diff --git a/-UdkFmZwUqA.txt b/-UdkFmZwUqA.txt
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--- /dev/null
+++ b/-UdkFmZwUqA.txt
@@ -0,0 +1,5991 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all
+
+ align:start position:0%
+ocw.mit.edu all
+ 
+
+ align:start position:0%
+ocw.mit.edu all
+right so as Professor Miller said our
+
+ align:start position:0%
+right so as Professor Miller said our
+ 
+
+ align:start position:0%
+right so as Professor Miller said our
+project was called number Square um we
+
+ align:start position:0%
+project was called number Square um we
+ 
+
+ align:start position:0%
+project was called number Square um we
+sort of like change the name to the end
+
+ align:start position:0%
+sort of like change the name to the end
+ 
+
+ align:start position:0%
+sort of like change the name to the end
+value game um basically our agenda for
+
+ align:start position:0%
+value game um basically our agenda for
+ 
+
+ align:start position:0%
+value game um basically our agenda for
+the day is going to be over over a few
+
+ align:start position:0%
+the day is going to be over over a few
+ 
+
+ align:start position:0%
+the day is going to be over over a few
+definitions to set up the problema is
+
+ align:start position:0%
+definitions to set up the problema is
+ 
+
+ align:start position:0%
+definitions to set up the problema is
+going to talk about the behavior of the
+
+ align:start position:0%
+going to talk about the behavior of the
+ 
+
+ align:start position:0%
+going to talk about the behavior of the
+three value game and then Matt is going
+
+ align:start position:0%
+three value game and then Matt is going
+ 
+
+ align:start position:0%
+three value game and then Matt is going
+to talk about the behavior of the four
+
+ align:start position:0%
+to talk about the behavior of the four
+ 
+
+ align:start position:0%
+to talk about the behavior of the four
+value game and also the end value game
+
+ align:start position:0%
+value game and also the end value game
+ 
+
+ align:start position:0%
+value game and also the end value game
+over the real numbers um but before we
+
+ align:start position:0%
+over the real numbers um but before we
+ 
+
+ align:start position:0%
+over the real numbers um but before we
+get started I wanted to just show a
+
+ align:start position:0%
+get started I wanted to just show a
+ 
+
+ align:start position:0%
+get started I wanted to just show a
+quick example of the four value game
+
+ align:start position:0%
+quick example of the four value game
+ 
+
+ align:start position:0%
+quick example of the four value game
+where we have four integers and so we're
+
+ align:start position:0%
+where we have four integers and so we're
+ 
+
+ align:start position:0%
+where we have four integers and so we're
+going to label these vertices 0
+
+ align:start position:0%
+going to label these vertices 0
+ 
+
+ align:start position:0%
+going to label these vertices 0
+3 sorry this
+
+ align:start position:0%
+3 sorry this
+ 
+
+ align:start position:0%
+3 sorry this
+isow 6 and three okay now in this game
+
+ align:start position:0%
+isow 6 and three okay now in this game
+ 
+
+ align:start position:0%
+isow 6 and three okay now in this game
+this dynamical system every time we move
+
+ align:start position:0%
+this dynamical system every time we move
+ 
+
+ align:start position:0%
+this dynamical system every time we move
+to a new state we simply take the
+
+ align:start position:0%
+to a new state we simply take the
+ 
+
+ align:start position:0%
+to a new state we simply take the
+vertices we make a a point at the
+
+ align:start position:0%
+vertices we make a a point at the
+ 
+
+ align:start position:0%
+vertices we make a a point at the
+midpoint and we label it with the
+
+ align:start position:0%
+midpoint and we label it with the
+ 
+
+ align:start position:0%
+midpoint and we label it with the
+absolute value of the difference here so
+
+ align:start position:0%
+absolute value of the difference here so
+ 
+
+ align:start position:0%
+absolute value of the difference here so
+this is going to give us three three
+
+ align:start position:0%
+this is going to give us three three
+ 
+
+ align:start position:0%
+this is going to give us three three
+three and three now if we iterate this
+
+ align:start position:0%
+three and three now if we iterate this
+ 
+
+ align:start position:0%
+three and three now if we iterate this
+once more we're going to go to
+
+ align:start position:0%
+once more we're going to go to
+ 
+
+ align:start position:0%
+once more we're going to go to
+z0 zero and we can see at this point
+
+ align:start position:0%
+z0 zero and we can see at this point
+ 
+
+ align:start position:0%
+z0 zero and we can see at this point
+that if we keep going we're only going
+
+ align:start position:0%
+that if we keep going we're only going
+ 
+
+ align:start position:0%
+that if we keep going we're only going
+to stay at this fix point 0 0 0 0 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so with that example a couple questions
+
+ align:start position:0%
+so with that example a couple questions
+ 
+
+ align:start position:0%
+so with that example a couple questions
+come to mind immediately you know we we
+
+ align:start position:0%
+come to mind immediately you know we we
+ 
+
+ align:start position:0%
+come to mind immediately you know we we
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+consider if different values on these
+
+ align:start position:0%
+consider if different values on these
+ 
+
+ align:start position:0%
+consider if different values on these
+vertices give us different long-term
+
+ align:start position:0%
+vertices give us different long-term
+ 
+
+ align:start position:0%
+vertices give us different long-term
+behaviors you know what we always go to
+
+ align:start position:0%
+behaviors you know what we always go to
+ 
+
+ align:start position:0%
+behaviors you know what we always go to
+this point this fixed point of all zeros
+
+ align:start position:0%
+this point this fixed point of all zeros
+ 
+
+ align:start position:0%
+this point this fixed point of all zeros
+or are there there values that we can
+
+ align:start position:0%
+or are there there values that we can
+ 
+
+ align:start position:0%
+or are there there values that we can
+choose for these vertices that that
+
+ align:start position:0%
+choose for these vertices that that
+ 
+
+ align:start position:0%
+choose for these vertices that that
+won't ever happen in order to sort of
+
+ align:start position:0%
+won't ever happen in order to sort of
+ 
+
+ align:start position:0%
+won't ever happen in order to sort of
+investigate these topics we first want
+
+ align:start position:0%
+investigate these topics we first want
+ 
+
+ align:start position:0%
+investigate these topics we first want
+to give the definitions of what we mean
+
+ align:start position:0%
+to give the definitions of what we mean
+ 
+
+ align:start position:0%
+to give the definitions of what we mean
+by state and game and transition um so
+
+ align:start position:0%
+by state and game and transition um so
+ 
+
+ align:start position:0%
+by state and game and transition um so
+the first thing is we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+so State s of the N value game is just
+
+ align:start position:0%
+so State s of the N value game is just
+ 
+
+ align:start position:0%
+so State s of the N value game is just
+an ordered list of the vertices A1
+
+ align:start position:0%
+an ordered list of the vertices A1
+ 
+
+ align:start position:0%
+an ordered list of the vertices A1
+A2 through a
+
+ align:start position:0%
+A2 through a
+ 
+
+ align:start position:0%
+A2 through a
+n okay so in this in the four value game
+
+ align:start position:0%
+n okay so in this in the four value game
+ 
+
+ align:start position:0%
+n okay so in this in the four value game
+example we start with A1 on the top left
+
+ align:start position:0%
+example we start with A1 on the top left
+ 
+
+ align:start position:0%
+example we start with A1 on the top left
+of the move by
+
+ align:start position:0%
+of the move by
+ 
+
+ align:start position:0%
+of the move by
+convention all right so the next thing
+
+ align:start position:0%
+convention all right so the next thing
+ 
+
+ align:start position:0%
+convention all right so the next thing
+we have for aate is the
+
+ align:start position:0%
+we have for aate is the
+ 
+
+ align:start position:0%
+we have for aate is the
+operator so we just call it t the
+
+ align:start position:0%
+operator so we just call it t the
+ 
+
+ align:start position:0%
+operator so we just call it t the
+upgrade T So this transitional T Works
+
+ align:start position:0%
+upgrade T So this transitional T Works
+ 
+
+ align:start position:0%
+upgrade T So this transitional T Works
+in the sense that t of s gives us the
+
+ align:start position:0%
+in the sense that t of s gives us the
+ 
+
+ align:start position:0%
+in the sense that t of s gives us the
+absolute difference of the adjacent
+
+ align:start position:0%
+absolute difference of the adjacent
+ 
+
+ align:start position:0%
+absolute difference of the adjacent
+veres we have A2
+
+ align:start position:0%
+veres we have A2
+ 
+
+ align:start position:0%
+veres we have A2
+A1 and then the last one loops around
+
+ align:start position:0%
+A1 and then the last one loops around
+ 
+
+ align:start position:0%
+A1 and then the last one loops around
+because we can see it here it's touching
+
+ align:start position:0%
+because we can see it here it's touching
+ 
+
+ align:start position:0%
+because we can see it here it's touching
+the first so we have A1 minus a
+
+ align:start position:0%
+the first so we have A1 minus a
+ 
+
+ align:start position:0%
+the first so we have A1 minus a
+n all right the last thing that we need
+
+ align:start position:0%
+n all right the last thing that we need
+ 
+
+ align:start position:0%
+n all right the last thing that we need
+to Define here is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game so game is just going to be the
+
+ align:start position:0%
+game so game is just going to be the
+ 
+
+ align:start position:0%
+game so game is just going to be the
+collection of the states s0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S1 all right so now that we have
+
+ align:start position:0%
+S1 all right so now that we have
+ 
+
+ align:start position:0%
+S1 all right so now that we have
+definition of the
+
+ align:start position:0%
+definition of the
+ 
+
+ align:start position:0%
+definition of the
+game what's the Rel
+
+ align:start position:0%
+game what's the Rel
+ 
+
+ align:start position:0%
+game what's the Rel
+okay that's good point all right so the
+
+ align:start position:0%
+okay that's good point all right so the
+ 
+
+ align:start position:0%
+okay that's good point all right so the
+relationship here between s0 S1 and SN
+
+ align:start position:0%
+relationship here between s0 S1 and SN
+ 
+
+ align:start position:0%
+relationship here between s0 S1 and SN
+is simply that s corresponds to M
+
+ align:start position:0%
+is simply that s corresponds to M
+ 
+
+ align:start position:0%
+is simply that s corresponds to M
+applications of our operator t on the
+
+ align:start position:0%
+applications of our operator t on the
+ 
+
+ align:start position:0%
+applications of our operator t on the
+initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State okay sorry about that um now the
+
+ align:start position:0%
+State okay sorry about that um now the
+ 
+
+ align:start position:0%
+State okay sorry about that um now the
+point of this this notation is we want
+
+ align:start position:0%
+point of this this notation is we want
+ 
+
+ align:start position:0%
+point of this this notation is we want
+to look at the long-term behavior of
+
+ align:start position:0%
+to look at the long-term behavior of
+ 
+
+ align:start position:0%
+to look at the long-term behavior of
+these caes um
+
+ align:start position:0%
+these caes um
+ 
+
+ align:start position:0%
+these caes um
+you know we we want to investigate
+
+ align:start position:0%
+you know we we want to investigate
+ 
+
+ align:start position:0%
+you know we we want to investigate
+whether or not it actually goes to the
+
+ align:start position:0%
+whether or not it actually goes to the
+ 
+
+ align:start position:0%
+whether or not it actually goes to the
+fix point and if it doesn't what other
+
+ align:start position:0%
+fix point and if it doesn't what other
+ 
+
+ align:start position:0%
+fix point and if it doesn't what other
+types of behaviors are possible so what
+
+ align:start position:0%
+types of behaviors are possible so what
+ 
+
+ align:start position:0%
+types of behaviors are possible so what
+we did was we defined our games to be
+
+ align:start position:0%
+we did was we defined our games to be
+ 
+
+ align:start position:0%
+we did was we defined our games to be
+something called K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cyclic so game is Cas
+
+ align:start position:0%
+cyclic so game is Cas
+ 
+
+ align:start position:0%
+cyclic so game is Cas
+cyclic if there exists some n such
+
+ align:start position:0%
+cyclic if there exists some n such
+ 
+
+ align:start position:0%
+cyclic if there exists some n such
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M plus K applications of the operator on
+
+ align:start position:0%
+M plus K applications of the operator on
+ 
+
+ align:start position:0%
+M plus K applications of the operator on
+the initial
+
+ align:start position:0%
+the initial
+ 
+
+ align:start position:0%
+the initial
+state is equal to M applications on the
+
+ align:start position:0%
+state is equal to M applications on the
+ 
+
+ align:start position:0%
+state is equal to M applications on the
+initial state so in our example above we
+
+ align:start position:0%
+initial state so in our example above we
+ 
+
+ align:start position:0%
+initial state so in our example above we
+have a one cylic G because we applied
+
+ align:start position:0%
+have a one cylic G because we applied
+ 
+
+ align:start position:0%
+have a one cylic G because we applied
+the operator twice and we got to the
+
+ align:start position:0%
+the operator twice and we got to the
+ 
+
+ align:start position:0%
+the operator twice and we got to the
+state the
+
+ align:start position:0%
+state the
+ 
+
+ align:start position:0%
+state the
+fix if we apply it a third time we're
+
+ align:start position:0%
+fix if we apply it a third time we're
+ 
+
+ align:start position:0%
+fix if we apply it a third time we're
+still at that same state okay
+
+ align:start position:0%
+still at that same state okay
+ 
+
+ align:start position:0%
+still at that same state okay
+so are there any questions about Cas
+
+ align:start position:0%
+so are there any questions about Cas
+ 
+
+ align:start position:0%
+so are there any questions about Cas
+cyclic all right so the opposite then
+
+ align:start position:0%
+cyclic all right so the opposite then
+ 
+
+ align:start position:0%
+cyclic all right so the opposite then
+the opposite if there doesn't exist an M
+
+ align:start position:0%
+the opposite if there doesn't exist an M
+ 
+
+ align:start position:0%
+the opposite if there doesn't exist an M
+such that this is true then we call
+
+ align:start position:0%
+such that this is true then we call
+ 
+
+ align:start position:0%
+such that this is true then we call
+these games non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repeat
+
+ align:start position:0%
+repeat
+ 
+
+ align:start position:0%
+repeat
+right so moving on from that we want
+
+ align:start position:0%
+right so moving on from that we want
+ 
+
+ align:start position:0%
+right so moving on from that we want
+to our goal of this is to study these
+
+ align:start position:0%
+to our goal of this is to study these
+ 
+
+ align:start position:0%
+to our goal of this is to study these
+these klic and non- repeating behaviors
+
+ align:start position:0%
+these klic and non- repeating behaviors
+ 
+
+ align:start position:0%
+these klic and non- repeating behaviors
+in in these different settings um in
+
+ align:start position:0%
+in in these different settings um in
+ 
+
+ align:start position:0%
+in in these different settings um in
+order to look at that in some of the the
+
+ align:start position:0%
+order to look at that in some of the the
+ 
+
+ align:start position:0%
+order to look at that in some of the the
+difference and errors we found it very
+
+ align:start position:0%
+difference and errors we found it very
+ 
+
+ align:start position:0%
+difference and errors we found it very
+useful to define a notion of equivalence
+
+ align:start position:0%
+useful to define a notion of equivalence
+ 
+
+ align:start position:0%
+useful to define a notion of equivalence
+so basically we want to say if we have
+
+ align:start position:0%
+so basically we want to say if we have
+ 
+
+ align:start position:0%
+so basically we want to say if we have
+two states X and Y when are they
+
+ align:start position:0%
+two states X and Y when are they
+ 
+
+ align:start position:0%
+two states X and Y when are they
+equivalent okay so the first thing that
+
+ align:start position:0%
+equivalent okay so the first thing that
+ 
+
+ align:start position:0%
+equivalent okay so the first thing that
+we realized was that there's something
+
+ align:start position:0%
+we realized was that there's something
+ 
+
+ align:start position:0%
+we realized was that there's something
+that we refer to as is equivalent by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+offset so if we have our
+
+ align:start position:0%
+offset so if we have our
+ 
+
+ align:start position:0%
+offset so if we have our
+state which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and then we add some constant value k
+
+ align:start position:0%
+is and then we add some constant value k
+ 
+
+ align:start position:0%
+is and then we add some constant value k
+each of the so we offset each of these
+
+ align:start position:0%
+each of the so we offset each of these
+ 
+
+ align:start position:0%
+each of the so we offset each of these
+vertices by K we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if we if we look at the operator
+
+ align:start position:0%
+well if we if we look at the operator
+ 
+
+ align:start position:0%
+well if we if we look at the operator
+appes s we
+
+ align:start position:0%
+appes s we
+ 
+
+ align:start position:0%
+appes s we
+get these differences from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before but it immediately follows from
+
+ align:start position:0%
+before but it immediately follows from
+ 
+
+ align:start position:0%
+before but it immediately follows from
+the definition of our operator that this
+
+ align:start position:0%
+the definition of our operator that this
+ 
+
+ align:start position:0%
+the definition of our operator that this
+K is going to fall out of every single
+
+ align:start position:0%
+K is going to fall out of every single
+ 
+
+ align:start position:0%
+K is going to fall out of every single
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+because you just look at the first we
+
+ align:start position:0%
+because you just look at the first we
+ 
+
+ align:start position:0%
+because you just look at the first we
+have an A2 plus
+
+ align:start position:0%
+have an A2 plus
+ 
+
+ align:start position:0%
+have an A2 plus
+Kus an A1 Plus K and this K is going to
+
+ align:start position:0%
+Kus an A1 Plus K and this K is going to
+ 
+
+ align:start position:0%
+Kus an A1 Plus K and this K is going to
+cancel for all of these
+
+ align:start position:0%
+cancel for all of these
+ 
+
+ align:start position:0%
+cancel for all of these
+veres okay so this is equivalent by
+
+ align:start position:0%
+veres okay so this is equivalent by
+ 
+
+ align:start position:0%
+veres okay so this is equivalent by
+opposite the next concept we had was the
+
+ align:start position:0%
+opposite the next concept we had was the
+ 
+
+ align:start position:0%
+opposite the next concept we had was the
+equivalence by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale so when we talk about scaling we
+
+ align:start position:0%
+scale so when we talk about scaling we
+ 
+
+ align:start position:0%
+scale so when we talk about scaling we
+want to use a number greater than zero
+
+ align:start position:0%
+want to use a number greater than zero
+ 
+
+ align:start position:0%
+want to use a number greater than zero
+and then we want to take our state s and
+
+ align:start position:0%
+and then we want to take our state s and
+ 
+
+ align:start position:0%
+and then we want to take our state s and
+transform it by multiplying scaling all
+
+ align:start position:0%
+transform it by multiplying scaling all
+ 
+
+ align:start position:0%
+transform it by multiplying scaling all
+the vertices such that we
+
+ align:start position:0%
+the vertices such that we
+ 
+
+ align:start position:0%
+the vertices such that we
+have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence now because R is greater than
+
+ align:start position:0%
+sequence now because R is greater than
+ 
+
+ align:start position:0%
+sequence now because R is greater than
+zero if we look at applying the
+
+ align:start position:0%
+zero if we look at applying the
+ 
+
+ align:start position:0%
+zero if we look at applying the
+operator to this scaled the scaled State
+
+ align:start position:0%
+operator to this scaled the scaled State
+ 
+
+ align:start position:0%
+operator to this scaled the scaled State
+we're going to get
+
+ align:start position:0%
+we're going to get
+ 
+
+ align:start position:0%
+we're going to get
+something that looks like
+
+ align:start position:0%
+something that looks like
+ 
+
+ align:start position:0%
+something that looks like
+this where the r can be factored out of
+
+ align:start position:0%
+this where the r can be factored out of
+ 
+
+ align:start position:0%
+this where the r can be factored out of
+both of these but because R is greater
+
+ align:start position:0%
+both of these but because R is greater
+ 
+
+ align:start position:0%
+both of these but because R is greater
+than zero we can actually Factor it out
+
+ align:start position:0%
+than zero we can actually Factor it out
+ 
+
+ align:start position:0%
+than zero we can actually Factor it out
+of the absolute value sign and this
+
+ align:start position:0%
+of the absolute value sign and this
+ 
+
+ align:start position:0%
+of the absolute value sign and this
+here is going to be equivalent to just
+
+ align:start position:0%
+here is going to be equivalent to just
+ 
+
+ align:start position:0%
+here is going to be equivalent to just
+scaling the resulting state from upon
+
+ align:start position:0%
+scaling the resulting state from upon
+ 
+
+ align:start position:0%
+scaling the resulting state from upon
+the operator what do you care why do you
+
+ align:start position:0%
+the operator what do you care why do you
+ 
+
+ align:start position:0%
+the operator what do you care why do you
+care if R is greater than zero doesn't
+
+ align:start position:0%
+care if R is greater than zero doesn't
+ 
+
+ align:start position:0%
+care if R is greater than zero doesn't
+it do the same thing if R
+
+ align:start position:0%
+it do the same thing if R
+ 
+
+ align:start position:0%
+it do the same thing if R
+is if R is less than zero we'll do the
+
+ align:start position:0%
+is if R is less than zero we'll do the
+ 
+
+ align:start position:0%
+is if R is less than zero we'll do the
+same thing I mean you won't it won't
+
+ align:start position:0%
+same thing I mean you won't it won't
+ 
+
+ align:start position:0%
+same thing I mean you won't it won't
+scale by R it scale by absolute R right
+
+ align:start position:0%
+scale by R it scale by absolute R right
+ 
+
+ align:start position:0%
+scale by R it scale by absolute R right
+am I missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something that's true what we want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraint yeah we so I mean for for our
+
+ align:start position:0%
+constraint yeah we so I mean for for our
+ 
+
+ align:start position:0%
+constraint yeah we so I mean for for our
+definitions we care about being greater
+
+ align:start position:0%
+definitions we care about being greater
+ 
+
+ align:start position:0%
+definitions we care about being greater
+than zero because when Matt wants to
+
+ align:start position:0%
+than zero because when Matt wants to
+ 
+
+ align:start position:0%
+than zero because when Matt wants to
+talk about the long-term behavior um
+
+ align:start position:0%
+talk about the long-term behavior um
+ 
+
+ align:start position:0%
+talk about the long-term behavior um
+this is going to be this notion here is
+
+ align:start position:0%
+this is going to be this notion here is
+ 
+
+ align:start position:0%
+this is going to be this notion here is
+going to be very important
+
+ align:start position:0%
+going to be very important
+ 
+
+ align:start position:0%
+going to be very important
+um okay so the last sort of bit of the
+
+ align:start position:0%
+um okay so the last sort of bit of the
+ 
+
+ align:start position:0%
+um okay so the last sort of bit of the
+the equivalence relation was also the
+
+ align:start position:0%
+the equivalence relation was also the
+ 
+
+ align:start position:0%
+the equivalence relation was also the
+trickiest part um and that's what we
+
+ align:start position:0%
+trickiest part um and that's what we
+ 
+
+ align:start position:0%
+trickiest part um and that's what we
+refer to as equivalent by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry so before explaining this um
+
+ align:start position:0%
+symmetry so before explaining this um
+ 
+
+ align:start position:0%
+symmetry so before explaining this um
+actually one of the the big things that
+
+ align:start position:0%
+actually one of the the big things that
+ 
+
+ align:start position:0%
+actually one of the the big things that
+we notice is when we look at say this
+
+ align:start position:0%
+we notice is when we look at say this
+ 
+
+ align:start position:0%
+we notice is when we look at say this
+example where we see this transition
+
+ align:start position:0%
+example where we see this transition
+ 
+
+ align:start position:0%
+example where we see this transition
+operator apply to the state each state
+
+ align:start position:0%
+operator apply to the state each state
+ 
+
+ align:start position:0%
+operator apply to the state each state
+only depends on its adjacent neighbors
+
+ align:start position:0%
+only depends on its adjacent neighbors
+ 
+
+ align:start position:0%
+only depends on its adjacent neighbors
+okay so when we talk about symmetry we
+
+ align:start position:0%
+okay so when we talk about symmetry we
+ 
+
+ align:start position:0%
+okay so when we talk about symmetry we
+talk about looking at permutations of
+
+ align:start position:0%
+talk about looking at permutations of
+ 
+
+ align:start position:0%
+talk about looking at permutations of
+the vertices such that we're preserving
+
+ align:start position:0%
+the vertices such that we're preserving
+ 
+
+ align:start position:0%
+the vertices such that we're preserving
+this property that the adjacent are are
+
+ align:start position:0%
+this property that the adjacent are are
+ 
+
+ align:start position:0%
+this property that the adjacent are are
+unchanged um so this is this is sort of
+
+ align:start position:0%
+unchanged um so this is this is sort of
+ 
+
+ align:start position:0%
+unchanged um so this is this is sort of
+easiest to see first uh by an example
+
+ align:start position:0%
+easiest to see first uh by an example
+ 
+
+ align:start position:0%
+easiest to see first uh by an example
+and so that's
+
+ align:start position:0%
+and so that's
+ 
+
+ align:start position:0%
+and so that's
+why actually why I drew this up here so
+
+ align:start position:0%
+why actually why I drew this up here so
+ 
+
+ align:start position:0%
+why actually why I drew this up here so
+these these eight pictures here
+
+ align:start position:0%
+these these eight pictures here
+ 
+
+ align:start position:0%
+these these eight pictures here
+represent all the possible symmetries of
+
+ align:start position:0%
+represent all the possible symmetries of
+ 
+
+ align:start position:0%
+represent all the possible symmetries of
+the four value the top four we can see
+
+ align:start position:0%
+the four value the top four we can see
+ 
+
+ align:start position:0%
+the four value the top four we can see
+are just a a rotation right so if we
+
+ align:start position:0%
+are just a a rotation right so if we
+ 
+
+ align:start position:0%
+are just a a rotation right so if we
+move to from the first one to the second
+
+ align:start position:0%
+move to from the first one to the second
+ 
+
+ align:start position:0%
+move to from the first one to the second
+one we simply rotate on count these ones
+
+ align:start position:0%
+one we simply rotate on count these ones
+ 
+
+ align:start position:0%
+one we simply rotate on count these ones
+here are just flipping about the the
+
+ align:start position:0%
+here are just flipping about the the
+ 
+
+ align:start position:0%
+here are just flipping about the the
+axis um but the examples that I wanted
+
+ align:start position:0%
+axis um but the examples that I wanted
+ 
+
+ align:start position:0%
+axis um but the examples that I wanted
+to show to to prove that this doesn't
+
+ align:start position:0%
+to show to to prove that this doesn't
+ 
+
+ align:start position:0%
+to show to to prove that this doesn't
+affect anything um is if we look at the
+
+ align:start position:0%
+affect anything um is if we look at the
+ 
+
+ align:start position:0%
+affect anything um is if we look at the
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isal 1 2 4
+
+ align:start position:0%
+isal 1 2 4
+ 
+
+ align:start position:0%
+isal 1 2 4
+7 now if we apply this
+
+ align:start position:0%
+7 now if we apply this
+ 
+
+ align:start position:0%
+7 now if we apply this
+transition we're going to get one in the
+
+ align:start position:0%
+transition we're going to get one in the
+ 
+
+ align:start position:0%
+transition we're going to get one in the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+two three and then
+
+ align:start position:0%
+two three and then
+ 
+
+ align:start position:0%
+two three and then
+six now the trick is if we if we then
+
+ align:start position:0%
+six now the trick is if we if we then
+ 
+
+ align:start position:0%
+six now the trick is if we if we then
+look at one of the permuted versions of
+
+ align:start position:0%
+look at one of the permuted versions of
+ 
+
+ align:start position:0%
+look at one of the permuted versions of
+s so say we look at and when we so when
+
+ align:start position:0%
+s so say we look at and when we so when
+ 
+
+ align:start position:0%
+s so say we look at and when we so when
+we talk about these permutations we're
+
+ align:start position:0%
+we talk about these permutations we're
+ 
+
+ align:start position:0%
+we talk about these permutations we're
+going to talk about permutation Sigma on
+
+ align:start position:0%
+going to talk about permutation Sigma on
+ 
+
+ align:start position:0%
+going to talk about permutation Sigma on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dial
+
+ align:start position:0%
+dial
+ 
+
+ align:start position:0%
+dial
+so those eight pictures right there are
+
+ align:start position:0%
+so those eight pictures right there are
+ 
+
+ align:start position:0%
+so those eight pictures right there are
+representing the dial group of eight
+
+ align:start position:0%
+representing the dial group of eight
+ 
+
+ align:start position:0%
+representing the dial group of eight
+okay so when we talk about this
+
+ align:start position:0%
+okay so when we talk about this
+ 
+
+ align:start position:0%
+okay so when we talk about this
+permutation Sigma on S one of the
+
+ align:start position:0%
+permutation Sigma on S one of the
+ 
+
+ align:start position:0%
+permutation Sigma on S one of the
+examples that we could look at is simply
+
+ align:start position:0%
+examples that we could look at is simply
+ 
+
+ align:start position:0%
+examples that we could look at is simply
+rewriting as 4 2 1 7 so this translates
+
+ align:start position:0%
+rewriting as 4 2 1 7 so this translates
+ 
+
+ align:start position:0%
+rewriting as 4 2 1 7 so this translates
+to flipping the first value and the
+
+ align:start position:0%
+to flipping the first value and the
+ 
+
+ align:start position:0%
+to flipping the first value and the
+third value which we see up here is
+
+ align:start position:0%
+third value which we see up here is
+ 
+
+ align:start position:0%
+third value which we see up here is
+simply this transformation okay so if we
+
+ align:start position:0%
+simply this transformation okay so if we
+ 
+
+ align:start position:0%
+simply this transformation okay so if we
+then apply the operator on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this we have 2
+
+ align:start position:0%
+this we have 2
+ 
+
+ align:start position:0%
+this we have 2
+one 6 and three which is itself just a
+
+ align:start position:0%
+one 6 and three which is itself just a
+ 
+
+ align:start position:0%
+one 6 and three which is itself just a
+permutation of this so we say
+
+ align:start position:0%
+permutation of this so we say
+ 
+
+ align:start position:0%
+permutation of this so we say
+that the operator plot here is another
+
+ align:start position:0%
+that the operator plot here is another
+ 
+
+ align:start position:0%
+that the operator plot here is another
+permutation appli to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resulting okay so one of
+
+ align:start position:0%
+resulting okay so one of
+ 
+
+ align:start position:0%
+resulting okay so one of
+the so the final thing then is to sum up
+
+ align:start position:0%
+the so the final thing then is to sum up
+ 
+
+ align:start position:0%
+the so the final thing then is to sum up
+all three of these nees of
+
+ align:start position:0%
+all three of these nees of
+ 
+
+ align:start position:0%
+all three of these nees of
+equivalent so we can say that two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states X is equ equivalent to Y if and
+
+ align:start position:0%
+states X is equ equivalent to Y if and
+ 
+
+ align:start position:0%
+states X is equ equivalent to Y if and
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+if there's than Z
+
+ align:start position:0%
+if there's than Z
+ 
+
+ align:start position:0%
+if there's than Z
+permutation from the dial group Sig X
+
+ align:start position:0%
+permutation from the dial group Sig X
+ 
+
+ align:start position:0%
+permutation from the dial group Sig X
+and a constant K such that we can get
+
+ align:start position:0%
+and a constant K such that we can get
+ 
+
+ align:start position:0%
+and a constant K such that we can get
+the exact thing
+
+ align:start position:0%
+the exact thing
+ 
+
+ align:start position:0%
+the exact thing
+y okay the thing given by negating all
+
+ align:start position:0%
+y okay the thing given by negating all
+ 
+
+ align:start position:0%
+y okay the thing given by negating all
+the entries is not aent what Thinking by
+
+ align:start position:0%
+the entries is not aent what Thinking by
+ 
+
+ align:start position:0%
+the entries is not aent what Thinking by
+negating all the initial ver vertex
+
+ align:start position:0%
+negating all the initial ver vertex
+ 
+
+ align:start position:0%
+negating all the initial ver vertex
+values is not
+
+ align:start position:0%
+values is not
+ 
+
+ align:start position:0%
+values is not
+equivalent um no so that's that become
+
+ align:start position:0%
+equivalent um no so that's that become
+ 
+
+ align:start position:0%
+equivalent um no so that's that become
+equivalent after one right so after one
+
+ align:start position:0%
+equivalent after one right so after one
+ 
+
+ align:start position:0%
+equivalent after one right so after one
+one application so the way that we
+
+ align:start position:0%
+one application so the way that we
+ 
+
+ align:start position:0%
+one application so the way that we
+avoided even considering that is we just
+
+ align:start position:0%
+avoided even considering that is we just
+ 
+
+ align:start position:0%
+avoided even considering that is we just
+restricted ourselves to only looking at
+
+ align:start position:0%
+restricted ourselves to only looking at
+ 
+
+ align:start position:0%
+restricted ourselves to only looking at
+positive value coures um because as you
+
+ align:start position:0%
+positive value coures um because as you
+ 
+
+ align:start position:0%
+positive value coures um because as you
+mentioned after one application with the
+
+ align:start position:0%
+mentioned after one application with the
+ 
+
+ align:start position:0%
+mentioned after one application with the
+absolute value operator all the various
+
+ align:start position:0%
+absolute value operator all the various
+ 
+
+ align:start position:0%
+absolute value operator all the various
+seats are going to be positive so any
+
+ align:start position:0%
+seats are going to be positive so any
+ 
+
+ align:start position:0%
+seats are going to be positive so any
+starting state that has negative entries
+
+ align:start position:0%
+starting state that has negative entries
+ 
+
+ align:start position:0%
+starting state that has negative entries
+can be transformed after one one
+
+ align:start position:0%
+can be transformed after one one
+ 
+
+ align:start position:0%
+can be transformed after one one
+application into a different state that
+
+ align:start position:0%
+application into a different state that
+ 
+
+ align:start position:0%
+application into a different state that
+is all positive um so yeah the one of
+
+ align:start position:0%
+is all positive um so yeah the one of
+ 
+
+ align:start position:0%
+is all positive um so yeah the one of
+the the quick things to know before EA
+
+ align:start position:0%
+the the quick things to know before EA
+ 
+
+ align:start position:0%
+the the quick things to know before EA
+gets into a three value game is this
+
+ align:start position:0%
+gets into a three value game is this
+ 
+
+ align:start position:0%
+gets into a three value game is this
+this notion of
+
+ align:start position:0%
+this notion of
+ 
+
+ align:start position:0%
+this notion of
+scaling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so scaling allowed us to immediately
+
+ align:start position:0%
+so scaling allowed us to immediately
+ 
+
+ align:start position:0%
+so scaling allowed us to immediately
+reduce the complexity of states that
+
+ align:start position:0%
+reduce the complexity of states that
+ 
+
+ align:start position:0%
+reduce the complexity of states that
+have integer values from the rationals
+
+ align:start position:0%
+have integer values from the rationals
+ 
+
+ align:start position:0%
+have integer values from the rationals
+so if we take our vertices as rational
+
+ align:start position:0%
+so if we take our vertices as rational
+ 
+
+ align:start position:0%
+so if we take our vertices as rational
+numbers we can simply get a common
+
+ align:start position:0%
+numbers we can simply get a common
+ 
+
+ align:start position:0%
+numbers we can simply get a common
+denominator and factor that out right so
+
+ align:start position:0%
+denominator and factor that out right so
+ 
+
+ align:start position:0%
+denominator and factor that out right so
+if we so we have some
+
+ align:start position:0%
+if we so we have some
+ 
+
+ align:start position:0%
+if we so we have some
+s isn't q and we can transform this into
+
+ align:start position:0%
+s isn't q and we can transform this into
+ 
+
+ align:start position:0%
+s isn't q and we can transform this into
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+state that is just on the Ines right
+
+ align:start position:0%
+state that is just on the Ines right
+ 
+
+ align:start position:0%
+state that is just on the Ines right
+because we factored out the common
+
+ align:start position:0%
+because we factored out the common
+ 
+
+ align:start position:0%
+because we factored out the common
+denom all right so with that you is
+
+ align:start position:0%
+denom all right so with that you is
+ 
+
+ align:start position:0%
+denom all right so with that you is
+going to talk about the behavior of the
+
+ align:start position:0%
+going to talk about the behavior of the
+ 
+
+ align:start position:0%
+going to talk about the behavior of the
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+value so as you can um uh imagine the
+
+ align:start position:0%
+value so as you can um uh imagine the
+ 
+
+ align:start position:0%
+value so as you can um uh imagine the
+three value game is just you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a a triangle and at the end of the
+
+ align:start position:0%
+a a triangle and at the end of the
+ 
+
+ align:start position:0%
+a a triangle and at the end of the
+points you have three values so I'm just
+
+ align:start position:0%
+points you have three values so I'm just
+ 
+
+ align:start position:0%
+points you have three values so I'm just
+going to give a quick
+
+ align:start position:0%
+going to give a quick
+ 
+
+ align:start position:0%
+going to give a quick
+example just random example so for this
+
+ align:start position:0%
+example just random example so for this
+ 
+
+ align:start position:0%
+example just random example so for this
+the game goes to two two and four and
+
+ align:start position:0%
+the game goes to two two and four and
+ 
+
+ align:start position:0%
+the game goes to two two and four and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you uh subtract the points again and so
+
+ align:start position:0%
+you uh subtract the points again and so
+ 
+
+ align:start position:0%
+you uh subtract the points again and so
+this would go to zero two and
+
+ align:start position:0%
+this would go to zero two and
+ 
+
+ align:start position:0%
+this would go to zero two and
+two and then if you do it one more time
+
+ align:start position:0%
+two and then if you do it one more time
+ 
+
+ align:start position:0%
+two and then if you do it one more time
+more iteration you get again
+
+ align:start position:0%
+more iteration you get again
+ 
+
+ align:start position:0%
+more iteration you get again
+220 and so you can probably see that um
+
+ align:start position:0%
+220 and so you can probably see that um
+ 
+
+ align:start position:0%
+220 and so you can probably see that um
+this particular three value game um has
+
+ align:start position:0%
+this particular three value game um has
+ 
+
+ align:start position:0%
+this particular three value game um has
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CycleOps 02 2
+
+ align:start position:0%
+CycleOps 02 2
+ 
+
+ align:start position:0%
+CycleOps 02 2
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so it's just for this particular game
+
+ align:start position:0%
+2 so it's just for this particular game
+ 
+
+ align:start position:0%
+2 so it's just for this particular game
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+the you enter a three cycle of this form
+
+ align:start position:0%
+the you enter a three cycle of this form
+ 
+
+ align:start position:0%
+the you enter a three cycle of this form
+right of 0 XX x0x um so we're going to
+
+ align:start position:0%
+right of 0 XX x0x um so we're going to
+ 
+
+ align:start position:0%
+right of 0 XX x0x um so we're going to
+talk about the end behavior of all three
+
+ align:start position:0%
+talk about the end behavior of all three
+ 
+
+ align:start position:0%
+talk about the end behavior of all three
+value games so
+
+ align:start position:0%
+value games so
+ 
+
+ align:start position:0%
+value games so
+um before we do that uh I wanted to go
+
+ align:start position:0%
+um before we do that uh I wanted to go
+ 
+
+ align:start position:0%
+um before we do that uh I wanted to go
+over some definitions so there are two
+
+ align:start position:0%
+over some definitions so there are two
+ 
+
+ align:start position:0%
+over some definitions so there are two
+key definitions so one is of a non- a
+
+ align:start position:0%
+key definitions so one is of a non- a
+ 
+
+ align:start position:0%
+key definitions so one is of a non- a
+trivial three valy game and one is of a
+
+ align:start position:0%
+trivial three valy game and one is of a
+ 
+
+ align:start position:0%
+trivial three valy game and one is of a
+non so a non
+
+ align:start position:0%
+non so a non
+ 
+
+ align:start position:0%
+non so a non
+trial
+
+ align:start position:0%
+trial
+ 
+
+ align:start position:0%
+trial
+let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tri so a three a trivial three value
+
+ align:start position:0%
+Tri so a three a trivial three value
+ 
+
+ align:start position:0%
+Tri so a three a trivial three value
+game is one in which the start state is
+
+ align:start position:0%
+game is one in which the start state is
+ 
+
+ align:start position:0%
+game is one in which the start state is
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form um XXX where X is positive integer
+
+ align:start position:0%
+form um XXX where X is positive integer
+ 
+
+ align:start position:0%
+form um XXX where X is positive integer
+so essentially with this game and only
+
+ align:start position:0%
+so essentially with this game and only
+ 
+
+ align:start position:0%
+so essentially with this game and only
+this game on the first step you have you
+
+ align:start position:0%
+this game on the first step you have you
+ 
+
+ align:start position:0%
+this game on the first step you have you
+know your
+
+ align:start position:0%
+know your
+ 
+
+ align:start position:0%
+know your
+transition times uh multip by the U
+
+ align:start position:0%
+transition times uh multip by the U
+ 
+
+ align:start position:0%
+transition times uh multip by the U
+start State gives you U 0 right and so a
+
+ align:start position:0%
+start State gives you U 0 right and so a
+ 
+
+ align:start position:0%
+start State gives you U 0 right and so a
+definition of a nontrivial d value game
+
+ align:start position:0%
+definition of a nontrivial d value game
+ 
+
+ align:start position:0%
+definition of a nontrivial d value game
+is just one you know in which you don't
+
+ align:start position:0%
+is just one you know in which you don't
+ 
+
+ align:start position:0%
+is just one you know in which you don't
+get as the um as a state after one
+
+ align:start position:0%
+get as the um as a state after one
+ 
+
+ align:start position:0%
+get as the um as a state after one
+iteration okay so what do you guys think
+
+ align:start position:0%
+iteration okay so what do you guys think
+ 
+
+ align:start position:0%
+iteration okay so what do you guys think
+happens um as end behavior for all three
+
+ align:start position:0%
+happens um as end behavior for all three
+ 
+
+ align:start position:0%
+happens um as end behavior for all three
+value games if you guys can kind of
+
+ align:start position:0%
+value games if you guys can kind of
+ 
+
+ align:start position:0%
+value games if you guys can kind of
+think about it really quickly since it's
+
+ align:start position:0%
+think about it really quickly since it's
+ 
+
+ align:start position:0%
+think about it really quickly since it's
+only three numbers you have to deal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with okay besides Z who's been working
+
+ align:start position:0%
+with okay besides Z who's been working
+ 
+
+ align:start position:0%
+with okay besides Z who's been working
+on this paper for about a month now
+
+ align:start position:0%
+on this paper for about a month now
+ 
+
+ align:start position:0%
+on this paper for about a month now
+anybody
+
+ align:start position:0%
+anybody
+ 
+
+ align:start position:0%
+anybody
+else they all have length zero or three
+
+ align:start position:0%
+else they all have length zero or three
+ 
+
+ align:start position:0%
+else they all have length zero or three
+or they all have length one or
+
+ align:start position:0%
+or they all have length one or
+ 
+
+ align:start position:0%
+or they all have length one or
+three one or three yeah um that is close
+
+ align:start position:0%
+three one or three yeah um that is close
+ 
+
+ align:start position:0%
+three one or three yeah um that is close
+but um they can have longer links but
+
+ align:start position:0%
+but um they can have longer links but
+ 
+
+ align:start position:0%
+but um they can have longer links but
+the end behavior of all of them um is is
+
+ align:start position:0%
+the end behavior of all of them um is is
+ 
+
+ align:start position:0%
+the end behavior of all of them um is is
+that they're going all um basically
+
+ align:start position:0%
+that they're going all um basically
+ 
+
+ align:start position:0%
+that they're going all um basically
+cycle in three
+
+ align:start position:0%
+cycle in three
+ 
+
+ align:start position:0%
+cycle in three
+cyc okay so I'm just going to prove this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+nontrivial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three value
+
+ align:start position:0%
+three value
+ 
+
+ align:start position:0%
+three value
+games um over positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers cycle or have a three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cycle so I didn't pick that because you
+
+ align:start position:0%
+cycle so I didn't pick that because you
+ 
+
+ align:start position:0%
+cycle so I didn't pick that because you
+know it was a random example all all
+
+ align:start position:0%
+know it was a random example all all
+ 
+
+ align:start position:0%
+know it was a random example all all
+three valy non-trivial three valy games
+
+ align:start position:0%
+three valy non-trivial three valy games
+ 
+
+ align:start position:0%
+three valy non-trivial three valy games
+are going to cycle in the form of Z XX
+
+ align:start position:0%
+are going to cycle in the form of Z XX
+ 
+
+ align:start position:0%
+are going to cycle in the form of Z XX
+so as I write these three cases down um
+
+ align:start position:0%
+so as I write these three cases down um
+ 
+
+ align:start position:0%
+so as I write these three cases down um
+try to you know think about what happens
+
+ align:start position:0%
+try to you know think about what happens
+ 
+
+ align:start position:0%
+try to you know think about what happens
+um after one or two itations of the of
+
+ align:start position:0%
+um after one or two itations of the of
+ 
+
+ align:start position:0%
+um after one or two itations of the of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and these states are be right before
+
+ align:start position:0%
+so and these states are be right before
+ 
+
+ align:start position:0%
+so and these states are be right before
+the trans
+
+ align:start position:0%
+the trans
+ 
+
+ align:start position:0%
+the trans
+position to the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+St and the X and Y they just represent
+
+ align:start position:0%
+St and the X and Y they just represent
+ 
+
+ align:start position:0%
+St and the X and Y they just represent
+different values um and different
+
+ align:start position:0%
+different values um and different
+ 
+
+ align:start position:0%
+different values um and different
+positive values and these two cases case
+
+ align:start position:0%
+positive values and these two cases case
+ 
+
+ align:start position:0%
+positive values and these two cases case
+two and case three are just going to
+
+ align:start position:0%
+two and case three are just going to
+ 
+
+ align:start position:0%
+two and case three are just going to
+enter um the case one after one
+
+ align:start position:0%
+enter um the case one after one
+ 
+
+ align:start position:0%
+enter um the case one after one
+iteration um we don't need to do an
+
+ align:start position:0%
+iteration um we don't need to do an
+ 
+
+ align:start position:0%
+iteration um we don't need to do an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so you can you can write this out a
+
+ align:start position:0%
+so you can you can write this out a
+ 
+
+ align:start position:0%
+so you can you can write this out a
+diagram and just so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is going to cycle into um and
+
+ align:start position:0%
+that this is going to cycle into um and
+ 
+
+ align:start position:0%
+that this is going to cycle into um and
+this is going to ENT a three cycle and
+
+ align:start position:0%
+this is going to ENT a three cycle and
+ 
+
+ align:start position:0%
+this is going to ENT a three cycle and
+these two cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're just going to transition into case
+
+ align:start position:0%
+we're just going to transition into case
+ 
+
+ align:start position:0%
+we're just going to transition into case
+one uh the more interest the more
+
+ align:start position:0%
+one uh the more interest the more
+ 
+
+ align:start position:0%
+one uh the more interest the more
+interesting case is case four and five
+
+ align:start position:0%
+interesting case is case four and five
+ 
+
+ align:start position:0%
+interesting case is case four and five
+so case four is actually just a
+
+ align:start position:0%
+so case four is actually just a
+ 
+
+ align:start position:0%
+so case four is actually just a
+um subset
+
+ align:start position:0%
+um subset
+ 
+
+ align:start position:0%
+um subset
+of case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um and in order to consider these two
+
+ align:start position:0%
+um and in order to consider these two
+ 
+
+ align:start position:0%
+um and in order to consider these two
+cases U it's it'll be useful to have
+
+ align:start position:0%
+cases U it's it'll be useful to have
+ 
+
+ align:start position:0%
+cases U it's it'll be useful to have
+another definition or final definition
+
+ align:start position:0%
+another definition or final definition
+ 
+
+ align:start position:0%
+another definition or final definition
+for this section and it's the definition
+
+ align:start position:0%
+for this section and it's the definition
+ 
+
+ align:start position:0%
+for this section and it's the definition
+for range so WR it right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so the range is uh essentially the
+
+ align:start position:0%
+here so the range is uh essentially the
+ 
+
+ align:start position:0%
+here so the range is uh essentially the
+largest positive difference between uh
+
+ align:start position:0%
+largest positive difference between uh
+ 
+
+ align:start position:0%
+largest positive difference between uh
+two values in a particular state so
+
+ align:start position:0%
+two values in a particular state so
+ 
+
+ align:start position:0%
+two values in a particular state so
+range can just be defined as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+max the max value in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game where s represents U that all the
+
+ align:start position:0%
+game where s represents U that all the
+ 
+
+ align:start position:0%
+game where s represents U that all the
+values in the game so as you can see um
+
+ align:start position:0%
+values in the game so as you can see um
+ 
+
+ align:start position:0%
+values in the game so as you can see um
+in this game uh if we if we assume that
+
+ align:start position:0%
+in this game uh if we if we assume that
+ 
+
+ align:start position:0%
+in this game uh if we if we assume that
+um you know X is is less than y and we
+
+ align:start position:0%
+um you know X is is less than y and we
+ 
+
+ align:start position:0%
+um you know X is is less than y and we
+can assume that because um like I said
+
+ align:start position:0%
+can assume that because um like I said
+ 
+
+ align:start position:0%
+can assume that because um like I said
+before when you're dealing with Bas
+
+ align:start position:0%
+before when you're dealing with Bas
+ 
+
+ align:start position:0%
+before when you're dealing with Bas
+essentially a a number line so if X and
+
+ align:start position:0%
+essentially a a number line so if X and
+ 
+
+ align:start position:0%
+essentially a a number line so if X and
+Y are in uh positions that make y uh
+
+ align:start position:0%
+Y are in uh positions that make y uh
+ 
+
+ align:start position:0%
+Y are in uh positions that make y uh
+make X larger than y then you can just
+
+ align:start position:0%
+make X larger than y then you can just
+ 
+
+ align:start position:0%
+make X larger than y then you can just
+uh basic essentially rotate the game so
+
+ align:start position:0%
+uh basic essentially rotate the game so
+ 
+
+ align:start position:0%
+uh basic essentially rotate the game so
+that you have uh this the second entry
+
+ align:start position:0%
+that you have uh this the second entry
+ 
+
+ align:start position:0%
+that you have uh this the second entry
+be smaller than the third entry right so
+
+ align:start position:0%
+be smaller than the third entry right so
+ 
+
+ align:start position:0%
+be smaller than the third entry right so
+if x is smaller than y then the range in
+
+ align:start position:0%
+if x is smaller than y then the range in
+ 
+
+ align:start position:0%
+if x is smaller than y then the range in
+this game before the transition is y
+
+ align:start position:0%
+this game before the transition is y
+ 
+
+ align:start position:0%
+this game before the transition is y
+right y- Z and so for case 4 and case
+
+ align:start position:0%
+right y- Z and so for case 4 and case
+ 
+
+ align:start position:0%
+right y- Z and so for case 4 and case
+five um the ranges uh after one
+
+ align:start position:0%
+five um the ranges uh after one
+ 
+
+ align:start position:0%
+five um the ranges uh after one
+iteration will decrease and after a
+
+ align:start position:0%
+iteration will decrease and after a
+ 
+
+ align:start position:0%
+iteration will decrease and after a
+second iteration also decrease so after
+
+ align:start position:0%
+second iteration also decrease so after
+ 
+
+ align:start position:0%
+second iteration also decrease so after
+every iteration if you're in case four
+
+ align:start position:0%
+every iteration if you're in case four
+ 
+
+ align:start position:0%
+every iteration if you're in case four
+case 5 the range will decrease and
+
+ align:start position:0%
+case 5 the range will decrease and
+ 
+
+ align:start position:0%
+case 5 the range will decrease and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um any wait any questions before I yeah
+
+ align:start position:0%
+um any wait any questions before I yeah
+ 
+
+ align:start position:0%
+um any wait any questions before I yeah
+yeah when would you ever get to case two
+
+ align:start position:0%
+yeah when would you ever get to case two
+ 
+
+ align:start position:0%
+yeah when would you ever get to case two
+if you're starting with exactly so for
+
+ align:start position:0%
+if you're starting with exactly so for
+ 
+
+ align:start position:0%
+if you're starting with exactly so for
+case two is case two is one of those
+
+ align:start position:0%
+case two is case two is one of those
+ 
+
+ align:start position:0%
+case two is case two is one of those
+cases where it's the initial you have to
+
+ align:start position:0%
+cases where it's the initial you have to
+ 
+
+ align:start position:0%
+cases where it's the initial you have to
+have the initial State being in case two
+
+ align:start position:0%
+have the initial State being in case two
+ 
+
+ align:start position:0%
+have the initial State being in case two
+in order for you to be in this but Wen
+
+ align:start position:0%
+in order for you to be in this but Wen
+ 
+
+ align:start position:0%
+in order for you to be in this but Wen
+you starting with
+
+ align:start position:0%
+you starting with
+ 
+
+ align:start position:0%
+you starting with
+positive yeah okay yeah so it's it's
+
+ align:start position:0%
+positive yeah okay yeah so it's it's
+ 
+
+ align:start position:0%
+positive yeah okay yeah so it's it's
+impossible like you said to get to this
+
+ align:start position:0%
+impossible like you said to get to this
+ 
+
+ align:start position:0%
+impossible like you said to get to this
+to case two which is a good observation
+
+ align:start position:0%
+to case two which is a good observation
+ 
+
+ align:start position:0%
+to case two which is a good observation
+from another case because in order to
+
+ align:start position:0%
+from another case because in order to
+ 
+
+ align:start position:0%
+from another case because in order to
+get two zeros you need to have um
+
+ align:start position:0%
+get two zeros you need to have um
+ 
+
+ align:start position:0%
+get two zeros you need to have um
+essentially four sets of
+
+ align:start position:0%
+essentially four sets of
+ 
+
+ align:start position:0%
+essentially four sets of
+numbers that you know you need to have
+
+ align:start position:0%
+numbers that you know you need to have
+ 
+
+ align:start position:0%
+numbers that you know you need to have
+um two pairs of numbers that are similar
+
+ align:start position:0%
+um two pairs of numbers that are similar
+ 
+
+ align:start position:0%
+um two pairs of numbers that are similar
+and you you only have three to do with
+
+ align:start position:0%
+and you you only have three to do with
+ 
+
+ align:start position:0%
+and you you only have three to do with
+right um
+
+ align:start position:0%
+right um
+ 
+
+ align:start position:0%
+right um
+so because um the first three cases uh
+
+ align:start position:0%
+so because um the first three cases uh
+ 
+
+ align:start position:0%
+so because um the first three cases uh
+enter the three cycle after the first
+
+ align:start position:0%
+enter the three cycle after the first
+ 
+
+ align:start position:0%
+enter the three cycle after the first
+iteration um and because case four and
+
+ align:start position:0%
+iteration um and because case four and
+ 
+
+ align:start position:0%
+iteration um and because case four and
+case 5 will always decrease in range
+
+ align:start position:0%
+case 5 will always decrease in range
+ 
+
+ align:start position:0%
+case 5 will always decrease in range
+until um you reach case three
+
+ align:start position:0%
+until um you reach case three
+ 
+
+ align:start position:0%
+until um you reach case three
+then you know that proves that the in
+
+ align:start position:0%
+then you know that proves that the in
+ 
+
+ align:start position:0%
+then you know that proves that the in
+the three value game um in a non-trivial
+
+ align:start position:0%
+the three value game um in a non-trivial
+ 
+
+ align:start position:0%
+the three value game um in a non-trivial
+three value game uh all the all the
+
+ align:start position:0%
+three value game uh all the all the
+ 
+
+ align:start position:0%
+three value game uh all the all the
+games enter a three cycle and you'll
+
+ align:start position:0%
+games enter a three cycle and you'll
+ 
+
+ align:start position:0%
+games enter a three cycle and you'll
+never enter um the form XXX from any of
+
+ align:start position:0%
+never enter um the form XXX from any of
+ 
+
+ align:start position:0%
+never enter um the form XXX from any of
+these cases because again if you think
+
+ align:start position:0%
+these cases because again if you think
+ 
+
+ align:start position:0%
+these cases because again if you think
+about it as U numbers on number line
+
+ align:start position:0%
+about it as U numbers on number line
+ 
+
+ align:start position:0%
+about it as U numbers on number line
+it's impossible to get three of the same
+
+ align:start position:0%
+it's impossible to get three of the same
+ 
+
+ align:start position:0%
+it's impossible to get three of the same
+numbers if you're subtracting um all
+
+ align:start position:0%
+numbers if you're subtracting um all
+ 
+
+ align:start position:0%
+numbers if you're subtracting um all
+perations of the numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and so with that uh I'll let Matt
+
+ align:start position:0%
+um and so with that uh I'll let Matt
+ 
+
+ align:start position:0%
+um and so with that uh I'll let Matt
+talk about the four value game so after
+
+ align:start position:0%
+talk about the four value game so after
+ 
+
+ align:start position:0%
+talk about the four value game so after
+answering some interesting questions
+
+ align:start position:0%
+answering some interesting questions
+ 
+
+ align:start position:0%
+answering some interesting questions
+about the three value game the next
+
+ align:start position:0%
+about the three value game the next
+ 
+
+ align:start position:0%
+about the three value game the next
+natural thing to ask is so what about
+
+ align:start position:0%
+natural thing to ask is so what about
+ 
+
+ align:start position:0%
+natural thing to ask is so what about
+the four value game we spent a lot of
+
+ align:start position:0%
+the four value game we spent a lot of
+ 
+
+ align:start position:0%
+the four value game we spent a lot of
+time building up to this but uh as it
+
+ align:start position:0%
+time building up to this but uh as it
+ 
+
+ align:start position:0%
+time building up to this but uh as it
+turns
+
+ align:start position:0%
+turns
+ 
+
+ align:start position:0%
+turns
+out uh it is not the case that the four
+
+ align:start position:0%
+out uh it is not the case that the four
+ 
+
+ align:start position:0%
+out uh it is not the case that the four
+value game demonstrates psychic Behavior
+
+ align:start position:0%
+value game demonstrates psychic Behavior
+ 
+
+ align:start position:0%
+value game demonstrates psychic Behavior
+specifically the four value game over
+
+ align:start position:0%
+specifically the four value game over
+ 
+
+ align:start position:0%
+specifically the four value game over
+the integers and we'll talk about the
+
+ align:start position:0%
+the integers and we'll talk about the
+ 
+
+ align:start position:0%
+the integers and we'll talk about the
+four value game over the integers and
+
+ align:start position:0%
+four value game over the integers and
+ 
+
+ align:start position:0%
+four value game over the integers and
+over the reals and there's a fund
+
+ align:start position:0%
+over the reals and there's a fund
+ 
+
+ align:start position:0%
+over the reals and there's a fund
+difference between those two sets that
+
+ align:start position:0%
+difference between those two sets that
+ 
+
+ align:start position:0%
+difference between those two sets that
+leads to some interesting
+
+ align:start position:0%
+leads to some interesting
+ 
+
+ align:start position:0%
+leads to some interesting
+properties but to start with we'll make
+
+ align:start position:0%
+properties but to start with we'll make
+ 
+
+ align:start position:0%
+properties but to start with we'll make
+a bold claim and that claim is the
+
+ align:start position:0%
+a bold claim and that claim is the
+ 
+
+ align:start position:0%
+a bold claim and that claim is the
+following theorem uh all four value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gains over the non- negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converge to F
+
+ align:start position:0%
+converge to F
+ 
+
+ align:start position:0%
+converge to F
+point0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z0 and the goal here is very similar to
+
+ align:start position:0%
+z0 and the goal here is very similar to
+ 
+
+ align:start position:0%
+z0 and the goal here is very similar to
+the the concept of the range in the last
+
+ align:start position:0%
+the the concept of the range in the last
+ 
+
+ align:start position:0%
+the the concept of the range in the last
+goal but in this case it's a little more
+
+ align:start position:0%
+goal but in this case it's a little more
+ 
+
+ align:start position:0%
+goal but in this case it's a little more
+direct we're going to show it in the
+
+ align:start position:0%
+direct we're going to show it in the
+ 
+
+ align:start position:0%
+direct we're going to show it in the
+following manner uh normally taking an
+
+ align:start position:0%
+following manner uh normally taking an
+ 
+
+ align:start position:0%
+following manner uh normally taking an
+application of one of our transition
+
+ align:start position:0%
+application of one of our transition
+ 
+
+ align:start position:0%
+application of one of our transition
+rules to a state is going to do one of
+
+ align:start position:0%
+rules to a state is going to do one of
+ 
+
+ align:start position:0%
+rules to a state is going to do one of
+two things it's either going to reduce
+
+ align:start position:0%
+two things it's either going to reduce
+ 
+
+ align:start position:0%
+two things it's either going to reduce
+the maximum value or it's going to leave
+
+ align:start position:0%
+the maximum value or it's going to leave
+ 
+
+ align:start position:0%
+the maximum value or it's going to leave
+the maximum value the same so one one
+
+ align:start position:0%
+the maximum value the same so one one
+ 
+
+ align:start position:0%
+the maximum value the same so one one
+case where it stays the same is suppose
+
+ align:start position:0%
+case where it stays the same is suppose
+ 
+
+ align:start position:0%
+case where it stays the same is suppose
+we have the state two 0
+
+ align:start position:0%
+we have the state two 0
+ 
+
+ align:start position:0%
+we have the state two 0
+to0 the transition here goes to 2222 and
+
+ align:start position:0%
+to0 the transition here goes to 2222 and
+ 
+
+ align:start position:0%
+to0 the transition here goes to 2222 and
+we haven't decreased it at all um it
+
+ align:start position:0%
+we haven't decreased it at all um it
+ 
+
+ align:start position:0%
+we haven't decreased it at all um it
+decreases maybe sorry
+
+ align:start position:0%
+decreases maybe sorry
+ 
+
+ align:start position:0%
+decreases maybe sorry
+4321 and this is going to go 2 1 one one
+
+ align:start position:0%
+4321 and this is going to go 2 1 one one
+ 
+
+ align:start position:0%
+4321 and this is going to go 2 1 one one
+3 so the maximum value has gone from
+
+ align:start position:0%
+3 so the maximum value has gone from
+ 
+
+ align:start position:0%
+3 so the maximum value has gone from
+four to three and because we're
+
+ align:start position:0%
+four to three and because we're
+ 
+
+ align:start position:0%
+four to three and because we're
+subtracting taking absent values is
+
+ align:start position:0%
+subtracting taking absent values is
+ 
+
+ align:start position:0%
+subtracting taking absent values is
+clearly not going to get lar so it' be
+
+ align:start position:0%
+clearly not going to get lar so it' be
+ 
+
+ align:start position:0%
+clearly not going to get lar so it' be
+nice to find some sort of uh sequence of
+
+ align:start position:0%
+nice to find some sort of uh sequence of
+ 
+
+ align:start position:0%
+nice to find some sort of uh sequence of
+steps that we can claim always decreases
+
+ align:start position:0%
+steps that we can claim always decreases
+ 
+
+ align:start position:0%
+steps that we can claim always decreases
+is the maximum value because if we have
+
+ align:start position:0%
+is the maximum value because if we have
+ 
+
+ align:start position:0%
+is the maximum value because if we have
+that then we have an inductive proof
+
+ align:start position:0%
+that then we have an inductive proof
+ 
+
+ align:start position:0%
+that then we have an inductive proof
+that basically says reduce the maximum
+
+ align:start position:0%
+that basically says reduce the maximum
+ 
+
+ align:start position:0%
+that basically says reduce the maximum
+value for each of them until you get to
+
+ align:start position:0%
+value for each of them until you get to
+ 
+
+ align:start position:0%
+value for each of them until you get to
+zero so it turns out such a sequence of
+
+ align:start position:0%
+zero so it turns out such a sequence of
+ 
+
+ align:start position:0%
+zero so it turns out such a sequence of
+steps exists and we're going to do it
+
+ align:start position:0%
+steps exists and we're going to do it
+ 
+
+ align:start position:0%
+steps exists and we're going to do it
+constructively by uh looking at
+
+ align:start position:0%
+constructively by uh looking at
+ 
+
+ align:start position:0%
+constructively by uh looking at
+pares so here's the proof uh we'll start
+
+ align:start position:0%
+pares so here's the proof uh we'll start
+ 
+
+ align:start position:0%
+pares so here's the proof uh we'll start
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L so given a state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a all entries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of four operations of this transition
+
+ align:start position:0%
+of four operations of this transition
+ 
+
+ align:start position:0%
+of four operations of this transition
+rule in a are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even so let's start with some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules for uh subtraction of even not
+
+ align:start position:0%
+rules for uh subtraction of even not
+ 
+
+ align:start position:0%
+rules for uh subtraction of even not
+numbers it's good to start with some of
+
+ align:start position:0%
+numbers it's good to start with some of
+ 
+
+ align:start position:0%
+numbers it's good to start with some of
+these uh we have an even number minus an
+
+ align:start position:0%
+these uh we have an even number minus an
+ 
+
+ align:start position:0%
+these uh we have an even number minus an
+even number is an even number an odd
+
+ align:start position:0%
+even number is an even number an odd
+ 
+
+ align:start position:0%
+even number is an even number an odd
+number minus an odd number is an odd
+
+ align:start position:0%
+number minus an odd number is an odd
+ 
+
+ align:start position:0%
+number minus an odd number is an odd
+number evenus odd is odd odd minus even
+
+ align:start position:0%
+number evenus odd is odd odd minus even
+ 
+
+ align:start position:0%
+number evenus odd is odd odd minus even
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+odd you mean odd minus odd is even odd
+
+ align:start position:0%
+odd you mean odd minus odd is even odd
+ 
+
+ align:start position:0%
+odd you mean odd minus odd is even odd
+minus odd is I do mean that
+
+ align:start position:0%
+minus odd is I do mean that
+ 
+
+ align:start position:0%
+minus odd is I do mean that
+yes lot of e and O's here um and so
+
+ align:start position:0%
+yes lot of e and O's here um and so
+ 
+
+ align:start position:0%
+yes lot of e and O's here um and so
+we'll do this by looking
+
+ align:start position:0%
+we'll do this by looking
+ 
+
+ align:start position:0%
+we'll do this by looking
+at some of the states that we'll need so
+
+ align:start position:0%
+at some of the states that we'll need so
+ 
+
+ align:start position:0%
+at some of the states that we'll need so
+clearly if I have a state that has uh
+
+ align:start position:0%
+clearly if I have a state that has uh
+ 
+
+ align:start position:0%
+clearly if I have a state that has uh
+four even numbers in it and we'll we'll
+
+ align:start position:0%
+four even numbers in it and we'll we'll
+ 
+
+ align:start position:0%
+four even numbers in it and we'll we'll
+use uh right here if we have four even
+
+ align:start position:0%
+use uh right here if we have four even
+ 
+
+ align:start position:0%
+use uh right here if we have four even
+numbers doing the subtraction we're
+
+ align:start position:0%
+numbers doing the subtraction we're
+ 
+
+ align:start position:0%
+numbers doing the subtraction we're
+always going to have even numbers so
+
+ align:start position:0%
+always going to have even numbers so
+ 
+
+ align:start position:0%
+always going to have even numbers so
+that that state goes to itself uh what
+
+ align:start position:0%
+that that state goes to itself uh what
+ 
+
+ align:start position:0%
+that that state goes to itself uh what
+state can we get that leads to four even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers any
+
+ align:start position:0%
+numbers any
+ 
+
+ align:start position:0%
+numbers any
+thoughts four odd four odd numbers yes
+
+ align:start position:0%
+thoughts four odd four odd numbers yes
+ 
+
+ align:start position:0%
+thoughts four odd four odd numbers yes
+okay okay what goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yeah even odd even
+
+ align:start position:0%
+here yeah even odd even
+ 
+
+ align:start position:0%
+here yeah even odd even
+odd okay and then what goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this one is even even odd
+
+ align:start position:0%
+here this one is even even odd
+ 
+
+ align:start position:0%
+here this one is even even odd
+odd uh and then we have the interesting
+
+ align:start position:0%
+odd uh and then we have the interesting
+ 
+
+ align:start position:0%
+odd uh and then we have the interesting
+case where there are in fact two things
+
+ align:start position:0%
+case where there are in fact two things
+ 
+
+ align:start position:0%
+case where there are in fact two things
+that go in here uh and one of these is
+
+ align:start position:0%
+that go in here uh and one of these is
+ 
+
+ align:start position:0%
+that go in here uh and one of these is
+even even even
+
+ align:start position:0%
+even even even
+ 
+
+ align:start position:0%
+even even even
+odd and the other one not surprisingly
+
+ align:start position:0%
+odd and the other one not surprisingly
+ 
+
+ align:start position:0%
+odd and the other one not surprisingly
+is odd odd odd even and so this sort of
+
+ align:start position:0%
+is odd odd odd even and so this sort of
+ 
+
+ align:start position:0%
+is odd odd odd even and so this sort of
+covers the universe of States this one
+
+ align:start position:0%
+covers the universe of States this one
+ 
+
+ align:start position:0%
+covers the universe of States this one
+has three evens this these two have the
+
+ align:start position:0%
+has three evens this these two have the
+ 
+
+ align:start position:0%
+has three evens this these two have the
+the cases where you have two evens you
+
+ align:start position:0%
+the cases where you have two evens you
+ 
+
+ align:start position:0%
+the cases where you have two evens you
+know the Symmetry this one has four
+
+ align:start position:0%
+know the Symmetry this one has four
+ 
+
+ align:start position:0%
+know the Symmetry this one has four
+evens this one has no even
+
+ align:start position:0%
+evens this one has no even
+ 
+
+ align:start position:0%
+evens this one has no even
+numbers so this is sort of proof by
+
+ align:start position:0%
+numbers so this is sort of proof by
+ 
+
+ align:start position:0%
+numbers so this is sort of proof by
+picture I can take four steps from any
+
+ align:start position:0%
+picture I can take four steps from any
+ 
+
+ align:start position:0%
+picture I can take four steps from any
+of these states and end up in a step
+
+ align:start position:0%
+of these states and end up in a step
+ 
+
+ align:start position:0%
+of these states and end up in a step
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+all okay great so now we're going to
+
+ align:start position:0%
+all okay great so now we're going to
+ 
+
+ align:start position:0%
+all okay great so now we're going to
+prove this this theorem up here that all
+
+ align:start position:0%
+prove this this theorem up here that all
+ 
+
+ align:start position:0%
+prove this this theorem up here that all
+four value gains conver to 0 and the
+
+ align:start position:0%
+four value gains conver to 0 and the
+ 
+
+ align:start position:0%
+four value gains conver to 0 and the
+trick uses the concept of equivalence
+
+ align:start position:0%
+trick uses the concept of equivalence
+ 
+
+ align:start position:0%
+trick uses the concept of equivalence
+that we talked about earlier so if I
+
+ align:start position:0%
+that we talked about earlier so if I
+ 
+
+ align:start position:0%
+that we talked about earlier so if I
+have some State a
+
+ align:start position:0%
+have some State a
+ 
+
+ align:start position:0%
+have some State a
+here uh I'm going to take four
+
+ align:start position:0%
+here uh I'm going to take four
+ 
+
+ align:start position:0%
+here uh I'm going to take four
+steps and I'm going to call this state a
+
+ align:start position:0%
+steps and I'm going to call this state a
+ 
+
+ align:start position:0%
+steps and I'm going to call this state a
+prime so a prime is guaranteed to have
+
+ align:start position:0%
+prime so a prime is guaranteed to have
+ 
+
+ align:start position:0%
+prime so a prime is guaranteed to have
+all even all even
+
+ align:start position:0%
+all even all even
+ 
+
+ align:start position:0%
+all even all even
+values uh and we're going to let the the
+
+ align:start position:0%
+values uh and we're going to let the the
+ 
+
+ align:start position:0%
+values uh and we're going to let the the
+maximum value in this original state so
+
+ align:start position:0%
+maximum value in this original state so
+ 
+
+ align:start position:0%
+maximum value in this original state so
+um maximum value over a will let this be
+
+ align:start position:0%
+um maximum value over a will let this be
+ 
+
+ align:start position:0%
+um maximum value over a will let this be
+now so after taking four steps I have a
+
+ align:start position:0%
+now so after taking four steps I have a
+ 
+
+ align:start position:0%
+now so after taking four steps I have a
+state that has all even values and I'd
+
+ align:start position:0%
+state that has all even values and I'd
+ 
+
+ align:start position:0%
+state that has all even values and I'd
+like to say uh well let's find an
+
+ align:start position:0%
+like to say uh well let's find an
+ 
+
+ align:start position:0%
+like to say uh well let's find an
+equivalent State a state that has the
+
+ align:start position:0%
+equivalent State a state that has the
+ 
+
+ align:start position:0%
+equivalent State a state that has the
+same long-term Behavior so I'm going to
+
+ align:start position:0%
+same long-term Behavior so I'm going to
+ 
+
+ align:start position:0%
+same long-term Behavior so I'm going to
+pull out a factor of two I'm going to
+
+ align:start position:0%
+pull out a factor of two I'm going to
+ 
+
+ align:start position:0%
+pull out a factor of two I'm going to
+you know this is this is equivalent to
+
+ align:start position:0%
+you know this is this is equivalent to
+ 
+
+ align:start position:0%
+you know this is this is equivalent to
+12 a prime so we'll we call this we'll
+
+ align:start position:0%
+12 a prime so we'll we call this we'll
+ 
+
+ align:start position:0%
+12 a prime so we'll we call this we'll
+call this state B the maximum value in B
+
+ align:start position:0%
+call this state B the maximum value in B
+ 
+
+ align:start position:0%
+call this state B the maximum value in B
+is guaranteed to be smaller than the
+
+ align:start position:0%
+is guaranteed to be smaller than the
+ 
+
+ align:start position:0%
+is guaranteed to be smaller than the
+maximum value in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is less than
+
+ align:start position:0%
+a is less than
+ 
+
+ align:start position:0%
+a is less than
+that so this is a way of of uh
+
+ align:start position:0%
+that so this is a way of of uh
+ 
+
+ align:start position:0%
+that so this is a way of of uh
+demonstrating inductively that we're
+
+ align:start position:0%
+demonstrating inductively that we're
+ 
+
+ align:start position:0%
+demonstrating inductively that we're
+going to you know we have this process
+
+ align:start position:0%
+going to you know we have this process
+ 
+
+ align:start position:0%
+going to you know we have this process
+that exists to decrease the maximum
+
+ align:start position:0%
+that exists to decrease the maximum
+ 
+
+ align:start position:0%
+that exists to decrease the maximum
+value and so now an a stute person might
+
+ align:start position:0%
+value and so now an a stute person might
+ 
+
+ align:start position:0%
+value and so now an a stute person might
+say how do I know this terminates well
+
+ align:start position:0%
+say how do I know this terminates well
+ 
+
+ align:start position:0%
+say how do I know this terminates well
+it turns out that the non- negative
+
+ align:start position:0%
+it turns out that the non- negative
+ 
+
+ align:start position:0%
+it turns out that the non- negative
+integers in fact have a least value
+
+ align:start position:0%
+integers in fact have a least value
+ 
+
+ align:start position:0%
+integers in fact have a least value
+which is zero and uh so we'll terminate
+
+ align:start position:0%
+which is zero and uh so we'll terminate
+ 
+
+ align:start position:0%
+which is zero and uh so we'll terminate
+at 0 0 0 0 this property does not exist
+
+ align:start position:0%
+at 0 0 0 0 this property does not exist
+ 
+
+ align:start position:0%
+at 0 0 0 0 this property does not exist
+for the real numbers so it's just
+
+ align:start position:0%
+for the real numbers so it's just
+ 
+
+ align:start position:0%
+for the real numbers so it's just
+something to keep in mind they're not uh
+
+ align:start position:0%
+something to keep in mind they're not uh
+ 
+
+ align:start position:0%
+something to keep in mind they're not uh
+they're not well
+
+ align:start position:0%
+they're not well
+ 
+
+ align:start position:0%
+they're not well
+ordered
+
+ align:start position:0%
+ordered
+ 
+
+ align:start position:0%
+ordered
+okay so hopefully this is a reasonably
+
+ align:start position:0%
+okay so hopefully this is a reasonably
+ 
+
+ align:start position:0%
+okay so hopefully this is a reasonably
+direct proof this actually gives a nice
+
+ align:start position:0%
+direct proof this actually gives a nice
+ 
+
+ align:start position:0%
+direct proof this actually gives a nice
+bound on how long one of these games
+
+ align:start position:0%
+bound on how long one of these games
+ 
+
+ align:start position:0%
+bound on how long one of these games
+will take to termin a um it's kind of a
+
+ align:start position:0%
+will take to termin a um it's kind of a
+ 
+
+ align:start position:0%
+will take to termin a um it's kind of a
+crude bound as we show in the paper but
+
+ align:start position:0%
+crude bound as we show in the paper but
+ 
+
+ align:start position:0%
+crude bound as we show in the paper but
+uh the you're going to take at most four
+
+ align:start position:0%
+uh the you're going to take at most four
+ 
+
+ align:start position:0%
+uh the you're going to take at most four
+steps at most log two time so you have
+
+ align:start position:0%
+steps at most log two time so you have
+ 
+
+ align:start position:0%
+steps at most log two time so you have
+the maximum value you're going to take
+
+ align:start position:0%
+the maximum value you're going to take
+ 
+
+ align:start position:0%
+the maximum value you're going to take
+it you're going to be able to have it at
+
+ align:start position:0%
+it you're going to be able to have it at
+ 
+
+ align:start position:0%
+it you're going to be able to have it at
+most log two times the max value so the
+
+ align:start position:0%
+most log two times the max value so the
+ 
+
+ align:start position:0%
+most log two times the max value so the
+the uh the maximum game length is at
+
+ align:start position:0%
+the uh the maximum game length is at
+ 
+
+ align:start position:0%
+the uh the maximum game length is at
+most um L is at most four steps time log
+
+ align:start position:0%
+most um L is at most four steps time log
+ 
+
+ align:start position:0%
+most um L is at most four steps time log
+two of the max
+
+ align:start position:0%
+two of the max
+ 
+
+ align:start position:0%
+two of the max
+value okay so now we'll talk about the
+
+ align:start position:0%
+value okay so now we'll talk about the
+ 
+
+ align:start position:0%
+value okay so now we'll talk about the
+uh the first we talk about the four
+
+ align:start position:0%
+uh the first we talk about the four
+ 
+
+ align:start position:0%
+uh the first we talk about the four
+value game on the real numbers and there
+
+ align:start position:0%
+value game on the real numbers and there
+ 
+
+ align:start position:0%
+value game on the real numbers and there
+will be a natural extension to fact the
+
+ align:start position:0%
+will be a natural extension to fact the
+ 
+
+ align:start position:0%
+will be a natural extension to fact the
+end value game on the real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the idea here is to sort of
+
+ align:start position:0%
+okay so the idea here is to sort of
+ 
+
+ align:start position:0%
+okay so the idea here is to sort of
+construct a generalization of this
+
+ align:start position:0%
+construct a generalization of this
+ 
+
+ align:start position:0%
+construct a generalization of this
+transition operator as a linear operator
+
+ align:start position:0%
+transition operator as a linear operator
+ 
+
+ align:start position:0%
+transition operator as a linear operator
+it' be really nice to have a linear
+
+ align:start position:0%
+it' be really nice to have a linear
+ 
+
+ align:start position:0%
+it' be really nice to have a linear
+operator now the absolute value function
+
+ align:start position:0%
+operator now the absolute value function
+ 
+
+ align:start position:0%
+operator now the absolute value function
+is not a linear function which is kind
+
+ align:start position:0%
+is not a linear function which is kind
+ 
+
+ align:start position:0%
+is not a linear function which is kind
+of a bummer but it turns out that we can
+
+ align:start position:0%
+of a bummer but it turns out that we can
+ 
+
+ align:start position:0%
+of a bummer but it turns out that we can
+put some constraints on the inputs to
+
+ align:start position:0%
+put some constraints on the inputs to
+ 
+
+ align:start position:0%
+put some constraints on the inputs to
+this linear operator that allow us to
+
+ align:start position:0%
+this linear operator that allow us to
+ 
+
+ align:start position:0%
+this linear operator that allow us to
+you know ignore the fact that the
+
+ align:start position:0%
+you know ignore the fact that the
+ 
+
+ align:start position:0%
+you know ignore the fact that the
+absolute value function is not linear
+
+ align:start position:0%
+absolute value function is not linear
+ 
+
+ align:start position:0%
+absolute value function is not linear
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+idea linearize t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's the one one direct way to do
+
+ align:start position:0%
+so let's the one one direct way to do
+ 
+
+ align:start position:0%
+so let's the one one direct way to do
+this is to say um I'm going to require
+
+ align:start position:0%
+this is to say um I'm going to require
+ 
+
+ align:start position:0%
+this is to say um I'm going to require
+all of the input states to be in
+
+ align:start position:0%
+all of the input states to be in
+ 
+
+ align:start position:0%
+all of the input states to be in
+increasing order now this seems like
+
+ align:start position:0%
+increasing order now this seems like
+ 
+
+ align:start position:0%
+increasing order now this seems like
+this isn't going anywhere but bear with
+
+ align:start position:0%
+this isn't going anywhere but bear with
+ 
+
+ align:start position:0%
+this isn't going anywhere but bear with
+me so if I have a less than or equal to
+
+ align:start position:0%
+me so if I have a less than or equal to
+ 
+
+ align:start position:0%
+me so if I have a less than or equal to
+B less than or equal to C less than or
+
+ align:start position:0%
+B less than or equal to C less than or
+ 
+
+ align:start position:0%
+B less than or equal to C less than or
+equal to D then the old transition
+
+ align:start position:0%
+equal to D then the old transition
+ 
+
+ align:start position:0%
+equal to D then the old transition
+operator would have you know a b c d is
+
+ align:start position:0%
+operator would have you know a b c d is
+ 
+
+ align:start position:0%
+operator would have you know a b c d is
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+to absolute value of B
+
+ align:start position:0%
+to absolute value of B
+ 
+
+ align:start position:0%
+to absolute value of B
+a absolute value of cus B absolute value
+
+ align:start position:0%
+a absolute value of cus B absolute value
+ 
+
+ align:start position:0%
+a absolute value of cus B absolute value
+of B minus C absolute value of a minus
+
+ align:start position:0%
+of B minus C absolute value of a minus
+ 
+
+ align:start position:0%
+of B minus C absolute value of a minus
+t if I have this constraint I can
+
+ align:start position:0%
+t if I have this constraint I can
+ 
+
+ align:start position:0%
+t if I have this constraint I can
+actually remove these absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signs so uh B is larger than a so this
+
+ align:start position:0%
+signs so uh B is larger than a so this
+ 
+
+ align:start position:0%
+signs so uh B is larger than a so this
+will be B minus a c is larger than b d
+
+ align:start position:0%
+will be B minus a c is larger than b d
+ 
+
+ align:start position:0%
+will be B minus a c is larger than b d
+is larger than C and then D is larger
+
+ align:start position:0%
+is larger than C and then D is larger
+ 
+
+ align:start position:0%
+is larger than C and then D is larger
+than a so this one flips sign here way I
+
+ align:start position:0%
+than a so this one flips sign here way I
+ 
+
+ align:start position:0%
+than a so this one flips sign here way I
+get D minus
+
+ align:start position:0%
+get D minus
+ 
+
+ align:start position:0%
+get D minus
+a so we can represent this transition as
+
+ align:start position:0%
+a so we can represent this transition as
+ 
+
+ align:start position:0%
+a so we can represent this transition as
+a matrix now so we'll let T and I'm
+
+ align:start position:0%
+a matrix now so we'll let T and I'm
+ 
+
+ align:start position:0%
+a matrix now so we'll let T and I'm
+going to specifically call this T4
+
+ align:start position:0%
+going to specifically call this T4
+ 
+
+ align:start position:0%
+going to specifically call this T4
+because we're going to be generalizing
+
+ align:start position:0%
+because we're going to be generalizing
+ 
+
+ align:start position:0%
+because we're going to be generalizing
+this transition to the end value game
+
+ align:start position:0%
+this transition to the end value game
+ 
+
+ align:start position:0%
+this transition to the end value game
+but T4 looks something like this so um
+
+ align:start position:0%
+but T4 looks something like this so um
+ 
+
+ align:start position:0%
+but T4 looks something like this so um
+we're going to be getting a minus a plus
+
+ align:start position:0%
+we're going to be getting a minus a plus
+ 
+
+ align:start position:0%
+we're going to be getting a minus a plus
+b here - b + C - C + D and then there's
+
+ align:start position:0%
+b here - b + C - C + D and then there's
+ 
+
+ align:start position:0%
+b here - b + C - C + D and then there's
+Min - A
+
+ align:start position:0%
+Min - A
+ 
+
+ align:start position:0%
+Min - A
+plus the Zer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and you guys can verify that if we
+
+ align:start position:0%
+here and you guys can verify that if we
+ 
+
+ align:start position:0%
+here and you guys can verify that if we
+multiply this by ABC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D we get
+
+ align:start position:0%
+D we get
+ 
+
+ align:start position:0%
+D we get
+out b - A cus B D- C tus
+
+ align:start position:0%
+out b - A cus B D- C tus
+ 
+
+ align:start position:0%
+out b - A cus B D- C tus
+a take a second and convince yourself
+
+ align:start position:0%
+a take a second and convince yourself
+ 
+
+ align:start position:0%
+a take a second and convince yourself
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+true switch minus signs okay and uh in
+
+ align:start position:0%
+true switch minus signs okay and uh in
+ 
+
+ align:start position:0%
+true switch minus signs okay and uh in
+in the general case we can extend this
+
+ align:start position:0%
+in the general case we can extend this
+ 
+
+ align:start position:0%
+in the general case we can extend this
+T4 the TN and the pattern of the Matrix
+
+ align:start position:0%
+T4 the TN and the pattern of the Matrix
+ 
+
+ align:start position:0%
+T4 the TN and the pattern of the Matrix
+is very similar you have a band of minus
+
+ align:start position:0%
+is very similar you have a band of minus
+ 
+
+ align:start position:0%
+is very similar you have a band of minus
+one one-1 oneus one one all the way down
+
+ align:start position:0%
+one one-1 oneus one one all the way down
+ 
+
+ align:start position:0%
+one one-1 oneus one one all the way down
+to the last row where you have a minus
+
+ align:start position:0%
+to the last row where you have a minus
+ 
+
+ align:start position:0%
+to the last row where you have a minus
+one in this bottom left corner and a one
+
+ align:start position:0%
+one in this bottom left corner and a one
+ 
+
+ align:start position:0%
+one in this bottom left corner and a one
+in the bottom right
+
+ align:start position:0%
+in the bottom right
+ 
+
+ align:start position:0%
+in the bottom right
+corner uh so now we'd like to talk
+
+ align:start position:0%
+corner uh so now we'd like to talk
+ 
+
+ align:start position:0%
+corner uh so now we'd like to talk
+reason a little bit about state so
+
+ align:start position:0%
+reason a little bit about state so
+ 
+
+ align:start position:0%
+reason a little bit about state so
+there's another problem with this a very
+
+ align:start position:0%
+there's another problem with this a very
+ 
+
+ align:start position:0%
+there's another problem with this a very
+obvious problem and that is if we have
+
+ align:start position:0%
+obvious problem and that is if we have
+ 
+
+ align:start position:0%
+obvious problem and that is if we have
+this constraint that the the inputs to
+
+ align:start position:0%
+this constraint that the the inputs to
+ 
+
+ align:start position:0%
+this constraint that the the inputs to
+this linear operator are in increasing
+
+ align:start position:0%
+this linear operator are in increasing
+ 
+
+ align:start position:0%
+this linear operator are in increasing
+order there's no guarantee that this
+
+ align:start position:0%
+order there's no guarantee that this
+ 
+
+ align:start position:0%
+order there's no guarantee that this
+output is increasing order but the the
+
+ align:start position:0%
+output is increasing order but the the
+ 
+
+ align:start position:0%
+output is increasing order but the the
+fix for this problem is to say well
+
+ align:start position:0%
+fix for this problem is to say well
+ 
+
+ align:start position:0%
+fix for this problem is to say well
+let's consider what what in what cases
+
+ align:start position:0%
+let's consider what what in what cases
+ 
+
+ align:start position:0%
+let's consider what what in what cases
+do we maintain that in variant and the
+
+ align:start position:0%
+do we maintain that in variant and the
+ 
+
+ align:start position:0%
+do we maintain that in variant and the
+case that then variance maintain is when
+
+ align:start position:0%
+case that then variance maintain is when
+ 
+
+ align:start position:0%
+case that then variance maintain is when
+this is an in a positive increasing I
+
+ align:start position:0%
+this is an in a positive increasing I
+ 
+
+ align:start position:0%
+this is an in a positive increasing I
+Vector of this transition Matrix so our
+
+ align:start position:0%
+Vector of this transition Matrix so our
+ 
+
+ align:start position:0%
+Vector of this transition Matrix so our
+our goal now is sort of to search or
+
+ align:start position:0%
+our goal now is sort of to search or
+ 
+
+ align:start position:0%
+our goal now is sort of to search or
+rather to prove that you know we can
+
+ align:start position:0%
+rather to prove that you know we can
+ 
+
+ align:start position:0%
+rather to prove that you know we can
+find some IG vectors that are positive
+
+ align:start position:0%
+find some IG vectors that are positive
+ 
+
+ align:start position:0%
+find some IG vectors that are positive
+and increasing along with a positive I
+
+ align:start position:0%
+and increasing along with a positive I
+ 
+
+ align:start position:0%
+and increasing along with a positive I
+can value and that that will actually
+
+ align:start position:0%
+can value and that that will actually
+ 
+
+ align:start position:0%
+can value and that that will actually
+give us something really cool if we can
+
+ align:start position:0%
+give us something really cool if we can
+ 
+
+ align:start position:0%
+give us something really cool if we can
+show that that exists for each one of
+
+ align:start position:0%
+show that that exists for each one of
+ 
+
+ align:start position:0%
+show that that exists for each one of
+these T subn matrices then we're going
+
+ align:start position:0%
+these T subn matrices then we're going
+ 
+
+ align:start position:0%
+these T subn matrices then we're going
+to have a non-re repeating sequence
+
+ align:start position:0%
+to have a non-re repeating sequence
+ 
+
+ align:start position:0%
+to have a non-re repeating sequence
+because we'll be able to operate
+
+ align:start position:0%
+because we'll be able to operate
+ 
+
+ align:start position:0%
+because we'll be able to operate
+multiple times and we'll basically form
+
+ align:start position:0%
+multiple times and we'll basically form
+ 
+
+ align:start position:0%
+multiple times and we'll basically form
+a geometric series with the values that
+
+ align:start position:0%
+a geometric series with the values that
+ 
+
+ align:start position:0%
+a geometric series with the values that
+will give us some cool States uh and so
+
+ align:start position:0%
+will give us some cool States uh and so
+ 
+
+ align:start position:0%
+will give us some cool States uh and so
+in the paper we actually do this you can
+
+ align:start position:0%
+in the paper we actually do this you can
+ 
+
+ align:start position:0%
+in the paper we actually do this you can
+you can work through the characteristic
+
+ align:start position:0%
+you can work through the characteristic
+ 
+
+ align:start position:0%
+you can work through the characteristic
+polinomial by expanding the determinant
+
+ align:start position:0%
+polinomial by expanding the determinant
+ 
+
+ align:start position:0%
+polinomial by expanding the determinant
+here and you'll get you know an upper
+
+ align:start position:0%
+here and you'll get you know an upper
+ 
+
+ align:start position:0%
+here and you'll get you know an upper
+triangular Matrix lower triangular
+
+ align:start position:0%
+triangular Matrix lower triangular
+ 
+
+ align:start position:0%
+triangular Matrix lower triangular
+Matrix and there's some nice math we're
+
+ align:start position:0%
+Matrix and there's some nice math we're
+ 
+
+ align:start position:0%
+Matrix and there's some nice math we're
+going to skip here it's pretty it's
+
+ align:start position:0%
+going to skip here it's pretty it's
+ 
+
+ align:start position:0%
+going to skip here it's pretty it's
+pretty algebra intensive it turns out
+
+ align:start position:0%
+pretty algebra intensive it turns out
+ 
+
+ align:start position:0%
+pretty algebra intensive it turns out
+that uh you you'll get um a
+
+ align:start position:0%
+that uh you you'll get um a
+ 
+
+ align:start position:0%
+that uh you you'll get um a
+characteristic polinomial for for t sub
+
+ align:start position:0%
+characteristic polinomial for for t sub
+ 
+
+ align:start position:0%
+characteristic polinomial for for t sub
+n 1 - lamb n * 1 + lamb n to the n- 1 =
+
+ align:start position:0%
+n 1 - lamb n * 1 + lamb n to the n- 1 =
+ 
+
+ align:start position:0%
+n 1 - lamb n * 1 + lamb n to the n- 1 =
+1 and then with a little more algebra
+
+ align:start position:0%
+1 and then with a little more algebra
+ 
+
+ align:start position:0%
+1 and then with a little more algebra
+bashing you can actually bound these
+
+ align:start position:0%
+bashing you can actually bound these
+ 
+
+ align:start position:0%
+bashing you can actually bound these
+igen values between zero and one uh and
+
+ align:start position:0%
+igen values between zero and one uh and
+ 
+
+ align:start position:0%
+igen values between zero and one uh and
+you can show that that these generate an
+
+ align:start position:0%
+you can show that that these generate an
+ 
+
+ align:start position:0%
+you can show that that these generate an
+igen Vector uh with the values 1 -
+
+ align:start position:0%
+igen Vector uh with the values 1 -
+ 
+
+ align:start position:0%
+igen Vector uh with the values 1 -
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+n 1 - Lambda n 1 + Lambda
+
+ align:start position:0%
+n 1 - Lambda n 1 + Lambda
+ 
+
+ align:start position:0%
+n 1 - Lambda n 1 + Lambda
+n 1 - lamb n 1 + plus lamb n^ 2 all the
+
+ align:start position:0%
+n 1 - lamb n 1 + plus lamb n^ 2 all the
+ 
+
+ align:start position:0%
+n 1 - lamb n 1 + plus lamb n^ 2 all the
+way down to
+
+ align:start position:0%
+way down to
+ 
+
+ align:start position:0%
+way down to
+1 uh so this is going to this sequence
+
+ align:start position:0%
+1 uh so this is going to this sequence
+ 
+
+ align:start position:0%
+1 uh so this is going to this sequence
+we verify that this is an increasing
+
+ align:start position:0%
+we verify that this is an increasing
+ 
+
+ align:start position:0%
+we verify that this is an increasing
+positive sequence uh and it is and uh so
+
+ align:start position:0%
+positive sequence uh and it is and uh so
+ 
+
+ align:start position:0%
+positive sequence uh and it is and uh so
+for the four value case let's look let's
+
+ align:start position:0%
+for the four value case let's look let's
+ 
+
+ align:start position:0%
+for the four value case let's look let's
+look in particular the I value Lambda 4
+
+ align:start position:0%
+look in particular the I value Lambda 4
+ 
+
+ align:start position:0%
+look in particular the I value Lambda 4
+is equal to like 89 I wrote down
+
+ align:start position:0%
+is equal to like 89 I wrote down
+ 
+
+ align:start position:0%
+is equal to like 89 I wrote down
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+8983 929 and the I Vector that that
+
+ align:start position:0%
+8983 929 and the I Vector that that
+ 
+
+ align:start position:0%
+8983 929 and the I Vector that that
+generates is uh 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+.60
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.295 uh
+
+ align:start position:0%
+0.295 uh
+ 
+
+ align:start position:0%
+0.295 uh
+0.543 and then one so this input to the
+
+ align:start position:0%
+0.543 and then one so this input to the
+ 
+
+ align:start position:0%
+0.543 and then one so this input to the
+four value problem on the reals will
+
+ align:start position:0%
+four value problem on the reals will
+ 
+
+ align:start position:0%
+four value problem on the reals will
+generate an infinite nonrepeating
+
+ align:start position:0%
+generate an infinite nonrepeating
+ 
+
+ align:start position:0%
+generate an infinite nonrepeating
+game uh using the equivalence relation
+
+ align:start position:0%
+game uh using the equivalence relation
+ 
+
+ align:start position:0%
+game uh using the equivalence relation
+that we talked about earlier you can
+
+ align:start position:0%
+that we talked about earlier you can
+ 
+
+ align:start position:0%
+that we talked about earlier you can
+actually generate infinitely many
+
+ align:start position:0%
+actually generate infinitely many
+ 
+
+ align:start position:0%
+actually generate infinitely many
+non-repeating infinite games I can
+
+ align:start position:0%
+non-repeating infinite games I can
+ 
+
+ align:start position:0%
+non-repeating infinite games I can
+offset this by whatever I want I can
+
+ align:start position:0%
+offset this by whatever I want I can
+ 
+
+ align:start position:0%
+offset this by whatever I want I can
+scale this by whatever I want and I can
+
+ align:start position:0%
+scale this by whatever I want and I can
+ 
+
+ align:start position:0%
+scale this by whatever I want and I can
+take any permutations from T4 uh so this
+
+ align:start position:0%
+take any permutations from T4 uh so this
+ 
+
+ align:start position:0%
+take any permutations from T4 uh so this
+is kind of a cool way to generate
+
+ align:start position:0%
+is kind of a cool way to generate
+ 
+
+ align:start position:0%
+is kind of a cool way to generate
+infinite families and infinite games and
+
+ align:start position:0%
+infinite families and infinite games and
+ 
+
+ align:start position:0%
+infinite families and infinite games and
+with that we'd like to ask us if there
+
+ align:start position:0%
+with that we'd like to ask us if there
+ 
+
+ align:start position:0%
+with that we'd like to ask us if there
+any questions and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yeah so I had another idea
+
+ align:start position:0%
+questions yeah so I had another idea
+ 
+
+ align:start position:0%
+questions yeah so I had another idea
+about playing this game on R um you said
+
+ align:start position:0%
+about playing this game on R um you said
+ 
+
+ align:start position:0%
+about playing this game on R um you said
+you're you're essentially looking at um
+
+ align:start position:0%
+you're you're essentially looking at um
+ 
+
+ align:start position:0%
+you're you're essentially looking at um
+and you're looking at two PS that are
+
+ align:start position:0%
+and you're looking at two PS that are
+ 
+
+ align:start position:0%
+and you're looking at two PS that are
+with each point taken from the line yeah
+
+ align:start position:0%
+with each point taken from the line yeah
+ 
+
+ align:start position:0%
+with each point taken from the line yeah
+if you allow yourself to use irrational
+
+ align:start position:0%
+if you allow yourself to use irrational
+ 
+
+ align:start position:0%
+if you allow yourself to use irrational
+numbers then you can take the you know
+
+ align:start position:0%
+numbers then you can take the you know
+ 
+
+ align:start position:0%
+numbers then you can take the you know
+the like lattice generated by these
+
+ align:start position:0%
+the like lattice generated by these
+ 
+
+ align:start position:0%
+the like lattice generated by these
+rational numbers in up to end
+
+ align:start position:0%
+rational numbers in up to end
+ 
+
+ align:start position:0%
+rational numbers in up to end
+dimensional space or like you know the
+
+ align:start position:0%
+dimensional space or like you know the
+ 
+
+ align:start position:0%
+dimensional space or like you know the
+rational Vector space whatever um and
+
+ align:start position:0%
+rational Vector space whatever um and
+ 
+
+ align:start position:0%
+rational Vector space whatever um and
+then you're playing the same game with
+
+ align:start position:0%
+then you're playing the same game with
+ 
+
+ align:start position:0%
+then you're playing the same game with
+the points taken from a lattice it's
+
+ align:start position:0%
+the points taken from a lattice it's
+ 
+
+ align:start position:0%
+the points taken from a lattice it's
+like a polytop like yeah yeah that kind
+
+ align:start position:0%
+like a polytop like yeah yeah that kind
+ 
+
+ align:start position:0%
+like a polytop like yeah yeah that kind
+of thing so um I I don't know maybe you
+
+ align:start position:0%
+of thing so um I I don't know maybe you
+ 
+
+ align:start position:0%
+of thing so um I I don't know maybe you
+can get some interesting geometric
+
+ align:start position:0%
+can get some interesting geometric
+ 
+
+ align:start position:0%
+can get some interesting geometric
+intuition about what playing the game on
+
+ align:start position:0%
+intuition about what playing the game on
+ 
+
+ align:start position:0%
+intuition about what playing the game on
+R looks like yeah we were we actually
+
+ align:start position:0%
+R looks like yeah we were we actually
+ 
+
+ align:start position:0%
+R looks like yeah we were we actually
+were spending a lot of time trying to
+
+ align:start position:0%
+were spending a lot of time trying to
+ 
+
+ align:start position:0%
+were spending a lot of time trying to
+get geometric insight to this problem
+
+ align:start position:0%
+get geometric insight to this problem
+ 
+
+ align:start position:0%
+get geometric insight to this problem
+and I think I think we didn't actually
+
+ align:start position:0%
+and I think I think we didn't actually
+ 
+
+ align:start position:0%
+and I think I think we didn't actually
+stumble ac across anything interesting
+
+ align:start position:0%
+stumble ac across anything interesting
+ 
+
+ align:start position:0%
+stumble ac across anything interesting
+but that lot harder though yeah
+
+ align:start position:0%
+but that lot harder though yeah
+ 
+
+ align:start position:0%
+but that lot harder though yeah
+especially you have these growing things
+
+ align:start position:0%
+especially you have these growing things
+ 
+
+ align:start position:0%
+especially you have these growing things
+with the I value like how would that
+
+ align:start position:0%
+with the I value like how would that
+ 
+
+ align:start position:0%
+with the I value like how would that
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay great thank you very much
+
+ align:start position:0%
+yeah okay great thank you very much
+ 
+
+ align:start position:0%
+yeah okay great thank you very much
+thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/1UD560RQ684.txt b/1UD560RQ684.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e4e1df6c60626c98932aad4451fe2afa34f19a4a
--- /dev/null
+++ b/1UD560RQ684.txt
@@ -0,0 +1,891 @@
+align:start position:0%
+ 
+let's now consider our rolling wheel and
+
+ align:start position:0%
+let's now consider our rolling wheel and
+ 
+
+ align:start position:0%
+let's now consider our rolling wheel and
+we want to look at some special
+
+ align:start position:0%
+we want to look at some special
+ 
+
+ align:start position:0%
+we want to look at some special
+conditions so at
+
+ align:start position:0%
+conditions so at
+ 
+
+ align:start position:0%
+conditions so at
+time T equals
+
+ align:start position:0%
+time T equals
+ 
+
+ align:start position:0%
+time T equals
+z and we'll have our wheel that's
+
+ align:start position:0%
+z and we'll have our wheel that's
+ 
+
+ align:start position:0%
+z and we'll have our wheel that's
+rolling here's the ground um let's say
+
+ align:start position:0%
+rolling here's the ground um let's say
+ 
+
+ align:start position:0%
+rolling here's the ground um let's say
+that our Point p is right up here at the
+
+ align:start position:0%
+that our Point p is right up here at the
+ 
+
+ align:start position:0%
+that our Point p is right up here at the
+top that's cm and we'll be in the ground
+
+ align:start position:0%
+top that's cm and we'll be in the ground
+ 
+
+ align:start position:0%
+top that's cm and we'll be in the ground
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+now and then at a later
+
+ align:start position:0%
+now and then at a later
+ 
+
+ align:start position:0%
+now and then at a later
+time time T the wheel has moved to the
+
+ align:start position:0%
+time time T the wheel has moved to the
+ 
+
+ align:start position:0%
+time time T the wheel has moved to the
+right so let's draw the wheel over
+
+ align:start position:0%
+right so let's draw the wheel over
+ 
+
+ align:start position:0%
+right so let's draw the wheel over
+here up the greatest picture of the
+
+ align:start position:0%
+here up the greatest picture of the
+ 
+
+ align:start position:0%
+here up the greatest picture of the
+wheel but we'll have the wheel over here
+
+ align:start position:0%
+wheel but we'll have the wheel over here
+ 
+
+ align:start position:0%
+wheel but we'll have the wheel over here
+and now the point P has
+
+ align:start position:0%
+and now the point P has
+ 
+
+ align:start position:0%
+and now the point P has
+moved some angle Delta Theta and we'll
+
+ align:start position:0%
+moved some angle Delta Theta and we'll
+ 
+
+ align:start position:0%
+moved some angle Delta Theta and we'll
+call this time interval delta
+
+ align:start position:0%
+call this time interval delta
+ 
+
+ align:start position:0%
+call this time interval delta
+T now the center of mass of the wheel
+
+ align:start position:0%
+T now the center of mass of the wheel
+ 
+
+ align:start position:0%
+T now the center of mass of the wheel
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+moved a distance X cm is the velocity of
+
+ align:start position:0%
+moved a distance X cm is the velocity of
+ 
+
+ align:start position:0%
+moved a distance X cm is the velocity of
+the center of mass time delta
+
+ align:start position:0%
+the center of mass time delta
+ 
+
+ align:start position:0%
+the center of mass time delta
+T and the point p on the
+
+ align:start position:0%
+T and the point p on the
+ 
+
+ align:start position:0%
+T and the point p on the
+rim this art change this length here on
+
+ align:start position:0%
+rim this art change this length here on
+ 
+
+ align:start position:0%
+rim this art change this length here on
+the rim that P is moved
+
+ align:start position:0%
+the rim that P is moved
+ 
+
+ align:start position:0%
+the rim that P is moved
+around um in the center of Mass frame is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R Delta
+
+ align:start position:0%
+R Delta
+ 
+
+ align:start position:0%
+R Delta
+Theta now we want to ask ourselves we'll
+
+ align:start position:0%
+Theta now we want to ask ourselves we'll
+ 
+
+ align:start position:0%
+Theta now we want to ask ourselves we'll
+call this Delta the X we now have three
+
+ align:start position:0%
+call this Delta the X we now have three
+ 
+
+ align:start position:0%
+call this Delta the X we now have three
+possible conditions we call
+
+ align:start position:0%
+possible conditions we call
+ 
+
+ align:start position:0%
+possible conditions we call
+rolling
+
+ align:start position:0%
+rolling
+ 
+
+ align:start position:0%
+rolling
+without
+
+ align:start position:0%
+without
+ 
+
+ align:start position:0%
+without
+slipping that will be our first case one
+
+ align:start position:0%
+slipping that will be our first case one
+ 
+
+ align:start position:0%
+slipping that will be our first case one
+and that's the case when the AR length
+
+ align:start position:0%
+and that's the case when the AR length
+ 
+
+ align:start position:0%
+and that's the case when the AR length
+Delta s is exactly equal to the distance
+
+ align:start position:0%
+Delta s is exactly equal to the distance
+ 
+
+ align:start position:0%
+Delta s is exactly equal to the distance
+along the
+
+ align:start position:0%
+along the
+ 
+
+ align:start position:0%
+along the
+ground so we have Delta X
+
+ align:start position:0%
+ground so we have Delta X
+ 
+
+ align:start position:0%
+ground so we have Delta X
+cm is Delta s and so we get V CM Delta
+
+ align:start position:0%
+cm is Delta s and so we get V CM Delta
+ 
+
+ align:start position:0%
+cm is Delta s and so we get V CM Delta
+tal R Delta Theta or V cm equal R Delta
+
+ align:start position:0%
+tal R Delta Theta or V cm equal R Delta
+ 
+
+ align:start position:0%
+tal R Delta Theta or V cm equal R Delta
+Theta over delta T now in the
+
+ align:start position:0%
+Theta over delta T now in the
+ 
+
+ align:start position:0%
+Theta over delta T now in the
+limit as delta T goes to zero we have
+
+ align:start position:0%
+limit as delta T goes to zero we have
+ 
+
+ align:start position:0%
+limit as delta T goes to zero we have
+that Delta Theta over delta T in this
+
+ align:start position:0%
+that Delta Theta over delta T in this
+ 
+
+ align:start position:0%
+that Delta Theta over delta T in this
+limit as delta T goes to zero is D Theta
+
+ align:start position:0%
+limit as delta T goes to zero is D Theta
+ 
+
+ align:start position:0%
+limit as delta T goes to zero is D Theta
+DT and that's what we called the angular
+
+ align:start position:0%
+DT and that's what we called the angular
+ 
+
+ align:start position:0%
+DT and that's what we called the angular
+speed so in our
+
+ align:start position:0%
+speed so in our
+ 
+
+ align:start position:0%
+speed so in our
+limit for as this wheel is rolling
+
+ align:start position:0%
+limit for as this wheel is rolling
+ 
+
+ align:start position:0%
+limit for as this wheel is rolling
+without slipping we have the condition
+
+ align:start position:0%
+without slipping we have the condition
+ 
+
+ align:start position:0%
+without slipping we have the condition
+that the velocity V cm
+
+ align:start position:0%
+that the velocity V cm
+ 
+
+ align:start position:0%
+that the velocity V cm
+equals R
+
+ align:start position:0%
+equals R
+ 
+
+ align:start position:0%
+equals R
+Omega so that's our first condition and
+
+ align:start position:0%
+Omega so that's our first condition and
+ 
+
+ align:start position:0%
+Omega so that's our first condition and
+we call this the rolling without
+
+ align:start position:0%
+we call this the rolling without
+ 
+
+ align:start position:0%
+we call this the rolling without
+slipping now what is the CM that's the
+
+ align:start position:0%
+slipping now what is the CM that's the
+ 
+
+ align:start position:0%
+slipping now what is the CM that's the
+velocity of the center of mass of the
+
+ align:start position:0%
+velocity of the center of mass of the
+ 
+
+ align:start position:0%
+velocity of the center of mass of the
+wheel and every single point on this
+
+ align:start position:0%
+wheel and every single point on this
+ 
+
+ align:start position:0%
+wheel and every single point on this
+wheel has that same speed
+
+ align:start position:0%
+wheel has that same speed
+ 
+
+ align:start position:0%
+wheel has that same speed
+and R Omega you can think of that as the
+
+ align:start position:0%
+and R Omega you can think of that as the
+ 
+
+ align:start position:0%
+and R Omega you can think of that as the
+tangential velocity in reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame CM this is just the speed in the
+
+ align:start position:0%
+frame CM this is just the speed in the
+ 
+
+ align:start position:0%
+frame CM this is just the speed in the
+reference frame moving with the center
+
+ align:start position:0%
+reference frame moving with the center
+ 
+
+ align:start position:0%
+reference frame moving with the center
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+mass so this is our condition for
+
+ align:start position:0%
+mass so this is our condition for
+ 
+
+ align:start position:0%
+mass so this is our condition for
+Rolling without
+
+ align:start position:0%
+Rolling without
+ 
+
+ align:start position:0%
+Rolling without
+slipping now if the wheel our second
+
+ align:start position:0%
+slipping now if the wheel our second
+ 
+
+ align:start position:0%
+slipping now if the wheel our second
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+is imagine that the ground that the
+
+ align:start position:0%
+is imagine that the ground that the
+ 
+
+ align:start position:0%
+is imagine that the ground that the
+wheel is not moving forward at all but
+
+ align:start position:0%
+wheel is not moving forward at all but
+ 
+
+ align:start position:0%
+wheel is not moving forward at all but
+it's just spinning that's what we call
+
+ align:start position:0%
+it's just spinning that's what we call
+ 
+
+ align:start position:0%
+it's just spinning that's what we call
+the wheel is slipping on the ground for
+
+ align:start position:0%
+the wheel is slipping on the ground for
+ 
+
+ align:start position:0%
+the wheel is slipping on the ground for
+instance if there were ice and so what
+
+ align:start position:0%
+instance if there were ice and so what
+ 
+
+ align:start position:0%
+instance if there were ice and so what
+we call slipping is a little bit more
+
+ align:start position:0%
+we call slipping is a little bit more
+ 
+
+ align:start position:0%
+we call slipping is a little bit more
+General it's whenever the wheel is
+
+ align:start position:0%
+General it's whenever the wheel is
+ 
+
+ align:start position:0%
+General it's whenever the wheel is
+spinning and the arc length is much
+
+ align:start position:0%
+spinning and the arc length is much
+ 
+
+ align:start position:0%
+spinning and the arc length is much
+greater than the horizontal distance
+
+ align:start position:0%
+greater than the horizontal distance
+ 
+
+ align:start position:0%
+greater than the horizontal distance
+that the wheel is moved so we have Delta
+
+ align:start position:0%
+that the wheel is moved so we have Delta
+ 
+
+ align:start position:0%
+that the wheel is moved so we have Delta
+s representing the arc length that the
+
+ align:start position:0%
+s representing the arc length that the
+ 
+
+ align:start position:0%
+s representing the arc length that the
+point is moved in the center of Mass
+
+ align:start position:0%
+point is moved in the center of Mass
+ 
+
+ align:start position:0%
+point is moved in the center of Mass
+frame is greater than how far the center
+
+ align:start position:0%
+frame is greater than how far the center
+ 
+
+ align:start position:0%
+frame is greater than how far the center
+of mass is moving and so again we have
+
+ align:start position:0%
+of mass is moving and so again we have
+ 
+
+ align:start position:0%
+of mass is moving and so again we have
+our Delta Theta is greater than b CM
+
+ align:start position:0%
+our Delta Theta is greater than b CM
+ 
+
+ align:start position:0%
+our Delta Theta is greater than b CM
+delta T or in the limit our Omega is
+
+ align:start position:0%
+delta T or in the limit our Omega is
+ 
+
+ align:start position:0%
+delta T or in the limit our Omega is
+greater than V CM you can say it's
+
+ align:start position:0%
+greater than V CM you can say it's
+ 
+
+ align:start position:0%
+greater than V CM you can say it's
+spinning faster than it's
+
+ align:start position:0%
+spinning faster than it's
+ 
+
+ align:start position:0%
+spinning faster than it's
+translating and
+
+ align:start position:0%
+translating and
+ 
+
+ align:start position:0%
+translating and
+finally the skidding condition
+
+ align:start position:0%
+finally the skidding condition
+ 
+
+ align:start position:0%
+finally the skidding condition
+skidding imagine that the wheel you're
+
+ align:start position:0%
+skidding imagine that the wheel you're
+ 
+
+ align:start position:0%
+skidding imagine that the wheel you're
+breaking a wheel the wheel is not
+
+ align:start position:0%
+breaking a wheel the wheel is not
+ 
+
+ align:start position:0%
+breaking a wheel the wheel is not
+spinning at all but it's just sliding
+
+ align:start position:0%
+spinning at all but it's just sliding
+ 
+
+ align:start position:0%
+spinning at all but it's just sliding
+along horizontally so the
+
+ align:start position:0%
+along horizontally so the
+ 
+
+ align:start position:0%
+along horizontally so the
+horizontal Delta X Center of mass is
+
+ align:start position:0%
+horizontal Delta X Center of mass is
+ 
+
+ align:start position:0%
+horizontal Delta X Center of mass is
+bigger than Delta s CM and so this is
+
+ align:start position:0%
+bigger than Delta s CM and so this is
+ 
+
+ align:start position:0%
+bigger than Delta s CM and so this is
+the case where Delta X cm how far it
+
+ align:start position:0%
+the case where Delta X cm how far it
+ 
+
+ align:start position:0%
+the case where Delta X cm how far it
+moved horizontally is greater than the
+
+ align:start position:0%
+moved horizontally is greater than the
+ 
+
+ align:start position:0%
+moved horizontally is greater than the
+amount of Arc Length that that point
+
+ align:start position:0%
+amount of Arc Length that that point
+ 
+
+ align:start position:0%
+amount of Arc Length that that point
+moved and so in the same type of
+
+ align:start position:0%
+moved and so in the same type of
+ 
+
+ align:start position:0%
+moved and so in the same type of
+argument when we put our conditions in
+
+ align:start position:0%
+argument when we put our conditions in
+ 
+
+ align:start position:0%
+argument when we put our conditions in
+we get that um V cm is greater than our
+
+ align:start position:0%
+we get that um V cm is greater than our
+ 
+
+ align:start position:0%
+we get that um V cm is greater than our
+Omega and again what that corresponds to
+
+ align:start position:0%
+Omega and again what that corresponds to
+ 
+
+ align:start position:0%
+Omega and again what that corresponds to
+in the skidding case imagine the limit
+
+ align:start position:0%
+in the skidding case imagine the limit
+ 
+
+ align:start position:0%
+in the skidding case imagine the limit
+where it's not rotating at all this
+
+ align:start position:0%
+where it's not rotating at all this
+ 
+
+ align:start position:0%
+where it's not rotating at all this
+would be zero and it's just skidding
+
+ align:start position:0%
+would be zero and it's just skidding
+ 
+
+ align:start position:0%
+would be zero and it's just skidding
+along the ground vcm so we have our
+
+ align:start position:0%
+along the ground vcm so we have our
+ 
+
+ align:start position:0%
+along the ground vcm so we have our
+three conditions we
+
+ align:start position:0%
+three conditions we
+ 
+
+ align:start position:0%
+three conditions we
+have the slipping condition where it's
+
+ align:start position:0%
+have the slipping condition where it's
+ 
+
+ align:start position:0%
+have the slipping condition where it's
+spinning
+
+ align:start position:0%
+spinning
+ 
+
+ align:start position:0%
+spinning
+faster than it's translating we have the
+
+ align:start position:0%
+faster than it's translating we have the
+ 
+
+ align:start position:0%
+faster than it's translating we have the
+skidding condition where it's
+
+ align:start position:0%
+skidding condition where it's
+ 
+
+ align:start position:0%
+skidding condition where it's
+translating faster than it's spinning
+
+ align:start position:0%
+translating faster than it's spinning
+ 
+
+ align:start position:0%
+translating faster than it's spinning
+and we have the rolling without slipping
+
+ align:start position:0%
+and we have the rolling without slipping
+ 
+
+ align:start position:0%
+and we have the rolling without slipping
+condition in
+
+ align:start position:0%
+condition in
+ 
+
+ align:start position:0%
+condition in
+which the arc
+
+ align:start position:0%
+which the arc
+ 
+
+ align:start position:0%
+which the arc
+length is exactly equal to the distance
+
+ align:start position:0%
+length is exactly equal to the distance
+ 
+
+ align:start position:0%
+length is exactly equal to the distance
+horizontal distance along the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ground
\ No newline at end of file
diff --git a/1_t7ixz5XRY.txt b/1_t7ixz5XRY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f37cdb70c5d0b6fdd8f44b8ab14e765b6c2e0b7
--- /dev/null
+++ b/1_t7ixz5XRY.txt
@@ -0,0 +1,4827 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ok I'm just going to get started first
+
+ align:start position:0%
+ok I'm just going to get started first
+ 
+
+ align:start position:0%
+ok I'm just going to get started first
+there are administrative stuff I
+
+ align:start position:0%
+there are administrative stuff I
+ 
+
+ align:start position:0%
+there are administrative stuff I
+definitely fewer people signed in on
+
+ align:start position:0%
+definitely fewer people signed in on
+ 
+
+ align:start position:0%
+definitely fewer people signed in on
+Monday then actually showed up in class
+
+ align:start position:0%
+Monday then actually showed up in class
+ 
+
+ align:start position:0%
+Monday then actually showed up in class
+so there were a bunch of people who just
+
+ align:start position:0%
+so there were a bunch of people who just
+ 
+
+ align:start position:0%
+so there were a bunch of people who just
+were going to sign it I tried to check
+
+ align:start position:0%
+were going to sign it I tried to check
+ 
+
+ align:start position:0%
+were going to sign it I tried to check
+off people that I remembered being in
+
+ align:start position:0%
+off people that I remembered being in
+ 
+
+ align:start position:0%
+off people that I remembered being in
+class but if you were in class and you
+
+ align:start position:0%
+class but if you were in class and you
+ 
+
+ align:start position:0%
+class but if you were in class and you
+think that you may not have signed it I
+
+ align:start position:0%
+think that you may not have signed it I
+ 
+
+ align:start position:0%
+think that you may not have signed it I
+have Monday's Monday signup sheet here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to attendance cheaters i believe yeah so
+
+ align:start position:0%
+to attendance cheaters i believe yeah so
+ 
+
+ align:start position:0%
+to attendance cheaters i believe yeah so
+make sure that that gets handed off to
+
+ align:start position:0%
+make sure that that gets handed off to
+ 
+
+ align:start position:0%
+make sure that that gets handed off to
+anybody who comes in later and i'm going
+
+ align:start position:0%
+anybody who comes in later and i'm going
+ 
+
+ align:start position:0%
+anybody who comes in later and i'm going
+to start off we're talking about the
+
+ align:start position:0%
+to start off we're talking about the
+ 
+
+ align:start position:0%
+to start off we're talking about the
+reading we're going to play some games
+
+ align:start position:0%
+reading we're going to play some games
+ 
+
+ align:start position:0%
+reading we're going to play some games
+are related to that reading and then
+
+ align:start position:0%
+are related to that reading and then
+ 
+
+ align:start position:0%
+are related to that reading and then
+we're going to take a break do your set
+
+ align:start position:0%
+we're going to take a break do your set
+ 
+
+ align:start position:0%
+we're going to take a break do your set
+up and I do be playtesting with each
+
+ align:start position:0%
+up and I do be playtesting with each
+ 
+
+ align:start position:0%
+up and I do be playtesting with each
+other all right who is on a team who
+
+ align:start position:0%
+other all right who is on a team who
+ 
+
+ align:start position:0%
+other all right who is on a team who
+doesn't have a game yet like you're
+
+ align:start position:0%
+doesn't have a game yet like you're
+ 
+
+ align:start position:0%
+doesn't have a game yet like you're
+waiting for team members to bring it in
+
+ align:start position:0%
+waiting for team members to bring it in
+ 
+
+ align:start position:0%
+waiting for team members to bring it in
+you don't think you're gonna have a game
+
+ align:start position:0%
+you don't think you're gonna have a game
+ 
+
+ align:start position:0%
+you don't think you're gonna have a game
+ready today you can do it ok ok all
+
+ align:start position:0%
+ready today you can do it ok ok all
+ 
+
+ align:start position:0%
+ready today you can do it ok ok all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+are those ways fine because because
+
+ align:start position:0%
+are those ways fine because because
+ 
+
+ align:start position:0%
+are those ways fine because because
+we're going to play testing the second
+
+ align:start position:0%
+we're going to play testing the second
+ 
+
+ align:start position:0%
+we're going to play testing the second
+half of class but by all anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we just do it on eyes on tiles see me
+
+ align:start position:0%
+so we just do it on eyes on tiles see me
+ 
+
+ align:start position:0%
+so we just do it on eyes on tiles see me
+hang out in all that oh okay because of
+
+ align:start position:0%
+hang out in all that oh okay because of
+ 
+
+ align:start position:0%
+hang out in all that oh okay because of
+the vibration ooh yeah
+
+ align:start position:0%
+the vibration ooh yeah
+ 
+
+ align:start position:0%
+the vibration ooh yeah
+all right let me sense absolutely that
+
+ align:start position:0%
+all right let me sense absolutely that
+ 
+
+ align:start position:0%
+all right let me sense absolutely that
+that will work fine alright so today's
+
+ align:start position:0%
+that will work fine alright so today's
+ 
+
+ align:start position:0%
+that will work fine alright so today's
+reading was partnered and some of you
+
+ align:start position:0%
+reading was partnered and some of you
+ 
+
+ align:start position:0%
+reading was partnered and some of you
+may be surprised that we jumped all the
+
+ align:start position:0%
+may be surprised that we jumped all the
+ 
+
+ align:start position:0%
+may be surprised that we jumped all the
+way back to chapter 1 but it's kind of
+
+ align:start position:0%
+way back to chapter 1 but it's kind of
+ 
+
+ align:start position:0%
+way back to chapter 1 but it's kind of
+revisiting an old topic right first of
+
+ align:start position:0%
+revisiting an old topic right first of
+ 
+
+ align:start position:0%
+revisiting an old topic right first of
+all he talks about the basic concepts of
+
+ align:start position:0%
+all he talks about the basic concepts of
+ 
+
+ align:start position:0%
+all he talks about the basic concepts of
+games and play and sports and I kind of
+
+ align:start position:0%
+games and play and sports and I kind of
+ 
+
+ align:start position:0%
+games and play and sports and I kind of
+want to go back to that but as I already
+
+ align:start position:0%
+want to go back to that but as I already
+ 
+
+ align:start position:0%
+want to go back to that but as I already
+voice my own opinion on the what is game
+
+ align:start position:0%
+voice my own opinion on the what is game
+ 
+
+ align:start position:0%
+voice my own opinion on the what is game
+question yes and I think it's not very
+
+ align:start position:0%
+question yes and I think it's not very
+ 
+
+ align:start position:0%
+question yes and I think it's not very
+productive to talk about what is a game
+
+ align:start position:0%
+productive to talk about what is a game
+ 
+
+ align:start position:0%
+productive to talk about what is a game
+because then you now have to decide what
+
+ align:start position:0%
+because then you now have to decide what
+ 
+
+ align:start position:0%
+because then you now have to decide what
+is it the games but what I do like to
+
+ align:start position:0%
+is it the games but what I do like to
+ 
+
+ align:start position:0%
+is it the games but what I do like to
+talk about all the different things that
+
+ align:start position:0%
+talk about all the different things that
+ 
+
+ align:start position:0%
+talk about all the different things that
+play and game can mean you know this is
+
+ align:start position:0%
+play and game can mean you know this is
+ 
+
+ align:start position:0%
+play and game can mean you know this is
+like certainly in the English language
+
+ align:start position:0%
+like certainly in the English language
+ 
+
+ align:start position:0%
+like certainly in the English language
+it's even in partnered he already talks
+
+ align:start position:0%
+it's even in partnered he already talks
+ 
+
+ align:start position:0%
+it's even in partnered he already talks
+about how it's a little bit weird and we
+
+ align:start position:0%
+about how it's a little bit weird and we
+ 
+
+ align:start position:0%
+about how it's a little bit weird and we
+have to two different words with two
+
+ align:start position:0%
+have to two different words with two
+ 
+
+ align:start position:0%
+have to two different words with two
+different origins to mean very related
+
+ align:start position:0%
+different origins to mean very related
+ 
+
+ align:start position:0%
+different origins to mean very related
+things but as a result of that these two
+
+ align:start position:0%
+things but as a result of that these two
+ 
+
+ align:start position:0%
+things but as a result of that these two
+words have kind of been used and reused
+
+ align:start position:0%
+words have kind of been used and reused
+ 
+
+ align:start position:0%
+words have kind of been used and reused
+to describe a whole bunch of related but
+
+ align:start position:0%
+to describe a whole bunch of related but
+ 
+
+ align:start position:0%
+to describe a whole bunch of related but
+not quite the same concepts and I just
+
+ align:start position:0%
+not quite the same concepts and I just
+ 
+
+ align:start position:0%
+not quite the same concepts and I just
+want to be able to run through that with
+
+ align:start position:0%
+want to be able to run through that with
+ 
+
+ align:start position:0%
+want to be able to run through that with
+you so today we have sport so that's not
+
+ align:start position:0%
+you so today we have sport so that's not
+ 
+
+ align:start position:0%
+you so today we have sport so that's not
+funny Paul be like the noun definitions
+
+ align:start position:0%
+funny Paul be like the noun definitions
+ 
+
+ align:start position:0%
+funny Paul be like the noun definitions
+like what's what are all the things that
+
+ align:start position:0%
+like what's what are all the things that
+ 
+
+ align:start position:0%
+like what's what are all the things that
+play can mean game and mean or sport can
+
+ align:start position:0%
+play can mean game and mean or sport can
+ 
+
+ align:start position:0%
+play can mean game and mean or sport can
+mean with what you are using it as it
+
+ align:start position:0%
+mean with what you are using it as it
+ 
+
+ align:start position:0%
+mean with what you are using it as it
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a spider like to spit game huh spit
+
+ align:start position:0%
+a spider like to spit game huh spit
+ 
+
+ align:start position:0%
+a spider like to spit game huh spit
+that's it backing so so that is okay I'm
+
+ align:start position:0%
+that's it backing so so that is okay I'm
+ 
+
+ align:start position:0%
+that's it backing so so that is okay I'm
+going to use whatsoever because I think
+
+ align:start position:0%
+going to use whatsoever because I think
+ 
+
+ align:start position:0%
+going to use whatsoever because I think
+it doesn't cost across well yeah that's
+
+ align:start position:0%
+it doesn't cost across well yeah that's
+ 
+
+ align:start position:0%
+it doesn't cost across well yeah that's
+that's kind of Ruby but yeah to to game
+
+ align:start position:0%
+that's kind of Ruby but yeah to to game
+ 
+
+ align:start position:0%
+that's kind of Ruby but yeah to to game
+to which which which means to sorry
+
+ align:start position:0%
+to which which which means to sorry
+ 
+
+ align:start position:0%
+to which which which means to sorry
+ritual how would you describe that
+
+ align:start position:0%
+ritual how would you describe that
+ 
+
+ align:start position:0%
+ritual how would you describe that
+that's the concept to game the system
+
+ align:start position:0%
+that's the concept to game the system
+ 
+
+ align:start position:0%
+that's the concept to game the system
+demon gaming this is loopholes exploits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay like a baseball player like you
+
+ align:start position:0%
+okay like a baseball player like you
+ 
+
+ align:start position:0%
+okay like a baseball player like you
+know that was a great play you know so
+
+ align:start position:0%
+know that was a great play you know so
+ 
+
+ align:start position:0%
+know that was a great play you know so
+so like my tactic wonder you actually
+
+ align:start position:0%
+so like my tactic wonder you actually
+ 
+
+ align:start position:0%
+so like my tactic wonder you actually
+have to execute it's not missing concept
+
+ align:start position:0%
+have to execute it's not missing concept
+ 
+
+ align:start position:0%
+have to execute it's not missing concept
+is something that I should have to
+
+ align:start position:0%
+is something that I should have to
+ 
+
+ align:start position:0%
+is something that I should have to
+happen like that performance if their
+
+ align:start position:0%
+happen like that performance if their
+ 
+
+ align:start position:0%
+happen like that performance if their
+performance also stage stage play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else if we play yes and this is not
+
+ align:start position:0%
+what else if we play yes and this is not
+ 
+
+ align:start position:0%
+what else if we play yes and this is not
+that serious okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a cosplay no there are this idea
+
+ align:start position:0%
+it's a cosplay no there are this idea
+ 
+
+ align:start position:0%
+it's a cosplay no there are this idea
+the thing that kids are doing most of
+
+ align:start position:0%
+the thing that kids are doing most of
+ 
+
+ align:start position:0%
+the thing that kids are doing most of
+the time this play in some sort of my
+
+ align:start position:0%
+the time this play in some sort of my
+ 
+
+ align:start position:0%
+the time this play in some sort of my
+general nonsense okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so so play as it to initiate as
+
+ align:start position:0%
+okay so so so play as it to initiate as
+ 
+
+ align:start position:0%
+okay so so so play as it to initiate as
+a sequence sometimes open apps a little
+
+ align:start position:0%
+a sequence sometimes open apps a little
+ 
+
+ align:start position:0%
+a sequence sometimes open apps a little
+bit with this because you can use play
+
+ align:start position:0%
+bit with this because you can use play
+ 
+
+ align:start position:0%
+bit with this because you can use play
+to describe something that happened in a
+
+ align:start position:0%
+to describe something that happened in a
+ 
+
+ align:start position:0%
+to describe something that happened in a
+pass or to make play alright
+
+ align:start position:0%
+pass or to make play alright
+ 
+
+ align:start position:0%
+pass or to make play alright
+crap I'll press play to you know
+
+ align:start position:0%
+crap I'll press play to you know
+ 
+
+ align:start position:0%
+crap I'll press play to you know
+actually that's that's a instead of sake
+
+ align:start position:0%
+actually that's that's a instead of sake
+ 
+
+ align:start position:0%
+actually that's that's a instead of sake
+initiate maybe you like this icon right
+
+ align:start position:0%
+initiate maybe you like this icon right
+ 
+
+ align:start position:0%
+initiate maybe you like this icon right
+this icon okay also so like sporting
+
+ align:start position:0%
+this icon okay also so like sporting
+ 
+
+ align:start position:0%
+this icon okay also so like sporting
+your colors okay so so like the display
+
+ align:start position:0%
+your colors okay so so like the display
+ 
+
+ align:start position:0%
+your colors okay so so like the display
+sorry I just put dad more in the verb
+
+ align:start position:0%
+sorry I just put dad more in the verb
+ 
+
+ align:start position:0%
+sorry I just put dad more in the verb
+site
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Something About You virtuous kind of
+
+ align:start position:0%
+Something About You virtuous kind of
+ 
+
+ align:start position:0%
+Something About You virtuous kind of
+thing yes I'm not sure if I got that
+
+ align:start position:0%
+thing yes I'm not sure if I got that
+ 
+
+ align:start position:0%
+thing yes I'm not sure if I got that
+right something for sport shooting for
+
+ align:start position:0%
+right something for sport shooting for
+ 
+
+ align:start position:0%
+right something for sport shooting for
+sport yeah an expert fishing for sport
+
+ align:start position:0%
+sport yeah an expert fishing for sport
+ 
+
+ align:start position:0%
+sport yeah an expert fishing for sport
+as opposed to sport fishing right those
+
+ align:start position:0%
+as opposed to sport fishing right those
+ 
+
+ align:start position:0%
+as opposed to sport fishing right those
+are you know that's another pun so I
+
+ align:start position:0%
+are you know that's another pun so I
+ 
+
+ align:start position:0%
+are you know that's another pun so I
+mean it's funny because often it is used
+
+ align:start position:0%
+mean it's funny because often it is used
+ 
+
+ align:start position:0%
+mean it's funny because often it is used
+to make something sound like it's for
+
+ align:start position:0%
+to make something sound like it's for
+ 
+
+ align:start position:0%
+to make something sound like it's for
+low stakes but it actually is very high
+
+ align:start position:0%
+low stakes but it actually is very high
+ 
+
+ align:start position:0%
+low stakes but it actually is very high
+stakes like you know oh we're going to
+
+ align:start position:0%
+stakes like you know oh we're going to
+ 
+
+ align:start position:0%
+stakes like you know oh we're going to
+hunt people for sport you know oh yeah I
+
+ align:start position:0%
+hunt people for sport you know oh yeah I
+ 
+
+ align:start position:0%
+hunt people for sport you know oh yeah I
+just think of like old light like 18th
+
+ align:start position:0%
+just think of like old light like 18th
+ 
+
+ align:start position:0%
+just think of like old light like 18th
+century this is sure when it comes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plays at you know it's often like he
+
+ align:start position:0%
+plays at you know it's often like he
+ 
+
+ align:start position:0%
+plays at you know it's often like he
+plays at relationships for sports or
+
+ align:start position:0%
+plays at relationships for sports or
+ 
+
+ align:start position:0%
+plays at relationships for sports or
+something like that right you know it's
+
+ align:start position:0%
+something like that right you know it's
+ 
+
+ align:start position:0%
+something like that right you know it's
+like something that supposed to be
+
+ align:start position:0%
+like something that supposed to be
+ 
+
+ align:start position:0%
+like something that supposed to be
+high-stakes but it's not ok so before I
+
+ align:start position:0%
+high-stakes but it's not ok so before I
+ 
+
+ align:start position:0%
+high-stakes but it's not ok so before I
+think maybe instead of how far now say
+
+ align:start position:0%
+think maybe instead of how far now say
+ 
+
+ align:start position:0%
+think maybe instead of how far now say
+for those things on those stakes okay
+
+ align:start position:0%
+for those things on those stakes okay
+ 
+
+ align:start position:0%
+for those things on those stakes okay
+which is bizarre because sport is
+
+ align:start position:0%
+which is bizarre because sport is
+ 
+
+ align:start position:0%
+which is bizarre because sport is
+usually very nicely what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a whole section in
+
+ align:start position:0%
+okay so this is a whole section in
+ 
+
+ align:start position:0%
+okay so this is a whole section in
+partland where he talks about the
+
+ align:start position:0%
+partland where he talks about the
+ 
+
+ align:start position:0%
+partland where he talks about the
+possibility that what game might have
+
+ align:start position:0%
+possibility that what game might have
+ 
+
+ align:start position:0%
+possibility that what game might have
+come from bending of the bending of
+
+ align:start position:0%
+come from bending of the bending of
+ 
+
+ align:start position:0%
+come from bending of the bending of
+these because cam is Welsh for a big
+
+ align:start position:0%
+these because cam is Welsh for a big
+ 
+
+ align:start position:0%
+these because cam is Welsh for a big
+game you can but but that's now nowadays
+
+ align:start position:0%
+game you can but but that's now nowadays
+ 
+
+ align:start position:0%
+game you can but but that's now nowadays
+more associated with some sort of
+
+ align:start position:0%
+more associated with some sort of
+ 
+
+ align:start position:0%
+more associated with some sort of
+physical it's physical activities that
+
+ align:start position:0%
+physical it's physical activities that
+ 
+
+ align:start position:0%
+physical it's physical activities that
+and sport tend to go together
+
+ align:start position:0%
+and sport tend to go together
+ 
+
+ align:start position:0%
+and sport tend to go together
+what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like poultry like like uh yeah so yeah
+
+ align:start position:0%
+like poultry like like uh yeah so yeah
+ 
+
+ align:start position:0%
+like poultry like like uh yeah so yeah
+game as in animal thank you yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other group Roosevelt positive I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something is also low states
+
+ align:start position:0%
+something is also low states
+ 
+
+ align:start position:0%
+something is also low states
+you think this is a game they have yeah
+
+ align:start position:0%
+you think this is a game they have yeah
+ 
+
+ align:start position:0%
+you think this is a game they have yeah
+so so so again something that is those
+
+ align:start position:0%
+so so so again something that is those
+ 
+
+ align:start position:0%
+so so so again something that is those
+things so it's inconsequential almost
+
+ align:start position:0%
+things so it's inconsequential almost
+ 
+
+ align:start position:0%
+things so it's inconsequential almost
+like it like like there's there's no
+
+ align:start position:0%
+like it like like there's there's no
+ 
+
+ align:start position:0%
+like it like like there's there's no
+penalty for having done this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along the same line what you're like
+
+ align:start position:0%
+along the same line what you're like
+ 
+
+ align:start position:0%
+along the same line what you're like
+specifically making that joke out of
+
+ align:start position:0%
+specifically making that joke out of
+ 
+
+ align:start position:0%
+specifically making that joke out of
+something like you know he's made in a
+
+ align:start position:0%
+something like you know he's made in a
+ 
+
+ align:start position:0%
+something like you know he's made in a
+game to do this right um hmm
+
+ align:start position:0%
+game to do this right um hmm
+ 
+
+ align:start position:0%
+game to do this right um hmm
+I guess sort of like an intention of
+
+ align:start position:0%
+I guess sort of like an intention of
+ 
+
+ align:start position:0%
+I guess sort of like an intention of
+like mocking oh I think that's related
+
+ align:start position:0%
+like mocking oh I think that's related
+ 
+
+ align:start position:0%
+like mocking oh I think that's related
+to this one because they're kind of when
+
+ align:start position:0%
+to this one because they're kind of when
+ 
+
+ align:start position:0%
+to this one because they're kind of when
+you make a game of something what you're
+
+ align:start position:0%
+you make a game of something what you're
+ 
+
+ align:start position:0%
+you make a game of something what you're
+really doing they're kind of belittling
+
+ align:start position:0%
+really doing they're kind of belittling
+ 
+
+ align:start position:0%
+really doing they're kind of belittling
+yeah so I think that's just a different
+
+ align:start position:0%
+yeah so I think that's just a different
+ 
+
+ align:start position:0%
+yeah so I think that's just a different
+application of the same but when you're
+
+ align:start position:0%
+application of the same but when you're
+ 
+
+ align:start position:0%
+application of the same but when you're
+making a game of something aren't you
+
+ align:start position:0%
+making a game of something aren't you
+ 
+
+ align:start position:0%
+making a game of something aren't you
+also care of it or is that a different
+
+ align:start position:0%
+also care of it or is that a different
+ 
+
+ align:start position:0%
+also care of it or is that a different
+is that different what you're saying
+
+ align:start position:0%
+is that different what you're saying
+ 
+
+ align:start position:0%
+is that different what you're saying
+yeah well I'm saying from like the sort
+
+ align:start position:0%
+yeah well I'm saying from like the sort
+ 
+
+ align:start position:0%
+yeah well I'm saying from like the sort
+of a mockery sense of it you know he's
+
+ align:start position:0%
+of a mockery sense of it you know he's
+ 
+
+ align:start position:0%
+of a mockery sense of it you know he's
+made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but but I think making a structure
+
+ align:start position:0%
+okay but but I think making a structure
+ 
+
+ align:start position:0%
+okay but but I think making a structure
+day is a different application right no
+
+ align:start position:0%
+day is a different application right no
+ 
+
+ align:start position:0%
+day is a different application right no
+it's like you you are applying rules to
+
+ align:start position:0%
+it's like you you are applying rules to
+ 
+
+ align:start position:0%
+it's like you you are applying rules to
+something that might have not needed it
+
+ align:start position:0%
+something that might have not needed it
+ 
+
+ align:start position:0%
+something that might have not needed it
+necessarily but you know now you're
+
+ align:start position:0%
+necessarily but you know now you're
+ 
+
+ align:start position:0%
+necessarily but you know now you're
+coming up with rules I going to make a
+
+ align:start position:0%
+coming up with rules I going to make a
+ 
+
+ align:start position:0%
+coming up with rules I going to make a
+game out because five people live in the
+
+ align:start position:0%
+game out because five people live in the
+ 
+
+ align:start position:0%
+game out because five people live in the
+Blitz
+
+ align:start position:0%
+Blitz
+ 
+
+ align:start position:0%
+Blitz
+all right big game right okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's all part of the game no I put it in
+
+ align:start position:0%
+it's all part of the game no I put it in
+ 
+
+ align:start position:0%
+it's all part of the game no I put it in
+sports but getting the game is almost
+
+ align:start position:0%
+sports but getting the game is almost
+ 
+
+ align:start position:0%
+sports but getting the game is almost
+certainly a bottle of something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unexpected or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right yeah so so that's the sort of like
+
+ align:start position:0%
+right yeah so so that's the sort of like
+ 
+
+ align:start position:0%
+right yeah so so that's the sort of like
+this thought that space where things are
+
+ align:start position:0%
+this thought that space where things are
+ 
+
+ align:start position:0%
+this thought that space where things are
+permitted like specific kinds of things
+
+ align:start position:0%
+permitted like specific kinds of things
+ 
+
+ align:start position:0%
+permitted like specific kinds of things
+that my this this introduces a concept
+
+ align:start position:0%
+that my this this introduces a concept
+ 
+
+ align:start position:0%
+that my this this introduces a concept
+that introduces the Magic Circle this is
+
+ align:start position:0%
+that introduces the Magic Circle this is
+ 
+
+ align:start position:0%
+that introduces the Magic Circle this is
+this is a mature we have a new beingness
+
+ align:start position:0%
+this is a mature we have a new beingness
+ 
+
+ align:start position:0%
+this is a mature we have a new beingness
+touched on this but this idea that a
+
+ align:start position:0%
+touched on this but this idea that a
+ 
+
+ align:start position:0%
+touched on this but this idea that a
+game is this bounded space where you can
+
+ align:start position:0%
+game is this bounded space where you can
+ 
+
+ align:start position:0%
+game is this bounded space where you can
+do things in it that you wouldn't
+
+ align:start position:0%
+do things in it that you wouldn't
+ 
+
+ align:start position:0%
+do things in it that you wouldn't
+necessarily be allowed to do in real
+
+ align:start position:0%
+necessarily be allowed to do in real
+ 
+
+ align:start position:0%
+necessarily be allowed to do in real
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+and similarly consequences that happen
+
+ align:start position:0%
+and similarly consequences that happen
+ 
+
+ align:start position:0%
+and similarly consequences that happen
+inside don't necessarily apply to
+
+ align:start position:0%
+inside don't necessarily apply to
+ 
+
+ align:start position:0%
+inside don't necessarily apply to
+outside I get incredibly important on
+
+ align:start position:0%
+outside I get incredibly important on
+ 
+
+ align:start position:0%
+outside I get incredibly important on
+the inside like the ball when the
+
+ align:start position:0%
+the inside like the ball when the
+ 
+
+ align:start position:0%
+the inside like the ball when the
+position of a ball is generally
+
+ align:start position:0%
+position of a ball is generally
+ 
+
+ align:start position:0%
+position of a ball is generally
+meaningless outside of the game but it's
+
+ align:start position:0%
+meaningless outside of the game but it's
+ 
+
+ align:start position:0%
+meaningless outside of the game but it's
+only games everything but you know you
+
+ align:start position:0%
+only games everything but you know you
+ 
+
+ align:start position:0%
+only games everything but you know you
+can you know bodycheck somebody in a
+
+ align:start position:0%
+can you know bodycheck somebody in a
+ 
+
+ align:start position:0%
+can you know bodycheck somebody in a
+hockey rink but you're not really
+
+ align:start position:0%
+hockey rink but you're not really
+ 
+
+ align:start position:0%
+hockey rink but you're not really
+allowed to do that on the cycle so that
+
+ align:start position:0%
+allowed to do that on the cycle so that
+ 
+
+ align:start position:0%
+allowed to do that on the cycle so that
+I think that is close to what do tons of
+
+ align:start position:0%
+I think that is close to what do tons of
+ 
+
+ align:start position:0%
+I think that is close to what do tons of
+all your application allowed to do this
+
+ align:start position:0%
+all your application allowed to do this
+ 
+
+ align:start position:0%
+all your application allowed to do this
+within these parameters because this is
+
+ align:start position:0%
+within these parameters because this is
+ 
+
+ align:start position:0%
+within these parameters because this is
+how the game is played all right where's
+
+ align:start position:0%
+how the game is played all right where's
+ 
+
+ align:start position:0%
+how the game is played all right where's
+yeah this I'm wondering about the game
+
+ align:start position:0%
+yeah this I'm wondering about the game
+ 
+
+ align:start position:0%
+yeah this I'm wondering about the game
+did this concept of the game as it the
+
+ align:start position:0%
+did this concept of the game as it the
+ 
+
+ align:start position:0%
+did this concept of the game as it the
+big game like a Super Bowl and I'm
+
+ align:start position:0%
+big game like a Super Bowl and I'm
+ 
+
+ align:start position:0%
+big game like a Super Bowl and I'm
+wondering if that's only is that only
+
+ align:start position:0%
+wondering if that's only is that only
+ 
+
+ align:start position:0%
+wondering if that's only is that only
+used in broadcast or is the sooner
+
+ align:start position:0%
+used in broadcast or is the sooner
+ 
+
+ align:start position:0%
+used in broadcast or is the sooner
+certain rights in sailors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but you get something like are you
+
+ align:start position:0%
+but but you get something like are you
+ 
+
+ align:start position:0%
+but but you get something like are you
+gonna come over to watch the game which
+
+ align:start position:0%
+gonna come over to watch the game which
+ 
+
+ align:start position:0%
+gonna come over to watch the game which
+doesn't necessarily be business Super
+
+ align:start position:0%
+doesn't necessarily be business Super
+ 
+
+ align:start position:0%
+doesn't necessarily be business Super
+Bowl yeah this weekly thing but it seems
+
+ align:start position:0%
+Bowl yeah this weekly thing but it seems
+ 
+
+ align:start position:0%
+Bowl yeah this weekly thing but it seems
+to be very TV related this this the game
+
+ align:start position:0%
+to be very TV related this this the game
+ 
+
+ align:start position:0%
+to be very TV related this this the game
+as this thing that you see on TV and
+
+ align:start position:0%
+as this thing that you see on TV and
+ 
+
+ align:start position:0%
+as this thing that you see on TV and
+this event is happening in a specific
+
+ align:start position:0%
+this event is happening in a specific
+ 
+
+ align:start position:0%
+this event is happening in a specific
+time rather than you've done and
+
+ align:start position:0%
+time rather than you've done and
+ 
+
+ align:start position:0%
+time rather than you've done and
+football in general isn't there some
+
+ align:start position:0%
+football in general isn't there some
+ 
+
+ align:start position:0%
+football in general isn't there some
+concept and then because think the stage
+
+ align:start position:0%
+concept and then because think the stage
+ 
+
+ align:start position:0%
+concept and then because think the stage
+aspect because you're watching it enough
+
+ align:start position:0%
+aspect because you're watching it enough
+ 
+
+ align:start position:0%
+aspect because you're watching it enough
+legs aspect yeah yeah so I'm just going
+
+ align:start position:0%
+legs aspect yeah yeah so I'm just going
+ 
+
+ align:start position:0%
+legs aspect yeah yeah so I'm just going
+to cook put TV things to them okay yeah
+
+ align:start position:0%
+to cook put TV things to them okay yeah
+ 
+
+ align:start position:0%
+to cook put TV things to them okay yeah
+I was gonna say game that's like still
+
+ align:start position:0%
+I was gonna say game that's like still
+ 
+
+ align:start position:0%
+I was gonna say game that's like still
+wasn't like he's got game I think that
+
+ align:start position:0%
+wasn't like he's got game I think that
+ 
+
+ align:start position:0%
+wasn't like he's got game I think that
+goes back to the swagger yeah a little
+
+ align:start position:0%
+goes back to the swagger yeah a little
+ 
+
+ align:start position:0%
+goes back to the swagger yeah a little
+bit kind of attitude I guess the
+
+ align:start position:0%
+bit kind of attitude I guess the
+ 
+
+ align:start position:0%
+bit kind of attitude I guess the
+assumption I think is that you that
+
+ align:start position:0%
+assumption I think is that you that
+ 
+
+ align:start position:0%
+assumption I think is that you that
+those two are related
+
+ align:start position:0%
+those two are related
+ 
+
+ align:start position:0%
+those two are related
+well once the appearance of skill that
+
+ align:start position:0%
+well once the appearance of skill that
+ 
+
+ align:start position:0%
+well once the appearance of skill that
+gave us that's good okay all right okay
+
+ align:start position:0%
+gave us that's good okay all right okay
+ 
+
+ align:start position:0%
+gave us that's good okay all right okay
+okay so actual skill versus oh that's
+
+ align:start position:0%
+okay so actual skill versus oh that's
+ 
+
+ align:start position:0%
+okay so actual skill versus oh that's
+that's a that's the dating I know
+
+ align:start position:0%
+that's a that's the dating I know
+ 
+
+ align:start position:0%
+that's a that's the dating I know
+there's a book that's very specifically
+
+ align:start position:0%
+there's a book that's very specifically
+ 
+
+ align:start position:0%
+there's a book that's very specifically
+called the game is I think I think that
+
+ align:start position:0%
+called the game is I think I think that
+ 
+
+ align:start position:0%
+called the game is I think I think that
+the use of them were the game to
+
+ align:start position:0%
+the use of them were the game to
+ 
+
+ align:start position:0%
+the use of them were the game to
+describe dating in general recreates
+
+ align:start position:0%
+describe dating in general recreates
+ 
+
+ align:start position:0%
+describe dating in general recreates
+that by far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plague also be referred to sports like
+
+ align:start position:0%
+plague also be referred to sports like
+ 
+
+ align:start position:0%
+plague also be referred to sports like
+like making football
+
+ align:start position:0%
+like making football
+ 
+
+ align:start position:0%
+like making football
+there's certainly yeah these things
+
+ align:start position:0%
+there's certainly yeah these things
+ 
+
+ align:start position:0%
+there's certainly yeah these things
+right yeah but but you're right you you
+
+ align:start position:0%
+right yeah but but you're right you you
+ 
+
+ align:start position:0%
+right yeah but but you're right you you
+you can write these things down you can
+
+ align:start position:0%
+you can write these things down you can
+ 
+
+ align:start position:0%
+you can write these things down you can
+talk about them as a vibratory offense
+
+ align:start position:0%
+talk about them as a vibratory offense
+ 
+
+ align:start position:0%
+talk about them as a vibratory offense
+that you can do there's the great game
+
+ align:start position:0%
+that you can do there's the great game
+ 
+
+ align:start position:0%
+that you can do there's the great game
+the Afghan or the curvy oh yeah so like
+
+ align:start position:0%
+the Afghan or the curvy oh yeah so like
+ 
+
+ align:start position:0%
+the Afghan or the curvy oh yeah so like
+the England versus Russia or a Napoleon
+
+ align:start position:0%
+the England versus Russia or a Napoleon
+ 
+
+ align:start position:0%
+the England versus Russia or a Napoleon
+versus Russia I forget exactly years of
+
+ align:start position:0%
+versus Russia I forget exactly years of
+ 
+
+ align:start position:0%
+versus Russia I forget exactly years of
+dates but it was a social political
+
+ align:start position:0%
+dates but it was a social political
+ 
+
+ align:start position:0%
+dates but it was a social political
+conflict going on so that there are
+
+ align:start position:0%
+conflict going on so that there are
+ 
+
+ align:start position:0%
+conflict going on so that there are
+system there are specific wars that are
+
+ align:start position:0%
+system there are specific wars that are
+ 
+
+ align:start position:0%
+system there are specific wars that are
+referred to as a Vikings game of thrones
+
+ align:start position:0%
+referred to as a Vikings game of thrones
+ 
+
+ align:start position:0%
+referred to as a Vikings game of thrones
+probably is related to that too although
+
+ align:start position:0%
+probably is related to that too although
+ 
+
+ align:start position:0%
+probably is related to that too although
+that's ineptitudes political I mean this
+
+ align:start position:0%
+that's ineptitudes political I mean this
+ 
+
+ align:start position:0%
+that's ineptitudes political I mean this
+even just on a down side we've gone
+
+ align:start position:0%
+even just on a down side we've gone
+ 
+
+ align:start position:0%
+even just on a down side we've gone
+through a lot
+
+ align:start position:0%
+through a lot
+ 
+
+ align:start position:0%
+through a lot
+somebody didn't include additives and
+
+ align:start position:0%
+somebody didn't include additives and
+ 
+
+ align:start position:0%
+somebody didn't include additives and
+we've run up a couple of additives so
+
+ align:start position:0%
+we've run up a couple of additives so
+ 
+
+ align:start position:0%
+we've run up a couple of additives so
+far far that also talks about how some
+
+ align:start position:0%
+far far that also talks about how some
+ 
+
+ align:start position:0%
+far far that also talks about how some
+people can say that you have a game like
+
+ align:start position:0%
+people can say that you have a game like
+ 
+
+ align:start position:0%
+people can say that you have a game like
+which means that you have a busted leg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's his extrapolation of where the work
+
+ align:start position:0%
+it's his extrapolation of where the work
+ 
+
+ align:start position:0%
+it's his extrapolation of where the work
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+comes up from from Celtic origins rather
+
+ align:start position:0%
+comes up from from Celtic origins rather
+ 
+
+ align:start position:0%
+comes up from from Celtic origins rather
+than back about groups sporting to sport
+
+ align:start position:0%
+than back about groups sporting to sport
+ 
+
+ align:start position:0%
+than back about groups sporting to sport
+well I guess we already did to sport
+
+ align:start position:0%
+well I guess we already did to sport
+ 
+
+ align:start position:0%
+well I guess we already did to sport
+although to game to play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+- in someone today right yeah exactly
+
+ align:start position:0%
+- in someone today right yeah exactly
+ 
+
+ align:start position:0%
+- in someone today right yeah exactly
+slang to execute like if you play make a
+
+ align:start position:0%
+slang to execute like if you play make a
+ 
+
+ align:start position:0%
+slang to execute like if you play make a
+play that's like the legal that it could
+
+ align:start position:0%
+play that's like the legal that it could
+ 
+
+ align:start position:0%
+play that's like the legal that it could
+be like a performance like it's playing
+
+ align:start position:0%
+be like a performance like it's playing
+ 
+
+ align:start position:0%
+be like a performance like it's playing
+this right okay yeah series of things
+
+ align:start position:0%
+this right okay yeah series of things
+ 
+
+ align:start position:0%
+this right okay yeah series of things
+you're executed stage planning for but
+
+ align:start position:0%
+you're executed stage planning for but
+ 
+
+ align:start position:0%
+you're executed stage planning for but
+to play something in a game seems like a
+
+ align:start position:0%
+to play something in a game seems like a
+ 
+
+ align:start position:0%
+to play something in a game seems like a
+much more time than better thing than to
+
+ align:start position:0%
+much more time than better thing than to
+ 
+
+ align:start position:0%
+much more time than better thing than to
+play a musical instrument
+
+ align:start position:0%
+play a musical instrument
+ 
+
+ align:start position:0%
+play a musical instrument
+this means kind of like a lifetime thing
+
+ align:start position:0%
+this means kind of like a lifetime thing
+ 
+
+ align:start position:0%
+this means kind of like a lifetime thing
+when I was like I play something I play
+
+ align:start position:0%
+when I was like I play something I play
+ 
+
+ align:start position:0%
+when I was like I play something I play
+the clarinet as if it has a very
+
+ align:start position:0%
+the clarinet as if it has a very
+ 
+
+ align:start position:0%
+the clarinet as if it has a very
+different product connotation from I
+
+ align:start position:0%
+different product connotation from I
+ 
+
+ align:start position:0%
+different product connotation from I
+played this Queen I played this card
+
+ align:start position:0%
+played this Queen I played this card
+ 
+
+ align:start position:0%
+played this Queen I played this card
+so those are two possibly on the same
+
+ align:start position:0%
+so those are two possibly on the same
+ 
+
+ align:start position:0%
+so those are two possibly on the same
+spectrum but they're like almost album
+
+ align:start position:0%
+spectrum but they're like almost album
+ 
+
+ align:start position:0%
+spectrum but they're like almost album
+on opposite ends closely related
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sporty
+
+ align:start position:0%
+sporty
+ 
+
+ align:start position:0%
+sporty
+supporting I generally associated again
+
+ align:start position:0%
+supporting I generally associated again
+ 
+
+ align:start position:0%
+supporting I generally associated again
+sort of like to be a good sport but you
+
+ align:start position:0%
+sort of like to be a good sport but you
+ 
+
+ align:start position:0%
+sort of like to be a good sport but you
+know this is this is morally fairness
+
+ align:start position:0%
+know this is this is morally fairness
+ 
+
+ align:start position:0%
+know this is this is morally fairness
+its forty gets up on a sporting chance
+
+ align:start position:0%
+its forty gets up on a sporting chance
+ 
+
+ align:start position:0%
+its forty gets up on a sporting chance
+anything is it is this just to punish
+
+ align:start position:0%
+anything is it is this just to punish
+ 
+
+ align:start position:0%
+anything is it is this just to punish
+you sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's funny how that this seems to be
+
+ align:start position:0%
+it's funny how that this seems to be
+ 
+
+ align:start position:0%
+it's funny how that this seems to be
+like the only connotation of game as a
+
+ align:start position:0%
+like the only connotation of game as a
+ 
+
+ align:start position:0%
+like the only connotation of game as a
+thoroughbred but
+
+ align:start position:0%
+thoroughbred but
+ 
+
+ align:start position:0%
+thoroughbred but
+Gaming is also kind of associated with
+
+ align:start position:0%
+Gaming is also kind of associated with
+ 
+
+ align:start position:0%
+Gaming is also kind of associated with
+the gambling industry if you talked if
+
+ align:start position:0%
+the gambling industry if you talked if
+ 
+
+ align:start position:0%
+the gambling industry if you talked if
+you go to a gaming conference what they
+
+ align:start position:0%
+you go to a gaming conference what they
+ 
+
+ align:start position:0%
+you go to a gaming conference what they
+actually mean is that you know they're
+
+ align:start position:0%
+actually mean is that you know they're
+ 
+
+ align:start position:0%
+actually mean is that you know they're
+talking about sticks sticks sticks a
+
+ align:start position:0%
+talking about sticks sticks sticks a
+ 
+
+ align:start position:0%
+talking about sticks sticks sticks a
+games to games like I play so that's
+
+ align:start position:0%
+games to games like I play so that's
+ 
+
+ align:start position:0%
+games to games like I play so that's
+Spanish imitating a fairly recent
+
+ align:start position:0%
+Spanish imitating a fairly recent
+ 
+
+ align:start position:0%
+Spanish imitating a fairly recent
+connotation is just just to you know
+
+ align:start position:0%
+connotation is just just to you know
+ 
+
+ align:start position:0%
+connotation is just just to you know
+usually in association with digital
+
+ align:start position:0%
+usually in association with digital
+ 
+
+ align:start position:0%
+usually in association with digital
+games but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so like when we say someone like I am a
+
+ align:start position:0%
+so like when we say someone like I am a
+ 
+
+ align:start position:0%
+so like when we say someone like I am a
+gamer right it's not implying that I
+
+ align:start position:0%
+gamer right it's not implying that I
+ 
+
+ align:start position:0%
+gamer right it's not implying that I
+other for loopholes and everything that
+
+ align:start position:0%
+other for loopholes and everything that
+ 
+
+ align:start position:0%
+other for loopholes and everything that
+I can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm pretty sure we can keep on going
+
+ align:start position:0%
+so I'm pretty sure we can keep on going
+ 
+
+ align:start position:0%
+so I'm pretty sure we can keep on going
+for a while I just think it's kind of
+
+ align:start position:0%
+for a while I just think it's kind of
+ 
+
+ align:start position:0%
+for a while I just think it's kind of
+neat that we have all of these different
+
+ align:start position:0%
+neat that we have all of these different
+ 
+
+ align:start position:0%
+neat that we have all of these different
+terminologies - they all use the same
+
+ align:start position:0%
+terminologies - they all use the same
+ 
+
+ align:start position:0%
+terminologies - they all use the same
+words they can they often can get
+
+ align:start position:0%
+words they can they often can get
+ 
+
+ align:start position:0%
+words they can they often can get
+confused in a sort of casual agent
+
+ align:start position:0%
+confused in a sort of casual agent
+ 
+
+ align:start position:0%
+confused in a sort of casual agent
+typically doesn't happen it doesn't get
+
+ align:start position:0%
+typically doesn't happen it doesn't get
+ 
+
+ align:start position:0%
+typically doesn't happen it doesn't get
+too confusing when you're talking to
+
+ align:start position:0%
+too confusing when you're talking to
+ 
+
+ align:start position:0%
+too confusing when you're talking to
+fellow designers or other people in game
+
+ align:start position:0%
+fellow designers or other people in game
+ 
+
+ align:start position:0%
+fellow designers or other people in game
+industry because the context of which
+
+ align:start position:0%
+industry because the context of which
+ 
+
+ align:start position:0%
+industry because the context of which
+they're using any one of these words
+
+ align:start position:0%
+they're using any one of these words
+ 
+
+ align:start position:0%
+they're using any one of these words
+typically is pretty clear and always
+
+ align:start position:0%
+typically is pretty clear and always
+ 
+
+ align:start position:0%
+typically is pretty clear and always
+thinking about the context when you say
+
+ align:start position:0%
+thinking about the context when you say
+ 
+
+ align:start position:0%
+thinking about the context when you say
+you know the gaming the system or the
+
+ align:start position:0%
+you know the gaming the system or the
+ 
+
+ align:start position:0%
+you know the gaming the system or the
+cupcake you know in any system it's very
+
+ align:start position:0%
+cupcake you know in any system it's very
+ 
+
+ align:start position:0%
+cupcake you know in any system it's very
+different it makes a threat here but I
+
+ align:start position:0%
+different it makes a threat here but I
+ 
+
+ align:start position:0%
+different it makes a threat here but I
+but I do think that part of the kind of
+
+ align:start position:0%
+but I do think that part of the kind of
+ 
+
+ align:start position:0%
+but I do think that part of the kind of
+slightly opens the pen the box in in
+
+ align:start position:0%
+slightly opens the pen the box in in
+ 
+
+ align:start position:0%
+slightly opens the pen the box in in
+today's and he tries to run shoot too
+
+ align:start position:0%
+today's and he tries to run shoot too
+ 
+
+ align:start position:0%
+today's and he tries to run shoot too
+into a sort of cross section of all
+
+ align:start position:0%
+into a sort of cross section of all
+ 
+
+ align:start position:0%
+into a sort of cross section of all
+these things that these words can
+
+ align:start position:0%
+these things that these words can
+ 
+
+ align:start position:0%
+these things that these words can
+possibly mean yeah and this is richer
+
+ align:start position:0%
+possibly mean yeah and this is richer
+ 
+
+ align:start position:0%
+possibly mean yeah and this is richer
+than that and the reason why he does
+
+ align:start position:0%
+than that and the reason why he does
+ 
+
+ align:start position:0%
+than that and the reason why he does
+that is so that he can actually get into
+
+ align:start position:0%
+that is so that he can actually get into
+ 
+
+ align:start position:0%
+that is so that he can actually get into
+the topic of his book which is poor news
+
+ align:start position:0%
+the topic of his book which is poor news
+ 
+
+ align:start position:0%
+the topic of his book which is poor news
+specifically he's breaking down it's
+
+ align:start position:0%
+specifically he's breaking down it's
+ 
+
+ align:start position:0%
+specifically he's breaking down it's
+like alright now that we know that games
+
+ align:start position:0%
+like alright now that we know that games
+ 
+
+ align:start position:0%
+like alright now that we know that games
+and play and sports and everything all
+
+ align:start position:0%
+and play and sports and everything all
+ 
+
+ align:start position:0%
+and play and sports and everything all
+kind of fuzzy and muddled they're not
+
+ align:start position:0%
+kind of fuzzy and muddled they're not
+ 
+
+ align:start position:0%
+kind of fuzzy and muddled they're not
+really very very clear how do we sort of
+
+ align:start position:0%
+really very very clear how do we sort of
+ 
+
+ align:start position:0%
+really very very clear how do we sort of
+at least clarify what we're talking
+
+ align:start position:0%
+at least clarify what we're talking
+ 
+
+ align:start position:0%
+at least clarify what we're talking
+about when I promised to meet workings
+
+ align:start position:0%
+about when I promised to meet workings
+ 
+
+ align:start position:0%
+about when I promised to meet workings
+anyone remember the five things that he
+
+ align:start position:0%
+anyone remember the five things that he
+ 
+
+ align:start position:0%
+anyone remember the five things that he
+ended up with the five or the five
+
+ align:start position:0%
+ended up with the five or the five
+ 
+
+ align:start position:0%
+ended up with the five or the five
+categories of projects that he kind of
+
+ align:start position:0%
+categories of projects that he kind of
+ 
+
+ align:start position:0%
+categories of projects that he kind of
+ended up ends up with for the Brian one
+
+ align:start position:0%
+ended up ends up with for the Brian one
+ 
+
+ align:start position:0%
+ended up ends up with for the Brian one
+minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+race games space games chess games at
+
+ align:start position:0%
+race games space games chess games at
+ 
+
+ align:start position:0%
+race games space games chess games at
+this place which which with which he
+
+ align:start position:0%
+this place which which with which he
+ 
+
+ align:start position:0%
+this place which which with which he
+admits he already came up he only gave
+
+ align:start position:0%
+admits he already came up he only gave
+ 
+
+ align:start position:0%
+admits he already came up he only gave
+that name because the price and then I'm
+
+ align:start position:0%
+that name because the price and then I'm
+ 
+
+ align:start position:0%
+that name because the price and then I'm
+five was like I think he just gave up at
+
+ align:start position:0%
+five was like I think he just gave up at
+ 
+
+ align:start position:0%
+five was like I think he just gave up at
+this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was interesting because he was kind
+
+ align:start position:0%
+it was interesting because he was kind
+ 
+
+ align:start position:0%
+it was interesting because he was kind
+of saying like here at these four that
+
+ align:start position:0%
+of saying like here at these four that
+ 
+
+ align:start position:0%
+of saying like here at these four that
+traditionally other scholars tend to
+
+ align:start position:0%
+traditionally other scholars tend to
+ 
+
+ align:start position:0%
+traditionally other scholars tend to
+ignore here here are these four which
+
+ align:start position:0%
+ignore here here are these four which
+ 
+
+ align:start position:0%
+ignore here here are these four which
+traditionally other scholars like to
+
+ align:start position:0%
+traditionally other scholars like to
+ 
+
+ align:start position:0%
+traditionally other scholars like to
+study because they are bereft of theme
+
+ align:start position:0%
+study because they are bereft of theme
+ 
+
+ align:start position:0%
+study because they are bereft of theme
+but then and yeah and they take in and
+
+ align:start position:0%
+but then and yeah and they take in and
+ 
+
+ align:start position:0%
+but then and yeah and they take in and
+they look at themed games and say like
+
+ align:start position:0%
+they look at themed games and say like
+ 
+
+ align:start position:0%
+they look at themed games and say like
+that thought worthy of study there's
+
+ align:start position:0%
+that thought worthy of study there's
+ 
+
+ align:start position:0%
+that thought worthy of study there's
+this whole chunk and and part that says
+
+ align:start position:0%
+this whole chunk and and part that says
+ 
+
+ align:start position:0%
+this whole chunk and and part that says
+wait a minute how you know first of all
+
+ align:start position:0%
+wait a minute how you know first of all
+ 
+
+ align:start position:0%
+wait a minute how you know first of all
+most of the games that you'll buy off
+
+ align:start position:0%
+most of the games that you'll buy off
+ 
+
+ align:start position:0%
+most of the games that you'll buy off
+the shelf right now from the theme games
+
+ align:start position:0%
+the shelf right now from the theme games
+ 
+
+ align:start position:0%
+the shelf right now from the theme games
+and the only reason why there is this
+
+ align:start position:0%
+and the only reason why there is this
+ 
+
+ align:start position:0%
+and the only reason why there is this
+interest in race games chase games the
+
+ align:start position:0%
+interest in race games chase games the
+ 
+
+ align:start position:0%
+interest in race games chase games the
+space games these games it's because a
+
+ align:start position:0%
+space games these games it's because a
+ 
+
+ align:start position:0%
+space games these games it's because a
+lot of those are he also describes those
+
+ align:start position:0%
+lot of those are he also describes those
+ 
+
+ align:start position:0%
+lot of those are he also describes those
+for positional games and positional
+
+ align:start position:0%
+for positional games and positional
+ 
+
+ align:start position:0%
+for positional games and positional
+games of the sort that scholars like to
+
+ align:start position:0%
+games of the sort that scholars like to
+ 
+
+ align:start position:0%
+games of the sort that scholars like to
+study it take to be fought games that
+
+ align:start position:0%
+study it take to be fought games that
+ 
+
+ align:start position:0%
+study it take to be fought games that
+have been handed down from generations
+
+ align:start position:0%
+have been handed down from generations
+ 
+
+ align:start position:0%
+have been handed down from generations
+yeah of course he's there we get down to
+
+ align:start position:0%
+yeah of course he's there we get down to
+ 
+
+ align:start position:0%
+yeah of course he's there we get down to
+ball games he's not including things
+
+ align:start position:0%
+ball games he's not including things
+ 
+
+ align:start position:0%
+ball games he's not including things
+like car games for Charles you know of
+
+ align:start position:0%
+like car games for Charles you know of
+ 
+
+ align:start position:0%
+like car games for Charles you know of
+which is also very rich
+
+ align:start position:0%
+which is also very rich
+ 
+
+ align:start position:0%
+which is also very rich
+tradition he has a whole separate book I
+
+ align:start position:0%
+tradition he has a whole separate book I
+ 
+
+ align:start position:0%
+tradition he has a whole separate book I
+think we also get to in this class there
+
+ align:start position:0%
+think we also get to in this class there
+ 
+
+ align:start position:0%
+think we also get to in this class there
+are mountain card games but this is just
+
+ align:start position:0%
+are mountain card games but this is just
+ 
+
+ align:start position:0%
+are mountain card games but this is just
+specifically his his port game work but
+
+ align:start position:0%
+specifically his his port game work but
+ 
+
+ align:start position:0%
+specifically his his port game work but
+he wants to start looking at the games
+
+ align:start position:0%
+he wants to start looking at the games
+ 
+
+ align:start position:0%
+he wants to start looking at the games
+and this was him introducing scholarship
+
+ align:start position:0%
+and this was him introducing scholarship
+ 
+
+ align:start position:0%
+and this was him introducing scholarship
+on the games later on on his book I just
+
+ align:start position:0%
+on the games later on on his book I just
+ 
+
+ align:start position:0%
+on the games later on on his book I just
+want to make you realize that you know
+
+ align:start position:0%
+want to make you realize that you know
+ 
+
+ align:start position:0%
+want to make you realize that you know
+the whole idea of studying games as a
+
+ align:start position:0%
+the whole idea of studying games as a
+ 
+
+ align:start position:0%
+the whole idea of studying games as a
+product we already talked a little bit
+
+ align:start position:0%
+product we already talked a little bit
+ 
+
+ align:start position:0%
+product we already talked a little bit
+about how that how the idea of a game as
+
+ align:start position:0%
+about how that how the idea of a game as
+ 
+
+ align:start position:0%
+about how that how the idea of a game as
+a product to begin with was fairly new
+
+ align:start position:0%
+a product to begin with was fairly new
+ 
+
+ align:start position:0%
+a product to begin with was fairly new
+we're talking about nineteen hundreds
+
+ align:start position:0%
+we're talking about nineteen hundreds
+ 
+
+ align:start position:0%
+we're talking about nineteen hundreds
+when that starts to become the thing but
+
+ align:start position:0%
+when that starts to become the thing but
+ 
+
+ align:start position:0%
+when that starts to become the thing but
+then the idea of studying something like
+
+ align:start position:0%
+then the idea of studying something like
+ 
+
+ align:start position:0%
+then the idea of studying something like
+that oh no I think we're talking about
+
+ align:start position:0%
+that oh no I think we're talking about
+ 
+
+ align:start position:0%
+that oh no I think we're talking about
+like fifties and sixties very very we
+
+ align:start position:0%
+like fifties and sixties very very we
+ 
+
+ align:start position:0%
+like fifties and sixties very very we
+said the idea that games as a product is
+
+ align:start position:0%
+said the idea that games as a product is
+ 
+
+ align:start position:0%
+said the idea that games as a product is
+something that we can study whereas
+
+ align:start position:0%
+something that we can study whereas
+ 
+
+ align:start position:0%
+something that we can study whereas
+things like games as a sport can
+
+ align:start position:0%
+things like games as a sport can
+ 
+
+ align:start position:0%
+things like games as a sport can
+probably call back a little bit further
+
+ align:start position:0%
+probably call back a little bit further
+ 
+
+ align:start position:0%
+probably call back a little bit further
+than that and you start start sistex for
+
+ align:start position:0%
+than that and you start start sistex for
+ 
+
+ align:start position:0%
+than that and you start start sistex for
+instance has it has been obsessed with
+
+ align:start position:0%
+instance has it has been obsessed with
+ 
+
+ align:start position:0%
+instance has it has been obsessed with
+baseball for later
+
+ align:start position:0%
+baseball for later
+ 
+
+ align:start position:0%
+baseball for later
+because it's very rich and we have the
+
+ align:start position:0%
+because it's very rich and we have the
+ 
+
+ align:start position:0%
+because it's very rich and we have the
+credits so I don't want to go too much
+
+ align:start position:0%
+credits so I don't want to go too much
+ 
+
+ align:start position:0%
+credits so I don't want to go too much
+into how he arrives at those definitions
+
+ align:start position:0%
+into how he arrives at those definitions
+ 
+
+ align:start position:0%
+into how he arrives at those definitions
+you know he takes a couple of
+
+ align:start position:0%
+you know he takes a couple of
+ 
+
+ align:start position:0%
+you know he takes a couple of
+definitions that other people have come
+
+ align:start position:0%
+definitions that other people have come
+ 
+
+ align:start position:0%
+definitions that other people have come
+up with and tries to build on them like
+
+ align:start position:0%
+up with and tries to build on them like
+ 
+
+ align:start position:0%
+up with and tries to build on them like
+no all scholars he's citing previous
+
+ align:start position:0%
+no all scholars he's citing previous
+ 
+
+ align:start position:0%
+no all scholars he's citing previous
+work but what I'd like to to have us
+
+ align:start position:0%
+work but what I'd like to to have us
+ 
+
+ align:start position:0%
+work but what I'd like to to have us
+played today are what I feel a couple of
+
+ align:start position:0%
+played today are what I feel a couple of
+ 
+
+ align:start position:0%
+played today are what I feel a couple of
+modern takes on those categories that he
+
+ align:start position:0%
+modern takes on those categories that he
+ 
+
+ align:start position:0%
+modern takes on those categories that he
+came up with so you know the race game
+
+ align:start position:0%
+came up with so you know the race game
+ 
+
+ align:start position:0%
+came up with so you know the race game
+what's a race thing if you I have to
+
+ align:start position:0%
+what's a race thing if you I have to
+ 
+
+ align:start position:0%
+what's a race thing if you I have to
+describe it in one sentence you get to
+
+ align:start position:0%
+describe it in one sentence you get to
+ 
+
+ align:start position:0%
+describe it in one sentence you get to
+the end point first right so this
+
+ align:start position:0%
+the end point first right so this
+ 
+
+ align:start position:0%
+the end point first right so this
+cottage a cottage an ax cut coffee get
+
+ align:start position:0%
+cottage a cottage an ax cut coffee get
+ 
+
+ align:start position:0%
+cottage a cottage an ax cut coffee get
+high if they don't think this okay so
+
+ align:start position:0%
+high if they don't think this okay so
+ 
+
+ align:start position:0%
+high if they don't think this okay so
+this is say if you if you look at the
+
+ align:start position:0%
+this is say if you if you look at the
+ 
+
+ align:start position:0%
+this is say if you if you look at the
+game that feels a little bit like a like
+
+ align:start position:0%
+game that feels a little bit like a like
+ 
+
+ align:start position:0%
+game that feels a little bit like a like
+a pile laying game because what you're
+
+ align:start position:0%
+a pile laying game because what you're
+ 
+
+ align:start position:0%
+a pile laying game because what you're
+really doing is you're trying to create
+
+ align:start position:0%
+really doing is you're trying to create
+ 
+
+ align:start position:0%
+really doing is you're trying to create
+this path from the jail that you're
+
+ align:start position:0%
+this path from the jail that you're
+ 
+
+ align:start position:0%
+this path from the jail that you're
+escaping you have a bunch of pirates
+
+ align:start position:0%
+escaping you have a bunch of pirates
+ 
+
+ align:start position:0%
+escaping you have a bunch of pirates
+from the jail they are sleeping all the
+
+ align:start position:0%
+from the jail they are sleeping all the
+ 
+
+ align:start position:0%
+from the jail they are sleeping all the
+way to the boat and then you know you
+
+ align:start position:0%
+way to the boat and then you know you
+ 
+
+ align:start position:0%
+way to the boat and then you know you
+can run or skip Oh Scott Scott for you
+
+ align:start position:0%
+can run or skip Oh Scott Scott for you
+ 
+
+ align:start position:0%
+can run or skip Oh Scott Scott for you
+but one of the core mechanics is that
+
+ align:start position:0%
+but one of the core mechanics is that
+ 
+
+ align:start position:0%
+but one of the core mechanics is that
+every player controls a different set of
+
+ align:start position:0%
+every player controls a different set of
+ 
+
+ align:start position:0%
+every player controls a different set of
+pirates you have a bunch of different
+
+ align:start position:0%
+pirates you have a bunch of different
+ 
+
+ align:start position:0%
+pirates you have a bunch of different
+colors you're all trying to get to the
+
+ align:start position:0%
+colors you're all trying to get to the
+ 
+
+ align:start position:0%
+colors you're all trying to get to the
+to the boat first so the first person to
+
+ align:start position:0%
+to the boat first so the first person to
+ 
+
+ align:start position:0%
+to the boat first so the first person to
+get your entire gang of pirates to the
+
+ align:start position:0%
+get your entire gang of pirates to the
+ 
+
+ align:start position:0%
+get your entire gang of pirates to the
+boat ways so it's risking everything
+
+ align:start position:0%
+boat ways so it's risking everything
+ 
+
+ align:start position:0%
+boat ways so it's risking everything
+against other people it just happens to
+
+ align:start position:0%
+against other people it just happens to
+ 
+
+ align:start position:0%
+against other people it just happens to
+be the track that you're racing a lot
+
+ align:start position:0%
+be the track that you're racing a lot
+ 
+
+ align:start position:0%
+be the track that you're racing a lot
+happens to be something that you build
+
+ align:start position:0%
+happens to be something that you build
+ 
+
+ align:start position:0%
+happens to be something that you build
+over time rather than something that's
+
+ align:start position:0%
+over time rather than something that's
+ 
+
+ align:start position:0%
+over time rather than something that's
+to each other so the interesting don't
+
+ align:start position:0%
+to each other so the interesting don't
+ 
+
+ align:start position:0%
+to each other so the interesting don't
+take nothing let me skip PowerGrid the
+
+ align:start position:0%
+take nothing let me skip PowerGrid the
+ 
+
+ align:start position:0%
+take nothing let me skip PowerGrid the
+other things or displace games I don't
+
+ align:start position:0%
+other things or displace games I don't
+ 
+
+ align:start position:0%
+other things or displace games I don't
+play pad when I struggle in this room
+
+ align:start position:0%
+play pad when I struggle in this room
+ 
+
+ align:start position:0%
+play pad when I struggle in this room
+okay I may need you to help explain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no my first semester okay all right just
+
+ align:start position:0%
+no my first semester okay all right just
+ 
+
+ align:start position:0%
+no my first semester okay all right just
+take a look at the rules again yeah this
+
+ align:start position:0%
+take a look at the rules again yeah this
+ 
+
+ align:start position:0%
+take a look at the rules again yeah this
+is it's it's a question a little a
+
+ align:start position:0%
+is it's it's a question a little a
+ 
+
+ align:start position:0%
+is it's it's a question a little a
+little bit of a tall order to ask
+
+ align:start position:0%
+little bit of a tall order to ask
+ 
+
+ align:start position:0%
+little bit of a tall order to ask
+someone to figure poet struggle in class
+
+ align:start position:0%
+someone to figure poet struggle in class
+ 
+
+ align:start position:0%
+someone to figure poet struggle in class
+but it's worth looking at Lisa Sayler
+
+ align:start position:0%
+but it's worth looking at Lisa Sayler
+ 
+
+ align:start position:0%
+but it's worth looking at Lisa Sayler
+design system you know this is a working
+
+ align:start position:0%
+design system you know this is a working
+ 
+
+ align:start position:0%
+design system you know this is a working
+you want give us a map of the world okay
+
+ align:start position:0%
+you want give us a map of the world okay
+ 
+
+ align:start position:0%
+you want give us a map of the world okay
+you are it is it's the Cold War 1945 to
+
+ align:start position:0%
+you are it is it's the Cold War 1945 to
+ 
+
+ align:start position:0%
+you are it is it's the Cold War 1945 to
+1989 and there's a whole bunch of things
+
+ align:start position:0%
+1989 and there's a whole bunch of things
+ 
+
+ align:start position:0%
+1989 and there's a whole bunch of things
+that come from modern game design like
+
+ align:start position:0%
+that come from modern game design like
+ 
+
+ align:start position:0%
+that come from modern game design like
+you have the event cards that recall
+
+ align:start position:0%
+you have the event cards that recall
+ 
+
+ align:start position:0%
+you have the event cards that recall
+important things that happened Cuban
+
+ align:start position:0%
+important things that happened Cuban
+ 
+
+ align:start position:0%
+important things that happened Cuban
+Missile Crisis Korean War pushing to
+
+ align:start position:0%
+Missile Crisis Korean War pushing to
+ 
+
+ align:start position:0%
+Missile Crisis Korean War pushing to
+rocket deploy things like that but in
+
+ align:start position:0%
+rocket deploy things like that but in
+ 
+
+ align:start position:0%
+rocket deploy things like that but in
+the end is about influence across a
+
+ align:start position:0%
+the end is about influence across a
+ 
+
+ align:start position:0%
+the end is about influence across a
+space which just happens to be laid out
+
+ align:start position:0%
+space which just happens to be laid out
+ 
+
+ align:start position:0%
+space which just happens to be laid out
+along on top of the map of the world to
+
+ align:start position:0%
+along on top of the map of the world to
+ 
+
+ align:start position:0%
+along on top of the map of the world to
+regions like the United States of
+
+ align:start position:0%
+regions like the United States of
+ 
+
+ align:start position:0%
+regions like the United States of
+America to South to South and Central
+
+ align:start position:0%
+America to South to South and Central
+ 
+
+ align:start position:0%
+America to South to South and Central
+America to Western Europe Eastern Europe
+
+ align:start position:0%
+America to Western Europe Eastern Europe
+ 
+
+ align:start position:0%
+America to Western Europe Eastern Europe
+and so on and so forth so so you are
+
+ align:start position:0%
+and so on and so forth so so you are
+ 
+
+ align:start position:0%
+and so on and so forth so so you are
+deploying influence points which is not
+
+ align:start position:0%
+deploying influence points which is not
+ 
+
+ align:start position:0%
+deploying influence points which is not
+all that different from the point what
+
+ align:start position:0%
+all that different from the point what
+ 
+
+ align:start position:0%
+all that different from the point what
+he calls man across the space and trying
+
+ align:start position:0%
+he calls man across the space and trying
+ 
+
+ align:start position:0%
+he calls man across the space and trying
+to be able to seize them to to push
+
+ align:start position:0%
+to be able to seize them to to push
+ 
+
+ align:start position:0%
+to be able to seize them to to push
+influence towards your actions rather
+
+ align:start position:0%
+influence towards your actions rather
+ 
+
+ align:start position:0%
+influence towards your actions rather
+than to the opposite depending on what
+
+ align:start position:0%
+than to the opposite depending on what
+ 
+
+ align:start position:0%
+than to the opposite depending on what
+airplane us all oh yes so display
+
+ align:start position:0%
+airplane us all oh yes so display
+ 
+
+ align:start position:0%
+airplane us all oh yes so display
+escapes justice place goes oh let me
+
+ align:start position:0%
+escapes justice place goes oh let me
+ 
+
+ align:start position:0%
+escapes justice place goes oh let me
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+such a this one Scotland Yard yeah I
+
+ align:start position:0%
+such a this one Scotland Yard yeah I
+ 
+
+ align:start position:0%
+such a this one Scotland Yard yeah I
+think this this might have been not
+
+ align:start position:0%
+think this this might have been not
+ 
+
+ align:start position:0%
+think this this might have been not
+business this is this was what I
+
+ align:start position:0%
+business this is this was what I
+ 
+
+ align:start position:0%
+business this is this was what I
+intended to bring out at this place but
+
+ align:start position:0%
+intended to bring out at this place but
+ 
+
+ align:start position:0%
+intended to bring out at this place but
+not so why did you capture any pieces in
+
+ align:start position:0%
+not so why did you capture any pieces in
+ 
+
+ align:start position:0%
+not so why did you capture any pieces in
+this you will capture it but then you
+
+ align:start position:0%
+this you will capture it but then you
+ 
+
+ align:start position:0%
+this you will capture it but then you
+can reintroduce it yeah yeah okay so
+
+ align:start position:0%
+can reintroduce it yeah yeah okay so
+ 
+
+ align:start position:0%
+can reintroduce it yeah yeah okay so
+this has been through this placement yes
+
+ align:start position:0%
+this has been through this placement yes
+ 
+
+ align:start position:0%
+this has been through this placement yes
+Scotland Yard which I believe we have
+
+ align:start position:0%
+Scotland Yard which I believe we have
+ 
+
+ align:start position:0%
+Scotland Yard which I believe we have
+mentioned in class before is kind of
+
+ align:start position:0%
+mentioned in class before is kind of
+ 
+
+ align:start position:0%
+mentioned in class before is kind of
+like a evolution of the chase game it is
+
+ align:start position:0%
+like a evolution of the chase game it is
+ 
+
+ align:start position:0%
+like a evolution of the chase game it is
+chase gives us super old some of the
+
+ align:start position:0%
+chase gives us super old some of the
+ 
+
+ align:start position:0%
+chase gives us super old some of the
+more famous ancient ones or Scandinavian
+
+ align:start position:0%
+more famous ancient ones or Scandinavian
+ 
+
+ align:start position:0%
+more famous ancient ones or Scandinavian
+in origin a lot of Norse a lot of Viking
+
+ align:start position:0%
+in origin a lot of Norse a lot of Viking
+ 
+
+ align:start position:0%
+in origin a lot of Norse a lot of Viking
+games where you have a king you have a
+
+ align:start position:0%
+games where you have a king you have a
+ 
+
+ align:start position:0%
+games where you have a king you have a
+couple of guards four bodyguards for the
+
+ align:start position:0%
+couple of guards four bodyguards for the
+ 
+
+ align:start position:0%
+couple of guards four bodyguards for the
+king they get a whole bunch of like
+
+ align:start position:0%
+king they get a whole bunch of like
+ 
+
+ align:start position:0%
+king they get a whole bunch of like
+low-level pawns all trying to flank the
+
+ align:start position:0%
+low-level pawns all trying to flank the
+ 
+
+ align:start position:0%
+low-level pawns all trying to flank the
+king that's that's the that's the theme
+
+ align:start position:0%
+king that's that's the that's the theme
+ 
+
+ align:start position:0%
+king that's that's the that's the theme
+of a whole genre of games couple of
+
+ align:start position:0%
+of a whole genre of games couple of
+ 
+
+ align:start position:0%
+of a whole genre of games couple of
+which chase games will form a big part
+
+ align:start position:0%
+which chase games will form a big part
+ 
+
+ align:start position:0%
+which chase games will form a big part
+of in this game you are a districts on
+
+ align:start position:0%
+of in this game you are a districts on
+ 
+
+ align:start position:0%
+of in this game you are a districts on
+the run from a bunch of Scotland Yard
+
+ align:start position:0%
+the run from a bunch of Scotland Yard
+ 
+
+ align:start position:0%
+the run from a bunch of Scotland Yard
+detectives and more importantly it's a
+
+ align:start position:0%
+detectives and more importantly it's a
+ 
+
+ align:start position:0%
+detectives and more importantly it's a
+blended public transport system and what
+
+ align:start position:0%
+blended public transport system and what
+ 
+
+ align:start position:0%
+blended public transport system and what
+you're trying to do is they're trying to
+
+ align:start position:0%
+you're trying to do is they're trying to
+ 
+
+ align:start position:0%
+you're trying to do is they're trying to
+go underground they're trying to catch
+
+ align:start position:0%
+go underground they're trying to catch
+ 
+
+ align:start position:0%
+go underground they're trying to catch
+cabs take buses and conceal where you
+
+ align:start position:0%
+cabs take buses and conceal where you
+ 
+
+ align:start position:0%
+cabs take buses and conceal where you
+are while the u.s. other players were
+
+ align:start position:0%
+are while the u.s. other players were
+ 
+
+ align:start position:0%
+are while the u.s. other players were
+all controlling the detectors actually
+
+ align:start position:0%
+all controlling the detectors actually
+ 
+
+ align:start position:0%
+all controlling the detectors actually
+yeah three to six players the people who
+
+ align:start position:0%
+yeah three to six players the people who
+ 
+
+ align:start position:0%
+yeah three to six players the people who
+are contrary to detectives such
+
+ align:start position:0%
+are contrary to detectives such
+ 
+
+ align:start position:0%
+are contrary to detectives such
+basically just trying to find you and so
+
+ align:start position:0%
+basically just trying to find you and so
+ 
+
+ align:start position:0%
+basically just trying to find you and so
+a nice little body revolution they they
+
+ align:start position:0%
+a nice little body revolution they they
+ 
+
+ align:start position:0%
+a nice little body revolution they they
+have a neat little do that which is a
+
+ align:start position:0%
+have a neat little do that which is a
+ 
+
+ align:start position:0%
+have a neat little do that which is a
+way to be able to track the moves that
+
+ align:start position:0%
+way to be able to track the moves that
+ 
+
+ align:start position:0%
+way to be able to track the moves that
+you made without revealing it
+
+ align:start position:0%
+you made without revealing it
+ 
+
+ align:start position:0%
+you made without revealing it
+opponents the bad guys position private
+
+ align:start position:0%
+opponents the bad guys position private
+ 
+
+ align:start position:0%
+opponents the bad guys position private
+republic it is funny but little bits of
+
+ align:start position:0%
+republic it is funny but little bits of
+ 
+
+ align:start position:0%
+republic it is funny but little bits of
+information about so you reveal that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+empire builder is a train game which one
+
+ align:start position:0%
+empire builder is a train game which one
+ 
+
+ align:start position:0%
+empire builder is a train game which one
+of our grad student allowance
+
+ align:start position:0%
+of our grad student allowance
+ 
+
+ align:start position:0%
+of our grad student allowance
+now all the physical studies but a very
+
+ align:start position:0%
+now all the physical studies but a very
+ 
+
+ align:start position:0%
+now all the physical studies but a very
+interesting kind general train train
+
+ align:start position:0%
+interesting kind general train train
+ 
+
+ align:start position:0%
+interesting kind general train train
+that you you may not have heard of
+
+ align:start position:0%
+that you you may not have heard of
+ 
+
+ align:start position:0%
+that you you may not have heard of
+concrete on rails where you got given a
+
+ align:start position:0%
+concrete on rails where you got given a
+ 
+
+ align:start position:0%
+concrete on rails where you got given a
+big sheet of plastic a plastic laminated
+
+ align:start position:0%
+big sheet of plastic a plastic laminated
+ 
+
+ align:start position:0%
+big sheet of plastic a plastic laminated
+board I guess it's kind of like a jigsaw
+
+ align:start position:0%
+board I guess it's kind of like a jigsaw
+ 
+
+ align:start position:0%
+board I guess it's kind of like a jigsaw
+and Anna Greece and Greece for yard but
+
+ align:start position:0%
+and Anna Greece and Greece for yard but
+ 
+
+ align:start position:0%
+and Anna Greece and Greece for yard but
+a piece for your invention criolla
+
+ align:start position:0%
+a piece for your invention criolla
+ 
+
+ align:start position:0%
+a piece for your invention criolla
+washable for you here we go
+
+ align:start position:0%
+washable for you here we go
+ 
+
+ align:start position:0%
+washable for you here we go
+you're just drawing your rails across
+
+ align:start position:0%
+you're just drawing your rails across
+ 
+
+ align:start position:0%
+you're just drawing your rails across
+the mat trying to establish your
+
+ align:start position:0%
+the mat trying to establish your
+ 
+
+ align:start position:0%
+the mat trying to establish your
+railroad Empire so this is this was the
+
+ align:start position:0%
+railroad Empire so this is this was the
+ 
+
+ align:start position:0%
+railroad Empire so this is this was the
+one that I was picking up as space
+
+ align:start position:0%
+one that I was picking up as space
+ 
+
+ align:start position:0%
+one that I was picking up as space
+because it's all about occupying space
+
+ align:start position:0%
+because it's all about occupying space
+ 
+
+ align:start position:0%
+because it's all about occupying space
+but you're occupying space with a
+
+ align:start position:0%
+but you're occupying space with a
+ 
+
+ align:start position:0%
+but you're occupying space with a
+network rather than occupying space
+
+ align:start position:0%
+network rather than occupying space
+ 
+
+ align:start position:0%
+network rather than occupying space
+they're just pieces that you're facing
+
+ align:start position:0%
+they're just pieces that you're facing
+ 
+
+ align:start position:0%
+they're just pieces that you're facing
+that creating lines across the United
+
+ align:start position:0%
+that creating lines across the United
+ 
+
+ align:start position:0%
+that creating lines across the United
+States while you're doing that so so I
+
+ align:start position:0%
+States while you're doing that so so I
+ 
+
+ align:start position:0%
+States while you're doing that so so I
+think train games are this particular
+
+ align:start position:0%
+think train games are this particular
+ 
+
+ align:start position:0%
+think train games are this particular
+genre of games are an interesting take
+
+ align:start position:0%
+genre of games are an interesting take
+ 
+
+ align:start position:0%
+genre of games are an interesting take
+on the space game there's a whole other
+
+ align:start position:0%
+on the space game there's a whole other
+ 
+
+ align:start position:0%
+on the space game there's a whole other
+genres of trade games that's really more
+
+ align:start position:0%
+genres of trade games that's really more
+ 
+
+ align:start position:0%
+genres of trade games that's really more
+about the economics of what it's like to
+
+ align:start position:0%
+about the economics of what it's like to
+ 
+
+ align:start position:0%
+about the economics of what it's like to
+be a robber baron
+
+ align:start position:0%
+be a robber baron
+ 
+
+ align:start position:0%
+be a robber baron
+train train Lord those are really
+
+ align:start position:0%
+train train Lord those are really
+ 
+
+ align:start position:0%
+train train Lord those are really
+fascinating as well those know kind of
+
+ align:start position:0%
+fascinating as well those know kind of
+ 
+
+ align:start position:0%
+fascinating as well those know kind of
+more on the economic sense which part
+
+ align:start position:0%
+more on the economic sense which part
+ 
+
+ align:start position:0%
+more on the economic sense which part
+that doesn't mean the address or maybe
+
+ align:start position:0%
+that doesn't mean the address or maybe
+ 
+
+ align:start position:0%
+that doesn't mean the address or maybe
+they'd all maybe those fall under this
+
+ align:start position:0%
+they'd all maybe those fall under this
+ 
+
+ align:start position:0%
+they'd all maybe those fall under this
+definition of teen games yeah
+
+ align:start position:0%
+definition of teen games yeah
+ 
+
+ align:start position:0%
+definition of teen games yeah
+and power grid is just this like huge
+
+ align:start position:0%
+and power grid is just this like huge
+ 
+
+ align:start position:0%
+and power grid is just this like huge
+mishmash of everything but I'm using it
+
+ align:start position:0%
+mishmash of everything but I'm using it
+ 
+
+ align:start position:0%
+mishmash of everything but I'm using it
+as an example of a theme game that kind
+
+ align:start position:0%
+as an example of a theme game that kind
+ 
+
+ align:start position:0%
+as an example of a theme game that kind
+of where if you play any of these games
+
+ align:start position:0%
+of where if you play any of these games
+ 
+
+ align:start position:0%
+of where if you play any of these games
+and you play however you'll see them
+
+ align:start position:0%
+and you play however you'll see them
+ 
+
+ align:start position:0%
+and you play however you'll see them
+you'll see the connections it's a game
+
+ align:start position:0%
+you'll see the connections it's a game
+ 
+
+ align:start position:0%
+you'll see the connections it's a game
+where you play on a network of Germany
+
+ align:start position:0%
+where you play on a network of Germany
+ 
+
+ align:start position:0%
+where you play on a network of Germany
+and you're basically supporting
+
+ align:start position:0%
+and you're basically supporting
+ 
+
+ align:start position:0%
+and you're basically supporting
+something else right and you're
+
+ align:start position:0%
+something else right and you're
+ 
+
+ align:start position:0%
+something else right and you're
+basically trying to create efficient
+
+ align:start position:0%
+basically trying to create efficient
+ 
+
+ align:start position:0%
+basically trying to create efficient
+links between different power stations
+
+ align:start position:0%
+links between different power stations
+ 
+
+ align:start position:0%
+links between different power stations
+that you are building and it's not all
+
+ align:start position:0%
+that you are building and it's not all
+ 
+
+ align:start position:0%
+that you are building and it's not all
+that different from creating in we all
+
+ align:start position:0%
+that different from creating in we all
+ 
+
+ align:start position:0%
+that different from creating in we all
+rode Empire you know it just happened to
+
+ align:start position:0%
+rode Empire you know it just happened to
+ 
+
+ align:start position:0%
+rode Empire you know it just happened to
+be trying to create energy generating
+
+ align:start position:0%
+be trying to create energy generating
+ 
+
+ align:start position:0%
+be trying to create energy generating
+Empire that going to use different
+
+ align:start position:0%
+Empire that going to use different
+ 
+
+ align:start position:0%
+Empire that going to use different
+commodities like you know on your way I
+
+ align:start position:0%
+commodities like you know on your way I
+ 
+
+ align:start position:0%
+commodities like you know on your way I
+think you can put a fuse yeah you can
+
+ align:start position:0%
+think you can put a fuse yeah you can
+ 
+
+ align:start position:0%
+think you can put a fuse yeah you can
+put in right here sample input you can
+
+ align:start position:0%
+put in right here sample input you can
+ 
+
+ align:start position:0%
+put in right here sample input you can
+pretty cool like you're playing on the
+
+ align:start position:0%
+pretty cool like you're playing on the
+ 
+
+ align:start position:0%
+pretty cool like you're playing on the
+same space you can occupy space so the
+
+ align:start position:0%
+same space you can occupy space so the
+ 
+
+ align:start position:0%
+same space you can occupy space so the
+way it's kind of like a space thing
+
+ align:start position:0%
+way it's kind of like a space thing
+ 
+
+ align:start position:0%
+way it's kind of like a space thing
+because once you take it space than what
+
+ align:start position:0%
+because once you take it space than what
+ 
+
+ align:start position:0%
+because once you take it space than what
+else they take it away from you but most
+
+ align:start position:0%
+else they take it away from you but most
+ 
+
+ align:start position:0%
+else they take it away from you but most
+of this game is about the economy rather
+
+ align:start position:0%
+of this game is about the economy rather
+ 
+
+ align:start position:0%
+of this game is about the economy rather
+than about these specific positions
+
+ align:start position:0%
+than about these specific positions
+ 
+
+ align:start position:0%
+than about these specific positions
+where you face although that's not very
+
+ align:start position:0%
+where you face although that's not very
+ 
+
+ align:start position:0%
+where you face although that's not very
+influence your economy so it's a
+
+ align:start position:0%
+influence your economy so it's a
+ 
+
+ align:start position:0%
+influence your economy so it's a
+complicated game it's very well designed
+
+ align:start position:0%
+complicated game it's very well designed
+ 
+
+ align:start position:0%
+complicated game it's very well designed
+if you have the right set of rules the
+
+ align:start position:0%
+if you have the right set of rules the
+ 
+
+ align:start position:0%
+if you have the right set of rules the
+rules that come in the box
+
+ align:start position:0%
+rules that come in the box
+ 
+
+ align:start position:0%
+rules that come in the box
+have misprints in them specifically they
+
+ align:start position:0%
+have misprints in them specifically they
+ 
+
+ align:start position:0%
+have misprints in them specifically they
+built they break things into turns
+
+ align:start position:0%
+built they break things into turns
+ 
+
+ align:start position:0%
+built they break things into turns
+phases and phases of steps and then they
+
+ align:start position:0%
+phases and phases of steps and then they
+ 
+
+ align:start position:0%
+phases and phases of steps and then they
+kind of don't use those words
+
+ align:start position:0%
+kind of don't use those words
+ 
+
+ align:start position:0%
+kind of don't use those words
+consistently if you are interested in
+
+ align:start position:0%
+consistently if you are interested in
+ 
+
+ align:start position:0%
+consistently if you are interested in
+seeing how fairly straightforward rules
+
+ align:start position:0%
+seeing how fairly straightforward rules
+ 
+
+ align:start position:0%
+seeing how fairly straightforward rules
+can be really really confusing take a
+
+ align:start position:0%
+can be really really confusing take a
+ 
+
+ align:start position:0%
+can be really really confusing take a
+look at the rules of it then take a look
+
+ align:start position:0%
+look at the rules of it then take a look
+ 
+
+ align:start position:0%
+look at the rules of it then take a look
+at the prison rules that I printed out
+
+ align:start position:0%
+at the prison rules that I printed out
+ 
+
+ align:start position:0%
+at the prison rules that I printed out
+from the printer because these are the
+
+ align:start position:0%
+from the printer because these are the
+ 
+
+ align:start position:0%
+from the printer because these are the
+Revised Rules these are the Revised
+
+ align:start position:0%
+Revised Rules these are the Revised
+ 
+
+ align:start position:0%
+Revised Rules these are the Revised
+Rules from Morgan Jeep that have some
+
+ align:start position:0%
+Rules from Morgan Jeep that have some
+ 
+
+ align:start position:0%
+Rules from Morgan Jeep that have some
+that are basically translation for the
+
+ align:start position:0%
+that are basically translation for the
+ 
+
+ align:start position:0%
+that are basically translation for the
+German rules a little bit more
+
+ align:start position:0%
+German rules a little bit more
+ 
+
+ align:start position:0%
+German rules a little bit more
+consistent it is a complicated game you
+
+ align:start position:0%
+consistent it is a complicated game you
+ 
+
+ align:start position:0%
+consistent it is a complicated game you
+might not be able to go through a full
+
+ align:start position:0%
+might not be able to go through a full
+ 
+
+ align:start position:0%
+might not be able to go through a full
+game and
+
+ align:start position:0%
+game and
+ 
+
+ align:start position:0%
+game and
+anyone here play powder I encourage you
+
+ align:start position:0%
+anyone here play powder I encourage you
+ 
+
+ align:start position:0%
+anyone here play powder I encourage you
+to set up the games to help more people
+
+ align:start position:0%
+to set up the games to help more people
+ 
+
+ align:start position:0%
+to set up the games to help more people
+do all right so what we're going to do
+
+ align:start position:0%
+do all right so what we're going to do
+ 
+
+ align:start position:0%
+do all right so what we're going to do
+actually any questions before we break
+
+ align:start position:0%
+actually any questions before we break
+ 
+
+ align:start position:0%
+actually any questions before we break
+on the new game game groups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'll play this until about
+
+ align:start position:0%
+okay so I'll play this until about
+ 
+
+ align:start position:0%
+okay so I'll play this until about
+actually I think all the windows 3
+
+ align:start position:0%
+actually I think all the windows 3
+ 
+
+ align:start position:0%
+actually I think all the windows 3
+probably are in these two 45 or so we'll
+
+ align:start position:0%
+probably are in these two 45 or so we'll
+ 
+
+ align:start position:0%
+probably are in these two 45 or so we'll
+call fire yeah we'll have about 15
+
+ align:start position:0%
+call fire yeah we'll have about 15
+ 
+
+ align:start position:0%
+call fire yeah we'll have about 15
+minutes for you to get all the pretest
+
+ align:start position:0%
+minutes for you to get all the pretest
+ 
+
+ align:start position:0%
+minutes for you to get all the pretest
+ready and in the last hours were you
+
+ align:start position:0%
+ready and in the last hours were you
+ 
+
+ align:start position:0%
+ready and in the last hours were you
+protesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you
\ No newline at end of file
diff --git a/1mw_Uo5ba58.txt b/1mw_Uo5ba58.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f7a7ed18096c6a1536773ed0ebf8ab6f0d4feec5
--- /dev/null
+++ b/1mw_Uo5ba58.txt
@@ -0,0 +1,763 @@
+align:start position:0%
+ 
+the next thing I want to talk about is
+
+ align:start position:0%
+the next thing I want to talk about is
+ 
+
+ align:start position:0%
+the next thing I want to talk about is
+what types of innovation are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we at the Massachusetts Institute
+
+ align:start position:0%
+there we at the Massachusetts Institute
+ 
+
+ align:start position:0%
+there we at the Massachusetts Institute
+of Technology think about technology but
+
+ align:start position:0%
+of Technology think about technology but
+ 
+
+ align:start position:0%
+of Technology think about technology but
+we also think about a lot of other
+
+ align:start position:0%
+we also think about a lot of other
+ 
+
+ align:start position:0%
+we also think about a lot of other
+things if you have types of innov
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technology but you can also have process
+
+ align:start position:0%
+technology but you can also have process
+ 
+
+ align:start position:0%
+technology but you can also have process
+Innovations as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you can have process Innovations
+
+ align:start position:0%
+well you can have process Innovations
+ 
+
+ align:start position:0%
+well you can have process Innovations
+where we change a process someone looks
+
+ align:start position:0%
+where we change a process someone looks
+ 
+
+ align:start position:0%
+where we change a process someone looks
+at something says this can be done
+
+ align:start position:0%
+at something says this can be done
+ 
+
+ align:start position:0%
+at something says this can be done
+differently we also can have business
+
+ align:start position:0%
+differently we also can have business
+ 
+
+ align:start position:0%
+differently we also can have business
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+Innovations this is probably one of the
+
+ align:start position:0%
+Innovations this is probably one of the
+ 
+
+ align:start position:0%
+Innovations this is probably one of the
+most interesting areas right now now
+
+ align:start position:0%
+most interesting areas right now now
+ 
+
+ align:start position:0%
+most interesting areas right now now
+because you see terrific um uh uh uh
+
+ align:start position:0%
+because you see terrific um uh uh uh
+ 
+
+ align:start position:0%
+because you see terrific um uh uh uh
+value Creation in innovative business
+
+ align:start position:0%
+value Creation in innovative business
+ 
+
+ align:start position:0%
+value Creation in innovative business
+models not just things like Blockbuster
+
+ align:start position:0%
+models not just things like Blockbuster
+ 
+
+ align:start position:0%
+models not just things like Blockbuster
+or Salesforce but the underlying
+
+ align:start position:0%
+or Salesforce but the underlying
+ 
+
+ align:start position:0%
+or Salesforce but the underlying
+Innovation at at Google that was
+
+ align:start position:0%
+Innovation at at Google that was
+ 
+
+ align:start position:0%
+Innovation at at Google that was
+creating value I would argue is the new
+
+ align:start position:0%
+creating value I would argue is the new
+ 
+
+ align:start position:0%
+creating value I would argue is the new
+way that they do advertising previously
+
+ align:start position:0%
+way that they do advertising previously
+ 
+
+ align:start position:0%
+way that they do advertising previously
+before that there were banner ads but
+
+ align:start position:0%
+before that there were banner ads but
+ 
+
+ align:start position:0%
+before that there were banner ads but
+Google again took the idea from Ure with
+
+ align:start position:0%
+Google again took the idea from Ure with
+ 
+
+ align:start position:0%
+Google again took the idea from Ure with
+Bill gross and commercialized that to
+
+ align:start position:0%
+Bill gross and commercialized that to
+ 
+
+ align:start position:0%
+Bill gross and commercialized that to
+change the name to change the game for
+
+ align:start position:0%
+change the name to change the game for
+ 
+
+ align:start position:0%
+change the name to change the game for
+business models how they extracted their
+
+ align:start position:0%
+business models how they extracted their
+ 
+
+ align:start position:0%
+business models how they extracted their
+value they did it by Google AdWords so
+
+ align:start position:0%
+value they did it by Google AdWords so
+ 
+
+ align:start position:0%
+value they did it by Google AdWords so
+they were charging they were advertising
+
+ align:start position:0%
+they were charging they were advertising
+ 
+
+ align:start position:0%
+they were charging they were advertising
+using the words as opposed to just the
+
+ align:start position:0%
+using the words as opposed to just the
+ 
+
+ align:start position:0%
+using the words as opposed to just the
+Real Estate another one that's very
+
+ align:start position:0%
+Real Estate another one that's very
+ 
+
+ align:start position:0%
+Real Estate another one that's very
+interesting when you talk about
+
+ align:start position:0%
+interesting when you talk about
+ 
+
+ align:start position:0%
+interesting when you talk about
+innovative business models one of the in
+
+ align:start position:0%
+innovative business models one of the in
+ 
+
+ align:start position:0%
+innovative business models one of the in
+in hindsight looking back at iTunes now
+
+ align:start position:0%
+in hindsight looking back at iTunes now
+ 
+
+ align:start position:0%
+in hindsight looking back at iTunes now
+one of the big breakthroughs that made
+
+ align:start position:0%
+one of the big breakthroughs that made
+ 
+
+ align:start position:0%
+one of the big breakthroughs that made
+iTunes successful was before them
+
+ align:start position:0%
+iTunes successful was before them
+ 
+
+ align:start position:0%
+iTunes successful was before them
+everybody was charging on a subscription
+
+ align:start position:0%
+everybody was charging on a subscription
+ 
+
+ align:start position:0%
+everybody was charging on a subscription
+basis for the music
+
+ align:start position:0%
+basis for the music
+ 
+
+ align:start position:0%
+basis for the music
+what what Apple did was they charged 99
+
+ align:start position:0%
+what what Apple did was they charged 99
+ 
+
+ align:start position:0%
+what what Apple did was they charged 99
+cents per song and you got to keep it
+
+ align:start position:0%
+cents per song and you got to keep it
+ 
+
+ align:start position:0%
+cents per song and you got to keep it
+turns out that was a very good business
+
+ align:start position:0%
+turns out that was a very good business
+ 
+
+ align:start position:0%
+turns out that was a very good business
+model Innovation as to how to price it
+
+ align:start position:0%
+model Innovation as to how to price it
+ 
+
+ align:start position:0%
+model Innovation as to how to price it
+and extract value because that made it
+
+ align:start position:0%
+and extract value because that made it
+ 
+
+ align:start position:0%
+and extract value because that made it
+more familiar with the past where they
+
+ align:start position:0%
+more familiar with the past where they
+ 
+
+ align:start position:0%
+more familiar with the past where they
+were buying CDs and other and the like
+
+ align:start position:0%
+were buying CDs and other and the like
+ 
+
+ align:start position:0%
+were buying CDs and other and the like
+so business model Innovation is a very
+
+ align:start position:0%
+so business model Innovation is a very
+ 
+
+ align:start position:0%
+so business model Innovation is a very
+interesting one um you can also
+
+ align:start position:0%
+interesting one um you can also
+ 
+
+ align:start position:0%
+interesting one um you can also
+have positioning how you position
+
+ align:start position:0%
+have positioning how you position
+ 
+
+ align:start position:0%
+have positioning how you position
+yourself and then we'll just say other
+
+ align:start position:0%
+yourself and then we'll just say other
+ 
+
+ align:start position:0%
+yourself and then we'll just say other
+cuz you it's hard to it's hard to limit
+
+ align:start position:0%
+cuz you it's hard to it's hard to limit
+ 
+
+ align:start position:0%
+cuz you it's hard to it's hard to limit
+your in your types of innovation now
+
+ align:start position:0%
+your in your types of innovation now
+ 
+
+ align:start position:0%
+your in your types of innovation now
+when you have types of innovation I
+
+ align:start position:0%
+when you have types of innovation I
+ 
+
+ align:start position:0%
+when you have types of innovation I
+would also say that we all we indeed we
+
+ align:start position:0%
+would also say that we all we indeed we
+ 
+
+ align:start position:0%
+would also say that we all we indeed we
+also have categories of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+innovation and in this case we have
+
+ align:start position:0%
+innovation and in this case we have
+ 
+
+ align:start position:0%
+innovation and in this case we have
+disruptive which
+
+ align:start position:0%
+disruptive which
+ 
+
+ align:start position:0%
+disruptive which
+is which is the word that we hear so
+
+ align:start position:0%
+is which is the word that we hear so
+ 
+
+ align:start position:0%
+is which is the word that we hear so
+often now this is disruptive this is
+
+ align:start position:0%
+often now this is disruptive this is
+ 
+
+ align:start position:0%
+often now this is disruptive this is
+disruptive that can be a very good thing
+
+ align:start position:0%
+disruptive that can be a very good thing
+ 
+
+ align:start position:0%
+disruptive that can be a very good thing
+if you're not the entrenched player if
+
+ align:start position:0%
+if you're not the entrenched player if
+ 
+
+ align:start position:0%
+if you're not the entrenched player if
+you're um if you're the new player in
+
+ align:start position:0%
+you're um if you're the new player in
+ 
+
+ align:start position:0%
+you're um if you're the new player in
+the market you want disruptive however
+
+ align:start position:0%
+the market you want disruptive however
+ 
+
+ align:start position:0%
+the market you want disruptive however
+if you're the entrenched player you're
+
+ align:start position:0%
+if you're the entrenched player you're
+ 
+
+ align:start position:0%
+if you're the entrenched player you're
+looking for incremental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Innovation that says this is 10% better
+
+ align:start position:0%
+Innovation that says this is 10% better
+ 
+
+ align:start position:0%
+Innovation that says this is 10% better
+20% better and the last one I'll say is
+
+ align:start position:0%
+20% better and the last one I'll say is
+ 
+
+ align:start position:0%
+20% better and the last one I'll say is
+that a very interesting one is what
+
+ align:start position:0%
+that a very interesting one is what
+ 
+
+ align:start position:0%
+that a very interesting one is what
+we'll call lateral Innovation or I think
+
+ align:start position:0%
+we'll call lateral Innovation or I think
+ 
+
+ align:start position:0%
+we'll call lateral Innovation or I think
+Stephan Tomy at Harvard calls it uh
+
+ align:start position:0%
+Stephan Tomy at Harvard calls it uh
+ 
+
+ align:start position:0%
+Stephan Tomy at Harvard calls it uh
+General Innovation and this is something
+
+ align:start position:0%
+General Innovation and this is something
+ 
+
+ align:start position:0%
+General Innovation and this is something
+that was an innovation that you saw in
+
+ align:start position:0%
+that was an innovation that you saw in
+ 
+
+ align:start position:0%
+that was an innovation that you saw in
+another industry and you're just
+
+ align:start position:0%
+another industry and you're just
+ 
+
+ align:start position:0%
+another industry and you're just
+bringing back into your indust into into
+
+ align:start position:0%
+bringing back into your indust into into
+ 
+
+ align:start position:0%
+bringing back into your indust into into
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+industry now why do I have types and
+
+ align:start position:0%
+industry now why do I have types and
+ 
+
+ align:start position:0%
+industry now why do I have types and
+categories because in this case you
+
+ align:start position:0%
+categories because in this case you
+ 
+
+ align:start position:0%
+categories because in this case you
+could have a technology that was
+
+ align:start position:0%
+could have a technology that was
+ 
+
+ align:start position:0%
+could have a technology that was
+disruptive innovation you could have a
+
+ align:start position:0%
+disruptive innovation you could have a
+ 
+
+ align:start position:0%
+disruptive innovation you could have a
+technology that's incremental or you
+
+ align:start position:0%
+technology that's incremental or you
+ 
+
+ align:start position:0%
+technology that's incremental or you
+could have a technology that's already
+
+ align:start position:0%
+could have a technology that's already
+ 
+
+ align:start position:0%
+could have a technology that's already
+worked in another industry and you bring
+
+ align:start position:0%
+worked in another industry and you bring
+ 
+
+ align:start position:0%
+worked in another industry and you bring
+it in so really what you have as a
+
+ align:start position:0%
+it in so really what you have as a
+ 
+
+ align:start position:0%
+it in so really what you have as a
+matrix where you have three different
+
+ align:start position:0%
+matrix where you have three different
+ 
+
+ align:start position:0%
+matrix where you have three different
+categories for each type and there could
+
+ align:start position:0%
+categories for each type and there could
+ 
+
+ align:start position:0%
+categories for each type and there could
+be more but my point here is is that as
+
+ align:start position:0%
+be more but my point here is is that as
+ 
+
+ align:start position:0%
+be more but my point here is is that as
+we're about to go through these 24 steps
+
+ align:start position:0%
+we're about to go through these 24 steps
+ 
+
+ align:start position:0%
+we're about to go through these 24 steps
+Innovation can be driven by a number of
+
+ align:start position:0%
+Innovation can be driven by a number of
+ 
+
+ align:start position:0%
+Innovation can be driven by a number of
+things it's not just technology and
+
+ align:start position:0%
+things it's not just technology and
+ 
+
+ align:start position:0%
+things it's not just technology and
+sometimes your Innovation can be
+
+ align:start position:0%
+sometimes your Innovation can be
+ 
+
+ align:start position:0%
+sometimes your Innovation can be
+disruptive and sometimes it can be
+
+ align:start position:0%
+disruptive and sometimes it can be
+ 
+
+ align:start position:0%
+disruptive and sometimes it can be
+incremental and sometimes it can be
+
+ align:start position:0%
+incremental and sometimes it can be
+ 
+
+ align:start position:0%
+incremental and sometimes it can be
+General all of these are good and it
+
+ align:start position:0%
+General all of these are good and it
+ 
+
+ align:start position:0%
+General all of these are good and it
+depends on your situation don't just
+
+ align:start position:0%
+depends on your situation don't just
+ 
+
+ align:start position:0%
+depends on your situation don't just
+look for disruptive technological
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+innovations
\ No newline at end of file
diff --git a/1xJJu5p3dD0.txt b/1xJJu5p3dD0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..96a16f4fa47d117a6cf911ec902ca343b81b32fc
--- /dev/null
+++ b/1xJJu5p3dD0.txt
@@ -0,0 +1,11154 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+today we are going to to talk about the
+
+ align:start position:0%
+today we are going to to talk about the
+ 
+
+ align:start position:0%
+today we are going to to talk about the
+vibration of continuous systems not
+
+ align:start position:0%
+vibration of continuous systems not
+ 
+
+ align:start position:0%
+vibration of continuous systems not
+covered on the quiz but uh it's a really
+
+ align:start position:0%
+covered on the quiz but uh it's a really
+ 
+
+ align:start position:0%
+covered on the quiz but uh it's a really
+important part of real world vibration
+
+ align:start position:0%
+important part of real world vibration
+ 
+
+ align:start position:0%
+important part of real world vibration
+and the most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh easiest one of the easiest ones to
+
+ align:start position:0%
+uh easiest one of the easiest ones to
+ 
+
+ align:start position:0%
+uh easiest one of the easiest ones to
+demonstrate I've shown you this one
+
+ align:start position:0%
+demonstrate I've shown you this one
+ 
+
+ align:start position:0%
+demonstrate I've shown you this one
+before is the Tau string but I want to
+
+ align:start position:0%
+before is the Tau string but I want to
+ 
+
+ align:start position:0%
+before is the Tau string but I want to
+show you something un unusual
+
+ align:start position:0%
+show you something un unusual
+ 
+
+ align:start position:0%
+show you something un unusual
+about something you may not know about
+
+ align:start position:0%
+about something you may not know about
+ 
+
+ align:start position:0%
+about something you may not know about
+strings wait till it calms down here a
+
+ align:start position:0%
+strings wait till it calms down here a
+ 
+
+ align:start position:0%
+strings wait till it calms down here a
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit okay so this is your guitar string
+
+ align:start position:0%
+bit okay so this is your guitar string
+ 
+
+ align:start position:0%
+bit okay so this is your guitar string
+or a piano string it's a it's under
+
+ align:start position:0%
+or a piano string it's a it's under
+ 
+
+ align:start position:0%
+or a piano string it's a it's under
+tension we've already seen that it
+
+ align:start position:0%
+tension we've already seen that it
+ 
+
+ align:start position:0%
+tension we've already seen that it
+exhibits natural frequencies in mode
+
+ align:start position:0%
+exhibits natural frequencies in mode
+ 
+
+ align:start position:0%
+exhibits natural frequencies in mode
+shape so there's the first mode looks
+
+ align:start position:0%
+shape so there's the first mode looks
+ 
+
+ align:start position:0%
+shape so there's the first mode looks
+like half a sine wave has a particular
+
+ align:start position:0%
+like half a sine wave has a particular
+ 
+
+ align:start position:0%
+like half a sine wave has a particular
+frequency associated with it the uh get
+
+ align:start position:0%
+frequency associated with it the uh get
+ 
+
+ align:start position:0%
+frequency associated with it the uh get
+it to stop doing that so I get to do but
+
+ align:start position:0%
+it to stop doing that so I get to do but
+ 
+
+ align:start position:0%
+it to stop doing that so I get to do but
+if I excited at twice the
+
+ align:start position:0%
+if I excited at twice the
+ 
+
+ align:start position:0%
+if I excited at twice the
+frequency and if I can do this there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go that turns out to be exactly twice
+
+ align:start position:0%
+go that turns out to be exactly twice
+ 
+
+ align:start position:0%
+go that turns out to be exactly twice
+the frequency of the first the mode
+
+ align:start position:0%
+the frequency of the first the mode
+ 
+
+ align:start position:0%
+the frequency of the first the mode
+shapes one full sine wave the mode
+
+ align:start position:0%
+shapes one full sine wave the mode
+ 
+
+ align:start position:0%
+shapes one full sine wave the mode
+shapes for a Tau string are s n pix over
+
+ align:start position:0%
+shapes for a Tau string are s n pix over
+ 
+
+ align:start position:0%
+shapes for a Tau string are s n pix over
+L but strings can do something else kind
+
+ align:start position:0%
+L but strings can do something else kind
+ 
+
+ align:start position:0%
+L but strings can do something else kind
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neat and that
+
+ align:start position:0%
+neat and that
+ 
+
+ align:start position:0%
+neat and that
+is if I hit this thing I wait till it
+
+ align:start position:0%
+is if I hit this thing I wait till it
+ 
+
+ align:start position:0%
+is if I hit this thing I wait till it
+calms down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here if I give this thing just a
+
+ align:start position:0%
+here if I give this thing just a
+ 
+
+ align:start position:0%
+here if I give this thing just a
+pulse what do you expect to
+
+ align:start position:0%
+pulse what do you expect to
+ 
+
+ align:start position:0%
+pulse what do you expect to
+see you going to see
+
+ align:start position:0%
+see you going to see
+ 
+
+ align:start position:0%
+see you going to see
+vibration tell me what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see what's that act what do you see
+
+ align:start position:0%
+see what's that act what do you see
+ 
+
+ align:start position:0%
+see what's that act what do you see
+happening something running back and
+
+ align:start position:0%
+happening something running back and
+ 
+
+ align:start position:0%
+happening something running back and
+forth right what you're seeing is wave
+
+ align:start position:0%
+forth right what you're seeing is wave
+ 
+
+ align:start position:0%
+forth right what you're seeing is wave
+propagation it's not really vibration
+
+ align:start position:0%
+propagation it's not really vibration
+ 
+
+ align:start position:0%
+propagation it's not really vibration
+vibration we see of its modes and
+
+ align:start position:0%
+vibration we see of its modes and
+ 
+
+ align:start position:0%
+vibration we see of its modes and
+standing waves and things like that
+
+ align:start position:0%
+standing waves and things like that
+ 
+
+ align:start position:0%
+standing waves and things like that
+right so the taught string behaves
+
+ align:start position:0%
+right so the taught string behaves
+ 
+
+ align:start position:0%
+right so the taught string behaves
+satisfies an equation of motion that's
+
+ align:start position:0%
+satisfies an equation of motion that's
+ 
+
+ align:start position:0%
+satisfies an equation of motion that's
+called the wave equation and we're going
+
+ align:start position:0%
+called the wave equation and we're going
+ 
+
+ align:start position:0%
+called the wave equation and we're going
+to talk about quite a bit about that
+
+ align:start position:0%
+to talk about quite a bit about that
+ 
+
+ align:start position:0%
+to talk about quite a bit about that
+this morning and the wave equation has
+
+ align:start position:0%
+this morning and the wave equation has
+ 
+
+ align:start position:0%
+this morning and the wave equation has
+has this name give something away the
+
+ align:start position:0%
+has this name give something away the
+ 
+
+ align:start position:0%
+has this name give something away the
+wave equation describes continuous
+
+ align:start position:0%
+wave equation describes continuous
+ 
+
+ align:start position:0%
+wave equation describes continuous
+systems of a particular kind that
+
+ align:start position:0%
+systems of a particular kind that
+ 
+
+ align:start position:0%
+systems of a particular kind that
+support traveling waves and so the
+
+ align:start position:0%
+support traveling waves and so the
+ 
+
+ align:start position:0%
+support traveling waves and so the
+string will both support I can give it a
+
+ align:start position:0%
+string will both support I can give it a
+ 
+
+ align:start position:0%
+string will both support I can give it a
+little pluck I'll try to just place it
+
+ align:start position:0%
+little pluck I'll try to just place it
+ 
+
+ align:start position:0%
+little pluck I'll try to just place it
+in a particular shape and let go there
+
+ align:start position:0%
+in a particular shape and let go there
+ 
+
+ align:start position:0%
+in a particular shape and let go there
+it is and that little pluck just goes
+
+ align:start position:0%
+it is and that little pluck just goes
+ 
+
+ align:start position:0%
+it is and that little pluck just goes
+back and forth and back and forth at a
+
+ align:start position:0%
+back and forth and back and forth at a
+ 
+
+ align:start position:0%
+back and forth and back and forth at a
+particular speed so is there a
+
+ align:start position:0%
+particular speed so is there a
+ 
+
+ align:start position:0%
+particular speed so is there a
+relationship between the speed at which
+
+ align:start position:0%
+relationship between the speed at which
+ 
+
+ align:start position:0%
+relationship between the speed at which
+things can travel in a string and the
+
+ align:start position:0%
+things can travel in a string and the
+ 
+
+ align:start position:0%
+things can travel in a string and the
+natural frequencies of a
+
+ align:start position:0%
+natural frequencies of a
+ 
+
+ align:start position:0%
+natural frequencies of a
+string we'll we'll get into that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+and I'm going
+
+ align:start position:0%
+and I'm going
+ 
+
+ align:start position:0%
+and I'm going
+to start by just showing you a little
+
+ align:start position:0%
+to start by just showing you a little
+ 
+
+ align:start position:0%
+to start by just showing you a little
+something that comes from my
+
+ align:start position:0%
+something that comes from my
+ 
+
+ align:start position:0%
+something that comes from my
+research and let's
+
+ align:start position:0%
+research and let's
+ 
+
+ align:start position:0%
+research and let's
+see let me do this I think this will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work can you hear that now what what's
+
+ align:start position:0%
+work can you hear that now what what's
+ 
+
+ align:start position:0%
+work can you hear that now what what's
+the as I go slower does frequency go up
+
+ align:start position:0%
+the as I go slower does frequency go up
+ 
+
+ align:start position:0%
+the as I go slower does frequency go up
+or down
+
+ align:start position:0%
+or down
+ 
+
+ align:start position:0%
+or down
+so that's kind of slow and I'm going to
+
+ align:start position:0%
+so that's kind of slow and I'm going to
+ 
+
+ align:start position:0%
+so that's kind of slow and I'm going to
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up all right goes up as the speed goes
+
+ align:start position:0%
+up all right goes up as the speed goes
+ 
+
+ align:start position:0%
+up all right goes up as the speed goes
+up so that's results of a phenomenon
+
+ align:start position:0%
+up so that's results of a phenomenon
+ 
+
+ align:start position:0%
+up so that's results of a phenomenon
+called flow induced
+
+ align:start position:0%
+called flow induced
+ 
+
+ align:start position:0%
+called flow induced
+vibration and if you have I'll give you
+
+ align:start position:0%
+vibration and if you have I'll give you
+ 
+
+ align:start position:0%
+vibration and if you have I'll give you
+a little very uh brief intro to flow
+
+ align:start position:0%
+a little very uh brief intro to flow
+ 
+
+ align:start position:0%
+a little very uh brief intro to flow
+induce vibration you have a cylinder
+
+ align:start position:0%
+induce vibration you have a cylinder
+ 
+
+ align:start position:0%
+induce vibration you have a cylinder
+sitting still flow coming by it water or
+
+ align:start position:0%
+sitting still flow coming by it water or
+ 
+
+ align:start position:0%
+sitting still flow coming by it water or
+air and it's let's see the cylinder is
+
+ align:start position:0%
+air and it's let's see the cylinder is
+ 
+
+ align:start position:0%
+air and it's let's see the cylinder is
+diameter
+
+ align:start position:0%
+diameter
+ 
+
+ align:start position:0%
+diameter
+D velocity U for the flow what happens
+
+ align:start position:0%
+D velocity U for the flow what happens
+ 
+
+ align:start position:0%
+D velocity U for the flow what happens
+be in the wake of that cylinder vortices
+
+ align:start position:0%
+be in the wake of that cylinder vortices
+ 
+
+ align:start position:0%
+be in the wake of that cylinder vortices
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+formed it's just like if you're paddling
+
+ align:start position:0%
+formed it's just like if you're paddling
+ 
+
+ align:start position:0%
+formed it's just like if you're paddling
+a canoe or something and stick paddle in
+
+ align:start position:0%
+a canoe or something and stick paddle in
+ 
+
+ align:start position:0%
+a canoe or something and stick paddle in
+the water you'll see vortices Shed off
+
+ align:start position:0%
+the water you'll see vortices Shed off
+ 
+
+ align:start position:0%
+the water you'll see vortices Shed off
+the side and if you first you get one
+
+ align:start position:0%
+the side and if you first you get one
+ 
+
+ align:start position:0%
+the side and if you first you get one
+that's positive and then one that's
+
+ align:start position:0%
+that's positive and then one that's
+ 
+
+ align:start position:0%
+that's positive and then one that's
+negative and so one full cycle of this
+
+ align:start position:0%
+negative and so one full cycle of this
+ 
+
+ align:start position:0%
+negative and so one full cycle of this
+is from here to here so that's there's a
+
+ align:start position:0%
+is from here to here so that's there's a
+ 
+
+ align:start position:0%
+is from here to here so that's there's a
+frequency to this shedding and the
+
+ align:start position:0%
+frequency to this shedding and the
+ 
+
+ align:start position:0%
+frequency to this shedding and the
+shedding frequency Fs in
+
+ align:start position:0%
+shedding frequency Fs in
+ 
+
+ align:start position:0%
+shedding frequency Fs in
+hertz can be predicted by a simple
+
+ align:start position:0%
+hertz can be predicted by a simple
+ 
+
+ align:start position:0%
+hertz can be predicted by a simple
+dimensionless parameter called the strw
+
+ align:start position:0%
+dimensionless parameter called the strw
+ 
+
+ align:start position:0%
+dimensionless parameter called the strw
+hul number St over D and that's
+
+ align:start position:0%
+hul number St over D and that's
+ 
+
+ align:start position:0%
+hul number St over D and that's
+approximately 2 U over D for stationary
+
+ align:start position:0%
+approximately 2 U over D for stationary
+ 
+
+ align:start position:0%
+approximately 2 U over D for stationary
+cylinders You can predict the frequency
+
+ align:start position:0%
+cylinders You can predict the frequency
+ 
+
+ align:start position:0%
+cylinders You can predict the frequency
+at which these vortices are shed now
+
+ align:start position:0%
+at which these vortices are shed now
+ 
+
+ align:start position:0%
+at which these vortices are shed now
+associated with the shedding of tices is
+
+ align:start position:0%
+associated with the shedding of tices is
+ 
+
+ align:start position:0%
+associated with the shedding of tices is
+a lift force and I'll call it as some FL
+
+ align:start position:0%
+a lift force and I'll call it as some FL
+ 
+
+ align:start position:0%
+a lift force and I'll call it as some FL
+L Co
+
+ align:start position:0%
+L Co
+ 
+
+ align:start position:0%
+L Co
+coine Omega T which is 2 pi FS * T So
+
+ align:start position:0%
+coine Omega T which is 2 pi FS * T So
+ 
+
+ align:start position:0%
+coine Omega T which is 2 pi FS * T So
+this at this frequency of Vortex
+
+ align:start position:0%
+this at this frequency of Vortex
+ 
+
+ align:start position:0%
+this at this frequency of Vortex
+shedding there is a transverse Force
+
+ align:start position:0%
+shedding there is a transverse Force
+ 
+
+ align:start position:0%
+shedding there is a transverse Force
+there's actually an inline Force also
+
+ align:start position:0%
+there's actually an inline Force also
+ 
+
+ align:start position:0%
+there's actually an inline Force also
+which I'll call FD for drag and it goes
+
+ align:start position:0%
+which I'll call FD for drag and it goes
+ 
+
+ align:start position:0%
+which I'll call FD for drag and it goes
+like cine 2 Omega s * T it's twice the
+
+ align:start position:0%
+like cine 2 Omega s * T it's twice the
+ 
+
+ align:start position:0%
+like cine 2 Omega s * T it's twice the
+frequency of that and so you get some
+
+ align:start position:0%
+frequency of that and so you get some
+ 
+
+ align:start position:0%
+frequency of that and so you get some
+inline oscillatory excitation and what
+
+ align:start position:0%
+inline oscillatory excitation and what
+ 
+
+ align:start position:0%
+inline oscillatory excitation and what
+we call cross flow oscillatory
+
+ align:start position:0%
+we call cross flow oscillatory
+ 
+
+ align:start position:0%
+we call cross flow oscillatory
+excitation and this is the this is the
+
+ align:start position:0%
+excitation and this is the this is the
+ 
+
+ align:start position:0%
+excitation and this is the this is the
+uh cause of lots of things that we the
+
+ align:start position:0%
+uh cause of lots of things that we the
+ 
+
+ align:start position:0%
+uh cause of lots of things that we the
+people who work on it call Flow induced
+
+ align:start position:0%
+people who work on it call Flow induced
+ 
+
+ align:start position:0%
+people who work on it call Flow induced
+vibration now an amazing thing
+
+ align:start position:0%
+vibration now an amazing thing
+ 
+
+ align:start position:0%
+vibration now an amazing thing
+happens is if this cylinder is
+
+ align:start position:0%
+happens is if this cylinder is
+ 
+
+ align:start position:0%
+happens is if this cylinder is
+elastically mounted or is
+
+ align:start position:0%
+elastically mounted or is
+ 
+
+ align:start position:0%
+elastically mounted or is
+flexible and that Force starts to act on
+
+ align:start position:0%
+flexible and that Force starts to act on
+ 
+
+ align:start position:0%
+flexible and that Force starts to act on
+it it will begin to
+
+ align:start position:0%
+it it will begin to
+ 
+
+ align:start position:0%
+it it will begin to
+vibrate and the amazing thing is it
+
+ align:start position:0%
+vibrate and the amazing thing is it
+ 
+
+ align:start position:0%
+vibrate and the amazing thing is it
+begins to vibrate it
+
+ align:start position:0%
+begins to vibrate it
+ 
+
+ align:start position:0%
+begins to vibrate it
+correlates the shedding of these
+
+ align:start position:0%
+correlates the shedding of these
+ 
+
+ align:start position:0%
+correlates the shedding of these
+vortices all along the cylinder so it's
+
+ align:start position:0%
+vortices all along the cylinder so it's
+ 
+
+ align:start position:0%
+vortices all along the cylinder so it's
+like soldiers Marching In Step going
+
+ align:start position:0%
+like soldiers Marching In Step going
+ 
+
+ align:start position:0%
+like soldiers Marching In Step going
+across the bridge and you if everybody's
+
+ align:start position:0%
+across the bridge and you if everybody's
+ 
+
+ align:start position:0%
+across the bridge and you if everybody's
+walking randomly then the bridge doesn't
+
+ align:start position:0%
+walking randomly then the bridge doesn't
+ 
+
+ align:start position:0%
+walking randomly then the bridge doesn't
+respond too much but if everybody
+
+ align:start position:0%
+respond too much but if everybody
+ 
+
+ align:start position:0%
+respond too much but if everybody
+marches together you can put a pretty
+
+ align:start position:0%
+marches together you can put a pretty
+ 
+
+ align:start position:0%
+marches together you can put a pretty
+good excitation into it well the motion
+
+ align:start position:0%
+good excitation into it well the motion
+ 
+
+ align:start position:0%
+good excitation into it well the motion
+of the cylinder itself organizes these
+
+ align:start position:0%
+of the cylinder itself organizes these
+ 
+
+ align:start position:0%
+of the cylinder itself organizes these
+Vortex shutting all along the cylinder
+
+ align:start position:0%
+Vortex shutting all along the cylinder
+ 
+
+ align:start position:0%
+Vortex shutting all along the cylinder
+so they're all Marching In step and that
+
+ align:start position:0%
+so they're all Marching In step and that
+ 
+
+ align:start position:0%
+so they're all Marching In step and that
+means the force is all correlated on the
+
+ align:start position:0%
+means the force is all correlated on the
+ 
+
+ align:start position:0%
+means the force is all correlated on the
+length and you can get some pretty
+
+ align:start position:0%
+length and you can get some pretty
+ 
+
+ align:start position:0%
+length and you can get some pretty
+substantial response so that's the
+
+ align:start position:0%
+substantial response so that's the
+ 
+
+ align:start position:0%
+substantial response so that's the
+subject called flow induced vibration
+
+ align:start position:0%
+subject called flow induced vibration
+ 
+
+ align:start position:0%
+subject called flow induced vibration
+and with that I going show you a few
+
+ align:start position:0%
+and with that I going show you a few
+ 
+
+ align:start position:0%
+and with that I going show you a few
+slides it'd be good if we let's dim the
+
+ align:start position:0%
+slides it'd be good if we let's dim the
+ 
+
+ align:start position:0%
+slides it'd be good if we let's dim the
+dim the lights a little bit if you
+
+ align:start position:0%
+dim the lights a little bit if you
+ 
+
+ align:start position:0%
+dim the lights a little bit if you
+could to see this there's some pictures
+
+ align:start position:0%
+could to see this there's some pictures
+ 
+
+ align:start position:0%
+could to see this there's some pictures
+I just want you to see better all right
+
+ align:start position:0%
+I just want you to see better all right
+ 
+
+ align:start position:0%
+I just want you to see better all right
+so I do flow induce vibration I've been
+
+ align:start position:0%
+so I do flow induce vibration I've been
+ 
+
+ align:start position:0%
+so I do flow induce vibration I've been
+doing this working on this for all my
+
+ align:start position:0%
+doing this working on this for all my
+ 
+
+ align:start position:0%
+doing this working on this for all my
+professional career and it's applied
+
+ align:start position:0%
+professional career and it's applied
+ 
+
+ align:start position:0%
+professional career and it's applied
+primarily to Big flexible cylinders in
+
+ align:start position:0%
+primarily to Big flexible cylinders in
+ 
+
+ align:start position:0%
+primarily to Big flexible cylinders in
+the particularly associated with the
+
+ align:start position:0%
+the particularly associated with the
+ 
+
+ align:start position:0%
+the particularly associated with the
+things the US Navy does long cables and
+
+ align:start position:0%
+things the US Navy does long cables and
+ 
+
+ align:start position:0%
+things the US Navy does long cables and
+things and also the offshore oil
+
+ align:start position:0%
+things and also the offshore oil
+ 
+
+ align:start position:0%
+things and also the offshore oil
+industry next slide can we dim the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lights can we dim the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lights I want you to be able to this is
+
+ align:start position:0%
+lights I want you to be able to this is
+ 
+
+ align:start position:0%
+lights I want you to be able to this is
+a tension leg platform it's one of the
+
+ align:start position:0%
+a tension leg platform it's one of the
+ 
+
+ align:start position:0%
+a tension leg platform it's one of the
+structures that's used in the offshore
+
+ align:start position:0%
+structures that's used in the offshore
+ 
+
+ align:start position:0%
+structures that's used in the offshore
+industry to produce oil and you it might
+
+ align:start position:0%
+industry to produce oil and you it might
+ 
+
+ align:start position:0%
+industry to produce oil and you it might
+might one of these might be mored in
+
+ align:start position:0%
+might one of these might be mored in
+ 
+
+ align:start position:0%
+might one of these might be mored in
+3,000 ft of water 1,000 M of water might
+
+ align:start position:0%
+3,000 ft of water 1,000 M of water might
+ 
+
+ align:start position:0%
+3,000 ft of water 1,000 M of water might
+weigh 20,000 tons and what's connecting
+
+ align:start position:0%
+weigh 20,000 tons and what's connecting
+ 
+
+ align:start position:0%
+weigh 20,000 tons and what's connecting
+it what holds it in place are steel
+
+ align:start position:0%
+it what holds it in place are steel
+ 
+
+ align:start position:0%
+it what holds it in place are steel
+cylinders a half a meter in diameter
+
+ align:start position:0%
+cylinders a half a meter in diameter
+ 
+
+ align:start position:0%
+cylinders a half a meter in diameter
+3,000 ft long going vertically down from
+
+ align:start position:0%
+3,000 ft long going vertically down from
+ 
+
+ align:start position:0%
+3,000 ft long going vertically down from
+each of those three pontoon legs
+
+ align:start position:0%
+each of those three pontoon legs
+ 
+
+ align:start position:0%
+each of those three pontoon legs
+sticking out and they're under a lot of
+
+ align:start position:0%
+sticking out and they're under a lot of
+ 
+
+ align:start position:0%
+sticking out and they're under a lot of
+tension and and in fact it pulls the
+
+ align:start position:0%
+tension and and in fact it pulls the
+ 
+
+ align:start position:0%
+tension and and in fact it pulls the
+thing down into the water so there's ex
+
+ align:start position:0%
+thing down into the water so there's ex
+ 
+
+ align:start position:0%
+thing down into the water so there's ex
+the the buoyancy of the whole thing puts
+
+ align:start position:0%
+the the buoyancy of the whole thing puts
+ 
+
+ align:start position:0%
+the the buoyancy of the whole thing puts
+tension on these cylinders but now what
+
+ align:start position:0%
+tension on these cylinders but now what
+ 
+
+ align:start position:0%
+tension on these cylinders but now what
+happens if an ocean current comes by
+
+ align:start position:0%
+happens if an ocean current comes by
+ 
+
+ align:start position:0%
+happens if an ocean current comes by
+those cylinders Vortex shedding and the
+
+ align:start position:0%
+those cylinders Vortex shedding and the
+ 
+
+ align:start position:0%
+those cylinders Vortex shedding and the
+cylinders vibrate and if they vibrate
+
+ align:start position:0%
+cylinders vibrate and if they vibrate
+ 
+
+ align:start position:0%
+cylinders vibrate and if they vibrate
+over time they will fatigue and fail
+
+ align:start position:0%
+over time they will fatigue and fail
+ 
+
+ align:start position:0%
+over time they will fatigue and fail
+okay next slide there's a picture of a
+
+ align:start position:0%
+okay next slide there's a picture of a
+ 
+
+ align:start position:0%
+okay next slide there's a picture of a
+real one that's a bigger one called
+
+ align:start position:0%
+real one that's a bigger one called
+ 
+
+ align:start position:0%
+real one that's a bigger one called
+Marco Polo it's on a launch ship it'll
+
+ align:start position:0%
+Marco Polo it's on a launch ship it'll
+ 
+
+ align:start position:0%
+Marco Polo it's on a launch ship it'll
+take it out to the site that it is and
+
+ align:start position:0%
+take it out to the site that it is and
+ 
+
+ align:start position:0%
+take it out to the site that it is and
+then uh it'll be ship will lower and
+
+ align:start position:0%
+then uh it'll be ship will lower and
+ 
+
+ align:start position:0%
+then uh it'll be ship will lower and
+it'll slide off so these are Big next
+
+ align:start position:0%
+it'll slide off so these are Big next
+ 
+
+ align:start position:0%
+it'll slide off so these are Big next
+slide this a a diagram of the Gulf of
+
+ align:start position:0%
+slide this a a diagram of the Gulf of
+ 
+
+ align:start position:0%
+slide this a a diagram of the Gulf of
+Mexico South America is at the bottom
+
+ align:start position:0%
+Mexico South America is at the bottom
+ 
+
+ align:start position:0%
+Mexico South America is at the bottom
+Yucatan Peninsula is sticking up there
+
+ align:start position:0%
+Yucatan Peninsula is sticking up there
+ 
+
+ align:start position:0%
+Yucatan Peninsula is sticking up there
+right in the middle of the bottom this
+
+ align:start position:0%
+right in the middle of the bottom this
+ 
+
+ align:start position:0%
+right in the middle of the bottom this
+is a picture satellite imagery of
+
+ align:start position:0%
+is a picture satellite imagery of
+ 
+
+ align:start position:0%
+is a picture satellite imagery of
+currents in the Gulf of Mexico there's a
+
+ align:start position:0%
+currents in the Gulf of Mexico there's a
+ 
+
+ align:start position:0%
+currents in the Gulf of Mexico there's a
+current that flows up off of South
+
+ align:start position:0%
+current that flows up off of South
+ 
+
+ align:start position:0%
+current that flows up off of South
+America into the Gulf of Mexico goes
+
+ align:start position:0%
+America into the Gulf of Mexico goes
+ 
+
+ align:start position:0%
+America into the Gulf of Mexico goes
+around in a loop and then come out you
+
+ align:start position:0%
+around in a loop and then come out you
+ 
+
+ align:start position:0%
+around in a loop and then come out you
+can see Florida sticking down in there
+
+ align:start position:0%
+can see Florida sticking down in there
+ 
+
+ align:start position:0%
+can see Florida sticking down in there
+on the right that current comes out of
+
+ align:start position:0%
+on the right that current comes out of
+ 
+
+ align:start position:0%
+on the right that current comes out of
+the gulf goes around the tip of Florida
+
+ align:start position:0%
+the gulf goes around the tip of Florida
+ 
+
+ align:start position:0%
+the gulf goes around the tip of Florida
+and goes up the Atlantic coast and is
+
+ align:start position:0%
+and goes up the Atlantic coast and is
+ 
+
+ align:start position:0%
+and goes up the Atlantic coast and is
+known as the Gulf
+
+ align:start position:0%
+known as the Gulf
+ 
+
+ align:start position:0%
+known as the Gulf
+Stream but it starts as a big current
+
+ align:start position:0%
+Stream but it starts as a big current
+ 
+
+ align:start position:0%
+Stream but it starts as a big current
+that comes into the Gulf of Mexico and
+
+ align:start position:0%
+that comes into the Gulf of Mexico and
+ 
+
+ align:start position:0%
+that comes into the Gulf of Mexico and
+every now and then that current pinches
+
+ align:start position:0%
+every now and then that current pinches
+ 
+
+ align:start position:0%
+every now and then that current pinches
+off an Eddy and that's what that red
+
+ align:start position:0%
+off an Eddy and that's what that red
+ 
+
+ align:start position:0%
+off an Eddy and that's what that red
+circle is in the middle and it's an Eddy
+
+ align:start position:0%
+circle is in the middle and it's an Eddy
+ 
+
+ align:start position:0%
+circle is in the middle and it's an Eddy
+that's many many kilometers in diameter
+
+ align:start position:0%
+that's many many kilometers in diameter
+ 
+
+ align:start position:0%
+that's many many kilometers in diameter
+with surface currents on the order of a
+
+ align:start position:0%
+with surface currents on the order of a
+ 
+
+ align:start position:0%
+with surface currents on the order of a
+meter per second or more and those are
+
+ align:start position:0%
+meter per second or more and those are
+ 
+
+ align:start position:0%
+meter per second or more and those are
+the most the biggest threat to for to in
+
+ align:start position:0%
+the most the biggest threat to for to in
+ 
+
+ align:start position:0%
+the most the biggest threat to for to in
+for causing flow induc vibration
+
+ align:start position:0%
+for causing flow induc vibration
+ 
+
+ align:start position:0%
+for causing flow induc vibration
+failures of long members from uh hanging
+
+ align:start position:0%
+failures of long members from uh hanging
+ 
+
+ align:start position:0%
+failures of long members from uh hanging
+off of offshore structures next so I've
+
+ align:start position:0%
+off of offshore structures next so I've
+ 
+
+ align:start position:0%
+off of offshore structures next so I've
+been doing research in this area for a
+
+ align:start position:0%
+been doing research in this area for a
+ 
+
+ align:start position:0%
+been doing research in this area for a
+long time this is a picture taken in the
+
+ align:start position:0%
+long time this is a picture taken in the
+ 
+
+ align:start position:0%
+long time this is a picture taken in the
+summer of
+
+ align:start position:0%
+summer of
+ 
+
+ align:start position:0%
+summer of
+1981 it is a piece of steel pipe about 2
+
+ align:start position:0%
+1981 it is a piece of steel pipe about 2
+ 
+
+ align:start position:0%
+1981 it is a piece of steel pipe about 2
+in in diameter and 75 ft long it's under
+
+ align:start position:0%
+in in diameter and 75 ft long it's under
+ 
+
+ align:start position:0%
+in in diameter and 75 ft long it's under
+750 pounds of tension and it's pinned at
+
+ align:start position:0%
+750 pounds of tension and it's pinned at
+ 
+
+ align:start position:0%
+750 pounds of tension and it's pinned at
+each end it is it behaves almost exactly
+
+ align:start position:0%
+each end it is it behaves almost exactly
+ 
+
+ align:start position:0%
+each end it is it behaves almost exactly
+like my rubber cord here has natural
+
+ align:start position:0%
+like my rubber cord here has natural
+ 
+
+ align:start position:0%
+like my rubber cord here has natural
+frequencies and it will vibrate if a
+
+ align:start position:0%
+frequencies and it will vibrate if a
+ 
+
+ align:start position:0%
+frequencies and it will vibrate if a
+current comes by it so this is actually
+
+ align:start position:0%
+current comes by it so this is actually
+ 
+
+ align:start position:0%
+current comes by it so this is actually
+a sandb bar and low tide we do all the
+
+ align:start position:0%
+a sandb bar and low tide we do all the
+ 
+
+ align:start position:0%
+a sandb bar and low tide we do all the
+work putting it up then as tide comes in
+
+ align:start position:0%
+work putting it up then as tide comes in
+ 
+
+ align:start position:0%
+work putting it up then as tide comes in
+the flow is perpendicular to the
+
+ align:start position:0%
+the flow is perpendicular to the
+ 
+
+ align:start position:0%
+the flow is perpendicular to the
+cylinder and vort vortices be start
+
+ align:start position:0%
+cylinder and vort vortices be start
+ 
+
+ align:start position:0%
+cylinder and vort vortices be start
+shedding and as the pipe begins to move
+
+ align:start position:0%
+shedding and as the pipe begins to move
+ 
+
+ align:start position:0%
+shedding and as the pipe begins to move
+they get organized all along the length
+
+ align:start position:0%
+they get organized all along the length
+ 
+
+ align:start position:0%
+they get organized all along the length
+and a typical response mode was when the
+
+ align:start position:0%
+and a typical response mode was when the
+ 
+
+ align:start position:0%
+and a typical response mode was when the
+vortex shedding frequency therefore the
+
+ align:start position:0%
+vortex shedding frequency therefore the
+ 
+
+ align:start position:0%
+vortex shedding frequency therefore the
+lift Force frequency coincided with the
+
+ align:start position:0%
+lift Force frequency coincided with the
+ 
+
+ align:start position:0%
+lift Force frequency coincided with the
+natural frequency then you'd expect it
+
+ align:start position:0%
+natural frequency then you'd expect it
+ 
+
+ align:start position:0%
+natural frequency then you'd expect it
+to give quite a bit of response the
+
+ align:start position:0%
+to give quite a bit of response the
+ 
+
+ align:start position:0%
+to give quite a bit of response the
+diagram on the left is if if you cut the
+
+ align:start position:0%
+diagram on the left is if if you cut the
+ 
+
+ align:start position:0%
+diagram on the left is if if you cut the
+cylinder and look down its axis this is
+
+ align:start position:0%
+cylinder and look down its axis this is
+ 
+
+ align:start position:0%
+cylinder and look down its axis this is
+the trajectory that you'd see the
+
+ align:start position:0%
+the trajectory that you'd see the
+ 
+
+ align:start position:0%
+the trajectory that you'd see the
+cylinder make it would sit there and
+
+ align:start position:0%
+cylinder make it would sit there and
+ 
+
+ align:start position:0%
+cylinder make it would sit there and
+just make big figure rates so up and
+
+ align:start position:0%
+just make big figure rates so up and
+ 
+
+ align:start position:0%
+just make big figure rates so up and
+down vertical is its vertical motion
+
+ align:start position:0%
+down vertical is its vertical motion
+ 
+
+ align:start position:0%
+down vertical is its vertical motion
+flows coming from say left to right
+
+ align:start position:0%
+flows coming from say left to right
+ 
+
+ align:start position:0%
+flows coming from say left to right
+vertical motion is up and down inline
+
+ align:start position:0%
+vertical motion is up and down inline
+ 
+
+ align:start position:0%
+vertical motion is up and down inline
+Motions like this and they are in
+
+ align:start position:0%
+Motions like this and they are in
+ 
+
+ align:start position:0%
+Motions like this and they are in
+exactly such a phase it just makes big
+
+ align:start position:0%
+exactly such a phase it just makes big
+ 
+
+ align:start position:0%
+exactly such a phase it just makes big
+beautiful figure rates that's the kind
+
+ align:start position:0%
+beautiful figure rates that's the kind
+ 
+
+ align:start position:0%
+beautiful figure rates that's the kind
+of motion you'd see okay so then um so
+
+ align:start position:0%
+of motion you'd see okay so then um so
+ 
+
+ align:start position:0%
+of motion you'd see okay so then um so
+very much what I was talking about a
+
+ align:start position:0%
+very much what I was talking about a
+ 
+
+ align:start position:0%
+very much what I was talking about a
+minute ago very much Behavior dominated
+
+ align:start position:0%
+minute ago very much Behavior dominated
+ 
+
+ align:start position:0%
+minute ago very much Behavior dominated
+by vibration vibration in the third mode
+
+ align:start position:0%
+by vibration vibration in the third mode
+ 
+
+ align:start position:0%
+by vibration vibration in the third mode
+cross flow was a typical one in fifth
+
+ align:start position:0%
+cross flow was a typical one in fifth
+ 
+
+ align:start position:0%
+cross flow was a typical one in fifth
+mode in line was typ difficult but
+
+ align:start position:0%
+mode in line was typ difficult but
+ 
+
+ align:start position:0%
+mode in line was typ difficult but
+that's a as cylinders go in the ocean
+
+ align:start position:0%
+that's a as cylinders go in the ocean
+ 
+
+ align:start position:0%
+that's a as cylinders go in the ocean
+that was kind of short third mode
+
+ align:start position:0%
+that was kind of short third mode
+ 
+
+ align:start position:0%
+that was kind of short third mode
+vibration is sort of
+
+ align:start position:0%
+vibration is sort of
+ 
+
+ align:start position:0%
+vibration is sort of
+low so as years have gone by and oil is
+
+ align:start position:0%
+low so as years have gone by and oil is
+ 
+
+ align:start position:0%
+low so as years have gone by and oil is
+being produced and deeper and deeper and
+
+ align:start position:0%
+being produced and deeper and deeper and
+ 
+
+ align:start position:0%
+being produced and deeper and deeper and
+deeper water the cylinders were putting
+
+ align:start position:0%
+deeper water the cylinders were putting
+ 
+
+ align:start position:0%
+deeper water the cylinders were putting
+out there get longer and longer and
+
+ align:start position:0%
+out there get longer and longer and
+ 
+
+ align:start position:0%
+out there get longer and longer and
+longer and longer and the modes that are
+
+ align:start position:0%
+longer and longer and the modes that are
+ 
+
+ align:start position:0%
+longer and longer and the modes that are
+excited by currents coming by get quite
+
+ align:start position:0%
+excited by currents coming by get quite
+ 
+
+ align:start position:0%
+excited by currents coming by get quite
+high so this is an experiment we did it
+
+ align:start position:0%
+high so this is an experiment we did it
+ 
+
+ align:start position:0%
+high so this is an experiment we did it
+was roughly a one10 scale model model is
+
+ align:start position:0%
+was roughly a one10 scale model model is
+ 
+
+ align:start position:0%
+was roughly a one10 scale model model is
+almost 2 Ines in diameter 500 ft long
+
+ align:start position:0%
+almost 2 Ines in diameter 500 ft long
+ 
+
+ align:start position:0%
+almost 2 Ines in diameter 500 ft long
+scale that up by factor of 10 you're up
+
+ align:start position:0%
+scale that up by factor of 10 you're up
+ 
+
+ align:start position:0%
+scale that up by factor of 10 you're up
+around 20 in in diameter and 5,000 ft
+
+ align:start position:0%
+around 20 in in diameter and 5,000 ft
+ 
+
+ align:start position:0%
+around 20 in in diameter and 5,000 ft
+long which is exactly the size of the
+
+ align:start position:0%
+long which is exactly the size of the
+ 
+
+ align:start position:0%
+long which is exactly the size of the
+drilling Riser that BP had hung off the
+
+ align:start position:0%
+drilling Riser that BP had hung off the
+ 
+
+ align:start position:0%
+drilling Riser that BP had hung off the
+drilling ship when the blowout occurred
+
+ align:start position:0%
+drilling ship when the blowout occurred
+ 
+
+ align:start position:0%
+drilling ship when the blowout occurred
+it's a piece of steel pipe 21 in in
+
+ align:start position:0%
+it's a piece of steel pipe 21 in in
+ 
+
+ align:start position:0%
+it's a piece of steel pipe 21 in in
+diameter 3/4 of an inch wall thickness
+
+ align:start position:0%
+diameter 3/4 of an inch wall thickness
+ 
+
+ align:start position:0%
+diameter 3/4 of an inch wall thickness
+5,000 ft long under a lot of tension and
+
+ align:start position:0%
+5,000 ft long under a lot of tension and
+ 
+
+ align:start position:0%
+5,000 ft long under a lot of tension and
+it when ocean currents come by it
+
+ align:start position:0%
+it when ocean currents come by it
+ 
+
+ align:start position:0%
+it when ocean currents come by it
+behaves just like this string okay and
+
+ align:start position:0%
+behaves just like this string okay and
+ 
+
+ align:start position:0%
+behaves just like this string okay and
+so we out this is a one10 scale model so
+
+ align:start position:0%
+so we out this is a one10 scale model so
+ 
+
+ align:start position:0%
+so we out this is a one10 scale model so
+we put a big weight on the bottom of a
+
+ align:start position:0%
+we put a big weight on the bottom of a
+ 
+
+ align:start position:0%
+we put a big weight on the bottom of a
+cylinder put it behind a boat and towed
+
+ align:start position:0%
+cylinder put it behind a boat and towed
+ 
+
+ align:start position:0%
+cylinder put it behind a boat and towed
+it in the Gulf Stream next
+
+ align:start position:0%
+it in the Gulf Stream next
+ 
+
+ align:start position:0%
+it in the Gulf Stream next
+picture so there's the boat it's an
+
+ align:start position:0%
+picture so there's the boat it's an
+ 
+
+ align:start position:0%
+picture so there's the boat it's an
+oceanographic vessel it's actually
+
+ align:start position:0%
+oceanographic vessel it's actually
+ 
+
+ align:start position:0%
+oceanographic vessel it's actually
+catamaran next this is a spool that had
+
+ align:start position:0%
+catamaran next this is a spool that had
+ 
+
+ align:start position:0%
+catamaran next this is a spool that had
+our test cylinder on it could lower that
+
+ align:start position:0%
+our test cylinder on it could lower that
+ 
+
+ align:start position:0%
+our test cylinder on it could lower that
+there's a reddish object down in the
+
+ align:start position:0%
+there's a reddish object down in the
+ 
+
+ align:start position:0%
+there's a reddish object down in the
+bottom which is where's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the that's a 750 pounds piece of
+
+ align:start position:0%
+the that's a 750 pounds piece of
+ 
+
+ align:start position:0%
+the that's a 750 pounds piece of
+railroad wheel and it's the weight on
+
+ align:start position:0%
+railroad wheel and it's the weight on
+ 
+
+ align:start position:0%
+railroad wheel and it's the weight on
+the bottom and so you'd spool this thing
+
+ align:start position:0%
+the bottom and so you'd spool this thing
+ 
+
+ align:start position:0%
+the bottom and so you'd spool this thing
+off lower it down and then do your test
+
+ align:start position:0%
+off lower it down and then do your test
+ 
+
+ align:start position:0%
+off lower it down and then do your test
+Next Top we measured tension
+
+ align:start position:0%
+Next Top we measured tension
+ 
+
+ align:start position:0%
+Next Top we measured tension
+inclination um and
+
+ align:start position:0%
+inclination um and
+ 
+
+ align:start position:0%
+inclination um and
+then it also had a it's a pin joint at
+
+ align:start position:0%
+then it also had a it's a pin joint at
+ 
+
+ align:start position:0%
+then it also had a it's a pin joint at
+the top so it would vibrate freely
+
+ align:start position:0%
+the top so it would vibrate freely
+ 
+
+ align:start position:0%
+the top so it would vibrate freely
+inside though were was fiber optics
+
+ align:start position:0%
+inside though were was fiber optics
+ 
+
+ align:start position:0%
+inside though were was fiber optics
+next we had eight Optical fibers and in
+
+ align:start position:0%
+next we had eight Optical fibers and in
+ 
+
+ align:start position:0%
+next we had eight Optical fibers and in
+those Optical fibers were what we call
+
+ align:start position:0%
+those Optical fibers were what we call
+ 
+
+ align:start position:0%
+those Optical fibers were what we call
+Optical strain gauges so we had 280
+
+ align:start position:0%
+Optical strain gauges so we had 280
+ 
+
+ align:start position:0%
+Optical strain gauges so we had 280
+Optical strain gauges instrumented up
+
+ align:start position:0%
+Optical strain gauges instrumented up
+ 
+
+ align:start position:0%
+Optical strain gauges instrumented up
+and down that pipe so we could measure
+
+ align:start position:0%
+and down that pipe so we could measure
+ 
+
+ align:start position:0%
+and down that pipe so we could measure
+its vibration and so you're looking at a
+
+ align:start position:0%
+its vibration and so you're looking at a
+ 
+
+ align:start position:0%
+its vibration and so you're looking at a
+cross-section of the pipe there were two
+
+ align:start position:0%
+cross-section of the pipe there were two
+ 
+
+ align:start position:0%
+cross-section of the pipe there were two
+Optical fibers in each quadrant and each
+
+ align:start position:0%
+Optical fibers in each quadrant and each
+ 
+
+ align:start position:0%
+Optical fibers in each quadrant and each
+one of those fibers had uh 35 sensors on
+
+ align:start position:0%
+one of those fibers had uh 35 sensors on
+ 
+
+ align:start position:0%
+one of those fibers had uh 35 sensors on
+it next so this is typical uh
+
+ align:start position:0%
+it next so this is typical uh
+ 
+
+ align:start position:0%
+it next so this is typical uh
+experimental case this is the surface
+
+ align:start position:0%
+experimental case this is the surface
+ 
+
+ align:start position:0%
+experimental case this is the surface
+this is 500 ft down this is the current
+
+ align:start position:0%
+this is 500 ft down this is the current
+ 
+
+ align:start position:0%
+this is 500 ft down this is the current
+profile so the flow velocity is about 2
+
+ align:start position:0%
+profile so the flow velocity is about 2
+ 
+
+ align:start position:0%
+profile so the flow velocity is about 2
+feet per second near the surface up to 4
+
+ align:start position:0%
+feet per second near the surface up to 4
+ 
+
+ align:start position:0%
+feet per second near the surface up to 4
+feet per second down on the bottom and
+
+ align:start position:0%
+feet per second down on the bottom and
+ 
+
+ align:start position:0%
+feet per second down on the bottom and
+this is the region where most of the
+
+ align:start position:0%
+this is the region where most of the
+ 
+
+ align:start position:0%
+this is the region where most of the
+excitation was coming from that would
+
+ align:start position:0%
+excitation was coming from that would
+ 
+
+ align:start position:0%
+excitation was coming from that would
+drive the flow induced vibration this is
+
+ align:start position:0%
+drive the flow induced vibration this is
+ 
+
+ align:start position:0%
+drive the flow induced vibration this is
+measured RMS strain caused to by the
+
+ align:start position:0%
+measured RMS strain caused to by the
+ 
+
+ align:start position:0%
+measured RMS strain caused to by the
+bending vibration of in the cylinder it
+
+ align:start position:0%
+bending vibration of in the cylinder it
+ 
+
+ align:start position:0%
+bending vibration of in the cylinder it
+Peak up about the maximum strain is
+
+ align:start position:0%
+Peak up about the maximum strain is
+ 
+
+ align:start position:0%
+Peak up about the maximum strain is
+about right there next typical response
+
+ align:start position:0%
+about right there next typical response
+ 
+
+ align:start position:0%
+about right there next typical response
+Spectrum basically the frequency content
+
+ align:start position:0%
+Spectrum basically the frequency content
+ 
+
+ align:start position:0%
+Spectrum basically the frequency content
+at three different locations down deep
+
+ align:start position:0%
+at three different locations down deep
+ 
+
+ align:start position:0%
+at three different locations down deep
+in the middle near the top this is
+
+ align:start position:0%
+in the middle near the top this is
+ 
+
+ align:start position:0%
+in the middle near the top this is
+frequency so this would be the peak that
+
+ align:start position:0%
+frequency so this would be the peak that
+ 
+
+ align:start position:0%
+frequency so this would be the peak that
+describes the principal cross flow
+
+ align:start position:0%
+describes the principal cross flow
+ 
+
+ align:start position:0%
+describes the principal cross flow
+vibration at the vortex shedding
+
+ align:start position:0%
+vibration at the vortex shedding
+ 
+
+ align:start position:0%
+vibration at the vortex shedding
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+next this pipe this is position bottom
+
+ align:start position:0%
+next this pipe this is position bottom
+ 
+
+ align:start position:0%
+next this pipe this is position bottom
+to top this is time and these are strain
+
+ align:start position:0%
+to top this is time and these are strain
+ 
+
+ align:start position:0%
+to top this is time and these are strain
+records from all all of those strain
+
+ align:start position:0%
+records from all all of those strain
+ 
+
+ align:start position:0%
+records from all all of those strain
+sensors there's a strain sensor about
+
+ align:start position:0%
+sensors there's a strain sensor about
+ 
+
+ align:start position:0%
+sensors there's a strain sensor about
+every uh 2 m along here but what you're
+
+ align:start position:0%
+every uh 2 m along here but what you're
+ 
+
+ align:start position:0%
+every uh 2 m along here but what you're
+seeing is this is evidence these red the
+
+ align:start position:0%
+seeing is this is evidence these red the
+ 
+
+ align:start position:0%
+seeing is this is evidence these red the
+red is the amplitude and red let's say
+
+ align:start position:0%
+red is the amplitude and red let's say
+ 
+
+ align:start position:0%
+red is the amplitude and red let's say
+red is positive strain and blue is
+
+ align:start position:0%
+red is positive strain and blue is
+ 
+
+ align:start position:0%
+red is positive strain and blue is
+negative strain and so at any location
+
+ align:start position:0%
+negative strain and so at any location
+ 
+
+ align:start position:0%
+negative strain and so at any location
+on the pipe where it's vibrating it's
+
+ align:start position:0%
+on the pipe where it's vibrating it's
+ 
+
+ align:start position:0%
+on the pipe where it's vibrating it's
+going to go from red to blue red to blue
+
+ align:start position:0%
+going to go from red to blue red to blue
+ 
+
+ align:start position:0%
+going to go from red to blue red to blue
+red to blue and but it's showing you
+
+ align:start position:0%
+red to blue and but it's showing you
+ 
+
+ align:start position:0%
+red to blue and but it's showing you
+that they're highly correlated all along
+
+ align:start position:0%
+that they're highly correlated all along
+ 
+
+ align:start position:0%
+that they're highly correlated all along
+the length that there's a red streak all
+
+ align:start position:0%
+the length that there's a red streak all
+ 
+
+ align:start position:0%
+the length that there's a red streak all
+lined up but it's not parallel to the
+
+ align:start position:0%
+lined up but it's not parallel to the
+ 
+
+ align:start position:0%
+lined up but it's not parallel to the
+pipe it's inclined this is showing you
+
+ align:start position:0%
+pipe it's inclined this is showing you
+ 
+
+ align:start position:0%
+pipe it's inclined this is showing you
+wave propagation the behavior of the
+
+ align:start position:0%
+wave propagation the behavior of the
+ 
+
+ align:start position:0%
+wave propagation the behavior of the
+pipe was completely dominated by wave
+
+ align:start position:0%
+pipe was completely dominated by wave
+ 
+
+ align:start position:0%
+pipe was completely dominated by wave
+propagation not by standing wave
+
+ align:start position:0%
+propagation not by standing wave
+ 
+
+ align:start position:0%
+propagation not by standing wave
+vibration so totally different than that
+
+ align:start position:0%
+vibration so totally different than that
+ 
+
+ align:start position:0%
+vibration so totally different than that
+short pipe
+
+ align:start position:0%
+short pipe
+ 
+
+ align:start position:0%
+short pipe
+1981 in the wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation so let's imagine we have a
+
+ align:start position:0%
+equation so let's imagine we have a
+ 
+
+ align:start position:0%
+equation so let's imagine we have a
+long pipe or string like that and it can
+
+ align:start position:0%
+long pipe or string like that and it can
+ 
+
+ align:start position:0%
+long pipe or string like that and it can
+carry waves traveling along it
+
+ align:start position:0%
+carry waves traveling along it
+ 
+
+ align:start position:0%
+carry waves traveling along it
+and the position at any location on here
+
+ align:start position:0%
+and the position at any location on here
+ 
+
+ align:start position:0%
+and the position at any location on here
+here's a coordinate X we describe the
+
+ align:start position:0%
+here's a coordinate X we describe the
+ 
+
+ align:start position:0%
+here's a coordinate X we describe the
+motion at a point by a coordinate W of x
+
+ align:start position:0%
+motion at a point by a coordinate W of x
+ 
+
+ align:start position:0%
+motion at a point by a coordinate W of x
+and t so it's a function of where it is
+
+ align:start position:0%
+and t so it's a function of where it is
+ 
+
+ align:start position:0%
+and t so it's a function of where it is
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+time and the way the what describes the
+
+ align:start position:0%
+time and the way the what describes the
+ 
+
+ align:start position:0%
+time and the way the what describes the
+motion of something which obeys the wave
+
+ align:start position:0%
+motion of something which obeys the wave
+ 
+
+ align:start position:0%
+motion of something which obeys the wave
+equation is the following equation
+
+ align:start position:0%
+equation is the following equation
+ 
+
+ align:start position:0%
+equation is the following equation
+partial squar
+
+ align:start position:0%
+partial squar
+ 
+
+ align:start position:0%
+partial squar
+W with respect to x
+
+ align:start position:0%
+W with respect to x
+ 
+
+ align:start position:0%
+W with respect to x
+s equal 1 /
+
+ align:start position:0%
+s equal 1 /
+ 
+
+ align:start position:0%
+s equal 1 /
+c^2 partial squar W with respect to
+
+ align:start position:0%
+c^2 partial squar W with respect to
+ 
+
+ align:start position:0%
+c^2 partial squar W with respect to
+t^2 that's what's known as the
+
+ align:start position:0%
+t^2 that's what's known as the
+ 
+
+ align:start position:0%
+t^2 that's what's known as the
+one-dimensional wave equation and the
+
+ align:start position:0%
+one-dimensional wave equation and the
+ 
+
+ align:start position:0%
+one-dimensional wave equation and the
+onedimensional wave equation governs
+
+ align:start position:0%
+onedimensional wave equation governs
+ 
+
+ align:start position:0%
+onedimensional wave equation governs
+incredibly broad category of of physical
+
+ align:start position:0%
+incredibly broad category of of physical
+ 
+
+ align:start position:0%
+incredibly broad category of of physical
+phenomena light
+
+ align:start position:0%
+phenomena light
+ 
+
+ align:start position:0%
+phenomena light
+behaves according to the wave equation
+
+ align:start position:0%
+behaves according to the wave equation
+ 
+
+ align:start position:0%
+behaves according to the wave equation
+sound propagating across the room to you
+
+ align:start position:0%
+sound propagating across the room to you
+ 
+
+ align:start position:0%
+sound propagating across the room to you
+is governed by the wave equation
+
+ align:start position:0%
+is governed by the wave equation
+ 
+
+ align:start position:0%
+is governed by the wave equation
+longitudinal vibration of rods torsional
+
+ align:start position:0%
+longitudinal vibration of rods torsional
+ 
+
+ align:start position:0%
+longitudinal vibration of rods torsional
+vibration of rods all governed by the
+
+ align:start position:0%
+vibration of rods all governed by the
+ 
+
+ align:start position:0%
+vibration of rods all governed by the
+wave equation so it's worthwhile to know
+
+ align:start position:0%
+wave equation so it's worthwhile to know
+ 
+
+ align:start position:0%
+wave equation so it's worthwhile to know
+a little bit about the wave
+
+ align:start position:0%
+a little bit about the wave
+ 
+
+ align:start position:0%
+a little bit about the wave
+equation and what I was showed you this
+
+ align:start position:0%
+equation and what I was showed you this
+ 
+
+ align:start position:0%
+equation and what I was showed you this
+morning it has this kind of Duality to
+
+ align:start position:0%
+morning it has this kind of Duality to
+ 
+
+ align:start position:0%
+morning it has this kind of Duality to
+it you can have things that vibrate with
+
+ align:start position:0%
+it you can have things that vibrate with
+ 
+
+ align:start position:0%
+it you can have things that vibrate with
+standing waves and mode shapes but the
+
+ align:start position:0%
+standing waves and mode shapes but the
+ 
+
+ align:start position:0%
+standing waves and mode shapes but the
+same system can support w waves that
+
+ align:start position:0%
+same system can support w waves that
+ 
+
+ align:start position:0%
+same system can support w waves that
+travel along it so let's figure out why
+
+ align:start position:0%
+travel along it so let's figure out why
+ 
+
+ align:start position:0%
+travel along it so let's figure out why
+why that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so I'm going to do the derivation for
+
+ align:start position:0%
+is so I'm going to do the derivation for
+ 
+
+ align:start position:0%
+is so I'm going to do the derivation for
+you of the uh of the wave equation for a
+
+ align:start position:0%
+you of the uh of the wave equation for a
+ 
+
+ align:start position:0%
+you of the uh of the wave equation for a
+string just so where you know it comes
+
+ align:start position:0%
+string just so where you know it comes
+ 
+
+ align:start position:0%
+string just so where you know it comes
+from because then that General
+
+ align:start position:0%
+from because then that General
+ 
+
+ align:start position:0%
+from because then that General
+derivation applies to all these
+
+ align:start position:0%
+derivation applies to all these
+ 
+
+ align:start position:0%
+derivation applies to all these
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+things so imagine you've got now a we're
+
+ align:start position:0%
+things so imagine you've got now a we're
+ 
+
+ align:start position:0%
+things so imagine you've got now a we're
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to we're interested in eventually
+
+ align:start position:0%
+to we're interested in eventually
+ 
+
+ align:start position:0%
+to we're interested in eventually
+getting the vibration so I'm going to
+
+ align:start position:0%
+getting the vibration so I'm going to
+ 
+
+ align:start position:0%
+getting the vibration so I'm going to
+make this a finite length
+
+ align:start position:0%
+make this a finite length
+ 
+
+ align:start position:0%
+make this a finite length
+string and it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has this position we'll describe as a w
+
+ align:start position:0%
+has this position we'll describe as a w
+ 
+
+ align:start position:0%
+has this position we'll describe as a w
+of x and t it has a tension
+
+ align:start position:0%
+of x and t it has a tension
+ 
+
+ align:start position:0%
+of x and t it has a tension
+t a mass per unit length M so this is
+
+ align:start position:0%
+t a mass per unit length M so this is
+ 
+
+ align:start position:0%
+t a mass per unit length M so this is
+like kilog per
+
+ align:start position:0%
+like kilog per
+ 
+
+ align:start position:0%
+like kilog per
+meter is the mass per unit length of
+
+ align:start position:0%
+meter is the mass per unit length of
+ 
+
+ align:start position:0%
+meter is the mass per unit length of
+this thing which can vibrate so tension
+
+ align:start position:0%
+this thing which can vibrate so tension
+ 
+
+ align:start position:0%
+this thing which can vibrate so tension
+mass per unit length uh
+
+ align:start position:0%
+mass per unit length uh
+ 
+
+ align:start position:0%
+mass per unit length uh
+L the length of it what other parameters
+
+ align:start position:0%
+L the length of it what other parameters
+ 
+
+ align:start position:0%
+L the length of it what other parameters
+do we need that'll that'll do for the
+
+ align:start position:0%
+do we need that'll that'll do for the
+ 
+
+ align:start position:0%
+do we need that'll that'll do for the
+moment now so let's draw it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+without in some
+
+ align:start position:0%
+without in some
+ 
+
+ align:start position:0%
+without in some
+displaced
+
+ align:start position:0%
+displaced
+ 
+
+ align:start position:0%
+displaced
+position and what's exciting it may be
+
+ align:start position:0%
+position and what's exciting it may be
+ 
+
+ align:start position:0%
+position and what's exciting it may be
+my Vortex shedding and so I'm going to
+
+ align:start position:0%
+my Vortex shedding and so I'm going to
+ 
+
+ align:start position:0%
+my Vortex shedding and so I'm going to
+draw on it excitation here and that will
+
+ align:start position:0%
+draw on it excitation here and that will
+ 
+
+ align:start position:0%
+draw on it excitation here and that will
+will describe as a f of x and t some
+
+ align:start position:0%
+will describe as a f of x and t some
+ 
+
+ align:start position:0%
+will describe as a f of x and t some
+Force per unit
+
+ align:start position:0%
+Force per unit
+ 
+
+ align:start position:0%
+Force per unit
+length so this has units of Newtons per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meter now in that
+
+ align:start position:0%
+meter now in that
+ 
+
+ align:start position:0%
+meter now in that
+little there may also be drag forces the
+
+ align:start position:0%
+little there may also be drag forces the
+ 
+
+ align:start position:0%
+little there may also be drag forces the
+fluid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+damping so I'm going to cut out a little
+
+ align:start position:0%
+damping so I'm going to cut out a little
+ 
+
+ align:start position:0%
+damping so I'm going to cut out a little
+piece of this cylinder and do a force
+
+ align:start position:0%
+piece of this cylinder and do a force
+ 
+
+ align:start position:0%
+piece of this cylinder and do a force
+balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on that piece of cylinder so basically f
+
+ align:start position:0%
+on that piece of cylinder so basically f
+ 
+
+ align:start position:0%
+on that piece of cylinder so basically f
+equals Ma we're just applying Newton to
+
+ align:start position:0%
+equals Ma we're just applying Newton to
+ 
+
+ align:start position:0%
+equals Ma we're just applying Newton to
+this piece of cylinder and I'll draw it
+
+ align:start position:0%
+this piece of cylinder and I'll draw it
+ 
+
+ align:start position:0%
+this piece of cylinder and I'll draw it
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+it's a little section of it it's
+
+ align:start position:0%
+it's a little section of it it's
+ 
+
+ align:start position:0%
+it's a little section of it it's
+curved here's
+
+ align:start position:0%
+curved here's
+ 
+
+ align:start position:0%
+curved here's
+horizontal there's horizontal we need to
+
+ align:start position:0%
+horizontal there's horizontal we need to
+ 
+
+ align:start position:0%
+horizontal there's horizontal we need to
+evaluate all the forces on
+
+ align:start position:0%
+evaluate all the forces on
+ 
+
+ align:start position:0%
+evaluate all the forces on
+it so the tension on this
+
+ align:start position:0%
+it so the tension on this
+ 
+
+ align:start position:0%
+it so the tension on this
+end is like that
+
+ align:start position:0%
+end is like that
+ 
+
+ align:start position:0%
+end is like that
+and the tension on this end is some
+
+ align:start position:0%
+and the tension on this end is some
+ 
+
+ align:start position:0%
+and the tension on this end is some
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+angle this will'll call Theta
+
+ align:start position:0%
+angle this will'll call Theta
+ 
+
+ align:start position:0%
+angle this will'll call Theta
+1 this we call Theta
+
+ align:start position:0%
+1 this we call Theta
+ 
+
+ align:start position:0%
+1 this we call Theta
+2 and along here are my excitation
+
+ align:start position:0%
+2 and along here are my excitation
+ 
+
+ align:start position:0%
+2 and along here are my excitation
+forces f of x and t there may be some
+
+ align:start position:0%
+forces f of x and t there may be some
+ 
+
+ align:start position:0%
+forces f of x and t there may be some
+resistance drag forces damping that'll
+
+ align:start position:0%
+resistance drag forces damping that'll
+ 
+
+ align:start position:0%
+resistance drag forces damping that'll
+be a damping constant R ofx which is
+
+ align:start position:0%
+be a damping constant R ofx which is
+ 
+
+ align:start position:0%
+be a damping constant R ofx which is
+force per unit length per unit velocity
+
+ align:start position:0%
+force per unit length per unit velocity
+ 
+
+ align:start position:0%
+force per unit length per unit velocity
+times uh the force on this would be have
+
+ align:start position:0%
+times uh the force on this would be have
+ 
+
+ align:start position:0%
+times uh the force on this would be have
+to be multiplied by the velocity so the
+
+ align:start position:0%
+to be multiplied by the velocity so the
+ 
+
+ align:start position:0%
+to be multiplied by the velocity so the
+derivative of the dis of this
+
+ align:start position:0%
+derivative of the dis of this
+ 
+
+ align:start position:0%
+derivative of the dis of this
+displacement with respect to time that's
+
+ align:start position:0%
+displacement with respect to time that's
+ 
+
+ align:start position:0%
+displacement with respect to time that's
+the force along here and it can vary
+
+ align:start position:0%
+the force along here and it can vary
+ 
+
+ align:start position:0%
+the force along here and it can vary
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+position and have we accounted for
+
+ align:start position:0%
+position and have we accounted for
+ 
+
+ align:start position:0%
+position and have we accounted for
+everything ah well we this is position X
+
+ align:start position:0%
+everything ah well we this is position X
+ 
+
+ align:start position:0%
+everything ah well we this is position X
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+at x + DX
+
+ align:start position:0%
+at x + DX
+ 
+
+ align:start position:0%
+at x + DX
+so this little element is DX in
+
+ align:start position:0%
+so this little element is DX in
+ 
+
+ align:start position:0%
+so this little element is DX in
+length and this is all for small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you assume small motions then you
+
+ align:start position:0%
+and if you assume small motions then you
+ 
+
+ align:start position:0%
+and if you assume small motions then you
+can say Theta 1 it's approximately equal
+
+ align:start position:0%
+can say Theta 1 it's approximately equal
+ 
+
+ align:start position:0%
+can say Theta 1 it's approximately equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh sin Theta 1 that's also approximately
+
+ align:start position:0%
+uh sin Theta 1 that's also approximately
+ 
+
+ align:start position:0%
+uh sin Theta 1 that's also approximately
+equal to tan Theta 1 and that's equal to
+
+ align:start position:0%
+equal to tan Theta 1 and that's equal to
+ 
+
+ align:start position:0%
+equal to tan Theta 1 and that's equal to
+the derivative of w with respect to X
+
+ align:start position:0%
+the derivative of w with respect to X
+ 
+
+ align:start position:0%
+the derivative of w with respect to X
+just the slope we're going to take
+
+ align:start position:0%
+just the slope we're going to take
+ 
+
+ align:start position:0%
+just the slope we're going to take
+advantage of that Theta 2 say same thing
+
+ align:start position:0%
+advantage of that Theta 2 say same thing
+ 
+
+ align:start position:0%
+advantage of that Theta 2 say same thing
+it's approximately equal to the uh to
+
+ align:start position:0%
+it's approximately equal to the uh to
+ 
+
+ align:start position:0%
+it's approximately equal to the uh to
+tan Theta 2 here and S and all those
+
+ align:start position:0%
+tan Theta 2 here and S and all those
+ 
+
+ align:start position:0%
+tan Theta 2 here and S and all those
+things but that
+
+ align:start position:0%
+things but that
+ 
+
+ align:start position:0%
+things but that
+then the slope has changed a little bit
+
+ align:start position:0%
+then the slope has changed a little bit
+ 
+
+ align:start position:0%
+then the slope has changed a little bit
+when you go from through DX and this is
+
+ align:start position:0%
+when you go from through DX and this is
+ 
+
+ align:start position:0%
+when you go from through DX and this is
+equal to the slope on the left hand
+
+ align:start position:0%
+equal to the slope on the left hand
+ 
+
+ align:start position:0%
+equal to the slope on the left hand
+side plus the rate of change of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope time
+
+ align:start position:0%
+slope time
+ 
+
+ align:start position:0%
+slope time
+DX okay so slope on the left this is now
+
+ align:start position:0%
+DX okay so slope on the left this is now
+ 
+
+ align:start position:0%
+DX okay so slope on the left this is now
+the slope on the right hand side and so
+
+ align:start position:0%
+the slope on the right hand side and so
+ 
+
+ align:start position:0%
+the slope on the right hand side and so
+now all it's left to do is to write a
+
+ align:start position:0%
+now all it's left to do is to write a
+ 
+
+ align:start position:0%
+now all it's left to do is to write a
+force balance for that little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+piece on the element
+
+ align:start position:0%
+piece on the element
+ 
+
+ align:start position:0%
+piece on the element
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+so positive upward we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t sin Theta but because sin Theta is
+
+ align:start position:0%
+t sin Theta but because sin Theta is
+ 
+
+ align:start position:0%
+t sin Theta but because sin Theta is
+approximately tan Theta is equal to dwdx
+
+ align:start position:0%
+approximately tan Theta is equal to dwdx
+ 
+
+ align:start position:0%
+approximately tan Theta is equal to dwdx
+then there's an upward force on the
+
+ align:start position:0%
+then there's an upward force on the
+ 
+
+ align:start position:0%
+then there's an upward force on the
+right hand side which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+and this turns into partial squared W
+
+ align:start position:0%
+and this turns into partial squared W
+ 
+
+ align:start position:0%
+and this turns into partial squared W
+with respect to X SAR DX so on the right
+
+ align:start position:0%
+with respect to X SAR DX so on the right
+ 
+
+ align:start position:0%
+with respect to X SAR DX so on the right
+hand side positive upwards you have t
+
+ align:start position:0%
+hand side positive upwards you have t
+ 
+
+ align:start position:0%
+hand side positive upwards you have t
+times the partial of
+
+ align:start position:0%
+times the partial of
+ 
+
+ align:start position:0%
+times the partial of
+w with respect to X Plus partial squar W
+
+ align:start position:0%
+w with respect to X Plus partial squar W
+ 
+
+ align:start position:0%
+w with respect to X Plus partial squar W
+respect to X
+
+ align:start position:0%
+respect to X
+ 
+
+ align:start position:0%
+respect to X
+SAR DX that's the upward force on the
+
+ align:start position:0%
+SAR DX that's the upward force on the
+ 
+
+ align:start position:0%
+SAR DX that's the upward force on the
+right hand side on the left hand side we
+
+ align:start position:0%
+right hand side on the left hand side we
+ 
+
+ align:start position:0%
+right hand side on the left hand side we
+have a downward Force minus t partial of
+
+ align:start position:0%
+have a downward Force minus t partial of
+ 
+
+ align:start position:0%
+have a downward Force minus t partial of
+w with respect to X and you notice that
+
+ align:start position:0%
+w with respect to X and you notice that
+ 
+
+ align:start position:0%
+w with respect to X and you notice that
+this one's going to cancel that one we
+
+ align:start position:0%
+this one's going to cancel that one we
+ 
+
+ align:start position:0%
+this one's going to cancel that one we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+minus r
+
+ align:start position:0%
+minus r
+ 
+
+ align:start position:0%
+minus r
+ofx partial W with respect to T that's
+
+ align:start position:0%
+ofx partial W with respect to T that's
+ 
+
+ align:start position:0%
+ofx partial W with respect to T that's
+the velocity DX long because that's
+
+ align:start position:0%
+the velocity DX long because that's
+ 
+
+ align:start position:0%
+the velocity DX long because that's
+Force per unit
+
+ align:start position:0%
+Force per unit
+ 
+
+ align:start position:0%
+Force per unit
+length and have we missed anything so
+
+ align:start position:0%
+length and have we missed anything so
+ 
+
+ align:start position:0%
+length and have we missed anything so
+that's the sum of the external forces on
+
+ align:start position:0%
+that's the sum of the external forces on
+ 
+
+ align:start position:0%
+that's the sum of the external forces on
+this little slice
+
+ align:start position:0%
+this little slice
+ 
+
+ align:start position:0%
+this little slice
+and that has to be equal to what did
+
+ align:start position:0%
+and that has to be equal to what did
+ 
+
+ align:start position:0%
+and that has to be equal to what did
+Newton
+
+ align:start position:0%
+Newton
+ 
+
+ align:start position:0%
+Newton
+say the mass which is the mass per unit
+
+ align:start position:0%
+say the mass which is the mass per unit
+ 
+
+ align:start position:0%
+say the mass which is the mass per unit
+length times DX is the total mass times
+
+ align:start position:0%
+length times DX is the total mass times
+ 
+
+ align:start position:0%
+length times DX is the total mass times
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+acceleration partial squared W with
+
+ align:start position:0%
+acceleration partial squared W with
+ 
+
+ align:start position:0%
+acceleration partial squared W with
+respect to t^
+
+ align:start position:0%
+respect to t^
+ 
+
+ align:start position:0%
+respect to t^
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay so this cancels this
+
+ align:start position:0%
+okay so this cancels this
+ 
+
+ align:start position:0%
+okay so this cancels this
+term and then you know notice I'm left
+
+ align:start position:0%
+term and then you know notice I'm left
+ 
+
+ align:start position:0%
+term and then you know notice I'm left
+with everything is just a function
+
+ align:start position:0%
+with everything is just a function
+ 
+
+ align:start position:0%
+with everything is just a function
+something DX something DX something DX
+
+ align:start position:0%
+something DX something DX something DX
+ 
+
+ align:start position:0%
+something DX something DX something DX
+get rid of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX's and I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write oh see did I leave I left out
+
+ align:start position:0%
+write oh see did I leave I left out
+ 
+
+ align:start position:0%
+write oh see did I leave I left out
+something I left out my distributed
+
+ align:start position:0%
+something I left out my distributed
+ 
+
+ align:start position:0%
+something I left out my distributed
+Force f of x and t DX it's positive as
+
+ align:start position:0%
+Force f of x and t DX it's positive as
+ 
+
+ align:start position:0%
+Force f of x and t DX it's positive as
+it's drawn it's over here also so this
+
+ align:start position:0%
+it's drawn it's over here also so this
+ 
+
+ align:start position:0%
+it's drawn it's over here also so this
+and I cancel out that DX so I put them
+
+ align:start position:0%
+and I cancel out that DX so I put them
+ 
+
+ align:start position:0%
+and I cancel out that DX so I put them
+all together now and assemble them I can
+
+ align:start position:0%
+all together now and assemble them I can
+ 
+
+ align:start position:0%
+all together now and assemble them I can
+write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down the equation that governs this
+
+ align:start position:0%
+down the equation that governs this
+ 
+
+ align:start position:0%
+down the equation that governs this
+motion so
+
+ align:start position:0%
+motion so
+ 
+
+ align:start position:0%
+motion so
+T partial squar W with respect to
+
+ align:start position:0%
+T partial squar W with respect to
+ 
+
+ align:start position:0%
+T partial squar W with respect to
+X2 minus r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx times velocity
+
+ align:start position:0%
+ofx times velocity
+ 
+
+ align:start position:0%
+ofx times velocity
+plus f x and
+
+ align:start position:0%
+plus f x and
+ 
+
+ align:start position:0%
+plus f x and
+t equals m partial squ W with respect to
+
+ align:start position:0%
+t equals m partial squ W with respect to
+ 
+
+ align:start position:0%
+t equals m partial squ W with respect to
+t^2 and that just says that the sum of
+
+ align:start position:0%
+t^2 and that just says that the sum of
+ 
+
+ align:start position:0%
+t^2 and that just says that the sum of
+the forces on the object equals its mass
+
+ align:start position:0%
+the forces on the object equals its mass
+ 
+
+ align:start position:0%
+the forces on the object equals its mass
+times its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration now if we're interested in
+
+ align:start position:0%
+acceleration now if we're interested in
+ 
+
+ align:start position:0%
+acceleration now if we're interested in
+natural frequencies and mode
+
+ align:start position:0%
+natural frequencies and mode
+ 
+
+ align:start position:0%
+natural frequencies and mode
+shapes how do when we when we've been
+
+ align:start position:0%
+shapes how do when we when we've been
+ 
+
+ align:start position:0%
+shapes how do when we when we've been
+doing one and two degree Freedom systems
+
+ align:start position:0%
+doing one and two degree Freedom systems
+ 
+
+ align:start position:0%
+doing one and two degree Freedom systems
+and we want to get the natural
+
+ align:start position:0%
+and we want to get the natural
+ 
+
+ align:start position:0%
+and we want to get the natural
+frequencies and mode shapes we
+
+ align:start position:0%
+frequencies and mode shapes we
+ 
+
+ align:start position:0%
+frequencies and mode shapes we
+temporarily let the damping be zero and
+
+ align:start position:0%
+temporarily let the damping be zero and
+ 
+
+ align:start position:0%
+temporarily let the damping be zero and
+the force be zero right so we want to do
+
+ align:start position:0%
+the force be zero right so we want to do
+ 
+
+ align:start position:0%
+the force be zero right so we want to do
+the same thing now we're interested in
+
+ align:start position:0%
+the same thing now we're interested in
+ 
+
+ align:start position:0%
+the same thing now we're interested in
+uh how do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find the Omega
+
+ align:start position:0%
+find the Omega
+ 
+
+ align:start position:0%
+find the Omega
+NS and what I call the S NS because now
+
+ align:start position:0%
+NS and what I call the S NS because now
+ 
+
+ align:start position:0%
+NS and what I call the S NS because now
+the mode shapes are functions and so
+
+ align:start position:0%
+the mode shapes are functions and so
+ 
+
+ align:start position:0%
+the mode shapes are functions and so
+this is the natural frequency and the
+
+ align:start position:0%
+this is the natural frequency and the
+ 
+
+ align:start position:0%
+this is the natural frequency and the
+mode shape for mode n we know there's
+
+ align:start position:0%
+mode shape for mode n we know there's
+ 
+
+ align:start position:0%
+mode shape for mode n we know there's
+lots of modes so we let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R ofx and F ofx and T be zero and when
+
+ align:start position:0%
+R ofx and F ofx and T be zero and when
+ 
+
+ align:start position:0%
+R ofx and F ofx and T be zero and when
+we do
+
+ align:start position:0%
+we do
+ 
+
+ align:start position:0%
+we do
+that I'm going to divide through by T
+
+ align:start position:0%
+that I'm going to divide through by T
+ 
+
+ align:start position:0%
+that I'm going to divide through by T
+when I do that this term goes away this
+
+ align:start position:0%
+when I do that this term goes away this
+ 
+
+ align:start position:0%
+when I do that this term goes away this
+term goes away I'm just left with t
+
+ align:start position:0%
+term goes away I'm just left with t
+ 
+
+ align:start position:0%
+term goes away I'm just left with t
+partial squ W respect X2 equals this and
+
+ align:start position:0%
+partial squ W respect X2 equals this and
+ 
+
+ align:start position:0%
+partial squ W respect X2 equals this and
+I'm going to divide through by T so I
+
+ align:start position:0%
+I'm going to divide through by T so I
+ 
+
+ align:start position:0%
+I'm going to divide through by T so I
+get partial squared
+
+ align:start position:0%
+get partial squared
+ 
+
+ align:start position:0%
+get partial squared
+W respect to X2 equal
+
+ align:start position:0%
+W respect to X2 equal
+ 
+
+ align:start position:0%
+W respect to X2 equal
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+over t/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M partial squar W with respect to t^
+
+ align:start position:0%
+M partial squar W with respect to t^
+ 
+
+ align:start position:0%
+M partial squar W with respect to t^
+2ar and this T over M
+
+ align:start position:0%
+2ar and this T over M
+ 
+
+ align:start position:0%
+2ar and this T over M
+quantity turns out to
+
+ align:start position:0%
+quantity turns out to
+ 
+
+ align:start position:0%
+quantity turns out to
+be the speed of wave propagation in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+medium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+that is the wave
+
+ align:start position:0%
+that is the wave
+ 
+
+ align:start position:0%
+that is the wave
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+right and as I've just so we've just
+
+ align:start position:0%
+right and as I've just so we've just
+ 
+
+ align:start position:0%
+right and as I've just so we've just
+found the wave equation for the string
+
+ align:start position:0%
+found the wave equation for the string
+ 
+
+ align:start position:0%
+found the wave equation for the string
+just by doing a simple applying Newton's
+
+ align:start position:0%
+just by doing a simple applying Newton's
+ 
+
+ align:start position:0%
+just by doing a simple applying Newton's
+law to a little section of string you
+
+ align:start position:0%
+law to a little section of string you
+ 
+
+ align:start position:0%
+law to a little section of string you
+can do that for the vibr you can do same
+
+ align:start position:0%
+can do that for the vibr you can do same
+ 
+
+ align:start position:0%
+can do that for the vibr you can do same
+thing cut out a little section of a beam
+
+ align:start position:0%
+thing cut out a little section of a beam
+ 
+
+ align:start position:0%
+thing cut out a little section of a beam
+C do the force balance on it set it
+
+ align:start position:0%
+C do the force balance on it set it
+ 
+
+ align:start position:0%
+C do the force balance on it set it
+equal to the mass times acceleration and
+
+ align:start position:0%
+equal to the mass times acceleration and
+ 
+
+ align:start position:0%
+equal to the mass times acceleration and
+for a beam you'll get a fourth order
+
+ align:start position:0%
+for a beam you'll get a fourth order
+ 
+
+ align:start position:0%
+for a beam you'll get a fourth order
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equation and it's not the wave
+
+ align:start position:0%
+equation and it's not the wave
+ 
+
+ align:start position:0%
+equation and it's not the wave
+equation still vibrates but it's not
+
+ align:start position:0%
+equation still vibrates but it's not
+ 
+
+ align:start position:0%
+equation still vibrates but it's not
+governed by what do we call the wave
+
+ align:start position:0%
+governed by what do we call the wave
+ 
+
+ align:start position:0%
+governed by what do we call the wave
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the one-dimensional wave
+
+ align:start position:0%
+okay so this is the one-dimensional wave
+ 
+
+ align:start position:0%
+okay so this is the one-dimensional wave
+equation this quantity T over m is the
+
+ align:start position:0%
+equation this quantity T over m is the
+ 
+
+ align:start position:0%
+equation this quantity T over m is the
+phase velocity it's called phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity you know that's a good one to
+
+ align:start position:0%
+velocity you know that's a good one to
+ 
+
+ align:start position:0%
+velocity you know that's a good one to
+remember for simple string the speed of
+
+ align:start position:0%
+remember for simple string the speed of
+ 
+
+ align:start position:0%
+remember for simple string the speed of
+phenoma running down the string is a
+
+ align:start position:0%
+phenoma running down the string is a
+ 
+
+ align:start position:0%
+phenoma running down the string is a
+square root of the tension divided by
+
+ align:start position:0%
+square root of the tension divided by
+ 
+
+ align:start position:0%
+square root of the tension divided by
+the mass per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length and if you had you know a long
+
+ align:start position:0%
+length and if you had you know a long
+ 
+
+ align:start position:0%
+length and if you had you know a long
+string and like I put that little pluck
+
+ align:start position:0%
+string and like I put that little pluck
+ 
+
+ align:start position:0%
+string and like I put that little pluck
+in it you can see that pluck running
+
+ align:start position:0%
+in it you can see that pluck running
+ 
+
+ align:start position:0%
+in it you can see that pluck running
+back and forth on it that's the speed
+
+ align:start position:0%
+back and forth on it that's the speed
+ 
+
+ align:start position:0%
+back and forth on it that's the speed
+it's going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at it's basically it's called the well
+
+ align:start position:0%
+at it's basically it's called the well
+ 
+
+ align:start position:0%
+at it's basically it's called the well
+so if I have my string and I put a
+
+ align:start position:0%
+so if I have my string and I put a
+ 
+
+ align:start position:0%
+so if I have my string and I put a
+little bump on it and that bump goes
+
+ align:start position:0%
+little bump on it and that bump goes
+ 
+
+ align:start position:0%
+little bump on it and that bump goes
+zipping along your eye will see this
+
+ align:start position:0%
+zipping along your eye will see this
+ 
+
+ align:start position:0%
+zipping along your eye will see this
+thing propagating at
+
+ align:start position:0%
+thing propagating at
+ 
+
+ align:start position:0%
+thing propagating at
+C all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so to get natural frequencies and
+
+ align:start position:0%
+right so to get natural frequencies and
+ 
+
+ align:start position:0%
+right so to get natural frequencies and
+mode shapes we basically need to solve
+
+ align:start position:0%
+mode shapes we basically need to solve
+ 
+
+ align:start position:0%
+mode shapes we basically need to solve
+solve this
+
+ align:start position:0%
+solve this
+ 
+
+ align:start position:0%
+solve this
+equation and it's quite straightforward
+
+ align:start position:0%
+equation and it's quite straightforward
+ 
+
+ align:start position:0%
+equation and it's quite straightforward
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do and a technique known as separation
+
+ align:start position:0%
+do and a technique known as separation
+ 
+
+ align:start position:0%
+do and a technique known as separation
+of variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Works which means that all you're doing
+
+ align:start position:0%
+Works which means that all you're doing
+ 
+
+ align:start position:0%
+Works which means that all you're doing
+is saying I believe that I going to be
+
+ align:start position:0%
+is saying I believe that I going to be
+ 
+
+ align:start position:0%
+is saying I believe that I going to be
+able to write the solution as some
+
+ align:start position:0%
+able to write the solution as some
+ 
+
+ align:start position:0%
+able to write the solution as some
+function of X only times some function
+
+ align:start position:0%
+function of X only times some function
+ 
+
+ align:start position:0%
+function of X only times some function
+of time only product of two terms and
+
+ align:start position:0%
+of time only product of two terms and
+ 
+
+ align:start position:0%
+of time only product of two terms and
+that in fact
+
+ align:start position:0%
+that in fact
+ 
+
+ align:start position:0%
+that in fact
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um because we are interested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+vibration you can tell me what the
+
+ align:start position:0%
+vibration you can tell me what the
+ 
+
+ align:start position:0%
+vibration you can tell me what the
+function of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is you're going to tell me half the
+
+ align:start position:0%
+is you're going to tell me half the
+ 
+
+ align:start position:0%
+is you're going to tell me half the
+solution just from observation what is
+
+ align:start position:0%
+solution just from observation what is
+ 
+
+ align:start position:0%
+solution just from observation what is
+it just the time dependent
+
+ align:start position:0%
+it just the time dependent
+ 
+
+ align:start position:0%
+it just the time dependent
+part it's the same as anything else that
+
+ align:start position:0%
+part it's the same as anything else that
+ 
+
+ align:start position:0%
+part it's the same as anything else that
+vibrat so single degree to Freedom
+
+ align:start position:0%
+vibrat so single degree to Freedom
+ 
+
+ align:start position:0%
+vibrat so single degree to Freedom
+system what is the time dependent
+
+ align:start position:0%
+system what is the time dependent
+ 
+
+ align:start position:0%
+system what is the time dependent
+function that we substitute in to find
+
+ align:start position:0%
+function that we substitute in to find
+ 
+
+ align:start position:0%
+function that we substitute in to find
+the natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency say
+
+ align:start position:0%
+frequency say
+ 
+
+ align:start position:0%
+frequency say
+again EA T would be just fine cosine
+
+ align:start position:0%
+again EA T would be just fine cosine
+ 
+
+ align:start position:0%
+again EA T would be just fine cosine
+Omega T Works s Omega T works but e
+
+ align:start position:0%
+Omega T Works s Omega T works but e
+ 
+
+ align:start position:0%
+Omega T Works s Omega T works but e
+Omega T is pretty easy to use because
+
+ align:start position:0%
+Omega T is pretty easy to use because
+ 
+
+ align:start position:0%
+Omega T is pretty easy to use because
+it's so simple to take the derivatives
+
+ align:start position:0%
+it's so simple to take the derivatives
+ 
+
+ align:start position:0%
+it's so simple to take the derivatives
+so we can guess that this is going to be
+
+ align:start position:0%
+so we can guess that this is going to be
+ 
+
+ align:start position:0%
+so we can guess that this is going to be
+some W of x
+
+ align:start position:0%
+some W of x
+ 
+
+ align:start position:0%
+some W of x
+times a e to the I Omega
+
+ align:start position:0%
+times a e to the I Omega
+ 
+
+ align:start position:0%
+times a e to the I Omega
+T right and plug it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in plug it into our wave equation over
+
+ align:start position:0%
+in plug it into our wave equation over
+ 
+
+ align:start position:0%
+in plug it into our wave equation over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so make sure I write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistently so we plug this into the
+
+ align:start position:0%
+consistently so we plug this into the
+ 
+
+ align:start position:0%
+consistently so we plug this into the
+first term it's two derivatives with
+
+ align:start position:0%
+first term it's two derivatives with
+ 
+
+ align:start position:0%
+first term it's two derivatives with
+respect to X so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just and the time dependent part just
+
+ align:start position:0%
+just and the time dependent part just
+ 
+
+ align:start position:0%
+just and the time dependent part just
+stays
+
+ align:start position:0%
+stays
+ 
+
+ align:start position:0%
+stays
+outside and on the uh right hand
+
+ align:start position:0%
+outside and on the uh right hand
+ 
+
+ align:start position:0%
+outside and on the uh right hand
+side when we plug it in here 1 over c^2
+
+ align:start position:0%
+side when we plug it in here 1 over c^2
+ 
+
+ align:start position:0%
+side when we plug it in here 1 over c^2
+two derivatives with respect to time
+
+ align:start position:0%
+two derivatives with respect to time
+ 
+
+ align:start position:0%
+two derivatives with respect to time
+it's going to give me minus Omega 2 so
+
+ align:start position:0%
+it's going to give me minus Omega 2 so
+ 
+
+ align:start position:0%
+it's going to give me minus Omega 2 so
+minus Omega 2 over C squ and then it
+
+ align:start position:0%
+minus Omega 2 over C squ and then it
+ 
+
+ align:start position:0%
+minus Omega 2 over C squ and then it
+gives me
+
+ align:start position:0%
+gives me
+ 
+
+ align:start position:0%
+gives me
+back W of X AE to the I Omega
+
+ align:start position:0%
+back W of X AE to the I Omega
+ 
+
+ align:start position:0%
+back W of X AE to the I Omega
+T and now I can get rid of the AE to the
+
+ align:start position:0%
+T and now I can get rid of the AE to the
+ 
+
+ align:start position:0%
+T and now I can get rid of the AE to the
+I Omega
+
+ align:start position:0%
+I Omega
+ 
+
+ align:start position:0%
+I Omega
+T's and I'm left with just an equation
+
+ align:start position:0%
+T's and I'm left with just an equation
+ 
+
+ align:start position:0%
+T's and I'm left with just an equation
+involving X only and it's an ordinary
+
+ align:start position:0%
+involving X only and it's an ordinary
+ 
+
+ align:start position:0%
+involving X only and it's an ordinary
+differential equation in W of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+so it turns into
+
+ align:start position:0%
+so it turns into
+ 
+
+ align:start position:0%
+so it turns into
+d2w
+
+ align:start position:0%
+d2w
+ 
+
+ align:start position:0%
+d2w
+dx2 plus Omega 2 over c^2
+
+ align:start position:0%
+dx2 plus Omega 2 over c^2
+ 
+
+ align:start position:0%
+dx2 plus Omega 2 over c^2
+W equal Z and that should that you've
+
+ align:start position:0%
+W equal Z and that should that you've
+ 
+
+ align:start position:0%
+W equal Z and that should that you've
+seen this equation before does this not
+
+ align:start position:0%
+seen this equation before does this not
+ 
+
+ align:start position:0%
+seen this equation before does this not
+look like uh have some similarity to MX
+
+ align:start position:0%
+look like uh have some similarity to MX
+ 
+
+ align:start position:0%
+look like uh have some similarity to MX
+double dot +
+
+ align:start position:0%
+double dot +
+ 
+
+ align:start position:0%
+double dot +
+KX equal Z okay the same basically the
+
+ align:start position:0%
+KX equal Z okay the same basically the
+ 
+
+ align:start position:0%
+KX equal Z okay the same basically the
+same equation this one's a function of X
+
+ align:start position:0%
+same equation this one's a function of X
+ 
+
+ align:start position:0%
+same equation this one's a function of X
+that one's a function of time okay and
+
+ align:start position:0%
+that one's a function of time okay and
+ 
+
+ align:start position:0%
+that one's a function of time okay and
+we know the solution to this one is some
+
+ align:start position:0%
+we know the solution to this one is some
+ 
+
+ align:start position:0%
+we know the solution to this one is some
+X of T is some
+
+ align:start position:0%
+X of T is some
+ 
+
+ align:start position:0%
+X of T is some
+amplitude e to the I Omega T so
+
+ align:start position:0%
+amplitude e to the I Omega T so
+ 
+
+ align:start position:0%
+amplitude e to the I Omega T so
+therefore we can guess that the solution
+
+ align:start position:0%
+therefore we can guess that the solution
+ 
+
+ align:start position:0%
+therefore we can guess that the solution
+to this one is W ofx is going to be I'll
+
+ align:start position:0%
+to this one is W ofx is going to be I'll
+ 
+
+ align:start position:0%
+to this one is W ofx is going to be I'll
+write it as uh some
+
+ align:start position:0%
+write it as uh some
+ 
+
+ align:start position:0%
+write it as uh some
+B and now I need a function of x X but
+
+ align:start position:0%
+B and now I need a function of x X but
+ 
+
+ align:start position:0%
+B and now I need a function of x X but
+it can be just like this e to the I and
+
+ align:start position:0%
+it can be just like this e to the I and
+ 
+
+ align:start position:0%
+it can be just like this e to the I and
+I'll say
+
+ align:start position:0%
+I'll say
+ 
+
+ align:start position:0%
+I'll say
+k x I know that's going to be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution so let's plug it in if I if I
+
+ align:start position:0%
+solution so let's plug it in if I if I
+ 
+
+ align:start position:0%
+solution so let's plug it in if I if I
+plug that in I get uh
+
+ align:start position:0%
+plug that in I get uh
+ 
+
+ align:start position:0%
+plug that in I get uh
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+b e to the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX plus Omega 2 over c^
+
+ align:start position:0%
+KX plus Omega 2 over c^
+ 
+
+ align:start position:0%
+KX plus Omega 2 over c^
+2 b e to the I KX =
+
+ align:start position:0%
+2 b e to the I KX =
+ 
+
+ align:start position:0%
+2 b e to the I KX =
+Z well now I get rid of
+
+ align:start position:0%
+Z well now I get rid of
+ 
+
+ align:start position:0%
+Z well now I get rid of
+these and what I found out is that K
+
+ align:start position:0%
+these and what I found out is that K
+ 
+
+ align:start position:0%
+these and what I found out is that K
+squ Omega 2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c^2 and
+
+ align:start position:0%
+c^2 and
+ 
+
+ align:start position:0%
+c^2 and
+this has a name
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k it's called The Wave
+
+ align:start position:0%
+k it's called The Wave
+ 
+
+ align:start position:0%
+k it's called The Wave
+number and I'm it also happens to be 2
+
+ align:start position:0%
+number and I'm it also happens to be 2
+ 
+
+ align:start position:0%
+number and I'm it also happens to be 2
+pi over Lambda we'll come back to that
+
+ align:start position:0%
+pi over Lambda we'll come back to that
+ 
+
+ align:start position:0%
+pi over Lambda we'll come back to that
+Lambda is the wavelength you have
+
+ align:start position:0%
+Lambda is the wavelength you have
+ 
+
+ align:start position:0%
+Lambda is the wavelength you have
+sinusal waves running through the
+
+ align:start position:0%
+sinusal waves running through the
+ 
+
+ align:start position:0%
+sinusal waves running through the
+medium 2 pi over Lambda is the same as
+
+ align:start position:0%
+medium 2 pi over Lambda is the same as
+ 
+
+ align:start position:0%
+medium 2 pi over Lambda is the same as
+Omega over C and this is called The
+
+ align:start position:0%
+Omega over C and this is called The
+ 
+
+ align:start position:0%
+Omega over C and this is called The
+Wave number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really important quantity if you're
+
+ align:start position:0%
+really important quantity if you're
+ 
+
+ align:start position:0%
+really important quantity if you're
+trying to understand wave propagation in
+
+ align:start position:0%
+trying to understand wave propagation in
+ 
+
+ align:start position:0%
+trying to understand wave propagation in
+systems and actually and this one this
+
+ align:start position:0%
+systems and actually and this one this
+ 
+
+ align:start position:0%
+systems and actually and this one this
+definition applies to all wave bearing
+
+ align:start position:0%
+definition applies to all wave bearing
+ 
+
+ align:start position:0%
+definition applies to all wave bearing
+systems whether or not they obey the
+
+ align:start position:0%
+systems whether or not they obey the
+ 
+
+ align:start position:0%
+systems whether or not they obey the
+wave equation it'll apply to waves
+
+ align:start position:0%
+wave equation it'll apply to waves
+ 
+
+ align:start position:0%
+wave equation it'll apply to waves
+traveling down a beam as well so the
+
+ align:start position:0%
+traveling down a beam as well so the
+ 
+
+ align:start position:0%
+traveling down a beam as well so the
+definition of wave number is frequency
+
+ align:start position:0%
+definition of wave number is frequency
+ 
+
+ align:start position:0%
+definition of wave number is frequency
+divided by speed or 2 pi over the
+
+ align:start position:0%
+divided by speed or 2 pi over the
+ 
+
+ align:start position:0%
+divided by speed or 2 pi over the
+wavelength well let's
+
+ align:start position:0%
+wavelength well let's
+ 
+
+ align:start position:0%
+wavelength well let's
+see we can't go much further
+
+ align:start position:0%
+see we can't go much further
+ 
+
+ align:start position:0%
+see we can't go much further
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+uh with just the wave equation itself we
+
+ align:start position:0%
+uh with just the wave equation itself we
+ 
+
+ align:start position:0%
+uh with just the wave equation itself we
+have in order to get the natural
+
+ align:start position:0%
+have in order to get the natural
+ 
+
+ align:start position:0%
+have in order to get the natural
+frequencies we have to invoke other
+
+ align:start position:0%
+frequencies we have to invoke other
+ 
+
+ align:start position:0%
+frequencies we have to invoke other
+information that we know in the problem
+
+ align:start position:0%
+information that we know in the problem
+ 
+
+ align:start position:0%
+information that we know in the problem
+in particular we know that in order to
+
+ align:start position:0%
+in particular we know that in order to
+ 
+
+ align:start position:0%
+in particular we know that in order to
+get natural frequencies we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to create conditions where this could
+
+ align:start position:0%
+to create conditions where this could
+ 
+
+ align:start position:0%
+to create conditions where this could
+vibrate in particular I fix that end and
+
+ align:start position:0%
+vibrate in particular I fix that end and
+ 
+
+ align:start position:0%
+vibrate in particular I fix that end and
+I fix this end and I put some tension on
+
+ align:start position:0%
+I fix this end and I put some tension on
+ 
+
+ align:start position:0%
+I fix this end and I put some tension on
+it and now it'll vibrate but it clearly
+
+ align:start position:0%
+it and now it'll vibrate but it clearly
+ 
+
+ align:start position:0%
+it and now it'll vibrate but it clearly
+has something to do with ends and its
+
+ align:start position:0%
+has something to do with ends and its
+ 
+
+ align:start position:0%
+has something to do with ends and its
+length and so this is a boundary value
+
+ align:start position:0%
+length and so this is a boundary value
+ 
+
+ align:start position:0%
+length and so this is a boundary value
+problem and we have to in invoke the
+
+ align:start position:0%
+problem and we have to in invoke the
+ 
+
+ align:start position:0%
+problem and we have to in invoke the
+boundary conditions to actually finish
+
+ align:start position:0%
+boundary conditions to actually finish
+ 
+
+ align:start position:0%
+boundary conditions to actually finish
+finding the natural frequencies and mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shapes apply the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+so this I assumed here that that my w of
+
+ align:start position:0%
+so this I assumed here that that my w of
+ 
+
+ align:start position:0%
+so this I assumed here that that my w of
+X was going to look something like that
+
+ align:start position:0%
+X was going to look something like that
+ 
+
+ align:start position:0%
+X was going to look something like that
+in order to I to get a little more
+
+ align:start position:0%
+in order to I to get a little more
+ 
+
+ align:start position:0%
+in order to I to get a little more
+information out of than this I'm going
+
+ align:start position:0%
+information out of than this I'm going
+ 
+
+ align:start position:0%
+information out of than this I'm going
+to write now W ofx in a form an
+
+ align:start position:0%
+to write now W ofx in a form an
+ 
+
+ align:start position:0%
+to write now W ofx in a form an
+alternate form that's equally valid and
+
+ align:start position:0%
+alternate form that's equally valid and
+ 
+
+ align:start position:0%
+alternate form that's equally valid and
+I'll call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B1 cine
+
+ align:start position:0%
+B1 cine
+ 
+
+ align:start position:0%
+B1 cine
+KX plus a
+
+ align:start position:0%
+KX plus a
+ 
+
+ align:start position:0%
+KX plus a
+B2 sin
+
+ align:start position:0%
+B2 sin
+ 
+
+ align:start position:0%
+B2 sin
+KX and I can relate that to you know e
+
+ align:start position:0%
+KX and I can relate that to you know e
+ 
+
+ align:start position:0%
+KX and I can relate that to you know e
+to the IX b e to the IX by real and
+
+ align:start position:0%
+to the IX b e to the IX by real and
+ 
+
+ align:start position:0%
+to the IX b e to the IX by real and
+imaginary parts and so forth this is a
+
+ align:start position:0%
+imaginary parts and so forth this is a
+ 
+
+ align:start position:0%
+imaginary parts and so forth this is a
+real part I'm saying in general could
+
+ align:start position:0%
+real part I'm saying in general could
+ 
+
+ align:start position:0%
+real part I'm saying in general could
+have a cosine part and also a sign part
+
+ align:start position:0%
+have a cosine part and also a sign part
+ 
+
+ align:start position:0%
+have a cosine part and also a sign part
+but now I know my boundary conditions
+
+ align:start position:0%
+but now I know my boundary conditions
+ 
+
+ align:start position:0%
+but now I know my boundary conditions
+are w at x equals 0 W of 0 is what
+
+ align:start position:0%
+are w at x equals 0 W of 0 is what
+ 
+
+ align:start position:0%
+are w at x equals 0 W of 0 is what
+what's the displacement of x equals
+
+ align:start position:0%
+what's the displacement of x equals
+ 
+
+ align:start position:0%
+what's the displacement of x equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+H zero that's the pin that's the end
+
+ align:start position:0%
+H zero that's the pin that's the end
+ 
+
+ align:start position:0%
+H zero that's the pin that's the end
+where it's fixed at and this is a we're
+
+ align:start position:0%
+where it's fixed at and this is a we're
+ 
+
+ align:start position:0%
+where it's fixed at and this is a we're
+started out here with a second order
+
+ align:start position:0%
+started out here with a second order
+ 
+
+ align:start position:0%
+started out here with a second order
+partial differential equation and a
+
+ align:start position:0%
+partial differential equation and a
+ 
+
+ align:start position:0%
+partial differential equation and a
+second order equation requires two
+
+ align:start position:0%
+second order equation requires two
+ 
+
+ align:start position:0%
+second order equation requires two
+boundary conditions a fourth order
+
+ align:start position:0%
+boundary conditions a fourth order
+ 
+
+ align:start position:0%
+boundary conditions a fourth order
+equation for the beam will require four
+
+ align:start position:0%
+equation for the beam will require four
+ 
+
+ align:start position:0%
+equation for the beam will require four
+boundary conditions we only have to find
+
+ align:start position:0%
+boundary conditions we only have to find
+ 
+
+ align:start position:0%
+boundary conditions we only have to find
+two one of them is it has no motion on
+
+ align:start position:0%
+two one of them is it has no motion on
+ 
+
+ align:start position:0%
+two one of them is it has no motion on
+the left so you plug in uh zero for x
+
+ align:start position:0%
+the left so you plug in uh zero for x
+ 
+
+ align:start position:0%
+the left so you plug in uh zero for x
+cosine of 0 is One S of 0 is zero so we
+
+ align:start position:0%
+cosine of 0 is One S of 0 is zero so we
+ 
+
+ align:start position:0%
+cosine of 0 is One S of 0 is zero so we
+find out that this is
+
+ align:start position:0%
+find out that this is
+ 
+
+ align:start position:0%
+find out that this is
+B1 * 1 but it has to be zero as the
+
+ align:start position:0%
+B1 * 1 but it has to be zero as the
+ 
+
+ align:start position:0%
+B1 * 1 but it has to be zero as the
+boundary condition so that implies
+
+ align:start position:0%
+boundary condition so that implies
+ 
+
+ align:start position:0%
+boundary condition so that implies
+B1 is zero there's no cosiness in this
+
+ align:start position:0%
+B1 is zero there's no cosiness in this
+ 
+
+ align:start position:0%
+B1 is zero there's no cosiness in this
+answer and W at L is zero and so that
+
+ align:start position:0%
+answer and W at L is zero and so that
+ 
+
+ align:start position:0%
+answer and W at L is zero and so that
+says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B2 sine k l equals z and that's true
+
+ align:start position:0%
+B2 sine k l equals z and that's true
+ 
+
+ align:start position:0%
+B2 sine k l equals z and that's true
+that's only true
+
+ align:start position:0%
+that's only true
+ 
+
+ align:start position:0%
+that's only true
+if k l equals n pi
+
+ align:start position:0%
+if k l equals n pi
+ 
+
+ align:start position:0%
+if k l equals n pi
+so now I found out that there's just for
+
+ align:start position:0%
+so now I found out that there's just for
+ 
+
+ align:start position:0%
+so now I found out that there's just for
+for vibration of a finite length string
+
+ align:start position:0%
+for vibration of a finite length string
+ 
+
+ align:start position:0%
+for vibration of a finite length string
+there's only particular values of K that
+
+ align:start position:0%
+there's only particular values of K that
+ 
+
+ align:start position:0%
+there's only particular values of K that
+work so that says that there
+
+ align:start position:0%
+work so that says that there
+ 
+
+ align:start position:0%
+work so that says that there
+are special values of K which I'll call
+
+ align:start position:0%
+are special values of K which I'll call
+ 
+
+ align:start position:0%
+are special values of K which I'll call
+K subn which are equal to n Pi /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and from that we now have our mode
+
+ align:start position:0%
+and from that we now have our mode
+ 
+
+ align:start position:0%
+and from that we now have our mode
+shapes because we can say ah well
+
+ align:start position:0%
+shapes because we can say ah well
+ 
+
+ align:start position:0%
+shapes because we can say ah well
+there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+special solution for this W of X that
+
+ align:start position:0%
+special solution for this W of X that
+ 
+
+ align:start position:0%
+special solution for this W of X that
+applies only when we satisfy the
+
+ align:start position:0%
+applies only when we satisfy the
+ 
+
+ align:start position:0%
+applies only when we satisfy the
+boundary conditions and that will be
+
+ align:start position:0%
+boundary conditions and that will be
+ 
+
+ align:start position:0%
+boundary conditions and that will be
+some undetermined
+
+ align:start position:0%
+some undetermined
+ 
+
+ align:start position:0%
+some undetermined
+amplitude B2 came from the S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those are our mode
+
+ align:start position:0%
+and those are our mode
+ 
+
+ align:start position:0%
+and those are our mode
+shapes and now the natural frequencies
+
+ align:start position:0%
+shapes and now the natural frequencies
+ 
+
+ align:start position:0%
+shapes and now the natural frequencies
+once you know mode shapes natural
+
+ align:start position:0%
+once you know mode shapes natural
+ 
+
+ align:start position:0%
+once you know mode shapes natural
+frequencies actually become pretty
+
+ align:start position:0%
+frequencies actually become pretty
+ 
+
+ align:start position:0%
+frequencies actually become pretty
+trivial to find in this case if we know
+
+ align:start position:0%
+trivial to find in this case if we know
+ 
+
+ align:start position:0%
+trivial to find in this case if we know
+that's the uh uh mode shape
+
+ align:start position:0%
+that's the uh uh mode shape
+ 
+
+ align:start position:0%
+that's the uh uh mode shape
+then how do we get the natural
+
+ align:start position:0%
+then how do we get the natural
+ 
+
+ align:start position:0%
+then how do we get the natural
+frequencies well we know that what's the
+
+ align:start position:0%
+frequencies well we know that what's the
+ 
+
+ align:start position:0%
+frequencies well we know that what's the
+definition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+therefore spe the particular values of K
+
+ align:start position:0%
+therefore spe the particular values of K
+ 
+
+ align:start position:0%
+therefore spe the particular values of K
+that's that were allowed Solutions here
+
+ align:start position:0%
+that's that were allowed Solutions here
+ 
+
+ align:start position:0%
+that's that were allowed Solutions here
+are going to be correspond to particular
+
+ align:start position:0%
+are going to be correspond to particular
+ 
+
+ align:start position:0%
+are going to be correspond to particular
+values of Omega
+
+ align:start position:0%
+values of Omega
+ 
+
+ align:start position:0%
+values of Omega
+n and therefore Omega n 2 is just k n^ 2
+
+ align:start position:0%
+n and therefore Omega n 2 is just k n^ 2
+ 
+
+ align:start position:0%
+n and therefore Omega n 2 is just k n^ 2
+c^
+
+ align:start position:0%
+c^
+ 
+
+ align:start position:0%
+c^
+2 and
+
+ align:start position:0%
+2 and
+ 
+
+ align:start position:0%
+2 and
+that's n pi over
+
+ align:start position:0%
+that's n pi over
+ 
+
+ align:start position:0%
+that's n pi over
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+squared T over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M that's Omega n
+
+ align:start position:0%
+M that's Omega n
+ 
+
+ align:start position:0%
+M that's Omega n
+SAR so the natural frequencies of a
+
+ align:start position:0%
+SAR so the natural frequencies of a
+ 
+
+ align:start position:0%
+SAR so the natural frequencies of a
+string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are n pi over lunk t/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and then in this is in radians per
+
+ align:start position:0%
+n and then in this is in radians per
+ 
+
+ align:start position:0%
+n and then in this is in radians per
+second and we like I like work in hertz
+
+ align:start position:0%
+second and we like I like work in hertz
+ 
+
+ align:start position:0%
+second and we like I like work in hertz
+sometimes so the natural frequencies in
+
+ align:start position:0%
+sometimes so the natural frequencies in
+ 
+
+ align:start position:0%
+sometimes so the natural frequencies in
+hertz Omega n over 2
+
+ align:start position:0%
+hertz Omega n over 2
+ 
+
+ align:start position:0%
+hertz Omega n over 2
+pi and that becomes
+
+ align:start position:0%
+pi and that becomes
+ 
+
+ align:start position:0%
+pi and that becomes
+n/ 2
+
+ align:start position:0%
+n/ 2
+ 
+
+ align:start position:0%
+n/ 2
+lunk T over
+
+ align:start position:0%
+lunk T over
+ 
+
+ align:start position:0%
+lunk T over
+M so the the first natural frequency
+
+ align:start position:0%
+M so the the first natural frequency
+ 
+
+ align:start position:0%
+M so the the first natural frequency
+fub1 is 1 over 2
+
+ align:start position:0%
+fub1 is 1 over 2
+ 
+
+ align:start position:0%
+fub1 is 1 over 2
+lunk T over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+now that let's go back let's draw what's
+
+ align:start position:0%
+now that let's go back let's draw what's
+ 
+
+ align:start position:0%
+now that let's go back let's draw what's
+the mode shape for the first mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's half a sine
+
+ align:start position:0%
+well it's half a sine
+ 
+
+ align:start position:0%
+well it's half a sine
+wave vibrates like that it's full
+
+ align:start position:0%
+wave vibrates like that it's full
+ 
+
+ align:start position:0%
+wave vibrates like that it's full
+wavelength it didn't leave myself quite
+
+ align:start position:0%
+wavelength it didn't leave myself quite
+ 
+
+ align:start position:0%
+wavelength it didn't leave myself quite
+enough room that's half a wavelength
+
+ align:start position:0%
+enough room that's half a wavelength
+ 
+
+ align:start position:0%
+enough room that's half a wavelength
+right of a sine wave so the full
+
+ align:start position:0%
+right of a sine wave so the full
+ 
+
+ align:start position:0%
+right of a sine wave so the full
+wavelength would be like that this is of
+
+ align:start position:0%
+wavelength would be like that this is of
+ 
+
+ align:start position:0%
+wavelength would be like that this is of
+length
+
+ align:start position:0%
+length
+ 
+
+ align:start position:0%
+length
+L and so is this piece over here so the
+
+ align:start position:0%
+L and so is this piece over here so the
+ 
+
+ align:start position:0%
+L and so is this piece over here so the
+length Lambda is 2 L for this particular
+
+ align:start position:0%
+length Lambda is 2 L for this particular
+ 
+
+ align:start position:0%
+length Lambda is 2 L for this particular
+problem how
+
+ align:start position:0%
+problem how
+ 
+
+ align:start position:0%
+problem how
+long let's see how do I want to pose
+
+ align:start position:0%
+long let's see how do I want to pose
+ 
+
+ align:start position:0%
+long let's see how do I want to pose
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question so how long does it
+
+ align:start position:0%
+question so how long does it
+ 
+
+ align:start position:0%
+question so how long does it
+take for a wave or disturbance to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+travel
+
+ align:start position:0%
+travel
+ 
+
+ align:start position:0%
+travel
+the length of the this finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string how long does it take to go down
+
+ align:start position:0%
+string how long does it take to go down
+ 
+
+ align:start position:0%
+string how long does it take to go down
+there and
+
+ align:start position:0%
+there and
+ 
+
+ align:start position:0%
+there and
+back how would you calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that distance equals rate time time
+
+ align:start position:0%
+that distance equals rate time time
+ 
+
+ align:start position:0%
+that distance equals rate time time
+what's the what's the distance 2 L
+
+ align:start position:0%
+what's the what's the distance 2 L
+ 
+
+ align:start position:0%
+what's the what's the distance 2 L
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+speed C so the length of time ought to
+
+ align:start position:0%
+speed C so the length of time ought to
+ 
+
+ align:start position:0%
+speed C so the length of time ought to
+be 2 L over C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+required
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 L / T over M but fub1 is T over m / 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L so the period so there is a direct
+
+ align:start position:0%
+L so the period so there is a direct
+ 
+
+ align:start position:0%
+L so the period so there is a direct
+connection
+
+ align:start position:0%
+connection
+ 
+
+ align:start position:0%
+connection
+between propagation speed
+
+ align:start position:0%
+between propagation speed
+ 
+
+ align:start position:0%
+between propagation speed
+frequencies wavelengths they're very
+
+ align:start position:0%
+frequencies wavelengths they're very
+ 
+
+ align:start position:0%
+frequencies wavelengths they're very
+closely related so the natural frequency
+
+ align:start position:0%
+closely related so the natural frequency
+ 
+
+ align:start position:0%
+closely related so the natural frequency
+of the first
+
+ align:start position:0%
+of the first
+ 
+
+ align:start position:0%
+of the first
+mode of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string that frequency is exactly one
+
+ align:start position:0%
+string that frequency is exactly one
+ 
+
+ align:start position:0%
+string that frequency is exactly one
+over the length of time it takes for a
+
+ align:start position:0%
+over the length of time it takes for a
+ 
+
+ align:start position:0%
+over the length of time it takes for a
+disturbance to travel down and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so with that depth of understanding
+
+ align:start position:0%
+okay so with that depth of understanding
+ 
+
+ align:start position:0%
+okay so with that depth of understanding
+of how
+
+ align:start position:0%
+of how
+ 
+
+ align:start position:0%
+of how
+um the wave equation behaves you
+
+ align:start position:0%
+um the wave equation behaves you
+ 
+
+ align:start position:0%
+um the wave equation behaves you
+can you can guess the
+
+ align:start position:0%
+can you can guess the
+ 
+
+ align:start position:0%
+can you can guess the
+behavior of lots of other things that
+
+ align:start position:0%
+behavior of lots of other things that
+ 
+
+ align:start position:0%
+behavior of lots of other things that
+behave like that like my rod here I'll
+
+ align:start position:0%
+behave like that like my rod here I'll
+ 
+
+ align:start position:0%
+behave like that like my rod here I'll
+do a little demo with it in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second so for example Le so this the
+
+ align:start position:0%
+second so for example Le so this the
+ 
+
+ align:start position:0%
+second so for example Le so this the
+longitudinal vibration stress waves
+
+ align:start position:0%
+longitudinal vibration stress waves
+ 
+
+ align:start position:0%
+longitudinal vibration stress waves
+running up and down this thing obey the
+
+ align:start position:0%
+running up and down this thing obey the
+ 
+
+ align:start position:0%
+running up and down this thing obey the
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+equation so if I
+
+ align:start position:0%
+equation so if I
+ 
+
+ align:start position:0%
+equation so if I
+take this thing and drop it on the floor
+
+ align:start position:0%
+take this thing and drop it on the floor
+ 
+
+ align:start position:0%
+take this thing and drop it on the floor
+it'll bounce off the floor how long does
+
+ align:start position:0%
+it'll bounce off the floor how long does
+ 
+
+ align:start position:0%
+it'll bounce off the floor how long does
+it take to bounce off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+floor so what do you think actually what
+
+ align:start position:0%
+floor so what do you think actually what
+ 
+
+ align:start position:0%
+floor so what do you think actually what
+physics has to have you know what's
+
+ align:start position:0%
+physics has to have you know what's
+ 
+
+ align:start position:0%
+physics has to have you know what's
+required to make this thing thing bounce
+
+ align:start position:0%
+required to make this thing thing bounce
+ 
+
+ align:start position:0%
+required to make this thing thing bounce
+off the floor so let we're going to
+
+ align:start position:0%
+off the floor so let we're going to
+ 
+
+ align:start position:0%
+off the floor so let we're going to
+consider the floor infinitely rigid it
+
+ align:start position:0%
+consider the floor infinitely rigid it
+ 
+
+ align:start position:0%
+consider the floor infinitely rigid it
+hits the floor it actually stays there
+
+ align:start position:0%
+hits the floor it actually stays there
+ 
+
+ align:start position:0%
+hits the floor it actually stays there
+for some finite length of time and then
+
+ align:start position:0%
+for some finite length of time and then
+ 
+
+ align:start position:0%
+for some finite length of time and then
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+leaves so physically when I was holding
+
+ align:start position:0%
+leaves so physically when I was holding
+ 
+
+ align:start position:0%
+leaves so physically when I was holding
+up my string if I smack the end what
+
+ align:start position:0%
+up my string if I smack the end what
+ 
+
+ align:start position:0%
+up my string if I smack the end what
+happened a pulse took off ran down the
+
+ align:start position:0%
+happened a pulse took off ran down the
+ 
+
+ align:start position:0%
+happened a pulse took off ran down the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+reflected came
+
+ align:start position:0%
+reflected came
+ 
+
+ align:start position:0%
+reflected came
+back and that was one round trip what
+
+ align:start position:0%
+back and that was one round trip what
+ 
+
+ align:start position:0%
+back and that was one round trip what
+you supposed happens
+
+ align:start position:0%
+you supposed happens
+ 
+
+ align:start position:0%
+you supposed happens
+here I put a pulse into the end
+
+ align:start position:0%
+here I put a pulse into the end
+ 
+
+ align:start position:0%
+here I put a pulse into the end
+is it tension or compression The Strain
+
+ align:start position:0%
+is it tension or compression The Strain
+ 
+
+ align:start position:0%
+is it tension or compression The Strain
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+felt compression so a little compression
+
+ align:start position:0%
+felt compression so a little compression
+ 
+
+ align:start position:0%
+felt compression so a little compression
+pulse is put into the end that
+
+ align:start position:0%
+pulse is put into the end that
+ 
+
+ align:start position:0%
+pulse is put into the end that
+compression pulse
+
+ align:start position:0%
+compression pulse
+ 
+
+ align:start position:0%
+compression pulse
+then when it first hits the compression
+
+ align:start position:0%
+then when it first hits the compression
+ 
+
+ align:start position:0%
+then when it first hits the compression
+and the speed of propagation is finite
+
+ align:start position:0%
+and the speed of propagation is finite
+ 
+
+ align:start position:0%
+and the speed of propagation is finite
+so that compression wave starts
+
+ align:start position:0%
+so that compression wave starts
+ 
+
+ align:start position:0%
+so that compression wave starts
+traveling up here behind the compression
+
+ align:start position:0%
+traveling up here behind the compression
+ 
+
+ align:start position:0%
+traveling up here behind the compression
+wave this Rod has come to a
+
+ align:start position:0%
+wave this Rod has come to a
+ 
+
+ align:start position:0%
+wave this Rod has come to a
+stop in front of the compression wave
+
+ align:start position:0%
+stop in front of the compression wave
+ 
+
+ align:start position:0%
+stop in front of the compression wave
+the rod doesn't know it hit the ground
+
+ align:start position:0%
+the rod doesn't know it hit the ground
+ 
+
+ align:start position:0%
+the rod doesn't know it hit the ground
+yet it's still moving down
+
+ align:start position:0%
+yet it's still moving down
+ 
+
+ align:start position:0%
+yet it's still moving down
+so the that compression wave travels up
+
+ align:start position:0%
+so the that compression wave travels up
+ 
+
+ align:start position:0%
+so the that compression wave travels up
+bring and it is decelerating each Little
+
+ align:start position:0%
+bring and it is decelerating each Little
+ 
+
+ align:start position:0%
+bring and it is decelerating each Little
+slice of mass as it passes through it
+
+ align:start position:0%
+slice of mass as it passes through it
+ 
+
+ align:start position:0%
+slice of mass as it passes through it
+brings it to a stop and so the
+
+ align:start position:0%
+brings it to a stop and so the
+ 
+
+ align:start position:0%
+brings it to a stop and so the
+compression red we reaches the top end
+
+ align:start position:0%
+compression red we reaches the top end
+ 
+
+ align:start position:0%
+compression red we reaches the top end
+the cylinder has come to a
+
+ align:start position:0%
+the cylinder has come to a
+ 
+
+ align:start position:0%
+the cylinder has come to a
+stop the end is free it can't take any
+
+ align:start position:0%
+stop the end is free it can't take any
+ 
+
+ align:start position:0%
+stop the end is free it can't take any
+strain so an equal and opposite tension
+
+ align:start position:0%
+strain so an equal and opposite tension
+ 
+
+ align:start position:0%
+strain so an equal and opposite tension
+wave has to start to make it the sum of
+
+ align:start position:0%
+wave has to start to make it the sum of
+ 
+
+ align:start position:0%
+wave has to start to make it the sum of
+them go to zero at the end the boundary
+
+ align:start position:0%
+them go to zero at the end the boundary
+ 
+
+ align:start position:0%
+them go to zero at the end the boundary
+condition of the end is no strin so it
+
+ align:start position:0%
+condition of the end is no strin so it
+ 
+
+ align:start position:0%
+condition of the end is no strin so it
+reflects as a tension wave now you have
+
+ align:start position:0%
+reflects as a tension wave now you have
+ 
+
+ align:start position:0%
+reflects as a tension wave now you have
+a tension wave going down and what it
+
+ align:start position:0%
+a tension wave going down and what it
+ 
+
+ align:start position:0%
+a tension wave going down and what it
+does is it accelerates every atom as it
+
+ align:start position:0%
+does is it accelerates every atom as it
+ 
+
+ align:start position:0%
+does is it accelerates every atom as it
+goes by as it goes past it so everything
+
+ align:start position:0%
+goes by as it goes past it so everything
+ 
+
+ align:start position:0%
+goes by as it goes past it so everything
+is stopped now now it starts down and
+
+ align:start position:0%
+is stopped now now it starts down and
+ 
+
+ align:start position:0%
+is stopped now now it starts down and
+this PE the part this thing starts
+
+ align:start position:0%
+this PE the part this thing starts
+ 
+
+ align:start position:0%
+this PE the part this thing starts
+rebounding from the top rebounds from
+
+ align:start position:0%
+rebounding from the top rebounds from
+ 
+
+ align:start position:0%
+rebounding from the top rebounds from
+the floor before the bottom does the top
+
+ align:start position:0%
+the floor before the bottom does the top
+ 
+
+ align:start position:0%
+the floor before the bottom does the top
+starts going up all of it more and more
+
+ align:start position:0%
+starts going up all of it more and more
+ 
+
+ align:start position:0%
+starts going up all of it more and more
+goes up and one hits the bottom the
+
+ align:start position:0%
+goes up and one hits the bottom the
+ 
+
+ align:start position:0%
+goes up and one hits the bottom the
+tension wave hits the floor it jumps off
+
+ align:start position:0%
+tension wave hits the floor it jumps off
+ 
+
+ align:start position:0%
+tension wave hits the floor it jumps off
+so how long does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and what do you guess the natural
+
+ align:start position:0%
+right and what do you guess the natural
+ 
+
+ align:start position:0%
+right and what do you guess the natural
+frequency of a free
+
+ align:start position:0%
+frequency of a free
+ 
+
+ align:start position:0%
+frequency of a free
+free Rod is now it has a funny mode
+
+ align:start position:0%
+free Rod is now it has a funny mode
+ 
+
+ align:start position:0%
+free Rod is now it has a funny mode
+shape the mode shape is not half a sign
+
+ align:start position:0%
+shape the mode shape is not half a sign
+ 
+
+ align:start position:0%
+shape the mode shape is not half a sign
+wave like this the the displacement of
+
+ align:start position:0%
+wave like this the the displacement of
+ 
+
+ align:start position:0%
+wave like this the the displacement of
+the rod it has free ends the ends are
+
+ align:start position:0%
+the rod it has free ends the ends are
+ 
+
+ align:start position:0%
+the rod it has free ends the ends are
+moving a
+
+ align:start position:0%
+moving a
+ 
+
+ align:start position:0%
+moving a
+lot but I give you a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clue I can hold it in the center and not
+
+ align:start position:0%
+clue I can hold it in the center and not
+ 
+
+ align:start position:0%
+clue I can hold it in the center and not
+damp it
+
+ align:start position:0%
+damp it
+ 
+
+ align:start position:0%
+damp it
+what do you think the mode shape looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like half a w link long ends are
+
+ align:start position:0%
+like half a w link long ends are
+ 
+
+ align:start position:0%
+like half a w link long ends are
+free cosine maximum displacement goes to
+
+ align:start position:0%
+free cosine maximum displacement goes to
+ 
+
+ align:start position:0%
+free cosine maximum displacement goes to
+zero maximum negative displacement so
+
+ align:start position:0%
+zero maximum negative displacement so
+ 
+
+ align:start position:0%
+zero maximum negative displacement so
+it's half a wavelength long but it's a
+
+ align:start position:0%
+it's half a wavelength long but it's a
+ 
+
+ align:start position:0%
+it's half a wavelength long but it's a
+cosine half a
+
+ align:start position:0%
+cosine half a
+ 
+
+ align:start position:0%
+cosine half a
+wavelength and the full wavelength is 2
+
+ align:start position:0%
+wavelength and the full wavelength is 2
+ 
+
+ align:start position:0%
+wavelength and the full wavelength is 2
+L all
+
+ align:start position:0%
+L all
+ 
+
+ align:start position:0%
+L all
+right so this has mode shapes the mode
+
+ align:start position:0%
+right so this has mode shapes the mode
+ 
+
+ align:start position:0%
+right so this has mode shapes the mode
+shapes I've applied different boundary
+
+ align:start position:0%
+shapes I've applied different boundary
+ 
+
+ align:start position:0%
+shapes I've applied different boundary
+conditions these are free free boundary
+
+ align:start position:0%
+conditions these are free free boundary
+ 
+
+ align:start position:0%
+conditions these are free free boundary
+conditions the mode shapes are coine n
+
+ align:start position:0%
+conditions the mode shapes are coine n
+ 
+
+ align:start position:0%
+conditions the mode shapes are coine n
+pi x over L but they have to obey a
+
+ align:start position:0%
+pi x over L but they have to obey a
+ 
+
+ align:start position:0%
+pi x over L but they have to obey a
+certain another law that we know about
+
+ align:start position:0%
+certain another law that we know about
+ 
+
+ align:start position:0%
+certain another law that we know about
+conservation of momentum if I'm I'm
+
+ align:start position:0%
+conservation of momentum if I'm I'm
+ 
+
+ align:start position:0%
+conservation of momentum if I'm I'm
+because I've got gravity to deal with I
+
+ align:start position:0%
+because I've got gravity to deal with I
+ 
+
+ align:start position:0%
+because I've got gravity to deal with I
+have to hang on to this thing but I've
+
+ align:start position:0%
+have to hang on to this thing but I've
+ 
+
+ align:start position:0%
+have to hang on to this thing but I've
+picked a place to hang on to it that
+
+ align:start position:0%
+picked a place to hang on to it that
+ 
+
+ align:start position:0%
+picked a place to hang on to it that
+you've you can hear it I am not
+
+ align:start position:0%
+you've you can hear it I am not
+ 
+
+ align:start position:0%
+you've you can hear it I am not
+affecting the motion there's no motion
+
+ align:start position:0%
+affecting the motion there's no motion
+ 
+
+ align:start position:0%
+affecting the motion there's no motion
+where I'm holding it so if I were out in
+
+ align:start position:0%
+where I'm holding it so if I were out in
+ 
+
+ align:start position:0%
+where I'm holding it so if I were out in
+space I could do
+
+ align:start position:0%
+space I could do
+ 
+
+ align:start position:0%
+space I could do
+this and just let it hang there in space
+
+ align:start position:0%
+this and just let it hang there in space
+ 
+
+ align:start position:0%
+this and just let it hang there in space
+right and it would sit there and ring
+
+ align:start position:0%
+right and it would sit there and ring
+ 
+
+ align:start position:0%
+right and it would sit there and ring
+what's is happening to the center of
+
+ align:start position:0%
+what's is happening to the center of
+ 
+
+ align:start position:0%
+what's is happening to the center of
+mass of this system as it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrates station stationary so half of
+
+ align:start position:0%
+vibrates station stationary so half of
+ 
+
+ align:start position:0%
+vibrates station stationary so half of
+the mass of this thing's got to be
+
+ align:start position:0%
+the mass of this thing's got to be
+ 
+
+ align:start position:0%
+the mass of this thing's got to be
+moving that way and half of the mass has
+
+ align:start position:0%
+moving that way and half of the mass has
+ 
+
+ align:start position:0%
+moving that way and half of the mass has
+to be moving that way so that the total
+
+ align:start position:0%
+to be moving that way so that the total
+ 
+
+ align:start position:0%
+to be moving that way so that the total
+Center of mass doesn't move well cosine
+
+ align:start position:0%
+Center of mass doesn't move well cosine
+ 
+
+ align:start position:0%
+Center of mass doesn't move well cosine
+mode shape positive here negative there
+
+ align:start position:0%
+mode shape positive here negative there
+ 
+
+ align:start position:0%
+mode shape positive here negative there
+perfectly symmetric Center Mass doesn't
+
+ align:start position:0%
+perfectly symmetric Center Mass doesn't
+ 
+
+ align:start position:0%
+perfectly symmetric Center Mass doesn't
+move so there's all sorts of neat little
+
+ align:start position:0%
+move so there's all sorts of neat little
+ 
+
+ align:start position:0%
+move so there's all sorts of neat little
+problems that you can solve uh to just
+
+ align:start position:0%
+problems that you can solve uh to just
+ 
+
+ align:start position:0%
+problems that you can solve uh to just
+by knowing the wave equation and
+
+ align:start position:0%
+by knowing the wave equation and
+ 
+
+ align:start position:0%
+by knowing the wave equation and
+figuring out boundary conditions okay
+
+ align:start position:0%
+figuring out boundary conditions okay
+ 
+
+ align:start position:0%
+figuring out boundary conditions okay
+how you know how many of you stand in
+
+ align:start position:0%
+how you know how many of you stand in
+ 
+
+ align:start position:0%
+how you know how many of you stand in
+the shower and hum and sing and you know
+
+ align:start position:0%
+the shower and hum and sing and you know
+ 
+
+ align:start position:0%
+the shower and hum and sing and you know
+and every now and then every now and
+
+ align:start position:0%
+and every now and then every now and
+ 
+
+ align:start position:0%
+and every now and then every now and
+then you hit a note man you just sound
+
+ align:start position:0%
+then you hit a note man you just sound
+ 
+
+ align:start position:0%
+then you hit a note man you just sound
+great right you know just all this
+
+ align:start position:0%
+great right you know just all this
+ 
+
+ align:start position:0%
+great right you know just all this
+reverberation how many have you done
+
+ align:start position:0%
+reverberation how many have you done
+ 
+
+ align:start position:0%
+reverberation how many have you done
+that okay right what's going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on you've hid a that somebody said
+
+ align:start position:0%
+on you've hid a that somebody said
+ 
+
+ align:start position:0%
+on you've hid a that somebody said
+natural frequency of
+
+ align:start position:0%
+natural frequency of
+ 
+
+ align:start position:0%
+natural frequency of
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh you've hit the N you the you have
+
+ align:start position:0%
+huh you've hit the N you the you have
+ 
+
+ align:start position:0%
+huh you've hit the N you the you have
+hit the natural frequency of the shower
+
+ align:start position:0%
+hit the natural frequency of the shower
+ 
+
+ align:start position:0%
+hit the natural frequency of the shower
+stall itself you know if the shower
+
+ align:start position:0%
+stall itself you know if the shower
+ 
+
+ align:start position:0%
+stall itself you know if the shower
+stall is a meter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+across pressure waves and you plot
+
+ align:start position:0%
+across pressure waves and you plot
+ 
+
+ align:start position:0%
+across pressure waves and you plot
+pressure inside of the uh shower the
+
+ align:start position:0%
+pressure inside of the uh shower the
+ 
+
+ align:start position:0%
+pressure inside of the uh shower the
+lowest mode if you plotting pressure
+
+ align:start position:0%
+lowest mode if you plotting pressure
+ 
+
+ align:start position:0%
+lowest mode if you plotting pressure
+well let's plot actually molecular
+
+ align:start position:0%
+well let's plot actually molecular
+ 
+
+ align:start position:0%
+well let's plot actually molecular
+movement what's the boundary condition
+
+ align:start position:0%
+movement what's the boundary condition
+ 
+
+ align:start position:0%
+movement what's the boundary condition
+at the wall the molecules at the
+
+ align:start position:0%
+at the wall the molecules at the
+ 
+
+ align:start position:0%
+at the wall the molecules at the
+wall can't move right zero so the
+
+ align:start position:0%
+wall can't move right zero so the
+ 
+
+ align:start position:0%
+wall can't move right zero so the
+molecular motion at resonance in the
+
+ align:start position:0%
+molecular motion at resonance in the
+ 
+
+ align:start position:0%
+molecular motion at resonance in the
+shower stall the molecules the pressure
+
+ align:start position:0%
+shower stall the molecules the pressure
+ 
+
+ align:start position:0%
+shower stall the molecules the pressure
+is making a move back and forth looks
+
+ align:start position:0%
+is making a move back and forth looks
+ 
+
+ align:start position:0%
+is making a move back and forth looks
+like back to the string again this is L
+
+ align:start position:0%
+like back to the string again this is L
+ 
+
+ align:start position:0%
+like back to the string again this is L
+the first natural frequency of sound
+
+ align:start position:0%
+the first natural frequency of sound
+ 
+
+ align:start position:0%
+the first natural frequency of sound
+waves bouncing off the walls in the
+
+ align:start position:0%
+waves bouncing off the walls in the
+ 
+
+ align:start position:0%
+waves bouncing off the walls in the
+stall is uh
+
+ align:start position:0%
+stall is uh
+ 
+
+ align:start position:0%
+stall is uh
+one over 2
+
+ align:start position:0%
+one over 2
+ 
+
+ align:start position:0%
+one over 2
+L uh root time C whatever C is and in C
+
+ align:start position:0%
+L uh root time C whatever C is and in C
+ 
+
+ align:start position:0%
+L uh root time C whatever C is and in C
+is the speed of sound in air which is
+
+ align:start position:0%
+is the speed of sound in air which is
+ 
+
+ align:start position:0%
+is the speed of sound in air which is
+340 m/s so 340 m/s divided 2 L so if
+
+ align:start position:0%
+340 m/s so 340 m/s divided 2 L so if
+ 
+
+ align:start position:0%
+340 m/s so 340 m/s divided 2 L so if
+it's 1 meter across here it's 340
+
+ align:start position:0%
+it's 1 meter across here it's 340
+ 
+
+ align:start position:0%
+it's 1 meter across here it's 340
+divided by 2 170 Hertz so that first
+
+ align:start position:0%
+divided by 2 170 Hertz so that first
+ 
+
+ align:start position:0%
+divided by 2 170 Hertz so that first
+note you can hit in the one meter across
+
+ align:start position:0%
+note you can hit in the one meter across
+ 
+
+ align:start position:0%
+note you can hit in the one meter across
+shower sty is about 170 htz pretty low
+
+ align:start position:0%
+shower sty is about 170 htz pretty low
+ 
+
+ align:start position:0%
+shower sty is about 170 htz pretty low
+okay but you can hit second mode be
+
+ align:start position:0%
+okay but you can hit second mode be
+ 
+
+ align:start position:0%
+okay but you can hit second mode be
+twice that and so forth okay what about
+
+ align:start position:0%
+twice that and so forth okay what about
+ 
+
+ align:start position:0%
+twice that and so forth okay what about
+an organ
+
+ align:start position:0%
+an organ
+ 
+
+ align:start position:0%
+an organ
+pipe this is an organ pipe wood it's got
+
+ align:start position:0%
+pipe this is an organ pipe wood it's got
+ 
+
+ align:start position:0%
+pipe this is an organ pipe wood it's got
+a stopper to
+
+ align:start position:0%
+a stopper to
+ 
+
+ align:start position:0%
+a stopper to
+end actually let's do it without the
+
+ align:start position:0%
+end actually let's do it without the
+ 
+
+ align:start position:0%
+end actually let's do it without the
+stopper now it's an open Organ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pipe base a wave equation how would you
+
+ align:start position:0%
+Pipe base a wave equation how would you
+ 
+
+ align:start position:0%
+Pipe base a wave equation how would you
+model its boundary
+
+ align:start position:0%
+model its boundary
+ 
+
+ align:start position:0%
+model its boundary
+conditions so you can talk about maybe
+
+ align:start position:0%
+conditions so you can talk about maybe
+ 
+
+ align:start position:0%
+conditions so you can talk about maybe
+particle Mo molecular motion just like
+
+ align:start position:0%
+particle Mo molecular motion just like
+ 
+
+ align:start position:0%
+particle Mo molecular motion just like
+this is now again it's just sound waves
+
+ align:start position:0%
+this is now again it's just sound waves
+ 
+
+ align:start position:0%
+this is now again it's just sound waves
+so air particles and this is now
+
+ align:start position:0%
+so air particles and this is now
+ 
+
+ align:start position:0%
+so air particles and this is now
+longitudinal things are moving inside so
+
+ align:start position:0%
+longitudinal things are moving inside so
+ 
+
+ align:start position:0%
+longitudinal things are moving inside so
+what's the boundary condition at this
+
+ align:start position:0%
+what's the boundary condition at this
+ 
+
+ align:start position:0%
+what's the boundary condition at this
+end free or fixed free and here it's
+
+ align:start position:0%
+end free or fixed free and here it's
+ 
+
+ align:start position:0%
+end free or fixed free and here it's
+quite open so the boundary condition
+
+ align:start position:0%
+quite open so the boundary condition
+ 
+
+ align:start position:0%
+quite open so the boundary condition
+down here is free so for the molecular
+
+ align:start position:0%
+down here is free so for the molecular
+ 
+
+ align:start position:0%
+down here is free so for the molecular
+motion in the organ free free Organ Pipe
+
+ align:start position:0%
+motion in the organ free free Organ Pipe
+ 
+
+ align:start position:0%
+motion in the organ free free Organ Pipe
+the um you're going to get back to that
+
+ align:start position:0%
+the um you're going to get back to that
+ 
+
+ align:start position:0%
+the um you're going to get back to that
+half a wavelength cosine thing and if
+
+ align:start position:0%
+half a wavelength cosine thing and if
+ 
+
+ align:start position:0%
+half a wavelength cosine thing and if
+you wanted to plot pressure instead
+
+ align:start position:0%
+you wanted to plot pressure instead
+ 
+
+ align:start position:0%
+you wanted to plot pressure instead
+instead you can write the wave equation
+
+ align:start position:0%
+instead you can write the wave equation
+ 
+
+ align:start position:0%
+instead you can write the wave equation
+in terms of pressure pressure is is this
+
+ align:start position:0%
+in terms of pressure pressure is is this
+ 
+
+ align:start position:0%
+in terms of pressure pressure is is this
+pressure relief here and pressure relief
+
+ align:start position:0%
+pressure relief here and pressure relief
+ 
+
+ align:start position:0%
+pressure relief here and pressure relief
+there so in fact this if this is
+
+ align:start position:0%
+there so in fact this if this is
+ 
+
+ align:start position:0%
+there so in fact this if this is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+displacement of the
+
+ align:start position:0%
+displacement of the
+ 
+
+ align:start position:0%
+displacement of the
+molecules pressure would plot like that
+
+ align:start position:0%
+molecules pressure would plot like that
+ 
+
+ align:start position:0%
+molecules pressure would plot like that
+you'd have pressure what's called a
+
+ align:start position:0%
+you'd have pressure what's called a
+ 
+
+ align:start position:0%
+you'd have pressure what's called a
+pressure relief boundary condition but
+
+ align:start position:0%
+pressure relief boundary condition but
+ 
+
+ align:start position:0%
+pressure relief boundary condition but
+again it's a half wavelength long what
+
+ align:start position:0%
+again it's a half wavelength long what
+ 
+
+ align:start position:0%
+again it's a half wavelength long what
+do you think the first natural frequency
+
+ align:start position:0%
+do you think the first natural frequency
+ 
+
+ align:start position:0%
+do you think the first natural frequency
+of this Organ Pipe
+
+ align:start position:0%
+of this Organ Pipe
+ 
+
+ align:start position:0%
+of this Organ Pipe
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the the period would be 2 L over C
+
+ align:start position:0%
+well the the period would be 2 L over C
+ 
+
+ align:start position:0%
+well the the period would be 2 L over C
+the frequency would be C over 2L okay so
+
+ align:start position:0%
+the frequency would be C over 2L okay so
+ 
+
+ align:start position:0%
+the frequency would be C over 2L okay so
+the frequency for the Organ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pipe
+
+ align:start position:0%
+Pipe
+ 
+
+ align:start position:0%
+Pipe
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+and fub1 is C over 2 L now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check your intuition I'm going to close
+
+ align:start position:0%
+check your intuition I'm going to close
+ 
+
+ align:start position:0%
+check your intuition I'm going to close
+the end still an organ pipe is the
+
+ align:start position:0%
+the end still an organ pipe is the
+ 
+
+ align:start position:0%
+the end still an organ pipe is the
+frequency now going to be higher or
+
+ align:start position:0%
+frequency now going to be higher or
+ 
+
+ align:start position:0%
+frequency now going to be higher or
+lower take a vote how many think the
+
+ align:start position:0%
+lower take a vote how many think the
+ 
+
+ align:start position:0%
+lower take a vote how many think the
+frequency is going to go up raise your
+
+ align:start position:0%
+frequency is going to go up raise your
+ 
+
+ align:start position:0%
+frequency is going to go up raise your
+hands commit all right
+
+ align:start position:0%
+hands commit all right
+ 
+
+ align:start position:0%
+hands commit all right
+down and a lot of uncertainty all right
+
+ align:start position:0%
+down and a lot of uncertainty all right
+ 
+
+ align:start position:0%
+down and a lot of uncertainty all right
+let's do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+come I find that actually kind of
+
+ align:start position:0%
+come I find that actually kind of
+ 
+
+ align:start position:0%
+come I find that actually kind of
+counterintuitive until I learned this I
+
+ align:start position:0%
+counterintuitive until I learned this I
+ 
+
+ align:start position:0%
+counterintuitive until I learned this I
+would have guessed the opposite way
+
+ align:start position:0%
+would have guessed the opposite way
+ 
+
+ align:start position:0%
+would have guessed the opposite way
+what's going on with pressure in a
+
+ align:start position:0%
+what's going on with pressure in a
+ 
+
+ align:start position:0%
+what's going on with pressure in a
+closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pipe well here at the orifice where the
+
+ align:start position:0%
+pipe well here at the orifice where the
+ 
+
+ align:start position:0%
+pipe well here at the orifice where the
+sound is actually generated it's the
+
+ align:start position:0%
+sound is actually generated it's the
+ 
+
+ align:start position:0%
+sound is actually generated it's the
+pressure we wanted to plot pressure at
+
+ align:start position:0%
+pressure we wanted to plot pressure at
+ 
+
+ align:start position:0%
+pressure we wanted to plot pressure at
+the opening that's a pressure relief
+
+ align:start position:0%
+the opening that's a pressure relief
+ 
+
+ align:start position:0%
+the opening that's a pressure relief
+place so it's zero but at the other end
+
+ align:start position:0%
+place so it's zero but at the other end
+ 
+
+ align:start position:0%
+place so it's zero but at the other end
+where the stopper is it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum how many wavelengths is
+
+ align:start position:0%
+maximum how many wavelengths is
+ 
+
+ align:start position:0%
+maximum how many wavelengths is
+that a
+
+ align:start position:0%
+that a
+ 
+
+ align:start position:0%
+that a
+quarter and so in order the length of
+
+ align:start position:0%
+quarter and so in order the length of
+ 
+
+ align:start position:0%
+quarter and so in order the length of
+time it takes for the thing to go
+
+ align:start position:0%
+time it takes for the thing to go
+ 
+
+ align:start position:0%
+time it takes for the thing to go
+through one complete period is going to
+
+ align:start position:0%
+through one complete period is going to
+ 
+
+ align:start position:0%
+through one complete period is going to
+be 4 L over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+half the frequency of the open
+
+ align:start position:0%
+half the frequency of the open
+ 
+
+ align:start position:0%
+half the frequency of the open
+pipe okay so the way you could the wave
+
+ align:start position:0%
+pipe okay so the way you could the wave
+ 
+
+ align:start position:0%
+pipe okay so the way you could the wave
+ofcl is really quite powerful governs
+
+ align:start position:0%
+ofcl is really quite powerful governs
+ 
+
+ align:start position:0%
+ofcl is really quite powerful governs
+lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things I want so I've got 105 minutes
+
+ align:start position:0%
+things I want so I've got 105 minutes
+ 
+
+ align:start position:0%
+things I want so I've got 105 minutes
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+here I don't want you to go away
+
+ align:start position:0%
+here I don't want you to go away
+ 
+
+ align:start position:0%
+here I don't want you to go away
+thinking that the whole world behaves
+
+ align:start position:0%
+thinking that the whole world behaves
+ 
+
+ align:start position:0%
+thinking that the whole world behaves
+like the wave equation because there are
+
+ align:start position:0%
+like the wave equation because there are
+ 
+
+ align:start position:0%
+like the wave equation because there are
+some important important other physical
+
+ align:start position:0%
+some important important other physical
+ 
+
+ align:start position:0%
+some important important other physical
+systems that we care about and the most
+
+ align:start position:0%
+systems that we care about and the most
+ 
+
+ align:start position:0%
+systems that we care about and the most
+I'm going to show you just one and
+
+ align:start position:0%
+I'm going to show you just one and
+ 
+
+ align:start position:0%
+I'm going to show you just one and
+that's the uh
+
+ align:start position:0%
+that's the uh
+ 
+
+ align:start position:0%
+that's the uh
+vibration of the
+
+ align:start position:0%
+vibration of the
+ 
+
+ align:start position:0%
+vibration of the
+beam so
+
+ align:start position:0%
+beam so
+ 
+
+ align:start position:0%
+beam so
+here's can't lever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam whole table's
+
+ align:start position:0%
+beam whole table's
+ 
+
+ align:start position:0%
+beam whole table's
+moving and you can see it up on the
+
+ align:start position:0%
+moving and you can see it up on the
+ 
+
+ align:start position:0%
+moving and you can see it up on the
+screen okay so it's it's first mode
+
+ align:start position:0%
+screen okay so it's it's first mode
+ 
+
+ align:start position:0%
+screen okay so it's it's first mode
+vibration tip moves maximum kind of
+
+ align:start position:0%
+vibration tip moves maximum kind of
+ 
+
+ align:start position:0%
+vibration tip moves maximum kind of
+looks like uh like a quarter wavelength
+
+ align:start position:0%
+looks like uh like a quarter wavelength
+ 
+
+ align:start position:0%
+looks like uh like a quarter wavelength
+roughly is but not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so let's draw a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Canever and you know most of you have
+
+ align:start position:0%
+Canever and you know most of you have
+ 
+
+ align:start position:0%
+Canever and you know most of you have
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+to1 so if you put a load P out
+
+ align:start position:0%
+to1 so if you put a load P out
+ 
+
+ align:start position:0%
+to1 so if you put a load P out
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+bends goes through a displacement Delta
+
+ align:start position:0%
+bends goes through a displacement Delta
+ 
+
+ align:start position:0%
+bends goes through a displacement Delta
+so you know that Delta equal
+
+ align:start position:0%
+so you know that Delta equal
+ 
+
+ align:start position:0%
+so you know that Delta equal
+p l Cub over 3 e i right and what's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I area moment of inertia right we now
+
+ align:start position:0%
+I area moment of inertia right we now
+ 
+
+ align:start position:0%
+I area moment of inertia right we now
+that You' got been doing Dynamics alter
+
+ align:start position:0%
+that You' got been doing Dynamics alter
+ 
+
+ align:start position:0%
+that You' got been doing Dynamics alter
+we talk about Mass moments of inertia
+
+ align:start position:0%
+we talk about Mass moments of inertia
+ 
+
+ align:start position:0%
+we talk about Mass moments of inertia
+there's also area moments of inertia so
+
+ align:start position:0%
+there's also area moments of inertia so
+ 
+
+ align:start position:0%
+there's also area moments of inertia so
+this is the area moment the of a beam in
+
+ align:start position:0%
+this is the area moment the of a beam in
+ 
+
+ align:start position:0%
+this is the area moment the of a beam in
+this case our beam is a little
+
+ align:start position:0%
+this case our beam is a little
+ 
+
+ align:start position:0%
+this case our beam is a little
+rectangular
+
+ align:start position:0%
+rectangular
+ 
+
+ align:start position:0%
+rectangular
+cross-section and and the neutral axis
+
+ align:start position:0%
+cross-section and and the neutral axis
+ 
+
+ align:start position:0%
+cross-section and and the neutral axis
+is here a little variable y a
+
+ align:start position:0%
+is here a little variable y a
+ 
+
+ align:start position:0%
+is here a little variable y a
+displacement I is the integral of Y
+
+ align:start position:0%
+displacement I is the integral of Y
+ 
+
+ align:start position:0%
+displacement I is the integral of Y
+sared da and da is just a little slice
+
+ align:start position:0%
+sared da and da is just a little slice
+ 
+
+ align:start position:0%
+sared da and da is just a little slice
+of area here
+
+ align:start position:0%
+of area here
+ 
+
+ align:start position:0%
+of area here
+da the integral of y s da is your
+
+ align:start position:0%
+da the integral of y s da is your
+ 
+
+ align:start position:0%
+da the integral of y s da is your
+cross-sectional area moment of inertia
+
+ align:start position:0%
+cross-sectional area moment of inertia
+ 
+
+ align:start position:0%
+cross-sectional area moment of inertia
+in the direction of bending okay it
+
+ align:start position:0%
+in the direction of bending okay it
+ 
+
+ align:start position:0%
+in the direction of bending okay it
+house so that is I I happens you can
+
+ align:start position:0%
+house so that is I I happens you can
+ 
+
+ align:start position:0%
+house so that is I I happens you can
+also write it as a Kappa squared a a and
+
+ align:start position:0%
+also write it as a Kappa squared a a and
+ 
+
+ align:start position:0%
+also write it as a Kappa squared a a and
+that's we had ran into this in Dynamics
+
+ align:start position:0%
+that's we had ran into this in Dynamics
+ 
+
+ align:start position:0%
+that's we had ran into this in Dynamics
+we called it the radius of gation you
+
+ align:start position:0%
+we called it the radius of gation you
+ 
+
+ align:start position:0%
+we called it the radius of gation you
+had the same thing in with area moments
+
+ align:start position:0%
+had the same thing in with area moments
+ 
+
+ align:start position:0%
+had the same thing in with area moments
+of inertia the radius of GTI this is
+
+ align:start position:0%
+of inertia the radius of GTI this is
+ 
+
+ align:start position:0%
+of inertia the radius of GTI this is
+going to be really helpful in a
+
+ align:start position:0%
+going to be really helpful in a
+ 
+
+ align:start position:0%
+going to be really helpful in a
+second so if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you solve the force balance for a beam
+
+ align:start position:0%
+you solve the force balance for a beam
+ 
+
+ align:start position:0%
+you solve the force balance for a beam
+like I did for the
+
+ align:start position:0%
+like I did for the
+ 
+
+ align:start position:0%
+like I did for the
+string take a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do force balance for transverse motions
+
+ align:start position:0%
+do force balance for transverse motions
+ 
+
+ align:start position:0%
+do force balance for transverse motions
+I'm not going to grind it out and and
+
+ align:start position:0%
+I'm not going to grind it out and and
+ 
+
+ align:start position:0%
+I'm not going to grind it out and and
+temporarily neglect external forces and
+
+ align:start position:0%
+temporarily neglect external forces and
+ 
+
+ align:start position:0%
+temporarily neglect external forces and
+damping I want to get to the Natural
+
+ align:start position:0%
+damping I want to get to the Natural
+ 
+
+ align:start position:0%
+damping I want to get to the Natural
+frequencies and mode shapes so the free
+
+ align:start position:0%
+frequencies and mode shapes so the free
+ 
+
+ align:start position:0%
+frequencies and mode shapes so the free
+vibration no damping equation looks like
+
+ align:start position:0%
+vibration no damping equation looks like
+ 
+
+ align:start position:0%
+vibration no damping equation looks like
+EI
+
+ align:start position:0%
+EI
+ 
+
+ align:start position:0%
+EI
+I partial
+
+ align:start position:0%
+I partial
+ 
+
+ align:start position:0%
+I partial
+for w with respect to x to the
+
+ align:start position:0%
+for w with respect to x to the
+ 
+
+ align:start position:0%
+for w with respect to x to the
+4th plus row a
+
+ align:start position:0%
+4th plus row a
+ 
+
+ align:start position:0%
+4th plus row a
+partial squar W with respect to t^2
+
+ align:start position:0%
+partial squar W with respect to t^2
+ 
+
+ align:start position:0%
+partial squar W with respect to t^2
+equals z now this is density mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density and the a this a is the area of
+
+ align:start position:0%
+density and the a this a is the area of
+ 
+
+ align:start position:0%
+density and the a this a is the area of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross-section you know so it's just some
+
+ align:start position:0%
+cross-section you know so it's just some
+ 
+
+ align:start position:0%
+cross-section you know so it's just some
+BH right with thick thickness times the
+
+ align:start position:0%
+BH right with thick thickness times the
+ 
+
+ align:start position:0%
+BH right with thick thickness times the
+width so row * a is mass per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length and so mass per unit length time
+
+ align:start position:0%
+length and so mass per unit length time
+ 
+
+ align:start position:0%
+length and so mass per unit length time
+DX would be the little Mass associated
+
+ align:start position:0%
+DX would be the little Mass associated
+ 
+
+ align:start position:0%
+DX would be the little Mass associated
+with the element times the acceleration
+
+ align:start position:0%
+with the element times the acceleration
+ 
+
+ align:start position:0%
+with the element times the acceleration
+should be the forces on the element so
+
+ align:start position:0%
+should be the forces on the element so
+ 
+
+ align:start position:0%
+should be the forces on the element so
+that's the fourth order partial
+
+ align:start position:0%
+that's the fourth order partial
+ 
+
+ align:start position:0%
+that's the fourth order partial
+differential equation that describes the
+
+ align:start position:0%
+differential equation that describes the
+ 
+
+ align:start position:0%
+differential equation that describes the
+vibration of a
+
+ align:start position:0%
+vibration of a
+ 
+
+ align:start position:0%
+vibration of a
+beam
+
+ align:start position:0%
+beam
+ 
+
+ align:start position:0%
+beam
+and you have to where we saw you have to
+
+ align:start position:0%
+and you have to where we saw you have to
+ 
+
+ align:start position:0%
+and you have to where we saw you have to
+apply the boundary conditions and for
+
+ align:start position:0%
+apply the boundary conditions and for
+ 
+
+ align:start position:0%
+apply the boundary conditions and for
+the string it was just a B1 cosine B2 s
+
+ align:start position:0%
+the string it was just a B1 cosine B2 s
+ 
+
+ align:start position:0%
+the string it was just a B1 cosine B2 s
+for the beam it's B1 cosine plus B2 sin
+
+ align:start position:0%
+for the beam it's B1 cosine plus B2 sin
+ 
+
+ align:start position:0%
+for the beam it's B1 cosine plus B2 sin
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+C2 Kos plus D2
+
+ align:start position:0%
+C2 Kos plus D2
+ 
+
+ align:start position:0%
+C2 Kos plus D2
+cinch X and then you have to apply four
+
+ align:start position:0%
+cinch X and then you have to apply four
+ 
+
+ align:start position:0%
+cinch X and then you have to apply four
+boundary conditions and solve for you
+
+ align:start position:0%
+boundary conditions and solve for you
+ 
+
+ align:start position:0%
+boundary conditions and solve for you
+know B1 B2 and so forth all four can all
+
+ align:start position:0%
+know B1 B2 and so forth all four can all
+ 
+
+ align:start position:0%
+know B1 B2 and so forth all four can all
+four of those I won't do it but it's how
+
+ align:start position:0%
+four of those I won't do it but it's how
+ 
+
+ align:start position:0%
+four of those I won't do it but it's how
+you do it separation and separation of
+
+ align:start position:0%
+you do it separation and separation of
+ 
+
+ align:start position:0%
+you do it separation and separation of
+variables works again so we solve this
+
+ align:start position:0%
+variables works again so we solve this
+ 
+
+ align:start position:0%
+variables works again so we solve this
+apply the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+apply the boundary conditions what are
+
+ align:start position:0%
+apply the boundary conditions what are
+ 
+
+ align:start position:0%
+apply the boundary conditions what are
+the boundary conditions just so you
+
+ align:start position:0%
+the boundary conditions just so you
+ 
+
+ align:start position:0%
+the boundary conditions just so you
+understand what I mean by the boundary
+
+ align:start position:0%
+understand what I mean by the boundary
+ 
+
+ align:start position:0%
+understand what I mean by the boundary
+conditions what are they for a free free
+
+ align:start position:0%
+conditions what are they for a free free
+ 
+
+ align:start position:0%
+conditions what are they for a free free
+beam zero motion at the
+
+ align:start position:0%
+beam zero motion at the
+ 
+
+ align:start position:0%
+beam zero motion at the
+wall
+
+ align:start position:0%
+wall
+ 
+
+ align:start position:0%
+wall
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+no strain at the end no bending moment
+
+ align:start position:0%
+no strain at the end no bending moment
+ 
+
+ align:start position:0%
+no strain at the end no bending moment
+at the end no sheer force at the end so
+
+ align:start position:0%
+at the end no sheer force at the end so
+ 
+
+ align:start position:0%
+at the end no sheer force at the end so
+there's no second derivative no third
+
+ align:start position:0%
+there's no second derivative no third
+ 
+
+ align:start position:0%
+there's no second derivative no third
+derivative uh and at the
+
+ align:start position:0%
+derivative uh and at the
+ 
+
+ align:start position:0%
+derivative uh and at the
+wall there the slope is zero the first
+
+ align:start position:0%
+wall there the slope is zero the first
+ 
+
+ align:start position:0%
+wall there the slope is zero the first
+derivative no slope comes into the wall
+
+ align:start position:0%
+derivative no slope comes into the wall
+ 
+
+ align:start position:0%
+derivative no slope comes into the wall
+but doesn't the slope is zero there so
+
+ align:start position:0%
+but doesn't the slope is zero there so
+ 
+
+ align:start position:0%
+but doesn't the slope is zero there so
+those are the different kind of boundary
+
+ align:start position:0%
+those are the different kind of boundary
+ 
+
+ align:start position:0%
+those are the different kind of boundary
+so every different you have a free free
+
+ align:start position:0%
+so every different you have a free free
+ 
+
+ align:start position:0%
+so every different you have a free free
+beam have no bending at either end and
+
+ align:start position:0%
+beam have no bending at either end and
+ 
+
+ align:start position:0%
+beam have no bending at either end and
+no strain at either
+
+ align:start position:0%
+no strain at either
+ 
+
+ align:start position:0%
+no strain at either
+end fix fix beam no displacement zero
+
+ align:start position:0%
+end fix fix beam no displacement zero
+ 
+
+ align:start position:0%
+end fix fix beam no displacement zero
+slopes at both ends and all different
+
+ align:start position:0%
+slopes at both ends and all different
+ 
+
+ align:start position:0%
+slopes at both ends and all different
+combinations and every different
+
+ align:start position:0%
+combinations and every different
+ 
+
+ align:start position:0%
+combinations and every different
+combination gives you different natural
+
+ align:start position:0%
+combination gives you different natural
+ 
+
+ align:start position:0%
+combination gives you different natural
+frequencies so you apply the boundary
+
+ align:start position:0%
+frequencies so you apply the boundary
+ 
+
+ align:start position:0%
+frequencies so you apply the boundary
+conditions and for a beam you find out
+
+ align:start position:0%
+conditions and for a beam you find out
+ 
+
+ align:start position:0%
+conditions and for a beam you find out
+that for all beams Omega n
+
+ align:start position:0%
+that for all beams Omega n
+ 
+
+ align:start position:0%
+that for all beams Omega n
+can be written as some beta n a
+
+ align:start position:0%
+can be written as some beta n a
+ 
+
+ align:start position:0%
+can be written as some beta n a
+parameter squared I'll call it times the
+
+ align:start position:0%
+parameter squared I'll call it times the
+ 
+
+ align:start position:0%
+parameter squared I'll call it times the
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+root of EI I over row a and this thing
+
+ align:start position:0%
+root of EI I over row a and this thing
+ 
+
+ align:start position:0%
+root of EI I over row a and this thing
+varies according to the boundary
+
+ align:start position:0%
+varies according to the boundary
+ 
+
+ align:start position:0%
+varies according to the boundary
+conditions okay now that's what you get
+
+ align:start position:0%
+conditions okay now that's what you get
+ 
+
+ align:start position:0%
+conditions okay now that's what you get
+shown in every textbook in the world
+
+ align:start position:0%
+shown in every textbook in the world
+ 
+
+ align:start position:0%
+shown in every textbook in the world
+which you what something but and I have
+
+ align:start position:0%
+which you what something but and I have
+ 
+
+ align:start position:0%
+which you what something but and I have
+a very hard time visualizing this you
+
+ align:start position:0%
+a very hard time visualizing this you
+ 
+
+ align:start position:0%
+a very hard time visualizing this you
+know you know getting physical intuition
+
+ align:start position:0%
+know you know getting physical intuition
+ 
+
+ align:start position:0%
+know you know getting physical intuition
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+that but so something you never see in a
+
+ align:start position:0%
+that but so something you never see in a
+ 
+
+ align:start position:0%
+that but so something you never see in a
+textbook but I often do is let's replace
+
+ align:start position:0%
+textbook but I often do is let's replace
+ 
+
+ align:start position:0%
+textbook but I often do is let's replace
+I with cap squ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and you get a square root of e over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row and a square root of I over a but I
+
+ align:start position:0%
+row and a square root of I over a but I
+ 
+
+ align:start position:0%
+row and a square root of I over a but I
+is Kappa squar a the A's cancel it's a
+
+ align:start position:0%
+is Kappa squar a the A's cancel it's a
+ 
+
+ align:start position:0%
+is Kappa squar a the A's cancel it's a
+square root of Kappa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C square of Capa squar so this and
+
+ align:start position:0%
+C square of Capa squar so this and
+ 
+
+ align:start position:0%
+C square of Capa squar so this and
+what's you know what e over row
+
+ align:start position:0%
+what's you know what e over row
+ 
+
+ align:start position:0%
+what's you know what e over row
+is e over
+
+ align:start position:0%
+is e over
+ 
+
+ align:start position:0%
+is e over
+row square root of e over row is the
+
+ align:start position:0%
+row square root of e over row is the
+ 
+
+ align:start position:0%
+row square root of e over row is the
+sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speed in a solid material so the speed
+
+ align:start position:0%
+speed in a solid material so the speed
+ 
+
+ align:start position:0%
+speed in a solid material so the speed
+of that stress waves traveling up and
+
+ align:start position:0%
+of that stress waves traveling up and
+ 
+
+ align:start position:0%
+of that stress waves traveling up and
+down this thing is the square root of e
+
+ align:start position:0%
+down this thing is the square root of e
+ 
+
+ align:start position:0%
+down this thing is the square root of e
+over row for this is a l about it's
+
+ align:start position:0%
+over row for this is a l about it's
+ 
+
+ align:start position:0%
+over row for this is a l about it's
+about 4,000 m a
+
+ align:start position:0%
+about 4,000 m a
+ 
+
+ align:start position:0%
+about 4,000 m a
+second so if you know just the
+
+ align:start position:0%
+second so if you know just the
+ 
+
+ align:start position:0%
+second so if you know just the
+properties of the material you have that
+
+ align:start position:0%
+properties of the material you have that
+ 
+
+ align:start position:0%
+properties of the material you have that
+and that says then the Omega n for beams
+
+ align:start position:0%
+and that says then the Omega n for beams
+ 
+
+ align:start position:0%
+and that says then the Omega n for beams
+is some beta n squar a parameter times
+
+ align:start position:0%
+is some beta n squar a parameter times
+ 
+
+ align:start position:0%
+is some beta n squar a parameter times
+Kappa CL and this thing this is often
+
+ align:start position:0%
+Kappa CL and this thing this is often
+ 
+
+ align:start position:0%
+Kappa CL and this thing this is often
+written CL it's the longitudinal Sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Speed this is Sound Speed for waves
+
+ align:start position:0%
+Speed this is Sound Speed for waves
+ 
+
+ align:start position:0%
+Speed this is Sound Speed for waves
+traveling through the
+
+ align:start position:0%
+traveling through the
+ 
+
+ align:start position:0%
+traveling through the
+medium so this tells you if you make the
+
+ align:start position:0%
+medium so this tells you if you make the
+ 
+
+ align:start position:0%
+medium so this tells you if you make the
+beam twice as thick what do you do to
+
+ align:start position:0%
+beam twice as thick what do you do to
+ 
+
+ align:start position:0%
+beam twice as thick what do you do to
+its natural
+
+ align:start position:0%
+its natural
+ 
+
+ align:start position:0%
+its natural
+frequencies doubles instantly you know
+
+ align:start position:0%
+frequencies doubles instantly you know
+ 
+
+ align:start position:0%
+frequencies doubles instantly you know
+that so bending properties depend a lot
+
+ align:start position:0%
+that so bending properties depend a lot
+ 
+
+ align:start position:0%
+that so bending properties depend a lot
+on the radius of gation and I'll give
+
+ align:start position:0%
+on the radius of gation and I'll give
+ 
+
+ align:start position:0%
+on the radius of gation and I'll give
+you a few natural frequencies for
+
+ align:start position:0%
+you a few natural frequencies for
+ 
+
+ align:start position:0%
+you a few natural frequencies for
+different boundary conditions just so
+
+ align:start position:0%
+different boundary conditions just so
+ 
+
+ align:start position:0%
+different boundary conditions just so
+you see what they behave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+pinned pin pin beam looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that so this is
+
+ align:start position:0%
+like that so this is
+ 
+
+ align:start position:0%
+like that so this is
+a you put a plank across
+
+ align:start position:0%
+a you put a plank across
+ 
+
+ align:start position:0%
+a you put a plank across
+the stream you know rocks on both sides
+
+ align:start position:0%
+the stream you know rocks on both sides
+ 
+
+ align:start position:0%
+the stream you know rocks on both sides
+you got a pin pin beam basically sit
+
+ align:start position:0%
+you got a pin pin beam basically sit
+ 
+
+ align:start position:0%
+you got a pin pin beam basically sit
+there and rock so some length L has
+
+ align:start position:0%
+there and rock so some length L has
+ 
+
+ align:start position:0%
+there and rock so some length L has
+properties EI so the natural frequencies
+
+ align:start position:0%
+properties EI so the natural frequencies
+ 
+
+ align:start position:0%
+properties EI so the natural frequencies
+for a pin pin beam the beta n's are just
+
+ align:start position:0%
+for a pin pin beam the beta n's are just
+ 
+
+ align:start position:0%
+for a pin pin beam the beta n's are just
+n pi over
+
+ align:start position:0%
+n pi over
+ 
+
+ align:start position:0%
+n pi over
+L and so your natural frequencies Omega
+
+ align:start position:0%
+L and so your natural frequencies Omega
+ 
+
+ align:start position:0%
+L and so your natural frequencies Omega
+n looks
+
+ align:start position:0%
+n looks
+ 
+
+ align:start position:0%
+n looks
+like n pi over L quantity squar Capa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CL and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the candle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lever
+
+ align:start position:0%
+lever
+ 
+
+ align:start position:0%
+lever
+for the Cal lever the natural
+
+ align:start position:0%
+for the Cal lever the natural
+ 
+
+ align:start position:0%
+for the Cal lever the natural
+frequencies look like Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n p pi^ 2 over 4 l^ 2 is the beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and I'll write it this way again EI I
+
+ align:start position:0%
+n and I'll write it this way again EI I
+ 
+
+ align:start position:0%
+n and I'll write it this way again EI I
+over row a you can always go back and do
+
+ align:start position:0%
+over row a you can always go back and do
+ 
+
+ align:start position:0%
+over row a you can always go back and do
+that or you can call it cap this is also
+
+ align:start position:0%
+that or you can call it cap this is also
+ 
+
+ align:start position:0%
+that or you can call it cap this is also
+Capa CL
+
+ align:start position:0%
+Capa CL
+ 
+
+ align:start position:0%
+Capa CL
+but then there's a there are some
+
+ align:start position:0%
+but then there's a there are some
+ 
+
+ align:start position:0%
+but then there's a there are some
+numbers you got to use here
+
+ align:start position:0%
+numbers you got to use here
+ 
+
+ align:start position:0%
+numbers you got to use here
+1.94 squared that's the first mode
+
+ align:start position:0%
+1.94 squared that's the first mode
+ 
+
+ align:start position:0%
+1.94 squared that's the first mode
+second mode
+
+ align:start position:0%
+second mode
+ 
+
+ align:start position:0%
+second mode
+2.9 88 squared and then after that 5
+
+ align:start position:0%
+2.9 88 squared and then after that 5
+ 
+
+ align:start position:0%
+2.9 88 squared and then after that 5
+squar 7 squar 9
+
+ align:start position:0%
+squar 7 squar 9
+ 
+
+ align:start position:0%
+squar 7 squar 9
+squar so that's the natural so this is
+
+ align:start position:0%
+squar so that's the natural so this is
+ 
+
+ align:start position:0%
+squar so that's the natural so this is
+the natural frequency of a candle lever
+
+ align:start position:0%
+the natural frequency of a candle lever
+ 
+
+ align:start position:0%
+the natural frequency of a candle lever
+p pi^ 2 over 4 l^ 2 *
+
+ align:start position:0%
+p pi^ 2 over 4 l^ 2 *
+ 
+
+ align:start position:0%
+p pi^ 2 over 4 l^ 2 *
+1.94
+
+ align:start position:0%
+1.94
+ 
+
+ align:start position:0%
+1.94
+Capac that's this natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency and a one final case because I
+
+ align:start position:0%
+frequency and a one final case because I
+ 
+
+ align:start position:0%
+frequency and a one final case because I
+can show it to you the free free
+
+ align:start position:0%
+can show it to you the free free
+ 
+
+ align:start position:0%
+can show it to you the free free
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+so that's a
+
+ align:start position:0%
+so that's a
+ 
+
+ align:start position:0%
+so that's a
+beam in bending that vibrates like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and I happen to know on a beam for
+
+ align:start position:0%
+that and I happen to know on a beam for
+ 
+
+ align:start position:0%
+that and I happen to know on a beam for
+the first mode of a beam this is first
+
+ align:start position:0%
+the first mode of a beam this is first
+ 
+
+ align:start position:0%
+the first mode of a beam this is first
+mode of a beam where these nodes are
+
+ align:start position:0%
+mode of a beam where these nodes are
+ 
+
+ align:start position:0%
+mode of a beam where these nodes are
+where there's no motion I should be able
+
+ align:start position:0%
+where there's no motion I should be able
+ 
+
+ align:start position:0%
+where there's no motion I should be able
+to hold it there and not damp it and
+
+ align:start position:0%
+to hold it there and not damp it and
+ 
+
+ align:start position:0%
+to hold it there and not damp it and
+that turns out to be at about the
+
+ align:start position:0%
+that turns out to be at about the
+ 
+
+ align:start position:0%
+that turns out to be at about the
+quarter
+
+ align:start position:0%
+quarter
+ 
+
+ align:start position:0%
+quarter
+points so whack it like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and do it
+
+ align:start position:0%
+that and do it
+ 
+
+ align:start position:0%
+that and do it
+again all right so I want you to hold
+
+ align:start position:0%
+again all right so I want you to hold
+ 
+
+ align:start position:0%
+again all right so I want you to hold
+it right
+
+ align:start position:0%
+it right
+ 
+
+ align:start position:0%
+it right
+there nope you can't hold it like that
+
+ align:start position:0%
+there nope you can't hold it like that
+ 
+
+ align:start position:0%
+there nope you can't hold it like that
+though just got to balance it because
+
+ align:start position:0%
+though just got to balance it because
+ 
+
+ align:start position:0%
+though just got to balance it because
+you C to be right where the Noe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is you can hear that little bit lower
+
+ align:start position:0%
+is you can hear that little bit lower
+ 
+
+ align:start position:0%
+is you can hear that little bit lower
+tone that's that free free bending mode
+
+ align:start position:0%
+tone that's that free free bending mode
+ 
+
+ align:start position:0%
+tone that's that free free bending mode
+and it's just sitting you can feel it
+
+ align:start position:0%
+and it's just sitting you can feel it
+ 
+
+ align:start position:0%
+and it's just sitting you can feel it
+vibrating a little bit right but not
+
+ align:start position:0%
+vibrating a little bit right but not
+ 
+
+ align:start position:0%
+vibrating a little bit right but not
+much you're when you're you're right in
+
+ align:start position:0%
+much you're when you're you're right in
+ 
+
+ align:start position:0%
+much you're when you're you're right in
+the right spot you're right on the mode
+
+ align:start position:0%
+the right spot you're right on the mode
+ 
+
+ align:start position:0%
+the right spot you're right on the mode
+shape you can almost see it if you hit
+
+ align:start position:0%
+shape you can almost see it if you hit
+ 
+
+ align:start position:0%
+shape you can almost see it if you hit
+it hard enough so that's the free free
+
+ align:start position:0%
+it hard enough so that's the free free
+ 
+
+ align:start position:0%
+it hard enough so that's the free free
+beam and the free free
+
+ align:start position:0%
+beam and the free free
+ 
+
+ align:start position:0%
+beam and the free free
+beam has natural frequencies Omega
+
+ align:start position:0%
+beam has natural frequencies Omega
+ 
+
+ align:start position:0%
+beam has natural frequencies Omega
+n again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi^ 2 over 4 L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Capac
+
+ align:start position:0%
+Capac
+ 
+
+ align:start position:0%
+Capac
+3.01 one2
+
+ align:start position:0%
+3.01 one2
+ 
+
+ align:start position:0%
+3.01 one2
+sared 5 squar 7 squar 9 squar so as you
+
+ align:start position:0%
+sared 5 squar 7 squar 9 squar so as you
+ 
+
+ align:start position:0%
+sared 5 squar 7 squar 9 squar so as you
+go up and in so that was are the natural
+
+ align:start position:0%
+go up and in so that was are the natural
+ 
+
+ align:start position:0%
+go up and in so that was are the natural
+frequencies of a free free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam oh one last Fact one last fact
+
+ align:start position:0%
+beam oh one last Fact one last fact
+ 
+
+ align:start position:0%
+beam oh one last Fact one last fact
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+beams so let's say I
+
+ align:start position:0%
+beams so let's say I
+ 
+
+ align:start position:0%
+beams so let's say I
+have this is
+
+ align:start position:0%
+have this is
+ 
+
+ align:start position:0%
+have this is
+now a steel
+
+ align:start position:0%
+now a steel
+ 
+
+ align:start position:0%
+now a steel
+beam under no tension it can support its
+
+ align:start position:0%
+beam under no tension it can support its
+ 
+
+ align:start position:0%
+beam under no tension it can support its
+own weight long though so it can can a
+
+ align:start position:0%
+own weight long though so it can can a
+ 
+
+ align:start position:0%
+own weight long though so it can can a
+beam support waves traveling down the
+
+ align:start position:0%
+beam support waves traveling down the
+ 
+
+ align:start position:0%
+beam support waves traveling down the
+beam transverse waves traveling down the
+
+ align:start position:0%
+beam transverse waves traveling down the
+ 
+
+ align:start position:0%
+beam transverse waves traveling down the
+beam what do you
+
+ align:start position:0%
+beam what do you
+ 
+
+ align:start position:0%
+beam what do you
+think well if it can support this can
+
+ align:start position:0%
+think well if it can support this can
+ 
+
+ align:start position:0%
+think well if it can support this can
+probably support waves right so waves
+
+ align:start position:0%
+probably support waves right so waves
+ 
+
+ align:start position:0%
+probably support waves right so waves
+will propagate in a beam even though
+
+ align:start position:0%
+will propagate in a beam even though
+ 
+
+ align:start position:0%
+will propagate in a beam even though
+this is fourth order part partial
+
+ align:start position:0%
+this is fourth order part partial
+ 
+
+ align:start position:0%
+this is fourth order part partial
+differential equation but how fast do
+
+ align:start position:0%
+differential equation but how fast do
+ 
+
+ align:start position:0%
+differential equation but how fast do
+they go that's the question okay so this
+
+ align:start position:0%
+they go that's the question okay so this
+ 
+
+ align:start position:0%
+they go that's the question okay so this
+is a beam and I want to know about waves
+
+ align:start position:0%
+is a beam and I want to know about waves
+ 
+
+ align:start position:0%
+is a beam and I want to know about waves
+traveling down it and I'm not going to
+
+ align:start position:0%
+traveling down it and I'm not going to
+ 
+
+ align:start position:0%
+traveling down it and I'm not going to
+go through this would take another hour
+
+ align:start position:0%
+go through this would take another hour
+ 
+
+ align:start position:0%
+go through this would take another hour
+so to show you where this comes from but
+
+ align:start position:0%
+so to show you where this comes from but
+ 
+
+ align:start position:0%
+so to show you where this comes from but
+the here's my
+
+ align:start position:0%
+the here's my
+ 
+
+ align:start position:0%
+the here's my
+beam here's a disturbance traveling
+
+ align:start position:0%
+beam here's a disturbance traveling
+ 
+
+ align:start position:0%
+beam here's a disturbance traveling
+along it with some speed that I'm going
+
+ align:start position:0%
+along it with some speed that I'm going
+ 
+
+ align:start position:0%
+along it with some speed that I'm going
+to call it I'm going to call it CT it's
+
+ align:start position:0%
+to call it I'm going to call it CT it's
+ 
+
+ align:start position:0%
+to call it I'm going to call it CT it's
+transverse wave speed it's the speed
+
+ align:start position:0%
+transverse wave speed it's the speed
+ 
+
+ align:start position:0%
+transverse wave speed it's the speed
+you'd see a crest of a wave moving at
+
+ align:start position:0%
+you'd see a crest of a wave moving at
+ 
+
+ align:start position:0%
+you'd see a crest of a wave moving at
+running down that
+
+ align:start position:0%
+running down that
+ 
+
+ align:start position:0%
+running down that
+beam CT for a
+
+ align:start position:0%
+beam CT for a
+ 
+
+ align:start position:0%
+beam CT for a
+beam square
+
+ align:start position:0%
+beam square
+ 
+
+ align:start position:0%
+beam square
+root of
+
+ align:start position:0%
+root of
+ 
+
+ align:start position:0%
+root of
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+Kappa
+
+ align:start position:0%
+Kappa
+ 
+
+ align:start position:0%
+Kappa
+CL and cl
+
+ align:start position:0%
+CL and cl
+ 
+
+ align:start position:0%
+CL and cl
+again is a square root of e over row
+
+ align:start position:0%
+again is a square root of e over row
+ 
+
+ align:start position:0%
+again is a square root of e over row
+it's a speed of sound in the material
+
+ align:start position:0%
+it's a speed of sound in the material
+ 
+
+ align:start position:0%
+it's a speed of sound in the material
+that property that just turns up in
+
+ align:start position:0%
+that property that just turns up in
+ 
+
+ align:start position:0%
+that property that just turns up in
+here so what does this tell you
+
+ align:start position:0%
+here so what does this tell you
+ 
+
+ align:start position:0%
+here so what does this tell you
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+uh frequency dependence of the
+
+ align:start position:0%
+uh frequency dependence of the
+ 
+
+ align:start position:0%
+uh frequency dependence of the
+speed does a speed change with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency Omega Capac right it's
+
+ align:start position:0%
+frequency Omega Capac right it's
+ 
+
+ align:start position:0%
+frequency Omega Capac right it's
+proportional to frequency high frequency
+
+ align:start position:0%
+proportional to frequency high frequency
+ 
+
+ align:start position:0%
+proportional to frequency high frequency
+waves go faster than low frequency waves
+
+ align:start position:0%
+waves go faster than low frequency waves
+ 
+
+ align:start position:0%
+waves go faster than low frequency waves
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+beam we I didn't emphasize it when we
+
+ align:start position:0%
+beam we I didn't emphasize it when we
+ 
+
+ align:start position:0%
+beam we I didn't emphasize it when we
+were talking about it but the wave
+
+ align:start position:0%
+were talking about it but the wave
+ 
+
+ align:start position:0%
+were talking about it but the wave
+equation what was C for the
+
+ align:start position:0%
+equation what was C for the
+ 
+
+ align:start position:0%
+equation what was C for the
+string for the wave equation the speed
+
+ align:start position:0%
+string for the wave equation the speed
+ 
+
+ align:start position:0%
+string for the wave equation the speed
+of sound the speed of wave propagation
+
+ align:start position:0%
+of sound the speed of wave propagation
+ 
+
+ align:start position:0%
+of sound the speed of wave propagation
+was Square Ro of T over M was it
+
+ align:start position:0%
+was Square Ro of T over M was it
+ 
+
+ align:start position:0%
+was Square Ro of T over M was it
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+dependent all Wes travel at the same
+
+ align:start position:0%
+dependent all Wes travel at the same
+ 
+
+ align:start position:0%
+dependent all Wes travel at the same
+speed and so there's an important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consequence so for anything that obeys
+
+ align:start position:0%
+consequence so for anything that obeys
+ 
+
+ align:start position:0%
+consequence so for anything that obeys
+the wave equation the speed of
+
+ align:start position:0%
+the wave equation the speed of
+ 
+
+ align:start position:0%
+the wave equation the speed of
+propagation is a constant and
+
+ align:start position:0%
+propagation is a constant and
+ 
+
+ align:start position:0%
+propagation is a constant and
+independent of
+
+ align:start position:0%
+independent of
+ 
+
+ align:start position:0%
+independent of
+frequency so I can make any initial
+
+ align:start position:0%
+frequency so I can make any initial
+ 
+
+ align:start position:0%
+frequency so I can make any initial
+shape that I make in this thing and let
+
+ align:start position:0%
+shape that I make in this thing and let
+ 
+
+ align:start position:0%
+shape that I make in this thing and let
+it go it's initial
+
+ align:start position:0%
+it go it's initial
+ 
+
+ align:start position:0%
+it go it's initial
+disturbance that little shape will stay
+
+ align:start position:0%
+disturbance that little shape will stay
+ 
+
+ align:start position:0%
+disturbance that little shape will stay
+that shape and run up and down the thing
+
+ align:start position:0%
+that shape and run up and down the thing
+ 
+
+ align:start position:0%
+that shape and run up and down the thing
+forever and that shape you can imagine a
+
+ align:start position:0%
+forever and that shape you can imagine a
+ 
+
+ align:start position:0%
+forever and that shape you can imagine a
+little pluck like this to start with you
+
+ align:start position:0%
+little pluck like this to start with you
+ 
+
+ align:start position:0%
+little pluck like this to start with you
+can imagine doing a make you know doing
+
+ align:start position:0%
+can imagine doing a make you know doing
+ 
+
+ align:start position:0%
+can imagine doing a make you know doing
+a 4ier series to approximate that it
+
+ align:start position:0%
+a 4ier series to approximate that it
+ 
+
+ align:start position:0%
+a 4ier series to approximate that it
+would be made up of a bunch of different
+
+ align:start position:0%
+would be made up of a bunch of different
+ 
+
+ align:start position:0%
+would be made up of a bunch of different
+fora components right um and yet for
+
+ align:start position:0%
+fora components right um and yet for
+ 
+
+ align:start position:0%
+fora components right um and yet for
+something that BS a wave equation that
+
+ align:start position:0%
+something that BS a wave equation that
+ 
+
+ align:start position:0%
+something that BS a wave equation that
+little pluck will just stay the shape of
+
+ align:start position:0%
+little pluck will just stay the shape of
+ 
+
+ align:start position:0%
+little pluck will just stay the shape of
+that pluck and run around forever but
+
+ align:start position:0%
+that pluck and run around forever but
+ 
+
+ align:start position:0%
+that pluck and run around forever but
+not so in a beam if you did that in a
+
+ align:start position:0%
+not so in a beam if you did that in a
+ 
+
+ align:start position:0%
+not so in a beam if you did that in a
+beam if you come up and put an Impulse
+
+ align:start position:0%
+beam if you come up and put an Impulse
+ 
+
+ align:start position:0%
+beam if you come up and put an Impulse
+into a
+
+ align:start position:0%
+into a
+ 
+
+ align:start position:0%
+into a
+beam all that energy would start out
+
+ align:start position:0%
+beam all that energy would start out
+ 
+
+ align:start position:0%
+beam all that energy would start out
+together but in very brief time the high
+
+ align:start position:0%
+together but in very brief time the high
+ 
+
+ align:start position:0%
+together but in very brief time the high
+frequency information would get out in
+
+ align:start position:0%
+frequency information would get out in
+ 
+
+ align:start position:0%
+frequency information would get out in
+front of the low frequency information
+
+ align:start position:0%
+front of the low frequency information
+ 
+
+ align:start position:0%
+front of the low frequency information
+and if you were way down this beam and
+
+ align:start position:0%
+and if you were way down this beam and
+ 
+
+ align:start position:0%
+and if you were way down this beam and
+somebody up a mile away whacks one end
+
+ align:start position:0%
+somebody up a mile away whacks one end
+ 
+
+ align:start position:0%
+somebody up a mile away whacks one end
+and you're down further along you'll say
+
+ align:start position:0%
+and you're down further along you'll say
+ 
+
+ align:start position:0%
+and you're down further along you'll say
+you'll see high frequency waves pass you
+
+ align:start position:0%
+you'll see high frequency waves pass you
+ 
+
+ align:start position:0%
+you'll see high frequency waves pass you
+and then lower frequency and finally
+
+ align:start position:0%
+and then lower frequency and finally
+ 
+
+ align:start position:0%
+and then lower frequency and finally
+really slow ones coming by the really
+
+ align:start position:0%
+really slow ones coming by the really
+ 
+
+ align:start position:0%
+really slow ones coming by the really
+long waves so that's called
+
+ align:start position:0%
+long waves so that's called
+ 
+
+ align:start position:0%
+long waves so that's called
+dispersion so beam waves are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dispersive things that b the wave
+
+ align:start position:0%
+dispersive things that b the wave
+ 
+
+ align:start position:0%
+dispersive things that b the wave
+equation are nondispersive the energy
+
+ align:start position:0%
+equation are nondispersive the energy
+ 
+
+ align:start position:0%
+equation are nondispersive the energy
+all travels at the same speed
+
+ align:start position:0%
+all travels at the same speed
+ 
+
+ align:start position:0%
+all travels at the same speed
+independent of frequency all right so
+
+ align:start position:0%
+independent of frequency all right so
+ 
+
+ align:start position:0%
+independent of frequency all right so
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+uh that's it for the term I'll see you
+
+ align:start position:0%
+uh that's it for the term I'll see you
+ 
+
+ align:start position:0%
+uh that's it for the term I'll see you
+guys on next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wednesday
\ No newline at end of file
diff --git a/2YPu29d8RZY.txt b/2YPu29d8RZY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b67c4a50aa3a4e085cdac58758666ef7d0a99592
--- /dev/null
+++ b/2YPu29d8RZY.txt
@@ -0,0 +1,651 @@
+align:start position:0%
+ 
+welcome back to a20 special relativity
+
+ align:start position:0%
+welcome back to a20 special relativity
+ 
+
+ align:start position:0%
+welcome back to a20 special relativity
+in this section we're going to take a
+
+ align:start position:0%
+in this section we're going to take a
+ 
+
+ align:start position:0%
+in this section we're going to take a
+journey through our solar system and
+
+ align:start position:0%
+journey through our solar system and
+ 
+
+ align:start position:0%
+journey through our solar system and
+beyond
+
+ align:start position:0%
+beyond
+ 
+
+ align:start position:0%
+beyond
+1977 marks the first fly of the voyager
+
+ align:start position:0%
+1977 marks the first fly of the voyager
+ 
+
+ align:start position:0%
+1977 marks the first fly of the voyager
+program voyager is an mit-led program
+
+ align:start position:0%
+program voyager is an mit-led program
+ 
+
+ align:start position:0%
+program voyager is an mit-led program
+with the original mission to study
+
+ align:start position:0%
+with the original mission to study
+ 
+
+ align:start position:0%
+with the original mission to study
+planetary systems
+
+ align:start position:0%
+planetary systems
+ 
+
+ align:start position:0%
+planetary systems
+now voyager 1 and voyager 2 to
+
+ align:start position:0%
+now voyager 1 and voyager 2 to
+ 
+
+ align:start position:0%
+now voyager 1 and voyager 2 to
+spacecrafts are studying the
+
+ align:start position:0%
+spacecrafts are studying the
+ 
+
+ align:start position:0%
+spacecrafts are studying the
+interstellar space
+
+ align:start position:0%
+interstellar space
+ 
+
+ align:start position:0%
+interstellar space
+those two probes are still sending back
+
+ align:start position:0%
+those two probes are still sending back
+ 
+
+ align:start position:0%
+those two probes are still sending back
+now more than 40 years later
+
+ align:start position:0%
+now more than 40 years later
+ 
+
+ align:start position:0%
+now more than 40 years later
+information about you know measurements
+
+ align:start position:0%
+information about you know measurements
+ 
+
+ align:start position:0%
+information about you know measurements
+of their surroundings back to earth
+
+ align:start position:0%
+of their surroundings back to earth
+ 
+
+ align:start position:0%
+of their surroundings back to earth
+those are the two you know furthest away
+
+ align:start position:0%
+those are the two you know furthest away
+ 
+
+ align:start position:0%
+those are the two you know furthest away
+objects were able to sort
+
+ align:start position:0%
+objects were able to sort
+ 
+
+ align:start position:0%
+objects were able to sort
+but we have we are in age 20 and it's
+
+ align:start position:0%
+but we have we are in age 20 and it's
+ 
+
+ align:start position:0%
+but we have we are in age 20 and it's
+irp so we are a little bit more
+
+ align:start position:0%
+irp so we are a little bit more
+ 
+
+ align:start position:0%
+irp so we are a little bit more
+ambitious
+
+ align:start position:0%
+ambitious
+ 
+
+ align:start position:0%
+ambitious
+our mission is to bring us to alpha
+
+ align:start position:0%
+our mission is to bring us to alpha
+ 
+
+ align:start position:0%
+our mission is to bring us to alpha
+centauri alpha centauri is the closest
+
+ align:start position:0%
+centauri alpha centauri is the closest
+ 
+
+ align:start position:0%
+centauri alpha centauri is the closest
+star and planetary system to our solar
+
+ align:start position:0%
+star and planetary system to our solar
+ 
+
+ align:start position:0%
+star and planetary system to our solar
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+it's actually not just one star but
+
+ align:start position:0%
+it's actually not just one star but
+ 
+
+ align:start position:0%
+it's actually not just one star but
+multiple stars
+
+ align:start position:0%
+multiple stars
+ 
+
+ align:start position:0%
+multiple stars
+and our journey brings us to proxima b
+
+ align:start position:0%
+and our journey brings us to proxima b
+ 
+
+ align:start position:0%
+and our journey brings us to proxima b
+which is a planet
+
+ align:start position:0%
+which is a planet
+ 
+
+ align:start position:0%
+which is a planet
+in the alpha centauri system
+
+ align:start position:0%
+in the alpha centauri system
+ 
+
+ align:start position:0%
+in the alpha centauri system
+so we have a very fancy spacecraft it's
+
+ align:start position:0%
+so we have a very fancy spacecraft it's
+ 
+
+ align:start position:0%
+so we have a very fancy spacecraft it's
+able to travel with the constant
+
+ align:start position:0%
+able to travel with the constant
+ 
+
+ align:start position:0%
+able to travel with the constant
+velocity of
+
+ align:start position:0%
+velocity of
+ 
+
+ align:start position:0%
+velocity of
+0.943
+
+ align:start position:0%
+0.943
+ 
+
+ align:start position:0%
+0.943
+c speed of light
+
+ align:start position:0%
+c speed of light
+ 
+
+ align:start position:0%
+c speed of light
+the gamma factor is 3 and the path which
+
+ align:start position:0%
+the gamma factor is 3 and the path which
+ 
+
+ align:start position:0%
+the gamma factor is 3 and the path which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+which we're going to take
+
+ align:start position:0%
+which we're going to take
+ 
+
+ align:start position:0%
+which we're going to take
+is five light years long
+
+ align:start position:0%
+is five light years long
+ 
+
+ align:start position:0%
+is five light years long
+alice
+
+ align:start position:0%
+alice
+ 
+
+ align:start position:0%
+alice
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+our ground control she is going to stay
+
+ align:start position:0%
+our ground control she is going to stay
+ 
+
+ align:start position:0%
+our ground control she is going to stay
+on earth and bob is going to take this
+
+ align:start position:0%
+on earth and bob is going to take this
+ 
+
+ align:start position:0%
+on earth and bob is going to take this
+journey
+
+ align:start position:0%
+journey
+ 
+
+ align:start position:0%
+journey
+with virgin galactic
+
+ align:start position:0%
+with virgin galactic
+ 
+
+ align:start position:0%
+with virgin galactic
+after some time bob is going to arrive
+
+ align:start position:0%
+after some time bob is going to arrive
+ 
+
+ align:start position:0%
+after some time bob is going to arrive
+on proxima b
+
+ align:start position:0%
+on proxima b
+ 
+
+ align:start position:0%
+on proxima b
+so your first charge
+
+ align:start position:0%
+so your first charge
+ 
+
+ align:start position:0%
+so your first charge
+is to now
+
+ align:start position:0%
+is to now
+ 
+
+ align:start position:0%
+is to now
+calculate how long does this trip take
+
+ align:start position:0%
+calculate how long does this trip take
+ 
+
+ align:start position:0%
+calculate how long does this trip take
+from analysis alice's and bob's
+
+ align:start position:0%
+from analysis alice's and bob's
+ 
+
+ align:start position:0%
+from analysis alice's and bob's
+perspective
+
+ align:start position:0%
+perspective
+ 
+
+ align:start position:0%
+perspective
+so i asked you to stop the video here
+
+ align:start position:0%
+so i asked you to stop the video here
+ 
+
+ align:start position:0%
+so i asked you to stop the video here
+and just works us out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for alice the time needed
+
+ align:start position:0%
+so for alice the time needed
+ 
+
+ align:start position:0%
+so for alice the time needed
+is 5 light years divided by 0.9 by the
+
+ align:start position:0%
+is 5 light years divided by 0.9 by the
+ 
+
+ align:start position:0%
+is 5 light years divided by 0.9 by the
+velocity of 0.943 times the speed of
+
+ align:start position:0%
+velocity of 0.943 times the speed of
+ 
+
+ align:start position:0%
+velocity of 0.943 times the speed of
+light and that gives us 5.3 years
+
+ align:start position:0%
+light and that gives us 5.3 years
+ 
+
+ align:start position:0%
+light and that gives us 5.3 years
+so after 5.3 years
+
+ align:start position:0%
+so after 5.3 years
+ 
+
+ align:start position:0%
+so after 5.3 years
+ali is observing bob's arrival on
+
+ align:start position:0%
+ali is observing bob's arrival on
+ 
+
+ align:start position:0%
+ali is observing bob's arrival on
+proxima b
+
+ align:start position:0%
+proxima b
+ 
+
+ align:start position:0%
+proxima b
+for bob the length of this path is
+
+ align:start position:0%
+for bob the length of this path is
+ 
+
+ align:start position:0%
+for bob the length of this path is
+lauren's
+
+ align:start position:0%
+lauren's
+ 
+
+ align:start position:0%
+lauren's
+lawrence contracted
+
+ align:start position:0%
+lawrence contracted
+ 
+
+ align:start position:0%
+lawrence contracted
+um five light years divided by three
+
+ align:start position:0%
+um five light years divided by three
+ 
+
+ align:start position:0%
+um five light years divided by three
+which is the gamma factor which results
+
+ align:start position:0%
+which is the gamma factor which results
+ 
+
+ align:start position:0%
+which is the gamma factor which results
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+1.67 light years
+
+ align:start position:0%
+1.67 light years
+ 
+
+ align:start position:0%
+1.67 light years
+so for him the journey takes
+
+ align:start position:0%
+so for him the journey takes
+ 
+
+ align:start position:0%
+so for him the journey takes
+only 1.77 years 1.67 light years divided
+
+ align:start position:0%
+only 1.77 years 1.67 light years divided
+ 
+
+ align:start position:0%
+only 1.77 years 1.67 light years divided
+by 0.943
+
+ align:start position:0%
+by 0.943
+ 
+
+ align:start position:0%
+by 0.943
+times the speed of light
+
+ align:start position:0%
+times the speed of light
+ 
+
+ align:start position:0%
+times the speed of light
+so apparently
+
+ align:start position:0%
+so apparently
+ 
+
+ align:start position:0%
+so apparently
+the time experienced by alice and bob
+
+ align:start position:0%
+the time experienced by alice and bob
+ 
+
+ align:start position:0%
+the time experienced by alice and bob
+for the very same journey is different
+
+ align:start position:0%
+for the very same journey is different
+ 
+
+ align:start position:0%
+for the very same journey is different
+so this now is the first part where we
+
+ align:start position:0%
+so this now is the first part where we
+ 
+
+ align:start position:0%
+so this now is the first part where we
+enter
+
+ align:start position:0%
+enter
+ 
+
+ align:start position:0%
+enter
+discussions of
+
+ align:start position:0%
+discussions of
+ 
+
+ align:start position:0%
+discussions of
+paradoxes in special relativity and this
+
+ align:start position:0%
+paradoxes in special relativity and this
+ 
+
+ align:start position:0%
+paradoxes in special relativity and this
+will bring us ultimately to an
+
+ align:start position:0%
+will bring us ultimately to an
+ 
+
+ align:start position:0%
+will bring us ultimately to an
+understanding of the twin paradox
+
+ align:start position:0%
+understanding of the twin paradox
+ 
+
+ align:start position:0%
+understanding of the twin paradox
+later in this course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/3eqYo1LCGdw.txt b/3eqYo1LCGdw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b68c87e4fb733b5b8b3c7446c453bfc08ac312aa
--- /dev/null
+++ b/3eqYo1LCGdw.txt
@@ -0,0 +1,3342 @@
+PROFESSOR: I'm sorry.
+
+I have to give this to you.
+
+Basically OK, except you
+didn't understand
+
+it the first time.
+
+OK.
+
+Good morning.
+
+Happy spring.
+
+Happy April.
+
+We're running a little late.
+
+I'll try to finish chapter
+nine today and start on
+
+chapter ten.
+
+Ashish may have chapter
+ten here later.
+
+If not, it'll be on the web.
+
+So we've been talking about
+convolutional codes.
+
+Specifically rate 1/n
+convolutional codes.
+
+One input n outputs.
+
+As you may imagine, there
+are also rate k/n
+
+convolutional codes.
+
+Generalization to k
+inputs n outputs.
+
+These have not been so much used
+in practice, because in
+
+general, we're using these
+binary codes in the power
+
+limited regime, and
+we want low rates.
+
+So 1/n is a good rate.
+
+1/2, 1/3, 1/4, or down to 1/6
+are common kinds of rates.
+
+So I haven't bothered to develop
+the more elaborate
+
+theory for rate k/n codes.
+
+The rate 1/n codes,
+just to review.
+
+The code is simply defined as
+the set of all possible output
+
+sequences of a convolutional
+encoder, whose N impulse
+
+responses are written as an
+n-tuple g of d as the inputs
+
+range over all Laurent
+
+sequences, bi-infinite sequences.
+
+And what we showed last time
+is that without loss of
+
+generality or optimality, we
+could always take this g of d
+
+to be of a particular
+canonical form.
+
+Namely, the g of d could be
+taken to be a set of n
+
+polynomials, g_j of d, that
+were relatively prime.
+
+And for any code, you can find
+such a canonical encoder by
+
+its unique [UNINTELLIGIBLE] two
+units, and specifies the
+
+code, clearly, by this.
+
+So that's a nice canonical
+encoder to take.
+
+It furthermore has the property
+that there's an
+
+obvious realization of
+this encoder in the
+
+[UNINTELLIGIBLE] register form
+with nu memory units.
+
+And therefore 2 to
+the nu states.
+
+And we will prove in chapter ten
+that this is the minimal
+
+possible encoder
+for this code.
+
+In other words, there are lots
+of different encoders that
+
+generate this code, but you
+can't possibly encode it with
+
+fewer than the state space of
+dimension less than nu.
+
+That's the way it's going
+to sound in chapter ten.
+
+So we haven't quite got there
+yet, but it's a minimal
+
+encoder, therefore,
+in that sense.
+
+All right.
+
+Today we're going to go now and
+exploit the finite state
+
+structure of this code, to get
+a very efficient maximum
+
+likelihood sequence decoding
+algorithm called the Viterbi
+
+algorithm, which I'm sure
+you've all heard of.
+
+It's become very famous, not
+only in this field, but really
+
+in any place where you're trying
+to observe a finite
+
+state machine in memory-less
+noise.
+
+A finite state hidden markov
+model, if you like.
+
+And so now it's used, for
+instance, in the detection of
+
+genomes, where the exons end and
+the introns start and so
+
+forth, and the garbage is.
+
+And people use it who have no
+idea that it was originally a
+
+digital communications
+algorithm.
+
+But it's a very obvious
+algorithm.
+
+It's come up in many different
+forms, and Viterbi, in a way,
+
+was just lucky to get
+his name on it.
+
+Because it would come up very
+easily as soon as you pose the
+
+problem correctly.
+
+Let's start out with terminated
+
+convolutional codes.
+
+Which I forget whether I started
+on this last time.
+
+I think I may have.
+
+But we'll start from
+scratch again.
+
+When I say terminated, I mean
+that we're going to take only
+
+a subset of the code words
+that start at a
+
+certain time --
+
+say, time 0 --
+
+continue for some finite
+time, and then end.
+
+And in this set up, with this
+canonical encoder, it's
+
+polynomial, the easy way to
+specify that is to let u of d
+
+be a finite sequence that
+starts at time 0.
+
+That's called a polynomial.
+
+and let's restrict
+its degree --
+
+degree u of d less than k.
+
+In other words, it looks like u0
+plus u1 d plus so forth up
+
+to uk minus 1 d.
+
+Therefore I've chosen k, so I
+really have k information bits
+
+or input bits.
+
+All right?
+
+So I specify u0 through
+uk minus 1.
+
+I use that as the input
+in my encoder.
+
+What is then my code,
+my truncated code,
+
+let's call it ck --
+
+that's not a very good notation,
+but we'll use it
+
+just for now --
+
+will be the set of all u of d,
+g of d such that u of d is
+
+polynomial and the degree of
+u of d is less than k.
+
+OK.
+
+So we ask what that code
+is going to be.
+
+And let's take some
+simple examples.
+
+Turns out when we terminate
+codes, we always choose
+
+polynomial encoders, so the code
+will naturally collapse
+
+back to the 0 state.
+
+How long?
+
+Nu time units after the
+input stops coming in.
+
+The outputs will be all 0 at
+that point and forevermore.
+
+The shift register will clear
+itself out nu time units
+
+later, and then they'll
+be all 0.
+
+So the code really starts
+at time 0 and ends
+
+at time k plus nu.
+
+So we aren't going to worry, in
+this case, whether the code
+
+is non-catastrophic or not.
+
+Here one of the principal
+properties that we had was
+
+this property guaranteed
+non-catastrophic.
+
+And in fact, is necessary
+for non-catastrophicity.
+
+So we spent a lot of time
+talking about why that would
+
+be a bad thing, to
+be catastrophic.
+
+OK.
+
+But let's take a catastrophic
+rate 1/1 encoder, which simply
+
+we have g of d equals
+1 plus d.
+
+You remember this encoder
+as nu equals 1.
+
+The input looks like this.
+
+uk, uk minus 1.
+
+And we simply add these, yk.
+
+So we get y of d equals
+1 plus d u of d.
+
+OK.
+
+Now, if the input to this is a
+finite sequence, a polynomial,
+
+let's see what this code
+can possibly be.
+
+What the code's going
+to look like.
+
+The code's going to start
+in state 0, at time 0.
+
+So here's the time.
+
+At the first time, we can either
+get a 0 in our a 1 in,
+
+and accordingly, it will
+go to state 0 or 1.
+
+At the second time, we can go
+to state 0 with another 0 or
+
+just state 1 with a 1.
+
+If we get a 1 in and we're in
+state 1, then the output is
+
+going to be 0, and we'll
+stay in state 1.
+
+If we get a 0 in, the output
+will be a 1, and we'll go back
+
+to state 0.
+
+So this is what a
+typical trellis
+
+section looks like here.
+
+We have all possible
+transitions
+
+between the two states.
+
+And so now it goes on for
+a while like this.
+
+Time invariantly.
+
+There are 1, dot dot dot, and
+then finally, at some time --
+
+say this is time k, or maybe
+it's time k minus 1 --
+
+time index is a little fuzzy
+here -- we don't
+
+put any more 1s in.
+
+We only put 0s on from
+that time forward.
+
+So we could have one more
+transition back to state 0,
+
+and then after that it just
+stays in state 0 forevermore.
+
+And this isn't very
+interesting.
+
+It was in time 0 all the
+time before here.
+
+It was in state 0 all the time
+before there and put out 0s.
+
+It was in state 0 all the time
+after here and put out 0s.
+
+And this is clearly not
+conveying any information.
+
+Not an interesting
+part of the code.
+
+So we're going to consider the
+code just to be defined over
+
+these k plus 1 units of time.
+
+And so y of d we're going
+to consider to be a
+
+polynomial of degree k.
+
+Now we're going to assume
+that they're k bits in.
+
+Then we're going to wait one
+more time to let the shift
+
+register clear out,
+which is nu.
+
+And at that time, we're going
+to take whatever y is, and
+
+then we're going to
+terminate it.
+
+So if we consider this now, we
+have a block code whose length
+
+is the number of non-zero
+coefficients of y of d.
+
+So we have n equals k plus
+1, we have k by design
+
+information bits, and
+what's the minimum
+
+non-zero weight of this?
+
+It's linear.
+
+What's its minimum
+non-zero weight,
+
+or its minimum distance?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: 1.
+
+Show me a code word
+of weight 1.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I claim the minimum
+non-zero weight is 2 by
+
+typical argument.
+
+I have the all 0 sequence.
+
+If I ever leave the all 0
+sequence, I accumulate 1 unit
+
+of Hamming weight.
+
+And I need to ultimately come
+back to the all 0 sequence,
+
+because I've made everything
+finite here.
+
+So in this case, I can make
+the argument that I always
+
+have to come back to
+the all 0 sequence.
+
+Whenever I merge back into
+the all 0 sequence, I'll
+
+accumulate another
+unit of weight.
+
+So this is a code with
+minimum distance 2.
+
+Minimum non-zero weight 2.
+
+And in fact, it's just the
+single parity-check code of
+
+length n equals k plus 1.
+
+OK?
+
+And if you ask yourself,
+can you generate any --
+
+this is supposedly the
+even weight code.
+
+It contains all even weight
+k plus 1-tuples.
+
+And I think you can convince
+yourself that you can generate
+
+any of these k plus 1 even
+weight k-tuples.
+
+In fact, the generator
+matrix for this code.
+
+Look.
+
+Here's a set of generators.
+
+1 1 is in the code.
+
+0 1 1 is in the code.
+
+0 0 1 1 in the code.
+
+So here's a set of generators.
+
+0 1 1.
+
+Generator matrix for the
+code looks like this.
+
+We just go like that.
+
+And with these k generators,
+you can generate any even
+
+weight code word.
+
+So we get a kind of
+convolutional form to the
+
+generator matrix.
+
+A sliding parity-check form
+to the generator matrix.
+
+OK.
+
+So I assert that this is the
+single parity-check code.
+
+So here's a trellis
+
+representation for a block code.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I'm sure I've got the
+time indices screwed up.
+
+But I put in k bits.
+
+I wait 1 more unit of time --
+
+nu equals 1 --
+
+for this to clear out.
+
+So I get out k plus 1 bits.
+
+Think of it in terms
+of this here.
+
+I put in k, the last input you
+think of as necessarily being
+
+0, and I take the outputs
+here for k plus 1 times.
+
+OK.
+
+So first of all, a couple
+points here.
+
+AUDIENCE: In general, the length
+will be k plus nu?
+
+PROFESSOR: In general, length
+will be k plus nu.
+
+So let's write that down.
+
+So in general, by terminating
+a rate 1/n --
+
+nu is called the constraint
+length --
+
+constraint length nu, or 2
+to the nu state code --
+
+convolutional code after k
+inputs, we get a binary linear
+
+block code whose parameters
+are --
+
+we have k information bits.
+
+We have k plus nu non-trivial
+output times.
+
+At each output time, I
+get n output bits.
+
+So it's n times k plus nu
+is the total effective
+
+length of the code.
+
+And the distance, we would have
+to say, is greater than
+
+or equal to the distance of the
+block code is greater than
+
+or equal to the distance of
+the convolutional code.
+
+Why?
+
+Because all of the words in this
+block code are actually
+
+sequences in the convolutional
+code.
+
+I'm assuming here that the code
+is not catastrophic, so
+
+it's sufficient to look at all
+the finite sequences in the
+
+convolutional code.
+
+All right.
+
+And in general, the block code
+distance is almost always
+
+going to be equal to the
+convolutional code distance.
+
+And this is just for
+finite code words.
+
+So as another example, suppose
+we take our standard rate 1/2,
+
+nu equals 2, distance equals
+5, convolutional code.
+
+Our example 1 that we've
+been using all along.
+
+Suppose I terminate with
+k equals 4, then I'm
+
+going to get what?
+
+I'm going to get a 2 times 6,
+I'm going to get a 12, 4, 5
+
+binary linear block code.
+
+That is not so bad, actually.
+
+There's a point that I'm
+not going to make
+
+very strongly here.
+
+But terminated convolutional
+codes can be good block codes.
+
+And in fact, asymptotically,
+by choosing the parameters
+
+correctly, you can show that you
+can get a random ensemble
+
+of terminated convolutional
+codes that is as good as the
+
+best possible random ensemble
+of block codes.
+
+So terminated convolutional
+codes is one way of
+
+constructing optimal block codes
+in the asymptotic limit.
+
+These parameters aren't bad.
+
+Here's a rate 1/3 code
+with distance 5.
+
+Not too long.
+
+You know, you might compare
+it to what?
+
+The BCH code?
+
+There's a 15 7 5 BCH code,
+which is clearly better,
+
+because it's higher rate.
+
+But if you shorten this code,
+you have to shorten this by 3,
+
+this by 3 to keep
+the distance.
+
+You would get the same code.
+
+So it's not optimum, but
+it's not too bad.
+
+And furthermore, from this
+construction, you get a
+
+trellis representation,
+which in this case
+
+would look like this.
+
+It looks like the trellis that
+we started to draw last time.
+
+Sorry.
+
+Doesn't look like that.
+
+This guy goes down here,
+this guy comes here,
+
+this guy goes here.
+
+This continues for a while.
+
+And then finally, when we start
+to enforce all zeros, we
+
+only have one possible output
+from each of these.
+
+And we get a trellis that
+looks like that.
+
+All right?
+
+Which is 1, 2, 3 --
+
+I did it correctly for
+this code, actually.
+
+Because each of these
+is going to have a
+
+2-tuple output on it.
+
+And that looked like 0,0
+0,0 0,0 0,0 0,0.
+
+Each of the information bits
+causes a two-way branch, no
+
+matter where you are
+in the trellis.
+
+So here's 1, here's 2,
+here's 3, here's 4.
+
+That's the end of them.
+
+We wait for nu equal 2 to let
+the states converge back to 0.
+
+So that's a trellis
+representation of this 12 4 5
+
+block code.
+
+OK.
+
+I want to talk about terminated
+block codes,
+
+terminated trellis codes,
+convolutional codes as block
+
+codes, for two reasons.
+
+One is to say we can get
+block codes that way.
+
+But the other is to introduce
+the Viterbi algorithm for
+
+terminated convolutional
+codes.
+
+I think it's easier first to
+look at how the algorithm
+
+works when you have a finite
+trellis like this, and then
+
+we'll go on and say, well, how
+would this work if we let the
+
+trellis become very long, or
+in principle, infinite?
+
+Would the Viterbi algorithm
+still work?
+
+And it becomes obvious
+that it does.
+
+So this is going to be a maximum
+likelihood sequence
+
+detection or decoding
+algorithm.
+
+We're going to assume that each
+time here, we get to see
+
+two things.
+
+Corresponding to the two
+bits we transmit.
+
+So we transmit yk according
+to which trellis
+
+branch we're on --
+
+y0 at this point -- and we
+receive a 2-tuple r0.
+
+If we were on a binary input
+additive white Gaussian
+
+channel, this would go into,
+actually, the 2-PAM map, two
+
+plus or minus alphas, and be
+received as two real numbers.
+
+And we do the same thing here.
+
+y1, we receive r1, and so forth,
+up to yk plus nu, or k
+
+plus nu minus 1, I think it
+is, rk plus nu minus 1.
+
+OK.
+
+So we have a transmit 2-tuple
+and a received
+
+2-tuple every time.
+
+And we're going to assume that
+the channel is memoryless so
+
+that the probabilities of
+receiving the various possible
+
+received values, the
+likelihoods, are independent
+
+from time unit to time unit.
+
+That's the only way
+this works.
+
+Then if I want to get the total
+probability of r given
+
+y, where now I'm talking about
+over the whole block, this
+
+factors into the probabilities
+of rk given yk, yes?
+
+That's what I'm going
+to depend on.
+
+This is what's called the
+memoryless condition,
+
+memoryless channel.
+
+The transition probabilities do
+not depend on what's been
+
+sent or received in
+previous blocks.
+
+Or it's more convenient to use
+the minus log likelihood
+
+equals now the sum of the minus
+log p of rk given yk.
+
+So maximum likelihood is
+equivalent to minimize the
+
+neg-log likelihood.
+
+OK.
+
+I receive only one thing
+in each time unit.
+
+And each trellis branch
+corresponds to transmitting a
+
+specific thing.
+
+So I can label each trellis
+branch with the appropriate
+
+minus log p of rk given yk.
+
+Do you see that?
+
+In other words, for this trellis
+branch down here,
+
+which is associated with y2
+equals 0 1, or s of y2 equals
+
+alpha minus alpha, suppose I
+receive r2 equals r1, r2, I
+
+would label this by, say, the
+Euclidean distance between
+
+what I transmitted for that
+branch and what I received.
+
+For instance, on the additive
+white Gaussian channel, this
+
+would simply be rk
+minus s of yk.
+
+The Euclidean distance
+squared.
+
+Or equivalently, minus the inner
+product, the correlation
+
+between rk and s of yk.
+
+You know, these are equivalent
+metrics.
+
+Or on a binary symmetric
+channel, might be the Hamming
+
+distance between what I
+received and what I
+
+transmitted, both of which
+would be binary
+
+2-tuples, in this case.
+
+It's just some measure
+of distance --
+
+Log likelihood distance,
+Euclidean distance, Hamming
+
+distance --
+
+between the particular thing I
+would have transmitted if I'd
+
+been on this branch and the
+particular thing that I
+
+actually did receive.
+
+So having received a whole block
+of data, I can now put a
+
+cost on each of these
+branches.
+
+What's the minus log likelihood
+cost if I say that
+
+the code word goes through
+that branch?
+
+What does it cost me?
+
+All right.
+
+Now what I'm basically depending
+on is note, there's
+
+a one-to-one map between
+code words y and
+
+c and trellis paths.
+
+For this specific trellis up
+here, how many paths are there
+
+through the trellis?
+
+Do you see that however I go
+through the trellis, I'm going
+
+to meet four two-way branches?
+
+All right?
+
+According to [UNINTELLIGIBLE],
+there
+
+are four yes-no questions.
+
+It's a binary tree.
+
+So there are 16 possible ways
+to get through this trellis
+
+from start to finish, if I view
+it as a maze problem.
+
+And they correspond --
+
+I haven't labeled all
+the branche --
+
+but they do correspond to all
+16 words in this block code.
+
+So now what is maximum
+likely decoding?
+
+I want to find the one of those
+16 words that has the
+
+greatest likelihood, or the
+least negative log likelihood,
+
+over all of these 12 received
+symbols or 6 received times.
+
+So what will that be?
+
+Once I've labeled each of these
+branches with a log
+
+likelihood cost, I simply want
+to find the least cost path
+
+through this trellis.
+
+And that will correspond to
+the most likely code word.
+
+This is the essence of it.
+
+Do you all see that?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: The independent
+transmission allows me to
+
+break it up into a
+symbol-by-symbol or
+
+time-by-time expression.
+
+So I can simply cumulate over
+this sum right here.
+
+And I'm just looking for the
+minimum sum over all the
+
+possible ways I could get
+through this trellis.
+
+So now we translated this into
+finding the minimum cost path
+
+through a graph.
+
+Through a graph with a very
+special structure, nice
+
+regular structure.
+
+OK.
+
+Once you've got that, then I
+think it's very obvious how to
+
+come up with a nice recursive
+algorithm for doing that.
+
+Here's my recursive algorithm.
+
+I'm going to start computing
+weights.
+
+I'm going to start here.
+
+I'm going to assign
+weight zero here.
+
+Right here I'm going to assign a
+weight which is equal to the
+
+cost of the best path to get
+to that node in the graph.
+
+In this case, it's just the
+cost of that branch.
+
+Similarly down here.
+
+Similarly I proceed
+to these four.
+
+There's only one way to get to
+each of these four, and I
+
+simply add up what the
+total weight is.
+
+Now here's the first point where
+it gets interesting,
+
+where I have two possible ways
+to get to this node.
+
+One way is via these three
+branches, and that has a
+
+certain cost.
+
+Another way is via these three
+branches, and that has a
+
+certain cost.
+
+Suppose the cost of these three
+branches is higher than
+
+the cost of these
+three branches.
+
+Just pair-wise.
+
+All right?
+
+Claim that I can pick the
+minimum cost path to this
+
+node, throw away the other
+possibility, and I can never
+
+have thrown away something which
+itself is part of the
+
+minimum cost path through
+the whole trellis.
+
+Clearly.
+
+Suppose this is the best
+path from here to here.
+
+This is worse.
+
+X, X, X, X X. And now I find the
+minimum cost path through
+
+the whole trellis goes
+through this node.
+
+Say it's like that.
+
+Could it have started
+with this?
+
+No.
+
+Because I can always replace
+this with a path that starts
+
+with that and get
+a better path.
+
+So at this point, I can make a
+decision between all the paths
+
+that get to that node
+and pick just one.
+
+The best one that gets
+to that node.
+
+And that's called
+the survivor.
+
+This is really the key concept
+that Viterbi introduced.
+
+We only need to say one, the
+best up to that time.
+
+We need to do it for all the
+2 to the nu possibilities.
+
+So we have 2 to the nu survivors
+at time k or time i,
+
+whatever your time index is.
+
+Used k for something else.
+
+OK.
+
+So I can throw away half
+the possibilities.
+
+Now each survivor, I remember
+what its past history is, and
+
+I remember what its cost
+is to that point.
+
+Now to proceed, the recursion
+is to proceed one time unit
+
+ahead, to add the incremental
+cost -- say, to make a
+
+decision here, I need to add
+the incremental cost to the
+
+two survivors that were
+here and here.
+
+So I add an incremental cost,
+according to what these
+
+branches are labeled with.
+
+And now I find the best of these
+two possibilities to get
+
+to this node.
+
+So the recursion is called an
+ACS operation for add, we add
+
+increments to each of these
+paths, we compare which is the
+
+best, and we select
+the best one.
+
+We keep that.
+
+We throw away the other.
+
+We now have a one unit longer
+best path to this node and its
+
+cost for all 2 the nu survivors
+at time i plus 1.
+
+And just proceeding in that way,
+we go through until we
+
+finally get to the
+terminating node.
+
+And at this point, when we've
+found the best path to this
+
+node, we've found the best path
+
+through the whole trellis.
+
+OK?
+
+So that's all it is.
+
+I believe it's just totally
+obvious once you reduce it to
+
+a search for a minimum cost
+path through the trellis.
+
+It's very well suited to the
+application of convolutional
+
+codes, because we really are
+thinking of sending these bits
+
+as a stream in time.
+
+And at the receiver, you can
+think of just proceeding
+
+forward one unit of time, 2 to
+the nu, add, compare, selects,
+
+and we've got a new
+set of survivors.
+
+There are nice implications of
+this that involve, you can
+
+build a computer for every
+node or for every pair of
+
+nodes to do the ACS operation,
+make a very fast recursion
+
+through here.
+
+So that's it.
+
+That's the Viterbi algorithm
+for terminated
+
+convolutional codes.
+
+Now let's ask about the
+VIterbi algorithm for
+
+unterminated convolutional
+codes.
+
+Suppose this trellis
+becomes very long.
+
+Across the whole page.
+
+What are these survivors
+going to look like?
+
+Suppose we start from a definite
+node here, and we've
+
+got a four state convolutional
+code, and we iterate and we
+
+iterate and we iterate with
+the Viterbi algorithm.
+
+After a long time, somewhere out
+here, we're going to have
+
+four survivors and
+their histories.
+
+And I've greatly simplified,
+but basically the histories
+
+are going to look schematically
+something --
+
+I don't know -- could
+be anything.
+
+Look like this.
+
+The point I'm illustrating here
+is that the histories
+
+will be distinct right
+at this time.
+
+They have to be, because
+they're going to
+
+four distinct stages.
+
+But as you go backwards in
+time, you will find they
+
+merge, any two histories will
+merge, at a certain time back.
+
+And this is a probablistic
+thing.
+
+It depends on what's happening
+on the channel and so forth.
+
+But with high probability, they
+will have merged not too
+
+far back in time.
+
+So even if we never get to a
+final node, even if we just
+
+let this process continue
+forever, at this point we can
+
+say, we can make a definite
+decision at this time.
+
+Right?
+
+Because all survivors
+start with a common
+
+initial part, up to here.
+
+So one way to operate the
+Viterbi algorithm would be
+
+just to, at this
+point, say, OK.
+
+I'm going to put out everything
+before this time.
+
+No matter how long I run the
+decoder, the first part of it
+
+is always going to
+be this part.
+
+So these are definitely decided
+up to this time.
+
+And then I still don't
+know about here.
+
+I'm going to have to go
+a little bit further.
+
+You proceed further, and after
+a while, you find more that's
+
+definitely done.
+
+In practice, that would lead
+to a sporadic output rate.
+
+That isn't really
+what you want.
+
+So in practice what you do is
+you establish a decision
+
+delay, delta.
+
+And what you put out is you hope
+that 99.999% of the time,
+
+that if you look back delta on
+all the survivors, they will
+
+all be a common path,
+delta back here.
+
+So there's a very
+high probability
+
+you will have converged.
+
+And so simply at this time, you
+put out what you decided
+
+on delta time units earlier.
+
+Next time you put out
+the next one.
+
+Next time you put out
+the next one.
+
+So you get a nice, regular,
+synchronous stream of data
+
+coming out of here.
+
+Every so often, it may happen
+that you get out to here and
+
+you still haven't
+made a decision.
+
+Then you have to do something.
+
+And it really doesn't matter
+terribly much what you do.
+
+You might pick the guy who has
+the best metric at this time,
+
+or you simply might say, well,
+I'm always going to pick the
+
+one that goes to all zeros.
+
+That wouldn't be symmetric.
+
+You can make any decision
+you like.
+
+And you could be wrong.
+
+But you pick delta large enough
+so that the probability
+
+of this happening is very rare,
+and this just adds a
+
+little bit to your error
+probability, and as long as
+
+the probability of making an
+error because of this kind of
+
+operation is much lower than
+your probability of making an
+
+ordinary decoding error, then
+you're going to be OK.
+
+For convolutional codes way back
+at the beginning of time,
+
+people decided that a decision
+delay a 5 times nu, 5 times
+
+the constraint length, was
+the right rule of thumb.
+
+And that's been the rule of
+thumb for rate 1/n codes
+
+forever after.
+
+The point is, delta should
+be a lot more than nu.
+
+You know, after one constraint
+length, you certainly won't
+
+have converged.
+
+After five constraint lengths,
+you're highly
+
+likely to have converged.
+
+And theoretically, the
+probability of not converging
+
+goes down exponentially
+with delta.
+
+So big enough is
+going to work.
+
+And a final point is that
+sometimes, you really care
+
+that what you put out to
+be a true code word.
+
+In that case, if you get to this
+situation, you have to
+
+make a choice, you make a choice
+here, then you have to
+
+actually eliminate all the
+survivors that are not
+
+consistent with that choice.
+
+And you can do that simply by
+putting an infinite metric on
+
+this guy here.
+
+Then he'll get wiped out as
+soon as he's compared with
+
+anybody else.
+
+And that will ensure that
+whatever you eventually put
+
+out, you keep the
+sequence being a
+
+legitimate code sequence.
+
+So that's a very fine point.
+
+OK.
+
+So there really isn't any
+serious problem with letting
+
+the Viterbi algorithm run
+indefinitely in time once
+
+you've got it started.
+
+How do you get it started?
+
+Suppose you came online and
+you simply had a stream of
+
+outputs, transmitted from a
+convolutional code over a
+
+channel, and you didn't know
+what state to start in.
+
+How do you use synchronize
+to a starting state?
+
+Well, this is not hard either.
+
+Basically you start, you're in
+one of four states, or 2 to
+
+the nu states.
+
+You don't know which one.
+
+Let's just give them all cost
+0 and start decoding, using
+
+the four state trellis.
+
+And we just start receiving
+2-tuples from here on.
+
+We get rk, r k plus
+1, and so forth.
+
+So how should we start?
+
+Well, we'll just start
+like that.
+
+And we get sort of the mirror
+image of this --
+
+that after a time, these will
+all converge to a single path.
+
+Or after a time, when we're way
+down here, this is what
+
+the situation will look like.
+
+These things will each have a
+different route over here, but
+
+they will have converged
+in here.
+
+There will be a long path over
+which they're all converged,
+
+and then towards the end,
+they'll be unrooted again.
+
+OK.
+
+Well, that's fine.
+
+What does that mean
+in practice?
+
+That means we make errors during
+the synchronization.
+
+But we say we're synchronized
+when we get this case where
+
+all the paths going to all the
+current survivors have a
+
+common central stage.
+
+And how long does it take
+to synchronize?
+
+Again, by analysis, it's exactly
+this same delta again.
+
+The probability of not being
+synchronized after delta goes
+
+down exponentially with delta
+in exactly the same way.
+
+It's just a mirror image from
+one end to the other.
+
+So from a practical point of
+view, this is no problem.
+
+And just starting the Viterbi
+decoder up, with arbitrary
+
+metrics here, and after five
+constraint lengths, if you
+
+like, it's highly likely to
+have gotten synchronized.
+
+You'll make errors for five
+constraint lengths and after
+
+that, you'll be OK, as though
+you knew the starting state.
+
+So the moral is, no problem.
+
+You can just set up the Viterbi
+
+algorithm and let it run.
+
+The costs will all, of course,
+increase without bound, which
+
+is [UNINTELLIGIBLE].
+
+You can always renormalize them,
+subtract a common cost
+
+from all of them.
+
+That won't change anything.
+
+Keep them within running time.
+
+So we don't need to terminate
+convolutional codes in order
+
+to run the Viterbi algorithm.
+
+We just let it self-synchronize
+and we make
+
+decisions with some
+decision delay.
+
+And the additional problems
+that we have
+
+are very, very small.
+
+There are no additional
+problems.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: At this point?
+
+Well, notice that we don't know
+that we've synchronized
+
+until we've continued further,
+and we've got --
+
+you know, where we've really
+synchronized is when we see
+
+that every survivor path
+has the common root.
+
+So at that point, there is
+really only one path here.
+
+And we can say that the
+synchronized part is
+
+definitely decoded.
+
+And we can't really say too
+much about this out here,
+
+because this depends on what's
+happened out in the past.
+
+So you say this is erasures,
+if you like.
+
+The stuff that we're pretty sure
+has a high probability of
+
+being wrong.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: There is
+only one decoded
+
+path during this interval.
+
+AUDIENCE: But before that
+interval there are branches
+
+and so on right.
+
+PROFESSOR: Well here, we
+don't know anything.
+
+Here we know the results
+of one computation.
+
+What are you suggesting?
+
+Just pick the best one
+at that point?
+
+AUDIENCE: And finally after
+you reach the [INAUDIBLE]?
+
+PROFESSOR: And finally?
+
+I'm just not sure
+exactly what the
+
+logic is of your algorithm.
+
+It's clear for this, it wouldn't
+make any difference
+
+if we just started off
+arbitrarily so, we're going to
+
+start in the zero state.
+
+And we only allow things to
+start in the zero state.
+
+Well, we'll eventually get
+to this path anyway.
+
+So it really doesn't matter
+how you start.
+
+You're going to have garbage for
+a while, and then you're
+
+going to be OK.
+
+There's no point in doing
+anything more
+
+sophisticated than that.
+
+I don't want to discuss what
+you're suggesting, because I
+
+think there's a flaw in it.
+
+Try to figure out what time
+you're going to make this
+
+decision at.
+
+OK.
+
+Do we all understand the
+Viterbi algorithm?
+
+Yes?
+
+Good.
+
+We can easily program it up.
+
+There will be an exercise
+on the homework.
+
+But now you can all do the
+Viterbi algorithm.
+
+All right.
+
+So --
+
+and oh.
+
+What's the complexity of
+the Viterbi algorithm?
+
+What is the complexity?
+
+We always want to be talking
+about performance versus
+
+complexity.
+
+So it's a recursive algorithm.
+
+We do exactly the same
+operations every unit of time.
+
+What do the operations
+consist of?
+
+They consist of add,
+compare, select.
+
+How many additions to
+we have to make?
+
+Additions are basically equal
+to the number of branches in
+
+each unit of time in the
+trellis, which is 2
+
+to the nu plus one.
+
+Is that clear?
+
+We have 2 to the nu states.
+
+Two branches out of, two
+branches into each state,
+
+always for rate one.
+
+So we have 2 to the nu
+plus 1 additions.
+
+We get 2 the nu compares,
+one for each state.
+
+Which is really, you can
+consider the select to be part
+
+of the compare.
+
+Overall, you can say the
+complexity is of the order of
+
+2 to the nu or 2 to
+the nu plus 1.
+
+This is the number of states
+or the state complexity.
+
+This is the number
+of branches.
+
+I will argue a little bit
+later that the branch
+
+complexity is really
+more fundamental.
+
+You've got to do at least one
+thing for each branch.
+
+So in different set up,
+the branch complexity.
+
+But these are practically the
+same thing, and so we say that
+
+the complexity of the Viterbi
+algorithm is basically like
+
+the number of states.
+
+We have a four state encoder,
+the complexity's like four, it
+
+goes up exponentially with
+the constraint length.
+
+This says, this is going to be
+nice, as long as we have short
+
+constraint length.
+
+For longer constraint lengths,
+you know, a constraint length
+
+20, it's going to be a pretty
+horrible algorithm.
+
+So we can only use the Viterbi
+algorithm relatively short
+
+constraint length codes,
+relatively
+
+small numbers of states.
+
+The biggest Viterbi algorithm
+that I'm aware has ever been
+
+built is a 2 the 14th
+state algorithm.
+
+The so-called big Viterbi
+decoder out at JPL.
+
+It was used for the Galileo
+space missions.
+
+It's in a rack that big.
+
+I'm sure nowadays you could
+practically get it on a chip,
+
+and you could maybe do
+2 the 20th states.
+
+But so this exponential
+complexity, in computer
+
+science terms, not really
+what we want.
+
+But when we're talking about
+moderate complexity decoders,
+
+these really have proved to be
+the most effective, and become
+
+the standard moderate
+complexity decoder.
+
+The advantage is that we can
+do true maximum likelihood
+
+decoding on a sequence basis,
+using soft decisions, using
+
+whatever reliability information
+the channel has,
+
+as long as it's memoryless.
+
+So last topic is to talk
+about performance.
+
+How are we going to evaluate
+the performance of
+
+convolutional codes?
+
+You remember what we
+did on block codes?
+
+We basically looked at the
+pairwise error probability
+
+between block code words, we
+then did the union bound,
+
+based on the pairwise
+error probabilities.
+
+And we observed that the union
+bound was typically dominated
+
+by the minimum distance error
+events, and so we get the
+
+union bound estimate, which
+was purely based on the
+
+minimum distance possible
+errors.
+
+And we can do exactly the
+same thing in the
+
+convolutional case.
+
+Convolutional case, again,
+is a linear code.
+
+That means it has the group
+property, has symmetry such
+
+that the distances from every
+possible code sequence to all
+
+other code sequences are going
+to be the same, since we're
+
+talking on a long or possibly
+infinite sequence basis.
+
+And we need to be just a little
+bit more careful about
+
+what an error consists of.
+
+We need to talk about
+error events.
+
+And this is a simple concept.
+
+Let us again draw a path
+corresponding to the
+
+transmitted code words.
+
+A very long path, potentially
+infinite, but it is some
+
+definite sequence.
+
+And let's run it through a
+memory list channel, use the
+
+Viterbi algorithm, and we're
+going to get some received
+
+code word, or decoded
+code word.
+
+This is one place where you
+might want to insist that the
+
+Viterbi algorithm actually
+put out a code word.
+
+What is that going
+to look like?
+
+Well, if you're running
+normally, the received code
+
+word is going to equal
+the transmitted code
+
+word most the time.
+
+Except it's going
+to make errors.
+
+And what will the errors
+look like?
+
+They'll look like a branch off
+through the trellis, and then
+
+eventually a reemerging
+into the same state.
+
+And similarly, you go on longer,
+and you might have
+
+another error.
+
+And any place where there's
+a difference --
+
+should have done a different
+color here --
+
+any place where there's
+difference, this is called an
+
+error event.
+
+So what I'm illustrating is a
+case when we had two disjoint
+
+error events.
+
+Is that concept clear?
+
+We're going to draw the trellis
+paths corresponding
+
+the transmitted code word and
+the decoded code word.
+
+Wherever they diverge over a
+period of time, we're going to
+
+call it an error event.
+
+But eventually they will
+re-merge again.
+
+So it could be a short time.
+
+Can't be any shorter than the
+constraint length plus 1.
+
+That would be the minimum
+length error event.
+
+Could be a longer time.
+
+Unbounded, actually.
+
+OK.
+
+What is going to be the
+probability of an error event
+
+starting at some time?
+
+And when I say an error event
+starting at time k, let's
+
+suppose I've been going along
+on the transmitted path, and
+
+the decoder has still
+got that there.
+
+I'm asking, what is the
+probability that this code
+
+word is actually more likely
+on a maximum likelihood
+
+sequence detection basis
+than this one?
+
+Well, simply the probability
+that the received sequence is
+
+closer to this one
+than this one.
+
+We know how to analyze that
+for a finite differences.
+
+What is the difference here?
+
+The difference, call this y
+of d and this y hat of d.
+
+What is y of d minus
+y hat of d?
+
+We'll call that e of d.
+
+This is a code word.
+
+This is a decoded code word.
+
+So the error event has
+to be a code word.
+
+Right?
+
+Decoder made a mistake.
+
+The mistake has to
+be a code word.
+
+So we're asking, what is the
+probability that y of d sent y
+
+hat of d decoded, where
+y hat of d equals y
+
+of d plus e of d?
+
+We'll just ask for that
+particular event.
+
+This is the probability that
+r of d closer to y hat
+
+of d than y of d.
+
+Now, making a big leap.
+
+This is equal to --
+
+we're just talking about two
+sequences in Euclidean space.
+
+All that matters is
+the Euclidean
+
+distance between them.
+
+What is the Euclidean distance
+between them?
+
+It's 4 alpha squared times the
+weight of this error event,
+
+the Hamming weight of
+this error event.
+
+And so if you remember how to
+calculate pairwise error
+
+probabilities, this is just
+alpha squared D over sigma
+
+squared, where D is the
+distance of e of d.
+
+The weight, the Hamming
+weight of e of d.
+
+Call it sigma squared.
+
+Remember something that
+looked like that?
+
+So once again, we go from the
+Hamming weight of a possible
+
+error event to a Euclidean
+weight, which is 4 alpha
+
+squared times the
+Hamming weight.
+
+We actually take the square root
+of that and we only need
+
+to make an error, a noise
+of half of that length.
+
+So that's where the
+4 disappears.
+
+And we just get q of d squared
+over sigma squared, where d is
+
+the distance to the
+decision boundary.
+
+Compressing a lot of steps,
+but it's all something you
+
+felt you knew well a
+few chapters ago.
+
+So the union bound would simply
+be the sum over all
+
+error events in the code
+such that the start --
+
+so e of d is --
+
+you want them to start
+at time 0, say.
+
+Let's ask for the probably
+of an error event
+
+starting at time 0.
+
+So we want it to be polynomial,
+have no non-zero
+
+negative coefficients, and have
+the coefficient at time 0
+
+be 1, or not 0.
+
+I'm doing this very roughly.
+
+Of q to the square root of alpha
+squared times the weight
+
+Hamming of e of d over
+sigma squared.
+
+Just as before.
+
+So to get the union bound, we
+sum up over the weights of all
+
+sequences that start
+at time 0.
+
+Let's do it for our
+favorite example.
+
+Suppose g of d is 1 plus d
+squared, 1 plus d plus d
+
+squared, then what are the
+possible e of d's that I'm
+
+talking about?
+
+I have this itself.
+
+1 plus d squared, 1 plus
+d plus d squared.
+
+This is weight equal to 5.
+
+What's my next possible
+error event?
+
+Would be 1 plus d times this.
+
+So it's going to be a table.
+
+We have g of d, 1 plus d times
+g of d, which is equal to 1
+
+plus d plus d squared plus d
+cubed, 1 plus d cubed, that
+
+has weight equals 6.
+
+What's my next longer one?
+
+1 plus d squared times g of d
+equals 1 plus d fourth, 1 plus
+
+d plus d third plus d fourth,
+that has weight 6.
+
+1 plus d plus d squared
+times g of d.
+
+1 plus d plus --
+
+this is 1 plus d plus --
+
+plus d third, plus d forth.
+
+I may be making a
+mistake here.
+
+1 plus d squared
+plus d fourth.
+
+It's hard to do this by
+hand after a while.
+
+OK.
+
+Notice, we start tabulating all
+the error events, which I
+
+can do in order of the degree of
+u of d, always keeping the
+
+non-zero, the time 0
+term equal to 1.
+
+So this is the only
+one of length 1.
+
+This is [UNINTELLIGIBLE]
+
+of degree 0.
+
+This is the only one
+of degree 1.
+
+There are two of them
+of degree 2.
+
+There will be four of them of
+degree 3, and so forth.
+
+So I can lay out what all the
+error events could be, and I
+
+look at what their
+weights are.
+
+Here's my minimum weight
+error event.
+
+Then I have two of weight
+six and so forth.
+
+So the union bound, I'd be
+adding up this term.
+
+I'd get one term where the
+weight is 5, two where the
+
+weight is 6, I don't know how
+many where the weight is 7.
+
+I happen to know there
+were only two
+
+weight 6 error events.
+
+And you simply have to find out
+what the weight profile is
+
+and put it in the union bound.
+
+Or you can use the union bound
+estimate, which is simply --
+
+let's just take k nd, the number
+of error events of
+
+minimum weight d, times q to
+the square root of alpha
+
+squared d, where d equals min
+weight over sigma squared.
+
+OK.
+
+In this case, nd equals
+1, d equals 6.
+
+Let me take this one
+step further.
+
+nd times q to the square
+root of --
+
+what is sigma squared
+equals n0 over 2?
+
+And Eb equals n times
+alpha squared.
+
+The energy per transmitted
+bit is alpha squared.
+
+We're going to transmit n bits
+for every information bit.
+
+So plugging those in, I get 2d
+over n times Eb over N0, which
+
+is again of the form nd q to the
+square root of 2 times the
+
+coding gain of the code
+times Eb over N0.
+
+Bottom line is I get precisely
+the same performance analysis,
+
+or I get a nominal
+coding gain of --
+
+in general, it's kd over n.
+
+If it were a rate k over n
+code, since we're only
+
+considering rate 1 over n codes,
+it's just d over n.
+
+And I get an error coefficient
+which equals the number of
+
+weight d code words,
+starting time 0.
+
+Of course an error event could
+start at any time.
+
+If there are nd starting
+at time 0, how many
+
+start at time 1?
+
+Time invariant code.
+
+So it's going to be the same
+numbers could possibly
+
+start at time 1.
+
+So what I'm computing here is
+the probability of an error
+
+event starting at a
+particular time.
+
+For this particular code,
+what do I have?
+
+I have one event of weight 5.
+
+So the nominal coding gain
+is 5 over n, which is 2.
+
+Which is --
+
+5 is 7 dB, 2 is 3 dB,
+so this is 4 dB.
+
+That's pretty good.
+
+Nominal coding gain of 4 dB with
+only a four state code.
+
+Obviously a very simple
+decoder for this code.
+
+And what is kd equals 1?
+
+That implies --
+
+again, we have the same argument
+about whatever the
+
+error coefficient is.
+
+You could plot this curve.
+
+The larger the error coefficient
+is, the more the
+
+curve moves up, and
+therefore over.
+
+You get an effective coding
+gain which is less.
+
+But this means since it's 1,
+you don't have to do that.
+
+The effective coding gain
+is the same as the
+
+nominal coding gain.
+
+It's still 4 dB.
+
+So it's a real 4 dB of coding
+gain for the simple little two
+
+state code.
+
+This code compares very directly
+with the 8 4 4
+
+Reed-Muller code, block code.
+
+This code also has rate 1/2.
+
+It has the same rate.
+
+We'll see that it also has a
+four-state trellis diagram.
+
+But it only has distance four,
+which means its nominal coding
+
+gain is only 2, 3 dB.
+
+And furthermore, it has 14
+minimum weight words, which
+
+even dividing by 4 to get the
+number per bit, there's still
+
+a factor of 3, still going to
+cost us another couple of
+
+tenths of a dB.
+
+Its effective coding gain is
+only about 2.6 or 2.7 dB.
+
+All right?
+
+So this code has much better
+performance for about the same
+
+complexity as this code,
+at the same rate.
+
+And this tends to be typical.
+
+Convolutional codes just beat
+block codes when you compare
+
+them in this way.
+
+Notice that we're assuming
+maximum likelihood decoding.
+
+We don't yet have a maximum
+likelihood decoding algorithm
+
+for this code.
+
+We'll find for this code, we can
+also decode it using the
+
+Viterbi algorithm with
+a four state decoder
+
+comparable to this one.
+
+So it would be, I would say,
+for maximum likelihood
+
+decoding --
+
+about same complexity.
+
+But we simply get much better
+performance with the
+
+convolutional.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Say again?
+
+AUDIENCE: What happened
+to the k?
+
+PROFESSOR: Why is
+k equal to 1?
+
+Which k?
+
+Over here?
+
+AUDIENCE: Yeah. kd
+[INAUDIBLE].
+
+PROFESSOR: All right.
+
+We're only considering
+rate 1/n codes.
+
+If it were a rate k/n code, we
+would get k over n, because
+
+this would be n over k
+times alpha squared.
+
+Just the same as before.
+
+In fact, I just want to wave my
+hand, say, everything goes
+
+through as before.
+
+As soon as you get the error
+event concept, you can reduce
+
+it to the calculation of
+pairwise error probabilities,
+
+and then the union bound
+estimate is as before.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Well, I had my
+little trellis here.
+
+And how long in real time
+does it take for
+
+two paths to merge?
+
+An error event has got to take
+at least nu plus 1 time units
+
+for two paths to diverge
+and then merge
+
+again in the trellis.
+
+Is that clear?
+
+Or put another way, the lowest
+degree of any possible error
+
+event is nu, which means it
+actually takes place over nu
+
+plus 1 time units.
+
+OK?
+
+From this.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Why is
+the lowest --?
+
+I'm taking g of d --
+
+the definition of nu is what?
+
+The maximum degree of g of d.
+
+OK?
+
+So if that's so, then the
+shortest length error event is
+
+1 times g of d, which takes nu
+plus 1 time units to run out.
+
+So error events have to be at
+least this long, and then they
+
+can be any integer length
+longer than that.
+
+You don't look totally happy.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You understand?
+
+OK.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: How I see it
+from this diagram?
+
+Where have I got a picture
+of a trellis?
+
+Here I've got a picture
+of a trellis.
+
+I've defined an error
+event by taking a
+
+transmitted code word.
+
+It's a code sequence.
+
+This is supposed to represent
+some path through the trellis.
+
+There's one-to-one
+correspondence between code
+
+sequences and trellis paths.
+
+Then I find another code
+sequence, which is the one I
+
+actually decided on.
+
+Call that the decoded
+code sequence.
+
+And I say, what's the minimum
+length of time they could be
+
+diverged from one another?
+
+All right?
+
+Let's take this particular
+trellis.
+
+What's the minimum length
+of time any two paths --
+
+say, here's the transmitted
+path.
+
+Suppose I try to find another
+path that diverges from it?
+
+Here's one.
+
+Comes back to it.
+
+Here's one.
+
+Another one.
+
+Comes back to it.
+
+I say that the minimum length
+of time it could
+
+take is nu plus 1.
+
+Why?
+
+Because the difference between
+these two paths is itself a
+
+code sequence, is therefore
+a non-zero polynomial
+
+multiple of g of d.
+
+OK?
+
+Same argument.
+
+OK.
+
+So I guess I'm not going to get
+into chapter 10, so I'll
+
+discourse a little bit more
+about convolutional codes
+
+versus block codes.
+
+How do you construct
+convolutional codes, actually?
+
+You see that really, what you
+want to do is to first of all,
+
+maximize the minimum distance
+for certain constraint length.
+
+Subject to that, you want to
+minimize the number of minimum
+
+distance words.
+
+You want to, in fact, get the
+best distance profile.
+
+Is there any block codes?
+
+We had nice, algebraic
+ways of doing this.
+
+Roots of polynomials,
+Reed-Solomon codes.
+
+We could develop an algebraic
+formula which told us what the
+
+minimum distance was.
+
+Do we have any nice algebraic
+constructions like that
+
+convolutional code?
+
+No.
+
+Basically, you've just got to
+search all the possible
+
+polynomials where the maximum
+degree is nu.
+
+Take pairs of polynomials.
+
+If you want a rate 1/2 code of
+degree nu, there's not that
+
+many things you have
+to search.
+
+All right?
+
+You just take all possible pairs
+of binary polynomials of
+
+degree nu or less, making sure
+that you don't take any two
+
+which have a common divisor, an
+untrivial common divisor,
+
+so you can wipe those out.
+
+You want to make sure that
+the constant term is 1.
+
+There's no point in sliding one
+over so it has a larger
+
+constant term than 1.
+
+But subject to those provisos,
+you simply try all pairs g1,
+
+g2, and you just do --
+
+as soon as you've assured
+yourself they're not
+
+catastrophic, they don't have a
+common divisor, then you can
+
+just list, you know, the finite
+code words are going to
+
+be the ones that are
+generated by
+
+finite information sequences.
+
+So you can just list all the
+code words, as I've started to
+
+do up here.
+
+Or since the trellis is, in
+fact, a way of listing all the
+
+code words, there's a one-to-one
+correspondence
+
+between code words and trellis
+paths, you can just start
+
+searching through the trellis
+and you will quickly find all
+
+the minimum weight code words,
+and thereby establish the
+
+minimum distance, the
+weight profile as
+
+far out as you like.
+
+And you choose the best.
+
+You try all possibilities.
+
+So Joseph Odenwalder did this
+as soon as people recognized
+
+that short convolutional codes
+could be practical, and he
+
+published the tables back in his
+PhD thesis in '69, so he
+
+got a PhD thesis out of this.
+
+It wasn't that hard, it's done
+once and for all, and the
+
+results are in the notes.
+
+The tables.
+
+And you can see from the
+tables that in terms of
+
+performance versus moderate
+complexity,
+
+things go pretty well.
+
+Here's this four state code.
+
+It already gets you 4 dB of
+effective coding gain.
+
+To get to 6 dB of effective
+coding gain, you need to go up
+
+to about 64 states.
+
+First person to do this was
+Jerry Heller at Jet Propulsion
+
+Laboratory.
+
+Again, about '68, immediately
+after Viterbi proposed his
+
+algorithm in '67, Heller was the
+first to go out and say,
+
+well, let's see how
+these perform.
+
+So he found a good 64 state
+rate 1/2 code, and he did
+
+probability of error versus Eb
+over N0, and he said, wow.
+
+I get a 6 dB coding gain.
+
+And Viterbi had no idea that his
+algorithm would actually
+
+be useful in practice.
+
+He was just using it
+to make a proof.
+
+And he didn't even know
+it was optimum.
+
+But he's always given the credit
+to Heller for realizing
+
+it could be practical.
+
+And so that 64 state rate 1/2
+code with Viterbi algorithm
+
+decoding became very popular
+in the '70s.
+
+Heller and Viterbi and Jacobs
+went off to form a company
+
+called Linkabit.
+
+And for the technology of the
+time, that seemed to be a very
+
+appropriate solution.
+
+You see you get approximately
+the same thing as a
+
+rate 1/3, rate 1/4.
+
+If you go lower in rate you
+can do marginally better.
+
+If you are after tenths of
+a dB, it's worthwhile.
+
+Later in the decade, is the best
+way to get more gain to
+
+go to more and more complicated
+
+convolutional codes?
+
+No.
+
+The best way is to use the
+concatenated idea.
+
+Once you use these maximum
+likelihood decoders, the
+
+Viterbi decoders, to get your
+error rate down to 10 to the
+
+minus 3 or something, 1 in 1000,
+at that point you have
+
+very few errors, and you can
+apply then an outer code to
+
+clean up the error events
+that do occur.
+
+You see, you're going to get
+bursts of errors in your
+
+decoded sequence.
+
+It's a very natural idea to have
+an outer code, which is
+
+based on gf of 256,
+say, 8 bit bytes.
+
+And so a Reed-Solomon code comes
+along and cleans up the
+
+errors that do occur, and drives
+the error probability
+
+down to 10 to the minus 12, to
+whatever you like it, with
+
+very little redundancy, very
+little additional cost.
+
+So that became the standard
+approach for space
+
+communications in the '70s
+and indeed '80s.
+
+I've already mentioned that
+around '90, they went up to
+
+this 2 to the fourteenth
+state Viterbi decoder.
+
+They went to much more powerful
+
+outer codes, much cleverer.
+
+And they were able to get to
+within about 2 or 3 dB of the
+
+Shannon limit.
+
+And that was the
+state-of-the-art on the eve of
+
+the discovery of turbo codes,
+which is where we're going in
+
+all of this.
+
+So from a practical point
+of view, in the moderate
+
+complexity regime, simple
+convolutional codes with
+
+moderate complexity Viterbi
+decoding are the best still
+
+that anybody knows how to do.
+
+They have all these
+system advantages.
+
+They work with nice synchronous
+streams of
+
+traffic, which is what you want
+for data transmission.
+
+They use soft decisions.
+
+They use any kind
+of reliability
+
+information you have.
+
+They're not limited
+by hard decisions.
+
+They're not limited by bounded
+systems as the algebraic
+
+schemes are.
+
+So it just proved to be a better
+way to go on channels
+
+like the additive white Gaussian
+noise channel.
+
+OK.
+
+So we didn't get into
+chapter 10.
+
+We'll start that next time.
\ No newline at end of file
diff --git a/5rjoqINtRbs.txt b/5rjoqINtRbs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e99d8282e0fd2ac29ddd79670a148ddc505626ff
--- /dev/null
+++ b/5rjoqINtRbs.txt
@@ -0,0 +1,13704 @@
+align:start position:0%
+ 
+okay so let me
+
+ align:start position:0%
+okay so let me
+ 
+
+ align:start position:0%
+okay so let me
+update where we are
+
+ align:start position:0%
+update where we are
+ 
+
+ align:start position:0%
+update where we are
+in terms of the
+
+ align:start position:0%
+in terms of the
+ 
+
+ align:start position:0%
+in terms of the
+calendar
+
+ align:start position:0%
+calendar
+ 
+
+ align:start position:0%
+calendar
+i guess a notable thing is that we have
+
+ align:start position:0%
+i guess a notable thing is that we have
+ 
+
+ align:start position:0%
+i guess a notable thing is that we have
+reached lecture 10 today thursday
+
+ align:start position:0%
+reached lecture 10 today thursday
+ 
+
+ align:start position:0%
+reached lecture 10 today thursday
+in terms of the reading list
+
+ align:start position:0%
+in terms of the reading list
+ 
+
+ align:start position:0%
+in terms of the reading list
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+having done all the risk sharing yeah
+
+ align:start position:0%
+having done all the risk sharing yeah
+ 
+
+ align:start position:0%
+having done all the risk sharing yeah
+we're at lecture 10 so there's a couple
+
+ align:start position:0%
+we're at lecture 10 so there's a couple
+ 
+
+ align:start position:0%
+we're at lecture 10 so there's a couple
+of things that are starred here
+
+ align:start position:0%
+of things that are starred here
+ 
+
+ align:start position:0%
+of things that are starred here
+and they obviously both come up in the
+
+ align:start position:0%
+and they obviously both come up in the
+ 
+
+ align:start position:0%
+and they obviously both come up in the
+lecture today
+
+ align:start position:0%
+lecture today
+ 
+
+ align:start position:0%
+lecture today
+one is the early version of this paper
+
+ align:start position:0%
+one is the early version of this paper
+ 
+
+ align:start position:0%
+one is the early version of this paper
+with alvarez and kawasuti pai sit on
+
+ align:start position:0%
+with alvarez and kawasuti pai sit on
+ 
+
+ align:start position:0%
+with alvarez and kawasuti pai sit on
+cash
+
+ align:start position:0%
+cash
+ 
+
+ align:start position:0%
+cash
+which has a star on it it's a little bit
+
+ align:start position:0%
+which has a star on it it's a little bit
+ 
+
+ align:start position:0%
+which has a star on it it's a little bit
+rough because it's kind of even then in
+
+ align:start position:0%
+rough because it's kind of even then in
+ 
+
+ align:start position:0%
+rough because it's kind of even then in
+the process of revision and i have added
+
+ align:start position:0%
+the process of revision and i have added
+ 
+
+ align:start position:0%
+the process of revision and i have added
+new material in the slides that haven't
+
+ align:start position:0%
+new material in the slides that haven't
+ 
+
+ align:start position:0%
+new material in the slides that haven't
+even made their way into the working
+
+ align:start position:0%
+even made their way into the working
+ 
+
+ align:start position:0%
+even made their way into the working
+paper yet and then there's some pandarak
+
+ align:start position:0%
+paper yet and then there's some pandarak
+ 
+
+ align:start position:0%
+paper yet and then there's some pandarak
+and townsend which is describing the
+
+ align:start position:0%
+and townsend which is describing the
+ 
+
+ align:start position:0%
+and townsend which is describing the
+tools we're going to be using a lot
+
+ align:start position:0%
+tools we're going to be using a lot
+ 
+
+ align:start position:0%
+tools we're going to be using a lot
+today these how to organize data think
+
+ align:start position:0%
+today these how to organize data think
+ 
+
+ align:start position:0%
+today these how to organize data think
+about flows and stocks
+
+ align:start position:0%
+about flows and stocks
+ 
+
+ align:start position:0%
+about flows and stocks
+in terms of financial accounts and so on
+
+ align:start position:0%
+in terms of financial accounts and so on
+ 
+
+ align:start position:0%
+in terms of financial accounts and so on
+so again the two starred readings other
+
+ align:start position:0%
+so again the two starred readings other
+ 
+
+ align:start position:0%
+so again the two starred readings other
+things you might enjoy time permitting
+
+ align:start position:0%
+things you might enjoy time permitting
+ 
+
+ align:start position:0%
+things you might enjoy time permitting
+there's something on kenya and pasa i
+
+ align:start position:0%
+there's something on kenya and pasa i
+ 
+
+ align:start position:0%
+there's something on kenya and pasa i
+have one slide describing actually two
+
+ align:start position:0%
+have one slide describing actually two
+ 
+
+ align:start position:0%
+have one slide describing actually two
+slides describing that today something
+
+ align:start position:0%
+slides describing that today something
+ 
+
+ align:start position:0%
+slides describing that today something
+on life cycle planning but none of those
+
+ align:start position:0%
+on life cycle planning but none of those
+ 
+
+ align:start position:0%
+on life cycle planning but none of those
+things have stars on them okay so that's
+
+ align:start position:0%
+things have stars on them okay so that's
+ 
+
+ align:start position:0%
+things have stars on them okay so that's
+the reading list
+
+ align:start position:0%
+the reading list
+ 
+
+ align:start position:0%
+the reading list
+the last thing
+
+ align:start position:0%
+the last thing
+ 
+
+ align:start position:0%
+the last thing
+turning to the study guide or the
+
+ align:start position:0%
+turning to the study guide or the
+ 
+
+ align:start position:0%
+turning to the study guide or the
+lecture from last time
+
+ align:start position:0%
+lecture from last time
+ 
+
+ align:start position:0%
+lecture from last time
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+which was risk in return in village
+
+ align:start position:0%
+which was risk in return in village
+ 
+
+ align:start position:0%
+which was risk in return in village
+thailand so
+
+ align:start position:0%
+thailand so
+ 
+
+ align:start position:0%
+thailand so
+explain intuitively in words why
+
+ align:start position:0%
+explain intuitively in words why
+ 
+
+ align:start position:0%
+explain intuitively in words why
+multiple technologies can be chosen to
+
+ align:start position:0%
+multiple technologies can be chosen to
+ 
+
+ align:start position:0%
+multiple technologies can be chosen to
+be operated simultaneously
+
+ align:start position:0%
+be operated simultaneously
+ 
+
+ align:start position:0%
+be operated simultaneously
+and why the rate of return on some might
+
+ align:start position:0%
+and why the rate of return on some might
+ 
+
+ align:start position:0%
+and why the rate of return on some might
+be higher than the rate of return
+
+ align:start position:0%
+be higher than the rate of return
+ 
+
+ align:start position:0%
+be higher than the rate of return
+for the others that are also operating
+
+ align:start position:0%
+for the others that are also operating
+ 
+
+ align:start position:0%
+for the others that are also operating
+and for that matter why some projects
+
+ align:start position:0%
+and for that matter why some projects
+ 
+
+ align:start position:0%
+and for that matter why some projects
+are not chosen at all
+
+ align:start position:0%
+are not chosen at all
+ 
+
+ align:start position:0%
+are not chosen at all
+if you can try to use the language of
+
+ align:start position:0%
+if you can try to use the language of
+ 
+
+ align:start position:0%
+if you can try to use the language of
+risk premium but don't you use it as
+
+ align:start position:0%
+risk premium but don't you use it as
+ 
+
+ align:start position:0%
+risk premium but don't you use it as
+jargon try to imagine you're telling
+
+ align:start position:0%
+jargon try to imagine you're telling
+ 
+
+ align:start position:0%
+jargon try to imagine you're telling
+someone in your household or a friend
+
+ align:start position:0%
+someone in your household or a friend
+ 
+
+ align:start position:0%
+someone in your household or a friend
+kind of what we're
+
+ align:start position:0%
+kind of what we're
+ 
+
+ align:start position:0%
+kind of what we're
+studying in class
+
+ align:start position:0%
+studying in class
+ 
+
+ align:start position:0%
+studying in class
+so i've been calling on people
+
+ align:start position:0%
+so i've been calling on people
+ 
+
+ align:start position:0%
+so i've been calling on people
+let me just ask for volunteers today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course i can call on people
+
+ align:start position:0%
+of course i can call on people
+ 
+
+ align:start position:0%
+of course i can call on people
+any volunteers
+
+ align:start position:0%
+any volunteers
+ 
+
+ align:start position:0%
+any volunteers
+carrie you want to take a crack at this
+
+ align:start position:0%
+carrie you want to take a crack at this
+ 
+
+ align:start position:0%
+carrie you want to take a crack at this
+um is it because like some technologies
+
+ align:start position:0%
+um is it because like some technologies
+ 
+
+ align:start position:0%
+um is it because like some technologies
+have a lower rate of return because like
+
+ align:start position:0%
+have a lower rate of return because like
+ 
+
+ align:start position:0%
+have a lower rate of return because like
+they're riskier and like the probability
+
+ align:start position:0%
+they're riskier and like the probability
+ 
+
+ align:start position:0%
+they're riskier and like the probability
+of a high rate of return is lower for
+
+ align:start position:0%
+of a high rate of return is lower for
+ 
+
+ align:start position:0%
+of a high rate of return is lower for
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+at first blush
+
+ align:start position:0%
+at first blush
+ 
+
+ align:start position:0%
+at first blush
+the rate of return is is simply all the
+
+ align:start position:0%
+the rate of return is is simply all the
+ 
+
+ align:start position:0%
+the rate of return is is simply all the
+possible returns multiplied by
+
+ align:start position:0%
+possible returns multiplied by
+ 
+
+ align:start position:0%
+possible returns multiplied by
+the effective probability so that's kind
+
+ align:start position:0%
+the effective probability so that's kind
+ 
+
+ align:start position:0%
+the effective probability so that's kind
+of inherent in the technology itself
+
+ align:start position:0%
+of inherent in the technology itself
+ 
+
+ align:start position:0%
+of inherent in the technology itself
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but if that were the only thing
+
+ align:start position:0%
+but if that were the only thing
+ 
+
+ align:start position:0%
+but if that were the only thing
+going on then why would they not choose
+
+ align:start position:0%
+going on then why would they not choose
+ 
+
+ align:start position:0%
+going on then why would they not choose
+the one with the highest expected return
+
+ align:start position:0%
+the one with the highest expected return
+ 
+
+ align:start position:0%
+the one with the highest expected return
+oh can you crack it
+
+ align:start position:0%
+oh can you crack it
+ 
+
+ align:start position:0%
+oh can you crack it
+yep well i i think like well
+
+ align:start position:0%
+yep well i i think like well
+ 
+
+ align:start position:0%
+yep well i i think like well
+yeah i'm i'm a bit behind the readings
+
+ align:start position:0%
+yeah i'm i'm a bit behind the readings
+ 
+
+ align:start position:0%
+yeah i'm i'm a bit behind the readings
+but what it looks like here is that you
+
+ align:start position:0%
+but what it looks like here is that you
+ 
+
+ align:start position:0%
+but what it looks like here is that you
+have some technologies that have a
+
+ align:start position:0%
+have some technologies that have a
+ 
+
+ align:start position:0%
+have some technologies that have a
+higher expected rate of return but more
+
+ align:start position:0%
+higher expected rate of return but more
+ 
+
+ align:start position:0%
+higher expected rate of return but more
+risk and some technologies that have the
+
+ align:start position:0%
+risk and some technologies that have the
+ 
+
+ align:start position:0%
+risk and some technologies that have the
+lower exposure rate rate turn a lower
+
+ align:start position:0%
+lower exposure rate rate turn a lower
+ 
+
+ align:start position:0%
+lower exposure rate rate turn a lower
+risk and
+
+ align:start position:0%
+risk and
+ 
+
+ align:start position:0%
+risk and
+basically and some of them like so some
+
+ align:start position:0%
+basically and some of them like so some
+ 
+
+ align:start position:0%
+basically and some of them like so some
+of them are like some people like some
+
+ align:start position:0%
+of them are like some people like some
+ 
+
+ align:start position:0%
+of them are like some people like some
+households might be more like like you
+
+ align:start position:0%
+households might be more like like you
+ 
+
+ align:start position:0%
+households might be more like like you
+can have like and if these aren't
+
+ align:start position:0%
+can have like and if these aren't
+ 
+
+ align:start position:0%
+can have like and if these aren't
+perfectly correlated then you might be
+
+ align:start position:0%
+perfectly correlated then you might be
+ 
+
+ align:start position:0%
+perfectly correlated then you might be
+able to like get a better sort of a less
+
+ align:start position:0%
+able to like get a better sort of a less
+ 
+
+ align:start position:0%
+able to like get a better sort of a less
+risky rate for the same less risk for
+
+ align:start position:0%
+risky rate for the same less risk for
+ 
+
+ align:start position:0%
+risky rate for the same less risk for
+the same rate of return by like
+
+ align:start position:0%
+the same rate of return by like
+ 
+
+ align:start position:0%
+the same rate of return by like
+diversification and like and then the re
+
+ align:start position:0%
+diversification and like and then the re
+ 
+
+ align:start position:0%
+diversification and like and then the re
+and the reason that like you would have
+
+ align:start position:0%
+and the reason that like you would have
+ 
+
+ align:start position:0%
+and the reason that like you would have
+lower you would have um you would have
+
+ align:start position:0%
+lower you would have um you would have
+ 
+
+ align:start position:0%
+lower you would have um you would have
+lower rate of return technologies in the
+
+ align:start position:0%
+lower rate of return technologies in the
+ 
+
+ align:start position:0%
+lower rate of return technologies in the
+same use at the same time as higher rate
+
+ align:start position:0%
+same use at the same time as higher rate
+ 
+
+ align:start position:0%
+same use at the same time as higher rate
+of return technologies as the lower
+
+ align:start position:0%
+of return technologies as the lower
+ 
+
+ align:start position:0%
+of return technologies as the lower
+rated return ones have a
+
+ align:start position:0%
+rated return ones have a
+ 
+
+ align:start position:0%
+rated return ones have a
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um the lower rate of return ones have
+
+ align:start position:0%
+um the lower rate of return ones have
+ 
+
+ align:start position:0%
+um the lower rate of return ones have
+a lower risk and the higher rate of
+
+ align:start position:0%
+a lower risk and the higher rate of
+ 
+
+ align:start position:0%
+a lower risk and the higher rate of
+returns one gets like you gotta
+
+ align:start position:0%
+returns one gets like you gotta
+ 
+
+ align:start position:0%
+returns one gets like you gotta
+basically pay a risk point there's a
+
+ align:start position:0%
+basically pay a risk point there's a
+ 
+
+ align:start position:0%
+basically pay a risk point there's a
+sort of wrist cream there which is why
+
+ align:start position:0%
+sort of wrist cream there which is why
+ 
+
+ align:start position:0%
+sort of wrist cream there which is why
+it's sort of less desirable or something
+
+ align:start position:0%
+it's sort of less desirable or something
+ 
+
+ align:start position:0%
+it's sort of less desirable or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+okay that's pretty good thank you
+
+ align:start position:0%
+okay that's pretty good thank you
+ 
+
+ align:start position:0%
+okay that's pretty good thank you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah you're what you're describing is
+
+ align:start position:0%
+yeah you're what you're describing is
+ 
+
+ align:start position:0%
+yeah you're what you're describing is
+correct there's like a sort of a mean
+
+ align:start position:0%
+correct there's like a sort of a mean
+ 
+
+ align:start position:0%
+correct there's like a sort of a mean
+variability trade-off here
+
+ align:start position:0%
+variability trade-off here
+ 
+
+ align:start position:0%
+variability trade-off here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+sort of a downward sloping frontier if
+
+ align:start position:0%
+sort of a downward sloping frontier if
+ 
+
+ align:start position:0%
+sort of a downward sloping frontier if
+you want to think about it that way as
+
+ align:start position:0%
+you want to think about it that way as
+ 
+
+ align:start position:0%
+you want to think about it that way as
+you move across different projects they
+
+ align:start position:0%
+you move across different projects they
+ 
+
+ align:start position:0%
+you move across different projects they
+may have higher and higher means
+
+ align:start position:0%
+may have higher and higher means
+ 
+
+ align:start position:0%
+may have higher and higher means
+but they come with higher and higher
+
+ align:start position:0%
+but they come with higher and higher
+ 
+
+ align:start position:0%
+but they come with higher and higher
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+so there's a trade-off
+
+ align:start position:0%
+so there's a trade-off
+ 
+
+ align:start position:0%
+so there's a trade-off
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and since households are risk-averse
+
+ align:start position:0%
+and since households are risk-averse
+ 
+
+ align:start position:0%
+and since households are risk-averse
+they don't like the variance
+
+ align:start position:0%
+they don't like the variance
+ 
+
+ align:start position:0%
+they don't like the variance
+so they pay attention to that
+
+ align:start position:0%
+so they pay attention to that
+ 
+
+ align:start position:0%
+so they pay attention to that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and and you've said this also you could
+
+ align:start position:0%
+and and you've said this also you could
+ 
+
+ align:start position:0%
+and and you've said this also you could
+have two technologies
+
+ align:start position:0%
+have two technologies
+ 
+
+ align:start position:0%
+have two technologies
+with the same mean return one with a
+
+ align:start position:0%
+with the same mean return one with a
+ 
+
+ align:start position:0%
+with the same mean return one with a
+higher variance than the other one and
+
+ align:start position:0%
+higher variance than the other one and
+ 
+
+ align:start position:0%
+higher variance than the other one and
+they would never do the higher
+
+ align:start position:0%
+they would never do the higher
+ 
+
+ align:start position:0%
+they would never do the higher
+variability one
+
+ align:start position:0%
+variability one
+ 
+
+ align:start position:0%
+variability one
+because then there's no trade-off
+
+ align:start position:0%
+because then there's no trade-off
+ 
+
+ align:start position:0%
+because then there's no trade-off
+since they get the same mean but at
+
+ align:start position:0%
+since they get the same mean but at
+ 
+
+ align:start position:0%
+since they get the same mean but at
+higher risk they wouldn't choose that
+
+ align:start position:0%
+higher risk they wouldn't choose that
+ 
+
+ align:start position:0%
+higher risk they wouldn't choose that
+there is
+
+ align:start position:0%
+there is
+ 
+
+ align:start position:0%
+there is
+a diversification aspect that we
+
+ align:start position:0%
+a diversification aspect that we
+ 
+
+ align:start position:0%
+a diversification aspect that we
+featured quite a bit in terms of
+
+ align:start position:0%
+featured quite a bit in terms of
+ 
+
+ align:start position:0%
+featured quite a bit in terms of
+land plots and how they want to
+
+ align:start position:0%
+land plots and how they want to
+ 
+
+ align:start position:0%
+land plots and how they want to
+diversify or in village india over
+
+ align:start position:0%
+diversify or in village india over
+ 
+
+ align:start position:0%
+diversify or in village india over
+crops and income sources and so on
+
+ align:start position:0%
+crops and income sources and so on
+ 
+
+ align:start position:0%
+crops and income sources and so on
+that's kind of captured here
+
+ align:start position:0%
+that's kind of captured here
+ 
+
+ align:start position:0%
+that's kind of captured here
+in a in a new way but it is in here
+
+ align:start position:0%
+in a in a new way but it is in here
+ 
+
+ align:start position:0%
+in a in a new way but it is in here
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+at a
+
+ align:start position:0%
+at a
+ 
+
+ align:start position:0%
+at a
+a guess
+
+ align:start position:0%
+a guess
+ 
+
+ align:start position:0%
+a guess
+of what technologies to operate overall
+
+ align:start position:0%
+of what technologies to operate overall
+ 
+
+ align:start position:0%
+of what technologies to operate overall
+you can compute the variability
+
+ align:start position:0%
+you can compute the variability
+ 
+
+ align:start position:0%
+you can compute the variability
+and then you look on the margin about
+
+ align:start position:0%
+and then you look on the margin about
+ 
+
+ align:start position:0%
+and then you look on the margin about
+whether to add or subtract one
+
+ align:start position:0%
+whether to add or subtract one
+ 
+
+ align:start position:0%
+whether to add or subtract one
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+and you look at its
+
+ align:start position:0%
+and you look at its
+ 
+
+ align:start position:0%
+and you look at its
+variability relative to this village
+
+ align:start position:0%
+variability relative to this village
+ 
+
+ align:start position:0%
+variability relative to this village
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if it's going to add to diversification
+
+ align:start position:0%
+if it's going to add to diversification
+ 
+
+ align:start position:0%
+if it's going to add to diversification
+uh it's going to have a return stream
+
+ align:start position:0%
+uh it's going to have a return stream
+ 
+
+ align:start position:0%
+uh it's going to have a return stream
+which is low
+
+ align:start position:0%
+which is low
+ 
+
+ align:start position:0%
+which is low
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+well say hi when the rest of the village
+
+ align:start position:0%
+well say hi when the rest of the village
+ 
+
+ align:start position:0%
+well say hi when the rest of the village
+is low
+
+ align:start position:0%
+is low
+ 
+
+ align:start position:0%
+is low
+so that's kind of the way the
+
+ align:start position:0%
+so that's kind of the way the
+ 
+
+ align:start position:0%
+so that's kind of the way the
+diversification aspect is coming out
+
+ align:start position:0%
+diversification aspect is coming out
+ 
+
+ align:start position:0%
+diversification aspect is coming out
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+mean variance framework
+
+ align:start position:0%
+mean variance framework
+ 
+
+ align:start position:0%
+mean variance framework
+but great that's very helpful
+
+ align:start position:0%
+but great that's very helpful
+ 
+
+ align:start position:0%
+but great that's very helpful
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's another one explain how it can be
+
+ align:start position:0%
+here's another one explain how it can be
+ 
+
+ align:start position:0%
+here's another one explain how it can be
+that while the magnitude of
+
+ align:start position:0%
+that while the magnitude of
+ 
+
+ align:start position:0%
+that while the magnitude of
+idiosyncratic risk
+
+ align:start position:0%
+idiosyncratic risk
+ 
+
+ align:start position:0%
+idiosyncratic risk
+is higher than the magnitude of
+
+ align:start position:0%
+is higher than the magnitude of
+ 
+
+ align:start position:0%
+is higher than the magnitude of
+aggregate risk
+
+ align:start position:0%
+aggregate risk
+ 
+
+ align:start position:0%
+aggregate risk
+nevertheless the
+
+ align:start position:0%
+nevertheless the
+ 
+
+ align:start position:0%
+nevertheless the
+idiosyncratic risk premium is smaller
+
+ align:start position:0%
+idiosyncratic risk premium is smaller
+ 
+
+ align:start position:0%
+idiosyncratic risk premium is smaller
+than the aggregate risk premium
+
+ align:start position:0%
+than the aggregate risk premium
+ 
+
+ align:start position:0%
+than the aggregate risk premium
+uh so again i'll take volunteers
+
+ align:start position:0%
+uh so again i'll take volunteers
+ 
+
+ align:start position:0%
+uh so again i'll take volunteers
+yeah um
+
+ align:start position:0%
+yeah um
+ 
+
+ align:start position:0%
+yeah um
+so uh is it so i i think it's because um
+
+ align:start position:0%
+so uh is it so i i think it's because um
+ 
+
+ align:start position:0%
+so uh is it so i i think it's because um
+uh when it come with idiosyncratic risk
+
+ align:start position:0%
+uh when it come with idiosyncratic risk
+ 
+
+ align:start position:0%
+uh when it come with idiosyncratic risk
+um it's possible for the village to sort
+
+ align:start position:0%
+um it's possible for the village to sort
+ 
+
+ align:start position:0%
+um it's possible for the village to sort
+of to sort to uh distribute their
+
+ align:start position:0%
+of to sort to uh distribute their
+ 
+
+ align:start position:0%
+of to sort to uh distribute their
+returns among amongst each other's like
+
+ align:start position:0%
+returns among amongst each other's like
+ 
+
+ align:start position:0%
+returns among amongst each other's like
+ex post
+
+ align:start position:0%
+ex post
+ 
+
+ align:start position:0%
+ex post
+whereas for aggregate risk um it's it's
+
+ align:start position:0%
+whereas for aggregate risk um it's it's
+ 
+
+ align:start position:0%
+whereas for aggregate risk um it's it's
+like it is risk affecting whole village
+
+ align:start position:0%
+like it is risk affecting whole village
+ 
+
+ align:start position:0%
+like it is risk affecting whole village
+and so there's no and so there's
+
+ align:start position:0%
+and so there's no and so there's
+ 
+
+ align:start position:0%
+and so there's no and so there's
+redistribution can't really benefit
+
+ align:start position:0%
+redistribution can't really benefit
+ 
+
+ align:start position:0%
+redistribution can't really benefit
+anyone uh when it comes to sort of
+
+ align:start position:0%
+anyone uh when it comes to sort of
+ 
+
+ align:start position:0%
+anyone uh when it comes to sort of
+things that affected those as well
+
+ align:start position:0%
+things that affected those as well
+ 
+
+ align:start position:0%
+things that affected those as well
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+perfect
+
+ align:start position:0%
+perfect
+ 
+
+ align:start position:0%
+perfect
+yeah the the last part of which i didn't
+
+ align:start position:0%
+yeah the the last part of which i didn't
+ 
+
+ align:start position:0%
+yeah the the last part of which i didn't
+read out explain in words what gifts and
+
+ align:start position:0%
+read out explain in words what gifts and
+ 
+
+ align:start position:0%
+read out explain in words what gifts and
+loans have to do with it but you kind of
+
+ align:start position:0%
+loans have to do with it but you kind of
+ 
+
+ align:start position:0%
+loans have to do with it but you kind of
+did already
+
+ align:start position:0%
+did already
+ 
+
+ align:start position:0%
+did already
+that's the sort of the way they pull
+
+ align:start position:0%
+that's the sort of the way they pull
+ 
+
+ align:start position:0%
+that's the sort of the way they pull
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+most if not all of the idiosyncratic
+
+ align:start position:0%
+most if not all of the idiosyncratic
+ 
+
+ align:start position:0%
+most if not all of the idiosyncratic
+risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whereas in the aggregate it's common
+
+ align:start position:0%
+whereas in the aggregate it's common
+ 
+
+ align:start position:0%
+whereas in the aggregate it's common
+it's hitting everyone so
+
+ align:start position:0%
+it's hitting everyone so
+ 
+
+ align:start position:0%
+it's hitting everyone so
+essentially you can't pull it away
+
+ align:start position:0%
+essentially you can't pull it away
+ 
+
+ align:start position:0%
+essentially you can't pull it away
+and and this next part is related to
+
+ align:start position:0%
+and and this next part is related to
+ 
+
+ align:start position:0%
+and and this next part is related to
+that is there full insurance in these
+
+ align:start position:0%
+that is there full insurance in these
+ 
+
+ align:start position:0%
+that is there full insurance in these
+thai village economies or not and to
+
+ align:start position:0%
+thai village economies or not and to
+ 
+
+ align:start position:0%
+thai village economies or not and to
+give it away a bit not and in particular
+
+ align:start position:0%
+give it away a bit not and in particular
+ 
+
+ align:start position:0%
+give it away a bit not and in particular
+what is it in the data
+
+ align:start position:0%
+what is it in the data
+ 
+
+ align:start position:0%
+what is it in the data
+that is inconsistent with full risk
+
+ align:start position:0%
+that is inconsistent with full risk
+ 
+
+ align:start position:0%
+that is inconsistent with full risk
+sharing
+
+ align:start position:0%
+sharing
+ 
+
+ align:start position:0%
+sharing
+volunteers
+
+ align:start position:0%
+volunteers
+ 
+
+ align:start position:0%
+volunteers
+um we find that in the data
+
+ align:start position:0%
+um we find that in the data
+ 
+
+ align:start position:0%
+um we find that in the data
+household consumption is still is
+
+ align:start position:0%
+household consumption is still is
+ 
+
+ align:start position:0%
+household consumption is still is
+positively correlated with
+
+ align:start position:0%
+positively correlated with
+ 
+
+ align:start position:0%
+positively correlated with
+the idiosyncratic
+
+ align:start position:0%
+the idiosyncratic
+ 
+
+ align:start position:0%
+the idiosyncratic
+um like shocks
+
+ align:start position:0%
+um like shocks
+ 
+
+ align:start position:0%
+um like shocks
+so that shows that it's not
+
+ align:start position:0%
+so that shows that it's not
+ 
+
+ align:start position:0%
+so that shows that it's not
+full risk sharing but there's still some
+
+ align:start position:0%
+full risk sharing but there's still some
+ 
+
+ align:start position:0%
+full risk sharing but there's still some
+risk sharing because the coefficient is
+
+ align:start position:0%
+risk sharing because the coefficient is
+ 
+
+ align:start position:0%
+risk sharing because the coefficient is
+really really small compared to other
+
+ align:start position:0%
+really really small compared to other
+ 
+
+ align:start position:0%
+really really small compared to other
+coefficients
+
+ align:start position:0%
+coefficients
+ 
+
+ align:start position:0%
+coefficients
+right compared to the coefficients on
+
+ align:start position:0%
+right compared to the coefficients on
+ 
+
+ align:start position:0%
+right compared to the coefficients on
+gifts and
+
+ align:start position:0%
+gifts and
+ 
+
+ align:start position:0%
+gifts and
+lending
+
+ align:start position:0%
+lending
+ 
+
+ align:start position:0%
+lending
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+absorbs the bulk of the risk
+
+ align:start position:0%
+absorbs the bulk of the risk
+ 
+
+ align:start position:0%
+absorbs the bulk of the risk
+so that's a perfect answer i'm so happy
+
+ align:start position:0%
+so that's a perfect answer i'm so happy
+ 
+
+ align:start position:0%
+so that's a perfect answer i'm so happy
+with this class i enjoy teaching you
+
+ align:start position:0%
+with this class i enjoy teaching you
+ 
+
+ align:start position:0%
+with this class i enjoy teaching you
+tremendously
+
+ align:start position:0%
+tremendously
+ 
+
+ align:start position:0%
+tremendously
+it's very gratifying
+
+ align:start position:0%
+it's very gratifying
+ 
+
+ align:start position:0%
+it's very gratifying
+uh okay thank you there's one more see
+
+ align:start position:0%
+uh okay thank you there's one more see
+ 
+
+ align:start position:0%
+uh okay thank you there's one more see
+if we can get it in
+
+ align:start position:0%
+if we can get it in
+ 
+
+ align:start position:0%
+if we can get it in
+describe one example from thai villages
+
+ align:start position:0%
+describe one example from thai villages
+ 
+
+ align:start position:0%
+describe one example from thai villages
+of propagation through networks that
+
+ align:start position:0%
+of propagation through networks that
+ 
+
+ align:start position:0%
+of propagation through networks that
+would be inconsistent with full risk
+
+ align:start position:0%
+would be inconsistent with full risk
+ 
+
+ align:start position:0%
+would be inconsistent with full risk
+sharing and investment efficiency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm abbreviating
+
+ align:start position:0%
+and i'm abbreviating
+ 
+
+ align:start position:0%
+and i'm abbreviating
+so this happened at the end of the
+
+ align:start position:0%
+so this happened at the end of the
+ 
+
+ align:start position:0%
+so this happened at the end of the
+lecture just as a hint
+
+ align:start position:0%
+lecture just as a hint
+ 
+
+ align:start position:0%
+lecture just as a hint
+can someone describe what we did at the
+
+ align:start position:0%
+can someone describe what we did at the
+ 
+
+ align:start position:0%
+can someone describe what we did at the
+end of the lecture
+
+ align:start position:0%
+end of the lecture
+ 
+
+ align:start position:0%
+end of the lecture
+well it's kind of given away here in
+
+ align:start position:0%
+well it's kind of given away here in
+ 
+
+ align:start position:0%
+well it's kind of given away here in
+this bullet point but i'll read it out
+
+ align:start position:0%
+this bullet point but i'll read it out
+ 
+
+ align:start position:0%
+this bullet point but i'll read it out
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+how can an individual specific illness
+
+ align:start position:0%
+how can an individual specific illness
+ 
+
+ align:start position:0%
+how can an individual specific illness
+shock turn into an aggregate village
+
+ align:start position:0%
+shock turn into an aggregate village
+ 
+
+ align:start position:0%
+shock turn into an aggregate village
+level downturn
+
+ align:start position:0%
+level downturn
+ 
+
+ align:start position:0%
+level downturn
+volunteers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think i think i think i think at the
+
+ align:start position:0%
+i think i think i think i think at the
+ 
+
+ align:start position:0%
+i think i think i think i think at the
+end of the class we were talking about
+
+ align:start position:0%
+end of the class we were talking about
+ 
+
+ align:start position:0%
+end of the class we were talking about
+how some of the networks uh how
+
+ align:start position:0%
+how some of the networks uh how
+ 
+
+ align:start position:0%
+how some of the networks uh how
+different kinds of networks are
+
+ align:start position:0%
+different kinds of networks are
+ 
+
+ align:start position:0%
+different kinds of networks are
+different from each other i'm not sure
+
+ align:start position:0%
+different from each other i'm not sure
+ 
+
+ align:start position:0%
+different from each other i'm not sure
+which specific networks were being
+
+ align:start position:0%
+which specific networks were being
+ 
+
+ align:start position:0%
+which specific networks were being
+compared but
+
+ align:start position:0%
+compared but
+ 
+
+ align:start position:0%
+compared but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so what happens do you recall when a
+
+ align:start position:0%
+so what happens do you recall when a
+ 
+
+ align:start position:0%
+so what happens do you recall when a
+household gets hit with an illness shock
+
+ align:start position:0%
+household gets hit with an illness shock
+ 
+
+ align:start position:0%
+household gets hit with an illness shock
+that increases its expenditure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nothing happened
+
+ align:start position:0%
+nothing happened
+ 
+
+ align:start position:0%
+nothing happened
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+do you remember or anyone else remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i remember that the
+
+ align:start position:0%
+i remember that the
+ 
+
+ align:start position:0%
+i remember that the
+households who
+
+ align:start position:0%
+households who
+ 
+
+ align:start position:0%
+households who
+are corrected directly corrected to the
+
+ align:start position:0%
+are corrected directly corrected to the
+ 
+
+ align:start position:0%
+are corrected directly corrected to the
+household who get illness jobs while the
+
+ align:start position:0%
+household who get illness jobs while the
+ 
+
+ align:start position:0%
+household who get illness jobs while the
+job done their working opportunity much
+
+ align:start position:0%
+job done their working opportunity much
+ 
+
+ align:start position:0%
+job done their working opportunity much
+more than households who are uncorrected
+
+ align:start position:0%
+more than households who are uncorrected
+ 
+
+ align:start position:0%
+more than households who are uncorrected
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+illness households so through the
+
+ align:start position:0%
+illness households so through the
+ 
+
+ align:start position:0%
+illness households so through the
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+households who are corrected
+
+ align:start position:0%
+households who are corrected
+ 
+
+ align:start position:0%
+households who are corrected
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+who are related
+
+ align:start position:0%
+who are related
+ 
+
+ align:start position:0%
+who are related
+to each other other much more maybe
+
+ align:start position:0%
+to each other other much more maybe
+ 
+
+ align:start position:0%
+to each other other much more maybe
+shock
+
+ align:start position:0%
+shock
+ 
+
+ align:start position:0%
+shock
+there was a negative shock between them
+
+ align:start position:0%
+there was a negative shock between them
+ 
+
+ align:start position:0%
+there was a negative shock between them
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+illness shocks to this hospitalism may
+
+ align:start position:0%
+illness shocks to this hospitalism may
+ 
+
+ align:start position:0%
+illness shocks to this hospitalism may
+transfer to the aggregate religion
+
+ align:start position:0%
+transfer to the aggregate religion
+ 
+
+ align:start position:0%
+transfer to the aggregate religion
+through the correlation
+
+ align:start position:0%
+through the correlation
+ 
+
+ align:start position:0%
+through the correlation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's pretty good it's a and it's a bit
+
+ align:start position:0%
+that's pretty good it's a and it's a bit
+ 
+
+ align:start position:0%
+that's pretty good it's a and it's a bit
+tricky this question
+
+ align:start position:0%
+tricky this question
+ 
+
+ align:start position:0%
+tricky this question
+uh because there are
+
+ align:start position:0%
+uh because there are
+ 
+
+ align:start position:0%
+uh because there are
+different networks in the village
+
+ align:start position:0%
+different networks in the village
+ 
+
+ align:start position:0%
+different networks in the village
+there's kind of the risk sharing
+
+ align:start position:0%
+there's kind of the risk sharing
+ 
+
+ align:start position:0%
+there's kind of the risk sharing
+insurance network there's the labor
+
+ align:start position:0%
+insurance network there's the labor
+ 
+
+ align:start position:0%
+insurance network there's the labor
+network there's the
+
+ align:start position:0%
+network there's the
+ 
+
+ align:start position:0%
+network there's the
+supply chain production network and and
+
+ align:start position:0%
+supply chain production network and and
+ 
+
+ align:start position:0%
+supply chain production network and and
+they don't
+
+ align:start position:0%
+they don't
+ 
+
+ align:start position:0%
+they don't
+coincide
+
+ align:start position:0%
+coincide
+ 
+
+ align:start position:0%
+coincide
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you got hit with an illness shock but
+
+ align:start position:0%
+if you got hit with an illness shock but
+ 
+
+ align:start position:0%
+if you got hit with an illness shock but
+nevertheless you're in this
+
+ align:start position:0%
+nevertheless you're in this
+ 
+
+ align:start position:0%
+nevertheless you're in this
+risk sharing insurance network then
+
+ align:start position:0%
+risk sharing insurance network then
+ 
+
+ align:start position:0%
+risk sharing insurance network then
+part of the or almost all of the shock
+
+ align:start position:0%
+part of the or almost all of the shock
+ 
+
+ align:start position:0%
+part of the or almost all of the shock
+gets covered
+
+ align:start position:0%
+gets covered
+ 
+
+ align:start position:0%
+gets covered
+in come the gifts just like we were
+
+ align:start position:0%
+in come the gifts just like we were
+ 
+
+ align:start position:0%
+in come the gifts just like we were
+describing with the production shops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however when
+
+ align:start position:0%
+however when
+ 
+
+ align:start position:0%
+however when
+that illness shock is not covered by
+
+ align:start position:0%
+that illness shock is not covered by
+ 
+
+ align:start position:0%
+that illness shock is not covered by
+gifts
+
+ align:start position:0%
+gifts
+ 
+
+ align:start position:0%
+gifts
+then the household has to respond on its
+
+ align:start position:0%
+then the household has to respond on its
+ 
+
+ align:start position:0%
+then the household has to respond on its
+own in some way and it does this by
+
+ align:start position:0%
+own in some way and it does this by
+ 
+
+ align:start position:0%
+own in some way and it does this by
+cutting
+
+ align:start position:0%
+cutting
+ 
+
+ align:start position:0%
+cutting
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+number of laborers that it hires and by
+
+ align:start position:0%
+number of laborers that it hires and by
+ 
+
+ align:start position:0%
+number of laborers that it hires and by
+shrinking
+
+ align:start position:0%
+shrinking
+ 
+
+ align:start position:0%
+shrinking
+sort of saving costs by shrinking its
+
+ align:start position:0%
+sort of saving costs by shrinking its
+ 
+
+ align:start position:0%
+sort of saving costs by shrinking its
+production operations
+
+ align:start position:0%
+production operations
+ 
+
+ align:start position:0%
+production operations
+and that is what spills over to other
+
+ align:start position:0%
+and that is what spills over to other
+ 
+
+ align:start position:0%
+and that is what spills over to other
+households along the production network
+
+ align:start position:0%
+households along the production network
+ 
+
+ align:start position:0%
+households along the production network
+so you know networks could be good or
+
+ align:start position:0%
+so you know networks could be good or
+ 
+
+ align:start position:0%
+so you know networks could be good or
+bad networks are good for
+
+ align:start position:0%
+bad networks are good for
+ 
+
+ align:start position:0%
+bad networks are good for
+sharing risk but they also can be bad
+
+ align:start position:0%
+sharing risk but they also can be bad
+ 
+
+ align:start position:0%
+sharing risk but they also can be bad
+because they propagate contagion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so if there was a full risk sharing then
+
+ align:start position:0%
+so if there was a full risk sharing then
+ 
+
+ align:start position:0%
+so if there was a full risk sharing then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+i then there were no effect on the
+
+ align:start position:0%
+i then there were no effect on the
+ 
+
+ align:start position:0%
+i then there were no effect on the
+employment
+
+ align:start position:0%
+employment
+ 
+
+ align:start position:0%
+employment
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+yeah for the householder who did not get
+
+ align:start position:0%
+yeah for the householder who did not get
+ 
+
+ align:start position:0%
+yeah for the householder who did not get
+any shock
+
+ align:start position:0%
+any shock
+ 
+
+ align:start position:0%
+any shock
+network i mean not work
+
+ align:start position:0%
+network i mean not work
+ 
+
+ align:start position:0%
+network i mean not work
+that was a factor those houses who did
+
+ align:start position:0%
+that was a factor those houses who did
+ 
+
+ align:start position:0%
+that was a factor those houses who did
+not get any shock because they are more
+
+ align:start position:0%
+not get any shock because they are more
+ 
+
+ align:start position:0%
+not get any shock because they are more
+related to the households with illness
+
+ align:start position:0%
+related to the households with illness
+ 
+
+ align:start position:0%
+related to the households with illness
+but if there was a full risk sharing
+
+ align:start position:0%
+but if there was a full risk sharing
+ 
+
+ align:start position:0%
+but if there was a full risk sharing
+those household will not have any effect
+
+ align:start position:0%
+those household will not have any effect
+ 
+
+ align:start position:0%
+those household will not have any effect
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+so the emphasis here is on you know a
+
+ align:start position:0%
+so the emphasis here is on you know a
+ 
+
+ align:start position:0%
+so the emphasis here is on you know a
+very specific household idiosyncratic
+
+ align:start position:0%
+very specific household idiosyncratic
+ 
+
+ align:start position:0%
+very specific household idiosyncratic
+shock
+
+ align:start position:0%
+shock
+ 
+
+ align:start position:0%
+shock
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+i do an analogy with you know covered 19
+
+ align:start position:0%
+i do an analogy with you know covered 19
+ 
+
+ align:start position:0%
+i do an analogy with you know covered 19
+but it's a bit unfair because covet as
+
+ align:start position:0%
+but it's a bit unfair because covet as
+ 
+
+ align:start position:0%
+but it's a bit unfair because covet as
+we know
+
+ align:start position:0%
+we know
+ 
+
+ align:start position:0%
+we know
+has a contagion effect literally in the
+
+ align:start position:0%
+has a contagion effect literally in the
+ 
+
+ align:start position:0%
+has a contagion effect literally in the
+health sense
+
+ align:start position:0%
+health sense
+ 
+
+ align:start position:0%
+health sense
+and you know if one person gets it
+
+ align:start position:0%
+and you know if one person gets it
+ 
+
+ align:start position:0%
+and you know if one person gets it
+people around that person get it so
+
+ align:start position:0%
+people around that person get it so
+ 
+
+ align:start position:0%
+people around that person get it so
+here though it's um you know
+
+ align:start position:0%
+here though it's um you know
+ 
+
+ align:start position:0%
+here though it's um you know
+it's a different kind of illness
+
+ align:start position:0%
+it's a different kind of illness
+ 
+
+ align:start position:0%
+it's a different kind of illness
+but it and it could be just an elderly
+
+ align:start position:0%
+but it and it could be just an elderly
+ 
+
+ align:start position:0%
+but it and it could be just an elderly
+person in the household but still
+
+ align:start position:0%
+person in the household but still
+ 
+
+ align:start position:0%
+person in the household but still
+there are big expenses double the normal
+
+ align:start position:0%
+there are big expenses double the normal
+ 
+
+ align:start position:0%
+there are big expenses double the normal
+expenses so they don't have the budget
+
+ align:start position:0%
+expenses so they don't have the budget
+ 
+
+ align:start position:0%
+expenses so they don't have the budget
+to manage and they have to start
+
+ align:start position:0%
+to manage and they have to start
+ 
+
+ align:start position:0%
+to manage and they have to start
+either getting a gift from someone or
+
+ align:start position:0%
+either getting a gift from someone or
+ 
+
+ align:start position:0%
+either getting a gift from someone or
+cutting
+
+ align:start position:0%
+cutting
+ 
+
+ align:start position:0%
+cutting
+so when they start cutting expenses
+
+ align:start position:0%
+so when they start cutting expenses
+ 
+
+ align:start position:0%
+so when they start cutting expenses
+that's when it spills over to other
+
+ align:start position:0%
+that's when it spills over to other
+ 
+
+ align:start position:0%
+that's when it spills over to other
+people that they hire or people so this
+
+ align:start position:0%
+people that they hire or people so this
+ 
+
+ align:start position:0%
+people that they hire or people so this
+is very reminiscent as i said in class
+
+ align:start position:0%
+is very reminiscent as i said in class
+ 
+
+ align:start position:0%
+is very reminiscent as i said in class
+of what's going on in the supply chain
+
+ align:start position:0%
+of what's going on in the supply chain
+ 
+
+ align:start position:0%
+of what's going on in the supply chain
+networks in the us for example
+
+ align:start position:0%
+networks in the us for example
+ 
+
+ align:start position:0%
+networks in the us for example
+and many other countries
+
+ align:start position:0%
+and many other countries
+ 
+
+ align:start position:0%
+and many other countries
+although that's more of a
+
+ align:start position:0%
+although that's more of a
+ 
+
+ align:start position:0%
+although that's more of a
+different kind of health shock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions about any other
+
+ align:start position:0%
+okay any questions about any other
+ 
+
+ align:start position:0%
+okay any questions about any other
+questions about that lecture
+
+ align:start position:0%
+questions about that lecture
+ 
+
+ align:start position:0%
+questions about that lecture
+okay so then we
+
+ align:start position:0%
+okay so then we
+ 
+
+ align:start position:0%
+okay so then we
+come to the lecture for today
+
+ align:start position:0%
+come to the lecture for today
+ 
+
+ align:start position:0%
+come to the lecture for today
+ledgers and management in fact there's a
+
+ align:start position:0%
+ledgers and management in fact there's a
+ 
+
+ align:start position:0%
+ledgers and management in fact there's a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+in the lecture today i would say i'm
+
+ align:start position:0%
+in the lecture today i would say i'm
+ 
+
+ align:start position:0%
+in the lecture today i would say i'm
+going to give you a tool to think about
+
+ align:start position:0%
+going to give you a tool to think about
+ 
+
+ align:start position:0%
+going to give you a tool to think about
+namely financial accounts
+
+ align:start position:0%
+namely financial accounts
+ 
+
+ align:start position:0%
+namely financial accounts
+income and balance sheet accounts in
+
+ align:start position:0%
+income and balance sheet accounts in
+ 
+
+ align:start position:0%
+income and balance sheet accounts in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+and then we'll go to the time monthly
+
+ align:start position:0%
+and then we'll go to the time monthly
+ 
+
+ align:start position:0%
+and then we'll go to the time monthly
+data that uh we were just talking about
+
+ align:start position:0%
+data that uh we were just talking about
+ 
+
+ align:start position:0%
+data that uh we were just talking about
+and use the tool to think about
+
+ align:start position:0%
+and use the tool to think about
+ 
+
+ align:start position:0%
+and use the tool to think about
+planning about wealth planning
+
+ align:start position:0%
+planning about wealth planning
+ 
+
+ align:start position:0%
+planning about wealth planning
+then we'll take a step back and add
+
+ align:start position:0%
+then we'll take a step back and add
+ 
+
+ align:start position:0%
+then we'll take a step back and add
+another account i'll motivate that
+
+ align:start position:0%
+another account i'll motivate that
+ 
+
+ align:start position:0%
+another account i'll motivate that
+account by thinking about bitcoin
+
+ align:start position:0%
+account by thinking about bitcoin
+ 
+
+ align:start position:0%
+account by thinking about bitcoin
+as i promised in lecture one
+
+ align:start position:0%
+as i promised in lecture one
+ 
+
+ align:start position:0%
+as i promised in lecture one
+and link the uh ledgers of bitcoin to
+
+ align:start position:0%
+and link the uh ledgers of bitcoin to
+ 
+
+ align:start position:0%
+and link the uh ledgers of bitcoin to
+the statement of cash flow
+
+ align:start position:0%
+the statement of cash flow
+ 
+
+ align:start position:0%
+the statement of cash flow
+and hence back to the thai villages in
+
+ align:start position:0%
+and hence back to the thai villages in
+ 
+
+ align:start position:0%
+and hence back to the thai villages in
+particular i'll talk about distributed
+
+ align:start position:0%
+particular i'll talk about distributed
+ 
+
+ align:start position:0%
+particular i'll talk about distributed
+ledgers which is a big part of
+
+ align:start position:0%
+ledgers which is a big part of
+ 
+
+ align:start position:0%
+ledgers which is a big part of
+bitcoin
+
+ align:start position:0%
+bitcoin
+ 
+
+ align:start position:0%
+bitcoin
+bitcoin blockchain and distributed
+
+ align:start position:0%
+bitcoin blockchain and distributed
+ 
+
+ align:start position:0%
+bitcoin blockchain and distributed
+ledgers
+
+ align:start position:0%
+ledgers
+ 
+
+ align:start position:0%
+ledgers
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+having introduced that concept i'll
+
+ align:start position:0%
+having introduced that concept i'll
+ 
+
+ align:start position:0%
+having introduced that concept i'll
+focus on
+
+ align:start position:0%
+focus on
+ 
+
+ align:start position:0%
+focus on
+the use almost exclusively of paper
+
+ align:start position:0%
+the use almost exclusively of paper
+ 
+
+ align:start position:0%
+the use almost exclusively of paper
+currency
+
+ align:start position:0%
+currency
+ 
+
+ align:start position:0%
+currency
+in thailand the use of almost
+
+ align:start position:0%
+in thailand the use of almost
+ 
+
+ align:start position:0%
+in thailand the use of almost
+exclusively electronic transfers in
+
+ align:start position:0%
+exclusively electronic transfers in
+ 
+
+ align:start position:0%
+exclusively electronic transfers in
+sweden
+
+ align:start position:0%
+sweden
+ 
+
+ align:start position:0%
+sweden
+and something in between in kenya which
+
+ align:start position:0%
+and something in between in kenya which
+ 
+
+ align:start position:0%
+and something in between in kenya which
+has two different kinds of monies
+
+ align:start position:0%
+has two different kinds of monies
+ 
+
+ align:start position:0%
+has two different kinds of monies
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+privately issued e-money from a cell
+
+ align:start position:0%
+privately issued e-money from a cell
+ 
+
+ align:start position:0%
+privately issued e-money from a cell
+phone provider and a public fiat money
+
+ align:start position:0%
+phone provider and a public fiat money
+ 
+
+ align:start position:0%
+phone provider and a public fiat money
+uh kenyan shillings and then i'll and
+
+ align:start position:0%
+uh kenyan shillings and then i'll and
+ 
+
+ align:start position:0%
+uh kenyan shillings and then i'll and
+and so these three things for thailand
+
+ align:start position:0%
+and so these three things for thailand
+ 
+
+ align:start position:0%
+and so these three things for thailand
+sweden and kenya are about cash various
+
+ align:start position:0%
+sweden and kenya are about cash various
+ 
+
+ align:start position:0%
+sweden and kenya are about cash various
+concepts of cash and cash management and
+
+ align:start position:0%
+concepts of cash and cash management and
+ 
+
+ align:start position:0%
+concepts of cash and cash management and
+then we'll come back to the ledgers
+
+ align:start position:0%
+then we'll come back to the ledgers
+ 
+
+ align:start position:0%
+then we'll come back to the ledgers
+again and talk about trusted third
+
+ align:start position:0%
+again and talk about trusted third
+ 
+
+ align:start position:0%
+again and talk about trusted third
+parties some problems in management that
+
+ align:start position:0%
+parties some problems in management that
+ 
+
+ align:start position:0%
+parties some problems in management that
+may or may not show up at the individual
+
+ align:start position:0%
+may or may not show up at the individual
+ 
+
+ align:start position:0%
+may or may not show up at the individual
+level but definitely show up at the
+
+ align:start position:0%
+level but definitely show up at the
+ 
+
+ align:start position:0%
+level but definitely show up at the
+wholesale level at the level of
+
+ align:start position:0%
+wholesale level at the level of
+ 
+
+ align:start position:0%
+wholesale level at the level of
+financial infrastructure okay
+
+ align:start position:0%
+financial infrastructure okay
+ 
+
+ align:start position:0%
+financial infrastructure okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's a statement of income
+
+ align:start position:0%
+here's a statement of income
+ 
+
+ align:start position:0%
+here's a statement of income
+and forgive me if this is a review for
+
+ align:start position:0%
+and forgive me if this is a review for
+ 
+
+ align:start position:0%
+and forgive me if this is a review for
+some of you these things aren't hard but
+
+ align:start position:0%
+some of you these things aren't hard but
+ 
+
+ align:start position:0%
+some of you these things aren't hard but
+they're a bit tedious
+
+ align:start position:0%
+they're a bit tedious
+ 
+
+ align:start position:0%
+they're a bit tedious
+so we talk about sources of income and
+
+ align:start position:0%
+so we talk about sources of income and
+ 
+
+ align:start position:0%
+so we talk about sources of income and
+uses of income and the sources of income
+
+ align:start position:0%
+uses of income and the sources of income
+ 
+
+ align:start position:0%
+uses of income and the sources of income
+as in the thai data come from
+
+ align:start position:0%
+as in the thai data come from
+ 
+
+ align:start position:0%
+as in the thai data come from
+cultivation livestock fish and shrimp
+
+ align:start position:0%
+cultivation livestock fish and shrimp
+ 
+
+ align:start position:0%
+cultivation livestock fish and shrimp
+this is a wage earning household
+
+ align:start position:0%
+this is a wage earning household
+ 
+
+ align:start position:0%
+this is a wage earning household
+primarily
+
+ align:start position:0%
+primarily
+ 
+
+ align:start position:0%
+primarily
+a little bit of livestock so most of the
+
+ align:start position:0%
+a little bit of livestock so most of the
+ 
+
+ align:start position:0%
+a little bit of livestock so most of the
+line entry here is almost entirely from
+
+ align:start position:0%
+line entry here is almost entirely from
+ 
+
+ align:start position:0%
+line entry here is almost entirely from
+wage labor income those are the sources
+
+ align:start position:0%
+wage labor income those are the sources
+ 
+
+ align:start position:0%
+wage labor income those are the sources
+and then the uses so to speak or you
+
+ align:start position:0%
+and then the uses so to speak or you
+ 
+
+ align:start position:0%
+and then the uses so to speak or you
+could say revenues versus costs
+
+ align:start position:0%
+could say revenues versus costs
+ 
+
+ align:start position:0%
+could say revenues versus costs
+you have expenses from each of the
+
+ align:start position:0%
+you have expenses from each of the
+ 
+
+ align:start position:0%
+you have expenses from each of the
+activities livestock you know if they're
+
+ align:start position:0%
+activities livestock you know if they're
+ 
+
+ align:start position:0%
+activities livestock you know if they're
+in debt they have interest expenses
+
+ align:start position:0%
+in debt they have interest expenses
+ 
+
+ align:start position:0%
+in debt they have interest expenses
+there's that depreciation and we talked
+
+ align:start position:0%
+there's that depreciation and we talked
+ 
+
+ align:start position:0%
+there's that depreciation and we talked
+about last time
+
+ align:start position:0%
+about last time
+ 
+
+ align:start position:0%
+about last time
+and then this is charges against revenue
+
+ align:start position:0%
+and then this is charges against revenue
+ 
+
+ align:start position:0%
+and then this is charges against revenue
+so in addition to having expenses for
+
+ align:start position:0%
+so in addition to having expenses for
+ 
+
+ align:start position:0%
+so in addition to having expenses for
+production they might pay taxes these
+
+ align:start position:0%
+production they might pay taxes these
+ 
+
+ align:start position:0%
+production they might pay taxes these
+guys don't but they can either consume
+
+ align:start position:0%
+guys don't but they can either consume
+ 
+
+ align:start position:0%
+guys don't but they can either consume
+the rest
+
+ align:start position:0%
+the rest
+ 
+
+ align:start position:0%
+the rest
+or save
+
+ align:start position:0%
+or save
+ 
+
+ align:start position:0%
+or save
+advantage of the financial accounts is
+
+ align:start position:0%
+advantage of the financial accounts is
+ 
+
+ align:start position:0%
+advantage of the financial accounts is
+that everything balances so in this case
+
+ align:start position:0%
+that everything balances so in this case
+ 
+
+ align:start position:0%
+that everything balances so in this case
+revenue is totally balanced by charges
+
+ align:start position:0%
+revenue is totally balanced by charges
+ 
+
+ align:start position:0%
+revenue is totally balanced by charges
+against revenue and if you're as we did
+
+ align:start position:0%
+against revenue and if you're as we did
+ 
+
+ align:start position:0%
+against revenue and if you're as we did
+taking the thai data and thinking you
+
+ align:start position:0%
+taking the thai data and thinking you
+ 
+
+ align:start position:0%
+taking the thai data and thinking you
+have all the line items then you're
+
+ align:start position:0%
+have all the line items then you're
+ 
+
+ align:start position:0%
+have all the line items then you're
+creating the accounts and if these left
+
+ align:start position:0%
+creating the accounts and if these left
+ 
+
+ align:start position:0%
+creating the accounts and if these left
+and right hand sides don't balance we
+
+ align:start position:0%
+and right hand sides don't balance we
+ 
+
+ align:start position:0%
+and right hand sides don't balance we
+know we did something wrong and we have
+
+ align:start position:0%
+know we did something wrong and we have
+ 
+
+ align:start position:0%
+know we did something wrong and we have
+to go back and iterate and figure out
+
+ align:start position:0%
+to go back and iterate and figure out
+ 
+
+ align:start position:0%
+to go back and iterate and figure out
+you know excluded a variable or put it
+
+ align:start position:0%
+you know excluded a variable or put it
+ 
+
+ align:start position:0%
+you know excluded a variable or put it
+in the inappropriate spot so it's a
+
+ align:start position:0%
+in the inappropriate spot so it's a
+ 
+
+ align:start position:0%
+in the inappropriate spot so it's a
+great discipline device the balance
+
+ align:start position:0%
+great discipline device the balance
+ 
+
+ align:start position:0%
+great discipline device the balance
+sheet is stocks of stuff at a point in
+
+ align:start position:0%
+sheet is stocks of stuff at a point in
+ 
+
+ align:start position:0%
+sheet is stocks of stuff at a point in
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+namely liabilities and assets
+
+ align:start position:0%
+namely liabilities and assets
+ 
+
+ align:start position:0%
+namely liabilities and assets
+so the obvious liability would be debt
+
+ align:start position:0%
+so the obvious liability would be debt
+ 
+
+ align:start position:0%
+so the obvious liability would be debt
+which this house household has this is
+
+ align:start position:0%
+which this house household has this is
+ 
+
+ align:start position:0%
+which this house household has this is
+really somebody's numbers right this is
+
+ align:start position:0%
+really somebody's numbers right this is
+ 
+
+ align:start position:0%
+really somebody's numbers right this is
+a real person i want to remind you
+
+ align:start position:0%
+a real person i want to remind you
+ 
+
+ align:start position:0%
+a real person i want to remind you
+more on that momentarily
+
+ align:start position:0%
+more on that momentarily
+ 
+
+ align:start position:0%
+more on that momentarily
+and the debt's about 37 000 baht
+
+ align:start position:0%
+and the debt's about 37 000 baht
+ 
+
+ align:start position:0%
+and the debt's about 37 000 baht
+and the assets that the household has
+
+ align:start position:0%
+and the assets that the household has
+ 
+
+ align:start position:0%
+and the assets that the household has
+could be real or
+
+ align:start position:0%
+could be real or
+ 
+
+ align:start position:0%
+could be real or
+financial the financial assets are a big
+
+ align:start position:0%
+financial the financial assets are a big
+ 
+
+ align:start position:0%
+financial the financial assets are a big
+chunk of it in
+
+ align:start position:0%
+chunk of it in
+ 
+
+ align:start position:0%
+chunk of it in
+paper currency and some deposits at the
+
+ align:start position:0%
+paper currency and some deposits at the
+ 
+
+ align:start position:0%
+paper currency and some deposits at the
+bank and real assets in this case
+
+ align:start position:0%
+bank and real assets in this case
+ 
+
+ align:start position:0%
+bank and real assets in this case
+household fixed assets
+
+ align:start position:0%
+household fixed assets
+ 
+
+ align:start position:0%
+household fixed assets
+so we went through some examples last
+
+ align:start position:0%
+so we went through some examples last
+ 
+
+ align:start position:0%
+so we went through some examples last
+time when we talked about rates of
+
+ align:start position:0%
+time when we talked about rates of
+ 
+
+ align:start position:0%
+time when we talked about rates of
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+because we had in the numerator
+
+ align:start position:0%
+because we had in the numerator
+ 
+
+ align:start position:0%
+because we had in the numerator
+profits which is on the previous account
+
+ align:start position:0%
+profits which is on the previous account
+ 
+
+ align:start position:0%
+profits which is on the previous account
+revenue minus expenses
+
+ align:start position:0%
+revenue minus expenses
+ 
+
+ align:start position:0%
+revenue minus expenses
+and here profits over capital and here
+
+ align:start position:0%
+and here profits over capital and here
+ 
+
+ align:start position:0%
+and here profits over capital and here
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+you know the
+
+ align:start position:0%
+you know the
+ 
+
+ align:start position:0%
+you know the
+real and also financial capital
+
+ align:start position:0%
+real and also financial capital
+ 
+
+ align:start position:0%
+real and also financial capital
+now you know again these things balance
+
+ align:start position:0%
+now you know again these things balance
+ 
+
+ align:start position:0%
+now you know again these things balance
+but here there's a big uh item that i
+
+ align:start position:0%
+but here there's a big uh item that i
+ 
+
+ align:start position:0%
+but here there's a big uh item that i
+deliberately didn't mention at first to
+
+ align:start position:0%
+deliberately didn't mention at first to
+ 
+
+ align:start position:0%
+deliberately didn't mention at first to
+get your attention
+
+ align:start position:0%
+get your attention
+ 
+
+ align:start position:0%
+get your attention
+which is if you take assets minus
+
+ align:start position:0%
+which is if you take assets minus
+ 
+
+ align:start position:0%
+which is if you take assets minus
+liabilities hopefully
+
+ align:start position:0%
+liabilities hopefully
+ 
+
+ align:start position:0%
+liabilities hopefully
+net worth is positive if liabilities
+
+ align:start position:0%
+net worth is positive if liabilities
+ 
+
+ align:start position:0%
+net worth is positive if liabilities
+were greater than assets this guy's
+
+ align:start position:0%
+were greater than assets this guy's
+ 
+
+ align:start position:0%
+were greater than assets this guy's
+bankrupt at least in the accounting
+
+ align:start position:0%
+bankrupt at least in the accounting
+ 
+
+ align:start position:0%
+bankrupt at least in the accounting
+sense so for almost all these households
+
+ align:start position:0%
+sense so for almost all these households
+ 
+
+ align:start position:0%
+sense so for almost all these households
+assets are greater than liabilities and
+
+ align:start position:0%
+assets are greater than liabilities and
+ 
+
+ align:start position:0%
+assets are greater than liabilities and
+the difference is something we call
+
+ align:start position:0%
+the difference is something we call
+ 
+
+ align:start position:0%
+the difference is something we call
+equity or net worth and that enters
+
+ align:start position:0%
+equity or net worth and that enters
+ 
+
+ align:start position:0%
+equity or net worth and that enters
+oddly on the right-hand side with
+
+ align:start position:0%
+oddly on the right-hand side with
+ 
+
+ align:start position:0%
+oddly on the right-hand side with
+liabilities precisely so that the two
+
+ align:start position:0%
+liabilities precisely so that the two
+ 
+
+ align:start position:0%
+liabilities precisely so that the two
+sides of the financial account of the
+
+ align:start position:0%
+sides of the financial account of the
+ 
+
+ align:start position:0%
+sides of the financial account of the
+balance sheet account are equal to each
+
+ align:start position:0%
+balance sheet account are equal to each
+ 
+
+ align:start position:0%
+balance sheet account are equal to each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now with the those concepts statement
+
+ align:start position:0%
+so now with the those concepts statement
+ 
+
+ align:start position:0%
+so now with the those concepts statement
+and balance sheet would take it to an
+
+ align:start position:0%
+and balance sheet would take it to an
+ 
+
+ align:start position:0%
+and balance sheet would take it to an
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+so this is a wealth planner which we
+
+ align:start position:0%
+so this is a wealth planner which we
+ 
+
+ align:start position:0%
+so this is a wealth planner which we
+implemented okay
+
+ align:start position:0%
+implemented okay
+ 
+
+ align:start position:0%
+implemented okay
+to that household and all of the other
+
+ align:start position:0%
+to that household and all of the other
+ 
+
+ align:start position:0%
+to that household and all of the other
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+what is the household we imagine to be
+
+ align:start position:0%
+what is the household we imagine to be
+ 
+
+ align:start position:0%
+what is the household we imagine to be
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+namely maximize discounted expected
+
+ align:start position:0%
+namely maximize discounted expected
+ 
+
+ align:start position:0%
+namely maximize discounted expected
+utility so you've kind of seen versions
+
+ align:start position:0%
+utility so you've kind of seen versions
+ 
+
+ align:start position:0%
+utility so you've kind of seen versions
+of this before you saw it first with
+
+ align:start position:0%
+of this before you saw it first with
+ 
+
+ align:start position:0%
+of this before you saw it first with
+respect to storage of seed and so on in
+
+ align:start position:0%
+respect to storage of seed and so on in
+ 
+
+ align:start position:0%
+respect to storage of seed and so on in
+the medieval village economy we've got a
+
+ align:start position:0%
+the medieval village economy we've got a
+ 
+
+ align:start position:0%
+the medieval village economy we've got a
+finite horizon here death happens but
+
+ align:start position:0%
+finite horizon here death happens but
+ 
+
+ align:start position:0%
+finite horizon here death happens but
+more on that momentarily so it's
+
+ align:start position:0%
+more on that momentarily so it's
+ 
+
+ align:start position:0%
+more on that momentarily so it's
+discounted utility this is constant
+
+ align:start position:0%
+discounted utility this is constant
+ 
+
+ align:start position:0%
+discounted utility this is constant
+relative risk aversion
+
+ align:start position:0%
+relative risk aversion
+ 
+
+ align:start position:0%
+relative risk aversion
+with a risk-averse coefficient of kappa
+
+ align:start position:0%
+with a risk-averse coefficient of kappa
+ 
+
+ align:start position:0%
+with a risk-averse coefficient of kappa
+delta is the discount rate
+
+ align:start position:0%
+delta is the discount rate
+ 
+
+ align:start position:0%
+delta is the discount rate
+and the end of life which is t
+
+ align:start position:0%
+and the end of life which is t
+ 
+
+ align:start position:0%
+and the end of life which is t
+they may bequest assets to their kids it
+
+ align:start position:0%
+they may bequest assets to their kids it
+ 
+
+ align:start position:0%
+they may bequest assets to their kids it
+looks like a similar function but
+
+ align:start position:0%
+looks like a similar function but
+ 
+
+ align:start position:0%
+looks like a similar function but
+there's an extra term here which is beta
+
+ align:start position:0%
+there's an extra term here which is beta
+ 
+
+ align:start position:0%
+there's an extra term here which is beta
+almost for bequest and again the
+
+ align:start position:0%
+almost for bequest and again the
+ 
+
+ align:start position:0%
+almost for bequest and again the
+notation changes from one lecture to the
+
+ align:start position:0%
+notation changes from one lecture to the
+ 
+
+ align:start position:0%
+notation changes from one lecture to the
+next but anyway so that's another
+
+ align:start position:0%
+next but anyway so that's another
+ 
+
+ align:start position:0%
+next but anyway so that's another
+parameter we have delta kappa and beta
+
+ align:start position:0%
+parameter we have delta kappa and beta
+ 
+
+ align:start position:0%
+parameter we have delta kappa and beta
+we're going to figure out what they are
+
+ align:start position:0%
+we're going to figure out what they are
+ 
+
+ align:start position:0%
+we're going to figure out what they are
+because they will impact the solution
+
+ align:start position:0%
+because they will impact the solution
+ 
+
+ align:start position:0%
+because they will impact the solution
+subject to the big constraint now again
+
+ align:start position:0%
+subject to the big constraint now again
+ 
+
+ align:start position:0%
+subject to the big constraint now again
+you've seen this a version of this in
+
+ align:start position:0%
+you've seen this a version of this in
+ 
+
+ align:start position:0%
+you've seen this a version of this in
+the medieval village economy because we
+
+ align:start position:0%
+the medieval village economy because we
+ 
+
+ align:start position:0%
+the medieval village economy because we
+had resources available today which they
+
+ align:start position:0%
+had resources available today which they
+ 
+
+ align:start position:0%
+had resources available today which they
+could eat or
+
+ align:start position:0%
+could eat or
+ 
+
+ align:start position:0%
+could eat or
+store in two different ways which would
+
+ align:start position:0%
+store in two different ways which would
+ 
+
+ align:start position:0%
+store in two different ways which would
+determine resources available next
+
+ align:start position:0%
+determine resources available next
+ 
+
+ align:start position:0%
+determine resources available next
+period here they have wealth today
+
+ align:start position:0%
+period here they have wealth today
+ 
+
+ align:start position:0%
+period here they have wealth today
+when they have resources available today
+
+ align:start position:0%
+when they have resources available today
+ 
+
+ align:start position:0%
+when they have resources available today
+which is the beginning of period stocks
+
+ align:start position:0%
+which is the beginning of period stocks
+ 
+
+ align:start position:0%
+which is the beginning of period stocks
+their wealth
+
+ align:start position:0%
+their wealth
+ 
+
+ align:start position:0%
+their wealth
+plus income more on that momentarily and
+
+ align:start position:0%
+plus income more on that momentarily and
+ 
+
+ align:start position:0%
+plus income more on that momentarily and
+they can either eat it and the
+
+ align:start position:0%
+they can either eat it and the
+ 
+
+ align:start position:0%
+they can either eat it and the
+difference between what they have and
+
+ align:start position:0%
+difference between what they have and
+ 
+
+ align:start position:0%
+difference between what they have and
+what they eat they invest so some
+
+ align:start position:0%
+what they eat they invest so some
+ 
+
+ align:start position:0%
+what they eat they invest so some
+fraction z
+
+ align:start position:0%
+fraction z
+ 
+
+ align:start position:0%
+fraction z
+goes into risky assets and the residual
+
+ align:start position:0%
+goes into risky assets and the residual
+ 
+
+ align:start position:0%
+goes into risky assets and the residual
+one minus z fraction goes into safe
+
+ align:start position:0%
+one minus z fraction goes into safe
+ 
+
+ align:start position:0%
+one minus z fraction goes into safe
+assets
+
+ align:start position:0%
+assets
+ 
+
+ align:start position:0%
+assets
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+life cycle portfolio allocation problem
+
+ align:start position:0%
+life cycle portfolio allocation problem
+ 
+
+ align:start position:0%
+life cycle portfolio allocation problem
+a little bit more detail about these
+
+ align:start position:0%
+a little bit more detail about these
+ 
+
+ align:start position:0%
+a little bit more detail about these
+numbers so
+
+ align:start position:0%
+numbers so
+ 
+
+ align:start position:0%
+numbers so
+the income term is the second and third
+
+ align:start position:0%
+the income term is the second and third
+ 
+
+ align:start position:0%
+the income term is the second and third
+term if gamma is equal to one then the
+
+ align:start position:0%
+term if gamma is equal to one then the
+ 
+
+ align:start position:0%
+term if gamma is equal to one then the
+mu which is the mean income cancels out
+
+ align:start position:0%
+mu which is the mean income cancels out
+ 
+
+ align:start position:0%
+mu which is the mean income cancels out
+and this household is entirely on its
+
+ align:start position:0%
+and this household is entirely on its
+ 
+
+ align:start position:0%
+and this household is entirely on its
+own with income fluctuations around the
+
+ align:start position:0%
+own with income fluctuations around the
+ 
+
+ align:start position:0%
+own with income fluctuations around the
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+when gamma is equal to zero this whole
+
+ align:start position:0%
+when gamma is equal to zero this whole
+ 
+
+ align:start position:0%
+when gamma is equal to zero this whole
+term is gone and the household has its
+
+ align:start position:0%
+term is gone and the household has its
+ 
+
+ align:start position:0%
+term is gone and the household has its
+mean income so gamma here between zero
+
+ align:start position:0%
+mean income so gamma here between zero
+ 
+
+ align:start position:0%
+mean income so gamma here between zero
+and one
+
+ align:start position:0%
+and one
+ 
+
+ align:start position:0%
+and one
+is capturing the risk sharing that we
+
+ align:start position:0%
+is capturing the risk sharing that we
+ 
+
+ align:start position:0%
+is capturing the risk sharing that we
+know is prevalent in the thai villages
+
+ align:start position:0%
+know is prevalent in the thai villages
+ 
+
+ align:start position:0%
+know is prevalent in the thai villages
+so that's the way all that risk sharing
+
+ align:start position:0%
+so that's the way all that risk sharing
+ 
+
+ align:start position:0%
+so that's the way all that risk sharing
+stuff entered into the individual
+
+ align:start position:0%
+stuff entered into the individual
+ 
+
+ align:start position:0%
+stuff entered into the individual
+program it looks like self-insurance
+
+ align:start position:0%
+program it looks like self-insurance
+ 
+
+ align:start position:0%
+program it looks like self-insurance
+but it isn't because the income stream
+
+ align:start position:0%
+but it isn't because the income stream
+ 
+
+ align:start position:0%
+but it isn't because the income stream
+can be attenuated
+
+ align:start position:0%
+can be attenuated
+ 
+
+ align:start position:0%
+can be attenuated
+due to the gifts but it can also vary
+
+ align:start position:0%
+due to the gifts but it can also vary
+ 
+
+ align:start position:0%
+due to the gifts but it can also vary
+about over households we have to elicit
+
+ align:start position:0%
+about over households we have to elicit
+ 
+
+ align:start position:0%
+about over households we have to elicit
+from the households how big or small
+
+ align:start position:0%
+from the households how big or small
+ 
+
+ align:start position:0%
+from the households how big or small
+gamma is
+
+ align:start position:0%
+gamma is
+ 
+
+ align:start position:0%
+gamma is
+this is a premium
+
+ align:start position:0%
+this is a premium
+ 
+
+ align:start position:0%
+this is a premium
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+sorry an indemnity if the household head
+
+ align:start position:0%
+sorry an indemnity if the household head
+ 
+
+ align:start position:0%
+sorry an indemnity if the household head
+dies these uh all these village
+
+ align:start position:0%
+dies these uh all these village
+ 
+
+ align:start position:0%
+dies these uh all these village
+villagers get together and contribute
+
+ align:start position:0%
+villagers get together and contribute
+ 
+
+ align:start position:0%
+villagers get together and contribute
+something to help the bereaved household
+
+ align:start position:0%
+something to help the bereaved household
+ 
+
+ align:start position:0%
+something to help the bereaved household
+with expenses and so on see his
+
+ align:start position:0%
+with expenses and so on see his
+ 
+
+ align:start position:0%
+with expenses and so on see his
+consumption big c is committed
+
+ align:start position:0%
+consumption big c is committed
+ 
+
+ align:start position:0%
+consumption big c is committed
+consumption so these are things the
+
+ align:start position:0%
+consumption so these are things the
+ 
+
+ align:start position:0%
+consumption so these are things the
+household tells us they're going to do
+
+ align:start position:0%
+household tells us they're going to do
+ 
+
+ align:start position:0%
+household tells us they're going to do
+no matter what and so we ended as a
+
+ align:start position:0%
+no matter what and so we ended as a
+ 
+
+ align:start position:0%
+no matter what and so we ended as a
+particular expense
+
+ align:start position:0%
+particular expense
+ 
+
+ align:start position:0%
+particular expense
+all right so here is a bit of what we
+
+ align:start position:0%
+all right so here is a bit of what we
+ 
+
+ align:start position:0%
+all right so here is a bit of what we
+show the household
+
+ align:start position:0%
+show the household
+ 
+
+ align:start position:0%
+show the household
+we explain to them
+
+ align:start position:0%
+we explain to them
+ 
+
+ align:start position:0%
+we explain to them
+we go and interview them and that we
+
+ align:start position:0%
+we go and interview them and that we
+ 
+
+ align:start position:0%
+we go and interview them and that we
+have we have been getting data from them
+
+ align:start position:0%
+have we have been getting data from them
+ 
+
+ align:start position:0%
+have we have been getting data from them
+all along but this is extra
+
+ align:start position:0%
+all along but this is extra
+ 
+
+ align:start position:0%
+all along but this is extra
+so we tell them we want to know how much
+
+ align:start position:0%
+so we tell them we want to know how much
+ 
+
+ align:start position:0%
+so we tell them we want to know how much
+they're planning to give to their kids
+
+ align:start position:0%
+they're planning to give to their kids
+ 
+
+ align:start position:0%
+they're planning to give to their kids
+if anything
+
+ align:start position:0%
+if anything
+ 
+
+ align:start position:0%
+if anything
+try to elicit their current income
+
+ align:start position:0%
+try to elicit their current income
+ 
+
+ align:start position:0%
+try to elicit their current income
+profile and future movements in income
+
+ align:start position:0%
+profile and future movements in income
+ 
+
+ align:start position:0%
+profile and future movements in income
+get their goals
+
+ align:start position:0%
+get their goals
+ 
+
+ align:start position:0%
+get their goals
+uh and get their current wealth
+
+ align:start position:0%
+uh and get their current wealth
+ 
+
+ align:start position:0%
+uh and get their current wealth
+and then we're going to tell them how
+
+ align:start position:0%
+and then we're going to tell them how
+ 
+
+ align:start position:0%
+and then we're going to tell them how
+much they should be saving
+
+ align:start position:0%
+much they should be saving
+ 
+
+ align:start position:0%
+much they should be saving
+and how to save it in risky versus safe
+
+ align:start position:0%
+and how to save it in risky versus safe
+ 
+
+ align:start position:0%
+and how to save it in risky versus safe
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+and particular whether they might want
+
+ align:start position:0%
+and particular whether they might want
+ 
+
+ align:start position:0%
+and particular whether they might want
+to be borrowing
+
+ align:start position:0%
+to be borrowing
+ 
+
+ align:start position:0%
+to be borrowing
+i don't know some people don't like
+
+ align:start position:0%
+i don't know some people don't like
+ 
+
+ align:start position:0%
+i don't know some people don't like
+these little cartoon characters it's an
+
+ align:start position:0%
+these little cartoon characters it's an
+ 
+
+ align:start position:0%
+these little cartoon characters it's an
+attempt to communicate
+
+ align:start position:0%
+attempt to communicate
+ 
+
+ align:start position:0%
+attempt to communicate
+clearly so we don't say tell us
+
+ align:start position:0%
+clearly so we don't say tell us
+ 
+
+ align:start position:0%
+clearly so we don't say tell us
+everything we say let us demonstrate for
+
+ align:start position:0%
+everything we say let us demonstrate for
+ 
+
+ align:start position:0%
+everything we say let us demonstrate for
+you how this works we'll show you the
+
+ align:start position:0%
+you how this works we'll show you the
+ 
+
+ align:start position:0%
+you how this works we'll show you the
+results of another villager
+
+ align:start position:0%
+results of another villager
+ 
+
+ align:start position:0%
+results of another villager
+we asked that household whether or not
+
+ align:start position:0%
+we asked that household whether or not
+ 
+
+ align:start position:0%
+we asked that household whether or not
+they want to leave money to their kids
+
+ align:start position:0%
+they want to leave money to their kids
+ 
+
+ align:start position:0%
+they want to leave money to their kids
+and this household said no
+
+ align:start position:0%
+and this household said no
+ 
+
+ align:start position:0%
+and this household said no
+my kids are going to be much richer than
+
+ align:start position:0%
+my kids are going to be much richer than
+ 
+
+ align:start position:0%
+my kids are going to be much richer than
+i am they're going to work in bangkok i
+
+ align:start position:0%
+i am they're going to work in bangkok i
+ 
+
+ align:start position:0%
+i am they're going to work in bangkok i
+don't think i need to leave anything to
+
+ align:start position:0%
+don't think i need to leave anything to
+ 
+
+ align:start position:0%
+don't think i need to leave anything to
+my children after my death
+
+ align:start position:0%
+my children after my death
+ 
+
+ align:start position:0%
+my children after my death
+so this household said zero bot
+
+ align:start position:0%
+so this household said zero bot
+ 
+
+ align:start position:0%
+so this household said zero bot
+i made the mistake once of having this
+
+ align:start position:0%
+i made the mistake once of having this
+ 
+
+ align:start position:0%
+i made the mistake once of having this
+interview with the mother and the
+
+ align:start position:0%
+interview with the mother and the
+ 
+
+ align:start position:0%
+interview with the mother and the
+daughter present in the room at the same
+
+ align:start position:0%
+daughter present in the room at the same
+ 
+
+ align:start position:0%
+daughter present in the room at the same
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+obviously that was awkward
+
+ align:start position:0%
+obviously that was awkward
+ 
+
+ align:start position:0%
+obviously that was awkward
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+collect input so we need to calibrate
+
+ align:start position:0%
+collect input so we need to calibrate
+ 
+
+ align:start position:0%
+collect input so we need to calibrate
+this income process
+
+ align:start position:0%
+this income process
+ 
+
+ align:start position:0%
+this income process
+and we give
+
+ align:start position:0%
+and we give
+ 
+
+ align:start position:0%
+and we give
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+chen now you're going to see some thai
+
+ align:start position:0%
+chen now you're going to see some thai
+ 
+
+ align:start position:0%
+chen now you're going to see some thai
+sorry anyway
+
+ align:start position:0%
+sorry anyway
+ 
+
+ align:start position:0%
+sorry anyway
+wage earners earn a regular income of 10
+
+ align:start position:0%
+wage earners earn a regular income of 10
+ 
+
+ align:start position:0%
+wage earners earn a regular income of 10
+000 baht
+
+ align:start position:0%
+000 baht
+ 
+
+ align:start position:0%
+000 baht
+uh expects to work to age 65 and then
+
+ align:start position:0%
+uh expects to work to age 65 and then
+ 
+
+ align:start position:0%
+uh expects to work to age 65 and then
+income you know drops to something very
+
+ align:start position:0%
+income you know drops to something very
+ 
+
+ align:start position:0%
+income you know drops to something very
+small with which is a pension so that's
+
+ align:start position:0%
+small with which is a pension so that's
+ 
+
+ align:start position:0%
+small with which is a pension so that's
+this picture ten thousand baht age 65
+
+ align:start position:0%
+this picture ten thousand baht age 65
+ 
+
+ align:start position:0%
+this picture ten thousand baht age 65
+the household is currently young
+
+ align:start position:0%
+the household is currently young
+ 
+
+ align:start position:0%
+the household is currently young
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+drops to zero or this guy
+
+ align:start position:0%
+drops to zero or this guy
+ 
+
+ align:start position:0%
+drops to zero or this guy
+different example has a little shop as a
+
+ align:start position:0%
+different example has a little shop as a
+ 
+
+ align:start position:0%
+different example has a little shop as a
+business very volatile income
+
+ align:start position:0%
+business very volatile income
+ 
+
+ align:start position:0%
+business very volatile income
+expects to keep its business running
+
+ align:start position:0%
+expects to keep its business running
+ 
+
+ align:start position:0%
+expects to keep its business running
+until age 60 currently age
+
+ align:start position:0%
+until age 60 currently age
+ 
+
+ align:start position:0%
+until age 60 currently age
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and then receive some small income again
+
+ align:start position:0%
+and then receive some small income again
+ 
+
+ align:start position:0%
+and then receive some small income again
+from from the kids oh yeah kids give
+
+ align:start position:0%
+from from the kids oh yeah kids give
+ 
+
+ align:start position:0%
+from from the kids oh yeah kids give
+money to the parents you guys you hear
+
+ align:start position:0%
+money to the parents you guys you hear
+ 
+
+ align:start position:0%
+money to the parents you guys you hear
+you hear that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+depends on where you're from whether you
+
+ align:start position:0%
+depends on where you're from whether you
+ 
+
+ align:start position:0%
+depends on where you're from whether you
+can relate to this another example this
+
+ align:start position:0%
+can relate to this another example this
+ 
+
+ align:start position:0%
+can relate to this another example this
+household has a regular increasing
+
+ align:start position:0%
+household has a regular increasing
+ 
+
+ align:start position:0%
+household has a regular increasing
+income for 30 years but again income
+
+ align:start position:0%
+income for 30 years but again income
+ 
+
+ align:start position:0%
+income for 30 years but again income
+starts to drop out however they're going
+
+ align:start position:0%
+starts to drop out however they're going
+ 
+
+ align:start position:0%
+starts to drop out however they're going
+to go into a second occupation and uh
+
+ align:start position:0%
+to go into a second occupation and uh
+ 
+
+ align:start position:0%
+to go into a second occupation and uh
+income only slowly so i stay you know we
+
+ align:start position:0%
+income only slowly so i stay you know we
+ 
+
+ align:start position:0%
+income only slowly so i stay you know we
+used to stay in the village with the
+
+ align:start position:0%
+used to stay in the village with the
+ 
+
+ align:start position:0%
+used to stay in the village with the
+head man but eventually thailand has
+
+ align:start position:0%
+head man but eventually thailand has
+ 
+
+ align:start position:0%
+head man but eventually thailand has
+motels and you'll often see an elderly
+
+ align:start position:0%
+motels and you'll often see an elderly
+ 
+
+ align:start position:0%
+motels and you'll often see an elderly
+couple running the motel
+
+ align:start position:0%
+couple running the motel
+ 
+
+ align:start position:0%
+couple running the motel
+that's now their new business relative
+
+ align:start position:0%
+that's now their new business relative
+ 
+
+ align:start position:0%
+that's now their new business relative
+to what they used to do etc
+
+ align:start position:0%
+to what they used to do etc
+ 
+
+ align:start position:0%
+to what they used to do etc
+so these are just three examples
+
+ align:start position:0%
+so these are just three examples
+ 
+
+ align:start position:0%
+so these are just three examples
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what about goals so
+
+ align:start position:0%
+what about goals so
+ 
+
+ align:start position:0%
+what about goals so
+do you expect to send your kids to
+
+ align:start position:0%
+do you expect to send your kids to
+ 
+
+ align:start position:0%
+do you expect to send your kids to
+college is that a planned expense or
+
+ align:start position:0%
+college is that a planned expense or
+ 
+
+ align:start position:0%
+college is that a planned expense or
+in the future open a business or buy a
+
+ align:start position:0%
+in the future open a business or buy a
+ 
+
+ align:start position:0%
+in the future open a business or buy a
+new tv
+
+ align:start position:0%
+new tv
+ 
+
+ align:start position:0%
+new tv
+but what we want are
+
+ align:start position:0%
+but what we want are
+ 
+
+ align:start position:0%
+but what we want are
+expenses they're going to do no matter
+
+ align:start position:0%
+expenses they're going to do no matter
+ 
+
+ align:start position:0%
+expenses they're going to do no matter
+what so yes or no
+
+ align:start position:0%
+what so yes or no
+ 
+
+ align:start position:0%
+what so yes or no
+depending
+
+ align:start position:0%
+depending
+ 
+
+ align:start position:0%
+depending
+and this particular example household we
+
+ align:start position:0%
+and this particular example household we
+ 
+
+ align:start position:0%
+and this particular example household we
+give them car purchase was that
+
+ align:start position:0%
+give them car purchase was that
+ 
+
+ align:start position:0%
+give them car purchase was that
+obligatory no send the kids to college
+
+ align:start position:0%
+obligatory no send the kids to college
+ 
+
+ align:start position:0%
+obligatory no send the kids to college
+yes if how many years away 15 years
+
+ align:start position:0%
+yes if how many years away 15 years
+ 
+
+ align:start position:0%
+yes if how many years away 15 years
+kids are young and it's gonna cost ten
+
+ align:start position:0%
+kids are young and it's gonna cost ten
+ 
+
+ align:start position:0%
+kids are young and it's gonna cost ten
+thousand dollars for for three years
+
+ align:start position:0%
+thousand dollars for for three years
+ 
+
+ align:start position:0%
+thousand dollars for for three years
+thirty thousand baht at that that's
+
+ align:start position:0%
+thirty thousand baht at that that's
+ 
+
+ align:start position:0%
+thirty thousand baht at that that's
+about yeah it's a lot less than u.s
+
+ align:start position:0%
+about yeah it's a lot less than u.s
+ 
+
+ align:start position:0%
+about yeah it's a lot less than u.s
+expenses let's it's not mit tuition
+
+ align:start position:0%
+expenses let's it's not mit tuition
+ 
+
+ align:start position:0%
+expenses let's it's not mit tuition
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+now we have wealth so w this is tricky
+
+ align:start position:0%
+now we have wealth so w this is tricky
+ 
+
+ align:start position:0%
+now we have wealth so w this is tricky
+money available to save or spend
+
+ align:start position:0%
+money available to save or spend
+ 
+
+ align:start position:0%
+money available to save or spend
+or invest so
+
+ align:start position:0%
+or invest so
+ 
+
+ align:start position:0%
+or invest so
+if you have a car it's worth ten
+
+ align:start position:0%
+if you have a car it's worth ten
+ 
+
+ align:start position:0%
+if you have a car it's worth ten
+thousand baht you think you know it's
+
+ align:start position:0%
+thousand baht you think you know it's
+ 
+
+ align:start position:0%
+thousand baht you think you know it's
+used but you could sell it easily then
+
+ align:start position:0%
+used but you could sell it easily then
+ 
+
+ align:start position:0%
+used but you could sell it easily then
+we would count that as a household asset
+
+ align:start position:0%
+we would count that as a household asset
+ 
+
+ align:start position:0%
+we would count that as a household asset
+or business asset it could be sold
+
+ align:start position:0%
+or business asset it could be sold
+ 
+
+ align:start position:0%
+or business asset it could be sold
+if they own land they
+
+ align:start position:0%
+if they own land they
+ 
+
+ align:start position:0%
+if they own land they
+worth a hundred thousand baht they may
+
+ align:start position:0%
+worth a hundred thousand baht they may
+ 
+
+ align:start position:0%
+worth a hundred thousand baht they may
+never plan to sell it it may not even be
+
+ align:start position:0%
+never plan to sell it it may not even be
+ 
+
+ align:start position:0%
+never plan to sell it it may not even be
+productive land so we don't count it
+
+ align:start position:0%
+productive land so we don't count it
+ 
+
+ align:start position:0%
+productive land so we don't count it
+unless they said it was
+
+ align:start position:0%
+unless they said it was
+ 
+
+ align:start position:0%
+unless they said it was
+if it's productive we have to we don't
+
+ align:start position:0%
+if it's productive we have to we don't
+ 
+
+ align:start position:0%
+if it's productive we have to we don't
+we want to avoid double counting so
+
+ align:start position:0%
+we want to avoid double counting so
+ 
+
+ align:start position:0%
+we want to avoid double counting so
+here's the thing
+
+ align:start position:0%
+here's the thing
+ 
+
+ align:start position:0%
+here's the thing
+you count the asset or you count the
+
+ align:start position:0%
+you count the asset or you count the
+ 
+
+ align:start position:0%
+you count the asset or you count the
+return stream you cannot count both
+
+ align:start position:0%
+return stream you cannot count both
+ 
+
+ align:start position:0%
+return stream you cannot count both
+value of land should be the
+
+ align:start position:0%
+value of land should be the
+ 
+
+ align:start position:0%
+value of land should be the
+discounted capitalized value of net
+
+ align:start position:0%
+discounted capitalized value of net
+ 
+
+ align:start position:0%
+discounted capitalized value of net
+profits from farming that's how much the
+
+ align:start position:0%
+profits from farming that's how much the
+ 
+
+ align:start position:0%
+profits from farming that's how much the
+land is worth
+
+ align:start position:0%
+land is worth
+ 
+
+ align:start position:0%
+land is worth
+you don't want to count both the land as
+
+ align:start position:0%
+you don't want to count both the land as
+ 
+
+ align:start position:0%
+you don't want to count both the land as
+an asset and also ask the households
+
+ align:start position:0%
+an asset and also ask the households
+ 
+
+ align:start position:0%
+an asset and also ask the households
+about the income stream so generally we
+
+ align:start position:0%
+about the income stream so generally we
+ 
+
+ align:start position:0%
+about the income stream so generally we
+don't count assets that we are using in
+
+ align:start position:0%
+don't count assets that we are using in
+ 
+
+ align:start position:0%
+don't count assets that we are using in
+calculating the income stream unless
+
+ align:start position:0%
+calculating the income stream unless
+ 
+
+ align:start position:0%
+calculating the income stream unless
+they say you know i'm going to stop
+
+ align:start position:0%
+they say you know i'm going to stop
+ 
+
+ align:start position:0%
+they say you know i'm going to stop
+farming at a certain date and how much
+
+ align:start position:0%
+farming at a certain date and how much
+ 
+
+ align:start position:0%
+farming at a certain date and how much
+would the land be worth then we count
+
+ align:start position:0%
+would the land be worth then we count
+ 
+
+ align:start position:0%
+would the land be worth then we count
+income up to that point then we count
+
+ align:start position:0%
+income up to that point then we count
+ 
+
+ align:start position:0%
+income up to that point then we count
+the land
+
+ align:start position:0%
+the land
+ 
+
+ align:start position:0%
+the land
+so let's run the planner
+
+ align:start position:0%
+so let's run the planner
+ 
+
+ align:start position:0%
+so let's run the planner
+i'll give you examples we created an
+
+ align:start position:0%
+i'll give you examples we created an
+ 
+
+ align:start position:0%
+i'll give you examples we created an
+excel spreadsheet with the answers to
+
+ align:start position:0%
+excel spreadsheet with the answers to
+ 
+
+ align:start position:0%
+excel spreadsheet with the answers to
+all the households questions
+
+ align:start position:0%
+all the households questions
+ 
+
+ align:start position:0%
+all the households questions
+and then enter it into the computer and
+
+ align:start position:0%
+and then enter it into the computer and
+ 
+
+ align:start position:0%
+and then enter it into the computer and
+run it i'm not showing you all of them
+
+ align:start position:0%
+run it i'm not showing you all of them
+ 
+
+ align:start position:0%
+run it i'm not showing you all of them
+the second household we told this
+
+ align:start position:0%
+the second household we told this
+ 
+
+ align:start position:0%
+the second household we told this
+household to cut its expenses on
+
+ align:start position:0%
+household to cut its expenses on
+ 
+
+ align:start position:0%
+household to cut its expenses on
+consumption quite a bit
+
+ align:start position:0%
+consumption quite a bit
+ 
+
+ align:start position:0%
+consumption quite a bit
+they weren't saving enough and to put
+
+ align:start position:0%
+they weren't saving enough and to put
+ 
+
+ align:start position:0%
+they weren't saving enough and to put
+almost all of it in safe assets
+
+ align:start position:0%
+almost all of it in safe assets
+ 
+
+ align:start position:0%
+almost all of it in safe assets
+more interesting is the life cycle
+
+ align:start position:0%
+more interesting is the life cycle
+ 
+
+ align:start position:0%
+more interesting is the life cycle
+picture so here's what the planner
+
+ align:start position:0%
+picture so here's what the planner
+ 
+
+ align:start position:0%
+picture so here's what the planner
+recommends that the household should do
+
+ align:start position:0%
+recommends that the household should do
+ 
+
+ align:start position:0%
+recommends that the household should do
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+let's start down here
+
+ align:start position:0%
+let's start down here
+ 
+
+ align:start position:0%
+let's start down here
+we've got income in red that's the
+
+ align:start position:0%
+we've got income in red that's the
+ 
+
+ align:start position:0%
+we've got income in red that's the
+elicited profile over time
+
+ align:start position:0%
+elicited profile over time
+ 
+
+ align:start position:0%
+elicited profile over time
+that i just told you about
+
+ align:start position:0%
+that i just told you about
+ 
+
+ align:start position:0%
+that i just told you about
+the consumption is endogenous variable
+
+ align:start position:0%
+the consumption is endogenous variable
+ 
+
+ align:start position:0%
+the consumption is endogenous variable
+obviously it's in black so here we told
+
+ align:start position:0%
+obviously it's in black so here we told
+ 
+
+ align:start position:0%
+obviously it's in black so here we told
+the household to cut its consumption
+
+ align:start position:0%
+the household to cut its consumption
+ 
+
+ align:start position:0%
+the household to cut its consumption
+expenditure a lot and much lower than
+
+ align:start position:0%
+expenditure a lot and much lower than
+ 
+
+ align:start position:0%
+expenditure a lot and much lower than
+its current income in order to build up
+
+ align:start position:0%
+its current income in order to build up
+ 
+
+ align:start position:0%
+its current income in order to build up
+the assets so here's the total level of
+
+ align:start position:0%
+the assets so here's the total level of
+ 
+
+ align:start position:0%
+the assets so here's the total level of
+assets and then when income drops to
+
+ align:start position:0%
+assets and then when income drops to
+ 
+
+ align:start position:0%
+assets and then when income drops to
+little or nothing
+
+ align:start position:0%
+little or nothing
+ 
+
+ align:start position:0%
+little or nothing
+they eat off the assets so this is just
+
+ align:start position:0%
+they eat off the assets so this is just
+ 
+
+ align:start position:0%
+they eat off the assets so this is just
+saving for retirement most of it's in
+
+ align:start position:0%
+saving for retirement most of it's in
+ 
+
+ align:start position:0%
+saving for retirement most of it's in
+safe assets not so much in risky and
+
+ align:start position:0%
+safe assets not so much in risky and
+ 
+
+ align:start position:0%
+safe assets not so much in risky and
+there's no borrowing another household
+
+ align:start position:0%
+there's no borrowing another household
+ 
+
+ align:start position:0%
+there's no borrowing another household
+basically had committed consumption that
+
+ align:start position:0%
+basically had committed consumption that
+ 
+
+ align:start position:0%
+basically had committed consumption that
+is going to get it in big trouble even
+
+ align:start position:0%
+is going to get it in big trouble even
+ 
+
+ align:start position:0%
+is going to get it in big trouble even
+though they said they were going to do
+
+ align:start position:0%
+though they said they were going to do
+ 
+
+ align:start position:0%
+though they said they were going to do
+it no matter what
+
+ align:start position:0%
+it no matter what
+ 
+
+ align:start position:0%
+it no matter what
+when we ran the planner at the time that
+
+ align:start position:0%
+when we ran the planner at the time that
+ 
+
+ align:start position:0%
+when we ran the planner at the time that
+they have this high expense i think it
+
+ align:start position:0%
+they have this high expense i think it
+ 
+
+ align:start position:0%
+they have this high expense i think it
+was for starting a business they really
+
+ align:start position:0%
+was for starting a business they really
+ 
+
+ align:start position:0%
+was for starting a business they really
+didn't have the resources to cover it
+
+ align:start position:0%
+didn't have the resources to cover it
+ 
+
+ align:start position:0%
+didn't have the resources to cover it
+now you know they try to
+
+ align:start position:0%
+now you know they try to
+ 
+
+ align:start position:0%
+now you know they try to
+increase their savings with income you
+
+ align:start position:0%
+increase their savings with income you
+ 
+
+ align:start position:0%
+increase their savings with income you
+know over consumption
+
+ align:start position:0%
+know over consumption
+ 
+
+ align:start position:0%
+know over consumption
+but it's you know in this sort of median
+
+ align:start position:0%
+but it's you know in this sort of median
+ 
+
+ align:start position:0%
+but it's you know in this sort of median
+simulation scenario it's just not enough
+
+ align:start position:0%
+simulation scenario it's just not enough
+ 
+
+ align:start position:0%
+simulation scenario it's just not enough
+so when that big expense comes on
+
+ align:start position:0%
+so when that big expense comes on
+ 
+
+ align:start position:0%
+so when that big expense comes on
+average they use up all of their assets
+
+ align:start position:0%
+average they use up all of their assets
+ 
+
+ align:start position:0%
+average they use up all of their assets
+you know consumption isn't dropping to
+
+ align:start position:0%
+you know consumption isn't dropping to
+ 
+
+ align:start position:0%
+you know consumption isn't dropping to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+remember it's constant relative risk
+
+ align:start position:0%
+remember it's constant relative risk
+ 
+
+ align:start position:0%
+remember it's constant relative risk
+aversion so marginal utility of
+
+ align:start position:0%
+aversion so marginal utility of
+ 
+
+ align:start position:0%
+aversion so marginal utility of
+consumption of zero is infinite although
+
+ align:start position:0%
+consumption of zero is infinite although
+ 
+
+ align:start position:0%
+consumption of zero is infinite although
+you can't see this but we gave them some
+
+ align:start position:0%
+you can't see this but we gave them some
+ 
+
+ align:start position:0%
+you can't see this but we gave them some
+subsistence bundle so they don't really
+
+ align:start position:0%
+subsistence bundle so they don't really
+ 
+
+ align:start position:0%
+subsistence bundle so they don't really
+go bankrupt they survive well they don't
+
+ align:start position:0%
+go bankrupt they survive well they don't
+ 
+
+ align:start position:0%
+go bankrupt they survive well they don't
+die
+
+ align:start position:0%
+die
+ 
+
+ align:start position:0%
+die
+when they go bankrupt they continue to
+
+ align:start position:0%
+when they go bankrupt they continue to
+ 
+
+ align:start position:0%
+when they go bankrupt they continue to
+survive because of that subsistence
+
+ align:start position:0%
+survive because of that subsistence
+ 
+
+ align:start position:0%
+survive because of that subsistence
+bundle
+
+ align:start position:0%
+bundle
+ 
+
+ align:start position:0%
+bundle
+uh what else is going on here this they
+
+ align:start position:0%
+uh what else is going on here this they
+ 
+
+ align:start position:0%
+uh what else is going on here this they
+kind of know in advance the planner
+
+ align:start position:0%
+kind of know in advance the planner
+ 
+
+ align:start position:0%
+kind of know in advance the planner
+knows state by state year by year
+
+ align:start position:0%
+knows state by state year by year
+ 
+
+ align:start position:0%
+knows state by state year by year
+that is that they're in trouble
+
+ align:start position:0%
+that is that they're in trouble
+ 
+
+ align:start position:0%
+that is that they're in trouble
+so actually they start borrowing of
+
+ align:start position:0%
+so actually they start borrowing of
+ 
+
+ align:start position:0%
+so actually they start borrowing of
+course given our subsistence consumption
+
+ align:start position:0%
+course given our subsistence consumption
+ 
+
+ align:start position:0%
+course given our subsistence consumption
+rule if the median scenario occurs
+
+ align:start position:0%
+rule if the median scenario occurs
+ 
+
+ align:start position:0%
+rule if the median scenario occurs
+they're not going to pay back the loan
+
+ align:start position:0%
+they're not going to pay back the loan
+ 
+
+ align:start position:0%
+they're not going to pay back the loan
+they get the default on the loan and
+
+ align:start position:0%
+they get the default on the loan and
+ 
+
+ align:start position:0%
+they get the default on the loan and
+they know that call this gambling for
+
+ align:start position:0%
+they know that call this gambling for
+ 
+
+ align:start position:0%
+they know that call this gambling for
+redemption they're starting to do
+
+ align:start position:0%
+redemption they're starting to do
+ 
+
+ align:start position:0%
+redemption they're starting to do
+risky things too
+
+ align:start position:0%
+risky things too
+ 
+
+ align:start position:0%
+risky things too
+and borrowing leveraging up you know
+
+ align:start position:0%
+and borrowing leveraging up you know
+ 
+
+ align:start position:0%
+and borrowing leveraging up you know
+with the idea that there's a good chance
+
+ align:start position:0%
+with the idea that there's a good chance
+ 
+
+ align:start position:0%
+with the idea that there's a good chance
+they're not going to make it not in here
+
+ align:start position:0%
+they're not going to make it not in here
+ 
+
+ align:start position:0%
+they're not going to make it not in here
+you know the planner is not the bank
+
+ align:start position:0%
+you know the planner is not the bank
+ 
+
+ align:start position:0%
+you know the planner is not the bank
+whether the bank would make this loan is
+
+ align:start position:0%
+whether the bank would make this loan is
+ 
+
+ align:start position:0%
+whether the bank would make this loan is
+is another issue anyway they survived
+
+ align:start position:0%
+is another issue anyway they survived
+ 
+
+ align:start position:0%
+is another issue anyway they survived
+this episode and continued to live
+
+ align:start position:0%
+this episode and continued to live
+ 
+
+ align:start position:0%
+this episode and continued to live
+another day with their fluctuating
+
+ align:start position:0%
+another day with their fluctuating
+ 
+
+ align:start position:0%
+another day with their fluctuating
+income so the rest of this looks like
+
+ align:start position:0%
+income so the rest of this looks like
+ 
+
+ align:start position:0%
+income so the rest of this looks like
+the other diagram to some extent
+
+ align:start position:0%
+the other diagram to some extent
+ 
+
+ align:start position:0%
+the other diagram to some extent
+okay so we show the households these
+
+ align:start position:0%
+okay so we show the households these
+ 
+
+ align:start position:0%
+okay so we show the households these
+pictures and um
+
+ align:start position:0%
+pictures and um
+ 
+
+ align:start position:0%
+pictures and um
+try to explain to them what's going on
+
+ align:start position:0%
+try to explain to them what's going on
+ 
+
+ align:start position:0%
+try to explain to them what's going on
+and and there are all kinds of
+
+ align:start position:0%
+and and there are all kinds of
+ 
+
+ align:start position:0%
+and and there are all kinds of
+households in the data and some of them
+
+ align:start position:0%
+households in the data and some of them
+ 
+
+ align:start position:0%
+households in the data and some of them
+in fact are very conservative and they
+
+ align:start position:0%
+in fact are very conservative and they
+ 
+
+ align:start position:0%
+in fact are very conservative and they
+have fluctuations in income and
+
+ align:start position:0%
+have fluctuations in income and
+ 
+
+ align:start position:0%
+have fluctuations in income and
+consumption consumption is never more
+
+ align:start position:0%
+consumption consumption is never more
+ 
+
+ align:start position:0%
+consumption consumption is never more
+than the lowest possible income draw and
+
+ align:start position:0%
+than the lowest possible income draw and
+ 
+
+ align:start position:0%
+than the lowest possible income draw and
+mostly a lot lower than their income
+
+ align:start position:0%
+mostly a lot lower than their income
+ 
+
+ align:start position:0%
+mostly a lot lower than their income
+draw so they're like saving like crazy
+
+ align:start position:0%
+draw so they're like saving like crazy
+ 
+
+ align:start position:0%
+draw so they're like saving like crazy
+and their net worth is growing at 20 per
+
+ align:start position:0%
+and their net worth is growing at 20 per
+ 
+
+ align:start position:0%
+and their net worth is growing at 20 per
+year sounds good to me by the way but
+
+ align:start position:0%
+year sounds good to me by the way but
+ 
+
+ align:start position:0%
+year sounds good to me by the way but
+they're probably over saving but i we
+
+ align:start position:0%
+they're probably over saving but i we
+ 
+
+ align:start position:0%
+they're probably over saving but i we
+we're very conservative about what we
+
+ align:start position:0%
+we're very conservative about what we
+ 
+
+ align:start position:0%
+we're very conservative about what we
+tell them we don't tell them that that's
+
+ align:start position:0%
+tell them we don't tell them that that's
+ 
+
+ align:start position:0%
+tell them we don't tell them that that's
+bad that's fine if they want to do that
+
+ align:start position:0%
+bad that's fine if they want to do that
+ 
+
+ align:start position:0%
+bad that's fine if they want to do that
+it's the ones who are eating too much
+
+ align:start position:0%
+it's the ones who are eating too much
+ 
+
+ align:start position:0%
+it's the ones who are eating too much
+and not saving
+
+ align:start position:0%
+and not saving
+ 
+
+ align:start position:0%
+and not saving
+that we're more worried about okay
+
+ align:start position:0%
+that we're more worried about okay
+ 
+
+ align:start position:0%
+that we're more worried about okay
+so this looks like thai villages but the
+
+ align:start position:0%
+so this looks like thai villages but the
+ 
+
+ align:start position:0%
+so this looks like thai villages but the
+life cycle model is universal
+
+ align:start position:0%
+life cycle model is universal
+ 
+
+ align:start position:0%
+life cycle model is universal
+and just to shift gears
+
+ align:start position:0%
+and just to shift gears
+ 
+
+ align:start position:0%
+and just to shift gears
+this is larry kotlikoff's
+
+ align:start position:0%
+this is larry kotlikoff's
+ 
+
+ align:start position:0%
+this is larry kotlikoff's
+website
+
+ align:start position:0%
+website
+ 
+
+ align:start position:0%
+website
+he's both a professor and an
+
+ align:start position:0%
+he's both a professor and an
+ 
+
+ align:start position:0%
+he's both a professor and an
+entrepreneur
+
+ align:start position:0%
+entrepreneur
+ 
+
+ align:start position:0%
+entrepreneur
+so he is selling this product
+
+ align:start position:0%
+so he is selling this product
+ 
+
+ align:start position:0%
+so he is selling this product
+this uh esp planner but he has a lot of
+
+ align:start position:0%
+this uh esp planner but he has a lot of
+ 
+
+ align:start position:0%
+this uh esp planner but he has a lot of
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+economic research on life cycle planning
+
+ align:start position:0%
+economic research on life cycle planning
+ 
+
+ align:start position:0%
+economic research on life cycle planning
+and you know
+
+ align:start position:0%
+and you know
+ 
+
+ align:start position:0%
+and you know
+no one wants to splurge today and starve
+
+ align:start position:0%
+no one wants to splurge today and starve
+ 
+
+ align:start position:0%
+no one wants to splurge today and starve
+tomorrow nor the opposite life cycle
+
+ align:start position:0%
+tomorrow nor the opposite life cycle
+ 
+
+ align:start position:0%
+tomorrow nor the opposite life cycle
+consumption smoothing balances our goals
+
+ align:start position:0%
+consumption smoothing balances our goals
+ 
+
+ align:start position:0%
+consumption smoothing balances our goals
+now you would think doesn't everyone do
+
+ align:start position:0%
+now you would think doesn't everyone do
+ 
+
+ align:start position:0%
+now you would think doesn't everyone do
+that the answer is no
+
+ align:start position:0%
+that the answer is no
+ 
+
+ align:start position:0%
+that the answer is no
+there's only two companies i know of in
+
+ align:start position:0%
+there's only two companies i know of in
+ 
+
+ align:start position:0%
+there's only two companies i know of in
+the us that do this
+
+ align:start position:0%
+the us that do this
+ 
+
+ align:start position:0%
+the us that do this
+and it's not vanguard it's not fidelity
+
+ align:start position:0%
+and it's not vanguard it's not fidelity
+ 
+
+ align:start position:0%
+and it's not vanguard it's not fidelity
+they're adopting kind of a rule of thumb
+
+ align:start position:0%
+they're adopting kind of a rule of thumb
+ 
+
+ align:start position:0%
+they're adopting kind of a rule of thumb
+they ask you
+
+ align:start position:0%
+they ask you
+ 
+
+ align:start position:0%
+they ask you
+what's your current expenses
+
+ align:start position:0%
+what's your current expenses
+ 
+
+ align:start position:0%
+what's your current expenses
+then you know say 70 percent of that is
+
+ align:start position:0%
+then you know say 70 percent of that is
+ 
+
+ align:start position:0%
+then you know say 70 percent of that is
+target for retirement
+
+ align:start position:0%
+target for retirement
+ 
+
+ align:start position:0%
+target for retirement
+and then how much do you have to save to
+
+ align:start position:0%
+and then how much do you have to save to
+ 
+
+ align:start position:0%
+and then how much do you have to save to
+make that goal
+
+ align:start position:0%
+make that goal
+ 
+
+ align:start position:0%
+make that goal
+and so consumption could be low because
+
+ align:start position:0%
+and so consumption could be low because
+ 
+
+ align:start position:0%
+and so consumption could be low because
+you're saving a lot
+
+ align:start position:0%
+you're saving a lot
+ 
+
+ align:start position:0%
+you're saving a lot
+and that can end up in a very imbalanced
+
+ align:start position:0%
+and that can end up in a very imbalanced
+ 
+
+ align:start position:0%
+and that can end up in a very imbalanced
+profile in which you're starving today
+
+ align:start position:0%
+profile in which you're starving today
+ 
+
+ align:start position:0%
+profile in which you're starving today
+in order to splurge tomorrow whereas you
+
+ align:start position:0%
+in order to splurge tomorrow whereas you
+ 
+
+ align:start position:0%
+in order to splurge tomorrow whereas you
+know we're using this strictly concave
+
+ align:start position:0%
+know we're using this strictly concave
+ 
+
+ align:start position:0%
+know we're using this strictly concave
+utility
+
+ align:start position:0%
+utility
+ 
+
+ align:start position:0%
+utility
+and so is larry to say you know we want
+
+ align:start position:0%
+and so is larry to say you know we want
+ 
+
+ align:start position:0%
+and so is larry to say you know we want
+to smooth over time just like we want to
+
+ align:start position:0%
+to smooth over time just like we want to
+ 
+
+ align:start position:0%
+to smooth over time just like we want to
+smooth over bad shocks we want to smooth
+
+ align:start position:0%
+smooth over bad shocks we want to smooth
+ 
+
+ align:start position:0%
+smooth over bad shocks we want to smooth
+over time
+
+ align:start position:0%
+over time
+ 
+
+ align:start position:0%
+over time
+as in the medieval village you know seed
+
+ align:start position:0%
+as in the medieval village you know seed
+ 
+
+ align:start position:0%
+as in the medieval village you know seed
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let me make a transition then to uh
+
+ align:start position:0%
+so let me make a transition then to uh
+ 
+
+ align:start position:0%
+so let me make a transition then to uh
+the other account which is cash flow and
+
+ align:start position:0%
+the other account which is cash flow and
+ 
+
+ align:start position:0%
+the other account which is cash flow and
+i'm going to do this by explaining a
+
+ align:start position:0%
+i'm going to do this by explaining a
+ 
+
+ align:start position:0%
+i'm going to do this by explaining a
+little bit about bitcoin and many of you
+
+ align:start position:0%
+little bit about bitcoin and many of you
+ 
+
+ align:start position:0%
+little bit about bitcoin and many of you
+probably know about this already so
+
+ align:start position:0%
+probably know about this already so
+ 
+
+ align:start position:0%
+probably know about this already so
+every transaction in bitcoin is an
+
+ align:start position:0%
+every transaction in bitcoin is an
+ 
+
+ align:start position:0%
+every transaction in bitcoin is an
+encoded message sent out with a
+
+ align:start position:0%
+encoded message sent out with a
+ 
+
+ align:start position:0%
+encoded message sent out with a
+generator with a private public key
+
+ align:start position:0%
+generator with a private public key
+ 
+
+ align:start position:0%
+generator with a private public key
+scheme which has the advantage that
+
+ align:start position:0%
+scheme which has the advantage that
+ 
+
+ align:start position:0%
+scheme which has the advantage that
+it's known which node sent the message
+
+ align:start position:0%
+it's known which node sent the message
+ 
+
+ align:start position:0%
+it's known which node sent the message
+and there's full commitment to the
+
+ align:start position:0%
+and there's full commitment to the
+ 
+
+ align:start position:0%
+and there's full commitment to the
+message you can't go back and deny that
+
+ align:start position:0%
+message you can't go back and deny that
+ 
+
+ align:start position:0%
+message you can't go back and deny that
+you sent it and it prevents fraud nobody
+
+ align:start position:0%
+you sent it and it prevents fraud nobody
+ 
+
+ align:start position:0%
+you sent it and it prevents fraud nobody
+can transact on your id because nobody
+
+ align:start position:0%
+can transact on your id because nobody
+ 
+
+ align:start position:0%
+can transact on your id because nobody
+else has the private key
+
+ align:start position:0%
+else has the private key
+ 
+
+ align:start position:0%
+else has the private key
+unless you get careless
+
+ align:start position:0%
+unless you get careless
+ 
+
+ align:start position:0%
+unless you get careless
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a transaction in bitcoin is the moving
+
+ align:start position:0%
+a transaction in bitcoin is the moving
+ 
+
+ align:start position:0%
+a transaction in bitcoin is the moving
+of the coin from one person to another
+
+ align:start position:0%
+of the coin from one person to another
+ 
+
+ align:start position:0%
+of the coin from one person to another
+the message sent might be i want to
+
+ align:start position:0%
+the message sent might be i want to
+ 
+
+ align:start position:0%
+the message sent might be i want to
+give the coin to person x arguably
+
+ align:start position:0%
+give the coin to person x arguably
+ 
+
+ align:start position:0%
+give the coin to person x arguably
+because person x is a merchant and
+
+ align:start position:0%
+because person x is a merchant and
+ 
+
+ align:start position:0%
+because person x is a merchant and
+you're buying something or whatever the
+
+ align:start position:0%
+you're buying something or whatever the
+ 
+
+ align:start position:0%
+you're buying something or whatever the
+various transactions are accumulated in
+
+ align:start position:0%
+various transactions are accumulated in
+ 
+
+ align:start position:0%
+various transactions are accumulated in
+to a block
+
+ align:start position:0%
+to a block
+ 
+
+ align:start position:0%
+to a block
+and the block is subject to a validation
+
+ align:start position:0%
+and the block is subject to a validation
+ 
+
+ align:start position:0%
+and the block is subject to a validation
+routine which is mining and
+
+ align:start position:0%
+routine which is mining and
+ 
+
+ align:start position:0%
+routine which is mining and
+and is quite costly i'll come back to
+
+ align:start position:0%
+and is quite costly i'll come back to
+ 
+
+ align:start position:0%
+and is quite costly i'll come back to
+that later
+
+ align:start position:0%
+that later
+ 
+
+ align:start position:0%
+that later
+the point here is that bitcoin is
+
+ align:start position:0%
+the point here is that bitcoin is
+ 
+
+ align:start position:0%
+the point here is that bitcoin is
+combining two different things one is
+
+ align:start position:0%
+combining two different things one is
+ 
+
+ align:start position:0%
+combining two different things one is
+the statement of cash flow as the coin
+
+ align:start position:0%
+the statement of cash flow as the coin
+ 
+
+ align:start position:0%
+the statement of cash flow as the coin
+moves from
+
+ align:start position:0%
+moves from
+ 
+
+ align:start position:0%
+moves from
+out or in
+
+ align:start position:0%
+out or in
+ 
+
+ align:start position:0%
+out or in
+to the person in question
+
+ align:start position:0%
+to the person in question
+ 
+
+ align:start position:0%
+to the person in question
+and the other is the balance sheet which
+
+ align:start position:0%
+and the other is the balance sheet which
+ 
+
+ align:start position:0%
+and the other is the balance sheet which
+is at a moment in time how many coins do
+
+ align:start position:0%
+is at a moment in time how many coins do
+ 
+
+ align:start position:0%
+is at a moment in time how many coins do
+you own
+
+ align:start position:0%
+you own
+ 
+
+ align:start position:0%
+you own
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so the accounting of the cash flow works
+
+ align:start position:0%
+so the accounting of the cash flow works
+ 
+
+ align:start position:0%
+so the accounting of the cash flow works
+for bitcoin it also works for paper
+
+ align:start position:0%
+for bitcoin it also works for paper
+ 
+
+ align:start position:0%
+for bitcoin it also works for paper
+currency in thailand so let me show you
+
+ align:start position:0%
+currency in thailand so let me show you
+ 
+
+ align:start position:0%
+currency in thailand so let me show you
+a statement of cash flow as an
+
+ align:start position:0%
+a statement of cash flow as an
+ 
+
+ align:start position:0%
+a statement of cash flow as an
+accounting statement remember before i
+
+ align:start position:0%
+accounting statement remember before i
+ 
+
+ align:start position:0%
+accounting statement remember before i
+show you income and balance sheet i
+
+ align:start position:0%
+show you income and balance sheet i
+ 
+
+ align:start position:0%
+show you income and balance sheet i
+haven't shown you the cash flow
+
+ align:start position:0%
+haven't shown you the cash flow
+ 
+
+ align:start position:0%
+haven't shown you the cash flow
+statement until now
+
+ align:start position:0%
+statement until now
+ 
+
+ align:start position:0%
+statement until now
+it's pretty small print let me just give
+
+ align:start position:0%
+it's pretty small print let me just give
+ 
+
+ align:start position:0%
+it's pretty small print let me just give
+you the big picture here we have cash
+
+ align:start position:0%
+you the big picture here we have cash
+ 
+
+ align:start position:0%
+you the big picture here we have cash
+flow from production which you can
+
+ align:start position:0%
+flow from production which you can
+ 
+
+ align:start position:0%
+flow from production which you can
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+if you sold something and got paper
+
+ align:start position:0%
+if you sold something and got paper
+ 
+
+ align:start position:0%
+if you sold something and got paper
+currency as a consequence you'd have a
+
+ align:start position:0%
+currency as a consequence you'd have a
+ 
+
+ align:start position:0%
+currency as a consequence you'd have a
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+if you're buying fertilizer to grow the
+
+ align:start position:0%
+if you're buying fertilizer to grow the
+ 
+
+ align:start position:0%
+if you're buying fertilizer to grow the
+rice you have a minus sign
+
+ align:start position:0%
+rice you have a minus sign
+ 
+
+ align:start position:0%
+rice you have a minus sign
+so you have inflows and outflows
+
+ align:start position:0%
+so you have inflows and outflows
+ 
+
+ align:start position:0%
+so you have inflows and outflows
+associated with production you can spend
+
+ align:start position:0%
+associated with production you can spend
+ 
+
+ align:start position:0%
+associated with production you can spend
+money on consumption that's typically an
+
+ align:start position:0%
+money on consumption that's typically an
+ 
+
+ align:start position:0%
+money on consumption that's typically an
+outflow you can spend money on
+
+ align:start position:0%
+outflow you can spend money on
+ 
+
+ align:start position:0%
+outflow you can spend money on
+investment also typically an outflow
+
+ align:start position:0%
+investment also typically an outflow
+ 
+
+ align:start position:0%
+investment also typically an outflow
+so we have cash flow from consumption
+
+ align:start position:0%
+so we have cash flow from consumption
+ 
+
+ align:start position:0%
+so we have cash flow from consumption
+and investment and then we have cash
+
+ align:start position:0%
+and investment and then we have cash
+ 
+
+ align:start position:0%
+and investment and then we have cash
+flow from financing which is you can put
+
+ align:start position:0%
+flow from financing which is you can put
+ 
+
+ align:start position:0%
+flow from financing which is you can put
+cash in the bank as a deposit or you
+
+ align:start position:0%
+cash in the bank as a deposit or you
+ 
+
+ align:start position:0%
+cash in the bank as a deposit or you
+could borrow cash hopefully you get it
+
+ align:start position:0%
+could borrow cash hopefully you get it
+ 
+
+ align:start position:0%
+could borrow cash hopefully you get it
+as an inflow they're gifts and so on so
+
+ align:start position:0%
+as an inflow they're gifts and so on so
+ 
+
+ align:start position:0%
+as an inflow they're gifts and so on so
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+cash flow from production consumption
+
+ align:start position:0%
+cash flow from production consumption
+ 
+
+ align:start position:0%
+cash flow from production consumption
+and financing are the three categories
+
+ align:start position:0%
+and financing are the three categories
+ 
+
+ align:start position:0%
+and financing are the three categories
+and this stuff up here is complicated
+
+ align:start position:0%
+and this stuff up here is complicated
+ 
+
+ align:start position:0%
+and this stuff up here is complicated
+when i said i'd shown you the income
+
+ align:start position:0%
+when i said i'd shown you the income
+ 
+
+ align:start position:0%
+when i said i'd shown you the income
+statement but not the cash flow
+
+ align:start position:0%
+statement but not the cash flow
+ 
+
+ align:start position:0%
+statement but not the cash flow
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+you may have been thinking well aren't
+
+ align:start position:0%
+you may have been thinking well aren't
+ 
+
+ align:start position:0%
+you may have been thinking well aren't
+they the same
+
+ align:start position:0%
+they the same
+ 
+
+ align:start position:0%
+they the same
+and the answer is well they could be but
+
+ align:start position:0%
+and the answer is well they could be but
+ 
+
+ align:start position:0%
+and the answer is well they could be but
+not necessarily so if you're a business
+
+ align:start position:0%
+not necessarily so if you're a business
+ 
+
+ align:start position:0%
+not necessarily so if you're a business
+and you sell something and the guy
+
+ align:start position:0%
+and you sell something and the guy
+ 
+
+ align:start position:0%
+and you sell something and the guy
+doesn't pay you
+
+ align:start position:0%
+doesn't pay you
+ 
+
+ align:start position:0%
+doesn't pay you
+then he's going to pay later that's an
+
+ align:start position:0%
+then he's going to pay later that's an
+ 
+
+ align:start position:0%
+then he's going to pay later that's an
+account receivable
+
+ align:start position:0%
+account receivable
+ 
+
+ align:start position:0%
+account receivable
+but there's no cash so the sale would
+
+ align:start position:0%
+but there's no cash so the sale would
+ 
+
+ align:start position:0%
+but there's no cash so the sale would
+count as revenue in the income statement
+
+ align:start position:0%
+count as revenue in the income statement
+ 
+
+ align:start position:0%
+count as revenue in the income statement
+using the accrued notion of accounting
+
+ align:start position:0%
+using the accrued notion of accounting
+ 
+
+ align:start position:0%
+using the accrued notion of accounting
+but it would not count as a cash inflow
+
+ align:start position:0%
+but it would not count as a cash inflow
+ 
+
+ align:start position:0%
+but it would not count as a cash inflow
+so oddly enough this top stuff here is
+
+ align:start position:0%
+so oddly enough this top stuff here is
+ 
+
+ align:start position:0%
+so oddly enough this top stuff here is
+just starting with the income statement
+
+ align:start position:0%
+just starting with the income statement
+ 
+
+ align:start position:0%
+just starting with the income statement
+and making adjustments to it according
+
+ align:start position:0%
+and making adjustments to it according
+ 
+
+ align:start position:0%
+and making adjustments to it according
+to whether the movement of cash you have
+
+ align:start position:0%
+to whether the movement of cash you have
+ 
+
+ align:start position:0%
+to whether the movement of cash you have
+to adjust one way or the other so i mean
+
+ align:start position:0%
+to adjust one way or the other so i mean
+ 
+
+ align:start position:0%
+to adjust one way or the other so i mean
+if you have an account receivable and
+
+ align:start position:0%
+if you have an account receivable and
+ 
+
+ align:start position:0%
+if you have an account receivable and
+you didn't get the cash then you have to
+
+ align:start position:0%
+you didn't get the cash then you have to
+ 
+
+ align:start position:0%
+you didn't get the cash then you have to
+subtract off from recruit income to get
+
+ align:start position:0%
+subtract off from recruit income to get
+ 
+
+ align:start position:0%
+subtract off from recruit income to get
+the cash flow because you're counting
+
+ align:start position:0%
+the cash flow because you're counting
+ 
+
+ align:start position:0%
+the cash flow because you're counting
+something that is not yet associated
+
+ align:start position:0%
+something that is not yet associated
+ 
+
+ align:start position:0%
+something that is not yet associated
+with the cash inflow
+
+ align:start position:0%
+with the cash inflow
+ 
+
+ align:start position:0%
+with the cash inflow
+all right mainly i'm just trying to give
+
+ align:start position:0%
+all right mainly i'm just trying to give
+ 
+
+ align:start position:0%
+all right mainly i'm just trying to give
+you the big picture here this is the
+
+ align:start position:0%
+you the big picture here this is the
+ 
+
+ align:start position:0%
+you the big picture here this is the
+statement of cash flow
+
+ align:start position:0%
+statement of cash flow
+ 
+
+ align:start position:0%
+statement of cash flow
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it is true and this is automatically
+
+ align:start position:0%
+it is true and this is automatically
+ 
+
+ align:start position:0%
+it is true and this is automatically
+true in bitcoin that you can check
+
+ align:start position:0%
+true in bitcoin that you can check
+ 
+
+ align:start position:0%
+true in bitcoin that you can check
+whether the change in cash holdings that
+
+ align:start position:0%
+whether the change in cash holdings that
+ 
+
+ align:start position:0%
+whether the change in cash holdings that
+come at the bottom line of the statement
+
+ align:start position:0%
+come at the bottom line of the statement
+ 
+
+ align:start position:0%
+come at the bottom line of the statement
+of cash flow are exactly equal or not to
+
+ align:start position:0%
+of cash flow are exactly equal or not to
+ 
+
+ align:start position:0%
+of cash flow are exactly equal or not to
+the change in cash that we have on the
+
+ align:start position:0%
+the change in cash that we have on the
+ 
+
+ align:start position:0%
+the change in cash that we have on the
+balance sheet so you have cash in a
+
+ align:start position:0%
+balance sheet so you have cash in a
+ 
+
+ align:start position:0%
+balance sheet so you have cash in a
+moment in time and then you have these
+
+ align:start position:0%
+moment in time and then you have these
+ 
+
+ align:start position:0%
+moment in time and then you have these
+inflows and outflows you have cash in
+
+ align:start position:0%
+inflows and outflows you have cash in
+ 
+
+ align:start position:0%
+inflows and outflows you have cash in
+the future period in each of those
+
+ align:start position:0%
+the future period in each of those
+ 
+
+ align:start position:0%
+the future period in each of those
+periods now and in the future you have
+
+ align:start position:0%
+periods now and in the future you have
+ 
+
+ align:start position:0%
+periods now and in the future you have
+two balance sheets take the difference
+
+ align:start position:0%
+two balance sheets take the difference
+ 
+
+ align:start position:0%
+two balance sheets take the difference
+in the balance sheet that's the change
+
+ align:start position:0%
+in the balance sheet that's the change
+ 
+
+ align:start position:0%
+in the balance sheet that's the change
+in the cash flow on the balance sheet
+
+ align:start position:0%
+in the cash flow on the balance sheet
+ 
+
+ align:start position:0%
+in the cash flow on the balance sheet
+and it should be exactly equal to what's
+
+ align:start position:0%
+and it should be exactly equal to what's
+ 
+
+ align:start position:0%
+and it should be exactly equal to what's
+showing up here in the cash flow from
+
+ align:start position:0%
+showing up here in the cash flow from
+ 
+
+ align:start position:0%
+showing up here in the cash flow from
+the statement of cash flow so we ran a
+
+ align:start position:0%
+the statement of cash flow so we ran a
+ 
+
+ align:start position:0%
+the statement of cash flow so we ran a
+check on the thai data and again if
+
+ align:start position:0%
+check on the thai data and again if
+ 
+
+ align:start position:0%
+check on the thai data and again if
+we're making a mistake these are not
+
+ align:start position:0%
+we're making a mistake these are not
+ 
+
+ align:start position:0%
+we're making a mistake these are not
+equal and that's a big guide to us i
+
+ align:start position:0%
+equal and that's a big guide to us i
+ 
+
+ align:start position:0%
+equal and that's a big guide to us i
+should save this for later but i will
+
+ align:start position:0%
+should save this for later but i will
+ 
+
+ align:start position:0%
+should save this for later but i will
+tell you that no top us survey does this
+
+ align:start position:0%
+tell you that no top us survey does this
+ 
+
+ align:start position:0%
+tell you that no top us survey does this
+not the survey of consumer finances
+
+ align:start position:0%
+not the survey of consumer finances
+ 
+
+ align:start position:0%
+not the survey of consumer finances
+not the psid
+
+ align:start position:0%
+not the psid
+ 
+
+ align:start position:0%
+not the psid
+they did not gather variables and check
+
+ align:start position:0%
+they did not gather variables and check
+ 
+
+ align:start position:0%
+they did not gather variables and check
+what they gathered against these
+
+ align:start position:0%
+what they gathered against these
+ 
+
+ align:start position:0%
+what they gathered against these
+comprehensive statements of integrated
+
+ align:start position:0%
+comprehensive statements of integrated
+ 
+
+ align:start position:0%
+comprehensive statements of integrated
+accounts
+
+ align:start position:0%
+accounts
+ 
+
+ align:start position:0%
+accounts
+and bitcoin is automatic because you
+
+ align:start position:0%
+and bitcoin is automatic because you
+ 
+
+ align:start position:0%
+and bitcoin is automatic because you
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+have it in your account and you spend it
+
+ align:start position:0%
+have it in your account and you spend it
+ 
+
+ align:start position:0%
+have it in your account and you spend it
+or you don't spend it and it's still in
+
+ align:start position:0%
+or you don't spend it and it's still in
+ 
+
+ align:start position:0%
+or you don't spend it and it's still in
+the account
+
+ align:start position:0%
+the account
+ 
+
+ align:start position:0%
+the account
+so that's kind of the
+
+ align:start position:0%
+so that's kind of the
+ 
+
+ align:start position:0%
+so that's kind of the
+unspoken advantage of bitcoin there is
+
+ align:start position:0%
+unspoken advantage of bitcoin there is
+ 
+
+ align:start position:0%
+unspoken advantage of bitcoin there is
+something that people talk about a lot
+
+ align:start position:0%
+something that people talk about a lot
+ 
+
+ align:start position:0%
+something that people talk about a lot
+uh on bitcoin
+
+ align:start position:0%
+uh on bitcoin
+ 
+
+ align:start position:0%
+uh on bitcoin
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+consensus
+
+ align:start position:0%
+consensus
+ 
+
+ align:start position:0%
+consensus
+so i keep giving this example in bitcoin
+
+ align:start position:0%
+so i keep giving this example in bitcoin
+ 
+
+ align:start position:0%
+so i keep giving this example in bitcoin
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+bob wants to transfer a coin to alice we
+
+ align:start position:0%
+bob wants to transfer a coin to alice we
+ 
+
+ align:start position:0%
+bob wants to transfer a coin to alice we
+have both
+
+ align:start position:0%
+have both
+ 
+
+ align:start position:0%
+have both
+alice's accounts and bob's account and
+
+ align:start position:0%
+alice's accounts and bob's account and
+ 
+
+ align:start position:0%
+alice's accounts and bob's account and
+what bob gives up is what alice gets
+
+ align:start position:0%
+what bob gives up is what alice gets
+ 
+
+ align:start position:0%
+what bob gives up is what alice gets
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the accounts have to be consistent with
+
+ align:start position:0%
+the accounts have to be consistent with
+ 
+
+ align:start position:0%
+the accounts have to be consistent with
+each other across the households
+
+ align:start position:0%
+each other across the households
+ 
+
+ align:start position:0%
+each other across the households
+and that is true in bitcoin
+
+ align:start position:0%
+and that is true in bitcoin
+ 
+
+ align:start position:0%
+and that is true in bitcoin
+but it is not well and again this is a
+
+ align:start position:0%
+but it is not well and again this is a
+ 
+
+ align:start position:0%
+but it is not well and again this is a
+bit technical for now but the whole
+
+ align:start position:0%
+bit technical for now but the whole
+ 
+
+ align:start position:0%
+bit technical for now but the whole
+thing about the mining and the
+
+ align:start position:0%
+thing about the mining and the
+ 
+
+ align:start position:0%
+thing about the mining and the
+validation of the transactions in
+
+ align:start position:0%
+validation of the transactions in
+ 
+
+ align:start position:0%
+validation of the transactions in
+bitcoin
+
+ align:start position:0%
+bitcoin
+ 
+
+ align:start position:0%
+bitcoin
+is to precisely be assured
+
+ align:start position:0%
+is to precisely be assured
+ 
+
+ align:start position:0%
+is to precisely be assured
+that bob is not double spending the coin
+
+ align:start position:0%
+that bob is not double spending the coin
+ 
+
+ align:start position:0%
+that bob is not double spending the coin
+can't spend it twice
+
+ align:start position:0%
+can't spend it twice
+ 
+
+ align:start position:0%
+can't spend it twice
+and they kind of figured out a way to do
+
+ align:start position:0%
+and they kind of figured out a way to do
+ 
+
+ align:start position:0%
+and they kind of figured out a way to do
+that very ingenious way to do that but
+
+ align:start position:0%
+that very ingenious way to do that but
+ 
+
+ align:start position:0%
+that very ingenious way to do that but
+anyway the the concept of reconciliation
+
+ align:start position:0%
+anyway the the concept of reconciliation
+ 
+
+ align:start position:0%
+anyway the the concept of reconciliation
+and validation could be taken
+
+ align:start position:0%
+and validation could be taken
+ 
+
+ align:start position:0%
+and validation could be taken
+to accounting in the thai villages in
+
+ align:start position:0%
+to accounting in the thai villages in
+ 
+
+ align:start position:0%
+to accounting in the thai villages in
+the sense that we really did try to
+
+ align:start position:0%
+the sense that we really did try to
+ 
+
+ align:start position:0%
+the sense that we really did try to
+measure all the transactions and when a
+
+ align:start position:0%
+measure all the transactions and when a
+ 
+
+ align:start position:0%
+measure all the transactions and when a
+household says that it boss something
+
+ align:start position:0%
+household says that it boss something
+ 
+
+ align:start position:0%
+household says that it boss something
+with cash if the person they bought it
+
+ align:start position:0%
+with cash if the person they bought it
+ 
+
+ align:start position:0%
+with cash if the person they bought it
+from is in the village then that person
+
+ align:start position:0%
+from is in the village then that person
+ 
+
+ align:start position:0%
+from is in the village then that person
+should get the cash while the person in
+
+ align:start position:0%
+should get the cash while the person in
+ 
+
+ align:start position:0%
+should get the cash while the person in
+question is giving it up so it should
+
+ align:start position:0%
+question is giving it up so it should
+ 
+
+ align:start position:0%
+question is giving it up so it should
+appear twice both in the accounts of the
+
+ align:start position:0%
+appear twice both in the accounts of the
+ 
+
+ align:start position:0%
+appear twice both in the accounts of the
+person buying and the accounts of the
+
+ align:start position:0%
+person buying and the accounts of the
+ 
+
+ align:start position:0%
+person buying and the accounts of the
+person selling so with one of your
+
+ align:start position:0%
+person selling so with one of your
+ 
+
+ align:start position:0%
+person selling so with one of your
+former classmates who was a student in
+
+ align:start position:0%
+former classmates who was a student in
+ 
+
+ align:start position:0%
+former classmates who was a student in
+this class about two years ago chad we
+
+ align:start position:0%
+this class about two years ago chad we
+ 
+
+ align:start position:0%
+this class about two years ago chad we
+set out he was wanted to help on these
+
+ align:start position:0%
+set out he was wanted to help on these
+ 
+
+ align:start position:0%
+set out he was wanted to help on these
+projects he was an r.a
+
+ align:start position:0%
+projects he was an r.a
+ 
+
+ align:start position:0%
+projects he was an r.a
+and yeah i'm not pushing that hard but
+
+ align:start position:0%
+and yeah i'm not pushing that hard but
+ 
+
+ align:start position:0%
+and yeah i'm not pushing that hard but
+if any of you are interested let me know
+
+ align:start position:0%
+if any of you are interested let me know
+ 
+
+ align:start position:0%
+if any of you are interested let me know
+it's a lot of interesting stuff to do so
+
+ align:start position:0%
+it's a lot of interesting stuff to do so
+ 
+
+ align:start position:0%
+it's a lot of interesting stuff to do so
+chad was very interested so here's what
+
+ align:start position:0%
+chad was very interested so here's what
+ 
+
+ align:start position:0%
+chad was very interested so here's what
+he did he looked literally to see
+
+ align:start position:0%
+he did he looked literally to see
+ 
+
+ align:start position:0%
+he did he looked literally to see
+whether what shows up in one person's
+
+ align:start position:0%
+whether what shows up in one person's
+ 
+
+ align:start position:0%
+whether what shows up in one person's
+account is also showing up in the other
+
+ align:start position:0%
+account is also showing up in the other
+ 
+
+ align:start position:0%
+account is also showing up in the other
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+or not and these are some of the details
+
+ align:start position:0%
+or not and these are some of the details
+ 
+
+ align:start position:0%
+or not and these are some of the details
+of going through and doing that as an
+
+ align:start position:0%
+of going through and doing that as an
+ 
+
+ align:start position:0%
+of going through and doing that as an
+algorithm he created these accounts he
+
+ align:start position:0%
+algorithm he created these accounts he
+ 
+
+ align:start position:0%
+algorithm he created these accounts he
+checks see if it's reported if not et
+
+ align:start position:0%
+checks see if it's reported if not et
+ 
+
+ align:start position:0%
+checks see if it's reported if not et
+cetera et cetera now right in the middle
+
+ align:start position:0%
+cetera et cetera now right in the middle
+ 
+
+ align:start position:0%
+cetera et cetera now right in the middle
+of this slide
+
+ align:start position:0%
+of this slide
+ 
+
+ align:start position:0%
+of this slide
+it jumps from thailand and
+
+ align:start position:0%
+it jumps from thailand and
+ 
+
+ align:start position:0%
+it jumps from thailand and
+and the thing that chad was doing
+
+ align:start position:0%
+and the thing that chad was doing
+ 
+
+ align:start position:0%
+and the thing that chad was doing
+to a very different application which is
+
+ align:start position:0%
+to a very different application which is
+ 
+
+ align:start position:0%
+to a very different application which is
+the stock market in australia
+
+ align:start position:0%
+the stock market in australia
+ 
+
+ align:start position:0%
+the stock market in australia
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the stock market in australia is about
+
+ align:start position:0%
+the stock market in australia is about
+ 
+
+ align:start position:0%
+the stock market in australia is about
+to run on distributed ledgers the way
+
+ align:start position:0%
+to run on distributed ledgers the way
+ 
+
+ align:start position:0%
+to run on distributed ledgers the way
+bitcoin does
+
+ align:start position:0%
+bitcoin does
+ 
+
+ align:start position:0%
+bitcoin does
+not using bitcoin but using the ledgers
+
+ align:start position:0%
+not using bitcoin but using the ledgers
+ 
+
+ align:start position:0%
+not using bitcoin but using the ledgers
+and so the idea is when someone owns the
+
+ align:start position:0%
+and so the idea is when someone owns the
+ 
+
+ align:start position:0%
+and so the idea is when someone owns the
+stock and there's a buyer and a seller
+
+ align:start position:0%
+stock and there's a buyer and a seller
+ 
+
+ align:start position:0%
+stock and there's a buyer and a seller
+the traditional legacy system
+
+ align:start position:0%
+the traditional legacy system
+ 
+
+ align:start position:0%
+the traditional legacy system
+is that they enter into a deal and then
+
+ align:start position:0%
+is that they enter into a deal and then
+ 
+
+ align:start position:0%
+is that they enter into a deal and then
+only uh after a day or maybe three the
+
+ align:start position:0%
+only uh after a day or maybe three the
+ 
+
+ align:start position:0%
+only uh after a day or maybe three the
+process of reconciliation kicks in and
+
+ align:start position:0%
+process of reconciliation kicks in and
+ 
+
+ align:start position:0%
+process of reconciliation kicks in and
+then they settle so the trade of the
+
+ align:start position:0%
+then they settle so the trade of the
+ 
+
+ align:start position:0%
+then they settle so the trade of the
+stocks is separate from the settlement
+
+ align:start position:0%
+stocks is separate from the settlement
+ 
+
+ align:start position:0%
+stocks is separate from the settlement
+of the stocks and believe it or not
+
+ align:start position:0%
+of the stocks and believe it or not
+ 
+
+ align:start position:0%
+of the stocks and believe it or not
+there's often huge discrepancies
+
+ align:start position:0%
+there's often huge discrepancies
+ 
+
+ align:start position:0%
+there's often huge discrepancies
+for one thing prices have moved so a
+
+ align:start position:0%
+for one thing prices have moved so a
+ 
+
+ align:start position:0%
+for one thing prices have moved so a
+household could claim i didn't buy it
+
+ align:start position:0%
+household could claim i didn't buy it
+ 
+
+ align:start position:0%
+household could claim i didn't buy it
+and in the new york financial markets
+
+ align:start position:0%
+and in the new york financial markets
+ 
+
+ align:start position:0%
+and in the new york financial markets
+there was an attempt to provide this in
+
+ align:start position:0%
+there was an attempt to provide this in
+ 
+
+ align:start position:0%
+there was an attempt to provide this in
+the repo market because every day in the
+
+ align:start position:0%
+the repo market because every day in the
+ 
+
+ align:start position:0%
+the repo market because every day in the
+u.s repo market with treasuries and so
+
+ align:start position:0%
+u.s repo market with treasuries and so
+ 
+
+ align:start position:0%
+u.s repo market with treasuries and so
+on they spend two hours at the end of
+
+ align:start position:0%
+on they spend two hours at the end of
+ 
+
+ align:start position:0%
+on they spend two hours at the end of
+each day
+
+ align:start position:0%
+each day
+ 
+
+ align:start position:0%
+each day
+after the end of trading trying to
+
+ align:start position:0%
+after the end of trading trying to
+ 
+
+ align:start position:0%
+after the end of trading trying to
+reconcile accounts state street bank
+
+ align:start position:0%
+reconcile accounts state street bank
+ 
+
+ align:start position:0%
+reconcile accounts state street bank
+here in boston is a big you know sort of
+
+ align:start position:0%
+here in boston is a big you know sort of
+ 
+
+ align:start position:0%
+here in boston is a big you know sort of
+third-party broker for people that hold
+
+ align:start position:0%
+third-party broker for people that hold
+ 
+
+ align:start position:0%
+third-party broker for people that hold
+accounts and it does this kind of
+
+ align:start position:0%
+accounts and it does this kind of
+ 
+
+ align:start position:0%
+accounts and it does this kind of
+reconciliation it's quite costly and
+
+ align:start position:0%
+reconciliation it's quite costly and
+ 
+
+ align:start position:0%
+reconciliation it's quite costly and
+tight and quite time consuming but
+
+ align:start position:0%
+tight and quite time consuming but
+ 
+
+ align:start position:0%
+tight and quite time consuming but
+if you're entering these trades on to
+
+ align:start position:0%
+if you're entering these trades on to
+ 
+
+ align:start position:0%
+if you're entering these trades on to
+the ledgers there's instantaneous
+
+ align:start position:0%
+the ledgers there's instantaneous
+ 
+
+ align:start position:0%
+the ledgers there's instantaneous
+reconciliation and so they could settle
+
+ align:start position:0%
+reconciliation and so they could settle
+ 
+
+ align:start position:0%
+reconciliation and so they could settle
+right away if they wanted to the
+
+ align:start position:0%
+right away if they wanted to the
+ 
+
+ align:start position:0%
+right away if they wanted to the
+decision to not pay for it is a credit
+
+ align:start position:0%
+decision to not pay for it is a credit
+ 
+
+ align:start position:0%
+decision to not pay for it is a credit
+decision they're not forced to to settle
+
+ align:start position:0%
+decision they're not forced to to settle
+ 
+
+ align:start position:0%
+decision they're not forced to to settle
+immediately but
+
+ align:start position:0%
+immediately but
+ 
+
+ align:start position:0%
+immediately but
+in principle trade and settlement can
+
+ align:start position:0%
+in principle trade and settlement can
+ 
+
+ align:start position:0%
+in principle trade and settlement can
+happen at exactly the same time all
+
+ align:start position:0%
+happen at exactly the same time all
+ 
+
+ align:start position:0%
+happen at exactly the same time all
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+distributed ledgers and the one in
+
+ align:start position:0%
+distributed ledgers and the one in
+ 
+
+ align:start position:0%
+distributed ledgers and the one in
+australia is able to process 115 million
+
+ align:start position:0%
+australia is able to process 115 million
+ 
+
+ align:start position:0%
+australia is able to process 115 million
+their daily trades at 6 300 trades per
+
+ align:start position:0%
+their daily trades at 6 300 trades per
+ 
+
+ align:start position:0%
+their daily trades at 6 300 trades per
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+continuously over five hours that well
+
+ align:start position:0%
+continuously over five hours that well
+ 
+
+ align:start position:0%
+continuously over five hours that well
+exceeds the volume in bitcoin bitcoin is
+
+ align:start position:0%
+exceeds the volume in bitcoin bitcoin is
+ 
+
+ align:start position:0%
+exceeds the volume in bitcoin bitcoin is
+not capable of doing this because of the
+
+ align:start position:0%
+not capable of doing this because of the
+ 
+
+ align:start position:0%
+not capable of doing this because of the
+mining but these other ledger
+
+ align:start position:0%
+mining but these other ledger
+ 
+
+ align:start position:0%
+mining but these other ledger
+technologies are a lot faster and a lot
+
+ align:start position:0%
+technologies are a lot faster and a lot
+ 
+
+ align:start position:0%
+technologies are a lot faster and a lot
+cheaper
+
+ align:start position:0%
+cheaper
+ 
+
+ align:start position:0%
+cheaper
+so let's come back to the village
+
+ align:start position:0%
+so let's come back to the village
+ 
+
+ align:start position:0%
+so let's come back to the village
+and think about how an individual
+
+ align:start position:0%
+and think about how an individual
+ 
+
+ align:start position:0%
+and think about how an individual
+household is managing its currency
+
+ align:start position:0%
+household is managing its currency
+ 
+
+ align:start position:0%
+household is managing its currency
+let me back up for a second
+
+ align:start position:0%
+let me back up for a second
+ 
+
+ align:start position:0%
+let me back up for a second
+that seemed like an abrupt transition
+
+ align:start position:0%
+that seemed like an abrupt transition
+ 
+
+ align:start position:0%
+that seemed like an abrupt transition
+you know i featured in lecture one that
+
+ align:start position:0%
+you know i featured in lecture one that
+ 
+
+ align:start position:0%
+you know i featured in lecture one that
+we will say a lot about bitcoin
+
+ align:start position:0%
+we will say a lot about bitcoin
+ 
+
+ align:start position:0%
+we will say a lot about bitcoin
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+currencies and it spread out you know
+
+ align:start position:0%
+currencies and it spread out you know
+ 
+
+ align:start position:0%
+currencies and it spread out you know
+throughout the lectures so bitcoin
+
+ align:start position:0%
+throughout the lectures so bitcoin
+ 
+
+ align:start position:0%
+throughout the lectures so bitcoin
+blockchain and distributed ledgers is
+
+ align:start position:0%
+blockchain and distributed ledgers is
+ 
+
+ align:start position:0%
+blockchain and distributed ledgers is
+the first time it really came up and i
+
+ align:start position:0%
+the first time it really came up and i
+ 
+
+ align:start position:0%
+the first time it really came up and i
+started with the ledger so when we're
+
+ align:start position:0%
+started with the ledger so when we're
+ 
+
+ align:start position:0%
+started with the ledger so when we're
+talking about financial accounts that's
+
+ align:start position:0%
+talking about financial accounts that's
+ 
+
+ align:start position:0%
+talking about financial accounts that's
+why i started to bring in bitcoin and we
+
+ align:start position:0%
+why i started to bring in bitcoin and we
+ 
+
+ align:start position:0%
+why i started to bring in bitcoin and we
+we will revisit bitcoin in other
+
+ align:start position:0%
+we will revisit bitcoin in other
+ 
+
+ align:start position:0%
+we will revisit bitcoin in other
+lectures when we talk about monetary
+
+ align:start position:0%
+lectures when we talk about monetary
+ 
+
+ align:start position:0%
+lectures when we talk about monetary
+economics and so on
+
+ align:start position:0%
+economics and so on
+ 
+
+ align:start position:0%
+economics and so on
+okay so now
+
+ align:start position:0%
+okay so now
+ 
+
+ align:start position:0%
+okay so now
+back to paper currency management you
+
+ align:start position:0%
+back to paper currency management you
+ 
+
+ align:start position:0%
+back to paper currency management you
+know i say paper currency just to
+
+ align:start position:0%
+know i say paper currency just to
+ 
+
+ align:start position:0%
+know i say paper currency just to
+constantly remind myself that cash is
+
+ align:start position:0%
+constantly remind myself that cash is
+ 
+
+ align:start position:0%
+constantly remind myself that cash is
+kind of ambiguous when you talk about
+
+ align:start position:0%
+kind of ambiguous when you talk about
+ 
+
+ align:start position:0%
+kind of ambiguous when you talk about
+cash in the us you mean currency yeah
+
+ align:start position:0%
+cash in the us you mean currency yeah
+ 
+
+ align:start position:0%
+cash in the us you mean currency yeah
+but also demand deposits and other very
+
+ align:start position:0%
+but also demand deposits and other very
+ 
+
+ align:start position:0%
+but also demand deposits and other very
+like maybe even debit cards but in
+
+ align:start position:0%
+like maybe even debit cards but in
+ 
+
+ align:start position:0%
+like maybe even debit cards but in
+thailand it's paper currency they love
+
+ align:start position:0%
+thailand it's paper currency they love
+ 
+
+ align:start position:0%
+thailand it's paper currency they love
+it that's what they use
+
+ align:start position:0%
+it that's what they use
+ 
+
+ align:start position:0%
+it that's what they use
+more on that momentarily so i'm gonna in
+
+ align:start position:0%
+more on that momentarily so i'm gonna in
+ 
+
+ align:start position:0%
+more on that momentarily so i'm gonna in
+notation describe a miller or model the
+
+ align:start position:0%
+notation describe a miller or model the
+ 
+
+ align:start position:0%
+notation describe a miller or model the
+management of cash for firms for
+
+ align:start position:0%
+management of cash for firms for
+ 
+
+ align:start position:0%
+management of cash for firms for
+business firms which do not have regular
+
+ align:start position:0%
+business firms which do not have regular
+ 
+
+ align:start position:0%
+business firms which do not have regular
+nor predictable flows and the result
+
+ align:start position:0%
+nor predictable flows and the result
+ 
+
+ align:start position:0%
+nor predictable flows and the result
+solving the model is rather intuitive
+
+ align:start position:0%
+solving the model is rather intuitive
+ 
+
+ align:start position:0%
+solving the model is rather intuitive
+there's going to be bounds so cash
+
+ align:start position:0%
+there's going to be bounds so cash
+ 
+
+ align:start position:0%
+there's going to be bounds so cash
+holdings can drift around but when they
+
+ align:start position:0%
+holdings can drift around but when they
+ 
+
+ align:start position:0%
+holdings can drift around but when they
+go above and upper bound it's time to
+
+ align:start position:0%
+go above and upper bound it's time to
+ 
+
+ align:start position:0%
+go above and upper bound it's time to
+make an adjustment and deposit the paper
+
+ align:start position:0%
+make an adjustment and deposit the paper
+ 
+
+ align:start position:0%
+make an adjustment and deposit the paper
+in the bank or lend it out and likewise
+
+ align:start position:0%
+in the bank or lend it out and likewise
+ 
+
+ align:start position:0%
+in the bank or lend it out and likewise
+when it goes below a lower bound they're
+
+ align:start position:0%
+when it goes below a lower bound they're
+ 
+
+ align:start position:0%
+when it goes below a lower bound they're
+going to have to withdraw money or call
+
+ align:start position:0%
+going to have to withdraw money or call
+ 
+
+ align:start position:0%
+going to have to withdraw money or call
+in a loan so sometimes that lower bound
+
+ align:start position:0%
+in a loan so sometimes that lower bound
+ 
+
+ align:start position:0%
+in a loan so sometimes that lower bound
+is zero obviously you can't run out of
+
+ align:start position:0%
+is zero obviously you can't run out of
+ 
+
+ align:start position:0%
+is zero obviously you can't run out of
+stock of something it can't go negative
+
+ align:start position:0%
+stock of something it can't go negative
+ 
+
+ align:start position:0%
+stock of something it can't go negative
+so that's going to be what the solution
+
+ align:start position:0%
+so that's going to be what the solution
+ 
+
+ align:start position:0%
+so that's going to be what the solution
+looks like so let me introduce a little
+
+ align:start position:0%
+looks like so let me introduce a little
+ 
+
+ align:start position:0%
+looks like so let me introduce a little
+bit of notation
+
+ align:start position:0%
+bit of notation
+ 
+
+ align:start position:0%
+bit of notation
+e being expenditure outflows of paper
+
+ align:start position:0%
+e being expenditure outflows of paper
+ 
+
+ align:start position:0%
+e being expenditure outflows of paper
+currency which looks like c but it's
+
+ align:start position:0%
+currency which looks like c but it's
+ 
+
+ align:start position:0%
+currency which looks like c but it's
+basically more than consumption it's all
+
+ align:start position:0%
+basically more than consumption it's all
+ 
+
+ align:start position:0%
+basically more than consumption it's all
+expenses out and then y being stuff
+
+ align:start position:0%
+expenses out and then y being stuff
+ 
+
+ align:start position:0%
+expenses out and then y being stuff
+coming in
+
+ align:start position:0%
+coming in
+ 
+
+ align:start position:0%
+coming in
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so expenditures outflows minus inflows
+
+ align:start position:0%
+so expenditures outflows minus inflows
+ 
+
+ align:start position:0%
+so expenditures outflows minus inflows
+which could be positive or negative so
+
+ align:start position:0%
+which could be positive or negative so
+ 
+
+ align:start position:0%
+which could be positive or negative so
+we postulate a stochastic process for
+
+ align:start position:0%
+we postulate a stochastic process for
+ 
+
+ align:start position:0%
+we postulate a stochastic process for
+the cash flows expenditure flows and
+
+ align:start position:0%
+the cash flows expenditure flows and
+ 
+
+ align:start position:0%
+the cash flows expenditure flows and
+estimate in the thai data
+
+ align:start position:0%
+estimate in the thai data
+ 
+
+ align:start position:0%
+estimate in the thai data
+we postulate that mostly things are
+
+ align:start position:0%
+we postulate that mostly things are
+ 
+
+ align:start position:0%
+we postulate that mostly things are
+pretty smooth and predictable delta
+
+ align:start position:0%
+pretty smooth and predictable delta
+ 
+
+ align:start position:0%
+pretty smooth and predictable delta
+refers to the length of the time
+
+ align:start position:0%
+refers to the length of the time
+ 
+
+ align:start position:0%
+refers to the length of the time
+interval and it's easier conceptually to
+
+ align:start position:0%
+interval and it's easier conceptually to
+ 
+
+ align:start position:0%
+interval and it's easier conceptually to
+think of delta as equal to one
+
+ align:start position:0%
+think of delta as equal to one
+ 
+
+ align:start position:0%
+think of delta as equal to one
+so with roughly probability one-half
+
+ align:start position:0%
+so with roughly probability one-half
+ 
+
+ align:start position:0%
+so with roughly probability one-half
+they're going to have an expenditure of
+
+ align:start position:0%
+they're going to have an expenditure of
+ 
+
+ align:start position:0%
+they're going to have an expenditure of
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+but it could be higher of order of
+
+ align:start position:0%
+but it could be higher of order of
+ 
+
+ align:start position:0%
+but it could be higher of order of
+magnitude sigma
+
+ align:start position:0%
+magnitude sigma
+ 
+
+ align:start position:0%
+magnitude sigma
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+with the residual probability roughly
+
+ align:start position:0%
+with the residual probability roughly
+ 
+
+ align:start position:0%
+with the residual probability roughly
+one-half
+
+ align:start position:0%
+one-half
+ 
+
+ align:start position:0%
+one-half
+it's c minus sigma so these are the ups
+
+ align:start position:0%
+it's c minus sigma so these are the ups
+ 
+
+ align:start position:0%
+it's c minus sigma so these are the ups
+and downs of expenditures you know
+
+ align:start position:0%
+and downs of expenditures you know
+ 
+
+ align:start position:0%
+and downs of expenditures you know
+probabilistic basis how big or small
+
+ align:start position:0%
+probabilistic basis how big or small
+ 
+
+ align:start position:0%
+probabilistic basis how big or small
+depends on how big sigma is
+
+ align:start position:0%
+depends on how big sigma is
+ 
+
+ align:start position:0%
+depends on how big sigma is
+i keep saying roughly probability one
+
+ align:start position:0%
+i keep saying roughly probability one
+ 
+
+ align:start position:0%
+i keep saying roughly probability one
+half because there are these zapper
+
+ align:start position:0%
+half because there are these zapper
+ 
+
+ align:start position:0%
+half because there are these zapper
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+that are very large inflows and outflows
+
+ align:start position:0%
+that are very large inflows and outflows
+ 
+
+ align:start position:0%
+that are very large inflows and outflows
+so expenditure is an outflow so positive
+
+ align:start position:0%
+so expenditure is an outflow so positive
+ 
+
+ align:start position:0%
+so expenditure is an outflow so positive
+zapper zp
+
+ align:start position:0%
+zapper zp
+ 
+
+ align:start position:0%
+zapper zp
+is a very large expenditure
+
+ align:start position:0%
+is a very large expenditure
+ 
+
+ align:start position:0%
+is a very large expenditure
+that happens with probability kappa
+
+ align:start position:0%
+that happens with probability kappa
+ 
+
+ align:start position:0%
+that happens with probability kappa
+again say delta equal one so this could
+
+ align:start position:0%
+again say delta equal one so this could
+ 
+
+ align:start position:0%
+again say delta equal one so this could
+be like two or three percent of the time
+
+ align:start position:0%
+be like two or three percent of the time
+ 
+
+ align:start position:0%
+be like two or three percent of the time
+there's an outflow which is more than
+
+ align:start position:0%
+there's an outflow which is more than
+ 
+
+ align:start position:0%
+there's an outflow which is more than
+two standard deviations away from the
+
+ align:start position:0%
+two standard deviations away from the
+ 
+
+ align:start position:0%
+two standard deviations away from the
+mean positive how flow
+
+ align:start position:0%
+mean positive how flow
+ 
+
+ align:start position:0%
+mean positive how flow
+it could be an inflow so these are rare
+
+ align:start position:0%
+it could be an inflow so these are rare
+ 
+
+ align:start position:0%
+it could be an inflow so these are rare
+revenues coming in
+
+ align:start position:0%
+revenues coming in
+ 
+
+ align:start position:0%
+revenues coming in
+with different kappas and different z's
+
+ align:start position:0%
+with different kappas and different z's
+ 
+
+ align:start position:0%
+with different kappas and different z's
+which will be estimated in the data and
+
+ align:start position:0%
+which will be estimated in the data and
+ 
+
+ align:start position:0%
+which will be estimated in the data and
+these shocks
+
+ align:start position:0%
+these shocks
+ 
+
+ align:start position:0%
+these shocks
+you take the probability of the positive
+
+ align:start position:0%
+you take the probability of the positive
+ 
+
+ align:start position:0%
+you take the probability of the positive
+outflow the probability of the negative
+
+ align:start position:0%
+outflow the probability of the negative
+ 
+
+ align:start position:0%
+outflow the probability of the negative
+outflow add them together delta say
+
+ align:start position:0%
+outflow add them together delta say
+ 
+
+ align:start position:0%
+outflow add them together delta say
+still equal to one so with probability
+
+ align:start position:0%
+still equal to one so with probability
+ 
+
+ align:start position:0%
+still equal to one so with probability
+one something happens
+
+ align:start position:0%
+one something happens
+ 
+
+ align:start position:0%
+one something happens
+with probability one minus the sum of
+
+ align:start position:0%
+with probability one minus the sum of
+ 
+
+ align:start position:0%
+with probability one minus the sum of
+those kappas you're in this middle
+
+ align:start position:0%
+those kappas you're in this middle
+ 
+
+ align:start position:0%
+those kappas you're in this middle
+branch and that's the one half adjusted
+
+ align:start position:0%
+branch and that's the one half adjusted
+ 
+
+ align:start position:0%
+branch and that's the one half adjusted
+up or down
+
+ align:start position:0%
+up or down
+ 
+
+ align:start position:0%
+up or down
+as always i'm assuming you will
+
+ align:start position:0%
+as always i'm assuming you will
+ 
+
+ align:start position:0%
+as always i'm assuming you will
+interrupt me things are not clear okay
+
+ align:start position:0%
+interrupt me things are not clear okay
+ 
+
+ align:start position:0%
+interrupt me things are not clear okay
+so let's think about how much cash they
+
+ align:start position:0%
+so let's think about how much cash they
+ 
+
+ align:start position:0%
+so let's think about how much cash they
+have in the house
+
+ align:start position:0%
+have in the house
+ 
+
+ align:start position:0%
+have in the house
+it's paper
+
+ align:start position:0%
+it's paper
+ 
+
+ align:start position:0%
+it's paper
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so they have a certain amount of cash in
+
+ align:start position:0%
+so they have a certain amount of cash in
+ 
+
+ align:start position:0%
+so they have a certain amount of cash in
+a moment in time
+
+ align:start position:0%
+a moment in time
+ 
+
+ align:start position:0%
+a moment in time
+they have an expenditure outflow which
+
+ align:start position:0%
+they have an expenditure outflow which
+ 
+
+ align:start position:0%
+they have an expenditure outflow which
+could be positive or negative
+
+ align:start position:0%
+could be positive or negative
+ 
+
+ align:start position:0%
+could be positive or negative
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+they're at t
+
+ align:start position:0%
+they're at t
+ 
+
+ align:start position:0%
+they're at t
+and we're gonna
+
+ align:start position:0%
+and we're gonna
+ 
+
+ align:start position:0%
+and we're gonna
+try to do the accounting for what how
+
+ align:start position:0%
+try to do the accounting for what how
+ 
+
+ align:start position:0%
+try to do the accounting for what how
+much money they would have at t plus
+
+ align:start position:0%
+much money they would have at t plus
+ 
+
+ align:start position:0%
+much money they would have at t plus
+delta where again delta could be equal
+
+ align:start position:0%
+delta where again delta could be equal
+ 
+
+ align:start position:0%
+delta where again delta could be equal
+to one okay
+
+ align:start position:0%
+to one okay
+ 
+
+ align:start position:0%
+to one okay
+money at t less outflows and then they
+
+ align:start position:0%
+money at t less outflows and then they
+ 
+
+ align:start position:0%
+money at t less outflows and then they
+could adjust
+
+ align:start position:0%
+could adjust
+ 
+
+ align:start position:0%
+could adjust
+they could either withdraw money or
+
+ align:start position:0%
+they could either withdraw money or
+ 
+
+ align:start position:0%
+they could either withdraw money or
+deposit it
+
+ align:start position:0%
+deposit it
+ 
+
+ align:start position:0%
+deposit it
+so these two things the w and d is
+
+ align:start position:0%
+so these two things the w and d is
+ 
+
+ align:start position:0%
+so these two things the w and d is
+endogenous
+
+ align:start position:0%
+endogenous
+ 
+
+ align:start position:0%
+endogenous
+and the model is going to have to solve
+
+ align:start position:0%
+and the model is going to have to solve
+ 
+
+ align:start position:0%
+and the model is going to have to solve
+for w and d when to do it as i was
+
+ align:start position:0%
+for w and d when to do it as i was
+ 
+
+ align:start position:0%
+for w and d when to do it as i was
+saying and how much to do and that will
+
+ align:start position:0%
+saying and how much to do and that will
+ 
+
+ align:start position:0%
+saying and how much to do and that will
+result in this
+
+ align:start position:0%
+result in this
+ 
+
+ align:start position:0%
+result in this
+endogenously determined statement of
+
+ align:start position:0%
+endogenously determined statement of
+ 
+
+ align:start position:0%
+endogenously determined statement of
+cash flow
+
+ align:start position:0%
+cash flow
+ 
+
+ align:start position:0%
+cash flow
+you can think about this like life cycle
+
+ align:start position:0%
+you can think about this like life cycle
+ 
+
+ align:start position:0%
+you can think about this like life cycle
+planning except now it's not you know
+
+ align:start position:0%
+planning except now it's not you know
+ 
+
+ align:start position:0%
+planning except now it's not you know
+over 50 years
+
+ align:start position:0%
+over 50 years
+ 
+
+ align:start position:0%
+over 50 years
+it may be a matter of a couple of weeks
+
+ align:start position:0%
+it may be a matter of a couple of weeks
+ 
+
+ align:start position:0%
+it may be a matter of a couple of weeks
+or 30 days and the data is 30 days
+
+ align:start position:0%
+or 30 days and the data is 30 days
+ 
+
+ align:start position:0%
+or 30 days and the data is 30 days
+because that's when we get the data
+
+ align:start position:0%
+because that's when we get the data
+ 
+
+ align:start position:0%
+because that's when we get the data
+they're trying to minimize costs now
+
+ align:start position:0%
+they're trying to minimize costs now
+ 
+
+ align:start position:0%
+they're trying to minimize costs now
+there's two costs
+
+ align:start position:0%
+there's two costs
+ 
+
+ align:start position:0%
+there's two costs
+one is kind of obvious really for
+
+ align:start position:0%
+one is kind of obvious really for
+ 
+
+ align:start position:0%
+one is kind of obvious really for
+economists which is
+
+ align:start position:0%
+economists which is
+ 
+
+ align:start position:0%
+economists which is
+if you're holding cash and it doesn't
+
+ align:start position:0%
+if you're holding cash and it doesn't
+ 
+
+ align:start position:0%
+if you're holding cash and it doesn't
+earn interest you've lost the interest
+
+ align:start position:0%
+earn interest you've lost the interest
+ 
+
+ align:start position:0%
+earn interest you've lost the interest
+you could have earned if you had
+
+ align:start position:0%
+you could have earned if you had
+ 
+
+ align:start position:0%
+you could have earned if you had
+deposited it in the bank so that's a
+
+ align:start position:0%
+deposited it in the bank so that's a
+ 
+
+ align:start position:0%
+deposited it in the bank so that's a
+real cost to the household that's the
+
+ align:start position:0%
+real cost to the household that's the
+ 
+
+ align:start position:0%
+real cost to the household that's the
+opportunity cost to the household
+
+ align:start position:0%
+opportunity cost to the household
+ 
+
+ align:start position:0%
+opportunity cost to the household
+we're going to let the interest rate in
+
+ align:start position:0%
+we're going to let the interest rate in
+ 
+
+ align:start position:0%
+we're going to let the interest rate in
+the bank be capital r
+
+ align:start position:0%
+the bank be capital r
+ 
+
+ align:start position:0%
+the bank be capital r
+show too much cash you're giving up a
+
+ align:start position:0%
+show too much cash you're giving up a
+ 
+
+ align:start position:0%
+show too much cash you're giving up a
+lot of foregone interest
+
+ align:start position:0%
+lot of foregone interest
+ 
+
+ align:start position:0%
+lot of foregone interest
+that's a cost
+
+ align:start position:0%
+that's a cost
+ 
+
+ align:start position:0%
+that's a cost
+there's also a physical adjustment cost
+
+ align:start position:0%
+there's also a physical adjustment cost
+ 
+
+ align:start position:0%
+there's also a physical adjustment cost
+to get to the bank which you can think
+
+ align:start position:0%
+to get to the bank which you can think
+ 
+
+ align:start position:0%
+to get to the bank which you can think
+of as the hassle or in these villages
+
+ align:start position:0%
+of as the hassle or in these villages
+ 
+
+ align:start position:0%
+of as the hassle or in these villages
+you got to get in your truck and drive
+
+ align:start position:0%
+you got to get in your truck and drive
+ 
+
+ align:start position:0%
+you got to get in your truck and drive
+to the village to the town et cetera so
+
+ align:start position:0%
+to the village to the town et cetera so
+ 
+
+ align:start position:0%
+to the village to the town et cetera so
+that should have had the notation here
+
+ align:start position:0%
+that should have had the notation here
+ 
+
+ align:start position:0%
+that should have had the notation here
+but it's little b you'll see little b
+
+ align:start position:0%
+but it's little b you'll see little b
+ 
+
+ align:start position:0%
+but it's little b you'll see little b
+momentarily
+
+ align:start position:0%
+momentarily
+ 
+
+ align:start position:0%
+momentarily
+so the next slide don't panic i'm going
+
+ align:start position:0%
+so the next slide don't panic i'm going
+ 
+
+ align:start position:0%
+so the next slide don't panic i'm going
+to walk you through the the value
+
+ align:start position:0%
+to walk you through the the value
+ 
+
+ align:start position:0%
+to walk you through the the value
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+it looks pretty intense at first they're
+
+ align:start position:0%
+it looks pretty intense at first they're
+ 
+
+ align:start position:0%
+it looks pretty intense at first they're
+sitting here
+
+ align:start position:0%
+sitting here
+ 
+
+ align:start position:0%
+sitting here
+with a certain amount of money m
+
+ align:start position:0%
+with a certain amount of money m
+ 
+
+ align:start position:0%
+with a certain amount of money m
+and then deciding whether they want to
+
+ align:start position:0%
+and then deciding whether they want to
+ 
+
+ align:start position:0%
+and then deciding whether they want to
+stay put
+
+ align:start position:0%
+stay put
+ 
+
+ align:start position:0%
+stay put
+and carry
+
+ align:start position:0%
+and carry
+ 
+
+ align:start position:0%
+and carry
+m into the second period or adjust
+
+ align:start position:0%
+m into the second period or adjust
+ 
+
+ align:start position:0%
+m into the second period or adjust
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if m is already negative they're in
+
+ align:start position:0%
+if m is already negative they're in
+ 
+
+ align:start position:0%
+if m is already negative they're in
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+can't go negative so they have to adjust
+
+ align:start position:0%
+can't go negative so they have to adjust
+ 
+
+ align:start position:0%
+can't go negative so they have to adjust
+and you get this cost b which is gone
+
+ align:start position:0%
+and you get this cost b which is gone
+ 
+
+ align:start position:0%
+and you get this cost b which is gone
+this cost function is not utility it's
+
+ align:start position:0%
+this cost function is not utility it's
+ 
+
+ align:start position:0%
+this cost function is not utility it's
+not net profits it's a cost and they're
+
+ align:start position:0%
+not net profits it's a cost and they're
+ 
+
+ align:start position:0%
+not net profits it's a cost and they're
+trying to minimize the cost
+
+ align:start position:0%
+trying to minimize the cost
+ 
+
+ align:start position:0%
+trying to minimize the cost
+so this is the enters positively because
+
+ align:start position:0%
+so this is the enters positively because
+ 
+
+ align:start position:0%
+so this is the enters positively because
+it's a cost
+
+ align:start position:0%
+it's a cost
+ 
+
+ align:start position:0%
+it's a cost
+they've gone to all the costs to getting
+
+ align:start position:0%
+they've gone to all the costs to getting
+ 
+
+ align:start position:0%
+they've gone to all the costs to getting
+to the bank they get to make an
+
+ align:start position:0%
+to the bank they get to make an
+ 
+
+ align:start position:0%
+to the bank they get to make an
+adjustment which means they can choose a
+
+ align:start position:0%
+adjustment which means they can choose a
+ 
+
+ align:start position:0%
+adjustment which means they can choose a
+new m prime going out and so they'll try
+
+ align:start position:0%
+new m prime going out and so they'll try
+ 
+
+ align:start position:0%
+new m prime going out and so they'll try
+to minimize
+
+ align:start position:0%
+to minimize
+ 
+
+ align:start position:0%
+to minimize
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+from that point on
+
+ align:start position:0%
+from that point on
+ 
+
+ align:start position:0%
+from that point on
+by that choice of m prime
+
+ align:start position:0%
+by that choice of m prime
+ 
+
+ align:start position:0%
+by that choice of m prime
+minimize the cost from that point on
+
+ align:start position:0%
+minimize the cost from that point on
+ 
+
+ align:start position:0%
+minimize the cost from that point on
+here m is positive but they still get to
+
+ align:start position:0%
+here m is positive but they still get to
+ 
+
+ align:start position:0%
+here m is positive but they still get to
+choose whether to adjust or not and if
+
+ align:start position:0%
+choose whether to adjust or not and if
+ 
+
+ align:start position:0%
+choose whether to adjust or not and if
+they don't adjust
+
+ align:start position:0%
+they don't adjust
+ 
+
+ align:start position:0%
+they don't adjust
+they keep it
+
+ align:start position:0%
+they keep it
+ 
+
+ align:start position:0%
+they keep it
+they suffer the opportunity cost the
+
+ align:start position:0%
+they suffer the opportunity cost the
+ 
+
+ align:start position:0%
+they suffer the opportunity cost the
+lost interest in the bank and then
+
+ align:start position:0%
+lost interest in the bank and then
+ 
+
+ align:start position:0%
+lost interest in the bank and then
+they'll have their value function
+
+ align:start position:0%
+they'll have their value function
+ 
+
+ align:start position:0%
+they'll have their value function
+tomorrow which is discounted by little r
+
+ align:start position:0%
+tomorrow which is discounted by little r
+ 
+
+ align:start position:0%
+tomorrow which is discounted by little r
+that's like a discount rate
+
+ align:start position:0%
+that's like a discount rate
+ 
+
+ align:start position:0%
+that's like a discount rate
+and things next period are stochastic so
+
+ align:start position:0%
+and things next period are stochastic so
+ 
+
+ align:start position:0%
+and things next period are stochastic so
+you take expectations over the future e
+
+ align:start position:0%
+you take expectations over the future e
+ 
+
+ align:start position:0%
+you take expectations over the future e
+values following that stochastic process
+
+ align:start position:0%
+values following that stochastic process
+ 
+
+ align:start position:0%
+values following that stochastic process
+so this is v of m minus e is all
+
+ align:start position:0%
+so this is v of m minus e is all
+ 
+
+ align:start position:0%
+so this is v of m minus e is all
+expectation is all written down here in
+
+ align:start position:0%
+expectation is all written down here in
+ 
+
+ align:start position:0%
+expectation is all written down here in
+terms of these branches which is you
+
+ align:start position:0%
+terms of these branches which is you
+ 
+
+ align:start position:0%
+terms of these branches which is you
+know positive zappers negative zappers
+
+ align:start position:0%
+know positive zappers negative zappers
+ 
+
+ align:start position:0%
+know positive zappers negative zappers
+you know ups and downs
+
+ align:start position:0%
+you know ups and downs
+ 
+
+ align:start position:0%
+you know ups and downs
+roughly probability one half etc so this
+
+ align:start position:0%
+roughly probability one half etc so this
+ 
+
+ align:start position:0%
+roughly probability one half etc so this
+is the expected cost in the future if
+
+ align:start position:0%
+is the expected cost in the future if
+ 
+
+ align:start position:0%
+is the expected cost in the future if
+you don't make a monetary adjustment
+
+ align:start position:0%
+you don't make a monetary adjustment
+ 
+
+ align:start position:0%
+you don't make a monetary adjustment
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+so this is the second or third time
+
+ align:start position:0%
+so this is the second or third time
+ 
+
+ align:start position:0%
+so this is the second or third time
+you've seen these value functions i
+
+ align:start position:0%
+you've seen these value functions i
+ 
+
+ align:start position:0%
+you've seen these value functions i
+introduced them at the end of the
+
+ align:start position:0%
+introduced them at the end of the
+ 
+
+ align:start position:0%
+introduced them at the end of the
+medieval village dynamic programming
+
+ align:start position:0%
+medieval village dynamic programming
+ 
+
+ align:start position:0%
+medieval village dynamic programming
+problem we then used that last class to
+
+ align:start position:0%
+problem we then used that last class to
+ 
+
+ align:start position:0%
+problem we then used that last class to
+talk about implications of risk sharing
+
+ align:start position:0%
+talk about implications of risk sharing
+ 
+
+ align:start position:0%
+talk about implications of risk sharing
+for production with the planner's value
+
+ align:start position:0%
+for production with the planner's value
+ 
+
+ align:start position:0%
+for production with the planner's value
+function this is the third time this is
+
+ align:start position:0%
+function this is the third time this is
+ 
+
+ align:start position:0%
+function this is the third time this is
+the value function for a household
+
+ align:start position:0%
+the value function for a household
+ 
+
+ align:start position:0%
+the value function for a household
+minimizing its costs
+
+ align:start position:0%
+minimizing its costs
+ 
+
+ align:start position:0%
+minimizing its costs
+more fun let me show you some pictures
+
+ align:start position:0%
+more fun let me show you some pictures
+ 
+
+ align:start position:0%
+more fun let me show you some pictures
+so these are real live people
+
+ align:start position:0%
+so these are real live people
+ 
+
+ align:start position:0%
+so these are real live people
+this is the cash flow this house the
+
+ align:start position:0%
+this is the cash flow this house the
+ 
+
+ align:start position:0%
+this is the cash flow this house the
+cash holdings of this household
+
+ align:start position:0%
+cash holdings of this household
+ 
+
+ align:start position:0%
+cash holdings of this household
+up and up and up and up she goes
+
+ align:start position:0%
+up and up and up and up she goes
+ 
+
+ align:start position:0%
+up and up and up and up she goes
+this one also had a trend and then boom
+
+ align:start position:0%
+this one also had a trend and then boom
+ 
+
+ align:start position:0%
+this one also had a trend and then boom
+down and then to zero
+
+ align:start position:0%
+down and then to zero
+ 
+
+ align:start position:0%
+down and then to zero
+and then back up again you can't see it
+
+ align:start position:0%
+and then back up again you can't see it
+ 
+
+ align:start position:0%
+and then back up again you can't see it
+very well i'm sorry the pictures are too
+
+ align:start position:0%
+very well i'm sorry the pictures are too
+ 
+
+ align:start position:0%
+very well i'm sorry the pictures are too
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+but what's plotted over here
+
+ align:start position:0%
+but what's plotted over here
+ 
+
+ align:start position:0%
+but what's plotted over here
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+net cash inflows or outflows along with
+
+ align:start position:0%
+net cash inflows or outflows along with
+ 
+
+ align:start position:0%
+net cash inflows or outflows along with
+you know say a deposit when you have a
+
+ align:start position:0%
+you know say a deposit when you have a
+ 
+
+ align:start position:0%
+you know say a deposit when you have a
+net inflow
+
+ align:start position:0%
+net inflow
+ 
+
+ align:start position:0%
+net inflow
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+a withdrawal
+
+ align:start position:0%
+a withdrawal
+ 
+
+ align:start position:0%
+a withdrawal
+when you have a net outflow so there's
+
+ align:start position:0%
+when you have a net outflow so there's
+ 
+
+ align:start position:0%
+when you have a net outflow so there's
+three lines here
+
+ align:start position:0%
+three lines here
+ 
+
+ align:start position:0%
+three lines here
+and sometimes you know things correspond
+
+ align:start position:0%
+and sometimes you know things correspond
+ 
+
+ align:start position:0%
+and sometimes you know things correspond
+the way i was just implying you're short
+
+ align:start position:0%
+the way i was just implying you're short
+ 
+
+ align:start position:0%
+the way i was just implying you're short
+so you withdraw
+
+ align:start position:0%
+so you withdraw
+ 
+
+ align:start position:0%
+so you withdraw
+etc so but when you can't see much here
+
+ align:start position:0%
+etc so but when you can't see much here
+ 
+
+ align:start position:0%
+etc so but when you can't see much here
+but when you integrate it out
+
+ align:start position:0%
+but when you integrate it out
+ 
+
+ align:start position:0%
+but when you integrate it out
+and look at the consequence for the
+
+ align:start position:0%
+and look at the consequence for the
+ 
+
+ align:start position:0%
+and look at the consequence for the
+levels you know using
+
+ align:start position:0%
+levels you know using
+ 
+
+ align:start position:0%
+levels you know using
+this flow equation
+
+ align:start position:0%
+this flow equation
+ 
+
+ align:start position:0%
+this flow equation
+then you can see what their stocks are
+
+ align:start position:0%
+then you can see what their stocks are
+ 
+
+ align:start position:0%
+then you can see what their stocks are
+it looks like a lot of money it is going
+
+ align:start position:0%
+it looks like a lot of money it is going
+ 
+
+ align:start position:0%
+it looks like a lot of money it is going
+to be unbelievable
+
+ align:start position:0%
+to be unbelievable
+ 
+
+ align:start position:0%
+to be unbelievable
+unbelievable in the sense of three years
+
+ align:start position:0%
+unbelievable in the sense of three years
+ 
+
+ align:start position:0%
+unbelievable in the sense of three years
+research running to try to understand
+
+ align:start position:0%
+research running to try to understand
+ 
+
+ align:start position:0%
+research running to try to understand
+this pattern
+
+ align:start position:0%
+this pattern
+ 
+
+ align:start position:0%
+this pattern
+so how much money does a typical
+
+ align:start position:0%
+so how much money does a typical
+ 
+
+ align:start position:0%
+so how much money does a typical
+household have currency paper squirrel
+
+ align:start position:0%
+household have currency paper squirrel
+ 
+
+ align:start position:0%
+household have currency paper squirrel
+away in the house in the rural villages
+
+ align:start position:0%
+away in the house in the rural villages
+ 
+
+ align:start position:0%
+away in the house in the rural villages
+that we were looking at
+
+ align:start position:0%
+that we were looking at
+ 
+
+ align:start position:0%
+that we were looking at
+roughly 32 months worth of consumption
+
+ align:start position:0%
+roughly 32 months worth of consumption
+ 
+
+ align:start position:0%
+roughly 32 months worth of consumption
+what's in your wallet you're gonna say a
+
+ align:start position:0%
+what's in your wallet you're gonna say a
+ 
+
+ align:start position:0%
+what's in your wallet you're gonna say a
+credit card these guys it's not in a
+
+ align:start position:0%
+credit card these guys it's not in a
+ 
+
+ align:start position:0%
+credit card these guys it's not in a
+wallet it's in the house or hidden in
+
+ align:start position:0%
+wallet it's in the house or hidden in
+ 
+
+ align:start position:0%
+wallet it's in the house or hidden in
+the backyard
+
+ align:start position:0%
+the backyard
+ 
+
+ align:start position:0%
+the backyard
+you know almost three years worth of
+
+ align:start position:0%
+you know almost three years worth of
+ 
+
+ align:start position:0%
+you know almost three years worth of
+expenditures in cash equivalent cash
+
+ align:start position:0%
+expenditures in cash equivalent cash
+ 
+
+ align:start position:0%
+expenditures in cash equivalent cash
+equivalent consumption we take we
+
+ align:start position:0%
+equivalent consumption we take we
+ 
+
+ align:start position:0%
+equivalent consumption we take we
+measure the consumption for each
+
+ align:start position:0%
+measure the consumption for each
+ 
+
+ align:start position:0%
+measure the consumption for each
+household and we see how much cash they
+
+ align:start position:0%
+household and we see how much cash they
+ 
+
+ align:start position:0%
+household and we see how much cash they
+have which we measured in the data 32
+
+ align:start position:0%
+have which we measured in the data 32
+ 
+
+ align:start position:0%
+have which we measured in the data 32
+months it's unbelievable okay and we
+
+ align:start position:0%
+months it's unbelievable okay and we
+ 
+
+ align:start position:0%
+months it's unbelievable okay and we
+also get deposits and withdrawals
+
+ align:start position:0%
+also get deposits and withdrawals
+ 
+
+ align:start position:0%
+also get deposits and withdrawals
+measured in the data that's a lot of
+
+ align:start position:0%
+measured in the data that's a lot of
+ 
+
+ align:start position:0%
+measured in the data that's a lot of
+detail to absorb let me show you kind of
+
+ align:start position:0%
+detail to absorb let me show you kind of
+ 
+
+ align:start position:0%
+detail to absorb let me show you kind of
+what's going on in the model
+
+ align:start position:0%
+what's going on in the model
+ 
+
+ align:start position:0%
+what's going on in the model
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+estimate the cash flow we recover all
+
+ align:start position:0%
+estimate the cash flow we recover all
+ 
+
+ align:start position:0%
+estimate the cash flow we recover all
+the parameters
+
+ align:start position:0%
+the parameters
+ 
+
+ align:start position:0%
+the parameters
+that we need
+
+ align:start position:0%
+that we need
+ 
+
+ align:start position:0%
+that we need
+take a stand on the interest rate in the
+
+ align:start position:0%
+take a stand on the interest rate in the
+ 
+
+ align:start position:0%
+take a stand on the interest rate in the
+bank
+
+ align:start position:0%
+bank
+ 
+
+ align:start position:0%
+bank
+and then look at you know how small or
+
+ align:start position:0%
+and then look at you know how small or
+ 
+
+ align:start position:0%
+and then look at you know how small or
+big the cost would be b uh is varying
+
+ align:start position:0%
+big the cost would be b uh is varying
+ 
+
+ align:start position:0%
+big the cost would be b uh is varying
+down here
+
+ align:start position:0%
+down here
+ 
+
+ align:start position:0%
+down here
+and the consequences for
+
+ align:start position:0%
+and the consequences for
+ 
+
+ align:start position:0%
+and the consequences for
+currency
+
+ align:start position:0%
+currency
+ 
+
+ align:start position:0%
+currency
+especially but also withdrawals and
+
+ align:start position:0%
+especially but also withdrawals and
+ 
+
+ align:start position:0%
+especially but also withdrawals and
+deposits
+
+ align:start position:0%
+deposits
+ 
+
+ align:start position:0%
+deposits
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+taking the reality to be the calibrated
+
+ align:start position:0%
+taking the reality to be the calibrated
+ 
+
+ align:start position:0%
+taking the reality to be the calibrated
+expenditure flows we see in the data
+
+ align:start position:0%
+expenditure flows we see in the data
+ 
+
+ align:start position:0%
+expenditure flows we see in the data
+along with a few other reasonable
+
+ align:start position:0%
+along with a few other reasonable
+ 
+
+ align:start position:0%
+along with a few other reasonable
+assumptions i assure you
+
+ align:start position:0%
+assumptions i assure you
+ 
+
+ align:start position:0%
+assumptions i assure you
+we can look at how much cash they should
+
+ align:start position:0%
+we can look at how much cash they should
+ 
+
+ align:start position:0%
+we can look at how much cash they should
+be holding relative to consumption
+
+ align:start position:0%
+be holding relative to consumption
+ 
+
+ align:start position:0%
+be holding relative to consumption
+that's this blue line
+
+ align:start position:0%
+that's this blue line
+ 
+
+ align:start position:0%
+that's this blue line
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+we can barely get it up to three
+
+ align:start position:0%
+we can barely get it up to three
+ 
+
+ align:start position:0%
+we can barely get it up to three
+the number in the data is 32.
+
+ align:start position:0%
+the number in the data is 32.
+ 
+
+ align:start position:0%
+the number in the data is 32.
+i mean you could imagine
+
+ align:start position:0%
+i mean you could imagine
+ 
+
+ align:start position:0%
+i mean you could imagine
+increasing those costs and decreasing
+
+ align:start position:0%
+increasing those costs and decreasing
+ 
+
+ align:start position:0%
+increasing those costs and decreasing
+the interest and you'll net you know
+
+ align:start position:0%
+the interest and you'll net you know
+ 
+
+ align:start position:0%
+the interest and you'll net you know
+this is like asymptoting out to
+
+ align:start position:0%
+this is like asymptoting out to
+ 
+
+ align:start position:0%
+this is like asymptoting out to
+something flat
+
+ align:start position:0%
+something flat
+ 
+
+ align:start position:0%
+something flat
+you know so you end up with something
+
+ align:start position:0%
+you know so you end up with something
+ 
+
+ align:start position:0%
+you know so you end up with something
+ridiculous
+
+ align:start position:0%
+ridiculous
+ 
+
+ align:start position:0%
+ridiculous
+the model isn't working you don't go to
+
+ align:start position:0%
+the model isn't working you don't go to
+ 
+
+ align:start position:0%
+the model isn't working you don't go to
+the bank and forego you know two years
+
+ align:start position:0%
+the bank and forego you know two years
+ 
+
+ align:start position:0%
+the bank and forego you know two years
+worth of consumption while you're doing
+
+ align:start position:0%
+worth of consumption while you're doing
+ 
+
+ align:start position:0%
+worth of consumption while you're doing
+your your banking transaction it's just
+
+ align:start position:0%
+your your banking transaction it's just
+ 
+
+ align:start position:0%
+your your banking transaction it's just
+not a reasonable value the sign is
+
+ align:start position:0%
+not a reasonable value the sign is
+ 
+
+ align:start position:0%
+not a reasonable value the sign is
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+the higher the cost
+
+ align:start position:0%
+the higher the cost
+ 
+
+ align:start position:0%
+the higher the cost
+be of going to the bank to either
+
+ align:start position:0%
+be of going to the bank to either
+ 
+
+ align:start position:0%
+be of going to the bank to either
+withdraw or deposit the less you're
+
+ align:start position:0%
+withdraw or deposit the less you're
+ 
+
+ align:start position:0%
+withdraw or deposit the less you're
+going to do it so when you do it the
+
+ align:start position:0%
+going to do it so when you do it the
+ 
+
+ align:start position:0%
+going to do it so when you do it the
+transactions are bigger and meanwhile
+
+ align:start position:0%
+transactions are bigger and meanwhile
+ 
+
+ align:start position:0%
+transactions are bigger and meanwhile
+you're holding more cash
+
+ align:start position:0%
+you're holding more cash
+ 
+
+ align:start position:0%
+you're holding more cash
+you know if b goes to infinity then you
+
+ align:start position:0%
+you know if b goes to infinity then you
+ 
+
+ align:start position:0%
+you know if b goes to infinity then you
+just it's all in cash
+
+ align:start position:0%
+just it's all in cash
+ 
+
+ align:start position:0%
+just it's all in cash
+forget the bank
+
+ align:start position:0%
+forget the bank
+ 
+
+ align:start position:0%
+forget the bank
+when you go rarely then you have to make
+
+ align:start position:0%
+when you go rarely then you have to make
+ 
+
+ align:start position:0%
+when you go rarely then you have to make
+up a big difference
+
+ align:start position:0%
+up a big difference
+ 
+
+ align:start position:0%
+up a big difference
+and this is the frequency which again as
+
+ align:start position:0%
+and this is the frequency which again as
+ 
+
+ align:start position:0%
+and this is the frequency which again as
+b goes up the frequency of going to the
+
+ align:start position:0%
+b goes up the frequency of going to the
+ 
+
+ align:start position:0%
+b goes up the frequency of going to the
+bank is going down
+
+ align:start position:0%
+bank is going down
+ 
+
+ align:start position:0%
+bank is going down
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+because we did that life cycle planner
+
+ align:start position:0%
+because we did that life cycle planner
+ 
+
+ align:start position:0%
+because we did that life cycle planner
+we wanted to evaluate as a randomized
+
+ align:start position:0%
+we wanted to evaluate as a randomized
+ 
+
+ align:start position:0%
+we wanted to evaluate as a randomized
+control trial
+
+ align:start position:0%
+control trial
+ 
+
+ align:start position:0%
+control trial
+how well or poorly it was working
+
+ align:start position:0%
+how well or poorly it was working
+ 
+
+ align:start position:0%
+how well or poorly it was working
+and in the process we gathered monthly
+
+ align:start position:0%
+and in the process we gathered monthly
+ 
+
+ align:start position:0%
+and in the process we gathered monthly
+data for the urban household so we're
+
+ align:start position:0%
+data for the urban household so we're
+ 
+
+ align:start position:0%
+data for the urban household so we're
+not in villages anymore we're in towns
+
+ align:start position:0%
+not in villages anymore we're in towns
+ 
+
+ align:start position:0%
+not in villages anymore we're in towns
+or even city neighborhoods
+
+ align:start position:0%
+or even city neighborhoods
+ 
+
+ align:start position:0%
+or even city neighborhoods
+in each of the four provinces
+
+ align:start position:0%
+in each of the four provinces
+ 
+
+ align:start position:0%
+in each of the four provinces
+you know we basically replicated all the
+
+ align:start position:0%
+you know we basically replicated all the
+ 
+
+ align:start position:0%
+you know we basically replicated all the
+existing surveys
+
+ align:start position:0%
+existing surveys
+ 
+
+ align:start position:0%
+existing surveys
+so the same questions are being asked
+
+ align:start position:0%
+so the same questions are being asked
+ 
+
+ align:start position:0%
+so the same questions are being asked
+and this is kind of buried here but if
+
+ align:start position:0%
+and this is kind of buried here but if
+ 
+
+ align:start position:0%
+and this is kind of buried here but if
+you look at the normalized cash in terms
+
+ align:start position:0%
+you look at the normalized cash in terms
+ 
+
+ align:start position:0%
+you look at the normalized cash in terms
+of consumption
+
+ align:start position:0%
+of consumption
+ 
+
+ align:start position:0%
+of consumption
+for the urban sample
+
+ align:start position:0%
+for the urban sample
+ 
+
+ align:start position:0%
+for the urban sample
+and look over here
+
+ align:start position:0%
+and look over here
+ 
+
+ align:start position:0%
+and look over here
+we get a number
+
+ align:start position:0%
+we get a number
+ 
+
+ align:start position:0%
+we get a number
+of 3.87
+
+ align:start position:0%
+of 3.87
+ 
+
+ align:start position:0%
+of 3.87
+much closer to 3. nothing like the 37
+
+ align:start position:0%
+much closer to 3. nothing like the 37
+ 
+
+ align:start position:0%
+much closer to 3. nothing like the 37
+well actually i should be over here at
+
+ align:start position:0%
+well actually i should be over here at
+ 
+
+ align:start position:0%
+well actually i should be over here at
+the median so it's
+
+ align:start position:0%
+the median so it's
+ 
+
+ align:start position:0%
+the median so it's
+1.94 we do some adjustments in the data
+
+ align:start position:0%
+1.94 we do some adjustments in the data
+ 
+
+ align:start position:0%
+1.94 we do some adjustments in the data
+i'm happy to tell you about them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's within reach of the model we
+
+ align:start position:0%
+that's within reach of the model we
+ 
+
+ align:start position:0%
+that's within reach of the model we
+calibrate the model again
+
+ align:start position:0%
+calibrate the model again
+ 
+
+ align:start position:0%
+calibrate the model again
+using the cache statistics you know
+
+ align:start position:0%
+using the cache statistics you know
+ 
+
+ align:start position:0%
+using the cache statistics you know
+these zapping
+
+ align:start position:0%
+these zapping
+ 
+
+ align:start position:0%
+these zapping
+big shocks small shocks how often they
+
+ align:start position:0%
+big shocks small shocks how often they
+ 
+
+ align:start position:0%
+big shocks small shocks how often they
+happen etc etc and get a model
+
+ align:start position:0%
+happen etc etc and get a model
+ 
+
+ align:start position:0%
+happen etc etc and get a model
+prediction and the implied value
+
+ align:start position:0%
+prediction and the implied value
+ 
+
+ align:start position:0%
+prediction and the implied value
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+is you know depending on whether you use
+
+ align:start position:0%
+is you know depending on whether you use
+ 
+
+ align:start position:0%
+is you know depending on whether you use
+the mean or the median
+
+ align:start position:0%
+the mean or the median
+ 
+
+ align:start position:0%
+the mean or the median
+is something like two so you know which
+
+ align:start position:0%
+is something like two so you know which
+ 
+
+ align:start position:0%
+is something like two so you know which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+close to what we're getting in the data
+
+ align:start position:0%
+close to what we're getting in the data
+ 
+
+ align:start position:0%
+close to what we're getting in the data
+so now we're in kind of business in the
+
+ align:start position:0%
+so now we're in kind of business in the
+ 
+
+ align:start position:0%
+so now we're in kind of business in the
+sense that a reasonable economic model
+
+ align:start position:0%
+sense that a reasonable economic model
+ 
+
+ align:start position:0%
+sense that a reasonable economic model
+is actually predicting pretty well how
+
+ align:start position:0%
+is actually predicting pretty well how
+ 
+
+ align:start position:0%
+is actually predicting pretty well how
+much cash they're holding whereas in the
+
+ align:start position:0%
+much cash they're holding whereas in the
+ 
+
+ align:start position:0%
+much cash they're holding whereas in the
+rural data was a disaster right we
+
+ align:start position:0%
+rural data was a disaster right we
+ 
+
+ align:start position:0%
+rural data was a disaster right we
+didn't get close so
+
+ align:start position:0%
+didn't get close so
+ 
+
+ align:start position:0%
+didn't get close so
+now we switch into sort of the
+
+ align:start position:0%
+now we switch into sort of the
+ 
+
+ align:start position:0%
+now we switch into sort of the
+how can we understand the error that the
+
+ align:start position:0%
+how can we understand the error that the
+ 
+
+ align:start position:0%
+how can we understand the error that the
+households are making with their cash
+
+ align:start position:0%
+households are making with their cash
+ 
+
+ align:start position:0%
+households are making with their cash
+management and the guess is federal
+
+ align:start position:0%
+management and the guess is federal
+ 
+
+ align:start position:0%
+management and the guess is federal
+guesses some turned out to be correct
+
+ align:start position:0%
+guesses some turned out to be correct
+ 
+
+ align:start position:0%
+guesses some turned out to be correct
+and some not
+
+ align:start position:0%
+and some not
+ 
+
+ align:start position:0%
+and some not
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+why would cash holdings be so much lower
+
+ align:start position:0%
+why would cash holdings be so much lower
+ 
+
+ align:start position:0%
+why would cash holdings be so much lower
+in the urban area relative to the rural
+
+ align:start position:0%
+in the urban area relative to the rural
+ 
+
+ align:start position:0%
+in the urban area relative to the rural
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+is it because households in the urban
+
+ align:start position:0%
+is it because households in the urban
+ 
+
+ align:start position:0%
+is it because households in the urban
+survey deposit more often and larger
+
+ align:start position:0%
+survey deposit more often and larger
+ 
+
+ align:start position:0%
+survey deposit more often and larger
+amounts or is it because they withdraw
+
+ align:start position:0%
+amounts or is it because they withdraw
+ 
+
+ align:start position:0%
+amounts or is it because they withdraw
+in the urban areas less and withdraw
+
+ align:start position:0%
+in the urban areas less and withdraw
+ 
+
+ align:start position:0%
+in the urban areas less and withdraw
+smaller amounts
+
+ align:start position:0%
+smaller amounts
+ 
+
+ align:start position:0%
+smaller amounts
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for deposits it turns out households in
+
+ align:start position:0%
+for deposits it turns out households in
+ 
+
+ align:start position:0%
+for deposits it turns out households in
+the rural area deposit more and not less
+
+ align:start position:0%
+the rural area deposit more and not less
+ 
+
+ align:start position:0%
+the rural area deposit more and not less
+and they deposit larger amounts this is
+
+ align:start position:0%
+and they deposit larger amounts this is
+ 
+
+ align:start position:0%
+and they deposit larger amounts this is
+exactly the opposite of what we would
+
+ align:start position:0%
+exactly the opposite of what we would
+ 
+
+ align:start position:0%
+exactly the opposite of what we would
+have predicted because the cash is going
+
+ align:start position:0%
+have predicted because the cash is going
+ 
+
+ align:start position:0%
+have predicted because the cash is going
+into the bank or into the local money
+
+ align:start position:0%
+into the bank or into the local money
+ 
+
+ align:start position:0%
+into the bank or into the local money
+market however for withdrawals it works
+
+ align:start position:0%
+market however for withdrawals it works
+ 
+
+ align:start position:0%
+market however for withdrawals it works
+the way we would have conjectured
+
+ align:start position:0%
+the way we would have conjectured
+ 
+
+ align:start position:0%
+the way we would have conjectured
+that when urban households put money in
+
+ align:start position:0%
+that when urban households put money in
+ 
+
+ align:start position:0%
+that when urban households put money in
+the bank they don't withdraw it very
+
+ align:start position:0%
+the bank they don't withdraw it very
+ 
+
+ align:start position:0%
+the bank they don't withdraw it very
+often and they withdraw a lot less
+
+ align:start position:0%
+often and they withdraw a lot less
+ 
+
+ align:start position:0%
+often and they withdraw a lot less
+it almost looks like they're putting
+
+ align:start position:0%
+it almost looks like they're putting
+ 
+
+ align:start position:0%
+it almost looks like they're putting
+their sort of proxy for their salary
+
+ align:start position:0%
+their sort of proxy for their salary
+ 
+
+ align:start position:0%
+their sort of proxy for their salary
+into the bank and any other money which
+
+ align:start position:0%
+into the bank and any other money which
+ 
+
+ align:start position:0%
+into the bank and any other money which
+they have from business and so on goes
+
+ align:start position:0%
+they have from business and so on goes
+ 
+
+ align:start position:0%
+they have from business and so on goes
+into the bank and stays there they they
+
+ align:start position:0%
+into the bank and stays there they they
+ 
+
+ align:start position:0%
+into the bank and stays there they they
+just withdraw what they need for
+
+ align:start position:0%
+just withdraw what they need for
+ 
+
+ align:start position:0%
+just withdraw what they need for
+consumption taking sort of the quote
+
+ align:start position:0%
+consumption taking sort of the quote
+ 
+
+ align:start position:0%
+consumption taking sort of the quote
+unquote salary equivalent out and
+
+ align:start position:0%
+unquote salary equivalent out and
+ 
+
+ align:start position:0%
+unquote salary equivalent out and
+leaving the rest in so this is why their
+
+ align:start position:0%
+leaving the rest in so this is why their
+ 
+
+ align:start position:0%
+leaving the rest in so this is why their
+money value is a lot lower
+
+ align:start position:0%
+money value is a lot lower
+ 
+
+ align:start position:0%
+money value is a lot lower
+there's still something to fix which you
+
+ align:start position:0%
+there's still something to fix which you
+ 
+
+ align:start position:0%
+there's still something to fix which you
+know just like in life cycle planner you
+
+ align:start position:0%
+know just like in life cycle planner you
+ 
+
+ align:start position:0%
+know just like in life cycle planner you
+know we could create from the research
+
+ align:start position:0%
+know we could create from the research
+ 
+
+ align:start position:0%
+know we could create from the research
+cash flow app and put it on the phone
+
+ align:start position:0%
+cash flow app and put it on the phone
+ 
+
+ align:start position:0%
+cash flow app and put it on the phone
+and tell households out of management
+
+ align:start position:0%
+and tell households out of management
+ 
+
+ align:start position:0%
+and tell households out of management
+and in fact you know the question is why
+
+ align:start position:0%
+and in fact you know the question is why
+ 
+
+ align:start position:0%
+and in fact you know the question is why
+are they having cash at all why don't
+
+ align:start position:0%
+are they having cash at all why don't
+ 
+
+ align:start position:0%
+are they having cash at all why don't
+they just put it on their cell phone and
+
+ align:start position:0%
+they just put it on their cell phone and
+ 
+
+ align:start position:0%
+they just put it on their cell phone and
+that brings us to
+
+ align:start position:0%
+that brings us to
+ 
+
+ align:start position:0%
+that brings us to
+oh and the costs
+
+ align:start position:0%
+oh and the costs
+ 
+
+ align:start position:0%
+oh and the costs
+of mismanagement of currency are very
+
+ align:start position:0%
+of mismanagement of currency are very
+ 
+
+ align:start position:0%
+of mismanagement of currency are very
+high something like nine and a half
+
+ align:start position:0%
+high something like nine and a half
+ 
+
+ align:start position:0%
+high something like nine and a half
+percent of monthly consumption that's
+
+ align:start position:0%
+percent of monthly consumption that's
+ 
+
+ align:start position:0%
+percent of monthly consumption that's
+huge in economics you know say
+
+ align:start position:0%
+huge in economics you know say
+ 
+
+ align:start position:0%
+huge in economics you know say
+exaggerate a bit 10 or call it five if
+
+ align:start position:0%
+exaggerate a bit 10 or call it five if
+ 
+
+ align:start position:0%
+exaggerate a bit 10 or call it five if
+you want five percent of monthly
+
+ align:start position:0%
+you want five percent of monthly
+ 
+
+ align:start position:0%
+you want five percent of monthly
+consumption could be saved or used for
+
+ align:start position:0%
+consumption could be saved or used for
+ 
+
+ align:start position:0%
+consumption could be saved or used for
+consumption if they just manage their
+
+ align:start position:0%
+consumption if they just manage their
+ 
+
+ align:start position:0%
+consumption if they just manage their
+currency better so you know one way to
+
+ align:start position:0%
+currency better so you know one way to
+ 
+
+ align:start position:0%
+currency better so you know one way to
+put this enormous cost of mismanagement
+
+ align:start position:0%
+put this enormous cost of mismanagement
+ 
+
+ align:start position:0%
+put this enormous cost of mismanagement
+of petty cash
+
+ align:start position:0%
+of petty cash
+ 
+
+ align:start position:0%
+of petty cash
+businesses get cash advisory services
+
+ align:start position:0%
+businesses get cash advisory services
+ 
+
+ align:start position:0%
+businesses get cash advisory services
+they pay for it you know why should
+
+ align:start position:0%
+they pay for it you know why should
+ 
+
+ align:start position:0%
+they pay for it you know why should
+these poor households not have access to
+
+ align:start position:0%
+these poor households not have access to
+ 
+
+ align:start position:0%
+these poor households not have access to
+better management tools
+
+ align:start position:0%
+better management tools
+ 
+
+ align:start position:0%
+better management tools
+okay sorry that's my view okay
+
+ align:start position:0%
+okay sorry that's my view okay
+ 
+
+ align:start position:0%
+okay sorry that's my view okay
+go to sweden
+
+ align:start position:0%
+go to sweden
+ 
+
+ align:start position:0%
+go to sweden
+how much paper currency they're using
+
+ align:start position:0%
+how much paper currency they're using
+ 
+
+ align:start position:0%
+how much paper currency they're using
+close to nothing they're gone it's gone
+
+ align:start position:0%
+close to nothing they're gone it's gone
+ 
+
+ align:start position:0%
+close to nothing they're gone it's gone
+this is the amount of currency relative
+
+ align:start position:0%
+this is the amount of currency relative
+ 
+
+ align:start position:0%
+this is the amount of currency relative
+to gdp
+
+ align:start position:0%
+to gdp
+ 
+
+ align:start position:0%
+to gdp
+ever declining this is the absolute
+
+ align:start position:0%
+ever declining this is the absolute
+ 
+
+ align:start position:0%
+ever declining this is the absolute
+level of of cash going down in an
+
+ align:start position:0%
+level of of cash going down in an
+ 
+
+ align:start position:0%
+level of of cash going down in an
+absolute not only relative basis so i
+
+ align:start position:0%
+absolute not only relative basis so i
+ 
+
+ align:start position:0%
+absolute not only relative basis so i
+got this and this slide from the
+
+ align:start position:0%
+got this and this slide from the
+ 
+
+ align:start position:0%
+got this and this slide from the
+governor of the rich bank in sweden
+
+ align:start position:0%
+governor of the rich bank in sweden
+ 
+
+ align:start position:0%
+governor of the rich bank in sweden
+so i don't know whether you'll
+
+ align:start position:0%
+so i don't know whether you'll
+ 
+
+ align:start position:0%
+so i don't know whether you'll
+appreciate the humor here but this is a
+
+ align:start position:0%
+appreciate the humor here but this is a
+ 
+
+ align:start position:0%
+appreciate the humor here but this is a
+picture of a stone so
+
+ align:start position:0%
+picture of a stone so
+ 
+
+ align:start position:0%
+picture of a stone so
+you know economists and others have
+
+ align:start position:0%
+you know economists and others have
+ 
+
+ align:start position:0%
+you know economists and others have
+written books about the first coins the
+
+ align:start position:0%
+written books about the first coins the
+ 
+
+ align:start position:0%
+written books about the first coins the
+first use of cash and there were claims
+
+ align:start position:0%
+first use of cash and there were claims
+ 
+
+ align:start position:0%
+first use of cash and there were claims
+on stones that were buried at the bottom
+
+ align:start position:0%
+on stones that were buried at the bottom
+ 
+
+ align:start position:0%
+on stones that were buried at the bottom
+of the lake so now in sweden they're
+
+ align:start position:0%
+of the lake so now in sweden they're
+ 
+
+ align:start position:0%
+of the lake so now in sweden they're
+transferring the stone around on their
+
+ align:start position:0%
+transferring the stone around on their
+ 
+
+ align:start position:0%
+transferring the stone around on their
+cell phone well not really it's swish
+
+ align:start position:0%
+cell phone well not really it's swish
+ 
+
+ align:start position:0%
+cell phone well not really it's swish
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+they have a bank account and for no
+
+ align:start position:0%
+they have a bank account and for no
+ 
+
+ align:start position:0%
+they have a bank account and for no
+money at all
+
+ align:start position:0%
+money at all
+ 
+
+ align:start position:0%
+money at all
+households can transfer cash to each
+
+ align:start position:0%
+households can transfer cash to each
+ 
+
+ align:start position:0%
+households can transfer cash to each
+other buy things and so on and it's
+
+ align:start position:0%
+other buy things and so on and it's
+ 
+
+ align:start position:0%
+other buy things and so on and it's
+replaced the paper currency it's
+
+ align:start position:0%
+replaced the paper currency it's
+ 
+
+ align:start position:0%
+replaced the paper currency it's
+actually a bit of a concern for them
+
+ align:start position:0%
+actually a bit of a concern for them
+ 
+
+ align:start position:0%
+actually a bit of a concern for them
+which is why they're thinking if there's
+
+ align:start position:0%
+which is why they're thinking if there's
+ 
+
+ align:start position:0%
+which is why they're thinking if there's
+no paper currency other than reserves
+
+ align:start position:0%
+no paper currency other than reserves
+ 
+
+ align:start position:0%
+no paper currency other than reserves
+there's no role for the central bank
+
+ align:start position:0%
+there's no role for the central bank
+ 
+
+ align:start position:0%
+there's no role for the central bank
+so they feel they should be providing a
+
+ align:start position:0%
+so they feel they should be providing a
+ 
+
+ align:start position:0%
+so they feel they should be providing a
+payment service as a backup so they're
+
+ align:start position:0%
+payment service as a backup so they're
+ 
+
+ align:start position:0%
+payment service as a backup so they're
+going to create almost surely a central
+
+ align:start position:0%
+going to create almost surely a central
+ 
+
+ align:start position:0%
+going to create almost surely a central
+bank digital currency so households will
+
+ align:start position:0%
+bank digital currency so households will
+ 
+
+ align:start position:0%
+bank digital currency so households will
+have digital accounts in the central
+
+ align:start position:0%
+have digital accounts in the central
+ 
+
+ align:start position:0%
+have digital accounts in the central
+bank which is what south africa is doing
+
+ align:start position:0%
+bank which is what south africa is doing
+ 
+
+ align:start position:0%
+bank which is what south africa is doing
+china has a different version of it and
+
+ align:start position:0%
+china has a different version of it and
+ 
+
+ align:start position:0%
+china has a different version of it and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+this has just happened in the bahamas
+
+ align:start position:0%
+this has just happened in the bahamas
+ 
+
+ align:start position:0%
+this has just happened in the bahamas
+they created something called the sand
+
+ align:start position:0%
+they created something called the sand
+ 
+
+ align:start position:0%
+they created something called the sand
+dollar
+
+ align:start position:0%
+dollar
+ 
+
+ align:start position:0%
+dollar
+the virus is accelerating this problem
+
+ align:start position:0%
+the virus is accelerating this problem
+ 
+
+ align:start position:0%
+the virus is accelerating this problem
+because people need government aid and
+
+ align:start position:0%
+because people need government aid and
+ 
+
+ align:start position:0%
+because people need government aid and
+they can't get the aid you know truck
+
+ align:start position:0%
+they can't get the aid you know truck
+ 
+
+ align:start position:0%
+they can't get the aid you know truck
+the paper currency over there this
+
+ align:start position:0%
+the paper currency over there this
+ 
+
+ align:start position:0%
+the paper currency over there this
+disastrous hurricane dorian destroyed an
+
+ align:start position:0%
+disastrous hurricane dorian destroyed an
+ 
+
+ align:start position:0%
+disastrous hurricane dorian destroyed an
+island in the bahamas they couldn't get
+
+ align:start position:0%
+island in the bahamas they couldn't get
+ 
+
+ align:start position:0%
+island in the bahamas they couldn't get
+emergency assistance so these are things
+
+ align:start position:0%
+emergency assistance so these are things
+ 
+
+ align:start position:0%
+emergency assistance so these are things
+that are happening all over the world
+
+ align:start position:0%
+that are happening all over the world
+ 
+
+ align:start position:0%
+that are happening all over the world
+right now this last slide is
+
+ align:start position:0%
+right now this last slide is
+ 
+
+ align:start position:0%
+right now this last slide is
+kenya and and i mentioned they have two
+
+ align:start position:0%
+kenya and and i mentioned they have two
+ 
+
+ align:start position:0%
+kenya and and i mentioned they have two
+kinds of currency one is kenyan
+
+ align:start position:0%
+kinds of currency one is kenyan
+ 
+
+ align:start position:0%
+kinds of currency one is kenyan
+shillings used to be a british colony
+
+ align:start position:0%
+shillings used to be a british colony
+ 
+
+ align:start position:0%
+shillings used to be a british colony
+and the other is e-credits at safaricom
+
+ align:start position:0%
+and the other is e-credits at safaricom
+ 
+
+ align:start position:0%
+and the other is e-credits at safaricom
+which is a cell phone provider
+
+ align:start position:0%
+which is a cell phone provider
+ 
+
+ align:start position:0%
+which is a cell phone provider
+so what you do is you take your
+
+ align:start position:0%
+so what you do is you take your
+ 
+
+ align:start position:0%
+so what you do is you take your
+shillings
+
+ align:start position:0%
+shillings
+ 
+
+ align:start position:0%
+shillings
+you go to this safari comm agent
+
+ align:start position:0%
+you go to this safari comm agent
+ 
+
+ align:start position:0%
+you go to this safari comm agent
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+give him your fiat money and you get
+
+ align:start position:0%
+give him your fiat money and you get
+ 
+
+ align:start position:0%
+give him your fiat money and you get
+credited sell accounts called impesa
+
+ align:start position:0%
+credited sell accounts called impesa
+ 
+
+ align:start position:0%
+credited sell accounts called impesa
+and then you can use that to give to
+
+ align:start position:0%
+and then you can use that to give to
+ 
+
+ align:start position:0%
+and then you can use that to give to
+your mom back in the village who goes to
+
+ align:start position:0%
+your mom back in the village who goes to
+ 
+
+ align:start position:0%
+your mom back in the village who goes to
+the agent there and transfers it back
+
+ align:start position:0%
+the agent there and transfers it back
+ 
+
+ align:start position:0%
+the agent there and transfers it back
+out into shillings or you can buy stuff
+
+ align:start position:0%
+out into shillings or you can buy stuff
+ 
+
+ align:start position:0%
+out into shillings or you can buy stuff
+so here you see you know the use of the
+
+ align:start position:0%
+so here you see you know the use of the
+ 
+
+ align:start position:0%
+so here you see you know the use of the
+paper currency but also this e-currency
+
+ align:start position:0%
+paper currency but also this e-currency
+ 
+
+ align:start position:0%
+paper currency but also this e-currency
+which is created by safari company
+
+ align:start position:0%
+which is created by safari company
+ 
+
+ align:start position:0%
+which is created by safari company
+and it has reached almost everybody
+
+ align:start position:0%
+and it has reached almost everybody
+ 
+
+ align:start position:0%
+and it has reached almost everybody
+some economies try to do this we kind of
+
+ align:start position:0%
+some economies try to do this we kind of
+ 
+
+ align:start position:0%
+some economies try to do this we kind of
+tried in thailand and i have not yet
+
+ align:start position:0%
+tried in thailand and i have not yet
+ 
+
+ align:start position:0%
+tried in thailand and i have not yet
+succeeded in kenya even the lowest
+
+ align:start position:0%
+succeeded in kenya even the lowest
+ 
+
+ align:start position:0%
+succeeded in kenya even the lowest
+income quartile we need to update this
+
+ align:start position:0%
+income quartile we need to update this
+ 
+
+ align:start position:0%
+income quartile we need to update this
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+with tom surry did this you know roughly
+
+ align:start position:0%
+with tom surry did this you know roughly
+ 
+
+ align:start position:0%
+with tom surry did this you know roughly
+85 percent of the pop low income
+
+ align:start position:0%
+85 percent of the pop low income
+ 
+
+ align:start position:0%
+85 percent of the pop low income
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+uh in a similar higher number for those
+
+ align:start position:0%
+uh in a similar higher number for those
+ 
+
+ align:start position:0%
+uh in a similar higher number for those
+with no bank accounts are using
+
+ align:start position:0%
+with no bank accounts are using
+ 
+
+ align:start position:0%
+with no bank accounts are using
+safaricom
+
+ align:start position:0%
+safaricom
+ 
+
+ align:start position:0%
+safaricom
+with no bank accounts in other words you
+
+ align:start position:0%
+with no bank accounts in other words you
+ 
+
+ align:start position:0%
+with no bank accounts in other words you
+don't need the traditional legacy
+
+ align:start position:0%
+don't need the traditional legacy
+ 
+
+ align:start position:0%
+don't need the traditional legacy
+infrastructure and this is again the
+
+ align:start position:0%
+infrastructure and this is again the
+ 
+
+ align:start position:0%
+infrastructure and this is again the
+allure
+
+ align:start position:0%
+allure
+ 
+
+ align:start position:0%
+allure
+the so-called disintermediation that the
+
+ align:start position:0%
+the so-called disintermediation that the
+ 
+
+ align:start position:0%
+the so-called disintermediation that the
+fintechs are bringing to the world
+
+ align:start position:0%
+fintechs are bringing to the world
+ 
+
+ align:start position:0%
+fintechs are bringing to the world
+of course commercial bankers don't like
+
+ align:start position:0%
+of course commercial bankers don't like
+ 
+
+ align:start position:0%
+of course commercial bankers don't like
+it much
+
+ align:start position:0%
+it much
+ 
+
+ align:start position:0%
+it much
+we talked about risk sharing and uh
+
+ align:start position:0%
+we talked about risk sharing and uh
+ 
+
+ align:start position:0%
+we talked about risk sharing and uh
+top nate and her co-author billy jack
+
+ align:start position:0%
+top nate and her co-author billy jack
+ 
+
+ align:start position:0%
+top nate and her co-author billy jack
+looked at how much consumption is being
+
+ align:start position:0%
+looked at how much consumption is being
+ 
+
+ align:start position:0%
+looked at how much consumption is being
+smoothed in kenya comparing households
+
+ align:start position:0%
+smoothed in kenya comparing households
+ 
+
+ align:start position:0%
+smoothed in kenya comparing households
+who have not yet gotten early on the
+
+ align:start position:0%
+who have not yet gotten early on the
+ 
+
+ align:start position:0%
+who have not yet gotten early on the
+impesa expansion versus those that did
+
+ align:start position:0%
+impesa expansion versus those that did
+ 
+
+ align:start position:0%
+impesa expansion versus those that did
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+there's a lot more smoother consumption
+
+ align:start position:0%
+there's a lot more smoother consumption
+ 
+
+ align:start position:0%
+there's a lot more smoother consumption
+but you see these common themes we did
+
+ align:start position:0%
+but you see these common themes we did
+ 
+
+ align:start position:0%
+but you see these common themes we did
+risk sharing we did gift giving in thai
+
+ align:start position:0%
+risk sharing we did gift giving in thai
+ 
+
+ align:start position:0%
+risk sharing we did gift giving in thai
+villages
+
+ align:start position:0%
+villages
+ 
+
+ align:start position:0%
+villages
+now people are giving gifts and
+
+ align:start position:0%
+now people are giving gifts and
+ 
+
+ align:start position:0%
+now people are giving gifts and
+transfers through
+
+ align:start position:0%
+transfers through
+ 
+
+ align:start position:0%
+transfers through
+kent to through impesa
+
+ align:start position:0%
+kent to through impesa
+ 
+
+ align:start position:0%
+kent to through impesa
+and so it has an impact
+
+ align:start position:0%
+and so it has an impact
+ 
+
+ align:start position:0%
+and so it has an impact
+say what's the big deal it's a big deal
+
+ align:start position:0%
+say what's the big deal it's a big deal
+ 
+
+ align:start position:0%
+say what's the big deal it's a big deal
+for kenya
+
+ align:start position:0%
+for kenya
+ 
+
+ align:start position:0%
+for kenya
+you know sweden already has its
+
+ align:start position:0%
+you know sweden already has its
+ 
+
+ align:start position:0%
+you know sweden already has its
+infrastructure it's not a big deal
+
+ align:start position:0%
+infrastructure it's not a big deal
+ 
+
+ align:start position:0%
+infrastructure it's not a big deal
+but it makes a big deal for low-income
+
+ align:start position:0%
+but it makes a big deal for low-income
+ 
+
+ align:start position:0%
+but it makes a big deal for low-income
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+there are some qualifications though
+
+ align:start position:0%
+there are some qualifications though
+ 
+
+ align:start position:0%
+there are some qualifications though
+first of all it's not on a distributed
+
+ align:start position:0%
+first of all it's not on a distributed
+ 
+
+ align:start position:0%
+first of all it's not on a distributed
+ledger so you have to trust safaricom to
+
+ align:start position:0%
+ledger so you have to trust safaricom to
+ 
+
+ align:start position:0%
+ledger so you have to trust safaricom to
+keep the accounts properly and they have
+
+ align:start position:0%
+keep the accounts properly and they have
+ 
+
+ align:start position:0%
+keep the accounts properly and they have
+the cash so
+
+ align:start position:0%
+the cash so
+ 
+
+ align:start position:0%
+the cash so
+they're supposed to put it in a
+
+ align:start position:0%
+they're supposed to put it in a
+ 
+
+ align:start position:0%
+they're supposed to put it in a
+commercial bank you trust them to do
+
+ align:start position:0%
+commercial bank you trust them to do
+ 
+
+ align:start position:0%
+commercial bank you trust them to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so you have to rely on a third-party
+
+ align:start position:0%
+so you have to rely on a third-party
+ 
+
+ align:start position:0%
+so you have to rely on a third-party
+vendor in kenya
+
+ align:start position:0%
+vendor in kenya
+ 
+
+ align:start position:0%
+vendor in kenya
+not only that the money's in the bank
+
+ align:start position:0%
+not only that the money's in the bank
+ 
+
+ align:start position:0%
+not only that the money's in the bank
+and kenya's subject to run so how safe
+
+ align:start position:0%
+and kenya's subject to run so how safe
+ 
+
+ align:start position:0%
+and kenya's subject to run so how safe
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+you may think you're going to get their
+
+ align:start position:0%
+you may think you're going to get their
+ 
+
+ align:start position:0%
+you may think you're going to get their
+money back but will you really
+
+ align:start position:0%
+money back but will you really
+ 
+
+ align:start position:0%
+money back but will you really
+and in other economies they don't have
+
+ align:start position:0%
+and in other economies they don't have
+ 
+
+ align:start position:0%
+and in other economies they don't have
+that kind of trust so it doesn't take
+
+ align:start position:0%
+that kind of trust so it doesn't take
+ 
+
+ align:start position:0%
+that kind of trust so it doesn't take
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+the other thing is those agents
+
+ align:start position:0%
+the other thing is those agents
+ 
+
+ align:start position:0%
+the other thing is those agents
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+they run out of stuff
+
+ align:start position:0%
+they run out of stuff
+ 
+
+ align:start position:0%
+they run out of stuff
+so you go and take your shillings and
+
+ align:start position:0%
+so you go and take your shillings and
+ 
+
+ align:start position:0%
+so you go and take your shillings and
+say i won and pessa and you know they
+
+ align:start position:0%
+say i won and pessa and you know they
+ 
+
+ align:start position:0%
+say i won and pessa and you know they
+can't create it there's no net creation
+
+ align:start position:0%
+can't create it there's no net creation
+ 
+
+ align:start position:0%
+can't create it there's no net creation
+it has to be a one-to-one transfer they
+
+ align:start position:0%
+it has to be a one-to-one transfer they
+ 
+
+ align:start position:0%
+it has to be a one-to-one transfer they
+have to have it in their account already
+
+ align:start position:0%
+have to have it in their account already
+ 
+
+ align:start position:0%
+have to have it in their account already
+and if they don't have in the account
+
+ align:start position:0%
+and if they don't have in the account
+ 
+
+ align:start position:0%
+and if they don't have in the account
+they got to say well wait or come back
+
+ align:start position:0%
+they got to say well wait or come back
+ 
+
+ align:start position:0%
+they got to say well wait or come back
+tomorrow likewise and perhaps more
+
+ align:start position:0%
+tomorrow likewise and perhaps more
+ 
+
+ align:start position:0%
+tomorrow likewise and perhaps more
+obviously for the currency withdrawal
+
+ align:start position:0%
+obviously for the currency withdrawal
+ 
+
+ align:start position:0%
+obviously for the currency withdrawal
+say here my here's my cell account i
+
+ align:start position:0%
+say here my here's my cell account i
+ 
+
+ align:start position:0%
+say here my here's my cell account i
+want to cash it out well i don't have
+
+ align:start position:0%
+want to cash it out well i don't have
+ 
+
+ align:start position:0%
+want to cash it out well i don't have
+that cash in my drawer you know tommy
+
+ align:start position:0%
+that cash in my drawer you know tommy
+ 
+
+ align:start position:0%
+that cash in my drawer you know tommy
+discovered is these agents are kind of
+
+ align:start position:0%
+discovered is these agents are kind of
+ 
+
+ align:start position:0%
+discovered is these agents are kind of
+linked to each other in an informal
+
+ align:start position:0%
+linked to each other in an informal
+ 
+
+ align:start position:0%
+linked to each other in an informal
+money market giving gifts to each other
+
+ align:start position:0%
+money market giving gifts to each other
+ 
+
+ align:start position:0%
+money market giving gifts to each other
+actually and borrowing and lending in
+
+ align:start position:0%
+actually and borrowing and lending in
+ 
+
+ align:start position:0%
+actually and borrowing and lending in
+order to smooth the fluctuation from
+
+ align:start position:0%
+order to smooth the fluctuation from
+ 
+
+ align:start position:0%
+order to smooth the fluctuation from
+smoothing at the household level to
+
+ align:start position:0%
+smoothing at the household level to
+ 
+
+ align:start position:0%
+smoothing at the household level to
+smoothing at the wholesale level and
+
+ align:start position:0%
+smoothing at the wholesale level and
+ 
+
+ align:start position:0%
+smoothing at the wholesale level and
+similar models would apply
+
+ align:start position:0%
+similar models would apply
+ 
+
+ align:start position:0%
+similar models would apply
+so so this brings us to the theme of
+
+ align:start position:0%
+so so this brings us to the theme of
+ 
+
+ align:start position:0%
+so so this brings us to the theme of
+building financial infrastructure
+
+ align:start position:0%
+building financial infrastructure
+ 
+
+ align:start position:0%
+building financial infrastructure
+how can we not just get currency on
+
+ align:start position:0%
+how can we not just get currency on
+ 
+
+ align:start position:0%
+how can we not just get currency on
+ledgers and transfer it around in a
+
+ align:start position:0%
+ledgers and transfer it around in a
+ 
+
+ align:start position:0%
+ledgers and transfer it around in a
+cheap way
+
+ align:start position:0%
+cheap way
+ 
+
+ align:start position:0%
+cheap way
+how can we build in the trust and how
+
+ align:start position:0%
+how can we build in the trust and how
+ 
+
+ align:start position:0%
+how can we build in the trust and how
+can we you know deal with this shortage
+
+ align:start position:0%
+can we you know deal with this shortage
+ 
+
+ align:start position:0%
+can we you know deal with this shortage
+problem among over-the-counter vendors
+
+ align:start position:0%
+problem among over-the-counter vendors
+ 
+
+ align:start position:0%
+problem among over-the-counter vendors
+and agents and so on and next lecture
+
+ align:start position:0%
+and agents and so on and next lecture
+ 
+
+ align:start position:0%
+and agents and so on and next lecture
+starting next time we're going to do
+
+ align:start position:0%
+starting next time we're going to do
+ 
+
+ align:start position:0%
+starting next time we're going to do
+mechanism design and private information
+
+ align:start position:0%
+mechanism design and private information
+ 
+
+ align:start position:0%
+mechanism design and private information
+and i'll tell you how to design at some
+
+ align:start position:0%
+and i'll tell you how to design at some
+ 
+
+ align:start position:0%
+and i'll tell you how to design at some
+point how to design this system
+
+ align:start position:0%
+point how to design this system
+ 
+
+ align:start position:0%
+point how to design this system
+all right went over by an extra minute
+
+ align:start position:0%
+all right went over by an extra minute
+ 
+
+ align:start position:0%
+all right went over by an extra minute
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so otherwise i'll see you next thursday
+
+ align:start position:0%
+so otherwise i'll see you next thursday
+ 
+
+ align:start position:0%
+so otherwise i'll see you next thursday
+or in my office momentarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/60vaGH3ULEU.txt b/60vaGH3ULEU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9dc00b359ad2126f9a0f9b787e9e388c63505187
--- /dev/null
+++ b/60vaGH3ULEU.txt
@@ -0,0 +1,5163 @@
+align:start position:0%
+ 
+the economics of demand and Supply if it
+
+ align:start position:0%
+the economics of demand and Supply if it
+ 
+
+ align:start position:0%
+the economics of demand and Supply if it
+was that easy everybody would be doing
+
+ align:start position:0%
+was that easy everybody would be doing
+ 
+
+ align:start position:0%
+was that easy everybody would be doing
+it it needs education it needs passion
+
+ align:start position:0%
+it it needs education it needs passion
+ 
+
+ align:start position:0%
+it it needs education it needs passion
+it needs commitment not just motivation
+
+ align:start position:0%
+it needs commitment not just motivation
+ 
+
+ align:start position:0%
+it needs commitment not just motivation
+you know you need to be motivated
+
+ align:start position:0%
+you know you need to be motivated
+ 
+
+ align:start position:0%
+you know you need to be motivated
+internally you need to be curious about
+
+ align:start position:0%
+internally you need to be curious about
+ 
+
+ align:start position:0%
+internally you need to be curious about
+the thing that you're learning if you're
+
+ align:start position:0%
+the thing that you're learning if you're
+ 
+
+ align:start position:0%
+the thing that you're learning if you're
+doing it just to get rich you're going
+
+ align:start position:0%
+doing it just to get rich you're going
+ 
+
+ align:start position:0%
+doing it just to get rich you're going
+to get way bored way before you know you
+
+ align:start position:0%
+to get way bored way before you know you
+ 
+
+ align:start position:0%
+to get way bored way before you know you
+ever actually get the opportunity to get
+
+ align:start position:0%
+ever actually get the opportunity to get
+ 
+
+ align:start position:0%
+ever actually get the opportunity to get
+your first
+
+ align:start position:0%
+your first
+ 
+
+ align:start position:0%
+your first
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+paycheck welcome to open liners a
+
+ align:start position:0%
+paycheck welcome to open liners a
+ 
+
+ align:start position:0%
+paycheck welcome to open liners a
+podcast that tells the story of Learners
+
+ align:start position:0%
+podcast that tells the story of Learners
+ 
+
+ align:start position:0%
+podcast that tells the story of Learners
+all over the world who use mit's open
+
+ align:start position:0%
+all over the world who use mit's open
+ 
+
+ align:start position:0%
+all over the world who use mit's open
+courseware I'm Emanuel Li kasigi an open
+
+ align:start position:0%
+courseware I'm Emanuel Li kasigi an open
+ 
+
+ align:start position:0%
+courseware I'm Emanuel Li kasigi an open
+learner myself from campella Uganda in
+
+ align:start position:0%
+learner myself from campella Uganda in
+ 
+
+ align:start position:0%
+learner myself from campella Uganda in
+East Africa and I'm Michael Jordan
+
+ align:start position:0%
+East Africa and I'm Michael Jordan
+ 
+
+ align:start position:0%
+East Africa and I'm Michael Jordan
+Pilgreen an open learner from Memphis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tennessee hey Emanuel hi Michael it's
+
+ align:start position:0%
+Tennessee hey Emanuel hi Michael it's
+ 
+
+ align:start position:0%
+Tennessee hey Emanuel hi Michael it's
+good to be back this is our third
+
+ align:start position:0%
+good to be back this is our third
+ 
+
+ align:start position:0%
+good to be back this is our third
+episode I'm very excited Emanuel you
+
+ align:start position:0%
+episode I'm very excited Emanuel you
+ 
+
+ align:start position:0%
+episode I'm very excited Emanuel you
+know today's learner is Nadar alawi
+
+ align:start position:0%
+know today's learner is Nadar alawi
+ 
+
+ align:start position:0%
+know today's learner is Nadar alawi
+Nadar is from Jordan and is currently
+
+ align:start position:0%
+Nadar is from Jordan and is currently
+ 
+
+ align:start position:0%
+Nadar is from Jordan and is currently
+living in
+
+ align:start position:0%
+living in
+ 
+
+ align:start position:0%
+living in
+oh nice and Michael Nadar is actually
+
+ align:start position:0%
+oh nice and Michael Nadar is actually
+ 
+
+ align:start position:0%
+oh nice and Michael Nadar is actually
+someone you've had the opportunity to
+
+ align:start position:0%
+someone you've had the opportunity to
+ 
+
+ align:start position:0%
+someone you've had the opportunity to
+work with outside of ocw can you tell us
+
+ align:start position:0%
+work with outside of ocw can you tell us
+ 
+
+ align:start position:0%
+work with outside of ocw can you tell us
+more about that sure I met Nadar through
+
+ align:start position:0%
+more about that sure I met Nadar through
+ 
+
+ align:start position:0%
+more about that sure I met Nadar through
+the micr Masters and finance program and
+
+ align:start position:0%
+the micr Masters and finance program and
+ 
+
+ align:start position:0%
+the micr Masters and finance program and
+I stayed in touch with him throughout
+
+ align:start position:0%
+I stayed in touch with him throughout
+ 
+
+ align:start position:0%
+I stayed in touch with him throughout
+that process once he graduated undergrad
+
+ align:start position:0%
+that process once he graduated undergrad
+ 
+
+ align:start position:0%
+that process once he graduated undergrad
+I knew we needed someone with his
+
+ align:start position:0%
+I knew we needed someone with his
+ 
+
+ align:start position:0%
+I knew we needed someone with his
+quantitative skills at Bon click so I
+
+ align:start position:0%
+quantitative skills at Bon click so I
+ 
+
+ align:start position:0%
+quantitative skills at Bon click so I
+recruited him to come work for me at Bon
+
+ align:start position:0%
+recruited him to come work for me at Bon
+ 
+
+ align:start position:0%
+recruited him to come work for me at Bon
+click amazing amazing uh cuz one of the
+
+ align:start position:0%
+click amazing amazing uh cuz one of the
+ 
+
+ align:start position:0%
+click amazing amazing uh cuz one of the
+reasons we wanted to start this podcast
+
+ align:start position:0%
+reasons we wanted to start this podcast
+ 
+
+ align:start position:0%
+reasons we wanted to start this podcast
+was to Showcase that ocw has the
+
+ align:start position:0%
+was to Showcase that ocw has the
+ 
+
+ align:start position:0%
+was to Showcase that ocw has the
+potential to be more than just an online
+
+ align:start position:0%
+potential to be more than just an online
+ 
+
+ align:start position:0%
+potential to be more than just an online
+learning platform it is a tool to build
+
+ align:start position:0%
+learning platform it is a tool to build
+ 
+
+ align:start position:0%
+learning platform it is a tool to build
+Global communities and Nadal story is a
+
+ align:start position:0%
+Global communities and Nadal story is a
+ 
+
+ align:start position:0%
+Global communities and Nadal story is a
+perfect example to include in our first
+
+ align:start position:0%
+perfect example to include in our first
+ 
+
+ align:start position:0%
+perfect example to include in our first
+season because it does exactly that
+
+ align:start position:0%
+season because it does exactly that
+ 
+
+ align:start position:0%
+season because it does exactly that
+exactly I think the power of the
+
+ align:start position:0%
+exactly I think the power of the
+ 
+
+ align:start position:0%
+exactly I think the power of the
+internet and MIT open courseware is that
+
+ align:start position:0%
+internet and MIT open courseware is that
+ 
+
+ align:start position:0%
+internet and MIT open courseware is that
+superpower of networking to connect with
+
+ align:start position:0%
+superpower of networking to connect with
+ 
+
+ align:start position:0%
+superpower of networking to connect with
+people all over the world unlike you and
+
+ align:start position:0%
+people all over the world unlike you and
+ 
+
+ align:start position:0%
+people all over the world unlike you and
+before you getting his current
+
+ align:start position:0%
+before you getting his current
+ 
+
+ align:start position:0%
+before you getting his current
+internship Nadar was already following a
+
+ align:start position:0%
+internship Nadar was already following a
+ 
+
+ align:start position:0%
+internship Nadar was already following a
+really inspiring path he's been
+
+ align:start position:0%
+really inspiring path he's been
+ 
+
+ align:start position:0%
+really inspiring path he's been
+passionate about Finance since he was a
+
+ align:start position:0%
+passionate about Finance since he was a
+ 
+
+ align:start position:0%
+passionate about Finance since he was a
+teenager but some life circumstances
+
+ align:start position:0%
+teenager but some life circumstances
+ 
+
+ align:start position:0%
+teenager but some life circumstances
+prevented him from really diving into
+
+ align:start position:0%
+prevented him from really diving into
+ 
+
+ align:start position:0%
+prevented him from really diving into
+his studies before he discovered mit's
+
+ align:start position:0%
+his studies before he discovered mit's
+ 
+
+ align:start position:0%
+his studies before he discovered mit's
+open learning resources he started open
+
+ align:start position:0%
+open learning resources he started open
+ 
+
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+courseware in 2020 at home in Jordan
+ 
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+while he was struggling to B balance
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+ align:start position:0%
+while he was struggling to B balance
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+ align:start position:0%
+while he was struggling to B balance
+high school with 19 hour shifts at a
+
+ align:start position:0%
+high school with 19 hour shifts at a
+ 
+
+ align:start position:0%
+high school with 19 hour shifts at a
+Falafel restaurant that's dedication in
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+Falafel restaurant that's dedication in
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+Falafel restaurant that's dedication in
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+Learners Journey NAD has completed a
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+Learners Journey NAD has completed a
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+micro Masters in finance he has taken a
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+mean it's just amazing mitw and MIT
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+mean it's just amazing mitw and MIT
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+programs from MIT but they're quite
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+programs from MIT but they're quite
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+different and complimentary to each
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+
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+different and complimentary to each
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+other so with ocwa a learner has access
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+
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+other so with ocwa a learner has access
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+to materials from thousands and
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+you know then there you can take a
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+mitx micr Masters program to get that
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+mitx micr Masters program to get that
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+
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+mitx micr Masters program to get that
+credential that you're looking for yeah
+
+ align:start position:0%
+credential that you're looking for yeah
+ 
+
+ align:start position:0%
+credential that you're looking for yeah
+Nadar is super impressive I'll let Nadar
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+ align:start position:0%
+Nadar is super impressive I'll let Nadar
+ 
+
+ align:start position:0%
+Nadar is super impressive I'll let Nadar
+tell the rest of his story himself but I
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+tell the rest of his story himself but I
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+
+ align:start position:0%
+tell the rest of his story himself but I
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+different place from where he started so
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+
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+different place from where he started so
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+
+ align:start position:0%
+let's get into it here is our
+ 
+
+ align:start position:0%
+let's get into it here is our
+conversation with Nadar alwi from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jordan so I'm NAD I'm from Jordan I'm 23
+
+ align:start position:0%
+Jordan so I'm NAD I'm from Jordan I'm 23
+ 
+
+ align:start position:0%
+Jordan so I'm NAD I'm from Jordan I'm 23
+years old I started my education journey
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+years old I started my education journey
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+and passion for for my career which is
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+
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+and passion for for my career which is
+finance when I was about 15 I used to
+
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+finance when I was about 15 I used to
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+
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+finance when I was about 15 I used to
+watch you know like random Youtube
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+watch you know like random Youtube
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+
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+watch you know like random Youtube
+videos about Warren Buffett and how he
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+videos about Warren Buffett and how he
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+
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+videos about Warren Buffett and how he
+invests and and stuff like that and then
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+invests and and stuff like that and then
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+invests and and stuff like that and then
+when I was going through High School
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+when I was going through High School
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+when I was going through High School
+I just had a a bit of trouble finishing
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+I just had a a bit of trouble finishing
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+
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+I just had a a bit of trouble finishing
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+it due to you know circumstances at home
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+
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+it due to you know circumstances at home
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+and financial issues so I was actually
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+
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+and financial issues so I was actually
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+working a couple of uh you know
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+
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+working a couple of uh you know
+different jobs minimum W jobs Feld
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+different jobs minimum W jobs Feld
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+
+ align:start position:0%
+different jobs minimum W jobs Feld
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+restaurant you know stuff like that then
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+University and as soon as I got into
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+
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+University I started discovering the
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+
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+University I started discovering the
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+various platforms that MIT has to
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+
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+various platforms that MIT has to
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+endorse open and free education across
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+
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+endorse open and free education across
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+the globe so that would be in I think
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+
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+the globe so that would be in I think
+September of 2020 during the
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+September of 2020 during the
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+September of 2020 during the
+pandemic and I found first MIT on edex I
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+pandemic and I found first MIT on edex I
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+pandemic and I found first MIT on edex I
+found the micromasters program in
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+found the micromasters program in
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+finance and I found you know
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+
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+ocw MIT open course whereare and I
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+ocw MIT open course whereare and I
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+ocw MIT open course whereare and I
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+started building into very know a lot of
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+started building into very know a lot of
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+
+ align:start position:0%
+various topics calculus statistics
+ 
+
+ align:start position:0%
+various topics calculus statistics
+Finance the most special thing for me
+
+ align:start position:0%
+Finance the most special thing for me
+ 
+
+ align:start position:0%
+Finance the most special thing for me
+about um the MIT micromasters program
+
+ align:start position:0%
+about um the MIT micromasters program
+ 
+
+ align:start position:0%
+about um the MIT micromasters program
+and the community that MIT Fosters
+
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+and the community that MIT Fosters
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+
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+and the community that MIT Fosters
+online is that you get to meet um
+
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+online is that you get to meet um
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+
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+online is that you get to meet um
+students from all around the world um
+
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+students from all around the world um
+ 
+
+ align:start position:0%
+students from all around the world um
+who have the same passion as you who's
+
+ align:start position:0%
+who have the same passion as you who's
+ 
+
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+who have the same passion as you who's
+trying to learn the same essential skill
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+ align:start position:0%
+trying to learn the same essential skill
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+
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+trying to learn the same essential skill
+that you are trying to learn every week
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+that you are trying to learn every week
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+that you are trying to learn every week
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+I would you know meet someone we chat up
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+I would you know meet someone we chat up
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+online and you know my the friend list
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+
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+online and you know my the friend list
+that I made throughout that uh program
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+ align:start position:0%
+that I made throughout that uh program
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+
+ align:start position:0%
+that I made throughout that uh program
+continued to grow and I some of them I
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+continued to grow and I some of them I
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+met in person some of them I me to meet
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+met in person some of them I me to meet
+in person like you Mike and Emanuel and
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+in person like you Mike and Emanuel and
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+in person like you Mike and Emanuel and
+after I finished the program I became a
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+after I finished the program I became a
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+
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+after I finished the program I became a
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+teaching assistant and interacted more
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+
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+with a lot of the students at MIT
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+
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+Community teaching assistant for the
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+microm Masters
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+
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+microm Masters
+program and you know that's when
+
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+program and you know that's when
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+
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+program and you know that's when
+opportunities started coming in all
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+opportunities started coming in all
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+
+ align:start position:0%
+opportunities started coming in all
+right let me let me ask one question
+
+ align:start position:0%
+right let me let me ask one question
+ 
+
+ align:start position:0%
+right let me let me ask one question
+just to get us contextualized within
+
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+just to get us contextualized within
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+
+ align:start position:0%
+just to get us contextualized within
+your journey so you know you said you
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+your journey so you know you said you
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+
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+your journey so you know you said you
+started finding these resources around
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+started finding these resources around
+September
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+September
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+
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+September
+2020 that year during the pandemic where
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+2020 that year during the pandemic where
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+
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+2020 that year during the pandemic where
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+were you what were you thinking about
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+
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+what was your daily life like at that
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+
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+what was your daily life like at that
+point in time you know I would wake up
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+point in time you know I would wake up
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+
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+point in time you know I would wake up
+at like 5:00 a.m. go to my job in the
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+at like 5:00 a.m. go to my job in the
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+at like 5:00 a.m. go to my job in the
+fla restaurant at 6 and you know work
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+fla restaurant at 6 and you know work
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+fla restaurant at 6 and you know work
+for 9 10 hours a day and I was slowly
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+for 9 10 hours a day and I was slowly
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+for 9 10 hours a day and I was slowly
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+doing high school at the time and once I
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+finished I had a bit of free time I quit
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+finished I had a bit of free time I quit
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+finished I had a bit of free time I quit
+my job and I decided that I want to
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+my job and I decided that I want to
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+my job and I decided that I want to
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+focus on my education so I was free I
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+bachelor started in September around the
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+
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+same time that the or October around the
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+same time that the or October around the
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+same time that I started the microman
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+same time that I started the microman
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+program it felt advanced you know it's
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+
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+program it felt advanced you know it's
+graduate level and I didn't even enter
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+graduate level and I didn't even enter
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+graduate level and I didn't even enter
+my bachelor's and I had problems you
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+my bachelor's and I had problems you
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+my bachelor's and I had problems you
+know with my high school so I wasn't
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+know with my high school so I wasn't
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+
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+know with my high school so I wasn't
+confident that I would be able to finish
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+confident that I would be able to finish
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+
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+confident that I would be able to finish
+the program but thankfully you know
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+ align:start position:0%
+the program but thankfully you know
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+
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+the program but thankfully you know
+after 10 20 30 hours a week of studying
+
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+after 10 20 30 hours a week of studying
+ 
+
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+after 10 20 30 hours a week of studying
+for a
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+
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+for a
+mighty exams I I was lucky enough to
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+mighty exams I I was lucky enough to
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+mighty exams I I was lucky enough to
+finish the program and you know that you
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+finish the program and you know that you
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+
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+finish the program and you know that you
+know really helped me gain a lot of
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+know really helped me gain a lot of
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+
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+know really helped me gain a lot of
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+
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+abilities and it helped me you know in
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+my undergraduate studies and helped me
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+
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+my undergraduate studies and helped me
+in other you know Finance specific
+
+ align:start position:0%
+in other you know Finance specific
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+
+ align:start position:0%
+in other you know Finance specific
+programs such as CFA and the FM going
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+programs such as CFA and the FM going
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+
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+
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+tackling graduate level work is like no
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+tackling graduate level work is like no
+small fee if you feel comfortable
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+small fee if you feel comfortable
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+
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+small fee if you feel comfortable
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+
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+sharing what were some of the
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+obstacles or problems you were having
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+
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+
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+during your high school education that
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+
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+it definitely was and you know at the
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+time my confidence was you know as I
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+
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+time my confidence was you know as I
+said was too low and the biggest problem
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+said was too low and the biggest problem
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+
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+said was too low and the biggest problem
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+I had was was just a lot of it was you
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+
+ align:start position:0%
+I had was was just a lot of it was you
+know family issues uh my dad had lost
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+ align:start position:0%
+know family issues uh my dad had lost
+ 
+
+ align:start position:0%
+know family issues uh my dad had lost
+his business we had to sell our house
+
+ align:start position:0%
+his business we had to sell our house
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+
+ align:start position:0%
+his business we had to sell our house
+and find a new one he went bankrupt
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+ align:start position:0%
+and find a new one he went bankrupt
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+
+ align:start position:0%
+and find a new one he went bankrupt
+unfortunately and that just caused a lot
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+ align:start position:0%
+unfortunately and that just caused a lot
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+
+ align:start position:0%
+unfortunately and that just caused a lot
+of stress and sort of havoc in my
+
+ align:start position:0%
+of stress and sort of havoc in my
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+personal life so I became just a little
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+
+ align:start position:0%
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+bit isolated trying to you know work so
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+ align:start position:0%
+bit isolated trying to you know work so
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+ align:start position:0%
+I can be able to support myself and my
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+ align:start position:0%
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+
+ align:start position:0%
+family and I didn't have the mental
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
+you know like when when you put it in
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+
+ align:start position:0%
+you know like when when you put it in
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+ align:start position:0%
+the you know normal context of yeah like
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+the you know normal context of yeah like
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+ align:start position:0%
+this is high school this is you know you
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+
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+this is high school this is you know you
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+
+ align:start position:0%
+got to finish this you know topics and
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+
+ align:start position:0%
+got to finish this you know topics and
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+ align:start position:0%
+pass those courses it was pretty boring
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+
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+you know I wasn't interested in it
+
+ align:start position:0%
+you know I wasn't interested in it
+ 
+
+ align:start position:0%
+you know I wasn't interested in it
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+
+ align:start position:0%
+really but when I started studying for
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+
+ align:start position:0%
+really but when I started studying for
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+
+ align:start position:0%
+MIT you know it seemed like this out of
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+
+ align:start position:0%
+MIT you know it seemed like this out of
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+ align:start position:0%
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+ align:start position:0%
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+happened September 2020 with the
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+ align:start position:0%
+happened September 2020 with the
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+ align:start position:0%
+happened September 2020 with the
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+
+ align:start position:0%
+lockdown I would like to touch a bit
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+is how are you as a human being and your
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+ align:start position:0%
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+know playing games
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+ align:start position:0%
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+
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+finishing that program and uh because of
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+once once you finish you know a quiz or
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+
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+ align:start position:0%
+you know translate into other aspects of
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+
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+you know translate into other aspects of
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+ align:start position:0%
+your life did it Inspire others in your
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+
+ align:start position:0%
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+Clos Circle did you even talk about it
+
+ align:start position:0%
+Clos Circle did you even talk about it
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+
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+ align:start position:0%
+with people in your closed Circle or was
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+
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+with people in your closed Circle or was
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+
+ align:start position:0%
+it more just a online thing oh yeah now
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+
+ align:start position:0%
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+
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+
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+
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+it that there was a lot of people um
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+
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+
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+
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+
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+
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+
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+
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
+country that that is you know not doing
+great economically I had access to the
+
+ align:start position:0%
+great economically I had access to the
+ 
+
+ align:start position:0%
+great economically I had access to the
+best education in the whole world and
+
+ align:start position:0%
+best education in the whole world and
+ 
+
+ align:start position:0%
+best education in the whole world and
+that education that I got manifested in
+
+ align:start position:0%
+that education that I got manifested in
+ 
+
+ align:start position:0%
+that education that I got manifested in
+me getting jobs and and working remotely
+
+ align:start position:0%
+me getting jobs and and working remotely
+ 
+
+ align:start position:0%
+me getting jobs and and working remotely
+with with companies in New York or
+
+ align:start position:0%
+with with companies in New York or
+ 
+
+ align:start position:0%
+with with companies in New York or
+Arizona or in Jordan or in Dubai um so
+
+ align:start position:0%
+Arizona or in Jordan or in Dubai um so
+ 
+
+ align:start position:0%
+Arizona or in Jordan or in Dubai um so
+now we're in a much more Global
+
+ align:start position:0%
+now we're in a much more Global
+ 
+
+ align:start position:0%
+now we're in a much more Global
+atmosphere where after also Co happened
+
+ align:start position:0%
+atmosphere where after also Co happened
+ 
+
+ align:start position:0%
+atmosphere where after also Co happened
+and work started being remote and you
+
+ align:start position:0%
+and work started being remote and you
+ 
+
+ align:start position:0%
+and work started being remote and you
+know people started being more
+
+ align:start position:0%
+know people started being more
+ 
+
+ align:start position:0%
+know people started being more
+collaborative online um so I think you
+
+ align:start position:0%
+collaborative online um so I think you
+ 
+
+ align:start position:0%
+collaborative online um so I think you
+know anyone with with a phone and
+
+ align:start position:0%
+know anyone with with a phone and
+ 
+
+ align:start position:0%
+know anyone with with a phone and
+internet connection and a passion now
+
+ align:start position:0%
+internet connection and a passion now
+ 
+
+ align:start position:0%
+internet connection and a passion now
+can can you know just pick up the
+
+ align:start position:0%
+can can you know just pick up the
+ 
+
+ align:start position:0%
+can can you know just pick up the
+resources that MIT has and the plenty of
+
+ align:start position:0%
+resources that MIT has and the plenty of
+ 
+
+ align:start position:0%
+resources that MIT has and the plenty of
+available online education in general
+
+ align:start position:0%
+available online education in general
+ 
+
+ align:start position:0%
+available online education in general
+resources that are free on the internet
+
+ align:start position:0%
+resources that are free on the internet
+ 
+
+ align:start position:0%
+resources that are free on the internet
+and you know learn any scale you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want you mentioned Finance alot do you
+
+ align:start position:0%
+want you mentioned Finance alot do you
+ 
+
+ align:start position:0%
+want you mentioned Finance alot do you
+you have a love for finance like
+
+ align:start position:0%
+you have a love for finance like
+ 
+
+ align:start position:0%
+you have a love for finance like
+naturally or it's just something you
+
+ align:start position:0%
+naturally or it's just something you
+ 
+
+ align:start position:0%
+naturally or it's just something you
+know it's where the money is it's what
+
+ align:start position:0%
+know it's where the money is it's what
+ 
+
+ align:start position:0%
+know it's where the money is it's what
+I'm going to do it's definitely where
+
+ align:start position:0%
+I'm going to do it's definitely where
+ 
+
+ align:start position:0%
+I'm going to do it's definitely where
+the money is yeah um but my passion for
+
+ align:start position:0%
+the money is yeah um but my passion for
+ 
+
+ align:start position:0%
+the money is yeah um but my passion for
+finance started when I was 15 I was I
+
+ align:start position:0%
+finance started when I was 15 I was I
+ 
+
+ align:start position:0%
+finance started when I was 15 I was I
+was just like always curious
+
+ align:start position:0%
+was just like always curious
+ 
+
+ align:start position:0%
+was just like always curious
+about how um you know financial markets
+
+ align:start position:0%
+about how um you know financial markets
+ 
+
+ align:start position:0%
+about how um you know financial markets
+function how the global economy can
+
+ align:start position:0%
+function how the global economy can
+ 
+
+ align:start position:0%
+function how the global economy can
+function you know when when I was six or
+
+ align:start position:0%
+function you know when when I was six or
+ 
+
+ align:start position:0%
+function you know when when I was six or
+whatever I whenever I would get like a
+
+ align:start position:0%
+whatever I whenever I would get like a
+ 
+
+ align:start position:0%
+whatever I whenever I would get like a
+huge bag of sh ships I would sell it to
+
+ align:start position:0%
+huge bag of sh ships I would sell it to
+ 
+
+ align:start position:0%
+huge bag of sh ships I would sell it to
+my friends um it's school or siblings I
+
+ align:start position:0%
+my friends um it's school or siblings I
+ 
+
+ align:start position:0%
+my friends um it's school or siblings I
+was always just interested in you know
+
+ align:start position:0%
+was always just interested in you know
+ 
+
+ align:start position:0%
+was always just interested in you know
+business in general especially finance
+
+ align:start position:0%
+business in general especially finance
+ 
+
+ align:start position:0%
+business in general especially finance
+and learning about the global economy
+
+ align:start position:0%
+and learning about the global economy
+ 
+
+ align:start position:0%
+and learning about the global economy
+yeah that's a nice one I I was like that
+
+ align:start position:0%
+yeah that's a nice one I I was like that
+ 
+
+ align:start position:0%
+yeah that's a nice one I I was like that
+too I also used to sell sweets to my
+
+ align:start position:0%
+too I also used to sell sweets to my
+ 
+
+ align:start position:0%
+too I also used to sell sweets to my
+classmates
+
+ align:start position:0%
+classmates
+ 
+
+ align:start position:0%
+classmates
+yeah so I understand so you are
+
+ align:start position:0%
+yeah so I understand so you are
+ 
+
+ align:start position:0%
+yeah so I understand so you are
+specifically looking for finance things
+
+ align:start position:0%
+specifically looking for finance things
+ 
+
+ align:start position:0%
+specifically looking for finance things
+when you founded ocw yep and ever since
+
+ align:start position:0%
+when you founded ocw yep and ever since
+ 
+
+ align:start position:0%
+when you founded ocw yep and ever since
+then have you taken anything out of your
+
+ align:start position:0%
+then have you taken anything out of your
+ 
+
+ align:start position:0%
+then have you taken anything out of your
+circles maybe something outside Finance
+
+ align:start position:0%
+circles maybe something outside Finance
+ 
+
+ align:start position:0%
+circles maybe something outside Finance
+yeah definitely um I did a lot of
+
+ align:start position:0%
+yeah definitely um I did a lot of
+ 
+
+ align:start position:0%
+yeah definitely um I did a lot of
+calculus I did a lot of probability and
+
+ align:start position:0%
+calculus I did a lot of probability and
+ 
+
+ align:start position:0%
+calculus I did a lot of probability and
+statistics programming Python and just
+
+ align:start position:0%
+statistics programming Python and just
+ 
+
+ align:start position:0%
+statistics programming Python and just
+other skills so because I want to become
+
+ align:start position:0%
+other skills so because I want to become
+ 
+
+ align:start position:0%
+other skills so because I want to become
+like a Quant I had to learn everything
+
+ align:start position:0%
+like a Quant I had to learn everything
+ 
+
+ align:start position:0%
+like a Quant I had to learn everything
+about technology learn everything about
+
+ align:start position:0%
+about technology learn everything about
+ 
+
+ align:start position:0%
+about technology learn everything about
+finance and sort of mix them together
+
+ align:start position:0%
+finance and sort of mix them together
+ 
+
+ align:start position:0%
+finance and sort of mix them together
+and MIT was the perfect place to do that
+
+ align:start position:0%
+and MIT was the perfect place to do that
+ 
+
+ align:start position:0%
+and MIT was the perfect place to do that
+because no other university in my
+
+ align:start position:0%
+because no other university in my
+ 
+
+ align:start position:0%
+because no other university in my
+country had you know that kind of wide
+
+ align:start position:0%
+country had you know that kind of wide
+ 
+
+ align:start position:0%
+country had you know that kind of wide
+range of you know offerings where you
+
+ align:start position:0%
+range of you know offerings where you
+ 
+
+ align:start position:0%
+range of you know offerings where you
+can choose in one degree for the all the
+
+ align:start position:0%
+can choose in one degree for the all the
+ 
+
+ align:start position:0%
+can choose in one degree for the all the
+assistant topics that I wanted to study
+
+ align:start position:0%
+assistant topics that I wanted to study
+ 
+
+ align:start position:0%
+assistant topics that I wanted to study
+nice so of all the things you've studed
+
+ align:start position:0%
+nice so of all the things you've studed
+ 
+
+ align:start position:0%
+nice so of all the things you've studed
+I know I personally have studed a lot I
+
+ align:start position:0%
+I know I personally have studed a lot I
+ 
+
+ align:start position:0%
+I know I personally have studed a lot I
+would take the most impactful for me I
+
+ align:start position:0%
+would take the most impactful for me I
+ 
+
+ align:start position:0%
+would take the most impactful for me I
+think were the AI lectures I've watched
+
+ align:start position:0%
+think were the AI lectures I've watched
+ 
+
+ align:start position:0%
+think were the AI lectures I've watched
+why would you say first of all was the
+
+ align:start position:0%
+why would you say first of all was the
+ 
+
+ align:start position:0%
+why would you say first of all was the
+most impactful and then the one that
+
+ align:start position:0%
+most impactful and then the one that
+ 
+
+ align:start position:0%
+most impactful and then the one that
+kind of had the most impact in the real
+
+ align:start position:0%
+kind of had the most impact in the real
+ 
+
+ align:start position:0%
+kind of had the most impact in the real
+life like when I took this course called
+
+ align:start position:0%
+life like when I took this course called
+ 
+
+ align:start position:0%
+life like when I took this course called
+disqualification is when I like went
+
+ align:start position:0%
+disqualification is when I like went
+ 
+
+ align:start position:0%
+disqualification is when I like went
+down the path I'm on now I think the
+
+ align:start position:0%
+down the path I'm on now I think the
+ 
+
+ align:start position:0%
+down the path I'm on now I think the
+course is named modern Financial Theory
+
+ align:start position:0%
+course is named modern Financial Theory
+ 
+
+ align:start position:0%
+course is named modern Financial Theory
+by uh Professor Andrew l i enrolled in
+
+ align:start position:0%
+by uh Professor Andrew l i enrolled in
+ 
+
+ align:start position:0%
+by uh Professor Andrew l i enrolled in
+the micromanage program but just before
+
+ align:start position:0%
+the micromanage program but just before
+ 
+
+ align:start position:0%
+the micromanage program but just before
+it had started I thought I would prepare
+
+ align:start position:0%
+it had started I thought I would prepare
+ 
+
+ align:start position:0%
+it had started I thought I would prepare
+myself with that course during that
+
+ align:start position:0%
+myself with that course during that
+ 
+
+ align:start position:0%
+myself with that course during that
+course during the time that they were
+
+ align:start position:0%
+course during the time that they were
+ 
+
+ align:start position:0%
+course during the time that they were
+fing those lectures the big financial
+
+ align:start position:0%
+fing those lectures the big financial
+ 
+
+ align:start position:0%
+fing those lectures the big financial
+crisis was happening in real time so
+
+ align:start position:0%
+crisis was happening in real time so
+ 
+
+ align:start position:0%
+crisis was happening in real time so
+we'd see a lot of you know meaningful
+
+ align:start position:0%
+we'd see a lot of you know meaningful
+ 
+
+ align:start position:0%
+we'd see a lot of you know meaningful
+interactions from the the MBA students
+
+ align:start position:0%
+interactions from the the MBA students
+ 
+
+ align:start position:0%
+interactions from the the MBA students
+that were taking the course and
+
+ align:start position:0%
+that were taking the course and
+ 
+
+ align:start position:0%
+that were taking the course and
+Professor Andrew Lou and all of the
+
+ align:start position:0%
+Professor Andrew Lou and all of the
+ 
+
+ align:start position:0%
+Professor Andrew Lou and all of the
+specific questions they would ask during
+
+ align:start position:0%
+specific questions they would ask during
+ 
+
+ align:start position:0%
+specific questions they would ask during
+that period it was such a coincidence
+
+ align:start position:0%
+that period it was such a coincidence
+ 
+
+ align:start position:0%
+that period it was such a coincidence
+very you know maybe happy or lucky
+
+ align:start position:0%
+very you know maybe happy or lucky
+ 
+
+ align:start position:0%
+very you know maybe happy or lucky
+coincidence that they started following
+
+ align:start position:0%
+coincidence that they started following
+ 
+
+ align:start position:0%
+coincidence that they started following
+the course just when the financial
+
+ align:start position:0%
+the course just when the financial
+ 
+
+ align:start position:0%
+the course just when the financial
+crisis was happening so how did you how
+
+ align:start position:0%
+crisis was happening so how did you how
+ 
+
+ align:start position:0%
+crisis was happening so how did you how
+did you end up in the finance internship
+
+ align:start position:0%
+did you end up in the finance internship
+ 
+
+ align:start position:0%
+did you end up in the finance internship
+so the first job I got as a quantitative
+
+ align:start position:0%
+so the first job I got as a quantitative
+ 
+
+ align:start position:0%
+so the first job I got as a quantitative
+analyst was with a startup in Jordan and
+
+ align:start position:0%
+analyst was with a startup in Jordan and
+ 
+
+ align:start position:0%
+analyst was with a startup in Jordan and
+it was actually in my second year of
+
+ align:start position:0%
+it was actually in my second year of
+ 
+
+ align:start position:0%
+it was actually in my second year of
+Bachelors just when I finished the MIT
+
+ align:start position:0%
+Bachelors just when I finished the MIT
+ 
+
+ align:start position:0%
+Bachelors just when I finished the MIT
+program and after a bit of time of being
+
+ align:start position:0%
+program and after a bit of time of being
+ 
+
+ align:start position:0%
+program and after a bit of time of being
+a community teaching assistant I worked
+
+ align:start position:0%
+a community teaching assistant I worked
+ 
+
+ align:start position:0%
+a community teaching assistant I worked
+with them for around six months you know
+
+ align:start position:0%
+with them for around six months you know
+ 
+
+ align:start position:0%
+with them for around six months you know
+building models for crypto trading and
+
+ align:start position:0%
+building models for crypto trading and
+ 
+
+ align:start position:0%
+building models for crypto trading and
+after that I I met Mike and he
+
+ align:start position:0%
+after that I I met Mike and he
+ 
+
+ align:start position:0%
+after that I I met Mike and he
+introduced me to an opportunity
+
+ align:start position:0%
+introduced me to an opportunity
+ 
+
+ align:start position:0%
+introduced me to an opportunity
+uh with with a company you know that
+
+ align:start position:0%
+uh with with a company you know that
+ 
+
+ align:start position:0%
+uh with with a company you know that
+works in in New York and on Wall Street
+
+ align:start position:0%
+works in in New York and on Wall Street
+ 
+
+ align:start position:0%
+works in in New York and on Wall Street
+and in the bond
+
+ align:start position:0%
+and in the bond
+ 
+
+ align:start position:0%
+and in the bond
+market and you know it took a couple of
+
+ align:start position:0%
+market and you know it took a couple of
+ 
+
+ align:start position:0%
+market and you know it took a couple of
+months of preparation and courses and
+
+ align:start position:0%
+months of preparation and courses and
+ 
+
+ align:start position:0%
+months of preparation and courses and
+education uh that that Mike suggested
+
+ align:start position:0%
+education uh that that Mike suggested
+ 
+
+ align:start position:0%
+education uh that that Mike suggested
+and after I finished those that's how I
+
+ align:start position:0%
+and after I finished those that's how I
+ 
+
+ align:start position:0%
+and after I finished those that's how I
+landed my current
+
+ align:start position:0%
+landed my current
+ 
+
+ align:start position:0%
+landed my current
+internship yeah and that that was that
+
+ align:start position:0%
+internship yeah and that that was that
+ 
+
+ align:start position:0%
+internship yeah and that that was that
+was a lot Kinder than the actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Journey so so you ended up graduating
+
+ align:start position:0%
+Journey so so you ended up graduating
+ 
+
+ align:start position:0%
+Journey so so you ended up graduating
+during that time from your undergrad and
+
+ align:start position:0%
+during that time from your undergrad and
+ 
+
+ align:start position:0%
+during that time from your undergrad and
+you know so my previous role was at a
+
+ align:start position:0%
+you know so my previous role was at a
+ 
+
+ align:start position:0%
+you know so my previous role was at a
+financial technology startup primarily
+
+ align:start position:0%
+financial technology startup primarily
+ 
+
+ align:start position:0%
+financial technology startup primarily
+focused on you know consolidating
+
+ align:start position:0%
+focused on you know consolidating
+ 
+
+ align:start position:0%
+focused on you know consolidating
+corporate bond information uh Nadar had
+
+ align:start position:0%
+corporate bond information uh Nadar had
+ 
+
+ align:start position:0%
+corporate bond information uh Nadar had
+been a standout student and teacher
+
+ align:start position:0%
+been a standout student and teacher
+ 
+
+ align:start position:0%
+been a standout student and teacher
+associate is that what they called it
+
+ align:start position:0%
+associate is that what they called it
+ 
+
+ align:start position:0%
+associate is that what they called it
+teaching assistant yeah teaching
+
+ align:start position:0%
+teaching assistant yeah teaching
+ 
+
+ align:start position:0%
+teaching assistant yeah teaching
+assistant teaching assistant and the
+
+ align:start position:0%
+assistant teaching assistant and the
+ 
+
+ align:start position:0%
+assistant teaching assistant and the
+microm Masters program we both started I
+
+ align:start position:0%
+microm Masters program we both started I
+ 
+
+ align:start position:0%
+microm Masters program we both started I
+think at the same time both September
+
+ align:start position:0%
+think at the same time both September
+ 
+
+ align:start position:0%
+think at the same time both September
+2020 so we were the same cohort of
+
+ align:start position:0%
+2020 so we were the same cohort of
+ 
+
+ align:start position:0%
+2020 so we were the same cohort of
+microm
+
+ align:start position:0%
+microm
+ 
+
+ align:start position:0%
+microm
+students and um as some of you may know
+
+ align:start position:0%
+students and um as some of you may know
+ 
+
+ align:start position:0%
+students and um as some of you may know
+I that's when I got my job at uh the
+
+ align:start position:0%
+I that's when I got my job at uh the
+ 
+
+ align:start position:0%
+I that's when I got my job at uh the
+financial technology
+
+ align:start position:0%
+financial technology
+ 
+
+ align:start position:0%
+financial technology
+startup so my cours workk sort of fell
+
+ align:start position:0%
+startup so my cours workk sort of fell
+ 
+
+ align:start position:0%
+startup so my cours workk sort of fell
+off because it became real life work for
+
+ align:start position:0%
+off because it became real life work for
+ 
+
+ align:start position:0%
+off because it became real life work for
+me you know I didn't end up passing a
+
+ align:start position:0%
+me you know I didn't end up passing a
+ 
+
+ align:start position:0%
+me you know I didn't end up passing a
+single course I don't think in that micr
+
+ align:start position:0%
+single course I don't think in that micr
+ 
+
+ align:start position:0%
+single course I don't think in that micr
+Masters meanwhile Nadar had been killing
+
+ align:start position:0%
+Masters meanwhile Nadar had been killing
+ 
+
+ align:start position:0%
+Masters meanwhile Nadar had been killing
+every single one uh
+
+ align:start position:0%
+every single one uh
+ 
+
+ align:start position:0%
+every single one uh
+you know we would touch face every 3
+
+ align:start position:0%
+you know we would touch face every 3
+ 
+
+ align:start position:0%
+you know we would touch face every 3
+months for a little while there and then
+
+ align:start position:0%
+months for a little while there and then
+ 
+
+ align:start position:0%
+months for a little while there and then
+once he graduated that was kind of when
+
+ align:start position:0%
+once he graduated that was kind of when
+ 
+
+ align:start position:0%
+once he graduated that was kind of when
+the program really opened up for him
+
+ align:start position:0%
+the program really opened up for him
+ 
+
+ align:start position:0%
+the program really opened up for him
+when he started working for us and
+
+ align:start position:0%
+when he started working for us and
+ 
+
+ align:start position:0%
+when he started working for us and
+solving some of these hard problems nice
+
+ align:start position:0%
+solving some of these hard problems nice
+ 
+
+ align:start position:0%
+solving some of these hard problems nice
+ad you mentioned something about people
+
+ align:start position:0%
+ad you mentioned something about people
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+around the world and for you you have an
+ 
+
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+
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+ 
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+
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+
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+
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+
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+met all these great people you've gotten
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+
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+met all these great people you've gotten
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+
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+part of it you're in Dubai but I want
+ 
+
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+
+ align:start position:0%
+you to use your own words and paint for
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+
+ align:start position:0%
+you to use your own words and paint for
+us your life after ocw a huge portion of
+
+ align:start position:0%
+us your life after ocw a huge portion of
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+
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+ align:start position:0%
+my life is is owed to ocw as well I did
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+a lot of programs not just the microm
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+Masters and finance I I did a forarm
+
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+Masters and finance I I did a forarm
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+
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+part one I did the CFA level one and I
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+
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+sometime while working as a Quant and
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+one time in real estate even under three
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+
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+CFA right I I didn't even know like what
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+
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+skills I need to to learn I didn't know
+ 
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+about you know big data and and how to
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+ align:start position:0%
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+
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+
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+
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+
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+
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+
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+ 
+
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+
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+
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+and having those conversation is what
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+
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+
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+
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+
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+
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+
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+
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+
+ align:start position:0%
+wasn't just about you know the material
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+
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+
+ align:start position:0%
+is all there you can learn anything
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
+learn in order to be successful and you
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+
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+
+ align:start position:0%
+know it wasn't just like you know
+ 
+
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+know it wasn't just like you know
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+
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+someone telling me that this program is
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+
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+someone telling me that this program is
+great and I would go to it I have a
+
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+great and I would go to it I have a
+ 
+
+ align:start position:0%
+great and I would go to it I have a
+friend for example his name is Deon uh
+
+ align:start position:0%
+friend for example his name is Deon uh
+ 
+
+ align:start position:0%
+friend for example his name is Deon uh
+we we studied together frm and CFA like
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+we we studied together frm and CFA like
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+
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+we we studied together frm and CFA like
+every single chapter like we would hop
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+ align:start position:0%
+every single chapter like we would hop
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+
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+every single chapter like we would hop
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+
+ align:start position:0%
+on a zoom call uh and you know we would
+ 
+
+ align:start position:0%
+on a zoom call uh and you know we would
+spend six hours together solving
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+spend six hours together solving
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+
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+spend six hours together solving
+questions and you know learning stuff uh
+
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+questions and you know learning stuff uh
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+
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+questions and you know learning stuff uh
+we did that for the microm Masters we
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+we did that for the microm Masters we
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+
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+we did that for the microm Masters we
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+
+ align:start position:0%
+did that for CFA we did that for frm and
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+
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+did that for CFA we did that for frm and
+I had a lot of you know many more
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+I had a lot of you know many more
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+
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+
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+friends that I you know had you know the
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+pleasure of studying with and
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+collaborating with so I I wouldn't have
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+done it alone without you know the
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+
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+
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+allowed me to survive right this this
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+allowed me to survive right this this
+very you know challenging program and
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+very you know challenging program and
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+
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+very you know challenging program and
+education Journey that's that's really
+
+ align:start position:0%
+education Journey that's that's really
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+
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+beautiful to think about that not only
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+
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+Resources by coursework material but you
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+
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+
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+that you could tap in that you could
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+
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+that you could tap in that you could
+leverage you could leverage an
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+leverage you could leverage an
+Executives experience you you know just
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+Executives experience you you know just
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+
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+your classmate right that that that
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+
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+your classmate right that that that
+really is a beautiful thing you know and
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+really is a beautiful thing you know and
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+really is a beautiful thing you know and
+just just we asked this question of
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+just just we asked this question of
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+just just we asked this question of
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+everyone that comes on the podcast and
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+
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+everyone that comes on the podcast and
+it was uh a question from Kurt Newton
+
+ align:start position:0%
+it was uh a question from Kurt Newton
+ 
+
+ align:start position:0%
+it was uh a question from Kurt Newton
+the director of open course sare if you
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+the director of open course sare if you
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+wand what would you add to open course
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+wand what would you add to open course
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+wand what would you add to open course
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+of Finance you know all of the C putting
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+of Finance you know all of the C putting
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+
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+of Finance you know all of the C putting
+it online I do it there is some
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+it online I do it there is some
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+it online I do it there is some
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+applications in the program where you
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+
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+applications in the program where you
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+
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+in the class more applied courses would
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+be um would be more you know appreciated
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+
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+be um would be more you know appreciated
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+and specifically courses that are
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+
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+and specifically courses that are
+centered around collaboration uh I've
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+centered around collaboration uh I've
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+centered around collaboration uh I've
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+centered around
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+centered around
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+because you know I I had an amazing
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+because you know I I had an amazing
+experience at uh MIT I think I made the
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+experience at uh MIT I think I made the
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+
+ align:start position:0%
+experience at uh MIT I think I made the
+most out of it there's still more to
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+most out of it there's still more to
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+
+ align:start position:0%
+most out of it there's still more to
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+learn and make more out of it but a lot
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+of students just you know didn't focus
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+
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+the social experience that I've had just
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+
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+material did the and exams and you know
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+they they left out it's not bad to do
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+they they left out it's not bad to do
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+
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+just you know increase the human touch
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+
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+just you know increase the human touch
+the human connection element that's
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+ align:start position:0%
+the human connection element that's
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+
+ align:start position:0%
+the human connection element that's
+that's really beautiful um do you have
+
+ align:start position:0%
+that's really beautiful um do you have
+ 
+
+ align:start position:0%
+that's really beautiful um do you have
+anything any message that you would want
+
+ align:start position:0%
+anything any message that you would want
+ 
+
+ align:start position:0%
+anything any message that you would want
+to share with your friends your family
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+ align:start position:0%
+to share with your friends your family
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+
+ align:start position:0%
+to share with your friends your family
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+the world around you if you have a dream
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+
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+you know just give it time stay
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+you know just give it time stay
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+
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+dedicated stay passionate stay don't
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+dedicated stay passionate stay don't
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+
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+dedicated stay passionate stay don't
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+
+ align:start position:0%
+don't let your passion die out don't get
+ 
+
+ align:start position:0%
+don't let your passion die out don't get
+turned down uh you know you know don't
+
+ align:start position:0%
+turned down uh you know you know don't
+ 
+
+ align:start position:0%
+turned down uh you know you know don't
+don't be too hard on yourself don't get
+
+ align:start position:0%
+don't be too hard on yourself don't get
+ 
+
+ align:start position:0%
+don't be too hard on yourself don't get
+turned down don't have doubts over the
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+ align:start position:0%
+turned down don't have doubts over the
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+
+ align:start position:0%
+turned down don't have doubts over the
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+ align:start position:0%
+long run if if you really just put the
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+
+ align:start position:0%
+long run if if you really just put the
+time put the effort in um you will make
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+ align:start position:0%
+time put the effort in um you will make
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+
+ align:start position:0%
+time put the effort in um you will make
+your dreams come true and you just need
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+ align:start position:0%
+your dreams come true and you just need
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+
+ align:start position:0%
+your dreams come true and you just need
+to you know get out there and show up
+
+ align:start position:0%
+to you know get out there and show up
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+
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+to you know get out there and show up
+every day um if you show up every day
+
+ align:start position:0%
+every day um if you show up every day
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+
+ align:start position:0%
+every day um if you show up every day
+and like if you do a little bit of work
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+ align:start position:0%
+and like if you do a little bit of work
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+ align:start position:0%
+and like if you do a little bit of work
+in your dream with enough time it's you
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+ align:start position:0%
+in your dream with enough time it's you
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+
+ align:start position:0%
+in your dream with enough time it's you
+know it's it's more than just a
+
+ align:start position:0%
+know it's it's more than just a
+ 
+
+ align:start position:0%
+know it's it's more than just a
+possibility to to make it true that
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+ align:start position:0%
+possibility to to make it true that
+ 
+
+ align:start position:0%
+possibility to to make it true that
+that's what happened with me here I
+
+ align:start position:0%
+that's what happened with me here I
+ 
+
+ align:start position:0%
+that's what happened with me here I
+remember having having dreaming of
+
+ align:start position:0%
+remember having having dreaming of
+ 
+
+ align:start position:0%
+remember having having dreaming of
+becoming a quantitative analyst on my
+
+ align:start position:0%
+becoming a quantitative analyst on my
+ 
+
+ align:start position:0%
+becoming a quantitative analyst on my
+LinkedIn bio when I just started out
+
+ align:start position:0%
+LinkedIn bio when I just started out
+ 
+
+ align:start position:0%
+LinkedIn bio when I just started out
+University three four years ago and I
+
+ align:start position:0%
+University three four years ago and I
+ 
+
+ align:start position:0%
+University three four years ago and I
+thought it's a silly dream that that
+
+ align:start position:0%
+thought it's a silly dream that that
+ 
+
+ align:start position:0%
+thought it's a silly dream that that
+would never achieve it but you know here
+
+ align:start position:0%
+would never achieve it but you know here
+ 
+
+ align:start position:0%
+would never achieve it but you know here
+I am being a Quant in the finance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+industry wow that was a full circle
+
+ align:start position:0%
+industry wow that was a full circle
+ 
+
+ align:start position:0%
+industry wow that was a full circle
+conversation uh we followed Nadal from
+
+ align:start position:0%
+conversation uh we followed Nadal from
+ 
+
+ align:start position:0%
+conversation uh we followed Nadal from
+the start of his ocw journey as a
+
+ align:start position:0%
+the start of his ocw journey as a
+ 
+
+ align:start position:0%
+the start of his ocw journey as a
+struggling high school student deep into
+
+ align:start position:0%
+struggling high school student deep into
+ 
+
+ align:start position:0%
+struggling high school student deep into
+his career as a Quant analyst pretty
+
+ align:start position:0%
+his career as a Quant analyst pretty
+ 
+
+ align:start position:0%
+his career as a Quant analyst pretty
+amazing if you ask me from all this
+
+ align:start position:0%
+amazing if you ask me from all this
+ 
+
+ align:start position:0%
+amazing if you ask me from all this
+what's your biggest takeaway from this
+
+ align:start position:0%
+what's your biggest takeaway from this
+ 
+
+ align:start position:0%
+what's your biggest takeaway from this
+conversation I think my biggest takeaway
+
+ align:start position:0%
+conversation I think my biggest takeaway
+ 
+
+ align:start position:0%
+conversation I think my biggest takeaway
+is exactly what nadara said in the last
+
+ align:start position:0%
+is exactly what nadara said in the last
+ 
+
+ align:start position:0%
+is exactly what nadara said in the last
+um answer to the question was if you
+
+ align:start position:0%
+um answer to the question was if you
+ 
+
+ align:start position:0%
+um answer to the question was if you
+have a dream give it time stay dedicated
+
+ align:start position:0%
+have a dream give it time stay dedicated
+ 
+
+ align:start position:0%
+have a dream give it time stay dedicated
+stay passionate don't let your passion
+
+ align:start position:0%
+stay passionate don't let your passion
+ 
+
+ align:start position:0%
+stay passionate don't let your passion
+die out and just keep pursuing it until
+
+ align:start position:0%
+die out and just keep pursuing it until
+ 
+
+ align:start position:0%
+die out and just keep pursuing it until
+you achieve it I conquer I conquer my
+
+ align:start position:0%
+you achieve it I conquer I conquer my
+ 
+
+ align:start position:0%
+you achieve it I conquer I conquer my
+biggest take out from all this is anyone
+
+ align:start position:0%
+biggest take out from all this is anyone
+ 
+
+ align:start position:0%
+biggest take out from all this is anyone
+can achieve this we're hearing a story
+
+ align:start position:0%
+can achieve this we're hearing a story
+ 
+
+ align:start position:0%
+can achieve this we're hearing a story
+of someone who started out all the way
+
+ align:start position:0%
+of someone who started out all the way
+ 
+
+ align:start position:0%
+of someone who started out all the way
+from Jordan didn't have much going for
+
+ align:start position:0%
+from Jordan didn't have much going for
+ 
+
+ align:start position:0%
+from Jordan didn't have much going for
+them but they stay dedicated putting in
+
+ align:start position:0%
+them but they stay dedicated putting in
+ 
+
+ align:start position:0%
+them but they stay dedicated putting in
+hours working insane hours at a
+
+ align:start position:0%
+hours working insane hours at a
+ 
+
+ align:start position:0%
+hours working insane hours at a
+restaurant but still having time to come
+
+ align:start position:0%
+restaurant but still having time to come
+ 
+
+ align:start position:0%
+restaurant but still having time to come
+back and do all these resources put in
+
+ align:start position:0%
+back and do all these resources put in
+ 
+
+ align:start position:0%
+back and do all these resources put in
+the time put in the work and it lat a
+
+ align:start position:0%
+the time put in the work and it lat a
+ 
+
+ align:start position:0%
+the time put in the work and it lat a
+paid off you have someone from Across
+
+ align:start position:0%
+paid off you have someone from Across
+ 
+
+ align:start position:0%
+paid off you have someone from Across
+the Nation ending up working for a
+
+ align:start position:0%
+the Nation ending up working for a
+ 
+
+ align:start position:0%
+the Nation ending up working for a
+company that is across the seas in
+
+ align:start position:0%
+company that is across the seas in
+ 
+
+ align:start position:0%
+company that is across the seas in
+another continent and is now living in a
+
+ align:start position:0%
+another continent and is now living in a
+ 
+
+ align:start position:0%
+another continent and is now living in a
+different place that is the power of
+
+ align:start position:0%
+different place that is the power of
+ 
+
+ align:start position:0%
+different place that is the power of
+what ocw gives you that's the power of
+
+ align:start position:0%
+what ocw gives you that's the power of
+ 
+
+ align:start position:0%
+what ocw gives you that's the power of
+the community and the internet to know
+
+ align:start position:0%
+the community and the internet to know
+ 
+
+ align:start position:0%
+the community and the internet to know
+that you can do it no matter where
+
+ align:start position:0%
+that you can do it no matter where
+ 
+
+ align:start position:0%
+that you can do it no matter where
+you're from no matter where you start
+
+ align:start position:0%
+you're from no matter where you start
+ 
+
+ align:start position:0%
+you're from no matter where you start
+you can access anyone on this planet
+
+ align:start position:0%
+you can access anyone on this planet
+ 
+
+ align:start position:0%
+you can access anyone on this planet
+from any corner of it and it's possible
+
+ align:start position:0%
+from any corner of it and it's possible
+ 
+
+ align:start position:0%
+from any corner of it and it's possible
+and ocw is giving everyone that power
+
+ align:start position:0%
+and ocw is giving everyone that power
+ 
+
+ align:start position:0%
+and ocw is giving everyone that power
+and that opportunity and I want to say
+
+ align:start position:0%
+and that opportunity and I want to say
+ 
+
+ align:start position:0%
+and that opportunity and I want to say
+thanks to everyone for tuning into our
+
+ align:start position:0%
+thanks to everyone for tuning into our
+ 
+
+ align:start position:0%
+thanks to everyone for tuning into our
+conversation with Nadar we will be back
+
+ align:start position:0%
+conversation with Nadar we will be back
+ 
+
+ align:start position:0%
+conversation with Nadar we will be back
+in two weeks with another story from a
+
+ align:start position:0%
+in two weeks with another story from a
+ 
+
+ align:start position:0%
+in two weeks with another story from a
+different Learner in the global open
+
+ align:start position:0%
+different Learner in the global open
+ 
+
+ align:start position:0%
+different Learner in the global open
+course for Community see you then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+open lers is produced by Alexis hot
+
+ align:start position:0%
+open lers is produced by Alexis hot
+ 
+
+ align:start position:0%
+open lers is produced by Alexis hot
+special thanks to the supporters and
+
+ align:start position:0%
+special thanks to the supporters and
+ 
+
+ align:start position:0%
+special thanks to the supporters and
+donors who make ocw possible to learn
+
+ align:start position:0%
+donors who make ocw possible to learn
+ 
+
+ align:start position:0%
+donors who make ocw possible to learn
+more about mit's Open course rare and to
+
+ align:start position:0%
+more about mit's Open course rare and to
+ 
+
+ align:start position:0%
+more about mit's Open course rare and to
+check out the courses mentioned in this
+
+ align:start position:0%
+check out the courses mentioned in this
+ 
+
+ align:start position:0%
+check out the courses mentioned in this
+episode visit the open coreware website
+
+ align:start position:0%
+episode visit the open coreware website
+ 
+
+ align:start position:0%
+episode visit the open coreware website
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a
\ No newline at end of file
diff --git a/64Kp4kgRdzs.txt b/64Kp4kgRdzs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e85d9c97f39f81cdc42fb696e979ffef361a9a47
--- /dev/null
+++ b/64Kp4kgRdzs.txt
@@ -0,0 +1,3903 @@
+PROFESSOR: All right,
+let's get started.
+
+We are continuing our
+theme of folding polygons
+
+into convex polyhedra.
+
+Let's do a quick
+reminder, we're talking
+
+about gluing up the boundary
+of a polygon to itself.
+
+And we were representing that
+with gluing trees last time.
+
+So I want to do an actual
+example of a gluing tree.
+
+So this is how you
+make a cube out
+
+of a cross, my favorite example.
+
+And a valid gluing,
+it's an Alexandroff
+
+gluing because it
+has no crossing, so
+
+its topologically a sphere.
+
+Everything is glued
+to everything.
+
+And it never glues more
+than 360 degrees of material
+
+to any point.
+
+In fact, it's going to
+be 270 at every point,
+
+because that's the curvature
+of every vertex of a cube.
+
+And the gluing tree was, if we
+sort of turned this inside out
+
+and think of the polygon as
+being on the outside instead
+
+of the inside, it's really
+hard to see here how to convert
+
+that into a gluing tree,
+though you can do it.
+
+It's the way that
+these arrows nest.
+
+But it's a little easier
+to think of on the sphere
+
+or on the polyhedron, because
+then turning inside out
+
+is just upside down.
+
+It's not a big deal.
+
+So if we look at where
+the cut are on the cube,
+
+it looks something like this.
+
+That should be a cross.
+
+This is the top
+of the cross, this
+
+is the bottom of the cross.
+
+It goes around the back side.
+
+So then the gluing tree is
+essentially this doubled.
+
+If we walk around the
+outside of the cuts,
+
+that is the gluing tree.
+
+So I can see, there's this
+segment, then this segment,
+
+then that segment.
+
+Then we're back here,
+then we go up one, two,
+
+and then we turn around.
+
+That's a leaf, and so it's
+going to look like this weird h
+
+shape.
+
+And these are vertices.
+
+That's right, all of
+these should be vertices.
+
+And locally you can see, ah,
+this is a 90 degree angle.
+
+This is actually the
+top of the cross,
+
+remember the polygon
+is now out here.
+
+That's going to
+be the top across.
+
+This is where it turns,
+it gets a little confusing
+
+because of the
+way I've drawn it.
+
+Here's the bottom of the cross.
+
+Those parts are easy to see.
+
+The rest is little awkward.
+
+But for algorithms,
+this is a great way
+
+to think about things.
+
+And also for proving bounds
+and how many different ways
+
+to fold, it's really useful
+to think about gluing trees.
+
+Of course, all of these
+views are equivalent,
+
+but a lot of things will
+be easier to analyze here.
+
+So, clear?
+
+Let me first tell you what
+we're going to prove today.
+
+We're going to do combinatorial
+bounds and algorithms
+
+for all of this.
+
+And let's see.
+
+So I want general gluings,
+general situation,
+
+edge-to-edge gluings, and a
+particular kind of polygon
+
+called bounded sharpness.
+
+And then I want two columns.
+
+The first question is, how
+many gluings are there?
+
+And whenever we get a bound
+on the number of gluings,
+
+we're also going to get
+an enumeration algorithm.
+
+Remember, there are three goals.
+
+The first goal was decision.
+
+Is there any folding?
+
+Second goal was enumeration,
+give me all the foldings.
+
+And third goal was
+counting, I think.
+
+How many different
+solutions are there?
+
+For [INAUDIBLE], this is mainly
+about decision and enumeration.
+
+And this number
+of gluings, that's
+
+the combinatorial problem.
+
+So it turns out, for
+everything the we'll do,
+
+these two have the same answer.
+
+So I'm going to put
+it in one column.
+
+But sometimes for
+a decision, you
+
+can do it a little faster
+than enumerating them.
+
+In particular, because
+the number of gluings
+
+can be exponential.
+
+We saw last time that it
+could actually be infinite.
+
+I'm going to fix
+that, don't worry.
+
+We'll make it finite.
+
+And then the right
+bound is exponential.
+
+There's upper and lower
+bounds of two to the theta n.
+
+And also here, bounded
+sharpness is interesting
+
+because it's polynomial.
+
+And so this is also polynomial.
+
+The one result here that
+is not tight is this one.
+
+It's an open question whether
+for the general setup, the most
+
+interesting scenario,
+just give you a polygon,
+
+is there any gluing?
+
+The best algorithm we
+know is exponential,
+
+even to decide whether
+there's a gluing.
+
+So I put a star
+there to say that.
+
+It is not tight.
+
+The open problem is, can
+you do it in polynomial?
+
+I suspect yes, but we worked on
+it a long time ago and failed.
+
+For the special case of
+edge-to-edge gluings, which
+
+is when you only glue
+whole edges of the polygons
+
+to other whole edges, there is
+a n to the order one algorithm.
+
+You can think of this as
+an edge-to-edge gluing
+
+if you imagine this
+as being two edges.
+
+If I actually draw
+a vertex there,
+
+then this is an
+edge-to-edge gluing.
+
+And then there's a polynomial
+algorithm to tell you,
+
+is there any folding?
+
+If you want to list all
+of the gluings though,
+
+you need exponential
+time because there
+
+can be exponentially many.
+
+But everything except
+this one result
+
+is the best you could hope for.
+
+Bounded sharpness
+is a natural sense
+
+in which this exponential
+is kind of cheating.
+
+Let's see, let me tell you
+about bounded sharpness.
+
+I want to bound how sharp an
+angle can be in a polygon.
+
+This is a really sharp angle.
+
+If every angle-- is that
+actually the sharpness I want?
+
+Actually, no.
+
+Sorry, I'm getting
+inside out already.
+
+Actually, what I care
+about are reflex vertices.
+
+I don't want to have a
+super big angles here.
+
+So if every angle
+is at least 360
+
+minus some epsilon--
+for a constant epsilon--
+
+then I call my polygon
+bounded sharpness.
+
+If your polygon has
+bounded sharpness,
+
+we get a polynomial bound
+on the number of gluings
+
+and a polynomial algorithm
+to list all the gluings.
+
+This is really the sense in
+which this is all practical.
+
+Give me a polygon that's going
+to have some sharpest angle,
+
+call that the bound.
+
+If epsilon gets really tiny, if
+your reflex angles get really
+
+close to 360, then
+this bound will go up.
+
+But as long as you're not
+too extreme, you're all set.
+
+I mean less than or
+equal to, yes, thank you.
+
+Yeah, that would
+be a weird polygon
+
+if all the angles were so big.
+
+I think that doesn't exist.
+
+So for example, convex polygons
+always have bounded sharpness.
+
+Epsilon is 180 in
+that situation.
+
+So, that's good.
+
+I told you about
+edge-to-edge gluings.
+
+Just glue whole
+edges to whole edges.
+
+What I haven't really told you
+is how we made this finite,
+
+so let me go to that.
+
+And when I say
+gluings here, I really
+
+mean a combinatorial
+type of gluing,
+
+because we had rolling belts.
+
+So there were infinitely
+many actual gluings,
+
+but I'm going to
+think of most of those
+
+as being the same thing and
+just distinguish essentially
+
+what the gluing tree looks
+like combinatorially.
+
+So let me define that.
+
+The first part is what I call
+the abstract gluing tree.
+
+So this is just what the
+picture looks like in general.
+
+So for example, the one
+over there-- the cube--
+
+combinatorially the
+tree looks like this.
+
+It has four leaves and a kind
+of wishbone configuration.
+
+So I'm not trying to measure
+the lengths or anything, just
+
+that's the abstract
+picture, no metric.
+
+And then the second
+part is I'm going
+
+to specify which polygon
+vertices and edges are where.
+
+And I'm going to specify that
+at things called junctions.
+
+So in particular, at
+leaves I want to say,
+
+oh this is vertex one.
+
+At places like this, where
+three edges come together,
+
+I want to specify for each
+one, oh this is vertex two,
+
+this is edge eight, this
+is vertex 10, whatever.
+
+I'm making up these numbers.
+
+They don't necessarily
+correspond,
+
+but they should appear in order
+because this is the polygon
+
+after all, just
+warped inside out.
+
+Also this one.
+
+Also, I didn't really draw
+this picture big enough,
+
+but if I have two parts
+of the gluing tree
+
+where a vertex glues
+against something--
+
+it could be another vertex
+or it could be an edge--
+
+I also consider those junctions.
+
+So junctions are going
+to be all the vertices--
+
+the only exception is when
+there's an edge gluing
+
+to an edge, I don't
+consider that a junction
+
+because there's going to
+be fairly many of those.
+
+I want there to be finite.
+
+So everything of
+degree one, everything
+
+of degree three or
+more, for degree two
+
+there has to be at
+least one vertex.
+
+So degree not equal to 2,
+or at least one vertex.
+
+Those are junctions.
+
+For each I'm going to
+mark where they are.
+
+That's part of my abstract
+gluing tree, specifying where
+
+the junctures are, how
+they're configured.
+
+And then for each
+one, wherever there's
+
+part of the polygon
+coming together,
+
+I specify which vertex
+or edge is coming there.
+
+Now when I specify
+an edge, I don't
+
+say what point on the edge,
+because that could be infinite.
+
+There could be a whole range
+of points, there could be.
+
+We'll worry about that later.
+
+I just specify that
+edge eight is there.
+
+So this is what I call
+combinatorial type of gluing.
+
+And in this case, there are
+only finitely many gluings,
+
+finitely many types, but
+it can be exponential.
+
+It's still big, just
+not quite as big.
+
+So just to get
+warmed up a little,
+
+let's prove this exponential
+upper bound that is only 2
+
+to the order n.
+
+That will in
+particular convince you
+
+that there's only
+finitely many of these,
+
+although I think that's probably
+obvious that it's finite.
+
+It's conceivable it could
+be more than exponential.
+
+This is not a particularly
+exciting bound,
+
+but we're going to use
+a lot of the same ideas
+
+in the other proofs, in
+particular this one which
+
+is more interesting.
+
+I want to look at
+leaves of my tree.
+
+And we have to remember back
+to the previous lecture, who
+
+can be at the leaves?
+
+Well, if could be a vertex
+or it could be an edge.
+
+When it was an edge, we
+called it a fold point.
+
+When we folded in the
+middle of an edge--
+
+so here's an edge of
+the polygon and I end up
+
+subdividing it and gluing
+the edge onto itself-- right
+
+there is 180 degrees
+of curvature.
+
+Total amount of
+curvature is 720,
+
+therefore I only
+have-- I can't count,
+
+I'm jetlagged-- four of them.
+
+At most four fold points.
+
+Everybody else is a vertex.
+
+So if I have n vertices, I
+have at most n plus 4 leaves.
+
+That's already feeling good.
+
+I pull a rabbit out
+of a hat and tell you
+
+that if I have only
+n plus 4 leaves,
+
+there are 2 to the order n
+trees on that many leaves.
+
+Actually, I should be
+a little more careful.
+
+If I can bound the number
+of nodes in the tree,
+
+then I'll get an exponential
+bound on the number of trees.
+
+And that will be part one,
+the abstract gluing tree.
+
+But right now I have a bound on
+the number of leaves, not the
+
+number of nodes.
+
+And there's a difference
+here, because if you
+
+have a tree which has
+a whole bunch of degree
+
+2 vertices, then that would be
+bad, because I only have two
+
+leaves I have
+arbitrarily many nodes.
+
+But every time I have one
+of these degree 2 nodes,
+
+we already threw away
+the degree 2 nodes that
+
+had no vertices at them, because
+there are infinitely many
+
+of those and those don't count.
+
+So once we throw that away,
+the only degree two junctions
+
+are the ones that have a vertex,
+which is why-- these dots are
+
+supposed to be the actual
+vertices of the polygon.
+
+So it might be an edge here,
+it might be an edge there.
+
+There's at least one
+vertex at each of them.
+
+So the total number of nodes
+here is indeed order n.
+
+I mean, it's probably actually
+at most n plus 4 again.
+
+But if we're sloppy you say,
+well the number of leaves
+
+is at most n plus 4.
+
+The number of degree
+2 nodes is at most n.
+
+Then there could be
+some degree three nodes.
+
+It's also at most
+n plus 4 in total,
+
+or n is all I care about.
+
+You could be more
+careful and figure out
+
+what the consonant is.
+
+But we get from this,
+this is order n nodes.
+
+And once you have that the tree
+has a linear number of nodes,
+
+I'll tell you this is one of
+the [? Kadhalan ?] problems,
+
+that there's only 2
+the order n such trees.
+
+But that's only part one
+of the combinatorial type
+
+of the gluing.
+
+We also have to worry about
+which vertices are where.
+
+I want to show that that
+is only exponential.
+
+So imagine at this
+point you've fixed
+
+the combinatorial
+structure of the tree,
+
+but you have no
+idea what's what.
+
+So in particular,
+at these points--
+
+and maybe also you've
+defined some degree 2
+
+junctions, which you
+know are supposed
+
+to have at least one vertex--
+the first thing I want
+
+to specify is, for each
+of these little dots that
+
+come together-- these are the
+junctions-- is it a vertex,
+
+or is it an edge?
+
+So that's just binary
+information for each one.
+
+I'll fill it in, say
+if it's a vertex,
+
+I'll leave it open
+if it's an edge.
+
+In fact, I know that at
+most one edge comes together
+
+at any point.
+
+Otherwise, you'd have too
+much material glued there.
+
+So maybe it looks
+something like this.
+
+It could be a fold point,
+maybe another fold point.
+
+Something like that.
+
+So that coloring, black
+and white, there's only 2
+
+to the order and such colorings.
+
+Call it a vertex edge
+coloring, because again there's
+
+order n dots.
+
+Each one, there's two choices,
+black or white, vertex or edge.
+
+And now what we
+really care about
+
+is where the vertices,
+because remember, this
+
+is the polygon in order.
+
+So if I could tell you, let's
+say which vertex is vertex one?
+
+Maybe this vertex is vertex one.
+
+Then I know this is vertex two,
+I know this is vertex three,
+
+I know this is edge
+three or whichever
+
+edge connects V3 three and V4.
+
+This is also edge
+three, and so on.
+
+I could just walk around
+and label them in order.
+
+All I needed to do is
+know where vertex one is.
+
+There's only n
+possibilities for that.
+
+There's n filled circles, which
+are where the vertices are.
+
+One of them is V1, so there's
+only n choices for it.
+
+You multiply all of these
+things together, n times 2
+
+to the order n, times
+2 to the order n,
+
+that result is 2 to
+the some other order n.
+
+That's total number of choices.
+
+So that's a rough
+but fine upper bound.
+
+I'm not going to try
+to tune this constant.
+
+I guess it would
+be an open problem
+
+to get a really good
+bound on the constant.
+
+I'm not sure if even
+one has been worked out,
+
+but what I will show you is
+that this is pretty much tight,
+
+so you can't hope to do
+much better than this
+
+because there's a 2 to
+the omega n lower bound
+
+on the number of gluings.
+
+And that is this crazy example.
+
+I'll draw it also on the board.
+
+It's a little tricky to draw.
+
+It's a very spiky star,
+something like that.
+
+So I have e points, and n
+spikes, n convex corners.
+
+The convex angle,
+I think, is alpha.
+
+Let me match the notation.
+
+Yes, convex angle is alpha.
+
+The reflex angle here is
+beta, but otherwise it's
+
+completely symmetric.
+
+So all the reflex
+angles are beta,
+
+all the convex angles are alpha.
+
+I have n spikes.
+
+I want these points--
+it's hard to draw,
+
+but I want them to be very,
+very close to the center.
+
+Take the limit.
+
+In the limit, alpha is 0.
+
+So alpha is going to be some
+very tiny amount epsilon.
+
+Beta.
+
+What's the limit of beta?
+
+180, 360?
+
+No, it's not 360.
+
+That's what's important.
+
+360 times 1 minus
+1 over n, yeah.
+
+It's like 360 minus 360 over n.
+
+Believe it or not,
+this is a big number,
+
+in that it doesn't
+depend on epsilon.
+
+So it's going to be, what,
+a little bit smaller--
+
+going to be some
+minus epsilon prime.
+
+But I really don't care
+about the epsilons.
+
+They're kind of irrelevant.
+
+Let me just cross them out,
+but they're really there.
+
+So alpha is basically 0, beta
+is a chunk less than 360.
+
+What this means is in the limit
+I can take one of these alphas
+
+and glue it into
+one of the betas,
+
+and it will still
+be less than 360.
+
+In fact I could
+glue n of the alpha.
+
+I could glue all of these
+spikes into one of these gaps.
+
+Remember, the limiting
+picture looks like this.
+
+That's maybe more convincing.
+
+It doesn't look that way here.
+
+This is nothing.
+
+Of course, I can fit arbitrarily
+many of them into this gap
+
+and it will still
+sum to less than 360.
+
+So this is kind of the key
+to why this example works.
+
+I've got tons a room for alphas
+in the complement of betas.
+
+Now, I would like to make
+this not only an exponential
+
+lower bound on the
+general case, but also
+
+on the edge-to-edge
+case, because that's
+
+a little bit stronger to say
+even edge-to-edge gluings there
+
+can be exponentially many.
+
+To do that, I'm going to
+take the midpoint of one
+
+of the edges, call
+that a vertex,
+
+and take the perimeter antipode,
+which is like here hopefully,
+
+more or less.
+
+So I want the left parameter
+and the right perimeter
+
+to be equal, also
+call that a vertex.
+
+And now one thing we know how
+to do is perimeter halving.
+
+Now, we were only supposed to
+do perimeter halving on convex
+
+polygons, but it turns out it
+will work on this polygon too.
+
+So I'm going to glue this
+half edge to this half edge,
+
+then I'm going to glue this
+edge to this edge, then
+
+this one to this one, and so on.
+
+So just do that gluing.
+
+And the only thing
+to worry about
+
+is that you glue
+two betas together.
+
+That would be more than 360.
+
+Anything else, beta to any
+number of alpha's is OK.
+
+At this point it is really
+helpful to draw a gluing tree,
+
+so let me do that.
+
+So gluing tree for
+perimeter halving is path.
+
+And do I give these guys
+names, probably x and y?
+
+Yeah, that's what
+I would call them,
+
+so naturally that's
+what I called them.
+
+We have x over here,
+we have y over here.
+
+And then we have the
+perimeter in between.
+
+So let's just
+check what happens.
+
+Here we get an
+alpha on one side--
+
+I'm going to say the right
+side is the bottom, let's say.
+
+I'm not going to try
+to think about it.
+
+So there's an alpha,
+and that meets a beta.
+
+And then it just
+alternates from there.
+
+There's an alpha, it meets a
+beta, but on the other side.
+
+And a beta meets
+an alpha and so on.
+
+At the end, it's probably the
+reverse, like alpha, beta.
+
+I've drawn it up
+here at the very top.
+
+The alpha's red, betas are black
+so you can distinguish them.
+
+But that's clearly an OK gluing
+because it's just one alpha
+
+gluing to one beta.
+
+We know we can glue tons
+of alphas into one beta.
+
+That's one gluing.
+
+The fun part is that
+there are exponentially
+
+many of these gluings which look
+like this, where you take some
+
+of the betas and turn
+them into leaves,
+
+kind of squeeze them out.
+
+And the result is that
+you get two alphas gluing
+
+to a beta, which is fine.
+
+The beta glues to
+itself, which is fine.
+
+I mean, it's a vertex.
+
+It's comforting that it
+has an angle almost 360.
+
+Therefore, there's very little
+curvature out at that leaf,
+
+but we don't really
+need to check that.
+
+It is just necessary
+for this to work.
+
+Of course, beta is less
+than 360 by itself.
+
+Here's an example where I
+squeezed two of the betas
+
+right next to each
+other, then three alpha's
+
+come together and
+glue to a beta.
+
+But what's nice is we don't
+have to think about the polygon.
+
+We just think about
+the gluing tree.
+
+And we say, well if
+I pull this down-- so
+
+I end up with
+that-- that's going
+
+to be just fine as long as
+I also pull one on the top.
+
+I have to squeeze the
+same number of betas
+
+on the top and the
+bottom, otherwise
+
+these links won't match up.
+
+As long as I do that,
+I get a valid gluing.
+
+So what I'm going to do,
+I have n betas total.
+
+So I have n over
+2 betas on the top
+
+and n over 2 betas
+on the bottom.
+
+I'm going to squeeze n over
+4 on the top and n over 4
+
+on the bottom, so half of them.
+
+That way the lengths
+will match up,
+
+and I happen to know there's
+a lot of ways to do this.
+
+The actual number is n over
+2 choose n over 4 for the top
+
+and the same for the bottom.
+
+So it's this
+squared, and I'm just
+
+going to tell you that
+is 2 to the theta n.
+
+Actually, I think you
+can be pretty precise.
+
+Can you?
+
+I've forgotten.
+
+Isn't n choose n over
+2-- it's very close to 2
+
+to the n over 2, I believe.
+
+Is that right?
+
+But not exactly, yeah.
+
+All right, I'm
+going to be sloppy.
+
+It's 2 to the theta n.
+
+You could figure out what
+the constant is there.
+
+I think I have a bound
+written down, maybe.
+
+Oh, it is the power of 2, yeah.
+
+It is equal, I believe,
+according to my notes.
+
+So this is going
+to be 2 to the n
+
+over 4 squared, which is
+2 to the n over 2 exactly.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: I only am allowed
+to squeeze betas, not alphas.
+
+But I can do whatever pattern I
+want on the top and separately
+
+any pattern I want
+on the bottom.
+
+Because what's key
+is by squeezing
+
+betas I preserve the parity,
+because when I squeeze away
+
+a beta I bring two
+alphas together.
+
+So the parity and who's matching
+whom on the top and the bottom
+
+is always the same.
+
+And the beta on
+the top will always
+
+be matching some number
+of alpha's on the bottom,
+
+and vice versa.
+
+So it doesn't matter what
+pattern I do on the top,
+
+or what pattern I
+do on the bottom.
+
+It just matters they
+have the same length,
+
+so I arbitrarily chose
+them to both be n over 4.
+
+Well, it wasn't
+arbitrary, but I chose
+
+it to be that
+because I knew there
+
+would be a lot of those choices.
+
+There are more, of course.
+
+Really I should sum this
+over all choices of n over 4,
+
+but this is good enough.
+
+That summation would not
+improve the bound by much.
+
+So that's sort of the bad news.
+
+These are really nasty polygons.
+
+They have exponentially
+many gluings.
+
+For fun, we actually
+did this for small n.
+
+It's been a while.
+
+This was some time ago
+that we made all these.
+
+I think it actually
+was before 2002,
+
+but that was when
+the paper appeared.
+
+So here is a four
+star, and these
+
+are I think all of
+the possible gluings.
+
+Maybe just some of
+them, it's been awhile,
+
+I could think about it.
+
+Not drawn as gluing trees
+here, but drawn as actual
+
+gulings on the polygon.
+
+Here instead of
+drawing the gluings
+
+on the outside, which
+is how they happen
+
+in the gluing three, I've
+drawn them on the inside,
+
+just because it's
+easier to draw.
+
+And then we built
+them in the same way
+
+that I built one like I showed
+you last time, where we just
+
+took a polygon, started
+taping edges together,
+
+and these are the
+roughly taped versions.
+
+And then you guess where
+the crease signs are,
+
+and then you can draw
+the crease lines on here.
+
+And two of them
+are drawn sort of
+
+worked out where exactly
+the crease lines have to be,
+
+according to getting all
+the edge links to match.
+
+And then you can
+make your polygons.
+
+That is n equals 4,
+then we did n equals 8.
+
+I guess we want n to be
+even here for convenience.
+
+And there's more, although
+still not a huge number.
+
+I think these are the top sides
+and these are the bottom sides.
+
+And you can see, in some
+cases it was a little tricky
+
+to tell where the creases
+are, because they were
+
+almost flat or possibly
+actually exactly flat.
+
+Like here they are flat.
+
+But it's a fun exercise.
+
+You can, whenever you
+have these gluings,
+
+reconstruct the polyhedra.
+
+Of course now that we have
+algorithms for Alexandroff's
+
+theorem, we could try plugging
+these into the programs
+
+and they should give us exact 3D
+polyhedra, from which we could
+
+figure out where the
+crease lines are.
+
+It would be a fun, small,
+mini-project, I guess,
+
+to do that.
+
+This is all from ages ago.
+
+At this point I want to move
+on to this result, which
+
+is the good news.
+
+This is sort of bad news
+that there are exponentially
+
+many different gluings.
+
+It's not so bad in that at
+least we can enumerate them
+
+in the same amount of time.
+
+We'll get to that later.
+
+While we're in the
+combinatorial streak,
+
+I want to prove
+that there's only
+
+a polynomial number
+of combinatorially
+
+distinct gluings for
+bounded sharpness polygons.
+
+So of course, this
+star polygon does not
+
+have bounded sharpness.
+
+We set beta to be very,
+very close to 360.
+
+It may be worth talking
+about this a little bit,
+
+because it wasn't exactly 360.
+
+It was bounded away from 360 by
+this value of 360 divided by n.
+
+Now I said that
+was a big number,
+
+because it was much,
+much bigger than alpha.
+
+Bigger than n times
+alpha even, because I
+
+can make alpha very close to 0.
+
+But it is not what we
+call bounded sharpness.
+
+Bounded sharpness was 360
+minus a constant-- I really
+
+shouldn't have called it
+epsilon because it's confusing.
+
+Let me call it gamma just
+got another Greek letter.
+
+Gamma is not arbitrarily small.
+
+It is a constant value, whereas
+over here it's not constant.
+
+It's a constant divided
+by n, that's sub-constant.
+
+So this is not bounded
+sharpness, just to check.
+
+But if we have all the
+reflex angles, at most 360
+
+minus an actual
+constant bigger than 0,
+
+then we can get a
+polynomial bound
+
+on the number of combinatorially
+distinct gluings.
+
+So let me show that to you.
+
+Here's the cool thing
+about bounded sharpness.
+
+How many leaves can
+the gluing tree have?
+
+Each leaf is either an edge,
+like it's a fold point.
+
+In that case, the
+curvature is 180 degrees.
+
+Or it's a vertex.
+
+If it's a vertex, the
+curvature at that point
+
+is 360 minus the
+angle at that point.
+
+360 minus the angle,
+let's call it alpha.
+
+Now, we know that every
+angle alpha is at most 360
+
+minus gamma.
+
+So if this is going to be
+at least 360 minus gamma,
+
+which is just gamma.
+
+So every vertex, every
+leaf of the tree,
+
+has curvature at least gamma.
+
+Gamma is a constant.
+
+Total curvature is 720, exactly.
+
+Therefore, the number
+of leaves is at most 720
+
+over gamma, which is a constant.
+
+That's going to help.
+
+We don't have to worry
+about trees with n leaves.
+
+We only have to
+worry about trees
+
+with 20 leaves, some
+constant number of leaves.
+
+Again, as the bound on sharpness
+goes down, the number of leaves
+
+will go up in this
+inverse proportional way,
+
+but it's a constant.
+
+So at least for part
+one, we're golden.
+
+I mean, the number
+of gluing trees,
+
+I said over here-- where is it?
+
+If I have n nodes
+in my tree, I'll
+
+only have 2 to
+the order n trees.
+
+So if I can reduce the
+number of nodes in my tree,
+
+I will reduce the number
+of trees correspondingly.
+
+If there's only a
+constant number of nodes,
+
+there will be a constant
+number of trees.
+
+It doesn't matter that a
+constant gets exponentiated,
+
+it'll still be constant.
+
+So that's good news,
+except we bounded again
+
+the number of leaves,
+not the number of nodes.
+
+So we have to be a
+little bit careful,
+
+because in particular we can
+have degree 2 junctions, which
+
+are real junctions--
+they might look like this
+
+where a vertex comes to an edge.
+
+There's got to be
+about n of those,
+
+because the vertices
+have to be somewhere.
+
+We're saying there aren't
+very many at the leaves.
+
+And therefore, at the degree
+three and higher junctions,
+
+there can't be very many.
+
+Maybe I haven't said
+this, but if you
+
+have a tree with
+L leaves, you'll
+
+only have at most L internal
+nodes, branching nodes.
+
+But degree two nodes, there
+could be arbitrarily many.
+
+So what we come to is, if
+I have L leaves in a tree,
+
+then I'll only get 2
+to the order L gluings.
+
+This is what we need to prove.
+
+It will tell us
+that in particular,
+
+if we have a constant
+number of leaves,
+
+as comes from the
+bounded sharpens case,
+
+I will get-- constant
+number of gluings?
+
+That's not right.
+
+There's some polynomial
+on n times 2 to the order
+
+L. Ah, that's why.
+
+I should look at my
+notes occasionally.
+
+The right bound to
+n to the order L.
+
+In fact, what I wrote
+is an open problem.
+
+I think maybe it's n to the
+order 1 times 2 to the order L.
+
+This is what you'd call a fixed
+parameter tractable bound,
+
+but no such upper
+bound is known.
+
+That might be fun to work
+on in the problem session.
+
+It might not be difficult,
+just at the time
+
+I didn't know those
+bounds were important.
+
+So we still have
+to prove this, n
+
+to the order L. This is the
+part where my notes are wrong.
+
+Here's the idea, we have
+a small number of leaves,
+
+we're worried about
+these degree 2 junctions.
+
+But I claim, actually
+there isn't a lot going on.
+
+Because one of the
+great things we can do,
+
+over here we said for
+every dot, was it a vertex
+
+or was it an edge?
+
+We can't afford that anymore,
+because there's n dots still.
+
+We can't afford
+2 to the order n.
+
+Where we can afford it is at
+the leaves, because there's only
+
+L of those, and at
+the branching nodes.
+
+So everything except
+these degree 2 problems
+
+we could specify.
+
+And really we could
+specify anything we want.
+
+So yeah, we could specify, is
+it a vertex or is it an edge?
+
+But we could make
+life even easier-- hm,
+
+I have an idea for
+solving this open problem.
+
+Do I want to solve it right now?
+
+Yeah, let's do it.
+
+Let me think for a second.
+
+I think that's going to work.
+
+OK, cool, cool.
+
+I needed to rewrite
+these notes anyway,
+
+so I might as well
+prove a stronger result.
+
+All right, so let
+me draw a picture.
+
+There's branching nodes, and I
+surely draw one of these longer
+
+so I can say, oh there's some
+degree two junctions here.
+
+Those are annoying,
+ignore those.
+
+For everything else-- the
+leaves and the branching
+
+nodes-- I'm going to specify
+the same binary thing.
+
+Is it a vertex,
+or is it an edge?
+
+But now there's only
+order L of them.
+
+There's L leaves, so there's at
+most L minus 1 internal nodes.
+
+Each of them has some
+degree, but the total number
+
+of these dots will be order
+L if I ignore the degree 2.
+
+So that's 2 to the order
+L vertex edge colorings,
+
+just like before
+except now with L,
+
+of leaves and branching nodes.
+
+Oh, I see the problem.
+
+Darn it.
+
+What I'd like to do is mimic
+the same proof and say, well
+
+choose where V1 is and then
+just label them around.
+
+There's a problem
+with that, though.
+
+Say V1 is here.
+
+Where's V2?
+
+Well, maybe this is an
+edge, maybe this is an edge.
+
+This, I have no idea.
+
+Is it an edge?
+
+Is it a vertex?
+
+I can't tell.
+
+At degree 2 junctions,
+I have a problem.
+
+That's kind of annoying.
+
+To fix that-- and so this is
+still going to be open, alas.
+
+To fix that I need to-- I
+really want to know which dot
+
+is which vertex for
+reasons to be determined.
+
+But in particular, that
+is part of number two.
+
+So I'm just going to give
+up and say, well there's
+
+2n different things that they
+could be, n vertices and edges.
+
+Do I want to do it that way?
+
+Maybe n choose order L. I'm
+just going to write down
+
+wherever I have a filled dot--
+I guess this one is not filled.
+
+Maybe this one's filled, filled.
+
+I just going to write down,
+what is the vertex number there?
+
+This is maybe V3, V5,
+V20, V21, whatever,
+
+for each of the filled
+dots among the vertices
+
+that I can see, ignoring again
+the degree two junctions.
+
+There's order L of them.
+
+I just going to for each one
+pick out one of the labels.
+
+Again, the order is
+determined, so this
+
+is the right number of them.
+
+And this is n to
+the order L at most.
+
+So this is where I'm
+being a bit wasteful.
+
+It would be interesting
+to try to get around that.
+
+This was actual
+vertex labelings.
+
+So now, among the
+vertices I can see--
+
+the degree three
+junctions, and the leaves,
+
+and higher degree
+junctions-- I know
+
+which vertices are glued there.
+
+I can also figure out
+which edges are glued there
+
+by similar labeling, although
+I don't think I actually care.
+
+No, I probably care, because
+it's part of number 2.
+
+So I do have to also label
+the open circles which
+
+edge is there.
+
+But a similar bound holds.
+
+What's left?
+
+What's left are the
+degree 2 vertices.
+
+I don't know
+anything about them.
+
+This is particularly tricky
+when I have some edge here.
+
+But let's first
+think about the case
+
+where I have a
+vertex, add a leaf,
+
+and I have these
+degree two junctions.
+
+And I don't know which edge
+is here, which vertex is here.
+
+In this case, because
+everything's small,
+
+I might be able to figure out.
+
+But here, where's the
+V3 to V4 transition?
+
+Could be here, or
+it could be here.
+
+It could be here.
+
+I can't afford to figure it out.
+
+Fortunately, I don't
+have to figure it out.
+
+It's not so obvious.
+
+From this picture you
+can't see what's going on,
+
+but this came from a polygon.
+
+This is an actual vertex,
+this is an actual vertex.
+
+So this edge length is the
+total perimeter from V3 to V5
+
+along the polygon.
+
+I know how long that is.
+
+So also if that was
+going clockwise from V3
+
+around the polygon--
+actually, that's
+
+probably counter-clockwise
+in the polygon
+
+because everything's inside out.
+
+If I go the other way--
+let's be relative-- from V3,
+
+I can measure out
+the same length.
+
+So in fact, I have
+some polygon-- maybe
+
+it looks like this, whatever.
+
+I go from V3 to V5, and I
+measure out that length.
+
+And I go the other
+way from V3, and I
+
+know this is getting
+glued to that.
+
+So I know where the vertices
+are from the lengths.
+
+I can figure out exactly
+what this picture must
+
+be when I have-- in
+this case, I happen
+
+to maybe get a vertex
+going to another vertex.
+
+In general, probably get some
+vertex gluing to some edge,
+
+and maybe vice versa.
+
+But if I can figure out
+exactly what that pattern is,
+
+I can figure out the
+label of these guys,
+
+because I know exactly
+what's happening there.
+
+So that's good.
+
+If it's a vertex to vertex edge
+in the gluing tree like this,
+
+I can figure out everything
+between that pair.
+
+Is that enough?
+
+Almost.
+
+So if I have a leaf where
+this is a vertex, which
+
+I was usually denoting
+by a filled circle,
+
+I have various
+degree 2 junctions
+
+which I ignore until I get
+to a degree three or higher
+
+junction.
+
+Now at this place,
+even just looking
+
+at this dot and this dot,
+I know at least one of them
+
+must be a vertex.
+
+Because I can't glue two edges
+together plus other stuff.
+
+I can glue at most one edge.
+
+So maybe this one's an
+edge, like in the picture
+
+that we did before.
+
+But one of them
+has to be a vertex.
+
+And then I can figure out
+exactly what's happening there,
+
+because I have this
+vertex to vertex thing.
+
+And I know the labels.
+
+I know this is V5 and
+this is V13, whatever.
+
+I know exactly what's
+happening on the right side, I
+
+measure backwards, I
+know exactly what's
+
+happening on the left side
+and who's going to what.
+
+So that determines everything.
+
+The problem is when
+I have an edge here,
+
+because then I don't know
+where it is along the edge.
+
+I can't measure lengths
+anymore, somewhere
+
+in the middle of the edge.
+
+And indeed, if I have
+something like this,
+
+where all of these angles--
+I mean this for example
+
+is in a convex polygon, this
+could be a perimeter halving--
+
+and it's not determined
+what's happening here
+
+because this is a rolling belt.
+
+I'll show you how
+undetermined it is.
+
+Suppose you have a bunch
+of vertices like this,
+
+and then some
+vertices like this.
+
+Depending on where I
+bend around for E5,
+
+these guys could be here.
+
+They could be here,
+or here, or here.
+
+They could be in the
+middle straddling this.
+
+In fact, there are about
+n squared different places
+
+where these guys could be,
+relative to these guys.
+
+Because there's going to be n
+transitions from-- if this is n
+
+and this is n-- n transitions
+from this versus that guy,
+
+then n transitions from
+these versus that guy,
+
+n transitions versus that
+guy, total of about n squared.
+
+Actually if this is n and this
+is n, it's exactly n squared.
+
+So we're not quite
+done, but I claim
+
+that there's really only
+order n squared left.
+
+It's always from
+the rolling belts.
+
+We know from last time there's
+at most three rolling belts,
+
+so at most quadratic per belt.
+
+So total outcome is
+polynomial for what's
+
+left, what we haven't specified,
+for how the degree 2 vertices
+
+behave.
+
+These are all
+degree 2 junctions.
+
+It's here, or they're
+here, we don't know.
+
+So if you want to get the full
+specification of what's where,
+
+you do all this work.
+
+And then for the
+degree two junctions,
+
+you have to deal with
+the rolling belts.
+
+The way to prove
+this is say, well,
+
+if I have a leaf that's a
+vertex, I can get rid of it
+
+and induct.
+
+In the end, I'll have
+at most four leaves
+
+because there's at
+most four fold points.
+
+So I have a constant
+number of leaves.
+
+You look at each
+belt, each of them
+
+is quadratic and polynomial.
+
+If you work out the
+bounds here-- we've
+
+tried to be a little
+more precise--
+
+you could prove an overall
+bound of n to the 2L minus 2
+
+for L leaves.
+
+And we have slightly better
+bounds for L equals 4
+
+and L equals 3, but
+that's pretty good.
+
+But the proof I gave is
+at least n to the order L.
+
+We could n to the order L
+count different things here,
+
+and then some N to the
+constant at the end.
+
+This ends the
+combinatorial part.
+
+Now we're going to
+get to algorithms.
+
+So we've proved all
+of these things.
+
+Exponential upper
+and lower bounds
+
+for the general case
+and edge-to-edge case,
+
+and polynomial for
+bounded sharpness,
+
+or when you have a reasonable
+number of leaves in your tree.
+
+I'm going to start with this
+edge-to-edge gluing algorithm.
+
+This is going to use a technique
+called dynamic programming,
+
+which some of you have seen
+before, some of you haven't.
+
+It's a very simple idea.
+
+You take your
+problem that you want
+
+to solve-- which is
+I have a polygon--
+
+and you split it up
+into sub-problems.
+
+You solve each of
+the sub-problems,
+
+and one of the sub-problems
+is actually the whole problem,
+
+and then you're done.
+
+In our case, a
+sub-problem is going
+
+to be some sub-chain
+from one vertex
+
+to another vertex
+of the polygon.
+
+So I have some
+polygon, and I just
+
+look at some interval of
+the boundary from VI to VJ.
+
+And the idea is, well suppose
+that VI is glued to VJ.
+
+How many different
+ways, or how should I
+
+glue the part in between?
+
+How should I glue
+this into itself?
+
+Because there's no
+crossings, there's
+
+going to be no gluings
+from inside to outside.
+
+So that's the sub-problem.
+
+And of course if I say from
+the interval from V1 to V1,
+
+that is the entire problem.
+
+Of course V1 is glued to V1.
+
+So in particular, the
+V1 to V1 sub-problem
+
+is what we want to solve.
+
+So this is our goal.
+
+So I'm going to tell
+you how to solve
+
+all of these sub-problems,
+and therefore
+
+how to solve what we
+actually want to solve.
+
+That's dynamic programming.
+
+So let's try to solve one of
+these sub-problems, VI to VJ.
+
+How are we going to solve it?
+
+So I'm going to draw a picture.
+
+It looks like this.
+
+This is now thinking
+about the gluing tree,
+
+so the polygon's on
+the outside here.
+
+That's one of the main reasons
+gluing trees were developed,
+
+just to describe this algorithm.
+
+This algorthim's
+actually quite old,
+
+1996 by [INAUDIBLE]
+and [INAUDIBLE].
+
+The edge-to-edge case was
+before I joined this group.
+
+And then later together
+we did the general case,
+
+unbounded sharpness, which
+is what we'll do next.
+
+So this is at the
+heart of everything.
+
+So we have VO to
+VJ glued together.
+
+We want to know how to
+glue together the rest.
+
+Well, maybe some vertices
+get glued in here in addition
+
+to VI and VJ, maybe not.
+
+Let's think about what
+gets glued to this edge.
+
+There's the edge
+from VI to VI plus 1.
+
+And this is an edge-to-edge
+gluing, so what
+
+gets glued there
+is an actual edge.
+
+What edge could it be?
+
+Some edge over here, I
+don't know which one.
+
+The power of the
+dynamic programming
+
+is you don't need to know.
+
+It's some edge, VK, VK
+plus 1 gets glued there.
+
+There's only one of them,
+it's out there somewhere.
+
+It has to have
+matching edge length,
+
+but there could be many
+choices, all of which
+
+have matching edge length.
+
+Maybe all the edge
+lengths are the same,
+
+but there's at most n
+choices for that edge.
+
+It's actually at most J
+minus I choices plus 1.
+
+But there's at most
+n edges in here,
+
+so there's at most n
+different possibilities.
+
+Just try them all.
+
+Think about all of them.
+
+I haven't said here whether
+I'm doing-- or I have?
+
+I guess I've been pointing here.
+
+I really want to do both of
+these algorithms at once,
+
+but I'll start with this
+one, which is just find
+
+all the gluings in
+exponential time, which
+
+is optimal in the worst
+case because there
+
+can be exponentially
+many outputs.
+
+So try all n choices
+for VK VK plus 1.
+
+What happens when
+I do one of them?
+
+I might choose one of them.
+
+Well, the new picture will
+be-- so the topological picture
+
+is I still have VI glued to VJ.
+
+Then I also have here VK and
+VI plus 1 glued together.
+
+And I have VI also
+glued to VK plus 1.
+
+Now it's possible
+actually VK plus 1 and VJ
+
+are the same thing, in which
+case there's no loop here.
+
+And that's the case
+when no extra vertex
+
+got glued in there.
+
+But this is the
+generic situation.
+
+If this is link 0, then
+these guys are the same.
+
+So really what I have now are
+two different sub-problems.
+
+There's this thing, which
+is VI plus 1, dot, dot, VK.
+
+And there's this one which
+is VK plus 1 dot, dot, VJ.
+
+The idea with the
+sub-problems is
+
+to solve the
+sub-problems in order
+
+by increasing chain length.
+
+So start with very short ones.
+
+And I saw longer and longer
+ones using the previous results.
+
+If I've already
+computed the answers
+
+to VK plus 1 to VJ
+because that is smaller
+
+than the original--
+look, there's
+
+two edges fewer at least.
+
+This thing is at least 2
+smaller than the original chain
+
+because here's two edges.
+
+So I wanted to solve VI to VJ.
+
+I guessed what VK
+to VK plus 1 was,
+
+meaning I tried all the
+possibilities for each one.
+
+I say, well what are all
+the possibilities for this?
+
+What are all the
+possibilities for this?
+
+Take the cross-product.
+
+Just multiply those
+sets together.
+
+Those are all the
+possible gluings.
+
+And then I sum that.
+
+I take all the options for
+all the different values of K.
+
+And that's it.
+
+That output is all
+the possible gluings.
+
+So this should actually
+give another way
+
+to prove that the number
+of different gluings
+
+is only exponential, but this is
+just for the edge-to-edge case.
+
+Maybe I should write that down.
+
+So we have for each
+choice of K output--
+
+let's say, and for each
+solution to the smaller
+
+sub-problem VK plus 1 to VJ.
+
+And then for each solution
+to VK plus 1 to VK output.
+
+This is very simple.
+
+This is just a product
+over various things.
+
+There's only order
+n choices here.
+
+This thing, it depends
+how many solutions there
+
+are to those sub-problems, but
+it's the product of the two.
+
+And then that's
+the total output.
+
+Believe me, this runs
+in exponential time.
+
+That's not very hard to prove.
+
+What's interesting
+is we can make
+
+the same algorithm with
+a little bit of tweaking
+
+get a polynomial time
+decision algorithm.
+
+That's cool.
+
+How do we make it a
+polynomial decision algorithm?
+
+I can't afford to store every
+solution for every sub-problem
+
+because there can be
+exponentially many.
+
+So I only get to store one
+solution for every sub-problem.
+
+So this is the great idea.
+
+Let's say for each sub-problem,
+let's say VI to VK only store
+
+the solution that
+minimizes the amount
+
+of stuff glued into VI VJ.
+
+So the sum of the
+angles glued at VI,
+
+which is the same thing as
+VJ because they are already
+
+glued together.
+
+That's what we were told.
+
+So I had many choices here.
+
+I had all the choices for
+K. I had all the choices
+
+for up here.
+
+I had all the
+choices for up here.
+
+Well actually now I'm just going
+to think about one choice up
+
+here, which is what
+is the choice that
+
+minimizes the angle glued here?
+
+And what is the
+choice over here that
+
+minimizes the angle glued there?
+
+Why the minimum?
+
+Because some of these are wrong.
+
+I should actually say
+output if it's Alexandroff.
+
+We only want to output
+Alexandroff gluings.
+
+We only want to
+output gluings where
+
+the total sum of the angles
+is less than or equal to 360.
+
+I need to check
+that for every one.
+
+If I want to have the most
+chance of it being Alexandroff,
+
+if I got the least possible
+angle glued here and glued
+
+here, that's my best
+hope of it working.
+
+Now I still have flexibility,
+which is I get to choose k.
+
+There's still n choices
+for k, but everything else
+
+is determined at that point.
+
+Once I fix K I see, well
+does this work, yes or no?
+
+If it works, that
+gives me one candidate
+
+for how much material
+gets glued here.
+
+It could be a lot,
+could be a little.
+
+I try for all K, I
+take the smallest one.
+
+So it's the same loop, except
+there's no four loops here.
+
+It's just for every
+choice of K, I
+
+look at the solution to VK plus
+1 to VJ, the solution for VI
+
+plus 1 to VK.
+
+If it's Alexandroff,
+I don't output it.
+
+But I check, is it the best
+solution so far in terms
+
+of the total angle
+glued of VI and VJ.
+
+I keep looping until I
+find the very best one,
+
+and I output that one.
+
+That would be the
+solution that I store.
+
+The result is, the running
+time is actually polynomial,
+
+because the number of
+sub-problems-- a sub-problem
+
+is determined by two vertices.
+
+There's only n of
+these, n of these.
+
+So the number of
+sub-problems is n squared.
+
+For each sub-problem I need to
+look at order n choices for K.
+
+And so the total
+running time is n
+
+squared times n,
+which is n cubed.
+
+And that will tell
+you if there's
+
+any hope of anything
+working, if there's
+
+any gluing this will find
+one, because it's always
+
+trying to minimize the angles
+that get glued together
+
+That's is edge-to-edge.
+
+Now we can generalize.
+
+It's a little bit
+messy, but we can
+
+generalize to arbitrary gluings.
+
+Let me sketch a little
+bit how that goes.
+
+So we've seen now this result
+for algorithms and this result
+
+for algorithms.
+
+And now I'm going to tell
+you about this result.
+
+I wish there was a result
+here to tell you about,
+
+but there isn't.
+
+So this last part that I did
+where the decision algorithm is
+
+very efficient, we don't
+know how to generalize that
+
+to the general case,
+arbitrary gluings.
+
+This only works
+for edge-to-edge.
+
+We assumed a whole
+edge, VK VK plus 1
+
+was glued to VI VI plus 1.
+
+But the enumeration
+part where we said,
+
+oh just give me
+all the solutions,
+
+that we can get to work.
+
+It's just slightly
+more complicated.
+
+Let me tell you how it
+gets more complicated.
+
+So one difference is that there
+are more kinds of sub-problems,
+
+this is the heart
+of the problem.
+
+We have the VI to VJ sub-problem
+just like before, that's easy.
+
+And then we have the
+VI to EJ sub-problem.
+
+So this one was VI was glued to
+VJ, very clear what that means.
+
+Here we have VI is
+glued to an edge EJ.
+
+The trouble with that is we
+don't know where on the edge
+
+it's glued.
+
+It's somewhere on the edge.
+
+This is where
+things get trickier.
+
+And there's also
+the symmetric case,
+
+of course, where it's EI to VJ.
+
+But we don't really
+need to worry about
+
+that, it's symmetric.
+
+So what does a
+solution look like?
+
+So before, a solution
+was an entire gluing.
+
+Now, because the
+gluings can be infinite.
+
+There can be infinitely
+many different gluings.
+
+I can't actually list
+every one explicitly.
+
+I've actually got to
+explain ranges of gluings
+
+if I have any hope of
+capturing all of them.
+
+So what a solution
+is going to look like
+
+is the combinatorial type of the
+gluing, which was this stuff.
+
+You have an abstract
+gluing tree,
+
+you get which vertices
+glue to what edges.
+
+So you have pretty
+much the whole picture,
+
+just not exactly where each
+vertex is glued to which edge.
+
+Then I also will tell
+you a total angle
+
+of material glued at VI so far.
+
+In both these cases,
+I want to know
+
+how much stuff in
+my gluing at VI
+
+so I can tell whether
+it's Alexandroff.
+
+And then in the case where I
+glue a vertex to an edge, what
+
+I'm going to do is
+give you an interval.
+
+The Interval's always
+going to be starting at 0,
+
+and going to some
+value x. x is less than
+
+or equal to the length
+of the edge, VJ.
+
+And this is the interval along
+the edge where VI can glue.
+
+So I'm going to tell
+you an actual interval
+
+here from the edge EJ.
+
+As long as you glue VI
+to somewhere between
+
+there and there,
+this stuff works.
+
+Whatever I specified
+works over there.
+
+You can't go beyond some point.
+
+That will turn out to be enough.
+
+So while there's the VI to VJ
+case, it's less interesting.
+
+Let's think about now if
+I want to actually solve
+
+the VI to EJ case.
+
+What could happen?
+
+Before there was
+only one-- we looked
+
+at what glues VI to VI
+plus 1 and it was one edge.
+
+It was a little
+easier to think about.
+
+Let's not think
+about the whole edge,
+
+but let's think about locally
+what happens just after VI.
+
+Something gets glued there.
+
+Now it could be EJ
+actually gets glued there.
+
+It could be we continue gluing.
+
+That's kind of like
+zipping, although not
+
+exactly what we were
+calling zipping before.
+
+Here I call it
+zipping, good choice.
+
+So one option is that you
+zip for a little while.
+
+Now, how long would you zip?
+
+A couple options.
+
+You zip until you
+hit a vertex, you
+
+can't stop in the
+middle of two edges.
+
+So maybe you hit a
+vertex here first,
+
+maybe you hit a
+vertex here first,
+
+and the next vertex
+here is farther away.
+
+So there's two pictures.
+
+Let me draw the two pictures.
+
+It could be hit you
+hit VI plus 1 first.
+
+So here's EJ.
+
+It could be you hit
+the vertex of EJ first.
+
+In this case, you
+get a sub-problem
+
+which is VI plus 1 to EJ.
+
+These are glued to each other.
+
+In this case, you get
+this vertex, which I think
+
+is VJ gets glued to the
+edge EI, which is just
+
+the symmetric case I
+was talking about here.
+
+Edge EI is glued to Vertex VJ.
+
+So those are smaller
+sub-problems.
+
+You solve those, and
+then from that you
+
+will see whether this
+actually gives you
+
+a solution to the
+original sub-problem
+
+you wanted to solve.
+
+That's the zip case.
+
+There's another case
+which we call tug.
+
+In the tug case-- so
+that was supposing,
+
+we'll maybe nothing
+else gets glued in here.
+
+But maybe another vertex gets
+glued in there, that's the tug.
+
+To pick a vertex, I pull it in.
+
+So in that case we get
+a picture like this.
+
+So here's EJ, here's
+VI, and now there's
+
+some other vertex VK
+that gets glued in there.
+
+Which vertex?
+
+I don't know, try them all.
+
+Just like before,
+before we were choosing
+
+an edge that gets glued in.
+
+Now it's not necessarily
+a whole edge,
+
+but if there's any
+vertex that glues in,
+
+pick who's the next one.
+
+And now I get a sub-problem
+here which is VI to VK.
+
+I get a sub-problem
+here which is VK to EJ.
+
+I solve each of those, I
+take the cross-product,
+
+I do that for all values
+of K just like I did here,
+
+except the labels have
+changed a little bit,
+
+and I find all the outputs.
+
+And again, you can show that
+it's exponential time at most.
+
+So that's an algorithm.
+
+Now, it's exponential time,
+but really it's not so bad
+
+because it's at most
+cubic like we had before.
+
+But we're doing
+extra work, which
+
+is something like the
+number of gluings dealt
+
+with at each stage
+per sub-problem.
+
+Now, it's not just the
+number of actual solutions,
+
+because we generate
+all possible solutions
+
+and then check whether
+they're Alexandroff.
+
+So if you have some example that
+happens to be unique in the way
+
+that it glues up, this bound
+will not actually be very good.
+
+It's still going to
+consider lots of options.
+
+But in the case of
+bounded sharpness,
+
+where the number of gluings
+is only polynomial--
+
+and it's polynomial
+for a strong reason
+
+that the trees can't
+get very complicated--
+
+then we can actually turn this
+into a polynomial algorithm.
+
+This will be n cubed
+times that bound.
+
+As long as your polygon
+is bounded sharpness,
+
+you can show that at every stage
+of course the number of gluings
+
+will also be polynomial.
+
+And so then even the
+number of gluings
+
+you have to consider and
+check will be polynomial.
+
+So the whole thing will
+be polynomial time,
+
+that is this result
+and this result.
+
+So if your polygon is
+vaguely reasonable,
+
+this is actually a
+really good algorithm.
+
+This algorithm has
+been implemented
+
+by two groups, one
+[INAUDIBLE] in mathematica
+
+and another [INAUDIBLE],
+which sadly is not--
+
+his implementation
+used to be on the web,
+
+I can't find it anymore.
+
+But you get either
+implementation,
+
+plug-in your
+polygon, and it just
+
+lists all the possible gluings.
+
+So that's all the
+theory for today.
+
+Now I want to show you a whole
+bunch of gluings for fun.
+
+Once you have all the stuff,
+we have these programs,
+
+you get to play.
+
+So our first play is not that.
+
+That was the last play.
+
+First thing, we saw this before.
+
+I'll just remind you
+what it looks like
+
+and tell you a little bit
+about what's going on here.
+
+So this was the cube.
+
+And then it's eventually
+going to fold into a cross.
+
+The real study here is
+for the Latin Cross--
+
+which is the picture
+I keep drawing
+
+at the beginning of lecture and
+which will now be unfolded--
+
+what other convex polyhedra
+can you glue that polygon into?
+
+So it's like you're not
+told what the creases are.
+
+You just want to look at
+gluings, the resulting creases.
+
+This is one convex
+polyhedron you can make.
+
+This is something that can
+come from Alexandroff's theorem
+
+that you actually get a flat,
+doubly-covered convex polygon.
+
+It's technically a polyhedron,
+according to Alexandroff.
+
+These are all edge-to-edge
+gluings if the length two edges
+
+are actually subdivided
+into two length one edges.
+
+And this video only enumerates
+the edge-to-edge gluings,
+
+because at this point we only
+had the edge-to-edge algorithm.
+
+I forget, this video
+is '98, I think.
+
+This algorithm was in '96, so
+they had just implemented that.
+
+And then that's when I joined.
+
+I was just starting out as
+a grad student and said,
+
+OK let's make a video.
+
+That would be cool.
+
+So I think there's one more.
+
+And this is the only
+one where we actually
+
+have the animations.
+
+This octahedron, this
+was tricky to find,
+
+beceause at this
+point there were
+
+no algorithms for
+Alexandroff's theorem.
+
+So we found it by taking
+a piece of cardboard,
+
+gluing it up,
+getting a protractor,
+
+and measuring all
+the dihedral angles,
+
+and then typing them in.
+
+And Lo and behold,
+in that animation
+
+they don't perfectly close
+up, but it's very close,
+
+up to the measurement
+error of the protractor.
+
+So for edge-to-edge
+gluings, there
+
+are exactly five
+convex polyhedra
+
+you can make from that cross.
+
+But if you allow
+non-edge-to-edge gluings--
+
+and so some years later when
+we came up with that algorithm
+
+and implemented it, we
+discovered there are 85 gluings
+
+of the cross.
+
+This is only six of them.
+
+We're going to do it
+starting with the cube,
+
+and then we're going to go
+in increasing order of faces.
+
+So there's two flat,
+doubly-covered quadrilaterals.
+
+They're different.
+
+Then there is a bunch of
+tetrahedra that you can make.
+
+None of them are regular.
+
+One of them was edge-to-edge,
+I think it might be this one.
+
+I think there's some more
+tetrahedra at the top there.
+
+The blue labels here
+say what they are.
+
+For each one of
+these we taped up
+
+the-- we knew what
+the gluing was.
+
+We taped it up, and
+then we played with it
+
+until we figured out,
+this must be the creases.
+
+Then we actually drew
+in that create pattern,
+
+folded it up, and verified
+that is the right answer.
+
+Because again, at this
+point no algorithm
+
+for Alexandroff's theorem.
+
+More tetrahedra.
+
+Here we get to the
+five-sided polyhedra.
+
+I think this one is edge-to-edge
+and is in the video.
+
+It's a little hard to
+tell from the-- actually,
+
+you can tell from the pictures.
+
+Here there's two sevens.
+
+That means seven glued to seven.
+
+That means this is a
+fold point, this edge
+
+is glued to that edge.
+
+Over here, every edge
+has only one label,
+
+where again this is
+considered two edges.
+
+So this was the
+edge-to-edge gluing.
+
+I think a couple more slides.
+
+We get another
+pentahedron and then
+
+starting to get hexahedra other
+than the cube, lots of them.
+
+Then we start getting octahedra.
+
+The last one in the
+video was octahedron.
+
+It's not this one, this
+one has some fold points.
+
+It must be-- these
+are all octahedra,
+
+so it's one of these.
+
+This guy.
+
+Of course, it's hard to
+tell from a static image,
+
+but yeah, obviously that was
+the octahedron from the video.
+
+And that is all.
+
+So actually, there's only
+23 distinct polyhedra
+
+you can make, but you can
+make them out of 85 gluings.
+
+So 85 gluings.
+
+If one of them is symmetric,
+the cube is symmetric.
+
+So that's one.
+
+And then the other
+84, there's everything
+
+and its reflectional
+inverse, because this polygon
+
+is symmetric.
+
+So it's 84 divided by 2,
+which is 42, a good number.
+
+42 actual honest
+gluings plus the cube.
+
+But those 42 gluings,
+a lot of them
+
+generate the same
+polyhedron, because there's
+
+only 23 distinct
+polyhedra in the end.
+
+I don't have it here,
+it's on my web page.
+
+You could look up
+all 85, and it says
+
+which ones are the
+same as which ones.
+
+And it was a real surprise
+when we were building them.
+
+It was like, wait
+this looks identical
+
+to this other
+polyhedron, and it's
+
+glued in a very different way.
+
+Sort of an extrasymmetry
+of that polyhedron,
+
+as opposed to the cross itself.
+
+It was pretty cool.
+
+An interesting
+thing to note here
+
+is that we only bisect
+the edges, right?
+
+There's a lot of
+edge-to-edge stuff,
+
+and then some of the
+edges get cut in half.
+
+And in this case actually, they
+look mostly like fold points,
+
+but that's not always the case.
+
+It turns out, if you have a
+polygon were all the edge links
+
+are the same like this and
+you look at non-edge-to-edge
+
+gluings, and there
+are no rolling belts--
+
+because if there's
+rolling belts,
+
+it's infinite because you're
+not going to have anything like
+
+this.
+
+Then it suffices to
+subdivide every edge in half.
+
+And then every non-edge-to-edge
+gluing will become
+
+an edge-to-edge gluing.
+
+This is called the [INAUDIBLE]
+half-length theorem
+
+in our book.
+
+It was proved by
+this guy [INAUDIBLE],
+
+who was one of the
+implementers of the algorithms
+
+for enumerating
+all these gluings.
+
+And he proved it afterward.
+
+The code doesn't actually
+exploit that fact,
+
+but it's kind of neat.
+
+All you have to worry
+about are half edges
+
+in this case where all the
+edge links are the same.
+
+All right, that's a cross.
+
+And it's kind of
+maybe even surprising
+
+that there's only finitely
+many different gluings,
+
+but there's no way to
+get a rolling belt here.
+
+Let's look at-- oh, here
+are all the polyhedra
+
+in a pretty 3D form.
+
+Here is a polygon
+which is convex.
+
+It is the equilateral triangle.
+
+And so, no surprise, there
+a rolling belts here.
+
+But here's the picture of
+how all the rolling belts fit
+
+together.
+
+In principle, you can
+extract this picture
+
+from this algorithm.
+
+Although combined with an
+algorithm for Alexandroff's
+
+theorem, that's the tricky part.
+
+So you have some
+very simple gluings,
+
+like could could fold
+the triangle in half,
+
+get this doubly-covered
+triangle,
+
+you can make a
+regular tetrahedron,
+
+or you can fold the triangle
+into a flat doubly-covered
+
+rectangle like at the top.
+
+And then there are
+rolling belts in between.
+
+So this is one
+rolling belt, this
+
+is another possible
+rolling belt,
+
+another possible rolling
+belt each with a gluing tree.
+
+They're not all drawn here.
+
+And this is sort of
+the topology of all
+
+of the possible gluings you
+could make, which is nice.
+
+So a triangle is
+relatively simple.
+
+The square is a little messier.
+
+There's again a bunch of
+particularly nice gluings
+
+like the [INAUDIBLE], the
+folding in half one way,
+
+folding in half the other
+way, making a letter,
+
+and some tetrahedra that
+are just drawn here.
+
+They're in the middle.
+
+And then there's these
+crazy rolling belts
+
+for how they fit together.
+
+So this is in unit square
+all the different gluings.
+
+And one of the fun things,
+some of them are octahedra,
+
+I have a list here.
+
+But I don't know actually
+which one of these belts
+
+has the octahedra.
+
+It might be a couple of them.
+
+And it turns out, for octahedra
+they actually figured out
+
+an algorithm just for octahedra
+to solve Alexandroff's theorem.
+
+This is again before
+Alexandroff theorem algorithms.
+
+And they wanted to compute, well
+if I take all these polyhdra,
+
+which one has the
+maximum volume?
+
+So if I take a
+square paper, what's
+
+the maximum volume
+shape you can make?
+
+And there it is.
+
+It's kind of fun.
+
+One of those octahedra.
+
+And this is a prettier picture
+of-- so here they actually
+
+computed all the polyhedra.
+
+Obviously not all
+infinitely many of them,
+
+but various snapshots
+along each rolling belt.
+
+And each of these
+rolling belts corresponds
+
+to one of the circles over here.
+
+And that's it.
+
+Any questions?
+
+So that's the end
+of fun with gluings.
+
+We'll look at other kinds of
+gluing problems next class.
\ No newline at end of file
diff --git a/6MssatXXAzc.txt b/6MssatXXAzc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..70e062e240d55ca820759cddb9f3054f33a08151
--- /dev/null
+++ b/6MssatXXAzc.txt
@@ -0,0 +1,9771 @@
+align:start position:0%
+ 
+so we just pick it up where we stopped
+
+ align:start position:0%
+so we just pick it up where we stopped
+ 
+
+ align:start position:0%
+so we just pick it up where we stopped
+last time so we are beginning to discuss
+
+ align:start position:0%
+last time so we are beginning to discuss
+ 
+
+ align:start position:0%
+last time so we are beginning to discuss
+how we are going to sort of do a
+
+ align:start position:0%
+how we are going to sort of do a
+ 
+
+ align:start position:0%
+how we are going to sort of do a
+geometrical approach to physics using a
+
+ align:start position:0%
+geometrical approach to physics using a
+ 
+
+ align:start position:0%
+geometrical approach to physics using a
+more general set of coordinates now so
+
+ align:start position:0%
+more general set of coordinates now so
+ 
+
+ align:start position:0%
+more general set of coordinates now so
+we began talking about how things change
+
+ align:start position:0%
+we began talking about how things change
+ 
+
+ align:start position:0%
+we began talking about how things change
+when I discuss special relativity so
+
+ align:start position:0%
+when I discuss special relativity so
+ 
+
+ align:start position:0%
+when I discuss special relativity so
+from the moment keeping ourselves just a
+
+ align:start position:0%
+from the moment keeping ourselves just a
+ 
+
+ align:start position:0%
+from the moment keeping ourselves just a
+special relativity we by the way are
+
+ align:start position:0%
+special relativity we by the way are
+ 
+
+ align:start position:0%
+special relativity we by the way are
+going to begin lifting our assumptions
+
+ align:start position:0%
+going to begin lifting our assumptions
+ 
+
+ align:start position:0%
+going to begin lifting our assumptions
+that it is simply special relativity
+
+ align:start position:0%
+that it is simply special relativity
+ 
+
+ align:start position:0%
+that it is simply special relativity
+fairly soon but to set that up I need to
+
+ align:start position:0%
+fairly soon but to set that up I need to
+ 
+
+ align:start position:0%
+fairly soon but to set that up I need to
+start thinking about how to work in more
+
+ align:start position:0%
+start thinking about how to work in more
+ 
+
+ align:start position:0%
+start thinking about how to work in more
+general coordinate systems okay so we're
+
+ align:start position:0%
+general coordinate systems okay so we're
+ 
+
+ align:start position:0%
+general coordinate systems okay so we're
+going to do it in the simplest possible
+
+ align:start position:0%
+going to do it in the simplest possible
+ 
+
+ align:start position:0%
+going to do it in the simplest possible
+curvilinear coordinates so it's
+
+ align:start position:0%
+curvilinear coordinates so it's
+ 
+
+ align:start position:0%
+curvilinear coordinates so it's
+basically just going from Cartesian
+
+ align:start position:0%
+basically just going from Cartesian
+ 
+
+ align:start position:0%
+basically just going from Cartesian
+coordinates and the spatial sector to
+
+ align:start position:0%
+coordinates and the spatial sector to
+ 
+
+ align:start position:0%
+coordinates and the spatial sector to
+plane polar coordinates one of the
+
+ align:start position:0%
+plane polar coordinates one of the
+ 
+
+ align:start position:0%
+plane polar coordinates one of the
+things which I have emphasized a few
+
+ align:start position:0%
+things which I have emphasized a few
+ 
+
+ align:start position:0%
+things which I have emphasized a few
+times and I'm going to continue to
+
+ align:start position:0%
+times and I'm going to continue to
+ 
+
+ align:start position:0%
+times and I'm going to continue to
+hammer on is that these are a little bit
+
+ align:start position:0%
+hammer on is that these are a little bit
+ 
+
+ align:start position:0%
+hammer on is that these are a little bit
+different from the curve little
+
+ align:start position:0%
+different from the curve little
+ 
+
+ align:start position:0%
+different from the curve little
+curvilinear coordinates that you are
+
+ align:start position:0%
+curvilinear coordinates that you are
+ 
+
+ align:start position:0%
+curvilinear coordinates that you are
+used to in your past life okay in
+
+ align:start position:0%
+used to in your past life okay in
+ 
+
+ align:start position:0%
+used to in your past life okay in
+particular if I write out the
+
+ align:start position:0%
+particular if I write out the
+ 
+
+ align:start position:0%
+particular if I write out the
+displacements the little vector of a
+
+ align:start position:0%
+displacements the little vector of a
+ 
+
+ align:start position:0%
+displacements the little vector of a
+displacement element in the usual way I
+
+ align:start position:0%
+displacement element in the usual way I
+ 
+
+ align:start position:0%
+displacement element in the usual way I
+am using what's called in a coordinate
+
+ align:start position:0%
+am using what's called in a coordinate
+ 
+
+ align:start position:0%
+am using what's called in a coordinate
+basis which means that the vector DX is
+
+ align:start position:0%
+basis which means that the vector DX is
+ 
+
+ align:start position:0%
+basis which means that the vector DX is
+related to the displacement the
+
+ align:start position:0%
+related to the displacement the
+ 
+
+ align:start position:0%
+related to the displacement the
+differential of the coordinates by just
+
+ align:start position:0%
+differential of the coordinates by just
+ 
+
+ align:start position:0%
+differential of the coordinates by just
+that thing contracted with all the basis
+
+ align:start position:0%
+that thing contracted with all the basis
+ 
+
+ align:start position:0%
+that thing contracted with all the basis
+vectors and so what that means is I've a
+
+ align:start position:0%
+vectors and so what that means is I've a
+ 
+
+ align:start position:0%
+vectors and so what that means is I've a
+little displacement in time which looks
+
+ align:start position:0%
+little displacement in time which looks
+ 
+
+ align:start position:0%
+little displacement in time which looks
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+displacement and radiation looks normal
+
+ align:start position:0%
+displacement and radiation looks normal
+ 
+
+ align:start position:0%
+displacement and radiation looks normal
+displacement in the Z direction which
+
+ align:start position:0%
+displacement in the Z direction which
+ 
+
+ align:start position:0%
+displacement in the Z direction which
+looks normal and a displacement an angle
+
+ align:start position:0%
+looks normal and a displacement an angle
+ 
+
+ align:start position:0%
+looks normal and a displacement an angle
+which does not okay in order for this
+
+ align:start position:0%
+which does not okay in order for this
+ 
+
+ align:start position:0%
+which does not okay in order for this
+whole thing to be dimensionally
+
+ align:start position:0%
+whole thing to be dimensionally
+ 
+
+ align:start position:0%
+whole thing to be dimensionally
+consistent that's telling me EF I has to
+
+ align:start position:0%
+consistent that's telling me EF I has to
+ 
+
+ align:start position:0%
+consistent that's telling me EF I has to
+have the dimensions of length and that
+
+ align:start position:0%
+have the dimensions of length and that
+ 
+
+ align:start position:0%
+have the dimensions of length and that
+is a feature not a bug okay we last time
+
+ align:start position:0%
+is a feature not a bug okay we last time
+ 
+
+ align:start position:0%
+is a feature not a bug okay we last time
+we introduced the matrix that allows me
+
+ align:start position:0%
+we introduced the matrix that allows me
+ 
+
+ align:start position:0%
+we introduced the matrix that allows me
+to convert between one coordinate system
+
+ align:start position:0%
+to convert between one coordinate system
+ 
+
+ align:start position:0%
+to convert between one coordinate system
+and another so just basically the the
+
+ align:start position:0%
+and another so just basically the the
+ 
+
+ align:start position:0%
+and another so just basically the the
+matrix it's sort of a Jacobian matrix
+
+ align:start position:0%
+matrix it's sort of a Jacobian matrix
+ 
+
+ align:start position:0%
+matrix it's sort of a Jacobian matrix
+just the matrix of partials between the
+
+ align:start position:0%
+just the matrix of partials between the
+ 
+
+ align:start position:0%
+just the matrix of partials between the
+two coordinate systems and this idea
+
+ align:start position:0%
+two coordinate systems and this idea
+ 
+
+ align:start position:0%
+two coordinate systems and this idea
+that things you know they they look a
+
+ align:start position:0%
+that things you know they they look a
+ 
+
+ align:start position:0%
+that things you know they they look a
+little weird right so the way I did that
+
+ align:start position:0%
+little weird right so the way I did that
+ 
+
+ align:start position:0%
+little weird right so the way I did that
+was I didn't actually write it out but I
+
+ align:start position:0%
+was I didn't actually write it out but I
+ 
+
+ align:start position:0%
+was I didn't actually write it out but I
+did the usual mapping between x y and r
+
+ align:start position:0%
+did the usual mapping between x y and r
+ 
+
+ align:start position:0%
+did the usual mapping between x y and r
+and phi worked out all of my of my
+
+ align:start position:0%
+and phi worked out all of my of my
+ 
+
+ align:start position:0%
+and phi worked out all of my of my
+derivatives and sure enough you got
+
+ align:start position:0%
+derivatives and sure enough you got
+ 
+
+ align:start position:0%
+derivatives and sure enough you got
+something that looks very standard with
+
+ align:start position:0%
+something that looks very standard with
+ 
+
+ align:start position:0%
+something that looks very standard with
+the possible exception of these ARS that
+
+ align:start position:0%
+the possible exception of these ARS that
+ 
+
+ align:start position:0%
+the possible exception of these ARS that
+are appearing in here so notice the
+
+ align:start position:0%
+are appearing in here so notice the
+ 
+
+ align:start position:0%
+are appearing in here so notice the
+elements of this matrix these do not
+
+ align:start position:0%
+elements of this matrix these do not
+ 
+
+ align:start position:0%
+elements of this matrix these do not
+have consistent units again feature not
+
+ align:start position:0%
+have consistent units again feature not
+ 
+
+ align:start position:0%
+have consistent units again feature not
+bug this guy is basically just the
+
+ align:start position:0%
+bug this guy is basically just the
+ 
+
+ align:start position:0%
+bug this guy is basically just the
+inverse of that this is the matrix that
+
+ align:start position:0%
+inverse of that this is the matrix that
+ 
+
+ align:start position:0%
+inverse of that this is the matrix that
+affects the cordon system the opposite
+
+ align:start position:0%
+affects the cordon system the opposite
+ 
+
+ align:start position:0%
+affects the cordon system the opposite
+direction and
+
+ align:start position:0%
+direction and
+ 
+
+ align:start position:0%
+direction and
+in this case you have some elements
+
+ align:start position:0%
+in this case you have some elements
+ 
+
+ align:start position:0%
+in this case you have some elements
+where their units are one over length
+
+ align:start position:0%
+where their units are one over length
+ 
+
+ align:start position:0%
+where their units are one over length
+okay so let's just continue to sort of
+
+ align:start position:0%
+okay so let's just continue to sort of
+ 
+
+ align:start position:0%
+okay so let's just continue to sort of
+catalog what some of the things we were
+
+ align:start position:0%
+catalog what some of the things we were
+ 
+
+ align:start position:0%
+catalog what some of the things we were
+going to be working with look like in
+
+ align:start position:0%
+going to be working with look like in
+ 
+
+ align:start position:0%
+going to be working with look like in
+this new coordinate representation and
+
+ align:start position:0%
+this new coordinate representation and
+ 
+
+ align:start position:0%
+this new coordinate representation and
+this will lead us to introduce one of
+
+ align:start position:0%
+this will lead us to introduce one of
+ 
+
+ align:start position:0%
+this will lead us to introduce one of
+the mathematical objects that we are
+
+ align:start position:0%
+the mathematical objects that we are
+ 
+
+ align:start position:0%
+the mathematical objects that we are
+going to use extensively as we move
+
+ align:start position:0%
+going to use extensively as we move
+ 
+
+ align:start position:0%
+going to use extensively as we move
+forward in studying this subject so what
+
+ align:start position:0%
+forward in studying this subject so what
+ 
+
+ align:start position:0%
+forward in studying this subject so what
+I want to do next is look at what my
+
+ align:start position:0%
+I want to do next is look at what my
+ 
+
+ align:start position:0%
+I want to do next is look at what my
+basis vectors look like so what I want
+
+ align:start position:0%
+basis vectors look like so what I want
+ 
+
+ align:start position:0%
+basis vectors look like so what I want
+to do is characterize what my er and my
+
+ align:start position:0%
+to do is characterize what my er and my
+ 
+
+ align:start position:0%
+to do is characterize what my er and my
+ePHI look like and these are gonna look
+
+ align:start position:0%
+ePHI look like and these are gonna look
+ 
+
+ align:start position:0%
+ePHI look like and these are gonna look
+very familiar from your intuition from
+
+ align:start position:0%
+very familiar from your intuition from
+ 
+
+ align:start position:0%
+very familiar from your intuition from
+having studied you know things like en
+
+ align:start position:0%
+having studied you know things like en
+ 
+
+ align:start position:0%
+having studied you know things like en
+em in non Cartesian coordinates so your
+
+ align:start position:0%
+em in non Cartesian coordinates so your
+ 
+
+ align:start position:0%
+em in non Cartesian coordinates so your
+er is just related to the original
+
+ align:start position:0%
+er is just related to the original
+ 
+
+ align:start position:0%
+er is just related to the original
+Cartesian basis vectors like so okay and
+
+ align:start position:0%
+Cartesian basis vectors like so okay and
+ 
+
+ align:start position:0%
+Cartesian basis vectors like so okay and
+if you like you can easily read that out
+
+ align:start position:0%
+if you like you can easily read that out
+ 
+
+ align:start position:0%
+if you like you can easily read that out
+by performing the following matrix
+
+ align:start position:0%
+by performing the following matrix
+ 
+
+ align:start position:0%
+by performing the following matrix
+multiplication on the original Cartesian
+
+ align:start position:0%
+multiplication on the original Cartesian
+ 
+
+ align:start position:0%
+multiplication on the original Cartesian
+basis vectors your ePHI perhaps looks a
+
+ align:start position:0%
+basis vectors your ePHI perhaps looks a
+ 
+
+ align:start position:0%
+basis vectors your ePHI perhaps looks a
+little wacky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you can see the length coming
+
+ align:start position:0%
+okay so you can see the length coming
+ 
+
+ align:start position:0%
+okay so you can see the length coming
+into play there a good way to think
+
+ align:start position:0%
+into play there a good way to think
+ 
+
+ align:start position:0%
+into play there a good way to think
+about this is if you sort of you know
+
+ align:start position:0%
+about this is if you sort of you know
+ 
+
+ align:start position:0%
+about this is if you sort of you know
+your intuition about unit vectors sorry
+
+ align:start position:0%
+your intuition about unit vectors sorry
+ 
+
+ align:start position:0%
+your intuition about unit vectors sorry
+your intuition about basis factors I
+
+ align:start position:0%
+your intuition about basis factors I
+ 
+
+ align:start position:0%
+your intuition about basis factors I
+have to be careful this language myself
+
+ align:start position:0%
+have to be careful this language myself
+ 
+
+ align:start position:0%
+have to be careful this language myself
+your intuition about basis vectors it's
+
+ align:start position:0%
+your intuition about basis vectors it's
+ 
+
+ align:start position:0%
+your intuition about basis vectors it's
+typically that they are unit factors
+
+ align:start position:0%
+typically that they are unit factors
+ 
+
+ align:start position:0%
+typically that they are unit factors
+okay these are not unit factors they do
+
+ align:start position:0%
+okay these are not unit factors they do
+ 
+
+ align:start position:0%
+okay these are not unit factors they do
+form a nice basis but they are not unit
+
+ align:start position:0%
+form a nice basis but they are not unit
+ 
+
+ align:start position:0%
+form a nice basis but they are not unit
+vectors in particular the basic idea
+
+ align:start position:0%
+vectors in particular the basic idea
+ 
+
+ align:start position:0%
+vectors in particular the basic idea
+we're gonna go with here is that ePHI
+
+ align:start position:0%
+we're gonna go with here is that ePHI
+ 
+
+ align:start position:0%
+we're gonna go with here is that ePHI
+you know it's always gonna sort of point
+
+ align:start position:0%
+you know it's always gonna sort of point
+ 
+
+ align:start position:0%
+you know it's always gonna sort of point
+in the tangential direction but no
+
+ align:start position:0%
+in the tangential direction but no
+ 
+
+ align:start position:0%
+in the tangential direction but no
+matter where I put it
+
+ align:start position:0%
+matter where I put it
+ 
+
+ align:start position:0%
+matter where I put it
+in radius I want that vector to always
+
+ align:start position:0%
+in radius I want that vector to always
+ 
+
+ align:start position:0%
+in radius I want that vector to always
+sort of sub ten the same amount of angle
+
+ align:start position:0%
+sort of sub ten the same amount of angle
+ 
+
+ align:start position:0%
+sort of sub ten the same amount of angle
+in order to do that it's length needs to
+
+ align:start position:0%
+in order to do that it's length needs to
+ 
+
+ align:start position:0%
+in order to do that it's length needs to
+grow with our okay so that's where
+
+ align:start position:0%
+grow with our okay so that's where
+ 
+
+ align:start position:0%
+grow with our okay so that's where
+that's a little bit different from your
+
+ align:start position:0%
+that's a little bit different from your
+ 
+
+ align:start position:0%
+that's a little bit different from your
+intuition oh and there's a bit there's a
+
+ align:start position:0%
+intuition oh and there's a bit there's a
+ 
+
+ align:start position:0%
+intuition oh and there's a bit there's a
+very good reason for this which we will
+
+ align:start position:0%
+very good reason for this which we will
+ 
+
+ align:start position:0%
+very good reason for this which we will
+get to hopefully well before the end of
+
+ align:start position:0%
+get to hopefully well before the end of
+ 
+
+ align:start position:0%
+get to hopefully well before the end of
+today's class so last time when we were
+
+ align:start position:0%
+today's class so last time when we were
+ 
+
+ align:start position:0%
+today's class so last time when we were
+talking about when we first began to
+
+ align:start position:0%
+talking about when we first began to
+ 
+
+ align:start position:0%
+talking about when we first began to
+talk about tensors a couple of lectures
+
+ align:start position:0%
+talk about tensors a couple of lectures
+ 
+
+ align:start position:0%
+talk about tensors a couple of lectures
+ago the first tensor I gave you so
+
+ align:start position:0%
+ago the first tensor I gave you so
+ 
+
+ align:start position:0%
+ago the first tensor I gave you so
+confining ourselves just to Cartesian
+
+ align:start position:0%
+confining ourselves just to Cartesian
+ 
+
+ align:start position:0%
+confining ourselves just to Cartesian
+coordinates was the metric which was
+
+ align:start position:0%
+coordinates was the metric which was
+ 
+
+ align:start position:0%
+coordinates was the metric which was
+originally introduced as this
+
+ align:start position:0%
+originally introduced as this
+ 
+
+ align:start position:0%
+originally introduced as this
+mathematical object that came at looking
+
+ align:start position:0%
+mathematical object that came at looking
+ 
+
+ align:start position:0%
+mathematical object that came at looking
+at dot products between basis factors
+
+ align:start position:0%
+at dot products between basis factors
+ 
+
+ align:start position:0%
+at dot products between basis factors
+it's essentially a tensor it allows me
+
+ align:start position:0%
+it's essentially a tensor it allows me
+ 
+
+ align:start position:0%
+it's essentially a tensor it allows me
+to feed in two displacements and get the
+
+ align:start position:0%
+to feed in two displacements and get the
+ 
+
+ align:start position:0%
+to feed in two displacements and get the
+the invariant interval between those
+
+ align:start position:0%
+the invariant interval between those
+ 
+
+ align:start position:0%
+the invariant interval between those
+displacements that comes out of that I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+am going to continue to call the dot
+
+ align:start position:0%
+am going to continue to call the dot
+ 
+
+ align:start position:0%
+am going to continue to call the dot
+product of two basis vectors the metric
+
+ align:start position:0%
+product of two basis vectors the metric
+ 
+
+ align:start position:0%
+product of two basis vectors the metric
+but I'm going to use a slightly
+
+ align:start position:0%
+but I'm going to use a slightly
+ 
+
+ align:start position:0%
+but I'm going to use a slightly
+different symbol for this I'm gonna call
+
+ align:start position:0%
+different symbol for this I'm gonna call
+ 
+
+ align:start position:0%
+different symbol for this I'm gonna call
+this G alpha beta okay
+
+ align:start position:0%
+this G alpha beta okay
+ 
+
+ align:start position:0%
+this G alpha beta okay
+in the coordinate representation that we
+
+ align:start position:0%
+in the coordinate representation that we
+ 
+
+ align:start position:0%
+in the coordinate representation that we
+are using right now so in plane polar
+
+ align:start position:0%
+are using right now so in plane polar
+ 
+
+ align:start position:0%
+are using right now so in plane polar
+coordinates this becomes whoops you can
+
+ align:start position:0%
+coordinates this becomes whoops you can
+ 
+
+ align:start position:0%
+coordinates this becomes whoops you can
+work it out from the what I've written
+
+ align:start position:0%
+work it out from the what I've written
+ 
+
+ align:start position:0%
+work it out from the what I've written
+down right here this is just the
+
+ align:start position:0%
+down right here this is just the
+ 
+
+ align:start position:0%
+down right here this is just the
+diagonal of minus one one R squared one
+
+ align:start position:0%
+diagonal of minus one one R squared one
+ 
+
+ align:start position:0%
+diagonal of minus one one R squared one
+okay so this equals dot here this is
+
+ align:start position:0%
+okay so this equals dot here this is
+ 
+
+ align:start position:0%
+okay so this equals dot here this is
+I'll put PPC for plane polar coordinates
+
+ align:start position:0%
+I'll put PPC for plane polar coordinates
+ 
+
+ align:start position:0%
+I'll put PPC for plane polar coordinates
+under that and then using that you know
+
+ align:start position:0%
+under that and then using that you know
+ 
+
+ align:start position:0%
+under that and then using that you know
+that you can always work out the
+
+ align:start position:0%
+that you can always work out the
+ 
+
+ align:start position:0%
+that you can always work out the
+invariant displacement between two
+
+ align:start position:0%
+invariant displacement between two
+ 
+
+ align:start position:0%
+invariant displacement between two
+events it's always going to be the
+
+ align:start position:0%
+events it's always going to be the
+ 
+
+ align:start position:0%
+events it's always going to be the
+metric contracted with the differential
+
+ align:start position:0%
+metric contracted with the differential
+ 
+
+ align:start position:0%
+metric contracted with the differential
+displacement interval actually this
+
+ align:start position:0%
+displacement interval actually this
+ 
+
+ align:start position:0%
+displacement interval actually this
+differential displacement element and
+
+ align:start position:0%
+differential displacement element and
+ 
+
+ align:start position:0%
+differential displacement element and
+this is going to be minus DT squared
+
+ align:start position:0%
+this is going to be minus DT squared
+ 
+
+ align:start position:0%
+this is going to be minus DT squared
+plus D R squared plus R squared 5
+
+ align:start position:0%
+plus D R squared plus R squared 5
+ 
+
+ align:start position:0%
+plus D R squared plus R squared 5
+squared plus DZ squared that I hope
+
+ align:start position:0%
+squared plus DZ squared that I hope
+ 
+
+ align:start position:0%
+squared plus DZ squared that I hope
+makes a lot of sense okay this is
+
+ align:start position:0%
+makes a lot of sense okay this is
+ 
+
+ align:start position:0%
+makes a lot of sense okay this is
+exactly what you would expect if I have
+
+ align:start position:0%
+exactly what you would expect if I have
+ 
+
+ align:start position:0%
+exactly what you would expect if I have
+two events that are separated in plane
+
+ align:start position:0%
+two events that are separated in plane
+ 
+
+ align:start position:0%
+two events that are separated in plane
+polar coordinates by DT D R D Phi D Z
+
+ align:start position:0%
+polar coordinates by DT D R D Phi D Z
+ 
+
+ align:start position:0%
+polar coordinates by DT D R D Phi D Z
+this is what the distance between them
+
+ align:start position:0%
+this is what the distance between them
+ 
+
+ align:start position:0%
+this is what the distance between them
+should be okay so the fact that my basis
+
+ align:start position:0%
+should be okay so the fact that my basis
+ 
+
+ align:start position:0%
+should be okay so the fact that my basis
+vectors have this slightly annoying form
+
+ align:start position:0%
+vectors have this slightly annoying form
+ 
+
+ align:start position:0%
+vectors have this slightly annoying form
+associated with them you know it all
+
+ align:start position:0%
+associated with them you know it all
+ 
+
+ align:start position:0%
+associated with them you know it all
+sort of comes out in the wash air
+
+ align:start position:0%
+sort of comes out in the wash air
+ 
+
+ align:start position:0%
+sort of comes out in the wash air
+remember at the end of the day if we
+
+ align:start position:0%
+remember at the end of the day if we
+ 
+
+ align:start position:0%
+remember at the end of the day if we
+think about quantities that are
+
+ align:start position:0%
+think about quantities that are
+ 
+
+ align:start position:0%
+think about quantities that are
+representation independent and that's
+
+ align:start position:0%
+representation independent and that's
+ 
+
+ align:start position:0%
+representation independent and that's
+going to be the key thing when you
+
+ align:start position:0%
+going to be the key thing when you
+ 
+
+ align:start position:0%
+going to be the key thing when you
+assemble scale or if you assemble the
+
+ align:start position:0%
+assemble scale or if you assemble the
+ 
+
+ align:start position:0%
+assemble scale or if you assemble the
+scalars out of these things you know the
+
+ align:start position:0%
+scalars out of these things you know the
+ 
+
+ align:start position:0%
+scalars out of these things you know the
+individual tensor components make me a
+
+ align:start position:0%
+individual tensor components make me a
+ 
+
+ align:start position:0%
+individual tensor components make me a
+little bit confusing sometimes okay they
+
+ align:start position:0%
+little bit confusing sometimes okay they
+ 
+
+ align:start position:0%
+little bit confusing sometimes okay they
+are not things that we measure they are
+
+ align:start position:0%
+are not things that we measure they are
+ 
+
+ align:start position:0%
+are not things that we measure they are
+not things that really characterize what
+
+ align:start position:0%
+not things that really characterize what
+ 
+
+ align:start position:0%
+not things that really characterize what
+we are going to be working with and we
+
+ align:start position:0%
+we are going to be working with and we
+ 
+
+ align:start position:0%
+we are going to be working with and we
+really want to get into the physics
+
+ align:start position:0%
+really want to get into the physics
+ 
+
+ align:start position:0%
+really want to get into the physics
+unless we're very careful about this is
+
+ align:start position:0%
+unless we're very careful about this is
+ 
+
+ align:start position:0%
+unless we're very careful about this is
+something you can measure okay and so
+
+ align:start position:0%
+something you can measure okay and so
+ 
+
+ align:start position:0%
+something you can measure okay and so
+sure enough it comes out and it's got a
+
+ align:start position:0%
+sure enough it comes out and it's got a
+ 
+
+ align:start position:0%
+sure enough it comes out and it's got a
+good meaning to it let me just wrap up
+
+ align:start position:0%
+good meaning to it let me just wrap up
+ 
+
+ align:start position:0%
+good meaning to it let me just wrap up
+one last thing before I talk about sort
+
+ align:start position:0%
+one last thing before I talk about sort
+ 
+
+ align:start position:0%
+one last thing before I talk about sort
+of where we're going with this so just
+
+ align:start position:0%
+of where we're going with this so just
+ 
+
+ align:start position:0%
+of where we're going with this so just
+for completeness let me write down the
+
+ align:start position:0%
+for completeness let me write down the
+ 
+
+ align:start position:0%
+for completeness let me write down the
+basis one forms just as the basis
+
+ align:start position:0%
+basis one forms just as the basis
+ 
+
+ align:start position:0%
+basis one forms just as the basis
+vectors had a bit of a funny form
+
+ align:start position:0%
+vectors had a bit of a funny form
+ 
+
+ align:start position:0%
+vectors had a bit of a funny form
+associated with them you're gonna find
+
+ align:start position:0%
+associated with them you're gonna find
+ 
+
+ align:start position:0%
+associated with them you're gonna find
+the basis one forms likewise have a bit
+
+ align:start position:0%
+the basis one forms likewise have a bit
+ 
+
+ align:start position:0%
+the basis one forms likewise have a bit
+of a funny form associate with them and
+
+ align:start position:0%
+of a funny form associate with them and
+ 
+
+ align:start position:0%
+of a funny form associate with them and
+the way I'm going to get these and so
+
+ align:start position:0%
+the way I'm going to get these and so
+ 
+
+ align:start position:0%
+the way I'm going to get these and so
+these are going to be the Cartesian
+
+ align:start position:0%
+these are going to be the Cartesian
+ 
+
+ align:start position:0%
+these are going to be the Cartesian
+basis one forms basically I just I'm not
+
+ align:start position:0%
+basis one forms basically I just I'm not
+ 
+
+ align:start position:0%
+basis one forms basically I just I'm not
+carefully proving all these relations
+
+ align:start position:0%
+carefully proving all these relations
+ 
+
+ align:start position:0%
+carefully proving all these relations
+just at this point okay you all know how
+
+ align:start position:0%
+just at this point okay you all know how
+ 
+
+ align:start position:0%
+just at this point okay you all know how
+to do that I'm just using line up the
+
+ align:start position:0%
+to do that I'm just using line up the
+ 
+
+ align:start position:0%
+to do that I'm just using line up the
+indices rule
+
+ align:start position:0%
+indices rule
+ 
+
+ align:start position:0%
+indices rule
+and then when you do that you get this
+
+ align:start position:0%
+and then when you do that you get this
+ 
+
+ align:start position:0%
+and then when you do that you get this
+and like why is your face it's one form
+
+ align:start position:0%
+and like why is your face it's one form
+ 
+
+ align:start position:0%
+and like why is your face it's one form
+for the axial direction I'll just write
+
+ align:start position:0%
+for the axial direction I'll just write
+ 
+
+ align:start position:0%
+for the axial direction I'll just write
+down the result it's gonna look like
+
+ align:start position:0%
+down the result it's gonna look like
+ 
+
+ align:start position:0%
+down the result it's gonna look like
+this okay so it's a key place where all
+
+ align:start position:0%
+this okay so it's a key place where all
+ 
+
+ align:start position:0%
+this okay so it's a key place where all
+of this so right now these are all just
+
+ align:start position:0%
+of this so right now these are all just
+ 
+
+ align:start position:0%
+of this so right now these are all just
+sort of definitions nothing I've done
+
+ align:start position:0%
+sort of definitions nothing I've done
+ 
+
+ align:start position:0%
+sort of definitions nothing I've done
+here should be anything that even
+
+ align:start position:0%
+here should be anything that even
+ 
+
+ align:start position:0%
+here should be anything that even
+approaches a surprise I hope you know
+
+ align:start position:0%
+approaches a surprise I hope you know
+ 
+
+ align:start position:0%
+approaches a surprise I hope you know
+just given that you guys have done the
+
+ align:start position:0%
+just given that you guys have done the
+ 
+
+ align:start position:0%
+just given that you guys have done the
+key thing that's probably new is just
+
+ align:start position:0%
+key thing that's probably new is just
+ 
+
+ align:start position:0%
+key thing that's probably new is just
+all this this garbage associated with
+
+ align:start position:0%
+all this this garbage associated with
+ 
+
+ align:start position:0%
+all this this garbage associated with
+coordinate basis these actor factors of
+
+ align:start position:0%
+coordinate basis these actor factors of
+ 
+
+ align:start position:0%
+coordinate basis these actor factors of
+R and 1 over R that are popping up but
+
+ align:start position:0%
+R and 1 over R that are popping up but
+ 
+
+ align:start position:0%
+R and 1 over R that are popping up but
+provided you're willing to sort of
+
+ align:start position:0%
+provided you're willing to sort of
+ 
+
+ align:start position:0%
+provided you're willing to sort of
+swallow your discomfort and go through
+
+ align:start position:0%
+swallow your discomfort and go through
+ 
+
+ align:start position:0%
+swallow your discomfort and go through
+the motions these are not difficult
+
+ align:start position:0%
+the motions these are not difficult
+ 
+
+ align:start position:0%
+the motions these are not difficult
+calculations at the key place where all
+
+ align:start position:0%
+calculations at the key place where all
+ 
+
+ align:start position:0%
+calculations at the key place where all
+of this really matters is going to be
+
+ align:start position:0%
+of this really matters is going to be
+ 
+
+ align:start position:0%
+of this really matters is going to be
+when we calculate derivatives of things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turn out there is an important role when
+
+ align:start position:0%
+turn out there is an important role when
+ 
+
+ align:start position:0%
+turn out there is an important role when
+we talk about integrals as well a little
+
+ align:start position:0%
+we talk about integrals as well a little
+ 
+
+ align:start position:0%
+we talk about integrals as well a little
+bit later let's just say that so now
+
+ align:start position:0%
+bit later let's just say that so now
+ 
+
+ align:start position:0%
+bit later let's just say that so now
+we'll focus on derivatives so all the
+
+ align:start position:0%
+we'll focus on derivatives so all the
+ 
+
+ align:start position:0%
+we'll focus on derivatives so all the
+derivatives that we've been looking at
+
+ align:start position:0%
+derivatives that we've been looking at
+ 
+
+ align:start position:0%
+derivatives that we've been looking at
+so far we have indeed done a couple
+
+ align:start position:0%
+so far we have indeed done a couple
+ 
+
+ align:start position:0%
+so far we have indeed done a couple
+calculations where we've computed the
+
+ align:start position:0%
+calculations where we've computed the
+ 
+
+ align:start position:0%
+calculations where we've computed the
+derivatives of various vector valued and
+
+ align:start position:0%
+derivatives of various vector valued and
+ 
+
+ align:start position:0%
+derivatives of various vector valued and
+tension valued quantities and it was
+
+ align:start position:0%
+tension valued quantities and it was
+ 
+
+ align:start position:0%
+tension valued quantities and it was
+helped by the fact that all the bases
+
+ align:start position:0%
+helped by the fact that all the bases
+ 
+
+ align:start position:0%
+helped by the fact that all the bases
+when I worked in Cartesian coordinates
+
+ align:start position:0%
+when I worked in Cartesian coordinates
+ 
+
+ align:start position:0%
+when I worked in Cartesian coordinates
+are constant well that's not the case
+
+ align:start position:0%
+are constant well that's not the case
+ 
+
+ align:start position:0%
+are constant well that's not the case
+now so now we need to account for the
+
+ align:start position:0%
+now so now we need to account for the
+ 
+
+ align:start position:0%
+now so now we need to account for the
+fact that the Basie's all vary with our
+
+ align:start position:0%
+fact that the Basie's all vary with our
+ 
+
+ align:start position:0%
+fact that the Basie's all vary with our
+coordinates so let me just quickly make
+
+ align:start position:0%
+coordinates so let me just quickly make
+ 
+
+ align:start position:0%
+coordinates so let me just quickly make
+a catalog of all the non-trivial there's
+
+ align:start position:0%
+a catalog of all the non-trivial there's
+ 
+
+ align:start position:0%
+a catalog of all the non-trivial there's
+basically four in this one where I'm
+
+ align:start position:0%
+basically four in this one where I'm
+ 
+
+ align:start position:0%
+basically four in this one where I'm
+just doing plain polar coordinates there
+
+ align:start position:0%
+just doing plain polar coordinates there
+ 
+
+ align:start position:0%
+just doing plain polar coordinates there
+are four non-trivial derivatives we need
+
+ align:start position:0%
+are four non-trivial derivatives we need
+ 
+
+ align:start position:0%
+are four non-trivial derivatives we need
+to worry about one of them actually
+
+ align:start position:0%
+to worry about one of them actually
+ 
+
+ align:start position:0%
+to worry about one of them actually
+turns out to be zero so the radial
+
+ align:start position:0%
+turns out to be zero so the radial
+ 
+
+ align:start position:0%
+turns out to be zero so the radial
+derivative of the radial unit vector is
+
+ align:start position:0%
+derivative of the radial unit vector is
+ 
+
+ align:start position:0%
+derivative of the radial unit vector is
+0 but the Phi derivative of the Phi unit
+
+ align:start position:0%
+0 but the Phi derivative of the Phi unit
+ 
+
+ align:start position:0%
+0 but the Phi derivative of the Phi unit
+vector is not okay you go and take the
+
+ align:start position:0%
+vector is not okay you go and take the
+ 
+
+ align:start position:0%
+vector is not okay you go and take the
+Phi derivative of this guy and you
+
+ align:start position:0%
+Phi derivative of this guy and you
+ 
+
+ align:start position:0%
+Phi derivative of this guy and you
+basically get take the v derivative this
+
+ align:start position:0%
+basically get take the v derivative this
+ 
+
+ align:start position:0%
+basically get take the v derivative this
+you're going to get this back module a
+
+ align:start position:0%
+you're going to get this back module a
+ 
+
+ align:start position:0%
+you're going to get this back module a
+factor of radius so I can write D er D
+
+ align:start position:0%
+factor of radius so I can write D er D
+ 
+
+ align:start position:0%
+factor of radius so I can write D er D
+Phi scuze me as ePHI over R if I take
+
+ align:start position:0%
+Phi scuze me as ePHI over R if I take
+ 
+
+ align:start position:0%
+Phi scuze me as ePHI over R if I take
+the derivative of e Phi with respect to
+
+ align:start position:0%
+the derivative of e Phi with respect to
+ 
+
+ align:start position:0%
+the derivative of e Phi with respect to
+R I get e Phi back divided by R so the
+
+ align:start position:0%
+R I get e Phi back divided by R so the
+ 
+
+ align:start position:0%
+R I get e Phi back divided by R so the
+simplest way to write this just like so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally if I take the Phi derivative
+
+ align:start position:0%
+and finally if I take the Phi derivative
+ 
+
+ align:start position:0%
+and finally if I take the Phi derivative
+of the Phi unit vector I get er back
+
+ align:start position:0%
+of the Phi unit vector I get er back
+ 
+
+ align:start position:0%
+of the Phi unit vector I get er back
+with an extra factor of R thrown aside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're gonna see a way of doing this
+
+ align:start position:0%
+so we're gonna see a way of doing this
+ 
+
+ align:start position:0%
+so we're gonna see a way of doing this
+it's a little bit system more systematic
+
+ align:start position:0%
+it's a little bit system more systematic
+ 
+
+ align:start position:0%
+it's a little bit system more systematic
+later but I want to just keep this
+
+ align:start position:0%
+later but I want to just keep this
+ 
+
+ align:start position:0%
+later but I want to just keep this
+simple example where we can just
+
+ align:start position:0%
+simple example where we can just
+ 
+
+ align:start position:0%
+simple example where we can just
+basically by hand calculate all the
+
+ align:start position:0%
+basically by hand calculate all the
+ 
+
+ align:start position:0%
+basically by hand calculate all the
+non-trivial derivatives easily of course
+
+ align:start position:0%
+non-trivial derivatives easily of course
+ 
+
+ align:start position:0%
+non-trivial derivatives easily of course
+there's also a T unit vector and a Z
+
+ align:start position:0%
+there's also a T unit vector and a Z
+ 
+
+ align:start position:0%
+there's also a T unit vector and a Z
+unit vector but they're constant so I'm
+
+ align:start position:0%
+unit vector but they're constant so I'm
+ 
+
+ align:start position:0%
+unit vector but they're constant so I'm
+not going to bother writing them out all
+
+ align:start position:0%
+not going to bother writing them out all
+ 
+
+ align:start position:0%
+not going to bother writing them out all
+the derivatives associated them are
+
+ align:start position:0%
+the derivatives associated them are
+ 
+
+ align:start position:0%
+the derivatives associated them are
+equal to zero so let's imagine now that
+
+ align:start position:0%
+equal to zero so let's imagine now that
+ 
+
+ align:start position:0%
+equal to zero so let's imagine now that
+I have assembled some vector so I had
+
+ align:start position:0%
+I have assembled some vector so I had
+ 
+
+ align:start position:0%
+I have assembled some vector so I had
+some vector field that lives in this
+
+ align:start position:0%
+some vector field that lives in this
+ 
+
+ align:start position:0%
+some vector field that lives in this
+space-time and I'm using this basis and
+
+ align:start position:0%
+space-time and I'm using this basis and
+ 
+
+ align:start position:0%
+space-time and I'm using this basis and
+so I would write this vector with
+
+ align:start position:0%
+so I would write this vector with
+ 
+
+ align:start position:0%
+so I would write this vector with
+components V alpha and let's let the so
+
+ align:start position:0%
+components V alpha and let's let the so
+ 
+
+ align:start position:0%
+components V alpha and let's let the so
+this is going to be a curvilinear
+
+ align:start position:0%
+this is going to be a curvilinear
+ 
+
+ align:start position:0%
+this is going to be a curvilinear
+coordinate system this will be plain
+
+ align:start position:0%
+coordinate system this will be plain
+ 
+
+ align:start position:0%
+coordinate system this will be plain
+polar coordinates being used here plain
+
+ align:start position:0%
+polar coordinates being used here plain
+ 
+
+ align:start position:0%
+polar coordinates being used here plain
+polar coordinate basis vectors and what
+
+ align:start position:0%
+polar coordinate basis vectors and what
+ 
+
+ align:start position:0%
+polar coordinate basis vectors and what
+I would like to do is assemble the
+
+ align:start position:0%
+I would like to do is assemble the
+ 
+
+ align:start position:0%
+I would like to do is assemble the
+tensor that you can think of essentially
+
+ align:start position:0%
+tensor that you can think of essentially
+ 
+
+ align:start position:0%
+tensor that you can think of essentially
+as the gradient of this vector so let's
+
+ align:start position:0%
+as the gradient of this vector so let's
+ 
+
+ align:start position:0%
+as the gradient of this vector so let's
+begin by doing this in a sort of
+
+ align:start position:0%
+begin by doing this in a sort of
+ 
+
+ align:start position:0%
+begin by doing this in a sort of
+abstract notation so the gradient of
+
+ align:start position:0%
+abstract notation so the gradient of
+ 
+
+ align:start position:0%
+abstract notation so the gradient of
+this guy this is sort of ugly notation
+
+ align:start position:0%
+this guy this is sort of ugly notation
+ 
+
+ align:start position:0%
+this guy this is sort of ugly notation
+but live with it you know following what
+
+ align:start position:0%
+but live with it you know following what
+ 
+
+ align:start position:0%
+but live with it you know following what
+we have been doing all along what you
+
+ align:start position:0%
+we have been doing all along what you
+ 
+
+ align:start position:0%
+we have been doing all along what you
+would want to do is just take the
+
+ align:start position:0%
+would want to do is just take the
+ 
+
+ align:start position:0%
+would want to do is just take the
+derivative of this whole thing it's
+
+ align:start position:0%
+derivative of this whole thing it's
+ 
+
+ align:start position:0%
+derivative of this whole thing it's
+gonna have a downstairs component on it
+
+ align:start position:0%
+gonna have a downstairs component on it
+ 
+
+ align:start position:0%
+gonna have a downstairs component on it
+so attached to it the basis one form
+
+ align:start position:0%
+so attached to it the basis one form
+ 
+
+ align:start position:0%
+so attached to it the basis one form
+okay if you prefer you can write it
+
+ align:start position:0%
+okay if you prefer you can write it
+ 
+
+ align:start position:0%
+okay if you prefer you can write it
+using the the denotation like I have
+
+ align:start position:0%
+using the the denotation like I have
+ 
+
+ align:start position:0%
+using the the denotation like I have
+there but I just wanna stick with the
+
+ align:start position:0%
+there but I just wanna stick with the
+ 
+
+ align:start position:0%
+there but I just wanna stick with the
+form I wrote in my notes looking at this
+
+ align:start position:0%
+form I wrote in my notes looking at this
+ 
+
+ align:start position:0%
+form I wrote in my notes looking at this
+the way I've sort of got this right now
+
+ align:start position:0%
+the way I've sort of got this right now
+ 
+
+ align:start position:0%
+the way I've sort of got this right now
+I sort of I can think of you know if I
+
+ align:start position:0%
+I sort of I can think of you know if I
+ 
+
+ align:start position:0%
+I sort of I can think of you know if I
+don't include the basis one forms here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this should be the components of a one
+
+ align:start position:0%
+this should be the components of a one
+ 
+
+ align:start position:0%
+this should be the components of a one
+form so this should be a tensorial kind
+
+ align:start position:0%
+form so this should be a tensorial kind
+ 
+
+ align:start position:0%
+form so this should be a tensorial kind
+of object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's just expand out that derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's write it like this so you just you
+
+ align:start position:0%
+let's write it like this so you just you
+ 
+
+ align:start position:0%
+let's write it like this so you just you
+know we haven't changed calculus right
+
+ align:start position:0%
+know we haven't changed calculus right
+ 
+
+ align:start position:0%
+know we haven't changed calculus right
+so when I do this I'm gonna basically
+
+ align:start position:0%
+so when I do this I'm gonna basically
+ 
+
+ align:start position:0%
+so when I do this I'm gonna basically
+use the old-fashioned Leibniz rule for
+
+ align:start position:0%
+use the old-fashioned Leibniz rule for
+ 
+
+ align:start position:0%
+use the old-fashioned Leibniz rule for
+expanding the derivative of the product
+
+ align:start position:0%
+expanding the derivative of the product
+ 
+
+ align:start position:0%
+expanding the derivative of the product
+of two things here's the key thing which
+
+ align:start position:0%
+of two things here's the key thing which
+ 
+
+ align:start position:0%
+of two things here's the key thing which
+I want to emphasize in order for this
+
+ align:start position:0%
+I want to emphasize in order for this
+ 
+
+ align:start position:0%
+I want to emphasize in order for this
+whole thing to be you know for this to
+
+ align:start position:0%
+whole thing to be you know for this to
+ 
+
+ align:start position:0%
+whole thing to be you know for this to
+be a tensorial object something that i
+
+ align:start position:0%
+be a tensorial object something that i
+ 
+
+ align:start position:0%
+be a tensorial object something that i
+couple to this basis one form the sum of
+
+ align:start position:0%
+couple to this basis one form the sum of
+ 
+
+ align:start position:0%
+couple to this basis one form the sum of
+these two objects must obey the rules
+
+ align:start position:0%
+these two objects must obey the rules
+ 
+
+ align:start position:0%
+these two objects must obey the rules
+for transforming tensors but the two
+
+ align:start position:0%
+for transforming tensors but the two
+ 
+
+ align:start position:0%
+for transforming tensors but the two
+objects individually will not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so this is an important point which I'm
+
+ align:start position:0%
+so this is an important point which I'm
+ 
+
+ align:start position:0%
+so this is an important point which I'm
+gonna emphasize in slightly different
+
+ align:start position:0%
+gonna emphasize in slightly different
+ 
+
+ align:start position:0%
+gonna emphasize in slightly different
+words in just a few moments again this
+
+ align:start position:0%
+words in just a few moments again this
+ 
+
+ align:start position:0%
+words in just a few moments again this
+is one of the key things I want you to
+
+ align:start position:0%
+is one of the key things I want you to
+ 
+
+ align:start position:0%
+is one of the key things I want you to
+get out of this lecture so that when I'm
+
+ align:start position:0%
+get out of this lecture so that when I'm
+ 
+
+ align:start position:0%
+get out of this lecture so that when I'm
+taking derivatives of things like this
+
+ align:start position:0%
+taking derivatives of things like this
+ 
+
+ align:start position:0%
+taking derivatives of things like this
+you got to be a little bit careful about
+
+ align:start position:0%
+you got to be a little bit careful about
+ 
+
+ align:start position:0%
+you got to be a little bit careful about
+what you consider B components of
+
+ align:start position:0%
+what you consider B components of
+ 
+
+ align:start position:0%
+what you consider B components of
+tensors and what is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now as written like that this is kind of
+
+ align:start position:0%
+now as written like that this is kind of
+ 
+
+ align:start position:0%
+now as written like that this is kind of
+annoying
+
+ align:start position:0%
+annoying
+ 
+
+ align:start position:0%
+annoying
+so my first object has a nice basis
+
+ align:start position:0%
+so my first object has a nice basis
+ 
+
+ align:start position:0%
+so my first object has a nice basis
+vector attached to it my second object
+
+ align:start position:0%
+vector attached to it my second object
+ 
+
+ align:start position:0%
+vector attached to it my second object
+involves a derivative of the basis
+
+ align:start position:0%
+involves a derivative of the basis
+ 
+
+ align:start position:0%
+involves a derivative of the basis
+vector however something we saw over
+
+ align:start position:0%
+vector however something we saw over
+ 
+
+ align:start position:0%
+vector however something we saw over
+here is that derivatives of basis
+
+ align:start position:0%
+here is that derivatives of basis
+ 
+
+ align:start position:0%
+here is that derivatives of basis
+vectors are themselves proportional to
+
+ align:start position:0%
+vectors are themselves proportional to
+ 
+
+ align:start position:0%
+vectors are themselves proportional to
+basis vectors so what I'm going to do is
+
+ align:start position:0%
+basis vectors so what I'm going to do is
+ 
+
+ align:start position:0%
+basis vectors so what I'm going to do is
+introduce a bit of notation so let me
+
+ align:start position:0%
+introduce a bit of notation so let me
+ 
+
+ align:start position:0%
+introduce a bit of notation so let me
+switch notation slightly here so the
+
+ align:start position:0%
+switch notation slightly here so the
+ 
+
+ align:start position:0%
+switch notation slightly here so the
+beta derivative of e alpha can be
+
+ align:start position:0%
+beta derivative of e alpha can be
+ 
+
+ align:start position:0%
+beta derivative of e alpha can be
+written as in general it can be written
+
+ align:start position:0%
+written as in general it can be written
+ 
+
+ align:start position:0%
+written as in general it can be written
+as a linear combination of basis factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we're going to do is define D
+
+ align:start position:0%
+so what we're going to do is define D
+ 
+
+ align:start position:0%
+so what we're going to do is define D
+want to make sure my Greek letters are
+
+ align:start position:0%
+want to make sure my Greek letters are
+ 
+
+ align:start position:0%
+want to make sure my Greek letters are
+legible to everyone in the room here so
+
+ align:start position:0%
+legible to everyone in the room here so
+ 
+
+ align:start position:0%
+legible to everyone in the room here so
+let me write this nice and clearly D
+
+ align:start position:0%
+let me write this nice and clearly D
+ 
+
+ align:start position:0%
+let me write this nice and clearly D
+beta of e alpha I'm gonna write that as
+
+ align:start position:0%
+beta of e alpha I'm gonna write that as
+ 
+
+ align:start position:0%
+beta of e alpha I'm gonna write that as
+capital gamma mu beta alpha email this
+
+ align:start position:0%
+capital gamma mu beta alpha email this
+ 
+
+ align:start position:0%
+capital gamma mu beta alpha email this
+gamma that I've just introduced here in
+
+ align:start position:0%
+gamma that I've just introduced here in
+ 
+
+ align:start position:0%
+gamma that I've just introduced here in
+this context is known as the Christoffel
+
+ align:start position:0%
+this context is known as the Christoffel
+ 
+
+ align:start position:0%
+this context is known as the Christoffel
+symbol fact I'm calling this a symbol
+
+ align:start position:0%
+symbol fact I'm calling this a symbol
+ 
+
+ align:start position:0%
+symbol fact I'm calling this a symbol
+it's got three indices on it you might
+
+ align:start position:0%
+it's got three indices on it you might
+ 
+
+ align:start position:0%
+it's got three indices on it you might
+look at in goose smells like a tensor
+
+ align:start position:0%
+look at in goose smells like a tensor
+ 
+
+ align:start position:0%
+look at in goose smells like a tensor
+okay be a little bit careful in much the
+
+ align:start position:0%
+okay be a little bit careful in much the
+ 
+
+ align:start position:0%
+okay be a little bit careful in much the
+same way that these two terms are not
+
+ align:start position:0%
+same way that these two terms are not
+ 
+
+ align:start position:0%
+same way that these two terms are not
+individually components of a tensor but
+
+ align:start position:0%
+individually components of a tensor but
+ 
+
+ align:start position:0%
+individually components of a tensor but
+their sum is this guy individually is
+
+ align:start position:0%
+their sum is this guy individually is
+ 
+
+ align:start position:0%
+their sum is this guy individually is
+actually not a compound of a tensor but
+
+ align:start position:0%
+actually not a compound of a tensor but
+ 
+
+ align:start position:0%
+actually not a compound of a tensor but
+when combined with other things it
+
+ align:start position:0%
+when combined with other things it
+ 
+
+ align:start position:0%
+when combined with other things it
+allows us to assemble tensors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for our plane polar coordinates there
+
+ align:start position:0%
+so for our plane polar coordinates there
+ 
+
+ align:start position:0%
+so for our plane polar coordinates there
+are exactly three nonzero Christoffel
+
+ align:start position:0%
+are exactly three nonzero Christoffel
+ 
+
+ align:start position:0%
+are exactly three nonzero Christoffel
+symbols so Gamma Phi R Phi is equal to
+
+ align:start position:0%
+symbols so Gamma Phi R Phi is equal to
+ 
+
+ align:start position:0%
+symbols so Gamma Phi R Phi is equal to
+one over R which is also equal to Gamma
+
+ align:start position:0%
+one over R which is also equal to Gamma
+ 
+
+ align:start position:0%
+one over R which is also equal to Gamma
+Phi Phi R gamma R Phi Phi is minus R and
+
+ align:start position:0%
+Phi Phi R gamma R Phi Phi is minus R and
+ 
+
+ align:start position:0%
+Phi Phi R gamma R Phi Phi is minus R and
+you can basically just read that out of
+
+ align:start position:0%
+you can basically just read that out of
+ 
+
+ align:start position:0%
+you can basically just read that out of
+that table that I wrote down over there
+
+ align:start position:0%
+that table that I wrote down over there
+ 
+
+ align:start position:0%
+that table that I wrote down over there
+all the others will be equal to zero now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from this example this sort of makes it
+
+ align:start position:0%
+from this example this sort of makes it
+ 
+
+ align:start position:0%
+from this example this sort of makes it
+smell like every time you introduce a
+
+ align:start position:0%
+smell like every time you introduce a
+ 
+
+ align:start position:0%
+smell like every time you introduce a
+new coordinate representation you're
+
+ align:start position:0%
+new coordinate representation you're
+ 
+
+ align:start position:0%
+new coordinate representation you're
+going to need to sit down for an hour
+
+ align:start position:0%
+going to need to sit down for an hour
+ 
+
+ align:start position:0%
+going to need to sit down for an hour
+and a half or something like that and
+
+ align:start position:0%
+and a half or something like that and
+ 
+
+ align:start position:0%
+and a half or something like that and
+just work out all the bloody derivatives
+
+ align:start position:0%
+just work out all the bloody derivatives
+ 
+
+ align:start position:0%
+just work out all the bloody derivatives
+and then go you know read out all the
+
+ align:start position:0%
+and then go you know read out all the
+ 
+
+ align:start position:0%
+and then go you know read out all the
+different components of this thing and
+
+ align:start position:0%
+different components of this thing and
+ 
+
+ align:start position:0%
+different components of this thing and
+assemble them together there actually is
+
+ align:start position:0%
+assemble them together there actually is
+ 
+
+ align:start position:0%
+assemble them together there actually is
+an algorithm that we will get to at the
+
+ align:start position:0%
+an algorithm that we will get to at the
+ 
+
+ align:start position:0%
+an algorithm that we will get to at the
+end of this class that allows you to
+
+ align:start position:0%
+end of this class that allows you to
+ 
+
+ align:start position:0%
+end of this class that allows you to
+easily extract the Christoffel symbols
+
+ align:start position:0%
+easily extract the Christoffel symbols
+ 
+
+ align:start position:0%
+easily extract the Christoffel symbols
+provided you know the metric but right
+
+ align:start position:0%
+provided you know the metric but right
+ 
+
+ align:start position:0%
+provided you know the metric but right
+now I just want to illustrate this thing
+
+ align:start position:0%
+now I just want to illustrate this thing
+ 
+
+ align:start position:0%
+now I just want to illustrate this thing
+conceptually the key thing which you
+
+ align:start position:0%
+conceptually the key thing which you
+ 
+
+ align:start position:0%
+conceptually the key thing which you
+which you should know about it is that
+
+ align:start position:0%
+which you should know about it is that
+ 
+
+ align:start position:0%
+which you should know about it is that
+it is essentially the that I almost said
+
+ align:start position:0%
+it is essentially the that I almost said
+ 
+
+ align:start position:0%
+it is essentially the that I almost said
+word matrix but it's got three indices
+
+ align:start position:0%
+word matrix but it's got three indices
+ 
+
+ align:start position:0%
+word matrix but it's got three indices
+it's a table of table of functions that
+
+ align:start position:0%
+it's a table of table of functions that
+ 
+
+ align:start position:0%
+it's a table of table of functions that
+allows me to relate derivatives of basis
+
+ align:start position:0%
+allows me to relate derivatives of basis
+ 
+
+ align:start position:0%
+allows me to relate derivatives of basis
+vectors to the basis factors okay so
+
+ align:start position:0%
+vectors to the basis factors okay so
+ 
+
+ align:start position:0%
+vectors to the basis factors okay so
+before I go on to talk about some of
+
+ align:start position:0%
+before I go on to talk about some of
+ 
+
+ align:start position:0%
+before I go on to talk about some of
+that stuff let's take a look at the
+
+ align:start position:0%
+that stuff let's take a look at the
+ 
+
+ align:start position:0%
+that stuff let's take a look at the
+derivative a little bit more carefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the derivative the vector so let's
+
+ align:start position:0%
+so the derivative the vector so let's
+ 
+
+ align:start position:0%
+so the derivative the vector so let's
+basically take what I've written out up
+
+ align:start position:0%
+basically take what I've written out up
+ 
+
+ align:start position:0%
+basically take what I've written out up
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+I'm gonna write this as beta derivative
+
+ align:start position:0%
+I'm gonna write this as beta derivative
+ 
+
+ align:start position:0%
+I'm gonna write this as beta derivative
+of vector V and I can write that as the
+
+ align:start position:0%
+of vector V and I can write that as the
+ 
+
+ align:start position:0%
+of vector V and I can write that as the
+beta derivative of e of V alpha so the
+
+ align:start position:0%
+beta derivative of e of V alpha so the
+ 
+
+ align:start position:0%
+beta derivative of e of V alpha so the
+first term where the derivative hits the
+
+ align:start position:0%
+first term where the derivative hits the
+ 
+
+ align:start position:0%
+first term where the derivative hits the
+vector components and then I've got a
+
+ align:start position:0%
+vector components and then I've got a
+ 
+
+ align:start position:0%
+vector components and then I've got a
+second term where the vector hits the
+
+ align:start position:0%
+second term where the vector hits the
+ 
+
+ align:start position:0%
+second term where the vector hits the
+basis to meet the derivative hits the
+
+ align:start position:0%
+basis to meet the derivative hits the
+ 
+
+ align:start position:0%
+basis to meet the derivative hits the
+basis I'm going to write this like so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is sort of annoying one term
+
+ align:start position:0%
+okay this is sort of annoying one term
+ 
+
+ align:start position:0%
+okay this is sort of annoying one term
+is proportionate to e alpha one is
+
+ align:start position:0%
+is proportionate to e alpha one is
+ 
+
+ align:start position:0%
+is proportionate to e alpha one is
+proportional to e mu but notice
+
+ align:start position:0%
+proportional to e mu but notice
+ 
+
+ align:start position:0%
+proportional to e mu but notice
+especially in this second term both
+
+ align:start position:0%
+especially in this second term both
+ 
+
+ align:start position:0%
+especially in this second term both
+alpha and nu are dummy indices so I'm
+
+ align:start position:0%
+alpha and nu are dummy indices so I'm
+ 
+
+ align:start position:0%
+alpha and nu are dummy indices so I'm
+free to label them so what I'm going to
+
+ align:start position:0%
+free to label them so what I'm going to
+ 
+
+ align:start position:0%
+free to label them so what I'm going to
+do is real able alpha and mu by
+
+ align:start position:0%
+do is real able alpha and mu by
+ 
+
+ align:start position:0%
+do is real able alpha and mu by
+exchanging them whoops as long as I do
+
+ align:start position:0%
+exchanging them whoops as long as I do
+ 
+
+ align:start position:0%
+exchanging them whoops as long as I do
+that consistently that is totally kosher
+
+ align:start position:0%
+that consistently that is totally kosher
+ 
+
+ align:start position:0%
+that consistently that is totally kosher
+and when I do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can factor out an overall factor of
+
+ align:start position:0%
+I can factor out an overall factor of
+ 
+
+ align:start position:0%
+I can factor out an overall factor of
+the basis object okay
+
+ align:start position:0%
+the basis object okay
+ 
+
+ align:start position:0%
+the basis object okay
+this combination it pops up here so we
+
+ align:start position:0%
+this combination it pops up here so we
+ 
+
+ align:start position:0%
+this combination it pops up here so we
+give this a name and this is a
+
+ align:start position:0%
+give this a name and this is a
+ 
+
+ align:start position:0%
+give this a name and this is a
+combination which by the time you have
+
+ align:start position:0%
+combination which by the time you have
+ 
+
+ align:start position:0%
+combination which by the time you have
+finished this semester if you don't have
+
+ align:start position:0%
+finished this semester if you don't have
+ 
+
+ align:start position:0%
+finished this semester if you don't have
+at least one nightmare in which this
+
+ align:start position:0%
+at least one nightmare in which this
+ 
+
+ align:start position:0%
+at least one nightmare in which this
+name appears I will not have done my job
+
+ align:start position:0%
+name appears I will not have done my job
+ 
+
+ align:start position:0%
+name appears I will not have done my job
+properly
+
+ align:start position:0%
+properly
+ 
+
+ align:start position:0%
+properly
+okay this shows up a lot at this point
+
+ align:start position:0%
+okay this shows up a lot at this point
+ 
+
+ align:start position:0%
+okay this shows up a lot at this point
+this is called the covariant derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we it shows up enough that we
+
+ align:start position:0%
+and we it shows up enough that we
+ 
+
+ align:start position:0%
+and we it shows up enough that we
+introduce a whole new notation for the
+
+ align:start position:0%
+introduce a whole new notation for the
+ 
+
+ align:start position:0%
+introduce a whole new notation for the
+derivative to take it into account I'm
+
+ align:start position:0%
+derivative to take it into account I'm
+ 
+
+ align:start position:0%
+derivative to take it into account I'm
+going to call this combination of the
+
+ align:start position:0%
+going to call this combination of the
+ 
+
+ align:start position:0%
+going to call this combination of the
+partial derivative of V and V coupled to
+
+ align:start position:0%
+partial derivative of V and V coupled to
+ 
+
+ align:start position:0%
+partial derivative of V and V coupled to
+the coupled to the Christoffel symbol
+
+ align:start position:0%
+the coupled to the Christoffel symbol
+ 
+
+ align:start position:0%
+the coupled to the Christoffel symbol
+I'm gonna write this using the if you're
+
+ align:start position:0%
+I'm gonna write this using the if you're
+ 
+
+ align:start position:0%
+I'm gonna write this using the if you're
+talking about this would be the Noblet
+
+ align:start position:0%
+talking about this would be the Noblet
+ 
+
+ align:start position:0%
+talking about this would be the Noblet
+operator so I made a point earlier when
+
+ align:start position:0%
+operator so I made a point earlier when
+ 
+
+ align:start position:0%
+operator so I made a point earlier when
+we were talking about derivatives a
+
+ align:start position:0%
+we were talking about derivatives a
+ 
+
+ align:start position:0%
+we were talking about derivatives a
+couple of weeks ago that we were
+
+ align:start position:0%
+couple of weeks ago that we were
+ 
+
+ align:start position:0%
+couple of weeks ago that we were
+reserving sort of the gradient symbol
+
+ align:start position:0%
+reserving sort of the gradient symbol
+ 
+
+ align:start position:0%
+reserving sort of the gradient symbol
+for a special purpose later here it is
+
+ align:start position:0%
+for a special purpose later here it is
+ 
+
+ align:start position:0%
+for a special purpose later here it is
+okay so whenever I make a derivative
+
+ align:start position:0%
+okay so whenever I make a derivative
+ 
+
+ align:start position:0%
+okay so whenever I make a derivative
+that involves the gradient symbol like
+
+ align:start position:0%
+that involves the gradient symbol like
+ 
+
+ align:start position:0%
+that involves the gradient symbol like
+this it is this covariant derivative and
+
+ align:start position:0%
+this it is this covariant derivative and
+ 
+
+ align:start position:0%
+this it is this covariant derivative and
+the covariant derivatives acting on
+
+ align:start position:0%
+the covariant derivatives acting on
+ 
+
+ align:start position:0%
+the covariant derivatives acting on
+acting on vector components it generates
+
+ align:start position:0%
+acting on vector components it generates
+ 
+
+ align:start position:0%
+acting on vector components it generates
+tensor components the partial derivative
+
+ align:start position:0%
+tensor components the partial derivative
+ 
+
+ align:start position:0%
+tensor components the partial derivative
+does not and what I'm going to do just
+
+ align:start position:0%
+does not and what I'm going to do just
+ 
+
+ align:start position:0%
+does not and what I'm going to do just
+in the interest of time it's one of
+
+ align:start position:0%
+in the interest of time it's one of
+ 
+
+ align:start position:0%
+in the interest of time it's one of
+those calculations that's
+
+ align:start position:0%
+those calculations that's
+ 
+
+ align:start position:0%
+those calculations that's
+straightforward but fairly tedious I
+
+ align:start position:0%
+straightforward but fairly tedious I
+ 
+
+ align:start position:0%
+straightforward but fairly tedious I
+have a set of notes that are actually
+
+ align:start position:0%
+have a set of notes that are actually
+ 
+
+ align:start position:0%
+have a set of notes that are actually
+meant to make ly before I head it over
+
+ align:start position:0%
+meant to make ly before I head it over
+ 
+
+ align:start position:0%
+meant to make ly before I head it over
+here but I forgot I have a set of notes
+
+ align:start position:0%
+here but I forgot I have a set of notes
+ 
+
+ align:start position:0%
+here but I forgot I have a set of notes
+that I'm going to show on the website by
+
+ align:start position:0%
+that I'm going to show on the website by
+ 
+
+ align:start position:0%
+that I'm going to show on the website by
+this evening which explicitly works out
+
+ align:start position:0%
+this evening which explicitly works out
+ 
+
+ align:start position:0%
+this evening which explicitly works out
+what happens when you apply the court in
+
+ align:start position:0%
+what happens when you apply the court in
+ 
+
+ align:start position:0%
+what happens when you apply the court in
+transformation using that's not it's
+
+ align:start position:0%
+transformation using that's not it's
+ 
+
+ align:start position:0%
+transformation using that's not it's
+been erased when you use that L matrix
+
+ align:start position:0%
+been erased when you use that L matrix
+ 
+
+ align:start position:0%
+been erased when you use that L matrix
+to construct the coordinate
+
+ align:start position:0%
+to construct the coordinate
+ 
+
+ align:start position:0%
+to construct the coordinate
+transformation between two
+
+ align:start position:0%
+transformation between two
+ 
+
+ align:start position:0%
+transformation between two
+representations
+
+ align:start position:0%
+representations
+ 
+
+ align:start position:0%
+representations
+if you try to do it to partial
+
+ align:start position:0%
+if you try to do it to partial
+ 
+
+ align:start position:0%
+if you try to do it to partial
+derivative of vector components
+
+ align:start position:0%
+derivative of vector components
+ 
+
+ align:start position:0%
+derivative of vector components
+basically what you find is that there's
+
+ align:start position:0%
+basically what you find is that there's
+ 
+
+ align:start position:0%
+basically what you find is that there's
+an extra term that spoils your ability
+
+ align:start position:0%
+an extra term that spoils your ability
+ 
+
+ align:start position:0%
+an extra term that spoils your ability
+to call that it spoils the tensor
+
+ align:start position:0%
+to call that it spoils the tensor
+ 
+
+ align:start position:0%
+to call that it spoils the tensor
+transformation law spoils your ability
+
+ align:start position:0%
+transformation law spoils your ability
+ 
+
+ align:start position:0%
+transformation law spoils your ability
+to call that a tensor component so the
+
+ align:start position:0%
+to call that a tensor component so the
+ 
+
+ align:start position:0%
+to call that a tensor component so the
+partial on its own doesn't let you you
+
+ align:start position:0%
+partial on its own doesn't let you you
+ 
+
+ align:start position:0%
+partial on its own doesn't let you you
+get some extra terms that come along and
+
+ align:start position:0%
+get some extra terms that come along and
+ 
+
+ align:start position:0%
+get some extra terms that come along and
+mess it all up on the next pset you guys
+
+ align:start position:0%
+mess it all up on the next pset you guys
+ 
+
+ align:start position:0%
+mess it all up on the next pset you guys
+are going to show that if you if you
+
+ align:start position:0%
+are going to show that if you if you
+ 
+
+ align:start position:0%
+are going to show that if you if you
+then try to apply the tensor
+
+ align:start position:0%
+then try to apply the tensor
+ 
+
+ align:start position:0%
+then try to apply the tensor
+transformation law to the Christoffel
+
+ align:start position:0%
+transformation law to the Christoffel
+ 
+
+ align:start position:0%
+transformation law to the Christoffel
+symbols you get something that looks
+
+ align:start position:0%
+symbols you get something that looks
+ 
+
+ align:start position:0%
+symbols you get something that looks
+tensorial but with an extra term that
+
+ align:start position:0%
+tensorial but with an extra term that
+ 
+
+ align:start position:0%
+tensorial but with an extra term that
+spoils your ability to call it truly
+
+ align:start position:0%
+spoils your ability to call it truly
+ 
+
+ align:start position:0%
+spoils your ability to call it truly
+tensorial there's a little bit of extra
+
+ align:start position:0%
+tensorial there's a little bit of extra
+ 
+
+ align:start position:0%
+tensorial there's a little bit of extra
+junk there but the two terms exactly
+
+ align:start position:0%
+junk there but the two terms exactly
+ 
+
+ align:start position:0%
+junk there but the two terms exactly
+conspire to cancel each other out so
+
+ align:start position:0%
+conspire to cancel each other out so
+ 
+
+ align:start position:0%
+conspire to cancel each other out so
+that the sum is tensorial okay so part 1
+
+ align:start position:0%
+that the sum is tensorial okay so part 1
+ 
+
+ align:start position:0%
+that the sum is tensorial okay so part 1
+of this will be notes that I post to the
+
+ align:start position:0%
+of this will be notes that I post to the
+ 
+
+ align:start position:0%
+of this will be notes that I post to the
+website no later than this evening part
+
+ align:start position:0%
+website no later than this evening part
+ 
+
+ align:start position:0%
+website no later than this evening part
+2 you guys will do on the P side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so just saying sort of in words or
+
+ align:start position:0%
+okay so just saying sort of in words or
+ 
+
+ align:start position:0%
+okay so just saying sort of in words or
+sorry saying in math what I just said in
+
+ align:start position:0%
+sorry saying in math what I just said in
+ 
+
+ align:start position:0%
+sorry saying in math what I just said in
+words if I do this like I said you
+
+ align:start position:0%
+words if I do this like I said you
+ 
+
+ align:start position:0%
+words if I do this like I said you
+basically will eventually reach the
+
+ align:start position:0%
+basically will eventually reach the
+ 
+
+ align:start position:0%
+basically will eventually reach the
+point where what I am writing out right
+
+ align:start position:0%
+point where what I am writing out right
+ 
+
+ align:start position:0%
+point where what I am writing out right
+now will become so automatic it will
+
+ align:start position:0%
+now will become so automatic it will
+ 
+
+ align:start position:0%
+now will become so automatic it will
+haunt your dreams wait a minute I screw
+
+ align:start position:0%
+haunt your dreams wait a minute I screw
+ 
+
+ align:start position:0%
+haunt your dreams wait a minute I screw
+that up so automatic I can't even write
+
+ align:start position:0%
+that up so automatic I can't even write
+ 
+
+ align:start position:0%
+that up so automatic I can't even write
+it properly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyhow something like that we'll modulo
+
+ align:start position:0%
+anyhow something like that we'll modulo
+ 
+
+ align:start position:0%
+anyhow something like that we'll modulo
+my typos that should become automatic
+
+ align:start position:0%
+my typos that should become automatic
+ 
+
+ align:start position:0%
+my typos that should become automatic
+and the key thing which I want to note
+
+ align:start position:0%
+and the key thing which I want to note
+ 
+
+ align:start position:0%
+and the key thing which I want to note
+is that if I take these guys and I
+
+ align:start position:0%
+is that if I take these guys and I
+ 
+
+ align:start position:0%
+is that if I take these guys and I
+attach the appropriate basis objects to
+
+ align:start position:0%
+attach the appropriate basis objects to
+ 
+
+ align:start position:0%
+attach the appropriate basis objects to
+them this is an honest-to-god tensor and
+
+ align:start position:0%
+them this is an honest-to-god tensor and
+ 
+
+ align:start position:0%
+them this is an honest-to-god tensor and
+so this derivative is itself an
+
+ align:start position:0%
+so this derivative is itself an
+ 
+
+ align:start position:0%
+so this derivative is itself an
+honest-to-god tensor a typical exact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is how do you compute a space-time
+
+ align:start position:0%
+is how do you compute a space-time
+ 
+
+ align:start position:0%
+is how do you compute a space-time
+divergence in these coordinate system so
+
+ align:start position:0%
+divergence in these coordinate system so
+ 
+
+ align:start position:0%
+divergence in these coordinate system so
+suppose I take the divergence of some
+
+ align:start position:0%
+suppose I take the divergence of some
+ 
+
+ align:start position:0%
+suppose I take the divergence of some
+vector field a that's give me a vector
+
+ align:start position:0%
+vector field a that's give me a vector
+ 
+
+ align:start position:0%
+vector field a that's give me a vector
+field V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you're gonna have four terms
+
+ align:start position:0%
+okay so you're gonna have four terms
+ 
+
+ align:start position:0%
+okay so you're gonna have four terms
+that are just the usual like when you
+
+ align:start position:0%
+that are just the usual like when you
+ 
+
+ align:start position:0%
+that are just the usual like when you
+guys learned how to do divergence and
+
+ align:start position:0%
+guys learned how to do divergence and
+ 
+
+ align:start position:0%
+guys learned how to do divergence and
+freshmen enm in Cartesian coordinates
+
+ align:start position:0%
+freshmen enm in Cartesian coordinates
+ 
+
+ align:start position:0%
+freshmen enm in Cartesian coordinates
+you get one term that's just no DV X DX
+
+ align:start position:0%
+you get one term that's just no DV X DX
+ 
+
+ align:start position:0%
+you get one term that's just no DV X DX
+DV Y dy etc so you got one term that
+
+ align:start position:0%
+DV Y dy etc so you got one term that
+ 
+
+ align:start position:0%
+DV Y dy etc so you got one term that
+looks just like that and they're gonna
+
+ align:start position:0%
+looks just like that and they're gonna
+ 
+
+ align:start position:0%
+looks just like that and they're gonna
+have something that brings in all of
+
+ align:start position:0%
+have something that brings in all of
+ 
+
+ align:start position:0%
+have something that brings in all of
+your Christoffel symbols notice the
+
+ align:start position:0%
+your Christoffel symbols notice the
+ 
+
+ align:start position:0%
+your Christoffel symbols notice the
+symmetry that we have on this one okay
+
+ align:start position:0%
+symmetry that we have on this one okay
+ 
+
+ align:start position:0%
+symmetry that we have on this one okay
+this is actually there is Einstein
+
+ align:start position:0%
+this is actually there is Einstein
+ 
+
+ align:start position:0%
+this is actually there is Einstein
+summation convention being imposed here
+
+ align:start position:0%
+summation convention being imposed here
+ 
+
+ align:start position:0%
+summation convention being imposed here
+but when we look at this there's
+
+ align:start position:0%
+but when we look at this there's
+ 
+
+ align:start position:0%
+but when we look at this there's
+actually only one Christoffel symbols
+
+ align:start position:0%
+actually only one Christoffel symbols
+ 
+
+ align:start position:0%
+actually only one Christoffel symbols
+that has repeated indices in that first
+
+ align:start position:0%
+that has repeated indices in that first
+ 
+
+ align:start position:0%
+that has repeated indices in that first
+position so when I put all this together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you wind up with something that looks
+
+ align:start position:0%
+you wind up with something that looks
+ 
+
+ align:start position:0%
+you wind up with something that looks
+like this so go back and check your copy
+
+ align:start position:0%
+like this so go back and check your copy
+ 
+
+ align:start position:0%
+like this so go back and check your copy
+of Jackson or Percell or Griffiths
+
+ align:start position:0%
+of Jackson or Percell or Griffiths
+ 
+
+ align:start position:0%
+of Jackson or Percell or Griffiths
+whatever your favorite E&M textbook is
+
+ align:start position:0%
+whatever your favorite E&M textbook is
+ 
+
+ align:start position:0%
+whatever your favorite E&M textbook is
+and you'll see when you work in
+
+ align:start position:0%
+and you'll see when you work in
+ 
+
+ align:start position:0%
+and you'll see when you work in
+cylindrical coordinates you indeed find
+
+ align:start position:0%
+cylindrical coordinates you indeed find
+ 
+
+ align:start position:0%
+cylindrical coordinates you indeed find
+that there's a correction to the radial
+
+ align:start position:0%
+that there's a correction to the radial
+ 
+
+ align:start position:0%
+that there's a correction to the radial
+term that involves a 1 over R that's
+
+ align:start position:0%
+term that involves a 1 over R that's
+ 
+
+ align:start position:0%
+term that involves a 1 over R that's
+popped out exactly like you think it
+
+ align:start position:0%
+popped out exactly like you think it
+ 
+
+ align:start position:0%
+popped out exactly like you think it
+should you have a bit of a wacky looking
+
+ align:start position:0%
+should you have a bit of a wacky looking
+ 
+
+ align:start position:0%
+should you have a bit of a wacky looking
+thing with your Phi component of course
+
+ align:start position:0%
+thing with your Phi component of course
+ 
+
+ align:start position:0%
+thing with your Phi component of course
+and let me just spend a second or two
+
+ align:start position:0%
+and let me just spend a second or two
+ 
+
+ align:start position:0%
+and let me just spend a second or two
+making sure it's often especially while
+
+ align:start position:0%
+making sure it's often especially while
+ 
+
+ align:start position:0%
+making sure it's often especially while
+we're developing intuition about working
+
+ align:start position:0%
+we're developing intuition about working
+ 
+
+ align:start position:0%
+we're developing intuition about working
+in a coordinate basis it's not a bad
+
+ align:start position:0%
+in a coordinate basis it's not a bad
+ 
+
+ align:start position:0%
+in a coordinate basis it's not a bad
+idea to do a little sanity check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's a standing check that I would
+
+ align:start position:0%
+so here's a standing check that I would
+ 
+
+ align:start position:0%
+so here's a standing check that I would
+do with this I am taking you know my
+
+ align:start position:0%
+do with this I am taking you know my
+ 
+
+ align:start position:0%
+do with this I am taking you know my
+take the the divergence I take a
+
+ align:start position:0%
+take the the divergence I take a
+ 
+
+ align:start position:0%
+take the the divergence I take a
+derivative of a vector field the final
+
+ align:start position:0%
+derivative of a vector field the final
+ 
+
+ align:start position:0%
+derivative of a vector field the final
+object that comes out of that should
+
+ align:start position:0%
+object that comes out of that should
+ 
+
+ align:start position:0%
+object that comes out of that should
+have the dimensions of that vector
+
+ align:start position:0%
+have the dimensions of that vector
+ 
+
+ align:start position:0%
+have the dimensions of that vector
+divided by length okay remembering C
+
+ align:start position:0%
+divided by length okay remembering C
+ 
+
+ align:start position:0%
+divided by length okay remembering C
+equals 1 that will clearly have that
+
+ align:start position:0%
+equals 1 that will clearly have that
+ 
+
+ align:start position:0%
+equals 1 that will clearly have that
+vector divided by length that will
+
+ align:start position:0%
+vector divided by length that will
+ 
+
+ align:start position:0%
+vector divided by length that will
+clearly have that vector divided by
+
+ align:start position:0%
+clearly have that vector divided by
+ 
+
+ align:start position:0%
+clearly have that vector divided by
+length vector divided by length
+
+ align:start position:0%
+length vector divided by length
+ 
+
+ align:start position:0%
+length vector divided by length
+explicitly vector divided by length
+
+ align:start position:0%
+explicitly vector divided by length
+ 
+
+ align:start position:0%
+explicitly vector divided by length
+that's weird but remember the basis
+
+ align:start position:0%
+that's weird but remember the basis
+ 
+
+ align:start position:0%
+that's weird but remember the basis
+objects themselves are a little weird
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of things we saw was that ePHI has
+
+ align:start position:0%
+one of things we saw was that ePHI has
+ 
+
+ align:start position:0%
+one of things we saw was that ePHI has
+the dimensions of length in order for
+
+ align:start position:0%
+the dimensions of length in order for
+ 
+
+ align:start position:0%
+the dimensions of length in order for
+the vector to itself be consistent V Phi
+
+ align:start position:0%
+the vector to itself be consistent V Phi
+ 
+
+ align:start position:0%
+the vector to itself be consistent V Phi
+must have the dimensions of V divided by
+
+ align:start position:0%
+must have the dimensions of V divided by
+ 
+
+ align:start position:0%
+must have the dimensions of V divided by
+length so in fact when I just take its
+
+ align:start position:0%
+length so in fact when I just take its
+ 
+
+ align:start position:0%
+length so in fact when I just take its
+Phi derivative I get something that
+
+ align:start position:0%
+Phi derivative I get something that
+ 
+
+ align:start position:0%
+Phi derivative I get something that
+looks exactly like it should if it is to
+
+ align:start position:0%
+looks exactly like it should if it is to
+ 
+
+ align:start position:0%
+looks exactly like it should if it is to
+be a divergence okay all right let's
+
+ align:start position:0%
+be a divergence okay all right let's
+ 
+
+ align:start position:0%
+be a divergence okay all right let's
+move on and think about how I take a
+
+ align:start position:0%
+move on and think about how I take a
+ 
+
+ align:start position:0%
+move on and think about how I take a
+covariant derivative of other kinds of
+
+ align:start position:0%
+covariant derivative of other kinds of
+ 
+
+ align:start position:0%
+covariant derivative of other kinds of
+tensorial objects okay this is all you
+
+ align:start position:0%
+tensorial objects okay this is all you
+ 
+
+ align:start position:0%
+tensorial objects okay this is all you
+need to know if you are worried about
+
+ align:start position:0%
+need to know if you are worried about
+ 
+
+ align:start position:0%
+need to know if you are worried about
+taking derivatives of vectors okay but
+
+ align:start position:0%
+taking derivatives of vectors okay but
+ 
+
+ align:start position:0%
+taking derivatives of vectors okay but
+we're gonna work with a lot of different
+
+ align:start position:0%
+we're gonna work with a lot of different
+ 
+
+ align:start position:0%
+we're gonna work with a lot of different
+kinds of tensor objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the most important lectures were
+
+ align:start position:0%
+one of the most important lectures were
+ 
+
+ align:start position:0%
+one of the most important lectures were
+gonna do in about a month actually
+
+ align:start position:0%
+gonna do in about a month actually
+ 
+
+ align:start position:0%
+gonna do in about a month actually
+involves looking at a bunch of covariant
+
+ align:start position:0%
+involves looking at a bunch of covariant
+ 
+
+ align:start position:0%
+involves looking at a bunch of covariant
+derivatives of some four index objects
+
+ align:start position:0%
+derivatives of some four index objects
+ 
+
+ align:start position:0%
+derivatives of some four index objects
+so it gets messy let's walk our way
+
+ align:start position:0%
+so it gets messy let's walk our way
+ 
+
+ align:start position:0%
+so it gets messy let's walk our way
+there so suppose I want to take the
+
+ align:start position:0%
+there so suppose I want to take the
+ 
+
+ align:start position:0%
+there so suppose I want to take the
+basis should we take the derivative of a
+
+ align:start position:0%
+basis should we take the derivative of a
+ 
+
+ align:start position:0%
+basis should we take the derivative of a
+scalar scalars have no basis object
+
+ align:start position:0%
+scalar scalars have no basis object
+ 
+
+ align:start position:0%
+scalar scalars have no basis object
+attached to them hey there's no basis
+
+ align:start position:0%
+attached to them hey there's no basis
+ 
+
+ align:start position:0%
+attached to them hey there's no basis
+objects when I take the derivative and I
+
+ align:start position:0%
+objects when I take the derivative and I
+ 
+
+ align:start position:0%
+objects when I take the derivative and I
+don't to worry about anything wiggling
+
+ align:start position:0%
+don't to worry about anything wiggling
+ 
+
+ align:start position:0%
+don't to worry about anything wiggling
+around no Christoffel symbols come in if
+
+ align:start position:0%
+around no Christoffel symbols come in if
+ 
+
+ align:start position:0%
+around no Christoffel symbols come in if
+I want to take the covariant derivative
+
+ align:start position:0%
+I want to take the covariant derivative
+ 
+
+ align:start position:0%
+I want to take the covariant derivative
+of some field Phi it is nothing more
+
+ align:start position:0%
+of some field Phi it is nothing more
+ 
+
+ align:start position:0%
+of some field Phi it is nothing more
+than the partial derivative of that
+
+ align:start position:0%
+than the partial derivative of that
+ 
+
+ align:start position:0%
+than the partial derivative of that
+field Phi boom happy days how about a
+
+ align:start position:0%
+field Phi boom happy days how about a
+ 
+
+ align:start position:0%
+field Phi boom happy days how about a
+one form the long way to do this would
+
+ align:start position:0%
+one form the long way to do this would
+ 
+
+ align:start position:0%
+one form the long way to do this would
+be to essentially say well the way I
+
+ align:start position:0%
+be to essentially say well the way I
+ 
+
+ align:start position:0%
+be to essentially say well the way I
+started this was by looking at how my
+
+ align:start position:0%
+started this was by looking at how my
+ 
+
+ align:start position:0%
+started this was by looking at how my
+basis vectors varied as I took their
+
+ align:start position:0%
+basis vectors varied as I took their
+ 
+
+ align:start position:0%
+basis vectors varied as I took their
+derivatives let's do the same thing for
+
+ align:start position:0%
+derivatives let's do the same thing for
+ 
+
+ align:start position:0%
+derivatives let's do the same thing for
+the basis one forms assemble my table do
+
+ align:start position:0%
+the basis one forms assemble my table do
+ 
+
+ align:start position:0%
+the basis one forms assemble my table do
+a lot of math blah blah blah knock
+
+ align:start position:0%
+a lot of math blah blah blah knock
+ 
+
+ align:start position:0%
+a lot of math blah blah blah knock
+yourselves out if that's what you want
+
+ align:start position:0%
+yourselves out if that's what you want
+ 
+
+ align:start position:0%
+yourselves out if that's what you want
+to do there's a shortcut let's use the
+
+ align:start position:0%
+to do there's a shortcut let's use the
+ 
+
+ align:start position:0%
+to do there's a shortcut let's use the
+fact that when I contract a one form on
+
+ align:start position:0%
+fact that when I contract a one form on
+ 
+
+ align:start position:0%
+fact that when I contract a one form on
+a vector I get a scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say I am looking at the beta
+
+ align:start position:0%
+so let's say I am looking at the beta
+ 
+
+ align:start position:0%
+so let's say I am looking at the beta
+covariant derivative of P alpha 1 a
+
+ align:start position:0%
+covariant derivative of P alpha 1 a
+ 
+
+ align:start position:0%
+covariant derivative of P alpha 1 a
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+that's a scalar so this is just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial derivative and the partial
+
+ align:start position:0%
+partial derivative and the partial
+ 
+
+ align:start position:0%
+partial derivative and the partial
+derivative of the product of something I
+
+ align:start position:0%
+derivative of the product of something I
+ 
+
+ align:start position:0%
+derivative of the product of something I
+can expand out real easily so using the
+
+ align:start position:0%
+can expand out real easily so using the
+ 
+
+ align:start position:0%
+can expand out real easily so using the
+fact that this just becomes the partial
+
+ align:start position:0%
+fact that this just becomes the partial
+ 
+
+ align:start position:0%
+fact that this just becomes the partial
+I can write this as a alpha D beta P
+
+ align:start position:0%
+I can write this as a alpha D beta P
+ 
+
+ align:start position:0%
+I can write this as a alpha D beta P
+alpha plus P okay so now what well let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rewrite this using the covariant
+
+ align:start position:0%
+rewrite this using the covariant
+ 
+
+ align:start position:0%
+rewrite this using the covariant
+derivative formula second one like you
+
+ align:start position:0%
+derivative formula second one like you
+ 
+
+ align:start position:0%
+derivative formula second one like you
+call it in my notes anywhere I can write
+
+ align:start position:0%
+call it in my notes anywhere I can write
+ 
+
+ align:start position:0%
+call it in my notes anywhere I can write
+this as the covariant derivative minus
+
+ align:start position:0%
+this as the covariant derivative minus
+ 
+
+ align:start position:0%
+this as the covariant derivative minus
+the correction that comes from that
+
+ align:start position:0%
+the correction that comes from that
+ 
+
+ align:start position:0%
+the correction that comes from that
+Christoffel symbol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay second there's a couple lines here
+
+ align:start position:0%
+okay second there's a couple lines here
+ 
+
+ align:start position:0%
+okay second there's a couple lines here
+I want to write out very neatly so I put
+
+ align:start position:0%
+I want to write out very neatly so I put
+ 
+
+ align:start position:0%
+I want to write out very neatly so I put
+this in whoops typo that last typo is
+
+ align:start position:0%
+this in whoops typo that last typo is
+ 
+
+ align:start position:0%
+this in whoops typo that last typo is
+important because I'm now going to do
+
+ align:start position:0%
+important because I'm now going to do
+ 
+
+ align:start position:0%
+important because I'm now going to do
+the relabeling trick okay so what I'm
+
+ align:start position:0%
+the relabeling trick okay so what I'm
+ 
+
+ align:start position:0%
+the relabeling trick okay so what I'm
+going to do is take advantage of the
+
+ align:start position:0%
+going to do is take advantage of the
+ 
+
+ align:start position:0%
+going to do is take advantage of the
+fact that in this last term alpha and nu
+
+ align:start position:0%
+fact that in this last term alpha and nu
+ 
+
+ align:start position:0%
+fact that in this last term alpha and nu
+are both dummy indices so on this last
+
+ align:start position:0%
+are both dummy indices so on this last
+ 
+
+ align:start position:0%
+are both dummy indices so on this last
+term that I have written down here I'm
+
+ align:start position:0%
+term that I have written down here I'm
+ 
+
+ align:start position:0%
+term that I have written down here I'm
+gonna swap out alpha and mu
+
+ align:start position:0%
+gonna swap out alpha and mu
+ 
+
+ align:start position:0%
+gonna swap out alpha and mu
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when I do that notice that the first
+
+ align:start position:0%
+when I do that notice that the first
+ 
+
+ align:start position:0%
+when I do that notice that the first
+term in the last term will both be
+
+ align:start position:0%
+term in the last term will both be
+ 
+
+ align:start position:0%
+term in the last term will both be
+proportional to the complement alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's require that the
+
+ align:start position:0%
+okay now let's require that the
+ 
+
+ align:start position:0%
+okay now let's require that the
+covariant derivative when an axle on two
+
+ align:start position:0%
+covariant derivative when an axle on two
+ 
+
+ align:start position:0%
+covariant derivative when an axle on two
+things that are multiplied together it's
+
+ align:start position:0%
+things that are multiplied together it's
+ 
+
+ align:start position:0%
+things that are multiplied together it's
+a derivative right so it should do what
+
+ align:start position:0%
+a derivative right so it should do what
+ 
+
+ align:start position:0%
+a derivative right so it should do what
+ordinary what derivatives ordinarily do
+
+ align:start position:0%
+ordinary what derivatives ordinarily do
+ 
+
+ align:start position:0%
+ordinary what derivatives ordinarily do
+so what we're going to do is require
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that when I take this covariant
+
+ align:start position:0%
+that when I take this covariant
+ 
+
+ align:start position:0%
+that when I take this covariant
+derivative I should be able to write the
+
+ align:start position:0%
+derivative I should be able to write the
+ 
+
+ align:start position:0%
+derivative I should be able to write the
+result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so okay it's a healthy thing for
+
+ align:start position:0%
+like so okay it's a healthy thing for
+ 
+
+ align:start position:0%
+like so okay it's a healthy thing for
+any just a little bit it's a healthy
+
+ align:start position:0%
+any just a little bit it's a healthy
+ 
+
+ align:start position:0%
+any just a little bit it's a healthy
+thing that any derivative should do so
+
+ align:start position:0%
+thing that any derivative should do so
+ 
+
+ align:start position:0%
+thing that any derivative should do so
+comparing I look at that and go oh I've
+
+ align:start position:0%
+comparing I look at that and go oh I've
+ 
+
+ align:start position:0%
+comparing I look at that and go oh I've
+got the covariant ribbon for my one form
+
+ align:start position:0%
+got the covariant ribbon for my one form
+ 
+
+ align:start position:0%
+got the covariant ribbon for my one form
+there just compare forms very very
+
+ align:start position:0%
+there just compare forms very very
+ 
+
+ align:start position:0%
+there just compare forms very very
+similar notice the minus sign okay so
+
+ align:start position:0%
+similar notice the minus sign okay so
+ 
+
+ align:start position:0%
+similar notice the minus sign okay so
+there's a minus sign that's been
+
+ align:start position:0%
+there's a minus sign that's been
+ 
+
+ align:start position:0%
+there's a minus sign that's been
+introduced there and that minus sign
+
+ align:start position:0%
+introduced there and that minus sign
+ 
+
+ align:start position:0%
+introduced there and that minus sign
+guarantees you know if you actually
+
+ align:start position:0%
+guarantees you know if you actually
+ 
+
+ align:start position:0%
+guarantees you know if you actually
+expand out that combination of covariant
+
+ align:start position:0%
+expand out that combination of covariant
+ 
+
+ align:start position:0%
+expand out that combination of covariant
+derivatives I have on the previous line
+
+ align:start position:0%
+derivatives I have on the previous line
+ 
+
+ align:start position:0%
+derivatives I have on the previous line
+there's a nice cancellation so that the
+
+ align:start position:0%
+there's a nice cancellation so that the
+ 
+
+ align:start position:0%
+there's a nice cancellation so that the
+scalar that I get when I contract P on a
+
+ align:start position:0%
+scalar that I get when I contract P on a
+ 
+
+ align:start position:0%
+scalar that I get when I contract P on a
+in fact doesn't have anything special
+
+ align:start position:0%
+in fact doesn't have anything special
+ 
+
+ align:start position:0%
+in fact doesn't have anything special
+going on when I do the covariant
+
+ align:start position:0%
+going on when I do the covariant
+ 
+
+ align:start position:0%
+going on when I do the covariant
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm gonna generalize this first let
+
+ align:start position:0%
+so I'm gonna generalize this first let
+ 
+
+ align:start position:0%
+so I'm gonna generalize this first let
+me just make a quick comment here I
+
+ align:start position:0%
+me just make a quick comment here I
+ 
+
+ align:start position:0%
+me just make a quick comment here I
+began this little calculation by saying
+
+ align:start position:0%
+began this little calculation by saying
+ 
+
+ align:start position:0%
+began this little calculation by saying
+you know given how we started our
+
+ align:start position:0%
+you know given how we started our
+ 
+
+ align:start position:0%
+you know given how we started our
+calculation of the covariant derivative
+
+ align:start position:0%
+calculation of the covariant derivative
+ 
+
+ align:start position:0%
+calculation of the covariant derivative
+of a vector we could have begun by just
+
+ align:start position:0%
+of a vector we could have begun by just
+ 
+
+ align:start position:0%
+of a vector we could have begun by just
+taking lots of derivatives at the basis
+
+ align:start position:0%
+taking lots of derivatives at the basis
+ 
+
+ align:start position:0%
+taking lots of derivatives at the basis
+one forms and assembling all these
+
+ align:start position:0%
+one forms and assembling all these
+ 
+
+ align:start position:0%
+one forms and assembling all these
+various tables and things like that if
+
+ align:start position:0%
+various tables and things like that if
+ 
+
+ align:start position:0%
+various tables and things like that if
+you had done this it's simple to find
+
+ align:start position:0%
+you had done this it's simple to find
+ 
+
+ align:start position:0%
+you had done this it's simple to find
+based on an analysis like this that if
+
+ align:start position:0%
+based on an analysis like this that if
+ 
+
+ align:start position:0%
+based on an analysis like this that if
+you take partial derivative of a one
+
+ align:start position:0%
+you take partial derivative of a one
+ 
+
+ align:start position:0%
+you take partial derivative of a one
+form that you get sort of a linear
+
+ align:start position:0%
+form that you get sort of a linear
+ 
+
+ align:start position:0%
+form that you get sort of a linear
+combination of one forms back looks just
+
+ align:start position:0%
+combination of one forms back looks just
+ 
+
+ align:start position:0%
+combination of one forms back looks just
+like what you got when you took a
+
+ align:start position:0%
+like what you got when you took a
+ 
+
+ align:start position:0%
+like what you got when you took a
+partial derivative of a basis factor but
+
+ align:start position:0%
+partial derivative of a basis factor but
+ 
+
+ align:start position:0%
+partial derivative of a basis factor but
+with a minus sign and what that minus
+
+ align:start position:0%
+with a minus sign and what that minus
+ 
+
+ align:start position:0%
+with a minus sign and what that minus
+sign does is it enforces if you go back
+
+ align:start position:0%
+sign does is it enforces if you go back
+ 
+
+ align:start position:0%
+sign does is it enforces if you go back
+to a lecture from ages ago
+
+ align:start position:0%
+to a lecture from ages ago
+ 
+
+ align:start position:0%
+to a lecture from ages ago
+when I first introduced basis one forms
+
+ align:start position:0%
+when I first introduced basis one forms
+ 
+
+ align:start position:0%
+when I first introduced basis one forms
+it enforces the idea that when I combine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis one forms with basis vectors I get
+
+ align:start position:0%
+basis one forms with basis vectors I get
+ 
+
+ align:start position:0%
+basis one forms with basis vectors I get
+an identity object out of this which is
+
+ align:start position:0%
+an identity object out of this which is
+ 
+
+ align:start position:0%
+an identity object out of this which is
+itself a constant okay if you like if
+
+ align:start position:0%
+itself a constant okay if you like if
+ 
+
+ align:start position:0%
+itself a constant okay if you like if
+you are the kind of person who likes
+
+ align:start position:0%
+you are the kind of person who likes
+ 
+
+ align:start position:0%
+you are the kind of person who likes
+that sort of mathematical rigor some
+
+ align:start position:0%
+that sort of mathematical rigor some
+ 
+
+ align:start position:0%
+that sort of mathematical rigor some
+textbooks will start with this and then
+
+ align:start position:0%
+textbooks will start with this and then
+ 
+
+ align:start position:0%
+textbooks will start with this and then
+derive other things from that okay sort
+
+ align:start position:0%
+derive other things from that okay sort
+ 
+
+ align:start position:0%
+derive other things from that okay sort
+of six of one half dozen of the other so
+
+ align:start position:0%
+of six of one half dozen of the other so
+ 
+
+ align:start position:0%
+of six of one half dozen of the other so
+we could go on at this point and I could
+
+ align:start position:0%
+we could go on at this point and I could
+ 
+
+ align:start position:0%
+we could go on at this point and I could
+say okay how do I do this with a tensor
+
+ align:start position:0%
+say okay how do I do this with a tensor
+ 
+
+ align:start position:0%
+say okay how do I do this with a tensor
+that has two indices in the upstairs
+
+ align:start position:0%
+that has two indices in the upstairs
+ 
+
+ align:start position:0%
+that has two indices in the upstairs
+position how do I do this with the
+
+ align:start position:0%
+position how do I do this with the
+ 
+
+ align:start position:0%
+position how do I do this with the
+tensor that has two indices in the
+
+ align:start position:0%
+tensor that has two indices in the
+ 
+
+ align:start position:0%
+tensor that has two indices in the
+downstairs position how do I do it for
+
+ align:start position:0%
+downstairs position how do I do it for
+ 
+
+ align:start position:0%
+downstairs position how do I do it for
+attention that's got 17 indices in the
+
+ align:start position:0%
+attention that's got 17 indices in the
+ 
+
+ align:start position:0%
+attention that's got 17 indices in the
+upstairs position and 38 in the
+
+ align:start position:0%
+upstairs position and 38 in the
+ 
+
+ align:start position:0%
+upstairs position and 38 in the
+downstairs position
+
+ align:start position:0%
+downstairs position
+ 
+
+ align:start position:0%
+downstairs position
+the answer is easily deduced from doing
+
+ align:start position:0%
+the answer is easily deduced from doing
+ 
+
+ align:start position:0%
+the answer is easily deduced from doing
+these kinds of rules so I'm just going
+
+ align:start position:0%
+these kinds of rules so I'm just going
+ 
+
+ align:start position:0%
+these kinds of rules so I'm just going
+to write down a couple of examples and
+
+ align:start position:0%
+to write down a couple of examples and
+ 
+
+ align:start position:0%
+to write down a couple of examples and
+state what it turns out today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically imagine I want to take the
+
+ align:start position:0%
+so basically imagine I want to take the
+ 
+
+ align:start position:0%
+so basically imagine I want to take the
+covariant derivative let's do the
+
+ align:start position:0%
+covariant derivative let's do the
+ 
+
+ align:start position:0%
+covariant derivative let's do the
+stress-energy tensor covariant
+
+ align:start position:0%
+stress-energy tensor covariant
+ 
+
+ align:start position:0%
+stress-energy tensor covariant
+derivative of team you know so remember
+
+ align:start position:0%
+derivative of team you know so remember
+ 
+
+ align:start position:0%
+derivative of team you know so remember
+the way that the Christoffel got into
+
+ align:start position:0%
+the way that the Christoffel got into
+ 
+
+ align:start position:0%
+the way that the Christoffel got into
+there is that when I looked at the
+
+ align:start position:0%
+there is that when I looked at the
+ 
+
+ align:start position:0%
+there is that when I looked at the
+derivative of a vector I was looking at
+
+ align:start position:0%
+derivative of a vector I was looking at
+ 
+
+ align:start position:0%
+derivative of a vector I was looking at
+derivatives of basis objects well now
+
+ align:start position:0%
+derivatives of basis objects well now
+ 
+
+ align:start position:0%
+derivatives of basis objects well now
+I'm gonna look at derivatives of two
+
+ align:start position:0%
+I'm gonna look at derivatives of two
+ 
+
+ align:start position:0%
+I'm gonna look at derivatives of two
+different basis objects so I'm gonna
+
+ align:start position:0%
+different basis objects so I'm gonna
+ 
+
+ align:start position:0%
+different basis objects so I'm gonna
+wind up with two Christoffel symbols you
+
+ align:start position:0%
+wind up with two Christoffel symbols you
+ 
+
+ align:start position:0%
+wind up with two Christoffel symbols you
+can kind of think of as coming along and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correcting each of these indices I can
+
+ align:start position:0%
+correcting each of these indices I can
+ 
+
+ align:start position:0%
+correcting each of these indices I can
+do this with the index in the doubt with
+
+ align:start position:0%
+do this with the index in the doubt with
+ 
+
+ align:start position:0%
+do this with the index in the doubt with
+the indices in the downstairs position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess what comes along and corrects all
+
+ align:start position:0%
+guess what comes along and corrects all
+ 
+
+ align:start position:0%
+guess what comes along and corrects all
+them with minus signs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just for completeness let me just write
+
+ align:start position:0%
+just for completeness let me just write
+ 
+
+ align:start position:0%
+just for completeness let me just write
+down the general rule if I am looking at
+
+ align:start position:0%
+down the general rule if I am looking at
+ 
+
+ align:start position:0%
+down the general rule if I am looking at
+the covariant derivative of a tensor
+
+ align:start position:0%
+the covariant derivative of a tensor
+ 
+
+ align:start position:0%
+the covariant derivative of a tensor
+with a gajillion upstairs indices and I
+
+ align:start position:0%
+with a gajillion upstairs indices and I
+ 
+
+ align:start position:0%
+with a gajillion upstairs indices and I
+kajillion downstairs indices you get one
+
+ align:start position:0%
+kajillion downstairs indices you get one
+ 
+
+ align:start position:0%
+kajillion downstairs indices you get one
+term this is the partial derivative of
+
+ align:start position:0%
+term this is the partial derivative of
+ 
+
+ align:start position:0%
+term this is the partial derivative of
+that guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you get a Christoffel coupling every
+
+ align:start position:0%
+and you get a Christoffel coupling every
+ 
+
+ align:start position:0%
+and you get a Christoffel coupling every
+one of these plus sign for all the
+
+ align:start position:0%
+one of these plus sign for all the
+ 
+
+ align:start position:0%
+one of these plus sign for all the
+upstairs minus sign for all the
+
+ align:start position:0%
+upstairs minus sign for all the
+ 
+
+ align:start position:0%
+upstairs minus sign for all the
+downstairs you basically just when I
+
+ align:start position:0%
+downstairs you basically just when I
+ 
+
+ align:start position:0%
+downstairs you basically just when I
+give you a tensor like that just kind of
+
+ align:start position:0%
+give you a tensor like that just kind of
+ 
+
+ align:start position:0%
+give you a tensor like that just kind of
+have to go through and it becomes sort
+
+ align:start position:0%
+have to go through and it becomes sort
+ 
+
+ align:start position:0%
+have to go through and it becomes sort
+of almost monkey work you just have to
+
+ align:start position:0%
+of almost monkey work you just have to
+ 
+
+ align:start position:0%
+of almost monkey work you just have to
+wrote li go through and correct every
+
+ align:start position:0%
+wrote li go through and correct every
+ 
+
+ align:start position:0%
+wrote li go through and correct every
+one of the indices using an algorithm
+
+ align:start position:0%
+one of the indices using an algorithm
+ 
+
+ align:start position:0%
+one of the indices using an algorithm
+that kind of looks like this all right
+
+ align:start position:0%
+that kind of looks like this all right
+ 
+
+ align:start position:0%
+that kind of looks like this all right
+oh jeez there's absolutely my sign a
+
+ align:start position:0%
+oh jeez there's absolutely my sign a
+ 
+
+ align:start position:0%
+oh jeez there's absolutely my sign a
+second one thank you appreciate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the way that we have done things so
+
+ align:start position:0%
+so the way that we have done things so
+ 
+
+ align:start position:0%
+so the way that we have done things so
+far and the kind of emphasizes sort of
+
+ align:start position:0%
+far and the kind of emphasizes sort of
+ 
+
+ align:start position:0%
+far and the kind of emphasizes sort of
+smells like the way to do this is you
+
+ align:start position:0%
+smells like the way to do this is you
+ 
+
+ align:start position:0%
+smells like the way to do this is you
+picked a new coordinate representation
+
+ align:start position:0%
+picked a new coordinate representation
+ 
+
+ align:start position:0%
+picked a new coordinate representation
+you throw together all of your all of
+
+ align:start position:0%
+you throw together all of your all of
+ 
+
+ align:start position:0%
+you throw together all of your all of
+your various basis objects and then you
+
+ align:start position:0%
+your various basis objects and then you
+ 
+
+ align:start position:0%
+your various basis objects and then you
+just start going we let's start taking
+
+ align:start position:0%
+just start going we let's start taking
+ 
+
+ align:start position:0%
+just start going we let's start taking
+derivatives and see how all these things
+
+ align:start position:0%
+derivatives and see how all these things
+ 
+
+ align:start position:0%
+derivatives and see how all these things
+vary it is back to each other
+
+ align:start position:0%
+vary it is back to each other
+ 
+
+ align:start position:0%
+vary it is back to each other
+assemble my table of the gammas and then
+
+ align:start position:0%
+assemble my table of the gammas and then
+ 
+
+ align:start position:0%
+assemble my table of the gammas and then
+do do my covariant derivatives okay if
+
+ align:start position:0%
+do do my covariant derivatives okay if
+ 
+
+ align:start position:0%
+do do my covariant derivatives okay if
+that were in fact the way we did it just
+
+ align:start position:0%
+that were in fact the way we did it just
+ 
+
+ align:start position:0%
+that were in fact the way we did it just
+I would not have chosen my research
+
+ align:start position:0%
+I would not have chosen my research
+ 
+
+ align:start position:0%
+I would not have chosen my research
+career to focus on this field okay that
+
+ align:start position:0%
+career to focus on this field okay that
+ 
+
+ align:start position:0%
+career to focus on this field okay that
+would suck certainly prior to prior to
+
+ align:start position:0%
+would suck certainly prior to prior to
+ 
+
+ align:start position:0%
+would suck certainly prior to prior to
+Odin providing us with Mathematica it
+
+ align:start position:0%
+Odin providing us with Mathematica it
+ 
+
+ align:start position:0%
+Odin providing us with Mathematica it
+would have been absolutely undoable you
+
+ align:start position:0%
+would have been absolutely undoable you
+ 
+
+ align:start position:0%
+would have been absolutely undoable you
+know even with it though it would be
+
+ align:start position:0%
+know even with it though it would be
+ 
+
+ align:start position:0%
+know even with it though it would be
+incredibly tedious so there is a better
+
+ align:start position:0%
+incredibly tedious so there is a better
+ 
+
+ align:start position:0%
+incredibly tedious so there is a better
+way to do this and it comes via the
+
+ align:start position:0%
+way to do this and it comes via the
+ 
+
+ align:start position:0%
+way to do this and it comes via the
+metric before I derive what the
+
+ align:start position:0%
+metric before I derive what the
+ 
+
+ align:start position:0%
+metric before I derive what the
+algorithm actually is I want to
+
+ align:start position:0%
+algorithm actually is I want to
+ 
+
+ align:start position:0%
+algorithm actually is I want to
+introduce an extremely important
+
+ align:start position:0%
+introduce an extremely important
+ 
+
+ align:start position:0%
+introduce an extremely important
+property of tensor relationships that we
+
+ align:start position:0%
+property of tensor relationships that we
+ 
+
+ align:start position:0%
+property of tensor relationships that we
+are going to come back to and use quite
+
+ align:start position:0%
+are going to come back to and use quite
+ 
+
+ align:start position:0%
+are going to come back to and use quite
+a bit in this course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is something that we have
+
+ align:start position:0%
+so this is something that we have
+ 
+
+ align:start position:0%
+so this is something that we have
+actually kind of alluded to repeatedly
+
+ align:start position:0%
+actually kind of alluded to repeatedly
+ 
+
+ align:start position:0%
+actually kind of alluded to repeatedly
+but I want to make it a little more
+
+ align:start position:0%
+but I want to make it a little more
+ 
+
+ align:start position:0%
+but I want to make it a little more
+formal and just clearly state it okay so
+
+ align:start position:0%
+formal and just clearly state it okay so
+ 
+
+ align:start position:0%
+formal and just clearly state it okay so
+this relationship but I'm going to use
+
+ align:start position:0%
+this relationship but I'm going to use
+ 
+
+ align:start position:0%
+this relationship but I'm going to use
+is some kind of a tensor equation a
+
+ align:start position:0%
+is some kind of a tensor equation a
+ 
+
+ align:start position:0%
+is some kind of a tensor equation a
+tensorial equation that holds in one
+
+ align:start position:0%
+tensorial equation that holds in one
+ 
+
+ align:start position:0%
+tensorial equation that holds in one
+representation must hold in all
+
+ align:start position:0%
+representation must hold in all
+ 
+
+ align:start position:0%
+representation must hold in all
+representations okay come back to the
+
+ align:start position:0%
+representations okay come back to the
+ 
+
+ align:start position:0%
+representations okay come back to the
+intuition when I first began describing
+
+ align:start position:0%
+intuition when I first began describing
+ 
+
+ align:start position:0%
+intuition when I first began describing
+physics in terms of geometric objects in
+
+ align:start position:0%
+physics in terms of geometric objects in
+ 
+
+ align:start position:0%
+physics in terms of geometric objects in
+space-time one of the key points I tried
+
+ align:start position:0%
+space-time one of the key points I tried
+ 
+
+ align:start position:0%
+space-time one of the key points I tried
+to really make the difference to
+
+ align:start position:0%
+to really make the difference to
+ 
+
+ align:start position:0%
+to really make the difference to
+emphasize the difference of is that I
+
+ align:start position:0%
+emphasize the difference of is that I
+ 
+
+ align:start position:0%
+emphasize the difference of is that I
+can have different we're going to say my
+
+ align:start position:0%
+can have different we're going to say my
+ 
+
+ align:start position:0%
+can have different we're going to say my
+arm is a particular vector in space-time
+
+ align:start position:0%
+arm is a particular vector in space-time
+ 
+
+ align:start position:0%
+arm is a particular vector in space-time
+okay someone running through the room at
+
+ align:start position:0%
+okay someone running through the room at
+ 
+
+ align:start position:0%
+okay someone running through the room at
+3/4 the speed of light will use
+
+ align:start position:0%
+3/4 the speed of light will use
+ 
+
+ align:start position:0%
+3/4 the speed of light will use
+different representations to describe my
+
+ align:start position:0%
+different representations to describe my
+ 
+
+ align:start position:0%
+different representations to describe my
+arm they will see length contractions
+
+ align:start position:0%
+arm they will see length contractions
+ 
+
+ align:start position:0%
+arm they will see length contractions
+they will see things sort of spanning
+
+ align:start position:0%
+they will see things sort of spanning
+ 
+
+ align:start position:0%
+they will see things sort of spanning
+different things but the geometric
+
+ align:start position:0%
+different things but the geometric
+ 
+
+ align:start position:0%
+different things but the geometric
+object the thing which is you know goes
+
+ align:start position:0%
+object the thing which is you know goes
+ 
+
+ align:start position:0%
+object the thing which is you know goes
+between two events and space-time that
+
+ align:start position:0%
+between two events and space-time that
+ 
+
+ align:start position:0%
+between two events and space-time that
+does not change even though the
+
+ align:start position:0%
+does not change even though the
+ 
+
+ align:start position:0%
+does not change even though the
+representation of those events might
+
+ align:start position:0%
+representation of those events might
+ 
+
+ align:start position:0%
+representation of those events might
+this remains true not just for Lorentz
+
+ align:start position:0%
+this remains true not just for Lorentz
+ 
+
+ align:start position:0%
+this remains true not just for Lorentz
+transformations but for all classes of
+
+ align:start position:0%
+transformations but for all classes of
+ 
+
+ align:start position:0%
+transformations but for all classes of
+transformations that we might care to
+
+ align:start position:0%
+transformations that we might care to
+ 
+
+ align:start position:0%
+transformations that we might care to
+use in our analysis changing the
+
+ align:start position:0%
+use in our analysis changing the
+ 
+
+ align:start position:0%
+use in our analysis changing the
+representation cannot change the
+
+ align:start position:0%
+representation cannot change the
+ 
+
+ align:start position:0%
+representation cannot change the
+equation you know written that way
+
+ align:start position:0%
+equation you know written that way
+ 
+
+ align:start position:0%
+equation you know written that way
+it's nice sounds like well duh but as
+
+ align:start position:0%
+it's nice sounds like well duh but as
+ 
+
+ align:start position:0%
+it's nice sounds like well duh but as
+well see it's got important consequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so as a warm-up exercise of how we might
+
+ align:start position:0%
+so as a warm-up exercise of how we might
+ 
+
+ align:start position:0%
+so as a warm-up exercise of how we might
+want to use this let's think about the
+
+ align:start position:0%
+want to use this let's think about the
+ 
+
+ align:start position:0%
+want to use this let's think about the
+double gradient of a scalar so let's
+
+ align:start position:0%
+double gradient of a scalar so let's
+ 
+
+ align:start position:0%
+double gradient of a scalar so let's
+define let's just say that this is the
+
+ align:start position:0%
+define let's just say that this is the
+ 
+
+ align:start position:0%
+define let's just say that this is the
+object that I want to compute let's
+
+ align:start position:0%
+object that I want to compute let's
+ 
+
+ align:start position:0%
+object that I want to compute let's
+first do this in a Cartesian
+
+ align:start position:0%
+first do this in a Cartesian
+ 
+
+ align:start position:0%
+first do this in a Cartesian
+representation in a Cartesian
+
+ align:start position:0%
+representation in a Cartesian
+ 
+
+ align:start position:0%
+representation in a Cartesian
+representation I just take two partial
+
+ align:start position:0%
+representation I just take two partial
+ 
+
+ align:start position:0%
+representation I just take two partial
+derivatives I've got a basis couple
+
+ align:start position:0%
+derivatives I've got a basis couple
+ 
+
+ align:start position:0%
+derivatives I've got a basis couple
+basis 1 forms for this ok so I've got
+
+ align:start position:0%
+basis 1 forms for this ok so I've got
+ 
+
+ align:start position:0%
+basis 1 forms for this ok so I've got
+something like this see what you want to
+
+ align:start position:0%
+something like this see what you want to
+ 
+
+ align:start position:0%
+something like this see what you want to
+emphasize is that as written in
+
+ align:start position:0%
+emphasize is that as written in
+ 
+
+ align:start position:0%
+emphasize is that as written in
+Cartesian coordinates D alpha D beta of
+
+ align:start position:0%
+Cartesian coordinates D alpha D beta of
+ 
+
+ align:start position:0%
+Cartesian coordinates D alpha D beta of
+Phi those are the components of a tensor
+
+ align:start position:0%
+Phi those are the components of a tensor
+ 
+
+ align:start position:0%
+Phi those are the components of a tensor
+in this representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the key thing is that they are
+
+ align:start position:0%
+and the key thing is that they are
+ 
+
+ align:start position:0%
+and the key thing is that they are
+obviously symmetric on exchange of the
+
+ align:start position:0%
+obviously symmetric on exchange of the
+ 
+
+ align:start position:0%
+obviously symmetric on exchange of the
+indices alpha and beta okay
+
+ align:start position:0%
+indices alpha and beta okay
+ 
+
+ align:start position:0%
+indices alpha and beta okay
+doesn't water if I'm just taking partial
+
+ align:start position:0%
+doesn't water if I'm just taking partial
+ 
+
+ align:start position:0%
+doesn't water if I'm just taking partial
+derivatives doesn't matter what order I
+
+ align:start position:0%
+derivatives doesn't matter what order I
+ 
+
+ align:start position:0%
+derivatives doesn't matter what order I
+take them in that's got to be symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's now look at the double gradient of
+
+ align:start position:0%
+let's now look at the double gradient of
+ 
+
+ align:start position:0%
+let's now look at the double gradient of
+a scalar in a more general
+
+ align:start position:0%
+a scalar in a more general
+ 
+
+ align:start position:0%
+a scalar in a more general
+representation so in a general
+
+ align:start position:0%
+representation so in a general
+ 
+
+ align:start position:0%
+representation so in a general
+representation I'm going to require
+
+ align:start position:0%
+representation I'm going to require
+ 
+
+ align:start position:0%
+representation I'm going to require
+these two derivatives to be covariant
+
+ align:start position:0%
+these two derivatives to be covariant
+ 
+
+ align:start position:0%
+these two derivatives to be covariant
+derivatives now we know one of them can
+
+ align:start position:0%
+derivatives now we know one of them can
+ 
+
+ align:start position:0%
+derivatives now we know one of them can
+be very trivially replaced with a
+
+ align:start position:0%
+be very trivially replaced with a
+ 
+
+ align:start position:0%
+be very trivially replaced with a
+partial but the other one cannot okay
+
+ align:start position:0%
+partial but the other one cannot okay
+ 
+
+ align:start position:0%
+partial but the other one cannot okay
+hold that thought for just a second if
+
+ align:start position:0%
+hold that thought for just a second if
+ 
+
+ align:start position:0%
+hold that thought for just a second if
+this thing is symmetric in the Cartesian
+
+ align:start position:0%
+this thing is symmetric in the Cartesian
+ 
+
+ align:start position:0%
+this thing is symmetric in the Cartesian
+representation I claim it must also be
+
+ align:start position:0%
+representation I claim it must also be
+ 
+
+ align:start position:0%
+representation I claim it must also be
+true in a general representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words exchanging the order of
+
+ align:start position:0%
+in other words exchanging the order of
+ 
+
+ align:start position:0%
+in other words exchanging the order of
+covariant derivatives when they act on a
+
+ align:start position:0%
+covariant derivatives when they act on a
+ 
+
+ align:start position:0%
+covariant derivatives when they act on a
+scaler should give me the same thing
+
+ align:start position:0%
+scaler should give me the same thing
+ 
+
+ align:start position:0%
+scaler should give me the same thing
+back let's see what this implies so if I
+
+ align:start position:0%
+back let's see what this implies so if I
+ 
+
+ align:start position:0%
+back let's see what this implies so if I
+require following to be true well that's
+
+ align:start position:0%
+require following to be true well that's
+ 
+
+ align:start position:0%
+require following to be true well that's
+saying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's expand this out one more
+
+ align:start position:0%
+okay so let's expand this out one more
+ 
+
+ align:start position:0%
+okay so let's expand this out one more
+level so now I'm correcting that
+
+ align:start position:0%
+level so now I'm correcting that
+ 
+
+ align:start position:0%
+level so now I'm correcting that
+downstairs index and over here okay so
+
+ align:start position:0%
+downstairs index and over here okay so
+ 
+
+ align:start position:0%
+downstairs index and over here okay so
+the terms involving nothing but partials
+
+ align:start position:0%
+the terms involving nothing but partials
+ 
+
+ align:start position:0%
+the terms involving nothing but partials
+they obviously cancel I have a common
+
+ align:start position:0%
+they obviously cancel I have a common
+ 
+
+ align:start position:0%
+they obviously cancel I have a common
+factor of D mu of Phi so let's move one
+
+ align:start position:0%
+factor of D mu of Phi so let's move one
+ 
+
+ align:start position:0%
+factor of D mu of Phi so let's move one
+of these over to the other side what
+
+ align:start position:0%
+of these over to the other side what
+ 
+
+ align:start position:0%
+of these over to the other side what
+we've learned is that this requirement
+
+ align:start position:0%
+we've learned is that this requirement
+ 
+
+ align:start position:0%
+we've learned is that this requirement
+that this combination of derivatives
+
+ align:start position:0%
+that this combination of derivatives
+ 
+
+ align:start position:0%
+that this combination of derivatives
+this combination of derivatives be
+
+ align:start position:0%
+this combination of derivatives be
+ 
+
+ align:start position:0%
+this combination of derivatives be
+symmetric tells me something about the
+
+ align:start position:0%
+symmetric tells me something about the
+ 
+
+ align:start position:0%
+symmetric tells me something about the
+symmetry of the Christoffel symbols
+
+ align:start position:0%
+symmetry of the Christoffel symbols
+ 
+
+ align:start position:0%
+symmetry of the Christoffel symbols
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you go back to that little table that
+
+ align:start position:0%
+if you go back to that little table that
+ 
+
+ align:start position:0%
+if you go back to that little table that
+I wrote down for playing polar
+
+ align:start position:0%
+I wrote down for playing polar
+ 
+
+ align:start position:0%
+I wrote down for playing polar
+coordinates okay that was one right it's
+
+ align:start position:0%
+coordinates okay that was one right it's
+ 
+
+ align:start position:0%
+coordinates okay that was one right it's
+calculated the only three non-trivial
+
+ align:start position:0%
+calculated the only three non-trivial
+ 
+
+ align:start position:0%
+calculated the only three non-trivial
+components but there was a symmetry in
+
+ align:start position:0%
+components but there was a symmetry in
+ 
+
+ align:start position:0%
+components but there was a symmetry in
+there and you go in you check it you
+
+ align:start position:0%
+there and you go in you check it you
+ 
+
+ align:start position:0%
+there and you go in you check it you
+will see it's consistent with I found
+
+ align:start position:0%
+will see it's consistent with I found
+ 
+
+ align:start position:0%
+will see it's consistent with I found
+right here pardon me just a second I
+
+ align:start position:0%
+right here pardon me just a second I
+ 
+
+ align:start position:0%
+right here pardon me just a second I
+want to organize a few of my notes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just use this as an
+
+ align:start position:0%
+so let me just use this as an
+ 
+
+ align:start position:0%
+so let me just use this as an
+opportunity to introduce a bit of
+
+ align:start position:0%
+opportunity to introduce a bit of
+ 
+
+ align:start position:0%
+opportunity to introduce a bit of
+notation whenever I give you a tensor
+
+ align:start position:0%
+notation whenever I give you a tensor
+ 
+
+ align:start position:0%
+notation whenever I give you a tensor
+that's got two indices if I write
+
+ align:start position:0%
+that's got two indices if I write
+ 
+
+ align:start position:0%
+that's got two indices if I write
+parentheses around those indices this is
+
+ align:start position:0%
+parentheses around those indices this is
+ 
+
+ align:start position:0%
+parentheses around those indices this is
+going to mean that I do what is called
+
+ align:start position:0%
+going to mean that I do what is called
+ 
+
+ align:start position:0%
+going to mean that I do what is called
+symmetry zation okay we're gonna use
+
+ align:start position:0%
+symmetry zation okay we're gonna use
+ 
+
+ align:start position:0%
+symmetry zation okay we're gonna use
+this from time to time if I write square
+
+ align:start position:0%
+this from time to time if I write square
+ 
+
+ align:start position:0%
+this from time to time if I write square
+braces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is what we call anti symmetry
+
+ align:start position:0%
+this is what we call anti symmetry
+ 
+
+ align:start position:0%
+this is what we call anti symmetry
+zation and so what we just learned is
+
+ align:start position:0%
+zation and so what we just learned is
+ 
+
+ align:start position:0%
+zation and so what we just learned is
+that gamma mu alpha beta is equal to MU
+
+ align:start position:0%
+that gamma mu alpha beta is equal to MU
+ 
+
+ align:start position:0%
+that gamma mu alpha beta is equal to MU
+alpha beta with symmetrization on those
+
+ align:start position:0%
+alpha beta with symmetrization on those
+ 
+
+ align:start position:0%
+alpha beta with symmetrization on those
+last two indices we have likewise
+
+ align:start position:0%
+last two indices we have likewise
+ 
+
+ align:start position:0%
+last two indices we have likewise
+learned that if I can track this against
+
+ align:start position:0%
+learned that if I can track this against
+ 
+
+ align:start position:0%
+learned that if I can track this against
+some object if these were anti symmetric
+
+ align:start position:0%
+some object if these were anti symmetric
+ 
+
+ align:start position:0%
+some object if these were anti symmetric
+I must get a zero out of it okay so
+
+ align:start position:0%
+I must get a zero out of it okay so
+ 
+
+ align:start position:0%
+I must get a zero out of it okay so
+that's a brief aside but these are
+
+ align:start position:0%
+that's a brief aside but these are
+ 
+
+ align:start position:0%
+that's a brief aside but these are
+important things I want to make sure you
+
+ align:start position:0%
+important things I want to make sure you
+ 
+
+ align:start position:0%
+important things I want to make sure you
+have a chance to see them okay so try to
+
+ align:start position:0%
+have a chance to see them okay so try to
+ 
+
+ align:start position:0%
+have a chance to see them okay so try to
+make a decision here about where I'm
+
+ align:start position:0%
+make a decision here about where I'm
+ 
+
+ align:start position:0%
+make a decision here about where I'm
+gonna want to sort of carry things
+
+ align:start position:0%
+gonna want to sort of carry things
+ 
+
+ align:start position:0%
+gonna want to sort of carry things
+forward we're approaching the end of one
+
+ align:start position:0%
+forward we're approaching the end of one
+ 
+
+ align:start position:0%
+forward we're approaching the end of one
+set of notes there's still one more
+
+ align:start position:0%
+set of notes there's still one more
+ 
+
+ align:start position:0%
+set of notes there's still one more
+thing I want to do alright so I set this
+
+ align:start position:0%
+thing I want to do alright so I set this
+ 
+
+ align:start position:0%
+thing I want to do alright so I set this
+whole thing up by saying that I wanted
+
+ align:start position:0%
+whole thing up by saying that I wanted
+ 
+
+ align:start position:0%
+whole thing up by saying that I wanted
+to give you guys an algorithm for how to
+
+ align:start position:0%
+to give you guys an algorithm for how to
+ 
+
+ align:start position:0%
+to give you guys an algorithm for how to
+generate the Christoffel symbols
+
+ align:start position:0%
+generate the Christoffel symbols
+ 
+
+ align:start position:0%
+generate the Christoffel symbols
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way I'm going to do this is by
+
+ align:start position:0%
+the way I'm going to do this is by
+ 
+
+ align:start position:0%
+the way I'm going to do this is by
+examining the gradient of the metric so
+
+ align:start position:0%
+examining the gradient of the metric so
+ 
+
+ align:start position:0%
+examining the gradient of the metric so
+suppose I want to compute following
+
+ align:start position:0%
+suppose I want to compute following
+ 
+
+ align:start position:0%
+suppose I want to compute following
+tensor quantity let's say G is the
+
+ align:start position:0%
+tensor quantity let's say G is the
+ 
+
+ align:start position:0%
+tensor quantity let's say G is the
+metric tensor written here in the fairly
+
+ align:start position:0%
+metric tensor written here in the fairly
+ 
+
+ align:start position:0%
+metric tensor written here in the fairly
+abstract notation and this is my full-on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tensor gradient of this thing so if you
+
+ align:start position:0%
+tensor gradient of this thing so if you
+ 
+
+ align:start position:0%
+tensor gradient of this thing so if you
+want to write this out and it's full
+
+ align:start position:0%
+want to write this out and it's full
+ 
+
+ align:start position:0%
+want to write this out and it's full
+glory you might write this as something
+
+ align:start position:0%
+glory you might write this as something
+ 
+
+ align:start position:0%
+glory you might write this as something
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if you stop and think about this for
+
+ align:start position:0%
+but if you stop and think about this for
+ 
+
+ align:start position:0%
+but if you stop and think about this for
+just a second let's go back to this
+
+ align:start position:0%
+just a second let's go back to this
+ 
+
+ align:start position:0%
+just a second let's go back to this
+principle an equation that is tensorial
+
+ align:start position:0%
+principle an equation that is tensorial
+ 
+
+ align:start position:0%
+principle an equation that is tensorial
+in one representation must be tensorial
+
+ align:start position:0%
+in one representation must be tensorial
+ 
+
+ align:start position:0%
+in one representation must be tensorial
+in all suppose I choose the the
+
+ align:start position:0%
+in all suppose I choose the the
+ 
+
+ align:start position:0%
+in all suppose I choose the the
+Cartesian representation of this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops here's what it looks like there
+
+ align:start position:0%
+whoops here's what it looks like there
+ 
+
+ align:start position:0%
+whoops here's what it looks like there
+but this is my constant right so if I do
+
+ align:start position:0%
+but this is my constant right so if I do
+ 
+
+ align:start position:0%
+but this is my constant right so if I do
+this in Cartesian coordinates it has to
+
+ align:start position:0%
+this in Cartesian coordinates it has to
+ 
+
+ align:start position:0%
+this in Cartesian coordinates it has to
+be a zero the only way that I can make
+
+ align:start position:0%
+be a zero the only way that I can make
+ 
+
+ align:start position:0%
+be a zero the only way that I can make
+this sort of comport with this principle
+
+ align:start position:0%
+this sort of comport with this principle
+ 
+
+ align:start position:0%
+this sort of comport with this principle
+that tends to represent an equation
+
+ align:start position:0%
+that tends to represent an equation
+ 
+
+ align:start position:0%
+that tends to represent an equation
+that's 10-story on one representation
+
+ align:start position:0%
+that's 10-story on one representation
+ 
+
+ align:start position:0%
+that's 10-story on one representation
+have it hold in all representations this
+
+ align:start position:0%
+have it hold in all representations this
+ 
+
+ align:start position:0%
+have it hold in all representations this
+leads me to say I need to require that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the covariant derivative of the metric
+
+ align:start position:0%
+the covariant derivative of the metric
+ 
+
+ align:start position:0%
+the covariant derivative of the metric
+be equal to zero we are going to use
+
+ align:start position:0%
+be equal to zero we are going to use
+ 
+
+ align:start position:0%
+be equal to zero we are going to use
+this and I think this will be sort of
+
+ align:start position:0%
+this and I think this will be sort of
+ 
+
+ align:start position:0%
+this and I think this will be sort of
+the last detailed calculation I do in
+
+ align:start position:0%
+the last detailed calculation I do in
+ 
+
+ align:start position:0%
+the last detailed calculation I do in
+today's lecture we're going to use this
+
+ align:start position:0%
+today's lecture we're going to use this
+ 
+
+ align:start position:0%
+today's lecture we're going to use this
+to find a way to get the Christoffel
+
+ align:start position:0%
+to find a way to get the Christoffel
+ 
+
+ align:start position:0%
+to find a way to get the Christoffel
+symbol from partial derivatives of the
+
+ align:start position:0%
+symbol from partial derivatives of the
+ 
+
+ align:start position:0%
+symbol from partial derivatives of the
+metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's a lot of terms here there's
+
+ align:start position:0%
+okay there's a lot of terms here there's
+ 
+
+ align:start position:0%
+okay there's a lot of terms here there's
+a lot of little indices so I'm gonna do
+
+ align:start position:0%
+a lot of little indices so I'm gonna do
+ 
+
+ align:start position:0%
+a lot of little indices so I'm gonna do
+my best to make my handwriting neat I'm
+
+ align:start position:0%
+my best to make my handwriting neat I'm
+ 
+
+ align:start position:0%
+my best to make my handwriting neat I'm
+gonna relay write down a relationship
+
+ align:start position:0%
+gonna relay write down a relationship
+ 
+
+ align:start position:0%
+gonna relay write down a relationship
+that I call Roman numeral one the
+
+ align:start position:0%
+that I call Roman numeral one the
+ 
+
+ align:start position:0%
+that I call Roman numeral one the
+covariant derivative in the Gamma
+
+ align:start position:0%
+covariant derivative in the Gamma
+ 
+
+ align:start position:0%
+covariant derivative in the Gamma
+direction of G alpha beta you know what
+
+ align:start position:0%
+direction of G alpha beta you know what
+ 
+
+ align:start position:0%
+direction of G alpha beta you know what
+let me put this down a little bit lower
+
+ align:start position:0%
+let me put this down a little bit lower
+ 
+
+ align:start position:0%
+let me put this down a little bit lower
+so I can get these two terms on the same
+
+ align:start position:0%
+so I can get these two terms on the same
+ 
+
+ align:start position:0%
+so I can get these two terms on the same
+line okay so I get this thing that
+
+ align:start position:0%
+line okay so I get this thing that
+ 
+
+ align:start position:0%
+line okay so I get this thing that
+involves two Christoffel symbols
+
+ align:start position:0%
+involves two Christoffel symbols
+ 
+
+ align:start position:0%
+involves two Christoffel symbols
+correcting those two indices this is one
+
+ align:start position:0%
+correcting those two indices this is one
+ 
+
+ align:start position:0%
+correcting those two indices this is one
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't really seem to have gotten very
+
+ align:start position:0%
+I don't really seem to have gotten very
+ 
+
+ align:start position:0%
+I don't really seem to have gotten very
+far okay this is true but I now have to
+
+ align:start position:0%
+far okay this is true but I now have to
+ 
+
+ align:start position:0%
+far okay this is true but I now have to
+bloody Christoffel symbols that I've
+
+ align:start position:0%
+bloody Christoffel symbols that I've
+ 
+
+ align:start position:0%
+bloody Christoffel symbols that I've
+somehow managed to work into this what
+
+ align:start position:0%
+somehow managed to work into this what
+ 
+
+ align:start position:0%
+somehow managed to work into this what
+I'm trying to do is find a way to get
+
+ align:start position:0%
+I'm trying to do is find a way to get
+ 
+
+ align:start position:0%
+I'm trying to do is find a way to get
+one and equate it to things involving
+
+ align:start position:0%
+one and equate it to things involving
+ 
+
+ align:start position:0%
+one and equate it to things involving
+derivative of the metric so this is sort
+
+ align:start position:0%
+derivative of the metric so this is sort
+ 
+
+ align:start position:0%
+derivative of the metric so this is sort
+of a rut row kind of moment but there's
+
+ align:start position:0%
+of a rut row kind of moment but there's
+ 
+
+ align:start position:0%
+of a rut row kind of moment but there's
+nothing special about this order of the
+
+ align:start position:0%
+nothing special about this order of the
+ 
+
+ align:start position:0%
+nothing special about this order of the
+indices so with the audacity that only
+
+ align:start position:0%
+indices so with the audacity that only
+ 
+
+ align:start position:0%
+indices so with the audacity that only
+comes from knowing the answer in advance
+
+ align:start position:0%
+comes from knowing the answer in advance
+ 
+
+ align:start position:0%
+comes from knowing the answer in advance
+what I'm going to do is permute the
+
+ align:start position:0%
+what I'm going to do is permute the
+ 
+
+ align:start position:0%
+what I'm going to do is permute the
+indices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bingo let's promote the indices once
+
+ align:start position:0%
+bingo let's promote the indices once
+ 
+
+ align:start position:0%
+bingo let's promote the indices once
+more so I'll give you guys a moment to
+
+ align:start position:0%
+more so I'll give you guys a moment to
+ 
+
+ align:start position:0%
+more so I'll give you guys a moment to
+catch up with me don't forget these
+
+ align:start position:0%
+catch up with me don't forget these
+ 
+
+ align:start position:0%
+catch up with me don't forget these
+notes will be scanned and added to the
+
+ align:start position:0%
+notes will be scanned and added to the
+ 
+
+ align:start position:0%
+notes will be scanned and added to the
+webpage so if you don't want to follow
+
+ align:start position:0%
+webpage so if you don't want to follow
+ 
+
+ align:start position:0%
+webpage so if you don't want to follow
+along writing down every little detail
+
+ align:start position:0%
+along writing down every little detail
+ 
+
+ align:start position:0%
+along writing down every little detail
+I understand although personally I find
+
+ align:start position:0%
+I understand although personally I find
+ 
+
+ align:start position:0%
+I understand although personally I find
+that these things gel a little bit
+
+ align:start position:0%
+that these things gel a little bit
+ 
+
+ align:start position:0%
+that these things gel a little bit
+better when you actually write them out
+
+ align:start position:0%
+better when you actually write them out
+ 
+
+ align:start position:0%
+better when you actually write them out
+yourself okay so those are three ways
+
+ align:start position:0%
+yourself okay so those are three ways
+ 
+
+ align:start position:0%
+yourself okay so those are three ways
+that I can assert that the metric has no
+
+ align:start position:0%
+that I can assert that the metric has no
+ 
+
+ align:start position:0%
+that I can assert that the metric has no
+covariant derivative okay
+
+ align:start position:0%
+covariant derivative okay
+ 
+
+ align:start position:0%
+covariant derivative okay
+they all are basically expressing that
+
+ align:start position:0%
+they all are basically expressing that
+ 
+
+ align:start position:0%
+they all are basically expressing that
+same physical fact I'm just permuting
+
+ align:start position:0%
+same physical fact I'm just permuting
+ 
+
+ align:start position:0%
+same physical fact I'm just permuting
+the indices now there's no better way to
+
+ align:start position:0%
+the indices now there's no better way to
+ 
+
+ align:start position:0%
+the indices now there's no better way to
+describe this then you sort of just
+
+ align:start position:0%
+describe this then you sort of just
+ 
+
+ align:start position:0%
+describe this then you sort of just
+stare at this for a few moments and then
+
+ align:start position:0%
+stare at this for a few moments and then
+ 
+
+ align:start position:0%
+stare at this for a few moments and then
+go gee I wonder what would happen if so
+
+ align:start position:0%
+go gee I wonder what would happen if so
+ 
+
+ align:start position:0%
+go gee I wonder what would happen if so
+stare at this for a little while and
+
+ align:start position:0%
+stare at this for a little while and
+ 
+
+ align:start position:0%
+stare at this for a little while and
+then construct you know I have three
+
+ align:start position:0%
+then construct you know I have three
+ 
+
+ align:start position:0%
+then construct you know I have three
+things that are equal to zero so I can
+
+ align:start position:0%
+things that are equal to zero so I can
+ 
+
+ align:start position:0%
+things that are equal to zero so I can
+add them together I can subtract one
+
+ align:start position:0%
+add them together I can subtract one
+ 
+
+ align:start position:0%
+add them together I can subtract one
+from the other I can add two and
+
+ align:start position:0%
+from the other I can add two and
+ 
+
+ align:start position:0%
+from the other I can add two and
+subtract one whatever they should all
+
+ align:start position:0%
+subtract one whatever they should all
+ 
+
+ align:start position:0%
+subtract one whatever they should all
+give me zero in particular combination I
+
+ align:start position:0%
+give me zero in particular combination I
+ 
+
+ align:start position:0%
+give me zero in particular combination I
+want to look at is what I get when I
+
+ align:start position:0%
+want to look at is what I get when I
+ 
+
+ align:start position:0%
+want to look at is what I get when I
+take relationship one and I subtract
+
+ align:start position:0%
+take relationship one and I subtract
+ 
+
+ align:start position:0%
+take relationship one and I subtract
+from it two and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to get one term there are
+
+ align:start position:0%
+so I'm going to get one term there are
+ 
+
+ align:start position:0%
+so I'm going to get one term there are
+just these three combinations of
+
+ align:start position:0%
+just these three combinations of
+ 
+
+ align:start position:0%
+just these three combinations of
+derivatives gamma okay and I get
+
+ align:start position:0%
+derivatives gamma okay and I get
+ 
+
+ align:start position:0%
+derivatives gamma okay and I get
+something that looks like so let me
+
+ align:start position:0%
+something that looks like so let me
+ 
+
+ align:start position:0%
+something that looks like so let me
+write this out and then pause and make a
+
+ align:start position:0%
+write this out and then pause and make a
+ 
+
+ align:start position:0%
+write this out and then pause and make a
+comment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I sort of made some lame jokes a
+
+ align:start position:0%
+okay so I sort of made some lame jokes a
+ 
+
+ align:start position:0%
+okay so I sort of made some lame jokes a
+few moments ago that essentially the
+
+ align:start position:0%
+few moments ago that essentially the
+ 
+
+ align:start position:0%
+few moments ago that essentially the
+only reason I was able to get this was
+
+ align:start position:0%
+only reason I was able to get this was
+ 
+
+ align:start position:0%
+only reason I was able to get this was
+by knowing the answer in the back of the
+
+ align:start position:0%
+by knowing the answer in the back of the
+ 
+
+ align:start position:0%
+by knowing the answer in the back of the
+book essentially and be perfectly blunt
+
+ align:start position:0%
+book essentially and be perfectly blunt
+ 
+
+ align:start position:0%
+book essentially and be perfectly blunt
+for me personally that's probably true
+
+ align:start position:0%
+for me personally that's probably true
+ 
+
+ align:start position:0%
+for me personally that's probably true
+when I first wrote this down I probably
+
+ align:start position:0%
+when I first wrote this down I probably
+ 
+
+ align:start position:0%
+when I first wrote this down I probably
+did need to follow an algorithm but if I
+
+ align:start position:0%
+did need to follow an algorithm but if I
+ 
+
+ align:start position:0%
+did need to follow an algorithm but if I
+was doing this ab initio if I was
+
+ align:start position:0%
+was doing this ab initio if I was
+ 
+
+ align:start position:0%
+was doing this ab initio if I was
+singing down to first do this what's
+
+ align:start position:0%
+singing down to first do this what's
+ 
+
+ align:start position:0%
+singing down to first do this what's
+really going on here is the reason I
+
+ align:start position:0%
+really going on here is the reason I
+ 
+
+ align:start position:0%
+really going on here is the reason I
+wrote out all these different
+
+ align:start position:0%
+wrote out all these different
+ 
+
+ align:start position:0%
+wrote out all these different
+combinations of things is that I was
+
+ align:start position:0%
+combinations of things is that I was
+ 
+
+ align:start position:0%
+combinations of things is that I was
+trying to gather terms together in such
+
+ align:start position:0%
+trying to gather terms together in such
+ 
+
+ align:start position:0%
+trying to gather terms together in such
+a way that I could take advantage of
+
+ align:start position:0%
+a way that I could take advantage of
+ 
+
+ align:start position:0%
+a way that I could take advantage of
+that symmetry okay a few moments ago we
+
+ align:start position:0%
+that symmetry okay a few moments ago we
+ 
+
+ align:start position:0%
+that symmetry okay a few moments ago we
+showed that the Christoffel symbols are
+
+ align:start position:0%
+showed that the Christoffel symbols are
+ 
+
+ align:start position:0%
+showed that the Christoffel symbols are
+symmetric on the lower two indices and
+
+ align:start position:0%
+symmetric on the lower two indices and
+ 
+
+ align:start position:0%
+symmetric on the lower two indices and
+so by putting out all these different
+
+ align:start position:0%
+so by putting out all these different
+ 
+
+ align:start position:0%
+so by putting out all these different
+combinations of things I was then able
+
+ align:start position:0%
+combinations of things I was then able
+ 
+
+ align:start position:0%
+combinations of things I was then able
+to combine them in such a way that
+
+ align:start position:0%
+to combine them in such a way that
+ 
+
+ align:start position:0%
+to combine them in such a way that
+certain terms look at this and go ah
+
+ align:start position:0%
+certain terms look at this and go ah
+ 
+
+ align:start position:0%
+certain terms look at this and go ah
+symmetry on alpha and gamma means this
+
+ align:start position:0%
+symmetry on alpha and gamma means this
+ 
+
+ align:start position:0%
+symmetry on alpha and gamma means this
+whole term dies symmetry on beta and
+
+ align:start position:0%
+whole term dies symmetry on beta and
+ 
+
+ align:start position:0%
+whole term dies symmetry on beta and
+gamma means this whole term dies
+
+ align:start position:0%
+gamma means this whole term dies
+ 
+
+ align:start position:0%
+gamma means this whole term dies
+symmetry on alpha and beta means these
+
+ align:start position:0%
+symmetry on alpha and beta means these
+ 
+
+ align:start position:0%
+symmetry on alpha and beta means these
+two guys combined and I get a factor of
+
+ align:start position:0%
+two guys combined and I get a factor of
+ 
+
+ align:start position:0%
+two guys combined and I get a factor of
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's clean up our algebra move a
+
+ align:start position:0%
+so let's clean up our algebra move a
+ 
+
+ align:start position:0%
+so let's clean up our algebra move a
+bunch of our terms to the other side of
+
+ align:start position:0%
+bunch of our terms to the other side of
+ 
+
+ align:start position:0%
+bunch of our terms to the other side of
+the equation since it's a blah blah blah
+
+ align:start position:0%
+the equation since it's a blah blah blah
+ 
+
+ align:start position:0%
+the equation since it's a blah blah blah
+equals zero what we get when we do this
+
+ align:start position:0%
+equals zero what we get when we do this
+ 
+
+ align:start position:0%
+equals zero what we get when we do this
+is G mu downstairs gamma this equals one
+
+ align:start position:0%
+is G mu downstairs gamma this equals one
+ 
+
+ align:start position:0%
+is G mu downstairs gamma this equals one
+half what we're going to do now is we
+
+ align:start position:0%
+half what we're going to do now is we
+ 
+
+ align:start position:0%
+half what we're going to do now is we
+will define everything on the right hand
+
+ align:start position:0%
+will define everything on the right hand
+ 
+
+ align:start position:0%
+will define everything on the right hand
+side I've kind of emphasized earlier
+
+ align:start position:0%
+side I've kind of emphasized earlier
+ 
+
+ align:start position:0%
+side I've kind of emphasized earlier
+that the crystals are not themselves
+
+ align:start position:0%
+that the crystals are not themselves
+ 
+
+ align:start position:0%
+that the crystals are not themselves
+tensors okay but we're going to imagine
+
+ align:start position:0%
+tensors okay but we're going to imagine
+ 
+
+ align:start position:0%
+tensors okay but we're going to imagine
+that we can nonetheless what I'm going
+
+ align:start position:0%
+that we can nonetheless what I'm going
+ 
+
+ align:start position:0%
+that we can nonetheless what I'm going
+to imagine we're just gonna define we're
+
+ align:start position:0%
+to imagine we're just gonna define we're
+ 
+
+ align:start position:0%
+to imagine we're just gonna define we're
+gonna say that we're allowed to raise
+
+ align:start position:0%
+gonna say that we're allowed to raise
+ 
+
+ align:start position:0%
+gonna say that we're allowed to raise
+and lower their indices using the metric
+
+ align:start position:0%
+and lower their indices using the metric
+ 
+
+ align:start position:0%
+and lower their indices using the metric
+in the same way that you guys have been
+
+ align:start position:0%
+in the same way that you guys have been
+ 
+
+ align:start position:0%
+in the same way that you guys have been
+doing with vectors and one forms and
+
+ align:start position:0%
+doing with vectors and one forms and
+ 
+
+ align:start position:0%
+doing with vectors and one forms and
+other kinds of tensors so let's call
+
+ align:start position:0%
+other kinds of tensors so let's call
+ 
+
+ align:start position:0%
+other kinds of tensors so let's call
+everything on the right hand side here
+
+ align:start position:0%
+everything on the right hand side here
+ 
+
+ align:start position:0%
+everything on the right hand side here
+gamma with all the indices in the
+
+ align:start position:0%
+gamma with all the indices in the
+ 
+
+ align:start position:0%
+gamma with all the indices in the
+downstairs position gamma sub gamma
+
+ align:start position:0%
+downstairs position gamma sub gamma
+ 
+
+ align:start position:0%
+downstairs position gamma sub gamma
+alpha beta and then this is simply what
+
+ align:start position:0%
+alpha beta and then this is simply what
+ 
+
+ align:start position:0%
+alpha beta and then this is simply what
+I get when I put all of these things
+
+ align:start position:0%
+I get when I put all of these things
+ 
+
+ align:start position:0%
+I get when I put all of these things
+together like so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you go and you look up the formulas
+
+ align:start position:0%
+if you go and you look up the formulas
+ 
+
+ align:start position:0%
+if you go and you look up the formulas
+for this in various textbooks they give
+
+ align:start position:0%
+for this in various textbooks they give
+ 
+
+ align:start position:0%
+for this in various textbooks they give
+give give these different kinds of
+
+ align:start position:0%
+give give these different kinds of
+ 
+
+ align:start position:0%
+give give these different kinds of
+formulas you will typically see it
+
+ align:start position:0%
+formulas you will typically see it
+ 
+
+ align:start position:0%
+formulas you will typically see it
+written as 1/2 G upstairs in the C's and
+
+ align:start position:0%
+written as 1/2 G upstairs in the C's and
+ 
+
+ align:start position:0%
+written as 1/2 G upstairs in the C's and
+then all this stuff in parentheses after
+
+ align:start position:0%
+then all this stuff in parentheses after
+ 
+
+ align:start position:0%
+then all this stuff in parentheses after
+that okay they often when you look at
+
+ align:start position:0%
+that okay they often when you look at
+ 
+
+ align:start position:0%
+that okay they often when you look at
+things up this is that the typical
+
+ align:start position:0%
+things up this is that the typical
+ 
+
+ align:start position:0%
+things up this is that the typical
+formula that is given in these books
+
+ align:start position:0%
+formula that is given in these books
+ 
+
+ align:start position:0%
+formula that is given in these books
+this is where it comes from okay so I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need to check one thing because it
+
+ align:start position:0%
+need to check one thing because it
+ 
+
+ align:start position:0%
+need to check one thing because it
+appears my notes are a little bit out of
+
+ align:start position:0%
+appears my notes are a little bit out of
+ 
+
+ align:start position:0%
+appears my notes are a little bit out of
+order here but nonetheless there is this
+
+ align:start position:0%
+order here but nonetheless there is this
+ 
+
+ align:start position:0%
+order here but nonetheless there is this
+is a good point since we've sort of just
+
+ align:start position:0%
+is a good point since we've sort of just
+ 
+
+ align:start position:0%
+is a good point since we've sort of just
+finished a pretty long calculation this
+
+ align:start position:0%
+finished a pretty long calculation this
+ 
+
+ align:start position:0%
+finished a pretty long calculation this
+is a good point to introduce an
+
+ align:start position:0%
+is a good point to introduce an
+ 
+
+ align:start position:0%
+is a good point to introduce an
+important physical point okay we're
+
+ align:start position:0%
+important physical point okay we're
+ 
+
+ align:start position:0%
+important physical point okay we're
+going to come back to this we're going
+
+ align:start position:0%
+going to come back to this we're going
+ 
+
+ align:start position:0%
+going to come back to this we're going
+to start this on Thursday but I want to
+
+ align:start position:0%
+to start this on Thursday but I want to
+ 
+
+ align:start position:0%
+to start this on Thursday but I want to
+begin making some physical points that
+
+ align:start position:0%
+begin making some physical points that
+ 
+
+ align:start position:0%
+begin making some physical points that
+are going to take us from special
+
+ align:start position:0%
+are going to take us from special
+ 
+
+ align:start position:0%
+are going to take us from special
+relativity to general relativity so
+
+ align:start position:0%
+relativity to general relativity so
+ 
+
+ align:start position:0%
+relativity to general relativity so
+despite the fact that I've introduced
+
+ align:start position:0%
+despite the fact that I've introduced
+ 
+
+ align:start position:0%
+despite the fact that I've introduced
+this new mathematical framework
+
+ align:start position:0%
+this new mathematical framework
+ 
+
+ align:start position:0%
+this new mathematical framework
+everything that I have done so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is in the context of special relativity
+
+ align:start position:0%
+is in the context of special relativity
+ 
+
+ align:start position:0%
+is in the context of special relativity
+I'm going to make a more precise
+
+ align:start position:0%
+I'm going to make a more precise
+ 
+
+ align:start position:0%
+I'm going to make a more precise
+definition of special relativity right
+
+ align:start position:0%
+definition of special relativity right
+ 
+
+ align:start position:0%
+definition of special relativity right
+now so special relativity we are going
+
+ align:start position:0%
+now so special relativity we are going
+ 
+
+ align:start position:0%
+now so special relativity we are going
+to think of this moving forward as the
+
+ align:start position:0%
+to think of this moving forward as the
+ 
+
+ align:start position:0%
+to think of this moving forward as the
+serie which allows us to cover the
+
+ align:start position:0%
+serie which allows us to cover the
+ 
+
+ align:start position:0%
+serie which allows us to cover the
+entire space-time manifold using
+
+ align:start position:0%
+entire space-time manifold using
+ 
+
+ align:start position:0%
+entire space-time manifold using
+inertial reference frames okay so we use
+
+ align:start position:0%
+inertial reference frames okay so we use
+ 
+
+ align:start position:0%
+inertial reference frames okay so we use
+inertial reference frames or essentially
+
+ align:start position:0%
+inertial reference frames or essentially
+ 
+
+ align:start position:0%
+inertial reference frames or essentially
+Lorentz reference frames it's saying
+
+ align:start position:0%
+Lorentz reference frames it's saying
+ 
+
+ align:start position:0%
+Lorentz reference frames it's saying
+that Lorentz coordinates are good
+
+ align:start position:0%
+that Lorentz coordinates are good
+ 
+
+ align:start position:0%
+that Lorentz coordinates are good
+everywhere we know we can go between
+
+ align:start position:0%
+everywhere we know we can go between
+ 
+
+ align:start position:0%
+everywhere we know we can go between
+different Lorentz reference frames using
+
+ align:start position:0%
+different Lorentz reference frames using
+ 
+
+ align:start position:0%
+different Lorentz reference frames using
+Lorentz transformations but the key
+
+ align:start position:0%
+Lorentz transformations but the key
+ 
+
+ align:start position:0%
+Lorentz transformations but the key
+thing is that if special relativity were
+
+ align:start position:0%
+thing is that if special relativity were
+ 
+
+ align:start position:0%
+thing is that if special relativity were
+correct the entire universe would be
+
+ align:start position:0%
+correct the entire universe would be
+ 
+
+ align:start position:0%
+correct the entire universe would be
+accurately described by any inertial
+
+ align:start position:0%
+accurately described by any inertial
+ 
+
+ align:start position:0%
+accurately described by any inertial
+reference frame you care to write down
+
+ align:start position:0%
+reference frame you care to write down
+ 
+
+ align:start position:0%
+reference frame you care to write down
+and I will probably only be able to do
+
+ align:start position:0%
+and I will probably only be able to do
+ 
+
+ align:start position:0%
+and I will probably only be able to do
+about half of this right now we'll pick
+
+ align:start position:0%
+about half of this right now we'll pick
+ 
+
+ align:start position:0%
+about half of this right now we'll pick
+it up next time if I cannot finish this
+
+ align:start position:0%
+it up next time if I cannot finish this
+ 
+
+ align:start position:0%
+it up next time if I cannot finish this
+key thing which I want to emphasize is
+
+ align:start position:0%
+key thing which I want to emphasize is
+ 
+
+ align:start position:0%
+key thing which I want to emphasize is
+gravity breaks this as soon as you put
+
+ align:start position:0%
+gravity breaks this as soon as you put
+ 
+
+ align:start position:0%
+gravity breaks this as soon as you put
+gravity into your theory of relativity
+
+ align:start position:0%
+gravity into your theory of relativity
+ 
+
+ align:start position:0%
+gravity into your theory of relativity
+you cannot have so we will call this a
+
+ align:start position:0%
+you cannot have so we will call this a
+ 
+
+ align:start position:0%
+you cannot have so we will call this a
+global inertial frame an inertial frame
+
+ align:start position:0%
+global inertial frame an inertial frame
+ 
+
+ align:start position:0%
+global inertial frame an inertial frame
+that is good everywhere so global in the
+
+ align:start position:0%
+that is good everywhere so global in the
+ 
+
+ align:start position:0%
+that is good everywhere so global in the
+mathematical sense not global in the
+
+ align:start position:0%
+mathematical sense not global in the
+ 
+
+ align:start position:0%
+mathematical sense not global in the
+Geographic sense not just earth the
+
+ align:start position:0%
+Geographic sense not just earth the
+ 
+
+ align:start position:0%
+Geographic sense not just earth the
+whole universe essentially soon as we
+
+ align:start position:0%
+whole universe essentially soon as we
+ 
+
+ align:start position:0%
+whole universe essentially soon as we
+put in gravity we no longer have global
+
+ align:start position:0%
+put in gravity we no longer have global
+ 
+
+ align:start position:0%
+put in gravity we no longer have global
+reference frames and global and there
+
+ align:start position:0%
+reference frames and global and there
+ 
+
+ align:start position:0%
+reference frames and global and there
+reference frames that word inertial is
+
+ align:start position:0%
+reference frames that word inertial is
+ 
+
+ align:start position:0%
+reference frames that word inertial is
+important but we are gonna be allowed to
+
+ align:start position:0%
+important but we are gonna be allowed to
+ 
+
+ align:start position:0%
+important but we are gonna be allowed to
+have local inertial frames I have not
+
+ align:start position:0%
+have local inertial frames I have not
+ 
+
+ align:start position:0%
+have local inertial frames I have not
+precisely to find the difference what
+
+ align:start position:0%
+precisely to find the difference what
+ 
+
+ align:start position:0%
+precisely to find the difference what
+local means in this case and I won't for
+
+ align:start position:0%
+local means in this case and I won't for
+ 
+
+ align:start position:0%
+local means in this case and I won't for
+a few lectures but to give you a preview
+
+ align:start position:0%
+a few lectures but to give you a preview
+ 
+
+ align:start position:0%
+a few lectures but to give you a preview
+is what that means it's essentially
+
+ align:start position:0%
+is what that means it's essentially
+ 
+
+ align:start position:0%
+is what that means it's essentially
+going to say that we can define an
+
+ align:start position:0%
+going to say that we can define an
+ 
+
+ align:start position:0%
+going to say that we can define an
+inertial coordinate system that is good
+
+ align:start position:0%
+inertial coordinate system that is good
+ 
+
+ align:start position:0%
+inertial coordinate system that is good
+over a particular region of space-time
+
+ align:start position:0%
+over a particular region of space-time
+ 
+
+ align:start position:0%
+over a particular region of space-time
+and we are going to have to discuss and
+
+ align:start position:0%
+and we are going to have to discuss and
+ 
+
+ align:start position:0%
+and we are going to have to discuss and
+come up with ways of understanding what
+
+ align:start position:0%
+come up with ways of understanding what
+ 
+
+ align:start position:0%
+come up with ways of understanding what
+the boundaries of that region are and
+
+ align:start position:0%
+the boundaries of that region are and
+ 
+
+ align:start position:0%
+the boundaries of that region are and
+how to make this precise so the
+
+ align:start position:0%
+how to make this precise so the
+ 
+
+ align:start position:0%
+how to make this precise so the
+statement that gravity breaks the
+
+ align:start position:0%
+statement that gravity breaks the
+ 
+
+ align:start position:0%
+statement that gravity breaks the
+existence of global Lorentz frames like
+
+ align:start position:0%
+existence of global Lorentz frames like
+ 
+
+ align:start position:0%
+existence of global Lorentz frames like
+I said it's a two part thing I'm going
+
+ align:start position:0%
+I said it's a two part thing I'm going
+ 
+
+ align:start position:0%
+I said it's a two part thing I'm going
+to use a very hand wavy argument which
+
+ align:start position:0%
+to use a very hand wavy argument which
+ 
+
+ align:start position:0%
+to use a very hand wavy argument which
+can be made quite rigorous later but I
+
+ align:start position:0%
+can be made quite rigorous later but I
+ 
+
+ align:start position:0%
+can be made quite rigorous later but I
+want to keep it to this hand-wavy level
+
+ align:start position:0%
+want to keep it to this hand-wavy level
+ 
+
+ align:start position:0%
+want to keep it to this hand-wavy level
+because first of all it actually was
+
+ align:start position:0%
+because first of all it actually was
+ 
+
+ align:start position:0%
+because first of all it actually was
+first done by a very high-level
+
+ align:start position:0%
+first done by a very high-level
+ 
+
+ align:start position:0%
+first done by a very high-level
+mathematical physicist named Alfred
+
+ align:start position:0%
+mathematical physicist named Alfred
+ 
+
+ align:start position:0%
+mathematical physicist named Alfred
+shield who worked in the early theory of
+
+ align:start position:0%
+shield who worked in the early theory of
+ 
+
+ align:start position:0%
+shield who worked in the early theory of
+relativity sort of like he was so
+
+ align:start position:0%
+relativity sort of like he was so
+ 
+
+ align:start position:0%
+relativity sort of like he was so
+mathematical was good enough for him
+
+ align:start position:0%
+mathematical was good enough for him
+ 
+
+ align:start position:0%
+mathematical was good enough for him
+that's good enough for me and it's I
+
+ align:start position:0%
+that's good enough for me and it's I
+ 
+
+ align:start position:0%
+that's good enough for me and it's I
+think you know even though it's a little
+
+ align:start position:0%
+think you know even though it's a little
+ 
+
+ align:start position:0%
+think you know even though it's a little
+hand wavy and kind of goofy in at least
+
+ align:start position:0%
+hand wavy and kind of goofy in at least
+ 
+
+ align:start position:0%
+hand wavy and kind of goofy in at least
+one place it gives a good physical sense
+
+ align:start position:0%
+one place it gives a good physical sense
+ 
+
+ align:start position:0%
+one place it gives a good physical sense
+as to why it is gravity begins to mess
+
+ align:start position:0%
+as to why it is gravity begins to mess
+ 
+
+ align:start position:0%
+as to why it is gravity begins to mess
+things up so part one is the fact that
+
+ align:start position:0%
+things up so part one is the fact that
+ 
+
+ align:start position:0%
+things up so part one is the fact that
+there exists a gravitational redshift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's where I'm going to be
+
+ align:start position:0%
+so here's where I'm going to be
+ 
+
+ align:start position:0%
+so here's where I'm going to be
+particularly silly but I will back up my
+
+ align:start position:0%
+particularly silly but I will back up my
+ 
+
+ align:start position:0%
+particularly silly but I will back up my
+silliness by the fact that everything
+
+ align:start position:0%
+silliness by the fact that everything
+ 
+
+ align:start position:0%
+silliness by the fact that everything
+silly that I say here has actually been
+
+ align:start position:0%
+silly that I say here has actually been
+ 
+
+ align:start position:0%
+silly that I say here has actually been
+experimentally verified or at least the
+
+ align:start position:0%
+experimentally verified or at least the
+ 
+
+ align:start position:0%
+experimentally verified or at least the
+key physical output of us so imagine you
+
+ align:start position:0%
+key physical output of us so imagine you
+ 
+
+ align:start position:0%
+key physical output of us so imagine you
+are on top of a tower and you drop a
+
+ align:start position:0%
+are on top of a tower and you drop a
+ 
+
+ align:start position:0%
+are on top of a tower and you drop a
+rock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excuse me of rest mass M off the top of
+
+ align:start position:0%
+excuse me of rest mass M off the top of
+ 
+
+ align:start position:0%
+excuse me of rest mass M off the top of
+this tower so here you are here's your
+
+ align:start position:0%
+this tower so here you are here's your
+ 
+
+ align:start position:0%
+this tower so here you are here's your
+rock the rock falls there's a wonderful
+
+ align:start position:0%
+rock the rock falls there's a wonderful
+ 
+
+ align:start position:0%
+rock the rock falls there's a wonderful
+device down here labeled with a P it's
+
+ align:start position:0%
+device down here labeled with a P it's
+ 
+
+ align:start position:0%
+device down here labeled with a P it's
+called a futon you later and what the
+
+ align:start position:0%
+called a futon you later and what the
+ 
+
+ align:start position:0%
+called a futon you later and what the
+photon you later does it converts the
+
+ align:start position:0%
+photon you later does it converts the
+ 
+
+ align:start position:0%
+photon you later does it converts the
+rock into a single photon and it does so
+
+ align:start position:0%
+rock into a single photon and it does so
+ 
+
+ align:start position:0%
+rock into a single photon and it does so
+conserving energy okay
+
+ align:start position:0%
+conserving energy okay
+ 
+
+ align:start position:0%
+conserving energy okay
+so when this rock falls the instant
+
+ align:start position:0%
+so when this rock falls the instant
+ 
+
+ align:start position:0%
+so when this rock falls the instant
+before it goes into your futon you later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just use Newtonian physics plus rest
+
+ align:start position:0%
+just use Newtonian physics plus rest
+ 
+
+ align:start position:0%
+just use Newtonian physics plus rest
+plus the a notion of rest energy so it's
+
+ align:start position:0%
+plus the a notion of rest energy so it's
+ 
+
+ align:start position:0%
+plus the a notion of rest energy so it's
+got a mass assuming it's got an energy
+
+ align:start position:0%
+got a mass assuming it's got an energy
+ 
+
+ align:start position:0%
+got a mass assuming it's got an energy
+of M MC squared if you prefer its rest
+
+ align:start position:0%
+of M MC squared if you prefer its rest
+ 
+
+ align:start position:0%
+of M MC squared if you prefer its rest
+energy plus what it acquired after
+
+ align:start position:0%
+energy plus what it acquired after
+ 
+
+ align:start position:0%
+energy plus what it acquired after
+falling pardon me I forgot to give you a
+
+ align:start position:0%
+falling pardon me I forgot to give you a
+ 
+
+ align:start position:0%
+falling pardon me I forgot to give you a
+distance here after following a distance
+
+ align:start position:0%
+distance here after following a distance
+ 
+
+ align:start position:0%
+distance here after following a distance
+H so that means that the photon that I
+
+ align:start position:0%
+H so that means that the photon that I
+ 
+
+ align:start position:0%
+H so that means that the photon that I
+shoot up from this thing so the instant
+
+ align:start position:0%
+shoot up from this thing so the instant
+ 
+
+ align:start position:0%
+shoot up from this thing so the instant
+did I create this photon this thing goes
+
+ align:start position:0%
+did I create this photon this thing goes
+ 
+
+ align:start position:0%
+did I create this photon this thing goes
+out and it's going to have a frequency
+
+ align:start position:0%
+out and it's going to have a frequency
+ 
+
+ align:start position:0%
+out and it's going to have a frequency
+Omega bottom which is simply related to
+
+ align:start position:0%
+Omega bottom which is simply related to
+ 
+
+ align:start position:0%
+Omega bottom which is simply related to
+that energy okay this photon immediately
+
+ align:start position:0%
+that energy okay this photon immediately
+ 
+
+ align:start position:0%
+that energy okay this photon immediately
+shot back up to the top where clever you
+
+ align:start position:0%
+shot back up to the top where clever you
+ 
+
+ align:start position:0%
+shot back up to the top where clever you
+you happen to have in your in your hands
+
+ align:start position:0%
+you happen to have in your in your hands
+ 
+
+ align:start position:0%
+you happen to have in your in your hands
+a rear ocular the rear ocular as a name
+
+ align:start position:0%
+a rear ocular the rear ocular as a name
+ 
+
+ align:start position:0%
+a rear ocular the rear ocular as a name
+obviously implies converse the photon
+
+ align:start position:0%
+obviously implies converse the photon
+ 
+
+ align:start position:0%
+obviously implies converse the photon
+back into a rock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now suppose it does so both the photon
+
+ align:start position:0%
+now suppose it does so both the photon
+ 
+
+ align:start position:0%
+now suppose it does so both the photon
+you later and the Reebok you later it's
+
+ align:start position:0%
+you later and the Reebok you later it's
+ 
+
+ align:start position:0%
+you later and the Reebok you later it's
+fine MIT engineering there are no losses
+
+ align:start position:0%
+fine MIT engineering there are no losses
+ 
+
+ align:start position:0%
+fine MIT engineering there are no losses
+anywhere in this thing so you know
+
+ align:start position:0%
+anywhere in this thing so you know
+ 
+
+ align:start position:0%
+anywhere in this thing so you know
+there's no friction there's no extra
+
+ align:start position:0%
+there's no friction there's no extra
+ 
+
+ align:start position:0%
+there's no friction there's no extra
+heat generated it does it conserving
+
+ align:start position:0%
+heat generated it does it conserving
+ 
+
+ align:start position:0%
+heat generated it does it conserving
+energy a hundred percent what is the
+
+ align:start position:0%
+energy a hundred percent what is the
+ 
+
+ align:start position:0%
+energy a hundred percent what is the
+energy at the top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you might naively say ah you know
+
+ align:start position:0%
+well you might naively say ah you know
+ 
+
+ align:start position:0%
+well you might naively say ah you know
+it's just gonna go up the top it's gonna
+
+ align:start position:0%
+it's just gonna go up the top it's gonna
+ 
+
+ align:start position:0%
+it's just gonna go up the top it's gonna
+have that same energy it might just have
+
+ align:start position:0%
+have that same energy it might just have
+ 
+
+ align:start position:0%
+have that same energy it might just have
+it in the form of a of a photon an Omega
+
+ align:start position:0%
+it in the form of a of a photon an Omega
+ 
+
+ align:start position:0%
+it in the form of a of a photon an Omega
+B there will be some frequency at the
+
+ align:start position:0%
+B there will be some frequency at the
+ 
+
+ align:start position:0%
+B there will be some frequency at the
+top and your initial guess might be it's
+
+ align:start position:0%
+top and your initial guess might be it's
+ 
+
+ align:start position:0%
+top and your initial guess might be it's
+going to be the same as the frequency at
+
+ align:start position:0%
+going to be the same as the frequency at
+ 
+
+ align:start position:0%
+going to be the same as the frequency at
+the bottom but if you do that you're
+
+ align:start position:0%
+the bottom but if you do that you're
+ 
+
+ align:start position:0%
+the bottom but if you do that you're
+gonna suddenly discover that your rock
+
+ align:start position:0%
+gonna suddenly discover that your rock
+ 
+
+ align:start position:0%
+gonna suddenly discover that your rock
+has more energy that started out with
+
+ align:start position:0%
+has more energy that started out with
+ 
+
+ align:start position:0%
+has more energy that started out with
+you can redirect it back down send it
+
+ align:start position:0%
+you can redirect it back down send it
+ 
+
+ align:start position:0%
+you can redirect it back down send it
+back up next thing you know you get
+
+ align:start position:0%
+back up next thing you know you get
+ 
+
+ align:start position:0%
+back up next thing you know you get
+yourself a perpetual motion machine okay
+
+ align:start position:0%
+yourself a perpetual motion machine okay
+ 
+
+ align:start position:0%
+yourself a perpetual motion machine okay
+so all you need to do is get your photon
+
+ align:start position:0%
+so all you need to do is get your photon
+ 
+
+ align:start position:0%
+so all you need to do is get your photon
+there and your rear ocular going you got
+
+ align:start position:0%
+there and your rear ocular going you got
+ 
+
+ align:start position:0%
+there and your rear ocular going you got
+yourself a perpetual motion machine here
+
+ align:start position:0%
+yourself a perpetual motion machine here
+ 
+
+ align:start position:0%
+yourself a perpetual motion machine here
+I'm grant that's probably not the
+
+ align:start position:0%
+I'm grant that's probably not the
+ 
+
+ align:start position:0%
+I'm grant that's probably not the
+weakest part of this argument huh
+
+ align:start position:0%
+weakest part of this argument huh
+ 
+
+ align:start position:0%
+weakest part of this argument huh
+suppose you had this I mean you look at
+
+ align:start position:0%
+suppose you had this I mean you look at
+ 
+
+ align:start position:0%
+suppose you had this I mean you look at
+this if you were if technology allows
+
+ align:start position:0%
+this if you were if technology allows
+ 
+
+ align:start position:0%
+this if you were if technology allows
+you to make these goofy devices you
+
+ align:start position:0%
+you to make these goofy devices you
+ 
+
+ align:start position:0%
+you to make these goofy devices you
+would instantly look at this and say
+
+ align:start position:0%
+would instantly look at this and say
+ 
+
+ align:start position:0%
+would instantly look at this and say
+look if I am NOT to have let's just say
+
+ align:start position:0%
+look if I am NOT to have let's just say
+ 
+
+ align:start position:0%
+look if I am NOT to have let's just say
+I live in a universe where I'm fine with
+
+ align:start position:0%
+I live in a universe where I'm fine with
+ 
+
+ align:start position:0%
+I live in a universe where I'm fine with
+photon you laters I'm finally free Locke
+
+ align:start position:0%
+photon you laters I'm finally free Locke
+ 
+
+ align:start position:0%
+photon you laters I'm finally free Locke
+you laters but dammit energy has to be
+
+ align:start position:0%
+you laters but dammit energy has to be
+ 
+
+ align:start position:0%
+you laters but dammit energy has to be
+conserved I am NOT fine with perpetual
+
+ align:start position:0%
+conserved I am NOT fine with perpetual
+ 
+
+ align:start position:0%
+conserved I am NOT fine with perpetual
+motion machines if that's the case we
+
+ align:start position:0%
+motion machines if that's the case we
+ 
+
+ align:start position:0%
+motion machines if that's the case we
+always fight perpetual motion we must
+
+ align:start position:0%
+always fight perpetual motion we must
+ 
+
+ align:start position:0%
+always fight perpetual motion we must
+have that the energy at the top is equal
+
+ align:start position:0%
+have that the energy at the top is equal
+ 
+
+ align:start position:0%
+have that the energy at the top is equal
+to the energy this guy started with when
+
+ align:start position:0%
+to the energy this guy started with when
+ 
+
+ align:start position:0%
+to the energy this guy started with when
+it sort of gets back into you imagine
+
+ align:start position:0%
+it sort of gets back into you imagine
+ 
+
+ align:start position:0%
+it sort of gets back into you imagine
+that your rear ocular is shaped like a
+
+ align:start position:0%
+that your rear ocular is shaped like a
+ 
+
+ align:start position:0%
+that your rear ocular is shaped like a
+baseball catchers net you know you want
+
+ align:start position:0%
+baseball catchers net you know you want
+ 
+
+ align:start position:0%
+baseball catchers net you know you want
+that thing to just land gently in your
+
+ align:start position:0%
+that thing to just land gently in your
+ 
+
+ align:start position:0%
+that thing to just land gently in your
+met right just be a perfectly gentle
+
+ align:start position:0%
+met right just be a perfectly gentle
+ 
+
+ align:start position:0%
+met right just be a perfectly gentle
+little landing there now when you put
+
+ align:start position:0%
+little landing there now when you put
+ 
+
+ align:start position:0%
+little landing there now when you put
+all this together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going through this taking advantage of
+
+ align:start position:0%
+going through this taking advantage of
+ 
+
+ align:start position:0%
+going through this taking advantage of
+the fact that in you know if you work in
+
+ align:start position:0%
+the fact that in you know if you work in
+ 
+
+ align:start position:0%
+the fact that in you know if you work in
+units where you put your C's back in
+
+ align:start position:0%
+units where you put your C's back in
+ 
+
+ align:start position:0%
+units where you put your C's back in
+there will be a factor of GH over C
+
+ align:start position:0%
+there will be a factor of GH over C
+ 
+
+ align:start position:0%
+there will be a factor of GH over C
+squared appearing in here what you find
+
+ align:start position:0%
+squared appearing in here what you find
+ 
+
+ align:start position:0%
+squared appearing in here what you find
+is that the frequency at the top is less
+
+ align:start position:0%
+is that the frequency at the top is less
+ 
+
+ align:start position:0%
+is that the frequency at the top is less
+than the frequency at the bottom in
+
+ align:start position:0%
+than the frequency at the bottom in
+ 
+
+ align:start position:0%
+than the frequency at the bottom in
+other words the light has gotten a
+
+ align:start position:0%
+other words the light has gotten a
+ 
+
+ align:start position:0%
+other words the light has gotten a
+little bit redder okay now I fully
+
+ align:start position:0%
+little bit redder okay now I fully
+ 
+
+ align:start position:0%
+little bit redder okay now I fully
+confess I did this via the props the
+
+ align:start position:0%
+confess I did this via the props the
+ 
+
+ align:start position:0%
+confess I did this via the props the
+silliest argument possible but I want to
+
+ align:start position:0%
+silliest argument possible but I want to
+ 
+
+ align:start position:0%
+silliest argument possible but I want to
+emphasize that this is one of the most
+
+ align:start position:0%
+emphasize that this is one of the most
+ 
+
+ align:start position:0%
+emphasize that this is one of the most
+precisely verified predictions of
+
+ align:start position:0%
+precisely verified predictions of
+ 
+
+ align:start position:0%
+precisely verified predictions of
+gravity and relativity theory okay this
+
+ align:start position:0%
+gravity and relativity theory okay this
+ 
+
+ align:start position:0%
+gravity and relativity theory okay this
+was first done actually up the street at
+
+ align:start position:0%
+was first done actually up the street at
+ 
+
+ align:start position:0%
+was first done actually up the street at
+Harvard by what's called the pound Rebka
+
+ align:start position:0%
+Harvard by what's called the pound Rebka
+ 
+
+ align:start position:0%
+Harvard by what's called the pound Rebka
+experiment and the basic principles of
+
+ align:start position:0%
+experiment and the basic principles of
+ 
+
+ align:start position:0%
+experiment and the basic principles of
+what is going on this right now you know
+
+ align:start position:0%
+what is going on this right now you know
+ 
+
+ align:start position:0%
+what is going on this right now you know
+I just took this out to make sure my
+
+ align:start position:0%
+I just took this out to make sure my
+ 
+
+ align:start position:0%
+I just took this out to make sure my
+alarm is not about to go off but I want
+
+ align:start position:0%
+alarm is not about to go off but I want
+ 
+
+ align:start position:0%
+alarm is not about to go off but I want
+to emphasize it's actually built into
+
+ align:start position:0%
+to emphasize it's actually built into
+ 
+
+ align:start position:0%
+to emphasize it's actually built into
+the working to the global positioning
+
+ align:start position:0%
+the working to the global positioning
+ 
+
+ align:start position:0%
+the working to the global positioning
+system okay because this fact that light
+
+ align:start position:0%
+system okay because this fact that light
+ 
+
+ align:start position:0%
+system okay because this fact that light
+signals when they travel out of a
+
+ align:start position:0%
+signals when they travel out of a
+ 
+
+ align:start position:0%
+signals when they travel out of a
+gravitational potential they they get
+
+ align:start position:0%
+gravitational potential they they get
+ 
+
+ align:start position:0%
+gravitational potential they they get
+redshift that needs to be taken into
+
+ align:start position:0%
+redshift that needs to be taken into
+ 
+
+ align:start position:0%
+redshift that needs to be taken into
+account in order to do the precise
+
+ align:start position:0%
+account in order to do the precise
+ 
+
+ align:start position:0%
+account in order to do the precise
+metrology the GPS allows now this is
+
+ align:start position:0%
+metrology the GPS allows now this is
+ 
+
+ align:start position:0%
+metrology the GPS allows now this is
+part one okay this idea that light gets
+
+ align:start position:0%
+part one okay this idea that light gets
+ 
+
+ align:start position:0%
+part one okay this idea that light gets
+redder as it climbs out of a
+
+ align:start position:0%
+redder as it climbs out of a
+ 
+
+ align:start position:0%
+redder as it climbs out of a
+gravitational field part two which I
+
+ align:start position:0%
+gravitational field part two which I
+ 
+
+ align:start position:0%
+gravitational field part two which I
+will do on Thursday is to show that if
+
+ align:start position:0%
+will do on Thursday is to show that if
+ 
+
+ align:start position:0%
+will do on Thursday is to show that if
+there is a global inertial frame there
+
+ align:start position:0%
+there is a global inertial frame there
+ 
+
+ align:start position:0%
+there is a global inertial frame there
+is no way for light to get redder as it
+
+ align:start position:0%
+is no way for light to get redder as it
+ 
+
+ align:start position:0%
+is no way for light to get redder as it
+climbs out of a gravitational potential
+
+ align:start position:0%
+climbs out of a gravitational potential
+ 
+
+ align:start position:0%
+climbs out of a gravitational potential
+you cannot have both gravity and a
+
+ align:start position:0%
+you cannot have both gravity and a
+ 
+
+ align:start position:0%
+you cannot have both gravity and a
+global inertial reference frame that's
+
+ align:start position:0%
+global inertial reference frame that's
+ 
+
+ align:start position:0%
+global inertial reference frame that's
+where I will pick it up on Thursday so
+
+ align:start position:0%
+where I will pick it up on Thursday so
+ 
+
+ align:start position:0%
+where I will pick it up on Thursday so
+you will do that and we will then begin
+
+ align:start position:0%
+you will do that and we will then begin
+ 
+
+ align:start position:0%
+you will do that and we will then begin
+talking about how we can try to put the
+
+ align:start position:0%
+talking about how we can try to put the
+ 
+
+ align:start position:0%
+talking about how we can try to put the
+principles of relativity and gravity
+
+ align:start position:0%
+principles of relativity and gravity
+ 
+
+ align:start position:0%
+principles of relativity and gravity
+together and in some sense this is when
+
+ align:start position:0%
+together and in some sense this is when
+ 
+
+ align:start position:0%
+together and in some sense this is when
+our study of general relativity will
+
+ align:start position:0%
+our study of general relativity will
+ 
+
+ align:start position:0%
+our study of general relativity will
+begin in earnest alright so let us stop
+
+ align:start position:0%
+begin in earnest alright so let us stop
+ 
+
+ align:start position:0%
+begin in earnest alright so let us stop
+there
\ No newline at end of file
diff --git a/781P9Ixmi0g.txt b/781P9Ixmi0g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e97fa5c8bd58fe40489771f21668eb6f0a49b3e8
--- /dev/null
+++ b/781P9Ixmi0g.txt
@@ -0,0 +1,186 @@
+Okay, we've figured out a way to design hardware
+to perform a particular computation:
+
+Draw the state transition diagram for an FSM
+that describes the sequence of operations
+
+needed to complete the computation.
+
+Then construct the appropriate datapath, using
+registers to store values and combinational
+
+logic to implement the needed operations.
+
+Finally build an FSM to generate the control
+signals required by the datapath.
+
+Is the datapath plus control logic itself
+an FSM?
+
+Well, it has registers and some combinational
+logic, so, yes, it is an FSM.
+
+Can we draw the truth table?
+
+In theory, yes.
+
+In practice, there are 66 bits of registers
+and hence 66 bits of state, so our truth table
+
+would need 2^66 rows!
+
+Hmm, not very likely that we'd be able to
+draw the truth table!
+
+The difficulty comes from thinking of the
+registers in the datapath as part of the state
+
+of our super-FSM.
+
+That's why we think about the datapath as
+being separate from the control FSM.
+
+So how do we generalize this approach so we
+can use one computer circuit to solve many
+
+different problems.
+
+Well, most problems would probably require
+more storage for operands and results.
+
+And a larger list of allowable operations
+would be handy.
+
+This is actually a bit tricky: what's the
+minimum set of operations we can get away
+
+with?
+
+As we'll see later, surprisingly simple hardware
+is sufficient to perform any realizable computation.
+
+At the other extreme, many complex operations
+(e.g., fast fourier transform) are best implemented
+
+as sequences of simpler operations (e.g.,
+add and multiply) rather than as a single
+
+massive combinational circuit.
+
+These sorts of design tradeoffs are what makes
+computer architecture fun!
+
+We'd then combine our larger storage with
+logic for our chosen set of operations into
+
+a general purpose datapath that could be reused
+to solve many different problems.
+
+Let's see how that would work…
+
+Here's a datapath with 4 data registers to
+hold results.
+
+The ASEL and BSEL multiplexers allow any of
+the data registers to be selected as either
+
+operand for our repertoire of arithmetic and
+boolean operations.
+
+The result is selected by the OPSEL MUX and
+can be written back into any of the data registers
+
+by setting the WEN control signal to 1 and
+using the 2-bit WSEL signal to select which
+
+data register will be loaded at the next rising
+clock edge.
+
+Note that the data registers have a load-enable
+control input.
+
+When this signal is 1, the register will load
+a new value from its D input, otherwise it
+
+ignores the D input and simply reloads its
+previous value.
+
+And, of course, we'll add a control FSM to
+generate the appropriate sequence of control
+
+signals for the datapath.
+
+The Z input from the datapath allows the system
+to perform data-dependent operations, where
+
+the sequence of operations can be influenced
+by the actual values in the data registers.
+
+Here's the state transition diagram for the
+control FSM we'd use if we wanted to use this
+
+datapath to compute factorial assuming the
+initial contents of the data registers are
+
+as shown.
+
+We need a few more states than in our initial
+implementation since this datapath can only
+
+perform one operation at each step.
+
+So we need three steps for each iteration:
+one for the multiply, one for the decrement,
+
+and one for the test to see if we're done.
+
+As seen here, it's often the case that general-purpose
+computer hardware will need more cycles and
+
+perhaps involve more hardware than an optimized
+single-purpose circuit.
+
+You can solve many different problems with
+this system:
+
+exponentiation, division, square root, and
+so on, so long as you don't need more than
+
+four data registers to hold input data, intermediate
+results, or the final answer.
+
+By designing a control FSM, we are in effect
+"programming" our digital system, specifying
+
+the sequence of operations it will perform.
+
+This is exactly how the early digital computers
+worked!
+
+Here's a picture of the ENIAC computer built
+in 1943 at the University of Pennsylvania.
+
+The Wikipedia article on the ENIAC tells us
+that "ENIAC could be programmed to perform
+
+complex sequences of operations, including
+loops, branches, and subroutines.
+
+The task of taking a problem and mapping it
+onto the machine was complex, and usually
+
+took weeks.
+
+After the program was figured out on paper,
+the process of getting the program into ENIAC
+
+by manipulating its switches and cables could
+take days.
+
+This was followed by a period of verification
+and debugging, aided by the ability to execute
+
+the program step by step."
+
+It's clear that we need a less cumbersome
+way to program our computer!
\ No newline at end of file
diff --git a/7Kq8BINVDiw.txt b/7Kq8BINVDiw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ad1f6d6b0d68e1e2830a79d189740becb15d3e6b
--- /dev/null
+++ b/7Kq8BINVDiw.txt
@@ -0,0 +1,379 @@
+align:start position:0%
+ 
+we just arrived this relation here the
+
+ align:start position:0%
+we just arrived this relation here the
+ 
+
+ align:start position:0%
+we just arrived this relation here the
+relation between the differential of the
+
+ align:start position:0%
+relation between the differential of the
+ 
+
+ align:start position:0%
+relation between the differential of the
+speed of the rocket sled and the
+
+ align:start position:0%
+speed of the rocket sled and the
+ 
+
+ align:start position:0%
+speed of the rocket sled and the
+differential of the mass of the rocket
+
+ align:start position:0%
+differential of the mass of the rocket
+ 
+
+ align:start position:0%
+differential of the mass of the rocket
+and we want to ultimately get the speed
+
+ align:start position:0%
+and we want to ultimately get the speed
+ 
+
+ align:start position:0%
+and we want to ultimately get the speed
+of the rocket so we have to do we have
+
+ align:start position:0%
+of the rocket so we have to do we have
+ 
+
+ align:start position:0%
+of the rocket so we have to do we have
+to apply a technique called separation
+
+ align:start position:0%
+to apply a technique called separation
+ 
+
+ align:start position:0%
+to apply a technique called separation
+of variables and then we want to
+
+ align:start position:0%
+of variables and then we want to
+ 
+
+ align:start position:0%
+of variables and then we want to
+integrate what we're going to do is
+
+ align:start position:0%
+integrate what we're going to do is
+ 
+
+ align:start position:0%
+integrate what we're going to do is
+first we're going to divide multiply by
+
+ align:start position:0%
+first we're going to divide multiply by
+ 
+
+ align:start position:0%
+first we're going to divide multiply by
+DT so that falls away and we're left
+
+ align:start position:0%
+DT so that falls away and we're left
+ 
+
+ align:start position:0%
+DT so that falls away and we're left
+with our DVR equals DM are you and we're
+
+ align:start position:0%
+with our DVR equals DM are you and we're
+ 
+
+ align:start position:0%
+with our DVR equals DM are you and we're
+going to shuffle the M on to the other
+
+ align:start position:0%
+going to shuffle the M on to the other
+ 
+
+ align:start position:0%
+going to shuffle the M on to the other
+side and we're left with DVR equals U is
+
+ align:start position:0%
+side and we're left with DVR equals U is
+ 
+
+ align:start position:0%
+side and we're left with DVR equals U is
+a constant so that goes up front and
+
+ align:start position:0%
+a constant so that goes up front and
+ 
+
+ align:start position:0%
+a constant so that goes up front and
+then we have R over m r that's an
+
+ align:start position:0%
+then we have R over m r that's an
+ 
+
+ align:start position:0%
+then we have R over m r that's an
+equation that we can integrate now and
+
+ align:start position:0%
+equation that we can integrate now and
+ 
+
+ align:start position:0%
+equation that we can integrate now and
+we can do that and the tricky bit is
+
+ align:start position:0%
+we can do that and the tricky bit is
+ 
+
+ align:start position:0%
+we can do that and the tricky bit is
+that we need to take care of the
+
+ align:start position:0%
+that we need to take care of the
+ 
+
+ align:start position:0%
+that we need to take care of the
+integration limits here we have V R and
+
+ align:start position:0%
+integration limits here we have V R and
+ 
+
+ align:start position:0%
+integration limits here we have V R and
+actually these now all primes so we have
+
+ align:start position:0%
+actually these now all primes so we have
+ 
+
+ align:start position:0%
+actually these now all primes so we have
+we are going from V naught that is our
+
+ align:start position:0%
+we are going from V naught that is our
+ 
+
+ align:start position:0%
+we are going from V naught that is our
+initial condition here to we r prime of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal V R of T and for the mass we have
+
+ align:start position:0%
+equal V R of T and for the mass we have
+ 
+
+ align:start position:0%
+equal V R of T and for the mass we have
+M R prime equals M not actually not
+
+ align:start position:0%
+M R prime equals M not actually not
+ 
+
+ align:start position:0%
+M R prime equals M not actually not
+quite am NOT it's to M naught because
+
+ align:start position:0%
+quite am NOT it's to M naught because
+ 
+
+ align:start position:0%
+quite am NOT it's to M naught because
+the initial mass of this is the dry mass
+
+ align:start position:0%
+the initial mass of this is the dry mass
+ 
+
+ align:start position:0%
+the initial mass of this is the dry mass
+and the fuel mass so that's two M naught
+
+ align:start position:0%
+and the fuel mass so that's two M naught
+ 
+
+ align:start position:0%
+and the fuel mass so that's two M naught
+so this is near the initial mass and
+
+ align:start position:0%
+so this is near the initial mass and
+ 
+
+ align:start position:0%
+so this is near the initial mass and
+then we go to M R prime equals F of V
+
+ align:start position:0%
+then we go to M R prime equals F of V
+ 
+
+ align:start position:0%
+then we go to M R prime equals F of V
+are alright so let's do that we're going
+
+ align:start position:0%
+are alright so let's do that we're going
+ 
+
+ align:start position:0%
+are alright so let's do that we're going
+to get VR minus
+
+ align:start position:0%
+to get VR minus
+ 
+
+ align:start position:0%
+to get VR minus
+V nought equals u 1 over m integrator
+
+ align:start position:0%
+V nought equals u 1 over m integrator
+ 
+
+ align:start position:0%
+V nought equals u 1 over m integrator
+gives us an LM so Ln and then we can
+
+ align:start position:0%
+gives us an LM so Ln and then we can
+ 
+
+ align:start position:0%
+gives us an LM so Ln and then we can
+immediately do this here over to not and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we ultimately want this so this is
+
+ align:start position:0%
+well we ultimately want this so this is
+ 
+
+ align:start position:0%
+well we ultimately want this so this is
+an V R of T of course and then we get V
+
+ align:start position:0%
+an V R of T of course and then we get V
+ 
+
+ align:start position:0%
+an V R of T of course and then we get V
+naught plus u Ln R over 2 m naught and
+
+ align:start position:0%
+naught plus u Ln R over 2 m naught and
+ 
+
+ align:start position:0%
+naught plus u Ln R over 2 m naught and
+that is our equation so what does this
+
+ align:start position:0%
+that is our equation so what does this
+ 
+
+ align:start position:0%
+that is our equation so what does this
+equation tell us M R the mass of the
+
+ align:start position:0%
+equation tell us M R the mass of the
+ 
+
+ align:start position:0%
+equation tell us M R the mass of the
+rocket is less later on than it was
+
+ align:start position:0%
+rocket is less later on than it was
+ 
+
+ align:start position:0%
+rocket is less later on than it was
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+which means this term here is going to
+
+ align:start position:0%
+which means this term here is going to
+ 
+
+ align:start position:0%
+which means this term here is going to
+be less than zero which means the
+
+ align:start position:0%
+be less than zero which means the
+ 
+
+ align:start position:0%
+be less than zero which means the
+velocity is our initial velocity minus
+
+ align:start position:0%
+velocity is our initial velocity minus
+ 
+
+ align:start position:0%
+velocity is our initial velocity minus
+something which means we have a decrease
+
+ align:start position:0%
+something which means we have a decrease
+ 
+
+ align:start position:0%
+something which means we have a decrease
+in velocity which means my sled will
+
+ align:start position:0%
+in velocity which means my sled will
+ 
+
+ align:start position:0%
+in velocity which means my sled will
+eventually come to a stop
\ No newline at end of file
diff --git a/7OHdAHWhPwQ.txt b/7OHdAHWhPwQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fca424c35ba5a7f9be854b59d3f2c4a17df74359
--- /dev/null
+++ b/7OHdAHWhPwQ.txt
@@ -0,0 +1,17579 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu easy one why should we not
+
+ align:start position:0%
+ocw.mit.edu easy one why should we not
+ 
+
+ align:start position:0%
+ocw.mit.edu easy one why should we not
+use the word Consciousness oh thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you more generally maybe we shouldn't
+
+ align:start position:0%
+you more generally maybe we shouldn't
+ 
+
+ align:start position:0%
+you more generally maybe we shouldn't
+use any word in popular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psychology should we use a word at
+
+ align:start position:0%
+psychology should we use a word at
+ 
+
+ align:start position:0%
+psychology should we use a word at
+all well in mathematics when you
+
+ align:start position:0%
+all well in mathematics when you
+ 
+
+ align:start position:0%
+all well in mathematics when you
+say the associative law people know what
+
+ align:start position:0%
+say the associative law people know what
+ 
+
+ align:start position:0%
+say the associative law people know what
+you mean if they know what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean but uh
+
+ align:start position:0%
+mean but uh
+ 
+
+ align:start position:0%
+mean but uh
+in the emotion machine I argue
+
+ align:start position:0%
+in the emotion machine I argue
+ 
+
+ align:start position:0%
+in the emotion machine I argue
+that to begin with almost every word
+
+ align:start position:0%
+that to begin with almost every word
+ 
+
+ align:start position:0%
+that to begin with almost every word
+except perhaps in mathematics where
+
+ align:start position:0%
+except perhaps in mathematics where
+ 
+
+ align:start position:0%
+except perhaps in mathematics where
+what's the difference between
+
+ align:start position:0%
+what's the difference between
+ 
+
+ align:start position:0%
+what's the difference between
+mathematics and the real world uh in
+
+ align:start position:0%
+mathematics and the real world uh in
+ 
+
+ align:start position:0%
+mathematics and the real world uh in
+mathematics you make the
+
+ align:start position:0%
+mathematics you make the
+ 
+
+ align:start position:0%
+mathematics you make the
+world and uh you define everything in it
+
+ align:start position:0%
+world and uh you define everything in it
+ 
+
+ align:start position:0%
+world and uh you define everything in it
+just about uh so then it's all right to
+
+ align:start position:0%
+just about uh so then it's all right to
+ 
+
+ align:start position:0%
+just about uh so then it's all right to
+make a definition because things aren't
+
+ align:start position:0%
+make a definition because things aren't
+ 
+
+ align:start position:0%
+make a definition because things aren't
+inher
+
+ align:start position:0%
+inher
+ 
+
+ align:start position:0%
+inher
+inherently ambiguous but you can't
+
+ align:start position:0%
+inherently ambiguous but you can't
+ 
+
+ align:start position:0%
+inherently ambiguous but you can't
+Define you can't Define a real
+
+ align:start position:0%
+Define you can't Define a real
+ 
+
+ align:start position:0%
+Define you can't Define a real
+thing uh what's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cat uh you can sort of narrow it down by
+
+ align:start position:0%
+cat uh you can sort of narrow it down by
+ 
+
+ align:start position:0%
+cat uh you can sort of narrow it down by
+saying it's a thing with such and such a
+
+ align:start position:0%
+saying it's a thing with such and such a
+ 
+
+ align:start position:0%
+saying it's a thing with such and such a
+genome but then the next cat doesn't
+
+ align:start position:0%
+genome but then the next cat doesn't
+ 
+
+ align:start position:0%
+genome but then the next cat doesn't
+have exactly that genome and so forth
+
+ align:start position:0%
+have exactly that genome and so forth
+ 
+
+ align:start position:0%
+have exactly that genome and so forth
+and there's a toy cat and a dead cat and
+
+ align:start position:0%
+and there's a toy cat and a dead cat and
+ 
+
+ align:start position:0%
+and there's a toy cat and a dead cat and
+all sorts of exceptions to whatever
+
+ align:start position:0%
+all sorts of exceptions to whatever
+ 
+
+ align:start position:0%
+all sorts of exceptions to whatever
+particular definition definition is a
+
+ align:start position:0%
+particular definition definition is a
+ 
+
+ align:start position:0%
+particular definition definition is a
+bunch of words
+
+ align:start position:0%
+bunch of words
+ 
+
+ align:start position:0%
+bunch of words
+and it more or less vaguely
+
+ align:start position:0%
+and it more or less vaguely
+ 
+
+ align:start position:0%
+and it more or less vaguely
+covers some things and not others
+
+ align:start position:0%
+covers some things and not others
+ 
+
+ align:start position:0%
+covers some things and not others
+and I think I mentioned an example of uh
+
+ align:start position:0%
+and I think I mentioned an example of uh
+ 
+
+ align:start position:0%
+and I think I mentioned an example of uh
+where does the Gulf of Mexico stop and
+
+ align:start position:0%
+where does the Gulf of Mexico stop and
+ 
+
+ align:start position:0%
+where does the Gulf of Mexico stop and
+and the Atlantic Ocean
+
+ align:start position:0%
+and the Atlantic Ocean
+ 
+
+ align:start position:0%
+and the Atlantic Ocean
+begin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and maybe that's something you can
+
+ align:start position:0%
+and maybe that's something you can
+ 
+
+ align:start position:0%
+and maybe that's something you can
+Define because there's no natural
+
+ align:start position:0%
+Define because there's no natural
+ 
+
+ align:start position:0%
+Define because there's no natural
+boundary and so you might say
+
+ align:start position:0%
+boundary and so you might say
+ 
+
+ align:start position:0%
+boundary and so you might say
+uh uh somewhere in the United States
+
+ align:start position:0%
+uh uh somewhere in the United States
+ 
+
+ align:start position:0%
+uh uh somewhere in the United States
+code there's several laws probably not
+
+ align:start position:0%
+code there's several laws probably not
+ 
+
+ align:start position:0%
+code there's several laws probably not
+in fact consistent which Define it and
+
+ align:start position:0%
+in fact consistent which Define it and
+ 
+
+ align:start position:0%
+in fact consistent which Define it and
+uh maybe Cuba has a law which defines
+
+ align:start position:0%
+uh maybe Cuba has a law which defines
+ 
+
+ align:start position:0%
+uh maybe Cuba has a law which defines
+the boundary different and so forth uh
+
+ align:start position:0%
+the boundary different and so forth uh
+ 
+
+ align:start position:0%
+the boundary different and so forth uh
+so I think generally uh Dustin's
+
+ align:start position:0%
+so I think generally uh Dustin's
+ 
+
+ align:start position:0%
+so I think generally uh Dustin's
+question is can
+
+ align:start position:0%
+question is can
+ 
+
+ align:start position:0%
+question is can
+you uh Define anything in Psychology and
+
+ align:start position:0%
+you uh Define anything in Psychology and
+ 
+
+ align:start position:0%
+you uh Define anything in Psychology and
+uh of course the emotion machine is
+
+ align:start position:0%
+uh of course the emotion machine is
+ 
+
+ align:start position:0%
+uh of course the emotion machine is
+complaining that the distinction
+
+ align:start position:0%
+complaining that the distinction
+ 
+
+ align:start position:0%
+complaining that the distinction
+between words like emotions
+
+ align:start position:0%
+between words like emotions
+ 
+
+ align:start position:0%
+between words like emotions
+feelings
+
+ align:start position:0%
+feelings
+ 
+
+ align:start position:0%
+feelings
+thoughts and uh subjective experiences
+
+ align:start position:0%
+thoughts and uh subjective experiences
+ 
+
+ align:start position:0%
+thoughts and uh subjective experiences
+all that sort of thing those
+
+ align:start position:0%
+all that sort of thing those
+ 
+
+ align:start position:0%
+all that sort of thing those
+are sort of old words most of them
+
+ align:start position:0%
+are sort of old words most of them
+ 
+
+ align:start position:0%
+are sort of old words most of them
+surely go back you can find Aristotle
+
+ align:start position:0%
+surely go back you can find Aristotle
+ 
+
+ align:start position:0%
+surely go back you can find Aristotle
+discussing somewhere I suppose the
+
+ align:start position:0%
+discussing somewhere I suppose the
+ 
+
+ align:start position:0%
+discussing somewhere I suppose the
+difference between Sensations and
+
+ align:start position:0%
+difference between Sensations and
+ 
+
+ align:start position:0%
+difference between Sensations and
+feelings
+
+ align:start position:0%
+feelings
+ 
+
+ align:start position:0%
+feelings
+but it seems to me that now that we know
+
+ align:start position:0%
+but it seems to me that now that we know
+ 
+
+ align:start position:0%
+but it seems to me that now that we know
+that the brain has hundreds of
+
+ align:start position:0%
+that the brain has hundreds of
+ 
+
+ align:start position:0%
+that the brain has hundreds of
+different uh areas as they're
+
+ align:start position:0%
+different uh areas as they're
+ 
+
+ align:start position:0%
+different uh areas as they're
+called hundreds of different uh kinds of
+
+ align:start position:0%
+called hundreds of different uh kinds of
+ 
+
+ align:start position:0%
+called hundreds of different uh kinds of
+Machinery linked in various ways that we
+
+ align:start position:0%
+Machinery linked in various ways that we
+ 
+
+ align:start position:0%
+Machinery linked in various ways that we
+don't understand uh it's
+
+ align:start position:0%
+don't understand uh it's
+ 
+
+ align:start position:0%
+don't understand uh it's
+it would be a wonderful coincidence if
+
+ align:start position:0%
+it would be a wonderful coincidence if
+ 
+
+ align:start position:0%
+it would be a wonderful coincidence if
+any of the words of Common Sense
+
+ align:start position:0%
+any of the words of Common Sense
+ 
+
+ align:start position:0%
+any of the words of Common Sense
+Psychology
+
+ align:start position:0%
+Psychology
+ 
+
+ align:start position:0%
+Psychology
+actually uh described anything that's
+
+ align:start position:0%
+actually uh described anything that's
+ 
+
+ align:start position:0%
+actually uh described anything that's
+clearly separate from you know like
+
+ align:start position:0%
+clearly separate from you know like
+ 
+
+ align:start position:0%
+clearly separate from you know like
+rational and emotional that's a typical
+
+ align:start position:0%
+rational and emotional that's a typical
+ 
+
+ align:start position:0%
+rational and emotional that's a typical
+dumbbell distinction that people
+
+ align:start position:0%
+dumbbell distinction that people
+ 
+
+ align:start position:0%
+dumbbell distinction that people
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+and uh I suppose the worst one which is
+
+ align:start position:0%
+and uh I suppose the worst one which is
+ 
+
+ align:start position:0%
+and uh I suppose the worst one which is
+only about 40 or 50 years old is the
+
+ align:start position:0%
+only about 40 or 50 years old is the
+ 
+
+ align:start position:0%
+only about 40 or 50 years old is the
+left Brown left brain versus right brain
+
+ align:start position:0%
+left Brown left brain versus right brain
+ 
+
+ align:start position:0%
+left Brown left brain versus right brain
+distinction which is wonderfully
+
+ align:start position:0%
+distinction which is wonderfully
+ 
+
+ align:start position:0%
+distinction which is wonderfully
+popular uh in the media and in non
+
+ align:start position:0%
+popular uh in the media and in non
+ 
+
+ align:start position:0%
+popular uh in the media and in non
+technical
+
+ align:start position:0%
+technical
+ 
+
+ align:start position:0%
+technical
+discussions but uh Sometimes some we'll
+
+ align:start position:0%
+discussions but uh Sometimes some we'll
+ 
+
+ align:start position:0%
+discussions but uh Sometimes some we'll
+talk about front brain and back brain
+
+ align:start position:0%
+talk about front brain and back brain
+ 
+
+ align:start position:0%
+talk about front brain and back brain
+because the front of the brain or the
+
+ align:start position:0%
+because the front of the brain or the
+ 
+
+ align:start position:0%
+because the front of the brain or the
+middle to to forward part of the brain
+
+ align:start position:0%
+middle to to forward part of the brain
+ 
+
+ align:start position:0%
+middle to to forward part of the brain
+is more involved with motor activities
+
+ align:start position:0%
+is more involved with motor activities
+ 
+
+ align:start position:0%
+is more involved with motor activities
+and the stuff
+
+ align:start position:0%
+and the stuff
+ 
+
+ align:start position:0%
+and the stuff
+in toward the back is more concerned
+
+ align:start position:0%
+in toward the back is more concerned
+ 
+
+ align:start position:0%
+in toward the back is more concerned
+with sensory activities in fact there
+
+ align:start position:0%
+with sensory activities in fact there
+ 
+
+ align:start position:0%
+with sensory activities in fact there
+are two language areas
+
+ align:start position:0%
+are two language areas
+ 
+
+ align:start position:0%
+are two language areas
+and there's a language area for uh
+
+ align:start position:0%
+and there's a language area for uh
+ 
+
+ align:start position:0%
+and there's a language area for uh
+dealing with hearing speech and one
+
+ align:start position:0%
+dealing with hearing speech and one
+ 
+
+ align:start position:0%
+dealing with hearing speech and one
+for which is more involved when you're
+
+ align:start position:0%
+for which is more involved when you're
+ 
+
+ align:start position:0%
+for which is more involved when you're
+actually talking yourself and uh those
+
+ align:start position:0%
+actually talking yourself and uh those
+ 
+
+ align:start position:0%
+actually talking yourself and uh those
+two are about an inch inch apart and
+
+ align:start position:0%
+two are about an inch inch apart and
+ 
+
+ align:start position:0%
+two are about an inch inch apart and
+they do tend to be the front for the
+
+ align:start position:0%
+they do tend to be the front for the
+ 
+
+ align:start position:0%
+they do tend to be the front for the
+motor activity and the back for the
+
+ align:start position:0%
+motor activity and the back for the
+ 
+
+ align:start position:0%
+motor activity and the back for the
+sensory and I think it's that lack
+
+ align:start position:0%
+sensory and I think it's that lack
+ 
+
+ align:start position:0%
+sensory and I think it's that lack
+of uh ways to unpack the suitcases
+
+ align:start position:0%
+of uh ways to unpack the suitcases
+ 
+
+ align:start position:0%
+of uh ways to unpack the suitcases
+overlapping uh collections of functions
+
+ align:start position:0%
+overlapping uh collections of functions
+ 
+
+ align:start position:0%
+overlapping uh collections of functions
+that the everyday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words uh point
+
+ align:start position:0%
+words uh point
+ 
+
+ align:start position:0%
+words uh point
+two uh that has made psychology very
+
+ align:start position:0%
+two uh that has made psychology very
+ 
+
+ align:start position:0%
+two uh that has made psychology very
+difficult and neurology difficult uh
+
+ align:start position:0%
+difficult and neurology difficult uh
+ 
+
+ align:start position:0%
+difficult and neurology difficult uh
+another trouble is that uh whatever the
+
+ align:start position:0%
+another trouble is that uh whatever the
+ 
+
+ align:start position:0%
+another trouble is that uh whatever the
+mind is it's very complicated ated or or
+
+ align:start position:0%
+mind is it's very complicated ated or or
+ 
+
+ align:start position:0%
+mind is it's very complicated ated or or
+rather uh it's a system with all sorts
+
+ align:start position:0%
+rather uh it's a system with all sorts
+ 
+
+ align:start position:0%
+rather uh it's a system with all sorts
+of very complicated
+
+ align:start position:0%
+of very complicated
+ 
+
+ align:start position:0%
+of very complicated
+processes and before
+
+ align:start position:0%
+processes and before
+ 
+
+ align:start position:0%
+processes and before
+1950 there
+
+ align:start position:0%
+1950 there
+ 
+
+ align:start position:0%
+1950 there
+wasn't there weren't any good terms for
+
+ align:start position:0%
+wasn't there weren't any good terms for
+ 
+
+ align:start position:0%
+wasn't there weren't any good terms for
+describing features of complicated
+
+ align:start position:0%
+describing features of complicated
+ 
+
+ align:start position:0%
+describing features of complicated
+processes what
+
+ align:start position:0%
+processes what
+ 
+
+ align:start position:0%
+processes what
+changed uh was that around
+
+ align:start position:0%
+changed uh was that around
+ 
+
+ align:start position:0%
+changed uh was that around
+1950 we were able to make complicated
+
+ align:start position:0%
+1950 we were able to make complicated
+ 
+
+ align:start position:0%
+1950 we were able to make complicated
+processes by programming
+
+ align:start position:0%
+processes by programming
+ 
+
+ align:start position:0%
+processes by programming
+computers and uh within a decade or
+
+ align:start position:0%
+computers and uh within a decade or
+ 
+
+ align:start position:0%
+computers and uh within a decade or
+two uh several hundred new words
+
+ align:start position:0%
+two uh several hundred new words
+ 
+
+ align:start position:0%
+two uh several hundred new words
+appeared and these new words described
+
+ align:start position:0%
+appeared and these new words described
+ 
+
+ align:start position:0%
+appeared and these new words described
+ideas about complicated
+
+ align:start position:0%
+ideas about complicated
+ 
+
+ align:start position:0%
+ideas about complicated
+machines uh most of which had never
+
+ align:start position:0%
+machines uh most of which had never
+ 
+
+ align:start position:0%
+machines uh most of which had never
+occurred to anyone that there could be
+
+ align:start position:0%
+occurred to anyone that there could be
+ 
+
+ align:start position:0%
+occurred to anyone that there could be
+such distinctions so a great distinction
+
+ align:start position:0%
+such distinctions so a great distinction
+ 
+
+ align:start position:0%
+such distinctions so a great distinction
+is the difference
+
+ align:start position:0%
+is the difference
+ 
+
+ align:start position:0%
+is the difference
+between compiler and
+
+ align:start position:0%
+between compiler and
+ 
+
+ align:start position:0%
+between compiler and
+interpreter if you are familiar with the
+
+ align:start position:0%
+interpreter if you are familiar with the
+ 
+
+ align:start position:0%
+interpreter if you are familiar with the
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+lisp uh you know that it's made of these
+
+ align:start position:0%
+lisp uh you know that it's made of these
+ 
+
+ align:start position:0%
+lisp uh you know that it's made of these
+uh descriptions of functions and
+
+ align:start position:0%
+uh descriptions of functions and
+ 
+
+ align:start position:0%
+uh descriptions of functions and
+variables arguments as they're
+
+ align:start position:0%
+variables arguments as they're
+ 
+
+ align:start position:0%
+variables arguments as they're
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+and uh somewhere early in your book
+
+ align:start position:0%
+and uh somewhere early in your book
+ 
+
+ align:start position:0%
+and uh somewhere early in your book
+about lisp there's a one-page program
+
+ align:start position:0%
+about lisp there's a one-page program
+ 
+
+ align:start position:0%
+about lisp there's a one-page program
+called The Interpreter which
+
+ align:start position:0%
+called The Interpreter which
+ 
+
+ align:start position:0%
+called The Interpreter which
+tells what does it do it says how can
+
+ align:start position:0%
+tells what does it do it says how can
+ 
+
+ align:start position:0%
+tells what does it do it says how can
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+uh get a computer to obey the
+
+ align:start position:0%
+uh get a computer to obey the
+ 
+
+ align:start position:0%
+uh get a computer to obey the
+instructions or the procedures described
+
+ align:start position:0%
+instructions or the procedures described
+ 
+
+ align:start position:0%
+instructions or the procedures described
+by the
+
+ align:start position:0%
+by the
+ 
+
+ align:start position:0%
+by the
+programs um I've talked to a lot of
+
+ align:start position:0%
+programs um I've talked to a lot of
+ 
+
+ align:start position:0%
+programs um I've talked to a lot of
+neuroscientists
+
+ align:start position:0%
+neuroscientists
+ 
+
+ align:start position:0%
+neuroscientists
+and um a lot of the younger ones know
+
+ align:start position:0%
+and um a lot of the younger ones know
+ 
+
+ align:start position:0%
+and um a lot of the younger ones know
+about the difference between a compiler
+
+ align:start position:0%
+about the difference between a compiler
+ 
+
+ align:start position:0%
+about the difference between a compiler
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+interpreter uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and I suspect that many higher level
+
+ align:start position:0%
+and and I suspect that many higher level
+ 
+
+ align:start position:0%
+and and I suspect that many higher level
+mental processes involve interpreters
+
+ align:start position:0%
+mental processes involve interpreters
+ 
+
+ align:start position:0%
+mental processes involve interpreters
+that is somewhere you've stored some
+
+ align:start position:0%
+that is somewhere you've stored some
+ 
+
+ align:start position:0%
+that is somewhere you've stored some
+structure that corresponds to a string
+
+ align:start position:0%
+structure that corresponds to a string
+ 
+
+ align:start position:0%
+structure that corresponds to a string
+of symbols or expressions and then
+
+ align:start position:0%
+of symbols or expressions and then
+ 
+
+ align:start position:0%
+of symbols or expressions and then
+there's another process that uh can
+
+ align:start position:0%
+there's another process that uh can
+ 
+
+ align:start position:0%
+there's another process that uh can
+convert that into a sequence of actions
+
+ align:start position:0%
+convert that into a sequence of actions
+ 
+
+ align:start position:0%
+convert that into a sequence of actions
+and what's the difference between an
+
+ align:start position:0%
+and what's the difference between an
+ 
+
+ align:start position:0%
+and what's the difference between an
+expert at something like someone who's
+
+ align:start position:0%
+expert at something like someone who's
+ 
+
+ align:start position:0%
+expert at something like someone who's
+very good at knitting and somebody who's
+
+ align:start position:0%
+very good at knitting and somebody who's
+ 
+
+ align:start position:0%
+very good at knitting and somebody who's
+just been told how to knit or a better
+
+ align:start position:0%
+just been told how to knit or a better
+ 
+
+ align:start position:0%
+just been told how to knit or a better
+example when the first interesting chest
+
+ align:start position:0%
+example when the first interesting chest
+ 
+
+ align:start position:0%
+example when the first interesting chest
+plate change playing program was uh
+
+ align:start position:0%
+plate change playing program was uh
+ 
+
+ align:start position:0%
+plate change playing program was uh
+written by Alan Newell and Herbert
+
+ align:start position:0%
+written by Alan Newell and Herbert
+ 
+
+ align:start position:0%
+written by Alan Newell and Herbert
+Simon
+
+ align:start position:0%
+Simon
+ 
+
+ align:start position:0%
+Simon
+uh it was on a computer that had only
+
+ align:start position:0%
+uh it was on a computer that had only
+ 
+
+ align:start position:0%
+uh it was on a computer that had only
+about a thousand words of memory and so
+
+ align:start position:0%
+about a thousand words of memory and so
+ 
+
+ align:start position:0%
+about a thousand words of memory and so
+there wasn't room for a chessboard so
+
+ align:start position:0%
+there wasn't room for a chessboard so
+ 
+
+ align:start position:0%
+there wasn't room for a chessboard so
+they had a 6x6 chess board I think they
+
+ align:start position:0%
+they had a 6x6 chess board I think they
+ 
+
+ align:start position:0%
+they had a 6x6 chess board I think they
+took out the Bishops or the knights not
+
+ align:start position:0%
+took out the Bishops or the knights not
+ 
+
+ align:start position:0%
+took out the Bishops or the knights not
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+which and
+
+ align:start position:0%
+which and
+ 
+
+ align:start position:0%
+which and
+um then they explained the rules of
+
+ align:start position:0%
+um then they explained the rules of
+ 
+
+ align:start position:0%
+um then they explained the rules of
+Chess to one of the
+
+ align:start position:0%
+Chess to one of the
+ 
+
+ align:start position:0%
+Chess to one of the
+secretaries and uh the program managed
+
+ align:start position:0%
+secretaries and uh the program managed
+ 
+
+ align:start position:0%
+secretaries and uh the program managed
+to beat
+
+ align:start position:0%
+to beat
+ 
+
+ align:start position:0%
+to beat
+her shortly a she had to look at the
+
+ align:start position:0%
+her shortly a she had to look at the
+ 
+
+ align:start position:0%
+her shortly a she had to look at the
+rules every now and then to see what
+
+ align:start position:0%
+rules every now and then to see what
+ 
+
+ align:start position:0%
+rules every now and then to see what
+were the legal moves so she was
+
+ align:start position:0%
+were the legal moves so she was
+ 
+
+ align:start position:0%
+were the legal moves so she was
+interpreting in some sense whereas a if
+
+ align:start position:0%
+interpreting in some sense whereas a if
+ 
+
+ align:start position:0%
+interpreting in some sense whereas a if
+you had some experience with chess and
+
+ align:start position:0%
+you had some experience with chess and
+ 
+
+ align:start position:0%
+you had some experience with chess and
+you look at the
+
+ align:start position:0%
+you look at the
+ 
+
+ align:start position:0%
+you look at the
+night I'm sure you each have a
+
+ align:start position:0%
+night I'm sure you each have a
+ 
+
+ align:start position:0%
+night I'm sure you each have a
+different uh representational experience
+
+ align:start position:0%
+different uh representational experience
+ 
+
+ align:start position:0%
+different uh representational experience
+when I see it the when I see a knight I
+
+ align:start position:0%
+when I see it the when I see a knight I
+ 
+
+ align:start position:0%
+when I see it the when I see a knight I
+see these eight squares light up around
+
+ align:start position:0%
+see these eight squares light up around
+ 
+
+ align:start position:0%
+see these eight squares light up around
+it and so it's in a little circle and
+
+ align:start position:0%
+it and so it's in a little circle and
+ 
+
+ align:start position:0%
+it and so it's in a little circle and
+when I look at a rook it's it's
+
+ align:start position:0%
+when I look at a rook it's it's
+ 
+
+ align:start position:0%
+when I look at a rook it's it's
+a big pair of coordinates and when I
+
+ align:start position:0%
+a big pair of coordinates and when I
+ 
+
+ align:start position:0%
+a big pair of coordinates and when I
+look at a bishop it's these diagonals
+
+ align:start position:0%
+look at a bishop it's these diagonals
+ 
+
+ align:start position:0%
+look at a bishop it's these diagonals
+and that happens without any in some
+
+ align:start position:0%
+and that happens without any in some
+ 
+
+ align:start position:0%
+and that happens without any in some
+sense as you move the bishop around uh
+
+ align:start position:0%
+sense as you move the bishop around uh
+ 
+
+ align:start position:0%
+sense as you move the bishop around uh
+you see these diagonal lines moving how
+
+ align:start position:0%
+you see these diagonal lines moving how
+ 
+
+ align:start position:0%
+you see these diagonal lines moving how
+many of you have images like that uh
+
+ align:start position:0%
+many of you have images like that uh
+ 
+
+ align:start position:0%
+many of you have images like that uh
+well of course the beginner doesn't and
+
+ align:start position:0%
+well of course the beginner doesn't and
+ 
+
+ align:start position:0%
+well of course the beginner doesn't and
+and he or she has to remember these
+
+ align:start position:0%
+and he or she has to remember these
+ 
+
+ align:start position:0%
+and he or she has to remember these
+rules and looking up uh for each move
+
+ align:start position:0%
+rules and looking up uh for each move
+ 
+
+ align:start position:0%
+rules and looking up uh for each move
+or uh each move that she's considering
+
+ align:start position:0%
+or uh each move that she's considering
+ 
+
+ align:start position:0%
+or uh each move that she's considering
+she has to think about that for a while
+
+ align:start position:0%
+she has to think about that for a while
+ 
+
+ align:start position:0%
+she has to think about that for a while
+uh there was a philosopher named Hubert
+
+ align:start position:0%
+uh there was a philosopher named Hubert
+ 
+
+ align:start position:0%
+uh there was a philosopher named Hubert
+dfus around in those days and uh he
+
+ align:start position:0%
+dfus around in those days and uh he
+ 
+
+ align:start position:0%
+dfus around in those days and uh he
+didn't believe a computer could ever
+
+ align:start position:0%
+didn't believe a computer could ever
+ 
+
+ align:start position:0%
+didn't believe a computer could ever
+play chess
+
+ align:start position:0%
+play chess
+ 
+
+ align:start position:0%
+play chess
+well and I have to say that in some
+
+ align:start position:0%
+well and I have to say that in some
+ 
+
+ align:start position:0%
+well and I have to say that in some
+sense no computer ever has played chess
+
+ align:start position:0%
+sense no computer ever has played chess
+ 
+
+ align:start position:0%
+sense no computer ever has played chess
+well uh Because deep blue uh didn't have
+
+ align:start position:0%
+well uh Because deep blue uh didn't have
+ 
+
+ align:start position:0%
+well uh Because deep blue uh didn't have
+any strategic ideas or barely any
+
+ align:start position:0%
+any strategic ideas or barely any
+ 
+
+ align:start position:0%
+any strategic ideas or barely any
+tactical ideas and it was in fact uh
+
+ align:start position:0%
+tactical ideas and it was in fact uh
+ 
+
+ align:start position:0%
+tactical ideas and it was in fact uh
+very little more than a an enormous
+
+ align:start position:0%
+very little more than a an enormous
+ 
+
+ align:start position:0%
+very little more than a an enormous
+super computer that could try billions
+
+ align:start position:0%
+super computer that could try billions
+ 
+
+ align:start position:0%
+super computer that could try billions
+of moves and could look
+
+ align:start position:0%
+of moves and could look
+ 
+
+ align:start position:0%
+of moves and could look
+ahead uh eight or nine moves or whatever
+
+ align:start position:0%
+ahead uh eight or nine moves or whatever
+ 
+
+ align:start position:0%
+ahead uh eight or nine moves or whatever
+it did I don't know and count how many
+
+ align:start position:0%
+it did I don't know and count how many
+ 
+
+ align:start position:0%
+it did I don't know and count how many
+pieces you had left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um or in some way compare two positions
+
+ align:start position:0%
+um or in some way compare two positions
+ 
+
+ align:start position:0%
+um or in some way compare two positions
+the standard way of comparing positions
+
+ align:start position:0%
+the standard way of comparing positions
+ 
+
+ align:start position:0%
+the standard way of comparing positions
+in chess was established back in the
+
+ align:start position:0%
+in chess was established back in the
+ 
+
+ align:start position:0%
+in chess was established back in the
+1950s and
+
+ align:start position:0%
+1950s and
+ 
+
+ align:start position:0%
+1950s and
+uh even in new new ignment program it
+
+ align:start position:0%
+uh even in new new ignment program it
+ 
+
+ align:start position:0%
+uh even in new new ignment program it
+scored the Val it said how good your
+
+ align:start position:0%
+scored the Val it said how good your
+ 
+
+ align:start position:0%
+scored the Val it said how good your
+position was one that that you're
+
+ align:start position:0%
+position was one that that you're
+ 
+
+ align:start position:0%
+position was one that that you're
+considering by considering how far
+
+ align:start position:0%
+considering by considering how far
+ 
+
+ align:start position:0%
+considering by considering how far
+Advanced the pawns were uh how much
+
+ align:start position:0%
+Advanced the pawns were uh how much
+ 
+
+ align:start position:0%
+Advanced the pawns were uh how much
+material you still had do you still have
+
+ align:start position:0%
+material you still had do you still have
+ 
+
+ align:start position:0%
+material you still had do you still have
+both U Bishops or Knights or queen or
+
+ align:start position:0%
+both U Bishops or Knights or queen or
+ 
+
+ align:start position:0%
+both U Bishops or Knights or queen or
+whatever it is
+
+ align:start position:0%
+whatever it is
+ 
+
+ align:start position:0%
+whatever it is
+and uh do you have Center control center
+
+ align:start position:0%
+and uh do you have Center control center
+ 
+
+ align:start position:0%
+and uh do you have Center control center
+control is the four squares in the
+
+ align:start position:0%
+control is the four squares in the
+ 
+
+ align:start position:0%
+control is the four squares in the
+middle of the chessboard and um the
+
+ align:start position:0%
+middle of the chessboard and um the
+ 
+
+ align:start position:0%
+middle of the chessboard and um the
+player who has more pieces that are
+
+ align:start position:0%
+player who has more pieces that are
+ 
+
+ align:start position:0%
+player who has more pieces that are
+potentially attacking those four squares
+
+ align:start position:0%
+potentially attacking those four squares
+ 
+
+ align:start position:0%
+potentially attacking those four squares
+is considered better
+
+ align:start position:0%
+is considered better
+ 
+
+ align:start position:0%
+is considered better
+uh there's one more I think it's
+
+ align:start position:0%
+uh there's one more I think it's
+ 
+
+ align:start position:0%
+uh there's one more I think it's
+uh did I mention the pawn
+
+ align:start position:0%
+uh did I mention the pawn
+ 
+
+ align:start position:0%
+uh did I mention the pawn
+structure if if your pawns are if one
+
+ align:start position:0%
+structure if if your pawns are if one
+ 
+
+ align:start position:0%
+structure if if your pawns are if one
+Pawn is two squares ahead of another uh
+
+ align:start position:0%
+Pawn is two squares ahead of another uh
+ 
+
+ align:start position:0%
+Pawn is two squares ahead of another uh
+then it's very vulnerable but if they're
+
+ align:start position:0%
+then it's very vulnerable but if they're
+ 
+
+ align:start position:0%
+then it's very vulnerable but if they're
+in little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triangles it's
+
+ align:start position:0%
+triangles it's
+ 
+
+ align:start position:0%
+triangles it's
+better and that's all that there were
+
+ align:start position:0%
+better and that's all that there were
+ 
+
+ align:start position:0%
+better and that's all that there were
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+uh the earliest chess programs later
+
+ align:start position:0%
+uh the earliest chess programs later
+ 
+
+ align:start position:0%
+uh the earliest chess programs later
+ones had a few more features for
+
+ align:start position:0%
+ones had a few more features for
+ 
+
+ align:start position:0%
+ones had a few more features for
+evaluating like if you have two Rooks on
+
+ align:start position:0%
+evaluating like if you have two Rooks on
+ 
+
+ align:start position:0%
+evaluating like if you have two Rooks on
+the same row or column that's called a
+
+ align:start position:0%
+the same row or column that's called a
+ 
+
+ align:start position:0%
+the same row or column that's called a
+double rook and that makes a nice strong
+
+ align:start position:0%
+double rook and that makes a nice strong
+ 
+
+ align:start position:0%
+double rook and that makes a nice strong
+position except that Rooks are so
+
+ align:start position:0%
+position except that Rooks are so
+ 
+
+ align:start position:0%
+position except that Rooks are so
+valuable
+
+ align:start position:0%
+valuable
+ 
+
+ align:start position:0%
+valuable
+that a bishop or Pawn can take one even
+
+ align:start position:0%
+that a bishop or Pawn can take one even
+ 
+
+ align:start position:0%
+that a bishop or Pawn can take one even
+if it's covered by another Rook so it's
+
+ align:start position:0%
+if it's covered by another Rook so it's
+ 
+
+ align:start position:0%
+if it's covered by another Rook so it's
+not that good but it does divide the
+
+ align:start position:0%
+not that good but it does divide the
+ 
+
+ align:start position:0%
+not that good but it does divide the
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+into two parts and pieces can't pass
+
+ align:start position:0%
+into two parts and pieces can't pass
+ 
+
+ align:start position:0%
+into two parts and pieces can't pass
+between them without some trouble anyway
+
+ align:start position:0%
+between them without some trouble anyway
+ 
+
+ align:start position:0%
+between them without some trouble anyway
+uh I'm rambling but what happened in in
+
+ align:start position:0%
+uh I'm rambling but what happened in in
+ 
+
+ align:start position:0%
+uh I'm rambling but what happened in in
+the 1950s and 60s is several hundred new
+
+ align:start position:0%
+the 1950s and 60s is several hundred new
+ 
+
+ align:start position:0%
+the 1950s and 60s is several hundred new
+words appeared for ideas
+
+ align:start position:0%
+words appeared for ideas
+ 
+
+ align:start position:0%
+words appeared for ideas
+about not just processes in general but
+
+ align:start position:0%
+about not just processes in general but
+ 
+
+ align:start position:0%
+about not just processes in general but
+the kinds you might expect to find in a
+
+ align:start position:0%
+the kinds you might expect to find in a
+ 
+
+ align:start position:0%
+the kinds you might expect to find in a
+brain and for example in
+
+ align:start position:0%
+brain and for example in
+ 
+
+ align:start position:0%
+brain and for example in
+memory how do you remember
+
+ align:start position:0%
+memory how do you remember
+ 
+
+ align:start position:0%
+memory how do you remember
+something uh you might store it in a
+
+ align:start position:0%
+something uh you might store it in a
+ 
+
+ align:start position:0%
+something uh you might store it in a
+list structure
+
+ align:start position:0%
+list structure
+ 
+
+ align:start position:0%
+list structure
+or uh you and where do you store it you
+
+ align:start position:0%
+or uh you and where do you store it you
+ 
+
+ align:start position:0%
+or uh you and where do you store it you
+might in uh in this kind of machine
+
+ align:start position:0%
+might in uh in this kind of machine
+ 
+
+ align:start position:0%
+might in uh in this kind of machine
+which I presume is a
+
+ align:start position:0%
+which I presume is a
+ 
+
+ align:start position:0%
+which I presume is a
+G4 uh it probably has three or four
+
+ align:start position:0%
+G4 uh it probably has three or four
+ 
+
+ align:start position:0%
+G4 uh it probably has three or four
+levels of cash uh two of which
+
+ align:start position:0%
+levels of cash uh two of which
+ 
+
+ align:start position:0%
+levels of cash uh two of which
+are sort of public and then inside the
+
+ align:start position:0%
+are sort of public and then inside the
+ 
+
+ align:start position:0%
+are sort of public and then inside the
+central processor there are things
+
+ align:start position:0%
+central processor there are things
+ 
+
+ align:start position:0%
+central processor there are things
+called registers which keep how many
+
+ align:start position:0%
+called registers which keep how many
+ 
+
+ align:start position:0%
+called registers which keep how many
+registers is in a PC these days anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know much the ands have something like
+
+ align:start position:0%
+know much the ands have something like
+ 
+
+ align:start position:0%
+know much the ands have something like
+64 128 okay in the early days of
+
+ align:start position:0%
+64 128 okay in the early days of
+ 
+
+ align:start position:0%
+64 128 okay in the early days of
+computers there were two and then there
+
+ align:start position:0%
+computers there were two and then there
+ 
+
+ align:start position:0%
+computers there were two and then there
+were eight and 16 and then after that
+
+ align:start position:0%
+were eight and 16 and then after that
+ 
+
+ align:start position:0%
+were eight and 16 and then after that
+nobody thought about it because they
+
+ align:start position:0%
+nobody thought about it because they
+ 
+
+ align:start position:0%
+nobody thought about it because they
+people stopped learning machine code and
+
+ align:start position:0%
+people stopped learning machine code and
+ 
+
+ align:start position:0%
+people stopped learning machine code and
+only the compiler writers knew what was
+
+ align:start position:0%
+only the compiler writers knew what was
+ 
+
+ align:start position:0%
+only the compiler writers knew what was
+actually going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on here's a question
+
+ align:start position:0%
+on here's a question
+ 
+
+ align:start position:0%
+on here's a question
+that John McCarthy once asked uh
+
+ align:start position:0%
+that John McCarthy once asked uh
+ 
+
+ align:start position:0%
+that John McCarthy once asked uh
+uh you could you can uh there are lots
+
+ align:start position:0%
+uh you could you can uh there are lots
+ 
+
+ align:start position:0%
+uh you could you can uh there are lots
+of theories of how knowledge is
+
+ align:start position:0%
+of theories of how knowledge is
+ 
+
+ align:start position:0%
+of theories of how knowledge is
+represented and how you retrieve it but
+
+ align:start position:0%
+represented and how you retrieve it but
+ 
+
+ align:start position:0%
+represented and how you retrieve it but
+he asked uh uh do you know Bill
+
+ align:start position:0%
+he asked uh uh do you know Bill
+ 
+
+ align:start position:0%
+he asked uh uh do you know Bill
+Clinton's phone
+
+ align:start position:0%
+Clinton's phone
+ 
+
+ align:start position:0%
+Clinton's phone
+number and there you're not ask I'm not
+
+ align:start position:0%
+number and there you're not ask I'm not
+ 
+
+ align:start position:0%
+number and there you're not ask I'm not
+asking you for Bill Clinton's phone
+
+ align:start position:0%
+asking you for Bill Clinton's phone
+ 
+
+ align:start position:0%
+asking you for Bill Clinton's phone
+number I'm asking
+
+ align:start position:0%
+number I'm asking
+ 
+
+ align:start position:0%
+number I'm asking
+you do you know it and presumably you
+
+ align:start position:0%
+you do you know it and presumably you
+ 
+
+ align:start position:0%
+you do you know it and presumably you
+don't and you can say so immediately so
+
+ align:start position:0%
+don't and you can say so immediately so
+ 
+
+ align:start position:0%
+don't and you can say so immediately so
+how do you do that
+
+ align:start position:0%
+how do you do that
+ 
+
+ align:start position:0%
+how do you do that
+and in computer science there is a
+
+ align:start position:0%
+and in computer science there is a
+ 
+
+ align:start position:0%
+and in computer science there is a
+gadget called hash coding who doesn't
+
+ align:start position:0%
+gadget called hash coding who doesn't
+ 
+
+ align:start position:0%
+gadget called hash coding who doesn't
+know about hash
+
+ align:start position:0%
+know about hash
+ 
+
+ align:start position:0%
+know about hash
+coding does it have another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+name or do people call it hash
+
+ align:start position:0%
+name or do people call it hash
+ 
+
+ align:start position:0%
+name or do people call it hash
+coding who has heard of hash
+
+ align:start position:0%
+coding who has heard of hash
+ 
+
+ align:start position:0%
+coding who has heard of hash
+coding okay uh I'm just wondering if
+
+ align:start position:0%
+coding okay uh I'm just wondering if
+ 
+
+ align:start position:0%
+coding okay uh I'm just wondering if
+there's a a more highly cultured name
+
+ align:start position:0%
+there's a a more highly cultured name
+ 
+
+ align:start position:0%
+there's a a more highly cultured name
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+it probably is in some textbook uh with
+
+ align:start position:0%
+it probably is in some textbook uh with
+ 
+
+ align:start position:0%
+it probably is in some textbook uh with
+hash coding what you do is you take uh
+
+ align:start position:0%
+hash coding what you do is you take uh
+ 
+
+ align:start position:0%
+hash coding what you do is you take uh
+some big bunch of
+
+ align:start position:0%
+some big bunch of
+ 
+
+ align:start position:0%
+some big bunch of
+data uh and compress it by a lossy
+
+ align:start position:0%
+data uh and compress it by a lossy
+ 
+
+ align:start position:0%
+data uh and compress it by a lossy
+compression into a small number of Bits
+
+ align:start position:0%
+compression into a small number of Bits
+ 
+
+ align:start position:0%
+compression into a small number of Bits
+And if you do that for every
+
+ align:start position:0%
+And if you do that for every
+ 
+
+ align:start position:0%
+And if you do that for every
+item uh that you put in memory like if
+
+ align:start position:0%
+item uh that you put in memory like if
+ 
+
+ align:start position:0%
+item uh that you put in memory like if
+it's linkoln Gettysburg Address you
+
+ align:start position:0%
+it's linkoln Gettysburg Address you
+ 
+
+ align:start position:0%
+it's linkoln Gettysburg Address you
+could hashcode the whole thing but that
+
+ align:start position:0%
+could hashcode the whole thing but that
+ 
+
+ align:start position:0%
+could hashcode the whole thing but that
+wouldn't be any use but if you took uh
+
+ align:start position:0%
+wouldn't be any use but if you took uh
+ 
+
+ align:start position:0%
+wouldn't be any use but if you took uh
+for scor in seven years ago which is a
+
+ align:start position:0%
+for scor in seven years ago which is a
+ 
+
+ align:start position:0%
+for scor in seven years ago which is a
+couple of hundred
+
+ align:start position:0%
+couple of hundred
+ 
+
+ align:start position:0%
+couple of hundred
+bits uh and compressed that into say a
+
+ align:start position:0%
+bits uh and compressed that into say a
+ 
+
+ align:start position:0%
+bits uh and compressed that into say a
+20 bit word then
+
+ align:start position:0%
+20 bit word then
+ 
+
+ align:start position:0%
+20 bit word then
+uh when I say four scor and seven years
+
+ align:start position:0%
+uh when I say four scor and seven years
+ 
+
+ align:start position:0%
+uh when I say four scor and seven years
+ago uh you could say oh I've heard that
+
+ align:start position:0%
+ago uh you could say oh I've heard that
+ 
+
+ align:start position:0%
+ago uh you could say oh I've heard that
+before because it lit up this 20 bit
+
+ align:start position:0%
+before because it lit up this 20 bit
+ 
+
+ align:start position:0%
+before because it lit up this 20 bit
+hash thing there's a one in a million
+
+ align:start position:0%
+hash thing there's a one in a million
+ 
+
+ align:start position:0%
+hash thing there's a one in a million
+chance when you add a new thing that it
+
+ align:start position:0%
+chance when you add a new thing that it
+ 
+
+ align:start position:0%
+chance when you add a new thing that it
+will get hashed into the same place but
+
+ align:start position:0%
+will get hashed into the same place but
+ 
+
+ align:start position:0%
+will get hashed into the same place but
+uh no human would be disturbed by making
+
+ align:start position:0%
+uh no human would be disturbed by making
+ 
+
+ align:start position:0%
+uh no human would be disturbed by making
+uh mistakes a few times in a million
+
+ align:start position:0%
+uh mistakes a few times in a million
+ 
+
+ align:start position:0%
+uh mistakes a few times in a million
+whereas uh accounting systems would get
+
+ align:start position:0%
+whereas uh accounting systems would get
+ 
+
+ align:start position:0%
+whereas uh accounting systems would get
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+distressed
+
+ align:start position:0%
+distressed
+ 
+
+ align:start position:0%
+distressed
+and in all my talks with neurologists
+
+ align:start position:0%
+and in all my talks with neurologists
+ 
+
+ align:start position:0%
+and in all my talks with neurologists
+neuroscientists I mean that might be an
+
+ align:start position:0%
+neuroscientists I mean that might be an
+ 
+
+ align:start position:0%
+neuroscientists I mean that might be an
+answer to McCarthy's question if you
+
+ align:start position:0%
+answer to McCarthy's question if you
+ 
+
+ align:start position:0%
+answer to McCarthy's question if you
+knew the number you would have hash
+
+ align:start position:0%
+knew the number you would have hash
+ 
+
+ align:start position:0%
+knew the number you would have hash
+coded some phrase like Bill Clinton's
+
+ align:start position:0%
+coded some phrase like Bill Clinton's
+ 
+
+ align:start position:0%
+coded some phrase like Bill Clinton's
+telephone number and uh
+
+ align:start position:0%
+telephone number and uh
+ 
+
+ align:start position:0%
+telephone number and uh
+but I don't think so I think you would
+
+ align:start position:0%
+but I don't think so I think you would
+ 
+
+ align:start position:0%
+but I don't think so I think you would
+say uh that's a heart to get to
+
+ align:start position:0%
+say uh that's a heart to get to
+ 
+
+ align:start position:0%
+say uh that's a heart to get to
+celebrity and uh he must be very busy
+
+ align:start position:0%
+celebrity and uh he must be very busy
+ 
+
+ align:start position:0%
+celebrity and uh he must be very busy
+and he surely doesn't tell anybody his
+
+ align:start position:0%
+and he surely doesn't tell anybody his
+ 
+
+ align:start position:0%
+and he surely doesn't tell anybody his
+phone number except uh his lawyer and a
+
+ align:start position:0%
+phone number except uh his lawyer and a
+ 
+
+ align:start position:0%
+phone number except uh his lawyer and a
+few other people and I've never had any
+
+ align:start position:0%
+few other people and I've never had any
+ 
+
+ align:start position:0%
+few other people and I've never had any
+occasion
+
+ align:start position:0%
+occasion
+ 
+
+ align:start position:0%
+occasion
+to in other words you you might be doing
+
+ align:start position:0%
+to in other words you you might be doing
+ 
+
+ align:start position:0%
+to in other words you you might be doing
+a fairly
+
+ align:start position:0%
+a fairly
+ 
+
+ align:start position:0%
+a fairly
+complicated uh analysis of if I knew
+
+ align:start position:0%
+complicated uh analysis of if I knew
+ 
+
+ align:start position:0%
+complicated uh analysis of if I knew
+that how would I have got it and I can't
+
+ align:start position:0%
+that how would I have got it and I can't
+ 
+
+ align:start position:0%
+that how would I have got it and I can't
+think of any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way it's hard the brain doesn't really
+
+ align:start position:0%
+way it's hard the brain doesn't really
+ 
+
+ align:start position:0%
+way it's hard the brain doesn't really
+have a have a process to enumerate
+
+ align:start position:0%
+have a have a process to enumerate
+ 
+
+ align:start position:0%
+have a have a process to enumerate
+everything I know about Bill Clinton no
+
+ align:start position:0%
+everything I know about Bill Clinton no
+ 
+
+ align:start position:0%
+everything I know about Bill Clinton no
+but it might have a hash Code
+
+ align:start position:0%
+but it might have a hash Code
+ 
+
+ align:start position:0%
+but it might have a hash Code
+system because that's so
+
+ align:start position:0%
+system because that's so
+ 
+
+ align:start position:0%
+system because that's so
+economical I didn't finish my sentence
+
+ align:start position:0%
+economical I didn't finish my sentence
+ 
+
+ align:start position:0%
+economical I didn't finish my sentence
+which is that uh I never met an older
+
+ align:start position:0%
+which is that uh I never met an older
+ 
+
+ align:start position:0%
+which is that uh I never met an older
+neuroscientist who knew that
+
+ align:start position:0%
+neuroscientist who knew that
+ 
+
+ align:start position:0%
+neuroscientist who knew that
+concept whereas uh all
+
+ align:start position:0%
+concept whereas uh all
+ 
+
+ align:start position:0%
+concept whereas uh all
+computer oriented people have known it
+
+ align:start position:0%
+computer oriented people have known it
+ 
+
+ align:start position:0%
+computer oriented people have known it
+for some 40 years so it takes a long
+
+ align:start position:0%
+for some 40 years so it takes a long
+ 
+
+ align:start position:0%
+for some 40 years so it takes a long
+time for a simple idea like that to
+
+ align:start position:0%
+time for a simple idea like that to
+ 
+
+ align:start position:0%
+time for a simple idea like that to
+cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the professional
+
+ align:start position:0%
+the professional
+ 
+
+ align:start position:0%
+the professional
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+and there are hundreds of such words for
+
+ align:start position:0%
+and there are hundreds of such words for
+ 
+
+ align:start position:0%
+and there are hundreds of such words for
+and and of course
+
+ align:start position:0%
+and and of course
+ 
+
+ align:start position:0%
+and and of course
+the uh the distinction
+
+ align:start position:0%
+the uh the distinction
+ 
+
+ align:start position:0%
+the uh the distinction
+between uh
+
+ align:start position:0%
+between uh
+ 
+
+ align:start position:0%
+between uh
+interpreted code and compiled code is
+
+ align:start position:0%
+interpreted code and compiled code is
+ 
+
+ align:start position:0%
+interpreted code and compiled code is
+very important and I was going to say
+
+ align:start position:0%
+very important and I was going to say
+ 
+
+ align:start position:0%
+very important and I was going to say
+that an expert is somebody who has
+
+ align:start position:0%
+that an expert is somebody who has
+ 
+
+ align:start position:0%
+that an expert is somebody who has
+compiled the procedures so
+
+ align:start position:0%
+compiled the procedures so
+ 
+
+ align:start position:0%
+compiled the procedures so
+that he or she or they or it can do it
+
+ align:start position:0%
+that he or she or they or it can do it
+ 
+
+ align:start position:0%
+that he or she or they or it can do it
+without thinking and uh one thing I
+
+ align:start position:0%
+without thinking and uh one thing I
+ 
+
+ align:start position:0%
+without thinking and uh one thing I
+mentioned a couple of times in the
+
+ align:start position:0%
+mentioned a couple of times in the
+ 
+
+ align:start position:0%
+mentioned a couple of times in the
+emotion machine is U there are other
+
+ align:start position:0%
+emotion machine is U there are other
+ 
+
+ align:start position:0%
+emotion machine is U there are other
+processes which psychiatrists probably
+
+ align:start position:0%
+processes which psychiatrists probably
+ 
+
+ align:start position:0%
+processes which psychiatrists probably
+do know about namely sensors and
+
+ align:start position:0%
+do know about namely sensors and
+ 
+
+ align:start position:0%
+do know about namely sensors and
+suppressors in some sense uh it might be
+
+ align:start position:0%
+suppressors in some sense uh it might be
+ 
+
+ align:start position:0%
+suppressors in some sense uh it might be
+that a large part of a of an expert
+
+ align:start position:0%
+that a large part of a of an expert
+ 
+
+ align:start position:0%
+that a large part of a of an expert
+person's knowledge is knowing what not
+
+ align:start position:0%
+person's knowledge is knowing what not
+ 
+
+ align:start position:0%
+person's knowledge is knowing what not
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do and
+
+ align:start position:0%
+do and
+ 
+
+ align:start position:0%
+do and
+uh I really haven't seen any discussion
+
+ align:start position:0%
+uh I really haven't seen any discussion
+ 
+
+ align:start position:0%
+uh I really haven't seen any discussion
+of that in the little cognitive
+
+ align:start position:0%
+of that in the little cognitive
+ 
+
+ align:start position:0%
+of that in the little cognitive
+psychology that I've read but uh an
+
+ align:start position:0%
+psychology that I've read but uh an
+ 
+
+ align:start position:0%
+psychology that I've read but uh an
+expert is someone who gets things done
+
+ align:start position:0%
+expert is someone who gets things done
+ 
+
+ align:start position:0%
+expert is someone who gets things done
+and doesn't make fatal mistakes Stakes
+
+ align:start position:0%
+and doesn't make fatal mistakes Stakes
+ 
+
+ align:start position:0%
+and doesn't make fatal mistakes Stakes
+U how many times have you jammed a
+
+ align:start position:0%
+U how many times have you jammed a
+ 
+
+ align:start position:0%
+U how many times have you jammed a
+screwdriver into your other Palm
+
+ align:start position:0%
+screwdriver into your other Palm
+ 
+
+ align:start position:0%
+screwdriver into your other Palm
+because you did this
+
+ align:start position:0%
+because you did this
+ 
+
+ align:start position:0%
+because you did this
+well every machinist has a few scars but
+
+ align:start position:0%
+well every machinist has a few scars but
+ 
+
+ align:start position:0%
+well every machinist has a few scars but
+not hundreds of them because uh after
+
+ align:start position:0%
+not hundreds of them because uh after
+ 
+
+ align:start position:0%
+not hundreds of them because uh after
+the second such accident you uh you do
+
+ align:start position:0%
+the second such accident you uh you do
+ 
+
+ align:start position:0%
+the second such accident you uh you do
+some mysterious process which uh builds
+
+ align:start position:0%
+some mysterious process which uh builds
+ 
+
+ align:start position:0%
+some mysterious process which uh builds
+a sensor so that you won't even think of
+
+ align:start position:0%
+a sensor so that you won't even think of
+ 
+
+ align:start position:0%
+a sensor so that you won't even think of
+pressing hard on
+
+ align:start position:0%
+pressing hard on
+ 
+
+ align:start position:0%
+pressing hard on
+a device that you're holding in your
+
+ align:start position:0%
+a device that you're holding in your
+ 
+
+ align:start position:0%
+a device that you're holding in your
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hand I don't know if you could read that
+
+ align:start position:0%
+hand I don't know if you could read that
+ 
+
+ align:start position:0%
+hand I don't know if you could read that
+first paragraph which I just found
+
+ align:start position:0%
+first paragraph which I just found
+ 
+
+ align:start position:0%
+first paragraph which I just found
+somewhere uh the prefrontal cortex
+
+ align:start position:0%
+somewhere uh the prefrontal cortex
+ 
+
+ align:start position:0%
+somewhere uh the prefrontal cortex
+or known as the frontal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lobe serves a specific function the
+
+ align:start position:0%
+lobe serves a specific function the
+ 
+
+ align:start position:0%
+lobe serves a specific function the
+active maintenance of patterns of
+
+ align:start position:0%
+active maintenance of patterns of
+ 
+
+ align:start position:0%
+active maintenance of patterns of
+activity that represent goals and the
+
+ align:start position:0%
+activity that represent goals and the
+ 
+
+ align:start position:0%
+activity that represent goals and the
+means of achieve them mean
+
+ align:start position:0%
+means of achieve them mean
+ 
+
+ align:start position:0%
+means of achieve them mean
+what was that
+
+ align:start position:0%
+what was that
+ 
+
+ align:start position:0%
+what was that
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably is it in there or is it in
+
+ align:start position:0%
+probably is it in there or is it in
+ 
+
+ align:start position:0%
+probably is it in there or is it in
+displays that's the wrong place energy
+
+ align:start position:0%
+displays that's the wrong place energy
+ 
+
+ align:start position:0%
+displays that's the wrong place energy
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+saver Microsoft is being socially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conscious
+
+ align:start position:0%
+conscious
+ 
+
+ align:start position:0%
+conscious
+where's the place which says never
+
+ align:start position:0%
+where's the place which says never
+ 
+
+ align:start position:0%
+where's the place which says never
+asleep
+
+ align:start position:0%
+asleep
+ 
+
+ align:start position:0%
+asleep
+here well it's saying never
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+asleep uh click off with the hard dis to
+
+ align:start position:0%
+asleep uh click off with the hard dis to
+ 
+
+ align:start position:0%
+asleep uh click off with the hard dis to
+sleep when possible yep do you think it
+
+ align:start position:0%
+sleep when possible yep do you think it
+ 
+
+ align:start position:0%
+sleep when possible yep do you think it
+did that yeah it didn't go totally well
+
+ align:start position:0%
+did that yeah it didn't go totally well
+ 
+
+ align:start position:0%
+did that yeah it didn't go totally well
+mysterious someday it will know when
+
+ align:start position:0%
+mysterious someday it will know when
+ 
+
+ align:start position:0%
+mysterious someday it will know when
+you it will have listened to the lecture
+
+ align:start position:0%
+you it will have listened to the lecture
+ 
+
+ align:start position:0%
+you it will have listened to the lecture
+and know that you're going to need it
+
+ align:start position:0%
+and know that you're going to need it
+ 
+
+ align:start position:0%
+and know that you're going to need it
+soon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then there's a strange
+
+ align:start position:0%
+but then there's a strange
+ 
+
+ align:start position:0%
+but then there's a strange
+Theory the maintenance of patterns of
+
+ align:start position:0%
+Theory the maintenance of patterns of
+ 
+
+ align:start position:0%
+Theory the maintenance of patterns of
+activity that represent goals and the
+
+ align:start position:0%
+activity that represent goals and the
+ 
+
+ align:start position:0%
+activity that represent goals and the
+means to achieve them them I like that
+
+ align:start position:0%
+means to achieve them them I like that
+ 
+
+ align:start position:0%
+means to achieve them them I like that
+they provide biou bias signals
+
+ align:start position:0%
+they provide biou bias signals
+ 
+
+ align:start position:0%
+they provide biou bias signals
+throughout much of the rest of the brain
+
+ align:start position:0%
+throughout much of the rest of the brain
+ 
+
+ align:start position:0%
+throughout much of the rest of the brain
+affecting not only visual processes but
+
+ align:start position:0%
+affecting not only visual processes but
+ 
+
+ align:start position:0%
+affecting not only visual processes but
+other sensory modalities and systems
+
+ align:start position:0%
+other sensory modalities and systems
+ 
+
+ align:start position:0%
+other sensory modalities and systems
+responsible
+
+ align:start position:0%
+responsible
+ 
+
+ align:start position:0%
+responsible
+for response me mem retrieval emotional
+
+ align:start position:0%
+for response me mem retrieval emotional
+ 
+
+ align:start position:0%
+for response me mem retrieval emotional
+evaluation and then he has
+
+ align:start position:0%
+evaluation and then he has
+ 
+
+ align:start position:0%
+evaluation and then he has
+a I used the word nutty in in some
+
+ align:start position:0%
+a I used the word nutty in in some
+ 
+
+ align:start position:0%
+a I used the word nutty in in some
+article by
+
+ align:start position:0%
+article by
+ 
+
+ align:start position:0%
+article by
+mistake and here's this nutty the
+
+ align:start position:0%
+mistake and here's this nutty the
+ 
+
+ align:start position:0%
+mistake and here's this nutty the
+aggregate effect of these bias signals
+
+ align:start position:0%
+aggregate effect of these bias signals
+ 
+
+ align:start position:0%
+aggregate effect of these bias signals
+is to guide the flow of neural
+
+ align:start position:0%
+is to guide the flow of neural
+ 
+
+ align:start position:0%
+is to guide the flow of neural
+activities along Pathways that establish
+
+ align:start position:0%
+activities along Pathways that establish
+ 
+
+ align:start position:0%
+activities along Pathways that establish
+the proper mappings between inputs
+
+ align:start position:0%
+the proper mappings between inputs
+ 
+
+ align:start position:0%
+the proper mappings between inputs
+internal States and outputs needed to
+
+ align:start position:0%
+internal States and outputs needed to
+ 
+
+ align:start position:0%
+internal States and outputs needed to
+perform a given task did you learn
+
+ align:start position:0%
+perform a given task did you learn
+ 
+
+ align:start position:0%
+perform a given task did you learn
+anything from that sentence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has no procedural Theory except this
+
+ align:start position:0%
+it has no procedural Theory except this
+ 
+
+ align:start position:0%
+it has no procedural Theory except this
+word bias which penetrates this this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paragraph well I just found that a
+
+ align:start position:0%
+paragraph well I just found that a
+ 
+
+ align:start position:0%
+paragraph well I just found that a
+couple of hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ago and I guess what I've been saying is
+
+ align:start position:0%
+ago and I guess what I've been saying is
+ 
+
+ align:start position:0%
+ago and I guess what I've been saying is
+that the words of everyday
+
+ align:start position:0%
+that the words of everyday
+ 
+
+ align:start position:0%
+that the words of everyday
+psychology are
+
+ align:start position:0%
+psychology are
+ 
+
+ align:start position:0%
+psychology are
+pre computer science they're from of
+
+ align:start position:0%
+pre computer science they're from of
+ 
+
+ align:start position:0%
+pre computer science they're from of
+course they're from the past Century but
+
+ align:start position:0%
+course they're from the past Century but
+ 
+
+ align:start position:0%
+course they're from the past Century but
+they're from the first half of the
+
+ align:start position:0%
+they're from the first half of the
+ 
+
+ align:start position:0%
+they're from the first half of the
+1900s and it's taking several
+
+ align:start position:0%
+1900s and it's taking several
+ 
+
+ align:start position:0%
+1900s and it's taking several
+generations for for other words about
+
+ align:start position:0%
+generations for for other words about
+ 
+
+ align:start position:0%
+generations for for other words about
+complicated processes to start uh
+
+ align:start position:0%
+complicated processes to start uh
+ 
+
+ align:start position:0%
+complicated processes to start uh
+getting into other
+
+ align:start position:0%
+getting into other
+ 
+
+ align:start position:0%
+getting into other
+fields computer science isn't about
+
+ align:start position:0%
+fields computer science isn't about
+ 
+
+ align:start position:0%
+fields computer science isn't about
+computers in this sense it's I think
+
+ align:start position:0%
+computers in this sense it's I think
+ 
+
+ align:start position:0%
+computers in this sense it's I think
+it's uh fantastic fantastically
+
+ align:start position:0%
+it's uh fantastic fantastically
+ 
+
+ align:start position:0%
+it's uh fantastic fantastically
+important step in the development of
+
+ align:start position:0%
+important step in the development of
+ 
+
+ align:start position:0%
+important step in the development of
+human knowledge and culture because
+
+ align:start position:0%
+human knowledge and culture because
+ 
+
+ align:start position:0%
+human knowledge and culture because
+there was no way to describe very
+
+ align:start position:0%
+there was no way to describe very
+ 
+
+ align:start position:0%
+there was no way to describe very
+complicated systems before
+
+ align:start position:0%
+complicated systems before
+ 
+
+ align:start position:0%
+complicated systems before
+1950 mathematics was good
+
+ align:start position:0%
+1950 mathematics was good
+ 
+
+ align:start position:0%
+1950 mathematics was good
+for what's mathematics good
+
+ align:start position:0%
+for what's mathematics good
+ 
+
+ align:start position:0%
+for what's mathematics good
+for uh pure mathematics is only good for
+
+ align:start position:0%
+for uh pure mathematics is only good for
+ 
+
+ align:start position:0%
+for uh pure mathematics is only good for
+describing systems that are very simple
+
+ align:start position:0%
+describing systems that are very simple
+ 
+
+ align:start position:0%
+describing systems that are very simple
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+sense I shouldn't say simple that
+
+ align:start position:0%
+sense I shouldn't say simple that
+ 
+
+ align:start position:0%
+sense I shouldn't say simple that
+everything's equally complicated in the
+
+ align:start position:0%
+everything's equally complicated in the
+ 
+
+ align:start position:0%
+everything's equally complicated in the
+end but uh systems that are described by
+
+ align:start position:0%
+end but uh systems that are described by
+ 
+
+ align:start position:0%
+end but uh systems that are described by
+three or four or five axioms so the
+
+ align:start position:0%
+three or four or five axioms so the
+ 
+
+ align:start position:0%
+three or four or five axioms so the
+group theory is this wonderful thing
+
+ align:start position:0%
+group theory is this wonderful thing
+ 
+
+ align:start position:0%
+group theory is this wonderful thing
+described by five aums and you uh these
+
+ align:start position:0%
+described by five aums and you uh these
+ 
+
+ align:start position:0%
+described by five aums and you uh these
+give the properties of a set of elements
+
+ align:start position:0%
+give the properties of a set of elements
+ 
+
+ align:start position:0%
+give the properties of a set of elements
+and an operation that has it inverse and
+
+ align:start position:0%
+and an operation that has it inverse and
+ 
+
+ align:start position:0%
+and an operation that has it inverse and
+is associative and so forth and uh given
+
+ align:start position:0%
+is associative and so forth and uh given
+ 
+
+ align:start position:0%
+is associative and so forth and uh given
+that definition of a group uh then in a
+
+ align:start position:0%
+that definition of a group uh then in a
+ 
+
+ align:start position:0%
+that definition of a group uh then in a
+few steps you can talk talk about uh say
+
+ align:start position:0%
+few steps you can talk talk about uh say
+ 
+
+ align:start position:0%
+few steps you can talk talk about uh say
+a concept that
+
+ align:start position:0%
+a concept that
+ 
+
+ align:start position:0%
+a concept that
+uh one group that a group may have a
+
+ align:start position:0%
+uh one group that a group may have a
+ 
+
+ align:start position:0%
+uh one group that a group may have a
+subgroup where you remove a lot of
+
+ align:start position:0%
+subgroup where you remove a lot of
+ 
+
+ align:start position:0%
+subgroup where you remove a lot of
+elements and you're still left with a
+
+ align:start position:0%
+elements and you're still left with a
+ 
+
+ align:start position:0%
+elements and you're still left with a
+group and uh you could consider that as
+
+ align:start position:0%
+group and uh you could consider that as
+ 
+
+ align:start position:0%
+group and uh you could consider that as
+like a divisor of the group and uh with
+
+ align:start position:0%
+like a divisor of the group and uh with
+ 
+
+ align:start position:0%
+like a divisor of the group and uh with
+a lot of effort you can prove everybody
+
+ align:start position:0%
+a lot of effort you can prove everybody
+ 
+
+ align:start position:0%
+a lot of effort you can prove everybody
+knows that an arithmetic if you have
+
+ align:start position:0%
+knows that an arithmetic if you have
+ 
+
+ align:start position:0%
+knows that an arithmetic if you have
+Prime if you have numbers any integer is
+
+ align:start position:0%
+Prime if you have numbers any integer is
+ 
+
+ align:start position:0%
+Prime if you have numbers any integer is
+unique divisible into primes uh well
+
+ align:start position:0%
+unique divisible into primes uh well
+ 
+
+ align:start position:0%
+unique divisible into primes uh well
+arithmetic is more complicated than
+
+ align:start position:0%
+arithmetic is more complicated than
+ 
+
+ align:start position:0%
+arithmetic is more complicated than
+groups and in some sense uh there's
+
+ align:start position:0%
+groups and in some sense uh there's
+ 
+
+ align:start position:0%
+groups and in some sense uh there's
+something called normal subgroups which
+
+ align:start position:0%
+something called normal subgroups which
+ 
+
+ align:start position:0%
+something called normal subgroups which
+correspond to a little bit to prime
+
+ align:start position:0%
+correspond to a little bit to prime
+ 
+
+ align:start position:0%
+correspond to a little bit to prime
+numbers and there's a beautiful theorem
+
+ align:start position:0%
+numbers and there's a beautiful theorem
+ 
+
+ align:start position:0%
+numbers and there's a beautiful theorem
+that is pretty hard to prove that uh if
+
+ align:start position:0%
+that is pretty hard to prove that uh if
+ 
+
+ align:start position:0%
+that is pretty hard to prove that uh if
+you have a big group it's uniquely
+
+ align:start position:0%
+you have a big group it's uniquely
+ 
+
+ align:start position:0%
+you have a big group it's uniquely
+divisible into these uh subgroups like
+
+ align:start position:0%
+divisible into these uh subgroups like
+ 
+
+ align:start position:0%
+divisible into these uh subgroups like
+primes and
+
+ align:start position:0%
+primes and
+ 
+
+ align:start position:0%
+primes and
+um then things get very hard after that
+
+ align:start position:0%
+um then things get very hard after that
+ 
+
+ align:start position:0%
+um then things get very hard after that
+and some problems about properties of
+
+ align:start position:0%
+and some problems about properties of
+ 
+
+ align:start position:0%
+and some problems about properties of
+groups uh haven't been solved for
+
+ align:start position:0%
+groups uh haven't been solved for
+ 
+
+ align:start position:0%
+groups uh haven't been solved for
+hundreds of years so actually the idea
+
+ align:start position:0%
+hundreds of years so actually the idea
+ 
+
+ align:start position:0%
+hundreds of years so actually the idea
+of an abstract group is just about 200
+
+ align:start position:0%
+of an abstract group is just about 200
+ 
+
+ align:start position:0%
+of an abstract group is just about 200
+years old and uh there's some problems
+
+ align:start position:0%
+years old and uh there's some problems
+ 
+
+ align:start position:0%
+years old and uh there's some problems
+about them that nobody's been able to
+
+ align:start position:0%
+about them that nobody's been able to
+ 
+
+ align:start position:0%
+about them that nobody's been able to
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+yet and
+
+ align:start position:0%
+yet and
+ 
+
+ align:start position:0%
+yet and
+uh so a little piece of mathematics
+
+ align:start position:0%
+uh so a little piece of mathematics
+ 
+
+ align:start position:0%
+uh so a little piece of mathematics
+something described by five axioms uh
+
+ align:start position:0%
+something described by five axioms uh
+ 
+
+ align:start position:0%
+something described by five axioms uh
+can consume lifetimes and is very
+
+ align:start position:0%
+can consume lifetimes and is very
+ 
+
+ align:start position:0%
+can consume lifetimes and is very
+complicated and if you have a 100
+
+ align:start position:0%
+complicated and if you have a 100
+ 
+
+ align:start position:0%
+complicated and if you have a 100
+axioms then it's hopeless you can't
+
+ align:start position:0%
+axioms then it's hopeless you can't
+ 
+
+ align:start position:0%
+axioms then it's hopeless you can't
+prove anything so mathematics in some
+
+ align:start position:0%
+prove anything so mathematics in some
+ 
+
+ align:start position:0%
+prove anything so mathematics in some
+sense is very powerful but what it is is
+
+ align:start position:0%
+sense is very powerful but what it is is
+ 
+
+ align:start position:0%
+sense is very powerful but what it is is
+for finding the complexity in things
+
+ align:start position:0%
+for finding the complexity in things
+ 
+
+ align:start position:0%
+for finding the complexity in things
+that uh that are caused by very simple
+
+ align:start position:0%
+that uh that are caused by very simple
+ 
+
+ align:start position:0%
+that uh that are caused by very simple
+causes and it doesn't get you very far
+
+ align:start position:0%
+causes and it doesn't get you very far
+ 
+
+ align:start position:0%
+causes and it doesn't get you very far
+so uh if the brain is constructed by
+
+ align:start position:0%
+so uh if the brain is constructed by
+ 
+
+ align:start position:0%
+so uh if the brain is constructed by
+20,000 genes or uh pieces of genes and
+
+ align:start position:0%
+20,000 genes or uh pieces of genes and
+ 
+
+ align:start position:0%
+20,000 genes or uh pieces of genes and
+so forth uh how could you ever
+
+ align:start position:0%
+so forth uh how could you ever
+ 
+
+ align:start position:0%
+so forth uh how could you ever
+understand such a thing well one way is
+
+ align:start position:0%
+understand such a thing well one way is
+ 
+
+ align:start position:0%
+understand such a thing well one way is
+you could say may maybe most of them
+
+ align:start position:0%
+you could say may maybe most of them
+ 
+
+ align:start position:0%
+you could say may maybe most of them
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+matter and uh another way
+
+ align:start position:0%
+matter and uh another way
+ 
+
+ align:start position:0%
+matter and uh another way
+is uh can I write a huge computer
+
+ align:start position:0%
+is uh can I write a huge computer
+ 
+
+ align:start position:0%
+is uh can I write a huge computer
+program and see if that program acts
+
+ align:start position:0%
+program and see if that program acts
+ 
+
+ align:start position:0%
+program and see if that program acts
+more or less and that raises lots of
+
+ align:start position:0%
+more or less and that raises lots of
+ 
+
+ align:start position:0%
+more or less and that raises lots of
+other problems uh what computer science
+
+ align:start position:0%
+other problems uh what computer science
+ 
+
+ align:start position:0%
+other problems uh what computer science
+did bring us was the ability to take a a
+
+ align:start position:0%
+did bring us was the ability to take a a
+ 
+
+ align:start position:0%
+did bring us was the ability to take a a
+fairly complicated system and simulate
+
+ align:start position:0%
+fairly complicated system and simulate
+ 
+
+ align:start position:0%
+fairly complicated system and simulate
+it and see what it did so that was
+
+ align:start position:0%
+it and see what it did so that was
+ 
+
+ align:start position:0%
+it and see what it did so that was
+wonderful but it but uh it also gave us
+
+ align:start position:0%
+wonderful but it but uh it also gave us
+ 
+
+ align:start position:0%
+wonderful but it but uh it also gave us
+these words and the dictionary of
+
+ align:start position:0%
+these words and the dictionary of
+ 
+
+ align:start position:0%
+these words and the dictionary of
+computer science words think probably
+
+ align:start position:0%
+computer science words think probably
+ 
+
+ align:start position:0%
+computer science words think probably
+has a couple of thousand Expressions
+
+ align:start position:0%
+has a couple of thousand Expressions
+ 
+
+ align:start position:0%
+has a couple of thousand Expressions
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh most of you know many of and each of
+
+ align:start position:0%
+uh most of you know many of and each of
+ 
+
+ align:start position:0%
+uh most of you know many of and each of
+these represents a an idea about the
+
+ align:start position:0%
+these represents a an idea about the
+ 
+
+ align:start position:0%
+these represents a an idea about the
+nature of some procedure or uh
+
+ align:start position:0%
+nature of some procedure or uh
+ 
+
+ align:start position:0%
+nature of some procedure or uh
+interaction or something like that
+
+ align:start position:0%
+interaction or something like that
+ 
+
+ align:start position:0%
+interaction or something like that
+between descriptions and the things they
+
+ align:start position:0%
+between descriptions and the things they
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+
+ align:start position:0%
+between descriptions and the things they
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+
+ align:start position:0%
+describ that that no one ever had a
+ 
+
+ align:start position:0%
+describ that that no one ever had a
+clear idea of in before the middle of
+
+ align:start position:0%
+clear idea of in before the middle of
+ 
+
+ align:start position:0%
+clear idea of in before the middle of
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+century um anyway
+
+ align:start position:0%
+century um anyway
+ 
+
+ align:start position:0%
+century um anyway
+uh nevertheless we have hundreds or
+
+ align:start position:0%
+uh nevertheless we have hundreds or
+ 
+
+ align:start position:0%
+uh nevertheless we have hundreds or
+thousands of words about the mind in
+
+ align:start position:0%
+thousands of words about the mind in
+ 
+
+ align:start position:0%
+thousands of words about the mind in
+popular psychology and uh one of those
+
+ align:start position:0%
+popular psychology and uh one of those
+ 
+
+ align:start position:0%
+popular psychology and uh one of those
+words is consciousness and uh here's a
+
+ align:start position:0%
+words is consciousness and uh here's a
+ 
+
+ align:start position:0%
+words is consciousness and uh here's a
+pretty nice paragraph
+
+ align:start position:0%
+pretty nice paragraph
+ 
+
+ align:start position:0%
+pretty nice paragraph
+about no no philosopher and hardly any
+
+ align:start position:0%
+about no no philosopher and hardly any
+ 
+
+ align:start position:0%
+about no no philosopher and hardly any
+novelist has ever managed to explain
+
+ align:start position:0%
+novelist has ever managed to explain
+ 
+
+ align:start position:0%
+novelist has ever managed to explain
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+consciousness
+
+ align:start position:0%
+consciousness
+ 
+
+ align:start position:0%
+consciousness
+uh that's pretty good she's putting the
+
+ align:start position:0%
+uh that's pretty good she's putting the
+ 
+
+ align:start position:0%
+uh that's pretty good she's putting the
+novelists just a little bit above the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+philosophers uh then here's a
+
+ align:start position:0%
+philosophers uh then here's a
+ 
+
+ align:start position:0%
+philosophers uh then here's a
+Mystic am I on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page anyone know S
+
+ align:start position:0%
+page anyone know S
+ 
+
+ align:start position:0%
+page anyone know S
+chinmoy I don't know much about him
+
+ align:start position:0%
+chinmoy I don't know much about him
+ 
+
+ align:start position:0%
+chinmoy I don't know much about him
+except that he has a bunch of books and
+
+ align:start position:0%
+except that he has a bunch of books and
+ 
+
+ align:start position:0%
+except that he has a bunch of books and
+and a sort
+
+ align:start position:0%
+and a sort
+ 
+
+ align:start position:0%
+and a sort
+of Fairly harmless looking
+
+ align:start position:0%
+of Fairly harmless looking
+ 
+
+ align:start position:0%
+of Fairly harmless looking
+cult Consciousness is the golden link
+
+ align:start position:0%
+cult Consciousness is the golden link
+ 
+
+ align:start position:0%
+cult Consciousness is the golden link
+within us that connects our highest and
+
+ align:start position:0%
+within us that connects our highest and
+ 
+
+ align:start position:0%
+within us that connects our highest and
+most illumined part with our lowest and
+
+ align:start position:0%
+most illumined part with our lowest and
+ 
+
+ align:start position:0%
+most illumined part with our lowest and
+most unilluminated
+
+ align:start position:0%
+most unilluminated
+ 
+
+ align:start position:0%
+most unilluminated
+part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foder foder is brilliant and almost
+
+ align:start position:0%
+foder foder is brilliant and almost
+ 
+
+ align:start position:0%
+foder foder is brilliant and almost
+always wrong as far as I can tell uh
+
+ align:start position:0%
+always wrong as far as I can tell uh
+ 
+
+ align:start position:0%
+always wrong as far as I can tell uh
+it's almost worth reading his papers
+
+ align:start position:0%
+it's almost worth reading his papers
+ 
+
+ align:start position:0%
+it's almost worth reading his papers
+to so that you can learn to avoid the
+
+ align:start position:0%
+to so that you can learn to avoid the
+ 
+
+ align:start position:0%
+to so that you can learn to avoid the
+most common
+
+ align:start position:0%
+most common
+ 
+
+ align:start position:0%
+most common
+mistakes no one has the slightest idea
+
+ align:start position:0%
+mistakes no one has the slightest idea
+ 
+
+ align:start position:0%
+mistakes no one has the slightest idea
+how anything material could be conscious
+
+ align:start position:0%
+how anything material could be conscious
+ 
+
+ align:start position:0%
+how anything material could be conscious
+nobody even know it would what it would
+
+ align:start position:0%
+nobody even know it would what it would
+ 
+
+ align:start position:0%
+nobody even know it would what it would
+be like to have the slightest idea about
+
+ align:start position:0%
+be like to have the slightest idea about
+ 
+
+ align:start position:0%
+be like to have the slightest idea about
+that what could that
+
+ align:start position:0%
+that what could that
+ 
+
+ align:start position:0%
+that what could that
+mean so much for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that some people think Consciousness is
+
+ align:start position:0%
+that some people think Consciousness is
+ 
+
+ align:start position:0%
+that some people think Consciousness is
+just in the nature of things and every
+
+ align:start position:0%
+just in the nature of things and every
+ 
+
+ align:start position:0%
+just in the nature of things and every
+object must be Consciousness or
+
+ align:start position:0%
+object must be Consciousness or
+ 
+
+ align:start position:0%
+object must be Consciousness or
+not I misspoke there we don't know where
+
+ align:start position:0%
+not I misspoke there we don't know where
+ 
+
+ align:start position:0%
+not I misspoke there we don't know where
+it starts in stops but clearly people
+
+ align:start position:0%
+it starts in stops but clearly people
+ 
+
+ align:start position:0%
+it starts in stops but clearly people
+are conscious and rocks are not and
+
+ align:start position:0%
+are conscious and rocks are not and
+ 
+
+ align:start position:0%
+are conscious and rocks are not and
+that's like the Gulf of Mexico problem
+
+ align:start position:0%
+that's like the Gulf of Mexico problem
+ 
+
+ align:start position:0%
+that's like the Gulf of Mexico problem
+uh at what magical point do creatures
+
+ align:start position:0%
+uh at what magical point do creatures
+ 
+
+ align:start position:0%
+uh at what magical point do creatures
+suddenly become conscious and there was
+
+ align:start position:0%
+suddenly become conscious and there was
+ 
+
+ align:start position:0%
+suddenly become conscious and there was
+a nice discussion
+
+ align:start position:0%
+a nice discussion
+ 
+
+ align:start position:0%
+a nice discussion
+on current discussion on a news group
+
+ align:start position:0%
+on current discussion on a news group
+ 
+
+ align:start position:0%
+on current discussion on a news group
+called comp AI
+
+ align:start position:0%
+called comp AI
+ 
+
+ align:start position:0%
+called comp AI
+philosophy uh where a graduate student
+
+ align:start position:0%
+philosophy uh where a graduate student
+ 
+
+ align:start position:0%
+philosophy uh where a graduate student
+named iray urel who's in Turkey uh is
+
+ align:start position:0%
+named iray urel who's in Turkey uh is
+ 
+
+ align:start position:0%
+named iray urel who's in Turkey uh is
+arguing with other people
+
+ align:start position:0%
+arguing with other people
+ 
+
+ align:start position:0%
+arguing with other people
+and I think that recently he said well
+
+ align:start position:0%
+and I think that recently he said well
+ 
+
+ align:start position:0%
+and I think that recently he said well
+if you had four simple neurons
+
+ align:start position:0%
+if you had four simple neurons
+ 
+
+ align:start position:0%
+if you had four simple neurons
+interacting with with each other would
+
+ align:start position:0%
+interacting with with each other would
+ 
+
+ align:start position:0%
+interacting with with each other would
+you say that that has a little bit of
+
+ align:start position:0%
+you say that that has a little bit of
+ 
+
+ align:start position:0%
+you say that that has a little bit of
+Consciousness and uh I don't think um
+
+ align:start position:0%
+Consciousness and uh I don't think um
+ 
+
+ align:start position:0%
+Consciousness and uh I don't think um
+he's sort of the moderator of the group
+
+ align:start position:0%
+he's sort of the moderator of the group
+ 
+
+ align:start position:0%
+he's sort of the moderator of the group
+and is trying to get them to take such
+
+ align:start position:0%
+and is trying to get them to take such
+ 
+
+ align:start position:0%
+and is trying to get them to take such
+questions not to take such questions
+
+ align:start position:0%
+questions not to take such questions
+ 
+
+ align:start position:0%
+questions not to take such questions
+seriously but to realize that if you
+
+ align:start position:0%
+seriously but to realize that if you
+ 
+
+ align:start position:0%
+seriously but to realize that if you
+assume that Consciousness is a matter of
+
+ align:start position:0%
+assume that Consciousness is a matter of
+ 
+
+ align:start position:0%
+assume that Consciousness is a matter of
+degree uh then
+
+ align:start position:0%
+degree uh then
+ 
+
+ align:start position:0%
+degree uh then
+uh then it might be not a valuable
+
+ align:start position:0%
+uh then it might be not a valuable
+ 
+
+ align:start position:0%
+uh then it might be not a valuable
+concept because if you can't tell when
+
+ align:start position:0%
+concept because if you can't tell when
+ 
+
+ align:start position:0%
+concept because if you can't tell when
+it starts or stops there's very little
+
+ align:start position:0%
+it starts or stops there's very little
+ 
+
+ align:start position:0%
+it starts or stops there's very little
+you can say about it everything has some
+
+ align:start position:0%
+you can say about it everything has some
+ 
+
+ align:start position:0%
+you can say about it everything has some
+Consciousness an atom has only a little
+
+ align:start position:0%
+Consciousness an atom has only a little
+ 
+
+ align:start position:0%
+Consciousness an atom has only a little
+bit while brains have
+
+ align:start position:0%
+bit while brains have
+ 
+
+ align:start position:0%
+bit while brains have
+more and then my favorite one
+
+ align:start position:0%
+more and then my favorite one
+ 
+
+ align:start position:0%
+more and then my favorite one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this criticism that's very popular
+
+ align:start position:0%
+this criticism that's very popular
+ 
+
+ align:start position:0%
+this criticism that's very popular
+that's what I sort of started the
+
+ align:start position:0%
+that's what I sort of started the
+ 
+
+ align:start position:0%
+that's what I sort of started the
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+about uh before you talk about
+
+ align:start position:0%
+about uh before you talk about
+ 
+
+ align:start position:0%
+about uh before you talk about
+Consciousness you really ought to Define
+
+ align:start position:0%
+Consciousness you really ought to Define
+ 
+
+ align:start position:0%
+Consciousness you really ought to Define
+it and
+
+ align:start position:0%
+it and
+ 
+
+ align:start position:0%
+it and
+uh people are always claiming to me if
+
+ align:start position:0%
+uh people are always claiming to me if
+ 
+
+ align:start position:0%
+uh people are always claiming to me if
+you're talking about artificial
+
+ align:start position:0%
+you're talking about artificial
+ 
+
+ align:start position:0%
+you're talking about artificial
+intelligence don't you need to Define
+
+ align:start position:0%
+intelligence don't you need to Define
+ 
+
+ align:start position:0%
+intelligence don't you need to Define
+intelligence
+
+ align:start position:0%
+intelligence
+ 
+
+ align:start position:0%
+intelligence
+and my answer is uh if you had such a
+
+ align:start position:0%
+and my answer is uh if you had such a
+ 
+
+ align:start position:0%
+and my answer is uh if you had such a
+definition what what would you do with
+
+ align:start position:0%
+definition what what would you do with
+ 
+
+ align:start position:0%
+definition what what would you do with
+it um so my definition
+
+ align:start position:0%
+it um so my definition
+ 
+
+ align:start position:0%
+it um so my definition
+is intelligence is not a word for a
+
+ align:start position:0%
+is intelligence is not a word for a
+ 
+
+ align:start position:0%
+is intelligence is not a word for a
+phenomenon it's a word for a social
+
+ align:start position:0%
+phenomenon it's a word for a social
+ 
+
+ align:start position:0%
+phenomenon it's a word for a social
+relationship uh if Jack's teacher says
+
+ align:start position:0%
+relationship uh if Jack's teacher says
+ 
+
+ align:start position:0%
+relationship uh if Jack's teacher says
+uh Shirley is very good at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+math that's a sort
+
+ align:start position:0%
+math that's a sort
+ 
+
+ align:start position:0%
+math that's a sort
+of what is that uh that
+
+ align:start position:0%
+of what is that uh that
+ 
+
+ align:start position:0%
+of what is that uh that
+saying uh being good at math is a skill
+
+ align:start position:0%
+saying uh being good at math is a skill
+ 
+
+ align:start position:0%
+saying uh being good at math is a skill
+that I wish I had a lot of uh like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh some mathematician you
+
+ align:start position:0%
+uh some mathematician you
+ 
+
+ align:start position:0%
+uh some mathematician you
+admire but to say someone is intelligent
+
+ align:start position:0%
+admire but to say someone is intelligent
+ 
+
+ align:start position:0%
+admire but to say someone is intelligent
+I think doesn't say anything very it's
+
+ align:start position:0%
+I think doesn't say anything very it's
+ 
+
+ align:start position:0%
+I think doesn't say anything very it's
+not a thing you can Define
+
+ align:start position:0%
+not a thing you can Define
+ 
+
+ align:start position:0%
+not a thing you can Define
+because uh it's a
+
+ align:start position:0%
+because uh it's a
+ 
+
+ align:start position:0%
+because uh it's a
+uh it's not a property it's a
+
+ align:start position:0%
+uh it's not a property it's a
+ 
+
+ align:start position:0%
+uh it's not a property it's a
+relationship this person is better at
+
+ align:start position:0%
+relationship this person is better at
+ 
+
+ align:start position:0%
+relationship this person is better at
+something than that person
+
+ align:start position:0%
+something than that person
+ 
+
+ align:start position:0%
+something than that person
+this person is generally better at
+
+ align:start position:0%
+this person is generally better at
+ 
+
+ align:start position:0%
+this person is generally better at
+everything than that person but uh what
+
+ align:start position:0%
+everything than that person but uh what
+ 
+
+ align:start position:0%
+everything than that person but uh what
+would you gain if you could say what
+
+ align:start position:0%
+would you gain if you could say what
+ 
+
+ align:start position:0%
+would you gain if you could say what
+what it was well you could say he is
+
+ align:start position:0%
+what it was well you could say he is
+ 
+
+ align:start position:0%
+what it was well you could say he is
+more resourceful at solving problems and
+
+ align:start position:0%
+more resourceful at solving problems and
+ 
+
+ align:start position:0%
+more resourceful at solving problems and
+if you went in that direction eventually
+
+ align:start position:0%
+if you went in that direction eventually
+ 
+
+ align:start position:0%
+if you went in that direction eventually
+somebody would say well
+
+ align:start position:0%
+somebody would say well
+ 
+
+ align:start position:0%
+somebody would say well
+uh what are the tricks can you tell me
+
+ align:start position:0%
+uh what are the tricks can you tell me
+ 
+
+ align:start position:0%
+uh what are the tricks can you tell me
+the tricks that this person uses to be
+
+ align:start position:0%
+the tricks that this person uses to be
+ 
+
+ align:start position:0%
+the tricks that this person uses to be
+better at something than someone else
+
+ align:start position:0%
+better at something than someone else
+ 
+
+ align:start position:0%
+better at something than someone else
+and then you'd start getting into
+
+ align:start position:0%
+and then you'd start getting into
+ 
+
+ align:start position:0%
+and then you'd start getting into
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this this is from chapter 4 and what
+
+ align:start position:0%
+so this this is from chapter 4 and what
+ 
+
+ align:start position:0%
+so this this is from chapter 4 and what
+I'm complaining is that you should be
+
+ align:start position:0%
+I'm complaining is that you should be
+ 
+
+ align:start position:0%
+I'm complaining is that you should be
+very careful not to Define your terms if
+
+ align:start position:0%
+very careful not to Define your terms if
+ 
+
+ align:start position:0%
+very careful not to Define your terms if
+you don't understand if you don't have a
+
+ align:start position:0%
+you don't understand if you don't have a
+ 
+
+ align:start position:0%
+you don't understand if you don't have a
+complete theory of what you're talking
+
+ align:start position:0%
+complete theory of what you're talking
+ 
+
+ align:start position:0%
+complete theory of what you're talking
+about because you're likely to make
+
+ align:start position:0%
+about because you're likely to make
+ 
+
+ align:start position:0%
+about because you're likely to make
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+worse uh a particular definition of
+
+ align:start position:0%
+worse uh a particular definition of
+ 
+
+ align:start position:0%
+worse uh a particular definition of
+intelligence
+
+ align:start position:0%
+intelligence
+ 
+
+ align:start position:0%
+intelligence
+if it gives some
+
+ align:start position:0%
+if it gives some
+ 
+
+ align:start position:0%
+if it gives some
+details is likely to trap you into doing
+
+ align:start position:0%
+details is likely to trap you into doing
+ 
+
+ align:start position:0%
+details is likely to trap you into doing
+some particular set of experiments and
+
+ align:start position:0%
+some particular set of experiments and
+ 
+
+ align:start position:0%
+some particular set of experiments and
+missing the abilities that someone else
+
+ align:start position:0%
+missing the abilities that someone else
+ 
+
+ align:start position:0%
+missing the abilities that someone else
+has who might be uh good at other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things so uh William Cal I don't know
+
+ align:start position:0%
+things so uh William Cal I don't know
+ 
+
+ align:start position:0%
+things so uh William Cal I don't know
+George ojan but Calvin is a neurologist
+
+ align:start position:0%
+George ojan but Calvin is a neurologist
+ 
+
+ align:start position:0%
+George ojan but Calvin is a neurologist
+who's uh does a lot of highlevel
+
+ align:start position:0%
+who's uh does a lot of highlevel
+ 
+
+ align:start position:0%
+who's uh does a lot of highlevel
+thinking and theories of how the brain
+
+ align:start position:0%
+thinking and theories of how the brain
+ 
+
+ align:start position:0%
+thinking and theories of how the brain
+evolved and some about how it
+
+ align:start position:0%
+evolved and some about how it
+ 
+
+ align:start position:0%
+evolved and some about how it
+works and he points out that you use the
+
+ align:start position:0%
+works and he points out that you use the
+ 
+
+ align:start position:0%
+works and he points out that you use the
+word for many different things like
+
+ align:start position:0%
+word for many different things like
+ 
+
+ align:start position:0%
+word for many different things like
+mental
+
+ align:start position:0%
+mental
+ 
+
+ align:start position:0%
+mental
+rehearsal focusing attention imagery
+
+ align:start position:0%
+rehearsal focusing attention imagery
+ 
+
+ align:start position:0%
+rehearsal focusing attention imagery
+decision
+
+ align:start position:0%
+decision
+ 
+
+ align:start position:0%
+decision
+making voluntary
+
+ align:start position:0%
+making voluntary
+ 
+
+ align:start position:0%
+making voluntary
+actions it goes on and uh that's a long
+
+ align:start position:0%
+actions it goes on and uh that's a long
+ 
+
+ align:start position:0%
+actions it goes on and uh that's a long
+list and the philosopher if that's a
+
+ align:start position:0%
+list and the philosopher if that's a
+ 
+
+ align:start position:0%
+list and the philosopher if that's a
+good word to use
+
+ align:start position:0%
+good word to use
+ 
+
+ align:start position:0%
+good word to use
+who I like to me there are two very good
+
+ align:start position:0%
+who I like to me there are two very good
+ 
+
+ align:start position:0%
+who I like to me there are two very good
+philosophers I don't know uh all the
+
+ align:start position:0%
+philosophers I don't know uh all the
+ 
+
+ align:start position:0%
+philosophers I don't know uh all the
+other ones and there probably some other
+
+ align:start position:0%
+other ones and there probably some other
+ 
+
+ align:start position:0%
+other ones and there probably some other
+good ones Aaron slowman at the
+
+ align:start position:0%
+good ones Aaron slowman at the
+ 
+
+ align:start position:0%
+good ones Aaron slowman at the
+University of Birmingham is full of
+
+ align:start position:0%
+University of Birmingham is full of
+ 
+
+ align:start position:0%
+University of Birmingham is full of
+ideas about such things and if you
+
+ align:start position:0%
+ideas about such things and if you
+ 
+
+ align:start position:0%
+ideas about such things and if you
+really get interested in this subject of
+
+ align:start position:0%
+really get interested in this subject of
+ 
+
+ align:start position:0%
+really get interested in this subject of
+making theories of
+
+ align:start position:0%
+making theories of
+ 
+
+ align:start position:0%
+making theories of
+mind then what should you do it's no use
+
+ align:start position:0%
+mind then what should you do it's no use
+ 
+
+ align:start position:0%
+mind then what should you do it's no use
+reading a textbook on AI
+
+ align:start position:0%
+reading a textbook on AI
+ 
+
+ align:start position:0%
+reading a textbook on AI
+because textbooks the existing textbooks
+
+ align:start position:0%
+because textbooks the existing textbooks
+ 
+
+ align:start position:0%
+because textbooks the existing textbooks
+are extremely
+
+ align:start position:0%
+are extremely
+ 
+
+ align:start position:0%
+are extremely
+conservative uh except maybe for Pat
+
+ align:start position:0%
+conservative uh except maybe for Pat
+ 
+
+ align:start position:0%
+conservative uh except maybe for Pat
+Winston's and
+
+ align:start position:0%
+Winston's and
+ 
+
+ align:start position:0%
+Winston's and
+uh how do you sell a
+
+ align:start position:0%
+uh how do you sell a
+ 
+
+ align:start position:0%
+uh how do you sell a
+textbook you have to have chapters that
+
+ align:start position:0%
+textbook you have to have chapters that
+ 
+
+ align:start position:0%
+textbook you have to have chapters that
+explain subjects that you can give
+
+ align:start position:0%
+explain subjects that you can give
+ 
+
+ align:start position:0%
+explain subjects that you can give
+homework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in now if a subject is not really very
+
+ align:start position:0%
+in now if a subject is not really very
+ 
+
+ align:start position:0%
+in now if a subject is not really very
+welld developed and I think it's fair to
+
+ align:start position:0%
+welld developed and I think it's fair to
+ 
+
+ align:start position:0%
+welld developed and I think it's fair to
+say that artificial intelligence
+
+ align:start position:0%
+say that artificial intelligence
+ 
+
+ align:start position:0%
+say that artificial intelligence
+isn't it's really very hard to think of
+
+ align:start position:0%
+isn't it's really very hard to think of
+ 
+
+ align:start position:0%
+isn't it's really very hard to think of
+things that gave that make good homework
+
+ align:start position:0%
+things that gave that make good homework
+ 
+
+ align:start position:0%
+things that gave that make good homework
+questions but these textbooks manag to
+
+ align:start position:0%
+questions but these textbooks manag to
+ 
+
+ align:start position:0%
+questions but these textbooks manag to
+confine themselves to uh topics that are
+
+ align:start position:0%
+confine themselves to uh topics that are
+ 
+
+ align:start position:0%
+confine themselves to uh topics that are
+very narrow like elements of probability
+
+ align:start position:0%
+very narrow like elements of probability
+ 
+
+ align:start position:0%
+very narrow like elements of probability
+Theory or elements of uh Elementary
+
+ align:start position:0%
+Theory or elements of uh Elementary
+ 
+
+ align:start position:0%
+Theory or elements of uh Elementary
+predicate logic or statistics
+
+ align:start position:0%
+predicate logic or statistics
+ 
+
+ align:start position:0%
+predicate logic or statistics
+or uh
+
+ align:start position:0%
+or uh
+ 
+
+ align:start position:0%
+or uh
+whatever and
+
+ align:start position:0%
+whatever and
+ 
+
+ align:start position:0%
+whatever and
+uh whereas Aaron slowman if you just
+
+ align:start position:0%
+uh whereas Aaron slowman if you just
+ 
+
+ align:start position:0%
+uh whereas Aaron slowman if you just
+Google for Aaron slowman and you'll find
+
+ align:start position:0%
+Google for Aaron slowman and you'll find
+ 
+
+ align:start position:0%
+Google for Aaron slowman and you'll find
+this page which has dozens of big
+
+ align:start position:0%
+this page which has dozens of big
+ 
+
+ align:start position:0%
+this page which has dozens of big
+profound essays and hundreds of little
+
+ align:start position:0%
+profound essays and hundreds of little
+ 
+
+ align:start position:0%
+profound essays and hundreds of little
+uh correspondences and uh messages on
+
+ align:start position:0%
+uh correspondences and uh messages on
+ 
+
+ align:start position:0%
+uh correspondences and uh messages on
+groups and so forth and uh that's that's
+
+ align:start position:0%
+groups and so forth and uh that's that's
+ 
+
+ align:start position:0%
+groups and so forth and uh that's that's
+a great Gold Mine of somebody who's
+
+ align:start position:0%
+a great Gold Mine of somebody who's
+ 
+
+ align:start position:0%
+a great Gold Mine of somebody who's
+thought about these things for many
+
+ align:start position:0%
+thought about these things for many
+ 
+
+ align:start position:0%
+thought about these things for many
+years and has filtered out he's very
+
+ align:start position:0%
+years and has filtered out he's very
+ 
+
+ align:start position:0%
+years and has filtered out he's very
+critical as well as constructive and
+
+ align:start position:0%
+critical as well as constructive and
+ 
+
+ align:start position:0%
+critical as well as constructive and
+pretty unique
+
+ align:start position:0%
+pretty unique
+ 
+
+ align:start position:0%
+pretty unique
+uh he never writes popular things so uh
+
+ align:start position:0%
+uh he never writes popular things so uh
+ 
+
+ align:start position:0%
+uh he never writes popular things so uh
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+philosopher if that's a good word uh is
+
+ align:start position:0%
+philosopher if that's a good word uh is
+ 
+
+ align:start position:0%
+philosopher if that's a good word uh is
+Daniel denned who writes a lot and he's
+
+ align:start position:0%
+Daniel denned who writes a lot and he's
+ 
+
+ align:start position:0%
+Daniel denned who writes a lot and he's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+as concise and or technical but uh he's
+
+ align:start position:0%
+as concise and or technical but uh he's
+ 
+
+ align:start position:0%
+as concise and or technical but uh he's
+the other person who is always full of
+
+ align:start position:0%
+the other person who is always full of
+ 
+
+ align:start position:0%
+the other person who is always full of
+new ideas about uh old problems and very
+
+ align:start position:0%
+new ideas about uh old problems and very
+ 
+
+ align:start position:0%
+new ideas about uh old problems and very
+constructive but if you want to learn
+
+ align:start position:0%
+constructive but if you want to learn
+ 
+
+ align:start position:0%
+constructive but if you want to learn
+things maybe
+
+ align:start position:0%
+things maybe
+ 
+
+ align:start position:0%
+things maybe
+slowman
+
+ align:start position:0%
+slowman
+ 
+
+ align:start position:0%
+slowman
+uh is the best person to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+read I thought I'd talk about
+
+ align:start position:0%
+read I thought I'd talk about
+ 
+
+ align:start position:0%
+read I thought I'd talk about
+Consciousness but uh after debugging
+
+ align:start position:0%
+Consciousness but uh after debugging
+ 
+
+ align:start position:0%
+Consciousness but uh after debugging
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+book right up to last November I don't
+
+ align:start position:0%
+book right up to last November I don't
+ 
+
+ align:start position:0%
+book right up to last November I don't
+think I have anything much to say that I
+
+ align:start position:0%
+think I have anything much to say that I
+ 
+
+ align:start position:0%
+think I have anything much to say that I
+didn't write in this chapter 4 which was
+
+ align:start position:0%
+didn't write in this chapter 4 which was
+ 
+
+ align:start position:0%
+didn't write in this chapter 4 which was
+the last one I worked on actually
+
+ align:start position:0%
+the last one I worked on actually
+ 
+
+ align:start position:0%
+the last one I worked on actually
+so here's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh everyday event where Joan is worried
+
+ align:start position:0%
+uh everyday event where Joan is worried
+ 
+
+ align:start position:0%
+uh everyday event where Joan is worried
+about missing her meeting and
+
+ align:start position:0%
+about missing her meeting and
+ 
+
+ align:start position:0%
+about missing her meeting and
+uh decides to cross the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+street
+
+ align:start position:0%
+street
+ 
+
+ align:start position:0%
+street
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh it might seem natural to ask what was
+
+ align:start position:0%
+uh it might seem natural to ask what was
+ 
+
+ align:start position:0%
+uh it might seem natural to ask what was
+Joan conscious of or how conscious was
+
+ align:start position:0%
+Joan conscious of or how conscious was
+ 
+
+ align:start position:0%
+Joan conscious of or how conscious was
+she of what she was
+
+ align:start position:0%
+she of what she was
+ 
+
+ align:start position:0%
+she of what she was
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+uh and then this is a sort of long
+
+ align:start position:0%
+uh and then this is a sort of long
+ 
+
+ align:start position:0%
+uh and then this is a sort of long
+section where I list about uh maybe 30
+
+ align:start position:0%
+section where I list about uh maybe 30
+ 
+
+ align:start position:0%
+section where I list about uh maybe 30
+or so different things that Joan was
+
+ align:start position:0%
+or so different things that Joan was
+ 
+
+ align:start position:0%
+or so different things that Joan was
+doing and you could ask uh how conscious
+
+ align:start position:0%
+doing and you could ask uh how conscious
+ 
+
+ align:start position:0%
+doing and you could ask uh how conscious
+was she of any of those and I didn't
+
+ align:start position:0%
+was she of any of those and I didn't
+ 
+
+ align:start position:0%
+was she of any of those and I didn't
+even try to uh answer that question I
+
+ align:start position:0%
+even try to uh answer that question I
+ 
+
+ align:start position:0%
+even try to uh answer that question I
+just made this big list of things that
+
+ align:start position:0%
+just made this big list of things that
+ 
+
+ align:start position:0%
+just made this big list of things that
+happened and what you notice is that
+
+ align:start position:0%
+happened and what you notice is that
+ 
+
+ align:start position:0%
+happened and what you notice is that
+whatever she's doing when she's thinking
+
+ align:start position:0%
+whatever she's doing when she's thinking
+ 
+
+ align:start position:0%
+whatever she's doing when she's thinking
+these thoughts
+
+ align:start position:0%
+these thoughts
+ 
+
+ align:start position:0%
+these thoughts
+uh there are a lot of different kinds of
+
+ align:start position:0%
+uh there are a lot of different kinds of
+ 
+
+ align:start position:0%
+uh there are a lot of different kinds of
+uh processes that you would have if you
+
+ align:start position:0%
+uh processes that you would have if you
+ 
+
+ align:start position:0%
+uh processes that you would have if you
+try to describe them in uh Common Sense
+
+ align:start position:0%
+try to describe them in uh Common Sense
+ 
+
+ align:start position:0%
+try to describe them in uh Common Sense
+uh English words so those are the words
+
+ align:start position:0%
+uh English words so those are the words
+ 
+
+ align:start position:0%
+uh English words so those are the words
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+italic uh the joke of course is the last
+
+ align:start position:0%
+italic uh the joke of course is the last
+ 
+
+ align:start position:0%
+italic uh the joke of course is the last
+sentence
+
+ align:start position:0%
+sentence
+ 
+
+ align:start position:0%
+sentence
+uh uh if I had uh done the wrong thing
+
+ align:start position:0%
+uh uh if I had uh done the wrong thing
+ 
+
+ align:start position:0%
+uh uh if I had uh done the wrong thing
+and got killed what would my friends
+
+ align:start position:0%
+and got killed what would my friends
+ 
+
+ align:start position:0%
+and got killed what would my friends
+have thought of me and that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's sort of interesting
+
+ align:start position:0%
+that's sort of interesting
+ 
+
+ align:start position:0%
+that's sort of interesting
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh is that really the most important
+
+ align:start position:0%
+uh is that really the most important
+ 
+
+ align:start position:0%
+uh is that really the most important
+consequence of your being killed you'd
+
+ align:start position:0%
+consequence of your being killed you'd
+ 
+
+ align:start position:0%
+consequence of your being killed you'd
+think that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what did she laugh after thinking
+
+ align:start position:0%
+uh what did she laugh after thinking
+ 
+
+ align:start position:0%
+uh what did she laugh after thinking
+that I think so uh but I was putting
+
+ align:start position:0%
+that I think so uh but I was putting
+ 
+
+ align:start position:0%
+that I think so uh but I was putting
+myself in her shoes or her knees in this
+
+ align:start position:0%
+myself in her shoes or her knees in this
+ 
+
+ align:start position:0%
+myself in her shoes or her knees in this
+case and uh I realized that that's one
+
+ align:start position:0%
+case and uh I realized that that's one
+ 
+
+ align:start position:0%
+case and uh I realized that that's one
+of the things things that you might
+
+ align:start position:0%
+of the things things that you might
+ 
+
+ align:start position:0%
+of the things things that you might
+actually think because your
+
+ align:start position:0%
+actually think because your
+ 
+
+ align:start position:0%
+actually think because your
+social uh social mind or at least in
+
+ align:start position:0%
+social uh social mind or at least in
+ 
+
+ align:start position:0%
+social uh social mind or at least in
+some people
+
+ align:start position:0%
+some people
+ 
+
+ align:start position:0%
+some people
+is whatever that means is as big as your
+
+ align:start position:0%
+is whatever that means is as big as your
+ 
+
+ align:start position:0%
+is whatever that means is as big as your
+uh common other Common Sense minds and U
+
+ align:start position:0%
+uh common other Common Sense minds and U
+ 
+
+ align:start position:0%
+uh common other Common Sense minds and U
+I'm attribut I'm worried that Joan is
+
+ align:start position:0%
+I'm attribut I'm worried that Joan is
+ 
+
+ align:start position:0%
+I'm attribut I'm worried that Joan is
+too concerned with with what other
+
+ align:start position:0%
+too concerned with with what other
+ 
+
+ align:start position:0%
+too concerned with with what other
+people think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+her was that
+
+ align:start position:0%
+her was that
+ 
+
+ align:start position:0%
+her was that
+there's a book is there a book by
+
+ align:start position:0%
+there's a book is there a book by
+ 
+
+ align:start position:0%
+there's a book is there a book by
+Richard Fineman called what do you care
+
+ align:start position:0%
+Richard Fineman called what do you care
+ 
+
+ align:start position:0%
+Richard Fineman called what do you care
+what other people think is that the
+
+ align:start position:0%
+what other people think is that the
+ 
+
+ align:start position:0%
+what other people think is that the
+whole actual title yes
+
+ align:start position:0%
+whole actual title yes
+ 
+
+ align:start position:0%
+whole actual title yes
+yes you shouldn't care what other people
+
+ align:start position:0%
+yes you shouldn't care what other people
+ 
+
+ align:start position:0%
+yes you shouldn't care what other people
+think except uh when you say it yeah
+
+ align:start position:0%
+think except uh when you say it yeah
+ 
+
+ align:start position:0%
+think except uh when you say it yeah
+well I was reading this section and uh
+
+ align:start position:0%
+well I was reading this section and uh
+ 
+
+ align:start position:0%
+well I was reading this section and uh
+one of the things I was curious about
+
+ align:start position:0%
+one of the things I was curious about
+ 
+
+ align:start position:0%
+one of the things I was curious about
+was uh examining what we would consider
+
+ align:start position:0%
+was uh examining what we would consider
+ 
+
+ align:start position:0%
+was uh examining what we would consider
+to be going on in Joan's mind as she was
+
+ align:start position:0%
+to be going on in Joan's mind as she was
+ 
+
+ align:start position:0%
+to be going on in Joan's mind as she was
+crossing the stre Street uh
+
+ align:start position:0%
+crossing the stre Street uh
+ 
+
+ align:start position:0%
+crossing the stre Street uh
+like uh for example at the top level I I
+
+ align:start position:0%
+like uh for example at the top level I I
+ 
+
+ align:start position:0%
+like uh for example at the top level I I
+would conjecture she was possibly
+
+ align:start position:0%
+would conjecture she was possibly
+ 
+
+ align:start position:0%
+would conjecture she was possibly
+thinking um I am late I want to do
+
+ align:start position:0%
+thinking um I am late I want to do
+ 
+
+ align:start position:0%
+thinking um I am late I want to do
+something I want to make make myself as
+
+ align:start position:0%
+something I want to make make myself as
+ 
+
+ align:start position:0%
+something I want to make make myself as
+least late as possible right and she may
+
+ align:start position:0%
+least late as possible right and she may
+ 
+
+ align:start position:0%
+least late as possible right and she may
+have compressed that
+
+ align:start position:0%
+have compressed that
+ 
+
+ align:start position:0%
+have compressed that
+into I I have to hurry but right and
+
+ align:start position:0%
+into I I have to hurry but right and
+ 
+
+ align:start position:0%
+into I I have to hurry but right and
+then that sort of makes
+
+ align:start position:0%
+then that sort of makes
+ 
+
+ align:start position:0%
+then that sort of makes
+um uh I kind of want to examine that um
+
+ align:start position:0%
+um uh I kind of want to examine that um
+ 
+
+ align:start position:0%
+um uh I kind of want to examine that um
+that perspective because
+
+ align:start position:0%
+that perspective because
+ 
+
+ align:start position:0%
+that perspective because
+um I when I looked at it it seemed makes
+
+ align:start position:0%
+um I when I looked at it it seemed makes
+ 
+
+ align:start position:0%
+um I when I looked at it it seemed makes
+sense to me as to why she did the thing
+
+ align:start position:0%
+sense to me as to why she did the thing
+ 
+
+ align:start position:0%
+sense to me as to why she did the thing
+she did because her priorities were
+
+ align:start position:0%
+she did because her priorities were
+ 
+
+ align:start position:0%
+she did because her priorities were
+about um not being late and that could
+
+ align:start position:0%
+about um not being late and that could
+ 
+
+ align:start position:0%
+about um not being late and that could
+percolate down to multiple levels of or
+
+ align:start position:0%
+percolate down to multiple levels of or
+ 
+
+ align:start position:0%
+percolate down to multiple levels of or
+or Consciousness um I think you were
+
+ align:start position:0%
+or Consciousness um I think you were
+ 
+
+ align:start position:0%
+or Consciousness um I think you were
+asking a profound question which is uh
+
+ align:start position:0%
+asking a profound question which is uh
+ 
+
+ align:start position:0%
+asking a profound question which is uh
+how many of the what does it mean to say
+
+ align:start position:0%
+how many of the what does it mean to say
+ 
+
+ align:start position:0%
+how many of the what does it mean to say
+that these were on her mind or or could
+
+ align:start position:0%
+that these were on her mind or or could
+ 
+
+ align:start position:0%
+that these were on her mind or or could
+they be retrieved in one step and we we
+
+ align:start position:0%
+they be retrieved in one step and we we
+ 
+
+ align:start position:0%
+they be retrieved in one step and we we
+can't tell I'm willing to say that there
+
+ align:start position:0%
+can't tell I'm willing to say that there
+ 
+
+ align:start position:0%
+can't tell I'm willing to say that there
+are um multiple things going on at
+
+ align:start position:0%
+are um multiple things going on at
+ 
+
+ align:start position:0%
+are um multiple things going on at
+different levels but I'm I'm sort of
+
+ align:start position:0%
+different levels but I'm I'm sort of
+ 
+
+ align:start position:0%
+different levels but I'm I'm sort of
+conjecturing at one level of quite great
+
+ align:start position:0%
+conjecturing at one level of quite great
+ 
+
+ align:start position:0%
+conjecturing at one level of quite great
+significance as she was crossing the
+
+ align:start position:0%
+significance as she was crossing the
+ 
+
+ align:start position:0%
+significance as she was crossing the
+street was I am late and I don't want to
+
+ align:start position:0%
+street was I am late and I don't want to
+ 
+
+ align:start position:0%
+street was I am late and I don't want to
+be that I don't don't want to be too
+
+ align:start position:0%
+be that I don't don't want to be too
+ 
+
+ align:start position:0%
+be that I don't don't want to be too
+late mhm um and then there are other
+
+ align:start position:0%
+late mhm um and then there are other
+ 
+
+ align:start position:0%
+late mhm um and then there are other
+things that or she might be even looking
+
+ align:start position:0%
+things that or she might be even looking
+ 
+
+ align:start position:0%
+things that or she might be even looking
+ahead a step and say what will they say
+
+ align:start position:0%
+ahead a step and say what will they say
+ 
+
+ align:start position:0%
+ahead a step and say what will they say
+if I'm late
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes well that's a nice question about
+
+ align:start position:0%
+yes well that's a nice question about
+ 
+
+ align:start position:0%
+yes well that's a nice question about
+uh various parts of your brain are have
+
+ align:start position:0%
+uh various parts of your brain are have
+ 
+
+ align:start position:0%
+uh various parts of your brain are have
+concerns I I think think it's safe to
+
+ align:start position:0%
+concerns I I think think it's safe to
+ 
+
+ align:start position:0%
+concerns I I think think it's safe to
+say and uh a nice question is are they
+
+ align:start position:0%
+say and uh a nice question is are they
+ 
+
+ align:start position:0%
+say and uh a nice question is are they
+ordered or are they parallel are you
+
+ align:start position:0%
+ordered or are they parallel are you
+ 
+
+ align:start position:0%
+ordered or are they parallel are you
+jumping around or uh because we're so
+
+ align:start position:0%
+jumping around or uh because we're so
+ 
+
+ align:start position:0%
+jumping around or uh because we're so
+we're such uh verbal animals that it
+
+ align:start position:0%
+we're such uh verbal animals that it
+ 
+
+ align:start position:0%
+we're such uh verbal animals that it
+might be that in the speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area what's in the speech area maybe
+
+ align:start position:0%
+area what's in the speech area maybe
+ 
+
+ align:start position:0%
+area what's in the speech area maybe
+there's a buffer that has the sentence
+
+ align:start position:0%
+there's a buffer that has the sentence
+ 
+
+ align:start position:0%
+there's a buffer that has the sentence
+that you're
+
+ align:start position:0%
+that you're
+ 
+
+ align:start position:0%
+that you're
+about to
+
+ align:start position:0%
+about to
+ 
+
+ align:start position:0%
+about to
+speak and it's in it's in an output
+
+ align:start position:0%
+speak and it's in it's in an output
+ 
+
+ align:start position:0%
+speak and it's in it's in an output
+buffer and it's all set and there's one
+
+ align:start position:0%
+buffer and it's all set and there's one
+ 
+
+ align:start position:0%
+buffer and it's all set and there's one
+that uh you're still constructing for
+
+ align:start position:0%
+that uh you're still constructing for
+ 
+
+ align:start position:0%
+that uh you're still constructing for
+saying next and then maybe there's four
+
+ align:start position:0%
+saying next and then maybe there's four
+ 
+
+ align:start position:0%
+saying next and then maybe there's four
+or five search processes which are
+
+ align:start position:0%
+or five search processes which are
+ 
+
+ align:start position:0%
+or five search processes which are
+saying and how could I justify that or
+
+ align:start position:0%
+saying and how could I justify that or
+ 
+
+ align:start position:0%
+saying and how could I justify that or
+what should I say after that or
+
+ align:start position:0%
+what should I say after that or
+ 
+
+ align:start position:0%
+what should I say after that or
+uh what's the probable reaction to the
+
+ align:start position:0%
+uh what's the probable reaction to the
+ 
+
+ align:start position:0%
+uh what's the probable reaction to the
+first one and should I change my goal
+
+ align:start position:0%
+first one and should I change my goal
+ 
+
+ align:start position:0%
+first one and should I change my goal
+I I've never seen good theories of this
+
+ align:start position:0%
+I I've never seen good theories of this
+ 
+
+ align:start position:0%
+I I've never seen good theories of this
+but I bet that in literary I think I
+
+ align:start position:0%
+but I bet that in literary I think I
+ 
+
+ align:start position:0%
+but I bet that in literary I think I
+mentioned that the other day in literary
+
+ align:start position:0%
+mentioned that the other day in literary
+ 
+
+ align:start position:0%
+mentioned that the other day in literary
+criticism there are writers and in
+
+ align:start position:0%
+criticism there are writers and in
+ 
+
+ align:start position:0%
+criticism there are writers and in
+poetry magazines few other
+
+ align:start position:0%
+poetry magazines few other
+ 
+
+ align:start position:0%
+poetry magazines few other
+places where would you find discussions
+
+ align:start position:0%
+places where would you find discussions
+ 
+
+ align:start position:0%
+places where would you find discussions
+of that sort of thing uh people trying
+
+ align:start position:0%
+of that sort of thing uh people trying
+ 
+
+ align:start position:0%
+of that sort of thing uh people trying
+to uh describe what's on their mind at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment I suppose it's in some Psy ology
+
+ align:start position:0%
+moment I suppose it's in some Psy ology
+ 
+
+ align:start position:0%
+moment I suppose it's in some Psy ology
+books but I've never found any attempt
+
+ align:start position:0%
+books but I've never found any attempt
+ 
+
+ align:start position:0%
+books but I've never found any attempt
+to sort of computerize it or to describe
+
+ align:start position:0%
+to sort of computerize it or to describe
+ 
+
+ align:start position:0%
+to sort of computerize it or to describe
+a structure with so many buffers and so
+
+ align:start position:0%
+a structure with so many buffers and so
+ 
+
+ align:start position:0%
+a structure with so many buffers and so
+many uh retrieval gadgets so forth what
+
+ align:start position:0%
+many uh retrieval gadgets so forth what
+ 
+
+ align:start position:0%
+many uh retrieval gadgets so forth what
+are psychology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+books they're mostly on a classification
+
+ align:start position:0%
+books they're mostly on a classification
+ 
+
+ align:start position:0%
+books they're mostly on a classification
+level and they're assuming that you
+
+ align:start position:0%
+level and they're assuming that you
+ 
+
+ align:start position:0%
+level and they're assuming that you
+know that you already have a theory of
+
+ align:start position:0%
+know that you already have a theory of
+ 
+
+ align:start position:0%
+know that you already have a theory of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+things I'm going I'm going to conjecture
+
+ align:start position:0%
+things I'm going I'm going to conjecture
+ 
+
+ align:start position:0%
+things I'm going I'm going to conjecture
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+chapters the relevant chapters in
+
+ align:start position:0%
+chapters the relevant chapters in
+ 
+
+ align:start position:0%
+chapters the relevant chapters in
+pychology text don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist I was curious to see um sort of
+
+ align:start position:0%
+exist I was curious to see um sort of
+ 
+
+ align:start position:0%
+exist I was curious to see um sort of
+a um a sort of an examination of what
+
+ align:start position:0%
+a um a sort of an examination of what
+ 
+
+ align:start position:0%
+a um a sort of an examination of what
+was going on in the state of Jon's mind
+
+ align:start position:0%
+was going on in the state of Jon's mind
+ 
+
+ align:start position:0%
+was going on in the state of Jon's mind
+as she was crossing the street um as
+
+ align:start position:0%
+as she was crossing the street um as
+ 
+
+ align:start position:0%
+as she was crossing the street um as
+viously as it's done here and then
+
+ align:start position:0%
+viously as it's done here and then
+ 
+
+ align:start position:0%
+viously as it's done here and then
+what's going on in Jon's mind after she
+
+ align:start position:0%
+what's going on in Jon's mind after she
+ 
+
+ align:start position:0%
+what's going on in Jon's mind after she
+crossed the street
+
+ align:start position:0%
+crossed the street
+ 
+
+ align:start position:0%
+crossed the street
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+had these thoughts what my friends have
+
+ align:start position:0%
+had these thoughts what my friends have
+ 
+
+ align:start position:0%
+had these thoughts what my friends have
+thought of me oh you're right uh I mean
+
+ align:start position:0%
+thought of me oh you're right uh I mean
+ 
+
+ align:start position:0%
+thought of me oh you're right uh I mean
+and then what the transitions were right
+
+ align:start position:0%
+and then what the transitions were right
+ 
+
+ align:start position:0%
+and then what the transitions were right
+so I said she later actually I have one
+
+ align:start position:0%
+so I said she later actually I have one
+ 
+
+ align:start position:0%
+so I said she later actually I have one
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+these but it's too hard to aim from here
+
+ align:start position:0%
+these but it's too hard to aim from here
+ 
+
+ align:start position:0%
+these but it's too hard to aim from here
+uh she might be reflecting on them while
+
+ align:start position:0%
+uh she might be reflecting on them while
+ 
+
+ align:start position:0%
+uh she might be reflecting on them while
+she's
+
+ align:start position:0%
+she's
+ 
+
+ align:start position:0%
+she's
+still I mean I just put that in
+
+ align:start position:0%
+still I mean I just put that in
+ 
+
+ align:start position:0%
+still I mean I just put that in
+gratuitously she might be thinking about
+
+ align:start position:0%
+gratuitously she might be thinking about
+ 
+
+ align:start position:0%
+gratuitously she might be thinking about
+getting killed while she's running
+
+ align:start position:0%
+getting killed while she's running
+ 
+
+ align:start position:0%
+getting killed while she's running
+across so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was just focusing on how funny it was
+
+ align:start position:0%
+I was just focusing on how funny it was
+ 
+
+ align:start position:0%
+I was just focusing on how funny it was
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+social uh concern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was it's like wondering what coffin
+
+ align:start position:0%
+was it's like wondering what coffin
+ 
+
+ align:start position:0%
+was it's like wondering what coffin
+you'll be buried
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in I mentioned that because I saw an
+
+ align:start position:0%
+in I mentioned that because I saw an
+ 
+
+ align:start position:0%
+in I mentioned that because I saw an
+article on green coffins I can't
+
+ align:start position:0%
+article on green coffins I can't
+ 
+
+ align:start position:0%
+article on green coffins I can't
+remember what it said but uh there's a a
+
+ align:start position:0%
+remember what it said but uh there's a a
+ 
+
+ align:start position:0%
+remember what it said but uh there's a a
+certain movement among
+
+ align:start position:0%
+certain movement among
+ 
+
+ align:start position:0%
+certain movement among
+funeral uh people about saying that
+
+ align:start position:0%
+funeral uh people about saying that
+ 
+
+ align:start position:0%
+funeral uh people about saying that
+their coffins are more or less
+
+ align:start position:0%
+their coffins are more or less
+ 
+
+ align:start position:0%
+their coffins are more or less
+biodegradable uh you have to have the
+
+ align:start position:0%
+biodegradable uh you have to have the
+ 
+
+ align:start position:0%
+biodegradable uh you have to have the
+right clientele to want a
+
+ align:start position:0%
+right clientele to want a
+ 
+
+ align:start position:0%
+right clientele to want a
+biodegradable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tomb well you've you've seen this huge
+
+ align:start position:0%
+tomb well you've you've seen this huge
+ 
+
+ align:start position:0%
+tomb well you've you've seen this huge
+list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is really descriptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of about 30 things that she might be
+
+ align:start position:0%
+of about 30 things that she might be
+ 
+
+ align:start position:0%
+of about 30 things that she might be
+concerned with and we need
+
+ align:start position:0%
+concerned with and we need
+ 
+
+ align:start position:0%
+concerned with and we need
+a to have a good model of of human
+
+ align:start position:0%
+a to have a good model of of human
+ 
+
+ align:start position:0%
+a to have a good model of of human
+thinking we need some way
+
+ align:start position:0%
+thinking we need some way
+ 
+
+ align:start position:0%
+thinking we need some way
+of do we need 30 different kinds of
+
+ align:start position:0%
+of do we need 30 different kinds of
+ 
+
+ align:start position:0%
+of do we need 30 different kinds of
+mechanisms or
+
+ align:start position:0%
+mechanisms or
+ 
+
+ align:start position:0%
+mechanisms or
+are or is this big collection of high of
+
+ align:start position:0%
+are or is this big collection of high of
+ 
+
+ align:start position:0%
+are or is this big collection of high of
+uh italicized words like learning
+
+ align:start position:0%
+uh italicized words like learning
+ 
+
+ align:start position:0%
+uh italicized words like learning
+recollecting expression
+
+ align:start position:0%
+recollecting expression
+ 
+
+ align:start position:0%
+recollecting expression
+narration those are all ordinary words
+
+ align:start position:0%
+narration those are all ordinary words
+ 
+
+ align:start position:0%
+narration those are all ordinary words
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh one image of how this field will
+
+ align:start position:0%
+uh one image of how this field will
+ 
+
+ align:start position:0%
+uh one image of how this field will
+eventually be successful is if that
+
+ align:start position:0%
+eventually be successful is if that
+ 
+
+ align:start position:0%
+eventually be successful is if that
+those get replaced by 30 technical Words
+
+ align:start position:0%
+those get replaced by 30 technical Words
+ 
+
+ align:start position:0%
+those get replaced by 30 technical Words
+which actually uh you can look up in
+
+ align:start position:0%
+which actually uh you can look up in
+ 
+
+ align:start position:0%
+which actually uh you can look up in
+some Encyclopedia of computer science
+
+ align:start position:0%
+some Encyclopedia of computer science
+ 
+
+ align:start position:0%
+some Encyclopedia of computer science
+and we'll say uh compiler a mechanism
+
+ align:start position:0%
+and we'll say uh compiler a mechanism
+ 
+
+ align:start position:0%
+and we'll say uh compiler a mechanism
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh converting a highlevel description
+
+ align:start position:0%
+uh converting a highlevel description
+ 
+
+ align:start position:0%
+uh converting a highlevel description
+into uh machine language code or
+
+ align:start position:0%
+into uh machine language code or
+ 
+
+ align:start position:0%
+into uh machine language code or
+whatever it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the uh one of the first great
+
+ align:start position:0%
+is the uh one of the first great
+ 
+
+ align:start position:0%
+is the uh one of the first great
+achievements in artificial intelligence
+
+ align:start position:0%
+achievements in artificial intelligence
+ 
+
+ align:start position:0%
+achievements in artificial intelligence
+was in the middle 1950s when uh a uh
+
+ align:start position:0%
+was in the middle 1950s when uh a uh
+ 
+
+ align:start position:0%
+was in the middle 1950s when uh a uh
+computer designer named Arthur Samuel
+
+ align:start position:0%
+computer designer named Arthur Samuel
+ 
+
+ align:start position:0%
+computer designer named Arthur Samuel
+wrote a checker playing
+
+ align:start position:0%
+wrote a checker playing
+ 
+
+ align:start position:0%
+wrote a checker playing
+program and uh
+
+ align:start position:0%
+program and uh
+ 
+
+ align:start position:0%
+program and uh
+he was also designing the IBM
+
+ align:start position:0%
+he was also designing the IBM
+ 
+
+ align:start position:0%
+he was also designing the IBM
+701 which was the first big big uh main
+
+ align:start position:0%
+701 which was the first big big uh main
+ 
+
+ align:start position:0%
+701 which was the first big big uh main
+frame that uh had hundreds of copies
+
+ align:start position:0%
+frame that uh had hundreds of copies
+ 
+
+ align:start position:0%
+frame that uh had hundreds of copies
+made made of
+
+ align:start position:0%
+made made of
+ 
+
+ align:start position:0%
+made made of
+it and he was he wrote the Checker
+
+ align:start position:0%
+it and he was he wrote the Checker
+ 
+
+ align:start position:0%
+it and he was he wrote the Checker
+program in machine language for that and
+
+ align:start position:0%
+program in machine language for that and
+ 
+
+ align:start position:0%
+program in machine language for that and
+discovered that he couldn't understand
+
+ align:start position:0%
+discovered that he couldn't understand
+ 
+
+ align:start position:0%
+discovered that he couldn't understand
+it uh a few days later because there
+
+ align:start position:0%
+it uh a few days later because there
+ 
+
+ align:start position:0%
+it uh a few days later because there
+wasn't room on punch card for comments
+
+ align:start position:0%
+wasn't room on punch card for comments
+ 
+
+ align:start position:0%
+wasn't room on punch card for comments
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+and uh so he wrote a symbolic
+
+ align:start position:0%
+and uh so he wrote a symbolic
+ 
+
+ align:start position:0%
+and uh so he wrote a symbolic
+disassembler everybody know what an
+
+ align:start position:0%
+disassembler everybody know what an
+ 
+
+ align:start position:0%
+disassembler everybody know what an
+assembly program
+
+ align:start position:0%
+assembly program
+ 
+
+ align:start position:0%
+assembly program
+is if you're writing machine code that's
+
+ align:start position:0%
+is if you're writing machine code that's
+ 
+
+ align:start position:0%
+is if you're writing machine code that's
+zeros and ones and there was a period
+
+ align:start position:0%
+zeros and ones and there was a period
+ 
+
+ align:start position:0%
+zeros and ones and there was a period
+when everybody who wrote programs just
+
+ align:start position:0%
+when everybody who wrote programs just
+ 
+
+ align:start position:0%
+when everybody who wrote programs just
+wrote these uh well they wrote them in
+
+ align:start position:0%
+wrote these uh well they wrote them in
+ 
+
+ align:start position:0%
+wrote these uh well they wrote them in
+HEX
+
+ align:start position:0%
+HEX
+ 
+
+ align:start position:0%
+HEX
+usually and or 16 base 16 and then
+
+ align:start position:0%
+usually and or 16 base 16 and then
+ 
+
+ align:start position:0%
+usually and or 16 base 16 and then
+people realized that if you refer into
+
+ align:start position:0%
+people realized that if you refer into
+ 
+
+ align:start position:0%
+people realized that if you refer into
+the same thing many times
+
+ align:start position:0%
+the same thing many times
+ 
+
+ align:start position:0%
+the same thing many times
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+X which is in some register then
+
+ align:start position:0%
+X which is in some register then
+ 
+
+ align:start position:0%
+X which is in some register then
+wouldn't it be nice if you could use the
+
+ align:start position:0%
+wouldn't it be nice if you could use the
+ 
+
+ align:start position:0%
+wouldn't it be nice if you could use the
+symbol X instead of the name of the
+
+ align:start position:0%
+symbol X instead of the name of the
+ 
+
+ align:start position:0%
+symbol X instead of the name of the
+register it's in so that was called
+
+ align:start position:0%
+register it's in so that was called
+ 
+
+ align:start position:0%
+register it's in so that was called
+symbolic assembly and Samuel wrote this
+
+ align:start position:0%
+symbolic assembly and Samuel wrote this
+ 
+
+ align:start position:0%
+symbolic assembly and Samuel wrote this
+uh program which must I've never seen it
+
+ align:start position:0%
+uh program which must I've never seen it
+ 
+
+ align:start position:0%
+uh program which must I've never seen it
+but it must have been uh a fantastic
+
+ align:start position:0%
+but it must have been uh a fantastic
+ 
+
+ align:start position:0%
+but it must have been uh a fantastic
+achievement which would look at machine
+
+ align:start position:0%
+achievement which would look at machine
+ 
+
+ align:start position:0%
+achievement which would look at machine
+code and notice that if the same address
+
+ align:start position:0%
+code and notice that if the same address
+ 
+
+ align:start position:0%
+code and notice that if the same address
+was used for several times well then he
+
+ align:start position:0%
+was used for several times well then he
+ 
+
+ align:start position:0%
+was used for several times well then he
+would assign a symbol to it and uh then
+
+ align:start position:0%
+would assign a symbol to it and uh then
+ 
+
+ align:start position:0%
+would assign a symbol to it and uh then
+it looked like assembly code instead of
+
+ align:start position:0%
+it looked like assembly code instead of
+ 
+
+ align:start position:0%
+it looked like assembly code instead of
+machine code and that way he could
+
+ align:start position:0%
+machine code and that way he could
+ 
+
+ align:start position:0%
+machine code and that way he could
+understand what he had written a few
+
+ align:start position:0%
+understand what he had written a few
+ 
+
+ align:start position:0%
+understand what he had written a few
+days
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ago I don't know if there's
+
+ align:start position:0%
+ago I don't know if there's
+ 
+
+ align:start position:0%
+ago I don't know if there's
+any are there great programs today which
+
+ align:start position:0%
+any are there great programs today which
+ 
+
+ align:start position:0%
+any are there great programs today which
+could look at a machine language program
+
+ align:start position:0%
+could look at a machine language program
+ 
+
+ align:start position:0%
+could look at a machine language program
+and and write some horrible C program to
+
+ align:start position:0%
+and and write some horrible C program to
+ 
+
+ align:start position:0%
+and and write some horrible C program to
+express it figure listen to that
+
+ align:start position:0%
+express it figure listen to that
+ 
+
+ align:start position:0%
+express it figure listen to that
+it disassembles itself into lisp uhuh
+
+ align:start position:0%
+it disassembles itself into lisp uhuh
+ 
+
+ align:start position:0%
+it disassembles itself into lisp uhuh
+well lisp is different from the other
+
+ align:start position:0%
+well lisp is different from the other
+ 
+
+ align:start position:0%
+well lisp is different from the other
+things because The Interpreter only
+
+ align:start position:0%
+things because The Interpreter only
+ 
+
+ align:start position:0%
+things because The Interpreter only
+needs what is it five or six
+
+ align:start position:0%
+needs what is it five or six
+ 
+
+ align:start position:0%
+needs what is it five or six
+Clauses but uh could you look at uh Java
+
+ align:start position:0%
+Clauses but uh could you look at uh Java
+ 
+
+ align:start position:0%
+Clauses but uh could you look at uh Java
+code and well maybe it's the same yeah
+
+ align:start position:0%
+code and well maybe it's the same yeah
+ 
+
+ align:start position:0%
+code and well maybe it's the same yeah
+jav I've I've actually lost code to Java
+
+ align:start position:0%
+jav I've I've actually lost code to Java
+ 
+
+ align:start position:0%
+jav I've I've actually lost code to Java
+programs and recovered it from machine
+
+ align:start position:0%
+programs and recovered it from machine
+ 
+
+ align:start position:0%
+programs and recovered it from machine
+code by Machine by a program Yeah by dis
+
+ align:start position:0%
+code by Machine by a program Yeah by dis
+ 
+
+ align:start position:0%
+code by Machine by a program Yeah by dis
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+great well if we could do that for our
+
+ align:start position:0%
+great well if we could do that for our
+ 
+
+ align:start position:0%
+great well if we could do that for our
+brains and find out uh why we thought of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something uh so much for that uh I guess
+
+ align:start position:0%
+something uh so much for that uh I guess
+ 
+
+ align:start position:0%
+something uh so much for that uh I guess
+I shouldn't go over this but one idea
+
+ align:start position:0%
+I shouldn't go over this but one idea
+ 
+
+ align:start position:0%
+I shouldn't go over this but one idea
+is one aspect the reason this is in the
+
+ align:start position:0%
+is one aspect the reason this is in the
+ 
+
+ align:start position:0%
+is one aspect the reason this is in the
+Consciousness chapter is uh people talk
+
+ align:start position:0%
+Consciousness chapter is uh people talk
+ 
+
+ align:start position:0%
+Consciousness chapter is uh people talk
+about self-awareness as being a feature
+
+ align:start position:0%
+about self-awareness as being a feature
+ 
+
+ align:start position:0%
+about self-awareness as being a feature
+of Consciousness and the question
+
+ align:start position:0%
+of Consciousness and the question
+ 
+
+ align:start position:0%
+of Consciousness and the question
+uh in what sense is a person
+
+ align:start position:0%
+uh in what sense is a person
+ 
+
+ align:start position:0%
+uh in what sense is a person
+self-aware they're clearly not aware of
+
+ align:start position:0%
+self-aware they're clearly not aware of
+ 
+
+ align:start position:0%
+self-aware they're clearly not aware of
+uh how their spinal cord
+
+ align:start position:0%
+uh how their spinal cord
+ 
+
+ align:start position:0%
+uh how their spinal cord
+sent decided to send signals to wiggle
+
+ align:start position:0%
+sent decided to send signals to wiggle
+ 
+
+ align:start position:0%
+sent decided to send signals to wiggle
+the little finger on your left hand
+
+ align:start position:0%
+the little finger on your left hand
+ 
+
+ align:start position:0%
+the little finger on your left hand
+except that now I'm
+
+ align:start position:0%
+except that now I'm
+ 
+
+ align:start position:0%
+except that now I'm
+aware uh I can think of in fact I don't
+
+ align:start position:0%
+aware uh I can think of in fact I don't
+ 
+
+ align:start position:0%
+aware uh I can think of in fact I don't
+know how it's done and I'm imagining a
+
+ align:start position:0%
+know how it's done and I'm imagining a
+ 
+
+ align:start position:0%
+know how it's done and I'm imagining a
+almost certainly wrong theory of what
+
+ align:start position:0%
+almost certainly wrong theory of what
+ 
+
+ align:start position:0%
+almost certainly wrong theory of what
+are the steps between saying I'm going
+
+ align:start position:0%
+are the steps between saying I'm going
+ 
+
+ align:start position:0%
+are the steps between saying I'm going
+to wiggle my finger in doing it so
+
+ align:start position:0%
+to wiggle my finger in doing it so
+ 
+
+ align:start position:0%
+to wiggle my finger in doing it so
+uh generally I don't think we're
+
+ align:start position:0%
+uh generally I don't think we're
+ 
+
+ align:start position:0%
+uh generally I don't think we're
+self-aware in a genuine sense hardly at
+
+ align:start position:0%
+self-aware in a genuine sense hardly at
+ 
+
+ align:start position:0%
+self-aware in a genuine sense hardly at
+all uh what happens is when uh when you
+
+ align:start position:0%
+all uh what happens is when uh when you
+ 
+
+ align:start position:0%
+all uh what happens is when uh when you
+quote experience something what you're
+
+ align:start position:0%
+quote experience something what you're
+ 
+
+ align:start position:0%
+quote experience something what you're
+doing is making up a uh baby theory of
+
+ align:start position:0%
+doing is making up a uh baby theory of
+ 
+
+ align:start position:0%
+doing is making up a uh baby theory of
+how it worked and that's your sense of
+
+ align:start position:0%
+how it worked and that's your sense of
+ 
+
+ align:start position:0%
+how it worked and that's your sense of
+of uh Insight is I've just thought of a
+
+ align:start position:0%
+of uh Insight is I've just thought of a
+ 
+
+ align:start position:0%
+of uh Insight is I've just thought of a
+really uh pretty simple uh model of what
+
+ align:start position:0%
+really uh pretty simple uh model of what
+ 
+
+ align:start position:0%
+really uh pretty simple uh model of what
+I did uh but I think it's very unlikely
+
+ align:start position:0%
+I did uh but I think it's very unlikely
+ 
+
+ align:start position:0%
+I did uh but I think it's very unlikely
+that anything like the language part of
+
+ align:start position:0%
+that anything like the language part of
+ 
+
+ align:start position:0%
+that anything like the language part of
+your brain has much idea of what
+
+ align:start position:0%
+your brain has much idea of what
+ 
+
+ align:start position:0%
+your brain has much idea of what
+happened in
+
+ align:start position:0%
+happened in
+ 
+
+ align:start position:0%
+happened in
+the uh that's in the front part of your
+
+ align:start position:0%
+the uh that's in the front part of your
+ 
+
+ align:start position:0%
+the uh that's in the front part of your
+brain has uh any really good ideas about
+
+ align:start position:0%
+brain has uh any really good ideas about
+ 
+
+ align:start position:0%
+brain has uh any really good ideas about
+what happened in the back half of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+so so in some sense when people talk
+
+ align:start position:0%
+so so in some sense when people talk
+ 
+
+ align:start position:0%
+so so in some sense when people talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+self-awareness that's an
+
+ align:start position:0%
+self-awareness that's an
+ 
+
+ align:start position:0%
+self-awareness that's an
+abbreviation for thinking that you know
+
+ align:start position:0%
+abbreviation for thinking that you know
+ 
+
+ align:start position:0%
+abbreviation for thinking that you know
+what just happened rather than really
+
+ align:start position:0%
+what just happened rather than really
+ 
+
+ align:start position:0%
+what just happened rather than really
+knowing what just
+
+ align:start position:0%
+knowing what just
+ 
+
+ align:start position:0%
+knowing what just
+happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh that leads
+
+ align:start position:0%
+and uh that leads
+ 
+
+ align:start position:0%
+and uh that leads
+to ideas
+
+ align:start position:0%
+to ideas
+ 
+
+ align:start position:0%
+to ideas
+about um maybe there are several layers
+
+ align:start position:0%
+about um maybe there are several layers
+ 
+
+ align:start position:0%
+about um maybe there are several layers
+of the brain uh Each of which gets
+
+ align:start position:0%
+of the brain uh Each of which gets
+ 
+
+ align:start position:0%
+of the brain uh Each of which gets
+inputs from the layer below it so that
+
+ align:start position:0%
+inputs from the layer below it so that
+ 
+
+ align:start position:0%
+inputs from the layer below it so that
+your highest
+
+ align:start position:0%
+your highest
+ 
+
+ align:start position:0%
+your highest
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+awareness is presumably actually uh
+
+ align:start position:0%
+awareness is presumably actually uh
+ 
+
+ align:start position:0%
+awareness is presumably actually uh
+recognitions of patterns in the at each
+
+ align:start position:0%
+recognitions of patterns in the at each
+ 
+
+ align:start position:0%
+recognitions of patterns in the at each
+level of patterns that are happening in
+
+ align:start position:0%
+level of patterns that are happening in
+ 
+
+ align:start position:0%
+level of patterns that are happening in
+the level below it there's a funny
+
+ align:start position:0%
+the level below it there's a funny
+ 
+
+ align:start position:0%
+the level below it there's a funny
+phenomenon in Vision called seeing
+
+ align:start position:0%
+phenomenon in Vision called seeing
+ 
+
+ align:start position:0%
+phenomenon in Vision called seeing
+through that uh if you look at a picture
+
+ align:start position:0%
+through that uh if you look at a picture
+ 
+
+ align:start position:0%
+through that uh if you look at a picture
+or if you look at a visual scene um
+
+ align:start position:0%
+or if you look at a visual scene um
+ 
+
+ align:start position:0%
+or if you look at a visual scene um
+I see the I see this hexagonal grid of
+
+ align:start position:0%
+I see the I see this hexagonal grid of
+ 
+
+ align:start position:0%
+I see the I see this hexagonal grid of
+little circles in those panels so I have
+
+ align:start position:0%
+little circles in those panels so I have
+ 
+
+ align:start position:0%
+little circles in those panels so I have
+a nice abstract theory that there
+
+ align:start position:0%
+a nice abstract theory that there
+ 
+
+ align:start position:0%
+a nice abstract theory that there
+are these sort of uh rectangles that are
+
+ align:start position:0%
+are these sort of uh rectangles that are
+ 
+
+ align:start position:0%
+are these sort of uh rectangles that are
+two and a half times as high as they are
+
+ align:start position:0%
+two and a half times as high as they are
+ 
+
+ align:start position:0%
+two and a half times as high as they are
+wide and each one uh is full of rows of
+
+ align:start position:0%
+wide and each one uh is full of rows of
+ 
+
+ align:start position:0%
+wide and each one uh is full of rows of
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+30 uh circles and those are arranged in
+
+ align:start position:0%
+30 uh circles and those are arranged in
+ 
+
+ align:start position:0%
+30 uh circles and those are arranged in
+a hexagonal pattern and so some some
+
+ align:start position:0%
+a hexagonal pattern and so some some
+ 
+
+ align:start position:0%
+a hexagonal pattern and so some some
+part of your brain is describing it that
+
+ align:start position:0%
+part of your brain is describing it that
+ 
+
+ align:start position:0%
+part of your brain is describing it that
+way and uh you have the feeling also
+
+ align:start position:0%
+way and uh you have the feeling also
+ 
+
+ align:start position:0%
+way and uh you have the feeling also
+that you're seeing all the holes
+
+ align:start position:0%
+that you're seeing all the holes
+ 
+
+ align:start position:0%
+that you're seeing all the holes
+separately and there probably are some
+
+ align:start position:0%
+separately and there probably are some
+ 
+
+ align:start position:0%
+separately and there probably are some
+parts of the brains that are uh noticing
+
+ align:start position:0%
+parts of the brains that are uh noticing
+ 
+
+ align:start position:0%
+parts of the brains that are uh noticing
+the roundness of the third hole to the
+
+ align:start position:0%
+the roundness of the third hole to the
+ 
+
+ align:start position:0%
+the roundness of the third hole to the
+left in the 15th
+
+ align:start position:0%
+left in the 15th
+ 
+
+ align:start position:0%
+left in the 15th
+row or maybe
+
+ align:start position:0%
+row or maybe
+ 
+
+ align:start position:0%
+row or maybe
+not and uh some of the visual people
+
+ align:start position:0%
+not and uh some of the visual people
+ 
+
+ align:start position:0%
+not and uh some of the visual people
+talk about the remarkable thing about
+
+ align:start position:0%
+talk about the remarkable thing about
+ 
+
+ align:start position:0%
+talk about the remarkable thing about
+human vision is that uh uh I can keep
+
+ align:start position:0%
+human vision is that uh uh I can keep
+ 
+
+ align:start position:0%
+human vision is that uh uh I can keep
+looking at the same scene but now I'm
+
+ align:start position:0%
+looking at the same scene but now I'm
+ 
+
+ align:start position:0%
+looking at the same scene but now I'm
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+1:00 on the one of those little holes
+
+ align:start position:0%
+1:00 on the one of those little holes
+ 
+
+ align:start position:0%
+1:00 on the one of those little holes
+and practically seeing the pixels there
+
+ align:start position:0%
+and practically seeing the pixels there
+ 
+
+ align:start position:0%
+and practically seeing the pixels there
+so how is it that you can see this high
+
+ align:start position:0%
+so how is it that you can see this high
+ 
+
+ align:start position:0%
+so how is it that you can see this high
+level pattern namely that's a textured
+
+ align:start position:0%
+level pattern namely that's a textured
+ 
+
+ align:start position:0%
+level pattern namely that's a textured
+wall and another level which is it's
+
+ align:start position:0%
+wall and another level which is it's
+ 
+
+ align:start position:0%
+wall and another level which is it's
+made of uh rectangles full of holes and
+
+ align:start position:0%
+made of uh rectangles full of holes and
+ 
+
+ align:start position:0%
+made of uh rectangles full of holes and
+another level where I can see the upper
+
+ align:start position:0%
+another level where I can see the upper
+ 
+
+ align:start position:0%
+another level where I can see the upper
+the 2:00 position in some particular
+
+ align:start position:0%
+the 2:00 position in some particular
+ 
+
+ align:start position:0%
+the 2:00 position in some particular
+hole and can you do those all
+
+ align:start position:0%
+hole and can you do those all
+ 
+
+ align:start position:0%
+hole and can you do those all
+simultaneously or what and uh I've there
+
+ align:start position:0%
+simultaneously or what and uh I've there
+ 
+
+ align:start position:0%
+simultaneously or what and uh I've there
+are a lot of theories about
+
+ align:start position:0%
+are a lot of theories about
+ 
+
+ align:start position:0%
+are a lot of theories about
+uh how you perceive edges and in fact
+
+ align:start position:0%
+uh how you perceive edges and in fact
+ 
+
+ align:start position:0%
+uh how you perceive edges and in fact
+uh really there are two parts of the
+
+ align:start position:0%
+uh really there are two parts of the
+ 
+
+ align:start position:0%
+uh really there are two parts of the
+brain that are pretty well understood
+
+ align:start position:0%
+brain that are pretty well understood
+ 
+
+ align:start position:0%
+brain that are pretty well understood
+and one is the lowest level visual
+
+ align:start position:0%
+and one is the lowest level visual
+ 
+
+ align:start position:0%
+and one is the lowest level visual
+processing stuff because they're uh you
+
+ align:start position:0%
+processing stuff because they're uh you
+ 
+
+ align:start position:0%
+processing stuff because they're uh you
+can experiment in lower animals and show
+
+ align:start position:0%
+can experiment in lower animals and show
+ 
+
+ align:start position:0%
+can experiment in lower animals and show
+patterns and and it's known that certain
+
+ align:start position:0%
+patterns and and it's known that certain
+ 
+
+ align:start position:0%
+patterns and and it's known that certain
+particular cells in the retina do such
+
+ align:start position:0%
+particular cells in the retina do such
+ 
+
+ align:start position:0%
+particular cells in the retina do such
+and such and it's also known that
+
+ align:start position:0%
+and such and it's also known that
+ 
+
+ align:start position:0%
+and such and it's also known that
+certain particular groups of cells in
+
+ align:start position:0%
+certain particular groups of cells in
+ 
+
+ align:start position:0%
+certain particular groups of cells in
+the visual cortex compute certain
+
+ align:start position:0%
+the visual cortex compute certain
+ 
+
+ align:start position:0%
+the visual cortex compute certain
+functions and that's fairly solid
+
+ align:start position:0%
+functions and that's fairly solid
+ 
+
+ align:start position:0%
+functions and that's fairly solid
+there's hardly any other area of the
+
+ align:start position:0%
+there's hardly any other area of the
+ 
+
+ align:start position:0%
+there's hardly any other area of the
+brain where you can say what any
+
+ align:start position:0%
+brain where you can say what any
+ 
+
+ align:start position:0%
+brain where you can say what any
+particular bunch of cells
+
+ align:start position:0%
+particular bunch of cells
+ 
+
+ align:start position:0%
+particular bunch of cells
+do auditory cortex is the auditory
+
+ align:start position:0%
+do auditory cortex is the auditory
+ 
+
+ align:start position:0%
+do auditory cortex is the auditory
+cortex also and there's a little there's
+
+ align:start position:0%
+cortex also and there's a little there's
+ 
+
+ align:start position:0%
+cortex also and there's a little there's
+rather lot known about the cerebellum
+
+ align:start position:0%
+rather lot known about the cerebellum
+ 
+
+ align:start position:0%
+rather lot known about the cerebellum
+but I haven't kept up with it
+
+ align:start position:0%
+but I haven't kept up with it
+ 
+
+ align:start position:0%
+but I haven't kept up with it
+uh but I don't think there's any
+
+ align:start position:0%
+uh but I don't think there's any
+ 
+
+ align:start position:0%
+uh but I don't think there's any
+substantial amount of knowledge about
+
+ align:start position:0%
+substantial amount of knowledge about
+ 
+
+ align:start position:0%
+substantial amount of knowledge about
+what happens in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the in the memory systems we don't know
+
+ align:start position:0%
+the in the memory systems we don't know
+ 
+
+ align:start position:0%
+the in the memory systems we don't know
+how anything's represented and in the uh
+
+ align:start position:0%
+how anything's represented and in the uh
+ 
+
+ align:start position:0%
+how anything's represented and in the uh
+reasoning systems and prediction systems
+
+ align:start position:0%
+reasoning systems and prediction systems
+ 
+
+ align:start position:0%
+reasoning systems and prediction systems
+in the frontal cortex so the sensory
+
+ align:start position:0%
+in the frontal cortex so the sensory
+ 
+
+ align:start position:0%
+in the frontal cortex so the sensory
+systems are nice because you can uh put
+
+ align:start position:0%
+systems are nice because you can uh put
+ 
+
+ align:start position:0%
+systems are nice because you can uh put
+a cat in a Vice and and have sensory
+
+ align:start position:0%
+a cat in a Vice and and have sensory
+ 
+
+ align:start position:0%
+a cat in a Vice and and have sensory
+inputs and see what happens it's much
+
+ align:start position:0%
+inputs and see what happens it's much
+ 
+
+ align:start position:0%
+inputs and see what happens it's much
+harder to get the cat to move its little
+
+ align:start position:0%
+harder to get the cat to move its little
+ 
+
+ align:start position:0%
+harder to get the cat to move its little
+finger and
+
+ align:start position:0%
+finger and
+ 
+
+ align:start position:0%
+finger and
+see how it decided to do that if you put
+
+ align:start position:0%
+see how it decided to do that if you put
+ 
+
+ align:start position:0%
+see how it decided to do that if you put
+a signal into the motor
+
+ align:start position:0%
+a signal into the motor
+ 
+
+ align:start position:0%
+a signal into the motor
+cortex uh you can find a place that
+
+ align:start position:0%
+cortex uh you can find a place that
+ 
+
+ align:start position:0%
+cortex uh you can find a place that
+makes that muscle move I'm not sure you
+
+ align:start position:0%
+makes that muscle move I'm not sure you
+ 
+
+ align:start position:0%
+makes that muscle move I'm not sure you
+can but you know certainly in the spinal
+
+ align:start position:0%
+can but you know certainly in the spinal
+ 
+
+ align:start position:0%
+can but you know certainly in the spinal
+cord you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can so that leads to the idea of mental
+
+ align:start position:0%
+can so that leads to the idea of mental
+ 
+
+ align:start position:0%
+can so that leads to the idea of mental
+critics and things like that which I
+
+ align:start position:0%
+critics and things like that which I
+ 
+
+ align:start position:0%
+critics and things like that which I
+really didn't develop till a couple of
+
+ align:start position:0%
+really didn't develop till a couple of
+ 
+
+ align:start position:0%
+really didn't develop till a couple of
+chapters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later the neuroscientists know a whole
+
+ align:start position:0%
+later the neuroscientists know a whole
+ 
+
+ align:start position:0%
+later the neuroscientists know a whole
+lot it seems like there's so much data
+
+ align:start position:0%
+lot it seems like there's so much data
+ 
+
+ align:start position:0%
+lot it seems like there's so much data
+that collected well but we don't know
+
+ align:start position:0%
+that collected well but we don't know
+ 
+
+ align:start position:0%
+that collected well but we don't know
+that they I'm not sure how much they
+
+ align:start position:0%
+that they I'm not sure how much they
+ 
+
+ align:start position:0%
+that they I'm not sure how much they
+know because their experiments are so
+
+ align:start position:0%
+know because their experiments are so
+ 
+
+ align:start position:0%
+know because their experiments are so
+ambiguous right it's not as very useful
+
+ align:start position:0%
+ambiguous right it's not as very useful
+ 
+
+ align:start position:0%
+ambiguous right it's not as very useful
+it's not put together but there's a lot
+
+ align:start position:0%
+it's not put together but there's a lot
+ 
+
+ align:start position:0%
+it's not put together but there's a lot
+of it just sitting there right there's a
+
+ align:start position:0%
+of it just sitting there right there's a
+ 
+
+ align:start position:0%
+of it just sitting there right there's a
+lot of experiments that's been done yeah
+
+ align:start position:0%
+lot of experiments that's been done yeah
+ 
+
+ align:start position:0%
+lot of experiments that's been done yeah
+but I'm not sure it has knowledge in
+
+ align:start position:0%
+but I'm not sure it has knowledge in
+ 
+
+ align:start position:0%
+but I'm not sure it has knowledge in
+other words if you don't if you don't
+
+ align:start position:0%
+other words if you don't if you don't
+ 
+
+ align:start position:0%
+other words if you don't if you don't
+design an experiment to see if you're
+
+ align:start position:0%
+design an experiment to see if you're
+ 
+
+ align:start position:0%
+design an experiment to see if you're
+using a hash code you'll never find it
+
+ align:start position:0%
+using a hash code you'll never find it
+ 
+
+ align:start position:0%
+using a hash code you'll never find it
+no matter how much data you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's well
+
+ align:start position:0%
+it's well
+ 
+
+ align:start position:0%
+it's well
+uh in fact there are people who are
+
+ align:start position:0%
+uh in fact there are people who are
+ 
+
+ align:start position:0%
+uh in fact there are people who are
+talking about making a Big Data Bank of
+
+ align:start position:0%
+talking about making a Big Data Bank of
+ 
+
+ align:start position:0%
+talking about making a Big Data Bank of
+all that stuff getting all the
+
+ align:start position:0%
+all that stuff getting all the
+ 
+
+ align:start position:0%
+all that stuff getting all the
+neurologists to give all their data and
+
+ align:start position:0%
+neurologists to give all their data and
+ 
+
+ align:start position:0%
+neurologists to give all their data and
+it's a open question of whether someone
+
+ align:start position:0%
+it's a open question of whether someone
+ 
+
+ align:start position:0%
+it's a open question of whether someone
+will discover something from it I think
+
+ align:start position:0%
+will discover something from it I think
+ 
+
+ align:start position:0%
+will discover something from it I think
+the you might discover a lot
+
+ align:start position:0%
+the you might discover a lot
+ 
+
+ align:start position:0%
+the you might discover a lot
+if sort of uh a little bit like what Deb
+
+ align:start position:0%
+if sort of uh a little bit like what Deb
+ 
+
+ align:start position:0%
+if sort of uh a little bit like what Deb
+Roy is
+
+ align:start position:0%
+Roy is
+ 
+
+ align:start position:0%
+Roy is
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+except if you had somebody wear an
+
+ align:start position:0%
+except if you had somebody wear an
+ 
+
+ align:start position:0%
+except if you had somebody wear an
+electro if you had somebody wearing a
+
+ align:start position:0%
+electro if you had somebody wearing a
+ 
+
+ align:start position:0%
+electro if you had somebody wearing a
+helmet that picked up say a couple of
+
+ align:start position:0%
+helmet that picked up say a couple of
+ 
+
+ align:start position:0%
+helmet that picked up say a couple of
+thousand signals from the
+
+ align:start position:0%
+thousand signals from the
+ 
+
+ align:start position:0%
+thousand signals from the
+brain I'm not sure you can do it from
+
+ align:start position:0%
+brain I'm not sure you can do it from
+ 
+
+ align:start position:0%
+brain I'm not sure you can do it from
+the scalp but I wouldn't be surprised if
+
+ align:start position:0%
+the scalp but I wouldn't be surprised if
+ 
+
+ align:start position:0%
+the scalp but I wouldn't be surprised if
+you could get a lot and then you have a
+
+ align:start position:0%
+you could get a lot and then you have a
+ 
+
+ align:start position:0%
+you could get a lot and then you have a
+person walk around for a year and record
+
+ align:start position:0%
+person walk around for a year and record
+ 
+
+ align:start position:0%
+person walk around for a year and record
+everything that the person sees and
+
+ align:start position:0%
+everything that the person sees and
+ 
+
+ align:start position:0%
+everything that the person sees and
+everything that they hear then maybe you
+
+ align:start position:0%
+everything that they hear then maybe you
+ 
+
+ align:start position:0%
+everything that they hear then maybe you
+could use something like the deep blue
+
+ align:start position:0%
+could use something like the deep blue
+ 
+
+ align:start position:0%
+could use something like the deep blue
+computer or the blue jean computer or
+
+ align:start position:0%
+computer or the blue jean computer or
+ 
+
+ align:start position:0%
+computer or the blue jean computer or
+whatever to look for correlations that
+
+ align:start position:0%
+whatever to look for correlations that
+ 
+
+ align:start position:0%
+whatever to look for correlations that
+say is there some complicated brain
+
+ align:start position:0%
+say is there some complicated brain
+ 
+
+ align:start position:0%
+say is there some complicated brain
+pattern that occurred most of the times
+
+ align:start position:0%
+pattern that occurred most of the times
+ 
+
+ align:start position:0%
+pattern that occurred most of the times
+when the person said I need coffee or
+
+ align:start position:0%
+when the person said I need coffee or
+ 
+
+ align:start position:0%
+when the person said I need coffee or
+what find some event that happens a few
+
+ align:start position:0%
+what find some event that happens a few
+ 
+
+ align:start position:0%
+what find some event that happens a few
+hundred times in the year and U see if
+
+ align:start position:0%
+hundred times in the year and U see if
+ 
+
+ align:start position:0%
+hundred times in the year and U see if
+you can track that down so I think a
+
+ align:start position:0%
+you can track that down so I think a
+ 
+
+ align:start position:0%
+you can track that down so I think a
+database like that might be good uh but
+
+ align:start position:0%
+database like that might be good uh but
+ 
+
+ align:start position:0%
+database like that might be good uh but
+paradoxically I think having a database
+
+ align:start position:0%
+paradoxically I think having a database
+ 
+
+ align:start position:0%
+paradoxically I think having a database
+of all the neurological
+
+ align:start position:0%
+of all the neurological
+ 
+
+ align:start position:0%
+of all the neurological
+experiences
+
+ align:start position:0%
+experiences
+ 
+
+ align:start position:0%
+experiences
+uh would tell you
+
+ align:start position:0%
+uh would tell you
+ 
+
+ align:start position:0%
+uh would tell you
+about would only confirm or disconfirm
+
+ align:start position:0%
+about would only confirm or disconfirm
+ 
+
+ align:start position:0%
+about would only confirm or disconfirm
+uh lowlevel Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in chapter 4 there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of what might be involved in the
+
+ align:start position:0%
+of of what might be involved in the
+ 
+
+ align:start position:0%
+of of what might be involved in the
+brain's Evolution and it's not a very
+
+ align:start position:0%
+brain's Evolution and it's not a very
+ 
+
+ align:start position:0%
+brain's Evolution and it's not a very
+good discussion because for some reason
+
+ align:start position:0%
+good discussion because for some reason
+ 
+
+ align:start position:0%
+good discussion because for some reason
+I cut
+
+ align:start position:0%
+I cut
+ 
+
+ align:start position:0%
+I cut
+out this important thing did I talk
+
+ align:start position:0%
+out this important thing did I talk
+ 
+
+ align:start position:0%
+out this important thing did I talk
+about this the other
+
+ align:start position:0%
+about this the other
+ 
+
+ align:start position:0%
+about this the other
+day that genetics is in some sense
+
+ align:start position:0%
+day that genetics is in some sense
+ 
+
+ align:start position:0%
+day that genetics is in some sense
+always at a dead
+
+ align:start position:0%
+always at a dead
+ 
+
+ align:start position:0%
+always at a dead
+end because uh if you take any
+
+ align:start position:0%
+end because uh if you take any
+ 
+
+ align:start position:0%
+end because uh if you take any
+particular piece of Machinery in the
+
+ align:start position:0%
+particular piece of Machinery in the
+ 
+
+ align:start position:0%
+particular piece of Machinery in the
+body it's probably been optimized for uh
+
+ align:start position:0%
+body it's probably been optimized for uh
+ 
+
+ align:start position:0%
+body it's probably been optimized for uh
+10,000 Years or or
+
+ align:start position:0%
+10,000 Years or or
+ 
+
+ align:start position:0%
+10,000 Years or or
+more because every now and then there's
+
+ align:start position:0%
+more because every now and then there's
+ 
+
+ align:start position:0%
+more because every now and then there's
+a little variation in some protein some
+
+ align:start position:0%
+a little variation in some protein some
+ 
+
+ align:start position:0%
+a little variation in some protein some
+Gene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which changes some protein which changes
+
+ align:start position:0%
+which changes some protein which changes
+ 
+
+ align:start position:0%
+which changes some protein which changes
+a little bit how something works and if
+
+ align:start position:0%
+a little bit how something works and if
+ 
+
+ align:start position:0%
+a little bit how something works and if
+this Gene is slightly
+
+ align:start position:0%
+this Gene is slightly
+ 
+
+ align:start position:0%
+this Gene is slightly
+better than the other Gene it has a
+
+ align:start position:0%
+better than the other Gene it has a
+ 
+
+ align:start position:0%
+better than the other Gene it has a
+fairly big chance of spreading through
+
+ align:start position:0%
+fairly big chance of spreading through
+ 
+
+ align:start position:0%
+fairly big chance of spreading through
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+population people used to think that
+
+ align:start position:0%
+population people used to think that
+ 
+
+ align:start position:0%
+population people used to think that
+Evolution was slow and then uh some new
+
+ align:start position:0%
+Evolution was slow and then uh some new
+ 
+
+ align:start position:0%
+Evolution was slow and then uh some new
+mathematical insights came along and it
+
+ align:start position:0%
+mathematical insights came along and it
+ 
+
+ align:start position:0%
+mathematical insights came along and it
+turns out that natural selection is
+
+ align:start position:0%
+turns out that natural selection is
+ 
+
+ align:start position:0%
+turns out that natural selection is
+pretty fast there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I mentioned Dawkins experience
+
+ align:start position:0%
+I think I mentioned Dawkins experience
+ 
+
+ align:start position:0%
+I think I mentioned Dawkins experience
+somewhere in the book when he wrote this
+
+ align:start position:0%
+somewhere in the book when he wrote this
+ 
+
+ align:start position:0%
+somewhere in the book when he wrote this
+uh he wrote an evolutionary
+
+ align:start position:0%
+uh he wrote an evolutionary
+ 
+
+ align:start position:0%
+uh he wrote an evolutionary
+program which made little animals on
+
+ align:start position:0%
+program which made little animals on
+ 
+
+ align:start position:0%
+program which made little animals on
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+screen and actually these animals don't
+
+ align:start position:0%
+screen and actually these animals don't
+ 
+
+ align:start position:0%
+screen and actually these animals don't
+function they're just Graphics but uh
+
+ align:start position:0%
+function they're just Graphics but uh
+ 
+
+ align:start position:0%
+function they're just Graphics but uh
+what the machine does what the program
+
+ align:start position:0%
+what the machine does what the program
+ 
+
+ align:start position:0%
+what the machine does what the program
+does is it makes uh more or less random
+
+ align:start position:0%
+does is it makes uh more or less random
+ 
+
+ align:start position:0%
+does is it makes uh more or less random
+variations of the description of a line
+
+ align:start position:0%
+variations of the description of a line
+ 
+
+ align:start position:0%
+variations of the description of a line
+drawing so uh it's like a it draws them
+
+ align:start position:0%
+drawing so uh it's like a it draws them
+ 
+
+ align:start position:0%
+drawing so uh it's like a it draws them
+like sort of like logo programs uh draw
+
+ align:start position:0%
+like sort of like logo programs uh draw
+ 
+
+ align:start position:0%
+like sort of like logo programs uh draw
+a line this long turn here uh Branch
+
+ align:start position:0%
+a line this long turn here uh Branch
+ 
+
+ align:start position:0%
+a line this long turn here uh Branch
+another one from it and so forth and uh
+
+ align:start position:0%
+another one from it and so forth and uh
+ 
+
+ align:start position:0%
+another one from it and so forth and uh
+so when you turn it on it puts up about
+
+ align:start position:0%
+so when you turn it on it puts up about
+ 
+
+ align:start position:0%
+so when you turn it on it puts up about
+20 lines which are sort of connected but
+
+ align:start position:0%
+20 lines which are sort of connected but
+ 
+
+ align:start position:0%
+20 lines which are sort of connected but
+don't make any sense and uh the idea was
+
+ align:start position:0%
+don't make any sense and uh the idea was
+ 
+
+ align:start position:0%
+don't make any sense and uh the idea was
+that it starts with one pattern you
+
+ align:start position:0%
+that it starts with one pattern you
+ 
+
+ align:start position:0%
+that it starts with one pattern you
+press this button and it makes 25
+
+ align:start position:0%
+press this button and it makes 25
+ 
+
+ align:start position:0%
+press this button and it makes 25
+variations of it the original is in the
+
+ align:start position:0%
+variations of it the original is in the
+ 
+
+ align:start position:0%
+variations of it the original is in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+that was because uh that's what he could
+
+ align:start position:0%
+that was because uh that's what he could
+ 
+
+ align:start position:0%
+that was because uh that's what he could
+do on
+
+ align:start position:0%
+do on
+ 
+
+ align:start position:0%
+do on
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh on the computer screens in the
+
+ align:start position:0%
+uh on the computer screens in the
+ 
+
+ align:start position:0%
+uh on the computer screens in the
+1980s 90s I guess and
+
+ align:start position:0%
+1980s 90s I guess and
+ 
+
+ align:start position:0%
+1980s 90s I guess and
+uh then you pick the one you like best
+
+ align:start position:0%
+uh then you pick the one you like best
+ 
+
+ align:start position:0%
+uh then you pick the one you like best
+of the 25 and here's what happens
+
+ align:start position:0%
+of the 25 and here's what happens
+ 
+
+ align:start position:0%
+of the 25 and here's what happens
+suppose there's this mess of of sort of
+
+ align:start position:0%
+suppose there's this mess of of sort of
+ 
+
+ align:start position:0%
+suppose there's this mess of of sort of
+little tree
+
+ align:start position:0%
+little tree
+ 
+
+ align:start position:0%
+little tree
+of uh that looks random and you say I'm
+
+ align:start position:0%
+of uh that looks random and you say I'm
+ 
+
+ align:start position:0%
+of uh that looks random and you say I'm
+thinking of a frog or I'm thinking of a
+
+ align:start position:0%
+thinking of a frog or I'm thinking of a
+ 
+
+ align:start position:0%
+thinking of a frog or I'm thinking of a
+spider or I'm thinking of a
+
+ align:start position:0%
+spider or I'm thinking of a
+ 
+
+ align:start position:0%
+spider or I'm thinking of a
+chair you say well uh I'd like to draw a
+
+ align:start position:0%
+chair you say well uh I'd like to draw a
+ 
+
+ align:start position:0%
+chair you say well uh I'd like to draw a
+chair and then you say well this is a
+
+ align:start position:0%
+chair and then you say well this is a
+ 
+
+ align:start position:0%
+chair and then you say well this is a
+little more like a chair than those
+
+ align:start position:0%
+little more like a chair than those
+ 
+
+ align:start position:0%
+little more like a chair than those
+other 24 you pick that and you type it
+
+ align:start position:0%
+other 24 you pick that and you type it
+ 
+
+ align:start position:0%
+other 24 you pick that and you type it
+again uh then you get mutations of that
+
+ align:start position:0%
+again uh then you get mutations of that
+ 
+
+ align:start position:0%
+again uh then you get mutations of that
+and you pick another one of the 25 guess
+
+ align:start position:0%
+and you pick another one of the 25 guess
+ 
+
+ align:start position:0%
+and you pick another one of the 25 guess
+how long it takes before it looks like a
+
+ align:start position:0%
+how long it takes before it looks like a
+ 
+
+ align:start position:0%
+how long it takes before it looks like a
+crab if that's what you were thinking
+
+ align:start position:0%
+crab if that's what you were thinking
+ 
+
+ align:start position:0%
+crab if that's what you were thinking
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's it's about 50 uh but sometimes
+
+ align:start position:0%
+well it's it's about 50 uh but sometimes
+ 
+
+ align:start position:0%
+well it's it's about 50 uh but sometimes
+20 it's not a
+
+ align:start position:0%
+20 it's not a
+ 
+
+ align:start position:0%
+20 it's not a
+thousand and uh Dawkins knew about
+
+ align:start position:0%
+thousand and uh Dawkins knew about
+ 
+
+ align:start position:0%
+thousand and uh Dawkins knew about
+genetics and uh all
+
+ align:start position:0%
+genetics and uh all
+ 
+
+ align:start position:0%
+genetics and uh all
+geneticists uh at that time thought
+
+ align:start position:0%
+geneticists uh at that time thought
+ 
+
+ align:start position:0%
+geneticists uh at that time thought
+evolution is fairly slow as far as I
+
+ align:start position:0%
+evolution is fairly slow as far as I
+ 
+
+ align:start position:0%
+evolution is fairly slow as far as I
+know U and he didn't expect this to
+
+ align:start position:0%
+know U and he didn't expect this to
+ 
+
+ align:start position:0%
+know U and he didn't expect this to
+happen in 20 or 50 trials it's and uh he
+
+ align:start position:0%
+happen in 20 or 50 trials it's and uh he
+ 
+
+ align:start position:0%
+happen in 20 or 50 trials it's and uh he
+said that was the uh most astonishing
+
+ align:start position:0%
+said that was the uh most astonishing
+ 
+
+ align:start position:0%
+said that was the uh most astonishing
+experience it was a
+
+ align:start position:0%
+experience it was a
+ 
+
+ align:start position:0%
+experience it was a
+revelation a religious conversion
+
+ align:start position:0%
+revelation a religious conversion
+ 
+
+ align:start position:0%
+revelation a religious conversion
+literally I
+
+ align:start position:0%
+literally I
+ 
+
+ align:start position:0%
+literally I
+suppose and uh quite a remarkable event
+
+ align:start position:0%
+suppose and uh quite a remarkable event
+ 
+
+ align:start position:0%
+suppose and uh quite a remarkable event
+uh you can get a copy of that I think
+
+ align:start position:0%
+uh you can get a copy of that I think
+ 
+
+ align:start position:0%
+uh you can get a copy of that I think
+somewhere is it on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+web I would look but I
+
+ align:start position:0%
+web I would look but I
+ 
+
+ align:start position:0%
+web I would look but I
+won't uh
+
+ align:start position:0%
+won't uh
+ 
+
+ align:start position:0%
+won't uh
+however the next step was that he said
+
+ align:start position:0%
+however the next step was that he said
+ 
+
+ align:start position:0%
+however the next step was that he said
+well of course this just looks like a
+
+ align:start position:0%
+well of course this just looks like a
+ 
+
+ align:start position:0%
+well of course this just looks like a
+frog uh I want one that can jump like a
+
+ align:start position:0%
+frog uh I want one that can jump like a
+ 
+
+ align:start position:0%
+frog uh I want one that can jump like a
+frog and so he was for years he thought
+
+ align:start position:0%
+frog and so he was for years he thought
+ 
+
+ align:start position:0%
+frog and so he was for years he thought
+about making the program such that the
+
+ align:start position:0%
+about making the program such that the
+ 
+
+ align:start position:0%
+about making the program such that the
+creatures actually did anything and he
+
+ align:start position:0%
+creatures actually did anything and he
+ 
+
+ align:start position:0%
+creatures actually did anything and he
+never got around to it and
+
+ align:start position:0%
+never got around to it and
+ 
+
+ align:start position:0%
+never got around to it and
+uh finally some other people did so he
+
+ align:start position:0%
+uh finally some other people did so he
+ 
+
+ align:start position:0%
+uh finally some other people did so he
+didn't have
+
+ align:start position:0%
+didn't have
+ 
+
+ align:start position:0%
+didn't have
+to what's Patty May's husband
+
+ align:start position:0%
+to what's Patty May's husband
+ 
+
+ align:start position:0%
+to what's Patty May's husband
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+damn what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h no h uh I'll remember before the end
+
+ align:start position:0%
+h no h uh I'll remember before the end
+ 
+
+ align:start position:0%
+h no h uh I'll remember before the end
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+um he made
+
+ align:start position:0%
+um he made
+ 
+
+ align:start position:0%
+um he made
+uh he made sort of little animals and he
+
+ align:start position:0%
+uh he made sort of little animals and he
+ 
+
+ align:start position:0%
+uh he made sort of little animals and he
+selected the ones that could win
+
+ align:start position:0%
+selected the ones that could win
+ 
+
+ align:start position:0%
+selected the ones that could win
+Races they would move at random and
+
+ align:start position:0%
+Races they would move at random and
+ 
+
+ align:start position:0%
+Races they would move at random and
+after a while some of them uh they had
+
+ align:start position:0%
+after a while some of them uh they had
+ 
+
+ align:start position:0%
+after a while some of them uh they had
+to cross a Finish
+
+ align:start position:0%
+to cross a Finish
+ 
+
+ align:start position:0%
+to cross a Finish
+Line uh then they would mutate their
+
+ align:start position:0%
+Line uh then they would mutate their
+ 
+
+ align:start position:0%
+Line uh then they would mutate their
+structure and add parts and crawl along
+
+ align:start position:0%
+structure and add parts and crawl along
+ 
+
+ align:start position:0%
+structure and add parts and crawl along
+and the Annoying Thing at least in the
+
+ align:start position:0%
+and the Annoying Thing at least in the
+ 
+
+ align:start position:0%
+and the Annoying Thing at least in the
+early stages is
+
+ align:start position:0%
+early stages is
+ 
+
+ align:start position:0%
+early stages is
+uh in his early experiments the thing
+
+ align:start position:0%
+uh in his early experiments the thing
+ 
+
+ align:start position:0%
+uh in his early experiments the thing
+that won was one that built that kept
+
+ align:start position:0%
+that won was one that built that kept
+ 
+
+ align:start position:0%
+that won was one that built that kept
+growing taller and taller until it fell
+
+ align:start position:0%
+growing taller and taller until it fell
+ 
+
+ align:start position:0%
+growing taller and taller until it fell
+over and its nose was across the finish
+
+ align:start position:0%
+over and its nose was across the finish
+ 
+
+ align:start position:0%
+over and its nose was across the finish
+line and uh all the other species were
+
+ align:start position:0%
+line and uh all the other species were
+ 
+
+ align:start position:0%
+line and uh all the other species were
+clumsily trying to learn to walk or
+
+ align:start position:0%
+clumsily trying to learn to walk or
+ 
+
+ align:start position:0%
+clumsily trying to learn to walk or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and this creature uh found another
+
+ align:start position:0%
+and this creature uh found another
+ 
+
+ align:start position:0%
+and this creature uh found another
+principle entirely of course it didn't
+
+ align:start position:0%
+principle entirely of course it didn't
+ 
+
+ align:start position:0%
+principle entirely of course it didn't
+know what it was
+
+ align:start position:0%
+know what it was
+ 
+
+ align:start position:0%
+know what it was
+doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh with real robots uh that's uh has a
+
+ align:start position:0%
+uh with real robots uh that's uh has a
+ 
+
+ align:start position:0%
+uh with real robots uh that's uh has a
+program that generates the shapes and
+
+ align:start position:0%
+program that generates the shapes and
+ 
+
+ align:start position:0%
+program that generates the shapes and
+then the 3D printer builds the actual
+
+ align:start position:0%
+then the 3D printer builds the actual
+ 
+
+ align:start position:0%
+then the 3D printer builds the actual
+yes yes that's uh Jordan Pollock at
+
+ align:start position:0%
+yes yes that's uh Jordan Pollock at
+ 
+
+ align:start position:0%
+yes yes that's uh Jordan Pollock at
+brandise or wherever he ising a coral
+
+ align:start position:0%
+brandise or wherever he ising a coral
+ 
+
+ align:start position:0%
+brandise or wherever he ising a coral
+well gu lots of people are doing this
+
+ align:start position:0%
+well gu lots of people are doing this
+ 
+
+ align:start position:0%
+well gu lots of people are doing this
+stuff maybe he's there now but it it was
+
+ align:start position:0%
+stuff maybe he's there now but it it was
+ 
+
+ align:start position:0%
+stuff maybe he's there now but it it was
+Jordan Paul like about two years ago I
+
+ align:start position:0%
+Jordan Paul like about two years ago I
+ 
+
+ align:start position:0%
+Jordan Paul like about two years ago I
+was really annoyed because got an
+
+ align:start position:0%
+was really annoyed because got an
+ 
+
+ align:start position:0%
+was really annoyed because got an
+enormous amount of attention and it
+
+ align:start position:0%
+enormous amount of attention and it
+ 
+
+ align:start position:0%
+enormous amount of attention and it
+didn't have any I mean he's a brilliant
+
+ align:start position:0%
+didn't have any I mean he's a brilliant
+ 
+
+ align:start position:0%
+didn't have any I mean he's a brilliant
+guy and he's uh he's the co-author of
+
+ align:start position:0%
+guy and he's uh he's the co-author of
+ 
+
+ align:start position:0%
+guy and he's uh he's the co-author of
+the Walts and Pollock
+
+ align:start position:0%
+the Walts and Pollock
+ 
+
+ align:start position:0%
+the Walts and Pollock
+Paper uh on micrones which or micro
+
+ align:start position:0%
+Paper uh on micrones which or micro
+ 
+
+ align:start position:0%
+Paper uh on micrones which or micro
+features which was a great idea about uh
+
+ align:start position:0%
+features which was a great idea about uh
+ 
+
+ align:start position:0%
+features which was a great idea about uh
+representing meanings but I was sort of
+
+ align:start position:0%
+representing meanings but I was sort of
+ 
+
+ align:start position:0%
+representing meanings but I was sort of
+annoyed because
+
+ align:start position:0%
+annoyed because
+ 
+
+ align:start position:0%
+annoyed because
+uh this particular stunt didn't have any
+
+ align:start position:0%
+uh this particular stunt didn't have any
+ 
+
+ align:start position:0%
+uh this particular stunt didn't have any
+new idea but it was Fusion of two great
+
+ align:start position:0%
+new idea but it was Fusion of two great
+ 
+
+ align:start position:0%
+new idea but it was Fusion of two great
+Technologies he had to put the motors in
+
+ align:start position:0%
+Technologies he had to put the motors in
+ 
+
+ align:start position:0%
+Technologies he had to put the motors in
+by hand
+
+ align:start position:0%
+by hand
+ 
+
+ align:start position:0%
+by hand
+though right so it evolved this thing
+
+ align:start position:0%
+though right so it evolved this thing
+ 
+
+ align:start position:0%
+though right so it evolved this thing
+and then the 3D printer made it and and
+
+ align:start position:0%
+and then the 3D printer made it and and
+ 
+
+ align:start position:0%
+and then the 3D printer made it and and
+it crawled
+
+ align:start position:0%
+it crawled
+ 
+
+ align:start position:0%
+it crawled
+around uh this is a very
+
+ align:start position:0%
+around uh this is a very
+ 
+
+ align:start position:0%
+around uh this is a very
+important principle that is probably not
+
+ align:start position:0%
+important principle that is probably not
+ 
+
+ align:start position:0%
+important principle that is probably not
+taught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in you know there's a great controversy
+
+ align:start position:0%
+in you know there's a great controversy
+ 
+
+ align:start position:0%
+in you know there's a great controversy
+about whether you should teach evolution
+
+ align:start position:0%
+about whether you should teach evolution
+ 
+
+ align:start position:0%
+about whether you should teach evolution
+in schools in the Bible
+
+ align:start position:0%
+in schools in the Bible
+ 
+
+ align:start position:0%
+in schools in the Bible
+Belt but one question is what are they
+
+ align:start position:0%
+Belt but one question is what are they
+ 
+
+ align:start position:0%
+Belt but one question is what are they
+going to teach because the Machinery of
+
+ align:start position:0%
+going to teach because the Machinery of
+ 
+
+ align:start position:0%
+going to teach because the Machinery of
+of genetics is really very complicated
+
+ align:start position:0%
+of genetics is really very complicated
+ 
+
+ align:start position:0%
+of genetics is really very complicated
+and clever by now and there are all
+
+ align:start position:0%
+and clever by now and there are all
+ 
+
+ align:start position:0%
+and clever by now and there are all
+sorts of uh wonderful pieces of
+
+ align:start position:0%
+sorts of uh wonderful pieces of
+ 
+
+ align:start position:0%
+sorts of uh wonderful pieces of
+Machinery in it and just
+
+ align:start position:0%
+Machinery in it and just
+ 
+
+ align:start position:0%
+Machinery in it and just
+teaching
+
+ align:start position:0%
+teaching
+ 
+
+ align:start position:0%
+teaching
+uh what a Dawkins call it the blind
+
+ align:start position:0%
+uh what a Dawkins call it the blind
+ 
+
+ align:start position:0%
+uh what a Dawkins call it the blind
+watch maker just showing that things can
+
+ align:start position:0%
+watch maker just showing that things can
+ 
+
+ align:start position:0%
+watch maker just showing that things can
+evolve
+
+ align:start position:0%
+evolve
+ 
+
+ align:start position:0%
+evolve
+uh doesn't uh tell you how wonderful
+
+ align:start position:0%
+uh doesn't uh tell you how wonderful
+ 
+
+ align:start position:0%
+uh doesn't uh tell you how wonderful
+the actual process that has evolved so
+
+ align:start position:0%
+the actual process that has evolved so
+ 
+
+ align:start position:0%
+the actual process that has evolved so
+this is an example of
+
+ align:start position:0%
+this is an example of
+ 
+
+ align:start position:0%
+this is an example of
+a a problem in genetics which is that uh
+
+ align:start position:0%
+a a problem in genetics which is that uh
+ 
+
+ align:start position:0%
+a a problem in genetics which is that uh
+almost all mutations are
+
+ align:start position:0%
+almost all mutations are
+ 
+
+ align:start position:0%
+almost all mutations are
+bad and the longer you wait the less
+
+ align:start position:0%
+bad and the longer you wait the less
+ 
+
+ align:start position:0%
+bad and the longer you wait the less
+likely you are to find a new mutation
+
+ align:start position:0%
+likely you are to find a new mutation
+ 
+
+ align:start position:0%
+likely you are to find a new mutation
+well usually evolution is described in
+
+ align:start position:0%
+well usually evolution is described in
+ 
+
+ align:start position:0%
+well usually evolution is described in
+terms of changing
+
+ align:start position:0%
+terms of changing
+ 
+
+ align:start position:0%
+terms of changing
+genes and those are now called point
+
+ align:start position:0%
+genes and those are now called point
+ 
+
+ align:start position:0%
+genes and those are now called point
+mutations but
+
+ align:start position:0%
+mutations but
+ 
+
+ align:start position:0%
+mutations but
+the uh this example says
+
+ align:start position:0%
+the uh this example says
+ 
+
+ align:start position:0%
+the uh this example says
+uh it's just a I just made it up I don't
+
+ align:start position:0%
+uh it's just a I just made it up I don't
+ 
+
+ align:start position:0%
+uh it's just a I just made it up I don't
+know if there's any such situation but
+
+ align:start position:0%
+know if there's any such situation but
+ 
+
+ align:start position:0%
+know if there's any such situation but
+imagine that there's a certain protein
+
+ align:start position:0%
+imagine that there's a certain protein
+ 
+
+ align:start position:0%
+imagine that there's a certain protein
+made by a certain Gene and you know if a
+
+ align:start position:0%
+made by a certain Gene and you know if a
+ 
+
+ align:start position:0%
+made by a certain Gene and you know if a
+gene can make a protein
+
+ align:start position:0%
+gene can make a protein
+ 
+
+ align:start position:0%
+gene can make a protein
+then uh every cell has all the genes
+
+ align:start position:0%
+then uh every cell has all the genes
+ 
+
+ align:start position:0%
+then uh every cell has all the genes
+pretty much but uh as your as the animal
+
+ align:start position:0%
+pretty much but uh as your as the animal
+ 
+
+ align:start position:0%
+pretty much but uh as your as the animal
+uh goes through embryonic stages and
+
+ align:start position:0%
+uh goes through embryonic stages and
+ 
+
+ align:start position:0%
+uh goes through embryonic stages and
+makes different
+
+ align:start position:0%
+makes different
+ 
+
+ align:start position:0%
+makes different
+tissues uh lots of genes get shut off
+
+ align:start position:0%
+tissues uh lots of genes get shut off
+ 
+
+ align:start position:0%
+tissues uh lots of genes get shut off
+and stay shut off so that
+
+ align:start position:0%
+and stay shut off so that
+ 
+
+ align:start position:0%
+and stay shut off so that
+uh the your a cell in your liver might
+
+ align:start position:0%
+uh the your a cell in your liver might
+ 
+
+ align:start position:0%
+uh the your a cell in your liver might
+Express 5,000 genes and a cell in your
+
+ align:start position:0%
+Express 5,000 genes and a cell in your
+ 
+
+ align:start position:0%
+Express 5,000 genes and a cell in your
+uh brain might Express uh 5,000 genes
+
+ align:start position:0%
+uh brain might Express uh 5,000 genes
+ 
+
+ align:start position:0%
+uh brain might Express uh 5,000 genes
+and they might not have well some of
+
+ align:start position:0%
+and they might not have well some of
+ 
+
+ align:start position:0%
+and they might not have well some of
+them will be in common namely the the
+
+ align:start position:0%
+them will be in common namely the the
+ 
+
+ align:start position:0%
+them will be in common namely the the
+basic ones that control respiration and
+
+ align:start position:0%
+basic ones that control respiration and
+ 
+
+ align:start position:0%
+basic ones that control respiration and
+and keeping the cell alive so uh and
+
+ align:start position:0%
+and keeping the cell alive so uh and
+ 
+
+ align:start position:0%
+and keeping the cell alive so uh and
+those will be those will be the same as
+
+ align:start position:0%
+those will be those will be the same as
+ 
+
+ align:start position:0%
+those will be those will be the same as
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+lettuce most of your genes uh are the
+
+ align:start position:0%
+lettuce most of your genes uh are the
+ 
+
+ align:start position:0%
+lettuce most of your genes uh are the
+same virtually identical to the ones in
+
+ align:start position:0%
+same virtually identical to the ones in
+ 
+
+ align:start position:0%
+same virtually identical to the ones in
+the average vegetable but the uh in each
+
+ align:start position:0%
+the average vegetable but the uh in each
+ 
+
+ align:start position:0%
+the average vegetable but the uh in each
+particular cell line there's some
+
+ align:start position:0%
+particular cell line there's some
+ 
+
+ align:start position:0%
+particular cell line there's some
+particular ones that get expressed so
+
+ align:start position:0%
+particular ones that get expressed so
+ 
+
+ align:start position:0%
+particular ones that get expressed so
+suppose there's some that uh a protein
+
+ align:start position:0%
+suppose there's some that uh a protein
+ 
+
+ align:start position:0%
+suppose there's some that uh a protein
+that's involved in making your heart
+
+ align:start position:0%
+that's involved in making your heart
+ 
+
+ align:start position:0%
+that's involved in making your heart
+controlling the shape of your heart
+
+ align:start position:0%
+controlling the shape of your heart
+ 
+
+ align:start position:0%
+controlling the shape of your heart
+valve your mitro valve
+
+ align:start position:0%
+valve your mitro valve
+ 
+
+ align:start position:0%
+valve your mitro valve
+say then uh over the last
+
+ align:start position:0%
+say then uh over the last
+ 
+
+ align:start position:0%
+say then uh over the last
+uh 40 or 50 million years ever since
+
+ align:start position:0%
+uh 40 or 50 million years ever since
+ 
+
+ align:start position:0%
+uh 40 or 50 million years ever since
+mammals had the kind of four chambered
+
+ align:start position:0%
+mammals had the kind of four chambered
+ 
+
+ align:start position:0%
+mammals had the kind of four chambered
+hearts that they
+
+ align:start position:0%
+hearts that they
+ 
+
+ align:start position:0%
+hearts that they
+do uh this valve has been tuned up and
+
+ align:start position:0%
+do uh this valve has been tuned up and
+ 
+
+ align:start position:0%
+do uh this valve has been tuned up and
+it's been optimized and probably the
+
+ align:start position:0%
+it's been optimized and probably the
+ 
+
+ align:start position:0%
+it's been optimized and probably the
+slightest change in that protein will
+
+ align:start position:0%
+slightest change in that protein will
+ 
+
+ align:start position:0%
+slightest change in that protein will
+make your heart slightly less efficient
+
+ align:start position:0%
+make your heart slightly less efficient
+ 
+
+ align:start position:0%
+make your heart slightly less efficient
+and you'll be like less likely to
+
+ align:start position:0%
+and you'll be like less likely to
+ 
+
+ align:start position:0%
+and you'll be like less likely to
+survive in as many
+
+ align:start position:0%
+survive in as many
+ 
+
+ align:start position:0%
+survive in as many
+environments and the very same protein
+
+ align:start position:0%
+environments and the very same protein
+ 
+
+ align:start position:0%
+environments and the very same protein
+might be involved in uh some connective
+
+ align:start position:0%
+might be involved in uh some connective
+ 
+
+ align:start position:0%
+might be involved in uh some connective
+uh molecules that hold some neuron in
+
+ align:start position:0%
+uh molecules that hold some neuron in
+ 
+
+ align:start position:0%
+uh molecules that hold some neuron in
+place or anchor it to another kind of
+
+ align:start position:0%
+place or anchor it to another kind of
+ 
+
+ align:start position:0%
+place or anchor it to another kind of
+cell in the brain so that it can get uh
+
+ align:start position:0%
+cell in the brain so that it can get uh
+ 
+
+ align:start position:0%
+cell in the brain so that it can get uh
+nutrients from there or whatever but you
+
+ align:start position:0%
+nutrients from there or whatever but you
+ 
+
+ align:start position:0%
+nutrients from there or whatever but you
+see the point you might be using the
+
+ align:start position:0%
+see the point you might be using the
+ 
+
+ align:start position:0%
+see the point you might be using the
+same protein for two different
+
+ align:start position:0%
+same protein for two different
+ 
+
+ align:start position:0%
+same protein for two different
+purposes and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's happened is uh now imagine a a
+
+ align:start position:0%
+what's happened is uh now imagine a a
+ 
+
+ align:start position:0%
+what's happened is uh now imagine a a
+spectrum of variations of that Gene for
+
+ align:start position:0%
+spectrum of variations of that Gene for
+ 
+
+ align:start position:0%
+spectrum of variations of that Gene for
+the heart it might look like this and
+
+ align:start position:0%
+the heart it might look like this and
+ 
+
+ align:start position:0%
+the heart it might look like this and
+for the brain it might look like this so
+
+ align:start position:0%
+for the brain it might look like this so
+ 
+
+ align:start position:0%
+for the brain it might look like this so
+there is a mutated version of that
+
+ align:start position:0%
+there is a mutated version of that
+ 
+
+ align:start position:0%
+there is a mutated version of that
+protein that would be make your heart
+
+ align:start position:0%
+protein that would be make your heart
+ 
+
+ align:start position:0%
+protein that would be make your heart
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+but this one but it would be fairly bad
+
+ align:start position:0%
+but this one but it would be fairly bad
+ 
+
+ align:start position:0%
+but this one but it would be fairly bad
+uh for your cognitive processes on the
+
+ align:start position:0%
+uh for your cognitive processes on the
+ 
+
+ align:start position:0%
+uh for your cognitive processes on the
+other hand there might
+
+ align:start position:0%
+other hand there might
+ 
+
+ align:start position:0%
+other hand there might
+be a variation this this this is the
+
+ align:start position:0%
+be a variation this this this is the
+ 
+
+ align:start position:0%
+be a variation this this this is the
+same protein there might be a mutation
+
+ align:start position:0%
+same protein there might be a mutation
+ 
+
+ align:start position:0%
+same protein there might be a mutation
+of this which is very good for your
+
+ align:start position:0%
+of this which is very good for your
+ 
+
+ align:start position:0%
+of this which is very good for your
+brain and it would make you
+
+ align:start position:0%
+brain and it would make you
+ 
+
+ align:start position:0%
+brain and it would make you
+smarter uh but uh you might die if you
+
+ align:start position:0%
+smarter uh but uh you might die if you
+ 
+
+ align:start position:0%
+smarter uh but uh you might die if you
+ran up a hill because you're not getting
+
+ align:start position:0%
+ran up a hill because you're not getting
+ 
+
+ align:start position:0%
+ran up a hill because you're not getting
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+oxygen so in this sense the the gene
+
+ align:start position:0%
+oxygen so in this sense the the gene
+ 
+
+ align:start position:0%
+oxygen so in this sense the the gene
+that you end up
+
+ align:start position:0%
+that you end up
+ 
+
+ align:start position:0%
+that you end up
+with is not so good either for your
+
+ align:start position:0%
+with is not so good either for your
+ 
+
+ align:start position:0%
+with is not so good either for your
+heart or your brain but you're stuck
+
+ align:start position:0%
+heart or your brain but you're stuck
+ 
+
+ align:start position:0%
+heart or your brain but you're stuck
+with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and any Gene that's used for two
+
+ align:start position:0%
+and any Gene that's used for two
+ 
+
+ align:start position:0%
+and any Gene that's used for two
+purposes uh you're probably stuck with
+
+ align:start position:0%
+purposes uh you're probably stuck with
+ 
+
+ align:start position:0%
+purposes uh you're probably stuck with
+it because it's optimized
+
+ align:start position:0%
+it because it's optimized
+ 
+
+ align:start position:0%
+it because it's optimized
+and of course I don't know how I'm just
+
+ align:start position:0%
+and of course I don't know how I'm just
+ 
+
+ align:start position:0%
+and of course I don't know how I'm just
+adding these graphs but what does that
+
+ align:start position:0%
+adding these graphs but what does that
+ 
+
+ align:start position:0%
+adding these graphs but what does that
+mean but you get the idea so although
+
+ align:start position:0%
+mean but you get the idea so although
+ 
+
+ align:start position:0%
+mean but you get the idea so although
+your genes are almost all
+
+ align:start position:0%
+your genes are almost all
+ 
+
+ align:start position:0%
+your genes are almost all
+optimized they're if any of them are
+
+ align:start position:0%
+optimized they're if any of them are
+ 
+
+ align:start position:0%
+optimized they're if any of them are
+used for two purposes uh they're far
+
+ align:start position:0%
+used for two purposes uh they're far
+ 
+
+ align:start position:0%
+used for two purposes uh they're far
+from optimal
+
+ align:start position:0%
+from optimal
+ 
+
+ align:start position:0%
+from optimal
+well there's another process that's very
+
+ align:start position:0%
+well there's another process that's very
+ 
+
+ align:start position:0%
+well there's another process that's very
+common in
+
+ align:start position:0%
+common in
+ 
+
+ align:start position:0%
+common in
+reproduction which is that when a
+
+ align:start position:0%
+reproduction which is that when a
+ 
+
+ align:start position:0%
+reproduction which is that when a
+chromosome is being
+
+ align:start position:0%
+chromosome is being
+ 
+
+ align:start position:0%
+chromosome is being
+copied because when a cell divides it
+
+ align:start position:0%
+copied because when a cell divides it
+ 
+
+ align:start position:0%
+copied because when a cell divides it
+makes another cop has to make a copy of
+
+ align:start position:0%
+makes another cop has to make a copy of
+ 
+
+ align:start position:0%
+makes another cop has to make a copy of
+all the genes um but it's copied
+
+ align:start position:0%
+all the genes um but it's copied
+ 
+
+ align:start position:0%
+all the genes um but it's copied
+serially by this uh little copying
+
+ align:start position:0%
+serially by this uh little copying
+ 
+
+ align:start position:0%
+serially by this uh little copying
+machine and every now and then uh the
+
+ align:start position:0%
+machine and every now and then uh the
+ 
+
+ align:start position:0%
+machine and every now and then uh the
+thing gets tangled up crosses itself and
+
+ align:start position:0%
+thing gets tangled up crosses itself and
+ 
+
+ align:start position:0%
+thing gets tangled up crosses itself and
+the poor what's it called uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I forget the name of
+
+ align:start position:0%
+I forget the name of
+ 
+
+ align:start position:0%
+I forget the name of
+the gadget that does this is it a
+
+ align:start position:0%
+the gadget that does this is it a
+ 
+
+ align:start position:0%
+the gadget that does this is it a
+ribosome
+
+ align:start position:0%
+ribosome
+ 
+
+ align:start position:0%
+ribosome
+no we're
+
+ align:start position:0%
+no we're
+ 
+
+ align:start position:0%
+no we're
+talking well I'm talking about the uh
+
+ align:start position:0%
+talking well I'm talking about the uh
+ 
+
+ align:start position:0%
+talking well I'm talking about the uh
+transcript days yeah it's the transcript
+
+ align:start position:0%
+transcript days yeah it's the transcript
+ 
+
+ align:start position:0%
+transcript days yeah it's the transcript
+days and it's attached to something so
+
+ align:start position:0%
+days and it's attached to something so
+ 
+
+ align:start position:0%
+days and it's attached to something so
+if if the uh chromosome got crossed
+
+ align:start position:0%
+if if the uh chromosome got crossed
+ 
+
+ align:start position:0%
+if if the uh chromosome got crossed
+itself incidentally there's a there's a
+
+ align:start position:0%
+itself incidentally there's a there's a
+ 
+
+ align:start position:0%
+itself incidentally there's a there's a
+whole separate piece of machinery when a
+
+ align:start position:0%
+whole separate piece of machinery when a
+ 
+
+ align:start position:0%
+whole separate piece of machinery when a
+chromosome crosses itself there's
+
+ align:start position:0%
+chromosome crosses itself there's
+ 
+
+ align:start position:0%
+chromosome crosses itself there's
+another enzyme that says oh it uh it's
+
+ align:start position:0%
+another enzyme that says oh it uh it's
+ 
+
+ align:start position:0%
+another enzyme that says oh it uh it's
+crossed and this one is under tension it
+
+ align:start position:0%
+crossed and this one is under tension it
+ 
+
+ align:start position:0%
+crossed and this one is under tension it
+actually cuts the other side and pulls
+
+ align:start position:0%
+actually cuts the other side and pulls
+ 
+
+ align:start position:0%
+actually cuts the other side and pulls
+it through and these are called top
+
+ align:start position:0%
+it through and these are called top
+ 
+
+ align:start position:0%
+it through and these are called top
+topazes and we're full of these these
+
+ align:start position:0%
+topazes and we're full of these these
+ 
+
+ align:start position:0%
+topazes and we're full of these these
+take the knots out of
+
+ align:start position:0%
+take the knots out of
+ 
+
+ align:start position:0%
+take the knots out of
+chromosomes who would have thought th uh
+
+ align:start position:0%
+chromosomes who would have thought th uh
+ 
+
+ align:start position:0%
+chromosomes who would have thought th uh
+so what happens is that uh it goes
+
+ align:start position:0%
+so what happens is that uh it goes
+ 
+
+ align:start position:0%
+so what happens is that uh it goes
+around the loop twice once once in a
+
+ align:start position:0%
+around the loop twice once once in a
+ 
+
+ align:start position:0%
+around the loop twice once once in a
+trillion times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and uh you get two copies of the same
+
+ align:start position:0%
+uh and uh you get two copies of the same
+ 
+
+ align:start position:0%
+uh and uh you get two copies of the same
+sequence of
+
+ align:start position:0%
+sequence of
+ 
+
+ align:start position:0%
+sequence of
+genes now
+
+ align:start position:0%
+genes now
+ 
+
+ align:start position:0%
+genes now
+uh if this happens to one of the
+
+ align:start position:0%
+uh if this happens to one of the
+ 
+
+ align:start position:0%
+uh if this happens to one of the
+chromosomes
+
+ align:start position:0%
+chromosomes
+ 
+
+ align:start position:0%
+chromosomes
+um then it might actually kill The
+
+ align:start position:0%
+um then it might actually kill The
+ 
+
+ align:start position:0%
+um then it might actually kill The
+Offspring because uh now the two
+
+ align:start position:0%
+Offspring because uh now the two
+ 
+
+ align:start position:0%
+Offspring because uh now the two
+chromosomes can't match up but uh it may
+
+ align:start position:0%
+chromosomes can't match up but uh it may
+ 
+
+ align:start position:0%
+chromosomes can't match up but uh it may
+not and even uh when that cell
+
+ align:start position:0%
+not and even uh when that cell
+ 
+
+ align:start position:0%
+not and even uh when that cell
+reproduces it
+
+ align:start position:0%
+reproduces it
+ 
+
+ align:start position:0%
+reproduces it
+um might make two copies of that one or
+
+ align:start position:0%
+um might make two copies of that one or
+ 
+
+ align:start position:0%
+um might make two copies of that one or
+uh something like that so now you get an
+
+ align:start position:0%
+uh something like that so now you get an
+ 
+
+ align:start position:0%
+uh something like that so now you get an
+animal that has an extra copy of of a
+
+ align:start position:0%
+animal that has an extra copy of of a
+ 
+
+ align:start position:0%
+animal that has an extra copy of of a
+whole block of
+
+ align:start position:0%
+whole block of
+ 
+
+ align:start position:0%
+whole block of
+genes and in some
+
+ align:start position:0%
+genes and in some
+ 
+
+ align:start position:0%
+genes and in some
+cases uh this is actually beneficial
+
+ align:start position:0%
+cases uh this is actually beneficial
+ 
+
+ align:start position:0%
+cases uh this is actually beneficial
+because although it was making this
+
+ align:start position:0%
+because although it was making this
+ 
+
+ align:start position:0%
+because although it was making this
+protein already U it may have moved to
+
+ align:start position:0%
+protein already U it may have moved to
+ 
+
+ align:start position:0%
+protein already U it may have moved to
+newer environment we're having uh two
+
+ align:start position:0%
+newer environment we're having uh two
+ 
+
+ align:start position:0%
+newer environment we're having uh two
+copies of uh of the new protein is
+
+ align:start position:0%
+copies of uh of the new protein is
+ 
+
+ align:start position:0%
+copies of uh of the new protein is
+better than one and uh that's that's
+
+ align:start position:0%
+better than one and uh that's that's
+ 
+
+ align:start position:0%
+better than one and uh that's that's
+something that wouldn't have been
+
+ align:start position:0%
+something that wouldn't have been
+ 
+
+ align:start position:0%
+something that wouldn't have been
+optimized okay so now you have two
+
+ align:start position:0%
+optimized okay so now you have two
+ 
+
+ align:start position:0%
+optimized okay so now you have two
+different places that are making these
+
+ align:start position:0%
+different places that are making these
+ 
+
+ align:start position:0%
+different places that are making these
+genes and you're still stuck on this
+
+ align:start position:0%
+genes and you're still stuck on this
+ 
+
+ align:start position:0%
+genes and you're still stuck on this
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+Optimum but then a single
+
+ align:start position:0%
+Optimum but then a single
+ 
+
+ align:start position:0%
+Optimum but then a single
+mutation in one or the other of those
+
+ align:start position:0%
+mutation in one or the other of those
+ 
+
+ align:start position:0%
+mutation in one or the other of those
+could cause it to be expressed in
+
+ align:start position:0%
+could cause it to be expressed in
+ 
+
+ align:start position:0%
+could cause it to be expressed in
+different cells because at the somewhere
+
+ align:start position:0%
+different cells because at the somewhere
+ 
+
+ align:start position:0%
+different cells because at the somewhere
+on the chromosome there's something
+
+ align:start position:0%
+on the chromosome there's something
+ 
+
+ align:start position:0%
+on the chromosome there's something
+which determines
+
+ align:start position:0%
+which determines
+ 
+
+ align:start position:0%
+which determines
+uh conditions under which it will
+
+ align:start position:0%
+uh conditions under which it will
+ 
+
+ align:start position:0%
+uh conditions under which it will
+actually make the protein so now you
+
+ align:start position:0%
+actually make the protein so now you
+ 
+
+ align:start position:0%
+actually make the protein so now you
+have two factories and if one of them if
+
+ align:start position:0%
+have two factories and if one of them if
+ 
+
+ align:start position:0%
+have two factories and if one of them if
+you could get this one to be activated
+
+ align:start position:0%
+you could get this one to be activated
+ 
+
+ align:start position:0%
+you could get this one to be activated
+in the heart and this one to be
+
+ align:start position:0%
+in the heart and this one to be
+ 
+
+ align:start position:0%
+in the heart and this one to be
+activated in the brain then you would
+
+ align:start position:0%
+activated in the brain then you would
+ 
+
+ align:start position:0%
+activated in the brain then you would
+have a really Superior or
+
+ align:start position:0%
+have a really Superior or
+ 
+
+ align:start position:0%
+have a really Superior or
+noticeably U more efficient animal and
+
+ align:start position:0%
+noticeably U more efficient animal and
+ 
+
+ align:start position:0%
+noticeably U more efficient animal and
+it would take off so it's things like
+
+ align:start position:0%
+it would take off so it's things like
+ 
+
+ align:start position:0%
+it would take off so it's things like
+that duplication and giving you a
+
+ align:start position:0%
+that duplication and giving you a
+ 
+
+ align:start position:0%
+that duplication and giving you a
+diversity of cell types that's probably
+
+ align:start position:0%
+diversity of cell types that's probably
+ 
+
+ align:start position:0%
+diversity of cell types that's probably
+at any particular point in evolution
+
+ align:start position:0%
+at any particular point in evolution
+ 
+
+ align:start position:0%
+at any particular point in evolution
+this is probably much more important
+
+ align:start position:0%
+this is probably much more important
+ 
+
+ align:start position:0%
+this is probably much more important
+than gene
+
+ align:start position:0%
+than gene
+ 
+
+ align:start position:0%
+than gene
+mutations now I bet that uh whatever
+
+ align:start position:0%
+mutations now I bet that uh whatever
+ 
+
+ align:start position:0%
+mutations now I bet that uh whatever
+they do teach in the high schools where
+
+ align:start position:0%
+they do teach in the high schools where
+ 
+
+ align:start position:0%
+they do teach in the high schools where
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+taught uh they just go back to
+
+ align:start position:0%
+taught uh they just go back to
+ 
+
+ align:start position:0%
+taught uh they just go back to
+whether two recessive genes will give
+
+ align:start position:0%
+whether two recessive genes will give
+ 
+
+ align:start position:0%
+whether two recessive genes will give
+you blue eyes and things like that and
+
+ align:start position:0%
+you blue eyes and things like that and
+ 
+
+ align:start position:0%
+you blue eyes and things like that and
+don't talk about uh details of the
+
+ align:start position:0%
+don't talk about uh details of the
+ 
+
+ align:start position:0%
+don't talk about uh details of the
+evolutionary process and there are
+
+ align:start position:0%
+evolutionary process and there are
+ 
+
+ align:start position:0%
+evolutionary process and there are
+dozens of mechanisms like this that have
+
+ align:start position:0%
+dozens of mechanisms like this that have
+ 
+
+ align:start position:0%
+dozens of mechanisms like this that have
+evolved U since the since the first
+
+ align:start position:0%
+evolved U since the since the first
+ 
+
+ align:start position:0%
+evolved U since the since the first
+plants and animals so that for
+
+ align:start position:0%
+plants and animals so that for
+ 
+
+ align:start position:0%
+plants and animals so that for
+example in your spinal cord
+
+ align:start position:0%
+example in your spinal cord
+ 
+
+ align:start position:0%
+example in your spinal cord
+or uh you have different sets of genes
+
+ align:start position:0%
+or uh you have different sets of genes
+ 
+
+ align:start position:0%
+or uh you have different sets of genes
+at for every vertebr and that's why you
+
+ align:start position:0%
+at for every vertebr and that's why you
+ 
+
+ align:start position:0%
+at for every vertebr and that's why you
+can have some sending nerves to the arms
+
+ align:start position:0%
+can have some sending nerves to the arms
+ 
+
+ align:start position:0%
+can have some sending nerves to the arms
+and some sending nerves to the legs and
+
+ align:start position:0%
+and some sending nerves to the legs and
+ 
+
+ align:start position:0%
+and some sending nerves to the legs and
+so forth forth so
+
+ align:start position:0%
+so forth forth so
+ 
+
+ align:start position:0%
+so forth forth so
+that's that's a fairly big deal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and well what's the point the point is
+
+ align:start position:0%
+and well what's the point the point is
+ 
+
+ align:start position:0%
+and well what's the point the point is
+that if you ask how did people get so
+
+ align:start position:0%
+that if you ask how did people get so
+ 
+
+ align:start position:0%
+that if you ask how did people get so
+smart as compared to squirrels
+
+ align:start position:0%
+smart as compared to squirrels
+ 
+
+ align:start position:0%
+smart as compared to squirrels
+or even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chimpanzees it would be nice to have a
+
+ align:start position:0%
+chimpanzees it would be nice to have a
+ 
+
+ align:start position:0%
+chimpanzees it would be nice to have a
+catalog of of
+
+ align:start position:0%
+catalog of of
+ 
+
+ align:start position:0%
+catalog of of
+uh what what because the human genome is
+
+ align:start position:0%
+uh what what because the human genome is
+ 
+
+ align:start position:0%
+uh what what because the human genome is
+not very different from the gorilla or
+
+ align:start position:0%
+not very different from the gorilla or
+ 
+
+ align:start position:0%
+not very different from the gorilla or
+the chimpanzee or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the orangutang or
+
+ align:start position:0%
+the orangutang or
+ 
+
+ align:start position:0%
+the orangutang or
+baboon it's just a few million
+
+ align:start position:0%
+baboon it's just a few million
+ 
+
+ align:start position:0%
+baboon it's just a few million
+years so what happened who has it what
+
+ align:start position:0%
+years so what happened who has it what
+ 
+
+ align:start position:0%
+years so what happened who has it what
+could it
+
+ align:start position:0%
+could it
+ 
+
+ align:start position:0%
+could it
+what anybody have some theories of what
+
+ align:start position:0%
+what anybody have some theories of what
+ 
+
+ align:start position:0%
+what anybody have some theories of what
+what made us so smart in just five
+
+ align:start position:0%
+what made us so smart in just five
+ 
+
+ align:start position:0%
+what made us so smart in just five
+million years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the stat yeah there are some theories
+
+ align:start position:0%
+the stat yeah there are some theories
+ 
+
+ align:start position:0%
+the stat yeah there are some theories
+that um there were intense periods of
+
+ align:start position:0%
+that um there were intense periods of
+ 
+
+ align:start position:0%
+that um there were intense periods of
+natural selection where our species was
+
+ align:start position:0%
+natural selection where our species was
+ 
+
+ align:start position:0%
+natural selection where our species was
+almost wiped out that happened several
+
+ align:start position:0%
+almost wiped out that happened several
+ 
+
+ align:start position:0%
+almost wiped out that happened several
+times yes so there were only you know
+
+ align:start position:0%
+times yes so there were only you know
+ 
+
+ align:start position:0%
+times yes so there were only you know
+during those periods most of our species
+
+ align:start position:0%
+during those periods most of our species
+ 
+
+ align:start position:0%
+during those periods most of our species
+were wiped out to the point where you
+
+ align:start position:0%
+were wiped out to the point where you
+ 
+
+ align:start position:0%
+were wiped out to the point where you
+just had a couple of thousand and when
+
+ align:start position:0%
+just had a couple of thousand and when
+ 
+
+ align:start position:0%
+just had a couple of thousand and when
+you just have a couple of thousand of
+
+ align:start position:0%
+you just have a couple of thousand of
+ 
+
+ align:start position:0%
+you just have a couple of thousand of
+any species you can have very rap
+
+ align:start position:0%
+any species you can have very rap
+ 
+
+ align:start position:0%
+any species you can have very rap
+mutation rates because they're such a
+
+ align:start position:0%
+mutation rates because they're such a
+ 
+
+ align:start position:0%
+mutation rates because they're such a
+small pool and then once they survive
+
+ align:start position:0%
+small pool and then once they survive
+ 
+
+ align:start position:0%
+small pool and then once they survive
+that it's spread out then it slows down
+
+ align:start position:0%
+that it's spread out then it slows down
+ 
+
+ align:start position:0%
+that it's spread out then it slows down
+again theories are that it happened five
+
+ align:start position:0%
+again theories are that it happened five
+ 
+
+ align:start position:0%
+again theories are that it happened five
+or six times maybe even and that's what
+
+ align:start position:0%
+or six times maybe even and that's what
+ 
+
+ align:start position:0%
+or six times maybe even and that's what
+helped increase our
+
+ align:start position:0%
+helped increase our
+ 
+
+ align:start position:0%
+helped increase our
+intelligence and U I think the main
+
+ align:start position:0%
+intelligence and U I think the main
+ 
+
+ align:start position:0%
+intelligence and U I think the main
+proponent of that thesis is this William
+
+ align:start position:0%
+proponent of that thesis is this William
+ 
+
+ align:start position:0%
+proponent of that thesis is this William
+Calvin in Seattle because he wrote a
+
+ align:start position:0%
+Calvin in Seattle because he wrote a
+ 
+
+ align:start position:0%
+Calvin in Seattle because he wrote a
+whole book
+
+ align:start position:0%
+whole book
+ 
+
+ align:start position:0%
+whole book
+about attempting to relate the ice ages
+
+ align:start position:0%
+about attempting to relate the ice ages
+ 
+
+ align:start position:0%
+about attempting to relate the ice ages
+in the last few million years to brain
+
+ align:start position:0%
+in the last few million years to brain
+ 
+
+ align:start position:0%
+in the last few million years to brain
+changes unfortunately we don't have
+
+ align:start position:0%
+changes unfortunately we don't have
+ 
+
+ align:start position:0%
+changes unfortunately we don't have
+enough we know something about the size
+
+ align:start position:0%
+enough we know something about the size
+ 
+
+ align:start position:0%
+enough we know something about the size
+of the uh brains but so that explains
+
+ align:start position:0%
+of the uh brains but so that explains
+ 
+
+ align:start position:0%
+of the uh brains but so that explains
+why it happened faster perhaps but what
+
+ align:start position:0%
+why it happened faster perhaps but what
+ 
+
+ align:start position:0%
+why it happened faster perhaps but what
+could of the important changes
+
+ align:start position:0%
+could of the important changes
+ 
+
+ align:start position:0%
+could of the important changes
+be usually people talk about the brain
+
+ align:start position:0%
+be usually people talk about the brain
+ 
+
+ align:start position:0%
+be usually people talk about the brain
+getting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger and but the question is then if
+
+ align:start position:0%
+bigger and but the question is then if
+ 
+
+ align:start position:0%
+bigger and but the question is then if
+that would make you smart Why didn't it
+
+ align:start position:0%
+that would make you smart Why didn't it
+ 
+
+ align:start position:0%
+that would make you smart Why didn't it
+happen 50 million years ago and in fact
+
+ align:start position:0%
+happen 50 million years ago and in fact
+ 
+
+ align:start position:0%
+happen 50 million years ago and in fact
+it did with for the
+
+ align:start position:0%
+it did with for the
+ 
+
+ align:start position:0%
+it did with for the
+Dolphins the there are enough fossil
+
+ align:start position:0%
+Dolphins the there are enough fossil
+ 
+
+ align:start position:0%
+Dolphins the there are enough fossil
+dolphins
+
+ align:start position:0%
+dolphins
+ 
+
+ align:start position:0%
+dolphins
+around that show us that I believe it's
+
+ align:start position:0%
+around that show us that I believe it's
+ 
+
+ align:start position:0%
+around that show us that I believe it's
+about 50 million years ago their brains
+
+ align:start position:0%
+about 50 million years ago their brains
+ 
+
+ align:start position:0%
+about 50 million years ago their brains
+rather rapidly got bigger until they're
+
+ align:start position:0%
+rather rapidly got bigger until they're
+ 
+
+ align:start position:0%
+rather rapidly got bigger until they're
+as big as now and then they stopped
+
+ align:start position:0%
+as big as now and then they stopped
+ 
+
+ align:start position:0%
+as big as now and then they stopped
+getting bigger and uh no one knows
+
+ align:start position:0%
+getting bigger and uh no one knows
+ 
+
+ align:start position:0%
+getting bigger and uh no one knows
+why uh yeah could it be that there was a
+
+ align:start position:0%
+why uh yeah could it be that there was a
+ 
+
+ align:start position:0%
+why uh yeah could it be that there was a
+technological change in the sense of
+
+ align:start position:0%
+technological change in the sense of
+ 
+
+ align:start position:0%
+technological change in the sense of
+maybe I don't know some kind of
+
+ align:start position:0%
+maybe I don't know some kind of
+ 
+
+ align:start position:0%
+maybe I don't know some kind of
+Agriculture was invented that allowed a
+
+ align:start position:0%
+Agriculture was invented that allowed a
+ 
+
+ align:start position:0%
+Agriculture was invented that allowed a
+stable environment to come into come
+
+ align:start position:0%
+stable environment to come into come
+ 
+
+ align:start position:0%
+stable environment to come into come
+into play and so that people could have
+
+ align:start position:0%
+into play and so that people could have
+ 
+
+ align:start position:0%
+into play and so that people could have
+a more stable existence would that
+
+ align:start position:0%
+a more stable existence would that
+ 
+
+ align:start position:0%
+a more stable existence would that
+certainly could to do
+
+ align:start position:0%
+certainly could to do
+ 
+
+ align:start position:0%
+certainly could to do
+agriculture uh you have to be able to
+
+ align:start position:0%
+agriculture uh you have to be able to
+ 
+
+ align:start position:0%
+agriculture uh you have to be able to
+think ahead for
+
+ align:start position:0%
+think ahead for
+ 
+
+ align:start position:0%
+think ahead for
+months and maybe we always maybe other
+
+ align:start position:0%
+months and maybe we always maybe other
+ 
+
+ align:start position:0%
+months and maybe we always maybe other
+animals get by just thinking of the next
+
+ align:start position:0%
+animals get by just thinking of the next
+ 
+
+ align:start position:0%
+animals get by just thinking of the next
+meal but I'm I'm not sure whether the
+
+ align:start position:0%
+meal but I'm I'm not sure whether the
+ 
+
+ align:start position:0%
+meal but I'm I'm not sure whether the
+cart would come before or after the
+
+ align:start position:0%
+cart would come before or after the
+ 
+
+ align:start position:0%
+cart would come before or after the
+horse there uh here here's uh here's one
+
+ align:start position:0%
+horse there uh here here's uh here's one
+ 
+
+ align:start position:0%
+horse there uh here here's uh here's one
+idea uh I bet that
+
+ align:start position:0%
+idea uh I bet that
+ 
+
+ align:start position:0%
+idea uh I bet that
+uh up till recently having a bigger
+
+ align:start position:0%
+uh up till recently having a bigger
+ 
+
+ align:start position:0%
+uh up till recently having a bigger
+brain would have let you remember
+
+ align:start position:0%
+brain would have let you remember
+ 
+
+ align:start position:0%
+brain would have let you remember
+more but if you just made the brain
+
+ align:start position:0%
+more but if you just made the brain
+ 
+
+ align:start position:0%
+more but if you just made the brain
+larger and made more uh it's like buying
+
+ align:start position:0%
+larger and made more uh it's like buying
+ 
+
+ align:start position:0%
+larger and made more uh it's like buying
+a terabyte for this Mac uh then I could
+
+ align:start position:0%
+a terabyte for this Mac uh then I could
+ 
+
+ align:start position:0%
+a terabyte for this Mac uh then I could
+uh keep all my
+
+ align:start position:0%
+uh keep all my
+ 
+
+ align:start position:0%
+uh keep all my
+movies but if you didn't have a good way
+
+ align:start position:0%
+movies but if you didn't have a good way
+ 
+
+ align:start position:0%
+movies but if you didn't have a good way
+to retrieve what you
+
+ align:start position:0%
+to retrieve what you
+ 
+
+ align:start position:0%
+to retrieve what you
+want then having more memory would
+
+ align:start position:0%
+want then having more memory would
+ 
+
+ align:start position:0%
+want then having more memory would
+actually be bad wouldn't it uh because
+
+ align:start position:0%
+actually be bad wouldn't it uh because
+ 
+
+ align:start position:0%
+actually be bad wouldn't it uh because
+you slow you down and you'd get more
+
+ align:start position:0%
+you slow you down and you'd get more
+ 
+
+ align:start position:0%
+you slow you down and you'd get more
+wrong things so one conjecture is that
+
+ align:start position:0%
+wrong things so one conjecture is that
+ 
+
+ align:start position:0%
+wrong things so one conjecture is that
+uh uh is that there was some change in
+
+ align:start position:0%
+uh uh is that there was some change in
+ 
+
+ align:start position:0%
+uh uh is that there was some change in
+our brain that made credit assignment
+
+ align:start position:0%
+our brain that made credit assignment
+ 
+
+ align:start position:0%
+our brain that made credit assignment
+better I forget what chapter I have
+
+ align:start position:0%
+better I forget what chapter I have
+ 
+
+ align:start position:0%
+better I forget what chapter I have
+credit assignment
+
+ align:start position:0%
+credit assignment
+ 
+
+ align:start position:0%
+credit assignment
+in it's somewhere that suggest that the
+
+ align:start position:0%
+in it's somewhere that suggest that the
+ 
+
+ align:start position:0%
+in it's somewhere that suggest that the
+important thing in learning is uh it's
+
+ align:start position:0%
+important thing in learning is uh it's
+ 
+
+ align:start position:0%
+important thing in learning is uh it's
+no use to remember something
+
+ align:start position:0%
+no use to remember something
+ 
+
+ align:start position:0%
+no use to remember something
+unless you uh connect it to something
+
+ align:start position:0%
+unless you uh connect it to something
+ 
+
+ align:start position:0%
+unless you uh connect it to something
+like a Critic which says in this
+
+ align:start position:0%
+like a Critic which says in this
+ 
+
+ align:start position:0%
+like a Critic which says in this
+situation this memory uh might provide a
+
+ align:start position:0%
+situation this memory uh might provide a
+ 
+
+ align:start position:0%
+situation this memory uh might provide a
+useful analogy so to solve this
+
+ align:start position:0%
+useful analogy so to solve this
+ 
+
+ align:start position:0%
+useful analogy so to solve this
+problem so my bet is that well that's so
+
+ align:start position:0%
+problem so my bet is that well that's so
+ 
+
+ align:start position:0%
+problem so my bet is that well that's so
+that's one hypothesis there was a
+
+ align:start position:0%
+that's one hypothesis there was a
+ 
+
+ align:start position:0%
+that's one hypothesis there was a
+mysterious Improvement in credit
+
+ align:start position:0%
+mysterious Improvement in credit
+ 
+
+ align:start position:0%
+mysterious Improvement in credit
+assignment namely which features of
+
+ align:start position:0%
+assignment namely which features of
+ 
+
+ align:start position:0%
+assignment namely which features of
+Which experiences to
+
+ align:start position:0%
+Which experiences to
+ 
+
+ align:start position:0%
+Which experiences to
+remember that suddenly made it okay to
+
+ align:start position:0%
+remember that suddenly made it okay to
+ 
+
+ align:start position:0%
+remember that suddenly made it okay to
+have a larger brain because it didn't
+
+ align:start position:0%
+have a larger brain because it didn't
+ 
+
+ align:start position:0%
+have a larger brain because it didn't
+matter now if you put twice as much junk
+
+ align:start position:0%
+matter now if you put twice as much junk
+ 
+
+ align:start position:0%
+matter now if you put twice as much junk
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+it uh provided that you were better at
+
+ align:start position:0%
+it uh provided that you were better at
+ 
+
+ align:start position:0%
+it uh provided that you were better at
+filtering out and picking out what you
+
+ align:start position:0%
+filtering out and picking out what you
+ 
+
+ align:start position:0%
+filtering out and picking out what you
+need so uh a good homework problem is
+
+ align:start position:0%
+need so uh a good homework problem is
+ 
+
+ align:start position:0%
+need so uh a good homework problem is
+uh CU presumably all animals uh
+
+ align:start position:0%
+uh CU presumably all animals uh
+ 
+
+ align:start position:0%
+uh CU presumably all animals uh
+potentially with a very small change
+
+ align:start position:0%
+potentially with a very small change
+ 
+
+ align:start position:0%
+potentially with a very small change
+could have a brain twice as big however
+
+ align:start position:0%
+could have a brain twice as big however
+ 
+
+ align:start position:0%
+could have a brain twice as big however
+if this didn't make them twice as smart
+
+ align:start position:0%
+if this didn't make them twice as smart
+ 
+
+ align:start position:0%
+if this didn't make them twice as smart
+uh they would be quickly wiped out
+
+ align:start position:0%
+uh they would be quickly wiped out
+ 
+
+ align:start position:0%
+uh they would be quickly wiped out
+because as you know brain our brain
+
+ align:start position:0%
+because as you know brain our brain
+ 
+
+ align:start position:0%
+because as you know brain our brain
+takes 20 or 25 watts to just keep going
+
+ align:start position:0%
+takes 20 or 25 watts to just keep going
+ 
+
+ align:start position:0%
+takes 20 or 25 watts to just keep going
+and uh a person the whole body takes
+
+ align:start position:0%
+and uh a person the whole body takes
+ 
+
+ align:start position:0%
+and uh a person the whole body takes
+about 100 Watts so the brain is a very
+
+ align:start position:0%
+about 100 Watts so the brain is a very
+ 
+
+ align:start position:0%
+about 100 Watts so the brain is a very
+you have feeding the brain is very
+
+ align:start position:0%
+you have feeding the brain is very
+ 
+
+ align:start position:0%
+you have feeding the brain is very
+expensive and you can't turn it off very
+
+ align:start position:0%
+expensive and you can't turn it off very
+ 
+
+ align:start position:0%
+expensive and you can't turn it off very
+well I'm not sure that the sleeping
+
+ align:start position:0%
+well I'm not sure that the sleeping
+ 
+
+ align:start position:0%
+well I'm not sure that the sleeping
+brain uses any less energy than the
+
+ align:start position:0%
+brain uses any less energy than the
+ 
+
+ align:start position:0%
+brain uses any less energy than the
+waking brain anybody
+
+ align:start position:0%
+waking brain anybody
+ 
+
+ align:start position:0%
+waking brain anybody
+know anyway uh so a good thing is can
+
+ align:start position:0%
+know anyway uh so a good thing is can
+ 
+
+ align:start position:0%
+know anyway uh so a good thing is can
+you think of a few
+
+ align:start position:0%
+you think of a few
+ 
+
+ align:start position:0%
+you think of a few
+other higher level cognitive features
+
+ align:start position:0%
+other higher level cognitive features
+ 
+
+ align:start position:0%
+other higher level cognitive features
+that might have sparked this rapid
+
+ align:start position:0%
+that might have sparked this rapid
+ 
+
+ align:start position:0%
+that might have sparked this rapid
+Evolution and uh yes this uh the other
+
+ align:start position:0%
+Evolution and uh yes this uh the other
+ 
+
+ align:start position:0%
+Evolution and uh yes this uh the other
+thing is reducing you to a small
+
+ align:start position:0%
+thing is reducing you to a small
+ 
+
+ align:start position:0%
+thing is reducing you to a small
+population makes selection more
+
+ align:start position:0%
+population makes selection more
+ 
+
+ align:start position:0%
+population makes selection more
+intense uh but when this happens to most
+
+ align:start position:0%
+intense uh but when this happens to most
+ 
+
+ align:start position:0%
+intense uh but when this happens to most
+species they die out so
+
+ align:start position:0%
+species they die out so
+ 
+
+ align:start position:0%
+species they die out so
+uh if the human population actually got
+
+ align:start position:0%
+uh if the human population actually got
+ 
+
+ align:start position:0%
+uh if the human population actually got
+down to a few thousand six times in the
+
+ align:start position:0%
+down to a few thousand six times in the
+ 
+
+ align:start position:0%
+down to a few thousand six times in the
+those glacial periods it's remarkable
+
+ align:start position:0%
+those glacial periods it's remarkable
+ 
+
+ align:start position:0%
+those glacial periods it's remarkable
+that anyone's left but um are thatw
+
+ align:start position:0%
+that anyone's left but um are thatw
+ 
+
+ align:start position:0%
+that anyone's left but um are thatw
+pictures any SYM there's some elephant
+
+ align:start position:0%
+pictures any SYM there's some elephant
+ 
+
+ align:start position:0%
+pictures any SYM there's some elephant
+that does paintings that they sell
+
+ align:start position:0%
+that does paintings that they sell
+ 
+
+ align:start position:0%
+that does paintings that they sell
+but say abstract yes I don't think
+
+ align:start position:0%
+but say abstract yes I don't think
+ 
+
+ align:start position:0%
+but say abstract yes I don't think
+anybody's uh claimed that it's
+
+ align:start position:0%
+anybody's uh claimed that it's
+ 
+
+ align:start position:0%
+anybody's uh claimed that it's
+portraying anything so I guess we always
+
+ align:start position:0%
+portraying anything so I guess we always
+ 
+
+ align:start position:0%
+portraying anything so I guess we always
+heard that like two two heads are better
+
+ align:start position:0%
+heard that like two two heads are better
+ 
+
+ align:start position:0%
+heard that like two two heads are better
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and consider pictures and writing over
+
+ align:start position:0%
+and consider pictures and writing over
+ 
+
+ align:start position:0%
+and consider pictures and writing over
+centuries they just imagine there a
+
+ align:start position:0%
+centuries they just imagine there a
+ 
+
+ align:start position:0%
+centuries they just imagine there a
+problem a pitfall that someone might go
+
+ align:start position:0%
+problem a pitfall that someone might go
+ 
+
+ align:start position:0%
+problem a pitfall that someone might go
+through and then someone gives you
+
+ align:start position:0%
+through and then someone gives you
+ 
+
+ align:start position:0%
+through and then someone gives you
+advice oh you probably shouldn't do that
+
+ align:start position:0%
+advice oh you probably shouldn't do that
+ 
+
+ align:start position:0%
+advice oh you probably shouldn't do that
+it's probably a bad idea to STI that
+
+ align:start position:0%
+it's probably a bad idea to STI that
+ 
+
+ align:start position:0%
+it's probably a bad idea to STI that
+fork in that socket and like other other
+
+ align:start position:0%
+fork in that socket and like other other
+ 
+
+ align:start position:0%
+fork in that socket and like other other
+really good advice over Generations kind
+
+ align:start position:0%
+really good advice over Generations kind
+ 
+
+ align:start position:0%
+really good advice over Generations kind
+of explains why we're quote unquote
+
+ align:start position:0%
+of explains why we're quote unquote
+ 
+
+ align:start position:0%
+of explains why we're quote unquote
+smarter because we're just taking
+
+ align:start position:0%
+smarter because we're just taking
+ 
+
+ align:start position:0%
+smarter because we're just taking
+advantage of like what everyone else
+
+ align:start position:0%
+advantage of like what everyone else
+ 
+
+ align:start position:0%
+advantage of like what everyone else
+figured out earlier but then like the
+
+ align:start position:0%
+figured out earlier but then like the
+ 
+
+ align:start position:0%
+figured out earlier but then like the
+original thing that made us paint or
+
+ align:start position:0%
+original thing that made us paint or
+ 
+
+ align:start position:0%
+original thing that made us paint or
+like draw symbols
+
+ align:start position:0%
+like draw symbols
+ 
+
+ align:start position:0%
+like draw symbols
+I that's a good point it might be that
+
+ align:start position:0%
+I that's a good point it might be that
+ 
+
+ align:start position:0%
+I that's a good point it might be that
+once people had just the least bit of
+
+ align:start position:0%
+once people had just the least bit of
+ 
+
+ align:start position:0%
+once people had just the least bit of
+communication they'd only say things
+
+ align:start position:0%
+communication they'd only say things
+ 
+
+ align:start position:0%
+communication they'd only say things
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+important and so in other words you
+
+ align:start position:0%
+important and so in other words you
+ 
+
+ align:start position:0%
+important and so in other words you
+could solve the credit assignment
+
+ align:start position:0%
+could solve the credit assignment
+ 
+
+ align:start position:0%
+could solve the credit assignment
+problem not by not by having something
+
+ align:start position:0%
+problem not by not by having something
+ 
+
+ align:start position:0%
+problem not by not by having something
+in your brain that does it well but just
+
+ align:start position:0%
+in your brain that does it well but just
+ 
+
+ align:start position:0%
+in your brain that does it well but just
+the fact that somebody says uh by the
+
+ align:start position:0%
+the fact that somebody says uh by the
+ 
+
+ align:start position:0%
+the fact that somebody says uh by the
+way there's a uh Raptor around the
+
+ align:start position:0%
+way there's a uh Raptor around the
+ 
+
+ align:start position:0%
+way there's a uh Raptor around the
+corner uh or Raptors hide in that
+
+ align:start position:0%
+corner uh or Raptors hide in that
+ 
+
+ align:start position:0%
+corner uh or Raptors hide in that
+particular kind of
+
+ align:start position:0%
+particular kind of
+ 
+
+ align:start position:0%
+particular kind of
+bush uh once you have communication I
+
+ align:start position:0%
+bush uh once you have communication I
+ 
+
+ align:start position:0%
+bush uh once you have communication I
+hadn't thought of that uh then it might
+
+ align:start position:0%
+hadn't thought of that uh then it might
+ 
+
+ align:start position:0%
+hadn't thought of that uh then it might
+be worth having a bigger brain because
+
+ align:start position:0%
+be worth having a bigger brain because
+ 
+
+ align:start position:0%
+be worth having a bigger brain because
+uh in the social thing people will only
+
+ align:start position:0%
+uh in the social thing people will only
+ 
+
+ align:start position:0%
+uh in the social thing people will only
+tell you about really important bad
+
+ align:start position:0%
+tell you about really important bad
+ 
+
+ align:start position:0%
+tell you about really important bad
+things yeah um on a tangent to that if
+
+ align:start position:0%
+things yeah um on a tangent to that if
+ 
+
+ align:start position:0%
+things yeah um on a tangent to that if
+there was only a few thousand
+
+ align:start position:0%
+there was only a few thousand
+ 
+
+ align:start position:0%
+there was only a few thousand
+individuals left or a small number of um
+
+ align:start position:0%
+individuals left or a small number of um
+ 
+
+ align:start position:0%
+individuals left or a small number of um
+people left wouldn't it make more sense
+
+ align:start position:0%
+people left wouldn't it make more sense
+ 
+
+ align:start position:0%
+people left wouldn't it make more sense
+to kind of band together humans are
+
+ align:start position:0%
+to kind of band together humans are
+ 
+
+ align:start position:0%
+to kind of band together humans are
+rather social animals if having bigger
+
+ align:start position:0%
+rather social animals if having bigger
+ 
+
+ align:start position:0%
+rather social animals if having bigger
+brains would allow us to be perhaps more
+
+ align:start position:0%
+brains would allow us to be perhaps more
+ 
+
+ align:start position:0%
+brains would allow us to be perhaps more
+social or to interact better with others
+
+ align:start position:0%
+social or to interact better with others
+ 
+
+ align:start position:0%
+social or to interact better with others
+of our species wouldn't that promote
+
+ align:start position:0%
+of our species wouldn't that promote
+ 
+
+ align:start position:0%
+of our species wouldn't that promote
+survival uh it's a good question uh in
+
+ align:start position:0%
+survival uh it's a good question uh in
+ 
+
+ align:start position:0%
+survival uh it's a good question uh in
+there's a guy named Martin Noak at
+
+ align:start position:0%
+there's a guy named Martin Noak at
+ 
+
+ align:start position:0%
+there's a guy named Martin Noak at
+Harvard who has an Institute for
+
+ align:start position:0%
+Harvard who has an Institute for
+ 
+
+ align:start position:0%
+Harvard who has an Institute for
+evolutionary
+
+ align:start position:0%
+evolutionary
+ 
+
+ align:start position:0%
+evolutionary
+uh mathematical evolutionary theories
+
+ align:start position:0%
+uh mathematical evolutionary theories
+ 
+
+ align:start position:0%
+uh mathematical evolutionary theories
+and there's some stuff related to that
+
+ align:start position:0%
+and there's some stuff related to that
+ 
+
+ align:start position:0%
+and there's some stuff related to that
+that's come up
+
+ align:start position:0%
+that's come up
+ 
+
+ align:start position:0%
+that's come up
+recently uh
+
+ align:start position:0%
+recently uh
+ 
+
+ align:start position:0%
+recently uh
+evolutionary theory is progressing very
+
+ align:start position:0%
+evolutionary theory is progressing very
+ 
+
+ align:start position:0%
+evolutionary theory is progressing very
+rapidly now that for the first time
+
+ align:start position:0%
+rapidly now that for the first time
+ 
+
+ align:start position:0%
+rapidly now that for the first time
+they're good mathematical models of
+
+ align:start position:0%
+they're good mathematical models of
+ 
+
+ align:start position:0%
+they're good mathematical models of
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+selection and a conjecture is that one
+
+ align:start position:0%
+selection and a conjecture is that one
+ 
+
+ align:start position:0%
+selection and a conjecture is that one
+of the features of human evolution is
+
+ align:start position:0%
+of the features of human evolution is
+ 
+
+ align:start position:0%
+of the features of human evolution is
+that uh before people had
+
+ align:start position:0%
+that uh before people had
+ 
+
+ align:start position:0%
+that uh before people had
+developed uh social communities very
+
+ align:start position:0%
+developed uh social communities very
+ 
+
+ align:start position:0%
+developed uh social communities very
+well uh two tribes might battle and uh
+
+ align:start position:0%
+well uh two tribes might battle and uh
+ 
+
+ align:start position:0%
+well uh two tribes might battle and uh
+and uh one would be defeated and run
+
+ align:start position:0%
+and uh one would be defeated and run
+ 
+
+ align:start position:0%
+and uh one would be defeated and run
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+but once you had
+
+ align:start position:0%
+but once you had
+ 
+
+ align:start position:0%
+but once you had
+cooperation then you could get the idea
+
+ align:start position:0%
+cooperation then you could get the idea
+ 
+
+ align:start position:0%
+cooperation then you could get the idea
+that uh if there's a neighboring tribe
+
+ align:start position:0%
+that uh if there's a neighboring tribe
+ 
+
+ align:start position:0%
+that uh if there's a neighboring tribe
+you don't like then you should go and
+
+ align:start position:0%
+you don't like then you should go and
+ 
+
+ align:start position:0%
+you don't like then you should go and
+kill every last one of them and that's a
+
+ align:start position:0%
+kill every last one of them and that's a
+ 
+
+ align:start position:0%
+kill every last one of them and that's a
+great idea people say wouldn't it be
+
+ align:start position:0%
+great idea people say wouldn't it be
+ 
+
+ align:start position:0%
+great idea people say wouldn't it be
+nice if we didn't have war and uh yes it
+
+ align:start position:0%
+nice if we didn't have war and uh yes it
+ 
+
+ align:start position:0%
+nice if we didn't have war and uh yes it
+would be nice for us maybe but uh in
+
+ align:start position:0%
+would be nice for us maybe but uh in
+ 
+
+ align:start position:0%
+would be nice for us maybe but uh in
+this there's a whole Spade of theories
+
+ align:start position:0%
+this there's a whole Spade of theories
+ 
+
+ align:start position:0%
+this there's a whole Spade of theories
+of group selection now and one of them
+
+ align:start position:0%
+of group selection now and one of them
+ 
+
+ align:start position:0%
+of group selection now and one of them
+is that when a tribe is smart enough to
+
+ align:start position:0%
+is that when a tribe is smart enough to
+ 
+
+ align:start position:0%
+is that when a tribe is smart enough to
+realize that if it can wipe out every
+
+ align:start position:0%
+realize that if it can wipe out every
+ 
+
+ align:start position:0%
+realize that if it can wipe out every
+one of the enemy then you've solved the
+
+ align:start position:0%
+one of the enemy then you've solved the
+ 
+
+ align:start position:0%
+one of the enemy then you've solved the
+problem for good and you can take over
+
+ align:start position:0%
+problem for good and you can take over
+ 
+
+ align:start position:0%
+problem for good and you can take over
+their land and uh so this kind of evil
+
+ align:start position:0%
+their land and uh so this kind of evil
+ 
+
+ align:start position:0%
+their land and uh so this kind of evil
+cooperation is a really unique feature
+
+ align:start position:0%
+cooperation is a really unique feature
+ 
+
+ align:start position:0%
+cooperation is a really unique feature
+and you don't U normally when species
+
+ align:start position:0%
+and you don't U normally when species
+ 
+
+ align:start position:0%
+and you don't U normally when species
+compete uh they're just hungry and they
+
+ align:start position:0%
+compete uh they're just hungry and they
+ 
+
+ align:start position:0%
+compete uh they're just hungry and they
+don't have the idea let's get rid of all
+
+ align:start position:0%
+don't have the idea let's get rid of all
+ 
+
+ align:start position:0%
+don't have the idea let's get rid of all
+of them for good yeah back to your
+
+ align:start position:0%
+of them for good yeah back to your
+ 
+
+ align:start position:0%
+of them for good yeah back to your
+question about what the maybe it had
+
+ align:start position:0%
+question about what the maybe it had
+ 
+
+ align:start position:0%
+question about what the maybe it had
+something to do with um Imagination and
+
+ align:start position:0%
+something to do with um Imagination and
+ 
+
+ align:start position:0%
+something to do with um Imagination and
+that uh imagination would maybe let you
+
+ align:start position:0%
+that uh imagination would maybe let you
+ 
+
+ align:start position:0%
+that uh imagination would maybe let you
+over what would normally be your
+
+ align:start position:0%
+over what would normally be your
+ 
+
+ align:start position:0%
+over what would normally be your
+instinct for how to do something so
+
+ align:start position:0%
+instinct for how to do something so
+ 
+
+ align:start position:0%
+instinct for how to do something so
+instead of um maybe hunting or gathering
+
+ align:start position:0%
+instead of um maybe hunting or gathering
+ 
+
+ align:start position:0%
+instead of um maybe hunting or gathering
+by Instinct you could use imagination to
+
+ align:start position:0%
+by Instinct you could use imagination to
+ 
+
+ align:start position:0%
+by Instinct you could use imagination to
+to think of a better way to do it yeah
+
+ align:start position:0%
+to think of a better way to do it yeah
+ 
+
+ align:start position:0%
+to think of a better way to do it yeah
+picking up that rock will help you hunt
+
+ align:start position:0%
+picking up that rock will help you hunt
+ 
+
+ align:start position:0%
+picking up that rock will help you hunt
+something certainly having reflective
+
+ align:start position:0%
+something certainly having reflective
+ 
+
+ align:start position:0%
+something certainly having reflective
+layers but why would that how would that
+
+ align:start position:0%
+layers but why would that how would that
+ 
+
+ align:start position:0%
+layers but why would that how would that
+promote the brain being
+
+ align:start position:0%
+promote the brain being
+ 
+
+ align:start position:0%
+promote the brain being
+bigger well if you remembered all your
+
+ align:start position:0%
+bigger well if you remembered all your
+ 
+
+ align:start position:0%
+bigger well if you remembered all your
+good ideas that would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I thought that sort of occurred to me
+
+ align:start position:0%
+I thought that sort of occurred to me
+ 
+
+ align:start position:0%
+I thought that sort of occurred to me
+when we went from the communication idea
+
+ align:start position:0%
+when we went from the communication idea
+ 
+
+ align:start position:0%
+when we went from the communication idea
+to the banding idea was
+
+ align:start position:0%
+to the banding idea was
+ 
+
+ align:start position:0%
+to the banding idea was
+that what about
+
+ align:start position:0%
+that what about
+ 
+
+ align:start position:0%
+that what about
+above if you consider the fact that you
+
+ align:start position:0%
+above if you consider the fact that you
+ 
+
+ align:start position:0%
+above if you consider the fact that you
+have yes you have small populations of
+
+ align:start position:0%
+have yes you have small populations of
+ 
+
+ align:start position:0%
+have yes you have small populations of
+humans that will survive better if they
+
+ align:start position:0%
+humans that will survive better if they
+ 
+
+ align:start position:0%
+humans that will survive better if they
+cooperate and S live together in bands
+
+ align:start position:0%
+cooperate and S live together in bands
+ 
+
+ align:start position:0%
+cooperate and S live together in bands
+um and would not little bands or bands
+
+ align:start position:0%
+um and would not little bands or bands
+ 
+
+ align:start position:0%
+um and would not little bands or bands
+of people work better they can
+
+ align:start position:0%
+of people work better they can
+ 
+
+ align:start position:0%
+of people work better they can
+communicate or if they specialize and
+
+ align:start position:0%
+communicate or if they specialize and
+ 
+
+ align:start position:0%
+communicate or if they specialize and
+cooperate so that somebody's good at
+
+ align:start position:0%
+cooperate so that somebody's good at
+ 
+
+ align:start position:0%
+cooperate so that somebody's good at
+knitting sweaters
+
+ align:start position:0%
+knitting sweaters
+ 
+
+ align:start position:0%
+knitting sweaters
+well you you make them do nothing but
+
+ align:start position:0%
+well you you make them do nothing but
+ 
+
+ align:start position:0%
+well you you make them do nothing but
+knit
+
+ align:start position:0%
+knit
+ 
+
+ align:start position:0%
+knit
+sweaters so I I I'm sort of inclined to
+
+ align:start position:0%
+sweaters so I I I'm sort of inclined to
+ 
+
+ align:start position:0%
+sweaters so I I I'm sort of inclined to
+believe that um the evolution of both
+
+ align:start position:0%
+believe that um the evolution of both
+ 
+
+ align:start position:0%
+believe that um the evolution of both
+ideas can progress together
+
+ align:start position:0%
+ideas can progress together
+ 
+
+ align:start position:0%
+ideas can progress together
+rapidly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MH another thing that comes to mind is
+
+ align:start position:0%
+MH another thing that comes to mind is
+ 
+
+ align:start position:0%
+MH another thing that comes to mind is
+that Humanity dwindles down to a th
+
+ align:start position:0%
+that Humanity dwindles down to a th
+ 
+
+ align:start position:0%
+that Humanity dwindles down to a th
+people six times the people that are
+
+ align:start position:0%
+people six times the people that are
+ 
+
+ align:start position:0%
+people six times the people that are
+left are probably the smartest ones yeah
+
+ align:start position:0%
+left are probably the smartest ones yeah
+ 
+
+ align:start position:0%
+left are probably the smartest ones yeah
+well they've been the idea is that they
+
+ align:start position:0%
+well they've been the idea is that they
+ 
+
+ align:start position:0%
+well they've been the idea is that they
+they've been selected to be more
+
+ align:start position:0%
+they've been selected to be more
+ 
+
+ align:start position:0%
+they've been selected to be more
+resourceful
+
+ align:start position:0%
+resourceful
+ 
+
+ align:start position:0%
+resourceful
+because but they might be the
+
+ align:start position:0%
+because but they might be the
+ 
+
+ align:start position:0%
+because but they might be the
+politicians well that's all
+
+ align:start position:0%
+politicians well that's all
+ 
+
+ align:start position:0%
+politicians well that's all
+right what are the only other species
+
+ align:start position:0%
+right what are the only other species
+ 
+
+ align:start position:0%
+right what are the only other species
+that um I guess only other species that
+
+ align:start position:0%
+that um I guess only other species that
+ 
+
+ align:start position:0%
+that um I guess only other species that
+has ever actually drawn pictures is our
+
+ align:start position:0%
+has ever actually drawn pictures is our
+ 
+
+ align:start position:0%
+has ever actually drawn pictures is our
+closest ancestor the Neanderthal I think
+
+ align:start position:0%
+closest ancestor the Neanderthal I think
+ 
+
+ align:start position:0%
+closest ancestor the Neanderthal I think
+they're off by one chromosome
+
+ align:start position:0%
+they're off by one chromosome
+ 
+
+ align:start position:0%
+they're off by one chromosome
+um half yeah there AR any anthropol
+
+ align:start position:0%
+um half yeah there AR any anthropol
+ 
+
+ align:start position:0%
+um half yeah there AR any anthropol
+pictures aren't there yeah lots of uh
+
+ align:start position:0%
+pictures aren't there yeah lots of uh
+ 
+
+ align:start position:0%
+pictures aren't there yeah lots of uh
+paintings um so they are that they were
+
+ align:start position:0%
+paintings um so they are that they were
+ 
+
+ align:start position:0%
+paintings um so they are that they were
+um I guess have have the same
+
+ align:start position:0%
+um I guess have have the same
+ 
+
+ align:start position:0%
+um I guess have have the same
+capabilities intellectually as a human
+
+ align:start position:0%
+capabilities intellectually as a human
+ 
+
+ align:start position:0%
+capabilities intellectually as a human
+being but they were more peaceful and
+
+ align:start position:0%
+being but they were more peaceful and
+ 
+
+ align:start position:0%
+being but they were more peaceful and
+passive and maybe the equiv of hisor
+
+ align:start position:0%
+passive and maybe the equiv of hisor
+ 
+
+ align:start position:0%
+passive and maybe the equiv of hisor
+well the latest theory is that that
+
+ align:start position:0%
+well the latest theory is that that
+ 
+
+ align:start position:0%
+well the latest theory is that that
+we're descended from across between
+
+ align:start position:0%
+we're descended from across between
+ 
+
+ align:start position:0%
+we're descended from across between
+neanderthals and Homo erectus but there
+
+ align:start position:0%
+neanderthals and Homo erectus but there
+ 
+
+ align:start position:0%
+neanderthals and Homo erectus but there
+aren't enough
+
+ align:start position:0%
+aren't enough
+ 
+
+ align:start position:0%
+aren't enough
+uh there aren't any fossils with genes
+
+ align:start position:0%
+uh there aren't any fossils with genes
+ 
+
+ align:start position:0%
+uh there aren't any fossils with genes
+in them yet for
+
+ align:start position:0%
+in them yet for
+ 
+
+ align:start position:0%
+in them yet for
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+the uh you remember that thing about the
+
+ align:start position:0%
+the uh you remember that thing about the
+ 
+
+ align:start position:0%
+the uh you remember that thing about the
+uh dinosaurs having soft tissue in their
+
+ align:start position:0%
+uh dinosaurs having soft tissue in their
+ 
+
+ align:start position:0%
+uh dinosaurs having soft tissue in their
+bones about three years
+
+ align:start position:0%
+bones about three years
+ 
+
+ align:start position:0%
+bones about three years
+ago so
+
+ align:start position:0%
+ago so
+ 
+
+ align:start position:0%
+ago so
+oh uh there was an there was an
+
+ align:start position:0%
+oh uh there was an there was an
+ 
+
+ align:start position:0%
+oh uh there was an there was an
+expedition that found a big thigh bone
+
+ align:start position:0%
+expedition that found a big thigh bone
+ 
+
+ align:start position:0%
+expedition that found a big thigh bone
+and it had some soft tissue in in a
+
+ align:start position:0%
+and it had some soft tissue in in a
+ 
+
+ align:start position:0%
+and it had some soft tissue in in a
+femur big big bone and there was a lot
+
+ align:start position:0%
+femur big big bone and there was a lot
+ 
+
+ align:start position:0%
+femur big big bone and there was a lot
+of stuff in the Press about this is this
+
+ align:start position:0%
+of stuff in the Press about this is this
+ 
+
+ align:start position:0%
+of stuff in the Press about this is this
+is terribly exciting because we might be
+
+ align:start position:0%
+is terribly exciting because we might be
+ 
+
+ align:start position:0%
+is terribly exciting because we might be
+able to uh find DNA in this 50 million
+
+ align:start position:0%
+able to uh find DNA in this 50 million
+ 
+
+ align:start position:0%
+able to uh find DNA in this 50 million
+year old dinosaur didn't it was in all
+
+ align:start position:0%
+year old dinosaur didn't it was in all
+ 
+
+ align:start position:0%
+year old dinosaur didn't it was in all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+papers U anyway they didn't find any it
+
+ align:start position:0%
+papers U anyway they didn't find any it
+ 
+
+ align:start position:0%
+papers U anyway they didn't find any it
+was Jack Jack Horner's project at the
+
+ align:start position:0%
+was Jack Jack Horner's project at the
+ 
+
+ align:start position:0%
+was Jack Jack Horner's project at the
+University
+
+ align:start position:0%
+University
+ 
+
+ align:start position:0%
+University
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Wyoming uh and there was some jelly like
+
+ align:start position:0%
+Wyoming uh and there was some jelly like
+ 
+
+ align:start position:0%
+Wyoming uh and there was some jelly like
+stuff but it wasn't the right
+
+ align:start position:0%
+stuff but it wasn't the right
+ 
+
+ align:start position:0%
+stuff but it wasn't the right
+stuff uh anyway if you could find
+
+ align:start position:0%
+stuff uh anyway if you could find
+ 
+
+ align:start position:0%
+stuff uh anyway if you could find
+if we could find some
+
+ align:start position:0%
+if we could find some
+ 
+
+ align:start position:0%
+if we could find some
+pranan and neandertal and other DNA
+
+ align:start position:0%
+pranan and neandertal and other DNA
+ 
+
+ align:start position:0%
+pranan and neandertal and other DNA
+then we could see how much
+
+ align:start position:0%
+then we could see how much
+ 
+
+ align:start position:0%
+then we could see how much
+of how many genes we have from each of
+
+ align:start position:0%
+of how many genes we have from each of
+ 
+
+ align:start position:0%
+of how many genes we have from each of
+them and that would be very
+
+ align:start position:0%
+them and that would be very
+ 
+
+ align:start position:0%
+them and that would be very
+exciting and the opposite would be
+
+ align:start position:0%
+exciting and the opposite would be
+ 
+
+ align:start position:0%
+exciting and the opposite would be
+exciting it could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make if we could push the ethicists
+
+ align:start position:0%
+make if we could push the ethicists
+ 
+
+ align:start position:0%
+make if we could push the ethicists
+aside then we could make some
+
+ align:start position:0%
+aside then we could make some
+ 
+
+ align:start position:0%
+aside then we could make some
+neanderthals and see how they do
+
+ align:start position:0%
+neanderthals and see how they do
+ 
+
+ align:start position:0%
+neanderthals and see how they do
+how useful 9.9% the same gen as chimp
+
+ align:start position:0%
+how useful 9.9% the same gen as chimp
+ 
+
+ align:start position:0%
+how useful 9.9% the same gen as chimp
+yes but the but the 360 genes must
+
+ align:start position:0%
+yes but the but the 360 genes must
+ 
+
+ align:start position:0%
+yes but the but the 360 genes must
+different must be very important I mean
+
+ align:start position:0%
+different must be very important I mean
+ 
+
+ align:start position:0%
+different must be very important I mean
+we have 80% in common with
+
+ align:start position:0%
+we have 80% in common with
+ 
+
+ align:start position:0%
+we have 80% in common with
+lettuce so it's it's the different ones
+
+ align:start position:0%
+lettuce so it's it's the different ones
+ 
+
+ align:start position:0%
+lettuce so it's it's the different ones
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh I don't know if if you've been
+
+ align:start position:0%
+uh I don't know if if you've been
+ 
+
+ align:start position:0%
+uh I don't know if if you've been
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+the at the scientific papers uh it's
+
+ align:start position:0%
+the at the scientific papers uh it's
+ 
+
+ align:start position:0%
+the at the scientific papers uh it's
+changing from month to month and
+
+ align:start position:0%
+changing from month to month and
+ 
+
+ align:start position:0%
+changing from month to month and
+somebody just announced that there's uh
+
+ align:start position:0%
+somebody just announced that there's uh
+ 
+
+ align:start position:0%
+somebody just announced that there's uh
+several thousand little fragments of
+
+ align:start position:0%
+several thousand little fragments of
+ 
+
+ align:start position:0%
+several thousand little fragments of
+something else uh in the genome that
+
+ align:start position:0%
+something else uh in the genome that
+ 
+
+ align:start position:0%
+something else uh in the genome that
+look like they might be regarded as
+
+ align:start position:0%
+look like they might be regarded as
+ 
+
+ align:start position:0%
+look like they might be regarded as
+genes and I forget what they're called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh but they're highly conserved
+
+ align:start position:0%
+but uh but they're highly conserved
+ 
+
+ align:start position:0%
+but uh but they're highly conserved
+they're not junk because they keep they
+
+ align:start position:0%
+they're not junk because they keep they
+ 
+
+ align:start position:0%
+they're not junk because they keep they
+haven't changed
+
+ align:start position:0%
+haven't changed
+ 
+
+ align:start position:0%
+haven't changed
+and no one knows what to do about them
+
+ align:start position:0%
+and no one knows what to do about them
+ 
+
+ align:start position:0%
+and no one knows what to do about them
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+month as far as genes go they found out
+
+ align:start position:0%
+month as far as genes go they found out
+ 
+
+ align:start position:0%
+month as far as genes go they found out
+that said the genome the
+
+ align:start position:0%
+that said the genome the
+ 
+
+ align:start position:0%
+that said the genome the
+prote the different gen can go for
+
+ align:start position:0%
+prote the different gen can go for
+ 
+
+ align:start position:0%
+prote the different gen can go for
+different protein in fact it's situation
+
+ align:start position:0%
+different protein in fact it's situation
+ 
+
+ align:start position:0%
+different protein in fact it's situation
+is pretty bad yeah you know so little
+
+ align:start position:0%
+is pretty bad yeah you know so little
+ 
+
+ align:start position:0%
+is pretty bad yeah you know so little
+about how to protect tertiary protein
+
+ align:start position:0%
+about how to protect tertiary protein
+ 
+
+ align:start position:0%
+about how to protect tertiary protein
+structure so that even like now with the
+
+ align:start position:0%
+structure so that even like now with the
+ 
+
+ align:start position:0%
+structure so that even like now with the
+the different genes that we can see
+
+ align:start position:0%
+the different genes that we can see
+ 
+
+ align:start position:0%
+the different genes that we can see
+between chanes and humans we still don't
+
+ align:start position:0%
+between chanes and humans we still don't
+ 
+
+ align:start position:0%
+between chanes and humans we still don't
+know anything even remotely close about
+
+ align:start position:0%
+know anything even remotely close about
+ 
+
+ align:start position:0%
+know anything even remotely close about
+the protein folding to give us any idea
+
+ align:start position:0%
+the protein folding to give us any idea
+ 
+
+ align:start position:0%
+the protein folding to give us any idea
+what the fundamental differences are
+
+ align:start position:0%
+what the fundamental differences are
+ 
+
+ align:start position:0%
+what the fundamental differences are
+between yeah I saw something about each
+
+ align:start position:0%
+between yeah I saw something about each
+ 
+
+ align:start position:0%
+between yeah I saw something about each
+gene uh being responsible for at least
+
+ align:start position:0%
+gene uh being responsible for at least
+ 
+
+ align:start position:0%
+gene uh being responsible for at least
+two and a half different proteins just
+
+ align:start position:0%
+two and a half different proteins just
+ 
+
+ align:start position:0%
+two and a half different proteins just
+by cutting and splicing so uh they're
+
+ align:start position:0%
+by cutting and splicing so uh they're
+ 
+
+ align:start position:0%
+by cutting and splicing so uh they're
+still talking about 30,000 genes but it
+
+ align:start position:0%
+still talking about 30,000 genes but it
+ 
+
+ align:start position:0%
+still talking about 30,000 genes but it
+makes 80,000 different
+
+ align:start position:0%
+makes 80,000 different
+ 
+
+ align:start position:0%
+makes 80,000 different
+proteins so uh also the whole issue of
+
+ align:start position:0%
+proteins so uh also the whole issue of
+ 
+
+ align:start position:0%
+proteins so uh also the whole issue of
+protein chaining where one protein
+
+ align:start position:0%
+protein chaining where one protein
+ 
+
+ align:start position:0%
+protein chaining where one protein
+enables another protein to enable a gene
+
+ align:start position:0%
+enables another protein to enable a gene
+ 
+
+ align:start position:0%
+enables another protein to enable a gene
+to make another protein and so on yes
+
+ align:start position:0%
+to make another protein and so on yes
+ 
+
+ align:start position:0%
+to make another protein and so on yes
+and if one of apparently if one of them
+
+ align:start position:0%
+and if one of apparently if one of them
+ 
+
+ align:start position:0%
+and if one of apparently if one of them
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+express some protein can get expressed
+
+ align:start position:0%
+express some protein can get expressed
+ 
+
+ align:start position:0%
+express some protein can get expressed
+which will cause a lot of other genes to
+
+ align:start position:0%
+which will cause a lot of other genes to
+ 
+
+ align:start position:0%
+which will cause a lot of other genes to
+to express their second protein rather
+
+ align:start position:0%
+to express their second protein rather
+ 
+
+ align:start position:0%
+to express their second protein rather
+than their first by making it skip some
+
+ align:start position:0%
+than their first by making it skip some
+ 
+
+ align:start position:0%
+than their first by making it skip some
+transcription thing so this big mess and
+
+ align:start position:0%
+transcription thing so this big mess and
+ 
+
+ align:start position:0%
+transcription thing so this big mess and
+uh at some point in evolution the
+
+ align:start position:0%
+uh at some point in evolution the
+ 
+
+ align:start position:0%
+uh at some point in evolution the
+appearance of
+
+ align:start position:0%
+appearance of
+ 
+
+ align:start position:0%
+appearance of
+editing editing genes must have appeared
+
+ align:start position:0%
+editing editing genes must have appeared
+ 
+
+ align:start position:0%
+editing editing genes must have appeared
+where instead of making a whole new
+
+ align:start position:0%
+where instead of making a whole new
+ 
+
+ align:start position:0%
+where instead of making a whole new
+Gene uh you can make a small protein
+
+ align:start position:0%
+Gene uh you can make a small protein
+ 
+
+ align:start position:0%
+Gene uh you can make a small protein
+that Snips out a little piece of an
+
+ align:start position:0%
+that Snips out a little piece of an
+ 
+
+ align:start position:0%
+that Snips out a little piece of an
+existing Gene and um so there's more
+
+ align:start position:0%
+existing Gene and um so there's more
+ 
+
+ align:start position:0%
+existing Gene and um so there's more
+information per bit than they thought
+
+ align:start position:0%
+information per bit than they thought
+ 
+
+ align:start position:0%
+information per bit than they thought
+before but it's it's still only a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gigabyte anyway uh I'm curious about
+
+ align:start position:0%
+gigabyte anyway uh I'm curious about
+ 
+
+ align:start position:0%
+gigabyte anyway uh I'm curious about
+whether with this great controversy
+
+ align:start position:0%
+whether with this great controversy
+ 
+
+ align:start position:0%
+whether with this great controversy
+whether you should teach Evolution or
+
+ align:start position:0%
+whether you should teach Evolution or
+ 
+
+ align:start position:0%
+whether you should teach Evolution or
+not I wonder if any High School courses
+
+ align:start position:0%
+not I wonder if any High School courses
+ 
+
+ align:start position:0%
+not I wonder if any High School courses
+because this hasn't reached the college
+
+ align:start position:0%
+because this hasn't reached the college
+ 
+
+ align:start position:0%
+because this hasn't reached the college
+level but I wonder if anybody talk I
+
+ align:start position:0%
+level but I wonder if anybody talk I
+ 
+
+ align:start position:0%
+level but I wonder if anybody talk I
+mean this is a this is a wonderfully
+
+ align:start position:0%
+mean this is a this is a wonderfully
+ 
+
+ align:start position:0%
+mean this is a this is a wonderfully
+simple idea
+
+ align:start position:0%
+simple idea
+ 
+
+ align:start position:0%
+simple idea
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+this guy Ono won a Nobel Prize
+
+ align:start position:0%
+this guy Ono won a Nobel Prize
+ 
+
+ align:start position:0%
+this guy Ono won a Nobel Prize
+for uh seeing how this works in the
+
+ align:start position:0%
+for uh seeing how this works in the
+ 
+
+ align:start position:0%
+for uh seeing how this works in the
+vertebrate structure uh when you make
+
+ align:start position:0%
+vertebrate structure uh when you make
+ 
+
+ align:start position:0%
+vertebrate structure uh when you make
+you know that vertebrates start out uh
+
+ align:start position:0%
+you know that vertebrates start out uh
+ 
+
+ align:start position:0%
+you know that vertebrates start out uh
+as a long tube with a lot of
+
+ align:start position:0%
+as a long tube with a lot of
+ 
+
+ align:start position:0%
+as a long tube with a lot of
+segments and then uh he discovers that
+
+ align:start position:0%
+segments and then uh he discovers that
+ 
+
+ align:start position:0%
+segments and then uh he discovers that
+there's four main areas which in fact
+
+ align:start position:0%
+there's four main areas which in fact
+ 
+
+ align:start position:0%
+there's four main areas which in fact
+have common names cervical
+
+ align:start position:0%
+have common names cervical
+ 
+
+ align:start position:0%
+have common names cervical
+thoracic something Lumber what's it in
+
+ align:start position:0%
+thoracic something Lumber what's it in
+ 
+
+ align:start position:0%
+thoracic something Lumber what's it in
+between lumber and
+
+ align:start position:0%
+between lumber and
+ 
+
+ align:start position:0%
+between lumber and
+sacral uh and those are activated in
+
+ align:start position:0%
+sacral uh and those are activated in
+ 
+
+ align:start position:0%
+sacral uh and those are activated in
+blocks and then uh each of those have
+
+ align:start position:0%
+blocks and then uh each of those have
+ 
+
+ align:start position:0%
+blocks and then uh each of those have
+three or four subblocks and each of
+
+ align:start position:0%
+three or four subblocks and each of
+ 
+
+ align:start position:0%
+three or four subblocks and each of
+those uh have
+
+ align:start position:0%
+those uh have
+ 
+
+ align:start position:0%
+those uh have
+specific effects for for different
+
+ align:start position:0%
+specific effects for for different
+ 
+
+ align:start position:0%
+specific effects for for different
+segments of the
+
+ align:start position:0%
+segments of the
+ 
+
+ align:start position:0%
+segments of the
+spine and apparently some of them are
+
+ align:start position:0%
+spine and apparently some of them are
+ 
+
+ align:start position:0%
+spine and apparently some of them are
+some of these are expressed because uh
+
+ align:start position:0%
+some of these are expressed because uh
+ 
+
+ align:start position:0%
+some of these are expressed because uh
+over here some chemical is expressed and
+
+ align:start position:0%
+over here some chemical is expressed and
+ 
+
+ align:start position:0%
+over here some chemical is expressed and
+has a high concentration here and less
+
+ align:start position:0%
+has a high concentration here and less
+ 
+
+ align:start position:0%
+has a high concentration here and less
+and less there and that uh affects so
+
+ align:start position:0%
+and less there and that uh affects so
+ 
+
+ align:start position:0%
+and less there and that uh affects so
+there's some analog stuff there too so
+
+ align:start position:0%
+there's some analog stuff there too so
+ 
+
+ align:start position:0%
+there's some analog stuff there too so
+that affects which genes get transcribed
+
+ align:start position:0%
+that affects which genes get transcribed
+ 
+
+ align:start position:0%
+that affects which genes get transcribed
+somehow
+
+ align:start position:0%
+somehow
+ 
+
+ align:start position:0%
+somehow
+uh but it seems to me
+
+ align:start position:0%
+uh but it seems to me
+ 
+
+ align:start position:0%
+uh but it seems to me
+that if you're going to teach Evolution
+
+ align:start position:0%
+that if you're going to teach Evolution
+ 
+
+ align:start position:0%
+that if you're going to teach Evolution
+at all you don't want to just say we're
+
+ align:start position:0%
+at all you don't want to just say we're
+ 
+
+ align:start position:0%
+at all you don't want to just say we're
+descended from chimpanzees but you want
+
+ align:start position:0%
+descended from chimpanzees but you want
+ 
+
+ align:start position:0%
+descended from chimpanzees but you want
+to say incidentally there's a really
+
+ align:start position:0%
+to say incidentally there's a really
+ 
+
+ align:start position:0%
+to say incidentally there's a really
+interesting thing and people are
+
+ align:start position:0%
+interesting thing and people are
+ 
+
+ align:start position:0%
+interesting thing and people are
+discovering I don't know why I mentioned
+
+ align:start position:0%
+discovering I don't know why I mentioned
+ 
+
+ align:start position:0%
+discovering I don't know why I mentioned
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but after I when I went to college I
+
+ align:start position:0%
+but after I when I went to college I
+ 
+
+ align:start position:0%
+but after I when I went to college I
+didn't know that people were still
+
+ align:start position:0%
+didn't know that people were still
+ 
+
+ align:start position:0%
+didn't know that people were still
+inventing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematics and so there are little
+
+ align:start position:0%
+mathematics and so there are little
+ 
+
+ align:start position:0%
+mathematics and so there are little
+things in education that just seem
+
+ align:start position:0%
+things in education that just seem
+ 
+
+ align:start position:0%
+things in education that just seem
+missing I went to
+
+ align:start position:0%
+missing I went to
+ 
+
+ align:start position:0%
+missing I went to
+a very Advanced school but somehow I
+
+ align:start position:0%
+a very Advanced school but somehow I
+ 
+
+ align:start position:0%
+a very Advanced school but somehow I
+didn't get the idea that oh look here's
+
+ align:start position:0%
+didn't get the idea that oh look here's
+ 
+
+ align:start position:0%
+didn't get the idea that oh look here's
+some mathematics you learn you can learn
+
+ align:start position:0%
+some mathematics you learn you can learn
+ 
+
+ align:start position:0%
+some mathematics you learn you can learn
+but you can also make it up and how many
+
+ align:start position:0%
+but you can also make it up and how many
+ 
+
+ align:start position:0%
+but you can also make it up and how many
+kids know that or do they think there's
+
+ align:start position:0%
+kids know that or do they think there's
+ 
+
+ align:start position:0%
+kids know that or do they think there's
+just high school algebra and and
+
+ align:start position:0%
+just high school algebra and and
+ 
+
+ align:start position:0%
+just high school algebra and and
+calculus and it's just all done
+
+ align:start position:0%
+calculus and it's just all done
+ 
+
+ align:start position:0%
+calculus and it's just all done
+and something funny about education did
+
+ align:start position:0%
+and something funny about education did
+ 
+
+ align:start position:0%
+and something funny about education did
+any of you how many of you knew that
+
+ align:start position:0%
+any of you how many of you knew that
+ 
+
+ align:start position:0%
+any of you how many of you knew that
+people were still in make making
+
+ align:start position:0%
+people were still in make making
+ 
+
+ align:start position:0%
+people were still in make making
+mathematics in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+school I probably had heard about it but
+
+ align:start position:0%
+school I probably had heard about it but
+ 
+
+ align:start position:0%
+school I probably had heard about it but
+I didn't really believe it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many of you have made up some
+
+ align:start position:0%
+how many of you have made up some
+ 
+
+ align:start position:0%
+how many of you have made up some
+mathematics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lately it kind of Mak sense think about
+
+ align:start position:0%
+lately it kind of Mak sense think about
+ 
+
+ align:start position:0%
+lately it kind of Mak sense think about
+Thomas Coon's book the structure of s
+
+ align:start position:0%
+Thomas Coon's book the structure of s
+ 
+
+ align:start position:0%
+Thomas Coon's book the structure of s
+revolutions and Paradigm shifts yes is
+
+ align:start position:0%
+revolutions and Paradigm shifts yes is
+ 
+
+ align:start position:0%
+revolutions and Paradigm shifts yes is
+that each new paradigm shift of
+
+ align:start position:0%
+that each new paradigm shift of
+ 
+
+ align:start position:0%
+that each new paradigm shift of
+knowledge like let's say there's a
+
+ align:start position:0%
+knowledge like let's say there's a
+ 
+
+ align:start position:0%
+knowledge like let's say there's a
+paradigm shift of mathematics or physics
+
+ align:start position:0%
+paradigm shift of mathematics or physics
+ 
+
+ align:start position:0%
+paradigm shift of mathematics or physics
+that entrenched itself as if it was the
+
+ align:start position:0%
+that entrenched itself as if it was the
+ 
+
+ align:start position:0%
+that entrenched itself as if it was the
+thing that always existed and then tries
+
+ align:start position:0%
+thing that always existed and then tries
+ 
+
+ align:start position:0%
+thing that always existed and then tries
+to produce itself to any other higher
+
+ align:start position:0%
+to produce itself to any other higher
+ 
+
+ align:start position:0%
+to produce itself to any other higher
+level organism so the reason like all
+
+ align:start position:0%
+level organism so the reason like all
+ 
+
+ align:start position:0%
+level organism so the reason like all
+the the entire sum all the paradigms and
+
+ align:start position:0%
+the the entire sum all the paradigms and
+ 
+
+ align:start position:0%
+the the entire sum all the paradigms and
+education just meant to sort of
+
+ align:start position:0%
+education just meant to sort of
+ 
+
+ align:start position:0%
+education just meant to sort of
+reproduce that and then someone will
+
+ align:start position:0%
+reproduce that and then someone will
+ 
+
+ align:start position:0%
+reproduce that and then someone will
+come along and say no that's not how to
+
+ align:start position:0%
+come along and say no that's not how to
+ 
+
+ align:start position:0%
+come along and say no that's not how to
+do it and they'll be like no you're
+
+ align:start position:0%
+do it and they'll be like no you're
+ 
+
+ align:start position:0%
+do it and they'll be like no you're
+wrong they prove that person right and
+
+ align:start position:0%
+wrong they prove that person right and
+ 
+
+ align:start position:0%
+wrong they prove that person right and
+they become parad and they become they
+
+ align:start position:0%
+they become parad and they become they
+ 
+
+ align:start position:0%
+they become parad and they become they
+entrench that as if that was the thing
+
+ align:start position:0%
+entrench that as if that was the thing
+ 
+
+ align:start position:0%
+entrench that as if that was the thing
+that was always
+
+ align:start position:0%
+that was always
+ 
+
+ align:start position:0%
+that was always
+yeah there certainly is a lot of
+
+ align:start position:0%
+yeah there certainly is a lot of
+ 
+
+ align:start position:0%
+yeah there certainly is a lot of
+rigidity
+
+ align:start position:0%
+rigidity
+ 
+
+ align:start position:0%
+rigidity
+about arithmetic and geometry and
+
+ align:start position:0%
+about arithmetic and geometry and
+ 
+
+ align:start position:0%
+about arithmetic and geometry and
+algebra and there are just so many other
+
+ align:start position:0%
+algebra and there are just so many other
+ 
+
+ align:start position:0%
+algebra and there are just so many other
+parts of
+
+ align:start position:0%
+parts of
+ 
+
+ align:start position:0%
+parts of
+math you can teach group Theory to fifth
+
+ align:start position:0%
+math you can teach group Theory to fifth
+ 
+
+ align:start position:0%
+math you can teach group Theory to fifth
+graders fourth graders and and uh it
+
+ align:start position:0%
+graders fourth graders and and uh it
+ 
+
+ align:start position:0%
+graders fourth graders and and uh it
+could be very liberating for some of
+
+ align:start position:0%
+could be very liberating for some of
+ 
+
+ align:start position:0%
+could be very liberating for some of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+because because you don't have to know
+
+ align:start position:0%
+because because you don't have to know
+ 
+
+ align:start position:0%
+because because you don't have to know
+anything to do grip Theory geometry sort
+
+ align:start position:0%
+anything to do grip Theory geometry sort
+ 
+
+ align:start position:0%
+anything to do grip Theory geometry sort
+of you have to understand the world and
+
+ align:start position:0%
+of you have to understand the world and
+ 
+
+ align:start position:0%
+of you have to understand the world and
+I don't know what I'm saying but but
+
+ align:start position:0%
+I don't know what I'm saying but but
+ 
+
+ align:start position:0%
+I don't know what I'm saying but but
+uh I don't think there's any point in
+
+ align:start position:0%
+uh I don't think there's any point in
+ 
+
+ align:start position:0%
+uh I don't think there's any point in
+there there are no moments in primary or
+
+ align:start position:0%
+there there are no moments in primary or
+ 
+
+ align:start position:0%
+there there are no moments in primary or
+secondary education where you get to
+
+ align:start position:0%
+secondary education where you get to
+ 
+
+ align:start position:0%
+secondary education where you get to
+invent some mathematics even if somebody
+
+ align:start position:0%
+invent some mathematics even if somebody
+ 
+
+ align:start position:0%
+invent some mathematics even if somebody
+else has invented it put people in a
+
+ align:start position:0%
+else has invented it put people in a
+ 
+
+ align:start position:0%
+else has invented it put people in a
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+where my daughter in high
+
+ align:start position:0%
+where my daughter in high
+ 
+
+ align:start position:0%
+where my daughter in high
+school I shouldn't discuss her but
+
+ align:start position:0%
+school I shouldn't discuss her but
+ 
+
+ align:start position:0%
+school I shouldn't discuss her but
+uh she got along very well with her
+
+ align:start position:0%
+uh she got along very well with her
+ 
+
+ align:start position:0%
+uh she got along very well with her
+English teacher
+
+ align:start position:0%
+English teacher
+ 
+
+ align:start position:0%
+English teacher
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh and uh he wanted to have some group
+
+ align:start position:0%
+uh and uh he wanted to have some group
+ 
+
+ align:start position:0%
+uh and uh he wanted to have some group
+activities so she
+
+ align:start position:0%
+activities so she
+ 
+
+ align:start position:0%
+activities so she
+invented a
+
+ align:start position:0%
+invented a
+ 
+
+ align:start position:0%
+invented a
+cute acute exercise that I mean she was
+
+ align:start position:0%
+cute acute exercise that I mean she was
+ 
+
+ align:start position:0%
+cute acute exercise that I mean she was
+she was good at programming already just
+
+ align:start position:0%
+she was good at programming already just
+ 
+
+ align:start position:0%
+she was good at programming already just
+runs in the family and uh so the English
+
+ align:start position:0%
+runs in the family and uh so the English
+ 
+
+ align:start position:0%
+runs in the family and uh so the English
+teacher agreed to give her the class
+
+ align:start position:0%
+teacher agreed to give her the class
+ 
+
+ align:start position:0%
+teacher agreed to give her the class
+class for a while and the game is this
+
+ align:start position:0%
+class for a while and the game is this
+ 
+
+ align:start position:0%
+class for a while and the game is this
+you uh you take pairs of students and
+
+ align:start position:0%
+you uh you take pairs of students and
+ 
+
+ align:start position:0%
+you uh you take pairs of students and
+you have a jigsaw puzzle and the
+
+ align:start position:0%
+you have a jigsaw puzzle and the
+ 
+
+ align:start position:0%
+you have a jigsaw puzzle and the
+students have a little phone booth they
+
+ align:start position:0%
+students have a little phone booth they
+ 
+
+ align:start position:0%
+students have a little phone booth they
+couldn't afford phone booths but uh but
+
+ align:start position:0%
+couldn't afford phone booths but uh but
+ 
+
+ align:start position:0%
+couldn't afford phone booths but uh but
+you could arrange it so they couldn't
+
+ align:start position:0%
+you could arrange it so they couldn't
+ 
+
+ align:start position:0%
+you could arrange it so they couldn't
+see each other and uh in each pair
+
+ align:start position:0%
+see each other and uh in each pair
+ 
+
+ align:start position:0%
+see each other and uh in each pair
+student a has to tell student B how to
+
+ align:start position:0%
+student a has to tell student B how to
+ 
+
+ align:start position:0%
+student a has to tell student B how to
+assemble this jigsaw puzzle it's a
+
+ align:start position:0%
+assemble this jigsaw puzzle it's a
+ 
+
+ align:start position:0%
+assemble this jigsaw puzzle it's a
+regular jigsaw puzzle and in order to do
+
+ align:start position:0%
+regular jigsaw puzzle and in order to do
+ 
+
+ align:start position:0%
+regular jigsaw puzzle and in order to do
+this you have to invent language for
+
+ align:start position:0%
+this you have to invent language for
+ 
+
+ align:start position:0%
+this you have to invent language for
+describing jigsaw puzzled parts and
+
+ align:start position:0%
+describing jigsaw puzzled parts and
+ 
+
+ align:start position:0%
+describing jigsaw puzzled parts and
+relations that's very simple and you
+
+ align:start position:0%
+relations that's very simple and you
+ 
+
+ align:start position:0%
+relations that's very simple and you
+know people would start out with uh the
+
+ align:start position:0%
+know people would start out with uh the
+ 
+
+ align:start position:0%
+know people would start out with uh the
+one with a bulge that looks like a head
+
+ align:start position:0%
+one with a bulge that looks like a head
+ 
+
+ align:start position:0%
+one with a bulge that looks like a head
+or whatever and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and some of the students in fact
+
+ align:start position:0%
+uh and some of the students in fact
+ 
+
+ align:start position:0%
+uh and some of the students in fact
+ended up uh defining little formal
+
+ align:start position:0%
+ended up uh defining little formal
+ 
+
+ align:start position:0%
+ended up uh defining little formal
+languages to describe the perimeters and
+
+ align:start position:0%
+languages to describe the perimeters and
+ 
+
+ align:start position:0%
+languages to describe the perimeters and
+and stuff like that and uh they did
+
+ align:start position:0%
+and stuff like that and uh they did
+ 
+
+ align:start position:0%
+and stuff like that and uh they did
+better than the ones who uh couldn't
+
+ align:start position:0%
+better than the ones who uh couldn't
+ 
+
+ align:start position:0%
+better than the ones who uh couldn't
+Express the
+
+ align:start position:0%
+Express the
+ 
+
+ align:start position:0%
+Express the
+shapes it's just a little point but uh
+
+ align:start position:0%
+shapes it's just a little point but uh
+ 
+
+ align:start position:0%
+shapes it's just a little point but uh
+how often do you ask students to make a
+
+ align:start position:0%
+how often do you ask students to make a
+ 
+
+ align:start position:0%
+how often do you ask students to make a
+formal
+
+ align:start position:0%
+formal
+ 
+
+ align:start position:0%
+formal
+language or and if you can make a formal
+
+ align:start position:0%
+language or and if you can make a formal
+ 
+
+ align:start position:0%
+language or and if you can make a formal
+language then you can probably prove
+
+ align:start position:0%
+language then you can probably prove
+ 
+
+ align:start position:0%
+language then you can probably prove
+something about it although I don't
+
+ align:start position:0%
+something about it although I don't
+ 
+
+ align:start position:0%
+something about it although I don't
+think they went that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far but I don't
+
+ align:start position:0%
+far but I don't
+ 
+
+ align:start position:0%
+far but I don't
+know don't know what they teach in
+
+ align:start position:0%
+know don't know what they teach in
+ 
+
+ align:start position:0%
+know don't know what they teach in
+math
+
+ align:start position:0%
+math
+ 
+
+ align:start position:0%
+math
+there was Professor lanu
+
+ align:start position:0%
+there was Professor lanu
+ 
+
+ align:start position:0%
+there was Professor lanu
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh who said he didn't learn arithmetic
+
+ align:start position:0%
+uh who said he didn't learn arithmetic
+ 
+
+ align:start position:0%
+uh who said he didn't learn arithmetic
+till he
+
+ align:start position:0%
+till he
+ 
+
+ align:start position:0%
+till he
+was 11 or
+
+ align:start position:0%
+was 11 or
+ 
+
+ align:start position:0%
+was 11 or
+12 and he became a great
+
+ align:start position:0%
+12 and he became a great
+ 
+
+ align:start position:0%
+12 and he became a great
+physicist and he said because in in his
+
+ align:start position:0%
+physicist and he said because in in his
+ 
+
+ align:start position:0%
+physicist and he said because in in his
+culture they didn't have that in
+
+ align:start position:0%
+culture they didn't have that in
+ 
+
+ align:start position:0%
+culture they didn't have that in
+elementary school in
+
+ align:start position:0%
+elementary school in
+ 
+
+ align:start position:0%
+elementary school in
+China and as far as he knew it was a big
+
+ align:start position:0%
+China and as far as he knew it was a big
+ 
+
+ align:start position:0%
+China and as far as he knew it was a big
+advantage
+
+ align:start position:0%
+advantage
+ 
+
+ align:start position:0%
+advantage
+AG
+
+ align:start position:0%
+AG
+ 
+
+ align:start position:0%
+AG
+because arithmetic is the main reason
+
+ align:start position:0%
+because arithmetic is the main reason
+ 
+
+ align:start position:0%
+because arithmetic is the main reason
+why almost all children hate
+
+ align:start position:0%
+why almost all children hate
+ 
+
+ align:start position:0%
+why almost all children hate
+mathematics it's really a very
+
+ align:start position:0%
+mathematics it's really a very
+ 
+
+ align:start position:0%
+mathematics it's really a very
+impoverished subject and you spend years
+
+ align:start position:0%
+impoverished subject and you spend years
+ 
+
+ align:start position:0%
+impoverished subject and you spend years
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+it maybe it's just wrong but uh anybody
+
+ align:start position:0%
+it maybe it's just wrong but uh anybody
+ 
+
+ align:start position:0%
+it maybe it's just wrong but uh anybody
+who tried not to teach it would be in
+
+ align:start position:0%
+who tried not to teach it would be in
+ 
+
+ align:start position:0%
+who tried not to teach it would be in
+jail it's the Paradigm is not just a
+
+ align:start position:0%
+jail it's the Paradigm is not just a
+ 
+
+ align:start position:0%
+jail it's the Paradigm is not just a
+cultural one but it's it's just about
+
+ align:start position:0%
+cultural one but it's it's just about
+ 
+
+ align:start position:0%
+cultural one but it's it's just about
+religion
+
+ align:start position:0%
+religion
+ 
+
+ align:start position:0%
+religion
+right in jail if you went against the
+
+ align:start position:0%
+right in jail if you went against the
+ 
+
+ align:start position:0%
+right in jail if you went against the
+Catholic church in 1500s now you go now
+
+ align:start position:0%
+Catholic church in 1500s now you go now
+ 
+
+ align:start position:0%
+Catholic church in 1500s now you go now
+you accepted if you went against the
+
+ align:start position:0%
+you accepted if you went against the
+ 
+
+ align:start position:0%
+you accepted if you went against the
+Orthodoxy that's entrenched as if that's
+
+ align:start position:0%
+Orthodoxy that's entrenched as if that's
+ 
+
+ align:start position:0%
+Orthodoxy that's entrenched as if that's
+the way it has to be naturally I'd say
+
+ align:start position:0%
+the way it has to be naturally I'd say
+ 
+
+ align:start position:0%
+the way it has to be naturally I'd say
+that the No Child Left Behind thing is
+
+ align:start position:0%
+that the No Child Left Behind thing is
+ 
+
+ align:start position:0%
+that the No Child Left Behind thing is
+is almost like a religious Dogma system
+
+ align:start position:0%
+is almost like a religious Dogma system
+ 
+
+ align:start position:0%
+is almost like a religious Dogma system
+this list list of exactly what you
+
+ align:start position:0%
+this list list of exactly what you
+ 
+
+ align:start position:0%
+this list list of exactly what you
+should learn it's also oxymoronic right
+
+ align:start position:0%
+should learn it's also oxymoronic right
+ 
+
+ align:start position:0%
+should learn it's also oxymoronic right
+No Child Left Behind they take money
+
+ align:start position:0%
+No Child Left Behind they take money
+ 
+
+ align:start position:0%
+No Child Left Behind they take money
+away from the schools doing bad it's
+
+ align:start position:0%
+away from the schools doing bad it's
+ 
+
+ align:start position:0%
+away from the schools doing bad it's
+very funny
+
+ align:start position:0%
+very funny
+ 
+
+ align:start position:0%
+very funny
+I feel that every child should learn
+
+ align:start position:0%
+I feel that every child should learn
+ 
+
+ align:start position:0%
+I feel that every child should learn
+what a diminished seventh chord is it's
+
+ align:start position:0%
+what a diminished seventh chord is it's
+ 
+
+ align:start position:0%
+what a diminished seventh chord is it's
+a little thing in music which allows you
+
+ align:start position:0%
+a little thing in music which allows you
+ 
+
+ align:start position:0%
+a little thing in music which allows you
+to get from any key to any other key in
+
+ align:start position:0%
+to get from any key to any other key in
+ 
+
+ align:start position:0%
+to get from any key to any other key in
+two steps and why isn't that just as
+
+ align:start position:0%
+two steps and why isn't that just as
+ 
+
+ align:start position:0%
+two steps and why isn't that just as
+important as whatever whatever they're
+
+ align:start position:0%
+important as whatever whatever they're
+ 
+
+ align:start position:0%
+important as whatever whatever they're
+teaching
+
+ align:start position:0%
+teaching
+ 
+
+ align:start position:0%
+teaching
+instead just so many things you could do
+
+ align:start position:0%
+instead just so many things you could do
+ 
+
+ align:start position:0%
+instead just so many things you could do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are that give you more power over
+
+ align:start position:0%
+are that give you more power over
+ 
+
+ align:start position:0%
+are that give you more power over
+something how many of you know how to
+
+ align:start position:0%
+something how many of you know how to
+ 
+
+ align:start position:0%
+something how many of you know how to
+use a diminish seventh Accord oh come on
+
+ align:start position:0%
+use a diminish seventh Accord oh come on
+ 
+
+ align:start position:0%
+use a diminish seventh Accord oh come on
+what now we
+
+ align:start position:0%
+what now we
+ 
+
+ align:start position:0%
+what now we
+do it to C E flat F sharp a if you
+
+ align:start position:0%
+do it to C E flat F sharp a if you
+ 
+
+ align:start position:0%
+do it to C E flat F sharp a if you
+change any note down you get a dominant
+
+ align:start position:0%
+change any note down you get a dominant
+ 
+
+ align:start position:0%
+change any note down you get a dominant
+seventh so you can go to Four Keys just
+
+ align:start position:0%
+seventh so you can go to Four Keys just
+ 
+
+ align:start position:0%
+seventh so you can go to Four Keys just
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+way uh and composers use it all the time
+
+ align:start position:0%
+way uh and composers use it all the time
+ 
+
+ align:start position:0%
+way uh and composers use it all the time
+whether they know it or not it's
+
+ align:start position:0%
+whether they know it or not it's
+ 
+
+ align:start position:0%
+whether they know it or not it's
+just because it's it's the top of a
+
+ align:start position:0%
+just because it's it's the top of a
+ 
+
+ align:start position:0%
+just because it's it's the top of a
+ninth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this what time is it this thing in
+
+ align:start position:0%
+uh this what time is it this thing in
+ 
+
+ align:start position:0%
+uh this what time is it this thing in
+the middle of chapter 4 is that clock
+
+ align:start position:0%
+the middle of chapter 4 is that clock
+ 
+
+ align:start position:0%
+the middle of chapter 4 is that clock
+right an
+
+ align:start position:0%
+right an
+ 
+
+ align:start position:0%
+right an
+hour I was I was wondering how I could
+
+ align:start position:0%
+hour I was I was wondering how I could
+ 
+
+ align:start position:0%
+hour I was I was wondering how I could
+have said so much in an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hour okay uh but I love this quotation
+
+ align:start position:0%
+hour okay uh but I love this quotation
+ 
+
+ align:start position:0%
+hour okay uh but I love this quotation
+by by Patrick Hayes
+
+ align:start position:0%
+by by Patrick Hayes
+ 
+
+ align:start position:0%
+by by Patrick Hayes
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh when people talk about Consciousness
+
+ align:start position:0%
+uh when people talk about Consciousness
+ 
+
+ align:start position:0%
+uh when people talk about Consciousness
+they assume that it's such a great thing
+
+ align:start position:0%
+they assume that it's such a great thing
+ 
+
+ align:start position:0%
+they assume that it's such a great thing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh you'll find that in chapter 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh why be in the engine room if we could
+
+ align:start position:0%
+uh why be in the engine room if we could
+ 
+
+ align:start position:0%
+uh why be in the engine room if we could
+be on the bridge he concludes it's it's
+
+ align:start position:0%
+be on the bridge he concludes it's it's
+ 
+
+ align:start position:0%
+be on the bridge he concludes it's it's
+a lovely lovely paragraph and uh then I
+
+ align:start position:0%
+a lovely lovely paragraph and uh then I
+ 
+
+ align:start position:0%
+a lovely lovely paragraph and uh then I
+have a I have a similar paragraph that I
+
+ align:start position:0%
+have a I have a similar paragraph that I
+ 
+
+ align:start position:0%
+have a I have a similar paragraph that I
+wrote for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+consider how you can drive a car without
+
+ align:start position:0%
+consider how you can drive a car without
+ 
+
+ align:start position:0%
+consider how you can drive a car without
+knowing how the engine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+and when you come to think of it we
+
+ align:start position:0%
+and when you come to think of it we
+ 
+
+ align:start position:0%
+and when you come to think of it we
+drive our bodies in this and Minds in
+
+ align:start position:0%
+drive our bodies in this and Minds in
+ 
+
+ align:start position:0%
+drive our bodies in this and Minds in
+the same way and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is maybe I didn't quote the whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the image is that you work your mind
+
+ align:start position:0%
+but the image is that you work your mind
+ 
+
+ align:start position:0%
+but the image is that you work your mind
+just the way uh you play a uh computer
+
+ align:start position:0%
+just the way uh you play a uh computer
+ 
+
+ align:start position:0%
+just the way uh you play a uh computer
+game on your
+
+ align:start position:0%
+game on your
+ 
+
+ align:start position:0%
+game on your
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+Xbox namely the so-called conscious mind
+
+ align:start position:0%
+Xbox namely the so-called conscious mind
+ 
+
+ align:start position:0%
+Xbox namely the so-called conscious mind
+is pressing little buttons and things
+
+ align:start position:0%
+is pressing little buttons and things
+ 
+
+ align:start position:0%
+is pressing little buttons and things
+appear and uh you get images and ideas
+
+ align:start position:0%
+appear and uh you get images and ideas
+ 
+
+ align:start position:0%
+appear and uh you get images and ideas
+and they pop up on your uh mental screen
+
+ align:start position:0%
+and they pop up on your uh mental screen
+ 
+
+ align:start position:0%
+and they pop up on your uh mental screen
+and people talk about how wonderful this
+
+ align:start position:0%
+and people talk about how wonderful this
+ 
+
+ align:start position:0%
+and people talk about how wonderful this
+is but it's
+
+ align:start position:0%
+is but it's
+ 
+
+ align:start position:0%
+is but it's
+as far as I can tell Consciousness is
+
+ align:start position:0%
+as far as I can tell Consciousness is
+ 
+
+ align:start position:0%
+as far as I can tell Consciousness is
+not very
+
+ align:start position:0%
+not very
+ 
+
+ align:start position:0%
+not very
+bright and uh it tells you Al it tells
+
+ align:start position:0%
+bright and uh it tells you Al it tells
+ 
+
+ align:start position:0%
+bright and uh it tells you Al it tells
+you things that are happening in some
+
+ align:start position:0%
+you things that are happening in some
+ 
+
+ align:start position:0%
+you things that are happening in some
+vague way but it doesn't tell you why
+
+ align:start position:0%
+vague way but it doesn't tell you why
+ 
+
+ align:start position:0%
+vague way but it doesn't tell you why
+they are happening at all and all this
+
+ align:start position:0%
+they are happening at all and all this
+ 
+
+ align:start position:0%
+they are happening at all and all this
+fuss about the uh wonders of subjective
+
+ align:start position:0%
+fuss about the uh wonders of subjective
+ 
+
+ align:start position:0%
+fuss about the uh wonders of subjective
+experience seem very shallow when you uh
+
+ align:start position:0%
+experience seem very shallow when you uh
+ 
+
+ align:start position:0%
+experience seem very shallow when you uh
+read these two paragraphs uh at least
+
+ align:start position:0%
+read these two paragraphs uh at least
+ 
+
+ align:start position:0%
+read these two paragraphs uh at least
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certainly the one by Patrick
+
+ align:start position:0%
+certainly the one by Patrick
+ 
+
+ align:start position:0%
+certainly the one by Patrick
+Hayes
+
+ align:start position:0%
+Hayes
+ 
+
+ align:start position:0%
+Hayes
+uh because he goes on to say in fact
+
+ align:start position:0%
+uh because he goes on to say in fact
+ 
+
+ align:start position:0%
+uh because he goes on to say in fact
+imagine if you did have to understand
+
+ align:start position:0%
+imagine if you did have to understand
+ 
+
+ align:start position:0%
+imagine if you did have to understand
+how your mind worked at every moment
+
+ align:start position:0%
+how your mind worked at every moment
+ 
+
+ align:start position:0%
+how your mind worked at every moment
+then you'd never get around to doing
+
+ align:start position:0%
+then you'd never get around to doing
+ 
+
+ align:start position:0%
+then you'd never get around to doing
+anything if you really had any self-
+
+ align:start position:0%
+anything if you really had any self-
+ 
+
+ align:start position:0%
+anything if you really had any self-
+insight you'd be so slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+I wrote the one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about this was from an introduction to a
+
+ align:start position:0%
+about this was from an introduction to a
+ 
+
+ align:start position:0%
+about this was from an introduction to a
+wonderful book by verer vingi who is
+
+ align:start position:0%
+wonderful book by verer vingi who is
+ 
+
+ align:start position:0%
+wonderful book by verer vingi who is
+science fiction writer wrote a a little
+
+ align:start position:0%
+science fiction writer wrote a a little
+ 
+
+ align:start position:0%
+science fiction writer wrote a a little
+novel called true names and true names
+
+ align:start position:0%
+novel called true names and true names
+ 
+
+ align:start position:0%
+novel called true names and true names
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+uh really it's the second or third novel
+
+ align:start position:0%
+uh really it's the second or third novel
+ 
+
+ align:start position:0%
+uh really it's the second or third novel
+which described what the web would be
+
+ align:start position:0%
+which described what the web would be
+ 
+
+ align:start position:0%
+which described what the web would be
+like there was Shockwave Rider by I
+
+ align:start position:0%
+like there was Shockwave Rider by I
+ 
+
+ align:start position:0%
+like there was Shockwave Rider by I
+forget who uh in
+
+ align:start position:0%
+forget who uh in
+ 
+
+ align:start position:0%
+forget who uh in
+the late 50s which described a worldwide
+
+ align:start position:0%
+the late 50s which described a worldwide
+ 
+
+ align:start position:0%
+the late 50s which described a worldwide
+web and uh various hackers Who were
+
+ align:start position:0%
+web and uh various hackers Who were
+ 
+
+ align:start position:0%
+web and uh various hackers Who were
+exploiting
+
+ align:start position:0%
+exploiting
+ 
+
+ align:start position:0%
+exploiting
+or sabotaging it in various ways verer
+
+ align:start position:0%
+or sabotaging it in various ways verer
+ 
+
+ align:start position:0%
+or sabotaging it in various ways verer
+vingi describes this worldwide game that
+
+ align:start position:0%
+vingi describes this worldwide game that
+ 
+
+ align:start position:0%
+vingi describes this worldwide game that
+everybody's playing the thing is called
+
+ align:start position:0%
+everybody's playing the thing is called
+ 
+
+ align:start position:0%
+everybody's playing the thing is called
+true name because the people get very
+
+ align:start position:0%
+true name because the people get very
+ 
+
+ align:start position:0%
+true name because the people get very
+wrapped up in this you know second world
+
+ align:start position:0%
+wrapped up in this you know second world
+ 
+
+ align:start position:0%
+wrapped up in this you know second world
+and uh millions of people on the planet
+
+ align:start position:0%
+and uh millions of people on the planet
+ 
+
+ align:start position:0%
+and uh millions of people on the planet
+are completely occupied with uh being
+
+ align:start position:0%
+are completely occupied with uh being
+ 
+
+ align:start position:0%
+are completely occupied with uh being
+successful at this game which goes
+
+ align:start position:0%
+successful at this game which goes
+ 
+
+ align:start position:0%
+successful at this game which goes
+everywhere and uh if some opponent is
+
+ align:start position:0%
+everywhere and uh if some opponent is
+ 
+
+ align:start position:0%
+everywhere and uh if some opponent is
+really uh frustrating you uh then if you
+
+ align:start position:0%
+really uh frustrating you uh then if you
+ 
+
+ align:start position:0%
+really uh frustrating you uh then if you
+could you'd actually go out and kill him
+
+ align:start position:0%
+could you'd actually go out and kill him
+ 
+
+ align:start position:0%
+could you'd actually go out and kill him
+so people have to use aliases and the
+
+ align:start position:0%
+so people have to use aliases and the
+ 
+
+ align:start position:0%
+so people have to use aliases and the
+novel's called true name because nobody
+
+ align:start position:0%
+novel's called true name because nobody
+ 
+
+ align:start position:0%
+novel's called true name because nobody
+ever logs in with their real name
+
+ align:start position:0%
+ever logs in with their real name
+ 
+
+ align:start position:0%
+ever logs in with their real name
+because they're afraid that other
+
+ align:start position:0%
+because they're afraid that other
+ 
+
+ align:start position:0%
+because they're afraid that other
+players will come in out and get them so
+
+ align:start position:0%
+players will come in out and get them so
+ 
+
+ align:start position:0%
+players will come in out and get them so
+U and I wrote that essay which you'll
+
+ align:start position:0%
+U and I wrote that essay which you'll
+ 
+
+ align:start position:0%
+U and I wrote that essay which you'll
+find it's in the Society of mine
+
+ align:start position:0%
+find it's in the Society of mine
+ 
+
+ align:start position:0%
+find it's in the Society of mine
+mostly because the publisher thought
+
+ align:start position:0%
+mostly because the publisher thought
+ 
+
+ align:start position:0%
+mostly because the publisher thought
+that verer vingi's book was too
+
+ align:start position:0%
+that verer vingi's book was too
+ 
+
+ align:start position:0%
+that verer vingi's book was too
+short and said oh it needs another 30 or
+
+ align:start position:0%
+short and said oh it needs another 30 or
+ 
+
+ align:start position:0%
+short and said oh it needs another 30 or
+40 pages or we won't publish
+
+ align:start position:0%
+40 pages or we won't publish
+ 
+
+ align:start position:0%
+40 pages or we won't publish
+it so that was a I would never have
+
+ align:start position:0%
+it so that was a I would never have
+ 
+
+ align:start position:0%
+it so that was a I would never have
+written that paper except that I thought
+
+ align:start position:0%
+written that paper except that I thought
+ 
+
+ align:start position:0%
+written that paper except that I thought
+this novel was so
+
+ align:start position:0%
+this novel was so
+ 
+
+ align:start position:0%
+this novel was so
+good well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess it's
+
+ align:start position:0%
+I guess it's
+ 
+
+ align:start position:0%
+I guess it's
+late
\ No newline at end of file
diff --git a/7XEUB_dTaK0.txt b/7XEUB_dTaK0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5aea6012698e2f383e6bdf5a91eff26189778e70
--- /dev/null
+++ b/7XEUB_dTaK0.txt
@@ -0,0 +1,427 @@
+align:start position:0%
+ 
+in this problem we are given a function
+
+ align:start position:0%
+in this problem we are given a function
+ 
+
+ align:start position:0%
+in this problem we are given a function
+Z equal to a or B and C the whole thing
+
+ align:start position:0%
+Z equal to a or B and C the whole thing
+ 
+
+ align:start position:0%
+Z equal to a or B and C the whole thing
+negated we are then asked to produce a
+
+ align:start position:0%
+negated we are then asked to produce a
+ 
+
+ align:start position:0%
+negated we are then asked to produce a
+CMOS circuit that implements the
+
+ align:start position:0%
+CMOS circuit that implements the
+ 
+
+ align:start position:0%
+CMOS circuit that implements the
+function Z we know that our CMOS
+
+ align:start position:0%
+function Z we know that our CMOS
+ 
+
+ align:start position:0%
+function Z we know that our CMOS
+circuits consists of a pulldown circuit
+
+ align:start position:0%
+circuits consists of a pulldown circuit
+ 
+
+ align:start position:0%
+circuits consists of a pulldown circuit
+made of purely event FETs and it is
+
+ align:start position:0%
+made of purely event FETs and it is
+ 
+
+ align:start position:0%
+made of purely event FETs and it is
+called pulled down because if it is on
+
+ align:start position:0%
+called pulled down because if it is on
+ 
+
+ align:start position:0%
+called pulled down because if it is on
+it connects the output to ground to
+
+ align:start position:0%
+it connects the output to ground to
+ 
+
+ align:start position:0%
+it connects the output to ground to
+produce a low or zero output we also
+
+ align:start position:0%
+produce a low or zero output we also
+ 
+
+ align:start position:0%
+produce a low or zero output we also
+have a pull-up circuit made up purely of
+
+ align:start position:0%
+have a pull-up circuit made up purely of
+ 
+
+ align:start position:0%
+have a pull-up circuit made up purely of
+P FETs and it is called a pull-up
+
+ align:start position:0%
+P FETs and it is called a pull-up
+ 
+
+ align:start position:0%
+P FETs and it is called a pull-up
+because if it is on it connects the
+
+ align:start position:0%
+because if it is on it connects the
+ 
+
+ align:start position:0%
+because if it is on it connects the
+output to VDD to produce a high or one
+
+ align:start position:0%
+output to VDD to produce a high or one
+ 
+
+ align:start position:0%
+output to VDD to produce a high or one
+output if Z equals not of a or B and C
+
+ align:start position:0%
+output if Z equals not of a or B and C
+ 
+
+ align:start position:0%
+output if Z equals not of a or B and C
+then not C equals a or b and C to draw
+
+ align:start position:0%
+then not C equals a or b and C to draw
+ 
+
+ align:start position:0%
+then not C equals a or b and C to draw
+the pulldown portion of the circuit we
+
+ align:start position:0%
+the pulldown portion of the circuit we
+ 
+
+ align:start position:0%
+the pulldown portion of the circuit we
+take a look at when the function
+
+ align:start position:0%
+take a look at when the function
+ 
+
+ align:start position:0%
+take a look at when the function
+produces Z equal to zero this occurs
+
+ align:start position:0%
+produces Z equal to zero this occurs
+ 
+
+ align:start position:0%
+produces Z equal to zero this occurs
+when a or B and C equals 1 so the
+
+ align:start position:0%
+when a or B and C equals 1 so the
+ 
+
+ align:start position:0%
+when a or B and C equals 1 so the
+pulldown circuitry should be on when a
+
+ align:start position:0%
+pulldown circuitry should be on when a
+ 
+
+ align:start position:0%
+pulldown circuitry should be on when a
+or B and C equals 1 so a or B equals 1
+
+ align:start position:0%
+or B and C equals 1 so a or B equals 1
+ 
+
+ align:start position:0%
+or B and C equals 1 so a or B equals 1
+and C equals 1 this means that we want a
+
+ align:start position:0%
+and C equals 1 this means that we want a
+ 
+
+ align:start position:0%
+and C equals 1 this means that we want a
+parallel a B in series with C circuit
+
+ align:start position:0%
+parallel a B in series with C circuit
+ 
+
+ align:start position:0%
+parallel a B in series with C circuit
+for our pulldown the parallel a B
+
+ align:start position:0%
+for our pulldown the parallel a B
+ 
+
+ align:start position:0%
+for our pulldown the parallel a B
+corresponds to a or B equal to 1 because
+
+ align:start position:0%
+corresponds to a or B equal to 1 because
+ 
+
+ align:start position:0%
+corresponds to a or B equal to 1 because
+if either A or B equals 1 then we have a
+
+ align:start position:0%
+if either A or B equals 1 then we have a
+ 
+
+ align:start position:0%
+if either A or B equals 1 then we have a
+path from z to the bottom of the
+
+ align:start position:0%
+path from z to the bottom of the
+ 
+
+ align:start position:0%
+path from z to the bottom of the
+parallel circuitry then if C is also 1
+
+ align:start position:0%
+parallel circuitry then if C is also 1
+ 
+
+ align:start position:0%
+parallel circuitry then if C is also 1
+we complete our path between Z and
+
+ align:start position:0%
+we complete our path between Z and
+ 
+
+ align:start position:0%
+we complete our path between Z and
+ground so if either a equals 1 and C
+
+ align:start position:0%
+ground so if either a equals 1 and C
+ 
+
+ align:start position:0%
+ground so if either a equals 1 and C
+equals 1 or B equals 1 and C equals 1 z
+
+ align:start position:0%
+equals 1 or B equals 1 and C equals 1 z
+ 
+
+ align:start position:0%
+equals 1 or B equals 1 and C equals 1 z
+is pulled down to ground and produces a
+
+ align:start position:0%
+is pulled down to ground and produces a
+ 
+
+ align:start position:0%
+is pulled down to ground and produces a
+0 output to generate our pull up we
+
+ align:start position:0%
+0 output to generate our pull up we
+ 
+
+ align:start position:0%
+0 output to generate our pull up we
+simply replace parallel circuits with
+
+ align:start position:0%
+simply replace parallel circuits with
+ 
+
+ align:start position:0%
+simply replace parallel circuits with
+series and series with parallel this
+
+ align:start position:0%
+series and series with parallel this
+ 
+
+ align:start position:0%
+series and series with parallel this
+will ensure that whenever our pulldown
+
+ align:start position:0%
+will ensure that whenever our pulldown
+ 
+
+ align:start position:0%
+will ensure that whenever our pulldown
+circuit is off our pull-up circuit is on
+
+ align:start position:0%
+circuit is off our pull-up circuit is on
+ 
+
+ align:start position:0%
+circuit is off our pull-up circuit is on
+so our pull up circuitry is series a B
+
+ align:start position:0%
+so our pull up circuitry is series a B
+ 
+
+ align:start position:0%
+so our pull up circuitry is series a B
+in parallel with C to convince ourselves
+
+ align:start position:0%
+in parallel with C to convince ourselves
+ 
+
+ align:start position:0%
+in parallel with C to convince ourselves
+that this is in fact the correct pull-up
+
+ align:start position:0%
+that this is in fact the correct pull-up
+ 
+
+ align:start position:0%
+that this is in fact the correct pull-up
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+we know that the pull-up must make Z
+
+ align:start position:0%
+we know that the pull-up must make Z
+ 
+
+ align:start position:0%
+we know that the pull-up must make Z
+equal to one Z equals one if a or B and
+
+ align:start position:0%
+equal to one Z equals one if a or B and
+ 
+
+ align:start position:0%
+equal to one Z equals one if a or B and
+C the whole thing negated equals one or
+
+ align:start position:0%
+C the whole thing negated equals one or
+ 
+
+ align:start position:0%
+C the whole thing negated equals one or
+a or B and C equals zero this is true
+
+ align:start position:0%
+a or B and C equals zero this is true
+ 
+
+ align:start position:0%
+a or B and C equals zero this is true
+when either A or B equals 0 or C equals
+
+ align:start position:0%
+when either A or B equals 0 or C equals
+ 
+
+ align:start position:0%
+when either A or B equals 0 or C equals
+0 this means that either a equals 0 and
+
+ align:start position:0%
+0 this means that either a equals 0 and
+ 
+
+ align:start position:0%
+0 this means that either a equals 0 and
+B equals 0 or just C equals 0 pull-up
+
+ align:start position:0%
+B equals 0 or just C equals 0 pull-up
+ 
+
+ align:start position:0%
+B equals 0 or just C equals 0 pull-up
+circuits use P FETs which are on when
+
+ align:start position:0%
+circuits use P FETs which are on when
+ 
+
+ align:start position:0%
+circuits use P FETs which are on when
+the input is low or zero so the
+
+ align:start position:0%
+the input is low or zero so the
+ 
+
+ align:start position:0%
+the input is low or zero so the
+equivalent circuit for this is series a
+
+ align:start position:0%
+equivalent circuit for this is series a
+ 
+
+ align:start position:0%
+equivalent circuit for this is series a
+B or D with C which is equal to series a
+
+ align:start position:0%
+B or D with C which is equal to series a
+ 
+
+ align:start position:0%
+B or D with C which is equal to series a
+B in parallel with C
\ No newline at end of file
diff --git a/8MWU1PxvaDY.txt b/8MWU1PxvaDY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f57854968c3e83c090ae9eb545d9b2704d82fcba
--- /dev/null
+++ b/8MWU1PxvaDY.txt
@@ -0,0 +1,221 @@
+Let's turn our attention to how the operating
+system (OS) deals with input/output devices.
+
+There are actually two parts to the discussion.
+
+First, we'll talk about how the OS interacts
+with the devices themselves.
+
+This will involve a combination of interrupt
+handlers and kernel buffers.
+
+Then we'll discuss how supervisor calls access
+the kernel buffers in response to requests
+
+from user-mode processes.
+
+As we'll see, this can get a bit tricky when
+the OS cannot complete the request at the
+
+time the SVC was executed.
+
+Here's the plan!
+
+When the user types a key on the keyboard,
+the keyboard triggers an interrupt request
+
+to the CPU.
+
+The interrupt suspends execution of the currently-running
+process and executes the handler whose job
+
+it is to deal with this particular I/O event.
+
+In this case, the keyboard handler reads the
+character from the keyboard and saves it in
+
+a kernel buffer associated with the process
+that has been chosen to receive incoming keystrokes.
+
+In the language of OSes, we'd say that process
+has the keyboard focus.
+
+This transfer takes just a handful of instructions
+and when the handler exits, we resume running
+
+the interrupted process.
+
+Assuming the interrupt request is serviced
+promptly, the CPU can easily keep up with
+
+the arrival of typed characters.
+
+Humans are pretty slow compared to the rate
+of executing instructions!
+
+But the buffer in the kernel can hold only
+so many characters before it fills up.
+
+What happens then?
+
+Well, there are a couple of choices.
+
+Overwriting characters received earlier doesn't
+make much sense: why keep later characters
+
+if the earlier ones have been discarded.
+
+Better that the CPU discard any characters
+received after the buffer was full, but it
+
+should give some indication that it's doing
+so.
+
+And, in fact, many systems beep at the user
+to signal that the character they've just
+
+typed is being ignored.
+
+At some later time, a user-mode program executes
+a ReadKey() supervisor call, requesting that
+
+the OS return the next character in R0.
+
+In the OS, the ReadKey SVC handler grabs the
+next character from the buffer, places it
+
+in the user's R0, and resumes execution at
+the instruction following the SVC.
+
+There are few tricky bits we need to figure
+out.
+
+The ReadKey() SVC is what we call a "blocking
+I/O" request, i.e., the program assumes that
+
+when the SVC returns, the next character is
+in R0.
+
+If there isn't (yet) a character to be returned,
+execution should be "blocked", i.e., suspended,
+
+until such time that a character is available.
+
+Many OSes also provide for non-blocking I/O
+requests, which always return immediately
+
+with both a status flag and a result.
+
+The program can check the status flag to see
+if there was a character and do the right
+
+thing if there wasn't, e.g., reissue the request
+at a later time.
+
+Note that the user-mode program didn't have
+any direct interaction with the keyboard,
+
+i.e., it's not constantly polling the device
+to see if there's a keystroke to be processed.
+
+Instead, we're using an "event-driven" approach,
+where the device signals the OS, via an interrupt,
+
+when it needs attention.
+
+This is an elegant separation of responsibilities.
+
+Imagine how cumbersome it would be if every
+program had to check constantly to see if
+
+there were pending I/O operations.
+
+Our event-driven organization provides for
+on-demand servicing of devices, but doesn't
+
+devote CPU resources to the I/O subsystem
+until there's actually work to be done.
+
+The interrupt-driven OS interactions with
+I/O devices are completely transparent to
+
+user programs.
+
+Here's sketch of what the OS keyboard handler
+code might actually look like.
+
+Depending on the hardware, the CPU might access
+device status and data using special I/O instructions
+
+in the ISA.
+
+For example, in the simulated Beta used for
+lab assignments, there's a RDCHAR() instruction
+
+for reading keyboard characters and a CLICK()
+instruction for reading the coordinates of
+
+a mouse click.
+
+Another common approach is to use "memory-mapped
+I/O", where a portion of the kernel address
+
+space is devoted to servicing I/O devices.
+
+In this scheme, ordinary LD and ST store instructions
+are used to access specific addresses, which
+
+the CPU recognizes as accesses to the keyboard
+or mouse device interfaces.
+
+This is the scheme shown in the code here.
+
+The C data structure represents the two I/O
+locations devoted to the keyboard: one for
+
+status and one for the actual keyboard data.
+
+The keyboard interrupt handler reads the keystroke
+data from the keyboard and places the character
+
+into the next location in the circular character
+buffer in the kernel.
+
+In real life keyboard processing is usually
+a bit more complicated.
+
+What one actually reads from a keyboard is
+a key number and a flag indicating whether
+
+the event is a key press or a key release.
+
+Knowing the keyboard layout, the OS translates
+the key number into the appropriate ASCII
+
+character,
+dealing with complications like holding down
+
+the shift key or control key to indicate a
+capital character or a control character.
+
+And certain combination of keystrokes, e.g.,
+CTRL-ALT-DEL on a Windows system, are interpreted
+
+as special user commands to start running
+particular applications like the Task Manager.
+
+Many OSes let the user specify whether they
+want "raw" keyboard input (i.e., the key numbers
+
+and status) or "digested" input (i.e., ASCII
+characters).
+
+Whew!
+
+Who knew that processing keystrokes could
+be so complicated!
+
+Next, we'll figure out how to code the associated
+supervisor call that lets user programs read
+
+characters.
\ No newline at end of file
diff --git a/8aNkTgarBis.txt b/8aNkTgarBis.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ae680fa1ac6c7fddf7312397a26c877289617f2c
--- /dev/null
+++ b/8aNkTgarBis.txt
@@ -0,0 +1,12952 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today we're doing Electric
+
+ align:start position:0%
+ocw.mit.edu today we're doing Electric
+ 
+
+ align:start position:0%
+ocw.mit.edu today we're doing Electric
+Power Systems sort of as they are and as
+
+ align:start position:0%
+Power Systems sort of as they are and as
+ 
+
+ align:start position:0%
+Power Systems sort of as they are and as
+they have been in 2010 Electric Power
+
+ align:start position:0%
+they have been in 2010 Electric Power
+ 
+
+ align:start position:0%
+they have been in 2010 Electric Power
+Systems were about 40% of I'm going to
+
+ align:start position:0%
+Systems were about 40% of I'm going to
+ 
+
+ align:start position:0%
+Systems were about 40% of I'm going to
+have to stand here and use the keyboard
+
+ align:start position:0%
+have to stand here and use the keyboard
+ 
+
+ align:start position:0%
+have to stand here and use the keyboard
+about 40% of primary
+
+ align:start position:0%
+about 40% of primary
+ 
+
+ align:start position:0%
+about 40% of primary
+energy and um 40% of CO2 emissions
+
+ align:start position:0%
+energy and um 40% of CO2 emissions
+ 
+
+ align:start position:0%
+energy and um 40% of CO2 emissions
+roughly most electricity goes to
+
+ align:start position:0%
+roughly most electricity goes to
+ 
+
+ align:start position:0%
+roughly most electricity goes to
+residential and Commercial sectors and
+
+ align:start position:0%
+residential and Commercial sectors and
+ 
+
+ align:start position:0%
+residential and Commercial sectors and
+applies about supplies about 46% of the
+
+ align:start position:0%
+applies about supplies about 46% of the
+ 
+
+ align:start position:0%
+applies about supplies about 46% of the
+energy they use what I want to do today
+
+ align:start position:0%
+energy they use what I want to do today
+ 
+
+ align:start position:0%
+energy they use what I want to do today
+is to talk about the essential features
+
+ align:start position:0%
+is to talk about the essential features
+ 
+
+ align:start position:0%
+is to talk about the essential features
+of these systems I'm guessing most of
+
+ align:start position:0%
+of these systems I'm guessing most of
+ 
+
+ align:start position:0%
+of these systems I'm guessing most of
+you haven't had a course in Power
+
+ align:start position:0%
+you haven't had a course in Power
+ 
+
+ align:start position:0%
+you haven't had a course in Power
+Systems since MIT doesn't teach a course
+
+ align:start position:0%
+Systems since MIT doesn't teach a course
+ 
+
+ align:start position:0%
+Systems since MIT doesn't teach a course
+in Power Systems really um and talk a
+
+ align:start position:0%
+in Power Systems really um and talk a
+ 
+
+ align:start position:0%
+in Power Systems really um and talk a
+little bit about the regulatory regime
+
+ align:start position:0%
+little bit about the regulatory regime
+ 
+
+ align:start position:0%
+little bit about the regulatory regime
+uh Monday will look forward what are
+
+ align:start position:0%
+uh Monday will look forward what are
+ 
+
+ align:start position:0%
+uh Monday will look forward what are
+some of the challenges what are some of
+
+ align:start position:0%
+some of the challenges what are some of
+ 
+
+ align:start position:0%
+some of the challenges what are some of
+the opportunities what are some of the
+
+ align:start position:0%
+the opportunities what are some of the
+ 
+
+ align:start position:0%
+the opportunities what are some of the
+policy issues so let's talk about the
+
+ align:start position:0%
+policy issues so let's talk about the
+ 
+
+ align:start position:0%
+policy issues so let's talk about the
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+system the one thing you really do have
+
+ align:start position:0%
+system the one thing you really do have
+ 
+
+ align:start position:0%
+system the one thing you really do have
+to keep in mind is despite all of the
+
+ align:start position:0%
+to keep in mind is despite all of the
+ 
+
+ align:start position:0%
+to keep in mind is despite all of the
+interest in storage and everybody talks
+
+ align:start position:0%
+interest in storage and everybody talks
+ 
+
+ align:start position:0%
+interest in storage and everybody talks
+about storage of electricity
+
+ align:start position:0%
+about storage of electricity
+ 
+
+ align:start position:0%
+about storage of electricity
+as a practical matter you simply can't
+
+ align:start position:0%
+as a practical matter you simply can't
+ 
+
+ align:start position:0%
+as a practical matter you simply can't
+store electricity in bulk at at a
+
+ align:start position:0%
+store electricity in bulk at at a
+ 
+
+ align:start position:0%
+store electricity in bulk at at a
+reasonable cost you can pump water
+
+ align:start position:0%
+reasonable cost you can pump water
+ 
+
+ align:start position:0%
+reasonable cost you can pump water
+uphill and use pumped hydro and that's
+
+ align:start position:0%
+uphill and use pumped hydro and that's
+ 
+
+ align:start position:0%
+uphill and use pumped hydro and that's
+pretty good that's pretty efficient it's
+
+ align:start position:0%
+pretty good that's pretty efficient it's
+ 
+
+ align:start position:0%
+pretty good that's pretty efficient it's
+very hard to build new pumped Hydro
+
+ align:start position:0%
+very hard to build new pumped Hydro
+ 
+
+ align:start position:0%
+very hard to build new pumped Hydro
+sites uh there's one in New England
+
+ align:start position:0%
+sites uh there's one in New England
+ 
+
+ align:start position:0%
+sites uh there's one in New England
+there are no plans for any others and as
+
+ align:start position:0%
+there are no plans for any others and as
+ 
+
+ align:start position:0%
+there are no plans for any others and as
+we'll see next time the value of storage
+
+ align:start position:0%
+we'll see next time the value of storage
+ 
+
+ align:start position:0%
+we'll see next time the value of storage
+goes up over time uh you can also Pump
+
+ align:start position:0%
+goes up over time uh you can also Pump
+ 
+
+ align:start position:0%
+goes up over time uh you can also Pump
+Air underground and that's there're like
+
+ align:start position:0%
+Air underground and that's there're like
+ 
+
+ align:start position:0%
+Air underground and that's there're like
+two of those in the world and there's a
+
+ align:start position:0%
+two of those in the world and there's a
+ 
+
+ align:start position:0%
+two of those in the world and there's a
+lot of research into batteries but so
+
+ align:start position:0%
+lot of research into batteries but so
+ 
+
+ align:start position:0%
+lot of research into batteries but so
+far nothing looks cheap so at the moment
+
+ align:start position:0%
+far nothing looks cheap so at the moment
+ 
+
+ align:start position:0%
+far nothing looks cheap so at the moment
+the system operates as effectively
+
+ align:start position:0%
+the system operates as effectively
+ 
+
+ align:start position:0%
+the system operates as effectively
+without
+
+ align:start position:0%
+without
+ 
+
+ align:start position:0%
+without
+storage um and this matters because
+
+ align:start position:0%
+storage um and this matters because
+ 
+
+ align:start position:0%
+storage um and this matters because
+demand varies over time in ways that
+
+ align:start position:0%
+demand varies over time in ways that
+ 
+
+ align:start position:0%
+demand varies over time in ways that
+aren't perfectly predictable here's some
+
+ align:start position:0%
+aren't perfectly predictable here's some
+ 
+
+ align:start position:0%
+aren't perfectly predictable here's some
+seasonal
+
+ align:start position:0%
+seasonal
+ 
+
+ align:start position:0%
+seasonal
+variation this is
+
+ align:start position:0%
+variation this is
+ 
+
+ align:start position:0%
+variation this is
+um a forecast for New
+
+ align:start position:0%
+um a forecast for New
+ 
+
+ align:start position:0%
+um a forecast for New
+England and you'll see that
+
+ align:start position:0%
+England and you'll see that
+ 
+
+ align:start position:0%
+England and you'll see that
+as it says there week eight is Late July
+
+ align:start position:0%
+as it says there week eight is Late July
+ 
+
+ align:start position:0%
+as it says there week eight is Late July
+week eight was forecast to be the peak
+
+ align:start position:0%
+week eight was forecast to be the peak
+ 
+
+ align:start position:0%
+week eight was forecast to be the peak
+and week 32 which is that sort of
+
+ align:start position:0%
+and week 32 which is that sort of
+ 
+
+ align:start position:0%
+and week 32 which is that sort of
+secondary Peak is early
+
+ align:start position:0%
+secondary Peak is early
+ 
+
+ align:start position:0%
+secondary Peak is early
+January most American systems now look
+
+ align:start position:0%
+January most American systems now look
+ 
+
+ align:start position:0%
+January most American systems now look
+like that they peak in the summertime
+
+ align:start position:0%
+like that they peak in the summertime
+ 
+
+ align:start position:0%
+like that they peak in the summertime
+that's air
+
+ align:start position:0%
+that's air
+ 
+
+ align:start position:0%
+that's air
+conditioning there's also a good deal of
+
+ align:start position:0%
+conditioning there's also a good deal of
+ 
+
+ align:start position:0%
+conditioning there's also a good deal of
+Vari so you have to follow that load you
+
+ align:start position:0%
+Vari so you have to follow that load you
+ 
+
+ align:start position:0%
+Vari so you have to follow that load you
+have to follow that variation in
+
+ align:start position:0%
+have to follow that variation in
+ 
+
+ align:start position:0%
+have to follow that variation in
+demand but hour by hour there's a lot of
+
+ align:start position:0%
+demand but hour by hour there's a lot of
+ 
+
+ align:start position:0%
+demand but hour by hour there's a lot of
+variation and that's sort of an
+
+ align:start position:0%
+variation and that's sort of an
+ 
+
+ align:start position:0%
+variation and that's sort of an
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+does the laser work no okay how long are
+
+ align:start position:0%
+does the laser work no okay how long are
+ 
+
+ align:start position:0%
+does the laser work no okay how long are
+my arms um that's sort of an interesting
+
+ align:start position:0%
+my arms um that's sort of an interesting
+ 
+
+ align:start position:0%
+my arms um that's sort of an interesting
+that's what last
+
+ align:start position:0%
+that's what last
+ 
+
+ align:start position:0%
+that's what last
+week uh for New England and you'll see
+
+ align:start position:0%
+week uh for New England and you'll see
+ 
+
+ align:start position:0%
+week uh for New England and you'll see
+first of all that the load in this
+
+ align:start position:0%
+first of all that the load in this
+ 
+
+ align:start position:0%
+first of all that the load in this
+relatively uneventful April week uh
+
+ align:start position:0%
+relatively uneventful April week uh
+ 
+
+ align:start position:0%
+relatively uneventful April week uh
+varied within a day between 9,000 and
+
+ align:start position:0%
+varied within a day between 9,000 and
+ 
+
+ align:start position:0%
+varied within a day between 9,000 and
+just about 16,000
+
+ align:start position:0%
+just about 16,000
+ 
+
+ align:start position:0%
+just about 16,000
+megawatts that's fairly fairly
+
+ align:start position:0%
+megawatts that's fairly fairly
+ 
+
+ align:start position:0%
+megawatts that's fairly fairly
+substantial you'll see the April 2nd was
+
+ align:start position:0%
+substantial you'll see the April 2nd was
+ 
+
+ align:start position:0%
+substantial you'll see the April 2nd was
+a Monday so you can see demand is higher
+
+ align:start position:0%
+a Monday so you can see demand is higher
+ 
+
+ align:start position:0%
+a Monday so you can see demand is higher
+during the week than the last two which
+
+ align:start position:0%
+during the week than the last two which
+ 
+
+ align:start position:0%
+during the week than the last two which
+are the
+
+ align:start position:0%
+are the
+ 
+
+ align:start position:0%
+are the
+weekends you'll also see the distinctive
+
+ align:start position:0%
+weekends you'll also see the distinctive
+ 
+
+ align:start position:0%
+weekends you'll also see the distinctive
+feature there's sort of a morning Peak
+
+ align:start position:0%
+feature there's sort of a morning Peak
+ 
+
+ align:start position:0%
+feature there's sort of a morning Peak
+and an evening Peak most days the
+
+ align:start position:0%
+and an evening Peak most days the
+ 
+
+ align:start position:0%
+and an evening Peak most days the
+evening Peak again focus on the um
+
+ align:start position:0%
+evening Peak again focus on the um
+ 
+
+ align:start position:0%
+evening Peak again focus on the um
+actual load the blue the evening Peak is
+
+ align:start position:0%
+actual load the blue the evening Peak is
+ 
+
+ align:start position:0%
+actual load the blue the evening Peak is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+higher um and the minimum occurs in the
+
+ align:start position:0%
+higher um and the minimum occurs in the
+ 
+
+ align:start position:0%
+higher um and the minimum occurs in the
+middle of the night not too surprisingly
+
+ align:start position:0%
+middle of the night not too surprisingly
+ 
+
+ align:start position:0%
+middle of the night not too surprisingly
+but the system has to track that the
+
+ align:start position:0%
+but the system has to track that the
+ 
+
+ align:start position:0%
+but the system has to track that the
+system has to track that the other thing
+
+ align:start position:0%
+system has to track that the other thing
+ 
+
+ align:start position:0%
+system has to track that the other thing
+you will see in terms of
+
+ align:start position:0%
+you will see in terms of
+ 
+
+ align:start position:0%
+you will see in terms of
+predictability forecast load I'm not
+
+ align:start position:0%
+predictability forecast load I'm not
+ 
+
+ align:start position:0%
+predictability forecast load I'm not
+sure how far ahead that forecast is but
+
+ align:start position:0%
+sure how far ahead that forecast is but
+ 
+
+ align:start position:0%
+sure how far ahead that forecast is but
+da is day ahead so the New England
+
+ align:start position:0%
+da is day ahead so the New England
+ 
+
+ align:start position:0%
+da is day ahead so the New England
+system operates with a market and
+
+ align:start position:0%
+system operates with a market and
+ 
+
+ align:start position:0%
+system operates with a market and
+there's a real time clearing which there
+
+ align:start position:0%
+there's a real time clearing which there
+ 
+
+ align:start position:0%
+there's a real time clearing which there
+has to be because you have to follow it
+
+ align:start position:0%
+has to be because you have to follow it
+ 
+
+ align:start position:0%
+has to be because you have to follow it
+second to second but there's also a day
+
+ align:start position:0%
+second to second but there's also a day
+ 
+
+ align:start position:0%
+second to second but there's also a day
+ahead market so the da gives you the the
+
+ align:start position:0%
+ahead market so the da gives you the the
+ 
+
+ align:start position:0%
+ahead market so the da gives you the the
+day in effect the day ahead
+
+ align:start position:0%
+day in effect the day ahead
+ 
+
+ align:start position:0%
+day in effect the day ahead
+forecast and you will see the difference
+
+ align:start position:0%
+forecast and you will see the difference
+ 
+
+ align:start position:0%
+forecast and you will see the difference
+between the green and the blue is
+
+ align:start position:0%
+between the green and the blue is
+ 
+
+ align:start position:0%
+between the green and the blue is
+usually small but not trivial not zero
+
+ align:start position:0%
+usually small but not trivial not zero
+ 
+
+ align:start position:0%
+usually small but not trivial not zero
+um what else to say any comments or
+
+ align:start position:0%
+um what else to say any comments or
+ 
+
+ align:start position:0%
+um what else to say any comments or
+questions so far on this yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jacob well it's got to be made up the
+
+ align:start position:0%
+Jacob well it's got to be made up the
+ 
+
+ align:start position:0%
+Jacob well it's got to be made up the
+question is that's a day ahead
+
+ align:start position:0%
+question is that's a day ahead
+ 
+
+ align:start position:0%
+question is that's a day ahead
+um some of this is going to be the
+
+ align:start position:0%
+um some of this is going to be the
+ 
+
+ align:start position:0%
+um some of this is going to be the
+actual load tended to be
+
+ align:start position:0%
+actual load tended to be
+ 
+
+ align:start position:0%
+actual load tended to be
+above um the day ahead which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggests well if this were If This Were
+
+ align:start position:0%
+suggests well if this were If This Were
+ 
+
+ align:start position:0%
+suggests well if this were If This Were
+the summertime I'd say this suggests uh
+
+ align:start position:0%
+the summertime I'd say this suggests uh
+ 
+
+ align:start position:0%
+the summertime I'd say this suggests uh
+warmer than expected which is sort of
+
+ align:start position:0%
+warmer than expected which is sort of
+ 
+
+ align:start position:0%
+warmer than expected which is sort of
+what it was that week uh you get better
+
+ align:start position:0%
+what it was that week uh you get better
+ 
+
+ align:start position:0%
+what it was that week uh you get better
+at forecasting the weather as you get
+
+ align:start position:0%
+at forecasting the weather as you get
+ 
+
+ align:start position:0%
+at forecasting the weather as you get
+closer so an hour or two ahead you know
+
+ align:start position:0%
+closer so an hour or two ahead you know
+ 
+
+ align:start position:0%
+closer so an hour or two ahead you know
+it's not like oh my God right now we've
+
+ align:start position:0%
+it's not like oh my God right now we've
+ 
+
+ align:start position:0%
+it's not like oh my God right now we've
+got to make a change but you may have a
+
+ align:start position:0%
+got to make a change but you may have a
+ 
+
+ align:start position:0%
+got to make a change but you may have a
+few hours warning that it's warmer than
+
+ align:start position:0%
+few hours warning that it's warmer than
+ 
+
+ align:start position:0%
+few hours warning that it's warmer than
+we thought so we really have to ramp
+
+ align:start position:0%
+we thought so we really have to ramp
+ 
+
+ align:start position:0%
+we thought so we really have to ramp
+stuff up but yes something has to follow
+
+ align:start position:0%
+stuff up but yes something has to follow
+ 
+
+ align:start position:0%
+stuff up but yes something has to follow
+that load could be Hydro could be gas
+
+ align:start position:0%
+that load could be Hydro could be gas
+ 
+
+ align:start position:0%
+that load could be Hydro could be gas
+turbin it's not going to be big coal
+
+ align:start position:0%
+turbin it's not going to be big coal
+ 
+
+ align:start position:0%
+turbin it's not going to be big coal
+plants because as I'll come to in a
+
+ align:start position:0%
+plants because as I'll come to in a
+ 
+
+ align:start position:0%
+plants because as I'll come to in a
+minute uh following load with big coal
+
+ align:start position:0%
+minute uh following load with big coal
+ 
+
+ align:start position:0%
+minute uh following load with big coal
+plants is very expensive there's a lot
+
+ align:start position:0%
+plants is very expensive there's a lot
+ 
+
+ align:start position:0%
+plants is very expensive there's a lot
+of stuff you get hot there's a lot of
+
+ align:start position:0%
+of stuff you get hot there's a lot of
+ 
+
+ align:start position:0%
+of stuff you get hot there's a lot of
+stuff spinning and to let that cool off
+
+ align:start position:0%
+stuff spinning and to let that cool off
+ 
+
+ align:start position:0%
+stuff spinning and to let that cool off
+and or slow down and then bring it back
+
+ align:start position:0%
+and or slow down and then bring it back
+ 
+
+ align:start position:0%
+and or slow down and then bring it back
+wastes a lot of energy so you want
+
+ align:start position:0%
+wastes a lot of energy so you want
+ 
+
+ align:start position:0%
+wastes a lot of energy so you want
+things that are quick that don't don't
+
+ align:start position:0%
+things that are quick that don't don't
+ 
+
+ align:start position:0%
+things that are quick that don't don't
+have a lot of parts to to a lot of
+
+ align:start position:0%
+have a lot of parts to to a lot of
+ 
+
+ align:start position:0%
+have a lot of parts to to a lot of
+rotating mass and they don't have a lot
+
+ align:start position:0%
+rotating mass and they don't have a lot
+ 
+
+ align:start position:0%
+rotating mass and they don't have a lot
+of stuff um uh that you have to heat and
+
+ align:start position:0%
+of stuff um uh that you have to heat and
+ 
+
+ align:start position:0%
+of stuff um uh that you have to heat and
+cool I have to heat and then
+
+ align:start position:0%
+cool I have to heat and then
+ 
+
+ align:start position:0%
+cool I have to heat and then
+reheat anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+santh why is there 10,000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+well it could what are these people
+
+ align:start position:0%
+well it could what are these people
+ 
+
+ align:start position:0%
+well it could what are these people
+doing I don't know this is this is you
+
+ align:start position:0%
+doing I don't know this is this is you
+ 
+
+ align:start position:0%
+doing I don't know this is this is you
+guys working late I guess
+
+ align:start position:0%
+guys working late I guess
+ 
+
+ align:start position:0%
+guys working late I guess
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh you got me some of that traditionally
+
+ align:start position:0%
+uh you got me some of that traditionally
+ 
+
+ align:start position:0%
+uh you got me some of that traditionally
+would be industrial load like if you're
+
+ align:start position:0%
+would be industrial load like if you're
+ 
+
+ align:start position:0%
+would be industrial load like if you're
+running a factory three shifts there's
+
+ align:start position:0%
+running a factory three shifts there's
+ 
+
+ align:start position:0%
+running a factory three shifts there's
+not that much of that in New England
+
+ align:start position:0%
+not that much of that in New England
+ 
+
+ align:start position:0%
+not that much of that in New England
+some of it may
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be HVAC in some buildings consuming
+
+ align:start position:0%
+be HVAC in some buildings consuming
+ 
+
+ align:start position:0%
+be HVAC in some buildings consuming
+electricity fans
+
+ align:start position:0%
+electricity fans
+ 
+
+ align:start position:0%
+electricity fans
+running um various various kinds of
+
+ align:start position:0%
+running um various various kinds of
+ 
+
+ align:start position:0%
+running um various various kinds of
+Machinery um there also these vampire
+
+ align:start position:0%
+Machinery um there also these vampire
+ 
+
+ align:start position:0%
+Machinery um there also these vampire
+load devices right when you have almost
+
+ align:start position:0%
+load devices right when you have almost
+ 
+
+ align:start position:0%
+load devices right when you have almost
+anything plugged in even if it's turned
+
+ align:start position:0%
+anything plugged in even if it's turned
+ 
+
+ align:start position:0%
+anything plugged in even if it's turned
+off at sucks power so those those loads
+
+ align:start position:0%
+off at sucks power so those those loads
+ 
+
+ align:start position:0%
+off at sucks power so those those loads
+have gone up uh I've never really seen
+
+ align:start position:0%
+have gone up uh I've never really seen
+ 
+
+ align:start position:0%
+have gone up uh I've never really seen
+an an analysis of 3 AM
+
+ align:start position:0%
+an an analysis of 3 AM
+ 
+
+ align:start position:0%
+an an analysis of 3 AM
+load um but you're you're right you
+
+ align:start position:0%
+load um but you're you're right you
+ 
+
+ align:start position:0%
+load um but you're you're right you
+could make a your consumption probably
+
+ align:start position:0%
+could make a your consumption probably
+ 
+
+ align:start position:0%
+could make a your consumption probably
+goes a lot lower uh your day-to-day VAR
+
+ align:start position:0%
+goes a lot lower uh your day-to-day VAR
+ 
+
+ align:start position:0%
+goes a lot lower uh your day-to-day VAR
+your within day variation is probably
+
+ align:start position:0%
+your within day variation is probably
+ 
+
+ align:start position:0%
+your within day variation is probably
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+that um and I'm trying to think about
+
+ align:start position:0%
+that um and I'm trying to think about
+ 
+
+ align:start position:0%
+that um and I'm trying to think about
+the apartment building where I live and
+
+ align:start position:0%
+the apartment building where I live and
+ 
+
+ align:start position:0%
+the apartment building where I live and
+what goes on at 3: in the morning and
+
+ align:start position:0%
+what goes on at 3: in the morning and
+ 
+
+ align:start position:0%
+what goes on at 3: in the morning and
+about all that's going on is in a warm
+
+ align:start position:0%
+about all that's going on is in a warm
+ 
+
+ align:start position:0%
+about all that's going on is in a warm
+period like this there may be some AC
+
+ align:start position:0%
+period like this there may be some AC
+ 
+
+ align:start position:0%
+period like this there may be some AC
+usage although ours wasn't on so I don't
+
+ align:start position:0%
+usage although ours wasn't on so I don't
+ 
+
+ align:start position:0%
+usage although ours wasn't on so I don't
+know and you know you got appliances
+
+ align:start position:0%
+know and you know you got appliances
+ 
+
+ align:start position:0%
+know and you know you got appliances
+running all night long refrigerators and
+
+ align:start position:0%
+running all night long refrigerators and
+ 
+
+ align:start position:0%
+running all night long refrigerators and
+such but I don't know anything else yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jacqueline the forecast is presumably
+
+ align:start position:0%
+Jacqueline the forecast is presumably
+ 
+
+ align:start position:0%
+Jacqueline the forecast is presumably
+and I should have checked before I put
+
+ align:start position:0%
+and I should have checked before I put
+ 
+
+ align:start position:0%
+and I should have checked before I put
+this up the forecast is presumably
+
+ align:start position:0%
+this up the forecast is presumably
+ 
+
+ align:start position:0%
+this up the forecast is presumably
+farther back in time than day ahead the
+
+ align:start position:0%
+farther back in time than day ahead the
+ 
+
+ align:start position:0%
+farther back in time than day ahead the
+forecast is a forecast this would be the
+
+ align:start position:0%
+forecast is a forecast this would be the
+ 
+
+ align:start position:0%
+forecast is a forecast this would be the
+the regional Authority and I'll talk
+
+ align:start position:0%
+the regional Authority and I'll talk
+ 
+
+ align:start position:0%
+the regional Authority and I'll talk
+about them a bit later the regional
+
+ align:start position:0%
+about them a bit later the regional
+ 
+
+ align:start position:0%
+about them a bit later the regional
+authorities guess maybe a week ahead or
+
+ align:start position:0%
+authorities guess maybe a week ahead or
+ 
+
+ align:start position:0%
+authorities guess maybe a week ahead or
+two weeks ahead day ahead cleared demand
+
+ align:start position:0%
+two weeks ahead day ahead cleared demand
+ 
+
+ align:start position:0%
+two weeks ahead day ahead cleared demand
+that's a market people bid to
+
+ align:start position:0%
+that's a market people bid to
+ 
+
+ align:start position:0%
+that's a market people bid to
+supply there's demand it clears at well
+
+ align:start position:0%
+supply there's demand it clears at well
+ 
+
+ align:start position:0%
+supply there's demand it clears at well
+it clears at a price we'll come to price
+
+ align:start position:0%
+it clears at a price we'll come to price
+ 
+
+ align:start position:0%
+it clears at a price we'll come to price
+later but that is a market that's a
+
+ align:start position:0%
+later but that is a market that's a
+ 
+
+ align:start position:0%
+later but that is a market that's a
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+outcome
+
+ align:start position:0%
+outcome
+ 
+
+ align:start position:0%
+outcome
+that's a that's a forecast outcome and I
+
+ align:start position:0%
+that's a that's a forecast outcome and I
+ 
+
+ align:start position:0%
+that's a that's a forecast outcome and I
+just don't know how far in advance but
+
+ align:start position:0%
+just don't know how far in advance but
+ 
+
+ align:start position:0%
+just don't know how far in advance but
+it's clearly by the regional Authority
+
+ align:start position:0%
+it's clearly by the regional Authority
+ 
+
+ align:start position:0%
+it's clearly by the regional Authority
+that runs the system and actual load is
+
+ align:start position:0%
+that runs the system and actual load is
+ 
+
+ align:start position:0%
+that runs the system and actual load is
+what actually happened when you turned
+
+ align:start position:0%
+what actually happened when you turned
+ 
+
+ align:start position:0%
+what actually happened when you turned
+on your computer so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um shortterm variation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um minute to
+
+ align:start position:0%
+um minute to
+ 
+
+ align:start position:0%
+um minute to
+minute the frequency right everything
+
+ align:start position:0%
+minute the frequency right everything
+ 
+
+ align:start position:0%
+minute the frequency right everything
+assumes that the system will run on
+
+ align:start position:0%
+assumes that the system will run on
+ 
+
+ align:start position:0%
+assumes that the system will run on
+every you all your equipment assumes
+
+ align:start position:0%
+every you all your equipment assumes
+ 
+
+ align:start position:0%
+every you all your equipment assumes
+your appliances assume that you'll be
+
+ align:start position:0%
+your appliances assume that you'll be
+ 
+
+ align:start position:0%
+your appliances assume that you'll be
+getting electricity that varies 60
+
+ align:start position:0%
+getting electricity that varies 60
+ 
+
+ align:start position:0%
+getting electricity that varies 60
+Cycles uh a second that frequency has to
+
+ align:start position:0%
+Cycles uh a second that frequency has to
+ 
+
+ align:start position:0%
+Cycles uh a second that frequency has to
+be maintained and it's mainly maintained
+
+ align:start position:0%
+be maintained and it's mainly maintained
+ 
+
+ align:start position:0%
+be maintained and it's mainly maintained
+by sort of automatic control at
+
+ align:start position:0%
+by sort of automatic control at
+ 
+
+ align:start position:0%
+by sort of automatic control at
+designated units but when you get big
+
+ align:start position:0%
+designated units but when you get big
+ 
+
+ align:start position:0%
+designated units but when you get big
+changes like that sort of Governors
+
+ align:start position:0%
+changes like that sort of Governors
+ 
+
+ align:start position:0%
+changes like that sort of Governors
+aren't going to do it uh and you will
+
+ align:start position:0%
+aren't going to do it uh and you will
+ 
+
+ align:start position:0%
+aren't going to do it uh and you will
+need to bring loow units on and off so
+
+ align:start position:0%
+need to bring loow units on and off so
+ 
+
+ align:start position:0%
+need to bring loow units on and off so
+let me talk about technology mix so we
+
+ align:start position:0%
+let me talk about technology mix so we
+ 
+
+ align:start position:0%
+let me talk about technology mix so we
+talked we mentioned a little earlier
+
+ align:start position:0%
+talked we mentioned a little earlier
+ 
+
+ align:start position:0%
+talked we mentioned a little earlier
+that uh you have
+
+ align:start position:0%
+that uh you have
+ 
+
+ align:start position:0%
+that uh you have
+fast fast
+
+ align:start position:0%
+fast fast
+ 
+
+ align:start position:0%
+fast fast
+responding uh uh generating units turbin
+
+ align:start position:0%
+responding uh uh generating units turbin
+ 
+
+ align:start position:0%
+responding uh uh generating units turbin
+say or diesels to respond to short-term
+
+ align:start position:0%
+say or diesels to respond to short-term
+ 
+
+ align:start position:0%
+say or diesels to respond to short-term
+variations in load but even if you could
+
+ align:start position:0%
+variations in load but even if you could
+ 
+
+ align:start position:0%
+variations in load but even if you could
+forecast the load you would want units
+
+ align:start position:0%
+forecast the load you would want units
+ 
+
+ align:start position:0%
+forecast the load you would want units
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as I mentioned it's EX it's
+
+ align:start position:0%
+and as I mentioned it's EX it's
+ 
+
+ align:start position:0%
+and as I mentioned it's EX it's
+expensive to vary the output from what
+
+ align:start position:0%
+expensive to vary the output from what
+ 
+
+ align:start position:0%
+expensive to vary the output from what
+are called base load units nuclear power
+
+ align:start position:0%
+are called base load units nuclear power
+ 
+
+ align:start position:0%
+are called base load units nuclear power
+plants big coal
+
+ align:start position:0%
+plants big coal
+ 
+
+ align:start position:0%
+plants big coal
+plants but not only that when you run
+
+ align:start position:0%
+plants but not only that when you run
+ 
+
+ align:start position:0%
+plants but not only that when you run
+them flat out they have very low running
+
+ align:start position:0%
+them flat out they have very low running
+ 
+
+ align:start position:0%
+them flat out they have very low running
+cost nuclear virtually zero coal pretty
+
+ align:start position:0%
+cost nuclear virtually zero coal pretty
+ 
+
+ align:start position:0%
+cost nuclear virtually zero coal pretty
+low you can buy turbines or
+
+ align:start position:0%
+low you can buy turbines or
+ 
+
+ align:start position:0%
+low you can buy turbines or
+diesels but they're very expensive to
+
+ align:start position:0%
+diesels but they're very expensive to
+ 
+
+ align:start position:0%
+diesels but they're very expensive to
+build these big units the little units
+
+ align:start position:0%
+build these big units the little units
+ 
+
+ align:start position:0%
+build these big units the little units
+peaking units or intermediate units but
+
+ align:start position:0%
+peaking units or intermediate units but
+ 
+
+ align:start position:0%
+peaking units or intermediate units but
+let me just assume two kinds think coal
+
+ align:start position:0%
+let me just assume two kinds think coal
+ 
+
+ align:start position:0%
+let me just assume two kinds think coal
+plants and gas turbin um they're cheap
+
+ align:start position:0%
+plants and gas turbin um they're cheap
+ 
+
+ align:start position:0%
+plants and gas turbin um they're cheap
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+build but they're expensive to run
+
+ align:start position:0%
+build but they're expensive to run
+ 
+
+ align:start position:0%
+build but they're expensive to run
+relatively on today's prices so you
+
+ align:start position:0%
+relatively on today's prices so you
+ 
+
+ align:start position:0%
+relatively on today's prices so you
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+want since load varies you're not going
+
+ align:start position:0%
+want since load varies you're not going
+ 
+
+ align:start position:0%
+want since load varies you're not going
+to run your whole Fleet all the time
+
+ align:start position:0%
+to run your whole Fleet all the time
+ 
+
+ align:start position:0%
+to run your whole Fleet all the time
+right if we didn't have those variations
+
+ align:start position:0%
+right if we didn't have those variations
+ 
+
+ align:start position:0%
+right if we didn't have those variations
+if demand were constant you just build
+
+ align:start position:0%
+if demand were constant you just build
+ 
+
+ align:start position:0%
+if demand were constant you just build
+well but for environmental issues you
+
+ align:start position:0%
+well but for environmental issues you
+ 
+
+ align:start position:0%
+well but for environmental issues you
+just build cheap coal plants cheap
+
+ align:start position:0%
+just build cheap coal plants cheap
+ 
+
+ align:start position:0%
+just build cheap coal plants cheap
+nuclear plants if you could find one uh
+
+ align:start position:0%
+nuclear plants if you could find one uh
+ 
+
+ align:start position:0%
+nuclear plants if you could find one uh
+combine cycle plants and run them all
+
+ align:start position:0%
+combine cycle plants and run them all
+ 
+
+ align:start position:0%
+combine cycle plants and run them all
+the time but since the load varies you
+
+ align:start position:0%
+the time but since the load varies you
+ 
+
+ align:start position:0%
+the time but since the load varies you
+know that you're not going to run your
+
+ align:start position:0%
+know that you're not going to run your
+ 
+
+ align:start position:0%
+know that you're not going to run your
+plants all the time so what do you do if
+
+ align:start position:0%
+plants all the time so what do you do if
+ 
+
+ align:start position:0%
+plants all the time so what do you do if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+look you look at imagine two plants of
+
+ align:start position:0%
+look you look at imagine two plants of
+ 
+
+ align:start position:0%
+look you look at imagine two plants of
+the same capacity one is I call it a
+
+ align:start position:0%
+the same capacity one is I call it a
+ 
+
+ align:start position:0%
+the same capacity one is I call it a
+peer but let it be a gas turbine and the
+
+ align:start position:0%
+peer but let it be a gas turbine and the
+ 
+
+ align:start position:0%
+peer but let it be a gas turbine and the
+other is a Bas load let it be a coal
+
+ align:start position:0%
+other is a Bas load let it be a coal
+ 
+
+ align:start position:0%
+other is a Bas load let it be a coal
+plant they don't tend to have the same
+
+ align:start position:0%
+plant they don't tend to have the same
+ 
+
+ align:start position:0%
+plant they don't tend to have the same
+capacities but for the sake of arguments
+
+ align:start position:0%
+capacities but for the sake of arguments
+ 
+
+ align:start position:0%
+capacities but for the sake of arguments
+suppose they do um you ask What's the
+
+ align:start position:0%
+suppose they do um you ask What's the
+ 
+
+ align:start position:0%
+suppose they do um you ask What's the
+total cost of this plant the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total the the more hours you run it the
+
+ align:start position:0%
+total the the more hours you run it the
+ 
+
+ align:start position:0%
+total the the more hours you run it the
+larger will be the fuel cost as a as a
+
+ align:start position:0%
+larger will be the fuel cost as a as a
+ 
+
+ align:start position:0%
+larger will be the fuel cost as a as a
+component of total cost right so the
+
+ align:start position:0%
+component of total cost right so the
+ 
+
+ align:start position:0%
+component of total cost right so the
+total cost consists of the cost of
+
+ align:start position:0%
+total cost consists of the cost of
+ 
+
+ align:start position:0%
+total cost consists of the cost of
+building the
+
+ align:start position:0%
+building the
+ 
+
+ align:start position:0%
+building the
+thing basically taken down to say a per
+
+ align:start position:0%
+thing basically taken down to say a per
+ 
+
+ align:start position:0%
+thing basically taken down to say a per
+day cost or a perear cost and then the
+
+ align:start position:0%
+day cost or a perear cost and then the
+ 
+
+ align:start position:0%
+day cost or a perear cost and then the
+slope is the marginal cost of running it
+
+ align:start position:0%
+slope is the marginal cost of running it
+ 
+
+ align:start position:0%
+slope is the marginal cost of running it
+so the height gives you the total cost
+
+ align:start position:0%
+so the height gives you the total cost
+ 
+
+ align:start position:0%
+so the height gives you the total cost
+if you're going to run all year long
+
+ align:start position:0%
+if you're going to run all year long
+ 
+
+ align:start position:0%
+if you're going to run all year long
+then the base load plant is the plant to
+
+ align:start position:0%
+then the base load plant is the plant to
+ 
+
+ align:start position:0%
+then the base load plant is the plant to
+build because you know way out here the
+
+ align:start position:0%
+build because you know way out here the
+ 
+
+ align:start position:0%
+build because you know way out here the
+fact that it's the fuel is cheap makes
+
+ align:start position:0%
+fact that it's the fuel is cheap makes
+ 
+
+ align:start position:0%
+fact that it's the fuel is cheap makes
+up for the capital
+
+ align:start position:0%
+up for the capital
+ 
+
+ align:start position:0%
+up for the capital
+cost but if you're only going to run it
+
+ align:start position:0%
+cost but if you're only going to run it
+ 
+
+ align:start position:0%
+cost but if you're only going to run it
+a little bit but you have to have it
+
+ align:start position:0%
+a little bit but you have to have it
+ 
+
+ align:start position:0%
+a little bit but you have to have it
+then you want to build a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peer right that notion clear the fact
+
+ align:start position:0%
+peer right that notion clear the fact
+ 
+
+ align:start position:0%
+peer right that notion clear the fact
+that there's output variation means you
+
+ align:start position:0%
+that there's output variation means you
+ 
+
+ align:start position:0%
+that there's output variation means you
+want to have plants of multiple types if
+
+ align:start position:0%
+want to have plants of multiple types if
+ 
+
+ align:start position:0%
+want to have plants of multiple types if
+you can get a base load plant to run
+
+ align:start position:0%
+you can get a base load plant to run
+ 
+
+ align:start position:0%
+you can get a base load plant to run
+almost all the time or all the time
+
+ align:start position:0%
+almost all the time or all the time
+ 
+
+ align:start position:0%
+almost all the time or all the time
+then you're in great shape but if you
+
+ align:start position:0%
+then you're in great shape but if you
+ 
+
+ align:start position:0%
+then you're in great shape but if you
+have to have plants that run only a
+
+ align:start position:0%
+have to have plants that run only a
+ 
+
+ align:start position:0%
+have to have plants that run only a
+little bit only a few hours per year
+
+ align:start position:0%
+little bit only a few hours per year
+ 
+
+ align:start position:0%
+little bit only a few hours per year
+then you got to have some of these and
+
+ align:start position:0%
+then you got to have some of these and
+ 
+
+ align:start position:0%
+then you got to have some of these and
+you've always got that mix we're going
+
+ align:start position:0%
+you've always got that mix we're going
+ 
+
+ align:start position:0%
+you've always got that mix we're going
+to talk about wind and solar next time
+
+ align:start position:0%
+to talk about wind and solar next time
+ 
+
+ align:start position:0%
+to talk about wind and solar next time
+they don't quite fit either of these
+
+ align:start position:0%
+they don't quite fit either of these
+ 
+
+ align:start position:0%
+they don't quite fit either of these
+categories if you think about it for a
+
+ align:start position:0%
+categories if you think about it for a
+ 
+
+ align:start position:0%
+categories if you think about it for a
+minute um but if that's
+
+ align:start position:0%
+minute um but if that's
+ 
+
+ align:start position:0%
+minute um but if that's
+clear then then let's look at
+
+ align:start position:0%
+clear then then let's look at
+ 
+
+ align:start position:0%
+clear then then let's look at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh the the red curve is what's called a
+
+ align:start position:0%
+uh the the red curve is what's called a
+ 
+
+ align:start position:0%
+uh the the red curve is what's called a
+load duration
+
+ align:start position:0%
+load duration
+ 
+
+ align:start position:0%
+load duration
+curve and it's the actual curve because
+
+ align:start position:0%
+curve and it's the actual curve because
+ 
+
+ align:start position:0%
+curve and it's the actual curve because
+I happen to find it it's the actual
+
+ align:start position:0%
+I happen to find it it's the actual
+ 
+
+ align:start position:0%
+I happen to find it it's the actual
+curve for it's probably England and
+
+ align:start position:0%
+curve for it's probably England and
+ 
+
+ align:start position:0%
+curve for it's probably England and
+Wales it says Great Britain um for
+
+ align:start position:0%
+Wales it says Great Britain um for
+ 
+
+ align:start position:0%
+Wales it says Great Britain um for
+2007 what a load duration curve is you
+
+ align:start position:0%
+2007 what a load duration curve is you
+ 
+
+ align:start position:0%
+2007 what a load duration curve is you
+look at how much electricity was
+
+ align:start position:0%
+look at how much electricity was
+ 
+
+ align:start position:0%
+look at how much electricity was
+consumed hour by hour
+
+ align:start position:0%
+consumed hour by hour
+ 
+
+ align:start position:0%
+consumed hour by hour
+and you basically convert those to a
+
+ align:start position:0%
+and you basically convert those to a
+ 
+
+ align:start position:0%
+and you basically convert those to a
+graph putting the hour with the highest
+
+ align:start position:0%
+graph putting the hour with the highest
+ 
+
+ align:start position:0%
+graph putting the hour with the highest
+consumption here then the second highest
+
+ align:start position:0%
+consumption here then the second highest
+ 
+
+ align:start position:0%
+consumption here then the second highest
+there you basically stack it
+
+ align:start position:0%
+there you basically stack it
+ 
+
+ align:start position:0%
+there you basically stack it
+up so out here at 100% you have the
+
+ align:start position:0%
+up so out here at 100% you have the
+ 
+
+ align:start position:0%
+up so out here at 100% you have the
+consumption of the demand and it's
+
+ align:start position:0%
+consumption of the demand and it's
+ 
+
+ align:start position:0%
+consumption of the demand and it's
+expressed as a percentage of peak to
+
+ align:start position:0%
+expressed as a percentage of peak to
+ 
+
+ align:start position:0%
+expressed as a percentage of peak to
+keep life simple the percentage of
+
+ align:start position:0%
+keep life simple the percentage of
+ 
+
+ align:start position:0%
+keep life simple the percentage of
+demand or the sorry the the percentage
+
+ align:start position:0%
+demand or the sorry the the percentage
+ 
+
+ align:start position:0%
+demand or the sorry the the percentage
+of peak demand at the lowest hour of the
+
+ align:start position:0%
+of peak demand at the lowest hour of the
+ 
+
+ align:start position:0%
+of peak demand at the lowest hour of the
+year presumably 3:00 in the morning on
+
+ align:start position:0%
+year presumably 3:00 in the morning on
+ 
+
+ align:start position:0%
+year presumably 3:00 in the morning on
+some day that was neither hot nor cold
+
+ align:start position:0%
+some day that was neither hot nor cold
+ 
+
+ align:start position:0%
+some day that was neither hot nor cold
+so nobody needed to run anything any
+
+ align:start position:0%
+so nobody needed to run anything any
+ 
+
+ align:start position:0%
+so nobody needed to run anything any
+HVAC and it was a holiday uh so there
+
+ align:start position:0%
+HVAC and it was a holiday uh so there
+ 
+
+ align:start position:0%
+HVAC and it was a holiday uh so there
+was no industrial work going on whatever
+
+ align:start position:0%
+was no industrial work going on whatever
+ 
+
+ align:start position:0%
+was no industrial work going on whatever
+so if you go back to this
+
+ align:start position:0%
+so if you go back to this
+ 
+
+ align:start position:0%
+so if you go back to this
+picture this picture says if you're
+
+ align:start position:0%
+picture this picture says if you're
+ 
+
+ align:start position:0%
+picture this picture says if you're
+going to run a plant fewer than H hour H
+
+ align:start position:0%
+going to run a plant fewer than H hour H
+ 
+
+ align:start position:0%
+going to run a plant fewer than H hour H
+Star hours a year you're going to want
+
+ align:start position:0%
+Star hours a year you're going to want
+ 
+
+ align:start position:0%
+Star hours a year you're going to want
+to peek it's going to have to be a PE
+
+ align:start position:0%
+to peek it's going to have to be a PE
+ 
+
+ align:start position:0%
+to peek it's going to have to be a PE
+it's going to it should be a peer rather
+
+ align:start position:0%
+it's going to it should be a peer rather
+ 
+
+ align:start position:0%
+it's going to it should be a peer rather
+than a Basel load
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come to this picture and you say okay
+
+ align:start position:0%
+come to this picture and you say okay
+ 
+
+ align:start position:0%
+come to this picture and you say okay
+let's suppose just because it fits the
+
+ align:start position:0%
+let's suppose just because it fits the
+ 
+
+ align:start position:0%
+let's suppose just because it fits the
+picture that if they're 8,760 hours in a
+
+ align:start position:0%
+picture that if they're 8,760 hours in a
+ 
+
+ align:start position:0%
+picture that if they're 8,760 hours in a
+year this is like 42 gallons in a barrel
+
+ align:start position:0%
+year this is like 42 gallons in a barrel
+ 
+
+ align:start position:0%
+year this is like 42 gallons in a barrel
+another one of those numbers you have to
+
+ align:start position:0%
+another one of those numbers you have to
+ 
+
+ align:start position:0%
+another one of those numbers you have to
+have 8760 hours in a
+
+ align:start position:0%
+have 8760 hours in a
+ 
+
+ align:start position:0%
+have 8760 hours in a
+year you
+
+ align:start position:0%
+year you
+ 
+
+ align:start position:0%
+year you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+that let's see if I can if I can do this
+
+ align:start position:0%
+that let's see if I can if I can do this
+ 
+
+ align:start position:0%
+that let's see if I can if I can do this
+if you build base load capacity up to
+
+ align:start position:0%
+if you build base load capacity up to
+ 
+
+ align:start position:0%
+if you build base load capacity up to
+this line
+
+ align:start position:0%
+this line
+ 
+
+ align:start position:0%
+this line
+you know that it will be
+
+ align:start position:0%
+you know that it will be
+ 
+
+ align:start position:0%
+you know that it will be
+running at least that fraction of of
+
+ align:start position:0%
+running at least that fraction of of
+ 
+
+ align:start position:0%
+running at least that fraction of of
+hours you'll have to cut it down
+
+ align:start position:0%
+hours you'll have to cut it down
+ 
+
+ align:start position:0%
+hours you'll have to cut it down
+somewhat in the really low hours but for
+
+ align:start position:0%
+somewhat in the really low hours but for
+ 
+
+ align:start position:0%
+somewhat in the really low hours but for
+but if you build that much base load
+
+ align:start position:0%
+but if you build that much base load
+ 
+
+ align:start position:0%
+but if you build that much base load
+capacity it will it will run for at
+
+ align:start position:0%
+capacity it will it will run for at
+ 
+
+ align:start position:0%
+capacity it will it will run for at
+least this many hours because demand
+
+ align:start position:0%
+least this many hours because demand
+ 
+
+ align:start position:0%
+least this many hours because demand
+exceeds that capacity for that fraction
+
+ align:start position:0%
+exceeds that capacity for that fraction
+ 
+
+ align:start position:0%
+exceeds that capacity for that fraction
+of the year right so we're
+
+ align:start position:0%
+of the year right so we're
+ 
+
+ align:start position:0%
+of the year right so we're
+asking
+
+ align:start position:0%
+asking
+ 
+
+ align:start position:0%
+asking
+you decide what you want to build in
+
+ align:start position:0%
+you decide what you want to build in
+ 
+
+ align:start position:0%
+you decide what you want to build in
+terms of Base load capacity as a
+
+ align:start position:0%
+terms of Base load capacity as a
+ 
+
+ align:start position:0%
+terms of Base load capacity as a
+fraction of the peak read across to the
+
+ align:start position:0%
+fraction of the peak read across to the
+ 
+
+ align:start position:0%
+fraction of the peak read across to the
+curve and come down and you get the
+
+ align:start position:0%
+curve and come down and you get the
+ 
+
+ align:start position:0%
+curve and come down and you get the
+fraction of hours of the year when
+
+ align:start position:0%
+fraction of hours of the year when
+ 
+
+ align:start position:0%
+fraction of hours of the year when
+demand is at least that
+
+ align:start position:0%
+demand is at least that
+ 
+
+ align:start position:0%
+demand is at least that
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+right so we've normalized we've
+
+ align:start position:0%
+right so we've normalized we've
+ 
+
+ align:start position:0%
+right so we've normalized we've
+normalized the load duration curve so
+
+ align:start position:0%
+normalized the load duration curve so
+ 
+
+ align:start position:0%
+normalized the load duration curve so
+the peak is 100 we also normalize time
+
+ align:start position:0%
+the peak is 100 we also normalize time
+ 
+
+ align:start position:0%
+the peak is 100 we also normalize time
+which is kind of awkward so that
+
+ align:start position:0%
+which is kind of awkward so that
+ 
+
+ align:start position:0%
+which is kind of awkward so that
+8,760 hours equal 100 so we can do
+
+ align:start position:0%
+8,760 hours equal 100 so we can do
+ 
+
+ align:start position:0%
+8,760 hours equal 100 so we can do
+percentages so again this is just
+
+ align:start position:0%
+percentages so again this is just
+ 
+
+ align:start position:0%
+percentages so again this is just
+stylized but but if if H star over 8760
+
+ align:start position:0%
+stylized but but if if H star over 8760
+ 
+
+ align:start position:0%
+stylized but but if if H star over 8760
+is here then that says you build half
+
+ align:start position:0%
+is here then that says you build half
+ 
+
+ align:start position:0%
+is here then that says you build half
+base load capacity and half peer
+
+ align:start position:0%
+base load capacity and half peer
+ 
+
+ align:start position:0%
+base load capacity and half peer
+capacity right the peers are only going
+
+ align:start position:0%
+capacity right the peers are only going
+ 
+
+ align:start position:0%
+capacity right the peers are only going
+to come into play when demand is
+
+ align:start position:0%
+to come into play when demand is
+ 
+
+ align:start position:0%
+to come into play when demand is
+above and this is where I need the laser
+
+ align:start position:0%
+above and this is where I need the laser
+ 
+
+ align:start position:0%
+above and this is where I need the laser
+is above that 50% point that's an
+
+ align:start position:0%
+is above that 50% point that's an
+ 
+
+ align:start position:0%
+is above that 50% point that's an
+artifact there's no this is just a this
+
+ align:start position:0%
+artifact there's no this is just a this
+ 
+
+ align:start position:0%
+artifact there's no this is just a this
+is stylized 50% has no no particular
+
+ align:start position:0%
+is stylized 50% has no no particular
+ 
+
+ align:start position:0%
+is stylized 50% has no no particular
+significance in life it just works out
+
+ align:start position:0%
+significance in life it just works out
+ 
+
+ align:start position:0%
+significance in life it just works out
+in this picture so you'd build half peer
+
+ align:start position:0%
+in this picture so you'd build half peer
+ 
+
+ align:start position:0%
+in this picture so you'd build half peer
+capacity and half base load the the peak
+
+ align:start position:0%
+capacity and half base load the the peak
+ 
+
+ align:start position:0%
+capacity and half base load the the peak
+units would be on for less than
+
+ align:start position:0%
+units would be on for less than
+ 
+
+ align:start position:0%
+units would be on for less than
+um eight Star hours a year or less than
+
+ align:start position:0%
+um eight Star hours a year or less than
+ 
+
+ align:start position:0%
+um eight Star hours a year or less than
+this fraction of hours per
+
+ align:start position:0%
+this fraction of hours per
+ 
+
+ align:start position:0%
+this fraction of hours per
+year does that make some
+
+ align:start position:0%
+year does that make some
+ 
+
+ align:start position:0%
+year does that make some
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+you see why you need the mix and this is
+
+ align:start position:0%
+you see why you need the mix and this is
+ 
+
+ align:start position:0%
+you see why you need the mix and this is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+mechanical to say if I know where the
+
+ align:start position:0%
+mechanical to say if I know where the
+ 
+
+ align:start position:0%
+mechanical to say if I know where the
+break point is then I got to say what
+
+ align:start position:0%
+break point is then I got to say what
+ 
+
+ align:start position:0%
+break point is then I got to say what
+fraction of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year I got to tr I got to use the low
+
+ align:start position:0%
+year I got to tr I got to use the low
+ 
+
+ align:start position:0%
+year I got to tr I got to use the low
+duration curve to go
+
+ align:start position:0%
+duration curve to go
+ 
+
+ align:start position:0%
+duration curve to go
+from the break
+
+ align:start position:0%
+from the break
+ 
+
+ align:start position:0%
+from the break
+point where I decide between the
+
+ align:start position:0%
+point where I decide between the
+ 
+
+ align:start position:0%
+point where I decide between the
+different Technologies the base load and
+
+ align:start position:0%
+different Technologies the base load and
+ 
+
+ align:start position:0%
+different Technologies the base load and
+the peer in this
+
+ align:start position:0%
+the peer in this
+ 
+
+ align:start position:0%
+the peer in this
+case and to get a capacity mix out of
+
+ align:start position:0%
+case and to get a capacity mix out of
+ 
+
+ align:start position:0%
+case and to get a capacity mix out of
+that for what fraction of the Year blah
+
+ align:start position:0%
+that for what fraction of the Year blah
+ 
+
+ align:start position:0%
+that for what fraction of the Year blah
+blah
+
+ align:start position:0%
+blah
+ 
+
+ align:start position:0%
+blah
+blah okay I know I
+
+ align:start position:0%
+blah okay I know I
+ 
+
+ align:start position:0%
+blah okay I know I
+want I want to build base load plants
+
+ align:start position:0%
+want I want to build base load plants
+ 
+
+ align:start position:0%
+want I want to build base load plants
+that will run this long at least this
+
+ align:start position:0%
+that will run this long at least this
+ 
+
+ align:start position:0%
+that will run this long at least this
+fraction sorry uh we'll run at least
+
+ align:start position:0%
+fraction sorry uh we'll run at least
+ 
+
+ align:start position:0%
+fraction sorry uh we'll run at least
+this fraction of the year uh I want
+
+ align:start position:0%
+this fraction of the year uh I want
+ 
+
+ align:start position:0%
+this fraction of the year uh I want
+peers that will run
+
+ align:start position:0%
+peers that will run
+ 
+
+ align:start position:0%
+peers that will run
+less uh the low duration curve
+
+ align:start position:0%
+less uh the low duration curve
+ 
+
+ align:start position:0%
+less uh the low duration curve
+translates that into
+
+ align:start position:0%
+translates that into
+ 
+
+ align:start position:0%
+translates that into
+capacity okay details not critical
+
+ align:start position:0%
+capacity okay details not critical
+ 
+
+ align:start position:0%
+capacity okay details not critical
+concept pretty critical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I'd have to use them both right I
+
+ align:start position:0%
+yeah I'd have to use them both right I
+ 
+
+ align:start position:0%
+yeah I'd have to use them both right I
+have to go back and say okay what are
+
+ align:start position:0%
+have to go back and say okay what are
+ 
+
+ align:start position:0%
+have to go back and say okay what are
+the characteristics of these
+
+ align:start position:0%
+the characteristics of these
+ 
+
+ align:start position:0%
+the characteristics of these
+Technologies where's the
+
+ align:start position:0%
+Technologies where's the
+ 
+
+ align:start position:0%
+Technologies where's the
+breakpoint where's the breakpoint um and
+
+ align:start position:0%
+breakpoint where's the breakpoint um and
+ 
+
+ align:start position:0%
+breakpoint where's the breakpoint um and
+then what I would do in fact if I'm
+
+ align:start position:0%
+then what I would do in fact if I'm
+ 
+
+ align:start position:0%
+then what I would do in fact if I'm
+doing this if I'm centrally planning and
+
+ align:start position:0%
+doing this if I'm centrally planning and
+ 
+
+ align:start position:0%
+doing this if I'm centrally planning and
+I'm not a market if if I'm centrally
+
+ align:start position:0%
+I'm not a market if if I'm centrally
+ 
+
+ align:start position:0%
+I'm not a market if if I'm centrally
+planning I would a allow for Reserve
+
+ align:start position:0%
+planning I would a allow for Reserve
+ 
+
+ align:start position:0%
+planning I would a allow for Reserve
+margin so I wouldn't build just capacity
+
+ align:start position:0%
+margin so I wouldn't build just capacity
+ 
+
+ align:start position:0%
+margin so I wouldn't build just capacity
+and I would allow for the fact that I
+
+ align:start position:0%
+and I would allow for the fact that I
+ 
+
+ align:start position:0%
+and I would allow for the fact that I
+don't know the load duration curve
+
+ align:start position:0%
+don't know the load duration curve
+ 
+
+ align:start position:0%
+don't know the load duration curve
+exactly so I'd do a little stochastic
+
+ align:start position:0%
+exactly so I'd do a little stochastic
+ 
+
+ align:start position:0%
+exactly so I'd do a little stochastic
+work here I'd say what do I need if the
+
+ align:start position:0%
+work here I'd say what do I need if the
+ 
+
+ align:start position:0%
+work here I'd say what do I need if the
+if the curve varies up and down by 20%
+
+ align:start position:0%
+if the curve varies up and down by 20%
+ 
+
+ align:start position:0%
+if the curve varies up and down by 20%
+what do I need to be sure and I'd work
+
+ align:start position:0%
+what do I need to be sure and I'd work
+ 
+
+ align:start position:0%
+what do I need to be sure and I'd work
+out a somewhat more complicated problem
+
+ align:start position:0%
+out a somewhat more complicated problem
+ 
+
+ align:start position:0%
+out a somewhat more complicated problem
+what I gave you was well if I've only
+
+ align:start position:0%
+what I gave you was well if I've only
+ 
+
+ align:start position:0%
+what I gave you was well if I've only
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+Technologies and the Slate's
+
+ align:start position:0%
+Technologies and the Slate's
+ 
+
+ align:start position:0%
+Technologies and the Slate's
+clean then I know how to choose based on
+
+ align:start position:0%
+clean then I know how to choose based on
+ 
+
+ align:start position:0%
+clean then I know how to choose based on
+how long the plant's going to
+
+ align:start position:0%
+how long the plant's going to
+ 
+
+ align:start position:0%
+how long the plant's going to
+run and I can go from how using this
+
+ align:start position:0%
+run and I can go from how using this
+ 
+
+ align:start position:0%
+run and I can go from how using this
+curve I can go from how long the plant's
+
+ align:start position:0%
+curve I can go from how long the plant's
+ 
+
+ align:start position:0%
+curve I can go from how long the plant's
+going to run to how much of it I
+
+ align:start position:0%
+going to run to how much of it I
+ 
+
+ align:start position:0%
+going to run to how much of it I
+need based on based on how many hours
+
+ align:start position:0%
+need based on based on how many hours
+ 
+
+ align:start position:0%
+need based on based on how many hours
+demand will be above and below certain
+
+ align:start position:0%
+demand will be above and below certain
+ 
+
+ align:start position:0%
+demand will be above and below certain
+levels right so yeah that's exactly what
+
+ align:start position:0%
+levels right so yeah that's exactly what
+ 
+
+ align:start position:0%
+levels right so yeah that's exactly what
+this exercise in the very simple case
+
+ align:start position:0%
+this exercise in the very simple case
+ 
+
+ align:start position:0%
+this exercise in the very simple case
+would do would optimize the
+
+ align:start position:0%
+would do would optimize the
+ 
+
+ align:start position:0%
+would do would optimize the
+fleet and you need both you need both
+
+ align:start position:0%
+fleet and you need both you need both
+ 
+
+ align:start position:0%
+fleet and you need both you need both
+even if you don't have to worry about
+
+ align:start position:0%
+even if you don't have to worry about
+ 
+
+ align:start position:0%
+even if you don't have to worry about
+quick response which is not present in
+
+ align:start position:0%
+quick response which is not present in
+ 
+
+ align:start position:0%
+quick response which is not present in
+this picture you'd need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this
+
+ align:start position:0%
+okay this
+ 
+
+ align:start position:0%
+okay this
+is in fact in real systems you have
+
+ align:start position:0%
+is in fact in real systems you have
+ 
+
+ align:start position:0%
+is in fact in real systems you have
+multiple Technologies and this is a very
+
+ align:start position:0%
+multiple Technologies and this is a very
+ 
+
+ align:start position:0%
+multiple Technologies and this is a very
+strange graph uh but it makes that point
+
+ align:start position:0%
+strange graph uh but it makes that point
+ 
+
+ align:start position:0%
+strange graph uh but it makes that point
+this shows in 2008
+
+ align:start position:0%
+this shows in 2008
+ 
+
+ align:start position:0%
+this shows in 2008
+supposedly
+
+ align:start position:0%
+supposedly
+ 
+
+ align:start position:0%
+supposedly
+ranked vertically by marginal cost and
+
+ align:start position:0%
+ranked vertically by marginal cost and
+ 
+
+ align:start position:0%
+ranked vertically by marginal cost and
+horizontally by
+
+ align:start position:0%
+horizontally by
+ 
+
+ align:start position:0%
+horizontally by
+capacity all the plants in the lower 48
+
+ align:start position:0%
+capacity all the plants in the lower 48
+ 
+
+ align:start position:0%
+capacity all the plants in the lower 48
+states and so it gives you a sort of a
+
+ align:start position:0%
+states and so it gives you a sort of a
+ 
+
+ align:start position:0%
+states and so it gives you a sort of a
+supply curve the lower 48 states are not
+
+ align:start position:0%
+supply curve the lower 48 states are not
+ 
+
+ align:start position:0%
+supply curve the lower 48 states are not
+a single market so it's a funny kind of
+
+ align:start position:0%
+a single market so it's a funny kind of
+ 
+
+ align:start position:0%
+a single market so it's a funny kind of
+supply curve but it gives you the
+
+ align:start position:0%
+supply curve but it gives you the
+ 
+
+ align:start position:0%
+supply curve but it gives you the
+it it shows Hydro there in the far
+
+ align:start position:0%
+it it shows Hydro there in the far
+ 
+
+ align:start position:0%
+it it shows Hydro there in the far
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+um which has essentially it has only an
+
+ align:start position:0%
+um which has essentially it has only an
+ 
+
+ align:start position:0%
+um which has essentially it has only an
+opportunity cost of running right if you
+
+ align:start position:0%
+opportunity cost of running right if you
+ 
+
+ align:start position:0%
+opportunity cost of running right if you
+let the water out now you don't have it
+
+ align:start position:0%
+let the water out now you don't have it
+ 
+
+ align:start position:0%
+let the water out now you don't have it
+tomorrow so there's a little bit of an
+
+ align:start position:0%
+tomorrow so there's a little bit of an
+ 
+
+ align:start position:0%
+tomorrow so there's a little bit of an
+opportunity cost but out of pocket is
+
+ align:start position:0%
+opportunity cost but out of pocket is
+ 
+
+ align:start position:0%
+opportunity cost but out of pocket is
+zero and then you've got
+
+ align:start position:0%
+zero and then you've got
+ 
+
+ align:start position:0%
+zero and then you've got
+nukes which have a very low running cost
+
+ align:start position:0%
+nukes which have a very low running cost
+ 
+
+ align:start position:0%
+nukes which have a very low running cost
+and then you've got this mixture of of
+
+ align:start position:0%
+and then you've got this mixture of of
+ 
+
+ align:start position:0%
+and then you've got this mixture of of
+coal and gas and others and then finally
+
+ align:start position:0%
+coal and gas and others and then finally
+ 
+
+ align:start position:0%
+coal and gas and others and then finally
+up here that vertical portion that's the
+
+ align:start position:0%
+up here that vertical portion that's the
+ 
+
+ align:start position:0%
+up here that vertical portion that's the
+oh my God start the Diesels portion
+
+ align:start position:0%
+oh my God start the Diesels portion
+ 
+
+ align:start position:0%
+oh my God start the Diesels portion
+that's the very hot summer day when very
+
+ align:start position:0%
+that's the very hot summer day when very
+ 
+
+ align:start position:0%
+that's the very hot summer day when very
+inefficient very dirty diesels that are
+
+ align:start position:0%
+inefficient very dirty diesels that are
+ 
+
+ align:start position:0%
+inefficient very dirty diesels that are
+kept around to run for only a few hours
+
+ align:start position:0%
+kept around to run for only a few hours
+ 
+
+ align:start position:0%
+kept around to run for only a few hours
+a year get fired up right so there are
+
+ align:start position:0%
+a year get fired up right so there are
+ 
+
+ align:start position:0%
+a year get fired up right so there are
+really expensive units that you keep on
+
+ align:start position:0%
+really expensive units that you keep on
+ 
+
+ align:start position:0%
+really expensive units that you keep on
+hand even though they're expensive to
+
+ align:start position:0%
+hand even though they're expensive to
+ 
+
+ align:start position:0%
+hand even though they're expensive to
+run because you've got them and on a hot
+
+ align:start position:0%
+run because you've got them and on a hot
+ 
+
+ align:start position:0%
+run because you've got them and on a hot
+summer day you may need them so in fact
+
+ align:start position:0%
+summer day you may need them so in fact
+ 
+
+ align:start position:0%
+summer day you may need them so in fact
+that two technology picture that I gave
+
+ align:start position:0%
+that two technology picture that I gave
+ 
+
+ align:start position:0%
+that two technology picture that I gave
+you is too simple because you'd want to
+
+ align:start position:0%
+you is too simple because you'd want to
+ 
+
+ align:start position:0%
+you is too simple because you'd want to
+build a more complicated mixture but you
+
+ align:start position:0%
+build a more complicated mixture but you
+ 
+
+ align:start position:0%
+build a more complicated mixture but you
+need a
+
+ align:start position:0%
+need a
+ 
+
+ align:start position:0%
+need a
+mixture
+
+ align:start position:0%
+mixture
+ 
+
+ align:start position:0%
+mixture
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+comments yeah Scott by capacity does it
+
+ align:start position:0%
+comments yeah Scott by capacity does it
+ 
+
+ align:start position:0%
+comments yeah Scott by capacity does it
+mean at what capacity you turn it on no
+
+ align:start position:0%
+mean at what capacity you turn it on no
+ 
+
+ align:start position:0%
+mean at what capacity you turn it on no
+it means the this tells you the total
+
+ align:start position:0%
+it means the this tells you the total
+ 
+
+ align:start position:0%
+it means the this tells you the total
+Hydro capacity this is the total nuclear
+
+ align:start position:0%
+Hydro capacity this is the total nuclear
+ 
+
+ align:start position:0%
+Hydro capacity this is the total nuclear
+capacity this distance so it's giving
+
+ align:start position:0%
+capacity this distance so it's giving
+ 
+
+ align:start position:0%
+capacity this distance so it's giving
+you a sense of how much you can get at
+
+ align:start position:0%
+you a sense of how much you can get at
+ 
+
+ align:start position:0%
+you a sense of how much you can get at
+different marginal costs so it is a
+
+ align:start position:0%
+different marginal costs so it is a
+ 
+
+ align:start position:0%
+different marginal costs so it is a
+supply curve in that sense
+
+ align:start position:0%
+supply curve in that sense
+ 
+
+ align:start position:0%
+supply curve in that sense
+if they were all in the same Market dot
+
+ align:start position:0%
+if they were all in the same Market dot
+ 
+
+ align:start position:0%
+if they were all in the same Market dot
+dot dot dot dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+um okay what's the grid look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um both the you can have multiple
+
+ align:start position:0%
+um both the you can have multiple
+ 
+
+ align:start position:0%
+um both the you can have multiple
+generating plants in any particular
+
+ align:start position:0%
+generating plants in any particular
+ 
+
+ align:start position:0%
+generating plants in any particular
+region but you really can't economically
+
+ align:start position:0%
+region but you really can't economically
+ 
+
+ align:start position:0%
+region but you really can't economically
+have multiple transmission systems and
+
+ align:start position:0%
+have multiple transmission systems and
+ 
+
+ align:start position:0%
+have multiple transmission systems and
+multiple Distribution Systems they are
+
+ align:start position:0%
+multiple Distribution Systems they are
+ 
+
+ align:start position:0%
+multiple Distribution Systems they are
+typically considered natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monopolies what a natural monopoly means
+
+ align:start position:0%
+monopolies what a natural monopoly means
+ 
+
+ align:start position:0%
+monopolies what a natural monopoly means
+is generally
+
+ align:start position:0%
+is generally
+ 
+
+ align:start position:0%
+is generally
+defined as having more than one of them
+
+ align:start position:0%
+defined as having more than one of them
+ 
+
+ align:start position:0%
+defined as having more than one of them
+would raise
+
+ align:start position:0%
+would raise
+ 
+
+ align:start position:0%
+would raise
+costs so if you think of the x's in that
+
+ align:start position:0%
+costs so if you think of the x's in that
+ 
+
+ align:start position:0%
+costs so if you think of the x's in that
+sub additivity bullet as
+
+ align:start position:0%
+sub additivity bullet as
+ 
+
+ align:start position:0%
+sub additivity bullet as
+basically uh electricity supplied two
+
+ align:start position:0%
+basically uh electricity supplied two
+ 
+
+ align:start position:0%
+basically uh electricity supplied two
+houses so each component is a house or a
+
+ align:start position:0%
+houses so each component is a house or a
+ 
+
+ align:start position:0%
+houses so each component is a house or a
+building um um rather than total
+
+ align:start position:0%
+building um um rather than total
+ 
+
+ align:start position:0%
+building um um rather than total
+kilowatt hours but but a vector of
+
+ align:start position:0%
+kilowatt hours but but a vector of
+ 
+
+ align:start position:0%
+kilowatt hours but but a vector of
+locations then sub additivity by that
+
+ align:start position:0%
+locations then sub additivity by that
+ 
+
+ align:start position:0%
+locations then sub additivity by that
+definition means it's cheaper to
+
+ align:start position:0%
+definition means it's cheaper to
+ 
+
+ align:start position:0%
+definition means it's cheaper to
+supply you you can't split the system
+
+ align:start position:0%
+supply you you can't split the system
+ 
+
+ align:start position:0%
+supply you you can't split the system
+without raising
+
+ align:start position:0%
+without raising
+ 
+
+ align:start position:0%
+without raising
+cost um the normal picture you get for
+
+ align:start position:0%
+cost um the normal picture you get for
+ 
+
+ align:start position:0%
+cost um the normal picture you get for
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is if if um uh the X's are scalers then
+
+ align:start position:0%
+is if if um uh the X's are scalers then
+ 
+
+ align:start position:0%
+is if if um uh the X's are scalers then
+it's just economies
+
+ align:start position:0%
+it's just economies
+ 
+
+ align:start position:0%
+it's just economies
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+so it's present in electri natural
+
+ align:start position:0%
+so it's present in electri natural
+ 
+
+ align:start position:0%
+so it's present in electri natural
+monopoly is present in electricity it's
+
+ align:start position:0%
+monopoly is present in electricity it's
+ 
+
+ align:start position:0%
+monopoly is present in electricity it's
+present in other areas as
+
+ align:start position:0%
+present in other areas as
+ 
+
+ align:start position:0%
+present in other areas as
+well let's do a minute on why there's a
+
+ align:start position:0%
+well let's do a minute on why there's a
+ 
+
+ align:start position:0%
+well let's do a minute on why there's a
+problem when you have a natural monopoly
+
+ align:start position:0%
+problem when you have a natural monopoly
+ 
+
+ align:start position:0%
+problem when you have a natural monopoly
+what's the policy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem why do we bother to talk about
+
+ align:start position:0%
+problem why do we bother to talk about
+ 
+
+ align:start position:0%
+problem why do we bother to talk about
+it Alex are you raising your hand or no
+
+ align:start position:0%
+it Alex are you raising your hand or no
+ 
+
+ align:start position:0%
+it Alex are you raising your hand or no
+you were not raising your hand you were
+
+ align:start position:0%
+you were not raising your hand you were
+ 
+
+ align:start position:0%
+you were not raising your hand you were
+thinking about raising your hand no not
+
+ align:start position:0%
+thinking about raising your hand no not
+ 
+
+ align:start position:0%
+thinking about raising your hand no not
+even that
+
+ align:start position:0%
+even that
+ 
+
+ align:start position:0%
+even that
+okay okay we're back in 1401 or1 Kristen
+
+ align:start position:0%
+okay okay we're back in 1401 or1 Kristen
+ 
+
+ align:start position:0%
+okay okay we're back in 1401 or1 Kristen
+Kristen and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+davidse monop to taking as much as they
+
+ align:start position:0%
+davidse monop to taking as much as they
+ 
+
+ align:start position:0%
+davidse monop to taking as much as they
+could so so what enables it to take as
+
+ align:start position:0%
+could so so what enables it to take as
+ 
+
+ align:start position:0%
+could so so what enables it to take as
+much as they as it could competition so
+
+ align:start position:0%
+much as they as it could competition so
+ 
+
+ align:start position:0%
+much as they as it could competition so
+you think there's no there would be no
+
+ align:start position:0%
+you think there's no there would be no
+ 
+
+ align:start position:0%
+you think there's no there would be no
+competition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they'd make a lot of money but we
+
+ align:start position:0%
+and they'd make a lot of money but we
+ 
+
+ align:start position:0%
+and they'd make a lot of money but we
+like making a lot of money don't
+
+ align:start position:0%
+like making a lot of money don't
+ 
+
+ align:start position:0%
+like making a lot of money don't
+we consumers don't so there'd be a
+
+ align:start position:0%
+we consumers don't so there'd be a
+ 
+
+ align:start position:0%
+we consumers don't so there'd be a
+there'd be a wellfare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loss
+
+ align:start position:0%
+loss
+ 
+
+ align:start position:0%
+loss
+David I mean yeah I was going to say
+
+ align:start position:0%
+David I mean yeah I was going to say
+ 
+
+ align:start position:0%
+David I mean yeah I was going to say
+they could just charge as much up to the
+
+ align:start position:0%
+they could just charge as much up to the
+ 
+
+ align:start position:0%
+they could just charge as much up to the
+point where it would be for another
+
+ align:start position:0%
+point where it would be for another
+ 
+
+ align:start position:0%
+point where it would be for another
+Monopoly for another firm to toer I mean
+
+ align:start position:0%
+Monopoly for another firm to toer I mean
+ 
+
+ align:start position:0%
+Monopoly for another firm to toer I mean
+it's actually interesting we always
+
+ align:start position:0%
+it's actually interesting we always
+ 
+
+ align:start position:0%
+it's actually interesting we always
+assume in these discussions that that
+
+ align:start position:0%
+assume in these discussions that that
+ 
+
+ align:start position:0%
+assume in these discussions that that
+you you that competition isn't viable um
+
+ align:start position:0%
+you you that competition isn't viable um
+ 
+
+ align:start position:0%
+you you that competition isn't viable um
+and cable television is a standard
+
+ align:start position:0%
+and cable television is a standard
+ 
+
+ align:start position:0%
+and cable television is a standard
+example of a natural monopoly local
+
+ align:start position:0%
+example of a natural monopoly local
+ 
+
+ align:start position:0%
+example of a natural monopoly local
+cable television distribution but there
+
+ align:start position:0%
+cable television distribution but there
+ 
+
+ align:start position:0%
+cable television distribution but there
+are a number of places where they're
+
+ align:start position:0%
+are a number of places where they're
+ 
+
+ align:start position:0%
+are a number of places where they're
+competing Cable Systems uh and that's
+
+ align:start position:0%
+competing Cable Systems uh and that's
+ 
+
+ align:start position:0%
+competing Cable Systems uh and that's
+wasteful but it may be less wasteful
+
+ align:start position:0%
+wasteful but it may be less wasteful
+ 
+
+ align:start position:0%
+wasteful but it may be less wasteful
+than having really high prices uh
+
+ align:start position:0%
+than having really high prices uh
+ 
+
+ align:start position:0%
+than having really high prices uh
+welfare lost because of
+
+ align:start position:0%
+welfare lost because of
+ 
+
+ align:start position:0%
+welfare lost because of
+high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prices well that's the same story right
+
+ align:start position:0%
+prices well that's the same story right
+ 
+
+ align:start position:0%
+prices well that's the same story right
+you raise the price you you supply less
+
+ align:start position:0%
+you raise the price you you supply less
+ 
+
+ align:start position:0%
+you raise the price you you supply less
+you you end up I can't draw it you might
+
+ align:start position:0%
+you you end up I can't draw it you might
+ 
+
+ align:start position:0%
+you you end up I can't draw it you might
+like to end
+
+ align:start position:0%
+like to end
+ 
+
+ align:start position:0%
+like to end
+up uh at some point like a and in fact
+
+ align:start position:0%
+up uh at some point like a and in fact
+ 
+
+ align:start position:0%
+up uh at some point like a and in fact
+what you might what the a monopoly in
+
+ align:start position:0%
+what you might what the a monopoly in
+ 
+
+ align:start position:0%
+what you might what the a monopoly in
+this situation might do is produce half
+
+ align:start position:0%
+this situation might do is produce half
+ 
+
+ align:start position:0%
+this situation might do is produce half
+that where the production would be B but
+
+ align:start position:0%
+that where the production would be B but
+ 
+
+ align:start position:0%
+that where the production would be B but
+the price would be notably higher than
+
+ align:start position:0%
+the price would be notably higher than
+ 
+
+ align:start position:0%
+the price would be notably higher than
+at a any
+
+ align:start position:0%
+at a any
+ 
+
+ align:start position:0%
+at a any
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+Environ good for the environment good
+
+ align:start position:0%
+Environ good for the environment good
+ 
+
+ align:start position:0%
+Environ good for the environment good
+for the environment so we should we
+
+ align:start position:0%
+for the environment so we should we
+ 
+
+ align:start position:0%
+for the environment so we should we
+should just deregulate electricity
+
+ align:start position:0%
+should just deregulate electricity
+ 
+
+ align:start position:0%
+should just deregulate electricity
+throughout because we'd spend a lot of
+
+ align:start position:0%
+throughout because we'd spend a lot of
+ 
+
+ align:start position:0%
+throughout because we'd spend a lot of
+money uh interesting point anybody else
+
+ align:start position:0%
+money uh interesting point anybody else
+ 
+
+ align:start position:0%
+money uh interesting point anybody else
+anything else that could go wrong in
+
+ align:start position:0%
+anything else that could go wrong in
+ 
+
+ align:start position:0%
+anything else that could go wrong in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+situation okay what about
+
+ align:start position:0%
+situation okay what about
+ 
+
+ align:start position:0%
+situation okay what about
+cost let's let's think about human
+
+ align:start position:0%
+cost let's let's think about human
+ 
+
+ align:start position:0%
+cost let's let's think about human
+beings running an
+
+ align:start position:0%
+beings running an
+ 
+
+ align:start position:0%
+beings running an
+organization and you have no competition
+
+ align:start position:0%
+organization and you have no competition
+ 
+
+ align:start position:0%
+organization and you have no competition
+and you're providing a
+
+ align:start position:0%
+and you're providing a
+ 
+
+ align:start position:0%
+and you're providing a
+necessity and your brother-in-law asks
+
+ align:start position:0%
+necessity and your brother-in-law asks
+ 
+
+ align:start position:0%
+necessity and your brother-in-law asks
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+job you hire your
+
+ align:start position:0%
+job you hire your
+ 
+
+ align:start position:0%
+job you hire your
+brother-in-law right there's a there's a
+
+ align:start position:0%
+brother-in-law right there's a there's a
+ 
+
+ align:start position:0%
+brother-in-law right there's a there's a
+cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem we always draw these curves like
+
+ align:start position:0%
+problem we always draw these curves like
+ 
+
+ align:start position:0%
+problem we always draw these curves like
+you know these these these come out of
+
+ align:start position:0%
+you know these these these come out of
+ 
+
+ align:start position:0%
+you know these these these come out of
+these come out of the sky and we March
+
+ align:start position:0%
+these come out of the sky and we March
+ 
+
+ align:start position:0%
+these come out of the sky and we March
+down cost Curves in fact these are
+
+ align:start position:0%
+down cost Curves in fact these are
+ 
+
+ align:start position:0%
+down cost Curves in fact these are
+determined by organizational
+
+ align:start position:0%
+determined by organizational
+ 
+
+ align:start position:0%
+determined by organizational
+decisions and when you have a monopoly
+
+ align:start position:0%
+decisions and when you have a monopoly
+ 
+
+ align:start position:0%
+decisions and when you have a monopoly
+uh the pressure to actually do
+
+ align:start position:0%
+uh the pressure to actually do
+ 
+
+ align:start position:0%
+uh the pressure to actually do
+unpleasant things like firing people or
+
+ align:start position:0%
+unpleasant things like firing people or
+ 
+
+ align:start position:0%
+unpleasant things like firing people or
+not hiring your
+
+ align:start position:0%
+not hiring your
+ 
+
+ align:start position:0%
+not hiring your
+brother-in-law uh those pressures are
+
+ align:start position:0%
+brother-in-law uh those pressures are
+ 
+
+ align:start position:0%
+brother-in-law uh those pressures are
+gone not gone they're
+
+ align:start position:0%
+gone not gone they're
+ 
+
+ align:start position:0%
+gone not gone they're
+diminished they're diminished so you
+
+ align:start position:0%
+diminished they're diminished so you
+ 
+
+ align:start position:0%
+diminished they're diminished so you
+expect high
+
+ align:start position:0%
+expect high
+ 
+
+ align:start position:0%
+expect high
+costs
+
+ align:start position:0%
+costs
+ 
+
+ align:start position:0%
+costs
+uh there's another reason and it's not
+
+ align:start position:0%
+uh there's another reason and it's not
+ 
+
+ align:start position:0%
+uh there's another reason and it's not
+true for all natural
+
+ align:start position:0%
+true for all natural
+ 
+
+ align:start position:0%
+true for all natural
+monopolies but it's true for the ones
+
+ align:start position:0%
+monopolies but it's true for the ones
+ 
+
+ align:start position:0%
+monopolies but it's true for the ones
+that we're mostly concerned about
+
+ align:start position:0%
+that we're mostly concerned about
+ 
+
+ align:start position:0%
+that we're mostly concerned about
+most of these things are called Public
+
+ align:start position:0%
+most of these things are called Public
+ 
+
+ align:start position:0%
+most of these things are called Public
+Utilities now it's not true for cable
+
+ align:start position:0%
+Utilities now it's not true for cable
+ 
+
+ align:start position:0%
+Utilities now it's not true for cable
+television
+
+ align:start position:0%
+television
+ 
+
+ align:start position:0%
+television
+yet electricity used to be a luxury good
+
+ align:start position:0%
+yet electricity used to be a luxury good
+ 
+
+ align:start position:0%
+yet electricity used to be a luxury good
+telephones used to be a luxury good
+
+ align:start position:0%
+telephones used to be a luxury good
+ 
+
+ align:start position:0%
+telephones used to be a luxury good
+they're not anymore they're mostly
+
+ align:start position:0%
+they're not anymore they're mostly
+ 
+
+ align:start position:0%
+they're not anymore they're mostly
+considered
+
+ align:start position:0%
+considered
+ 
+
+ align:start position:0%
+considered
+necessities and when you raise the price
+
+ align:start position:0%
+necessities and when you raise the price
+ 
+
+ align:start position:0%
+necessities and when you raise the price
+as Kirsten wanted them to do to raise
+
+ align:start position:0%
+as Kirsten wanted them to do to raise
+ 
+
+ align:start position:0%
+as Kirsten wanted them to do to raise
+the price to for Necessities you're
+
+ align:start position:0%
+the price to for Necessities you're
+ 
+
+ align:start position:0%
+the price to for Necessities you're
+basically taking money out of poor
+
+ align:start position:0%
+basically taking money out of poor
+ 
+
+ align:start position:0%
+basically taking money out of poor
+people's pockets and giving them to Rich
+
+ align:start position:0%
+people's pockets and giving them to Rich
+ 
+
+ align:start position:0%
+people's pockets and giving them to Rich
+shareholders so these are the problems
+
+ align:start position:0%
+shareholders so these are the problems
+ 
+
+ align:start position:0%
+shareholders so these are the problems
+that people mostly worry
+
+ align:start position:0%
+that people mostly worry
+ 
+
+ align:start position:0%
+that people mostly worry
+about um and that business about
+
+ align:start position:0%
+about um and that business about
+ 
+
+ align:start position:0%
+about um and that business about
+triangles and rectangles let me just
+
+ align:start position:0%
+triangles and rectangles let me just
+ 
+
+ align:start position:0%
+triangles and rectangles let me just
+remind
+
+ align:start position:0%
+remind
+ 
+
+ align:start position:0%
+remind
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me hold let let let let for some
+
+ align:start position:0%
+um let me hold let let let let for some
+ 
+
+ align:start position:0%
+um let me hold let let let let for some
+reason let this be marginal cost equals
+
+ align:start position:0%
+reason let this be marginal cost equals
+ 
+
+ align:start position:0%
+reason let this be marginal cost equals
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+cost and this
+
+ align:start position:0%
+cost and this
+ 
+
+ align:start position:0%
+cost and this
+is the demand curve and this is of
+
+ align:start position:0%
+is the demand curve and this is of
+ 
+
+ align:start position:0%
+is the demand curve and this is of
+course what you'd
+
+ align:start position:0%
+course what you'd
+ 
+
+ align:start position:0%
+course what you'd
+like right you'd like production at the
+
+ align:start position:0%
+like right you'd like production at the
+ 
+
+ align:start position:0%
+like right you'd like production at the
+point where price equals marginal cost
+
+ align:start position:0%
+point where price equals marginal cost
+ 
+
+ align:start position:0%
+point where price equals marginal cost
+um and this is the price axis and this
+
+ align:start position:0%
+um and this is the price axis and this
+ 
+
+ align:start position:0%
+um and this is the price axis and this
+is the quantity
+
+ align:start position:0%
+is the quantity
+ 
+
+ align:start position:0%
+is the quantity
+axis the classic thing that a monopoly
+
+ align:start position:0%
+axis the classic thing that a monopoly
+ 
+
+ align:start position:0%
+axis the classic thing that a monopoly
+might do is to
+
+ align:start position:0%
+might do is to
+ 
+
+ align:start position:0%
+might do is to
+produce say
+
+ align:start position:0%
+produce say
+ 
+
+ align:start position:0%
+produce say
+qm and charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pm and then the the dead weight loss
+
+ align:start position:0%
+pm and then the the dead weight loss
+ 
+
+ align:start position:0%
+pm and then the the dead weight loss
+this triangle over here I'm hoping I'm
+
+ align:start position:0%
+this triangle over here I'm hoping I'm
+ 
+
+ align:start position:0%
+this triangle over here I'm hoping I'm
+reminding you uh it's the difference
+
+ align:start position:0%
+reminding you uh it's the difference
+ 
+
+ align:start position:0%
+reminding you uh it's the difference
+between what people were willing to pay
+
+ align:start position:0%
+between what people were willing to pay
+ 
+
+ align:start position:0%
+between what people were willing to pay
+and what it would have cost to produce
+
+ align:start position:0%
+and what it would have cost to produce
+ 
+
+ align:start position:0%
+and what it would have cost to produce
+this output that's not produced so
+
+ align:start position:0%
+this output that's not produced so
+ 
+
+ align:start position:0%
+this output that's not produced so
+that's that's a loss right if you if you
+
+ align:start position:0%
+that's that's a loss right if you if you
+ 
+
+ align:start position:0%
+that's that's a loss right if you if you
+reduce output from say
+
+ align:start position:0%
+reduce output from say
+ 
+
+ align:start position:0%
+reduce output from say
+qar to qm you lose that
+
+ align:start position:0%
+qar to qm you lose that
+ 
+
+ align:start position:0%
+qar to qm you lose that
+triangle but suppose what in fact
+
+ align:start position:0%
+triangle but suppose what in fact
+ 
+
+ align:start position:0%
+triangle but suppose what in fact
+happens is the monopolist is really
+
+ align:start position:0%
+happens is the monopolist is really
+ 
+
+ align:start position:0%
+happens is the monopolist is really
+lazy and costs go up to to
+
+ align:start position:0%
+lazy and costs go up to to
+ 
+
+ align:start position:0%
+lazy and costs go up to to
+PM well in that case you lose the
+
+ align:start position:0%
+PM well in that case you lose the
+ 
+
+ align:start position:0%
+PM well in that case you lose the
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+too and in most reason able cases the
+
+ align:start position:0%
+too and in most reason able cases the
+ 
+
+ align:start position:0%
+too and in most reason able cases the
+rectangles are bigger than the
+
+ align:start position:0%
+rectangles are bigger than the
+ 
+
+ align:start position:0%
+rectangles are bigger than the
+triangles so that if I can't resist
+
+ align:start position:0%
+triangles so that if I can't resist
+ 
+
+ align:start position:0%
+triangles so that if I can't resist
+hiring my brother-in-law neither can
+
+ align:start position:0%
+hiring my brother-in-law neither can
+ 
+
+ align:start position:0%
+hiring my brother-in-law neither can
+anybody else that could be much worse
+
+ align:start position:0%
+anybody else that could be much worse
+ 
+
+ align:start position:0%
+anybody else that could be much worse
+aside from the the rich poor
+
+ align:start position:0%
+aside from the the rich poor
+ 
+
+ align:start position:0%
+aside from the the rich poor
+issue than the fact that I'm pricing
+
+ align:start position:0%
+issue than the fact that I'm pricing
+ 
+
+ align:start position:0%
+issue than the fact that I'm pricing
+High okay so these are things you're
+
+ align:start position:0%
+High okay so these are things you're
+ 
+
+ align:start position:0%
+High okay so these are things you're
+worry
+
+ align:start position:0%
+worry
+ 
+
+ align:start position:0%
+worry
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um what do you do about
+
+ align:start position:0%
+um what do you do about
+ 
+
+ align:start position:0%
+um what do you do about
+it Water Supplies like this you could
+
+ align:start position:0%
+it Water Supplies like this you could
+ 
+
+ align:start position:0%
+it Water Supplies like this you could
+argue bus services like this telephone
+
+ align:start position:0%
+argue bus services like this telephone
+ 
+
+ align:start position:0%
+argue bus services like this telephone
+distribution is like this electricity
+
+ align:start position:0%
+distribution is like this electricity
+ 
+
+ align:start position:0%
+distribution is like this electricity
+distribution is like this electricity
+
+ align:start position:0%
+distribution is like this electricity
+ 
+
+ align:start position:0%
+distribution is like this electricity
+transmission is like this now we're
+
+ align:start position:0%
+transmission is like this now we're
+ 
+
+ align:start position:0%
+transmission is like this now we're
+mostly about energy but it is a general
+
+ align:start position:0%
+mostly about energy but it is a general
+ 
+
+ align:start position:0%
+mostly about energy but it is a general
+problem what are some of the
+
+ align:start position:0%
+problem what are some of the
+ 
+
+ align:start position:0%
+problem what are some of the
+solutions right this
+
+ align:start position:0%
+solutions right this
+ 
+
+ align:start position:0%
+solutions right this
+this difficulty a natural monopoly
+
+ align:start position:0%
+this difficulty a natural monopoly
+ 
+
+ align:start position:0%
+this difficulty a natural monopoly
+arises across time and space and
+
+ align:start position:0%
+arises across time and space and
+ 
+
+ align:start position:0%
+arises across time and space and
+industries uh
+
+ align:start position:0%
+industries uh
+ 
+
+ align:start position:0%
+industries uh
+and a variety of mechanisms have been
+
+ align:start position:0%
+and a variety of mechanisms have been
+ 
+
+ align:start position:0%
+and a variety of mechanisms have been
+adopted what might you
+
+ align:start position:0%
+adopted what might you
+ 
+
+ align:start position:0%
+adopted what might you
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we could have a private
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+firm and we could regulate
+
+ align:start position:0%
+firm and we could regulate
+ 
+
+ align:start position:0%
+firm and we could regulate
+it okay anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Brendan well that's not going to what
+
+ align:start position:0%
+Brendan well that's not going to what
+ 
+
+ align:start position:0%
+Brendan well that's not going to what
+what am I going to do if I can't have
+
+ align:start position:0%
+what am I going to do if I can't have
+ 
+
+ align:start position:0%
+what am I going to do if I can't have
+competition as an economic matter I can
+
+ align:start position:0%
+competition as an economic matter I can
+ 
+
+ align:start position:0%
+competition as an economic matter I can
+split it
+
+ align:start position:0%
+split it
+ 
+
+ align:start position:0%
+split it
+you're saying Force
+
+ align:start position:0%
+you're saying Force
+ 
+
+ align:start position:0%
+you're saying Force
+competition well what if what if I split
+
+ align:start position:0%
+competition well what if what if I split
+ 
+
+ align:start position:0%
+competition well what if what if I split
+it and in fact one of them goes out of
+
+ align:start position:0%
+it and in fact one of them goes out of
+ 
+
+ align:start position:0%
+it and in fact one of them goes out of
+business see the problem with this if
+
+ align:start position:0%
+business see the problem with this if
+ 
+
+ align:start position:0%
+business see the problem with this if
+you go back to this
+
+ align:start position:0%
+you go back to this
+ 
+
+ align:start position:0%
+you go back to this
+picture the if I've got two firms and
+
+ align:start position:0%
+picture the if I've got two firms and
+ 
+
+ align:start position:0%
+picture the if I've got two firms and
+they're both on this cost curve the
+
+ align:start position:0%
+they're both on this cost curve the
+ 
+
+ align:start position:0%
+they're both on this cost curve the
+larger one always has a cost
+
+ align:start position:0%
+larger one always has a cost
+ 
+
+ align:start position:0%
+larger one always has a cost
+Advantage so that it you can imagine
+
+ align:start position:0%
+Advantage so that it you can imagine
+ 
+
+ align:start position:0%
+Advantage so that it you can imagine
+competition working but you could also
+
+ align:start position:0%
+competition working but you could also
+ 
+
+ align:start position:0%
+competition working but you could also
+Imagine the larger firm drives a smaller
+
+ align:start position:0%
+Imagine the larger firm drives a smaller
+ 
+
+ align:start position:0%
+Imagine the larger firm drives a smaller
+firm out just competing
+
+ align:start position:0%
+firm out just competing
+ 
+
+ align:start position:0%
+firm out just competing
+and nobody comes in because they have a
+
+ align:start position:0%
+and nobody comes in because they have a
+ 
+
+ align:start position:0%
+and nobody comes in because they have a
+big cost disadvantage if they come in so
+
+ align:start position:0%
+big cost disadvantage if they come in so
+ 
+
+ align:start position:0%
+big cost disadvantage if they come in so
+that's a tough one most Industries
+
+ align:start position:0%
+that's a tough one most Industries
+ 
+
+ align:start position:0%
+that's a tough one most Industries
+that's what you want to do and that's
+
+ align:start position:0%
+that's what you want to do and that's
+ 
+
+ align:start position:0%
+that's what you want to do and that's
+what's done but that's tough here
+
+ align:start position:0%
+what's done but that's tough here
+ 
+
+ align:start position:0%
+what's done but that's tough here
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+Max you could you could have a
+
+ align:start position:0%
+Max you could you could have a
+ 
+
+ align:start position:0%
+Max you could you could have a
+government government
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+run uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Enterprise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me drill down a little bit on
+
+ align:start position:0%
+let me drill down a little bit on
+ 
+
+ align:start position:0%
+let me drill down a little bit on
+regulation how might you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regulate
+
+ align:start position:0%
+regulate
+ 
+
+ align:start position:0%
+regulate
+Max well no you actually probably don't
+
+ align:start position:0%
+Max well no you actually probably don't
+ 
+
+ align:start position:0%
+Max well no you actually probably don't
+want to price
+
+ align:start position:0%
+want to price
+ 
+
+ align:start position:0%
+want to price
+floor price ceiling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe oh you want them to raise prices
+
+ align:start position:0%
+maybe oh you want them to raise prices
+ 
+
+ align:start position:0%
+maybe oh you want them to raise prices
+to bring in
+
+ align:start position:0%
+to bring in
+ 
+
+ align:start position:0%
+to bring in
+entry oo oo that could be really
+
+ align:start position:0%
+entry oo oo that could be really
+ 
+
+ align:start position:0%
+entry oo oo that could be really
+expensive right remember the higher the
+
+ align:start position:0%
+expensive right remember the higher the
+ 
+
+ align:start position:0%
+expensive right remember the higher the
+if you split you've raised costs and now
+
+ align:start position:0%
+if you split you've raised costs and now
+ 
+
+ align:start position:0%
+if you split you've raised costs and now
+you're going to raise the price to make
+
+ align:start position:0%
+you're going to raise the price to make
+ 
+
+ align:start position:0%
+you're going to raise the price to make
+sure that you can survive with higher
+
+ align:start position:0%
+sure that you can survive with higher
+ 
+
+ align:start position:0%
+sure that you can survive with higher
+costs you'll get more companies
+
+ align:start position:0%
+costs you'll get more companies
+ 
+
+ align:start position:0%
+costs you'll get more companies
+in do you want there actually have been
+
+ align:start position:0%
+in do you want there actually have been
+ 
+
+ align:start position:0%
+in do you want there actually have been
+examples of competing telephone systems
+
+ align:start position:0%
+examples of competing telephone systems
+ 
+
+ align:start position:0%
+examples of competing telephone systems
+historically uh I don't know of any
+
+ align:start position:0%
+historically uh I don't know of any
+ 
+
+ align:start position:0%
+historically uh I don't know of any
+competing I don't know off hand of any
+
+ align:start position:0%
+competing I don't know off hand of any
+ 
+
+ align:start position:0%
+competing I don't know off hand of any
+competing electric Distribution Systems
+
+ align:start position:0%
+competing electric Distribution Systems
+ 
+
+ align:start position:0%
+competing electric Distribution Systems
+there are competing Cable Systems it's
+
+ align:start position:0%
+there are competing Cable Systems it's
+ 
+
+ align:start position:0%
+there are competing Cable Systems it's
+it's expensive right I mean you're
+
+ align:start position:0%
+it's expensive right I mean you're
+ 
+
+ align:start position:0%
+it's expensive right I mean you're
+duplicating you're duplicating so most
+
+ align:start position:0%
+duplicating you're duplicating so most
+ 
+
+ align:start position:0%
+duplicating you're duplicating so most
+people say that's triangles versus
+
+ align:start position:0%
+people say that's triangles versus
+ 
+
+ align:start position:0%
+people say that's triangles versus
+rectangles you're saying I'll tolerate
+
+ align:start position:0%
+rectangles you're saying I'll tolerate
+ 
+
+ align:start position:0%
+rectangles you're saying I'll tolerate
+I'll tolerate a higher
+
+ align:start position:0%
+I'll tolerate a higher
+ 
+
+ align:start position:0%
+I'll tolerate a higher
+cost as as long as they're not making
+
+ align:start position:0%
+cost as as long as they're not making
+ 
+
+ align:start position:0%
+cost as as long as they're not making
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+money well I don't want to pay a higher
+
+ align:start position:0%
+money well I don't want to pay a higher
+ 
+
+ align:start position:0%
+money well I don't want to pay a higher
+price Max I'm sorry I I'm happy that
+
+ align:start position:0%
+price Max I'm sorry I I'm happy that
+ 
+
+ align:start position:0%
+price Max I'm sorry I I'm happy that
+they're not making profits but what
+
+ align:start position:0%
+they're not making profits but what
+ 
+
+ align:start position:0%
+they're not making profits but what
+you're managing to do is to raise the
+
+ align:start position:0%
+you're managing to do is to raise the
+ 
+
+ align:start position:0%
+you're managing to do is to raise the
+cost and that's the natural monopoly
+
+ align:start position:0%
+cost and that's the natural monopoly
+ 
+
+ align:start position:0%
+cost and that's the natural monopoly
+problem that's the core of it that the
+
+ align:start position:0%
+problem that's the core of it that the
+ 
+
+ align:start position:0%
+problem that's the core of it that the
+if you get competition in you will have
+
+ align:start position:0%
+if you get competition in you will have
+ 
+
+ align:start position:0%
+if you get competition in you will have
+it at a higher
+
+ align:start position:0%
+it at a higher
+ 
+
+ align:start position:0%
+it at a higher
+cost and sometimes if you think
+
+ align:start position:0%
+cost and sometimes if you think
+ 
+
+ align:start position:0%
+cost and sometimes if you think
+about ways that curve could
+
+ align:start position:0%
+about ways that curve could
+ 
+
+ align:start position:0%
+about ways that curve could
+look sometimes in fact if that curve is
+
+ align:start position:0%
+look sometimes in fact if that curve is
+ 
+
+ align:start position:0%
+look sometimes in fact if that curve is
+shallow
+
+ align:start position:0%
+shallow
+ 
+
+ align:start position:0%
+shallow
+enough you're you'd be right let's have
+
+ align:start position:0%
+enough you're you'd be right let's have
+ 
+
+ align:start position:0%
+enough you're you'd be right let's have
+a little competition the costs will go
+
+ align:start position:0%
+a little competition the costs will go
+ 
+
+ align:start position:0%
+a little competition the costs will go
+up but the incentives will be
+
+ align:start position:0%
+up but the incentives will be
+ 
+
+ align:start position:0%
+up but the incentives will be
+stronger they will not hire their
+
+ align:start position:0%
+stronger they will not hire their
+ 
+
+ align:start position:0%
+stronger they will not hire their
+brothers-in-law and the yeah the the
+
+ align:start position:0%
+brothers-in-law and the yeah the the
+ 
+
+ align:start position:0%
+brothers-in-law and the yeah the the
+costs will be up but the pressure on
+
+ align:start position:0%
+costs will be up but the pressure on
+ 
+
+ align:start position:0%
+costs will be up but the pressure on
+prices will overwhelm it mostly that's
+
+ align:start position:0%
+prices will overwhelm it mostly that's
+ 
+
+ align:start position:0%
+prices will overwhelm it mostly that's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+true I mean telephone it might be uh
+
+ align:start position:0%
+true I mean telephone it might be uh
+ 
+
+ align:start position:0%
+true I mean telephone it might be uh
+wireless IT surely is that's why we have
+
+ align:start position:0%
+wireless IT surely is that's why we have
+ 
+
+ align:start position:0%
+wireless IT surely is that's why we have
+so many we can have competing wireless
+
+ align:start position:0%
+so many we can have competing wireless
+ 
+
+ align:start position:0%
+so many we can have competing wireless
+companies we have maybe three in Europe
+
+ align:start position:0%
+companies we have maybe three in Europe
+ 
+
+ align:start position:0%
+companies we have maybe three in Europe
+they tend to have more uh that's easy
+
+ align:start position:0%
+they tend to have more uh that's easy
+ 
+
+ align:start position:0%
+they tend to have more uh that's easy
+but wi line that's tough um let me come
+
+ align:start position:0%
+but wi line that's tough um let me come
+ 
+
+ align:start position:0%
+but wi line that's tough um let me come
+back to yeah
+
+ align:start position:0%
+back to yeah
+ 
+
+ align:start position:0%
+back to yeah
+David the shareholders are the the
+
+ align:start position:0%
+David the shareholders are the the
+ 
+
+ align:start position:0%
+David the shareholders are the the
+people who are using the
+
+ align:start position:0%
+people who are using the
+ 
+
+ align:start position:0%
+people who are using the
+services well that would be a
+
+ align:start position:0%
+services well that would be a
+ 
+
+ align:start position:0%
+services well that would be a
+Cooperative model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's exactly The Cooperative model um
+
+ align:start position:0%
+that's exactly The Cooperative model um
+ 
+
+ align:start position:0%
+that's exactly The Cooperative model um
+and it's it's uh you do see it you do
+
+ align:start position:0%
+and it's it's uh you do see it you do
+ 
+
+ align:start position:0%
+and it's it's uh you do see it you do
+see it um let me just mention there are
+
+ align:start position:0%
+see it um let me just mention there are
+ 
+
+ align:start position:0%
+see it um let me just mention there are
+a number of different ways those are the
+
+ align:start position:0%
+a number of different ways those are the
+ 
+
+ align:start position:0%
+a number of different ways those are the
+three main Alternatives there are a
+
+ align:start position:0%
+three main Alternatives there are a
+ 
+
+ align:start position:0%
+three main Alternatives there are a
+number of different ways to skin this
+
+ align:start position:0%
+number of different ways to skin this
+ 
+
+ align:start position:0%
+number of different ways to skin this
+one to to regulate and I'll just say a
+
+ align:start position:0%
+one to to regulate and I'll just say a
+ 
+
+ align:start position:0%
+one to to regulate and I'll just say a
+little bit not go into too much
+
+ align:start position:0%
+little bit not go into too much
+ 
+
+ align:start position:0%
+little bit not go into too much
+detail
+
+ align:start position:0%
+detail
+ 
+
+ align:start position:0%
+detail
+um regulation so I've got government
+
+ align:start position:0%
+um regulation so I've got government
+ 
+
+ align:start position:0%
+um regulation so I've got government
+ownership at the top and cooperatives at
+
+ align:start position:0%
+ownership at the top and cooperatives at
+ 
+
+ align:start position:0%
+ownership at the top and cooperatives at
+the bottom I didn't talk about franchise
+
+ align:start position:0%
+the bottom I didn't talk about franchise
+ 
+
+ align:start position:0%
+the bottom I didn't talk about franchise
+bidding I think that'll take us a little
+
+ align:start position:0%
+bidding I think that'll take us a little
+ 
+
+ align:start position:0%
+bidding I think that'll take us a little
+too far a field but that's the U uh bid
+
+ align:start position:0%
+too far a field but that's the U uh bid
+ 
+
+ align:start position:0%
+too far a field but that's the U uh bid
+for the right to provide
+
+ align:start position:0%
+for the right to provide
+ 
+
+ align:start position:0%
+for the right to provide
+electricity um different kinds of
+
+ align:start position:0%
+electricity um different kinds of
+ 
+
+ align:start position:0%
+electricity um different kinds of
+Regulation you could
+
+ align:start position:0%
+Regulation you could
+ 
+
+ align:start position:0%
+Regulation you could
+do the early street cars and buses and
+
+ align:start position:0%
+do the early street cars and buses and
+ 
+
+ align:start position:0%
+do the early street cars and buses and
+Electric Power Systems and cable systems
+
+ align:start position:0%
+Electric Power Systems and cable systems
+ 
+
+ align:start position:0%
+Electric Power Systems and cable systems
+were regulated by
+
+ align:start position:0%
+were regulated by
+ 
+
+ align:start position:0%
+were regulated by
+cities and the city had jurisdiction
+
+ align:start position:0%
+cities and the city had jurisdiction
+ 
+
+ align:start position:0%
+cities and the city had jurisdiction
+because they needed to use the
+
+ align:start position:0%
+because they needed to use the
+ 
+
+ align:start position:0%
+because they needed to use the
+streets so yes you can put up your your
+
+ align:start position:0%
+streets so yes you can put up your your
+ 
+
+ align:start position:0%
+streets so yes you can put up your your
+uh um uh phone lines yes you can run the
+
+ align:start position:0%
+uh um uh phone lines yes you can run the
+ 
+
+ align:start position:0%
+uh um uh phone lines yes you can run the
+street cars but you need
+
+ align:start position:0%
+street cars but you need
+ 
+
+ align:start position:0%
+street cars but you need
+to uh comply with certain
+
+ align:start position:0%
+to uh comply with certain
+ 
+
+ align:start position:0%
+to uh comply with certain
+restrictions I will talk about rate of
+
+ align:start position:0%
+restrictions I will talk about rate of
+ 
+
+ align:start position:0%
+restrictions I will talk about rate of
+return regulation that's been the
+
+ align:start position:0%
+return regulation that's been the
+ 
+
+ align:start position:0%
+return regulation that's been the
+dominant way electric electricity has
+
+ align:start position:0%
+dominant way electric electricity has
+ 
+
+ align:start position:0%
+dominant way electric electricity has
+been regulated since the early 20th
+
+ align:start position:0%
+been regulated since the early 20th
+ 
+
+ align:start position:0%
+been regulated since the early 20th
+century it's focused on
+
+ align:start position:0%
+century it's focused on
+ 
+
+ align:start position:0%
+century it's focused on
+profits um and incentive regulation is
+
+ align:start position:0%
+profits um and incentive regulation is
+ 
+
+ align:start position:0%
+profits um and incentive regulation is
+to try to be a little to hold prices
+
+ align:start position:0%
+to try to be a little to hold prices
+ 
+
+ align:start position:0%
+to try to be a little to hold prices
+constant for a while to give incentives
+
+ align:start position:0%
+constant for a while to give incentives
+ 
+
+ align:start position:0%
+constant for a while to give incentives
+to cut price to cut cost I I I will
+
+ align:start position:0%
+to cut price to cut cost I I I will
+ 
+
+ align:start position:0%
+to cut price to cut cost I I I will
+cycle back to this I will cycle back but
+
+ align:start position:0%
+cycle back to this I will cycle back but
+ 
+
+ align:start position:0%
+cycle back to this I will cycle back but
+just to know that there are a whole set
+
+ align:start position:0%
+just to know that there are a whole set
+ 
+
+ align:start position:0%
+just to know that there are a whole set
+of approaches that have been used they
+
+ align:start position:0%
+of approaches that have been used they
+ 
+
+ align:start position:0%
+of approaches that have been used they
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+political they involve decisions made by
+
+ align:start position:0%
+political they involve decisions made by
+ 
+
+ align:start position:0%
+political they involve decisions made by
+people they involve decisions made by
+
+ align:start position:0%
+people they involve decisions made by
+ 
+
+ align:start position:0%
+people they involve decisions made by
+people who uh are U subject to voters
+
+ align:start position:0%
+people who uh are U subject to voters
+ 
+
+ align:start position:0%
+people who uh are U subject to voters
+typically one way or another either
+
+ align:start position:0%
+typically one way or another either
+ 
+
+ align:start position:0%
+typically one way or another either
+government Enterprise or they are
+
+ align:start position:0%
+government Enterprise or they are
+ 
+
+ align:start position:0%
+government Enterprise or they are
+regulated uh or the co-op s um uh the
+
+ align:start position:0%
+regulated uh or the co-op s um uh the
+ 
+
+ align:start position:0%
+regulated uh or the co-op s um uh the
+co-op members vote so one of the things
+
+ align:start position:0%
+co-op members vote so one of the things
+ 
+
+ align:start position:0%
+co-op members vote so one of the things
+you want to do is as little of this as
+
+ align:start position:0%
+you want to do is as little of this as
+ 
+
+ align:start position:0%
+you want to do is as little of this as
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+so transmission and distribution natural
+
+ align:start position:0%
+so transmission and distribution natural
+ 
+
+ align:start position:0%
+so transmission and distribution natural
+monopolies poses a policy
+
+ align:start position:0%
+monopolies poses a policy
+ 
+
+ align:start position:0%
+monopolies poses a policy
+problem um in terms of the architecture
+
+ align:start position:0%
+problem um in terms of the architecture
+ 
+
+ align:start position:0%
+problem um in terms of the architecture
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+just I don't know why
+
+ align:start position:0%
+just I don't know why
+ 
+
+ align:start position:0%
+just I don't know why
+I'm this is a Blackboard
+
+ align:start position:0%
+I'm this is a Blackboard
+ 
+
+ align:start position:0%
+I'm this is a Blackboard
+talk but when I say that low voltage
+
+ align:start position:0%
+talk but when I say that low voltage
+ 
+
+ align:start position:0%
+talk but when I say that low voltage
+Distribution Systems are a tree there'll
+
+ align:start position:0%
+Distribution Systems are a tree there'll
+ 
+
+ align:start position:0%
+Distribution Systems are a tree there'll
+be a
+
+ align:start position:0%
+be a
+ 
+
+ align:start position:0%
+be a
+substation and feeders go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out to serve neighborhoods and houses
+
+ align:start position:0%
+out to serve neighborhoods and houses
+ 
+
+ align:start position:0%
+out to serve neighborhoods and houses
+and so forth um the transmission system
+
+ align:start position:0%
+and so forth um the transmission system
+ 
+
+ align:start position:0%
+and so forth um the transmission system
+if you look at I'll show you a map in a
+
+ align:start position:0%
+if you look at I'll show you a map in a
+ 
+
+ align:start position:0%
+if you look at I'll show you a map in a
+little bit but you might have a
+
+ align:start position:0%
+little bit but you might have a
+ 
+
+ align:start position:0%
+little bit but you might have a
+generator here you might have City or
+
+ align:start position:0%
+generator here you might have City or
+ 
+
+ align:start position:0%
+generator here you might have City or
+load here and load there and another
+
+ align:start position:0%
+load here and load there and another
+ 
+
+ align:start position:0%
+load here and load there and another
+generator here here the transmission
+
+ align:start position:0%
+generator here here the transmission
+ 
+
+ align:start position:0%
+generator here here the transmission
+system will be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mesh it's a it's a different
+
+ align:start position:0%
+mesh it's a it's a different
+ 
+
+ align:start position:0%
+mesh it's a it's a different
+architecture it means there are multiple
+
+ align:start position:0%
+architecture it means there are multiple
+ 
+
+ align:start position:0%
+architecture it means there are multiple
+paths in the tree structure you'd have a
+
+ align:start position:0%
+paths in the tree structure you'd have a
+ 
+
+ align:start position:0%
+paths in the tree structure you'd have a
+substation and this would be a house
+
+ align:start position:0%
+substation and this would be a house
+ 
+
+ align:start position:0%
+substation and this would be a house
+there's only one path there are multiple
+
+ align:start position:0%
+there's only one path there are multiple
+ 
+
+ align:start position:0%
+there's only one path there are multiple
+paths well in this case three from this
+
+ align:start position:0%
+paths well in this case three from this
+ 
+
+ align:start position:0%
+paths well in this case three from this
+generator to this load
+
+ align:start position:0%
+generator to this load
+ 
+
+ align:start position:0%
+generator to this load
+um the reason for multiple Paths of
+
+ align:start position:0%
+um the reason for multiple Paths of
+ 
+
+ align:start position:0%
+um the reason for multiple Paths of
+course is
+
+ align:start position:0%
+course is
+ 
+
+ align:start position:0%
+course is
+reliability the reason for a tree
+
+ align:start position:0%
+reliability the reason for a tree
+ 
+
+ align:start position:0%
+reliability the reason for a tree
+structure is
+
+ align:start position:0%
+structure is
+ 
+
+ align:start position:0%
+structure is
+cost um in some dense urban areas the
+
+ align:start position:0%
+cost um in some dense urban areas the
+ 
+
+ align:start position:0%
+cost um in some dense urban areas the
+distribution system is a mesh because
+
+ align:start position:0%
+distribution system is a mesh because
+ 
+
+ align:start position:0%
+distribution system is a mesh because
+the lines are short and you might as
+
+ align:start position:0%
+the lines are short and you might as
+ 
+
+ align:start position:0%
+the lines are short and you might as
+well but if you think any rural or
+
+ align:start position:0%
+well but if you think any rural or
+ 
+
+ align:start position:0%
+well but if you think any rural or
+suburban area it's a
+
+ align:start position:0%
+suburban area it's a
+ 
+
+ align:start position:0%
+suburban area it's a
+tree um the pa the transmission system I
+
+ align:start position:0%
+tree um the pa the transmission system I
+ 
+
+ align:start position:0%
+tree um the pa the transmission system I
+have to say for most of us it takes a
+
+ align:start position:0%
+have to say for most of us it takes a
+ 
+
+ align:start position:0%
+have to say for most of us it takes a
+little getting used to
+
+ align:start position:0%
+little getting used to
+ 
+
+ align:start position:0%
+little getting used to
+you don't switch
+
+ align:start position:0%
+you don't switch
+ 
+
+ align:start position:0%
+you don't switch
+current right the if you do the you do
+
+ align:start position:0%
+current right the if you do the you do
+ 
+
+ align:start position:0%
+current right the if you do the you do
+the analysis power from this generator
+
+ align:start position:0%
+the analysis power from this generator
+ 
+
+ align:start position:0%
+the analysis power from this generator
+to this load goes on all three
+
+ align:start position:0%
+to this load goes on all three
+ 
+
+ align:start position:0%
+to this load goes on all three
+paths depending on the characteristics
+
+ align:start position:0%
+paths depending on the characteristics
+ 
+
+ align:start position:0%
+paths depending on the characteristics
+of the path you can change those
+
+ align:start position:0%
+of the path you can change those
+ 
+
+ align:start position:0%
+of the path you can change those
+characteristics with expensive
+
+ align:start position:0%
+characteristics with expensive
+ 
+
+ align:start position:0%
+characteristics with expensive
+technology but mostly it's
+
+ align:start position:0%
+technology but mostly it's
+ 
+
+ align:start position:0%
+technology but mostly it's
+passive that
+
+ align:start position:0%
+passive that
+ 
+
+ align:start position:0%
+passive that
+means um well it means two things let me
+
+ align:start position:0%
+means um well it means two things let me
+ 
+
+ align:start position:0%
+means um well it means two things let me
+do that means if
+
+ align:start position:0%
+do that means if
+ 
+
+ align:start position:0%
+do that means if
+I demand more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I demand the demand goes up
+
+ align:start position:0%
+here I demand the demand goes up
+ 
+
+ align:start position:0%
+here I demand the demand goes up
+here and I increase generation
+
+ align:start position:0%
+here and I increase generation
+ 
+
+ align:start position:0%
+here and I increase generation
+here I could in fact cause a problem on
+
+ align:start position:0%
+here I could in fact cause a problem on
+ 
+
+ align:start position:0%
+here I could in fact cause a problem on
+this line because some power will flow
+
+ align:start position:0%
+this line because some power will flow
+ 
+
+ align:start position:0%
+this line because some power will flow
+through it and if that line can't handle
+
+ align:start position:0%
+through it and if that line can't handle
+ 
+
+ align:start position:0%
+through it and if that line can't handle
+it I could run into it could overheat it
+
+ align:start position:0%
+it I could run into it could overheat it
+ 
+
+ align:start position:0%
+it I could run into it could overheat it
+could sag this is called Loop flow when
+
+ align:start position:0%
+could sag this is called Loop flow when
+ 
+
+ align:start position:0%
+could sag this is called Loop flow when
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+electricity over multiple paths uh
+
+ align:start position:0%
+electricity over multiple paths uh
+ 
+
+ align:start position:0%
+electricity over multiple paths uh
+causes problems particularly if say
+
+ align:start position:0%
+causes problems particularly if say
+ 
+
+ align:start position:0%
+causes problems particularly if say
+that's a national
+
+ align:start position:0%
+that's a national
+ 
+
+ align:start position:0%
+that's a national
+border okay so I can cause congestion
+
+ align:start position:0%
+border okay so I can cause congestion
+ 
+
+ align:start position:0%
+border okay so I can cause congestion
+over here I can cause a problem over
+
+ align:start position:0%
+over here I can cause a problem over
+ 
+
+ align:start position:0%
+over here I can cause a problem over
+here when I increase demand and
+
+ align:start position:0%
+here when I increase demand and
+ 
+
+ align:start position:0%
+here when I increase demand and
+generation here now you might say well
+
+ align:start position:0%
+generation here now you might say well
+ 
+
+ align:start position:0%
+generation here now you might say well
+can't we fix that the answer is a little
+
+ align:start position:0%
+can't we fix that the answer is a little
+ 
+
+ align:start position:0%
+can't we fix that the answer is a little
+bit we can fix that now with Power
+
+ align:start position:0%
+bit we can fix that now with Power
+ 
+
+ align:start position:0%
+bit we can fix that now with Power
+Electronics we can we can change some of
+
+ align:start position:0%
+Electronics we can we can change some of
+ 
+
+ align:start position:0%
+Electronics we can we can change some of
+the characteristics of these lines but
+
+ align:start position:0%
+the characteristics of these lines but
+ 
+
+ align:start position:0%
+the characteristics of these lines but
+it's expensive and it's not much done
+
+ align:start position:0%
+it's expensive and it's not much done
+ 
+
+ align:start position:0%
+it's expensive and it's not much done
+okay so it's a strange system right it's
+
+ align:start position:0%
+okay so it's a strange system right it's
+ 
+
+ align:start position:0%
+okay so it's a strange system right it's
+not not intuitive not
+
+ align:start position:0%
+not not intuitive not
+ 
+
+ align:start position:0%
+not not intuitive not
+intuitive question about the
+
+ align:start position:0%
+intuitive question about the
+ 
+
+ align:start position:0%
+intuitive question about the
+architecture or about the
+
+ align:start position:0%
+architecture or about the
+ 
+
+ align:start position:0%
+architecture or about the
+problem okay here's the picture
+
+ align:start position:0%
+problem okay here's the picture
+ 
+
+ align:start position:0%
+problem okay here's the picture
+yeah they're about 170,000 miles in the
+
+ align:start position:0%
+yeah they're about 170,000 miles in the
+ 
+
+ align:start position:0%
+yeah they're about 170,000 miles in the
+US of high voltage I think it's 200k is
+
+ align:start position:0%
+US of high voltage I think it's 200k is
+ 
+
+ align:start position:0%
+US of high voltage I think it's 200k is
+the 200,000 volts 230,000 volts is the
+
+ align:start position:0%
+the 200,000 volts 230,000 volts is the
+ 
+
+ align:start position:0%
+the 200,000 volts 230,000 volts is the
+is the threshold for
+
+ align:start position:0%
+is the threshold for
+ 
+
+ align:start position:0%
+is the threshold for
+transmission um you will
+
+ align:start position:0%
+transmission um you will
+ 
+
+ align:start position:0%
+transmission um you will
+note that the country is divided into
+
+ align:start position:0%
+note that the country is divided into
+ 
+
+ align:start position:0%
+note that the country is divided into
+three things that are labeled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interconnect technical
+
+ align:start position:0%
+interconnect technical
+ 
+
+ align:start position:0%
+interconnect technical
+description they are the interconnects
+
+ align:start position:0%
+description they are the interconnects
+ 
+
+ align:start position:0%
+description they are the interconnects
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+connected uh with relatively low
+
+ align:start position:0%
+connected uh with relatively low
+ 
+
+ align:start position:0%
+connected uh with relatively low
+capacity direct current lines in a
+
+ align:start position:0%
+capacity direct current lines in a
+ 
+
+ align:start position:0%
+capacity direct current lines in a
+couple of
+
+ align:start position:0%
+couple of
+ 
+
+ align:start position:0%
+couple of
+places each
+
+ align:start position:0%
+places each
+ 
+
+ align:start position:0%
+places each
+interconnect is basically one big
+
+ align:start position:0%
+interconnect is basically one big
+ 
+
+ align:start position:0%
+interconnect is basically one big
+machine everything's turning together
+
+ align:start position:0%
+machine everything's turning together
+ 
+
+ align:start position:0%
+machine everything's turning together
+everything's synchronized all the
+
+ align:start position:0%
+everything's synchronized all the
+ 
+
+ align:start position:0%
+everything's synchronized all the
+generators all the frequency little
+
+ align:start position:0%
+generators all the frequency little
+ 
+
+ align:start position:0%
+generators all the frequency little
+variations but not
+
+ align:start position:0%
+variations but not
+ 
+
+ align:start position:0%
+variations but not
+much um it's easy to see why there's an
+
+ align:start position:0%
+much um it's easy to see why there's an
+ 
+
+ align:start position:0%
+much um it's easy to see why there's an
+Eastern and a western right because you
+
+ align:start position:0%
+Eastern and a western right because you
+ 
+
+ align:start position:0%
+Eastern and a western right because you
+got the Rocky Mountains relatively low
+
+ align:start position:0%
+got the Rocky Mountains relatively low
+ 
+
+ align:start position:0%
+got the Rocky Mountains relatively low
+population density relatively it didn't
+
+ align:start position:0%
+population density relatively it didn't
+ 
+
+ align:start position:0%
+population density relatively it didn't
+make a lot of sense to try to connect
+
+ align:start position:0%
+make a lot of sense to try to connect
+ 
+
+ align:start position:0%
+make a lot of sense to try to connect
+New York and Los Angeles in the same
+
+ align:start position:0%
+New York and Los Angeles in the same
+ 
+
+ align:start position:0%
+New York and Los Angeles in the same
+synchronized system certainly didn't 50
+
+ align:start position:0%
+synchronized system certainly didn't 50
+ 
+
+ align:start position:0%
+synchronized system certainly didn't 50
+years ago probably doesn't now why is
+
+ align:start position:0%
+years ago probably doesn't now why is
+ 
+
+ align:start position:0%
+years ago probably doesn't now why is
+Texas Independent why is Texas a
+
+ align:start position:0%
+Texas Independent why is Texas a
+ 
+
+ align:start position:0%
+Texas Independent why is Texas a
+separate interconnect why isn't Texas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+synchronized oh take a jump take a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shot was a political deal made in the
+
+ align:start position:0%
+shot was a political deal made in the
+ 
+
+ align:start position:0%
+shot was a political deal made in the
+30s it was a political deal made in the
+
+ align:start position:0%
+30s it was a political deal made in the
+ 
+
+ align:start position:0%
+30s it was a political deal made in the
+30s that has
+
+ align:start position:0%
+30s that has
+ 
+
+ align:start position:0%
+30s that has
+the fiction but near truth that
+
+ align:start position:0%
+the fiction but near truth that
+ 
+
+ align:start position:0%
+the fiction but near truth that
+electrons don't cross state L don't
+
+ align:start position:0%
+electrons don't cross state L don't
+ 
+
+ align:start position:0%
+electrons don't cross state L don't
+cross the boundaries of this
+
+ align:start position:0%
+cross the boundaries of this
+ 
+
+ align:start position:0%
+cross the boundaries of this
+area therefore what goes on in here is
+
+ align:start position:0%
+area therefore what goes on in here is
+ 
+
+ align:start position:0%
+area therefore what goes on in here is
+not subject to Federal Regulation
+
+ align:start position:0%
+not subject to Federal Regulation
+ 
+
+ align:start position:0%
+not subject to Federal Regulation
+because it's wholly within one
+
+ align:start position:0%
+because it's wholly within one
+ 
+
+ align:start position:0%
+because it's wholly within one
+state does that make electrical sense no
+
+ align:start position:0%
+state does that make electrical sense no
+ 
+
+ align:start position:0%
+state does that make electrical sense no
+is it an obvious should it be obvious
+
+ align:start position:0%
+is it an obvious should it be obvious
+ 
+
+ align:start position:0%
+is it an obvious should it be obvious
+that Texas and Louisiana should be
+
+ align:start position:0%
+that Texas and Louisiana should be
+ 
+
+ align:start position:0%
+that Texas and Louisiana should be
+separate electrically
+
+ align:start position:0%
+separate electrically
+ 
+
+ align:start position:0%
+separate electrically
+no but in the 30s it was part of getting
+
+ align:start position:0%
+no but in the 30s it was part of getting
+ 
+
+ align:start position:0%
+no but in the 30s it was part of getting
+a deal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done whenever you see something like
+
+ align:start position:0%
+done whenever you see something like
+ 
+
+ align:start position:0%
+done whenever you see something like
+this do not assume it's a technical
+
+ align:start position:0%
+this do not assume it's a technical
+ 
+
+ align:start position:0%
+this do not assume it's a technical
+reason because it usually isn't there
+
+ align:start position:0%
+reason because it usually isn't there
+ 
+
+ align:start position:0%
+reason because it usually isn't there
+are I I'll give you one other example
+
+ align:start position:0%
+are I I'll give you one other example
+ 
+
+ align:start position:0%
+are I I'll give you one other example
+and then we'll I'll I'll take your your
+
+ align:start position:0%
+and then we'll I'll I'll take your your
+ 
+
+ align:start position:0%
+and then we'll I'll I'll take your your
+question um within the country there are
+
+ align:start position:0%
+question um within the country there are
+ 
+
+ align:start position:0%
+question um within the country there are
+about 107 so-called balancing areas each
+
+ align:start position:0%
+about 107 so-called balancing areas each
+ 
+
+ align:start position:0%
+about 107 so-called balancing areas each
+balancing area is a control center
+
+ align:start position:0%
+balancing area is a control center
+ 
+
+ align:start position:0%
+balancing area is a control center
+that's responsible for electrical flows
+
+ align:start position:0%
+that's responsible for electrical flows
+ 
+
+ align:start position:0%
+that's responsible for electrical flows
+across its boundary right have certain
+
+ align:start position:0%
+across its boundary right have certain
+ 
+
+ align:start position:0%
+across its boundary right have certain
+obligations like not sending a lot out
+
+ align:start position:0%
+obligations like not sending a lot out
+ 
+
+ align:start position:0%
+obligations like not sending a lot out
+or not bringing a lot in so there's one
+
+ align:start position:0%
+or not bringing a lot in so there's one
+ 
+
+ align:start position:0%
+or not bringing a lot in so there's one
+control there's one balancing area in
+
+ align:start position:0%
+control there's one balancing area in
+ 
+
+ align:start position:0%
+control there's one balancing area in
+New England there's one balancing area
+
+ align:start position:0%
+New England there's one balancing area
+ 
+
+ align:start position:0%
+New England there's one balancing area
+in New York there are eight balancing
+
+ align:start position:0%
+in New York there are eight balancing
+ 
+
+ align:start position:0%
+in New York there are eight balancing
+areas in
+
+ align:start position:0%
+areas in
+ 
+
+ align:start position:0%
+areas in
+Arkansas that is not the answer to any
+
+ align:start position:0%
+Arkansas that is not the answer to any
+ 
+
+ align:start position:0%
+Arkansas that is not the answer to any
+technical question okay
+
+ align:start position:0%
+technical question okay
+ 
+
+ align:start position:0%
+technical question okay
+Brendan this
+
+ align:start position:0%
+Brendan this
+ 
+
+ align:start position:0%
+Brendan this
+system a higher lower cost electricity
+
+ align:start position:0%
+system a higher lower cost electricity
+ 
+
+ align:start position:0%
+system a higher lower cost electricity
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+I I would say trying to figure out
+
+ align:start position:0%
+I I would say trying to figure out
+ 
+
+ align:start position:0%
+I I would say trying to figure out
+whether this system has had any effect
+
+ align:start position:0%
+whether this system has had any effect
+ 
+
+ align:start position:0%
+whether this system has had any effect
+on Texas costs uh is probably
+
+ align:start position:0%
+on Texas costs uh is probably
+ 
+
+ align:start position:0%
+on Texas costs uh is probably
+impossible Texas rates are reasonably
+
+ align:start position:0%
+impossible Texas rates are reasonably
+ 
+
+ align:start position:0%
+impossible Texas rates are reasonably
+low Texas Burns a lot of
+
+ align:start position:0%
+low Texas Burns a lot of
+ 
+
+ align:start position:0%
+low Texas Burns a lot of
+coal um uh Texas is big
+
+ align:start position:0%
+coal um uh Texas is big
+ 
+
+ align:start position:0%
+coal um uh Texas is big
+enough that the reliability implications
+
+ align:start position:0%
+enough that the reliability implications
+ 
+
+ align:start position:0%
+enough that the reliability implications
+aren't that great right if you decided
+
+ align:start position:0%
+aren't that great right if you decided
+ 
+
+ align:start position:0%
+aren't that great right if you decided
+to make Belmont Massachusetts separate
+
+ align:start position:0%
+to make Belmont Massachusetts separate
+ 
+
+ align:start position:0%
+to make Belmont Massachusetts separate
+from the rest of the country with say
+
+ align:start position:0%
+from the rest of the country with say
+ 
+
+ align:start position:0%
+from the rest of the country with say
+one generating plant if Belmont has one
+
+ align:start position:0%
+one generating plant if Belmont has one
+ 
+
+ align:start position:0%
+one generating plant if Belmont has one
+you would expect reliability problems
+
+ align:start position:0%
+you would expect reliability problems
+ 
+
+ align:start position:0%
+you would expect reliability problems
+just because if that plant goes down
+
+ align:start position:0%
+just because if that plant goes down
+ 
+
+ align:start position:0%
+just because if that plant goes down
+which it has to occasionally the system
+
+ align:start position:0%
+which it has to occasionally the system
+ 
+
+ align:start position:0%
+which it has to occasionally the system
+goes down Texas is big enough that that
+
+ align:start position:0%
+goes down Texas is big enough that that
+ 
+
+ align:start position:0%
+goes down Texas is big enough that that
+hasn't been an issue Texas has a lot of
+
+ align:start position:0%
+hasn't been an issue Texas has a lot of
+ 
+
+ align:start position:0%
+hasn't been an issue Texas has a lot of
+Renewables which is kind of a surprise
+
+ align:start position:0%
+Renewables which is kind of a surprise
+ 
+
+ align:start position:0%
+Renewables which is kind of a surprise
+but Texas has a lot of wind power that's
+
+ align:start position:0%
+but Texas has a lot of wind power that's
+ 
+
+ align:start position:0%
+but Texas has a lot of wind power that's
+an issue it also is a cost issue but so
+
+ align:start position:0%
+an issue it also is a cost issue but so
+ 
+
+ align:start position:0%
+an issue it also is a cost issue but so
+I don't think this has much to do with
+
+ align:start position:0%
+I don't think this has much to do with
+ 
+
+ align:start position:0%
+I don't think this has much to do with
+with the price of electricity in Texas
+
+ align:start position:0%
+with the price of electricity in Texas
+ 
+
+ align:start position:0%
+with the price of electricity in Texas
+it's just a really interesting odity and
+
+ align:start position:0%
+it's just a really interesting odity and
+ 
+
+ align:start position:0%
+it's just a really interesting odity and
+is I hope uh uh always a cautionary flag
+
+ align:start position:0%
+is I hope uh uh always a cautionary flag
+ 
+
+ align:start position:0%
+is I hope uh uh always a cautionary flag
+when you see something that looks like
+
+ align:start position:0%
+when you see something that looks like
+ 
+
+ align:start position:0%
+when you see something that looks like
+it's weird uh it's either a political
+
+ align:start position:0%
+it's weird uh it's either a political
+ 
+
+ align:start position:0%
+it's weird uh it's either a political
+deal or a consequence of the tax system
+
+ align:start position:0%
+deal or a consequence of the tax system
+ 
+
+ align:start position:0%
+deal or a consequence of the tax system
+uh is my my rule of thumb and this is a
+
+ align:start position:0%
+uh is my my rule of thumb and this is a
+ 
+
+ align:start position:0%
+uh is my my rule of thumb and this is a
+deal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah it's a good question I don't
+
+ align:start position:0%
+yeah yeah it's a good question I don't
+ 
+
+ align:start position:0%
+yeah yeah it's a good question I don't
+know I don't know you wonder why I say I
+
+ align:start position:0%
+know I don't know you wonder why I say I
+ 
+
+ align:start position:0%
+know I don't know you wonder why I say I
+think that's that's amarilla up there
+
+ align:start position:0%
+think that's that's amarilla up there
+ 
+
+ align:start position:0%
+think that's that's amarilla up there
+that top Dot and I do not know why
+
+ align:start position:0%
+that top Dot and I do not know why
+ 
+
+ align:start position:0%
+that top Dot and I do not know why
+whoever made the
+
+ align:start position:0%
+whoever made the
+ 
+
+ align:start position:0%
+whoever made the
+deal wrote off North Texas i
+
+ align:start position:0%
+deal wrote off North Texas i
+ 
+
+ align:start position:0%
+deal wrote off North Texas i
+h same boundary yeah boundary haven't
+
+ align:start position:0%
+h same boundary yeah boundary haven't
+ 
+
+ align:start position:0%
+h same boundary yeah boundary haven't
+changed no no
+
+ align:start position:0%
+changed no no
+ 
+
+ align:start position:0%
+changed no no
+it you you don't want to say that too
+
+ align:start position:0%
+it you you don't want to say that too
+ 
+
+ align:start position:0%
+it you you don't want to say that too
+close to Texas I mean Texas is when I
+
+ align:start position:0%
+close to Texas I mean Texas is when I
+ 
+
+ align:start position:0%
+close to Texas I mean Texas is when I
+asked this question the first year I
+
+ align:start position:0%
+asked this question the first year I
+ 
+
+ align:start position:0%
+asked this question the first year I
+taught this I taught the course the
+
+ align:start position:0%
+taught this I taught the course the
+ 
+
+ align:start position:0%
+taught this I taught the course the
+answer from a Texan was so we can
+
+ align:start position:0%
+answer from a Texan was so we can
+ 
+
+ align:start position:0%
+answer from a Texan was so we can
+secede
+
+ align:start position:0%
+secede
+ 
+
+ align:start position:0%
+secede
+uh I don't know I don't know why they
+
+ align:start position:0%
+uh I don't know I don't know why they
+ 
+
+ align:start position:0%
+uh I don't know I don't know why they
+wouldn't take amarilla with them and and
+
+ align:start position:0%
+wouldn't take amarilla with them and and
+ 
+
+ align:start position:0%
+wouldn't take amarilla with them and and
+who whoever that second dot is I don't
+
+ align:start position:0%
+who whoever that second dot is I don't
+ 
+
+ align:start position:0%
+who whoever that second dot is I don't
+know who that is either um uh I don't
+
+ align:start position:0%
+know who that is either um uh I don't
+ 
+
+ align:start position:0%
+know who that is either um uh I don't
+have an answer it my guess is that that
+
+ align:start position:0%
+have an answer it my guess is that that
+ 
+
+ align:start position:0%
+have an answer it my guess is that that
+actually was an electrical response that
+
+ align:start position:0%
+actually was an electrical response that
+ 
+
+ align:start position:0%
+actually was an electrical response that
+that part of Texas may have had closer
+
+ align:start position:0%
+that part of Texas may have had closer
+ 
+
+ align:start position:0%
+that part of Texas may have had closer
+electrical connections outside the state
+
+ align:start position:0%
+electrical connections outside the state
+ 
+
+ align:start position:0%
+electrical connections outside the state
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+inside um and somebody said look that
+
+ align:start position:0%
+inside um and somebody said look that
+ 
+
+ align:start position:0%
+inside um and somebody said look that
+would be really stupid to kind of
+
+ align:start position:0%
+would be really stupid to kind of
+ 
+
+ align:start position:0%
+would be really stupid to kind of
+reconfigure the transmission
+
+ align:start position:0%
+reconfigure the transmission
+ 
+
+ align:start position:0%
+reconfigure the transmission
+system I'm guessing I don't know
+
+ align:start position:0%
+system I'm guessing I don't know
+ 
+
+ align:start position:0%
+system I'm guessing I don't know
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um all right let
+
+ align:start position:0%
+um all right let
+ 
+
+ align:start position:0%
+um all right let
+me spend most of the rest of the time on
+
+ align:start position:0%
+me spend most of the rest of the time on
+ 
+
+ align:start position:0%
+me spend most of the rest of the time on
+sort of how we got here and walk through
+
+ align:start position:0%
+sort of how we got here and walk through
+ 
+
+ align:start position:0%
+sort of how we got here and walk through
+the regulatory history
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um First Central Generating Station
+
+ align:start position:0%
+um First Central Generating Station
+ 
+
+ align:start position:0%
+um First Central Generating Station
+Thomas Edison New York uh 59 customers
+
+ align:start position:0%
+Thomas Edison New York uh 59 customers
+ 
+
+ align:start position:0%
+Thomas Edison New York uh 59 customers
+lighting and by the way you think you
+
+ align:start position:0%
+lighting and by the way you think you
+ 
+
+ align:start position:0%
+lighting and by the way you think you
+had a load variation you have a load
+
+ align:start position:0%
+had a load variation you have a load
+ 
+
+ align:start position:0%
+had a load variation you have a load
+variation problem now with those New
+
+ align:start position:0%
+variation problem now with those New
+ 
+
+ align:start position:0%
+variation problem now with those New
+England things think about when your
+
+ align:start position:0%
+England things think about when your
+ 
+
+ align:start position:0%
+England things think about when your
+only product is
+
+ align:start position:0%
+only product is
+ 
+
+ align:start position:0%
+only product is
+lighting you shut the whole system down
+
+ align:start position:0%
+lighting you shut the whole system down
+ 
+
+ align:start position:0%
+lighting you shut the whole system down
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+daytime this is not a good way to use
+
+ align:start position:0%
+daytime this is not a good way to use
+ 
+
+ align:start position:0%
+daytime this is not a good way to use
+your assets so one of the first things
+
+ align:start position:0%
+your assets so one of the first things
+ 
+
+ align:start position:0%
+your assets so one of the first things
+things they did was push for electric
+
+ align:start position:0%
+things they did was push for electric
+ 
+
+ align:start position:0%
+things they did was push for electric
+street cars um these early systems
+
+ align:start position:0%
+street cars um these early systems
+ 
+
+ align:start position:0%
+street cars um these early systems
+direct current systems were regulated
+
+ align:start position:0%
+direct current systems were regulated
+ 
+
+ align:start position:0%
+direct current systems were regulated
+mostly by
+
+ align:start position:0%
+mostly by
+ 
+
+ align:start position:0%
+mostly by
+cities they were local they were direct
+
+ align:start position:0%
+cities they were local they were direct
+ 
+
+ align:start position:0%
+cities they were local they were direct
+current direct current at low voltage
+
+ align:start position:0%
+current direct current at low voltage
+ 
+
+ align:start position:0%
+current direct current at low voltage
+doesn't travel very far efficiently so
+
+ align:start position:0%
+doesn't travel very far efficiently so
+ 
+
+ align:start position:0%
+doesn't travel very far efficiently so
+they were and you don't want to put high
+
+ align:start position:0%
+they were and you don't want to put high
+ 
+
+ align:start position:0%
+they were and you don't want to put high
+voltage into people's homes
+
+ align:start position:0%
+voltage into people's homes
+ 
+
+ align:start position:0%
+voltage into people's homes
+um so we had a bunch of cities City
+
+ align:start position:0%
+um so we had a bunch of cities City
+ 
+
+ align:start position:0%
+um so we had a bunch of cities City
+regulated systems and then we had a
+
+ align:start position:0%
+regulated systems and then we had a
+ 
+
+ align:start position:0%
+regulated systems and then we had a
+bunch of City run
+
+ align:start position:0%
+bunch of City run
+ 
+
+ align:start position:0%
+bunch of City run
+systems uh so in 1900 as far as I can
+
+ align:start position:0%
+systems uh so in 1900 as far as I can
+ 
+
+ align:start position:0%
+systems uh so in 1900 as far as I can
+tell the peak of Municipal systems
+
+ align:start position:0%
+tell the peak of Municipal systems
+ 
+
+ align:start position:0%
+tell the peak of Municipal systems
+Belmont has one Los Angeles has one they
+
+ align:start position:0%
+Belmont has one Los Angeles has one they
+ 
+
+ align:start position:0%
+Belmont has one Los Angeles has one they
+peaked at 8% of generation in
+
+ align:start position:0%
+peaked at 8% of generation in
+ 
+
+ align:start position:0%
+peaked at 8% of generation in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um as alternating current came in and
+
+ align:start position:0%
+um as alternating current came in and
+ 
+
+ align:start position:0%
+um as alternating current came in and
+the big thing with alternating current
+
+ align:start position:0%
+the big thing with alternating current
+ 
+
+ align:start position:0%
+the big thing with alternating current
+is you can change its
+
+ align:start position:0%
+is you can change its
+ 
+
+ align:start position:0%
+is you can change its
+voltage relatively easily so you can
+
+ align:start position:0%
+voltage relatively easily so you can
+ 
+
+ align:start position:0%
+voltage relatively easily so you can
+have high voltage to send it long
+
+ align:start position:0%
+have high voltage to send it long
+ 
+
+ align:start position:0%
+have high voltage to send it long
+distances and then you can take it down
+
+ align:start position:0%
+distances and then you can take it down
+ 
+
+ align:start position:0%
+distances and then you can take it down
+for use in home so the Transformer
+
+ align:start position:0%
+for use in home so the Transformer
+ 
+
+ align:start position:0%
+for use in home so the Transformer
+really uh makes alternating current the
+
+ align:start position:0%
+really uh makes alternating current the
+ 
+
+ align:start position:0%
+really uh makes alternating current the
+winner now you can take DC up and down
+
+ align:start position:0%
+winner now you can take DC up and down
+ 
+
+ align:start position:0%
+winner now you can take DC up and down
+but it's more expensive and you couldn't
+
+ align:start position:0%
+but it's more expensive and you couldn't
+ 
+
+ align:start position:0%
+but it's more expensive and you couldn't
+do it for a long time uh so alternating
+
+ align:start position:0%
+do it for a long time uh so alternating
+ 
+
+ align:start position:0%
+do it for a long time uh so alternating
+current winds and as you
+
+ align:start position:0%
+current winds and as you
+ 
+
+ align:start position:0%
+current winds and as you
+begin to make it technically possible to
+
+ align:start position:0%
+begin to make it technically possible to
+ 
+
+ align:start position:0%
+begin to make it technically possible to
+go beyond a city right if you're doing
+
+ align:start position:0%
+go beyond a city right if you're doing
+ 
+
+ align:start position:0%
+go beyond a city right if you're doing
+direct current you're building a
+
+ align:start position:0%
+direct current you're building a
+ 
+
+ align:start position:0%
+direct current you're building a
+Generating Station you're serving a
+
+ align:start position:0%
+Generating Station you're serving a
+ 
+
+ align:start position:0%
+Generating Station you're serving a
+neighborhood we talked about the London
+
+ align:start position:0%
+neighborhood we talked about the London
+ 
+
+ align:start position:0%
+neighborhood we talked about the London
+system and how it's stayed that way for
+
+ align:start position:0%
+system and how it's stayed that way for
+ 
+
+ align:start position:0%
+system and how it's stayed that way for
+a long time time that's how they grow up
+
+ align:start position:0%
+a long time time that's how they grow up
+ 
+
+ align:start position:0%
+a long time time that's how they grow up
+right you build a generator to serve a
+
+ align:start position:0%
+right you build a generator to serve a
+ 
+
+ align:start position:0%
+right you build a generator to serve a
+neighborhood then maybe you go to
+
+ align:start position:0%
+neighborhood then maybe you go to
+ 
+
+ align:start position:0%
+neighborhood then maybe you go to
+alternating current but technically once
+
+ align:start position:0%
+alternating current but technically once
+ 
+
+ align:start position:0%
+alternating current but technically once
+you can do higher voltages you can
+
+ align:start position:0%
+you can do higher voltages you can
+ 
+
+ align:start position:0%
+you can do higher voltages you can
+expand you can link up separate cities
+
+ align:start position:0%
+expand you can link up separate cities
+ 
+
+ align:start position:0%
+expand you can link up separate cities
+and that began to happen after the turn
+
+ align:start position:0%
+and that began to happen after the turn
+ 
+
+ align:start position:0%
+and that began to happen after the turn
+of the century and States took over
+
+ align:start position:0%
+of the century and States took over
+ 
+
+ align:start position:0%
+of the century and States took over
+regulation from
+
+ align:start position:0%
+regulation from
+ 
+
+ align:start position:0%
+regulation from
+cities the idea was we'd set up these
+
+ align:start position:0%
+cities the idea was we'd set up these
+ 
+
+ align:start position:0%
+cities the idea was we'd set up these
+impartial
+
+ align:start position:0%
+impartial
+ 
+
+ align:start position:0%
+impartial
+commissions and these impartial non iCal
+
+ align:start position:0%
+commissions and these impartial non iCal
+ 
+
+ align:start position:0%
+commissions and these impartial non iCal
+public utility commissions not elected
+
+ align:start position:0%
+public utility commissions not elected
+ 
+
+ align:start position:0%
+public utility commissions not elected
+in Most states not subject to removal by
+
+ align:start position:0%
+in Most states not subject to removal by
+ 
+
+ align:start position:0%
+in Most states not subject to removal by
+the government independent commissions
+
+ align:start position:0%
+the government independent commissions
+ 
+
+ align:start position:0%
+the government independent commissions
+were it was an in an invention that
+
+ align:start position:0%
+were it was an in an invention that
+ 
+
+ align:start position:0%
+were it was an in an invention that
+started I'm now forgetting I think
+
+ align:start position:0%
+started I'm now forgetting I think
+ 
+
+ align:start position:0%
+started I'm now forgetting I think
+Wisconsin in 1907 and by 1920 everybody
+
+ align:start position:0%
+Wisconsin in 1907 and by 1920 everybody
+ 
+
+ align:start position:0%
+Wisconsin in 1907 and by 1920 everybody
+almost everybody had them does anybody
+
+ align:start position:0%
+almost everybody had them does anybody
+ 
+
+ align:start position:0%
+almost everybody had them does anybody
+here from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nebraska okay Nebraska doesn't have a
+
+ align:start position:0%
+Nebraska okay Nebraska doesn't have a
+ 
+
+ align:start position:0%
+Nebraska okay Nebraska doesn't have a
+Public Utility Commission because no
+
+ align:start position:0%
+Public Utility Commission because no
+ 
+
+ align:start position:0%
+Public Utility Commission because no
+private firm is selling electricity in
+
+ align:start position:0%
+private firm is selling electricity in
+ 
+
+ align:start position:0%
+private firm is selling electricity in
+Nebraska it's all government and co-ops
+
+ align:start position:0%
+Nebraska it's all government and co-ops
+ 
+
+ align:start position:0%
+Nebraska it's all government and co-ops
+but everybody else has
+
+ align:start position:0%
+but everybody else has
+ 
+
+ align:start position:0%
+but everybody else has
+one the Europeans didn't do
+
+ align:start position:0%
+one the Europeans didn't do
+ 
+
+ align:start position:0%
+one the Europeans didn't do
+this what happened the European systems
+
+ align:start position:0%
+this what happened the European systems
+ 
+
+ align:start position:0%
+this what happened the European systems
+started out like this started out local
+
+ align:start position:0%
+started out like this started out local
+ 
+
+ align:start position:0%
+started out like this started out local
+began to
+
+ align:start position:0%
+began to
+ 
+
+ align:start position:0%
+began to
+grow and became government
+
+ align:start position:0%
+grow and became government
+ 
+
+ align:start position:0%
+grow and became government
+Enterprises
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why okay you figure that's the answer to
+
+ align:start position:0%
+why okay you figure that's the answer to
+ 
+
+ align:start position:0%
+why okay you figure that's the answer to
+an engineering
+
+ align:start position:0%
+an engineering
+ 
+
+ align:start position:0%
+an engineering
+question that is not the answer to an
+
+ align:start position:0%
+question that is not the answer to an
+ 
+
+ align:start position:0%
+question that is not the answer to an
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+question same electrons same
+
+ align:start position:0%
+question same electrons same
+ 
+
+ align:start position:0%
+question same electrons same
+technology similar densities in many
+
+ align:start position:0%
+technology similar densities in many
+ 
+
+ align:start position:0%
+technology similar densities in many
+areas Jacob save me here oh although
+
+ align:start position:0%
+areas Jacob save me here oh although
+ 
+
+ align:start position:0%
+areas Jacob save me here oh although
+they may have like provinces they're not
+
+ align:start position:0%
+they may have like provinces they're not
+ 
+
+ align:start position:0%
+they may have like provinces they're not
+as independent government institutions
+
+ align:start position:0%
+as independent government institutions
+ 
+
+ align:start position:0%
+as independent government institutions
+as they are in the United States well
+
+ align:start position:0%
+as they are in the United States well
+ 
+
+ align:start position:0%
+as they are in the United States well
+that's that's true to some extent
+
+ align:start position:0%
+that's that's true to some extent
+ 
+
+ align:start position:0%
+that's that's true to some extent
+although take Germany Germany is is and
+
+ align:start position:0%
+although take Germany Germany is is and
+ 
+
+ align:start position:0%
+although take Germany Germany is is and
+has been to the extent that it was uh
+
+ align:start position:0%
+has been to the extent that it was uh
+ 
+
+ align:start position:0%
+has been to the extent that it was uh
+well it wasn't Democratic for a long
+
+ align:start position:0%
+well it wasn't Democratic for a long
+ 
+
+ align:start position:0%
+well it wasn't Democratic for a long
+time but it has it began as a set of
+
+ align:start position:0%
+time but it has it began as a set of
+ 
+
+ align:start position:0%
+time but it has it began as a set of
+independent countries that became the L
+
+ align:start position:0%
+independent countries that became the L
+ 
+
+ align:start position:0%
+independent countries that became the L
+became a federal system so when it
+
+ align:start position:0%
+became a federal system so when it
+ 
+
+ align:start position:0%
+became a federal system so when it
+became when when the government took
+
+ align:start position:0%
+became when when the government took
+ 
+
+ align:start position:0%
+became when when the government took
+over the Berlin system it was the Berlin
+
+ align:start position:0%
+over the Berlin system it was the Berlin
+ 
+
+ align:start position:0%
+over the Berlin system it was the Berlin
+government it wasn't the national
+
+ align:start position:0%
+government it wasn't the national
+ 
+
+ align:start position:0%
+government it wasn't the national
+government so not all of these
+
+ align:start position:0%
+government so not all of these
+ 
+
+ align:start position:0%
+government so not all of these
+government Enterprises were National
+
+ align:start position:0%
+government Enterprises were National
+ 
+
+ align:start position:0%
+government Enterprises were National
+it's a good point the political
+
+ align:start position:0%
+it's a good point the political
+ 
+
+ align:start position:0%
+it's a good point the political
+structures differed and in the US was in
+
+ align:start position:0%
+structures differed and in the US was in
+ 
+
+ align:start position:0%
+structures differed and in the US was in
+in if not unique then it's stood out as
+
+ align:start position:0%
+in if not unique then it's stood out as
+ 
+
+ align:start position:0%
+in if not unique then it's stood out as
+having this whole state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure uh it's just an ID an
+
+ align:start position:0%
+structure uh it's just an ID an
+ 
+
+ align:start position:0%
+structure uh it's just an ID an
+ideological difference an ideological
+
+ align:start position:0%
+ideological difference an ideological
+ 
+
+ align:start position:0%
+ideological difference an ideological
+difference the US had a strong
+
+ align:start position:0%
+difference the US had a strong
+ 
+
+ align:start position:0%
+difference the US had a strong
+preference for private Enterprise Europe
+
+ align:start position:0%
+preference for private Enterprise Europe
+ 
+
+ align:start position:0%
+preference for private Enterprise Europe
+had a less strong
+
+ align:start position:0%
+had a less strong
+ 
+
+ align:start position:0%
+had a less strong
+preference
+
+ align:start position:0%
+preference
+ 
+
+ align:start position:0%
+preference
+um you know we uh uh it was a big debate
+
+ align:start position:0%
+um you know we uh uh it was a big debate
+ 
+
+ align:start position:0%
+um you know we uh uh it was a big debate
+in the US through the 30s should this
+
+ align:start position:0%
+in the US through the 30s should this
+ 
+
+ align:start position:0%
+in the US through the 30s should this
+stuff be government or should it be
+
+ align:start position:0%
+stuff be government or should it be
+ 
+
+ align:start position:0%
+stuff be government or should it be
+private private mostly one in the US
+
+ align:start position:0%
+private private mostly one in the US
+ 
+
+ align:start position:0%
+private private mostly one in the US
+government mostly W in Europe uh there's
+
+ align:start position:0%
+government mostly W in Europe uh there's
+ 
+
+ align:start position:0%
+government mostly W in Europe uh there's
+no you could make arguments both
+
+ align:start position:0%
+no you could make arguments both
+ 
+
+ align:start position:0%
+no you could make arguments both
+ways I talked about various solutions to
+
+ align:start position:0%
+ways I talked about various solutions to
+ 
+
+ align:start position:0%
+ways I talked about various solutions to
+Natural monopolies the government
+
+ align:start position:0%
+Natural monopolies the government
+ 
+
+ align:start position:0%
+Natural monopolies the government
+solution is look there are no
+
+ align:start position:0%
+solution is look there are no
+ 
+
+ align:start position:0%
+solution is look there are no
+shareholders trying to rape and pillage
+
+ align:start position:0%
+shareholders trying to rape and pillage
+ 
+
+ align:start position:0%
+shareholders trying to rape and pillage
+here we're just all trying to serve the
+
+ align:start position:0%
+here we're just all trying to serve the
+ 
+
+ align:start position:0%
+here we're just all trying to serve the
+customers the private response is yes
+
+ align:start position:0%
+customers the private response is yes
+ 
+
+ align:start position:0%
+customers the private response is yes
+and you're all hiring your
+
+ align:start position:0%
+and you're all hiring your
+ 
+
+ align:start position:0%
+and you're all hiring your
+brothers-in-law the costs are high you
+
+ align:start position:0%
+brothers-in-law the costs are high you
+ 
+
+ align:start position:0%
+brothers-in-law the costs are high you
+have no pre you have no stockholder
+
+ align:start position:0%
+have no pre you have no stockholder
+ 
+
+ align:start position:0%
+have no pre you have no stockholder
+pressure to be efficient costs will be
+
+ align:start position:0%
+pressure to be efficient costs will be
+ 
+
+ align:start position:0%
+pressure to be efficient costs will be
+too high that debate ran for 30 40 years
+
+ align:start position:0%
+too high that debate ran for 30 40 years
+ 
+
+ align:start position:0%
+too high that debate ran for 30 40 years
+still goes on in some quarters one side
+
+ align:start position:0%
+still goes on in some quarters one side
+ 
+
+ align:start position:0%
+still goes on in some quarters one side
+one in Europe one side one in the US
+
+ align:start position:0%
+one in Europe one side one in the US
+ 
+
+ align:start position:0%
+one in Europe one side one in the US
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so far the states now the
+
+ align:start position:0%
+okay so far the states now the
+ 
+
+ align:start position:0%
+okay so far the states now the
+feds the federal role federal government
+
+ align:start position:0%
+feds the federal role federal government
+ 
+
+ align:start position:0%
+feds the federal role federal government
+got into electricity first in 1906
+
+ align:start position:0%
+got into electricity first in 1906
+ 
+
+ align:start position:0%
+got into electricity first in 1906
+selling cheap Surplus power from
+
+ align:start position:0%
+selling cheap Surplus power from
+ 
+
+ align:start position:0%
+selling cheap Surplus power from
+irrigation projects it gave preference
+
+ align:start position:0%
+irrigation projects it gave preference
+ 
+
+ align:start position:0%
+irrigation projects it gave preference
+to municipalities rather than private
+
+ align:start position:0%
+to municipalities rather than private
+ 
+
+ align:start position:0%
+to municipalities rather than private
+buyers why was it cheap do you think why
+
+ align:start position:0%
+buyers why was it cheap do you think why
+ 
+
+ align:start position:0%
+buyers why was it cheap do you think why
+was the power cheap from irrigation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projects okay today is quirky political
+
+ align:start position:0%
+projects okay today is quirky political
+ 
+
+ align:start position:0%
+projects okay today is quirky political
+explanations
+
+ align:start position:0%
+explanations
+ 
+
+ align:start position:0%
+explanations
+day in calculating the cost of building
+
+ align:start position:0%
+day in calculating the cost of building
+ 
+
+ align:start position:0%
+day in calculating the cost of building
+something the government tends to use
+
+ align:start position:0%
+something the government tends to use
+ 
+
+ align:start position:0%
+something the government tends to use
+its borrowing
+
+ align:start position:0%
+its borrowing
+ 
+
+ align:start position:0%
+its borrowing
+rate the cost of capital to the
+
+ align:start position:0%
+rate the cost of capital to the
+ 
+
+ align:start position:0%
+rate the cost of capital to the
+government which has the power to tax is
+
+ align:start position:0%
+government which has the power to tax is
+ 
+
+ align:start position:0%
+government which has the power to tax is
+lower than the cost of capital to
+
+ align:start position:0%
+lower than the cost of capital to
+ 
+
+ align:start position:0%
+lower than the cost of capital to
+private firms that
+
+ align:start position:0%
+private firms that
+ 
+
+ align:start position:0%
+private firms that
+don't so all else equal the government
+
+ align:start position:0%
+don't so all else equal the government
+ 
+
+ align:start position:0%
+don't so all else equal the government
+can produce power cheaper and if the
+
+ align:start position:0%
+can produce power cheaper and if the
+ 
+
+ align:start position:0%
+can produce power cheaper and if the
+main cost is capital which it is for a
+
+ align:start position:0%
+main cost is capital which it is for a
+ 
+
+ align:start position:0%
+main cost is capital which it is for a
+high Hydro facility it can be a lot
+
+ align:start position:0%
+high Hydro facility it can be a lot
+ 
+
+ align:start position:0%
+high Hydro facility it can be a lot
+cheaper so the government says we're not
+
+ align:start position:0%
+cheaper so the government says we're not
+ 
+
+ align:start position:0%
+cheaper so the government says we're not
+making any money we will sell it cheaply
+
+ align:start position:0%
+making any money we will sell it cheaply
+ 
+
+ align:start position:0%
+making any money we will sell it cheaply
+but then you got to figure out who gets
+
+ align:start position:0%
+but then you got to figure out who gets
+ 
+
+ align:start position:0%
+but then you got to figure out who gets
+it and the decision was Municipal
+
+ align:start position:0%
+it and the decision was Municipal
+ 
+
+ align:start position:0%
+it and the decision was Municipal
+Utilities
+
+ align:start position:0%
+Utilities
+ 
+
+ align:start position:0%
+Utilities
+um during the run up to the 20s and
+
+ align:start position:0%
+um during the run up to the 20s and
+ 
+
+ align:start position:0%
+um during the run up to the 20s and
+that's an amazing period if you think
+
+ align:start position:0%
+that's an amazing period if you think
+ 
+
+ align:start position:0%
+that's an amazing period if you think
+about growth industries I just ran the
+
+ align:start position:0%
+about growth industries I just ran the
+ 
+
+ align:start position:0%
+about growth industries I just ran the
+numbers the growth in electric power
+
+ align:start position:0%
+numbers the growth in electric power
+ 
+
+ align:start position:0%
+numbers the growth in electric power
+between 19 1900 1929 averaged 14% a year
+
+ align:start position:0%
+between 19 1900 1929 averaged 14% a year
+ 
+
+ align:start position:0%
+between 19 1900 1929 averaged 14% a year
+that's a boom that's a long boom that
+
+ align:start position:0%
+that's a boom that's a long boom that
+ 
+
+ align:start position:0%
+that's a boom that's a long boom that
+was fun uh it was fun except that these
+
+ align:start position:0%
+was fun uh it was fun except that these
+ 
+
+ align:start position:0%
+was fun uh it was fun except that these
+guys were being regulated so their
+
+ align:start position:0%
+guys were being regulated so their
+ 
+
+ align:start position:0%
+guys were being regulated so their
+response was we're being regulated by
+
+ align:start position:0%
+response was we're being regulated by
+ 
+
+ align:start position:0%
+response was we're being regulated by
+States let's have holding companies that
+
+ align:start position:0%
+States let's have holding companies that
+ 
+
+ align:start position:0%
+States let's have holding companies that
+operate in multiple States so we can
+
+ align:start position:0%
+operate in multiple States so we can
+ 
+
+ align:start position:0%
+operate in multiple States so we can
+kind of hide the ball from
+
+ align:start position:0%
+kind of hide the ball from
+ 
+
+ align:start position:0%
+kind of hide the ball from
+regulators and it was used to uh to Fuel
+
+ align:start position:0%
+regulators and it was used to uh to Fuel
+ 
+
+ align:start position:0%
+regulators and it was used to uh to Fuel
+stock speculation so that was they had a
+
+ align:start position:0%
+stock speculation so that was they had a
+ 
+
+ align:start position:0%
+stock speculation so that was they had a
+lot of fun they built these big holding
+
+ align:start position:0%
+lot of fun they built these big holding
+ 
+
+ align:start position:0%
+lot of fun they built these big holding
+companies um I'll come back to that the
+
+ align:start position:0%
+companies um I'll come back to that the
+ 
+
+ align:start position:0%
+companies um I'll come back to that the
+the Federal power Commission Now the
+
+ align:start position:0%
+the Federal power Commission Now the
+ 
+
+ align:start position:0%
+the Federal power Commission Now the
+firk was formed in 1920 because all
+
+ align:start position:0%
+firk was formed in 1920 because all
+ 
+
+ align:start position:0%
+firk was formed in 1920 because all
+navigable waterways are federal it began
+
+ align:start position:0%
+navigable waterways are federal it began
+ 
+
+ align:start position:0%
+navigable waterways are federal it began
+to do some regulation from
+
+ align:start position:0%
+to do some regulation from
+ 
+
+ align:start position:0%
+to do some regulation from
+1935 in 1935 in response to these
+
+ align:start position:0%
+1935 in 1935 in response to these
+ 
+
+ align:start position:0%
+1935 in 1935 in response to these
+holding companies which really were
+
+ align:start position:0%
+holding companies which really were
+ 
+
+ align:start position:0%
+holding companies which really were
+weird creatures federal law was and they
+
+ align:start position:0%
+weird creatures federal law was and they
+ 
+
+ align:start position:0%
+weird creatures federal law was and they
+were blamed for the stock market crash
+
+ align:start position:0%
+were blamed for the stock market crash
+ 
+
+ align:start position:0%
+were blamed for the stock market crash
+of 1929 you always need to find a
+
+ align:start position:0%
+of 1929 you always need to find a
+ 
+
+ align:start position:0%
+of 1929 you always need to find a
+scapegoat so the scapegoat was these
+
+ align:start position:0%
+scapegoat so the scapegoat was these
+ 
+
+ align:start position:0%
+scapegoat so the scapegoat was these
+utility comp they were broken they were
+
+ align:start position:0%
+utility comp they were broken they were
+ 
+
+ align:start position:0%
+utility comp they were broken they were
+broken up you had to operate in one
+
+ align:start position:0%
+broken up you had to operate in one
+ 
+
+ align:start position:0%
+broken up you had to operate in one
+contiguous area you you couldn't have a
+
+ align:start position:0%
+contiguous area you you couldn't have a
+ 
+
+ align:start position:0%
+contiguous area you you couldn't have a
+company here and a company there under
+
+ align:start position:0%
+company here and a company there under
+ 
+
+ align:start position:0%
+company here and a company there under
+the same umbrella well that really
+
+ align:start position:0%
+the same umbrella well that really
+ 
+
+ align:start position:0%
+the same umbrella well that really
+enforced what was the the vertically
+
+ align:start position:0%
+enforced what was the the vertically
+ 
+
+ align:start position:0%
+enforced what was the the vertically
+integrated Monopoly structure the same
+
+ align:start position:0%
+integrated Monopoly structure the same
+ 
+
+ align:start position:0%
+integrated Monopoly structure the same
+company would generate the power
+
+ align:start position:0%
+company would generate the power
+ 
+
+ align:start position:0%
+company would generate the power
+transmit the power and sell you the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power in the 30s we
+
+ align:start position:0%
+power in the 30s we
+ 
+
+ align:start position:0%
+power in the 30s we
+also one of Roosevelt's
+
+ align:start position:0%
+also one of Roosevelt's
+ 
+
+ align:start position:0%
+also one of Roosevelt's
+initiatives was to get power to rural
+
+ align:start position:0%
+initiatives was to get power to rural
+ 
+
+ align:start position:0%
+initiatives was to get power to rural
+areas one of his priorities the existing
+
+ align:start position:0%
+areas one of his priorities the existing
+ 
+
+ align:start position:0%
+areas one of his priorities the existing
+utilities weren't interested in doing it
+
+ align:start position:0%
+utilities weren't interested in doing it
+ 
+
+ align:start position:0%
+utilities weren't interested in doing it
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+expensive and the their current
+
+ align:start position:0%
+expensive and the their current
+ 
+
+ align:start position:0%
+expensive and the their current
+customers didn't want to pay higher
+
+ align:start position:0%
+customers didn't want to pay higher
+ 
+
+ align:start position:0%
+customers didn't want to pay higher
+prices so the farmer in the next County
+
+ align:start position:0%
+prices so the farmer in the next County
+ 
+
+ align:start position:0%
+prices so the farmer in the next County
+can get
+
+ align:start position:0%
+can get
+ 
+
+ align:start position:0%
+can get
+power what the federal remedy was will
+
+ align:start position:0%
+power what the federal remedy was will
+ 
+
+ align:start position:0%
+power what the federal remedy was will
+will enable a set of
+
+ align:start position:0%
+will enable a set of
+ 
+
+ align:start position:0%
+will enable a set of
+co-ops and we'll sell them cheap power
+
+ align:start position:0%
+co-ops and we'll sell them cheap power
+ 
+
+ align:start position:0%
+co-ops and we'll sell them cheap power
+from federal
+
+ align:start position:0%
+from federal
+ 
+
+ align:start position:0%
+from federal
+facilities that's what was done TVA is
+
+ align:start position:0%
+facilities that's what was done TVA is
+ 
+
+ align:start position:0%
+facilities that's what was done TVA is
+the most visible sort of will generate
+
+ align:start position:0%
+the most visible sort of will generate
+ 
+
+ align:start position:0%
+the most visible sort of will generate
+from federal facilities and sell cheap
+
+ align:start position:0%
+from federal facilities and sell cheap
+ 
+
+ align:start position:0%
+from federal facilities and sell cheap
+but we did a bunch of
+
+ align:start position:0%
+but we did a bunch of
+ 
+
+ align:start position:0%
+but we did a bunch of
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+and in 1950 when it peaked the federal
+
+ align:start position:0%
+and in 1950 when it peaked the federal
+ 
+
+ align:start position:0%
+and in 1950 when it peaked the federal
+government generated 12% of us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electricity
+
+ align:start position:0%
+electricity
+ 
+
+ align:start position:0%
+electricity
+okay so far so good that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+history State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regulation so the the
+
+ align:start position:0%
+regulation so the the
+ 
+
+ align:start position:0%
+regulation so the the
+bulk
+
+ align:start position:0%
+bulk
+ 
+
+ align:start position:0%
+bulk
+of the regulatory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effort from 1907 particularly after 1935
+
+ align:start position:0%
+effort from 1907 particularly after 1935
+ 
+
+ align:start position:0%
+effort from 1907 particularly after 1935
+that's puka always pronounced puka um
+
+ align:start position:0%
+that's puka always pronounced puka um
+ 
+
+ align:start position:0%
+that's puka always pronounced puka um
+State Regulators required just and
+
+ align:start position:0%
+State Regulators required just and
+ 
+
+ align:start position:0%
+State Regulators required just and
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+rates this was rate of return
+
+ align:start position:0%
+rates this was rate of return
+ 
+
+ align:start position:0%
+rates this was rate of return
+regulation they would set
+
+ align:start position:0%
+regulation they would set
+ 
+
+ align:start position:0%
+regulation they would set
+prices in principle so that the utility
+
+ align:start position:0%
+prices in principle so that the utility
+ 
+
+ align:start position:0%
+prices in principle so that the utility
+would just earn a fair rate of return
+
+ align:start position:0%
+would just earn a fair rate of return
+ 
+
+ align:start position:0%
+would just earn a fair rate of return
+right you got to have some profits
+
+ align:start position:0%
+right you got to have some profits
+ 
+
+ align:start position:0%
+right you got to have some profits
+what's a fair profit well we know what
+
+ align:start position:0%
+what's a fair profit well we know what
+ 
+
+ align:start position:0%
+what's a fair profit well we know what
+your cost of capital is we'll figure out
+
+ align:start position:0%
+your cost of capital is we'll figure out
+ 
+
+ align:start position:0%
+your cost of capital is we'll figure out
+what that is and we'll set the rates so
+
+ align:start position:0%
+what that is and we'll set the rates so
+ 
+
+ align:start position:0%
+what that is and we'll set the rates so
+you just earn
+
+ align:start position:0%
+you just earn
+ 
+
+ align:start position:0%
+you just earn
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what might go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong Alex surely you're about to raise
+
+ align:start position:0%
+wrong Alex surely you're about to raise
+ 
+
+ align:start position:0%
+wrong Alex surely you're about to raise
+your hand now I keep watching this hand
+
+ align:start position:0%
+your hand now I keep watching this hand
+ 
+
+ align:start position:0%
+your hand now I keep watching this hand
+going what do you think what could go
+
+ align:start position:0%
+going what do you think what could go
+ 
+
+ align:start position:0%
+going what do you think what could go
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+anything we're going to
+
+ align:start position:0%
+anything we're going to
+ 
+
+ align:start position:0%
+anything we're going to
+set we're going to set prices so that
+
+ align:start position:0%
+set we're going to set prices so that
+ 
+
+ align:start position:0%
+set we're going to set prices so that
+you just earn
+
+ align:start position:0%
+you just earn
+ 
+
+ align:start position:0%
+you just earn
+a reasonable rate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return you could get it wrong we'll set
+
+ align:start position:0%
+return you could get it wrong we'll set
+ 
+
+ align:start position:0%
+return you could get it wrong we'll set
+a we'll set a we'll set a price and uh
+
+ align:start position:0%
+a we'll set a we'll set a price and uh
+ 
+
+ align:start position:0%
+a we'll set a we'll set a price and uh
+we'll let it we we'll well we'll set a
+
+ align:start position:0%
+we'll let it we we'll well we'll set a
+ 
+
+ align:start position:0%
+we'll let it we we'll well we'll set a
+price and let's suppose we adjust it
+
+ align:start position:0%
+price and let's suppose we adjust it
+ 
+
+ align:start position:0%
+price and let's suppose we adjust it
+when we get surprises or let's so we
+
+ align:start position:0%
+when we get surprises or let's so we
+ 
+
+ align:start position:0%
+when we get surprises or let's so we
+we're worried about and this is what
+
+ align:start position:0%
+we're worried about and this is what
+ 
+
+ align:start position:0%
+we're worried about and this is what
+they did do after a while we know that
+
+ align:start position:0%
+they did do after a while we know that
+ 
+
+ align:start position:0%
+they did do after a while we know that
+you can't control your cost of fuel
+
+ align:start position:0%
+you can't control your cost of fuel
+ 
+
+ align:start position:0%
+you can't control your cost of fuel
+that's on the open market so we'll pass
+
+ align:start position:0%
+that's on the open market so we'll pass
+ 
+
+ align:start position:0%
+that's on the open market so we'll pass
+that through
+
+ align:start position:0%
+that through
+ 
+
+ align:start position:0%
+that through
+automatically anything else anything
+
+ align:start position:0%
+automatically anything else anything
+ 
+
+ align:start position:0%
+automatically anything else anything
+else that could go wrong if I make sure
+
+ align:start position:0%
+else that could go wrong if I make sure
+ 
+
+ align:start position:0%
+else that could go wrong if I make sure
+you just earn a reasonable rate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return okay let me not torture you think
+
+ align:start position:0%
+return okay let me not torture you think
+ 
+
+ align:start position:0%
+return okay let me not torture you think
+about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so you would expect the big problem
+
+ align:start position:0%
+yes so you would expect the big problem
+ 
+
+ align:start position:0%
+yes so you would expect the big problem
+would be that a cost would be too high
+
+ align:start position:0%
+would be that a cost would be too high
+ 
+
+ align:start position:0%
+would be that a cost would be too high
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose and we can even sharpen that a
+
+ align:start position:0%
+suppose and we can even sharpen that a
+ 
+
+ align:start position:0%
+suppose and we can even sharpen that a
+little bit and that is the main the main
+
+ align:start position:0%
+little bit and that is the main the main
+ 
+
+ align:start position:0%
+little bit and that is the main the main
+uh uh defect in that form of Regulation
+
+ align:start position:0%
+uh uh defect in that form of Regulation
+ 
+
+ align:start position:0%
+uh uh defect in that form of Regulation
+um so suppose we we recognize the
+
+ align:start position:0%
+um so suppose we we recognize the
+ 
+
+ align:start position:0%
+um so suppose we we recognize the
+following if I say that a reasonable
+
+ align:start position:0%
+following if I say that a reasonable
+ 
+
+ align:start position:0%
+following if I say that a reasonable
+rate of return is below your cost of
+
+ align:start position:0%
+rate of return is below your cost of
+ 
+
+ align:start position:0%
+rate of return is below your cost of
+capital then you can't you can't
+
+ align:start position:0%
+capital then you can't you can't
+ 
+
+ align:start position:0%
+capital then you can't you can't
+function right if you can't raise money
+
+ align:start position:0%
+function right if you can't raise money
+ 
+
+ align:start position:0%
+function right if you can't raise money
+to invest because you can't earn enough
+
+ align:start position:0%
+to invest because you can't earn enough
+ 
+
+ align:start position:0%
+to invest because you can't earn enough
+on it if I've set the rate of return too
+
+ align:start position:0%
+on it if I've set the rate of return too
+ 
+
+ align:start position:0%
+on it if I've set the rate of return too
+low you can't go forward so I don't want
+
+ align:start position:0%
+low you can't go forward so I don't want
+ 
+
+ align:start position:0%
+low you can't go forward so I don't want
+that to happen
+
+ align:start position:0%
+that to happen
+ 
+
+ align:start position:0%
+that to happen
+so I make sure you earn more than your
+
+ align:start position:0%
+so I make sure you earn more than your
+ 
+
+ align:start position:0%
+so I make sure you earn more than your
+cost of capital on the Investments I
+
+ align:start position:0%
+cost of capital on the Investments I
+ 
+
+ align:start position:0%
+cost of capital on the Investments I
+have to make sure that every dollar you
+
+ align:start position:0%
+have to make sure that every dollar you
+ 
+
+ align:start position:0%
+have to make sure that every dollar you
+invest earns more
+
+ align:start position:0%
+invest earns more
+ 
+
+ align:start position:0%
+invest earns more
+than what it cost you to raise that
+
+ align:start position:0%
+than what it cost you to raise that
+ 
+
+ align:start position:0%
+than what it cost you to raise that
+dollar what might that lead to just
+
+ align:start position:0%
+dollar what might that lead to just
+ 
+
+ align:start position:0%
+dollar what might that lead to just
+intuitively David overinvestment
+
+ align:start position:0%
+intuitively David overinvestment
+ 
+
+ align:start position:0%
+intuitively David overinvestment
+overinvestment which they referred to in
+
+ align:start position:0%
+overinvestment which they referred to in
+ 
+
+ align:start position:0%
+overinvestment which they referred to in
+the literature as gold plating right if
+
+ align:start position:0%
+the literature as gold plating right if
+ 
+
+ align:start position:0%
+the literature as gold plating right if
+I have a choice of doing it with three
+
+ align:start position:0%
+I have a choice of doing it with three
+ 
+
+ align:start position:0%
+I have a choice of doing it with three
+people or a $5 million investment I'll
+
+ align:start position:0%
+people or a $5 million investment I'll
+ 
+
+ align:start position:0%
+people or a $5 million investment I'll
+do a five million investment because
+
+ align:start position:0%
+do a five million investment because
+ 
+
+ align:start position:0%
+do a five million investment because
+I'll earn money on that and I won't earn
+
+ align:start position:0%
+I'll earn money on that and I won't earn
+ 
+
+ align:start position:0%
+I'll earn money on that and I won't earn
+any money on the three people so you
+
+ align:start position:0%
+any money on the three people so you
+ 
+
+ align:start position:0%
+any money on the three people so you
+have a tendency you would expect to have
+
+ align:start position:0%
+have a tendency you would expect to have
+ 
+
+ align:start position:0%
+have a tendency you would expect to have
+capital investment too high there are a
+
+ align:start position:0%
+capital investment too high there are a
+ 
+
+ align:start position:0%
+capital investment too high there are a
+couple other problems we've hit two of
+
+ align:start position:0%
+couple other problems we've hit two of
+ 
+
+ align:start position:0%
+couple other problems we've hit two of
+them I'll just mention the others um
+
+ align:start position:0%
+them I'll just mention the others um
+ 
+
+ align:start position:0%
+them I'll just mention the others um
+when people talk about this
+
+ align:start position:0%
+when people talk about this
+ 
+
+ align:start position:0%
+when people talk about this
+system they talk about
+
+ align:start position:0%
+system they talk about
+ 
+
+ align:start position:0%
+system they talk about
+capture uh
+
+ align:start position:0%
+capture uh
+ 
+
+ align:start position:0%
+capture uh
+because well I I actually gave a talk at
+
+ align:start position:0%
+because well I I actually gave a talk at
+ 
+
+ align:start position:0%
+because well I I actually gave a talk at
+the the Massachusetts Commission
+
+ align:start position:0%
+the the Massachusetts Commission
+ 
+
+ align:start position:0%
+the the Massachusetts Commission
+uh a couple of weeks ago
+
+ align:start position:0%
+uh a couple of weeks ago
+ 
+
+ align:start position:0%
+uh a couple of weeks ago
+and turns out there's a little office
+
+ align:start position:0%
+and turns out there's a little office
+ 
+
+ align:start position:0%
+and turns out there's a little office
+complex inside South Station you don't
+
+ align:start position:0%
+complex inside South Station you don't
+ 
+
+ align:start position:0%
+complex inside South Station you don't
+see it but you kind of go around the
+
+ align:start position:0%
+see it but you kind of go around the
+ 
+
+ align:start position:0%
+see it but you kind of go around the
+corner and you go up and they have some
+
+ align:start position:0%
+corner and you go up and they have some
+ 
+
+ align:start position:0%
+corner and you go up and they have some
+offices who do you think goes into those
+
+ align:start position:0%
+offices who do you think goes into those
+ 
+
+ align:start position:0%
+offices who do you think goes into those
+offices the companies they
+
+ align:start position:0%
+offices the companies they
+ 
+
+ align:start position:0%
+offices the companies they
+regulate who do you
+
+ align:start position:0%
+regulate who do you
+ 
+
+ align:start position:0%
+regulate who do you
+think says nice things to them talks to
+
+ align:start position:0%
+think says nice things to them talks to
+ 
+
+ align:start position:0%
+think says nice things to them talks to
+them has any relationship with them at
+
+ align:start position:0%
+them has any relationship with them at
+ 
+
+ align:start position:0%
+them has any relationship with them at
+all to people they regulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who has lots of lawyers and lots of PR
+
+ align:start position:0%
+who has lots of lawyers and lots of PR
+ 
+
+ align:start position:0%
+who has lots of lawyers and lots of PR
+people to make a lot of noise if they're
+
+ align:start position:0%
+people to make a lot of noise if they're
+ 
+
+ align:start position:0%
+people to make a lot of noise if they're
+unhappy the people they
+
+ align:start position:0%
+unhappy the people they
+ 
+
+ align:start position:0%
+unhappy the people they
+regulate so a strong model not an
+
+ align:start position:0%
+regulate so a strong model not an
+ 
+
+ align:start position:0%
+regulate so a strong model not an
+entirely accurate model but not an
+
+ align:start position:0%
+entirely accurate model but not an
+ 
+
+ align:start position:0%
+entirely accurate model but not an
+entirely crazy model is after a while
+
+ align:start position:0%
+entirely crazy model is after a while
+ 
+
+ align:start position:0%
+entirely crazy model is after a while
+The Regulators serve the serve the folks
+
+ align:start position:0%
+The Regulators serve the serve the folks
+ 
+
+ align:start position:0%
+The Regulators serve the serve the folks
+they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regulate because you want to make them
+
+ align:start position:0%
+regulate because you want to make them
+ 
+
+ align:start position:0%
+regulate because you want to make them
+happy you see them every day they come
+
+ align:start position:0%
+happy you see them every day they come
+ 
+
+ align:start position:0%
+happy you see them every day they come
+in your office you could imagine a
+
+ align:start position:0%
+in your office you could imagine a
+ 
+
+ align:start position:0%
+in your office you could imagine a
+different kind of relationship and
+
+ align:start position:0%
+different kind of relationship and
+ 
+
+ align:start position:0%
+different kind of relationship and
+sometimes you see
+
+ align:start position:0%
+sometimes you see
+ 
+
+ align:start position:0%
+sometimes you see
+it but one argument is you know all the
+
+ align:start position:0%
+it but one argument is you know all the
+ 
+
+ align:start position:0%
+it but one argument is you know all the
+consumers are not organized the utility
+
+ align:start position:0%
+consumers are not organized the utility
+ 
+
+ align:start position:0%
+consumers are not organized the utility
+is the electric companies are organized
+
+ align:start position:0%
+is the electric companies are organized
+ 
+
+ align:start position:0%
+is the electric companies are organized
+they have their lawyers they have their
+
+ align:start position:0%
+they have their lawyers they have their
+ 
+
+ align:start position:0%
+they have their lawyers they have their
+lobbyists they're in every day they
+
+ align:start position:0%
+lobbyists they're in every day they
+ 
+
+ align:start position:0%
+lobbyists they're in every day they
+write the
+
+ align:start position:0%
+write the
+ 
+
+ align:start position:0%
+write the
+stuff those of us who only pay bills
+
+ align:start position:0%
+stuff those of us who only pay bills
+ 
+
+ align:start position:0%
+stuff those of us who only pay bills
+aren't in there every day so that's one
+
+ align:start position:0%
+aren't in there every day so that's one
+ 
+
+ align:start position:0%
+aren't in there every day so that's one
+problem the other problem is um it's a
+
+ align:start position:0%
+problem the other problem is um it's a
+ 
+
+ align:start position:0%
+problem the other problem is um it's a
+more subtle problem is who determines
+
+ align:start position:0%
+more subtle problem is who determines
+ 
+
+ align:start position:0%
+more subtle problem is who determines
+who pays what price and the simplest
+
+ align:start position:0%
+who pays what price and the simplest
+ 
+
+ align:start position:0%
+who pays what price and the simplest
+example is prices to Industry versus
+
+ align:start position:0%
+example is prices to Industry versus
+ 
+
+ align:start position:0%
+example is prices to Industry versus
+prices to
+
+ align:start position:0%
+prices to
+ 
+
+ align:start position:0%
+prices to
+Consumers industry takes power at higher
+
+ align:start position:0%
+Consumers industry takes power at higher
+ 
+
+ align:start position:0%
+Consumers industry takes power at higher
+voltages so they ought to pay a lower
+
+ align:start position:0%
+voltages so they ought to pay a lower
+ 
+
+ align:start position:0%
+voltages so they ought to pay a lower
+price what's the price difference well I
+
+ align:start position:0%
+price what's the price difference well I
+ 
+
+ align:start position:0%
+price what's the price difference well I
+submit to that price difference is a
+
+ align:start position:0%
+submit to that price difference is a
+ 
+
+ align:start position:0%
+submit to that price difference is a
+political decision as much as it is
+
+ align:start position:0%
+political decision as much as it is
+ 
+
+ align:start position:0%
+political decision as much as it is
+anything and under a regul regulated
+
+ align:start position:0%
+anything and under a regul regulated
+ 
+
+ align:start position:0%
+anything and under a regul regulated
+regime it's hard to see how it could be
+
+ align:start position:0%
+regime it's hard to see how it could be
+ 
+
+ align:start position:0%
+regime it's hard to see how it could be
+anything else okay so those
+
+ align:start position:0%
+anything else okay so those
+ 
+
+ align:start position:0%
+anything else okay so those
+are this system actually worked and I'm
+
+ align:start position:0%
+are this system actually worked and I'm
+ 
+
+ align:start position:0%
+are this system actually worked and I'm
+going to answer this question just in
+
+ align:start position:0%
+going to answer this question just in
+ 
+
+ align:start position:0%
+going to answer this question just in
+the interest of our leaving today this
+
+ align:start position:0%
+the interest of our leaving today this
+ 
+
+ align:start position:0%
+the interest of our leaving today this
+system generated almost no complaints
+
+ align:start position:0%
+system generated almost no complaints
+ 
+
+ align:start position:0%
+system generated almost no complaints
+until the 1970s in electric power
+
+ align:start position:0%
+until the 1970s in electric power
+ 
+
+ align:start position:0%
+until the 1970s in electric power
+despite all of these well-known well
+
+ align:start position:0%
+despite all of these well-known well
+ 
+
+ align:start position:0%
+despite all of these well-known well
+documented
+
+ align:start position:0%
+documented
+ 
+
+ align:start position:0%
+documented
+problems and the reason for that is in
+
+ align:start position:0%
+problems and the reason for that is in
+ 
+
+ align:start position:0%
+problems and the reason for that is in
+electricity technical change was very
+
+ align:start position:0%
+electricity technical change was very
+ 
+
+ align:start position:0%
+electricity technical change was very
+rapid energy costs were pretty stable
+
+ align:start position:0%
+rapid energy costs were pretty stable
+ 
+
+ align:start position:0%
+rapid energy costs were pretty stable
+and so the price of electricity was
+
+ align:start position:0%
+and so the price of electricity was
+ 
+
+ align:start position:0%
+and so the price of electricity was
+dropping very often the utility would
+
+ align:start position:0%
+dropping very often the utility would
+ 
+
+ align:start position:0%
+dropping very often the utility would
+come in and ask for a rate
+
+ align:start position:0%
+come in and ask for a rate
+ 
+
+ align:start position:0%
+come in and ask for a rate
+decrease right if you fixed my price and
+
+ align:start position:0%
+decrease right if you fixed my price and
+ 
+
+ align:start position:0%
+decrease right if you fixed my price and
+my costs keep dropping there comes a
+
+ align:start position:0%
+my costs keep dropping there comes a
+ 
+
+ align:start position:0%
+my costs keep dropping there comes a
+point at which the price is
+
+ align:start position:0%
+point at which the price is
+ 
+
+ align:start position:0%
+point at which the price is
+embarrassingly high above the Monopoly
+
+ align:start position:0%
+embarrassingly high above the Monopoly
+ 
+
+ align:start position:0%
+embarrassingly high above the Monopoly
+price going to make me too much money to
+
+ align:start position:0%
+price going to make me too much money to
+ 
+
+ align:start position:0%
+price going to make me too much money to
+survive political scrutiny I'll ask for
+
+ align:start position:0%
+survive political scrutiny I'll ask for
+ 
+
+ align:start position:0%
+survive political scrutiny I'll ask for
+a lower
+
+ align:start position:0%
+a lower
+ 
+
+ align:start position:0%
+a lower
+price so an awful lot of that happened
+
+ align:start position:0%
+price so an awful lot of that happened
+ 
+
+ align:start position:0%
+price so an awful lot of that happened
+that's a great system The Regulators
+
+ align:start position:0%
+that's a great system The Regulators
+ 
+
+ align:start position:0%
+that's a great system The Regulators
+don't have to do much the utility comes
+
+ align:start position:0%
+don't have to do much the utility comes
+ 
+
+ align:start position:0%
+don't have to do much the utility comes
+in and says may we please lower our
+
+ align:start position:0%
+in and says may we please lower our
+ 
+
+ align:start position:0%
+in and says may we please lower our
+price we do a big fuss we have lawyers
+
+ align:start position:0%
+price we do a big fuss we have lawyers
+ 
+
+ align:start position:0%
+price we do a big fuss we have lawyers
+we write briefs after a while we say
+
+ align:start position:0%
+we write briefs after a while we say
+ 
+
+ align:start position:0%
+we write briefs after a while we say
+yeah lower your price we all go out to
+
+ align:start position:0%
+yeah lower your price we all go out to
+ 
+
+ align:start position:0%
+yeah lower your price we all go out to
+lunch this is a good system it didn't
+
+ align:start position:0%
+lunch this is a good system it didn't
+ 
+
+ align:start position:0%
+lunch this is a good system it didn't
+work in the 70s very well when fuel cost
+
+ align:start position:0%
+work in the 70s very well when fuel cost
+ 
+
+ align:start position:0%
+work in the 70s very well when fuel cost
+began to rise and the utilities came in
+
+ align:start position:0%
+began to rise and the utilities came in
+ 
+
+ align:start position:0%
+began to rise and the utilities came in
+and said now let us raise our
+
+ align:start position:0%
+and said now let us raise our
+ 
+
+ align:start position:0%
+and said now let us raise our
+prices and then people began to say wait
+
+ align:start position:0%
+prices and then people began to say wait
+ 
+
+ align:start position:0%
+prices and then people began to say wait
+a minute your costs are too high your
+
+ align:start position:0%
+a minute your costs are too high your
+ 
+
+ align:start position:0%
+a minute your costs are too high your
+goldplated blah blah blah and it began
+
+ align:start position:0%
+goldplated blah blah blah and it began
+ 
+
+ align:start position:0%
+goldplated blah blah blah and it began
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+nasty okay
+
+ align:start position:0%
+nasty okay
+ 
+
+ align:start position:0%
+nasty okay
+um so let me let me take this up to date
+
+ align:start position:0%
+um so let me let me take this up to date
+ 
+
+ align:start position:0%
+um so let me let me take this up to date
+um in the
+
+ align:start position:0%
+um in the
+ 
+
+ align:start position:0%
+um in the
+1970s
+
+ align:start position:0%
+1970s
+ 
+
+ align:start position:0%
+1970s
+we deregulated a lot of things in this
+
+ align:start position:0%
+we deregulated a lot of things in this
+ 
+
+ align:start position:0%
+we deregulated a lot of things in this
+economy we deregulated Airlines we
+
+ align:start position:0%
+economy we deregulated Airlines we
+ 
+
+ align:start position:0%
+economy we deregulated Airlines we
+deregulated Trucking we deregulated
+
+ align:start position:0%
+deregulated Trucking we deregulated
+ 
+
+ align:start position:0%
+deregulated Trucking we deregulated
+railroads we deregulated the Wellhead
+
+ align:start position:0%
+railroads we deregulated the Wellhead
+ 
+
+ align:start position:0%
+railroads we deregulated the Wellhead
+price of natural
+
+ align:start position:0%
+price of natural
+ 
+
+ align:start position:0%
+price of natural
+gas and most of those
+
+ align:start position:0%
+gas and most of those
+ 
+
+ align:start position:0%
+gas and most of those
+worked price of natural gas went up but
+
+ align:start position:0%
+worked price of natural gas went up but
+ 
+
+ align:start position:0%
+worked price of natural gas went up but
+we stopped having shortages airline
+
+ align:start position:0%
+we stopped having shortages airline
+ 
+
+ align:start position:0%
+we stopped having shortages airline
+prices came down Trucking prices came
+
+ align:start position:0%
+prices came down Trucking prices came
+ 
+
+ align:start position:0%
+prices came down Trucking prices came
+down railroad prices came down costs
+
+ align:start position:0%
+down railroad prices came down costs
+ 
+
+ align:start position:0%
+down railroad prices came down costs
+came down
+
+ align:start position:0%
+came down
+ 
+
+ align:start position:0%
+came down
+so and electricity prices were going up
+
+ align:start position:0%
+so and electricity prices were going up
+ 
+
+ align:start position:0%
+so and electricity prices were going up
+fuel costs were going up there was
+
+ align:start position:0%
+fuel costs were going up there was
+ 
+
+ align:start position:0%
+fuel costs were going up there was
+excess capacity people had to pay for
+
+ align:start position:0%
+excess capacity people had to pay for
+ 
+
+ align:start position:0%
+excess capacity people had to pay for
+that capacity there became a move to
+
+ align:start position:0%
+that capacity there became a move to
+ 
+
+ align:start position:0%
+that capacity there became a move to
+deregulate
+
+ align:start position:0%
+deregulate
+ 
+
+ align:start position:0%
+deregulate
+electricity but I just told you it was a
+
+ align:start position:0%
+electricity but I just told you it was a
+ 
+
+ align:start position:0%
+electricity but I just told you it was a
+natural monopoly um so the F step was
+
+ align:start position:0%
+natural monopoly um so the F step was
+ 
+
+ align:start position:0%
+natural monopoly um so the F step was
+this law that said you have to buy from
+
+ align:start position:0%
+this law that said you have to buy from
+ 
+
+ align:start position:0%
+this law that said you have to buy from
+Renewables and you have to buy from
+
+ align:start position:0%
+Renewables and you have to buy from
+ 
+
+ align:start position:0%
+Renewables and you have to buy from
+combined heat and power co-generation
+
+ align:start position:0%
+combined heat and power co-generation
+ 
+
+ align:start position:0%
+combined heat and power co-generation
+hexion type units at avoided cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's avoided cost well each state got
+
+ align:start position:0%
+what's avoided cost well each state got
+ 
+
+ align:start position:0%
+what's avoided cost well each state got
+to determine that big mess there were no
+
+ align:start position:0%
+to determine that big mess there were no
+ 
+
+ align:start position:0%
+to determine that big mess there were no
+markets but an interesting
+
+ align:start position:0%
+markets but an interesting
+ 
+
+ align:start position:0%
+markets but an interesting
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+um early 80s and I will cite myself here
+
+ align:start position:0%
+um early 80s and I will cite myself here
+ 
+
+ align:start position:0%
+um early 80s and I will cite myself here
+because I do tend to get cited for this
+
+ align:start position:0%
+because I do tend to get cited for this
+ 
+
+ align:start position:0%
+because I do tend to get cited for this
+in the early 80s Paul josca and I were
+
+ align:start position:0%
+in the early 80s Paul josca and I were
+ 
+
+ align:start position:0%
+in the early 80s Paul josca and I were
+working in this area and we began to
+
+ align:start position:0%
+working in this area and we began to
+ 
+
+ align:start position:0%
+working in this area and we began to
+hear from people in the reaged
+
+ align:start position:0%
+hear from people in the reaged
+ 
+
+ align:start position:0%
+hear from people in the reaged
+administration all this other stuff
+
+ align:start position:0%
+administration all this other stuff
+ 
+
+ align:start position:0%
+administration all this other stuff
+worked we deregulated gas and Trucking
+
+ align:start position:0%
+worked we deregulated gas and Trucking
+ 
+
+ align:start position:0%
+worked we deregulated gas and Trucking
+and Airlines why don't we just
+
+ align:start position:0%
+and Airlines why don't we just
+ 
+
+ align:start position:0%
+and Airlines why don't we just
+deregulate
+
+ align:start position:0%
+deregulate
+ 
+
+ align:start position:0%
+deregulate
+electricity why don't we just let the
+
+ align:start position:0%
+electricity why don't we just let the
+ 
+
+ align:start position:0%
+electricity why don't we just let the
+market determine electricity prices I
+
+ align:start position:0%
+market determine electricity prices I
+ 
+
+ align:start position:0%
+market determine electricity prices I
+have to say you know the words natural
+
+ align:start position:0%
+have to say you know the words natural
+ 
+
+ align:start position:0%
+have to say you know the words natural
+monopoly came to mind it's you you're
+
+ align:start position:0%
+monopoly came to mind it's you you're
+ 
+
+ align:start position:0%
+monopoly came to mind it's you you're
+not going to have competition in
+
+ align:start position:0%
+not going to have competition in
+ 
+
+ align:start position:0%
+not going to have competition in
+transmission you're not going to have
+
+ align:start position:0%
+transmission you're not going to have
+ 
+
+ align:start position:0%
+transmission you're not going to have
+competition in
+
+ align:start position:0%
+competition in
+ 
+
+ align:start position:0%
+competition in
+distribution but you know you could have
+
+ align:start position:0%
+distribution but you know you could have
+ 
+
+ align:start position:0%
+distribution but you know you could have
+competition in
+
+ align:start position:0%
+competition in
+ 
+
+ align:start position:0%
+competition in
+generation it's not like there's only
+
+ align:start position:0%
+generation it's not like there's only
+ 
+
+ align:start position:0%
+generation it's not like there's only
+one generating plant per City or per
+
+ align:start position:0%
+one generating plant per City or per
+ 
+
+ align:start position:0%
+one generating plant per City or per
+state there are a bunch of them so maybe
+
+ align:start position:0%
+state there are a bunch of them so maybe
+ 
+
+ align:start position:0%
+state there are a bunch of them so maybe
+you could so we actually wrote a book
+
+ align:start position:0%
+you could so we actually wrote a book
+ 
+
+ align:start position:0%
+you could so we actually wrote a book
+called markets for power that uh people
+
+ align:start position:0%
+called markets for power that uh people
+ 
+
+ align:start position:0%
+called markets for power that uh people
+tell me was influential more outside the
+
+ align:start position:0%
+tell me was influential more outside the
+ 
+
+ align:start position:0%
+tell me was influential more outside the
+US than in uh but we said well you know
+
+ align:start position:0%
+US than in uh but we said well you know
+ 
+
+ align:start position:0%
+US than in uh but we said well you know
+you could do it if you were careful if
+
+ align:start position:0%
+you could do it if you were careful if
+ 
+
+ align:start position:0%
+you could do it if you were careful if
+you were careful and you worried about
+
+ align:start position:0%
+you were careful and you worried about
+ 
+
+ align:start position:0%
+you were careful and you worried about
+Market power and you worried about the
+
+ align:start position:0%
+Market power and you worried about the
+ 
+
+ align:start position:0%
+Market power and you worried about the
+proper rules and you worried about about
+
+ align:start position:0%
+proper rules and you worried about about
+ 
+
+ align:start position:0%
+proper rules and you worried about about
+a half a dozen other things you could
+
+ align:start position:0%
+a half a dozen other things you could
+ 
+
+ align:start position:0%
+a half a dozen other things you could
+actually deregulate
+
+ align:start position:0%
+actually deregulate
+ 
+
+ align:start position:0%
+actually deregulate
+Generation Well it
+
+ align:start position:0%
+Generation Well it
+ 
+
+ align:start position:0%
+Generation Well it
+happened and I don't claim credit for
+
+ align:start position:0%
+happened and I don't claim credit for
+ 
+
+ align:start position:0%
+happened and I don't claim credit for
+this it was mostly because the Thatcher
+
+ align:start position:0%
+this it was mostly because the Thatcher
+ 
+
+ align:start position:0%
+this it was mostly because the Thatcher
+Administration in England needed money
+
+ align:start position:0%
+Administration in England needed money
+ 
+
+ align:start position:0%
+Administration in England needed money
+so they sold they sold the electric
+
+ align:start position:0%
+so they sold they sold the electric
+ 
+
+ align:start position:0%
+so they sold they sold the electric
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+system this was a shock it had happened
+
+ align:start position:0%
+system this was a shock it had happened
+ 
+
+ align:start position:0%
+system this was a shock it had happened
+in Chile a few years earlier nobody
+
+ align:start position:0%
+in Chile a few years earlier nobody
+ 
+
+ align:start position:0%
+in Chile a few years earlier nobody
+noticed Chile besides they did it in
+
+ align:start position:0%
+noticed Chile besides they did it in
+ 
+
+ align:start position:0%
+noticed Chile besides they did it in
+Spanish so but in England and Wales they
+
+ align:start position:0%
+Spanish so but in England and Wales they
+ 
+
+ align:start position:0%
+Spanish so but in England and Wales they
+did it they they kept the grid the
+
+ align:start position:0%
+did it they they kept the grid the
+ 
+
+ align:start position:0%
+did it they they kept the grid the
+transmission system together they
+
+ align:start position:0%
+transmission system together they
+ 
+
+ align:start position:0%
+transmission system together they
+regulated the distribution companies but
+
+ align:start position:0%
+regulated the distribution companies but
+ 
+
+ align:start position:0%
+regulated the distribution companies but
+they sold the
+
+ align:start position:0%
+they sold the
+ 
+
+ align:start position:0%
+they sold the
+generators they sold the
+
+ align:start position:0%
+generators they sold the
+ 
+
+ align:start position:0%
+generators they sold the
+generators uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this was pretty exciting stuff and it
+
+ align:start position:0%
+this was pretty exciting stuff and it
+ 
+
+ align:start position:0%
+this was pretty exciting stuff and it
+actually worked not perfectly they had
+
+ align:start position:0%
+actually worked not perfectly they had
+ 
+
+ align:start position:0%
+actually worked not perfectly they had
+Monopoly power problems in generation in
+
+ align:start position:0%
+Monopoly power problems in generation in
+ 
+
+ align:start position:0%
+Monopoly power problems in generation in
+some areas they had to make changes but
+
+ align:start position:0%
+some areas they had to make changes but
+ 
+
+ align:start position:0%
+some areas they had to make changes but
+it sort of
+
+ align:start position:0%
+it sort of
+ 
+
+ align:start position:0%
+it sort of
+worked other count started to follow we
+
+ align:start position:0%
+worked other count started to follow we
+ 
+
+ align:start position:0%
+worked other count started to follow we
+started to
+
+ align:start position:0%
+started to
+ 
+
+ align:start position:0%
+started to
+follow um uh suddenly you had to
+
+ align:start position:0%
+follow um uh suddenly you had to
+ 
+
+ align:start position:0%
+follow um uh suddenly you had to
+transmission lines had to be able to
+
+ align:start position:0%
+transmission lines had to be able to
+ 
+
+ align:start position:0%
+transmission lines had to be able to
+carry be willing to carry anybody's
+
+ align:start position:0%
+carry be willing to carry anybody's
+ 
+
+ align:start position:0%
+carry be willing to carry anybody's
+power from anybody to anybody just like
+
+ align:start position:0%
+power from anybody to anybody just like
+ 
+
+ align:start position:0%
+power from anybody to anybody just like
+trucks do um the FK set up independent
+
+ align:start position:0%
+trucks do um the FK set up independent
+ 
+
+ align:start position:0%
+trucks do um the FK set up independent
+system operators they set up a regime
+
+ align:start position:0%
+system operators they set up a regime
+ 
+
+ align:start position:0%
+system operators they set up a regime
+where you could have one entity run the
+
+ align:start position:0%
+where you could have one entity run the
+ 
+
+ align:start position:0%
+where you could have one entity run the
+system not own it but run it uh and you
+
+ align:start position:0%
+system not own it but run it uh and you
+ 
+
+ align:start position:0%
+system not own it but run it uh and you
+could have wholesale markets for
+
+ align:start position:0%
+could have wholesale markets for
+ 
+
+ align:start position:0%
+could have wholesale markets for
+electricity um some people did it and
+
+ align:start position:0%
+electricity um some people did it and
+ 
+
+ align:start position:0%
+electricity um some people did it and
+I'll show you what happened then we had
+
+ align:start position:0%
+I'll show you what happened then we had
+ 
+
+ align:start position:0%
+I'll show you what happened then we had
+California who's from
+
+ align:start position:0%
+California who's from
+ 
+
+ align:start position:0%
+California who's from
+California was that fun that was not fun
+
+ align:start position:0%
+California was that fun that was not fun
+ 
+
+ align:start position:0%
+California was that fun that was not fun
+prices went crazy in California around
+
+ align:start position:0%
+prices went crazy in California around
+ 
+
+ align:start position:0%
+prices went crazy in California around
+2201 uh there were blackouts there was
+
+ align:start position:0%
+2201 uh there were blackouts there was
+ 
+
+ align:start position:0%
+2201 uh there were blackouts there was
+screaming there was political crisis
+
+ align:start position:0%
+screaming there was political crisis
+ 
+
+ align:start position:0%
+screaming there was political crisis
+there was Enron doing various
+
+ align:start position:0%
+there was Enron doing various
+ 
+
+ align:start position:0%
+there was Enron doing various
+interesting things there's litigation
+
+ align:start position:0%
+interesting things there's litigation
+ 
+
+ align:start position:0%
+interesting things there's litigation
+which may now have finished I'm not sure
+
+ align:start position:0%
+which may now have finished I'm not sure
+ 
+
+ align:start position:0%
+which may now have finished I'm not sure
+about who did what to
+
+ align:start position:0%
+about who did what to
+ 
+
+ align:start position:0%
+about who did what to
+whom
+
+ align:start position:0%
+whom
+ 
+
+ align:start position:0%
+whom
+um reform
+
+ align:start position:0%
+um reform
+ 
+
+ align:start position:0%
+um reform
+stopped uh we'll say a little bit about
+
+ align:start position:0%
+stopped uh we'll say a little bit about
+ 
+
+ align:start position:0%
+stopped uh we'll say a little bit about
+it but let me just say sort of where we
+
+ align:start position:0%
+it but let me just say sort of where we
+ 
+
+ align:start position:0%
+it but let me just say sort of where we
+are um so basically nothing's happened
+
+ align:start position:0%
+are um so basically nothing's happened
+ 
+
+ align:start position:0%
+are um so basically nothing's happened
+since California to a first
+
+ align:start position:0%
+since California to a first
+ 
+
+ align:start position:0%
+since California to a first
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+but a lot happened before
+
+ align:start position:0%
+but a lot happened before
+ 
+
+ align:start position:0%
+but a lot happened before
+California so there is competition in
+
+ align:start position:0%
+California so there is competition in
+ 
+
+ align:start position:0%
+California so there is competition in
+generation generators sell into a
+
+ align:start position:0%
+generation generators sell into a
+ 
+
+ align:start position:0%
+generation generators sell into a
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+um in England and Wales it's the core
+
+ align:start position:0%
+um in England and Wales it's the core
+ 
+
+ align:start position:0%
+um in England and Wales it's the core
+European Union policy all these
+
+ align:start position:0%
+European Union policy all these
+ 
+
+ align:start position:0%
+European Union policy all these
+state-owned monopolies are moving toward
+
+ align:start position:0%
+state-owned monopolies are moving toward
+ 
+
+ align:start position:0%
+state-owned monopolies are moving toward
+markets dramatically dramatically uh and
+
+ align:start position:0%
+markets dramatically dramatically uh and
+ 
+
+ align:start position:0%
+markets dramatically dramatically uh and
+about two-thirds of us consumers are
+
+ align:start position:0%
+about two-thirds of us consumers are
+ 
+
+ align:start position:0%
+about two-thirds of us consumers are
+served by markets this is the the
+
+ align:start position:0%
+served by markets this is the the
+ 
+
+ align:start position:0%
+served by markets this is the the
+picture the colored areas are roughly
+
+ align:start position:0%
+picture the colored areas are roughly
+ 
+
+ align:start position:0%
+picture the colored areas are roughly
+they change slightly over time uh
+
+ align:start position:0%
+they change slightly over time uh
+ 
+
+ align:start position:0%
+they change slightly over time uh
+roughly the boundaries of organized
+
+ align:start position:0%
+roughly the boundaries of organized
+ 
+
+ align:start position:0%
+roughly the boundaries of organized
+wholesale markets so in New England I
+
+ align:start position:0%
+wholesale markets so in New England I
+ 
+
+ align:start position:0%
+wholesale markets so in New England I
+you know I showed you these day ahead
+
+ align:start position:0%
+you know I showed you these day ahead
+ 
+
+ align:start position:0%
+you know I showed you these day ahead
+clearing uh demands and I'll show you
+
+ align:start position:0%
+clearing uh demands and I'll show you
+ 
+
+ align:start position:0%
+clearing uh demands and I'll show you
+some prices in a little bit um Texas
+
+ align:start position:0%
+some prices in a little bit um Texas
+ 
+
+ align:start position:0%
+some prices in a little bit um Texas
+runs this part of Texas runs runs a very
+
+ align:start position:0%
+runs this part of Texas runs runs a very
+ 
+
+ align:start position:0%
+runs this part of Texas runs runs a very
+nice Market
+
+ align:start position:0%
+nice Market
+ 
+
+ align:start position:0%
+nice Market
+California a after a while
+
+ align:start position:0%
+California a after a while
+ 
+
+ align:start position:0%
+California a after a while
+restarted this part of the country is
+
+ align:start position:0%
+restarted this part of the country is
+ 
+
+ align:start position:0%
+restarted this part of the country is
+traditional vertically integrated we
+
+ align:start position:0%
+traditional vertically integrated we
+ 
+
+ align:start position:0%
+traditional vertically integrated we
+generate we transmit we distribute
+
+ align:start position:0%
+generate we transmit we distribute
+ 
+
+ align:start position:0%
+generate we transmit we distribute
+what's a market uh Utilities in the west
+
+ align:start position:0%
+what's a market uh Utilities in the west
+ 
+
+ align:start position:0%
+what's a market uh Utilities in the west
+the federal government has a huge
+
+ align:start position:0%
+the federal government has a huge
+ 
+
+ align:start position:0%
+the federal government has a huge
+presence operates a lot of the
+
+ align:start position:0%
+presence operates a lot of the
+ 
+
+ align:start position:0%
+presence operates a lot of the
+transmission system um there's sort of
+
+ align:start position:0%
+transmission system um there's sort of
+ 
+
+ align:start position:0%
+transmission system um there's sort of
+elements of Market but not really and
+
+ align:start position:0%
+elements of Market but not really and
+ 
+
+ align:start position:0%
+elements of Market but not really and
+there's a awful lot of preference power
+
+ align:start position:0%
+there's a awful lot of preference power
+ 
+
+ align:start position:0%
+there's a awful lot of preference power
+because there's a lot of
+
+ align:start position:0%
+because there's a lot of
+ 
+
+ align:start position:0%
+because there's a lot of
+government-owned
+
+ align:start position:0%
+government-owned
+ 
+
+ align:start position:0%
+government-owned
+hydro if you go up the Columbia River
+
+ align:start position:0%
+hydro if you go up the Columbia River
+ 
+
+ align:start position:0%
+hydro if you go up the Columbia River
+you pass Dam after Dam after Dam uh
+
+ align:start position:0%
+you pass Dam after Dam after Dam uh
+ 
+
+ align:start position:0%
+you pass Dam after Dam after Dam uh
+which you all own um so New England is
+
+ align:start position:0%
+which you all own um so New England is
+ 
+
+ align:start position:0%
+which you all own um so New England is
+one of the earlier
+
+ align:start position:0%
+one of the earlier
+ 
+
+ align:start position:0%
+one of the earlier
+ones very nice little market
+
+ align:start position:0%
+ones very nice little market
+ 
+
+ align:start position:0%
+ones very nice little market
+um these are wholesale average wholesale
+
+ align:start position:0%
+um these are wholesale average wholesale
+ 
+
+ align:start position:0%
+um these are wholesale average wholesale
+prices in New England uh for the last
+
+ align:start position:0%
+prices in New England uh for the last
+ 
+
+ align:start position:0%
+prices in New England uh for the last
+year the prices are hourly I think maybe
+
+ align:start position:0%
+year the prices are hourly I think maybe
+ 
+
+ align:start position:0%
+year the prices are hourly I think maybe
+they've gone down to 15 minutes now but
+
+ align:start position:0%
+they've gone down to 15 minutes now but
+ 
+
+ align:start position:0%
+they've gone down to 15 minutes now but
+at least hourly they also can are
+
+ align:start position:0%
+at least hourly they also can are
+ 
+
+ align:start position:0%
+at least hourly they also can are
+differentiated by
+
+ align:start position:0%
+differentiated by
+ 
+
+ align:start position:0%
+differentiated by
+region uh if there's a problem
+
+ align:start position:0%
+region uh if there's a problem
+ 
+
+ align:start position:0%
+region uh if there's a problem
+transmitting power from A to B the
+
+ align:start position:0%
+transmitting power from A to B the
+ 
+
+ align:start position:0%
+transmitting power from A to B the
+prices in A and B can differ if there is
+
+ align:start position:0%
+prices in A and B can differ if there is
+ 
+
+ align:start position:0%
+prices in A and B can differ if there is
+no problem they're they differ trivially
+
+ align:start position:0%
+no problem they're they differ trivially
+ 
+
+ align:start position:0%
+no problem they're they differ trivially
+so again this is the day ahead price and
+
+ align:start position:0%
+so again this is the day ahead price and
+ 
+
+ align:start position:0%
+so again this is the day ahead price and
+this is the real time
+
+ align:start position:0%
+this is the real time
+ 
+
+ align:start position:0%
+this is the real time
+price so you'll
+
+ align:start position:0%
+price so you'll
+ 
+
+ align:start position:0%
+price so you'll
+see I don't know what happened last
+
+ align:start position:0%
+see I don't know what happened last
+ 
+
+ align:start position:0%
+see I don't know what happened last
+August whether that was a particularly
+
+ align:start position:0%
+August whether that was a particularly
+ 
+
+ align:start position:0%
+August whether that was a particularly
+or Late July whether that was a
+
+ align:start position:0%
+or Late July whether that was a
+ 
+
+ align:start position:0%
+or Late July whether that was a
+particularly hot day it was clearly
+
+ align:start position:0%
+particularly hot day it was clearly
+ 
+
+ align:start position:0%
+particularly hot day it was clearly
+anticipated you see the blue shot up as
+
+ align:start position:0%
+anticipated you see the blue shot up as
+ 
+
+ align:start position:0%
+anticipated you see the blue shot up as
+well uh as as the green uh sometimes the
+
+ align:start position:0%
+well uh as as the green uh sometimes the
+ 
+
+ align:start position:0%
+well uh as as the green uh sometimes the
+day ahead is too high sometimes the day
+
+ align:start position:0%
+day ahead is too high sometimes the day
+ 
+
+ align:start position:0%
+day ahead is too high sometimes the day
+ahead is too low there is a day ahead
+
+ align:start position:0%
+ahead is too low there is a day ahead
+ 
+
+ align:start position:0%
+ahead is too low there is a day ahead
+market and then there is what actually
+
+ align:start position:0%
+market and then there is what actually
+ 
+
+ align:start position:0%
+market and then there is what actually
+has to happen to follow the load so you
+
+ align:start position:0%
+has to happen to follow the load so you
+ 
+
+ align:start position:0%
+has to happen to follow the load so you
+know sometimes uh the day ahead market
+
+ align:start position:0%
+know sometimes uh the day ahead market
+ 
+
+ align:start position:0%
+know sometimes uh the day ahead market
+overestimates demand and thus cost
+
+ align:start position:0%
+overestimates demand and thus cost
+ 
+
+ align:start position:0%
+overestimates demand and thus cost
+sometimes it underestimates but those
+
+ align:start position:0%
+sometimes it underestimates but those
+ 
+
+ align:start position:0%
+sometimes it underestimates but those
+are daily
+
+ align:start position:0%
+are daily
+ 
+
+ align:start position:0%
+are daily
+prices um I'll show you some hourly
+
+ align:start position:0%
+prices um I'll show you some hourly
+ 
+
+ align:start position:0%
+prices um I'll show you some hourly
+prices on
+
+ align:start position:0%
+prices on
+ 
+
+ align:start position:0%
+prices on
+Monday um and here's what the US looks
+
+ align:start position:0%
+Monday um and here's what the US looks
+ 
+
+ align:start position:0%
+Monday um and here's what the US looks
+like this is no other country has a
+
+ align:start position:0%
+like this is no other country has a
+ 
+
+ align:start position:0%
+like this is no other country has a
+system that is this fragmented and
+
+ align:start position:0%
+system that is this fragmented and
+ 
+
+ align:start position:0%
+system that is this fragmented and
+diverse with the possible exception of
+
+ align:start position:0%
+diverse with the possible exception of
+ 
+
+ align:start position:0%
+diverse with the possible exception of
+Japan depending on how you count
+
+ align:start position:0%
+Japan depending on how you count
+ 
+
+ align:start position:0%
+Japan depending on how you count
+fragmentation and diversity since half
+
+ align:start position:0%
+fragmentation and diversity since half
+ 
+
+ align:start position:0%
+fragmentation and diversity since half
+of Japan runs on 50 Cycles a second and
+
+ align:start position:0%
+of Japan runs on 50 Cycles a second and
+ 
+
+ align:start position:0%
+of Japan runs on 50 Cycles a second and
+half of Japan runs on 60 Cycles we we at
+
+ align:start position:0%
+half of Japan runs on 60 Cycles we we at
+ 
+
+ align:start position:0%
+half of Japan runs on 60 Cycles we we at
+least beat that but uh so about 2third
+
+ align:start position:0%
+least beat that but uh so about 2third
+ 
+
+ align:start position:0%
+least beat that but uh so about 2third
+are served by organized markets ISO is
+
+ align:start position:0%
+are served by organized markets ISO is
+ 
+
+ align:start position:0%
+are served by organized markets ISO is
+independent system operator RTO is
+
+ align:start position:0%
+independent system operator RTO is
+ 
+
+ align:start position:0%
+independent system operator RTO is
+regional transmission operator
+
+ align:start position:0%
+regional transmission operator
+ 
+
+ align:start position:0%
+regional transmission operator
+differences are
+
+ align:start position:0%
+differences are
+ 
+
+ align:start position:0%
+differences are
+immaterial we have a transmission system
+
+ align:start position:0%
+immaterial we have a transmission system
+ 
+
+ align:start position:0%
+immaterial we have a transmission system
+owned by about 450 different entities
+
+ align:start position:0%
+owned by about 450 different entities
+ 
+
+ align:start position:0%
+owned by about 450 different entities
+some federal some local some State some
+
+ align:start position:0%
+some federal some local some State some
+ 
+
+ align:start position:0%
+some federal some local some State some
+private about 2third of the system is
+
+ align:start position:0%
+private about 2third of the system is
+ 
+
+ align:start position:0%
+private about 2third of the system is
+owned by private
+
+ align:start position:0%
+owned by private
+ 
+
+ align:start position:0%
+owned by private
+firms we
+
+ align:start position:0%
+firms we
+ 
+
+ align:start position:0%
+firms we
+have on the order of 3200 entities
+
+ align:start position:0%
+have on the order of 3200 entities
+ 
+
+ align:start position:0%
+have on the order of 3200 entities
+selling
+
+ align:start position:0%
+selling
+ 
+
+ align:start position:0%
+selling
+electricity 3,200 entities selling
+
+ align:start position:0%
+electricity 3,200 entities selling
+ 
+
+ align:start position:0%
+electricity 3,200 entities selling
+electricity um cooperatives aren't
+
+ align:start position:0%
+electricity um cooperatives aren't
+ 
+
+ align:start position:0%
+electricity um cooperatives aren't
+regulated by anybody investor-owned
+
+ align:start position:0%
+regulated by anybody investor-owned
+ 
+
+ align:start position:0%
+regulated by anybody investor-owned
+utilities are which are about 2/3
+
+ align:start position:0%
+utilities are which are about 2/3
+ 
+
+ align:start position:0%
+utilities are which are about 2/3
+regulated by States and by feds
+
+ align:start position:0%
+regulated by States and by feds
+ 
+
+ align:start position:0%
+regulated by States and by feds
+the munis and the federal systems are
+
+ align:start position:0%
+the munis and the federal systems are
+ 
+
+ align:start position:0%
+the munis and the federal systems are
+not regulated by
+
+ align:start position:0%
+not regulated by
+ 
+
+ align:start position:0%
+not regulated by
+anybody uh and that
+
+ align:start position:0%
+anybody uh and that
+ 
+
+ align:start position:0%
+anybody uh and that
+retail competitors at the bottom is a
+
+ align:start position:0%
+retail competitors at the bottom is a
+ 
+
+ align:start position:0%
+retail competitors at the bottom is a
+development that was underway before
+
+ align:start position:0%
+development that was underway before
+ 
+
+ align:start position:0%
+development that was underway before
+California has gotten stalled because of
+
+ align:start position:0%
+California has gotten stalled because of
+ 
+
+ align:start position:0%
+California has gotten stalled because of
+California um but this is in Texas is
+
+ align:start position:0%
+California um but this is in Texas is
+ 
+
+ align:start position:0%
+California um but this is in Texas is
+where it's it's most
+
+ align:start position:0%
+where it's it's most
+ 
+
+ align:start position:0%
+where it's it's most
+prevalent um you can buy electricity
+
+ align:start position:0%
+prevalent um you can buy electricity
+ 
+
+ align:start position:0%
+prevalent um you can buy electricity
+from any one of a number of competing
+
+ align:start position:0%
+from any one of a number of competing
+ 
+
+ align:start position:0%
+from any one of a number of competing
+firms it'll be delivered by the Monopoly
+
+ align:start position:0%
+firms it'll be delivered by the Monopoly
+ 
+
+ align:start position:0%
+firms it'll be delivered by the Monopoly
+Distribution
+
+ align:start position:0%
+Distribution
+ 
+
+ align:start position:0%
+Distribution
+Company but you will pay for it to some
+
+ align:start position:0%
+Company but you will pay for it to some
+ 
+
+ align:start position:0%
+Company but you will pay for it to some
+other firm that's responsible for making
+
+ align:start position:0%
+other firm that's responsible for making
+ 
+
+ align:start position:0%
+other firm that's responsible for making
+sure there's a l electricity to serve
+
+ align:start position:0%
+sure there's a l electricity to serve
+ 
+
+ align:start position:0%
+sure there's a l electricity to serve
+its customers that's the model in Europe
+
+ align:start position:0%
+its customers that's the model in Europe
+ 
+
+ align:start position:0%
+its customers that's the model in Europe
+it exists in Massachusetts but isn't
+
+ align:start position:0%
+it exists in Massachusetts but isn't
+ 
+
+ align:start position:0%
+it exists in Massachusetts but isn't
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+effective I got just last week I got my
+
+ align:start position:0%
+effective I got just last week I got my
+ 
+
+ align:start position:0%
+effective I got just last week I got my
+first solicitation this has been 10
+
+ align:start position:0%
+first solicitation this has been 10
+ 
+
+ align:start position:0%
+first solicitation this has been 10
+years to switch suppliers and because I
+
+ align:start position:0%
+years to switch suppliers and because I
+ 
+
+ align:start position:0%
+years to switch suppliers and because I
+believe in competition I did but so so
+
+ align:start position:0%
+believe in competition I did but so so
+ 
+
+ align:start position:0%
+believe in competition I did but so so
+there's enough retail competition that
+
+ align:start position:0%
+there's enough retail competition that
+ 
+
+ align:start position:0%
+there's enough retail competition that
+people people who don't own wires sold
+
+ align:start position:0%
+people people who don't own wires sold
+ 
+
+ align:start position:0%
+people people who don't own wires sold
+plus I thought I'd see what would happen
+
+ align:start position:0%
+plus I thought I'd see what would happen
+ 
+
+ align:start position:0%
+plus I thought I'd see what would happen
+plus uh people who don't own wires sold
+
+ align:start position:0%
+plus uh people who don't own wires sold
+ 
+
+ align:start position:0%
+plus uh people who don't own wires sold
+8% of the electricity in the company in
+
+ align:start position:0%
+8% of the electricity in the company in
+ 
+
+ align:start position:0%
+8% of the electricity in the company in
+the country in 200 I think these are
+
+ align:start position:0%
+the country in 200 I think these are
+ 
+
+ align:start position:0%
+the country in 200 I think these are
+2010 numbers that's a uh that's a big
+
+ align:start position:0%
+2010 numbers that's a uh that's a big
+ 
+
+ align:start position:0%
+2010 numbers that's a uh that's a big
+change that was Zero the bigger change
+
+ align:start position:0%
+change that was Zero the bigger change
+ 
+
+ align:start position:0%
+change that was Zero the bigger change
+is on the generation
+
+ align:start position:0%
+is on the generation
+ 
+
+ align:start position:0%
+is on the generation
+side so you have government systems and
+
+ align:start position:0%
+side so you have government systems and
+ 
+
+ align:start position:0%
+side so you have government systems and
+this is a big number 16% not all federal
+
+ align:start position:0%
+this is a big number 16% not all federal
+ 
+
+ align:start position:0%
+this is a big number 16% not all federal
+some State some municip Los Angeles for
+
+ align:start position:0%
+some State some municip Los Angeles for
+ 
+
+ align:start position:0%
+some State some municip Los Angeles for
+instance 16% investor owned utilities
+
+ align:start position:0%
+instance 16% investor owned utilities
+ 
+
+ align:start position:0%
+instance 16% investor owned utilities
+with retail sales 42% Independent
+
+ align:start position:0%
+with retail sales 42% Independent
+ 
+
+ align:start position:0%
+with retail sales 42% Independent
+Producers folks who have entered the
+
+ align:start position:0%
+Producers folks who have entered the
+ 
+
+ align:start position:0%
+Producers folks who have entered the
+wholesale Market who do not sell
+
+ align:start position:0%
+wholesale Market who do not sell
+ 
+
+ align:start position:0%
+wholesale Market who do not sell
+directly to retail customers 42% of
+
+ align:start position:0%
+directly to retail customers 42% of
+ 
+
+ align:start position:0%
+directly to retail customers 42% of
+generation so we have moved a fairly
+
+ align:start position:0%
+generation so we have moved a fairly
+ 
+
+ align:start position:0%
+generation so we have moved a fairly
+long way toward a market-based
+
+ align:start position:0%
+long way toward a market-based
+ 
+
+ align:start position:0%
+long way toward a market-based
+system but we're not quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
\ No newline at end of file
diff --git a/9KNmqar0Dd8.txt b/9KNmqar0Dd8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..155cdd2e04e3942247946a56e35584d0f68432fe
--- /dev/null
+++ b/9KNmqar0Dd8.txt
@@ -0,0 +1,18499 @@
+align:start position:0%
+ 
+so the topic is basically complete the
+
+ align:start position:0%
+so the topic is basically complete the
+ 
+
+ align:start position:0%
+so the topic is basically complete the
+title is complex traits what to believe
+
+ align:start position:0%
+title is complex traits what to believe
+ 
+
+ align:start position:0%
+title is complex traits what to believe
+which I think tries to get the gist of
+
+ align:start position:0%
+which I think tries to get the gist of
+ 
+
+ align:start position:0%
+which I think tries to get the gist of
+of the one of the main messages
+
+ align:start position:0%
+of the one of the main messages
+ 
+
+ align:start position:0%
+of the one of the main messages
+uh here and fit into the number of
+
+ align:start position:0%
+uh here and fit into the number of
+ 
+
+ align:start position:0%
+uh here and fit into the number of
+characters I'm allotted uh for a title
+
+ align:start position:0%
+characters I'm allotted uh for a title
+ 
+
+ align:start position:0%
+characters I'm allotted uh for a title
+of a lecture
+
+ align:start position:0%
+of a lecture
+ 
+
+ align:start position:0%
+of a lecture
+um and it basically uh has to do with uh
+
+ align:start position:0%
+um and it basically uh has to do with uh
+ 
+
+ align:start position:0%
+um and it basically uh has to do with uh
+current efforts in human genetics to
+
+ align:start position:0%
+current efforts in human genetics to
+ 
+
+ align:start position:0%
+current efforts in human genetics to
+understand uh the role that inherited
+
+ align:start position:0%
+understand uh the role that inherited
+ 
+
+ align:start position:0%
+understand uh the role that inherited
+DNA sequence variation plays in
+
+ align:start position:0%
+DNA sequence variation plays in
+ 
+
+ align:start position:0%
+DNA sequence variation plays in
+regulating what are called complex
+
+ align:start position:0%
+regulating what are called complex
+ 
+
+ align:start position:0%
+regulating what are called complex
+traits
+
+ align:start position:0%
+traits
+ 
+
+ align:start position:0%
+traits
+um and let me just go through all that
+
+ align:start position:0%
+um and let me just go through all that
+ 
+
+ align:start position:0%
+um and let me just go through all that
+so this is basically
+
+ align:start position:0%
+so this is basically
+ 
+
+ align:start position:0%
+so this is basically
+the plan for the uh
+
+ align:start position:0%
+the plan for the uh
+ 
+
+ align:start position:0%
+the plan for the uh
+talk at least as it stands now just give
+
+ align:start position:0%
+talk at least as it stands now just give
+ 
+
+ align:start position:0%
+talk at least as it stands now just give
+you a little bit of introduction into
+
+ align:start position:0%
+you a little bit of introduction into
+ 
+
+ align:start position:0%
+you a little bit of introduction into
+complex traits and common disease and
+
+ align:start position:0%
+complex traits and common disease and
+ 
+
+ align:start position:0%
+complex traits and common disease and
+how they relate to each other
+
+ align:start position:0%
+how they relate to each other
+ 
+
+ align:start position:0%
+how they relate to each other
+so here's a list of uh somewhat random
+
+ align:start position:0%
+so here's a list of uh somewhat random
+ 
+
+ align:start position:0%
+so here's a list of uh somewhat random
+list of diseases that you might see in a
+
+ align:start position:0%
+list of diseases that you might see in a
+ 
+
+ align:start position:0%
+list of diseases that you might see in a
+hospital or in a in a doctor's office
+
+ align:start position:0%
+hospital or in a in a doctor's office
+ 
+
+ align:start position:0%
+hospital or in a in a doctor's office
+and account for you know a lot of
+
+ align:start position:0%
+and account for you know a lot of
+ 
+
+ align:start position:0%
+and account for you know a lot of
+morbidity mortality and it turns out
+
+ align:start position:0%
+morbidity mortality and it turns out
+ 
+
+ align:start position:0%
+morbidity mortality and it turns out
+that most of these diseases cluster in
+
+ align:start position:0%
+that most of these diseases cluster in
+ 
+
+ align:start position:0%
+that most of these diseases cluster in
+families in ways that tell us that
+
+ align:start position:0%
+families in ways that tell us that
+ 
+
+ align:start position:0%
+families in ways that tell us that
+genetics plays a role in regulating who
+
+ align:start position:0%
+genetics plays a role in regulating who
+ 
+
+ align:start position:0%
+genetics plays a role in regulating who
+will and will not come down with these
+
+ align:start position:0%
+will and will not come down with these
+ 
+
+ align:start position:0%
+will and will not come down with these
+diseases same thing is true for things
+
+ align:start position:0%
+diseases same thing is true for things
+ 
+
+ align:start position:0%
+diseases same thing is true for things
+that aren't diseases but are
+
+ align:start position:0%
+that aren't diseases but are
+ 
+
+ align:start position:0%
+that aren't diseases but are
+quantitative traits that you can measure
+
+ align:start position:0%
+quantitative traits that you can measure
+ 
+
+ align:start position:0%
+quantitative traits that you can measure
+some of these however are very
+
+ align:start position:0%
+some of these however are very
+ 
+
+ align:start position:0%
+some of these however are very
+significant risk factors I list here
+
+ align:start position:0%
+significant risk factors I list here
+ 
+
+ align:start position:0%
+significant risk factors I list here
+just things that are relevant to
+
+ align:start position:0%
+just things that are relevant to
+ 
+
+ align:start position:0%
+just things that are relevant to
+Endocrinology which is one of my
+
+ align:start position:0%
+Endocrinology which is one of my
+ 
+
+ align:start position:0%
+Endocrinology which is one of my
+interests but you know things like blood
+
+ align:start position:0%
+interests but you know things like blood
+ 
+
+ align:start position:0%
+interests but you know things like blood
+pressure obviously if you have high
+
+ align:start position:0%
+pressure obviously if you have high
+ 
+
+ align:start position:0%
+pressure obviously if you have high
+blood pressure that's a huge risk factor
+
+ align:start position:0%
+blood pressure that's a huge risk factor
+ 
+
+ align:start position:0%
+blood pressure that's a huge risk factor
+for heart disease stroke et cetera et
+
+ align:start position:0%
+for heart disease stroke et cetera et
+ 
+
+ align:start position:0%
+for heart disease stroke et cetera et
+cetera increased obesity is a huge risk
+
+ align:start position:0%
+cetera increased obesity is a huge risk
+ 
+
+ align:start position:0%
+cetera increased obesity is a huge risk
+factor for death and diabetes and heart
+
+ align:start position:0%
+factor for death and diabetes and heart
+ 
+
+ align:start position:0%
+factor for death and diabetes and heart
+disease and many of these other things
+
+ align:start position:0%
+disease and many of these other things
+ 
+
+ align:start position:0%
+disease and many of these other things
+also have to do with future diseases and
+
+ align:start position:0%
+also have to do with future diseases and
+ 
+
+ align:start position:0%
+also have to do with future diseases and
+these also cluster in families in ways
+
+ align:start position:0%
+these also cluster in families in ways
+ 
+
+ align:start position:0%
+these also cluster in families in ways
+that tell us that genetics plays a role
+
+ align:start position:0%
+that tell us that genetics plays a role
+ 
+
+ align:start position:0%
+that tell us that genetics plays a role
+but for all of these whether it's
+
+ align:start position:0%
+but for all of these whether it's
+ 
+
+ align:start position:0%
+but for all of these whether it's
+disease susceptibility or the
+
+ align:start position:0%
+disease susceptibility or the
+ 
+
+ align:start position:0%
+disease susceptibility or the
+quantitative trait Illustrated here
+
+ align:start position:0%
+quantitative trait Illustrated here
+ 
+
+ align:start position:0%
+quantitative trait Illustrated here
+adult height
+
+ align:start position:0%
+adult height
+ 
+
+ align:start position:0%
+adult height
+um we know also from the way that they
+
+ align:start position:0%
+um we know also from the way that they
+ 
+
+ align:start position:0%
+um we know also from the way that they
+cluster in families that multiple genes
+
+ align:start position:0%
+cluster in families that multiple genes
+ 
+
+ align:start position:0%
+cluster in families that multiple genes
+are involved and furthermore that
+
+ align:start position:0%
+are involved and furthermore that
+ 
+
+ align:start position:0%
+are involved and furthermore that
+environmental and other non-genetic
+
+ align:start position:0%
+environmental and other non-genetic
+ 
+
+ align:start position:0%
+environmental and other non-genetic
+influences must play a role as well so
+
+ align:start position:0%
+influences must play a role as well so
+ 
+
+ align:start position:0%
+influences must play a role as well so
+this is not quite so simple a pictures
+
+ align:start position:0%
+this is not quite so simple a pictures
+ 
+
+ align:start position:0%
+this is not quite so simple a pictures
+for example trying to track down the
+
+ align:start position:0%
+for example trying to track down the
+ 
+
+ align:start position:0%
+for example trying to track down the
+gene that's responsible for Cystic
+
+ align:start position:0%
+gene that's responsible for Cystic
+ 
+
+ align:start position:0%
+gene that's responsible for Cystic
+Fibrosis or for Tay Sachs disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the goal uh that a lot of people
+
+ align:start position:0%
+and so the goal uh that a lot of people
+ 
+
+ align:start position:0%
+and so the goal uh that a lot of people
+in genetics have is to try to make this
+
+ align:start position:0%
+in genetics have is to try to make this
+ 
+
+ align:start position:0%
+in genetics have is to try to make this
+connection there's variation uh in the
+
+ align:start position:0%
+connection there's variation uh in the
+ 
+
+ align:start position:0%
+connection there's variation uh in the
+human genome which I'll talk quite
+
+ align:start position:0%
+human genome which I'll talk quite
+ 
+
+ align:start position:0%
+human genome which I'll talk quite
+extensively about and there's variation
+
+ align:start position:0%
+extensively about and there's variation
+ 
+
+ align:start position:0%
+extensively about and there's variation
+that we observe out in the world and we
+
+ align:start position:0%
+that we observe out in the world and we
+ 
+
+ align:start position:0%
+that we observe out in the world and we
+know there's a connection here and it's
+
+ align:start position:0%
+know there's a connection here and it's
+ 
+
+ align:start position:0%
+know there's a connection here and it's
+a question of making that connection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you compare genomes as again as
+
+ align:start position:0%
+and if you compare genomes as again as
+ 
+
+ align:start position:0%
+and if you compare genomes as again as
+I'll get to in a little bit
+
+ align:start position:0%
+I'll get to in a little bit
+ 
+
+ align:start position:0%
+I'll get to in a little bit
+I find that people are mostly uh the
+
+ align:start position:0%
+I find that people are mostly uh the
+ 
+
+ align:start position:0%
+I find that people are mostly uh the
+same but there are differences uh
+
+ align:start position:0%
+same but there are differences uh
+ 
+
+ align:start position:0%
+same but there are differences uh
+between every person and again most of
+
+ align:start position:0%
+between every person and again most of
+ 
+
+ align:start position:0%
+between every person and again most of
+these differences are random spelling
+
+ align:start position:0%
+these differences are random spelling
+ 
+
+ align:start position:0%
+these differences are random spelling
+differences in the in the genetic code
+
+ align:start position:0%
+differences in the in the genetic code
+ 
+
+ align:start position:0%
+differences in the in the genetic code
+that have no consequence but some of
+
+ align:start position:0%
+that have no consequence but some of
+ 
+
+ align:start position:0%
+that have no consequence but some of
+them do have biological consequences
+
+ align:start position:0%
+them do have biological consequences
+ 
+
+ align:start position:0%
+them do have biological consequences
+again the challenge is to figure out
+
+ align:start position:0%
+again the challenge is to figure out
+ 
+
+ align:start position:0%
+again the challenge is to figure out
+which one of these differences matter
+
+ align:start position:0%
+which one of these differences matter
+ 
+
+ align:start position:0%
+which one of these differences matter
+so I said that we know that genetics
+
+ align:start position:0%
+so I said that we know that genetics
+ 
+
+ align:start position:0%
+so I said that we know that genetics
+plays a role I just want to briefly get
+
+ align:start position:0%
+plays a role I just want to briefly get
+ 
+
+ align:start position:0%
+plays a role I just want to briefly get
+into how do we know that actually
+
+ align:start position:0%
+into how do we know that actually
+ 
+
+ align:start position:0%
+into how do we know that actually
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+one way is from something called twin
+
+ align:start position:0%
+one way is from something called twin
+ 
+
+ align:start position:0%
+one way is from something called twin
+studies I forgot the little English this
+
+ align:start position:0%
+studies I forgot the little English this
+ 
+
+ align:start position:0%
+studies I forgot the little English this
+is from some country music group that I
+
+ align:start position:0%
+is from some country music group that I
+ 
+
+ align:start position:0%
+is from some country music group that I
+have no affiliation with and have never
+
+ align:start position:0%
+have no affiliation with and have never
+ 
+
+ align:start position:0%
+have no affiliation with and have never
+heard called the Taylor Brothers but
+
+ align:start position:0%
+heard called the Taylor Brothers but
+ 
+
+ align:start position:0%
+heard called the Taylor Brothers but
+notable for the part of their
+
+ align:start position:0%
+notable for the part of their
+ 
+
+ align:start position:0%
+notable for the part of their
+uh promotions that their identical twins
+
+ align:start position:0%
+uh promotions that their identical twins
+ 
+
+ align:start position:0%
+uh promotions that their identical twins
+um and you know you can see things like
+
+ align:start position:0%
+um and you know you can see things like
+ 
+
+ align:start position:0%
+um and you know you can see things like
+they're you know they look the same
+
+ align:start position:0%
+they're you know they look the same
+ 
+
+ align:start position:0%
+they're you know they look the same
+they're about the same height I'm not
+
+ align:start position:0%
+they're about the same height I'm not
+ 
+
+ align:start position:0%
+they're about the same height I'm not
+sure whether you can tell whether they
+
+ align:start position:0%
+sure whether you can tell whether they
+ 
+
+ align:start position:0%
+sure whether you can tell whether they
+have the same preference in clothing or
+
+ align:start position:0%
+have the same preference in clothing or
+ 
+
+ align:start position:0%
+have the same preference in clothing or
+not from this but
+
+ align:start position:0%
+not from this but
+ 
+
+ align:start position:0%
+not from this but
+um you know they may have some of the
+
+ align:start position:0%
+um you know they may have some of the
+ 
+
+ align:start position:0%
+um you know they may have some of the
+same aptitude so and what you can do is
+
+ align:start position:0%
+same aptitude so and what you can do is
+ 
+
+ align:start position:0%
+same aptitude so and what you can do is
+you can do twin studies where you
+
+ align:start position:0%
+you can do twin studies where you
+ 
+
+ align:start position:0%
+you can do twin studies where you
+compare identical twins to twins who are
+
+ align:start position:0%
+compare identical twins to twins who are
+ 
+
+ align:start position:0%
+compare identical twins to twins who are
+uh what are called dizygotic twins
+
+ align:start position:0%
+uh what are called dizygotic twins
+ 
+
+ align:start position:0%
+uh what are called dizygotic twins
+basically what are also commonly called
+
+ align:start position:0%
+basically what are also commonly called
+ 
+
+ align:start position:0%
+basically what are also commonly called
+fraternal twins We compare same-sex
+
+ align:start position:0%
+fraternal twins We compare same-sex
+ 
+
+ align:start position:0%
+fraternal twins We compare same-sex
+fraternal twins and identical twins
+
+ align:start position:0%
+fraternal twins and identical twins
+ 
+
+ align:start position:0%
+fraternal twins and identical twins
+they're in theory raised in about the
+
+ align:start position:0%
+they're in theory raised in about the
+ 
+
+ align:start position:0%
+they're in theory raised in about the
+same amount of shared environments
+
+ align:start position:0%
+same amount of shared environments
+ 
+
+ align:start position:0%
+same amount of shared environments
+they're both raised in the same
+
+ align:start position:0%
+they're both raised in the same
+ 
+
+ align:start position:0%
+they're both raised in the same
+household and that's the thing but
+
+ align:start position:0%
+household and that's the thing but
+ 
+
+ align:start position:0%
+household and that's the thing but
+identical twins or monos they got a twin
+
+ align:start position:0%
+identical twins or monos they got a twin
+ 
+
+ align:start position:0%
+identical twins or monos they got a twin
+share 100 of their DNA whereas dizygotic
+
+ align:start position:0%
+share 100 of their DNA whereas dizygotic
+ 
+
+ align:start position:0%
+share 100 of their DNA whereas dizygotic
+twins share only 50 of their DNA they
+
+ align:start position:0%
+twins share only 50 of their DNA they
+ 
+
+ align:start position:0%
+twins share only 50 of their DNA they
+share the same as as siblings and so if
+
+ align:start position:0%
+share the same as as siblings and so if
+ 
+
+ align:start position:0%
+share the same as as siblings and so if
+there are things that are more
+
+ align:start position:0%
+there are things that are more
+ 
+
+ align:start position:0%
+there are things that are more
+concordant uh or more similar in
+
+ align:start position:0%
+concordant uh or more similar in
+ 
+
+ align:start position:0%
+concordant uh or more similar in
+monozygotic twins than in dizygotic
+
+ align:start position:0%
+monozygotic twins than in dizygotic
+ 
+
+ align:start position:0%
+monozygotic twins than in dizygotic
+twins the usual conclusion is is that
+
+ align:start position:0%
+twins the usual conclusion is is that
+ 
+
+ align:start position:0%
+twins the usual conclusion is is that
+genetics plays a role in that similarity
+
+ align:start position:0%
+genetics plays a role in that similarity
+ 
+
+ align:start position:0%
+genetics plays a role in that similarity
+so for example if you look at type 2
+
+ align:start position:0%
+so for example if you look at type 2
+ 
+
+ align:start position:0%
+so for example if you look at type 2
+diabetes if you look at non-zygotic
+
+ align:start position:0%
+diabetes if you look at non-zygotic
+ 
+
+ align:start position:0%
+diabetes if you look at non-zygotic
+twins and follow them over their
+
+ align:start position:0%
+twins and follow them over their
+ 
+
+ align:start position:0%
+twins and follow them over their
+lifetime there's at least an 80 percent
+
+ align:start position:0%
+lifetime there's at least an 80 percent
+ 
+
+ align:start position:0%
+lifetime there's at least an 80 percent
+and some people think it's actually
+
+ align:start position:0%
+and some people think it's actually
+ 
+
+ align:start position:0%
+and some people think it's actually
+close to 100 concordance rate what that
+
+ align:start position:0%
+close to 100 concordance rate what that
+ 
+
+ align:start position:0%
+close to 100 concordance rate what that
+means is actually sort of striking which
+
+ align:start position:0%
+means is actually sort of striking which
+ 
+
+ align:start position:0%
+means is actually sort of striking which
+means that if
+
+ align:start position:0%
+means that if
+ 
+
+ align:start position:0%
+means that if
+um that there is a particular set of
+
+ align:start position:0%
+um that there is a particular set of
+ 
+
+ align:start position:0%
+um that there is a particular set of
+genotypes which is incredibly predictive
+
+ align:start position:0%
+genotypes which is incredibly predictive
+ 
+
+ align:start position:0%
+genotypes which is incredibly predictive
+of getting diabetes yes thank you sorry
+
+ align:start position:0%
+of getting diabetes yes thank you sorry
+ 
+
+ align:start position:0%
+of getting diabetes yes thank you sorry
+I found a I found a I found a little
+
+ align:start position:0%
+I found a I found a I found a little
+ 
+
+ align:start position:0%
+I found a I found a I found a little
+cable so uh one right one and one wrong
+
+ align:start position:0%
+cable so uh one right one and one wrong
+ 
+
+ align:start position:0%
+cable so uh one right one and one wrong
+one so I am all right
+
+ align:start position:0%
+one so I am all right
+ 
+
+ align:start position:0%
+one so I am all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+whereas if you look at dizygotic twins
+
+ align:start position:0%
+whereas if you look at dizygotic twins
+ 
+
+ align:start position:0%
+whereas if you look at dizygotic twins
+there's a lot of concordance and part of
+
+ align:start position:0%
+there's a lot of concordance and part of
+ 
+
+ align:start position:0%
+there's a lot of concordance and part of
+that is because they share 50 of their
+
+ align:start position:0%
+that is because they share 50 of their
+ 
+
+ align:start position:0%
+that is because they share 50 of their
+genetic material and part of it's
+
+ align:start position:0%
+genetic material and part of it's
+ 
+
+ align:start position:0%
+genetic material and part of it's
+probably because they share the
+
+ align:start position:0%
+probably because they share the
+ 
+
+ align:start position:0%
+probably because they share the
+environment that they shared but they
+
+ align:start position:0%
+environment that they shared but they
+ 
+
+ align:start position:0%
+environment that they shared but they
+concentrate is much much higher for
+
+ align:start position:0%
+concentrate is much much higher for
+ 
+
+ align:start position:0%
+concentrate is much much higher for
+monozygotic twins so that says that
+
+ align:start position:0%
+monozygotic twins so that says that
+ 
+
+ align:start position:0%
+monozygotic twins so that says that
+there's uh a strong genetic influence
+
+ align:start position:0%
+there's uh a strong genetic influence
+ 
+
+ align:start position:0%
+there's uh a strong genetic influence
+and you can do other studies that don't
+
+ align:start position:0%
+and you can do other studies that don't
+ 
+
+ align:start position:0%
+and you can do other studies that don't
+depend on twin studies and you can also
+
+ align:start position:0%
+depend on twin studies and you can also
+ 
+
+ align:start position:0%
+depend on twin studies and you can also
+do twin studies where they're
+
+ align:start position:0%
+do twin studies where they're
+ 
+
+ align:start position:0%
+do twin studies where they're
+monosygotic twins reared apart but those
+
+ align:start position:0%
+monosygotic twins reared apart but those
+ 
+
+ align:start position:0%
+monosygotic twins reared apart but those
+are much less common but basically
+
+ align:start position:0%
+are much less common but basically
+ 
+
+ align:start position:0%
+are much less common but basically
+family studies where you look at if
+
+ align:start position:0%
+family studies where you look at if
+ 
+
+ align:start position:0%
+family studies where you look at if
+somebody has diabetes what's the risk to
+
+ align:start position:0%
+somebody has diabetes what's the risk to
+ 
+
+ align:start position:0%
+somebody has diabetes what's the risk to
+their sibling for getting diabetes as
+
+ align:start position:0%
+their sibling for getting diabetes as
+ 
+
+ align:start position:0%
+their sibling for getting diabetes as
+opposed to the risk of somebody next
+
+ align:start position:0%
+opposed to the risk of somebody next
+ 
+
+ align:start position:0%
+opposed to the risk of somebody next
+door for example and again it's much
+
+ align:start position:0%
+door for example and again it's much
+ 
+
+ align:start position:0%
+door for example and again it's much
+greater for siblings than it is for uh
+
+ align:start position:0%
+greater for siblings than it is for uh
+ 
+
+ align:start position:0%
+greater for siblings than it is for uh
+the general population that's something
+
+ align:start position:0%
+the general population that's something
+ 
+
+ align:start position:0%
+the general population that's something
+that ratio is something called Lambda s
+
+ align:start position:0%
+that ratio is something called Lambda s
+ 
+
+ align:start position:0%
+that ratio is something called Lambda s
+and you can estimate also something
+
+ align:start position:0%
+and you can estimate also something
+ 
+
+ align:start position:0%
+and you can estimate also something
+called heritability which is uh purports
+
+ align:start position:0%
+called heritability which is uh purports
+ 
+
+ align:start position:0%
+called heritability which is uh purports
+to be the percentage of variation that's
+
+ align:start position:0%
+to be the percentage of variation that's
+ 
+
+ align:start position:0%
+to be the percentage of variation that's
+attributable to genetic factors and
+
+ align:start position:0%
+attributable to genetic factors and
+ 
+
+ align:start position:0%
+attributable to genetic factors and
+actually certain types of genetic
+
+ align:start position:0%
+actually certain types of genetic
+ 
+
+ align:start position:0%
+actually certain types of genetic
+factors
+
+ align:start position:0%
+factors
+ 
+
+ align:start position:0%
+factors
+okay so that's basically an introduction
+
+ align:start position:0%
+okay so that's basically an introduction
+ 
+
+ align:start position:0%
+okay so that's basically an introduction
+so these their most common diseases are
+
+ align:start position:0%
+so these their most common diseases are
+ 
+
+ align:start position:0%
+so these their most common diseases are
+these complex genetic traits where we
+
+ align:start position:0%
+these complex genetic traits where we
+ 
+
+ align:start position:0%
+these complex genetic traits where we
+know genes play a role and we also know
+
+ align:start position:0%
+know genes play a role and we also know
+ 
+
+ align:start position:0%
+know genes play a role and we also know
+from those family studies they don't
+
+ align:start position:0%
+from those family studies they don't
+ 
+
+ align:start position:0%
+from those family studies they don't
+just segregate in a simple pattern where
+
+ align:start position:0%
+just segregate in a simple pattern where
+ 
+
+ align:start position:0%
+just segregate in a simple pattern where
+you know if the father if the father has
+
+ align:start position:0%
+you know if the father if the father has
+ 
+
+ align:start position:0%
+you know if the father if the father has
+it half of the children will have it and
+
+ align:start position:0%
+it half of the children will have it and
+ 
+
+ align:start position:0%
+it half of the children will have it and
+the half of their children will have it
+
+ align:start position:0%
+the half of their children will have it
+ 
+
+ align:start position:0%
+the half of their children will have it
+Etc and or in a simple recessive pattern
+
+ align:start position:0%
+Etc and or in a simple recessive pattern
+ 
+
+ align:start position:0%
+Etc and or in a simple recessive pattern
+but it's clearly multifactorial
+
+ align:start position:0%
+but it's clearly multifactorial
+ 
+
+ align:start position:0%
+but it's clearly multifactorial
+so the next section is basically uh why
+
+ align:start position:0%
+so the next section is basically uh why
+ 
+
+ align:start position:0%
+so the next section is basically uh why
+we think that there might be a
+
+ align:start position:0%
+we think that there might be a
+ 
+
+ align:start position:0%
+we think that there might be a
+connection between common genetic
+
+ align:start position:0%
+connection between common genetic
+ 
+
+ align:start position:0%
+connection between common genetic
+variation and these common diseases
+
+ align:start position:0%
+variation and these common diseases
+ 
+
+ align:start position:0%
+variation and these common diseases
+so this is a stretch of a genome I think
+
+ align:start position:0%
+so this is a stretch of a genome I think
+ 
+
+ align:start position:0%
+so this is a stretch of a genome I think
+I borrowed this from
+
+ align:start position:0%
+I borrowed this from
+ 
+
+ align:start position:0%
+I borrowed this from
+David alshell or Eric Lander I'm not
+
+ align:start position:0%
+David alshell or Eric Lander I'm not
+ 
+
+ align:start position:0%
+David alshell or Eric Lander I'm not
+sure uh and this is what genetic
+
+ align:start position:0%
+sure uh and this is what genetic
+ 
+
+ align:start position:0%
+sure uh and this is what genetic
+variation looks like okay so you have a
+
+ align:start position:0%
+variation looks like okay so you have a
+ 
+
+ align:start position:0%
+variation looks like okay so you have a
+long stretch here and if you compare two
+
+ align:start position:0%
+long stretch here and if you compare two
+ 
+
+ align:start position:0%
+long stretch here and if you compare two
+stretches taken from different people
+
+ align:start position:0%
+stretches taken from different people
+ 
+
+ align:start position:0%
+stretches taken from different people
+you'll find that there's a one place
+
+ align:start position:0%
+you'll find that there's a one place
+ 
+
+ align:start position:0%
+you'll find that there's a one place
+here and one place here where maybe they
+
+ align:start position:0%
+here and one place here where maybe they
+ 
+
+ align:start position:0%
+here and one place here where maybe they
+differ
+
+ align:start position:0%
+differ
+ 
+
+ align:start position:0%
+differ
+okay and most of those variants change a
+
+ align:start position:0%
+okay and most of those variants change a
+ 
+
+ align:start position:0%
+okay and most of those variants change a
+single nucleotide or single DNA letter
+
+ align:start position:0%
+single nucleotide or single DNA letter
+ 
+
+ align:start position:0%
+single nucleotide or single DNA letter
+it's called therefore single nucleotide
+
+ align:start position:0%
+it's called therefore single nucleotide
+ 
+
+ align:start position:0%
+it's called therefore single nucleotide
+polymorphism
+
+ align:start position:0%
+polymorphism
+ 
+
+ align:start position:0%
+polymorphism
+um and uh means many forms or in this
+
+ align:start position:0%
+um and uh means many forms or in this
+ 
+
+ align:start position:0%
+um and uh means many forms or in this
+case would be just two forms or a snip
+
+ align:start position:0%
+case would be just two forms or a snip
+ 
+
+ align:start position:0%
+case would be just two forms or a snip
+for short and what you might find is
+
+ align:start position:0%
+for short and what you might find is
+ 
+
+ align:start position:0%
+for short and what you might find is
+there's a stretch of DNA where
+
+ align:start position:0%
+there's a stretch of DNA where
+ 
+
+ align:start position:0%
+there's a stretch of DNA where
+everybody's the same and then if this
+
+ align:start position:0%
+everybody's the same and then if this
+ 
+
+ align:start position:0%
+everybody's the same and then if this
+nucleotide some people have a c and some
+
+ align:start position:0%
+nucleotide some people have a c and some
+ 
+
+ align:start position:0%
+nucleotide some people have a c and some
+people have a t and what we want to know
+
+ align:start position:0%
+people have a t and what we want to know
+ 
+
+ align:start position:0%
+people have a t and what we want to know
+is of all these different genetic
+
+ align:start position:0%
+is of all these different genetic
+ 
+
+ align:start position:0%
+is of all these different genetic
+variants which ones are going to be the
+
+ align:start position:0%
+variants which ones are going to be the
+ 
+
+ align:start position:0%
+variants which ones are going to be the
+ones that are going to affect things
+
+ align:start position:0%
+ones that are going to affect things
+ 
+
+ align:start position:0%
+ones that are going to affect things
+that we care about so you know here's
+
+ align:start position:0%
+that we care about so you know here's
+ 
+
+ align:start position:0%
+that we care about so you know here's
+something that we should all be
+
+ align:start position:0%
+something that we should all be
+ 
+
+ align:start position:0%
+something that we should all be
+passionate about in the next few months
+
+ align:start position:0%
+passionate about in the next few months
+ 
+
+ align:start position:0%
+passionate about in the next few months
+um so you know whether you're you know
+
+ align:start position:0%
+um so you know whether you're you know
+ 
+
+ align:start position:0%
+um so you know whether you're you know
+happy or sad that A-Rod went to the
+
+ align:start position:0%
+happy or sad that A-Rod went to the
+ 
+
+ align:start position:0%
+happy or sad that A-Rod went to the
+Yankees or something like that but no in
+
+ align:start position:0%
+Yankees or something like that but no in
+ 
+
+ align:start position:0%
+Yankees or something like that but no in
+seriousness you know if this were you
+
+ align:start position:0%
+seriousness you know if this were you
+ 
+
+ align:start position:0%
+seriousness you know if this were you
+know healthy and disease not to say
+
+ align:start position:0%
+know healthy and disease not to say
+ 
+
+ align:start position:0%
+know healthy and disease not to say
+which is which here
+
+ align:start position:0%
+which is which here
+ 
+
+ align:start position:0%
+which is which here
+um then we would be interested to see
+
+ align:start position:0%
+um then we would be interested to see
+ 
+
+ align:start position:0%
+um then we would be interested to see
+which variants track along with disease
+
+ align:start position:0%
+which variants track along with disease
+ 
+
+ align:start position:0%
+which variants track along with disease
+and that's going to be the general gist
+
+ align:start position:0%
+and that's going to be the general gist
+ 
+
+ align:start position:0%
+and that's going to be the general gist
+of what what people are trying to do
+
+ align:start position:0%
+of what what people are trying to do
+ 
+
+ align:start position:0%
+of what what people are trying to do
+so I said that there's a connection
+
+ align:start position:0%
+so I said that there's a connection
+ 
+
+ align:start position:0%
+so I said that there's a connection
+between common variants and disease and
+
+ align:start position:0%
+between common variants and disease and
+ 
+
+ align:start position:0%
+between common variants and disease and
+so one question is why why might we be
+
+ align:start position:0%
+so one question is why why might we be
+ 
+
+ align:start position:0%
+so one question is why why might we be
+interested in common variants and if you
+
+ align:start position:0%
+interested in common variants and if you
+ 
+
+ align:start position:0%
+interested in common variants and if you
+think about it before you begin
+
+ align:start position:0%
+think about it before you begin
+ 
+
+ align:start position:0%
+think about it before you begin
+what's known so far about genetic
+
+ align:start position:0%
+what's known so far about genetic
+ 
+
+ align:start position:0%
+what's known so far about genetic
+disease you might say well that's kind
+
+ align:start position:0%
+disease you might say well that's kind
+ 
+
+ align:start position:0%
+disease you might say well that's kind
+of the wrong place to look because if
+
+ align:start position:0%
+of the wrong place to look because if
+ 
+
+ align:start position:0%
+of the wrong place to look because if
+you look at things like Tay Sachs or
+
+ align:start position:0%
+you look at things like Tay Sachs or
+ 
+
+ align:start position:0%
+you look at things like Tay Sachs or
+cystic fibrosis
+
+ align:start position:0%
+cystic fibrosis
+ 
+
+ align:start position:0%
+cystic fibrosis
+um those are mostly caused uh by genetic
+
+ align:start position:0%
+um those are mostly caused uh by genetic
+ 
+
+ align:start position:0%
+um those are mostly caused uh by genetic
+variants they're quite rare in the
+
+ align:start position:0%
+variants they're quite rare in the
+ 
+
+ align:start position:0%
+variants they're quite rare in the
+population they're severe uh deleterious
+
+ align:start position:0%
+population they're severe uh deleterious
+ 
+
+ align:start position:0%
+population they're severe uh deleterious
+mutations that cause these severe
+
+ align:start position:0%
+mutations that cause these severe
+ 
+
+ align:start position:0%
+mutations that cause these severe
+diseases so if those genetic diseases
+
+ align:start position:0%
+diseases so if those genetic diseases
+ 
+
+ align:start position:0%
+diseases so if those genetic diseases
+are caused by Rare variants why wouldn't
+
+ align:start position:0%
+are caused by Rare variants why wouldn't
+ 
+
+ align:start position:0%
+are caused by Rare variants why wouldn't
+things like diabetes be caused by Rare
+
+ align:start position:0%
+things like diabetes be caused by Rare
+ 
+
+ align:start position:0%
+things like diabetes be caused by Rare
+variants and there's an open question
+
+ align:start position:0%
+variants and there's an open question
+ 
+
+ align:start position:0%
+variants and there's an open question
+I'll get into that but let me just take
+
+ align:start position:0%
+I'll get into that but let me just take
+ 
+
+ align:start position:0%
+I'll get into that but let me just take
+you through at least some of the
+
+ align:start position:0%
+you through at least some of the
+ 
+
+ align:start position:0%
+you through at least some of the
+background
+
+ align:start position:0%
+background
+ 
+
+ align:start position:0%
+background
+so I showed you earlier that if you
+
+ align:start position:0%
+so I showed you earlier that if you
+ 
+
+ align:start position:0%
+so I showed you earlier that if you
+sequence a stretch of genome imagine
+
+ align:start position:0%
+sequence a stretch of genome imagine
+ 
+
+ align:start position:0%
+sequence a stretch of genome imagine
+this is about a thousand bases from two
+
+ align:start position:0%
+this is about a thousand bases from two
+ 
+
+ align:start position:0%
+this is about a thousand bases from two
+different chromosomes it could be two
+
+ align:start position:0%
+different chromosomes it could be two
+ 
+
+ align:start position:0%
+different chromosomes it could be two
+chromosomes from the same person or it
+
+ align:start position:0%
+chromosomes from the same person or it
+ 
+
+ align:start position:0%
+chromosomes from the same person or it
+could be one chromosome from somebody
+
+ align:start position:0%
+could be one chromosome from somebody
+ 
+
+ align:start position:0%
+could be one chromosome from somebody
+here and one chromosome from somebody
+
+ align:start position:0%
+here and one chromosome from somebody
+ 
+
+ align:start position:0%
+here and one chromosome from somebody
+around the world you get the same answer
+
+ align:start position:0%
+around the world you get the same answer
+ 
+
+ align:start position:0%
+around the world you get the same answer
+more or less which is that on average
+
+ align:start position:0%
+more or less which is that on average
+ 
+
+ align:start position:0%
+more or less which is that on average
+you'd see about one every 1200 bases
+
+ align:start position:0%
+you'd see about one every 1200 bases
+ 
+
+ align:start position:0%
+you'd see about one every 1200 bases
+would be different
+
+ align:start position:0%
+would be different
+ 
+
+ align:start position:0%
+would be different
+you can then ask the question well
+
+ align:start position:0%
+you can then ask the question well
+ 
+
+ align:start position:0%
+you can then ask the question well
+having identified these two alleles the
+
+ align:start position:0%
+having identified these two alleles the
+ 
+
+ align:start position:0%
+having identified these two alleles the
+C allele and the a allele
+
+ align:start position:0%
+C allele and the a allele
+ 
+
+ align:start position:0%
+C allele and the a allele
+if I then look in the same thousand
+
+ align:start position:0%
+if I then look in the same thousand
+ 
+
+ align:start position:0%
+if I then look in the same thousand
+bases at lots of other chromosomes is it
+
+ align:start position:0%
+bases at lots of other chromosomes is it
+ 
+
+ align:start position:0%
+bases at lots of other chromosomes is it
+that this allele or maybe this C allele
+
+ align:start position:0%
+that this allele or maybe this C allele
+ 
+
+ align:start position:0%
+that this allele or maybe this C allele
+is just a really unique event that's
+
+ align:start position:0%
+is just a really unique event that's
+ 
+
+ align:start position:0%
+is just a really unique event that's
+private to one of these chromosomes or
+
+ align:start position:0%
+private to one of these chromosomes or
+ 
+
+ align:start position:0%
+private to one of these chromosomes or
+do I see both alleles uh around the
+
+ align:start position:0%
+do I see both alleles uh around the
+ 
+
+ align:start position:0%
+do I see both alleles uh around the
+whole world
+
+ align:start position:0%
+whole world
+ 
+
+ align:start position:0%
+whole world
+um and the answer most of the time about
+
+ align:start position:0%
+um and the answer most of the time about
+ 
+
+ align:start position:0%
+um and the answer most of the time about
+90 of the time is that you see both
+
+ align:start position:0%
+90 of the time is that you see both
+ 
+
+ align:start position:0%
+90 of the time is that you see both
+alleles around the world and so what
+
+ align:start position:0%
+alleles around the world and so what
+ 
+
+ align:start position:0%
+alleles around the world and so what
+that means is that most of the
+
+ align:start position:0%
+that means is that most of the
+ 
+
+ align:start position:0%
+that means is that most of the
+differences that you can find between
+
+ align:start position:0%
+differences that you can find between
+ 
+
+ align:start position:0%
+differences that you can find between
+two chromosomes are explainable or
+
+ align:start position:0%
+two chromosomes are explainable or
+ 
+
+ align:start position:0%
+two chromosomes are explainable or
+attributable to the variation that those
+
+ align:start position:0%
+attributable to the variation that those
+ 
+
+ align:start position:0%
+attributable to the variation that those
+variants that are common that are shared
+
+ align:start position:0%
+variants that are common that are shared
+ 
+
+ align:start position:0%
+variants that are common that are shared
+throughout the world that are not like
+
+ align:start position:0%
+throughout the world that are not like
+ 
+
+ align:start position:0%
+throughout the world that are not like
+the tay-sax mutations but they're
+
+ align:start position:0%
+the tay-sax mutations but they're
+ 
+
+ align:start position:0%
+the tay-sax mutations but they're
+actually old variants that happened a
+
+ align:start position:0%
+actually old variants that happened a
+ 
+
+ align:start position:0%
+actually old variants that happened a
+long time ago and are present in
+
+ align:start position:0%
+long time ago and are present in
+ 
+
+ align:start position:0%
+long time ago and are present in
+multiple populations around the world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right and that's basically what that
+
+ align:start position:0%
+so right and that's basically what that
+ 
+
+ align:start position:0%
+so right and that's basically what that
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+and so this has led to a hypothesis so
+
+ align:start position:0%
+and so this has led to a hypothesis so
+ 
+
+ align:start position:0%
+and so this has led to a hypothesis so
+the assumptions are as follows first of
+
+ align:start position:0%
+the assumptions are as follows first of
+ 
+
+ align:start position:0%
+the assumptions are as follows first of
+all that most variation in the genome is
+
+ align:start position:0%
+all that most variation in the genome is
+ 
+
+ align:start position:0%
+all that most variation in the genome is
+evolutionarily neutral that actually may
+
+ align:start position:0%
+evolutionarily neutral that actually may
+ 
+
+ align:start position:0%
+evolutionarily neutral that actually may
+or may not be true but it for it
+
+ align:start position:0%
+or may not be true but it for it
+ 
+
+ align:start position:0%
+or may not be true but it for it
+actually whether that uh as long as it's
+
+ align:start position:0%
+actually whether that uh as long as it's
+ 
+
+ align:start position:0%
+actually whether that uh as long as it's
+not most Evolution most variation is
+
+ align:start position:0%
+not most Evolution most variation is
+ 
+
+ align:start position:0%
+not most Evolution most variation is
+evolutionarily beneficial we're okay but
+
+ align:start position:0%
+evolutionarily beneficial we're okay but
+ 
+
+ align:start position:0%
+evolutionarily beneficial we're okay but
+let's assume there's some background uh
+
+ align:start position:0%
+let's assume there's some background uh
+ 
+
+ align:start position:0%
+let's assume there's some background uh
+for the for the genome
+
+ align:start position:0%
+for the for the genome
+ 
+
+ align:start position:0%
+for the for the genome
+um so that you know you have a snip
+
+ align:start position:0%
+um so that you know you have a snip
+ 
+
+ align:start position:0%
+um so that you know you have a snip
+that's you know
+
+ align:start position:0%
+that's you know
+ 
+
+ align:start position:0%
+that's you know
+22 KB away from the nearest Gene and
+
+ align:start position:0%
+22 KB away from the nearest Gene and
+ 
+
+ align:start position:0%
+22 KB away from the nearest Gene and
+probably doesn't affect the function of
+
+ align:start position:0%
+probably doesn't affect the function of
+ 
+
+ align:start position:0%
+probably doesn't affect the function of
+that Gene at all let's assume that
+
+ align:start position:0%
+that Gene at all let's assume that
+ 
+
+ align:start position:0%
+that Gene at all let's assume that
+evolution is not particularly cared
+
+ align:start position:0%
+evolution is not particularly cared
+ 
+
+ align:start position:0%
+evolution is not particularly cared
+about that that base change
+
+ align:start position:0%
+about that that base change
+ 
+
+ align:start position:0%
+about that that base change
+we know that most of this variation most
+
+ align:start position:0%
+we know that most of this variation most
+ 
+
+ align:start position:0%
+we know that most of this variation most
+of the background variations probably
+
+ align:start position:0%
+of the background variations probably
+ 
+
+ align:start position:0%
+of the background variations probably
+what you call this rather than neutral
+
+ align:start position:0%
+what you call this rather than neutral
+ 
+
+ align:start position:0%
+what you call this rather than neutral
+is due to these common variants that's
+
+ align:start position:0%
+is due to these common variants that's
+ 
+
+ align:start position:0%
+is due to these common variants that's
+what I just showed you that 90 of that
+
+ align:start position:0%
+what I just showed you that 90 of that
+ 
+
+ align:start position:0%
+what I just showed you that 90 of that
+variation is due to the common variance
+
+ align:start position:0%
+variation is due to the common variance
+ 
+
+ align:start position:0%
+variation is due to the common variance
+we know also what I've been telling with
+
+ align:start position:0%
+we know also what I've been telling with
+ 
+
+ align:start position:0%
+we know also what I've been telling with
+the Tay Sachs disease that traits under
+
+ align:start position:0%
+the Tay Sachs disease that traits under
+ 
+
+ align:start position:0%
+the Tay Sachs disease that traits under
+negative selection will in fact be
+
+ align:start position:0%
+negative selection will in fact be
+ 
+
+ align:start position:0%
+negative selection will in fact be
+largely due to rare variants and there's
+
+ align:start position:0%
+largely due to rare variants and there's
+ 
+
+ align:start position:0%
+largely due to rare variants and there's
+a nice description of why this should be
+
+ align:start position:0%
+a nice description of why this should be
+ 
+
+ align:start position:0%
+a nice description of why this should be
+true in an article by Jonathan Pritchard
+
+ align:start position:0%
+true in an article by Jonathan Pritchard
+ 
+
+ align:start position:0%
+true in an article by Jonathan Pritchard
+well there's a hypothesis the traits are
+
+ align:start position:0%
+well there's a hypothesis the traits are
+ 
+
+ align:start position:0%
+well there's a hypothesis the traits are
+that are not under negative selection or
+
+ align:start position:0%
+that are not under negative selection or
+ 
+
+ align:start position:0%
+that are not under negative selection or
+at least not under severe negative
+
+ align:start position:0%
+at least not under severe negative
+ 
+
+ align:start position:0%
+at least not under severe negative
+selection will actually be
+
+ align:start position:0%
+selection will actually be
+ 
+
+ align:start position:0%
+selection will actually be
+due to variants that look more like the
+
+ align:start position:0%
+due to variants that look more like the
+ 
+
+ align:start position:0%
+due to variants that look more like the
+background so that our common variants
+
+ align:start position:0%
+background so that our common variants
+ 
+
+ align:start position:0%
+background so that our common variants
+um and so this is what's called the
+
+ align:start position:0%
+um and so this is what's called the
+ 
+
+ align:start position:0%
+um and so this is what's called the
+common disease common variant hypothesis
+
+ align:start position:0%
+common disease common variant hypothesis
+ 
+
+ align:start position:0%
+common disease common variant hypothesis
+and one of the more forceful I would say
+
+ align:start position:0%
+and one of the more forceful I would say
+ 
+
+ align:start position:0%
+and one of the more forceful I would say
+uh descriptions of it is a paper
+
+ align:start position:0%
+uh descriptions of it is a paper
+ 
+
+ align:start position:0%
+uh descriptions of it is a paper
+vibration Lander Trends in genetics 2002
+
+ align:start position:0%
+vibration Lander Trends in genetics 2002
+ 
+
+ align:start position:0%
+vibration Lander Trends in genetics 2002
+and the idea for why common diseases
+
+ align:start position:0%
+and the idea for why common diseases
+ 
+
+ align:start position:0%
+and the idea for why common diseases
+might be like might be have be due to
+
+ align:start position:0%
+might be like might be have be due to
+ 
+
+ align:start position:0%
+might be like might be have be due to
+alleles that are not under severe
+
+ align:start position:0%
+alleles that are not under severe
+ 
+
+ align:start position:0%
+alleles that are not under severe
+negative selection goes like this first
+
+ align:start position:0%
+negative selection goes like this first
+ 
+
+ align:start position:0%
+negative selection goes like this first
+of all
+
+ align:start position:0%
+of all
+ 
+
+ align:start position:0%
+of all
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they're actually common so in some sense
+
+ align:start position:0%
+they're actually common so in some sense
+ 
+
+ align:start position:0%
+they're actually common so in some sense
+it sounds taught logical but it's
+
+ align:start position:0%
+it sounds taught logical but it's
+ 
+
+ align:start position:0%
+it sounds taught logical but it's
+actually not
+
+ align:start position:0%
+actually not
+ 
+
+ align:start position:0%
+actually not
+they can't be that evolutionarily
+
+ align:start position:0%
+they can't be that evolutionarily
+ 
+
+ align:start position:0%
+they can't be that evolutionarily
+deleterious if they're extremely if
+
+ align:start position:0%
+deleterious if they're extremely if
+ 
+
+ align:start position:0%
+deleterious if they're extremely if
+they're extremely common that's one
+
+ align:start position:0%
+they're extremely common that's one
+ 
+
+ align:start position:0%
+they're extremely common that's one
+argument two is that they're
+
+ align:start position:0%
+argument two is that they're
+ 
+
+ align:start position:0%
+argument two is that they're
+multifactorial so each gene that
+
+ align:start position:0%
+multifactorial so each gene that
+ 
+
+ align:start position:0%
+multifactorial so each gene that
+contributes to these common diseases
+
+ align:start position:0%
+contributes to these common diseases
+ 
+
+ align:start position:0%
+contributes to these common diseases
+actually only contributes a little bit
+
+ align:start position:0%
+actually only contributes a little bit
+ 
+
+ align:start position:0%
+actually only contributes a little bit
+to susceptibility and that's going to be
+
+ align:start position:0%
+to susceptibility and that's going to be
+ 
+
+ align:start position:0%
+to susceptibility and that's going to be
+a theme that'll run through this whole
+
+ align:start position:0%
+a theme that'll run through this whole
+ 
+
+ align:start position:0%
+a theme that'll run through this whole
+talk so even if it were even if they
+
+ align:start position:0%
+talk so even if it were even if they
+ 
+
+ align:start position:0%
+talk so even if it were even if they
+were somewhat evolutionarily deleterious
+
+ align:start position:0%
+were somewhat evolutionarily deleterious
+ 
+
+ align:start position:0%
+were somewhat evolutionarily deleterious
+each individual allele would only be
+
+ align:start position:0%
+each individual allele would only be
+ 
+
+ align:start position:0%
+each individual allele would only be
+contributing a small fraction of that
+
+ align:start position:0%
+contributing a small fraction of that
+ 
+
+ align:start position:0%
+contributing a small fraction of that
+third is they often tend to be late
+
+ align:start position:0%
+third is they often tend to be late
+ 
+
+ align:start position:0%
+third is they often tend to be late
+onset or um you know so after
+
+ align:start position:0%
+onset or um you know so after
+ 
+
+ align:start position:0%
+onset or um you know so after
+reproductive age so again Evolution
+
+ align:start position:0%
+reproductive age so again Evolution
+ 
+
+ align:start position:0%
+reproductive age so again Evolution
+cares less about stuff like that and
+
+ align:start position:0%
+cares less about stuff like that and
+ 
+
+ align:start position:0%
+cares less about stuff like that and
+although we don't know maybe good to
+
+ align:start position:0%
+although we don't know maybe good to
+ 
+
+ align:start position:0%
+although we don't know maybe good to
+have had your grandfather around in
+
+ align:start position:0%
+have had your grandfather around in
+ 
+
+ align:start position:0%
+have had your grandfather around in
+Africa 50 000 years ago so it could be
+
+ align:start position:0%
+Africa 50 000 years ago so it could be
+ 
+
+ align:start position:0%
+Africa 50 000 years ago so it could be
+the late onset diseases were bad
+
+ align:start position:0%
+the late onset diseases were bad
+ 
+
+ align:start position:0%
+the late onset diseases were bad
+another thing is that it's been
+
+ align:start position:0%
+another thing is that it's been
+ 
+
+ align:start position:0%
+another thing is that it's been
+hypothesized that some of these diseases
+
+ align:start position:0%
+hypothesized that some of these diseases
+ 
+
+ align:start position:0%
+hypothesized that some of these diseases
+like hypertension or diabetes actually
+
+ align:start position:0%
+like hypertension or diabetes actually
+ 
+
+ align:start position:0%
+like hypertension or diabetes actually
+have what's called balancing selection
+
+ align:start position:0%
+have what's called balancing selection
+ 
+
+ align:start position:0%
+have what's called balancing selection
+which is that
+
+ align:start position:0%
+which is that
+ 
+
+ align:start position:0%
+which is that
+um yeah they give you diabetes late in
+
+ align:start position:0%
+um yeah they give you diabetes late in
+ 
+
+ align:start position:0%
+um yeah they give you diabetes late in
+life but the reason that they give you
+
+ align:start position:0%
+life but the reason that they give you
+ 
+
+ align:start position:0%
+life but the reason that they give you
+diabetes is because
+
+ align:start position:0%
+diabetes is because
+ 
+
+ align:start position:0%
+diabetes is because
+um they uh help make you uh hold on to
+
+ align:start position:0%
+um they uh help make you uh hold on to
+ 
+
+ align:start position:0%
+um they uh help make you uh hold on to
+calories better so that gives you
+
+ align:start position:0%
+calories better so that gives you
+ 
+
+ align:start position:0%
+calories better so that gives you
+obesity now when we have McDonald's
+
+ align:start position:0%
+obesity now when we have McDonald's
+ 
+
+ align:start position:0%
+obesity now when we have McDonald's
+around uh but uh you know 100 000 years
+
+ align:start position:0%
+around uh but uh you know 100 000 years
+ 
+
+ align:start position:0%
+around uh but uh you know 100 000 years
+ago when food was scarce maybe that was
+
+ align:start position:0%
+ago when food was scarce maybe that was
+ 
+
+ align:start position:0%
+ago when food was scarce maybe that was
+really good there's something called the
+
+ align:start position:0%
+really good there's something called the
+ 
+
+ align:start position:0%
+really good there's something called the
+Thrifty Gene hypothesis it's only for
+
+ align:start position:0%
+Thrifty Gene hypothesis it's only for
+ 
+
+ align:start position:0%
+Thrifty Gene hypothesis it's only for
+hypertension maybe it's good to hold on
+
+ align:start position:0%
+hypertension maybe it's good to hold on
+ 
+
+ align:start position:0%
+hypertension maybe it's good to hold on
+to Salt if you lived in a desert that
+
+ align:start position:0%
+to Salt if you lived in a desert that
+ 
+
+ align:start position:0%
+to Salt if you lived in a desert that
+sort of thing
+
+ align:start position:0%
+sort of thing
+ 
+
+ align:start position:0%
+sort of thing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if we're looking for a common variation
+
+ align:start position:0%
+if we're looking for a common variation
+ 
+
+ align:start position:0%
+if we're looking for a common variation
+um or thinking about that this may be a
+
+ align:start position:0%
+um or thinking about that this may be a
+ 
+
+ align:start position:0%
+um or thinking about that this may be a
+good place to look for the genetic
+
+ align:start position:0%
+good place to look for the genetic
+ 
+
+ align:start position:0%
+good place to look for the genetic
+variants that underlie common disease
+
+ align:start position:0%
+variants that underlie common disease
+ 
+
+ align:start position:0%
+variants that underlie common disease
+and again this is this hypothesis does
+
+ align:start position:0%
+and again this is this hypothesis does
+ 
+
+ align:start position:0%
+and again this is this hypothesis does
+not say that rare variation won't also
+
+ align:start position:0%
+not say that rare variation won't also
+ 
+
+ align:start position:0%
+not say that rare variation won't also
+contribute to common disease just as a
+
+ align:start position:0%
+contribute to common disease just as a
+ 
+
+ align:start position:0%
+contribute to common disease just as a
+common variation will be part of the
+
+ align:start position:0%
+common variation will be part of the
+ 
+
+ align:start position:0%
+common variation will be part of the
+contributors so if we're looking for it
+
+ align:start position:0%
+contributors so if we're looking for it
+ 
+
+ align:start position:0%
+contributors so if we're looking for it
+it's been estimated that there are about
+
+ align:start position:0%
+it's been estimated that there are about
+ 
+
+ align:start position:0%
+it's been estimated that there are about
+10 million common Snips within where
+
+ align:start position:0%
+10 million common Snips within where
+ 
+
+ align:start position:0%
+10 million common Snips within where
+both alleles are found at more than one
+
+ align:start position:0%
+both alleles are found at more than one
+ 
+
+ align:start position:0%
+both alleles are found at more than one
+percent in the general population
+
+ align:start position:0%
+percent in the general population
+ 
+
+ align:start position:0%
+percent in the general population
+about 6 million of those are actually
+
+ align:start position:0%
+about 6 million of those are actually
+ 
+
+ align:start position:0%
+about 6 million of those are actually
+already in databases so it's actually
+
+ align:start position:0%
+already in databases so it's actually
+ 
+
+ align:start position:0%
+already in databases so it's actually
+most a good fraction has been found and
+
+ align:start position:0%
+most a good fraction has been found and
+ 
+
+ align:start position:0%
+most a good fraction has been found and
+as you'll see there's a lot of
+
+ align:start position:0%
+as you'll see there's a lot of
+ 
+
+ align:start position:0%
+as you'll see there's a lot of
+redundancy between Snips so probably a
+
+ align:start position:0%
+redundancy between Snips so probably a
+ 
+
+ align:start position:0%
+redundancy between Snips so probably a
+very high fraction of the variation
+
+ align:start position:0%
+very high fraction of the variation
+ 
+
+ align:start position:0%
+very high fraction of the variation
+common variation The genome actually has
+
+ align:start position:0%
+common variation The genome actually has
+ 
+
+ align:start position:0%
+common variation The genome actually has
+been cataloged which is a remarkable
+
+ align:start position:0%
+been cataloged which is a remarkable
+ 
+
+ align:start position:0%
+been cataloged which is a remarkable
+thing when I started uh in this field in
+
+ align:start position:0%
+thing when I started uh in this field in
+ 
+
+ align:start position:0%
+thing when I started uh in this field in
+not very long ago I think six years ago
+
+ align:start position:0%
+not very long ago I think six years ago
+ 
+
+ align:start position:0%
+not very long ago I think six years ago
+there was a paper that came out of the
+
+ align:start position:0%
+there was a paper that came out of the
+ 
+
+ align:start position:0%
+there was a paper that came out of the
+Lander lab uh
+
+ align:start position:0%
+Lander lab uh
+ 
+
+ align:start position:0%
+Lander lab uh
+uh which is a massive tour de force
+
+ align:start position:0%
+uh which is a massive tour de force
+ 
+
+ align:start position:0%
+uh which is a massive tour de force
+cataloging cataloging 2 000 Snips across
+
+ align:start position:0%
+cataloging cataloging 2 000 Snips across
+ 
+
+ align:start position:0%
+cataloging cataloging 2 000 Snips across
+the genome and this you know quintuple
+
+ align:start position:0%
+the genome and this you know quintuple
+ 
+
+ align:start position:0%
+the genome and this you know quintuple
+the number of snips that were known okay
+
+ align:start position:0%
+the number of snips that were known okay
+ 
+
+ align:start position:0%
+the number of snips that were known okay
+so this is now this is three thousand
+
+ align:start position:0%
+so this is now this is three thousand
+ 
+
+ align:start position:0%
+so this is now this is three thousand
+times as many now and just in the last
+
+ align:start position:0%
+times as many now and just in the last
+ 
+
+ align:start position:0%
+times as many now and just in the last
+six years and you can find all of these
+
+ align:start position:0%
+six years and you can find all of these
+ 
+
+ align:start position:0%
+six years and you can find all of these
+in websites like dbsnap or the UCSC
+
+ align:start position:0%
+in websites like dbsnap or the UCSC
+ 
+
+ align:start position:0%
+in websites like dbsnap or the UCSC
+genome browser and CPI has a genome
+
+ align:start position:0%
+genome browser and CPI has a genome
+ 
+
+ align:start position:0%
+genome browser and CPI has a genome
+browser and they're uh all right there
+
+ align:start position:0%
+browser and they're uh all right there
+ 
+
+ align:start position:0%
+browser and they're uh all right there
+so this is a screenshot from the UCSC
+
+ align:start position:0%
+so this is a screenshot from the UCSC
+ 
+
+ align:start position:0%
+so this is a screenshot from the UCSC
+genome browser each one of these little
+
+ align:start position:0%
+genome browser each one of these little
+ 
+
+ align:start position:0%
+genome browser each one of these little
+lines is a snip and this is probably
+
+ align:start position:0%
+lines is a snip and this is probably
+ 
+
+ align:start position:0%
+lines is a snip and this is probably
+already out of date even though I took
+
+ align:start position:0%
+already out of date even though I took
+ 
+
+ align:start position:0%
+already out of date even though I took
+it not too long ago from the uh from
+
+ align:start position:0%
+it not too long ago from the uh from
+ 
+
+ align:start position:0%
+it not too long ago from the uh from
+there and this is just in one gene each
+
+ align:start position:0%
+there and this is just in one gene each
+ 
+
+ align:start position:0%
+there and this is just in one gene each
+of these are are on each of these two
+
+ align:start position:0%
+of these are are on each of these two
+ 
+
+ align:start position:0%
+of these are are on each of these two
+columns is a snip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+if we want to use this catalog of common
+
+ align:start position:0%
+if we want to use this catalog of common
+ 
+
+ align:start position:0%
+if we want to use this catalog of common
+variation to try to find the alleles
+
+ align:start position:0%
+variation to try to find the alleles
+ 
+
+ align:start position:0%
+variation to try to find the alleles
+that are responsible for disease
+
+ align:start position:0%
+that are responsible for disease
+ 
+
+ align:start position:0%
+that are responsible for disease
+how can we do that well one way would
+
+ align:start position:0%
+how can we do that well one way would
+ 
+
+ align:start position:0%
+how can we do that well one way would
+actually be just try to study every
+
+ align:start position:0%
+actually be just try to study every
+ 
+
+ align:start position:0%
+actually be just try to study every
+variant or at least every common variant
+
+ align:start position:0%
+variant or at least every common variant
+ 
+
+ align:start position:0%
+variant or at least every common variant
+this would be great it would be an
+
+ align:start position:0%
+this would be great it would be an
+ 
+
+ align:start position:0%
+this would be great it would be an
+unbiased search of the entire genome
+
+ align:start position:0%
+unbiased search of the entire genome
+ 
+
+ align:start position:0%
+unbiased search of the entire genome
+basically the entire universe of common
+
+ align:start position:0%
+basically the entire universe of common
+ 
+
+ align:start position:0%
+basically the entire universe of common
+variation
+
+ align:start position:0%
+variation
+ 
+
+ align:start position:0%
+variation
+and this we would this would be great if
+
+ align:start position:0%
+and this we would this would be great if
+ 
+
+ align:start position:0%
+and this we would this would be great if
+we could do it but it's not currently
+
+ align:start position:0%
+we could do it but it's not currently
+ 
+
+ align:start position:0%
+we could do it but it's not currently
+practical 10 million people sorry 10
+
+ align:start position:0%
+practical 10 million people sorry 10
+ 
+
+ align:start position:0%
+practical 10 million people sorry 10
+million variants and as I'll show you
+
+ align:start position:0%
+million variants and as I'll show you
+ 
+
+ align:start position:0%
+million variants and as I'll show you
+you need many thousands of people to do
+
+ align:start position:0%
+you need many thousands of people to do
+ 
+
+ align:start position:0%
+you need many thousands of people to do
+this so it actually works out to you
+
+ align:start position:0%
+this so it actually works out to you
+ 
+
+ align:start position:0%
+this so it actually works out to you
+know hundreds of billions of genotypes
+
+ align:start position:0%
+know hundreds of billions of genotypes
+ 
+
+ align:start position:0%
+know hundreds of billions of genotypes
+so that's something like you know the
+
+ align:start position:0%
+so that's something like you know the
+ 
+
+ align:start position:0%
+so that's something like you know the
+the Pentagon budget or something for a
+
+ align:start position:0%
+the Pentagon budget or something for a
+ 
+
+ align:start position:0%
+the Pentagon budget or something for a
+year to do one study so NIH doesn't like
+
+ align:start position:0%
+year to do one study so NIH doesn't like
+ 
+
+ align:start position:0%
+year to do one study so NIH doesn't like
+grants like that so basically until this
+
+ align:start position:0%
+grants like that so basically until this
+ 
+
+ align:start position:0%
+grants like that so basically until this
+gets much cheaper and or we apply some
+
+ align:start position:0%
+gets much cheaper and or we apply some
+ 
+
+ align:start position:0%
+gets much cheaper and or we apply some
+of the shortcuts that I'll tell you
+
+ align:start position:0%
+of the shortcuts that I'll tell you
+ 
+
+ align:start position:0%
+of the shortcuts that I'll tell you
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh you need to pick which genes and
+
+ align:start position:0%
+uh you need to pick which genes and
+ 
+
+ align:start position:0%
+uh you need to pick which genes and
+variants we're going to study
+
+ align:start position:0%
+variants we're going to study
+ 
+
+ align:start position:0%
+variants we're going to study
+all right so this brings into methods
+
+ align:start position:0%
+all right so this brings into methods
+ 
+
+ align:start position:0%
+all right so this brings into methods
+for finding traits any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're on the on the track of
+
+ align:start position:0%
+okay so we're on the on the track of
+ 
+
+ align:start position:0%
+okay so we're on the on the track of
+trying to find which of these common
+
+ align:start position:0%
+trying to find which of these common
+ 
+
+ align:start position:0%
+trying to find which of these common
+variants might be contributing to to
+
+ align:start position:0%
+variants might be contributing to to
+ 
+
+ align:start position:0%
+variants might be contributing to to
+common diseases
+
+ align:start position:0%
+common diseases
+ 
+
+ align:start position:0%
+common diseases
+so really kind of three uh approaches
+
+ align:start position:0%
+so really kind of three uh approaches
+ 
+
+ align:start position:0%
+so really kind of three uh approaches
+two of which have to do with common
+
+ align:start position:0%
+two of which have to do with common
+ 
+
+ align:start position:0%
+two of which have to do with common
+variance one actually which explicitly
+
+ align:start position:0%
+variance one actually which explicitly
+ 
+
+ align:start position:0%
+variance one actually which explicitly
+has to do with rare variance and I'll
+
+ align:start position:0%
+has to do with rare variance and I'll
+ 
+
+ align:start position:0%
+has to do with rare variance and I'll
+get to get to that at the end
+
+ align:start position:0%
+get to get to that at the end
+ 
+
+ align:start position:0%
+get to get to that at the end
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the traditional approach to finding
+
+ align:start position:0%
+so the traditional approach to finding
+ 
+
+ align:start position:0%
+so the traditional approach to finding
+uh genes for disease has actually been
+
+ align:start position:0%
+uh genes for disease has actually been
+ 
+
+ align:start position:0%
+uh genes for disease has actually been
+something called linkage and have you
+
+ align:start position:0%
+something called linkage and have you
+ 
+
+ align:start position:0%
+something called linkage and have you
+guys done linkage is that something
+
+ align:start position:0%
+guys done linkage is that something
+ 
+
+ align:start position:0%
+guys done linkage is that something
+that's been done here yes no so I'll
+
+ align:start position:0%
+that's been done here yes no so I'll
+ 
+
+ align:start position:0%
+that's been done here yes no so I'll
+briefly go through linkage
+
+ align:start position:0%
+briefly go through linkage
+ 
+
+ align:start position:0%
+briefly go through linkage
+um so linkage requires families where
+
+ align:start position:0%
+um so linkage requires families where
+ 
+
+ align:start position:0%
+um so linkage requires families where
+you have uh in the case of disease
+
+ align:start position:0%
+you have uh in the case of disease
+ 
+
+ align:start position:0%
+you have uh in the case of disease
+multiple affected relatives in the same
+
+ align:start position:0%
+multiple affected relatives in the same
+ 
+
+ align:start position:0%
+multiple affected relatives in the same
+family okay so those could be brother
+
+ align:start position:0%
+family okay so those could be brother
+ 
+
+ align:start position:0%
+family okay so those could be brother
+sister or it could be cousins or uh you
+
+ align:start position:0%
+sister or it could be cousins or uh you
+ 
+
+ align:start position:0%
+sister or it could be cousins or uh you
+know an uncle and a niece or something
+
+ align:start position:0%
+know an uncle and a niece or something
+ 
+
+ align:start position:0%
+know an uncle and a niece or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+the idea is that there is a single
+
+ align:start position:0%
+the idea is that there is a single
+ 
+
+ align:start position:0%
+the idea is that there is a single
+disease-causing allele that's
+
+ align:start position:0%
+disease-causing allele that's
+ 
+
+ align:start position:0%
+disease-causing allele that's
+segregating in that family so it's being
+
+ align:start position:0%
+segregating in that family so it's being
+ 
+
+ align:start position:0%
+segregating in that family so it's being
+passed on to some of the people in the
+
+ align:start position:0%
+passed on to some of the people in the
+ 
+
+ align:start position:0%
+passed on to some of the people in the
+family and not others
+
+ align:start position:0%
+family and not others
+ 
+
+ align:start position:0%
+family and not others
+and the other assumption is that the
+
+ align:start position:0%
+and the other assumption is that the
+ 
+
+ align:start position:0%
+and the other assumption is that the
+disease will more or less doesn't have
+
+ align:start position:0%
+disease will more or less doesn't have
+ 
+
+ align:start position:0%
+disease will more or less doesn't have
+to be perfect but it has to be pretty
+
+ align:start position:0%
+to be perfect but it has to be pretty
+ 
+
+ align:start position:0%
+to be perfect but it has to be pretty
+good will more or less track with that
+
+ align:start position:0%
+good will more or less track with that
+ 
+
+ align:start position:0%
+good will more or less track with that
+allele
+
+ align:start position:0%
+allele
+ 
+
+ align:start position:0%
+allele
+now for linkage you're not actually
+
+ align:start position:0%
+now for linkage you're not actually
+ 
+
+ align:start position:0%
+now for linkage you're not actually
+typing the allele itself what you're
+
+ align:start position:0%
+typing the allele itself what you're
+ 
+
+ align:start position:0%
+typing the allele itself what you're
+doing you're typing markers that
+
+ align:start position:0%
+doing you're typing markers that
+ 
+
+ align:start position:0%
+doing you're typing markers that
+surround the allele so they may be
+
+ align:start position:0%
+surround the allele so they may be
+ 
+
+ align:start position:0%
+surround the allele so they may be
+a couple of million bases away actually
+
+ align:start position:0%
+a couple of million bases away actually
+ 
+
+ align:start position:0%
+a couple of million bases away actually
+and that's sort of a typical thing is
+
+ align:start position:0%
+and that's sort of a typical thing is
+ 
+
+ align:start position:0%
+and that's sort of a typical thing is
+ever is about marker spaced every 10
+
+ align:start position:0%
+ever is about marker spaced every 10
+ 
+
+ align:start position:0%
+ever is about marker spaced every 10
+million every sort of few to 10 million
+
+ align:start position:0%
+million every sort of few to 10 million
+ 
+
+ align:start position:0%
+million every sort of few to 10 million
+bases
+
+ align:start position:0%
+bases
+ 
+
+ align:start position:0%
+bases
+and the idea is that since you're just
+
+ align:start position:0%
+and the idea is that since you're just
+ 
+
+ align:start position:0%
+and the idea is that since you're just
+looking in a family
+
+ align:start position:0%
+looking in a family
+ 
+
+ align:start position:0%
+looking in a family
+um it turns out that a million bases is
+
+ align:start position:0%
+um it turns out that a million bases is
+ 
+
+ align:start position:0%
+um it turns out that a million bases is
+what's called one centimorgan which
+
+ align:start position:0%
+what's called one centimorgan which
+ 
+
+ align:start position:0%
+what's called one centimorgan which
+means the recombination events happens
+
+ align:start position:0%
+means the recombination events happens
+ 
+
+ align:start position:0%
+means the recombination events happens
+once every hundred meiosis okay so
+
+ align:start position:0%
+once every hundred meiosis okay so
+ 
+
+ align:start position:0%
+once every hundred meiosis okay so
+within a few Centum organs there's
+
+ align:start position:0%
+within a few Centum organs there's
+ 
+
+ align:start position:0%
+within a few Centum organs there's
+generally not going to be any
+
+ align:start position:0%
+generally not going to be any
+ 
+
+ align:start position:0%
+generally not going to be any
+recombination events within a family so
+
+ align:start position:0%
+recombination events within a family so
+ 
+
+ align:start position:0%
+recombination events within a family so
+the marker that's a few million bases
+
+ align:start position:0%
+the marker that's a few million bases
+ 
+
+ align:start position:0%
+the marker that's a few million bases
+away will travel with the disease allele
+
+ align:start position:0%
+away will travel with the disease allele
+ 
+
+ align:start position:0%
+away will travel with the disease allele
+in the family so you use that marker as
+
+ align:start position:0%
+in the family so you use that marker as
+ 
+
+ align:start position:0%
+in the family so you use that marker as
+a surrogate for the disease allele and
+
+ align:start position:0%
+a surrogate for the disease allele and
+ 
+
+ align:start position:0%
+a surrogate for the disease allele and
+you follow the marker through the family
+
+ align:start position:0%
+you follow the marker through the family
+ 
+
+ align:start position:0%
+you follow the marker through the family
+and you say which of these markers so
+
+ align:start position:0%
+and you say which of these markers so
+ 
+
+ align:start position:0%
+and you say which of these markers so
+this marker is traveling with disease
+
+ align:start position:0%
+this marker is traveling with disease
+ 
+
+ align:start position:0%
+this marker is traveling with disease
+you say maybe that's pretty close to the
+
+ align:start position:0%
+you say maybe that's pretty close to the
+ 
+
+ align:start position:0%
+you say maybe that's pretty close to the
+disease allele but a marker on some
+
+ align:start position:0%
+disease allele but a marker on some
+ 
+
+ align:start position:0%
+disease allele but a marker on some
+other chromosome won't be segregating
+
+ align:start position:0%
+other chromosome won't be segregating
+ 
+
+ align:start position:0%
+other chromosome won't be segregating
+with the disease so you'll say that
+
+ align:start position:0%
+with the disease so you'll say that
+ 
+
+ align:start position:0%
+with the disease so you'll say that
+region isn't linked so that's linkage
+
+ align:start position:0%
+region isn't linked so that's linkage
+ 
+
+ align:start position:0%
+region isn't linked so that's linkage
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so traditionally it's been
+
+ align:start position:0%
+so traditionally it's been
+ 
+
+ align:start position:0%
+so traditionally it's been
+microsatellites which are uh markers
+
+ align:start position:0%
+microsatellites which are uh markers
+ 
+
+ align:start position:0%
+microsatellites which are uh markers
+that are things like repeats of the
+
+ align:start position:0%
+that are things like repeats of the
+ 
+
+ align:start position:0%
+that are things like repeats of the
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+t-a-t-a-t-a-t-a-t-a and some people have
+
+ align:start position:0%
+t-a-t-a-t-a-t-a-t-a and some people have
+ 
+
+ align:start position:0%
+t-a-t-a-t-a-t-a-t-a and some people have
+DNA polymerase doesn't like to copy
+
+ align:start position:0%
+DNA polymerase doesn't like to copy
+ 
+
+ align:start position:0%
+DNA polymerase doesn't like to copy
+those very well so some people have 50
+
+ align:start position:0%
+those very well so some people have 50
+ 
+
+ align:start position:0%
+those very well so some people have 50
+copied some people have 44 some people
+
+ align:start position:0%
+copied some people have 44 some people
+ 
+
+ align:start position:0%
+copied some people have 44 some people
+have 53 that sort of thing and you can
+
+ align:start position:0%
+have 53 that sort of thing and you can
+ 
+
+ align:start position:0%
+have 53 that sort of thing and you can
+type those those are a pain in the ass
+
+ align:start position:0%
+type those those are a pain in the ass
+ 
+
+ align:start position:0%
+type those those are a pain in the ass
+to work with actually and so people are
+
+ align:start position:0%
+to work with actually and so people are
+ 
+
+ align:start position:0%
+to work with actually and so people are
+shifting over starting to to use
+
+ align:start position:0%
+shifting over starting to to use
+ 
+
+ align:start position:0%
+shifting over starting to to use
+snip-based uh linkage analysis because
+
+ align:start position:0%
+snip-based uh linkage analysis because
+ 
+
+ align:start position:0%
+snip-based uh linkage analysis because
+all you need is basically a marker that
+
+ align:start position:0%
+all you need is basically a marker that
+ 
+
+ align:start position:0%
+all you need is basically a marker that
+lets you distinguish
+
+ align:start position:0%
+lets you distinguish
+ 
+
+ align:start position:0%
+lets you distinguish
+each of the chromosomes that are
+
+ align:start position:0%
+each of the chromosomes that are
+ 
+
+ align:start position:0%
+each of the chromosomes that are
+segregating in the family so
+
+ align:start position:0%
+segregating in the family so
+ 
+
+ align:start position:0%
+segregating in the family so
+probably microsatellites are it's gonna
+
+ align:start position:0%
+probably microsatellites are it's gonna
+ 
+
+ align:start position:0%
+probably microsatellites are it's gonna
+there's gonna be a shift
+
+ align:start position:0%
+there's gonna be a shift
+ 
+
+ align:start position:0%
+there's gonna be a shift
+but there's been wildly successful for
+
+ align:start position:0%
+but there's been wildly successful for
+ 
+
+ align:start position:0%
+but there's been wildly successful for
+single Gene disorders and the reason
+
+ align:start position:0%
+single Gene disorders and the reason
+ 
+
+ align:start position:0%
+single Gene disorders and the reason
+it's been successful is because there's
+
+ align:start position:0%
+it's been successful is because there's
+ 
+
+ align:start position:0%
+it's been successful is because there's
+always just a single copy in a family of
+
+ align:start position:0%
+always just a single copy in a family of
+ 
+
+ align:start position:0%
+always just a single copy in a family of
+the disease allele and the segregation
+
+ align:start position:0%
+the disease allele and the segregation
+ 
+
+ align:start position:0%
+the disease allele and the segregation
+with disease and that marker is really
+
+ align:start position:0%
+with disease and that marker is really
+ 
+
+ align:start position:0%
+with disease and that marker is really
+very good because if you have the
+
+ align:start position:0%
+very good because if you have the
+ 
+
+ align:start position:0%
+very good because if you have the
+disease-causing allele you get disease
+
+ align:start position:0%
+disease-causing allele you get disease
+ 
+
+ align:start position:0%
+disease-causing allele you get disease
+and if you don't you don't so for common
+
+ align:start position:0%
+and if you don't you don't so for common
+ 
+
+ align:start position:0%
+and if you don't you don't so for common
+diseases none of those things are true
+
+ align:start position:0%
+diseases none of those things are true
+ 
+
+ align:start position:0%
+diseases none of those things are true
+first of all uh because multiple genes
+
+ align:start position:0%
+first of all uh because multiple genes
+ 
+
+ align:start position:0%
+first of all uh because multiple genes
+are involved you might not have the
+
+ align:start position:0%
+are involved you might not have the
+ 
+
+ align:start position:0%
+are involved you might not have the
+disease causing allele but get the
+
+ align:start position:0%
+disease causing allele but get the
+ 
+
+ align:start position:0%
+disease causing allele but get the
+disease anyway and vice versa you might
+
+ align:start position:0%
+disease anyway and vice versa you might
+ 
+
+ align:start position:0%
+disease anyway and vice versa you might
+have the disease susceptibility allele
+
+ align:start position:0%
+have the disease susceptibility allele
+ 
+
+ align:start position:0%
+have the disease susceptibility allele
+really it should be called
+
+ align:start position:0%
+really it should be called
+ 
+
+ align:start position:0%
+really it should be called
+and not get the disease and furthermore
+
+ align:start position:0%
+and not get the disease and furthermore
+ 
+
+ align:start position:0%
+and not get the disease and furthermore
+there might be multiple because it might
+
+ align:start position:0%
+there might be multiple because it might
+ 
+
+ align:start position:0%
+there might be multiple because it might
+be a common variant there actually might
+
+ align:start position:0%
+be a common variant there actually might
+ 
+
+ align:start position:0%
+be a common variant there actually might
+be multiple copies of the susceptibility
+
+ align:start position:0%
+be multiple copies of the susceptibility
+ 
+
+ align:start position:0%
+be multiple copies of the susceptibility
+oil traveling in the same family so the
+
+ align:start position:0%
+oil traveling in the same family so the
+ 
+
+ align:start position:0%
+oil traveling in the same family so the
+markers that are a couple million bases
+
+ align:start position:0%
+markers that are a couple million bases
+ 
+
+ align:start position:0%
+markers that are a couple million bases
+away now no longer perfectly Mark the
+
+ align:start position:0%
+away now no longer perfectly Mark the
+ 
+
+ align:start position:0%
+away now no longer perfectly Mark the
+the disease susceptibility allele
+
+ align:start position:0%
+the disease susceptibility allele
+ 
+
+ align:start position:0%
+the disease susceptibility allele
+because maybe on this side of the family
+
+ align:start position:0%
+because maybe on this side of the family
+ 
+
+ align:start position:0%
+because maybe on this side of the family
+it's marked by you know it travels with
+
+ align:start position:0%
+it's marked by you know it travels with
+ 
+
+ align:start position:0%
+it's marked by you know it travels with
+this marker this allele but then on this
+
+ align:start position:0%
+this marker this allele but then on this
+ 
+
+ align:start position:0%
+this marker this allele but then on this
+side of the family where it's
+
+ align:start position:0%
+side of the family where it's
+ 
+
+ align:start position:0%
+side of the family where it's
+segregating it travels with a different
+
+ align:start position:0%
+segregating it travels with a different
+ 
+
+ align:start position:0%
+segregating it travels with a different
+marker so all these things conspire
+
+ align:start position:0%
+marker so all these things conspire
+ 
+
+ align:start position:0%
+marker so all these things conspire
+against you for common diseases
+
+ align:start position:0%
+against you for common diseases
+ 
+
+ align:start position:0%
+against you for common diseases
+nonetheless people have found a couple
+
+ align:start position:0%
+nonetheless people have found a couple
+ 
+
+ align:start position:0%
+nonetheless people have found a couple
+of things through linkage of common
+
+ align:start position:0%
+of things through linkage of common
+ 
+
+ align:start position:0%
+of things through linkage of common
+diseases and tracked it down decode
+
+ align:start position:0%
+diseases and tracked it down decode
+ 
+
+ align:start position:0%
+diseases and tracked it down decode
+genetics in Iceland is probably the most
+
+ align:start position:0%
+genetics in Iceland is probably the most
+ 
+
+ align:start position:0%
+genetics in Iceland is probably the most
+prolific example of that
+
+ align:start position:0%
+prolific example of that
+ 
+
+ align:start position:0%
+prolific example of that
+so if linkage isn't working it brings us
+
+ align:start position:0%
+so if linkage isn't working it brings us
+ 
+
+ align:start position:0%
+so if linkage isn't working it brings us
+to the other main approach that's used
+
+ align:start position:0%
+to the other main approach that's used
+ 
+
+ align:start position:0%
+to the other main approach that's used
+which I'll spend a lot of the talk
+
+ align:start position:0%
+which I'll spend a lot of the talk
+ 
+
+ align:start position:0%
+which I'll spend a lot of the talk
+talking about because it is the main
+
+ align:start position:0%
+talking about because it is the main
+ 
+
+ align:start position:0%
+talking about because it is the main
+method it's called Association studies
+
+ align:start position:0%
+method it's called Association studies
+ 
+
+ align:start position:0%
+method it's called Association studies
+and basically what this means is that
+
+ align:start position:0%
+and basically what this means is that
+ 
+
+ align:start position:0%
+and basically what this means is that
+rather than searching through the whole
+
+ align:start position:0%
+rather than searching through the whole
+ 
+
+ align:start position:0%
+rather than searching through the whole
+genome you pick candidate genes and this
+
+ align:start position:0%
+genome you pick candidate genes and this
+ 
+
+ align:start position:0%
+genome you pick candidate genes and this
+is Richard maracangus have shown that
+
+ align:start position:0%
+is Richard maracangus have shown that
+ 
+
+ align:start position:0%
+is Richard maracangus have shown that
+this is much better suited than linkage
+
+ align:start position:0%
+this is much better suited than linkage
+ 
+
+ align:start position:0%
+this is much better suited than linkage
+to things where this scenario where you
+
+ align:start position:0%
+to things where this scenario where you
+ 
+
+ align:start position:0%
+to things where this scenario where you
+have common alleles that have only
+
+ align:start position:0%
+have common alleles that have only
+ 
+
+ align:start position:0%
+have common alleles that have only
+modest effects on disease what's called
+
+ align:start position:0%
+modest effects on disease what's called
+ 
+
+ align:start position:0%
+modest effects on disease what's called
+modest penetrance
+
+ align:start position:0%
+modest penetrance
+ 
+
+ align:start position:0%
+modest penetrance
+and then there's another approach that
+
+ align:start position:0%
+and then there's another approach that
+ 
+
+ align:start position:0%
+and then there's another approach that
+people are taking which is they say okay
+
+ align:start position:0%
+people are taking which is they say okay
+ 
+
+ align:start position:0%
+people are taking which is they say okay
+I'm gonna I understand linkage might not
+
+ align:start position:0%
+I'm gonna I understand linkage might not
+ 
+
+ align:start position:0%
+I'm gonna I understand linkage might not
+be the best way to go but I don't
+
+ align:start position:0%
+be the best way to go but I don't
+ 
+
+ align:start position:0%
+be the best way to go but I don't
+believe this common variant stuff I want
+
+ align:start position:0%
+believe this common variant stuff I want
+ 
+
+ align:start position:0%
+believe this common variant stuff I want
+to look for rare variants that
+
+ align:start position:0%
+to look for rare variants that
+ 
+
+ align:start position:0%
+to look for rare variants that
+contribute to Z's and so there what you
+
+ align:start position:0%
+contribute to Z's and so there what you
+ 
+
+ align:start position:0%
+contribute to Z's and so there what you
+are doing is again you're picking the
+
+ align:start position:0%
+are doing is again you're picking the
+ 
+
+ align:start position:0%
+are doing is again you're picking the
+genes to look at but instead of just
+
+ align:start position:0%
+genes to look at but instead of just
+ 
+
+ align:start position:0%
+genes to look at but instead of just
+taking Snips off the public map and
+
+ align:start position:0%
+taking Snips off the public map and
+ 
+
+ align:start position:0%
+taking Snips off the public map and
+looking for common variation they're
+
+ align:start position:0%
+looking for common variation they're
+ 
+
+ align:start position:0%
+looking for common variation they're
+actually resequencing to try to find
+
+ align:start position:0%
+actually resequencing to try to find
+ 
+
+ align:start position:0%
+actually resequencing to try to find
+those rare variants that are present
+
+ align:start position:0%
+those rare variants that are present
+ 
+
+ align:start position:0%
+those rare variants that are present
+only in disease and the best examples of
+
+ align:start position:0%
+only in disease and the best examples of
+ 
+
+ align:start position:0%
+only in disease and the best examples of
+this are brca1 for breast cancer which
+
+ align:start position:0%
+this are brca1 for breast cancer which
+ 
+
+ align:start position:0%
+this are brca1 for breast cancer which
+actually originally identified by
+
+ align:start position:0%
+actually originally identified by
+ 
+
+ align:start position:0%
+actually originally identified by
+linkage but you that's sort of a rare
+
+ align:start position:0%
+linkage but you that's sort of a rare
+ 
+
+ align:start position:0%
+linkage but you that's sort of a rare
+disease and also uh mc4r mutations this
+
+ align:start position:0%
+disease and also uh mc4r mutations this
+ 
+
+ align:start position:0%
+disease and also uh mc4r mutations this
+lanacortin4 receptor Gene where there's
+
+ align:start position:0%
+lanacortin4 receptor Gene where there's
+ 
+
+ align:start position:0%
+lanacortin4 receptor Gene where there's
+a lot of rare variants that contribute
+
+ align:start position:0%
+a lot of rare variants that contribute
+ 
+
+ align:start position:0%
+a lot of rare variants that contribute
+to early onset particularly severe
+
+ align:start position:0%
+to early onset particularly severe
+ 
+
+ align:start position:0%
+to early onset particularly severe
+obesity the difficulty with this
+
+ align:start position:0%
+obesity the difficulty with this
+ 
+
+ align:start position:0%
+obesity the difficulty with this
+approach right now is it's very
+
+ align:start position:0%
+approach right now is it's very
+ 
+
+ align:start position:0%
+approach right now is it's very
+expensive it's much more expensive to
+
+ align:start position:0%
+expensive it's much more expensive to
+ 
+
+ align:start position:0%
+expensive it's much more expensive to
+resequence uh than it is to do
+
+ align:start position:0%
+resequence uh than it is to do
+ 
+
+ align:start position:0%
+resequence uh than it is to do
+genotyping of polymorphisms and at the
+
+ align:start position:0%
+genotyping of polymorphisms and at the
+ 
+
+ align:start position:0%
+genotyping of polymorphisms and at the
+expense were flipped people would
+
+ align:start position:0%
+expense were flipped people would
+ 
+
+ align:start position:0%
+expense were flipped people would
+probably do this resequencing because
+
+ align:start position:0%
+probably do this resequencing because
+ 
+
+ align:start position:0%
+probably do this resequencing because
+this gets you the common variance as
+
+ align:start position:0%
+this gets you the common variance as
+ 
+
+ align:start position:0%
+this gets you the common variance as
+well and it's really just it's largely
+
+ align:start position:0%
+well and it's really just it's largely
+ 
+
+ align:start position:0%
+well and it's really just it's largely
+an expense issue that we can't do this
+
+ align:start position:0%
+an expense issue that we can't do this
+ 
+
+ align:start position:0%
+an expense issue that we can't do this
+so you know I talked about the study
+
+ align:start position:0%
+so you know I talked about the study
+ 
+
+ align:start position:0%
+so you know I talked about the study
+that would take you know just the
+
+ align:start position:0%
+that would take you know just the
+ 
+
+ align:start position:0%
+that would take you know just the
+Pentagon budget if you were going to do
+
+ align:start position:0%
+Pentagon budget if you were going to do
+ 
+
+ align:start position:0%
+Pentagon budget if you were going to do
+this this would take you know probably
+
+ align:start position:0%
+this this would take you know probably
+ 
+
+ align:start position:0%
+this this would take you know probably
+the GDP for the history of the United
+
+ align:start position:0%
+the GDP for the history of the United
+ 
+
+ align:start position:0%
+the GDP for the history of the United
+States or something like that so we're
+
+ align:start position:0%
+States or something like that so we're
+ 
+
+ align:start position:0%
+States or something like that so we're
+still a ways away from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm just saying that if you if you
+
+ align:start position:0%
+so I'm just saying that if you if you
+ 
+
+ align:start position:0%
+so I'm just saying that if you if you
+choose to I I don't mean to say that the
+
+ align:start position:0%
+choose to I I don't mean to say that the
+ 
+
+ align:start position:0%
+choose to I I don't mean to say that the
+hypothesis has been proven I believe
+
+ align:start position:0%
+hypothesis has been proven I believe
+ 
+
+ align:start position:0%
+hypothesis has been proven I believe
+that common rates contribute to common
+
+ align:start position:0%
+that common rates contribute to common
+ 
+
+ align:start position:0%
+that common rates contribute to common
+disease there are still people who
+
+ align:start position:0%
+disease there are still people who
+ 
+
+ align:start position:0%
+disease there are still people who
+believe that that's not true at all and
+
+ align:start position:0%
+believe that that's not true at all and
+ 
+
+ align:start position:0%
+believe that that's not true at all and
+that really this is the only thing
+
+ align:start position:0%
+that really this is the only thing
+ 
+
+ align:start position:0%
+that really this is the only thing
+that's ever going to yield anything
+
+ align:start position:0%
+that's ever going to yield anything
+ 
+
+ align:start position:0%
+that's ever going to yield anything
+um is is looking for rare variants
+
+ align:start position:0%
+um is is looking for rare variants
+ 
+
+ align:start position:0%
+um is is looking for rare variants
+um so and there are definitely you know
+
+ align:start position:0%
+um so and there are definitely you know
+ 
+
+ align:start position:0%
+um so and there are definitely you know
+a couple of cases where this has been
+
+ align:start position:0%
+a couple of cases where this has been
+ 
+
+ align:start position:0%
+a couple of cases where this has been
+true and this really hasn't been
+
+ align:start position:0%
+true and this really hasn't been
+ 
+
+ align:start position:0%
+true and this really hasn't been
+explored to any degree just because it's
+
+ align:start position:0%
+explored to any degree just because it's
+ 
+
+ align:start position:0%
+explored to any degree just because it's
+so expensive and I put it there just
+
+ align:start position:0%
+so expensive and I put it there just
+ 
+
+ align:start position:0%
+so expensive and I put it there just
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if all of a sudden to sequence
+
+ align:start position:0%
+if all of a sudden to sequence
+ 
+
+ align:start position:0%
+if all of a sudden to sequence
+somebody's genome for a hundred dollars
+
+ align:start position:0%
+somebody's genome for a hundred dollars
+ 
+
+ align:start position:0%
+somebody's genome for a hundred dollars
+became feasible you would take a
+
+ align:start position:0%
+became feasible you would take a
+ 
+
+ align:start position:0%
+became feasible you would take a
+thousand people with diabetes and
+
+ align:start position:0%
+thousand people with diabetes and
+ 
+
+ align:start position:0%
+thousand people with diabetes and
+sequence their genomes and that would be
+
+ align:start position:0%
+sequence their genomes and that would be
+ 
+
+ align:start position:0%
+sequence their genomes and that would be
+the way you do the experiment so
+
+ align:start position:0%
+the way you do the experiment so
+ 
+
+ align:start position:0%
+the way you do the experiment so
+that's why it's on there
+
+ align:start position:0%
+that's why it's on there
+ 
+
+ align:start position:0%
+that's why it's on there
+okay so this is sort of a cartoon
+
+ align:start position:0%
+okay so this is sort of a cartoon
+ 
+
+ align:start position:0%
+okay so this is sort of a cartoon
+version of what I just told you linkage
+
+ align:start position:0%
+version of what I just told you linkage
+ 
+
+ align:start position:0%
+version of what I just told you linkage
+analysis lets you search the whole
+
+ align:start position:0%
+analysis lets you search the whole
+ 
+
+ align:start position:0%
+analysis lets you search the whole
+genome and points you to a region
+
+ align:start position:0%
+genome and points you to a region
+ 
+
+ align:start position:0%
+genome and points you to a region
+although it does not point you to the
+
+ align:start position:0%
+although it does not point you to the
+ 
+
+ align:start position:0%
+although it does not point you to the
+gene so remember those markers are 10 10
+
+ align:start position:0%
+gene so remember those markers are 10 10
+ 
+
+ align:start position:0%
+gene so remember those markers are 10 10
+million bases apart and in fact because
+
+ align:start position:0%
+million bases apart and in fact because
+ 
+
+ align:start position:0%
+million bases apart and in fact because
+of some of the vagaries of complex trait
+
+ align:start position:0%
+of some of the vagaries of complex trait
+ 
+
+ align:start position:0%
+of some of the vagaries of complex trait
+genetics and uh the reasons that linkage
+
+ align:start position:0%
+genetics and uh the reasons that linkage
+ 
+
+ align:start position:0%
+genetics and uh the reasons that linkage
+isn't that well suited usually you get
+
+ align:start position:0%
+isn't that well suited usually you get
+ 
+
+ align:start position:0%
+isn't that well suited usually you get
+about a 20 centimorgan region or about
+
+ align:start position:0%
+about a 20 centimorgan region or about
+ 
+
+ align:start position:0%
+about a 20 centimorgan region or about
+20 million basis which can have
+
+ align:start position:0%
+20 million basis which can have
+ 
+
+ align:start position:0%
+20 million basis which can have
+something like 200 genes in it
+
+ align:start position:0%
+something like 200 genes in it
+ 
+
+ align:start position:0%
+something like 200 genes in it
+um and it'll say somewhere in that in
+
+ align:start position:0%
+um and it'll say somewhere in that in
+ 
+
+ align:start position:0%
+um and it'll say somewhere in that in
+those 200 genes there's something that's
+
+ align:start position:0%
+those 200 genes there's something that's
+ 
+
+ align:start position:0%
+those 200 genes there's something that's
+contributing to disease
+
+ align:start position:0%
+contributing to disease
+ 
+
+ align:start position:0%
+contributing to disease
+whereas Association
+
+ align:start position:0%
+whereas Association
+ 
+
+ align:start position:0%
+whereas Association
+you're looking one gene at a time so
+
+ align:start position:0%
+you're looking one gene at a time so
+ 
+
+ align:start position:0%
+you're looking one gene at a time so
+you're not but you have to guess
+
+ align:start position:0%
+you're not but you have to guess
+ 
+
+ align:start position:0%
+you're not but you have to guess
+correctly where to go and so you know
+
+ align:start position:0%
+correctly where to go and so you know
+ 
+
+ align:start position:0%
+correctly where to go and so you know
+you have to so there's this Haystack
+
+ align:start position:0%
+you have to so there's this Haystack
+ 
+
+ align:start position:0%
+you have to so there's this Haystack
+here of 30 000 genes
+
+ align:start position:0%
+here of 30 000 genes
+ 
+
+ align:start position:0%
+here of 30 000 genes
+um or 30 000 straws and you can pull one
+
+ align:start position:0%
+um or 30 000 straws and you can pull one
+ 
+
+ align:start position:0%
+um or 30 000 straws and you can pull one
+out and say you know is that a straw or
+
+ align:start position:0%
+out and say you know is that a straw or
+ 
+
+ align:start position:0%
+out and say you know is that a straw or
+a needle no it's a straw next one and
+
+ align:start position:0%
+a needle no it's a straw next one and
+ 
+
+ align:start position:0%
+a needle no it's a straw next one and
+and look and obviously the success
+
+ align:start position:0%
+and look and obviously the success
+ 
+
+ align:start position:0%
+and look and obviously the success
+depends on you being able to guess
+
+ align:start position:0%
+depends on you being able to guess
+ 
+
+ align:start position:0%
+depends on you being able to guess
+correctly but we actually at least for
+
+ align:start position:0%
+correctly but we actually at least for
+ 
+
+ align:start position:0%
+correctly but we actually at least for
+the first time we know what the 30 000
+
+ align:start position:0%
+the first time we know what the 30 000
+ 
+
+ align:start position:0%
+the first time we know what the 30 000
+straws are right so that you know
+
+ align:start position:0%
+straws are right so that you know
+ 
+
+ align:start position:0%
+straws are right so that you know
+there's a website now with the entire
+
+ align:start position:0%
+there's a website now with the entire
+ 
+
+ align:start position:0%
+there's a website now with the entire
+genome on it and we're getting pretty
+
+ align:start position:0%
+genome on it and we're getting pretty
+ 
+
+ align:start position:0%
+genome on it and we're getting pretty
+good as I'll tell you it telling whether
+
+ align:start position:0%
+good as I'll tell you it telling whether
+ 
+
+ align:start position:0%
+good as I'll tell you it telling whether
+um whether things are real contributors
+
+ align:start position:0%
+um whether things are real contributors
+ 
+
+ align:start position:0%
+um whether things are real contributors
+to disease or not but it's this
+
+ align:start position:0%
+to disease or not but it's this
+ 
+
+ align:start position:0%
+to disease or not but it's this
+interpretation of whether this is a
+
+ align:start position:0%
+interpretation of whether this is a
+ 
+
+ align:start position:0%
+interpretation of whether this is a
+straw or a needle
+
+ align:start position:0%
+straw or a needle
+ 
+
+ align:start position:0%
+straw or a needle
+um that uh is going to be the focus of a
+
+ align:start position:0%
+um that uh is going to be the focus of a
+ 
+
+ align:start position:0%
+um that uh is going to be the focus of a
+lot of the talk because that's what
+
+ align:start position:0%
+lot of the talk because that's what
+ 
+
+ align:start position:0%
+lot of the talk because that's what
+that's the study that a lot of people do
+
+ align:start position:0%
+that's the study that a lot of people do
+ 
+
+ align:start position:0%
+that's the study that a lot of people do
+is they pick aging and they test it and
+
+ align:start position:0%
+is they pick aging and they test it and
+ 
+
+ align:start position:0%
+is they pick aging and they test it and
+they claim it either does or does not
+
+ align:start position:0%
+they claim it either does or does not
+ 
+
+ align:start position:0%
+they claim it either does or does not
+have a role in disease and I sort of
+
+ align:start position:0%
+have a role in disease and I sort of
+ 
+
+ align:start position:0%
+have a role in disease and I sort of
+want to until you give you some uh
+
+ align:start position:0%
+want to until you give you some uh
+ 
+
+ align:start position:0%
+want to until you give you some uh
+hopefully some sophistication in Reading
+
+ align:start position:0%
+hopefully some sophistication in Reading
+ 
+
+ align:start position:0%
+hopefully some sophistication in Reading
+those sorts of studies to try to say
+
+ align:start position:0%
+those sorts of studies to try to say
+ 
+
+ align:start position:0%
+those sorts of studies to try to say
+should you believe everything that you
+
+ align:start position:0%
+should you believe everything that you
+ 
+
+ align:start position:0%
+should you believe everything that you
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+the obvious answer is no but so this is
+
+ align:start position:0%
+the obvious answer is no but so this is
+ 
+
+ align:start position:0%
+the obvious answer is no but so this is
+what an association study is you can
+
+ align:start position:0%
+what an association study is you can
+ 
+
+ align:start position:0%
+what an association study is you can
+imagine that you had healthy individuals
+
+ align:start position:0%
+imagine that you had healthy individuals
+ 
+
+ align:start position:0%
+imagine that you had healthy individuals
+and people with Alzheimer's disease
+
+ align:start position:0%
+and people with Alzheimer's disease
+ 
+
+ align:start position:0%
+and people with Alzheimer's disease
+and there's a common variant in the apoe
+
+ align:start position:0%
+and there's a common variant in the apoe
+ 
+
+ align:start position:0%
+and there's a common variant in the apoe
+gene called apoe4 it encodes apoelectric
+
+ align:start position:0%
+gene called apoe4 it encodes apoelectric
+ 
+
+ align:start position:0%
+gene called apoe4 it encodes apoelectric
+protein e and it is a common variant
+
+ align:start position:0%
+protein e and it is a common variant
+ 
+
+ align:start position:0%
+protein e and it is a common variant
+because if you look in uh the the
+
+ align:start position:0%
+because if you look in uh the the
+ 
+
+ align:start position:0%
+because if you look in uh the the
+control population you'll see it's there
+
+ align:start position:0%
+control population you'll see it's there
+ 
+
+ align:start position:0%
+control population you'll see it's there
+about 10 percent of the time something
+
+ align:start position:0%
+about 10 percent of the time something
+ 
+
+ align:start position:0%
+about 10 percent of the time something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+but if you look at people of Alzheimer's
+
+ align:start position:0%
+but if you look at people of Alzheimer's
+ 
+
+ align:start position:0%
+but if you look at people of Alzheimer's
+disease you'll see those frequencies
+
+ align:start position:0%
+disease you'll see those frequencies
+ 
+
+ align:start position:0%
+disease you'll see those frequencies
+increased increased about threefold and
+
+ align:start position:0%
+increased increased about threefold and
+ 
+
+ align:start position:0%
+increased increased about threefold and
+so this is the this is the Paradigm for
+
+ align:start position:0%
+so this is the this is the Paradigm for
+ 
+
+ align:start position:0%
+so this is the this is the Paradigm for
+associations of common disease and
+
+ align:start position:0%
+associations of common disease and
+ 
+
+ align:start position:0%
+associations of common disease and
+common variants and this has been seen
+
+ align:start position:0%
+common variants and this has been seen
+ 
+
+ align:start position:0%
+common variants and this has been seen
+over and over again you look in just
+
+ align:start position:0%
+over and over again you look in just
+ 
+
+ align:start position:0%
+over and over again you look in just
+about every study that's been done
+
+ align:start position:0%
+about every study that's been done
+ 
+
+ align:start position:0%
+about every study that's been done
+you see this increase in Risk
+
+ align:start position:0%
+you see this increase in Risk
+ 
+
+ align:start position:0%
+you see this increase in Risk
+yep sorry no no sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually yeah so there's there's a
+
+ align:start position:0%
+so actually yeah so there's there's a
+ 
+
+ align:start position:0%
+so actually yeah so there's there's a
+little bit of a subtlety to even this
+
+ align:start position:0%
+little bit of a subtlety to even this
+ 
+
+ align:start position:0%
+little bit of a subtlety to even this
+Association so it has been seen in other
+
+ align:start position:0%
+Association so it has been seen in other
+ 
+
+ align:start position:0%
+Association so it has been seen in other
+ethnicities it looks although the the
+
+ align:start position:0%
+ethnicities it looks although the the
+ 
+
+ align:start position:0%
+ethnicities it looks although the the
+last time I looked at this the data were
+
+ align:start position:0%
+last time I looked at this the data were
+ 
+
+ align:start position:0%
+last time I looked at this the data were
+not strong enough to say that there was
+
+ align:start position:0%
+not strong enough to say that there was
+ 
+
+ align:start position:0%
+not strong enough to say that there was
+definitely a difference but it looks
+
+ align:start position:0%
+definitely a difference but it looks
+ 
+
+ align:start position:0%
+definitely a difference but it looks
+like the association with Alzheimer's
+
+ align:start position:0%
+like the association with Alzheimer's
+ 
+
+ align:start position:0%
+like the association with Alzheimer's
+disease might be a little bit weaker in
+
+ align:start position:0%
+disease might be a little bit weaker in
+ 
+
+ align:start position:0%
+disease might be a little bit weaker in
+African derived populations
+
+ align:start position:0%
+African derived populations
+ 
+
+ align:start position:0%
+African derived populations
+there could be a wide variety of reasons
+
+ align:start position:0%
+there could be a wide variety of reasons
+ 
+
+ align:start position:0%
+there could be a wide variety of reasons
+why that's true and I'll go through a
+
+ align:start position:0%
+why that's true and I'll go through a
+ 
+
+ align:start position:0%
+why that's true and I'll go through a
+bunch of them just in general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh no you would so that the the rate the
+
+ align:start position:0%
+uh no you would so that the the rate the
+ 
+
+ align:start position:0%
+uh no you would so that the the rate the
+frequency of apoe4 in this case doesn't
+
+ align:start position:0%
+frequency of apoe4 in this case doesn't
+ 
+
+ align:start position:0%
+frequency of apoe4 in this case doesn't
+actually vary that much across
+
+ align:start position:0%
+actually vary that much across
+ 
+
+ align:start position:0%
+actually vary that much across
+populations it's an old allele some
+
+ align:start position:0%
+populations it's an old allele some
+ 
+
+ align:start position:0%
+populations it's an old allele some
+alleles do and you're getting into
+
+ align:start position:0%
+alleles do and you're getting into
+ 
+
+ align:start position:0%
+alleles do and you're getting into
+something called Ethnic admixture which
+
+ align:start position:0%
+something called Ethnic admixture which
+ 
+
+ align:start position:0%
+something called Ethnic admixture which
+I'll definitely get to in a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+as I said you have to guess right
+
+ align:start position:0%
+as I said you have to guess right
+ 
+
+ align:start position:0%
+as I said you have to guess right
+um so there's an issue of which genes do
+
+ align:start position:0%
+um so there's an issue of which genes do
+ 
+
+ align:start position:0%
+um so there's an issue of which genes do
+you guess and ideally again one would
+
+ align:start position:0%
+you guess and ideally again one would
+ 
+
+ align:start position:0%
+you guess and ideally again one would
+like to do all of them and it's getting
+
+ align:start position:0%
+like to do all of them and it's getting
+ 
+
+ align:start position:0%
+like to do all of them and it's getting
+closer to be able to do that but yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can study and find that region
+
+ align:start position:0%
+we can study and find that region
+ 
+
+ align:start position:0%
+we can study and find that region
+so that's definitely one thing you would
+
+ align:start position:0%
+so that's definitely one thing you would
+ 
+
+ align:start position:0%
+so that's definitely one thing you would
+do so it's actually been hard enough
+
+ align:start position:0%
+do so it's actually been hard enough
+ 
+
+ align:start position:0%
+do so it's actually been hard enough
+until
+
+ align:start position:0%
+until
+ 
+
+ align:start position:0%
+until
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+basically this year
+
+ align:start position:0%
+basically this year
+ 
+
+ align:start position:0%
+basically this year
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to do that so you know you have 200
+
+ align:start position:0%
+to do that so you know you have 200
+ 
+
+ align:start position:0%
+to do that so you know you have 200
+genes and to to thoroughly go through a
+
+ align:start position:0%
+genes and to to thoroughly go through a
+ 
+
+ align:start position:0%
+genes and to to thoroughly go through a
+gene and uh
+
+ align:start position:0%
+gene and uh
+ 
+
+ align:start position:0%
+gene and uh
+basically look at all 200 of them has
+
+ align:start position:0%
+basically look at all 200 of them has
+ 
+
+ align:start position:0%
+basically look at all 200 of them has
+been something that's just basically
+
+ align:start position:0%
+been something that's just basically
+ 
+
+ align:start position:0%
+been something that's just basically
+been Out Of Reach just to give you an
+
+ align:start position:0%
+been Out Of Reach just to give you an
+ 
+
+ align:start position:0%
+been Out Of Reach just to give you an
+example I just got I think funded to do
+
+ align:start position:0%
+example I just got I think funded to do
+ 
+
+ align:start position:0%
+example I just got I think funded to do
+exactly that for an OPC linkage Peak and
+
+ align:start position:0%
+exactly that for an OPC linkage Peak and
+ 
+
+ align:start position:0%
+exactly that for an OPC linkage Peak and
+we couldn't have really written to do
+
+ align:start position:0%
+we couldn't have really written to do
+ 
+
+ align:start position:0%
+we couldn't have really written to do
+that sort of a part of a regular r01
+
+ align:start position:0%
+that sort of a part of a regular r01
+ 
+
+ align:start position:0%
+that sort of a part of a regular r01
+type Grant we could not have written an
+
+ align:start position:0%
+type Grant we could not have written an
+ 
+
+ align:start position:0%
+type Grant we could not have written an
+r01 to do that a year ago it was just
+
+ align:start position:0%
+r01 to do that a year ago it was just
+ 
+
+ align:start position:0%
+r01 to do that a year ago it was just
+too expensive and too hard
+
+ align:start position:0%
+too expensive and too hard
+ 
+
+ align:start position:0%
+too expensive and too hard
+um just the information about which
+
+ align:start position:0%
+um just the information about which
+ 
+
+ align:start position:0%
+um just the information about which
+variants to type and I'll go through
+
+ align:start position:0%
+variants to type and I'll go through
+ 
+
+ align:start position:0%
+variants to type and I'll go through
+again using Apple types and stuff like
+
+ align:start position:0%
+again using Apple types and stuff like
+ 
+
+ align:start position:0%
+again using Apple types and stuff like
+that to do it uh the information just
+
+ align:start position:0%
+that to do it uh the information just
+ 
+
+ align:start position:0%
+that to do it uh the information just
+wasn't there and the expense was too
+
+ align:start position:0%
+wasn't there and the expense was too
+ 
+
+ align:start position:0%
+wasn't there and the expense was too
+high but yes I agree those would be the
+
+ align:start position:0%
+high but yes I agree those would be the
+ 
+
+ align:start position:0%
+high but yes I agree those would be the
+first candidates so this is you know you
+
+ align:start position:0%
+first candidates so this is you know you
+ 
+
+ align:start position:0%
+first candidates so this is you know you
+would use information from linkage
+
+ align:start position:0%
+would use information from linkage
+ 
+
+ align:start position:0%
+would use information from linkage
+studies and you might just say you know
+
+ align:start position:0%
+studies and you might just say you know
+ 
+
+ align:start position:0%
+studies and you might just say you know
+I don't care about anything else that
+
+ align:start position:0%
+I don't care about anything else that
+ 
+
+ align:start position:0%
+I don't care about anything else that
+anybody says I'm going to take linkage
+
+ align:start position:0%
+anybody says I'm going to take linkage
+ 
+
+ align:start position:0%
+anybody says I'm going to take linkage
+you know if you're a complex trade your
+
+ align:start position:0%
+you know if you're a complex trade your
+ 
+
+ align:start position:0%
+you know if you're a complex trade your
+common disease is fortunate enough to
+
+ align:start position:0%
+common disease is fortunate enough to
+ 
+
+ align:start position:0%
+common disease is fortunate enough to
+have a linkage Peak that you believe
+
+ align:start position:0%
+have a linkage Peak that you believe
+ 
+
+ align:start position:0%
+have a linkage Peak that you believe
+which is not true for most of them
+
+ align:start position:0%
+which is not true for most of them
+ 
+
+ align:start position:0%
+which is not true for most of them
+actually but
+
+ align:start position:0%
+actually but
+ 
+
+ align:start position:0%
+actually but
+um some of them it is you would say okay
+
+ align:start position:0%
+um some of them it is you would say okay
+ 
+
+ align:start position:0%
+um some of them it is you would say okay
+those are the 200 best genes I'm going
+
+ align:start position:0%
+those are the 200 best genes I'm going
+ 
+
+ align:start position:0%
+those are the 200 best genes I'm going
+to go for those that's definitely an
+
+ align:start position:0%
+to go for those that's definitely an
+ 
+
+ align:start position:0%
+to go for those that's definitely an
+approach
+
+ align:start position:0%
+approach
+ 
+
+ align:start position:0%
+approach
+um you might say well you know linkage
+
+ align:start position:0%
+um you might say well you know linkage
+ 
+
+ align:start position:0%
+um you might say well you know linkage
+is pretty is not very well powered for
+
+ align:start position:0%
+is pretty is not very well powered for
+ 
+
+ align:start position:0%
+is pretty is not very well powered for
+common disease probably most of the
+
+ align:start position:0%
+common disease probably most of the
+ 
+
+ align:start position:0%
+common disease probably most of the
+genes are not under linkage Peaks
+
+ align:start position:0%
+genes are not under linkage Peaks
+ 
+
+ align:start position:0%
+genes are not under linkage Peaks
+and most of the genes under the linkage
+
+ align:start position:0%
+and most of the genes under the linkage
+ 
+
+ align:start position:0%
+and most of the genes under the linkage
+Peak are not the right one
+
+ align:start position:0%
+Peak are not the right one
+ 
+
+ align:start position:0%
+Peak are not the right one
+so I'm going to ignore that I'm going to
+
+ align:start position:0%
+so I'm going to ignore that I'm going to
+ 
+
+ align:start position:0%
+so I'm going to ignore that I'm going to
+go for things that you know I'm going to
+
+ align:start position:0%
+go for things that you know I'm going to
+ 
+
+ align:start position:0%
+go for things that you know I'm going to
+say 100 Years of research has meant
+
+ align:start position:0%
+say 100 Years of research has meant
+ 
+
+ align:start position:0%
+say 100 Years of research has meant
+something and if I'm studying diabetes
+
+ align:start position:0%
+something and if I'm studying diabetes
+ 
+
+ align:start position:0%
+something and if I'm studying diabetes
+I'm going to do the insulin signaling
+
+ align:start position:0%
+I'm going to do the insulin signaling
+ 
+
+ align:start position:0%
+I'm going to do the insulin signaling
+pathway and beta cell function and you
+
+ align:start position:0%
+pathway and beta cell function and you
+ 
+
+ align:start position:0%
+pathway and beta cell function and you
+know obesity you know fat cell
+
+ align:start position:0%
+know obesity you know fat cell
+ 
+
+ align:start position:0%
+know obesity you know fat cell
+differentiation genes and stuff like
+
+ align:start position:0%
+differentiation genes and stuff like
+ 
+
+ align:start position:0%
+differentiation genes and stuff like
+that and those are the genes I'm going
+
+ align:start position:0%
+that and those are the genes I'm going
+ 
+
+ align:start position:0%
+that and those are the genes I'm going
+to go for or you might say well you know
+
+ align:start position:0%
+to go for or you might say well you know
+ 
+
+ align:start position:0%
+to go for or you might say well you know
+this is just you know Lamppost science
+
+ align:start position:0%
+this is just you know Lamppost science
+ 
+
+ align:start position:0%
+this is just you know Lamppost science
+because it's the biology that people
+
+ align:start position:0%
+because it's the biology that people
+ 
+
+ align:start position:0%
+because it's the biology that people
+have been doing and this is not very
+
+ align:start position:0%
+have been doing and this is not very
+ 
+
+ align:start position:0%
+have been doing and this is not very
+powered but this is a genome-wide tool
+
+ align:start position:0%
+powered but this is a genome-wide tool
+ 
+
+ align:start position:0%
+powered but this is a genome-wide tool
+we can use expression analysis so survey
+
+ align:start position:0%
+we can use expression analysis so survey
+ 
+
+ align:start position:0%
+we can use expression analysis so survey
+all the genes find things that are
+
+ align:start position:0%
+all the genes find things that are
+ 
+
+ align:start position:0%
+all the genes find things that are
+expressed at different levels in disease
+
+ align:start position:0%
+expressed at different levels in disease
+ 
+
+ align:start position:0%
+expressed at different levels in disease
+versus uh healthy people and say that
+
+ align:start position:0%
+versus uh healthy people and say that
+ 
+
+ align:start position:0%
+versus uh healthy people and say that
+you know some of those while all right
+
+ align:start position:0%
+you know some of those while all right
+ 
+
+ align:start position:0%
+you know some of those while all right
+many of those changes might be secondary
+
+ align:start position:0%
+many of those changes might be secondary
+ 
+
+ align:start position:0%
+many of those changes might be secondary
+to the disease State maybe some of those
+
+ align:start position:0%
+to the disease State maybe some of those
+ 
+
+ align:start position:0%
+to the disease State maybe some of those
+represent a primary regulatory variant
+
+ align:start position:0%
+represent a primary regulatory variant
+ 
+
+ align:start position:0%
+represent a primary regulatory variant
+that affects disease and so I'm going to
+
+ align:start position:0%
+that affects disease and so I'm going to
+ 
+
+ align:start position:0%
+that affects disease and so I'm going to
+look for those and you know what we're
+
+ align:start position:0%
+look for those and you know what we're
+ 
+
+ align:start position:0%
+look for those and you know what we're
+trying to do and and other people are
+
+ align:start position:0%
+trying to do and and other people are
+ 
+
+ align:start position:0%
+trying to do and and other people are
+trying to do is actually the most
+
+ align:start position:0%
+trying to do is actually the most
+ 
+
+ align:start position:0%
+trying to do is actually the most
+interesting genes are probably the ones
+
+ align:start position:0%
+interesting genes are probably the ones
+ 
+
+ align:start position:0%
+interesting genes are probably the ones
+that happen to fall in here although
+
+ align:start position:0%
+that happen to fall in here although
+ 
+
+ align:start position:0%
+that happen to fall in here although
+there's no saying that you know that
+
+ align:start position:0%
+there's no saying that you know that
+ 
+
+ align:start position:0%
+there's no saying that you know that
+they have to fall into this intersection
+
+ align:start position:0%
+they have to fall into this intersection
+ 
+
+ align:start position:0%
+they have to fall into this intersection
+maybe they've Fallen here or they're
+
+ align:start position:0%
+maybe they've Fallen here or they're
+ 
+
+ align:start position:0%
+maybe they've Fallen here or they're
+they're even just one of these or you
+
+ align:start position:0%
+they're even just one of these or you
+ 
+
+ align:start position:0%
+they're even just one of these or you
+know in the universe outside
+
+ align:start position:0%
+know in the universe outside
+ 
+
+ align:start position:0%
+know in the universe outside
+all together
+
+ align:start position:0%
+all together
+ 
+
+ align:start position:0%
+all together
+but I'll just give you an example for
+
+ align:start position:0%
+but I'll just give you an example for
+ 
+
+ align:start position:0%
+but I'll just give you an example for
+type 2 diabetes just because we are
+
+ align:start position:0%
+type 2 diabetes just because we are
+ 
+
+ align:start position:0%
+type 2 diabetes just because we are
+actually doing this sort of thing so
+
+ align:start position:0%
+actually doing this sort of thing so
+ 
+
+ align:start position:0%
+actually doing this sort of thing so
+there's there is a hundreds of years of
+
+ align:start position:0%
+there's there is a hundreds of years of
+ 
+
+ align:start position:0%
+there's there is a hundreds of years of
+biology or 100 Years of biology probably
+
+ align:start position:0%
+biology or 100 Years of biology probably
+ 
+
+ align:start position:0%
+biology or 100 Years of biology probably
+on Diabetes a lot of mouse models uh
+
+ align:start position:0%
+on Diabetes a lot of mouse models uh
+ 
+
+ align:start position:0%
+on Diabetes a lot of mouse models uh
+single Gene disorders that cause the
+
+ align:start position:0%
+single Gene disorders that cause the
+ 
+
+ align:start position:0%
+single Gene disorders that cause the
+disease so that's another sort of thing
+
+ align:start position:0%
+disease so that's another sort of thing
+ 
+
+ align:start position:0%
+disease so that's another sort of thing
+if severe variation causes a severe form
+
+ align:start position:0%
+if severe variation causes a severe form
+ 
+
+ align:start position:0%
+if severe variation causes a severe form
+of the disease maybe mild variation
+
+ align:start position:0%
+of the disease maybe mild variation
+ 
+
+ align:start position:0%
+of the disease maybe mild variation
+caused the late onset form
+
+ align:start position:0%
+caused the late onset form
+ 
+
+ align:start position:0%
+caused the late onset form
+so you can there's a list of genes there
+
+ align:start position:0%
+so you can there's a list of genes there
+ 
+
+ align:start position:0%
+so you can there's a list of genes there
+so for diabetes this is one of those
+
+ align:start position:0%
+so for diabetes this is one of those
+ 
+
+ align:start position:0%
+so for diabetes this is one of those
+things where there really isn't a
+
+ align:start position:0%
+things where there really isn't a
+ 
+
+ align:start position:0%
+things where there really isn't a
+perfect linkage Peak to go under there's
+
+ align:start position:0%
+perfect linkage Peak to go under there's
+ 
+
+ align:start position:0%
+perfect linkage Peak to go under there's
+a Graham Bells group uh identified the
+
+ align:start position:0%
+a Graham Bells group uh identified the
+ 
+
+ align:start position:0%
+a Graham Bells group uh identified the
+cow pain 10 Gene by going under a peak
+
+ align:start position:0%
+cow pain 10 Gene by going under a peak
+ 
+
+ align:start position:0%
+cow pain 10 Gene by going under a peak
+where they had significant linkage
+
+ align:start position:0%
+where they had significant linkage
+ 
+
+ align:start position:0%
+where they had significant linkage
+although if you actually put all the
+
+ align:start position:0%
+although if you actually put all the
+ 
+
+ align:start position:0%
+although if you actually put all the
+linkage evidence together from everybody
+
+ align:start position:0%
+linkage evidence together from everybody
+ 
+
+ align:start position:0%
+linkage evidence together from everybody
+you would not have said that there was
+
+ align:start position:0%
+you would not have said that there was
+ 
+
+ align:start position:0%
+you would not have said that there was
+any significant linkage diabetes there
+
+ align:start position:0%
+any significant linkage diabetes there
+ 
+
+ align:start position:0%
+any significant linkage diabetes there
+that Association is probably true uh but
+
+ align:start position:0%
+that Association is probably true uh but
+ 
+
+ align:start position:0%
+that Association is probably true uh but
+um uh not you know so that you can you
+
+ align:start position:0%
+um uh not you know so that you can you
+ 
+
+ align:start position:0%
+um uh not you know so that you can you
+can do this but it's it's not the
+
+ align:start position:0%
+can do this but it's it's not the
+ 
+
+ align:start position:0%
+can do this but it's it's not the
+end-all
+
+ align:start position:0%
+end-all
+ 
+
+ align:start position:0%
+end-all
+and then uh there's been expression
+
+ align:start position:0%
+and then uh there's been expression
+ 
+
+ align:start position:0%
+and then uh there's been expression
+studies and diabetes is pointed to a
+
+ align:start position:0%
+studies and diabetes is pointed to a
+ 
+
+ align:start position:0%
+studies and diabetes is pointed to a
+pathway of oxidative phosphorylation
+
+ align:start position:0%
+pathway of oxidative phosphorylation
+ 
+
+ align:start position:0%
+pathway of oxidative phosphorylation
+um uh some call uh so uh some colleagues
+
+ align:start position:0%
+um uh some call uh so uh some colleagues
+ 
+
+ align:start position:0%
+um uh some call uh so uh some colleagues
+of of my fancy Mutha David all Chiller
+
+ align:start position:0%
+of of my fancy Mutha David all Chiller
+ 
+
+ align:start position:0%
+of of my fancy Mutha David all Chiller
+life groups Lindgren and others and also
+
+ align:start position:0%
+life groups Lindgren and others and also
+ 
+
+ align:start position:0%
+life groups Lindgren and others and also
+paper from the Joslin uh Mary Elizabeth
+
+ align:start position:0%
+paper from the Joslin uh Mary Elizabeth
+ 
+
+ align:start position:0%
+paper from the Joslin uh Mary Elizabeth
+Patty's pointed to that pathway and
+
+ align:start position:0%
+Patty's pointed to that pathway and
+ 
+
+ align:start position:0%
+Patty's pointed to that pathway and
+there are genes that are actually in
+
+ align:start position:0%
+there are genes that are actually in
+ 
+
+ align:start position:0%
+there are genes that are actually in
+this you know red area a few of them so
+
+ align:start position:0%
+this you know red area a few of them so
+ 
+
+ align:start position:0%
+this you know red area a few of them so
+you know we're going after those genes
+
+ align:start position:0%
+you know we're going after those genes
+ 
+
+ align:start position:0%
+you know we're going after those genes
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+so that's kind of picking genes and it's
+
+ align:start position:0%
+so that's kind of picking genes and it's
+ 
+
+ align:start position:0%
+so that's kind of picking genes and it's
+sort of more of a at this point more of
+
+ align:start position:0%
+sort of more of a at this point more of
+ 
+
+ align:start position:0%
+sort of more of a at this point more of
+kind of a you know
+
+ align:start position:0%
+kind of a you know
+ 
+
+ align:start position:0%
+kind of a you know
+art form than you know any computerized
+
+ align:start position:0%
+art form than you know any computerized
+ 
+
+ align:start position:0%
+art form than you know any computerized
+algorithm uh to do it although just even
+
+ align:start position:0%
+algorithm uh to do it although just even
+ 
+
+ align:start position:0%
+algorithm uh to do it although just even
+getting all that information into one
+
+ align:start position:0%
+getting all that information into one
+ 
+
+ align:start position:0%
+getting all that information into one
+place where you could even do the
+
+ align:start position:0%
+place where you could even do the
+ 
+
+ align:start position:0%
+place where you could even do the
+queries of what is what genes are under
+
+ align:start position:0%
+queries of what is what genes are under
+ 
+
+ align:start position:0%
+queries of what is what genes are under
+linkage Peak what genes are
+
+ align:start position:0%
+linkage Peak what genes are
+ 
+
+ align:start position:0%
+linkage Peak what genes are
+differentially expressed what genes are
+
+ align:start position:0%
+differentially expressed what genes are
+ 
+
+ align:start position:0%
+differentially expressed what genes are
+in known Pathways that's actually tools
+
+ align:start position:0%
+in known Pathways that's actually tools
+ 
+
+ align:start position:0%
+in known Pathways that's actually tools
+that don't that we're sort of just
+
+ align:start position:0%
+that don't that we're sort of just
+ 
+
+ align:start position:0%
+that don't that we're sort of just
+trying to develop
+
+ align:start position:0%
+trying to develop
+ 
+
+ align:start position:0%
+trying to develop
+it's okay so which genes and then which
+
+ align:start position:0%
+it's okay so which genes and then which
+ 
+
+ align:start position:0%
+it's okay so which genes and then which
+variants so ideally you have the disease
+
+ align:start position:0%
+variants so ideally you have the disease
+ 
+
+ align:start position:0%
+variants so ideally you have the disease
+causing allele in your hand and you're
+
+ align:start position:0%
+causing allele in your hand and you're
+ 
+
+ align:start position:0%
+causing allele in your hand and you're
+genotyping it and you test it because
+
+ align:start position:0%
+genotyping it and you test it because
+ 
+
+ align:start position:0%
+genotyping it and you test it because
+there the marker that you're testing as
+
+ align:start position:0%
+there the marker that you're testing as
+ 
+
+ align:start position:0%
+there the marker that you're testing as
+opposed to being you know a distance
+
+ align:start position:0%
+opposed to being you know a distance
+ 
+
+ align:start position:0%
+opposed to being you know a distance
+away is perfectly Carly with the
+
+ align:start position:0%
+away is perfectly Carly with the
+ 
+
+ align:start position:0%
+away is perfectly Carly with the
+variance that's the ideal situation and
+
+ align:start position:0%
+variance that's the ideal situation and
+ 
+
+ align:start position:0%
+variance that's the ideal situation and
+so that implies that maybe we should
+
+ align:start position:0%
+so that implies that maybe we should
+ 
+
+ align:start position:0%
+so that implies that maybe we should
+actually really concentrate our efforts
+
+ align:start position:0%
+actually really concentrate our efforts
+ 
+
+ align:start position:0%
+actually really concentrate our efforts
+on finding the variants that are most
+
+ align:start position:0%
+on finding the variants that are most
+ 
+
+ align:start position:0%
+on finding the variants that are most
+likely to be functional so similar to
+
+ align:start position:0%
+likely to be functional so similar to
+ 
+
+ align:start position:0%
+likely to be functional so similar to
+the way you might try to find the genes
+
+ align:start position:0%
+the way you might try to find the genes
+ 
+
+ align:start position:0%
+the way you might try to find the genes
+that are most likely to be responsible
+
+ align:start position:0%
+that are most likely to be responsible
+ 
+
+ align:start position:0%
+that are most likely to be responsible
+the most obvious things are missense
+
+ align:start position:0%
+the most obvious things are missense
+ 
+
+ align:start position:0%
+the most obvious things are missense
+variants
+
+ align:start position:0%
+variants
+ 
+
+ align:start position:0%
+variants
+and these are easy to recognize it's
+
+ align:start position:0%
+and these are easy to recognize it's
+ 
+
+ align:start position:0%
+and these are easy to recognize it's
+been shown if you look at their they're
+
+ align:start position:0%
+been shown if you look at their they're
+ 
+
+ align:start position:0%
+been shown if you look at their they're
+much rarer than they should be which
+
+ align:start position:0%
+much rarer than they should be which
+ 
+
+ align:start position:0%
+much rarer than they should be which
+means Evolution has cared about them to
+
+ align:start position:0%
+means Evolution has cared about them to
+ 
+
+ align:start position:0%
+means Evolution has cared about them to
+suppress them so many of them are
+
+ align:start position:0%
+suppress them so many of them are
+ 
+
+ align:start position:0%
+suppress them so many of them are
+actually mildly deleterious maybe you
+
+ align:start position:0%
+actually mildly deleterious maybe you
+ 
+
+ align:start position:0%
+actually mildly deleterious maybe you
+know they're not severe deleterious but
+
+ align:start position:0%
+know they're not severe deleterious but
+ 
+
+ align:start position:0%
+know they're not severe deleterious but
+maybe this is just the right balance of
+
+ align:start position:0%
+maybe this is just the right balance of
+ 
+
+ align:start position:0%
+maybe this is just the right balance of
+things to cause common disease
+
+ align:start position:0%
+things to cause common disease
+ 
+
+ align:start position:0%
+things to cause common disease
+and even if you're doing rare variants
+
+ align:start position:0%
+and even if you're doing rare variants
+ 
+
+ align:start position:0%
+and even if you're doing rare variants
+you can recognize them and group them
+
+ align:start position:0%
+you can recognize them and group them
+ 
+
+ align:start position:0%
+you can recognize them and group them
+together and study them as a class if
+
+ align:start position:0%
+together and study them as a class if
+ 
+
+ align:start position:0%
+together and study them as a class if
+you want to say if you have the model
+
+ align:start position:0%
+you want to say if you have the model
+ 
+
+ align:start position:0%
+you want to say if you have the model
+that rare variants cause disease
+
+ align:start position:0%
+that rare variants cause disease
+ 
+
+ align:start position:0%
+that rare variants cause disease
+so but we know and there are plenty of
+
+ align:start position:0%
+so but we know and there are plenty of
+ 
+
+ align:start position:0%
+so but we know and there are plenty of
+cases now where the variant that's been
+
+ align:start position:0%
+cases now where the variant that's been
+ 
+
+ align:start position:0%
+cases now where the variant that's been
+finally identified is actually for a
+
+ align:start position:0%
+finally identified is actually for a
+ 
+
+ align:start position:0%
+finally identified is actually for a
+complex trait has not been a misens
+
+ align:start position:0%
+complex trait has not been a misens
+ 
+
+ align:start position:0%
+complex trait has not been a misens
+variant but it's been a regulatory
+
+ align:start position:0%
+variant but it's been a regulatory
+ 
+
+ align:start position:0%
+variant but it's been a regulatory
+variant that affects the level of the
+
+ align:start position:0%
+variant that affects the level of the
+ 
+
+ align:start position:0%
+variant that affects the level of the
+gene but not the structure of the
+
+ align:start position:0%
+gene but not the structure of the
+ 
+
+ align:start position:0%
+gene but not the structure of the
+protein it encodes there's a great
+
+ align:start position:0%
+protein it encodes there's a great
+ 
+
+ align:start position:0%
+protein it encodes there's a great
+example from type 1 diabetes from John
+
+ align:start position:0%
+example from type 1 diabetes from John
+ 
+
+ align:start position:0%
+example from type 1 diabetes from John
+Todd this group and others where there
+
+ align:start position:0%
+Todd this group and others where there
+ 
+
+ align:start position:0%
+Todd this group and others where there
+was a misense variant that was thought
+
+ align:start position:0%
+was a misense variant that was thought
+ 
+
+ align:start position:0%
+was a misense variant that was thought
+to be the right variant but then they
+
+ align:start position:0%
+to be the right variant but then they
+ 
+
+ align:start position:0%
+to be the right variant but then they
+did a huge study and showed that in fact
+
+ align:start position:0%
+did a huge study and showed that in fact
+ 
+
+ align:start position:0%
+did a huge study and showed that in fact
+all of the association that they saw
+
+ align:start position:0%
+all of the association that they saw
+ 
+
+ align:start position:0%
+all of the association that they saw
+with the missense brain was actually
+
+ align:start position:0%
+with the missense brain was actually
+ 
+
+ align:start position:0%
+with the missense brain was actually
+explained by something in the three
+
+ align:start position:0%
+explained by something in the three
+ 
+
+ align:start position:0%
+explained by something in the three
+prime utr and infected the level of the
+
+ align:start position:0%
+prime utr and infected the level of the
+ 
+
+ align:start position:0%
+prime utr and infected the level of the
+gene
+
+ align:start position:0%
+gene
+ 
+
+ align:start position:0%
+gene
+so the question is well these are hard
+
+ align:start position:0%
+so the question is well these are hard
+ 
+
+ align:start position:0%
+so the question is well these are hard
+to recognize there's lots of variation
+
+ align:start position:0%
+to recognize there's lots of variation
+ 
+
+ align:start position:0%
+to recognize there's lots of variation
+out there we have no idea how to reach
+
+ align:start position:0%
+out there we have no idea how to reach
+ 
+
+ align:start position:0%
+out there we have no idea how to reach
+so the reason we can recognize misense
+
+ align:start position:0%
+so the reason we can recognize misense
+ 
+
+ align:start position:0%
+so the reason we can recognize misense
+variants right is we we know the genetic
+
+ align:start position:0%
+variants right is we we know the genetic
+ 
+
+ align:start position:0%
+variants right is we we know the genetic
+code right they crack that you know soon
+
+ align:start position:0%
+code right they crack that you know soon
+ 
+
+ align:start position:0%
+code right they crack that you know soon
+after DNA
+
+ align:start position:0%
+after DNA
+ 
+
+ align:start position:0%
+after DNA
+um but we don't know the regulatory code
+
+ align:start position:0%
+um but we don't know the regulatory code
+ 
+
+ align:start position:0%
+um but we don't know the regulatory code
+um so there's some effort now to try to
+
+ align:start position:0%
+um so there's some effort now to try to
+ 
+
+ align:start position:0%
+um so there's some effort now to try to
+crack essentially the regulatory code by
+
+ align:start position:0%
+crack essentially the regulatory code by
+ 
+
+ align:start position:0%
+crack essentially the regulatory code by
+using multiple species and doing
+
+ align:start position:0%
+using multiple species and doing
+ 
+
+ align:start position:0%
+using multiple species and doing
+comparisons this is from Eddie Rubens
+
+ align:start position:0%
+comparisons this is from Eddie Rubens
+ 
+
+ align:start position:0%
+comparisons this is from Eddie Rubens
+group uh this is a great website it's
+
+ align:start position:0%
+group uh this is a great website it's
+ 
+
+ align:start position:0%
+group uh this is a great website it's
+called the ECR browser and you can see
+
+ align:start position:0%
+called the ECR browser and you can see
+ 
+
+ align:start position:0%
+called the ECR browser and you can see
+uh what you see here is Regions that are
+
+ align:start position:0%
+uh what you see here is Regions that are
+ 
+
+ align:start position:0%
+uh what you see here is Regions that are
+actually evolutionarily conserved across
+
+ align:start position:0%
+actually evolutionarily conserved across
+ 
+
+ align:start position:0%
+actually evolutionarily conserved across
+species and therefore may be important
+
+ align:start position:0%
+species and therefore may be important
+ 
+
+ align:start position:0%
+species and therefore may be important
+Evolution has tried has cared about them
+
+ align:start position:0%
+Evolution has tried has cared about them
+ 
+
+ align:start position:0%
+Evolution has tried has cared about them
+again so they may be important
+
+ align:start position:0%
+again so they may be important
+ 
+
+ align:start position:0%
+again so they may be important
+regulatory regions and there's
+
+ align:start position:0%
+regulatory regions and there's
+ 
+
+ align:start position:0%
+regulatory regions and there's
+experimental backup for that hypothesis
+
+ align:start position:0%
+experimental backup for that hypothesis
+ 
+
+ align:start position:0%
+experimental backup for that hypothesis
+so basically that would suggest that we
+
+ align:start position:0%
+so basically that would suggest that we
+ 
+
+ align:start position:0%
+so basically that would suggest that we
+should and Russian boxing have suggested
+
+ align:start position:0%
+should and Russian boxing have suggested
+ 
+
+ align:start position:0%
+should and Russian boxing have suggested
+this Approach at least for missense
+
+ align:start position:0%
+this Approach at least for missense
+ 
+
+ align:start position:0%
+this Approach at least for missense
+variants then we should resequence uh
+
+ align:start position:0%
+variants then we should resequence uh
+ 
+
+ align:start position:0%
+variants then we should resequence uh
+targeted regions try to find every
+
+ align:start position:0%
+targeted regions try to find every
+ 
+
+ align:start position:0%
+targeted regions try to find every
+variant that's in there and make sure we
+
+ align:start position:0%
+variant that's in there and make sure we
+ 
+
+ align:start position:0%
+variant that's in there and make sure we
+type all of them
+
+ align:start position:0%
+type all of them
+ 
+
+ align:start position:0%
+type all of them
+um and again the issue is that
+
+ align:start position:0%
+um and again the issue is that
+ 
+
+ align:start position:0%
+um and again the issue is that
+resequencing is expensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we might not have the causal variant in
+
+ align:start position:0%
+we might not have the causal variant in
+ 
+
+ align:start position:0%
+we might not have the causal variant in
+hand if we don't go through this
+
+ align:start position:0%
+hand if we don't go through this
+ 
+
+ align:start position:0%
+hand if we don't go through this
+approach or if we're bad at guessing
+
+ align:start position:0%
+approach or if we're bad at guessing
+ 
+
+ align:start position:0%
+approach or if we're bad at guessing
+what the regulatory variants are so we
+
+ align:start position:0%
+what the regulatory variants are so we
+ 
+
+ align:start position:0%
+what the regulatory variants are so we
+should try to understand also the
+
+ align:start position:0%
+should try to understand also the
+ 
+
+ align:start position:0%
+should try to understand also the
+correlation between variants I alluded
+
+ align:start position:0%
+correlation between variants I alluded
+ 
+
+ align:start position:0%
+correlation between variants I alluded
+to the fact that Snips are redundant
+
+ align:start position:0%
+to the fact that Snips are redundant
+ 
+
+ align:start position:0%
+to the fact that Snips are redundant
+with each other
+
+ align:start position:0%
+with each other
+ 
+
+ align:start position:0%
+with each other
+so if you have the causal variant that
+
+ align:start position:0%
+so if you have the causal variant that
+ 
+
+ align:start position:0%
+so if you have the causal variant that
+hasn't been genotyped you have to infer
+
+ align:start position:0%
+hasn't been genotyped you have to infer
+ 
+
+ align:start position:0%
+hasn't been genotyped you have to infer
+its effect by genotyping neighboring
+
+ align:start position:0%
+its effect by genotyping neighboring
+ 
+
+ align:start position:0%
+its effect by genotyping neighboring
+snips
+
+ align:start position:0%
+snips
+ 
+
+ align:start position:0%
+snips
+and so they have to be correlated or
+
+ align:start position:0%
+and so they have to be correlated or
+ 
+
+ align:start position:0%
+and so they have to be correlated or
+what's called a linkage disequilibrium
+
+ align:start position:0%
+what's called a linkage disequilibrium
+ 
+
+ align:start position:0%
+what's called a linkage disequilibrium
+with the causal variant
+
+ align:start position:0%
+with the causal variant
+ 
+
+ align:start position:0%
+with the causal variant
+it turns out that a lot of the times
+
+ align:start position:0%
+it turns out that a lot of the times
+ 
+
+ align:start position:0%
+it turns out that a lot of the times
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+so this is actually what the genome uh
+
+ align:start position:0%
+so this is actually what the genome uh
+ 
+
+ align:start position:0%
+so this is actually what the genome uh
+looks like most of the time or most of
+
+ align:start position:0%
+looks like most of the time or most of
+ 
+
+ align:start position:0%
+looks like most of the time or most of
+the genome where this is it meant that
+
+ align:start position:0%
+the genome where this is it meant that
+ 
+
+ align:start position:0%
+the genome where this is it meant that
+that slide that I showed you before I
+
+ align:start position:0%
+that slide that I showed you before I
+ 
+
+ align:start position:0%
+that slide that I showed you before I
+imagine this is now zoomed out we're
+
+ align:start position:0%
+imagine this is now zoomed out we're
+ 
+
+ align:start position:0%
+imagine this is now zoomed out we're
+looking at 30 000 faces of a bunch of
+
+ align:start position:0%
+looking at 30 000 faces of a bunch of
+ 
+
+ align:start position:0%
+looking at 30 000 faces of a bunch of
+different chromosomes you see as if you
+
+ align:start position:0%
+different chromosomes you see as if you
+ 
+
+ align:start position:0%
+different chromosomes you see as if you
+have a c here and a c here you can
+
+ align:start position:0%
+have a c here and a c here you can
+ 
+
+ align:start position:0%
+have a c here and a c here you can
+predict that you can have a g here A C
+
+ align:start position:0%
+predict that you can have a g here A C
+ 
+
+ align:start position:0%
+predict that you can have a g here A C
+here an a here to C there and these
+
+ align:start position:0%
+here an a here to C there and these
+ 
+
+ align:start position:0%
+here an a here to C there and these
+patterns of alleles are called
+
+ align:start position:0%
+patterns of alleles are called
+ 
+
+ align:start position:0%
+patterns of alleles are called
+haplotypes and in most of the genome
+
+ align:start position:0%
+haplotypes and in most of the genome
+ 
+
+ align:start position:0%
+haplotypes and in most of the genome
+there are these blocks of correlation or
+
+ align:start position:0%
+there are these blocks of correlation or
+ 
+
+ align:start position:0%
+there are these blocks of correlation or
+blocks of linkages equilibrium where
+
+ align:start position:0%
+blocks of linkages equilibrium where
+ 
+
+ align:start position:0%
+blocks of linkages equilibrium where
+there are only a few common haplotypes
+
+ align:start position:0%
+there are only a few common haplotypes
+ 
+
+ align:start position:0%
+there are only a few common haplotypes
+in this case the red the blue and the
+
+ align:start position:0%
+in this case the red the blue and the
+ 
+
+ align:start position:0%
+in this case the red the blue and the
+yellow and occasionally there's uh
+
+ align:start position:0%
+yellow and occasionally there's uh
+ 
+
+ align:start position:0%
+yellow and occasionally there's uh
+shuffling it by recombination these were
+
+ align:start position:0%
+shuffling it by recombination these were
+ 
+
+ align:start position:0%
+shuffling it by recombination these were
+first identified but more daily and
+
+ align:start position:0%
+first identified but more daily and
+ 
+
+ align:start position:0%
+first identified but more daily and
+colleagues and genetics and then this
+
+ align:start position:0%
+colleagues and genetics and then this
+ 
+
+ align:start position:0%
+colleagues and genetics and then this
+sort of shown to be true on a
+
+ align:start position:0%
+sort of shown to be true on a
+ 
+
+ align:start position:0%
+sort of shown to be true on a
+genome-like scale is Stacy Gabriel about
+
+ align:start position:0%
+genome-like scale is Stacy Gabriel about
+ 
+
+ align:start position:0%
+genome-like scale is Stacy Gabriel about
+and the reason this is useful is that if
+
+ align:start position:0%
+and the reason this is useful is that if
+ 
+
+ align:start position:0%
+and the reason this is useful is that if
+there's a causal polymorphism but not
+
+ align:start position:0%
+there's a causal polymorphism but not
+ 
+
+ align:start position:0%
+there's a causal polymorphism but not
+one that you've typed You can predict it
+
+ align:start position:0%
+one that you've typed You can predict it
+ 
+
+ align:start position:0%
+one that you've typed You can predict it
+pretty well by the neighboring markers
+
+ align:start position:0%
+pretty well by the neighboring markers
+ 
+
+ align:start position:0%
+pretty well by the neighboring markers
+that if you have a c here and an a here
+
+ align:start position:0%
+that if you have a c here and an a here
+ 
+
+ align:start position:0%
+that if you have a c here and an a here
+then you probably are carrying this
+
+ align:start position:0%
+then you probably are carrying this
+ 
+
+ align:start position:0%
+then you probably are carrying this
+causal polymorphism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I'll take you through briefly uh but I'm
+
+ align:start position:0%
+I'll take you through briefly uh but I'm
+ 
+
+ align:start position:0%
+I'll take you through briefly uh but I'm
+going to blow through this a little bit
+
+ align:start position:0%
+going to blow through this a little bit
+ 
+
+ align:start position:0%
+going to blow through this a little bit
+just the uh range of uh
+
+ align:start position:0%
+just the uh range of uh
+ 
+
+ align:start position:0%
+just the uh range of uh
+what what these patterns look like
+
+ align:start position:0%
+what what these patterns look like
+ 
+
+ align:start position:0%
+what what these patterns look like
+there's a measure of correlation which
+
+ align:start position:0%
+there's a measure of correlation which
+ 
+
+ align:start position:0%
+there's a measure of correlation which
+is not important to understand called D
+
+ align:start position:0%
+is not important to understand called D
+ 
+
+ align:start position:0%
+is not important to understand called D
+Prime basically red means that the Snips
+
+ align:start position:0%
+Prime basically red means that the Snips
+ 
+
+ align:start position:0%
+Prime basically red means that the Snips
+are correlated with each other and any
+
+ align:start position:0%
+are correlated with each other and any
+ 
+
+ align:start position:0%
+are correlated with each other and any
+other color means that you're not sure
+
+ align:start position:0%
+other color means that you're not sure
+ 
+
+ align:start position:0%
+other color means that you're not sure
+if they are and I'll show you a little a
+
+ align:start position:0%
+if they are and I'll show you a little a
+ 
+
+ align:start position:0%
+if they are and I'll show you a little a
+little plot like this where this is the
+
+ align:start position:0%
+little plot like this where this is the
+ 
+
+ align:start position:0%
+little plot like this where this is the
+data for markers one and two and uh this
+
+ align:start position:0%
+data for markers one and two and uh this
+ 
+
+ align:start position:0%
+data for markers one and two and uh this
+is the data for markers three and five
+
+ align:start position:0%
+is the data for markers three and five
+ 
+
+ align:start position:0%
+is the data for markers three and five
+and this is what blocks look like where
+
+ align:start position:0%
+and this is what blocks look like where
+ 
+
+ align:start position:0%
+and this is what blocks look like where
+you see a whole bunch of red triangle
+
+ align:start position:0%
+you see a whole bunch of red triangle
+ 
+
+ align:start position:0%
+you see a whole bunch of red triangle
+here which means that all the markers
+
+ align:start position:0%
+here which means that all the markers
+ 
+
+ align:start position:0%
+here which means that all the markers
+one to six or correlated with each other
+
+ align:start position:0%
+one to six or correlated with each other
+ 
+
+ align:start position:0%
+one to six or correlated with each other
+and then here 8 to 13 are all correlated
+
+ align:start position:0%
+and then here 8 to 13 are all correlated
+ 
+
+ align:start position:0%
+and then here 8 to 13 are all correlated
+with each other and that corresponds
+
+ align:start position:0%
+with each other and that corresponds
+ 
+
+ align:start position:0%
+with each other and that corresponds
+they're being two blocks of linkages
+
+ align:start position:0%
+they're being two blocks of linkages
+ 
+
+ align:start position:0%
+they're being two blocks of linkages
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and if you again from the Gabriel paper
+
+ align:start position:0%
+and if you again from the Gabriel paper
+ 
+
+ align:start position:0%
+and if you again from the Gabriel paper
+if you look just concentrate on the
+
+ align:start position:0%
+if you look just concentrate on the
+ 
+
+ align:start position:0%
+if you look just concentrate on the
+figure on the right
+
+ align:start position:0%
+figure on the right
+ 
+
+ align:start position:0%
+figure on the right
+um in uh for example a European
+
+ align:start position:0%
+um in uh for example a European
+ 
+
+ align:start position:0%
+um in uh for example a European
+population or Asian population uh over
+
+ align:start position:0%
+population or Asian population uh over
+ 
+
+ align:start position:0%
+population or Asian population uh over
+almost 40 percent of the genome is found
+
+ align:start position:0%
+almost 40 percent of the genome is found
+ 
+
+ align:start position:0%
+almost 40 percent of the genome is found
+in blocks of over 50 KB and the average
+
+ align:start position:0%
+in blocks of over 50 KB and the average
+ 
+
+ align:start position:0%
+in blocks of over 50 KB and the average
+block size is about 22 KB so on average
+
+ align:start position:0%
+block size is about 22 KB so on average
+ 
+
+ align:start position:0%
+block size is about 22 KB so on average
+if you look in the genome this this
+
+ align:start position:0%
+if you look in the genome this this
+ 
+
+ align:start position:0%
+if you look in the genome this this
+correlation that extends for tens of
+
+ align:start position:0%
+correlation that extends for tens of
+ 
+
+ align:start position:0%
+correlation that extends for tens of
+thousands of bases sort of on the order
+
+ align:start position:0%
+thousands of bases sort of on the order
+ 
+
+ align:start position:0%
+thousands of bases sort of on the order
+of the size of a gene although it
+
+ align:start position:0%
+of the size of a gene although it
+ 
+
+ align:start position:0%
+of the size of a gene although it
+doesn't necessarily correlate perfectly
+
+ align:start position:0%
+doesn't necessarily correlate perfectly
+ 
+
+ align:start position:0%
+doesn't necessarily correlate perfectly
+with genes
+
+ align:start position:0%
+with genes
+ 
+
+ align:start position:0%
+with genes
+and within those blocks as I showed you
+
+ align:start position:0%
+and within those blocks as I showed you
+ 
+
+ align:start position:0%
+and within those blocks as I showed you
+with that red blue and yellow pattern
+
+ align:start position:0%
+with that red blue and yellow pattern
+ 
+
+ align:start position:0%
+with that red blue and yellow pattern
+there's only a few uh common haplotypes
+
+ align:start position:0%
+there's only a few uh common haplotypes
+ 
+
+ align:start position:0%
+there's only a few uh common haplotypes
+uh present so you know sort of in the
+
+ align:start position:0%
+uh present so you know sort of in the
+ 
+
+ align:start position:0%
+uh present so you know sort of in the
+order of three to four for non-african
+
+ align:start position:0%
+order of three to four for non-african
+ 
+
+ align:start position:0%
+order of three to four for non-african
+populations and one or two more for
+
+ align:start position:0%
+populations and one or two more for
+ 
+
+ align:start position:0%
+populations and one or two more for
+African populations and they explain the
+
+ align:start position:0%
+African populations and they explain the
+ 
+
+ align:start position:0%
+African populations and they explain the
+vast majority of the chromosomes in that
+
+ align:start position:0%
+vast majority of the chromosomes in that
+ 
+
+ align:start position:0%
+vast majority of the chromosomes in that
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+and furthermore the the haplotypes
+
+ align:start position:0%
+and furthermore the the haplotypes
+ 
+
+ align:start position:0%
+and furthermore the the haplotypes
+themselves are generally shared again
+
+ align:start position:0%
+themselves are generally shared again
+ 
+
+ align:start position:0%
+themselves are generally shared again
+Africans have a little bit more and this
+
+ align:start position:0%
+Africans have a little bit more and this
+ 
+
+ align:start position:0%
+Africans have a little bit more and this
+is because when uh humans emerge from
+
+ align:start position:0%
+is because when uh humans emerge from
+ 
+
+ align:start position:0%
+is because when uh humans emerge from
+Africa only a subset of the genetic
+
+ align:start position:0%
+Africa only a subset of the genetic
+ 
+
+ align:start position:0%
+Africa only a subset of the genetic
+diversity went with them so Africa is
+
+ align:start position:0%
+diversity went with them so Africa is
+ 
+
+ align:start position:0%
+diversity went with them so Africa is
+actually more diverse uh continent than
+
+ align:start position:0%
+actually more diverse uh continent than
+ 
+
+ align:start position:0%
+actually more diverse uh continent than
+the rest of the world is
+
+ align:start position:0%
+the rest of the world is
+ 
+
+ align:start position:0%
+the rest of the world is
+and I won't go through the reasons that
+
+ align:start position:0%
+and I won't go through the reasons that
+ 
+
+ align:start position:0%
+and I won't go through the reasons that
+blocks exist but basically it has to do
+
+ align:start position:0%
+blocks exist but basically it has to do
+ 
+
+ align:start position:0%
+blocks exist but basically it has to do
+with sort of the nature of recombination
+
+ align:start position:0%
+with sort of the nature of recombination
+ 
+
+ align:start position:0%
+with sort of the nature of recombination
+the fact that there are hot spots for
+
+ align:start position:0%
+the fact that there are hot spots for
+ 
+
+ align:start position:0%
+the fact that there are hot spots for
+combination and
+
+ align:start position:0%
+combination and
+ 
+
+ align:start position:0%
+combination and
+and this uh emergence uh This Out of
+
+ align:start position:0%
+and this uh emergence uh This Out of
+ 
+
+ align:start position:0%
+and this uh emergence uh This Out of
+Africa pattern
+
+ align:start position:0%
+Africa pattern
+ 
+
+ align:start position:0%
+Africa pattern
+and so that's led to a proposal that
+
+ align:start position:0%
+and so that's led to a proposal that
+ 
+
+ align:start position:0%
+and so that's led to a proposal that
+basically if you can recognize these red
+
+ align:start position:0%
+basically if you can recognize these red
+ 
+
+ align:start position:0%
+basically if you can recognize these red
+blue and yellow patterns
+
+ align:start position:0%
+blue and yellow patterns
+ 
+
+ align:start position:0%
+blue and yellow patterns
+you can then identify a few tag Snips in
+
+ align:start position:0%
+you can then identify a few tag Snips in
+ 
+
+ align:start position:0%
+you can then identify a few tag Snips in
+this case two which distinguish those
+
+ align:start position:0%
+this case two which distinguish those
+ 
+
+ align:start position:0%
+this case two which distinguish those
+patterns so if you have the red variant
+
+ align:start position:0%
+patterns so if you have the red variant
+ 
+
+ align:start position:0%
+patterns so if you have the red variant
+you're if you if you have the variant
+
+ align:start position:0%
+you're if you if you have the variant
+ 
+
+ align:start position:0%
+you're if you if you have the variant
+for text of one you're red if you have
+
+ align:start position:0%
+for text of one you're red if you have
+ 
+
+ align:start position:0%
+for text of one you're red if you have
+the variant protects and two you're
+
+ align:start position:0%
+the variant protects and two you're
+ 
+
+ align:start position:0%
+the variant protects and two you're
+yellow and if you don't have either
+
+ align:start position:0%
+yellow and if you don't have either
+ 
+
+ align:start position:0%
+yellow and if you don't have either
+variant you must have been blue
+
+ align:start position:0%
+variant you must have been blue
+ 
+
+ align:start position:0%
+variant you must have been blue
+and so this means that if you can
+
+ align:start position:0%
+and so this means that if you can
+ 
+
+ align:start position:0%
+and so this means that if you can
+type enough markers to distinguish these
+
+ align:start position:0%
+type enough markers to distinguish these
+ 
+
+ align:start position:0%
+type enough markers to distinguish these
+patterns you can then identify these tag
+
+ align:start position:0%
+patterns you can then identify these tag
+ 
+
+ align:start position:0%
+patterns you can then identify these tag
+Snips that greatly reduces the effort
+
+ align:start position:0%
+Snips that greatly reduces the effort
+ 
+
+ align:start position:0%
+Snips that greatly reduces the effort
+you need to cover a region
+
+ align:start position:0%
+you need to cover a region
+ 
+
+ align:start position:0%
+you need to cover a region
+and so that's the goal of the human
+
+ align:start position:0%
+and so that's the goal of the human
+ 
+
+ align:start position:0%
+and so that's the goal of the human
+haplotype map which is ongoing is 100
+
+ align:start position:0%
+haplotype map which is ongoing is 100
+ 
+
+ align:start position:0%
+haplotype map which is ongoing is 100
+million dollar International project
+
+ align:start position:0%
+million dollar International project
+ 
+
+ align:start position:0%
+million dollar International project
+it's basically to type about a million
+
+ align:start position:0%
+it's basically to type about a million
+ 
+
+ align:start position:0%
+it's basically to type about a million
+or more markers in three different
+
+ align:start position:0%
+or more markers in three different
+ 
+
+ align:start position:0%
+or more markers in three different
+reference populations
+
+ align:start position:0%
+reference populations
+ 
+
+ align:start position:0%
+reference populations
+um European American West African and
+
+ align:start position:0%
+um European American West African and
+ 
+
+ align:start position:0%
+um European American West African and
+then East Asian which is Japanese and
+
+ align:start position:0%
+then East Asian which is Japanese and
+ 
+
+ align:start position:0%
+then East Asian which is Japanese and
+Chinese and you can go to the hapmap
+
+ align:start position:0%
+Chinese and you can go to the hapmap
+ 
+
+ align:start position:0%
+Chinese and you can go to the hapmap
+website or see this nature description
+
+ align:start position:0%
+website or see this nature description
+ 
+
+ align:start position:0%
+website or see this nature description
+for this goal is to identify all these
+
+ align:start position:0%
+for this goal is to identify all these
+ 
+
+ align:start position:0%
+for this goal is to identify all these
+tag snips
+
+ align:start position:0%
+tag snips
+ 
+
+ align:start position:0%
+tag snips
+and so the approach we basically take
+
+ align:start position:0%
+and so the approach we basically take
+ 
+
+ align:start position:0%
+and so the approach we basically take
+the steps from the database
+
+ align:start position:0%
+the steps from the database
+ 
+
+ align:start position:0%
+the steps from the database
+genotype these Snips and reference
+
+ align:start position:0%
+genotype these Snips and reference
+ 
+
+ align:start position:0%
+genotype these Snips and reference
+panels
+
+ align:start position:0%
+panels
+ 
+
+ align:start position:0%
+panels
+uh measure the linkages of equilibrium
+
+ align:start position:0%
+uh measure the linkages of equilibrium
+ 
+
+ align:start position:0%
+uh measure the linkages of equilibrium
+and then identify the tag Snips and then
+
+ align:start position:0%
+and then identify the tag Snips and then
+ 
+
+ align:start position:0%
+and then identify the tag Snips and then
+select them and then take those Snips
+
+ align:start position:0%
+select them and then take those Snips
+ 
+
+ align:start position:0%
+select them and then take those Snips
+and type them in population
+
+ align:start position:0%
+and type them in population
+ 
+
+ align:start position:0%
+and type them in population
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's kind of how one would set up
+
+ align:start position:0%
+so that's kind of how one would set up
+ 
+
+ align:start position:0%
+so that's kind of how one would set up
+in 2004 to do an association study where
+
+ align:start position:0%
+in 2004 to do an association study where
+ 
+
+ align:start position:0%
+in 2004 to do an association study where
+you pick genes you would understand the
+
+ align:start position:0%
+you pick genes you would understand the
+ 
+
+ align:start position:0%
+you pick genes you would understand the
+haplotype structure you might even do
+
+ align:start position:0%
+haplotype structure you might even do
+ 
+
+ align:start position:0%
+haplotype structure you might even do
+some resequencing to make sure you had
+
+ align:start position:0%
+some resequencing to make sure you had
+ 
+
+ align:start position:0%
+some resequencing to make sure you had
+all the missense variants and then you
+
+ align:start position:0%
+all the missense variants and then you
+ 
+
+ align:start position:0%
+all the missense variants and then you
+would take some set some subset of
+
+ align:start position:0%
+would take some set some subset of
+ 
+
+ align:start position:0%
+would take some set some subset of
+variants and type them in populations
+
+ align:start position:0%
+variants and type them in populations
+ 
+
+ align:start position:0%
+variants and type them in populations
+do your Association study
+
+ align:start position:0%
+do your Association study
+ 
+
+ align:start position:0%
+do your Association study
+the problem is that if what after you've
+
+ align:start position:0%
+the problem is that if what after you've
+ 
+
+ align:start position:0%
+the problem is that if what after you've
+done all that work to set up to do this
+
+ align:start position:0%
+done all that work to set up to do this
+ 
+
+ align:start position:0%
+done all that work to set up to do this
+you do an association and you publish it
+
+ align:start position:0%
+you do an association and you publish it
+ 
+
+ align:start position:0%
+you do an association and you publish it
+and you find that it's very difficult
+
+ align:start position:0%
+and you find that it's very difficult
+ 
+
+ align:start position:0%
+and you find that it's very difficult
+for anybody else to reproduce it okay so
+
+ align:start position:0%
+for anybody else to reproduce it okay so
+ 
+
+ align:start position:0%
+for anybody else to reproduce it okay so
+that was a lot of work for nothing right
+
+ align:start position:0%
+that was a lot of work for nothing right
+ 
+
+ align:start position:0%
+that was a lot of work for nothing right
+um so we wanted to understand if we were
+
+ align:start position:0%
+um so we wanted to understand if we were
+ 
+
+ align:start position:0%
+um so we wanted to understand if we were
+going to try to use this as a tool well
+
+ align:start position:0%
+going to try to use this as a tool well
+ 
+
+ align:start position:0%
+going to try to use this as a tool well
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+why are Association studies not uh
+
+ align:start position:0%
+why are Association studies not uh
+ 
+
+ align:start position:0%
+why are Association studies not uh
+reproduced and there's really
+
+ align:start position:0%
+reproduced and there's really
+ 
+
+ align:start position:0%
+reproduced and there's really
+three possible explanations one is could
+
+ align:start position:0%
+three possible explanations one is could
+ 
+
+ align:start position:0%
+three possible explanations one is could
+be false positive so when you did your
+
+ align:start position:0%
+be false positive so when you did your
+ 
+
+ align:start position:0%
+be false positive so when you did your
+Association it was just wrong okay you
+
+ align:start position:0%
+Association it was just wrong okay you
+ 
+
+ align:start position:0%
+Association it was just wrong okay you
+know maybe you've tested a lot of genes
+
+ align:start position:0%
+know maybe you've tested a lot of genes
+ 
+
+ align:start position:0%
+know maybe you've tested a lot of genes
+and tested a lot of variants in a lot of
+
+ align:start position:0%
+and tested a lot of variants in a lot of
+ 
+
+ align:start position:0%
+and tested a lot of variants in a lot of
+genes and by chance you got a p-value of
+
+ align:start position:0%
+genes and by chance you got a p-value of
+ 
+
+ align:start position:0%
+genes and by chance you got a p-value of
+0.01 okay so you go ahead and you
+
+ align:start position:0%
+0.01 okay so you go ahead and you
+ 
+
+ align:start position:0%
+0.01 okay so you go ahead and you
+publish it and it was just because you'd
+
+ align:start position:0%
+publish it and it was just because you'd
+ 
+
+ align:start position:0%
+publish it and it was just because you'd
+flip the coin a bunch of times and
+
+ align:start position:0%
+flip the coin a bunch of times and
+ 
+
+ align:start position:0%
+flip the coin a bunch of times and
+you've got a row you got a run of heads
+
+ align:start position:0%
+you've got a row you got a run of heads
+ 
+
+ align:start position:0%
+you've got a row you got a run of heads
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh it doesn't mean the coin is
+
+ align:start position:0%
+uh it doesn't mean the coin is
+ 
+
+ align:start position:0%
+uh it doesn't mean the coin is
+two-headed
+
+ align:start position:0%
+two-headed
+ 
+
+ align:start position:0%
+two-headed
+it could mean that in fact you were
+
+ align:start position:0%
+it could mean that in fact you were
+ 
+
+ align:start position:0%
+it could mean that in fact you were
+right but then the people who came after
+
+ align:start position:0%
+right but then the people who came after
+ 
+
+ align:start position:0%
+right but then the people who came after
+you had little small studies and they
+
+ align:start position:0%
+you had little small studies and they
+ 
+
+ align:start position:0%
+you had little small studies and they
+were they were looking for a modest
+
+ align:start position:0%
+were they were looking for a modest
+ 
+
+ align:start position:0%
+were they were looking for a modest
+effect and they just didn't have enough
+
+ align:start position:0%
+effect and they just didn't have enough
+ 
+
+ align:start position:0%
+effect and they just didn't have enough
+power okay so it actually was the coin
+
+ align:start position:0%
+power okay so it actually was the coin
+ 
+
+ align:start position:0%
+power okay so it actually was the coin
+was unfair right so it does come up
+
+ align:start position:0%
+was unfair right so it does come up
+ 
+
+ align:start position:0%
+was unfair right so it does come up
+heads more often than Tails but they
+
+ align:start position:0%
+heads more often than Tails but they
+ 
+
+ align:start position:0%
+heads more often than Tails but they
+only flipped it five times and it came
+
+ align:start position:0%
+only flipped it five times and it came
+ 
+
+ align:start position:0%
+only flipped it five times and it came
+up tails you know or they only flipped
+
+ align:start position:0%
+up tails you know or they only flipped
+ 
+
+ align:start position:0%
+up tails you know or they only flipped
+it six times and came up heads three
+
+ align:start position:0%
+it six times and came up heads three
+ 
+
+ align:start position:0%
+it six times and came up heads three
+times in Tails three times this
+
+ align:start position:0%
+times in Tails three times this
+ 
+
+ align:start position:0%
+times in Tails three times this
+equivalent of doing a study with not
+
+ align:start position:0%
+equivalent of doing a study with not
+ 
+
+ align:start position:0%
+equivalent of doing a study with not
+very many people okay so that's a sort
+
+ align:start position:0%
+very many people okay so that's a sort
+ 
+
+ align:start position:0%
+very many people okay so that's a sort
+of lack of power and then there could be
+
+ align:start position:0%
+of lack of power and then there could be
+ 
+
+ align:start position:0%
+of lack of power and then there could be
+true differences between populations so
+
+ align:start position:0%
+true differences between populations so
+ 
+
+ align:start position:0%
+true differences between populations so
+that the marker really is associated
+
+ align:start position:0%
+that the marker really is associated
+ 
+
+ align:start position:0%
+that the marker really is associated
+with disease in your population but not
+
+ align:start position:0%
+with disease in your population but not
+ 
+
+ align:start position:0%
+with disease in your population but not
+in the population that somebody else
+
+ align:start position:0%
+in the population that somebody else
+ 
+
+ align:start position:0%
+in the population that somebody else
+studied
+
+ align:start position:0%
+studied
+ 
+
+ align:start position:0%
+studied
+so we set out to kind of overview these
+
+ align:start position:0%
+so we set out to kind of overview these
+ 
+
+ align:start position:0%
+so we set out to kind of overview these
+the association study literature and say
+
+ align:start position:0%
+the association study literature and say
+ 
+
+ align:start position:0%
+the association study literature and say
+well what what explanations are actually
+
+ align:start position:0%
+well what what explanations are actually
+ 
+
+ align:start position:0%
+well what what explanations are actually
+going on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and we identified uh as a 2000 or 2001
+
+ align:start position:0%
+and we identified uh as a 2000 or 2001
+ 
+
+ align:start position:0%
+and we identified uh as a 2000 or 2001
+just over 600 associations between
+
+ align:start position:0%
+just over 600 associations between
+ 
+
+ align:start position:0%
+just over 600 associations between
+common variants and disease and they're
+
+ align:start position:0%
+common variants and disease and they're
+ 
+
+ align:start position:0%
+common variants and disease and they're
+way more than this now
+
+ align:start position:0%
+way more than this now
+ 
+
+ align:start position:0%
+way more than this now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there were 166 that have been studied at
+
+ align:start position:0%
+there were 166 that have been studied at
+ 
+
+ align:start position:0%
+there were 166 that have been studied at
+least three times so we could get a
+
+ align:start position:0%
+least three times so we could get a
+ 
+
+ align:start position:0%
+least three times so we could get a
+handle on the reproducibility
+
+ align:start position:0%
+handle on the reproducibility
+ 
+
+ align:start position:0%
+handle on the reproducibility
+and the first thing we noticed about of
+
+ align:start position:0%
+and the first thing we noticed about of
+ 
+
+ align:start position:0%
+and the first thing we noticed about of
+those 166 only six were actually highly
+
+ align:start position:0%
+those 166 only six were actually highly
+ 
+
+ align:start position:0%
+those 166 only six were actually highly
+consistently producible so only six were
+
+ align:start position:0%
+consistently producible so only six were
+ 
+
+ align:start position:0%
+consistently producible so only six were
+seen three quarters of the time
+
+ align:start position:0%
+seen three quarters of the time
+ 
+
+ align:start position:0%
+seen three quarters of the time
+so you could say well this is just
+
+ align:start position:0%
+so you could say well this is just
+ 
+
+ align:start position:0%
+so you could say well this is just
+terrible okay almost all associations
+
+ align:start position:0%
+terrible okay almost all associations
+ 
+
+ align:start position:0%
+terrible okay almost all associations
+just are not really reproducible
+
+ align:start position:0%
+just are not really reproducible
+ 
+
+ align:start position:0%
+just are not really reproducible
+um or you could say well you know
+
+ align:start position:0%
+um or you could say well you know
+ 
+
+ align:start position:0%
+um or you could say well you know
+actually you've only tested 166 things
+
+ align:start position:0%
+actually you've only tested 166 things
+ 
+
+ align:start position:0%
+actually you've only tested 166 things
+you found six real ones that's pretty
+
+ align:start position:0%
+you found six real ones that's pretty
+ 
+
+ align:start position:0%
+you found six real ones that's pretty
+good you know they're they're a lot
+
+ align:start position:0%
+good you know they're they're a lot
+ 
+
+ align:start position:0%
+good you know they're they're a lot
+there's 10 million things to test out
+
+ align:start position:0%
+there's 10 million things to test out
+ 
+
+ align:start position:0%
+there's 10 million things to test out
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+these are the six and one of them is
+
+ align:start position:0%
+these are the six and one of them is
+ 
+
+ align:start position:0%
+these are the six and one of them is
+this Paradigm that I showed you apoe4
+
+ align:start position:0%
+this Paradigm that I showed you apoe4
+ 
+
+ align:start position:0%
+this Paradigm that I showed you apoe4
+and then there's things like ccr5 Delta
+
+ align:start position:0%
+and then there's things like ccr5 Delta
+ 
+
+ align:start position:0%
+and then there's things like ccr5 Delta
+32 this dtla4 interesting this is that
+
+ align:start position:0%
+32 this dtla4 interesting this is that
+ 
+
+ align:start position:0%
+32 this dtla4 interesting this is that
+missense variant that I told you about
+
+ align:start position:0%
+missense variant that I told you about
+ 
+
+ align:start position:0%
+missense variant that I told you about
+that actually now this should be
+
+ align:start position:0%
+that actually now this should be
+ 
+
+ align:start position:0%
+that actually now this should be
+corrected to the three prime utr so even
+
+ align:start position:0%
+corrected to the three prime utr so even
+ 
+
+ align:start position:0%
+corrected to the three prime utr so even
+though they didn't have the right
+
+ align:start position:0%
+though they didn't have the right
+ 
+
+ align:start position:0%
+though they didn't have the right
+variant it was still pretty reproducible
+
+ align:start position:0%
+variant it was still pretty reproducible
+ 
+
+ align:start position:0%
+variant it was still pretty reproducible
+um Factor five uh and deepiness
+
+ align:start position:0%
+um Factor five uh and deepiness
+ 
+
+ align:start position:0%
+um Factor five uh and deepiness
+thrombosis and a couple of others and
+
+ align:start position:0%
+thrombosis and a couple of others and
+ 
+
+ align:start position:0%
+thrombosis and a couple of others and
+they're more on this list now although
+
+ align:start position:0%
+they're more on this list now although
+ 
+
+ align:start position:0%
+they're more on this list now although
+not many
+
+ align:start position:0%
+not many
+ 
+
+ align:start position:0%
+not many
+um that are that highly consistently
+
+ align:start position:0%
+um that are that highly consistently
+ 
+
+ align:start position:0%
+um that are that highly consistently
+reproducible
+
+ align:start position:0%
+reproducible
+ 
+
+ align:start position:0%
+reproducible
+so what about the other 160 are they
+
+ align:start position:0%
+so what about the other 160 are they
+ 
+
+ align:start position:0%
+so what about the other 160 are they
+just complete nonsense or or what why
+
+ align:start position:0%
+just complete nonsense or or what why
+ 
+
+ align:start position:0%
+just complete nonsense or or what why
+are they why are they not reproducible
+
+ align:start position:0%
+are they why are they not reproducible
+ 
+
+ align:start position:0%
+are they why are they not reproducible
+well the next thing we noticed was that
+
+ align:start position:0%
+well the next thing we noticed was that
+ 
+
+ align:start position:0%
+well the next thing we noticed was that
+of the 160 91 of them were actually seen
+
+ align:start position:0%
+of the 160 91 of them were actually seen
+ 
+
+ align:start position:0%
+of the 160 91 of them were actually seen
+multiple times so not just by the person
+
+ align:start position:0%
+multiple times so not just by the person
+ 
+
+ align:start position:0%
+multiple times so not just by the person
+who reported them but by somebody else
+
+ align:start position:0%
+who reported them but by somebody else
+ 
+
+ align:start position:0%
+who reported them but by somebody else
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+and so that suggested that maybe there
+
+ align:start position:0%
+and so that suggested that maybe there
+ 
+
+ align:start position:0%
+and so that suggested that maybe there
+was something real going on but we
+
+ align:start position:0%
+was something real going on but we
+ 
+
+ align:start position:0%
+was something real going on but we
+wanted to look at that in sort of a more
+
+ align:start position:0%
+wanted to look at that in sort of a more
+ 
+
+ align:start position:0%
+wanted to look at that in sort of a more
+formal way
+
+ align:start position:0%
+formal way
+ 
+
+ align:start position:0%
+formal way
+and so to do that we basically uh picked
+
+ align:start position:0%
+and so to do that we basically uh picked
+ 
+
+ align:start position:0%
+and so to do that we basically uh picked
+25 of these 160 associations for some
+
+ align:start position:0%
+25 of these 160 associations for some
+ 
+
+ align:start position:0%
+25 of these 160 associations for some
+diseases we cared about and some others
+
+ align:start position:0%
+diseases we cared about and some others
+ 
+
+ align:start position:0%
+diseases we cared about and some others
+at random
+
+ align:start position:0%
+at random
+ 
+
+ align:start position:0%
+at random
+and we got rid of the first person
+
+ align:start position:0%
+and we got rid of the first person
+ 
+
+ align:start position:0%
+and we got rid of the first person
+reported and we said of all the other
+
+ align:start position:0%
+reported and we said of all the other
+ 
+
+ align:start position:0%
+reported and we said of all the other
+people who tried to replicate it
+
+ align:start position:0%
+people who tried to replicate it
+ 
+
+ align:start position:0%
+people who tried to replicate it
+how well did they do
+
+ align:start position:0%
+how well did they do
+ 
+
+ align:start position:0%
+how well did they do
+um so there were 301 studies for these
+
+ align:start position:0%
+um so there were 301 studies for these
+ 
+
+ align:start position:0%
+um so there were 301 studies for these
+25 associations and if all those 25
+
+ align:start position:0%
+25 associations and if all those 25
+ 
+
+ align:start position:0%
+25 associations and if all those 25
+associations were incorrect we would
+
+ align:start position:0%
+associations were incorrect we would
+ 
+
+ align:start position:0%
+associations were incorrect we would
+expect that the follow-up studies in
+
+ align:start position:0%
+expect that the follow-up studies in
+ 
+
+ align:start position:0%
+expect that the follow-up studies in
+theory or naively should have five
+
+ align:start position:0%
+theory or naively should have five
+ 
+
+ align:start position:0%
+theory or naively should have five
+percent of them should have again been
+
+ align:start position:0%
+percent of them should have again been
+ 
+
+ align:start position:0%
+percent of them should have again been
+statistically significant with a p-val
+
+ align:start position:0%
+statistically significant with a p-val
+ 
+
+ align:start position:0%
+statistically significant with a p-val
+of 0.05 one percent should have had a
+
+ align:start position:0%
+of 0.05 one percent should have had a
+ 
+
+ align:start position:0%
+of 0.05 one percent should have had a
+p-value 0.01 Etc et cetera
+
+ align:start position:0%
+p-value 0.01 Etc et cetera
+ 
+
+ align:start position:0%
+p-value 0.01 Etc et cetera
+so what did we see
+
+ align:start position:0%
+so what did we see
+ 
+
+ align:start position:0%
+so what did we see
+we actually found that about a fifth of
+
+ align:start position:0%
+we actually found that about a fifth of
+ 
+
+ align:start position:0%
+we actually found that about a fifth of
+them had P values less than 0.5 this is
+
+ align:start position:0%
+them had P values less than 0.5 this is
+ 
+
+ align:start position:0%
+them had P values less than 0.5 this is
+way way more than you would expect this
+
+ align:start position:0%
+way way more than you would expect this
+ 
+
+ align:start position:0%
+way way more than you would expect this
+is not just by chance and encouragingly
+
+ align:start position:0%
+is not just by chance and encouragingly
+ 
+
+ align:start position:0%
+is not just by chance and encouragingly
+most of the associations were in the
+
+ align:start position:0%
+most of the associations were in the
+ 
+
+ align:start position:0%
+most of the associations were in the
+same direction so it was the same allele
+
+ align:start position:0%
+same direction so it was the same allele
+ 
+
+ align:start position:0%
+same direction so it was the same allele
+that was associated with diseases was in
+
+ align:start position:0%
+that was associated with diseases was in
+ 
+
+ align:start position:0%
+that was associated with diseases was in
+the original report okay so it's
+
+ align:start position:0%
+the original report okay so it's
+ 
+
+ align:start position:0%
+the original report okay so it's
+actually that would only happen not one
+
+ align:start position:0%
+actually that would only happen not one
+ 
+
+ align:start position:0%
+actually that would only happen not one
+in 20 times but one in 40 times
+
+ align:start position:0%
+in 20 times but one in 40 times
+ 
+
+ align:start position:0%
+in 20 times but one in 40 times
+and furthermore it wasn't that each of
+
+ align:start position:0%
+and furthermore it wasn't that each of
+ 
+
+ align:start position:0%
+and furthermore it wasn't that each of
+the 25 had a few replications it was
+
+ align:start position:0%
+the 25 had a few replications it was
+ 
+
+ align:start position:0%
+the 25 had a few replications it was
+that there was a sub-fraction of them
+
+ align:start position:0%
+that there was a sub-fraction of them
+ 
+
+ align:start position:0%
+that there was a sub-fraction of them
+that had a lot of replications and then
+
+ align:start position:0%
+that had a lot of replications and then
+ 
+
+ align:start position:0%
+that had a lot of replications and then
+the rest of them were never seen again
+
+ align:start position:0%
+the rest of them were never seen again
+ 
+
+ align:start position:0%
+the rest of them were never seen again
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you might say could this be
+
+ align:start position:0%
+so you might say could this be
+ 
+
+ align:start position:0%
+so you might say could this be
+publication bias
+
+ align:start position:0%
+publication bias
+ 
+
+ align:start position:0%
+publication bias
+um so we we obviously could only look at
+
+ align:start position:0%
+um so we we obviously could only look at
+ 
+
+ align:start position:0%
+um so we we obviously could only look at
+the reports that were published so it
+
+ align:start position:0%
+the reports that were published so it
+ 
+
+ align:start position:0%
+the reports that were published so it
+might be that there were lots of people
+
+ align:start position:0%
+might be that there were lots of people
+ 
+
+ align:start position:0%
+might be that there were lots of people
+doing these studies out there and when
+
+ align:start position:0%
+doing these studies out there and when
+ 
+
+ align:start position:0%
+doing these studies out there and when
+they got a P value of less than 0.05
+
+ align:start position:0%
+they got a P value of less than 0.05
+ 
+
+ align:start position:0%
+they got a P value of less than 0.05
+they broke out the champagne celebrated
+
+ align:start position:0%
+they broke out the champagne celebrated
+ 
+
+ align:start position:0%
+they broke out the champagne celebrated
+and sent the journal sent the uh report
+
+ align:start position:0%
+and sent the journal sent the uh report
+ 
+
+ align:start position:0%
+and sent the journal sent the uh report
+off to the journal but maybe if they did
+
+ align:start position:0%
+off to the journal but maybe if they did
+ 
+
+ align:start position:0%
+off to the journal but maybe if they did
+it and the p-value wasn't over 0.05 it
+
+ align:start position:0%
+it and the p-value wasn't over 0.05 it
+ 
+
+ align:start position:0%
+it and the p-value wasn't over 0.05 it
+lingered in the desk drawer and that's
+
+ align:start position:0%
+lingered in the desk drawer and that's
+ 
+
+ align:start position:0%
+lingered in the desk drawer and that's
+actually the formal name for this thing
+
+ align:start position:0%
+actually the formal name for this thing
+ 
+
+ align:start position:0%
+actually the formal name for this thing
+it's the desk drawer phenomenon and so
+
+ align:start position:0%
+it's the desk drawer phenomenon and so
+ 
+
+ align:start position:0%
+it's the desk drawer phenomenon and so
+what we asked was could there be a
+
+ align:start position:0%
+what we asked was could there be a
+ 
+
+ align:start position:0%
+what we asked was could there be a
+universe of unpublished studies
+
+ align:start position:0%
+universe of unpublished studies
+ 
+
+ align:start position:0%
+universe of unpublished studies
+lingering in desk drawers around the
+
+ align:start position:0%
+lingering in desk drawers around the
+ 
+
+ align:start position:0%
+lingering in desk drawers around the
+world that would explain why we saw so
+
+ align:start position:0%
+world that would explain why we saw so
+ 
+
+ align:start position:0%
+world that would explain why we saw so
+many of these studies how many
+
+ align:start position:0%
+many of these studies how many
+ 
+
+ align:start position:0%
+many of these studies how many
+unpublished studies would we have to
+
+ align:start position:0%
+unpublished studies would we have to
+ 
+
+ align:start position:0%
+unpublished studies would we have to
+hypothesize per Association to explain
+
+ align:start position:0%
+hypothesize per Association to explain
+ 
+
+ align:start position:0%
+hypothesize per Association to explain
+the fraction we saw was it one or two or
+
+ align:start position:0%
+the fraction we saw was it one or two or
+ 
+
+ align:start position:0%
+the fraction we saw was it one or two or
+three or was it just you know a
+
+ align:start position:0%
+three or was it just you know a
+ 
+
+ align:start position:0%
+three or was it just you know a
+ludicrous number of studies out there
+
+ align:start position:0%
+ludicrous number of studies out there
+ 
+
+ align:start position:0%
+ludicrous number of studies out there
+and it turned out actually you would
+
+ align:start position:0%
+and it turned out actually you would
+ 
+
+ align:start position:0%
+and it turned out actually you would
+have to postulate a ludicrous number of
+
+ align:start position:0%
+have to postulate a ludicrous number of
+ 
+
+ align:start position:0%
+have to postulate a ludicrous number of
+studies uh to explain the positives we
+
+ align:start position:0%
+studies uh to explain the positives we
+ 
+
+ align:start position:0%
+studies uh to explain the positives we
+saw you would have to explain possibly
+
+ align:start position:0%
+saw you would have to explain possibly
+ 
+
+ align:start position:0%
+saw you would have to explain possibly
+about 40 to 80 unpublished negative
+
+ align:start position:0%
+about 40 to 80 unpublished negative
+ 
+
+ align:start position:0%
+about 40 to 80 unpublished negative
+studies lingering in desk drawers around
+
+ align:start position:0%
+studies lingering in desk drawers around
+ 
+
+ align:start position:0%
+studies lingering in desk drawers around
+the world and there just aren't even
+
+ align:start position:0%
+the world and there just aren't even
+ 
+
+ align:start position:0%
+the world and there just aren't even
+that many people doing Association
+
+ align:start position:0%
+that many people doing Association
+ 
+
+ align:start position:0%
+that many people doing Association
+studies for any any of these diseases so
+
+ align:start position:0%
+studies for any any of these diseases so
+ 
+
+ align:start position:0%
+studies for any any of these diseases so
+we think this is and we did some other
+
+ align:start position:0%
+we think this is and we did some other
+ 
+
+ align:start position:0%
+we think this is and we did some other
+work to show this is not publication
+
+ align:start position:0%
+work to show this is not publication
+ 
+
+ align:start position:0%
+work to show this is not publication
+bias
+
+ align:start position:0%
+bias
+ 
+
+ align:start position:0%
+bias
+okay so you you'd asked about ethnic
+
+ align:start position:0%
+okay so you you'd asked about ethnic
+ 
+
+ align:start position:0%
+okay so you you'd asked about ethnic
+admixture stratification so I want to
+
+ align:start position:0%
+admixture stratification so I want to
+ 
+
+ align:start position:0%
+admixture stratification so I want to
+talk about that for a little bit yeah
+
+ align:start position:0%
+talk about that for a little bit yeah
+ 
+
+ align:start position:0%
+talk about that for a little bit yeah
+sure go right ahead yep
+
+ align:start position:0%
+sure go right ahead yep
+ 
+
+ align:start position:0%
+sure go right ahead yep
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so yeah it's not a common
+
+ align:start position:0%
+yeah yeah so yeah it's not a common
+ 
+
+ align:start position:0%
+yeah yeah so yeah it's not a common
+disease you're right so it's a very
+
+ align:start position:0%
+disease you're right so it's a very
+ 
+
+ align:start position:0%
+disease you're right so it's a very
+environmental disease right so that what
+
+ align:start position:0%
+environmental disease right so that what
+ 
+
+ align:start position:0%
+environmental disease right so that what
+it is is actually it's probably a common
+
+ align:start position:0%
+it is is actually it's probably a common
+ 
+
+ align:start position:0%
+it is is actually it's probably a common
+disease but just the environmental
+
+ align:start position:0%
+disease but just the environmental
+ 
+
+ align:start position:0%
+disease but just the environmental
+exposure that's required is rare
+
+ align:start position:0%
+exposure that's required is rare
+ 
+
+ align:start position:0%
+exposure that's required is rare
+um so it's sort of like and you actually
+
+ align:start position:0%
+um so it's sort of like and you actually
+ 
+
+ align:start position:0%
+um so it's sort of like and you actually
+another one was HIV which unfortunately
+
+ align:start position:0%
+another one was HIV which unfortunately
+ 
+
+ align:start position:0%
+another one was HIV which unfortunately
+is not a rare disease now because the
+
+ align:start position:0%
+is not a rare disease now because the
+ 
+
+ align:start position:0%
+is not a rare disease now because the
+environmental exposure is so common but
+
+ align:start position:0%
+environmental exposure is so common but
+ 
+
+ align:start position:0%
+environmental exposure is so common but
+you could imagine if
+
+ align:start position:0%
+you could imagine if
+ 
+
+ align:start position:0%
+you could imagine if
+the world were a different place would
+
+ align:start position:0%
+the world were a different place would
+ 
+
+ align:start position:0%
+the world were a different place would
+be a rare disease and the same same sort
+
+ align:start position:0%
+be a rare disease and the same same sort
+ 
+
+ align:start position:0%
+be a rare disease and the same same sort
+of thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it may be the same thing as diabetes you
+
+ align:start position:0%
+it may be the same thing as diabetes you
+ 
+
+ align:start position:0%
+it may be the same thing as diabetes you
+know type 2 diabetes may be a common
+
+ align:start position:0%
+know type 2 diabetes may be a common
+ 
+
+ align:start position:0%
+know type 2 diabetes may be a common
+disease in part because the
+
+ align:start position:0%
+disease in part because the
+ 
+
+ align:start position:0%
+disease in part because the
+environmental exposures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it turns out it's actually it's
+
+ align:start position:0%
+yeah so it turns out it's actually it's
+ 
+
+ align:start position:0%
+yeah so it turns out it's actually it's
+actually a huge risk factor it's a huge
+
+ align:start position:0%
+actually a huge risk factor it's a huge
+ 
+
+ align:start position:0%
+actually a huge risk factor it's a huge
+genetic risk factor
+
+ align:start position:0%
+genetic risk factor
+ 
+
+ align:start position:0%
+genetic risk factor
+um there's an interesting article in
+
+ align:start position:0%
+um there's an interesting article in
+ 
+
+ align:start position:0%
+um there's an interesting article in
+science looking at this variant showing
+
+ align:start position:0%
+science looking at this variant showing
+ 
+
+ align:start position:0%
+science looking at this variant showing
+that there's been waves of selection in
+
+ align:start position:0%
+that there's been waves of selection in
+ 
+
+ align:start position:0%
+that there's been waves of selection in
+favor of the resistance variant in
+
+ align:start position:0%
+favor of the resistance variant in
+ 
+
+ align:start position:0%
+favor of the resistance variant in
+tribes that uh where uh uh Prime
+
+ align:start position:0%
+tribes that uh where uh uh Prime
+ 
+
+ align:start position:0%
+tribes that uh where uh uh Prime
+diseases are are endemic
+
+ align:start position:0%
+diseases are are endemic
+ 
+
+ align:start position:0%
+diseases are are endemic
+yeah it's pretty common and uh it turns
+
+ align:start position:0%
+yeah it's pretty common and uh it turns
+ 
+
+ align:start position:0%
+yeah it's pretty common and uh it turns
+out that it's it's a big effect so
+
+ align:start position:0%
+out that it's it's a big effect so
+ 
+
+ align:start position:0%
+out that it's it's a big effect so
+that's how you get power so that even if
+
+ align:start position:0%
+that's how you get power so that even if
+ 
+
+ align:start position:0%
+that's how you get power so that even if
+you know and they're enough sporadic you
+
+ align:start position:0%
+you know and they're enough sporadic you
+ 
+
+ align:start position:0%
+you know and they're enough sporadic you
+know there's sort of people collect like
+
+ align:start position:0%
+know there's sort of people collect like
+ 
+
+ align:start position:0%
+know there's sort of people collect like
+a couple hundred sporadic cases here and
+
+ align:start position:0%
+a couple hundred sporadic cases here and
+ 
+
+ align:start position:0%
+a couple hundred sporadic cases here and
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um and it's just it's just a big effect
+
+ align:start position:0%
+um and it's just it's just a big effect
+ 
+
+ align:start position:0%
+um and it's just it's just a big effect
+and that's why they were able to see it
+
+ align:start position:0%
+and that's why they were able to see it
+ 
+
+ align:start position:0%
+and that's why they were able to see it
+so even rare diseases can have common
+
+ align:start position:0%
+so even rare diseases can have common
+ 
+
+ align:start position:0%
+so even rare diseases can have common
+variants that contribute to them
+
+ align:start position:0%
+variants that contribute to them
+ 
+
+ align:start position:0%
+variants that contribute to them
+okay so ethnic admixture what is that
+
+ align:start position:0%
+okay so ethnic admixture what is that
+ 
+
+ align:start position:0%
+okay so ethnic admixture what is that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is sort of an ideal
+
+ align:start position:0%
+so this is sort of an ideal
+ 
+
+ align:start position:0%
+so this is sort of an ideal
+uh epidemiology study so when people
+
+ align:start position:0%
+uh epidemiology study so when people
+ 
+
+ align:start position:0%
+uh epidemiology study so when people
+collect cases and controls
+
+ align:start position:0%
+collect cases and controls
+ 
+
+ align:start position:0%
+collect cases and controls
+um they often will ask about ethnicity
+
+ align:start position:0%
+um they often will ask about ethnicity
+ 
+
+ align:start position:0%
+um they often will ask about ethnicity
+and they have what's called
+
+ align:start position:0%
+and they have what's called
+ 
+
+ align:start position:0%
+and they have what's called
+self-described ethnicity
+
+ align:start position:0%
+self-described ethnicity
+ 
+
+ align:start position:0%
+self-described ethnicity
+and the ideal thing is that you would
+
+ align:start position:0%
+and the ideal thing is that you would
+ 
+
+ align:start position:0%
+and the ideal thing is that you would
+you know clearly everybody matches on
+
+ align:start position:0%
+you know clearly everybody matches on
+ 
+
+ align:start position:0%
+you know clearly everybody matches on
+what people put down but people will
+
+ align:start position:0%
+what people put down but people will
+ 
+
+ align:start position:0%
+what people put down but people will
+self-describe differently and there may
+
+ align:start position:0%
+self-describe differently and there may
+ 
+
+ align:start position:0%
+self-describe differently and there may
+not be an accurate self-description for
+
+ align:start position:0%
+not be an accurate self-description for
+ 
+
+ align:start position:0%
+not be an accurate self-description for
+what people's actual ethnic and you know
+
+ align:start position:0%
+what people's actual ethnic and you know
+ 
+
+ align:start position:0%
+what people's actual ethnic and you know
+genetic backgrounds are so you hope that
+
+ align:start position:0%
+genetic backgrounds are so you hope that
+ 
+
+ align:start position:0%
+genetic backgrounds are so you hope that
+somehow just you know that this
+
+ align:start position:0%
+somehow just you know that this
+ 
+
+ align:start position:0%
+somehow just you know that this
+self-described ethnicity is good enough
+
+ align:start position:0%
+self-described ethnicity is good enough
+ 
+
+ align:start position:0%
+self-described ethnicity is good enough
+that you actually have a good match but
+
+ align:start position:0%
+that you actually have a good match but
+ 
+
+ align:start position:0%
+that you actually have a good match but
+you can imagine that within some ethnic
+
+ align:start position:0%
+you can imagine that within some ethnic
+ 
+
+ align:start position:0%
+you can imagine that within some ethnic
+group there might be a couple of
+
+ align:start position:0%
+group there might be a couple of
+ 
+
+ align:start position:0%
+group there might be a couple of
+subgroups and this is obviously the
+
+ align:start position:0%
+subgroups and this is obviously the
+ 
+
+ align:start position:0%
+subgroups and this is obviously the
+distinctions are I've drawn this as you
+
+ align:start position:0%
+distinctions are I've drawn this as you
+ 
+
+ align:start position:0%
+distinctions are I've drawn this as you
+know there's you know the blue subgroup
+
+ align:start position:0%
+know there's you know the blue subgroup
+ 
+
+ align:start position:0%
+know there's you know the blue subgroup
+and the green subgroup but in real
+
+ align:start position:0%
+and the green subgroup but in real
+ 
+
+ align:start position:0%
+and the green subgroup but in real
+reality would probably some you know
+
+ align:start position:0%
+reality would probably some you know
+ 
+
+ align:start position:0%
+reality would probably some you know
+shading from Blue to blue green to green
+
+ align:start position:0%
+shading from Blue to blue green to green
+ 
+
+ align:start position:0%
+shading from Blue to blue green to green
+blue to you know Green
+
+ align:start position:0%
+blue to you know Green
+ 
+
+ align:start position:0%
+blue to you know Green
+um so you can imagine that there might
+
+ align:start position:0%
+um so you can imagine that there might
+ 
+
+ align:start position:0%
+um so you can imagine that there might
+be some different ethnic subgroups and
+
+ align:start position:0%
+be some different ethnic subgroups and
+ 
+
+ align:start position:0%
+be some different ethnic subgroups and
+you could think about this for example
+
+ align:start position:0%
+you could think about this for example
+ 
+
+ align:start position:0%
+you could think about this for example
+European might be northern European and
+
+ align:start position:0%
+European might be northern European and
+ 
+
+ align:start position:0%
+European might be northern European and
+Southern European or something like that
+
+ align:start position:0%
+Southern European or something like that
+ 
+
+ align:start position:0%
+Southern European or something like that
+and there might be diseases where the
+
+ align:start position:0%
+and there might be diseases where the
+ 
+
+ align:start position:0%
+and there might be diseases where the
+disease actually is more prevalent let's
+
+ align:start position:0%
+disease actually is more prevalent let's
+ 
+
+ align:start position:0%
+disease actually is more prevalent let's
+say in northern Europe so you might have
+
+ align:start position:0%
+say in northern Europe so you might have
+ 
+
+ align:start position:0%
+say in northern Europe so you might have
+more cases from the northern European
+
+ align:start position:0%
+more cases from the northern European
+ 
+
+ align:start position:0%
+more cases from the northern European
+ancestry and more controls the southern
+
+ align:start position:0%
+ancestry and more controls the southern
+ 
+
+ align:start position:0%
+ancestry and more controls the southern
+European ancestry and that's for example
+
+ align:start position:0%
+European ancestry and that's for example
+ 
+
+ align:start position:0%
+European ancestry and that's for example
+type 1 diabetes might fit uh fit this
+
+ align:start position:0%
+type 1 diabetes might fit uh fit this
+ 
+
+ align:start position:0%
+type 1 diabetes might fit uh fit this
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+a much more common in Finland than in
+
+ align:start position:0%
+a much more common in Finland than in
+ 
+
+ align:start position:0%
+a much more common in Finland than in
+south of France for example
+
+ align:start position:0%
+south of France for example
+ 
+
+ align:start position:0%
+south of France for example
+so if you then had a marker that was um
+
+ align:start position:0%
+so if you then had a marker that was um
+ 
+
+ align:start position:0%
+so if you then had a marker that was um
+tracked genetically with uh
+
+ align:start position:0%
+tracked genetically with uh
+ 
+
+ align:start position:0%
+tracked genetically with uh
+uh northern European ancestry but not
+
+ align:start position:0%
+uh northern European ancestry but not
+ 
+
+ align:start position:0%
+uh northern European ancestry but not
+with Southern European ancestry and
+
+ align:start position:0%
+with Southern European ancestry and
+ 
+
+ align:start position:0%
+with Southern European ancestry and
+there are not a lot of markers like that
+
+ align:start position:0%
+there are not a lot of markers like that
+ 
+
+ align:start position:0%
+there are not a lot of markers like that
+but there are at least one that I know
+
+ align:start position:0%
+but there are at least one that I know
+ 
+
+ align:start position:0%
+but there are at least one that I know
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um then you might find that that marker
+
+ align:start position:0%
+um then you might find that that marker
+ 
+
+ align:start position:0%
+um then you might find that that marker
+would be overrepresented in the cases
+
+ align:start position:0%
+would be overrepresented in the cases
+ 
+
+ align:start position:0%
+would be overrepresented in the cases
+relative to the controls just because
+
+ align:start position:0%
+relative to the controls just because
+ 
+
+ align:start position:0%
+relative to the controls just because
+the that that ethnic group was
+
+ align:start position:0%
+the that that ethnic group was
+ 
+
+ align:start position:0%
+the that that ethnic group was
+overrepresented and this uh is thought
+
+ align:start position:0%
+overrepresented and this uh is thought
+ 
+
+ align:start position:0%
+overrepresented and this uh is thought
+to be more of a problem also in
+
+ align:start position:0%
+to be more of a problem also in
+ 
+
+ align:start position:0%
+to be more of a problem also in
+populations that have had recent
+
+ align:start position:0%
+populations that have had recent
+ 
+
+ align:start position:0%
+populations that have had recent
+admixture like African-American
+
+ align:start position:0%
+admixture like African-American
+ 
+
+ align:start position:0%
+admixture like African-American
+populations or Latino populations uh
+
+ align:start position:0%
+populations or Latino populations uh
+ 
+
+ align:start position:0%
+populations or Latino populations uh
+where uh instead of this being northern
+
+ align:start position:0%
+where uh instead of this being northern
+ 
+
+ align:start position:0%
+where uh instead of this being northern
+European Southern European this might be
+
+ align:start position:0%
+European Southern European this might be
+ 
+
+ align:start position:0%
+European Southern European this might be
+degree of uh ancestry uh so what
+
+ align:start position:0%
+degree of uh ancestry uh so what
+ 
+
+ align:start position:0%
+degree of uh ancestry uh so what
+fraction of your chromosomes are have
+
+ align:start position:0%
+fraction of your chromosomes are have
+ 
+
+ align:start position:0%
+fraction of your chromosomes are have
+alleles that are more common in Europe
+
+ align:start position:0%
+alleles that are more common in Europe
+ 
+
+ align:start position:0%
+alleles that are more common in Europe
+versus alleles that are more common in
+
+ align:start position:0%
+versus alleles that are more common in
+ 
+
+ align:start position:0%
+versus alleles that are more common in
+Africa and you can end up with this same
+
+ align:start position:0%
+Africa and you can end up with this same
+ 
+
+ align:start position:0%
+Africa and you can end up with this same
+setup so you can get in theory false
+
+ align:start position:0%
+setup so you can get in theory false
+ 
+
+ align:start position:0%
+setup so you can get in theory false
+positive associations from that
+
+ align:start position:0%
+positive associations from that
+ 
+
+ align:start position:0%
+positive associations from that
+so there are ways around it now so the
+
+ align:start position:0%
+so there are ways around it now so the
+ 
+
+ align:start position:0%
+so there are ways around it now so the
+first way that was proposed by Rich
+
+ align:start position:0%
+first way that was proposed by Rich
+ 
+
+ align:start position:0%
+first way that was proposed by Rich
+Spielman and then a whole bunch of other
+
+ align:start position:0%
+Spielman and then a whole bunch of other
+ 
+
+ align:start position:0%
+Spielman and then a whole bunch of other
+people is to use what are called family
+
+ align:start position:0%
+people is to use what are called family
+ 
+
+ align:start position:0%
+people is to use what are called family
+taste test based family-based tests of
+
+ align:start position:0%
+taste test based family-based tests of
+ 
+
+ align:start position:0%
+taste test based family-based tests of
+Association I'm not going to go through
+
+ align:start position:0%
+Association I'm not going to go through
+ 
+
+ align:start position:0%
+Association I'm not going to go through
+the details of those other than them to
+
+ align:start position:0%
+the details of those other than them to
+ 
+
+ align:start position:0%
+the details of those other than them to
+tell you that they are immune to this
+
+ align:start position:0%
+tell you that they are immune to this
+ 
+
+ align:start position:0%
+tell you that they are immune to this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the other way is to basically if
+
+ align:start position:0%
+and the other way is to basically if
+ 
+
+ align:start position:0%
+and the other way is to basically if
+you're doing if you can't do the
+
+ align:start position:0%
+you're doing if you can't do the
+ 
+
+ align:start position:0%
+you're doing if you can't do the
+family-based test and there are a lot of
+
+ align:start position:0%
+family-based test and there are a lot of
+ 
+
+ align:start position:0%
+family-based test and there are a lot of
+reasons you might not be able to uh you
+
+ align:start position:0%
+reasons you might not be able to uh you
+ 
+
+ align:start position:0%
+reasons you might not be able to uh you
+can use something called genomic control
+
+ align:start position:0%
+can use something called genomic control
+ 
+
+ align:start position:0%
+can use something called genomic control
+where you type a lot of random markers
+
+ align:start position:0%
+where you type a lot of random markers
+ 
+
+ align:start position:0%
+where you type a lot of random markers
+and you see well do those random markers
+
+ align:start position:0%
+and you see well do those random markers
+ 
+
+ align:start position:0%
+and you see well do those random markers
+give you these spurious associations and
+
+ align:start position:0%
+give you these spurious associations and
+ 
+
+ align:start position:0%
+give you these spurious associations and
+you can use those to correct your
+
+ align:start position:0%
+you can use those to correct your
+ 
+
+ align:start position:0%
+you can use those to correct your
+Association results or even to renatch
+
+ align:start position:0%
+Association results or even to renatch
+ 
+
+ align:start position:0%
+Association results or even to renatch
+your cases and controls to make sure
+
+ align:start position:0%
+your cases and controls to make sure
+ 
+
+ align:start position:0%
+your cases and controls to make sure
+that they're genetic uh regardless of
+
+ align:start position:0%
+that they're genetic uh regardless of
+ 
+
+ align:start position:0%
+that they're genetic uh regardless of
+what the self-described ethnicity is you
+
+ align:start position:0%
+what the self-described ethnicity is you
+ 
+
+ align:start position:0%
+what the self-described ethnicity is you
+can match them sort of by their genetic
+
+ align:start position:0%
+can match them sort of by their genetic
+ 
+
+ align:start position:0%
+can match them sort of by their genetic
+background is assessed by these hundred
+
+ align:start position:0%
+background is assessed by these hundred
+ 
+
+ align:start position:0%
+background is assessed by these hundred
+markers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we actually looked at least for our
+
+ align:start position:0%
+so we actually looked at least for our
+ 
+
+ align:start position:0%
+so we actually looked at least for our
+little study most of the things that
+
+ align:start position:0%
+little study most of the things that
+ 
+
+ align:start position:0%
+little study most of the things that
+have replicated are actually seen in
+
+ align:start position:0%
+have replicated are actually seen in
+ 
+
+ align:start position:0%
+have replicated are actually seen in
+family-based studies or in multiple
+
+ align:start position:0%
+family-based studies or in multiple
+ 
+
+ align:start position:0%
+family-based studies or in multiple
+ethnic groups which makes admixture less
+
+ align:start position:0%
+ethnic groups which makes admixture less
+ 
+
+ align:start position:0%
+ethnic groups which makes admixture less
+likely but it doesn't mean that this
+
+ align:start position:0%
+likely but it doesn't mean that this
+ 
+
+ align:start position:0%
+likely but it doesn't mean that this
+isn't going on in a rampant way and like
+
+ align:start position:0%
+isn't going on in a rampant way and like
+ 
+
+ align:start position:0%
+isn't going on in a rampant way and like
+you know for example the ones that were
+
+ align:start position:0%
+you know for example the ones that were
+ 
+
+ align:start position:0%
+you know for example the ones that were
+never replicated could well be that some
+
+ align:start position:0%
+never replicated could well be that some
+ 
+
+ align:start position:0%
+never replicated could well be that some
+of those false positives are due to
+
+ align:start position:0%
+of those false positives are due to
+ 
+
+ align:start position:0%
+of those false positives are due to
+admixture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there's sort of a a true population
+
+ align:start position:0%
+then there's sort of a a true population
+ 
+
+ align:start position:0%
+then there's sort of a a true population
+differences that could be uh uh could be
+
+ align:start position:0%
+differences that could be uh uh could be
+ 
+
+ align:start position:0%
+differences that could be uh uh could be
+coming into play there's a lot of
+
+ align:start position:0%
+coming into play there's a lot of
+ 
+
+ align:start position:0%
+coming into play there's a lot of
+different things it could be you know
+
+ align:start position:0%
+different things it could be you know
+ 
+
+ align:start position:0%
+different things it could be you know
+different diets and different
+
+ align:start position:0%
+different diets and different
+ 
+
+ align:start position:0%
+different diets and different
+populations uh it could be that uh there
+
+ align:start position:0%
+populations uh it could be that uh there
+ 
+
+ align:start position:0%
+populations uh it could be that uh there
+are other genes that are more common in
+
+ align:start position:0%
+are other genes that are more common in
+ 
+
+ align:start position:0%
+are other genes that are more common in
+one population than in another and
+
+ align:start position:0%
+one population than in another and
+ 
+
+ align:start position:0%
+one population than in another and
+there's some interaction between what
+
+ align:start position:0%
+there's some interaction between what
+ 
+
+ align:start position:0%
+there's some interaction between what
+you're looking at and that
+
+ align:start position:0%
+you're looking at and that
+ 
+
+ align:start position:0%
+you're looking at and that
+um and I want to talk about one very
+
+ align:start position:0%
+um and I want to talk about one very
+ 
+
+ align:start position:0%
+um and I want to talk about one very
+specific uh type of difference that at
+
+ align:start position:0%
+specific uh type of difference that at
+ 
+
+ align:start position:0%
+specific uh type of difference that at
+least we could address which is that
+
+ align:start position:0%
+least we could address which is that
+ 
+
+ align:start position:0%
+least we could address which is that
+there might be different patterns of
+
+ align:start position:0%
+there might be different patterns of
+ 
+
+ align:start position:0%
+there might be different patterns of
+correlation in different populations and
+
+ align:start position:0%
+correlation in different populations and
+ 
+
+ align:start position:0%
+correlation in different populations and
+the marker that's being used might not
+
+ align:start position:0%
+the marker that's being used might not
+ 
+
+ align:start position:0%
+the marker that's being used might not
+be the causal marker it might be
+
+ align:start position:0%
+be the causal marker it might be
+ 
+
+ align:start position:0%
+be the causal marker it might be
+something which is correlated so I
+
+ align:start position:0%
+something which is correlated so I
+ 
+
+ align:start position:0%
+something which is correlated so I
+showed you this diagram where you could
+
+ align:start position:0%
+showed you this diagram where you could
+ 
+
+ align:start position:0%
+showed you this diagram where you could
+use the ca haplotype these you know if
+
+ align:start position:0%
+use the ca haplotype these you know if
+ 
+
+ align:start position:0%
+use the ca haplotype these you know if
+you look at this two marker haplotype
+
+ align:start position:0%
+you look at this two marker haplotype
+ 
+
+ align:start position:0%
+you look at this two marker haplotype
+use this CA haplotype to try to predict
+
+ align:start position:0%
+use this CA haplotype to try to predict
+ 
+
+ align:start position:0%
+use this CA haplotype to try to predict
+uh whether the causal polymorphism is
+
+ align:start position:0%
+uh whether the causal polymorphism is
+ 
+
+ align:start position:0%
+uh whether the causal polymorphism is
+there and does pretty well because there
+
+ align:start position:0%
+there and does pretty well because there
+ 
+
+ align:start position:0%
+there and does pretty well because there
+wasn't very much of this recombinant
+
+ align:start position:0%
+wasn't very much of this recombinant
+ 
+
+ align:start position:0%
+wasn't very much of this recombinant
+haplotype here so here actually the
+
+ align:start position:0%
+haplotype here so here actually the
+ 
+
+ align:start position:0%
+haplotype here so here actually the
+prediction I haven't drawn the arrows
+
+ align:start position:0%
+prediction I haven't drawn the arrows
+ 
+
+ align:start position:0%
+prediction I haven't drawn the arrows
+but the prediction would actually not be
+
+ align:start position:0%
+but the prediction would actually not be
+ 
+
+ align:start position:0%
+but the prediction would actually not be
+right for this one chromosome but most
+
+ align:start position:0%
+right for this one chromosome but most
+ 
+
+ align:start position:0%
+right for this one chromosome but most
+the time the correlation is pretty good
+
+ align:start position:0%
+the time the correlation is pretty good
+ 
+
+ align:start position:0%
+the time the correlation is pretty good
+but what if there was a lot of that
+
+ align:start position:0%
+but what if there was a lot of that
+ 
+
+ align:start position:0%
+but what if there was a lot of that
+recombinant chromosome in some other
+
+ align:start position:0%
+recombinant chromosome in some other
+ 
+
+ align:start position:0%
+recombinant chromosome in some other
+population now all of a sudden
+
+ align:start position:0%
+population now all of a sudden
+ 
+
+ align:start position:0%
+population now all of a sudden
+you have to see a common CA haplotype
+
+ align:start position:0%
+you have to see a common CA haplotype
+ 
+
+ align:start position:0%
+you have to see a common CA haplotype
+without the causal snip and so in
+
+ align:start position:0%
+without the causal snip and so in
+ 
+
+ align:start position:0%
+without the causal snip and so in
+addition to you know being the
+
+ align:start position:0%
+addition to you know being the
+ 
+
+ align:start position:0%
+addition to you know being the
+correlation is now no longer so good so
+
+ align:start position:0%
+correlation is now no longer so good so
+ 
+
+ align:start position:0%
+correlation is now no longer so good so
+you might not see an association so
+
+ align:start position:0%
+you might not see an association so
+ 
+
+ align:start position:0%
+you might not see an association so
+that's at least one possible thing to
+
+ align:start position:0%
+that's at least one possible thing to
+ 
+
+ align:start position:0%
+that's at least one possible thing to
+keep in mind is that the marker that
+
+ align:start position:0%
+keep in mind is that the marker that
+ 
+
+ align:start position:0%
+keep in mind is that the marker that
+you're looking at might not be the
+
+ align:start position:0%
+you're looking at might not be the
+ 
+
+ align:start position:0%
+you're looking at might not be the
+causal thing so basically understanding
+
+ align:start position:0%
+causal thing so basically understanding
+ 
+
+ align:start position:0%
+causal thing so basically understanding
+the LD patterns around an association so
+
+ align:start position:0%
+the LD patterns around an association so
+ 
+
+ align:start position:0%
+the LD patterns around an association so
+once an association's been found typing
+
+ align:start position:0%
+once an association's been found typing
+ 
+
+ align:start position:0%
+once an association's been found typing
+lots of other markers in there and
+
+ align:start position:0%
+lots of other markers in there and
+ 
+
+ align:start position:0%
+lots of other markers in there and
+seeing is there another marker that
+
+ align:start position:0%
+seeing is there another marker that
+ 
+
+ align:start position:0%
+seeing is there another marker that
+explains it better
+
+ align:start position:0%
+explains it better
+ 
+
+ align:start position:0%
+explains it better
+will become important and almost Nobody
+
+ align:start position:0%
+will become important and almost Nobody
+ 
+
+ align:start position:0%
+will become important and almost Nobody
+Does that right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then finally the last thing that we
+
+ align:start position:0%
+and then finally the last thing that we
+ 
+
+ align:start position:0%
+and then finally the last thing that we
+looked at was could it be that some of
+
+ align:start position:0%
+looked at was could it be that some of
+ 
+
+ align:start position:0%
+looked at was could it be that some of
+the associations that we were seeing in
+
+ align:start position:0%
+the associations that we were seeing in
+ 
+
+ align:start position:0%
+the associations that we were seeing in
+our meta-analysis were actually true but
+
+ align:start position:0%
+our meta-analysis were actually true but
+ 
+
+ align:start position:0%
+our meta-analysis were actually true but
+the studies that said that there was no
+
+ align:start position:0%
+the studies that said that there was no
+ 
+
+ align:start position:0%
+the studies that said that there was no
+association were actually incorrect
+
+ align:start position:0%
+association were actually incorrect
+ 
+
+ align:start position:0%
+association were actually incorrect
+and so to try to get a sense for this
+
+ align:start position:0%
+and so to try to get a sense for this
+ 
+
+ align:start position:0%
+and so to try to get a sense for this
+what that requires is that uh the sample
+
+ align:start position:0%
+what that requires is that uh the sample
+ 
+
+ align:start position:0%
+what that requires is that uh the sample
+sizes were too small to detect the
+
+ align:start position:0%
+sizes were too small to detect the
+ 
+
+ align:start position:0%
+sizes were too small to detect the
+association which means in turn that the
+
+ align:start position:0%
+association which means in turn that the
+ 
+
+ align:start position:0%
+association which means in turn that the
+association must have been a weak
+
+ align:start position:0%
+association must have been a weak
+ 
+
+ align:start position:0%
+association must have been a weak
+associations or modest a modest effect
+
+ align:start position:0%
+associations or modest a modest effect
+ 
+
+ align:start position:0%
+associations or modest a modest effect
+so we estimated the effects for all of
+
+ align:start position:0%
+so we estimated the effects for all of
+ 
+
+ align:start position:0%
+so we estimated the effects for all of
+these associations
+
+ align:start position:0%
+these associations
+ 
+
+ align:start position:0%
+these associations
+and by pooling all the data and so eight
+
+ align:start position:0%
+and by pooling all the data and so eight
+ 
+
+ align:start position:0%
+and by pooling all the data and so eight
+of them replicated and the question was
+
+ align:start position:0%
+of them replicated and the question was
+ 
+
+ align:start position:0%
+of them replicated and the question was
+what was the effect sizes and basically
+
+ align:start position:0%
+what was the effect sizes and basically
+ 
+
+ align:start position:0%
+what was the effect sizes and basically
+all eight increased the risk of disease
+
+ align:start position:0%
+all eight increased the risk of disease
+ 
+
+ align:start position:0%
+all eight increased the risk of disease
+by less than two-fold and some of them
+
+ align:start position:0%
+by less than two-fold and some of them
+ 
+
+ align:start position:0%
+by less than two-fold and some of them
+was like just a 10 increased risk of
+
+ align:start position:0%
+was like just a 10 increased risk of
+ 
+
+ align:start position:0%
+was like just a 10 increased risk of
+disease uh associated with having the
+
+ align:start position:0%
+disease uh associated with having the
+ 
+
+ align:start position:0%
+disease uh associated with having the
+allele and for 10 for example you need
+
+ align:start position:0%
+allele and for 10 for example you need
+ 
+
+ align:start position:0%
+allele and for 10 for example you need
+thousands of cases and controls and
+
+ align:start position:0%
+thousands of cases and controls and
+ 
+
+ align:start position:0%
+thousands of cases and controls and
+almost none of the studies we looked at
+
+ align:start position:0%
+almost none of the studies we looked at
+ 
+
+ align:start position:0%
+almost none of the studies we looked at
+had that so almost all the studies were
+
+ align:start position:0%
+had that so almost all the studies were
+ 
+
+ align:start position:0%
+had that so almost all the studies were
+underpowered for almost all the
+
+ align:start position:0%
+underpowered for almost all the
+ 
+
+ align:start position:0%
+underpowered for almost all the
+associations we looked at so lack of
+
+ align:start position:0%
+associations we looked at so lack of
+ 
+
+ align:start position:0%
+associations we looked at so lack of
+power is rampant in this field and a
+
+ align:start position:0%
+power is rampant in this field and a
+ 
+
+ align:start position:0%
+power is rampant in this field and a
+negative study by itself unless it's got
+
+ align:start position:0%
+negative study by itself unless it's got
+ 
+
+ align:start position:0%
+negative study by itself unless it's got
+many thousands of people
+
+ align:start position:0%
+many thousands of people
+ 
+
+ align:start position:0%
+many thousands of people
+really can't be taken to be worth much
+
+ align:start position:0%
+really can't be taken to be worth much
+ 
+
+ align:start position:0%
+really can't be taken to be worth much
+other than by itself it can be worth a
+
+ align:start position:0%
+other than by itself it can be worth a
+ 
+
+ align:start position:0%
+other than by itself it can be worth a
+lot in context of other studies
+
+ align:start position:0%
+lot in context of other studies
+ 
+
+ align:start position:0%
+lot in context of other studies
+one last thing that I want to just take
+
+ align:start position:0%
+one last thing that I want to just take
+ 
+
+ align:start position:0%
+one last thing that I want to just take
+you through again because an important
+
+ align:start position:0%
+you through again because an important
+ 
+
+ align:start position:0%
+you through again because an important
+issue thinking about interpreting the
+
+ align:start position:0%
+issue thinking about interpreting the
+ 
+
+ align:start position:0%
+issue thinking about interpreting the
+literature
+
+ align:start position:0%
+literature
+ 
+
+ align:start position:0%
+literature
+when we did this estimation of what was
+
+ align:start position:0%
+when we did this estimation of what was
+ 
+
+ align:start position:0%
+when we did this estimation of what was
+the actual genetic effect and then we
+
+ align:start position:0%
+the actual genetic effect and then we
+ 
+
+ align:start position:0%
+the actual genetic effect and then we
+compared those less than two-fold risks
+
+ align:start position:0%
+compared those less than two-fold risks
+ 
+
+ align:start position:0%
+compared those less than two-fold risks
+to what the first report had claimed
+
+ align:start position:0%
+to what the first report had claimed
+ 
+
+ align:start position:0%
+to what the first report had claimed
+almost always the first positive report
+
+ align:start position:0%
+almost always the first positive report
+ 
+
+ align:start position:0%
+almost always the first positive report
+had overestimated the actual genetic
+
+ align:start position:0%
+had overestimated the actual genetic
+ 
+
+ align:start position:0%
+had overestimated the actual genetic
+effect okay and we want to know if this
+
+ align:start position:0%
+effect okay and we want to know if this
+ 
+
+ align:start position:0%
+effect okay and we want to know if this
+consistent with a phenomenon called the
+
+ align:start position:0%
+consistent with a phenomenon called the
+ 
+
+ align:start position:0%
+consistent with a phenomenon called the
+Winner's curse
+
+ align:start position:0%
+Winner's curse
+ 
+
+ align:start position:0%
+Winner's curse
+so winners care is best described for
+
+ align:start position:0%
+so winners care is best described for
+ 
+
+ align:start position:0%
+so winners care is best described for
+auction Theory and it goes like this
+
+ align:start position:0%
+auction Theory and it goes like this
+ 
+
+ align:start position:0%
+auction Theory and it goes like this
+imagine that there are a bunch of people
+
+ align:start position:0%
+imagine that there are a bunch of people
+ 
+
+ align:start position:0%
+imagine that there are a bunch of people
+who are bidding on an item okay and they
+
+ align:start position:0%
+who are bidding on an item okay and they
+ 
+
+ align:start position:0%
+who are bidding on an item okay and they
+all have an accurate I'm sorry yes an
+
+ align:start position:0%
+all have an accurate I'm sorry yes an
+ 
+
+ align:start position:0%
+all have an accurate I'm sorry yes an
+unbiased estimate of the value of that
+
+ align:start position:0%
+unbiased estimate of the value of that
+ 
+
+ align:start position:0%
+unbiased estimate of the value of that
+item okay but it's not that precise so
+
+ align:start position:0%
+item okay but it's not that precise so
+ 
+
+ align:start position:0%
+item okay but it's not that precise so
+people are just as likely to
+
+ align:start position:0%
+people are just as likely to
+ 
+
+ align:start position:0%
+people are just as likely to
+overestimate its value as underestimated
+
+ align:start position:0%
+overestimate its value as underestimated
+ 
+
+ align:start position:0%
+overestimate its value as underestimated
+and they all placed bids and those
+
+ align:start position:0%
+and they all placed bids and those
+ 
+
+ align:start position:0%
+and they all placed bids and those
+unbiased bids will therefore and let's
+
+ align:start position:0%
+unbiased bids will therefore and let's
+ 
+
+ align:start position:0%
+unbiased bids will therefore and let's
+say they bid what they think they think
+
+ align:start position:0%
+say they bid what they think they think
+ 
+
+ align:start position:0%
+say they bid what they think they think
+what the item is actually worth
+
+ align:start position:0%
+what the item is actually worth
+ 
+
+ align:start position:0%
+what the item is actually worth
+those unbiased bits will fluctuate
+
+ align:start position:0%
+those unbiased bits will fluctuate
+ 
+
+ align:start position:0%
+those unbiased bits will fluctuate
+around the True Value and then one of
+
+ align:start position:0%
+around the True Value and then one of
+ 
+
+ align:start position:0%
+around the True Value and then one of
+those will have fluctuated up the most
+
+ align:start position:0%
+those will have fluctuated up the most
+ 
+
+ align:start position:0%
+those will have fluctuated up the most
+and that will be the winning bid okay so
+
+ align:start position:0%
+and that will be the winning bid okay so
+ 
+
+ align:start position:0%
+and that will be the winning bid okay so
+it over the winning bid conditional on
+
+ align:start position:0%
+it over the winning bid conditional on
+ 
+
+ align:start position:0%
+it over the winning bid conditional on
+it being the winning bid
+
+ align:start position:0%
+it being the winning bid
+ 
+
+ align:start position:0%
+it being the winning bid
+will almost always have overestimated
+
+ align:start position:0%
+will almost always have overestimated
+ 
+
+ align:start position:0%
+will almost always have overestimated
+the value and this the best description
+
+ align:start position:0%
+the value and this the best description
+ 
+
+ align:start position:0%
+the value and this the best description
+this is uh uh Samuelson article called
+
+ align:start position:0%
+this is uh uh Samuelson article called
+ 
+
+ align:start position:0%
+this is uh uh Samuelson article called
+um I won the auction but don't want the
+
+ align:start position:0%
+um I won the auction but don't want the
+ 
+
+ align:start position:0%
+um I won the auction but don't want the
+prize
+
+ align:start position:0%
+prize
+ 
+
+ align:start position:0%
+prize
+um so you know beware on eBay
+
+ align:start position:0%
+um so you know beware on eBay
+ 
+
+ align:start position:0%
+um so you know beware on eBay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but so in in uh Association studies
+
+ align:start position:0%
+but so in in uh Association studies
+ 
+
+ align:start position:0%
+but so in in uh Association studies
+basically the winning bid is equivalent
+
+ align:start position:0%
+basically the winning bid is equivalent
+ 
+
+ align:start position:0%
+basically the winning bid is equivalent
+to the first person who gets an exciting
+
+ align:start position:0%
+to the first person who gets an exciting
+ 
+
+ align:start position:0%
+to the first person who gets an exciting
+enough result that they can publish it
+
+ align:start position:0%
+enough result that they can publish it
+ 
+
+ align:start position:0%
+enough result that they can publish it
+quickly and in a prominent journal and
+
+ align:start position:0%
+quickly and in a prominent journal and
+ 
+
+ align:start position:0%
+quickly and in a prominent journal and
+that sort of thing and conditional on
+
+ align:start position:0%
+that sort of thing and conditional on
+ 
+
+ align:start position:0%
+that sort of thing and conditional on
+them having found something interesting
+
+ align:start position:0%
+them having found something interesting
+ 
+
+ align:start position:0%
+them having found something interesting
+it's likely that they overestimated the
+
+ align:start position:0%
+it's likely that they overestimated the
+ 
+
+ align:start position:0%
+it's likely that they overestimated the
+true value and the True Value might
+
+ align:start position:0%
+true value and the True Value might
+ 
+
+ align:start position:0%
+true value and the True Value might
+either be a weak effect a weaker effect
+
+ align:start position:0%
+either be a weak effect a weaker effect
+ 
+
+ align:start position:0%
+either be a weak effect a weaker effect
+or actually no effect at all and that
+
+ align:start position:0%
+or actually no effect at all and that
+ 
+
+ align:start position:0%
+or actually no effect at all and that
+that time time only time can tell and so
+
+ align:start position:0%
+that time time only time can tell and so
+ 
+
+ align:start position:0%
+that time time only time can tell and so
+we found that this was it was consistent
+
+ align:start position:0%
+we found that this was it was consistent
+ 
+
+ align:start position:0%
+we found that this was it was consistent
+that the degree by which they
+
+ align:start position:0%
+that the degree by which they
+ 
+
+ align:start position:0%
+that the degree by which they
+overestimated was generally consistent
+
+ align:start position:0%
+overestimated was generally consistent
+ 
+
+ align:start position:0%
+overestimated was generally consistent
+with the Winner's curse phenomenon
+
+ align:start position:0%
+with the Winner's curse phenomenon
+ 
+
+ align:start position:0%
+with the Winner's curse phenomenon
+so this is kind of the take-home
+
+ align:start position:0%
+so this is kind of the take-home
+ 
+
+ align:start position:0%
+so this is kind of the take-home
+messages from Reading you know for
+
+ align:start position:0%
+messages from Reading you know for
+ 
+
+ align:start position:0%
+messages from Reading you know for
+reading the association study literature
+
+ align:start position:0%
+reading the association study literature
+ 
+
+ align:start position:0%
+reading the association study literature
+so if you pick up
+
+ align:start position:0%
+so if you pick up
+ 
+
+ align:start position:0%
+so if you pick up
+a paper and it says that something is
+
+ align:start position:0%
+a paper and it says that something is
+ 
+
+ align:start position:0%
+a paper and it says that something is
+associated with disease
+
+ align:start position:0%
+associated with disease
+ 
+
+ align:start position:0%
+associated with disease
+there is a possibility that it will be
+
+ align:start position:0%
+there is a possibility that it will be
+ 
+
+ align:start position:0%
+there is a possibility that it will be
+true okay but it's I would say well
+
+ align:start position:0%
+true okay but it's I would say well
+ 
+
+ align:start position:0%
+true okay but it's I would say well
+under 50 okay it's not zero percent
+
+ align:start position:0%
+under 50 okay it's not zero percent
+ 
+
+ align:start position:0%
+under 50 okay it's not zero percent
+either but it's it's well under 50
+
+ align:start position:0%
+either but it's it's well under 50
+ 
+
+ align:start position:0%
+either but it's it's well under 50
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the genetic effects for associations are
+
+ align:start position:0%
+the genetic effects for associations are
+ 
+
+ align:start position:0%
+the genetic effects for associations are
+likely to be quite modest so if
+
+ align:start position:0%
+likely to be quite modest so if
+ 
+
+ align:start position:0%
+likely to be quite modest so if
+somebody's claiming a uh
+
+ align:start position:0%
+somebody's claiming a uh
+ 
+
+ align:start position:0%
+somebody's claiming a uh
+a five-fold effect and their confidence
+
+ align:start position:0%
+a five-fold effect and their confidence
+ 
+
+ align:start position:0%
+a five-fold effect and their confidence
+intervals go from 1.1 to 40. it's
+
+ align:start position:0%
+intervals go from 1.1 to 40. it's
+ 
+
+ align:start position:0%
+intervals go from 1.1 to 40. it's
+probably closer to 1.1
+
+ align:start position:0%
+probably closer to 1.1
+ 
+
+ align:start position:0%
+probably closer to 1.1
+uh if not one uh and then because of
+
+ align:start position:0%
+uh if not one uh and then because of
+ 
+
+ align:start position:0%
+uh if not one uh and then because of
+these modest effects we need large study
+
+ align:start position:0%
+these modest effects we need large study
+ 
+
+ align:start position:0%
+these modest effects we need large study
+sites to detect these reliably and also
+
+ align:start position:0%
+sites to detect these reliably and also
+ 
+
+ align:start position:0%
+sites to detect these reliably and also
+to narrow those confidence intervals
+
+ align:start position:0%
+to narrow those confidence intervals
+ 
+
+ align:start position:0%
+to narrow those confidence intervals
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+I'll just give you an example our
+
+ align:start position:0%
+I'll just give you an example our
+ 
+
+ align:start position:0%
+I'll just give you an example our
+favorite example uh for an association
+
+ align:start position:0%
+favorite example uh for an association
+ 
+
+ align:start position:0%
+favorite example uh for an association
+of a missense polymorphism or we think
+
+ align:start position:0%
+of a missense polymorphism or we think
+ 
+
+ align:start position:0%
+of a missense polymorphism or we think
+that's the causal polymorphism uh and
+
+ align:start position:0%
+that's the causal polymorphism uh and
+ 
+
+ align:start position:0%
+that's the causal polymorphism uh and
+type 2 diabetes is in the gene called
+
+ align:start position:0%
+type 2 diabetes is in the gene called
+ 
+
+ align:start position:0%
+type 2 diabetes is in the gene called
+PPR gamma which is important for fat
+
+ align:start position:0%
+PPR gamma which is important for fat
+ 
+
+ align:start position:0%
+PPR gamma which is important for fat
+cell differentiation and uh is a nuclear
+
+ align:start position:0%
+cell differentiation and uh is a nuclear
+ 
+
+ align:start position:0%
+cell differentiation and uh is a nuclear
+hormone receptor probably binds fatty
+
+ align:start position:0%
+hormone receptor probably binds fatty
+ 
+
+ align:start position:0%
+hormone receptor probably binds fatty
+acids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the first study that was published is
+
+ align:start position:0%
+the first study that was published is
+ 
+
+ align:start position:0%
+the first study that was published is
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+um so each line is a study the point is
+
+ align:start position:0%
+um so each line is a study the point is
+ 
+
+ align:start position:0%
+um so each line is a study the point is
+the point estimate for the uh effect on
+
+ align:start position:0%
+the point estimate for the uh effect on
+ 
+
+ align:start position:0%
+the point estimate for the uh effect on
+diabetes and actually in this case
+
+ align:start position:0%
+diabetes and actually in this case
+ 
+
+ align:start position:0%
+diabetes and actually in this case
+anything to the left of this line uh is
+
+ align:start position:0%
+anything to the left of this line uh is
+ 
+
+ align:start position:0%
+anything to the left of this line uh is
+is an association with diabetes
+
+ align:start position:0%
+is an association with diabetes
+ 
+
+ align:start position:0%
+is an association with diabetes
+and the line around the point represents
+
+ align:start position:0%
+and the line around the point represents
+ 
+
+ align:start position:0%
+and the line around the point represents
+the confidence interval around that
+
+ align:start position:0%
+the confidence interval around that
+ 
+
+ align:start position:0%
+the confidence interval around that
+estimate okay so for example this study
+
+ align:start position:0%
+estimate okay so for example this study
+ 
+
+ align:start position:0%
+estimate okay so for example this study
+up here even though it shows that it
+
+ align:start position:0%
+up here even though it shows that it
+ 
+
+ align:start position:0%
+up here even though it shows that it
+Trends towards Association was
+
+ align:start position:0%
+Trends towards Association was
+ 
+
+ align:start position:0%
+Trends towards Association was
+considered negative because this line
+
+ align:start position:0%
+considered negative because this line
+ 
+
+ align:start position:0%
+considered negative because this line
+crosses uh the 95 confident will crosses
+
+ align:start position:0%
+crosses uh the 95 confident will crosses
+ 
+
+ align:start position:0%
+crosses uh the 95 confident will crosses
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+this is the first study which you can
+
+ align:start position:0%
+this is the first study which you can
+ 
+
+ align:start position:0%
+this is the first study which you can
+see the Winner's curse in action here
+
+ align:start position:0%
+see the Winner's curse in action here
+ 
+
+ align:start position:0%
+see the Winner's curse in action here
+overestimates the uh is is the strongest
+
+ align:start position:0%
+overestimates the uh is is the strongest
+ 
+
+ align:start position:0%
+overestimates the uh is is the strongest
+estimate of risk and it was followed by
+
+ align:start position:0%
+estimate of risk and it was followed by
+ 
+
+ align:start position:0%
+estimate of risk and it was followed by
+I believe these three and a bunch of
+
+ align:start position:0%
+I believe these three and a bunch of
+ 
+
+ align:start position:0%
+I believe these three and a bunch of
+other studies all of which were
+
+ align:start position:0%
+other studies all of which were
+ 
+
+ align:start position:0%
+other studies all of which were
+considered to be negative because
+
+ align:start position:0%
+considered to be negative because
+ 
+
+ align:start position:0%
+considered to be negative because
+they're 95 composite intervals across
+
+ align:start position:0%
+they're 95 composite intervals across
+ 
+
+ align:start position:0%
+they're 95 composite intervals across
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um we then did a pretty big study where
+
+ align:start position:0%
+um we then did a pretty big study where
+ 
+
+ align:start position:0%
+um we then did a pretty big study where
+we showed an association we actually
+
+ align:start position:0%
+we showed an association we actually
+ 
+
+ align:start position:0%
+we showed an association we actually
+pointed out that all the literature to
+
+ align:start position:0%
+pointed out that all the literature to
+ 
+
+ align:start position:0%
+pointed out that all the literature to
+date was consistent with an association
+
+ align:start position:0%
+date was consistent with an association
+ 
+
+ align:start position:0%
+date was consistent with an association
+somewhere in this range much weaker than
+
+ align:start position:0%
+somewhere in this range much weaker than
+ 
+
+ align:start position:0%
+somewhere in this range much weaker than
+originally described but uh modest
+
+ align:start position:0%
+originally described but uh modest
+ 
+
+ align:start position:0%
+originally described but uh modest
+enough that these studies didn't have
+
+ align:start position:0%
+enough that these studies didn't have
+ 
+
+ align:start position:0%
+enough that these studies didn't have
+power to pick it up and in fact as you
+
+ align:start position:0%
+power to pick it up and in fact as you
+ 
+
+ align:start position:0%
+power to pick it up and in fact as you
+get larger and larger samples what you
+
+ align:start position:0%
+get larger and larger samples what you
+ 
+
+ align:start position:0%
+get larger and larger samples what you
+can see is that the confidence intervals
+
+ align:start position:0%
+can see is that the confidence intervals
+ 
+
+ align:start position:0%
+can see is that the confidence intervals
+is that the things tend to really focus
+
+ align:start position:0%
+is that the things tend to really focus
+ 
+
+ align:start position:0%
+is that the things tend to really focus
+in and you put all the data together you
+
+ align:start position:0%
+in and you put all the data together you
+ 
+
+ align:start position:0%
+in and you put all the data together you
+get a pretty narrow confidence interval
+
+ align:start position:0%
+get a pretty narrow confidence interval
+ 
+
+ align:start position:0%
+get a pretty narrow confidence interval
+and now the p-value for Association is
+
+ align:start position:0%
+and now the p-value for Association is
+ 
+
+ align:start position:0%
+and now the p-value for Association is
+like 10 to the minus nine so it's it's
+
+ align:start position:0%
+like 10 to the minus nine so it's it's
+ 
+
+ align:start position:0%
+like 10 to the minus nine so it's it's
+real but it took 20 000 alleles from
+
+ align:start position:0%
+real but it took 20 000 alleles from
+ 
+
+ align:start position:0%
+real but it took 20 000 alleles from
+people with diabetes and controls to get
+
+ align:start position:0%
+people with diabetes and controls to get
+ 
+
+ align:start position:0%
+people with diabetes and controls to get
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for diabetes the definition of
+
+ align:start position:0%
+so for diabetes the definition of
+ 
+
+ align:start position:0%
+so for diabetes the definition of
+diabetes is pretty clear there's a who
+
+ align:start position:0%
+diabetes is pretty clear there's a who
+ 
+
+ align:start position:0%
+diabetes is pretty clear there's a who
+consensus and they're more or less the
+
+ align:start position:0%
+consensus and they're more or less the
+ 
+
+ align:start position:0%
+consensus and they're more or less the
+same definition uh I would say close
+
+ align:start position:0%
+same definition uh I would say close
+ 
+
+ align:start position:0%
+same definition uh I would say close
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+the allele itself is clearly the same
+
+ align:start position:0%
+the allele itself is clearly the same
+ 
+
+ align:start position:0%
+the allele itself is clearly the same
+variant and uh you know assuming that
+
+ align:start position:0%
+variant and uh you know assuming that
+ 
+
+ align:start position:0%
+variant and uh you know assuming that
+the quality of genotyping was good
+
+ align:start position:0%
+the quality of genotyping was good
+ 
+
+ align:start position:0%
+the quality of genotyping was good
+um probably they were looking at the
+
+ align:start position:0%
+um probably they were looking at the
+ 
+
+ align:start position:0%
+um probably they were looking at the
+same thing there
+
+ align:start position:0%
+same thing there
+ 
+
+ align:start position:0%
+same thing there
+obviously the populations are different
+
+ align:start position:0%
+obviously the populations are different
+ 
+
+ align:start position:0%
+obviously the populations are different
+so I talked about population differences
+
+ align:start position:0%
+so I talked about population differences
+ 
+
+ align:start position:0%
+so I talked about population differences
+so it turns out also one of the best
+
+ align:start position:0%
+so it turns out also one of the best
+ 
+
+ align:start position:0%
+so it turns out also one of the best
+examples of heterogeneity between
+
+ align:start position:0%
+examples of heterogeneity between
+ 
+
+ align:start position:0%
+examples of heterogeneity between
+populations is for this polymorphism not
+
+ align:start position:0%
+populations is for this polymorphism not
+ 
+
+ align:start position:0%
+populations is for this polymorphism not
+so much in diabetes although it hasn't
+
+ align:start position:0%
+so much in diabetes although it hasn't
+ 
+
+ align:start position:0%
+so much in diabetes although it hasn't
+really been looked that well but
+
+ align:start position:0%
+really been looked that well but
+ 
+
+ align:start position:0%
+really been looked that well but
+actually obesity so this has been looked
+
+ align:start position:0%
+actually obesity so this has been looked
+ 
+
+ align:start position:0%
+actually obesity so this has been looked
+at a lot for obesity and wildly
+
+ align:start position:0%
+at a lot for obesity and wildly
+ 
+
+ align:start position:0%
+at a lot for obesity and wildly
+Divergent results it turns out that how
+
+ align:start position:0%
+Divergent results it turns out that how
+ 
+
+ align:start position:0%
+Divergent results it turns out that how
+much trans fatty acids you eat or
+
+ align:start position:0%
+much trans fatty acids you eat or
+ 
+
+ align:start position:0%
+much trans fatty acids you eat or
+saturated unsaturated fatty acids
+
+ align:start position:0%
+saturated unsaturated fatty acids
+ 
+
+ align:start position:0%
+saturated unsaturated fatty acids
+affects whether this polymorphism has an
+
+ align:start position:0%
+affects whether this polymorphism has an
+ 
+
+ align:start position:0%
+affects whether this polymorphism has an
+effect on Obesity I can't remember right
+
+ align:start position:0%
+effect on Obesity I can't remember right
+ 
+
+ align:start position:0%
+effect on Obesity I can't remember right
+now which way it goes basically on a on
+
+ align:start position:0%
+now which way it goes basically on a on
+ 
+
+ align:start position:0%
+now which way it goes basically on a on
+one diet which is much more common in
+
+ align:start position:0%
+one diet which is much more common in
+ 
+
+ align:start position:0%
+one diet which is much more common in
+Western countries there's I think no
+
+ align:start position:0%
+Western countries there's I think no
+ 
+
+ align:start position:0%
+Western countries there's I think no
+effect and on another diet which is much
+
+ align:start position:0%
+effect and on another diet which is much
+ 
+
+ align:start position:0%
+effect and on another diet which is much
+more common in Asian countries uh there
+
+ align:start position:0%
+more common in Asian countries uh there
+ 
+
+ align:start position:0%
+more common in Asian countries uh there
+is an effect on Obesity so you can
+
+ align:start position:0%
+is an effect on Obesity so you can
+ 
+
+ align:start position:0%
+is an effect on Obesity so you can
+imagine that they're you know and
+
+ align:start position:0%
+imagine that they're you know and
+ 
+
+ align:start position:0%
+imagine that they're you know and
+actually if you look it turns out that
+
+ align:start position:0%
+actually if you look it turns out that
+ 
+
+ align:start position:0%
+actually if you look it turns out that
+the these three are all in uh Asian
+
+ align:start position:0%
+the these three are all in uh Asian
+ 
+
+ align:start position:0%
+the these three are all in uh Asian
+populations so it could be that there is
+
+ align:start position:0%
+populations so it could be that there is
+ 
+
+ align:start position:0%
+populations so it could be that there is
+some heterogeneity going on there
+
+ align:start position:0%
+some heterogeneity going on there
+ 
+
+ align:start position:0%
+some heterogeneity going on there
+although it's statistically marginally
+
+ align:start position:0%
+although it's statistically marginally
+ 
+
+ align:start position:0%
+although it's statistically marginally
+significant whether any of these studies
+
+ align:start position:0%
+significant whether any of these studies
+ 
+
+ align:start position:0%
+significant whether any of these studies
+are different than any any of the others
+
+ align:start position:0%
+are different than any any of the others
+ 
+
+ align:start position:0%
+are different than any any of the others
+so these are mostly consistent with if
+
+ align:start position:0%
+so these are mostly consistent with if
+ 
+
+ align:start position:0%
+so these are mostly consistent with if
+you took you know darts and threw them
+
+ align:start position:0%
+you took you know darts and threw them
+ 
+
+ align:start position:0%
+you took you know darts and threw them
+all at the same odds ratio you might end
+
+ align:start position:0%
+all at the same odds ratio you might end
+ 
+
+ align:start position:0%
+all at the same odds ratio you might end
+up with points that look more or less
+
+ align:start position:0%
+up with points that look more or less
+ 
+
+ align:start position:0%
+up with points that look more or less
+like that so but it could well be that
+
+ align:start position:0%
+like that so but it could well be that
+ 
+
+ align:start position:0%
+like that so but it could well be that
+there are differences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for things like you know for Less well
+
+ align:start position:0%
+for things like you know for Less well
+ 
+
+ align:start position:0%
+for things like you know for Less well
+so for Alzheimer's disease there's a
+
+ align:start position:0%
+so for Alzheimer's disease there's a
+ 
+
+ align:start position:0%
+so for Alzheimer's disease there's a
+little more debate sometimes of whether
+
+ align:start position:0%
+little more debate sometimes of whether
+ 
+
+ align:start position:0%
+little more debate sometimes of whether
+it's pathology confirmed or not and that
+
+ align:start position:0%
+it's pathology confirmed or not and that
+ 
+
+ align:start position:0%
+it's pathology confirmed or not and that
+sort of thing so
+
+ align:start position:0%
+sort of thing so
+ 
+
+ align:start position:0%
+sort of thing so
+all right so what to believe is the kind
+
+ align:start position:0%
+all right so what to believe is the kind
+ 
+
+ align:start position:0%
+all right so what to believe is the kind
+of the question so should you believe it
+
+ align:start position:0%
+of the question so should you believe it
+ 
+
+ align:start position:0%
+of the question so should you believe it
+I would say initial skepticism is
+
+ align:start position:0%
+I would say initial skepticism is
+ 
+
+ align:start position:0%
+I would say initial skepticism is
+warranted replication especially with
+
+ align:start position:0%
+warranted replication especially with
+ 
+
+ align:start position:0%
+warranted replication especially with
+low P values and maybe we can discuss
+
+ align:start position:0%
+low P values and maybe we can discuss
+ 
+
+ align:start position:0%
+low P values and maybe we can discuss
+what that means is encouraging large
+
+ align:start position:0%
+what that means is encouraging large
+ 
+
+ align:start position:0%
+what that means is encouraging large
+sample sizes are crucial so if you take
+
+ align:start position:0%
+sample sizes are crucial so if you take
+ 
+
+ align:start position:0%
+sample sizes are crucial so if you take
+anything home there you go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want to quickly um this is a
+
+ align:start position:0%
+okay so I want to quickly um this is a
+ 
+
+ align:start position:0%
+okay so I want to quickly um this is a
+sort of quantitatively oriented
+
+ align:start position:0%
+sort of quantitatively oriented
+ 
+
+ align:start position:0%
+sort of quantitatively oriented
+um class talk about applying Bayes
+
+ align:start position:0%
+um class talk about applying Bayes
+ 
+
+ align:start position:0%
+um class talk about applying Bayes
+theorem to interpreting Association
+
+ align:start position:0%
+theorem to interpreting Association
+ 
+
+ align:start position:0%
+theorem to interpreting Association
+studies so Bayes theorem um is basically
+
+ align:start position:0%
+studies so Bayes theorem um is basically
+ 
+
+ align:start position:0%
+studies so Bayes theorem um is basically
+is you know one of the fundamental
+
+ align:start position:0%
+is you know one of the fundamental
+ 
+
+ align:start position:0%
+is you know one of the fundamental
+theorems of probability
+
+ align:start position:0%
+theorems of probability
+ 
+
+ align:start position:0%
+theorems of probability
+um and in this case what I've done is
+
+ align:start position:0%
+um and in this case what I've done is
+ 
+
+ align:start position:0%
+um and in this case what I've done is
+I've substituted in the words causal and
+
+ align:start position:0%
+I've substituted in the words causal and
+ 
+
+ align:start position:0%
+I've substituted in the words causal and
+a soap for associate for uh uh
+
+ align:start position:0%
+a soap for associate for uh uh
+ 
+
+ align:start position:0%
+a soap for associate for uh uh
+probability of observing Association and
+
+ align:start position:0%
+probability of observing Association and
+ 
+
+ align:start position:0%
+probability of observing Association and
+causal is the probability that the
+
+ align:start position:0%
+causal is the probability that the
+ 
+
+ align:start position:0%
+causal is the probability that the
+variant that you're looking at actually
+
+ align:start position:0%
+variant that you're looking at actually
+ 
+
+ align:start position:0%
+variant that you're looking at actually
+is causal
+
+ align:start position:0%
+is causal
+ 
+
+ align:start position:0%
+is causal
+so if you go through just plugging it
+
+ align:start position:0%
+so if you go through just plugging it
+ 
+
+ align:start position:0%
+so if you go through just plugging it
+into Bayes theorem this is what you get
+
+ align:start position:0%
+into Bayes theorem this is what you get
+ 
+
+ align:start position:0%
+into Bayes theorem this is what you get
+and what you're interested in is
+
+ align:start position:0%
+and what you're interested in is
+ 
+
+ align:start position:0%
+and what you're interested in is
+basically given that I've seen an
+
+ align:start position:0%
+basically given that I've seen an
+ 
+
+ align:start position:0%
+basically given that I've seen an
+association what's the likelihood that
+
+ align:start position:0%
+association what's the likelihood that
+ 
+
+ align:start position:0%
+association what's the likelihood that
+it's true right that's what you want to
+
+ align:start position:0%
+it's true right that's what you want to
+ 
+
+ align:start position:0%
+it's true right that's what you want to
+know when you pick up the paper
+
+ align:start position:0%
+know when you pick up the paper
+ 
+
+ align:start position:0%
+know when you pick up the paper
+so this has to do with three terms one
+
+ align:start position:0%
+so this has to do with three terms one
+ 
+
+ align:start position:0%
+so this has to do with three terms one
+is the probability that something's
+
+ align:start position:0%
+is the probability that something's
+ 
+
+ align:start position:0%
+is the probability that something's
+Associated given that it was causal so
+
+ align:start position:0%
+Associated given that it was causal so
+ 
+
+ align:start position:0%
+Associated given that it was causal so
+that's the power of the study right so
+
+ align:start position:0%
+that's the power of the study right so
+ 
+
+ align:start position:0%
+that's the power of the study right so
+would you see an association if it were
+
+ align:start position:0%
+would you see an association if it were
+ 
+
+ align:start position:0%
+would you see an association if it were
+causal
+
+ align:start position:0%
+causal
+ 
+
+ align:start position:0%
+causal
+would I have seen this Association date
+
+ align:start position:0%
+would I have seen this Association date
+ 
+
+ align:start position:0%
+would I have seen this Association date
+if it were not causable that's the
+
+ align:start position:0%
+if it were not causable that's the
+ 
+
+ align:start position:0%
+if it were not causable that's the
+p-value the probability of observing the
+
+ align:start position:0%
+p-value the probability of observing the
+ 
+
+ align:start position:0%
+p-value the probability of observing the
+data by chance
+
+ align:start position:0%
+data by chance
+ 
+
+ align:start position:0%
+data by chance
+and then the probability that's causal
+
+ align:start position:0%
+and then the probability that's causal
+ 
+
+ align:start position:0%
+and then the probability that's causal
+to begin with which is your prior
+
+ align:start position:0%
+to begin with which is your prior
+ 
+
+ align:start position:0%
+to begin with which is your prior
+probabilities this is the key to Bayes
+
+ align:start position:0%
+probabilities this is the key to Bayes
+ 
+
+ align:start position:0%
+probabilities this is the key to Bayes
+theorem which is that you have to
+
+ align:start position:0%
+theorem which is that you have to
+ 
+
+ align:start position:0%
+theorem which is that you have to
+specify the priors which is of course
+
+ align:start position:0%
+specify the priors which is of course
+ 
+
+ align:start position:0%
+specify the priors which is of course
+always the hardest part it's very easy
+
+ align:start position:0%
+always the hardest part it's very easy
+ 
+
+ align:start position:0%
+always the hardest part it's very easy
+to write down Bayes theorem but then
+
+ align:start position:0%
+to write down Bayes theorem but then
+ 
+
+ align:start position:0%
+to write down Bayes theorem but then
+specifying your prior distribution can
+
+ align:start position:0%
+specifying your prior distribution can
+ 
+
+ align:start position:0%
+specifying your prior distribution can
+sometimes be quite tricky
+
+ align:start position:0%
+sometimes be quite tricky
+ 
+
+ align:start position:0%
+sometimes be quite tricky
+all right so I'm going to take you
+
+ align:start position:0%
+all right so I'm going to take you
+ 
+
+ align:start position:0%
+all right so I'm going to take you
+through what I believe prior
+
+ align:start position:0%
+through what I believe prior
+ 
+
+ align:start position:0%
+through what I believe prior
+distributions look like within a couple
+
+ align:start position:0%
+distributions look like within a couple
+ 
+
+ align:start position:0%
+distributions look like within a couple
+of orders of magnitude
+
+ align:start position:0%
+of orders of magnitude
+ 
+
+ align:start position:0%
+of orders of magnitude
+so what are the prior probabilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I'm going to say they're about 600 000
+
+ align:start position:0%
+I'm going to say they're about 600 000
+ 
+
+ align:start position:0%
+I'm going to say they're about 600 000
+independent common variants that has to
+
+ align:start position:0%
+independent common variants that has to
+ 
+
+ align:start position:0%
+independent common variants that has to
+do with the degree of redundancy that's
+
+ align:start position:0%
+do with the degree of redundancy that's
+ 
+
+ align:start position:0%
+do with the degree of redundancy that's
+been determined by the hap map and stuff
+
+ align:start position:0%
+been determined by the hap map and stuff
+ 
+
+ align:start position:0%
+been determined by the hap map and stuff
+like that there are 10 million in total
+
+ align:start position:0%
+like that there are 10 million in total
+ 
+
+ align:start position:0%
+like that there are 10 million in total
+some of them aren't that common so I'm
+
+ align:start position:0%
+some of them aren't that common so I'm
+ 
+
+ align:start position:0%
+some of them aren't that common so I'm
+going to kind of shove those under the
+
+ align:start position:0%
+going to kind of shove those under the
+ 
+
+ align:start position:0%
+going to kind of shove those under the
+rug for a little bit uh and of the rest
+
+ align:start position:0%
+rug for a little bit uh and of the rest
+ 
+
+ align:start position:0%
+rug for a little bit uh and of the rest
+there's enough correlation that I'm
+
+ align:start position:0%
+there's enough correlation that I'm
+ 
+
+ align:start position:0%
+there's enough correlation that I'm
+going to say there's about 600 000
+
+ align:start position:0%
+going to say there's about 600 000
+ 
+
+ align:start position:0%
+going to say there's about 600 000
+variants that you can type
+
+ align:start position:0%
+variants that you can type
+ 
+
+ align:start position:0%
+variants that you can type
+the other assumption is that at least a
+
+ align:start position:0%
+the other assumption is that at least a
+ 
+
+ align:start position:0%
+the other assumption is that at least a
+few of those are going to be causal so
+
+ align:start position:0%
+few of those are going to be causal so
+ 
+
+ align:start position:0%
+few of those are going to be causal so
+I'm assuming the common variance Place
+
+ align:start position:0%
+I'm assuming the common variance Place
+ 
+
+ align:start position:0%
+I'm assuming the common variance Place
+some role in disease okay so I'm going
+
+ align:start position:0%
+some role in disease okay so I'm going
+ 
+
+ align:start position:0%
+some role in disease okay so I'm going
+to say somewhere between 6 and 60. it
+
+ align:start position:0%
+to say somewhere between 6 and 60. it
+ 
+
+ align:start position:0%
+to say somewhere between 6 and 60. it
+may be more uh but and I would say
+
+ align:start position:0%
+may be more uh but and I would say
+ 
+
+ align:start position:0%
+may be more uh but and I would say
+causal to a degree where you have any
+
+ align:start position:0%
+causal to a degree where you have any
+ 
+
+ align:start position:0%
+causal to a degree where you have any
+power to detect them at all because
+
+ align:start position:0%
+power to detect them at all because
+ 
+
+ align:start position:0%
+power to detect them at all because
+obviously you have no power to detect
+
+ align:start position:0%
+obviously you have no power to detect
+ 
+
+ align:start position:0%
+obviously you have no power to detect
+them they may as well not exist from the
+
+ align:start position:0%
+them they may as well not exist from the
+ 
+
+ align:start position:0%
+them they may as well not exist from the
+point of view of this study okay because
+
+ align:start position:0%
+point of view of this study okay because
+ 
+
+ align:start position:0%
+point of view of this study okay because
+if you're if you plug in 0 for your
+
+ align:start position:0%
+if you're if you plug in 0 for your
+ 
+
+ align:start position:0%
+if you're if you plug in 0 for your
+power then all everything starts
+
+ align:start position:0%
+power then all everything starts
+ 
+
+ align:start position:0%
+power then all everything starts
+canceling out
+
+ align:start position:0%
+canceling out
+ 
+
+ align:start position:0%
+canceling out
+okay so that's you're probably one in
+
+ align:start position:0%
+okay so that's you're probably one in
+ 
+
+ align:start position:0%
+okay so that's you're probably one in
+ten thousand to one in a hundred
+
+ align:start position:0%
+ten thousand to one in a hundred
+ 
+
+ align:start position:0%
+ten thousand to one in a hundred
+thousand more or less how about
+
+ align:start position:0%
+thousand more or less how about
+ 
+
+ align:start position:0%
+thousand more or less how about
+candidate genes let's say well you know
+
+ align:start position:0%
+candidate genes let's say well you know
+ 
+
+ align:start position:0%
+candidate genes let's say well you know
+I'm not studying to say this paper is
+
+ align:start position:0%
+I'm not studying to say this paper is
+ 
+
+ align:start position:0%
+I'm not studying to say this paper is
+not studying some some stinking random
+
+ align:start position:0%
+not studying some some stinking random
+ 
+
+ align:start position:0%
+not studying some some stinking random
+variant this is like the greatest
+
+ align:start position:0%
+variant this is like the greatest
+ 
+
+ align:start position:0%
+variant this is like the greatest
+candidate Gene in the whole world
+
+ align:start position:0%
+candidate Gene in the whole world
+ 
+
+ align:start position:0%
+candidate Gene in the whole world
+well so we've gone through the exercise
+
+ align:start position:0%
+well so we've gone through the exercise
+ 
+
+ align:start position:0%
+well so we've gone through the exercise
+of writing down all the candidate genes
+
+ align:start position:0%
+of writing down all the candidate genes
+ 
+
+ align:start position:0%
+of writing down all the candidate genes
+that we think are great candidate genes
+
+ align:start position:0%
+that we think are great candidate genes
+ 
+
+ align:start position:0%
+that we think are great candidate genes
+for diseases and you usually come up
+
+ align:start position:0%
+for diseases and you usually come up
+ 
+
+ align:start position:0%
+for diseases and you usually come up
+with somewhere between say 100 and 500
+
+ align:start position:0%
+with somewhere between say 100 and 500
+ 
+
+ align:start position:0%
+with somewhere between say 100 and 500
+genes so let's say 300 that you come up
+
+ align:start position:0%
+genes so let's say 300 that you come up
+ 
+
+ align:start position:0%
+genes so let's say 300 that you come up
+with and I would argue that you could
+
+ align:start position:0%
+with and I would argue that you could
+ 
+
+ align:start position:0%
+with and I would argue that you could
+tell as equally beautiful a story about
+
+ align:start position:0%
+tell as equally beautiful a story about
+ 
+
+ align:start position:0%
+tell as equally beautiful a story about
+almost all 300 of those genes once you
+
+ align:start position:0%
+almost all 300 of those genes once you
+ 
+
+ align:start position:0%
+almost all 300 of those genes once you
+knew post-hoc that there was an
+
+ align:start position:0%
+knew post-hoc that there was an
+ 
+
+ align:start position:0%
+knew post-hoc that there was an
+association
+
+ align:start position:0%
+association
+ 
+
+ align:start position:0%
+association
+okay so you can say oh of course that's
+
+ align:start position:0%
+okay so you can say oh of course that's
+ 
+
+ align:start position:0%
+okay so you can say oh of course that's
+why protein kinase C Theta is the key to
+
+ align:start position:0%
+why protein kinase C Theta is the key to
+ 
+
+ align:start position:0%
+why protein kinase C Theta is the key to
+diabetes you know and you write your
+
+ align:start position:0%
+diabetes you know and you write your
+ 
+
+ align:start position:0%
+diabetes you know and you write your
+story so I'm going to say that there are
+
+ align:start position:0%
+story so I'm going to say that there are
+ 
+
+ align:start position:0%
+story so I'm going to say that there are
+300 candidate genes all of them about
+
+ align:start position:0%
+300 candidate genes all of them about
+ 
+
+ align:start position:0%
+300 candidate genes all of them about
+equally likely to be Associated again
+
+ align:start position:0%
+equally likely to be Associated again
+ 
+
+ align:start position:0%
+equally likely to be Associated again
+using some things about there are about
+
+ align:start position:0%
+using some things about there are about
+ 
+
+ align:start position:0%
+using some things about there are about
+three or four blocks of linguistic
+
+ align:start position:0%
+three or four blocks of linguistic
+ 
+
+ align:start position:0%
+three or four blocks of linguistic
+equilibrium report for per Gene about
+
+ align:start position:0%
+equilibrium report for per Gene about
+ 
+
+ align:start position:0%
+equilibrium report for per Gene about
+three or four haplotypes for genome and
+
+ align:start position:0%
+three or four haplotypes for genome and
+ 
+
+ align:start position:0%
+three or four haplotypes for genome and
+say they're about 12 independent
+
+ align:start position:0%
+say they're about 12 independent
+ 
+
+ align:start position:0%
+say they're about 12 independent
+variants per Gene
+
+ align:start position:0%
+variants per Gene
+ 
+
+ align:start position:0%
+variants per Gene
+so there's about 3 600 candidate
+
+ align:start position:0%
+so there's about 3 600 candidate
+ 
+
+ align:start position:0%
+so there's about 3 600 candidate
+variants on your list of 300 genes that
+
+ align:start position:0%
+variants on your list of 300 genes that
+ 
+
+ align:start position:0%
+variants on your list of 300 genes that
+you've just made
+
+ align:start position:0%
+you've just made
+ 
+
+ align:start position:0%
+you've just made
+let's assume and this is I think
+
+ align:start position:0%
+let's assume and this is I think
+ 
+
+ align:start position:0%
+let's assume and this is I think
+somewhat generous but you know let's
+
+ align:start position:0%
+somewhat generous but you know let's
+ 
+
+ align:start position:0%
+somewhat generous but you know let's
+assume that all that biology that went
+
+ align:start position:0%
+assume that all that biology that went
+ 
+
+ align:start position:0%
+assume that all that biology that went
+into making those that list is
+
+ align:start position:0%
+into making those that list is
+ 
+
+ align:start position:0%
+into making those that list is
+worthwhile
+
+ align:start position:0%
+worthwhile
+ 
+
+ align:start position:0%
+worthwhile
+and that half of all the causal variants
+
+ align:start position:0%
+and that half of all the causal variants
+ 
+
+ align:start position:0%
+and that half of all the causal variants
+are in the candidate genes well then if
+
+ align:start position:0%
+are in the candidate genes well then if
+ 
+
+ align:start position:0%
+are in the candidate genes well then if
+you do all the multiplication the prior
+
+ align:start position:0%
+you do all the multiplication the prior
+ 
+
+ align:start position:0%
+you do all the multiplication the prior
+probability is about 10 times higher for
+
+ align:start position:0%
+probability is about 10 times higher for
+ 
+
+ align:start position:0%
+probability is about 10 times higher for
+candidate Gene as it is for a random
+
+ align:start position:0%
+candidate Gene as it is for a random
+ 
+
+ align:start position:0%
+candidate Gene as it is for a random
+Gene one and a hundred to one in a
+
+ align:start position:0%
+Gene one and a hundred to one in a
+ 
+
+ align:start position:0%
+Gene one and a hundred to one in a
+thousand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then what are the prior
+
+ align:start position:0%
+and then what are the prior
+ 
+
+ align:start position:0%
+and then what are the prior
+probabilities you suggested looking
+
+ align:start position:0%
+probabilities you suggested looking
+ 
+
+ align:start position:0%
+probabilities you suggested looking
+under a linkage Peak let's go do all the
+
+ align:start position:0%
+under a linkage Peak let's go do all the
+ 
+
+ align:start position:0%
+under a linkage Peak let's go do all the
+genes under a linkage Peak well what are
+
+ align:start position:0%
+genes under a linkage Peak well what are
+ 
+
+ align:start position:0%
+genes under a linkage Peak well what are
+the prior probabilities there let's say
+
+ align:start position:0%
+the prior probabilities there let's say
+ 
+
+ align:start position:0%
+the prior probabilities there let's say
+actually not 200 genes let's say they're
+
+ align:start position:0%
+actually not 200 genes let's say they're
+ 
+
+ align:start position:0%
+actually not 200 genes let's say they're
+only 100 genes that are linkage Peak
+
+ align:start position:0%
+only 100 genes that are linkage Peak
+ 
+
+ align:start position:0%
+only 100 genes that are linkage Peak
+again the same 12 variants per Gene but
+
+ align:start position:0%
+again the same 12 variants per Gene but
+ 
+
+ align:start position:0%
+again the same 12 variants per Gene but
+this time there's only one the
+
+ align:start position:0%
+this time there's only one the
+ 
+
+ align:start position:0%
+this time there's only one the
+assumption is only one gene or one
+
+ align:start position:0%
+assumption is only one gene or one
+ 
+
+ align:start position:0%
+assumption is only one gene or one
+variant that's under that linkage Peak
+
+ align:start position:0%
+variant that's under that linkage Peak
+ 
+
+ align:start position:0%
+variant that's under that linkage Peak
+that's actually contributing so again
+
+ align:start position:0%
+that's actually contributing so again
+ 
+
+ align:start position:0%
+that's actually contributing so again
+the probability works out to be about
+
+ align:start position:0%
+the probability works out to be about
+ 
+
+ align:start position:0%
+the probability works out to be about
+the same as a candidate Gene one in a
+
+ align:start position:0%
+the same as a candidate Gene one in a
+ 
+
+ align:start position:0%
+the same as a candidate Gene one in a
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's I would say you should probably at
+
+ align:start position:0%
+it's I would say you should probably at
+ 
+
+ align:start position:0%
+it's I would say you should probably at
+this point be agnostic as to whether
+
+ align:start position:0%
+this point be agnostic as to whether
+ 
+
+ align:start position:0%
+this point be agnostic as to whether
+you're focusing all your effort under
+
+ align:start position:0%
+you're focusing all your effort under
+ 
+
+ align:start position:0%
+you're focusing all your effort under
+linkage Peak or on a list of candidate
+
+ align:start position:0%
+linkage Peak or on a list of candidate
+ 
+
+ align:start position:0%
+linkage Peak or on a list of candidate
+genes that you've uh come up with
+
+ align:start position:0%
+genes that you've uh come up with
+ 
+
+ align:start position:0%
+genes that you've uh come up with
+through biology
+
+ align:start position:0%
+through biology
+ 
+
+ align:start position:0%
+through biology
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's assume that you now do your study
+
+ align:start position:0%
+let's assume that you now do your study
+ 
+
+ align:start position:0%
+let's assume that you now do your study
+and you achieve some magical p-value
+
+ align:start position:0%
+and you achieve some magical p-value
+ 
+
+ align:start position:0%
+and you achieve some magical p-value
+0.05 what's the likelihood that there
+
+ align:start position:0%
+0.05 what's the likelihood that there
+ 
+
+ align:start position:0%
+0.05 what's the likelihood that there
+was an association that was correct Okay
+
+ align:start position:0%
+was an association that was correct Okay
+ 
+
+ align:start position:0%
+was an association that was correct Okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the greatest candidate Gene in the world
+
+ align:start position:0%
+the greatest candidate Gene in the world
+ 
+
+ align:start position:0%
+the greatest candidate Gene in the world
+so this is actually you know I'm going
+
+ align:start position:0%
+so this is actually you know I'm going
+ 
+
+ align:start position:0%
+so this is actually you know I'm going
+to give you 10 times more likelihood
+
+ align:start position:0%
+to give you 10 times more likelihood
+ 
+
+ align:start position:0%
+to give you 10 times more likelihood
+that this was correct than your typical
+
+ align:start position:0%
+that this was correct than your typical
+ 
+
+ align:start position:0%
+that this was correct than your typical
+candidate Gene prior probably 0.01
+
+ align:start position:0%
+candidate Gene prior probably 0.01
+ 
+
+ align:start position:0%
+candidate Gene prior probably 0.01
+p-value 0.05 posterior probability this
+
+ align:start position:0%
+p-value 0.05 posterior probability this
+ 
+
+ align:start position:0%
+p-value 0.05 posterior probability this
+is assuming also perfect power to detect
+
+ align:start position:0%
+is assuming also perfect power to detect
+ 
+
+ align:start position:0%
+is assuming also perfect power to detect
+your Association which means you did
+
+ align:start position:0%
+your Association which means you did
+ 
+
+ align:start position:0%
+your Association which means you did
+this in a big study if you do it in a
+
+ align:start position:0%
+this in a big study if you do it in a
+ 
+
+ align:start position:0%
+this in a big study if you do it in a
+small study this number goes down
+
+ align:start position:0%
+small study this number goes down
+ 
+
+ align:start position:0%
+small study this number goes down
+because the power this this thing scales
+
+ align:start position:0%
+because the power this this thing scales
+ 
+
+ align:start position:0%
+because the power this this thing scales
+with power suppose you're probably a
+
+ align:start position:0%
+with power suppose you're probably a
+ 
+
+ align:start position:0%
+with power suppose you're probably a
+chance that you're right about 15 okay
+
+ align:start position:0%
+chance that you're right about 15 okay
+ 
+
+ align:start position:0%
+chance that you're right about 15 okay
+so that's a little bit
+
+ align:start position:0%
+so that's a little bit
+ 
+
+ align:start position:0%
+so that's a little bit
+um disheartening Maybe
+
+ align:start position:0%
+um disheartening Maybe
+ 
+
+ align:start position:0%
+um disheartening Maybe
+how about a typical candidate Gene this
+
+ align:start position:0%
+how about a typical candidate Gene this
+ 
+
+ align:start position:0%
+how about a typical candidate Gene this
+is sort of the typical Association study
+
+ align:start position:0%
+is sort of the typical Association study
+ 
+
+ align:start position:0%
+is sort of the typical Association study
+that's done there's about a one percent
+
+ align:start position:0%
+that's done there's about a one percent
+ 
+
+ align:start position:0%
+that's done there's about a one percent
+chance that a p-value 0.05 represents a
+
+ align:start position:0%
+chance that a p-value 0.05 represents a
+ 
+
+ align:start position:0%
+chance that a p-value 0.05 represents a
+true Association okay Canada or linkage
+
+ align:start position:0%
+true Association okay Canada or linkage
+ 
+
+ align:start position:0%
+true Association okay Canada or linkage
+Peak So Cal pane 10
+
+ align:start position:0%
+Peak So Cal pane 10
+ 
+
+ align:start position:0%
+Peak So Cal pane 10
+one percent chance okay in a with a P
+
+ align:start position:0%
+one percent chance okay in a with a P
+ 
+
+ align:start position:0%
+one percent chance okay in a with a P
+value 0.05 now their P value is lower
+
+ align:start position:0%
+value 0.05 now their P value is lower
+ 
+
+ align:start position:0%
+value 0.05 now their P value is lower
+but still that's sort of not much lower
+
+ align:start position:0%
+but still that's sort of not much lower
+ 
+
+ align:start position:0%
+but still that's sort of not much lower
+random Gene in the genome
+
+ align:start position:0%
+random Gene in the genome
+ 
+
+ align:start position:0%
+random Gene in the genome
+basically guaranteed to be wrong
+
+ align:start position:0%
+basically guaranteed to be wrong
+ 
+
+ align:start position:0%
+basically guaranteed to be wrong
+um with a p-value 0.05
+
+ align:start position:0%
+um with a p-value 0.05
+ 
+
+ align:start position:0%
+um with a p-value 0.05
+. so what kind of P values do you need
+
+ align:start position:0%
+. so what kind of P values do you need
+ 
+
+ align:start position:0%
+. so what kind of P values do you need
+to actually have pretty good posterior
+
+ align:start position:0%
+to actually have pretty good posterior
+ 
+
+ align:start position:0%
+to actually have pretty good posterior
+problems again this is assuming good
+
+ align:start position:0%
+problems again this is assuming good
+ 
+
+ align:start position:0%
+problems again this is assuming good
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+so basically what you need is p values
+
+ align:start position:0%
+so basically what you need is p values
+ 
+
+ align:start position:0%
+so basically what you need is p values
+that are somewhere in the range of 10 to
+
+ align:start position:0%
+that are somewhere in the range of 10 to
+ 
+
+ align:start position:0%
+that are somewhere in the range of 10 to
+the minus four to ten to the minus six
+
+ align:start position:0%
+the minus four to ten to the minus six
+ 
+
+ align:start position:0%
+the minus four to ten to the minus six
+and this could be a single study or all
+
+ align:start position:0%
+and this could be a single study or all
+ 
+
+ align:start position:0%
+and this could be a single study or all
+studies put together
+
+ align:start position:0%
+studies put together
+ 
+
+ align:start position:0%
+studies put together
+okay so that's so basically most report
+
+ align:start position:0%
+okay so that's so basically most report
+ 
+
+ align:start position:0%
+okay so that's so basically most report
+associations are probably incorrect
+
+ align:start position:0%
+associations are probably incorrect
+ 
+
+ align:start position:0%
+associations are probably incorrect
+but not all of them some will turn out
+
+ align:start position:0%
+but not all of them some will turn out
+ 
+
+ align:start position:0%
+but not all of them some will turn out
+to be correct and I would say that if
+
+ align:start position:0%
+to be correct and I would say that if
+ 
+
+ align:start position:0%
+to be correct and I would say that if
+you have low P values replicated or
+
+ align:start position:0%
+you have low P values replicated or
+ 
+
+ align:start position:0%
+you have low P values replicated or
+there's a really really really really
+
+ align:start position:0%
+there's a really really really really
+ 
+
+ align:start position:0%
+there's a really really really really
+good reason for plausibility then that
+
+ align:start position:0%
+good reason for plausibility then that
+ 
+
+ align:start position:0%
+good reason for plausibility then that
+makes it much more likely to be right
+
+ align:start position:0%
+makes it much more likely to be right
+ 
+
+ align:start position:0%
+makes it much more likely to be right
+and then just this last Point genes
+
+ align:start position:0%
+and then just this last Point genes
+ 
+
+ align:start position:0%
+and then just this last Point genes
+under leakage Peaks are about the same
+
+ align:start position:0%
+under leakage Peaks are about the same
+ 
+
+ align:start position:0%
+under leakage Peaks are about the same
+as any other kind of candidate obviously
+
+ align:start position:0%
+as any other kind of candidate obviously
+ 
+
+ align:start position:0%
+as any other kind of candidate obviously
+if you have a candidate that's in a good
+
+ align:start position:0%
+if you have a candidate that's in a good
+ 
+
+ align:start position:0%
+if you have a candidate that's in a good
+pathway and it's under a linkage Peak
+
+ align:start position:0%
+pathway and it's under a linkage Peak
+ 
+
+ align:start position:0%
+pathway and it's under a linkage Peak
+you know probably raises its prior
+
+ align:start position:0%
+you know probably raises its prior
+ 
+
+ align:start position:0%
+you know probably raises its prior
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+oh sorry
+
+ align:start position:0%
+oh sorry
+ 
+
+ align:start position:0%
+oh sorry
+probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I haven't talked to all I only
+
+ align:start position:0%
+yeah so I haven't talked to all I only
+ 
+
+ align:start position:0%
+yeah so I haven't talked to all I only
+alluded briefly to Gene environment
+
+ align:start position:0%
+alluded briefly to Gene environment
+ 
+
+ align:start position:0%
+alluded briefly to Gene environment
+interaction right but the PPR gamma on
+
+ align:start position:0%
+interaction right but the PPR gamma on
+ 
+
+ align:start position:0%
+interaction right but the PPR gamma on
+the diet thing and I haven't talked at
+
+ align:start position:0%
+the diet thing and I haven't talked at
+ 
+
+ align:start position:0%
+the diet thing and I haven't talked at
+all about Gene Gene interaction
+
+ align:start position:0%
+all about Gene Gene interaction
+ 
+
+ align:start position:0%
+all about Gene Gene interaction
+so there's a hot debate going on in the
+
+ align:start position:0%
+so there's a hot debate going on in the
+ 
+
+ align:start position:0%
+so there's a hot debate going on in the
+field I would say about whether one
+
+ align:start position:0%
+field I would say about whether one
+ 
+
+ align:start position:0%
+field I would say about whether one
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+look for Gene Gene interaction without
+
+ align:start position:0%
+look for Gene Gene interaction without
+ 
+
+ align:start position:0%
+look for Gene Gene interaction without
+any evidence that either Gene is
+
+ align:start position:0%
+any evidence that either Gene is
+ 
+
+ align:start position:0%
+any evidence that either Gene is
+involved which basically involves doing
+
+ align:start position:0%
+involved which basically involves doing
+ 
+
+ align:start position:0%
+involved which basically involves doing
+all the pairwise at least if not
+
+ align:start position:0%
+all the pairwise at least if not
+ 
+
+ align:start position:0%
+all the pairwise at least if not
+three-way or four-way or n-way
+
+ align:start position:0%
+three-way or four-way or n-way
+ 
+
+ align:start position:0%
+three-way or four-way or n-way
+combinations
+
+ align:start position:0%
+combinations
+ 
+
+ align:start position:0%
+combinations
+and the challenge for that becomes
+
+ align:start position:0%
+and the challenge for that becomes
+ 
+
+ align:start position:0%
+and the challenge for that becomes
+apparent when you say that they're
+
+ align:start position:0%
+apparent when you say that they're
+ 
+
+ align:start position:0%
+apparent when you say that they're
+actually like 600 000 independent
+
+ align:start position:0%
+actually like 600 000 independent
+ 
+
+ align:start position:0%
+actually like 600 000 independent
+variants across the genome so even if
+
+ align:start position:0%
+variants across the genome so even if
+ 
+
+ align:start position:0%
+variants across the genome so even if
+you're just doing pairwise that's 6
+
+ align:start position:0%
+you're just doing pairwise that's 6
+ 
+
+ align:start position:0%
+you're just doing pairwise that's 6
+times 10 to the fifth so it ends up
+
+ align:start position:0%
+times 10 to the fifth so it ends up
+ 
+
+ align:start position:0%
+times 10 to the fifth so it ends up
+being 3.6 times 10 to the 11th variance
+
+ align:start position:0%
+being 3.6 times 10 to the 11th variance
+ 
+
+ align:start position:0%
+being 3.6 times 10 to the 11th variance
+uh sorry pairwise combinations that you
+
+ align:start position:0%
+uh sorry pairwise combinations that you
+ 
+
+ align:start position:0%
+uh sorry pairwise combinations that you
+have to look for and so you know that
+
+ align:start position:0%
+have to look for and so you know that
+ 
+
+ align:start position:0%
+have to look for and so you know that
+you're actually going to get a p-value
+
+ align:start position:0%
+you're actually going to get a p-value
+ 
+
+ align:start position:0%
+you're actually going to get a p-value
+of 10 to the minus 11th for interaction
+
+ align:start position:0%
+of 10 to the minus 11th for interaction
+ 
+
+ align:start position:0%
+of 10 to the minus 11th for interaction
+at some point
+
+ align:start position:0%
+at some point
+ 
+
+ align:start position:0%
+at some point
+um just because that's how many pairs
+
+ align:start position:0%
+um just because that's how many pairs
+ 
+
+ align:start position:0%
+um just because that's how many pairs
+you test in fact you you know you get
+
+ align:start position:0%
+you test in fact you you know you get
+ 
+
+ align:start position:0%
+you test in fact you you know you get
+3.6 of them
+
+ align:start position:0%
+3.6 of them
+ 
+
+ align:start position:0%
+3.6 of them
+um so uh it becomes a issue of power
+
+ align:start position:0%
+um so uh it becomes a issue of power
+ 
+
+ align:start position:0%
+um so uh it becomes a issue of power
+again uh in that to correct for all the
+
+ align:start position:0%
+again uh in that to correct for all the
+ 
+
+ align:start position:0%
+again uh in that to correct for all the
+different hypotheses that you'd be
+
+ align:start position:0%
+different hypotheses that you'd be
+ 
+
+ align:start position:0%
+different hypotheses that you'd be
+testing you need an enormous sample size
+
+ align:start position:0%
+testing you need an enormous sample size
+ 
+
+ align:start position:0%
+testing you need an enormous sample size
+or you need to hope that the the some
+
+ align:start position:0%
+or you need to hope that the the some
+ 
+
+ align:start position:0%
+or you need to hope that the the some
+the interaction effect is just so
+
+ align:start position:0%
+the interaction effect is just so
+ 
+
+ align:start position:0%
+the interaction effect is just so
+enormous that you actually get a p-value
+
+ align:start position:0%
+enormous that you actually get a p-value
+ 
+
+ align:start position:0%
+enormous that you actually get a p-value
+that survives that correction a multiple
+
+ align:start position:0%
+that survives that correction a multiple
+ 
+
+ align:start position:0%
+that survives that correction a multiple
+hypothesis testing
+
+ align:start position:0%
+hypothesis testing
+ 
+
+ align:start position:0%
+hypothesis testing
+um which might be the case but then the
+
+ align:start position:0%
+um which might be the case but then the
+ 
+
+ align:start position:0%
+um which might be the case but then the
+question is if that interaction is so
+
+ align:start position:0%
+question is if that interaction is so
+ 
+
+ align:start position:0%
+question is if that interaction is so
+enormous
+
+ align:start position:0%
+enormous
+ 
+
+ align:start position:0%
+enormous
+you have to draw very strange models
+
+ align:start position:0%
+you have to draw very strange models
+ 
+
+ align:start position:0%
+you have to draw very strange models
+that you wouldn't also pick up at least
+
+ align:start position:0%
+that you wouldn't also pick up at least
+ 
+
+ align:start position:0%
+that you wouldn't also pick up at least
+one of the two as being causal now what
+
+ align:start position:0%
+one of the two as being causal now what
+ 
+
+ align:start position:0%
+one of the two as being causal now what
+should be done but isn't is that once
+
+ align:start position:0%
+should be done but isn't is that once
+ 
+
+ align:start position:0%
+should be done but isn't is that once
+you have something that you really
+
+ align:start position:0%
+you have something that you really
+ 
+
+ align:start position:0%
+you have something that you really
+believe so for example we work in the
+
+ align:start position:0%
+believe so for example we work in the
+ 
+
+ align:start position:0%
+believe so for example we work in the
+diabetes field and we really believe
+
+ align:start position:0%
+diabetes field and we really believe
+ 
+
+ align:start position:0%
+diabetes field and we really believe
+people are gamma Pro 12 Ally but yet we
+
+ align:start position:0%
+people are gamma Pro 12 Ally but yet we
+ 
+
+ align:start position:0%
+people are gamma Pro 12 Ally but yet we
+do not yet and we should test for
+
+ align:start position:0%
+do not yet and we should test for
+ 
+
+ align:start position:0%
+do not yet and we should test for
+pairwise interactions for every single
+
+ align:start position:0%
+pairwise interactions for every single
+ 
+
+ align:start position:0%
+pairwise interactions for every single
+thing we genotype and P and Pro 12 Ally
+
+ align:start position:0%
+thing we genotype and P and Pro 12 Ally
+ 
+
+ align:start position:0%
+thing we genotype and P and Pro 12 Ally
+because you can draw plenty of con of
+
+ align:start position:0%
+because you can draw plenty of con of
+ 
+
+ align:start position:0%
+because you can draw plenty of con of
+reasonable models where you would only
+
+ align:start position:0%
+reasonable models where you would only
+ 
+
+ align:start position:0%
+reasonable models where you would only
+detect one of the two things that are
+
+ align:start position:0%
+detect one of the two things that are
+ 
+
+ align:start position:0%
+detect one of the two things that are
+interacting and the other one would be
+
+ align:start position:0%
+interacting and the other one would be
+ 
+
+ align:start position:0%
+interacting and the other one would be
+completely masked or largely masked so
+
+ align:start position:0%
+completely masked or largely masked so
+ 
+
+ align:start position:0%
+completely masked or largely masked so
+we don't do that and we should and but I
+
+ align:start position:0%
+we don't do that and we should and but I
+ 
+
+ align:start position:0%
+we don't do that and we should and but I
+would say that if you're again if you're
+
+ align:start position:0%
+would say that if you're again if you're
+ 
+
+ align:start position:0%
+would say that if you're again if you're
+picking up a paper which says we didn't
+
+ align:start position:0%
+picking up a paper which says we didn't
+ 
+
+ align:start position:0%
+picking up a paper which says we didn't
+see anything with either one of these
+
+ align:start position:0%
+see anything with either one of these
+ 
+
+ align:start position:0%
+see anything with either one of these
+variants but then we did the pairwise
+
+ align:start position:0%
+variants but then we did the pairwise
+ 
+
+ align:start position:0%
+variants but then we did the pairwise
+test and we see an interaction think
+
+ align:start position:0%
+test and we see an interaction think
+ 
+
+ align:start position:0%
+test and we see an interaction think
+about your prior probability that that
+
+ align:start position:0%
+about your prior probability that that
+ 
+
+ align:start position:0%
+about your prior probability that that
+pairwise test was actually Associated
+
+ align:start position:0%
+pairwise test was actually Associated
+ 
+
+ align:start position:0%
+pairwise test was actually Associated
+okay the number of pairs in the genome
+
+ align:start position:0%
+okay the number of pairs in the genome
+ 
+
+ align:start position:0%
+okay the number of pairs in the genome
+versus the number they're actually going
+
+ align:start position:0%
+versus the number they're actually going
+ 
+
+ align:start position:0%
+versus the number they're actually going
+to be causal your prior probabilities
+
+ align:start position:0%
+to be causal your prior probabilities
+ 
+
+ align:start position:0%
+to be causal your prior probabilities
+are probably several orders of magnitude
+
+ align:start position:0%
+are probably several orders of magnitude
+ 
+
+ align:start position:0%
+are probably several orders of magnitude
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+so unless there's again some really
+
+ align:start position:0%
+so unless there's again some really
+ 
+
+ align:start position:0%
+so unless there's again some really
+great reason to know that these genetic
+
+ align:start position:0%
+great reason to know that these genetic
+ 
+
+ align:start position:0%
+great reason to know that these genetic
+variants interact so that's my
+
+ align:start position:0%
+variants interact so that's my
+ 
+
+ align:start position:0%
+variants interact so that's my
+incredibly biased answer to that
+
+ align:start position:0%
+incredibly biased answer to that
+ 
+
+ align:start position:0%
+incredibly biased answer to that
+um or not biased but opinionated answer
+
+ align:start position:0%
+um or not biased but opinionated answer
+ 
+
+ align:start position:0%
+um or not biased but opinionated answer
+to that question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I won't go through why you get the
+
+ align:start position:0%
+um I won't go through why you get the
+ 
+
+ align:start position:0%
+um I won't go through why you get the
+same sort of winners curse and things
+
+ align:start position:0%
+same sort of winners curse and things
+ 
+
+ align:start position:0%
+same sort of winners curse and things
+like that in linkage but just to take
+
+ align:start position:0%
+like that in linkage but just to take
+ 
+
+ align:start position:0%
+like that in linkage but just to take
+you through rare rare variant uh
+
+ align:start position:0%
+you through rare rare variant uh
+ 
+
+ align:start position:0%
+you through rare rare variant uh
+Association studies again just in case
+
+ align:start position:0%
+Association studies again just in case
+ 
+
+ align:start position:0%
+Association studies again just in case
+you pick up literature on this
+
+ align:start position:0%
+you pick up literature on this
+ 
+
+ align:start position:0%
+you pick up literature on this
+so this is the typical rare variant
+
+ align:start position:0%
+so this is the typical rare variant
+ 
+
+ align:start position:0%
+so this is the typical rare variant
+Association study as it is practiced in
+
+ align:start position:0%
+Association study as it is practiced in
+ 
+
+ align:start position:0%
+Association study as it is practiced in
+2004.
+
+ align:start position:0%
+2004.
+ 
+
+ align:start position:0%
+2004.
+genes are are resequenced and affected
+
+ align:start position:0%
+genes are are resequenced and affected
+ 
+
+ align:start position:0%
+genes are are resequenced and affected
+individuals to try to find say missense
+
+ align:start position:0%
+individuals to try to find say missense
+ 
+
+ align:start position:0%
+individuals to try to find say missense
+variants and then those missense
+
+ align:start position:0%
+variants and then those missense
+ 
+
+ align:start position:0%
+variants and then those missense
+variants are then taken and typed in
+
+ align:start position:0%
+variants are then taken and typed in
+ 
+
+ align:start position:0%
+variants are then taken and typed in
+unaffected individuals that sequencing
+
+ align:start position:0%
+unaffected individuals that sequencing
+ 
+
+ align:start position:0%
+unaffected individuals that sequencing
+here genotyping here okay and what's
+
+ align:start position:0%
+here genotyping here okay and what's
+ 
+
+ align:start position:0%
+here genotyping here okay and what's
+often observed is that they're not there
+
+ align:start position:0%
+often observed is that they're not there
+ 
+
+ align:start position:0%
+often observed is that they're not there
+so I'll take you through a
+
+ align:start position:0%
+so I'll take you through a
+ 
+
+ align:start position:0%
+so I'll take you through a
+possible resequencing Association study
+
+ align:start position:0%
+possible resequencing Association study
+ 
+
+ align:start position:0%
+possible resequencing Association study
+let's resequence your favorite Gene Gene
+
+ align:start position:0%
+let's resequence your favorite Gene Gene
+ 
+
+ align:start position:0%
+let's resequence your favorite Gene Gene
+x 200 diabetic individuals and lo and
+
+ align:start position:0%
+x 200 diabetic individuals and lo and
+ 
+
+ align:start position:0%
+x 200 diabetic individuals and lo and
+behold you actually find 10 rare
+
+ align:start position:0%
+behold you actually find 10 rare
+ 
+
+ align:start position:0%
+behold you actually find 10 rare
+missense variants each seen in one
+
+ align:start position:0%
+missense variants each seen in one
+ 
+
+ align:start position:0%
+missense variants each seen in one
+person with diabetes
+
+ align:start position:0%
+person with diabetes
+ 
+
+ align:start position:0%
+person with diabetes
+you then type 200 healthy individuals
+
+ align:start position:0%
+you then type 200 healthy individuals
+ 
+
+ align:start position:0%
+you then type 200 healthy individuals
+those variants are not seen at all so
+
+ align:start position:0%
+those variants are not seen at all so
+ 
+
+ align:start position:0%
+those variants are not seen at all so
+you conclude
+
+ align:start position:0%
+you conclude
+ 
+
+ align:start position:0%
+you conclude
+uh thank you okay uh the rare missed
+
+ align:start position:0%
+uh thank you okay uh the rare missed
+ 
+
+ align:start position:0%
+uh thank you okay uh the rare missed
+experience in GNX cause diabetes okay so
+
+ align:start position:0%
+experience in GNX cause diabetes okay so
+ 
+
+ align:start position:0%
+experience in GNX cause diabetes okay so
+now I'm going to take you through
+
+ align:start position:0%
+now I'm going to take you through
+ 
+
+ align:start position:0%
+now I'm going to take you through
+an equally possible resequencing study
+
+ align:start position:0%
+an equally possible resequencing study
+ 
+
+ align:start position:0%
+an equally possible resequencing study
+resequence Gene X in 200 Red Sox fans
+
+ align:start position:0%
+resequence Gene X in 200 Red Sox fans
+ 
+
+ align:start position:0%
+resequence Gene X in 200 Red Sox fans
+you will identify
+
+ align:start position:0%
+you will identify
+ 
+
+ align:start position:0%
+you will identify
+uh if this is a gene that happens to
+
+ align:start position:0%
+uh if this is a gene that happens to
+ 
+
+ align:start position:0%
+uh if this is a gene that happens to
+tolerate rare missense variation you
+
+ align:start position:0%
+tolerate rare missense variation you
+ 
+
+ align:start position:0%
+tolerate rare missense variation you
+will identify 10 rare missense variants
+
+ align:start position:0%
+will identify 10 rare missense variants
+ 
+
+ align:start position:0%
+will identify 10 rare missense variants
+you might Identify some common variance
+
+ align:start position:0%
+you might Identify some common variance
+ 
+
+ align:start position:0%
+you might Identify some common variance
+but you might not many genes don't have
+
+ align:start position:0%
+but you might not many genes don't have
+ 
+
+ align:start position:0%
+but you might not many genes don't have
+any commonness experience
+
+ align:start position:0%
+any commonness experience
+ 
+
+ align:start position:0%
+any commonness experience
+if you then take those 10 missense
+
+ align:start position:0%
+if you then take those 10 missense
+ 
+
+ align:start position:0%
+if you then take those 10 missense
+variants and type them in 200 other
+
+ align:start position:0%
+variants and type them in 200 other
+ 
+
+ align:start position:0%
+variants and type them in 200 other
+people say Yankees fans you will not see
+
+ align:start position:0%
+people say Yankees fans you will not see
+ 
+
+ align:start position:0%
+people say Yankees fans you will not see
+those variants okay so this is very
+
+ align:start position:0%
+those variants okay so this is very
+ 
+
+ align:start position:0%
+those variants okay so this is very
+plausible
+
+ align:start position:0%
+plausible
+ 
+
+ align:start position:0%
+plausible
+and you will conclude that rare variants
+
+ align:start position:0%
+and you will conclude that rare variants
+ 
+
+ align:start position:0%
+and you will conclude that rare variants
+in gene X make you root for the Red Sox
+
+ align:start position:0%
+in gene X make you root for the Red Sox
+ 
+
+ align:start position:0%
+in gene X make you root for the Red Sox
+which of course is not the correct
+
+ align:start position:0%
+which of course is not the correct
+ 
+
+ align:start position:0%
+which of course is not the correct
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+um and the reason for this
+
+ align:start position:0%
+um and the reason for this
+ 
+
+ align:start position:0%
+um and the reason for this
+is has to do with the fact that in
+
+ align:start position:0%
+is has to do with the fact that in
+ 
+
+ align:start position:0%
+is has to do with the fact that in
+identifying these rare variants you have
+
+ align:start position:0%
+identifying these rare variants you have
+ 
+
+ align:start position:0%
+identifying these rare variants you have
+to go to very great depth in doing the
+
+ align:start position:0%
+to go to very great depth in doing the
+ 
+
+ align:start position:0%
+to go to very great depth in doing the
+resequencing so you get common variants
+
+ align:start position:0%
+resequencing so you get common variants
+ 
+
+ align:start position:0%
+resequencing so you get common variants
+if you sequence two chromosomes that's
+
+ align:start position:0%
+if you sequence two chromosomes that's
+ 
+
+ align:start position:0%
+if you sequence two chromosomes that's
+what I showed you at the very beginning
+
+ align:start position:0%
+what I showed you at the very beginning
+ 
+
+ align:start position:0%
+what I showed you at the very beginning
+of the talk right so if you just compare
+
+ align:start position:0%
+of the talk right so if you just compare
+ 
+
+ align:start position:0%
+of the talk right so if you just compare
+two chromosomes and then look are those
+
+ align:start position:0%
+two chromosomes and then look are those
+ 
+
+ align:start position:0%
+two chromosomes and then look are those
+variants common in the rest of the
+
+ align:start position:0%
+variants common in the rest of the
+ 
+
+ align:start position:0%
+variants common in the rest of the
+population the answer is almost always
+
+ align:start position:0%
+population the answer is almost always
+ 
+
+ align:start position:0%
+population the answer is almost always
+yes the average allele frequency is
+
+ align:start position:0%
+yes the average allele frequency is
+ 
+
+ align:start position:0%
+yes the average allele frequency is
+about one in five so average is 20
+
+ align:start position:0%
+about one in five so average is 20
+ 
+
+ align:start position:0%
+about one in five so average is 20
+percent for both for the minor allele
+
+ align:start position:0%
+percent for both for the minor allele
+ 
+
+ align:start position:0%
+percent for both for the minor allele
+and 80 of the other allele but if you
+
+ align:start position:0%
+and 80 of the other allele but if you
+ 
+
+ align:start position:0%
+and 80 of the other allele but if you
+then sequence a large group of people
+
+ align:start position:0%
+then sequence a large group of people
+ 
+
+ align:start position:0%
+then sequence a large group of people
+you obviously find all these common
+
+ align:start position:0%
+you obviously find all these common
+ 
+
+ align:start position:0%
+you obviously find all these common
+variants you find those in like the
+
+ align:start position:0%
+variants you find those in like the
+ 
+
+ align:start position:0%
+variants you find those in like the
+first four chromosomes you do you
+
+ align:start position:0%
+first four chromosomes you do you
+ 
+
+ align:start position:0%
+first four chromosomes you do you
+basically run through all the common
+
+ align:start position:0%
+basically run through all the common
+ 
+
+ align:start position:0%
+basically run through all the common
+grains but you actually keep finding
+
+ align:start position:0%
+grains but you actually keep finding
+ 
+
+ align:start position:0%
+grains but you actually keep finding
+variants as you go every once in a while
+
+ align:start position:0%
+variants as you go every once in a while
+ 
+
+ align:start position:0%
+variants as you go every once in a while
+and this has to do with population
+
+ align:start position:0%
+and this has to do with population
+ 
+
+ align:start position:0%
+and this has to do with population
+genetics and what the allele frequency
+
+ align:start position:0%
+genetics and what the allele frequency
+ 
+
+ align:start position:0%
+genetics and what the allele frequency
+distributions are and stuff like that
+
+ align:start position:0%
+distributions are and stuff like that
+ 
+
+ align:start position:0%
+distributions are and stuff like that
+but you most of the variants you find if
+
+ align:start position:0%
+but you most of the variants you find if
+ 
+
+ align:start position:0%
+but you most of the variants you find if
+you do debris sequencing end up being
+
+ align:start position:0%
+you do debris sequencing end up being
+ 
+
+ align:start position:0%
+you do debris sequencing end up being
+these rare variants they don't account
+
+ align:start position:0%
+these rare variants they don't account
+ 
+
+ align:start position:0%
+these rare variants they don't account
+for most of the heterozygosity because
+
+ align:start position:0%
+for most of the heterozygosity because
+ 
+
+ align:start position:0%
+for most of the heterozygosity because
+they're so rare and in fact their
+
+ align:start position:0%
+they're so rare and in fact their
+ 
+
+ align:start position:0%
+they're so rare and in fact their
+average frequency is something like one
+
+ align:start position:0%
+average frequency is something like one
+ 
+
+ align:start position:0%
+average frequency is something like one
+in ten thousand so if you type them in
+
+ align:start position:0%
+in ten thousand so if you type them in
+ 
+
+ align:start position:0%
+in ten thousand so if you type them in
+200 people you're never going to see any
+
+ align:start position:0%
+200 people you're never going to see any
+ 
+
+ align:start position:0%
+200 people you're never going to see any
+of them again
+
+ align:start position:0%
+of them again
+ 
+
+ align:start position:0%
+of them again
+so what needs to get done is basically
+
+ align:start position:0%
+so what needs to get done is basically
+ 
+
+ align:start position:0%
+so what needs to get done is basically
+you need to resequence the controls as
+
+ align:start position:0%
+you need to resequence the controls as
+ 
+
+ align:start position:0%
+you need to resequence the controls as
+well there are other ways of doing it
+
+ align:start position:0%
+well there are other ways of doing it
+ 
+
+ align:start position:0%
+well there are other ways of doing it
+for example if you have families you can
+
+ align:start position:0%
+for example if you have families you can
+ 
+
+ align:start position:0%
+for example if you have families you can
+see that the uh that the rare variants
+
+ align:start position:0%
+see that the uh that the rare variants
+ 
+
+ align:start position:0%
+see that the uh that the rare variants
+actually segregate with disease that's
+
+ align:start position:0%
+actually segregate with disease that's
+ 
+
+ align:start position:0%
+actually segregate with disease that's
+sort of equivalent to resequencing
+
+ align:start position:0%
+sort of equivalent to resequencing
+ 
+
+ align:start position:0%
+sort of equivalent to resequencing
+control so that's that's one way around
+
+ align:start position:0%
+control so that's that's one way around
+ 
+
+ align:start position:0%
+control so that's that's one way around
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+uh but that's basically what you need to
+
+ align:start position:0%
+uh but that's basically what you need to
+ 
+
+ align:start position:0%
+uh but that's basically what you need to
+do and furthermore
+
+ align:start position:0%
+do and furthermore
+ 
+
+ align:start position:0%
+do and furthermore
+you know what I said there in that
+
+ align:start position:0%
+you know what I said there in that
+ 
+
+ align:start position:0%
+you know what I said there in that
+previous service you identified you know
+
+ align:start position:0%
+previous service you identified you know
+ 
+
+ align:start position:0%
+previous service you identified you know
+10 missense variants what if you
+
+ align:start position:0%
+10 missense variants what if you
+ 
+
+ align:start position:0%
+10 missense variants what if you
+identified 11 but one of them was common
+
+ align:start position:0%
+identified 11 but one of them was common
+ 
+
+ align:start position:0%
+identified 11 but one of them was common
+okay and you said well that's a common
+
+ align:start position:0%
+okay and you said well that's a common
+ 
+
+ align:start position:0%
+okay and you said well that's a common
+one and it's present in cases and
+
+ align:start position:0%
+one and it's present in cases and
+ 
+
+ align:start position:0%
+one and it's present in cases and
+controls that's probably not functional
+
+ align:start position:0%
+controls that's probably not functional
+ 
+
+ align:start position:0%
+controls that's probably not functional
+you know that's probably and I'll just
+
+ align:start position:0%
+you know that's probably and I'll just
+ 
+
+ align:start position:0%
+you know that's probably and I'll just
+concentrate on the ones that are only
+
+ align:start position:0%
+concentrate on the ones that are only
+ 
+
+ align:start position:0%
+concentrate on the ones that are only
+present in cases let's obviously
+
+ align:start position:0%
+present in cases let's obviously
+ 
+
+ align:start position:0%
+present in cases let's obviously
+rigging the results beforehand right so
+
+ align:start position:0%
+rigging the results beforehand right so
+ 
+
+ align:start position:0%
+rigging the results beforehand right so
+you could if you limit yourself to just
+
+ align:start position:0%
+you could if you limit yourself to just
+ 
+
+ align:start position:0%
+you could if you limit yourself to just
+those variants that are present in cases
+
+ align:start position:0%
+those variants that are present in cases
+ 
+
+ align:start position:0%
+those variants that are present in cases
+and say those are the only ones that
+
+ align:start position:0%
+and say those are the only ones that
+ 
+
+ align:start position:0%
+and say those are the only ones that
+matter obviously they're only going to
+
+ align:start position:0%
+matter obviously they're only going to
+ 
+
+ align:start position:0%
+matter obviously they're only going to
+be present in cases so you have to have
+
+ align:start position:0%
+be present in cases so you have to have
+ 
+
+ align:start position:0%
+be present in cases so you have to have
+some way of grouping these rare variants
+
+ align:start position:0%
+some way of grouping these rare variants
+ 
+
+ align:start position:0%
+some way of grouping these rare variants
+for analysis before you know the results
+
+ align:start position:0%
+for analysis before you know the results
+ 
+
+ align:start position:0%
+for analysis before you know the results
+of the association study of you know
+
+ align:start position:0%
+of the association study of you know
+ 
+
+ align:start position:0%
+of the association study of you know
+which ones are in cases and which ones
+
+ align:start position:0%
+which ones are in cases and which ones
+ 
+
+ align:start position:0%
+which ones are in cases and which ones
+are in controls so something like either
+
+ align:start position:0%
+are in controls so something like either
+ 
+
+ align:start position:0%
+are in controls so something like either
+I'll only look at friendships or
+
+ align:start position:0%
+I'll only look at friendships or
+ 
+
+ align:start position:0%
+I'll only look at friendships or
+nonsense mutations or I'll only look at
+
+ align:start position:0%
+nonsense mutations or I'll only look at
+ 
+
+ align:start position:0%
+nonsense mutations or I'll only look at
+things that have this particular in
+
+ align:start position:0%
+things that have this particular in
+ 
+
+ align:start position:0%
+things that have this particular in
+vitro functional property or something
+
+ align:start position:0%
+vitro functional property or something
+ 
+
+ align:start position:0%
+vitro functional property or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+okay so just in the last
+
+ align:start position:0%
+okay so just in the last
+ 
+
+ align:start position:0%
+okay so just in the last
+couple of minutes
+
+ align:start position:0%
+couple of minutes
+ 
+
+ align:start position:0%
+couple of minutes
+um or how actually how I'm actually way
+
+ align:start position:0%
+um or how actually how I'm actually way
+ 
+
+ align:start position:0%
+um or how actually how I'm actually way
+ahead
+
+ align:start position:0%
+ahead
+ 
+
+ align:start position:0%
+ahead
+oh no not way ahead good 12 30. good I
+
+ align:start position:0%
+oh no not way ahead good 12 30. good I
+ 
+
+ align:start position:0%
+oh no not way ahead good 12 30. good I
+was for a minute I thought I had like 37
+
+ align:start position:0%
+was for a minute I thought I had like 37
+ 
+
+ align:start position:0%
+was for a minute I thought I had like 37
+minutes left I was like I've been
+
+ align:start position:0%
+minutes left I was like I've been
+ 
+
+ align:start position:0%
+minutes left I was like I've been
+talking longer than that okay so what
+
+ align:start position:0%
+talking longer than that okay so what
+ 
+
+ align:start position:0%
+talking longer than that okay so what
+could what could we learn and I think
+
+ align:start position:0%
+could what could we learn and I think
+ 
+
+ align:start position:0%
+could what could we learn and I think
+this is also uh important to think about
+
+ align:start position:0%
+this is also uh important to think about
+ 
+
+ align:start position:0%
+this is also uh important to think about
+and kind of what it what are the goals
+
+ align:start position:0%
+and kind of what it what are the goals
+ 
+
+ align:start position:0%
+and kind of what it what are the goals
+and what are the likely outcomes there's
+
+ align:start position:0%
+and what are the likely outcomes there's
+ 
+
+ align:start position:0%
+and what are the likely outcomes there's
+a lot of hype around the whole field of
+
+ align:start position:0%
+a lot of hype around the whole field of
+ 
+
+ align:start position:0%
+a lot of hype around the whole field of
+genomics and Snips and common disease
+
+ align:start position:0%
+genomics and Snips and common disease
+ 
+
+ align:start position:0%
+genomics and Snips and common disease
+and just to try to take a look at what
+
+ align:start position:0%
+and just to try to take a look at what
+ 
+
+ align:start position:0%
+and just to try to take a look at what
+what is and is what is not likely so I
+
+ align:start position:0%
+what is and is what is not likely so I
+ 
+
+ align:start position:0%
+what is and is what is not likely so I
+don't know if anybody's seen the movie
+
+ align:start position:0%
+don't know if anybody's seen the movie
+ 
+
+ align:start position:0%
+don't know if anybody's seen the movie
+Gattaca
+
+ align:start position:0%
+Gattaca
+ 
+
+ align:start position:0%
+Gattaca
+um so so gatic I think people actually
+
+ align:start position:0%
+um so so gatic I think people actually
+ 
+
+ align:start position:0%
+um so so gatic I think people actually
+have Gattaca in the back of their mind
+
+ align:start position:0%
+have Gattaca in the back of their mind
+ 
+
+ align:start position:0%
+have Gattaca in the back of their mind
+when they are are thinking about this
+
+ align:start position:0%
+when they are are thinking about this
+ 
+
+ align:start position:0%
+when they are are thinking about this
+which is that we should be able to tell
+
+ align:start position:0%
+which is that we should be able to tell
+ 
+
+ align:start position:0%
+which is that we should be able to tell
+by you know genotyping if we could
+
+ align:start position:0%
+by you know genotyping if we could
+ 
+
+ align:start position:0%
+by you know genotyping if we could
+sequence somebody's genome we will be
+
+ align:start position:0%
+sequence somebody's genome we will be
+ 
+
+ align:start position:0%
+sequence somebody's genome we will be
+able to predict you know if you if you
+
+ align:start position:0%
+able to predict you know if you if you
+ 
+
+ align:start position:0%
+able to predict you know if you if you
+look at the opening scene in that movie
+
+ align:start position:0%
+look at the opening scene in that movie
+ 
+
+ align:start position:0%
+look at the opening scene in that movie
+it's like you know probably if coronary
+
+ align:start position:0%
+it's like you know probably if coronary
+ 
+
+ align:start position:0%
+it's like you know probably if coronary
+artery disease like 98 you know
+
+ align:start position:0%
+artery disease like 98 you know
+ 
+
+ align:start position:0%
+artery disease like 98 you know
+probability of you know stroke 100 you
+
+ align:start position:0%
+probability of you know stroke 100 you
+ 
+
+ align:start position:0%
+probability of you know stroke 100 you
+know this sort of thing so we already
+
+ align:start position:0%
+know this sort of thing so we already
+ 
+
+ align:start position:0%
+know this sort of thing so we already
+know that genetic variation actually
+
+ align:start position:0%
+know that genetic variation actually
+ 
+
+ align:start position:0%
+know that genetic variation actually
+even if we had perfect information only
+
+ align:start position:0%
+even if we had perfect information only
+ 
+
+ align:start position:0%
+even if we had perfect information only
+explains like 30 to 50 of common disease
+
+ align:start position:0%
+explains like 30 to 50 of common disease
+ 
+
+ align:start position:0%
+explains like 30 to 50 of common disease
+but what's even the likelihood that
+
+ align:start position:0%
+but what's even the likelihood that
+ 
+
+ align:start position:0%
+but what's even the likelihood that
+we'll get that good a prediction I think
+
+ align:start position:0%
+we'll get that good a prediction I think
+ 
+
+ align:start position:0%
+we'll get that good a prediction I think
+it's probably not that great because
+
+ align:start position:0%
+it's probably not that great because
+ 
+
+ align:start position:0%
+it's probably not that great because
+it's probably a lot of alleles that are
+
+ align:start position:0%
+it's probably a lot of alleles that are
+ 
+
+ align:start position:0%
+it's probably a lot of alleles that are
+going to interact in complex ways that
+
+ align:start position:0%
+going to interact in complex ways that
+ 
+
+ align:start position:0%
+going to interact in complex ways that
+we may not be able to figure out for a
+
+ align:start position:0%
+we may not be able to figure out for a
+ 
+
+ align:start position:0%
+we may not be able to figure out for a
+very long time
+
+ align:start position:0%
+very long time
+ 
+
+ align:start position:0%
+very long time
+but nonetheless there is some thought
+
+ align:start position:0%
+but nonetheless there is some thought
+ 
+
+ align:start position:0%
+but nonetheless there is some thought
+that we maybe I'll identify people who
+
+ align:start position:0%
+that we maybe I'll identify people who
+ 
+
+ align:start position:0%
+that we maybe I'll identify people who
+are high risk or particularly people who
+
+ align:start position:0%
+are high risk or particularly people who
+ 
+
+ align:start position:0%
+are high risk or particularly people who
+might be at low risk
+
+ align:start position:0%
+might be at low risk
+ 
+
+ align:start position:0%
+might be at low risk
+if that were the case and I've shown
+
+ align:start position:0%
+if that were the case and I've shown
+ 
+
+ align:start position:0%
+if that were the case and I've shown
+here a probably very optimistic scenario
+
+ align:start position:0%
+here a probably very optimistic scenario
+ 
+
+ align:start position:0%
+here a probably very optimistic scenario
+which is that you could enrich this much
+
+ align:start position:0%
+which is that you could enrich this much
+ 
+
+ align:start position:0%
+which is that you could enrich this much
+for the high-risk people you might say
+
+ align:start position:0%
+for the high-risk people you might say
+ 
+
+ align:start position:0%
+for the high-risk people you might say
+that these people would get a more
+
+ align:start position:0%
+that these people would get a more
+ 
+
+ align:start position:0%
+that these people would get a more
+aggressive intervention preventive
+
+ align:start position:0%
+aggressive intervention preventive
+ 
+
+ align:start position:0%
+aggressive intervention preventive
+measure and these people might get the
+
+ align:start position:0%
+measure and these people might get the
+ 
+
+ align:start position:0%
+measure and these people might get the
+standard of care or might even be able
+
+ align:start position:0%
+standard of care or might even be able
+ 
+
+ align:start position:0%
+standard of care or might even be able
+to get slightly less aggressive
+
+ align:start position:0%
+to get slightly less aggressive
+ 
+
+ align:start position:0%
+to get slightly less aggressive
+interventions depending on how the risk
+
+ align:start position:0%
+interventions depending on how the risk
+ 
+
+ align:start position:0%
+interventions depending on how the risk
+benefit played out this obviously
+
+ align:start position:0%
+benefit played out this obviously
+ 
+
+ align:start position:0%
+benefit played out this obviously
+requires that there be effective
+
+ align:start position:0%
+requires that there be effective
+ 
+
+ align:start position:0%
+requires that there be effective
+preventive measures and things like that
+
+ align:start position:0%
+preventive measures and things like that
+ 
+
+ align:start position:0%
+preventive measures and things like that
+but you could imagine you know for
+
+ align:start position:0%
+but you could imagine you know for
+ 
+
+ align:start position:0%
+but you could imagine you know for
+things like diabetes you could say you
+
+ align:start position:0%
+things like diabetes you could say you
+ 
+
+ align:start position:0%
+things like diabetes you could say you
+know you really are at high risk for
+
+ align:start position:0%
+know you really are at high risk for
+ 
+
+ align:start position:0%
+know you really are at high risk for
+getting diabetes you really need to you
+
+ align:start position:0%
+getting diabetes you really need to you
+ 
+
+ align:start position:0%
+getting diabetes you really need to you
+know exercise and lose weight maybe that
+
+ align:start position:0%
+know exercise and lose weight maybe that
+ 
+
+ align:start position:0%
+know exercise and lose weight maybe that
+would you know there would be some you
+
+ align:start position:0%
+would you know there would be some you
+ 
+
+ align:start position:0%
+would you know there would be some you
+know you could hook that person up with
+
+ align:start position:0%
+know you could hook that person up with
+ 
+
+ align:start position:0%
+know you could hook that person up with
+nutritionist and all the uh you know
+
+ align:start position:0%
+nutritionist and all the uh you know
+ 
+
+ align:start position:0%
+nutritionist and all the uh you know
+personal trainer and all that sort of
+
+ align:start position:0%
+personal trainer and all that sort of
+ 
+
+ align:start position:0%
+personal trainer and all that sort of
+stuff and might not be something that we
+
+ align:start position:0%
+stuff and might not be something that we
+ 
+
+ align:start position:0%
+stuff and might not be something that we
+as Society could afford for everybody
+
+ align:start position:0%
+as Society could afford for everybody
+ 
+
+ align:start position:0%
+as Society could afford for everybody
+but maybe at least for the people of the
+
+ align:start position:0%
+but maybe at least for the people of the
+ 
+
+ align:start position:0%
+but maybe at least for the people of the
+highest risk we could afford it
+
+ align:start position:0%
+highest risk we could afford it
+ 
+
+ align:start position:0%
+highest risk we could afford it
+if we could get there but I don't think
+
+ align:start position:0%
+if we could get there but I don't think
+ 
+
+ align:start position:0%
+if we could get there but I don't think
+that this is necessarily really where
+
+ align:start position:0%
+that this is necessarily really where
+ 
+
+ align:start position:0%
+that this is necessarily really where
+the true promised lies there's another
+
+ align:start position:0%
+the true promised lies there's another
+ 
+
+ align:start position:0%
+the true promised lies there's another
+possibility
+
+ align:start position:0%
+possibility
+ 
+
+ align:start position:0%
+possibility
+um this is sort of called
+
+ align:start position:0%
+um this is sort of called
+ 
+
+ align:start position:0%
+um this is sort of called
+pharmacogenomics which basically
+
+ align:start position:0%
+pharmacogenomics which basically
+ 
+
+ align:start position:0%
+pharmacogenomics which basically
+reclassification of individuals to guide
+
+ align:start position:0%
+reclassification of individuals to guide
+ 
+
+ align:start position:0%
+reclassification of individuals to guide
+therapy so you have this mix of people
+
+ align:start position:0%
+therapy so you have this mix of people
+ 
+
+ align:start position:0%
+therapy so you have this mix of people
+who have some disease like type 2
+
+ align:start position:0%
+who have some disease like type 2
+ 
+
+ align:start position:0%
+who have some disease like type 2
+diabetes but it turns out it's actually
+
+ align:start position:0%
+diabetes but it turns out it's actually
+ 
+
+ align:start position:0%
+diabetes but it turns out it's actually
+type 2 a to b2c and 2D maybe we could
+
+ align:start position:0%
+type 2 a to b2c and 2D maybe we could
+ 
+
+ align:start position:0%
+type 2 a to b2c and 2D maybe we could
+classify them by DNA sequence or you
+
+ align:start position:0%
+classify them by DNA sequence or you
+ 
+
+ align:start position:0%
+classify them by DNA sequence or you
+know expression profile or some genomic
+
+ align:start position:0%
+know expression profile or some genomic
+ 
+
+ align:start position:0%
+know expression profile or some genomic
+method we can say well these people will
+
+ align:start position:0%
+method we can say well these people will
+ 
+
+ align:start position:0%
+method we can say well these people will
+do best with treatment a these people
+
+ align:start position:0%
+do best with treatment a these people
+ 
+
+ align:start position:0%
+do best with treatment a these people
+with B these with c and these would be
+
+ align:start position:0%
+with B these with c and these would be
+ 
+
+ align:start position:0%
+with B these with c and these would be
+again that may or may not come to pass
+
+ align:start position:0%
+again that may or may not come to pass
+ 
+
+ align:start position:0%
+again that may or may not come to pass
+and certainly people are looking at it I
+
+ align:start position:0%
+and certainly people are looking at it I
+ 
+
+ align:start position:0%
+and certainly people are looking at it I
+think it's going to partially come to
+
+ align:start position:0%
+think it's going to partially come to
+ 
+
+ align:start position:0%
+think it's going to partially come to
+pass I'll just give you one real life
+
+ align:start position:0%
+pass I'll just give you one real life
+ 
+
+ align:start position:0%
+pass I'll just give you one real life
+example that actually is not in the
+
+ align:start position:0%
+example that actually is not in the
+ 
+
+ align:start position:0%
+example that actually is not in the
+clinic yet but I'm not sure why not
+
+ align:start position:0%
+clinic yet but I'm not sure why not
+ 
+
+ align:start position:0%
+clinic yet but I'm not sure why not
+um so this is there's a gene called
+
+ align:start position:0%
+um so this is there's a gene called
+ 
+
+ align:start position:0%
+um so this is there's a gene called
+sip2c9 which actually metabolizes
+
+ align:start position:0%
+sip2c9 which actually metabolizes
+ 
+
+ align:start position:0%
+sip2c9 which actually metabolizes
+Warfarin which is used commonly to treat
+
+ align:start position:0%
+Warfarin which is used commonly to treat
+ 
+
+ align:start position:0%
+Warfarin which is used commonly to treat
+conditions uh involved with thrombosis
+
+ align:start position:0%
+conditions uh involved with thrombosis
+ 
+
+ align:start position:0%
+conditions uh involved with thrombosis
+or blood clotting it's an anti-clotting
+
+ align:start position:0%
+or blood clotting it's an anti-clotting
+ 
+
+ align:start position:0%
+or blood clotting it's an anti-clotting
+agent
+
+ align:start position:0%
+agent
+ 
+
+ align:start position:0%
+agent
+uh actually vitamin K uh
+
+ align:start position:0%
+uh actually vitamin K uh
+ 
+
+ align:start position:0%
+uh actually vitamin K uh
+and this didn't quite I'm sorry the
+
+ align:start position:0%
+and this didn't quite I'm sorry the
+ 
+
+ align:start position:0%
+and this didn't quite I'm sorry the
+white on yellow is not a good color
+
+ align:start position:0%
+white on yellow is not a good color
+ 
+
+ align:start position:0%
+white on yellow is not a good color
+scheme but basically most of the
+
+ align:start position:0%
+scheme but basically most of the
+ 
+
+ align:start position:0%
+scheme but basically most of the
+population has zero low activity alleles
+
+ align:start position:0%
+population has zero low activity alleles
+ 
+
+ align:start position:0%
+population has zero low activity alleles
+20 of population is one more activity
+
+ align:start position:0%
+20 of population is one more activity
+ 
+
+ align:start position:0%
+20 of population is one more activity
+within five percent of the population
+
+ align:start position:0%
+within five percent of the population
+ 
+
+ align:start position:0%
+within five percent of the population
+have too low activity alleles
+
+ align:start position:0%
+have too low activity alleles
+ 
+
+ align:start position:0%
+have too low activity alleles
+and if you look at the average dosage
+
+ align:start position:0%
+and if you look at the average dosage
+ 
+
+ align:start position:0%
+and if you look at the average dosage
+that people end up on by their genotype
+
+ align:start position:0%
+that people end up on by their genotype
+ 
+
+ align:start position:0%
+that people end up on by their genotype
+so this dosage is not based on their
+
+ align:start position:0%
+so this dosage is not based on their
+ 
+
+ align:start position:0%
+so this dosage is not based on their
+genotype it's like there's trial and
+
+ align:start position:0%
+genotype it's like there's trial and
+ 
+
+ align:start position:0%
+genotype it's like there's trial and
+error by The Physician and they find you
+
+ align:start position:0%
+error by The Physician and they find you
+ 
+
+ align:start position:0%
+error by The Physician and they find you
+know oh you know you're all of a sudden
+
+ align:start position:0%
+know oh you know you're all of a sudden
+ 
+
+ align:start position:0%
+know oh you know you're all of a sudden
+you know you're you know you have a
+
+ align:start position:0%
+you know you're you know you have a
+ 
+
+ align:start position:0%
+you know you're you know you have a
+nosebleed that won't stop maybe your
+
+ align:start position:0%
+nosebleed that won't stop maybe your
+ 
+
+ align:start position:0%
+nosebleed that won't stop maybe your
+Warfarin dose is too high or your PT
+
+ align:start position:0%
+Warfarin dose is too high or your PT
+ 
+
+ align:start position:0%
+Warfarin dose is too high or your PT
+value is too high we have to cut the
+
+ align:start position:0%
+value is too high we have to cut the
+ 
+
+ align:start position:0%
+value is too high we have to cut the
+dose
+
+ align:start position:0%
+dose
+ 
+
+ align:start position:0%
+dose
+you see that there's a huge there's a
+
+ align:start position:0%
+you see that there's a huge there's a
+ 
+
+ align:start position:0%
+you see that there's a huge there's a
+very nice
+
+ align:start position:0%
+very nice
+ 
+
+ align:start position:0%
+very nice
+allele versus dose correlation here so
+
+ align:start position:0%
+allele versus dose correlation here so
+ 
+
+ align:start position:0%
+allele versus dose correlation here so
+that you know if you have two low
+
+ align:start position:0%
+that you know if you have two low
+ 
+
+ align:start position:0%
+that you know if you have two low
+activity alleles and you get put on the
+
+ align:start position:0%
+activity alleles and you get put on the
+ 
+
+ align:start position:0%
+activity alleles and you get put on the
+typical five milligram dose you're going
+
+ align:start position:0%
+typical five milligram dose you're going
+ 
+
+ align:start position:0%
+typical five milligram dose you're going
+to have bleeding problems okay in fact
+
+ align:start position:0%
+to have bleeding problems okay in fact
+ 
+
+ align:start position:0%
+to have bleeding problems okay in fact
+you're going to be at six times the risk
+
+ align:start position:0%
+you're going to be at six times the risk
+ 
+
+ align:start position:0%
+you're going to be at six times the risk
+of serious complications so personally
+
+ align:start position:0%
+of serious complications so personally
+ 
+
+ align:start position:0%
+of serious complications so personally
+if I were going on Warfarin I would
+
+ align:start position:0%
+if I were going on Warfarin I would
+ 
+
+ align:start position:0%
+if I were going on Warfarin I would
+probably want to know what my sip2c9
+
+ align:start position:0%
+probably want to know what my sip2c9
+ 
+
+ align:start position:0%
+probably want to know what my sip2c9
+genotype was but it's not yet standard
+
+ align:start position:0%
+genotype was but it's not yet standard
+ 
+
+ align:start position:0%
+genotype was but it's not yet standard
+practice the only one of the only cases
+
+ align:start position:0%
+practice the only one of the only cases
+ 
+
+ align:start position:0%
+practice the only one of the only cases
+that I know that is is actually if you
+
+ align:start position:0%
+that I know that is is actually if you
+ 
+
+ align:start position:0%
+that I know that is is actually if you
+have cancer and you're getting six more
+
+ align:start position:0%
+have cancer and you're getting six more
+ 
+
+ align:start position:0%
+have cancer and you're getting six more
+Capital purine or related drugs there's
+
+ align:start position:0%
+Capital purine or related drugs there's
+ 
+
+ align:start position:0%
+Capital purine or related drugs there's
+a gene called TPMT which again
+
+ align:start position:0%
+a gene called TPMT which again
+ 
+
+ align:start position:0%
+a gene called TPMT which again
+metabolizes that uh into a toxic
+
+ align:start position:0%
+metabolizes that uh into a toxic
+ 
+
+ align:start position:0%
+metabolizes that uh into a toxic
+intermediate and that has now become
+
+ align:start position:0%
+intermediate and that has now become
+ 
+
+ align:start position:0%
+intermediate and that has now become
+pretty much the standard of care because
+
+ align:start position:0%
+pretty much the standard of care because
+ 
+
+ align:start position:0%
+pretty much the standard of care because
+again the risk of death uh is is higher
+
+ align:start position:0%
+again the risk of death uh is is higher
+ 
+
+ align:start position:0%
+again the risk of death uh is is higher
+if you have the wrong genotype so death
+
+ align:start position:0%
+if you have the wrong genotype so death
+ 
+
+ align:start position:0%
+if you have the wrong genotype so death
+gets people's attention quite quite
+
+ align:start position:0%
+gets people's attention quite quite
+ 
+
+ align:start position:0%
+gets people's attention quite quite
+vigorously
+
+ align:start position:0%
+vigorously
+ 
+
+ align:start position:0%
+vigorously
+yeah so there's a range oh absolutely
+
+ align:start position:0%
+yeah so there's a range oh absolutely
+ 
+
+ align:start position:0%
+yeah so there's a range oh absolutely
+yeah so I have to say I should have put
+
+ align:start position:0%
+yeah so I have to say I should have put
+ 
+
+ align:start position:0%
+yeah so I have to say I should have put
+error bars on here I was looking at that
+
+ align:start position:0%
+error bars on here I was looking at that
+ 
+
+ align:start position:0%
+error bars on here I was looking at that
+and just noticing I did not have them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah so right so so if this were if you
+
+ align:start position:0%
+ah so right so so if this were if you
+ 
+
+ align:start position:0%
+ah so right so so if this were if you
+could say well Physicians can do this
+
+ align:start position:0%
+could say well Physicians can do this
+ 
+
+ align:start position:0%
+could say well Physicians can do this
+without knowing ahead of time then this
+
+ align:start position:0%
+without knowing ahead of time then this
+ 
+
+ align:start position:0%
+without knowing ahead of time then this
+should not happen right
+
+ align:start position:0%
+should not happen right
+ 
+
+ align:start position:0%
+should not happen right
+oh yeah yeah so if yeah so this is the
+
+ align:start position:0%
+oh yeah yeah so if yeah so this is the
+ 
+
+ align:start position:0%
+oh yeah yeah so if yeah so this is the
+argument is oh well you know Physicians
+
+ align:start position:0%
+argument is oh well you know Physicians
+ 
+
+ align:start position:0%
+argument is oh well you know Physicians
+are kind of going to be good at this
+
+ align:start position:0%
+are kind of going to be good at this
+ 
+
+ align:start position:0%
+are kind of going to be good at this
+anyway they're not they suck at it okay
+
+ align:start position:0%
+anyway they're not they suck at it okay
+ 
+
+ align:start position:0%
+anyway they're not they suck at it okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I think the other the other thing
+
+ align:start position:0%
+but I think the other the other thing
+ 
+
+ align:start position:0%
+but I think the other the other thing
+that um is potentially useful so if you
+
+ align:start position:0%
+that um is potentially useful so if you
+ 
+
+ align:start position:0%
+that um is potentially useful so if you
+look at at least the two most uh
+
+ align:start position:0%
+look at at least the two most uh
+ 
+
+ align:start position:0%
+look at at least the two most uh
+well-established uh risk alleles for
+
+ align:start position:0%
+well-established uh risk alleles for
+ 
+
+ align:start position:0%
+well-established uh risk alleles for
+type 2 diabetes turns out they're both
+
+ align:start position:0%
+type 2 diabetes turns out they're both
+ 
+
+ align:start position:0%
+type 2 diabetes turns out they're both
+in drug targets now this is admittedly a
+
+ align:start position:0%
+in drug targets now this is admittedly a
+ 
+
+ align:start position:0%
+in drug targets now this is admittedly a
+little bit circular because the reason
+
+ align:start position:0%
+little bit circular because the reason
+ 
+
+ align:start position:0%
+little bit circular because the reason
+they were looked at was because it was
+
+ align:start position:0%
+they were looked at was because it was
+ 
+
+ align:start position:0%
+they were looked at was because it was
+known ahead of time they were drug
+
+ align:start position:0%
+known ahead of time they were drug
+ 
+
+ align:start position:0%
+known ahead of time they were drug
+targets so they made sense as being good
+
+ align:start position:0%
+targets so they made sense as being good
+ 
+
+ align:start position:0%
+targets so they made sense as being good
+candidate chains but it is interesting
+
+ align:start position:0%
+candidate chains but it is interesting
+ 
+
+ align:start position:0%
+candidate chains but it is interesting
+that you know two of the major drugs
+
+ align:start position:0%
+that you know two of the major drugs
+ 
+
+ align:start position:0%
+that you know two of the major drugs
+that are used to treat type 2 diabetes
+
+ align:start position:0%
+that are used to treat type 2 diabetes
+ 
+
+ align:start position:0%
+that are used to treat type 2 diabetes
+there's variants in their targets that
+
+ align:start position:0%
+there's variants in their targets that
+ 
+
+ align:start position:0%
+there's variants in their targets that
+affect the genetic susceptibility to
+
+ align:start position:0%
+affect the genetic susceptibility to
+ 
+
+ align:start position:0%
+affect the genetic susceptibility to
+diabetes and of course the promise here
+
+ align:start position:0%
+diabetes and of course the promise here
+ 
+
+ align:start position:0%
+diabetes and of course the promise here
+is that if you could find all of the
+
+ align:start position:0%
+is that if you could find all of the
+ 
+
+ align:start position:0%
+is that if you could find all of the
+other genetic Pathways even if they only
+
+ align:start position:0%
+other genetic Pathways even if they only
+ 
+
+ align:start position:0%
+other genetic Pathways even if they only
+had a 1.1 fold effect on disease so PPR
+
+ align:start position:0%
+had a 1.1 fold effect on disease so PPR
+ 
+
+ align:start position:0%
+had a 1.1 fold effect on disease so PPR
+gamma is only about a 25 risk effect on
+
+ align:start position:0%
+gamma is only about a 25 risk effect on
+ 
+
+ align:start position:0%
+gamma is only about a 25 risk effect on
+on risk of disease
+
+ align:start position:0%
+on risk of disease
+ 
+
+ align:start position:0%
+on risk of disease
+but you could easily imagine you come up
+
+ align:start position:0%
+but you could easily imagine you come up
+ 
+
+ align:start position:0%
+but you could easily imagine you come up
+with a pharmacologic event intervention
+
+ align:start position:0%
+with a pharmacologic event intervention
+ 
+
+ align:start position:0%
+with a pharmacologic event intervention
+that does a lot more than the genetic
+
+ align:start position:0%
+that does a lot more than the genetic
+ 
+
+ align:start position:0%
+that does a lot more than the genetic
+polymorphism does so there's you know
+
+ align:start position:0%
+polymorphism does so there's you know
+ 
+
+ align:start position:0%
+polymorphism does so there's you know
+only so much tolerance for
+
+ align:start position:0%
+only so much tolerance for
+ 
+
+ align:start position:0%
+only so much tolerance for
+how much genetic variation Evolution
+
+ align:start position:0%
+how much genetic variation Evolution
+ 
+
+ align:start position:0%
+how much genetic variation Evolution
+will will let happen but it might be
+
+ align:start position:0%
+will will let happen but it might be
+ 
+
+ align:start position:0%
+will will let happen but it might be
+that you could you know giving
+
+ align:start position:0%
+that you could you know giving
+ 
+
+ align:start position:0%
+that you could you know giving
+thiazoline diodes might be like you know
+
+ align:start position:0%
+thiazoline diodes might be like you know
+ 
+
+ align:start position:0%
+thiazoline diodes might be like you know
+having you know 10 times as much of an
+
+ align:start position:0%
+having you know 10 times as much of an
+ 
+
+ align:start position:0%
+having you know 10 times as much of an
+effect as having an alanine allele does
+
+ align:start position:0%
+effect as having an alanine allele does
+ 
+
+ align:start position:0%
+effect as having an alanine allele does
+so the idea is that hopefully by
+
+ align:start position:0%
+so the idea is that hopefully by
+ 
+
+ align:start position:0%
+so the idea is that hopefully by
+identifying the genes that are
+
+ align:start position:0%
+identifying the genes that are
+ 
+
+ align:start position:0%
+identifying the genes that are
+responsible and this is true for for
+
+ align:start position:0%
+responsible and this is true for for
+ 
+
+ align:start position:0%
+responsible and this is true for for
+severe forms of the disease as well you
+
+ align:start position:0%
+severe forms of the disease as well you
+ 
+
+ align:start position:0%
+severe forms of the disease as well you
+might identify drug targets
+
+ align:start position:0%
+might identify drug targets
+ 
+
+ align:start position:0%
+might identify drug targets
+and finally of course you know this
+
+ align:start position:0%
+and finally of course you know this
+ 
+
+ align:start position:0%
+and finally of course you know this
+helps just understand human biology and
+
+ align:start position:0%
+helps just understand human biology and
+ 
+
+ align:start position:0%
+helps just understand human biology and
+that's always a worthy goal so
+
+ align:start position:0%
+that's always a worthy goal so
+ 
+
+ align:start position:0%
+that's always a worthy goal so
+um should uh talk about potential
+
+ align:start position:0%
+um should uh talk about potential
+ 
+
+ align:start position:0%
+um should uh talk about potential
+difficulties from all these uh from all
+
+ align:start position:0%
+difficulties from all these uh from all
+ 
+
+ align:start position:0%
+difficulties from all these uh from all
+these advances
+
+ align:start position:0%
+these advances
+ 
+
+ align:start position:0%
+these advances
+they're obviously concerns about privacy
+
+ align:start position:0%
+they're obviously concerns about privacy
+ 
+
+ align:start position:0%
+they're obviously concerns about privacy
+with genetic data and I don't know what
+
+ align:start position:0%
+with genetic data and I don't know what
+ 
+
+ align:start position:0%
+with genetic data and I don't know what
+time to go into it but obviously there's
+
+ align:start position:0%
+time to go into it but obviously there's
+ 
+
+ align:start position:0%
+time to go into it but obviously there's
+uh the big fear is has to do with
+
+ align:start position:0%
+uh the big fear is has to do with
+ 
+
+ align:start position:0%
+uh the big fear is has to do with
+insurance discrimination and employers
+
+ align:start position:0%
+insurance discrimination and employers
+ 
+
+ align:start position:0%
+insurance discrimination and employers
+uh knowing about genetic diseases and
+
+ align:start position:0%
+uh knowing about genetic diseases and
+ 
+
+ align:start position:0%
+uh knowing about genetic diseases and
+there's bills that keep making it almost
+
+ align:start position:0%
+there's bills that keep making it almost
+ 
+
+ align:start position:0%
+there's bills that keep making it almost
+all the way through Congress and not
+
+ align:start position:0%
+all the way through Congress and not
+ 
+
+ align:start position:0%
+all the way through Congress and not
+quite to deal with this it's a Lobby or
+
+ align:start position:0%
+quite to deal with this it's a Lobby or
+ 
+
+ align:start position:0%
+quite to deal with this it's a Lobby or
+congressman
+
+ align:start position:0%
+congressman
+ 
+
+ align:start position:0%
+congressman
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's sort of the Gattaca mindset
+
+ align:start position:0%
+there's sort of the Gattaca mindset
+ 
+
+ align:start position:0%
+there's sort of the Gattaca mindset
+about you know improper interpretation
+
+ align:start position:0%
+about you know improper interpretation
+ 
+
+ align:start position:0%
+about you know improper interpretation
+of predictive information how predictive
+
+ align:start position:0%
+of predictive information how predictive
+ 
+
+ align:start position:0%
+of predictive information how predictive
+genetic information is
+
+ align:start position:0%
+genetic information is
+ 
+
+ align:start position:0%
+genetic information is
+um there are companies that will try to
+
+ align:start position:0%
+um there are companies that will try to
+ 
+
+ align:start position:0%
+um there are companies that will try to
+sell you that you should be on diet a or
+
+ align:start position:0%
+sell you that you should be on diet a or
+ 
+
+ align:start position:0%
+sell you that you should be on diet a or
+diet based on Snapchat Gene types that
+
+ align:start position:0%
+diet based on Snapchat Gene types that
+ 
+
+ align:start position:0%
+diet based on Snapchat Gene types that
+are in those irreproducible associations
+
+ align:start position:0%
+are in those irreproducible associations
+ 
+
+ align:start position:0%
+are in those irreproducible associations
+um there can be you know psychological
+
+ align:start position:0%
+um there can be you know psychological
+ 
+
+ align:start position:0%
+um there can be you know psychological
+impacts of if you say you know you have
+
+ align:start position:0%
+impacts of if you say you know you have
+ 
+
+ align:start position:0%
+impacts of if you say you know you have
+the high risk allele for diabetes that
+
+ align:start position:0%
+the high risk allele for diabetes that
+ 
+
+ align:start position:0%
+the high risk allele for diabetes that
+might without an understanding that this
+
+ align:start position:0%
+might without an understanding that this
+ 
+
+ align:start position:0%
+might without an understanding that this
+is a correlative rather than a perfectly
+
+ align:start position:0%
+is a correlative rather than a perfectly
+ 
+
+ align:start position:0%
+is a correlative rather than a perfectly
+predictive measure That Could That Could
+
+ align:start position:0%
+predictive measure That Could That Could
+ 
+
+ align:start position:0%
+predictive measure That Could That Could
+Have significant harm as well as impact
+
+ align:start position:0%
+Have significant harm as well as impact
+ 
+
+ align:start position:0%
+Have significant harm as well as impact
+on reproductive choices again uh
+
+ align:start position:0%
+on reproductive choices again uh
+ 
+
+ align:start position:0%
+on reproductive choices again uh
+depending on how predictive people
+
+ align:start position:0%
+depending on how predictive people
+ 
+
+ align:start position:0%
+depending on how predictive people
+things think things are there are huge
+
+ align:start position:0%
+things think things are there are huge
+ 
+
+ align:start position:0%
+things think things are there are huge
+interactions with concepts of race and
+
+ align:start position:0%
+interactions with concepts of race and
+ 
+
+ align:start position:0%
+interactions with concepts of race and
+ethnicity we alluded to this a little
+
+ align:start position:0%
+ethnicity we alluded to this a little
+ 
+
+ align:start position:0%
+ethnicity we alluded to this a little
+bit with different allele frequencies in
+
+ align:start position:0%
+bit with different allele frequencies in
+ 
+
+ align:start position:0%
+bit with different allele frequencies in
+different populations most alleles are
+
+ align:start position:0%
+different populations most alleles are
+ 
+
+ align:start position:0%
+different populations most alleles are
+present around the world and you can't
+
+ align:start position:0%
+present around the world and you can't
+ 
+
+ align:start position:0%
+present around the world and you can't
+use generally any one variant to tell
+
+ align:start position:0%
+use generally any one variant to tell
+ 
+
+ align:start position:0%
+use generally any one variant to tell
+different ethnic groups apart but there
+
+ align:start position:0%
+different ethnic groups apart but there
+ 
+
+ align:start position:0%
+different ethnic groups apart but there
+are definitely differences in real
+
+ align:start position:0%
+are definitely differences in real
+ 
+
+ align:start position:0%
+are definitely differences in real
+frequencies between populations and that
+
+ align:start position:0%
+frequencies between populations and that
+ 
+
+ align:start position:0%
+frequencies between populations and that
+has a significant interaction
+
+ align:start position:0%
+has a significant interaction
+ 
+
+ align:start position:0%
+has a significant interaction
+significant implications and then
+
+ align:start position:0%
+significant implications and then
+ 
+
+ align:start position:0%
+significant implications and then
+finally
+
+ align:start position:0%
+finally
+ 
+
+ align:start position:0%
+finally
+you know I certainly don't study the
+
+ align:start position:0%
+you know I certainly don't study the
+ 
+
+ align:start position:0%
+you know I certainly don't study the
+genetics of performance but you could
+
+ align:start position:0%
+genetics of performance but you could
+ 
+
+ align:start position:0%
+genetics of performance but you could
+imagine that if people started getting
+
+ align:start position:0%
+imagine that if people started getting
+ 
+
+ align:start position:0%
+imagine that if people started getting
+into that
+
+ align:start position:0%
+into that
+ 
+
+ align:start position:0%
+into that
+um they could be quite dicey
+
+ align:start position:0%
+um they could be quite dicey
+ 
+
+ align:start position:0%
+um they could be quite dicey
+um and even if the science were perfect
+
+ align:start position:0%
+um and even if the science were perfect
+ 
+
+ align:start position:0%
+um and even if the science were perfect
+uh from a technical standpoint uh it
+
+ align:start position:0%
+uh from a technical standpoint uh it
+ 
+
+ align:start position:0%
+uh from a technical standpoint uh it
+might uh create a lot of trouble
+
+ align:start position:0%
+might uh create a lot of trouble
+ 
+
+ align:start position:0%
+might uh create a lot of trouble
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+David alchair is uh collaborated with me
+
+ align:start position:0%
+David alchair is uh collaborated with me
+ 
+
+ align:start position:0%
+David alchair is uh collaborated with me
+on the diabetes work and also very
+
+ align:start position:0%
+on the diabetes work and also very
+ 
+
+ align:start position:0%
+on the diabetes work and also very
+involved in the Hat map with the work
+
+ align:start position:0%
+involved in the Hat map with the work
+ 
+
+ align:start position:0%
+involved in the Hat map with the work
+that was done by Stacy Gabriel Mark
+
+ align:start position:0%
+that was done by Stacy Gabriel Mark
+ 
+
+ align:start position:0%
+that was done by Stacy Gabriel Mark
+Daley Steve Shaffer on hapl type blocks
+
+ align:start position:0%
+Daley Steve Shaffer on hapl type blocks
+ 
+
+ align:start position:0%
+Daley Steve Shaffer on hapl type blocks
+the diabetes group also is Noel Leif
+
+ align:start position:0%
+the diabetes group also is Noel Leif
+ 
+
+ align:start position:0%
+the diabetes group also is Noel Leif
+Cecilia bombsi did some expression stuff
+
+ align:start position:0%
+Cecilia bombsi did some expression stuff
+ 
+
+ align:start position:0%
+Cecilia bombsi did some expression stuff
+and Kirk and Lee and Eric were on the
+
+ align:start position:0%
+and Kirk and Lee and Eric were on the
+ 
+
+ align:start position:0%
+and Kirk and Lee and Eric were on the
+meta-analysis of Association setting
+
+ align:start position:0%
+meta-analysis of Association setting
+ 
+
+ align:start position:0%
+meta-analysis of Association setting
+there are a lot of Genome Project type
+
+ align:start position:0%
+there are a lot of Genome Project type
+ 
+
+ align:start position:0%
+there are a lot of Genome Project type
+things that are obviously giving us all
+
+ align:start position:0%
+things that are obviously giving us all
+ 
+
+ align:start position:0%
+things that are obviously giving us all
+the tools to do this too thanks
\ No newline at end of file
diff --git a/BW_EHmZf2pM.txt b/BW_EHmZf2pM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a714f24c894d03a0729848f8f063701a93651c19
--- /dev/null
+++ b/BW_EHmZf2pM.txt
@@ -0,0 +1,1402 @@
+align:start position:0%
+ 
+in this video we continue our
+
+ align:start position:0%
+in this video we continue our
+ 
+
+ align:start position:0%
+in this video we continue our
+exploration of quantities of interest
+
+ align:start position:0%
+exploration of quantities of interest
+ 
+
+ align:start position:0%
+exploration of quantities of interest
+associated with the short-term behavior
+
+ align:start position:0%
+associated with the short-term behavior
+ 
+
+ align:start position:0%
+associated with the short-term behavior
+of Markov chain
+
+ align:start position:0%
+of Markov chain
+ 
+
+ align:start position:0%
+of Markov chain
+this time we suppose that we have a
+
+ align:start position:0%
+this time we suppose that we have a
+ 
+
+ align:start position:0%
+this time we suppose that we have a
+Markov chain composed of a single
+
+ align:start position:0%
+Markov chain composed of a single
+ 
+
+ align:start position:0%
+Markov chain composed of a single
+recurrent class such as this one here we
+
+ align:start position:0%
+recurrent class such as this one here we
+ 
+
+ align:start position:0%
+recurrent class such as this one here we
+have our recurrent class and these are
+
+ align:start position:0%
+have our recurrent class and these are
+ 
+
+ align:start position:0%
+have our recurrent class and these are
+transient States we also assume that we
+
+ align:start position:0%
+transient States we also assume that we
+ 
+
+ align:start position:0%
+transient States we also assume that we
+are interesting in a specific recurrent
+
+ align:start position:0%
+are interesting in a specific recurrent
+ 
+
+ align:start position:0%
+are interesting in a specific recurrent
+State let's say nine so this is my state
+
+ align:start position:0%
+State let's say nine so this is my state
+ 
+
+ align:start position:0%
+State let's say nine so this is my state
+s and we will assume that the Markov
+
+ align:start position:0%
+s and we will assume that the Markov
+ 
+
+ align:start position:0%
+s and we will assume that the Markov
+chains start from a given initial state
+
+ align:start position:0%
+chains start from a given initial state
+ 
+
+ align:start position:0%
+chains start from a given initial state
+state I and assume that I is one now the
+
+ align:start position:0%
+state I and assume that I is one now the
+ 
+
+ align:start position:0%
+state I and assume that I is one now the
+question we ask is given that you
+
+ align:start position:0%
+question we ask is given that you
+ 
+
+ align:start position:0%
+question we ask is given that you
+started in one house is it going to take
+
+ align:start position:0%
+started in one house is it going to take
+ 
+
+ align:start position:0%
+started in one house is it going to take
+to reach nine for the first time we know
+
+ align:start position:0%
+to reach nine for the first time we know
+ 
+
+ align:start position:0%
+to reach nine for the first time we know
+this is a recurrent class so we know
+
+ align:start position:0%
+this is a recurrent class so we know
+ 
+
+ align:start position:0%
+this is a recurrent class so we know
+that the Markov chain eventually will
+
+ align:start position:0%
+that the Markov chain eventually will
+ 
+
+ align:start position:0%
+that the Markov chain eventually will
+come to that class and circulate here so
+
+ align:start position:0%
+come to that class and circulate here so
+ 
+
+ align:start position:0%
+come to that class and circulate here so
+you know that the Markov chain will get
+
+ align:start position:0%
+you know that the Markov chain will get
+ 
+
+ align:start position:0%
+you know that the Markov chain will get
+to that state nine you are interested in
+
+ align:start position:0%
+to that state nine you are interested in
+ 
+
+ align:start position:0%
+to that state nine you are interested in
+knowing when it does so for the first
+
+ align:start position:0%
+knowing when it does so for the first
+ 
+
+ align:start position:0%
+knowing when it does so for the first
+time of course we don't know for sure
+
+ align:start position:0%
+time of course we don't know for sure
+ 
+
+ align:start position:0%
+time of course we don't know for sure
+this is random it is a random variable
+
+ align:start position:0%
+this is random it is a random variable
+ 
+
+ align:start position:0%
+this is random it is a random variable
+and let's try to calculate the expected
+
+ align:start position:0%
+and let's try to calculate the expected
+ 
+
+ align:start position:0%
+and let's try to calculate the expected
+value of this random variable more
+
+ align:start position:0%
+value of this random variable more
+ 
+
+ align:start position:0%
+value of this random variable more
+precisely this is what we would like to
+
+ align:start position:0%
+precisely this is what we would like to
+ 
+
+ align:start position:0%
+precisely this is what we would like to
+do we would like to find the mean first
+
+ align:start position:0%
+do we would like to find the mean first
+ 
+
+ align:start position:0%
+do we would like to find the mean first
+passage time from I to s from any
+
+ align:start position:0%
+passage time from I to s from any
+ 
+
+ align:start position:0%
+passage time from I to s from any
+starting state i here we're going to
+
+ align:start position:0%
+starting state i here we're going to
+ 
+
+ align:start position:0%
+starting state i here we're going to
+illustrate that with 1 and
+
+ align:start position:0%
+illustrate that with 1 and
+ 
+
+ align:start position:0%
+illustrate that with 1 and
+mathematically this is what we have here
+
+ align:start position:0%
+mathematically this is what we have here
+ 
+
+ align:start position:0%
+mathematically this is what we have here
+so here again what you have is that the
+
+ align:start position:0%
+so here again what you have is that the
+ 
+
+ align:start position:0%
+so here again what you have is that the
+Markov chain started in state I at time
+
+ align:start position:0%
+Markov chain started in state I at time
+ 
+
+ align:start position:0%
+Markov chain started in state I at time
+0 and now you are looking at this set
+
+ align:start position:0%
+0 and now you are looking at this set
+ 
+
+ align:start position:0%
+0 and now you are looking at this set
+here and this set records all the time n
+
+ align:start position:0%
+here and this set records all the time n
+ 
+
+ align:start position:0%
+here and this set records all the time n
+such that your Markov chain xn is in the
+
+ align:start position:0%
+such that your Markov chain xn is in the
+ 
+
+ align:start position:0%
+such that your Markov chain xn is in the
+state s of interest so out of this set
+
+ align:start position:0%
+state s of interest so out of this set
+ 
+
+ align:start position:0%
+state s of interest so out of this set
+you are looking at the minimum and that
+
+ align:start position:0%
+you are looking at the minimum and that
+ 
+
+ align:start position:0%
+you are looking at the minimum and that
+verifies that so this is going to be a
+
+ align:start position:0%
+verifies that so this is going to be a
+ 
+
+ align:start position:0%
+verifies that so this is going to be a
+random variable and you take the
+
+ align:start position:0%
+random variable and you take the
+ 
+
+ align:start position:0%
+random variable and you take the
+expected value of that and this is what
+
+ align:start position:0%
+expected value of that and this is what
+ 
+
+ align:start position:0%
+expected value of that and this is what
+we call the mean first passage time from
+
+ align:start position:0%
+we call the mean first passage time from
+ 
+
+ align:start position:0%
+we call the mean first passage time from
+I to s again this is the expected number
+
+ align:start position:0%
+I to s again this is the expected number
+ 
+
+ align:start position:0%
+I to s again this is the expected number
+of steps in order to get from I to s for
+
+ align:start position:0%
+of steps in order to get from I to s for
+ 
+
+ align:start position:0%
+of steps in order to get from I to s for
+the first time
+
+ align:start position:0%
+the first time
+ 
+
+ align:start position:0%
+the first time
+so how do we go about calculating such a
+
+ align:start position:0%
+so how do we go about calculating such a
+ 
+
+ align:start position:0%
+so how do we go about calculating such a
+quantity well let us think a little bit
+
+ align:start position:0%
+quantity well let us think a little bit
+ 
+
+ align:start position:0%
+quantity well let us think a little bit
+we are looking at the events that you
+
+ align:start position:0%
+we are looking at the events that you
+ 
+
+ align:start position:0%
+we are looking at the events that you
+will visit nine from one for the first
+
+ align:start position:0%
+will visit nine from one for the first
+ 
+
+ align:start position:0%
+will visit nine from one for the first
+time what happened after visiting nine
+
+ align:start position:0%
+time what happened after visiting nine
+ 
+
+ align:start position:0%
+time what happened after visiting nine
+is of no relevance in our calculation in
+
+ align:start position:0%
+is of no relevance in our calculation in
+ 
+
+ align:start position:0%
+is of no relevance in our calculation in
+other words our calculation will never
+
+ align:start position:0%
+other words our calculation will never
+ 
+
+ align:start position:0%
+other words our calculation will never
+involve this arc and will not involve
+
+ align:start position:0%
+involve this arc and will not involve
+ 
+
+ align:start position:0%
+involve this arc and will not involve
+this art either because in order for the
+
+ align:start position:0%
+this art either because in order for the
+ 
+
+ align:start position:0%
+this art either because in order for the
+Markov chain to traverse this arc or
+
+ align:start position:0%
+Markov chain to traverse this arc or
+ 
+
+ align:start position:0%
+Markov chain to traverse this arc or
+this one it would have to visit nine
+
+ align:start position:0%
+this one it would have to visit nine
+ 
+
+ align:start position:0%
+this one it would have to visit nine
+first so what it means is that we can
+
+ align:start position:0%
+first so what it means is that we can
+ 
+
+ align:start position:0%
+first so what it means is that we can
+forget about this arc and we can forget
+
+ align:start position:0%
+forget about this arc and we can forget
+ 
+
+ align:start position:0%
+forget about this arc and we can forget
+about this arc in a sense that they
+
+ align:start position:0%
+about this arc in a sense that they
+ 
+
+ align:start position:0%
+about this arc in a sense that they
+don't matter in the calculation of the
+
+ align:start position:0%
+don't matter in the calculation of the
+ 
+
+ align:start position:0%
+don't matter in the calculation of the
+mean first passage time to s now
+
+ align:start position:0%
+mean first passage time to s now
+ 
+
+ align:start position:0%
+mean first passage time to s now
+removing these arcs entirely means that
+
+ align:start position:0%
+removing these arcs entirely means that
+ 
+
+ align:start position:0%
+removing these arcs entirely means that
+you would have to increase the
+
+ align:start position:0%
+you would have to increase the
+ 
+
+ align:start position:0%
+you would have to increase the
+probability of that cell transition from
+
+ align:start position:0%
+probability of that cell transition from
+ 
+
+ align:start position:0%
+probability of that cell transition from
+zero to two one so what do you get
+
+ align:start position:0%
+zero to two one so what do you get
+ 
+
+ align:start position:0%
+zero to two one so what do you get
+well you get this following graph we
+
+ align:start position:0%
+well you get this following graph we
+ 
+
+ align:start position:0%
+well you get this following graph we
+have removed this arcs and we have
+
+ align:start position:0%
+have removed this arcs and we have
+ 
+
+ align:start position:0%
+have removed this arcs and we have
+increased the priority 0.2 here to 1 and
+
+ align:start position:0%
+increased the priority 0.2 here to 1 and
+ 
+
+ align:start position:0%
+increased the priority 0.2 here to 1 and
+again we have argued that calculating
+
+ align:start position:0%
+again we have argued that calculating
+ 
+
+ align:start position:0%
+again we have argued that calculating
+the mean first passage time from I to s
+
+ align:start position:0%
+the mean first passage time from I to s
+ 
+
+ align:start position:0%
+the mean first passage time from I to s
+in this graph is the same as doing the
+
+ align:start position:0%
+in this graph is the same as doing the
+ 
+
+ align:start position:0%
+in this graph is the same as doing the
+same thing for this graph but here we
+
+ align:start position:0%
+same thing for this graph but here we
+ 
+
+ align:start position:0%
+same thing for this graph but here we
+have a very special structure we have
+
+ align:start position:0%
+have a very special structure we have
+ 
+
+ align:start position:0%
+have a very special structure we have
+only one recurrent state left which is
+
+ align:start position:0%
+only one recurrent state left which is
+ 
+
+ align:start position:0%
+only one recurrent state left which is
+state 9 and that state is an absorbing
+
+ align:start position:0%
+state 9 and that state is an absorbing
+ 
+
+ align:start position:0%
+state 9 and that state is an absorbing
+state all the other state this one was
+
+ align:start position:0%
+state all the other state this one was
+ 
+
+ align:start position:0%
+state all the other state this one was
+transient transient transient this one
+
+ align:start position:0%
+transient transient transient this one
+ 
+
+ align:start position:0%
+transient transient transient this one
+becomes a transient state and this one
+
+ align:start position:0%
+becomes a transient state and this one
+ 
+
+ align:start position:0%
+becomes a transient state and this one
+is also a transient state in this new
+
+ align:start position:0%
+is also a transient state in this new
+ 
+
+ align:start position:0%
+is also a transient state in this new
+transition priority diagram so we get a
+
+ align:start position:0%
+transition priority diagram so we get a
+ 
+
+ align:start position:0%
+transition priority diagram so we get a
+situation where we have one single
+
+ align:start position:0%
+situation where we have one single
+ 
+
+ align:start position:0%
+situation where we have one single
+absorbing state and we are interested in
+
+ align:start position:0%
+absorbing state and we are interested in
+ 
+
+ align:start position:0%
+absorbing state and we are interested in
+calculating the priority starting from I
+
+ align:start position:0%
+calculating the priority starting from I
+ 
+
+ align:start position:0%
+calculating the priority starting from I
+to reach that absorbing state and also
+
+ align:start position:0%
+to reach that absorbing state and also
+ 
+
+ align:start position:0%
+to reach that absorbing state and also
+the number of steps it takes to do that
+
+ align:start position:0%
+the number of steps it takes to do that
+ 
+
+ align:start position:0%
+the number of steps it takes to do that
+which is what we did in the previous
+
+ align:start position:0%
+which is what we did in the previous
+ 
+
+ align:start position:0%
+which is what we did in the previous
+video so let us repeat what we had seen
+
+ align:start position:0%
+video so let us repeat what we had seen
+ 
+
+ align:start position:0%
+video so let us repeat what we had seen
+before so this is going to be the unique
+
+ align:start position:0%
+before so this is going to be the unique
+ 
+
+ align:start position:0%
+before so this is going to be the unique
+solution to this system T of s equals 0
+
+ align:start position:0%
+solution to this system T of s equals 0
+ 
+
+ align:start position:0%
+solution to this system T of s equals 0
+of course since you start from s you are
+
+ align:start position:0%
+of course since you start from s you are
+ 
+
+ align:start position:0%
+of course since you start from s you are
+in s and so that not in the matter
+
+ align:start position:0%
+in s and so that not in the matter
+ 
+
+ align:start position:0%
+in s and so that not in the matter
+time it takes to get to s is zero and
+
+ align:start position:0%
+time it takes to get to s is zero and
+ 
+
+ align:start position:0%
+time it takes to get to s is zero and
+otherwise for all the other states that
+
+ align:start position:0%
+otherwise for all the other states that
+ 
+
+ align:start position:0%
+otherwise for all the other states that
+are not s this is the resulting system
+
+ align:start position:0%
+are not s this is the resulting system
+ 
+
+ align:start position:0%
+are not s this is the resulting system
+of equation that we have and the unique
+
+ align:start position:0%
+of equation that we have and the unique
+ 
+
+ align:start position:0%
+of equation that we have and the unique
+solution of this system gives you the
+
+ align:start position:0%
+solution of this system gives you the
+ 
+
+ align:start position:0%
+solution of this system gives you the
+result of finding the expected amount of
+
+ align:start position:0%
+result of finding the expected amount of
+ 
+
+ align:start position:0%
+result of finding the expected amount of
+time to go to the absorbing state s so
+
+ align:start position:0%
+time to go to the absorbing state s so
+ 
+
+ align:start position:0%
+time to go to the absorbing state s so
+using this simple trick we have been
+
+ align:start position:0%
+using this simple trick we have been
+ 
+
+ align:start position:0%
+using this simple trick we have been
+able to use the previous calculation to
+
+ align:start position:0%
+able to use the previous calculation to
+ 
+
+ align:start position:0%
+able to use the previous calculation to
+calculate something else let us consider
+
+ align:start position:0%
+calculate something else let us consider
+ 
+
+ align:start position:0%
+calculate something else let us consider
+a belated question which we call the
+
+ align:start position:0%
+a belated question which we call the
+ 
+
+ align:start position:0%
+a belated question which we call the
+mean recurrence time of s here let's go
+
+ align:start position:0%
+mean recurrence time of s here let's go
+ 
+
+ align:start position:0%
+mean recurrence time of s here let's go
+back to the original graph and this is
+
+ align:start position:0%
+back to the original graph and this is
+ 
+
+ align:start position:0%
+back to the original graph and this is
+our state s and now the question is the
+
+ align:start position:0%
+our state s and now the question is the
+ 
+
+ align:start position:0%
+our state s and now the question is the
+following given that you are in S what
+
+ align:start position:0%
+following given that you are in S what
+ 
+
+ align:start position:0%
+following given that you are in S what
+is the amount of time it will take for
+
+ align:start position:0%
+is the amount of time it will take for
+ 
+
+ align:start position:0%
+is the amount of time it will take for
+the Markov chain to return to s for the
+
+ align:start position:0%
+the Markov chain to return to s for the
+ 
+
+ align:start position:0%
+the Markov chain to return to s for the
+first time so for this question the
+
+ align:start position:0%
+first time so for this question the
+ 
+
+ align:start position:0%
+first time so for this question the
+Markov chain is currently in nine and
+
+ align:start position:0%
+Markov chain is currently in nine and
+ 
+
+ align:start position:0%
+Markov chain is currently in nine and
+you ask yourself how long is it going to
+
+ align:start position:0%
+you ask yourself how long is it going to
+ 
+
+ align:start position:0%
+you ask yourself how long is it going to
+take once you leave nine to return to
+
+ align:start position:0%
+take once you leave nine to return to
+ 
+
+ align:start position:0%
+take once you leave nine to return to
+nine here again we don't know for sure
+
+ align:start position:0%
+nine here again we don't know for sure
+ 
+
+ align:start position:0%
+nine here again we don't know for sure
+it's a random variable and we are
+
+ align:start position:0%
+it's a random variable and we are
+ 
+
+ align:start position:0%
+it's a random variable and we are
+interested in the expectation of that
+
+ align:start position:0%
+interested in the expectation of that
+ 
+
+ align:start position:0%
+interested in the expectation of that
+random variable in other words in the
+
+ align:start position:0%
+random variable in other words in the
+ 
+
+ align:start position:0%
+random variable in other words in the
+expected number of steps it takes in
+
+ align:start position:0%
+expected number of steps it takes in
+ 
+
+ align:start position:0%
+expected number of steps it takes in
+order to get back to nine once you are
+
+ align:start position:0%
+order to get back to nine once you are
+ 
+
+ align:start position:0%
+order to get back to nine once you are
+in nine and this is what we mean by the
+
+ align:start position:0%
+in nine and this is what we mean by the
+ 
+
+ align:start position:0%
+in nine and this is what we mean by the
+mean recurrence time of s and
+
+ align:start position:0%
+mean recurrence time of s and
+ 
+
+ align:start position:0%
+mean recurrence time of s and
+mathematically this is what it is it is
+
+ align:start position:0%
+mathematically this is what it is it is
+ 
+
+ align:start position:0%
+mathematically this is what it is it is
+almost the same formula as the one that
+
+ align:start position:0%
+almost the same formula as the one that
+ 
+
+ align:start position:0%
+almost the same formula as the one that
+you had here except that here you have n
+
+ align:start position:0%
+you had here except that here you have n
+ 
+
+ align:start position:0%
+you had here except that here you have n
+greater than equals to one as opposed to
+
+ align:start position:0%
+greater than equals to one as opposed to
+ 
+
+ align:start position:0%
+greater than equals to one as opposed to
+n greater than equal to zero it simply
+
+ align:start position:0%
+n greater than equal to zero it simply
+ 
+
+ align:start position:0%
+n greater than equal to zero it simply
+means that you are not interested in the
+
+ align:start position:0%
+means that you are not interested in the
+ 
+
+ align:start position:0%
+means that you are not interested in the
+first time that joini is because you
+
+ align:start position:0%
+first time that joini is because you
+ 
+
+ align:start position:0%
+first time that joini is because you
+start from s so you want to have and
+
+ align:start position:0%
+start from s so you want to have and
+ 
+
+ align:start position:0%
+start from s so you want to have and
+greater than equals to one N equals zero
+
+ align:start position:0%
+greater than equals to one N equals zero
+ 
+
+ align:start position:0%
+greater than equals to one N equals zero
+that work tsf star would have been zero
+
+ align:start position:0%
+that work tsf star would have been zero
+ 
+
+ align:start position:0%
+that work tsf star would have been zero
+so how would you solve that problem well
+
+ align:start position:0%
+so how would you solve that problem well
+ 
+
+ align:start position:0%
+so how would you solve that problem well
+here again you use the same trick that
+
+ align:start position:0%
+here again you use the same trick that
+ 
+
+ align:start position:0%
+here again you use the same trick that
+we use before and think in terms of tree
+
+ align:start position:0%
+we use before and think in terms of tree
+ 
+
+ align:start position:0%
+we use before and think in terms of tree
+let's look at the mock of chain in state
+
+ align:start position:0%
+let's look at the mock of chain in state
+ 
+
+ align:start position:0%
+let's look at the mock of chain in state
+nine what can happen next from nine it
+
+ align:start position:0%
+nine what can happen next from nine it
+ 
+
+ align:start position:0%
+nine what can happen next from nine it
+can go to three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or it can go to five or it can jump on
+
+ align:start position:0%
+or it can go to five or it can jump on
+ 
+
+ align:start position:0%
+or it can go to five or it can jump on
+itself so this is what the part is you
+
+ align:start position:0%
+itself so this is what the part is you
+ 
+
+ align:start position:0%
+itself so this is what the part is you
+point to this is where the priority 0.2
+
+ align:start position:0%
+point to this is where the priority 0.2
+ 
+
+ align:start position:0%
+point to this is where the priority 0.2
+and this is who the priority of 0.6 and
+
+ align:start position:0%
+and this is who the priority of 0.6 and
+ 
+
+ align:start position:0%
+and this is who the priority of 0.6 and
+now after you make one transition so
+
+ align:start position:0%
+now after you make one transition so
+ 
+
+ align:start position:0%
+now after you make one transition so
+that you are in three now what is the
+
+ align:start position:0%
+that you are in three now what is the
+ 
+
+ align:start position:0%
+that you are in three now what is the
+time to get to nine
+
+ align:start position:0%
+time to get to nine
+ 
+
+ align:start position:0%
+time to get to nine
+well it's exactly T three where the T is
+
+ align:start position:0%
+well it's exactly T three where the T is
+ 
+
+ align:start position:0%
+well it's exactly T three where the T is
+the solution here of that previous
+
+ align:start position:0%
+the solution here of that previous
+ 
+
+ align:start position:0%
+the solution here of that previous
+system what about from 5g5
+
+ align:start position:0%
+system what about from 5g5
+ 
+
+ align:start position:0%
+system what about from 5g5
+and what about from nine forty nine
+
+ align:start position:0%
+and what about from nine forty nine
+ 
+
+ align:start position:0%
+and what about from nine forty nine
+ninety nine was zero so from that tree
+
+ align:start position:0%
+ninety nine was zero so from that tree
+ 
+
+ align:start position:0%
+ninety nine was zero so from that tree
+what you have is T nine star will be
+
+ align:start position:0%
+what you have is T nine star will be
+ 
+
+ align:start position:0%
+what you have is T nine star will be
+zero point two times T three plus zero
+
+ align:start position:0%
+zero point two times T three plus zero
+ 
+
+ align:start position:0%
+zero point two times T three plus zero
+point six times T five plus zero point
+
+ align:start position:0%
+point six times T five plus zero point
+ 
+
+ align:start position:0%
+point six times T five plus zero point
+two times T 9 plus of course one because
+
+ align:start position:0%
+two times T 9 plus of course one because
+ 
+
+ align:start position:0%
+two times T 9 plus of course one because
+you have done one transition where again
+
+ align:start position:0%
+you have done one transition where again
+ 
+
+ align:start position:0%
+you have done one transition where again
+this value of T three T 5 and T nine are
+
+ align:start position:0%
+this value of T three T 5 and T nine are
+ 
+
+ align:start position:0%
+this value of T three T 5 and T nine are
+the one corresponding to this solution
+
+ align:start position:0%
+the one corresponding to this solution
+ 
+
+ align:start position:0%
+the one corresponding to this solution
+here so of course T nine is zero so what
+
+ align:start position:0%
+here so of course T nine is zero so what
+ 
+
+ align:start position:0%
+here so of course T nine is zero so what
+we have shown here that in general this
+
+ align:start position:0%
+we have shown here that in general this
+ 
+
+ align:start position:0%
+we have shown here that in general this
+is actually what you would have and this
+
+ align:start position:0%
+is actually what you would have and this
+ 
+
+ align:start position:0%
+is actually what you would have and this
+is exactly what we have written here TS
+
+ align:start position:0%
+is exactly what we have written here TS
+ 
+
+ align:start position:0%
+is exactly what we have written here TS
+f star is one plus the summation of PS G
+
+ align:start position:0%
+f star is one plus the summation of PS G
+ 
+
+ align:start position:0%
+f star is one plus the summation of PS G
+of T of G where T of j is the solution
+
+ align:start position:0%
+of T of G where T of j is the solution
+ 
+
+ align:start position:0%
+of T of G where T of j is the solution
+to this system so again you start from
+
+ align:start position:0%
+to this system so again you start from
+ 
+
+ align:start position:0%
+to this system so again you start from
+nine you have to do a transition first
+
+ align:start position:0%
+nine you have to do a transition first
+ 
+
+ align:start position:0%
+nine you have to do a transition first
+you can do a transition onto yourself
+
+ align:start position:0%
+you can do a transition onto yourself
+ 
+
+ align:start position:0%
+you can do a transition onto yourself
+you can go to three or you can go to six
+
+ align:start position:0%
+you can go to three or you can go to six
+ 
+
+ align:start position:0%
+you can go to three or you can go to six
+after that transition which counts for
+
+ align:start position:0%
+after that transition which counts for
+ 
+
+ align:start position:0%
+after that transition which counts for
+the number one here what happened is you
+
+ align:start position:0%
+the number one here what happened is you
+ 
+
+ align:start position:0%
+the number one here what happened is you
+are trying to find the solution to this
+
+ align:start position:0%
+are trying to find the solution to this
+ 
+
+ align:start position:0%
+are trying to find the solution to this
+system which is the mean first passage
+
+ align:start position:0%
+system which is the mean first passage
+ 
+
+ align:start position:0%
+system which is the mean first passage
+time from the current state where you
+
+ align:start position:0%
+time from the current state where you
+ 
+
+ align:start position:0%
+time from the current state where you
+are to nine and then when you put these
+
+ align:start position:0%
+are to nine and then when you put these
+ 
+
+ align:start position:0%
+are to nine and then when you put these
+two things together will you get the
+
+ align:start position:0%
+two things together will you get the
+ 
+
+ align:start position:0%
+two things together will you get the
+mean recurrence time of
+
+ align:start position:0%
+mean recurrence time of
+ 
+
+ align:start position:0%
+mean recurrence time of
\ No newline at end of file
diff --git a/BatYGepHsnc.txt b/BatYGepHsnc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23bcc44df6492049e64aac7cc09417d136452eac
--- /dev/null
+++ b/BatYGepHsnc.txt
@@ -0,0 +1,2854 @@
+YUFEI ZHAO: OK, we are
+still on our journey
+
+to proving Freiman theorem.
+
+Right?
+
+So we've been
+looking at some tools
+
+for analyzing sets
+of small doubling.
+
+And last time, we showed
+the following result,
+
+that if a has small doubling,
+then there exists a prime.
+
+It's not too much
+bigger than a, such
+
+that a big subset of a, of
+at least 1/8 proportion,
+
+a big subset of a is Freiman
+8-isomorphic to a subset
+
+of this small cyclic group.
+
+So last time, we developed this
+tool called of modeling lemma,
+
+so Ruzsa's modeling
+lemma that allows
+
+us to pass from a set of small
+doubling, which could have
+
+elements very spread
+out in the integers,
+
+to something that is much more
+compact, a much tighter set.
+
+That's a subset, a
+positive proportionate
+
+subset of a small cyclic group.
+
+And remember, the last time we
+defined this notion of Freiman
+
+8-isomorphic, Freiman
+isomorphism, in this case,
+
+it just means that it preserves
+partially additive structure.
+
+It preserves additive
+structure when
+
+you look at most 8-wise sums.
+
+All right.
+
+Well, this is where
+we left off last time.
+
+If you start with
+small doubling,
+
+then I can model a big
+portion of this set
+
+by a large fraction of
+a small cyclic group.
+
+All right.
+
+So now, we're in
+the setting where
+
+we are looking at some space,
+a cyclic group, for instance.
+
+And now, we have
+positive proportion,
+
+a constant proportion
+subset of that group.
+
+And we would like to extract
+some additional additive
+
+structure from this large set.
+
+And that should
+remind you of things
+
+we've discussed when we
+talked about Roth's theorem.
+
+Right?
+
+So Roth's theorem
+also had this form.
+
+If you start with Z mod n or
+in the finite field setting,
+
+and you have a constant
+proportion of the space,
+
+then you must find a three-term
+arithmetic progression.
+
+In fact, you must
+find many three-APs.
+
+So we're going to do something
+very similar, at least
+
+in spirit, here.
+
+We're starting from this large
+proportion of some space.
+
+We're going to extract a very
+large additive structure, just
+
+from the size alone.
+
+So let me begin by motivating
+it with a question.
+
+And we're going to start,
+as we've done in the past,
+
+with a finite field model, where
+things are much easier to state
+
+and to analyze.
+
+The question is, suppose
+you have a set a, which
+
+is a subset of f2 to the m.
+
+And a is an alpha proportion
+of the space where you think
+
+of alpha as some constant.
+
+Question is, OK,
+suppose this is true.
+
+And must it be the case
+that a plus a the subset--
+
+all right, so a itself,
+just because it's
+
+a large proportion of the space.
+
+So just because it's
+the 1% of the space,
+
+doesn't mean that it contains
+any large structures.
+
+It doesn't contain necessarily
+any large sub-spaces,
+
+because it could be a more
+random subset of f to the m.
+
+But there's a general principle
+in additive combinatorics
+
+or even analysis where if
+you start with a set that
+
+is quite large, and it might be
+a bit rough, a is a bit rough,
+
+it's all over the place.
+
+If you add a to itself,
+it smooths out the set.
+
+So a plus a is much
+smoother than a.
+
+And the question is, must A
+plus A contain a large subspace?
+
+And here, by "large,"
+I mean the following.
+
+Because we're looking
+at constant proportions
+
+of the entire
+space, by "large," I
+
+would also want a constant
+proportion of the entire space.
+
+So does there
+exist some subspace
+
+of bounded codimension?
+
+So if alpha is a
+constant, I want
+
+a bounded codimensional subspace
+that lives inside A plus A.
+
+It turns out the answer is no.
+
+So there exists sets that, even
+though there are very large
+
+and you add it to
+itself, it still
+
+doesn't have large subspaces.
+
+So let me give you an example.
+
+And this construction
+is called a nivo set.
+
+So let's take A sub n to be the
+set of points in F2 to the n
+
+who's Hamming weight--
+
+so Hamming weight here
+is just the number
+
+of 1's or it's a number
+of non-zero elements--
+
+number of 1's in
+x or, in general,
+
+the number of non-zero
+elements among the coordinates
+
+of x, so the number of
+non-zero coordinates.
+
+And I want the Hamming weight
+to be less than this quantity
+
+here.
+
+So visually, what
+this looks like is
+
+I'm thinking of the
+Hamming cube placed
+
+so that the all-zero
+vector is here,
+
+the all-ones vector is up there.
+
+And then it's sorted
+by Hamming weight.
+
+So this is called
+a Boolean lattice.
+
+And I'm looking at
+all the elements, A,
+
+which are within a Hamming
+ball of the 0 vector.
+
+So this is the set.
+
+It's not too hard to
+calculate the size of the set,
+
+because I'm taking everything
+with Hamming weight
+
+less than this quantity over
+here by central limit theorem.
+
+The number of elements
+in the set is of the form
+
+a constant fraction
+of the entire space,
+
+where alpha is some
+constant if c is a constant.
+
+So it has the desired size.
+
+But also, A added
+to itself consists
+
+of points in the Boolean
+cube whose Hamming weight
+
+is at most n minus c root n.
+
+And I claim that
+this sumset does not
+
+contain any subspace of
+dimension larger than n minus c
+
+root n.
+
+So this is the final claim.
+
+It's something that's, again,
+one of these linear algebraic
+
+exercises that we've actually
+seen earlier when we discussed
+
+the proof of a cap set, right,
+so the polynomial method
+
+proof of cap set.
+
+If you have a
+subspace of dimension
+
+greater than some
+quantity, then you
+
+should be able to find a
+vector in that subspace whose
+
+support has size at
+least the dimension.
+
+OK.
+
+So you see, in
+particular, we do not
+
+have any bounded codimensional
+subspaces in this A plus A.
+
+So even though the
+philosophy is roughly right
+
+that if you start with a set
+A and you add it to itself,
+
+it smooths out
+the set, it should
+
+contain-- we expect it to
+contain some large structure.
+
+That's not quite true.
+
+But what turns out to be true,
+and this is the first result
+
+that I will show today,
+is that if you add A
+
+to itself a few more
+times, that, indeed,
+
+you can get large subspaces.
+
+And this is an important step
+in a proof of Freiman's theorem.
+
+And this step is known
+as Bogolyubov's lemma.
+
+So Bogolyubov's lemma, in
+the case of F2 to the n,
+
+says that if you
+have a subset A of F2
+
+to the n of fraction alpha of
+the space, then 2A minus 2A
+
+contains a bounded codimensional
+subspace, so a very large
+
+subspace.
+
+so 2A minus 2A contains
+a subspace of codimension
+
+less than 1 over alpha squared.
+
+Here, I write 2A minus 2A
+even though we're in F2.
+
+So this is the same as 4A.
+
+But in general-- and you'll
+see later on when we do it
+
+in integers--
+
+2A minus 2A is the right
+expression to look at.
+
+So 2A minus 2A, something
+that works in every group.
+
+But for F2 to the n,
+it's the same as 4A.
+
+So the main philosophy here
+is that adding is smoothing.
+
+You start with a large
+subset of F2 to the n.
+
+It's large.
+
+Does it contain
+large structures?
+
+Not necessarily.
+
+But you add it to itself, and
+it smooths out the picture.
+
+So it has a rough spot.
+
+It smooths it out.
+
+And if you keep
+adding A to itself,
+
+it smooths it out even further.
+
+You add it to
+itself enough times,
+
+and then it will contain
+a large structure
+
+and just from the
+size of A alone.
+
+And there is a very
+similar idea, which
+
+comes up all over the
+place in analysis,
+
+is that convolutions
+are smoothing.
+
+So you start with some function
+that might be very rough.
+
+If you convolve it
+with itself and if you
+
+do it many more times,
+you get something
+
+that is much smoother.
+
+And in fact, adding
+and convolutions
+
+are almost the same things.
+
+And I'll explain
+that in a second.
+
+So this is an important idea
+to take away from all of this.
+
+So when we do these free
+analytic calculations--
+
+so there will be some free
+analytic calculations--
+
+the first time you see
+them, they might just
+
+seem like calculations.
+
+So you push the symbols around,
+and you get some inequalities.
+
+You get some answers.
+
+But that's no way to
+learn the subject.
+
+So you need to
+figure out, what is
+
+the intuition behind each step?
+
+Because when you need
+to work on it yourself,
+
+you're not just guessing the
+right symbols to put down.
+
+You have to understand
+the intuition, like why,
+
+intuitively, each inequality
+should be expected to hold?
+
+And this is an important
+idea that adding is smoothing
+
+and convolution is smoothing.
+
+All right.
+
+So let me remind you
+about convolutions.
+
+So recall, in a
+general abelian group,
+
+if I have two functions,
+f and g, on the group--
+
+so complex value functions--
+then the convolution
+
+is given by the
+following formula.
+
+So that's the convolution.
+
+And it behaves very
+well with respect
+
+to the Fourier transform.
+
+The Fourier transform
+turns convolutions
+
+into multiplications.
+
+So this means, point
+wise, I have that.
+
+Convolutions also relate to
+some sets, because if I--
+
+and this is the
+interpretation of convolutions
+
+that I want you to keep
+in mind for the purpose
+
+of additive combinatorics.
+
+If you have two
+sets, A and B, then
+
+look at the convolution
+of their indicators.
+
+It has an interpretation.
+
+So if you read out
+what this value says,
+
+then what this comes
+out to is 1 divided
+
+by the size of the group over
+the number of pairs in A and B
+
+such that their sum is x.
+
+So up to normalization,
+convolution records
+
+some sets with multiplicities.
+
+So the convolution
+tells you how many ways
+
+are there to express x in
+terms of a sum of one element
+
+from A and another
+element from B.
+
+And in particular,
+this function here
+
+is supported on the
+sumset A plus B.
+
+So this is the way that
+convolutions and sumsets
+
+are intimately
+related to each other.
+
+So that's proof
+Bogolyubov's lemma.
+
+We're going to be looking at
+this sumset, which is related
+
+to the following convolution.
+
+So let f be this convolution
+of indicators, AA minus A minus
+
+A. Of course, in
+F2 to the n, you
+
+don't need to worry
+about the minus signs.
+
+But I'll keep them there
+for future reference.
+
+Here, by what we said
+earlier, the support of f
+
+is 2A minus 2A.
+
+It's not too hard to evaluate
+the Fourier transform of f,
+
+because Fourier transform plays
+very well with convolutions.
+
+So in this case, it is the
+Fourier transform of A squared,
+
+Fourier transform
+of minus A squared.
+
+The Fourier transform of minus
+A, if you look at the formula,
+
+is the conjugate.
+
+It's a complex conjugate of
+the Fourier transform of A.
+
+So again, in F2 to the n,
+they're actually the same.
+
+But in general, it's
+the complex conjugate.
+
+So we always have
+this formula here.
+
+So we always have that.
+
+So by the Fourier
+inversion formula,
+
+we can write f in terms
+of its Fourier transform.
+
+Here, I'm using that.
+
+We're now using that.
+
+We're in F2, so that's
+what the inverse Fourier
+
+transform looks like.
+
+And so we have the
+following formula
+
+for the value of f in terms
+of the Fourier transform
+
+of the original set.
+
+OK.
+
+We want to show that f, whose
+support is the 2A minus 2A
+
+we're interested in--
+
+we want to show the
+support of f contains
+
+a large subspace, a small,
+codimensional subspace.
+
+So observe that if f has
+positive value, then--
+
+if f of x is positive,
+then x lies in its support.
+
+So we just want to
+find a large subspace
+
+on which f is positive.
+
+But we can choose our
+subspace by looking
+
+at Fourier coefficients
+according to their size.
+
+So what we can do is let R
+be the set of, essentially,
+
+Fourier characters whose
+corresponding value
+
+in the Fourier
+transform is large.
+
+So it's at least
+alpha to the 3/2.
+
+And that value
+will come up later.
+
+So let's look at
+this R. And what
+
+we're going to do is
+we're going to look
+
+at the orthogonal
+complement of R
+
+and show that f is positive on
+the orthogonal complement of R.
+
+First, R is not too large.
+
+The size of R is, I claim,
+less than 1 over alpha squared.
+
+Why's that?
+
+So this is an important
+trick that we've
+
+seen a few times before.
+
+The number of large Fourier
+coefficients cannot be too
+
+large, because they're Parseval,
+which tells us that the sum
+
+of the squares of the Fourier
+coefficients is equal to the L2
+
+norm of the original
+function, which, in this case,
+
+is just the density
+of A. So that's alpha.
+
+So just looking at that, the
+number of large terms cannot be
+
+too many.
+
+OK.
+
+So we have this small set, R,
+on which f has large Fourier
+
+transform values.
+
+Now, let's look at f of x.
+
+So let's look at f of x.
+
+We want to find out, when
+can we control f of x
+
+to make sure it is positive?
+
+Well, for the values of r--
+
+little r-- not in big R or
+0, we see that the Fourier
+
+transform--
+
+we would like to upper bound
+this quantity here so that this
+
+is negligible.
+
+This is a small term.
+
+Again, this is a
+computation that we've
+
+seen several times
+earlier in this course.
+
+All of these terms are small.
+
+So I want to show that
+the whole sum is small.
+
+I don't want to bound each term
+individually and then sum up
+
+all the possible contributions.
+
+That will be too big.
+
+But we've seen this trick
+before where we just take out
+
+some subset of the factors.
+
+So in particular, I'll
+take out two of the factors
+
+and get alpha cubed upper bound
+plus the remaining factors.
+
+And once again, use Parseval
+on this very last sum,
+
+keeping in mind that
+I'm throwing away
+
+some of the r's, including 0.
+
+So it will be a
+strict inequality.
+
+OK.
+
+Yeah.
+
+So this step should be
+reminiscent of very similar
+
+computations that we did in
+the proof of Roth's theorem.
+
+So if x lies in the orthogonal
+complement of uppercase R, then
+
+f of x--
+
+well, let's evaluate f of x from
+the Fourier inversion formula.
+
+We have this.
+
+So I can now split the sum as
+the 0-th term, the large terms.
+
+Now, you see, for
+the large terms,
+
+because we're in the
+orthogonal complement of A,
+
+I can make sure that they all
+come with a positive sign.
+
+And finally, the small terms.
+
+And you see that the main
+term is alpha to the 4.
+
+This term is always
+non-negative.
+
+And the error terms,
+the small terms,
+
+are strictly less than alpha
+to the 4th in magnitude.
+
+So as a result, this
+whole sum is positive.
+
+Yeah.
+
+AUDIENCE: These 1's are
+also 1 sub A's, right?
+
+YUFEI ZHAO: Thank you.
+
+The 1's are 1 sub A's.
+
+Yeah.
+
+So this is the very
+similar philosophy
+
+to when we proved
+Roth's theorem.
+
+We look at a sum like this,
+so some trigonometric series,
+
+some Fourier series.
+
+And we decompose it
+into several terms
+
+based on how large their
+Fourier coefficients are.
+
+We can control the small ones
+using what essentially amounts
+
+to a counting lemma and show
+that the small ones cannot ever
+
+annihilate the large,
+dominant terms.
+
+So as a result, f
+of x is positive
+
+on the orthogonal
+complement of R.
+
+So thus R lies in
+the support of f,
+
+which is equal to 2A minus 2A.
+
+And furthermore, the
+codimension of R is at most--
+
+so it could be some
+linear dependencies--
+
+is at most the size of R,
+which is strictly less than 1
+
+over alpha squared.
+
+And that proves
+Bogolyubov's lemma.
+
+So if you have a large
+subset of F2 to the n,
+
+you add it to
+itself enough times
+
+so that it's a
+smoothing operation.
+
+And then eventually, you
+must find a large structure.
+
+And we only start by
+assuming the size of it.
+
+If it's just large
+enough, then we
+
+can find a large structure
+within this iterated sumset.
+
+Any questions?
+
+Yeah?
+
+AUDIENCE: Isn't R in
+support of R [INAUDIBLE]??
+
+YUFEI ZHAO: Sorry, come again?
+
+AUDIENCE: You got that the
+orthogonal complement of R--
+
+YUFEI ZHAO: Sorry.
+
+The orthogonal complement
+of R is in the support.
+
+Yeah.
+
+So R lives in the
+character space.
+
+OK, great.
+
+So this is the proof
+of Bogolyubov's lemma
+
+in the finite field
+setting, working
+
+in F2 to the n, which is fine.
+
+It's a useful setting as a
+playground for us to work in.
+
+But ultimately, we
+want to understand
+
+what happens in the integers.
+
+So if you look at where
+we left off last time,
+
+we started in the
+cyclic group, Z mod n.
+
+So we would like to know how
+to formulate a similar result
+
+but in the cyclic group where
+there are no more subspaces.
+
+We encountered a
+similar situation,
+
+although we didn't
+go into it, when
+
+we discussed Roth's theorem.
+
+In the first proof
+of Roth's theorem
+
+that we showed, in the
+first Fourier analytic proof
+
+in the finite field
+setting, the proof
+
+won by restricting to
+subspaces, to hyperplanes.
+
+And then we keep on iterating
+by restricting to hyperplanes.
+
+So you can stay in subspaces.
+
+And the finite field setting
+has lots of subspaces.
+
+And we said that to get that
+proof to work in the integers,
+
+we had to do
+something different.
+
+And we did something by
+restricting to intervals.
+
+But I also mentioned
+that, somehow, that's
+
+not the natural
+analog of subspaces.
+
+The natural analog of subspaces
+is something called a Bohr set.
+
+And so I want to explore
+this idea further now.
+
+So the natural analog
+of subspaces in Z mod n
+
+are these objects
+called Bohr sets.
+
+And they're defined as follows.
+
+So suppose you are given
+some R, a subset of Z mod n.
+
+We define a Bohr set,
+denoted like this, so
+
+Bohr of R and epsilon, to
+be the subset of Z mod n,
+
+so including elements
+x, such that rx
+
+is pretty close to
+a multiple of n.
+
+So here, we're looking
+at the R mod Z norm.
+
+So this is the distance to
+the closest integer such
+
+that this fraction is very close
+to an integer for all little r
+
+and big R. You see, this
+is the analog of subspaces,
+
+because in the finite field
+setting, the finite field
+
+vector space, even if I
+set epsilon to equal to 0
+
+and turn this into
+an inner product,
+
+then Bohr sets are exactly
+subspaces-- namely,
+
+the orthogonal
+complement of the set R.
+
+But now we're in the integers,
+where you don't have exact 0.
+
+But I just want that quantity,
+that norm, to be small enough.
+
+So let me give you some names.
+
+So given the Bohr set,
+which, technically
+
+speaking, is more
+than just the set
+
+itself but also includes the
+information of R and epsilon--
+
+so it's the entire data
+written on the board--
+
+we call the size of the R
+the dimension of the Bohr set
+
+and epsilon, the width.
+
+Bogolyubov's lemma for Z mod n
+now takes the following form.
+
+If you start with a subset A of
+Z mod n, and all I need to know
+
+is that A is a constant
+fraction of the cyclic group,
+
+then the iterated
+sumset 2A minus 2A
+
+contains some Bohr
+set Bohr R of 1/4
+
+with the size of R less
+than 1 over alpha squared.
+
+So earlier, we said that if
+you have a large subset of F2
+
+to the n, then 2A minus 2A
+contains a large subspace.
+
+And now we say that
+if A is a large subset
+
+of the cyclic group,
+then 2A minus 2A
+
+contains a large Bohr
+set of small dimension.
+
+And so this terminology
+may be slightly confusing.
+
+The dimension corresponds
+to codimension previously.
+
+So if you do this
+translation, this dimension--
+
+I mean, if R were a set
+of independent vectors
+
+and you have 2 to
+the n, then that'll
+
+be the codimension of the
+corresponding subspace.
+
+But this is the terminology
+that we're stuck with.
+
+OK.
+
+Any questions about
+the statement?
+
+You see, even the bounds are
+exactly the same, 1 over alpha
+
+squared.
+
+And I mean, the
+proof is going to be
+
+pretty much exactly
+the same once you
+
+make the correct
+notational modifications.
+
+So we're going to do that.
+
+So I'm going to write on
+top of this earlier proof
+
+and show you what are the
+notational modifications so
+
+that you can get exactly
+the same result here
+
+but with Bohr sets
+instead of a subspace.
+
+The thing to keep in mind
+is that we have a somewhat
+
+different Fourier transform.
+
+So let me now use
+different colored chalk.
+
+So the Fourier transform of
+a function f from Z mod n,
+
+so a complex value,
+is a function
+
+also on Z mod n defined by f
+hat of r equal to expectation
+
+over x in Z mod n of
+f of x times omega
+
+to the minus rx, where omega
+is a primitive n root of unity.
+
+And you also had the
+Fourier inversion formula.
+
+It's what you expect.
+
+I won't bother writing it down.
+
+So we go back to the proof.
+
+And pretty much everything
+will read exactly the same.
+
+So f is still the same f.
+
+And the Fourier transform
+has the same property.
+
+So all of these nice properties
+of the Fourier transform hold.
+
+For inversion, it's
+basically the same
+
+except that the formula
+is slightly different.
+
+So instead of minus
+1 to the r dot
+
+x, what we have now
+is omega to the rx.
+
+So here, we have
+omega to the rx.
+
+OK.
+
+Great.
+
+The next part is the
+same, where we define r.
+
+So now we define r to consist
+of elements of z mod n, whose
+
+Fourier transform is large.
+
+I can take out 0.
+
+OK.
+
+This part is still the same.
+
+It's the same calculation.
+
+Now, it's the very
+last part that needs
+
+to be just slightly changed.
+
+Where does the 1/4 come in?
+
+So where does this come in?
+
+So observe that if x is in
+the Bohr set with width 1/4,
+
+then rx divided by n is--
+
+OK, so by definition,
+all of these fractions
+
+are within the
+1/4 of an integer.
+
+And if you think about what
+happens on the unit circle,
+
+if you are within
+1/4 of the integer,
+
+then that means the
+corresponding place on the unit
+
+circle is on the
+left half circle.
+
+So in particular, the cosine
+of 2rx over n is non-negative.
+
+So it has non-negative
+real part.
+
+So now we go back to
+this part of the proof,
+
+where we're applying Fourier
+inversion formula to f of x.
+
+So we had the Fourier
+inversion formula up there.
+
+But because f of x is real,
+it's really the cosine
+
+that should come in play.
+
+It should be a cosine.
+
+And now, for the next step,
+we have no negative sign here,
+
+because this step--
+
+OK, let me just cross
+out this step over there.
+
+All of these terms,
+the terms that
+
+correspond to
+little r and big R,
+
+they have non-negative
+contribution.
+
+Whatever the contributions
+here, it's non-negative.
+
+So I cross out this term.
+
+All I'm left with
+is the main term,
+
+corresponding to the
+density, and the error term,
+
+so to speak, the minor terms,
+which is less than alpha
+
+to the 4th in absolute value.
+
+OK.
+
+So it's positive.
+
+So basically the same proof.
+
+Once you make the
+appropriate modifications,
+
+it's the same proof in Z mod n.
+
+OK, great.
+
+So this concludes our discussion
+of Bogolyubov's lemma.
+
+So it says that--
+
+OK, so continuing
+our previous thread,
+
+we start with a subset of z
+mod n of constant proportion.
+
+Then 2A minus 2A necessarily
+contains a large Bohr set.
+
+And the next thing I want to do
+is to start with this Bohr set.
+
+So that's the definition
+of a Bohr set.
+
+But what does it look like?
+
+So it's a bit hard to imagine.
+
+So what does it look like?
+
+In the finite field setting,
+we know it's a subspace.
+
+But in the Z mod n
+setting, right now, it's
+
+just some subset of Z mod n.
+
+OK, so in the next
+step, we want to extract
+
+some geometric structure
+from this Bohr set.
+
+So we're going to
+show that this Bohr
+
+set will contain a large,
+generalized arithmetic
+
+progression.
+
+So you asked something
+earlier about--
+
+something seems a bit fishy
+about the general strategy.
+
+Seems like our
+goal for proving--
+
+we want to prove
+Freiman's theorem, which
+
+says that the
+conclusion is that A
+
+is contained in some GAP,
+some fairly compact additive
+
+structure.
+
+And we're already
+losing quite a bit.
+
+So we pass down
+to 1/8 of A. So it
+
+seems like even if
+you contain the rest,
+
+even if you can contain this
+fraction, this large fraction
+
+of A, what are you going
+to do about the rest of A?
+
+That's an unanswered question.
+
+A second unanswered
+question-- so right now,
+
+what I've told you,
+the strategy is
+
+we're going to find a large
+GAP inside 2A minus 2A,
+
+which is not quite the
+thing that we want to do.
+
+We want to contain
+A in a small GAP.
+
+But at least it's
+some progress, right?
+
+It's some progress to
+find some structure.
+
+I mean, the name of
+the game is to try
+
+to find additive structure.
+
+So in the theme of
+this whole semester
+
+course is trying to understand
+the dichotomy between structure
+
+and pseudorandomness.
+
+And when you have structure,
+let's use that structure.
+
+See if you can boost
+that structure.
+
+So there will be an
+additional argument, which
+
+I will show you at the
+beginning of next lecture
+
+at the conclusion of the proof
+of Freiman's theorem, which
+
+will allow you to start with the
+structure on a small part of A,
+
+but not too small-- it's
+a constant fraction of A--
+
+and pass it up to
+the whole of A.
+
+And we've actually
+already seen a tool
+
+that allows us to do that.
+
+So I want to cover all
+of A. So last time, we
+
+did something called
+the covering lemma,
+
+Ruzsa covering
+lemma, that tells us
+
+that if you have some
+nice control on A
+
+and you can cover some
+part of A very well,
+
+then I can cover the
+entirety of A very well.
+
+So those tools
+will come in hand.
+
+I mean, so similar
+to actually how we
+
+proved Freiman's theorem in
+groups with bounded exponent.
+
+And so we're going
+to use the covering
+
+lemma to conclude the theorem.
+
+But now I want to
+get into the issue
+
+of the geometry of numbers.
+
+OK.
+
+I want to tell you
+some necessary tools
+
+that we'll need to find a
+large GAP inside 2A minus 2A.
+
+Now, it will seem like
+a bit of a digression,
+
+but we'll come back into
+additive combinatorics
+
+in a bit.
+
+So the geometry of numbers
+concerns the study of lattices.
+
+So it concerns the study of
+lattices and convex bodies.
+
+So this is a really important
+area of mathematics, especially
+
+about a century ago with
+mathematicians like Minkowski
+
+playing foundational
+roles in the subject.
+
+So number theorists were
+very interested in trying
+
+to understand how
+lattices behave.
+
+So I'll tell you some
+very classical results
+
+that we'll use for
+proving Freiman's theorem.
+
+So first, what is a lattice?
+
+So let me give you the following
+definition of a lattice in R
+
+to the d.
+
+It's a structure on a group,
+if you will, as an integer
+
+span of d independent vectors.
+
+So I start with v1
+through vd vectors
+
+that are linearly independent.
+
+And I look at
+their integer span.
+
+I think this is best
+explained with a picture.
+
+So if I have a bunch of--
+
+so here, I'm drawing
+a picture in R2.
+
+And this picture extends
+in all directions.
+
+If I start with two vectors, v1
+and v2, linearly independent,
+
+and look at their integer
+span, so that's a lattice.
+
+So that's what a lattice is.
+
+You can come up with all
+sorts of fancy definitions,
+
+like a discrete
+subgroup of R to the n.
+
+But this is what it is.
+
+So just to emphasize this
+definition for a bit--
+
+and also, one more
+definition that we'll need
+
+is the determinant of a lattice.
+
+So what's the
+determinant of a lattice?
+
+One way to define it is you
+look at these v's, and you
+
+construct a matrix with
+the v's as columns.
+
+And you evaluate the absolute
+value of this determinant.
+
+More visually, the determinant
+of a lattice is also equal
+
+to the volume of its
+fundamental parallelepiped,
+
+which is a
+parallelepiped-- well,
+
+in the two-dimensional
+case, it's a parallelogram--
+
+which is spanned by v1 and
+v2 or these v's, although you
+
+have more choices, right?
+
+So you could have
+chosen a different set
+
+of generating vectors.
+
+For example, you could have
+chosen these two vectors,
+
+and they also generate
+the same lattice.
+
+And that's also a
+fundamental parallelepiped.
+
+And they will have
+the same volume.
+
+You can make some wrong
+choices, and then they
+
+will not have the right volume.
+
+So if you had chosen
+these two, so this
+
+is not a fundamental
+parallelepiped.
+
+Great.
+
+So let me give
+you some examples.
+
+The simplest lattice is just
+the integer lattice, Zd,
+
+which has determinant 1.
+
+If I'm in the
+complex plane, which
+
+is viewed as two-dimensional
+real plane, then if I take,
+
+let's say, omega being
+the 3rd root of unity,
+
+I have a triangular lattice.
+
+And the fundamental
+parallelepiped
+
+of this lattice,
+that's one example.
+
+And you can evaluate
+its determinant
+
+as the area of
+that parallelogram.
+
+If I take two nonlinearly
+independent vectors--
+
+so for example, if
+I'm in one dimension
+
+and I look at the integer
+span of 1 and root 2,
+
+this is not a lattice.
+
+Now, the next definition
+will initially
+
+be slightly confusing.
+
+But I will explain
+it through an example
+
+or at least try to help you
+visualize what's going on.
+
+So if I give you a centrally
+symmetric convex body--
+
+"centrally symmetric" means
+that k equals to minus k.
+
+So centrally symmetric
+convex body, OK.
+
+So here, centrally
+symmetric is x in k
+
+if and only if minus x is in k.
+
+And I'm in d dimensions.
+
+Let me define the i-th
+successive minimum
+
+to be lambda i.
+
+OK, so i-th successive minimum
+of k with respect to lambda
+
+to be the infimum of all
+non-negative lambda such that
+
+the dimension of the span of the
+intersection of lambda k and--
+
+well, little o lambda
+k and the lattice--
+
+has dimension at least i.
+
+OK.
+
+So let me explain.
+
+I start with a lattice.
+
+So I start with some lattice.
+
+And I have some convex body.
+
+So this is 0, let's say.
+
+So I have some convex body,
+a centrally symmetric convex
+
+body like that.
+
+I initially could
+be bigger, as well,
+
+but that's scale it so that
+it's quite small initially.
+
+And let's consider an animation
+where I look at lambda k
+
+where k lambda goes
+from 0 to infinity.
+
+This is k.
+
+So initially, lambda
+k is very, very small.
+
+And I imagine it growing.
+
+It gets bigger and
+bigger and bigger.
+
+So it gets bigger and bigger.
+
+And let's think
+about the first time
+
+that this growing body
+hits a lattice point,
+
+a non-zero lattice point.
+
+At that point, I
+freeze the animation.
+
+And I record this vector.
+
+I record this vector where
+I've hit a lattice point.
+
+And now I continue
+the animation.
+
+It's going to keep on
+growing and growing
+
+and growing until when I
+hit a vector in a direction
+
+I haven't seen before.
+
+So it's going to keep growing.
+
+And then the next time I hit
+a vector in a new direction,
+
+I stop the animation.
+
+And I look at the other vector.
+
+So I keep growing this ball
+until I hit new vectors,
+
+keep growing this convex body.
+
+So for example, if your initial
+convex body is very elongated,
+
+if that's your k--
+
+so you keep growing, growing--
+
+you might initially
+hit that vector.
+
+And then you keep on growing it.
+
+And the next vector
+you hit might still
+
+be in the same direction.
+
+But I don't count it.
+
+I don't stop the
+animation here, because I
+
+didn't see a new direction yet.
+
+I only stop the animation
+when I see a new direction.
+
+So I keep growing until
+I see a new direction.
+
+And I stop the animation there.
+
+So think about this growing
+body, and stop in every place
+
+when you see a new direction
+contained in your lambda k.
+
+And the places where
+you stop the animations,
+
+they're the successive
+minimum of k.
+
+Yeah?
+
+AUDIENCE: Is this defined
+if i is greater than d?
+
+YUFEI ZHAO: Is this defined
+when i is greater than d?
+
+No.
+
+So you only have exactly
+d successive minimum.
+
+Now, sometimes you might
+see two new directions
+
+at the same time.
+
+That's OK.
+
+But once you exhaust
+all d directions,
+
+then there's no more new
+directions you can explore.
+
+We also consider the
+vectors that you see.
+
+So let me also call
+these so that we can--
+
+OK, so we can select
+these lattice vectors bi.
+
+I am going to use
+underscore to denote.
+
+So I'm going to use this
+underline to denote boldface.
+
+So it's a vector bi, which
+is in, basically, this.
+
+You should think of bi as
+the new vector that you see.
+
+And it will have the property
+such that b1 through bd
+
+form a basis of Rd.
+
+So I keep growing
+this convex body.
+
+When I see a vector in a new
+direction, I record lambda.
+
+And I record the vector bi.
+
+I keep on going,
+keep going, keep
+
+going until I exhaust
+all d directions.
+
+I call these b's the
+directional basis.
+
+OK.
+
+Any questions?
+
+All right.
+
+So the result from the
+geometry of numbers
+
+that we're going to
+need is something called
+
+Minkowski's second theorem.
+
+So Minkowski's
+second theorem says
+
+that if you have
+lambda, a lattice,
+
+in Rd and k, a centrally
+symmetric body, also in Rd,
+
+such that lambda
+1 through lambda
+
+d are the successive minima
+of k with respect to lambda,
+
+then one has the inequality
+lambda 1, lambda 2.
+
+So the product of
+these successive minima
+
+times the volume of k
+is upper bounded by 2
+
+to the d times the
+determinant of lambda.
+
+For example, and here is
+a very easy case of this
+
+Minkowski's second theorem, if
+your k is an axis-aligned box--
+
+namely, it is a box where the
+width in the i-th direction is
+
+2 over lambda i--
+
+so then you see that the
+successive minima of this box
+
+are exactly the lambda i's.
+
+And you can check that for--
+
+this inequality is
+actually an equality.
+
+OK.
+
+So actually, in this
+case, lambda, the lattice,
+
+is the integer lattice.
+
+Now, this is a pretty easy case
+of Minkowski's second theorem.
+
+But the general case, which
+we're not going to prove,
+
+is actually quite subtle.
+
+I mean, the proof
+itself is not so long.
+
+It's worth looking up and trying
+to see what the proof is about.
+
+But it's actually
+rather counterintuitive
+
+to think about.
+
+It's one of those theorems
+where you sit down
+
+for half an hour or an hour.
+
+You're trying to prove.
+
+You think you might have
+come up with a proof.
+
+And then on closer
+examination, it'll
+
+be very likely that you
+made some very subtle error.
+
+So it's not so easy to
+get all the details right.
+
+And we're going
+to skip the proof.
+
+But any questions
+about the statement?
+
+OK.
+
+We're going to use
+Minkowski's second theorem
+
+to show that a large Bohr
+set contains a large GAP.
+
+And specifically, we will
+prove that every Bohr
+
+set of dimension d
+and width epsilon--
+
+epsilon is between 0 and 1--
+
+in Z mod nZ contains a proper
+GAP with dimension at most d
+
+and size at least
+this quantity, which
+
+is epsilon divided by d raised
+to the power of d fraction
+
+of the cyclic group.
+
+So just to step
+back a bit and see
+
+where we're going,
+from everything
+
+that we've done earlier, we
+conclude that 2A minus 2A
+
+contains a large Bohr set.
+
+Here, epsilon is 1/4.
+
+So epsilon is a constant.
+
+And R is also going
+to be a constant.
+
+It's depending on the
+doubling constant.
+
+And this proposition
+will tell us
+
+that inside this 2A
+minus 2A, we will
+
+be able to find a very
+large, proper GAP.
+
+So "proper" means that in
+this generalized arithmetic
+
+progression, all the
+individual terms are distinct,
+
+or you don't have collisions.
+
+So you're going to find
+this proper GAP that
+
+is constant dimension
+and at least
+
+a constant fraction of the
+size of the group, so pretty
+
+large GAP.
+
+To find this GAP, we
+will set up a lattice
+
+and apply Minkowski's
+second theorem.
+
+Suppose the Bohr
+set is given by R
+
+where the individual
+elements, I'm
+
+going to denote by little
+r1 through little rd.
+
+And let uppercase lambda be
+a lattice explicitly given
+
+as follows.
+
+It consists of all points in
+Rd that are congruent mod 1
+
+to some integer multiple of the
+vector r1 over n, r2 over n,
+
+through rd over n,
+so congruent mod 1.
+
+So for example, in two
+dimensions, which is all
+
+I can draw on the board,
+if r1 and r2 are 1 and 3
+
+and n equals to
+5, then basically,
+
+what we're going to have is
+a refinement of the integer
+
+lattice, where this box is
+going to be the integer lattice.
+
+And I'm going to tell you some
+additional lattice vectors.
+
+And here, it's going to repeat,
+or it's going to tile all over.
+
+So I start with 1, 3.
+
+And I look at multiples of it.
+
+But I mod 1.
+
+So I would end up with these
+points and then repeat it.
+
+And so you would have--
+
+so that's the lattice.
+
+So you have this
+lattice, lambda.
+
+What is the volume?
+
+What is the determinant
+of this lattice?
+
+So the determinant
+of the lattice,
+
+remember, is the volume of its
+fundamental parallelepiped.
+
+So I claim that the determinant
+is exactly 1 over n.
+
+There are a few
+ways to see this.
+
+So one is that, originally,
+I had the integer
+
+lattice as determinant 1.
+
+And now I put--
+
+instead of one point,
+I have endpoints
+
+in each original parallelepiped.
+
+So the determinant has to
+go down by a factor of n.
+
+Or you can construct an explicit
+fundamental parallelepiped
+
+like that.
+
+And then you use
+base times height.
+
+OK.
+
+We're going to apply
+Minkowski's second theorem.
+
+And I will need to tell you--
+
+I don't need the definition
+of Bohr set up there.
+
+So I want to tell you what
+to use as the convex body.
+
+The convex body that
+we're going to use
+
+is k being this box
+of width 2 epsilon.
+
+So that's the lattice.
+
+That's the convex body.
+
+And we're going to apply
+Minkowski's second theorem.
+
+So let's let little lowercase
+lambda 1 through lambda d--
+
+so n is d--
+
+be the successive minima
+of k with respect to lambda
+
+and b be the
+directional vectors,
+
+the rational basis corresponding
+to those successive minima.
+
+I claim that the
+L-infinity norm of bj
+
+is at most lambda j
+epsilon for each j.
+
+And this is basically
+because of the definition.
+
+I mean, if you look at the
+definition of successive minima
+
+and directional
+basis, this is k.
+
+I grow k, grow it by
+a factor of lambda j.
+
+And that's the first
+point when I see b sub j.
+
+So every coordinate
+of b sub j has
+
+to be at most this
+quantity in absolute value.
+
+So now let me denote
+uppercase L sub j
+
+to be 1 over lambda
+jd rounded up.
+
+And I claim that if little
+l is less than big L--
+
+lj, Lj-- then little lj--
+
+OK, so if I dilate the bj
+vector by factor little l,
+
+so if I plug it in and just
+look at these two inequalities,
+
+I obtain an upper
+bound of epsilon
+
+over d on the L-infinity
+norm of lj bj,
+
+so just looking at this bound
+here and the size of lj.
+
+And if this holds for
+all j, then summing up
+
+all of these individual
+inequalities,
+
+we find that the sum of
+these lj bj's is at most
+
+epsilon in L-infinity norm.
+
+So the point here
+is that we want
+
+to find the GAP
+in this Bohr set.
+
+And how does one
+think of a Bohr set?
+
+So it's kind of hard to
+imagine, because the Bohr set
+
+is a subset of Z mod n.
+
+But the right way to
+think about a Bohr set
+
+is in a higher dimensional lift,
+because a Bohr set is defined
+
+by looking at these numbers
+for R different values,
+
+R different coordinates.
+
+So we think of each r
+as its own coordinate.
+
+So we think of there
+being capital uppercase
+
+R many coordinates.
+
+And we want to
+consider the set of x's
+
+so that all the coordinate
+values are small.
+
+So instead of considering
+a one-dimensional picture,
+
+as we do in the Bohr sets,
+we're considering a higher
+
+dimensional or
+d-dimensional picture
+
+and then eventually
+projecting what happens up
+
+there down to this Bohr set.
+
+So what does Minkowski's
+second theorem
+
+have to do with anything?
+
+Well, once you have this higher
+dimensional lattice, what we're
+
+going to do is find a large
+lattice parallelepiped,
+
+so a large structure inside
+this higher dimensional
+
+lattice, and then
+project it down
+
+onto one-dimensional Z mod n.
+
+So this is the process of--
+
+so you already see some
+aspects of a GAP in here.
+
+So these guys,
+they're essentially
+
+the GAP that we're going
+to eventually wish to find.
+
+And right now, they live in
+this higher dimensional lattice.
+
+But we're going to pull
+them down to Z mod n.
+
+All right.
+
+Now, where do these
+b's come from?
+
+So each b sub j is congruent to
+some x sub j times this vector
+
+mod 1 where x sub
+j is an integer
+
+between 0 and uppercase N.
+
+So this inequality
+up here, star.
+
+So the i-th
+coordinate for star--
+
+"coordinate" meaning this
+is an L-infinity bound,
+
+so the i-th coordinate is
+upper bounded by epsilon.
+
+But the i-th coordinate
+bound implies
+
+that if you look at this sum
+over here times Ri divided
+
+by N, this quantity,
+whatever it is,
+
+is very close to an
+integer for each i.
+
+So the i-th coordinates
+implies this inequality,
+
+and it's true for every i.
+
+Thus what we find is
+that the GAP, which you
+
+already see in this
+formula over here--
+
+so the GAP is given like that.
+
+So this GAP is contained
+in the Bohr set.
+
+So we found a large
+structure in the lattice.
+
+But the lattice came
+from this construction,
+
+which was directly
+motivated by the Bohr set.
+
+So we find a large
+GAP in the Bohr set.
+
+Well, we haven't shown yet it
+is large or that it is proper.
+
+So we need to check
+those two things.
+
+To check that this GAP
+that we found is large,
+
+we're going to apply
+Minkowski's second theorem.
+
+Let's check GAP is large.
+
+So by Minkowski's
+second theorem,
+
+we find that the size of the
+GAP, which is, by definition,
+
+the product of these
+upper case L's--
+
+so if you look at how the
+uppercase L's is defined,
+
+you see that this
+quantity is at least 1
+
+over the product of the
+successive minima times
+
+denominator d to the d.
+
+And now we apply
+Minkowski's second.
+
+And we find that this
+quantity is at least
+
+the volume of k
+divided by 2 to the d
+
+times the determinant of the
+lattice times d to the d.
+
+But we saw what is the
+determinant of the lattice.
+
+It is 1 over N. You have
+d to the d, 2 to the d.
+
+And the volume of k,
+well, k is just that box.
+
+So the volume of k is
+2 epsilon raised to d.
+
+So putting everything
+together, we
+
+find that the size of this
+GAP is the claimed quantity.
+
+It's a constant fraction
+of the entire group.
+
+The second thing that we
+need to check is properness.
+
+So what does it
+mean to be proper?
+
+So we just want to
+know that you don't
+
+have two different
+ways of representing
+
+the same term in the GAP.
+
+So if I have the
+following congruence,
+
+so if this combination
+of the x's is
+
+congruent to a different
+combination of the x's where
+
+these little l's
+are between 1 and--
+
+OK, so I want to show-- so
+to check that it's proper--
+
+so we're in Z mod n--
+
+we just need to check
+that if this holds,
+
+then all the corresponding
+little l's must
+
+be the same as their primes.
+
+Well, if it is
+true, then setting--
+
+let's go back to the lattice--
+
+setting the vector b to
+be a vector originally
+
+that corresponds to the
+difference of these two
+
+numbers--
+
+so if we set b to be the
+difference of these two
+
+numbers, we find that, first
+of all, it lies in Z to the d,
+
+because these two numbers are
+congruent to each other mod n.
+
+And furthermore, the L-infinity
+norm of b is upper bounded by--
+
+I mean, each one of them
+has small l-infinity norm.
+
+And this is some
+number that is bounded.
+
+It's less than uppercase L.
+
+So the whole thing, this whole
+sum, the L-infinity norm,
+
+cannot be larger than
+this quantity over here,
+
+where I essentially use the
+triangle inequality to analyze
+
+this b term by term.
+
+All of these numbers
+are very small,
+
+because if you look at what we
+saw up there, so the size of b,
+
+we see that this whole
+thing is at most epsilon.
+
+And epsilon is
+strictly less than 1.
+
+So you have some vector b,
+which is an integer vector,
+
+such that all of its coordinates
+have L-infinity norms strictly
+
+less than 1.
+
+So that means that
+b is equal to 0.
+
+So b is the 0 vector.
+
+So b is a zero vector.
+
+Thus this thing
+here equals to 0.
+
+So this sum here equals to 0.
+
+And since the bi's
+form a basis, we
+
+find that the li's
+and l prime i's
+
+are equal to each
+other for all i.
+
+And this checks the
+properness of this GAP.
+
+Yeah.
+
+So this argument, it's not hard.
+
+But you need to
+check the details.
+
+So you need to wrap your
+mind around changing
+
+from working in a higher
+dimensional lattice setting
+
+to going back down to Z mod n.
+
+And the main takeaway
+here is that the right way
+
+to think about a Bohr set
+is to not stay in Z mod n
+
+but to think about what
+happens in d-dimensional space
+
+where d is the dimension
+of the Bohr set.
+
+OK.
+
+So now we have pretty
+much all the ingredients
+
+that we need to prove
+Freiman's theorem.
+
+And that's what we'll do at
+the beginning of next lecture.
+
+We'll conclude the proof
+of Freiman's theorem.
+
+And then I'll tell you also
+about an important conjecture
+
+in additive combinatorics called
+a polynomial Freiman-Ruzsa
+
+conjecture, which
+many people think
+
+is the most important
+open conjecture
+
+in additive combinatorics.
\ No newline at end of file
diff --git a/Brmq13Waa_Y.txt b/Brmq13Waa_Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4f3b726f6f01f8593f9b1565f34d1b62f4f5b09d
--- /dev/null
+++ b/Brmq13Waa_Y.txt
@@ -0,0 +1,4595 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi our lecture today is on the one hand
+
+ align:start position:0%
+hi our lecture today is on the one hand
+ 
+
+ align:start position:0%
+hi our lecture today is on the one hand
+deceptively simple on the other hand
+
+ align:start position:0%
+deceptively simple on the other hand
+ 
+
+ align:start position:0%
+deceptively simple on the other hand
+deceptively hard that from a certain
+
+ align:start position:0%
+deceptively hard that from a certain
+ 
+
+ align:start position:0%
+deceptively hard that from a certain
+point of view to talk about the
+
+ align:start position:0%
+point of view to talk about the
+ 
+
+ align:start position:0%
+point of view to talk about the
+equations of lines and planes is first
+
+ align:start position:0%
+equations of lines and planes is first
+ 
+
+ align:start position:0%
+equations of lines and planes is first
+of all uh a topic that many people say
+
+ align:start position:0%
+of all uh a topic that many people say
+ 
+
+ align:start position:0%
+of all uh a topic that many people say
+I'm not interested in studying geometry
+
+ align:start position:0%
+I'm not interested in studying geometry
+ 
+
+ align:start position:0%
+I'm not interested in studying geometry
+when are we going to get back to
+
+ align:start position:0%
+when are we going to get back to
+ 
+
+ align:start position:0%
+when are we going to get back to
+calculus this is very analogous to our
+
+ align:start position:0%
+calculus this is very analogous to our
+ 
+
+ align:start position:0%
+calculus this is very analogous to our
+problem of part one in Calculus if you
+
+ align:start position:0%
+problem of part one in Calculus if you
+ 
+
+ align:start position:0%
+problem of part one in Calculus if you
+recall where we started with analytic
+
+ align:start position:0%
+recall where we started with analytic
+ 
+
+ align:start position:0%
+recall where we started with analytic
+geometry and the question came up why do
+
+ align:start position:0%
+geometry and the question came up why do
+ 
+
+ align:start position:0%
+geometry and the question came up why do
+we need geometry when what we really
+
+ align:start position:0%
+we need geometry when what we really
+ 
+
+ align:start position:0%
+we need geometry when what we really
+wanted to study was calculus and the
+
+ align:start position:0%
+wanted to study was calculus and the
+ 
+
+ align:start position:0%
+wanted to study was calculus and the
+idea of graphs played a very important
+
+ align:start position:0%
+idea of graphs played a very important
+ 
+
+ align:start position:0%
+idea of graphs played a very important
+role in calculus we found out for
+
+ align:start position:0%
+role in calculus we found out for
+ 
+
+ align:start position:0%
+role in calculus we found out for
+example also that the relatively
+
+ align:start position:0%
+example also that the relatively
+ 
+
+ align:start position:0%
+example also that the relatively
+harmless straight line was a rather
+
+ align:start position:0%
+harmless straight line was a rather
+ 
+
+ align:start position:0%
+harmless straight line was a rather
+crucial curve namely given any curve no
+
+ align:start position:0%
+crucial curve namely given any curve no
+ 
+
+ align:start position:0%
+crucial curve namely given any curve no
+matter how random in the plane provided
+
+ align:start position:0%
+matter how random in the plane provided
+ 
+
+ align:start position:0%
+matter how random in the plane provided
+only that it was smooth we were able to
+
+ align:start position:0%
+only that it was smooth we were able to
+ 
+
+ align:start position:0%
+only that it was smooth we were able to
+approximate that curve by a sequence of
+
+ align:start position:0%
+approximate that curve by a sequence of
+ 
+
+ align:start position:0%
+approximate that curve by a sequence of
+t tent lines to various points and in a
+
+ align:start position:0%
+t tent lines to various points and in a
+ 
+
+ align:start position:0%
+t tent lines to various points and in a
+similar way one finds that planes will
+
+ align:start position:0%
+similar way one finds that planes will
+ 
+
+ align:start position:0%
+similar way one finds that planes will
+do for functions of two real variables
+
+ align:start position:0%
+do for functions of two real variables
+ 
+
+ align:start position:0%
+do for functions of two real variables
+what the equations of lines did for
+
+ align:start position:0%
+what the equations of lines did for
+ 
+
+ align:start position:0%
+what the equations of lines did for
+functions of a single real variable
+
+ align:start position:0%
+functions of a single real variable
+ 
+
+ align:start position:0%
+functions of a single real variable
+we'll as I say we'll talk about that in
+
+ align:start position:0%
+we'll as I say we'll talk about that in
+ 
+
+ align:start position:0%
+we'll as I say we'll talk about that in
+more detail as we go along the other
+
+ align:start position:0%
+more detail as we go along the other
+ 
+
+ align:start position:0%
+more detail as we go along the other
+nice part about this lesson is the fact
+
+ align:start position:0%
+nice part about this lesson is the fact
+ 
+
+ align:start position:0%
+nice part about this lesson is the fact
+that we can now take some of our Vector
+
+ align:start position:0%
+that we can now take some of our Vector
+ 
+
+ align:start position:0%
+that we can now take some of our Vector
+properties that we've learned from the
+
+ align:start position:0%
+properties that we've learned from the
+ 
+
+ align:start position:0%
+properties that we've learned from the
+past lessons and hit what I call the
+
+ align:start position:0%
+past lessons and hit what I call the
+ 
+
+ align:start position:0%
+past lessons and hit what I call the
+Home Run ball once and for all now
+
+ align:start position:0%
+Home Run ball once and for all now
+ 
+
+ align:start position:0%
+Home Run ball once and for all now
+finish off what we've started and that
+
+ align:start position:0%
+finish off what we've started and that
+ 
+
+ align:start position:0%
+finish off what we've started and that
+is in the study of three-dimensional
+
+ align:start position:0%
+is in the study of three-dimensional
+ 
+
+ align:start position:0%
+is in the study of three-dimensional
+Geometry The crucial characteristics are
+
+ align:start position:0%
+Geometry The crucial characteristics are
+ 
+
+ align:start position:0%
+Geometry The crucial characteristics are
+those building blocks called lines and
+
+ align:start position:0%
+those building blocks called lines and
+ 
+
+ align:start position:0%
+those building blocks called lines and
+planes and by finding convenient recipes
+
+ align:start position:0%
+planes and by finding convenient recipes
+ 
+
+ align:start position:0%
+planes and by finding convenient recipes
+for expressing lines and planes will be
+
+ align:start position:0%
+for expressing lines and planes will be
+ 
+
+ align:start position:0%
+for expressing lines and planes will be
+most of the way home as far as using
+
+ align:start position:0%
+most of the way home as far as using
+ 
+
+ align:start position:0%
+most of the way home as far as using
+this material is concerned again we'll
+
+ align:start position:0%
+this material is concerned again we'll
+ 
+
+ align:start position:0%
+this material is concerned again we'll
+hit mainly the Highlights today the
+
+ align:start position:0%
+hit mainly the Highlights today the
+ 
+
+ align:start position:0%
+hit mainly the Highlights today the
+remainder of the material will be
+
+ align:start position:0%
+remainder of the material will be
+ 
+
+ align:start position:0%
+remainder of the material will be
+covered I hope adequately between the
+
+ align:start position:0%
+covered I hope adequately between the
+ 
+
+ align:start position:0%
+covered I hope adequately between the
+text and the exercises at any rate then
+
+ align:start position:0%
+text and the exercises at any rate then
+ 
+
+ align:start position:0%
+text and the exercises at any rate then
+uh the lesson today is equations of
+
+ align:start position:0%
+uh the lesson today is equations of
+ 
+
+ align:start position:0%
+uh the lesson today is equations of
+lines and planes and to refresh what I
+
+ align:start position:0%
+lines and planes and to refresh what I
+ 
+
+ align:start position:0%
+lines and planes and to refresh what I
+just said before the little ratio planes
+
+ align:start position:0%
+just said before the little ratio planes
+ 
+
+ align:start position:0%
+just said before the little ratio planes
+are to surfaces what lines are two
+
+ align:start position:0%
+are to surfaces what lines are two
+ 
+
+ align:start position:0%
+are to surfaces what lines are two
+curves that we're going approximate
+
+ align:start position:0%
+curves that we're going approximate
+ 
+
+ align:start position:0%
+curves that we're going approximate
+curves by tangent lines we can
+
+ align:start position:0%
+curves by tangent lines we can
+ 
+
+ align:start position:0%
+curves by tangent lines we can
+approximate smooth surfaces by tangent
+
+ align:start position:0%
+approximate smooth surfaces by tangent
+ 
+
+ align:start position:0%
+approximate smooth surfaces by tangent
+planes now what we would like to do is
+
+ align:start position:0%
+planes now what we would like to do is
+ 
+
+ align:start position:0%
+planes now what we would like to do is
+go back to cartisian coordinates and
+
+ align:start position:0%
+go back to cartisian coordinates and
+ 
+
+ align:start position:0%
+go back to cartisian coordinates and
+find the equation of a plane the first
+
+ align:start position:0%
+find the equation of a plane the first
+ 
+
+ align:start position:0%
+find the equation of a plane the first
+question that we asked before before we
+
+ align:start position:0%
+question that we asked before before we
+ 
+
+ align:start position:0%
+question that we asked before before we
+even use a any coordinate system is just
+
+ align:start position:0%
+even use a any coordinate system is just
+ 
+
+ align:start position:0%
+even use a any coordinate system is just
+how much information do you need before
+
+ align:start position:0%
+how much information do you need before
+ 
+
+ align:start position:0%
+how much information do you need before
+you can determine a plane well one way
+
+ align:start position:0%
+you can determine a plane well one way
+ 
+
+ align:start position:0%
+you can determine a plane well one way
+we know of is to know three points in
+
+ align:start position:0%
+we know of is to know three points in
+ 
+
+ align:start position:0%
+we know of is to know three points in
+the plane another way is analogous to
+
+ align:start position:0%
+the plane another way is analogous to
+ 
+
+ align:start position:0%
+the plane another way is analogous to
+the line case where to determine a line
+
+ align:start position:0%
+the line case where to determine a line
+ 
+
+ align:start position:0%
+the line case where to determine a line
+you needed a point and a slope one way
+
+ align:start position:0%
+you needed a point and a slope one way
+ 
+
+ align:start position:0%
+you needed a point and a slope one way
+of determining a plane is to know what a
+
+ align:start position:0%
+of determining a plane is to know what a
+ 
+
+ align:start position:0%
+of determining a plane is to know what a
+point in the plane and the direction of
+
+ align:start position:0%
+point in the plane and the direction of
+ 
+
+ align:start position:0%
+point in the plane and the direction of
+the plane and one way of getting the
+
+ align:start position:0%
+the plane and one way of getting the
+ 
+
+ align:start position:0%
+the plane and one way of getting the
+direction of the plane is to fix a
+
+ align:start position:0%
+direction of the plane is to fix a
+ 
+
+ align:start position:0%
+direction of the plane is to fix a
+normal a perpendicular to the plane in
+
+ align:start position:0%
+normal a perpendicular to the plane in
+ 
+
+ align:start position:0%
+normal a perpendicular to the plane in
+other words the approach that we're
+
+ align:start position:0%
+other words the approach that we're
+ 
+
+ align:start position:0%
+other words the approach that we're
+going to use is let's suppose that we
+
+ align:start position:0%
+going to use is let's suppose that we
+ 
+
+ align:start position:0%
+going to use is let's suppose that we
+know a point that we want to be in our
+
+ align:start position:0%
+know a point that we want to be in our
+ 
+
+ align:start position:0%
+know a point that we want to be in our
+plane and we'll call that point p 0
+
+ align:start position:0%
+plane and we'll call that point p 0
+ 
+
+ align:start position:0%
+plane and we'll call that point p 0
+we'll denote it generically by x0 y0 z0
+
+ align:start position:0%
+we'll denote it generically by x0 y0 z0
+ 
+
+ align:start position:0%
+we'll denote it generically by x0 y0 z0
+and let's let capital N denote the
+
+ align:start position:0%
+and let's let capital N denote the
+ 
+
+ align:start position:0%
+and let's let capital N denote the
+vector a i plus BJ plus c k which is
+
+ align:start position:0%
+vector a i plus BJ plus c k which is
+ 
+
+ align:start position:0%
+vector a i plus BJ plus c k which is
+perpendicular to our plane okay so we're
+
+ align:start position:0%
+perpendicular to our plane okay so we're
+ 
+
+ align:start position:0%
+perpendicular to our plane okay so we're
+given a vector perpendicular to the
+
+ align:start position:0%
+given a vector perpendicular to the
+ 
+
+ align:start position:0%
+given a vector perpendicular to the
+plane we're given a point in the plane
+
+ align:start position:0%
+plane we're given a point in the plane
+ 
+
+ align:start position:0%
+plane we're given a point in the plane
+and now in cartisian coordinates we
+
+ align:start position:0%
+and now in cartisian coordinates we
+ 
+
+ align:start position:0%
+and now in cartisian coordinates we
+would like to know the equation of the
+
+ align:start position:0%
+would like to know the equation of the
+ 
+
+ align:start position:0%
+would like to know the equation of the
+plane and as we do so often we simply
+
+ align:start position:0%
+plane and as we do so often we simply
+ 
+
+ align:start position:0%
+plane and as we do so often we simply
+come back to a little diagram here that
+
+ align:start position:0%
+come back to a little diagram here that
+ 
+
+ align:start position:0%
+come back to a little diagram here that
+will utilize Vector geometry what we say
+
+ align:start position:0%
+will utilize Vector geometry what we say
+ 
+
+ align:start position:0%
+will utilize Vector geometry what we say
+is okay here's a little diagram here his
+
+ align:start position:0%
+is okay here's a little diagram here his
+ 
+
+ align:start position:0%
+is okay here's a little diagram here his
+P0 in the plane his n normal to the
+
+ align:start position:0%
+P0 in the plane his n normal to the
+ 
+
+ align:start position:0%
+P0 in the plane his n normal to the
+plane now we pick any point P whatsoever
+
+ align:start position:0%
+plane now we pick any point P whatsoever
+ 
+
+ align:start position:0%
+plane now we pick any point P whatsoever
+any point in the whole world whatsoever
+
+ align:start position:0%
+any point in the whole world whatsoever
+ 
+
+ align:start position:0%
+any point in the whole world whatsoever
+as long as long as it's in space
+
+ align:start position:0%
+as long as long as it's in space
+ 
+
+ align:start position:0%
+as long as long as it's in space
+threedimensional space and what we say
+
+ align:start position:0%
+threedimensional space and what we say
+ 
+
+ align:start position:0%
+threedimensional space and what we say
+is what does it mean for the point P to
+
+ align:start position:0%
+is what does it mean for the point P to
+ 
+
+ align:start position:0%
+is what does it mean for the point P to
+be in the plane well in Vector language
+
+ align:start position:0%
+be in the plane well in Vector language
+ 
+
+ align:start position:0%
+be in the plane well in Vector language
+for the point P to be in the
+
+ align:start position:0%
+for the point P to be in the
+ 
+
+ align:start position:0%
+for the point P to be in the
+plane I think it's rather
+
+ align:start position:0%
+plane I think it's rather
+ 
+
+ align:start position:0%
+plane I think it's rather
+obvious that p 0 P had better be
+
+ align:start position:0%
+obvious that p 0 P had better be
+ 
+
+ align:start position:0%
+obvious that p 0 P had better be
+perpendicular to n on the other hand in
+
+ align:start position:0%
+perpendicular to n on the other hand in
+ 
+
+ align:start position:0%
+perpendicular to n on the other hand in
+dot product language what does it mean
+
+ align:start position:0%
+dot product language what does it mean
+ 
+
+ align:start position:0%
+dot product language what does it mean
+to say that n is perpendicular to p 0 P
+
+ align:start position:0%
+to say that n is perpendicular to p 0 P
+ 
+
+ align:start position:0%
+to say that n is perpendicular to p 0 P
+that says that the dotproduct of N and
+
+ align:start position:0%
+that says that the dotproduct of N and
+ 
+
+ align:start position:0%
+that says that the dotproduct of N and
+P0 P must be zero now just to economize
+
+ align:start position:0%
+P0 P must be zero now just to economize
+ 
+
+ align:start position:0%
+P0 P must be zero now just to economize
+space let me utilize the notation that
+
+ align:start position:0%
+space let me utilize the notation that
+ 
+
+ align:start position:0%
+space let me utilize the notation that
+we've talked about in the notes and in
+
+ align:start position:0%
+we've talked about in the notes and in
+ 
+
+ align:start position:0%
+we've talked about in the notes and in
+the exercises where in cartisian
+
+ align:start position:0%
+the exercises where in cartisian
+ 
+
+ align:start position:0%
+the exercises where in cartisian
+coordinates I'll abbreviate a vector in
+
+ align:start position:0%
+coordinates I'll abbreviate a vector in
+ 
+
+ align:start position:0%
+coordinates I'll abbreviate a vector in
+i j and k components just by writing
+
+ align:start position:0%
+i j and k components just by writing
+ 
+
+ align:start position:0%
+i j and k components just by writing
+down its components in other words let
+
+ align:start position:0%
+down its components in other words let
+ 
+
+ align:start position:0%
+down its components in other words let
+me abbreviate n by a comma B comma C
+
+ align:start position:0%
+me abbreviate n by a comma B comma C
+ 
+
+ align:start position:0%
+me abbreviate n by a comma B comma C
+which stands for a i plus BJ plus c k
+
+ align:start position:0%
+which stands for a i plus BJ plus c k
+ 
+
+ align:start position:0%
+which stands for a i plus BJ plus c k
+Etc notice the beauty now of our
+
+ align:start position:0%
+Etc notice the beauty now of our
+ 
+
+ align:start position:0%
+Etc notice the beauty now of our
+cartisian coordinate system n is the
+
+ align:start position:0%
+cartisian coordinate system n is the
+ 
+
+ align:start position:0%
+cartisian coordinate system n is the
+vector whose components are a b and c
+
+ align:start position:0%
+vector whose components are a b and c
+ 
+
+ align:start position:0%
+vector whose components are a b and c
+what about p 0 P well that's the vector
+
+ align:start position:0%
+what about p 0 P well that's the vector
+ 
+
+ align:start position:0%
+what about p 0 P well that's the vector
+whose components are x - x0 y - y0 and Z
+
+ align:start position:0%
+whose components are x - x0 y - y0 and Z
+ 
+
+ align:start position:0%
+whose components are x - x0 y - y0 and Z
+minus z0 that beauty of cartisian
+
+ align:start position:0%
+minus z0 that beauty of cartisian
+ 
+
+ align:start position:0%
+minus z0 that beauty of cartisian
+coordinates again consequently I want
+
+ align:start position:0%
+coordinates again consequently I want
+ 
+
+ align:start position:0%
+coordinates again consequently I want
+the dotproduct of these two vectors to
+
+ align:start position:0%
+the dotproduct of these two vectors to
+ 
+
+ align:start position:0%
+the dotproduct of these two vectors to
+be zero but in cartisian coordinates we
+
+ align:start position:0%
+be zero but in cartisian coordinates we
+ 
+
+ align:start position:0%
+be zero but in cartisian coordinates we
+know that to dot two vectors we simply
+
+ align:start position:0%
+know that to dot two vectors we simply
+ 
+
+ align:start position:0%
+know that to dot two vectors we simply
+multiply corresponding components and
+
+ align:start position:0%
+multiply corresponding components and
+ 
+
+ align:start position:0%
+multiply corresponding components and
+add and that results in what a * x - x0
+
+ align:start position:0%
+add and that results in what a * x - x0
+ 
+
+ align:start position:0%
+add and that results in what a * x - x0
+plus b * y - y0 plus C * z- Z 0 = 0 by
+
+ align:start position:0%
+plus b * y - y0 plus C * z- Z 0 = 0 by
+ 
+
+ align:start position:0%
+plus b * y - y0 plus C * z- Z 0 = 0 by
+the way each of these steps is
+
+ align:start position:0%
+the way each of these steps is
+ 
+
+ align:start position:0%
+the way each of these steps is
+reversible meaning that under these
+
+ align:start position:0%
+reversible meaning that under these
+ 
+
+ align:start position:0%
+reversible meaning that under these
+given conditions the point
+
+ align:start position:0%
+given conditions the point
+ 
+
+ align:start position:0%
+given conditions the point
+XYZ is in the given plane if and only if
+
+ align:start position:0%
+XYZ is in the given plane if and only if
+ 
+
+ align:start position:0%
+XYZ is in the given plane if and only if
+this equation here is satisfied another
+
+ align:start position:0%
+this equation here is satisfied another
+ 
+
+ align:start position:0%
+this equation here is satisfied another
+way of saying that is what if we if a b
+
+ align:start position:0%
+way of saying that is what if we if a b
+ 
+
+ align:start position:0%
+way of saying that is what if we if a b
+c x0 y0 and z0 are given constants then
+
+ align:start position:0%
+c x0 y0 and z0 are given constants then
+ 
+
+ align:start position:0%
+c x0 y0 and z0 are given constants then
+a * x - x0 + B * y - y0 + C * Z - Z 0 =
+
+ align:start position:0%
+a * x - x0 + B * y - y0 + C * Z - Z 0 =
+ 
+
+ align:start position:0%
+a * x - x0 + B * y - y0 + C * Z - Z 0 =
+0 is the equation of the plane which
+
+ align:start position:0%
+0 is the equation of the plane which
+ 
+
+ align:start position:0%
+0 is the equation of the plane which
+passes through the point x0 y0
+
+ align:start position:0%
+passes through the point x0 y0
+ 
+
+ align:start position:0%
+passes through the point x0 y0
+z0 and which has the vector AI plus BJ
+
+ align:start position:0%
+z0 and which has the vector AI plus BJ
+ 
+
+ align:start position:0%
+z0 and which has the vector AI plus BJ
+plus CK as its normal vector and perhaps
+
+ align:start position:0%
+plus CK as its normal vector and perhaps
+ 
+
+ align:start position:0%
+plus CK as its normal vector and perhaps
+the easiest way to illustrate this is
+
+ align:start position:0%
+the easiest way to illustrate this is
+ 
+
+ align:start position:0%
+the easiest way to illustrate this is
+Again by means of an example let me
+
+ align:start position:0%
+Again by means of an example let me
+ 
+
+ align:start position:0%
+Again by means of an example let me
+simply write down a linear expression
+
+ align:start position:0%
+simply write down a linear expression
+ 
+
+ align:start position:0%
+simply write down a linear expression
+I'll write down 2 * x - 1 + 3 * y + 2 +
+
+ align:start position:0%
+I'll write down 2 * x - 1 + 3 * y + 2 +
+ 
+
+ align:start position:0%
+I'll write down 2 * x - 1 + 3 * y + 2 +
+4 * Z - 5 my claim is that this is the
+
+ align:start position:0%
+4 * Z - 5 my claim is that this is the
+ 
+
+ align:start position:0%
+4 * Z - 5 my claim is that this is the
+special case where a B and C are played
+
+ align:start position:0%
+special case where a B and C are played
+ 
+
+ align:start position:0%
+special case where a B and C are played
+by two 3 and four respectively x0 y0 and
+
+ align:start position:0%
+by two 3 and four respectively x0 y0 and
+ 
+
+ align:start position:0%
+by two 3 and four respectively x0 y0 and
+z0 are played by one -2 and5 the same
+
+ align:start position:0%
+z0 are played by one -2 and5 the same
+ 
+
+ align:start position:0%
+z0 are played by one -2 and5 the same
+thing as in our previous study of
+
+ align:start position:0%
+thing as in our previous study of
+ 
+
+ align:start position:0%
+thing as in our previous study of
+ordinary uh two-dimensional geometry
+
+ align:start position:0%
+ordinary uh two-dimensional geometry
+ 
+
+ align:start position:0%
+ordinary uh two-dimensional geometry
+remember that the standard form of our
+
+ align:start position:0%
+remember that the standard form of our
+ 
+
+ align:start position:0%
+remember that the standard form of our
+equation uses a minus sign consequently
+
+ align:start position:0%
+equation uses a minus sign consequently
+ 
+
+ align:start position:0%
+equation uses a minus sign consequently
+to use the equation where we see y + 2
+
+ align:start position:0%
+to use the equation where we see y + 2
+ 
+
+ align:start position:0%
+to use the equation where we see y + 2
+we should rewrite that as Yus -2 and
+
+ align:start position:0%
+we should rewrite that as Yus -2 and
+ 
+
+ align:start position:0%
+we should rewrite that as Yus -2 and
+what we're saying is that this equation
+
+ align:start position:0%
+what we're saying is that this equation
+ 
+
+ align:start position:0%
+what we're saying is that this equation
+is then what it passes through the point
+
+ align:start position:0%
+is then what it passes through the point
+ 
+
+ align:start position:0%
+is then what it passes through the point
+1 - 2
+
+ align:start position:0%
+1 - 2
+ 
+
+ align:start position:0%
+1 - 2
+5 and has as its normal the vector 2 I +
+
+ align:start position:0%
+5 and has as its normal the vector 2 I +
+ 
+
+ align:start position:0%
+5 and has as its normal the vector 2 I +
+3 J +
+
+ align:start position:0%
+3 J +
+ 
+
+ align:start position:0%
+3 J +
+4K actually this is not a very difficult
+
+ align:start position:0%
+4K actually this is not a very difficult
+ 
+
+ align:start position:0%
+4K actually this is not a very difficult
+concept cep once you try a few examples
+
+ align:start position:0%
+concept cep once you try a few examples
+ 
+
+ align:start position:0%
+concept cep once you try a few examples
+and see what's happening over here by
+
+ align:start position:0%
+and see what's happening over here by
+ 
+
+ align:start position:0%
+and see what's happening over here by
+the way uh before I go on I just want to
+
+ align:start position:0%
+the way uh before I go on I just want to
+ 
+
+ align:start position:0%
+the way uh before I go on I just want to
+make a note that I'm going to return to
+
+ align:start position:0%
+make a note that I'm going to return to
+ 
+
+ align:start position:0%
+make a note that I'm going to return to
+later on notice by the way there is
+
+ align:start position:0%
+later on notice by the way there is
+ 
+
+ align:start position:0%
+later on notice by the way there is
+nothing sacred about the right hand side
+
+ align:start position:0%
+nothing sacred about the right hand side
+ 
+
+ align:start position:0%
+nothing sacred about the right hand side
+of this equation being zero notice that
+
+ align:start position:0%
+of this equation being zero notice that
+ 
+
+ align:start position:0%
+of this equation being zero notice that
+somehow or other the really important
+
+ align:start position:0%
+somehow or other the really important
+ 
+
+ align:start position:0%
+somehow or other the really important
+factor was 2x + 3 y + 4 Z in other words
+
+ align:start position:0%
+factor was 2x + 3 y + 4 Z in other words
+ 
+
+ align:start position:0%
+factor was 2x + 3 y + 4 Z in other words
+notice that the other terms led to a
+
+ align:start position:0%
+notice that the other terms led to a
+ 
+
+ align:start position:0%
+notice that the other terms led to a
+constant which could have been
+
+ align:start position:0%
+constant which could have been
+ 
+
+ align:start position:0%
+constant which could have been
+transposed onto the right hand side of
+
+ align:start position:0%
+transposed onto the right hand side of
+ 
+
+ align:start position:0%
+transposed onto the right hand side of
+the equation and that somehow or other I
+
+ align:start position:0%
+the equation and that somehow or other I
+ 
+
+ align:start position:0%
+the equation and that somehow or other I
+can change the constant but if these
+
+ align:start position:0%
+can change the constant but if these
+ 
+
+ align:start position:0%
+can change the constant but if these
+multipliers in front the two three and
+
+ align:start position:0%
+multipliers in front the two three and
+ 
+
+ align:start position:0%
+multipliers in front the two three and
+four stay the same see notice what I'm
+
+ align:start position:0%
+four stay the same see notice what I'm
+ 
+
+ align:start position:0%
+four stay the same see notice what I'm
+driving at here no matter how I let me
+
+ align:start position:0%
+driving at here no matter how I let me
+ 
+
+ align:start position:0%
+driving at here no matter how I let me
+go back up here for a second no matter
+
+ align:start position:0%
+go back up here for a second no matter
+ 
+
+ align:start position:0%
+go back up here for a second no matter
+how I change x0 y0
+
+ align:start position:0%
+how I change x0 y0
+ 
+
+ align:start position:0%
+how I change x0 y0
+z0 whatever plane this is it still has
+
+ align:start position:0%
+z0 whatever plane this is it still has
+ 
+
+ align:start position:0%
+z0 whatever plane this is it still has
+AI plus BJ plus CK as a normal Vector
+
+ align:start position:0%
+AI plus BJ plus CK as a normal Vector
+ 
+
+ align:start position:0%
+AI plus BJ plus CK as a normal Vector
+what I can change is what point the
+
+ align:start position:0%
+what I can change is what point the
+ 
+
+ align:start position:0%
+what I can change is what point the
+plane passes through in other words
+
+ align:start position:0%
+plane passes through in other words
+ 
+
+ align:start position:0%
+plane passes through in other words
+somehow or other if I leave a b and c
+
+ align:start position:0%
+somehow or other if I leave a b and c
+ 
+
+ align:start position:0%
+somehow or other if I leave a b and c
+fixed but I vary x0 y0 z0 I generate a
+
+ align:start position:0%
+fixed but I vary x0 y0 z0 I generate a
+ 
+
+ align:start position:0%
+fixed but I vary x0 y0 z0 I generate a
+family of parallel planes and that can
+
+ align:start position:0%
+family of parallel planes and that can
+ 
+
+ align:start position:0%
+family of parallel planes and that can
+be State restated somewhat differently
+
+ align:start position:0%
+be State restated somewhat differently
+ 
+
+ align:start position:0%
+be State restated somewhat differently
+well I guess if it wasn't somewhat
+
+ align:start position:0%
+well I guess if it wasn't somewhat
+ 
+
+ align:start position:0%
+well I guess if it wasn't somewhat
+differently that wouldn't be called
+
+ align:start position:0%
+differently that wouldn't be called
+ 
+
+ align:start position:0%
+differently that wouldn't be called
+restated would it let's just note this
+
+ align:start position:0%
+restated would it let's just note this
+ 
+
+ align:start position:0%
+restated would it let's just note this
+way for fixed a b and c ax the equation
+
+ align:start position:0%
+way for fixed a b and c ax the equation
+ 
+
+ align:start position:0%
+way for fixed a b and c ax the equation
+ax + b y + c z equals D see forget about
+
+ align:start position:0%
+ax + b y + c z equals D see forget about
+ 
+
+ align:start position:0%
+ax + b y + c z equals D see forget about
+the zero on the right hand side let DB
+
+ align:start position:0%
+the zero on the right hand side let DB
+ 
+
+ align:start position:0%
+the zero on the right hand side let DB
+an arbitrary constant what I'm saying is
+
+ align:start position:0%
+an arbitrary constant what I'm saying is
+ 
+
+ align:start position:0%
+an arbitrary constant what I'm saying is
+that this equation is a family of
+
+ align:start position:0%
+that this equation is a family of
+ 
+
+ align:start position:0%
+that this equation is a family of
+parallel planes and why is it a family
+
+ align:start position:0%
+parallel planes and why is it a family
+ 
+
+ align:start position:0%
+parallel planes and why is it a family
+of parallel planes because every plane
+
+ align:start position:0%
+of parallel planes because every plane
+ 
+
+ align:start position:0%
+of parallel planes because every plane
+in this family has as a normal Vector AI
+
+ align:start position:0%
+in this family has as a normal Vector AI
+ 
+
+ align:start position:0%
+in this family has as a normal Vector AI
+plus BJ plus CK AI plus BJ plus
+
+ align:start position:0%
+plus BJ plus CK AI plus BJ plus
+ 
+
+ align:start position:0%
+plus BJ plus CK AI plus BJ plus
+CK okay the second point I would like to
+
+ align:start position:0%
+CK okay the second point I would like to
+ 
+
+ align:start position:0%
+CK okay the second point I would like to
+emphasize about the equation of our
+
+ align:start position:0%
+emphasize about the equation of our
+ 
+
+ align:start position:0%
+emphasize about the equation of our
+plane is that it's called a linear
+
+ align:start position:0%
+plane is that it's called a linear
+ 
+
+ align:start position:0%
+plane is that it's called a linear
+equation meaning and I don't know why I
+
+ align:start position:0%
+equation meaning and I don't know why I
+ 
+
+ align:start position:0%
+equation meaning and I don't know why I
+suddenly switched to small letters here
+
+ align:start position:0%
+suddenly switched to small letters here
+ 
+
+ align:start position:0%
+suddenly switched to small letters here
+but that certainly doesn't make any
+
+ align:start position:0%
+but that certainly doesn't make any
+ 
+
+ align:start position:0%
+but that certainly doesn't make any
+difference with a b c and d is constants
+
+ align:start position:0%
+difference with a b c and d is constants
+ 
+
+ align:start position:0%
+difference with a b c and d is constants
+observe that ax + b y + C zal D is what
+
+ align:start position:0%
+observe that ax + b y + C zal D is what
+ 
+
+ align:start position:0%
+observe that ax + b y + C zal D is what
+we call a linear algebraic equation in
+
+ align:start position:0%
+we call a linear algebraic equation in
+ 
+
+ align:start position:0%
+we call a linear algebraic equation in
+the variables X Y and Z namely each one
+
+ align:start position:0%
+the variables X Y and Z namely each one
+ 
+
+ align:start position:0%
+the variables X Y and Z namely each one
+appears each variable appears multiplied
+
+ align:start position:0%
+appears each variable appears multiplied
+ 
+
+ align:start position:0%
+appears each variable appears multiplied
+only by a constant and we add these
+
+ align:start position:0%
+only by a constant and we add these
+ 
+
+ align:start position:0%
+only by a constant and we add these
+things up and notice that in a way a
+
+ align:start position:0%
+things up and notice that in a way a
+ 
+
+ align:start position:0%
+things up and notice that in a way a
+plane should be linear meaning there's
+
+ align:start position:0%
+plane should be linear meaning there's
+ 
+
+ align:start position:0%
+plane should be linear meaning there's
+no curvature to a plane once it's fixed
+
+ align:start position:0%
+no curvature to a plane once it's fixed
+ 
+
+ align:start position:0%
+no curvature to a plane once it's fixed
+in space and this sort of generalizes
+
+ align:start position:0%
+in space and this sort of generalizes
+ 
+
+ align:start position:0%
+in space and this sort of generalizes
+the idea of the line remember the
+
+ align:start position:0%
+the idea of the line remember the
+ 
+
+ align:start position:0%
+the idea of the line remember the
+general definition of a line was of the
+
+ align:start position:0%
+general definition of a line was of the
+ 
+
+ align:start position:0%
+general definition of a line was of the
+form what ax plus b y equals a constant
+
+ align:start position:0%
+form what ax plus b y equals a constant
+ 
+
+ align:start position:0%
+form what ax plus b y equals a constant
+that was a two-dimensional linear
+
+ align:start position:0%
+that was a two-dimensional linear
+ 
+
+ align:start position:0%
+that was a two-dimensional linear
+equation the plane is a
+
+ align:start position:0%
+equation the plane is a
+ 
+
+ align:start position:0%
+equation the plane is a
+three-dimensional linear equation and
+
+ align:start position:0%
+three-dimensional linear equation and
+ 
+
+ align:start position:0%
+three-dimensional linear equation and
+one of the subjects that we return to
+
+ align:start position:0%
+one of the subjects that we return to
+ 
+
+ align:start position:0%
+one of the subjects that we return to
+later in the course but I just mentioned
+
+ align:start position:0%
+later in the course but I just mentioned
+ 
+
+ align:start position:0%
+later in the course but I just mentioned
+it in passing now is that even though
+
+ align:start position:0%
+it in passing now is that even though
+ 
+
+ align:start position:0%
+it in passing now is that even though
+you can't draw in more than
+
+ align:start position:0%
+you can't draw in more than
+ 
+
+ align:start position:0%
+you can't draw in more than
+three-dimensional space if you have 15
+
+ align:start position:0%
+three-dimensional space if you have 15
+ 
+
+ align:start position:0%
+three-dimensional space if you have 15
+variables you can certainly have a
+
+ align:start position:0%
+variables you can certainly have a
+ 
+
+ align:start position:0%
+variables you can certainly have a
+linear equation in 15 unknowns and the
+
+ align:start position:0%
+linear equation in 15 unknowns and the
+ 
+
+ align:start position:0%
+linear equation in 15 unknowns and the
+interesting point in calculus of several
+
+ align:start position:0%
+interesting point in calculus of several
+ 
+
+ align:start position:0%
+interesting point in calculus of several
+variables is that even when you run out
+
+ align:start position:0%
+variables is that even when you run out
+ 
+
+ align:start position:0%
+variables is that even when you run out
+of pictures when you can't draw the
+
+ align:start position:0%
+of pictures when you can't draw the
+ 
+
+ align:start position:0%
+of pictures when you can't draw the
+situation the linear equation plays a
+
+ align:start position:0%
+situation the linear equation plays a
+ 
+
+ align:start position:0%
+situation the linear equation plays a
+very very special role in the
+
+ align:start position:0%
+very very special role in the
+ 
+
+ align:start position:0%
+very very special role in the
+development of calculus of several
+
+ align:start position:0%
+development of calculus of several
+ 
+
+ align:start position:0%
+development of calculus of several
+variables analogous to what a line does
+
+ align:start position:0%
+variables analogous to what a line does
+ 
+
+ align:start position:0%
+variables analogous to what a line does
+for a curve in the case of one variable
+
+ align:start position:0%
+for a curve in the case of one variable
+ 
+
+ align:start position:0%
+for a curve in the case of one variable
+and what a plane does for a surface in
+
+ align:start position:0%
+and what a plane does for a surface in
+ 
+
+ align:start position:0%
+and what a plane does for a surface in
+the case of two variables what I want to
+
+ align:start position:0%
+the case of two variables what I want to
+ 
+
+ align:start position:0%
+the case of two variables what I want to
+emphasize though also and we'll come
+
+ align:start position:0%
+emphasize though also and we'll come
+ 
+
+ align:start position:0%
+emphasize though also and we'll come
+back to this in very short order is that
+
+ align:start position:0%
+back to this in very short order is that
+ 
+
+ align:start position:0%
+back to this in very short order is that
+a plane has two degrees of freedom
+
+ align:start position:0%
+a plane has two degrees of freedom
+ 
+
+ align:start position:0%
+a plane has two degrees of freedom
+meaning what that in a plane observe
+
+ align:start position:0%
+meaning what that in a plane observe
+ 
+
+ align:start position:0%
+meaning what that in a plane observe
+that given the linear equation you have
+
+ align:start position:0%
+that given the linear equation you have
+ 
+
+ align:start position:0%
+that given the linear equation you have
+what one linear equation and three
+
+ align:start position:0%
+what one linear equation and three
+ 
+
+ align:start position:0%
+what one linear equation and three
+unknowns it
+
+ align:start position:0%
+unknowns it
+ 
+
+ align:start position:0%
+unknowns it
+requires that you pick two of the
+
+ align:start position:0%
+requires that you pick two of the
+ 
+
+ align:start position:0%
+requires that you pick two of the
+variables before the rest of the
+
+ align:start position:0%
+variables before the rest of the
+ 
+
+ align:start position:0%
+variables before the rest of the
+equation is determined in other words if
+
+ align:start position:0%
+equation is determined in other words if
+ 
+
+ align:start position:0%
+equation is determined in other words if
+given x + 2 y + 3 Z = 6 if I say let X
+
+ align:start position:0%
+given x + 2 y + 3 Z = 6 if I say let X
+ 
+
+ align:start position:0%
+given x + 2 y + 3 Z = 6 if I say let X
+be 15 notice that I have what 15 + 2 y +
+
+ align:start position:0%
+be 15 notice that I have what 15 + 2 y +
+ 
+
+ align:start position:0%
+be 15 notice that I have what 15 + 2 y +
+3 Z = 6 which gives me one equation in
+
+ align:start position:0%
+3 Z = 6 which gives me one equation in
+ 
+
+ align:start position:0%
+3 Z = 6 which gives me one equation in
+the two unknowns Y and Z that to
+
+ align:start position:0%
+the two unknowns Y and Z that to
+ 
+
+ align:start position:0%
+the two unknowns Y and Z that to
+actually uniquely fix anything I must
+
+ align:start position:0%
+actually uniquely fix anything I must
+ 
+
+ align:start position:0%
+actually uniquely fix anything I must
+specify what two of the three variables
+
+ align:start position:0%
+specify what two of the three variables
+ 
+
+ align:start position:0%
+specify what two of the three variables
+are in other words in this equation I
+
+ align:start position:0%
+are in other words in this equation I
+ 
+
+ align:start position:0%
+are in other words in this equation I
+can choose any two of the three
+
+ align:start position:0%
+can choose any two of the three
+ 
+
+ align:start position:0%
+can choose any two of the three
+variables at random and solve for the
+
+ align:start position:0%
+variables at random and solve for the
+ 
+
+ align:start position:0%
+variables at random and solve for the
+third by the way if anybody is having
+
+ align:start position:0%
+third by the way if anybody is having
+ 
+
+ align:start position:0%
+third by the way if anybody is having
+difficulty understanding the difference
+
+ align:start position:0%
+difficulty understanding the difference
+ 
+
+ align:start position:0%
+difficulty understanding the difference
+between the six being on the right hand
+
+ align:start position:0%
+between the six being on the right hand
+ 
+
+ align:start position:0%
+between the six being on the right hand
+side as we have it now and the zero as
+
+ align:start position:0%
+side as we have it now and the zero as
+ 
+
+ align:start position:0%
+side as we have it now and the zero as
+we used it
+
+ align:start position:0%
+we used it
+ 
+
+ align:start position:0%
+we used it
+originally notice that we can very
+
+ align:start position:0%
+originally notice that we can very
+ 
+
+ align:start position:0%
+originally notice that we can very
+quickly find a point which passes which
+
+ align:start position:0%
+quickly find a point which passes which
+ 
+
+ align:start position:0%
+quickly find a point which passes which
+is p plane passes through for example
+
+ align:start position:0%
+is p plane passes through for example
+ 
+
+ align:start position:0%
+is p plane passes through for example
+among other things just set Y and Z
+
+ align:start position:0%
+among other things just set Y and Z
+ 
+
+ align:start position:0%
+among other things just set Y and Z
+equal to zero in which case X is 6 so
+
+ align:start position:0%
+equal to zero in which case X is 6 so
+ 
+
+ align:start position:0%
+equal to zero in which case X is 6 so
+certainly one point in this plane is 6 0
+
+ align:start position:0%
+certainly one point in this plane is 6 0
+ 
+
+ align:start position:0%
+certainly one point in this plane is 6 0
+0 what is is a vector perpendicular to
+
+ align:start position:0%
+0 what is is a vector perpendicular to
+ 
+
+ align:start position:0%
+0 what is is a vector perpendicular to
+this plane it's the vector 1 I + 2 J + 3
+
+ align:start position:0%
+this plane it's the vector 1 I + 2 J + 3
+ 
+
+ align:start position:0%
+this plane it's the vector 1 I + 2 J + 3
+K so using the standard form we could
+
+ align:start position:0%
+K so using the standard form we could
+ 
+
+ align:start position:0%
+K so using the standard form we could
+write what x - 6 + 2 * y - 0 + 3 * z- 0
+
+ align:start position:0%
+write what x - 6 + 2 * y - 0 + 3 * z- 0
+ 
+
+ align:start position:0%
+write what x - 6 + 2 * y - 0 + 3 * z- 0
+= 0 notice by the way that algebraically
+
+ align:start position:0%
+= 0 notice by the way that algebraically
+ 
+
+ align:start position:0%
+= 0 notice by the way that algebraically
+these two equations are equivalent but
+
+ align:start position:0%
+these two equations are equivalent but
+ 
+
+ align:start position:0%
+these two equations are equivalent but
+that in this form this tell tells me
+
+ align:start position:0%
+that in this form this tell tells me
+ 
+
+ align:start position:0%
+that in this form this tell tells me
+what this specifies a point that the
+
+ align:start position:0%
+what this specifies a point that the
+ 
+
+ align:start position:0%
+what this specifies a point that the
+plane passes through namely what this is
+
+ align:start position:0%
+plane passes through namely what this is
+ 
+
+ align:start position:0%
+plane passes through namely what this is
+the plane that passes through 6 0 and
+
+ align:start position:0%
+the plane that passes through 6 0 and
+ 
+
+ align:start position:0%
+the plane that passes through 6 0 and
+has the vector I + 2 J + 3 K as a normal
+
+ align:start position:0%
+has the vector I + 2 J + 3 K as a normal
+ 
+
+ align:start position:0%
+has the vector I + 2 J + 3 K as a normal
+by the way you could do this in
+
+ align:start position:0%
+by the way you could do this in
+ 
+
+ align:start position:0%
+by the way you could do this in
+different ways some person might say why
+
+ align:start position:0%
+different ways some person might say why
+ 
+
+ align:start position:0%
+different ways some person might say why
+couldn't you have transposed the six
+
+ align:start position:0%
+couldn't you have transposed the six
+ 
+
+ align:start position:0%
+couldn't you have transposed the six
+over here then Taken 3 Z minus
+
+ align:start position:0%
+over here then Taken 3 Z minus
+ 
+
+ align:start position:0%
+over here then Taken 3 Z minus
+6 you see why don't you let X and Y be
+
+ align:start position:0%
+6 you see why don't you let X and Y be
+ 
+
+ align:start position:0%
+6 you see why don't you let X and Y be
+zero and solve this equation and get
+
+ align:start position:0%
+zero and solve this equation and get
+ 
+
+ align:start position:0%
+zero and solve this equation and get
+that Z = 2 in other words isn't 0 02
+
+ align:start position:0%
+that Z = 2 in other words isn't 0 02
+ 
+
+ align:start position:0%
+that Z = 2 in other words isn't 0 02
+also a point on the in the plane and the
+
+ align:start position:0%
+also a point on the in the plane and the
+ 
+
+ align:start position:0%
+also a point on the in the plane and the
+answer is yes it is and you could have
+
+ align:start position:0%
+answer is yes it is and you could have
+ 
+
+ align:start position:0%
+answer is yes it is and you could have
+written the equation now as what x - 0 +
+
+ align:start position:0%
+written the equation now as what x - 0 +
+ 
+
+ align:start position:0%
+written the equation now as what x - 0 +
+t y - 0 + 3 * Z - 2 = 0 that would be
+
+ align:start position:0%
+t y - 0 + 3 * Z - 2 = 0 that would be
+ 
+
+ align:start position:0%
+t y - 0 + 3 * Z - 2 = 0 that would be
+what the equation of the plane that
+
+ align:start position:0%
+what the equation of the plane that
+ 
+
+ align:start position:0%
+what the equation of the plane that
+passed through 0
+
+ align:start position:0%
+passed through 0
+ 
+
+ align:start position:0%
+passed through 0
+02 and had as its normal I + 2 J + 3 K
+
+ align:start position:0%
+02 and had as its normal I + 2 J + 3 K
+ 
+
+ align:start position:0%
+02 and had as its normal I + 2 J + 3 K
+of course what happened happens is that
+
+ align:start position:0%
+of course what happened happens is that
+ 
+
+ align:start position:0%
+of course what happened happens is that
+6 and 002 belong to the same plane I
+
+ align:start position:0%
+6 and 002 belong to the same plane I
+ 
+
+ align:start position:0%
+6 and 002 belong to the same plane I
+mean that's another thing to keep in
+
+ align:start position:0%
+mean that's another thing to keep in
+ 
+
+ align:start position:0%
+mean that's another thing to keep in
+mind here that the plane that we're
+
+ align:start position:0%
+mind here that the plane that we're
+ 
+
+ align:start position:0%
+mind here that the plane that we're
+talking about passes through more than
+
+ align:start position:0%
+talking about passes through more than
+ 
+
+ align:start position:0%
+talking about passes through more than
+one point so x0 y0 z0 can be played by
+
+ align:start position:0%
+one point so x0 y0 z0 can be played by
+ 
+
+ align:start position:0%
+one point so x0 y0 z0 can be played by
+an Infinity of choices at any rate let's
+
+ align:start position:0%
+an Infinity of choices at any rate let's
+ 
+
+ align:start position:0%
+an Infinity of choices at any rate let's
+let that go now as the equation of our
+
+ align:start position:0%
+let that go now as the equation of our
+ 
+
+ align:start position:0%
+let that go now as the equation of our
+plane and let's talk now about the
+
+ align:start position:0%
+plane and let's talk now about the
+ 
+
+ align:start position:0%
+plane and let's talk now about the
+equation of a line that's a plane let's
+
+ align:start position:0%
+equation of a line that's a plane let's
+ 
+
+ align:start position:0%
+equation of a line that's a plane let's
+talk about the equation of a line how do
+
+ align:start position:0%
+talk about the equation of a line how do
+ 
+
+ align:start position:0%
+talk about the equation of a line how do
+we determine a line in two-dimensional
+
+ align:start position:0%
+we determine a line in two-dimensional
+ 
+
+ align:start position:0%
+we determine a line in two-dimensional
+space we said we needed to know a point
+
+ align:start position:0%
+space we said we needed to know a point
+ 
+
+ align:start position:0%
+space we said we needed to know a point
+on the line and the slope and another
+
+ align:start position:0%
+on the line and the slope and another
+ 
+
+ align:start position:0%
+on the line and the slope and another
+way of saying that is we need to know a
+
+ align:start position:0%
+way of saying that is we need to know a
+ 
+
+ align:start position:0%
+way of saying that is we need to know a
+point on the line and we would like to
+
+ align:start position:0%
+point on the line and we would like to
+ 
+
+ align:start position:0%
+point on the line and we would like to
+know a line parallel to the given line
+
+ align:start position:0%
+know a line parallel to the given line
+ 
+
+ align:start position:0%
+know a line parallel to the given line
+in Vector language what we say is okay
+
+ align:start position:0%
+in Vector language what we say is okay
+ 
+
+ align:start position:0%
+in Vector language what we say is okay
+let's suppose we're given the line L and
+
+ align:start position:0%
+let's suppose we're given the line L and
+ 
+
+ align:start position:0%
+let's suppose we're given the line L and
+we know that the vector v whose
+
+ align:start position:0%
+we know that the vector v whose
+ 
+
+ align:start position:0%
+we know that the vector v whose
+components are a b and c that that
+
+ align:start position:0%
+components are a b and c that that
+ 
+
+ align:start position:0%
+components are a b and c that that
+Vector is parallel to L and at the point
+
+ align:start position:0%
+Vector is parallel to L and at the point
+ 
+
+ align:start position:0%
+Vector is parallel to L and at the point
+p 0 whose coordinates are x0 y0 z0 that
+
+ align:start position:0%
+p 0 whose coordinates are x0 y0 z0 that
+ 
+
+ align:start position:0%
+p 0 whose coordinates are x0 y0 z0 that
+that point is on the line L then the
+
+ align:start position:0%
+that point is on the line L then the
+ 
+
+ align:start position:0%
+that point is on the line L then the
+question is how do we find the equation
+
+ align:start position:0%
+question is how do we find the equation
+ 
+
+ align:start position:0%
+question is how do we find the equation
+of the line L and again Vector methods
+
+ align:start position:0%
+of the line L and again Vector methods
+ 
+
+ align:start position:0%
+of the line L and again Vector methods
+come to our Aid very nicely what we say
+
+ align:start position:0%
+come to our Aid very nicely what we say
+ 
+
+ align:start position:0%
+come to our Aid very nicely what we say
+is let's pick any other point p in space
+
+ align:start position:0%
+is let's pick any other point p in space
+ 
+
+ align:start position:0%
+is let's pick any other point p in space
+all right what does it mean if the point
+
+ align:start position:0%
+all right what does it mean if the point
+ 
+
+ align:start position:0%
+all right what does it mean if the point
+p is on the line L if the point p is on
+
+ align:start position:0%
+p is on the line L if the point p is on
+ 
+
+ align:start position:0%
+p is on the line L if the point p is on
+the line L since we want to use Vector
+
+ align:start position:0%
+the line L since we want to use Vector
+ 
+
+ align:start position:0%
+the line L since we want to use Vector
+methods let's simply observe that
+
+ align:start position:0%
+methods let's simply observe that
+ 
+
+ align:start position:0%
+methods let's simply observe that
+since L is parallel to V the vector p 0
+
+ align:start position:0%
+since L is parallel to V the vector p 0
+ 
+
+ align:start position:0%
+since L is parallel to V the vector p 0
+P being parallel to V must be a Scala
+
+ align:start position:0%
+P being parallel to V must be a Scala
+ 
+
+ align:start position:0%
+P being parallel to V must be a Scala
+multiple of V that's what parallel means
+
+ align:start position:0%
+multiple of V that's what parallel means
+ 
+
+ align:start position:0%
+multiple of V that's what parallel means
+for vectors Scala multiple so p 0 p is
+
+ align:start position:0%
+for vectors Scala multiple so p 0 p is
+ 
+
+ align:start position:0%
+for vectors Scala multiple so p 0 p is
+equal to some constant time V and let me
+
+ align:start position:0%
+equal to some constant time V and let me
+ 
+
+ align:start position:0%
+equal to some constant time V and let me
+pause here for a moment to point out
+
+ align:start position:0%
+pause here for a moment to point out
+ 
+
+ align:start position:0%
+pause here for a moment to point out
+that this constant is really a variable
+
+ align:start position:0%
+that this constant is really a variable
+ 
+
+ align:start position:0%
+that this constant is really a variable
+that sounds awful how can a constant be
+
+ align:start position:0%
+that sounds awful how can a constant be
+ 
+
+ align:start position:0%
+that sounds awful how can a constant be
+a variable what I mean of course is that
+
+ align:start position:0%
+a variable what I mean of course is that
+ 
+
+ align:start position:0%
+a variable what I mean of course is that
+P was any point in this line notice that
+
+ align:start position:0%
+P was any point in this line notice that
+ 
+
+ align:start position:0%
+P was any point in this line notice that
+that t determines the length of p 0 p
+
+ align:start position:0%
+that t determines the length of p 0 p
+ 
+
+ align:start position:0%
+that t determines the length of p 0 p
+and how long p 0 p is is going to depend
+
+ align:start position:0%
+and how long p 0 p is is going to depend
+ 
+
+ align:start position:0%
+and how long p 0 p is is going to depend
+on where I choose p in other words for
+
+ align:start position:0%
+on where I choose p in other words for
+ 
+
+ align:start position:0%
+on where I choose p in other words for
+different choices of p i get a different
+
+ align:start position:0%
+different choices of p i get a different
+ 
+
+ align:start position:0%
+different choices of p i get a different
+scal of multiple and by the way if I
+
+ align:start position:0%
+scal of multiple and by the way if I
+ 
+
+ align:start position:0%
+scal of multiple and by the way if I
+choose p on the wrong side of p 0 as
+
+ align:start position:0%
+choose p on the wrong side of p 0 as
+ 
+
+ align:start position:0%
+choose p on the wrong side of p 0 as
+I've deliberately done over here notice
+
+ align:start position:0%
+I've deliberately done over here notice
+ 
+
+ align:start position:0%
+I've deliberately done over here notice
+that p 0 P has the opposite sense of V
+
+ align:start position:0%
+that p 0 P has the opposite sense of V
+ 
+
+ align:start position:0%
+that p 0 P has the opposite sense of V
+so that t can even be negative in other
+
+ align:start position:0%
+so that t can even be negative in other
+ 
+
+ align:start position:0%
+so that t can even be negative in other
+words not only is t a variable but if
+
+ align:start position:0%
+words not only is t a variable but if
+ 
+
+ align:start position:0%
+words not only is t a variable but if
+it's negative it means that p 0 P has
+
+ align:start position:0%
+it's negative it means that p 0 P has
+ 
+
+ align:start position:0%
+it's negative it means that p 0 P has
+the opposite sense of V if it's positive
+
+ align:start position:0%
+the opposite sense of V if it's positive
+ 
+
+ align:start position:0%
+the opposite sense of V if it's positive
+they have the same sense but I'm not
+
+ align:start position:0%
+they have the same sense but I'm not
+ 
+
+ align:start position:0%
+they have the same sense but I'm not
+going to belay with that point what I'm
+
+ align:start position:0%
+going to belay with that point what I'm
+ 
+
+ align:start position:0%
+going to belay with that point what I'm
+now going to do is in cartisian
+
+ align:start position:0%
+now going to do is in cartisian
+ 
+
+ align:start position:0%
+now going to do is in cartisian
+coordinates see what this equation tells
+
+ align:start position:0%
+coordinates see what this equation tells
+ 
+
+ align:start position:0%
+coordinates see what this equation tells
+me and right away it tells me what that
+
+ align:start position:0%
+me and right away it tells me what that
+ 
+
+ align:start position:0%
+me and right away it tells me what that
+p 0 p is that Vector whose components
+
+ align:start position:0%
+p 0 p is that Vector whose components
+ 
+
+ align:start position:0%
+p 0 p is that Vector whose components
+are x - x 0 y - y0 and z- Z 0 what
+
+ align:start position:0%
+are x - x 0 y - y0 and z- Z 0 what
+ 
+
+ align:start position:0%
+are x - x 0 y - y0 and z- Z 0 what
+Vector is T * V well V we saw had as
+
+ align:start position:0%
+Vector is T * V well V we saw had as
+ 
+
+ align:start position:0%
+Vector is T * V well V we saw had as
+components a b and c
+
+ align:start position:0%
+components a b and c
+ 
+
+ align:start position:0%
+components a b and c
+and in cartisian coordinates multiplying
+
+ align:start position:0%
+and in cartisian coordinates multiplying
+ 
+
+ align:start position:0%
+and in cartisian coordinates multiplying
+a vector by a scalar simply multiplies
+
+ align:start position:0%
+a vector by a scalar simply multiplies
+ 
+
+ align:start position:0%
+a vector by a scalar simply multiplies
+each component by that scalar so in
+
+ align:start position:0%
+each component by that scalar so in
+ 
+
+ align:start position:0%
+each component by that scalar so in
+other words T * V is the vector whose
+
+ align:start position:0%
+other words T * V is the vector whose
+ 
+
+ align:start position:0%
+other words T * V is the vector whose
+components are TA TB and
+
+ align:start position:0%
+components are TA TB and
+ 
+
+ align:start position:0%
+components are TA TB and
+TC we also know in cartisian coordinates
+
+ align:start position:0%
+TC we also know in cartisian coordinates
+ 
+
+ align:start position:0%
+TC we also know in cartisian coordinates
+that the only way that two vectors can
+
+ align:start position:0%
+that the only way that two vectors can
+ 
+
+ align:start position:0%
+that the only way that two vectors can
+be equal is component by component and
+
+ align:start position:0%
+be equal is component by component and
+ 
+
+ align:start position:0%
+be equal is component by component and
+that tells us what that x - x0 must
+
+ align:start position:0%
+that tells us what that x - x0 must
+ 
+
+ align:start position:0%
+that tells us what that x - x0 must
+equal T * a y - y 0 must equal T * B and
+
+ align:start position:0%
+equal T * a y - y 0 must equal T * B and
+ 
+
+ align:start position:0%
+equal T * a y - y 0 must equal T * B and
+Z minus z0 must equal T * C that's these
+
+ align:start position:0%
+Z minus z0 must equal T * C that's these
+ 
+
+ align:start position:0%
+Z minus z0 must equal T * C that's these
+three equations here what do all of
+
+ align:start position:0%
+three equations here what do all of
+ 
+
+ align:start position:0%
+three equations here what do all of
+these three equations have in common
+
+ align:start position:0%
+these three equations have in common
+ 
+
+ align:start position:0%
+these three equations have in common
+numerically they all have the factor T
+
+ align:start position:0%
+numerically they all have the factor T
+ 
+
+ align:start position:0%
+numerically they all have the factor T
+and consequently I can solve each of
+
+ align:start position:0%
+and consequently I can solve each of
+ 
+
+ align:start position:0%
+and consequently I can solve each of
+these three equations for T namely what
+
+ align:start position:0%
+these three equations for T namely what
+ 
+
+ align:start position:0%
+these three equations for T namely what
+divide both sides of this equation by a
+
+ align:start position:0%
+divide both sides of this equation by a
+ 
+
+ align:start position:0%
+divide both sides of this equation by a
+both sides of this equation by B both
+
+ align:start position:0%
+both sides of this equation by B both
+ 
+
+ align:start position:0%
+both sides of this equation by B both
+sides of this equation by C being very
+
+ align:start position:0%
+sides of this equation by C being very
+ 
+
+ align:start position:0%
+sides of this equation by C being very
+careful that neither a b nor C are zero
+
+ align:start position:0%
+careful that neither a b nor C are zero
+ 
+
+ align:start position:0%
+careful that neither a b nor C are zero
+by the way if they are zero
+
+ align:start position:0%
+by the way if they are zero
+ 
+
+ align:start position:0%
+by the way if they are zero
+straightforward ramifications take place
+
+ align:start position:0%
+straightforward ramifications take place
+ 
+
+ align:start position:0%
+straightforward ramifications take place
+that we leave for the textbook to
+
+ align:start position:0%
+that we leave for the textbook to
+ 
+
+ align:start position:0%
+that we leave for the textbook to
+explain don't worry about that part
+
+ align:start position:0%
+explain don't worry about that part
+ 
+
+ align:start position:0%
+explain don't worry about that part
+right now we don't want to get bogged
+
+ align:start position:0%
+right now we don't want to get bogged
+ 
+
+ align:start position:0%
+right now we don't want to get bogged
+down in that but at any rate if we now
+
+ align:start position:0%
+down in that but at any rate if we now
+ 
+
+ align:start position:0%
+down in that but at any rate if we now
+go from here to see what that says we
+
+ align:start position:0%
+go from here to see what that says we
+ 
+
+ align:start position:0%
+go from here to see what that says we
+now wind up with the standard equation
+
+ align:start position:0%
+now wind up with the standard equation
+ 
+
+ align:start position:0%
+now wind up with the standard equation
+of the straight line
+
+ align:start position:0%
+of the straight line
+ 
+
+ align:start position:0%
+of the straight line
+namely if you have x - x0 / a = y - y y
+
+ align:start position:0%
+namely if you have x - x0 / a = y - y y
+ 
+
+ align:start position:0%
+namely if you have x - x0 / a = y - y y
+0/ b = zus z0 / C equals some constant T
+
+ align:start position:0%
+0/ b = zus z0 / C equals some constant T
+ 
+
+ align:start position:0%
+0/ b = zus z0 / C equals some constant T
+that particular form is called the
+
+ align:start position:0%
+that particular form is called the
+ 
+
+ align:start position:0%
+that particular form is called the
+standard equation for a straight line
+
+ align:start position:0%
+standard equation for a straight line
+ 
+
+ align:start position:0%
+standard equation for a straight line
+what straight line is it it's the line
+
+ align:start position:0%
+what straight line is it it's the line
+ 
+
+ align:start position:0%
+what straight line is it it's the line
+which passes through the point x0 y0
+
+ align:start position:0%
+which passes through the point x0 y0
+ 
+
+ align:start position:0%
+which passes through the point x0 y0
+z0 and is parallel to the vector a i +
+
+ align:start position:0%
+z0 and is parallel to the vector a i +
+ 
+
+ align:start position:0%
+z0 and is parallel to the vector a i +
+BJ plus c k by means of an example x -1
+
+ align:start position:0%
+BJ plus c k by means of an example x -1
+ 
+
+ align:start position:0%
+BJ plus c k by means of an example x -1
+over4 = y - 5 over3 equal Z - 6/ 7 is
+
+ align:start position:0%
+over4 = y - 5 over3 equal Z - 6/ 7 is
+ 
+
+ align:start position:0%
+over4 = y - 5 over3 equal Z - 6/ 7 is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+equation it's one equation really it's
+
+ align:start position:0%
+equation it's one equation really it's
+ 
+
+ align:start position:0%
+equation it's one equation really it's
+the equation of a line which has what
+
+ align:start position:0%
+the equation of a line which has what
+ 
+
+ align:start position:0%
+the equation of a line which has what
+property it passes through the point 1
+
+ align:start position:0%
+property it passes through the point 1
+ 
+
+ align:start position:0%
+property it passes through the point 1
+comma 5 comma 6 and is parallel to the
+
+ align:start position:0%
+comma 5 comma 6 and is parallel to the
+ 
+
+ align:start position:0%
+comma 5 comma 6 and is parallel to the
+vector 4 I + 3 J + 7 K and by the way I
+
+ align:start position:0%
+vector 4 I + 3 J + 7 K and by the way I
+ 
+
+ align:start position:0%
+vector 4 I + 3 J + 7 K and by the way I
+have to be very very on my God
+
+ align:start position:0%
+have to be very very on my God
+ 
+
+ align:start position:0%
+have to be very very on my God
+here the there's something very
+
+ align:start position:0%
+here the there's something very
+ 
+
+ align:start position:0%
+here the there's something very
+deceptive here the equation of a plane
+
+ align:start position:0%
+deceptive here the equation of a plane
+ 
+
+ align:start position:0%
+deceptive here the equation of a plane
+and a line are very very much different
+
+ align:start position:0%
+and a line are very very much different
+ 
+
+ align:start position:0%
+and a line are very very much different
+but they look enough alike so it may
+
+ align:start position:0%
+but they look enough alike so it may
+ 
+
+ align:start position:0%
+but they look enough alike so it may
+confuse you you know it reminds me of my
+
+ align:start position:0%
+confuse you you know it reminds me of my
+ 
+
+ align:start position:0%
+confuse you you know it reminds me of my
+daughter who I get a lot of stories from
+
+ align:start position:0%
+daughter who I get a lot of stories from
+ 
+
+ align:start position:0%
+daughter who I get a lot of stories from
+was eating a sandwich one day and I
+
+ align:start position:0%
+was eating a sandwich one day and I
+ 
+
+ align:start position:0%
+was eating a sandwich one day and I
+asked her what kind of a sandwich she
+
+ align:start position:0%
+asked her what kind of a sandwich she
+ 
+
+ align:start position:0%
+asked her what kind of a sandwich she
+was eating and she said it was like a
+
+ align:start position:0%
+was eating and she said it was like a
+ 
+
+ align:start position:0%
+was eating and she said it was like a
+peanut butter and jelly sandwich and I
+
+ align:start position:0%
+peanut butter and jelly sandwich and I
+ 
+
+ align:start position:0%
+peanut butter and jelly sandwich and I
+never heard of a sandwich that was like
+
+ align:start position:0%
+never heard of a sandwich that was like
+ 
+
+ align:start position:0%
+never heard of a sandwich that was like
+a peanut butter and jelly sandwich so I
+
+ align:start position:0%
+a peanut butter and jelly sandwich so I
+ 
+
+ align:start position:0%
+a peanut butter and jelly sandwich so I
+looked at it to see what it wasn't it
+
+ align:start position:0%
+looked at it to see what it wasn't it
+ 
+
+ align:start position:0%
+looked at it to see what it wasn't it
+was ham and cheese I say why did you say
+
+ align:start position:0%
+was ham and cheese I say why did you say
+ 
+
+ align:start position:0%
+was ham and cheese I say why did you say
+it was like peanut butter and jelly she
+
+ align:start position:0%
+it was like peanut butter and jelly she
+ 
+
+ align:start position:0%
+it was like peanut butter and jelly she
+said well there was two things in it all
+
+ align:start position:0%
+said well there was two things in it all
+ 
+
+ align:start position:0%
+said well there was two things in it all
+right look it the equation of a line in
+
+ align:start position:0%
+right look it the equation of a line in
+ 
+
+ align:start position:0%
+right look it the equation of a line in
+the plane have three things in it x y
+
+ align:start position:0%
+the plane have three things in it x y
+ 
+
+ align:start position:0%
+the plane have three things in it x y
+and z Z but to just to position these
+
+ align:start position:0%
+and z Z but to just to position these
+ 
+
+ align:start position:0%
+and z Z but to just to position these
+let me write down the two things that
+
+ align:start position:0%
+let me write down the two things that
+ 
+
+ align:start position:0%
+let me write down the two things that
+may look
+
+ align:start position:0%
+may look
+ 
+
+ align:start position:0%
+may look
+confusing let's suppose I write this
+
+ align:start position:0%
+confusing let's suppose I write this
+ 
+
+ align:start position:0%
+confusing let's suppose I write this
+down you see what I'm doing now what I'm
+
+ align:start position:0%
+down you see what I'm doing now what I'm
+ 
+
+ align:start position:0%
+down you see what I'm doing now what I'm
+doing now is I'm changing the equal
+
+ align:start position:0%
+doing now is I'm changing the equal
+ 
+
+ align:start position:0%
+doing now is I'm changing the equal
+signs here to plus signs and bringing up
+
+ align:start position:0%
+signs here to plus signs and bringing up
+ 
+
+ align:start position:0%
+signs here to plus signs and bringing up
+the denominators here see this is a line
+
+ align:start position:0%
+the denominators here see this is a line
+ 
+
+ align:start position:0%
+the denominators here see this is a line
+This is a plane what plane is this this
+
+ align:start position:0%
+This is a plane what plane is this this
+ 
+
+ align:start position:0%
+This is a plane what plane is this this
+is the plane which passes through the
+
+ align:start position:0%
+is the plane which passes through the
+ 
+
+ align:start position:0%
+is the plane which passes through the
+point 1 comma 5 comma 6 and has the line
+
+ align:start position:0%
+point 1 comma 5 comma 6 and has the line
+ 
+
+ align:start position:0%
+point 1 comma 5 comma 6 and has the line
+are the vector 4 i+ 3 J plus 7 K as it's
+
+ align:start position:0%
+are the vector 4 i+ 3 J plus 7 K as it's
+ 
+
+ align:start position:0%
+are the vector 4 i+ 3 J plus 7 K as it's
+normal how can I best explain this to
+
+ align:start position:0%
+normal how can I best explain this to
+ 
+
+ align:start position:0%
+normal how can I best explain this to
+you to keep this straight in your mind
+
+ align:start position:0%
+you to keep this straight in your mind
+ 
+
+ align:start position:0%
+you to keep this straight in your mind
+well I think the easiest way and again
+
+ align:start position:0%
+well I think the easiest way and again
+ 
+
+ align:start position:0%
+well I think the easiest way and again
+notice what I'm saying see the X y's and
+
+ align:start position:0%
+notice what I'm saying see the X y's and
+ 
+
+ align:start position:0%
+notice what I'm saying see the X y's and
+Z's here the X y's and Z's here which is
+
+ align:start position:0%
+Z's here the X y's and Z's here which is
+ 
+
+ align:start position:0%
+Z's here the X y's and Z's here which is
+which the easiest way is to keep track
+
+ align:start position:0%
+which the easiest way is to keep track
+ 
+
+ align:start position:0%
+which the easiest way is to keep track
+of degrees of freedom remember in the
+
+ align:start position:0%
+of degrees of freedom remember in the
+ 
+
+ align:start position:0%
+of degrees of freedom remember in the
+plane we said look at you can pick two
+
+ align:start position:0%
+plane we said look at you can pick two
+ 
+
+ align:start position:0%
+plane we said look at you can pick two
+of the variables at random and solve for
+
+ align:start position:0%
+of the variables at random and solve for
+ 
+
+ align:start position:0%
+of the variables at random and solve for
+the third I claim in this system in this
+
+ align:start position:0%
+the third I claim in this system in this
+ 
+
+ align:start position:0%
+the third I claim in this system in this
+system here there is only one degree of
+
+ align:start position:0%
+system here there is only one degree of
+ 
+
+ align:start position:0%
+system here there is only one degree of
+Freedom the line has one degree of
+
+ align:start position:0%
+Freedom the line has one degree of
+ 
+
+ align:start position:0%
+Freedom the line has one degree of
+Freedom namely let's repeat this example
+
+ align:start position:0%
+Freedom namely let's repeat this example
+ 
+
+ align:start position:0%
+Freedom namely let's repeat this example
+so we don't have to keep looking back to
+
+ align:start position:0%
+so we don't have to keep looking back to
+ 
+
+ align:start position:0%
+so we don't have to keep looking back to
+the board here x let's take x -1 over4 =
+
+ align:start position:0%
+the board here x let's take x -1 over4 =
+ 
+
+ align:start position:0%
+the board here x let's take x -1 over4 =
+y - 5 over 3 = Z - 6 over 7 and since we
+
+ align:start position:0%
+y - 5 over 3 = Z - 6 over 7 and since we
+ 
+
+ align:start position:0%
+y - 5 over 3 = Z - 6 over 7 and since we
+don't like to work with fractions I'll
+
+ align:start position:0%
+don't like to work with fractions I'll
+ 
+
+ align:start position:0%
+don't like to work with fractions I'll
+pick a number that works out
+
+ align:start position:0%
+pick a number that works out
+ 
+
+ align:start position:0%
+pick a number that works out
+nicely see I say okay let's see what
+
+ align:start position:0%
+nicely see I say okay let's see what
+ 
+
+ align:start position:0%
+nicely see I say okay let's see what
+happens when X is n now here's the whole
+
+ align:start position:0%
+happens when X is n now here's the whole
+ 
+
+ align:start position:0%
+happens when X is n now here's the whole
+point as soon as I say let x equals 9 as
+
+ align:start position:0%
+point as soon as I say let x equals 9 as
+ 
+
+ align:start position:0%
+point as soon as I say let x equals 9 as
+soon as I let x equal 9 this is
+
+ align:start position:0%
+soon as I let x equal 9 this is
+ 
+
+ align:start position:0%
+soon as I let x equal 9 this is
+fixed right in fact what does it become
+
+ align:start position:0%
+fixed right in fact what does it become
+ 
+
+ align:start position:0%
+fixed right in fact what does it become
+fixed as soon as I do this as soon as x
+
+ align:start position:0%
+fixed as soon as I do this as soon as x
+ 
+
+ align:start position:0%
+fixed as soon as I do this as soon as x
+= 9 x - 1 over 4 is 2 now notice that y
+
+ align:start position:0%
+= 9 x - 1 over 4 is 2 now notice that y
+ 
+
+ align:start position:0%
+= 9 x - 1 over 4 is 2 now notice that y
+- 5 over3 has to equal two well I have
+
+ align:start position:0%
+- 5 over3 has to equal two well I have
+ 
+
+ align:start position:0%
+- 5 over3 has to equal two well I have
+no more Choice then if y - 5 over3 has
+
+ align:start position:0%
+no more Choice then if y - 5 over3 has
+ 
+
+ align:start position:0%
+no more Choice then if y - 5 over3 has
+to equal two and also Z - 6 over 7 has
+
+ align:start position:0%
+to equal two and also Z - 6 over 7 has
+ 
+
+ align:start position:0%
+to equal two and also Z - 6 over 7 has
+to equal two you see what I'm saying
+
+ align:start position:0%
+to equal two you see what I'm saying
+ 
+
+ align:start position:0%
+to equal two you see what I'm saying
+here this fixes the fact that y must be
+
+ align:start position:0%
+here this fixes the fact that y must be
+ 
+
+ align:start position:0%
+here this fixes the fact that y must be
+11 and that Z must be 20 in other words
+
+ align:start position:0%
+11 and that Z must be 20 in other words
+ 
+
+ align:start position:0%
+11 and that Z must be 20 in other words
+the choice of xal 9 forces me to make y
+
+ align:start position:0%
+the choice of xal 9 forces me to make y
+ 
+
+ align:start position:0%
+the choice of xal 9 forces me to make y
+equal 11 and Z equal 20 one degree of
+
+ align:start position:0%
+equal 11 and Z equal 20 one degree of
+ 
+
+ align:start position:0%
+equal 11 and Z equal 20 one degree of
+freedom and by the way if you want to
+
+ align:start position:0%
+freedom and by the way if you want to
+ 
+
+ align:start position:0%
+freedom and by the way if you want to
+see this thing from a geometrical point
+
+ align:start position:0%
+see this thing from a geometrical point
+ 
+
+ align:start position:0%
+see this thing from a geometrical point
+of view what we're saying is visualize
+
+ align:start position:0%
+of view what we're saying is visualize
+ 
+
+ align:start position:0%
+of view what we're saying is visualize
+this line cutting through space all
+
+ align:start position:0%
+this line cutting through space all
+ 
+
+ align:start position:0%
+this line cutting through space all
+right notice that directly on that line
+
+ align:start position:0%
+right notice that directly on that line
+ 
+
+ align:start position:0%
+right notice that directly on that line
+only one point will have its x
+
+ align:start position:0%
+only one point will have its x
+ 
+
+ align:start position:0%
+only one point will have its x
+coordinate equal to 9 and what we're
+
+ align:start position:0%
+coordinate equal to 9 and what we're
+ 
+
+ align:start position:0%
+coordinate equal to 9 and what we're
+saying is the point on that line whose x
+
+ align:start position:0%
+saying is the point on that line whose x
+ 
+
+ align:start position:0%
+saying is the point on that line whose x
+coordinate is 9 is the point 9 comma 11
+
+ align:start position:0%
+coordinate is 9 is the point 9 comma 11
+ 
+
+ align:start position:0%
+coordinate is 9 is the point 9 comma 11
+comma 20 okay one degree of Freedom
+
+ align:start position:0%
+comma 20 okay one degree of Freedom
+ 
+
+ align:start position:0%
+comma 20 okay one degree of Freedom
+again that's very very crucial for you
+
+ align:start position:0%
+again that's very very crucial for you
+ 
+
+ align:start position:0%
+again that's very very crucial for you
+to see by the way I guess one thing that
+
+ align:start position:0%
+to see by the way I guess one thing that
+ 
+
+ align:start position:0%
+to see by the way I guess one thing that
+bothers a lot of students is the fact
+
+ align:start position:0%
+bothers a lot of students is the fact
+ 
+
+ align:start position:0%
+bothers a lot of students is the fact
+that they read this as two separate
+
+ align:start position:0%
+that they read this as two separate
+ 
+
+ align:start position:0%
+that they read this as two separate
+equations they say you know why isn't
+
+ align:start position:0%
+equations they say you know why isn't
+ 
+
+ align:start position:0%
+equations they say you know why isn't
+this x -1 over4 = y - 5 over3 why can't
+
+ align:start position:0%
+this x -1 over4 = y - 5 over3 why can't
+ 
+
+ align:start position:0%
+this x -1 over4 = y - 5 over3 why can't
+I treat that as one equation or why
+
+ align:start position:0%
+I treat that as one equation or why
+ 
+
+ align:start position:0%
+I treat that as one equation or why
+couldn't I take y - 53 = Z - 6/ 7 or why
+
+ align:start position:0%
+couldn't I take y - 53 = Z - 6/ 7 or why
+ 
+
+ align:start position:0%
+couldn't I take y - 53 = Z - 6/ 7 or why
+couldn't I take x -14 and say that's
+
+ align:start position:0%
+couldn't I take x -14 and say that's
+ 
+
+ align:start position:0%
+couldn't I take x -14 and say that's
+equal Z - 6/ 7 and the answer is that by
+
+ align:start position:0%
+equal Z - 6/ 7 and the answer is that by
+ 
+
+ align:start position:0%
+equal Z - 6/ 7 and the answer is that by
+itself isn't enough but rather than give
+
+ align:start position:0%
+itself isn't enough but rather than give
+ 
+
+ align:start position:0%
+itself isn't enough but rather than give
+you a negative answer let me give you a
+
+ align:start position:0%
+you a negative answer let me give you a
+ 
+
+ align:start position:0%
+you a negative answer let me give you a
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+one let me close today's lesson with
+
+ align:start position:0%
+one let me close today's lesson with
+ 
+
+ align:start position:0%
+one let me close today's lesson with
+this particular illustration suppose we
+
+ align:start position:0%
+this particular illustration suppose we
+ 
+
+ align:start position:0%
+this particular illustration suppose we
+had solved x -14 = y - 5 over 3 what we
+
+ align:start position:0%
+had solved x -14 = y - 5 over 3 what we
+ 
+
+ align:start position:0%
+had solved x -14 = y - 5 over 3 what we
+would have obtained is the equation 4 y
+
+ align:start position:0%
+would have obtained is the equation 4 y
+ 
+
+ align:start position:0%
+would have obtained is the equation 4 y
+- 3x = 17 now this is very dangerous
+
+ align:start position:0%
+- 3x = 17 now this is very dangerous
+ 
+
+ align:start position:0%
+- 3x = 17 now this is very dangerous
+when you look at the equation 4 y - 3x =
+
+ align:start position:0%
+when you look at the equation 4 y - 3x =
+ 
+
+ align:start position:0%
+when you look at the equation 4 y - 3x =
+17 I'll bet your dollars to Donuts you
+
+ align:start position:0%
+17 I'll bet your dollars to Donuts you
+ 
+
+ align:start position:0%
+17 I'll bet your dollars to Donuts you
+tend to think of this as a as a line
+
+ align:start position:0%
+tend to think of this as a as a line
+ 
+
+ align:start position:0%
+tend to think of this as a as a line
+rather than as a plane but the
+
+ align:start position:0%
+rather than as a plane but the
+ 
+
+ align:start position:0%
+rather than as a plane but the
+interesting thing is notice that the way
+
+ align:start position:0%
+interesting thing is notice that the way
+ 
+
+ align:start position:0%
+interesting thing is notice that the way
+we got this equation was ignoring the Z
+
+ align:start position:0%
+we got this equation was ignoring the Z
+ 
+
+ align:start position:0%
+we got this equation was ignoring the Z
+coordinate of our points and what what
+
+ align:start position:0%
+coordinate of our points and what what
+ 
+
+ align:start position:0%
+coordinate of our points and what what
+we're really saying is let's forget
+
+ align:start position:0%
+we're really saying is let's forget
+ 
+
+ align:start position:0%
+we're really saying is let's forget
+about the Z coordinate in other words 3
+
+ align:start position:0%
+about the Z coordinate in other words 3
+ 
+
+ align:start position:0%
+about the Z coordinate in other words 3
+4 y - 3x = 17 may be viewed as a line
+
+ align:start position:0%
+4 y - 3x = 17 may be viewed as a line
+ 
+
+ align:start position:0%
+4 y - 3x = 17 may be viewed as a line
+but in this particular case it's a plane
+
+ align:start position:0%
+but in this particular case it's a plane
+ 
+
+ align:start position:0%
+but in this particular case it's a plane
+in fact what plane is it it's the plane
+
+ align:start position:0%
+in fact what plane is it it's the plane
+ 
+
+ align:start position:0%
+in fact what plane is it it's the plane
+that goes through the line 3 y 4 y - 3x
+
+ align:start position:0%
+that goes through the line 3 y 4 y - 3x
+ 
+
+ align:start position:0%
+that goes through the line 3 y 4 y - 3x
+= 17 which lies in the XY plane it's the
+
+ align:start position:0%
+= 17 which lies in the XY plane it's the
+ 
+
+ align:start position:0%
+= 17 which lies in the XY plane it's the
+plane that goes through that line
+
+ align:start position:0%
+plane that goes through that line
+ 
+
+ align:start position:0%
+plane that goes through that line
+perpendicular to the XY plane the by the
+
+ align:start position:0%
+perpendicular to the XY plane the by the
+ 
+
+ align:start position:0%
+perpendicular to the XY plane the by the
+way again if you go back to part one of
+
+ align:start position:0%
+way again if you go back to part one of
+ 
+
+ align:start position:0%
+way again if you go back to part one of
+this course where we stress sets the
+
+ align:start position:0%
+this course where we stress sets the
+ 
+
+ align:start position:0%
+this course where we stress sets the
+language of sets comes to our rescue
+
+ align:start position:0%
+language of sets comes to our rescue
+ 
+
+ align:start position:0%
+language of sets comes to our rescue
+very nicely the difference between
+
+ align:start position:0%
+very nicely the difference between
+ 
+
+ align:start position:0%
+very nicely the difference between
+whether for y - 3x = 17 is a plane or
+
+ align:start position:0%
+whether for y - 3x = 17 is a plane or
+ 
+
+ align:start position:0%
+whether for y - 3x = 17 is a plane or
+whether it's a line hinges on whether
+
+ align:start position:0%
+whether it's a line hinges on whether
+ 
+
+ align:start position:0%
+whether it's a line hinges on whether
+we're talking about the set of pairs X
+
+ align:start position:0%
+we're talking about the set of pairs X
+ 
+
+ align:start position:0%
+we're talking about the set of pairs X
+comma y such that 4 y - 3x = 17 or
+
+ align:start position:0%
+comma y such that 4 y - 3x = 17 or
+ 
+
+ align:start position:0%
+comma y such that 4 y - 3x = 17 or
+whether we're talking about the set of
+
+ align:start position:0%
+whether we're talking about the set of
+ 
+
+ align:start position:0%
+whether we're talking about the set of
+triplets XYZ such that 4 y - 3x = 17 in
+
+ align:start position:0%
+triplets XYZ such that 4 y - 3x = 17 in
+ 
+
+ align:start position:0%
+triplets XYZ such that 4 y - 3x = 17 in
+this particular example we're talking
+
+ align:start position:0%
+this particular example we're talking
+ 
+
+ align:start position:0%
+this particular example we're talking
+about points in space in other words our
+
+ align:start position:0%
+about points in space in other words our
+ 
+
+ align:start position:0%
+about points in space in other words our
+universe of discourse are the points X
+
+ align:start position:0%
+universe of discourse are the points X
+ 
+
+ align:start position:0%
+universe of discourse are the points X
+comma y y comma Z not the points X comma
+
+ align:start position:0%
+comma y y comma Z not the points X comma
+ 
+
+ align:start position:0%
+comma y y comma Z not the points X comma
+y well anyway rather than to belabor
+
+ align:start position:0%
+y well anyway rather than to belabor
+ 
+
+ align:start position:0%
+y well anyway rather than to belabor
+this point what I'm saying is in the
+
+ align:start position:0%
+this point what I'm saying is in the
+ 
+
+ align:start position:0%
+this point what I'm saying is in the
+same way that this equation represents a
+
+ align:start position:0%
+same way that this equation represents a
+ 
+
+ align:start position:0%
+same way that this equation represents a
+plane in a similar way had we equated y
+
+ align:start position:0%
+plane in a similar way had we equated y
+ 
+
+ align:start position:0%
+plane in a similar way had we equated y
+- 5 = 3 with Z - 6 y - 5 over3 = Z - 6
+
+ align:start position:0%
+- 5 = 3 with Z - 6 y - 5 over3 = Z - 6
+ 
+
+ align:start position:0%
+- 5 = 3 with Z - 6 y - 5 over3 = Z - 6
+over 7 we would have obtained the
+
+ align:start position:0%
+over 7 we would have obtained the
+ 
+
+ align:start position:0%
+over 7 we would have obtained the
+plane 7 y - 3 Z = 17 so if you don't
+
+ align:start position:0%
+plane 7 y - 3 Z = 17 so if you don't
+ 
+
+ align:start position:0%
+plane 7 y - 3 Z = 17 so if you don't
+like look at our set of three equations
+
+ align:start position:0%
+like look at our set of three equations
+ 
+
+ align:start position:0%
+like look at our set of three equations
+if you'd like to look at these three
+
+ align:start position:0%
+if you'd like to look at these three
+ 
+
+ align:start position:0%
+if you'd like to look at these three
+equations in
+
+ align:start position:0%
+equations in
+ 
+
+ align:start position:0%
+equations in
+pairs you see if you want to look at
+
+ align:start position:0%
+pairs you see if you want to look at
+ 
+
+ align:start position:0%
+pairs you see if you want to look at
+these three equations and pairs another
+
+ align:start position:0%
+these three equations and pairs another
+ 
+
+ align:start position:0%
+these three equations and pairs another
+way of saying it is this that the triple
+
+ align:start position:0%
+way of saying it is this that the triple
+ 
+
+ align:start position:0%
+way of saying it is this that the triple
+equality X - 1 over4 = y - 5 over3 = Z -
+
+ align:start position:0%
+equality X - 1 over4 = y - 5 over3 = Z -
+ 
+
+ align:start position:0%
+equality X - 1 over4 = y - 5 over3 = Z -
+6 over 7 that that may be viewed as the
+
+ align:start position:0%
+6 over 7 that that may be viewed as the
+ 
+
+ align:start position:0%
+6 over 7 that that may be viewed as the
+intersection of the two planes namely
+
+ align:start position:0%
+intersection of the two planes namely
+ 
+
+ align:start position:0%
+intersection of the two planes namely
+the plane determined by this equation
+
+ align:start position:0%
+the plane determined by this equation
+ 
+
+ align:start position:0%
+the plane determined by this equation
+and the plane determined by this
+
+ align:start position:0%
+and the plane determined by this
+ 
+
+ align:start position:0%
+and the plane determined by this
+equation of course someone can also say
+
+ align:start position:0%
+equation of course someone can also say
+ 
+
+ align:start position:0%
+equation of course someone can also say
+isn't there a plane determined by this
+
+ align:start position:0%
+isn't there a plane determined by this
+ 
+
+ align:start position:0%
+isn't there a plane determined by this
+one and this one and the answer is yes
+
+ align:start position:0%
+one and this one and the answer is yes
+ 
+
+ align:start position:0%
+one and this one and the answer is yes
+there is notice that whereas you have
+
+ align:start position:0%
+there is notice that whereas you have
+ 
+
+ align:start position:0%
+there is notice that whereas you have
+three equalities here only two of them
+
+ align:start position:0%
+three equalities here only two of them
+ 
+
+ align:start position:0%
+three equalities here only two of them
+are independent namely as soon as the
+
+ align:start position:0%
+are independent namely as soon as the
+ 
+
+ align:start position:0%
+are independent namely as soon as the
+first equals the second and the second
+
+ align:start position:0%
+first equals the second and the second
+ 
+
+ align:start position:0%
+first equals the second and the second
+equals the third the first must equal
+
+ align:start position:0%
+equals the third the first must equal
+ 
+
+ align:start position:0%
+equals the third the first must equal
+the third okay but the whole idea is can
+
+ align:start position:0%
+the third okay but the whole idea is can
+ 
+
+ align:start position:0%
+the third okay but the whole idea is can
+you now see the difference the easiest
+
+ align:start position:0%
+you now see the difference the easiest
+ 
+
+ align:start position:0%
+you now see the difference the easiest
+way I know of to distinguish the
+
+ align:start position:0%
+way I know of to distinguish the
+ 
+
+ align:start position:0%
+way I know of to distinguish the
+difference between the equation of a
+
+ align:start position:0%
+difference between the equation of a
+ 
+
+ align:start position:0%
+difference between the equation of a
+line and a plane the plane has two
+
+ align:start position:0%
+line and a plane the plane has two
+ 
+
+ align:start position:0%
+line and a plane the plane has two
+degrees of freedom the line has but one
+
+ align:start position:0%
+degrees of freedom the line has but one
+ 
+
+ align:start position:0%
+degrees of freedom the line has but one
+degree of freedom and that triple
+
+ align:start position:0%
+degree of freedom and that triple
+ 
+
+ align:start position:0%
+degree of freedom and that triple
+equality says as soon as you've picked
+
+ align:start position:0%
+equality says as soon as you've picked
+ 
+
+ align:start position:0%
+equality says as soon as you've picked
+one of the unknowns you've determined
+
+ align:start position:0%
+one of the unknowns you've determined
+ 
+
+ align:start position:0%
+one of the unknowns you've determined
+all of the others whereas that string of
+
+ align:start position:0%
+all of the others whereas that string of
+ 
+
+ align:start position:0%
+all of the others whereas that string of
+plus sign says that once you've
+
+ align:start position:0%
+plus sign says that once you've
+ 
+
+ align:start position:0%
+plus sign says that once you've
+determined one you still have some
+
+ align:start position:0%
+determined one you still have some
+ 
+
+ align:start position:0%
+determined one you still have some
+Freedom left now what we're going to do
+
+ align:start position:0%
+Freedom left now what we're going to do
+ 
+
+ align:start position:0%
+Freedom left now what we're going to do
+is next time start a new phase of
+
+ align:start position:0%
+is next time start a new phase of
+ 
+
+ align:start position:0%
+is next time start a new phase of
+vectors for the time being what we have
+
+ align:start position:0%
+vectors for the time being what we have
+ 
+
+ align:start position:0%
+vectors for the time being what we have
+now done is finished at least for the
+
+ align:start position:0%
+now done is finished at least for the
+ 
+
+ align:start position:0%
+now done is finished at least for the
+moment our preliminary investigation of
+
+ align:start position:0%
+moment our preliminary investigation of
+ 
+
+ align:start position:0%
+moment our preliminary investigation of
+three-dimensional space as seen Through
+
+ align:start position:0%
+three-dimensional space as seen Through
+ 
+
+ align:start position:0%
+three-dimensional space as seen Through
+The Eyes of cartisian coordinates at any
+
+ align:start position:0%
+The Eyes of cartisian coordinates at any
+ 
+
+ align:start position:0%
+The Eyes of cartisian coordinates at any
+rate until next time
+
+ align:start position:0%
+rate until next time
+ 
+
+ align:start position:0%
+rate until next time
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continued to provide
+
+ align:start position:0%
+foundation help ocw continued to provide
+ 
+
+ align:start position:0%
+foundation help ocw continued to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/BvZlP1ZyToo.txt b/BvZlP1ZyToo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..84fbf28a7a7f214c808de286926f12715120c98e
--- /dev/null
+++ b/BvZlP1ZyToo.txt
@@ -0,0 +1,723 @@
+align:start position:0%
+ 
+so let's begin modeling this problem as
+
+ align:start position:0%
+so let's begin modeling this problem as
+ 
+
+ align:start position:0%
+so let's begin modeling this problem as
+a linear optimization problem in terms
+
+ align:start position:0%
+a linear optimization problem in terms
+ 
+
+ align:start position:0%
+a linear optimization problem in terms
+of the framework that we have seen in
+
+ align:start position:0%
+of the framework that we have seen in
+ 
+
+ align:start position:0%
+of the framework that we have seen in
+the lectures our objective is to
+
+ align:start position:0%
+the lectures our objective is to
+ 
+
+ align:start position:0%
+the lectures our objective is to
+maximize the revenue to Google our
+
+ align:start position:0%
+maximize the revenue to Google our
+ 
+
+ align:start position:0%
+maximize the revenue to Google our
+decision is for each advertiser in each
+
+ align:start position:0%
+decision is for each advertiser in each
+ 
+
+ align:start position:0%
+decision is for each advertiser in each
+query to decide the number of times that
+
+ align:start position:0%
+query to decide the number of times that
+ 
+
+ align:start position:0%
+query to decide the number of times that
+advertisers ad will be displayed for
+
+ align:start position:0%
+advertisers ad will be displayed for
+ 
+
+ align:start position:0%
+advertisers ad will be displayed for
+that query our constraints are of two
+
+ align:start position:0%
+that query our constraints are of two
+ 
+
+ align:start position:0%
+that query our constraints are of two
+types
+
+ align:start position:0%
+types
+ 
+
+ align:start position:0%
+types
+our first constraint is that the average
+
+ align:start position:0%
+our first constraint is that the average
+ 
+
+ align:start position:0%
+our first constraint is that the average
+amount paid by each advertiser based on
+
+ align:start position:0%
+amount paid by each advertiser based on
+ 
+
+ align:start position:0%
+amount paid by each advertiser based on
+the number of times Google displays
+
+ align:start position:0%
+the number of times Google displays
+ 
+
+ align:start position:0%
+the number of times Google displays
+their ad for each query cannot exceed
+
+ align:start position:0%
+their ad for each query cannot exceed
+ 
+
+ align:start position:0%
+their ad for each query cannot exceed
+the budget of that advertiser our second
+
+ align:start position:0%
+the budget of that advertiser our second
+ 
+
+ align:start position:0%
+the budget of that advertiser our second
+constraint is that the total number of
+
+ align:start position:0%
+constraint is that the total number of
+ 
+
+ align:start position:0%
+constraint is that the total number of
+ads we display for a query cannot exceed
+
+ align:start position:0%
+ads we display for a query cannot exceed
+ 
+
+ align:start position:0%
+ads we display for a query cannot exceed
+our estimate over the number of requests
+
+ align:start position:0%
+our estimate over the number of requests
+ 
+
+ align:start position:0%
+our estimate over the number of requests
+that we expect to see for that query
+
+ align:start position:0%
+that we expect to see for that query
+ 
+
+ align:start position:0%
+that we expect to see for that query
+let's quickly review our problem data we
+
+ align:start position:0%
+let's quickly review our problem data we
+ 
+
+ align:start position:0%
+let's quickly review our problem data we
+have the average price per display for
+
+ align:start position:0%
+have the average price per display for
+ 
+
+ align:start position:0%
+have the average price per display for
+each advertiser in each query we have
+
+ align:start position:0%
+each advertiser in each query we have
+ 
+
+ align:start position:0%
+each advertiser in each query we have
+the budget of each advertiser and we
+
+ align:start position:0%
+the budget of each advertiser and we
+ 
+
+ align:start position:0%
+the budget of each advertiser and we
+have estimates of the number of requests
+
+ align:start position:0%
+have estimates of the number of requests
+ 
+
+ align:start position:0%
+have estimates of the number of requests
+for each query so let's now think about
+
+ align:start position:0%
+for each query so let's now think about
+ 
+
+ align:start position:0%
+for each query so let's now think about
+how to model all the pieces of our
+
+ align:start position:0%
+how to model all the pieces of our
+ 
+
+ align:start position:0%
+how to model all the pieces of our
+problem first how should we define our
+
+ align:start position:0%
+problem first how should we define our
+ 
+
+ align:start position:0%
+problem first how should we define our
+decision variables well we should define
+
+ align:start position:0%
+decision variables well we should define
+ 
+
+ align:start position:0%
+decision variables well we should define
+them for each advertiser in each query
+
+ align:start position:0%
+them for each advertiser in each query
+ 
+
+ align:start position:0%
+them for each advertiser in each query
+so for example one of our decision
+
+ align:start position:0%
+so for example one of our decision
+ 
+
+ align:start position:0%
+so for example one of our decision
+variables will be XA 1 XA 1 is a number
+
+ align:start position:0%
+variables will be XA 1 XA 1 is a number
+ 
+
+ align:start position:0%
+variables will be XA 1 XA 1 is a number
+of times we will display a TN t--'s ad
+
+ align:start position:0%
+of times we will display a TN t--'s ad
+ 
+
+ align:start position:0%
+of times we will display a TN t--'s ad
+for query 1 similarly we can define X a
+
+ align:start position:0%
+for query 1 similarly we can define X a
+ 
+
+ align:start position:0%
+for query 1 similarly we can define X a
+2 and X a 3 these are the numbers of
+
+ align:start position:0%
+2 and X a 3 these are the numbers of
+ 
+
+ align:start position:0%
+2 and X a 3 these are the numbers of
+times that we will display a TN t--'s ad
+
+ align:start position:0%
+times that we will display a TN t--'s ad
+ 
+
+ align:start position:0%
+times that we will display a TN t--'s ad
+for queries 2 and 3 respectively now of
+
+ align:start position:0%
+for queries 2 and 3 respectively now of
+ 
+
+ align:start position:0%
+for queries 2 and 3 respectively now of
+course we have three different
+
+ align:start position:0%
+course we have three different
+ 
+
+ align:start position:0%
+course we have three different
+advertisers so we will have variables XT
+
+ align:start position:0%
+advertisers so we will have variables XT
+ 
+
+ align:start position:0%
+advertisers so we will have variables XT
+1 XT 2 and XT three these variables
+
+ align:start position:0%
+1 XT 2 and XT three these variables
+ 
+
+ align:start position:0%
+1 XT 2 and XT three these variables
+represent the number of times that we
+
+ align:start position:0%
+represent the number of times that we
+ 
+
+ align:start position:0%
+represent the number of times that we
+display
+
+ align:start position:0%
+display
+ 
+
+ align:start position:0%
+display
+t-mobile's ad for queries one two and
+
+ align:start position:0%
+t-mobile's ad for queries one two and
+ 
+
+ align:start position:0%
+t-mobile's ad for queries one two and
+three respectively and of course our
+
+ align:start position:0%
+three respectively and of course our
+ 
+
+ align:start position:0%
+three respectively and of course our
+last advertisers Verizon so we will have
+
+ align:start position:0%
+last advertisers Verizon so we will have
+ 
+
+ align:start position:0%
+last advertisers Verizon so we will have
+variables X v1 x v2 and x v3 which are
+
+ align:start position:0%
+variables X v1 x v2 and x v3 which are
+ 
+
+ align:start position:0%
+variables X v1 x v2 and x v3 which are
+the numbers of times that we display
+
+ align:start position:0%
+the numbers of times that we display
+ 
+
+ align:start position:0%
+the numbers of times that we display
+horizons at 4 queries one two and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now how do we compute the revenue to
+
+ align:start position:0%
+now how do we compute the revenue to
+ 
+
+ align:start position:0%
+now how do we compute the revenue to
+Google which is our objective
+
+ align:start position:0%
+Google which is our objective
+ 
+
+ align:start position:0%
+Google which is our objective
+well we know the average price per
+
+ align:start position:0%
+well we know the average price per
+ 
+
+ align:start position:0%
+well we know the average price per
+display and our decision variables tell
+
+ align:start position:0%
+display and our decision variables tell
+ 
+
+ align:start position:0%
+display and our decision variables tell
+us exactly how many times will display
+
+ align:start position:0%
+us exactly how many times will display
+ 
+
+ align:start position:0%
+us exactly how many times will display
+each ad for each query so all we need to
+
+ align:start position:0%
+each ad for each query so all we need to
+ 
+
+ align:start position:0%
+each ad for each query so all we need to
+do is we need to multiply each decision
+
+ align:start position:0%
+do is we need to multiply each decision
+ 
+
+ align:start position:0%
+do is we need to multiply each decision
+variable whether its corresponding
+
+ align:start position:0%
+variable whether its corresponding
+ 
+
+ align:start position:0%
+variable whether its corresponding
+average price per display and add them
+
+ align:start position:0%
+average price per display and add them
+ 
+
+ align:start position:0%
+average price per display and add them
+all up if we did this we would have 0.5
+
+ align:start position:0%
+all up if we did this we would have 0.5
+ 
+
+ align:start position:0%
+all up if we did this we would have 0.5
+x a1 plus 0.5 x a2 plus 1 point 6 X a3
+
+ align:start position:0%
+x a1 plus 0.5 x a2 plus 1 point 6 X a3
+ 
+
+ align:start position:0%
+x a1 plus 0.5 x a2 plus 1 point 6 X a3
+plus 1 X t1 and we can continue this and
+
+ align:start position:0%
+plus 1 X t1 and we can continue this and
+ 
+
+ align:start position:0%
+plus 1 X t1 and we can continue this and
+the last term in our sum will be 5 times
+
+ align:start position:0%
+the last term in our sum will be 5 times
+ 
+
+ align:start position:0%
+the last term in our sum will be 5 times
+X v3 to get the constraints we use a
+
+ align:start position:0%
+X v3 to get the constraints we use a
+ 
+
+ align:start position:0%
+X v3 to get the constraints we use a
+similar process for instance to get how
+
+ align:start position:0%
+similar process for instance to get how
+ 
+
+ align:start position:0%
+similar process for instance to get how
+much AT&T pays we multiply the AT&T
+
+ align:start position:0%
+much AT&T pays we multiply the AT&T
+ 
+
+ align:start position:0%
+much AT&T pays we multiply the AT&T
+variables where their average prices per
+
+ align:start position:0%
+variables where their average prices per
+ 
+
+ align:start position:0%
+variables where their average prices per
+display and add them up so we'd get 0.5
+
+ align:start position:0%
+display and add them up so we'd get 0.5
+ 
+
+ align:start position:0%
+display and add them up so we'd get 0.5
+x a1 plus 0.5 x a2 plus 1.6
+
+ align:start position:0%
+x a1 plus 0.5 x a2 plus 1.6
+ 
+
+ align:start position:0%
+x a1 plus 0.5 x a2 plus 1.6
+XA 3 now one of our constraints as you
+
+ align:start position:0%
+XA 3 now one of our constraints as you
+ 
+
+ align:start position:0%
+XA 3 now one of our constraints as you
+will recall is that this cannot exceed
+
+ align:start position:0%
+will recall is that this cannot exceed
+ 
+
+ align:start position:0%
+will recall is that this cannot exceed
+18 T's budget which is 170 dollars so
+
+ align:start position:0%
+18 T's budget which is 170 dollars so
+ 
+
+ align:start position:0%
+18 T's budget which is 170 dollars so
+our model would have the constraint 0.5
+
+ align:start position:0%
+our model would have the constraint 0.5
+ 
+
+ align:start position:0%
+our model would have the constraint 0.5
+X a1 plus 0.5 X a2 plus 1 point 6 X a 3
+
+ align:start position:0%
+X a1 plus 0.5 X a2 plus 1 point 6 X a 3
+ 
+
+ align:start position:0%
+X a1 plus 0.5 X a2 plus 1 point 6 X a 3
+is less than 117 we can repeat this to
+
+ align:start position:0%
+is less than 117 we can repeat this to
+ 
+
+ align:start position:0%
+is less than 117 we can repeat this to
+get the same kind of budget constraint
+
+ align:start position:0%
+get the same kind of budget constraint
+ 
+
+ align:start position:0%
+get the same kind of budget constraint
+for t-mobile and Verizon now to get the
+
+ align:start position:0%
+for t-mobile and Verizon now to get the
+ 
+
+ align:start position:0%
+for t-mobile and Verizon now to get the
+number of times query 2 is used we add
+
+ align:start position:0%
+number of times query 2 is used we add
+ 
+
+ align:start position:0%
+number of times query 2 is used we add
+up the decision variables corresponding
+
+ align:start position:0%
+up the decision variables corresponding
+ 
+
+ align:start position:0%
+up the decision variables corresponding
+to query 2 so we have x a2 the number of
+
+ align:start position:0%
+to query 2 so we have x a2 the number of
+ 
+
+ align:start position:0%
+to query 2 so we have x a2 the number of
+times AT&T is paired with query 2 we
+
+ align:start position:0%
+times AT&T is paired with query 2 we
+ 
+
+ align:start position:0%
+times AT&T is paired with query 2 we
+have X t2 which is a number of times
+
+ align:start position:0%
+have X t2 which is a number of times
+ 
+
+ align:start position:0%
+have X t2 which is a number of times
+t-mobile is paired with query 2 and X V
+
+ align:start position:0%
+t-mobile is paired with query 2 and X V
+ 
+
+ align:start position:0%
+t-mobile is paired with query 2 and X V
+2 which is the number of times Verizon
+
+ align:start position:0%
+2 which is the number of times Verizon
+ 
+
+ align:start position:0%
+2 which is the number of times Verizon
+this pair of good query 2 now one of our
+
+ align:start position:0%
+this pair of good query 2 now one of our
+ 
+
+ align:start position:0%
+this pair of good query 2 now one of our
+constraints is that this cannot exceed
+
+ align:start position:0%
+constraints is that this cannot exceed
+ 
+
+ align:start position:0%
+constraints is that this cannot exceed
+number of requests for query - which is
+
+ align:start position:0%
+number of requests for query - which is
+ 
+
+ align:start position:0%
+number of requests for query - which is
+80 sir model would have the constraint
+
+ align:start position:0%
+80 sir model would have the constraint
+ 
+
+ align:start position:0%
+80 sir model would have the constraint
+XA 2 + xt 2 + XV - all less than 80 we
+
+ align:start position:0%
+XA 2 + xt 2 + XV - all less than 80 we
+ 
+
+ align:start position:0%
+XA 2 + xt 2 + XV - all less than 80 we
+can do this for the other queries so we
+
+ align:start position:0%
+can do this for the other queries so we
+ 
+
+ align:start position:0%
+can do this for the other queries so we
+can do this for query 1 and query 3 and
+
+ align:start position:0%
+can do this for query 1 and query 3 and
+ 
+
+ align:start position:0%
+can do this for query 1 and query 3 and
+this is all that we really need so now
+
+ align:start position:0%
+this is all that we really need so now
+ 
+
+ align:start position:0%
+this is all that we really need so now
+let's take this problem - libre office
+
+ align:start position:0%
+let's take this problem - libre office
+ 
+
+ align:start position:0%
+let's take this problem - libre office
+and actually solve it
\ No newline at end of file
diff --git a/CALYA11terw.txt b/CALYA11terw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..306320935aa90d136808fb811fa70034ff5af01c
--- /dev/null
+++ b/CALYA11terw.txt
@@ -0,0 +1,8051 @@
+align:start position:0%
+ 
+okay I just want to just highlight your
+
+ align:start position:0%
+okay I just want to just highlight your
+ 
+
+ align:start position:0%
+okay I just want to just highlight your
+attention to things like every day I get
+
+ align:start position:0%
+attention to things like every day I get
+ 
+
+ align:start position:0%
+attention to things like every day I get
+the MIT news feed I get a couple of
+
+ align:start position:0%
+the MIT news feed I get a couple of
+ 
+
+ align:start position:0%
+the MIT news feed I get a couple of
+other news feeds and I just thought this
+
+ align:start position:0%
+other news feeds and I just thought this
+ 
+
+ align:start position:0%
+other news feeds and I just thought this
+was really sort of a striking image and
+
+ align:start position:0%
+was really sort of a striking image and
+ 
+
+ align:start position:0%
+was really sort of a striking image and
+I think a great way to convey science
+
+ align:start position:0%
+I think a great way to convey science
+ 
+
+ align:start position:0%
+I think a great way to convey science
+and engineering is through sort of
+
+ align:start position:0%
+and engineering is through sort of
+ 
+
+ align:start position:0%
+and engineering is through sort of
+really eye-catching imagery and this but
+
+ align:start position:0%
+really eye-catching imagery and this but
+ 
+
+ align:start position:0%
+really eye-catching imagery and this but
+these are this is a synapse which is
+
+ align:start position:0%
+these are this is a synapse which is
+ 
+
+ align:start position:0%
+these are this is a synapse which is
+where nerves contact our other nerves or
+
+ align:start position:0%
+where nerves contact our other nerves or
+ 
+
+ align:start position:0%
+where nerves contact our other nerves or
+to the neuromuscular Junction in order
+
+ align:start position:0%
+to the neuromuscular Junction in order
+ 
+
+ align:start position:0%
+to the neuromuscular Junction in order
+to trigger activity and this is a piece
+
+ align:start position:0%
+to trigger activity and this is a piece
+ 
+
+ align:start position:0%
+to trigger activity and this is a piece
+of research out of the Seema whoops go
+
+ align:start position:0%
+of research out of the Seema whoops go
+ 
+
+ align:start position:0%
+of research out of the Seema whoops go
+back one oops go back one more between
+
+ align:start position:0%
+back one oops go back one more between
+ 
+
+ align:start position:0%
+back one oops go back one more between
+the FEMA and Langer labs where they've
+
+ align:start position:0%
+the FEMA and Langer labs where they've
+ 
+
+ align:start position:0%
+the FEMA and Langer labs where they've
+designed a little tiny microchip probes
+
+ align:start position:0%
+designed a little tiny microchip probes
+ 
+
+ align:start position:0%
+designed a little tiny microchip probes
+they're about 10 microns big that can be
+
+ align:start position:0%
+they're about 10 microns big that can be
+ 
+
+ align:start position:0%
+they're about 10 microns big that can be
+planted in the brain in different sites
+
+ align:start position:0%
+planted in the brain in different sites
+ 
+
+ align:start position:0%
+planted in the brain in different sites
+non hopefully non invasively but and
+
+ align:start position:0%
+non hopefully non invasively but and
+ 
+
+ align:start position:0%
+non hopefully non invasively but and
+they could report on concentrations of
+
+ align:start position:0%
+they could report on concentrations of
+ 
+
+ align:start position:0%
+they could report on concentrations of
+this neurotransmitter dopamine and the
+
+ align:start position:0%
+this neurotransmitter dopamine and the
+ 
+
+ align:start position:0%
+this neurotransmitter dopamine and the
+reason you might want to be able to do
+
+ align:start position:0%
+reason you might want to be able to do
+ 
+
+ align:start position:0%
+reason you might want to be able to do
+that is that there is a dopamine deficit
+
+ align:start position:0%
+that is that there is a dopamine deficit
+ 
+
+ align:start position:0%
+that is that there is a dopamine deficit
+in a lot of neurologic disorders so you
+
+ align:start position:0%
+in a lot of neurologic disorders so you
+ 
+
+ align:start position:0%
+in a lot of neurologic disorders so you
+would like to understand what the
+
+ align:start position:0%
+would like to understand what the
+ 
+
+ align:start position:0%
+would like to understand what the
+deficits are and pinpoint points of the
+
+ align:start position:0%
+deficits are and pinpoint points of the
+ 
+
+ align:start position:0%
+deficits are and pinpoint points of the
+brain where there may be issues and in
+
+ align:start position:0%
+brain where there may be issues and in
+ 
+
+ align:start position:0%
+brain where there may be issues and in
+fact they used it to track Parkinson's
+
+ align:start position:0%
+fact they used it to track Parkinson's
+ 
+
+ align:start position:0%
+fact they used it to track Parkinson's
+disease because Parkinson's disease some
+
+ align:start position:0%
+disease because Parkinson's disease some
+ 
+
+ align:start position:0%
+disease because Parkinson's disease some
+of the therapeutic approaches involve
+
+ align:start position:0%
+of the therapeutic approaches involve
+ 
+
+ align:start position:0%
+of the therapeutic approaches involve
+deep brain stimulation but you can't
+
+ align:start position:0%
+deep brain stimulation but you can't
+ 
+
+ align:start position:0%
+deep brain stimulation but you can't
+really tell if it's working unless you
+
+ align:start position:0%
+really tell if it's working unless you
+ 
+
+ align:start position:0%
+really tell if it's working unless you
+can measure something and the thing that
+
+ align:start position:0%
+can measure something and the thing that
+ 
+
+ align:start position:0%
+can measure something and the thing that
+you could measure would be the absolute
+
+ align:start position:0%
+you could measure would be the absolute
+ 
+
+ align:start position:0%
+you could measure would be the absolute
+levels of this neurotransmitter dopamine
+
+ align:start position:0%
+levels of this neurotransmitter dopamine
+ 
+
+ align:start position:0%
+levels of this neurotransmitter dopamine
+which by the way is originated from the
+
+ align:start position:0%
+which by the way is originated from the
+ 
+
+ align:start position:0%
+which by the way is originated from the
+amino acid tyrosine you could sort of
+
+ align:start position:0%
+amino acid tyrosine you could sort of
+ 
+
+ align:start position:0%
+amino acid tyrosine you could sort of
+spot some of the parts of that that
+
+ align:start position:0%
+spot some of the parts of that that
+ 
+
+ align:start position:0%
+spot some of the parts of that that
+would be the carbon becomes a cotton is
+
+ align:start position:0%
+would be the carbon becomes a cotton is
+ 
+
+ align:start position:0%
+would be the carbon becomes a cotton is
+a carboxylate and an amine
+
+ align:start position:0%
+a carboxylate and an amine
+ 
+
+ align:start position:0%
+a carboxylate and an amine
+oh I've drawn I've drawn the alcohol
+
+ align:start position:0%
+oh I've drawn I've drawn the alcohol
+ 
+
+ align:start position:0%
+oh I've drawn I've drawn the alcohol
+this should be an nh-2 group sorry I
+
+ align:start position:0%
+this should be an nh-2 group sorry I
+ 
+
+ align:start position:0%
+this should be an nh-2 group sorry I
+just added this at last minute so
+
+ align:start position:0%
+just added this at last minute so
+ 
+
+ align:start position:0%
+just added this at last minute so
+dopamine actually though originates from
+
+ align:start position:0%
+dopamine actually though originates from
+ 
+
+ align:start position:0%
+dopamine actually though originates from
+tyrosine so I just thought you would be
+
+ align:start position:0%
+tyrosine so I just thought you would be
+ 
+
+ align:start position:0%
+tyrosine so I just thought you would be
+interested because when I talk about
+
+ align:start position:0%
+interested because when I talk about
+ 
+
+ align:start position:0%
+interested because when I talk about
+highlighting things that are in the news
+
+ align:start position:0%
+highlighting things that are in the news
+ 
+
+ align:start position:0%
+highlighting things that are in the news
+I mean
+
+ align:start position:0%
+I mean
+ 
+
+ align:start position:0%
+I mean
+things like this where we're all kind of
+
+ align:start position:0%
+things like this where we're all kind of
+ 
+
+ align:start position:0%
+things like this where we're all kind of
+interesting it's cool it's relevant to
+
+ align:start position:0%
+interesting it's cool it's relevant to
+ 
+
+ align:start position:0%
+interesting it's cool it's relevant to
+what we do and it really combines the
+
+ align:start position:0%
+what we do and it really combines the
+ 
+
+ align:start position:0%
+what we do and it really combines the
+efforts of scientists and engineers to
+
+ align:start position:0%
+efforts of scientists and engineers to
+ 
+
+ align:start position:0%
+efforts of scientists and engineers to
+make tools and methods and invent
+
+ align:start position:0%
+make tools and methods and invent
+ 
+
+ align:start position:0%
+make tools and methods and invent
+methods to make measurements that are
+
+ align:start position:0%
+methods to make measurements that are
+ 
+
+ align:start position:0%
+methods to make measurements that are
+quantitative enough to guide the
+
+ align:start position:0%
+quantitative enough to guide the
+ 
+
+ align:start position:0%
+quantitative enough to guide the
+analysis of a disorder so I just want to
+
+ align:start position:0%
+analysis of a disorder so I just want to
+ 
+
+ align:start position:0%
+analysis of a disorder so I just want to
+wrap up a little bit on the aspects I'm
+
+ align:start position:0%
+wrap up a little bit on the aspects I'm
+ 
+
+ align:start position:0%
+wrap up a little bit on the aspects I'm
+showing you the energy diagrams in the
+
+ align:start position:0%
+showing you the energy diagrams in the
+ 
+
+ align:start position:0%
+showing you the energy diagrams in the
+last class and telling you how enzymes
+
+ align:start position:0%
+last class and telling you how enzymes
+ 
+
+ align:start position:0%
+last class and telling you how enzymes
+affect the course of a reaction by
+
+ align:start position:0%
+affect the course of a reaction by
+ 
+
+ align:start position:0%
+affect the course of a reaction by
+lowering the energy of activation by
+
+ align:start position:0%
+lowering the energy of activation by
+ 
+
+ align:start position:0%
+lowering the energy of activation by
+stabilizing a transition state or a high
+
+ align:start position:0%
+stabilizing a transition state or a high
+ 
+
+ align:start position:0%
+stabilizing a transition state or a high
+energy intermediate state so the energy
+
+ align:start position:0%
+energy intermediate state so the energy
+ 
+
+ align:start position:0%
+energy intermediate state so the energy
+of activation becomes smaller in the
+
+ align:start position:0%
+of activation becomes smaller in the
+ 
+
+ align:start position:0%
+of activation becomes smaller in the
+catalyzed reaction therefore faster than
+
+ align:start position:0%
+catalyzed reaction therefore faster than
+ 
+
+ align:start position:0%
+catalyzed reaction therefore faster than
+in the other catalysts reaction and I
+
+ align:start position:0%
+in the other catalysts reaction and I
+ 
+
+ align:start position:0%
+in the other catalysts reaction and I
+did not give you this number last time
+
+ align:start position:0%
+did not give you this number last time
+ 
+
+ align:start position:0%
+did not give you this number last time
+enzymes catalyze reactions through about
+
+ align:start position:0%
+enzymes catalyze reactions through about
+ 
+
+ align:start position:0%
+enzymes catalyze reactions through about
+10 to the 6 a million to 10 to the 10
+
+ align:start position:0%
+10 to the 6 a million to 10 to the 10
+ 
+
+ align:start position:0%
+10 to the 6 a million to 10 to the 10
+folds so these are dramatic increases in
+
+ align:start position:0%
+folds so these are dramatic increases in
+ 
+
+ align:start position:0%
+folds so these are dramatic increases in
+rates that are really fizzy we depend on
+
+ align:start position:0%
+rates that are really fizzy we depend on
+ 
+
+ align:start position:0%
+rates that are really fizzy we depend on
+physiologically they ensure specificity
+
+ align:start position:0%
+physiologically they ensure specificity
+ 
+
+ align:start position:0%
+physiologically they ensure specificity
+and they're essential in all systems and
+
+ align:start position:0%
+and they're essential in all systems and
+ 
+
+ align:start position:0%
+and they're essential in all systems and
+the way we discuss energetic changes in
+
+ align:start position:0%
+the way we discuss energetic changes in
+ 
+
+ align:start position:0%
+the way we discuss energetic changes in
+reaction diagrams is by looking at
+
+ align:start position:0%
+reaction diagrams is by looking at
+ 
+
+ align:start position:0%
+reaction diagrams is by looking at
+what's known as the Delta G it's the
+
+ align:start position:0%
+what's known as the Delta G it's the
+ 
+
+ align:start position:0%
+what's known as the Delta G it's the
+change in free energy what I show you
+
+ align:start position:0%
+change in free energy what I show you
+ 
+
+ align:start position:0%
+change in free energy what I show you
+here is an exergonic reaction where it
+
+ align:start position:0%
+here is an exergonic reaction where it
+ 
+
+ align:start position:0%
+here is an exergonic reaction where it
+is a negative Delta G I didn't reinforce
+
+ align:start position:0%
+is a negative Delta G I didn't reinforce
+ 
+
+ align:start position:0%
+is a negative Delta G I didn't reinforce
+that point in that last time the energy
+
+ align:start position:0%
+that point in that last time the energy
+ 
+
+ align:start position:0%
+that point in that last time the energy
+of the products is lower than the energy
+
+ align:start position:0%
+of the products is lower than the energy
+ 
+
+ align:start position:0%
+of the products is lower than the energy
+of the substrates so energy is given out
+
+ align:start position:0%
+of the substrates so energy is given out
+ 
+
+ align:start position:0%
+of the substrates so energy is given out
+at the end of the transformation that
+
+ align:start position:0%
+at the end of the transformation that
+ 
+
+ align:start position:0%
+at the end of the transformation that
+means the reaction is favorable with
+
+ align:start position:0%
+means the reaction is favorable with
+ 
+
+ align:start position:0%
+means the reaction is favorable with
+respect to an equilibrium a
+
+ align:start position:0%
+respect to an equilibrium a
+ 
+
+ align:start position:0%
+respect to an equilibrium a
+thermodynamic parameter and then it's
+
+ align:start position:0%
+thermodynamic parameter and then it's
+ 
+
+ align:start position:0%
+thermodynamic parameter and then it's
+the enzyme that takes care of the
+
+ align:start position:0%
+the enzyme that takes care of the
+ 
+
+ align:start position:0%
+the enzyme that takes care of the
+kinetic aspects of the reaction so just
+
+ align:start position:0%
+kinetic aspects of the reaction so just
+ 
+
+ align:start position:0%
+kinetic aspects of the reaction so just
+to sort of show you the correlate an
+
+ align:start position:0%
+to sort of show you the correlate an
+ 
+
+ align:start position:0%
+to sort of show you the correlate an
+endergonic reaction would look like this
+
+ align:start position:0%
+endergonic reaction would look like this
+ 
+
+ align:start position:0%
+endergonic reaction would look like this
+where the Delta G is positive the
+
+ align:start position:0%
+where the Delta G is positive the
+ 
+
+ align:start position:0%
+where the Delta G is positive the
+products are less stable than the
+
+ align:start position:0%
+products are less stable than the
+ 
+
+ align:start position:0%
+products are less stable than the
+starting materials which would mean the
+
+ align:start position:0%
+starting materials which would mean the
+ 
+
+ align:start position:0%
+starting materials which would mean the
+reaction is not favourable but it will
+
+ align:start position:0%
+reaction is not favourable but it will
+ 
+
+ align:start position:0%
+reaction is not favourable but it will
+still proceed in the presence of a
+
+ align:start position:0%
+still proceed in the presence of a
+ 
+
+ align:start position:0%
+still proceed in the presence of a
+catalyst
+
+ align:start position:0%
+catalyst
+ 
+
+ align:start position:0%
+catalyst
+and in this next small bit where we talk
+
+ align:start position:0%
+and in this next small bit where we talk
+ 
+
+ align:start position:0%
+and in this next small bit where we talk
+about pathways and different aspects of
+
+ align:start position:0%
+about pathways and different aspects of
+ 
+
+ align:start position:0%
+about pathways and different aspects of
+metabolism I'm going to tell you how we
+
+ align:start position:0%
+metabolism I'm going to tell you how we
+ 
+
+ align:start position:0%
+metabolism I'm going to tell you how we
+get around the unfavorable equilibrium
+
+ align:start position:0%
+get around the unfavorable equilibrium
+ 
+
+ align:start position:0%
+get around the unfavorable equilibrium
+problem because that's obviously a big
+
+ align:start position:0%
+problem because that's obviously a big
+ 
+
+ align:start position:0%
+problem because that's obviously a big
+predicament in biochemistry if reactions
+
+ align:start position:0%
+predicament in biochemistry if reactions
+ 
+
+ align:start position:0%
+predicament in biochemistry if reactions
+aren't favorable why do they why do they
+
+ align:start position:0%
+aren't favorable why do they why do they
+ 
+
+ align:start position:0%
+aren't favorable why do they why do they
+go far enough to be useful to us in in
+
+ align:start position:0%
+go far enough to be useful to us in in
+ 
+
+ align:start position:0%
+go far enough to be useful to us in in
+metabolism and so that reaction would
+
+ align:start position:0%
+metabolism and so that reaction would
+ 
+
+ align:start position:0%
+metabolism and so that reaction would
+have a positive Delta G and then I also
+
+ align:start position:0%
+have a positive Delta G and then I also
+ 
+
+ align:start position:0%
+have a positive Delta G and then I also
+mentioned these two terms anabolic
+
+ align:start position:0%
+mentioned these two terms anabolic
+ 
+
+ align:start position:0%
+mentioned these two terms anabolic
+refers to the end argon the endergonic
+
+ align:start position:0%
+refers to the end argon the endergonic
+ 
+
+ align:start position:0%
+refers to the end argon the endergonic
+reactions I don't know why you're doing
+
+ align:start position:0%
+reactions I don't know why you're doing
+ 
+
+ align:start position:0%
+reactions I don't know why you're doing
+this to me the endergonic reactions and
+
+ align:start position:0%
+this to me the endergonic reactions and
+ 
+
+ align:start position:0%
+this to me the endergonic reactions and
+catabolic refers to the exergonic
+
+ align:start position:0%
+catabolic refers to the exergonic
+ 
+
+ align:start position:0%
+catabolic refers to the exergonic
+reactions okay then this last point I
+
+ align:start position:0%
+reactions okay then this last point I
+ 
+
+ align:start position:0%
+reactions okay then this last point I
+showed you this slide last time but I
+
+ align:start position:0%
+showed you this slide last time but I
+ 
+
+ align:start position:0%
+showed you this slide last time but I
+think it was important to think about
+
+ align:start position:0%
+think it was important to think about
+ 
+
+ align:start position:0%
+think it was important to think about
+why our enzyme so big and I want to give
+
+ align:start position:0%
+why our enzyme so big and I want to give
+ 
+
+ align:start position:0%
+why our enzyme so big and I want to give
+you some example of an additional
+
+ align:start position:0%
+you some example of an additional
+ 
+
+ align:start position:0%
+you some example of an additional
+genetic mutation that causes a human
+
+ align:start position:0%
+genetic mutation that causes a human
+ 
+
+ align:start position:0%
+genetic mutation that causes a human
+disorder where I at least show you how
+
+ align:start position:0%
+disorder where I at least show you how
+ 
+
+ align:start position:0%
+disorder where I at least show you how
+the mutations are spread quite a
+
+ align:start position:0%
+the mutations are spread quite a
+ 
+
+ align:start position:0%
+the mutations are spread quite a
+distance from the reaction center to
+
+ align:start position:0%
+distance from the reaction center to
+ 
+
+ align:start position:0%
+distance from the reaction center to
+show you that all of that structure that
+
+ align:start position:0%
+show you that all of that structure that
+ 
+
+ align:start position:0%
+show you that all of that structure that
+you see in an enzyme as it interacts
+
+ align:start position:0%
+you see in an enzyme as it interacts
+ 
+
+ align:start position:0%
+you see in an enzyme as it interacts
+with a small substrate is critical for
+
+ align:start position:0%
+with a small substrate is critical for
+ 
+
+ align:start position:0%
+with a small substrate is critical for
+catalysis so we see small substrates in
+
+ align:start position:0%
+catalysis so we see small substrates in
+ 
+
+ align:start position:0%
+catalysis so we see small substrates in
+each case but we have this very large
+
+ align:start position:0%
+each case but we have this very large
+ 
+
+ align:start position:0%
+each case but we have this very large
+enzyme which is many many times its size
+
+ align:start position:0%
+enzyme which is many many times its size
+ 
+
+ align:start position:0%
+enzyme which is many many times its size
+all engaged in catalysis but what's the
+
+ align:start position:0%
+all engaged in catalysis but what's the
+ 
+
+ align:start position:0%
+all engaged in catalysis but what's the
+proof of that so why are enzyme so big
+
+ align:start position:0%
+proof of that so why are enzyme so big
+ 
+
+ align:start position:0%
+proof of that so why are enzyme so big
+so phenylketonuria is human disorder
+
+ align:start position:0%
+so phenylketonuria is human disorder
+ 
+
+ align:start position:0%
+so phenylketonuria is human disorder
+it's one of those disorders that
+
+ align:start position:0%
+it's one of those disorders that
+ 
+
+ align:start position:0%
+it's one of those disorders that
+neonates Brad newborns are tested for
+
+ align:start position:0%
+neonates Brad newborns are tested for
+ 
+
+ align:start position:0%
+neonates Brad newborns are tested for
+they they're checked for the genetic
+
+ align:start position:0%
+they they're checked for the genetic
+ 
+
+ align:start position:0%
+they they're checked for the genetic
+signal that shows that the protein will
+
+ align:start position:0%
+signal that shows that the protein will
+ 
+
+ align:start position:0%
+signal that shows that the protein will
+have mutations in its structure and
+
+ align:start position:0%
+have mutations in its structure and
+ 
+
+ align:start position:0%
+have mutations in its structure and
+there are many mutations associated with
+
+ align:start position:0%
+there are many mutations associated with
+ 
+
+ align:start position:0%
+there are many mutations associated with
+a defect in this particular protein and
+
+ align:start position:0%
+a defect in this particular protein and
+ 
+
+ align:start position:0%
+a defect in this particular protein and
+the protein that I'm talking about is
+
+ align:start position:0%
+the protein that I'm talking about is
+ 
+
+ align:start position:0%
+the protein that I'm talking about is
+phenylalanine hydroxylase so the
+
+ align:start position:0%
+phenylalanine hydroxylase so the
+ 
+
+ align:start position:0%
+phenylalanine hydroxylase so the
+disorder is related to defects in
+
+ align:start position:0%
+disorder is related to defects in
+ 
+
+ align:start position:0%
+disorder is related to defects in
+phenylalanine hydroxylase now what does
+
+ align:start position:0%
+phenylalanine hydroxylase now what does
+ 
+
+ align:start position:0%
+phenylalanine hydroxylase now what does
+that enzyme do it takes phenylalanine
+
+ align:start position:0%
+that enzyme do it takes phenylalanine
+ 
+
+ align:start position:0%
+that enzyme do it takes phenylalanine
+and installs a hydroxyl group opposite
+
+ align:start position:0%
+and installs a hydroxyl group opposite
+ 
+
+ align:start position:0%
+and installs a hydroxyl group opposite
+to where it's attached to the amino acid
+
+ align:start position:0%
+to where it's attached to the amino acid
+ 
+
+ align:start position:0%
+to where it's attached to the amino acid
+so this is the hydrophobic amino acid
+
+ align:start position:0%
+so this is the hydrophobic amino acid
+ 
+
+ align:start position:0%
+so this is the hydrophobic amino acid
+phenylalanine and this is another one of
+
+ align:start position:0%
+phenylalanine and this is another one of
+ 
+
+ align:start position:0%
+phenylalanine and this is another one of
+the hydrophobic amino acids in a similar
+
+ align:start position:0%
+the hydrophobic amino acids in a similar
+ 
+
+ align:start position:0%
+the hydrophobic amino acids in a similar
+family that's tyrosine and in fact it's
+
+ align:start position:0%
+family that's tyrosine and in fact it's
+ 
+
+ align:start position:0%
+family that's tyrosine and in fact it's
+the precursor to dopamine
+
+ align:start position:0%
+the precursor to dopamine
+ 
+
+ align:start position:0%
+the precursor to dopamine
+physiologically now it turns out in this
+
+ align:start position:0%
+physiologically now it turns out in this
+ 
+
+ align:start position:0%
+physiologically now it turns out in this
+kid there can always be too much of a
+
+ align:start position:0%
+kid there can always be too much of a
+ 
+
+ align:start position:0%
+kid there can always be too much of a
+good thing so if you have too much
+
+ align:start position:0%
+good thing so if you have too much
+ 
+
+ align:start position:0%
+good thing so if you have too much
+phenylalanine it has to be converted to
+
+ align:start position:0%
+phenylalanine it has to be converted to
+ 
+
+ align:start position:0%
+phenylalanine it has to be converted to
+a different amino acid because the build
+
+ align:start position:0%
+a different amino acid because the build
+ 
+
+ align:start position:0%
+a different amino acid because the build
+up of phenylalanine gets to a certain
+
+ align:start position:0%
+up of phenylalanine gets to a certain
+ 
+
+ align:start position:0%
+up of phenylalanine gets to a certain
+stage where it is converted itself to a
+
+ align:start position:0%
+stage where it is converted itself to a
+ 
+
+ align:start position:0%
+stage where it is converted itself to a
+toxic by-product that actually causes
+
+ align:start position:0%
+toxic by-product that actually causes
+ 
+
+ align:start position:0%
+toxic by-product that actually causes
+severe mental disorders and seizures so
+
+ align:start position:0%
+severe mental disorders and seizures so
+ 
+
+ align:start position:0%
+severe mental disorders and seizures so
+you need to the body needs to monitor
+
+ align:start position:0%
+you need to the body needs to monitor
+ 
+
+ align:start position:0%
+you need to the body needs to monitor
+the levels of phenylalanine and at a
+
+ align:start position:0%
+the levels of phenylalanine and at a
+ 
+
+ align:start position:0%
+the levels of phenylalanine and at a
+certain stage phenylalanine hydroxylase
+
+ align:start position:0%
+certain stage phenylalanine hydroxylase
+ 
+
+ align:start position:0%
+certain stage phenylalanine hydroxylase
+will convert it to tyrosine so even
+
+ align:start position:0%
+will convert it to tyrosine so even
+ 
+
+ align:start position:0%
+will convert it to tyrosine so even
+though phenylalanine is essential
+
+ align:start position:0%
+though phenylalanine is essential
+ 
+
+ align:start position:0%
+though phenylalanine is essential
+too much phenylalanine is a bad thing so
+
+ align:start position:0%
+too much phenylalanine is a bad thing so
+ 
+
+ align:start position:0%
+too much phenylalanine is a bad thing so
+that enzyme is the one that is
+
+ align:start position:0%
+that enzyme is the one that is
+ 
+
+ align:start position:0%
+that enzyme is the one that is
+associated with defects that with
+
+ align:start position:0%
+associated with defects that with
+ 
+
+ align:start position:0%
+associated with defects that with
+mutations that lower the activity of the
+
+ align:start position:0%
+mutations that lower the activity of the
+ 
+
+ align:start position:0%
+mutations that lower the activity of the
+phenylalanine hydroxylase and end you up
+
+ align:start position:0%
+phenylalanine hydroxylase and end you up
+ 
+
+ align:start position:0%
+phenylalanine hydroxylase and end you up
+accumulating phenylalanine to high and
+
+ align:start position:0%
+accumulating phenylalanine to high and
+ 
+
+ align:start position:0%
+accumulating phenylalanine to high and
+so the pah regulates the clearance from
+
+ align:start position:0%
+so the pah regulates the clearance from
+ 
+
+ align:start position:0%
+so the pah regulates the clearance from
+the body converting it to tyrosine so
+
+ align:start position:0%
+the body converting it to tyrosine so
+ 
+
+ align:start position:0%
+the body converting it to tyrosine so
+why you know I just I told you I would
+
+ align:start position:0%
+why you know I just I told you I would
+ 
+
+ align:start position:0%
+why you know I just I told you I would
+give you some insight into how entire
+
+ align:start position:0%
+give you some insight into how entire
+ 
+
+ align:start position:0%
+give you some insight into how entire
+enzymes are in fact critical for
+
+ align:start position:0%
+enzymes are in fact critical for
+ 
+
+ align:start position:0%
+enzymes are in fact critical for
+catalysis so what I'm showing you on
+
+ align:start position:0%
+catalysis so what I'm showing you on
+ 
+
+ align:start position:0%
+catalysis so what I'm showing you on
+this little movie is that the sites
+
+ align:start position:0%
+this little movie is that the sites
+ 
+
+ align:start position:0%
+this little movie is that the sites
+shown in magenta all around this protein
+
+ align:start position:0%
+shown in magenta all around this protein
+ 
+
+ align:start position:0%
+shown in magenta all around this protein
+the active site would be where this big
+
+ align:start position:0%
+the active site would be where this big
+ 
+
+ align:start position:0%
+the active site would be where this big
+ball is it's actually cofactor iron but
+
+ align:start position:0%
+ball is it's actually cofactor iron but
+ 
+
+ align:start position:0%
+ball is it's actually cofactor iron but
+the sites that are involved in the
+
+ align:start position:0%
+the sites that are involved in the
+ 
+
+ align:start position:0%
+the sites that are involved in the
+reduction of activity of phenylalanine
+
+ align:start position:0%
+reduction of activity of phenylalanine
+ 
+
+ align:start position:0%
+reduction of activity of phenylalanine
+hydroxylase away out on the protein out
+
+ align:start position:0%
+hydroxylase away out on the protein out
+ 
+
+ align:start position:0%
+hydroxylase away out on the protein out
+on its perimeters so this protein is
+
+ align:start position:0%
+on its perimeters so this protein is
+ 
+
+ align:start position:0%
+on its perimeters so this protein is
+about 49 angstroms 4.9 nanometers across
+
+ align:start position:0%
+about 49 angstroms 4.9 nanometers across
+ 
+
+ align:start position:0%
+about 49 angstroms 4.9 nanometers across
+but the sites that cause a reduction in
+
+ align:start position:0%
+but the sites that cause a reduction in
+ 
+
+ align:start position:0%
+but the sites that cause a reduction in
+activity are a long way away 10
+
+ align:start position:0%
+activity are a long way away 10
+ 
+
+ align:start position:0%
+activity are a long way away 10
+angstroms longer 15 angstroms 16 so it
+
+ align:start position:0%
+angstroms longer 15 angstroms 16 so it
+ 
+
+ align:start position:0%
+angstroms longer 15 angstroms 16 so it
+turns out that enzymes as catalysts
+
+ align:start position:0%
+turns out that enzymes as catalysts
+ 
+
+ align:start position:0%
+turns out that enzymes as catalysts
+don't just use the local environment
+
+ align:start position:0%
+don't just use the local environment
+ 
+
+ align:start position:0%
+don't just use the local environment
+right near where chemistry happens the
+
+ align:start position:0%
+right near where chemistry happens the
+ 
+
+ align:start position:0%
+right near where chemistry happens the
+entire protein collaborates to make the
+
+ align:start position:0%
+entire protein collaborates to make the
+ 
+
+ align:start position:0%
+entire protein collaborates to make the
+changes happen in catalysis so enzymes
+
+ align:start position:0%
+changes happen in catalysis so enzymes
+ 
+
+ align:start position:0%
+changes happen in catalysis so enzymes
+are big because you're not just using
+
+ align:start position:0%
+are big because you're not just using
+ 
+
+ align:start position:0%
+are big because you're not just using
+this inner shell of functional groups
+
+ align:start position:0%
+this inner shell of functional groups
+ 
+
+ align:start position:0%
+this inner shell of functional groups
+where the substrate binds you're
+
+ align:start position:0%
+where the substrate binds you're
+ 
+
+ align:start position:0%
+where the substrate binds you're
+actually using a lot of the dynamics of
+
+ align:start position:0%
+actually using a lot of the dynamics of
+ 
+
+ align:start position:0%
+actually using a lot of the dynamics of
+the enzyme to promote catalysis and just
+
+ align:start position:0%
+the enzyme to promote catalysis and just
+ 
+
+ align:start position:0%
+the enzyme to promote catalysis and just
+this sort of visual shows you how far
+
+ align:start position:0%
+this sort of visual shows you how far
+ 
+
+ align:start position:0%
+this sort of visual shows you how far
+away things can be where they suppress
+
+ align:start position:0%
+away things can be where they suppress
+ 
+
+ align:start position:0%
+away things can be where they suppress
+the activity of a protein and make it a
+
+ align:start position:0%
+the activity of a protein and make it a
+ 
+
+ align:start position:0%
+the activity of a protein and make it a
+poor a catalyst okay so as I said this
+
+ align:start position:0%
+poor a catalyst okay so as I said this
+ 
+
+ align:start position:0%
+poor a catalyst okay so as I said this
+is one of the dis disorders that the
+
+ align:start position:0%
+is one of the dis disorders that the
+ 
+
+ align:start position:0%
+is one of the dis disorders that the
+genetic mutations that tested is tested
+
+ align:start position:0%
+genetic mutations that tested is tested
+ 
+
+ align:start position:0%
+genetic mutations that tested is tested
+for at birth if you have one of these
+
+ align:start position:0%
+for at birth if you have one of these
+ 
+
+ align:start position:0%
+for at birth if you have one of these
+set of mutations you immediately have to
+
+ align:start position:0%
+set of mutations you immediately have to
+ 
+
+ align:start position:0%
+set of mutations you immediately have to
+be put on a diet that's low in
+
+ align:start position:0%
+be put on a diet that's low in
+ 
+
+ align:start position:0%
+be put on a diet that's low in
+phenylalanine so you don't bombard your
+
+ align:start position:0%
+phenylalanine so you don't bombard your
+ 
+
+ align:start position:0%
+phenylalanine so you don't bombard your
+body with too much phenylalanine
+
+ align:start position:0%
+body with too much phenylalanine
+ 
+
+ align:start position:0%
+body with too much phenylalanine
+allowing this is not allowing the
+
+ align:start position:0%
+allowing this is not allowing the
+ 
+
+ align:start position:0%
+allowing this is not allowing the
+phenylalanine to build up too much but
+
+ align:start position:0%
+phenylalanine to build up too much but
+ 
+
+ align:start position:0%
+phenylalanine to build up too much but
+there I don't know if any of you have
+
+ align:start position:0%
+there I don't know if any of you have
+ 
+
+ align:start position:0%
+there I don't know if any of you have
+lately grabbed a can of coca-cola that's
+
+ align:start position:0%
+lately grabbed a can of coca-cola that's
+ 
+
+ align:start position:0%
+lately grabbed a can of coca-cola that's
+got a Spartan as a sweetener it turns
+
+ align:start position:0%
+got a Spartan as a sweetener it turns
+ 
+
+ align:start position:0%
+got a Spartan as a sweetener it turns
+out that sweetener nutrasweet rather is
+
+ align:start position:0%
+out that sweetener nutrasweet rather is
+ 
+
+ align:start position:0%
+out that sweetener nutrasweet rather is
+a dipeptide see but it contains
+
+ align:start position:0%
+a dipeptide see but it contains
+ 
+
+ align:start position:0%
+a dipeptide see but it contains
+phenylalanine so if you drink a ton of
+
+ align:start position:0%
+phenylalanine so if you drink a ton of
+ 
+
+ align:start position:0%
+phenylalanine so if you drink a ton of
+diet drinks that include a nutrasweet
+
+ align:start position:0%
+diet drinks that include a nutrasweet
+ 
+
+ align:start position:0%
+diet drinks that include a nutrasweet
+you are actually bombing yourself with
+
+ align:start position:0%
+you are actually bombing yourself with
+ 
+
+ align:start position:0%
+you are actually bombing yourself with
+high levels of phenylalanine that the
+
+ align:start position:0%
+high levels of phenylalanine that the
+ 
+
+ align:start position:0%
+high levels of phenylalanine that the
+body can't deal with so people who have
+
+ align:start position:0%
+body can't deal with so people who have
+ 
+
+ align:start position:0%
+body can't deal with so people who have
+phenylketonuria ie a defect in that
+
+ align:start position:0%
+phenylketonuria ie a defect in that
+ 
+
+ align:start position:0%
+phenylketonuria ie a defect in that
+enzyme shouldn't be drinking or using
+
+ align:start position:0%
+enzyme shouldn't be drinking or using
+ 
+
+ align:start position:0%
+enzyme shouldn't be drinking or using
+NutraSweet type sweeteners because they
+
+ align:start position:0%
+NutraSweet type sweeteners because they
+ 
+
+ align:start position:0%
+NutraSweet type sweeteners because they
+actually give you too much penile
+
+ align:start position:0%
+actually give you too much penile
+ 
+
+ align:start position:0%
+actually give you too much penile
+alanine at once that you can't mitigate
+
+ align:start position:0%
+alanine at once that you can't mitigate
+ 
+
+ align:start position:0%
+alanine at once that you can't mitigate
+the levels of so I want to just tell you
+
+ align:start position:0%
+the levels of so I want to just tell you
+ 
+
+ align:start position:0%
+the levels of so I want to just tell you
+about these genetic disorders there's a
+
+ align:start position:0%
+about these genetic disorders there's a
+ 
+
+ align:start position:0%
+about these genetic disorders there's a
+fairly decent set that are tested for a
+
+ align:start position:0%
+fairly decent set that are tested for a
+ 
+
+ align:start position:0%
+fairly decent set that are tested for a
+birth but the ones that are tested are
+
+ align:start position:0%
+birth but the ones that are tested are
+ 
+
+ align:start position:0%
+birth but the ones that are tested are
+the ones that you can make dietary
+
+ align:start position:0%
+the ones that you can make dietary
+ 
+
+ align:start position:0%
+the ones that you can make dietary
+modifications or lifestyle modifications
+
+ align:start position:0%
+modifications or lifestyle modifications
+ 
+
+ align:start position:0%
+modifications or lifestyle modifications
+and mitigate the the symptoms and so
+
+ align:start position:0%
+and mitigate the the symptoms and so
+ 
+
+ align:start position:0%
+and mitigate the the symptoms and so
+that's a very important thing to know
+
+ align:start position:0%
+that's a very important thing to know
+ 
+
+ align:start position:0%
+that's a very important thing to know
+you're not tested for things you don't
+
+ align:start position:0%
+you're not tested for things you don't
+ 
+
+ align:start position:0%
+you're not tested for things you don't
+know how to fix because that wouldn't be
+
+ align:start position:0%
+know how to fix because that wouldn't be
+ 
+
+ align:start position:0%
+know how to fix because that wouldn't be
+that wouldn't be appropriate alright any
+
+ align:start position:0%
+that wouldn't be appropriate alright any
+ 
+
+ align:start position:0%
+that wouldn't be appropriate alright any
+questions about that
+
+ align:start position:0%
+questions about that
+ 
+
+ align:start position:0%
+questions about that
+yeah oh you know that was me being
+
+ align:start position:0%
+yeah oh you know that was me being
+ 
+
+ align:start position:0%
+yeah oh you know that was me being
+clunky with her because you guys notice
+
+ align:start position:0%
+clunky with her because you guys notice
+ 
+
+ align:start position:0%
+clunky with her because you guys notice
+everything this morning I was
+
+ align:start position:0%
+everything this morning I was
+ 
+
+ align:start position:0%
+everything this morning I was
+making everybody let's go forward
+
+ align:start position:0%
+making everybody let's go forward
+ 
+
+ align:start position:0%
+making everybody let's go forward
+learned and that and I know what I know
+
+ align:start position:0%
+learned and that and I know what I know
+ 
+
+ align:start position:0%
+learned and that and I know what I know
+exactly what you're talking about this
+
+ align:start position:0%
+exactly what you're talking about this
+ 
+
+ align:start position:0%
+exactly what you're talking about this
+little curve down yeah that's that's me
+
+ align:start position:0%
+little curve down yeah that's that's me
+ 
+
+ align:start position:0%
+little curve down yeah that's that's me
+shaking when I'm doing the Kendra or
+
+ align:start position:0%
+shaking when I'm doing the Kendra or
+ 
+
+ align:start position:0%
+shaking when I'm doing the Kendra or
+drawing it should be a flat but thank
+
+ align:start position:0%
+drawing it should be a flat but thank
+ 
+
+ align:start position:0%
+drawing it should be a flat but thank
+you for noticing that just so that's not
+
+ align:start position:0%
+you for noticing that just so that's not
+ 
+
+ align:start position:0%
+you for noticing that just so that's not
+ambiguous there should not be there
+
+ align:start position:0%
+ambiguous there should not be there
+ 
+
+ align:start position:0%
+ambiguous there should not be there
+could be actually a little dip when
+
+ align:start position:0%
+could be actually a little dip when
+ 
+
+ align:start position:0%
+could be actually a little dip when
+substrates bind to enzymes but I didn't
+
+ align:start position:0%
+substrates bind to enzymes but I didn't
+ 
+
+ align:start position:0%
+substrates bind to enzymes but I didn't
+mean to imply it okay anything else okay
+
+ align:start position:0%
+mean to imply it okay anything else okay
+ 
+
+ align:start position:0%
+mean to imply it okay anything else okay
+so what I want to talk about now is the
+
+ align:start position:0%
+so what I want to talk about now is the
+ 
+
+ align:start position:0%
+so what I want to talk about now is the
+equilibrium problem and what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we have reactions that are
+
+ align:start position:0%
+so if we have reactions that are
+ 
+
+ align:start position:0%
+so if we have reactions that are
+endergonic so we have one of these
+
+ align:start position:0%
+endergonic so we have one of these
+ 
+
+ align:start position:0%
+endergonic so we have one of these
+situations where we have a substrate
+
+ align:start position:0%
+situations where we have a substrate
+ 
+
+ align:start position:0%
+situations where we have a substrate
+going to a product that's higher energy
+
+ align:start position:0%
+going to a product that's higher energy
+ 
+
+ align:start position:0%
+going to a product that's higher energy
+what that means is at equilibrium
+
+ align:start position:0%
+what that means is at equilibrium
+ 
+
+ align:start position:0%
+what that means is at equilibrium
+between substrate and product which is
+
+ align:start position:0%
+between substrate and product which is
+ 
+
+ align:start position:0%
+between substrate and product which is
+defined by the Delta G you have
+
+ align:start position:0%
+defined by the Delta G you have
+ 
+
+ align:start position:0%
+defined by the Delta G you have
+substrate going to product but mostly
+
+ align:start position:0%
+substrate going to product but mostly
+ 
+
+ align:start position:0%
+substrate going to product but mostly
+you've got a lot of substrate there
+
+ align:start position:0%
+you've got a lot of substrate there
+ 
+
+ align:start position:0%
+you've got a lot of substrate there
+which is the amount of each of these is
+
+ align:start position:0%
+which is the amount of each of these is
+ 
+
+ align:start position:0%
+which is the amount of each of these is
+defined by this energy difference okay
+
+ align:start position:0%
+defined by this energy difference okay
+ 
+
+ align:start position:0%
+defined by this energy difference okay
+so how do we survive with these kinds of
+
+ align:start position:0%
+so how do we survive with these kinds of
+ 
+
+ align:start position:0%
+so how do we survive with these kinds of
+transformations when we really want the
+
+ align:start position:0%
+transformations when we really want the
+ 
+
+ align:start position:0%
+transformations when we really want the
+flux through an enzyme to be in the
+
+ align:start position:0%
+flux through an enzyme to be in the
+ 
+
+ align:start position:0%
+flux through an enzyme to be in the
+forwards direction because if we need
+
+ align:start position:0%
+forwards direction because if we need
+ 
+
+ align:start position:0%
+forwards direction because if we need
+the product we need to move things
+
+ align:start position:0%
+the product we need to move things
+ 
+
+ align:start position:0%
+the product we need to move things
+forward so nature deals with this by
+
+ align:start position:0%
+forward so nature deals with this by
+ 
+
+ align:start position:0%
+forward so nature deals with this by
+coupling reactions to other reactions so
+
+ align:start position:0%
+coupling reactions to other reactions so
+ 
+
+ align:start position:0%
+coupling reactions to other reactions so
+it finds ways around the equilibrium
+
+ align:start position:0%
+it finds ways around the equilibrium
+ 
+
+ align:start position:0%
+it finds ways around the equilibrium
+problem by for example putting a series
+
+ align:start position:0%
+problem by for example putting a series
+ 
+
+ align:start position:0%
+problem by for example putting a series
+of reactions for example let's go from A
+
+ align:start position:0%
+of reactions for example let's go from A
+ 
+
+ align:start position:0%
+of reactions for example let's go from A
+to B to C so these are three
+
+ align:start position:0%
+to B to C so these are three
+ 
+
+ align:start position:0%
+to B to C so these are three
+intermediates catalyzed by enzyme one
+
+ align:start position:0%
+intermediates catalyzed by enzyme one
+ 
+
+ align:start position:0%
+intermediates catalyzed by enzyme one
+enzyme to okay and let's just say this
+
+ align:start position:0%
+enzyme to okay and let's just say this
+ 
+
+ align:start position:0%
+enzyme to okay and let's just say this
+has an unfavorable Delta G so we don't
+
+ align:start position:0%
+has an unfavorable Delta G so we don't
+ 
+
+ align:start position:0%
+has an unfavorable Delta G so we don't
+make we have a lot of a we have very
+
+ align:start position:0%
+make we have a lot of a we have very
+ 
+
+ align:start position:0%
+make we have a lot of a we have very
+little B
+
+ align:start position:0%
+little B
+ 
+
+ align:start position:0%
+little B
+and then what happens how are we gonna
+
+ align:start position:0%
+and then what happens how are we gonna
+ 
+
+ align:start position:0%
+and then what happens how are we gonna
+and then let's just say for example this
+
+ align:start position:0%
+and then let's just say for example this
+ 
+
+ align:start position:0%
+and then let's just say for example this
+reaction is favorable all right so let's
+
+ align:start position:0%
+reaction is favorable all right so let's
+ 
+
+ align:start position:0%
+reaction is favorable all right so let's
+say the Delta G here is positive the
+
+ align:start position:0%
+say the Delta G here is positive the
+ 
+
+ align:start position:0%
+say the Delta G here is positive the
+Delta G here is negative all right so by
+
+ align:start position:0%
+Delta G here is negative all right so by
+ 
+
+ align:start position:0%
+Delta G here is negative all right so by
+plus bei mean positive and negative so
+
+ align:start position:0%
+plus bei mean positive and negative so
+ 
+
+ align:start position:0%
+plus bei mean positive and negative so
+this is a favorable reaction whereas
+
+ align:start position:0%
+this is a favorable reaction whereas
+ 
+
+ align:start position:0%
+this is a favorable reaction whereas
+this is an unfavorable reaction how does
+
+ align:start position:0%
+this is an unfavorable reaction how does
+ 
+
+ align:start position:0%
+this is an unfavorable reaction how does
+putting two reactions adjacent to each
+
+ align:start position:0%
+putting two reactions adjacent to each
+ 
+
+ align:start position:0%
+putting two reactions adjacent to each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+happening on the same substrate moving
+
+ align:start position:0%
+happening on the same substrate moving
+ 
+
+ align:start position:0%
+happening on the same substrate moving
+through helped that situation yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perfect so the answer here is that as
+
+ align:start position:0%
+perfect so the answer here is that as
+ 
+
+ align:start position:0%
+perfect so the answer here is that as
+you take whatever B you have and turn it
+
+ align:start position:0%
+you take whatever B you have and turn it
+ 
+
+ align:start position:0%
+you take whatever B you have and turn it
+into C a has a has the e one has to make
+
+ align:start position:0%
+into C a has a has the e one has to make
+ 
+
+ align:start position:0%
+into C a has a has the e one has to make
+more B so you solve the equilibrium
+
+ align:start position:0%
+more B so you solve the equilibrium
+ 
+
+ align:start position:0%
+more B so you solve the equilibrium
+problem in that way to a certain extent
+
+ align:start position:0%
+problem in that way to a certain extent
+ 
+
+ align:start position:0%
+problem in that way to a certain extent
+by just opening the tap at the other end
+
+ align:start position:0%
+by just opening the tap at the other end
+ 
+
+ align:start position:0%
+by just opening the tap at the other end
+of the series a nature organizes a ton
+
+ align:start position:0%
+of the series a nature organizes a ton
+ 
+
+ align:start position:0%
+of the series a nature organizes a ton
+of reactions in sequential pathways to
+
+ align:start position:0%
+of reactions in sequential pathways to
+ 
+
+ align:start position:0%
+of reactions in sequential pathways to
+get around these kinds of problems so
+
+ align:start position:0%
+get around these kinds of problems so
+ 
+
+ align:start position:0%
+get around these kinds of problems so
+this is done by coupling reactions and
+
+ align:start position:0%
+this is done by coupling reactions and
+ 
+
+ align:start position:0%
+this is done by coupling reactions and
+so there are some reactions that are
+
+ align:start position:0%
+so there are some reactions that are
+ 
+
+ align:start position:0%
+so there are some reactions that are
+highly favorable highly exothermic where
+
+ align:start position:0%
+highly favorable highly exothermic where
+ 
+
+ align:start position:0%
+highly favorable highly exothermic where
+you can really sort of guarantee flux
+
+ align:start position:0%
+you can really sort of guarantee flux
+ 
+
+ align:start position:0%
+you can really sort of guarantee flux
+through that enzyme a lot of these
+
+ align:start position:0%
+through that enzyme a lot of these
+ 
+
+ align:start position:0%
+through that enzyme a lot of these
+enzymes are ATP dependent they use and
+
+ align:start position:0%
+enzymes are ATP dependent they use and
+ 
+
+ align:start position:0%
+enzymes are ATP dependent they use and
+burn ATP so you get a lot of energy out
+
+ align:start position:0%
+burn ATP so you get a lot of energy out
+ 
+
+ align:start position:0%
+burn ATP so you get a lot of energy out
+and they drive the flux through enzyme
+
+ align:start position:0%
+and they drive the flux through enzyme
+ 
+
+ align:start position:0%
+and they drive the flux through enzyme
+one by enzyme to being an exergonic
+
+ align:start position:0%
+one by enzyme to being an exergonic
+ 
+
+ align:start position:0%
+one by enzyme to being an exergonic
+reaction while enzyme one is endergonic
+
+ align:start position:0%
+reaction while enzyme one is endergonic
+ 
+
+ align:start position:0%
+reaction while enzyme one is endergonic
+so flux is guaranteed and a lot of
+
+ align:start position:0%
+so flux is guaranteed and a lot of
+ 
+
+ align:start position:0%
+so flux is guaranteed and a lot of
+pathways sort of set up to be in this
+
+ align:start position:0%
+pathways sort of set up to be in this
+ 
+
+ align:start position:0%
+pathways sort of set up to be in this
+way with this coupling of the
+
+ align:start position:0%
+way with this coupling of the
+ 
+
+ align:start position:0%
+way with this coupling of the
+chemistry's so what we find is that
+
+ align:start position:0%
+chemistry's so what we find is that
+ 
+
+ align:start position:0%
+chemistry's so what we find is that
+enzymes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all work in pathways where they
+
+ align:start position:0%
+first of all work in pathways where they
+ 
+
+ align:start position:0%
+first of all work in pathways where they
+are co-located in certain places they
+
+ align:start position:0%
+are co-located in certain places they
+ 
+
+ align:start position:0%
+are co-located in certain places they
+may be for example who localized to
+
+ align:start position:0%
+may be for example who localized to
+ 
+
+ align:start position:0%
+may be for example who localized to
+certain organelles in a human cell they
+
+ align:start position:0%
+certain organelles in a human cell they
+ 
+
+ align:start position:0%
+certain organelles in a human cell they
+may be Co localized in the mitochondria
+
+ align:start position:0%
+may be Co localized in the mitochondria
+ 
+
+ align:start position:0%
+may be Co localized in the mitochondria
+or in some organelle and we'll talk more
+
+ align:start position:0%
+or in some organelle and we'll talk more
+ 
+
+ align:start position:0%
+or in some organelle and we'll talk more
+about organelles and mitochondria later
+
+ align:start position:0%
+about organelles and mitochondria later
+ 
+
+ align:start position:0%
+about organelles and mitochondria later
+they could be Co localized at a membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you ensure that the enzymes are
+
+ align:start position:0%
+and so you ensure that the enzymes are
+ 
+
+ align:start position:0%
+and so you ensure that the enzymes are
+together by putting them in the same
+
+ align:start position:0%
+together by putting them in the same
+ 
+
+ align:start position:0%
+together by putting them in the same
+place and then nature also evolves ways
+
+ align:start position:0%
+place and then nature also evolves ways
+ 
+
+ align:start position:0%
+place and then nature also evolves ways
+where the enzymes physically interact
+
+ align:start position:0%
+where the enzymes physically interact
+ 
+
+ align:start position:0%
+where the enzymes physically interact
+with each other either covalently or
+
+ align:start position:0%
+with each other either covalently or
+ 
+
+ align:start position:0%
+with each other either covalently or
+non-covalently so they could be
+
+ align:start position:0%
+non-covalently so they could be
+ 
+
+ align:start position:0%
+non-covalently so they could be
+associated in the pathway by some kind
+
+ align:start position:0%
+associated in the pathway by some kind
+ 
+
+ align:start position:0%
+associated in the pathway by some kind
+of non covalent interaction or you may
+
+ align:start position:0%
+of non covalent interaction or you may
+ 
+
+ align:start position:0%
+of non covalent interaction or you may
+actually link enzymes to make them
+
+ align:start position:0%
+actually link enzymes to make them
+ 
+
+ align:start position:0%
+actually link enzymes to make them
+single species so if this is enzyme one
+
+ align:start position:0%
+single species so if this is enzyme one
+ 
+
+ align:start position:0%
+single species so if this is enzyme one
+and this is enzyme 2 here you have an
+
+ align:start position:0%
+and this is enzyme 2 here you have an
+ 
+
+ align:start position:0%
+and this is enzyme 2 here you have an
+enzyme one enzyme two single long
+
+ align:start position:0%
+enzyme one enzyme two single long
+ 
+
+ align:start position:0%
+enzyme one enzyme two single long
+polypeptide chain that has two domains
+
+ align:start position:0%
+polypeptide chain that has two domains
+ 
+
+ align:start position:0%
+polypeptide chain that has two domains
+they can't get away from each other
+
+ align:start position:0%
+they can't get away from each other
+ 
+
+ align:start position:0%
+they can't get away from each other
+because they're joined covalently and
+
+ align:start position:0%
+because they're joined covalently and
+ 
+
+ align:start position:0%
+because they're joined covalently and
+they catalyze sequential reactions this
+
+ align:start position:0%
+they catalyze sequential reactions this
+ 
+
+ align:start position:0%
+they catalyze sequential reactions this
+just doesn't happen with just three
+
+ align:start position:0%
+just doesn't happen with just three
+ 
+
+ align:start position:0%
+just doesn't happen with just three
+enzymes it can happen with ten enzymes
+
+ align:start position:0%
+enzymes it can happen with ten enzymes
+ 
+
+ align:start position:0%
+enzymes it can happen with ten enzymes
+or more so they're very clever ways to
+
+ align:start position:0%
+or more so they're very clever ways to
+ 
+
+ align:start position:0%
+or more so they're very clever ways to
+ensure the plucks occurs through
+
+ align:start position:0%
+ensure the plucks occurs through
+ 
+
+ align:start position:0%
+ensure the plucks occurs through
+pathways but don't forget all along that
+
+ align:start position:0%
+pathways but don't forget all along that
+ 
+
+ align:start position:0%
+pathways but don't forget all along that
+each of these enzymes is responsible for
+
+ align:start position:0%
+each of these enzymes is responsible for
+ 
+
+ align:start position:0%
+each of these enzymes is responsible for
+a single transformation that's important
+
+ align:start position:0%
+a single transformation that's important
+ 
+
+ align:start position:0%
+a single transformation that's important
+there's another phenomenon that having
+
+ align:start position:0%
+there's another phenomenon that having
+ 
+
+ align:start position:0%
+there's another phenomenon that having
+flux through pathways is very useful for
+
+ align:start position:0%
+flux through pathways is very useful for
+ 
+
+ align:start position:0%
+flux through pathways is very useful for
+is to deal with toxic intermediates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because that makes it very advantageous
+
+ align:start position:0%
+because that makes it very advantageous
+ 
+
+ align:start position:0%
+because that makes it very advantageous
+again to couple reactions so let's say
+
+ align:start position:0%
+again to couple reactions so let's say
+ 
+
+ align:start position:0%
+again to couple reactions so let's say
+product B is toxic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't want it hanging around much we
+
+ align:start position:0%
+we don't want it hanging around much we
+ 
+
+ align:start position:0%
+we don't want it hanging around much we
+don't want it released from an enzyme to
+
+ align:start position:0%
+don't want it released from an enzyme to
+ 
+
+ align:start position:0%
+don't want it released from an enzyme to
+go do damage somewhere in the cell
+
+ align:start position:0%
+go do damage somewhere in the cell
+ 
+
+ align:start position:0%
+go do damage somewhere in the cell
+so having flux through a pathway
+
+ align:start position:0%
+so having flux through a pathway
+ 
+
+ align:start position:0%
+so having flux through a pathway
+basically ensures the B never gets out
+
+ align:start position:0%
+basically ensures the B never gets out
+ 
+
+ align:start position:0%
+basically ensures the B never gets out
+of the game it just goes straight to
+
+ align:start position:0%
+of the game it just goes straight to
+ 
+
+ align:start position:0%
+of the game it just goes straight to
+enzyme 2 so that's another another
+
+ align:start position:0%
+enzyme 2 so that's another another
+ 
+
+ align:start position:0%
+enzyme 2 so that's another another
+physical advantage of those processes
+
+ align:start position:0%
+physical advantage of those processes
+ 
+
+ align:start position:0%
+physical advantage of those processes
+being linked together and finally the
+
+ align:start position:0%
+being linked together and finally the
+ 
+
+ align:start position:0%
+being linked together and finally the
+process also ensures a very nice
+
+ align:start position:0%
+process also ensures a very nice
+ 
+
+ align:start position:0%
+process also ensures a very nice
+opportunity to do regulation so here we
+
+ align:start position:0%
+opportunity to do regulation so here we
+ 
+
+ align:start position:0%
+opportunity to do regulation so here we
+on this slide I show you this sort of
+
+ align:start position:0%
+on this slide I show you this sort of
+ 
+
+ align:start position:0%
+on this slide I show you this sort of
+mega mess of metabolic pathways in
+
+ align:start position:0%
+mega mess of metabolic pathways in
+ 
+
+ align:start position:0%
+mega mess of metabolic pathways in
+physiology that there would be the
+
+ align:start position:0%
+physiology that there would be the
+ 
+
+ align:start position:0%
+physiology that there would be the
+critter the krebs cycle but all the
+
+ align:start position:0%
+critter the krebs cycle but all the
+ 
+
+ align:start position:0%
+critter the krebs cycle but all the
+metabolic pathways that are all
+
+ align:start position:0%
+metabolic pathways that are all
+ 
+
+ align:start position:0%
+metabolic pathways that are all
+interlinked and many of these pathways
+
+ align:start position:0%
+interlinked and many of these pathways
+ 
+
+ align:start position:0%
+interlinked and many of these pathways
+will be Co localized but steps in these
+
+ align:start position:0%
+will be Co localized but steps in these
+ 
+
+ align:start position:0%
+will be Co localized but steps in these
+pathways will be Co localized as
+
+ align:start position:0%
+pathways will be Co localized as
+ 
+
+ align:start position:0%
+pathways will be Co localized as
+clusters and so that deals tells you how
+
+ align:start position:0%
+clusters and so that deals tells you how
+ 
+
+ align:start position:0%
+clusters and so that deals tells you how
+we can solve the equilibrium problem by
+
+ align:start position:0%
+we can solve the equilibrium problem by
+ 
+
+ align:start position:0%
+we can solve the equilibrium problem by
+linking enzymes for flux through
+
+ align:start position:0%
+linking enzymes for flux through
+ 
+
+ align:start position:0%
+linking enzymes for flux through
+pathways and one of the best examples is
+
+ align:start position:0%
+pathways and one of the best examples is
+ 
+
+ align:start position:0%
+pathways and one of the best examples is
+in aerobic glycolysis we're in the early
+
+ align:start position:0%
+in aerobic glycolysis we're in the early
+ 
+
+ align:start position:0%
+in aerobic glycolysis we're in the early
+steps they're not energetically
+
+ align:start position:0%
+steps they're not energetically
+ 
+
+ align:start position:0%
+steps they're not energetically
+favorable you use ATP to start to break
+
+ align:start position:0%
+favorable you use ATP to start to break
+ 
+
+ align:start position:0%
+favorable you use ATP to start to break
+down glucose then you get to a certain
+
+ align:start position:0%
+down glucose then you get to a certain
+ 
+
+ align:start position:0%
+down glucose then you get to a certain
+intermediate where it's conversion to a
+
+ align:start position:0%
+intermediate where it's conversion to a
+ 
+
+ align:start position:0%
+intermediate where it's conversion to a
+smaller molecule generates ATP with very
+
+ align:start position:0%
+smaller molecule generates ATP with very
+ 
+
+ align:start position:0%
+smaller molecule generates ATP with very
+favorable reactions so glycolysis is a
+
+ align:start position:0%
+favorable reactions so glycolysis is a
+ 
+
+ align:start position:0%
+favorable reactions so glycolysis is a
+really great example of this now the
+
+ align:start position:0%
+really great example of this now the
+ 
+
+ align:start position:0%
+really great example of this now the
+other thing that I just want to describe
+
+ align:start position:0%
+other thing that I just want to describe
+ 
+
+ align:start position:0%
+other thing that I just want to describe
+to you is the issue of feedback and I
+
+ align:start position:0%
+to you is the issue of feedback and I
+ 
+
+ align:start position:0%
+to you is the issue of feedback and I
+describe this here on this slide and so
+
+ align:start position:0%
+describe this here on this slide and so
+ 
+
+ align:start position:0%
+describe this here on this slide and so
+we'll talk about it on this slide so if
+
+ align:start position:0%
+we'll talk about it on this slide so if
+ 
+
+ align:start position:0%
+we'll talk about it on this slide so if
+we are working with a pathway that goes
+
+ align:start position:0%
+we are working with a pathway that goes
+ 
+
+ align:start position:0%
+we are working with a pathway that goes
+through multiple steps to make an end
+
+ align:start position:0%
+through multiple steps to make an end
+ 
+
+ align:start position:0%
+through multiple steps to make an end
+product five steps three steps over here
+
+ align:start position:0%
+product five steps three steps over here
+ 
+
+ align:start position:0%
+product five steps three steps over here
+and you've made too much of that you've
+
+ align:start position:0%
+and you've made too much of that you've
+ 
+
+ align:start position:0%
+and you've made too much of that you've
+already made a lot of that product and
+
+ align:start position:0%
+already made a lot of that product and
+ 
+
+ align:start position:0%
+already made a lot of that product and
+you don't need anymore nature also has
+
+ align:start position:0%
+you don't need anymore nature also has
+ 
+
+ align:start position:0%
+you don't need anymore nature also has
+in place a regulatory mechanism to
+
+ align:start position:0%
+in place a regulatory mechanism to
+ 
+
+ align:start position:0%
+in place a regulatory mechanism to
+feedback and stop slot
+
+ align:start position:0%
+feedback and stop slot
+ 
+
+ align:start position:0%
+feedback and stop slot
+through the pathway you don't just stop
+
+ align:start position:0%
+through the pathway you don't just stop
+ 
+
+ align:start position:0%
+through the pathway you don't just stop
+all the enzymes you find a way to stop
+
+ align:start position:0%
+all the enzymes you find a way to stop
+ 
+
+ align:start position:0%
+all the enzymes you find a way to stop
+the first enzyme so this is a very
+
+ align:start position:0%
+the first enzyme so this is a very
+ 
+
+ align:start position:0%
+the first enzyme so this is a very
+important paradigm in biochemistry and
+
+ align:start position:0%
+important paradigm in biochemistry and
+ 
+
+ align:start position:0%
+important paradigm in biochemistry and
+that's called negative feedback so I'm
+
+ align:start position:0%
+that's called negative feedback so I'm
+ 
+
+ align:start position:0%
+that's called negative feedback so I'm
+showing you it here just in a very
+
+ align:start position:0%
+showing you it here just in a very
+ 
+
+ align:start position:0%
+showing you it here just in a very
+simple cartoon form in the isoleucine
+
+ align:start position:0%
+simple cartoon form in the isoleucine
+ 
+
+ align:start position:0%
+simple cartoon form in the isoleucine
+biosynthesis pathway that's one of the
+
+ align:start position:0%
+biosynthesis pathway that's one of the
+ 
+
+ align:start position:0%
+biosynthesis pathway that's one of the
+hydrophobic amino acids this is an
+
+ align:start position:0%
+hydrophobic amino acids this is an
+ 
+
+ align:start position:0%
+hydrophobic amino acids this is an
+intermediate that is on its way from
+
+ align:start position:0%
+intermediate that is on its way from
+ 
+
+ align:start position:0%
+intermediate that is on its way from
+this amino acid that is polar but not
+
+ align:start position:0%
+this amino acid that is polar but not
+ 
+
+ align:start position:0%
+this amino acid that is polar but not
+charged threonine so threonine gets
+
+ align:start position:0%
+charged threonine so threonine gets
+ 
+
+ align:start position:0%
+charged threonine so threonine gets
+converted to isoleucine we need
+
+ align:start position:0%
+converted to isoleucine we need
+ 
+
+ align:start position:0%
+converted to isoleucine we need
+threonine to make isoleucine but once we
+
+ align:start position:0%
+threonine to make isoleucine but once we
+ 
+
+ align:start position:0%
+threonine to make isoleucine but once we
+got a lot of isoleucine it binds to the
+
+ align:start position:0%
+got a lot of isoleucine it binds to the
+ 
+
+ align:start position:0%
+got a lot of isoleucine it binds to the
+very first enzyme in the pathway and
+
+ align:start position:0%
+very first enzyme in the pathway and
+ 
+
+ align:start position:0%
+very first enzyme in the pathway and
+acts as an arrow low steric regulator
+
+ align:start position:0%
+acts as an arrow low steric regulator
+ 
+
+ align:start position:0%
+acts as an arrow low steric regulator
+that dampens activity so in this case I
+
+ align:start position:0%
+that dampens activity so in this case I
+ 
+
+ align:start position:0%
+that dampens activity so in this case I
+just want to point out to you that I'm
+
+ align:start position:0%
+just want to point out to you that I'm
+ 
+
+ align:start position:0%
+just want to point out to you that I'm
+showing a very common way we know tape
+
+ align:start position:0%
+showing a very common way we know tape
+ 
+
+ align:start position:0%
+showing a very common way we know tape
+things when we are talking about
+
+ align:start position:0%
+things when we are talking about
+ 
+
+ align:start position:0%
+things when we are talking about
+inhibiting a reaction we draw it like
+
+ align:start position:0%
+inhibiting a reaction we draw it like
+ 
+
+ align:start position:0%
+inhibiting a reaction we draw it like
+this we align and then align to the so
+
+ align:start position:0%
+this we align and then align to the so
+ 
+
+ align:start position:0%
+this we align and then align to the so
+the arrow just which means you've
+
+ align:start position:0%
+the arrow just which means you've
+ 
+
+ align:start position:0%
+the arrow just which means you've
+stopped the activity so you'll see this
+
+ align:start position:0%
+stopped the activity so you'll see this
+ 
+
+ align:start position:0%
+stopped the activity so you'll see this
+again and again you're gonna see it a
+
+ align:start position:0%
+again and again you're gonna see it a
+ 
+
+ align:start position:0%
+again and again you're gonna see it a
+lot in signaling pathways because things
+
+ align:start position:0%
+lot in signaling pathways because things
+ 
+
+ align:start position:0%
+lot in signaling pathways because things
+often feedback so another thing that
+
+ align:start position:0%
+often feedback so another thing that
+ 
+
+ align:start position:0%
+often feedback so another thing that
+nature ensures in additions are not
+
+ align:start position:0%
+nature ensures in additions are not
+ 
+
+ align:start position:0%
+nature ensures in additions are not
+building up toxic products and dealing
+
+ align:start position:0%
+building up toxic products and dealing
+ 
+
+ align:start position:0%
+building up toxic products and dealing
+with the equilibria is that you don't
+
+ align:start position:0%
+with the equilibria is that you don't
+ 
+
+ align:start position:0%
+with the equilibria is that you don't
+want a ton of enzymes working to make
+
+ align:start position:0%
+want a ton of enzymes working to make
+ 
+
+ align:start position:0%
+want a ton of enzymes working to make
+something you don't need anymore so you
+
+ align:start position:0%
+something you don't need anymore so you
+ 
+
+ align:start position:0%
+something you don't need anymore so you
+might as well take the end product and
+
+ align:start position:0%
+might as well take the end product and
+ 
+
+ align:start position:0%
+might as well take the end product and
+use it to stop the first enzyme as that
+
+ align:start position:0%
+use it to stop the first enzyme as that
+ 
+
+ align:start position:0%
+use it to stop the first enzyme as that
+end product becomes scarce it
+
+ align:start position:0%
+end product becomes scarce it
+ 
+
+ align:start position:0%
+end product becomes scarce it
+dissociates from the first enzyme and it
+
+ align:start position:0%
+dissociates from the first enzyme and it
+ 
+
+ align:start position:0%
+dissociates from the first enzyme and it
+turns the pathway back on again and I
+
+ align:start position:0%
+turns the pathway back on again and I
+ 
+
+ align:start position:0%
+turns the pathway back on again and I
+think that's a really neat way of making
+
+ align:start position:0%
+think that's a really neat way of making
+ 
+
+ align:start position:0%
+think that's a really neat way of making
+that happen and also in these cases the
+
+ align:start position:0%
+that happen and also in these cases the
+ 
+
+ align:start position:0%
+that happen and also in these cases the
+enzymes have to be clustered as a group
+
+ align:start position:0%
+enzymes have to be clustered as a group
+ 
+
+ align:start position:0%
+enzymes have to be clustered as a group
+because you wouldn't get those local
+
+ align:start position:0%
+because you wouldn't get those local
+ 
+
+ align:start position:0%
+because you wouldn't get those local
+concentrations to be so advantageous if
+
+ align:start position:0%
+concentrations to be so advantageous if
+ 
+
+ align:start position:0%
+concentrations to be so advantageous if
+the enzymes weren't co-localize does
+
+ align:start position:0%
+the enzymes weren't co-localize does
+ 
+
+ align:start position:0%
+the enzymes weren't co-localize does
+that make sense if they weren't in a
+
+ align:start position:0%
+that make sense if they weren't in a
+ 
+
+ align:start position:0%
+that make sense if they weren't in a
+really near location that enzyme that
+
+ align:start position:0%
+really near location that enzyme that
+ 
+
+ align:start position:0%
+really near location that enzyme that
+pursuit produces isoleucine that
+
+ align:start position:0%
+pursuit produces isoleucine that
+ 
+
+ align:start position:0%
+pursuit produces isoleucine that
+isoleucine couldn't bind back to the
+
+ align:start position:0%
+isoleucine couldn't bind back to the
+ 
+
+ align:start position:0%
+isoleucine couldn't bind back to the
+first enzyme in the pathway if they were
+
+ align:start position:0%
+first enzyme in the pathway if they were
+ 
+
+ align:start position:0%
+first enzyme in the pathway if they were
+in different compartments of the cell
+
+ align:start position:0%
+in different compartments of the cell
+ 
+
+ align:start position:0%
+in different compartments of the cell
+okay everyone good with that
+
+ align:start position:0%
+okay everyone good with that
+ 
+
+ align:start position:0%
+okay everyone good with that
+good alright okay so now we are moving
+
+ align:start position:0%
+good alright okay so now we are moving
+ 
+
+ align:start position:0%
+good alright okay so now we are moving
+on to carbohydrates it's a pretty
+
+ align:start position:0%
+on to carbohydrates it's a pretty
+ 
+
+ align:start position:0%
+on to carbohydrates it's a pretty
+strange word carbohydrate but actually
+
+ align:start position:0%
+strange word carbohydrate but actually
+ 
+
+ align:start position:0%
+strange word carbohydrate but actually
+it relates to early findings that
+
+ align:start position:0%
+it relates to early findings that
+ 
+
+ align:start position:0%
+it relates to early findings that
+glucose is a carbohydrate and its
+
+ align:start position:0%
+glucose is a carbohydrate and its
+ 
+
+ align:start position:0%
+glucose is a carbohydrate and its
+molecular formula is c6h12o6 so they
+
+ align:start position:0%
+molecular formula is c6h12o6 so they
+ 
+
+ align:start position:0%
+molecular formula is c6h12o6 so they
+called it a hydrate of carbon before
+
+ align:start position:0%
+called it a hydrate of carbon before
+ 
+
+ align:start position:0%
+called it a hydrate of carbon before
+when they knew the elemental composition
+
+ align:start position:0%
+when they knew the elemental composition
+ 
+
+ align:start position:0%
+when they knew the elemental composition
+but they didn't know anything about the
+
+ align:start position:0%
+but they didn't know anything about the
+ 
+
+ align:start position:0%
+but they didn't know anything about the
+structure there's a lot of carbohydrates
+
+ align:start position:0%
+structure there's a lot of carbohydrates
+ 
+
+ align:start position:0%
+structure there's a lot of carbohydrates
+that don't be hey doughnut BAE this rule
+
+ align:start position:0%
+that don't be hey doughnut BAE this rule
+ 
+
+ align:start position:0%
+that don't be hey doughnut BAE this rule
+but that's where the name comes from a
+
+ align:start position:0%
+but that's where the name comes from a
+ 
+
+ align:start position:0%
+but that's where the name comes from a
+hydrate of carbon all right now
+
+ align:start position:0%
+hydrate of carbon all right now
+ 
+
+ align:start position:0%
+hydrate of carbon all right now
+carbohydrates are account for what do
+
+ align:start position:0%
+carbohydrates are account for what do
+ 
+
+ align:start position:0%
+carbohydrates are account for what do
+they have here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25% of the mass of macromolecules so a
+
+ align:start position:0%
+25% of the mass of macromolecules so a
+ 
+
+ align:start position:0%
+25% of the mass of macromolecules so a
+good amount there are very very
+
+ align:start position:0%
+good amount there are very very
+ 
+
+ align:start position:0%
+good amount there are very very
+important carbohydrates in central
+
+ align:start position:0%
+important carbohydrates in central
+ 
+
+ align:start position:0%
+important carbohydrates in central
+metabolism we use carbohydrates as a
+
+ align:start position:0%
+metabolism we use carbohydrates as a
+ 
+
+ align:start position:0%
+metabolism we use carbohydrates as a
+source of energy but also carbohydrates
+
+ align:start position:0%
+source of energy but also carbohydrates
+ 
+
+ align:start position:0%
+source of energy but also carbohydrates
+a part of storage of energy in the form
+
+ align:start position:0%
+a part of storage of energy in the form
+ 
+
+ align:start position:0%
+a part of storage of energy in the form
+of polymeric structures that I'll
+
+ align:start position:0%
+of polymeric structures that I'll
+ 
+
+ align:start position:0%
+of polymeric structures that I'll
+describe to you there are different ones
+
+ align:start position:0%
+describe to you there are different ones
+ 
+
+ align:start position:0%
+describe to you there are different ones
+in plants and in humans
+
+ align:start position:0%
+in plants and in humans
+ 
+
+ align:start position:0%
+in plants and in humans
+one is glycogen one is cellulose but
+
+ align:start position:0%
+one is glycogen one is cellulose but
+ 
+
+ align:start position:0%
+one is glycogen one is cellulose but
+carbohydrates have an increasingly
+
+ align:start position:0%
+carbohydrates have an increasingly
+ 
+
+ align:start position:0%
+carbohydrates have an increasingly
+important role in the extracellular
+
+ align:start position:0%
+important role in the extracellular
+ 
+
+ align:start position:0%
+important role in the extracellular
+matrix in these polymers that are
+
+ align:start position:0%
+matrix in these polymers that are
+ 
+
+ align:start position:0%
+matrix in these polymers that are
+wrapped around your cells and also a
+
+ align:start position:0%
+wrapped around your cells and also a
+ 
+
+ align:start position:0%
+wrapped around your cells and also a
+signaling entities both inside and
+
+ align:start position:0%
+signaling entities both inside and
+ 
+
+ align:start position:0%
+signaling entities both inside and
+outside the cell so we used to think of
+
+ align:start position:0%
+outside the cell so we used to think of
+ 
+
+ align:start position:0%
+outside the cell so we used to think of
+carbohydrates and straightaway connect
+
+ align:start position:0%
+carbohydrates and straightaway connect
+ 
+
+ align:start position:0%
+carbohydrates and straightaway connect
+this with metabolism but the story is
+
+ align:start position:0%
+this with metabolism but the story is
+ 
+
+ align:start position:0%
+this with metabolism but the story is
+far greater than that and I'll try to
+
+ align:start position:0%
+far greater than that and I'll try to
+ 
+
+ align:start position:0%
+far greater than that and I'll try to
+explain to you why and it's because of
+
+ align:start position:0%
+explain to you why and it's because of
+ 
+
+ align:start position:0%
+explain to you why and it's because of
+the richness of functional groups in a
+
+ align:start position:0%
+the richness of functional groups in a
+ 
+
+ align:start position:0%
+the richness of functional groups in a
+carbohydrate so the simplest
+
+ align:start position:0%
+carbohydrate so the simplest
+ 
+
+ align:start position:0%
+carbohydrate so the simplest
+carbohydrate before I go up there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a three carbon molecule this would
+
+ align:start position:0%
+is a three carbon molecule this would
+ 
+
+ align:start position:0%
+is a three carbon molecule this would
+actually be called glyceraldehyde but
+
+ align:start position:0%
+actually be called glyceraldehyde but
+ 
+
+ align:start position:0%
+actually be called glyceraldehyde but
+don't worry about that other name for it
+
+ align:start position:0%
+don't worry about that other name for it
+ 
+
+ align:start position:0%
+don't worry about that other name for it
+it's a three carbon carbohydrate and
+
+ align:start position:0%
+it's a three carbon carbohydrate and
+ 
+
+ align:start position:0%
+it's a three carbon carbohydrate and
+this molecule would be called a triose
+
+ align:start position:0%
+this molecule would be called a triose
+ 
+
+ align:start position:0%
+this molecule would be called a triose
+so we've got a couple of new a new
+
+ align:start position:0%
+so we've got a couple of new a new
+ 
+
+ align:start position:0%
+so we've got a couple of new a new
+suffix because anything that there's a
+
+ align:start position:0%
+suffix because anything that there's a
+ 
+
+ align:start position:0%
+suffix because anything that there's a
+carbohydrate ends with the suffix OSE
+
+ align:start position:0%
+carbohydrate ends with the suffix OSE
+ 
+
+ align:start position:0%
+carbohydrate ends with the suffix OSE
+not to be confused with the suffix ASE
+
+ align:start position:0%
+not to be confused with the suffix ASE
+ 
+
+ align:start position:0%
+not to be confused with the suffix ASE
+which is an enzyme so look carefully
+
+ align:start position:0%
+which is an enzyme so look carefully
+ 
+
+ align:start position:0%
+which is an enzyme so look carefully
+whether it's an A or an O because it's
+
+ align:start position:0%
+whether it's an A or an O because it's
+ 
+
+ align:start position:0%
+whether it's an A or an O because it's
+the difference between a big protein
+
+ align:start position:0%
+the difference between a big protein
+ 
+
+ align:start position:0%
+the difference between a big protein
+that catalyzes a reaction and a
+
+ align:start position:0%
+that catalyzes a reaction and a
+ 
+
+ align:start position:0%
+that catalyzes a reaction and a
+carbohydrate so a triose would be a
+
+ align:start position:0%
+carbohydrate so a triose would be a
+ 
+
+ align:start position:0%
+carbohydrate so a triose would be a
+carbohydrate with three carbons they
+
+ align:start position:0%
+carbohydrate with three carbons they
+ 
+
+ align:start position:0%
+carbohydrate with three carbons they
+have an aldehyde or let's just say they
+
+ align:start position:0%
+have an aldehyde or let's just say they
+ 
+
+ align:start position:0%
+have an aldehyde or let's just say they
+have a carbonyl functionality so
+
+ align:start position:0%
+have a carbonyl functionality so
+ 
+
+ align:start position:0%
+have a carbonyl functionality so
+remember the that there would be lone
+
+ align:start position:0%
+remember the that there would be lone
+ 
+
+ align:start position:0%
+remember the that there would be lone
+pair electrons on those OHS similarly on
+
+ align:start position:0%
+pair electrons on those OHS similarly on
+ 
+
+ align:start position:0%
+pair electrons on those OHS similarly on
+these and remember that each of these
+
+ align:start position:0%
+these and remember that each of these
+ 
+
+ align:start position:0%
+these and remember that each of these
+vertices corresponds to a carbon it's
+
+ align:start position:0%
+vertices corresponds to a carbon it's
+ 
+
+ align:start position:0%
+vertices corresponds to a carbon it's
+some the way you recognize carbohydrates
+
+ align:start position:0%
+some the way you recognize carbohydrates
+ 
+
+ align:start position:0%
+some the way you recognize carbohydrates
+is most commonly is that they are rich
+
+ align:start position:0%
+is most commonly is that they are rich
+ 
+
+ align:start position:0%
+is most commonly is that they are rich
+in carbon - o H bonds which are
+
+ align:start position:0%
+in carbon - o H bonds which are
+ 
+
+ align:start position:0%
+in carbon - o H bonds which are
+hydroxyls which makes them polar
+
+ align:start position:0%
+hydroxyls which makes them polar
+ 
+
+ align:start position:0%
+hydroxyls which makes them polar
+molecules likely to be highly so baited
+
+ align:start position:0%
+molecules likely to be highly so baited
+ 
+
+ align:start position:0%
+molecules likely to be highly so baited
+in water and very different for the from
+
+ align:start position:0%
+in water and very different for the from
+ 
+
+ align:start position:0%
+in water and very different for the from
+the compounds that are rich in just CH
+
+ align:start position:0%
+the compounds that are rich in just CH
+ 
+
+ align:start position:0%
+the compounds that are rich in just CH
+bonds that don't have such opportunities
+
+ align:start position:0%
+bonds that don't have such opportunities
+ 
+
+ align:start position:0%
+bonds that don't have such opportunities
+so if you see a molecule and it's got a
+
+ align:start position:0%
+so if you see a molecule and it's got a
+ 
+
+ align:start position:0%
+so if you see a molecule and it's got a
+bunch of CHS but not a bunch of OHS it's
+
+ align:start position:0%
+bunch of CHS but not a bunch of OHS it's
+ 
+
+ align:start position:0%
+bunch of CHS but not a bunch of OHS it's
+probably a lipid if you see a com a
+
+ align:start position:0%
+probably a lipid if you see a com a
+ 
+
+ align:start position:0%
+probably a lipid if you see a com a
+compound that's rich in OHS it's likely
+
+ align:start position:0%
+compound that's rich in OHS it's likely
+ 
+
+ align:start position:0%
+compound that's rich in OHS it's likely
+to be a carbohydrate the story gets a
+
+ align:start position:0%
+to be a carbohydrate the story gets a
+ 
+
+ align:start position:0%
+to be a carbohydrate the story gets a
+little bit more interesting as we move
+
+ align:start position:0%
+little bit more interesting as we move
+ 
+
+ align:start position:0%
+little bit more interesting as we move
+up to some of the different
+
+ align:start position:0%
+up to some of the different
+ 
+
+ align:start position:0%
+up to some of the different
+carbohydrates which I've shown you there
+
+ align:start position:0%
+carbohydrates which I've shown you there
+ 
+
+ align:start position:0%
+carbohydrates which I've shown you there
+on that screen and I'm going to go
+
+ align:start position:0%
+on that screen and I'm going to go
+ 
+
+ align:start position:0%
+on that screen and I'm going to go
+forward to talk about those because this
+
+ align:start position:0%
+forward to talk about those because this
+ 
+
+ align:start position:0%
+forward to talk about those because this
+triose is important in primary
+
+ align:start position:0%
+triose is important in primary
+ 
+
+ align:start position:0%
+triose is important in primary
+metabolism
+
+ align:start position:0%
+metabolism
+ 
+
+ align:start position:0%
+metabolism
+we break down carbon carbohydrates that
+
+ align:start position:0%
+we break down carbon carbohydrates that
+ 
+
+ align:start position:0%
+we break down carbon carbohydrates that
+have six sugars to small carbohydrates
+
+ align:start position:0%
+have six sugars to small carbohydrates
+ 
+
+ align:start position:0%
+have six sugars to small carbohydrates
+that have three excuse me
+
+ align:start position:0%
+that have three excuse me
+ 
+
+ align:start position:0%
+that have three excuse me
+carbohydrates that have six carbons two
+
+ align:start position:0%
+carbohydrates that have six carbons two
+ 
+
+ align:start position:0%
+carbohydrates that have six carbons two
+carbohydrates that have three carbons
+
+ align:start position:0%
+carbohydrates that have three carbons
+ 
+
+ align:start position:0%
+carbohydrates that have three carbons
+and that's where these three carbon
+
+ align:start position:0%
+and that's where these three carbon
+ 
+
+ align:start position:0%
+and that's where these three carbon
+entities crop up but I want to focus you
+
+ align:start position:0%
+entities crop up but I want to focus you
+ 
+
+ align:start position:0%
+entities crop up but I want to focus you
+in on two sets of carbohydrates the
+
+ align:start position:0%
+in on two sets of carbohydrates the
+ 
+
+ align:start position:0%
+in on two sets of carbohydrates the
+hexoses and the pentoses so we
+
+ align:start position:0%
+hexoses and the pentoses so we
+ 
+
+ align:start position:0%
+hexoses and the pentoses so we
+immediately know their carbohydrates
+
+ align:start position:0%
+immediately know their carbohydrates
+ 
+
+ align:start position:0%
+immediately know their carbohydrates
+right OSE the hexoses obviously has six
+
+ align:start position:0%
+right OSE the hexoses obviously has six
+ 
+
+ align:start position:0%
+right OSE the hexoses obviously has six
+carbons and the pentoses have five
+
+ align:start position:0%
+carbons and the pentoses have five
+ 
+
+ align:start position:0%
+carbons and the pentoses have five
+carbons and these are the most important
+
+ align:start position:0%
+carbons and these are the most important
+ 
+
+ align:start position:0%
+carbons and these are the most important
+of the carbohydrates yes there are
+
+ align:start position:0%
+of the carbohydrates yes there are
+ 
+
+ align:start position:0%
+of the carbohydrates yes there are
+carbohydrates with four carbons and then
+
+ align:start position:0%
+carbohydrates with four carbons and then
+ 
+
+ align:start position:0%
+carbohydrates with four carbons and then
+there were ones with seven eight nine
+
+ align:start position:0%
+there were ones with seven eight nine
+ 
+
+ align:start position:0%
+there were ones with seven eight nine
+carbons but these are the ones we'll
+
+ align:start position:0%
+carbons but these are the ones we'll
+ 
+
+ align:start position:0%
+carbons but these are the ones we'll
+totally focus on in 701 six because
+
+ align:start position:0%
+totally focus on in 701 six because
+ 
+
+ align:start position:0%
+totally focus on in 701 six because
+these are very important in different
+
+ align:start position:0%
+these are very important in different
+ 
+
+ align:start position:0%
+these are very important in different
+biopolymers and hexoses are important
+
+ align:start position:0%
+biopolymers and hexoses are important
+ 
+
+ align:start position:0%
+biopolymers and hexoses are important
+components for example of cellulose and
+
+ align:start position:0%
+components for example of cellulose and
+ 
+
+ align:start position:0%
+components for example of cellulose and
+glycogen but where are the pentose
+
+ align:start position:0%
+glycogen but where are the pentose
+ 
+
+ align:start position:0%
+glycogen but where are the pentose
+carbons where are they so important
+
+ align:start position:0%
+carbons where are they so important
+ 
+
+ align:start position:0%
+carbons where are they so important
+actually I need to draw this as it's
+
+ align:start position:0%
+actually I need to draw this as it's
+ 
+
+ align:start position:0%
+actually I need to draw this as it's
+straight chain inversion cuz I'll Drive
+
+ align:start position:0%
+straight chain inversion cuz I'll Drive
+ 
+
+ align:start position:0%
+straight chain inversion cuz I'll Drive
+you crazy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this sugar here is a pentose one two
+
+ align:start position:0%
+so this sugar here is a pentose one two
+ 
+
+ align:start position:0%
+so this sugar here is a pentose one two
+three four five carbons bunch of OHS
+
+ align:start position:0%
+three four five carbons bunch of OHS
+ 
+
+ align:start position:0%
+three four five carbons bunch of OHS
+aldehyde at one end commonly
+
+ align:start position:0%
+aldehyde at one end commonly
+ 
+
+ align:start position:0%
+aldehyde at one end commonly
+carbohydrates will fold up into a cyclic
+
+ align:start position:0%
+carbohydrates will fold up into a cyclic
+ 
+
+ align:start position:0%
+carbohydrates will fold up into a cyclic
+structure through an equilibrium I won't
+
+ align:start position:0%
+structure through an equilibrium I won't
+ 
+
+ align:start position:0%
+structure through an equilibrium I won't
+worry you too much with the chemistry
+
+ align:start position:0%
+worry you too much with the chemistry
+ 
+
+ align:start position:0%
+worry you too much with the chemistry
+but I'm just gonna show you that
+
+ align:start position:0%
+but I'm just gonna show you that
+ 
+
+ align:start position:0%
+but I'm just gonna show you that
+structure looks like this a five
+
+ align:start position:0%
+structure looks like this a five
+ 
+
+ align:start position:0%
+structure looks like this a five
+membered ring so this the inter
+
+ align:start position:0%
+membered ring so this the inter
+ 
+
+ align:start position:0%
+membered ring so this the inter
+conversion of these two is an
+
+ align:start position:0%
+conversion of these two is an
+ 
+
+ align:start position:0%
+conversion of these two is an
+equilibrium process and those
+
+ align:start position:0%
+equilibrium process and those
+ 
+
+ align:start position:0%
+equilibrium process and those
+carbohydrates are incredibly important
+
+ align:start position:0%
+carbohydrates are incredibly important
+ 
+
+ align:start position:0%
+carbohydrates are incredibly important
+where yeah
+
+ align:start position:0%
+where yeah
+ 
+
+ align:start position:0%
+where yeah
+nucleic acids so your phosphodiester
+
+ align:start position:0%
+nucleic acids so your phosphodiester
+ 
+
+ align:start position:0%
+nucleic acids so your phosphodiester
+backbone is attached to sugars that are
+
+ align:start position:0%
+backbone is attached to sugars that are
+ 
+
+ align:start position:0%
+backbone is attached to sugars that are
+attached to better to purines and
+
+ align:start position:0%
+attached to better to purines and
+ 
+
+ align:start position:0%
+attached to better to purines and
+pyrimidines and we'll see those
+
+ align:start position:0%
+pyrimidines and we'll see those
+ 
+
+ align:start position:0%
+pyrimidines and we'll see those
+structures later but an absolutely
+
+ align:start position:0%
+structures later but an absolutely
+ 
+
+ align:start position:0%
+structures later but an absolutely
+essential feature of that polymer is
+
+ align:start position:0%
+essential feature of that polymer is
+ 
+
+ align:start position:0%
+essential feature of that polymer is
+this five membered ring carbohydrates
+
+ align:start position:0%
+this five membered ring carbohydrates
+ 
+
+ align:start position:0%
+this five membered ring carbohydrates
+that are known as ribose which is what
+
+ align:start position:0%
+that are known as ribose which is what
+ 
+
+ align:start position:0%
+that are known as ribose which is what
+that guy is and two deoxyribose where
+
+ align:start position:0%
+that guy is and two deoxyribose where
+ 
+
+ align:start position:0%
+that guy is and two deoxyribose where
+one of the hydroxyls is actually a
+
+ align:start position:0%
+one of the hydroxyls is actually a
+ 
+
+ align:start position:0%
+one of the hydroxyls is actually a
+hydrogen it's not a hydroxyl and it's
+
+ align:start position:0%
+hydrogen it's not a hydroxyl and it's
+ 
+
+ align:start position:0%
+hydrogen it's not a hydroxyl and it's
+this one so instead of being a no H it's
+
+ align:start position:0%
+this one so instead of being a no H it's
+ 
+
+ align:start position:0%
+this one so instead of being a no H it's
+a an H and we number carbohydrates and
+
+ align:start position:0%
+a an H and we number carbohydrates and
+ 
+
+ align:start position:0%
+a an H and we number carbohydrates and
+your I'll reinforce this much more when
+
+ align:start position:0%
+your I'll reinforce this much more when
+ 
+
+ align:start position:0%
+your I'll reinforce this much more when
+we talk about carbohydrate about nucleic
+
+ align:start position:0%
+we talk about carbohydrate about nucleic
+ 
+
+ align:start position:0%
+we talk about carbohydrate about nucleic
+acids there's a numbering system so two
+
+ align:start position:0%
+acids there's a numbering system so two
+ 
+
+ align:start position:0%
+acids there's a numbering system so two
+deoxyribose is in your DNA and ribose
+
+ align:start position:0%
+deoxyribose is in your DNA and ribose
+ 
+
+ align:start position:0%
+deoxyribose is in your DNA and ribose
+itself is in your RNA okay so obviously
+
+ align:start position:0%
+itself is in your RNA okay so obviously
+ 
+
+ align:start position:0%
+itself is in your RNA okay so obviously
+we need to worry about carbohydrates and
+
+ align:start position:0%
+we need to worry about carbohydrates and
+ 
+
+ align:start position:0%
+we need to worry about carbohydrates and
+learn a little bit about them based on
+
+ align:start position:0%
+learn a little bit about them based on
+ 
+
+ align:start position:0%
+learn a little bit about them based on
+that key criterion okay let's move now
+
+ align:start position:0%
+that key criterion okay let's move now
+ 
+
+ align:start position:0%
+that key criterion okay let's move now
+to the hexoses I'm not gonna make you
+
+ align:start position:0%
+to the hexoses I'm not gonna make you
+ 
+
+ align:start position:0%
+to the hexoses I'm not gonna make you
+keep drawing hexoses and things I'm
+
+ align:start position:0%
+keep drawing hexoses and things I'm
+ 
+
+ align:start position:0%
+keep drawing hexoses and things I'm
+gonna just to tell you a little bit
+
+ align:start position:0%
+gonna just to tell you a little bit
+ 
+
+ align:start position:0%
+gonna just to tell you a little bit
+about them with respect to their
+
+ align:start position:0%
+about them with respect to their
+ 
+
+ align:start position:0%
+about them with respect to their
+structures so I've shown you on the
+
+ align:start position:0%
+structures so I've shown you on the
+ 
+
+ align:start position:0%
+structures so I've shown you on the
+board the cyclic form of a pentose this
+
+ align:start position:0%
+board the cyclic form of a pentose this
+ 
+
+ align:start position:0%
+board the cyclic form of a pentose this
+is the linear form and the cyclic form
+
+ align:start position:0%
+is the linear form and the cyclic form
+ 
+
+ align:start position:0%
+is the linear form and the cyclic form
+let me write that down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by the way in your DNA it's always
+
+ align:start position:0%
+and by the way in your DNA it's always
+ 
+
+ align:start position:0%
+and by the way in your DNA it's always
+in the cyclic form it's not in the
+
+ align:start position:0%
+in the cyclic form it's not in the
+ 
+
+ align:start position:0%
+in the cyclic form it's not in the
+linear form and the hexoses also have a
+
+ align:start position:0%
+linear form and the hexoses also have a
+ 
+
+ align:start position:0%
+linear form and the hexoses also have a
+linear in a cyclic form and I show you
+
+ align:start position:0%
+linear in a cyclic form and I show you
+ 
+
+ align:start position:0%
+linear in a cyclic form and I show you
+that equilibrium for glucose you see six
+
+ align:start position:0%
+that equilibrium for glucose you see six
+ 
+
+ align:start position:0%
+that equilibrium for glucose you see six
+carbons I've got them numbered and they
+
+ align:start position:0%
+carbons I've got them numbered and they
+ 
+
+ align:start position:0%
+carbons I've got them numbered and they
+form favorably into the six membered
+
+ align:start position:0%
+form favorably into the six membered
+ 
+
+ align:start position:0%
+form favorably into the six membered
+ring this is the cyclic form of glucose
+
+ align:start position:0%
+ring this is the cyclic form of glucose
+ 
+
+ align:start position:0%
+ring this is the cyclic form of glucose
+this is the linear form of glucose when
+
+ align:start position:0%
+this is the linear form of glucose when
+ 
+
+ align:start position:0%
+this is the linear form of glucose when
+glucose associates into polymers it
+
+ align:start position:0%
+glucose associates into polymers it
+ 
+
+ align:start position:0%
+glucose associates into polymers it
+becomes these things like cellulose or
+
+ align:start position:0%
+becomes these things like cellulose or
+ 
+
+ align:start position:0%
+becomes these things like cellulose or
+glycogen and
+
+ align:start position:0%
+glycogen and
+ 
+
+ align:start position:0%
+glycogen and
+depends a lot on the linkages and those
+
+ align:start position:0%
+depends a lot on the linkages and those
+ 
+
+ align:start position:0%
+depends a lot on the linkages and those
+polymers to define which one it is now
+
+ align:start position:0%
+polymers to define which one it is now
+ 
+
+ align:start position:0%
+polymers to define which one it is now
+as I mentioned carbohydrates aren't
+
+ align:start position:0%
+as I mentioned carbohydrates aren't
+ 
+
+ align:start position:0%
+as I mentioned carbohydrates aren't
+always just a series of Oh H groups
+
+ align:start position:0%
+always just a series of Oh H groups
+ 
+
+ align:start position:0%
+always just a series of Oh H groups
+there sometimes are the functionality so
+
+ align:start position:0%
+there sometimes are the functionality so
+ 
+
+ align:start position:0%
+there sometimes are the functionality so
+I'm just going to quickly draw those and
+
+ align:start position:0%
+I'm just going to quickly draw those and
+ 
+
+ align:start position:0%
+I'm just going to quickly draw those and
+if you've got them on your handout you
+
+ align:start position:0%
+if you've got them on your handout you
+ 
+
+ align:start position:0%
+if you've got them on your handout you
+can play along with me here so sometimes
+
+ align:start position:0%
+can play along with me here so sometimes
+ 
+
+ align:start position:0%
+can play along with me here so sometimes
+there's an nh-2 there that's called
+
+ align:start position:0%
+there's an nh-2 there that's called
+ 
+
+ align:start position:0%
+there's an nh-2 there that's called
+glucosamine very creatively sometimes
+
+ align:start position:0%
+glucosamine very creatively sometimes
+ 
+
+ align:start position:0%
+glucosamine very creatively sometimes
+that NH 2 is converted to an amide like
+
+ align:start position:0%
+that NH 2 is converted to an amide like
+ 
+
+ align:start position:0%
+that NH 2 is converted to an amide like
+that bond in a peptide so it's glucose a
+
+ align:start position:0%
+that bond in a peptide so it's glucose a
+ 
+
+ align:start position:0%
+that bond in a peptide so it's glucose a
+bit right and sometimes so you can draw
+
+ align:start position:0%
+bit right and sometimes so you can draw
+ 
+
+ align:start position:0%
+bit right and sometimes so you can draw
+these on your handout because the six
+
+ align:start position:0%
+these on your handout because the six
+ 
+
+ align:start position:0%
+these on your handout because the six
+membered rings are there this stays as a
+
+ align:start position:0%
+membered rings are there this stays as a
+ 
+
+ align:start position:0%
+membered rings are there this stays as a
+no H but this Oh H here is that a
+
+ align:start position:0%
+no H but this Oh H here is that a
+ 
+
+ align:start position:0%
+no H but this Oh H here is that a
+different oxidation state don't worry
+
+ align:start position:0%
+different oxidation state don't worry
+ 
+
+ align:start position:0%
+different oxidation state don't worry
+about that terminology but what's
+
+ align:start position:0%
+about that terminology but what's
+ 
+
+ align:start position:0%
+about that terminology but what's
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+it's glucuronic acid so it can be
+
+ align:start position:0%
+it's glucuronic acid so it can be
+ 
+
+ align:start position:0%
+it's glucuronic acid so it can be
+negatively charged positively charged
+
+ align:start position:0%
+negatively charged positively charged
+ 
+
+ align:start position:0%
+negatively charged positively charged
+neutral so there are variations on a lot
+
+ align:start position:0%
+neutral so there are variations on a lot
+ 
+
+ align:start position:0%
+neutral so there are variations on a lot
+of our hexoses basically meaning this
+
+ align:start position:0%
+of our hexoses basically meaning this
+ 
+
+ align:start position:0%
+of our hexoses basically meaning this
+carbohydrate molecular formula doesn't
+
+ align:start position:0%
+carbohydrate molecular formula doesn't
+ 
+
+ align:start position:0%
+carbohydrate molecular formula doesn't
+work anymore but the term is stuck all
+
+ align:start position:0%
+work anymore but the term is stuck all
+ 
+
+ align:start position:0%
+work anymore but the term is stuck all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so there's quite a variety of different
+
+ align:start position:0%
+so there's quite a variety of different
+ 
+
+ align:start position:0%
+so there's quite a variety of different
+carbohydrates with slight differences
+
+ align:start position:0%
+carbohydrates with slight differences
+ 
+
+ align:start position:0%
+carbohydrates with slight differences
+and the intriguing thing is that the
+
+ align:start position:0%
+and the intriguing thing is that the
+ 
+
+ align:start position:0%
+and the intriguing thing is that the
+carbohydrates that you and I use in all
+
+ align:start position:0%
+carbohydrates that you and I use in all
+ 
+
+ align:start position:0%
+carbohydrates that you and I use in all
+of our physiologic processes are much
+
+ align:start position:0%
+of our physiologic processes are much
+ 
+
+ align:start position:0%
+of our physiologic processes are much
+simpler than the carbohydrates the
+
+ align:start position:0%
+simpler than the carbohydrates the
+ 
+
+ align:start position:0%
+simpler than the carbohydrates the
+bacteria use there's an expansion of
+
+ align:start position:0%
+bacteria use there's an expansion of
+ 
+
+ align:start position:0%
+bacteria use there's an expansion of
+like 10 to the 2 or 10 to the 3 in the
+
+ align:start position:0%
+like 10 to the 2 or 10 to the 3 in the
+ 
+
+ align:start position:0%
+like 10 to the 2 or 10 to the 3 in the
+variety of sugars that bacteria use and
+
+ align:start position:0%
+variety of sugars that bacteria use and
+ 
+
+ align:start position:0%
+variety of sugars that bacteria use and
+that's definitely a story for another
+
+ align:start position:0%
+that's definitely a story for another
+ 
+
+ align:start position:0%
+that's definitely a story for another
+day so let me now move on to thinking
+
+ align:start position:0%
+day so let me now move on to thinking
+ 
+
+ align:start position:0%
+day so let me now move on to thinking
+about carbohydrates not as the monomers
+
+ align:start position:0%
+about carbohydrates not as the monomers
+ 
+
+ align:start position:0%
+about carbohydrates not as the monomers
+that you metabolize but rather as the
+
+ align:start position:0%
+that you metabolize but rather as the
+ 
+
+ align:start position:0%
+that you metabolize but rather as the
+polymers that are involved in many other
+
+ align:start position:0%
+polymers that are involved in many other
+ 
+
+ align:start position:0%
+polymers that are involved in many other
+different types of processes and when we
+
+ align:start position:0%
+different types of processes and when we
+ 
+
+ align:start position:0%
+different types of processes and when we
+think about the polymers we want to
+
+ align:start position:0%
+think about the polymers we want to
+ 
+
+ align:start position:0%
+think about the polymers we want to
+think about how they're polymers differ
+
+ align:start position:0%
+think about how they're polymers differ
+ 
+
+ align:start position:0%
+think about how they're polymers differ
+from the polymers
+
+ align:start position:0%
+from the polymers
+ 
+
+ align:start position:0%
+from the polymers
+of nucleic acids or proteins because
+
+ align:start position:0%
+of nucleic acids or proteins because
+ 
+
+ align:start position:0%
+of nucleic acids or proteins because
+this will tell you why carbohydrates are
+
+ align:start position:0%
+this will tell you why carbohydrates are
+ 
+
+ align:start position:0%
+this will tell you why carbohydrates are
+so complicated right when you may take a
+
+ align:start position:0%
+so complicated right when you may take a
+ 
+
+ align:start position:0%
+so complicated right when you may take a
+bunch of amino acids and make a polymer
+
+ align:start position:0%
+bunch of amino acids and make a polymer
+ 
+
+ align:start position:0%
+bunch of amino acids and make a polymer
+it's a linear polymer right every unit
+
+ align:start position:0%
+it's a linear polymer right every unit
+ 
+
+ align:start position:0%
+it's a linear polymer right every unit
+is joined to the next by an ami there's
+
+ align:start position:0%
+is joined to the next by an ami there's
+ 
+
+ align:start position:0%
+is joined to the next by an ami there's
+no branching there it's just a linear
+
+ align:start position:0%
+no branching there it's just a linear
+ 
+
+ align:start position:0%
+no branching there it's just a linear
+polymer so the diversity is not enormous
+
+ align:start position:0%
+polymer so the diversity is not enormous
+ 
+
+ align:start position:0%
+polymer so the diversity is not enormous
+or it's pretty enormous but it's not as
+
+ align:start position:0%
+or it's pretty enormous but it's not as
+ 
+
+ align:start position:0%
+or it's pretty enormous but it's not as
+big as it could be if it were a branched
+
+ align:start position:0%
+big as it could be if it were a branched
+ 
+
+ align:start position:0%
+big as it could be if it were a branched
+polymer with different types of side
+
+ align:start position:0%
+polymer with different types of side
+ 
+
+ align:start position:0%
+polymer with different types of side
+chains we will see next week that the
+
+ align:start position:0%
+chains we will see next week that the
+ 
+
+ align:start position:0%
+chains we will see next week that the
+polymers of the nucleic acids here's the
+
+ align:start position:0%
+polymers of the nucleic acids here's the
+ 
+
+ align:start position:0%
+polymers of the nucleic acids here's the
+basic structure there's the ribose by
+
+ align:start position:0%
+basic structure there's the ribose by
+ 
+
+ align:start position:0%
+basic structure there's the ribose by
+the way the R could be an OHA char NH
+
+ align:start position:0%
+the way the R could be an OHA char NH
+ 
+
+ align:start position:0%
+the way the R could be an OHA char NH
+attached to a base a purine or
+
+ align:start position:0%
+attached to a base a purine or
+ 
+
+ align:start position:0%
+attached to a base a purine or
+pyrimidine you don't need to know that
+
+ align:start position:0%
+pyrimidine you don't need to know that
+ 
+
+ align:start position:0%
+pyrimidine you don't need to know that
+yet you'll know it next week and then to
+
+ align:start position:0%
+yet you'll know it next week and then to
+ 
+
+ align:start position:0%
+yet you'll know it next week and then to
+a phosphate but those again are linear
+
+ align:start position:0%
+a phosphate but those again are linear
+ 
+
+ align:start position:0%
+a phosphate but those again are linear
+polymers you only have you don't have
+
+ align:start position:0%
+polymers you only have you don't have
+ 
+
+ align:start position:0%
+polymers you only have you don't have
+branching you just have a single
+
+ align:start position:0%
+branching you just have a single
+ 
+
+ align:start position:0%
+branching you just have a single
+continuous chain the crazy thing about
+
+ align:start position:0%
+continuous chain the crazy thing about
+ 
+
+ align:start position:0%
+continuous chain the crazy thing about
+sugars is they can branch from any of
+
+ align:start position:0%
+sugars is they can branch from any of
+ 
+
+ align:start position:0%
+sugars is they can branch from any of
+those OHS so there's much more diversity
+
+ align:start position:0%
+those OHS so there's much more diversity
+ 
+
+ align:start position:0%
+those OHS so there's much more diversity
+of structure and function within with
+
+ align:start position:0%
+of structure and function within with
+ 
+
+ align:start position:0%
+of structure and function within with
+wrapped in the carbohydrates which makes
+
+ align:start position:0%
+wrapped in the carbohydrates which makes
+ 
+
+ align:start position:0%
+wrapped in the carbohydrates which makes
+them real trouble to study okay I want
+
+ align:start position:0%
+them real trouble to study okay I want
+ 
+
+ align:start position:0%
+them real trouble to study okay I want
+to now introduce you to another feature
+
+ align:start position:0%
+to now introduce you to another feature
+ 
+
+ align:start position:0%
+to now introduce you to another feature
+the other thing is when we join amino
+
+ align:start position:0%
+the other thing is when we join amino
+ 
+
+ align:start position:0%
+the other thing is when we join amino
+acids or we join nucleic acid building
+
+ align:start position:0%
+acids or we join nucleic acid building
+ 
+
+ align:start position:0%
+acids or we join nucleic acid building
+blocks nuclear sides there's no
+
+ align:start position:0%
+blocks nuclear sides there's no
+ 
+
+ align:start position:0%
+blocks nuclear sides there's no
+difference in the shapes that we can
+
+ align:start position:0%
+difference in the shapes that we can
+ 
+
+ align:start position:0%
+difference in the shapes that we can
+form we don't have variety there but in
+
+ align:start position:0%
+form we don't have variety there but in
+ 
+
+ align:start position:0%
+form we don't have variety there but in
+sugars we can make different kinds of
+
+ align:start position:0%
+sugars we can make different kinds of
+ 
+
+ align:start position:0%
+sugars we can make different kinds of
+linkages depending on how to O H groups
+
+ align:start position:0%
+linkages depending on how to O H groups
+ 
+
+ align:start position:0%
+linkages depending on how to O H groups
+in a sugar are joined so for example if
+
+ align:start position:0%
+in a sugar are joined so for example if
+ 
+
+ align:start position:0%
+in a sugar are joined so for example if
+you join two glucose Asst in this kind
+
+ align:start position:0%
+you join two glucose Asst in this kind
+ 
+
+ align:start position:0%
+you join two glucose Asst in this kind
+of linkage that would give you maltose
+
+ align:start position:0%
+of linkage that would give you maltose
+ 
+
+ align:start position:0%
+of linkage that would give you maltose
+but if you join two glucoses in that
+
+ align:start position:0%
+but if you join two glucoses in that
+ 
+
+ align:start position:0%
+but if you join two glucoses in that
+kind of linkage it would give you
+
+ align:start position:0%
+kind of linkage it would give you
+ 
+
+ align:start position:0%
+kind of linkage it would give you
+lactose and those are different
+
+ align:start position:0%
+lactose and those are different
+ 
+
+ align:start position:0%
+lactose and those are different
+compounds they serve different types of
+
+ align:start position:0%
+compounds they serve different types of
+ 
+
+ align:start position:0%
+compounds they serve different types of
+physiologic roles and there are enzymes
+
+ align:start position:0%
+physiologic roles and there are enzymes
+ 
+
+ align:start position:0%
+physiologic roles and there are enzymes
+that will make these bonds and then
+
+ align:start position:0%
+that will make these bonds and then
+ 
+
+ align:start position:0%
+that will make these bonds and then
+enzymes the world break these bonds
+
+ align:start position:0%
+enzymes the world break these bonds
+ 
+
+ align:start position:0%
+enzymes the world break these bonds
+there is a common disorder that people
+
+ align:start position:0%
+there is a common disorder that people
+ 
+
+ align:start position:0%
+there is a common disorder that people
+have as they grow older the enzyme that
+
+ align:start position:0%
+have as they grow older the enzyme that
+ 
+
+ align:start position:0%
+have as they grow older the enzyme that
+breaks the lactase the lactose bond the
+
+ align:start position:0%
+breaks the lactase the lactose bond the
+ 
+
+ align:start position:0%
+breaks the lactase the lactose bond the
+gets turned off it doesn't work anymore
+
+ align:start position:0%
+gets turned off it doesn't work anymore
+ 
+
+ align:start position:0%
+gets turned off it doesn't work anymore
+and that's the enzyme lactose so when
+
+ align:start position:0%
+and that's the enzyme lactose so when
+ 
+
+ align:start position:0%
+and that's the enzyme lactose so when
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+intolerance to sugars lactose is the
+
+ align:start position:0%
+intolerance to sugars lactose is the
+ 
+
+ align:start position:0%
+intolerance to sugars lactose is the
+sugar in milk and they can't digest
+
+ align:start position:0%
+sugar in milk and they can't digest
+ 
+
+ align:start position:0%
+sugar in milk and they can't digest
+dairy products because lactase doesn't
+
+ align:start position:0%
+dairy products because lactase doesn't
+ 
+
+ align:start position:0%
+dairy products because lactase doesn't
+work anymore or you can take supplements
+
+ align:start position:0%
+work anymore or you can take supplements
+ 
+
+ align:start position:0%
+work anymore or you can take supplements
+so that's how that relates to physiology
+
+ align:start position:0%
+so that's how that relates to physiology
+ 
+
+ align:start position:0%
+so that's how that relates to physiology
+the reaction between two glucose is to
+
+ align:start position:0%
+the reaction between two glucose is to
+ 
+
+ align:start position:0%
+the reaction between two glucose is to
+make the disaccharide is actually a
+
+ align:start position:0%
+make the disaccharide is actually a
+ 
+
+ align:start position:0%
+make the disaccharide is actually a
+condensation because when you join that
+
+ align:start position:0%
+condensation because when you join that
+ 
+
+ align:start position:0%
+condensation because when you join that
+bond you kick out water as a side
+
+ align:start position:0%
+bond you kick out water as a side
+ 
+
+ align:start position:0%
+bond you kick out water as a side
+product or when you break that bond you
+
+ align:start position:0%
+product or when you break that bond you
+ 
+
+ align:start position:0%
+product or when you break that bond you
+release water so this is another one of
+
+ align:start position:0%
+release water so this is another one of
+ 
+
+ align:start position:0%
+release water so this is another one of
+the condensation reactions so underline
+
+ align:start position:0%
+the condensation reactions so underline
+ 
+
+ align:start position:0%
+the condensation reactions so underline
+that on the slide because a condensation
+
+ align:start position:0%
+that on the slide because a condensation
+ 
+
+ align:start position:0%
+that on the slide because a condensation
+means a reaction that proceeds and
+
+ align:start position:0%
+means a reaction that proceeds and
+ 
+
+ align:start position:0%
+means a reaction that proceeds and
+produces you a molecule of water okay
+
+ align:start position:0%
+produces you a molecule of water okay
+ 
+
+ align:start position:0%
+produces you a molecule of water okay
+all right and this just sums up the
+
+ align:start position:0%
+all right and this just sums up the
+ 
+
+ align:start position:0%
+all right and this just sums up the
+lactase problem where you can't digest
+
+ align:start position:0%
+lactase problem where you can't digest
+ 
+
+ align:start position:0%
+lactase problem where you can't digest
+lactose the milk sugar okay so those are
+
+ align:start position:0%
+lactose the milk sugar okay so those are
+ 
+
+ align:start position:0%
+lactose the milk sugar okay so those are
+monomers now let's think about polymers
+
+ align:start position:0%
+monomers now let's think about polymers
+ 
+
+ align:start position:0%
+monomers now let's think about polymers
+and complex structures of sugars and I
+
+ align:start position:0%
+and complex structures of sugars and I
+ 
+
+ align:start position:0%
+and complex structures of sugars and I
+put these all on the slides because it's
+
+ align:start position:0%
+put these all on the slides because it's
+ 
+
+ align:start position:0%
+put these all on the slides because it's
+just impossible for you to keep drawing
+
+ align:start position:0%
+just impossible for you to keep drawing
+ 
+
+ align:start position:0%
+just impossible for you to keep drawing
+them and I'm just gonna give you sort of
+
+ align:start position:0%
+them and I'm just gonna give you sort of
+ 
+
+ align:start position:0%
+them and I'm just gonna give you sort of
+one of my pet peeves
+
+ align:start position:0%
+one of my pet peeves
+ 
+
+ align:start position:0%
+one of my pet peeves
+I draw sugars like this a lot of other
+
+ align:start position:0%
+I draw sugars like this a lot of other
+ 
+
+ align:start position:0%
+I draw sugars like this a lot of other
+people draw sugars like that and I don't
+
+ align:start position:0%
+people draw sugars like that and I don't
+ 
+
+ align:start position:0%
+people draw sugars like that and I don't
+like that because this is what they look
+
+ align:start position:0%
+like that because this is what they look
+ 
+
+ align:start position:0%
+like that because this is what they look
+like so if you see this and you go I
+
+ align:start position:0%
+like so if you see this and you go I
+ 
+
+ align:start position:0%
+like so if you see this and you go I
+haven't seen sugars looking like that
+
+ align:start position:0%
+haven't seen sugars looking like that
+ 
+
+ align:start position:0%
+haven't seen sugars looking like that
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+it's because this is the way to draw
+
+ align:start position:0%
+it's because this is the way to draw
+ 
+
+ align:start position:0%
+it's because this is the way to draw
+them that actually represents their
+
+ align:start position:0%
+them that actually represents their
+ 
+
+ align:start position:0%
+them that actually represents their
+shape so if it's unusual format to you
+
+ align:start position:0%
+shape so if it's unusual format to you
+ 
+
+ align:start position:0%
+shape so if it's unusual format to you
+I'm not going to ask you to construct
+
+ align:start position:0%
+I'm not going to ask you to construct
+ 
+
+ align:start position:0%
+I'm not going to ask you to construct
+these I just want you to be familiar
+
+ align:start position:0%
+these I just want you to be familiar
+ 
+
+ align:start position:0%
+these I just want you to be familiar
+with looking at them like this rather
+
+ align:start position:0%
+with looking at them like this rather
+ 
+
+ align:start position:0%
+with looking at them like this rather
+than like this because to me that's the
+
+ align:start position:0%
+than like this because to me that's the
+ 
+
+ align:start position:0%
+than like this because to me that's the
+best way to render them alright okay so
+
+ align:start position:0%
+best way to render them alright okay so
+ 
+
+ align:start position:0%
+best way to render them alright okay so
+polymers of sugars I just mentioned to
+
+ align:start position:0%
+polymers of sugars I just mentioned to
+ 
+
+ align:start position:0%
+polymers of sugars I just mentioned to
+you there are polymers of sugars that
+
+ align:start position:0%
+you there are polymers of sugars that
+ 
+
+ align:start position:0%
+you there are polymers of sugars that
+are important as storage so when we have
+
+ align:start position:0%
+are important as storage so when we have
+ 
+
+ align:start position:0%
+are important as storage so when we have
+excess glucose we store glucose as
+
+ align:start position:0%
+excess glucose we store glucose as
+ 
+
+ align:start position:0%
+excess glucose we store glucose as
+glycogen in the liver and stored in the
+
+ align:start position:0%
+glycogen in the liver and stored in the
+ 
+
+ align:start position:0%
+glycogen in the liver and stored in the
+liver and later on in the semester we'll
+
+ align:start position:0%
+liver and later on in the semester we'll
+ 
+
+ align:start position:0%
+liver and later on in the semester we'll
+see how a bolt of adrenaline does sets
+
+ align:start position:0%
+see how a bolt of adrenaline does sets
+ 
+
+ align:start position:0%
+see how a bolt of adrenaline does sets
+all the processes in motion to chew up
+
+ align:start position:0%
+all the processes in motion to chew up
+ 
+
+ align:start position:0%
+all the processes in motion to chew up
+glycogen to release
+
+ align:start position:0%
+glycogen to release
+ 
+
+ align:start position:0%
+glycogen to release
+more glucose so you can have a lot of
+
+ align:start position:0%
+more glucose so you can have a lot of
+ 
+
+ align:start position:0%
+more glucose so you can have a lot of
+energy quickly so in that in that
+
+ align:start position:0%
+energy quickly so in that in that
+ 
+
+ align:start position:0%
+energy quickly so in that in that
+polymer the sugars are linked in a
+
+ align:start position:0%
+polymer the sugars are linked in a
+ 
+
+ align:start position:0%
+polymer the sugars are linked in a
+different way the common polymer in
+
+ align:start position:0%
+different way the common polymer in
+ 
+
+ align:start position:0%
+different way the common polymer in
+plants and in fact accounts for a
+
+ align:start position:0%
+plants and in fact accounts for a
+ 
+
+ align:start position:0%
+plants and in fact accounts for a
+massive proportion of the biomass is a
+
+ align:start position:0%
+massive proportion of the biomass is a
+ 
+
+ align:start position:0%
+massive proportion of the biomass is a
+different polymer of glucose where the
+
+ align:start position:0%
+different polymer of glucose where the
+ 
+
+ align:start position:0%
+different polymer of glucose where the
+linkages are Beatle that we would call
+
+ align:start position:0%
+linkages are Beatle that we would call
+ 
+
+ align:start position:0%
+linkages are Beatle that we would call
+this a beta linkage but that's the way
+
+ align:start position:0%
+this a beta linkage but that's the way
+ 
+
+ align:start position:0%
+this a beta linkage but that's the way
+it looks
+
+ align:start position:0%
+it looks
+ 
+
+ align:start position:0%
+it looks
+and that would be cellulose and it's a
+
+ align:start position:0%
+and that would be cellulose and it's a
+ 
+
+ align:start position:0%
+and that would be cellulose and it's a
+linear polymer coming down here glycogen
+
+ align:start position:0%
+linear polymer coming down here glycogen
+ 
+
+ align:start position:0%
+linear polymer coming down here glycogen
+is often a branched polymer with
+
+ align:start position:0%
+is often a branched polymer with
+ 
+
+ align:start position:0%
+is often a branched polymer with
+different kinds of linkages with
+
+ align:start position:0%
+different kinds of linkages with
+ 
+
+ align:start position:0%
+different kinds of linkages with
+different aspects or different shapes so
+
+ align:start position:0%
+different aspects or different shapes so
+ 
+
+ align:start position:0%
+different aspects or different shapes so
+the glycogen that we store and can break
+
+ align:start position:0%
+the glycogen that we store and can break
+ 
+
+ align:start position:0%
+the glycogen that we store and can break
+down in order to produce glucose to make
+
+ align:start position:0%
+down in order to produce glucose to make
+ 
+
+ align:start position:0%
+down in order to produce glucose to make
+energy as glycogen we cannot break down
+
+ align:start position:0%
+energy as glycogen we cannot break down
+ 
+
+ align:start position:0%
+energy as glycogen we cannot break down
+cellulose we don't digest plant
+
+ align:start position:0%
+cellulose we don't digest plant
+ 
+
+ align:start position:0%
+cellulose we don't digest plant
+cellulose because we don't have those
+
+ align:start position:0%
+cellulose because we don't have those
+ 
+
+ align:start position:0%
+cellulose because we don't have those
+enzymes which is why we don't get
+
+ align:start position:0%
+enzymes which is why we don't get
+ 
+
+ align:start position:0%
+enzymes which is why we don't get
+nutritional value out of the cellulose
+
+ align:start position:0%
+nutritional value out of the cellulose
+ 
+
+ align:start position:0%
+nutritional value out of the cellulose
+the same way we can we can put the
+
+ align:start position:0%
+the same way we can we can put the
+ 
+
+ align:start position:0%
+the same way we can we can put the
+forces in action to break down glucose
+
+ align:start position:0%
+forces in action to break down glucose
+ 
+
+ align:start position:0%
+forces in action to break down glucose
+so the way those bond looks bonds look
+
+ align:start position:0%
+so the way those bond looks bonds look
+ 
+
+ align:start position:0%
+so the way those bond looks bonds look
+is absolutely critical for how you can
+
+ align:start position:0%
+is absolutely critical for how you can
+ 
+
+ align:start position:0%
+is absolutely critical for how you can
+use the energy that's within them by
+
+ align:start position:0%
+use the energy that's within them by
+ 
+
+ align:start position:0%
+use the energy that's within them by
+using enzymes to break those bonds okay
+
+ align:start position:0%
+using enzymes to break those bonds okay
+ 
+
+ align:start position:0%
+using enzymes to break those bonds okay
+so in general I've just said that
+
+ align:start position:0%
+so in general I've just said that
+ 
+
+ align:start position:0%
+so in general I've just said that
+glucose can be stored a cellulose or as
+
+ align:start position:0%
+glucose can be stored a cellulose or as
+ 
+
+ align:start position:0%
+glucose can be stored a cellulose or as
+glycogen the process of photosynthesis
+
+ align:start position:0%
+glycogen the process of photosynthesis
+ 
+
+ align:start position:0%
+glycogen the process of photosynthesis
+converts energy and sunlight into glue
+
+ align:start position:0%
+converts energy and sunlight into glue
+ 
+
+ align:start position:0%
+converts energy and sunlight into glue
+into glucose and then you can make the
+
+ align:start position:0%
+into glucose and then you can make the
+ 
+
+ align:start position:0%
+into glucose and then you can make the
+polymers of glucose and what I'm showing
+
+ align:start position:0%
+polymers of glucose and what I'm showing
+ 
+
+ align:start position:0%
+polymers of glucose and what I'm showing
+you here in these polymers is a
+
+ align:start position:0%
+you here in these polymers is a
+ 
+
+ align:start position:0%
+you here in these polymers is a
+simplified view I want to introduce to
+
+ align:start position:0%
+simplified view I want to introduce to
+ 
+
+ align:start position:0%
+simplified view I want to introduce to
+you one other term and that term is
+
+ align:start position:0%
+you one other term and that term is
+ 
+
+ align:start position:0%
+you one other term and that term is
+glycan and that basically refers to
+
+ align:start position:0%
+glycan and that basically refers to
+ 
+
+ align:start position:0%
+glycan and that basically refers to
+something that is more than one sugar
+
+ align:start position:0%
+something that is more than one sugar
+ 
+
+ align:start position:0%
+something that is more than one sugar
+one carbohydrate I was looking at the
+
+ align:start position:0%
+one carbohydrate I was looking at the
+ 
+
+ align:start position:0%
+one carbohydrate I was looking at the
+videos of my lectures I realized my
+
+ align:start position:0%
+videos of my lectures I realized my
+ 
+
+ align:start position:0%
+videos of my lectures I realized my
+handwriting is horrible so I'm really
+
+ align:start position:0%
+handwriting is horrible so I'm really
+ 
+
+ align:start position:0%
+handwriting is horrible so I'm really
+trying very hard to make it a little bit
+
+ align:start position:0%
+trying very hard to make it a little bit
+ 
+
+ align:start position:0%
+trying very hard to make it a little bit
+neater today so glycan is just the name
+
+ align:start position:0%
+neater today so glycan is just the name
+ 
+
+ align:start position:0%
+neater today so glycan is just the name
+for a polymer of sugars but they can
+
+ align:start position:0%
+for a polymer of sugars but they can
+ 
+
+ align:start position:0%
+for a polymer of sugars but they can
+also be called
+
+ align:start position:0%
+also be called
+ 
+
+ align:start position:0%
+also be called
+polysaccharides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but glycan now is the commonly accepted
+
+ align:start position:0%
+but glycan now is the commonly accepted
+ 
+
+ align:start position:0%
+but glycan now is the commonly accepted
+term for a lot of sugars now I told you
+
+ align:start position:0%
+term for a lot of sugars now I told you
+ 
+
+ align:start position:0%
+term for a lot of sugars now I told you
+about energy storage
+
+ align:start position:0%
+about energy storage
+ 
+
+ align:start position:0%
+about energy storage
+I've told you about simple disaccharides
+
+ align:start position:0%
+I've told you about simple disaccharides
+ 
+
+ align:start position:0%
+I've told you about simple disaccharides
+and monosaccharides and metabolism but
+
+ align:start position:0%
+and monosaccharides and metabolism but
+ 
+
+ align:start position:0%
+and monosaccharides and metabolism but
+what I want to do now is give you a
+
+ align:start position:0%
+what I want to do now is give you a
+ 
+
+ align:start position:0%
+what I want to do now is give you a
+little overview of all the different
+
+ align:start position:0%
+little overview of all the different
+ 
+
+ align:start position:0%
+little overview of all the different
+places where sugars feature in a Cell
+
+ align:start position:0%
+places where sugars feature in a Cell
+ 
+
+ align:start position:0%
+places where sugars feature in a Cell
+because I think it's really important to
+
+ align:start position:0%
+because I think it's really important to
+ 
+
+ align:start position:0%
+because I think it's really important to
+realize that sugars form a great sort of
+
+ align:start position:0%
+realize that sugars form a great sort of
+ 
+
+ align:start position:0%
+realize that sugars form a great sort of
+set of Communicator molecules for
+
+ align:start position:0%
+set of Communicator molecules for
+ 
+
+ align:start position:0%
+set of Communicator molecules for
+communication so I'm gonna go around
+
+ align:start position:0%
+communication so I'm gonna go around
+ 
+
+ align:start position:0%
+communication so I'm gonna go around
+this sort of funny-looking square cell
+
+ align:start position:0%
+this sort of funny-looking square cell
+ 
+
+ align:start position:0%
+this sort of funny-looking square cell
+and this would be a eukaryotic cell
+
+ align:start position:0%
+and this would be a eukaryotic cell
+ 
+
+ align:start position:0%
+and this would be a eukaryotic cell
+because it's got a nucleus and there are
+
+ align:start position:0%
+because it's got a nucleus and there are
+ 
+
+ align:start position:0%
+because it's got a nucleus and there are
+different compartments so within the
+
+ align:start position:0%
+different compartments so within the
+ 
+
+ align:start position:0%
+different compartments so within the
+cell the cell sits in what's known as an
+
+ align:start position:0%
+cell the cell sits in what's known as an
+ 
+
+ align:start position:0%
+cell the cell sits in what's known as an
+extracellular matrix
+
+ align:start position:0%
+extracellular matrix
+ 
+
+ align:start position:0%
+extracellular matrix
+it's a meshwork of sugar polymers that
+
+ align:start position:0%
+it's a meshwork of sugar polymers that
+ 
+
+ align:start position:0%
+it's a meshwork of sugar polymers that
+actually is important for the cells and
+
+ align:start position:0%
+actually is important for the cells and
+ 
+
+ align:start position:0%
+actually is important for the cells and
+important for trapping signals that come
+
+ align:start position:0%
+important for trapping signals that come
+ 
+
+ align:start position:0%
+important for trapping signals that come
+from cells and go to other cells so
+
+ align:start position:0%
+from cells and go to other cells so
+ 
+
+ align:start position:0%
+from cells and go to other cells so
+those are all predominantly made up of
+
+ align:start position:0%
+those are all predominantly made up of
+ 
+
+ align:start position:0%
+those are all predominantly made up of
+carbohydrate the next thing to look at
+
+ align:start position:0%
+carbohydrate the next thing to look at
+ 
+
+ align:start position:0%
+carbohydrate the next thing to look at
+is that there are sugar there are
+
+ align:start position:0%
+is that there are sugar there are
+ 
+
+ align:start position:0%
+is that there are sugar there are
+proteins within the cell that can become
+
+ align:start position:0%
+proteins within the cell that can become
+ 
+
+ align:start position:0%
+proteins within the cell that can become
+modified with a sugar and go to the
+
+ align:start position:0%
+modified with a sugar and go to the
+ 
+
+ align:start position:0%
+modified with a sugar and go to the
+nucleus or leave the nucleus so there is
+
+ align:start position:0%
+nucleus or leave the nucleus so there is
+ 
+
+ align:start position:0%
+nucleus or leave the nucleus so there is
+a type of signaling that is based on
+
+ align:start position:0%
+a type of signaling that is based on
+ 
+
+ align:start position:0%
+a type of signaling that is based on
+adding a sugar or taking it off a
+
+ align:start position:0%
+adding a sugar or taking it off a
+ 
+
+ align:start position:0%
+adding a sugar or taking it off a
+protein we'll see later in the semester
+
+ align:start position:0%
+protein we'll see later in the semester
+ 
+
+ align:start position:0%
+protein we'll see later in the semester
+how also phosphorylation does a lot of
+
+ align:start position:0%
+how also phosphorylation does a lot of
+ 
+
+ align:start position:0%
+how also phosphorylation does a lot of
+functions that look like that there are
+
+ align:start position:0%
+functions that look like that there are
+ 
+
+ align:start position:0%
+functions that look like that there are
+sugars that are displayed on cell
+
+ align:start position:0%
+sugars that are displayed on cell
+ 
+
+ align:start position:0%
+sugars that are displayed on cell
+surface polymers and that's where
+
+ align:start position:0%
+surface polymers and that's where
+ 
+
+ align:start position:0%
+surface polymers and that's where
+signaling becomes important because
+
+ align:start position:0%
+signaling becomes important because
+ 
+
+ align:start position:0%
+signaling becomes important because
+sugars may be attached to lipids you
+
+ align:start position:0%
+sugars may be attached to lipids you
+ 
+
+ align:start position:0%
+sugars may be attached to lipids you
+remember we've talked about
+
+ align:start position:0%
+remember we've talked about
+ 
+
+ align:start position:0%
+remember we've talked about
+phospholipids being part of the membrane
+
+ align:start position:0%
+phospholipids being part of the membrane
+ 
+
+ align:start position:0%
+phospholipids being part of the membrane
+sugars can be attached to lipids that
+
+ align:start position:0%
+sugars can be attached to lipids that
+ 
+
+ align:start position:0%
+sugars can be attached to lipids that
+sit in the membrane and face out and
+
+ align:start position:0%
+sit in the membrane and face out and
+ 
+
+ align:start position:0%
+sit in the membrane and face out and
+it's how cell-cell communication occurs
+
+ align:start position:0%
+it's how cell-cell communication occurs
+ 
+
+ align:start position:0%
+it's how cell-cell communication occurs
+in some instances or they may be
+
+ align:start position:0%
+in some instances or they may be
+ 
+
+ align:start position:0%
+in some instances or they may be
+attached to proteins that are also
+
+ align:start position:0%
+attached to proteins that are also
+ 
+
+ align:start position:0%
+attached to proteins that are also
+displayed on the surface of the cell so
+
+ align:start position:0%
+displayed on the surface of the cell so
+ 
+
+ align:start position:0%
+displayed on the surface of the cell so
+this tells you a little bit about where
+
+ align:start position:0%
+this tells you a little bit about where
+ 
+
+ align:start position:0%
+this tells you a little bit about where
+we put these sugars is what's
+
+ align:start position:0%
+we put these sugars is what's
+ 
+
+ align:start position:0%
+we put these sugars is what's
+responsible for communication because
+
+ align:start position:0%
+responsible for communication because
+ 
+
+ align:start position:0%
+responsible for communication because
+they're there on the surface and the
+
+ align:start position:0%
+they're there on the surface and the
+ 
+
+ align:start position:0%
+they're there on the surface and the
+cell were their sides out and then the
+
+ align:start position:0%
+cell were their sides out and then the
+ 
+
+ align:start position:0%
+cell were their sides out and then the
+final thing I want to talk about is the
+
+ align:start position:0%
+final thing I want to talk about is the
+ 
+
+ align:start position:0%
+final thing I want to talk about is the
+blood group system
+
+ align:start position:0%
+blood group system
+ 
+
+ align:start position:0%
+blood group system
+a lot of you may be aware of blood
+
+ align:start position:0%
+a lot of you may be aware of blood
+ 
+
+ align:start position:0%
+a lot of you may be aware of blood
+groups there are four principle blood
+
+ align:start position:0%
+groups there are four principle blood
+ 
+
+ align:start position:0%
+groups there are four principle blood
+groups and those the differences between
+
+ align:start position:0%
+groups and those the differences between
+ 
+
+ align:start position:0%
+groups and those the differences between
+the blood in a B a B and O blood groups
+
+ align:start position:0%
+the blood in a B a B and O blood groups
+ 
+
+ align:start position:0%
+the blood in a B a B and O blood groups
+a differences in just the sugars that
+
+ align:start position:0%
+a differences in just the sugars that
+ 
+
+ align:start position:0%
+a differences in just the sugars that
+are attached to the surface of the cell
+
+ align:start position:0%
+are attached to the surface of the cell
+ 
+
+ align:start position:0%
+are attached to the surface of the cell
+so let me describe those and then we'll
+
+ align:start position:0%
+so let me describe those and then we'll
+ 
+
+ align:start position:0%
+so let me describe those and then we'll
+talk about blood groups and things that
+
+ align:start position:0%
+talk about blood groups and things that
+ 
+
+ align:start position:0%
+talk about blood groups and things that
+are being done to enhance the supplies
+
+ align:start position:0%
+are being done to enhance the supplies
+ 
+
+ align:start position:0%
+are being done to enhance the supplies
+of red blood cells in cases of emergency
+
+ align:start position:0%
+of red blood cells in cases of emergency
+ 
+
+ align:start position:0%
+of red blood cells in cases of emergency
+I have a nice little video I'm hoping to
+
+ align:start position:0%
+I have a nice little video I'm hoping to
+ 
+
+ align:start position:0%
+I have a nice little video I'm hoping to
+get to so on the surface of the cell you
+
+ align:start position:0%
+get to so on the surface of the cell you
+ 
+
+ align:start position:0%
+get to so on the surface of the cell you
+might have different sugars this is a
+
+ align:start position:0%
+might have different sugars this is a
+ 
+
+ align:start position:0%
+might have different sugars this is a
+trisaccharide all right you can see one
+
+ align:start position:0%
+trisaccharide all right you can see one
+ 
+
+ align:start position:0%
+trisaccharide all right you can see one
+two three sugars they have different
+
+ align:start position:0%
+two three sugars they have different
+ 
+
+ align:start position:0%
+two three sugars they have different
+linkages but you can pick out the sugars
+
+ align:start position:0%
+linkages but you can pick out the sugars
+ 
+
+ align:start position:0%
+linkages but you can pick out the sugars
+and they are joined by a bond called a
+
+ align:start position:0%
+and they are joined by a bond called a
+ 
+
+ align:start position:0%
+and they are joined by a bond called a
+glycoside bond and those join sugars so
+
+ align:start position:0%
+glycoside bond and those join sugars so
+ 
+
+ align:start position:0%
+glycoside bond and those join sugars so
+what do you think the enzyme that
+
+ align:start position:0%
+what do you think the enzyme that
+ 
+
+ align:start position:0%
+what do you think the enzyme that
+Cleaves a glycoside is like a side like
+
+ align:start position:0%
+Cleaves a glycoside is like a side like
+ 
+
+ align:start position:0%
+Cleaves a glycoside is like a side like
+OC days you would think like us today is
+
+ align:start position:0%
+OC days you would think like us today is
+ 
+
+ align:start position:0%
+OC days you would think like us today is
+I would say glycoside days but they are
+
+ align:start position:0%
+I would say glycoside days but they are
+ 
+
+ align:start position:0%
+I would say glycoside days but they are
+the same thing so and that's gonna be
+
+ align:start position:0%
+the same thing so and that's gonna be
+ 
+
+ align:start position:0%
+the same thing so and that's gonna be
+pertinent in a minute so remember if in
+
+ align:start position:0%
+pertinent in a minute so remember if in
+ 
+
+ align:start position:0%
+pertinent in a minute so remember if in
+doubt guess and stick a's at the end if
+
+ align:start position:0%
+doubt guess and stick a's at the end if
+ 
+
+ align:start position:0%
+doubt guess and stick a's at the end if
+i ask you the name of an enzyme because
+
+ align:start position:0%
+i ask you the name of an enzyme because
+ 
+
+ align:start position:0%
+i ask you the name of an enzyme because
+that works pretty well so if you have a
+
+ align:start position:0%
+that works pretty well so if you have a
+ 
+
+ align:start position:0%
+that works pretty well so if you have a
+blood group you would have exclusively
+
+ align:start position:0%
+blood group you would have exclusively
+ 
+
+ align:start position:0%
+blood group you would have exclusively
+this trisaccharide on your red blood
+
+ align:start position:0%
+this trisaccharide on your red blood
+ 
+
+ align:start position:0%
+this trisaccharide on your red blood
+cells if you have the a blood group you
+
+ align:start position:0%
+cells if you have the a blood group you
+ 
+
+ align:start position:0%
+cells if you have the a blood group you
+have an extra sugar attached to that
+
+ align:start position:0%
+have an extra sugar attached to that
+ 
+
+ align:start position:0%
+have an extra sugar attached to that
+trisaccharide and it's a glucosamine
+
+ align:start position:0%
+trisaccharide and it's a glucosamine
+ 
+
+ align:start position:0%
+trisaccharide and it's a glucosamine
+glucosamine sugar there's an extra
+
+ align:start position:0%
+glucosamine sugar there's an extra
+ 
+
+ align:start position:0%
+glucosamine sugar there's an extra
+carbonyl group with on on an amide and
+
+ align:start position:0%
+carbonyl group with on on an amide and
+ 
+
+ align:start position:0%
+carbonyl group with on on an amide and
+if you have B blood group
+
+ align:start position:0%
+if you have B blood group
+ 
+
+ align:start position:0%
+if you have B blood group
+it's gluco it's a sugar it's actually
+
+ align:start position:0%
+it's gluco it's a sugar it's actually
+ 
+
+ align:start position:0%
+it's gluco it's a sugar it's actually
+called galactose that has all age groups
+
+ align:start position:0%
+called galactose that has all age groups
+ 
+
+ align:start position:0%
+called galactose that has all age groups
+so the difference is between if your oh
+
+ align:start position:0%
+so the difference is between if your oh
+ 
+
+ align:start position:0%
+so the difference is between if your oh
+group if you're a group or if your B
+
+ align:start position:0%
+group if you're a group or if your B
+ 
+
+ align:start position:0%
+group if you're a group or if your B
+group are just those differences in
+
+ align:start position:0%
+group are just those differences in
+ 
+
+ align:start position:0%
+group are just those differences in
+sugars and then people who have a B
+
+ align:start position:0%
+sugars and then people who have a B
+ 
+
+ align:start position:0%
+sugars and then people who have a B
+blood group have a composite they have a
+
+ align:start position:0%
+blood group have a composite they have a
+ 
+
+ align:start position:0%
+blood group have a composite they have a
+Mik
+
+ align:start position:0%
+Mik
+ 
+
+ align:start position:0%
+Mik
+of the a and the B blood group all right
+
+ align:start position:0%
+of the a and the B blood group all right
+ 
+
+ align:start position:0%
+of the a and the B blood group all right
+so yeah question that's a second marker
+
+ align:start position:0%
+so yeah question that's a second marker
+ 
+
+ align:start position:0%
+so yeah question that's a second marker
+so and which we won't talk about but
+
+ align:start position:0%
+so and which we won't talk about but
+ 
+
+ align:start position:0%
+so and which we won't talk about but
+it's uh so it's a plus a different plus
+
+ align:start position:0%
+it's uh so it's a plus a different plus
+ 
+
+ align:start position:0%
+it's uh so it's a plus a different plus
+another marker that's either one type or
+
+ align:start position:0%
+another marker that's either one type or
+ 
+
+ align:start position:0%
+another marker that's either one type or
+another type all right but the a B and O
+
+ align:start position:0%
+another type all right but the a B and O
+ 
+
+ align:start position:0%
+another type all right but the a B and O
+are defined by the sugars yeah good
+
+ align:start position:0%
+are defined by the sugars yeah good
+ 
+
+ align:start position:0%
+are defined by the sugars yeah good
+question okay so the people know their
+
+ align:start position:0%
+question okay so the people know their
+ 
+
+ align:start position:0%
+question okay so the people know their
+blood group it's good to know
+
+ align:start position:0%
+blood group it's good to know
+ 
+
+ align:start position:0%
+blood group it's good to know
+frankly because you know someone you
+
+ align:start position:0%
+frankly because you know someone you
+ 
+
+ align:start position:0%
+frankly because you know someone you
+know you may cut yourself on someone
+
+ align:start position:0%
+know you may cut yourself on someone
+ 
+
+ align:start position:0%
+know you may cut yourself on someone
+says do you know your blood group and
+
+ align:start position:0%
+says do you know your blood group and
+ 
+
+ align:start position:0%
+says do you know your blood group and
+you go yes and they'll give you an
+
+ align:start position:0%
+you go yes and they'll give you an
+ 
+
+ align:start position:0%
+you go yes and they'll give you an
+on-site transfusion and I've been
+
+ align:start position:0%
+on-site transfusion and I've been
+ 
+
+ align:start position:0%
+on-site transfusion and I've been
+watching too much Jack Bauer but you
+
+ align:start position:0%
+watching too much Jack Bauer but you
+ 
+
+ align:start position:0%
+watching too much Jack Bauer but you
+know that's a story for another day as
+
+ align:start position:0%
+know that's a story for another day as
+ 
+
+ align:start position:0%
+know that's a story for another day as
+well so if so it turns out that
+
+ align:start position:0%
+well so if so it turns out that
+ 
+
+ align:start position:0%
+well so if so it turns out that
+depending on blood groups you can either
+
+ align:start position:0%
+depending on blood groups you can either
+ 
+
+ align:start position:0%
+depending on blood groups you can either
+be a universal donor or a universal
+
+ align:start position:0%
+be a universal donor or a universal
+ 
+
+ align:start position:0%
+be a universal donor or a universal
+acceptor so the people with the O blood
+
+ align:start position:0%
+acceptor so the people with the O blood
+ 
+
+ align:start position:0%
+acceptor so the people with the O blood
+group can give anyone their blood
+
+ align:start position:0%
+group can give anyone their blood
+ 
+
+ align:start position:0%
+group can give anyone their blood
+people with O a B and a B but
+
+ align:start position:0%
+people with O a B and a B but
+ 
+
+ align:start position:0%
+people with O a B and a B but
+unfortunately for the poor people with
+
+ align:start position:0%
+unfortunately for the poor people with
+ 
+
+ align:start position:0%
+unfortunately for the poor people with
+Oh blood group is they could they cannot
+
+ align:start position:0%
+Oh blood group is they could they cannot
+ 
+
+ align:start position:0%
+Oh blood group is they could they cannot
+receive blood from blood group a B or a
+
+ align:start position:0%
+receive blood from blood group a B or a
+ 
+
+ align:start position:0%
+receive blood from blood group a B or a
+B and I wanted to show this and I hope I
+
+ align:start position:0%
+B and I wanted to show this and I hope I
+ 
+
+ align:start position:0%
+B and I wanted to show this and I hope I
+can get it working because we have just
+
+ align:start position:0%
+can get it working because we have just
+ 
+
+ align:start position:0%
+can get it working because we have just
+the right amount of time which makes me
+
+ align:start position:0%
+the right amount of time which makes me
+ 
+
+ align:start position:0%
+the right amount of time which makes me
+really happy because I don't really
+
+ align:start position:0%
+really happy because I don't really
+ 
+
+ align:start position:0%
+really happy because I don't really
+program things that well sometimes there
+
+ align:start position:0%
+program things that well sometimes there
+ 
+
+ align:start position:0%
+program things that well sometimes there
+was a P there was um at the latest
+
+ align:start position:0%
+was a P there was um at the latest
+ 
+
+ align:start position:0%
+was a P there was um at the latest
+American camera other disasters were
+
+ align:start position:0%
+American camera other disasters were
+ 
+
+ align:start position:0%
+American camera other disasters were
+affected by crisis usually need for
+
+ align:start position:0%
+affected by crisis usually need for
+ 
+
+ align:start position:0%
+affected by crisis usually need for
+vital things food shelter water and
+
+ align:start position:0%
+vital things food shelter water and
+ 
+
+ align:start position:0%
+vital things food shelter water and
+blood in particular o type blood because
+
+ align:start position:0%
+blood in particular o type blood because
+ 
+
+ align:start position:0%
+blood in particular o type blood because
+it can be safely given to any patient
+
+ align:start position:0%
+it can be safely given to any patient
+ 
+
+ align:start position:0%
+it can be safely given to any patient
+now scientists say they have identified
+
+ align:start position:0%
+now scientists say they have identified
+ 
+
+ align:start position:0%
+now scientists say they have identified
+enzymes from the human gut that can turn
+
+ align:start position:0%
+enzymes from the human gut that can turn
+ 
+
+ align:start position:0%
+enzymes from the human gut that can turn
+Type A and B blood into Type O up to 30
+
+ align:start position:0%
+Type A and B blood into Type O up to 30
+ 
+
+ align:start position:0%
+Type A and B blood into Type O up to 30
+times more efficiently than previously
+
+ align:start position:0%
+times more efficiently than previously
+ 
+
+ align:start position:0%
+times more efficiently than previously
+studied enzymes type A or B blood has
+
+ align:start position:0%
+studied enzymes type A or B blood has
+ 
+
+ align:start position:0%
+studied enzymes type A or B blood has
+specific sugars on the outside of itself
+
+ align:start position:0%
+specific sugars on the outside of itself
+ 
+
+ align:start position:0%
+specific sugars on the outside of itself
+these sugars are recognized by the
+
+ align:start position:0%
+these sugars are recognized by the
+ 
+
+ align:start position:0%
+these sugars are recognized by the
+immune system and if they don't match
+
+ align:start position:0%
+immune system and if they don't match
+ 
+
+ align:start position:0%
+immune system and if they don't match
+the type of blood that's already in an
+
+ align:start position:0%
+the type of blood that's already in an
+ 
+
+ align:start position:0%
+the type of blood that's already in an
+individual those cells are destroyed
+
+ align:start position:0%
+individual those cells are destroyed
+ 
+
+ align:start position:0%
+individual those cells are destroyed
+because these sugars are recognized by
+
+ align:start position:0%
+because these sugars are recognized by
+ 
+
+ align:start position:0%
+because these sugars are recognized by
+the immune system
+
+ align:start position:0%
+the immune system
+ 
+
+ align:start position:0%
+the immune system
+they're called antigens type a B blood
+
+ align:start position:0%
+they're called antigens type a B blood
+ 
+
+ align:start position:0%
+they're called antigens type a B blood
+has both antigens and type O blood has
+
+ align:start position:0%
+has both antigens and type O blood has
+ 
+
+ align:start position:0%
+has both antigens and type O blood has
+none the researchers presented these
+
+ align:start position:0%
+none the researchers presented these
+ 
+
+ align:start position:0%
+none the researchers presented these
+findings at the recent American Chemical
+
+ align:start position:0%
+findings at the recent American Chemical
+ 
+
+ align:start position:0%
+findings at the recent American Chemical
+Society national meeting in Boston
+
+ align:start position:0%
+Society national meeting in Boston
+ 
+
+ align:start position:0%
+Society national meeting in Boston
+Stephen withers from the University of
+
+ align:start position:0%
+Stephen withers from the University of
+ 
+
+ align:start position:0%
+Stephen withers from the University of
+British Columbia has been
+
+ align:start position:0%
+British Columbia has been
+ 
+
+ align:start position:0%
+British Columbia has been
+studying enzymes that remove a or b
+
+ align:start position:0%
+studying enzymes that remove a or b
+ 
+
+ align:start position:0%
+studying enzymes that remove a or b
+antigens from red blood cells
+
+ align:start position:0%
+antigens from red blood cells
+ 
+
+ align:start position:0%
+antigens from red blood cells
+if those antigens can be removed then
+
+ align:start position:0%
+if those antigens can be removed then
+ 
+
+ align:start position:0%
+if those antigens can be removed then
+type A or B can be converted to type O
+
+ align:start position:0%
+type A or B can be converted to type O
+ 
+
+ align:start position:0%
+type A or B can be converted to type O
+blood to find the enzymes more quickly
+
+ align:start position:0%
+blood to find the enzymes more quickly
+ 
+
+ align:start position:0%
+blood to find the enzymes more quickly
+withers in a colleague at his
+
+ align:start position:0%
+withers in a colleague at his
+ 
+
+ align:start position:0%
+withers in a colleague at his
+institution used a technique called
+
+ align:start position:0%
+institution used a technique called
+ 
+
+ align:start position:0%
+institution used a technique called
+metagenomics which allows scientists to
+
+ align:start position:0%
+metagenomics which allows scientists to
+ 
+
+ align:start position:0%
+metagenomics which allows scientists to
+sample the genes of millions of
+
+ align:start position:0%
+sample the genes of millions of
+ 
+
+ align:start position:0%
+sample the genes of millions of
+microorganisms without the need for
+
+ align:start position:0%
+microorganisms without the need for
+ 
+
+ align:start position:0%
+microorganisms without the need for
+individual coal so that tells you
+
+ align:start position:0%
+individual coal so that tells you
+ 
+
+ align:start position:0%
+individual coal so that tells you
+something about technology and
+
+ align:start position:0%
+something about technology and
+ 
+
+ align:start position:0%
+something about technology and
+engineering and understanding structures
+
+ align:start position:0%
+engineering and understanding structures
+ 
+
+ align:start position:0%
+engineering and understanding structures
+so it would be really advantageous the
+
+ align:start position:0%
+so it would be really advantageous the
+ 
+
+ align:start position:0%
+so it would be really advantageous the
+state of which you really need blood
+
+ align:start position:0%
+state of which you really need blood
+ 
+
+ align:start position:0%
+state of which you really need blood
+supplies is to take all the blood in the
+
+ align:start position:0%
+supplies is to take all the blood in the
+ 
+
+ align:start position:0%
+supplies is to take all the blood in the
+blood banks and turn everything into a
+
+ align:start position:0%
+blood banks and turn everything into a
+ 
+
+ align:start position:0%
+blood banks and turn everything into a
+universal donor but the blood banks keep
+
+ align:start position:0%
+universal donor but the blood banks keep
+ 
+
+ align:start position:0%
+universal donor but the blood banks keep
+these differentiated supplies of blood
+
+ align:start position:0%
+these differentiated supplies of blood
+ 
+
+ align:start position:0%
+these differentiated supplies of blood
+but what if you needle you know you need
+
+ align:start position:0%
+but what if you needle you know you need
+ 
+
+ align:start position:0%
+but what if you needle you know you need
+something that you can give everyone
+
+ align:start position:0%
+something that you can give everyone
+ 
+
+ align:start position:0%
+something that you can give everyone
+safely and so there are enzymes in the
+
+ align:start position:0%
+safely and so there are enzymes in the
+ 
+
+ align:start position:0%
+safely and so there are enzymes in the
+guards there excuse me bacteria in the
+
+ align:start position:0%
+guards there excuse me bacteria in the
+ 
+
+ align:start position:0%
+guards there excuse me bacteria in the
+gut
+
+ align:start position:0%
+gut
+ 
+
+ align:start position:0%
+gut
+that actually live off of sugars that
+
+ align:start position:0%
+that actually live off of sugars that
+ 
+
+ align:start position:0%
+that actually live off of sugars that
+they chopped off cells in and the matrix
+
+ align:start position:0%
+they chopped off cells in and the matrix
+ 
+
+ align:start position:0%
+they chopped off cells in and the matrix
+in the in the in the in the in GI system
+
+ align:start position:0%
+in the in the in the in the in GI system
+ 
+
+ align:start position:0%
+in the in the in the in the in GI system
+and so what the withers group did was to
+
+ align:start position:0%
+and so what the withers group did was to
+ 
+
+ align:start position:0%
+and so what the withers group did was to
+screen a lot of different enzymes from
+
+ align:start position:0%
+screen a lot of different enzymes from
+ 
+
+ align:start position:0%
+screen a lot of different enzymes from
+bacteria in the gut and find ones that
+
+ align:start position:0%
+bacteria in the gut and find ones that
+ 
+
+ align:start position:0%
+bacteria in the gut and find ones that
+had a really good specificity for
+
+ align:start position:0%
+had a really good specificity for
+ 
+
+ align:start position:0%
+had a really good specificity for
+removing those sugars then they did
+
+ align:start position:0%
+removing those sugars then they did
+ 
+
+ align:start position:0%
+removing those sugars then they did
+protein engineering work to make them
+
+ align:start position:0%
+protein engineering work to make them
+ 
+
+ align:start position:0%
+protein engineering work to make them
+more efficient thus creating something
+
+ align:start position:0%
+more efficient thus creating something
+ 
+
+ align:start position:0%
+more efficient thus creating something
+that was proposed a long time ago could
+
+ align:start position:0%
+that was proposed a long time ago could
+ 
+
+ align:start position:0%
+that was proposed a long time ago could
+be useful but now really making it
+
+ align:start position:0%
+be useful but now really making it
+ 
+
+ align:start position:0%
+be useful but now really making it
+useful because those enzymes are much
+
+ align:start position:0%
+useful because those enzymes are much
+ 
+
+ align:start position:0%
+useful because those enzymes are much
+more efficient they really catalyze
+
+ align:start position:0%
+more efficient they really catalyze
+ 
+
+ align:start position:0%
+more efficient they really catalyze
+reactions a great speed so they're much
+
+ align:start position:0%
+reactions a great speed so they're much
+ 
+
+ align:start position:0%
+reactions a great speed so they're much
+more efficient engineering enzymes to
+
+ align:start position:0%
+more efficient engineering enzymes to
+ 
+
+ align:start position:0%
+more efficient engineering enzymes to
+treat your blood cells to make sure you
+
+ align:start position:0%
+treat your blood cells to make sure you
+ 
+
+ align:start position:0%
+treat your blood cells to make sure you
+get rid of all the features that are
+
+ align:start position:0%
+get rid of all the features that are
+ 
+
+ align:start position:0%
+get rid of all the features that are
+characteristic of the a the B and the a
+
+ align:start position:0%
+characteristic of the a the B and the a
+ 
+
+ align:start position:0%
+characteristic of the a the B and the a
+B antigens because you if you don't do a
+
+ align:start position:0%
+B antigens because you if you don't do a
+ 
+
+ align:start position:0%
+B antigens because you if you don't do a
+good job of it then the human immune
+
+ align:start position:0%
+good job of it then the human immune
+ 
+
+ align:start position:0%
+good job of it then the human immune
+system will recognize the little bits
+
+ align:start position:0%
+system will recognize the little bits
+ 
+
+ align:start position:0%
+system will recognize the little bits
+that sneak in and start triggering an
+
+ align:start position:0%
+that sneak in and start triggering an
+ 
+
+ align:start position:0%
+that sneak in and start triggering an
+immune response so the efficiency of the
+
+ align:start position:0%
+immune response so the efficiency of the
+ 
+
+ align:start position:0%
+immune response so the efficiency of the
+enzymes that cleave those sugars off is
+
+ align:start position:0%
+enzymes that cleave those sugars off is
+ 
+
+ align:start position:0%
+enzymes that cleave those sugars off is
+absolutely paramount and that's what I
+
+ align:start position:0%
+absolutely paramount and that's what I
+ 
+
+ align:start position:0%
+absolutely paramount and that's what I
+have for you today I will see you Monday
+
+ align:start position:0%
+have for you today I will see you Monday
+ 
+
+ align:start position:0%
+have for you today I will see you Monday
+so don't forget the P sets due at 3:00
+
+ align:start position:0%
+so don't forget the P sets due at 3:00
+ 
+
+ align:start position:0%
+so don't forget the P sets due at 3:00
+Monday I would like for you to have a
+
+ align:start position:0%
+Monday I would like for you to have a
+ 
+
+ align:start position:0%
+Monday I would like for you to have a
+preview of the whoops
+
+ align:start position:0%
+preview of the whoops
+ 
+
+ align:start position:0%
+preview of the whoops
+of the DNA reading material I don't know
+
+ align:start position:0%
+of the DNA reading material I don't know
+ 
+
+ align:start position:0%
+of the DNA reading material I don't know
+if any of you do this but I think it's
+
+ align:start position:0%
+if any of you do this but I think it's
+ 
+
+ align:start position:0%
+if any of you do this but I think it's
+really handy so there's just some very
+
+ align:start position:0%
+really handy so there's just some very
+ 
+
+ align:start position:0%
+really handy so there's just some very
+little sections and we'll give you a bit
+
+ align:start position:0%
+little sections and we'll give you a bit
+ 
+
+ align:start position:0%
+little sections and we'll give you a bit
+of exposure to nucleic acids it'll just
+
+ align:start position:0%
+of exposure to nucleic acids it'll just
+ 
+
+ align:start position:0%
+of exposure to nucleic acids it'll just
+make the lecture a little bit more kind
+
+ align:start position:0%
+make the lecture a little bit more kind
+ 
+
+ align:start position:0%
+make the lecture a little bit more kind
+of familiar but that's what we're up for
+
+ align:start position:0%
+of familiar but that's what we're up for
+ 
+
+ align:start position:0%
+of familiar but that's what we're up for
+Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/D1WF9YKqf3o.txt b/D1WF9YKqf3o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..21d8cd49b042f0ae6fa91303d9896a772aaabcd5
--- /dev/null
+++ b/D1WF9YKqf3o.txt
@@ -0,0 +1,2021 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: In the last two
+lectures, we saw how periodic
+
+and non periodic signals could
+be represented as linear
+
+combinations of complex
+exponentials.
+
+And this led to the Fourier
+series representation, in the
+
+periodic case, and it led
+to the Fourier transform
+
+representation in the
+aperiodic case.
+
+And then, in fact, what we did
+was to incorporate the Fourier
+
+series within the framework
+of the Fourier transform.
+
+What I'd like to do in today's
+lecture is look at the Fourier
+
+transform more closely, in
+particular with regard to some
+
+of its properties.
+
+So let me begin by reminding
+you of the analysis and
+
+synthesis equations for the
+Fourier transform, as I've
+
+summarized them here.
+
+The synthesis equation being an
+equation the tells us how
+
+to build the time function out
+of, in essence, a linear
+
+combination of complex
+exponentials.
+
+And the analysis equation
+telling us how to get the
+
+amplitudes of those complex
+exponentials from the
+
+associated time function.
+
+So essentially, in the
+decomposition of x of t as a
+
+linear combination of complex
+exponentials, the complex
+
+amplitudes of those are, in
+effect, the Fourier transform
+
+scaled by the differential and
+scaled by 1 over 2 pi.
+
+As I indicated last time, the
+Fourier transform is a complex
+
+function of frequency.
+
+And in particular, the complex
+function of frequency has an
+
+important and very useful
+symmetry property.
+
+The symmetry of the Fourier
+transform, when x of t is
+
+real, is what is referred to
+as conjugate symmetric.
+
+In other words, if we take the
+complex function, f of omega,
+
+and its complex conjugate,
+that's equivalent to replacing
+
+omega by minus omega.
+
+And a consequence of that, if we
+think in terms of the real
+
+part of the Fourier transform,
+the real part is an even
+
+function of frequency, and the
+magnitude is an even function
+
+of frequency.
+
+Whereas the imaginary part is an
+odd function of frequency,
+
+and the phase angle is an odd
+function of frequency.
+
+So we have this symmetry
+relationship that, for x of t
+
+real, if we think of either the
+real part or the magnitude
+
+of the Fourier transform,
+it's even symmetric.
+
+And the imaginary part, or the
+phase angle, either one, is
+
+odd symmetric.
+
+In other words, if we flip it,
+we multiply by a minus sign.
+
+Let's look at an example, in the
+context of an example that
+
+we worked last time for
+the Fourier transform.
+
+We took the case of a real
+exponential of the form e to
+
+the minus at times the step.
+
+And the Fourier transform, as we
+found, was of the algebraic
+
+form 1 over a plus j omega.
+
+And, incidentally, the Fourier
+transform integral only
+
+converged for a greater
+than 0.
+
+In other words, for this
+exponential decaying.
+
+And I illustrated the magnitude
+and angle, and what
+
+we see is that e to the minus
+at is a real time function,
+
+therefore its magnitude should
+be an even function of
+
+frequency, and indeed it is.
+
+And its phase angle,
+shown below, is an
+
+odd function of frequency.
+
+So in fact, although I stressed
+last time that the
+
+complex exponentials is required
+to build a time
+
+function require exponentials of
+both positive and negative
+
+frequencies, for x of t real
+what we see is that, because
+
+of these symmetry properties,
+either for the real and
+
+imaginary or magnitude and
+angle, we can specify the
+
+Fourier transform for, let's say
+only positive frequencies,
+
+and the symmetry, then, implies,
+or tells us, what the
+
+Fourier transform, then, would
+be for the negative
+
+frequencies.
+
+This same example, the
+decaying exponential,
+
+demonstrates another important
+and often useful property of
+
+the Fourier transform.
+
+Specifically, let's rewrite,
+algebraically, this example as
+
+I indicate here.
+
+So we have, again, the
+exponential, whose Fourier
+
+transform is 1 over
+a plus j omega.
+
+And if I just simply divide
+numerator and denominator by
+
+a, I can rewrite it in
+the form shown here.
+
+And what we notice is that in
+the time function we have a
+
+term of the form a times t, and
+in the frequency function
+
+we have a term of the form
+omega divided by a.
+
+Or equivalently, we could think
+of the time function,
+
+which I show here, and as the
+parameter a gets smaller, the
+
+exponential gets spread
+out in time.
+
+Whereas its Fourier transform,
+or the magnitude of its
+
+Fourier transform, has the
+inverse property that as a
+
+gets smaller, in fact, this
+scales down in frequency.
+
+Well, this is a general property
+of the Fourier
+
+transform, namely the fact that
+a linear scaling in time
+
+generates the inverse linear
+scaling in frequency.
+
+And the general statement of
+this time frequency scaling is
+
+what I show at the top of the
+transparency, namely the
+
+equation that if we scale the
+time function in time, then we
+
+apply an inverse scaling
+in frequency.
+
+This, in fact, is probably a
+result that you're already
+
+possibly familiar with,
+in somewhat
+
+of a different context.
+
+Essentially, you could think
+of this as an example, or a
+
+generalization, rather, of the
+notion that if, let's say I
+
+had a signal that was recorded
+on a tape player, and if I
+
+play the tape back at, let's
+say, twice the speed, which
+
+means that I'm compressing
+the time axis linearly
+
+by a factor of 2.
+
+Then, in fact, what happens is
+that the frequencies that we
+
+observe get pushed up
+by a factor of 2.
+
+And, in fact, let me
+illustrate that.
+
+I have here a glockenspiel, and
+anyone who loves a parade
+
+certainly knows what
+a glockenspiel is.
+
+And this particular glockenspiel
+has three a's,
+
+separated each by an octave.
+
+There's a middle a, a
+high a, and a low a.
+
+And what I've done is to record
+the middle a on a tape
+
+at 7 and 1/2 inches
+per second.
+
+And what I'd like to demonstrate
+is that as we play
+
+that back, either at twice or
+half speed, the effective note
+
+gets moved down or
+up by an octave.
+
+So let me first play the
+note at the speed at
+
+which it was recorded.
+
+And so what we'll hear is the
+middle a as I've recorded it.
+
+And let me just start
+the tape player.
+
+Let me stop it, and hopefully
+what you heard is the same
+
+note from the tape recorder as
+the note that I played on the
+
+glockenspiel.
+
+Now I'll rewind the tape, and
+we'll go back to the beginning
+
+of that portion.
+
+And now, if I change the tape
+speed to half the speed, so
+
+from 7 and 1/2 inches per
+second, I'll change the tape
+
+speed to 3 and 3/4 inches
+per second.
+
+And now when I play the tape
+back, because of the inverse
+
+relationship between time and
+frequency scaling, we're now
+
+scaling in time by stretching
+out, we would expect the
+
+frequencies to be lowered
+by a factor of 2.
+
+We should now expect the taped
+note to be an octave lower,
+
+matching this lower a.
+
+So let's just play that.
+
+Let me stop it, and, again,
+we'll rewind the tape.
+
+Go back to the beginning,
+and now we'll play this
+
+at twice the speed.
+
+So I'll change from 3 and 3/4
+to 15 inches per second.
+
+And now when I play it, we would
+expect that to match the
+
+upper note.
+
+And let's just do that.
+
+Although that's a result that,
+intuitively, probably makes
+
+considerable sense, in fact,
+what that is is an
+
+illustration of the inverse
+relationship between time
+
+scaling and frequency scaling.
+
+And also, by the way, it was
+finally my opportunity to play
+
+the glockenspiel
+on television.
+
+In addition, there is another
+very important relationship
+
+between the time and frequency
+domains, namely what is
+
+referred to as a duality
+relationship.
+
+And the duality relationship
+between time and frequency
+
+falls out, more or less
+directly, from the equations,
+
+the analysis and synthesis
+equations.
+
+In particular, if we look at the
+synthesis equation, which
+
+I repeat here, and the analysis
+equation, which I
+
+repeat below it, what we observe
+is that, in fact,
+
+these equations are basically
+identical, except for the fact
+
+that in the top integral we have
+things as a function of
+
+omega, in the bottom integral
+as a function of t, and
+
+there's a factor of 1 over
+2 pi, and, by the
+
+way, a minus sign.
+
+You can look at the algebra
+more carefully at your
+
+leisure, but essentially what
+this says is that if x of
+
+omega is the Fourier transform
+of a time function x of t,
+
+then, in fact, x of t is very
+much like the Fourier
+
+transform of x of omega.
+
+In fact, it's the Fourier
+transform of x of minus omega
+
+to account for this
+minus sign.
+
+And, by the way, there's
+just an additional
+
+factor of 1 over 2 pi.
+
+So the duality relationship
+which follows from these two
+
+equations, in fact, says that if
+x of t and x of omega are a
+
+Fourier transform pair, if x and
+X are a Fourier transform
+
+pair, then X, in fact, has a
+Fourier transform which is
+
+proportional to x
+turned around.
+
+This duality in the continuous
+time Fourier
+
+transform is very important.
+
+It's very useful.
+
+It, by the way, is not a duality
+that surfaced in the
+
+Fourier series, because, as you
+recall, the Fourier series
+
+begins with a continuous time
+function and in the frequency
+
+domain generates a sequence,
+which would just naturally
+
+have problems associated with
+it if we attempted to
+
+interpret a duality.
+
+And we'll see, also, that in the
+discrete time case, one of
+
+the important differences
+between continuous time and
+
+discrete time Fourier transforms
+is the fact that in
+
+continuous time we have duality,
+in the discrete time
+
+Fourier transform we don't.
+
+Let's illustrate this
+with an example.
+
+Here are, in fact, two examples
+of Fourier transform
+
+pairs taken from examples
+in the text.
+
+The top one being example 4.11
+from the text, and it's a time
+
+function which is a sine x
+over x type of function.
+
+And its Fourier transform
+corresponds to a rectangular
+
+shape in the frequency domain.
+
+There's also another example in
+the text, the example that
+
+precedes this one, which
+is example 4.10.
+
+And in example 4.10, we begin
+with a rectangle, and its
+
+Fourier transform is
+of the form of a
+
+sine x over x function.
+
+So in fact, if we look at these
+two examples together,
+
+what we see is the duality
+very evident.
+
+In other words, if we take this
+time function and instead
+
+think of a frequency function
+that has the same form, then
+
+we simply interchange the roles
+of time and frequency in
+
+the other domains.
+
+So the fact that these two
+correspond means that these
+
+two correspond.
+
+Of course in this particular
+example, because of the fact
+
+that we picked a symmetric
+function, an even function, in
+
+fact, the additional twist of
+the time axis being reversed
+
+didn't show up in duality
+with this example.
+
+One thing this says, of course,
+is that essentially
+
+any time you've calculated the
+Fourier transform of one time
+
+function, then you've actually
+calculated the Fourier
+
+transform of two
+time functions.
+
+Another one being the dual
+example to the one that you
+
+just calculated.
+
+Also somewhat related to duality
+is what is referred to
+
+as Parseval's relation
+for the continuous
+
+time Fourier transform.
+
+And essentially, what Parseval's
+relationship says,
+
+as a summary of it, says that
+the energy in a time function
+
+and the energy in its Fourier
+transform are proportional,
+
+the proportionality factor
+being a factor of 2 pi.
+
+That's summarized here.
+
+What's meant by the energy is,
+of course, the integral of the
+
+magnitude squared of x of t.
+
+And the statement of Parseval's
+relation is that
+
+that integral, the energy in x
+of t, is proportional to this
+
+integral, which is the
+energy in x of omega.
+
+Although we've incorporated the
+Fourier series within a
+
+framework of the Fourier
+transform, Parseval's relation
+
+needs to be modified slightly
+for Fourier series, because of
+
+the fact that a periodic signal
+has an infinite amount
+
+of energy in it, and,
+essentially, that form of
+
+Parseval's relationship for the
+periodic case would say
+
+infinity equals infinity,
+which isn't too useful.
+
+However, it can be modified so
+that Parseval's relationship
+
+to the periodic case says,
+essentially, that the energy
+
+in one period of the periodic
+time function is proportional
+
+with, this is the
+proportionality factor,
+
+proportional to the sum of the
+magnitude squared of the
+
+coefficients.
+
+In other words, the energy in
+one period is proportional to
+
+the energy in the sequence that
+represents the Fourier
+
+series coefficients.
+
+There are lots of other
+properties, and they're
+
+developed in the text and
+in the study guide.
+
+A number of properties that we
+want to make particular use of
+
+during this lecture, and in
+later lectures, are ones that
+
+I summarize here.
+
+And I won't demonstrate the
+proofs, but principally focus
+
+on some of the interpretation
+as the lecture goes on.
+
+The first property that I have
+listed here is what's referred
+
+to as the time shifting
+property.
+
+And the time shifting property
+says, if I have a time
+
+function with a Fourier
+transform x of omega, if I
+
+shift that time function in
+time, then that corresponds to
+
+multiplying the Fourier
+transform by this factor.
+
+As you examine this factor, what
+you can see is that this
+
+factor has magnitude unity and
+it has a phase, which is
+
+linear with frequency, and
+a slope of minus t0.
+
+So a statement to remember, that
+will come up many times
+
+throughout the course, is
+that a time shift, or a
+
+displacement in time,
+corresponds to a linear change
+
+in phase and frequency.
+
+Another property and, in fact,
+a pair of properties that
+
+we'll make reference to as we
+turn our attention toward the
+
+end of this lecture to solving
+differential equations using
+
+the Fourier transform, is what's
+referred to as the
+
+differentiation property and
+its companion, which is the
+
+integration property.
+
+The differentiation property
+says, again, if we have a time
+
+function with Fourier transform
+x of omega, the
+
+Fourier transform of the time
+derivative of that corresponds
+
+to multiplying the Fourier
+transform by a linear function
+
+of frequency.
+
+So here it's a linear amplitude
+change that
+
+corresponds to differentiation.
+
+At first glance, what you
+might think is that the
+
+integration property is just
+the reverse of that.
+
+If for the differentiation
+property you multiply by j
+
+omega, then for integration you
+must divide by j omega.
+
+And that's almost correct,
+except not quite.
+
+And the reason for the not quite
+is that recall that if
+
+you differentiate, what happens,
+of course, is that
+
+you lose a constant.
+
+And if we have a time function
+that's some finite energy
+
+signal plus a constant,
+differentiating will destroy
+
+the constant.
+
+The integration property,
+in essence, tries
+
+to bring that back.
+
+So the integration property,
+which is the inverse of the
+
+differentiation property, says
+that we divide the transform
+
+by j omega, and then if, in
+fact, there was a constant
+
+added to x of t, we have to
+account for that by inserting
+
+an impulse into the
+Fourier transform.
+
+And the final property that I
+want to draw your attention to
+
+on this view graph is the
+linearity property, which is
+
+very straightforward to
+demonstrate from the analysis
+
+and synthesis equations, which
+simply says if x1 of omega is
+
+the Fourier transform x1 of t,
+and x2 of omega is the Fourier
+
+transform of x2 of t, then the
+Fourier transform of a linear
+
+combination is a linear
+combination of the Fourier
+
+transforms.
+
+Let me emphasize, also, that
+these properties, for the most
+
+part, apply both to Fourier
+series and Fourier transforms
+
+because, in fact, what we've
+done is to incorporate the
+
+Fourier series within
+the framework
+
+of the Fourier transform.
+
+We'll be using a number of these
+properties shortly, when
+
+we turn our attention to linear
+constant coefficient
+
+differential equations.
+
+However, before we do that
+I'd like to focus on two
+
+additional major properties, and
+these are what I refer to
+
+as the convolution property and
+the modulation property.
+
+And in fact, the convolution
+property, as I'm about to
+
+introduce it, forms the
+mathematical and conceptual
+
+basis for the whole notion of
+filtering, which, in fact,
+
+will be a topic by itself in a
+set of lectures, and, in fact,
+
+is a chapter by itself
+in the textbook.
+
+Similarly, what I'll refer to
+as the modulation property,
+
+again, will occupy its own set
+of lectures as we go through
+
+the course, and, in
+fact, has its own
+
+chapter in the textbook.
+
+Let me just indicate what the
+convolution property is.
+
+And what the convolution
+property tells us is that the
+
+Fourier transform of the
+convolution of two time
+
+functions is the product of
+their Fourier transforms.
+
+So it says, for example, that
+if I have a linear time
+
+invariant system, and I have
+an input x of t, an impulse
+
+response h of t, and the output,
+of course, being the
+
+convolution, then, in fact,
+if I look at this in the
+
+frequency domain, the Fourier
+transform of the output is the
+
+Fourier transform of the input
+times the Fourier transform of
+
+the impulse response.
+
+You can demonstrate this
+property algebraically by
+
+essentially taking the
+convolution integral and
+
+applying the Fourier transform
+and doing the appropriate
+
+interchanging of the order of
+integration, et cetera.
+
+But what I'd like to draw your
+attention to is a somewhat
+
+more intuitive interpretation
+of the property.
+
+And the intuitive interpretation
+stems from the
+
+relationship between the Fourier
+transform of the
+
+impulse response and what
+we've referred to as the
+
+frequency response.
+
+Recall that one of the things
+that led us to use complex
+
+exponentials as building blocks
+was the fact that
+
+they're eigenfunctions
+of linear
+
+time and variant systems.
+
+In other words, if we have a
+linear time invariant system,
+
+and I have an input which is
+a complex exponential, the
+
+output is a complex exponential
+of the same
+
+frequency multiplied
+by what we call
+
+the frequency response.
+
+And, in fact, the expression for
+the frequency response is
+
+identical to the expression for
+the Fourier transform of
+
+the impulse response.
+
+In other words, the frequency
+response is the Fourier
+
+transform of the impulse
+response.
+
+Now in that context, how
+can we interpret
+
+the convolution property?
+
+Well, remember what I said at
+the beginning of the lecture,
+
+when I pointed to the synthesis
+equation and I said,
+
+in essence, the synthesis
+equation tells us how to
+
+decompose x of t as a linear
+combination of complex
+
+exponentials.
+
+What are the complex amplitudes
+of those complex
+
+exponentials?
+
+In terms of our notation here,
+the complex amplitude of those
+
+complex exponentials is x of
+omega, or proportional to x of
+
+omega, in particular it's x of
+omega, d omega, and then a
+
+factor of 2 pi.
+
+As this signal goes through
+this linear time invariant
+
+system, what happens to each of
+those exponential is each
+
+one gets multiplied by the
+frequency response at the
+
+associated frequency.
+
+What comes out is the amplitude
+of the complex
+
+exponentials that are used
+to build the output.
+
+So in fact, the convolution
+property simply is telling us
+
+that, in terms of the
+decomposition of the signal,
+
+in terms of complex
+exponentials, as we push that
+
+signal through a linear time
+invariant system, we're
+
+separately multiplying by the
+frequency response, the
+
+amplitudes of the exponential
+components used
+
+to build the input.
+
+And that sum, in turn, is the
+decomposition of the output in
+
+terms of complex exponentials.
+
+I understand that going through
+that involves a little
+
+bit of sorting out, and I
+strongly encourage you to try
+
+to understand and interpret the
+convolution property in
+
+those conceptual terms, rather
+than simply by applying the
+
+mathematics to the convolution
+integral and seeing the terms
+
+match up on both sides.
+
+As I indicated, the convolution
+property forms the
+
+basis for what's referred
+to as filtering.
+
+And this is a topic that we'll
+be treating in a considerable
+
+amount of detail after we've
+also gone through a discussion
+
+of the discrete time Fourier
+transform in the
+
+next several lectures.
+
+However, what I'd like to do
+is just indicate, now, a
+
+little bit of the conceptual
+ideas involved.
+
+Essentially, conceptually,
+what filtering, as it's
+
+typically referred to,
+corresponds to is modifying
+
+separately the individual
+frequency
+
+components in a signal.
+
+The convolution property told
+us that if we look at the
+
+individual frequency components,
+they get
+
+multiplied by the frequency
+response, and so what that
+
+says is that we can amplify
+or attenuate any of those
+
+components separately using a
+linear time invariant system.
+
+For example, what I've
+illustrated here is the
+
+frequency response of what is
+commonly referred to as an
+
+ideal low pass filter.
+
+What an ideal low pass filter
+does is to pass exactly
+
+frequencies in one frequency
+range and eliminate totally
+
+frequencies outside
+that range.
+
+Another filter which is not so
+ideal might, for example,
+
+attenuate components in
+this band but not
+
+totally eliminate them.
+
+In terms of filtering, we
+can think back to the
+
+differentiation property
+and, in fact, interpret
+
+differentiator as a filter.
+
+Recall that the differentiation
+property said
+
+that the Fourier transform of
+the differentiated signal is
+
+the Fourier transform of
+the original signal
+
+multiplied by j omega.
+
+So what that says, then,
+is that if we have a
+
+differentiator, the frequency
+response of that is j omega.
+
+In other words, the Fourier
+transform of the output is j
+
+omega times the Fourier
+transform of the input.
+
+And so the frequency response
+of the differentiator looks
+
+like this, in terms
+of its magnitude.
+
+And what it does, of course,
+is it amplifies high
+
+frequencies and attenuates
+low frequencies.
+
+Let me just, to cement some of
+these ideas, illustrate them
+
+in the context of one kind of
+signal, namely a signal which,
+
+in fact, is a spatial signal
+rather than a time signal.
+
+And this also gives me an
+opportunity to introduce you
+
+to our colleague, J.
+B. J. Fourier.
+
+So if we could look at our
+colleague, Mr. Fourier, who,
+
+by the way, is not only a person
+who had tremendously
+
+brilliant insights, and his
+insights, in fact, have led to
+
+forming the foundation of the
+developments that is the basis
+
+for this course.
+
+He was also a very
+
+interesting, fascinating person.
+
+And there's a certain amount of
+historical discussion about
+
+Fourier and his background,
+which you might enjoy reading
+
+in the text.
+
+In any case, what you're
+looking at, of
+
+course, is a signal.
+
+And the signal is a spatial
+signal, and it has high
+
+frequencies and low
+frequencies.
+
+High frequencies corresponding
+to things that are varying
+
+rapidly spatially, and
+low frequencies
+
+varying slowly spatially.
+
+And so, for example, we could
+low pass filter this picture
+
+simply by asking the video crew
+if they could be slightly
+
+defocus it.
+
+And what you see as the picture
+is defocused, if you
+
+could hold it there, is that
+we've lost edges, which is the
+
+rapid variation.
+
+And what we've retained is the
+broader, slow variation.
+
+And now let's take out the
+defocusing low pass filter and
+
+go back to a focused image.
+
+What we can also consider is
+what would happen if we looked
+
+at the differentiated image.
+
+And there are several ways
+we can think about this.
+
+One is that a differentiator--
+
+Of course the output of a
+differentiator is larger where
+
+the discontinuity, or where
+the variation, is faster.
+
+And so we would expect the edges
+to be enhanced if, in
+
+fact, we differentiated
+the image.
+
+Or if we interpret
+differentiation in the context
+
+of our filter, then what we're
+saying is that, in effect,
+
+what's happening is that the
+differentiator is accentuating
+
+the high frequencies because of
+the frequency shape of the
+
+differentiator.
+
+Recall that this all fits
+together as a nice package.
+
+We expect intuitively
+that differentiation
+
+will enhance edges.
+
+When we talked about square
+waves and we saw how the
+
+Fourier series built up a square
+wave, we saw that it
+
+was the high frequencies that
+were required in order to
+
+build up the sharp edges.
+
+And so either viewed as a
+filter, or viewed intuitively,
+
+we would expect that the
+differentiated image would, in
+
+fact, attenuate this slowly
+varying background and amplify
+
+the rapidly varying edges.
+
+So let's look again at our
+original image, just to remind
+
+you of the fact that there are
+edges, of course, and there is
+
+a more slowly varying
+background.
+
+And now let's look at the result
+of passing that through
+
+a differentiator.
+
+And, as I think is very evident
+in the resulting
+
+image, clearly it's the edges
+that are retained and the
+
+slower background variations
+are destroyed, which is
+
+consistent with everything
+that we've said.
+
+I've emphasized that we'll be
+returning to a much broader
+
+discussion of filtering at a
+later point in the course.
+
+I'd now like to comment on
+another property, which is
+
+also, as I indicated, a topic
+in its own right, and which
+
+really is the dual property to
+the convolution property, and,
+
+in fact, could be argued
+directly from duality.
+
+And that is what's referred to
+as the modulation property.
+
+The convolution property told us
+that if we convolve in the
+
+time domain, we multiply in
+the frequency domain.
+
+And we know that time and
+frequency domains are
+
+interchangeable because of
+duality, so what that would
+
+suggest is that if we multiply
+in the time domain, that would
+
+correspond to convolution
+in the frequency domain.
+
+And, in fact, that is
+exactly what the
+
+modulation property is.
+
+I have it summarized here that
+if we multiply a time function
+
+by another time function,
+then in the
+
+frequency domain we convolve.
+
+Whereas the convolution property
+is just the dual of
+
+that, namely convolving in the
+time domain corresponds to
+
+multiplication in the
+frequency domain.
+
+The convolution property
+is the basis, as I
+
+indicated, for filtering.
+
+The modulation property, as I've
+summarized it here, in
+
+fact, is the entire basis for
+amplitude modulation systems
+
+as used almost universally
+in communications.
+
+And what the modulation
+property, as we'll see when we
+
+explore it in more detail, tells
+us is that if we have a
+
+signal with a certain spectrum,
+and we multiply by a
+
+sinusoidal signal whose Fourier
+transform is a set of
+
+impulses, then in a frequency
+domain we convolve.
+
+And that corresponds to taking
+the original spectrum and
+
+translating it, shifting it in
+frequency up to the frequency
+
+of the carrier, namely the
+sinusoidal signal.
+
+And as I said, we'll come to
+that in much more detail in a
+
+number of lectures.
+
+We've seen a number of
+properties, and I indicated
+
+sometime earlier when we talked
+about differential
+
+equations, that, in fact, it's
+the properties of the Fourier
+
+transform that provide us with
+a very useful and important
+
+mechanism for solving linear
+constant coefficient
+
+differential equations.
+
+And what I'd like to do now is
+illustrate the procedure, the
+
+basis for that, and I think what
+we'll do is illustrate it
+
+simply in the context
+of several examples.
+
+What I've indicated is a
+system with an impulse
+
+response h of t, or frequency
+response h of omega.
+
+And, of course, we know that
+in the time domain it's
+
+described through convolution,
+in the frequency domain it's
+
+described through
+multiplication.
+
+And I, in essence, am assuming
+that we're talking about a
+
+linear time invariant system.
+
+And we're also going to assume
+then it's characterized by a
+
+linear constant coefficient
+differential equation, where
+
+we're going to impose the
+condition that it's causal
+
+linear and time invariant, or
+equivalently that the initial
+
+conditions are consistent
+with the initial rest.
+
+And it's because of the fact
+that we're assuming that it's
+
+a linear time invariant system
+that we can describe it in the
+
+frequency domain through the
+convolution property, and we
+
+can use the properties of
+the Fourier transform.
+
+So let's take, as our example,
+a first order differential
+
+equation as I indicate here.
+
+So the derivative of the output
+plus a times the output
+
+is equal to the input.
+
+And now we can use the
+differentiation property.
+
+If we Fourier transform this
+entire expression, the
+
+differentiation property tells
+us that the Fourier transform
+
+of the derivative of the
+output is the Fourier
+
+transform of the output
+multiplied by j omega.
+
+And linearity will let us write
+the Fourier transform of
+
+this as a times y of omega.
+
+And since these are added
+together, and since we have
+
+the linearity property, these
+are added together.
+
+And x of omega is the Fourier
+transform of x of t.
+
+So what we've used is the
+differentiation property, and
+
+we've used the linearity
+property.
+
+We can solve this equation
+for y of omega.
+
+The Fourier transform of the
+output in terms of x of omega,
+
+the Fourier transform of the
+input, and a simple algebraic
+
+step gets us to this
+expression.
+
+So the Fourier transform of the
+output is 1 over j omega
+
+plus a times the Fourier
+transform of the input.
+
+And I've just simply repeated
+that equation up here.
+
+So far this is algebra, and the
+question is, now, how do
+
+we interpret this?
+
+Well, we know that the Fourier
+transform of the output is the
+
+Fourier transform of the input
+times the Fourier transform of
+
+the impulse response of
+the system, namely
+
+the frequency response.
+
+So, in fact, if we think of
+h of t and h of omega as a
+
+Fourier transform pair, it's the
+convolution property that
+
+lets us equate this term
+with h of omega.
+
+So here we're using the
+convolution property.
+
+So we know what the Fourier
+transform of the impulse
+
+response is, namely 1
+over j omega plus a.
+
+We may have, for example, wanted
+in our problem, instead
+
+of getting the frequency
+response, to
+
+get the impulse response.
+
+And there are a variety of
+ways that we can do this.
+
+We can attempt to go through the
+inverse Fourier transform
+
+expression.
+
+But in fact, one of the most
+useful ways is formally called
+
+the inspection method.
+
+Informally it's called, if you
+worked it out going one way,
+
+then you ought to remember the
+answer so that you know how to
+
+get back method.
+
+So what that says is, remember
+that we worked an example, and
+
+in fact I showed you the
+example earlier in the
+
+lecture, that the Fourier
+transform of e to the minus at
+
+times the step is 1 over
+j omega plus a?
+
+So what is the inverse Fourier
+transfer of 1 over
+
+j omega plus a?
+
+Well, it's e to the minus
+at times a unit step.
+
+And that's just simply
+remembering, in essence, this
+
+particular transform pair.
+
+I've drawn, graphically, the
+magnitude of the Fourier
+
+transform here.
+
+And below it we have the
+impulse response.
+
+The impulse response is, as I
+just indicated, e to the minus
+
+at times u of t.
+
+Now let's go back up and look
+at the magnitude of the
+
+frequency response.
+
+And given just the little bit
+of discussion that we had
+
+previously about filtering, you
+should be able to infer
+
+something about the filtering
+characteristics of this
+
+simple, first order differential
+equation.
+
+In particular, if you look at
+that frequency response, the
+
+frequency response falls off
+with frequency and so what it
+
+tends to do is attenuate high
+frequencies and retain low
+
+frequencies.
+
+So in fact, you could think of
+the defocusing that we did on
+
+the image of Fourier, you
+could think of that,
+
+approximately, as similar to the
+kind of filtering action
+
+that you would get by passing a
+signal through a first order
+
+differential equation.
+
+Just to illustrate one
+additional step in both
+
+evaluating inverse transforms
+and using Fourier transform
+
+properties to solve linear
+constant coefficient
+
+differential equations, let's
+take the same example and,
+
+rather than finding the impulse
+response, let's find
+
+the response to another
+exponential input.
+
+We could, of course,
+do that using
+
+the convolution integral.
+
+We've just gotten the impulse
+response, and we could put
+
+that through the convolution
+integral to get the response
+
+to this input.
+
+But let's do it, instead,
+by going back to the
+
+differential equation.
+
+And so here I'm taking a
+differential equation.
+
+I'll choose, just to have
+some numbers to work
+
+with, a equal to 2.
+
+And now I'll choose an
+exponential on the right hand
+
+side, e to the minus
+t times u of t.
+
+And again, we Fourier transform
+the equation.
+
+And we can remember
+this particular
+
+Fourier transform pair.
+
+It's just the one we worked
+out previously, now with a
+
+equal to 1.
+
+Clearly we're getting a lot of
+mileage out of that example.
+
+And now, if we want to determine
+what the output y of
+
+t is, we can do that by solving
+for y of omega and
+
+then generating the inverse
+Fourier transform.
+
+Let's solve this algebraically
+for y of omega, and that gets
+
+us to this expression.
+
+And this is not a Fourier
+transform that we've worked
+
+out before.
+
+And this is the second part to
+the inspection procedure.
+
+What we have is a Fourier
+transform which is a product
+
+of two terms, each of which
+we can recognize.
+
+And what we can consider doing
+is expanding that out in a
+
+partial fraction expansion,
+namely as a sum of terms.
+
+Because of the linearity
+property associated with the
+
+Fourier transform, the inverse
+transform is then the sum of
+
+the inverse transform of
+each of those terms.
+
+So if we expand this out in a
+partial fraction expansion,
+
+and you can just verify that if
+you add these two together
+
+you'll get back to
+where we started.
+
+We now have the sum of two
+terms, and if we now
+
+recognize, by inspection, the
+inverse Fourier transform of
+
+this, we see that it's simply
+minus e to the minus 2t times
+
+the unit step.
+
+This one is plus e to the minus
+t times the unit step.
+
+And so, in fact, it's the sum
+of these two terms which are
+
+the inverse transforms of the
+individual terms in the
+
+partial fraction expansion that
+then give us the output.
+
+So this is y of t, which
+is the sum of these two
+
+exponentials, and this is the
+inverse Fourier transform of y
+
+of omega as we calculated
+it previously.
+
+Hopefully you're beginning to
+get some sense, now, of how
+
+powerful and also beautiful
+the Fourier transform is.
+
+We've seen already a glimpse
+of how it plays a role in
+
+filtering, modulation, how its
+properties help us with linear
+
+constant coefficient
+differential
+
+equations, et cetera.
+
+What we will do, beginning
+with the next lecture, is
+
+develop a similar set of tools
+for the discrete time case.
+
+And there are some very strong
+similarities to what we've
+
+done in continuous time, also
+some very important
+
+differences.
+
+And then, after we have the
+continuous time and discrete
+
+time Fourier transforms, we'll
+then see how the concepts
+
+involved and the properties
+involved lead to very
+
+important and powerful notions
+of filtering, modulation,
+
+sampling, and other signal
+processing ideas.
+
+Thank you.
\ No newline at end of file
diff --git a/DKDcpkK3pM8.txt b/DKDcpkK3pM8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..64a4ed524170140c90936b139f2211e466e4c6e4
--- /dev/null
+++ b/DKDcpkK3pM8.txt
@@ -0,0 +1,2041 @@
+PROFESSOR: Do them individually
+so I can continue
+
+to put names and
+faces together.
+
+I'm happy to announce that
+the registrar has now got
+
+everybody's photograph
+online for
+
+registration in the course.
+
+So anonymity is a thing of the
+past, so you have to watch
+
+your step from now on.
+
+I handed back, to those who
+didn't get it, problem set
+
+number four, which asked you
+to tackle some patterns,
+
+nontrivial patterns.
+
+And actually, that was a dirty
+trick, because we hadn't, at
+
+that point, derived the plane
+groups, and you really didn't
+
+know what to do or
+what to look for.
+
+But nevertheless, it got you
+thinking about patterns and
+
+some of the symmetry elements
+which we had discussed up to
+
+that point.
+
+At this point we have derived
+exhaustively every last one of
+
+the 17 plane groups.
+
+So now you are armed with this
+new-found power, and when
+
+faced with a pattern, you should
+know exactly what to
+
+look for and how to go
+about deciding what
+
+plane group it is.
+
+At the very least, you'll
+have the drawings of the
+
+arrangement of symmetry elements
+in the plane groups
+
+before you, and you can work by
+the process of elimination.
+
+For example, high symmetry
+usually hits you right between
+
+the eyes, and if something is
+square-ish, you can pretty
+
+quickly guess that it's based
+on a square lattice.
+
+And if it has a square lattice,
+there jolly well
+
+better be a 4-fold axis in there
+that makes it square.
+
+If you can find the 4-fold axis,
+then you have to ask
+
+yourself only three questions.
+
+So 4-fold axis, fine.
+
+Is there a mirror
+line in there?
+
+Yeah.
+
+Does the mirror line go through
+the 4-fold axis?
+
+Then it is P 4 MM.
+
+And you know just where to
+look for everything else,
+
+including these very
+subtle glide planes
+
+that are hard to spot.
+
+If there is a mirror plane
+there, but it doesn't go
+
+through the 4-fold axis,
+then it's P 4 MG.
+
+And if there is no mirror
+plane, then it's P 4.
+
+So just by asking one or two
+simple questions, you can
+
+narrow it down to what the
+plane group has to be.
+
+This is another indication that
+the informed intellect is
+
+always more than a match
+for sheer, raw native
+
+intelligence.
+
+If you know what to look
+for, it's a lot easier.
+
+Because you really didn't have
+much practice with patterns,
+
+we're having a quiz, as you
+know, next Thursday, that will
+
+cover up through completion of
+the plane groups and not the
+
+material we've been doing now.
+
+So I think it might be of use
+to you to have some practice
+
+analyzing a few more patterns.
+
+So there are four additional
+patterns in this problem set.
+
+As always, it's optional, but if
+you would like to try them,
+
+and you want to see if you've
+got them right, come in and
+
+see me tomorrow or on
+Thursday morning.
+
+I'd be happy to go over them
+with you on the spot.
+
+So this is for practice.
+
+And some of you did
+extraordinarily well
+
+on the first try.
+
+Others, I think, could use
+the additional practice.
+
+There were a few people who
+identified the plane group
+
+correctly, but got the name
+that's assigned to it wrong.
+
+And one other very confusing
+thing is that there is one
+
+plane group that has the symbols
+G and M, and another
+
+plane group which has
+the symbols M and G.
+
+So if you found a mirror plane
+and a glide plane is an
+
+independent symmetry plane,
+when is it MG,
+
+and when is it GM?
+
+I have a little mnemonic
+device.
+
+GM, general manager, is the
+guy who sits on top of the
+
+organization.
+
+So GM should be the
+plane group that
+
+has the highest symmetry.
+
+P 4 GM, P 4 general manager.
+
+Now that is--
+
+hey, it works for me.
+
+But another way of saying it
+is that there are two plane
+
+groups, one has MG and the other
+has GM, and I like cars,
+
+and I think an MG is much
+classier than anything that
+
+General Motors, GM, puts out,
+so MG should be the one of
+
+highest quality, highest
+symmetry.
+
+And that's just the reverse.
+
+But whatever works for you.
+
+You could keep them straight
+through that simple algorithm.
+
+And as they say, if it works for
+me, but if it doesn't work
+
+for you, don't use it.
+
+All right.
+
+What I will bring in during
+intermission, for those of you
+
+had trouble identifying
+translations in the patterns
+
+that we handed out earlier, I've
+taken these and put them
+
+on overhead transparencies.
+
+And I'll have two of each.
+
+So if you don't see the symmetry
+or translations that
+
+are present, you can actually
+take one pattern and
+
+physically move it and lay it
+on top of the other one, and
+
+that's a good way to convince
+yourself what a translation
+
+looks like when it occurs
+in a pattern.
+
+So I'll bring those in at
+our break between class.
+
+All right, any questions
+before we move on?
+
+Any questions that have arisen
+as you have gotten
+
+ready for the quiz?
+
+You haven't gotten ready
+for the quiz yet, so
+
+there are no questions.
+
+That's OK.
+
+I know how things work at MIT.
+
+You deal with one crisis
+at a time.
+
+Any questions?
+
+Anything you want to go over?
+
+There was one interesting
+wrinkle in a problem that I
+
+had not encountered before,
+and this was the one that
+
+asked you to look at, in two
+dimensions, a plane with
+
+indices h and k.
+
+And then, when h and k were
+mutually prime, to move that
+
+plane by the translations plus
+T1 and plus and minus T2, and
+
+then show that the number of
+intervals between the origin
+
+and the intercept plane, the one
+that hit lattice points on
+
+both translations, was equal
+to h times k if they were
+
+mutually prime.
+
+That is true only if the
+lattice is primitive.
+
+And what the problem said was to
+pick one of the cells that
+
+you used in the first
+problem, number one.
+
+Well, that problem asked you
+to begin with identifying
+
+different primitive cells.
+
+If you take a multiple cell,
+this operation of going plus
+
+and minus T1 does not put a
+lattice line through each of
+
+the lattice points.
+
+If you picked a double cell,
+that process decorated only
+
+half of the lattice points with
+planes, and the other
+
+half sat there with nothing
+hanging on them at all.
+
+The key to the difference, if
+you looked at a double cell,
+
+was that if h plus k was even,
+then you automatically got a
+
+plane on every lattice point.
+
+If h plus k was odd, as it would
+have been for the plane
+
+2,1 for example, 2 plus 1 is 3--
+hey, this isn't even one
+
+of my good days--
+
+then half of the lattice points
+did not have planes
+
+hanging on them.
+
+Now, there's great relevance
+of this observation to
+
+diffraction, and you probably
+are all familiar, if only
+
+vaguely, with the magic rules
+that say, if h plus k is equal
+
+to 3 pi plus 4, then the
+intensity is identically 0.
+
+Well, for a double cell, the
+lattice planes that are
+
+repeated by translation diffract
+x-rays, and there is
+
+no reason why the intensity
+should be
+
+something other than 0.
+
+So here comes, a la Bragg, an
+x-ray beam coming in at angle
+
+theta, and then you say you
+get diffraction when
+
+scattering from this lattice
+plane is exactly in
+
+phase with this one.
+
+And this gives the familiar
+relation that an integral
+
+number of wavelengths is equal
+to 2 d sine of theta when the
+
+crystal diffracts.
+
+So there is exactly-- this
+says there's exactly 2 pi
+
+phase difference or n lambda
+path difference between these
+
+two planes.
+
+Now, if the lattice would be a
+double cell, then there is an
+
+additional lattice point in here
+that does not get a plane
+
+hung on it.
+
+So if the lattice is a double
+cell, there's another plane
+
+that has to hang on this lattice
+point, and that one is
+
+exactly out of phase with this
+plane, and the intensity is 0.
+
+So this observation that a
+non-primitive lattice has a
+
+interplanar spacing that is a
+sub-multiple of that of a
+
+primitive lattice gives some
+insight into why certain
+
+reflections--
+
+certain diffraction maxima-- are
+identically 0 in intensity
+
+for a crystal that has a
+non-primitive lattice.
+
+So that is something I had
+not noticed before.
+
+I should have, but I will phrase
+the problem a little
+
+bit more precisely
+in the future.
+
+All right.
+
+So to conclude my preamble, I
+hope you'll try playing with
+
+some of the four additional
+patterns that I handed out,
+
+just to give yourself
+some practice.
+
+And the implication of this is
+that you're going to see a
+
+pattern on the quiz, and I will
+tell you that you will.
+
+So if you want to see how you
+did on the patterns that I
+
+distributed, please come in
+and talk to me about them.
+
+All right then.
+
+Let me remind you where
+we were last time.
+
+We started to begin to build a
+framework of symmetry elements
+
+in three dimensions.
+
+And we asked the question, what
+would happen if we take a
+
+first rotation axis, A alpha,
+combine it with a second
+
+rotation axis, B beta, in
+such a way that they
+
+intersect at a point.
+
+This means that their operation
+and reproducing
+
+atoms or motifs is going to
+leave at least one point in
+
+space unchanged, and that will
+be the point of intersection.
+
+We ask ourselves, what will
+be the combined effect--
+
+we have two operations
+in space--
+
+what would be the combined
+effect of rotating alpha
+
+degrees about A followed
+immediately by beta degrees
+
+about B.
+
+So what we're going to do then
+is to take a first motif--
+
+and let's say it's
+left handed.
+
+Being a left-handed person, I
+like to give right handed
+
+motifs and left handed
+motifs equal time.
+
+If we rotate that through an
+angle alpha, and this is
+
+number 2, it will stay
+left handed.
+
+Then if we rotate that by B
+beta, it'll move it over here
+
+to number 3 and it will stay
+left handed as well.
+
+And the question is then, what
+net operation is equivalent to
+
+the combined operation of these
+two transformations?
+
+And to specify the type of
+operation is really a
+
+no-brainer.
+
+All of these motifs are of the
+same corality so the only
+
+thing that can relate them is
+
+translation or another rotation.
+
+And clearly the first and the
+third have no reason to be
+
+parallel to one another, and the
+distance between them is
+
+going to depend on how far they
+are away from the axis,
+
+so translation won't do the
+job, a and the only thing
+
+that's left as a net operation
+that's equivalent to those two
+
+steps is rotation about
+a third axis C.
+
+And what we're going to do today
+is answer the question,
+
+where is axis C located, and
+what is the angle of rotation,
+
+given the value of alpha and
+beta and the angle between
+
+these two axes?
+
+And let's define that
+as a lowercase c.
+
+So clearly the location of the
+axis and the amount of the
+
+rotation is going to be a
+function of alpha, beta, and
+
+the angle between them.
+
+We want this to be a combination
+of operations that
+
+exists in a symmetry
+operation.
+
+And if this is to be a
+crystallographic symmetry,
+
+these will be restricted to
+the angular throws of a
+
+1-fold, 2-fold, 3-fold,
+4-fold, a 6-fold axis.
+
+We can take these two at a time,
+ask what the net effect
+
+is if we combine at
+a given angle c.
+
+And what comes out here must
+be a rotation which is also
+
+crystallographic.
+
+So there are going to be severe
+constraints on this
+
+combination.
+
+Two rotations about an
+intersecting point will always
+
+be a third rotation, but if
+this is to be a set of
+
+operations in a symmetry group,
+the result must be
+
+crystallographic.
+
+That's a tough problem, and how
+will we undertake it is
+
+going to be non-intuitive.
+
+OK, the problem is most readily
+treated with spherical
+
+trigonometry.
+
+So on the surface of a sphere,
+I'm going to map the point at
+
+which A alpha protrudes--
+
+and I'll call this point A--
+
+and then I'll mark out the point
+where axis B beta exits
+
+the sphere, and I'll mark that
+point B. And this is the angle
+
+C.
+
+And we said that in spherical
+trigonometry, the measure of
+
+the length of the arc separating
+A and B is given by
+
+the angle subtended at the
+center, so the length of this
+
+distance between A and
+B is the angle c.
+
+Again, it sort of boggles the
+mind when you measure lengths
+
+in terms of degrees rather
+than some metric unit.
+
+All right.
+
+So I will now not bother to show
+the sphere on which the
+
+geometry is taking place.
+
+I'll just draw A and B,
+and this is the arc
+
+between them, c.
+
+And somewhere or other there
+will be some third axis, C,
+
+which is going to be the
+combined effect of the
+
+rotation about axis A and axis
+B. So what I would like to do
+
+is to locate the position
+of this axis C.
+
+In order to do that, I'll have
+to know what the angle between
+
+A and C is, and I'll call that,
+by analogy to what I've
+
+done here, I'll call that b.
+
+And I'll want to know what the
+angle between B and C is, and
+
+I'll call that angle a.
+
+So again, going back to three
+dimensions momentarily, if
+
+this is the rotation operation
+C gamma, and this is A alpha,
+
+and this is B beta, the axis c
+is this, the angle b is this,
+
+and the angle a is this.
+
+OK.
+
+It's a non-trivial problem and
+it is not by accident that the
+
+solution to this problem was
+first given by a very, very
+
+famous mathematician, Leonhard
+Euler, and this construction
+
+that we're about to go through
+is called Euler's
+
+construction.
+
+All right.
+
+Let me find where these
+different locations
+
+are going to be.
+
+We've specified the location of
+point A and the location of
+
+point B, and we know that the
+angle between them is the
+
+length of the arc ab, which is
+the angle between A and C. So
+
+let me now do some
+constructions.
+
+Let me find a great circle that
+by design is alpha over 2
+
+away from the arc ab, and
+that is by construction.
+
+And I'm going to say, then, that
+if A alpha works in this
+
+direction, the operation of A
+alpha is going to take this
+
+great circle and move it over
+to a great circle which is
+
+alpha over 2 on the other
+side of the arc ab.
+
+Fine, you say, so what?
+
+Well, just going to leave
+those there for now.
+
+I'll have B beta work
+in the same sense.
+
+And I'm now going to create a
+line here that by construction
+
+is beta over 2 on one side of
+the arc ab, and if I let B
+
+beta go to work, that will map
+this great circle over to a
+
+new location beta over
+2 on the other side.
+
+What has this done for me, other
+than perhaps confuse me
+
+and clutter the diagram?
+
+Well, now I'm going to determine
+unequivocally the
+
+location of the axis C, and
+where it emerges from the
+
+reference here.
+
+And how will I do that?
+
+I'm going to use a definition
+that may have seemed trivial
+
+the first time we made
+the observation.
+
+I said that a symmetry element
+is the locus of points that is
+
+left unmoved by an operation.
+
+OK?
+
+I rotated by A alpha from here
+to here, that took everything
+
+along this line and mapped it
+to a new location here.
+
+I took this line and rotated
+it by B beta, and that took
+
+everything along this line and
+moved it to a new location.
+
+So my question now is if I
+rotate by A alpha and then
+
+rotate in the same direction
+by B beta, what
+
+point is left unmoved?
+
+It's only one point that can
+make that claim, and that is
+
+where these two great
+circles intersect.
+
+The rotation A alpha will
+take this location--
+
+and I'm going to call it C
+because I've identified now
+
+what it is-- it's going to take
+C and move it over to
+
+here, call that C prime, and
+then B beta takes that point
+
+and only that point, and
+restores it back to its
+
+original location.
+
+So this, then, ladies and
+gentlemen, is where the
+
+rotation axis C gamma pokes
+out of the sphere of
+
+reflection.
+
+Still don't know what this angle
+is in here, and I would
+
+dearly love to know what these
+arcs b and a are, and then I
+
+will have specified all three
+of the interaxial angles
+
+between A, B and C.
+
+OK, let me do something quite
+similar to what I did before.
+
+I'm going to again let A alpha
+work on a particular point,
+
+and then let B beta map it.
+
+So here's A alpha,
+here's B beta.
+
+And now I'm going to look
+specifically at how these two
+
+rotations transform point A,
+where A is the point at which
+
+axis A alpha pokes out
+of the sphere.
+
+A alpha, when it acts on this
+point, does nothing to it.
+
+It leaves it alone.
+
+B beta is going to map A to
+a new location, A prime.
+
+Now, doing A alpha and following
+up by B beta is
+
+supposed to be equal to
+the rotation C gamma.
+
+So that says that this point and
+this point must be related
+
+by the rotation gamma.
+
+So say that again.
+
+We're doing exactly what we did
+here except we're starting
+
+with an initial point, not this
+arc, but we're starting
+
+with the specific point A,
+operate on it by A alpha, it
+
+twirled around but stays put.
+
+Rotate that by B beta, it goes
+through a total angle beta to
+
+this location here.
+
+The net effect of getting from A
+to A prime is supposed to be
+
+the rotation C gamma, so this
+angle is then gamma and this
+
+is the location of C. OK?
+
+OK, one other step that's
+a fairly easy one.
+
+This length is equal to this
+length, because they were
+
+produced by rotation.
+
+This side is common to these two
+triangles, and this angle
+
+then is beta over 2, this
+is beta over 2.
+
+And if these two triangles, A,
+B, and C, that triangle is
+
+similar to A prime BC, and
+therefore I can say that angle
+
+A prime CA is identical to ACB,
+so therefore this angle
+
+has to equal this angle, and if
+the total angle is gamma,
+
+this is gamma over 2, and
+this is gamma over 2.
+
+So now let me extract from this
+the information that I
+
+would like to use.
+
+Here are three axes, A alpha,
+B beta, and C gamma.
+
+This angle in here
+is gamma over 2.
+
+This angle in here is beta over
+2, and this angle in here
+
+is alpha over 2.
+
+And let me emphasize that in
+this magic triangle, out of
+
+which we're going to extract
+some dazzlingly profound
+
+stuff, it is half the angular
+throw of the rotation axes
+
+that appear in here as these
+spherical angles, and not the
+
+entire angle of rotation.
+
+So here's how properties of the
+three rotation axes are
+
+related one to another.
+
+And now, we introduced without
+proof last time something
+
+called the law of cosines in
+spherical trigonometry.
+
+And I not only do not want to
+prove it, but I have no idea
+
+how I would go about doing so,
+but that doesn't prevent me
+
+from using it.
+
+So if here are three edges, a,
+b, c, and three angles in
+
+there, A, B, and C, we said
+that the law of cosines in
+
+spherical trigonometry,
+analogous in a way to the law
+
+of cosines and plane geometry,
+except since the lengths of
+
+the triangles are measured
+in degrees, there are
+
+trigonometric functions of these
+angles that appear in
+
+the law of cosines.
+
+This says that cosine of b
+cosine of c plus sine b sine
+
+of c times cosine of a is
+equal to cosine of a.
+
+So this now is an interesting
+relation that we can apply to
+
+this spherical triangle, which
+connects together the three
+
+rotation axes.
+
+Let me apply it to find the
+angle c which we have picked
+
+as the angle between the initial
+two axes a and b.
+
+That says that this should be
+equal to cosine of b cosine of
+
+c, the angle between the other
+two axes, plus sine of b sine
+
+of c times the cosine of angle
+a, and angle a is cosine of
+
+alpha over 2.
+
+So all these quantities that
+we'd like to determine are
+
+hooked together by the
+law of cosines.
+
+And this is a lovely relation,
+but it doesn't do us a bit of
+
+good, because in this relation
+we know only one quantity, and
+
+that is the rotation
+angle of a.
+
+We can pick the angle between
+a and b, that's this, but I
+
+have no idea what these
+other angles are.
+
+That's what I'd like
+to find out.
+
+I'd like to find out the
+angles at which three
+
+rotations have to be combined
+in order that rotation about
+
+one followed by rotation about
+the second be the third.
+
+So this equation is a beautiful
+equation, but it
+
+involves everything that I
+don't know and only one
+
+quantity that I do know.
+
+So it looks as though
+we're up the creek.
+
+Yes, sir?
+
+AUDIENCE: So you're looking for
+cosine c, so shouldn't it
+
+be cosine b cosine a?
+
+PROFESSOR: Oh, I'm sorry.
+
+Yeah, I did that wrong.
+
+Yeah.
+
+You're absolutely right.
+
+This should be cosine of a,
+and this a goes with this
+
+alpha over 2.
+
+Absolutely.
+
+Sorry about that.
+
+So anyway, the point still
+stands that what this equation
+
+involves is the three interaxial
+angles, and I would
+
+like to know how I could combine
+a and b to get it to
+
+come out to a crystallographic
+rotation c, and where that
+
+location is relative to
+the first two axes.
+
+So it involves everything I
+don't know, and only one
+
+thing that I do.
+
+But now we introduce another
+curious aspect of spherical
+
+triangles, which I mentioned
+last time.
+
+You may have thought
+that that's
+
+interesting, but who cares?
+
+Here are the three points, A,
+B, and C, and these are the
+
+three arcs little c, little
+a and little b.
+
+And then we said we could
+construct something called the
+
+polar triangle of ABC.
+
+And what we would do, we would
+find the pole of arc b, and
+
+that will be some
+point B prime.
+
+We'll find the pole of arc
+a, and that will be
+
+some point A prime.
+
+We'll find, similarly, the pole
+of arc c, and that will
+
+be some point C prime.
+
+And now we can connect together
+A prime, B prime, and
+
+C prime, and get something
+that's
+
+called the polar triangle.
+
+And now comes the useful part.
+
+We said that a curious property
+of the polar triangle
+
+is that the side of the polar
+triangle plus the angle
+
+opposite it add up
+to 180 degrees.
+
+In my original triangle, this is
+beta over 2, this is gamma
+
+over 2, and this is
+alpha over 2.
+
+So the length of this side is
+going to be 180 degrees minus
+
+beta over 2, the length of this
+side is going to be 180
+
+degrees minus alpha over 2, and
+the length of this side is
+
+going to be 180 degrees
+minus gamma over 2.
+
+And now let's use these angles
+and these lengths in the law
+
+of cosines, and I'll leave
+out the little bit
+
+of intervening algebra.
+
+And what we will get out of
+this is that cosine of c--
+
+and I'll solve for that--
+
+is equal to cosine of alpha over
+2 cosine of beta over 2
+
+plus cosine of gamma over 2
+divided by sine alpha over 2
+
+sine beta over 2.
+
+And that is something we can
+sink our teeth into and run
+
+with, because now I can ask the
+question, suppose I want a
+
+to be a 2-fold rotation axis,
+b to be a 3-fold rotation
+
+axis, and c be a 4-fold
+rotation axis?
+
+Then the value of alpha over 2
+is half of 180 degrees or 90.
+
+Well, you can see I put
+in half the value of
+
+the rotation axes.
+
+And then I solve for c, and that
+is the angle at which I
+
+have to put axis a and b
+together to get c to turn out
+
+to be whatever angle
+gamma over 2 is.
+
+So I can do this
+
+systematically now without thinking.
+
+And I can set up the problem by
+taking the crystallographic
+
+rotation axes and combining them
+together three at a time
+
+in all possible combinations.
+
+Right?
+
+In addition to this relation,
+I have two other relations.
+
+And let me assemble them off to
+the left, because we have
+
+to solve three equations to
+find out the nature of the
+
+combination that is required.
+
+So just permuting terms, the
+angle between A and B, c, has
+
+to follow from cosine of c
+equals cosine of alpha over 2
+
+cosine of beta over 2 plus
+cosine of gamma over 2.
+
+Notice that the single term by
+itself is the cosine of half
+
+the angle of the opposite
+rotation axis c.
+
+Then in the denominator is the
+sine of these two angles.
+
+And so just permuting terms, one
+can see that cosine of b
+
+is going to turn out to be
+cosine of alpha over 2 cosine
+
+of gamma over 2 plus cosine of
+theta over 2 divided by sine
+
+of alpha over 2 sine
+of gamma over 2.
+
+And a third analogous expression
+will give me the
+
+angle that will be the one
+between B and C. And this will
+
+be cosine of beta over 2 cosine
+gamma over 2 plus
+
+cosine of alpha over 2 divided
+by sine beta over 2
+
+sine gamma over 2.
+
+OK?
+
+So now we don't have
+to think anymore.
+
+It's just plug and chug.
+
+And I'll pause to suck in air
+and let you catch up, and then
+
+we'll set up the problem and
+look at a few solutions.
+
+And all this, in the event
+that you're thoroughly
+
+bewildered, is in the
+set of notes that I
+
+handed out last time.
+
+So you can read it over
+at your leisure.
+
+AUDIENCE: Will this stuff
+be on the quiz?
+
+PROFESSOR: No.
+
+Quiz will go up to the end of
+the two-dimensional plane
+
+groups and stop.
+
+We won't say anything
+three dimensional.
+
+OK, let's, then, if there's no
+objection or complaint, look
+
+at possible values for--
+
+let me do it the same way that
+I did it in the notes so that
+
+it's consistent--
+
+let's put down the value for
+axis b, the rank of axis b and
+
+the rank of axis a.
+
+And A could be a 1-fold axis,
+B could be a 1-fold access,
+
+and we could take a 1 with a 1
+with a 1, a 1 with a 1 with a
+
+2, a 1 with a 1 with a 3, a 1
+with a 1 with a 4, and a 1
+
+with a 1 with a 6.
+
+This is clearly impossible.
+
+If I did nothing, and followed
+it by doing nothing, and
+
+wanted it to come out to be a
+6-fold rotation, you'd all be
+
+spinning on your axes
+like tops right now.
+
+So you can't do nothing and
+follow it by doing nothing and
+
+have it come out to
+be a net rotation.
+
+So these are impossible.
+
+So we don't have to
+consider those.
+
+A could be a 2, though, and I
+don't want to do 2, 1, 1,
+
+because I've got
+a 1, 1, 2 here.
+
+The order doesn't make
+any difference.
+
+So I'll start with a 2, 1,
+2, a 2, 1, 3, a 2, 1,
+
+4, and a 2, 1, 6.
+
+So those are four combinations
+that I should be examining.
+
+I could look at a 3 with a--
+
+2 with a 1, I have here in the
+form of 2, 1, 3, so the next
+
+one I would want to look at
+is a 3, 1, 3, a 3, 1,
+
+4, and a 3, 1, 6.
+
+And let me put in a
+couple more here.
+
+If B were a 2, I should look at
+a 2 with a 2 with a 2, a 2
+
+with a 2 with a 3, a 2
+with a 2 with a 4, 2
+
+with a 2 with a 6.
+
+And then A 3 with a 2--
+
+and I've got 3, 2, 2 up here, so
+I'll start with 3, 2, 3, 3,
+
+2, 4, 3, 2, 6, run out of room
+here, but there should be a
+
+similar entry with
+a 4 and a 6.
+
+So this sets up the problem.
+
+If you count up the number of
+ways one can do this, we only
+
+have to consider the
+off-diagonal boxes here,
+
+because interchanging a and b,
+for example, looking at 3, 1,
+
+3, that's going to be the
+same as 1, 3, 3 up here.
+
+So it's just the off-diagonal
+boxes
+
+that we have to consider.
+
+So there should be a 3,
+3, 3 in here, a 3, 3,
+
+4, and a 3, 3, 6.
+
+So what we would have to do in
+order to determine the unique
+
+combinations is to look at all
+of these combinations in turn,
+
+and I'm going to not
+try all of them.
+
+I will do one that's going
+to be clearly impossible.
+
+So let's look at 2, 1, 4.
+
+So here A corresponds to a
+2-fold axis, B corresponds to
+
+a 1-fold axis, and C would
+correspond to a 4-fold axis.
+
+So could we combine these three
+axes at appropriate
+
+angles such that a 2-fold
+followed by a 1-fold is
+
+equivalent to a 4-fold?
+
+This clearly isn't
+going to work.
+
+If I do a 180-degree rotation
+then don't do anything and ask
+
+is that equivalent to a 4-fold
+rotation, that is saying that
+
+the 2-fold axis should be
+identical to the 4-fold axis,
+
+and that is not going to work.
+
+So let me do now a generic
+family that I know turns out
+
+to be possible.
+
+Let me look at an n-fold axis
+with a 2-fold axis with a
+
+2-fold axis, and I can show
+that this combination is
+
+possible for any integer
+n whatsoever.
+
+So this will include a lot
+of non-crystallographic
+
+symmetries.
+
+So let's say that this is C,
+this is A, and this is B. But
+
+make it C, B, A if you'd like.
+
+OK, so my first equation says
+that cosine of c, the angle
+
+between A and B, should be equal
+to the cosine of alpha
+
+over 2 times the cosine of beta
+over 2 plus the cosine of
+
+gamma over 2 divided by sine
+of alpha over 2 sine
+
+of beta over 2.
+
+B is a 2-fold axis, so alpha
+is equal to 180 degrees.
+
+A is a 2-fold--
+
+I'm sorry.
+
+B beta, A alpha.
+
+Beta is equal to 180 degrees,
+the angular
+
+throw of a 2-fold axis.
+
+Alpha is equal to 180
+degrees, the angular
+
+throw of a 2-fold axis.
+
+And gamma is equal to whatever
+2 pi over n would be.
+
+That's the throw of the n-fold
+axis than I'm letting be equal
+
+to C.
+
+So the cosine of A and B, to get
+the result of rotation A
+
+followed by rotation B being
+equal to the net rotation of
+
+an n-fold axis is that the
+cosine of c should be the
+
+cosine of 180 degrees over 2
+times the cosine of 180 over 2
+
+plus the cosine of gamma over
+2, and gamma is whatever the
+
+rank of the axis determines, and
+that's divided by sine of
+
+alpha over 2, and alpha is 180
+and sine beta over 2, and
+
+that's 180 over 2.
+
+So the cosine of c is going to
+be the cosine of 90, which is
+
+0, times the cosine of 90, which
+is 0, plus the cosine of
+
+gamma over 2, whatever that
+might be, over the sine of 90
+
+which is 1, sine of
+90 which is 1.
+
+So this says that cosine
+of c is equal to cosine
+
+of gamma over 2.
+
+So the angle between axis A and
+axis B ought to be equal
+
+to one half the angular throw
+of rotation axis C. So let's
+
+start putting down some
+of this information.
+
+This says that if this is axis
+C gamma, then A pi and B pi,
+
+the 2 180-degree rotations,
+should be at an
+
+angle gamma over 2.
+
+We still need values
+for b, and we still
+
+need a value for a.
+
+So let's find out
+what those are.
+
+And let me start over here at
+the left again, because I've
+
+got the relation that I need
+for b sitting here.
+
+The cosine of b is equal to the
+cosine of alpha over 2,
+
+and that is the cosine of pi
+over 2, plus alpha is a
+
+90-degree rotation.
+
+Then cosine of gamma over 2,
+whatever gamma happens to be,
+
+plus the cosine of beta over
+2, and that's cosine of pi
+
+over 2, and this is all over
+sine of pi over 2 times the
+
+sine of gamma over 2.
+
+So this is going to be cosine of
+pi over 2, which is 0, plus
+
+cosine of pi over 2 divided by
+sine of pi over 2, which is 1.
+
+This gamma over 2--
+
+no, cosine of pi over 2 is 0.
+
+So this is 0 plus 0 times sine
+of gamma over 2, whatever that
+
+turns out to be.
+
+So cosine of b is 0, and that
+says that the angle b between
+
+axis A and axis C turns
+out to be 90 degrees.
+
+So in order to get pi followed
+by c gamma to be equal to b
+
+pi, I've got to make b be
+equal to pi over 2.
+
+And if I put it in this
+orientation, then a pi
+
+followed by c gamma is going
+to be equal to b pi.
+
+One final angle, and that's
+the value for a.
+
+OK, cosine of a should be equal
+to the cosine of beta
+
+over 2, that's pi over 2 times
+the cosine of gamma over 2,
+
+whatever it is, plus the cosine
+of beta over 2, and
+
+that's cosine of pi over 2, over
+sine pi over 2 sine of
+
+gamma over 2.
+
+And this, as for b, turns out
+to be 0 plus 0 over sine pi
+
+over 2, which is 1 times
+sine of gamma over 2.
+
+So cosine of a turns out to be
+0, and this says that the
+
+angle a is also pi over 2.
+
+So we've got a whole--
+
+Yeah.
+
+AUDIENCE: Did you really
+need to go
+
+through all three equations?
+
+PROFESSOR: Yeah, because I had
+to show that all three work.
+
+And in general, if I combine,
+let's say, a 4-fold with a
+
+3-fold with a 2-fold, which is
+something I want to do, all
+
+three angles a, b, and
+c, will be different.
+
+OK?
+
+So the answer is yes.
+
+And there will be a few cases
+where a value for one angle
+
+will exist and the value for the
+one or two others will be
+
+impossible.
+
+And that's also something
+that I have to know.
+
+So repetitious as the exercise
+might be, the answer is yeah,
+
+you do have to do all three.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Oh, you don't have to
+do different permutations.
+
+That's just a question
+of labeling.
+
+OK?
+
+So n with a 2 with a 2 is the
+same as a 2 with an n with a 2
+
+is the same as a 2
+with a 2 with an
+
+n, that's just labeling.
+
+So that's why my boxes, when I
+filled them out, the list got
+
+shorter and shorter, until
+finally for a 6-fold axis, it
+
+would be just 6, 1, 1, 6, 1,
+2, 6, 1, 3, and so on.
+
+Just that one entry in the box
+where I enumerated what should
+
+be considered.
+
+Well, here is a whole slew of
+possible solutions and a lot
+
+of them are
+non-crystallographic, but
+
+still possible.
+
+This says that a combination
+of a 2-fold axis--
+
+but remember now that these are
+equations and operations.
+
+But the only operation that's
+present for a 2-fold axis is a
+
+rotation a pi, b pi or c pi.
+
+So I could combine three 2-fold
+axes that are mutually
+
+orthogonal, and that is an
+allowable combination.
+
+And what we are obtaining here
+is a sort of scaffolding, a
+
+framework, based on pure
+rotation operations, that by
+
+themselves will be an allowable
+3-dimensional point
+
+group, but which also provides a
+framework, a Christmas tree,
+
+that we can decorate with mirror
+planes and inversion
+
+centers to get still additional
+
+groups of higher symmetry.
+
+So here's one possible
+crystallographic o combination
+
+of rotation axes.
+
+What we will use to denote this
+combination is the same
+
+rule that we use for
+our other notation.
+
+We will make a running list of
+the independent operations
+
+that are present, and what we
+have combined here are three
+
+distinct independent
+2-fold axes.
+
+A solid that would have this
+symmetry plus some other
+
+symmetry would be an orthogonal
+brick with one
+
+2-fold axis coming out here.
+
+This is the operation c pi,
+another 2-fold axis coming out
+
+the front, and this would be
+the operation a pi, and
+
+another 2-fold axis coming out
+of this face, and this would
+
+be the operation b pi.
+
+Now let me show you-- it's
+rather amusing-- that what we
+
+have done really works.
+
+We've shown supposedly that a pi
+followed by b pi should be
+
+equal to a net rotation c
+pi about an axis that's
+
+orthogonal to the first two.
+
+So let's pick a motif, and for
+convenience I'll put it at one
+
+corner of this brick.
+
+Here's object 1, I rotate it
+by 180 degrees about a.
+
+Here sits object number 2,
+same corality, and then I
+
+rotate it 180 degrees about B
+beta, and that's going to give
+
+me number 3.
+
+What is the net way of
+getting from 1 to 3?
+
+Holy mackerel.
+
+It's a net 180-degree
+rotation about c pi.
+
+It really works.
+
+Or I could do the operations
+in a different order.
+
+I could rotate by d, rotate by
+c, and the way I get from the
+
+first to the third is
+a rotation a pi.
+
+So that is a self consistent
+set of rotation axes.
+
+That is 2, 2, 2.
+
+Let me do one more.
+
+Well, no, let me take a break
+here and let you absorb all
+
+this, and then we'll look at
+some remaining ones, and this
+
+will include some that are
+non- crystallographic.
+
+And that's perfectly OK.
+
+But they're lovely groups, they
+constitute groups, but
+
+they won't be groups
+that can occur in
+
+combination with a lattice.
\ No newline at end of file
diff --git a/EAWpLeor4Zk.txt b/EAWpLeor4Zk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..345139ded2dc8c6ff3079b3eb2390d624129fe0b
--- /dev/null
+++ b/EAWpLeor4Zk.txt
@@ -0,0 +1,9835 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+good morning today there is a bit of an
+
+ align:start position:0%
+good morning today there is a bit of an
+ 
+
+ align:start position:0%
+good morning today there is a bit of an
+overview on the iCub robot and so it
+
+ align:start position:0%
+overview on the iCub robot and so it
+ 
+
+ align:start position:0%
+overview on the iCub robot and so it
+will be about 1 1 hour 1 hour and out
+
+ align:start position:0%
+will be about 1 1 hour 1 hour and out
+ 
+
+ align:start position:0%
+will be about 1 1 hour 1 hour and out
+and we have organized the schedule for
+
+ align:start position:0%
+and we have organized the schedule for
+ 
+
+ align:start position:0%
+and we have organized the schedule for
+this time in periods of poor small talk
+
+ align:start position:0%
+this time in periods of poor small talk
+ 
+
+ align:start position:0%
+this time in periods of poor small talk
+and and then a demo from the item like
+
+ align:start position:0%
+and and then a demo from the item like
+ 
+
+ align:start position:0%
+and and then a demo from the item like
+them so I will give you an overview of
+
+ align:start position:0%
+them so I will give you an overview of
+ 
+
+ align:start position:0%
+them so I will give you an overview of
+the the kind of shielding capabilities
+
+ align:start position:0%
+the the kind of shielding capabilities
+ 
+
+ align:start position:0%
+the the kind of shielding capabilities
+that they are cam has developed so far
+
+ align:start position:0%
+that they are cam has developed so far
+ 
+
+ align:start position:0%
+that they are cam has developed so far
+and while Alexandra fellow and Julia
+
+ align:start position:0%
+and while Alexandra fellow and Julia
+ 
+
+ align:start position:0%
+and while Alexandra fellow and Julia
+will show you a bit what's going on
+
+ align:start position:0%
+will show you a bit what's going on
+ 
+
+ align:start position:0%
+will show you a bit what's going on
+right now on the icon part of what's
+
+ align:start position:0%
+right now on the icon part of what's
+ 
+
+ align:start position:0%
+right now on the icon part of what's
+going on on the robot so they're going
+
+ align:start position:0%
+going on on the robot so they're going
+ 
+
+ align:start position:0%
+going on on the robot so they're going
+to talk about their their recent work so
+
+ align:start position:0%
+to talk about their their recent work so
+ 
+
+ align:start position:0%
+to talk about their their recent work so
+let's start with the presentation this
+
+ align:start position:0%
+let's start with the presentation this
+ 
+
+ align:start position:0%
+let's start with the presentation this
+is the iCub which is a child numeron
+
+ align:start position:0%
+is the iCub which is a child numeron
+ 
+
+ align:start position:0%
+is the iCub which is a child numeron
+robot beyond the size and the the
+
+ align:start position:0%
+robot beyond the size and the the
+ 
+
+ align:start position:0%
+robot beyond the size and the the
+project of the item mm pork and the icon
+
+ align:start position:0%
+project of the item mm pork and the icon
+ 
+
+ align:start position:0%
+project of the item mm pork and the icon
+actually the icon because there are many
+
+ align:start position:0%
+actually the icon because there are many
+ 
+
+ align:start position:0%
+actually the icon because there are many
+of them there are built in Genoa at the
+
+ align:start position:0%
+of them there are built in Genoa at the
+ 
+
+ align:start position:0%
+of them there are built in Genoa at the
+Italian Institute of Technology and the
+
+ align:start position:0%
+Italian Institute of Technology and the
+ 
+
+ align:start position:0%
+Italian Institute of Technology and the
+main motivation behind the creation the
+
+ align:start position:0%
+main motivation behind the creation the
+ 
+
+ align:start position:0%
+main motivation behind the creation the
+design of this platform was to actually
+
+ align:start position:0%
+design of this platform was to actually
+ 
+
+ align:start position:0%
+design of this platform was to actually
+have a in autonomous it was a way to
+
+ align:start position:0%
+have a in autonomous it was a way to
+ 
+
+ align:start position:0%
+have a in autonomous it was a way to
+have a platform in order to study to
+
+ align:start position:0%
+have a platform in order to study to
+ 
+
+ align:start position:0%
+have a platform in order to study to
+study how intelligent how cognition
+
+ align:start position:0%
+study how intelligent how cognition
+ 
+
+ align:start position:0%
+study how intelligent how cognition
+emerges in artificial embodied systems
+
+ align:start position:0%
+emerges in artificial embodied systems
+ 
+
+ align:start position:0%
+emerges in artificial embodied systems
+so Julie sondini
+
+ align:start position:0%
+so Julie sondini
+ 
+
+ align:start position:0%
+so Julie sondini
+and Georgia mater that you consider are
+
+ align:start position:0%
+and Georgia mater that you consider are
+ 
+
+ align:start position:0%
+and Georgia mater that you consider are
+the actual original founders of the of
+
+ align:start position:0%
+the actual original founders of the of
+ 
+
+ align:start position:0%
+the actual original founders of the of
+the old hike aboard so they are both
+
+ align:start position:0%
+the old hike aboard so they are both
+ 
+
+ align:start position:0%
+the old hike aboard so they are both
+directors at the IAT and this is a bit
+
+ align:start position:0%
+directors at the IAT and this is a bit
+ 
+
+ align:start position:0%
+directors at the IAT and this is a bit
+of a timeline that I drew actually there
+
+ align:start position:0%
+of a timeline that I drew actually there
+ 
+
+ align:start position:0%
+of a timeline that I drew actually there
+are many other things going on
+
+ align:start position:0%
+are many other things going on
+ 
+
+ align:start position:0%
+are many other things going on
+during all these 11 years this is a
+
+ align:start position:0%
+during all these 11 years this is a
+ 
+
+ align:start position:0%
+during all these 11 years this is a
+video celebrating the the actual first
+
+ align:start position:0%
+video celebrating the the actual first
+ 
+
+ align:start position:0%
+video celebrating the the actual first
+10 years of the project and and actually
+
+ align:start position:0%
+10 years of the project and and actually
+ 
+
+ align:start position:0%
+10 years of the project and and actually
+you can see many more things that the
+
+ align:start position:0%
+you can see many more things that the
+ 
+
+ align:start position:0%
+you can see many more things that the
+icon will be able to but I selected this
+
+ align:start position:0%
+icon will be able to but I selected this
+ 
+
+ align:start position:0%
+icon will be able to but I selected this
+part because I think they could be
+
+ align:start position:0%
+part because I think they could be
+ 
+
+ align:start position:0%
+part because I think they could be
+useful also if you are interested in
+
+ align:start position:0%
+useful also if you are interested in
+ 
+
+ align:start position:0%
+useful also if you are interested in
+doing project with a robot to have an
+
+ align:start position:0%
+doing project with a robot to have an
+ 
+
+ align:start position:0%
+doing project with a robot to have an
+idea of the kind of skills and the kind
+
+ align:start position:0%
+idea of the kind of skills and the kind
+ 
+
+ align:start position:0%
+idea of the kind of skills and the kind
+of feedback that the robot can can
+
+ align:start position:0%
+of feedback that the robot can can
+ 
+
+ align:start position:0%
+of feedback that the robot can can
+provide you to do my experiment so I
+
+ align:start position:0%
+provide you to do my experiment so I
+ 
+
+ align:start position:0%
+provide you to do my experiment so I
+told you I can post built with the idea
+
+ align:start position:0%
+told you I can post built with the idea
+ 
+
+ align:start position:0%
+told you I can post built with the idea
+of replicating sometimes a in artificial
+
+ align:start position:0%
+of replicating sometimes a in artificial
+ 
+
+ align:start position:0%
+of replicating sometimes a in artificial
+embodied system that could explore the
+
+ align:start position:0%
+embodied system that could explore the
+ 
+
+ align:start position:0%
+embodied system that could explore the
+environment and learn from it so it has
+
+ align:start position:0%
+environment and learn from it so it has
+ 
+
+ align:start position:0%
+environment and learn from it so it has
+many different sensors these are some of
+
+ align:start position:0%
+many different sensors these are some of
+ 
+
+ align:start position:0%
+many different sensors these are some of
+them so in the end in the head we have
+
+ align:start position:0%
+them so in the end in the head we have
+ 
+
+ align:start position:0%
+them so in the end in the head we have
+an accelerometer and the gyroscope to in
+
+ align:start position:0%
+an accelerometer and the gyroscope to in
+ 
+
+ align:start position:0%
+an accelerometer and the gyroscope to in
+order to provide the inertial feedback
+
+ align:start position:0%
+order to provide the inertial feedback
+ 
+
+ align:start position:0%
+order to provide the inertial feedback
+to the system and to dragonfly cameras
+
+ align:start position:0%
+to the system and to dragonfly cameras
+ 
+
+ align:start position:0%
+to the system and to dragonfly cameras
+that provide the medium resolution
+
+ align:start position:0%
+that provide the medium resolution
+ 
+
+ align:start position:0%
+that provide the medium resolution
+images and as you can see there is it's
+
+ align:start position:0%
+images and as you can see there is it's
+ 
+
+ align:start position:0%
+images and as you can see there is it's
+all about one meter one meter is
+
+ align:start position:0%
+all about one meter one meter is
+ 
+
+ align:start position:0%
+all about one meter one meter is
+something and it's pretty light
+
+ align:start position:0%
+something and it's pretty light
+ 
+
+ align:start position:0%
+something and it's pretty light
+difference kilograms and as lots of
+
+ align:start position:0%
+difference kilograms and as lots of
+ 
+
+ align:start position:0%
+difference kilograms and as lots of
+degrees of freedom so 53 degrees of
+
+ align:start position:0%
+degrees of freedom so 53 degrees of
+ 
+
+ align:start position:0%
+degrees of freedom so 53 degrees of
+freedom and they allowed it the robot to
+
+ align:start position:0%
+freedom and they allowed it the robot to
+ 
+
+ align:start position:0%
+freedom and they allowed it the robot to
+perform many complicated many complex
+
+ align:start position:0%
+perform many complicated many complex
+ 
+
+ align:start position:0%
+perform many complicated many complex
+actions it's provided with torque and
+
+ align:start position:0%
+actions it's provided with torque and
+ 
+
+ align:start position:0%
+actions it's provided with torque and
+force sensors and I'll go over these in
+
+ align:start position:0%
+force sensors and I'll go over these in
+ 
+
+ align:start position:0%
+force sensors and I'll go over these in
+in a minute and also is bold body or it
+
+ align:start position:0%
+in a minute and also is bold body or it
+ 
+
+ align:start position:0%
+in a minute and also is bold body or it
+lives in the discoverer part of the
+
+ align:start position:0%
+lives in the discoverer part of the
+ 
+
+ align:start position:0%
+lives in the discoverer part of the
+robot that the black part that you can
+
+ align:start position:0%
+robot that the black part that you can
+ 
+
+ align:start position:0%
+robot that the black part that you can
+see there are all covered in artificial
+
+ align:start position:0%
+see there are all covered in artificial
+ 
+
+ align:start position:0%
+see there are all covered in artificial
+skin so then they provide feedback about
+
+ align:start position:0%
+skin so then they provide feedback about
+ 
+
+ align:start position:0%
+skin so then they provide feedback about
+contact with the external world and it
+
+ align:start position:0%
+contact with the external world and it
+ 
+
+ align:start position:0%
+contact with the external world and it
+is also microphones mounted on the end
+
+ align:start position:0%
+is also microphones mounted on the end
+ 
+
+ align:start position:0%
+is also microphones mounted on the end
+but probably for found a special
+
+ align:start position:0%
+but probably for found a special
+ 
+
+ align:start position:0%
+but probably for found a special
+missions whether to use a direct micro
+
+ align:start position:0%
+missions whether to use a direct micro
+ 
+
+ align:start position:0%
+missions whether to use a direct micro
+feedback at the moment because of of
+
+ align:start position:0%
+feedback at the moment because of of
+ 
+
+ align:start position:0%
+feedback at the moment because of of
+course noise canceling problems and so
+
+ align:start position:0%
+course noise canceling problems and so
+ 
+
+ align:start position:0%
+course noise canceling problems and so
+if you're interested in to pitch and in
+
+ align:start position:0%
+if you're interested in to pitch and in
+ 
+
+ align:start position:0%
+if you're interested in to pitch and in
+sound feedback we are going to be used
+
+ align:start position:0%
+sound feedback we are going to be used
+ 
+
+ align:start position:0%
+sound feedback we are going to be used
+other kind of microphone so during these
+
+ align:start position:0%
+other kind of microphone so during these
+ 
+
+ align:start position:0%
+other kind of microphone so during these
+11 years I Kevin's been involved in many
+
+ align:start position:0%
+11 years I Kevin's been involved in many
+ 
+
+ align:start position:0%
+11 years I Kevin's been involved in many
+many projects and the indeed part of
+
+ align:start position:0%
+many projects and the indeed part of
+ 
+
+ align:start position:0%
+many projects and the indeed part of
+what I'm going to show you it's the
+
+ align:start position:0%
+what I'm going to show you it's the
+ 
+
+ align:start position:0%
+what I'm going to show you it's the
+results of the joint efforts of many lab
+
+ align:start position:0%
+results of the joint efforts of many lab
+ 
+
+ align:start position:0%
+results of the joint efforts of many lab
+mainly in Europe mostly European
+
+ align:start position:0%
+mainly in Europe mostly European
+ 
+
+ align:start position:0%
+mainly in Europe mostly European
+projects but I can be sold to in the
+
+ align:start position:0%
+projects but I can be sold to in the
+ 
+
+ align:start position:0%
+projects but I can be sold to in the
+international partner or of the Indian
+
+ align:start position:0%
+international partner or of the Indian
+ 
+
+ align:start position:0%
+international partner or of the Indian
+project attempted so regarding Porter
+
+ align:start position:0%
+project attempted so regarding Porter
+ 
+
+ align:start position:0%
+project attempted so regarding Porter
+standard they are big and so that you
+
+ align:start position:0%
+standard they are big and so that you
+ 
+
+ align:start position:0%
+standard they are big and so that you
+can interaction with the world and
+
+ align:start position:0%
+can interaction with the world and
+ 
+
+ align:start position:0%
+can interaction with the world and
+indeed with this kind of object into
+
+ align:start position:0%
+indeed with this kind of object into
+ 
+
+ align:start position:0%
+indeed with this kind of object into
+many different things top written in
+
+ align:start position:0%
+many different things top written in
+ 
+
+ align:start position:0%
+many different things top written in
+these and this video I'm showing an
+
+ align:start position:0%
+these and this video I'm showing an
+ 
+
+ align:start position:0%
+these and this video I'm showing an
+example of how the team but provided by
+
+ align:start position:0%
+example of how the team but provided by
+ 
+
+ align:start position:0%
+example of how the team but provided by
+the porters tensor can be used to guide
+
+ align:start position:0%
+the porters tensor can be used to guide
+ 
+
+ align:start position:0%
+the porters tensor can be used to guide
+the robot and teach to learn different
+
+ align:start position:0%
+the robot and teach to learn different
+ 
+
+ align:start position:0%
+the robot and teach to learn different
+kind of of action like in this case
+
+ align:start position:0%
+kind of of action like in this case
+ 
+
+ align:start position:0%
+kind of of action like in this case
+pouring action and then repeat it and
+
+ align:start position:0%
+pouring action and then repeat it and
+ 
+
+ align:start position:0%
+pouring action and then repeat it and
+maybe try to generalize it so Porter
+
+ align:start position:0%
+maybe try to generalize it so Porter
+ 
+
+ align:start position:0%
+maybe try to generalize it so Porter
+centers provide the robot feedback about
+
+ align:start position:0%
+centers provide the robot feedback about
+ 
+
+ align:start position:0%
+centers provide the robot feedback about
+the intensity of the interaction with us
+
+ align:start position:0%
+the intensity of the interaction with us
+ 
+
+ align:start position:0%
+the intensity of the interaction with us
+in the external world but they don't I
+
+ align:start position:0%
+in the external world but they don't I
+ 
+
+ align:start position:0%
+in the external world but they don't I
+mean they do not allow to have the robot
+
+ align:start position:0%
+mean they do not allow to have the robot
+ 
+
+ align:start position:0%
+mean they do not allow to have the robot
+have an idea of where this kind of
+
+ align:start position:0%
+have an idea of where this kind of
+ 
+
+ align:start position:0%
+have an idea of where this kind of
+interaction is occurring so for this we
+
+ align:start position:0%
+interaction is occurring so for this we
+ 
+
+ align:start position:0%
+interaction is occurring so for this we
+have artificial skin covering the robot
+
+ align:start position:0%
+have artificial skin covering the robot
+ 
+
+ align:start position:0%
+have artificial skin covering the robot
+as I told you and and the technology
+
+ align:start position:0%
+as I told you and and the technology
+ 
+
+ align:start position:0%
+as I told you and and the technology
+used for for this kind of pin that you
+
+ align:start position:0%
+used for for this kind of pin that you
+ 
+
+ align:start position:0%
+used for for this kind of pin that you
+can see here for the palm of the end of
+
+ align:start position:0%
+can see here for the palm of the end of
+ 
+
+ align:start position:0%
+can see here for the palm of the end of
+the robot is capacitive and it's similar
+
+ align:start position:0%
+the robot is capacitive and it's similar
+ 
+
+ align:start position:0%
+the robot is capacitive and it's similar
+to what to the technology used for cell
+
+ align:start position:0%
+to what to the technology used for cell
+ 
+
+ align:start position:0%
+to what to the technology used for cell
+phone for smartphone and it is is
+
+ align:start position:0%
+phone for smartphone and it is is
+ 
+
+ align:start position:0%
+phone for smartphone and it is is
+basically a
+
+ align:start position:0%
+basically a
+ 
+
+ align:start position:0%
+basically a
+it's using if you can see this yellow
+
+ align:start position:0%
+it's using if you can see this yellow
+ 
+
+ align:start position:0%
+it's using if you can see this yellow
+dot they are all a lecture that together
+
+ align:start position:0%
+dot they are all a lecture that together
+ 
+
+ align:start position:0%
+dot they are all a lecture that together
+with with another armor they deform a
+
+ align:start position:0%
+with with another armor they deform a
+ 
+
+ align:start position:0%
+with with another armor they deform a
+capacitor and entered poorer the the the
+
+ align:start position:0%
+capacitor and entered poorer the the the
+ 
+
+ align:start position:0%
+capacitor and entered poorer the the the
+way these the armors of this capacitor
+
+ align:start position:0%
+way these the armors of this capacitor
+ 
+
+ align:start position:0%
+way these the armors of this capacitor
+are deformed when when there is an
+
+ align:start position:0%
+are deformed when when there is an
+ 
+
+ align:start position:0%
+are deformed when when there is an
+interaction with environment allowed to
+
+ align:start position:0%
+interaction with environment allowed to
+ 
+
+ align:start position:0%
+interaction with environment allowed to
+provide the feedback of the kind of
+
+ align:start position:0%
+provide the feedback of the kind of
+ 
+
+ align:start position:0%
+provide the feedback of the kind of
+intensity providing information about
+
+ align:start position:0%
+intensity providing information about
+ 
+
+ align:start position:0%
+intensity providing information about
+where is the interaction is occurring
+
+ align:start position:0%
+where is the interaction is occurring
+ 
+
+ align:start position:0%
+where is the interaction is occurring
+and the artificial skin it's actually
+
+ align:start position:0%
+and the artificial skin it's actually
+ 
+
+ align:start position:0%
+and the artificial skin it's actually
+really useful for for an embodied agent
+
+ align:start position:0%
+really useful for for an embodied agent
+ 
+
+ align:start position:0%
+really useful for for an embodied agent
+and for instance like in in this video
+
+ align:start position:0%
+and for instance like in in this video
+ 
+
+ align:start position:0%
+and for instance like in in this video
+without using this feedback if you have
+
+ align:start position:0%
+without using this feedback if you have
+ 
+
+ align:start position:0%
+without using this feedback if you have
+a very light object the robot is not
+
+ align:start position:0%
+a very light object the robot is not
+ 
+
+ align:start position:0%
+a very light object the robot is not
+able to detect the fact that it is
+
+ align:start position:0%
+able to detect the fact that it is
+ 
+
+ align:start position:0%
+able to detect the fact that it is
+interacting with something is just
+
+ align:start position:0%
+interacting with something is just
+ 
+
+ align:start position:0%
+interacting with something is just
+closing the end and it doesn't have any
+
+ align:start position:0%
+closing the end and it doesn't have any
+ 
+
+ align:start position:0%
+closing the end and it doesn't have any
+feedback is crushing the the object
+
+ align:start position:0%
+feedback is crushing the the object
+ 
+
+ align:start position:0%
+feedback is crushing the the object
+while by using the sensors on the
+
+ align:start position:0%
+while by using the sensors on the
+ 
+
+ align:start position:0%
+while by using the sensors on the
+fingertips of the Rope of all be hand
+
+ align:start position:0%
+fingertips of the Rope of all be hand
+ 
+
+ align:start position:0%
+fingertips of the Rope of all be hand
+the robot is able to detect that is
+
+ align:start position:0%
+the robot is able to detect that is
+ 
+
+ align:start position:0%
+the robot is able to detect that is
+actually touching something and under
+
+ align:start position:0%
+actually touching something and under
+ 
+
+ align:start position:0%
+actually touching something and under
+Forrest is talking in its action without
+
+ align:start position:0%
+Forrest is talking in its action without
+ 
+
+ align:start position:0%
+Forrest is talking in its action without
+crashing he objects so other other
+
+ align:start position:0%
+crashing he objects so other other
+ 
+
+ align:start position:0%
+crashing he objects so other other
+useful things that can be done with the
+
+ align:start position:0%
+useful things that can be done with the
+ 
+
+ align:start position:0%
+useful things that can be done with the
+artificial skin so this is an example of
+
+ align:start position:0%
+artificial skin so this is an example of
+ 
+
+ align:start position:0%
+artificial skin so this is an example of
+combining the information from the first
+
+ align:start position:0%
+combining the information from the first
+ 
+
+ align:start position:0%
+combining the information from the first
+or sensor and 15 so the diffidence he
+
+ align:start position:0%
+or sensor and 15 so the diffidence he
+ 
+
+ align:start position:0%
+or sensor and 15 so the diffidence he
+allowed to detect wear and a bit the
+
+ align:start position:0%
+allowed to detect wear and a bit the
+ 
+
+ align:start position:0%
+allowed to detect wear and a bit the
+direction of the kind of port that is he
+
+ align:start position:0%
+direction of the kind of port that is he
+ 
+
+ align:start position:0%
+direction of the kind of port that is he
+to the robot and in this case the robot
+
+ align:start position:0%
+to the robot and in this case the robot
+ 
+
+ align:start position:0%
+to the robot and in this case the robot
+is counterbalancing the negating the
+
+ align:start position:0%
+is counterbalancing the negating the
+ 
+
+ align:start position:0%
+is counterbalancing the negating the
+effect of gravity and of internal forces
+
+ align:start position:0%
+effect of gravity and of internal forces
+ 
+
+ align:start position:0%
+effect of gravity and of internal forces
+so it's basically having his term
+
+ align:start position:0%
+so it's basically having his term
+ 
+
+ align:start position:0%
+so it's basically having his term
+floating around like if it was in space
+
+ align:start position:0%
+floating around like if it was in space
+ 
+
+ align:start position:0%
+floating around like if it was in space
+and there is no friction so the by
+
+ align:start position:0%
+and there is no friction so the by
+ 
+
+ align:start position:0%
+and there is no friction so the by
+touching the arm of the robot we have
+
+ align:start position:0%
+touching the arm of the robot we have
+ 
+
+ align:start position:0%
+touching the arm of the robot we have
+the arm drifting in the direction
+
+ align:start position:0%
+the arm drifting in the direction
+ 
+
+ align:start position:0%
+the arm drifting in the direction
+opposed to where the the force is
+
+ align:start position:0%
+opposed to where the the force is
+ 
+
+ align:start position:0%
+opposed to where the the force is
+applied or the torque you can see they
+
+ align:start position:0%
+applied or the torque you can see they
+ 
+
+ align:start position:0%
+applied or the torque you can see they
+are not turning but as you can
+
+ align:start position:0%
+are not turning but as you can
+ 
+
+ align:start position:0%
+are not turning but as you can
+like if it was in paste without any
+
+ align:start position:0%
+like if it was in paste without any
+ 
+
+ align:start position:0%
+like if it was in paste without any
+friction because exactly it's negating
+
+ align:start position:0%
+friction because exactly it's negating
+ 
+
+ align:start position:0%
+friction because exactly it's negating
+both gravity and internal portion so and
+
+ align:start position:0%
+both gravity and internal portion so and
+ 
+
+ align:start position:0%
+both gravity and internal portion so and
+finally again about artificial skin it's
+
+ align:start position:0%
+finally again about artificial skin it's
+ 
+
+ align:start position:0%
+finally again about artificial skin it's
+some work by Alessandro but he's going
+
+ align:start position:0%
+some work by Alessandro but he's going
+ 
+
+ align:start position:0%
+some work by Alessandro but he's going
+to talk about something else but I found
+
+ align:start position:0%
+to talk about something else but I found
+ 
+
+ align:start position:0%
+to talk about something else but I found
+this particularly interesting to show so
+
+ align:start position:0%
+this particularly interesting to show so
+ 
+
+ align:start position:0%
+this particularly interesting to show so
+this is an example of the robot self
+
+ align:start position:0%
+this is an example of the robot self
+ 
+
+ align:start position:0%
+this is an example of the robot self
+calibrating the its own model or the
+
+ align:start position:0%
+calibrating the its own model or the
+ 
+
+ align:start position:0%
+calibrating the its own model or the
+model of its own body with respect to to
+
+ align:start position:0%
+model of its own body with respect to to
+ 
+
+ align:start position:0%
+model of its own body with respect to to
+its own end so it the idea is to have
+
+ align:start position:0%
+its own end so it the idea is to have
+ 
+
+ align:start position:0%
+its own end so it the idea is to have
+the robot use the tactile feedback from
+
+ align:start position:0%
+the robot use the tactile feedback from
+ 
+
+ align:start position:0%
+the robot use the tactile feedback from
+the fingertip and the king of it forearm
+
+ align:start position:0%
+the fingertip and the king of it forearm
+ 
+
+ align:start position:0%
+the fingertip and the king of it forearm
+for instance to learn the relation
+
+ align:start position:0%
+for instance to learn the relation
+ 
+
+ align:start position:0%
+for instance to learn the relation
+directed the position that there exists
+
+ align:start position:0%
+directed the position that there exists
+ 
+
+ align:start position:0%
+directed the position that there exists
+between the fingertip and in the arm and
+
+ align:start position:0%
+between the fingertip and in the arm and
+ 
+
+ align:start position:0%
+between the fingertip and in the arm and
+therefore a table in first by attaching
+
+ align:start position:0%
+therefore a table in first by attaching
+ 
+
+ align:start position:0%
+therefore a table in first by attaching
+itself to learn this correspondence and
+
+ align:start position:0%
+itself to learn this correspondence and
+ 
+
+ align:start position:0%
+itself to learn this correspondence and
+then to to actually show that it has
+
+ align:start position:0%
+then to to actually show that it has
+ 
+
+ align:start position:0%
+then to to actually show that it has
+learned this this kind of correlation by
+
+ align:start position:0%
+learned this this kind of correlation by
+ 
+
+ align:start position:0%
+learned this this kind of correlation by
+reaching that point when someone else
+
+ align:start position:0%
+reaching that point when someone else
+ 
+
+ align:start position:0%
+reaching that point when someone else
+touches the same point and tries to
+
+ align:start position:0%
+touches the same point and tries to
+ 
+
+ align:start position:0%
+touches the same point and tries to
+reach it and therefore this can be seen
+
+ align:start position:0%
+reach it and therefore this can be seen
+ 
+
+ align:start position:0%
+reach it and therefore this can be seen
+as a way of collaborating without the
+
+ align:start position:0%
+as a way of collaborating without the
+ 
+
+ align:start position:0%
+as a way of collaborating without the
+need of a model of the kinematics of the
+
+ align:start position:0%
+need of a model of the kinematics of the
+ 
+
+ align:start position:0%
+need of a model of the kinematics of the
+robot the robot would just be able to
+
+ align:start position:0%
+robot the robot would just be able to
+ 
+
+ align:start position:0%
+robot the robot would just be able to
+explore itself and and learn how
+
+ align:start position:0%
+explore itself and and learn how
+ 
+
+ align:start position:0%
+explore itself and and learn how
+different parts of its body relate one
+
+ align:start position:0%
+different parts of its body relate one
+ 
+
+ align:start position:0%
+different parts of its body relate one
+to the other and again related to to
+
+ align:start position:0%
+to the other and again related to to
+ 
+
+ align:start position:0%
+to the other and again related to to
+tell calibration sometimes but this is
+
+ align:start position:0%
+tell calibration sometimes but this is
+ 
+
+ align:start position:0%
+tell calibration sometimes but this is
+more of a calibration between vision and
+
+ align:start position:0%
+more of a calibration between vision and
+ 
+
+ align:start position:0%
+more of a calibration between vision and
+motor activity this is a work of by
+
+ align:start position:0%
+motor activity this is a work of by
+ 
+
+ align:start position:0%
+motor activity this is a work of by
+appeared in 2014 in which basically the
+
+ align:start position:0%
+appeared in 2014 in which basically the
+ 
+
+ align:start position:0%
+appeared in 2014 in which basically the
+correlation between the kind of actions
+
+ align:start position:0%
+correlation between the kind of actions
+ 
+
+ align:start position:0%
+correlation between the kind of actions
+that the robot is able to perform is
+
+ align:start position:0%
+that the robot is able to perform is
+ 
+
+ align:start position:0%
+that the robot is able to perform is
+calibrated with respect to its ability
+
+ align:start position:0%
+calibrated with respect to its ability
+ 
+
+ align:start position:0%
+calibrated with respect to its ability
+to see the world to perceive the world
+
+ align:start position:0%
+to see the world to perceive the world
+ 
+
+ align:start position:0%
+to see the world to perceive the world
+so in this in this kind of videos I'm
+
+ align:start position:0%
+so in this in this kind of videos I'm
+ 
+
+ align:start position:0%
+so in this in this kind of videos I'm
+going to show the robot is trying to
+
+ align:start position:0%
+going to show the robot is trying to
+ 
+
+ align:start position:0%
+going to show the robot is trying to
+reach for an object and it's failing in
+
+ align:start position:0%
+reach for an object and it's failing in
+ 
+
+ align:start position:0%
+reach for an object and it's failing in
+instruction because because the actual
+
+ align:start position:0%
+instruction because because the actual
+ 
+
+ align:start position:0%
+instruction because because the actual
+model of the word that is used to
+
+ align:start position:0%
+model of the word that is used to
+ 
+
+ align:start position:0%
+model of the word that is used to
+perform the reaching is is not aligned
+
+ align:start position:0%
+perform the reaching is is not aligned
+ 
+
+ align:start position:0%
+perform the reaching is is not aligned
+with the 3d model provided
+
+ align:start position:0%
+with the 3d model provided
+ 
+
+ align:start position:0%
+with the 3d model provided
+vision and and this can happen due to
+
+ align:start position:0%
+vision and and this can happen due to
+ 
+
+ align:start position:0%
+vision and and this can happen due to
+small errors in the kinematics or in the
+
+ align:start position:0%
+small errors in the kinematics or in the
+ 
+
+ align:start position:0%
+small errors in the kinematics or in the
+or in the vision and under poor we even
+
+ align:start position:0%
+or in the vision and under poor we even
+ 
+
+ align:start position:0%
+or in the vision and under poor we even
+just small errors caused a complete
+
+ align:start position:0%
+just small errors caused a complete
+ 
+
+ align:start position:0%
+just small errors caused a complete
+failure of the system and therefore by
+
+ align:start position:0%
+failure of the system and therefore by
+ 
+
+ align:start position:0%
+failure of the system and therefore by
+by trying to correlate the two
+
+ align:start position:0%
+by trying to correlate the two
+ 
+
+ align:start position:0%
+by trying to correlate the two
+information the one from the kinematics
+
+ align:start position:0%
+information the one from the kinematics
+ 
+
+ align:start position:0%
+information the one from the kinematics
+in this case the robot is using his own
+
+ align:start position:0%
+in this case the robot is using his own
+ 
+
+ align:start position:0%
+in this case the robot is using his own
+fingertip to to see where it actually it
+
+ align:start position:0%
+fingertip to to see where it actually it
+ 
+
+ align:start position:0%
+fingertip to to see where it actually it
+hand is in the image and and when the
+
+ align:start position:0%
+hand is in the image and and when the
+ 
+
+ align:start position:0%
+hand is in the image and and when the
+kinematic model predicts the hand should
+
+ align:start position:0%
+kinematic model predicts the hand should
+ 
+
+ align:start position:0%
+kinematic model predicts the hand should
+be so the green dot is the point
+
+ align:start position:0%
+be so the green dot is the point
+ 
+
+ align:start position:0%
+be so the green dot is the point
+predicted by kinematic so where the
+
+ align:start position:0%
+predicted by kinematic so where the
+ 
+
+ align:start position:0%
+predicted by kinematic so where the
+system expects the fingertip to be and
+
+ align:start position:0%
+system expects the fingertip to be and
+ 
+
+ align:start position:0%
+system expects the fingertip to be and
+where actually the fingertip is so of
+
+ align:start position:0%
+where actually the fingertip is so of
+ 
+
+ align:start position:0%
+where actually the fingertip is so of
+course by by learning these relations
+
+ align:start position:0%
+course by by learning these relations
+ 
+
+ align:start position:0%
+course by by learning these relations
+the D robot is able to cope with with
+
+ align:start position:0%
+the D robot is able to cope with with
+ 
+
+ align:start position:0%
+the D robot is able to cope with with
+this kind of misalignment and and
+
+ align:start position:0%
+this kind of misalignment and and
+ 
+
+ align:start position:0%
+this kind of misalignment and and
+therefore after a first calibration
+
+ align:start position:0%
+therefore after a first calibration
+ 
+
+ align:start position:0%
+therefore after a first calibration
+phase it's able to to perform the reach
+
+ align:start position:0%
+phase it's able to to perform the reach
+ 
+
+ align:start position:0%
+phase it's able to to perform the reach
+interaction as we will see in a moment
+
+ align:start position:0%
+interaction as we will see in a moment
+ 
+
+ align:start position:0%
+interaction as we will see in a moment
+so also this kind of ability of
+
+ align:start position:0%
+so also this kind of ability of
+ 
+
+ align:start position:0%
+so also this kind of ability of
+calibrating would be pretty useful in
+
+ align:start position:0%
+calibrating would be pretty useful in
+ 
+
+ align:start position:0%
+calibrating would be pretty useful in
+case of situations in which the robot is
+
+ align:start position:0%
+case of situations in which the robot is
+ 
+
+ align:start position:0%
+case of situations in which the robot is
+damaged and for the actual model changes
+
+ align:start position:0%
+damaged and for the actual model changes
+ 
+
+ align:start position:0%
+damaged and for the actual model changes
+completely and yeah as you can see now
+
+ align:start position:0%
+completely and yeah as you can see now
+ 
+
+ align:start position:0%
+completely and yeah as you can see now
+it's reaching and and it's performing
+
+ align:start position:0%
+it's reaching and and it's performing
+ 
+
+ align:start position:0%
+it's reaching and and it's performing
+the de grasper wracking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so finally before going with the actual
+
+ align:start position:0%
+so finally before going with the actual
+ 
+
+ align:start position:0%
+so finally before going with the actual
+talk I'm going to show you a final video
+
+ align:start position:0%
+talk I'm going to show you a final video
+ 
+
+ align:start position:0%
+talk I'm going to show you a final video
+about balancing some of you have asked
+
+ align:start position:0%
+about balancing some of you have asked
+ 
+
+ align:start position:0%
+about balancing some of you have asked
+that if the robot work and the robot is
+
+ align:start position:0%
+that if the robot work and the robot is
+ 
+
+ align:start position:0%
+that if the robot work and the robot is
+currently not it's not able to work but
+
+ align:start position:0%
+currently not it's not able to work but
+ 
+
+ align:start position:0%
+currently not it's not able to work but
+this is a video from the people from the
+
+ align:start position:0%
+this is a video from the people from the
+ 
+
+ align:start position:0%
+this is a video from the people from the
+group that is actually in charge of
+
+ align:start position:0%
+group that is actually in charge of
+ 
+
+ align:start position:0%
+group that is actually in charge of
+making the robot work and the the first
+
+ align:start position:0%
+making the robot work and the the first
+ 
+
+ align:start position:0%
+making the robot work and the the first
+step of course will be balancing and
+
+ align:start position:0%
+step of course will be balancing and
+ 
+
+ align:start position:0%
+step of course will be balancing and
+this is an example of it so it's
+
+ align:start position:0%
+this is an example of it so it's
+ 
+
+ align:start position:0%
+this is an example of it so it's
+actually a one tooth balancing where
+
+ align:start position:0%
+actually a one tooth balancing where
+ 
+
+ align:start position:0%
+actually a one tooth balancing where
+multiple component of the skiff that of
+
+ align:start position:0%
+multiple component of the skiff that of
+ 
+
+ align:start position:0%
+multiple component of the skiff that of
+the component of what I'm showing you
+
+ align:start position:0%
+the component of what I'm showing you
+ 
+
+ align:start position:0%
+the component of what I'm showing you
+about the eye comes to Forrester
+
+ align:start position:0%
+about the eye comes to Forrester
+ 
+
+ align:start position:0%
+about the eye comes to Forrester
+stenting inertial sensing are combined
+
+ align:start position:0%
+stenting inertial sensing are combined
+ 
+
+ align:start position:0%
+stenting inertial sensing are combined
+together to have the robot stand on one
+
+ align:start position:0%
+together to have the robot stand on one
+ 
+
+ align:start position:0%
+together to have the robot stand on one
+foot and and also be able to cope with
+
+ align:start position:0%
+foot and and also be able to cope with
+ 
+
+ align:start position:0%
+foot and and also be able to cope with
+the interaction external forces that
+
+ align:start position:0%
+the interaction external forces that
+ 
+
+ align:start position:0%
+the interaction external forces that
+that could try to to make it pop to to
+
+ align:start position:0%
+that could try to to make it pop to to
+ 
+
+ align:start position:0%
+that could try to to make it pop to to
+have it pull yeah yeah they're applying
+
+ align:start position:0%
+have it pull yeah yeah they're applying
+ 
+
+ align:start position:0%
+have it pull yeah yeah they're applying
+forces to their robot and they feel able
+
+ align:start position:0%
+forces to their robot and they feel able
+ 
+
+ align:start position:0%
+forces to their robot and they feel able
+to to detect the forces to cooperate
+
+ align:start position:0%
+to to detect the forces to cooperate
+ 
+
+ align:start position:0%
+to to detect the forces to cooperate
+with the forces but to pay table okay so
+
+ align:start position:0%
+with the forces but to pay table okay so
+ 
+
+ align:start position:0%
+with the forces but to pay table okay so
+this was just a brief overview of some
+
+ align:start position:0%
+this was just a brief overview of some
+ 
+
+ align:start position:0%
+this was just a brief overview of some
+things that can be done with the icon
+
+ align:start position:0%
+things that can be done with the icon
+ 
+
+ align:start position:0%
+things that can be done with the icon
+and actually the next talk will be a bit
+
+ align:start position:0%
+and actually the next talk will be a bit
+ 
+
+ align:start position:0%
+and actually the next talk will be a bit
+more about what's going on with with it
+
+ align:start position:0%
+more about what's going on with with it
+ 
+
+ align:start position:0%
+more about what's going on with with it
+so yes dizzy teeth yeah I want to talk
+
+ align:start position:0%
+so yes dizzy teeth yeah I want to talk
+ 
+
+ align:start position:0%
+so yes dizzy teeth yeah I want to talk
+about part of my PhD project that was
+
+ align:start position:0%
+about part of my PhD project that was
+ 
+
+ align:start position:0%
+about part of my PhD project that was
+about tackling the perception problem
+
+ align:start position:0%
+about tackling the perception problem
+ 
+
+ align:start position:0%
+about tackling the perception problem
+sound coming out okay
+
+ align:start position:0%
+sound coming out okay
+ 
+
+ align:start position:0%
+sound coming out okay
+ the perception problem but
+
+ align:start position:0%
+ the perception problem but
+ 
+
+ align:start position:0%
+ the perception problem but
+through the use of multi-sensory
+
+ align:start position:0%
+through the use of multi-sensory
+ 
+
+ align:start position:0%
+through the use of multi-sensory
+integration and specifically I nailed
+
+ align:start position:0%
+integration and specifically I nailed
+ 
+
+ align:start position:0%
+integration and specifically I nailed
+down this big problem by implementing a
+
+ align:start position:0%
+down this big problem by implementing a
+ 
+
+ align:start position:0%
+down this big problem by implementing a
+model of cry fastness based on the iCub
+
+ align:start position:0%
+model of cry fastness based on the iCub
+ 
+
+ align:start position:0%
+model of cry fastness based on the iCub
+that is being inspired approach
+
+ align:start position:0%
+that is being inspired approach
+ 
+
+ align:start position:0%
+that is being inspired approach
+professional space is a concept that is
+
+ align:start position:0%
+professional space is a concept that is
+ 
+
+ align:start position:0%
+professional space is a concept that is
+administered in neuroscience and
+
+ align:start position:0%
+administered in neuroscience and
+ 
+
+ align:start position:0%
+administered in neuroscience and
+psychology for years and so let me start
+
+ align:start position:0%
+psychology for years and so let me start
+ 
+
+ align:start position:0%
+psychology for years and so let me start
+is what my personal space is and why it
+
+ align:start position:0%
+is what my personal space is and why it
+ 
+
+ align:start position:0%
+is what my personal space is and why it
+is so important for humans and animals
+
+ align:start position:0%
+is so important for humans and animals
+ 
+
+ align:start position:0%
+is so important for humans and animals
+it is defined as the space around us
+
+ align:start position:0%
+it is defined as the space around us
+ 
+
+ align:start position:0%
+it is defined as the space around us
+within which objects can be grasped and
+
+ align:start position:0%
+within which objects can be grasped and
+ 
+
+ align:start position:0%
+within which objects can be grasped and
+manipulated is an interface basically
+
+ align:start position:0%
+manipulated is an interface basically
+ 
+
+ align:start position:0%
+manipulated is an interface basically
+between our body and the external world
+
+ align:start position:0%
+between our body and the external world
+ 
+
+ align:start position:0%
+between our body and the external world
+and for this reason it benefits from a
+
+ align:start position:0%
+and for this reason it benefits from a
+ 
+
+ align:start position:0%
+and for this reason it benefits from a
+multimodal integrated representation
+
+ align:start position:0%
+multimodal integrated representation
+ 
+
+ align:start position:0%
+multimodal integrated representation
+that merges information between
+
+ align:start position:0%
+that merges information between
+ 
+
+ align:start position:0%
+that merges information between
+different modalities and historically
+
+ align:start position:0%
+different modalities and historically
+ 
+
+ align:start position:0%
+different modalities and historically
+these have been the vision system the
+
+ align:start position:0%
+these have been the vision system the
+ 
+
+ align:start position:0%
+these have been the vision system the
+tactile system the perception auditory
+
+ align:start position:0%
+tactile system the perception auditory
+ 
+
+ align:start position:0%
+tactile system the perception auditory
+system and even the motor system
+
+ align:start position:0%
+system and even the motor system
+ 
+
+ align:start position:0%
+system and even the motor system
+historically it has been studied by two
+
+ align:start position:0%
+historically it has been studied by two
+ 
+
+ align:start position:0%
+historically it has been studied by two
+different field the neurophysiology on
+
+ align:start position:0%
+different field the neurophysiology on
+ 
+
+ align:start position:0%
+different field the neurophysiology on
+one side one side and all the
+
+ align:start position:0%
+one side one side and all the
+ 
+
+ align:start position:0%
+one side one side and all the
+disciplines related to psychology and
+
+ align:start position:0%
+disciplines related to psychology and
+ 
+
+ align:start position:0%
+disciplines related to psychology and
+developmental psychology on the other
+
+ align:start position:0%
+developmental psychology on the other
+ 
+
+ align:start position:0%
+developmental psychology on the other
+they basically follow the two different
+
+ align:start position:0%
+they basically follow the two different
+ 
+
+ align:start position:0%
+they basically follow the two different
+approaches the former being button up or
+
+ align:start position:0%
+approaches the former being button up or
+ 
+
+ align:start position:0%
+approaches the former being button up or
+the latter being top-down and they came
+
+ align:start position:0%
+the latter being top-down and they came
+ 
+
+ align:start position:0%
+the latter being top-down and they came
+out with different outcomes
+
+ align:start position:0%
+out with different outcomes
+ 
+
+ align:start position:0%
+out with different outcomes
+the former emphasizes the role of the
+
+ align:start position:0%
+the former emphasizes the role of the
+ 
+
+ align:start position:0%
+the former emphasizes the role of the
+perception and it interplay with the
+
+ align:start position:0%
+perception and it interplay with the
+ 
+
+ align:start position:0%
+perception and it interplay with the
+motor system in the control of movement
+
+ align:start position:0%
+motor system in the control of movement
+ 
+
+ align:start position:0%
+motor system in the control of movement
+whereas the latter was focusing mainly
+
+ align:start position:0%
+whereas the latter was focusing mainly
+ 
+
+ align:start position:0%
+whereas the latter was focusing mainly
+on the multi-sensory after that is how
+
+ align:start position:0%
+on the multi-sensory after that is how
+ 
+
+ align:start position:0%
+on the multi-sensory after that is how
+different modalities were combined
+
+ align:start position:0%
+different modalities were combined
+ 
+
+ align:start position:0%
+different modalities were combined
+together in order to form a coherent
+
+ align:start position:0%
+together in order to form a coherent
+ 
+
+ align:start position:0%
+together in order to form a coherent
+view of the body and the nearby space
+
+ align:start position:0%
+view of the body and the nearby space
+ 
+
+ align:start position:0%
+view of the body and the nearby space
+likely in the recent years they started
+
+ align:start position:0%
+likely in the recent years they started
+ 
+
+ align:start position:0%
+likely in the recent years they started
+to converge to a common ground and the
+
+ align:start position:0%
+to converge to a common ground and the
+ 
+
+ align:start position:0%
+to converge to a common ground and the
+shared interpretation and for the
+
+ align:start position:0%
+shared interpretation and for the
+ 
+
+ align:start position:0%
+shared interpretation and for the
+purposes of my work I would like to
+
+ align:start position:0%
+purposes of my work I would like to
+ 
+
+ align:start position:0%
+purposes of my work I would like to
+highlight three main track firstly and
+
+ align:start position:0%
+highlight three main track firstly and
+ 
+
+ align:start position:0%
+highlight three main track firstly and
+this one is might be of interest from an
+
+ align:start position:0%
+this one is might be of interest from an
+ 
+
+ align:start position:0%
+this one is might be of interest from an
+engineering perspective so a personal
+
+ align:start position:0%
+engineering perspective so a personal
+ 
+
+ align:start position:0%
+engineering perspective so a personal
+space is made from is made of different
+
+ align:start position:0%
+space is made from is made of different
+ 
+
+ align:start position:0%
+space is made from is made of different
+reference frames that are located in
+
+ align:start position:0%
+reference frames that are located in
+ 
+
+ align:start position:0%
+reference frames that are located in
+different regions of the brain and there
+
+ align:start position:0%
+different regions of the brain and there
+ 
+
+ align:start position:0%
+different regions of the brain and there
+might be a way for the brain to switch
+
+ align:start position:0%
+might be a way for the brain to switch
+ 
+
+ align:start position:0%
+might be a way for the brain to switch
+from one to another according to
+
+ align:start position:0%
+from one to another according to
+ 
+
+ align:start position:0%
+from one to another according to
+different contact angles and secondly as
+
+ align:start position:0%
+different contact angles and secondly as
+ 
+
+ align:start position:0%
+different contact angles and secondly as
+I was saying my personal space benefit
+
+ align:start position:0%
+I was saying my personal space benefit
+ 
+
+ align:start position:0%
+I was saying my personal space benefit
+from a multi-sensory integration in
+
+ align:start position:0%
+from a multi-sensory integration in
+ 
+
+ align:start position:0%
+from a multi-sensory integration in
+order to form a coherent view of the
+
+ align:start position:0%
+order to form a coherent view of the
+ 
+
+ align:start position:0%
+order to form a coherent view of the
+body and the surrounding space in this
+
+ align:start position:0%
+body and the surrounding space in this
+ 
+
+ align:start position:0%
+body and the surrounding space in this
+experiment made by pegasi in 1886 the
+
+ align:start position:0%
+experiment made by pegasi in 1886 the
+ 
+
+ align:start position:0%
+experiment made by pegasi in 1886 the
+they basically found a number of
+
+ align:start position:0%
+they basically found a number of
+ 
+
+ align:start position:0%
+they basically found a number of
+so-called visual tactile neurons that
+
+ align:start position:0%
+so-called visual tactile neurons that
+ 
+
+ align:start position:0%
+so-called visual tactile neurons that
+are a set of neurons that fire both
+
+ align:start position:0%
+are a set of neurons that fire both
+ 
+
+ align:start position:0%
+are a set of neurons that fire both
+related in a specific team part and if
+
+ align:start position:0%
+related in a specific team part and if
+ 
+
+ align:start position:0%
+related in a specific team part and if
+an object is presented in the
+
+ align:start position:0%
+an object is presented in the
+ 
+
+ align:start position:0%
+an object is presented in the
+surrounding space so this means that
+
+ align:start position:0%
+surrounding space so this means that
+ 
+
+ align:start position:0%
+surrounding space so this means that
+these kneels and could both the visual
+
+ align:start position:0%
+these kneels and could both the visual
+ 
+
+ align:start position:0%
+these kneels and could both the visual
+information and the tactile information
+
+ align:start position:0%
+information and the tactile information
+ 
+
+ align:start position:0%
+information and the tactile information
+but they also have some perceptive
+
+ align:start position:0%
+but they also have some perceptive
+ 
+
+ align:start position:0%
+but they also have some perceptive
+information because they are basically
+
+ align:start position:0%
+information because they are basically
+ 
+
+ align:start position:0%
+information because they are basically
+attached to the body part they belong to
+
+ align:start position:0%
+attached to the body part they belong to
+ 
+
+ align:start position:0%
+attached to the body part they belong to
+lastly one of the main properties of
+
+ align:start position:0%
+lastly one of the main properties of
+ 
+
+ align:start position:0%
+lastly one of the main properties of
+this representation is in tasting
+
+ align:start position:0%
+this representation is in tasting
+ 
+
+ align:start position:0%
+this representation is in tasting
+plasticity and for example in this
+
+ align:start position:0%
+plasticity and for example in this
+ 
+
+ align:start position:0%
+plasticity and for example in this
+experiment to me by Erie T 10 years ago
+
+ align:start position:0%
+experiment to me by Erie T 10 years ago
+ 
+
+ align:start position:0%
+experiment to me by Erie T 10 years ago
+the extension of this adaptive T in the
+
+ align:start position:0%
+the extension of this adaptive T in the
+ 
+
+ align:start position:0%
+the extension of this adaptive T in the
+visual space 20 surrounding space after
+
+ align:start position:0%
+visual space 20 surrounding space after
+ 
+
+ align:start position:0%
+visual space 20 surrounding space after
+training with the Eric have been shown
+
+ align:start position:0%
+training with the Eric have been shown
+ 
+
+ align:start position:0%
+training with the Eric have been shown
+to grow up to enclose the tool as if
+
+ align:start position:0%
+to grow up to enclose the tool as if
+ 
+
+ align:start position:0%
+to grow up to enclose the tool as if
+this tool becomes part of the body so to
+
+ align:start position:0%
+this tool becomes part of the body so to
+ 
+
+ align:start position:0%
+this tool becomes part of the body so to
+experience and to to use the monkey was
+
+ align:start position:0%
+experience and to to use the monkey was
+ 
+
+ align:start position:0%
+experience and to to use the monkey was
+able to grow this receptive field okay
+
+ align:start position:0%
+able to grow this receptive field okay
+ 
+
+ align:start position:0%
+able to grow this receptive field okay
+and in robotic I mean those are
+
+ align:start position:0%
+and in robotic I mean those are
+ 
+
+ align:start position:0%
+and in robotic I mean those are
+properties that very nice and we would
+
+ align:start position:0%
+properties that very nice and we would
+ 
+
+ align:start position:0%
+properties that very nice and we would
+like them to be available for the robot
+
+ align:start position:0%
+like them to be available for the robot
+ 
+
+ align:start position:0%
+like them to be available for the robot
+and in general in robotic work slated to
+
+ align:start position:0%
+and in general in robotic work slated to
+ 
+
+ align:start position:0%
+and in general in robotic work slated to
+professional space can be divided into
+
+ align:start position:0%
+professional space can be divided into
+ 
+
+ align:start position:0%
+professional space can be divided into
+two groups and on one side there are the
+
+ align:start position:0%
+two groups and on one side there are the
+ 
+
+ align:start position:0%
+two groups and on one side there are the
+models and the simulations basically the
+
+ align:start position:0%
+models and the simulations basically the
+ 
+
+ align:start position:0%
+models and the simulations basically the
+closest one to my work was the one from
+
+ align:start position:0%
+closest one to my work was the one from
+ 
+
+ align:start position:0%
+closest one to my work was the one from
+Phuket and colleagues that are from
+
+ align:start position:0%
+Phuket and colleagues that are from
+ 
+
+ align:start position:0%
+Phuket and colleagues that are from
+Masada's lab in which they used
+
+ align:start position:0%
+Masada's lab in which they used
+ 
+
+ align:start position:0%
+Masada's lab in which they used
+stimulated the robot in order to model
+
+ align:start position:0%
+stimulated the robot in order to model
+ 
+
+ align:start position:0%
+stimulated the robot in order to model
+the mechanism that are leading to these
+
+ align:start position:0%
+the mechanism that are leading to these
+ 
+
+ align:start position:0%
+the mechanism that are leading to these
+visual representations on the other side
+
+ align:start position:0%
+visual representations on the other side
+ 
+
+ align:start position:0%
+visual representations on the other side
+there are the engineering approaches
+
+ align:start position:0%
+there are the engineering approaches
+ 
+
+ align:start position:0%
+there are the engineering approaches
+that appeal the closest one is this one
+
+ align:start position:0%
+that appeal the closest one is this one
+ 
+
+ align:start position:0%
+that appeal the closest one is this one
+by Mitterrand or from God on shanks lab
+
+ align:start position:0%
+by Mitterrand or from God on shanks lab
+ 
+
+ align:start position:0%
+by Mitterrand or from God on shanks lab
+in which they firstly developed a
+
+ align:start position:0%
+in which they firstly developed a
+ 
+
+ align:start position:0%
+in which they firstly developed a
+multi-modal skin so they develop the
+
+ align:start position:0%
+multi-modal skin so they develop the
+ 
+
+ align:start position:0%
+multi-modal skin so they develop the
+hardware able to do that and then they
+
+ align:start position:0%
+hardware able to do that and then they
+ 
+
+ align:start position:0%
+hardware able to do that and then they
+used it in order to trigger local
+
+ align:start position:0%
+used it in order to trigger local
+ 
+
+ align:start position:0%
+used it in order to trigger local
+avoidance responses some practice to
+
+ align:start position:0%
+avoidance responses some practice to
+ 
+
+ align:start position:0%
+avoidance responses some practice to
+incoming object s tape we are trying to
+
+ align:start position:0%
+incoming object s tape we are trying to
+ 
+
+ align:start position:0%
+incoming object s tape we are trying to
+position our start in the middle let's
+
+ align:start position:0%
+position our start in the middle let's
+ 
+
+ align:start position:0%
+position our start in the middle let's
+say we are not trying to create a
+
+ align:start position:0%
+say we are not trying to create a
+ 
+
+ align:start position:0%
+say we are not trying to create a
+perfect model of my personal space from
+
+ align:start position:0%
+perfect model of my personal space from
+ 
+
+ align:start position:0%
+perfect model of my personal space from
+bio biological
+
+ align:start position:0%
+bio biological
+ 
+
+ align:start position:0%
+bio biological
+active but on the other side we would
+
+ align:start position:0%
+active but on the other side we would
+ 
+
+ align:start position:0%
+active but on the other side we would
+like to have something that is also
+
+ align:start position:0%
+like to have something that is also
+ 
+
+ align:start position:0%
+like to have something that is also
+working on the yellow of it and useful
+
+ align:start position:0%
+working on the yellow of it and useful
+ 
+
+ align:start position:0%
+working on the yellow of it and useful
+for our proposal so from now on I will
+
+ align:start position:0%
+for our proposal so from now on I will
+ 
+
+ align:start position:0%
+for our proposal so from now on I will
+divide this presentation in two parts
+
+ align:start position:0%
+divide this presentation in two parts
+ 
+
+ align:start position:0%
+divide this presentation in two parts
+the first one will be about the modal
+
+ align:start position:0%
+the first one will be about the modal
+ 
+
+ align:start position:0%
+the first one will be about the modal
+estab so what we think will be useful
+
+ align:start position:0%
+estab so what we think will be useful
+ 
+
+ align:start position:0%
+estab so what we think will be useful
+for tackling the problem on the other
+
+ align:start position:0%
+for tackling the problem on the other
+ 
+
+ align:start position:0%
+for tackling the problem on the other
+side I will show you an application of
+
+ align:start position:0%
+side I will show you an application of
+ 
+
+ align:start position:0%
+side I will show you an application of
+this model that is basically using this
+
+ align:start position:0%
+this model that is basically using this
+ 
+
+ align:start position:0%
+this model that is basically using this
+local representation in order to trigger
+
+ align:start position:0%
+local representation in order to trigger
+ 
+
+ align:start position:0%
+local representation in order to trigger
+avoidance responses or reaching
+
+ align:start position:0%
+avoidance responses or reaching
+ 
+
+ align:start position:0%
+avoidance responses or reaching
+responses distributed throughout the
+
+ align:start position:0%
+responses distributed throughout the
+ 
+
+ align:start position:0%
+responses distributed throughout the
+body and so let me start with this the
+
+ align:start position:0%
+body and so let me start with this the
+ 
+
+ align:start position:0%
+body and so let me start with this the
+proposed model of personal space loose
+
+ align:start position:0%
+proposed model of personal space loose
+ 
+
+ align:start position:0%
+proposed model of personal space loose
+inspired by the neurophysiological
+
+ align:start position:0%
+inspired by the neurophysiological
+ 
+
+ align:start position:0%
+inspired by the neurophysiological
+findings I discussed before we developed
+
+ align:start position:0%
+findings I discussed before we developed
+ 
+
+ align:start position:0%
+findings I discussed before we developed
+this personal space representation by
+
+ align:start position:0%
+this personal space representation by
+ 
+
+ align:start position:0%
+this personal space representation by
+means of a set of facial especially
+
+ align:start position:0%
+means of a set of facial especially
+ 
+
+ align:start position:0%
+means of a set of facial especially
+safety pins that were going out from the
+
+ align:start position:0%
+safety pins that were going out from the
+ 
+
+ align:start position:0%
+safety pins that were going out from the
+robots esteem so basically they were
+
+ align:start position:0%
+robots esteem so basically they were
+ 
+
+ align:start position:0%
+robots esteem so basically they were
+extending the tactile domain into nearby
+
+ align:start position:0%
+extending the tactile domain into nearby
+ 
+
+ align:start position:0%
+extending the tactile domain into nearby
+face each tactile that is each pass the
+
+ align:start position:0%
+face each tactile that is each pass the
+ 
+
+ align:start position:0%
+face each tactile that is each pass the
+iCub skin is composed of will experience
+
+ align:start position:0%
+iCub skin is composed of will experience
+ 
+
+ align:start position:0%
+iCub skin is composed of will experience
+a set of multi-sensory events so
+
+ align:start position:0%
+a set of multi-sensory events so
+ 
+
+ align:start position:0%
+a set of multi-sensory events so
+basically we were training the Latino
+
+ align:start position:0%
+basically we were training the Latino
+ 
+
+ align:start position:0%
+basically we were training the Latino
+learn these visual associations by
+
+ align:start position:0%
+learn these visual associations by
+ 
+
+ align:start position:0%
+learn these visual associations by
+taking an object and making it contact
+
+ align:start position:0%
+taking an object and making it contact
+ 
+
+ align:start position:0%
+taking an object and making it contact
+on the steam part and it will learn by
+
+ align:start position:0%
+on the steam part and it will learn by
+ 
+
+ align:start position:0%
+on the steam part and it will learn by
+thanks to this experience he will learn
+
+ align:start position:0%
+thanks to this experience he will learn
+ 
+
+ align:start position:0%
+thanks to this experience he will learn
+a sort of probability of being attacked
+
+ align:start position:0%
+a sort of probability of being attacked
+ 
+
+ align:start position:0%
+a sort of probability of being attacked
+and it's basically a prior to contact
+
+ align:start position:0%
+and it's basically a prior to contact
+ 
+
+ align:start position:0%
+and it's basically a prior to contact
+activation when a new incoming object is
+
+ align:start position:0%
+activation when a new incoming object is
+ 
+
+ align:start position:0%
+activation when a new incoming object is
+presented to the stand we basically
+
+ align:start position:0%
+presented to the stand we basically
+ 
+
+ align:start position:0%
+presented to the stand we basically
+created this cone-shaped receptive field
+
+ align:start position:0%
+created this cone-shaped receptive field
+ 
+
+ align:start position:0%
+created this cone-shaped receptive field
+that is going out from each of the taxol
+
+ align:start position:0%
+that is going out from each of the taxol
+ 
+
+ align:start position:0%
+that is going out from each of the taxol
+and for any object that is entering this
+
+ align:start position:0%
+and for any object that is entering this
+ 
+
+ align:start position:0%
+and for any object that is entering this
+receptive field we created we call the
+
+ align:start position:0%
+receptive field we created we call the
+ 
+
+ align:start position:0%
+receptive field we created we call the
+buffer of the second the path so
+
+ align:start position:0%
+buffer of the second the path so
+ 
+
+ align:start position:0%
+buffer of the second the path so
+basically the idea is that the robot has
+
+ align:start position:0%
+basically the idea is that the robot has
+ 
+
+ align:start position:0%
+basically the idea is that the robot has
+some information from what was going on
+
+ align:start position:0%
+some information from what was going on
+ 
+
+ align:start position:0%
+some information from what was going on
+before the touch they caught the actual
+
+ align:start position:0%
+before the touch they caught the actual
+ 
+
+ align:start position:0%
+before the touch they caught the actual
+contact and if this object eventually
+
+ align:start position:0%
+contact and if this object eventually
+ 
+
+ align:start position:0%
+contact and if this object eventually
+ends up touching the tactile this will
+
+ align:start position:0%
+ends up touching the tactile this will
+ 
+
+ align:start position:0%
+ends up touching the tactile this will
+be labeled as a positive event that will
+
+ align:start position:0%
+be labeled as a positive event that will
+ 
+
+ align:start position:0%
+be labeled as a positive event that will
+enforce the probability of
+
+ align:start position:0%
+enforce the probability of
+ 
+
+ align:start position:0%
+enforce the probability of
+event ending up touching the doctor if
+
+ align:start position:0%
+event ending up touching the doctor if
+ 
+
+ align:start position:0%
+event ending up touching the doctor if
+not for example it might be that the
+
+ align:start position:0%
+not for example it might be that the
+ 
+
+ align:start position:0%
+not for example it might be that the
+object enters this establishment at the
+
+ align:start position:0%
+object enters this establishment at the
+ 
+
+ align:start position:0%
+object enters this establishment at the
+end and stop touching a new table in a
+
+ align:start position:0%
+end and stop touching a new table in a
+ 
+
+ align:start position:0%
+end and stop touching a new table in a
+detector this will be labeled as
+
+ align:start position:0%
+detector this will be labeled as
+ 
+
+ align:start position:0%
+detector this will be labeled as
+negative so at the end we will have a
+
+ align:start position:0%
+negative so at the end we will have a
+ 
+
+ align:start position:0%
+negative so at the end we will have a
+set of positive and negative events the
+
+ align:start position:0%
+set of positive and negative events the
+ 
+
+ align:start position:0%
+set of positive and negative events the
+doctor can learn from this is a
+
+ align:start position:0%
+doctor can learn from this is a
+ 
+
+ align:start position:0%
+doctor can learn from this is a
+three-dimensional space because the
+
+ align:start position:0%
+three-dimensional space because the
+ 
+
+ align:start position:0%
+three-dimensional space because the
+distance is a dimensional and we now add
+
+ align:start position:0%
+distance is a dimensional and we now add
+ 
+
+ align:start position:0%
+distance is a dimensional and we now add
+it down to a one dimensional domain by
+
+ align:start position:0%
+it down to a one dimensional domain by
+ 
+
+ align:start position:0%
+it down to a one dimensional domain by
+basically taking the norm of the
+
+ align:start position:0%
+basically taking the norm of the
+ 
+
+ align:start position:0%
+basically taking the norm of the
+distance but also the relative position
+
+ align:start position:0%
+distance but also the relative position
+ 
+
+ align:start position:0%
+distance but also the relative position
+of the object with an the taxol in order
+
+ align:start position:0%
+of the object with an the taxol in order
+ 
+
+ align:start position:0%
+of the object with an the taxol in order
+for us to be able to cope with
+
+ align:start position:0%
+for us to be able to cope with
+ 
+
+ align:start position:0%
+for us to be able to cope with
+calibration errors that were amounting
+
+ align:start position:0%
+calibration errors that were amounting
+ 
+
+ align:start position:0%
+calibration errors that were amounting
+up to a couple centimeters so we're
+
+ align:start position:0%
+up to a couple centimeters so we're
+ 
+
+ align:start position:0%
+up to a couple centimeters so we're
+significant and so this one-dimensional
+
+ align:start position:0%
+significant and so this one-dimensional
+ 
+
+ align:start position:0%
+significant and so this one-dimensional
+variable has been disguised in a set of
+
+ align:start position:0%
+variable has been disguised in a set of
+ 
+
+ align:start position:0%
+variable has been disguised in a set of
+bills and for each bin we computed the
+
+ align:start position:0%
+bills and for each bin we computed the
+ 
+
+ align:start position:0%
+bills and for each bin we computed the
+probability of an event belonging to
+
+ align:start position:0%
+probability of an event belonging to
+ 
+
+ align:start position:0%
+probability of an event belonging to
+that bin of being touched so the idea is
+
+ align:start position:0%
+that bin of being touched so the idea is
+ 
+
+ align:start position:0%
+that bin of being touched so the idea is
+that a 20-centimeter the probability of
+
+ align:start position:0%
+that a 20-centimeter the probability of
+ 
+
+ align:start position:0%
+that a 20-centimeter the probability of
+being touch would be lower than a zero
+
+ align:start position:0%
+being touch would be lower than a zero
+ 
+
+ align:start position:0%
+being touch would be lower than a zero
+centimeter this is the intuitive idea
+
+ align:start position:0%
+centimeter this is the intuitive idea
+ 
+
+ align:start position:0%
+centimeter this is the intuitive idea
+and over this one-dimensional villain
+
+ align:start position:0%
+and over this one-dimensional villain
+ 
+
+ align:start position:0%
+and over this one-dimensional villain
+ization we used the person window
+
+ align:start position:0%
+ization we used the person window
+ 
+
+ align:start position:0%
+ization we used the person window
+interpolation technique in order to
+
+ align:start position:0%
+interpolation technique in order to
+ 
+
+ align:start position:0%
+interpolation technique in order to
+provide us with this two dimensional
+
+ align:start position:0%
+provide us with this two dimensional
+ 
+
+ align:start position:0%
+provide us with this two dimensional
+function that's at the end will give us
+
+ align:start position:0%
+function that's at the end will give us
+ 
+
+ align:start position:0%
+function that's at the end will give us
+a an activation value that is
+
+ align:start position:0%
+a an activation value that is
+ 
+
+ align:start position:0%
+a an activation value that is
+proportional to the width the distance
+
+ align:start position:0%
+proportional to the width the distance
+ 
+
+ align:start position:0%
+proportional to the width the distance
+of the of the object so as soon as a new
+
+ align:start position:0%
+of the of the object so as soon as a new
+ 
+
+ align:start position:0%
+of the of the object so as soon as a new
+object will enter the receptive field I
+
+ align:start position:0%
+object will enter the receptive field I
+ 
+
+ align:start position:0%
+object will enter the receptive field I
+will have and the fact that will fire
+
+ align:start position:0%
+will have and the fact that will fire
+ 
+
+ align:start position:0%
+will have and the fact that will fire
+before being contacted before being
+
+ align:start position:0%
+before being contacted before being
+ 
+
+ align:start position:0%
+before being contacted before being
+contacted but we did the basically two
+
+ align:start position:0%
+contacted but we did the basically two
+ 
+
+ align:start position:0%
+contacted but we did the basically two
+experiment that initially we created we
+
+ align:start position:0%
+experiment that initially we created we
+ 
+
+ align:start position:0%
+experiment that initially we created we
+did the stimulation MATLAB internet was
+
+ align:start position:0%
+did the stimulation MATLAB internet was
+ 
+
+ align:start position:0%
+did the stimulation MATLAB internet was
+test the convergence on the long term
+
+ align:start position:0%
+test the convergence on the long term
+ 
+
+ align:start position:0%
+test the convergence on the long term
+learning the one-shot learning behavior
+
+ align:start position:0%
+learning the one-shot learning behavior
+ 
+
+ align:start position:0%
+learning the one-shot learning behavior
+to assess if our model was able to cope
+
+ align:start position:0%
+to assess if our model was able to cope
+ 
+
+ align:start position:0%
+to assess if our model was able to cope
+with noise with different calibration
+
+ align:start position:0%
+with noise with different calibration
+ 
+
+ align:start position:0%
+with noise with different calibration
+errors and then we went on their yellow
+
+ align:start position:0%
+errors and then we went on their yellow
+ 
+
+ align:start position:0%
+errors and then we went on their yellow
+robot we presented a robot with the
+
+ align:start position:0%
+robot we presented a robot with the
+ 
+
+ align:start position:0%
+robot we presented a robot with the
+different object and we were basically
+
+ align:start position:0%
+different object and we were basically
+ 
+
+ align:start position:0%
+different object and we were basically
+touching the robot for under time in
+
+ align:start position:0%
+touching the robot for under time in
+ 
+
+ align:start position:0%
+touching the robot for under time in
+order to make it learn these
+
+ align:start position:0%
+order to make it learn these
+ 
+
+ align:start position:0%
+order to make it learn these
+representations so
+
+ align:start position:0%
+representations so
+ 
+
+ align:start position:0%
+representations so
+trust me I don't want to bother you with
+
+ align:start position:0%
+trust me I don't want to bother you with
+ 
+
+ align:start position:0%
+trust me I don't want to bother you with
+this kind of technicalities but we did a
+
+ align:start position:0%
+this kind of technicalities but we did a
+ 
+
+ align:start position:0%
+this kind of technicalities but we did a
+lot of work on it what this is basically
+
+ align:start position:0%
+lot of work on it what this is basically
+ 
+
+ align:start position:0%
+lot of work on it what this is basically
+the MATLAB result and so let me go on
+
+ align:start position:0%
+the MATLAB result and so let me go on
+ 
+
+ align:start position:0%
+the MATLAB result and so let me go on
+the second part in which the robot the
+
+ align:start position:0%
+the second part in which the robot the
+ 
+
+ align:start position:0%
+the second part in which the robot the
+main problem was for the robot to detect
+
+ align:start position:0%
+main problem was for the robot to detect
+ 
+
+ align:start position:0%
+main problem was for the robot to detect
+the object visually in order for us to
+
+ align:start position:0%
+the object visually in order for us to
+ 
+
+ align:start position:0%
+the object visually in order for us to
+do that we developed a third attacking
+
+ align:start position:0%
+do that we developed a third attacking
+ 
+
+ align:start position:0%
+do that we developed a third attacking
+algorithm that was enabled to talk about
+
+ align:start position:0%
+algorithm that was enabled to talk about
+ 
+
+ align:start position:0%
+algorithm that was enabled to talk about
+an object basically to design that we
+
+ align:start position:0%
+an object basically to design that we
+ 
+
+ align:start position:0%
+an object basically to design that we
+used some software the toaster is
+
+ align:start position:0%
+used some software the toaster is
+ 
+
+ align:start position:0%
+used some software the toaster is
+available in the i-cubs of the
+
+ align:start position:0%
+available in the i-cubs of the
+ 
+
+ align:start position:0%
+available in the i-cubs of the
+repository that the in general provides
+
+ align:start position:0%
+repository that the in general provides
+ 
+
+ align:start position:0%
+repository that the in general provides
+you with some basic algorithm that you
+
+ align:start position:0%
+you with some basic algorithm that you
+ 
+
+ align:start position:0%
+you with some basic algorithm that you
+can play with and namely we used a three
+
+ align:start position:0%
+can play with and namely we used a three
+ 
+
+ align:start position:0%
+can play with and namely we used a three
+dimensional optical flow made by carlo
+
+ align:start position:0%
+dimensional optical flow made by carlo
+ 
+
+ align:start position:0%
+dimensional optical flow made by carlo
+and a 2d particle printer and a 3d
+
+ align:start position:0%
+and a 2d particle printer and a 3d
+ 
+
+ align:start position:0%
+and a 2d particle printer and a 3d
+stereo vision algorithm that is
+
+ align:start position:0%
+stereo vision algorithm that is
+ 
+
+ align:start position:0%
+stereo vision algorithm that is
+basically the same as I was showing
+
+ align:start position:0%
+basically the same as I was showing
+ 
+
+ align:start position:0%
+basically the same as I was showing
+before doing the actual condition day in
+
+ align:start position:0%
+before doing the actual condition day in
+ 
+
+ align:start position:0%
+before doing the actual condition day in
+game and this basically was feeding a 3d
+
+ align:start position:0%
+game and this basically was feeding a 3d
+ 
+
+ align:start position:0%
+game and this basically was feeding a 3d
+Kalman filter in order to provide us
+
+ align:start position:0%
+Kalman filter in order to provide us
+ 
+
+ align:start position:0%
+Kalman filter in order to provide us
+with a robot estimation of the 3d
+
+ align:start position:0%
+with a robot estimation of the 3d
+ 
+
+ align:start position:0%
+with a robot estimation of the 3d
+position of the object so the idea is
+
+ align:start position:0%
+position of the object so the idea is
+ 
+
+ align:start position:0%
+position of the object so the idea is
+that the motion detected from the
+
+ align:start position:0%
+that the motion detected from the
+ 
+
+ align:start position:0%
+that the motion detected from the
+optical probe act as a trigger for the
+
+ align:start position:0%
+optical probe act as a trigger for the
+ 
+
+ align:start position:0%
+optical probe act as a trigger for the
+subsequent pipeline in which basically
+
+ align:start position:0%
+subsequent pipeline in which basically
+ 
+
+ align:start position:0%
+subsequent pipeline in which basically
+after a consistent enough motion in this
+
+ align:start position:0%
+after a consistent enough motion in this
+ 
+
+ align:start position:0%
+after a consistent enough motion in this
+optical flow mode module this will be a
+
+ align:start position:0%
+optical flow mode module this will be a
+ 
+
+ align:start position:0%
+optical flow mode module this will be a
+template that start to be tucked in the
+
+ align:start position:0%
+template that start to be tucked in the
+ 
+
+ align:start position:0%
+template that start to be tucked in the
+visual in the 2d visual world by this
+
+ align:start position:0%
+visual in the 2d visual world by this
+ 
+
+ align:start position:0%
+visual in the 2d visual world by this
+then this information is sent to the 3d
+
+ align:start position:0%
+then this information is sent to the 3d
+ 
+
+ align:start position:0%
+then this information is sent to the 3d
+death map and this would be we'll be
+
+ align:start position:0%
+death map and this would be we'll be
+ 
+
+ align:start position:0%
+death map and this would be we'll be
+feeding the camera filter in order to
+
+ align:start position:0%
+feeding the camera filter in order to
+ 
+
+ align:start position:0%
+feeding the camera filter in order to
+provide us with this table presentation
+
+ align:start position:0%
+provide us with this table presentation
+ 
+
+ align:start position:0%
+provide us with this table presentation
+because obviously the system doesn't
+
+ align:start position:0%
+because obviously the system doesn't
+ 
+
+ align:start position:0%
+because obviously the system doesn't
+work that good in our contact and this
+
+ align:start position:0%
+work that good in our contact and this
+ 
+
+ align:start position:0%
+work that good in our contact and this
+if it worked no yeah okay on my laptop
+
+ align:start position:0%
+if it worked no yeah okay on my laptop
+ 
+
+ align:start position:0%
+if it worked no yeah okay on my laptop
+it worked okay now it works ok this is
+
+ align:start position:0%
+it worked okay now it works ok this is
+ 
+
+ align:start position:0%
+it worked okay now it works ok this is
+the idea so I was basically waving
+
+ align:start position:0%
+the idea so I was basically waving
+ 
+
+ align:start position:0%
+the idea so I was basically waving
+moving the object in the beginning of
+
+ align:start position:0%
+moving the object in the beginning of
+ 
+
+ align:start position:0%
+moving the object in the beginning of
+our abilities it's ok then when it is
+
+ align:start position:0%
+our abilities it's ok then when it is
+ 
+
+ align:start position:0%
+our abilities it's ok then when it is
+detected this fiber and start
+
+ align:start position:0%
+detected this fiber and start
+ 
+
+ align:start position:0%
+detected this fiber and start
+and you can see here the talking this is
+
+ align:start position:0%
+and you can see here the talking this is
+ 
+
+ align:start position:0%
+and you can see here the talking this is
+the television this is the final outcome
+
+ align:start position:0%
+the television this is the final outcome
+ 
+
+ align:start position:0%
+the television this is the final outcome
+this was used for the learning we did a
+
+ align:start position:0%
+this was used for the learning we did a
+ 
+
+ align:start position:0%
+this was used for the learning we did a
+lot of iterations of these objects
+
+ align:start position:0%
+lot of iterations of these objects
+ 
+
+ align:start position:0%
+lot of iterations of these objects
+washing the skin on different body fast
+
+ align:start position:0%
+washing the skin on different body fast
+ 
+
+ align:start position:0%
+washing the skin on different body fast
+this is the dagger I don't want to talk
+
+ align:start position:0%
+this is the dagger I don't want to talk
+ 
+
+ align:start position:0%
+this is the dagger I don't want to talk
+about that so let me start with the
+
+ align:start position:0%
+about that so let me start with the
+ 
+
+ align:start position:0%
+about that so let me start with the
+video this is basically the skin and
+
+ align:start position:0%
+video this is basically the skin and
+ 
+
+ align:start position:0%
+video this is basically the skin and
+this is the Python was showing before
+
+ align:start position:0%
+this is the Python was showing before
+ 
+
+ align:start position:0%
+this is the Python was showing before
+when there is a contact there is a red
+
+ align:start position:0%
+when there is a contact there is a red
+ 
+
+ align:start position:0%
+when there is a contact there is a red
+activation here you can see here the
+
+ align:start position:0%
+activation here you can see here the
+ 
+
+ align:start position:0%
+activation here you can see here the
+creation and soon after this this thing
+
+ align:start position:0%
+creation and soon after this this thing
+ 
+
+ align:start position:0%
+creation and soon after this this thing
+worked also with one example the tactile
+
+ align:start position:0%
+worked also with one example the tactile
+ 
+
+ align:start position:0%
+worked also with one example the tactile
+starts firing before the contact and
+
+ align:start position:0%
+starts firing before the contact and
+ 
+
+ align:start position:0%
+starts firing before the contact and
+obviously this is improved over the time
+
+ align:start position:0%
+obviously this is improved over the time
+ 
+
+ align:start position:0%
+obviously this is improved over the time
+and it depends on the body spot that is
+
+ align:start position:0%
+and it depends on the body spot that is
+ 
+
+ align:start position:0%
+and it depends on the body spot that is
+attached day for example if I touch here
+
+ align:start position:0%
+attached day for example if I touch here
+ 
+
+ align:start position:0%
+attached day for example if I touch here
+I mean coming from the top so the
+
+ align:start position:0%
+I mean coming from the top so the
+ 
+
+ align:start position:0%
+I mean coming from the top so the
+presentation start spying mainly here
+
+ align:start position:0%
+presentation start spying mainly here
+ 
+
+ align:start position:0%
+presentation start spying mainly here
+and and this obviously depends on the
+
+ align:start position:0%
+and and this obviously depends on the
+ 
+
+ align:start position:0%
+and and this obviously depends on the
+specific body part now I think that I'm
+
+ align:start position:0%
+specific body part now I think that I'm
+ 
+
+ align:start position:0%
+specific body part now I think that I'm
+going to touch the hand and so after a
+
+ align:start position:0%
+going to touch the hand and so after a
+ 
+
+ align:start position:0%
+going to touch the hand and so after a
+while you will I will have an activation
+
+ align:start position:0%
+while you will I will have an activation
+ 
+
+ align:start position:0%
+while you will I will have an activation
+of the hand obviously I will have also
+
+ align:start position:0%
+of the hand obviously I will have also
+ 
+
+ align:start position:0%
+of the hand obviously I will have also
+some activation the program because I
+
+ align:start position:0%
+some activation the program because I
+ 
+
+ align:start position:0%
+some activation the program because I
+was getting closer to the forearm and as
+
+ align:start position:0%
+was getting closer to the forearm and as
+ 
+
+ align:start position:0%
+was getting closer to the forearm and as
+an application of this this one is
+
+ align:start position:0%
+an application of this this one is
+ 
+
+ align:start position:0%
+an application of this this one is
+basically simple simple presentation so
+
+ align:start position:0%
+basically simple simple presentation so
+ 
+
+ align:start position:0%
+basically simple simple presentation so
+it's not that useful
+
+ align:start position:0%
+it's not that useful
+ 
+
+ align:start position:0%
+it's not that useful
+we basically exploited it in order to
+
+ align:start position:0%
+we basically exploited it in order to
+ 
+
+ align:start position:0%
+we basically exploited it in order to
+develop an avoidance imagine of safety
+
+ align:start position:0%
+develop an avoidance imagine of safety
+ 
+
+ align:start position:0%
+develop an avoidance imagine of safety
+around the body let's say if the tactile
+
+ align:start position:0%
+around the body let's say if the tactile
+ 
+
+ align:start position:0%
+around the body let's say if the tactile
+is filing I will like it to go away from
+
+ align:start position:0%
+is filing I will like it to go away from
+ 
+
+ align:start position:0%
+is filing I will like it to go away from
+the object assuming that this can be a
+
+ align:start position:0%
+the object assuming that this can be a
+ 
+
+ align:start position:0%
+the object assuming that this can be a
+potentially harmful object and on the
+
+ align:start position:0%
+potentially harmful object and on the
+ 
+
+ align:start position:0%
+potentially harmful object and on the
+other way I would like it to be able to
+
+ align:start position:0%
+other way I would like it to be able to
+ 
+
+ align:start position:0%
+other way I would like it to be able to
+eat with any body part the object under
+
+ align:start position:0%
+eat with any body part the object under
+ 
+
+ align:start position:0%
+eat with any body part the object under
+consideration so to this end we
+
+ align:start position:0%
+consideration so to this end we
+ 
+
+ align:start position:0%
+consideration so to this end we
+developed an avoidance eye-catching
+
+ align:start position:0%
+developed an avoidance eye-catching
+ 
+
+ align:start position:0%
+developed an avoidance eye-catching
+controller that was able to leverage on
+
+ align:start position:0%
+controller that was able to leverage on
+ 
+
+ align:start position:0%
+controller that was able to leverage on
+the distributed information and perform
+
+ align:start position:0%
+the distributed information and perform
+ 
+
+ align:start position:0%
+the distributed information and perform
+a sensory based guidance of the motor
+
+ align:start position:0%
+a sensory based guidance of the motor
+ 
+
+ align:start position:0%
+a sensory based guidance of the motor
+actions by mist of these visual tactile
+
+ align:start position:0%
+actions by mist of these visual tactile
+ 
+
+ align:start position:0%
+actions by mist of these visual tactile
+associations and this is basically how
+
+ align:start position:0%
+associations and this is basically how
+ 
+
+ align:start position:0%
+associations and this is basically how
+it works so this is at the testing stage
+
+ align:start position:0%
+it works so this is at the testing stage
+ 
+
+ align:start position:0%
+it works so this is at the testing stage
+so I already learned
+
+ align:start position:0%
+so I already learned
+ 
+
+ align:start position:0%
+so I already learned
+imitation as soon as I get closer the
+
+ align:start position:0%
+imitation as soon as I get closer the
+ 
+
+ align:start position:0%
+imitation as soon as I get closer the
+tactile thought firing because of the
+
+ align:start position:0%
+tactile thought firing because of the
+ 
+
+ align:start position:0%
+tactile thought firing because of the
+probabilities I was learning and the
+
+ align:start position:0%
+probabilities I was learning and the
+ 
+
+ align:start position:0%
+probabilities I was learning and the
+harm goes away
+
+ align:start position:0%
+harm goes away
+ 
+
+ align:start position:0%
+harm goes away
+obviously the movement depends on the
+
+ align:start position:0%
+obviously the movement depends on the
+ 
+
+ align:start position:0%
+obviously the movement depends on the
+specific team part that has been touched
+
+ align:start position:0%
+specific team part that has been touched
+ 
+
+ align:start position:0%
+specific team part that has been touched
+if I touching here the Opera go away
+
+ align:start position:0%
+if I touching here the Opera go away
+ 
+
+ align:start position:0%
+if I touching here the Opera go away
+from here if I'm taking from if I'm
+
+ align:start position:0%
+from here if I'm taking from if I'm
+ 
+
+ align:start position:0%
+from here if I'm taking from if I'm
+coming from the top I think this one was
+
+ align:start position:0%
+coming from the top I think this one was
+ 
+
+ align:start position:0%
+coming from the top I think this one was
+doing from the top yes the robot will go
+
+ align:start position:0%
+doing from the top yes the robot will go
+ 
+
+ align:start position:0%
+doing from the top yes the robot will go
+away in this direction from the back
+
+ align:start position:0%
+away in this direction from the back
+ 
+
+ align:start position:0%
+away in this direction from the back
+there are between going away from
+
+ align:start position:0%
+there are between going away from
+ 
+
+ align:start position:0%
+there are between going away from
+another direction and the idea is not to
+
+ align:start position:0%
+another direction and the idea is not to
+ 
+
+ align:start position:0%
+another direction and the idea is not to
+explicitly tackle the problem from a
+
+ align:start position:0%
+explicitly tackle the problem from a
+ 
+
+ align:start position:0%
+explicitly tackle the problem from a
+classical robotics approach but
+
+ align:start position:0%
+classical robotics approach but
+ 
+
+ align:start position:0%
+classical robotics approach but
+basically this behavior emerges from the
+
+ align:start position:0%
+basically this behavior emerges from the
+ 
+
+ align:start position:0%
+basically this behavior emerges from the
+learning and the idea was very simple we
+
+ align:start position:0%
+learning and the idea was very simple we
+ 
+
+ align:start position:0%
+learning and the idea was very simple we
+basically we were basically looking at
+
+ align:start position:0%
+basically we were basically looking at
+ 
+
+ align:start position:0%
+basically we were basically looking at
+the taxa that work we were firing if
+
+ align:start position:0%
+the taxa that work we were firing if
+ 
+
+ align:start position:0%
+the taxa that work we were firing if
+they were finding enough we were
+
+ align:start position:0%
+they were finding enough we were
+ 
+
+ align:start position:0%
+they were finding enough we were
+recording their position and we were
+
+ align:start position:0%
+recording their position and we were
+ 
+
+ align:start position:0%
+recording their position and we were
+doing a basically a population coding
+
+ align:start position:0%
+doing a basically a population coding
+ 
+
+ align:start position:0%
+doing a basically a population coding
+that is a weighted average according to
+
+ align:start position:0%
+that is a weighted average according to
+ 
+
+ align:start position:0%
+that is a weighted average according to
+daya activation and dire prediction we
+
+ align:start position:0%
+daya activation and dire prediction we
+ 
+
+ align:start position:0%
+daya activation and dire prediction we
+did that both for the position of the
+
+ align:start position:0%
+did that both for the position of the
+ 
+
+ align:start position:0%
+did that both for the position of the
+taxon and the normal so at the enemy if
+
+ align:start position:0%
+taxon and the normal so at the enemy if
+ 
+
+ align:start position:0%
+taxon and the normal so at the enemy if
+you have a bunch of taxes here we will
+
+ align:start position:0%
+you have a bunch of taxes here we will
+ 
+
+ align:start position:0%
+you have a bunch of taxes here we will
+end up with one point to go away with
+
+ align:start position:0%
+end up with one point to go away with
+ 
+
+ align:start position:0%
+end up with one point to go away with
+from and on the other side the caching
+
+ align:start position:0%
+from and on the other side the caching
+ 
+
+ align:start position:0%
+from and on the other side the caching
+the etching was basically the same but
+
+ align:start position:0%
+the etching was basically the same but
+ 
+
+ align:start position:0%
+the etching was basically the same but
+in the opposite direction so if I want
+
+ align:start position:0%
+in the opposite direction so if I want
+ 
+
+ align:start position:0%
+in the opposite direction so if I want
+to avoid I do this if I want to catch I
+
+ align:start position:0%
+to avoid I do this if I want to catch I
+ 
+
+ align:start position:0%
+to avoid I do this if I want to catch I
+will do this obvious if you do it in the
+
+ align:start position:0%
+will do this obvious if you do it in the
+ 
+
+ align:start position:0%
+will do this obvious if you do it in the
+hand this will be a stand of the
+
+ align:start position:0%
+hand this will be a stand of the
+ 
+
+ align:start position:0%
+hand this will be a stand of the
+reaching robotic reaching but this
+
+ align:start position:0%
+reaching robotic reaching but this
+ 
+
+ align:start position:0%
+reaching robotic reaching but this
+actually can be tailored also in
+
+ align:start position:0%
+actually can be tailored also in
+ 
+
+ align:start position:0%
+actually can be tailored also in
+different body parts as you can see here
+
+ align:start position:0%
+different body parts as you can see here
+ 
+
+ align:start position:0%
+different body parts as you can see here
+I get a vehicle activation and then a
+
+ align:start position:0%
+I get a vehicle activation and then a
+ 
+
+ align:start position:0%
+I get a vehicle activation and then a
+physical contact and and yes basically
+
+ align:start position:0%
+physical contact and and yes basically
+ 
+
+ align:start position:0%
+physical contact and and yes basically
+the our design was to do to use the same
+
+ align:start position:0%
+the our design was to do to use the same
+ 
+
+ align:start position:0%
+the our design was to do to use the same
+controller for both of the OT of the
+
+ align:start position:0%
+controller for both of the OT of the
+ 
+
+ align:start position:0%
+controller for both of the OT of the
+behaviors so this is the okay this is
+
+ align:start position:0%
+behaviors so this is the okay this is
+ 
+
+ align:start position:0%
+behaviors so this is the okay this is
+also some technicalities that I don't
+
+ align:start position:0%
+also some technicalities that I don't
+ 
+
+ align:start position:0%
+also some technicalities that I don't
+want to show you so in conclusion the
+
+ align:start position:0%
+want to show you so in conclusion the
+ 
+
+ align:start position:0%
+want to show you so in conclusion the
+architecture presented here is to our
+
+ align:start position:0%
+architecture presented here is to our
+ 
+
+ align:start position:0%
+architecture presented here is to our
+knowledge the first attempt at creating
+
+ align:start position:0%
+knowledge the first attempt at creating
+ 
+
+ align:start position:0%
+knowledge the first attempt at creating
+a distant alized multi-sensory visual
+
+ align:start position:0%
+a distant alized multi-sensory visual
+ 
+
+ align:start position:0%
+a distant alized multi-sensory visual
+tactile presentation for a robot and
+
+ align:start position:0%
+tactile presentation for a robot and
+ 
+
+ align:start position:0%
+tactile presentation for a robot and
+it's nearby space by means of the
+
+ align:start position:0%
+it's nearby space by means of the
+ 
+
+ align:start position:0%
+it's nearby space by means of the
+distributed cane
+
+ align:start position:0%
+distributed cane
+ 
+
+ align:start position:0%
+distributed cane
+and interaction with the environment one
+
+ align:start position:0%
+and interaction with the environment one
+ 
+
+ align:start position:0%
+and interaction with the environment one
+of the actors of our presentation is
+
+ align:start position:0%
+of the actors of our presentation is
+ 
+
+ align:start position:0%
+of the actors of our presentation is
+that learning is fast and you were
+
+ align:start position:0%
+that learning is fast and you were
+ 
+
+ align:start position:0%
+that learning is fast and you were
+saying it was can learn also from one
+
+ align:start position:0%
+saying it was can learn also from one
+ 
+
+ align:start position:0%
+saying it was can learn also from one
+single example it's in parallel to for
+
+ align:start position:0%
+single example it's in parallel to for
+ 
+
+ align:start position:0%
+single example it's in parallel to for
+the world body in the sense that every
+
+ align:start position:0%
+the world body in the sense that every
+ 
+
+ align:start position:0%
+the world body in the sense that every
+taxa learn independently its own a
+
+ align:start position:0%
+taxa learn independently its own a
+ 
+
+ align:start position:0%
+taxa learn independently its own a
+presentation at least incremental in a
+
+ align:start position:0%
+presentation at least incremental in a
+ 
+
+ align:start position:0%
+presentation at least incremental in a
+sense that it converges towards a stable
+
+ align:start position:0%
+sense that it converges towards a stable
+ 
+
+ align:start position:0%
+sense that it converges towards a stable
+representation over the time and
+
+ align:start position:0%
+representation over the time and
+ 
+
+ align:start position:0%
+representation over the time and
+importantly it is adapted from
+
+ align:start position:0%
+importantly it is adapted from
+ 
+
+ align:start position:0%
+importantly it is adapted from
+experience and so basically it can
+
+ align:start position:0%
+experience and so basically it can
+ 
+
+ align:start position:0%
+experience and so basically it can
+automatically compensate for errors in
+
+ align:start position:0%
+automatically compensate for errors in
+ 
+
+ align:start position:0%
+automatically compensate for errors in
+the model that for human robots is one
+
+ align:start position:0%
+the model that for human robots is one
+ 
+
+ align:start position:0%
+the model that for human robots is one
+of the main problems when merging
+
+ align:start position:0%
+of the main problems when merging
+ 
+
+ align:start position:0%
+of the main problems when merging
+different modalities okay thank you
+
+ align:start position:0%
+different modalities okay thank you
+ 
+
+ align:start position:0%
+different modalities okay thank you
+if you have any question people learning
+
+ align:start position:0%
+if you have any question people learning
+ 
+
+ align:start position:0%
+if you have any question people learning
+and robotics in particular some subsets
+
+ align:start position:0%
+and robotics in particular some subsets
+ 
+
+ align:start position:0%
+and robotics in particular some subsets
+of machine learning which are a large
+
+ align:start position:0%
+of machine learning which are a large
+ 
+
+ align:start position:0%
+of machine learning which are a large
+scale learning and incremental learning
+
+ align:start position:0%
+scale learning and incremental learning
+ 
+
+ align:start position:0%
+scale learning and incremental learning
+but what do we expect from a modern
+
+ align:start position:0%
+but what do we expect from a modern
+ 
+
+ align:start position:0%
+but what do we expect from a modern
+robot and how can machine learning help
+
+ align:start position:0%
+robot and how can machine learning help
+ 
+
+ align:start position:0%
+robot and how can machine learning help
+out with with this well respect modern
+
+ align:start position:0%
+out with with this well respect modern
+ 
+
+ align:start position:0%
+out with with this well respect modern
+robots to work in particularly
+
+ align:start position:0%
+robots to work in particularly
+ 
+
+ align:start position:0%
+robots to work in particularly
+unstructured environments which they
+
+ align:start position:0%
+unstructured environments which they
+ 
+
+ align:start position:0%
+unstructured environments which they
+have never seen before
+
+ align:start position:0%
+have never seen before
+ 
+
+ align:start position:0%
+have never seen before
+and to learn new tasks on the fly
+
+ align:start position:0%
+and to learn new tasks on the fly
+ 
+
+ align:start position:0%
+and to learn new tasks on the fly
+depending on the particular needs
+
+ align:start position:0%
+depending on the particular needs
+ 
+
+ align:start position:0%
+depending on the particular needs
+throughout the operation of the of the
+
+ align:start position:0%
+throughout the operation of the of the
+ 
+
+ align:start position:0%
+throughout the operation of the of the
+robot itself and across different
+
+ align:start position:0%
+robot itself and across different
+ 
+
+ align:start position:0%
+robot itself and across different
+modalities for instance vision of course
+
+ align:start position:0%
+modalities for instance vision of course
+ 
+
+ align:start position:0%
+modalities for instance vision of course
+but also tactile sensing which is
+
+ align:start position:0%
+but also tactile sensing which is
+ 
+
+ align:start position:0%
+but also tactile sensing which is
+available on the iCub and also
+
+ align:start position:0%
+available on the iCub and also
+ 
+
+ align:start position:0%
+available on the iCub and also
+proprioceptive the sensing including
+
+ align:start position:0%
+proprioceptive the sensing including
+ 
+
+ align:start position:0%
+proprioceptive the sensing including
+first sensing pneumatics and so on and
+
+ align:start position:0%
+first sensing pneumatics and so on and
+ 
+
+ align:start position:0%
+first sensing pneumatics and so on and
+so forth and we'd want to do all of
+
+ align:start position:0%
+so forth and we'd want to do all of
+ 
+
+ align:start position:0%
+so forth and we'd want to do all of
+these throughout a very long time span
+
+ align:start position:0%
+these throughout a very long time span
+ 
+
+ align:start position:0%
+these throughout a very long time span
+potentially because we expect troubles
+
+ align:start position:0%
+potentially because we expect troubles
+ 
+
+ align:start position:0%
+potentially because we expect troubles
+to be companions of humans in the real
+
+ align:start position:0%
+to be companions of humans in the real
+ 
+
+ align:start position:0%
+to be companions of humans in the real
+world operating for maybe years or more
+
+ align:start position:0%
+world operating for maybe years or more
+ 
+
+ align:start position:0%
+world operating for maybe years or more
+and this poses a lot of challenges
+
+ align:start position:0%
+and this poses a lot of challenges
+ 
+
+ align:start position:0%
+and this poses a lot of challenges
+especially from the computational point
+
+ align:start position:0%
+especially from the computational point
+ 
+
+ align:start position:0%
+especially from the computational point
+of view and machine learning can
+
+ align:start position:0%
+of view and machine learning can
+ 
+
+ align:start position:0%
+of view and machine learning can
+actually help with this with tackling
+
+ align:start position:0%
+actually help with this with tackling
+ 
+
+ align:start position:0%
+actually help with this with tackling
+these challenges for instance there are
+
+ align:start position:0%
+these challenges for instance there are
+ 
+
+ align:start position:0%
+these challenges for instance there are
+large scale learning methods which
+
+ align:start position:0%
+large scale learning methods which
+ 
+
+ align:start position:0%
+large scale learning methods which
+enables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which are algorithms which can work with
+
+ align:start position:0%
+which are algorithms which can work with
+ 
+
+ align:start position:0%
+which are algorithms which can work with
+large very large scale data types for
+
+ align:start position:0%
+large very large scale data types for
+ 
+
+ align:start position:0%
+large very large scale data types for
+instance if we have millions of points
+
+ align:start position:0%
+instance if we have millions of points
+ 
+
+ align:start position:0%
+instance if we have millions of points
+gathered by the robot cameras throughout
+
+ align:start position:0%
+gathered by the robot cameras throughout
+ 
+
+ align:start position:0%
+gathered by the robot cameras throughout
+10 days and we want to process them well
+
+ align:start position:0%
+10 days and we want to process them well
+ 
+
+ align:start position:0%
+10 days and we want to process them well
+if we use standard machine learning
+
+ align:start position:0%
+if we use standard machine learning
+ 
+
+ align:start position:0%
+if we use standard machine learning
+methods that will be a very difficult
+
+ align:start position:0%
+methods that will be a very difficult
+ 
+
+ align:start position:0%
+methods that will be a very difficult
+problem to solve if we don't use for
+
+ align:start position:0%
+problem to solve if we don't use for
+ 
+
+ align:start position:0%
+problem to solve if we don't use for
+instance randomized methods and and so
+
+ align:start position:0%
+instance randomized methods and and so
+ 
+
+ align:start position:0%
+instance randomized methods and and so
+on and so forth we also want much
+
+ align:start position:0%
+on and so forth we also want much
+ 
+
+ align:start position:0%
+on and so forth we also want much
+learning also has incremental algorithms
+
+ align:start position:0%
+learning also has incremental algorithms
+ 
+
+ align:start position:0%
+learning also has incremental algorithms
+which can be allowed demote the learned
+
+ align:start position:0%
+which can be allowed demote the learned
+ 
+
+ align:start position:0%
+which can be allowed demote the learned
+model to be updated as new privily
+
+ align:start position:0%
+model to be updated as new privily
+ 
+
+ align:start position:0%
+model to be updated as new privily
+previously and seen features are
+
+ align:start position:0%
+previously and seen features are
+ 
+
+ align:start position:0%
+previously and seen features are
+presented to the to the agent and also
+
+ align:start position:0%
+presented to the to the agent and also
+ 
+
+ align:start position:0%
+presented to the to the agent and also
+there is a subfield of transfer learning
+
+ align:start position:0%
+there is a subfield of transfer learning
+ 
+
+ align:start position:0%
+there is a subfield of transfer learning
+which allows knowledge no knowledge
+
+ align:start position:0%
+which allows knowledge no knowledge
+ 
+
+ align:start position:0%
+which allows knowledge no knowledge
+learned for a particular task to be used
+
+ align:start position:0%
+learned for a particular task to be used
+ 
+
+ align:start position:0%
+learned for a particular task to be used
+for serving another related task without
+
+ align:start position:0%
+for serving another related task without
+ 
+
+ align:start position:0%
+for serving another related task without
+the need for seeing many new examples
+
+ align:start position:0%
+the need for seeing many new examples
+ 
+
+ align:start position:0%
+the need for seeing many new examples
+for the new task so my main research
+
+ align:start position:0%
+for the new task so my main research
+ 
+
+ align:start position:0%
+for the new task so my main research
+focuses are especially in in machine
+
+ align:start position:0%
+focuses are especially in in machine
+ 
+
+ align:start position:0%
+focuses are especially in in machine
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+I work especially in large-scale
+
+ align:start position:0%
+I work especially in large-scale
+ 
+
+ align:start position:0%
+I work especially in large-scale
+learning methods incremental learning
+
+ align:start position:0%
+learning methods incremental learning
+ 
+
+ align:start position:0%
+learning methods incremental learning
+and in the design of the algorithms
+
+ align:start position:0%
+and in the design of the algorithms
+ 
+
+ align:start position:0%
+and in the design of the algorithms
+which allow for computational and
+
+ align:start position:0%
+which allow for computational and
+ 
+
+ align:start position:0%
+which allow for computational and
+accuracy trade-off I will explain this a
+
+ align:start position:0%
+accuracy trade-off I will explain this a
+ 
+
+ align:start position:0%
+accuracy trade-off I will explain this a
+bit more later and as concerns robotics
+
+ align:start position:0%
+bit more later and as concerns robotics
+ 
+
+ align:start position:0%
+bit more later and as concerns robotics
+applications I work with julia carlo and
+
+ align:start position:0%
+applications I work with julia carlo and
+ 
+
+ align:start position:0%
+applications I work with julia carlo and
+others on incremental object recognition
+
+ align:start position:0%
+others on incremental object recognition
+ 
+
+ align:start position:0%
+others on incremental object recognition
+so in a setting in which the robot is
+
+ align:start position:0%
+so in a setting in which the robot is
+ 
+
+ align:start position:0%
+so in a setting in which the robot is
+presented new objects throughout a long
+
+ align:start position:0%
+presented new objects throughout a long
+ 
+
+ align:start position:0%
+presented new objects throughout a long
+time span and it has to
+
+ align:start position:0%
+time span and it has to
+ 
+
+ align:start position:0%
+time span and it has to
+learn them on the slide and also I'm
+
+ align:start position:0%
+learn them on the slide and also I'm
+ 
+
+ align:start position:0%
+learn them on the slide and also I'm
+working in a more systematic I'm working
+
+ align:start position:0%
+working in a more systematic I'm working
+ 
+
+ align:start position:0%
+working in a more systematic I'm working
+in a system identification setting which
+
+ align:start position:0%
+in a system identification setting which
+ 
+
+ align:start position:0%
+in a system identification setting which
+really I will explain later related to
+
+ align:start position:0%
+really I will explain later related to
+ 
+
+ align:start position:0%
+really I will explain later related to
+the more strength of the robot so this
+
+ align:start position:0%
+the more strength of the robot so this
+ 
+
+ align:start position:0%
+the more strength of the robot so this
+is one of the works which has occupied
+
+ align:start position:0%
+is one of the works which has occupied
+ 
+
+ align:start position:0%
+is one of the works which has occupied
+nine last year and it is related to
+
+ align:start position:0%
+nine last year and it is related to
+ 
+
+ align:start position:0%
+nine last year and it is related to
+large-scale learning so when if we
+
+ align:start position:0%
+large-scale learning so when if we
+ 
+
+ align:start position:0%
+large-scale learning so when if we
+consider that we may have a very large n
+
+ align:start position:0%
+consider that we may have a very large n
+ 
+
+ align:start position:0%
+consider that we may have a very large n
+which is the number of examples we have
+
+ align:start position:0%
+which is the number of examples we have
+ 
+
+ align:start position:0%
+which is the number of examples we have
+access to and in the setting of kernel
+
+ align:start position:0%
+access to and in the setting of kernel
+ 
+
+ align:start position:0%
+access to and in the setting of kernel
+methods we may have to store a huge
+
+ align:start position:0%
+methods we may have to store a huge
+ 
+
+ align:start position:0%
+methods we may have to store a huge
+matrix the matrix K which is n by n
+
+ align:start position:0%
+matrix the matrix K which is n by n
+ 
+
+ align:start position:0%
+matrix the matrix K which is n by n
+which could be simply impossible to
+
+ align:start position:0%
+which could be simply impossible to
+ 
+
+ align:start position:0%
+which could be simply impossible to
+store
+
+ align:start position:0%
+store
+ 
+
+ align:start position:0%
+store
+so there are randomized methods like the
+
+ align:start position:0%
+so there are randomized methods like the
+ 
+
+ align:start position:0%
+so there are randomized methods like the
+Nystrom method which enable to compute a
+
+ align:start position:0%
+Nystrom method which enable to compute a
+ 
+
+ align:start position:0%
+Nystrom method which enable to compute a
+low-rank approximation of the kernel
+
+ align:start position:0%
+low-rank approximation of the kernel
+ 
+
+ align:start position:0%
+low-rank approximation of the kernel
+matrix by drawing by simply by drawing a
+
+ align:start position:0%
+matrix by drawing by simply by drawing a
+ 
+
+ align:start position:0%
+matrix by drawing by simply by drawing a
+few points and at random few samples and
+
+ align:start position:0%
+few points and at random few samples and
+ 
+
+ align:start position:0%
+few points and at random few samples and
+at random and building the matrix K and
+
+ align:start position:0%
+at random and building the matrix K and
+ 
+
+ align:start position:0%
+at random and building the matrix K and
+M which is much smaller because I missed
+
+ align:start position:0%
+M which is much smaller because I missed
+ 
+
+ align:start position:0%
+M which is much smaller because I missed
+much smaller than n and this is a
+
+ align:start position:0%
+much smaller than n and this is a
+ 
+
+ align:start position:0%
+much smaller than n and this is a
+well-known method in in machine learning
+
+ align:start position:0%
+well-known method in in machine learning
+ 
+
+ align:start position:0%
+well-known method in in machine learning
+but we try to see it from a different
+
+ align:start position:0%
+but we try to see it from a different
+ 
+
+ align:start position:0%
+but we try to see it from a different
+point of view than usual
+
+ align:start position:0%
+point of view than usual
+ 
+
+ align:start position:0%
+point of view than usual
+usually this is seen just from a
+
+ align:start position:0%
+usually this is seen just from a
+ 
+
+ align:start position:0%
+usually this is seen just from a
+computational point of view in order to
+
+ align:start position:0%
+computational point of view in order to
+ 
+
+ align:start position:0%
+computational point of view in order to
+fit difficult problem inside limited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+considers with limited capabilities
+
+ align:start position:0%
+considers with limited capabilities
+ 
+
+ align:start position:0%
+considers with limited capabilities
+while we
+
+ align:start position:0%
+while we
+ 
+
+ align:start position:0%
+while we
+proposed to cidney some approximation as
+
+ align:start position:0%
+proposed to cidney some approximation as
+ 
+
+ align:start position:0%
+proposed to cidney some approximation as
+regularization opera creation itself the
+
+ align:start position:0%
+regularization opera creation itself the
+ 
+
+ align:start position:0%
+regularization opera creation itself the
+usual way to in which the national
+
+ align:start position:0%
+usual way to in which the national
+ 
+
+ align:start position:0%
+usual way to in which the national
+method is applied for instance with the
+
+ align:start position:0%
+method is applied for instance with the
+ 
+
+ align:start position:0%
+method is applied for instance with the
+kernel regularized least squares the
+
+ align:start position:0%
+kernel regularized least squares the
+ 
+
+ align:start position:0%
+kernel regularized least squares the
+parameter M so the number of examples we
+
+ align:start position:0%
+parameter M so the number of examples we
+ 
+
+ align:start position:0%
+parameter M so the number of examples we
+are taking at random is usually taking
+
+ align:start position:0%
+are taking at random is usually taking
+ 
+
+ align:start position:0%
+are taking at random is usually taking
+as big as large as possible in order to
+
+ align:start position:0%
+as big as large as possible in order to
+ 
+
+ align:start position:0%
+as big as large as possible in order to
+just to fit in fit the memory of the
+
+ align:start position:0%
+just to fit in fit the memory of the
+ 
+
+ align:start position:0%
+just to fit in fit the memory of the
+available machines while actually after
+
+ align:start position:0%
+available machines while actually after
+ 
+
+ align:start position:0%
+available machines while actually after
+choosing a large m it is also necessary
+
+ align:start position:0%
+choosing a large m it is also necessary
+ 
+
+ align:start position:0%
+choosing a large m it is also necessary
+to regularize with Tikhonov
+
+ align:start position:0%
+to regularize with Tikhonov
+ 
+
+ align:start position:0%
+to regularize with Tikhonov
+regularization for instance and this
+
+ align:start position:0%
+regularization for instance and this
+ 
+
+ align:start position:0%
+regularization for instance and this
+sounds a bit like a waste of time and
+
+ align:start position:0%
+sounds a bit like a waste of time and
+ 
+
+ align:start position:0%
+sounds a bit like a waste of time and
+memory because actually what
+
+ align:start position:0%
+memory because actually what
+ 
+
+ align:start position:0%
+memory because actually what
+regularization roughly speaking does is
+
+ align:start position:0%
+regularization roughly speaking does is
+ 
+
+ align:start position:0%
+regularization roughly speaking does is
+to discard the irrelevant eigen
+
+ align:start position:0%
+to discard the irrelevant eigen
+ 
+
+ align:start position:0%
+to discard the irrelevant eigen
+components of the kernel matrix so we
+
+ align:start position:0%
+components of the kernel matrix so we
+ 
+
+ align:start position:0%
+components of the kernel matrix so we
+can do we observe that we can do this by
+
+ align:start position:0%
+can do we observe that we can do this by
+ 
+
+ align:start position:0%
+can do we observe that we can do this by
+just less random examples and so having
+
+ align:start position:0%
+just less random examples and so having
+ 
+
+ align:start position:0%
+just less random examples and so having
+a smaller model which can be computed
+
+ align:start position:0%
+a smaller model which can be computed
+ 
+
+ align:start position:0%
+a smaller model which can be computed
+more efficiently and without having to
+
+ align:start position:0%
+more efficiently and without having to
+ 
+
+ align:start position:0%
+more efficiently and without having to
+trigger eyes again later
+
+ align:start position:0%
+trigger eyes again later
+ 
+
+ align:start position:0%
+trigger eyes again later
+so M the number of the examples which
+
+ align:start position:0%
+so M the number of the examples which
+ 
+
+ align:start position:0%
+so M the number of the examples which
+are used controls both the
+
+ align:start position:0%
+are used controls both the
+ 
+
+ align:start position:0%
+are used controls both the
+regularization and the computational
+
+ align:start position:0%
+regularization and the computational
+ 
+
+ align:start position:0%
+regularization and the computational
+complexity of our algorithm this is very
+
+ align:start position:0%
+complexity of our algorithm this is very
+ 
+
+ align:start position:0%
+complexity of our algorithm this is very
+useful in in a robotic setting in which
+
+ align:start position:0%
+useful in in a robotic setting in which
+ 
+
+ align:start position:0%
+useful in in a robotic setting in which
+we have to deal with lots of data as
+
+ align:start position:0%
+we have to deal with lots of data as
+ 
+
+ align:start position:0%
+we have to deal with lots of data as
+regards the incremental object
+
+ align:start position:0%
+regards the incremental object
+ 
+
+ align:start position:0%
+regards the incremental object
+recognition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tasks this is a another work project I'm
+
+ align:start position:0%
+tasks this is a another work project I'm
+ 
+
+ align:start position:0%
+tasks this is a another work project I'm
+working on and imagine that the robot
+
+ align:start position:0%
+working on and imagine that the robot
+ 
+
+ align:start position:0%
+working on and imagine that the robot
+has to work in an unknown environment
+
+ align:start position:0%
+has to work in an unknown environment
+ 
+
+ align:start position:0%
+has to work in an unknown environment
+and it is presented novel objects on the
+
+ align:start position:0%
+and it is presented novel objects on the
+ 
+
+ align:start position:0%
+and it is presented novel objects on the
+fly and it has to update its object
+
+ align:start position:0%
+fly and it has to update its object
+ 
+
+ align:start position:0%
+fly and it has to update its object
+recognition model in an efficient way
+
+ align:start position:0%
+recognition model in an efficient way
+ 
+
+ align:start position:0%
+recognition model in an efficient way
+without retraining from scratch every
+
+ align:start position:0%
+without retraining from scratch every
+ 
+
+ align:start position:0%
+without retraining from scratch every
+time a new object arrives so this can be
+
+ align:start position:0%
+time a new object arrives so this can be
+ 
+
+ align:start position:0%
+time a new object arrives so this can be
+done easily by a slight association of
+
+ align:start position:0%
+done easily by a slight association of
+ 
+
+ align:start position:0%
+done easily by a slight association of
+regular right of the regularized list
+
+ align:start position:0%
+regular right of the regularized list
+ 
+
+ align:start position:0%
+regular right of the regularized list
+algorithm and properly waiting it an
+
+ align:start position:0%
+algorithm and properly waiting it an
+ 
+
+ align:start position:0%
+algorithm and properly waiting it an
+open question is how to change the
+
+ align:start position:0%
+open question is how to change the
+ 
+
+ align:start position:0%
+open question is how to change the
+regularization as n grows because we
+
+ align:start position:0%
+regularization as n grows because we
+ 
+
+ align:start position:0%
+regularization as n grows because we
+didn't find yet a way to efficiently
+
+ align:start position:0%
+didn't find yet a way to efficiently
+ 
+
+ align:start position:0%
+didn't find yet a way to efficiently
+update the regularization parameter in
+
+ align:start position:0%
+update the regularization parameter in
+ 
+
+ align:start position:0%
+update the regularization parameter in
+this case so we are still working on
+
+ align:start position:0%
+this case so we are still working on
+ 
+
+ align:start position:0%
+this case so we are still working on
+this the last project I'll talk about is
+
+ align:start position:0%
+this the last project I'll talk about is
+ 
+
+ align:start position:0%
+this the last project I'll talk about is
+more related to physics and motion so we
+
+ align:start position:0%
+more related to physics and motion so we
+ 
+
+ align:start position:0%
+more related to physics and motion so we
+need we have an arbitrary limb of the
+
+ align:start position:0%
+need we have an arbitrary limb of the
+ 
+
+ align:start position:0%
+need we have an arbitrary limb of the
+robot twisting the arm and our task is
+
+ align:start position:0%
+robot twisting the arm and our task is
+ 
+
+ align:start position:0%
+robot twisting the arm and our task is
+to learn a model we can provide as an
+
+ align:start position:0%
+to learn a model we can provide as an
+ 
+
+ align:start position:0%
+to learn a model we can provide as an
+inverse dynamics model so it can predict
+
+ align:start position:0%
+inverse dynamics model so it can predict
+ 
+
+ align:start position:0%
+inverse dynamics model so it can predict
+the inner forces of the armor during
+
+ align:start position:0%
+the inner forces of the armor during
+ 
+
+ align:start position:0%
+the inner forces of the armor during
+motion this is useful for instance in
+
+ align:start position:0%
+motion this is useful for instance in
+ 
+
+ align:start position:0%
+motion this is useful for instance in
+contact detective setting so when the
+
+ align:start position:0%
+contact detective setting so when the
+ 
+
+ align:start position:0%
+contact detective setting so when the
+sensor readings are different from the
+
+ align:start position:0%
+sensor readings are different from the
+ 
+
+ align:start position:0%
+sensor readings are different from the
+predicted one that means that there may
+
+ align:start position:0%
+predicted one that means that there may
+ 
+
+ align:start position:0%
+predicted one that means that there may
+be a contact or for external force a
+
+ align:start position:0%
+be a contact or for external force a
+ 
+
+ align:start position:0%
+be a contact or for external force a
+semester or for example for the
+
+ align:start position:0%
+semester or for example for the
+ 
+
+ align:start position:0%
+semester or for example for the
+identification of the mass of a
+
+ align:start position:0%
+identification of the mass of a
+ 
+
+ align:start position:0%
+identification of the mass of a
+manipulator dog so we had some
+
+ align:start position:0%
+manipulator dog so we had some
+ 
+
+ align:start position:0%
+manipulator dog so we had some
+challenges / Purdy's project we have to
+
+ align:start position:0%
+challenges / Purdy's project we have to
+ 
+
+ align:start position:0%
+challenges / Purdy's project we have to
+devise a model which could be
+
+ align:start position:0%
+devise a model which could be
+ 
+
+ align:start position:0%
+devise a model which could be
+interpretable so in which the rigid body
+
+ align:start position:0%
+interpretable so in which the rigid body
+ 
+
+ align:start position:0%
+interpretable so in which the rigid body
+dynamics
+
+ align:start position:0%
+dynamics
+ 
+
+ align:start position:0%
+dynamics
+a parameter would be understandable and
+
+ align:start position:0%
+a parameter would be understandable and
+ 
+
+ align:start position:0%
+a parameter would be understandable and
+intelligible for control purposes and we
+
+ align:start position:0%
+intelligible for control purposes and we
+ 
+
+ align:start position:0%
+intelligible for control purposes and we
+wanted this model to be more accurate
+
+ align:start position:0%
+wanted this model to be more accurate
+ 
+
+ align:start position:0%
+wanted this model to be more accurate
+than standard multi-body dynamic frigid
+
+ align:start position:0%
+than standard multi-body dynamic frigid
+ 
+
+ align:start position:0%
+than standard multi-body dynamic frigid
+for the dynamic model you know and also
+
+ align:start position:0%
+for the dynamic model you know and also
+ 
+
+ align:start position:0%
+for the dynamic model you know and also
+we wanted it to adapt to changing
+
+ align:start position:0%
+we wanted it to adapt to changing
+ 
+
+ align:start position:0%
+we wanted it to adapt to changing
+conditions throughout time for instance
+
+ align:start position:0%
+conditions throughout time for instance
+ 
+
+ align:start position:0%
+conditions throughout time for instance
+during the operation of the robot after
+
+ align:start position:0%
+during the operation of the robot after
+ 
+
+ align:start position:0%
+during the operation of the robot after
+one hour the changes in temperature that
+
+ align:start position:0%
+one hour the changes in temperature that
+ 
+
+ align:start position:0%
+one hour the changes in temperature that
+determine change also in the dynamic
+
+ align:start position:0%
+determine change also in the dynamic
+ 
+
+ align:start position:0%
+determine change also in the dynamic
+properties of the the mechanical
+
+ align:start position:0%
+properties of the the mechanical
+ 
+
+ align:start position:0%
+properties of the the mechanical
+properties of the arm and we want to
+
+ align:start position:0%
+properties of the arm and we want to
+ 
+
+ align:start position:0%
+properties of the arm and we want to
+accommodate for this in an in an
+
+ align:start position:0%
+accommodate for this in an in an
+ 
+
+ align:start position:0%
+accommodate for this in an in an
+incremental way so this is what we did
+
+ align:start position:0%
+incremental way so this is what we did
+ 
+
+ align:start position:0%
+incremental way so this is what we did
+we implemented the semi parametric model
+
+ align:start position:0%
+we implemented the semi parametric model
+ 
+
+ align:start position:0%
+we implemented the semi parametric model
+which the first part with test priority
+
+ align:start position:0%
+which the first part with test priority
+ 
+
+ align:start position:0%
+which the first part with test priority
+is a simple incremental parametric model
+
+ align:start position:0%
+is a simple incremental parametric model
+ 
+
+ align:start position:0%
+is a simple incremental parametric model
+and then we used random features for
+
+ align:start position:0%
+and then we used random features for
+ 
+
+ align:start position:0%
+and then we used random features for
+building nonparametric incremental model
+
+ align:start position:0%
+building nonparametric incremental model
+ 
+
+ align:start position:0%
+building nonparametric incremental model
+which can be updated in an efficient way
+
+ align:start position:0%
+which can be updated in an efficient way
+ 
+
+ align:start position:0%
+which can be updated in an efficient way
+and we turn with the several firm that
+
+ align:start position:0%
+and we turn with the several firm that
+ 
+
+ align:start position:0%
+and we turn with the several firm that
+destiny parametric model works as well
+
+ align:start position:0%
+destiny parametric model works as well
+ 
+
+ align:start position:0%
+destiny parametric model works as well
+as the nonparametric one but it started
+
+ align:start position:0%
+as the nonparametric one but it started
+ 
+
+ align:start position:0%
+as the nonparametric one but it started
+to converge because it has and in each
+
+ align:start position:0%
+to converge because it has and in each
+ 
+
+ align:start position:0%
+to converge because it has and in each
+other knowledge about the 50 top and it
+
+ align:start position:0%
+other knowledge about the 50 top and it
+ 
+
+ align:start position:0%
+other knowledge about the 50 top and it
+is also better than the fully parametric
+
+ align:start position:0%
+is also better than the fully parametric
+ 
+
+ align:start position:0%
+is also better than the fully parametric
+one because it was two models a pre
+
+ align:start position:0%
+one because it was two models a pre
+ 
+
+ align:start position:0%
+one because it was two models a pre
+temple dynamical effect due to the
+
+ align:start position:0%
+temple dynamical effect due to the
+ 
+
+ align:start position:0%
+temple dynamical effect due to the
+flexibility of the bodies and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and dynamic effect which are usually not
+
+ align:start position:0%
+and dynamic effect which are usually not
+ 
+
+ align:start position:0%
+and dynamic effect which are usually not
+modeled by okay another thing I'm doing
+
+ align:start position:0%
+modeled by okay another thing I'm doing
+ 
+
+ align:start position:0%
+modeled by okay another thing I'm doing
+is maintaining the grand unified
+
+ align:start position:0%
+is maintaining the grand unified
+ 
+
+ align:start position:0%
+is maintaining the grand unified
+rigorously first library which is a
+
+ align:start position:0%
+rigorously first library which is a
+ 
+
+ align:start position:0%
+rigorously first library which is a
+library for regularized least squares it
+
+ align:start position:0%
+library for regularized least squares it
+ 
+
+ align:start position:0%
+library for regularized least squares it
+supports a large scale data sheet it was
+
+ align:start position:0%
+supports a large scale data sheet it was
+ 
+
+ align:start position:0%
+supports a large scale data sheet it was
+developed in joint between MIT and IIT
+
+ align:start position:0%
+developed in joint between MIT and IIT
+ 
+
+ align:start position:0%
+developed in joint between MIT and IIT
+some years ago and by others and it has
+
+ align:start position:0%
+some years ago and by others and it has
+ 
+
+ align:start position:0%
+some years ago and by others and it has
+a MATLAB and a C++ interface you want to
+
+ align:start position:0%
+a MATLAB and a C++ interface you want to
+ 
+
+ align:start position:0%
+a MATLAB and a C++ interface you want to
+have a look at how these methods work I
+
+ align:start position:0%
+have a look at how these methods work I
+ 
+
+ align:start position:0%
+have a look at how these methods work I
+suggest you to try our tutorials which
+
+ align:start position:0%
+suggest you to try our tutorials which
+ 
+
+ align:start position:0%
+suggest you to try our tutorials which
+are available on github I'm Julia and I
+
+ align:start position:0%
+are available on github I'm Julia and I
+ 
+
+ align:start position:0%
+are available on github I'm Julia and I
+work on the iCub robot with my
+
+ align:start position:0%
+work on the iCub robot with my
+ 
+
+ align:start position:0%
+work on the iCub robot with my
+colleagues especially on vision and in
+
+ align:start position:0%
+colleagues especially on vision and in
+ 
+
+ align:start position:0%
+colleagues especially on vision and in
+particular on visual recognition I work
+
+ align:start position:0%
+particular on visual recognition I work
+ 
+
+ align:start position:0%
+particular on visual recognition I work
+under the supervision of learning so
+
+ align:start position:0%
+under the supervision of learning so
+ 
+
+ align:start position:0%
+under the supervision of learning so
+Natalia and the Lawrence Rose asked who
+
+ align:start position:0%
+Natalia and the Lawrence Rose asked who
+ 
+
+ align:start position:0%
+Natalia and the Lawrence Rose asked who
+both will be here for a few days in the
+
+ align:start position:0%
+both will be here for a few days in the
+ 
+
+ align:start position:0%
+both will be here for a few days in the
+following weeks and the work that I'm
+
+ align:start position:0%
+following weeks and the work that I'm
+ 
+
+ align:start position:0%
+following weeks and the work that I'm
+going to present has been done in
+
+ align:start position:0%
+going to present has been done in
+ 
+
+ align:start position:0%
+going to present has been done in
+collaboration with catalog and also
+
+ align:start position:0%
+collaboration with catalog and also
+ 
+
+ align:start position:0%
+collaboration with catalog and also
+Francesca Dona from the University of
+
+ align:start position:0%
+Francesca Dona from the University of
+ 
+
+ align:start position:0%
+Francesca Dona from the University of
+Geneva so in the last couple of years
+
+ align:start position:0%
+Geneva so in the last couple of years
+ 
+
+ align:start position:0%
+Geneva so in the last couple of years
+computer vision methods based on deep
+
+ align:start position:0%
+computer vision methods based on deep
+ 
+
+ align:start position:0%
+computer vision methods based on deep
+convolutional neural networks have
+
+ align:start position:0%
+convolutional neural networks have
+ 
+
+ align:start position:0%
+convolutional neural networks have
+achieved the remarkable performance in
+
+ align:start position:0%
+achieved the remarkable performance in
+ 
+
+ align:start position:0%
+achieved the remarkable performance in
+tasks such as large-scale image
+
+ align:start position:0%
+tasks such as large-scale image
+ 
+
+ align:start position:0%
+tasks such as large-scale image
+classification and retrieval and the
+
+ align:start position:0%
+classification and retrieval and the
+ 
+
+ align:start position:0%
+classification and retrieval and the
+extreme success of these methods is
+
+ align:start position:0%
+extreme success of these methods is
+ 
+
+ align:start position:0%
+extreme success of these methods is
+mainly due to the increasing
+
+ align:start position:0%
+mainly due to the increasing
+ 
+
+ align:start position:0%
+mainly due to the increasing
+availability of always larger data sets
+
+ align:start position:0%
+availability of always larger data sets
+ 
+
+ align:start position:0%
+availability of always larger data sets
+and in particular I'm referring to the
+
+ align:start position:0%
+and in particular I'm referring to the
+ 
+
+ align:start position:0%
+and in particular I'm referring to the
+image not one which is composed by
+
+ align:start position:0%
+image not one which is composed by
+ 
+
+ align:start position:0%
+image not one which is composed by
+millions of examples labelled into
+
+ align:start position:0%
+millions of examples labelled into
+ 
+
+ align:start position:0%
+millions of examples labelled into
+thousands of categories through
+
+ align:start position:0%
+thousands of categories through
+ 
+
+ align:start position:0%
+thousands of categories through
+crowdsourcing methods such as the Amazon
+
+ align:start position:0%
+crowdsourcing methods such as the Amazon
+ 
+
+ align:start position:0%
+crowdsourcing methods such as the Amazon
+Turk and in particular the increased
+
+ align:start position:0%
+Turk and in particular the increased
+ 
+
+ align:start position:0%
+Turk and in particular the increased
+data availability together with the
+
+ align:start position:0%
+data availability together with the
+ 
+
+ align:start position:0%
+data availability together with the
+increased computational power has
+
+ align:start position:0%
+increased computational power has
+ 
+
+ align:start position:0%
+increased computational power has
+allowed to Train deep networks
+
+ align:start position:0%
+allowed to Train deep networks
+ 
+
+ align:start position:0%
+allowed to Train deep networks
+characterized by
+
+ align:start position:0%
+characterized by
+ 
+
+ align:start position:0%
+characterized by
+Souths parameters in a supervised way
+
+ align:start position:0%
+Souths parameters in a supervised way
+ 
+
+ align:start position:0%
+Souths parameters in a supervised way
+from the image up to the final label
+
+ align:start position:0%
+from the image up to the final label
+ 
+
+ align:start position:0%
+from the image up to the final label
+through the backpropagation algorithm
+
+ align:start position:0%
+through the backpropagation algorithm
+ 
+
+ align:start position:0%
+through the backpropagation algorithm
+and this has allowed to mark
+
+ align:start position:0%
+and this has allowed to mark
+ 
+
+ align:start position:0%
+and this has allowed to mark
+breakthrough in particular in 2012 when
+
+ align:start position:0%
+breakthrough in particular in 2012 when
+ 
+
+ align:start position:0%
+breakthrough in particular in 2012 when
+Alex Krzyzewski proposed for the first
+
+ align:start position:0%
+Alex Krzyzewski proposed for the first
+ 
+
+ align:start position:0%
+Alex Krzyzewski proposed for the first
+time kind of a network of this kind
+
+ align:start position:0%
+time kind of a network of this kind
+ 
+
+ align:start position:0%
+time kind of a network of this kind
+trained on image not dataset and
+
+ align:start position:0%
+trained on image not dataset and
+ 
+
+ align:start position:0%
+trained on image not dataset and
+definitely warned the image not
+
+ align:start position:0%
+definitely warned the image not
+ 
+
+ align:start position:0%
+definitely warned the image not
+large-scale in the visual recognition
+
+ align:start position:0%
+large-scale in the visual recognition
+ 
+
+ align:start position:0%
+large-scale in the visual recognition
+challenge in this way and the trend has
+
+ align:start position:0%
+challenge in this way and the trend has
+ 
+
+ align:start position:0%
+challenge in this way and the trend has
+been confirmed in the following years
+
+ align:start position:0%
+been confirmed in the following years
+ 
+
+ align:start position:0%
+been confirmed in the following years
+so that nowadays problems such as
+
+ align:start position:0%
+so that nowadays problems such as
+ 
+
+ align:start position:0%
+so that nowadays problems such as
+large-scale image classification or
+
+ align:start position:0%
+large-scale image classification or
+ 
+
+ align:start position:0%
+large-scale image classification or
+detection are usually tackled following
+
+ align:start position:0%
+detection are usually tackled following
+ 
+
+ align:start position:0%
+detection are usually tackled following
+this deep learning approach and not only
+
+ align:start position:0%
+this deep learning approach and not only
+ 
+
+ align:start position:0%
+this deep learning approach and not only
+it has been also demonstrated at least
+
+ align:start position:0%
+it has been also demonstrated at least
+ 
+
+ align:start position:0%
+it has been also demonstrated at least
+empirically I'm sorry that maybe this is
+
+ align:start position:0%
+empirically I'm sorry that maybe this is
+ 
+
+ align:start position:0%
+empirically I'm sorry that maybe this is
+not particularly clear but that this is
+
+ align:start position:0%
+not particularly clear but that this is
+ 
+
+ align:start position:0%
+not particularly clear but that this is
+decretive key Network models of networks
+
+ align:start position:0%
+decretive key Network models of networks
+ 
+
+ align:start position:0%
+decretive key Network models of networks
+of this kind trained on large datasets
+
+ align:start position:0%
+of this kind trained on large datasets
+ 
+
+ align:start position:0%
+of this kind trained on large datasets
+such as the image not one do provide
+
+ align:start position:0%
+such as the image not one do provide
+ 
+
+ align:start position:0%
+such as the image not one do provide
+also very good general and powerful
+
+ align:start position:0%
+also very good general and powerful
+ 
+
+ align:start position:0%
+also very good general and powerful
+image descriptors to be applied also on
+
+ align:start position:0%
+image descriptors to be applied also on
+ 
+
+ align:start position:0%
+image descriptors to be applied also on
+other tasks and datasets in particular
+
+ align:start position:0%
+other tasks and datasets in particular
+ 
+
+ align:start position:0%
+other tasks and datasets in particular
+it is possible to use the convolutional
+
+ align:start position:0%
+it is possible to use the convolutional
+ 
+
+ align:start position:0%
+it is possible to use the convolutional
+neural network trained on image not
+
+ align:start position:0%
+neural network trained on image not
+ 
+
+ align:start position:0%
+neural network trained on image not
+dataset feed it with images and using it
+
+ align:start position:0%
+dataset feed it with images and using it
+ 
+
+ align:start position:0%
+dataset feed it with images and using it
+as a black box extracting the vectorial
+
+ align:start position:0%
+as a black box extracting the vectorial
+ 
+
+ align:start position:0%
+as a black box extracting the vectorial
+representation of the incoming images as
+
+ align:start position:0%
+representation of the incoming images as
+ 
+
+ align:start position:0%
+representation of the incoming images as
+the output of one of the intermediate
+
+ align:start position:0%
+the output of one of the intermediate
+ 
+
+ align:start position:0%
+the output of one of the intermediate
+layers or even better it is possible to
+
+ align:start position:0%
+layers or even better it is possible to
+ 
+
+ align:start position:0%
+layers or even better it is possible to
+start from a network model trained on
+
+ align:start position:0%
+start from a network model trained on
+ 
+
+ align:start position:0%
+start from a network model trained on
+the image metadata set and fine-tune its
+
+ align:start position:0%
+the image metadata set and fine-tune its
+ 
+
+ align:start position:0%
+the image metadata set and fine-tune its
+parameters on a new data set for a new
+
+ align:start position:0%
+parameters on a new data set for a new
+ 
+
+ align:start position:0%
+parameters on a new data set for a new
+task and achieving and surpassing the
+
+ align:start position:0%
+task and achieving and surpassing the
+ 
+
+ align:start position:0%
+task and achieving and surpassing the
+state of the art for example also on the
+
+ align:start position:0%
+state of the art for example also on the
+ 
+
+ align:start position:0%
+state of the art for example also on the
+Pascal data set and other
+
+ align:start position:0%
+Pascal data set and other
+ 
+
+ align:start position:0%
+Pascal data set and other
+tasks following this approach so it is
+
+ align:start position:0%
+tasks following this approach so it is
+ 
+
+ align:start position:0%
+tasks following this approach so it is
+natural to ask at this point why instead
+
+ align:start position:0%
+natural to ask at this point why instead
+ 
+
+ align:start position:0%
+natural to ask at this point why instead
+in robotics providing robots with robust
+
+ align:start position:0%
+in robotics providing robots with robust
+ 
+
+ align:start position:0%
+in robotics providing robots with robust
+and accurate visual recognition
+
+ align:start position:0%
+and accurate visual recognition
+ 
+
+ align:start position:0%
+and accurate visual recognition
+capabilities in the real world is still
+
+ align:start position:0%
+capabilities in the real world is still
+ 
+
+ align:start position:0%
+capabilities in the real world is still
+one of the greatest challenges that
+
+ align:start position:0%
+one of the greatest challenges that
+ 
+
+ align:start position:0%
+one of the greatest challenges that
+prevents use of autonomous agents for
+
+ align:start position:0%
+prevents use of autonomous agents for
+ 
+
+ align:start position:0%
+prevents use of autonomous agents for
+concrete applications and actually this
+
+ align:start position:0%
+concrete applications and actually this
+ 
+
+ align:start position:0%
+concrete applications and actually this
+is a problem that is not only related to
+
+ align:start position:0%
+is a problem that is not only related to
+ 
+
+ align:start position:0%
+is a problem that is not only related to
+the iCub platform but it is also a
+
+ align:start position:0%
+the iCub platform but it is also a
+ 
+
+ align:start position:0%
+the iCub platform but it is also a
+limiting factor that effects the
+
+ align:start position:0%
+limiting factor that effects the
+ 
+
+ align:start position:0%
+limiting factor that effects the
+performance of latest robotics platforms
+
+ align:start position:0%
+performance of latest robotics platforms
+ 
+
+ align:start position:0%
+performance of latest robotics platforms
+such as the ones that have been
+
+ align:start position:0%
+such as the ones that have been
+ 
+
+ align:start position:0%
+such as the ones that have been
+participating for example - the DARPA
+
+ align:start position:0%
+participating for example - the DARPA
+ 
+
+ align:start position:0%
+participating for example - the DARPA
+Robotics Challenge indeed as you can see
+
+ align:start position:0%
+Robotics Challenge indeed as you can see
+ 
+
+ align:start position:0%
+Robotics Challenge indeed as you can see
+here robots are still either highly
+
+ align:start position:0%
+here robots are still either highly
+ 
+
+ align:start position:0%
+here robots are still either highly
+teleoperated or complex methods - for
+
+ align:start position:0%
+teleoperated or complex methods - for
+ 
+
+ align:start position:0%
+teleoperated or complex methods - for
+example map the 3d structure of the
+
+ align:start position:0%
+example map the 3d structure of the
+ 
+
+ align:start position:0%
+example map the 3d structure of the
+environment and label it a priori must
+
+ align:start position:0%
+environment and label it a priori must
+ 
+
+ align:start position:0%
+environment and label it a priori must
+be implemented in order to enable
+
+ align:start position:0%
+be implemented in order to enable
+ 
+
+ align:start position:0%
+be implemented in order to enable
+autonomous agents to act in very
+
+ align:start position:0%
+autonomous agents to act in very
+ 
+
+ align:start position:0%
+autonomous agents to act in very
+controlled environment so we decided to
+
+ align:start position:0%
+controlled environment so we decided to
+ 
+
+ align:start position:0%
+controlled environment so we decided to
+focus on very simple settings we are in
+
+ align:start position:0%
+focus on very simple settings we are in
+ 
+
+ align:start position:0%
+focus on very simple settings we are in
+principle computer vision methods as the
+
+ align:start position:0%
+principle computer vision methods as the
+ 
+
+ align:start position:0%
+principle computer vision methods as the
+ones that have been describing you
+
+ align:start position:0%
+ones that have been describing you
+ 
+
+ align:start position:0%
+ones that have been describing you
+should be mmm at least well should
+
+ align:start position:0%
+should be mmm at least well should
+ 
+
+ align:start position:0%
+should be mmm at least well should
+provide very good performances because
+
+ align:start position:0%
+provide very good performances because
+ 
+
+ align:start position:0%
+provide very good performances because
+here the setting is pretty simple and we
+
+ align:start position:0%
+here the setting is pretty simple and we
+ 
+
+ align:start position:0%
+here the setting is pretty simple and we
+try to evaluate the performance of these
+
+ align:start position:0%
+try to evaluate the performance of these
+ 
+
+ align:start position:0%
+try to evaluate the performance of these
+deep learning methods in these settings
+
+ align:start position:0%
+deep learning methods in these settings
+ 
+
+ align:start position:0%
+deep learning methods in these settings
+here you can see the robot that one
+
+ align:start position:0%
+here you can see the robot that one
+ 
+
+ align:start position:0%
+here you can see the robot that one
+standing in front of a table there is a
+
+ align:start position:0%
+standing in front of a table there is a
+ 
+
+ align:start position:0%
+standing in front of a table there is a
+human which gives verbal instruction to
+
+ align:start position:0%
+human which gives verbal instruction to
+ 
+
+ align:start position:0%
+human which gives verbal instruction to
+the robot and also for example in
+
+ align:start position:0%
+the robot and also for example in
+ 
+
+ align:start position:0%
+the robot and also for example in
+Caze the label of the object to be
+
+ align:start position:0%
+Caze the label of the object to be
+ 
+
+ align:start position:0%
+Caze the label of the object to be
+either learned or recognized and the
+
+ align:start position:0%
+either learned or recognized and the
+ 
+
+ align:start position:0%
+either learned or recognized and the
+robot can focus his attention on
+
+ align:start position:0%
+robot can focus his attention on
+ 
+
+ align:start position:0%
+robot can focus his attention on
+potential objects through bottom-up the
+
+ align:start position:0%
+potential objects through bottom-up the
+ 
+
+ align:start position:0%
+potential objects through bottom-up the
+segmentation techniques for example in
+
+ align:start position:0%
+segmentation techniques for example in
+ 
+
+ align:start position:0%
+segmentation techniques for example in
+this case color or other saliency based
+
+ align:start position:0%
+this case color or other saliency based
+ 
+
+ align:start position:0%
+this case color or other saliency based
+segmentation methods not going into the
+
+ align:start position:0%
+segmentation methods not going into the
+ 
+
+ align:start position:0%
+segmentation methods not going into the
+detail of this setting because you will
+
+ align:start position:0%
+detail of this setting because you will
+ 
+
+ align:start position:0%
+detail of this setting because you will
+see a demo after my talk of this another
+
+ align:start position:0%
+see a demo after my talk of this another
+ 
+
+ align:start position:0%
+see a demo after my talk of this another
+setting that we are considering is
+
+ align:start position:0%
+setting that we are considering is
+ 
+
+ align:start position:0%
+setting that we are considering is
+similar to the previous one but this
+
+ align:start position:0%
+similar to the previous one but this
+ 
+
+ align:start position:0%
+similar to the previous one but this
+time there is a human standing in front
+
+ align:start position:0%
+time there is a human standing in front
+ 
+
+ align:start position:0%
+time there is a human standing in front
+of the robot and there is no table and
+
+ align:start position:0%
+of the robot and there is no table and
+ 
+
+ align:start position:0%
+of the robot and there is no table and
+the human he's holding the objects in
+
+ align:start position:0%
+the human he's holding the objects in
+ 
+
+ align:start position:0%
+the human he's holding the objects in
+his hands and showing one object after
+
+ align:start position:0%
+his hands and showing one object after
+ 
+
+ align:start position:0%
+his hands and showing one object after
+the other to the robot providing the
+
+ align:start position:0%
+the other to the robot providing the
+ 
+
+ align:start position:0%
+the other to the robot providing the
+verbal annotation for that objects the
+
+ align:start position:0%
+verbal annotation for that objects the
+ 
+
+ align:start position:0%
+verbal annotation for that objects the
+robot in this way for example here can
+
+ align:start position:0%
+robot in this way for example here can
+ 
+
+ align:start position:0%
+robot in this way for example here can
+exploit a motion detection techniques in
+
+ align:start position:0%
+exploit a motion detection techniques in
+ 
+
+ align:start position:0%
+exploit a motion detection techniques in
+order to localize the object in the
+
+ align:start position:0%
+order to localize the object in the
+ 
+
+ align:start position:0%
+order to localize the object in the
+visual field and focus on it
+
+ align:start position:0%
+visual field and focus on it
+ 
+
+ align:start position:0%
+visual field and focus on it
+Grob attracts the objector continuously
+
+ align:start position:0%
+Grob attracts the objector continuously
+ 
+
+ align:start position:0%
+Grob attracts the objector continuously
+acquiring in this way crop the frames
+
+ align:start position:0%
+acquiring in this way crop the frames
+ 
+
+ align:start position:0%
+acquiring in this way crop the frames
+around the object that are the training
+
+ align:start position:0%
+around the object that are the training
+ 
+
+ align:start position:0%
+around the object that are the training
+examples that will be used to learn the
+
+ align:start position:0%
+examples that will be used to learn the
+ 
+
+ align:start position:0%
+examples that will be used to learn the
+objects appearance so in general this is
+
+ align:start position:0%
+objects appearance so in general this is
+ 
+
+ align:start position:0%
+objects appearance so in general this is
+the recognition pipeline that is
+
+ align:start position:0%
+the recognition pipeline that is
+ 
+
+ align:start position:0%
+the recognition pipeline that is
+implemented to perform both the two
+
+ align:start position:0%
+implemented to perform both the two
+ 
+
+ align:start position:0%
+implemented to perform both the two
+behaviors that have been showing you as
+
+ align:start position:0%
+behaviors that have been showing you as
+ 
+
+ align:start position:0%
+behaviors that have been showing you as
+you can see the input is the image the
+
+ align:start position:0%
+you can see the input is the image the
+ 
+
+ align:start position:0%
+you can see the input is the image the
+stream of images from one of the two
+
+ align:start position:0%
+stream of images from one of the two
+ 
+
+ align:start position:0%
+stream of images from one of the two
+cameras then there is the verbal
+
+ align:start position:0%
+cameras then there is the verbal
+ 
+
+ align:start position:0%
+cameras then there is the verbal
+supervision of the teacher then there
+
+ align:start position:0%
+supervision of the teacher then there
+ 
+
+ align:start position:0%
+supervision of the teacher then there
+are segmentation techniques in order to
+
+ align:start position:0%
+are segmentation techniques in order to
+ 
+
+ align:start position:0%
+are segmentation techniques in order to
+crop region of interest from the
+
+ align:start position:0%
+crop region of interest from the
+ 
+
+ align:start position:0%
+crop region of interest from the
+incoming frame and feed this crop to a
+
+ align:start position:0%
+incoming frame and feed this crop to a
+ 
+
+ align:start position:0%
+incoming frame and feed this crop to a
+convolutional neural network in this
+
+ align:start position:0%
+convolutional neural network in this
+ 
+
+ align:start position:0%
+convolutional neural network in this
+case we are using the famous preserve
+
+ align:start position:0%
+case we are using the famous preserve
+ 
+
+ align:start position:0%
+case we are using the famous preserve
+scheme model then we encode each
+
+ align:start position:0%
+scheme model then we encode each
+ 
+
+ align:start position:0%
+scheme model then we encode each
+incoming craft in a vector as the output
+
+ align:start position:0%
+incoming craft in a vector as the output
+ 
+
+ align:start position:0%
+incoming craft in a vector as the output
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of the latest layers of the network and
+
+ align:start position:0%
+of the latest layers of the network and
+ 
+
+ align:start position:0%
+of the latest layers of the network and
+we feed all these vectors to a linear
+
+ align:start position:0%
+we feed all these vectors to a linear
+ 
+
+ align:start position:0%
+we feed all these vectors to a linear
+classifier which is linear because in
+
+ align:start position:0%
+classifier which is linear because in
+ 
+
+ align:start position:0%
+classifier which is linear because in
+principle the representation that we are
+
+ align:start position:0%
+principle the representation that we are
+ 
+
+ align:start position:0%
+principle the representation that we are
+extracting is good enough for the
+
+ align:start position:0%
+extracting is good enough for the
+ 
+
+ align:start position:0%
+extracting is good enough for the
+discrimination that we want to perform
+
+ align:start position:0%
+discrimination that we want to perform
+ 
+
+ align:start position:0%
+discrimination that we want to perform
+and so the classifier uses these
+
+ align:start position:0%
+and so the classifier uses these
+ 
+
+ align:start position:0%
+and so the classifier uses these
+incoming vectors either other examples
+
+ align:start position:0%
+incoming vectors either other examples
+ 
+
+ align:start position:0%
+incoming vectors either other examples
+to be easier as examples for the change
+
+ align:start position:0%
+to be easier as examples for the change
+ 
+
+ align:start position:0%
+to be easier as examples for the change
+that or assigns to each vector the
+
+ align:start position:0%
+that or assigns to each vector the
+ 
+
+ align:start position:0%
+that or assigns to each vector the
+prediction the yeah the prediction label
+
+ align:start position:0%
+prediction the yeah the prediction label
+ 
+
+ align:start position:0%
+prediction the yeah the prediction label
+and the output is an Instagram with the
+
+ align:start position:0%
+and the output is an Instagram with the
+ 
+
+ align:start position:0%
+and the output is an Instagram with the
+probabilities of all the classes and the
+
+ align:start position:0%
+probabilities of all the classes and the
+ 
+
+ align:start position:0%
+probabilities of all the classes and the
+final outcome is the the one with the
+
+ align:start position:0%
+final outcome is the the one with the
+ 
+
+ align:start position:0%
+final outcome is the the one with the
+highest probability and the histogram is
+
+ align:start position:0%
+highest probability and the histogram is
+ 
+
+ align:start position:0%
+highest probability and the histogram is
+updated in real time so this pie pan can
+
+ align:start position:0%
+updated in real time so this pie pan can
+ 
+
+ align:start position:0%
+updated in real time so this pie pan can
+be used either for one or the other
+
+ align:start position:0%
+be used either for one or the other
+ 
+
+ align:start position:0%
+be used either for one or the other
+settings that have been described you so
+
+ align:start position:0%
+settings that have been described you so
+ 
+
+ align:start position:0%
+settings that have been described you so
+in particular we started from trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to list some requirements that according
+
+ align:start position:0%
+to list some requirements that according
+ 
+
+ align:start position:0%
+to list some requirements that according
+to us are fundamental in order to
+
+ align:start position:0%
+to us are fundamental in order to
+ 
+
+ align:start position:0%
+to us are fundamental in order to
+implement a sort of ideal robotic visual
+
+ align:start position:0%
+implement a sort of ideal robotic visual
+ 
+
+ align:start position:0%
+implement a sort of ideal robotic visual
+recognition system and these
+
+ align:start position:0%
+recognition system and these
+ 
+
+ align:start position:0%
+recognition system and these
+requirements are usually not considered
+
+ align:start position:0%
+requirements are usually not considered
+ 
+
+ align:start position:0%
+requirements are usually not considered
+by typical computer vision methods as
+
+ align:start position:0%
+by typical computer vision methods as
+ 
+
+ align:start position:0%
+by typical computer vision methods as
+the ones that have been described you
+
+ align:start position:0%
+the ones that have been described you
+ 
+
+ align:start position:0%
+the ones that have been described you
+but are the same fundamental if we want
+
+ align:start position:0%
+but are the same fundamental if we want
+ 
+
+ align:start position:0%
+but are the same fundamental if we want
+to achieve human-level performances in
+
+ align:start position:0%
+to achieve human-level performances in
+ 
+
+ align:start position:0%
+to achieve human-level performances in
+the settings that I've been showing you
+
+ align:start position:0%
+the settings that I've been showing you
+ 
+
+ align:start position:0%
+the settings that I've been showing you
+for example first of all the system
+
+ align:start position:0%
+for example first of all the system
+ 
+
+ align:start position:0%
+for example first of all the system
+should be as you have seen as much as
+
+ align:start position:0%
+should be as you have seen as much as
+ 
+
+ align:start position:0%
+should be as you have seen as much as
+possible self supervised meaning that
+
+ align:start position:0%
+possible self supervised meaning that
+ 
+
+ align:start position:0%
+possible self supervised meaning that
+there must be techniques in order to
+
+ align:start position:0%
+there must be techniques in order to
+ 
+
+ align:start position:0%
+there must be techniques in order to
+focus the robot's attention on the
+
+ align:start position:0%
+focus the robot's attention on the
+ 
+
+ align:start position:0%
+focus the robot's attention on the
+object of interest and isolate them from
+
+ align:start position:0%
+object of interest and isolate them from
+ 
+
+ align:start position:0%
+object of interest and isolate them from
+the visual field then hopefully we would
+
+ align:start position:0%
+the visual field then hopefully we would
+ 
+
+ align:start position:0%
+the visual field then hopefully we would
+like to come out with a system that is
+
+ align:start position:0%
+like to come out with a system that is
+ 
+
+ align:start position:0%
+like to come out with a system that is
+reliable and robust to the variations in
+
+ align:start position:0%
+reliable and robust to the variations in
+ 
+
+ align:start position:0%
+reliable and robust to the variations in
+the environment and also in the objects
+
+ align:start position:0%
+the environment and also in the objects
+ 
+
+ align:start position:0%
+the environment and also in the objects
+appearance then also as we are in the
+
+ align:start position:0%
+appearance then also as we are in the
+ 
+
+ align:start position:0%
+appearance then also as we are in the
+real
+
+ align:start position:0%
+real
+ 
+
+ align:start position:0%
+real
+world we would like a system able to
+
+ align:start position:0%
+world we would like a system able to
+ 
+
+ align:start position:0%
+world we would like a system able to
+exploit the contextual information that
+
+ align:start position:0%
+exploit the contextual information that
+ 
+
+ align:start position:0%
+exploit the contextual information that
+is available for example the fact that
+
+ align:start position:0%
+is available for example the fact that
+ 
+
+ align:start position:0%
+is available for example the fact that
+we are actually dealing with videos so
+
+ align:start position:0%
+we are actually dealing with videos so
+ 
+
+ align:start position:0%
+we are actually dealing with videos so
+the frames are temporally correlated and
+
+ align:start position:0%
+the frames are temporally correlated and
+ 
+
+ align:start position:0%
+the frames are temporally correlated and
+we are not dealing with images in the
+
+ align:start position:0%
+we are not dealing with images in the
+ 
+
+ align:start position:0%
+we are not dealing with images in the
+wild does the image nutcase and finally
+
+ align:start position:0%
+wild does the image nutcase and finally
+ 
+
+ align:start position:0%
+wild does the image nutcase and finally
+as a fellow was mentioning we would like
+
+ align:start position:0%
+as a fellow was mentioning we would like
+ 
+
+ align:start position:0%
+as a fellow was mentioning we would like
+to have a system that is able to learn
+
+ align:start position:0%
+to have a system that is able to learn
+ 
+
+ align:start position:0%
+to have a system that is able to learn
+incrementally to build always richer
+
+ align:start position:0%
+incrementally to build always richer
+ 
+
+ align:start position:0%
+incrementally to build always richer
+models of the object through time so we
+
+ align:start position:0%
+models of the object through time so we
+ 
+
+ align:start position:0%
+models of the object through time so we
+decided to evaluate this recognition
+
+ align:start position:0%
+decided to evaluate this recognition
+ 
+
+ align:start position:0%
+decided to evaluate this recognition
+pipeline according to the criteria that
+
+ align:start position:0%
+pipeline according to the criteria that
+ 
+
+ align:start position:0%
+pipeline according to the criteria that
+have been described in you and in order
+
+ align:start position:0%
+have been described in you and in order
+ 
+
+ align:start position:0%
+have been described in you and in order
+to provide reproducibility to our study
+
+ align:start position:0%
+to provide reproducibility to our study
+ 
+
+ align:start position:0%
+to provide reproducibility to our study
+we decided to acquire a data set on
+
+ align:start position:0%
+we decided to acquire a data set on
+ 
+
+ align:start position:0%
+we decided to acquire a data set on
+which to perform our analysis however we
+
+ align:start position:0%
+which to perform our analysis however we
+ 
+
+ align:start position:0%
+which to perform our analysis however we
+would like also to be confident enough
+
+ align:start position:0%
+would like also to be confident enough
+ 
+
+ align:start position:0%
+would like also to be confident enough
+that the result that we obtain on our
+
+ align:start position:0%
+that the result that we obtain on our
+ 
+
+ align:start position:0%
+that the result that we obtain on our
+benchmark will hold also in real usage
+
+ align:start position:0%
+benchmark will hold also in real usage
+ 
+
+ align:start position:0%
+benchmark will hold also in real usage
+of our system and this is the reason why
+
+ align:start position:0%
+of our system and this is the reason why
+ 
+
+ align:start position:0%
+of our system and this is the reason why
+we decided to acquire our dataset in the
+
+ align:start position:0%
+we decided to acquire our dataset in the
+ 
+
+ align:start position:0%
+we decided to acquire our dataset in the
+same application setting where the robot
+
+ align:start position:0%
+same application setting where the robot
+ 
+
+ align:start position:0%
+same application setting where the robot
+usually operates so this is the iCub
+
+ align:start position:0%
+usually operates so this is the iCub
+ 
+
+ align:start position:0%
+usually operates so this is the iCub
+word 28 data set that I acquired the
+
+ align:start position:0%
+word 28 data set that I acquired the
+ 
+
+ align:start position:0%
+word 28 data set that I acquired the
+last year as you can see is composed by
+
+ align:start position:0%
+last year as you can see is composed by
+ 
+
+ align:start position:0%
+last year as you can see is composed by
+28 objects divided into seven categories
+
+ align:start position:0%
+28 objects divided into seven categories
+ 
+
+ align:start position:0%
+28 objects divided into seven categories
+and four instances per category and I
+
+ align:start position:0%
+and four instances per category and I
+ 
+
+ align:start position:0%
+and four instances per category and I
+acquired it for four different days in
+
+ align:start position:0%
+acquired it for four different days in
+ 
+
+ align:start position:0%
+acquired it for four different days in
+order to test also incremental learning
+
+ align:start position:0%
+order to test also incremental learning
+ 
+
+ align:start position:0%
+order to test also incremental learning
+capabilities the data set is available
+
+ align:start position:0%
+capabilities the data set is available
+ 
+
+ align:start position:0%
+capabilities the data set is available
+on the i-80 website and you can also use
+
+ align:start position:0%
+on the i-80 website and you can also use
+ 
+
+ align:start position:0%
+on the i-80 website and you can also use
+it for example for the project of trust
+
+ align:start position:0%
+it for example for the project of trust
+ 
+
+ align:start position:0%
+it for example for the project of trust
+five if you are interested and this is
+
+ align:start position:0%
+five if you are interested and this is
+ 
+
+ align:start position:0%
+five if you are interested and this is
+an example of the kind of videos that I
+
+ align:start position:0%
+an example of the kind of videos that I
+ 
+
+ align:start position:0%
+an example of the kind of videos that I
+acquired them considering one of the 28
+
+ align:start position:0%
+acquired them considering one of the 28
+ 
+
+ align:start position:0%
+acquired them considering one of the 28
+objects there are four videos for the
+
+ align:start position:0%
+objects there are four videos for the
+ 
+
+ align:start position:0%
+objects there are four videos for the
+Train
+
+ align:start position:0%
+Train
+ 
+
+ align:start position:0%
+Train
+four for the test acquiring four
+
+ align:start position:0%
+four for the test acquiring four
+ 
+
+ align:start position:0%
+four for the test acquiring four
+different conditions the object is
+
+ align:start position:0%
+different conditions the object is
+ 
+
+ align:start position:0%
+different conditions the object is
+undergoing random transformations mainly
+
+ align:start position:0%
+undergoing random transformations mainly
+ 
+
+ align:start position:0%
+undergoing random transformations mainly
+limited to 3d rotations and as you can
+
+ align:start position:0%
+limited to 3d rotations and as you can
+ 
+
+ align:start position:0%
+limited to 3d rotations and as you can
+see the difference between the
+
+ align:start position:0%
+see the difference between the
+ 
+
+ align:start position:0%
+see the difference between the
+dey's is mainly limited to the fact that
+
+ align:start position:0%
+dey's is mainly limited to the fact that
+ 
+
+ align:start position:0%
+dey's is mainly limited to the fact that
+we are just changing the conditions in
+
+ align:start position:0%
+we are just changing the conditions in
+ 
+
+ align:start position:0%
+we are just changing the conditions in
+the environment for example the
+
+ align:start position:0%
+the environment for example the
+ 
+
+ align:start position:0%
+the environment for example the
+background or the lighting conditions
+
+ align:start position:0%
+background or the lighting conditions
+ 
+
+ align:start position:0%
+background or the lighting conditions
+and we acquired eight videos for each of
+
+ align:start position:0%
+and we acquired eight videos for each of
+ 
+
+ align:start position:0%
+and we acquired eight videos for each of
+the 28 objects that I'll show you so
+
+ align:start position:0%
+the 28 objects that I'll show you so
+ 
+
+ align:start position:0%
+the 28 objects that I'll show you so
+first of all we try to find a measure as
+
+ align:start position:0%
+first of all we try to find a measure as
+ 
+
+ align:start position:0%
+first of all we try to find a measure as
+I was saying before to quantify the
+
+ align:start position:0%
+I was saying before to quantify the
+ 
+
+ align:start position:0%
+I was saying before to quantify the
+confidence with which we can expect that
+
+ align:start position:0%
+confidence with which we can expect that
+ 
+
+ align:start position:0%
+confidence with which we can expect that
+the results and the performance that we
+
+ align:start position:0%
+the results and the performance that we
+ 
+
+ align:start position:0%
+the results and the performance that we
+observe on this benchmark will also hold
+
+ align:start position:0%
+observe on this benchmark will also hold
+ 
+
+ align:start position:0%
+observe on this benchmark will also hold
+the in the real usage of the system and
+
+ align:start position:0%
+the in the real usage of the system and
+ 
+
+ align:start position:0%
+the in the real usage of the system and
+to do this we first of all we focused
+
+ align:start position:0%
+to do this we first of all we focused
+ 
+
+ align:start position:0%
+to do this we first of all we focused
+only on object identification for the
+
+ align:start position:0%
+only on object identification for the
+ 
+
+ align:start position:0%
+only on object identification for the
+moment so the task is to discriminate
+
+ align:start position:0%
+moment so the task is to discriminate
+ 
+
+ align:start position:0%
+moment so the task is to discriminate
+the specific instances of objects among
+
+ align:start position:0%
+the specific instances of objects among
+ 
+
+ align:start position:0%
+the specific instances of objects among
+the pool of 28 and we decided to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimate for an increasing number of
+
+ align:start position:0%
+estimate for an increasing number of
+ 
+
+ align:start position:0%
+estimate for an increasing number of
+objects to be discriminated from to 228
+
+ align:start position:0%
+objects to be discriminated from to 228
+ 
+
+ align:start position:0%
+objects to be discriminated from to 228
+the empirical probability distribution
+
+ align:start position:0%
+the empirical probability distribution
+ 
+
+ align:start position:0%
+the empirical probability distribution
+of the identification of curacy that we
+
+ align:start position:0%
+of the identification of curacy that we
+ 
+
+ align:start position:0%
+of the identification of curacy that we
+can observe statistically for fix the
+
+ align:start position:0%
+can observe statistically for fix the
+ 
+
+ align:start position:0%
+can observe statistically for fix the
+number of objects that is depicted here
+
+ align:start position:0%
+number of objects that is depicted here
+ 
+
+ align:start position:0%
+number of objects that is depicted here
+in the form of box plots and also we
+
+ align:start position:0%
+in the form of box plots and also we
+ 
+
+ align:start position:0%
+in the form of box plots and also we
+estimated for each fixed number of
+
+ align:start position:0%
+estimated for each fixed number of
+ 
+
+ align:start position:0%
+estimated for each fixed number of
+objects to be discriminated the minimum
+
+ align:start position:0%
+objects to be discriminated the minimum
+ 
+
+ align:start position:0%
+objects to be discriminated the minimum
+accuracy that we can expect to achieve
+
+ align:start position:0%
+accuracy that we can expect to achieve
+ 
+
+ align:start position:0%
+accuracy that we can expect to achieve
+within increasing confidence levels and
+
+ align:start position:0%
+within increasing confidence levels and
+ 
+
+ align:start position:0%
+within increasing confidence levels and
+this is a sort of datasheet the idea is
+
+ align:start position:0%
+this is a sort of datasheet the idea is
+ 
+
+ align:start position:0%
+this is a sort of datasheet the idea is
+to provide is to provide an idea to an
+
+ align:start position:0%
+to provide is to provide an idea to an
+ 
+
+ align:start position:0%
+to provide is to provide an idea to an
+apathetic
+
+ align:start position:0%
+apathetic
+ 
+
+ align:start position:0%
+apathetic
+user of the robot of the identification
+
+ align:start position:0%
+user of the robot of the identification
+ 
+
+ align:start position:0%
+user of the robot of the identification
+accuracy that can be expected
+
+ align:start position:0%
+accuracy that can be expected
+ 
+
+ align:start position:0%
+accuracy that can be expected
+given a certain pool of objects to be
+
+ align:start position:0%
+given a certain pool of objects to be
+ 
+
+ align:start position:0%
+given a certain pool of objects to be
+discriminated so the second point that
+
+ align:start position:0%
+discriminated so the second point that
+ 
+
+ align:start position:0%
+discriminated so the second point that
+i'm briefly strategies the fact that we
+
+ align:start position:0%
+i'm briefly strategies the fact that we
+ 
+
+ align:start position:0%
+i'm briefly strategies the fact that we
+investigated the effect of having more
+
+ align:start position:0%
+investigated the effect of having more
+ 
+
+ align:start position:0%
+investigated the effect of having more
+or less precise segments
+
+ align:start position:0%
+or less precise segments
+ 
+
+ align:start position:0%
+or less precise segments
+in the image so we evaluated the task of
+
+ align:start position:0%
+in the image so we evaluated the task of
+ 
+
+ align:start position:0%
+in the image so we evaluated the task of
+identifying the 28 objects with
+
+ align:start position:0%
+identifying the 28 objects with
+ 
+
+ align:start position:0%
+identifying the 28 objects with
+different levels of segmentation
+
+ align:start position:0%
+different levels of segmentation
+ 
+
+ align:start position:0%
+different levels of segmentation
+starting from the world image up to a
+
+ align:start position:0%
+starting from the world image up to a
+ 
+
+ align:start position:0%
+starting from the world image up to a
+very precise manual segmentation of the
+
+ align:start position:0%
+very precise manual segmentation of the
+ 
+
+ align:start position:0%
+very precise manual segmentation of the
+objects it can be seen that indeed even
+
+ align:start position:0%
+objects it can be seen that indeed even
+ 
+
+ align:start position:0%
+objects it can be seen that indeed even
+if in principle these convolutional
+
+ align:start position:0%
+if in principle these convolutional
+ 
+
+ align:start position:0%
+if in principle these convolutional
+networks are trained to classify objects
+
+ align:start position:0%
+networks are trained to classify objects
+ 
+
+ align:start position:0%
+networks are trained to classify objects
+in the world images it is in the image
+
+ align:start position:0%
+in the world images it is in the image
+ 
+
+ align:start position:0%
+in the world images it is in the image
+not data set it is still true that in
+
+ align:start position:0%
+not data set it is still true that in
+ 
+
+ align:start position:0%
+not data set it is still true that in
+our case we observed that there is a
+
+ align:start position:0%
+our case we observed that there is a
+ 
+
+ align:start position:0%
+our case we observed that there is a
+still a large benefit from having a
+
+ align:start position:0%
+still a large benefit from having a
+ 
+
+ align:start position:0%
+still a large benefit from having a
+fine-grained segmentation so probably
+
+ align:start position:0%
+fine-grained segmentation so probably
+ 
+
+ align:start position:0%
+fine-grained segmentation so probably
+the network is not able to completely
+
+ align:start position:0%
+the network is not able to completely
+ 
+
+ align:start position:0%
+the network is not able to completely
+discard the non relevant information
+
+ align:start position:0%
+discard the non relevant information
+ 
+
+ align:start position:0%
+discard the non relevant information
+that is in the background so this is a
+
+ align:start position:0%
+that is in the background so this is a
+ 
+
+ align:start position:0%
+that is in the background so this is a
+possible interesting directions of
+
+ align:start position:0%
+possible interesting directions of
+ 
+
+ align:start position:0%
+possible interesting directions of
+research and finally the last point the
+
+ align:start position:0%
+research and finally the last point the
+ 
+
+ align:start position:0%
+research and finally the last point the
+time decided to tell you I will skip on
+
+ align:start position:0%
+time decided to tell you I will skip on
+ 
+
+ align:start position:0%
+time decided to tell you I will skip on
+the incremental part because it's still
+
+ align:start position:0%
+the incremental part because it's still
+ 
+
+ align:start position:0%
+the incremental part because it's still
+an ongoing work that I'm doing with our
+
+ align:start position:0%
+an ongoing work that I'm doing with our
+ 
+
+ align:start position:0%
+an ongoing work that I'm doing with our
+file is about the exploitation of the
+
+ align:start position:0%
+file is about the exploitation of the
+ 
+
+ align:start position:0%
+file is about the exploitation of the
+temporal contextual information here you
+
+ align:start position:0%
+temporal contextual information here you
+ 
+
+ align:start position:0%
+temporal contextual information here you
+can see the same kind of plot that I
+
+ align:start position:0%
+can see the same kind of plot that I
+ 
+
+ align:start position:0%
+can see the same kind of plot that I
+showed you before so the task is object
+
+ align:start position:0%
+showed you before so the task is object
+ 
+
+ align:start position:0%
+showed you before so the task is object
+identification increasing number of
+
+ align:start position:0%
+identification increasing number of
+ 
+
+ align:start position:0%
+identification increasing number of
+objects and the dot black line represent
+
+ align:start position:0%
+objects and the dot black line represent
+ 
+
+ align:start position:0%
+objects and the dot black line represent
+the accuracy that you obtain if you
+
+ align:start position:0%
+the accuracy that you obtain if you
+ 
+
+ align:start position:0%
+the accuracy that you obtain if you
+consider as you are asking before the
+
+ align:start position:0%
+consider as you are asking before the
+ 
+
+ align:start position:0%
+consider as you are asking before the
+classification of each frame
+
+ align:start position:0%
+classification of each frame
+ 
+
+ align:start position:0%
+classification of each frame
+independently so you can see that in
+
+ align:start position:0%
+independently so you can see that in
+ 
+
+ align:start position:0%
+independently so you can see that in
+this case the accuracy that you get is
+
+ align:start position:0%
+this case the accuracy that you get is
+ 
+
+ align:start position:0%
+this case the accuracy that you get is
+pretty low considering that we have to
+
+ align:start position:0%
+pretty low considering that we have to
+ 
+
+ align:start position:0%
+pretty low considering that we have to
+describe discriminate between only 28
+
+ align:start position:0%
+describe discriminate between only 28
+ 
+
+ align:start position:0%
+describe discriminate between only 28
+objects however it is also true that as
+
+ align:start position:0%
+objects however it is also true that as
+ 
+
+ align:start position:0%
+objects however it is also true that as
+soon as you start considering instead of
+
+ align:start position:0%
+soon as you start considering instead of
+ 
+
+ align:start position:0%
+soon as you start considering instead of
+the prediction given looking only at the
+
+ align:start position:0%
+the prediction given looking only at the
+ 
+
+ align:start position:0%
+the prediction given looking only at the
+current frame the most frequent
+
+ align:start position:0%
+current frame the most frequent
+ 
+
+ align:start position:0%
+current frame the most frequent
+prediction occurred in a temporal window
+
+ align:start position:0%
+prediction occurred in a temporal window
+ 
+
+ align:start position:0%
+prediction occurred in a temporal window
+so in the previous let's say 50 frames
+
+ align:start position:0%
+so in the previous let's say 50 frames
+ 
+
+ align:start position:0%
+so in the previous let's say 50 frames
+you can boost your recognition of curacy
+
+ align:start position:0%
+you can boost your recognition of curacy
+ 
+
+ align:start position:0%
+you can boost your recognition of curacy
+a lot a
+
+ align:start position:0%
+a lot a
+ 
+
+ align:start position:0%
+a lot a
+you can see here from green to red
+
+ align:start position:0%
+you can see here from green to red
+ 
+
+ align:start position:0%
+you can see here from green to red
+increasing the length of the temporal
+
+ align:start position:0%
+increasing the length of the temporal
+ 
+
+ align:start position:0%
+increasing the length of the temporal
+window increases the recognition
+
+ align:start position:0%
+window increases the recognition
+ 
+
+ align:start position:0%
+window increases the recognition
+accuracy that you got this is a very
+
+ align:start position:0%
+accuracy that you got this is a very
+ 
+
+ align:start position:0%
+accuracy that you got this is a very
+simple approach but it is showing that
+
+ align:start position:0%
+simple approach but it is showing that
+ 
+
+ align:start position:0%
+simple approach but it is showing that
+actually it is relevant the fact that
+
+ align:start position:0%
+actually it is relevant the fact that
+ 
+
+ align:start position:0%
+actually it is relevant the fact that
+you are actually dealing with videos
+
+ align:start position:0%
+you are actually dealing with videos
+ 
+
+ align:start position:0%
+you are actually dealing with videos
+instead of images in the wild and it is
+
+ align:start position:0%
+instead of images in the wild and it is
+ 
+
+ align:start position:0%
+instead of images in the wild and it is
+in other directions of research so
+
+ align:start position:0%
+in other directions of research so
+ 
+
+ align:start position:0%
+in other directions of research so
+finally in the last part of my talk I
+
+ align:start position:0%
+finally in the last part of my talk I
+ 
+
+ align:start position:0%
+finally in the last part of my talk I
+would like to tell you about the work
+
+ align:start position:0%
+would like to tell you about the work
+ 
+
+ align:start position:0%
+would like to tell you about the work
+that I'm actually doing now which is
+
+ align:start position:0%
+that I'm actually doing now which is
+ 
+
+ align:start position:0%
+that I'm actually doing now which is
+concerning about most object
+
+ align:start position:0%
+concerning about most object
+ 
+
+ align:start position:0%
+concerning about most object
+categorization tasks instead of
+
+ align:start position:0%
+categorization tasks instead of
+ 
+
+ align:start position:0%
+categorization tasks instead of
+identification and this is the reason
+
+ align:start position:0%
+identification and this is the reason
+ 
+
+ align:start position:0%
+identification and this is the reason
+why we decided to acquire a new dataset
+
+ align:start position:0%
+why we decided to acquire a new dataset
+ 
+
+ align:start position:0%
+why we decided to acquire a new dataset
+which is larger than the previous ones
+
+ align:start position:0%
+which is larger than the previous ones
+ 
+
+ align:start position:0%
+which is larger than the previous ones
+because it is composed not only by more
+
+ align:start position:0%
+because it is composed not only by more
+ 
+
+ align:start position:0%
+because it is composed not only by more
+categories but in particular by more
+
+ align:start position:0%
+categories but in particular by more
+ 
+
+ align:start position:0%
+categories but in particular by more
+instances per category in order to be
+
+ align:start position:0%
+instances per category in order to be
+ 
+
+ align:start position:0%
+instances per category in order to be
+able to perform categorization
+
+ align:start position:0%
+able to perform categorization
+ 
+
+ align:start position:0%
+able to perform categorization
+experiments as I told you here you can
+
+ align:start position:0%
+experiments as I told you here you can
+ 
+
+ align:start position:0%
+experiments as I told you here you can
+see the categories were with which we
+
+ align:start position:0%
+see the categories were with which we
+ 
+
+ align:start position:0%
+see the categories were with which we
+are starting our 28 divided into seven
+
+ align:start position:0%
+are starting our 28 divided into seven
+ 
+
+ align:start position:0%
+are starting our 28 divided into seven
+macro categories at same but the idea of
+
+ align:start position:0%
+macro categories at same but the idea of
+ 
+
+ align:start position:0%
+macro categories at same but the idea of
+this dataset is to have continuously
+
+ align:start position:0%
+this dataset is to have continuously
+ 
+
+ align:start position:0%
+this dataset is to have continuously
+expandable in time dataset so there is a
+
+ align:start position:0%
+expandable in time dataset so there is a
+ 
+
+ align:start position:0%
+expandable in time dataset so there is a
+an application that we use to acquire
+
+ align:start position:0%
+an application that we use to acquire
+ 
+
+ align:start position:0%
+an application that we use to acquire
+this dataset and the idea is to perform
+
+ align:start position:0%
+this dataset and the idea is to perform
+ 
+
+ align:start position:0%
+this dataset and the idea is to perform
+periodical acquisitions in order to
+
+ align:start position:0%
+periodical acquisitions in order to
+ 
+
+ align:start position:0%
+periodical acquisitions in order to
+incremental and reach the knowledge of
+
+ align:start position:0%
+incremental and reach the knowledge of
+ 
+
+ align:start position:0%
+incremental and reach the knowledge of
+the robot about the objects in the scene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also another important factor regarding
+
+ align:start position:0%
+also another important factor regarding
+ 
+
+ align:start position:0%
+also another important factor regarding
+this dataset is that differently from
+
+ align:start position:0%
+this dataset is that differently from
+ 
+
+ align:start position:0%
+this dataset is that differently from
+the previous one this will be divided
+
+ align:start position:0%
+the previous one this will be divided
+ 
+
+ align:start position:0%
+the previous one this will be divided
+and tagged by nuisance factors and in
+
+ align:start position:0%
+and tagged by nuisance factors and in
+ 
+
+ align:start position:0%
+and tagged by nuisance factors and in
+particular for each object we are
+
+ align:start position:0%
+particular for each object we are
+ 
+
+ align:start position:0%
+particular for each object we are
+acquiring different videos where we
+
+ align:start position:0%
+acquiring different videos where we
+ 
+
+ align:start position:0%
+acquiring different videos where we
+isolate the different transformations
+
+ align:start position:0%
+isolate the different transformations
+ 
+
+ align:start position:0%
+isolate the different transformations
+that the object is undergoing so we have
+
+ align:start position:0%
+that the object is undergoing so we have
+ 
+
+ align:start position:0%
+that the object is undergoing so we have
+a video where the object is just
+
+ align:start position:0%
+a video where the object is just
+ 
+
+ align:start position:0%
+a video where the object is just
+a different scale than it is rotating on
+
+ align:start position:0%
+a different scale than it is rotating on
+ 
+
+ align:start position:0%
+a different scale than it is rotating on
+the plane
+
+ align:start position:0%
+the plane
+ 
+
+ align:start position:0%
+the plane
+outside the plane it is translating and
+
+ align:start position:0%
+outside the plane it is translating and
+ 
+
+ align:start position:0%
+outside the plane it is translating and
+then there is a final video where all of
+
+ align:start position:0%
+then there is a final video where all of
+ 
+
+ align:start position:0%
+then there is a final video where all of
+this transformation occurs
+
+ align:start position:0%
+this transformation occurs
+ 
+
+ align:start position:0%
+this transformation occurs
+simultaneously and finally to acquire
+
+ align:start position:0%
+simultaneously and finally to acquire
+ 
+
+ align:start position:0%
+simultaneously and finally to acquire
+this dataset we decided to use the Deaf
+
+ align:start position:0%
+this dataset we decided to use the Deaf
+ 
+
+ align:start position:0%
+this dataset we decided to use the Deaf
+information so that in the end we
+
+ align:start position:0%
+information so that in the end we
+ 
+
+ align:start position:0%
+information so that in the end we
+acquired both the left and the right two
+
+ align:start position:0%
+acquired both the left and the right two
+ 
+
+ align:start position:0%
+acquired both the left and the right two
+cameras and in principle that this
+
+ align:start position:0%
+cameras and in principle that this
+ 
+
+ align:start position:0%
+cameras and in principle that this
+information could be used to obtain the
+
+ align:start position:0%
+information could be used to obtain the
+ 
+
+ align:start position:0%
+information could be used to obtain the
+3d structure of the objects and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the idea that we used in order to make
+
+ align:start position:0%
+the idea that we used in order to make
+ 
+
+ align:start position:0%
+the idea that we used in order to make
+the robot focusing on the object of
+
+ align:start position:0%
+the robot focusing on the object of
+ 
+
+ align:start position:0%
+the robot focusing on the object of
+interest using disparity this parrot is
+
+ align:start position:0%
+interest using disparity this parrot is
+ 
+
+ align:start position:0%
+interest using disparity this parrot is
+very useful in this case because it
+
+ align:start position:0%
+very useful in this case because it
+ 
+
+ align:start position:0%
+very useful in this case because it
+allows to detect unknown objects just
+
+ align:start position:0%
+allows to detect unknown objects just
+ 
+
+ align:start position:0%
+allows to detect unknown objects just
+given the fact that we know that we want
+
+ align:start position:0%
+given the fact that we know that we want
+ 
+
+ align:start position:0%
+given the fact that we know that we want
+the robot focused on the most on the
+
+ align:start position:0%
+the robot focused on the most on the
+ 
+
+ align:start position:0%
+the robot focused on the most on the
+closest object in the scene so it is a
+
+ align:start position:0%
+closest object in the scene so it is a
+ 
+
+ align:start position:0%
+closest object in the scene so it is a
+very powerful method in order to have
+
+ align:start position:0%
+very powerful method in order to have
+ 
+
+ align:start position:0%
+very powerful method in order to have
+the robot tracking unknown objects with
+
+ align:start position:0%
+the robot tracking unknown objects with
+ 
+
+ align:start position:0%
+the robot tracking unknown objects with
+all different lighting conditions and so
+
+ align:start position:0%
+all different lighting conditions and so
+ 
+
+ align:start position:0%
+all different lighting conditions and so
+on and yeah here you can see this is the
+
+ align:start position:0%
+on and yeah here you can see this is the
+ 
+
+ align:start position:0%
+on and yeah here you can see this is the
+left camera this is the disparity map
+
+ align:start position:0%
+left camera this is the disparity map
+ 
+
+ align:start position:0%
+left camera this is the disparity map
+this is it's a segmentation which
+
+ align:start position:0%
+this is it's a segmentation which
+ 
+
+ align:start position:0%
+this is it's a segmentation which
+provides an approximate region of
+
+ align:start position:0%
+provides an approximate region of
+ 
+
+ align:start position:0%
+provides an approximate region of
+interest around the object and this is
+
+ align:start position:0%
+interest around the object and this is
+ 
+
+ align:start position:0%
+interest around the object and this is
+the final output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I started acquiring the first well it
+
+ align:start position:0%
+so I started acquiring the first well it
+ 
+
+ align:start position:0%
+so I started acquiring the first well it
+should be red but it's not very clear I
+
+ align:start position:0%
+should be red but it's not very clear I
+ 
+
+ align:start position:0%
+should be red but it's not very clear I
+mean I started recording the first five
+
+ align:start position:0%
+mean I started recording the first five
+ 
+
+ align:start position:0%
+mean I started recording the first five
+categories among these 21 listed here
+
+ align:start position:0%
+categories among these 21 listed here
+ 
+
+ align:start position:0%
+categories among these 21 listed here
+which are the squeezer prior the cream
+
+ align:start position:0%
+which are the squeezer prior the cream
+ 
+
+ align:start position:0%
+which are the squeezer prior the cream
+the oven cloth and the bottle for each
+
+ align:start position:0%
+the oven cloth and the bottle for each
+ 
+
+ align:start position:0%
+the oven cloth and the bottle for each
+row you see the ten instances that I
+
+ align:start position:0%
+row you see the ten instances that I
+ 
+
+ align:start position:0%
+row you see the ten instances that I
+collected and the idea is to continue
+
+ align:start position:0%
+collected and the idea is to continue
+ 
+
+ align:start position:0%
+collected and the idea is to continue
+acquiring them when I come back
+
+ align:start position:0%
+acquiring them when I come back
+ 
+
+ align:start position:0%
+acquiring them when I come back
+in Geneva and so here you can see an
+
+ align:start position:0%
+in Geneva and so here you can see an
+ 
+
+ align:start position:0%
+in Geneva and so here you can see an
+example of the five videos actually
+
+ align:start position:0%
+example of the five videos actually
+ 
+
+ align:start position:0%
+example of the five videos actually
+acquired ten videos per object five for
+
+ align:start position:0%
+acquired ten videos per object five for
+ 
+
+ align:start position:0%
+acquired ten videos per object five for
+the training set and five for the test
+
+ align:start position:0%
+the training set and five for the test
+ 
+
+ align:start position:0%
+the training set and five for the test
+set and you can see that in the
+
+ align:start position:0%
+set and you can see that in the
+ 
+
+ align:start position:0%
+set and you can see that in the
+different videos the object is
+
+ align:start position:0%
+different videos the object is
+ 
+
+ align:start position:0%
+different videos the object is
+undergoing different transformations and
+
+ align:start position:0%
+undergoing different transformations and
+ 
+
+ align:start position:0%
+undergoing different transformations and
+this is the final one while this
+
+ align:start position:0%
+this is the final one while this
+ 
+
+ align:start position:0%
+this is the final one while this
+transformation are mixed them oh these
+
+ align:start position:0%
+transformation are mixed them oh these
+ 
+
+ align:start position:0%
+transformation are mixed them oh these
+are the images here are not segmented
+
+ align:start position:0%
+are the images here are not segmented
+ 
+
+ align:start position:0%
+are the images here are not segmented
+yet so you can see the world image but
+
+ align:start position:0%
+yet so you can see the world image but
+ 
+
+ align:start position:0%
+yet so you can see the world image but
+in the end also the information about
+
+ align:start position:0%
+in the end also the information about
+ 
+
+ align:start position:0%
+in the end also the information about
+the segmentation and disparity and so on
+
+ align:start position:0%
+the segmentation and disparity and so on
+ 
+
+ align:start position:0%
+the segmentation and disparity and so on
+will be available and this dataset
+
+ align:start position:0%
+will be available and this dataset
+ 
+
+ align:start position:0%
+will be available and this dataset
+regarding the 50 objects that I acquired
+
+ align:start position:0%
+regarding the 50 objects that I acquired
+ 
+
+ align:start position:0%
+regarding the 50 objects that I acquired
+together with the application that I'm
+
+ align:start position:0%
+together with the application that I'm
+ 
+
+ align:start position:0%
+together with the application that I'm
+using to acquire the dataset are
+
+ align:start position:0%
+using to acquire the dataset are
+ 
+
+ align:start position:0%
+using to acquire the dataset are
+available if you are willing to use them
+
+ align:start position:0%
+available if you are willing to use them
+ 
+
+ align:start position:0%
+available if you are willing to use them
+for the projects in trust five for
+
+ align:start position:0%
+for the projects in trust five for
+ 
+
+ align:start position:0%
+for the projects in trust five for
+example in order to investigate an
+
+ align:start position:0%
+example in order to investigate an
+ 
+
+ align:start position:0%
+example in order to investigate an
+invariant properties of the different
+
+ align:start position:0%
+invariant properties of the different
+ 
+
+ align:start position:0%
+invariant properties of the different
+representations and so that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/EObHWIEKGjA.txt b/EObHWIEKGjA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e6c5247a7120c6ed25e01250559ecd323233728f
--- /dev/null
+++ b/EObHWIEKGjA.txt
@@ -0,0 +1,2496 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, good morning.
+
+So today, we're going to have
+a fairly packed lecture.
+
+We are going to conclude
+with chapter two,
+
+discrete random variables.
+
+And we will be talking
+mostly about
+
+multiple random variables.
+
+And this is also the
+last lecture as far
+
+as quiz one is concerned.
+
+So it's going to cover the
+material until today, and of
+
+course the next recitation
+and tutorial as well.
+
+OK, so we're going to review
+quickly what we introduced at
+
+the end of last lecture, where
+we talked about the joint PMF
+
+of two random variables.
+
+We're going to talk about the
+case of more than two random
+
+variables as well.
+
+We're going to talk about
+the familiar concepts of
+
+conditioning and independence,
+but applied to random
+
+variables instead of events.
+
+We're going to look at the
+expectations once more, talk
+
+about a few properties that they
+have, and then solve a
+
+couple of problems and calculate
+a few things in
+
+somewhat clever ways.
+
+So the first point I want to
+make is that, to a large
+
+extent, whatever is happening
+in our chapter on discrete
+
+random variables is just an
+exercise in notation.
+
+There is stuff and concepts that
+you are already familiar
+
+with-- probabilities,
+probabilities of two things
+
+happening, conditional
+probabilities.
+
+And all that we're doing, to
+some extent, is rewriting
+
+those familiar concepts
+in new notation.
+
+So for example, this
+is the joint PMF
+
+of two random variable.
+
+It gives us, for any pair or
+possible values of those
+
+random variables, the
+probability that that pair
+
+occurs simultaneously.
+
+So it's the probability that
+simultaneously x takes that
+
+value, and y takes
+that other value.
+
+And similarly, we have the
+notion of the conditional PMF,
+
+which is just a list of the --
+condition of -- the various
+
+conditional probabilities
+of interest, conditional
+
+probability that one random
+variable takes this value
+
+given that the other random
+variable takes that value.
+
+Now, a remark about conditional
+probabilities.
+
+Conditional probabilities
+generally are like ordinary
+
+probabilities.
+
+You condition on something
+particular.
+
+So here we condition
+on a particular y.
+
+So think of little y as
+a fixed quantity.
+
+And then look at this
+as a function of x.
+
+So given that y, which we
+condition on, given our new
+
+universe, we're considering the
+various possibilities for
+
+x and the probabilities
+that they have.
+
+Now, the probabilities over
+all x's, of course,
+
+needs to add to 1.
+
+So we should have a relation
+of this kind.
+
+So they're just like ordinary
+probabilities over the
+
+different x's in a universe
+where we are told the value of
+
+the random variable y.
+
+Now, how are these related?
+
+So we call these the marginal,
+these the joint, these the
+
+conditional.
+
+And there are some relations
+between these.
+
+For example, to find the
+marginal from the joint, it's
+
+pretty straightforward.
+
+The probability that x takes a
+particular value is the sum of
+
+the probabilities of all of the
+different ways that this
+
+particular value may occur.
+
+What are the different ways?
+
+Well, it may occur together with
+a certain y, or together
+
+with some other y, or together
+with some other y.
+
+So you look at all the possible
+y's that can go
+
+together with this x, and add
+the probabilities of all of
+
+those pairs for which we get
+this particular value of x.
+
+And then there's a relation
+between that connects these
+
+two probabilities with the
+conditional probability.
+
+And it's this relation.
+
+It's nothing new.
+
+It's just new notation for
+writing what we already know,
+
+that the probability of two
+things happening is the
+
+probability that the first thing
+happens, and then given
+
+that the first thing happens,
+the probability that the
+
+second one happened.
+
+So how do we go from
+one to the other?
+
+Think of A as being the event
+that X takes the value, little
+
+x, and B being the event that
+Y takes the value, little y.
+
+So the joint probability is the
+probability that these two
+
+things happen simultaneously.
+
+It's the probability that X
+takes this value times the
+
+conditional probability that Y
+takes this value, given that X
+
+took that first value.
+
+So it's the familiar
+multiplication rule, but just
+
+transcribed in our
+new notation.
+
+So nothing new so far.
+
+OK, why did we go through this
+exercise and this notation?
+
+It's because in the experiments
+where we're
+
+interested in the real world,
+typically there's going to be
+
+lots of uncertain quantities.
+
+There's going to be multiple
+random variables.
+
+And we want to be able to talk
+about them simultaneously.
+
+Okay.
+
+Why two and not more than two?
+
+How about three random
+variables?
+
+Well, if you understand what's
+going on in this slide, you
+
+should be able to kind of
+automatically generalize this
+
+to the case of multiple
+random variables.
+
+So for example, if we have three
+random variables, X, Y,
+
+and Z, and you see an expression
+like this, it
+
+should be clear what it means.
+
+It's the probability that
+X takes this value and
+
+simultaneously Y takes that
+value and simultaneously Z
+
+takes that value.
+
+I guess that's an uppercase Z
+here, that's a lowercase z.
+
+And if I ask you to find the
+marginal of X, if I tell you
+
+the joint PMF of the three
+random variables and I ask you
+
+for this value, how
+would you find it?
+
+Well, you will try to generalize
+this relation here.
+
+The probability that x occurs
+is the sum of the
+
+probabilities of all events
+that make X to take that
+
+particular value.
+
+So what are all the events?
+
+Well, this particular x can
+happen together with some y
+
+and some z.
+
+We don't care which y and z.
+
+Any y and z will do.
+
+So when we consider all
+possibilities, we need to add
+
+here over all possible values
+of y's and z's.
+
+So consider all triples,
+x, y, z.
+
+Fix x and consider all the
+possibilities for the
+
+remaining variables, y and z,
+add these up, and that gives
+
+you the marginal PMF of X. And
+then there's other things that
+
+you can do.
+
+This is the multiplication
+rule for two events.
+
+We saw back in chapter one that
+there's a multiplication
+
+rule when you talk about
+more than two events.
+
+And you can write a chain of
+conditional probabilities.
+
+We can certainly do the same
+in our new notation.
+
+So let's look at this
+rule up here.
+
+Multiplication rule for three
+random variables,
+
+what does it say?
+
+The probability of three
+things happening
+
+simultaneously, X, Y, Z taking
+specific values, little x,
+
+little y, little z, that
+probability is the probability
+
+that the first thing happens,
+that X takes that value.
+
+Given that X takes that value,
+we multiply it with the
+
+probability that Y takes
+also a certain value.
+
+And now, given that X and Y have
+taken those particular
+
+values, we multiply with a
+conditional probability that
+
+the third thing happens,
+given that the
+
+first two things happen.
+
+So this is just the
+multiplication rule for three
+
+events, which would be
+probability of A intersection
+
+B intersection C equals--
+
+you know the rest
+of the formula.
+
+You just rewrite this formula
+in PMF notation.
+
+Probability of A intersection
+B intersection C is the
+
+probability of A, which
+corresponds to this term,
+
+times the probability of B given
+A, times the probability
+
+of C given A and B.
+
+So what else is there that's
+left from chapter one that we
+
+can or should generalize
+to random variables?
+
+Well, there's the notion
+of independence.
+
+So let's define what
+independence means.
+
+Instead of talking about just
+two random variables, let's go
+
+directly to the case of multiple
+random variables.
+
+When we talked about events,
+things were a little
+
+complicated.
+
+We had a simple definition for
+independence of two events.
+
+Two events are independent if
+the probability of both is
+
+equal to the product of
+the probabilities.
+
+But for three events, it
+was kind of messy.
+
+We needed to write down
+lots of conditions.
+
+For random variables,
+things in some sense
+
+are a little simpler.
+
+We only need to write down one
+formula and take this as the
+
+definition of independence.
+
+Three random variables are
+independent if and only if, by
+
+definition, their joint
+probability mass function
+
+factors out into individual
+probability mass functions.
+
+So the probability that all
+three things happen is the
+
+product of the individual
+probabilities that each one of
+
+these three things
+is happening.
+
+So independence means
+mathematically that you can
+
+just multiply probabilities to
+get to the probability of
+
+several things happening
+simultaneously.
+
+So with three events, we have
+to write a huge number of
+
+equations, of equalities
+that have to hold.
+
+How can it be that with random
+variables we can only manage
+
+with one equality?
+
+Well, the catch is
+that this is not
+
+really just one equality.
+
+We require this to be true for
+every little x, y, and z.
+
+So in some sense, this is a
+bunch of conditions that are
+
+being put on the joint PMF, a
+bunch of conditions that we
+
+need to check.
+
+So this is the mathematical
+definition.
+
+What is the intuitive content
+of this definition?
+
+The intuitive content is
+the same as for events.
+
+Random variables are independent
+if knowing
+
+something about the realized
+values of some of these random
+
+variables does not change our
+beliefs about the likelihood
+
+of various values for the
+remaining random variables.
+
+So independence would translate,
+for example, to a
+
+condition such as the
+conditional PMF of X , given
+
+y, should be equal to the
+marginal PMF of X. What is
+
+this saying?
+
+That you have some original
+beliefs about how likely it is
+
+for X to take this value.
+
+Now, someone comes and
+tells you that Y took
+
+on a certain value.
+
+This causes you, in principle,
+to revise your beliefs.
+
+And your new beliefs will be
+captured by the conditional
+
+PMF, or the conditional
+probabilities.
+
+Independence means that your
+revised beliefs actually will
+
+be the same as your
+original beliefs.
+
+Telling you information about
+the value of Y doesn't change
+
+what you expect for the
+random variable X.
+
+Why didn't we use this
+definition for independence?
+
+Well, because this definition
+only makes sense when this
+
+conditional is well-defined.
+
+And this conditional is only
+well-defined if the events
+
+that Y takes on that particular
+value has positive
+
+probability.
+
+We cannot condition on events
+that have zero probability, so
+
+conditional probabilities are
+only defined for y's that are
+
+likely to occur, that have
+a positive probability.
+
+Now, similarly, with multiple
+random variables, if they're
+
+independent, you would have
+relations such as the
+
+conditional of X, given y and
+z, should be the same as the
+
+marginal of X. What
+is this saying?
+
+Again, that if I tell you the
+values, the realized values of
+
+random variables Y and Z, this
+is not going to change your
+
+beliefs about how likely
+x is to occur.
+
+Whatever you believed in the
+beginning, you're going to
+
+believe the same thing
+afterwards.
+
+So it's important to keep that
+intuition in mind, because
+
+sometimes this way you can tell
+whether random variables
+
+are independent without having
+to do calculations and to
+
+check this formula.
+
+OK, so let's check our concepts
+
+with a simple example.
+
+Let's look at two random
+variables that are discrete,
+
+take values between
+one and for each.
+
+And this is a table that
+gives us the joint PMF.
+
+So it tells us the probability
+that X equals to 2 and Y
+
+equals to 1 happening
+simultaneously.
+
+It's an event that has
+probability 1/20.
+
+Are these two random variables
+independent?
+
+You can try to check a
+condition like this.
+
+But can we tell directly
+from the table?
+
+If I tell you a value of Y,
+could that give you useful
+
+information about X?
+
+Certainly.
+
+If I tell you that Y is equal
+to 1, this tells you that X
+
+must be equal to 2.
+
+But if I tell you that Y was
+equal to 3, this tells you
+
+that, still, X could
+be anything.
+
+So telling you the value of
+Y kind of changes what you
+
+expect or what you consider
+possible for the values of the
+
+other random variable.
+
+So by just inspecting here, we
+can tell that the random
+
+variables are not independent.
+
+Okay.
+
+What's the other concept we
+introduced in chapter one?
+
+We introduced the concept of
+conditional independence.
+
+And conditional independence is
+like ordinary independence
+
+but applied to a conditional
+universe where we're given
+
+some information.
+
+So suppose someone tells you
+that the outcome of the
+
+experiment is such that X is
+less than or equal to 2 and Y
+
+is larger than or equal to 3.
+
+So we are given the information
+that we now live
+
+inside this universe.
+
+So what happens inside
+this universe?
+
+Inside this universe, our random
+variables are going to
+
+have a new joint PMF which is
+conditioned on the event that
+
+we were told that
+it has occurred.
+
+So let A correspond to this
+sort of event here.
+
+And now we're dealing with
+conditional probabilities.
+
+What are those conditional
+probabilities?
+
+We can put them in a table.
+
+So it's a two by two table,
+since we only have two
+
+possible values.
+
+What are they going to be?
+
+Well, these probabilities
+show up in the ratios
+
+1, 2, 2, and 4.
+
+Those ratios have to
+stay the same.
+
+The probabilities need
+to add up to one.
+
+So what should the denominators
+be since these
+
+numbers add up to nine?
+
+These are the conditional
+probabilities.
+
+So this is the conditional
+PMF in this example.
+
+Now, in this conditional
+universe, is x
+
+independent from y?
+
+If I tell you that y takes this
+value, so we live in this
+
+universe, what do you
+know about x?
+
+What you know about x is at this
+value is twice as likely
+
+as that value.
+
+If I condition on y taking this
+value, so we're living
+
+here, what do you
+know about x?
+
+What you know about x is that
+this value is twice as likely
+
+as that value.
+
+So it's the same.
+
+Whether we live here or we live
+there, this x is twice as
+
+likely as that x.
+
+So the conditional PMF in this
+new universe, the conditional
+
+PMF of X given y, in the new
+universe is the same as the
+
+marginal PMF of X, but of course
+in the new universe.
+
+So no matter what y is,
+the conditional
+
+PMF of X is the same.
+
+And that conditional
+PMF is 1/3 and 2/3.
+
+This is the conditional PMF of
+X in the new universe no
+
+matter what y occurs.
+
+So Y does not give us any
+information about X, doesn't
+
+cause us to change our beliefs
+inside this little universe.
+
+And therefore the two random
+variables are independent.
+
+Now, the other way that you
+can verify that we have
+
+independence is to find the
+marginal PMFs of the two
+
+random variables.
+
+The marginal PMF of
+X, you find it by
+
+adding those two terms.
+
+You get 1/3.
+
+Adding those two terms,
+you get 2/3.
+
+Marginal PMF of Y, you find it,
+you add these two terms,
+
+and you get 1/3.
+
+And the marginal PMF of Y
+here is going to be 2/3.
+
+And then you ask the question,
+is the joint the product of
+
+the marginals?
+
+And indeed it is.
+
+This times this gives you 1/9.
+
+This times this gives you 2/9.
+
+So the values in the table with
+the joint PMFs is the
+
+product of the marginal PMFs of
+X and Y in this universe,
+
+so the two random variables are
+
+independent inside this universe.
+
+So we say that they're
+conditionally independent.
+
+All right.
+
+Now let's move to the new topic,
+to the new concept that
+
+we introduce in this chapter,
+which is the concept of
+
+expectations.
+
+So what are the things
+to know here?
+
+One is the general idea.
+
+The way to think about
+expectations is that it's
+
+something like the average value
+for random variable if
+
+you do an experiment over and
+over, and if you interpret
+
+probabilities as frequencies.
+
+So you get x's over and over
+with a certain frequency --
+
+P(x) --
+
+a particular value, little
+x, gets realized.
+
+And each time that this happens,
+you get x dollars.
+
+How many dollars do you
+get on the average?
+
+Well, this formula gives you
+that particular average.
+
+So first thing we do is to write
+down a definition for
+
+this sort of concept.
+
+But then the other things you
+need to know is how to
+
+calculate expectations using
+shortcuts sometimes, and what
+
+properties they have.
+
+The most important shortcut
+there is is that, if you want
+
+to calculate the expected value,
+the average value for a
+
+random variable, you do not need
+to find the PMF of that
+
+random variable.
+
+But you can work directly with
+the x's and the y's.
+
+So you do the experiment
+over and over.
+
+The outcome of the experiment
+is a pair (x,y).
+
+And each time that a certain
+(x,y) happens,
+
+you get so many dollars.
+
+So this fraction of the time,
+a certain (x,y) happens.
+
+And that fraction of the time,
+you get so many dollars, so
+
+this is the average number
+of dollars that you get.
+
+So what you end up, since it
+is the average, then that
+
+means that it corresponds
+to the expected value.
+
+Now, this is something that, of
+course, needs a little bit
+
+of mathematical proof.
+
+But this is just a different
+way of accounting.
+
+And it turns out we give
+you the right answer.
+
+And it's a very useful
+shortcut.
+
+Now, when we're talking about
+functions of random variables,
+
+in general, we cannot speak
+just about averages.
+
+That is, the expected value
+of a function of a random
+
+variable is not the same
+as the function of
+
+the expected values.
+
+A function of averages is
+not the same as the
+
+average of a function.
+
+So in general, this
+is not true.
+
+But what it's important to know
+is to know the exceptions
+
+to this rule.
+
+And the important exceptions
+are mainly two.
+
+One is the case of linear
+
+functions of a random variable.
+
+We discussed this last time.
+
+So the expected value of
+temperature in Celsius is, you
+
+first find the expected value of
+temperature in Fahrenheit,
+
+and then you do the conversion
+to Celsius.
+
+So whether you first average and
+then do the conversion to
+
+the new units or not, it
+shouldn't matter when you get
+
+the result.
+
+The other property that turns
+out to be true when you talk
+
+about multiple random variables
+is that expectation
+
+still behaves linearly.
+
+So let X, Y, and Z be the score
+of a random student at
+
+each one of the three
+sections of the SAT.
+
+So the overall SAT score is X
+plus Y plus Z. This is the
+
+average score, the average
+total SAT score.
+
+Another way to calculate that
+average is to look at the
+
+first section of the SAT and
+see what was the average.
+
+Look at the second section, look
+at what was the average,
+
+and so the third, and
+add the averages.
+
+So you can do the averages for
+each section separately, add
+
+the averages, or you can find
+total scores for each student
+
+and average them.
+
+So I guess you probably believe
+that this is correct
+
+if you talk just about
+averaging scores.
+
+Since expectations are just the
+variation of averages, it
+
+turns out that this is
+also true in general.
+
+And the derivation of this is
+very simple, based on the
+
+expected value rule.
+
+And you can look at
+it in the notes.
+
+So this is one exception,
+which is linearity.
+
+The second important exception
+is the case of independent
+
+random variables, that the
+product of two random
+
+variables has an expectation
+which is the product of the
+
+expectations.
+
+In general, this is not true.
+
+But for the case where we have
+independence, the expectation
+
+works out as follows.
+
+Using the expected value rule,
+this is how you calculate the
+
+expected value of a function
+of a random variable.
+
+So think of this as being your
+g(X, Y) and this being your
+
+g(little x, y).
+
+So this is something that's
+generally true.
+
+Now, if we have independence,
+then the PMFs factor out, and
+
+then you can separate this sum
+by bringing together the x
+
+terms, bring them outside
+the y summation.
+
+And you find that this is the
+same as expected value of X
+
+times the expected value of Y.
+So independence is used in
+
+this step here.
+
+OK, now what if X and Y are
+independent, but instead of
+
+taking the expectation of
+X times Y, we take the
+
+expectation of the product of
+two functions of X and Y?
+
+I claim that the expected value
+of the product is still
+
+going to be the product of
+the expected values.
+
+How do we show that?
+
+We could show it by just redoing
+this derivation here.
+
+Instead of X and Y, we would
+have g(X) and h(Y), so the
+
+algebra goes through.
+
+But there's a better way to
+think about it which is more
+
+conceptual.
+
+And here's the idea.
+
+If X and Y are independent,
+what does it mean?
+
+X does not convey any
+information about Y. If X
+
+conveys no information about Y,
+does X convey information
+
+about h(Y)?
+
+No.
+
+If X tells me nothing about Y,
+nothing new, it shouldn't tell
+
+me anything about h(Y).
+
+Now, if X tells me nothing about
+h of h(Y), could g(X)
+
+tell me something about h(Y)?
+
+No.
+
+So the idea is that, if X is
+unrelated to Y, doesn't have
+
+any useful information, then
+g(X) could not have any useful
+
+information for h(Y).
+
+So if X and Y are independent,
+then g(X) and h(Y) are also
+
+independent.
+
+So this is something that
+one can try to prove
+
+mathematically, but it's more
+important to understand
+
+conceptually why this is so.
+
+It's in terms of conveying
+information.
+
+So if X tells me nothing about
+Y, X cannot tell me anything
+
+about Y cubed, or X cannot
+tell me anything by Y
+
+squared, and so on.
+
+That's the idea.
+
+And once we are convinced that
+g(X) and h(Y) are independent,
+
+then we can apply our previous
+rule, that for independent
+
+random variables, expectations
+multiply the right way.
+
+Apply the previous rule, but
+apply it now to these two
+
+independent random variables.
+
+And we get the conclusion
+that we wanted.
+
+Now, besides expectations, we
+also introduced the concept of
+
+the variance.
+
+And if you remember the
+definition of the variance,
+
+let me write down the formula
+for the variance of aX.
+
+It's the expected value of the
+random variable that we're
+
+looking at minus the expected
+value of the random variable
+
+that we're looking at.
+
+So this is the difference
+of the random
+
+variable from its mean.
+
+And we take that difference
+and square it, so it's the
+
+squared distance from the
+mean, and then take
+
+expectations of the
+whole thing.
+
+So when you look at that
+expression, you realize that a
+
+can be pulled out of
+those expressions.
+
+And because there is a squared,
+when you pull out the
+
+a, it's going to come
+out as an a-squared.
+
+So that gives us the rule for
+finding the variance of a
+
+scale or product of
+a random variable.
+
+The variance captures the idea
+of how wide, how spread out a
+
+certain distribution is.
+
+Bigger variance means it's
+more spread out.
+
+Now, if you take a random
+variable and the constants to
+
+it, what does it do to
+its distribution?
+
+It just shifts it, but it
+doesn't change its width.
+
+So intuitively it
+means that the
+
+variance should not change.
+
+You can check that
+mathematically, but it should
+
+also make sense intuitively.
+
+So the variance, when you add
+the constant, does not change.
+
+Now, can you add variances is
+the way we added expectations?
+
+Does variance behave linearly?
+
+It turns out that not always.
+
+Here, we need a condition.
+
+It's only in special cases--
+
+for example, when the two
+random variables are
+
+independent--
+
+that you can add variances.
+
+The variance of the sum is the
+sum of the variances if X and
+
+Y are independent.
+
+The derivation of this is,
+again, very short and simple.
+
+We'll skip it, but it's an
+important fact to remember.
+
+Now, to appreciate why this
+equality is not true always,
+
+we can think of some
+extreme examples.
+
+Suppose that X is the same as
+Y. What's going to be the
+
+variance of X plus Y?
+
+Well, X plus Y, in this case,
+is the same as 2X, so we're
+
+going to get 4 times the
+variance of X, which is
+
+different than the variance of
+X plus the variance of X.
+
+So that expression would give
+us twice the variance of X.
+
+But actually now it's 4 times
+the variance of X. The other
+
+extreme would be if X is equal
+to -Y. Then the variance is
+
+the variance of the random
+variable, which is always
+
+equal to 0.
+
+Now, a random variable which
+is always equal to 0 has no
+
+uncertainty.
+
+It is always equal to its mean
+value, so the variance, in
+
+this case, turns out to be 0.
+
+So in both of these cases,
+of course we have random
+
+variables that are extremely
+dependent.
+
+Why are they dependent?
+
+Because if I tell you something
+about Y, it tells
+
+you an awful lot about the value
+of X. There's a lot of
+
+information about X if
+I tell you Y, in this
+
+case or in that case.
+
+And finally, a short drill.
+
+If I tell you that the random
+variables are independent and
+
+you want to calculate the
+variance of a linear
+
+combination of this kind,
+then how do you argue?
+
+You argue that, since X and Y
+are independent, this means
+
+that X and 3Y are also
+independent.
+
+X has no information about Y, so
+X has no information about
+
+-Y. X has no information about
+-Y, so X should not have any
+
+information about -3Y.
+
+So X and -3Y are independent.
+
+So the variance of Z should be
+the variance of X plus the
+
+variance of -3Y, which is the
+variance of X plus 9 times the
+
+variance of Y. The important
+thing to note here is that no
+
+matter what happens, you
+end up getting a
+
+plus here, not a minus.
+
+So that's the sort of important
+thing to remember in
+
+this type of calculation.
+
+So this has been all concepts,
+reviews, new
+
+concepts and all that.
+
+It's the usual fire hose.
+
+Now let's use them to do
+something useful finally.
+
+So let's revisit our old
+example, the binomial
+
+distribution, which counts the
+number of successes in
+
+independent trials of a coin.
+
+It's a biased coin that has
+a probability of heads, or
+
+probability of success, equal
+to p at each trial.
+
+Finally, we can go through the
+exercise of calculating the
+
+expected value of this
+random variable.
+
+And there's the way of
+calculating that expectation
+
+that would be the favorite
+of those people who enjoy
+
+algebra, which is to write down
+the definition of the
+
+expected value.
+
+We add over all possible values
+of the random variable,
+
+over all the possible k's, and
+weigh them according to the
+
+probabilities that this
+particular k occurs.
+
+The probability that X takes on
+a particular value k is, of
+
+course, the binomial
+PMF, which is
+
+this familiar formula.
+
+Clearly, that would be a messy
+and challenging calculation.
+
+Can we find a shortcut?
+
+There's a very clever trick.
+
+There's lots of problems in
+probability that you can
+
+approach really nicely by
+breaking up the random
+
+variable of interest into a
+sum of simpler and more
+
+manageable random variables.
+
+And if you can make it to be a
+sum of random variables that
+
+are just 0's or 1's,
+so much the better.
+
+Life is easier.
+
+Random variables that take
+values 0 or 1, we call them
+
+indicator variables.
+
+They indicate whether an event
+has occurred or not.
+
+In this case, we look at each
+coin flip one at a time.
+
+For the i-th flip, if it
+resulted in heads or a
+
+success, we record it 1.
+
+If not, we record it 0.
+
+And then we look at the
+random variable.
+
+If we take the sum of the Xi's,
+what is it going to be?
+
+We add one each time that we get
+a success, so the sum is
+
+going to be the total
+number of successes.
+
+So we break up the random
+variable of interest as a sum
+
+of really nice and simple
+random variables.
+
+And now we can use the linearity
+of expectations.
+
+We're going to find the
+expectation of X by finding
+
+the expectation of the Xi's
+and then adding the
+
+expectations.
+
+What's the expected
+value of Xi?
+
+Well, Xi takes the value 1 with
+probability p, and takes
+
+the value 0 with probability
+1-p.
+
+So the expected value
+of Xi is just p.
+
+So the expected value of X is
+going to be just n times p.
+
+Because X is the sum of n terms,
+each one of which has
+
+expectation p, the expected
+value of the sum is the sum of
+
+the expected values.
+
+So I guess that's a pretty good
+shortcut for doing this
+
+horrendous calculation
+up there.
+
+So in case you didn't realize
+it, that's what we just
+
+established without
+doing any algebra.
+
+Good.
+
+How about the variance
+of X, of Xi?
+
+Two ways to calculate it.
+
+One is by using directly the
+formula for the variance,
+
+which would be --
+
+let's see what it would be.
+
+With probability
+p, you get a 1.
+
+And in this case, you are
+so far from the mean.
+
+That's your squared distance
+from the mean.
+
+With probability 1-p, you
+get a 0, which is so far
+
+away from the mean.
+
+And then you can simplify that
+formula and get an answer.
+
+How about a slightly easier
+way of doing it.
+
+Instead of doing the algebra
+here, let me indicate the
+
+slightly easier way.
+
+We have a formula for the
+variance that tells us that we
+
+can find the variance by
+proceeding this way.
+
+That's a formula that's
+generally true for variances.
+
+Why is this easier?
+
+What's the expected value
+of Xi squared?
+
+Backtrack.
+
+What is Xi squared, after all?
+
+It's the same thing as Xi.
+
+Since Xi takes value 0 and 1, Xi
+squared also takes the same
+
+values, 0 and 1.
+
+So the expected value of Xi
+squared is the same as the
+
+expected value of Xi,
+which is equal to p.
+
+And the expected value of Xi
+squared is p squared, so we
+
+get the final answer,
+p times (1-p).
+
+If you were to work through and
+do the cancellations in
+
+this messy expression here,
+after one line you would also
+
+get to the same formula.
+
+But this sort of illustrates
+that working with this formula
+
+for the variance, sometimes
+things work
+
+out a little faster.
+
+Finally, are we in business?
+
+Can we calculate the variance
+of the random
+
+variable X as well?
+
+Well, we have the rule that
+for independent random
+
+variables, the variance
+of the sum is
+
+the sum of the variances.
+
+So to find the variance of X,
+we just need to add the
+
+variances of the Xi's.
+
+We have n Xi's, and each
+one of them has
+
+variance p_n times (1-p).
+
+And we are done.
+
+So this way, we have calculated
+both the mean and
+
+the variance of the binomial
+random variable.
+
+It's interesting to look at this
+particular formula and
+
+see what it tells us.
+
+If you are to plot the variance
+of X as a function of
+
+p, it has this shape.
+
+And the maximum is
+here at 1/2.
+
+p times (1-p) is 0 when
+p is equal to 0.
+
+And when p equals to 1, it's a
+quadratic, so it must have
+
+this particular shape.
+
+So what does it tell us?
+
+If you think about variance as
+a measure of uncertainty, it
+
+tells you that coin flips
+are most uncertain when
+
+your coin is fair.
+
+When p is equal to 1/2, that's
+when you have the most
+
+randomness.
+
+And this is kind of intuitive.
+
+if on the other hand I tell you
+that the coin is extremely
+
+biased, p very close to 1, which
+means it almost always
+
+gives you heads, then
+that would be
+
+a case of low variance.
+
+There's low variability
+in the results.
+
+There's little uncertainty about
+what's going to happen.
+
+It's going to be mostly heads
+with some occasional tails.
+
+So p equals 1/2.
+
+Fair coin, that's the coin which
+is the most uncertain of
+
+all coins, in some sense.
+
+And it corresponds to the
+biggest variance.
+
+It corresponds to an X that has
+the widest distribution.
+
+Now that we're on a roll and we
+can calculate such hugely
+
+complicated sums in simple ways,
+let us try to push our
+
+luck and do a problem with
+this flavor, but a little
+
+harder than that.
+
+So you go to one of those
+
+old-fashioned cocktail parties.
+
+All males at least will have
+those standard big hats which
+
+look identical.
+
+They check them in when
+they walk in.
+
+And when they walk out, since
+they look pretty identical,
+
+they just pick a random
+hat and go home.
+
+So n people, they pick their
+hats completely at random,
+
+quote, unquote, and
+then leave.
+
+And the question is, to say
+something about the number of
+
+people who end up, by accident
+or by luck, to get back their
+
+own hat, the exact same hat
+that they checked in.
+
+OK, first what do we mean
+completely at random?
+
+Completely at random, we
+basically mean that any
+
+permutation of the hats
+is equally likely.
+
+Any way of distributing those
+n hats to the n people, any
+
+particular way is as likely
+as any other way.
+
+So there's complete symmetry
+between hats and people.
+
+So what we want to do is to
+calculate the expected value
+
+and the variance of this random
+variable X. Let's start
+
+with the expected value.
+
+Let's reuse the trick from
+the binomial case.
+
+So total number of hats picked,
+we're going to think
+
+of total number of hats
+picked as a sum of
+
+(0, 1) random variables.
+
+X1 tells us whether person
+1 got their own hat back.
+
+If they did, we record a 1.
+
+X2, the same thing.
+
+By adding all X's is how many
+1's did we get, which counts
+
+how many people selected
+their own hats.
+
+So we broke down the random
+variable of interest, the
+
+number of people who get their
+own hats back, as a sum of
+
+random variables.
+
+And these random variables,
+again, are easy to handle,
+
+because they're binary.
+
+The only take two values.
+
+What's the probability that Xi
+is equal to 1, the i-th person
+
+has a probability that they
+get their own hat?
+
+There's n hats by symmetry.
+
+The chance is that they end up
+getting their own hat, as
+
+opposed to any one of the
+other n - 1 hats,
+
+is going to be 1/n.
+
+So what's the expected
+value of Xi?
+
+It's one times 1/n.
+
+With probability 1/n, you get
+your own hat, or you get a
+
+value of 0 with probability
+1-1/n, which is 1/n.
+
+All right, so we got the
+expected value of the Xi's.
+
+And remember, we want to do is
+to calculate the expected
+
+value of X by using this
+decomposition?
+
+Are the random variables Xi
+independent of each other?
+
+You can try to answer that
+question by writing down a
+
+joint PMF for the X's,
+but I'm sure that
+
+you will not succeed.
+
+But can you think intuitively?
+
+If I tell you information about
+some of the Xi's, does
+
+it give you information about
+the remaining ones?
+
+Yeah.
+
+If I tell you that out of 10
+people, 9 of them got their
+
+own hat back, does that
+tell you something
+
+about the 10th person?
+
+Yes.
+
+If 9 got their own hat, then the
+10th must also have gotten
+
+their own hat back.
+
+So the first 9 random variables
+tell you something
+
+about the 10th one.
+
+And conveying information of
+this sort, that's the case of
+
+dependence.
+
+All right, so the random
+variables are not independent.
+
+Are we stuck?
+
+Can we still calculate the
+expected value of X?
+
+Yes, we can.
+
+And the reason we can is that
+expectations are linear.
+
+Expectation of a sum of random
+variables is the sum of the
+
+expectations.
+
+And that's always true.
+
+There's no independence
+assumption that's being used
+
+to apply that rule.
+
+So we have that the expected
+value of X is the sum of the
+
+expected value of the Xi's.
+
+And this is a property
+that's always true.
+
+You don't need independence.
+
+You don't care.
+
+So we're adding n terms,
+each one of which has
+
+expected value 1/n.
+
+And the final answer is 1.
+
+So out of the 100 people who
+selected hats at random, on
+
+the average, you expect only one
+of them to end up getting
+
+their own hat back.
+
+Very good.
+
+So since we are succeeding so
+far, let's try to see if we
+
+can succeed in calculating
+the variance as well.
+
+And of course, we will.
+
+But it's going to be a little
+more complicated.
+
+The reason it's going to be a
+little more complicated is
+
+because the Xi's are not
+independent, so the variance
+
+of the sum is not the same as
+the sum of the variances.
+
+So it's not enough to find the
+variances of the Xi's.
+
+We'll have to do more work.
+
+And here's what's involved.
+
+Let's start with the general
+formula for the variance,
+
+which, as I mentioned before,
+it's usually the simpler way
+
+to go about calculating
+variances.
+
+So we need to calculate the
+expected value for X-squared,
+
+and subtract from it the
+expectation squared.
+
+Well, we already found the
+expected value of X. It's
+
+equal to 1.
+
+So 1-squared gives us just 1.
+
+So we're left with the task of
+calculating the expected value
+
+of X-squared, the random
+variable X-squared.
+
+Let's try to follow
+the same idea.
+
+Write this messy random
+variable, X-squared, as a sum
+
+of hopefully simpler
+random variables.
+
+So X is the sum of the
+Xi's, so you square
+
+both sides of this.
+
+And then you expand the
+right-hand side.
+
+When you expand the right-hand
+side, you get the squares of
+
+the terms that appear here.
+
+And then you get all
+the cross-terms.
+
+For every pair of (i,j) that
+are different, i different
+
+than j, you're going to have
+a cross-term in the sum.
+
+So now, in order to calculate
+the expected value of
+
+X-squared, what does
+our task reduce to?
+
+It reduces to calculating the
+expected value of this term
+
+and calculating the expected
+value of that term.
+
+So let's do them
+one at a time.
+
+Expected value of Xi squared,
+what is it going to be?
+
+Same trick as before.
+
+Xi takes value 0 or 1, so Xi
+squared takes just the same
+
+values, 0 or 1.
+
+So that's the easy one.
+
+That's the same as expected
+value of Xi, which we already
+
+know to be 1/n.
+
+So this gives us a first
+contribution down here.
+
+The expected value of this
+term is going to be what?
+
+We have n terms in
+the summation.
+
+And each one of these terms
+has an expectation of 1/n.
+
+So we did a piece
+of the puzzle.
+
+So now let's deal with the
+second piece of the puzzle.
+
+Let's find the expected
+value of Xi times Xj.
+
+Now by symmetry, the expected
+value of Xi times Xj is going
+
+to be the same no matter
+what i and j you see.
+
+So let's just think about X1
+and X2 and try to find the
+
+expected value of X1 and X2.
+
+X1 times X2 is a random
+variable.
+
+What values does it take?
+
+Only 0 or 1?
+
+Since X1 and X2 are 0 or 1,
+their product can only take
+
+the values of 0 or 1.
+
+So to find the probability
+distribution of this random
+
+variable, it's just sufficient
+to find the probability that
+
+it takes the value of 1.
+
+Now, what does X1 times
+X2 equal to 1 mean?
+
+It means that X1 was
+1 and X2 was 1.
+
+The only way that you can get
+a product of 1 is if both of
+
+them turned out to be 1's.
+
+So that's the same as saying,
+persons 1 and 2 both picked
+
+their own hats.
+
+The probability that person 1
+and person 2 both pick their
+
+own hats is the probability of
+two things happening, which is
+
+the product of the first thing
+happening times the
+
+conditional probability
+of the second, given
+
+that the first happened.
+
+And in words, this is the
+probability that the first
+
+person picked their own hat
+times the probability that the
+
+second person picks their own
+hat, given that the first
+
+person already picked
+their own.
+
+So what's the probability
+that the first person
+
+picks their own hat?
+
+We know that it's 1/n.
+
+Now, how about the
+second person?
+
+If I tell you that one person
+has their own hat, and that
+
+person takes their hat and goes
+away, from the point of
+
+view of the second person,
+there's n - 1 people left
+
+looking at n - 1 hats.
+
+And they're getting just
+hats at random.
+
+What's the chance that
+I will get my own?
+
+It's 1/n - 1.
+
+So think of them as person 1
+goes, picks a hat at random,
+
+it happens to be their
+own, and it leaves.
+
+You're left with n - 1 people,
+and there are n
+
+- 1 hats out there.
+
+Person 2 goes and picks a hat
+at random, with probability
+
+1/n - 1, is going to
+pick his own hat.
+
+So the expected value now of
+this random variable is,
+
+again, that same number,
+because this is
+
+a 0, 1 random variable.
+
+So this is the same as expected
+value of Xi times Xj
+
+when i different than j.
+
+So here, all that's left to do
+is to add the expectations of
+
+these terms.
+
+Each one of these terms has an
+expected value that's 1/n
+
+times (1/n - 1).
+
+And how many terms do we have?
+
+How many of these are
+we adding up?
+
+It's n-squared - n.
+
+When you expand the quadratic,
+there's a total
+
+of n-squared terms.
+
+Some are self-terms,
+n of them.
+
+And the remaining number of
+terms is n-squared - n.
+
+So here we got n-squared
+- n terms.
+
+And so we need to multiply
+here with n-squared - n.
+
+And after you realize that this
+number here is 1, and you
+
+realize that this is the same
+as the denominator, you get
+
+the answer that the expected
+value of X squared equals 2.
+
+And then, finally going up to
+the top formula, we get the
+
+expected value of X squared,
+which is 2 - 1, and the
+
+variance is just equal to 1.
+
+So the variance of this random
+variable, number of people who
+
+get their own hats back,
+is also equal to 1,
+
+equal to the mean.
+
+Looks like magic.
+
+Why is this the case?
+
+Well, there's a deeper
+explanation why these two
+
+numbers should come out
+to be the same.
+
+But this is something that would
+probably have to wait a
+
+couple of chapters before we
+could actually explain it.
+
+And so I'll stop here.
\ No newline at end of file
diff --git a/Eki8KqKxGQg.txt b/Eki8KqKxGQg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..71eb3ae00fd3187e8a6a459a15731928c53a50b3
--- /dev/null
+++ b/Eki8KqKxGQg.txt
@@ -0,0 +1,15115 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+opencourseware under a Creative Commons
+
+ align:start position:0%
+opencourseware under a Creative Commons
+ 
+
+ align:start position:0%
+opencourseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have what I think of as a couple of
+
+ align:start position:0%
+I have what I think of as a couple of
+ 
+
+ align:start position:0%
+I have what I think of as a couple of
+fascinating questions that I will
+
+ align:start position:0%
+fascinating questions that I will
+ 
+
+ align:start position:0%
+fascinating questions that I will
+use to occupy us for the next for the
+
+ align:start position:0%
+use to occupy us for the next for the
+ 
+
+ align:start position:0%
+use to occupy us for the next for the
+last couple of lectures of the course
+
+ align:start position:0%
+last couple of lectures of the course
+ 
+
+ align:start position:0%
+last couple of lectures of the course
+um in in the context of talking about
+
+ align:start position:0%
+um in in the context of talking about
+ 
+
+ align:start position:0%
+um in in the context of talking about
+sleep and dreams I I mentioned that the
+
+ align:start position:0%
+sleep and dreams I I mentioned that the
+ 
+
+ align:start position:0%
+sleep and dreams I I mentioned that the
+the drive the hunger Drive is strong but
+
+ align:start position:0%
+the drive the hunger Drive is strong but
+ 
+
+ align:start position:0%
+the drive the hunger Drive is strong but
+it's not so strong that if you wanted to
+
+ align:start position:0%
+it's not so strong that if you wanted to
+ 
+
+ align:start position:0%
+it's not so strong that if you wanted to
+um you couldn't starve yourself to death
+
+ align:start position:0%
+um you couldn't starve yourself to death
+ 
+
+ align:start position:0%
+um you couldn't starve yourself to death
+but an interesting question would be
+
+ align:start position:0%
+but an interesting question would be
+ 
+
+ align:start position:0%
+but an interesting question would be
+why a an otherwise healthy adolescent
+
+ align:start position:0%
+why a an otherwise healthy adolescent
+ 
+
+ align:start position:0%
+why a an otherwise healthy adolescent
+girl would do that and why in doing that
+
+ align:start position:0%
+girl would do that and why in doing that
+ 
+
+ align:start position:0%
+girl would do that and why in doing that
+she would argue
+
+ align:start position:0%
+she would argue
+ 
+
+ align:start position:0%
+she would argue
+um vociferously that there was nothing
+
+ align:start position:0%
+um vociferously that there was nothing
+ 
+
+ align:start position:0%
+um vociferously that there was nothing
+wrong with her and that she wasn't
+
+ align:start position:0%
+wrong with her and that she wasn't
+ 
+
+ align:start position:0%
+wrong with her and that she wasn't
+hungry even while starving herself
+
+ align:start position:0%
+hungry even while starving herself
+ 
+
+ align:start position:0%
+hungry even while starving herself
+um potentially to death
+
+ align:start position:0%
+um potentially to death
+ 
+
+ align:start position:0%
+um potentially to death
+um that's that's one question that will
+
+ align:start position:0%
+um that's that's one question that will
+ 
+
+ align:start position:0%
+um that's that's one question that will
+occupy probably today
+
+ align:start position:0%
+occupy probably today
+ 
+
+ align:start position:0%
+occupy probably today
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you'll see that I did handouts for both
+
+ align:start position:0%
+you'll see that I did handouts for both
+ 
+
+ align:start position:0%
+you'll see that I did handouts for both
+this lecture and the next lecture rolled
+
+ align:start position:0%
+this lecture and the next lecture rolled
+ 
+
+ align:start position:0%
+this lecture and the next lecture rolled
+together in case I get to the next one
+
+ align:start position:0%
+together in case I get to the next one
+ 
+
+ align:start position:0%
+together in case I get to the next one
+today the second question
+
+ align:start position:0%
+today the second question
+ 
+
+ align:start position:0%
+today the second question
+um is well you might uh you you might
+
+ align:start position:0%
+um is well you might uh you you might
+ 
+
+ align:start position:0%
+um is well you might uh you you might
+have found the evolutionary psych
+
+ align:start position:0%
+have found the evolutionary psych
+ 
+
+ align:start position:0%
+have found the evolutionary psych
+argument about uh asymmetries between
+
+ align:start position:0%
+argument about uh asymmetries between
+ 
+
+ align:start position:0%
+argument about uh asymmetries between
+the uh between the sexes in terms of
+
+ align:start position:0%
+the uh between the sexes in terms of
+ 
+
+ align:start position:0%
+the uh between the sexes in terms of
+what they want in relationships to be
+
+ align:start position:0%
+what they want in relationships to be
+ 
+
+ align:start position:0%
+what they want in relationships to be
+reasonably compelling that argument
+
+ align:start position:0%
+reasonably compelling that argument
+ 
+
+ align:start position:0%
+reasonably compelling that argument
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um guys wanting to uh prop well
+
+ align:start position:0%
+um guys wanting to uh prop well
+ 
+
+ align:start position:0%
+um guys wanting to uh prop well
+everybody wanting to propagate their
+
+ align:start position:0%
+everybody wanting to propagate their
+ 
+
+ align:start position:0%
+everybody wanting to propagate their
+genes but because women get pregnant and
+
+ align:start position:0%
+genes but because women get pregnant and
+ 
+
+ align:start position:0%
+genes but because women get pregnant and
+are thus tied up with the baby for an
+
+ align:start position:0%
+are thus tied up with the baby for an
+ 
+
+ align:start position:0%
+are thus tied up with the baby for an
+extended period of time that you end up
+
+ align:start position:0%
+extended period of time that you end up
+ 
+
+ align:start position:0%
+extended period of time that you end up
+with an asymmetry that would cause males
+
+ align:start position:0%
+with an asymmetry that would cause males
+ 
+
+ align:start position:0%
+with an asymmetry that would cause males
+to want
+
+ align:start position:0%
+to want
+ 
+
+ align:start position:0%
+to want
+um uh more sex more often with more
+
+ align:start position:0%
+um uh more sex more often with more
+ 
+
+ align:start position:0%
+um uh more sex more often with more
+Partners than women you might have found
+
+ align:start position:0%
+Partners than women you might have found
+ 
+
+ align:start position:0%
+Partners than women you might have found
+that appealing
+
+ align:start position:0%
+that appealing
+ 
+
+ align:start position:0%
+that appealing
+um at least as an intellectual
+
+ align:start position:0%
+um at least as an intellectual
+ 
+
+ align:start position:0%
+um at least as an intellectual
+um construct but how would we explain
+
+ align:start position:0%
+um construct but how would we explain
+ 
+
+ align:start position:0%
+um construct but how would we explain
+would that explain how might it explain
+
+ align:start position:0%
+would that explain how might it explain
+ 
+
+ align:start position:0%
+would that explain how might it explain
+why at least uh some males end up
+
+ align:start position:0%
+why at least uh some males end up
+ 
+
+ align:start position:0%
+why at least uh some males end up
+engaging in coercive sexual behavior
+
+ align:start position:0%
+engaging in coercive sexual behavior
+ 
+
+ align:start position:0%
+engaging in coercive sexual behavior
+sexual behavior that does not appear to
+
+ align:start position:0%
+sexual behavior that does not appear to
+ 
+
+ align:start position:0%
+sexual behavior that does not appear to
+be consensual between
+
+ align:start position:0%
+be consensual between
+ 
+
+ align:start position:0%
+be consensual between
+um between the partners and that's
+
+ align:start position:0%
+um between the partners and that's
+ 
+
+ align:start position:0%
+um between the partners and that's
+what's going to occupy us for the uh for
+
+ align:start position:0%
+what's going to occupy us for the uh for
+ 
+
+ align:start position:0%
+what's going to occupy us for the uh for
+the last lecture of the course now these
+
+ align:start position:0%
+the last lecture of the course now these
+ 
+
+ align:start position:0%
+the last lecture of the course now these
+are very different problems the problem
+
+ align:start position:0%
+are very different problems the problem
+ 
+
+ align:start position:0%
+are very different problems the problem
+of Eating Disorders on one hand and and
+
+ align:start position:0%
+of Eating Disorders on one hand and and
+ 
+
+ align:start position:0%
+of Eating Disorders on one hand and and
+um coercive sexual behavior or more
+
+ align:start position:0%
+um coercive sexual behavior or more
+ 
+
+ align:start position:0%
+um coercive sexual behavior or more
+colloquially date rape on on the on the
+
+ align:start position:0%
+colloquially date rape on on the on the
+ 
+
+ align:start position:0%
+colloquially date rape on on the on the
+other side but they do have some
+
+ align:start position:0%
+other side but they do have some
+ 
+
+ align:start position:0%
+other side but they do have some
+interesting parallels one with the other
+
+ align:start position:0%
+interesting parallels one with the other
+ 
+
+ align:start position:0%
+interesting parallels one with the other
+uh they are these are outlined a bit and
+
+ align:start position:0%
+uh they are these are outlined a bit and
+ 
+
+ align:start position:0%
+uh they are these are outlined a bit and
+the I guess in the abstract part of um
+
+ align:start position:0%
+the I guess in the abstract part of um
+ 
+
+ align:start position:0%
+the I guess in the abstract part of um
+of the handout they're both
+
+ align:start position:0%
+of the handout they're both
+ 
+
+ align:start position:0%
+of the handout they're both
+um problems that are gender specific uh
+
+ align:start position:0%
+um problems that are gender specific uh
+ 
+
+ align:start position:0%
+um problems that are gender specific uh
+the overwhelming uh number of eating
+
+ align:start position:0%
+the overwhelming uh number of eating
+ 
+
+ align:start position:0%
+the overwhelming uh number of eating
+disorder patients are female and the
+
+ align:start position:0%
+disorder patients are female and the
+ 
+
+ align:start position:0%
+disorder patients are female and the
+overwhelming number of
+
+ align:start position:0%
+overwhelming number of
+ 
+
+ align:start position:0%
+overwhelming number of
+um people who get into into trouble
+
+ align:start position:0%
+um people who get into into trouble
+ 
+
+ align:start position:0%
+um people who get into into trouble
+um for or you know brought up on charges
+
+ align:start position:0%
+um for or you know brought up on charges
+ 
+
+ align:start position:0%
+um for or you know brought up on charges
+in in coercive sexual behavior cases for
+
+ align:start position:0%
+in in coercive sexual behavior cases for
+ 
+
+ align:start position:0%
+in in coercive sexual behavior cases for
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+um are male so they're gender specific
+
+ align:start position:0%
+um are male so they're gender specific
+ 
+
+ align:start position:0%
+um are male so they're gender specific
+that's uh that's of some interest
+
+ align:start position:0%
+that's uh that's of some interest
+ 
+
+ align:start position:0%
+that's uh that's of some interest
+um they are both
+
+ align:start position:0%
+um they are both
+ 
+
+ align:start position:0%
+um they are both
+they both serve a useful function at the
+
+ align:start position:0%
+they both serve a useful function at the
+ 
+
+ align:start position:0%
+they both serve a useful function at the
+end of the course because they're both
+
+ align:start position:0%
+end of the course because they're both
+ 
+
+ align:start position:0%
+end of the course because they're both
+useful for uh for bringing back theme
+
+ align:start position:0%
+useful for uh for bringing back theme
+ 
+
+ align:start position:0%
+useful for uh for bringing back theme
+after theme that we've seen throughout
+
+ align:start position:0%
+after theme that we've seen throughout
+ 
+
+ align:start position:0%
+after theme that we've seen throughout
+the uh um throughout the course uh
+
+ align:start position:0%
+the uh um throughout the course uh
+ 
+
+ align:start position:0%
+the uh um throughout the course uh
+themes like yeah the the revisiting you
+
+ align:start position:0%
+themes like yeah the the revisiting you
+ 
+
+ align:start position:0%
+themes like yeah the the revisiting you
+know is it nature is it nurture um you
+
+ align:start position:0%
+know is it nature is it nurture um you
+ 
+
+ align:start position:0%
+know is it nature is it nurture um you
+know is it biology or is is it uh
+
+ align:start position:0%
+know is it biology or is is it uh
+ 
+
+ align:start position:0%
+know is it biology or is is it uh
+sociology and the answer always turns
+
+ align:start position:0%
+sociology and the answer always turns
+ 
+
+ align:start position:0%
+sociology and the answer always turns
+out to be or often turns out to be that
+
+ align:start position:0%
+out to be or often turns out to be that
+ 
+
+ align:start position:0%
+out to be or often turns out to be that
+these are complicated
+
+ align:start position:0%
+these are complicated
+ 
+
+ align:start position:0%
+these are complicated
+um interactions and the problems of
+
+ align:start position:0%
+um interactions and the problems of
+ 
+
+ align:start position:0%
+um interactions and the problems of
+eating disorders and and coercive sex
+
+ align:start position:0%
+eating disorders and and coercive sex
+ 
+
+ align:start position:0%
+eating disorders and and coercive sex
+turn out to be particularly Rich
+
+ align:start position:0%
+turn out to be particularly Rich
+ 
+
+ align:start position:0%
+turn out to be particularly Rich
+um interactions between a number of uh
+
+ align:start position:0%
+um interactions between a number of uh
+ 
+
+ align:start position:0%
+um interactions between a number of uh
+of factors
+
+ align:start position:0%
+of factors
+ 
+
+ align:start position:0%
+of factors
+um and by the same token neither of them
+
+ align:start position:0%
+um and by the same token neither of them
+ 
+
+ align:start position:0%
+um and by the same token neither of them
+is uh well dealt with in any
+
+ align:start position:0%
+is uh well dealt with in any
+ 
+
+ align:start position:0%
+is uh well dealt with in any
+simple-minded oh give them a pill for
+
+ align:start position:0%
+simple-minded oh give them a pill for
+ 
+
+ align:start position:0%
+simple-minded oh give them a pill for
+instance kind of uh of way and they're
+
+ align:start position:0%
+instance kind of uh of way and they're
+ 
+
+ align:start position:0%
+instance kind of uh of way and they're
+both what could be described as
+
+ align:start position:0%
+both what could be described as
+ 
+
+ align:start position:0%
+both what could be described as
+um as being successful disasters I'll
+
+ align:start position:0%
+um as being successful disasters I'll
+ 
+
+ align:start position:0%
+um as being successful disasters I'll
+elaborate on that later but but uh both
+
+ align:start position:0%
+elaborate on that later but but uh both
+ 
+
+ align:start position:0%
+elaborate on that later but but uh both
+of them are in a perverse sense
+
+ align:start position:0%
+of them are in a perverse sense
+ 
+
+ align:start position:0%
+of them are in a perverse sense
+successful behaviors and in a more
+
+ align:start position:0%
+successful behaviors and in a more
+ 
+
+ align:start position:0%
+successful behaviors and in a more
+obvious sense
+
+ align:start position:0%
+obvious sense
+ 
+
+ align:start position:0%
+obvious sense
+um disasters unsuccessful so let me um
+
+ align:start position:0%
+um disasters unsuccessful so let me um
+ 
+
+ align:start position:0%
+um disasters unsuccessful so let me um
+uh well let let me start by by sketching
+
+ align:start position:0%
+uh well let let me start by by sketching
+ 
+
+ align:start position:0%
+uh well let let me start by by sketching
+a uh
+
+ align:start position:0%
+a uh
+ 
+
+ align:start position:0%
+a uh
+a portrait of what would be one a
+
+ align:start position:0%
+a portrait of what would be one a
+ 
+
+ align:start position:0%
+a portrait of what would be one a
+typical patient
+
+ align:start position:0%
+typical patient
+ 
+
+ align:start position:0%
+typical patient
+um with a diagnosis of anorexia nervosa
+
+ align:start position:0%
+um with a diagnosis of anorexia nervosa
+ 
+
+ align:start position:0%
+um with a diagnosis of anorexia nervosa
+the term simply means anorexia means a
+
+ align:start position:0%
+the term simply means anorexia means a
+ 
+
+ align:start position:0%
+the term simply means anorexia means a
+lack of appetite nervosa is just what
+
+ align:start position:0%
+lack of appetite nervosa is just what
+ 
+
+ align:start position:0%
+lack of appetite nervosa is just what
+you stick on when uh it's of nervous
+
+ align:start position:0%
+you stick on when uh it's of nervous
+ 
+
+ align:start position:0%
+you stick on when uh it's of nervous
+Origins it's a you know it's it's uh you
+
+ align:start position:0%
+Origins it's a you know it's it's uh you
+ 
+
+ align:start position:0%
+Origins it's a you know it's it's uh you
+could have called it psychogenic or
+
+ align:start position:0%
+could have called it psychogenic or
+ 
+
+ align:start position:0%
+could have called it psychogenic or
+something like that it's uh
+
+ align:start position:0%
+something like that it's uh
+ 
+
+ align:start position:0%
+something like that it's uh
+it just means a loss of appetite that
+
+ align:start position:0%
+it just means a loss of appetite that
+ 
+
+ align:start position:0%
+it just means a loss of appetite that
+you're not going to explain
+
+ align:start position:0%
+you're not going to explain
+ 
+
+ align:start position:0%
+you're not going to explain
+by some organic cause a typical patient
+
+ align:start position:0%
+by some organic cause a typical patient
+ 
+
+ align:start position:0%
+by some organic cause a typical patient
+would be an adolescent girl say 14 15
+
+ align:start position:0%
+would be an adolescent girl say 14 15
+ 
+
+ align:start position:0%
+would be an adolescent girl say 14 15
+16.
+
+ align:start position:0%
+16.
+ 
+
+ align:start position:0%
+16.
+um who gets brought typically by her
+
+ align:start position:0%
+um who gets brought typically by her
+ 
+
+ align:start position:0%
+um who gets brought typically by her
+family to the doctor
+
+ align:start position:0%
+family to the doctor
+ 
+
+ align:start position:0%
+family to the doctor
+um very skinny
+
+ align:start position:0%
+um very skinny
+ 
+
+ align:start position:0%
+um very skinny
+part of the characteristics you can see
+
+ align:start position:0%
+part of the characteristics you can see
+ 
+
+ align:start position:0%
+part of the characteristics you can see
+on the clinical criteria for for the
+
+ align:start position:0%
+on the clinical criteria for for the
+ 
+
+ align:start position:0%
+on the clinical criteria for for the
+diagnosis
+
+ align:start position:0%
+diagnosis
+ 
+
+ align:start position:0%
+diagnosis
+um part of the characteristic is a a
+
+ align:start position:0%
+um part of the characteristic is a a
+ 
+
+ align:start position:0%
+um part of the characteristic is a a
+refusal to maintain what's considered a
+
+ align:start position:0%
+refusal to maintain what's considered a
+ 
+
+ align:start position:0%
+refusal to maintain what's considered a
+normal body weight so maybe you know for
+
+ align:start position:0%
+normal body weight so maybe you know for
+ 
+
+ align:start position:0%
+normal body weight so maybe you know for
+heightened at her height and age she
+
+ align:start position:0%
+heightened at her height and age she
+ 
+
+ align:start position:0%
+heightened at her height and age she
+should weigh about a hundred pounds she
+
+ align:start position:0%
+should weigh about a hundred pounds she
+ 
+
+ align:start position:0%
+should weigh about a hundred pounds she
+might come in weighing 75 pounds looking
+
+ align:start position:0%
+might come in weighing 75 pounds looking
+ 
+
+ align:start position:0%
+might come in weighing 75 pounds looking
+to all the world
+
+ align:start position:0%
+to all the world
+ 
+
+ align:start position:0%
+to all the world
+um like she is emaciated looking to all
+
+ align:start position:0%
+um like she is emaciated looking to all
+ 
+
+ align:start position:0%
+um like she is emaciated looking to all
+the world but one like she's emaciated
+
+ align:start position:0%
+the world but one like she's emaciated
+ 
+
+ align:start position:0%
+the world but one like she's emaciated
+one of the characteristics is a um uh
+
+ align:start position:0%
+one of the characteristics is a um uh
+ 
+
+ align:start position:0%
+one of the characteristics is a um uh
+well I think it's on the handout is yes
+
+ align:start position:0%
+well I think it's on the handout is yes
+ 
+
+ align:start position:0%
+well I think it's on the handout is yes
+Distortion of body image a denial that
+
+ align:start position:0%
+Distortion of body image a denial that
+ 
+
+ align:start position:0%
+Distortion of body image a denial that
+you're actually skinny and it's not just
+
+ align:start position:0%
+you're actually skinny and it's not just
+ 
+
+ align:start position:0%
+you're actually skinny and it's not just
+um you know some sort of a uh uh a a
+
+ align:start position:0%
+um you know some sort of a uh uh a a
+ 
+
+ align:start position:0%
+um you know some sort of a uh uh a a
+cranky you know
+
+ align:start position:0%
+cranky you know
+ 
+
+ align:start position:0%
+cranky you know
+you know what did you get in in biology
+
+ align:start position:0%
+you know what did you get in in biology
+ 
+
+ align:start position:0%
+you know what did you get in in biology
+this term now did you did you Funk
+
+ align:start position:0%
+this term now did you did you Funk
+ 
+
+ align:start position:0%
+this term now did you did you Funk
+biology this term no I didn't flunk
+
+ align:start position:0%
+biology this term no I didn't flunk
+ 
+
+ align:start position:0%
+biology this term no I didn't flunk
+biology this term when you can see on
+
+ align:start position:0%
+biology this term when you can see on
+ 
+
+ align:start position:0%
+biology this term when you can see on
+the report card that it says F or
+
+ align:start position:0%
+the report card that it says F or
+ 
+
+ align:start position:0%
+the report card that it says F or
+something like that it's not that kind
+
+ align:start position:0%
+something like that it's not that kind
+ 
+
+ align:start position:0%
+something like that it's not that kind
+of of denial it's almost like a
+
+ align:start position:0%
+of of denial it's almost like a
+ 
+
+ align:start position:0%
+of of denial it's almost like a
+perceptual disorder
+
+ align:start position:0%
+perceptual disorder
+ 
+
+ align:start position:0%
+perceptual disorder
+um where uh a a young girl who looks to
+
+ align:start position:0%
+um where uh a a young girl who looks to
+ 
+
+ align:start position:0%
+um where uh a a young girl who looks to
+everybody else like she is
+
+ align:start position:0%
+everybody else like she is
+ 
+
+ align:start position:0%
+everybody else like she is
+um a famine victim looks at herself in
+
+ align:start position:0%
+um a famine victim looks at herself in
+ 
+
+ align:start position:0%
+um a famine victim looks at herself in
+the mirror and says I look fat
+
+ align:start position:0%
+the mirror and says I look fat
+ 
+
+ align:start position:0%
+the mirror and says I look fat
+see as as though she was seeing
+
+ align:start position:0%
+see as as though she was seeing
+ 
+
+ align:start position:0%
+see as as though she was seeing
+something that literally
+
+ align:start position:0%
+something that literally
+ 
+
+ align:start position:0%
+something that literally
+um wasn't there
+
+ align:start position:0%
+um wasn't there
+ 
+
+ align:start position:0%
+um wasn't there
+um this is combined with an intense fear
+
+ align:start position:0%
+um this is combined with an intense fear
+ 
+
+ align:start position:0%
+um this is combined with an intense fear
+of of being fat of being overweight
+
+ align:start position:0%
+of of being fat of being overweight
+ 
+
+ align:start position:0%
+of of being fat of being overweight
+um and and one of the official
+
+ align:start position:0%
+um and and one of the official
+ 
+
+ align:start position:0%
+um and and one of the official
+diagnostic Criterion is a cessation of
+
+ align:start position:0%
+diagnostic Criterion is a cessation of
+ 
+
+ align:start position:0%
+diagnostic Criterion is a cessation of
+menstrual cycles for more than
+
+ align:start position:0%
+menstrual cycles for more than
+ 
+
+ align:start position:0%
+menstrual cycles for more than
+um three months there was an interesting
+
+ align:start position:0%
+um three months there was an interesting
+ 
+
+ align:start position:0%
+um three months there was an interesting
+article Bo you sent it around right the
+
+ align:start position:0%
+article Bo you sent it around right the
+ 
+
+ align:start position:0%
+article Bo you sent it around right the
+the did you send around that the New
+
+ align:start position:0%
+the did you send around that the New
+ 
+
+ align:start position:0%
+the did you send around that the New
+York Times thing about ednas
+
+ align:start position:0%
+York Times thing about ednas
+ 
+
+ align:start position:0%
+York Times thing about ednas
+um the uh an interesting article in the
+
+ align:start position:0%
+um the uh an interesting article in the
+ 
+
+ align:start position:0%
+um the uh an interesting article in the
+New York Times science section last week
+
+ align:start position:0%
+New York Times science section last week
+ 
+
+ align:start position:0%
+New York Times science section last week
+pointing out one of the problems in
+
+ align:start position:0%
+pointing out one of the problems in
+ 
+
+ align:start position:0%
+pointing out one of the problems in
+psychiatric diagnosis suppose you got a
+
+ align:start position:0%
+psychiatric diagnosis suppose you got a
+ 
+
+ align:start position:0%
+psychiatric diagnosis suppose you got a
+patient she's 15 years old skinny as a
+
+ align:start position:0%
+patient she's 15 years old skinny as a
+ 
+
+ align:start position:0%
+patient she's 15 years old skinny as a
+rail
+
+ align:start position:0%
+rail
+ 
+
+ align:start position:0%
+rail
+um intense fear of being uh uh uh being
+
+ align:start position:0%
+um intense fear of being uh uh uh being
+ 
+
+ align:start position:0%
+um intense fear of being uh uh uh being
+fat
+
+ align:start position:0%
+fat
+ 
+
+ align:start position:0%
+fat
+um says she looks fat
+
+ align:start position:0%
+um says she looks fat
+ 
+
+ align:start position:0%
+um says she looks fat
+and her her monthly Cycles are irregular
+
+ align:start position:0%
+and her her monthly Cycles are irregular
+ 
+
+ align:start position:0%
+and her her monthly Cycles are irregular
+but they've never disappeared for a full
+
+ align:start position:0%
+but they've never disappeared for a full
+ 
+
+ align:start position:0%
+but they've never disappeared for a full
+three months under the official rules of
+
+ align:start position:0%
+three months under the official rules of
+ 
+
+ align:start position:0%
+three months under the official rules of
+the game you can't give her a diagnosis
+
+ align:start position:0%
+the game you can't give her a diagnosis
+ 
+
+ align:start position:0%
+the game you can't give her a diagnosis
+of of anorexia because she doesn't meet
+
+ align:start position:0%
+of of anorexia because she doesn't meet
+ 
+
+ align:start position:0%
+of of anorexia because she doesn't meet
+all the diagnostic criteria clearly has
+
+ align:start position:0%
+all the diagnostic criteria clearly has
+ 
+
+ align:start position:0%
+all the diagnostic criteria clearly has
+an eating disorder what you end up uh
+
+ align:start position:0%
+an eating disorder what you end up uh
+ 
+
+ align:start position:0%
+an eating disorder what you end up uh
+labeling her as is eating disorder not
+
+ align:start position:0%
+labeling her as is eating disorder not
+ 
+
+ align:start position:0%
+labeling her as is eating disorder not
+otherwise specify ednas is the official
+
+ align:start position:0%
+otherwise specify ednas is the official
+ 
+
+ align:start position:0%
+otherwise specify ednas is the official
+category for this
+
+ align:start position:0%
+category for this
+ 
+
+ align:start position:0%
+category for this
+um it's it's an issue it becomes an
+
+ align:start position:0%
+um it's it's an issue it becomes an
+ 
+
+ align:start position:0%
+um it's it's an issue it becomes an
+issue in in the uh in the economics of
+
+ align:start position:0%
+issue in in the uh in the economics of
+ 
+
+ align:start position:0%
+issue in in the uh in the economics of
+health care because what you can get
+
+ align:start position:0%
+health care because what you can get
+ 
+
+ align:start position:0%
+health care because what you can get
+reimbursed for what you can treat for
+
+ align:start position:0%
+reimbursed for what you can treat for
+ 
+
+ align:start position:0%
+reimbursed for what you can treat for
+are real diseases you can't I mean
+
+ align:start position:0%
+are real diseases you can't I mean
+ 
+
+ align:start position:0%
+are real diseases you can't I mean
+reasonably enough you can't go to your
+
+ align:start position:0%
+reasonably enough you can't go to your
+ 
+
+ align:start position:0%
+reasonably enough you can't go to your
+doctor and say you know uh I want a pile
+
+ align:start position:0%
+doctor and say you know uh I want a pile
+ 
+
+ align:start position:0%
+doctor and say you know uh I want a pile
+of drugs in therapy that I want somebody
+
+ align:start position:0%
+of drugs in therapy that I want somebody
+ 
+
+ align:start position:0%
+of drugs in therapy that I want somebody
+else to pay for because uh BBB because I
+
+ align:start position:0%
+else to pay for because uh BBB because I
+ 
+
+ align:start position:0%
+else to pay for because uh BBB because I
+I I I I hate my calculus ta
+
+ align:start position:0%
+I I I I hate my calculus ta
+ 
+
+ align:start position:0%
+I I I I hate my calculus ta
+pathologically
+
+ align:start position:0%
+pathologically
+ 
+
+ align:start position:0%
+pathologically
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+right yeah okay you know you can't just
+
+ align:start position:0%
+right yeah okay you know you can't just
+ 
+
+ align:start position:0%
+right yeah okay you know you can't just
+decide that yeah but you can just decide
+
+ align:start position:0%
+decide that yeah but you can just decide
+ 
+
+ align:start position:0%
+decide that yeah but you can just decide
+that you're ill in some fact or you
+
+ align:start position:0%
+that you're ill in some fact or you
+ 
+
+ align:start position:0%
+that you're ill in some fact or you
+can't just walk in and and and and and
+
+ align:start position:0%
+can't just walk in and and and and and
+ 
+
+ align:start position:0%
+can't just walk in and and and and and
+and say you know I want you to treat me
+
+ align:start position:0%
+and say you know I want you to treat me
+ 
+
+ align:start position:0%
+and say you know I want you to treat me
+um I I desperately need you to to change
+
+ align:start position:0%
+um I I desperately need you to to change
+ 
+
+ align:start position:0%
+um I I desperately need you to to change
+the shape of my nose and you know I'm
+
+ align:start position:0%
+the shape of my nose and you know I'm
+ 
+
+ align:start position:0%
+the shape of my nose and you know I'm
+not thrilled with my rear end and and
+
+ align:start position:0%
+not thrilled with my rear end and and
+ 
+
+ align:start position:0%
+not thrilled with my rear end and and
+and and and you know I kind of want you
+
+ align:start position:0%
+and and and you know I kind of want you
+ 
+
+ align:start position:0%
+and and and you know I kind of want you
+to reshape my whole body because because
+
+ align:start position:0%
+to reshape my whole body because because
+ 
+
+ align:start position:0%
+to reshape my whole body because because
+you know I just my body it's just not
+
+ align:start position:0%
+you know I just my body it's just not
+ 
+
+ align:start position:0%
+you know I just my body it's just not
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+yeah you have to get a diagnosis of you
+
+ align:start position:0%
+yeah you have to get a diagnosis of you
+ 
+
+ align:start position:0%
+yeah you have to get a diagnosis of you
+know body dysmorphic disorder or
+
+ align:start position:0%
+know body dysmorphic disorder or
+ 
+
+ align:start position:0%
+know body dysmorphic disorder or
+something like that before you can
+
+ align:start position:0%
+something like that before you can
+ 
+
+ align:start position:0%
+something like that before you can
+persuade the third party payers to do it
+
+ align:start position:0%
+persuade the third party payers to do it
+ 
+
+ align:start position:0%
+persuade the third party payers to do it
+anyway in psychiatric land this is a big
+
+ align:start position:0%
+anyway in psychiatric land this is a big
+ 
+
+ align:start position:0%
+anyway in psychiatric land this is a big
+problem because it's it's very difficult
+
+ align:start position:0%
+problem because it's it's very difficult
+ 
+
+ align:start position:0%
+problem because it's it's very difficult
+to come up with you know there's no
+
+ align:start position:0%
+to come up with you know there's no
+ 
+
+ align:start position:0%
+to come up with you know there's no
+blood test
+
+ align:start position:0%
+blood test
+ 
+
+ align:start position:0%
+blood test
+right you can if you've got polio
+
+ align:start position:0%
+right you can if you've got polio
+ 
+
+ align:start position:0%
+right you can if you've got polio
+there's a polio virus somewhere to look
+
+ align:start position:0%
+there's a polio virus somewhere to look
+ 
+
+ align:start position:0%
+there's a polio virus somewhere to look
+for if you've got an eating disorder
+
+ align:start position:0%
+for if you've got an eating disorder
+ 
+
+ align:start position:0%
+for if you've got an eating disorder
+there's not and and so exactly how to
+
+ align:start position:0%
+there's not and and so exactly how to
+ 
+
+ align:start position:0%
+there's not and and so exactly how to
+label people is a is is a substantial
+
+ align:start position:0%
+label people is a is is a substantial
+ 
+
+ align:start position:0%
+label people is a is is a substantial
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+um but I'm not going to say more about
+
+ align:start position:0%
+um but I'm not going to say more about
+ 
+
+ align:start position:0%
+um but I'm not going to say more about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+in any case
+
+ align:start position:0%
+in any case
+ 
+
+ align:start position:0%
+in any case
+um it's uh so so you you've got here's
+
+ align:start position:0%
+um it's uh so so you you've got here's
+ 
+
+ align:start position:0%
+um it's uh so so you you've got here's
+here's a patient is an interesting uh
+
+ align:start position:0%
+here's a patient is an interesting uh
+ 
+
+ align:start position:0%
+here's a patient is an interesting uh
+this this disorder is is interesting as
+
+ align:start position:0%
+this this disorder is is interesting as
+ 
+
+ align:start position:0%
+this this disorder is is interesting as
+an interplay of of Mind and Body in many
+
+ align:start position:0%
+an interplay of of Mind and Body in many
+ 
+
+ align:start position:0%
+an interplay of of Mind and Body in many
+many ways part of the reason that it's
+
+ align:start position:0%
+many ways part of the reason that it's
+ 
+
+ align:start position:0%
+many ways part of the reason that it's
+interesting is because
+
+ align:start position:0%
+interesting is because
+ 
+
+ align:start position:0%
+interesting is because
+um there are all sorts of
+
+ align:start position:0%
+um there are all sorts of
+ 
+
+ align:start position:0%
+um there are all sorts of
+psychiatric consequences that just arise
+
+ align:start position:0%
+psychiatric consequences that just arise
+ 
+
+ align:start position:0%
+psychiatric consequences that just arise
+from the fact that this uh this girl
+
+ align:start position:0%
+from the fact that this uh this girl
+ 
+
+ align:start position:0%
+from the fact that this uh this girl
+I'll stick with it being a female
+
+ align:start position:0%
+I'll stick with it being a female
+ 
+
+ align:start position:0%
+I'll stick with it being a female
+patient because it's a anorexia is about
+
+ align:start position:0%
+patient because it's a anorexia is about
+ 
+
+ align:start position:0%
+patient because it's a anorexia is about
+eight to one nine to one female
+
+ align:start position:0%
+eight to one nine to one female
+ 
+
+ align:start position:0%
+eight to one nine to one female
+um because she's starving herself for
+
+ align:start position:0%
+um because she's starving herself for
+ 
+
+ align:start position:0%
+um because she's starving herself for
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+starving yourself is depressing
+
+ align:start position:0%
+starving yourself is depressing
+ 
+
+ align:start position:0%
+starving yourself is depressing
+you because if you are really hungry you
+
+ align:start position:0%
+you because if you are really hungry you
+ 
+
+ align:start position:0%
+you because if you are really hungry you
+also tend to have have more symptoms of
+
+ align:start position:0%
+also tend to have have more symptoms of
+ 
+
+ align:start position:0%
+also tend to have have more symptoms of
+clinical depression is depression part
+
+ align:start position:0%
+clinical depression is depression part
+ 
+
+ align:start position:0%
+clinical depression is depression part
+of the eating disorder pattern which cut
+
+ align:start position:0%
+of the eating disorder pattern which cut
+ 
+
+ align:start position:0%
+of the eating disorder pattern which cut
+you know is is it uh is it part of the
+
+ align:start position:0%
+you know is is it uh is it part of the
+ 
+
+ align:start position:0%
+you know is is it uh is it part of the
+pathology or is it a side effect of of
+
+ align:start position:0%
+pathology or is it a side effect of of
+ 
+
+ align:start position:0%
+pathology or is it a side effect of of
+the pathology
+
+ align:start position:0%
+the pathology
+ 
+
+ align:start position:0%
+the pathology
+in any case it is not an uncommon
+
+ align:start position:0%
+in any case it is not an uncommon
+ 
+
+ align:start position:0%
+in any case it is not an uncommon
+disorder
+
+ align:start position:0%
+disorder
+ 
+
+ align:start position:0%
+disorder
+um Point prevalence is jargon for saying
+
+ align:start position:0%
+um Point prevalence is jargon for saying
+ 
+
+ align:start position:0%
+um Point prevalence is jargon for saying
+if I go and look at a population at this
+
+ align:start position:0%
+if I go and look at a population at this
+ 
+
+ align:start position:0%
+if I go and look at a population at this
+point in time how many people have the
+
+ align:start position:0%
+point in time how many people have the
+ 
+
+ align:start position:0%
+point in time how many people have the
+disorder I'm looking for and if you look
+
+ align:start position:0%
+disorder I'm looking for and if you look
+ 
+
+ align:start position:0%
+disorder I'm looking for and if you look
+at a population of young women the point
+
+ align:start position:0%
+at a population of young women the point
+ 
+
+ align:start position:0%
+at a population of young women the point
+prevalence of anorexia is about half of
+
+ align:start position:0%
+prevalence of anorexia is about half of
+ 
+
+ align:start position:0%
+prevalence of anorexia is about half of
+a percent if you broaden it to this
+
+ align:start position:0%
+a percent if you broaden it to this
+ 
+
+ align:start position:0%
+a percent if you broaden it to this
+ednas eating disorder not otherwise
+
+ align:start position:0%
+ednas eating disorder not otherwise
+ 
+
+ align:start position:0%
+ednas eating disorder not otherwise
+specified category that can go up to
+
+ align:start position:0%
+specified category that can go up to
+ 
+
+ align:start position:0%
+specified category that can go up to
+anywhere between two and five percent
+
+ align:start position:0%
+anywhere between two and five percent
+ 
+
+ align:start position:0%
+anywhere between two and five percent
+depending on what you read
+
+ align:start position:0%
+depending on what you read
+ 
+
+ align:start position:0%
+depending on what you read
+if you look at prevalence rates as I say
+
+ align:start position:0%
+if you look at prevalence rates as I say
+ 
+
+ align:start position:0%
+if you look at prevalence rates as I say
+they're about eight to one female to uh
+
+ align:start position:0%
+they're about eight to one female to uh
+ 
+
+ align:start position:0%
+they're about eight to one female to uh
+to male so it's very heavily uh female
+
+ align:start position:0%
+to male so it's very heavily uh female
+ 
+
+ align:start position:0%
+to male so it's very heavily uh female
+disorder
+
+ align:start position:0%
+disorder
+ 
+
+ align:start position:0%
+disorder
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and um and it's a dangerous disorder uh
+
+ align:start position:0%
+and um and it's a dangerous disorder uh
+ 
+
+ align:start position:0%
+and um and it's a dangerous disorder uh
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+for patients with full-blown full-blown
+
+ align:start position:0%
+for patients with full-blown full-blown
+ 
+
+ align:start position:0%
+for patients with full-blown full-blown
+anorexia diagnosis the mortality rate
+
+ align:start position:0%
+anorexia diagnosis the mortality rate
+ 
+
+ align:start position:0%
+anorexia diagnosis the mortality rate
+can be as high as about five percent
+
+ align:start position:0%
+can be as high as about five percent
+ 
+
+ align:start position:0%
+can be as high as about five percent
+that's very high for a disorder of a
+
+ align:start position:0%
+that's very high for a disorder of a
+ 
+
+ align:start position:0%
+that's very high for a disorder of a
+population that's otherwise you know
+
+ align:start position:0%
+population that's otherwise you know
+ 
+
+ align:start position:0%
+population that's otherwise you know
+Health you know young healthy women
+
+ align:start position:0%
+Health you know young healthy women
+ 
+
+ align:start position:0%
+Health you know young healthy women
+um what kills you by the way is not
+
+ align:start position:0%
+um what kills you by the way is not
+ 
+
+ align:start position:0%
+um what kills you by the way is not
+um uh not starving to death but but
+
+ align:start position:0%
+um uh not starving to death but but
+ 
+
+ align:start position:0%
+um uh not starving to death but but
+things like heart attack
+
+ align:start position:0%
+things like heart attack
+ 
+
+ align:start position:0%
+things like heart attack
+um your the electrolytes get in your
+
+ align:start position:0%
+um your the electrolytes get in your
+ 
+
+ align:start position:0%
+um your the electrolytes get in your
+your electrolytes get to be so out of
+
+ align:start position:0%
+your electrolytes get to be so out of
+ 
+
+ align:start position:0%
+your electrolytes get to be so out of
+balance that your heart fails to work
+
+ align:start position:0%
+balance that your heart fails to work
+ 
+
+ align:start position:0%
+balance that your heart fails to work
+and things of that sort it is also a
+
+ align:start position:0%
+and things of that sort it is also a
+ 
+
+ align:start position:0%
+and things of that sort it is also a
+disorder like in a sense like multiple
+
+ align:start position:0%
+disorder like in a sense like multiple
+ 
+
+ align:start position:0%
+disorder like in a sense like multiple
+personality disorder that has changed
+
+ align:start position:0%
+personality disorder that has changed
+ 
+
+ align:start position:0%
+personality disorder that has changed
+greatly in its um uh frequency in the
+
+ align:start position:0%
+greatly in its um uh frequency in the
+ 
+
+ align:start position:0%
+greatly in its um uh frequency in the
+population in
+
+ align:start position:0%
+population in
+ 
+
+ align:start position:0%
+population in
+um in historical time like the last 40
+
+ align:start position:0%
+um in historical time like the last 40
+ 
+
+ align:start position:0%
+um in historical time like the last 40
+years it's different from multiple
+
+ align:start position:0%
+years it's different from multiple
+ 
+
+ align:start position:0%
+years it's different from multiple
+personality disorder in the this change
+
+ align:start position:0%
+personality disorder in the this change
+ 
+
+ align:start position:0%
+personality disorder in the this change
+may be a real change in incidents
+
+ align:start position:0%
+may be a real change in incidents
+ 
+
+ align:start position:0%
+may be a real change in incidents
+remember the argument was that in
+
+ align:start position:0%
+remember the argument was that in
+ 
+
+ align:start position:0%
+remember the argument was that in
+multiple personality disorder
+
+ align:start position:0%
+multiple personality disorder
+ 
+
+ align:start position:0%
+multiple personality disorder
+um dissociative disorder had been there
+
+ align:start position:0%
+um dissociative disorder had been there
+ 
+
+ align:start position:0%
+um dissociative disorder had been there
+all along
+
+ align:start position:0%
+all along
+ 
+
+ align:start position:0%
+all along
+and that multiple personality was merely
+
+ align:start position:0%
+and that multiple personality was merely
+ 
+
+ align:start position:0%
+and that multiple personality was merely
+the way that it manifests itself that
+
+ align:start position:0%
+the way that it manifests itself that
+ 
+
+ align:start position:0%
+the way that it manifests itself that
+the dissociate the dissociative disorder
+
+ align:start position:0%
+the dissociate the dissociative disorder
+ 
+
+ align:start position:0%
+the dissociate the dissociative disorder
+manifested itself in um in modern
+
+ align:start position:0%
+manifested itself in um in modern
+ 
+
+ align:start position:0%
+manifested itself in um in modern
+Western
+
+ align:start position:0%
+Western
+ 
+
+ align:start position:0%
+Western
+um culture
+
+ align:start position:0%
+um culture
+ 
+
+ align:start position:0%
+um culture
+um in the case of Eating Disorders it
+
+ align:start position:0%
+um in the case of Eating Disorders it
+ 
+
+ align:start position:0%
+um in the case of Eating Disorders it
+rarely may be that the disorder is
+
+ align:start position:0%
+rarely may be that the disorder is
+ 
+
+ align:start position:0%
+rarely may be that the disorder is
+itself more frequent
+
+ align:start position:0%
+itself more frequent
+ 
+
+ align:start position:0%
+itself more frequent
+um than it than it's been in the past
+
+ align:start position:0%
+um than it than it's been in the past
+ 
+
+ align:start position:0%
+um than it than it's been in the past
+um it is certainly a uh
+
+ align:start position:0%
+um it is certainly a uh
+ 
+
+ align:start position:0%
+um it is certainly a uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it depends on what Society you are in it
+
+ align:start position:0%
+it depends on what Society you are in it
+ 
+
+ align:start position:0%
+it depends on what Society you are in it
+was characteristically oh you know is
+
+ align:start position:0%
+was characteristically oh you know is
+ 
+
+ align:start position:0%
+was characteristically oh you know is
+even as recently as probably 20 years
+
+ align:start position:0%
+even as recently as probably 20 years
+ 
+
+ align:start position:0%
+even as recently as probably 20 years
+ago it was absolutely characteristically
+
+ align:start position:0%
+ago it was absolutely characteristically
+ 
+
+ align:start position:0%
+ago it was absolutely characteristically
+a disease of middle class white girls
+
+ align:start position:0%
+a disease of middle class white girls
+ 
+
+ align:start position:0%
+a disease of middle class white girls
+um it has since managed to
+
+ align:start position:0%
+um it has since managed to
+ 
+
+ align:start position:0%
+um it has since managed to
+um Embrace diversity and um and reach
+
+ align:start position:0%
+um Embrace diversity and um and reach
+ 
+
+ align:start position:0%
+um Embrace diversity and um and reach
+out to other groups in in Western
+
+ align:start position:0%
+out to other groups in in Western
+ 
+
+ align:start position:0%
+out to other groups in in Western
+culture for instance virtually unknown
+
+ align:start position:0%
+culture for instance virtually unknown
+ 
+
+ align:start position:0%
+culture for instance virtually unknown
+in Japan
+
+ align:start position:0%
+in Japan
+ 
+
+ align:start position:0%
+in Japan
+um until fairly recently but now is a
+
+ align:start position:0%
+um until fairly recently but now is a
+ 
+
+ align:start position:0%
+um until fairly recently but now is a
+disorder showing up in in Japan I think
+
+ align:start position:0%
+disorder showing up in in Japan I think
+ 
+
+ align:start position:0%
+disorder showing up in in Japan I think
+I just read something that is even more
+
+ align:start position:0%
+I just read something that is even more
+ 
+
+ align:start position:0%
+I just read something that is even more
+recently now starting to show up in uh
+
+ align:start position:0%
+recently now starting to show up in uh
+ 
+
+ align:start position:0%
+recently now starting to show up in uh
+in mainland China where it was unknown
+
+ align:start position:0%
+in mainland China where it was unknown
+ 
+
+ align:start position:0%
+in mainland China where it was unknown
+one of the requirements for a good
+
+ align:start position:0%
+one of the requirements for a good
+ 
+
+ align:start position:0%
+one of the requirements for a good
+eating disorder population by the way is
+
+ align:start position:0%
+eating disorder population by the way is
+ 
+
+ align:start position:0%
+eating disorder population by the way is
+a culture where there's lots of food you
+
+ align:start position:0%
+a culture where there's lots of food you
+ 
+
+ align:start position:0%
+a culture where there's lots of food you
+don't have people with eating disorders
+
+ align:start position:0%
+don't have people with eating disorders
+ 
+
+ align:start position:0%
+don't have people with eating disorders
+of this sort in
+
+ align:start position:0%
+of this sort in
+ 
+
+ align:start position:0%
+of this sort in
+um in famine yeah you you can be 75
+
+ align:start position:0%
+um in famine yeah you you can be 75
+ 
+
+ align:start position:0%
+um in famine yeah you you can be 75
+pounds when you're supposed to be 100
+
+ align:start position:0%
+pounds when you're supposed to be 100
+ 
+
+ align:start position:0%
+pounds when you're supposed to be 100
+pounds because there isn't enough food
+
+ align:start position:0%
+pounds because there isn't enough food
+ 
+
+ align:start position:0%
+pounds because there isn't enough food
+but it's not because you're you're
+
+ align:start position:0%
+but it's not because you're you're
+ 
+
+ align:start position:0%
+but it's not because you're you're
+refusing to uh to maintain your body
+
+ align:start position:0%
+refusing to uh to maintain your body
+ 
+
+ align:start position:0%
+refusing to uh to maintain your body
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+um so it it is a disorder of a society
+
+ align:start position:0%
+um so it it is a disorder of a society
+ 
+
+ align:start position:0%
+um so it it is a disorder of a society
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+um feeding everybody uh six that would
+
+ align:start position:0%
+um feeding everybody uh six that would
+ 
+
+ align:start position:0%
+um feeding everybody uh six that would
+be able to feed everybody
+
+ align:start position:0%
+be able to feed everybody
+ 
+
+ align:start position:0%
+be able to feed everybody
+successfully
+
+ align:start position:0%
+successfully
+ 
+
+ align:start position:0%
+successfully
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+where does this come from what's its
+
+ align:start position:0%
+where does this come from what's its
+ 
+
+ align:start position:0%
+where does this come from what's its
+etiology what are the risk factors that
+
+ align:start position:0%
+etiology what are the risk factors that
+ 
+
+ align:start position:0%
+etiology what are the risk factors that
+that that that that contribute here
+
+ align:start position:0%
+that that that that contribute here
+ 
+
+ align:start position:0%
+that that that that contribute here
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can tell it must be time to flip pages
+
+ align:start position:0%
+I can tell it must be time to flip pages
+ 
+
+ align:start position:0%
+I can tell it must be time to flip pages
+on the handout right look at that what's
+
+ align:start position:0%
+on the handout right look at that what's
+ 
+
+ align:start position:0%
+on the handout right look at that what's
+the causes
+
+ align:start position:0%
+the causes
+ 
+
+ align:start position:0%
+the causes
+um and it reminds me to uh about to to
+
+ align:start position:0%
+um and it reminds me to uh about to to
+ 
+
+ align:start position:0%
+um and it reminds me to uh about to to
+caution
+
+ align:start position:0%
+caution
+ 
+
+ align:start position:0%
+caution
+um to step back for a couple of
+
+ align:start position:0%
+um to step back for a couple of
+ 
+
+ align:start position:0%
+um to step back for a couple of
+questions the primary caution here is
+
+ align:start position:0%
+questions the primary caution here is
+ 
+
+ align:start position:0%
+questions the primary caution here is
+um that this is not
+
+ align:start position:0%
+um that this is not
+ 
+
+ align:start position:0%
+um that this is not
+um intended to be talking about uh you
+
+ align:start position:0%
+um intended to be talking about uh you
+ 
+
+ align:start position:0%
+um intended to be talking about uh you
+specifically
+
+ align:start position:0%
+specifically
+ 
+
+ align:start position:0%
+specifically
+um because well all right dear well
+
+ align:start position:0%
+um because well all right dear well
+ 
+
+ align:start position:0%
+um because well all right dear well
+let's Jump Ahead uh we can say stuff
+
+ align:start position:0%
+let's Jump Ahead uh we can say stuff
+ 
+
+ align:start position:0%
+let's Jump Ahead uh we can say stuff
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um the uh uh again typically the girl
+
+ align:start position:0%
+um the uh uh again typically the girl
+ 
+
+ align:start position:0%
+um the uh uh again typically the girl
+who is a patient
+
+ align:start position:0%
+who is a patient
+ 
+
+ align:start position:0%
+who is a patient
+um there are characteristics that not
+
+ align:start position:0%
+um there are characteristics that not
+ 
+
+ align:start position:0%
+um there are characteristics that not
+not every you know it's a big wide
+
+ align:start position:0%
+not every you know it's a big wide
+ 
+
+ align:start position:0%
+not every you know it's a big wide
+distribution as usual but we can say
+
+ align:start position:0%
+distribution as usual but we can say
+ 
+
+ align:start position:0%
+distribution as usual but we can say
+something about where the where where
+
+ align:start position:0%
+something about where the where where
+ 
+
+ align:start position:0%
+something about where the where where
+where the the sort of typical patient
+
+ align:start position:0%
+where the the sort of typical patient
+ 
+
+ align:start position:0%
+where the the sort of typical patient
+might lie typically she is
+
+ align:start position:0%
+might lie typically she is
+ 
+
+ align:start position:0%
+might lie typically she is
+um uh adolescent shortly at you know
+
+ align:start position:0%
+um uh adolescent shortly at you know
+ 
+
+ align:start position:0%
+um uh adolescent shortly at you know
+sometime after the onset of puberty is
+
+ align:start position:0%
+sometime after the onset of puberty is
+ 
+
+ align:start position:0%
+sometime after the onset of puberty is
+is is the uh sort of risk period for the
+
+ align:start position:0%
+is is the uh sort of risk period for the
+ 
+
+ align:start position:0%
+is is the uh sort of risk period for the
+onset of and anorexia typically
+
+ align:start position:0%
+onset of and anorexia typically
+ 
+
+ align:start position:0%
+onset of and anorexia typically
+described as a good girl something of a
+
+ align:start position:0%
+described as a good girl something of a
+ 
+
+ align:start position:0%
+described as a good girl something of a
+perfectionist the one who never gave any
+
+ align:start position:0%
+perfectionist the one who never gave any
+ 
+
+ align:start position:0%
+perfectionist the one who never gave any
+trouble and now you should be
+
+ align:start position:0%
+trouble and now you should be
+ 
+
+ align:start position:0%
+trouble and now you should be
+immediately able to see why I put this
+
+ align:start position:0%
+immediately able to see why I put this
+ 
+
+ align:start position:0%
+immediately able to see why I put this
+caution in that I'm not talking about
+
+ align:start position:0%
+caution in that I'm not talking about
+ 
+
+ align:start position:0%
+caution in that I'm not talking about
+you who in the world gets to MIT by
+
+ align:start position:0%
+you who in the world gets to MIT by
+ 
+
+ align:start position:0%
+you who in the world gets to MIT by
+being a a bad evil non-perfectionist
+
+ align:start position:0%
+being a a bad evil non-perfectionist
+ 
+
+ align:start position:0%
+being a a bad evil non-perfectionist
+well you know there's a couple of you
+
+ align:start position:0%
+well you know there's a couple of you
+ 
+
+ align:start position:0%
+well you know there's a couple of you
+here maybe who you know just got through
+
+ align:start position:0%
+here maybe who you know just got through
+ 
+
+ align:start position:0%
+here maybe who you know just got through
+because your brilliant bad evil
+
+ align:start position:0%
+because your brilliant bad evil
+ 
+
+ align:start position:0%
+because your brilliant bad evil
+non-perfectionist or something like that
+
+ align:start position:0%
+non-perfectionist or something like that
+ 
+
+ align:start position:0%
+non-perfectionist or something like that
+but the rest of you spent your those
+
+ align:start position:0%
+but the rest of you spent your those
+ 
+
+ align:start position:0%
+but the rest of you spent your those
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+adolescent years
+
+ align:start position:0%
+adolescent years
+ 
+
+ align:start position:0%
+adolescent years
+um being very those of you who were
+
+ align:start position:0%
+um being very those of you who were
+ 
+
+ align:start position:0%
+um being very those of you who were
+women the rest of you didn't spend your
+
+ align:start position:0%
+women the rest of you didn't spend your
+ 
+
+ align:start position:0%
+women the rest of you didn't spend your
+time being women
+
+ align:start position:0%
+time being women
+ 
+
+ align:start position:0%
+time being women
+um but but
+
+ align:start position:0%
+um but but
+ 
+
+ align:start position:0%
+um but but
+um you know you spent your time being
+
+ align:start position:0%
+um you know you spent your time being
+ 
+
+ align:start position:0%
+um you know you spent your time being
+good and doing your homework and not
+
+ align:start position:0%
+good and doing your homework and not
+ 
+
+ align:start position:0%
+good and doing your homework and not
+raising a lot of trouble and stuff like
+
+ align:start position:0%
+raising a lot of trouble and stuff like
+ 
+
+ align:start position:0%
+raising a lot of trouble and stuff like
+that oh great now let's talk about the
+
+ align:start position:0%
+that oh great now let's talk about the
+ 
+
+ align:start position:0%
+that oh great now let's talk about the
+family a bit the family this is it's an
+
+ align:start position:0%
+family a bit the family this is it's an
+ 
+
+ align:start position:0%
+family a bit the family this is it's an
+interesting disorder because it's
+
+ align:start position:0%
+interesting disorder because it's
+ 
+
+ align:start position:0%
+interesting disorder because it's
+interesting it turns out to be important
+
+ align:start position:0%
+interesting it turns out to be important
+ 
+
+ align:start position:0%
+interesting it turns out to be important
+to talk about the family if you are
+
+ align:start position:0%
+to talk about the family if you are
+ 
+
+ align:start position:0%
+to talk about the family if you are
+dealing with a lot of other uh health
+
+ align:start position:0%
+dealing with a lot of other uh health
+ 
+
+ align:start position:0%
+dealing with a lot of other uh health
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+your family background is of some
+
+ align:start position:0%
+your family background is of some
+ 
+
+ align:start position:0%
+your family background is of some
+interest particularly for sort of
+
+ align:start position:0%
+interest particularly for sort of
+ 
+
+ align:start position:0%
+interest particularly for sort of
+genetic reasons
+
+ align:start position:0%
+genetic reasons
+ 
+
+ align:start position:0%
+genetic reasons
+um but the structure of your family is
+
+ align:start position:0%
+um but the structure of your family is
+ 
+
+ align:start position:0%
+um but the structure of your family is
+typically not desperately important here
+
+ align:start position:0%
+typically not desperately important here
+ 
+
+ align:start position:0%
+typically not desperately important here
+it may really be important the family
+
+ align:start position:0%
+it may really be important the family
+ 
+
+ align:start position:0%
+it may really be important the family
+again wide range possible but the
+
+ align:start position:0%
+again wide range possible but the
+ 
+
+ align:start position:0%
+again wide range possible but the
+typical family would be one that's
+
+ align:start position:0%
+typical family would be one that's
+ 
+
+ align:start position:0%
+typical family would be one that's
+described as what have I got here
+
+ align:start position:0%
+described as what have I got here
+ 
+
+ align:start position:0%
+described as what have I got here
+overprotective and
+
+ align:start position:0%
+overprotective and
+ 
+
+ align:start position:0%
+overprotective and
+um also perfectionist achievement
+
+ align:start position:0%
+um also perfectionist achievement
+ 
+
+ align:start position:0%
+um also perfectionist achievement
+oriented and you're sitting there saying
+
+ align:start position:0%
+oriented and you're sitting there saying
+ 
+
+ align:start position:0%
+oriented and you're sitting there saying
+oh my God Not only was I good but my
+
+ align:start position:0%
+oh my God Not only was I good but my
+ 
+
+ align:start position:0%
+oh my God Not only was I good but my
+family they're overprotective and and
+
+ align:start position:0%
+family they're overprotective and and
+ 
+
+ align:start position:0%
+family they're overprotective and and
+their achievement oriented and when I
+
+ align:start position:0%
+their achievement oriented and when I
+ 
+
+ align:start position:0%
+their achievement oriented and when I
+said that you know what I really wanted
+
+ align:start position:0%
+said that you know what I really wanted
+ 
+
+ align:start position:0%
+said that you know what I really wanted
+to do was go to the Community College
+
+ align:start position:0%
+to do was go to the Community College
+ 
+
+ align:start position:0%
+to do was go to the Community College
+they they they locked me in my room for
+
+ align:start position:0%
+they they they locked me in my room for
+ 
+
+ align:start position:0%
+they they they locked me in my room for
+three days until I finished the MIT
+
+ align:start position:0%
+three days until I finished the MIT
+ 
+
+ align:start position:0%
+three days until I finished the MIT
+application and stuff
+
+ align:start position:0%
+application and stuff
+ 
+
+ align:start position:0%
+application and stuff
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+this this this is our history these are
+
+ align:start position:0%
+this this this is our history these are
+ 
+
+ align:start position:0%
+this this this is our history these are
+our people we know them
+
+ align:start position:0%
+our people we know them
+ 
+
+ align:start position:0%
+our people we know them
+um the the other characteristic to
+
+ align:start position:0%
+um the the other characteristic to
+ 
+
+ align:start position:0%
+um the the other characteristic to
+introduce a little piece of jargon here
+
+ align:start position:0%
+introduce a little piece of jargon here
+ 
+
+ align:start position:0%
+introduce a little piece of jargon here
+um the family are described as enmeshed
+
+ align:start position:0%
+um the family are described as enmeshed
+ 
+
+ align:start position:0%
+um the family are described as enmeshed
+this is a piece of jargon that I
+
+ align:start position:0%
+this is a piece of jargon that I
+ 
+
+ align:start position:0%
+this is a piece of jargon that I
+understand well because I come from a a
+
+ align:start position:0%
+understand well because I come from a a
+ 
+
+ align:start position:0%
+understand well because I come from a a
+family that that is beautifully
+
+ align:start position:0%
+family that that is beautifully
+ 
+
+ align:start position:0%
+family that that is beautifully
+described you know beautifully fits the
+
+ align:start position:0%
+described you know beautifully fits the
+ 
+
+ align:start position:0%
+described you know beautifully fits the
+enmeshed idea I don't understand how my
+
+ align:start position:0%
+enmeshed idea I don't understand how my
+ 
+
+ align:start position:0%
+enmeshed idea I don't understand how my
+sisters got through their their um you
+
+ align:start position:0%
+sisters got through their their um you
+ 
+
+ align:start position:0%
+sisters got through their their um you
+know youth without an eating disorder
+
+ align:start position:0%
+know youth without an eating disorder
+ 
+
+ align:start position:0%
+know youth without an eating disorder
+because if I every year when I talk
+
+ align:start position:0%
+because if I every year when I talk
+ 
+
+ align:start position:0%
+because if I every year when I talk
+about this if I talk about the risk
+
+ align:start position:0%
+about this if I talk about the risk
+ 
+
+ align:start position:0%
+about this if I talk about the risk
+factors you know it just sounds like my
+
+ align:start position:0%
+factors you know it just sounds like my
+ 
+
+ align:start position:0%
+factors you know it just sounds like my
+family
+
+ align:start position:0%
+family
+ 
+
+ align:start position:0%
+family
+um our nice achievement oriented
+
+ align:start position:0%
+um our nice achievement oriented
+ 
+
+ align:start position:0%
+um our nice achievement oriented
+enmeshed family imeshed means a family
+
+ align:start position:0%
+enmeshed family imeshed means a family
+ 
+
+ align:start position:0%
+enmeshed family imeshed means a family
+where people imagine a family like yours
+
+ align:start position:0%
+where people imagine a family like yours
+ 
+
+ align:start position:0%
+where people imagine a family like yours
+may be where people finish each other's
+
+ align:start position:0%
+may be where people finish each other's
+ 
+
+ align:start position:0%
+may be where people finish each other's
+sentences and stuff like that they're
+
+ align:start position:0%
+sentences and stuff like that they're
+ 
+
+ align:start position:0%
+sentences and stuff like that they're
+sort of all over each other
+
+ align:start position:0%
+sort of all over each other
+ 
+
+ align:start position:0%
+sort of all over each other
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+psychologically they know
+
+ align:start position:0%
+psychologically they know
+ 
+
+ align:start position:0%
+psychologically they know
+um you know what uh what they want they
+
+ align:start position:0%
+um you know what uh what they want they
+ 
+
+ align:start position:0%
+um you know what uh what they want they
+know what you want and everybody you
+
+ align:start position:0%
+know what you want and everybody you
+ 
+
+ align:start position:0%
+know what you want and everybody you
+know look the place to see it in in the
+
+ align:start position:0%
+know look the place to see it in in the
+ 
+
+ align:start position:0%
+know look the place to see it in in the
+wolf family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um as as my my wife who of course
+
+ align:start position:0%
+um as as my my wife who of course
+ 
+
+ align:start position:0%
+um as as my my wife who of course
+married into this found out is go out to
+
+ align:start position:0%
+married into this found out is go out to
+ 
+
+ align:start position:0%
+married into this found out is go out to
+dinner with them
+
+ align:start position:0%
+dinner with them
+ 
+
+ align:start position:0%
+dinner with them
+you don't want to do this because it's
+
+ align:start position:0%
+you don't want to do this because it's
+ 
+
+ align:start position:0%
+you don't want to do this because it's
+pathological first you got to decide
+
+ align:start position:0%
+pathological first you got to decide
+ 
+
+ align:start position:0%
+pathological first you got to decide
+where to go for dinner right so
+
+ align:start position:0%
+where to go for dinner right so
+ 
+
+ align:start position:0%
+where to go for dinner right so
+everybody gets together you decide where
+
+ align:start position:0%
+everybody gets together you decide where
+ 
+
+ align:start position:0%
+everybody gets together you decide where
+to go to dinner you've almost got a
+
+ align:start position:0%
+to go to dinner you've almost got a
+ 
+
+ align:start position:0%
+to go to dinner you've almost got a
+consensus you're gonna go to like Legal
+
+ align:start position:0%
+consensus you're gonna go to like Legal
+ 
+
+ align:start position:0%
+consensus you're gonna go to like Legal
+Seafood or something at which point one
+
+ align:start position:0%
+Seafood or something at which point one
+ 
+
+ align:start position:0%
+Seafood or something at which point one
+of us it might well be me points out
+
+ align:start position:0%
+of us it might well be me points out
+ 
+
+ align:start position:0%
+of us it might well be me points out
+my mother doesn't really like fish is my
+
+ align:start position:0%
+my mother doesn't really like fish is my
+ 
+
+ align:start position:0%
+my mother doesn't really like fish is my
+mother fussing about this no my mother's
+
+ align:start position:0%
+mother fussing about this no my mother's
+ 
+
+ align:start position:0%
+mother fussing about this no my mother's
+perfectly happy to go along with what
+
+ align:start position:0%
+perfectly happy to go along with what
+ 
+
+ align:start position:0%
+perfectly happy to go along with what
+everybody else wants but you know I'll
+
+ align:start position:0%
+everybody else wants but you know I'll
+ 
+
+ align:start position:0%
+everybody else wants but you know I'll
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+but but mom doesn't like fish well
+
+ align:start position:0%
+but but mom doesn't like fish well
+ 
+
+ align:start position:0%
+but but mom doesn't like fish well
+actually these days I would say but Gaga
+
+ align:start position:0%
+actually these days I would say but Gaga
+ 
+
+ align:start position:0%
+actually these days I would say but Gaga
+doesn't like fish my eldest child when
+
+ align:start position:0%
+doesn't like fish my eldest child when
+ 
+
+ align:start position:0%
+doesn't like fish my eldest child when
+he was a toddler named my mother Gaga
+
+ align:start position:0%
+he was a toddler named my mother Gaga
+ 
+
+ align:start position:0%
+he was a toddler named my mother Gaga
+and that's been her name ever since
+
+ align:start position:0%
+and that's been her name ever since
+ 
+
+ align:start position:0%
+and that's been her name ever since
+which is you know she deals with it
+
+ align:start position:0%
+which is you know she deals with it
+ 
+
+ align:start position:0%
+which is you know she deals with it
+um anyway
+
+ align:start position:0%
+um anyway
+ 
+
+ align:start position:0%
+um anyway
+um so all right so all right we gotta
+
+ align:start position:0%
+um so all right so all right we gotta
+ 
+
+ align:start position:0%
+um so all right so all right we gotta
+cancel that one so now the whole
+
+ align:start position:0%
+cancel that one so now the whole
+ 
+
+ align:start position:0%
+cancel that one so now the whole
+conversation starts again and you can do
+
+ align:start position:0%
+conversation starts again and you can do
+ 
+
+ align:start position:0%
+conversation starts again and you can do
+this for hours
+
+ align:start position:0%
+this for hours
+ 
+
+ align:start position:0%
+this for hours
+right if Julie my spouse learned the
+
+ align:start position:0%
+right if Julie my spouse learned the
+ 
+
+ align:start position:0%
+right if Julie my spouse learned the
+best thing to do particularly if we're
+
+ align:start position:0%
+best thing to do particularly if we're
+ 
+
+ align:start position:0%
+best thing to do particularly if we're
+like out somewhere you're wandering
+
+ align:start position:0%
+like out somewhere you're wandering
+ 
+
+ align:start position:0%
+like out somewhere you're wandering
+around trying to decide where to go to a
+
+ align:start position:0%
+around trying to decide where to go to a
+ 
+
+ align:start position:0%
+around trying to decide where to go to a
+restaurant is just drop about five six
+
+ align:start position:0%
+restaurant is just drop about five six
+ 
+
+ align:start position:0%
+restaurant is just drop about five six
+Paces back you just don't want to be in
+
+ align:start position:0%
+Paces back you just don't want to be in
+ 
+
+ align:start position:0%
+Paces back you just don't want to be in
+this conversation but eventually if
+
+ align:start position:0%
+this conversation but eventually if
+ 
+
+ align:start position:0%
+this conversation but eventually if
+eventually we'll end up at a restaurant
+
+ align:start position:0%
+eventually we'll end up at a restaurant
+ 
+
+ align:start position:0%
+eventually we'll end up at a restaurant
+at which point everybody's ordering for
+
+ align:start position:0%
+at which point everybody's ordering for
+ 
+
+ align:start position:0%
+at which point everybody's ordering for
+everybody else
+
+ align:start position:0%
+everybody else
+ 
+
+ align:start position:0%
+everybody else
+and is ordering stuff that they don't
+
+ align:start position:0%
+and is ordering stuff that they don't
+ 
+
+ align:start position:0%
+and is ordering stuff that they don't
+necessarily want to
+
+ align:start position:0%
+necessarily want to
+ 
+
+ align:start position:0%
+necessarily want to
+but they think somebody else might want
+
+ align:start position:0%
+but they think somebody else might want
+ 
+
+ align:start position:0%
+but they think somebody else might want
+to eat my mother is the queen of this my
+
+ align:start position:0%
+to eat my mother is the queen of this my
+ 
+
+ align:start position:0%
+to eat my mother is the queen of this my
+mother will will order things she
+
+ align:start position:0%
+mother will will order things she
+ 
+
+ align:start position:0%
+mother will will order things she
+doesn't even like because she thinks one
+
+ align:start position:0%
+doesn't even like because she thinks one
+ 
+
+ align:start position:0%
+doesn't even like because she thinks one
+of her children wants to try it or
+
+ align:start position:0%
+of her children wants to try it or
+ 
+
+ align:start position:0%
+of her children wants to try it or
+something like that and this is still
+
+ align:start position:0%
+something like that and this is still
+ 
+
+ align:start position:0%
+something like that and this is still
+true now that her children are in their
+
+ align:start position:0%
+true now that her children are in their
+ 
+
+ align:start position:0%
+true now that her children are in their
+late 40s right yeah it's it's okay Ma
+
+ align:start position:0%
+late 40s right yeah it's it's okay Ma
+ 
+
+ align:start position:0%
+late 40s right yeah it's it's okay Ma
+I'm I'm not I'm not starving anymore
+
+ align:start position:0%
+I'm I'm not I'm not starving anymore
+ 
+
+ align:start position:0%
+I'm I'm not I'm not starving anymore
+um anyway that's enmeshed and that um
+
+ align:start position:0%
+um anyway that's enmeshed and that um
+ 
+
+ align:start position:0%
+um anyway that's enmeshed and that um
+the these these families are also
+
+ align:start position:0%
+the these these families are also
+ 
+
+ align:start position:0%
+the these these families are also
+characteristically
+
+ align:start position:0%
+characteristically
+ 
+
+ align:start position:0%
+characteristically
+um intolerant of expressions of of of of
+
+ align:start position:0%
+um intolerant of expressions of of of of
+ 
+
+ align:start position:0%
+um intolerant of expressions of of of of
+conflict and anger it's not that there
+
+ align:start position:0%
+conflict and anger it's not that there
+ 
+
+ align:start position:0%
+conflict and anger it's not that there
+aren't conflicts in these in in these
+
+ align:start position:0%
+aren't conflicts in these in in these
+ 
+
+ align:start position:0%
+aren't conflicts in these in in these
+settings but the family will will act as
+
+ align:start position:0%
+settings but the family will will act as
+ 
+
+ align:start position:0%
+settings but the family will will act as
+a unit to smooth them out this is not a
+
+ align:start position:0%
+a unit to smooth them out this is not a
+ 
+
+ align:start position:0%
+a unit to smooth them out this is not a
+uh uh you know a dramatic family where
+
+ align:start position:0%
+uh uh you know a dramatic family where
+ 
+
+ align:start position:0%
+uh uh you know a dramatic family where
+people throw Crocker at each other
+
+ align:start position:0%
+people throw Crocker at each other
+ 
+
+ align:start position:0%
+people throw Crocker at each other
+um and and and then uh you know in Act
+
+ align:start position:0%
+um and and and then uh you know in Act
+ 
+
+ align:start position:0%
+um and and and then uh you know in Act
+five they all hug or something like that
+
+ align:start position:0%
+five they all hug or something like that
+ 
+
+ align:start position:0%
+five they all hug or something like that
+this is a family where where if there's
+
+ align:start position:0%
+this is a family where where if there's
+ 
+
+ align:start position:0%
+this is a family where where if there's
+an issue it's it's dealt with in some
+
+ align:start position:0%
+an issue it's it's dealt with in some
+ 
+
+ align:start position:0%
+an issue it's it's dealt with in some
+quiet perhaps even subterranean
+
+ align:start position:0%
+quiet perhaps even subterranean
+ 
+
+ align:start position:0%
+quiet perhaps even subterranean
+kind of a way
+
+ align:start position:0%
+kind of a way
+ 
+
+ align:start position:0%
+kind of a way
+um so um
+
+ align:start position:0%
+um so um
+ 
+
+ align:start position:0%
+um so um
+so those that that's sort of the the the
+
+ align:start position:0%
+so those that that's sort of the the the
+ 
+
+ align:start position:0%
+so those that that's sort of the the the
+the patient and and and the family and
+
+ align:start position:0%
+the patient and and and the family and
+ 
+
+ align:start position:0%
+the patient and and and the family and
+uh and and then you've got to ask in a
+
+ align:start position:0%
+uh and and then you've got to ask in a
+ 
+
+ align:start position:0%
+uh and and then you've got to ask in a
+uh we're given a disorder that has been
+
+ align:start position:0%
+uh we're given a disorder that has been
+ 
+
+ align:start position:0%
+uh we're given a disorder that has been
+a disorder of
+
+ align:start position:0%
+a disorder of
+ 
+
+ align:start position:0%
+a disorder of
+um Western middle class culture you've
+
+ align:start position:0%
+um Western middle class culture you've
+ 
+
+ align:start position:0%
+um Western middle class culture you've
+got to ask what it is about the culture
+
+ align:start position:0%
+got to ask what it is about the culture
+ 
+
+ align:start position:0%
+got to ask what it is about the culture
+that might be contributory here
+
+ align:start position:0%
+that might be contributory here
+ 
+
+ align:start position:0%
+that might be contributory here
+again that's uh
+
+ align:start position:0%
+again that's uh
+ 
+
+ align:start position:0%
+again that's uh
+there there are other situations in
+
+ align:start position:0%
+there there are other situations in
+ 
+
+ align:start position:0%
+there there are other situations in
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+um uh the the broader environment is
+
+ align:start position:0%
+um uh the the broader environment is
+ 
+
+ align:start position:0%
+um uh the the broader environment is
+important like is it putting stress on
+
+ align:start position:0%
+important like is it putting stress on
+ 
+
+ align:start position:0%
+important like is it putting stress on
+on on on on you in some sort of global
+
+ align:start position:0%
+on on on on you in some sort of global
+ 
+
+ align:start position:0%
+on on on on you in some sort of global
+kind of a way but here the specific
+
+ align:start position:0%
+kind of a way but here the specific
+ 
+
+ align:start position:0%
+kind of a way but here the specific
+demands of the culture turn out to be of
+
+ align:start position:0%
+demands of the culture turn out to be of
+ 
+
+ align:start position:0%
+demands of the culture turn out to be of
+particular interest
+
+ align:start position:0%
+particular interest
+ 
+
+ align:start position:0%
+particular interest
+um and the particular demand that um
+
+ align:start position:0%
+um and the particular demand that um
+ 
+
+ align:start position:0%
+um and the particular demand that um
+that people
+
+ align:start position:0%
+that people
+ 
+
+ align:start position:0%
+that people
+focus on is the
+
+ align:start position:0%
+focus on is the
+ 
+
+ align:start position:0%
+focus on is the
+degree to which
+
+ align:start position:0%
+degree to which
+ 
+
+ align:start position:0%
+degree to which
+um American culture more broadly Western
+
+ align:start position:0%
+um American culture more broadly Western
+ 
+
+ align:start position:0%
+um American culture more broadly Western
+culture is simultaneously obsessed with
+
+ align:start position:0%
+culture is simultaneously obsessed with
+ 
+
+ align:start position:0%
+culture is simultaneously obsessed with
+both food and thinness this is a
+
+ align:start position:0%
+both food and thinness this is a
+ 
+
+ align:start position:0%
+both food and thinness this is a
+difficult combination
+
+ align:start position:0%
+difficult combination
+ 
+
+ align:start position:0%
+difficult combination
+right so um what's what's the how do we
+
+ align:start position:0%
+right so um what's what's the how do we
+ 
+
+ align:start position:0%
+right so um what's what's the how do we
+know that you're that this is a culture
+
+ align:start position:0%
+know that you're that this is a culture
+ 
+
+ align:start position:0%
+know that you're that this is a culture
+obsessed with thinness
+
+ align:start position:0%
+obsessed with thinness
+ 
+
+ align:start position:0%
+obsessed with thinness
+um one of the most telling ways is to
+
+ align:start position:0%
+um one of the most telling ways is to
+ 
+
+ align:start position:0%
+um one of the most telling ways is to
+take a look at
+
+ align:start position:0%
+take a look at
+ 
+
+ align:start position:0%
+take a look at
+um the so the ideals of female Beauty
+
+ align:start position:0%
+um the so the ideals of female Beauty
+ 
+
+ align:start position:0%
+um the so the ideals of female Beauty
+what is it that that makes uh that that
+
+ align:start position:0%
+what is it that that makes uh that that
+ 
+
+ align:start position:0%
+what is it that that makes uh that that
+the society as a whole declares to be
+
+ align:start position:0%
+the society as a whole declares to be
+ 
+
+ align:start position:0%
+the society as a whole declares to be
+beautiful in um
+
+ align:start position:0%
+beautiful in um
+ 
+
+ align:start position:0%
+beautiful in um
+in women
+
+ align:start position:0%
+in women
+ 
+
+ align:start position:0%
+in women
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you do uh something like I don't have
+
+ align:start position:0%
+if you do uh something like I don't have
+ 
+
+ align:start position:0%
+if you do uh something like I don't have
+to I should check if there's a cool
+
+ align:start position:0%
+to I should check if there's a cool
+ 
+
+ align:start position:0%
+to I should check if there's a cool
+website for this
+
+ align:start position:0%
+website for this
+ 
+
+ align:start position:0%
+website for this
+um if you just line up the pictures of
+
+ align:start position:0%
+um if you just line up the pictures of
+ 
+
+ align:start position:0%
+um if you just line up the pictures of
+Miss America for instance
+
+ align:start position:0%
+Miss America for instance
+ 
+
+ align:start position:0%
+Miss America for instance
+um over the last uh uh you know 50 60
+
+ align:start position:0%
+um over the last uh uh you know 50 60
+ 
+
+ align:start position:0%
+um over the last uh uh you know 50 60
+years if you take a look at Miss America
+
+ align:start position:0%
+years if you take a look at Miss America
+ 
+
+ align:start position:0%
+years if you take a look at Miss America
+from the 1940s you would agree that
+
+ align:start position:0%
+from the 1940s you would agree that
+ 
+
+ align:start position:0%
+from the 1940s you would agree that
+she's a perfectly attractive looking
+
+ align:start position:0%
+she's a perfectly attractive looking
+ 
+
+ align:start position:0%
+she's a perfectly attractive looking
+woman but you'd think she looks a little
+
+ align:start position:0%
+woman but you'd think she looks a little
+ 
+
+ align:start position:0%
+woman but you'd think she looks a little
+chunky
+
+ align:start position:0%
+chunky
+ 
+
+ align:start position:0%
+chunky
+um she there's a lot more on her than
+
+ align:start position:0%
+um she there's a lot more on her than
+ 
+
+ align:start position:0%
+um she there's a lot more on her than
+um than would be the case for uh for a
+
+ align:start position:0%
+um than would be the case for uh for a
+ 
+
+ align:start position:0%
+um than would be the case for uh for a
+modern Miss America or a modern oh open
+
+ align:start position:0%
+modern Miss America or a modern oh open
+ 
+
+ align:start position:0%
+modern Miss America or a modern oh open
+up a a a a fashion magazine at random
+
+ align:start position:0%
+up a a a a fashion magazine at random
+ 
+
+ align:start position:0%
+up a a a a fashion magazine at random
+and look at the models
+
+ align:start position:0%
+and look at the models
+ 
+
+ align:start position:0%
+and look at the models
+um much skinnier than the ideal would
+
+ align:start position:0%
+um much skinnier than the ideal would
+ 
+
+ align:start position:0%
+um much skinnier than the ideal would
+have been a couple of generations ago or
+
+ align:start position:0%
+have been a couple of generations ago or
+ 
+
+ align:start position:0%
+have been a couple of generations ago or
+take a look at um one that was uh
+
+ align:start position:0%
+take a look at um one that was uh
+ 
+
+ align:start position:0%
+take a look at um one that was uh
+that I learned about when my children
+
+ align:start position:0%
+that I learned about when my children
+ 
+
+ align:start position:0%
+that I learned about when my children
+became big fans of the James Bond movies
+
+ align:start position:0%
+became big fans of the James Bond movies
+ 
+
+ align:start position:0%
+became big fans of the James Bond movies
+so in every James Bond movie there's the
+
+ align:start position:0%
+so in every James Bond movie there's the
+ 
+
+ align:start position:0%
+so in every James Bond movie there's the
+girl right she's been getting a lot
+
+ align:start position:0%
+girl right she's been getting a lot
+ 
+
+ align:start position:0%
+girl right she's been getting a lot
+skinnier over the years if you go back
+
+ align:start position:0%
+skinnier over the years if you go back
+ 
+
+ align:start position:0%
+skinnier over the years if you go back
+to the early ones I don't know how many
+
+ align:start position:0%
+to the early ones I don't know how many
+ 
+
+ align:start position:0%
+to the early ones I don't know how many
+of you agreed James Bond aficionados but
+
+ align:start position:0%
+of you agreed James Bond aficionados but
+ 
+
+ align:start position:0%
+of you agreed James Bond aficionados but
+if you go back and look at at a movie
+
+ align:start position:0%
+if you go back and look at at a movie
+ 
+
+ align:start position:0%
+if you go back and look at at a movie
+like Goldfinger
+
+ align:start position:0%
+like Goldfinger
+ 
+
+ align:start position:0%
+like Goldfinger
+I will not recite all the names of the
+
+ align:start position:0%
+I will not recite all the names of the
+ 
+
+ align:start position:0%
+I will not recite all the names of the
+characters because they're all
+
+ align:start position:0%
+characters because they're all
+ 
+
+ align:start position:0%
+characters because they're all
+bad lewd puns I'm realizing as I'm
+
+ align:start position:0%
+bad lewd puns I'm realizing as I'm
+ 
+
+ align:start position:0%
+bad lewd puns I'm realizing as I'm
+thinking about this but if you if you go
+
+ align:start position:0%
+thinking about this but if you if you go
+ 
+
+ align:start position:0%
+thinking about this but if you if you go
+back and and and look at that at the the
+
+ align:start position:0%
+back and and and look at that at the the
+ 
+
+ align:start position:0%
+back and and and look at that at the the
+the girl in Goldfinger
+
+ align:start position:0%
+the girl in Goldfinger
+ 
+
+ align:start position:0%
+the girl in Goldfinger
+um or or in doctor no or something like
+
+ align:start position:0%
+um or or in doctor no or something like
+ 
+
+ align:start position:0%
+um or or in doctor no or something like
+that you will find again see that's from
+
+ align:start position:0%
+that you will find again see that's from
+ 
+
+ align:start position:0%
+that you will find again see that's from
+the early 60s mid 60s you'll find that
+
+ align:start position:0%
+the early 60s mid 60s you'll find that
+ 
+
+ align:start position:0%
+the early 60s mid 60s you'll find that
+she looks you know a perfectly
+
+ align:start position:0%
+she looks you know a perfectly
+ 
+
+ align:start position:0%
+she looks you know a perfectly
+attractive woman but again there's more
+
+ align:start position:0%
+attractive woman but again there's more
+ 
+
+ align:start position:0%
+attractive woman but again there's more
+of her than there would be in Who's the
+
+ align:start position:0%
+of her than there would be in Who's the
+ 
+
+ align:start position:0%
+of her than there would be in Who's the
+who is the the tarte in the most recent
+
+ align:start position:0%
+who is the the tarte in the most recent
+ 
+
+ align:start position:0%
+who is the the tarte in the most recent
+well it's actually the Haley Berry yes
+
+ align:start position:0%
+well it's actually the Haley Berry yes
+ 
+
+ align:start position:0%
+well it's actually the Haley Berry yes
+nothing there right she's pretty skinny
+
+ align:start position:0%
+nothing there right she's pretty skinny
+ 
+
+ align:start position:0%
+nothing there right she's pretty skinny
+the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another move in the in the James Bond
+
+ align:start position:0%
+another move in the in the James Bond
+ 
+
+ align:start position:0%
+another move in the in the James Bond
+thing which is an interesting thing in
+
+ align:start position:0%
+thing which is an interesting thing in
+ 
+
+ align:start position:0%
+thing which is an interesting thing in
+its own right which is that uh the they
+
+ align:start position:0%
+its own right which is that uh the they
+ 
+
+ align:start position:0%
+its own right which is that uh the they
+still they still have to end up together
+
+ align:start position:0%
+still they still have to end up together
+ 
+
+ align:start position:0%
+still they still have to end up together
+by the end of the movie but they're
+
+ align:start position:0%
+by the end of the movie but they're
+ 
+
+ align:start position:0%
+by the end of the movie but they're
+getting a lot
+
+ align:start position:0%
+getting a lot
+ 
+
+ align:start position:0%
+getting a lot
+crankier about the whole business right
+
+ align:start position:0%
+crankier about the whole business right
+ 
+
+ align:start position:0%
+crankier about the whole business right
+they said it's like they get into this
+
+ align:start position:0%
+they said it's like they get into this
+ 
+
+ align:start position:0%
+they said it's like they get into this
+movie and they realized it by the end of
+
+ align:start position:0%
+movie and they realized it by the end of
+ 
+
+ align:start position:0%
+movie and they realized it by the end of
+the movie I've gotta you know be in one
+
+ align:start position:0%
+the movie I've gotta you know be in one
+ 
+
+ align:start position:0%
+the movie I've gotta you know be in one
+of those silly scenes with whoever is
+
+ align:start position:0%
+of those silly scenes with whoever is
+ 
+
+ align:start position:0%
+of those silly scenes with whoever is
+playing bond this week but he's a jerk
+
+ align:start position:0%
+playing bond this week but he's a jerk
+ 
+
+ align:start position:0%
+playing bond this week but he's a jerk
+really but anyway that's a separate
+
+ align:start position:0%
+really but anyway that's a separate
+ 
+
+ align:start position:0%
+really but anyway that's a separate
+issue anyway they've been getting
+
+ align:start position:0%
+issue anyway they've been getting
+ 
+
+ align:start position:0%
+issue anyway they've been getting
+skinnier and skinnier
+
+ align:start position:0%
+skinnier and skinnier
+ 
+
+ align:start position:0%
+skinnier and skinnier
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Barbie has been skinny forever but gets
+
+ align:start position:0%
+Barbie has been skinny forever but gets
+ 
+
+ align:start position:0%
+Barbie has been skinny forever but gets
+blamed uh you know is held up literally
+
+ align:start position:0%
+blamed uh you know is held up literally
+ 
+
+ align:start position:0%
+blamed uh you know is held up literally
+as an icon for this problem you know
+
+ align:start position:0%
+as an icon for this problem you know
+ 
+
+ align:start position:0%
+as an icon for this problem you know
+women do not look like Barbie if you
+
+ align:start position:0%
+women do not look like Barbie if you
+ 
+
+ align:start position:0%
+women do not look like Barbie if you
+scale Barbie up to um uh to human size
+
+ align:start position:0%
+scale Barbie up to um uh to human size
+ 
+
+ align:start position:0%
+scale Barbie up to um uh to human size
+there are serious biomechanical problems
+
+ align:start position:0%
+there are serious biomechanical problems
+ 
+
+ align:start position:0%
+there are serious biomechanical problems
+that ensue apparently
+
+ align:start position:0%
+that ensue apparently
+ 
+
+ align:start position:0%
+that ensue apparently
+um somebody wrote a marvelous there's a
+
+ align:start position:0%
+um somebody wrote a marvelous there's a
+ 
+
+ align:start position:0%
+um somebody wrote a marvelous there's a
+great engineering piece on that
+
+ align:start position:0%
+great engineering piece on that
+ 
+
+ align:start position:0%
+great engineering piece on that
+somewhere that I saw once upon a time
+
+ align:start position:0%
+somewhere that I saw once upon a time
+ 
+
+ align:start position:0%
+somewhere that I saw once upon a time
+there there are cantilevering problems
+
+ align:start position:0%
+there there are cantilevering problems
+ 
+
+ align:start position:0%
+there there are cantilevering problems
+and all anyway all sorts of very bad
+
+ align:start position:0%
+and all anyway all sorts of very bad
+ 
+
+ align:start position:0%
+and all anyway all sorts of very bad
+problems with Barbie if you scale her up
+
+ align:start position:0%
+problems with Barbie if you scale her up
+ 
+
+ align:start position:0%
+problems with Barbie if you scale her up
+um so but the notion is that that that
+
+ align:start position:0%
+um so but the notion is that that that
+ 
+
+ align:start position:0%
+um so but the notion is that that that
+the ideal of what is beautiful has been
+
+ align:start position:0%
+the ideal of what is beautiful has been
+ 
+
+ align:start position:0%
+the ideal of what is beautiful has been
+getting skinnier and skinnier at the
+
+ align:start position:0%
+getting skinnier and skinnier at the
+ 
+
+ align:start position:0%
+getting skinnier and skinnier at the
+same time there has been
+
+ align:start position:0%
+same time there has been
+ 
+
+ align:start position:0%
+same time there has been
+this surge in uh both the availability
+
+ align:start position:0%
+this surge in uh both the availability
+ 
+
+ align:start position:0%
+this surge in uh both the availability
+and the diversity of food available so
+
+ align:start position:0%
+and the diversity of food available so
+ 
+
+ align:start position:0%
+and the diversity of food available so
+you're you're expected to be skinny
+
+ align:start position:0%
+you're you're expected to be skinny
+ 
+
+ align:start position:0%
+you're you're expected to be skinny
+while plunked down at the uh at the
+
+ align:start position:0%
+while plunked down at the uh at the
+ 
+
+ align:start position:0%
+while plunked down at the uh at the
+spectacular all-you-can-eat buffet
+
+ align:start position:0%
+spectacular all-you-can-eat buffet
+ 
+
+ align:start position:0%
+spectacular all-you-can-eat buffet
+um and and that's uh you know you can
+
+ align:start position:0%
+um and and that's uh you know you can
+ 
+
+ align:start position:0%
+um and and that's uh you know you can
+imagine that there are a certain amount
+
+ align:start position:0%
+imagine that there are a certain amount
+ 
+
+ align:start position:0%
+imagine that there are a certain amount
+of problems there there are
+
+ align:start position:0%
+of problems there there are
+ 
+
+ align:start position:0%
+of problems there there are
+specific populations and these are
+
+ align:start position:0%
+specific populations and these are
+ 
+
+ align:start position:0%
+specific populations and these are
+unsurprising specific populations where
+
+ align:start position:0%
+unsurprising specific populations where
+ 
+
+ align:start position:0%
+unsurprising specific populations where
+you see higher than average rates of
+
+ align:start position:0%
+you see higher than average rates of
+ 
+
+ align:start position:0%
+you see higher than average rates of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Eating Disorders so for instance
+
+ align:start position:0%
+Eating Disorders so for instance
+ 
+
+ align:start position:0%
+Eating Disorders so for instance
+gymnasts
+
+ align:start position:0%
+gymnasts
+ 
+
+ align:start position:0%
+gymnasts
+um are uh the Eating Disorders are over
+
+ align:start position:0%
+um are uh the Eating Disorders are over
+ 
+
+ align:start position:0%
+um are uh the Eating Disorders are over
+represented in that population
+
+ align:start position:0%
+represented in that population
+ 
+
+ align:start position:0%
+represented in that population
+um if you're looking for male uh eating
+
+ align:start position:0%
+um if you're looking for male uh eating
+ 
+
+ align:start position:0%
+um if you're looking for male uh eating
+disorder patients a great place to look
+
+ align:start position:0%
+disorder patients a great place to look
+ 
+
+ align:start position:0%
+disorder patients a great place to look
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um in uh in the wrestling population
+
+ align:start position:0%
+um in uh in the wrestling population
+ 
+
+ align:start position:0%
+um in uh in the wrestling population
+why is that well if you're wrestling in
+
+ align:start position:0%
+why is that well if you're wrestling in
+ 
+
+ align:start position:0%
+why is that well if you're wrestling in
+a weight class and you have to be
+
+ align:start position:0%
+a weight class and you have to be
+ 
+
+ align:start position:0%
+a weight class and you have to be
+exactly this weight particularly since
+
+ align:start position:0%
+exactly this weight particularly since
+ 
+
+ align:start position:0%
+exactly this weight particularly since
+there's a pressure to to wrestle in in
+
+ align:start position:0%
+there's a pressure to to wrestle in in
+ 
+
+ align:start position:0%
+there's a pressure to to wrestle in in
+the lightest weight class you can sort
+
+ align:start position:0%
+the lightest weight class you can sort
+ 
+
+ align:start position:0%
+the lightest weight class you can sort
+of get away with there's going to be a
+
+ align:start position:0%
+of get away with there's going to be a
+ 
+
+ align:start position:0%
+of get away with there's going to be a
+lot of pressure
+
+ align:start position:0%
+lot of pressure
+ 
+
+ align:start position:0%
+lot of pressure
+um of the sort that that's similar to
+
+ align:start position:0%
+um of the sort that that's similar to
+ 
+
+ align:start position:0%
+um of the sort that that's similar to
+this uh um pressure that you might
+
+ align:start position:0%
+this uh um pressure that you might
+ 
+
+ align:start position:0%
+this uh um pressure that you might
+imagine being applied by an ideal of
+
+ align:start position:0%
+imagine being applied by an ideal of
+ 
+
+ align:start position:0%
+imagine being applied by an ideal of
+female Beauty that's that's
+
+ align:start position:0%
+female Beauty that's that's
+ 
+
+ align:start position:0%
+female Beauty that's that's
+um that's very skinny
+
+ align:start position:0%
+um that's very skinny
+ 
+
+ align:start position:0%
+um that's very skinny
+um so there are these pressure yes yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they measure you some number of hours
+
+ align:start position:0%
+they measure you some number of hours
+ 
+
+ align:start position:0%
+they measure you some number of hours
+before the actual match
+
+ align:start position:0%
+before the actual match
+ 
+
+ align:start position:0%
+before the actual match
+yeah yes there are all sorts of reasons
+
+ align:start position:0%
+yeah yes there are all sorts of reasons
+ 
+
+ align:start position:0%
+yeah yes there are all sorts of reasons
+why this is not inclined to produce
+
+ align:start position:0%
+why this is not inclined to produce
+ 
+
+ align:start position:0%
+why this is not inclined to produce
+wholesome eating Behavior as I
+
+ align:start position:0%
+wholesome eating Behavior as I
+ 
+
+ align:start position:0%
+wholesome eating Behavior as I
+understand it my my own personal
+
+ align:start position:0%
+understand it my my own personal
+ 
+
+ align:start position:0%
+understand it my my own personal
+wrestling career
+
+ align:start position:0%
+wrestling career
+ 
+
+ align:start position:0%
+wrestling career
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why are they all laughing
+
+ align:start position:0%
+why are they all laughing
+ 
+
+ align:start position:0%
+why are they all laughing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well you know it's it's it's only mildly
+
+ align:start position:0%
+well you know it's it's it's only mildly
+ 
+
+ align:start position:0%
+well you know it's it's it's only mildly
+well I suppose maybe it's completely
+
+ align:start position:0%
+well I suppose maybe it's completely
+ 
+
+ align:start position:0%
+well I suppose maybe it's completely
+hilarious you know the the it was clear
+
+ align:start position:0%
+hilarious you know the the it was clear
+ 
+
+ align:start position:0%
+hilarious you know the the it was clear
+that I wasn't going to wrestle
+
+ align:start position:0%
+that I wasn't going to wrestle
+ 
+
+ align:start position:0%
+that I wasn't going to wrestle
+heavyweight right but you know that the
+
+ align:start position:0%
+heavyweight right but you know that the
+ 
+
+ align:start position:0%
+heavyweight right but you know that the
+world is full of these you know little
+
+ align:start position:0%
+world is full of these you know little
+ 
+
+ align:start position:0%
+world is full of these you know little
+little tough guys as opposed to just
+
+ align:start position:0%
+little tough guys as opposed to just
+ 
+
+ align:start position:0%
+little tough guys as opposed to just
+merely little guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+letter I was writing for you
+
+ align:start position:0%
+letter I was writing for you
+ 
+
+ align:start position:0%
+letter I was writing for you
+it's really bad when the people in your
+
+ align:start position:0%
+it's really bad when the people in your
+ 
+
+ align:start position:0%
+it's really bad when the people in your
+lab are the ones who are becoming
+
+ align:start position:0%
+lab are the ones who are becoming
+ 
+
+ align:start position:0%
+lab are the ones who are becoming
+hysterical and
+
+ align:start position:0%
+hysterical and
+ 
+
+ align:start position:0%
+hysterical and
+anyway um I might as well complete this
+
+ align:start position:0%
+anyway um I might as well complete this
+ 
+
+ align:start position:0%
+anyway um I might as well complete this
+embarrassing story uh high school high
+
+ align:start position:0%
+embarrassing story uh high school high
+ 
+
+ align:start position:0%
+embarrassing story uh high school high
+school wrestling
+
+ align:start position:0%
+school wrestling
+ 
+
+ align:start position:0%
+school wrestling
+um high school wrestling was was the gym
+
+ align:start position:0%
+um high school wrestling was was the gym
+ 
+
+ align:start position:0%
+um high school wrestling was was the gym
+teachers were always weird people
+
+ align:start position:0%
+teachers were always weird people
+ 
+
+ align:start position:0%
+teachers were always weird people
+um and and and so high school wrestling
+
+ align:start position:0%
+um and and and so high school wrestling
+ 
+
+ align:start position:0%
+um and and and so high school wrestling
+you had to wrestle by weight class right
+
+ align:start position:0%
+you had to wrestle by weight class right
+ 
+
+ align:start position:0%
+you had to wrestle by weight class right
+that made sense but but but our our guy
+
+ align:start position:0%
+that made sense but but but our our guy
+ 
+
+ align:start position:0%
+that made sense but but but our our guy
+thought it was like a circle
+
+ align:start position:0%
+thought it was like a circle
+ 
+
+ align:start position:0%
+thought it was like a circle
+so you wrestled the guy next to you and
+
+ align:start position:0%
+so you wrestled the guy next to you and
+ 
+
+ align:start position:0%
+so you wrestled the guy next to you and
+wait well if you were the lightest guy
+
+ align:start position:0%
+wait well if you were the lightest guy
+ 
+
+ align:start position:0%
+wait well if you were the lightest guy
+it's gonna be a hoot let's get him to
+
+ align:start position:0%
+it's gonna be a hoot let's get him to
+ 
+
+ align:start position:0%
+it's gonna be a hoot let's get him to
+wrestle the heaviest guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which was actually okay because the
+
+ align:start position:0%
+which was actually okay because the
+ 
+
+ align:start position:0%
+which was actually okay because the
+heaviest guy was just about as
+
+ align:start position:0%
+heaviest guy was just about as
+ 
+
+ align:start position:0%
+heaviest guy was just about as
+athletically talented as I was
+
+ align:start position:0%
+athletically talented as I was
+ 
+
+ align:start position:0%
+athletically talented as I was
+um and and the the major danger was that
+
+ align:start position:0%
+um and and the the major danger was that
+ 
+
+ align:start position:0%
+um and and the the major danger was that
+he would fall on me right because then
+
+ align:start position:0%
+he would fall on me right because then
+ 
+
+ align:start position:0%
+he would fall on me right because then
+then it was just going to be all over so
+
+ align:start position:0%
+then it was just going to be all over so
+ 
+
+ align:start position:0%
+then it was just going to be all over so
+he's I'm I'm I'm this Athletics was not
+
+ align:start position:0%
+he's I'm I'm I'm this Athletics was not
+ 
+
+ align:start position:0%
+he's I'm I'm I'm this Athletics was not
+my strong suit so there was no danger
+
+ align:start position:0%
+my strong suit so there was no danger
+ 
+
+ align:start position:0%
+my strong suit so there was no danger
+that I was going to do him any serious
+
+ align:start position:0%
+that I was going to do him any serious
+ 
+
+ align:start position:0%
+that I was going to do him any serious
+damage
+
+ align:start position:0%
+damage
+ 
+
+ align:start position:0%
+damage
+um there was and and there was no
+
+ align:start position:0%
+um there was and and there was no
+ 
+
+ align:start position:0%
+um there was and and there was no
+serious danger that as long as he didn't
+
+ align:start position:0%
+serious danger that as long as he didn't
+ 
+
+ align:start position:0%
+serious danger that as long as he didn't
+fall on me I was gonna get hurt so I I
+
+ align:start position:0%
+fall on me I was gonna get hurt so I I
+ 
+
+ align:start position:0%
+fall on me I was gonna get hurt so I I
+figured out a way to get on his back and
+
+ align:start position:0%
+figured out a way to get on his back and
+ 
+
+ align:start position:0%
+figured out a way to get on his back and
+sort of wrote him around for a while
+
+ align:start position:0%
+sort of wrote him around for a while
+ 
+
+ align:start position:0%
+sort of wrote him around for a while
+um and and sort of manly things that
+
+ align:start position:0%
+um and and sort of manly things that
+ 
+
+ align:start position:0%
+um and and sort of manly things that
+look like I might be trying to flip him
+
+ align:start position:0%
+look like I might be trying to flip him
+ 
+
+ align:start position:0%
+look like I might be trying to flip him
+but that wasn't ever gonna happen the uh
+
+ align:start position:0%
+but that wasn't ever gonna happen the uh
+ 
+
+ align:start position:0%
+but that wasn't ever gonna happen the uh
+it was it was a great moment
+
+ align:start position:0%
+it was it was a great moment
+ 
+
+ align:start position:0%
+it was it was a great moment
+um made made greater of course by the
+
+ align:start position:0%
+um made made greater of course by the
+ 
+
+ align:start position:0%
+um made made greater of course by the
+fact that that this was pop uh never
+
+ align:start position:0%
+fact that that this was pop uh never
+ 
+
+ align:start position:0%
+fact that that this was pop uh never
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+um we no I should continue that this was
+
+ align:start position:0%
+um we no I should continue that this was
+ 
+
+ align:start position:0%
+um we no I should continue that this was
+also he was uh um this this was full of
+
+ align:start position:0%
+also he was uh um this this was full of
+ 
+
+ align:start position:0%
+also he was uh um this this was full of
+this guy he was a deeply homophobic um
+
+ align:start position:0%
+this guy he was a deeply homophobic um
+ 
+
+ align:start position:0%
+this guy he was a deeply homophobic um
+gym teacher who also uh was fond of
+
+ align:start position:0%
+gym teacher who also uh was fond of
+ 
+
+ align:start position:0%
+gym teacher who also uh was fond of
+explaining that
+
+ align:start position:0%
+explaining that
+ 
+
+ align:start position:0%
+explaining that
+um how hard you wrestled was just showed
+
+ align:start position:0%
+um how hard you wrestled was just showed
+ 
+
+ align:start position:0%
+um how hard you wrestled was just showed
+whether you were a real guy
+
+ align:start position:0%
+whether you were a real guy
+ 
+
+ align:start position:0%
+whether you were a real guy
+um and and anyway it goes It goes
+
+ align:start position:0%
+um and and anyway it goes It goes
+ 
+
+ align:start position:0%
+um and and anyway it goes It goes
+downhill from there
+
+ align:start position:0%
+downhill from there
+ 
+
+ align:start position:0%
+downhill from there
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in any case the uh where were we oh
+
+ align:start position:0%
+so in any case the uh where were we oh
+ 
+
+ align:start position:0%
+so in any case the uh where were we oh
+yes uh this is this explains why my
+
+ align:start position:0%
+yes uh this is this explains why my
+ 
+
+ align:start position:0%
+yes uh this is this explains why my
+wrestling career did not produce any
+
+ align:start position:0%
+wrestling career did not produce any
+ 
+
+ align:start position:0%
+wrestling career did not produce any
+eating disorders in my case
+
+ align:start position:0%
+eating disorders in my case
+ 
+
+ align:start position:0%
+eating disorders in my case
+um so there are these societal or or
+
+ align:start position:0%
+um so there are these societal or or
+ 
+
+ align:start position:0%
+um so there are these societal or or
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+um cultural factors that might be
+
+ align:start position:0%
+um cultural factors that might be
+ 
+
+ align:start position:0%
+um cultural factors that might be
+pushing one towards these sort of
+
+ align:start position:0%
+pushing one towards these sort of
+ 
+
+ align:start position:0%
+pushing one towards these sort of
+disorders
+
+ align:start position:0%
+disorders
+ 
+
+ align:start position:0%
+disorders
+um and and then there are
+
+ align:start position:0%
+um and and then there are
+ 
+
+ align:start position:0%
+um and and then there are
+then there's the
+
+ align:start position:0%
+then there's the
+ 
+
+ align:start position:0%
+then there's the
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+actor there is there some sort of a
+
+ align:start position:0%
+actor there is there some sort of a
+ 
+
+ align:start position:0%
+actor there is there some sort of a
+genetic predisposition
+
+ align:start position:0%
+genetic predisposition
+ 
+
+ align:start position:0%
+genetic predisposition
+um towards this
+
+ align:start position:0%
+um towards this
+ 
+
+ align:start position:0%
+um towards this
+um the sorts of things that people point
+
+ align:start position:0%
+um the sorts of things that people point
+ 
+
+ align:start position:0%
+um the sorts of things that people point
+to are
+
+ align:start position:0%
+to are
+ 
+
+ align:start position:0%
+to are
+data for instance that there are there
+
+ align:start position:0%
+data for instance that there are there
+ 
+
+ align:start position:0%
+data for instance that there are there
+there's there are family histories of
+
+ align:start position:0%
+there's there are family histories of
+ 
+
+ align:start position:0%
+there's there are family histories of
+depression more depression showing up in
+
+ align:start position:0%
+depression more depression showing up in
+ 
+
+ align:start position:0%
+depression more depression showing up in
+uh eating disorder in in the in the
+
+ align:start position:0%
+uh eating disorder in in the in the
+ 
+
+ align:start position:0%
+uh eating disorder in in the in the
+families of eating disorder patients
+
+ align:start position:0%
+families of eating disorder patients
+ 
+
+ align:start position:0%
+families of eating disorder patients
+than in the general population there's
+
+ align:start position:0%
+than in the general population there's
+ 
+
+ align:start position:0%
+than in the general population there's
+also more depression in eating disorder
+
+ align:start position:0%
+also more depression in eating disorder
+ 
+
+ align:start position:0%
+also more depression in eating disorder
+patients themselves but as I've said
+
+ align:start position:0%
+patients themselves but as I've said
+ 
+
+ align:start position:0%
+patients themselves but as I've said
+that's hard to
+
+ align:start position:0%
+that's hard to
+ 
+
+ align:start position:0%
+that's hard to
+um disentangle from the effects of of
+
+ align:start position:0%
+um disentangle from the effects of of
+ 
+
+ align:start position:0%
+um disentangle from the effects of of
+starvation that that itself produces
+
+ align:start position:0%
+starvation that that itself produces
+ 
+
+ align:start position:0%
+starvation that that itself produces
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh just uh problems
+
+ align:start position:0%
+uh just uh problems
+ 
+
+ align:start position:0%
+uh just uh problems
+um in any case there are uh well
+
+ align:start position:0%
+um in any case there are uh well
+ 
+
+ align:start position:0%
+um in any case there are uh well
+actually there is
+
+ align:start position:0%
+actually there is
+ 
+
+ align:start position:0%
+actually there is
+one thing that is potentially a a
+
+ align:start position:0%
+one thing that is potentially a a
+ 
+
+ align:start position:0%
+one thing that is potentially a a
+biological
+
+ align:start position:0%
+biological
+ 
+
+ align:start position:0%
+biological
+underpinning
+
+ align:start position:0%
+underpinning
+ 
+
+ align:start position:0%
+underpinning
+has nothing to do with the brain at all
+
+ align:start position:0%
+has nothing to do with the brain at all
+ 
+
+ align:start position:0%
+has nothing to do with the brain at all
+but is simply well in in um in in uh
+
+ align:start position:0%
+but is simply well in in um in in uh
+ 
+
+ align:start position:0%
+but is simply well in in um in in uh
+a diet land these are known as set point
+
+ align:start position:0%
+a diet land these are known as set point
+ 
+
+ align:start position:0%
+a diet land these are known as set point
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+um there's a notion that people uh come
+
+ align:start position:0%
+um there's a notion that people uh come
+ 
+
+ align:start position:0%
+um there's a notion that people uh come
+with some sort of uh weight that that is
+
+ align:start position:0%
+with some sort of uh weight that that is
+ 
+
+ align:start position:0%
+with some sort of uh weight that that is
+sort of the weight that they are set for
+
+ align:start position:0%
+sort of the weight that they are set for
+ 
+
+ align:start position:0%
+sort of the weight that they are set for
+the little thermostat in the
+
+ align:start position:0%
+the little thermostat in the
+ 
+
+ align:start position:0%
+the little thermostat in the
+hypothalamus is set to say you know
+
+ align:start position:0%
+hypothalamus is set to say you know
+ 
+
+ align:start position:0%
+hypothalamus is set to say you know
+you're going to be 180 pounds or
+
+ align:start position:0%
+you're going to be 180 pounds or
+ 
+
+ align:start position:0%
+you're going to be 180 pounds or
+whatever you can push this around but
+
+ align:start position:0%
+whatever you can push this around but
+ 
+
+ align:start position:0%
+whatever you can push this around but
+this is this is where we we want to be
+
+ align:start position:0%
+this is this is where we we want to be
+ 
+
+ align:start position:0%
+this is this is where we we want to be
+it's related to the fact that that there
+
+ align:start position:0%
+it's related to the fact that that there
+ 
+
+ align:start position:0%
+it's related to the fact that that there
+are certainly genetic factors that are
+
+ align:start position:0%
+are certainly genetic factors that are
+ 
+
+ align:start position:0%
+are certainly genetic factors that are
+making you one body shape versus another
+
+ align:start position:0%
+making you one body shape versus another
+ 
+
+ align:start position:0%
+making you one body shape versus another
+body shape and if you are one shape and
+
+ align:start position:0%
+body shape and if you are one shape and
+ 
+
+ align:start position:0%
+body shape and if you are one shape and
+you're feeling strongly pressured to be
+
+ align:start position:0%
+you're feeling strongly pressured to be
+ 
+
+ align:start position:0%
+you're feeling strongly pressured to be
+another shape that is not the shape that
+
+ align:start position:0%
+another shape that is not the shape that
+ 
+
+ align:start position:0%
+another shape that is not the shape that
+you were sort of built to be that's
+
+ align:start position:0%
+you were sort of built to be that's
+ 
+
+ align:start position:0%
+you were sort of built to be that's
+considered to possibly be a biological
+
+ align:start position:0%
+considered to possibly be a biological
+ 
+
+ align:start position:0%
+considered to possibly be a biological
+factor pushing people towards uh
+
+ align:start position:0%
+factor pushing people towards uh
+ 
+
+ align:start position:0%
+factor pushing people towards uh
+um towards eating disorder that's not a
+
+ align:start position:0%
+um towards eating disorder that's not a
+ 
+
+ align:start position:0%
+um towards eating disorder that's not a
+factor that that's not like the the sort
+
+ align:start position:0%
+factor that that's not like the the sort
+ 
+
+ align:start position:0%
+factor that that's not like the the sort
+of factors we're thinking about as a a a
+
+ align:start position:0%
+of factors we're thinking about as a a a
+ 
+
+ align:start position:0%
+of factors we're thinking about as a a a
+genetic predisposition to something like
+
+ align:start position:0%
+genetic predisposition to something like
+ 
+
+ align:start position:0%
+genetic predisposition to something like
+schizophrenia that's really an
+
+ align:start position:0%
+schizophrenia that's really an
+ 
+
+ align:start position:0%
+schizophrenia that's really an
+interaction of of body type which these
+
+ align:start position:0%
+interaction of of body type which these
+ 
+
+ align:start position:0%
+interaction of of body type which these
+these sort of cultural
+
+ align:start position:0%
+these sort of cultural
+ 
+
+ align:start position:0%
+these sort of cultural
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+cultural pressures all right so you've
+
+ align:start position:0%
+cultural pressures all right so you've
+ 
+
+ align:start position:0%
+cultural pressures all right so you've
+got stuff you've got characteristics of
+
+ align:start position:0%
+got stuff you've got characteristics of
+ 
+
+ align:start position:0%
+got stuff you've got characteristics of
+of family uh patient the culture as a
+
+ align:start position:0%
+of family uh patient the culture as a
+ 
+
+ align:start position:0%
+of family uh patient the culture as a
+whole possibly biological underpinnings
+
+ align:start position:0%
+whole possibly biological underpinnings
+ 
+
+ align:start position:0%
+whole possibly biological underpinnings
+how might all of this contribute to
+
+ align:start position:0%
+how might all of this contribute to
+ 
+
+ align:start position:0%
+how might all of this contribute to
+producing
+
+ align:start position:0%
+producing
+ 
+
+ align:start position:0%
+producing
+um an an actual disorder one way to
+
+ align:start position:0%
+um an an actual disorder one way to
+ 
+
+ align:start position:0%
+um an an actual disorder one way to
+think about this is to think about it as
+
+ align:start position:0%
+think about this is to think about it as
+ 
+
+ align:start position:0%
+think about this is to think about it as
+a trap that that uh that some subset of
+
+ align:start position:0%
+a trap that that uh that some subset of
+ 
+
+ align:start position:0%
+a trap that that uh that some subset of
+of girls fall into not consciously
+
+ align:start position:0%
+of girls fall into not consciously
+ 
+
+ align:start position:0%
+of girls fall into not consciously
+nobody wakes up in the morning and says
+
+ align:start position:0%
+nobody wakes up in the morning and says
+ 
+
+ align:start position:0%
+nobody wakes up in the morning and says
+gee I think I'll have an eating disorder
+
+ align:start position:0%
+gee I think I'll have an eating disorder
+ 
+
+ align:start position:0%
+gee I think I'll have an eating disorder
+um but the the unconscious uh process
+
+ align:start position:0%
+um but the the unconscious uh process
+ 
+
+ align:start position:0%
+um but the the unconscious uh process
+might run something like the following
+
+ align:start position:0%
+might run something like the following
+ 
+
+ align:start position:0%
+might run something like the following
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you hit puberty it's all right so you've
+
+ align:start position:0%
+you hit puberty it's all right so you've
+ 
+
+ align:start position:0%
+you hit puberty it's all right so you've
+been this sort of perfectionist good
+
+ align:start position:0%
+been this sort of perfectionist good
+ 
+
+ align:start position:0%
+been this sort of perfectionist good
+girl
+
+ align:start position:0%
+girl
+ 
+
+ align:start position:0%
+girl
+um all along
+
+ align:start position:0%
+um all along
+ 
+
+ align:start position:0%
+um all along
+um you hit puberty
+
+ align:start position:0%
+um you hit puberty
+ 
+
+ align:start position:0%
+um you hit puberty
+um and uh that's a sort of a time that
+
+ align:start position:0%
+um and uh that's a sort of a time that
+ 
+
+ align:start position:0%
+um and uh that's a sort of a time that
+that stretches uh or strains Perfection
+
+ align:start position:0%
+that stretches uh or strains Perfection
+ 
+
+ align:start position:0%
+that stretches uh or strains Perfection
+all together
+
+ align:start position:0%
+all together
+ 
+
+ align:start position:0%
+all together
+um your
+
+ align:start position:0%
+um your
+ 
+
+ align:start position:0%
+um your
+being perfect requires a certain amount
+
+ align:start position:0%
+being perfect requires a certain amount
+ 
+
+ align:start position:0%
+being perfect requires a certain amount
+of self-control and you may recall the
+
+ align:start position:0%
+of self-control and you may recall the
+ 
+
+ align:start position:0%
+of self-control and you may recall the
+the the you know the the sort of wash of
+
+ align:start position:0%
+the the you know the the sort of wash of
+ 
+
+ align:start position:0%
+the the you know the the sort of wash of
+hormones that accompanies the onset of
+
+ align:start position:0%
+hormones that accompanies the onset of
+ 
+
+ align:start position:0%
+hormones that accompanies the onset of
+puberty is not particularly good for for
+
+ align:start position:0%
+puberty is not particularly good for for
+ 
+
+ align:start position:0%
+puberty is not particularly good for for
+um self-control so the sense of control
+
+ align:start position:0%
+um self-control so the sense of control
+ 
+
+ align:start position:0%
+um self-control so the sense of control
+is is is not what it used to be your
+
+ align:start position:0%
+is is is not what it used to be your
+ 
+
+ align:start position:0%
+is is is not what it used to be your
+body is changing in ways that that you
+
+ align:start position:0%
+body is changing in ways that that you
+ 
+
+ align:start position:0%
+body is changing in ways that that you
+don't control and you're in this family
+
+ align:start position:0%
+don't control and you're in this family
+ 
+
+ align:start position:0%
+don't control and you're in this family
+where the set of ways that you can act
+
+ align:start position:0%
+where the set of ways that you can act
+ 
+
+ align:start position:0%
+where the set of ways that you can act
+out is very limited there are lots of
+
+ align:start position:0%
+out is very limited there are lots of
+ 
+
+ align:start position:0%
+out is very limited there are lots of
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+um that to deal to start to act out in
+
+ align:start position:0%
+um that to deal to start to act out in
+ 
+
+ align:start position:0%
+um that to deal to start to act out in
+in in adolescence but you're in a family
+
+ align:start position:0%
+in in adolescence but you're in a family
+ 
+
+ align:start position:0%
+in in adolescence but you're in a family
+where most of them are sort of not not
+
+ align:start position:0%
+where most of them are sort of not not
+ 
+
+ align:start position:0%
+where most of them are sort of not not
+sanctioned
+
+ align:start position:0%
+sanctioned
+ 
+
+ align:start position:0%
+sanctioned
+um so one way to sort of re-exert a
+
+ align:start position:0%
+um so one way to sort of re-exert a
+ 
+
+ align:start position:0%
+um so one way to sort of re-exert a
+sense of control a very culturally
+
+ align:start position:0%
+sense of control a very culturally
+ 
+
+ align:start position:0%
+sense of control a very culturally
+endorsed one is well let's go on a diet
+
+ align:start position:0%
+endorsed one is well let's go on a diet
+ 
+
+ align:start position:0%
+endorsed one is well let's go on a diet
+right the percentage of women in this
+
+ align:start position:0%
+right the percentage of women in this
+ 
+
+ align:start position:0%
+right the percentage of women in this
+country on diets at any time is huge and
+
+ align:start position:0%
+country on diets at any time is huge and
+ 
+
+ align:start position:0%
+country on diets at any time is huge and
+that goes down to school girl age
+
+ align:start position:0%
+that goes down to school girl age
+ 
+
+ align:start position:0%
+that goes down to school girl age
+and if you ask
+
+ align:start position:0%
+and if you ask
+ 
+
+ align:start position:0%
+and if you ask
+um you go and talk to uh uh Middle
+
+ align:start position:0%
+um you go and talk to uh uh Middle
+ 
+
+ align:start position:0%
+um you go and talk to uh uh Middle
+School boys about you know diet
+
+ align:start position:0%
+School boys about you know diet
+ 
+
+ align:start position:0%
+School boys about you know diet
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+I'm gonna sort of grunt at you or
+
+ align:start position:0%
+I'm gonna sort of grunt at you or
+ 
+
+ align:start position:0%
+I'm gonna sort of grunt at you or
+something go talk to middle school girls
+
+ align:start position:0%
+something go talk to middle school girls
+ 
+
+ align:start position:0%
+something go talk to middle school girls
+about diet and they can talk your ear
+
+ align:start position:0%
+about diet and they can talk your ear
+ 
+
+ align:start position:0%
+about diet and they can talk your ear
+off whether or not they're on some sort
+
+ align:start position:0%
+off whether or not they're on some sort
+ 
+
+ align:start position:0%
+off whether or not they're on some sort
+of a diet they know all about it and
+
+ align:start position:0%
+of a diet they know all about it and
+ 
+
+ align:start position:0%
+of a diet they know all about it and
+then any other this it's it's it's it's
+
+ align:start position:0%
+then any other this it's it's it's it's
+ 
+
+ align:start position:0%
+then any other this it's it's it's it's
+it's there in fact you might go on a
+
+ align:start position:0%
+it's there in fact you might go on a
+ 
+
+ align:start position:0%
+it's there in fact you might go on a
+diet endorsed by mom my mom might say
+
+ align:start position:0%
+diet endorsed by mom my mom might say
+ 
+
+ align:start position:0%
+diet endorsed by mom my mom might say
+you're in here looking a little chunky
+
+ align:start position:0%
+you're in here looking a little chunky
+ 
+
+ align:start position:0%
+you're in here looking a little chunky
+and and that you know let's we can do it
+
+ align:start position:0%
+and and that you know let's we can do it
+ 
+
+ align:start position:0%
+and and that you know let's we can do it
+together it's a mother-daughter kind of
+
+ align:start position:0%
+together it's a mother-daughter kind of
+ 
+
+ align:start position:0%
+together it's a mother-daughter kind of
+thing well you know particularly since
+
+ align:start position:0%
+thing well you know particularly since
+ 
+
+ align:start position:0%
+thing well you know particularly since
+you know we're really enmeshed here
+
+ align:start position:0%
+you know we're really enmeshed here
+ 
+
+ align:start position:0%
+you know we're really enmeshed here
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+um all right well you can sort of
+
+ align:start position:0%
+um all right well you can sort of
+ 
+
+ align:start position:0%
+um all right well you can sort of
+imagine that a perfectionist on a diet
+
+ align:start position:0%
+imagine that a perfectionist on a diet
+ 
+
+ align:start position:0%
+imagine that a perfectionist on a diet
+um under the right circumstances could
+
+ align:start position:0%
+um under the right circumstances could
+ 
+
+ align:start position:0%
+um under the right circumstances could
+be a a a a a a a a recipe for uh
+
+ align:start position:0%
+be a a a a a a a a recipe for uh
+ 
+
+ align:start position:0%
+be a a a a a a a a recipe for uh
+disaster
+
+ align:start position:0%
+disaster
+ 
+
+ align:start position:0%
+disaster
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+it's it's sort of like MIT and sleeping
+
+ align:start position:0%
+it's it's sort of like MIT and sleeping
+ 
+
+ align:start position:0%
+it's it's sort of like MIT and sleeping
+you know people out there say
+
+ align:start position:0%
+you know people out there say
+ 
+
+ align:start position:0%
+you know people out there say
+all right I need to do a little extra
+
+ align:start position:0%
+all right I need to do a little extra
+ 
+
+ align:start position:0%
+all right I need to do a little extra
+work so I'll stay up an extra hour MIT
+
+ align:start position:0%
+work so I'll stay up an extra hour MIT
+ 
+
+ align:start position:0%
+work so I'll stay up an extra hour MIT
+student says I don't need to sleep you
+
+ align:start position:0%
+student says I don't need to sleep you
+ 
+
+ align:start position:0%
+student says I don't need to sleep you
+know most people out in the world say ah
+
+ align:start position:0%
+know most people out in the world say ah
+ 
+
+ align:start position:0%
+know most people out in the world say ah
+diet okay we'll cut out the uh the
+
+ align:start position:0%
+diet okay we'll cut out the uh the
+ 
+
+ align:start position:0%
+diet okay we'll cut out the uh the
+double dip uh the Double you know Double
+
+ align:start position:0%
+double dip uh the Double you know Double
+ 
+
+ align:start position:0%
+double dip uh the Double you know Double
+Stuffed to Oreos and and okay we won't
+
+ align:start position:0%
+Stuffed to Oreos and and okay we won't
+ 
+
+ align:start position:0%
+Stuffed to Oreos and and okay we won't
+deep fry the pizza
+
+ align:start position:0%
+deep fry the pizza
+ 
+
+ align:start position:0%
+deep fry the pizza
+um and and and that that and and and and
+
+ align:start position:0%
+um and and and that that and and and and
+ 
+
+ align:start position:0%
+um and and and that that and and and and
+you did this hypothetical perfectionist
+
+ align:start position:0%
+you did this hypothetical perfectionist
+ 
+
+ align:start position:0%
+you did this hypothetical perfectionist
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+Water Lettuce and water
+
+ align:start position:0%
+Water Lettuce and water
+ 
+
+ align:start position:0%
+Water Lettuce and water
+that'll work right so anyway you can
+
+ align:start position:0%
+that'll work right so anyway you can
+ 
+
+ align:start position:0%
+that'll work right so anyway you can
+imagine that the diet could be and what
+
+ align:start position:0%
+imagine that the diet could be and what
+ 
+
+ align:start position:0%
+imagine that the diet could be and what
+happens in in when this is spiraling
+
+ align:start position:0%
+happens in in when this is spiraling
+ 
+
+ align:start position:0%
+happens in in when this is spiraling
+downwards this diet can become
+
+ align:start position:0%
+downwards this diet can become
+ 
+
+ align:start position:0%
+downwards this diet can become
+increasingly severe
+
+ align:start position:0%
+increasingly severe
+ 
+
+ align:start position:0%
+increasingly severe
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and at some point it becomes an uh a a
+
+ align:start position:0%
+and at some point it becomes an uh a a
+ 
+
+ align:start position:0%
+and at some point it becomes an uh a a
+real issue it becomes a source of
+
+ align:start position:0%
+real issue it becomes a source of
+ 
+
+ align:start position:0%
+real issue it becomes a source of
+conflict in the family because
+
+ align:start position:0%
+conflict in the family because
+ 
+
+ align:start position:0%
+conflict in the family because
+um it becomes clearly unhealthy it's
+
+ align:start position:0%
+um it becomes clearly unhealthy it's
+ 
+
+ align:start position:0%
+um it becomes clearly unhealthy it's
+it's clear to anybody except for the
+
+ align:start position:0%
+it's clear to anybody except for the
+ 
+
+ align:start position:0%
+it's clear to anybody except for the
+patient that this is unhealthy but at
+
+ align:start position:0%
+patient that this is unhealthy but at
+ 
+
+ align:start position:0%
+patient that this is unhealthy but at
+that point this is be if you regard this
+
+ align:start position:0%
+that point this is be if you regard this
+ 
+
+ align:start position:0%
+that point this is be if you regard this
+as as some sort of an assertion of
+
+ align:start position:0%
+as as some sort of an assertion of
+ 
+
+ align:start position:0%
+as as some sort of an assertion of
+autonomy this is the last place where
+
+ align:start position:0%
+autonomy this is the last place where
+ 
+
+ align:start position:0%
+autonomy this is the last place where
+this girl has managed to find a place
+
+ align:start position:0%
+this girl has managed to find a place
+ 
+
+ align:start position:0%
+this girl has managed to find a place
+where she can carve out some place where
+
+ align:start position:0%
+where she can carve out some place where
+ 
+
+ align:start position:0%
+where she can carve out some place where
+where she's in control now the family is
+
+ align:start position:0%
+where she's in control now the family is
+ 
+
+ align:start position:0%
+where she's in control now the family is
+saying you can't do that either and and
+
+ align:start position:0%
+saying you can't do that either and and
+ 
+
+ align:start position:0%
+saying you can't do that either and and
+and she draws the Line This is where I'm
+
+ align:start position:0%
+and she draws the Line This is where I'm
+ 
+
+ align:start position:0%
+and she draws the Line This is where I'm
+going to make my stand
+
+ align:start position:0%
+going to make my stand
+ 
+
+ align:start position:0%
+going to make my stand
+um and um and it it becomes it can
+
+ align:start position:0%
+um and um and it it becomes it can
+ 
+
+ align:start position:0%
+um and um and it it becomes it can
+become a a clearly pathological State uh
+
+ align:start position:0%
+become a a clearly pathological State uh
+ 
+
+ align:start position:0%
+become a a clearly pathological State uh
+people in in full blast and anorexia
+
+ align:start position:0%
+people in in full blast and anorexia
+ 
+
+ align:start position:0%
+people in in full blast and anorexia
+deny that they are hungry in spite of
+
+ align:start position:0%
+deny that they are hungry in spite of
+ 
+
+ align:start position:0%
+deny that they are hungry in spite of
+being strongly
+
+ align:start position:0%
+being strongly
+ 
+
+ align:start position:0%
+being strongly
+um malnourished uh the the the rituals
+
+ align:start position:0%
+um malnourished uh the the the rituals
+ 
+
+ align:start position:0%
+um malnourished uh the the the rituals
+around eating the rituals that get built
+
+ align:start position:0%
+around eating the rituals that get built
+ 
+
+ align:start position:0%
+around eating the rituals that get built
+up around eating be extremely elaborate
+
+ align:start position:0%
+up around eating be extremely elaborate
+ 
+
+ align:start position:0%
+up around eating be extremely elaborate
+and extremely time consuming along with
+
+ align:start position:0%
+and extremely time consuming along with
+ 
+
+ align:start position:0%
+and extremely time consuming along with
+for instance uh very vigorous exercise
+
+ align:start position:0%
+for instance uh very vigorous exercise
+ 
+
+ align:start position:0%
+for instance uh very vigorous exercise
+regimens
+
+ align:start position:0%
+regimens
+ 
+
+ align:start position:0%
+regimens
+um that that basically it takes over
+
+ align:start position:0%
+um that that basically it takes over
+ 
+
+ align:start position:0%
+um that that basically it takes over
+your life plus being starved not only
+
+ align:start position:0%
+your life plus being starved not only
+ 
+
+ align:start position:0%
+your life plus being starved not only
+makes you tends to make you depressed
+
+ align:start position:0%
+makes you tends to make you depressed
+ 
+
+ align:start position:0%
+makes you tends to make you depressed
+but um it also can make you delusional
+
+ align:start position:0%
+but um it also can make you delusional
+ 
+
+ align:start position:0%
+but um it also can make you delusional
+in a variety of ways
+
+ align:start position:0%
+in a variety of ways
+ 
+
+ align:start position:0%
+in a variety of ways
+so it's it's clearly not a good place to
+
+ align:start position:0%
+so it's it's clearly not a good place to
+ 
+
+ align:start position:0%
+so it's it's clearly not a good place to
+be so that's a sense in which it's a
+
+ align:start position:0%
+be so that's a sense in which it's a
+ 
+
+ align:start position:0%
+be so that's a sense in which it's a
+disaster it's also in a sense
+
+ align:start position:0%
+disaster it's also in a sense
+ 
+
+ align:start position:0%
+disaster it's also in a sense
+um the sense in which it's a success
+
+ align:start position:0%
+um the sense in which it's a success
+ 
+
+ align:start position:0%
+um the sense in which it's a success
+this notion of it being a successful
+
+ align:start position:0%
+this notion of it being a successful
+ 
+
+ align:start position:0%
+this notion of it being a successful
+disaster the notion the way the sense in
+
+ align:start position:0%
+disaster the notion the way the sense in
+ 
+
+ align:start position:0%
+disaster the notion the way the sense in
+which it's a success is if you regard
+
+ align:start position:0%
+which it's a success is if you regard
+ 
+
+ align:start position:0%
+which it's a success is if you regard
+this as an issue about control
+
+ align:start position:0%
+this as an issue about control
+ 
+
+ align:start position:0%
+this as an issue about control
+in some sense
+
+ align:start position:0%
+in some sense
+ 
+
+ align:start position:0%
+in some sense
+um the the
+
+ align:start position:0%
+um the the
+ 
+
+ align:start position:0%
+um the the
+patient the daughter has managed to take
+
+ align:start position:0%
+patient the daughter has managed to take
+ 
+
+ align:start position:0%
+patient the daughter has managed to take
+control over the family that wasn't her
+
+ align:start position:0%
+control over the family that wasn't her
+ 
+
+ align:start position:0%
+control over the family that wasn't her
+goal but there's nothing like a a
+
+ align:start position:0%
+goal but there's nothing like a a
+ 
+
+ align:start position:0%
+goal but there's nothing like a a
+life-threatening condition to Galvanize
+
+ align:start position:0%
+life-threatening condition to Galvanize
+ 
+
+ align:start position:0%
+life-threatening condition to Galvanize
+the attention of of of a family and here
+
+ align:start position:0%
+the attention of of of a family and here
+ 
+
+ align:start position:0%
+the attention of of of a family and here
+um in this in this clearly pathological
+
+ align:start position:0%
+um in this in this clearly pathological
+ 
+
+ align:start position:0%
+um in this in this clearly pathological
+way the daughter has become the center
+
+ align:start position:0%
+way the daughter has become the center
+ 
+
+ align:start position:0%
+way the daughter has become the center
+of the family's attention
+
+ align:start position:0%
+of the family's attention
+ 
+
+ align:start position:0%
+of the family's attention
+there's this quiet never caused any
+
+ align:start position:0%
+there's this quiet never caused any
+ 
+
+ align:start position:0%
+there's this quiet never caused any
+trouble you know
+
+ align:start position:0%
+trouble you know
+ 
+
+ align:start position:0%
+trouble you know
+bury the problems elsewhere daughter has
+
+ align:start position:0%
+bury the problems elsewhere daughter has
+ 
+
+ align:start position:0%
+bury the problems elsewhere daughter has
+now successfully taken over
+
+ align:start position:0%
+now successfully taken over
+ 
+
+ align:start position:0%
+now successfully taken over
+um the family the problem with that
+
+ align:start position:0%
+um the family the problem with that
+ 
+
+ align:start position:0%
+um the family the problem with that
+success is it's clearly desperately
+
+ align:start position:0%
+success is it's clearly desperately
+ 
+
+ align:start position:0%
+success is it's clearly desperately
+maladaptive and and potentially
+
+ align:start position:0%
+maladaptive and and potentially
+ 
+
+ align:start position:0%
+maladaptive and and potentially
+dangerous well what do you do
+
+ align:start position:0%
+dangerous well what do you do
+ 
+
+ align:start position:0%
+dangerous well what do you do
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as you can imagine
+
+ align:start position:0%
+as you can imagine
+ 
+
+ align:start position:0%
+as you can imagine
+um virtually
+
+ align:start position:0%
+um virtually
+ 
+
+ align:start position:0%
+um virtually
+every major uh psychotherapeutic
+
+ align:start position:0%
+every major uh psychotherapeutic
+ 
+
+ align:start position:0%
+every major uh psychotherapeutic
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+regimen has been tried in some fashion
+
+ align:start position:0%
+regimen has been tried in some fashion
+ 
+
+ align:start position:0%
+regimen has been tried in some fashion
+the the the the the punch line the
+
+ align:start position:0%
+the the the the the punch line the
+ 
+
+ align:start position:0%
+the the the the the punch line the
+bottom line is that
+
+ align:start position:0%
+bottom line is that
+ 
+
+ align:start position:0%
+bottom line is that
+um my understanding of best practice is
+
+ align:start position:0%
+um my understanding of best practice is
+ 
+
+ align:start position:0%
+um my understanding of best practice is
+that nothing by itself Works terribly
+
+ align:start position:0%
+that nothing by itself Works terribly
+ 
+
+ align:start position:0%
+that nothing by itself Works terribly
+well and that what what you do is uh
+
+ align:start position:0%
+well and that what what you do is uh
+ 
+
+ align:start position:0%
+well and that what what you do is uh
+some of everything
+
+ align:start position:0%
+some of everything
+ 
+
+ align:start position:0%
+some of everything
+um now what is everything well one bit
+
+ align:start position:0%
+um now what is everything well one bit
+ 
+
+ align:start position:0%
+um now what is everything well one bit
+of everything is you've got to get
+
+ align:start position:0%
+of everything is you've got to get
+ 
+
+ align:start position:0%
+of everything is you've got to get
+um the patients to eat
+
+ align:start position:0%
+um the patients to eat
+ 
+
+ align:start position:0%
+um the patients to eat
+then by the time you've got an eating
+
+ align:start position:0%
+then by the time you've got an eating
+ 
+
+ align:start position:0%
+then by the time you've got an eating
+disorder patient who has reached
+
+ align:start position:0%
+disorder patient who has reached
+ 
+
+ align:start position:0%
+disorder patient who has reached
+the point of being in medical care
+
+ align:start position:0%
+the point of being in medical care
+ 
+
+ align:start position:0%
+the point of being in medical care
+um this is a a potentially
+
+ align:start position:0%
+um this is a a potentially
+ 
+
+ align:start position:0%
+um this is a a potentially
+life-threatening situation and the
+
+ align:start position:0%
+life-threatening situation and the
+ 
+
+ align:start position:0%
+life-threatening situation and the
+patients often get hospitalized under
+
+ align:start position:0%
+patients often get hospitalized under
+ 
+
+ align:start position:0%
+patients often get hospitalized under
+Hospital settings one of the things that
+
+ align:start position:0%
+Hospital settings one of the things that
+ 
+
+ align:start position:0%
+Hospital settings one of the things that
+works really well and one of the things
+
+ align:start position:0%
+works really well and one of the things
+ 
+
+ align:start position:0%
+works really well and one of the things
+that was once upon a time touted is a
+
+ align:start position:0%
+that was once upon a time touted is a
+ 
+
+ align:start position:0%
+that was once upon a time touted is a
+magic you know Silver Bullet cure
+
+ align:start position:0%
+magic you know Silver Bullet cure
+ 
+
+ align:start position:0%
+magic you know Silver Bullet cure
+um comes straight out of
+
+ align:start position:0%
+um comes straight out of
+ 
+
+ align:start position:0%
+um comes straight out of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Skinner boxes and behaviorist uh Theory
+
+ align:start position:0%
+Skinner boxes and behaviorist uh Theory
+ 
+
+ align:start position:0%
+Skinner boxes and behaviorist uh Theory
+learning theory and that is
+
+ align:start position:0%
+learning theory and that is
+ 
+
+ align:start position:0%
+learning theory and that is
+um to set up the ward well basically is
+
+ align:start position:0%
+um to set up the ward well basically is
+ 
+
+ align:start position:0%
+um to set up the ward well basically is
+a giant Skinner box okay there's stuff
+
+ align:start position:0%
+a giant Skinner box okay there's stuff
+ 
+
+ align:start position:0%
+a giant Skinner box okay there's stuff
+you want right you want to be able to
+
+ align:start position:0%
+you want right you want to be able to
+ 
+
+ align:start position:0%
+you want right you want to be able to
+call your friends good here's what you
+
+ align:start position:0%
+call your friends good here's what you
+ 
+
+ align:start position:0%
+call your friends good here's what you
+got to eat you want to be able to
+
+ align:start position:0%
+got to eat you want to be able to
+ 
+
+ align:start position:0%
+got to eat you want to be able to
+um uh watch TV
+
+ align:start position:0%
+um uh watch TV
+ 
+
+ align:start position:0%
+um uh watch TV
+good here's the weight standard you have
+
+ align:start position:0%
+good here's the weight standard you have
+ 
+
+ align:start position:0%
+good here's the weight standard you have
+to reach and so you set up a clearly
+
+ align:start position:0%
+to reach and so you set up a clearly
+ 
+
+ align:start position:0%
+to reach and so you set up a clearly
+defined set of rewards in response for
+
+ align:start position:0%
+defined set of rewards in response for
+ 
+
+ align:start position:0%
+defined set of rewards in response for
+eating behaviors and it works very
+
+ align:start position:0%
+eating behaviors and it works very
+ 
+
+ align:start position:0%
+eating behaviors and it works very
+nicely in many cases you can get people
+
+ align:start position:0%
+nicely in many cases you can get people
+ 
+
+ align:start position:0%
+nicely in many cases you can get people
+back up to weights that are appropriate
+
+ align:start position:0%
+back up to weights that are appropriate
+ 
+
+ align:start position:0%
+back up to weights that are appropriate
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+um you know age and height
+
+ align:start position:0%
+um you know age and height
+ 
+
+ align:start position:0%
+um you know age and height
+um works just fine why isn't it a Magic
+
+ align:start position:0%
+um works just fine why isn't it a Magic
+ 
+
+ align:start position:0%
+um works just fine why isn't it a Magic
+Bullet
+
+ align:start position:0%
+Bullet
+ 
+
+ align:start position:0%
+Bullet
+well what happens when you go out of the
+
+ align:start position:0%
+well what happens when you go out of the
+ 
+
+ align:start position:0%
+well what happens when you go out of the
+hospital you go out of the hospital
+
+ align:start position:0%
+hospital you go out of the hospital
+ 
+
+ align:start position:0%
+hospital you go out of the hospital
+you're back in the environment that
+
+ align:start position:0%
+you're back in the environment that
+ 
+
+ align:start position:0%
+you're back in the environment that
+produced the disorder in some sense
+
+ align:start position:0%
+produced the disorder in some sense
+ 
+
+ align:start position:0%
+produced the disorder in some sense
+um and it tends to fall apart the
+
+ align:start position:0%
+um and it tends to fall apart the
+ 
+
+ align:start position:0%
+um and it tends to fall apart the
+problem was that relapse rates were uh
+
+ align:start position:0%
+problem was that relapse rates were uh
+ 
+
+ align:start position:0%
+problem was that relapse rates were uh
+were very great
+
+ align:start position:0%
+were very great
+ 
+
+ align:start position:0%
+were very great
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+well so one of the things you're going
+
+ align:start position:0%
+well so one of the things you're going
+ 
+
+ align:start position:0%
+well so one of the things you're going
+to want to do is not just treat people
+
+ align:start position:0%
+to want to do is not just treat people
+ 
+
+ align:start position:0%
+to want to do is not just treat people
+aren't pigeons you don't want to treat
+
+ align:start position:0%
+aren't pigeons you don't want to treat
+ 
+
+ align:start position:0%
+aren't pigeons you don't want to treat
+them just as pigeons
+
+ align:start position:0%
+them just as pigeons
+ 
+
+ align:start position:0%
+them just as pigeons
+um you can train your pigeon to to do
+
+ align:start position:0%
+um you can train your pigeon to to do
+ 
+
+ align:start position:0%
+um you can train your pigeon to to do
+whatever with a nice schedule of
+
+ align:start position:0%
+whatever with a nice schedule of
+ 
+
+ align:start position:0%
+whatever with a nice schedule of
+reinforcement and probably that doesn't
+
+ align:start position:0%
+reinforcement and probably that doesn't
+ 
+
+ align:start position:0%
+reinforcement and probably that doesn't
+work too well when you release the
+
+ align:start position:0%
+work too well when you release the
+ 
+
+ align:start position:0%
+work too well when you release the
+pigeon into the wild either with a human
+
+ align:start position:0%
+pigeon into the wild either with a human
+ 
+
+ align:start position:0%
+pigeon into the wild either with a human
+it's nice to talk to them so
+
+ align:start position:0%
+it's nice to talk to them so
+ 
+
+ align:start position:0%
+it's nice to talk to them so
+psychotherapeutic approaches have been
+
+ align:start position:0%
+psychotherapeutic approaches have been
+ 
+
+ align:start position:0%
+psychotherapeutic approaches have been
+you know various forms of talk therapy
+
+ align:start position:0%
+you know various forms of talk therapy
+ 
+
+ align:start position:0%
+you know various forms of talk therapy
+have been tried Freudian therapy
+
+ align:start position:0%
+have been tried Freudian therapy
+ 
+
+ align:start position:0%
+have been tried Freudian therapy
+centered around the idea that what what
+
+ align:start position:0%
+centered around the idea that what what
+ 
+
+ align:start position:0%
+centered around the idea that what what
+the the the core issue here was a fear
+
+ align:start position:0%
+the the the core issue here was a fear
+ 
+
+ align:start position:0%
+the the the core issue here was a fear
+of growing up
+
+ align:start position:0%
+of growing up
+ 
+
+ align:start position:0%
+of growing up
+um in in the in the sort of typical
+
+ align:start position:0%
+um in in the in the sort of typical
+ 
+
+ align:start position:0%
+um in in the in the sort of typical
+Freudian
+
+ align:start position:0%
+Freudian
+ 
+
+ align:start position:0%
+Freudian
+um uh tendency to sexualize everything
+
+ align:start position:0%
+um uh tendency to sexualize everything
+ 
+
+ align:start position:0%
+um uh tendency to sexualize everything
+under the sun this gets described as a
+
+ align:start position:0%
+under the sun this gets described as a
+ 
+
+ align:start position:0%
+under the sun this gets described as a
+fear of of of pregnancy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that well you know if if you manage
+
+ align:start position:0%
+um that well you know if if you manage
+ 
+
+ align:start position:0%
+um that well you know if if you manage
+to suppress
+
+ align:start position:0%
+to suppress
+ 
+
+ align:start position:0%
+to suppress
+um menstrual cycles and things like that
+
+ align:start position:0%
+um menstrual cycles and things like that
+ 
+
+ align:start position:0%
+um menstrual cycles and things like that
+you're not going to become pregnant
+
+ align:start position:0%
+you're not going to become pregnant
+ 
+
+ align:start position:0%
+you're not going to become pregnant
+um and and by starving yourself your
+
+ align:start position:0%
+um and and by starving yourself your
+ 
+
+ align:start position:0%
+um and and by starving yourself your
+body will be more like that of of a
+
+ align:start position:0%
+body will be more like that of of a
+ 
+
+ align:start position:0%
+body will be more like that of of a
+little girl it's it's a little like the
+
+ align:start position:0%
+little girl it's it's a little like the
+ 
+
+ align:start position:0%
+little girl it's it's a little like the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um the sort of metaphoric senses of
+
+ align:start position:0%
+um the sort of metaphoric senses of
+ 
+
+ align:start position:0%
+um the sort of metaphoric senses of
+trying of Snow White's evil stepmother
+
+ align:start position:0%
+trying of Snow White's evil stepmother
+ 
+
+ align:start position:0%
+trying of Snow White's evil stepmother
+trying to keep Snow White as a little
+
+ align:start position:0%
+trying to keep Snow White as a little
+ 
+
+ align:start position:0%
+trying to keep Snow White as a little
+girl but anyway the Freudian notion was
+
+ align:start position:0%
+girl but anyway the Freudian notion was
+ 
+
+ align:start position:0%
+girl but anyway the Freudian notion was
+that that there's a certain Terror about
+
+ align:start position:0%
+that that there's a certain Terror about
+ 
+
+ align:start position:0%
+that that there's a certain Terror about
+getting older uh you know growing up
+
+ align:start position:0%
+getting older uh you know growing up
+ 
+
+ align:start position:0%
+getting older uh you know growing up
+um that that the that the patients are
+
+ align:start position:0%
+um that that the that the patients are
+ 
+
+ align:start position:0%
+um that that the that the patients are
+dealing with
+
+ align:start position:0%
+dealing with
+ 
+
+ align:start position:0%
+dealing with
+um just talking to him about it didn't
+
+ align:start position:0%
+um just talking to him about it didn't
+ 
+
+ align:start position:0%
+um just talking to him about it didn't
+turn out to be a huge success in part
+
+ align:start position:0%
+turn out to be a huge success in part
+ 
+
+ align:start position:0%
+turn out to be a huge success in part
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+patients who are that
+
+ align:start position:0%
+patients who are that
+ 
+
+ align:start position:0%
+patients who are that
+undernourished are a little like
+
+ align:start position:0%
+undernourished are a little like
+ 
+
+ align:start position:0%
+undernourished are a little like
+schizophrenic patients they're not good
+
+ align:start position:0%
+schizophrenic patients they're not good
+ 
+
+ align:start position:0%
+schizophrenic patients they're not good
+candidates for psychoanalysis or for
+
+ align:start position:0%
+candidates for psychoanalysis or for
+ 
+
+ align:start position:0%
+candidates for psychoanalysis or for
+much other in the way of talking therapy
+
+ align:start position:0%
+much other in the way of talking therapy
+ 
+
+ align:start position:0%
+much other in the way of talking therapy
+delusional people are not great at
+
+ align:start position:0%
+delusional people are not great at
+ 
+
+ align:start position:0%
+delusional people are not great at
+Insight
+
+ align:start position:0%
+Insight
+ 
+
+ align:start position:0%
+Insight
+um and and
+
+ align:start position:0%
+um and and
+ 
+
+ align:start position:0%
+um and and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+combining
+
+ align:start position:0%
+combining
+ 
+
+ align:start position:0%
+combining
+some sort of conversation some sort of
+
+ align:start position:0%
+some sort of conversation some sort of
+ 
+
+ align:start position:0%
+some sort of conversation some sort of
+therapeutic conversation with something
+
+ align:start position:0%
+therapeutic conversation with something
+ 
+
+ align:start position:0%
+therapeutic conversation with something
+like the the behavioral modification
+
+ align:start position:0%
+like the the behavioral modification
+ 
+
+ align:start position:0%
+like the the behavioral modification
+technique that helps
+
+ align:start position:0%
+technique that helps
+ 
+
+ align:start position:0%
+technique that helps
+um there is evidence that uh
+
+ align:start position:0%
+um there is evidence that uh
+ 
+
+ align:start position:0%
+um there is evidence that uh
+pharmacology helps there is an obsessive
+
+ align:start position:0%
+pharmacology helps there is an obsessive
+ 
+
+ align:start position:0%
+pharmacology helps there is an obsessive
+quality to the thought processes of of
+
+ align:start position:0%
+quality to the thought processes of of
+ 
+
+ align:start position:0%
+quality to the thought processes of of
+anorexic patients that deeply obsessed
+
+ align:start position:0%
+anorexic patients that deeply obsessed
+ 
+
+ align:start position:0%
+anorexic patients that deeply obsessed
+with with food in fact you get these
+
+ align:start position:0%
+with with food in fact you get these
+ 
+
+ align:start position:0%
+with with food in fact you get these
+fascinating case histories where
+
+ align:start position:0%
+fascinating case histories where
+ 
+
+ align:start position:0%
+fascinating case histories where
+um the the anorexic is doing all the
+
+ align:start position:0%
+um the the anorexic is doing all the
+ 
+
+ align:start position:0%
+um the the anorexic is doing all the
+cooking for the family right she loves
+
+ align:start position:0%
+cooking for the family right she loves
+ 
+
+ align:start position:0%
+cooking for the family right she loves
+to cook for for everybody she just
+
+ align:start position:0%
+to cook for for everybody she just
+ 
+
+ align:start position:0%
+to cook for for everybody she just
+doesn't eat any of this you know
+
+ align:start position:0%
+doesn't eat any of this you know
+ 
+
+ align:start position:0%
+doesn't eat any of this you know
+absolutely obsessed with food uh
+
+ align:start position:0%
+absolutely obsessed with food uh
+ 
+
+ align:start position:0%
+absolutely obsessed with food uh
+swearing they're not hungry and and and
+
+ align:start position:0%
+swearing they're not hungry and and and
+ 
+
+ align:start position:0%
+swearing they're not hungry and and and
+and and uh
+
+ align:start position:0%
+and and uh
+ 
+
+ align:start position:0%
+and and uh
+and engaging in elaborate rituals around
+
+ align:start position:0%
+and engaging in elaborate rituals around
+ 
+
+ align:start position:0%
+and engaging in elaborate rituals around
+eating
+
+ align:start position:0%
+eating
+ 
+
+ align:start position:0%
+eating
+um you know that's an obsessive kind of
+
+ align:start position:0%
+um you know that's an obsessive kind of
+ 
+
+ align:start position:0%
+um you know that's an obsessive kind of
+behavior that is uh that turns out to be
+
+ align:start position:0%
+behavior that is uh that turns out to be
+ 
+
+ align:start position:0%
+behavior that is uh that turns out to be
+broken up
+
+ align:start position:0%
+broken up
+ 
+
+ align:start position:0%
+broken up
+um by Prozac and similar drugs quite
+
+ align:start position:0%
+um by Prozac and similar drugs quite
+ 
+
+ align:start position:0%
+um by Prozac and similar drugs quite
+well so one thing to do is to feed them
+
+ align:start position:0%
+well so one thing to do is to feed them
+ 
+
+ align:start position:0%
+well so one thing to do is to feed them
+an antidepressant like Prozac in part
+
+ align:start position:0%
+an antidepressant like Prozac in part
+ 
+
+ align:start position:0%
+an antidepressant like Prozac in part
+because they may be depressed and in
+
+ align:start position:0%
+because they may be depressed and in
+ 
+
+ align:start position:0%
+because they may be depressed and in
+part because it acts against the
+
+ align:start position:0%
+part because it acts against the
+ 
+
+ align:start position:0%
+part because it acts against the
+obsessive thoughts just feeding them uh
+
+ align:start position:0%
+obsessive thoughts just feeding them uh
+ 
+
+ align:start position:0%
+obsessive thoughts just feeding them uh
+uh an antidepressant by itself has no
+
+ align:start position:0%
+uh an antidepressant by itself has no
+ 
+
+ align:start position:0%
+uh an antidepressant by itself has no
+great track record but all right let's
+
+ align:start position:0%
+great track record but all right let's
+ 
+
+ align:start position:0%
+great track record but all right let's
+combine a little antidepressant
+
+ align:start position:0%
+combine a little antidepressant
+ 
+
+ align:start position:0%
+combine a little antidepressant
+medication with a little behavior
+
+ align:start position:0%
+medication with a little behavior
+ 
+
+ align:start position:0%
+medication with a little behavior
+modification a little talk therapy this
+
+ align:start position:0%
+modification a little talk therapy this
+ 
+
+ align:start position:0%
+modification a little talk therapy this
+is all working this this this all might
+
+ align:start position:0%
+is all working this this this all might
+ 
+
+ align:start position:0%
+is all working this this this all might
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+meat to it one of the things that um
+
+ align:start position:0%
+meat to it one of the things that um
+ 
+
+ align:start position:0%
+meat to it one of the things that um
+seems to
+
+ align:start position:0%
+seems to
+ 
+
+ align:start position:0%
+seems to
+be an interesting part of treatment
+
+ align:start position:0%
+be an interesting part of treatment
+ 
+
+ align:start position:0%
+be an interesting part of treatment
+regimens in Eating Disorders more so
+
+ align:start position:0%
+regimens in Eating Disorders more so
+ 
+
+ align:start position:0%
+regimens in Eating Disorders more so
+perhaps than elsewhere is it's often
+
+ align:start position:0%
+perhaps than elsewhere is it's often
+ 
+
+ align:start position:0%
+perhaps than elsewhere is it's often
+useful in in anorexia particularly to
+
+ align:start position:0%
+useful in in anorexia particularly to
+ 
+
+ align:start position:0%
+useful in in anorexia particularly to
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+to tomly also because that family
+
+ align:start position:0%
+to tomly also because that family
+ 
+
+ align:start position:0%
+to tomly also because that family
+they're they're actually
+
+ align:start position:0%
+they're they're actually
+ 
+
+ align:start position:0%
+they're they're actually
+um there there are clinicians who argue
+
+ align:start position:0%
+um there there are clinicians who argue
+ 
+
+ align:start position:0%
+um there there are clinicians who argue
+that um that uh anorexia is a disorder
+
+ align:start position:0%
+that um that uh anorexia is a disorder
+ 
+
+ align:start position:0%
+that um that uh anorexia is a disorder
+of the family where it just happens to
+
+ align:start position:0%
+of the family where it just happens to
+ 
+
+ align:start position:0%
+of the family where it just happens to
+be that the girl is the designated
+
+ align:start position:0%
+be that the girl is the designated
+ 
+
+ align:start position:0%
+be that the girl is the designated
+patient that the family as a system is
+
+ align:start position:0%
+patient that the family as a system is
+ 
+
+ align:start position:0%
+patient that the family as a system is
+sick
+
+ align:start position:0%
+sick
+ 
+
+ align:start position:0%
+sick
+and that the daughter is showing the
+
+ align:start position:0%
+and that the daughter is showing the
+ 
+
+ align:start position:0%
+and that the daughter is showing the
+symptom and that if you want to uh if
+
+ align:start position:0%
+symptom and that if you want to uh if
+ 
+
+ align:start position:0%
+symptom and that if you want to uh if
+you want to have this work out
+
+ align:start position:0%
+you want to have this work out
+ 
+
+ align:start position:0%
+you want to have this work out
+um that what you need to do is is to
+
+ align:start position:0%
+um that what you need to do is is to
+ 
+
+ align:start position:0%
+um that what you need to do is is to
+treat the uh is to treat the family and
+
+ align:start position:0%
+treat the uh is to treat the family and
+ 
+
+ align:start position:0%
+treat the uh is to treat the family and
+and get the family
+
+ align:start position:0%
+and get the family
+ 
+
+ align:start position:0%
+and get the family
+um out of each other's faces uh a little
+
+ align:start position:0%
+um out of each other's faces uh a little
+ 
+
+ align:start position:0%
+um out of each other's faces uh a little
+more and more willing to express uh
+
+ align:start position:0%
+more and more willing to express uh
+ 
+
+ align:start position:0%
+more and more willing to express uh
+feelings to each other perhaps and
+
+ align:start position:0%
+feelings to each other perhaps and
+ 
+
+ align:start position:0%
+feelings to each other perhaps and
+things of that sort
+
+ align:start position:0%
+things of that sort
+ 
+
+ align:start position:0%
+things of that sort
+um the prognosis is
+
+ align:start position:0%
+um the prognosis is
+ 
+
+ align:start position:0%
+um the prognosis is
+um is is a little reminiscent of Anna oh
+
+ align:start position:0%
+um is is a little reminiscent of Anna oh
+ 
+
+ align:start position:0%
+um is is a little reminiscent of Anna oh
+if you if uh you remember that story
+
+ align:start position:0%
+if you if uh you remember that story
+ 
+
+ align:start position:0%
+if you if uh you remember that story
+from from the history of of Freud's
+
+ align:start position:0%
+from from the history of of Freud's
+ 
+
+ align:start position:0%
+from from the history of of Freud's
+development Anna oh had patient had
+
+ align:start position:0%
+development Anna oh had patient had
+ 
+
+ align:start position:0%
+development Anna oh had patient had
+symptoms that Freud and broyer could
+
+ align:start position:0%
+symptoms that Freud and broyer could
+ 
+
+ align:start position:0%
+symptoms that Freud and broyer could
+treat
+
+ align:start position:0%
+treat
+ 
+
+ align:start position:0%
+treat
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+when those were treated something new
+
+ align:start position:0%
+when those were treated something new
+ 
+
+ align:start position:0%
+when those were treated something new
+popped up there's a flavor of that in
+
+ align:start position:0%
+popped up there's a flavor of that in
+ 
+
+ align:start position:0%
+popped up there's a flavor of that in
+and when you read about case histories
+
+ align:start position:0%
+and when you read about case histories
+ 
+
+ align:start position:0%
+and when you read about case histories
+of of anorexia that you can most
+
+ align:start position:0%
+of of anorexia that you can most
+ 
+
+ align:start position:0%
+of of anorexia that you can most
+patients recover
+
+ align:start position:0%
+patients recover
+ 
+
+ align:start position:0%
+patients recover
+right they they become non-anorexic but
+
+ align:start position:0%
+right they they become non-anorexic but
+ 
+
+ align:start position:0%
+right they they become non-anorexic but
+they're uh but the population sees more
+
+ align:start position:0%
+they're uh but the population sees more
+ 
+
+ align:start position:0%
+they're uh but the population sees more
+depression going forward than a typical
+
+ align:start position:0%
+depression going forward than a typical
+ 
+
+ align:start position:0%
+depression going forward than a typical
+Pro population the population sees more
+
+ align:start position:0%
+Pro population the population sees more
+ 
+
+ align:start position:0%
+Pro population the population sees more
+other Eating Disorders than a typical
+
+ align:start position:0%
+other Eating Disorders than a typical
+ 
+
+ align:start position:0%
+other Eating Disorders than a typical
+population as if there's something that
+
+ align:start position:0%
+population as if there's something that
+ 
+
+ align:start position:0%
+population as if there's something that
+was not dealt with
+
+ align:start position:0%
+was not dealt with
+ 
+
+ align:start position:0%
+was not dealt with
+and exactly what that is we clearly
+
+ align:start position:0%
+and exactly what that is we clearly
+ 
+
+ align:start position:0%
+and exactly what that is we clearly
+don't really know
+
+ align:start position:0%
+don't really know
+ 
+
+ align:start position:0%
+don't really know
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but that that this
+
+ align:start position:0%
+but that that this
+ 
+
+ align:start position:0%
+but that that this
+um that that anorexia was the particular
+
+ align:start position:0%
+um that that anorexia was the particular
+ 
+
+ align:start position:0%
+um that that anorexia was the particular
+crisis and that there are issues that
+
+ align:start position:0%
+crisis and that there are issues that
+ 
+
+ align:start position:0%
+crisis and that there are issues that
+may need to be uh dealt with on on a uh
+
+ align:start position:0%
+may need to be uh dealt with on on a uh
+ 
+
+ align:start position:0%
+may need to be uh dealt with on on a uh
+on a long-term basis now one of the
+
+ align:start position:0%
+on a long-term basis now one of the
+ 
+
+ align:start position:0%
+on a long-term basis now one of the
+disorders
+
+ align:start position:0%
+disorders
+ 
+
+ align:start position:0%
+disorders
+that um that you can sort of progress to
+
+ align:start position:0%
+that um that you can sort of progress to
+ 
+
+ align:start position:0%
+that um that you can sort of progress to
+if you like
+
+ align:start position:0%
+if you like
+ 
+
+ align:start position:0%
+if you like
+um not infrequently or you can manage to
+
+ align:start position:0%
+um not infrequently or you can manage to
+ 
+
+ align:start position:0%
+um not infrequently or you can manage to
+generate it all by itself is bulimia or
+
+ align:start position:0%
+generate it all by itself is bulimia or
+ 
+
+ align:start position:0%
+generate it all by itself is bulimia or
+more technically bulimia nervosa though
+
+ align:start position:0%
+more technically bulimia nervosa though
+ 
+
+ align:start position:0%
+more technically bulimia nervosa though
+it anorexia nervosa gets called anorexia
+
+ align:start position:0%
+it anorexia nervosa gets called anorexia
+ 
+
+ align:start position:0%
+it anorexia nervosa gets called anorexia
+nervosa bulimia often just calls gets
+
+ align:start position:0%
+nervosa bulimia often just calls gets
+ 
+
+ align:start position:0%
+nervosa bulimia often just calls gets
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+um bulimia oh did we just switch oh look
+
+ align:start position:0%
+um bulimia oh did we just switch oh look
+ 
+
+ align:start position:0%
+um bulimia oh did we just switch oh look
+at that we it's so much fun to watch
+
+ align:start position:0%
+at that we it's so much fun to watch
+ 
+
+ align:start position:0%
+at that we it's so much fun to watch
+everybody go
+
+ align:start position:0%
+everybody go
+ 
+
+ align:start position:0%
+everybody go
+glad to know you're following along
+
+ align:start position:0%
+glad to know you're following along
+ 
+
+ align:start position:0%
+glad to know you're following along
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so bulimia is is one of the reasons the
+
+ align:start position:0%
+so bulimia is is one of the reasons the
+ 
+
+ align:start position:0%
+so bulimia is is one of the reasons the
+follow-on disorder well I don't know
+
+ align:start position:0%
+follow-on disorder well I don't know
+ 
+
+ align:start position:0%
+follow-on disorder well I don't know
+it's a reason
+
+ align:start position:0%
+it's a reason
+ 
+
+ align:start position:0%
+it's a reason
+um it's not surprising it's a follow-on
+
+ align:start position:0%
+um it's not surprising it's a follow-on
+ 
+
+ align:start position:0%
+um it's not surprising it's a follow-on
+disorder it's characteristic of an older
+
+ align:start position:0%
+disorder it's characteristic of an older
+ 
+
+ align:start position:0%
+disorder it's characteristic of an older
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+um typical onset in uh uh in in college
+
+ align:start position:0%
+um typical onset in uh uh in in college
+ 
+
+ align:start position:0%
+um typical onset in uh uh in in college
+age or 20s
+
+ align:start position:0%
+age or 20s
+ 
+
+ align:start position:0%
+age or 20s
+um and and a a different kind of uh a
+
+ align:start position:0%
+um and and a a different kind of uh a
+ 
+
+ align:start position:0%
+um and and a a different kind of uh a
+sort of a different story uh so one
+
+ align:start position:0%
+sort of a different story uh so one
+ 
+
+ align:start position:0%
+sort of a different story uh so one
+important characteristic is these are
+
+ align:start position:0%
+important characteristic is these are
+ 
+
+ align:start position:0%
+important characteristic is these are
+patients typically who are outside of
+
+ align:start position:0%
+patients typically who are outside of
+ 
+
+ align:start position:0%
+patients typically who are outside of
+the family situation they're not
+
+ align:start position:0%
+the family situation they're not
+ 
+
+ align:start position:0%
+the family situation they're not
+embedded in their family they've gone
+
+ align:start position:0%
+embedded in their family they've gone
+ 
+
+ align:start position:0%
+embedded in their family they've gone
+off to college or they've gone off to
+
+ align:start position:0%
+off to college or they've gone off to
+ 
+
+ align:start position:0%
+off to college or they've gone off to
+work or something uh of of that sort
+
+ align:start position:0%
+work or something uh of of that sort
+ 
+
+ align:start position:0%
+work or something uh of of that sort
+um a bit insecure let's go back to this
+
+ align:start position:0%
+um a bit insecure let's go back to this
+ 
+
+ align:start position:0%
+um a bit insecure let's go back to this
+we're not necessarily talking about you
+
+ align:start position:0%
+we're not necessarily talking about you
+ 
+
+ align:start position:0%
+we're not necessarily talking about you
+thing a bit insecure right who isn't the
+
+ align:start position:0%
+thing a bit insecure right who isn't the
+ 
+
+ align:start position:0%
+thing a bit insecure right who isn't the
+ones who aren't a little bit insecure
+
+ align:start position:0%
+ones who aren't a little bit insecure
+ 
+
+ align:start position:0%
+ones who aren't a little bit insecure
+are the people you know near and dear to
+
+ align:start position:0%
+are the people you know near and dear to
+ 
+
+ align:start position:0%
+are the people you know near and dear to
+us who are insufferable
+
+ align:start position:0%
+us who are insufferable
+ 
+
+ align:start position:0%
+us who are insufferable
+um but so a little bit insecure maybe
+
+ align:start position:0%
+um but so a little bit insecure maybe
+ 
+
+ align:start position:0%
+um but so a little bit insecure maybe
+maybe a bit more insecure than usual uh
+
+ align:start position:0%
+maybe a bit more insecure than usual uh
+ 
+
+ align:start position:0%
+maybe a bit more insecure than usual uh
+a bit impulsive
+
+ align:start position:0%
+a bit impulsive
+ 
+
+ align:start position:0%
+a bit impulsive
+um what's impulsive all right when you
+
+ align:start position:0%
+um what's impulsive all right when you
+ 
+
+ align:start position:0%
+um what's impulsive all right when you
+get that family history sorry the
+
+ align:start position:0%
+get that family history sorry the
+ 
+
+ align:start position:0%
+get that family history sorry the
+patient's history you you get uh uh
+
+ align:start position:0%
+patient's history you you get uh uh
+ 
+
+ align:start position:0%
+patient's history you you get uh uh
+these anecdotes about uh you know dumb
+
+ align:start position:0%
+these anecdotes about uh you know dumb
+ 
+
+ align:start position:0%
+these anecdotes about uh you know dumb
+impulsive things oh I shop you know I I
+
+ align:start position:0%
+impulsive things oh I shop you know I I
+ 
+
+ align:start position:0%
+impulsive things oh I shop you know I I
+don't know where my shoplifted once it's
+
+ align:start position:0%
+don't know where my shoplifted once it's
+ 
+
+ align:start position:0%
+don't know where my shoplifted once it's
+not like I'm a a a a chronic shoplifter
+
+ align:start position:0%
+not like I'm a a a a chronic shoplifter
+ 
+
+ align:start position:0%
+not like I'm a a a a chronic shoplifter
+but dumb you you get sort of dumb single
+
+ align:start position:0%
+but dumb you you get sort of dumb single
+ 
+
+ align:start position:0%
+but dumb you you get sort of dumb single
+incident kind of things
+
+ align:start position:0%
+incident kind of things
+ 
+
+ align:start position:0%
+incident kind of things
+um in these in these reports
+
+ align:start position:0%
+um in these in these reports
+ 
+
+ align:start position:0%
+um in these in these reports
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and uh not
+
+ align:start position:0%
+and uh not
+ 
+
+ align:start position:0%
+and uh not
+self-esteem not great and uh wants to
+
+ align:start position:0%
+self-esteem not great and uh wants to
+ 
+
+ align:start position:0%
+self-esteem not great and uh wants to
+fit in which of course qualifies for
+
+ align:start position:0%
+fit in which of course qualifies for
+ 
+
+ align:start position:0%
+fit in which of course qualifies for
+most of us also at least the ones to fit
+
+ align:start position:0%
+most of us also at least the ones to fit
+ 
+
+ align:start position:0%
+most of us also at least the ones to fit
+in part
+
+ align:start position:0%
+in part
+ 
+
+ align:start position:0%
+in part
+um so the Dilemma faced by this woman
+
+ align:start position:0%
+um so the Dilemma faced by this woman
+ 
+
+ align:start position:0%
+um so the Dilemma faced by this woman
+now living independently is that that
+
+ align:start position:0%
+now living independently is that that
+ 
+
+ align:start position:0%
+now living independently is that that
+the fitting in peace involves
+
+ align:start position:0%
+the fitting in peace involves
+ 
+
+ align:start position:0%
+the fitting in peace involves
+um socializing and the socializing
+
+ align:start position:0%
+um socializing and the socializing
+ 
+
+ align:start position:0%
+um socializing and the socializing
+involves a lot of uh eating and drinking
+
+ align:start position:0%
+involves a lot of uh eating and drinking
+ 
+
+ align:start position:0%
+involves a lot of uh eating and drinking
+um fitting in also involves rather
+
+ align:start position:0%
+um fitting in also involves rather
+ 
+
+ align:start position:0%
+um fitting in also involves rather
+literally fitting in to those those
+
+ align:start position:0%
+literally fitting in to those those
+ 
+
+ align:start position:0%
+literally fitting in to those those
+genes or whatever that were designed for
+
+ align:start position:0%
+genes or whatever that were designed for
+ 
+
+ align:start position:0%
+genes or whatever that were designed for
+uh some half-starved model in the
+
+ align:start position:0%
+uh some half-starved model in the
+ 
+
+ align:start position:0%
+uh some half-starved model in the
+fashion magazines somewhere and so
+
+ align:start position:0%
+fashion magazines somewhere and so
+ 
+
+ align:start position:0%
+fashion magazines somewhere and so
+you've got this conflict between food
+
+ align:start position:0%
+you've got this conflict between food
+ 
+
+ align:start position:0%
+you've got this conflict between food
+and and and and thinness
+
+ align:start position:0%
+and and and and thinness
+ 
+
+ align:start position:0%
+and and and and thinness
+um made quite concrete and um
+
+ align:start position:0%
+um made quite concrete and um
+ 
+
+ align:start position:0%
+um made quite concrete and um
+and these are our our patients who in a
+
+ align:start position:0%
+and these are our our patients who in a
+ 
+
+ align:start position:0%
+and these are our our patients who in a
+sense stumble on a trick and the trick
+
+ align:start position:0%
+sense stumble on a trick and the trick
+ 
+
+ align:start position:0%
+sense stumble on a trick and the trick
+is that if you eat and then you get rid
+
+ align:start position:0%
+is that if you eat and then you get rid
+ 
+
+ align:start position:0%
+is that if you eat and then you get rid
+of the food
+
+ align:start position:0%
+of the food
+ 
+
+ align:start position:0%
+of the food
+those calories don't end up on your hips
+
+ align:start position:0%
+those calories don't end up on your hips
+ 
+
+ align:start position:0%
+those calories don't end up on your hips
+right so if you eat and then
+
+ align:start position:0%
+right so if you eat and then
+ 
+
+ align:start position:0%
+right so if you eat and then
+um take a laxative or or throw up then
+
+ align:start position:0%
+um take a laxative or or throw up then
+ 
+
+ align:start position:0%
+um take a laxative or or throw up then
+then you don't get the calories right
+
+ align:start position:0%
+then you don't get the calories right
+ 
+
+ align:start position:0%
+then you don't get the calories right
+now that's a solution but it's not a
+
+ align:start position:0%
+now that's a solution but it's not a
+ 
+
+ align:start position:0%
+now that's a solution but it's not a
+really great solution it's not a great
+
+ align:start position:0%
+really great solution it's not a great
+ 
+
+ align:start position:0%
+really great solution it's not a great
+solution for any number of reasons one
+
+ align:start position:0%
+solution for any number of reasons one
+ 
+
+ align:start position:0%
+solution for any number of reasons one
+of them is that interestingly it feels
+
+ align:start position:0%
+of them is that interestingly it feels
+ 
+
+ align:start position:0%
+of them is that interestingly it feels
+shameful
+
+ align:start position:0%
+shameful
+ 
+
+ align:start position:0%
+shameful
+um now it's that's interesting because
+
+ align:start position:0%
+um now it's that's interesting because
+ 
+
+ align:start position:0%
+um now it's that's interesting because
+you could go on to a whole thing about
+
+ align:start position:0%
+you could go on to a whole thing about
+ 
+
+ align:start position:0%
+you could go on to a whole thing about
+why no no I'm I suppose no is probably
+
+ align:start position:0%
+why no no I'm I suppose no is probably
+ 
+
+ align:start position:0%
+why no no I'm I suppose no is probably
+too strong a typical bulimic is not
+
+ align:start position:0%
+too strong a typical bulimic is not
+ 
+
+ align:start position:0%
+too strong a typical bulimic is not
+going to have a buddy bulimic who yo let
+
+ align:start position:0%
+going to have a buddy bulimic who yo let
+ 
+
+ align:start position:0%
+going to have a buddy bulimic who yo let
+you know let's go off and and go to this
+
+ align:start position:0%
+you know let's go off and and go to this
+ 
+
+ align:start position:0%
+you know let's go off and and go to this
+party and eat and go throw up together
+
+ align:start position:0%
+party and eat and go throw up together
+ 
+
+ align:start position:0%
+party and eat and go throw up together
+um I mean it even sounds it sounds weird
+
+ align:start position:0%
+um I mean it even sounds it sounds weird
+ 
+
+ align:start position:0%
+um I mean it even sounds it sounds weird
+oh by the way though this is not unknown
+
+ align:start position:0%
+oh by the way though this is not unknown
+ 
+
+ align:start position:0%
+oh by the way though this is not unknown
+culturally
+
+ align:start position:0%
+culturally
+ 
+
+ align:start position:0%
+culturally
+um though I realized talking to my
+
+ align:start position:0%
+um though I realized talking to my
+ 
+
+ align:start position:0%
+um though I realized talking to my
+Concourse class this morning that it's
+
+ align:start position:0%
+Concourse class this morning that it's
+ 
+
+ align:start position:0%
+Concourse class this morning that it's
+apparently much less known than I
+
+ align:start position:0%
+apparently much less known than I
+ 
+
+ align:start position:0%
+apparently much less known than I
+thought
+
+ align:start position:0%
+thought
+ 
+
+ align:start position:0%
+thought
+um because my eight-year-old
+
+ align:start position:0%
+um because my eight-year-old
+ 
+
+ align:start position:0%
+um because my eight-year-old
+can tell you all about this
+
+ align:start position:0%
+can tell you all about this
+ 
+
+ align:start position:0%
+can tell you all about this
+um but uh in in in
+
+ align:start position:0%
+um but uh in in in
+ 
+
+ align:start position:0%
+um but uh in in in
+Roman culture sort of high Roman Empire
+
+ align:start position:0%
+Roman culture sort of high Roman Empire
+ 
+
+ align:start position:0%
+Roman culture sort of high Roman Empire
+culture
+
+ align:start position:0%
+culture
+ 
+
+ align:start position:0%
+culture
+um there there were I don't know how
+
+ align:start position:0%
+um there there were I don't know how
+ 
+
+ align:start position:0%
+um there there were I don't know how
+widespread this was but certainly in in
+
+ align:start position:0%
+widespread this was but certainly in in
+ 
+
+ align:start position:0%
+widespread this was but certainly in in
+in in the in the orgy class
+
+ align:start position:0%
+in in the in the orgy class
+ 
+
+ align:start position:0%
+in in the in the orgy class
+um there was a a custom of having these
+
+ align:start position:0%
+um there was a a custom of having these
+ 
+
+ align:start position:0%
+um there was a a custom of having these
+you know very elaborate parties where
+
+ align:start position:0%
+you know very elaborate parties where
+ 
+
+ align:start position:0%
+you know very elaborate parties where
+you'd eat and eat and eat and then you
+
+ align:start position:0%
+you'd eat and eat and eat and then you
+ 
+
+ align:start position:0%
+you'd eat and eat and eat and then you
+couldn't eat anymore well but you wanted
+
+ align:start position:0%
+couldn't eat anymore well but you wanted
+ 
+
+ align:start position:0%
+couldn't eat anymore well but you wanted
+to keep eating so you went to the next
+
+ align:start position:0%
+to keep eating so you went to the next
+ 
+
+ align:start position:0%
+to keep eating so you went to the next
+room you threw up and you came back and
+
+ align:start position:0%
+room you threw up and you came back and
+ 
+
+ align:start position:0%
+room you threw up and you came back and
+you ate some more
+
+ align:start position:0%
+you ate some more
+ 
+
+ align:start position:0%
+you ate some more
+um and and and uh so uh there are even
+
+ align:start position:0%
+um and and and uh so uh there are even
+ 
+
+ align:start position:0%
+um and and and uh so uh there are even
+villas with rooms that are designated as
+
+ align:start position:0%
+villas with rooms that are designated as
+ 
+
+ align:start position:0%
+villas with rooms that are designated as
+the vomitorium
+
+ align:start position:0%
+the vomitorium
+ 
+
+ align:start position:0%
+the vomitorium
+um and and so how many people knew about
+
+ align:start position:0%
+um and and so how many people knew about
+ 
+
+ align:start position:0%
+um and and so how many people knew about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+oh yeah all right so this is a minority
+
+ align:start position:0%
+oh yeah all right so this is a minority
+ 
+
+ align:start position:0%
+oh yeah all right so this is a minority
+I did it's absolutely fascinating to a
+
+ align:start position:0%
+I did it's absolutely fascinating to a
+ 
+
+ align:start position:0%
+I did it's absolutely fascinating to a
+certain round of eight eight-year-old
+
+ align:start position:0%
+certain round of eight eight-year-old
+ 
+
+ align:start position:0%
+certain round of eight eight-year-old
+boys
+
+ align:start position:0%
+boys
+ 
+
+ align:start position:0%
+boys
+um who who think this is you know
+
+ align:start position:0%
+um who who think this is you know
+ 
+
+ align:start position:0%
+um who who think this is you know
+really very interesting not something
+
+ align:start position:0%
+really very interesting not something
+ 
+
+ align:start position:0%
+really very interesting not something
+they want to try thank you but but you
+
+ align:start position:0%
+they want to try thank you but but you
+ 
+
+ align:start position:0%
+they want to try thank you but but you
+know oh that's really well like other
+
+ align:start position:0%
+know oh that's really well like other
+ 
+
+ align:start position:0%
+know oh that's really well like other
+gross stuff anyway the problem is that
+
+ align:start position:0%
+gross stuff anyway the problem is that
+ 
+
+ align:start position:0%
+gross stuff anyway the problem is that
+first of all it's it's not it's it's
+
+ align:start position:0%
+first of all it's it's not it's it's
+ 
+
+ align:start position:0%
+first of all it's it's not it's it's
+something that feels shameful and needs
+
+ align:start position:0%
+something that feels shameful and needs
+ 
+
+ align:start position:0%
+something that feels shameful and needs
+to be done in private
+
+ align:start position:0%
+to be done in private
+ 
+
+ align:start position:0%
+to be done in private
+um it's not a um
+
+ align:start position:0%
+um it's not a um
+ 
+
+ align:start position:0%
+um it's not a um
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is it's clearly a sort of an odd
+
+ align:start position:0%
+it is it's clearly a sort of an odd
+ 
+
+ align:start position:0%
+it is it's clearly a sort of an odd
+solution so maybe you try a more
+
+ align:start position:0%
+solution so maybe you try a more
+ 
+
+ align:start position:0%
+solution so maybe you try a more
+mainstream solution let's go on a diet
+
+ align:start position:0%
+mainstream solution let's go on a diet
+ 
+
+ align:start position:0%
+mainstream solution let's go on a diet
+and maybe it becomes a fairly severe
+
+ align:start position:0%
+and maybe it becomes a fairly severe
+ 
+
+ align:start position:0%
+and maybe it becomes a fairly severe
+diet but
+
+ align:start position:0%
+diet but
+ 
+
+ align:start position:0%
+diet but
+um unlike anorexics who deny their
+
+ align:start position:0%
+um unlike anorexics who deny their
+ 
+
+ align:start position:0%
+um unlike anorexics who deny their
+hunger and really don't seem to feel
+
+ align:start position:0%
+hunger and really don't seem to feel
+ 
+
+ align:start position:0%
+hunger and really don't seem to feel
+that hunger bulimics feel hungry they
+
+ align:start position:0%
+that hunger bulimics feel hungry they
+ 
+
+ align:start position:0%
+that hunger bulimics feel hungry they
+feel really hungry and so the diet
+
+ align:start position:0%
+feel really hungry and so the diet
+ 
+
+ align:start position:0%
+feel really hungry and so the diet
+doesn't work and and what you end up
+
+ align:start position:0%
+doesn't work and and what you end up
+ 
+
+ align:start position:0%
+doesn't work and and what you end up
+with is that the diet breaks down at
+
+ align:start position:0%
+with is that the diet breaks down at
+ 
+
+ align:start position:0%
+with is that the diet breaks down at
+some point you go off the diet perhaps
+
+ align:start position:0%
+some point you go off the diet perhaps
+ 
+
+ align:start position:0%
+some point you go off the diet perhaps
+in some spectacular bingy kind of a way
+
+ align:start position:0%
+in some spectacular bingy kind of a way
+ 
+
+ align:start position:0%
+in some spectacular bingy kind of a way
+well that feels lousy too
+
+ align:start position:0%
+well that feels lousy too
+ 
+
+ align:start position:0%
+well that feels lousy too
+and so you
+
+ align:start position:0%
+and so you
+ 
+
+ align:start position:0%
+and so you
+um and so well you figured out this
+
+ align:start position:0%
+um and so well you figured out this
+ 
+
+ align:start position:0%
+um and so well you figured out this
+trick once uh you go and Purge again
+
+ align:start position:0%
+trick once uh you go and Purge again
+ 
+
+ align:start position:0%
+trick once uh you go and Purge again
+um in some fashion
+
+ align:start position:0%
+um in some fashion
+ 
+
+ align:start position:0%
+um in some fashion
+um and and that gives you some transient
+
+ align:start position:0%
+um and and that gives you some transient
+ 
+
+ align:start position:0%
+um and and that gives you some transient
+relief from the shame of having broken
+
+ align:start position:0%
+relief from the shame of having broken
+ 
+
+ align:start position:0%
+relief from the shame of having broken
+the diet but again the the purging thing
+
+ align:start position:0%
+the diet but again the the purging thing
+ 
+
+ align:start position:0%
+the diet but again the the purging thing
+isn't isn't isn't great either
+
+ align:start position:0%
+isn't isn't isn't great either
+ 
+
+ align:start position:0%
+isn't isn't isn't great either
+um but this can become and in in full
+
+ align:start position:0%
+um but this can become and in in full
+ 
+
+ align:start position:0%
+um but this can become and in in full
+blast bulimia becomes a very ritualized
+
+ align:start position:0%
+blast bulimia becomes a very ritualized
+ 
+
+ align:start position:0%
+blast bulimia becomes a very ritualized
+behavior in its in its own right
+
+ align:start position:0%
+behavior in its in its own right
+ 
+
+ align:start position:0%
+behavior in its in its own right
+actually somebody was telling me that
+
+ align:start position:0%
+actually somebody was telling me that
+ 
+
+ align:start position:0%
+actually somebody was telling me that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+some some bulimics
+
+ align:start position:0%
+some some bulimics
+ 
+
+ align:start position:0%
+some some bulimics
+um plan things very carefully so that
+
+ align:start position:0%
+um plan things very carefully so that
+ 
+
+ align:start position:0%
+um plan things very carefully so that
+they eat the nutritive foods first
+
+ align:start position:0%
+they eat the nutritive foods first
+ 
+
+ align:start position:0%
+they eat the nutritive foods first
+um and and in a in a sort of a binging
+
+ align:start position:0%
+um and and in a in a sort of a binging
+ 
+
+ align:start position:0%
+um and and in a in a sort of a binging
+session and then finish up with the half
+
+ align:start position:0%
+session and then finish up with the half
+ 
+
+ align:start position:0%
+session and then finish up with the half
+gallon of ice cream and and the jar of
+
+ align:start position:0%
+gallon of ice cream and and the jar of
+ 
+
+ align:start position:0%
+gallon of ice cream and and the jar of
+mayonnaise I mean the things you read
+
+ align:start position:0%
+mayonnaise I mean the things you read
+ 
+
+ align:start position:0%
+mayonnaise I mean the things you read
+people seriously the things you read the
+
+ align:start position:0%
+people seriously the things you read the
+ 
+
+ align:start position:0%
+people seriously the things you read the
+people eating on on bulimic binges are
+
+ align:start position:0%
+people eating on on bulimic binges are
+ 
+
+ align:start position:0%
+people eating on on bulimic binges are
+really quite amazing I mean if you've
+
+ align:start position:0%
+really quite amazing I mean if you've
+ 
+
+ align:start position:0%
+really quite amazing I mean if you've
+got imagining sitting down and eating a
+
+ align:start position:0%
+got imagining sitting down and eating a
+ 
+
+ align:start position:0%
+got imagining sitting down and eating a
+thing of mayonnaise is just very odd but
+
+ align:start position:0%
+thing of mayonnaise is just very odd but
+ 
+
+ align:start position:0%
+thing of mayonnaise is just very odd but
+this is the sort of thing that gets that
+
+ align:start position:0%
+this is the sort of thing that gets that
+ 
+
+ align:start position:0%
+this is the sort of thing that gets that
+apparently is that anyway but you you
+
+ align:start position:0%
+apparently is that anyway but you you
+ 
+
+ align:start position:0%
+apparently is that anyway but you you
+stagger it in such a way so that you get
+
+ align:start position:0%
+stagger it in such a way so that you get
+ 
+
+ align:start position:0%
+stagger it in such a way so that you get
+at least enough of the nutrients that
+
+ align:start position:0%
+at least enough of the nutrients that
+ 
+
+ align:start position:0%
+at least enough of the nutrients that
+you need before you go and Purge that
+
+ align:start position:0%
+you need before you go and Purge that
+ 
+
+ align:start position:0%
+you need before you go and Purge that
+you're not starving yourself and bulimia
+
+ align:start position:0%
+you're not starving yourself and bulimia
+ 
+
+ align:start position:0%
+you're not starving yourself and bulimia
+unlike anorexia can be a very long-term
+
+ align:start position:0%
+unlike anorexia can be a very long-term
+ 
+
+ align:start position:0%
+unlike anorexia can be a very long-term
+disorder people can maintain body weight
+
+ align:start position:0%
+disorder people can maintain body weight
+ 
+
+ align:start position:0%
+disorder people can maintain body weight
+for a uh
+
+ align:start position:0%
+for a uh
+ 
+
+ align:start position:0%
+for a uh
+a long time doing this
+
+ align:start position:0%
+a long time doing this
+ 
+
+ align:start position:0%
+a long time doing this
+um it's clearly not uh adaptive I mean
+
+ align:start position:0%
+um it's clearly not uh adaptive I mean
+ 
+
+ align:start position:0%
+um it's clearly not uh adaptive I mean
+it's it's a success in again uh in in a
+
+ align:start position:0%
+it's it's a success in again uh in in a
+ 
+
+ align:start position:0%
+it's it's a success in again uh in in a
+limited sense lets you eat and lets you
+
+ align:start position:0%
+limited sense lets you eat and lets you
+ 
+
+ align:start position:0%
+limited sense lets you eat and lets you
+maintain this this this skinny weight
+
+ align:start position:0%
+maintain this this this skinny weight
+ 
+
+ align:start position:0%
+maintain this this this skinny weight
+but in many other ways it's a disaster
+
+ align:start position:0%
+but in many other ways it's a disaster
+ 
+
+ align:start position:0%
+but in many other ways it's a disaster
+first of all repeated purging is very
+
+ align:start position:0%
+first of all repeated purging is very
+ 
+
+ align:start position:0%
+first of all repeated purging is very
+bad uh for that you know do a variety of
+
+ align:start position:0%
+bad uh for that you know do a variety of
+ 
+
+ align:start position:0%
+bad uh for that you know do a variety of
+bits of permanent damage to you
+
+ align:start position:0%
+bits of permanent damage to you
+ 
+
+ align:start position:0%
+bits of permanent damage to you
+um physiologically
+
+ align:start position:0%
+um physiologically
+ 
+
+ align:start position:0%
+um physiologically
+um it carries with it its own risk of of
+
+ align:start position:0%
+um it carries with it its own risk of of
+ 
+
+ align:start position:0%
+um it carries with it its own risk of of
+mortality again typically from heart
+
+ align:start position:0%
+mortality again typically from heart
+ 
+
+ align:start position:0%
+mortality again typically from heart
+attack from getting electrolytes
+
+ align:start position:0%
+attack from getting electrolytes
+ 
+
+ align:start position:0%
+attack from getting electrolytes
+sufficiently imbalanced to stop the
+
+ align:start position:0%
+sufficiently imbalanced to stop the
+ 
+
+ align:start position:0%
+sufficiently imbalanced to stop the
+heart
+
+ align:start position:0%
+heart
+ 
+
+ align:start position:0%
+heart
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+um and it does really bad things to that
+
+ align:start position:0%
+um and it does really bad things to that
+ 
+
+ align:start position:0%
+um and it does really bad things to that
+uh hunger Drive circuitry in in places
+
+ align:start position:0%
+uh hunger Drive circuitry in in places
+ 
+
+ align:start position:0%
+uh hunger Drive circuitry in in places
+like your hypothalamus because what
+
+ align:start position:0%
+like your hypothalamus because what
+ 
+
+ align:start position:0%
+like your hypothalamus because what
+happens is the the body is smart
+
+ align:start position:0%
+happens is the the body is smart
+ 
+
+ align:start position:0%
+happens is the the body is smart
+it says
+
+ align:start position:0%
+it says
+ 
+
+ align:start position:0%
+it says
+we ate
+
+ align:start position:0%
+we ate
+ 
+
+ align:start position:0%
+we ate
+a half gallon of ice cream
+
+ align:start position:0%
+a half gallon of ice cream
+ 
+
+ align:start position:0%
+a half gallon of ice cream
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a thing of mayonnaise and we got
+
+ align:start position:0%
+a thing of mayonnaise and we got
+ 
+
+ align:start position:0%
+a thing of mayonnaise and we got
+this much caloric bounce out of that
+
+ align:start position:0%
+this much caloric bounce out of that
+ 
+
+ align:start position:0%
+this much caloric bounce out of that
+you know that's that's that's that's
+
+ align:start position:0%
+you know that's that's that's that's
+ 
+
+ align:start position:0%
+you know that's that's that's that's
+that's odd I don't know what the problem
+
+ align:start position:0%
+that's odd I don't know what the problem
+ 
+
+ align:start position:0%
+that's odd I don't know what the problem
+here is but I know how to adapt to that
+
+ align:start position:0%
+here is but I know how to adapt to that
+ 
+
+ align:start position:0%
+here is but I know how to adapt to that
+right if it is the case that huge
+
+ align:start position:0%
+right if it is the case that huge
+ 
+
+ align:start position:0%
+right if it is the case that huge
+amounts of food are not providing me
+
+ align:start position:0%
+amounts of food are not providing me
+ 
+
+ align:start position:0%
+amounts of food are not providing me
+with with the calories I I need me up in
+
+ align:start position:0%
+with with the calories I I need me up in
+ 
+
+ align:start position:0%
+with with the calories I I need me up in
+the hypothalamus here well the answer is
+
+ align:start position:0%
+the hypothalamus here well the answer is
+ 
+
+ align:start position:0%
+the hypothalamus here well the answer is
+something's wrong in the gut but the
+
+ align:start position:0%
+something's wrong in the gut but the
+ 
+
+ align:start position:0%
+something's wrong in the gut but the
+answer is I better eat more I gotta get
+
+ align:start position:0%
+answer is I better eat more I gotta get
+ 
+
+ align:start position:0%
+answer is I better eat more I gotta get
+make this sucker hungrier ramp up the
+
+ align:start position:0%
+make this sucker hungrier ramp up the
+ 
+
+ align:start position:0%
+make this sucker hungrier ramp up the
+hunger bulimia the word comes from to
+
+ align:start position:0%
+hunger bulimia the word comes from to
+ 
+
+ align:start position:0%
+hunger bulimia the word comes from to
+have an appetite like an ox like a bowl
+
+ align:start position:0%
+have an appetite like an ox like a bowl
+ 
+
+ align:start position:0%
+have an appetite like an ox like a bowl
+um because what happens is that the body
+
+ align:start position:0%
+um because what happens is that the body
+ 
+
+ align:start position:0%
+um because what happens is that the body
+learns that food isn't doing it for you
+
+ align:start position:0%
+learns that food isn't doing it for you
+ 
+
+ align:start position:0%
+learns that food isn't doing it for you
+anymore and you just keep eating it you
+
+ align:start position:0%
+anymore and you just keep eating it you
+ 
+
+ align:start position:0%
+anymore and you just keep eating it you
+just so it's a vicious cycle you gotta
+
+ align:start position:0%
+just so it's a vicious cycle you gotta
+ 
+
+ align:start position:0%
+just so it's a vicious cycle you gotta
+eat more and more while this other says
+
+ align:start position:0%
+eat more and more while this other says
+ 
+
+ align:start position:0%
+eat more and more while this other says
+it's two chunks of your brain fighting
+
+ align:start position:0%
+it's two chunks of your brain fighting
+ 
+
+ align:start position:0%
+it's two chunks of your brain fighting
+right the the this hardwired chunk of
+
+ align:start position:0%
+right the the this hardwired chunk of
+ 
+
+ align:start position:0%
+right the the this hardwired chunk of
+hunger Drive is saying need this many
+
+ align:start position:0%
+hunger Drive is saying need this many
+ 
+
+ align:start position:0%
+hunger Drive is saying need this many
+calories if it takes you know this many
+
+ align:start position:0%
+calories if it takes you know this many
+ 
+
+ align:start position:0%
+calories if it takes you know this many
+truckloads of food to get it well go out
+
+ align:start position:0%
+truckloads of food to get it well go out
+ 
+
+ align:start position:0%
+truckloads of food to get it well go out
+and eat that truckload and you got this
+
+ align:start position:0%
+and eat that truckload and you got this
+ 
+
+ align:start position:0%
+and eat that truckload and you got this
+other chunk of the brain saying we're
+
+ align:start position:0%
+other chunk of the brain saying we're
+ 
+
+ align:start position:0%
+other chunk of the brain saying we're
+getting In Those Jeans man so go and
+
+ align:start position:0%
+getting In Those Jeans man so go and
+ 
+
+ align:start position:0%
+getting In Those Jeans man so go and
+throw up again and these two are
+
+ align:start position:0%
+throw up again and these two are
+ 
+
+ align:start position:0%
+throw up again and these two are
+fighting with each other in a way that's
+
+ align:start position:0%
+fighting with each other in a way that's
+ 
+
+ align:start position:0%
+fighting with each other in a way that's
+clearly at this point
+
+ align:start position:0%
+clearly at this point
+ 
+
+ align:start position:0%
+clearly at this point
+um maladaptive now we have this the the
+
+ align:start position:0%
+um maladaptive now we have this the the
+ 
+
+ align:start position:0%
+um maladaptive now we have this the the
+the the regular
+
+ align:start position:0%
+the the regular
+ 
+
+ align:start position:0%
+the the regular
+population away from the eating disorder
+
+ align:start position:0%
+population away from the eating disorder
+ 
+
+ align:start position:0%
+population away from the eating disorder
+population runs into the same problem by
+
+ align:start position:0%
+population runs into the same problem by
+ 
+
+ align:start position:0%
+population runs into the same problem by
+the way with diet foods
+
+ align:start position:0%
+the way with diet foods
+ 
+
+ align:start position:0%
+the way with diet foods
+right diet foods
+
+ align:start position:0%
+right diet foods
+ 
+
+ align:start position:0%
+right diet foods
+don't give you the caloric punch of
+
+ align:start position:0%
+don't give you the caloric punch of
+ 
+
+ align:start position:0%
+don't give you the caloric punch of
+regular Foods that's the whole idea
+
+ align:start position:0%
+regular Foods that's the whole idea
+ 
+
+ align:start position:0%
+regular Foods that's the whole idea
+right so these little chunks of the
+
+ align:start position:0%
+right so these little chunks of the
+ 
+
+ align:start position:0%
+right so these little chunks of the
+brain say
+
+ align:start position:0%
+brain say
+ 
+
+ align:start position:0%
+brain say
+hey
+
+ align:start position:0%
+hey
+ 
+
+ align:start position:0%
+hey
+eat twice as many
+
+ align:start position:0%
+eat twice as many
+ 
+
+ align:start position:0%
+eat twice as many
+all right see the label it says half as
+
+ align:start position:0%
+all right see the label it says half as
+ 
+
+ align:start position:0%
+all right see the label it says half as
+much fat
+
+ align:start position:0%
+much fat
+ 
+
+ align:start position:0%
+much fat
+brain says eat twice as many
+
+ align:start position:0%
+brain says eat twice as many
+ 
+
+ align:start position:0%
+brain says eat twice as many
+this is not this and and the other thing
+
+ align:start position:0%
+this is not this and and the other thing
+ 
+
+ align:start position:0%
+this is not this and and the other thing
+it says is you know what do you like
+
+ align:start position:0%
+it says is you know what do you like
+ 
+
+ align:start position:0%
+it says is you know what do you like
+well you're built to like brain says we
+
+ align:start position:0%
+well you're built to like brain says we
+ 
+
+ align:start position:0%
+well you're built to like brain says we
+like double stuffed Cheerios Cheerios
+
+ align:start position:0%
+like double stuffed Cheerios Cheerios
+ 
+
+ align:start position:0%
+like double stuffed Cheerios Cheerios
+Oreos there's probably Double Stuffed
+
+ align:start position:0%
+Oreos there's probably Double Stuffed
+ 
+
+ align:start position:0%
+Oreos there's probably Double Stuffed
+Cheerios now too anyway we love double
+
+ align:start position:0%
+Cheerios now too anyway we love double
+ 
+
+ align:start position:0%
+Cheerios now too anyway we love double
+stuffed Oreos because they've got lots
+
+ align:start position:0%
+stuffed Oreos because they've got lots
+ 
+
+ align:start position:0%
+stuffed Oreos because they've got lots
+of calories and and we're this little
+
+ align:start position:0%
+of calories and and we're this little
+ 
+
+ align:start position:0%
+of calories and and we're this little
+piece of my brain is still sound you
+
+ align:start position:0%
+piece of my brain is still sound you
+ 
+
+ align:start position:0%
+piece of my brain is still sound you
+know foraging around on the Savannah and
+
+ align:start position:0%
+know foraging around on the Savannah and
+ 
+
+ align:start position:0%
+know foraging around on the Savannah and
+and and when I found Double Stuffed uh
+
+ align:start position:0%
+and and when I found Double Stuffed uh
+ 
+
+ align:start position:0%
+and and when I found Double Stuffed uh
+Oreos on the Savannah man I could live
+
+ align:start position:0%
+Oreos on the Savannah man I could live
+ 
+
+ align:start position:0%
+Oreos on the Savannah man I could live
+for a week off of one of those suckers
+
+ align:start position:0%
+for a week off of one of those suckers
+ 
+
+ align:start position:0%
+for a week off of one of those suckers
+um yeah it's great stuff now you're
+
+ align:start position:0%
+um yeah it's great stuff now you're
+ 
+
+ align:start position:0%
+um yeah it's great stuff now you're
+eating the the low fat reduced
+
+ align:start position:0%
+eating the the low fat reduced
+ 
+
+ align:start position:0%
+eating the the low fat reduced
+everything version of this and the brain
+
+ align:start position:0%
+everything version of this and the brain
+ 
+
+ align:start position:0%
+everything version of this and the brain
+is saying
+
+ align:start position:0%
+is saying
+ 
+
+ align:start position:0%
+is saying
+there's lousy stuff man you're eating
+
+ align:start position:0%
+there's lousy stuff man you're eating
+ 
+
+ align:start position:0%
+there's lousy stuff man you're eating
+barks and twigs barking Twigs here
+
+ align:start position:0%
+barks and twigs barking Twigs here
+ 
+
+ align:start position:0%
+barks and twigs barking Twigs here
+so it doesn't taste good to me no more
+
+ align:start position:0%
+so it doesn't taste good to me no more
+ 
+
+ align:start position:0%
+so it doesn't taste good to me no more
+even though it tasted perfectly this is
+
+ align:start position:0%
+even though it tasted perfectly this is
+ 
+
+ align:start position:0%
+even though it tasted perfectly this is
+one of the reasons why diet foods cycle
+
+ align:start position:0%
+one of the reasons why diet foods cycle
+ 
+
+ align:start position:0%
+one of the reasons why diet foods cycle
+through the supermarket much more
+
+ align:start position:0%
+through the supermarket much more
+ 
+
+ align:start position:0%
+through the supermarket much more
+rapidly than high fat foods
+
+ align:start position:0%
+rapidly than high fat foods
+ 
+
+ align:start position:0%
+rapidly than high fat foods
+which is that any diet food tends to
+
+ align:start position:0%
+which is that any diet food tends to
+ 
+
+ align:start position:0%
+which is that any diet food tends to
+have a fall off in its appeal to the
+
+ align:start position:0%
+have a fall off in its appeal to the
+ 
+
+ align:start position:0%
+have a fall off in its appeal to the
+population fairly rapidly
+
+ align:start position:0%
+population fairly rapidly
+ 
+
+ align:start position:0%
+population fairly rapidly
+um now the the the the Oreos stay there
+
+ align:start position:0%
+um now the the the the Oreos stay there
+ 
+
+ align:start position:0%
+um now the the the the Oreos stay there
+forever because people love them
+
+ align:start position:0%
+forever because people love them
+ 
+
+ align:start position:0%
+forever because people love them
+they reduced fat all twig Oreos
+
+ align:start position:0%
+they reduced fat all twig Oreos
+ 
+
+ align:start position:0%
+they reduced fat all twig Oreos
+have to be replaced next week by the you
+
+ align:start position:0%
+have to be replaced next week by the you
+ 
+
+ align:start position:0%
+have to be replaced next week by the you
+know low carb reduced fat High cardboard
+
+ align:start position:0%
+know low carb reduced fat High cardboard
+ 
+
+ align:start position:0%
+know low carb reduced fat High cardboard
+Oreos or something in a brand new
+
+ align:start position:0%
+Oreos or something in a brand new
+ 
+
+ align:start position:0%
+Oreos or something in a brand new
+package so that you'll go out and try it
+
+ align:start position:0%
+package so that you'll go out and try it
+ 
+
+ align:start position:0%
+package so that you'll go out and try it
+because well you know those low-fat ones
+
+ align:start position:0%
+because well you know those low-fat ones
+ 
+
+ align:start position:0%
+because well you know those low-fat ones
+they were okay for a while but but my
+
+ align:start position:0%
+they were okay for a while but but my
+ 
+
+ align:start position:0%
+they were okay for a while but but my
+hypothalamus is now telling me they
+
+ align:start position:0%
+hypothalamus is now telling me they
+ 
+
+ align:start position:0%
+hypothalamus is now telling me they
+weren't that good so you have to keep
+
+ align:start position:0%
+weren't that good so you have to keep
+ 
+
+ align:start position:0%
+weren't that good so you have to keep
+churning the product line in order to to
+
+ align:start position:0%
+churning the product line in order to to
+ 
+
+ align:start position:0%
+churning the product line in order to to
+keep you happy
+
+ align:start position:0%
+keep you happy
+ 
+
+ align:start position:0%
+keep you happy
+um treatment turns out to be much the
+
+ align:start position:0%
+um treatment turns out to be much the
+ 
+
+ align:start position:0%
+um treatment turns out to be much the
+same story
+
+ align:start position:0%
+same story
+ 
+
+ align:start position:0%
+same story
+um as as with with uh
+
+ align:start position:0%
+um as as with with uh
+ 
+
+ align:start position:0%
+um as as with with uh
+um anorexia Nothing by itself Works uh
+
+ align:start position:0%
+um anorexia Nothing by itself Works uh
+ 
+
+ align:start position:0%
+um anorexia Nothing by itself Works uh
+one there are a couple of big
+
+ align:start position:0%
+one there are a couple of big
+ 
+
+ align:start position:0%
+one there are a couple of big
+differences one is as I said before you
+
+ align:start position:0%
+differences one is as I said before you
+ 
+
+ align:start position:0%
+differences one is as I said before you
+can go for a very long time without
+
+ align:start position:0%
+can go for a very long time without
+ 
+
+ align:start position:0%
+can go for a very long time without
+seeking treatment because
+
+ align:start position:0%
+seeking treatment because
+ 
+
+ align:start position:0%
+seeking treatment because
+um it's not as acute a disorder as full
+
+ align:start position:0%
+um it's not as acute a disorder as full
+ 
+
+ align:start position:0%
+um it's not as acute a disorder as full
+blast anorexia uh is it's not good for
+
+ align:start position:0%
+blast anorexia uh is it's not good for
+ 
+
+ align:start position:0%
+blast anorexia uh is it's not good for
+you but you can maintain this plus it's
+
+ align:start position:0%
+you but you can maintain this plus it's
+ 
+
+ align:start position:0%
+you but you can maintain this plus it's
+a very private disorder and so you can
+
+ align:start position:0%
+a very private disorder and so you can
+ 
+
+ align:start position:0%
+a very private disorder and so you can
+tend to maintain it all by your little
+
+ align:start position:0%
+tend to maintain it all by your little
+ 
+
+ align:start position:0%
+tend to maintain it all by your little
+lonesome for a fairly long period of
+
+ align:start position:0%
+lonesome for a fairly long period of
+ 
+
+ align:start position:0%
+lonesome for a fairly long period of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um the other thing is that it no longer
+
+ align:start position:0%
+um the other thing is that it no longer
+ 
+
+ align:start position:0%
+um the other thing is that it no longer
+turns out to be desperately interesting
+
+ align:start position:0%
+turns out to be desperately interesting
+ 
+
+ align:start position:0%
+turns out to be desperately interesting
+to talk to the family about this you're
+
+ align:start position:0%
+to talk to the family about this you're
+ 
+
+ align:start position:0%
+to talk to the family about this you're
+outside the family but in place of that
+
+ align:start position:0%
+outside the family but in place of that
+ 
+
+ align:start position:0%
+outside the family but in place of that
+what turns out to be an interesting
+
+ align:start position:0%
+what turns out to be an interesting
+ 
+
+ align:start position:0%
+what turns out to be an interesting
+component of treatment is group therapy
+
+ align:start position:0%
+component of treatment is group therapy
+ 
+
+ align:start position:0%
+component of treatment is group therapy
+this has been a very isolating disorder
+
+ align:start position:0%
+this has been a very isolating disorder
+ 
+
+ align:start position:0%
+this has been a very isolating disorder
+and when you finally come to treatment
+
+ align:start position:0%
+and when you finally come to treatment
+ 
+
+ align:start position:0%
+and when you finally come to treatment
+you say to yourself in some fashion I am
+
+ align:start position:0%
+you say to yourself in some fashion I am
+ 
+
+ align:start position:0%
+you say to yourself in some fashion I am
+so weird there's nobody else like me in
+
+ align:start position:0%
+so weird there's nobody else like me in
+ 
+
+ align:start position:0%
+so weird there's nobody else like me in
+the world and that doesn't help you
+
+ align:start position:0%
+the world and that doesn't help you
+ 
+
+ align:start position:0%
+the world and that doesn't help you
+right that that that's just depressing
+
+ align:start position:0%
+right that that that's just depressing
+ 
+
+ align:start position:0%
+right that that that's just depressing
+and and and off-putting in its own right
+
+ align:start position:0%
+and and and off-putting in its own right
+ 
+
+ align:start position:0%
+and and and off-putting in its own right
+if you're with a group of other people
+
+ align:start position:0%
+if you're with a group of other people
+ 
+
+ align:start position:0%
+if you're with a group of other people
+with a similar disorder you're saying
+
+ align:start position:0%
+with a similar disorder you're saying
+ 
+
+ align:start position:0%
+with a similar disorder you're saying
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+it turns out there are other people like
+
+ align:start position:0%
+it turns out there are other people like
+ 
+
+ align:start position:0%
+it turns out there are other people like
+this we'll work through this thing
+
+ align:start position:0%
+this we'll work through this thing
+ 
+
+ align:start position:0%
+this we'll work through this thing
+together and that turns out to have some
+
+ align:start position:0%
+together and that turns out to have some
+ 
+
+ align:start position:0%
+together and that turns out to have some
+therapeutic value again like anorexia
+
+ align:start position:0%
+therapeutic value again like anorexia
+ 
+
+ align:start position:0%
+therapeutic value again like anorexia
+people tend to get over this and then
+
+ align:start position:0%
+people tend to get over this and then
+ 
+
+ align:start position:0%
+people tend to get over this and then
+tend to have to to need to sort of be
+
+ align:start position:0%
+tend to have to to need to sort of be
+ 
+
+ align:start position:0%
+tend to have to to need to sort of be
+vigilant about food issues and Vigilant
+
+ align:start position:0%
+vigilant about food issues and Vigilant
+ 
+
+ align:start position:0%
+vigilant about food issues and Vigilant
+about other such issues
+
+ align:start position:0%
+about other such issues
+ 
+
+ align:start position:0%
+about other such issues
+um ongoing past that as if there were
+
+ align:start position:0%
+um ongoing past that as if there were
+ 
+
+ align:start position:0%
+um ongoing past that as if there were
+some underlying issue that that hasn't
+
+ align:start position:0%
+some underlying issue that that hasn't
+ 
+
+ align:start position:0%
+some underlying issue that that hasn't
+uh hasn't quite been
+
+ align:start position:0%
+uh hasn't quite been
+ 
+
+ align:start position:0%
+uh hasn't quite been
+addressed so
+
+ align:start position:0%
+addressed so
+ 
+
+ align:start position:0%
+addressed so
+well I think I think what I will do
+
+ align:start position:0%
+well I think I think what I will do
+ 
+
+ align:start position:0%
+well I think I think what I will do
+unless there's some Oh no I got to all
+
+ align:start position:0%
+unless there's some Oh no I got to all
+ 
+
+ align:start position:0%
+unless there's some Oh no I got to all
+the various words on the handout look at
+
+ align:start position:0%
+the various words on the handout look at
+ 
+
+ align:start position:0%
+the various words on the handout look at
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um let's let's take a break and then
+
+ align:start position:0%
+um let's let's take a break and then
+ 
+
+ align:start position:0%
+um let's let's take a break and then
+what I'll do is at least set up the uh
+
+ align:start position:0%
+what I'll do is at least set up the uh
+ 
+
+ align:start position:0%
+what I'll do is at least set up the uh
+the problem of of uh coercive sexual
+
+ align:start position:0%
+the problem of of uh coercive sexual
+ 
+
+ align:start position:0%
+the problem of of uh coercive sexual
+behavior and and and we'll go on from
+
+ align:start position:0%
+behavior and and and we'll go on from
+ 
+
+ align:start position:0%
+behavior and and and we'll go on from
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh did I okay I could say a word about
+
+ align:start position:0%
+oh did I okay I could say a word about
+ 
+
+ align:start position:0%
+oh did I okay I could say a word about
+that yes because otherwise somebody will
+
+ align:start position:0%
+that yes because otherwise somebody will
+ 
+
+ align:start position:0%
+that yes because otherwise somebody will
+get it on when they're reviewing and
+
+ align:start position:0%
+get it on when they're reviewing and
+ 
+
+ align:start position:0%
+get it on when they're reviewing and
+want not want to know something about it
+
+ align:start position:0%
+want not want to know something about it
+ 
+
+ align:start position:0%
+want not want to know something about it
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two roughly two-thirds second half one
+
+ align:start position:0%
+two roughly two-thirds second half one
+ 
+
+ align:start position:0%
+two roughly two-thirds second half one
+third first half but that's rough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evolutionary type reasons
+
+ align:start position:0%
+evolutionary type reasons
+ 
+
+ align:start position:0%
+evolutionary type reasons
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mainline argument I think is is
+
+ align:start position:0%
+the mainline argument I think is is
+ 
+
+ align:start position:0%
+the mainline argument I think is is
+um that the pressures are exerted on
+
+ align:start position:0%
+um that the pressures are exerted on
+ 
+
+ align:start position:0%
+um that the pressures are exerted on
+girls much more than boys that if if the
+
+ align:start position:0%
+girls much more than boys that if if the
+ 
+
+ align:start position:0%
+girls much more than boys that if if the
+ideal guy had there are sort of just
+
+ align:start position:0%
+ideal guy had there are sort of just
+ 
+
+ align:start position:0%
+ideal guy had there are sort of just
+there there are uh sort of muscle
+
+ align:start position:0%
+there there are uh sort of muscle
+ 
+
+ align:start position:0%
+there there are uh sort of muscle
+building-ish disorders and guys that
+
+ align:start position:0%
+building-ish disorders and guys that
+ 
+
+ align:start position:0%
+building-ish disorders and guys that
+that might be comfortable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is it formally diagnosed I don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I I I I would I would be amazed if it
+
+ align:start position:0%
+I I I I I would I would be amazed if it
+ 
+
+ align:start position:0%
+I I I I I would I would be amazed if it
+wasn't because everything is formally
+
+ align:start position:0%
+wasn't because everything is formally
+ 
+
+ align:start position:0%
+wasn't because everything is formally
+diagnosed somewhere
+
+ align:start position:0%
+diagnosed somewhere
+ 
+
+ align:start position:0%
+diagnosed somewhere
+um but you know what really shows up
+
+ align:start position:0%
+um but you know what really shows up
+ 
+
+ align:start position:0%
+um but you know what really shows up
+there I think is is uh substance abuse
+
+ align:start position:0%
+there I think is is uh substance abuse
+ 
+
+ align:start position:0%
+there I think is is uh substance abuse
+right that that it's it's it's in this
+
+ align:start position:0%
+right that that it's it's it's in this
+ 
+
+ align:start position:0%
+right that that it's it's it's in this
+culture it's much less that you get
+
+ align:start position:0%
+culture it's much less that you get
+ 
+
+ align:start position:0%
+culture it's much less that you get
+somebody who's pathologically working
+
+ align:start position:0%
+somebody who's pathologically working
+ 
+
+ align:start position:0%
+somebody who's pathologically working
+out in the gym though I'm sure that
+
+ align:start position:0%
+out in the gym though I'm sure that
+ 
+
+ align:start position:0%
+out in the gym though I'm sure that
+happens they go and popping up steroids
+
+ align:start position:0%
+happens they go and popping up steroids
+ 
+
+ align:start position:0%
+happens they go and popping up steroids
+to get themselves into trouble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+well okay there's a whole I don't
+
+ align:start position:0%
+well okay there's a whole I don't
+ 
+
+ align:start position:0%
+well okay there's a whole I don't
+actually know much about the whole set
+
+ align:start position:0%
+actually know much about the whole set
+ 
+
+ align:start position:0%
+actually know much about the whole set
+of self-harming disorders actually I
+
+ align:start position:0%
+of self-harming disorders actually I
+ 
+
+ align:start position:0%
+of self-harming disorders actually I
+should probably sometimes teach myself
+
+ align:start position:0%
+should probably sometimes teach myself
+ 
+
+ align:start position:0%
+should probably sometimes teach myself
+something about it because there's
+
+ align:start position:0%
+something about it because there's
+ 
+
+ align:start position:0%
+something about it because there's
+another pathology that is
+
+ align:start position:0%
+another pathology that is
+ 
+
+ align:start position:0%
+another pathology that is
+um uh new I think uh that or if it's not
+
+ align:start position:0%
+um uh new I think uh that or if it's not
+ 
+
+ align:start position:0%
+um uh new I think uh that or if it's not
+new it was it was it was deeply hidden
+
+ align:start position:0%
+new it was it was it was deeply hidden
+ 
+
+ align:start position:0%
+new it was it was it was deeply hidden
+before the the notion of people cutting
+
+ align:start position:0%
+before the the notion of people cutting
+ 
+
+ align:start position:0%
+before the the notion of people cutting
+themselves and things like that
+
+ align:start position:0%
+themselves and things like that
+ 
+
+ align:start position:0%
+themselves and things like that
+um so it may be that there's there's a I
+
+ align:start position:0%
+um so it may be that there's there's a I
+ 
+
+ align:start position:0%
+um so it may be that there's there's a I
+don't know anything about it but there
+
+ align:start position:0%
+don't know anything about it but there
+ 
+
+ align:start position:0%
+don't know anything about it but there
+may well be a a make yourself throw up
+
+ align:start position:0%
+may well be a a make yourself throw up
+ 
+
+ align:start position:0%
+may well be a a make yourself throw up
+in the self-harming kind of category but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I read an article about it at one point
+
+ align:start position:0%
+I read an article about it at one point
+ 
+
+ align:start position:0%
+I read an article about it at one point
+where people are busy encouraging each
+
+ align:start position:0%
+where people are busy encouraging each
+ 
+
+ align:start position:0%
+where people are busy encouraging each
+other in their Eating Disorders not
+
+ align:start position:0%
+other in their Eating Disorders not
+ 
+
+ align:start position:0%
+other in their Eating Disorders not
+wholesome I wouldn't say but
+
+ align:start position:0%
+wholesome I wouldn't say but
+ 
+
+ align:start position:0%
+wholesome I wouldn't say but
+I don't know
+
+ align:start position:0%
+I don't know
+ 
+
+ align:start position:0%
+I don't know
+I don't know I don't know and I don't
+
+ align:start position:0%
+I don't know I don't know and I don't
+ 
+
+ align:start position:0%
+I don't know I don't know and I don't
+know if it's widespread enough to be I
+
+ align:start position:0%
+know if it's widespread enough to be I
+ 
+
+ align:start position:0%
+know if it's widespread enough to be I
+mean I I I've just seen a couple of uh
+
+ align:start position:0%
+mean I I I've just seen a couple of uh
+ 
+
+ align:start position:0%
+mean I I I've just seen a couple of uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+I think sort of popular press things
+
+ align:start position:0%
+I think sort of popular press things
+ 
+
+ align:start position:0%
+I think sort of popular press things
+about it I I just don't know how
+
+ align:start position:0%
+about it I I just don't know how
+ 
+
+ align:start position:0%
+about it I I just don't know how
+widespread that is I know who to ask at
+
+ align:start position:0%
+widespread that is I know who to ask at
+ 
+
+ align:start position:0%
+widespread that is I know who to ask at
+MIT but there are a couple of people who
+
+ align:start position:0%
+MIT but there are a couple of people who
+ 
+
+ align:start position:0%
+MIT but there are a couple of people who
+are good experts on that at MIT but
+
+ align:start position:0%
+are good experts on that at MIT but
+ 
+
+ align:start position:0%
+are good experts on that at MIT but
+anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+The Dangers the dangers of relatively
+
+ align:start position:0%
+The Dangers the dangers of relatively
+ 
+
+ align:start position:0%
+The Dangers the dangers of relatively
+complete uh
+
+ align:start position:0%
+complete uh
+ 
+
+ align:start position:0%
+complete uh
+handouts or comparatively complete
+
+ align:start position:0%
+handouts or comparatively complete
+ 
+
+ align:start position:0%
+handouts or comparatively complete
+handouts is that if I don't then hit all
+
+ align:start position:0%
+handouts is that if I don't then hit all
+ 
+
+ align:start position:0%
+handouts is that if I don't then hit all
+the lines on the handout
+
+ align:start position:0%
+the lines on the handout
+ 
+
+ align:start position:0%
+the lines on the handout
+um there there's a danger that
+
+ align:start position:0%
+um there there's a danger that
+ 
+
+ align:start position:0%
+um there there's a danger that
+somebody's going to want to know what I
+
+ align:start position:0%
+somebody's going to want to know what I
+ 
+
+ align:start position:0%
+somebody's going to want to know what I
+meant by Magic cures for imperfections
+
+ align:start position:0%
+meant by Magic cures for imperfections
+ 
+
+ align:start position:0%
+meant by Magic cures for imperfections
+and the Superwoman myth so let's jump
+
+ align:start position:0%
+and the Superwoman myth so let's jump
+ 
+
+ align:start position:0%
+and the Superwoman myth so let's jump
+back to societal pressures for uh for uh
+
+ align:start position:0%
+back to societal pressures for uh for uh
+ 
+
+ align:start position:0%
+back to societal pressures for uh for uh
+pushing people towards anorexia
+
+ align:start position:0%
+pushing people towards anorexia
+ 
+
+ align:start position:0%
+pushing people towards anorexia
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one of the the the magical cure thing uh
+
+ align:start position:0%
+one of the the the magical cure thing uh
+ 
+
+ align:start position:0%
+one of the the the magical cure thing uh
+is is the notion that we're a culture
+
+ align:start position:0%
+is is the notion that we're a culture
+ 
+
+ align:start position:0%
+is is the notion that we're a culture
+that firmly believes that you should be
+
+ align:start position:0%
+that firmly believes that you should be
+ 
+
+ align:start position:0%
+that firmly believes that you should be
+able to cure your problems right now and
+
+ align:start position:0%
+able to cure your problems right now and
+ 
+
+ align:start position:0%
+able to cure your problems right now and
+without too much real hard work
+
+ align:start position:0%
+without too much real hard work
+ 
+
+ align:start position:0%
+without too much real hard work
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+um if you are not sexy enough here is
+
+ align:start position:0%
+um if you are not sexy enough here is
+ 
+
+ align:start position:0%
+um if you are not sexy enough here is
+the mouthwash the um uh the the the the
+
+ align:start position:0%
+the mouthwash the um uh the the the the
+ 
+
+ align:start position:0%
+the mouthwash the um uh the the the the
+the clothes and and the uh and the six
+
+ align:start position:0%
+the clothes and and the uh and the six
+ 
+
+ align:start position:0%
+the clothes and and the uh and the six
+amazing acts that you can perform in the
+
+ align:start position:0%
+amazing acts that you can perform in the
+ 
+
+ align:start position:0%
+amazing acts that you can perform in the
+privacy of your own room
+
+ align:start position:0%
+privacy of your own room
+ 
+
+ align:start position:0%
+privacy of your own room
+um that will will do it all for you and
+
+ align:start position:0%
+um that will will do it all for you and
+ 
+
+ align:start position:0%
+um that will will do it all for you and
+you can read these at the supermarket
+
+ align:start position:0%
+you can read these at the supermarket
+ 
+
+ align:start position:0%
+you can read these at the supermarket
+checkout right one of my favorite I mean
+
+ align:start position:0%
+checkout right one of my favorite I mean
+ 
+
+ align:start position:0%
+checkout right one of my favorite I mean
+you get stuck at the supermarket check
+
+ align:start position:0%
+you get stuck at the supermarket check
+ 
+
+ align:start position:0%
+you get stuck at the supermarket check
+out I I love bouncing down the the uh
+
+ align:start position:0%
+out I I love bouncing down the the uh
+ 
+
+ align:start position:0%
+out I I love bouncing down the the uh
+just the the headlines of of the uh what
+
+ align:start position:0%
+just the the headlines of of the uh what
+ 
+
+ align:start position:0%
+just the the headlines of of the uh what
+what are described as the women's
+
+ align:start position:0%
+what are described as the women's
+ 
+
+ align:start position:0%
+what are described as the women's
+magazines Cosmo being the best of these
+
+ align:start position:0%
+magazines Cosmo being the best of these
+ 
+
+ align:start position:0%
+magazines Cosmo being the best of these
+because Cosmo is always willing to make
+
+ align:start position:0%
+because Cosmo is always willing to make
+ 
+
+ align:start position:0%
+because Cosmo is always willing to make
+you completely sexy by next month and
+
+ align:start position:0%
+you completely sexy by next month and
+ 
+
+ align:start position:0%
+you completely sexy by next month and
+amazingly they need to do it all again
+
+ align:start position:0%
+amazingly they need to do it all again
+ 
+
+ align:start position:0%
+amazingly they need to do it all again
+the next month but
+
+ align:start position:0%
+the next month but
+ 
+
+ align:start position:0%
+the next month but
+um you know this move will drive your
+
+ align:start position:0%
+um you know this move will drive your
+ 
+
+ align:start position:0%
+um you know this move will drive your
+man wild
+
+ align:start position:0%
+man wild
+ 
+
+ align:start position:0%
+man wild
+once a month on on the uh uh anyway it's
+
+ align:start position:0%
+once a month on on the uh uh anyway it's
+ 
+
+ align:start position:0%
+once a month on on the uh uh anyway it's
+great stuff
+
+ align:start position:0%
+great stuff
+ 
+
+ align:start position:0%
+great stuff
+um at least I suppose it's great stuff I
+
+ align:start position:0%
+um at least I suppose it's great stuff I
+ 
+
+ align:start position:0%
+um at least I suppose it's great stuff I
+don't get to read the journal much it's
+
+ align:start position:0%
+don't get to read the journal much it's
+ 
+
+ align:start position:0%
+don't get to read the journal much it's
+not it's not one of the technical
+
+ align:start position:0%
+not it's not one of the technical
+ 
+
+ align:start position:0%
+not it's not one of the technical
+journals in my field
+
+ align:start position:0%
+journals in my field
+ 
+
+ align:start position:0%
+journals in my field
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+all right so there's the magic cure
+
+ align:start position:0%
+all right so there's the magic cure
+ 
+
+ align:start position:0%
+all right so there's the magic cure
+piece and then the the Superwoman myth
+
+ align:start position:0%
+piece and then the the Superwoman myth
+ 
+
+ align:start position:0%
+piece and then the the Superwoman myth
+which uh which many
+
+ align:start position:0%
+which uh which many
+ 
+
+ align:start position:0%
+which uh which many
+um of these superwomen here may relate
+
+ align:start position:0%
+um of these superwomen here may relate
+ 
+
+ align:start position:0%
+um of these superwomen here may relate
+to is the uh uh is is a I can't remember
+
+ align:start position:0%
+to is the uh uh is is a I can't remember
+ 
+
+ align:start position:0%
+to is the uh uh is is a I can't remember
+who coined the term but the idea it's
+
+ align:start position:0%
+who coined the term but the idea it's
+ 
+
+ align:start position:0%
+who coined the term but the idea it's
+it's the idea of the woman or the guy
+
+ align:start position:0%
+it's the idea of the woman or the guy
+ 
+
+ align:start position:0%
+it's the idea of the woman or the guy
+for that matter who can do it all right
+
+ align:start position:0%
+for that matter who can do it all right
+ 
+
+ align:start position:0%
+for that matter who can do it all right
+she's she's got the high-powered uh uh
+
+ align:start position:0%
+she's she's got the high-powered uh uh
+ 
+
+ align:start position:0%
+she's she's got the high-powered uh uh
+career based on her great MIT degree
+
+ align:start position:0%
+career based on her great MIT degree
+ 
+
+ align:start position:0%
+career based on her great MIT degree
+um and she also is the mother of 15
+
+ align:start position:0%
+um and she also is the mother of 15
+ 
+
+ align:start position:0%
+um and she also is the mother of 15
+um and and and and uh making it to all
+
+ align:start position:0%
+um and and and and uh making it to all
+ 
+
+ align:start position:0%
+um and and and and uh making it to all
+the school plays and and and and making
+
+ align:start position:0%
+the school plays and and and and making
+ 
+
+ align:start position:0%
+the school plays and and and and making
+the food and of course knitting the
+
+ align:start position:0%
+the food and of course knitting the
+ 
+
+ align:start position:0%
+the food and of course knitting the
+clothes by hand and and stuff like that
+
+ align:start position:0%
+clothes by hand and and stuff like that
+ 
+
+ align:start position:0%
+clothes by hand and and stuff like that
+um there's typically not a similar
+
+ align:start position:0%
+um there's typically not a similar
+ 
+
+ align:start position:0%
+um there's typically not a similar
+Superman myth because even in in these
+
+ align:start position:0%
+Superman myth because even in in these
+ 
+
+ align:start position:0%
+Superman myth because even in in these
+more egalitarian days it Still Remains
+
+ align:start position:0%
+more egalitarian days it Still Remains
+ 
+
+ align:start position:0%
+more egalitarian days it Still Remains
+the case that the burden of child
+
+ align:start position:0%
+the case that the burden of child
+ 
+
+ align:start position:0%
+the case that the burden of child
+rearing Falls more heavily on the on the
+
+ align:start position:0%
+rearing Falls more heavily on the on the
+ 
+
+ align:start position:0%
+rearing Falls more heavily on the on the
+female than on the male typically across
+
+ align:start position:0%
+female than on the male typically across
+ 
+
+ align:start position:0%
+female than on the male typically across
+um across culture across across across
+
+ align:start position:0%
+um across culture across across across
+ 
+
+ align:start position:0%
+um across culture across across across
+this culture
+
+ align:start position:0%
+this culture
+ 
+
+ align:start position:0%
+this culture
+um so if anybody is going to be
+
+ align:start position:0%
+um so if anybody is going to be
+ 
+
+ align:start position:0%
+um so if anybody is going to be
+massively stressed out by trying to
+
+ align:start position:0%
+massively stressed out by trying to
+ 
+
+ align:start position:0%
+massively stressed out by trying to
+balance the home and and career thing
+
+ align:start position:0%
+balance the home and and career thing
+ 
+
+ align:start position:0%
+balance the home and and career thing
+it's more likely to be the woman at
+
+ align:start position:0%
+it's more likely to be the woman at
+ 
+
+ align:start position:0%
+it's more likely to be the woman at
+least uh that that's the argument that's
+
+ align:start position:0%
+least uh that that's the argument that's
+ 
+
+ align:start position:0%
+least uh that that's the argument that's
+being made here
+
+ align:start position:0%
+being made here
+ 
+
+ align:start position:0%
+being made here
+um all right let me jump then to this uh
+
+ align:start position:0%
+um all right let me jump then to this uh
+ 
+
+ align:start position:0%
+um all right let me jump then to this uh
+this other topic
+
+ align:start position:0%
+this other topic
+ 
+
+ align:start position:0%
+this other topic
+of of coercive sexual behavior and
+
+ align:start position:0%
+of of coercive sexual behavior and
+ 
+
+ align:start position:0%
+of of coercive sexual behavior and
+um Let me let me Advocate that you
+
+ align:start position:0%
+um Let me let me Advocate that you
+ 
+
+ align:start position:0%
+um Let me let me Advocate that you
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+um take advantage of your time in
+
+ align:start position:0%
+um take advantage of your time in
+ 
+
+ align:start position:0%
+um take advantage of your time in
+Cambridge sometime to go to the American
+
+ align:start position:0%
+Cambridge sometime to go to the American
+ 
+
+ align:start position:0%
+Cambridge sometime to go to the American
+Repertory Theater
+
+ align:start position:0%
+Repertory Theater
+ 
+
+ align:start position:0%
+Repertory Theater
+um just off the Harvard campus across
+
+ align:start position:0%
+um just off the Harvard campus across
+ 
+
+ align:start position:0%
+um just off the Harvard campus across
+the street from uh um Radcliffe
+
+ align:start position:0%
+the street from uh um Radcliffe
+ 
+
+ align:start position:0%
+the street from uh um Radcliffe
+um because I think my recollection is
+
+ align:start position:0%
+um because I think my recollection is
+ 
+
+ align:start position:0%
+um because I think my recollection is
+actually I haven't checked lately
+
+ align:start position:0%
+actually I haven't checked lately
+ 
+
+ align:start position:0%
+actually I haven't checked lately
+because I haven't been a student for a
+
+ align:start position:0%
+because I haven't been a student for a
+ 
+
+ align:start position:0%
+because I haven't been a student for a
+long time students used to get in
+
+ align:start position:0%
+long time students used to get in
+ 
+
+ align:start position:0%
+long time students used to get in
+amazingly cheaply
+
+ align:start position:0%
+amazingly cheaply
+ 
+
+ align:start position:0%
+amazingly cheaply
+um and and so you should do this they
+
+ align:start position:0%
+um and and so you should do this they
+ 
+
+ align:start position:0%
+um and and so you should do this they
+they put on a range of plays from Modern
+
+ align:start position:0%
+they put on a range of plays from Modern
+ 
+
+ align:start position:0%
+they put on a range of plays from Modern
+to Classic but almost always with some
+
+ align:start position:0%
+to Classic but almost always with some
+ 
+
+ align:start position:0%
+to Classic but almost always with some
+kind of out there attitude about it so I
+
+ align:start position:0%
+kind of out there attitude about it so I
+ 
+
+ align:start position:0%
+kind of out there attitude about it so I
+I remember this great production of um
+
+ align:start position:0%
+I remember this great production of um
+ 
+
+ align:start position:0%
+I remember this great production of um
+of handle yeah handles uh handle Opera
+
+ align:start position:0%
+of handle yeah handles uh handle Opera
+ 
+
+ align:start position:0%
+of handle yeah handles uh handle Opera
+um which they had decided to set
+
+ align:start position:0%
+um which they had decided to set
+ 
+
+ align:start position:0%
+um which they had decided to set
+um act one was set in a uh trailer park
+
+ align:start position:0%
+um act one was set in a uh trailer park
+ 
+
+ align:start position:0%
+um act one was set in a uh trailer park
+in in a Florida swamp
+
+ align:start position:0%
+in in a Florida swamp
+ 
+
+ align:start position:0%
+in in a Florida swamp
+um and act two was set on Mars
+
+ align:start position:0%
+um and act two was set on Mars
+ 
+
+ align:start position:0%
+um and act two was set on Mars
+um neither of which I believe were
+
+ align:start position:0%
+um neither of which I believe were
+ 
+
+ align:start position:0%
+um neither of which I believe were
+described as the settings in the
+
+ align:start position:0%
+described as the settings in the
+ 
+
+ align:start position:0%
+described as the settings in the
+original libretto
+
+ align:start position:0%
+original libretto
+ 
+
+ align:start position:0%
+original libretto
+um somebody had said that that kind of
+
+ align:start position:0%
+um somebody had said that that kind of
+ 
+
+ align:start position:0%
+um somebody had said that that kind of
+thing anyway some years ago
+
+ align:start position:0%
+thing anyway some years ago
+ 
+
+ align:start position:0%
+thing anyway some years ago
+um I I saw a production of Shakespeare's
+
+ align:start position:0%
+um I I saw a production of Shakespeare's
+ 
+
+ align:start position:0%
+um I I saw a production of Shakespeare's
+Midsummer Night stream there
+
+ align:start position:0%
+Midsummer Night stream there
+ 
+
+ align:start position:0%
+Midsummer Night stream there
+um and at the beginning of the play what
+
+ align:start position:0%
+um and at the beginning of the play what
+ 
+
+ align:start position:0%
+um and at the beginning of the play what
+they had done is they staged
+
+ align:start position:0%
+they had done is they staged
+ 
+
+ align:start position:0%
+they had done is they staged
+um up a a a practice fight it was clear
+
+ align:start position:0%
+um up a a a practice fight it was clear
+ 
+
+ align:start position:0%
+um up a a a practice fight it was clear
+that these were
+
+ align:start position:0%
+that these were
+ 
+
+ align:start position:0%
+that these were
+um two uh two nights
+
+ align:start position:0%
+um two uh two nights
+ 
+
+ align:start position:0%
+um two uh two nights
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know practicing rather than fighting
+
+ align:start position:0%
+you know practicing rather than fighting
+ 
+
+ align:start position:0%
+you know practicing rather than fighting
+in an actual battle sparring with each
+
+ align:start position:0%
+in an actual battle sparring with each
+ 
+
+ align:start position:0%
+in an actual battle sparring with each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+um and they're whacking away at each
+
+ align:start position:0%
+um and they're whacking away at each
+ 
+
+ align:start position:0%
+um and they're whacking away at each
+other the lights come up and they're
+
+ align:start position:0%
+other the lights come up and they're
+ 
+
+ align:start position:0%
+other the lights come up and they're
+whacking away at each other and finally
+
+ align:start position:0%
+whacking away at each other and finally
+ 
+
+ align:start position:0%
+whacking away at each other and finally
+one of them flattens the other and and
+
+ align:start position:0%
+one of them flattens the other and and
+ 
+
+ align:start position:0%
+one of them flattens the other and and
+uh pulls a sword as it is at the neck of
+
+ align:start position:0%
+uh pulls a sword as it is at the neck of
+ 
+
+ align:start position:0%
+uh pulls a sword as it is at the neck of
+of of of of of of of of the guy on the
+
+ align:start position:0%
+of of of of of of of of the guy on the
+ 
+
+ align:start position:0%
+of of of of of of of of the guy on the
+ground and at that point
+
+ align:start position:0%
+ground and at that point
+ 
+
+ align:start position:0%
+ground and at that point
+um the lines you hear are hippolyta I
+
+ align:start position:0%
+um the lines you hear are hippolyta I
+ 
+
+ align:start position:0%
+um the lines you hear are hippolyta I
+would be with my sword and one thy love
+
+ align:start position:0%
+would be with my sword and one thy love
+ 
+
+ align:start position:0%
+would be with my sword and one thy love
+doing the injuries but I will wed thee
+
+ align:start position:0%
+doing the injuries but I will wed thee
+ 
+
+ align:start position:0%
+doing the injuries but I will wed thee
+in another key with pomp with Triumph
+
+ align:start position:0%
+in another key with pomp with Triumph
+ 
+
+ align:start position:0%
+in another key with pomp with Triumph
+and with reveling
+
+ align:start position:0%
+and with reveling
+ 
+
+ align:start position:0%
+and with reveling
+um what the art had done
+
+ align:start position:0%
+um what the art had done
+ 
+
+ align:start position:0%
+um what the art had done
+was at the moment that the fight was
+
+ align:start position:0%
+was at the moment that the fight was
+ 
+
+ align:start position:0%
+was at the moment that the fight was
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+um the guy on the floor is reciting
+
+ align:start position:0%
+um the guy on the floor is reciting
+ 
+
+ align:start position:0%
+um the guy on the floor is reciting
+those lines and
+
+ align:start position:0%
+those lines and
+ 
+
+ align:start position:0%
+those lines and
+um the other person takes off her helmet
+
+ align:start position:0%
+um the other person takes off her helmet
+ 
+
+ align:start position:0%
+um the other person takes off her helmet
+and of course to make it dramatic her
+
+ align:start position:0%
+and of course to make it dramatic her
+ 
+
+ align:start position:0%
+and of course to make it dramatic her
+big hair fluffs out all over the place
+
+ align:start position:0%
+big hair fluffs out all over the place
+ 
+
+ align:start position:0%
+big hair fluffs out all over the place
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+um the the beginning of of
+
+ align:start position:0%
+um the the beginning of of
+ 
+
+ align:start position:0%
+um the the beginning of of
+um Midsummer Night's Dream is the setup
+
+ align:start position:0%
+um Midsummer Night's Dream is the setup
+ 
+
+ align:start position:0%
+um Midsummer Night's Dream is the setup
+that the setup is that there's going to
+
+ align:start position:0%
+that the setup is that there's going to
+ 
+
+ align:start position:0%
+that the setup is that there's going to
+be a wedding between Theseus Duke of
+
+ align:start position:0%
+be a wedding between Theseus Duke of
+ 
+
+ align:start position:0%
+be a wedding between Theseus Duke of
+Athens and hippolyta the queen of the
+
+ align:start position:0%
+Athens and hippolyta the queen of the
+ 
+
+ align:start position:0%
+Athens and hippolyta the queen of the
+Amazons who he has conquered and is now
+
+ align:start position:0%
+Amazons who he has conquered and is now
+ 
+
+ align:start position:0%
+Amazons who he has conquered and is now
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+um marry but the notion of I Ruled thee
+
+ align:start position:0%
+um marry but the notion of I Ruled thee
+ 
+
+ align:start position:0%
+um marry but the notion of I Ruled thee
+with my sword and ones I love doing the
+
+ align:start position:0%
+with my sword and ones I love doing the
+ 
+
+ align:start position:0%
+with my sword and ones I love doing the
+injuries does not sit well in uh in in
+
+ align:start position:0%
+injuries does not sit well in uh in in
+ 
+
+ align:start position:0%
+injuries does not sit well in uh in in
+at least not in a Cambridge academic
+
+ align:start position:0%
+at least not in a Cambridge academic
+ 
+
+ align:start position:0%
+at least not in a Cambridge academic
+kind of setting
+
+ align:start position:0%
+kind of setting
+ 
+
+ align:start position:0%
+kind of setting
+um and and so uh the art played this
+
+ align:start position:0%
+um and and so uh the art played this
+ 
+
+ align:start position:0%
+um and and so uh the art played this
+against type right with with Theseus on
+
+ align:start position:0%
+against type right with with Theseus on
+ 
+
+ align:start position:0%
+against type right with with Theseus on
+on the floor yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+but it's an interesting
+
+ align:start position:0%
+but it's an interesting
+ 
+
+ align:start position:0%
+but it's an interesting
+curious thought that you might woo
+
+ align:start position:0%
+curious thought that you might woo
+ 
+
+ align:start position:0%
+curious thought that you might woo
+somebody with your sword and win their
+
+ align:start position:0%
+somebody with your sword and win their
+ 
+
+ align:start position:0%
+somebody with your sword and win their
+love doing them injuries
+
+ align:start position:0%
+love doing them injuries
+ 
+
+ align:start position:0%
+love doing them injuries
+um it's uh I I suspect there aren't very
+
+ align:start position:0%
+um it's uh I I suspect there aren't very
+ 
+
+ align:start position:0%
+um it's uh I I suspect there aren't very
+many women present who might uh who who
+
+ align:start position:0%
+many women present who might uh who who
+ 
+
+ align:start position:0%
+many women present who might uh who who
+would subscribe to the notion that that
+
+ align:start position:0%
+would subscribe to the notion that that
+ 
+
+ align:start position:0%
+would subscribe to the notion that that
+would be a marvelous form of courtship
+
+ align:start position:0%
+would be a marvelous form of courtship
+ 
+
+ align:start position:0%
+would be a marvelous form of courtship
+um and and and maybe not even an awful
+
+ align:start position:0%
+um and and and maybe not even an awful
+ 
+
+ align:start position:0%
+um and and and maybe not even an awful
+lot of guys but
+
+ align:start position:0%
+lot of guys but
+ 
+
+ align:start position:0%
+lot of guys but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+forms of relations that become coercive
+
+ align:start position:0%
+forms of relations that become coercive
+ 
+
+ align:start position:0%
+forms of relations that become coercive
+are by no means unheard of and the place
+
+ align:start position:0%
+are by no means unheard of and the place
+ 
+
+ align:start position:0%
+are by no means unheard of and the place
+we typically end up hearing about them
+
+ align:start position:0%
+we typically end up hearing about them
+ 
+
+ align:start position:0%
+we typically end up hearing about them
+is when they end up in court how do they
+
+ align:start position:0%
+is when they end up in court how do they
+ 
+
+ align:start position:0%
+is when they end up in court how do they
+end up in court well let me tell you a
+
+ align:start position:0%
+end up in court well let me tell you a
+ 
+
+ align:start position:0%
+end up in court well let me tell you a
+court case this this happened
+
+ align:start position:0%
+court case this this happened
+ 
+
+ align:start position:0%
+court case this this happened
+um about 10 years ago now this is a
+
+ align:start position:0%
+um about 10 years ago now this is a
+ 
+
+ align:start position:0%
+um about 10 years ago now this is a
+court case
+
+ align:start position:0%
+court case
+ 
+
+ align:start position:0%
+court case
+where a woman is suing a a collection of
+
+ align:start position:0%
+where a woman is suing a a collection of
+ 
+
+ align:start position:0%
+where a woman is suing a a collection of
+uh just suing them or no I think I think
+
+ align:start position:0%
+uh just suing them or no I think I think
+ 
+
+ align:start position:0%
+uh just suing them or no I think I think
+this was actually a rape case in
+
+ align:start position:0%
+this was actually a rape case in
+ 
+
+ align:start position:0%
+this was actually a rape case in
+Criminal Court
+
+ align:start position:0%
+Criminal Court
+ 
+
+ align:start position:0%
+Criminal Court
+um they're they're charged with rape
+
+ align:start position:0%
+um they're they're charged with rape
+ 
+
+ align:start position:0%
+um they're they're charged with rape
+um and and and she's the plaintiff what
+
+ align:start position:0%
+um and and and she's the plaintiff what
+ 
+
+ align:start position:0%
+um and and and she's the plaintiff what
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+um well
+
+ align:start position:0%
+um well
+ 
+
+ align:start position:0%
+um well
+considerable disagreement about what
+
+ align:start position:0%
+considerable disagreement about what
+ 
+
+ align:start position:0%
+considerable disagreement about what
+happened when you end up in court but
+
+ align:start position:0%
+happened when you end up in court but
+ 
+
+ align:start position:0%
+happened when you end up in court but
+what basically seems to have happened is
+
+ align:start position:0%
+what basically seems to have happened is
+ 
+
+ align:start position:0%
+what basically seems to have happened is
+that these that
+
+ align:start position:0%
+that these that
+ 
+
+ align:start position:0%
+that these that
+um the woman and one of the guys met at
+
+ align:start position:0%
+um the woman and one of the guys met at
+ 
+
+ align:start position:0%
+um the woman and one of the guys met at
+uh I think it was rifle practice some
+
+ align:start position:0%
+uh I think it was rifle practice some
+ 
+
+ align:start position:0%
+uh I think it was rifle practice some
+sort of athletic practice
+
+ align:start position:0%
+sort of athletic practice
+ 
+
+ align:start position:0%
+sort of athletic practice
+um he invited her back to his uh his
+
+ align:start position:0%
+um he invited her back to his uh his
+ 
+
+ align:start position:0%
+um he invited her back to his uh his
+residence
+
+ align:start position:0%
+residence
+ 
+
+ align:start position:0%
+residence
+um alcohol followed and
+
+ align:start position:0%
+um alcohol followed and
+ 
+
+ align:start position:0%
+um alcohol followed and
+um she ended up having some variety of
+
+ align:start position:0%
+um she ended up having some variety of
+ 
+
+ align:start position:0%
+um she ended up having some variety of
+sexual relations with like six different
+
+ align:start position:0%
+sexual relations with like six different
+ 
+
+ align:start position:0%
+sexual relations with like six different
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+um and subsequently
+
+ align:start position:0%
+um and subsequently
+ 
+
+ align:start position:0%
+um and subsequently
+um uh it subsequently charged them with
+
+ align:start position:0%
+um uh it subsequently charged them with
+ 
+
+ align:start position:0%
+um uh it subsequently charged them with
+rape
+
+ align:start position:0%
+rape
+ 
+
+ align:start position:0%
+rape
+um she argued that uh um that she had
+
+ align:start position:0%
+um she argued that uh um that she had
+ 
+
+ align:start position:0%
+um she argued that uh um that she had
+been passing in and out of Consciousness
+
+ align:start position:0%
+been passing in and out of Consciousness
+ 
+
+ align:start position:0%
+been passing in and out of Consciousness
+and and that they had basically abused
+
+ align:start position:0%
+and and that they had basically abused
+ 
+
+ align:start position:0%
+and and that they had basically abused
+her they argued that this was consensual
+
+ align:start position:0%
+her they argued that this was consensual
+ 
+
+ align:start position:0%
+her they argued that this was consensual
+um I think what happened in this
+
+ align:start position:0%
+um I think what happened in this
+ 
+
+ align:start position:0%
+um I think what happened in this
+particular case
+
+ align:start position:0%
+particular case
+ 
+
+ align:start position:0%
+particular case
+um by the way is that there was no
+
+ align:start position:0%
+um by the way is that there was no
+ 
+
+ align:start position:0%
+um by the way is that there was no
+conviction for rape but uh but several
+
+ align:start position:0%
+conviction for rape but uh but several
+ 
+
+ align:start position:0%
+conviction for rape but uh but several
+of the guys ended up being expelled from
+
+ align:start position:0%
+of the guys ended up being expelled from
+ 
+
+ align:start position:0%
+of the guys ended up being expelled from
+school um yeah
+
+ align:start position:0%
+school um yeah
+ 
+
+ align:start position:0%
+school um yeah
+there are lots of things one could talk
+
+ align:start position:0%
+there are lots of things one could talk
+ 
+
+ align:start position:0%
+there are lots of things one could talk
+about here I'm not in the business
+
+ align:start position:0%
+about here I'm not in the business
+ 
+
+ align:start position:0%
+about here I'm not in the business
+um for for a psych course of of giving
+
+ align:start position:0%
+um for for a psych course of of giving
+ 
+
+ align:start position:0%
+um for for a psych course of of giving
+is sort of an RO week lecture about
+
+ align:start position:0%
+is sort of an RO week lecture about
+ 
+
+ align:start position:0%
+is sort of an RO week lecture about
+about you know good behavior or
+
+ align:start position:0%
+about you know good behavior or
+ 
+
+ align:start position:0%
+about you know good behavior or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+um but the the interesting issue well
+
+ align:start position:0%
+um but the the interesting issue well
+ 
+
+ align:start position:0%
+um but the the interesting issue well
+there are lots of interesting psych
+
+ align:start position:0%
+there are lots of interesting psych
+ 
+
+ align:start position:0%
+there are lots of interesting psych
+issues the interesting psych issue that
+
+ align:start position:0%
+issues the interesting psych issue that
+ 
+
+ align:start position:0%
+issues the interesting psych issue that
+I want to focus on is the question of
+
+ align:start position:0%
+I want to focus on is the question of
+ 
+
+ align:start position:0%
+I want to focus on is the question of
+how this could come to pass given that
+
+ align:start position:0%
+how this could come to pass given that
+ 
+
+ align:start position:0%
+how this could come to pass given that
+probably nobody wanted it to come to
+
+ align:start position:0%
+probably nobody wanted it to come to
+ 
+
+ align:start position:0%
+probably nobody wanted it to come to
+pass it is extremely unlikely that
+
+ align:start position:0%
+pass it is extremely unlikely that
+ 
+
+ align:start position:0%
+pass it is extremely unlikely that
+um she went to whatever it was rifle
+
+ align:start position:0%
+um she went to whatever it was rifle
+ 
+
+ align:start position:0%
+um she went to whatever it was rifle
+practice saying oh gee I think I'll go
+
+ align:start position:0%
+practice saying oh gee I think I'll go
+ 
+
+ align:start position:0%
+practice saying oh gee I think I'll go
+home with this guy get smashed out of my
+
+ align:start position:0%
+home with this guy get smashed out of my
+ 
+
+ align:start position:0%
+home with this guy get smashed out of my
+mind and have sex with all of his
+
+ align:start position:0%
+mind and have sex with all of his
+ 
+
+ align:start position:0%
+mind and have sex with all of his
+roommates it just doesn't seem likely it
+
+ align:start position:0%
+roommates it just doesn't seem likely it
+ 
+
+ align:start position:0%
+roommates it just doesn't seem likely it
+does and minor does it seem very likely
+
+ align:start position:0%
+does and minor does it seem very likely
+ 
+
+ align:start position:0%
+does and minor does it seem very likely
+that he said to himself oh I think I'll
+
+ align:start position:0%
+that he said to himself oh I think I'll
+ 
+
+ align:start position:0%
+that he said to himself oh I think I'll
+take this friend of mine home and we'll
+
+ align:start position:0%
+take this friend of mine home and we'll
+ 
+
+ align:start position:0%
+take this friend of mine home and we'll
+all have too much to drink and and and
+
+ align:start position:0%
+all have too much to drink and and and
+ 
+
+ align:start position:0%
+all have too much to drink and and and
+and she'll have sex with everybody Under
+
+ align:start position:0%
+and she'll have sex with everybody Under
+ 
+
+ align:start position:0%
+and she'll have sex with everybody Under
+the Sun so it it's pretty clear that
+
+ align:start position:0%
+the Sun so it it's pretty clear that
+ 
+
+ align:start position:0%
+the Sun so it it's pretty clear that
+this is not what
+
+ align:start position:0%
+this is not what
+ 
+
+ align:start position:0%
+this is not what
+um anybody particularly had in mind
+
+ align:start position:0%
+um anybody particularly had in mind
+ 
+
+ align:start position:0%
+um anybody particularly had in mind
+how does it come to pass oh look at that
+
+ align:start position:0%
+how does it come to pass oh look at that
+ 
+
+ align:start position:0%
+how does it come to pass oh look at that
+I must have said that on the handout
+
+ align:start position:0%
+I must have said that on the handout
+ 
+
+ align:start position:0%
+I must have said that on the handout
+what am I talking about next
+
+ align:start position:0%
+what am I talking about next
+ 
+
+ align:start position:0%
+what am I talking about next
+lots of questions most of which we
+
+ align:start position:0%
+lots of questions most of which we
+ 
+
+ align:start position:0%
+lots of questions most of which we
+cannot address
+
+ align:start position:0%
+cannot address
+ 
+
+ align:start position:0%
+cannot address
+um all right
+
+ align:start position:0%
+um all right
+ 
+
+ align:start position:0%
+um all right
+so let's address some of the ones we can
+
+ align:start position:0%
+so let's address some of the ones we can
+ 
+
+ align:start position:0%
+so let's address some of the ones we can
+address as it says they're very gender
+
+ align:start position:0%
+address as it says they're very gender
+ 
+
+ align:start position:0%
+address as it says they're very gender
+specific problem there is there are
+
+ align:start position:0%
+specific problem there is there are
+ 
+
+ align:start position:0%
+specific problem there is there are
+certainly instances of
+
+ align:start position:0%
+certainly instances of
+ 
+
+ align:start position:0%
+certainly instances of
+um sexual coercion going the other uh
+
+ align:start position:0%
+um sexual coercion going the other uh
+ 
+
+ align:start position:0%
+um sexual coercion going the other uh
+female on male sexual coercion and
+
+ align:start position:0%
+female on male sexual coercion and
+ 
+
+ align:start position:0%
+female on male sexual coercion and
+within homosexual relationships there
+
+ align:start position:0%
+within homosexual relationships there
+ 
+
+ align:start position:0%
+within homosexual relationships there
+are certainly instances of of sexual
+
+ align:start position:0%
+are certainly instances of of sexual
+ 
+
+ align:start position:0%
+are certainly instances of of sexual
+coercion but the great bulk of these
+
+ align:start position:0%
+coercion but the great bulk of these
+ 
+
+ align:start position:0%
+coercion but the great bulk of these
+cases are male on on female coercion
+
+ align:start position:0%
+cases are male on on female coercion
+ 
+
+ align:start position:0%
+cases are male on on female coercion
+um and in in fact uh the female on male
+
+ align:start position:0%
+um and in in fact uh the female on male
+ 
+
+ align:start position:0%
+um and in in fact uh the female on male
+coercion uh
+
+ align:start position:0%
+coercion uh
+ 
+
+ align:start position:0%
+coercion uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+incidents is vastly higher
+
+ align:start position:0%
+incidents is vastly higher
+ 
+
+ align:start position:0%
+incidents is vastly higher
+um in in in the erotic literature than
+
+ align:start position:0%
+um in in in the erotic literature than
+ 
+
+ align:start position:0%
+um in in in the erotic literature than
+it is in reality apparently now the
+
+ align:start position:0%
+it is in reality apparently now the
+ 
+
+ align:start position:0%
+it is in reality apparently now the
+because because well if it's remember
+
+ align:start position:0%
+because because well if it's remember
+ 
+
+ align:start position:0%
+because because well if it's remember
+the example from earlier on about
+
+ align:start position:0%
+the example from earlier on about
+ 
+
+ align:start position:0%
+the example from earlier on about
+imagine that
+
+ align:start position:0%
+imagine that
+ 
+
+ align:start position:0%
+imagine that
+um you're going you're on on the subway
+
+ align:start position:0%
+um you're going you're on on the subway
+ 
+
+ align:start position:0%
+um you're going you're on on the subway
+and some uh member of the sex that you
+
+ align:start position:0%
+and some uh member of the sex that you
+ 
+
+ align:start position:0%
+and some uh member of the sex that you
+find active begins to touch you
+
+ align:start position:0%
+find active begins to touch you
+ 
+
+ align:start position:0%
+find active begins to touch you
+surreptitiously on a crowded subway car
+
+ align:start position:0%
+surreptitiously on a crowded subway car
+ 
+
+ align:start position:0%
+surreptitiously on a crowded subway car
+is this a good thing or a bad thing
+
+ align:start position:0%
+is this a good thing or a bad thing
+ 
+
+ align:start position:0%
+is this a good thing or a bad thing
+women uniformly say this is not good and
+
+ align:start position:0%
+women uniformly say this is not good and
+ 
+
+ align:start position:0%
+women uniformly say this is not good and
+guys well not quite uniformly say okay
+
+ align:start position:0%
+guys well not quite uniformly say okay
+ 
+
+ align:start position:0%
+guys well not quite uniformly say okay
+it's you can get similar data
+
+ align:start position:0%
+it's you can get similar data
+ 
+
+ align:start position:0%
+it's you can get similar data
+um you can get similar data with with
+
+ align:start position:0%
+um you can get similar data with with
+ 
+
+ align:start position:0%
+um you can get similar data with with
+um with coercive uh
+
+ align:start position:0%
+um with coercive uh
+ 
+
+ align:start position:0%
+um with coercive uh
+relations
+
+ align:start position:0%
+relations
+ 
+
+ align:start position:0%
+relations
+um you know the uh it's the the the the
+
+ align:start position:0%
+um you know the uh it's the the the the
+ 
+
+ align:start position:0%
+um you know the uh it's the the the the
+leather-bound woman who shows up and
+
+ align:start position:0%
+leather-bound woman who shows up and
+ 
+
+ align:start position:0%
+leather-bound woman who shows up and
+says you're having sex with me right now
+
+ align:start position:0%
+says you're having sex with me right now
+ 
+
+ align:start position:0%
+says you're having sex with me right now
+is is is a fantasy figure right the
+
+ align:start position:0%
+is is is a fantasy figure right the
+ 
+
+ align:start position:0%
+is is is a fantasy figure right the
+leather-bound guy who comes up to a
+
+ align:start position:0%
+leather-bound guy who comes up to a
+ 
+
+ align:start position:0%
+leather-bound guy who comes up to a
+woman and says you're having sex with me
+
+ align:start position:0%
+woman and says you're having sex with me
+ 
+
+ align:start position:0%
+woman and says you're having sex with me
+right now is not typically a fantasy
+
+ align:start position:0%
+right now is not typically a fantasy
+ 
+
+ align:start position:0%
+right now is not typically a fantasy
+figure not in this right so there's
+
+ align:start position:0%
+figure not in this right so there's
+ 
+
+ align:start position:0%
+figure not in this right so there's
+there's this there's this odd asymmetry
+
+ align:start position:0%
+there's this there's this odd asymmetry
+ 
+
+ align:start position:0%
+there's this there's this odd asymmetry
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+there are lots of ways to understand
+
+ align:start position:0%
+there are lots of ways to understand
+ 
+
+ align:start position:0%
+there are lots of ways to understand
+how this could um
+
+ align:start position:0%
+how this could um
+ 
+
+ align:start position:0%
+how this could um
+uh could come to pass one of the reasons
+
+ align:start position:0%
+uh could come to pass one of the reasons
+ 
+
+ align:start position:0%
+uh could come to pass one of the reasons
+as I said earlier for making this a uh
+
+ align:start position:0%
+as I said earlier for making this a uh
+ 
+
+ align:start position:0%
+as I said earlier for making this a uh
+an end of the term kind of topic is it
+
+ align:start position:0%
+an end of the term kind of topic is it
+ 
+
+ align:start position:0%
+an end of the term kind of topic is it
+it is it does sort of neatly
+
+ align:start position:0%
+it is it does sort of neatly
+ 
+
+ align:start position:0%
+it is it does sort of neatly
+recapitulate an awful lot of the themes
+
+ align:start position:0%
+recapitulate an awful lot of the themes
+ 
+
+ align:start position:0%
+recapitulate an awful lot of the themes
+about causality that that have shown up
+
+ align:start position:0%
+about causality that that have shown up
+ 
+
+ align:start position:0%
+about causality that that have shown up
+in in the
+
+ align:start position:0%
+in in the
+ 
+
+ align:start position:0%
+in in the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in the course of the term and then what
+
+ align:start position:0%
+in the course of the term and then what
+ 
+
+ align:start position:0%
+in the course of the term and then what
+I'll probably oh very clearly do next
+
+ align:start position:0%
+I'll probably oh very clearly do next
+ 
+
+ align:start position:0%
+I'll probably oh very clearly do next
+time is is weave a story that combines
+
+ align:start position:0%
+time is is weave a story that combines
+ 
+
+ align:start position:0%
+time is is weave a story that combines
+many different threads into one let me
+
+ align:start position:0%
+many different threads into one let me
+ 
+
+ align:start position:0%
+many different threads into one let me
+let me just say a word about
+
+ align:start position:0%
+let me just say a word about
+ 
+
+ align:start position:0%
+let me just say a word about
+um incidents today and then we'll go on
+
+ align:start position:0%
+um incidents today and then we'll go on
+ 
+
+ align:start position:0%
+um incidents today and then we'll go on
+to etiology
+
+ align:start position:0%
+to etiology
+ 
+
+ align:start position:0%
+to etiology
+um when we when we pick up next time how
+
+ align:start position:0%
+um when we when we pick up next time how
+ 
+
+ align:start position:0%
+um when we when we pick up next time how
+common is this as a problem well you've
+
+ align:start position:0%
+common is this as a problem well you've
+ 
+
+ align:start position:0%
+common is this as a problem well you've
+got a real problem here which I have
+
+ align:start position:0%
+got a real problem here which I have
+ 
+
+ align:start position:0%
+got a real problem here which I have
+mentioned before which is the data on
+
+ align:start position:0%
+mentioned before which is the data on
+ 
+
+ align:start position:0%
+mentioned before which is the data on
+sexual behavior are lousy
+
+ align:start position:0%
+sexual behavior are lousy
+ 
+
+ align:start position:0%
+sexual behavior are lousy
+um because people don't well first of
+
+ align:start position:0%
+um because people don't well first of
+ 
+
+ align:start position:0%
+um because people don't well first of
+all we don't collect that much of it and
+
+ align:start position:0%
+all we don't collect that much of it and
+ 
+
+ align:start position:0%
+all we don't collect that much of it and
+second of all people lie
+
+ align:start position:0%
+second of all people lie
+ 
+
+ align:start position:0%
+second of all people lie
+um recall that if you ask males how many
+
+ align:start position:0%
+um recall that if you ask males how many
+ 
+
+ align:start position:0%
+um recall that if you ask males how many
+sexual partners have you had and you ask
+
+ align:start position:0%
+sexual partners have you had and you ask
+ 
+
+ align:start position:0%
+sexual partners have you had and you ask
+females how many sexual partners have
+
+ align:start position:0%
+females how many sexual partners have
+ 
+
+ align:start position:0%
+females how many sexual partners have
+you had you discover that there's a
+
+ align:start position:0%
+you had you discover that there's a
+ 
+
+ align:start position:0%
+you had you discover that there's a
+third sex out there somewhere
+
+ align:start position:0%
+third sex out there somewhere
+ 
+
+ align:start position:0%
+third sex out there somewhere
+um because the math doesn't add up you
+
+ align:start position:0%
+um because the math doesn't add up you
+ 
+
+ align:start position:0%
+um because the math doesn't add up you
+see that too
+
+ align:start position:0%
+see that too
+ 
+
+ align:start position:0%
+see that too
+um in uh well maybe you see that in in
+
+ align:start position:0%
+um in uh well maybe you see that in in
+ 
+
+ align:start position:0%
+um in uh well maybe you see that in in
+the data on on uh that's gotten
+
+ align:start position:0%
+the data on on uh that's gotten
+ 
+
+ align:start position:0%
+the data on on uh that's gotten
+basically from survey data
+
+ align:start position:0%
+basically from survey data
+ 
+
+ align:start position:0%
+basically from survey data
+um on on coercive sex if you ask females
+
+ align:start position:0%
+um on on coercive sex if you ask females
+ 
+
+ align:start position:0%
+um on on coercive sex if you ask females
+how many
+
+ align:start position:0%
+how many
+ 
+
+ align:start position:0%
+how many
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+have you ever been coerced into uh in
+
+ align:start position:0%
+have you ever been coerced into uh in
+ 
+
+ align:start position:0%
+have you ever been coerced into uh in
+into sexual intercourse uh in at least
+
+ align:start position:0%
+into sexual intercourse uh in at least
+ 
+
+ align:start position:0%
+into sexual intercourse uh in at least
+one study the answer is 15 of women say
+
+ align:start position:0%
+one study the answer is 15 of women say
+ 
+
+ align:start position:0%
+one study the answer is 15 of women say
+yes if you ask men how many of you have
+
+ align:start position:0%
+yes if you ask men how many of you have
+ 
+
+ align:start position:0%
+yes if you ask men how many of you have
+you ever coerced anybody into having
+
+ align:start position:0%
+you ever coerced anybody into having
+ 
+
+ align:start position:0%
+you ever coerced anybody into having
+sexual intercourse only seven percent of
+
+ align:start position:0%
+sexual intercourse only seven percent of
+ 
+
+ align:start position:0%
+sexual intercourse only seven percent of
+males say yes now there are a number of
+
+ align:start position:0%
+males say yes now there are a number of
+ 
+
+ align:start position:0%
+males say yes now there are a number of
+possible explanations like serial
+
+ align:start position:0%
+possible explanations like serial
+ 
+
+ align:start position:0%
+possible explanations like serial
+coercers or things of that sort but you
+
+ align:start position:0%
+coercers or things of that sort but you
+ 
+
+ align:start position:0%
+coercers or things of that sort but you
+can see that there may be reporting
+
+ align:start position:0%
+can see that there may be reporting
+ 
+
+ align:start position:0%
+can see that there may be reporting
+issues that are difficult there one last
+
+ align:start position:0%
+issues that are difficult there one last
+ 
+
+ align:start position:0%
+issues that are difficult there one last
+point on this if you ask on the
+
+ align:start position:0%
+point on this if you ask on the
+ 
+
+ align:start position:0%
+point on this if you ask on the
+incidence point if you ask
+
+ align:start position:0%
+incidence point if you ask
+ 
+
+ align:start position:0%
+incidence point if you ask
+um have you ever well 25 percent of
+
+ align:start position:0%
+um have you ever well 25 percent of
+ 
+
+ align:start position:0%
+um have you ever well 25 percent of
+women in in one study back from the mid
+
+ align:start position:0%
+women in in one study back from the mid
+ 
+
+ align:start position:0%
+women in in one study back from the mid
+80s reported
+
+ align:start position:0%
+80s reported
+ 
+
+ align:start position:0%
+80s reported
+intercourse because
+
+ align:start position:0%
+intercourse because
+ 
+
+ align:start position:0%
+intercourse because
+um quote they were overwhelmed by a
+
+ align:start position:0%
+um quote they were overwhelmed by a
+ 
+
+ align:start position:0%
+um quote they were overwhelmed by a
+man's continual arguments and pressure
+
+ align:start position:0%
+man's continual arguments and pressure
+ 
+
+ align:start position:0%
+man's continual arguments and pressure
+that's an interesting statistic in a
+
+ align:start position:0%
+that's an interesting statistic in a
+ 
+
+ align:start position:0%
+that's an interesting statistic in a
+couple of ways first of all it's
+
+ align:start position:0%
+couple of ways first of all it's
+ 
+
+ align:start position:0%
+couple of ways first of all it's
+interesting because it's quite High
+
+ align:start position:0%
+interesting because it's quite High
+ 
+
+ align:start position:0%
+interesting because it's quite High
+second of all it's interesting because
+
+ align:start position:0%
+second of all it's interesting because
+ 
+
+ align:start position:0%
+second of all it's interesting because
+it points out the very distinct status
+
+ align:start position:0%
+it points out the very distinct status
+ 
+
+ align:start position:0%
+it points out the very distinct status
+of sexual relationships if I am coerced
+
+ align:start position:0%
+of sexual relationships if I am coerced
+ 
+
+ align:start position:0%
+of sexual relationships if I am coerced
+into buying a used car by the man's
+
+ align:start position:0%
+into buying a used car by the man's
+ 
+
+ align:start position:0%
+into buying a used car by the man's
+continual arguments and pressure
+
+ align:start position:0%
+continual arguments and pressure
+ 
+
+ align:start position:0%
+continual arguments and pressure
+that's too bad right
+
+ align:start position:0%
+that's too bad right
+ 
+
+ align:start position:0%
+that's too bad right
+if I decide that I'm gonna strangle who
+
+ align:start position:0%
+if I decide that I'm gonna strangle who
+ 
+
+ align:start position:0%
+if I decide that I'm gonna strangle who
+am I going to strangle oh I don't know I
+
+ align:start position:0%
+am I going to strangle oh I don't know I
+ 
+
+ align:start position:0%
+am I going to strangle oh I don't know I
+won't strangle anybody particular oh
+
+ align:start position:0%
+won't strangle anybody particular oh
+ 
+
+ align:start position:0%
+won't strangle anybody particular oh
+maybe I'll strangle Kristen because she
+
+ align:start position:0%
+maybe I'll strangle Kristen because she
+ 
+
+ align:start position:0%
+maybe I'll strangle Kristen because she
+was laughing at me earlier
+
+ align:start position:0%
+was laughing at me earlier
+ 
+
+ align:start position:0%
+was laughing at me earlier
+um I I I'll I'll strangle Kristen um
+
+ align:start position:0%
+um I I I'll I'll strangle Kristen um
+ 
+
+ align:start position:0%
+um I I I'll I'll strangle Kristen um
+because I was pressured by Anna's
+
+ align:start position:0%
+because I was pressured by Anna's
+ 
+
+ align:start position:0%
+because I was pressured by Anna's
+continuous verbal demands or something
+
+ align:start position:0%
+continuous verbal demands or something
+ 
+
+ align:start position:0%
+continuous verbal demands or something
+like that to do this
+
+ align:start position:0%
+like that to do this
+ 
+
+ align:start position:0%
+like that to do this
+um you know I can make the case that
+
+ align:start position:0%
+um you know I can make the case that
+ 
+
+ align:start position:0%
+um you know I can make the case that
+that it was her demands that made me do
+
+ align:start position:0%
+that it was her demands that made me do
+ 
+
+ align:start position:0%
+that it was her demands that made me do
+this but I'm still going to jail it's
+
+ align:start position:0%
+this but I'm still going to jail it's
+ 
+
+ align:start position:0%
+this but I'm still going to jail it's
+not it doesn't explain away my behavior
+
+ align:start position:0%
+not it doesn't explain away my behavior
+ 
+
+ align:start position:0%
+not it doesn't explain away my behavior
+sexual sexual relations are
+
+ align:start position:0%
+sexual sexual relations are
+ 
+
+ align:start position:0%
+sexual sexual relations are
+interestingly different from other
+
+ align:start position:0%
+interestingly different from other
+ 
+
+ align:start position:0%
+interestingly different from other
+relations in that way
+
+ align:start position:0%
+relations in that way
+ 
+
+ align:start position:0%
+relations in that way
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and okay we'll pick up on on at our last
+
+ align:start position:0%
+and okay we'll pick up on on at our last
+ 
+
+ align:start position:0%
+and okay we'll pick up on on at our last
+meeting on on how this all comes to pass
\ No newline at end of file
diff --git a/FJCVSswFXyE.txt b/FJCVSswFXyE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2e37c68eaf7a945d00c7fcf86a526454fdc16b44
--- /dev/null
+++ b/FJCVSswFXyE.txt
@@ -0,0 +1,7067 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so uh Collective knowledge
+
+ align:start position:0%
+ocw.mit.edu so uh Collective knowledge
+ 
+
+ align:start position:0%
+ocw.mit.edu so uh Collective knowledge
+got us a bunch more
+
+ align:start position:0%
+got us a bunch more
+ 
+
+ align:start position:0%
+got us a bunch more
+points so these uh the rules for
+
+ align:start position:0%
+points so these uh the rules for
+ 
+
+ align:start position:0%
+points so these uh the rules for
+significant figures are on the back page
+
+ align:start position:0%
+significant figures are on the back page
+ 
+
+ align:start position:0%
+significant figures are on the back page
+of the handout from Friday and so we
+
+ align:start position:0%
+of the handout from Friday and so we
+ 
+
+ align:start position:0%
+of the handout from Friday and so we
+want to think about how many are after
+
+ align:start position:0%
+want to think about how many are after
+ 
+
+ align:start position:0%
+want to think about how many are after
+the decimal point here so there are
+
+ align:start position:0%
+the decimal point here so there are
+ 
+
+ align:start position:0%
+the decimal point here so there are
+three after the decimal point which
+
+ align:start position:0%
+three after the decimal point which
+ 
+
+ align:start position:0%
+three after the decimal point which
+gives you three here in your answer log
+
+ align:start position:0%
+gives you three here in your answer log
+ 
+
+ align:start position:0%
+gives you three here in your answer log
+significant figure rules yes so in acid
+
+ align:start position:0%
+significant figure rules yes so in acid
+ 
+
+ align:start position:0%
+significant figure rules yes so in acid
+base and some in chemical equilibrium
+
+ align:start position:0%
+base and some in chemical equilibrium
+ 
+
+ align:start position:0%
+base and some in chemical equilibrium
+which are all kind of the same thing you
+
+ align:start position:0%
+which are all kind of the same thing you
+ 
+
+ align:start position:0%
+which are all kind of the same thing you
+can have
+
+ align:start position:0%
+can have
+ 
+
+ align:start position:0%
+can have
+subtraction and
+
+ align:start position:0%
+subtraction and
+ 
+
+ align:start position:0%
+subtraction and
+addition then multiplication and
+
+ align:start position:0%
+addition then multiplication and
+ 
+
+ align:start position:0%
+addition then multiplication and
+division and then end your answer with
+
+ align:start position:0%
+division and then end your answer with
+ 
+
+ align:start position:0%
+division and then end your answer with
+logs three significant figure rules in
+
+ align:start position:0%
+logs three significant figure rules in
+ 
+
+ align:start position:0%
+logs three significant figure rules in
+one problem yes it's coming so uh want
+
+ align:start position:0%
+one problem yes it's coming so uh want
+ 
+
+ align:start position:0%
+one problem yes it's coming so uh want
+to get get those get those rules
+
+ align:start position:0%
+to get get those get those rules
+ 
+
+ align:start position:0%
+to get get those get those rules
+down okay so today we're going to talk
+
+ align:start position:0%
+down okay so today we're going to talk
+ 
+
+ align:start position:0%
+down okay so today we're going to talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+solubility and this is really a direct
+
+ align:start position:0%
+solubility and this is really a direct
+ 
+
+ align:start position:0%
+solubility and this is really a direct
+kind of uh growth out of thermodynamics
+
+ align:start position:0%
+kind of uh growth out of thermodynamics
+ 
+
+ align:start position:0%
+kind of uh growth out of thermodynamics
+and chemical equilibrium you're going to
+
+ align:start position:0%
+and chemical equilibrium you're going to
+ 
+
+ align:start position:0%
+and chemical equilibrium you're going to
+be seeing a lot of the same ideas in
+
+ align:start position:0%
+be seeing a lot of the same ideas in
+ 
+
+ align:start position:0%
+be seeing a lot of the same ideas in
+solubility and then at the end of the
+
+ align:start position:0%
+solubility and then at the end of the
+ 
+
+ align:start position:0%
+solubility and then at the end of the
+class we're going to start acid bases
+
+ align:start position:0%
+class we're going to start acid bases
+ 
+
+ align:start position:0%
+class we're going to start acid bases
+okay so so far we have been discussing
+
+ align:start position:0%
+okay so so far we have been discussing
+ 
+
+ align:start position:0%
+okay so so far we have been discussing
+mostly pure substances and that is all
+
+ align:start position:0%
+mostly pure substances and that is all
+ 
+
+ align:start position:0%
+mostly pure substances and that is all
+changing right now because most
+
+ align:start position:0%
+changing right now because most
+ 
+
+ align:start position:0%
+changing right now because most
+substances are actually mixtures so most
+
+ align:start position:0%
+substances are actually mixtures so most
+ 
+
+ align:start position:0%
+substances are actually mixtures so most
+of the time you have two things mixed
+
+ align:start position:0%
+of the time you have two things mixed
+ 
+
+ align:start position:0%
+of the time you have two things mixed
+together so so mixtures you have a
+
+ align:start position:0%
+together so so mixtures you have a
+ 
+
+ align:start position:0%
+together so so mixtures you have a
+homogeneous mixture of something
+
+ align:start position:0%
+homogeneous mixture of something
+ 
+
+ align:start position:0%
+homogeneous mixture of something
+something's dissolved in something
+
+ align:start position:0%
+something's dissolved in something
+ 
+
+ align:start position:0%
+something's dissolved in something
+else and and you have a or solution is a
+
+ align:start position:0%
+else and and you have a or solution is a
+ 
+
+ align:start position:0%
+else and and you have a or solution is a
+homogeneous
+
+ align:start position:0%
+homogeneous
+ 
+
+ align:start position:0%
+homogeneous
+mixture um and so in your solution you
+
+ align:start position:0%
+mixture um and so in your solution you
+ 
+
+ align:start position:0%
+mixture um and so in your solution you
+have a solvent which is the thing that
+
+ align:start position:0%
+have a solvent which is the thing that
+ 
+
+ align:start position:0%
+have a solvent which is the thing that
+is dissolving the other thing and the
+
+ align:start position:0%
+is dissolving the other thing and the
+ 
+
+ align:start position:0%
+is dissolving the other thing and the
+other thing is the solute so the solute
+
+ align:start position:0%
+other thing is the solute so the solute
+ 
+
+ align:start position:0%
+other thing is the solute so the solute
+is any dissolved substance in a solution
+
+ align:start position:0%
+is any dissolved substance in a solution
+ 
+
+ align:start position:0%
+is any dissolved substance in a solution
+and the solvent is the substance that
+
+ align:start position:0%
+and the solvent is the substance that
+ 
+
+ align:start position:0%
+and the solvent is the substance that
+does the dissolving and water is a great
+
+ align:start position:0%
+does the dissolving and water is a great
+ 
+
+ align:start position:0%
+does the dissolving and water is a great
+solvent one of the most common solvents
+
+ align:start position:0%
+solvent one of the most common solvents
+ 
+
+ align:start position:0%
+solvent one of the most common solvents
+is water so when you have your salute in
+
+ align:start position:0%
+is water so when you have your salute in
+ 
+
+ align:start position:0%
+is water so when you have your salute in
+your solvent and it's nicely dissolved
+
+ align:start position:0%
+your solvent and it's nicely dissolved
+ 
+
+ align:start position:0%
+your solvent and it's nicely dissolved
+then you have a solution so let's look
+
+ align:start position:0%
+then you have a solution so let's look
+ 
+
+ align:start position:0%
+then you have a solution so let's look
+at examples of things that dissolve in
+
+ align:start position:0%
+at examples of things that dissolve in
+ 
+
+ align:start position:0%
+at examples of things that dissolve in
+other things and first we're going to
+
+ align:start position:0%
+other things and first we're going to
+ 
+
+ align:start position:0%
+other things and first we're going to
+talk about NAC common table salt
+
+ align:start position:0%
+talk about NAC common table salt
+ 
+
+ align:start position:0%
+talk about NAC common table salt
+dissolving in water so NAC is held
+
+ align:start position:0%
+dissolving in water so NAC is held
+ 
+
+ align:start position:0%
+dissolving in water so NAC is held
+together by an ionic bond and it forms
+
+ align:start position:0%
+together by an ionic bond and it forms
+ 
+
+ align:start position:0%
+together by an ionic bond and it forms
+crystals where we have these beautiful
+
+ align:start position:0%
+crystals where we have these beautiful
+ 
+
+ align:start position:0%
+crystals where we have these beautiful
+arrangement of our
+
+ align:start position:0%
+arrangement of our
+ 
+
+ align:start position:0%
+arrangement of our
+sodium plus and our CL
+
+ align:start position:0%
+sodium plus and our CL
+ 
+
+ align:start position:0%
+sodium plus and our CL
+minus and a polar solvent like water
+
+ align:start position:0%
+minus and a polar solvent like water
+ 
+
+ align:start position:0%
+minus and a polar solvent like water
+will what's called hydrate the ions and
+
+ align:start position:0%
+will what's called hydrate the ions and
+ 
+
+ align:start position:0%
+will what's called hydrate the ions and
+pry them away from the surface so if we
+
+ align:start position:0%
+pry them away from the surface so if we
+ 
+
+ align:start position:0%
+pry them away from the surface so if we
+look at this picture and we have our
+
+ align:start position:0%
+look at this picture and we have our
+ 
+
+ align:start position:0%
+look at this picture and we have our
+sodium and our chlorides around it in
+
+ align:start position:0%
+sodium and our chlorides around it in
+ 
+
+ align:start position:0%
+sodium and our chlorides around it in
+our salt crystal we have water which is
+
+ align:start position:0%
+our salt crystal we have water which is
+ 
+
+ align:start position:0%
+our salt crystal we have water which is
+red with those two little white dots
+
+ align:start position:0%
+red with those two little white dots
+ 
+
+ align:start position:0%
+red with those two little white dots
+which are the hydrogens on the water and
+
+ align:start position:0%
+which are the hydrogens on the water and
+ 
+
+ align:start position:0%
+which are the hydrogens on the water and
+so we have our bent uh geometry for our
+
+ align:start position:0%
+so we have our bent uh geometry for our
+ 
+
+ align:start position:0%
+so we have our bent uh geometry for our
+polar water molecule and the water is
+
+ align:start position:0%
+polar water molecule and the water is
+ 
+
+ align:start position:0%
+polar water molecule and the water is
+coming in and it's hydrating the ions
+
+ align:start position:0%
+coming in and it's hydrating the ions
+ 
+
+ align:start position:0%
+coming in and it's hydrating the ions
+and so here you see the edge of the salt
+
+ align:start position:0%
+and so here you see the edge of the salt
+ 
+
+ align:start position:0%
+and so here you see the edge of the salt
+crystal and now the water is kind of
+
+ align:start position:0%
+crystal and now the water is kind of
+ 
+
+ align:start position:0%
+crystal and now the water is kind of
+pulling one of the the ions apart and
+
+ align:start position:0%
+pulling one of the the ions apart and
+ 
+
+ align:start position:0%
+pulling one of the the ions apart and
+here you see the ions are coming out of
+
+ align:start position:0%
+here you see the ions are coming out of
+ 
+
+ align:start position:0%
+here you see the ions are coming out of
+the salt crystal and dissolving in your
+
+ align:start position:0%
+the salt crystal and dissolving in your
+ 
+
+ align:start position:0%
+the salt crystal and dissolving in your
+solution so a polar uh solvent like
+
+ align:start position:0%
+solution so a polar uh solvent like
+ 
+
+ align:start position:0%
+solution so a polar uh solvent like
+water can just pry that uh Crystal
+
+ align:start position:0%
+water can just pry that uh Crystal
+ 
+
+ align:start position:0%
+water can just pry that uh Crystal
+apart so stirring can speed up this
+
+ align:start position:0%
+apart so stirring can speed up this
+ 
+
+ align:start position:0%
+apart so stirring can speed up this
+process it doesn't often change uh the
+
+ align:start position:0%
+process it doesn't often change uh the
+ 
+
+ align:start position:0%
+process it doesn't often change uh the
+properties it doesn't make things more
+
+ align:start position:0%
+properties it doesn't make things more
+ 
+
+ align:start position:0%
+properties it doesn't make things more
+soluble but it'll speed it up because if
+
+ align:start position:0%
+soluble but it'll speed it up because if
+ 
+
+ align:start position:0%
+soluble but it'll speed it up because if
+you stir it you're going to get more of
+
+ align:start position:0%
+you stir it you're going to get more of
+ 
+
+ align:start position:0%
+you stir it you're going to get more of
+that water having access to the edges of
+
+ align:start position:0%
+that water having access to the edges of
+ 
+
+ align:start position:0%
+that water having access to the edges of
+the salt crystals and helping to to pry
+
+ align:start position:0%
+the salt crystals and helping to to pry
+ 
+
+ align:start position:0%
+the salt crystals and helping to to pry
+apart um and hydrate those ions so that
+
+ align:start position:0%
+apart um and hydrate those ions so that
+ 
+
+ align:start position:0%
+apart um and hydrate those ions so that
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+solubilize we have uh an equilibrium
+
+ align:start position:0%
+solubilize we have uh an equilibrium
+ 
+
+ align:start position:0%
+solubilize we have uh an equilibrium
+expression for solubility so we're just
+
+ align:start position:0%
+expression for solubility so we're just
+ 
+
+ align:start position:0%
+expression for solubility so we're just
+following right along with chemical
+
+ align:start position:0%
+following right along with chemical
+ 
+
+ align:start position:0%
+following right along with chemical
+equilibrium and so we have our solid NAC
+
+ align:start position:0%
+equilibrium and so we have our solid NAC
+ 
+
+ align:start position:0%
+equilibrium and so we have our solid NAC
+going to our hydrated ions are our na+
+
+ align:start position:0%
+going to our hydrated ions are our na+
+ 
+
+ align:start position:0%
+going to our hydrated ions are our na+
+that was pulled out by water and our CL
+
+ align:start position:0%
+that was pulled out by water and our CL
+ 
+
+ align:start position:0%
+that was pulled out by water and our CL
+minus and this in here it says aous
+
+ align:start position:0%
+minus and this in here it says aous
+ 
+
+ align:start position:0%
+minus and this in here it says aous
+abbreviation from aquous so we have our
+
+ align:start position:0%
+abbreviation from aquous so we have our
+ 
+
+ align:start position:0%
+abbreviation from aquous so we have our
+dissolved ions that's how we would
+
+ align:start position:0%
+dissolved ions that's how we would
+ 
+
+ align:start position:0%
+dissolved ions that's how we would
+interpret that and S here is for um
+
+ align:start position:0%
+interpret that and S here is for um
+ 
+
+ align:start position:0%
+interpret that and S here is for um
+solid so we've also not paid much
+
+ align:start position:0%
+solid so we've also not paid much
+ 
+
+ align:start position:0%
+solid so we've also not paid much
+attention to phase of things at this
+
+ align:start position:0%
+attention to phase of things at this
+ 
+
+ align:start position:0%
+attention to phase of things at this
+point a little bit when we were talking
+
+ align:start position:0%
+point a little bit when we were talking
+ 
+
+ align:start position:0%
+point a little bit when we were talking
+about increasing entropy we're talking
+
+ align:start position:0%
+about increasing entropy we're talking
+ 
+
+ align:start position:0%
+about increasing entropy we're talking
+about gases going to liquids and solids
+
+ align:start position:0%
+about gases going to liquids and solids
+ 
+
+ align:start position:0%
+about gases going to liquids and solids
+and vice versa and predicting the uh
+
+ align:start position:0%
+and vice versa and predicting the uh
+ 
+
+ align:start position:0%
+and vice versa and predicting the uh
+change in in uh entropy for those
+
+ align:start position:0%
+change in in uh entropy for those
+ 
+
+ align:start position:0%
+change in in uh entropy for those
+processes but now we're going to spend a
+
+ align:start position:0%
+processes but now we're going to spend a
+ 
+
+ align:start position:0%
+processes but now we're going to spend a
+lot of time paying attention to the
+
+ align:start position:0%
+lot of time paying attention to the
+ 
+
+ align:start position:0%
+lot of time paying attention to the
+phase um and so solubility something
+
+ align:start position:0%
+phase um and so solubility something
+ 
+
+ align:start position:0%
+phase um and so solubility something
+solid going to its aquous ions so we can
+
+ align:start position:0%
+solid going to its aquous ions so we can
+ 
+
+ align:start position:0%
+solid going to its aquous ions so we can
+write an equilibrium expression for this
+
+ align:start position:0%
+write an equilibrium expression for this
+ 
+
+ align:start position:0%
+write an equilibrium expression for this
+and it has a special name KSP where SP
+
+ align:start position:0%
+and it has a special name KSP where SP
+ 
+
+ align:start position:0%
+and it has a special name KSP where SP
+stands for solubility product and so KSP
+
+ align:start position:0%
+stands for solubility product and so KSP
+ 
+
+ align:start position:0%
+stands for solubility product and so KSP
+would be equal to the concentration of
+
+ align:start position:0%
+would be equal to the concentration of
+ 
+
+ align:start position:0%
+would be equal to the concentration of
+sodium ions and the concentration of CHL
+
+ align:start position:0%
+sodium ions and the concentration of CHL
+ 
+
+ align:start position:0%
+sodium ions and the concentration of CHL
+times the concentration of chloride ions
+
+ align:start position:0%
+times the concentration of chloride ions
+ 
+
+ align:start position:0%
+times the concentration of chloride ions
+and so and equilibrium constants are
+
+ align:start position:0%
+and so and equilibrium constants are
+ 
+
+ align:start position:0%
+and so and equilibrium constants are
+products over reactants we don't have
+
+ align:start position:0%
+products over reactants we don't have
+ 
+
+ align:start position:0%
+products over reactants we don't have
+our reactant in this equation because it
+
+ align:start position:0%
+our reactant in this equation because it
+ 
+
+ align:start position:0%
+our reactant in this equation because it
+is a solid so it doesn't appear um in
+
+ align:start position:0%
+is a solid so it doesn't appear um in
+ 
+
+ align:start position:0%
+is a solid so it doesn't appear um in
+the equilibrium expression so our
+
+ align:start position:0%
+the equilibrium expression so our
+ 
+
+ align:start position:0%
+the equilibrium expression so our
+equilibrium expression which here has
+
+ align:start position:0%
+equilibrium expression which here has
+ 
+
+ align:start position:0%
+equilibrium expression which here has
+the SE special name of KSP um is just
+
+ align:start position:0%
+the SE special name of KSP um is just
+ 
+
+ align:start position:0%
+the SE special name of KSP um is just
+those ions in solution the concentration
+
+ align:start position:0%
+those ions in solution the concentration
+ 
+
+ align:start position:0%
+those ions in solution the concentration
+of each ion times each other all right
+
+ align:start position:0%
+of each ion times each other all right
+ 
+
+ align:start position:0%
+of each ion times each other all right
+so let's have a little practice with
+
+ align:start position:0%
+so let's have a little practice with
+ 
+
+ align:start position:0%
+so let's have a little practice with
+writing KSP P's and so we have a clicker
+
+ align:start position:0%
+writing KSP P's and so we have a clicker
+ 
+
+ align:start position:0%
+writing KSP P's and so we have a clicker
+question on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great yep so again we don't want to have
+
+ align:start position:0%
+great yep so again we don't want to have
+ 
+
+ align:start position:0%
+great yep so again we don't want to have
+the solid in the expression and we need
+
+ align:start position:0%
+the solid in the expression and we need
+ 
+
+ align:start position:0%
+the solid in the expression and we need
+to remember the stochiometry always need
+
+ align:start position:0%
+to remember the stochiometry always need
+ 
+
+ align:start position:0%
+to remember the stochiometry always need
+to remember the
+
+ align:start position:0%
+to remember the
+ 
+
+ align:start position:0%
+to remember the
+stochiometry okay so their
+
+ align:start position:0%
+stochiometry okay so their
+ 
+
+ align:start position:0%
+stochiometry okay so their
+solubility uh
+
+ align:start position:0%
+solubility uh
+ 
+
+ align:start position:0%
+solubility uh
+product okay so now let's think about
+
+ align:start position:0%
+product okay so now let's think about
+ 
+
+ align:start position:0%
+product okay so now let's think about
+something that is not ionic let's think
+
+ align:start position:0%
+something that is not ionic let's think
+ 
+
+ align:start position:0%
+something that is not ionic let's think
+about glucose
+
+ align:start position:0%
+about glucose
+ 
+
+ align:start position:0%
+about glucose
+we've talked a lot about glucose let's
+
+ align:start position:0%
+we've talked a lot about glucose let's
+ 
+
+ align:start position:0%
+we've talked a lot about glucose let's
+think about glucose dissolving in water
+
+ align:start position:0%
+think about glucose dissolving in water
+ 
+
+ align:start position:0%
+think about glucose dissolving in water
+and here I have a picture of two beakers
+
+ align:start position:0%
+and here I have a picture of two beakers
+ 
+
+ align:start position:0%
+and here I have a picture of two beakers
+a beaker where it's clear and a beaker
+
+ align:start position:0%
+a beaker where it's clear and a beaker
+ 
+
+ align:start position:0%
+a beaker where it's clear and a beaker
+where there's a lot of glucose sitting
+
+ align:start position:0%
+where there's a lot of glucose sitting
+ 
+
+ align:start position:0%
+where there's a lot of glucose sitting
+on the bottom and so we can think about
+
+ align:start position:0%
+on the bottom and so we can think about
+ 
+
+ align:start position:0%
+on the bottom and so we can think about
+the solubility here so how can this
+
+ align:start position:0%
+the solubility here so how can this
+ 
+
+ align:start position:0%
+the solubility here so how can this
+dissolve it can't form ions it's not
+
+ align:start position:0%
+dissolve it can't form ions it's not
+ 
+
+ align:start position:0%
+dissolve it can't form ions it's not
+made up of ions like sodium chloride so
+
+ align:start position:0%
+made up of ions like sodium chloride so
+ 
+
+ align:start position:0%
+made up of ions like sodium chloride so
+how does it dissolve well it can
+
+ align:start position:0%
+how does it dissolve well it can
+ 
+
+ align:start position:0%
+how does it dissolve well it can
+dissolve again water molecules water is
+
+ align:start position:0%
+dissolve again water molecules water is
+ 
+
+ align:start position:0%
+dissolve again water molecules water is
+amazing water molecules form hydrogen
+
+ align:start position:0%
+amazing water molecules form hydrogen
+ 
+
+ align:start position:0%
+amazing water molecules form hydrogen
+bonds with the glucose and pull one of
+
+ align:start position:0%
+bonds with the glucose and pull one of
+ 
+
+ align:start position:0%
+bonds with the glucose and pull one of
+the glucose molecules that is at the
+
+ align:start position:0%
+the glucose molecules that is at the
+ 
+
+ align:start position:0%
+the glucose molecules that is at the
+edge of the solid piece of glucose pulls
+
+ align:start position:0%
+edge of the solid piece of glucose pulls
+ 
+
+ align:start position:0%
+edge of the solid piece of glucose pulls
+it out into Solution by hydrogen bonding
+
+ align:start position:0%
+it out into Solution by hydrogen bonding
+ 
+
+ align:start position:0%
+it out into Solution by hydrogen bonding
+to it so again it's solubilizing the
+
+ align:start position:0%
+to it so again it's solubilizing the
+ 
+
+ align:start position:0%
+to it so again it's solubilizing the
+glucose that's in this solid form by
+
+ align:start position:0%
+glucose that's in this solid form by
+ 
+
+ align:start position:0%
+glucose that's in this solid form by
+interacting at the surface and prying
+
+ align:start position:0%
+interacting at the surface and prying
+ 
+
+ align:start position:0%
+interacting at the surface and prying
+layers of glucose molecules off by
+
+ align:start position:0%
+layers of glucose molecules off by
+ 
+
+ align:start position:0%
+layers of glucose molecules off by
+hydrogen bonding to them luckily you
+
+ align:start position:0%
+hydrogen bonding to them luckily you
+ 
+
+ align:start position:0%
+hydrogen bonding to them luckily you
+know all about hydrogen bond so just to
+
+ align:start position:0%
+know all about hydrogen bond so just to
+ 
+
+ align:start position:0%
+know all about hydrogen bond so just to
+do a little clicker practice um why
+
+ align:start position:0%
+do a little clicker practice um why
+ 
+
+ align:start position:0%
+do a little clicker practice um why
+don't you tell me what kind of hydro
+
+ align:start position:0%
+don't you tell me what kind of hydro
+ 
+
+ align:start position:0%
+don't you tell me what kind of hydro
+bonds glucose is capable of forming if
+
+ align:start position:0%
+bonds glucose is capable of forming if
+ 
+
+ align:start position:0%
+bonds glucose is capable of forming if
+it is in fact capable of forming but I
+
+ align:start position:0%
+it is in fact capable of forming but I
+ 
+
+ align:start position:0%
+it is in fact capable of forming but I
+kind of gave away one of the answers
+
+ align:start position:0%
+kind of gave away one of the answers
+ 
+
+ align:start position:0%
+kind of gave away one of the answers
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all right good zero put four
+
+ align:start position:0%
+seconds all right good zero put four
+ 
+
+ align:start position:0%
+seconds all right good zero put four
+that's awesome you were listening to
+
+ align:start position:0%
+that's awesome you were listening to
+ 
+
+ align:start position:0%
+that's awesome you were listening to
+what I was saying um yes so that is
+
+ align:start position:0%
+what I was saying um yes so that is
+ 
+
+ align:start position:0%
+what I was saying um yes so that is
+correct and uh if we uh look back at the
+
+ align:start position:0%
+correct and uh if we uh look back at the
+ 
+
+ align:start position:0%
+correct and uh if we uh look back at the
+molecule for a minute so it's a hydrogen
+
+ align:start position:0%
+molecule for a minute so it's a hydrogen
+ 
+
+ align:start position:0%
+molecule for a minute so it's a hydrogen
+bond donor because of these o groups all
+
+ align:start position:0%
+bond donor because of these o groups all
+ 
+
+ align:start position:0%
+bond donor because of these o groups all
+along here and so o there's an electron
+
+ align:start position:0%
+along here and so o there's an electron
+ 
+
+ align:start position:0%
+along here and so o there's an electron
+negativity difference of greater than 04
+
+ align:start position:0%
+negativity difference of greater than 04
+ 
+
+ align:start position:0%
+negativity difference of greater than 04
+so it's capable of being a hydrogen bond
+
+ align:start position:0%
+so it's capable of being a hydrogen bond
+ 
+
+ align:start position:0%
+so it's capable of being a hydrogen bond
+donor but this double bonded o here it's
+
+ align:start position:0%
+donor but this double bonded o here it's
+ 
+
+ align:start position:0%
+donor but this double bonded o here it's
+not a complete Lew structure it's
+
+ align:start position:0%
+not a complete Lew structure it's
+ 
+
+ align:start position:0%
+not a complete Lew structure it's
+missing its lone pairs but it has lone
+
+ align:start position:0%
+missing its lone pairs but it has lone
+ 
+
+ align:start position:0%
+missing its lone pairs but it has lone
+pairs on that oxygen and that could be a
+
+ align:start position:0%
+pairs on that oxygen and that could be a
+ 
+
+ align:start position:0%
+pairs on that oxygen and that could be a
+hydrogen bond acceptor so we have
+
+ align:start position:0%
+hydrogen bond acceptor so we have
+ 
+
+ align:start position:0%
+hydrogen bond acceptor so we have
+hydrogen bond donors and hydrogen bond
+
+ align:start position:0%
+hydrogen bond donors and hydrogen bond
+ 
+
+ align:start position:0%
+hydrogen bond donors and hydrogen bond
+acceptors in this molecule and water can
+
+ align:start position:0%
+acceptors in this molecule and water can
+ 
+
+ align:start position:0%
+acceptors in this molecule and water can
+also be a hydrogen bond donor and
+
+ align:start position:0%
+also be a hydrogen bond donor and
+ 
+
+ align:start position:0%
+also be a hydrogen bond donor and
+acceptor it has two Hy two um hydrogens
+
+ align:start position:0%
+acceptor it has two Hy two um hydrogens
+ 
+
+ align:start position:0%
+acceptor it has two Hy two um hydrogens
+that can form hydrogen bond and also has
+
+ align:start position:0%
+that can form hydrogen bond and also has
+ 
+
+ align:start position:0%
+that can form hydrogen bond and also has
+two lone pairs which gives it its bent
+
+ align:start position:0%
+two lone pairs which gives it its bent
+ 
+
+ align:start position:0%
+two lone pairs which gives it its bent
+shape so it can be a donor and acceptor
+
+ align:start position:0%
+shape so it can be a donor and acceptor
+ 
+
+ align:start position:0%
+shape so it can be a donor and acceptor
+so it's capable of interacting with
+
+ align:start position:0%
+so it's capable of interacting with
+ 
+
+ align:start position:0%
+so it's capable of interacting with
+glucose and pulling that solid glucose
+
+ align:start position:0%
+glucose and pulling that solid glucose
+ 
+
+ align:start position:0%
+glucose and pulling that solid glucose
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+solution so if we look at these two
+
+ align:start position:0%
+solution so if we look at these two
+ 
+
+ align:start position:0%
+solution so if we look at these two
+pictures this could be glucose nicely in
+
+ align:start position:0%
+pictures this could be glucose nicely in
+ 
+
+ align:start position:0%
+pictures this could be glucose nicely in
+solution you can't see any glucose but
+
+ align:start position:0%
+solution you can't see any glucose but
+ 
+
+ align:start position:0%
+solution you can't see any glucose but
+here you see a level of glucose at the
+
+ align:start position:0%
+here you see a level of glucose at the
+ 
+
+ align:start position:0%
+here you see a level of glucose at the
+bottom and a solution is considered
+
+ align:start position:0%
+bottom and a solution is considered
+ 
+
+ align:start position:0%
+bottom and a solution is considered
+saturated when all of the solvent has
+
+ align:start position:0%
+saturated when all of the solvent has
+ 
+
+ align:start position:0%
+saturated when all of the solvent has
+dissolved as much as it can but a little
+
+ align:start position:0%
+dissolved as much as it can but a little
+ 
+
+ align:start position:0%
+dissolved as much as it can but a little
+bit of undissolved solute remains so
+
+ align:start position:0%
+bit of undissolved solute remains so
+ 
+
+ align:start position:0%
+bit of undissolved solute remains so
+this this is not really this is
+
+ align:start position:0%
+this this is not really this is
+ 
+
+ align:start position:0%
+this this is not really this is
+oversaturated um often it's just
+
+ align:start position:0%
+oversaturated um often it's just
+ 
+
+ align:start position:0%
+oversaturated um often it's just
+saturated when you have just a little
+
+ align:start position:0%
+saturated when you have just a little
+ 
+
+ align:start position:0%
+saturated when you have just a little
+bit more than can be dissolved you've
+
+ align:start position:0%
+bit more than can be dissolved you've
+ 
+
+ align:start position:0%
+bit more than can be dissolved you've
+gone past that point you can't get any
+
+ align:start position:0%
+gone past that point you can't get any
+ 
+
+ align:start position:0%
+gone past that point you can't get any
+more dissolved in that volume of water
+
+ align:start position:0%
+more dissolved in that volume of water
+ 
+
+ align:start position:0%
+more dissolved in that volume of water
+this has a pretty large excess so
+
+ align:start position:0%
+this has a pretty large excess so
+ 
+
+ align:start position:0%
+this has a pretty large excess so
+sometimes when you you get your solution
+
+ align:start position:0%
+sometimes when you you get your solution
+ 
+
+ align:start position:0%
+sometimes when you you get your solution
+you get your solution clear your um
+
+ align:start position:0%
+you get your solution clear your um
+ 
+
+ align:start position:0%
+you get your solution clear your um
+glucose has dissolved or whatever it is
+
+ align:start position:0%
+glucose has dissolved or whatever it is
+ 
+
+ align:start position:0%
+glucose has dissolved or whatever it is
+you're working on has dissolved and then
+
+ align:start position:0%
+you're working on has dissolved and then
+ 
+
+ align:start position:0%
+you're working on has dissolved and then
+you maybe add a little bit too much and
+
+ align:start position:0%
+you maybe add a little bit too much and
+ 
+
+ align:start position:0%
+you maybe add a little bit too much and
+it all crashes out a solution again you
+
+ align:start position:0%
+it all crashes out a solution again you
+ 
+
+ align:start position:0%
+it all crashes out a solution again you
+have the precipitant just coming out so
+
+ align:start position:0%
+have the precipitant just coming out so
+ 
+
+ align:start position:0%
+have the precipitant just coming out so
+undissolved solute another name for that
+
+ align:start position:0%
+undissolved solute another name for that
+ 
+
+ align:start position:0%
+undissolved solute another name for that
+the name that's used more often is
+
+ align:start position:0%
+the name that's used more often is
+ 
+
+ align:start position:0%
+the name that's used more often is
+precipitate so it precipitates out of
+
+ align:start position:0%
+precipitate so it precipitates out of
+ 
+
+ align:start position:0%
+precipitate so it precipitates out of
+solution if it has too much in it so if
+
+ align:start position:0%
+solution if it has too much in it so if
+ 
+
+ align:start position:0%
+solution if it has too much in it so if
+you are not part of the solution you are
+
+ align:start position:0%
+you are not part of the solution you are
+ 
+
+ align:start position:0%
+you are not part of the solution you are
+part of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precipitate that's my t-shirt
+
+ align:start position:0%
+precipitate that's my t-shirt
+ 
+
+ align:start position:0%
+precipitate that's my t-shirt
+no okay so dissolved and undissolved
+
+ align:start position:0%
+no okay so dissolved and undissolved
+ 
+
+ align:start position:0%
+no okay so dissolved and undissolved
+solute they're not doing nothing they're
+
+ align:start position:0%
+solute they're not doing nothing they're
+ 
+
+ align:start position:0%
+solute they're not doing nothing they're
+in dynamic equilibrium just like all
+
+ align:start position:0%
+in dynamic equilibrium just like all
+ 
+
+ align:start position:0%
+in dynamic equilibrium just like all
+other kind of chemical equilibrium
+
+ align:start position:0%
+other kind of chemical equilibrium
+ 
+
+ align:start position:0%
+other kind of chemical equilibrium
+there's no net change but the process is
+
+ align:start position:0%
+there's no net change but the process is
+ 
+
+ align:start position:0%
+there's no net change but the process is
+still going forward and back in fact the
+
+ align:start position:0%
+still going forward and back in fact the
+ 
+
+ align:start position:0%
+still going forward and back in fact the
+rate going forward is equal to the rate
+
+ align:start position:0%
+rate going forward is equal to the rate
+ 
+
+ align:start position:0%
+rate going forward is equal to the rate
+going back the same is true here the
+
+ align:start position:0%
+going back the same is true here the
+ 
+
+ align:start position:0%
+going back the same is true here the
+dissolved and undissolved
+
+ align:start position:0%
+dissolved and undissolved
+ 
+
+ align:start position:0%
+dissolved and undissolved
+um solute are in dynamic equilibrium
+
+ align:start position:0%
+um solute are in dynamic equilibrium
+ 
+
+ align:start position:0%
+um solute are in dynamic equilibrium
+with each
+
+ align:start position:0%
+with each
+ 
+
+ align:start position:0%
+with each
+other so how much can you get in there
+
+ align:start position:0%
+other so how much can you get in there
+ 
+
+ align:start position:0%
+other so how much can you get in there
+how much solute can you get into your
+
+ align:start position:0%
+how much solute can you get into your
+ 
+
+ align:start position:0%
+how much solute can you get into your
+solvent and that depends on the
+
+ align:start position:0%
+solvent and that depends on the
+ 
+
+ align:start position:0%
+solvent and that depends on the
+particular substance and its molar
+
+ align:start position:0%
+particular substance and its molar
+ 
+
+ align:start position:0%
+particular substance and its molar
+solubility and Molar solubility is
+
+ align:start position:0%
+solubility and Molar solubility is
+ 
+
+ align:start position:0%
+solubility and Molar solubility is
+defined as s either little s or big S I
+
+ align:start position:0%
+defined as s either little s or big S I
+ 
+
+ align:start position:0%
+defined as s either little s or big S I
+seen it both ways in textbooks um so the
+
+ align:start position:0%
+seen it both ways in textbooks um so the
+ 
+
+ align:start position:0%
+seen it both ways in textbooks um so the
+molar solubility s is the molar
+
+ align:start position:0%
+molar solubility s is the molar
+ 
+
+ align:start position:0%
+molar solubility s is the molar
+concentration in that saturated solution
+
+ align:start position:0%
+concentration in that saturated solution
+ 
+
+ align:start position:0%
+concentration in that saturated solution
+where you've put just a little more in
+
+ align:start position:0%
+where you've put just a little more in
+ 
+
+ align:start position:0%
+where you've put just a little more in
+um than can be completely dissolved and
+
+ align:start position:0%
+um than can be completely dissolved and
+ 
+
+ align:start position:0%
+um than can be completely dissolved and
+so that represents the limit of the
+
+ align:start position:0%
+so that represents the limit of the
+ 
+
+ align:start position:0%
+so that represents the limit of the
+ability of that solvent to dissolve that
+
+ align:start position:0%
+ability of that solvent to dissolve that
+ 
+
+ align:start position:0%
+ability of that solvent to dissolve that
+solute that particular compound and its
+
+ align:start position:0%
+solute that particular compound and its
+ 
+
+ align:start position:0%
+solute that particular compound and its
+units are perhaps unsurprisingly given
+
+ align:start position:0%
+units are perhaps unsurprisingly given
+ 
+
+ align:start position:0%
+units are perhaps unsurprisingly given
+its name is molar moles per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liter so molar solubility is related to
+
+ align:start position:0%
+liter so molar solubility is related to
+ 
+
+ align:start position:0%
+liter so molar solubility is related to
+our friend KSP but it's not the same
+
+ align:start position:0%
+our friend KSP but it's not the same
+ 
+
+ align:start position:0%
+our friend KSP but it's not the same
+thing or at least most of the time I
+
+ align:start position:0%
+thing or at least most of the time I
+ 
+
+ align:start position:0%
+thing or at least most of the time I
+think none of the time exactly the same
+
+ align:start position:0%
+think none of the time exactly the same
+ 
+
+ align:start position:0%
+think none of the time exactly the same
+so when you're talking about the molar
+
+ align:start position:0%
+so when you're talking about the molar
+ 
+
+ align:start position:0%
+so when you're talking about the molar
+solubility of either ion you're talking
+
+ align:start position:0%
+solubility of either ion you're talking
+ 
+
+ align:start position:0%
+solubility of either ion you're talking
+about that concentration of sodium Plus
+
+ align:start position:0%
+about that concentration of sodium Plus
+ 
+
+ align:start position:0%
+about that concentration of sodium Plus
+or chlorine minus so you're talking
+
+ align:start position:0%
+or chlorine minus so you're talking
+ 
+
+ align:start position:0%
+or chlorine minus so you're talking
+about the moles per liter that can be
+
+ align:start position:0%
+about the moles per liter that can be
+ 
+
+ align:start position:0%
+about the moles per liter that can be
+dissolved in that particular amount of
+
+ align:start position:0%
+dissolved in that particular amount of
+ 
+
+ align:start position:0%
+dissolved in that particular amount of
+solvent or kind of solvent and so those
+
+ align:start position:0%
+solvent or kind of solvent and so those
+ 
+
+ align:start position:0%
+solvent or kind of solvent and so those
+concentrations are the molar solubility
+
+ align:start position:0%
+concentrations are the molar solubility
+ 
+
+ align:start position:0%
+concentrations are the molar solubility
+and again our KSP is going to be equal
+
+ align:start position:0%
+and again our KSP is going to be equal
+ 
+
+ align:start position:0%
+and again our KSP is going to be equal
+to the concentration of the sodium um in
+
+ align:start position:0%
+to the concentration of the sodium um in
+ 
+
+ align:start position:0%
+to the concentration of the sodium um in
+solution and the concentration of that
+
+ align:start position:0%
+solution and the concentration of that
+ 
+
+ align:start position:0%
+solution and the concentration of that
+chloride that's dissolved so in this
+
+ align:start position:0%
+chloride that's dissolved so in this
+ 
+
+ align:start position:0%
+chloride that's dissolved so in this
+case the relationship is that KSP would
+
+ align:start position:0%
+case the relationship is that KSP would
+ 
+
+ align:start position:0%
+case the relationship is that KSP would
+equal the molar solubility squared the
+
+ align:start position:0%
+equal the molar solubility squared the
+ 
+
+ align:start position:0%
+equal the molar solubility squared the
+molar solubility of this times the molar
+
+ align:start position:0%
+molar solubility of this times the molar
+ 
+
+ align:start position:0%
+molar solubility of this times the molar
+solubility of that so you can derive if
+
+ align:start position:0%
+solubility of that so you can derive if
+ 
+
+ align:start position:0%
+solubility of that so you can derive if
+you know one you can derive the other
+
+ align:start position:0%
+you know one you can derive the other
+ 
+
+ align:start position:0%
+you know one you can derive the other
+and you can do that on a problem set in
+
+ align:start position:0%
+and you can do that on a problem set in
+ 
+
+ align:start position:0%
+and you can do that on a problem set in
+particular so those are the definitions
+
+ align:start position:0%
+particular so those are the definitions
+ 
+
+ align:start position:0%
+particular so those are the definitions
+of those terms so molar solubility how
+
+ align:start position:0%
+of those terms so molar solubility how
+ 
+
+ align:start position:0%
+of those terms so molar solubility how
+much of something dissolves in another
+
+ align:start position:0%
+much of something dissolves in another
+ 
+
+ align:start position:0%
+much of something dissolves in another
+whether it dissolves at all will depend
+
+ align:start position:0%
+whether it dissolves at all will depend
+ 
+
+ align:start position:0%
+whether it dissolves at all will depend
+on again the nature of the material and
+
+ align:start position:0%
+on again the nature of the material and
+ 
+
+ align:start position:0%
+on again the nature of the material and
+the nature of the solvent are they
+
+ align:start position:0%
+the nature of the solvent are they
+ 
+
+ align:start position:0%
+the nature of the solvent are they
+missable do they is there a way like
+
+ align:start position:0%
+missable do they is there a way like
+ 
+
+ align:start position:0%
+missable do they is there a way like
+water getting in there um and forming
+
+ align:start position:0%
+water getting in there um and forming
+ 
+
+ align:start position:0%
+water getting in there um and forming
+hydrogen bonds for example and this
+
+ align:start position:0%
+hydrogen bonds for example and this
+ 
+
+ align:start position:0%
+hydrogen bonds for example and this
+leads to a rule that a lot of people um
+
+ align:start position:0%
+leads to a rule that a lot of people um
+ 
+
+ align:start position:0%
+leads to a rule that a lot of people um
+tend to know which is like dissolves
+
+ align:start position:0%
+tend to know which is like dissolves
+ 
+
+ align:start position:0%
+tend to know which is like dissolves
+like rule so if water if it's a non
+
+ align:start position:0%
+like rule so if water if it's a non
+ 
+
+ align:start position:0%
+like rule so if water if it's a non
+ionic substance and you need to uh pull
+
+ align:start position:0%
+ionic substance and you need to uh pull
+ 
+
+ align:start position:0%
+ionic substance and you need to uh pull
+it out of of the solid by hydrogen
+
+ align:start position:0%
+it out of of the solid by hydrogen
+ 
+
+ align:start position:0%
+it out of of the solid by hydrogen
+bonding if that material is nothing to
+
+ align:start position:0%
+bonding if that material is nothing to
+ 
+
+ align:start position:0%
+bonding if that material is nothing to
+hydrogen bond too if it's completely
+
+ align:start position:0%
+hydrogen bond too if it's completely
+ 
+
+ align:start position:0%
+hydrogen bond too if it's completely
+non-polar water's not going to be able
+
+ align:start position:0%
+non-polar water's not going to be able
+ 
+
+ align:start position:0%
+non-polar water's not going to be able
+to solubilize it so polar things polar
+
+ align:start position:0%
+to solubilize it so polar things polar
+ 
+
+ align:start position:0%
+to solubilize it so polar things polar
+liquids like water are generally the
+
+ align:start position:0%
+liquids like water are generally the
+ 
+
+ align:start position:0%
+liquids like water are generally the
+best solvents for things that are ionic
+
+ align:start position:0%
+best solvents for things that are ionic
+ 
+
+ align:start position:0%
+best solvents for things that are ionic
+like salts or polar compounds so it
+
+ align:start position:0%
+like salts or polar compounds so it
+ 
+
+ align:start position:0%
+like salts or polar compounds so it
+doesn't have to be a salt it can be a
+
+ align:start position:0%
+doesn't have to be a salt it can be a
+ 
+
+ align:start position:0%
+doesn't have to be a salt it can be a
+compound made of carbon but it needs to
+
+ align:start position:0%
+compound made of carbon but it needs to
+ 
+
+ align:start position:0%
+compound made of carbon but it needs to
+be a polar compound so that the water
+
+ align:start position:0%
+be a polar compound so that the water
+ 
+
+ align:start position:0%
+be a polar compound so that the water
+can get in there and form those hydrogen
+
+ align:start position:0%
+can get in there and form those hydrogen
+ 
+
+ align:start position:0%
+can get in there and form those hydrogen
+bonds so you can see that knowing what
+
+ align:start position:0%
+bonds so you can see that knowing what
+ 
+
+ align:start position:0%
+bonds so you can see that knowing what
+is capable of forming hydrogen bonds can
+
+ align:start position:0%
+is capable of forming hydrogen bonds can
+ 
+
+ align:start position:0%
+is capable of forming hydrogen bonds can
+be really useful to think about what's
+
+ align:start position:0%
+be really useful to think about what's
+ 
+
+ align:start position:0%
+be really useful to think about what's
+going to be dissolved in what other type
+
+ align:start position:0%
+going to be dissolved in what other type
+ 
+
+ align:start position:0%
+going to be dissolved in what other type
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+material so non-polar liquids like
+
+ align:start position:0%
+material so non-polar liquids like
+ 
+
+ align:start position:0%
+material so non-polar liquids like
+hexane um for example um are better for
+
+ align:start position:0%
+hexane um for example um are better for
+ 
+
+ align:start position:0%
+hexane um for example um are better for
+nonpolar so non-polar like dissolves
+
+ align:start position:0%
+nonpolar so non-polar like dissolves
+ 
+
+ align:start position:0%
+nonpolar so non-polar like dissolves
+likes and so that's why people go to dry
+
+ align:start position:0%
+likes and so that's why people go to dry
+ 
+
+ align:start position:0%
+likes and so that's why people go to dry
+cleaners because you know you don't you
+
+ align:start position:0%
+cleaners because you know you don't you
+ 
+
+ align:start position:0%
+cleaners because you know you don't you
+don't want to use water to wash certain
+
+ align:start position:0%
+don't want to use water to wash certain
+ 
+
+ align:start position:0%
+don't want to use water to wash certain
+things you want to use
+
+ align:start position:0%
+things you want to use
+ 
+
+ align:start position:0%
+things you want to use
+um you want to be dry you want to get
+
+ align:start position:0%
+um you want to be dry you want to get
+ 
+
+ align:start position:0%
+um you want to be dry you want to get
+your non-polar stains out so this is
+
+ align:start position:0%
+your non-polar stains out so this is
+ 
+
+ align:start position:0%
+your non-polar stains out so this is
+very important there's a number of
+
+ align:start position:0%
+very important there's a number of
+ 
+
+ align:start position:0%
+very important there's a number of
+applications of these principles um this
+
+ align:start position:0%
+applications of these principles um this
+ 
+
+ align:start position:0%
+applications of these principles um this
+is important in the pharmaceutical
+
+ align:start position:0%
+is important in the pharmaceutical
+ 
+
+ align:start position:0%
+is important in the pharmaceutical
+industry so um we talked about some of
+
+ align:start position:0%
+industry so um we talked about some of
+ 
+
+ align:start position:0%
+industry so um we talked about some of
+the molecules that are used as uh
+
+ align:start position:0%
+the molecules that are used as uh
+ 
+
+ align:start position:0%
+the molecules that are used as uh
+pharmaceutical um in terms of being
+
+ align:start position:0%
+pharmaceutical um in terms of being
+ 
+
+ align:start position:0%
+pharmaceutical um in terms of being
+polar and nonpolar and vitamins the same
+
+ align:start position:0%
+polar and nonpolar and vitamins the same
+ 
+
+ align:start position:0%
+polar and nonpolar and vitamins the same
+way so when you're designing a molecule
+
+ align:start position:0%
+way so when you're designing a molecule
+ 
+
+ align:start position:0%
+way so when you're designing a molecule
+that you want to get into the body and
+
+ align:start position:0%
+that you want to get into the body and
+ 
+
+ align:start position:0%
+that you want to get into the body and
+react with a Target if you design
+
+ align:start position:0%
+react with a Target if you design
+ 
+
+ align:start position:0%
+react with a Target if you design
+something that is really non-polar it's
+
+ align:start position:0%
+something that is really non-polar it's
+ 
+
+ align:start position:0%
+something that is really non-polar it's
+not the human body there's a lot of
+
+ align:start position:0%
+not the human body there's a lot of
+ 
+
+ align:start position:0%
+not the human body there's a lot of
+water parts and it's not going to
+
+ align:start position:0%
+water parts and it's not going to
+ 
+
+ align:start position:0%
+water parts and it's not going to
+necessarily get to where you want it to
+
+ align:start position:0%
+necessarily get to where you want it to
+ 
+
+ align:start position:0%
+necessarily get to where you want it to
+go and but if it's too uh too non-polar
+
+ align:start position:0%
+go and but if it's too uh too non-polar
+ 
+
+ align:start position:0%
+go and but if it's too uh too non-polar
+or too polar it might just get washed
+
+ align:start position:0%
+or too polar it might just get washed
+ 
+
+ align:start position:0%
+or too polar it might just get washed
+out so you want the right amount of
+
+ align:start position:0%
+out so you want the right amount of
+ 
+
+ align:start position:0%
+out so you want the right amount of
+polar non-polar to stay in the body long
+
+ align:start position:0%
+polar non-polar to stay in the body long
+ 
+
+ align:start position:0%
+polar non-polar to stay in the body long
+enough but also get to where it needs to
+
+ align:start position:0%
+enough but also get to where it needs to
+ 
+
+ align:start position:0%
+enough but also get to where it needs to
+go so a lot of people who are designing
+
+ align:start position:0%
+go so a lot of people who are designing
+ 
+
+ align:start position:0%
+go so a lot of people who are designing
+molecules to treat disease are very
+
+ align:start position:0%
+molecules to treat disease are very
+ 
+
+ align:start position:0%
+molecules to treat disease are very
+concerned about can we make this
+
+ align:start position:0%
+concerned about can we make this
+ 
+
+ align:start position:0%
+concerned about can we make this
+molecule more polar can we make it more
+
+ align:start position:0%
+molecule more polar can we make it more
+ 
+
+ align:start position:0%
+molecule more polar can we make it more
+soluble it's a great it hits our Target
+
+ align:start position:0%
+soluble it's a great it hits our Target
+ 
+
+ align:start position:0%
+soluble it's a great it hits our Target
+beautifully it really destroys that
+
+ align:start position:0%
+beautifully it really destroys that
+ 
+
+ align:start position:0%
+beautifully it really destroys that
+enzyme it would be a fantastic
+
+ align:start position:0%
+enzyme it would be a fantastic
+ 
+
+ align:start position:0%
+enzyme it would be a fantastic
+chemotherapeutic agent but we need to
+
+ align:start position:0%
+chemotherapeutic agent but we need to
+ 
+
+ align:start position:0%
+chemotherapeutic agent but we need to
+figure out how to make it get into the
+
+ align:start position:0%
+figure out how to make it get into the
+ 
+
+ align:start position:0%
+figure out how to make it get into the
+cell that it needs to
+
+ align:start position:0%
+cell that it needs to
+ 
+
+ align:start position:0%
+cell that it needs to
+Target and of course so if you're going
+
+ align:start position:0%
+Target and of course so if you're going
+ 
+
+ align:start position:0%
+Target and of course so if you're going
+to go into drug design or medicine you
+
+ align:start position:0%
+to go into drug design or medicine you
+ 
+
+ align:start position:0%
+to go into drug design or medicine you
+care about this if you're going to
+
+ align:start position:0%
+care about this if you're going to
+ 
+
+ align:start position:0%
+care about this if you're going to
+become a parent you care a lot about
+
+ align:start position:0%
+become a parent you care a lot about
+ 
+
+ align:start position:0%
+become a parent you care a lot about
+cleaning um and you become you know it's
+
+ align:start position:0%
+cleaning um and you become you know it's
+ 
+
+ align:start position:0%
+cleaning um and you become you know it's
+a daily event how am I going to get this
+
+ align:start position:0%
+a daily event how am I going to get this
+ 
+
+ align:start position:0%
+a daily event how am I going to get this
+stain out of my child's clothes every
+
+ align:start position:0%
+stain out of my child's clothes every
+ 
+
+ align:start position:0%
+stain out of my child's clothes every
+day this is a question um so this is
+
+ align:start position:0%
+day this is a question um so this is
+ 
+
+ align:start position:0%
+day this is a question um so this is
+important all right and one one other
+
+ align:start position:0%
+important all right and one one other
+ 
+
+ align:start position:0%
+important all right and one one other
+example in the Longs of cleaning I just
+
+ align:start position:0%
+example in the Longs of cleaning I just
+ 
+
+ align:start position:0%
+example in the Longs of cleaning I just
+want to share with you a short story
+
+ align:start position:0%
+want to share with you a short story
+ 
+
+ align:start position:0%
+want to share with you a short story
+about a chemist Robert H black and a
+
+ align:start position:0%
+about a chemist Robert H black and a
+ 
+
+ align:start position:0%
+about a chemist Robert H black and a
+life altering event that happened to him
+
+ align:start position:0%
+life altering event that happened to him
+ 
+
+ align:start position:0%
+life altering event that happened to him
+so one day Mrs black said to Mr
+
+ align:start position:0%
+so one day Mrs black said to Mr
+ 
+
+ align:start position:0%
+so one day Mrs black said to Mr
+Black clean the
+
+ align:start position:0%
+Black clean the
+ 
+
+ align:start position:0%
+Black clean the
+bathtub this was an unprecedented event
+
+ align:start position:0%
+bathtub this was an unprecedented event
+ 
+
+ align:start position:0%
+bathtub this was an unprecedented event
+in the black
+
+ align:start position:0%
+in the black
+ 
+
+ align:start position:0%
+in the black
+household so Robert black went in to
+
+ align:start position:0%
+household so Robert black went in to
+ 
+
+ align:start position:0%
+household so Robert black went in to
+clean his
+
+ align:start position:0%
+clean his
+ 
+
+ align:start position:0%
+clean his
+bathtub and it was really hard and he
+
+ align:start position:0%
+bathtub and it was really hard and he
+ 
+
+ align:start position:0%
+bathtub and it was really hard and he
+scrubbed and he scrubbed and he scrubbed
+
+ align:start position:0%
+scrubbed and he scrubbed and he scrubbed
+ 
+
+ align:start position:0%
+scrubbed and he scrubbed and he scrubbed
+and he scrubbed and he was a chemist so
+
+ align:start position:0%
+and he scrubbed and he was a chemist so
+ 
+
+ align:start position:0%
+and he scrubbed and he was a chemist so
+he knew what kind of uh chemicals you
+
+ align:start position:0%
+he knew what kind of uh chemicals you
+ 
+
+ align:start position:0%
+he knew what kind of uh chemicals you
+would need to uh to clean a bathtub you
+
+ align:start position:0%
+would need to uh to clean a bathtub you
+ 
+
+ align:start position:0%
+would need to uh to clean a bathtub you
+want to have things to dissolve your
+
+ align:start position:0%
+want to have things to dissolve your
+ 
+
+ align:start position:0%
+want to have things to dissolve your
+likes and uh you know so you want to
+
+ align:start position:0%
+likes and uh you know so you want to
+ 
+
+ align:start position:0%
+likes and uh you know so you want to
+have your polar and non-polar you want
+
+ align:start position:0%
+have your polar and non-polar you want
+ 
+
+ align:start position:0%
+have your polar and non-polar you want
+to have a a Keating agent to pull the
+
+ align:start position:0%
+to have a a Keating agent to pull the
+ 
+
+ align:start position:0%
+to have a a Keating agent to pull the
+heavy metals out of the tub scum a
+
+ align:start position:0%
+heavy metals out of the tub scum a
+ 
+
+ align:start position:0%
+heavy metals out of the tub scum a
+surfactant to make them beat up so you
+
+ align:start position:0%
+surfactant to make them beat up so you
+ 
+
+ align:start position:0%
+surfactant to make them beat up so you
+can wash them away um alcohols to remove
+
+ align:start position:0%
+can wash them away um alcohols to remove
+ 
+
+ align:start position:0%
+can wash them away um alcohols to remove
+sort of the more greasy kind of stains
+
+ align:start position:0%
+sort of the more greasy kind of stains
+ 
+
+ align:start position:0%
+sort of the more greasy kind of stains
+so he knew all this but he realized that
+
+ align:start position:0%
+so he knew all this but he realized that
+ 
+
+ align:start position:0%
+so he knew all this but he realized that
+if you didn't apply cleaner on a regular
+
+ align:start position:0%
+if you didn't apply cleaner on a regular
+ 
+
+ align:start position:0%
+if you didn't apply cleaner on a regular
+basis the tub scum got so thick and so
+
+ align:start position:0%
+basis the tub scum got so thick and so
+ 
+
+ align:start position:0%
+basis the tub scum got so thick and so
+nasty that the cleaner couldn't
+
+ align:start position:0%
+nasty that the cleaner couldn't
+ 
+
+ align:start position:0%
+nasty that the cleaner couldn't
+penetrate the scum and you need surface
+
+ align:start position:0%
+penetrate the scum and you need surface
+ 
+
+ align:start position:0%
+penetrate the scum and you need surface
+area these things work by dissolving out
+
+ align:start position:0%
+area these things work by dissolving out
+ 
+
+ align:start position:0%
+area these things work by dissolving out
+they touch the surface so you need to
+
+ align:start position:0%
+they touch the surface so you need to
+ 
+
+ align:start position:0%
+they touch the surface so you need to
+have a surface so he had this idea that
+
+ align:start position:0%
+have a surface so he had this idea that
+ 
+
+ align:start position:0%
+have a surface so he had this idea that
+instead of having having this tub scum
+
+ align:start position:0%
+instead of having having this tub scum
+ 
+
+ align:start position:0%
+instead of having having this tub scum
+build up so much that it was a real
+
+ align:start position:0%
+build up so much that it was a real
+ 
+
+ align:start position:0%
+build up so much that it was a real
+problem to clean it that you could take
+
+ align:start position:0%
+problem to clean it that you could take
+ 
+
+ align:start position:0%
+problem to clean it that you could take
+all of these things that were chemists
+
+ align:start position:0%
+all of these things that were chemists
+ 
+
+ align:start position:0%
+all of these things that were chemists
+knew would be useful and package them in
+
+ align:start position:0%
+knew would be useful and package them in
+ 
+
+ align:start position:0%
+knew would be useful and package them in
+something that was a daily cleaner so he
+
+ align:start position:0%
+something that was a daily cleaner so he
+ 
+
+ align:start position:0%
+something that was a daily cleaner so he
+advertised these things that every time
+
+ align:start position:0%
+advertised these things that every time
+ 
+
+ align:start position:0%
+advertised these things that every time
+you take a shower you just spray the
+
+ align:start position:0%
+you take a shower you just spray the
+ 
+
+ align:start position:0%
+you take a shower you just spray the
+shower or the tub and then you never
+
+ align:start position:0%
+shower or the tub and then you never
+ 
+
+ align:start position:0%
+shower or the tub and then you never
+have to scrub your tub again because you
+
+ align:start position:0%
+have to scrub your tub again because you
+ 
+
+ align:start position:0%
+have to scrub your tub again because you
+do a little bit every day where there's
+
+ align:start position:0%
+do a little bit every day where there's
+ 
+
+ align:start position:0%
+do a little bit every day where there's
+not a lot of surface so it gets it right
+
+ align:start position:0%
+not a lot of surface so it gets it right
+ 
+
+ align:start position:0%
+not a lot of surface so it gets it right
+off right away
+
+ align:start position:0%
+off right away
+ 
+
+ align:start position:0%
+off right away
+and Mr Black and his wife never had to
+
+ align:start position:0%
+and Mr Black and his wife never had to
+ 
+
+ align:start position:0%
+and Mr Black and his wife never had to
+clean their tub again because this
+
+ align:start position:0%
+clean their tub again because this
+ 
+
+ align:start position:0%
+clean their tub again because this
+resulted in sales of about $70 million
+
+ align:start position:0%
+resulted in sales of about $70 million
+ 
+
+ align:start position:0%
+resulted in sales of about $70 million
+per year and it's important to point out
+
+ align:start position:0%
+per year and it's important to point out
+ 
+
+ align:start position:0%
+per year and it's important to point out
+that he wasn't using anything new he was
+
+ align:start position:0%
+that he wasn't using anything new he was
+ 
+
+ align:start position:0%
+that he wasn't using anything new he was
+just packaging his chemicals for daily
+
+ align:start position:0%
+just packaging his chemicals for daily
+ 
+
+ align:start position:0%
+just packaging his chemicals for daily
+use rather than say for weekly or
+
+ align:start position:0%
+use rather than say for weekly or
+ 
+
+ align:start position:0%
+use rather than say for weekly or
+monthly use so I think there's a couple
+
+ align:start position:0%
+monthly use so I think there's a couple
+ 
+
+ align:start position:0%
+monthly use so I think there's a couple
+important lessons from this one it's
+
+ align:start position:0%
+important lessons from this one it's
+ 
+
+ align:start position:0%
+important lessons from this one it's
+always important to clean your bathroom
+
+ align:start position:0%
+always important to clean your bathroom
+ 
+
+ align:start position:0%
+always important to clean your bathroom
+two you never know where chem istry
+
+ align:start position:0%
+two you never know where chem istry
+ 
+
+ align:start position:0%
+two you never know where chem istry
+knowledge is going to come what life
+
+ align:start position:0%
+knowledge is going to come what life
+ 
+
+ align:start position:0%
+knowledge is going to come what life
+altering event will cause you to realize
+
+ align:start position:0%
+altering event will cause you to realize
+ 
+
+ align:start position:0%
+altering event will cause you to realize
+that you have in your mind chemistry
+
+ align:start position:0%
+that you have in your mind chemistry
+ 
+
+ align:start position:0%
+that you have in your mind chemistry
+knowledge that can make you $70 million
+
+ align:start position:0%
+knowledge that can make you $70 million
+ 
+
+ align:start position:0%
+knowledge that can make you $70 million
+a year and when that life altering event
+
+ align:start position:0%
+a year and when that life altering event
+ 
+
+ align:start position:0%
+a year and when that life altering event
+occurs remember that I take cash and
+
+ align:start position:0%
+occurs remember that I take cash and
+ 
+
+ align:start position:0%
+occurs remember that I take cash and
+checks and stock options I added the
+
+ align:start position:0%
+checks and stock options I added the
+ 
+
+ align:start position:0%
+checks and stock options I added the
+last one I thought cash and checks I
+
+ align:start position:0%
+last one I thought cash and checks I
+ 
+
+ align:start position:0%
+last one I thought cash and checks I
+should be more flexible so I'm also
+
+ align:start position:0%
+should be more flexible so I'm also
+ 
+
+ align:start position:0%
+should be more flexible so I'm also
+going to take stock options and this is
+
+ align:start position:0%
+going to take stock options and this is
+ 
+
+ align:start position:0%
+going to take stock options and this is
+why I teach you all the fundamentals of
+
+ align:start position:0%
+why I teach you all the fundamentals of
+ 
+
+ align:start position:0%
+why I teach you all the fundamentals of
+chemistry cover everything that's it's
+
+ align:start position:0%
+chemistry cover everything that's it's
+ 
+
+ align:start position:0%
+chemistry cover everything that's it's
+really important for you to know because
+
+ align:start position:0%
+really important for you to know because
+ 
+
+ align:start position:0%
+really important for you to know because
+then if you use any of it you've learned
+
+ align:start position:0%
+then if you use any of it you've learned
+ 
+
+ align:start position:0%
+then if you use any of it you've learned
+it from
+
+ align:start position:0%
+it from
+ 
+
+ align:start position:0%
+it from
+me okay so just keep that in mind one
+
+ align:start position:0%
+me okay so just keep that in mind one
+ 
+
+ align:start position:0%
+me okay so just keep that in mind one
+never knows what life event is ahead of
+
+ align:start position:0%
+never knows what life event is ahead of
+ 
+
+ align:start position:0%
+never knows what life event is ahead of
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+so what about gas solubility we talked
+
+ align:start position:0%
+so what about gas solubility we talked
+ 
+
+ align:start position:0%
+so what about gas solubility we talked
+about solids now let's talk about
+
+ align:start position:0%
+about solids now let's talk about
+ 
+
+ align:start position:0%
+about solids now let's talk about
+gases so whether a a gas is going to be
+
+ align:start position:0%
+gases so whether a a gas is going to be
+ 
+
+ align:start position:0%
+gases so whether a a gas is going to be
+soluble is going to depend on Henry's
+
+ align:start position:0%
+soluble is going to depend on Henry's
+ 
+
+ align:start position:0%
+soluble is going to depend on Henry's
+law or we can find out about its
+
+ align:start position:0%
+law or we can find out about its
+ 
+
+ align:start position:0%
+law or we can find out about its
+solubility so the solubility of a gas
+
+ align:start position:0%
+solubility so the solubility of a gas
+ 
+
+ align:start position:0%
+solubility so the solubility of a gas
+we're going to call that little s that's
+
+ align:start position:0%
+we're going to call that little s that's
+ 
+
+ align:start position:0%
+we're going to call that little s that's
+our solubility is directly proportional
+
+ align:start position:0%
+our solubility is directly proportional
+ 
+
+ align:start position:0%
+our solubility is directly proportional
+to the partial pressure of the gas and a
+
+ align:start position:0%
+to the partial pressure of the gas and a
+ 
+
+ align:start position:0%
+to the partial pressure of the gas and a
+constant called Henry's constant and
+
+ align:start position:0%
+constant called Henry's constant and
+ 
+
+ align:start position:0%
+constant called Henry's constant and
+that depends on the nature of the gas
+
+ align:start position:0%
+that depends on the nature of the gas
+ 
+
+ align:start position:0%
+that depends on the nature of the gas
+and the solvent and the temperature so
+
+ align:start position:0%
+and the solvent and the temperature so
+ 
+
+ align:start position:0%
+and the solvent and the temperature so
+let's think about this this rule in this
+
+ align:start position:0%
+let's think about this this rule in this
+ 
+
+ align:start position:0%
+let's think about this this rule in this
+plot in a clicker question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right just take 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds awesome
+
+ align:start position:0%
+seconds awesome
+ 
+
+ align:start position:0%
+seconds awesome
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+okay so let's just take a look at that
+
+ align:start position:0%
+okay so let's just take a look at that
+ 
+
+ align:start position:0%
+okay so let's just take a look at that
+so one of one of the clicker questions
+
+ align:start position:0%
+so one of one of the clicker questions
+ 
+
+ align:start position:0%
+so one of one of the clicker questions
+was just kind of getting you to read the
+
+ align:start position:0%
+was just kind of getting you to read the
+ 
+
+ align:start position:0%
+was just kind of getting you to read the
+graph um and so it was asking say at 05
+
+ align:start position:0%
+graph um and so it was asking say at 05
+ 
+
+ align:start position:0%
+graph um and so it was asking say at 05
+atmospheres um it said oxygen is more
+
+ align:start position:0%
+atmospheres um it said oxygen is more
+ 
+
+ align:start position:0%
+atmospheres um it said oxygen is more
+soluble than helium this is molar
+
+ align:start position:0%
+soluble than helium this is molar
+ 
+
+ align:start position:0%
+soluble than helium this is molar
+solubility versus partial pressure at 05
+
+ align:start position:0%
+solubility versus partial pressure at 05
+ 
+
+ align:start position:0%
+solubility versus partial pressure at 05
+sure enough oxygen is more soluble so
+
+ align:start position:0%
+sure enough oxygen is more soluble so
+ 
+
+ align:start position:0%
+sure enough oxygen is more soluble so
+that was just reading the plot the other
+
+ align:start position:0%
+that was just reading the plot the other
+ 
+
+ align:start position:0%
+that was just reading the plot the other
+um one was just interpreting Henry's law
+
+ align:start position:0%
+um one was just interpreting Henry's law
+ 
+
+ align:start position:0%
+um one was just interpreting Henry's law
+again that solubility if solubility
+
+ align:start position:0%
+again that solubility if solubility
+ 
+
+ align:start position:0%
+again that solubility if solubility
+would increase as partial pressure
+
+ align:start position:0%
+would increase as partial pressure
+ 
+
+ align:start position:0%
+would increase as partial pressure
+increases you can see that from the
+
+ align:start position:0%
+increases you can see that from the
+ 
+
+ align:start position:0%
+increases you can see that from the
+equation but you can also think about
+
+ align:start position:0%
+equation but you can also think about
+ 
+
+ align:start position:0%
+equation but you can also think about
+why that's true and why it's true is the
+
+ align:start position:0%
+why that's true and why it's true is the
+ 
+
+ align:start position:0%
+why that's true and why it's true is the
+answer to three that the solubility of
+
+ align:start position:0%
+answer to three that the solubility of
+ 
+
+ align:start position:0%
+answer to three that the solubility of
+gas is proportional to its partial
+
+ align:start position:0%
+gas is proportional to its partial
+ 
+
+ align:start position:0%
+gas is proportional to its partial
+pressure an increase in pressure
+
+ align:start position:0%
+pressure an increase in pressure
+ 
+
+ align:start position:0%
+pressure an increase in pressure
+corresponds to an increase in rate at
+
+ align:start position:0%
+corresponds to an increase in rate at
+ 
+
+ align:start position:0%
+corresponds to an increase in rate at
+which the gas molecules strike the
+
+ align:start position:0%
+which the gas molecules strike the
+ 
+
+ align:start position:0%
+which the gas molecules strike the
+surface and that makes them more soluble
+
+ align:start position:0%
+surface and that makes them more soluble
+ 
+
+ align:start position:0%
+surface and that makes them more soluble
+so again ability really has to do with
+
+ align:start position:0%
+so again ability really has to do with
+ 
+
+ align:start position:0%
+so again ability really has to do with
+getting at that surface if you get at
+
+ align:start position:0%
+getting at that surface if you get at
+ 
+
+ align:start position:0%
+getting at that surface if you get at
+the surface then you can dissolve your
+
+ align:start position:0%
+the surface then you can dissolve your
+ 
+
+ align:start position:0%
+the surface then you can dissolve your
+material all right so why should you
+
+ align:start position:0%
+material all right so why should you
+ 
+
+ align:start position:0%
+material all right so why should you
+care about the solubility of gases and
+
+ align:start position:0%
+care about the solubility of gases and
+ 
+
+ align:start position:0%
+care about the solubility of gases and
+um I'm going to give you an example um
+
+ align:start position:0%
+um I'm going to give you an example um
+ 
+
+ align:start position:0%
+um I'm going to give you an example um
+this is another in your own word so
+
+ align:start position:0%
+this is another in your own word so
+ 
+
+ align:start position:0%
+this is another in your own word so
+we'll watch the video and I think
+
+ align:start position:0%
+we'll watch the video and I think
+ 
+
+ align:start position:0%
+we'll watch the video and I think
+tonight there's some kind of big climate
+
+ align:start position:0%
+tonight there's some kind of big climate
+ 
+
+ align:start position:0%
+tonight there's some kind of big climate
+change thing I've seen Flyers around I
+
+ align:start position:0%
+change thing I've seen Flyers around I
+ 
+
+ align:start position:0%
+change thing I've seen Flyers around I
+haven't paid enough attention to what's
+
+ align:start position:0%
+haven't paid enough attention to what's
+ 
+
+ align:start position:0%
+haven't paid enough attention to what's
+going on but climate change is certainly
+
+ align:start position:0%
+going on but climate change is certainly
+ 
+
+ align:start position:0%
+going on but climate change is certainly
+a very um Hot Topic if you'll ex excuse
+
+ align:start position:0%
+a very um Hot Topic if you'll ex excuse
+ 
+
+ align:start position:0%
+a very um Hot Topic if you'll ex excuse
+that um right now I didn't really mean
+
+ align:start position:0%
+that um right now I didn't really mean
+ 
+
+ align:start position:0%
+that um right now I didn't really mean
+it it just kind of came out um but CO2
+
+ align:start position:0%
+it it just kind of came out um but CO2
+ 
+
+ align:start position:0%
+it it just kind of came out um but CO2
+is a greenhouse gas it's a big problem
+
+ align:start position:0%
+is a greenhouse gas it's a big problem
+ 
+
+ align:start position:0%
+is a greenhouse gas it's a big problem
+and so a number of researchers here at
+
+ align:start position:0%
+and so a number of researchers here at
+ 
+
+ align:start position:0%
+and so a number of researchers here at
+MIT are thinking about ways that you can
+
+ align:start position:0%
+MIT are thinking about ways that you can
+ 
+
+ align:start position:0%
+MIT are thinking about ways that you can
+capture and store it somewhere get it
+
+ align:start position:0%
+capture and store it somewhere get it
+ 
+
+ align:start position:0%
+capture and store it somewhere get it
+out of our atmosphere other people are
+
+ align:start position:0%
+out of our atmosphere other people are
+ 
+
+ align:start position:0%
+out of our atmosphere other people are
+thinking about ways that you can change
+
+ align:start position:0%
+thinking about ways that you can change
+ 
+
+ align:start position:0%
+thinking about ways that you can change
+industrial processes to make less CO2
+
+ align:start position:0%
+industrial processes to make less CO2
+ 
+
+ align:start position:0%
+industrial processes to make less CO2
+there's a lot of research going on so
+
+ align:start position:0%
+there's a lot of research going on so
+ 
+
+ align:start position:0%
+there's a lot of research going on so
+today you'll hear from Hector Hernandez
+
+ align:start position:0%
+today you'll hear from Hector Hernandez
+ 
+
+ align:start position:0%
+today you'll hear from Hector Hernandez
+who had a PhD in chemistry from the
+
+ align:start position:0%
+who had a PhD in chemistry from the
+ 
+
+ align:start position:0%
+who had a PhD in chemistry from the
+chemistry Department here at MIT did his
+
+ align:start position:0%
+chemistry Department here at MIT did his
+ 
+
+ align:start position:0%
+chemistry Department here at MIT did his
+postto here at MIT in chemical
+
+ align:start position:0%
+postto here at MIT in chemical
+ 
+
+ align:start position:0%
+postto here at MIT in chemical
+engineering um and is now a professor of
+
+ align:start position:0%
+engineering um and is now a professor of
+ 
+
+ align:start position:0%
+engineering um and is now a professor of
+chemical engineering at mastar Institute
+
+ align:start position:0%
+chemical engineering at mastar Institute
+ 
+
+ align:start position:0%
+chemical engineering at mastar Institute
+in the uh United Arab Emirates so this
+
+ align:start position:0%
+in the uh United Arab Emirates so this
+ 
+
+ align:start position:0%
+in the uh United Arab Emirates so this
+is one of the MIT satellite universities
+
+ align:start position:0%
+is one of the MIT satellite universities
+ 
+
+ align:start position:0%
+is one of the MIT satellite universities
+that are popping up all over the world
+
+ align:start position:0%
+that are popping up all over the world
+ 
+
+ align:start position:0%
+that are popping up all over the world
+um so Hector was born I think in
+
+ align:start position:0%
+um so Hector was born I think in
+ 
+
+ align:start position:0%
+um so Hector was born I think in
+Honduras and then lived in Florida ended
+
+ align:start position:0%
+Honduras and then lived in Florida ended
+ 
+
+ align:start position:0%
+Honduras and then lived in Florida ended
+up in MIT and now he's at the United
+
+ align:start position:0%
+up in MIT and now he's at the United
+ 
+
+ align:start position:0%
+up in MIT and now he's at the United
+Arab Emirates so that's just another
+
+ align:start position:0%
+Arab Emirates so that's just another
+ 
+
+ align:start position:0%
+Arab Emirates so that's just another
+example of one never knows what's going
+
+ align:start position:0%
+example of one never knows what's going
+ 
+
+ align:start position:0%
+example of one never knows what's going
+to happen to you all right so you can
+
+ align:start position:0%
+to happen to you all right so you can
+ 
+
+ align:start position:0%
+to happen to you all right so you can
+hear from Hector in his own
+
+ align:start position:0%
+hear from Hector in his own
+ 
+
+ align:start position:0%
+hear from Hector in his own
+words so um another there's Hector's
+
+ align:start position:0%
+words so um another there's Hector's
+ 
+
+ align:start position:0%
+words so um another there's Hector's
+video is is on personal videos online I
+
+ align:start position:0%
+video is is on personal videos online I
+ 
+
+ align:start position:0%
+video is is on personal videos online I
+think it's a fun one to watch there's a
+
+ align:start position:0%
+think it's a fun one to watch there's a
+ 
+
+ align:start position:0%
+think it's a fun one to watch there's a
+couple of things that are really
+
+ align:start position:0%
+couple of things that are really
+ 
+
+ align:start position:0%
+couple of things that are really
+interesting about his personal story
+
+ align:start position:0%
+interesting about his personal story
+ 
+
+ align:start position:0%
+interesting about his personal story
+including the fact that as he mentioned
+
+ align:start position:0%
+including the fact that as he mentioned
+ 
+
+ align:start position:0%
+including the fact that as he mentioned
+in past life he did some construction he
+
+ align:start position:0%
+in past life he did some construction he
+ 
+
+ align:start position:0%
+in past life he did some construction he
+started undergrad at age age 30 I think
+
+ align:start position:0%
+started undergrad at age age 30 I think
+ 
+
+ align:start position:0%
+started undergrad at age age 30 I think
+where he was he was basically building
+
+ align:start position:0%
+where he was he was basically building
+ 
+
+ align:start position:0%
+where he was he was basically building
+houses and fixing cars and he realized
+
+ align:start position:0%
+houses and fixing cars and he realized
+ 
+
+ align:start position:0%
+houses and fixing cars and he realized
+that uh his back might not survive this
+
+ align:start position:0%
+that uh his back might not survive this
+ 
+
+ align:start position:0%
+that uh his back might not survive this
+being his permanent career so he decided
+
+ align:start position:0%
+being his permanent career so he decided
+ 
+
+ align:start position:0%
+being his permanent career so he decided
+to use his brain instead of his back and
+
+ align:start position:0%
+to use his brain instead of his back and
+ 
+
+ align:start position:0%
+to use his brain instead of his back and
+so started undergraduate now he's a
+
+ align:start position:0%
+so started undergraduate now he's a
+ 
+
+ align:start position:0%
+so started undergraduate now he's a
+professor so it just shows there's a lot
+
+ align:start position:0%
+professor so it just shows there's a lot
+ 
+
+ align:start position:0%
+professor so it just shows there's a lot
+of different paths uh to success all
+
+ align:start position:0%
+of different paths uh to success all
+ 
+
+ align:start position:0%
+of different paths uh to success all
+right so CO2 big problem you were trying
+
+ align:start position:0%
+right so CO2 big problem you were trying
+ 
+
+ align:start position:0%
+right so CO2 big problem you were trying
+to use in in that case he was interested
+
+ align:start position:0%
+to use in in that case he was interested
+ 
+
+ align:start position:0%
+to use in in that case he was interested
+in turning into biofuels or interested
+
+ align:start position:0%
+in turning into biofuels or interested
+ 
+
+ align:start position:0%
+in turning into biofuels or interested
+in ways to store for it you care about
+
+ align:start position:0%
+in ways to store for it you care about
+ 
+
+ align:start position:0%
+in ways to store for it you care about
+solubility of gases and you care about
+
+ align:start position:0%
+solubility of gases and you care about
+ 
+
+ align:start position:0%
+solubility of gases and you care about
+later's principle of driving things the
+
+ align:start position:0%
+later's principle of driving things the
+ 
+
+ align:start position:0%
+later's principle of driving things the
+direction that you want to make the
+
+ align:start position:0%
+direction that you want to make the
+ 
+
+ align:start position:0%
+direction that you want to make the
+products you want okay so let's think
+
+ align:start position:0%
+products you want okay so let's think
+ 
+
+ align:start position:0%
+products you want okay so let's think
+more about these factors that affect
+
+ align:start position:0%
+more about these factors that affect
+ 
+
+ align:start position:0%
+more about these factors that affect
+solubility and one thing that's very
+
+ align:start position:0%
+solubility and one thing that's very
+ 
+
+ align:start position:0%
+solubility and one thing that's very
+important for sure is
+
+ align:start position:0%
+important for sure is
+ 
+
+ align:start position:0%
+important for sure is
+temperature so
+
+ align:start position:0%
+temperature so
+ 
+
+ align:start position:0%
+temperature so
+temperature most substances dissolve
+
+ align:start position:0%
+temperature most substances dissolve
+ 
+
+ align:start position:0%
+temperature most substances dissolve
+more quickly at higher temperature which
+
+ align:start position:0%
+more quickly at higher temperature which
+ 
+
+ align:start position:0%
+more quickly at higher temperature which
+is often what you want but it doesn't
+
+ align:start position:0%
+is often what you want but it doesn't
+ 
+
+ align:start position:0%
+is often what you want but it doesn't
+always mean if you increase the
+
+ align:start position:0%
+always mean if you increase the
+ 
+
+ align:start position:0%
+always mean if you increase the
+temperature that you're going to make it
+
+ align:start position:0%
+temperature that you're going to make it
+ 
+
+ align:start position:0%
+temperature that you're going to make it
+more soluble you may just make it
+
+ align:start position:0%
+more soluble you may just make it
+ 
+
+ align:start position:0%
+more soluble you may just make it
+dissolve faster but not actually change
+
+ align:start position:0%
+dissolve faster but not actually change
+ 
+
+ align:start position:0%
+dissolve faster but not actually change
+the end product some things are more
+
+ align:start position:0%
+the end product some things are more
+ 
+
+ align:start position:0%
+the end product some things are more
+sensitive to temperature than others so
+
+ align:start position:0%
+sensitive to temperature than others so
+ 
+
+ align:start position:0%
+sensitive to temperature than others so
+most gases for example are less soluble
+
+ align:start position:0%
+most gases for example are less soluble
+ 
+
+ align:start position:0%
+most gases for example are less soluble
+in warm water than in cold water but
+
+ align:start position:0%
+in warm water than in cold water but
+ 
+
+ align:start position:0%
+in warm water than in cold water but
+with solids it's much harder to predict
+
+ align:start position:0%
+with solids it's much harder to predict
+ 
+
+ align:start position:0%
+with solids it's much harder to predict
+that what effect temperature might have
+
+ align:start position:0%
+that what effect temperature might have
+ 
+
+ align:start position:0%
+that what effect temperature might have
+on their solubility even though for many
+
+ align:start position:0%
+on their solubility even though for many
+ 
+
+ align:start position:0%
+on their solubility even though for many
+things it will make it faster
+
+ align:start position:0%
+things it will make it faster
+ 
+
+ align:start position:0%
+things it will make it faster
+so let's think now about how to drive a
+
+ align:start position:0%
+so let's think now about how to drive a
+ 
+
+ align:start position:0%
+so let's think now about how to drive a
+reaction and what what what factors are
+
+ align:start position:0%
+reaction and what what what factors are
+ 
+
+ align:start position:0%
+reaction and what what what factors are
+involved and what's favorable and what's
+
+ align:start position:0%
+involved and what's favorable and what's
+ 
+
+ align:start position:0%
+involved and what's favorable and what's
+not favorable and when we're talking
+
+ align:start position:0%
+not favorable and when we're talking
+ 
+
+ align:start position:0%
+not favorable and when we're talking
+about those things we're going to be
+
+ align:start position:0%
+about those things we're going to be
+ 
+
+ align:start position:0%
+about those things we're going to be
+back to our thermodynamics back to
+
+ align:start position:0%
+back to our thermodynamics back to
+ 
+
+ align:start position:0%
+back to our thermodynamics back to
+enthalpy entropy and Gibbs free energy
+
+ align:start position:0%
+enthalpy entropy and Gibbs free energy
+ 
+
+ align:start position:0%
+enthalpy entropy and Gibbs free energy
+so all these have little special
+
+ align:start position:0%
+so all these have little special
+ 
+
+ align:start position:0%
+so all these have little special
+subnames so when we're talking about
+
+ align:start position:0%
+subnames so when we're talking about
+ 
+
+ align:start position:0%
+subnames so when we're talking about
+Delta H and we're talking about
+
+ align:start position:0%
+Delta H and we're talking about
+ 
+
+ align:start position:0%
+Delta H and we're talking about
+Solutions things dissolving we're
+
+ align:start position:0%
+Solutions things dissolving we're
+ 
+
+ align:start position:0%
+Solutions things dissolving we're
+talking about Delta H subs for uh
+
+ align:start position:0%
+talking about Delta H subs for uh
+ 
+
+ align:start position:0%
+talking about Delta H subs for uh
+solution or if you could think of it as
+
+ align:start position:0%
+solution or if you could think of it as
+ 
+
+ align:start position:0%
+solution or if you could think of it as
+solubility and one point that I'll make
+
+ align:start position:0%
+solubility and one point that I'll make
+ 
+
+ align:start position:0%
+solubility and one point that I'll make
+a lot of times when people are learning
+
+ align:start position:0%
+a lot of times when people are learning
+ 
+
+ align:start position:0%
+a lot of times when people are learning
+a new field they're like oh there's so
+
+ align:start position:0%
+a new field they're like oh there's so
+ 
+
+ align:start position:0%
+a new field they're like oh there's so
+much to learn but it you get to some
+
+ align:start position:0%
+much to learn but it you get to some
+ 
+
+ align:start position:0%
+much to learn but it you get to some
+point everything is just kind of like a
+
+ align:start position:0%
+point everything is just kind of like a
+ 
+
+ align:start position:0%
+point everything is just kind of like a
+subtle difference in something you've
+
+ align:start position:0%
+subtle difference in something you've
+ 
+
+ align:start position:0%
+subtle difference in something you've
+already learned so if you already
+
+ align:start position:0%
+already learned so if you already
+ 
+
+ align:start position:0%
+already learned so if you already
+learned about Delta H this is just a
+
+ align:start position:0%
+learned about Delta H this is just a
+ 
+
+ align:start position:0%
+learned about Delta H this is just a
+slight modification of what you learned
+
+ align:start position:0%
+slight modification of what you learned
+ 
+
+ align:start position:0%
+slight modification of what you learned
+it's not you don't have to learn a whole
+
+ align:start position:0%
+it's not you don't have to learn a whole
+ 
+
+ align:start position:0%
+it's not you don't have to learn a whole
+new thing so that's one of the good
+
+ align:start position:0%
+new thing so that's one of the good
+ 
+
+ align:start position:0%
+new thing so that's one of the good
+things about the course you start
+
+ align:start position:0%
+things about the course you start
+ 
+
+ align:start position:0%
+things about the course you start
+recognizing already I already pretty
+
+ align:start position:0%
+recognizing already I already pretty
+ 
+
+ align:start position:0%
+recognizing already I already pretty
+much know know this I just need to to
+
+ align:start position:0%
+much know know this I just need to to
+ 
+
+ align:start position:0%
+much know know this I just need to to
+add a little saw to the end okay so
+
+ align:start position:0%
+add a little saw to the end okay so
+ 
+
+ align:start position:0%
+add a little saw to the end okay so
+Delta h of solution can be measured um
+
+ align:start position:0%
+Delta h of solution can be measured um
+ 
+
+ align:start position:0%
+Delta h of solution can be measured um
+you can measure it from heat released
+
+ align:start position:0%
+you can measure it from heat released
+ 
+
+ align:start position:0%
+you can measure it from heat released
+when something dissolves or measure it
+
+ align:start position:0%
+when something dissolves or measure it
+ 
+
+ align:start position:0%
+when something dissolves or measure it
+by the heat absorbed and at constant
+
+ align:start position:0%
+by the heat absorbed and at constant
+ 
+
+ align:start position:0%
+by the heat absorbed and at constant
+pressure and so the sign of Delta H Sol
+
+ align:start position:0%
+pressure and so the sign of Delta H Sol
+ 
+
+ align:start position:0%
+pressure and so the sign of Delta H Sol
+will tell you about whether heat is
+
+ align:start position:0%
+will tell you about whether heat is
+ 
+
+ align:start position:0%
+will tell you about whether heat is
+released or heat is is um required when
+
+ align:start position:0%
+released or heat is is um required when
+ 
+
+ align:start position:0%
+released or heat is is um required when
+something dissolves so a negative
+
+ align:start position:0%
+something dissolves so a negative
+ 
+
+ align:start position:0%
+something dissolves so a negative
+enthalpy of solution tells us that heat
+
+ align:start position:0%
+enthalpy of solution tells us that heat
+ 
+
+ align:start position:0%
+enthalpy of solution tells us that heat
+is released when something dissolves and
+
+ align:start position:0%
+is released when something dissolves and
+ 
+
+ align:start position:0%
+is released when something dissolves and
+many of you may have just experienced
+
+ align:start position:0%
+many of you may have just experienced
+ 
+
+ align:start position:0%
+many of you may have just experienced
+this if you're holding you're mixing
+
+ align:start position:0%
+this if you're holding you're mixing
+ 
+
+ align:start position:0%
+this if you're holding you're mixing
+something together and you're holding
+
+ align:start position:0%
+something together and you're holding
+ 
+
+ align:start position:0%
+something together and you're holding
+the container and all of a sudden it
+
+ align:start position:0%
+the container and all of a sudden it
+ 
+
+ align:start position:0%
+the container and all of a sudden it
+heats up so then you know Delta h of Sal
+
+ align:start position:0%
+heats up so then you know Delta h of Sal
+ 
+
+ align:start position:0%
+heats up so then you know Delta h of Sal
+is a negative value and of course a
+
+ align:start position:0%
+is a negative value and of course a
+ 
+
+ align:start position:0%
+is a negative value and of course a
+positive value tells you that um that
+
+ align:start position:0%
+positive value tells you that um that
+ 
+
+ align:start position:0%
+positive value tells you that um that
+energy is absorbed and sometimes things
+
+ align:start position:0%
+energy is absorbed and sometimes things
+ 
+
+ align:start position:0%
+energy is absorbed and sometimes things
+can get very very cold when they're
+
+ align:start position:0%
+can get very very cold when they're
+ 
+
+ align:start position:0%
+can get very very cold when they're
+dissolving so you already kind of knew
+
+ align:start position:0%
+dissolving so you already kind of knew
+ 
+
+ align:start position:0%
+dissolving so you already kind of knew
+that that negative Delta H tells you
+
+ align:start position:0%
+that that negative Delta H tells you
+ 
+
+ align:start position:0%
+that that negative Delta H tells you
+that heat is released and positive Delta
+
+ align:start position:0%
+that heat is released and positive Delta
+ 
+
+ align:start position:0%
+that heat is released and positive Delta
+H tells you that heat is absorbed so
+
+ align:start position:0%
+H tells you that heat is absorbed so
+ 
+
+ align:start position:0%
+H tells you that heat is absorbed so
+this is basically the same thing that
+
+ align:start position:0%
+this is basically the same thing that
+ 
+
+ align:start position:0%
+this is basically the same thing that
+you already learned um it just applies
+
+ align:start position:0%
+you already learned um it just applies
+ 
+
+ align:start position:0%
+you already learned um it just applies
+to things dissolving just the same as it
+
+ align:start position:0%
+to things dissolving just the same as it
+ 
+
+ align:start position:0%
+to things dissolving just the same as it
+does to any reaction all right now
+
+ align:start position:0%
+does to any reaction all right now
+ 
+
+ align:start position:0%
+does to any reaction all right now
+suppose we want to know whether the
+
+ align:start position:0%
+suppose we want to know whether the
+ 
+
+ align:start position:0%
+suppose we want to know whether the
+reaction is going to be spontaneous at
+
+ align:start position:0%
+reaction is going to be spontaneous at
+ 
+
+ align:start position:0%
+reaction is going to be spontaneous at
+constant pressure or temperature if we
+
+ align:start position:0%
+constant pressure or temperature if we
+ 
+
+ align:start position:0%
+constant pressure or temperature if we
+want to know if the dissolving whether
+
+ align:start position:0%
+want to know if the dissolving whether
+ 
+
+ align:start position:0%
+want to know if the dissolving whether
+it will dissolve
+
+ align:start position:0%
+it will dissolve
+ 
+
+ align:start position:0%
+it will dissolve
+spontaneously what am I asking about
+
+ align:start position:0%
+spontaneously what am I asking about
+ 
+
+ align:start position:0%
+spontaneously what am I asking about
+what term do I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know I want to know about Delta G I sure
+
+ align:start position:0%
+know I want to know about Delta G I sure
+ 
+
+ align:start position:0%
+know I want to know about Delta G I sure
+do Delta G tells us whether things are
+
+ align:start position:0%
+do Delta G tells us whether things are
+ 
+
+ align:start position:0%
+do Delta G tells us whether things are
+spontaneous or not it does with
+
+ align:start position:0%
+spontaneous or not it does with
+ 
+
+ align:start position:0%
+spontaneous or not it does with
+thermodynamics it does with solubility
+
+ align:start position:0%
+thermodynamics it does with solubility
+ 
+
+ align:start position:0%
+thermodynamics it does with solubility
+Delta G is the predictor of whether
+
+ align:start position:0%
+Delta G is the predictor of whether
+ 
+
+ align:start position:0%
+Delta G is the predictor of whether
+something is going to be spont aneous or
+
+ align:start position:0%
+something is going to be spont aneous or
+ 
+
+ align:start position:0%
+something is going to be spont aneous or
+nonspontaneous by the sign of Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G so entropy don't want to leave out
+
+ align:start position:0%
+G so entropy don't want to leave out
+ 
+
+ align:start position:0%
+G so entropy don't want to leave out
+entropy never leave out entropy my
+
+ align:start position:0%
+entropy never leave out entropy my
+ 
+
+ align:start position:0%
+entropy never leave out entropy my
+t-shirts still unaccounted for after
+
+ align:start position:0%
+t-shirts still unaccounted for after
+ 
+
+ align:start position:0%
+t-shirts still unaccounted for after
+they got back to Massachusetts they left
+
+ align:start position:0%
+they got back to Massachusetts they left
+ 
+
+ align:start position:0%
+they got back to Massachusetts they left
+for New Jersey and Cincinnati again last
+
+ align:start position:0%
+for New Jersey and Cincinnati again last
+ 
+
+ align:start position:0%
+for New Jersey and Cincinnati again last
+time I checked they were still in
+
+ align:start position:0%
+time I checked they were still in
+ 
+
+ align:start position:0%
+time I checked they were still in
+Ohio
+
+ align:start position:0%
+Ohio
+ 
+
+ align:start position:0%
+Ohio
+entropy all right so since disorder
+
+ align:start position:0%
+entropy all right so since disorder
+ 
+
+ align:start position:0%
+entropy all right so since disorder
+typically increases when when a solvent
+
+ align:start position:0%
+typically increases when when a solvent
+ 
+
+ align:start position:0%
+typically increases when when a solvent
+dissolves typically entropy should
+
+ align:start position:0%
+dissolves typically entropy should
+ 
+
+ align:start position:0%
+dissolves typically entropy should
+increase and there's a little star and
+
+ align:start position:0%
+increase and there's a little star and
+ 
+
+ align:start position:0%
+increase and there's a little star and
+we'll get back to the star because
+
+ align:start position:0%
+we'll get back to the star because
+ 
+
+ align:start position:0%
+we'll get back to the star because
+doesn't always increase but typically it
+
+ align:start position:0%
+doesn't always increase but typically it
+ 
+
+ align:start position:0%
+doesn't always increase but typically it
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+increase so if we're looking at these
+
+ align:start position:0%
+increase so if we're looking at these
+ 
+
+ align:start position:0%
+increase so if we're looking at these
+pictures here over here you have your
+
+ align:start position:0%
+pictures here over here you have your
+ 
+
+ align:start position:0%
+pictures here over here you have your
+nice uh molecules all lined up in your
+
+ align:start position:0%
+nice uh molecules all lined up in your
+ 
+
+ align:start position:0%
+nice uh molecules all lined up in your
+solvent in your solid and it's going to
+
+ align:start position:0%
+solvent in your solid and it's going to
+ 
+
+ align:start position:0%
+solvent in your solid and it's going to
+then dissolve and you can see that when
+
+ align:start position:0%
+then dissolve and you can see that when
+ 
+
+ align:start position:0%
+then dissolve and you can see that when
+it's dissolved that's a lot more entropy
+
+ align:start position:0%
+it's dissolved that's a lot more entropy
+ 
+
+ align:start position:0%
+it's dissolved that's a lot more entropy
+over there there a lot more freedom
+
+ align:start position:0%
+over there there a lot more freedom
+ 
+
+ align:start position:0%
+over there there a lot more freedom
+moving around this is more constraint
+
+ align:start position:0%
+moving around this is more constraint
+ 
+
+ align:start position:0%
+moving around this is more constraint
+so typically entropy increases when
+
+ align:start position:0%
+so typically entropy increases when
+ 
+
+ align:start position:0%
+so typically entropy increases when
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+dissolve so if Delta H is negative and
+
+ align:start position:0%
+dissolve so if Delta H is negative and
+ 
+
+ align:start position:0%
+dissolve so if Delta H is negative and
+Delta s increases when a solute
+
+ align:start position:0%
+Delta s increases when a solute
+ 
+
+ align:start position:0%
+Delta s increases when a solute
+dissolves then what do we expect about
+
+ align:start position:0%
+dissolves then what do we expect about
+ 
+
+ align:start position:0%
+dissolves then what do we expect about
+the dissolving process and that's a
+
+ align:start position:0%
+the dissolving process and that's a
+ 
+
+ align:start position:0%
+the dissolving process and that's a
+clicker question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so most people have so we'll take
+
+ align:start position:0%
+yeah so most people have so we'll take
+ 
+
+ align:start position:0%
+yeah so most people have so we'll take
+10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds okay so let's look at both of
+
+ align:start position:0%
+seconds okay so let's look at both of
+ 
+
+ align:start position:0%
+seconds okay so let's look at both of
+them because we're going to do this one
+
+ align:start position:0%
+them because we're going to do this one
+ 
+
+ align:start position:0%
+them because we're going to do this one
+in a few minutes um so let's uh let's
+
+ align:start position:0%
+in a few minutes um so let's uh let's
+ 
+
+ align:start position:0%
+in a few minutes um so let's uh let's
+just continue with our notes and we're
+
+ align:start position:0%
+just continue with our notes and we're
+ 
+
+ align:start position:0%
+just continue with our notes and we're
+going to come back to that one I don't
+
+ align:start position:0%
+going to come back to that one I don't
+ 
+
+ align:start position:0%
+going to come back to that one I don't
+know could we just leave that one up
+
+ align:start position:0%
+know could we just leave that one up
+ 
+
+ align:start position:0%
+know could we just leave that one up
+maybe um for a minute I don't know how
+
+ align:start position:0%
+maybe um for a minute I don't know how
+ 
+
+ align:start position:0%
+maybe um for a minute I don't know how
+long it was going to take to me to get
+
+ align:start position:0%
+long it was going to take to me to get
+ 
+
+ align:start position:0%
+long it was going to take to me to get
+there all right so when we're talking
+
+ align:start position:0%
+there all right so when we're talking
+ 
+
+ align:start position:0%
+there all right so when we're talking
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+oops so if uh we'll just keep things in
+
+ align:start position:0%
+oops so if uh we'll just keep things in
+ 
+
+ align:start position:0%
+oops so if uh we'll just keep things in
+the notes and we'll come back to that
+
+ align:start position:0%
+the notes and we'll come back to that
+ 
+
+ align:start position:0%
+the notes and we'll come back to that
+one so if this is if this is negative
+
+ align:start position:0%
+one so if this is if this is negative
+ 
+
+ align:start position:0%
+one so if this is if this is negative
+and Delta s is increasing so if this is
+
+ align:start position:0%
+and Delta s is increasing so if this is
+ 
+
+ align:start position:0%
+and Delta s is increasing so if this is
+negative and this is positive then
+
+ align:start position:0%
+negative and this is positive then
+ 
+
+ align:start position:0%
+negative and this is positive then
+you're going to have a spont anous
+
+ align:start position:0%
+you're going to have a spont anous
+ 
+
+ align:start position:0%
+you're going to have a spont anous
+process here so if you can put in your
+
+ align:start position:0%
+process here so if you can put in your
+ 
+
+ align:start position:0%
+process here so if you can put in your
+notes that this should be spontaneous
+
+ align:start position:0%
+notes that this should be spontaneous
+ 
+
+ align:start position:0%
+notes that this should be spontaneous
+under these
+
+ align:start position:0%
+under these
+ 
+
+ align:start position:0%
+under these
+circumstances all right so now let's uh
+
+ align:start position:0%
+circumstances all right so now let's uh
+ 
+
+ align:start position:0%
+circumstances all right so now let's uh
+continue on and think about getting
+
+ align:start position:0%
+continue on and think about getting
+ 
+
+ align:start position:0%
+continue on and think about getting
+around to the next one so
+
+ align:start position:0%
+around to the next one so
+ 
+
+ align:start position:0%
+around to the next one so
+um in some cases I don't know hopefully
+
+ align:start position:0%
+um in some cases I don't know hopefully
+ 
+
+ align:start position:0%
+um in some cases I don't know hopefully
+if people can see this in some cases
+
+ align:start position:0%
+if people can see this in some cases
+ 
+
+ align:start position:0%
+if people can see this in some cases
+entropy of the system is actually
+
+ align:start position:0%
+entropy of the system is actually
+ 
+
+ align:start position:0%
+entropy of the system is actually
+lowered when something dissolves and
+
+ align:start position:0%
+lowered when something dissolves and
+ 
+
+ align:start position:0%
+lowered when something dissolves and
+this is because of what's known as this
+
+ align:start position:0%
+this is because of what's known as this
+ 
+
+ align:start position:0%
+this is because of what's known as this
+cage effect if you have water molecules
+
+ align:start position:0%
+cage effect if you have water molecules
+ 
+
+ align:start position:0%
+cage effect if you have water molecules
+when something dissolves sometimes order
+
+ align:start position:0%
+when something dissolves sometimes order
+ 
+
+ align:start position:0%
+when something dissolves sometimes order
+around the thing and so the water
+
+ align:start position:0%
+around the thing and so the water
+ 
+
+ align:start position:0%
+around the thing and so the water
+entropy is uh determining the process
+
+ align:start position:0%
+entropy is uh determining the process
+ 
+
+ align:start position:0%
+entropy is uh determining the process
+and so it's uh it's it's you have this
+
+ align:start position:0%
+and so it's uh it's it's you have this
+ 
+
+ align:start position:0%
+and so it's uh it's it's you have this
+new order because of the water structure
+
+ align:start position:0%
+new order because of the water structure
+ 
+
+ align:start position:0%
+new order because of the water structure
+so this can change so it's not always
+
+ align:start position:0%
+so this can change so it's not always
+ 
+
+ align:start position:0%
+so this can change so it's not always
+the case that entropy of the overall
+
+ align:start position:0%
+the case that entropy of the overall
+ 
+
+ align:start position:0%
+the case that entropy of the overall
+system is uh going to increase so here
+
+ align:start position:0%
+system is uh going to increase so here
+ 
+
+ align:start position:0%
+system is uh going to increase so here
+even if this is a negative value Delta H
+
+ align:start position:0%
+even if this is a negative value Delta H
+ 
+
+ align:start position:0%
+even if this is a negative value Delta H
+solution is negative Delta G might be
+
+ align:start position:0%
+solution is negative Delta G might be
+ 
+
+ align:start position:0%
+solution is negative Delta G might be
+positive it might not be a spontaneous
+
+ align:start position:0%
+positive it might not be a spontaneous
+ 
+
+ align:start position:0%
+positive it might not be a spontaneous
+system and so the cage effect is why
+
+ align:start position:0%
+system and so the cage effect is why
+ 
+
+ align:start position:0%
+system and so the cage effect is why
+some things that are hydrophobic you
+
+ align:start position:0%
+some things that are hydrophobic you
+ 
+
+ align:start position:0%
+some things that are hydrophobic you
+just you're having a hard time
+
+ align:start position:0%
+just you're having a hard time
+ 
+
+ align:start position:0%
+just you're having a hard time
+dissolving them even if they have a
+
+ align:start position:0%
+dissolving them even if they have a
+ 
+
+ align:start position:0%
+dissolving them even if they have a
+negative enthalpy even if you would just
+
+ align:start position:0%
+negative enthalpy even if you would just
+ 
+
+ align:start position:0%
+negative enthalpy even if you would just
+look at the negative enthalpy and
+
+ align:start position:0%
+look at the negative enthalpy and
+ 
+
+ align:start position:0%
+look at the negative enthalpy and
+predict that it should be spontaneous
+
+ align:start position:0%
+predict that it should be spontaneous
+ 
+
+ align:start position:0%
+predict that it should be spontaneous
+because even if this is NE if this is
+
+ align:start position:0%
+because even if this is NE if this is
+ 
+
+ align:start position:0%
+because even if this is NE if this is
+negative if Delta s is also negative
+
+ align:start position:0%
+negative if Delta s is also negative
+ 
+
+ align:start position:0%
+negative if Delta s is also negative
+because you have more order due to the
+
+ align:start position:0%
+because you have more order due to the
+ 
+
+ align:start position:0%
+because you have more order due to the
+water molecules then the overall term
+
+ align:start position:0%
+water molecules then the overall term
+ 
+
+ align:start position:0%
+water molecules then the overall term
+can be positive it would depend on the
+
+ align:start position:0%
+can be positive it would depend on the
+ 
+
+ align:start position:0%
+can be positive it would depend on the
+magnet nitudes of of these and of the
+
+ align:start position:0%
+magnet nitudes of of these and of the
+ 
+
+ align:start position:0%
+magnet nitudes of of these and of the
+temperature so then um this is actually
+
+ align:start position:0%
+temperature so then um this is actually
+ 
+
+ align:start position:0%
+temperature so then um this is actually
+more slides than I remembered before we
+
+ align:start position:0%
+more slides than I remembered before we
+ 
+
+ align:start position:0%
+more slides than I remembered before we
+get to the next oh this is the last one
+
+ align:start position:0%
+get to the next oh this is the last one
+ 
+
+ align:start position:0%
+get to the next oh this is the last one
+okay so uh when gases are in liquids uh
+
+ align:start position:0%
+okay so uh when gases are in liquids uh
+ 
+
+ align:start position:0%
+okay so uh when gases are in liquids uh
+dissolved in a liquid there's much less
+
+ align:start position:0%
+dissolved in a liquid there's much less
+ 
+
+ align:start position:0%
+dissolved in a liquid there's much less
+Freedom gases not dissolved can be
+
+ align:start position:0%
+Freedom gases not dissolved can be
+ 
+
+ align:start position:0%
+Freedom gases not dissolved can be
+anywhere um but when they're in a liquid
+
+ align:start position:0%
+anywhere um but when they're in a liquid
+ 
+
+ align:start position:0%
+anywhere um but when they're in a liquid
+then there's much less freedom and so
+
+ align:start position:0%
+then there's much less freedom and so
+ 
+
+ align:start position:0%
+then there's much less freedom and so
+the entropy then is going to be negative
+
+ align:start position:0%
+the entropy then is going to be negative
+ 
+
+ align:start position:0%
+the entropy then is going to be negative
+and the solubility will decrease um as
+
+ align:start position:0%
+and the solubility will decrease um as
+ 
+
+ align:start position:0%
+and the solubility will decrease um as
+the temperature rises and so that brings
+
+ align:start position:0%
+the temperature rises and so that brings
+ 
+
+ align:start position:0%
+the temperature rises and so that brings
+us then to our question about Delta h of
+
+ align:start position:0%
+us then to our question about Delta h of
+ 
+
+ align:start position:0%
+us then to our question about Delta h of
+solution being positive and now we can
+
+ align:start position:0%
+solution being positive and now we can
+ 
+
+ align:start position:0%
+solution being positive and now we can
+look at the answer to
+
+ align:start position:0%
+look at the answer to
+ 
+
+ align:start position:0%
+look at the answer to
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+so now I guess we can go maybe to the
+
+ align:start position:0%
+so now I guess we can go maybe to the
+ 
+
+ align:start position:0%
+so now I guess we can go maybe to the
+other slide so that was the question
+
+ align:start position:0%
+other slide so that was the question
+ 
+
+ align:start position:0%
+other slide so that was the question
+that you had here and um I've just put
+
+ align:start position:0%
+that you had here and um I've just put
+ 
+
+ align:start position:0%
+that you had here and um I've just put
+up the answers so here Delta H is
+
+ align:start position:0%
+up the answers so here Delta H is
+ 
+
+ align:start position:0%
+up the answers so here Delta H is
+positive and so we have positive minus t
+
+ align:start position:0%
+positive and so we have positive minus t
+ 
+
+ align:start position:0%
+positive and so we have positive minus t
+Delta s again we don't it we weren't
+
+ align:start position:0%
+Delta s again we don't it we weren't
+ 
+
+ align:start position:0%
+Delta s again we don't it we weren't
+told anything about Delta s in this
+
+ align:start position:0%
+told anything about Delta s in this
+ 
+
+ align:start position:0%
+told anything about Delta s in this
+particular just ask what if it's
+
+ align:start position:0%
+particular just ask what if it's
+ 
+
+ align:start position:0%
+particular just ask what if it's
+positive um and so one for the first one
+
+ align:start position:0%
+positive um and so one for the first one
+ 
+
+ align:start position:0%
+positive um and so one for the first one
+said dissolving is never spontaneous and
+
+ align:start position:0%
+said dissolving is never spontaneous and
+ 
+
+ align:start position:0%
+said dissolving is never spontaneous and
+that isn't necessarily true um because
+
+ align:start position:0%
+that isn't necessarily true um because
+ 
+
+ align:start position:0%
+that isn't necessarily true um because
+you don't know what Delta s is
+
+ align:start position:0%
+you don't know what Delta s is
+ 
+
+ align:start position:0%
+you don't know what Delta s is
+dissolving is only spontaneous if T
+
+ align:start position:0%
+dissolving is only spontaneous if T
+ 
+
+ align:start position:0%
+dissolving is only spontaneous if T
+Delta s is positive and larger than
+
+ align:start position:0%
+Delta s is positive and larger than
+ 
+
+ align:start position:0%
+Delta s is positive and larger than
+Delta H solution and that was the
+
+ align:start position:0%
+Delta H solution and that was the
+ 
+
+ align:start position:0%
+Delta H solution and that was the
+correct answer if this is a big term
+
+ align:start position:0%
+correct answer if this is a big term
+ 
+
+ align:start position:0%
+correct answer if this is a big term
+here um it's larger than that term and
+
+ align:start position:0%
+here um it's larger than that term and
+ 
+
+ align:start position:0%
+here um it's larger than that term and
+this is a positive value then you would
+
+ align:start position:0%
+this is a positive value then you would
+ 
+
+ align:start position:0%
+this is a positive value then you would
+get a negative Delta G and it would be
+
+ align:start position:0%
+get a negative Delta G and it would be
+ 
+
+ align:start position:0%
+get a negative Delta G and it would be
+uh a spontaneous process if we look at
+
+ align:start position:0%
+uh a spontaneous process if we look at
+ 
+
+ align:start position:0%
+uh a spontaneous process if we look at
+number three here dissolving is only
+
+ align:start position:0%
+number three here dissolving is only
+ 
+
+ align:start position:0%
+number three here dissolving is only
+spontaneous if this is negative that
+
+ align:start position:0%
+spontaneous if this is negative that
+ 
+
+ align:start position:0%
+spontaneous if this is negative that
+does not help us at all um and the rate
+
+ align:start position:0%
+does not help us at all um and the rate
+ 
+
+ align:start position:0%
+does not help us at all um and the rate
+will be slower Delta H is not going to
+
+ align:start position:0%
+will be slower Delta H is not going to
+ 
+
+ align:start position:0%
+will be slower Delta H is not going to
+going to tell us anything about rates
+
+ align:start position:0%
+going to tell us anything about rates
+ 
+
+ align:start position:0%
+going to tell us anything about rates
+rates are determined by kinetics
+
+ align:start position:0%
+rates are determined by kinetics
+ 
+
+ align:start position:0%
+rates are determined by kinetics
+temperature can affect the rates for
+
+ align:start position:0%
+temperature can affect the rates for
+ 
+
+ align:start position:0%
+temperature can affect the rates for
+sure stirring can affect the rates for
+
+ align:start position:0%
+sure stirring can affect the rates for
+ 
+
+ align:start position:0%
+sure stirring can affect the rates for
+sure but Delta H is not telling us about
+
+ align:start position:0%
+sure but Delta H is not telling us about
+ 
+
+ align:start position:0%
+sure but Delta H is not telling us about
+being T Delta H being positive is not
+
+ align:start position:0%
+being T Delta H being positive is not
+ 
+
+ align:start position:0%
+being T Delta H being positive is not
+telling us about the rates so you'll see
+
+ align:start position:0%
+telling us about the rates so you'll see
+ 
+
+ align:start position:0%
+telling us about the rates so you'll see
+in this um in this particular unit when
+
+ align:start position:0%
+in this um in this particular unit when
+ 
+
+ align:start position:0%
+in this um in this particular unit when
+you're thinking about solubility you're
+
+ align:start position:0%
+you're thinking about solubility you're
+ 
+
+ align:start position:0%
+you're thinking about solubility you're
+thinking about equilibrium Expressions a
+
+ align:start position:0%
+thinking about equilibrium Expressions a
+ 
+
+ align:start position:0%
+thinking about equilibrium Expressions a
+special equilibrium expression KSP
+
+ align:start position:0%
+special equilibrium expression KSP
+ 
+
+ align:start position:0%
+special equilibrium expression KSP
+you're thinking about um partial
+
+ align:start position:0%
+you're thinking about um partial
+ 
+
+ align:start position:0%
+you're thinking about um partial
+pressures again you're thinking about
+
+ align:start position:0%
+pressures again you're thinking about
+ 
+
+ align:start position:0%
+pressures again you're thinking about
+effects on um the solubility that have
+
+ align:start position:0%
+effects on um the solubility that have
+ 
+
+ align:start position:0%
+effects on um the solubility that have
+to do with temperatures you're thinking
+
+ align:start position:0%
+to do with temperatures you're thinking
+ 
+
+ align:start position:0%
+to do with temperatures you're thinking
+about Delta H Delta s and Delta G so
+
+ align:start position:0%
+about Delta H Delta s and Delta G so
+ 
+
+ align:start position:0%
+about Delta H Delta s and Delta G so
+it's really an outgrowth of
+
+ align:start position:0%
+it's really an outgrowth of
+ 
+
+ align:start position:0%
+it's really an outgrowth of
+thermodynamics and chemical equilibrium
+
+ align:start position:0%
+thermodynamics and chemical equilibrium
+ 
+
+ align:start position:0%
+thermodynamics and chemical equilibrium
+but you're just applying really what
+
+ align:start position:0%
+but you're just applying really what
+ 
+
+ align:start position:0%
+but you're just applying really what
+you've already learned to thinking about
+
+ align:start position:0%
+you've already learned to thinking about
+ 
+
+ align:start position:0%
+you've already learned to thinking about
+a solute dissolving in a solvent um so
+
+ align:start position:0%
+a solute dissolving in a solvent um so
+ 
+
+ align:start position:0%
+a solute dissolving in a solvent um so
+that's one of the things that that's
+
+ align:start position:0%
+that's one of the things that that's
+ 
+
+ align:start position:0%
+that's one of the things that that's
+really great about the course in the
+
+ align:start position:0%
+really great about the course in the
+ 
+
+ align:start position:0%
+really great about the course in the
+next couple units is that everything's
+
+ align:start position:0%
+next couple units is that everything's
+ 
+
+ align:start position:0%
+next couple units is that everything's
+very connected so we can just briefly
+
+ align:start position:0%
+very connected so we can just briefly
+ 
+
+ align:start position:0%
+very connected so we can just briefly
+introduce you to the next unit and we're
+
+ align:start position:0%
+introduce you to the next unit and we're
+ 
+
+ align:start position:0%
+introduce you to the next unit and we're
+going to be talking about acids and
+
+ align:start position:0%
+going to be talking about acids and
+ 
+
+ align:start position:0%
+going to be talking about acids and
+bases now for several lectures um and I
+
+ align:start position:0%
+bases now for several lectures um and I
+ 
+
+ align:start position:0%
+bases now for several lectures um and I
+have to say that this is one of the
+
+ align:start position:0%
+have to say that this is one of the
+ 
+
+ align:start position:0%
+have to say that this is one of the
+units when we get to kind of acid based
+
+ align:start position:0%
+units when we get to kind of acid based
+ 
+
+ align:start position:0%
+units when we get to kind of acid based
+titrations that MIT students seem to
+
+ align:start position:0%
+titrations that MIT students seem to
+ 
+
+ align:start position:0%
+titrations that MIT students seem to
+struggle with so um we're going to spend
+
+ align:start position:0%
+struggle with so um we're going to spend
+ 
+
+ align:start position:0%
+struggle with so um we're going to spend
+we're going to slow this down and really
+
+ align:start position:0%
+we're going to slow this down and really
+ 
+
+ align:start position:0%
+we're going to slow this down and really
+go over it and have you be awesome at
+
+ align:start position:0%
+go over it and have you be awesome at
+ 
+
+ align:start position:0%
+go over it and have you be awesome at
+acids and bases all right so
+
+ align:start position:0%
+acids and bases all right so
+ 
+
+ align:start position:0%
+acids and bases all right so
+um and I'll I'll I'll mention that one
+
+ align:start position:0%
+um and I'll I'll I'll mention that one
+ 
+
+ align:start position:0%
+um and I'll I'll I'll mention that one
+of the reasons why I spend time on
+
+ align:start position:0%
+of the reasons why I spend time on
+ 
+
+ align:start position:0%
+of the reasons why I spend time on
+solubility and acids bases because these
+
+ align:start position:0%
+solubility and acids bases because these
+ 
+
+ align:start position:0%
+solubility and acids bases because these
+are topics that are really important for
+
+ align:start position:0%
+are topics that are really important for
+ 
+
+ align:start position:0%
+are topics that are really important for
+medical school and I know a lot of you
+
+ align:start position:0%
+medical school and I know a lot of you
+ 
+
+ align:start position:0%
+medical school and I know a lot of you
+are not Premed but I want everybody in
+
+ align:start position:0%
+are not Premed but I want everybody in
+ 
+
+ align:start position:0%
+are not Premed but I want everybody in
+this class to have that background that
+
+ align:start position:0%
+this class to have that background that
+ 
+
+ align:start position:0%
+this class to have that background that
+they could go to med school if they
+
+ align:start position:0%
+they could go to med school if they
+ 
+
+ align:start position:0%
+they could go to med school if they
+wanted to or they could um just advocate
+
+ align:start position:0%
+wanted to or they could um just advocate
+ 
+
+ align:start position:0%
+wanted to or they could um just advocate
+for their own health um U with a doctor
+
+ align:start position:0%
+for their own health um U with a doctor
+ 
+
+ align:start position:0%
+for their own health um U with a doctor
+who doesn't know about acids and bases
+
+ align:start position:0%
+who doesn't know about acids and bases
+ 
+
+ align:start position:0%
+who doesn't know about acids and bases
+and I'll tell you a story about that a
+
+ align:start position:0%
+and I'll tell you a story about that a
+ 
+
+ align:start position:0%
+and I'll tell you a story about that a
+little later um
+
+ align:start position:0%
+little later um
+ 
+
+ align:start position:0%
+little later um
+anyway okay so acids and bases we're
+
+ align:start position:0%
+anyway okay so acids and bases we're
+ 
+
+ align:start position:0%
+anyway okay so acids and bases we're
+just going to do some
+
+ align:start position:0%
+just going to do some
+ 
+
+ align:start position:0%
+just going to do some
+definitions so um the simplest um
+
+ align:start position:0%
+definitions so um the simplest um
+ 
+
+ align:start position:0%
+definitions so um the simplest um
+definition of this is that an acid is a
+
+ align:start position:0%
+definition of this is that an acid is a
+ 
+
+ align:start position:0%
+definition of this is that an acid is a
+substance that when dissolved in water
+
+ align:start position:0%
+substance that when dissolved in water
+ 
+
+ align:start position:0%
+substance that when dissolved in water
+increases the concentration of hydrogen
+
+ align:start position:0%
+increases the concentration of hydrogen
+ 
+
+ align:start position:0%
+increases the concentration of hydrogen
+ions
+
+ align:start position:0%
+ions
+ 
+
+ align:start position:0%
+ions
+H+ whereas a base is a substance that
+
+ align:start position:0%
+H+ whereas a base is a substance that
+ 
+
+ align:start position:0%
+H+ whereas a base is a substance that
+increases the hydroxide concentration o
+
+ align:start position:0%
+increases the hydroxide concentration o
+ 
+
+ align:start position:0%
+increases the hydroxide concentration o
+minus so there are acids and bases that
+
+ align:start position:0%
+minus so there are acids and bases that
+ 
+
+ align:start position:0%
+minus so there are acids and bases that
+definitely fit this description but this
+
+ align:start position:0%
+definitely fit this description but this
+ 
+
+ align:start position:0%
+definitely fit this description but this
+is a very narrow description of acids
+
+ align:start position:0%
+is a very narrow description of acids
+ 
+
+ align:start position:0%
+is a very narrow description of acids
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+bases the next one the bronzee Lowry is
+
+ align:start position:0%
+bases the next one the bronzee Lowry is
+ 
+
+ align:start position:0%
+bases the next one the bronzee Lowry is
+a bit
+
+ align:start position:0%
+a bit
+ 
+
+ align:start position:0%
+a bit
+broader so an acid is something that
+
+ align:start position:0%
+broader so an acid is something that
+ 
+
+ align:start position:0%
+broader so an acid is something that
+donates a hydrogen ion
+
+ align:start position:0%
+donates a hydrogen ion
+ 
+
+ align:start position:0%
+donates a hydrogen ion
+H+ and a bronzed lowy base is something
+
+ align:start position:0%
+H+ and a bronzed lowy base is something
+ 
+
+ align:start position:0%
+H+ and a bronzed lowy base is something
+that accepts a hydrogen ion and this is
+
+ align:start position:0%
+that accepts a hydrogen ion and this is
+ 
+
+ align:start position:0%
+that accepts a hydrogen ion and this is
+really the definition we'll be spending
+
+ align:start position:0%
+really the definition we'll be spending
+ 
+
+ align:start position:0%
+really the definition we'll be spending
+the most time with in the the class so
+
+ align:start position:0%
+the most time with in the the class so
+ 
+
+ align:start position:0%
+the most time with in the the class so
+let's look at some examples of
+
+ align:start position:0%
+let's look at some examples of
+ 
+
+ align:start position:0%
+let's look at some examples of
+this so here we have an
+
+ align:start position:0%
+this so here we have an
+ 
+
+ align:start position:0%
+this so here we have an
+acid and if it's an acid it's going to
+
+ align:start position:0%
+acid and if it's an acid it's going to
+ 
+
+ align:start position:0%
+acid and if it's an acid it's going to
+be donating a hydrogen ion and it's
+
+ align:start position:0%
+be donating a hydrogen ion and it's
+ 
+
+ align:start position:0%
+be donating a hydrogen ion and it's
+going to donate it here to the water the
+
+ align:start position:0%
+going to donate it here to the water the
+ 
+
+ align:start position:0%
+going to donate it here to the water the
+water acts as a base in that it accepts
+
+ align:start position:0%
+water acts as a base in that it accepts
+ 
+
+ align:start position:0%
+water acts as a base in that it accepts
+the hydrogen ion when it accepts the
+
+ align:start position:0%
+the hydrogen ion when it accepts the
+ 
+
+ align:start position:0%
+the hydrogen ion when it accepts the
+hydrogen ion it has one extra hydrogen
+
+ align:start position:0%
+hydrogen ion it has one extra hydrogen
+ 
+
+ align:start position:0%
+hydrogen ion it has one extra hydrogen
+ion so it's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h3o+ and when the acid loses its
+
+ align:start position:0%
+h3o+ and when the acid loses its
+ 
+
+ align:start position:0%
+h3o+ and when the acid loses its
+hydrogen ion it becomes this base over
+
+ align:start position:0%
+hydrogen ion it becomes this base over
+ 
+
+ align:start position:0%
+hydrogen ion it becomes this base over
+here the same molecule minus the
+
+ align:start position:0%
+here the same molecule minus the
+ 
+
+ align:start position:0%
+here the same molecule minus the
+hydrogen ion so now it has a negative
+
+ align:start position:0%
+hydrogen ion so now it has a negative
+ 
+
+ align:start position:0%
+hydrogen ion so now it has a negative
+charge and so this uh we're you'll see
+
+ align:start position:0%
+charge and so this uh we're you'll see
+ 
+
+ align:start position:0%
+charge and so this uh we're you'll see
+hydronium ions quite a bit which is
+
+ align:start position:0%
+hydronium ions quite a bit which is
+ 
+
+ align:start position:0%
+hydronium ions quite a bit which is
+h3o+ that's really the more accurate
+
+ align:start position:0%
+h3o+ that's really the more accurate
+ 
+
+ align:start position:0%
+h3o+ that's really the more accurate
+form rather than just writing H+
+
+ align:start position:0%
+form rather than just writing H+
+ 
+
+ align:start position:0%
+form rather than just writing H+
+somewhere so that's the kind of true
+
+ align:start position:0%
+somewhere so that's the kind of true
+ 
+
+ align:start position:0%
+somewhere so that's the kind of true
+nature of things so let me just show you
+
+ align:start position:0%
+nature of things so let me just show you
+ 
+
+ align:start position:0%
+nature of things so let me just show you
+a little anim of this happening I think
+
+ align:start position:0%
+a little anim of this happening I think
+ 
+
+ align:start position:0%
+a little anim of this happening I think
+it's kind of cute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so here we have our water molecules
+
+ align:start position:0%
+um so here we have our water molecules
+ 
+
+ align:start position:0%
+um so here we have our water molecules
+and we have um our our uh acid it
+
+ align:start position:0%
+and we have um our our uh acid it
+ 
+
+ align:start position:0%
+and we have um our our uh acid it
+donated a hydrogen ion to this and then
+
+ align:start position:0%
+donated a hydrogen ion to this and then
+ 
+
+ align:start position:0%
+donated a hydrogen ion to this and then
+another water came and stole it away and
+
+ align:start position:0%
+another water came and stole it away and
+ 
+
+ align:start position:0%
+another water came and stole it away and
+so there's our
+
+ align:start position:0%
+so there's our
+ 
+
+ align:start position:0%
+so there's our
+h3o+ and so in solution you have this
+
+ align:start position:0%
+h3o+ and so in solution you have this
+ 
+
+ align:start position:0%
+h3o+ and so in solution you have this
+exchange of hydrogen atoms the acid is
+
+ align:start position:0%
+exchange of hydrogen atoms the acid is
+ 
+
+ align:start position:0%
+exchange of hydrogen atoms the acid is
+donating the base is accepting and as
+
+ align:start position:0%
+donating the base is accepting and as
+ 
+
+ align:start position:0%
+donating the base is accepting and as
+they donate and accept they become
+
+ align:start position:0%
+they donate and accept they become
+ 
+
+ align:start position:0%
+they donate and accept they become
+different molecules so that gives rise
+
+ align:start position:0%
+different molecules so that gives rise
+ 
+
+ align:start position:0%
+different molecules so that gives rise
+to this idea of conjugate acid base
+
+ align:start position:0%
+to this idea of conjugate acid base
+ 
+
+ align:start position:0%
+to this idea of conjugate acid base
+pairs so here you see that um this acid
+
+ align:start position:0%
+pairs so here you see that um this acid
+ 
+
+ align:start position:0%
+pairs so here you see that um this acid
+is paired with this base over here
+
+ align:start position:0%
+is paired with this base over here
+ 
+
+ align:start position:0%
+is paired with this base over here
+they're the same except that one has the
+
+ align:start position:0%
+they're the same except that one has the
+ 
+
+ align:start position:0%
+they're the same except that one has the
+hydrogen ion and one does not and then
+
+ align:start position:0%
+hydrogen ion and one does not and then
+ 
+
+ align:start position:0%
+hydrogen ion and one does not and then
+the other pair is here it's a it's
+
+ align:start position:0%
+the other pair is here it's a it's
+ 
+
+ align:start position:0%
+the other pair is here it's a it's
+another acid base pair we have water and
+
+ align:start position:0%
+another acid base pair we have water and
+ 
+
+ align:start position:0%
+another acid base pair we have water and
+hydronium ion that also differ by H+ so
+
+ align:start position:0%
+hydronium ion that also differ by H+ so
+ 
+
+ align:start position:0%
+hydronium ion that also differ by H+ so
+every time an acid donates a hydrogen
+
+ align:start position:0%
+every time an acid donates a hydrogen
+ 
+
+ align:start position:0%
+every time an acid donates a hydrogen
+ion or proton it becomes its conjugate
+
+ align:start position:0%
+ion or proton it becomes its conjugate
+ 
+
+ align:start position:0%
+ion or proton it becomes its conjugate
+base every time a base accepts a
+
+ align:start position:0%
+base every time a base accepts a
+ 
+
+ align:start position:0%
+base every time a base accepts a
+hydrogen ion or proton it becomes its
+
+ align:start position:0%
+hydrogen ion or proton it becomes its
+ 
+
+ align:start position:0%
+hydrogen ion or proton it becomes its
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+acid so the conjugate base of any acid
+
+ align:start position:0%
+acid so the conjugate base of any acid
+ 
+
+ align:start position:0%
+acid so the conjugate base of any acid
+is the base that is formed when the acid
+
+ align:start position:0%
+is the base that is formed when the acid
+ 
+
+ align:start position:0%
+is the base that is formed when the acid
+acid has donated hydrogen ion or proton
+
+ align:start position:0%
+acid has donated hydrogen ion or proton
+ 
+
+ align:start position:0%
+acid has donated hydrogen ion or proton
+the conjugate acid of a base is the acid
+
+ align:start position:0%
+the conjugate acid of a base is the acid
+ 
+
+ align:start position:0%
+the conjugate acid of a base is the acid
+that forms when the base accepts a
+
+ align:start position:0%
+that forms when the base accepts a
+ 
+
+ align:start position:0%
+that forms when the base accepts a
+hydrogen ion or proton
+
+ align:start position:0%
+hydrogen ion or proton
+ 
+
+ align:start position:0%
+hydrogen ion or proton
+so let's take a look at one more example
+
+ align:start position:0%
+so let's take a look at one more example
+ 
+
+ align:start position:0%
+so let's take a look at one more example
+if this over here is this acting as an
+
+ align:start position:0%
+if this over here is this acting as an
+ 
+
+ align:start position:0%
+if this over here is this acting as an
+acid or base this molecule here what do
+
+ align:start position:0%
+acid or base this molecule here what do
+ 
+
+ align:start position:0%
+acid or base this molecule here what do
+you think you can just yell it
+
+ align:start position:0%
+you think you can just yell it
+ 
+
+ align:start position:0%
+you think you can just yell it
+out it's acting as an acid right this is
+
+ align:start position:0%
+out it's acting as an acid right this is
+ 
+
+ align:start position:0%
+out it's acting as an acid right this is
+acting then as the base when this base
+
+ align:start position:0%
+acting then as the base when this base
+ 
+
+ align:start position:0%
+acting then as the base when this base
+accepts the hydrogen ion it forms its
+
+ align:start position:0%
+accepts the hydrogen ion it forms its
+ 
+
+ align:start position:0%
+accepts the hydrogen ion it forms its
+conjugate acid and this then forms its
+
+ align:start position:0%
+conjugate acid and this then forms its
+ 
+
+ align:start position:0%
+conjugate acid and this then forms its
+conjugate base which differs by H+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why don't you why don't you try one
+
+ align:start position:0%
+so why don't you why don't you try one
+ 
+
+ align:start position:0%
+so why don't you why don't you try one
+of these then on your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+own 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can go back to that over
+
+ align:start position:0%
+okay so we can go back to that over
+ 
+
+ align:start position:0%
+okay so we can go back to that over
+there so you most people got this this
+
+ align:start position:0%
+there so you most people got this this
+ 
+
+ align:start position:0%
+there so you most people got this this
+right and so you're looking at what's
+
+ align:start position:0%
+right and so you're looking at what's
+ 
+
+ align:start position:0%
+right and so you're looking at what's
+acting as the base and what's acting as
+
+ align:start position:0%
+acting as the base and what's acting as
+ 
+
+ align:start position:0%
+acting as the base and what's acting as
+the acid again the base is going to be
+
+ align:start position:0%
+the acid again the base is going to be
+ 
+
+ align:start position:0%
+the acid again the base is going to be
+accepting a hydrogen ion so this is
+
+ align:start position:0%
+accepting a hydrogen ion so this is
+ 
+
+ align:start position:0%
+accepting a hydrogen ion so this is
+acting as the acid this forms its
+
+ align:start position:0%
+acting as the acid this forms its
+ 
+
+ align:start position:0%
+acting as the acid this forms its
+conjugate and this and um I'll just uh
+
+ align:start position:0%
+conjugate and this and um I'll just uh
+ 
+
+ align:start position:0%
+conjugate and this and um I'll just uh
+end quickly with the idea of something
+
+ align:start position:0%
+end quickly with the idea of something
+ 
+
+ align:start position:0%
+end quickly with the idea of something
+that's amphoteric which is a molecule
+
+ align:start position:0%
+that's amphoteric which is a molecule
+ 
+
+ align:start position:0%
+that's amphoteric which is a molecule
+that can act as an acid or a base you
+
+ align:start position:0%
+that can act as an acid or a base you
+ 
+
+ align:start position:0%
+that can act as an acid or a base you
+just saw some nice examples of that and
+
+ align:start position:0%
+just saw some nice examples of that and
+ 
+
+ align:start position:0%
+just saw some nice examples of that and
+finally just one last definition um for
+
+ align:start position:0%
+finally just one last definition um for
+ 
+
+ align:start position:0%
+finally just one last definition um for
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+bases and um I don't want to we'll we'll
+
+ align:start position:0%
+bases and um I don't want to we'll we'll
+ 
+
+ align:start position:0%
+bases and um I don't want to we'll we'll
+just uh put this up and then we'll
+
+ align:start position:0%
+just uh put this up and then we'll
+ 
+
+ align:start position:0%
+just uh put this up and then we'll
+that's kind of the end um so the final
+
+ align:start position:0%
+that's kind of the end um so the final
+ 
+
+ align:start position:0%
+that's kind of the end um so the final
+definition the ls Bas donates a lone
+
+ align:start position:0%
+definition the ls Bas donates a lone
+ 
+
+ align:start position:0%
+definition the ls Bas donates a lone
+pair whereas a Lewis acid accepts such
+
+ align:start position:0%
+pair whereas a Lewis acid accepts such
+ 
+
+ align:start position:0%
+pair whereas a Lewis acid accepts such
+electrons
\ No newline at end of file
diff --git a/Fj7pbLwbSmU.txt b/Fj7pbLwbSmU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f5eb768e66051e6c7a70f62fb942bccc90f20d7d
--- /dev/null
+++ b/Fj7pbLwbSmU.txt
@@ -0,0 +1,1643 @@
+align:start position:0%
+ 
+welcome back to recitation today we're
+
+ align:start position:0%
+welcome back to recitation today we're
+ 
+
+ align:start position:0%
+welcome back to recitation today we're
+going to talk about something you've
+
+ align:start position:0%
+going to talk about something you've
+ 
+
+ align:start position:0%
+going to talk about something you've
+been seeing in the lectures specifically
+
+ align:start position:0%
+been seeing in the lectures specifically
+ 
+
+ align:start position:0%
+been seeing in the lectures specifically
+we're going to talk about continuity and
+
+ align:start position:0%
+we're going to talk about continuity and
+ 
+
+ align:start position:0%
+we're going to talk about continuity and
+differentiability and we're going to use
+
+ align:start position:0%
+differentiability and we're going to use
+ 
+
+ align:start position:0%
+differentiability and we're going to use
+an example to see uh a little bit what
+
+ align:start position:0%
+an example to see uh a little bit what
+ 
+
+ align:start position:0%
+an example to see uh a little bit what
+the difference is that how you can be
+
+ align:start position:0%
+the difference is that how you can be
+ 
+
+ align:start position:0%
+the difference is that how you can be
+continuous and not necessarily
+
+ align:start position:0%
+continuous and not necessarily
+ 
+
+ align:start position:0%
+continuous and not necessarily
+differentiable and how it's a little
+
+ align:start position:0%
+differentiable and how it's a little
+ 
+
+ align:start position:0%
+differentiable and how it's a little
+stronger to to have differentiability so
+
+ align:start position:0%
+stronger to to have differentiability so
+ 
+
+ align:start position:0%
+stronger to to have differentiability so
+we're going to deal with a piecewise
+
+ align:start position:0%
+we're going to deal with a piecewise
+ 
+
+ align:start position:0%
+we're going to deal with a piecewise
+function so I'm going to ask a question
+
+ align:start position:0%
+function so I'm going to ask a question
+ 
+
+ align:start position:0%
+function so I'm going to ask a question
+uh I'll give you a little bit of time to
+
+ align:start position:0%
+uh I'll give you a little bit of time to
+ 
+
+ align:start position:0%
+uh I'll give you a little bit of time to
+work on it and then we'll come back so
+
+ align:start position:0%
+work on it and then we'll come back so
+ 
+
+ align:start position:0%
+work on it and then we'll come back so
+the question is the following for what
+
+ align:start position:0%
+the question is the following for what
+ 
+
+ align:start position:0%
+the question is the following for what
+values of A and B is the following
+
+ align:start position:0%
+values of A and B is the following
+ 
+
+ align:start position:0%
+values of A and B is the following
+function either first continuous or
+
+ align:start position:0%
+function either first continuous or
+ 
+
+ align:start position:0%
+function either first continuous or
+second differentiable so the function is
+
+ align:start position:0%
+second differentiable so the function is
+ 
+
+ align:start position:0%
+second differentiable so the function is
+defined in the following way f ofx is
+
+ align:start position:0%
+defined in the following way f ofx is
+ 
+
+ align:start position:0%
+defined in the following way f ofx is
+going to be equal to the function x^2 +
+
+ align:start position:0%
+going to be equal to the function x^2 +
+ 
+
+ align:start position:0%
+going to be equal to the function x^2 +
+1 when X is bigger than one and it's
+
+ align:start position:0%
+1 when X is bigger than one and it's
+ 
+
+ align:start position:0%
+1 when X is bigger than one and it's
+going to be equal to a linear function
+
+ align:start position:0%
+going to be equal to a linear function
+ 
+
+ align:start position:0%
+going to be equal to a linear function
+where you get to pick the a which is the
+
+ align:start position:0%
+where you get to pick the a which is the
+ 
+
+ align:start position:0%
+where you get to pick the a which is the
+slope and you get to pick the B which is
+
+ align:start position:0%
+slope and you get to pick the B which is
+ 
+
+ align:start position:0%
+slope and you get to pick the B which is
+the Y intercept if x is less than or
+
+ align:start position:0%
+the Y intercept if x is less than or
+ 
+
+ align:start position:0%
+the Y intercept if x is less than or
+equal to one so what I've drawn so far
+
+ align:start position:0%
+equal to one so what I've drawn so far
+ 
+
+ align:start position:0%
+equal to one so what I've drawn so far
+so that you can see is that I've drawn
+
+ align:start position:0%
+so that you can see is that I've drawn
+ 
+
+ align:start position:0%
+so that you can see is that I've drawn
+the part of x^2 + 1 If X is bigger than
+
+ align:start position:0%
+the part of x^2 + 1 If X is bigger than
+ 
+
+ align:start position:0%
+the part of x^2 + 1 If X is bigger than
+one so I've taken the X squ function
+
+ align:start position:0%
+one so I've taken the X squ function
+ 
+
+ align:start position:0%
+one so I've taken the X squ function
+that starts at 0 0 or the vertex is at 0
+
+ align:start position:0%
+that starts at 0 0 or the vertex is at 0
+ 
+
+ align:start position:0%
+that starts at 0 0 or the vertex is at 0
+0 I've shifted it up one unit and then
+
+ align:start position:0%
+0 I've shifted it up one unit and then
+ 
+
+ align:start position:0%
+0 I've shifted it up one unit and then
+I've chopped off everything left of and
+
+ align:start position:0%
+I've chopped off everything left of and
+ 
+
+ align:start position:0%
+I've chopped off everything left of and
+including the value at x equal one so my
+
+ align:start position:0%
+including the value at x equal one so my
+ 
+
+ align:start position:0%
+including the value at x equal one so my
+my question again is what choices do I
+
+ align:start position:0%
+my question again is what choices do I
+ 
+
+ align:start position:0%
+my question again is what choices do I
+have for A and B to either first figure
+
+ align:start position:0%
+have for A and B to either first figure
+ 
+
+ align:start position:0%
+have for A and B to either first figure
+out what choices for A and B allow this
+
+ align:start position:0%
+out what choices for A and B allow this
+ 
+
+ align:start position:0%
+out what choices for A and B allow this
+function to be continuous when I put in
+
+ align:start position:0%
+function to be continuous when I put in
+ 
+
+ align:start position:0%
+function to be continuous when I put in
+the the left part so the values when it
+
+ align:start position:0%
+the the left part so the values when it
+ 
+
+ align:start position:0%
+the the left part so the values when it
+X is less than or equal to one and what
+
+ align:start position:0%
+X is less than or equal to one and what
+ 
+
+ align:start position:0%
+X is less than or equal to one and what
+uh what values for A and B allow this
+
+ align:start position:0%
+uh what values for A and B allow this
+ 
+
+ align:start position:0%
+uh what values for A and B allow this
+function to be differentiable so I'm
+
+ align:start position:0%
+function to be differentiable so I'm
+ 
+
+ align:start position:0%
+function to be differentiable so I'm
+going to give you a moment to work on it
+
+ align:start position:0%
+going to give you a moment to work on it
+ 
+
+ align:start position:0%
+going to give you a moment to work on it
+yourself then we'll come back and I'll
+
+ align:start position:0%
+yourself then we'll come back and I'll
+ 
+
+ align:start position:0%
+yourself then we'll come back and I'll
+work through them for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you okay so what we were doing again is
+
+ align:start position:0%
+you okay so what we were doing again is
+ 
+
+ align:start position:0%
+you okay so what we were doing again is
+we were trying to answer this question
+
+ align:start position:0%
+we were trying to answer this question
+ 
+
+ align:start position:0%
+we were trying to answer this question
+uh choose values for a and b um that
+
+ align:start position:0%
+uh choose values for a and b um that
+ 
+
+ align:start position:0%
+uh choose values for a and b um that
+make first let's look at the continuity
+
+ align:start position:0%
+make first let's look at the continuity
+ 
+
+ align:start position:0%
+make first let's look at the continuity
+question okay so what we really need is
+
+ align:start position:0%
+question okay so what we really need is
+ 
+
+ align:start position:0%
+question okay so what we really need is
+we need to have a linear function that
+
+ align:start position:0%
+we need to have a linear function that
+ 
+
+ align:start position:0%
+we need to have a linear function that
+ultimately goes through this point
+
+ align:start position:0%
+ultimately goes through this point
+ 
+
+ align:start position:0%
+ultimately goes through this point
+whatever this point is so we have to
+
+ align:start position:0%
+whatever this point is so we have to
+ 
+
+ align:start position:0%
+whatever this point is so we have to
+figure out what that point is and then
+
+ align:start position:0%
+figure out what that point is and then
+ 
+
+ align:start position:0%
+figure out what that point is and then
+we can figure out what values of A and B
+
+ align:start position:0%
+we can figure out what values of A and B
+ 
+
+ align:start position:0%
+we can figure out what values of A and B
+will allow that to work so if I want uh
+
+ align:start position:0%
+will allow that to work so if I want uh
+ 
+
+ align:start position:0%
+will allow that to work so if I want uh
+if I want a continuous
+
+ align:start position:0%
+if I want a continuous
+ 
+
+ align:start position:0%
+if I want a continuous
+function these a a and b again they have
+
+ align:start position:0%
+function these a a and b again they have
+ 
+
+ align:start position:0%
+function these a a and b again they have
+to be such that the line goes straight
+
+ align:start position:0%
+to be such that the line goes straight
+ 
+
+ align:start position:0%
+to be such that the line goes straight
+through that point so what is that point
+
+ align:start position:0%
+through that point so what is that point
+ 
+
+ align:start position:0%
+through that point so what is that point
+well the x value is one so what what
+
+ align:start position:0%
+well the x value is one so what what
+ 
+
+ align:start position:0%
+well the x value is one so what what
+would the y value have to be in order to
+
+ align:start position:0%
+would the y value have to be in order to
+ 
+
+ align:start position:0%
+would the y value have to be in order to
+fill in that Circle we can actually look
+
+ align:start position:0%
+fill in that Circle we can actually look
+ 
+
+ align:start position:0%
+fill in that Circle we can actually look
+at F ofx and we can say well if I wanted
+
+ align:start position:0%
+at F ofx and we can say well if I wanted
+ 
+
+ align:start position:0%
+at F ofx and we can say well if I wanted
+it to be continuous then the yvalue I
+
+ align:start position:0%
+it to be continuous then the yvalue I
+ 
+
+ align:start position:0%
+it to be continuous then the yvalue I
+need here I need at x equal 1 is going
+
+ align:start position:0%
+need here I need at x equal 1 is going
+ 
+
+ align:start position:0%
+need here I need at x equal 1 is going
+to be whatever the y- value is here at x
+
+ align:start position:0%
+to be whatever the y- value is here at x
+ 
+
+ align:start position:0%
+to be whatever the y- value is here at x
+equal 1 so let me write that make a
+
+ align:start position:0%
+equal 1 so let me write that make a
+ 
+
+ align:start position:0%
+equal 1 so let me write that make a
+little space over here so to answer
+
+ align:start position:0%
+little space over here so to answer
+ 
+
+ align:start position:0%
+little space over here so to answer
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one I Need A and
+
+ align:start position:0%
+one I Need A and
+ 
+
+ align:start position:0%
+one I Need A and
+B so that
+
+ align:start position:0%
+B so that
+ 
+
+ align:start position:0%
+B so that
+at x =
+
+ align:start position:0%
+at x =
+ 
+
+ align:start position:0%
+at x =
+1 Y is equal to well if I put in one
+
+ align:start position:0%
+1 Y is equal to well if I put in one
+ 
+
+ align:start position:0%
+1 Y is equal to well if I put in one
+here what do I get I get 1^ 2ar + 1 so I
+
+ align:start position:0%
+here what do I get I get 1^ 2ar + 1 so I
+ 
+
+ align:start position:0%
+here what do I get I get 1^ 2ar + 1 so I
+get two so I need y to equal two when X
+
+ align:start position:0%
+get two so I need y to equal two when X
+ 
+
+ align:start position:0%
+get two so I need y to equal two when X
+is equal to 1 okay so in other words
+
+ align:start position:0%
+is equal to 1 okay so in other words
+ 
+
+ align:start position:0%
+is equal to 1 okay so in other words
+down here so again let me just say
+
+ align:start position:0%
+down here so again let me just say
+ 
+
+ align:start position:0%
+down here so again let me just say
+before I go on this point is one comma
+
+ align:start position:0%
+before I go on this point is one comma
+ 
+
+ align:start position:0%
+before I go on this point is one comma
+two so what I need is a line that goes
+
+ align:start position:0%
+two so what I need is a line that goes
+ 
+
+ align:start position:0%
+two so what I need is a line that goes
+through the point one comma two okay so
+
+ align:start position:0%
+through the point one comma two okay so
+ 
+
+ align:start position:0%
+through the point one comma two okay so
+what is that that would be in this case
+
+ align:start position:0%
+what is that that would be in this case
+ 
+
+ align:start position:0%
+what is that that would be in this case
+that would be the output is 2 and the
+
+ align:start position:0%
+that would be the output is 2 and the
+ 
+
+ align:start position:0%
+that would be the output is 2 and the
+input is a * well X is 1 1 plus b so
+
+ align:start position:0%
+input is a * well X is 1 1 plus b so
+ 
+
+ align:start position:0%
+input is a * well X is 1 1 plus b so
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+means a plus B has to equal
+
+ align:start position:0%
+means a plus B has to equal
+ 
+
+ align:start position:0%
+means a plus B has to equal
+two and that actually uh represents all
+
+ align:start position:0%
+two and that actually uh represents all
+ 
+
+ align:start position:0%
+two and that actually uh represents all
+the solutions so there are an infinite
+
+ align:start position:0%
+the solutions so there are an infinite
+ 
+
+ align:start position:0%
+the solutions so there are an infinite
+number of solutions I could have and if
+
+ align:start position:0%
+number of solutions I could have and if
+ 
+
+ align:start position:0%
+number of solutions I could have and if
+you think about it I could draw some of
+
+ align:start position:0%
+you think about it I could draw some of
+ 
+
+ align:start position:0%
+you think about it I could draw some of
+these I could draw some of these lines
+
+ align:start position:0%
+these I could draw some of these lines
+ 
+
+ align:start position:0%
+these I could draw some of these lines
+so let's take for instance
+
+ align:start position:0%
+so let's take for instance
+ 
+
+ align:start position:0%
+so let's take for instance
+um b equals 2 and a equals zero when B
+
+ align:start position:0%
+um b equals 2 and a equals zero when B
+ 
+
+ align:start position:0%
+um b equals 2 and a equals zero when B
+is two and a is zero it's the constant
+
+ align:start position:0%
+is two and a is zero it's the constant
+ 
+
+ align:start position:0%
+is two and a is zero it's the constant
+it's the constant function f ofx equals
+
+ align:start position:0%
+it's the constant function f ofx equals
+ 
+
+ align:start position:0%
+it's the constant function f ofx equals
+2 it's a straight line that would graph
+
+ align:start position:0%
+2 it's a straight line that would graph
+ 
+
+ align:start position:0%
+2 it's a straight line that would graph
+going to graph that
+
+ align:start position:0%
+going to graph that
+ 
+
+ align:start position:0%
+going to graph that
+here that would graph straight
+
+ align:start position:0%
+here that would graph straight
+ 
+
+ align:start position:0%
+here that would graph straight
+across and that would fill in right here
+
+ align:start position:0%
+across and that would fill in right here
+ 
+
+ align:start position:0%
+across and that would fill in right here
+and this would be if we had on this side
+
+ align:start position:0%
+and this would be if we had on this side
+ 
+
+ align:start position:0%
+and this would be if we had on this side
+this is f ofx equals 2
+
+ align:start position:0%
+this is f ofx equals 2
+ 
+
+ align:start position:0%
+this is f ofx equals 2
+okay I could also have chosen uh a plus
+
+ align:start position:0%
+okay I could also have chosen uh a plus
+ 
+
+ align:start position:0%
+okay I could also have chosen uh a plus
+Bal 2 I could also have chosen AAL 1 and
+
+ align:start position:0%
+Bal 2 I could also have chosen AAL 1 and
+ 
+
+ align:start position:0%
+Bal 2 I could also have chosen AAL 1 and
+Bal 1 so I could have slope one and
+
+ align:start position:0%
+Bal 1 so I could have slope one and
+ 
+
+ align:start position:0%
+Bal 1 so I could have slope one and
+intercept one notice by the way this one
+
+ align:start position:0%
+intercept one notice by the way this one
+ 
+
+ align:start position:0%
+intercept one notice by the way this one
+is not differentiable right it's
+
+ align:start position:0%
+is not differentiable right it's
+ 
+
+ align:start position:0%
+is not differentiable right it's
+obviously there's a there's a
+
+ align:start position:0%
+obviously there's a there's a
+ 
+
+ align:start position:0%
+obviously there's a there's a
+significant break there we'll see also
+
+ align:start position:0%
+significant break there we'll see also
+ 
+
+ align:start position:0%
+significant break there we'll see also
+with a equal 1 and b equals 1 it's also
+
+ align:start position:0%
+with a equal 1 and b equals 1 it's also
+ 
+
+ align:start position:0%
+with a equal 1 and b equals 1 it's also
+not differentiable so a equals 1 is
+
+ align:start position:0%
+not differentiable so a equals 1 is
+ 
+
+ align:start position:0%
+not differentiable so a equals 1 is
+slope one and b equals 1 as intercept is
+
+ align:start position:0%
+slope one and b equals 1 as intercept is
+ 
+
+ align:start position:0%
+slope one and b equals 1 as intercept is
+one that's this line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is kind of running out of room
+
+ align:start position:0%
+so this is kind of running out of room
+ 
+
+ align:start position:0%
+so this is kind of running out of room
+but f
+
+ align:start position:0%
+but f
+ 
+
+ align:start position:0%
+but f
+ofx equals
+
+ align:start position:0%
+ofx equals
+ 
+
+ align:start position:0%
+ofx equals
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+Plus 1 hopefully you can see that F of
+
+ align:start position:0%
+Plus 1 hopefully you can see that F of
+ 
+
+ align:start position:0%
+Plus 1 hopefully you can see that F of
+xal X+ one f ofx equals 2 this one looks
+
+ align:start position:0%
+xal X+ one f ofx equals 2 this one looks
+ 
+
+ align:start position:0%
+xal X+ one f ofx equals 2 this one looks
+a little bit closer to being almost like
+
+ align:start position:0%
+a little bit closer to being almost like
+ 
+
+ align:start position:0%
+a little bit closer to being almost like
+the tangent lines are going to match up
+
+ align:start position:0%
+the tangent lines are going to match up
+ 
+
+ align:start position:0%
+the tangent lines are going to match up
+there but it's not quite and we'll
+
+ align:start position:0%
+there but it's not quite and we'll
+ 
+
+ align:start position:0%
+there but it's not quite and we'll
+see uh in a second what we will need so
+
+ align:start position:0%
+see uh in a second what we will need so
+ 
+
+ align:start position:0%
+see uh in a second what we will need so
+this was we answered the continuity
+
+ align:start position:0%
+this was we answered the continuity
+ 
+
+ align:start position:0%
+this was we answered the continuity
+question okay so now let's answer the
+
+ align:start position:0%
+question okay so now let's answer the
+ 
+
+ align:start position:0%
+question okay so now let's answer the
+differentiability question okay notice
+
+ align:start position:0%
+differentiability question okay notice
+ 
+
+ align:start position:0%
+differentiability question okay notice
+again continuous we have a lot of lines
+
+ align:start position:0%
+again continuous we have a lot of lines
+ 
+
+ align:start position:0%
+again continuous we have a lot of lines
+that will work
+
+ align:start position:0%
+that will work
+ 
+
+ align:start position:0%
+that will work
+okay but to answer the differentiability
+
+ align:start position:0%
+okay but to answer the differentiability
+ 
+
+ align:start position:0%
+okay but to answer the differentiability
+question I need the derivative as I come
+
+ align:start position:0%
+question I need the derivative as I come
+ 
+
+ align:start position:0%
+question I need the derivative as I come
+in from the left to be equal to the
+
+ align:start position:0%
+in from the left to be equal to the
+ 
+
+ align:start position:0%
+in from the left to be equal to the
+derivative as I come in from the right
+
+ align:start position:0%
+derivative as I come in from the right
+ 
+
+ align:start position:0%
+derivative as I come in from the right
+so actually I think I did that backwards
+
+ align:start position:0%
+so actually I think I did that backwards
+ 
+
+ align:start position:0%
+so actually I think I did that backwards
+this is as I come in from the right I
+
+ align:start position:0%
+this is as I come in from the right I
+ 
+
+ align:start position:0%
+this is as I come in from the right I
+need this derivative gives me a certain
+
+ align:start position:0%
+need this derivative gives me a certain
+ 
+
+ align:start position:0%
+need this derivative gives me a certain
+value as I come in from the left I need
+
+ align:start position:0%
+value as I come in from the left I need
+ 
+
+ align:start position:0%
+value as I come in from the left I need
+a derivative coming this direction I
+
+ align:start position:0%
+a derivative coming this direction I
+ 
+
+ align:start position:0%
+a derivative coming this direction I
+need them to be the same
+
+ align:start position:0%
+need them to be the same
+ 
+
+ align:start position:0%
+need them to be the same
+that's what it would mean for the
+
+ align:start position:0%
+that's what it would mean for the
+ 
+
+ align:start position:0%
+that's what it would mean for the
+function to be differentiable I can
+
+ align:start position:0%
+function to be differentiable I can
+ 
+
+ align:start position:0%
+function to be differentiable I can
+write that in
+
+ align:start position:0%
+write that in
+ 
+
+ align:start position:0%
+write that in
+words the limit as X goes to one from
+
+ align:start position:0%
+words the limit as X goes to one from
+ 
+
+ align:start position:0%
+words the limit as X goes to one from
+the left of frime of X has to equal the
+
+ align:start position:0%
+the left of frime of X has to equal the
+ 
+
+ align:start position:0%
+the left of frime of X has to equal the
+limit as X goes to one from the right of
+
+ align:start position:0%
+limit as X goes to one from the right of
+ 
+
+ align:start position:0%
+limit as X goes to one from the right of
+frime of
+
+ align:start position:0%
+frime of
+ 
+
+ align:start position:0%
+frime of
+X I'm not sure I think you saw this
+
+ align:start position:0%
+X I'm not sure I think you saw this
+ 
+
+ align:start position:0%
+X I'm not sure I think you saw this
+notation already limits coming in from
+
+ align:start position:0%
+notation already limits coming in from
+ 
+
+ align:start position:0%
+notation already limits coming in from
+the left are designated by a minus sign
+
+ align:start position:0%
+the left are designated by a minus sign
+ 
+
+ align:start position:0%
+the left are designated by a minus sign
+coming in from the right are designated
+
+ align:start position:0%
+coming in from the right are designated
+ 
+
+ align:start position:0%
+coming in from the right are designated
+by a plus sign so we need these two
+
+ align:start position:0%
+by a plus sign so we need these two
+ 
+
+ align:start position:0%
+by a plus sign so we need these two
+limits to agree in order for the
+
+ align:start position:0%
+limits to agree in order for the
+ 
+
+ align:start position:0%
+limits to agree in order for the
+function to have a a well- defined
+
+ align:start position:0%
+function to have a a well- defined
+ 
+
+ align:start position:0%
+function to have a a well- defined
+derivative at that point so let's figure
+
+ align:start position:0%
+derivative at that point so let's figure
+ 
+
+ align:start position:0%
+derivative at that point so let's figure
+out what this is because we have the
+
+ align:start position:0%
+out what this is because we have the
+ 
+
+ align:start position:0%
+out what this is because we have the
+function here the function to the right
+
+ align:start position:0%
+function here the function to the right
+ 
+
+ align:start position:0%
+function here the function to the right
+of one is x^2 + 1 we know its derivative
+
+ align:start position:0%
+of one is x^2 + 1 we know its derivative
+ 
+
+ align:start position:0%
+of one is x^2 + 1 we know its derivative
+its derivative is 2x so on this
+
+ align:start position:0%
+its derivative is 2x so on this
+ 
+
+ align:start position:0%
+its derivative is 2x so on this
+side we have the limit as X goes to one
+
+ align:start position:0%
+side we have the limit as X goes to one
+ 
+
+ align:start position:0%
+side we have the limit as X goes to one
+from the right of
+
+ align:start position:0%
+from the right of
+ 
+
+ align:start position:0%
+from the right of
+2x and now we can fill that in what is
+
+ align:start position:0%
+2x and now we can fill that in what is
+ 
+
+ align:start position:0%
+2x and now we can fill that in what is
+that well I just evaluate at xal 1 and I
+
+ align:start position:0%
+that well I just evaluate at xal 1 and I
+ 
+
+ align:start position:0%
+that well I just evaluate at xal 1 and I
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+two okay and now that means I need the
+
+ align:start position:0%
+two okay and now that means I need the
+ 
+
+ align:start position:0%
+two okay and now that means I need the
+limit as X goes to one from the left of
+
+ align:start position:0%
+limit as X goes to one from the left of
+ 
+
+ align:start position:0%
+limit as X goes to one from the left of
+the derivative to also be two so let's
+
+ align:start position:0%
+the derivative to also be two so let's
+ 
+
+ align:start position:0%
+the derivative to also be two so let's
+fill in this side the function on the
+
+ align:start position:0%
+fill in this side the function on the
+ 
+
+ align:start position:0%
+fill in this side the function on the
+left at the left of one is ax plus b so
+
+ align:start position:0%
+left at the left of one is ax plus b so
+ 
+
+ align:start position:0%
+left at the left of one is ax plus b so
+what is its derivative its derivative is
+
+ align:start position:0%
+what is its derivative its derivative is
+ 
+
+ align:start position:0%
+what is its derivative its derivative is
+just a right because the derivative of b
+
+ align:start position:0%
+just a right because the derivative of b
+ 
+
+ align:start position:0%
+just a right because the derivative of b
+b is a constant that derivative zero the
+
+ align:start position:0%
+b is a constant that derivative zero the
+ 
+
+ align:start position:0%
+b is a constant that derivative zero the
+derivative of this is a okay so we get
+
+ align:start position:0%
+derivative of this is a okay so we get
+ 
+
+ align:start position:0%
+derivative of this is a okay so we get
+the limit as X goes to one from the left
+
+ align:start position:0%
+the limit as X goes to one from the left
+ 
+
+ align:start position:0%
+the limit as X goes to one from the left
+of a that's what this left hand
+
+ align:start position:0%
+of a that's what this left hand
+ 
+
+ align:start position:0%
+of a that's what this left hand
+expression is well if I evaluate a at x
+
+ align:start position:0%
+expression is well if I evaluate a at x
+ 
+
+ align:start position:0%
+expression is well if I evaluate a at x
+equal 1 I can actually just plug it in
+
+ align:start position:0%
+equal 1 I can actually just plug it in
+ 
+
+ align:start position:0%
+equal 1 I can actually just plug it in
+there's no X there this is a constant
+
+ align:start position:0%
+there's no X there this is a constant
+ 
+
+ align:start position:0%
+there's no X there this is a constant
+function so as X goes to one from the
+
+ align:start position:0%
+function so as X goes to one from the
+ 
+
+ align:start position:0%
+function so as X goes to one from the
+left I just get a so that tells me that
+
+ align:start position:0%
+left I just get a so that tells me that
+ 
+
+ align:start position:0%
+left I just get a so that tells me that
+a has to equal two
+
+ align:start position:0%
+a has to equal two
+ 
+
+ align:start position:0%
+a has to equal two
+here okay so in order to make the
+
+ align:start position:0%
+here okay so in order to make the
+ 
+
+ align:start position:0%
+here okay so in order to make the
+function differentiable I only have one
+
+ align:start position:0%
+function differentiable I only have one
+ 
+
+ align:start position:0%
+function differentiable I only have one
+value of a I'm allowed to use and that's
+
+ align:start position:0%
+value of a I'm allowed to use and that's
+ 
+
+ align:start position:0%
+value of a I'm allowed to use and that's
+when a equals 2 okay so I didn't draw
+
+ align:start position:0%
+when a equals 2 okay so I didn't draw
+ 
+
+ align:start position:0%
+when a equals 2 okay so I didn't draw
+this one yet I didn't draw it on purpose
+
+ align:start position:0%
+this one yet I didn't draw it on purpose
+ 
+
+ align:start position:0%
+this one yet I didn't draw it on purpose
+because I wanted to save that for last
+
+ align:start position:0%
+because I wanted to save that for last
+ 
+
+ align:start position:0%
+because I wanted to save that for last
+so when a is two what's B have to be
+
+ align:start position:0%
+so when a is two what's B have to be
+ 
+
+ align:start position:0%
+so when a is two what's B have to be
+well in order to be differentiable it
+
+ align:start position:0%
+well in order to be differentiable it
+ 
+
+ align:start position:0%
+well in order to be differentiable it
+first has to be continuous so it has to
+
+ align:start position:0%
+first has to be continuous so it has to
+ 
+
+ align:start position:0%
+first has to be continuous so it has to
+satisfy this a equals 2 and it has to
+
+ align:start position:0%
+satisfy this a equals 2 and it has to
+ 
+
+ align:start position:0%
+satisfy this a equals 2 and it has to
+satisfy this a plus b equals two so that
+
+ align:start position:0%
+satisfy this a plus b equals two so that
+ 
+
+ align:start position:0%
+satisfy this a plus b equals two so that
+tells me a equals 2 that tells me B has
+
+ align:start position:0%
+tells me a equals 2 that tells me B has
+ 
+
+ align:start position:0%
+tells me a equals 2 that tells me B has
+to equal zero
+
+ align:start position:0%
+to equal zero
+ 
+
+ align:start position:0%
+to equal zero
+that comes from our work in number one
+
+ align:start position:0%
+that comes from our work in number one
+ 
+
+ align:start position:0%
+that comes from our work in number one
+okay what does that represent that's a
+
+ align:start position:0%
+okay what does that represent that's a
+ 
+
+ align:start position:0%
+okay what does that represent that's a
+line with intercept zero and slope two
+
+ align:start position:0%
+line with intercept zero and slope two
+ 
+
+ align:start position:0%
+line with intercept zero and slope two
+so I'll draw that one last goes through
+
+ align:start position:0%
+so I'll draw that one last goes through
+ 
+
+ align:start position:0%
+so I'll draw that one last goes through
+zero has slope two so it goes through
+
+ align:start position:0%
+zero has slope two so it goes through
+ 
+
+ align:start position:0%
+zero has slope two so it goes through
+this point and if I draw those if I
+
+ align:start position:0%
+this point and if I draw those if I
+ 
+
+ align:start position:0%
+this point and if I draw those if I
+connect those
+
+ align:start position:0%
+connect those
+ 
+
+ align:start position:0%
+connect those
+up maybe this
+
+ align:start position:0%
+up maybe this
+ 
+
+ align:start position:0%
+up maybe this
+is we see if we continued we see that
+
+ align:start position:0%
+is we see if we continued we see that
+ 
+
+ align:start position:0%
+is we see if we continued we see that
+the tangent lines there agree exactly
+
+ align:start position:0%
+the tangent lines there agree exactly
+ 
+
+ align:start position:0%
+the tangent lines there agree exactly
+but the function itself is just this
+
+ align:start position:0%
+but the function itself is just this
+ 
+
+ align:start position:0%
+but the function itself is just this
+part it's the right hand side is is x^2
+
+ align:start position:0%
+part it's the right hand side is is x^2
+ 
+
+ align:start position:0%
+part it's the right hand side is is x^2
++ 1 the left hand side is y = 2x so
+
+ align:start position:0%
++ 1 the left hand side is y = 2x so
+ 
+
+ align:start position:0%
++ 1 the left hand side is y = 2x so
+we've now figured out how to make this
+
+ align:start position:0%
+we've now figured out how to make this
+ 
+
+ align:start position:0%
+we've now figured out how to make this
+pie wise function both continuous and
+
+ align:start position:0%
+pie wise function both continuous and
+ 
+
+ align:start position:0%
+pie wise function both continuous and
+differentiable and we'll stop there
\ No newline at end of file
diff --git a/FwIKZIWJfg8.txt b/FwIKZIWJfg8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77912755695e9f5062274e740c7633b8e906dca0
--- /dev/null
+++ b/FwIKZIWJfg8.txt
@@ -0,0 +1,1392 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT Open
+Courseware continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT Open Courseware at
+
+ocw.mit.edu.
+
+Hi there.
+
+Welcome.
+
+I'm Brian Spatocco.
+
+We're going to be going
+over exam 2 from
+
+the fall 2009 semester.
+
+The logical place to start on
+this exam is problem 1.
+
+And what I usually do for all
+the problems is discuss the
+
+things we need to know
+before we start it.
+
+So I would recommend reviewing
+these concepts before
+
+attempting the problem.
+
+And then attempt the
+problem and then
+
+identify your weak spots.
+
+So here's what I personally
+found to be important
+
+information to know before
+attempting the problem.
+
+So I call it what I need, (W
+I N), if you want to win.
+
+There's four things.
+
+The first are Miller Indices.
+
+This is a crystallographic
+notation for figuring out and
+
+communicating planes and
+directions in crystals.
+
+So review Miller Indices
+
+We have plane/direction
+notation.
+
+I'll explain a little bit more
+what that is in a second.
+
+Definition of planar density.
+
+And for that matter, linear and
+
+three-dimensional density as well.
+
+And 4, the concept of
+a crystal basis.
+
+And this is actually the concept
+that most students had
+
+trouble with on this particular
+question.
+
+So those are the things I would
+recommend you look at
+
+before starting.
+
+And if you haven't,
+check it out now.
+
+So let's start off with
+part a of problem 1.
+
+And so the question asks us to
+draw the crystallographic
+
+feature indicated and
+label it clearly.
+
+It doesn't actually say if
+we're drawing planes or
+
+directions and that's left to
+the exam taker to identify.
+
+So the first thing I note on
+that problem, part a, is that
+
+we're asked to draw
+0, 1 bar, 2 bar.
+
+And 1 1 1 bar.
+
+So the first thing I notice
+about these two particular
+
+crystallographic features
+is how they're actually
+
+encapsulated.
+
+So the first one is
+in parentheses.
+
+The next one is in
+square brackets.
+
+That actually tells us some
+information about the problem.
+
+The first part, a part one,
+is 0 1 bar 2 bar.
+
+So you actually need to know
+what this implies.
+
+Parentheses mean we're looking
+at a particular plane
+
+orientation.
+
+Now I'm not saying a plane.
+
+I'm saying a plane
+orientation.
+
+Which means there are infinitely
+many planes in a
+
+crystal which have
+this orientation.
+
+OK so that's distinguishing
+between just
+
+one plane and a crystal.
+
+The second part, b, we
+have square brackets.
+
+That implies we're either
+looking at a direction or a
+
+place in a crystal.
+
+We also have things like this,
+which we're not seeing on the
+
+exam this time but may
+show up later.
+
+We have these curly brackets
+and we have
+
+these angled brackets.
+
+The curly brackets denote
+a family of planes.
+
+And the angled brackets denote
+a family of directions.
+
+And it's markedly different
+than a particular or plane
+
+orientation and a particular
+direction.
+
+So let's do some visuals here
+to explain what we mean.
+
+So let's start off with a 1.
+
+Now we're asked for
+0 1 bar 2 bar.
+
+Now the bars indicate
+negative signs.
+
+So you would know that from your
+Miller Indices review.
+
+Now the way to do
+this problem--
+
+what I find is the easiest way
+we reviewed in recitation--
+
+was to not be afraid to
+move your origin.
+
+A lot of people are afraid to
+move their origin around but
+
+we have to remember in a
+crystal, basically what a
+
+crystal is, it's a unit lattice
+repeated infinitely in
+
+three dimensions.
+
+So it's OK to move your origin
+as long as you choose some
+
+reasonable point.
+
+So in this problem we're looking
+in the back bottom
+
+left corner.
+
+That's our defined origin
+on the paper.
+
+But to do this problem,
+I would recommend
+
+choosing a new origin.
+
+I chose this one.
+
+And that's really going to
+facilitate doing this problem
+
+a lot more easily.
+
+So let's look at what
+we have to dran now.
+
+0 1 bar 2 bar.
+
+The 0 indicates that we're never
+actually intersecting
+
+the x-axis.
+
+OK, so at no point
+will this plane--
+
+we know it's a plane because
+the parentheses--
+
+intersect the x-axis.
+
+The 1 bar indicates that we are
+intersecting the y-axis at
+
+1 lattice parameter spacing.
+
+Miller Indices are a little
+tricky because they're
+
+somewhat inverted.
+
+1 implies you are
+going the full
+
+distance of the unit cell.
+
+2 implies you're going
+half the distance.
+
+3 implies you are going
+1/3 the distance and
+
+so on and so forth.
+
+So for 1, we're going to
+go the distance of 1.
+
+We're going to move
+negative 1 in y.
+
+So we're going to
+move negative 1.
+
+We're going to go to here.
+
+That's in our y.
+
+And when we actually make
+this a little clearer.
+
+I've chosen a new origin.
+
+So here's my y prime.
+
+Here's my z prime.
+
+Here's my x prime.
+
+So we're moving negative
+1 and y.
+
+We're going to move half,
+negative 1/2 and z.
+
+And we're also told that
+this plane doesn't
+
+intersect the x-axis.
+
+So it must run parallel
+to that asix.
+
+Which tells me that it's going
+to run along the x-axis.
+
+We're going to get a
+plane like this.
+
+And here's our plane.
+
+That's the answer to part a 1.
+
+Pretty easy and most students
+got this correct.
+
+For part a 2 we're asked to draw
+a direction or point to a
+
+particular place in space.
+
+I also moved my origin
+on this problem.
+
+And I found it easiest to
+redefine my origin up here.
+
+Which means that my new set
+of axes are going to
+
+be x prime, y prime.
+
+I'm going to keep z because
+z didn't move at all.
+
+OK note how, when I'm drawing
+these things--
+
+we're going to draw
+this one now--
+
+that the way I choose to move
+my origin generally tracks
+
+with the negative signs that I
+have. This problem I had a
+
+negative y and negative z, I
+moved in the negative y,
+
+negative z directions.
+
+Here I had a negative z.
+
+So I just moved up in
+the negative z.
+
+That kind of told me how
+to move my origin.
+
+It made life a little easier.
+
+And now it's pretty
+easy from here.
+
+Now what we're going to do is
+draw 1 in the x, we'll go 1 in
+
+the y, we'll go negative
+1 in z.
+
+We're pointing to this point.
+
+There we go.
+
+That's our direction.
+
+So pretty easy.
+
+Part a 1.
+
+Part a 2.
+
+So we're batting
+100 right now.
+
+And just don't be afraid
+to move your origin.
+
+That's the take-away
+from this part.
+
+The problem, of course,
+gets a little harder.
+
+That's something that we pride
+ourselves on in 3.091.
+
+If it was always this easy,
+everyone would pass the class
+
+and get 100s.
+
+So the second part, part b, is
+asking us to calculate the
+
+density of atoms in a plane.
+
+So this gets back to what
+I was saying before.
+
+We need to understand the
+
+definition of a planar density.
+
+OK, so I've sort of
+defined it here.
+
+This is rho.
+
+Not p. rho planar.
+
+And rho planar, I define--
+
+to help me, maybe
+it'll help you--
+
+is the number of full atoms
+in a particular plane--
+
+in this case we're looking
+at 0 0 1--
+
+divided by some area.
+
+Because the plane is denoted
+by an area not a volume.
+
+Don't be afraid, I mean
+densities don't always have to
+
+be mass over volume.
+
+It can be some unit
+over some specific
+
+distance or area or volume.
+
+So that's general density.
+
+So we're looking at the number
+of full items in a plane
+
+divided by the area.
+
+We're told that we're looking
+at Dalium, of course named
+
+after Salvador Dali.
+
+And so we're also told
+that we're looking
+
+at the 0 0 1 plane.
+
+I've drawn a bcc crystal here.
+
+As a scientist or an engineer,
+when you're given a bcc fcc,
+
+simple cubic, the first thing
+you put on that paper is the
+
+actual crystal structure.
+
+So I drew the Dalium up here.
+
+Not a real element, but
+a make-believe one.
+
+And we're going to identify
+our 0 0 1 plane.
+
+This is good practice.
+
+So there's our x, y and
+our z is right here.
+
+Our 0 0 1 plane, so we're
+not intersecting x.
+
+We're not intersecting y.
+
+We're only intersecting z.
+
+So here's our 0 0 1 plane.
+
+Let me sort of bring
+this down for you.
+
+So we can look down
+on it from above.
+
+It's a square, with sides a.
+
+And here's our atoms. So now the
+question is, how many full
+
+atoms do we have and
+what's the area?
+
+The area's obviously
+a squared.
+
+And the number of full atoms in
+this area is we have four
+
+quarters of an atom.
+
+When you're in two-dimensional
+space an atom looks like a
+
+circle to you.
+
+When you're in three-dimensional
+space it
+
+looks like a sphere.
+
+So if you lived in the
+two-dimensional plane, you
+
+would see a quarter of an
+atom, a quarter of an
+
+atom, and so on.
+
+You'd have one full atom
+in this plane.
+
+So this is sort of what
+we're looking for.
+
+And you say, oh,
+well I'm done.
+
+A lot people left it at that.
+
+But that's not the answer
+we're looking for.
+
+We want an actual numerical
+answer.
+
+So the question now becomes,
+what is a?
+
+So we're going to digress and
+find a and then we'll know
+
+exactly the answer to
+the planar density.
+
+So a--
+
+this is where you have to
+be a little clever.
+
+How do you find a?
+
+The lattice parameter,
+the lattice spacing.
+
+So the best way to do this is to
+think both small scale and
+
+large scale.
+
+So first let's think
+about a unit cell.
+
+Let me ask you, what's
+the three-dimensional
+
+density of a unit cell.
+
+So how many atoms do we
+have per unit cell?
+
+We have our bcc.
+
+We know in bcc there are two
+atoms. We have eight corner
+
+atoms and they're each 1/8.
+
+We have one body atom.
+
+So there's two atoms. So
+we have 2 atoms per--
+
+what's the volume--
+
+well the volume is a cubed.
+
+Now we got a cubed.
+
+We didn't really make any
+progress here, we still have
+
+an unknown variable.
+
+But the question is, how do
+we get solved for a cubed.
+
+So let's zoom out from
+that unit cell.
+
+Let's zoom out to a
+mole of material.
+
+OK, so a mole of material,
+how many atoms are
+
+in a mole of material?
+
+Well by definition, it's
+Avogadro's Number.
+
+6.02 times 10 to the 23.
+
+And then what's the volume
+of a mole of material?
+
+Well looking back at
+the problem, we're
+
+given the molar volume.
+
+Which is something that I would
+
+recommend you write down.
+
+You know all the information
+you're given,
+
+see what you've got.
+
+The volume of a mole
+is the molar
+
+volume, which we're given.
+
+So now it's pretty easy.
+
+We know Avogadro's, we
+know molar volume.
+
+So we can solve for a.
+
+So not too bad.
+
+You'll find that a is about 2.8
+times 10 to the negative 8
+
+centimeters.
+
+You could give me 2.85, 2.79.
+
+We're worried about
+the concepts
+
+here, not the numbers.
+
+So don't go back and
+waste a lot of time
+
+getting the exact number.
+
+That's our a.
+
+And now that we've got a, we've
+got our planar density.
+
+Very easy.
+
+I'm going to write rho plan,
+just to save some time.
+
+And that equals 1 over
+this number squared.
+
+That's one atom, by the way.
+
+And that's all squared.
+
+And we're going to find in the
+end that our planar density is
+
+going to be equal to 1.27
+times 10 to the 15.
+
+And the units are important.
+
+That's atoms per centimeter,
+squared.
+
+If you don't give us the units
+then we have no idea if you're
+
+right or wrong.
+
+So always include your
+units at the end.
+
+So hopefully that helped.
+
+We're going to take a second
+and clean off the boards.
+
+And we're going to start
+with part c.
+
+OK we're back.
+
+We're going to finish problem
+1 now from the 2009 exam 2.
+
+We're on part c.
+
+So thus far in part a, we've
+talked about Miller Indices,
+
+we've talked about the plane
+and direction notation with
+
+the parentheses and
+the brackets.
+
+We've also talked about
+planar density.
+
+And I would invite you to
+review those things.
+
+Now we're going to go to part c,
+which is really the concept
+
+of the crystal basis.
+
+And this was the part of the
+problem that most students
+
+lost points on.
+
+So it's the thing that
+I would emphasize the
+
+most on this problem.
+
+The problem asks us to--
+
+and I put a sad face because
+that's how people felt after
+
+this part--
+
+the problem asks us to
+draw a particular
+
+plane in a fcc crystal.
+
+So we're given Magnesia, MgO.
+
+They want us to draw that plane
+and show the atoms. And
+
+we also want you to show the
+relative sizes of the atoms.
+
+You know we have anions
+and cations.
+
+And we actually give you the
+sizes of those ions, so it
+
+shouldn't be too tricky
+on that part.
+
+But I think the best way to
+start is to go over the answer
+
+that was given that was wrong.
+
+And then we're going to talk
+about why it was wrong and how
+
+to get the right answer.
+
+So to start off, we want you
+to draw this crystal.
+
+The best place to start is by
+actually drawing the crystal
+
+in 3-D and then we're
+going to take the
+
+projection after that.
+
+So people think, MgO, they see
+fcc, and they say, oh that's
+
+not so bad.
+
+I know what fcc looks like.
+
+Let me draw fcc.
+
+I'm going to use for this
+problem, I'm going to use this
+
+red chalk to represent magnesium
+and the blue chalk
+
+to represent oxygen.
+
+OK so magnesium, we're
+going to have it as
+
+a circle like this.
+
+This is magnesium, 2 plus.
+
+And we're going to
+have the oxygen--
+
+it's going to be slightly bigger
+because it's an anion.
+
+This is O 2 minus.
+
+Maybe I'll color this in too.
+
+People said, OK easy. fcc.
+
+This is a simple problem,
+easy points.
+
+They drew what they thought
+to be an fcc crystal.
+
+So they did--
+
+let's say they put the
+Mgs on the corners.
+
+And they said, OK now
+I need my faces.
+
+So maybe the oxygen
+are the faces.
+
+So I'm going to put in my 6 face
+atoms. So here are my 1
+
+side here, and I've got the
+bottom and the top.
+
+There's my 6 faces.
+
+And they said, OK, easy.
+
+I'm done.
+
+And then they took the
+projection of 0 1 1.
+
+We also know, when you
+put the axes on here
+
+just to make it clear.
+
+And here's our z, You know
+0 1 1, we know it doesn't
+
+intersect the x but it
+intersects the y and the z at
+
+one lattice spacing.
+
+So x doesn't intersect.
+
+It intersects z here,
+intersects y here's.
+
+We've got this kind of
+plane going on here.
+
+We've got something like this.
+
+And they just drew this.
+
+It's a little bit of 3-D
+visualization But they drew
+
+that and they got 0 points.
+
+The reason that that is not a
+correct answer is because that
+
+is not what MgO-- it's rock salt
+structure-- that's not
+
+what it looks like.
+
+And the reason they got it wrong
+is because they didn't
+
+understand the concept
+of the basis.
+
+So I'm going to make a
+statement right now.
+
+This is a really important
+statements so I urge you to
+
+think about it.
+
+A crystal equals a lattice
+plus a basis.
+
+Here's the difference.
+
+A lattice is a collection
+of points.
+
+So you have an fcc lattice, you
+have a bcc lattice, you
+
+have a simple cubic lattice.
+
+Those are points where atoms--
+
+I use atoms plurally,
+perhaps--
+
+can exist.
+
+OK, a basis I like to
+think of as a stamp.
+
+A basis represents the most
+fundamental pattern that you
+
+stamp at every lattice point.
+
+So let's draw an fcc lattice.
+
+So I'm going to drawn
+an fcc lattice on
+
+this cube right here.
+
+I'm going to put points.
+
+So I'm going to make
+them white.
+
+They're just points.
+
+I got all the corners.
+
+They're hard to see.
+
+But they're all the corners.
+
+I got the faces.
+
+Side, back, front and bottom.
+
+You're saying to yourself,
+that's like the same
+
+thing you just drew.
+
+It's really not.
+
+What I drew the first time,
+I put atoms in.
+
+That's a crystal I drew.
+
+I just a lattice right now.
+
+This isn't a crystal,
+this is a lattice.
+
+So to actually answer the
+question, we want to figure
+
+out, we want to draw the 2-D
+projection of a crystal.
+
+So we've got to draw the
+crystal eventually.
+
+Now we're dealing with MgO.
+
+We're told MgO is face-centered
+cubic.
+
+Which means that our basis must
+have 1 Mg and 1 O atom.
+
+So I'm going to do
+that right now.
+
+I'm going to draw what I'm going
+to call to be my stamp.
+
+You can use whatever method you
+think is best. But I call
+
+this my stamp.
+
+I'm going to draw
+it like this.
+
+So here's an oxygen atom.
+
+Here's a Magnesium atom.
+
+And this little white dot
+is the point that's
+
+going to get stamped.
+
+And here's my stamp.
+
+And the idea is I'm going to
+take the stamp, this basis--
+
+that's what it is,
+it's a basis--
+
+and I'm going to stamp it
+at every lattice point.
+
+OK so note I have 8 corner
+lattice points and I have 6
+
+face lattice points so I'm going
+to be stamping 14 times.
+
+So I'll do the first
+couple very slowly.
+
+I'll take my stamp and
+I'll stamp here.
+
+Here is my O.
+
+Here's my Mg.
+
+I'll stamp over at
+this corner.
+
+Here's my O, here's my Mg.
+
+I'll stamp in the face.
+
+Here's the face, the
+front face one.
+
+Here's my O, here's my Mg.
+
+So you can see what's
+happening.
+
+Let me just circle it for you.
+
+I'll circle one of them.
+
+Here's my stamp.
+
+I'm going to go ahead,
+I'm going to finish
+
+drawing this in.
+
+It's going to get a little
+messy for a board.
+
+But I hope that you can go home
+and do it on some graph
+
+paper as well.
+
+All four corners.
+
+The face is here.
+
+I have a tendency to leave
+off faces sometimes.
+
+Let me make sure I've
+got them all.
+
+I already did that one.
+
+Yep that's right.
+
+Is that right?
+
+No.
+
+OK, now let me finish with the
+magnesiums. The magnesiums--
+
+it's going to be hard to
+see-- exist at the
+
+center of every edge.
+
+So it's a little tricky but
+let me explain what we're
+
+looking at.
+
+What you should be looking at.
+
+We have what looks to be oxygen
+in the face center
+
+cubic arrangement.
+
+And we have magnesium
+at all the edges.
+
+So you're thinking,
+this is weird this
+
+isn't face center cubic.
+
+Look at the magnesium,
+this doesn't
+
+look face center cubic.
+
+Well the thing I would challenge
+you to do at home is
+
+actually draw this unit
+cell out 4 more times.
+
+And then you will actually be
+able to find face center cubic
+
+magnesium lattic cell in
+that larger unit cell.
+
+So this is actually
+the answer.
+
+This is what a rock salt
+structure looks like.
+
+This is MgO.
+
+You have oxygen,
+looks like your
+
+traditional face center cubic.
+
+And you've got these magnesium
+stuck on all the edges.
+
+So now we're just going to
+take our projection.
+
+Let me use white
+chalk for that.
+
+Or rather we're going
+to take our plane.
+
+We're looking at the
+0 1 1 plane.
+
+Here's our axes again.
+
+Remember it's always
+right-handed.
+
+We're going to do 0 1 1.
+
+Not intersecting the
+x and were going to
+
+intersect z and y.
+
+So we're going to come
+down across the face.
+
+We've got this.
+
+This is pretty terrible
+looking.
+
+But this is one of the tricks
+of the problem.
+
+You have to be able to visualize
+these in 3-D space.
+
+So let's slowly transcribe what
+this plane here looks
+
+like projected out
+on the board.
+
+We know that at our corners and
+also at the faces of this
+
+cube, we've got oxygen.
+
+So here's a corner.
+
+These are our corners.
+
+At the faces, two faces,
+we've got oxygen.
+
+What else do we have?
+
+We know we must be hitting
+some magnesium.
+
+Well we know that at
+all the edges--
+
+here's an edge, here's
+an edge--
+
+we've got some magnesium.
+
+What about the center?
+
+Well the center we do too
+because we know that when we
+
+made this stamp, the bottom face
+with this oxygen, we also
+
+stamped halfway up
+a magnesium.
+
+So there's actually a magnesium
+right here.
+
+It's there.
+
+It's right there.
+
+Believe me.
+
+There's our magnesium.
+
+And this is what we've got.
+
+This is the answer
+to the problem.
+
+Notice how I've giving my
+oxygens larger than my
+
+magnesiums and I've got
+it looking like this.
+
+In fact let me let me emphasize
+this even more.
+
+The fact that you could actually
+have drawn this
+
+differently.
+
+You could have drawn
+it like this.
+
+And it would have been exactly
+the same thing.
+
+You would have gotten
+full credit.
+
+You could have drawn this.
+
+This is the thing that I would
+recommend you try at home to
+
+prove that this is true.
+
+These two are equivalent
+It's the same thing.
+
+It all depends on what you
+choose as your stamp point.
+
+So I could have chosen
+to put my red at
+
+every point, my magnesium.
+
+So this is the answer
+to part c.
+
+This part, most people
+did not get correct.
+
+Less than half the class
+got this correct.
+
+So think about a little bit.
+
+Identify crystal as lattice
+plus basis.
+
+And then think about the full
+scope of the problem.
+
+What do we go over? when went
+over Miller Indices, went over
+
+designation and crystallographic
+notation, so
+
+plane and direction notation.
+
+We went over the definition
+of planar density.
+
+Think about what linear density
+means, think about
+
+what three-dimensional
+density means.
+
+Don't be afraid to
+not use mass.
+
+And the last thing we just
+covered was the crystal basis.
+
+So review those and hopefully
+you did well.
+
+Thanks.
\ No newline at end of file
diff --git a/Gd0QPYVYnQg.txt b/Gd0QPYVYnQg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..227cbcfbcd279a00624a4eb65ba27aebb81fd3cd
--- /dev/null
+++ b/Gd0QPYVYnQg.txt
@@ -0,0 +1,8739 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
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+a Creative Commons license your support
+ 
+
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+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
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+will help MIT OpenCourseWare continue to
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+to make a donation or to view additional
+materials from hundreds of MIT courses
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+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'd like to do a quick two or three
+
+ align:start position:0%
+so I'd like to do a quick two or three
+ 
+
+ align:start position:0%
+so I'd like to do a quick two or three
+minute review of the stuff we did last
+
+ align:start position:0%
+minute review of the stuff we did last
+ 
+
+ align:start position:0%
+minute review of the stuff we did last
+time to get you back into where we were
+
+ align:start position:0%
+time to get you back into where we were
+ 
+
+ align:start position:0%
+time to get you back into where we were
+we were talking about different types of
+
+ align:start position:0%
+we were talking about different types of
+ 
+
+ align:start position:0%
+we were talking about different types of
+technologies that use the stuff field
+
+ align:start position:0%
+technologies that use the stuff field
+ 
+
+ align:start position:0%
+technologies that use the stuff field
+the youth learning in 2201 everything
+
+ align:start position:0%
+the youth learning in 2201 everything
+ 
+
+ align:start position:0%
+the youth learning in 2201 everything
+ranging from nuclear reactors for
+
+ align:start position:0%
+ranging from nuclear reactors for
+ 
+
+ align:start position:0%
+ranging from nuclear reactors for
+producing power and the Cherenkov
+
+ align:start position:0%
+producing power and the Cherenkov
+ 
+
+ align:start position:0%
+producing power and the Cherenkov
+radiation that tells you well that the
+
+ align:start position:0%
+radiation that tells you well that the
+ 
+
+ align:start position:0%
+radiation that tells you well that the
+beta particles are moving faster than
+
+ align:start position:0%
+beta particles are moving faster than
+ 
+
+ align:start position:0%
+beta particles are moving faster than
+the speed of light in water is a neat
+
+ align:start position:0%
+the speed of light in water is a neat
+ 
+
+ align:start position:0%
+the speed of light in water is a neat
+thing - I've actually been to this
+
+ align:start position:0%
+thing - I've actually been to this
+ 
+
+ align:start position:0%
+thing - I've actually been to this
+reactor at Idaho - the spent fuel pool
+
+ align:start position:0%
+reactor at Idaho - the spent fuel pool
+ 
+
+ align:start position:0%
+reactor at Idaho - the spent fuel pool
+even the spent fuel once it comes out of
+
+ align:start position:0%
+even the spent fuel once it comes out of
+ 
+
+ align:start position:0%
+even the spent fuel once it comes out of
+the reactor is still giving off betas
+
+ align:start position:0%
+the reactor is still giving off betas
+ 
+
+ align:start position:0%
+the reactor is still giving off betas
+and still giving off Cherenkov radiation
+
+ align:start position:0%
+and still giving off Cherenkov radiation
+ 
+
+ align:start position:0%
+and still giving off Cherenkov radiation
+and you can tell how long it's been out
+
+ align:start position:0%
+and you can tell how long it's been out
+ 
+
+ align:start position:0%
+and you can tell how long it's been out
+of the reactor by how dim the glow gets
+
+ align:start position:0%
+of the reactor by how dim the glow gets
+ 
+
+ align:start position:0%
+of the reactor by how dim the glow gets
+which is pretty cool so you can tell how
+
+ align:start position:0%
+which is pretty cool so you can tell how
+ 
+
+ align:start position:0%
+which is pretty cool so you can tell how
+all the fuel assembly is by the blue
+
+ align:start position:0%
+all the fuel assembly is by the blue
+ 
+
+ align:start position:0%
+all the fuel assembly is by the blue
+glow so remember I told you guys if
+
+ align:start position:0%
+glow so remember I told you guys if
+ 
+
+ align:start position:0%
+glow so remember I told you guys if
+someone says oh your nuclear do you glow
+
+ align:start position:0%
+someone says oh your nuclear do you glow
+ 
+
+ align:start position:0%
+someone says oh your nuclear do you glow
+green you could be like no it's blue
+
+ align:start position:0%
+green you could be like no it's blue
+ 
+
+ align:start position:0%
+green you could be like no it's blue
+that's the right way of things we talked
+
+ align:start position:0%
+that's the right way of things we talked
+ 
+
+ align:start position:0%
+that's the right way of things we talked
+about fusion energy and got into some of
+
+ align:start position:0%
+about fusion energy and got into some of
+ 
+
+ align:start position:0%
+about fusion energy and got into some of
+the nuclear reactions involved in fusion
+
+ align:start position:0%
+the nuclear reactions involved in fusion
+ 
+
+ align:start position:0%
+the nuclear reactions involved in fusion
+energy and I'll be teaching you more
+
+ align:start position:0%
+energy and I'll be teaching you more
+ 
+
+ align:start position:0%
+energy and I'll be teaching you more
+about these today
+
+ align:start position:0%
+about these today
+ 
+
+ align:start position:0%
+about these today
+why fission and fusion work it all has
+
+ align:start position:0%
+why fission and fusion work it all has
+ 
+
+ align:start position:0%
+why fission and fusion work it all has
+to do with the stability and binding
+
+ align:start position:0%
+to do with the stability and binding
+ 
+
+ align:start position:0%
+to do with the stability and binding
+energy of the nuclei involved and
+
+ align:start position:0%
+energy of the nuclei involved and
+ 
+
+ align:start position:0%
+energy of the nuclei involved and
+that'll be the main topic for today is
+
+ align:start position:0%
+that'll be the main topic for today is
+ 
+
+ align:start position:0%
+that'll be the main topic for today is
+excess mass binding energy nuclear
+
+ align:start position:0%
+excess mass binding energy nuclear
+ 
+
+ align:start position:0%
+excess mass binding energy nuclear
+stability we looked at medical uses of
+
+ align:start position:0%
+stability we looked at medical uses of
+ 
+
+ align:start position:0%
+stability we looked at medical uses of
+radiation from implanting radioactive
+
+ align:start position:0%
+radiation from implanting radioactive
+ 
+
+ align:start position:0%
+radiation from implanting radioactive
+seeds of called brachytherapy seeds in
+
+ align:start position:0%
+seeds of called brachytherapy seeds in
+ 
+
+ align:start position:0%
+seeds of called brachytherapy seeds in
+certain places to destroy tumors to
+
+ align:start position:0%
+certain places to destroy tumors to
+ 
+
+ align:start position:0%
+certain places to destroy tumors to
+imaging to x-ray therapy to proton
+
+ align:start position:0%
+imaging to x-ray therapy to proton
+ 
+
+ align:start position:0%
+imaging to x-ray therapy to proton
+therapy using accelerators or cyclotrons
+
+ align:start position:0%
+therapy using accelerators or cyclotrons
+ 
+
+ align:start position:0%
+therapy using accelerators or cyclotrons
+to accelerate protons and send them into
+
+ align:start position:0%
+to accelerate protons and send them into
+ 
+
+ align:start position:0%
+to accelerate protons and send them into
+people if you remember last time we ran
+
+ align:start position:0%
+people if you remember last time we ran
+ 
+
+ align:start position:0%
+people if you remember last time we ran
+the srem code of the stopping range of
+
+ align:start position:0%
+the srem code of the stopping range of
+ 
+
+ align:start position:0%
+the srem code of the stopping range of
+ions and matter and actually showed that
+
+ align:start position:0%
+ions and matter and actually showed that
+ 
+
+ align:start position:0%
+ions and matter and actually showed that
+protons all stop at a certain distance
+
+ align:start position:0%
+protons all stop at a certain distance
+ 
+
+ align:start position:0%
+protons all stop at a certain distance
+in tissue depending on their energy and
+
+ align:start position:0%
+in tissue depending on their energy and
+ 
+
+ align:start position:0%
+in tissue depending on their energy and
+what you're sending them into let's see
+
+ align:start position:0%
+what you're sending them into let's see
+ 
+
+ align:start position:0%
+what you're sending them into let's see
+talked about brachytherapy we talked
+
+ align:start position:0%
+talked about brachytherapy we talked
+ 
+
+ align:start position:0%
+talked about brachytherapy we talked
+about radiotracers and this is going to
+
+ align:start position:0%
+about radiotracers and this is going to
+ 
+
+ align:start position:0%
+about radiotracers and this is going to
+be one of the other main topics for
+
+ align:start position:0%
+be one of the other main topics for
+ 
+
+ align:start position:0%
+be one of the other main topics for
+today is these decay diagrams and
+
+ align:start position:0%
+today is these decay diagrams and
+ 
+
+ align:start position:0%
+today is these decay diagrams and
+figuring out not only what products are
+
+ align:start position:0%
+figuring out not only what products are
+ 
+
+ align:start position:0%
+figuring out not only what products are
+made but what energy levels - the nuclei
+
+ align:start position:0%
+made but what energy levels - the nuclei
+ 
+
+ align:start position:0%
+made but what energy levels - the nuclei
+have and how do you calculate the energy
+
+ align:start position:0%
+have and how do you calculate the energy
+ 
+
+ align:start position:0%
+have and how do you calculate the energy
+of the radioactive decay products and
+
+ align:start position:0%
+of the radioactive decay products and
+ 
+
+ align:start position:0%
+of the radioactive decay products and
+the recoil nuclei which do take away
+
+ align:start position:0%
+the recoil nuclei which do take away
+ 
+
+ align:start position:0%
+the recoil nuclei which do take away
+some of the energy we talked about one
+
+ align:start position:0%
+some of the energy we talked about one
+ 
+
+ align:start position:0%
+some of the energy we talked about one
+way to get rich if you guys can figure
+
+ align:start position:0%
+way to get rich if you guys can figure
+ 
+
+ align:start position:0%
+way to get rich if you guys can figure
+out one of the ways to solve this Molly
+
+ align:start position:0%
+out one of the ways to solve this Molly
+ 
+
+ align:start position:0%
+out one of the ways to solve this Molly
+99 shortage right now it's mostly
+
+ align:start position:0%
+99 shortage right now it's mostly
+ 
+
+ align:start position:0%
+99 shortage right now it's mostly
+and reactors the future has got to be
+
+ align:start position:0%
+and reactors the future has got to be
+ 
+
+ align:start position:0%
+and reactors the future has got to be
+accelerators or some sort of switchable
+
+ align:start position:0%
+accelerators or some sort of switchable
+ 
+
+ align:start position:0%
+accelerators or some sort of switchable
+device where you don't need to construct
+
+ align:start position:0%
+device where you don't need to construct
+ 
+
+ align:start position:0%
+device where you don't need to construct
+a reactor to make these medical isotopes
+
+ align:start position:0%
+a reactor to make these medical isotopes
+ 
+
+ align:start position:0%
+a reactor to make these medical isotopes
+for imaging and tracers and such and
+
+ align:start position:0%
+for imaging and tracers and such and
+ 
+
+ align:start position:0%
+for imaging and tracers and such and
+finally we got all the way up to space
+
+ align:start position:0%
+finally we got all the way up to space
+ 
+
+ align:start position:0%
+finally we got all the way up to space
+applications shielding crazy different
+
+ align:start position:0%
+applications shielding crazy different
+ 
+
+ align:start position:0%
+applications shielding crazy different
+types of shielding like electromagnetic
+
+ align:start position:0%
+types of shielding like electromagnetic
+ 
+
+ align:start position:0%
+types of shielding like electromagnetic
+shielding to protect from high-energy
+
+ align:start position:0%
+shielding to protect from high-energy
+ 
+
+ align:start position:0%
+shielding to protect from high-energy
+protons all the way to radio thermal
+
+ align:start position:0%
+protons all the way to radio thermal
+ 
+
+ align:start position:0%
+protons all the way to radio thermal
+generators which use alpha decay to
+
+ align:start position:0%
+generators which use alpha decay to
+ 
+
+ align:start position:0%
+generators which use alpha decay to
+produce a constant amount of energy on
+
+ align:start position:0%
+produce a constant amount of energy on
+ 
+
+ align:start position:0%
+produce a constant amount of energy on
+the order of 1 to 200 watts for like a
+
+ align:start position:0%
+the order of 1 to 200 watts for like a
+ 
+
+ align:start position:0%
+the order of 1 to 200 watts for like a
+hundred years and finally to a different
+
+ align:start position:0%
+hundred years and finally to a different
+ 
+
+ align:start position:0%
+hundred years and finally to a different
+configuration of nuclear reactors where
+
+ align:start position:0%
+configuration of nuclear reactors where
+ 
+
+ align:start position:0%
+configuration of nuclear reactors where
+you can design them to produce thrust
+
+ align:start position:0%
+you can design them to produce thrust
+ 
+
+ align:start position:0%
+you can design them to produce thrust
+not necessarily electricity and that's
+
+ align:start position:0%
+not necessarily electricity and that's
+ 
+
+ align:start position:0%
+not necessarily electricity and that's
+where we stopped on Friday so let's move
+
+ align:start position:0%
+where we stopped on Friday so let's move
+ 
+
+ align:start position:0%
+where we stopped on Friday so let's move
+on to one of the things I'd alluded to
+
+ align:start position:0%
+on to one of the things I'd alluded to
+ 
+
+ align:start position:0%
+on to one of the things I'd alluded to
+earlier which is semiconductor
+
+ align:start position:0%
+earlier which is semiconductor
+ 
+
+ align:start position:0%
+earlier which is semiconductor
+processing this is actually a diagram
+
+ align:start position:0%
+processing this is actually a diagram
+ 
+
+ align:start position:0%
+processing this is actually a diagram
+from the MIT reactor because we have
+
+ align:start position:0%
+from the MIT reactor because we have
+ 
+
+ align:start position:0%
+from the MIT reactor because we have
+this beam port here
+
+ align:start position:0%
+this beam port here
+ 
+
+ align:start position:0%
+this beam port here
+has anyone got to see the silicon beam
+
+ align:start position:0%
+has anyone got to see the silicon beam
+ 
+
+ align:start position:0%
+has anyone got to see the silicon beam
+port at the MIT reactor about seven
+
+ align:start position:0%
+port at the MIT reactor about seven
+ 
+
+ align:start position:0%
+port at the MIT reactor about seven
+eight okay about how for you for those
+
+ align:start position:0%
+eight okay about how for you for those
+ 
+
+ align:start position:0%
+eight okay about how for you for those
+who have and who here has not had a
+
+ align:start position:0%
+who have and who here has not had a
+ 
+
+ align:start position:0%
+who have and who here has not had a
+nuclear reactor tour oh man okay well
+
+ align:start position:0%
+nuclear reactor tour oh man okay well
+ 
+
+ align:start position:0%
+nuclear reactor tour oh man okay well
+you'll get one when you get to control
+
+ align:start position:0%
+you'll get one when you get to control
+ 
+
+ align:start position:0%
+you'll get one when you get to control
+the thing in early October so you
+
+ align:start position:0%
+the thing in early October so you
+ 
+
+ align:start position:0%
+the thing in early October so you
+actually get to go down to the control
+
+ align:start position:0%
+actually get to go down to the control
+ 
+
+ align:start position:0%
+actually get to go down to the control
+room and see the rest of what's going on
+
+ align:start position:0%
+room and see the rest of what's going on
+ 
+
+ align:start position:0%
+room and see the rest of what's going on
+so make sure to ask them show us the
+
+ align:start position:0%
+so make sure to ask them show us the
+ 
+
+ align:start position:0%
+so make sure to ask them show us the
+beam port for silicate ingots and I
+
+ align:start position:0%
+beam port for silicate ingots and I
+ 
+
+ align:start position:0%
+beam port for silicate ingots and I
+think I already told you the story about
+
+ align:start position:0%
+think I already told you the story about
+ 
+
+ align:start position:0%
+think I already told you the story about
+the pour UROP who held the ingots up to
+
+ align:start position:0%
+the pour UROP who held the ingots up to
+ 
+
+ align:start position:0%
+the pour UROP who held the ingots up to
+their chest getting about ten months of
+
+ align:start position:0%
+their chest getting about ten months of
+ 
+
+ align:start position:0%
+their chest getting about ten months of
+dose which is not dangerous but it meant
+
+ align:start position:0%
+dose which is not dangerous but it meant
+ 
+
+ align:start position:0%
+dose which is not dangerous but it meant
+that for ten months they can have no
+
+ align:start position:0%
+that for ten months they can have no
+ 
+
+ align:start position:0%
+that for ten months they can have no
+radiation exposure and they had to
+
+ align:start position:0%
+radiation exposure and they had to
+ 
+
+ align:start position:0%
+radiation exposure and they had to
+answer the phone so that's how we ensure
+
+ align:start position:0%
+answer the phone so that's how we ensure
+ 
+
+ align:start position:0%
+answer the phone so that's how we ensure
+safety around here there's other ones
+
+ align:start position:0%
+safety around here there's other ones
+ 
+
+ align:start position:0%
+safety around here there's other ones
+that applications that you're probably
+
+ align:start position:0%
+that applications that you're probably
+ 
+
+ align:start position:0%
+that applications that you're probably
+carrying around in your pocket you can
+
+ align:start position:0%
+carrying around in your pocket you can
+ 
+
+ align:start position:0%
+carrying around in your pocket you can
+use the fact that charge particles have
+
+ align:start position:0%
+use the fact that charge particles have
+ 
+
+ align:start position:0%
+use the fact that charge particles have
+very finite ranges and matter to
+
+ align:start position:0%
+very finite ranges and matter to
+ 
+
+ align:start position:0%
+very finite ranges and matter to
+separate little bits of that matter from
+
+ align:start position:0%
+separate little bits of that matter from
+ 
+
+ align:start position:0%
+separate little bits of that matter from
+other things so this is actually how
+
+ align:start position:0%
+other things so this is actually how
+ 
+
+ align:start position:0%
+other things so this is actually how
+single crystal sapphires can be
+
+ align:start position:0%
+single crystal sapphires can be
+ 
+
+ align:start position:0%
+single crystal sapphires can be
+separated in little slivers for
+
+ align:start position:0%
+separated in little slivers for
+ 
+
+ align:start position:0%
+separated in little slivers for
+protective phone covers because
+
+ align:start position:0%
+protective phone covers because
+ 
+
+ align:start position:0%
+protective phone covers because
+sapphires one of the most the hardest of
+
+ align:start position:0%
+sapphires one of the most the hardest of
+ 
+
+ align:start position:0%
+sapphires one of the most the hardest of
+the most scratch resistant materials
+
+ align:start position:0%
+the most scratch resistant materials
+ 
+
+ align:start position:0%
+the most scratch resistant materials
+there is single crystal sapphire is
+
+ align:start position:0%
+there is single crystal sapphire is
+ 
+
+ align:start position:0%
+there is single crystal sapphire is
+exceptionally strong and optically
+
+ align:start position:0%
+exceptionally strong and optically
+ 
+
+ align:start position:0%
+exceptionally strong and optically
+transparent and expensive I know that
+
+ align:start position:0%
+transparent and expensive I know that
+ 
+
+ align:start position:0%
+transparent and expensive I know that
+because on one of our experiments we use
+
+ align:start position:0%
+because on one of our experiments we use
+ 
+
+ align:start position:0%
+because on one of our experiments we use
+a single crystal sapphire window to see
+
+ align:start position:0%
+a single crystal sapphire window to see
+ 
+
+ align:start position:0%
+a single crystal sapphire window to see
+into reactor conditions at like 150
+
+ align:start position:0%
+into reactor conditions at like 150
+ 
+
+ align:start position:0%
+into reactor conditions at like 150
+atmospheres
+
+ align:start position:0%
+atmospheres
+ 
+
+ align:start position:0%
+atmospheres
+and 350 degrees Celsius and pretty
+
+ align:start position:0%
+and 350 degrees Celsius and pretty
+ 
+
+ align:start position:0%
+and 350 degrees Celsius and pretty
+corrosive chemistry so you want to use
+
+ align:start position:0%
+corrosive chemistry so you want to use
+ 
+
+ align:start position:0%
+corrosive chemistry so you want to use
+as little as possible so you can use a
+
+ align:start position:0%
+as little as possible so you can use a
+ 
+
+ align:start position:0%
+as little as possible so you can use a
+big expensive accelerator to limit the
+
+ align:start position:0%
+big expensive accelerator to limit the
+ 
+
+ align:start position:0%
+big expensive accelerator to limit the
+amount of sapphire that you use and this
+
+ align:start position:0%
+amount of sapphire that you use and this
+ 
+
+ align:start position:0%
+amount of sapphire that you use and this
+is actually done here in Boston there's
+
+ align:start position:0%
+is actually done here in Boston there's
+ 
+
+ align:start position:0%
+is actually done here in Boston there's
+a facility not far from here that uses
+
+ align:start position:0%
+a facility not far from here that uses
+ 
+
+ align:start position:0%
+a facility not far from here that uses
+an accelerator and this is their super
+
+ align:start position:0%
+an accelerator and this is their super
+ 
+
+ align:start position:0%
+an accelerator and this is their super
+detailed diagram of what the radiation
+
+ align:start position:0%
+detailed diagram of what the radiation
+ 
+
+ align:start position:0%
+detailed diagram of what the radiation
+looks like yeah whatever but what they
+
+ align:start position:0%
+looks like yeah whatever but what they
+ 
+
+ align:start position:0%
+looks like yeah whatever but what they
+do is they take they accelerate protons
+
+ align:start position:0%
+do is they take they accelerate protons
+ 
+
+ align:start position:0%
+do is they take they accelerate protons
+they send them through bending magnets
+
+ align:start position:0%
+they send them through bending magnets
+ 
+
+ align:start position:0%
+they send them through bending magnets
+to steer that beam path and then they
+
+ align:start position:0%
+to steer that beam path and then they
+ 
+
+ align:start position:0%
+to steer that beam path and then they
+send them into a large piece of single
+
+ align:start position:0%
+send them into a large piece of single
+ 
+
+ align:start position:0%
+send them into a large piece of single
+crystal sapphire which is exceptionally
+
+ align:start position:0%
+crystal sapphire which is exceptionally
+ 
+
+ align:start position:0%
+crystal sapphire which is exceptionally
+expensive to make and they can actually
+
+ align:start position:0%
+expensive to make and they can actually
+ 
+
+ align:start position:0%
+expensive to make and they can actually
+lift off a thin sliver with micron
+
+ align:start position:0%
+lift off a thin sliver with micron
+ 
+
+ align:start position:0%
+lift off a thin sliver with micron
+precision the reason for that is the
+
+ align:start position:0%
+precision the reason for that is the
+ 
+
+ align:start position:0%
+precision the reason for that is the
+same reason that we showed with that
+
+ align:start position:0%
+same reason that we showed with that
+ 
+
+ align:start position:0%
+same reason that we showed with that
+srem code if you to have this exact
+
+ align:start position:0%
+srem code if you to have this exact
+ 
+
+ align:start position:0%
+srem code if you to have this exact
+energy of protons going into well-known
+
+ align:start position:0%
+energy of protons going into well-known
+ 
+
+ align:start position:0%
+energy of protons going into well-known
+matter you know what its range is going
+
+ align:start position:0%
+matter you know what its range is going
+ 
+
+ align:start position:0%
+matter you know what its range is going
+to be with an uncertainty or so of about
+
+ align:start position:0%
+to be with an uncertainty or so of about
+ 
+
+ align:start position:0%
+to be with an uncertainty or so of about
+a micron so you can have things that
+
+ align:start position:0%
+a micron so you can have things that
+ 
+
+ align:start position:0%
+a micron so you can have things that
+come out thin uniformly and thick and
+
+ align:start position:0%
+come out thin uniformly and thick and
+ 
+
+ align:start position:0%
+come out thin uniformly and thick and
+smooth right away
+
+ align:start position:0%
+smooth right away
+ 
+
+ align:start position:0%
+smooth right away
+there's some other really wacky products
+
+ align:start position:0%
+there's some other really wacky products
+ 
+
+ align:start position:0%
+there's some other really wacky products
+like if anyone heard of these beta
+
+ align:start position:0%
+like if anyone heard of these beta
+ 
+
+ align:start position:0%
+like if anyone heard of these beta
+voltaic batteries no they rely on beta
+
+ align:start position:0%
+voltaic batteries no they rely on beta
+ 
+
+ align:start position:0%
+voltaic batteries no they rely on beta
+decay or the direct capture and
+
+ align:start position:0%
+decay or the direct capture and
+ 
+
+ align:start position:0%
+decay or the direct capture and
+electricity generation from a radiation
+
+ align:start position:0%
+electricity generation from a radiation
+ 
+
+ align:start position:0%
+electricity generation from a radiation
+source like radioactive tritium so in
+
+ align:start position:0%
+source like radioactive tritium so in
+ 
+
+ align:start position:0%
+source like radioactive tritium so in
+this little chip is about two Curie's
+
+ align:start position:0%
+this little chip is about two Curie's
+ 
+
+ align:start position:0%
+this little chip is about two Curie's
+worth of tritium you guys will learn in
+
+ align:start position:0%
+worth of tritium you guys will learn in
+ 
+
+ align:start position:0%
+worth of tritium you guys will learn in
+oh about a week how to go from activity
+
+ align:start position:0%
+oh about a week how to go from activity
+ 
+
+ align:start position:0%
+oh about a week how to go from activity
+and Curie's into mass or something like
+
+ align:start position:0%
+and Curie's into mass or something like
+ 
+
+ align:start position:0%
+and Curie's into mass or something like
+that and so this chip actually contains
+
+ align:start position:0%
+that and so this chip actually contains
+ 
+
+ align:start position:0%
+that and so this chip actually contains
+a lot of radioactive tritium that
+
+ align:start position:0%
+a lot of radioactive tritium that
+ 
+
+ align:start position:0%
+a lot of radioactive tritium that
+directly creates electricity so you can
+
+ align:start position:0%
+directly creates electricity so you can
+ 
+
+ align:start position:0%
+directly creates electricity so you can
+hook into that chip and produce nano
+
+ align:start position:0%
+hook into that chip and produce nano
+ 
+
+ align:start position:0%
+hook into that chip and produce nano
+watts for years so it's one of these
+
+ align:start position:0%
+watts for years so it's one of these
+ 
+
+ align:start position:0%
+watts for years so it's one of these
+batteries that lasts well as long as a
+
+ align:start position:0%
+batteries that lasts well as long as a
+ 
+
+ align:start position:0%
+batteries that lasts well as long as a
+couple half-lives of the isotope that's
+
+ align:start position:0%
+couple half-lives of the isotope that's
+ 
+
+ align:start position:0%
+couple half-lives of the isotope that's
+inside now there's a trade-off here the
+
+ align:start position:0%
+inside now there's a trade-off here the
+ 
+
+ align:start position:0%
+inside now there's a trade-off here the
+shorter the half-life the more active a
+
+ align:start position:0%
+shorter the half-life the more active a
+ 
+
+ align:start position:0%
+shorter the half-life the more active a
+given isotope will be for the same
+
+ align:start position:0%
+given isotope will be for the same
+ 
+
+ align:start position:0%
+given isotope will be for the same
+number of atoms but the shorter it will
+
+ align:start position:0%
+number of atoms but the shorter it will
+ 
+
+ align:start position:0%
+number of atoms but the shorter it will
+last so you can have higher power for
+
+ align:start position:0%
+last so you can have higher power for
+ 
+
+ align:start position:0%
+last so you can have higher power for
+lower time or lower pi or Howard time
+
+ align:start position:0%
+lower time or lower pi or Howard time
+ 
+
+ align:start position:0%
+lower time or lower pi or Howard time
+it's the classic energy trade-off works
+
+ align:start position:0%
+it's the classic energy trade-off works
+ 
+
+ align:start position:0%
+it's the classic energy trade-off works
+the same way with irradiation and so now
+
+ align:start position:0%
+the same way with irradiation and so now
+ 
+
+ align:start position:0%
+the same way with irradiation and so now
+I wanted to get into some of the more
+
+ align:start position:0%
+I wanted to get into some of the more
+ 
+
+ align:start position:0%
+I wanted to get into some of the more
+technical stuff where we'll be talking
+
+ align:start position:0%
+technical stuff where we'll be talking
+ 
+
+ align:start position:0%
+technical stuff where we'll be talking
+about nuclear mass and stability and
+
+ align:start position:0%
+about nuclear mass and stability and
+ 
+
+ align:start position:0%
+about nuclear mass and stability and
+this is where the nuclear stuff really
+
+ align:start position:0%
+this is where the nuclear stuff really
+ 
+
+ align:start position:0%
+this is where the nuclear stuff really
+begins in 2201 first I want to make sure
+
+ align:start position:0%
+begins in 2201 first I want to make sure
+ 
+
+ align:start position:0%
+begins in 2201 first I want to make sure
+that we all agree on
+
+ align:start position:0%
+that we all agree on
+ 
+
+ align:start position:0%
+that we all agree on
+so I'll be writing isotopes in this sort
+
+ align:start position:0%
+so I'll be writing isotopes in this sort
+ 
+
+ align:start position:0%
+so I'll be writing isotopes in this sort
+of fashion or we referred to a as the
+
+ align:start position:0%
+of fashion or we referred to a as the
+ 
+
+ align:start position:0%
+of fashion or we referred to a as the
+atomic mass or just the total number of
+
+ align:start position:0%
+atomic mass or just the total number of
+ 
+
+ align:start position:0%
+atomic mass or just the total number of
+nucleons this is not the exact mass of a
+
+ align:start position:0%
+nucleons this is not the exact mass of a
+ 
+
+ align:start position:0%
+nucleons this is not the exact mass of a
+nucleus it just refers to the sum of the
+
+ align:start position:0%
+nucleus it just refers to the sum of the
+ 
+
+ align:start position:0%
+nucleus it just refers to the sum of the
+protons and neutrons in the nucleus
+
+ align:start position:0%
+protons and neutrons in the nucleus
+ 
+
+ align:start position:0%
+protons and neutrons in the nucleus
+itself and a lot of what we'll be
+
+ align:start position:0%
+itself and a lot of what we'll be
+ 
+
+ align:start position:0%
+itself and a lot of what we'll be
+talking about today is the difference
+
+ align:start position:0%
+talking about today is the difference
+ 
+
+ align:start position:0%
+talking about today is the difference
+between this nice integer mass number
+
+ align:start position:0%
+between this nice integer mass number
+ 
+
+ align:start position:0%
+between this nice integer mass number
+and the actual mass of the nucleus and
+
+ align:start position:0%
+and the actual mass of the nucleus and
+ 
+
+ align:start position:0%
+and the actual mass of the nucleus and
+that difference is given by the binding
+
+ align:start position:0%
+that difference is given by the binding
+ 
+
+ align:start position:0%
+that difference is given by the binding
+energy or the excess mass which are
+
+ align:start position:0%
+energy or the excess mass which are
+ 
+
+ align:start position:0%
+energy or the excess mass which are
+directly related Z is just referred to
+
+ align:start position:0%
+directly related Z is just referred to
+ 
+
+ align:start position:0%
+directly related Z is just referred to
+as the atomic number or the number of
+
+ align:start position:0%
+as the atomic number or the number of
+ 
+
+ align:start position:0%
+as the atomic number or the number of
+protons it's what makes the element what
+
+ align:start position:0%
+protons it's what makes the element what
+ 
+
+ align:start position:0%
+protons it's what makes the element what
+it is which makes the name kind of
+
+ align:start position:0%
+it is which makes the name kind of
+ 
+
+ align:start position:0%
+it is which makes the name kind of
+redundant but it's so humans learn by
+
+ align:start position:0%
+redundant but it's so humans learn by
+ 
+
+ align:start position:0%
+redundant but it's so humans learn by
+association it's easier to remember
+
+ align:start position:0%
+association it's easier to remember
+ 
+
+ align:start position:0%
+association it's easier to remember
+element names or symbols than which
+
+ align:start position:0%
+element names or symbols than which
+ 
+
+ align:start position:0%
+element names or symbols than which
+element is which just by the number of
+
+ align:start position:0%
+element is which just by the number of
+ 
+
+ align:start position:0%
+element is which just by the number of
+protons so a lot of times we'll use the
+
+ align:start position:0%
+protons so a lot of times we'll use the
+ 
+
+ align:start position:0%
+protons so a lot of times we'll use the
+name or at least the symbol just so we
+
+ align:start position:0%
+name or at least the symbol just so we
+ 
+
+ align:start position:0%
+name or at least the symbol just so we
+know what's going on and anything up
+
+ align:start position:0%
+know what's going on and anything up
+ 
+
+ align:start position:0%
+know what's going on and anything up
+here is some sort of a charge I do want
+
+ align:start position:0%
+here is some sort of a charge I do want
+ 
+
+ align:start position:0%
+here is some sort of a charge I do want
+to warn you guys of the dreaded multiple
+
+ align:start position:0%
+to warn you guys of the dreaded multiple
+ 
+
+ align:start position:0%
+to warn you guys of the dreaded multiple
+symbol use or multiple use of symbols
+
+ align:start position:0%
+symbol use or multiple use of symbols
+ 
+
+ align:start position:0%
+symbol use or multiple use of symbols
+I'll try to stick for a lowercase Q will
+
+ align:start position:0%
+I'll try to stick for a lowercase Q will
+ 
+
+ align:start position:0%
+I'll try to stick for a lowercase Q will
+be charged an uppercase Q is going to
+
+ align:start position:0%
+be charged an uppercase Q is going to
+ 
+
+ align:start position:0%
+be charged an uppercase Q is going to
+refer to the Q value or the energy
+
+ align:start position:0%
+refer to the Q value or the energy
+ 
+
+ align:start position:0%
+refer to the Q value or the energy
+consumed or released by a nuclear
+
+ align:start position:0%
+consumed or released by a nuclear
+ 
+
+ align:start position:0%
+consumed or released by a nuclear
+reaction so they're both Q's but we're
+
+ align:start position:0%
+reaction so they're both Q's but we're
+ 
+
+ align:start position:0%
+reaction so they're both Q's but we're
+gonna keep one upper and lowercase and
+
+ align:start position:0%
+gonna keep one upper and lowercase and
+ 
+
+ align:start position:0%
+gonna keep one upper and lowercase and
+like we mentioned before let's say we
+
+ align:start position:0%
+like we mentioned before let's say we
+ 
+
+ align:start position:0%
+like we mentioned before let's say we
+were to write a typical nuclear reaction
+
+ align:start position:0%
+were to write a typical nuclear reaction
+ 
+
+ align:start position:0%
+were to write a typical nuclear reaction
+like the capture of neutrons by boron to
+
+ align:start position:0%
+like the capture of neutrons by boron to
+ 
+
+ align:start position:0%
+like the capture of neutrons by boron to
+produce lithium seven helium four better
+
+ align:start position:0%
+produce lithium seven helium four better
+ 
+
+ align:start position:0%
+produce lithium seven helium four better
+known as an alpha particle and some
+
+ align:start position:0%
+known as an alpha particle and some
+ 
+
+ align:start position:0%
+known as an alpha particle and some
+amount of energy there's two places
+
+ align:start position:0%
+amount of energy there's two places
+ 
+
+ align:start position:0%
+amount of energy there's two places
+where we actually use this reaction one
+
+ align:start position:0%
+where we actually use this reaction one
+ 
+
+ align:start position:0%
+where we actually use this reaction one
+of them is as control rods Alana
+
+ align:start position:0%
+of them is as control rods Alana
+ 
+
+ align:start position:0%
+of them is as control rods Alana
+reactors use boron for carbide or this
+
+ align:start position:0%
+reactors use boron for carbide or this
+ 
+
+ align:start position:0%
+reactors use boron for carbide or this
+compound B for C which is conveniently
+
+ align:start position:0%
+compound B for C which is conveniently
+ 
+
+ align:start position:0%
+compound B for C which is conveniently
+solid fairly dense and contains a whole
+
+ align:start position:0%
+solid fairly dense and contains a whole
+ 
+
+ align:start position:0%
+solid fairly dense and contains a whole
+lot of boron in one place specifically
+
+ align:start position:0%
+lot of boron in one place specifically
+ 
+
+ align:start position:0%
+lot of boron in one place specifically
+enriched in boron 10 because boron 10
+
+ align:start position:0%
+enriched in boron 10 because boron 10
+ 
+
+ align:start position:0%
+enriched in boron 10 because boron 10
+has a high cross-section or probability
+
+ align:start position:0%
+has a high cross-section or probability
+ 
+
+ align:start position:0%
+has a high cross-section or probability
+for Neutron capture and the other one is
+
+ align:start position:0%
+for Neutron capture and the other one is
+ 
+
+ align:start position:0%
+for Neutron capture and the other one is
+in what's called boron Neutron capture
+
+ align:start position:0%
+in what's called boron Neutron capture
+ 
+
+ align:start position:0%
+in what's called boron Neutron capture
+therapy if I discuss this with you guys
+
+ align:start position:0%
+therapy if I discuss this with you guys
+ 
+
+ align:start position:0%
+therapy if I discuss this with you guys
+already BNCT
+
+ align:start position:0%
+already BNCT
+ 
+
+ align:start position:0%
+already BNCT
+good because that's what we'll be
+
+ align:start position:0%
+good because that's what we'll be
+ 
+
+ align:start position:0%
+good because that's what we'll be
+talking about for a few slides and to
+
+ align:start position:0%
+talking about for a few slides and to
+ 
+
+ align:start position:0%
+talking about for a few slides and to
+write this whole reaction is the same
+
+ align:start position:0%
+write this whole reaction is the same
+ 
+
+ align:start position:0%
+write this whole reaction is the same
+thing as writing this shorthand nuclear
+
+ align:start position:0%
+thing as writing this shorthand nuclear
+ 
+
+ align:start position:0%
+thing as writing this shorthand nuclear
+reaction so this is often how you see
+
+ align:start position:0%
+reaction so this is often how you see
+ 
+
+ align:start position:0%
+reaction so this is often how you see
+them in the reading and in papers
+
+ align:start position:0%
+them in the reading and in papers
+ 
+
+ align:start position:0%
+them in the reading and in papers
+because it's shorter to do that but it's
+
+ align:start position:0%
+because it's shorter to do that but it's
+ 
+
+ align:start position:0%
+because it's shorter to do that but it's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+exact same thing so I have a couple
+
+ align:start position:0%
+exact same thing so I have a couple
+ 
+
+ align:start position:0%
+exact same thing so I have a couple
+questions for you guys then I have this
+
+ align:start position:0%
+questions for you guys then I have this
+ 
+
+ align:start position:0%
+questions for you guys then I have this
+extra queue here where does that queue
+
+ align:start position:0%
+extra queue here where does that queue
+ 
+
+ align:start position:0%
+extra queue here where does that queue
+actually go so let's say boron and
+
+ align:start position:0%
+actually go so let's say boron and
+ 
+
+ align:start position:0%
+actually go so let's say boron and
+neutron absorb it produces two nuclei
+
+ align:start position:0%
+neutron absorb it produces two nuclei
+ 
+
+ align:start position:0%
+neutron absorb it produces two nuclei
+with different binding energies what
+
+ align:start position:0%
+with different binding energies what
+ 
+
+ align:start position:0%
+with different binding energies what
+happens to the excess energy created
+
+ align:start position:0%
+happens to the excess energy created
+ 
+
+ align:start position:0%
+happens to the excess energy created
+from the conversion of mass to energy
+
+ align:start position:0%
+from the conversion of mass to energy
+ 
+
+ align:start position:0%
+from the conversion of mass to energy
+yeah Alex yep and heat more specifically
+
+ align:start position:0%
+yeah Alex yep and heat more specifically
+ 
+
+ align:start position:0%
+yeah Alex yep and heat more specifically
+kinetic energy of the radiation released
+
+ align:start position:0%
+kinetic energy of the radiation released
+ 
+
+ align:start position:0%
+kinetic energy of the radiation released
+and so that kinetic energy is actually
+
+ align:start position:0%
+and so that kinetic energy is actually
+ 
+
+ align:start position:0%
+and so that kinetic energy is actually
+used to our benefit in BNCT or boron
+
+ align:start position:0%
+used to our benefit in BNCT or boron
+ 
+
+ align:start position:0%
+used to our benefit in BNCT or boron
+Neutron capture therapy the way this
+
+ align:start position:0%
+Neutron capture therapy the way this
+ 
+
+ align:start position:0%
+Neutron capture therapy the way this
+works once I hit play is you can either
+
+ align:start position:0%
+works once I hit play is you can either
+ 
+
+ align:start position:0%
+works once I hit play is you can either
+use any sort of source of neutrons
+
+ align:start position:0%
+use any sort of source of neutrons
+ 
+
+ align:start position:0%
+use any sort of source of neutrons
+either a reactor or an accelerator
+
+ align:start position:0%
+either a reactor or an accelerator
+ 
+
+ align:start position:0%
+either a reactor or an accelerator
+through a lower complex chain of events
+
+ align:start position:0%
+through a lower complex chain of events
+ 
+
+ align:start position:0%
+through a lower complex chain of events
+like this in this case an accelerator so
+
+ align:start position:0%
+like this in this case an accelerator so
+ 
+
+ align:start position:0%
+like this in this case an accelerator so
+you don't need a whole reactor fires a
+
+ align:start position:0%
+you don't need a whole reactor fires a
+ 
+
+ align:start position:0%
+you don't need a whole reactor fires a
+beam of high-energy protons into a
+
+ align:start position:0%
+beam of high-energy protons into a
+ 
+
+ align:start position:0%
+beam of high-energy protons into a
+beryllium target that sound fairly
+
+ align:start position:0%
+beryllium target that sound fairly
+ 
+
+ align:start position:0%
+beryllium target that sound fairly
+familiar firing something at beryllium
+
+ align:start position:0%
+familiar firing something at beryllium
+ 
+
+ align:start position:0%
+familiar firing something at beryllium
+releasing neutrons like what Chadwick
+
+ align:start position:0%
+releasing neutrons like what Chadwick
+ 
+
+ align:start position:0%
+releasing neutrons like what Chadwick
+was doing except he was firing alpha
+
+ align:start position:0%
+was doing except he was firing alpha
+ 
+
+ align:start position:0%
+was doing except he was firing alpha
+particles into it this releases neutrons
+
+ align:start position:0%
+particles into it this releases neutrons
+ 
+
+ align:start position:0%
+particles into it this releases neutrons
+what they don't have labeled here is
+
+ align:start position:0%
+what they don't have labeled here is
+ 
+
+ align:start position:0%
+what they don't have labeled here is
+slowing down stuff or probably
+
+ align:start position:0%
+slowing down stuff or probably
+ 
+
+ align:start position:0%
+slowing down stuff or probably
+hydrogenous material so that the
+
+ align:start position:0%
+hydrogenous material so that the
+ 
+
+ align:start position:0%
+hydrogenous material so that the
+neutrons slow down to a lower energy and
+
+ align:start position:0%
+neutrons slow down to a lower energy and
+ 
+
+ align:start position:0%
+neutrons slow down to a lower energy and
+their probability of capture increases
+
+ align:start position:0%
+their probability of capture increases
+ 
+
+ align:start position:0%
+their probability of capture increases
+or their cross-section increases if you
+
+ align:start position:0%
+or their cross-section increases if you
+ 
+
+ align:start position:0%
+or their cross-section increases if you
+don't know what a cross-section is the
+
+ align:start position:0%
+don't know what a cross-section is the
+ 
+
+ align:start position:0%
+don't know what a cross-section is the
+definition is two slides away and the
+
+ align:start position:0%
+definition is two slides away and the
+ 
+
+ align:start position:0%
+definition is two slides away and the
+idea here is that these neutrons then
+
+ align:start position:0%
+idea here is that these neutrons then
+ 
+
+ align:start position:0%
+idea here is that these neutrons then
+enter the brain or wherever the tumour
+
+ align:start position:0%
+enter the brain or wherever the tumour
+ 
+
+ align:start position:0%
+enter the brain or wherever the tumour
+happens to be and we rely on the fact
+
+ align:start position:0%
+happens to be and we rely on the fact
+ 
+
+ align:start position:0%
+happens to be and we rely on the fact
+that tumor cells consume resources much
+
+ align:start position:0%
+that tumor cells consume resources much
+ 
+
+ align:start position:0%
+that tumor cells consume resources much
+faster than regular cells especially
+
+ align:start position:0%
+faster than regular cells especially
+ 
+
+ align:start position:0%
+faster than regular cells especially
+neurons which after you're about five
+
+ align:start position:0%
+neurons which after you're about five
+ 
+
+ align:start position:0%
+neurons which after you're about five
+don't tend to grow very much so it's all
+
+ align:start position:0%
+don't tend to grow very much so it's all
+ 
+
+ align:start position:0%
+don't tend to grow very much so it's all
+downhill by the time you enter
+
+ align:start position:0%
+downhill by the time you enter
+ 
+
+ align:start position:0%
+downhill by the time you enter
+kindergarten and we use that to our
+
+ align:start position:0%
+kindergarten and we use that to our
+ 
+
+ align:start position:0%
+kindergarten and we use that to our
+advantage so that the neutrons coming in
+
+ align:start position:0%
+advantage so that the neutrons coming in
+ 
+
+ align:start position:0%
+advantage so that the neutrons coming in
+will hit the cancer cells which will
+
+ align:start position:0%
+will hit the cancer cells which will
+ 
+
+ align:start position:0%
+will hit the cancer cells which will
+preferentially uptake the bohr aidid
+
+ align:start position:0%
+preferentially uptake the bohr aidid
+ 
+
+ align:start position:0%
+preferentially uptake the bohr aidid
+compounds leaving most of the normal
+
+ align:start position:0%
+compounds leaving most of the normal
+ 
+
+ align:start position:0%
+compounds leaving most of the normal
+cells intact and the difference in dose
+
+ align:start position:0%
+cells intact and the difference in dose
+ 
+
+ align:start position:0%
+cells intact and the difference in dose
+can be a factor of five or a factor of
+
+ align:start position:0%
+can be a factor of five or a factor of
+ 
+
+ align:start position:0%
+can be a factor of five or a factor of
+ten so that the cancer gets fried while
+
+ align:start position:0%
+ten so that the cancer gets fried while
+ 
+
+ align:start position:0%
+ten so that the cancer gets fried while
+doing as little damage as possible that
+
+ align:start position:0%
+doing as little damage as possible that
+ 
+
+ align:start position:0%
+doing as little damage as possible that
+the remaining brain cells of which we
+
+ align:start position:0%
+the remaining brain cells of which we
+ 
+
+ align:start position:0%
+the remaining brain cells of which we
+have fewer and fewer every day so I say
+
+ align:start position:0%
+have fewer and fewer every day so I say
+ 
+
+ align:start position:0%
+have fewer and fewer every day so I say
+statistically speaking you guys are
+
+ align:start position:0%
+statistically speaking you guys are
+ 
+
+ align:start position:0%
+statistically speaking you guys are
+probably smarter than me if we go by
+
+ align:start position:0%
+probably smarter than me if we go by
+ 
+
+ align:start position:0%
+probably smarter than me if we go by
+number of neurons in your brain because
+
+ align:start position:0%
+number of neurons in your brain because
+ 
+
+ align:start position:0%
+number of neurons in your brain because
+I think I'm the oldest person in the
+
+ align:start position:0%
+I think I'm the oldest person in the
+ 
+
+ align:start position:0%
+I think I'm the oldest person in the
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+and so now we can start to explain how
+
+ align:start position:0%
+and so now we can start to explain how
+ 
+
+ align:start position:0%
+and so now we can start to explain how
+does BNCT work and why did we make the
+
+ align:start position:0%
+does BNCT work and why did we make the
+ 
+
+ align:start position:0%
+does BNCT work and why did we make the
+choices that we did for example they use
+
+ align:start position:0%
+choices that we did for example they use
+ 
+
+ align:start position:0%
+choices that we did for example they use
+30 MeV protons in order to induce these
+
+ align:start position:0%
+30 MeV protons in order to induce these
+ 
+
+ align:start position:0%
+30 MeV protons in order to induce these
+neutrons so we have a nuclear reaction
+
+ align:start position:0%
+neutrons so we have a nuclear reaction
+ 
+
+ align:start position:0%
+neutrons so we have a nuclear reaction
+that looks something like this we start
+
+ align:start position:0%
+that looks something like this we start
+ 
+
+ align:start position:0%
+that looks something like this we start
+off with beryllium 9 plus a proton let's
+
+ align:start position:0%
+off with beryllium 9 plus a proton let's
+ 
+
+ align:start position:0%
+off with beryllium 9 plus a proton let's
+just call it hydrogen to stick with our
+
+ align:start position:0%
+just call it hydrogen to stick with our
+ 
+
+ align:start position:0%
+just call it hydrogen to stick with our
+normal notation and becomes well can
+
+ align:start position:0%
+normal notation and becomes well can
+ 
+
+ align:start position:0%
+normal notation and becomes well can
+someone help me balance this reaction we
+
+ align:start position:0%
+someone help me balance this reaction we
+ 
+
+ align:start position:0%
+someone help me balance this reaction we
+know we get a neutron what else is left
+
+ align:start position:0%
+know we get a neutron what else is left
+ 
+
+ align:start position:0%
+know we get a neutron what else is left
+no Monica what would you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even just say number of protons and
+
+ align:start position:0%
+even just say number of protons and
+ 
+
+ align:start position:0%
+even just say number of protons and
+neutrons and we'll figure out the symbol
+
+ align:start position:0%
+neutrons and we'll figure out the symbol
+ 
+
+ align:start position:0%
+neutrons and we'll figure out the symbol
+leader sorry oh that's a yep five
+
+ align:start position:0%
+leader sorry oh that's a yep five
+ 
+
+ align:start position:0%
+leader sorry oh that's a yep five
+protons which means it's boron and
+
+ align:start position:0%
+protons which means it's boron and
+ 
+
+ align:start position:0%
+protons which means it's boron and
+number of neutrons in the nucleus
+
+ align:start position:0%
+number of neutrons in the nucleus
+ 
+
+ align:start position:0%
+number of neutrons in the nucleus
+someone else yeah nine so we have boron
+
+ align:start position:0%
+someone else yeah nine so we have boron
+ 
+
+ align:start position:0%
+someone else yeah nine so we have boron
+nine not a stable isotope of boron but
+
+ align:start position:0%
+nine not a stable isotope of boron but
+ 
+
+ align:start position:0%
+nine not a stable isotope of boron but
+doesn't really matter because boron nine
+
+ align:start position:0%
+doesn't really matter because boron nine
+ 
+
+ align:start position:0%
+doesn't really matter because boron nine
+almost immediately decays into an alpha
+
+ align:start position:0%
+almost immediately decays into an alpha
+ 
+
+ align:start position:0%
+almost immediately decays into an alpha
+and an alpha and a hydrogen but this
+
+ align:start position:0%
+and an alpha and a hydrogen but this
+ 
+
+ align:start position:0%
+and an alpha and a hydrogen but this
+nuclear reaction right here is what
+
+ align:start position:0%
+nuclear reaction right here is what
+ 
+
+ align:start position:0%
+nuclear reaction right here is what
+we'll be studying for a little bit and
+
+ align:start position:0%
+we'll be studying for a little bit and
+ 
+
+ align:start position:0%
+we'll be studying for a little bit and
+they'll also be some amount of energy
+
+ align:start position:0%
+they'll also be some amount of energy
+ 
+
+ align:start position:0%
+they'll also be some amount of energy
+and this Q can actually be positive or
+
+ align:start position:0%
+and this Q can actually be positive or
+ 
+
+ align:start position:0%
+and this Q can actually be positive or
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+no one said there had to be energy
+
+ align:start position:0%
+no one said there had to be energy
+ 
+
+ align:start position:0%
+no one said there had to be energy
+released in a nuclear reaction because
+
+ align:start position:0%
+released in a nuclear reaction because
+ 
+
+ align:start position:0%
+released in a nuclear reaction because
+in this case we actually start off with
+
+ align:start position:0%
+in this case we actually start off with
+ 
+
+ align:start position:0%
+in this case we actually start off with
+thirty MeV protons and roughly zero and
+
+ align:start position:0%
+thirty MeV protons and roughly zero and
+ 
+
+ align:start position:0%
+thirty MeV protons and roughly zero and
+maybe beryllium if you want to get
+
+ align:start position:0%
+maybe beryllium if you want to get
+ 
+
+ align:start position:0%
+maybe beryllium if you want to get
+really exact it's on the order of about
+
+ align:start position:0%
+really exact it's on the order of about
+ 
+
+ align:start position:0%
+really exact it's on the order of about
+0.01 evey which is why we neglect the
+
+ align:start position:0%
+0.01 evey which is why we neglect the
+ 
+
+ align:start position:0%
+0.01 evey which is why we neglect the
+kinetic energy of beryllium at room
+
+ align:start position:0%
+kinetic energy of beryllium at room
+ 
+
+ align:start position:0%
+kinetic energy of beryllium at room
+temperature there are other reactions
+
+ align:start position:0%
+temperature there are other reactions
+ 
+
+ align:start position:0%
+temperature there are other reactions
+that when you fire a proton into them
+
+ align:start position:0%
+that when you fire a proton into them
+ 
+
+ align:start position:0%
+that when you fire a proton into them
+will produce neutrons such as the
+
+ align:start position:0%
+will produce neutrons such as the
+ 
+
+ align:start position:0%
+will produce neutrons such as the
+absorption of lithium but can anyone
+
+ align:start position:0%
+absorption of lithium but can anyone
+ 
+
+ align:start position:0%
+absorption of lithium but can anyone
+think of why we'd want to use beryllium
+
+ align:start position:0%
+think of why we'd want to use beryllium
+ 
+
+ align:start position:0%
+think of why we'd want to use beryllium
+instead of lithium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Kristen what do you think what could be
+
+ align:start position:0%
+Kristen what do you think what could be
+ 
+
+ align:start position:0%
+Kristen what do you think what could be
+a bad thing about using lithium you ever
+
+ align:start position:0%
+a bad thing about using lithium you ever
+ 
+
+ align:start position:0%
+a bad thing about using lithium you ever
+throw it in water okay then I should
+
+ align:start position:0%
+throw it in water okay then I should
+ 
+
+ align:start position:0%
+throw it in water okay then I should
+show you what happens when you throw it
+
+ align:start position:0%
+show you what happens when you throw it
+ 
+
+ align:start position:0%
+show you what happens when you throw it
+in water there's a few bad things about
+
+ align:start position:0%
+in water there's a few bad things about
+ 
+
+ align:start position:0%
+in water there's a few bad things about
+lithium it does this when you throw it
+
+ align:start position:0%
+lithium it does this when you throw it
+ 
+
+ align:start position:0%
+lithium it does this when you throw it
+in water it's one of the alkali metals
+
+ align:start position:0%
+in water it's one of the alkali metals
+ 
+
+ align:start position:0%
+in water it's one of the alkali metals
+it's got an awfully low melting point it
+
+ align:start position:0%
+it's got an awfully low melting point it
+ 
+
+ align:start position:0%
+it's got an awfully low melting point it
+reacts with oxygen to produce an oxide
+
+ align:start position:0%
+reacts with oxygen to produce an oxide
+ 
+
+ align:start position:0%
+reacts with oxygen to produce an oxide
+almost instantaneously so if you ever
+
+ align:start position:0%
+almost instantaneously so if you ever
+ 
+
+ align:start position:0%
+almost instantaneously so if you ever
+take a lift the embargo riah part which
+
+ align:start position:0%
+take a lift the embargo riah part which
+ 
+
+ align:start position:0%
+take a lift the embargo riah part which
+you shouldn't but if you watch the video
+
+ align:start position:0%
+you shouldn't but if you watch the video
+ 
+
+ align:start position:0%
+you shouldn't but if you watch the video
+of somebody else doing it you'll see
+
+ align:start position:0%
+of somebody else doing it you'll see
+ 
+
+ align:start position:0%
+of somebody else doing it you'll see
+that the lithium foil turns black almost
+
+ align:start position:0%
+that the lithium foil turns black almost
+ 
+
+ align:start position:0%
+that the lithium foil turns black almost
+instantly it also has a pretty poor
+
+ align:start position:0%
+instantly it also has a pretty poor
+ 
+
+ align:start position:0%
+instantly it also has a pretty poor
+thermal conductivity and doesn't hold
+
+ align:start position:0%
+thermal conductivity and doesn't hold
+ 
+
+ align:start position:0%
+thermal conductivity and doesn't hold
+its structural integrity when it melts
+
+ align:start position:0%
+its structural integrity when it melts
+ 
+
+ align:start position:0%
+its structural integrity when it melts
+so it's not that good of a target to use
+
+ align:start position:0%
+so it's not that good of a target to use
+ 
+
+ align:start position:0%
+so it's not that good of a target to use
+beryllium is pretty cool and that it's
+
+ align:start position:0%
+beryllium is pretty cool and that it's
+ 
+
+ align:start position:0%
+beryllium is pretty cool and that it's
+the lightest structural material there
+
+ align:start position:0%
+the lightest structural material there
+ 
+
+ align:start position:0%
+the lightest structural material there
+is folks tend to make satellites out of
+
+ align:start position:0%
+is folks tend to make satellites out of
+ 
+
+ align:start position:0%
+is folks tend to make satellites out of
+it because it costs a lot of money to
+
+ align:start position:0%
+it because it costs a lot of money to
+ 
+
+ align:start position:0%
+it because it costs a lot of money to
+launch things into space and if you want
+
+ align:start position:0%
+launch things into space and if you want
+ 
+
+ align:start position:0%
+launch things into space and if you want
+something that has a high melting point
+
+ align:start position:0%
+something that has a high melting point
+ 
+
+ align:start position:0%
+something that has a high melting point
+and is light and is structural beryllium
+
+ align:start position:0%
+and is light and is structural beryllium
+ 
+
+ align:start position:0%
+and is light and is structural beryllium
+is your way to go it also happens to be
+
+ align:start position:0%
+is your way to go it also happens to be
+ 
+
+ align:start position:0%
+is your way to go it also happens to be
+a great neutron generator and then why
+
+ align:start position:0%
+a great neutron generator and then why
+ 
+
+ align:start position:0%
+a great neutron generator and then why
+30 MeV in this case we're going to look
+
+ align:start position:0%
+30 MeV in this case we're going to look
+ 
+
+ align:start position:0%
+30 MeV in this case we're going to look
+use a table called Janus which I've got
+
+ align:start position:0%
+use a table called Janus which I've got
+ 
+
+ align:start position:0%
+use a table called Janus which I've got
+open over here and I just have to clone
+
+ align:start position:0%
+open over here and I just have to clone
+ 
+
+ align:start position:0%
+open over here and I just have to clone
+my screen so you can see it this is a
+
+ align:start position:0%
+my screen so you can see it this is a
+ 
+
+ align:start position:0%
+my screen so you can see it this is a
+resource that I think you guys are going
+
+ align:start position:0%
+resource that I think you guys are going
+ 
+
+ align:start position:0%
+resource that I think you guys are going
+to be using quite a lot in this course
+
+ align:start position:0%
+to be using quite a lot in this course
+ 
+
+ align:start position:0%
+to be using quite a lot in this course
+we have a link to it on the learning
+
+ align:start position:0%
+we have a link to it on the learning
+ 
+
+ align:start position:0%
+we have a link to it on the learning
+module site and I'm gonna show you how
+
+ align:start position:0%
+module site and I'm gonna show you how
+ 
+
+ align:start position:0%
+module site and I'm gonna show you how
+it works right now so I tend to use the
+
+ align:start position:0%
+it works right now so I tend to use the
+ 
+
+ align:start position:0%
+it works right now so I tend to use the
+web version because it works on any
+
+ align:start position:0%
+web version because it works on any
+ 
+
+ align:start position:0%
+web version because it works on any
+browser or any computer and now you can
+
+ align:start position:0%
+browser or any computer and now you can
+ 
+
+ align:start position:0%
+browser or any computer and now you can
+start to pick which nuclear reaction
+
+ align:start position:0%
+start to pick which nuclear reaction
+ 
+
+ align:start position:0%
+start to pick which nuclear reaction
+you're looking at and you can get
+
+ align:start position:0%
+you're looking at and you can get
+ 
+
+ align:start position:0%
+you're looking at and you can get
+tabulated cross-sections so I'm gonna
+
+ align:start position:0%
+tabulated cross-sections so I'm gonna
+ 
+
+ align:start position:0%
+tabulated cross-sections so I'm gonna
+start by zooming all the way out we can
+
+ align:start position:0%
+start by zooming all the way out we can
+ 
+
+ align:start position:0%
+start by zooming all the way out we can
+pick our incident particle since in this
+
+ align:start position:0%
+pick our incident particle since in this
+ 
+
+ align:start position:0%
+pick our incident particle since in this
+case we're looking at the firing of
+
+ align:start position:0%
+case we're looking at the firing of
+ 
+
+ align:start position:0%
+case we're looking at the firing of
+protons into beryllium I'll pick the
+
+ align:start position:0%
+protons into beryllium I'll pick the
+ 
+
+ align:start position:0%
+protons into beryllium I'll pick the
+incident proton data right here there's
+
+ align:start position:0%
+incident proton data right here there's
+ 
+
+ align:start position:0%
+incident proton data right here there's
+a lot of different databases with
+
+ align:start position:0%
+a lot of different databases with
+ 
+
+ align:start position:0%
+a lot of different databases with
+sometimes conflicting information I tend
+
+ align:start position:0%
+sometimes conflicting information I tend
+ 
+
+ align:start position:0%
+sometimes conflicting information I tend
+to go with the most recent one you can
+
+ align:start position:0%
+to go with the most recent one you can
+ 
+
+ align:start position:0%
+to go with the most recent one you can
+find and click on cross-sections and
+
+ align:start position:0%
+find and click on cross-sections and
+ 
+
+ align:start position:0%
+find and click on cross-sections and
+this is again another table of nuclides
+
+ align:start position:0%
+this is again another table of nuclides
+ 
+
+ align:start position:0%
+this is again another table of nuclides
+anything in green there's data for
+
+ align:start position:0%
+anything in green there's data for
+ 
+
+ align:start position:0%
+anything in green there's data for
+anything in gray there isn't so let's go
+
+ align:start position:0%
+anything in gray there isn't so let's go
+ 
+
+ align:start position:0%
+anything in gray there isn't so let's go
+all the way back to the light nuclei
+
+ align:start position:0%
+all the way back to the light nuclei
+ 
+
+ align:start position:0%
+all the way back to the light nuclei
+zoom in
+
+ align:start position:0%
+zoom in
+ 
+
+ align:start position:0%
+zoom in
+go back down to the light nuclei again
+
+ align:start position:0%
+go back down to the light nuclei again
+ 
+
+ align:start position:0%
+go back down to the light nuclei again
+until we find beryllium 9 double-click
+
+ align:start position:0%
+until we find beryllium 9 double-click
+ 
+
+ align:start position:0%
+until we find beryllium 9 double-click
+on that and let's look for the anything
+
+ align:start position:0%
+on that and let's look for the anything
+ 
+
+ align:start position:0%
+on that and let's look for the anything
+cross-section and this is a pretty wide
+
+ align:start position:0%
+cross-section and this is a pretty wide
+ 
+
+ align:start position:0%
+cross-section and this is a pretty wide
+energy scale so you can actually change
+
+ align:start position:0%
+energy scale so you can actually change
+ 
+
+ align:start position:0%
+energy scale so you can actually change
+your x minimum and maximum so let's
+
+ align:start position:0%
+your x minimum and maximum so let's
+ 
+
+ align:start position:0%
+your x minimum and maximum so let's
+change it to a minimum and maximum I
+
+ align:start position:0%
+change it to a minimum and maximum I
+ 
+
+ align:start position:0%
+change it to a minimum and maximum I
+don't know a maximum of fifty MeV we
+
+ align:start position:0%
+don't know a maximum of fifty MeV we
+ 
+
+ align:start position:0%
+don't know a maximum of fifty MeV we
+don't have to see all of that other
+
+ align:start position:0%
+don't have to see all of that other
+ 
+
+ align:start position:0%
+don't have to see all of that other
+stuff going on fifty MeV and maybe a
+
+ align:start position:0%
+stuff going on fifty MeV and maybe a
+ 
+
+ align:start position:0%
+stuff going on fifty MeV and maybe a
+minimum of ten if you notice actually
+
+ align:start position:0%
+minimum of ten if you notice actually
+ 
+
+ align:start position:0%
+minimum of ten if you notice actually
+I'll go back to one and I want to point
+
+ align:start position:0%
+I'll go back to one and I want to point
+ 
+
+ align:start position:0%
+I'll go back to one and I want to point
+something out it you can actually get a
+
+ align:start position:0%
+something out it you can actually get a
+ 
+
+ align:start position:0%
+something out it you can actually get a
+good yield of beryllium let's say you
+
+ align:start position:0%
+good yield of beryllium let's say you
+ 
+
+ align:start position:0%
+good yield of beryllium let's say you
+can actually get a good yield of
+
+ align:start position:0%
+can actually get a good yield of
+ 
+
+ align:start position:0%
+can actually get a good yield of
+neutrons by firing protons at beryllium
+
+ align:start position:0%
+neutrons by firing protons at beryllium
+ 
+
+ align:start position:0%
+neutrons by firing protons at beryllium
+and lower energies but I noticed there's
+
+ align:start position:0%
+and lower energies but I noticed there's
+ 
+
+ align:start position:0%
+and lower energies but I noticed there's
+this interesting feature right around
+
+ align:start position:0%
+this interesting feature right around
+ 
+
+ align:start position:0%
+this interesting feature right around
+there the cross-sections flatter and so
+
+ align:start position:0%
+there the cross-sections flatter and so
+ 
+
+ align:start position:0%
+there the cross-sections flatter and so
+if you want to get an insurer that you
+
+ align:start position:0%
+if you want to get an insurer that you
+ 
+
+ align:start position:0%
+if you want to get an insurer that you
+get the right dose you might want to
+
+ align:start position:0%
+get the right dose you might want to
+ 
+
+ align:start position:0%
+get the right dose you might want to
+deal with a flatter cross section or a
+
+ align:start position:0%
+deal with a flatter cross section or a
+ 
+
+ align:start position:0%
+deal with a flatter cross section or a
+flatter probability region so that you
+
+ align:start position:0%
+flatter probability region so that you
+ 
+
+ align:start position:0%
+flatter probability region so that you
+have something more predictable instead
+
+ align:start position:0%
+have something more predictable instead
+ 
+
+ align:start position:0%
+have something more predictable instead
+of in a really high slope region but
+
+ align:start position:0%
+of in a really high slope region but
+ 
+
+ align:start position:0%
+of in a really high slope region but
+some of these nuclear reactions actually
+
+ align:start position:0%
+some of these nuclear reactions actually
+ 
+
+ align:start position:0%
+some of these nuclear reactions actually
+take extra energy in order to move
+
+ align:start position:0%
+take extra energy in order to move
+ 
+
+ align:start position:0%
+take extra energy in order to move
+forward and we'll show you another
+
+ align:start position:0%
+forward and we'll show you another
+ 
+
+ align:start position:0%
+forward and we'll show you another
+example pretty quickly let's go back to
+
+ align:start position:0%
+example pretty quickly let's go back to
+ 
+
+ align:start position:0%
+example pretty quickly let's go back to
+our slides here then another question is
+
+ align:start position:0%
+our slides here then another question is
+ 
+
+ align:start position:0%
+our slides here then another question is
+how does the boron only get into the
+
+ align:start position:0%
+how does the boron only get into the
+ 
+
+ align:start position:0%
+how does the boron only get into the
+cancer cells like we mentioned before
+
+ align:start position:0%
+cancer cells like we mentioned before
+ 
+
+ align:start position:0%
+cancer cells like we mentioned before
+cancer cells are actively growing which
+
+ align:start position:0%
+cancer cells are actively growing which
+ 
+
+ align:start position:0%
+cancer cells are actively growing which
+means they need a very large and active
+
+ align:start position:0%
+means they need a very large and active
+ 
+
+ align:start position:0%
+means they need a very large and active
+blood supply and so it's one way for
+
+ align:start position:0%
+blood supply and so it's one way for
+ 
+
+ align:start position:0%
+blood supply and so it's one way for
+things to let's say not quite cross the
+
+ align:start position:0%
+things to let's say not quite cross the
+ 
+
+ align:start position:0%
+things to let's say not quite cross the
+blood-brain barrier if the cancer cells
+
+ align:start position:0%
+blood-brain barrier if the cancer cells
+ 
+
+ align:start position:0%
+blood-brain barrier if the cancer cells
+are growing and your neurons aren't then
+
+ align:start position:0%
+are growing and your neurons aren't then
+ 
+
+ align:start position:0%
+are growing and your neurons aren't then
+your cancer cells are going to use more
+
+ align:start position:0%
+your cancer cells are going to use more
+ 
+
+ align:start position:0%
+your cancer cells are going to use more
+energy take in more sugar which might be
+
+ align:start position:0%
+energy take in more sugar which might be
+ 
+
+ align:start position:0%
+energy take in more sugar which might be
+doped with boron or some other compound
+
+ align:start position:0%
+doped with boron or some other compound
+ 
+
+ align:start position:0%
+doped with boron or some other compound
+doped with boron and that's how you can
+
+ align:start position:0%
+doped with boron and that's how you can
+ 
+
+ align:start position:0%
+doped with boron and that's how you can
+get the boron into the cells that you
+
+ align:start position:0%
+get the boron into the cells that you
+ 
+
+ align:start position:0%
+get the boron into the cells that you
+want and then why was boron selected for
+
+ align:start position:0%
+want and then why was boron selected for
+ 
+
+ align:start position:0%
+want and then why was boron selected for
+the therapy let's think about that what
+
+ align:start position:0%
+the therapy let's think about that what
+ 
+
+ align:start position:0%
+the therapy let's think about that what
+happens after the neutron is created and
+
+ align:start position:0%
+happens after the neutron is created and
+ 
+
+ align:start position:0%
+happens after the neutron is created and
+let's write the next stage of the
+
+ align:start position:0%
+let's write the next stage of the
+ 
+
+ align:start position:0%
+let's write the next stage of the
+reaction and boron Neutron capture
+
+ align:start position:0%
+reaction and boron Neutron capture
+ 
+
+ align:start position:0%
+reaction and boron Neutron capture
+therapy we rely on doping the patient
+
+ align:start position:0%
+therapy we rely on doping the patient
+ 
+
+ align:start position:0%
+therapy we rely on doping the patient
+with boron 10 to release an alpha
+
+ align:start position:0%
+with boron 10 to release an alpha
+ 
+
+ align:start position:0%
+with boron 10 to release an alpha
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+and lithium-7
+
+ align:start position:0%
+and lithium-7
+ 
+
+ align:start position:0%
+and lithium-7
+and a gamma-ray so now what we can start
+
+ align:start position:0%
+and a gamma-ray so now what we can start
+ 
+
+ align:start position:0%
+and a gamma-ray so now what we can start
+doing is look at the table of nuclides
+
+ align:start position:0%
+doing is look at the table of nuclides
+ 
+
+ align:start position:0%
+doing is look at the table of nuclides
+which I'm going to teach you how to read
+
+ align:start position:0%
+which I'm going to teach you how to read
+ 
+
+ align:start position:0%
+which I'm going to teach you how to read
+now to figure out let's say that this
+
+ align:start position:0%
+now to figure out let's say that this
+ 
+
+ align:start position:0%
+now to figure out let's say that this
+neutron had an energy of about 0a v and
+
+ align:start position:0%
+neutron had an energy of about 0a v and
+ 
+
+ align:start position:0%
+neutron had an energy of about 0a v and
+the boron nucleus had an energy of about
+
+ align:start position:0%
+the boron nucleus had an energy of about
+ 
+
+ align:start position:0%
+the boron nucleus had an energy of about
+0a v and in the end all this stuff here
+
+ align:start position:0%
+0a v and in the end all this stuff here
+ 
+
+ align:start position:0%
+0a v and in the end all this stuff here
+has gained or lost some sort of energy Q
+
+ align:start position:0%
+has gained or lost some sort of energy Q
+ 
+
+ align:start position:0%
+has gained or lost some sort of energy Q
+and today we're gonna teach you how to
+
+ align:start position:0%
+and today we're gonna teach you how to
+ 
+
+ align:start position:0%
+and today we're gonna teach you how to
+calculate this Q so I'm gonna skip ahead
+
+ align:start position:0%
+calculate this Q so I'm gonna skip ahead
+ 
+
+ align:start position:0%
+calculate this Q so I'm gonna skip ahead
+to how to read the table of nuclides so
+
+ align:start position:0%
+to how to read the table of nuclides so
+ 
+
+ align:start position:0%
+to how to read the table of nuclides so
+there's all this is like the poster
+
+ align:start position:0%
+there's all this is like the poster
+ 
+
+ align:start position:0%
+there's all this is like the poster
+you'll see in every nuclear building
+
+ align:start position:0%
+you'll see in every nuclear building
+ 
+
+ align:start position:0%
+you'll see in every nuclear building
+it's kind of what makes us us what
+
+ align:start position:0%
+it's kind of what makes us us what
+ 
+
+ align:start position:0%
+it's kind of what makes us us what
+you'll notice is that there's a whole
+
+ align:start position:0%
+you'll notice is that there's a whole
+ 
+
+ align:start position:0%
+you'll notice is that there's a whole
+lot of nuclei at the lower left there
+
+ align:start position:0%
+lot of nuclei at the lower left there
+ 
+
+ align:start position:0%
+lot of nuclei at the lower left there
+are the light ones at the upper right
+
+ align:start position:0%
+are the light ones at the upper right
+ 
+
+ align:start position:0%
+are the light ones at the upper right
+there the heavier ones and they're
+
+ align:start position:0%
+there the heavier ones and they're
+ 
+
+ align:start position:0%
+there the heavier ones and they're
+colored by half-life in general the blue
+
+ align:start position:0%
+colored by half-life in general the blue
+ 
+
+ align:start position:0%
+colored by half-life in general the blue
+ones will be stable and the further away
+
+ align:start position:0%
+ones will be stable and the further away
+ 
+
+ align:start position:0%
+ones will be stable and the further away
+you get from blue the less stable they
+
+ align:start position:0%
+you get from blue the less stable they
+ 
+
+ align:start position:0%
+you get from blue the less stable they
+get so right away without even delving
+
+ align:start position:0%
+get so right away without even delving
+ 
+
+ align:start position:0%
+get so right away without even delving
+deeper what patterns do you guys notice
+
+ align:start position:0%
+deeper what patterns do you guys notice
+ 
+
+ align:start position:0%
+deeper what patterns do you guys notice
+here yeah Alex yeah there's a whole
+
+ align:start position:0%
+here yeah Alex yeah there's a whole
+ 
+
+ align:start position:0%
+here yeah Alex yeah there's a whole
+section where there's no more blue there
+
+ align:start position:0%
+section where there's no more blue there
+ 
+
+ align:start position:0%
+section where there's no more blue there
+are no stable elements so stability
+
+ align:start position:0%
+are no stable elements so stability
+ 
+
+ align:start position:0%
+are no stable elements so stability
+drops off after a certain point and what
+
+ align:start position:0%
+drops off after a certain point and what
+ 
+
+ align:start position:0%
+drops off after a certain point and what
+about in the region of stable isotopes
+
+ align:start position:0%
+about in the region of stable isotopes
+ 
+
+ align:start position:0%
+about in the region of stable isotopes
+does anybody notice any repeating
+
+ align:start position:0%
+does anybody notice any repeating
+ 
+
+ align:start position:0%
+does anybody notice any repeating
+patterns here take a look at every other
+
+ align:start position:0%
+patterns here take a look at every other
+ 
+
+ align:start position:0%
+patterns here take a look at every other
+row there's a bunch of blues and then
+
+ align:start position:0%
+row there's a bunch of blues and then
+ 
+
+ align:start position:0%
+row there's a bunch of blues and then
+one and then a bunch and then one and
+
+ align:start position:0%
+one and then a bunch and then one and
+ 
+
+ align:start position:0%
+one and then a bunch and then one and
+then more and then none that must be
+
+ align:start position:0%
+then more and then none that must be
+ 
+
+ align:start position:0%
+then more and then none that must be
+technetium so that's the only element
+
+ align:start position:0%
+technetium so that's the only element
+ 
+
+ align:start position:0%
+technetium so that's the only element
+around there that doesn't have any and
+
+ align:start position:0%
+around there that doesn't have any and
+ 
+
+ align:start position:0%
+around there that doesn't have any and
+then a bunch of Blues so every other row
+
+ align:start position:0%
+then a bunch of Blues so every other row
+ 
+
+ align:start position:0%
+then a bunch of Blues so every other row
+and in this case it's increasing number
+
+ align:start position:0%
+and in this case it's increasing number
+ 
+
+ align:start position:0%
+and in this case it's increasing number
+of protons has more or fewer stable
+
+ align:start position:0%
+of protons has more or fewer stable
+ 
+
+ align:start position:0%
+of protons has more or fewer stable
+isotopes it turns out that the
+
+ align:start position:0%
+isotopes it turns out that the
+ 
+
+ align:start position:0%
+isotopes it turns out that the
+even-numbered isotopes have a lot more
+
+ align:start position:0%
+even-numbered isotopes have a lot more
+ 
+
+ align:start position:0%
+even-numbered isotopes have a lot more
+stable ones for reasons that we'll get
+
+ align:start position:0%
+stable ones for reasons that we'll get
+ 
+
+ align:start position:0%
+stable ones for reasons that we'll get
+into pretty soon if you zoom in a little
+
+ align:start position:0%
+into pretty soon if you zoom in a little
+ 
+
+ align:start position:0%
+into pretty soon if you zoom in a little
+bit you can see all the different
+
+ align:start position:0%
+bit you can see all the different
+ 
+
+ align:start position:0%
+bit you can see all the different
+isotopes so you can select which ones
+
+ align:start position:0%
+isotopes so you can select which ones
+ 
+
+ align:start position:0%
+isotopes so you can select which ones
+you want and again if you look really
+
+ align:start position:0%
+you want and again if you look really
+ 
+
+ align:start position:0%
+you want and again if you look really
+closely that lets say neon right here
+
+ align:start position:0%
+closely that lets say neon right here
+ 
+
+ align:start position:0%
+closely that lets say neon right here
+has got a few stable ones sodium has one
+
+ align:start position:0%
+has got a few stable ones sodium has one
+ 
+
+ align:start position:0%
+has got a few stable ones sodium has one
+magnesium has three
+
+ align:start position:0%
+magnesium has three
+ 
+
+ align:start position:0%
+magnesium has three
+aluminum has one and this pattern
+
+ align:start position:0%
+aluminum has one and this pattern
+ 
+
+ align:start position:0%
+aluminum has one and this pattern
+repeats all the way up to the point
+
+ align:start position:0%
+repeats all the way up to the point
+ 
+
+ align:start position:0%
+repeats all the way up to the point
+where you don't really get any more
+
+ align:start position:0%
+where you don't really get any more
+ 
+
+ align:start position:0%
+where you don't really get any more
+stable isotopes if you double click on
+
+ align:start position:0%
+stable isotopes if you double click on
+ 
+
+ align:start position:0%
+stable isotopes if you double click on
+one of them you get all the information
+
+ align:start position:0%
+one of them you get all the information
+ 
+
+ align:start position:0%
+one of them you get all the information
+that you'll need for the next 3 or so
+
+ align:start position:0%
+that you'll need for the next 3 or so
+ 
+
+ align:start position:0%
+that you'll need for the next 3 or so
+weeks of the course so in this case I
+
+ align:start position:0%
+weeks of the course so in this case I
+ 
+
+ align:start position:0%
+weeks of the course so in this case I
+picked on sulfur 32 one of the stable
+
+ align:start position:0%
+picked on sulfur 32 one of the stable
+ 
+
+ align:start position:0%
+picked on sulfur 32 one of the stable
+isotopes of sulfur so if you notice it
+
+ align:start position:0%
+isotopes of sulfur so if you notice it
+ 
+
+ align:start position:0%
+isotopes of sulfur so if you notice it
+doesn't have any decay mechanisms here
+
+ align:start position:0%
+doesn't have any decay mechanisms here
+ 
+
+ align:start position:0%
+doesn't have any decay mechanisms here
+but it does say it's atomic abundance so
+
+ align:start position:0%
+but it does say it's atomic abundance so
+ 
+
+ align:start position:0%
+but it does say it's atomic abundance so
+you can know how what percentage is
+
+ align:start position:0%
+you can know how what percentage is
+ 
+
+ align:start position:0%
+you can know how what percentage is
+normally found in nature and then
+
+ align:start position:0%
+normally found in nature and then
+ 
+
+ align:start position:0%
+normally found in nature and then
+there's a few other quantities that is
+
+ align:start position:0%
+there's a few other quantities that is
+ 
+
+ align:start position:0%
+there's a few other quantities that is
+going to be the topic of what's going on
+
+ align:start position:0%
+going to be the topic of what's going on
+ 
+
+ align:start position:0%
+going to be the topic of what's going on
+here let's start with the atomic mass if
+
+ align:start position:0%
+here let's start with the atomic mass if
+ 
+
+ align:start position:0%
+here let's start with the atomic mass if
+you notice the atomic mass is slightly
+
+ align:start position:0%
+you notice the atomic mass is slightly
+ 
+
+ align:start position:0%
+you notice the atomic mass is slightly
+less than 32 32 being the mass number or
+
+ align:start position:0%
+less than 32 32 being the mass number or
+ 
+
+ align:start position:0%
+less than 32 32 being the mass number or
+the total number of protons plus
+
+ align:start position:0%
+the total number of protons plus
+ 
+
+ align:start position:0%
+the total number of protons plus
+neutrons in the nucleus the actual mass
+
+ align:start position:0%
+neutrons in the nucleus the actual mass
+ 
+
+ align:start position:0%
+neutrons in the nucleus the actual mass
+is a little lower by that amount right
+
+ align:start position:0%
+is a little lower by that amount right
+ 
+
+ align:start position:0%
+is a little lower by that amount right
+there the binding energy it might be a
+
+ align:start position:0%
+there the binding energy it might be a
+ 
+
+ align:start position:0%
+there the binding energy it might be a
+little funny because I've given you a
+
+ align:start position:0%
+little funny because I've given you a
+ 
+
+ align:start position:0%
+little funny because I've given you a
+mass an amu and a binding energy and
+
+ align:start position:0%
+mass an amu and a binding energy and
+ 
+
+ align:start position:0%
+mass an amu and a binding energy and
+kill electron volts I want to remind you
+
+ align:start position:0%
+kill electron volts I want to remind you
+ 
+
+ align:start position:0%
+kill electron volts I want to remind you
+that these are the same thing the
+
+ align:start position:0%
+that these are the same thing the
+ 
+
+ align:start position:0%
+that these are the same thing the
+conversion factor you'll be using over
+
+ align:start position:0%
+conversion factor you'll be using over
+ 
+
+ align:start position:0%
+conversion factor you'll be using over
+and over again throughout this course
+
+ align:start position:0%
+and over again throughout this course
+ 
+
+ align:start position:0%
+and over again throughout this course
+especially on the next P sets is one
+
+ align:start position:0%
+especially on the next P sets is one
+ 
+
+ align:start position:0%
+especially on the next P sets is one
+atomic mass unit is 930 1.49 mb v c
+
+ align:start position:0%
+atomic mass unit is 930 1.49 mb v c
+ 
+
+ align:start position:0%
+atomic mass unit is 930 1.49 mb v c
+squared yeah I'm sorry
+
+ align:start position:0%
+squared yeah I'm sorry
+ 
+
+ align:start position:0%
+squared yeah I'm sorry
+yeah nevermind put that there so then
+
+ align:start position:0%
+yeah nevermind put that there so then
+ 
+
+ align:start position:0%
+yeah nevermind put that there so then
+again one don't round because we've had
+
+ align:start position:0%
+again one don't round because we've had
+ 
+
+ align:start position:0%
+again one don't round because we've had
+times when folks said oh this is about
+
+ align:start position:0%
+times when folks said oh this is about
+ 
+
+ align:start position:0%
+times when folks said oh this is about
+931 and when you're off by half an MeV
+
+ align:start position:0%
+931 and when you're off by half an MeV
+ 
+
+ align:start position:0%
+931 and when you're off by half an MeV
+you could be at a totally different
+
+ align:start position:0%
+you could be at a totally different
+ 
+
+ align:start position:0%
+you could be at a totally different
+decay level or get a positive Q when it
+
+ align:start position:0%
+decay level or get a positive Q when it
+ 
+
+ align:start position:0%
+decay level or get a positive Q when it
+should be negative or vice versa and
+
+ align:start position:0%
+should be negative or vice versa and
+ 
+
+ align:start position:0%
+should be negative or vice versa and
+let's take a quick look here to say if
+
+ align:start position:0%
+let's take a quick look here to say if
+ 
+
+ align:start position:0%
+let's take a quick look here to say if
+this atomic mass is thirty one point
+
+ align:start position:0%
+this atomic mass is thirty one point
+ 
+
+ align:start position:0%
+this atomic mass is thirty one point
+nine seven two O 707 amu this is why I
+
+ align:start position:0%
+nine seven two O 707 amu this is why I
+ 
+
+ align:start position:0%
+nine seven two O 707 amu this is why I
+brought a calculator normally I do
+
+ align:start position:0%
+brought a calculator normally I do
+ 
+
+ align:start position:0%
+brought a calculator normally I do
+mental math but since I told you guys
+
+ align:start position:0%
+mental math but since I told you guys
+ 
+
+ align:start position:0%
+mental math but since I told you guys
+don't round I can't do eight significant
+
+ align:start position:0%
+don't round I can't do eight significant
+ 
+
+ align:start position:0%
+don't round I can't do eight significant
+digits in my head so I'm going to get
+
+ align:start position:0%
+digits in my head so I'm going to get
+ 
+
+ align:start position:0%
+digits in my head so I'm going to get
+that in there
+
+ align:start position:0%
+that in there
+ 
+
+ align:start position:0%
+that in there
+oh seven oh seven if any you guys want
+
+ align:start position:0%
+oh seven oh seven if any you guys want
+ 
+
+ align:start position:0%
+oh seven oh seven if any you guys want
+to follow along I encourage you to and
+
+ align:start position:0%
+to follow along I encourage you to and
+ 
+
+ align:start position:0%
+to follow along I encourage you to and
+say minus 32 which is the mass number so
+
+ align:start position:0%
+say minus 32 which is the mass number so
+ 
+
+ align:start position:0%
+say minus 32 which is the mass number so
+in this case we're taking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the actual atomic mass - the actual
+
+ align:start position:0%
+the actual atomic mass - the actual
+ 
+
+ align:start position:0%
+the actual atomic mass - the actual
+amount the mass number in this case is
+
+ align:start position:0%
+amount the mass number in this case is
+ 
+
+ align:start position:0%
+amount the mass number in this case is
+32 in this case it's 31 point nine seven
+
+ align:start position:0%
+32 in this case it's 31 point nine seven
+ 
+
+ align:start position:0%
+32 in this case it's 31 point nine seven
+two oh seven oh seven and we end up with
+
+ align:start position:0%
+two oh seven oh seven and we end up with
+ 
+
+ align:start position:0%
+two oh seven oh seven and we end up with
+minus 0.02 put all the digits here - 9 3
+
+ align:start position:0%
+minus 0.02 put all the digits here - 9 3
+ 
+
+ align:start position:0%
+minus 0.02 put all the digits here - 9 3
+amu if we convert this to MeV times nine
+
+ align:start position:0%
+amu if we convert this to MeV times nine
+ 
+
+ align:start position:0%
+amu if we convert this to MeV times nine
+thirty one point four nine we get minus
+
+ align:start position:0%
+thirty one point four nine we get minus
+ 
+
+ align:start position:0%
+thirty one point four nine we get minus
+twenty six point oh one five nine MeV
+
+ align:start position:0%
+twenty six point oh one five nine MeV
+ 
+
+ align:start position:0%
+twenty six point oh one five nine MeV
+see this number anywhere on the khari
+
+ align:start position:0%
+see this number anywhere on the khari
+ 
+
+ align:start position:0%
+see this number anywhere on the khari
+table right there
+
+ align:start position:0%
+table right there
+ 
+
+ align:start position:0%
+table right there
+that's the excess mass and in this case
+
+ align:start position:0%
+that's the excess mass and in this case
+ 
+
+ align:start position:0%
+that's the excess mass and in this case
+we usually give this the symbol Delta
+
+ align:start position:0%
+we usually give this the symbol Delta
+ 
+
+ align:start position:0%
+we usually give this the symbol Delta
+for the excess mass and these are how
+
+ align:start position:0%
+for the excess mass and these are how
+ 
+
+ align:start position:0%
+for the excess mass and these are how
+these quantities are directly related
+
+ align:start position:0%
+these quantities are directly related
+ 
+
+ align:start position:0%
+these quantities are directly related
+the excess mass well actually what does
+
+ align:start position:0%
+the excess mass well actually what does
+ 
+
+ align:start position:0%
+the excess mass well actually what does
+the excess mass really mean it's the
+
+ align:start position:0%
+the excess mass really mean it's the
+ 
+
+ align:start position:0%
+the excess mass really mean it's the
+difference between the actual mass and a
+
+ align:start position:0%
+difference between the actual mass and a
+ 
+
+ align:start position:0%
+difference between the actual mass and a
+fairly poor approximation of the mass so
+
+ align:start position:0%
+fairly poor approximation of the mass so
+ 
+
+ align:start position:0%
+fairly poor approximation of the mass so
+the excess mass doesn't really have that
+
+ align:start position:0%
+the excess mass doesn't really have that
+ 
+
+ align:start position:0%
+the excess mass doesn't really have that
+much of a physical connotation but it is
+
+ align:start position:0%
+much of a physical connotation but it is
+ 
+
+ align:start position:0%
+much of a physical connotation but it is
+nice because if you know very well the
+
+ align:start position:0%
+nice because if you know very well the
+ 
+
+ align:start position:0%
+nice because if you know very well the
+tabulated atomic number I'm sorry the
+
+ align:start position:0%
+tabulated atomic number I'm sorry the
+ 
+
+ align:start position:0%
+tabulated atomic number I'm sorry the
+yeah the mass number and the excess mass
+
+ align:start position:0%
+yeah the mass number and the excess mass
+ 
+
+ align:start position:0%
+yeah the mass number and the excess mass
+you can figure out let's see yeah you
+
+ align:start position:0%
+you can figure out let's see yeah you
+ 
+
+ align:start position:0%
+you can figure out let's see yeah you
+can figure out what the real atomic mass
+
+ align:start position:0%
+can figure out what the real atomic mass
+ 
+
+ align:start position:0%
+can figure out what the real atomic mass
+is and I want to switch now to the
+
+ align:start position:0%
+is and I want to switch now to the
+ 
+
+ align:start position:0%
+is and I want to switch now to the
+actual table of nuclides and show you
+
+ align:start position:0%
+actual table of nuclides and show you
+ 
+
+ align:start position:0%
+actual table of nuclides and show you
+one example if you want to very quickly
+
+ align:start position:0%
+one example if you want to very quickly
+ 
+
+ align:start position:0%
+one example if you want to very quickly
+jump between isotopes you can type them
+
+ align:start position:0%
+jump between isotopes you can type them
+ 
+
+ align:start position:0%
+jump between isotopes you can type them
+in right up here and does anyone know
+
+ align:start position:0%
+in right up here and does anyone know
+ 
+
+ align:start position:0%
+in right up here and does anyone know
+what the gold standard for atomic mass
+
+ align:start position:0%
+what the gold standard for atomic mass
+ 
+
+ align:start position:0%
+what the gold standard for atomic mass
+is and I'll give you a hint it's not
+
+ align:start position:0%
+is and I'll give you a hint it's not
+ 
+
+ align:start position:0%
+is and I'll give you a hint it's not
+gold yep carbon-12 what do you think the
+
+ align:start position:0%
+gold yep carbon-12 what do you think the
+ 
+
+ align:start position:0%
+gold yep carbon-12 what do you think the
+the excess mass of carbon 12 is going to
+
+ align:start position:0%
+the excess mass of carbon 12 is going to
+ 
+
+ align:start position:0%
+the excess mass of carbon 12 is going to
+be without doing any calculations
+
+ align:start position:0%
+be without doing any calculations
+ 
+
+ align:start position:0%
+be without doing any calculations
+exactly zero so if we go to carbon-12
+
+ align:start position:0%
+exactly zero so if we go to carbon-12
+ 
+
+ align:start position:0%
+exactly zero so if we go to carbon-12
+because that is set as the standard the
+
+ align:start position:0%
+because that is set as the standard the
+ 
+
+ align:start position:0%
+because that is set as the standard the
+way atomic masses were done was
+
+ align:start position:0%
+way atomic masses were done was
+ 
+
+ align:start position:0%
+way atomic masses were done was
+carbon-12 weighs exactly 12 amu the
+
+ align:start position:0%
+carbon-12 weighs exactly 12 amu the
+ 
+
+ align:start position:0%
+carbon-12 weighs exactly 12 amu the
+excess mass here is zero and that's why
+
+ align:start position:0%
+excess mass here is zero and that's why
+ 
+
+ align:start position:0%
+excess mass here is zero and that's why
+the atomic
+
+ align:start position:0%
+the atomic
+ 
+
+ align:start position:0%
+the atomic
+12.0 to as many decimals as we care to
+
+ align:start position:0%
+12.0 to as many decimals as we care to
+ 
+
+ align:start position:0%
+12.0 to as many decimals as we care to
+note so is everyone clear on what excess
+
+ align:start position:0%
+note so is everyone clear on what excess
+ 
+
+ align:start position:0%
+note so is everyone clear on what excess
+mass is yep so mass does not actually
+
+ align:start position:0%
+mass is yep so mass does not actually
+ 
+
+ align:start position:0%
+mass is yep so mass does not actually
+equal alright and it's actually on the
+
+ align:start position:0%
+equal alright and it's actually on the
+ 
+
+ align:start position:0%
+equal alright and it's actually on the
+my chalk - it's actually down below the
+
+ align:start position:0%
+my chalk - it's actually down below the
+ 
+
+ align:start position:0%
+my chalk - it's actually down below the
+point is that energy is related to mass
+
+ align:start position:0%
+point is that energy is related to mass
+ 
+
+ align:start position:0%
+point is that energy is related to mass
+by C squared so there are not the same
+
+ align:start position:0%
+by C squared so there are not the same
+ 
+
+ align:start position:0%
+by C squared so there are not the same
+units but they're directly convertible
+
+ align:start position:0%
+units but they're directly convertible
+ 
+
+ align:start position:0%
+units but they're directly convertible
+yep and so this way you have an e over a
+
+ align:start position:0%
+yep and so this way you have an e over a
+ 
+
+ align:start position:0%
+yep and so this way you have an e over a
+C squared you get an M and there we go I
+
+ align:start position:0%
+C squared you get an M and there we go I
+ 
+
+ align:start position:0%
+C squared you get an M and there we go I
+have the unit's upside down however calm
+
+ align:start position:0%
+have the unit's upside down however calm
+ 
+
+ align:start position:0%
+have the unit's upside down however calm
+carbon-12 does not have a zero binding
+
+ align:start position:0%
+carbon-12 does not have a zero binding
+ 
+
+ align:start position:0%
+carbon-12 does not have a zero binding
+energy yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MeV per C squared yeah yeah that's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's it is funny right the binding
+
+ align:start position:0%
+so it's it is funny right the binding
+ 
+
+ align:start position:0%
+so it's it is funny right the binding
+energies give it in ke V and that's
+
+ align:start position:0%
+energies give it in ke V and that's
+ 
+
+ align:start position:0%
+energies give it in ke V and that's
+correct and energies and energy and
+
+ align:start position:0%
+correct and energies and energy and
+ 
+
+ align:start position:0%
+correct and energies and energy and
+excess mass it really should say ke V
+
+ align:start position:0%
+excess mass it really should say ke V
+ 
+
+ align:start position:0%
+excess mass it really should say ke V
+per C squared because if we're talking
+
+ align:start position:0%
+per C squared because if we're talking
+ 
+
+ align:start position:0%
+per C squared because if we're talking
+in units of mass it's got to be in m or
+
+ align:start position:0%
+in units of mass it's got to be in m or
+ 
+
+ align:start position:0%
+in units of mass it's got to be in m or
+using this way you could say M is an
+
+ align:start position:0%
+using this way you could say M is an
+ 
+
+ align:start position:0%
+using this way you could say M is an
+energy per C squared so this to me is a
+
+ align:start position:0%
+energy per C squared so this to me is a
+ 
+
+ align:start position:0%
+energy per C squared so this to me is a
+semantic inconsistency in the table but
+
+ align:start position:0%
+semantic inconsistency in the table but
+ 
+
+ align:start position:0%
+semantic inconsistency in the table but
+you guys will know that a mass is always
+
+ align:start position:0%
+you guys will know that a mass is always
+ 
+
+ align:start position:0%
+you guys will know that a mass is always
+going to be in AMU or kilograms or MeV
+
+ align:start position:0%
+going to be in AMU or kilograms or MeV
+ 
+
+ align:start position:0%
+going to be in AMU or kilograms or MeV
+per C squared and energies will be in
+
+ align:start position:0%
+per C squared and energies will be in
+ 
+
+ align:start position:0%
+per C squared and energies will be in
+MeV ke V some sort of Eevee usually in
+
+ align:start position:0%
+MeV ke V some sort of Eevee usually in
+ 
+
+ align:start position:0%
+MeV ke V some sort of Eevee usually in
+this course the binding energy though
+
+ align:start position:0%
+this course the binding energy though
+ 
+
+ align:start position:0%
+this course the binding energy though
+that's that's correct that's in ke V
+
+ align:start position:0%
+that's that's correct that's in ke V
+ 
+
+ align:start position:0%
+that's that's correct that's in ke V
+because that's an actual energy now then
+
+ align:start position:0%
+because that's an actual energy now then
+ 
+
+ align:start position:0%
+because that's an actual energy now then
+the question is what is the binding
+
+ align:start position:0%
+the question is what is the binding
+ 
+
+ align:start position:0%
+the question is what is the binding
+energy actually represent does anyone
+
+ align:start position:0%
+energy actually represent does anyone
+ 
+
+ align:start position:0%
+energy actually represent does anyone
+remember from Friday or Thursday I can
+
+ align:start position:0%
+remember from Friday or Thursday I can
+ 
+
+ align:start position:0%
+remember from Friday or Thursday I can
+refresh your memory that's what I'm here
+
+ align:start position:0%
+refresh your memory that's what I'm here
+ 
+
+ align:start position:0%
+refresh your memory that's what I'm here
+to do the binding energy is as if let's
+
+ align:start position:0%
+to do the binding energy is as if let's
+ 
+
+ align:start position:0%
+to do the binding energy is as if let's
+say we're assembling carbon-12 from its
+
+ align:start position:0%
+say we're assembling carbon-12 from its
+ 
+
+ align:start position:0%
+say we're assembling carbon-12 from its
+constituent nucleons there's going to be
+
+ align:start position:0%
+constituent nucleons there's going to be
+ 
+
+ align:start position:0%
+constituent nucleons there's going to be
+12 of them let's say we had six protons
+
+ align:start position:0%
+12 of them let's say we had six protons
+ 
+
+ align:start position:0%
+12 of them let's say we had six protons
+and six neutrons we can calculate the
+
+ align:start position:0%
+and six neutrons we can calculate the
+ 
+
+ align:start position:0%
+and six neutrons we can calculate the
+total mass energy of this ensemble of
+
+ align:start position:0%
+total mass energy of this ensemble of
+ 
+
+ align:start position:0%
+total mass energy of this ensemble of
+nucleons when they're infinitely far
+
+ align:start position:0%
+nucleons when they're infinitely far
+ 
+
+ align:start position:0%
+nucleons when they're infinitely far
+apart from each other and forgive the
+
+ align:start position:0%
+apart from each other and forgive the
+ 
+
+ align:start position:0%
+apart from each other and forgive the
+low it's not to scale but they are
+
+ align:start position:0%
+low it's not to scale but they are
+ 
+
+ align:start position:0%
+low it's not to scale but they are
+infinitely far apart from each other and
+
+ align:start position:0%
+infinitely far apart from each other and
+ 
+
+ align:start position:0%
+infinitely far apart from each other and
+we can say that let's say there's Z
+
+ align:start position:0%
+we can say that let's say there's Z
+ 
+
+ align:start position:0%
+we can say that let's say there's Z
+number of protons so we'll say the
+
+ align:start position:0%
+number of protons so we'll say the
+ 
+
+ align:start position:0%
+number of protons so we'll say the
+binding energy is the number of protons
+
+ align:start position:0%
+binding energy is the number of protons
+ 
+
+ align:start position:0%
+binding energy is the number of protons
+times the mass of a proton plus the
+
+ align:start position:0%
+times the mass of a proton plus the
+ 
+
+ align:start position:0%
+times the mass of a proton plus the
+number of neutrons a minus C times the
+
+ align:start position:0%
+number of neutrons a minus C times the
+ 
+
+ align:start position:0%
+number of neutrons a minus C times the
+mass of a neutron minus the energy of
+
+ align:start position:0%
+mass of a neutron minus the energy of
+ 
+
+ align:start position:0%
+mass of a neutron minus the energy of
+the assembled carbon-12 nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's actually a measurable
+
+ align:start position:0%
+so there's actually a measurable
+ 
+
+ align:start position:0%
+so there's actually a measurable
+difference in mass between six protons
+
+ align:start position:0%
+difference in mass between six protons
+ 
+
+ align:start position:0%
+difference in mass between six protons
+and six neutrons and the actual mass of
+
+ align:start position:0%
+and six neutrons and the actual mass of
+ 
+
+ align:start position:0%
+and six neutrons and the actual mass of
+a nucleus with atomic number a and I'm
+
+ align:start position:0%
+a nucleus with atomic number a and I'm
+ 
+
+ align:start position:0%
+a nucleus with atomic number a and I'm
+sorry with atomic number Z and mass
+
+ align:start position:0%
+sorry with atomic number Z and mass
+ 
+
+ align:start position:0%
+sorry with atomic number Z and mass
+number a C squared so is everyone clear
+
+ align:start position:0%
+number a C squared so is everyone clear
+ 
+
+ align:start position:0%
+number a C squared so is everyone clear
+on how we arrived at this formula it's
+
+ align:start position:0%
+on how we arrived at this formula it's
+ 
+
+ align:start position:0%
+on how we arrived at this formula it's
+effectively the energy released when you
+
+ align:start position:0%
+effectively the energy released when you
+ 
+
+ align:start position:0%
+effectively the energy released when you
+take the individual nucleons assemble
+
+ align:start position:0%
+take the individual nucleons assemble
+ 
+
+ align:start position:0%
+take the individual nucleons assemble
+the nucleus you don't have as much mass
+
+ align:start position:0%
+the nucleus you don't have as much mass
+ 
+
+ align:start position:0%
+the nucleus you don't have as much mass
+as when you start it or in some cases
+
+ align:start position:0%
+as when you start it or in some cases
+ 
+
+ align:start position:0%
+as when you start it or in some cases
+you might have a little more mass than
+
+ align:start position:0%
+you might have a little more mass than
+ 
+
+ align:start position:0%
+you might have a little more mass than
+when you started
+
+ align:start position:0%
+when you started
+ 
+
+ align:start position:0%
+when you started
+if things are particularly unstable and
+
+ align:start position:0%
+if things are particularly unstable and
+ 
+
+ align:start position:0%
+if things are particularly unstable and
+you can use the excess mass and binding
+
+ align:start position:0%
+you can use the excess mass and binding
+ 
+
+ align:start position:0%
+you can use the excess mass and binding
+energies and relative amounts to see is
+
+ align:start position:0%
+energies and relative amounts to see is
+ 
+
+ align:start position:0%
+energies and relative amounts to see is
+a nucleus going to be stable for example
+
+ align:start position:0%
+a nucleus going to be stable for example
+ 
+
+ align:start position:0%
+a nucleus going to be stable for example
+let's look at iron 55 I'm gonna jump
+
+ align:start position:0%
+let's look at iron 55 I'm gonna jump
+ 
+
+ align:start position:0%
+let's look at iron 55 I'm gonna jump
+here make it a little bigger so it the
+
+ align:start position:0%
+here make it a little bigger so it the
+ 
+
+ align:start position:0%
+here make it a little bigger so it the
+important stuff is easier to see and if
+
+ align:start position:0%
+important stuff is easier to see and if
+ 
+
+ align:start position:0%
+important stuff is easier to see and if
+you notice the binding energy of iron 55
+
+ align:start position:0%
+you notice the binding energy of iron 55
+ 
+
+ align:start position:0%
+you notice the binding energy of iron 55
+there's quite a bit of it it's very well
+
+ align:start position:0%
+there's quite a bit of it it's very well
+ 
+
+ align:start position:0%
+there's quite a bit of it it's very well
+bound in fact this is one of the most
+
+ align:start position:0%
+bound in fact this is one of the most
+ 
+
+ align:start position:0%
+bound in fact this is one of the most
+well bound nuclei in the whole chart of
+
+ align:start position:0%
+well bound nuclei in the whole chart of
+ 
+
+ align:start position:0%
+well bound nuclei in the whole chart of
+nuclides let's look at something that we
+
+ align:start position:0%
+nuclides let's look at something that we
+ 
+
+ align:start position:0%
+nuclides let's look at something that we
+know to be particularly unstable someone
+
+ align:start position:0%
+know to be particularly unstable someone
+ 
+
+ align:start position:0%
+know to be particularly unstable someone
+have any idea let's just add like 20
+
+ align:start position:0%
+have any idea let's just add like 20
+ 
+
+ align:start position:0%
+have any idea let's just add like 20
+neutrons to iron let's see if it even
+
+ align:start position:0%
+neutrons to iron let's see if it even
+ 
+
+ align:start position:0%
+neutrons to iron let's see if it even
+exists no doesn't happen let's try
+
+ align:start position:0%
+exists no doesn't happen let's try
+ 
+
+ align:start position:0%
+exists no doesn't happen let's try
+adding 10 neutrons to iron go even
+
+ align:start position:0%
+adding 10 neutrons to iron go even
+ 
+
+ align:start position:0%
+adding 10 neutrons to iron go even
+crazier
+
+ align:start position:0%
+crazier
+ 
+
+ align:start position:0%
+crazier
+what about 70 to small all right let's
+
+ align:start position:0%
+what about 70 to small all right let's
+ 
+
+ align:start position:0%
+what about 70 to small all right let's
+meet somewhere in the middle
+
+ align:start position:0%
+meet somewhere in the middle
+ 
+
+ align:start position:0%
+meet somewhere in the middle
+68 still a pretty high binding energy
+
+ align:start position:0%
+68 still a pretty high binding energy
+ 
+
+ align:start position:0%
+68 still a pretty high binding energy
+but you can look at it as a difference
+
+ align:start position:0%
+but you can look at it as a difference
+ 
+
+ align:start position:0%
+but you can look at it as a difference
+in binding energy per nucleon so in this
+
+ align:start position:0%
+in binding energy per nucleon so in this
+ 
+
+ align:start position:0%
+in binding energy per nucleon so in this
+case the binding energy per nucleon if
+
+ align:start position:0%
+case the binding energy per nucleon if
+ 
+
+ align:start position:0%
+case the binding energy per nucleon if
+you take the binding energy and divided
+
+ align:start position:0%
+you take the binding energy and divided
+ 
+
+ align:start position:0%
+you take the binding energy and divided
+by the total number of nucleons will
+
+ align:start position:0%
+by the total number of nucleons will
+ 
+
+ align:start position:0%
+by the total number of nucleons will
+give you a relative measure of how
+
+ align:start position:0%
+give you a relative measure of how
+ 
+
+ align:start position:0%
+give you a relative measure of how
+tightly bound that nucleus is now these
+
+ align:start position:0%
+tightly bound that nucleus is now these
+ 
+
+ align:start position:0%
+tightly bound that nucleus is now these
+are not absolute things you can't just
+
+ align:start position:0%
+are not absolute things you can't just
+ 
+
+ align:start position:0%
+are not absolute things you can't just
+say certain binding energy leads to
+
+ align:start position:0%
+say certain binding energy leads to
+ 
+
+ align:start position:0%
+say certain binding energy leads to
+certain stability but they do give you
+
+ align:start position:0%
+certain stability but they do give you
+ 
+
+ align:start position:0%
+certain stability but they do give you
+pretty good trends to follow and we're
+
+ align:start position:0%
+pretty good trends to follow and we're
+ 
+
+ align:start position:0%
+pretty good trends to follow and we're
+actually going to be coming up with
+
+ align:start position:0%
+actually going to be coming up with
+ 
+
+ align:start position:0%
+actually going to be coming up with
+probably on Thursday a semi empirical
+
+ align:start position:0%
+probably on Thursday a semi empirical
+ 
+
+ align:start position:0%
+probably on Thursday a semi empirical
+formula to
+
+ align:start position:0%
+formula to
+ 
+
+ align:start position:0%
+formula to
+get the rough binding energy of any
+
+ align:start position:0%
+get the rough binding energy of any
+ 
+
+ align:start position:0%
+get the rough binding energy of any
+particular assembly of protons and
+
+ align:start position:0%
+particular assembly of protons and
+ 
+
+ align:start position:0%
+particular assembly of protons and
+neutrons and it follows experimental
+
+ align:start position:0%
+neutrons and it follows experimental
+ 
+
+ align:start position:0%
+neutrons and it follows experimental
+calc calculations pretty well
+
+ align:start position:0%
+calc calculations pretty well
+ 
+
+ align:start position:0%
+calc calculations pretty well
+surprisingly so I want to jump back to
+
+ align:start position:0%
+surprisingly so I want to jump back to
+ 
+
+ align:start position:0%
+surprisingly so I want to jump back to
+here because I've mentioned
+
+ align:start position:0%
+here because I've mentioned
+ 
+
+ align:start position:0%
+here because I've mentioned
+cross-sections and I want to actually
+
+ align:start position:0%
+cross-sections and I want to actually
+ 
+
+ align:start position:0%
+cross-sections and I want to actually
+define what a cross-section is because
+
+ align:start position:0%
+define what a cross-section is because
+ 
+
+ align:start position:0%
+define what a cross-section is because
+this is a quantity that you're going to
+
+ align:start position:0%
+this is a quantity that you're going to
+ 
+
+ align:start position:0%
+this is a quantity that you're going to
+be using everywhere let's say that we
+
+ align:start position:0%
+be using everywhere let's say that we
+ 
+
+ align:start position:0%
+be using everywhere let's say that we
+fired a beam of particles it doesn't
+
+ align:start position:0%
+fired a beam of particles it doesn't
+ 
+
+ align:start position:0%
+fired a beam of particles it doesn't
+matter what it is at a target of other
+
+ align:start position:0%
+matter what it is at a target of other
+ 
+
+ align:start position:0%
+matter what it is at a target of other
+particles let's say that the beam
+
+ align:start position:0%
+particles let's say that the beam
+ 
+
+ align:start position:0%
+particles let's say that the beam
+particles are atom a and the target
+
+ align:start position:0%
+particles are atom a and the target
+ 
+
+ align:start position:0%
+particles are atom a and the target
+particles are atom B and once these a
+
+ align:start position:0%
+particles are atom B and once these a
+ 
+
+ align:start position:0%
+particles are atom B and once these a
+particles pass through the target B a
+
+ align:start position:0%
+particles pass through the target B a
+ 
+
+ align:start position:0%
+particles pass through the target B a
+little bit fewer of them come out the
+
+ align:start position:0%
+little bit fewer of them come out the
+ 
+
+ align:start position:0%
+little bit fewer of them come out the
+other side unreacted or unscathed or unn
+
+ align:start position:0%
+other side unreacted or unscathed or unn
+ 
+
+ align:start position:0%
+other side unreacted or unscathed or unn
+scattered and some of them are absorbed
+
+ align:start position:0%
+scattered and some of them are absorbed
+ 
+
+ align:start position:0%
+scattered and some of them are absorbed
+or scattered or bounced off or scattered
+
+ align:start position:0%
+or scattered or bounced off or scattered
+ 
+
+ align:start position:0%
+or scattered or bounced off or scattered
+backwards or what have you we can write
+
+ align:start position:0%
+backwards or what have you we can write
+ 
+
+ align:start position:0%
+backwards or what have you we can write
+the sort of proportionality constant
+
+ align:start position:0%
+the sort of proportionality constant
+ 
+
+ align:start position:0%
+the sort of proportionality constant
+between the change in intensity of our a
+
+ align:start position:0%
+between the change in intensity of our a
+ 
+
+ align:start position:0%
+between the change in intensity of our a
+beam and the thickness of our slab and
+
+ align:start position:0%
+beam and the thickness of our slab and
+ 
+
+ align:start position:0%
+beam and the thickness of our slab and
+we give that proportionality constant
+
+ align:start position:0%
+we give that proportionality constant
+ 
+
+ align:start position:0%
+we give that proportionality constant
+this symbol little Sigma I'll get
+
+ align:start position:0%
+this symbol little Sigma I'll get
+ 
+
+ align:start position:0%
+this symbol little Sigma I'll get
+something going up here little Sigma
+
+ align:start position:0%
+something going up here little Sigma
+ 
+
+ align:start position:0%
+something going up here little Sigma
+which we call the microscopic cross
+
+ align:start position:0%
+which we call the microscopic cross
+ 
+
+ align:start position:0%
+which we call the microscopic cross
+section it's in effect a constant of
+
+ align:start position:0%
+section it's in effect a constant of
+ 
+
+ align:start position:0%
+section it's in effect a constant of
+proportionality that relates the
+
+ align:start position:0%
+proportionality that relates the
+ 
+
+ align:start position:0%
+proportionality that relates the
+probability of absorbing an atom from
+
+ align:start position:0%
+probability of absorbing an atom from
+ 
+
+ align:start position:0%
+probability of absorbing an atom from
+this beam i from this beam of atoms a
+
+ align:start position:0%
+this beam i from this beam of atoms a
+ 
+
+ align:start position:0%
+this beam i from this beam of atoms a
+threw a slab of B and then if you take
+
+ align:start position:0%
+threw a slab of B and then if you take
+ 
+
+ align:start position:0%
+threw a slab of B and then if you take
+this formula you divide by that Delta X
+
+ align:start position:0%
+this formula you divide by that Delta X
+ 
+
+ align:start position:0%
+this formula you divide by that Delta X
+so I'm going to take what's on there and
+
+ align:start position:0%
+so I'm going to take what's on there and
+ 
+
+ align:start position:0%
+so I'm going to take what's on there and
+say Delta I over Delta x equals minus
+
+ align:start position:0%
+say Delta I over Delta x equals minus
+ 
+
+ align:start position:0%
+say Delta I over Delta x equals minus
+cross section a B n which refers here to
+
+ align:start position:0%
+cross section a B n which refers here to
+ 
+
+ align:start position:0%
+cross section a B n which refers here to
+the number density so I'll keep our
+
+ align:start position:0%
+the number density so I'll keep our
+ 
+
+ align:start position:0%
+the number density so I'll keep our
+table of symbols all together so it's a
+
+ align:start position:0%
+table of symbols all together so it's a
+ 
+
+ align:start position:0%
+table of symbols all together so it's a
+little easier to follow and as our
+
+ align:start position:0%
+little easier to follow and as our
+ 
+
+ align:start position:0%
+little easier to follow and as our
+number density which means the number of
+
+ align:start position:0%
+number density which means the number of
+ 
+
+ align:start position:0%
+number density which means the number of
+atoms per unit volume usually in nuclear
+
+ align:start position:0%
+atoms per unit volume usually in nuclear
+ 
+
+ align:start position:0%
+atoms per unit volume usually in nuclear
+quantities we use centimeters because
+
+ align:start position:0%
+quantities we use centimeters because
+ 
+
+ align:start position:0%
+quantities we use centimeters because
+these are things that are actually
+
+ align:start position:0%
+these are things that are actually
+ 
+
+ align:start position:0%
+these are things that are actually
+fairly measurable and cross-sections are
+
+ align:start position:0%
+fairly measurable and cross-sections are
+ 
+
+ align:start position:0%
+fairly measurable and cross-sections are
+actually in you
+
+ align:start position:0%
+actually in you
+ 
+
+ align:start position:0%
+actually in you
+it's of centimeters squared and let me
+
+ align:start position:0%
+it's of centimeters squared and let me
+ 
+
+ align:start position:0%
+it's of centimeters squared and let me
+finish that expression we had the number
+
+ align:start position:0%
+finish that expression we had the number
+ 
+
+ align:start position:0%
+finish that expression we had the number
+density of our target B we had our
+
+ align:start position:0%
+density of our target B we had our
+ 
+
+ align:start position:0%
+density of our target B we had our
+initial intensity and that's it anyone
+
+ align:start position:0%
+initial intensity and that's it anyone
+ 
+
+ align:start position:0%
+initial intensity and that's it anyone
+know how to solve this differential
+
+ align:start position:0%
+know how to solve this differential
+ 
+
+ align:start position:0%
+know how to solve this differential
+equation if we take the limit of small
+
+ align:start position:0%
+equation if we take the limit of small
+ 
+
+ align:start position:0%
+equation if we take the limit of small
+deltas should start to look like a
+
+ align:start position:0%
+deltas should start to look like a
+ 
+
+ align:start position:0%
+deltas should start to look like a
+differential equation the final answer
+
+ align:start position:0%
+differential equation the final answer
+ 
+
+ align:start position:0%
+differential equation the final answer
+is up there on the screen was anyone
+
+ align:start position:0%
+is up there on the screen was anyone
+ 
+
+ align:start position:0%
+is up there on the screen was anyone
+remember the method to actually solve
+
+ align:start position:0%
+remember the method to actually solve
+ 
+
+ align:start position:0%
+remember the method to actually solve
+this differential equation this is the
+
+ align:start position:0%
+this differential equation this is the
+ 
+
+ align:start position:0%
+this differential equation this is the
+easy one separate the variables so in
+
+ align:start position:0%
+easy one separate the variables so in
+ 
+
+ align:start position:0%
+easy one separate the variables so in
+this case we can divide each side by I
+
+ align:start position:0%
+this case we can divide each side by I
+ 
+
+ align:start position:0%
+this case we can divide each side by I
+of X multiply each side by X I'm going
+
+ align:start position:0%
+of X multiply each side by X I'm going
+ 
+
+ align:start position:0%
+of X multiply each side by X I'm going
+to bring this up so I'm not bending down
+
+ align:start position:0%
+to bring this up so I'm not bending down
+ 
+
+ align:start position:0%
+to bring this up so I'm not bending down
+so we have di over I equals minus Sigma
+
+ align:start position:0%
+so we have di over I equals minus Sigma
+ 
+
+ align:start position:0%
+so we have di over I equals minus Sigma
+a B and of B times DX integrate both
+
+ align:start position:0%
+a B and of B times DX integrate both
+ 
+
+ align:start position:0%
+a B and of B times DX integrate both
+sides and we get log of I equals minus
+
+ align:start position:0%
+sides and we get log of I equals minus
+ 
+
+ align:start position:0%
+sides and we get log of I equals minus
+Sigma a B and of B X and some
+
+ align:start position:0%
+Sigma a B and of B X and some
+ 
+
+ align:start position:0%
+Sigma a B and of B X and some
+integration constant you can apply an
+
+ align:start position:0%
+integration constant you can apply an
+ 
+
+ align:start position:0%
+integration constant you can apply an
+initial boundary condition to say that
+
+ align:start position:0%
+initial boundary condition to say that
+ 
+
+ align:start position:0%
+initial boundary condition to say that
+it's equals 0 the intensity of the beam
+
+ align:start position:0%
+it's equals 0 the intensity of the beam
+ 
+
+ align:start position:0%
+it's equals 0 the intensity of the beam
+X was some intensity I not whatever
+
+ align:start position:0%
+X was some intensity I not whatever
+ 
+
+ align:start position:0%
+X was some intensity I not whatever
+intensity of the beam that we initially
+
+ align:start position:0%
+intensity of the beam that we initially
+ 
+
+ align:start position:0%
+intensity of the beam that we initially
+fired at the target and by combining
+
+ align:start position:0%
+fired at the target and by combining
+ 
+
+ align:start position:0%
+fired at the target and by combining
+these two you end up with the expression
+
+ align:start position:0%
+these two you end up with the expression
+ 
+
+ align:start position:0%
+these two you end up with the expression
+you get right there which is that the
+
+ align:start position:0%
+you get right there which is that the
+ 
+
+ align:start position:0%
+you get right there which is that the
+intensity of the beam coming out is the
+
+ align:start position:0%
+intensity of the beam coming out is the
+ 
+
+ align:start position:0%
+intensity of the beam coming out is the
+initial intensity times e to the minus
+
+ align:start position:0%
+initial intensity times e to the minus
+ 
+
+ align:start position:0%
+initial intensity times e to the minus
+Sigma a b-and-b X and we've kind of
+
+ align:start position:0%
+Sigma a b-and-b X and we've kind of
+ 
+
+ align:start position:0%
+Sigma a b-and-b X and we've kind of
+derived the idea of exponential
+
+ align:start position:0%
+derived the idea of exponential
+ 
+
+ align:start position:0%
+derived the idea of exponential
+attenuation for those who haven't seen
+
+ align:start position:0%
+attenuation for those who haven't seen
+ 
+
+ align:start position:0%
+attenuation for those who haven't seen
+that word before attenuation or the
+
+ align:start position:0%
+that word before attenuation or the
+ 
+
+ align:start position:0%
+that word before attenuation or the
+gradual removal of the beam of incident
+
+ align:start position:0%
+gradual removal of the beam of incident
+ 
+
+ align:start position:0%
+gradual removal of the beam of incident
+particles by whatever the target happens
+
+ align:start position:0%
+particles by whatever the target happens
+ 
+
+ align:start position:0%
+particles by whatever the target happens
+to be this quantity right here we
+
+ align:start position:0%
+to be this quantity right here we
+ 
+
+ align:start position:0%
+to be this quantity right here we
+actually have another symbol for
+
+ align:start position:0%
+actually have another symbol for
+ 
+
+ align:start position:0%
+actually have another symbol for
+which ah which we give big Sigma and in
+
+ align:start position:0%
+which ah which we give big Sigma and in
+ 
+
+ align:start position:0%
+which ah which we give big Sigma and in
+this case big Sigma we call the
+
+ align:start position:0%
+this case big Sigma we call the
+ 
+
+ align:start position:0%
+this case big Sigma we call the
+macroscopic cross-section I'll draw a
+
+ align:start position:0%
+macroscopic cross-section I'll draw a
+ 
+
+ align:start position:0%
+macroscopic cross-section I'll draw a
+box around these so we know these are
+
+ align:start position:0%
+box around these so we know these are
+ 
+
+ align:start position:0%
+box around these so we know these are
+our symbols that were keeping defined
+
+ align:start position:0%
+our symbols that were keeping defined
+ 
+
+ align:start position:0%
+our symbols that were keeping defined
+here and so you may see that the
+
+ align:start position:0%
+here and so you may see that the
+ 
+
+ align:start position:0%
+here and so you may see that the
+microscopic cross-section just depends
+
+ align:start position:0%
+microscopic cross-section just depends
+ 
+
+ align:start position:0%
+microscopic cross-section just depends
+on single reactions between the incoming
+
+ align:start position:0%
+on single reactions between the incoming
+ 
+
+ align:start position:0%
+on single reactions between the incoming
+atoms a and the target atoms be the
+
+ align:start position:0%
+atoms a and the target atoms be the
+ 
+
+ align:start position:0%
+atoms a and the target atoms be the
+macroscopic cross-section depends on how
+
+ align:start position:0%
+macroscopic cross-section depends on how
+ 
+
+ align:start position:0%
+macroscopic cross-section depends on how
+much B is there so if you want to get
+
+ align:start position:0%
+much B is there so if you want to get
+ 
+
+ align:start position:0%
+much B is there so if you want to get
+per atom probabilities of absorption
+
+ align:start position:0%
+per atom probabilities of absorption
+ 
+
+ align:start position:0%
+per atom probabilities of absorption
+scattering whatever thing you're looking
+
+ align:start position:0%
+scattering whatever thing you're looking
+ 
+
+ align:start position:0%
+scattering whatever thing you're looking
+at you use the microscopic cross-section
+
+ align:start position:0%
+at you use the microscopic cross-section
+ 
+
+ align:start position:0%
+at you use the microscopic cross-section
+and if you have a finite amount of stuff
+
+ align:start position:0%
+and if you have a finite amount of stuff
+ 
+
+ align:start position:0%
+and if you have a finite amount of stuff
+there and you know the number density of
+
+ align:start position:0%
+there and you know the number density of
+ 
+
+ align:start position:0%
+there and you know the number density of
+your substance B you can use the macro
+
+ align:start position:0%
+your substance B you can use the macro
+ 
+
+ align:start position:0%
+your substance B you can use the macro
+macroscopic cross section to get actual
+
+ align:start position:0%
+macroscopic cross section to get actual
+ 
+
+ align:start position:0%
+macroscopic cross section to get actual
+total probabilities of beam attenuation
+
+ align:start position:0%
+total probabilities of beam attenuation
+ 
+
+ align:start position:0%
+total probabilities of beam attenuation
+or to calculate exponential attenuation
+
+ align:start position:0%
+or to calculate exponential attenuation
+ 
+
+ align:start position:0%
+or to calculate exponential attenuation
+we're gonna see this again in another
+
+ align:start position:0%
+we're gonna see this again in another
+ 
+
+ align:start position:0%
+we're gonna see this again in another
+form when we talk about designing
+
+ align:start position:0%
+form when we talk about designing
+ 
+
+ align:start position:0%
+form when we talk about designing
+shielding and how much shielding do you
+
+ align:start position:0%
+shielding and how much shielding do you
+ 
+
+ align:start position:0%
+shielding and how much shielding do you
+need to remove how much of the beam well
+
+ align:start position:0%
+need to remove how much of the beam well
+ 
+
+ align:start position:0%
+need to remove how much of the beam well
+this quantity right here there's
+
+ align:start position:0%
+this quantity right here there's
+ 
+
+ align:start position:0%
+this quantity right here there's
+actually tabulated values for a lot of
+
+ align:start position:0%
+actually tabulated values for a lot of
+ 
+
+ align:start position:0%
+actually tabulated values for a lot of
+this stuff at on the NIST website and I
+
+ align:start position:0%
+this stuff at on the NIST website and I
+ 
+
+ align:start position:0%
+this stuff at on the NIST website and I
+have links to that as well on the
+
+ align:start position:0%
+have links to that as well on the
+ 
+
+ align:start position:0%
+have links to that as well on the
+stellar website so that you can instead
+
+ align:start position:0%
+stellar website so that you can instead
+ 
+
+ align:start position:0%
+stellar website so that you can instead
+of having to look these all up on janus
+
+ align:start position:0%
+of having to look these all up on janus
+ 
+
+ align:start position:0%
+of having to look these all up on janus
+and multiply number densities there are
+
+ align:start position:0%
+and multiply number densities there are
+ 
+
+ align:start position:0%
+and multiply number densities there are
+some easier graphical functions you can
+
+ align:start position:0%
+some easier graphical functions you can
+ 
+
+ align:start position:0%
+some easier graphical functions you can
+just find the value for but we'll get
+
+ align:start position:0%
+just find the value for but we'll get
+ 
+
+ align:start position:0%
+just find the value for but we'll get
+back to that in a few days so anyway on
+
+ align:start position:0%
+back to that in a few days so anyway on
+ 
+
+ align:start position:0%
+back to that in a few days so anyway on
+reading the Kairi table there's a few
+
+ align:start position:0%
+reading the Kairi table there's a few
+ 
+
+ align:start position:0%
+reading the Kairi table there's a few
+quantities right there I we've already
+
+ align:start position:0%
+quantities right there I we've already
+ 
+
+ align:start position:0%
+quantities right there I we've already
+defined what the excess mass and the
+
+ align:start position:0%
+defined what the excess mass and the
+ 
+
+ align:start position:0%
+defined what the excess mass and the
+binding energy is and I want to note
+
+ align:start position:0%
+binding energy is and I want to note
+ 
+
+ align:start position:0%
+binding energy is and I want to note
+right here if you want to actually
+
+ align:start position:0%
+right here if you want to actually
+ 
+
+ align:start position:0%
+right here if you want to actually
+calculate binding energies by hand which
+
+ align:start position:0%
+calculate binding energies by hand which
+ 
+
+ align:start position:0%
+calculate binding energies by hand which
+I'm going to ask you to do a bit on
+
+ align:start position:0%
+I'm going to ask you to do a bit on
+ 
+
+ align:start position:0%
+I'm going to ask you to do a bit on
+problem set two you'll need to know what
+
+ align:start position:0%
+problem set two you'll need to know what
+ 
+
+ align:start position:0%
+problem set two you'll need to know what
+the mass of the proton and the neutron
+
+ align:start position:0%
+the mass of the proton and the neutron
+ 
+
+ align:start position:0%
+the mass of the proton and the neutron
+and the electron are to again usually
+
+ align:start position:0%
+and the electron are to again usually
+ 
+
+ align:start position:0%
+and the electron are to again usually
+like six or seven digits is the is the
+
+ align:start position:0%
+like six or seven digits is the is the
+ 
+
+ align:start position:0%
+like six or seven digits is the is the
+idea behind this course notice that
+
+ align:start position:0%
+idea behind this course notice that
+ 
+
+ align:start position:0%
+idea behind this course notice that
+they're not exactly one atomic mass unit
+
+ align:start position:0%
+they're not exactly one atomic mass unit
+ 
+
+ align:start position:0%
+they're not exactly one atomic mass unit
+because one atomic mass unit again was
+
+ align:start position:0%
+because one atomic mass unit again was
+ 
+
+ align:start position:0%
+because one atomic mass unit again was
+set with that carbon-12 standard I'm not
+
+ align:start position:0%
+set with that carbon-12 standard I'm not
+ 
+
+ align:start position:0%
+set with that carbon-12 standard I'm not
+going to use the word gold standard
+
+ align:start position:0%
+going to use the word gold standard
+ 
+
+ align:start position:0%
+going to use the word gold standard
+because that's a misnomer in this field
+
+ align:start position:0%
+because that's a misnomer in this field
+ 
+
+ align:start position:0%
+because that's a misnomer in this field
+and so like I said what does excess mass
+
+ align:start position:0%
+and so like I said what does excess mass
+ 
+
+ align:start position:0%
+and so like I said what does excess mass
+really mean physically not much because
+
+ align:start position:0%
+really mean physically not much because
+ 
+
+ align:start position:0%
+really mean physically not much because
+it's the comparison to an arbitrary
+
+ align:start position:0%
+it's the comparison to an arbitrary
+ 
+
+ align:start position:0%
+it's the comparison to an arbitrary
+standard or a rather poor approximation
+
+ align:start position:0%
+standard or a rather poor approximation
+ 
+
+ align:start position:0%
+standard or a rather poor approximation
+of the mass the binding energy actually
+
+ align:start position:0%
+of the mass the binding energy actually
+ 
+
+ align:start position:0%
+of the mass the binding energy actually
+does represent the conversion of math to
+
+ align:start position:0%
+does represent the conversion of math to
+ 
+
+ align:start position:0%
+does represent the conversion of math to
+energy when you assemble a nucleus like
+
+ align:start position:0%
+energy when you assemble a nucleus like
+ 
+
+ align:start position:0%
+energy when you assemble a nucleus like
+Voltron style from its constituent
+
+ align:start position:0%
+Voltron style from its constituent
+ 
+
+ align:start position:0%
+Voltron style from its constituent
+nucleons so let's try a few examples in
+
+ align:start position:0%
+nucleons so let's try a few examples in
+ 
+
+ align:start position:0%
+nucleons so let's try a few examples in
+class right here I'd like you guys to
+
+ align:start position:0%
+class right here I'd like you guys to
+ 
+
+ align:start position:0%
+class right here I'd like you guys to
+follow around and try and calculate the
+
+ align:start position:0%
+follow around and try and calculate the
+ 
+
+ align:start position:0%
+follow around and try and calculate the
+binding energy of each of these three
+
+ align:start position:0%
+binding energy of each of these three
+ 
+
+ align:start position:0%
+binding energy of each of these three
+nuclei of sulfur let me get a better
+
+ align:start position:0%
+nuclei of sulfur let me get a better
+ 
+
+ align:start position:0%
+nuclei of sulfur let me get a better
+blank board you can follow along and
+
+ align:start position:0%
+blank board you can follow along and
+ 
+
+ align:start position:0%
+blank board you can follow along and
+there's a few different ways of
+
+ align:start position:0%
+there's a few different ways of
+ 
+
+ align:start position:0%
+there's a few different ways of
+calculating that binding energy you can
+
+ align:start position:0%
+calculating that binding energy you can
+ 
+
+ align:start position:0%
+calculating that binding energy you can
+do it by the excess mass you can do it
+
+ align:start position:0%
+do it by the excess mass you can do it
+ 
+
+ align:start position:0%
+do it by the excess mass you can do it
+by let's go back to the table of
+
+ align:start position:0%
+by let's go back to the table of
+ 
+
+ align:start position:0%
+by let's go back to the table of
+nuclides so I can show you how I would
+
+ align:start position:0%
+nuclides so I can show you how I would
+ 
+
+ align:start position:0%
+nuclides so I can show you how I would
+do it let's start with sulfur 32 and
+
+ align:start position:0%
+do it let's start with sulfur 32 and
+ 
+
+ align:start position:0%
+do it let's start with sulfur 32 and
+we'll write up the quantities that were
+
+ align:start position:0%
+we'll write up the quantities that were
+ 
+
+ align:start position:0%
+we'll write up the quantities that were
+that we know let's say the excess mass
+
+ align:start position:0%
+that we know let's say the excess mass
+ 
+
+ align:start position:0%
+that we know let's say the excess mass
+is the actual mass minus the mass number
+
+ align:start position:0%
+is the actual mass minus the mass number
+ 
+
+ align:start position:0%
+is the actual mass minus the mass number
+the binding energy is Z times mass of
+
+ align:start position:0%
+the binding energy is Z times mass of
+ 
+
+ align:start position:0%
+the binding energy is Z times mass of
+hydrogen plus a minus Z mass of a
+
+ align:start position:0%
+hydrogen plus a minus Z mass of a
+ 
+
+ align:start position:0%
+hydrogen plus a minus Z mass of a
+neutron minus the actual mass of that
+
+ align:start position:0%
+neutron minus the actual mass of that
+ 
+
+ align:start position:0%
+neutron minus the actual mass of that
+nucleus with a Z Z squared and then what
+
+ align:start position:0%
+nucleus with a Z Z squared and then what
+ 
+
+ align:start position:0%
+nucleus with a Z Z squared and then what
+we can do is rearrange this excess mass
+
+ align:start position:0%
+we can do is rearrange this excess mass
+ 
+
+ align:start position:0%
+we can do is rearrange this excess mass
+isolating the mass term right here and
+
+ align:start position:0%
+isolating the mass term right here and
+ 
+
+ align:start position:0%
+isolating the mass term right here and
+make a substitution so we can say the
+
+ align:start position:0%
+make a substitution so we can say the
+ 
+
+ align:start position:0%
+make a substitution so we can say the
+mass is actually the excess mass plus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stick that in right there and now we can
+
+ align:start position:0%
+stick that in right there and now we can
+ 
+
+ align:start position:0%
+stick that in right there and now we can
+calculate and confirm the binding
+
+ align:start position:0%
+calculate and confirm the binding
+ 
+
+ align:start position:0%
+calculate and confirm the binding
+energies that we see right here from
+
+ align:start position:0%
+energies that we see right here from
+ 
+
+ align:start position:0%
+energies that we see right here from
+tabulated excess mass values atomic
+
+ align:start position:0%
+tabulated excess mass values atomic
+ 
+
+ align:start position:0%
+tabulated excess mass values atomic
+number mass number and the masses of a
+
+ align:start position:0%
+number mass number and the masses of a
+ 
+
+ align:start position:0%
+number mass number and the masses of a
+hydrogen atom and a neutron which for
+
+ align:start position:0%
+hydrogen atom and a neutron which for
+ 
+
+ align:start position:0%
+hydrogen atom and a neutron which for
+reference all right up here as well so
+
+ align:start position:0%
+reference all right up here as well so
+ 
+
+ align:start position:0%
+reference all right up here as well so
+the mass of a hydrogen is the mass of a
+
+ align:start position:0%
+the mass of a hydrogen is the mass of a
+ 
+
+ align:start position:0%
+the mass of a hydrogen is the mass of a
+proton plus an electron so one point
+
+ align:start position:0%
+proton plus an electron so one point
+ 
+
+ align:start position:0%
+proton plus an electron so one point
+zero seven two
+
+ align:start position:0%
+zero seven two
+ 
+
+ align:start position:0%
+zero seven two
+oh seven - seven six plus point
+
+ align:start position:0%
+oh seven - seven six plus point
+ 
+
+ align:start position:0%
+oh seven - seven six plus point
+Oh Oh Oh make that a little easier to
+
+ align:start position:0%
+Oh Oh Oh make that a little easier to
+ 
+
+ align:start position:0%
+Oh Oh Oh make that a little easier to
+read how many zeros ooo five four eight
+
+ align:start position:0%
+read how many zeros ooo five four eight
+ 
+
+ align:start position:0%
+read how many zeros ooo five four eight
+five eight am you massive a neutron
+
+ align:start position:0%
+five eight am you massive a neutron
+ 
+
+ align:start position:0%
+five eight am you massive a neutron
+surprisingly close to Chadwicks
+
+ align:start position:0%
+surprisingly close to Chadwicks
+ 
+
+ align:start position:0%
+surprisingly close to Chadwicks
+prediction eight six six four amu so now
+
+ align:start position:0%
+prediction eight six six four amu so now
+ 
+
+ align:start position:0%
+prediction eight six six four amu so now
+I'll head back to the table of nuclides
+
+ align:start position:0%
+I'll head back to the table of nuclides
+ 
+
+ align:start position:0%
+I'll head back to the table of nuclides
+and let's see if you guys can follow
+
+ align:start position:0%
+and let's see if you guys can follow
+ 
+
+ align:start position:0%
+and let's see if you guys can follow
+along what we want to do is try to
+
+ align:start position:0%
+along what we want to do is try to
+ 
+
+ align:start position:0%
+along what we want to do is try to
+confirm this binding energy using the
+
+ align:start position:0%
+confirm this binding energy using the
+ 
+
+ align:start position:0%
+confirm this binding energy using the
+atomic mass the excess mass or if we
+
+ align:start position:0%
+atomic mass the excess mass or if we
+ 
+
+ align:start position:0%
+atomic mass the excess mass or if we
+don't even know the atomic mass we can
+
+ align:start position:0%
+don't even know the atomic mass we can
+ 
+
+ align:start position:0%
+don't even know the atomic mass we can
+use the excess mass plus a right there
+
+ align:start position:0%
+use the excess mass plus a right there
+ 
+
+ align:start position:0%
+use the excess mass plus a right there
+so let's see Z in this case for sulphur
+
+ align:start position:0%
+so let's see Z in this case for sulphur
+ 
+
+ align:start position:0%
+so let's see Z in this case for sulphur
+is 16 times the mass of hydrogen this is
+
+ align:start position:0%
+is 16 times the mass of hydrogen this is
+ 
+
+ align:start position:0%
+is 16 times the mass of hydrogen this is
+definitely a calculator moment because
+
+ align:start position:0%
+definitely a calculator moment because
+ 
+
+ align:start position:0%
+definitely a calculator moment because
+like I said I don't know about you guys
+
+ align:start position:0%
+like I said I don't know about you guys
+ 
+
+ align:start position:0%
+like I said I don't know about you guys
+but I can't do eight significant digits
+
+ align:start position:0%
+but I can't do eight significant digits
+ 
+
+ align:start position:0%
+but I can't do eight significant digits
+in my head oh five four eight five eight
+
+ align:start position:0%
+in my head oh five four eight five eight
+ 
+
+ align:start position:0%
+in my head oh five four eight five eight
+one point zero seven eight two fives
+
+ align:start position:0%
+one point zero seven eight two fives
+ 
+
+ align:start position:0%
+one point zero seven eight two fives
+probably enough digits plus sixteen
+
+ align:start position:0%
+probably enough digits plus sixteen
+ 
+
+ align:start position:0%
+probably enough digits plus sixteen
+because there's mass number here is 32
+
+ align:start position:0%
+because there's mass number here is 32
+ 
+
+ align:start position:0%
+because there's mass number here is 32
+the atomic number 16 that leaves us with
+
+ align:start position:0%
+the atomic number 16 that leaves us with
+ 
+
+ align:start position:0%
+the atomic number 16 that leaves us with
+16 neutrons times the mass of a neutron
+
+ align:start position:0%
+16 neutrons times the mass of a neutron
+ 
+
+ align:start position:0%
+16 neutrons times the mass of a neutron
+Oh 8 6 6 4 minus the excess mass which
+
+ align:start position:0%
+Oh 8 6 6 4 minus the excess mass which
+ 
+
+ align:start position:0%
+Oh 8 6 6 4 minus the excess mass which
+in this case is 26 point oh one 5 MeV
+
+ align:start position:0%
+in this case is 26 point oh one 5 MeV
+ 
+
+ align:start position:0%
+in this case is 26 point oh one 5 MeV
+oh one 5 MeV / C squared so thanks to
+
+ align:start position:0%
+oh one 5 MeV / C squared so thanks to
+ 
+
+ align:start position:0%
+oh one 5 MeV / C squared so thanks to
+that same Garrett for that question
+
+ align:start position:0%
+that same Garrett for that question
+ 
+
+ align:start position:0%
+that same Garrett for that question
+because indeed the excess mass if you
+
+ align:start position:0%
+because indeed the excess mass if you
+ 
+
+ align:start position:0%
+because indeed the excess mass if you
+want to write it in terms of a mass
+
+ align:start position:0%
+want to write it in terms of a mass
+ 
+
+ align:start position:0%
+want to write it in terms of a mass
+should be in MeV or ke V / C squared
+
+ align:start position:0%
+should be in MeV or ke V / C squared
+ 
+
+ align:start position:0%
+should be in MeV or ke V / C squared
+minus a which is 32 times C squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do all this out shouldn't take
+
+ align:start position:0%
+so let's do all this out shouldn't take
+ 
+
+ align:start position:0%
+so let's do all this out shouldn't take
+too long oh seven eight to five that's
+
+ align:start position:0%
+too long oh seven eight to five that's
+ 
+
+ align:start position:0%
+too long oh seven eight to five that's
+one point oh eight six six four - 32 -
+
+ align:start position:0%
+one point oh eight six six four - 32 -
+ 
+
+ align:start position:0%
+one point oh eight six six four - 32 -
+twenty six point zero one five divided
+
+ align:start position:0%
+twenty six point zero one five divided
+ 
+
+ align:start position:0%
+twenty six point zero one five divided
+by C squared it's basically nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives us on the order of let's see times
+
+ align:start position:0%
+gives us on the order of let's see times
+ 
+
+ align:start position:0%
+gives us on the order of let's see times
+C squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where do we get right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see believe it is because we have
+
+ align:start position:0%
+let's see believe it is because we have
+ 
+
+ align:start position:0%
+let's see believe it is because we have
+to subtract the mass and we're
+
+ align:start position:0%
+to subtract the mass and we're
+ 
+
+ align:start position:0%
+to subtract the mass and we're
+substituting in this Delta oh good point
+
+ align:start position:0%
+substituting in this Delta oh good point
+ 
+
+ align:start position:0%
+substituting in this Delta oh good point
+there is a negative there so that's
+
+ align:start position:0%
+there is a negative there so that's
+ 
+
+ align:start position:0%
+there is a negative there so that's
+minus negative that and a is 32 thank
+
+ align:start position:0%
+minus negative that and a is 32 thank
+ 
+
+ align:start position:0%
+minus negative that and a is 32 thank
+you yeah good point let me try this
+
+ align:start position:0%
+you yeah good point let me try this
+ 
+
+ align:start position:0%
+you yeah good point let me try this
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah I know what I'm doing wrong this part
+
+ align:start position:0%
+ah I know what I'm doing wrong this part
+ 
+
+ align:start position:0%
+ah I know what I'm doing wrong this part
+right here we want to convert to amu
+
+ align:start position:0%
+right here we want to convert to amu
+ 
+
+ align:start position:0%
+right here we want to convert to amu
+so we can take our - thank you twenty
+
+ align:start position:0%
+so we can take our - thank you twenty
+ 
+
+ align:start position:0%
+so we can take our - thank you twenty
+six point oh one five MeV per C squared
+
+ align:start position:0%
+six point oh one five MeV per C squared
+ 
+
+ align:start position:0%
+six point oh one five MeV per C squared
+and divided by our conversion factor
+
+ align:start position:0%
+and divided by our conversion factor
+ 
+
+ align:start position:0%
+and divided by our conversion factor
+nine thirty one point four nine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the MeV per C squared per amu what
+
+ align:start position:0%
+it's the MeV per C squared per amu what
+ 
+
+ align:start position:0%
+it's the MeV per C squared per amu what
+does that give us twenty six point oh
+
+ align:start position:0%
+does that give us twenty six point oh
+ 
+
+ align:start position:0%
+does that give us twenty six point oh
+one five over that 0.027 9:00 to 8:00
+
+ align:start position:0%
+one five over that 0.027 9:00 to 8:00
+ 
+
+ align:start position:0%
+one five over that 0.027 9:00 to 8:00
+a.m. you- let's put that in and see how
+
+ align:start position:0%
+a.m. you- let's put that in and see how
+ 
+
+ align:start position:0%
+a.m. you- let's put that in and see how
+we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so plus 0.02 798 minus 32 and then we
+
+ align:start position:0%
+so plus 0.02 798 minus 32 and then we
+ 
+
+ align:start position:0%
+so plus 0.02 798 minus 32 and then we
+get to 71 point I'll just say 764 MeV I
+
+ align:start position:0%
+get to 71 point I'll just say 764 MeV I
+ 
+
+ align:start position:0%
+get to 71 point I'll just say 764 MeV I
+think six digits is enough the actual
+
+ align:start position:0%
+think six digits is enough the actual
+ 
+
+ align:start position:0%
+think six digits is enough the actual
+binding energy to 70 1.78 Oh MeV so
+
+ align:start position:0%
+binding energy to 70 1.78 Oh MeV so
+ 
+
+ align:start position:0%
+binding energy to 70 1.78 Oh MeV so
+we're off by 16 electron volts close
+
+ align:start position:0%
+we're off by 16 electron volts close
+ 
+
+ align:start position:0%
+we're off by 16 electron volts close
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+also note that I used a five digit
+
+ align:start position:0%
+also note that I used a five digit
+ 
+
+ align:start position:0%
+also note that I used a five digit
+accurate conversion factor that might be
+
+ align:start position:0%
+accurate conversion factor that might be
+ 
+
+ align:start position:0%
+accurate conversion factor that might be
+part of the source of it someone have a
+
+ align:start position:0%
+part of the source of it someone have a
+ 
+
+ align:start position:0%
+part of the source of it someone have a
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah I actually added the two so the
+
+ align:start position:0%
+oh yeah I actually added the two so the
+ 
+
+ align:start position:0%
+oh yeah I actually added the two so the
+mass of an electron since it's got that
+
+ align:start position:0%
+mass of an electron since it's got that
+ 
+
+ align:start position:0%
+mass of an electron since it's got that
+extra zero makes so much of a so the
+
+ align:start position:0%
+extra zero makes so much of a so the
+ 
+
+ align:start position:0%
+extra zero makes so much of a so the
+mass of oh yeah a massive hydrogen would
+
+ align:start position:0%
+mass of oh yeah a massive hydrogen would
+ 
+
+ align:start position:0%
+mass of oh yeah a massive hydrogen would
+be the proton plus the electron right
+
+ align:start position:0%
+be the proton plus the electron right
+ 
+
+ align:start position:0%
+be the proton plus the electron right
+there oh because it's there's an
+
+ align:start position:0%
+there oh because it's there's an
+ 
+
+ align:start position:0%
+there oh because it's there's an
+electron there too now this can usually
+
+ align:start position:0%
+electron there too now this can usually
+ 
+
+ align:start position:0%
+electron there too now this can usually
+be neglected because it's such small
+
+ align:start position:0%
+be neglected because it's such small
+ 
+
+ align:start position:0%
+be neglected because it's such small
+fraction compared to everything else so
+
+ align:start position:0%
+fraction compared to everything else so
+ 
+
+ align:start position:0%
+fraction compared to everything else so
+now we're talking about what the fifth
+
+ align:start position:0%
+now we're talking about what the fifth
+ 
+
+ align:start position:0%
+now we're talking about what the fifth
+or sixth decimal place but just for
+
+ align:start position:0%
+or sixth decimal place but just for
+ 
+
+ align:start position:0%
+or sixth decimal place but just for
+exactness I could stuck them in yeah in
+
+ align:start position:0%
+exactness I could stuck them in yeah in
+ 
+
+ align:start position:0%
+exactness I could stuck them in yeah in
+your calculation you can try with and
+
+ align:start position:0%
+your calculation you can try with and
+ 
+
+ align:start position:0%
+your calculation you can try with and
+without and I think you'll find that it
+
+ align:start position:0%
+without and I think you'll find that it
+ 
+
+ align:start position:0%
+without and I think you'll find that it
+doesn't matter that much because in the
+
+ align:start position:0%
+doesn't matter that much because in the
+ 
+
+ align:start position:0%
+doesn't matter that much because in the
+end we get the binding energy that we
+
+ align:start position:0%
+end we get the binding energy that we
+ 
+
+ align:start position:0%
+end we get the binding energy that we
+see on the table to within 16 electron
+
+ align:start position:0%
+see on the table to within 16 electron
+ 
+
+ align:start position:0%
+see on the table to within 16 electron
+volts for a total of yeah 271 MeV that's
+
+ align:start position:0%
+volts for a total of yeah 271 MeV that's
+ 
+
+ align:start position:0%
+volts for a total of yeah 271 MeV that's
+pretty accurate
+
+ align:start position:0%
+pretty accurate
+ 
+
+ align:start position:0%
+pretty accurate
+yeah that's the next slide I'll get
+
+ align:start position:0%
+yeah that's the next slide I'll get
+ 
+
+ align:start position:0%
+yeah that's the next slide I'll get
+right there yeah so you hear you're
+
+ align:start position:0%
+right there yeah so you hear you're
+ 
+
+ align:start position:0%
+right there yeah so you hear you're
+catching on to where we're going so once
+
+ align:start position:0%
+catching on to where we're going so once
+ 
+
+ align:start position:0%
+catching on to where we're going so once
+you can calculate either the excess mass
+
+ align:start position:0%
+you can calculate either the excess mass
+ 
+
+ align:start position:0%
+you can calculate either the excess mass
+or the binding energy or the total mass
+
+ align:start position:0%
+or the binding energy or the total mass
+ 
+
+ align:start position:0%
+or the binding energy or the total mass
+of any nucleus you can start to put them
+
+ align:start position:0%
+of any nucleus you can start to put them
+ 
+
+ align:start position:0%
+of any nucleus you can start to put them
+together into nuclear reactions so since
+
+ align:start position:0%
+together into nuclear reactions so since
+ 
+
+ align:start position:0%
+together into nuclear reactions so since
+you asked let's take a quick look at
+
+ align:start position:0%
+you asked let's take a quick look at
+ 
+
+ align:start position:0%
+you asked let's take a quick look at
+them where is our nuclear reaction board
+
+ align:start position:0%
+them where is our nuclear reaction board
+ 
+
+ align:start position:0%
+them where is our nuclear reaction board
+anyone mind if I hide this board for now
+
+ align:start position:0%
+anyone mind if I hide this board for now
+ 
+
+ align:start position:0%
+anyone mind if I hide this board for now
+so we can go back to our original okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a look at this reaction right
+
+ align:start position:0%
+let's take a look at this reaction right
+ 
+
+ align:start position:0%
+let's take a look at this reaction right
+here the actual boron Neutron capture
+
+ align:start position:0%
+here the actual boron Neutron capture
+ 
+
+ align:start position:0%
+here the actual boron Neutron capture
+therapy reaction and now we can get
+
+ align:start position:0%
+therapy reaction and now we can get
+ 
+
+ align:start position:0%
+therapy reaction and now we can get
+towards calculating this Q what the
+
+ align:start position:0%
+towards calculating this Q what the
+ 
+
+ align:start position:0%
+towards calculating this Q what the
+difference is between the energies of
+
+ align:start position:0%
+difference is between the energies of
+ 
+
+ align:start position:0%
+difference is between the energies of
+total energies of the products and the
+
+ align:start position:0%
+total energies of the products and the
+ 
+
+ align:start position:0%
+total energies of the products and the
+reactants and where does that go so now
+
+ align:start position:0%
+reactants and where does that go so now
+ 
+
+ align:start position:0%
+reactants and where does that go so now
+we can either look up or calculate the
+
+ align:start position:0%
+we can either look up or calculate the
+ 
+
+ align:start position:0%
+we can either look up or calculate the
+binding energy of each of these nuclei
+
+ align:start position:0%
+binding energy of each of these nuclei
+ 
+
+ align:start position:0%
+binding energy of each of these nuclei
+subtract off the energy of the gamma
+
+ align:start position:0%
+subtract off the energy of the gamma
+ 
+
+ align:start position:0%
+subtract off the energy of the gamma
+which I've looked up already is about
+
+ align:start position:0%
+which I've looked up already is about
+ 
+
+ align:start position:0%
+which I've looked up already is about
+0.478 MeV and we can figure out what the
+
+ align:start position:0%
+0.478 MeV and we can figure out what the
+ 
+
+ align:start position:0%
+0.478 MeV and we can figure out what the
+total Q of this reaction is so in this
+
+ align:start position:0%
+total Q of this reaction is so in this
+ 
+
+ align:start position:0%
+total Q of this reaction is so in this
+case I'll skip ahead to the slide where
+
+ align:start position:0%
+case I'll skip ahead to the slide where
+ 
+
+ align:start position:0%
+case I'll skip ahead to the slide where
+I've got it because that way all right
+
+ align:start position:0%
+I've got it because that way all right
+ 
+
+ align:start position:0%
+I've got it because that way all right
+anything wrong
+
+ align:start position:0%
+anything wrong
+ 
+
+ align:start position:0%
+anything wrong
+the board got everything right up here
+
+ align:start position:0%
+the board got everything right up here
+ 
+
+ align:start position:0%
+the board got everything right up here
+we assume that both boron and the
+
+ align:start position:0%
+we assume that both boron and the
+ 
+
+ align:start position:0%
+we assume that both boron and the
+neutron have roughly zero kinetic energy
+
+ align:start position:0%
+neutron have roughly zero kinetic energy
+ 
+
+ align:start position:0%
+neutron have roughly zero kinetic energy
+and at the end they come out with some
+
+ align:start position:0%
+and at the end they come out with some
+ 
+
+ align:start position:0%
+and at the end they come out with some
+other kinetic energies as well as this
+
+ align:start position:0%
+other kinetic energies as well as this
+ 
+
+ align:start position:0%
+other kinetic energies as well as this
+gamma ray the sum of this energy
+
+ align:start position:0%
+gamma ray the sum of this energy
+ 
+
+ align:start position:0%
+gamma ray the sum of this energy
+difference as we refer to as Q and we
+
+ align:start position:0%
+difference as we refer to as Q and we
+ 
+
+ align:start position:0%
+difference as we refer to as Q and we
+can actually confirm this total Q with a
+
+ align:start position:0%
+can actually confirm this total Q with a
+ 
+
+ align:start position:0%
+can actually confirm this total Q with a
+few different methods in this case it's
+
+ align:start position:0%
+few different methods in this case it's
+ 
+
+ align:start position:0%
+few different methods in this case it's
+always conserved something that's the
+
+ align:start position:0%
+always conserved something that's the
+ 
+
+ align:start position:0%
+always conserved something that's the
+the whole theme of this course that you
+
+ align:start position:0%
+the whole theme of this course that you
+ 
+
+ align:start position:0%
+the whole theme of this course that you
+can conserve total masses you can
+
+ align:start position:0%
+can conserve total masses you can
+ 
+
+ align:start position:0%
+can conserve total masses you can
+conserve total kinetic energies we may
+
+ align:start position:0%
+conserve total kinetic energies we may
+ 
+
+ align:start position:0%
+conserve total kinetic energies we may
+not know those but tabulated in the in
+
+ align:start position:0%
+not know those but tabulated in the in
+ 
+
+ align:start position:0%
+not know those but tabulated in the in
+the Kairi table are the binding energies
+
+ align:start position:0%
+the Kairi table are the binding energies
+ 
+
+ align:start position:0%
+the Kairi table are the binding energies
+of each of these nuclei so let's try
+
+ align:start position:0%
+of each of these nuclei so let's try
+ 
+
+ align:start position:0%
+of each of these nuclei so let's try
+that out right now so let's look at the
+
+ align:start position:0%
+that out right now so let's look at the
+ 
+
+ align:start position:0%
+that out right now so let's look at the
+binding energies of each of these nuclei
+
+ align:start position:0%
+binding energies of each of these nuclei
+ 
+
+ align:start position:0%
+binding energies of each of these nuclei
+and see what the difference is the total
+
+ align:start position:0%
+and see what the difference is the total
+ 
+
+ align:start position:0%
+and see what the difference is the total
+energy released first of all what's the
+
+ align:start position:0%
+energy released first of all what's the
+ 
+
+ align:start position:0%
+energy released first of all what's the
+binding energy of a lone Neutron anyone
+
+ align:start position:0%
+binding energy of a lone Neutron anyone
+ 
+
+ align:start position:0%
+binding energy of a lone Neutron anyone
+have any idea see a lot of these zero
+
+ align:start position:0%
+have any idea see a lot of these zero
+ 
+
+ align:start position:0%
+have any idea see a lot of these zero
+yeah you haven't assembled the nucleus
+
+ align:start position:0%
+yeah you haven't assembled the nucleus
+ 
+
+ align:start position:0%
+yeah you haven't assembled the nucleus
+out of a lone Neutron so we'll go with
+
+ align:start position:0%
+out of a lone Neutron so we'll go with
+ 
+
+ align:start position:0%
+out of a lone Neutron so we'll go with
+the neutron has a binding energy of zero
+
+ align:start position:0%
+the neutron has a binding energy of zero
+ 
+
+ align:start position:0%
+the neutron has a binding energy of zero
+MeV boron not quite the case but we can
+
+ align:start position:0%
+MeV boron not quite the case but we can
+ 
+
+ align:start position:0%
+MeV boron not quite the case but we can
+go back to the table of nuclides and
+
+ align:start position:0%
+go back to the table of nuclides and
+ 
+
+ align:start position:0%
+go back to the table of nuclides and
+punch that in boron 10 we can look up
+
+ align:start position:0%
+punch that in boron 10 we can look up
+ 
+
+ align:start position:0%
+punch that in boron 10 we can look up
+its binding energy which is about sixty
+
+ align:start position:0%
+its binding energy which is about sixty
+ 
+
+ align:start position:0%
+its binding energy which is about sixty
+four point seven 507 I keep saying about
+
+ align:start position:0%
+four point seven 507 I keep saying about
+ 
+
+ align:start position:0%
+four point seven 507 I keep saying about
+which is exactly 64 point 7 507 MeV and
+
+ align:start position:0%
+which is exactly 64 point 7 507 MeV and
+ 
+
+ align:start position:0%
+which is exactly 64 point 7 507 MeV and
+then our other two nuclei helium-4 so
+
+ align:start position:0%
+then our other two nuclei helium-4 so
+ 
+
+ align:start position:0%
+then our other two nuclei helium-4 so
+you can punch in helium four here it's
+
+ align:start position:0%
+you can punch in helium four here it's
+ 
+
+ align:start position:0%
+you can punch in helium four here it's
+got a binding energy of exactly 28 point
+
+ align:start position:0%
+got a binding energy of exactly 28 point
+ 
+
+ align:start position:0%
+got a binding energy of exactly 28 point
+two nine five 673 MeV and finally
+
+ align:start position:0%
+two nine five 673 MeV and finally
+ 
+
+ align:start position:0%
+two nine five 673 MeV and finally
+lithium seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's punch that in think you guys are
+
+ align:start position:0%
+let's punch that in think you guys are
+ 
+
+ align:start position:0%
+let's punch that in think you guys are
+gonna get very familiar with this table
+
+ align:start position:0%
+gonna get very familiar with this table
+ 
+
+ align:start position:0%
+gonna get very familiar with this table
+there's a few versions out there there's
+
+ align:start position:0%
+there's a few versions out there there's
+ 
+
+ align:start position:0%
+there's a few versions out there there's
+a new slick Java version that I found a
+
+ align:start position:0%
+a new slick Java version that I found a
+ 
+
+ align:start position:0%
+a new slick Java version that I found a
+little hard to use so I like the
+
+ align:start position:0%
+little hard to use so I like the
+ 
+
+ align:start position:0%
+little hard to use so I like the
+text-only version because it's just as
+
+ align:start position:0%
+text-only version because it's just as
+ 
+
+ align:start position:0%
+text-only version because it's just as
+simple and fast as it gets thirty nine
+
+ align:start position:0%
+simple and fast as it gets thirty nine
+ 
+
+ align:start position:0%
+simple and fast as it gets thirty nine
+point two four four five to six five to
+
+ align:start position:0%
+point two four four five to six five to
+ 
+
+ align:start position:0%
+point two four four five to six five to
+six so any sort of increase in total
+
+ align:start position:0%
+six so any sort of increase in total
+ 
+
+ align:start position:0%
+six so any sort of increase in total
+amount of binding energy between the
+
+ align:start position:0%
+amount of binding energy between the
+ 
+
+ align:start position:0%
+amount of binding energy between the
+reactants and the products
+
+ align:start position:0%
+reactants and the products
+ 
+
+ align:start position:0%
+reactants and the products
+is going to release or absorb energy now
+
+ align:start position:0%
+is going to release or absorb energy now
+ 
+
+ align:start position:0%
+is going to release or absorb energy now
+because boron does capture a thermal
+
+ align:start position:0%
+because boron does capture a thermal
+ 
+
+ align:start position:0%
+because boron does capture a thermal
+Neutron or a neutron with approximately
+
+ align:start position:0%
+Neutron or a neutron with approximately
+ 
+
+ align:start position:0%
+Neutron or a neutron with approximately
+zero evie of kinetic energy does anyone
+
+ align:start position:0%
+zero evie of kinetic energy does anyone
+ 
+
+ align:start position:0%
+zero evie of kinetic energy does anyone
+have any idea whether this would release
+
+ align:start position:0%
+have any idea whether this would release
+ 
+
+ align:start position:0%
+have any idea whether this would release
+or consume energy in other words you
+
+ align:start position:0%
+or consume energy in other words you
+ 
+
+ align:start position:0%
+or consume energy in other words you
+think this is an exothermic or an
+
+ align:start position:0%
+think this is an exothermic or an
+ 
+
+ align:start position:0%
+think this is an exothermic or an
+endothermic reaction
+
+ align:start position:0%
+endothermic reaction
+ 
+
+ align:start position:0%
+endothermic reaction
+yeah Alex okay indeed if the total Q
+
+ align:start position:0%
+yeah Alex okay indeed if the total Q
+ 
+
+ align:start position:0%
+yeah Alex okay indeed if the total Q
+value is greater than zero we refer to
+
+ align:start position:0%
+value is greater than zero we refer to
+ 
+
+ align:start position:0%
+value is greater than zero we refer to
+this as exothermic kind of like in
+
+ align:start position:0%
+this as exothermic kind of like in
+ 
+
+ align:start position:0%
+this as exothermic kind of like in
+chemistry and if Q is less than zero we
+
+ align:start position:0%
+chemistry and if Q is less than zero we
+ 
+
+ align:start position:0%
+chemistry and if Q is less than zero we
+refer to this as endothermic so let's do
+
+ align:start position:0%
+refer to this as endothermic so let's do
+ 
+
+ align:start position:0%
+refer to this as endothermic so let's do
+our binding energy subtraction now we
+
+ align:start position:0%
+our binding energy subtraction now we
+ 
+
+ align:start position:0%
+our binding energy subtraction now we
+want to figure out how much excess
+
+ align:start position:0%
+want to figure out how much excess
+ 
+
+ align:start position:0%
+want to figure out how much excess
+binding energy is released so I'm going
+
+ align:start position:0%
+binding energy is released so I'm going
+ 
+
+ align:start position:0%
+binding energy is released so I'm going
+to take the reactants I'm sorry I'm
+
+ align:start position:0%
+to take the reactants I'm sorry I'm
+ 
+
+ align:start position:0%
+to take the reactants I'm sorry I'm
+gonna take the products so helium two
+
+ align:start position:0%
+gonna take the products so helium two
+ 
+
+ align:start position:0%
+gonna take the products so helium two
+nine five six seven three add lithium 2
+
+ align:start position:0%
+nine five six seven three add lithium 2
+ 
+
+ align:start position:0%
+nine five six seven three add lithium 2
+4 4 5 2 6 subtract boron seven 507
+
+ align:start position:0%
+4 4 5 2 6 subtract boron seven 507
+ 
+
+ align:start position:0%
+4 4 5 2 6 subtract boron seven 507
+subtract the neutron which is zero and
+
+ align:start position:0%
+subtract the neutron which is zero and
+ 
+
+ align:start position:0%
+subtract the neutron which is zero and
+we're left with two point seven nine MeV
+
+ align:start position:0%
+we're left with two point seven nine MeV
+ 
+
+ align:start position:0%
+we're left with two point seven nine MeV
+and because it's positive this is an
+
+ align:start position:0%
+and because it's positive this is an
+ 
+
+ align:start position:0%
+and because it's positive this is an
+exothermic reaction which is what we'd
+
+ align:start position:0%
+exothermic reaction which is what we'd
+ 
+
+ align:start position:0%
+exothermic reaction which is what we'd
+expect because this reaction actually
+
+ align:start position:0%
+expect because this reaction actually
+ 
+
+ align:start position:0%
+expect because this reaction actually
+happens if this was an endothermic
+
+ align:start position:0%
+happens if this was an endothermic
+ 
+
+ align:start position:0%
+happens if this was an endothermic
+reaction what could you do to make it
+
+ align:start position:0%
+reaction what could you do to make it
+ 
+
+ align:start position:0%
+reaction what could you do to make it
+occur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah like with temperature or what do
+
+ align:start position:0%
+yeah like with temperature or what do
+ 
+
+ align:start position:0%
+yeah like with temperature or what do
+you mean there you go
+
+ align:start position:0%
+you mean there you go
+ 
+
+ align:start position:0%
+you mean there you go
+so actually yeah you kind of said the
+
+ align:start position:0%
+so actually yeah you kind of said the
+ 
+
+ align:start position:0%
+so actually yeah you kind of said the
+same thing twice heating things up does
+
+ align:start position:0%
+same thing twice heating things up does
+ 
+
+ align:start position:0%
+same thing twice heating things up does
+give them higher kinetic energy if you
+
+ align:start position:0%
+give them higher kinetic energy if you
+ 
+
+ align:start position:0%
+give them higher kinetic energy if you
+rely on temperature you'll be imparting
+
+ align:start position:0%
+rely on temperature you'll be imparting
+ 
+
+ align:start position:0%
+rely on temperature you'll be imparting
+Evi worth of kinetic energy but if you
+
+ align:start position:0%
+Evi worth of kinetic energy but if you
+ 
+
+ align:start position:0%
+Evi worth of kinetic energy but if you
+accelerate them or get them from a
+
+ align:start position:0%
+accelerate them or get them from a
+ 
+
+ align:start position:0%
+accelerate them or get them from a
+different nuclear reaction and you get
+
+ align:start position:0%
+different nuclear reaction and you get
+ 
+
+ align:start position:0%
+different nuclear reaction and you get
+them up to the MeV level where whatever
+
+ align:start position:0%
+them up to the MeV level where whatever
+ 
+
+ align:start position:0%
+them up to the MeV level where whatever
+this Q value could be might be negative
+
+ align:start position:0%
+this Q value could be might be negative
+ 
+
+ align:start position:0%
+this Q value could be might be negative
+then you can get the reaction to occur
+
+ align:start position:0%
+then you can get the reaction to occur
+ 
+
+ align:start position:0%
+then you can get the reaction to occur
+for example what is the Q of that
+
+ align:start position:0%
+for example what is the Q of that
+ 
+
+ align:start position:0%
+for example what is the Q of that
+reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative that so in this case if you
+
+ align:start position:0%
+negative that so in this case if you
+ 
+
+ align:start position:0%
+negative that so in this case if you
+want lithium to absorb an alpha particle
+
+ align:start position:0%
+want lithium to absorb an alpha particle
+ 
+
+ align:start position:0%
+want lithium to absorb an alpha particle
+and make boron and a neutron you would
+
+ align:start position:0%
+and make boron and a neutron you would
+ 
+
+ align:start position:0%
+and make boron and a neutron you would
+have to accelerate the alphas to that
+
+ align:start position:0%
+have to accelerate the alphas to that
+ 
+
+ align:start position:0%
+have to accelerate the alphas to that
+same amount of energy in order to get
+
+ align:start position:0%
+same amount of energy in order to get
+ 
+
+ align:start position:0%
+same amount of energy in order to get
+this to occur
+
+ align:start position:0%
+this to occur
+ 
+
+ align:start position:0%
+this to occur
+so nuclear reactions do go both ways
+
+ align:start position:0%
+so nuclear reactions do go both ways
+ 
+
+ align:start position:0%
+so nuclear reactions do go both ways
+just not as easily kind of like chemical
+
+ align:start position:0%
+just not as easily kind of like chemical
+ 
+
+ align:start position:0%
+just not as easily kind of like chemical
+reactions you can drive them in
+
+ align:start position:0%
+reactions you can drive them in
+ 
+
+ align:start position:0%
+reactions you can drive them in
+different directions by changing the
+
+ align:start position:0%
+different directions by changing the
+ 
+
+ align:start position:0%
+different directions by changing the
+temperature changing the concentration
+
+ align:start position:0%
+temperature changing the concentration
+ 
+
+ align:start position:0%
+temperature changing the concentration
+of the reactants here the concentration
+
+ align:start position:0%
+of the reactants here the concentration
+ 
+
+ align:start position:0%
+of the reactants here the concentration
+doesn't matter but the kinetic energy
+
+ align:start position:0%
+doesn't matter but the kinetic energy
+ 
+
+ align:start position:0%
+doesn't matter but the kinetic energy
+related directly to the temperature
+
+ align:start position:0%
+related directly to the temperature
+ 
+
+ align:start position:0%
+related directly to the temperature
+definitely is and so in this case it's
+
+ align:start position:0%
+definitely is and so in this case it's
+ 
+
+ align:start position:0%
+definitely is and so in this case it's
+2.79 MeV if I tell you the gamma ray
+
+ align:start position:0%
+2.79 MeV if I tell you the gamma ray
+ 
+
+ align:start position:0%
+2.79 MeV if I tell you the gamma ray
+takes off 0.478 MeV of that we're left
+
+ align:start position:0%
+takes off 0.478 MeV of that we're left
+ 
+
+ align:start position:0%
+takes off 0.478 MeV of that we're left
+with two point three one MeV between the
+
+ align:start position:0%
+with two point three one MeV between the
+ 
+
+ align:start position:0%
+with two point three one MeV between the
+lithium nucleus and the helium nucleus
+
+ align:start position:0%
+lithium nucleus and the helium nucleus
+ 
+
+ align:start position:0%
+lithium nucleus and the helium nucleus
+now my next question of my last question
+
+ align:start position:0%
+now my next question of my last question
+ 
+
+ align:start position:0%
+now my next question of my last question
+for you today oh man is what's the split
+
+ align:start position:0%
+for you today oh man is what's the split
+ 
+
+ align:start position:0%
+for you today oh man is what's the split
+I think I don't want to keep you longer
+
+ align:start position:0%
+I think I don't want to keep you longer
+ 
+
+ align:start position:0%
+I think I don't want to keep you longer
+because it's one minute of 10 so this is
+
+ align:start position:0%
+because it's one minute of 10 so this is
+ 
+
+ align:start position:0%
+because it's one minute of 10 so this is
+the question that we're gonna pick up
+
+ align:start position:0%
+the question that we're gonna pick up
+ 
+
+ align:start position:0%
+the question that we're gonna pick up
+with on Thursday which is how much of
+
+ align:start position:0%
+with on Thursday which is how much of
+ 
+
+ align:start position:0%
+with on Thursday which is how much of
+the energy is taken off by helium and
+
+ align:start position:0%
+the energy is taken off by helium and
+ 
+
+ align:start position:0%
+the energy is taken off by helium and
+how much is taken off by lithium sorry I
+
+ align:start position:0%
+how much is taken off by lithium sorry I
+ 
+
+ align:start position:0%
+how much is taken off by lithium sorry I
+should have kept better track of the
+
+ align:start position:0%
+should have kept better track of the
+ 
+
+ align:start position:0%
+should have kept better track of the
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/H6eR3sG524M.txt b/H6eR3sG524M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a784cfa42b42ee02708c2785876288d77dd2af39
--- /dev/null
+++ b/H6eR3sG524M.txt
@@ -0,0 +1,11567 @@
+align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+welcome to tuesday so uh hopefully
+
+ align:start position:0%
+welcome to tuesday so uh hopefully
+ 
+
+ align:start position:0%
+welcome to tuesday so uh hopefully
+you've all saw the brief announcement i
+
+ align:start position:0%
+you've all saw the brief announcement i
+ 
+
+ align:start position:0%
+you've all saw the brief announcement i
+sent to the class
+
+ align:start position:0%
+sent to the class
+ 
+
+ align:start position:0%
+sent to the class
+um i have to introduce a colloquium
+
+ align:start position:0%
+um i have to introduce a colloquium
+ 
+
+ align:start position:0%
+um i have to introduce a colloquium
+speaker over in astrophysics
+
+ align:start position:0%
+speaker over in astrophysics
+ 
+
+ align:start position:0%
+speaker over in astrophysics
+basically at the second this class
+
+ align:start position:0%
+basically at the second this class
+ 
+
+ align:start position:0%
+basically at the second this class
+officially ends so i will be wrapping
+
+ align:start position:0%
+officially ends so i will be wrapping
+ 
+
+ align:start position:0%
+officially ends so i will be wrapping
+things up a little bit early so that i
+
+ align:start position:0%
+things up a little bit early so that i
+ 
+
+ align:start position:0%
+things up a little bit early so that i
+can take into account the
+
+ align:start position:0%
+can take into account the
+ 
+
+ align:start position:0%
+can take into account the
+spatial separation and uh get back there
+
+ align:start position:0%
+spatial separation and uh get back there
+ 
+
+ align:start position:0%
+spatial separation and uh get back there
+in time to actually
+
+ align:start position:0%
+in time to actually
+ 
+
+ align:start position:0%
+in time to actually
+do the introduction um i've already
+
+ align:start position:0%
+do the introduction um i've already
+ 
+
+ align:start position:0%
+do the introduction um i've already
+posted
+
+ align:start position:0%
+posted
+ 
+
+ align:start position:0%
+posted
+the lecture notes of material i'm going
+
+ align:start position:0%
+the lecture notes of material i'm going
+ 
+
+ align:start position:0%
+the lecture notes of material i'm going
+to be covering uh
+
+ align:start position:0%
+to be covering uh
+ 
+
+ align:start position:0%
+to be covering uh
+today and probably still you know i i
+
+ align:start position:0%
+today and probably still you know i i
+ 
+
+ align:start position:0%
+today and probably still you know i i
+hope to wrap it all up today but it's
+
+ align:start position:0%
+hope to wrap it all up today but it's
+ 
+
+ align:start position:0%
+hope to wrap it all up today but it's
+possible we'll spill a little bit into
+
+ align:start position:0%
+possible we'll spill a little bit into
+ 
+
+ align:start position:0%
+possible we'll spill a little bit into
+thursday so
+
+ align:start position:0%
+thursday so
+ 
+
+ align:start position:0%
+thursday so
+um if you've already looked at those
+
+ align:start position:0%
+um if you've already looked at those
+ 
+
+ align:start position:0%
+um if you've already looked at those
+notes today will essentially just be
+
+ align:start position:0%
+notes today will essentially just be
+ 
+
+ align:start position:0%
+notes today will essentially just be
+sort of my guided tour through that
+
+ align:start position:0%
+sort of my guided tour through that
+ 
+
+ align:start position:0%
+sort of my guided tour through that
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+so i want to pick it up with where i
+
+ align:start position:0%
+so i want to pick it up with where i
+ 
+
+ align:start position:0%
+so i want to pick it up with where i
+left things last time so we covered a
+
+ align:start position:0%
+left things last time so we covered a
+ 
+
+ align:start position:0%
+left things last time so we covered a
+bunch of material that
+
+ align:start position:0%
+bunch of material that
+ 
+
+ align:start position:0%
+bunch of material that
+again i kind of emphasize what we're
+
+ align:start position:0%
+again i kind of emphasize what we're
+ 
+
+ align:start position:0%
+again i kind of emphasize what we're
+doing right now is just laying the
+
+ align:start position:0%
+doing right now is just laying the
+ 
+
+ align:start position:0%
+doing right now is just laying the
+mathematical foundations in a very
+
+ align:start position:0%
+mathematical foundations in a very
+ 
+
+ align:start position:0%
+mathematical foundations in a very
+thorough almost excessively thorough way
+
+ align:start position:0%
+thorough almost excessively thorough way
+ 
+
+ align:start position:0%
+thorough almost excessively thorough way
+in order that we have a very strong
+
+ align:start position:0%
+in order that we have a very strong
+ 
+
+ align:start position:0%
+in order that we have a very strong
+structure as we begin to move
+
+ align:start position:0%
+structure as we begin to move
+ 
+
+ align:start position:0%
+structure as we begin to move
+into more physically complicated
+
+ align:start position:0%
+into more physically complicated
+ 
+
+ align:start position:0%
+into more physically complicated
+situations than the special relativity
+
+ align:start position:0%
+situations than the special relativity
+ 
+
+ align:start position:0%
+situations than the special relativity
+that we're focusing on right now
+
+ align:start position:0%
+that we're focusing on right now
+ 
+
+ align:start position:0%
+that we're focusing on right now
+so we talked about this definition of an
+
+ align:start position:0%
+so we talked about this definition of an
+ 
+
+ align:start position:0%
+so we talked about this definition of an
+inner product between
+
+ align:start position:0%
+inner product between
+ 
+
+ align:start position:0%
+inner product between
+two four vectors two vectors in space
+
+ align:start position:0%
+two four vectors two vectors in space
+ 
+
+ align:start position:0%
+two four vectors two vectors in space
+time okay and
+
+ align:start position:0%
+time okay and
+ 
+
+ align:start position:0%
+time okay and
+it looks just like the uh the inner
+
+ align:start position:0%
+it looks just like the uh the inner
+ 
+
+ align:start position:0%
+it looks just like the uh the inner
+product between two vectors that you are
+
+ align:start position:0%
+product between two vectors that you are
+ 
+
+ align:start position:0%
+product between two vectors that you are
+used to from your euclidean three-space
+
+ align:start position:0%
+used to from your euclidean three-space
+ 
+
+ align:start position:0%
+used to from your euclidean three-space
+intuition
+
+ align:start position:0%
+intuition
+ 
+
+ align:start position:0%
+intuition
+it's just that we have an extra bit
+
+ align:start position:0%
+it's just that we have an extra bit
+ 
+
+ align:start position:0%
+it's just that we have an extra bit
+there that enters with a minus sign
+
+ align:start position:0%
+there that enters with a minus sign
+ 
+
+ align:start position:0%
+there that enters with a minus sign
+having to do with the time-like
+
+ align:start position:0%
+having to do with the time-like
+ 
+
+ align:start position:0%
+having to do with the time-like
+components of those two
+
+ align:start position:0%
+components of those two
+ 
+
+ align:start position:0%
+components of those two
+four vectors um and then using the fact
+
+ align:start position:0%
+four vectors um and then using the fact
+ 
+
+ align:start position:0%
+four vectors um and then using the fact
+that i can write my four vector as
+
+ align:start position:0%
+that i can write my four vector as
+ 
+
+ align:start position:0%
+that i can write my four vector as
+components contracted onto
+
+ align:start position:0%
+components contracted onto
+ 
+
+ align:start position:0%
+components contracted onto
+elements of a set of basis vectors i can
+
+ align:start position:0%
+elements of a set of basis vectors i can
+ 
+
+ align:start position:0%
+elements of a set of basis vectors i can
+use this to define
+
+ align:start position:0%
+use this to define
+ 
+
+ align:start position:0%
+use this to define
+a tensor which i will get to the
+
+ align:start position:0%
+a tensor which i will get to the
+ 
+
+ align:start position:0%
+a tensor which i will get to the
+mathematical definition of more
+
+ align:start position:0%
+mathematical definition of more
+ 
+
+ align:start position:0%
+mathematical definition of more
+precisely in just a moment the dot
+
+ align:start position:0%
+precisely in just a moment the dot
+ 
+
+ align:start position:0%
+precisely in just a moment the dot
+product of any two basis vectors i will
+
+ align:start position:0%
+product of any two basis vectors i will
+ 
+
+ align:start position:0%
+product of any two basis vectors i will
+call that the tensor component
+
+ align:start position:0%
+call that the tensor component
+ 
+
+ align:start position:0%
+call that the tensor component
+eta alpha beta okay and so this is the
+
+ align:start position:0%
+eta alpha beta okay and so this is the
+ 
+
+ align:start position:0%
+eta alpha beta okay and so this is the
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+tensor of special relativity at least in
+
+ align:start position:0%
+tensor of special relativity at least in
+ 
+
+ align:start position:0%
+tensor of special relativity at least in
+rectilinear coordinates rectilinear
+
+ align:start position:0%
+rectilinear coordinates rectilinear
+ 
+
+ align:start position:0%
+rectilinear coordinates rectilinear
+basically just means cartesian
+
+ align:start position:0%
+basically just means cartesian
+ 
+
+ align:start position:0%
+basically just means cartesian
+but throwing time in there as well okay
+
+ align:start position:0%
+but throwing time in there as well okay
+ 
+
+ align:start position:0%
+but throwing time in there as well okay
+when we
+
+ align:start position:0%
+when we
+ 
+
+ align:start position:0%
+when we
+start talking about special relativity
+
+ align:start position:0%
+start talking about special relativity
+ 
+
+ align:start position:0%
+start talking about special relativity
+and curvilinear coordinates it'll get a
+
+ align:start position:0%
+and curvilinear coordinates it'll get a
+ 
+
+ align:start position:0%
+and curvilinear coordinates it'll get a
+little bit more complicated than that
+
+ align:start position:0%
+little bit more complicated than that
+ 
+
+ align:start position:0%
+little bit more complicated than that
+and i will not use the symbol eta in
+
+ align:start position:0%
+and i will not use the symbol eta in
+ 
+
+ align:start position:0%
+and i will not use the symbol eta in
+that case i'm going to reserve eta
+
+ align:start position:0%
+that case i'm going to reserve eta
+ 
+
+ align:start position:0%
+that case i'm going to reserve eta
+for this particular this particular form
+
+ align:start position:0%
+for this particular this particular form
+ 
+
+ align:start position:0%
+for this particular this particular form
+of the metric in these in this
+
+ align:start position:0%
+of the metric in these in this
+ 
+
+ align:start position:0%
+of the metric in these in this
+coordinate system
+
+ align:start position:0%
+coordinate system
+ 
+
+ align:start position:0%
+coordinate system
+and of course when you actually write
+
+ align:start position:0%
+and of course when you actually write
+ 
+
+ align:start position:0%
+and of course when you actually write
+out these components
+
+ align:start position:0%
+out these components
+ 
+
+ align:start position:0%
+out these components
+a very compact way of writing this is is
+
+ align:start position:0%
+a very compact way of writing this is is
+ 
+
+ align:start position:0%
+a very compact way of writing this is is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+the matrix that has the elements minus
+
+ align:start position:0%
+the matrix that has the elements minus
+ 
+
+ align:start position:0%
+the matrix that has the elements minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+one one one down the diagonal
+
+ align:start position:0%
+one one one down the diagonal
+ 
+
+ align:start position:0%
+one one one down the diagonal
+and zeros everywhere else okay this is a
+
+ align:start position:0%
+and zeros everywhere else okay this is a
+ 
+
+ align:start position:0%
+and zeros everywhere else okay this is a
+fairly common way of writing a diagonal
+
+ align:start position:0%
+fairly common way of writing a diagonal
+ 
+
+ align:start position:0%
+fairly common way of writing a diagonal
+matrix this just takes into account the
+
+ align:start position:0%
+matrix this just takes into account the
+ 
+
+ align:start position:0%
+matrix this just takes into account the
+fact that there's zeros everywhere else
+
+ align:start position:0%
+fact that there's zeros everywhere else
+ 
+
+ align:start position:0%
+fact that there's zeros everywhere else
+okay so i call this the metric tensor
+
+ align:start position:0%
+okay so i call this the metric tensor
+ 
+
+ align:start position:0%
+okay so i call this the metric tensor
+which kind of begs the question what's a
+
+ align:start position:0%
+which kind of begs the question what's a
+ 
+
+ align:start position:0%
+which kind of begs the question what's a
+tensor so this is where we concluded
+
+ align:start position:0%
+tensor so this is where we concluded
+ 
+
+ align:start position:0%
+tensor so this is where we concluded
+things last time i'm going to generally
+
+ align:start position:0%
+things last time i'm going to generally
+ 
+
+ align:start position:0%
+things last time i'm going to generally
+define a tensor of type
+
+ align:start position:0%
+define a tensor of type
+ 
+
+ align:start position:0%
+define a tensor of type
+0n we're going to change that 0 to
+
+ align:start position:0%
+0n we're going to change that 0 to
+ 
+
+ align:start position:0%
+0n we're going to change that 0 to
+something else by the end of today's
+
+ align:start position:0%
+something else by the end of today's
+ 
+
+ align:start position:0%
+something else by the end of today's
+lecture you can you'll be able to see
+
+ align:start position:0%
+lecture you can you'll be able to see
+ 
+
+ align:start position:0%
+lecture you can you'll be able to see
+where i'm going probably from a mile
+
+ align:start position:0%
+where i'm going probably from a mile
+ 
+
+ align:start position:0%
+where i'm going probably from a mile
+away let's just leave it like this for
+
+ align:start position:0%
+away let's just leave it like this for
+ 
+
+ align:start position:0%
+away let's just leave it like this for
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so a tensor of type 0n is
+
+ align:start position:0%
+so a tensor of type 0n is
+ 
+
+ align:start position:0%
+so a tensor of type 0n is
+you can think of as a function or a
+
+ align:start position:0%
+you can think of as a function or a
+ 
+
+ align:start position:0%
+you can think of as a function or a
+mapping of n vectors into lorentz
+
+ align:start position:0%
+mapping of n vectors into lorentz
+ 
+
+ align:start position:0%
+mapping of n vectors into lorentz
+invariant scalars
+
+ align:start position:0%
+invariant scalars
+ 
+
+ align:start position:0%
+invariant scalars
+which is linear in its n arguments
+
+ align:start position:0%
+which is linear in its n arguments
+ 
+
+ align:start position:0%
+which is linear in its n arguments
+okay so the inner product clearly falls
+
+ align:start position:0%
+okay so the inner product clearly falls
+ 
+
+ align:start position:0%
+okay so the inner product clearly falls
+into this category
+
+ align:start position:0%
+into this category
+ 
+
+ align:start position:0%
+into this category
+if i think of a dot b
+
+ align:start position:0%
+if i think of a dot b
+ 
+
+ align:start position:0%
+if i think of a dot b
+let's say this inner product is some
+
+ align:start position:0%
+let's say this inner product is some
+ 
+
+ align:start position:0%
+let's say this inner product is some
+number lowercase a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a will be a lowrance invariant okay uh i
+
+ align:start position:0%
+a will be a lowrance invariant okay uh i
+ 
+
+ align:start position:0%
+a will be a lowrance invariant okay uh i
+forgot to say this but the reason we
+
+ align:start position:0%
+forgot to say this but the reason we
+ 
+
+ align:start position:0%
+forgot to say this but the reason we
+defined the inner product in this way
+
+ align:start position:0%
+defined the inner product in this way
+ 
+
+ align:start position:0%
+defined the inner product in this way
+was that we are motivated by
+
+ align:start position:0%
+was that we are motivated by
+ 
+
+ align:start position:0%
+was that we are motivated by
+the invariant interval in space and time
+
+ align:start position:0%
+the invariant interval in space and time
+ 
+
+ align:start position:0%
+the invariant interval in space and time
+between two events we wanted to find a
+
+ align:start position:0%
+between two events we wanted to find a
+ 
+
+ align:start position:0%
+between two events we wanted to find a
+an inner product that duplicates its
+
+ align:start position:0%
+an inner product that duplicates its
+ 
+
+ align:start position:0%
+an inner product that duplicates its
+mathematical structure
+
+ align:start position:0%
+mathematical structure
+ 
+
+ align:start position:0%
+mathematical structure
+if i take one of these vectors multiply
+
+ align:start position:0%
+if i take one of these vectors multiply
+ 
+
+ align:start position:0%
+if i take one of these vectors multiply
+it by some scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linearity linearity is going to hold
+
+ align:start position:0%
+linearity linearity is going to hold
+ 
+
+ align:start position:0%
+linearity linearity is going to hold
+this will just be
+
+ align:start position:0%
+this will just be
+ 
+
+ align:start position:0%
+this will just be
+eta alpha beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is terrible notation i'm using
+
+ align:start position:0%
+okay this is terrible notation i'm using
+ 
+
+ align:start position:0%
+okay this is terrible notation i'm using
+divorce symbol alpha for both a
+
+ align:start position:0%
+divorce symbol alpha for both a
+ 
+
+ align:start position:0%
+divorce symbol alpha for both a
+pre-factor
+
+ align:start position:0%
+pre-factor
+ 
+
+ align:start position:0%
+pre-factor
+and an index minus five points to me
+
+ align:start position:0%
+and an index minus five points to me
+ 
+
+ align:start position:0%
+and an index minus five points to me
+let's call this gamma
+
+ align:start position:0%
+let's call this gamma
+ 
+
+ align:start position:0%
+let's call this gamma
+okay you can quickly convince yourself
+
+ align:start position:0%
+okay you can quickly convince yourself
+ 
+
+ align:start position:0%
+okay you can quickly convince yourself
+that just comes out and you get a factor
+
+ align:start position:0%
+that just comes out and you get a factor
+ 
+
+ align:start position:0%
+that just comes out and you get a factor
+of gamma on this you can do the same
+
+ align:start position:0%
+of gamma on this you can do the same
+ 
+
+ align:start position:0%
+of gamma on this you can do the same
+thing on the second slot
+
+ align:start position:0%
+thing on the second slot
+ 
+
+ align:start position:0%
+thing on the second slot
+uh if i take the dot product of
+
+ align:start position:0%
+uh if i take the dot product of
+ 
+
+ align:start position:0%
+uh if i take the dot product of
+a with the sum of two vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay etc you can keep going all the
+
+ align:start position:0%
+okay etc you can keep going all the
+ 
+
+ align:start position:0%
+okay etc you can keep going all the
+rules for linearity are going to hold
+
+ align:start position:0%
+rules for linearity are going to hold
+ 
+
+ align:start position:0%
+rules for linearity are going to hold
+i'm not going to step through them all
+
+ align:start position:0%
+i'm not going to step through them all
+ 
+
+ align:start position:0%
+i'm not going to step through them all
+you can sort of see where they all go so
+
+ align:start position:0%
+you can sort of see where they all go so
+ 
+
+ align:start position:0%
+you can sort of see where they all go so
+whenever i'm going to define a tensor
+
+ align:start position:0%
+whenever i'm going to define a tensor
+ 
+
+ align:start position:0%
+whenever i'm going to define a tensor
+in my head i'm imagining it's got
+
+ align:start position:0%
+in my head i'm imagining it's got
+ 
+
+ align:start position:0%
+in my head i'm imagining it's got
+properties like this that come along for
+
+ align:start position:0%
+properties like this that come along for
+ 
+
+ align:start position:0%
+properties like this that come along for
+the ride
+
+ align:start position:0%
+the ride
+ 
+
+ align:start position:0%
+the ride
+now especially when you see this defined
+
+ align:start position:0%
+now especially when you see this defined
+ 
+
+ align:start position:0%
+now especially when you see this defined
+in certain textbooks
+
+ align:start position:0%
+in certain textbooks
+ 
+
+ align:start position:0%
+in certain textbooks
+mtw is particularly fond of doing this
+
+ align:start position:0%
+mtw is particularly fond of doing this
+ 
+
+ align:start position:0%
+mtw is particularly fond of doing this
+so we come back to this idea that it's
+
+ align:start position:0%
+so we come back to this idea that it's
+ 
+
+ align:start position:0%
+so we come back to this idea that it's
+sort of a function or a mapping
+
+ align:start position:0%
+sort of a function or a mapping
+ 
+
+ align:start position:0%
+sort of a function or a mapping
+you can almost abstractly define
+
+ align:start position:0%
+you can almost abstractly define
+ 
+
+ align:start position:0%
+you can almost abstractly define
+the tensor as
+
+ align:start position:0%
+the tensor as
+ 
+
+ align:start position:0%
+the tensor as
+a mathematical sort of machine that's
+
+ align:start position:0%
+a mathematical sort of machine that's
+ 
+
+ align:start position:0%
+a mathematical sort of machine that's
+got two slots in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so several of the recommended textbooks
+
+ align:start position:0%
+so several of the recommended textbooks
+ 
+
+ align:start position:0%
+so several of the recommended textbooks
+we'll write down equations
+
+ align:start position:0%
+we'll write down equations
+ 
+
+ align:start position:0%
+we'll write down equations
+i'm going to put two lines over the
+
+ align:start position:0%
+i'm going to put two lines over the
+ 
+
+ align:start position:0%
+i'm going to put two lines over the
+symbol to sort of if you actually read
+
+ align:start position:0%
+symbol to sort of if you actually read
+ 
+
+ align:start position:0%
+symbol to sort of if you actually read
+this in for instance mtw or carol or
+
+ align:start position:0%
+this in for instance mtw or carol or
+ 
+
+ align:start position:0%
+this in for instance mtw or carol or
+something like that this will be written
+
+ align:start position:0%
+something like that this will be written
+ 
+
+ align:start position:0%
+something like that this will be written
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+boldface symbol it's hard to do on the
+
+ align:start position:0%
+boldface symbol it's hard to do on the
+ 
+
+ align:start position:0%
+boldface symbol it's hard to do on the
+blackboard so i'm just going to write
+
+ align:start position:0%
+blackboard so i'm just going to write
+ 
+
+ align:start position:0%
+blackboard so i'm just going to write
+double bars over it
+
+ align:start position:0%
+double bars over it
+ 
+
+ align:start position:0%
+double bars over it
+so if i imagine this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with my slots filled with these it's got
+
+ align:start position:0%
+with my slots filled with these it's got
+ 
+
+ align:start position:0%
+with my slots filled with these it's got
+two slots associated with it i fill it
+
+ align:start position:0%
+two slots associated with it i fill it
+ 
+
+ align:start position:0%
+two slots associated with it i fill it
+with those two vectors
+
+ align:start position:0%
+with those two vectors
+ 
+
+ align:start position:0%
+with those two vectors
+that is equivalent to saying
+
+ align:start position:0%
+that is equivalent to saying
+ 
+
+ align:start position:0%
+that is equivalent to saying
+a dot b which is equivalent to it in
+
+ align:start position:0%
+a dot b which is equivalent to it in
+ 
+
+ align:start position:0%
+a dot b which is equivalent to it in
+this component notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have repeatedly and the little bit of
+
+ align:start position:0%
+we have repeatedly and the little bit of
+ 
+
+ align:start position:0%
+we have repeatedly and the little bit of
+time we spent together i should say i
+
+ align:start position:0%
+time we spent together i should say i
+ 
+
+ align:start position:0%
+time we spent together i should say i
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+repeatedly a little bit of time we spent
+
+ align:start position:0%
+repeatedly a little bit of time we spent
+ 
+
+ align:start position:0%
+repeatedly a little bit of time we spent
+together emphasize the distinction
+
+ align:start position:0%
+together emphasize the distinction
+ 
+
+ align:start position:0%
+together emphasize the distinction
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+frame independent geometric objects
+
+ align:start position:0%
+frame independent geometric objects
+ 
+
+ align:start position:0%
+frame independent geometric objects
+things that reside in the manifold and
+
+ align:start position:0%
+things that reside in the manifold and
+ 
+
+ align:start position:0%
+things that reside in the manifold and
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+kind of an integral physical geometric
+
+ align:start position:0%
+kind of an integral physical geometric
+ 
+
+ align:start position:0%
+kind of an integral physical geometric
+sensibility of their own and their
+
+ align:start position:0%
+sensibility of their own and their
+ 
+
+ align:start position:0%
+sensibility of their own and their
+representations
+
+ align:start position:0%
+representations
+ 
+
+ align:start position:0%
+representations
+i have emphasized quite strongly that
+
+ align:start position:0%
+i have emphasized quite strongly that
+ 
+
+ align:start position:0%
+i have emphasized quite strongly that
+you should think
+
+ align:start position:0%
+you should think
+ 
+
+ align:start position:0%
+you should think
+of the vectors a and b as being
+
+ align:start position:0%
+of the vectors a and b as being
+ 
+
+ align:start position:0%
+of the vectors a and b as being
+geometric objects okay this is some
+
+ align:start position:0%
+geometric objects okay this is some
+ 
+
+ align:start position:0%
+geometric objects okay this is some
+thing that is pointing in space time we
+
+ align:start position:0%
+thing that is pointing in space time we
+ 
+
+ align:start position:0%
+thing that is pointing in space time we
+all agree that this points if that's a
+
+ align:start position:0%
+all agree that this points if that's a
+ 
+
+ align:start position:0%
+all agree that this points if that's a
+displacement vector
+
+ align:start position:0%
+displacement vector
+ 
+
+ align:start position:0%
+displacement vector
+it points from event a to from event one
+
+ align:start position:0%
+it points from event a to from event one
+ 
+
+ align:start position:0%
+it points from event a to from event one
+to event two okay
+
+ align:start position:0%
+to event two okay
+ 
+
+ align:start position:0%
+to event two okay
+everyone agrees on that geometric
+
+ align:start position:0%
+everyone agrees on that geometric
+ 
+
+ align:start position:0%
+everyone agrees on that geometric
+reality of this
+
+ align:start position:0%
+reality of this
+ 
+
+ align:start position:0%
+reality of this
+uh different observers may represent it
+
+ align:start position:0%
+uh different observers may represent it
+ 
+
+ align:start position:0%
+uh different observers may represent it
+using different components okay and
+
+ align:start position:0%
+using different components okay and
+ 
+
+ align:start position:0%
+using different components okay and
+that's just because they're using
+
+ align:start position:0%
+that's just because they're using
+ 
+
+ align:start position:0%
+that's just because they're using
+different coordinate systems
+
+ align:start position:0%
+different coordinate systems
+ 
+
+ align:start position:0%
+different coordinate systems
+so when i write down something like this
+
+ align:start position:0%
+so when i write down something like this
+ 
+
+ align:start position:0%
+so when i write down something like this
+so let's go back to where i wrote before
+
+ align:start position:0%
+so let's go back to where i wrote before
+ 
+
+ align:start position:0%
+so let's go back to where i wrote before
+this is going to turn into some frame
+
+ align:start position:0%
+this is going to turn into some frame
+ 
+
+ align:start position:0%
+this is going to turn into some frame
+independence
+
+ align:start position:0%
+independence
+ 
+
+ align:start position:0%
+independence
+lorentz scalar a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what i like to call a frame
+
+ align:start position:0%
+so this is what i like to call a frame
+ 
+
+ align:start position:0%
+so this is what i like to call a frame
+independent object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame a lorenz independent geometric
+
+ align:start position:0%
+frame a lorenz independent geometric
+ 
+
+ align:start position:0%
+frame a lorenz independent geometric
+object as is this scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so therefore the tensor must be a
+
+ align:start position:0%
+and so therefore the tensor must be a
+ 
+
+ align:start position:0%
+and so therefore the tensor must be a
+frame independent geometric object as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's a lot of words around the
+
+ align:start position:0%
+okay that's a lot of words around the
+ 
+
+ align:start position:0%
+okay that's a lot of words around the
+blackboard but i really want to nail
+
+ align:start position:0%
+blackboard but i really want to nail
+ 
+
+ align:start position:0%
+blackboard but i really want to nail
+that point home
+
+ align:start position:0%
+that point home
+ 
+
+ align:start position:0%
+that point home
+so tensors just like vectors
+
+ align:start position:0%
+so tensors just like vectors
+ 
+
+ align:start position:0%
+so tensors just like vectors
+think of them as geometric objects that
+
+ align:start position:0%
+think of them as geometric objects that
+ 
+
+ align:start position:0%
+think of them as geometric objects that
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+you know an intrinsic sort of geometric
+
+ align:start position:0%
+you know an intrinsic sort of geometric
+ 
+
+ align:start position:0%
+you know an intrinsic sort of geometric
+meaning associated with them that lives
+
+ align:start position:0%
+meaning associated with them that lives
+ 
+
+ align:start position:0%
+meaning associated with them that lives
+in space time
+
+ align:start position:0%
+in space time
+ 
+
+ align:start position:0%
+in space time
+we will talk about certain examples of
+
+ align:start position:0%
+we will talk about certain examples of
+ 
+
+ align:start position:0%
+we will talk about certain examples of
+them okay you guys all have some
+
+ align:start position:0%
+them okay you guys all have some
+ 
+
+ align:start position:0%
+them okay you guys all have some
+intuition about vectors because you've
+
+ align:start position:0%
+intuition about vectors because you've
+ 
+
+ align:start position:0%
+intuition about vectors because you've
+been doing vectors ever since you took
+
+ align:start position:0%
+been doing vectors ever since you took
+ 
+
+ align:start position:0%
+been doing vectors ever since you took
+your first kindergarten
+
+ align:start position:0%
+your first kindergarten
+ 
+
+ align:start position:0%
+your first kindergarten
+physics course and so you know that
+
+ align:start position:0%
+physics course and so you know that
+ 
+
+ align:start position:0%
+physics course and so you know that
+there's some kind of an object that
+
+ align:start position:0%
+there's some kind of an object that
+ 
+
+ align:start position:0%
+there's some kind of an object that
+points in a certain direction
+
+ align:start position:0%
+points in a certain direction
+ 
+
+ align:start position:0%
+points in a certain direction
+tensors are a little bit more
+
+ align:start position:0%
+tensors are a little bit more
+ 
+
+ align:start position:0%
+tensors are a little bit more
+challenging in many cases to develop an
+
+ align:start position:0%
+challenging in many cases to develop an
+ 
+
+ align:start position:0%
+challenging in many cases to develop an
+intuition for
+
+ align:start position:0%
+intuition for
+ 
+
+ align:start position:0%
+intuition for
+okay some of them really do have a
+
+ align:start position:0%
+okay some of them really do have a
+ 
+
+ align:start position:0%
+okay some of them really do have a
+fairly simple geometric interpretation
+
+ align:start position:0%
+fairly simple geometric interpretation
+ 
+
+ align:start position:0%
+fairly simple geometric interpretation
+you can kind of think of them as
+
+ align:start position:0%
+you can kind of think of them as
+ 
+
+ align:start position:0%
+you can kind of think of them as
+for instance we're going to introduce
+
+ align:start position:0%
+for instance we're going to introduce
+ 
+
+ align:start position:0%
+for instance we're going to introduce
+one a little bit which describes the
+
+ align:start position:0%
+one a little bit which describes the
+ 
+
+ align:start position:0%
+one a little bit which describes the
+flow of energy and
+
+ align:start position:0%
+flow of energy and
+ 
+
+ align:start position:0%
+flow of energy and
+momentum in space time and so it'll have
+
+ align:start position:0%
+momentum in space time and so it'll have
+ 
+
+ align:start position:0%
+momentum in space time and so it'll have
+two in this indices associated with it
+
+ align:start position:0%
+two in this indices associated with it
+ 
+
+ align:start position:0%
+two in this indices associated with it
+and those indices
+
+ align:start position:0%
+and those indices
+ 
+
+ align:start position:0%
+and those indices
+tell me about what component of energy
+
+ align:start position:0%
+tell me about what component of energy
+ 
+
+ align:start position:0%
+tell me about what component of energy
+or momentum is flowing in a particular
+
+ align:start position:0%
+or momentum is flowing in a particular
+ 
+
+ align:start position:0%
+or momentum is flowing in a particular
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+really easy to interpret that some of
+
+ align:start position:0%
+really easy to interpret that some of
+ 
+
+ align:start position:0%
+really easy to interpret that some of
+the others not so much okay
+
+ align:start position:0%
+the others not so much okay
+ 
+
+ align:start position:0%
+the others not so much okay
+um nonetheless they do have this
+
+ align:start position:0%
+um nonetheless they do have this
+ 
+
+ align:start position:0%
+um nonetheless they do have this
+geometric meaning
+
+ align:start position:0%
+geometric meaning
+ 
+
+ align:start position:0%
+geometric meaning
+underneath the hood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's bound up in the fact that if
+
+ align:start position:0%
+and that's bound up in the fact that if
+ 
+
+ align:start position:0%
+and that's bound up in the fact that if
+i put
+
+ align:start position:0%
+i put
+ 
+
+ align:start position:0%
+i put
+frame independent geometric objects into
+
+ align:start position:0%
+frame independent geometric objects into
+ 
+
+ align:start position:0%
+frame independent geometric objects into
+all the slots i get a real num
+
+ align:start position:0%
+all the slots i get a real num
+ 
+
+ align:start position:0%
+all the slots i get a real num
+a lorentz and variant number out of it
+
+ align:start position:0%
+a lorentz and variant number out of it
+ 
+
+ align:start position:0%
+a lorentz and variant number out of it
+it's the only way that that can sort of
+
+ align:start position:0%
+it's the only way that that can sort of
+ 
+
+ align:start position:0%
+it's the only way that that can sort of
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+um but one reason why i'm going through
+
+ align:start position:0%
+um but one reason why i'm going through
+ 
+
+ align:start position:0%
+um but one reason why i'm going through
+this is that just like with vectors
+
+ align:start position:0%
+this is that just like with vectors
+ 
+
+ align:start position:0%
+this is that just like with vectors
+different observers different frames
+
+ align:start position:0%
+different observers different frames
+ 
+
+ align:start position:0%
+different observers different frames
+will get different
+
+ align:start position:0%
+will get different
+ 
+
+ align:start position:0%
+will get different
+components in general so there will be
+
+ align:start position:0%
+components in general so there will be
+ 
+
+ align:start position:0%
+components in general so there will be
+different representations
+
+ align:start position:0%
+different representations
+ 
+
+ align:start position:0%
+different representations
+according to different observers write
+
+ align:start position:0%
+according to different observers write
+ 
+
+ align:start position:0%
+according to different observers write
+down the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you want to get a particular
+
+ align:start position:0%
+so if you want to get a particular
+ 
+
+ align:start position:0%
+so if you want to get a particular
+observer's
+
+ align:start position:0%
+observer's
+ 
+
+ align:start position:0%
+observer's
+components out of the tensor there's
+
+ align:start position:0%
+components out of the tensor there's
+ 
+
+ align:start position:0%
+components out of the tensor there's
+actually a very simple recipe for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all you do is you take your tensor
+
+ align:start position:0%
+all you do is you take your tensor
+ 
+
+ align:start position:0%
+all you do is you take your tensor
+and into its slots you plug in
+
+ align:start position:0%
+and into its slots you plug in
+ 
+
+ align:start position:0%
+and into its slots you plug in
+the basis vectors that that observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if i want to get
+
+ align:start position:0%
+okay so if i want to get
+ 
+
+ align:start position:0%
+okay so if i want to get
+the components and this unfortunately is
+
+ align:start position:0%
+the components and this unfortunately is
+ 
+
+ align:start position:0%
+the components and this unfortunately is
+a fairly stupid example
+
+ align:start position:0%
+a fairly stupid example
+ 
+
+ align:start position:0%
+a fairly stupid example
+but it's the only one we've got at the
+
+ align:start position:0%
+but it's the only one we've got at the
+ 
+
+ align:start position:0%
+but it's the only one we've got at the
+moment so let's just work with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i take the tensor eta the special
+
+ align:start position:0%
+if i take the tensor eta the special
+ 
+
+ align:start position:0%
+if i take the tensor eta the special
+relativity
+
+ align:start position:0%
+relativity
+ 
+
+ align:start position:0%
+relativity
+basis give me the special relativity
+
+ align:start position:0%
+basis give me the special relativity
+ 
+
+ align:start position:0%
+basis give me the special relativity
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+i plug in some observers basis vectors
+
+ align:start position:0%
+i plug in some observers basis vectors
+ 
+
+ align:start position:0%
+i plug in some observers basis vectors
+into this thing
+
+ align:start position:0%
+into this thing
+ 
+
+ align:start position:0%
+into this thing
+this by definition is eta alpha beta
+
+ align:start position:0%
+this by definition is eta alpha beta
+ 
+
+ align:start position:0%
+this by definition is eta alpha beta
+suppose i have a different observer who
+
+ align:start position:0%
+suppose i have a different observer who
+ 
+
+ align:start position:0%
+suppose i have a different observer who
+comes along okay someone who we're doing
+
+ align:start position:0%
+comes along okay someone who we're doing
+ 
+
+ align:start position:0%
+comes along okay someone who we're doing
+special relativity so someone who's
+
+ align:start position:0%
+special relativity so someone who's
+ 
+
+ align:start position:0%
+special relativity so someone who's
+dashing through the room at three
+
+ align:start position:0%
+dashing through the room at three
+ 
+
+ align:start position:0%
+dashing through the room at three
+quarters of the speed of light
+
+ align:start position:0%
+quarters of the speed of light
+ 
+
+ align:start position:0%
+quarters of the speed of light
+i want to know what their uh
+
+ align:start position:0%
+i want to know what their uh
+ 
+
+ align:start position:0%
+i want to know what their uh
+what their components would be well
+
+ align:start position:0%
+what their components would be well
+ 
+
+ align:start position:0%
+what their components would be well
+what i do is i just plug into the slots
+
+ align:start position:0%
+what i do is i just plug into the slots
+ 
+
+ align:start position:0%
+what i do is i just plug into the slots
+let's put bars on the components to
+
+ align:start position:0%
+let's put bars on the components to
+ 
+
+ align:start position:0%
+let's put bars on the components to
+denote this other observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay do this operation for this
+
+ align:start position:0%
+okay do this operation for this
+ 
+
+ align:start position:0%
+okay do this operation for this
+other observer set of basis vectors and
+
+ align:start position:0%
+other observer set of basis vectors and
+ 
+
+ align:start position:0%
+other observer set of basis vectors and
+you will get the complements that they
+
+ align:start position:0%
+you will get the complements that they
+ 
+
+ align:start position:0%
+you will get the complements that they
+will measure
+
+ align:start position:0%
+will measure
+ 
+
+ align:start position:0%
+will measure
+now one reason why i'm going through
+
+ align:start position:0%
+now one reason why i'm going through
+ 
+
+ align:start position:0%
+now one reason why i'm going through
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that last time we talked about how to
+
+ align:start position:0%
+is that last time we talked about how to
+ 
+
+ align:start position:0%
+is that last time we talked about how to
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+basis vectors between different
+
+ align:start position:0%
+basis vectors between different
+ 
+
+ align:start position:0%
+basis vectors between different
+reference frames okay we know that these
+
+ align:start position:0%
+reference frames okay we know that these
+ 
+
+ align:start position:0%
+reference frames okay we know that these
+guys are just related to one another
+
+ align:start position:0%
+guys are just related to one another
+ 
+
+ align:start position:0%
+guys are just related to one another
+by a lawrence transformation matrix so
+
+ align:start position:0%
+by a lawrence transformation matrix so
+ 
+
+ align:start position:0%
+by a lawrence transformation matrix so
+let's just take this a step further so
+
+ align:start position:0%
+let's just take this a step further so
+ 
+
+ align:start position:0%
+let's just take this a step further so
+this is telling me
+
+ align:start position:0%
+this is telling me
+ 
+
+ align:start position:0%
+this is telling me
+that the components of the metric
+
+ align:start position:0%
+that the components of the metric
+ 
+
+ align:start position:0%
+that the components of the metric
+in this barred frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're going to be what i get when i
+
+ align:start position:0%
+they're going to be what i get when i
+ 
+
+ align:start position:0%
+they're going to be what i get when i
+put into the slots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay those are the basis vectors in the
+
+ align:start position:0%
+okay those are the basis vectors in the
+ 
+
+ align:start position:0%
+okay those are the basis vectors in the
+bard frame using the lorentz
+
+ align:start position:0%
+bard frame using the lorentz
+ 
+
+ align:start position:0%
+bard frame using the lorentz
+transformation matrix to go from the
+
+ align:start position:0%
+transformation matrix to go from the
+ 
+
+ align:start position:0%
+transformation matrix to go from the
+onboard frame to the bart frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now remember again this is one of those
+
+ align:start position:0%
+now remember again this is one of those
+ 
+
+ align:start position:0%
+now remember again this is one of those
+places where if you're sort of just
+
+ align:start position:0%
+places where if you're sort of just
+ 
+
+ align:start position:0%
+places where if you're sort of just
+becoming comfortable with
+
+ align:start position:0%
+becoming comfortable with
+ 
+
+ align:start position:0%
+becoming comfortable with
+the index notation your temptation at
+
+ align:start position:0%
+the index notation your temptation at
+ 
+
+ align:start position:0%
+the index notation your temptation at
+this stage is always to go these are
+
+ align:start position:0%
+this stage is always to go these are
+ 
+
+ align:start position:0%
+this stage is always to go these are
+matrices i should start doing matrix
+
+ align:start position:0%
+matrices i should start doing matrix
+ 
+
+ align:start position:0%
+matrices i should start doing matrix
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+okay if you set that urge
+
+ align:start position:0%
+okay if you set that urge
+ 
+
+ align:start position:0%
+okay if you set that urge
+within you aside you go no no no those
+
+ align:start position:0%
+within you aside you go no no no those
+ 
+
+ align:start position:0%
+within you aside you go no no no those
+are just a set of 16 numbers
+
+ align:start position:0%
+are just a set of 16 numbers
+ 
+
+ align:start position:0%
+are just a set of 16 numbers
+okay for any particular set of
+
+ align:start position:0%
+okay for any particular set of
+ 
+
+ align:start position:0%
+okay for any particular set of
+components i can just pull them out
+
+ align:start position:0%
+components i can just pull them out
+ 
+
+ align:start position:0%
+components i can just pull them out
+so because of the linearity of all these
+
+ align:start position:0%
+so because of the linearity of all these
+ 
+
+ align:start position:0%
+so because of the linearity of all these
+slots with this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this just becomes those two lorentz
+
+ align:start position:0%
+this just becomes those two lorentz
+ 
+
+ align:start position:0%
+this just becomes those two lorentz
+transformation matrices
+
+ align:start position:0%
+transformation matrices
+ 
+
+ align:start position:0%
+transformation matrices
+acting on the abstract metric tensor
+
+ align:start position:0%
+acting on the abstract metric tensor
+ 
+
+ align:start position:0%
+acting on the abstract metric tensor
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the unbarred uh basis vectors in its
+
+ align:start position:0%
+the unbarred uh basis vectors in its
+ 
+
+ align:start position:0%
+the unbarred uh basis vectors in its
+slots
+
+ align:start position:0%
+slots
+ 
+
+ align:start position:0%
+slots
+and this we already know okay this is by
+
+ align:start position:0%
+and this we already know okay this is by
+ 
+
+ align:start position:0%
+and this we already know okay this is by
+definition this is just
+
+ align:start position:0%
+definition this is just
+ 
+
+ align:start position:0%
+definition this is just
+adam you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repeat this exercise for any tensor you
+
+ align:start position:0%
+repeat this exercise for any tensor you
+ 
+
+ align:start position:0%
+repeat this exercise for any tensor you
+care to write down any zero end tensor
+
+ align:start position:0%
+care to write down any zero end tensor
+ 
+
+ align:start position:0%
+care to write down any zero end tensor
+you care to write down
+
+ align:start position:0%
+you care to write down
+ 
+
+ align:start position:0%
+you care to write down
+go through all this kind of uh
+
+ align:start position:0%
+go through all this kind of uh
+ 
+
+ align:start position:0%
+go through all this kind of uh
+manipulation and you
+
+ align:start position:0%
+manipulation and you
+ 
+
+ align:start position:0%
+manipulation and you
+always find that there's a very simple
+
+ align:start position:0%
+always find that there's a very simple
+ 
+
+ align:start position:0%
+always find that there's a very simple
+algorithm for getting
+
+ align:start position:0%
+algorithm for getting
+ 
+
+ align:start position:0%
+algorithm for getting
+the components in let's call it the bard
+
+ align:start position:0%
+the components in let's call it the bard
+ 
+
+ align:start position:0%
+the components in let's call it the bard
+observers frame as
+
+ align:start position:0%
+observers frame as
+ 
+
+ align:start position:0%
+observers frame as
+converted from the unbarred observers
+
+ align:start position:0%
+converted from the unbarred observers
+ 
+
+ align:start position:0%
+converted from the unbarred observers
+frame essentially you just hit it with a
+
+ align:start position:0%
+frame essentially you just hit it with a
+ 
+
+ align:start position:0%
+frame essentially you just hit it with a
+bunch of lorentz transfer matrices
+
+ align:start position:0%
+bunch of lorentz transfer matrices
+ 
+
+ align:start position:0%
+bunch of lorentz transfer matrices
+and you know as an old professor of mine
+
+ align:start position:0%
+and you know as an old professor of mine
+ 
+
+ align:start position:0%
+and you know as an old professor of mine
+like to say at this point line up the
+
+ align:start position:0%
+like to say at this point line up the
+ 
+
+ align:start position:0%
+like to say at this point line up the
+indices
+
+ align:start position:0%
+indices
+ 
+
+ align:start position:0%
+indices
+that's really all we're doing is we're
+
+ align:start position:0%
+that's really all we're doing is we're
+ 
+
+ align:start position:0%
+that's really all we're doing is we're
+just going to line up the muse to
+
+ align:start position:0%
+just going to line up the muse to
+ 
+
+ align:start position:0%
+just going to line up the muse to
+convert them to alpha bars alpha bar
+
+ align:start position:0%
+convert them to alpha bars alpha bar
+ 
+
+ align:start position:0%
+convert them to alpha bars alpha bar
+here mu there
+
+ align:start position:0%
+here mu there
+ 
+
+ align:start position:0%
+here mu there
+put this guy here i want to convert my
+
+ align:start position:0%
+put this guy here i want to convert my
+ 
+
+ align:start position:0%
+put this guy here i want to convert my
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+into a beta bar i put my matrix there
+
+ align:start position:0%
+into a beta bar i put my matrix there
+ 
+
+ align:start position:0%
+into a beta bar i put my matrix there
+boom just line up the indices and we're
+
+ align:start position:0%
+boom just line up the indices and we're
+ 
+
+ align:start position:0%
+boom just line up the indices and we're
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+now this is as i kind of emphasized
+
+ align:start position:0%
+now this is as i kind of emphasized
+ 
+
+ align:start position:0%
+now this is as i kind of emphasized
+a fairly stupid example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you take
+
+ align:start position:0%
+because if you take
+ 
+
+ align:start position:0%
+because if you take
+the diagonal of minus one one one one
+
+ align:start position:0%
+the diagonal of minus one one one one
+ 
+
+ align:start position:0%
+the diagonal of minus one one one one
+and you apply the most god-awful
+
+ align:start position:0%
+and you apply the most god-awful
+ 
+
+ align:start position:0%
+and you apply the most god-awful
+lawrence transformation you care to
+
+ align:start position:0%
+lawrence transformation you care to
+ 
+
+ align:start position:0%
+lawrence transformation you care to
+write down to it you do all the matrix
+
+ align:start position:0%
+write down to it you do all the matrix
+ 
+
+ align:start position:0%
+write down to it you do all the matrix
+uh manipulation and you line it all up
+
+ align:start position:0%
+uh manipulation and you line it all up
+ 
+
+ align:start position:0%
+uh manipulation and you line it all up
+what you'll end up finding
+
+ align:start position:0%
+what you'll end up finding
+ 
+
+ align:start position:0%
+what you'll end up finding
+is that this is the diagonal of minus
+
+ align:start position:0%
+is that this is the diagonal of minus
+ 
+
+ align:start position:0%
+is that this is the diagonal of minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+one one one in all frames
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's actually one of the defining
+
+ align:start position:0%
+okay that's actually one of the defining
+ 
+
+ align:start position:0%
+okay that's actually one of the defining
+characteristics of the metric of special
+
+ align:start position:0%
+characteristics of the metric of special
+ 
+
+ align:start position:0%
+characteristics of the metric of special
+relativity if you're working
+
+ align:start position:0%
+relativity if you're working
+ 
+
+ align:start position:0%
+relativity if you're working
+curvilinear coordinates the metric is
+
+ align:start position:0%
+curvilinear coordinates the metric is
+ 
+
+ align:start position:0%
+curvilinear coordinates the metric is
+always minus one one one one to
+
+ align:start position:0%
+always minus one one one one to
+ 
+
+ align:start position:0%
+always minus one one one one to
+all observers so
+
+ align:start position:0%
+all observers so
+ 
+
+ align:start position:0%
+all observers so
+you know the recipe holds in general
+
+ align:start position:0%
+you know the recipe holds in general
+ 
+
+ align:start position:0%
+you know the recipe holds in general
+this will hold whenever we are studying
+
+ align:start position:0%
+this will hold whenever we are studying
+ 
+
+ align:start position:0%
+this will hold whenever we are studying
+tensors from now and from henceforth
+
+ align:start position:0%
+tensors from now and from henceforth
+ 
+
+ align:start position:0%
+tensors from now and from henceforth
+just so happens that this first example
+
+ align:start position:0%
+just so happens that this first example
+ 
+
+ align:start position:0%
+just so happens that this first example
+we were given is a kind of a dumb one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonetheless learn the lesson
+
+ align:start position:0%
+nonetheless learn the lesson
+ 
+
+ align:start position:0%
+nonetheless learn the lesson
+and overlook the example and wisdom
+
+ align:start position:0%
+and overlook the example and wisdom
+ 
+
+ align:start position:0%
+and overlook the example and wisdom
+shall be yours
+
+ align:start position:0%
+shall be yours
+ 
+
+ align:start position:0%
+shall be yours
+okay i want to spend a few moments
+
+ align:start position:0%
+okay i want to spend a few moments
+ 
+
+ align:start position:0%
+okay i want to spend a few moments
+talking about a particular
+
+ align:start position:0%
+talking about a particular
+ 
+
+ align:start position:0%
+talking about a particular
+subset of tensors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the zero end tensors
+
+ align:start position:0%
+of the zero end tensors
+ 
+
+ align:start position:0%
+of the zero end tensors
+where n equals one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a subset of tensors in general
+
+ align:start position:0%
+this is a subset of tensors in general
+ 
+
+ align:start position:0%
+this is a subset of tensors in general
+that is known in many textbooks as
+
+ align:start position:0%
+that is known in many textbooks as
+ 
+
+ align:start position:0%
+that is known in many textbooks as
+one forms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for reasons that i will elaborate on in
+
+ align:start position:0%
+for reasons that i will elaborate on in
+ 
+
+ align:start position:0%
+for reasons that i will elaborate on in
+probably 10 or so minutes
+
+ align:start position:0%
+probably 10 or so minutes
+ 
+
+ align:start position:0%
+probably 10 or so minutes
+these are also sometimes called dual
+
+ align:start position:0%
+these are also sometimes called dual
+ 
+
+ align:start position:0%
+these are also sometimes called dual
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just set if that's sort of making
+
+ align:start position:0%
+and just set if that's sort of making
+ 
+
+ align:start position:0%
+and just set if that's sort of making
+some neurons uh
+
+ align:start position:0%
+some neurons uh
+ 
+
+ align:start position:0%
+some neurons uh
+light up in your head okay set that
+
+ align:start position:0%
+light up in your head okay set that
+ 
+
+ align:start position:0%
+light up in your head okay set that
+aside for a moment
+
+ align:start position:0%
+aside for a moment
+ 
+
+ align:start position:0%
+aside for a moment
+i want to uh carefully go through them
+
+ align:start position:0%
+i want to uh carefully go through them
+ 
+
+ align:start position:0%
+i want to uh carefully go through them
+before i indicate the manner in which
+
+ align:start position:0%
+before i indicate the manner in which
+ 
+
+ align:start position:0%
+before i indicate the manner in which
+there is a duality
+
+ align:start position:0%
+there is a duality
+ 
+
+ align:start position:0%
+there is a duality
+that is being applied here so if we go
+
+ align:start position:0%
+that is being applied here so if we go
+ 
+
+ align:start position:0%
+that is being applied here so if we go
+back to the
+
+ align:start position:0%
+back to the
+ 
+
+ align:start position:0%
+back to the
+uh the definition of a tensor
+
+ align:start position:0%
+uh the definition of a tensor
+ 
+
+ align:start position:0%
+uh the definition of a tensor
+this tells us that a one form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a mapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from a single vector
+
+ align:start position:0%
+from a single vector
+ 
+
+ align:start position:0%
+from a single vector
+to the lorenz invariant scalars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so using some notation that i will
+
+ align:start position:0%
+so using some notation that i will
+ 
+
+ align:start position:0%
+so using some notation that i will
+probably only use in this lecture
+
+ align:start position:0%
+probably only use in this lecture
+ 
+
+ align:start position:0%
+probably only use in this lecture
+because we're going to sort of move past
+
+ align:start position:0%
+because we're going to sort of move past
+ 
+
+ align:start position:0%
+because we're going to sort of move past
+this notation pretty soon
+
+ align:start position:0%
+this notation pretty soon
+ 
+
+ align:start position:0%
+this notation pretty soon
+let's say a one form i'm going to denote
+
+ align:start position:0%
+let's say a one form i'm going to denote
+ 
+
+ align:start position:0%
+let's say a one form i'm going to denote
+this with an over tilde on it
+
+ align:start position:0%
+this with an over tilde on it
+ 
+
+ align:start position:0%
+this with an over tilde on it
+so let's say p is a one form
+
+ align:start position:0%
+so let's say p is a one form
+ 
+
+ align:start position:0%
+so let's say p is a one form
+it will have in this sort of abstract
+
+ align:start position:0%
+it will have in this sort of abstract
+ 
+
+ align:start position:0%
+it will have in this sort of abstract
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+a single slot so i put the vector a into
+
+ align:start position:0%
+a single slot so i put the vector a into
+ 
+
+ align:start position:0%
+a single slot so i put the vector a into
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and this then gives me some
+
+ align:start position:0%
+and this then gives me some
+ 
+
+ align:start position:0%
+and this then gives me some
+scalar out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops yeah whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meant to use to the other board so in my
+
+ align:start position:0%
+meant to use to the other board so in my
+ 
+
+ align:start position:0%
+meant to use to the other board so in my
+notes i go through some stuff indicating
+
+ align:start position:0%
+notes i go through some stuff indicating
+ 
+
+ align:start position:0%
+notes i go through some stuff indicating
+that this guy
+
+ align:start position:0%
+that this guy
+ 
+
+ align:start position:0%
+that this guy
+is it's a linear operation but that's
+
+ align:start position:0%
+is it's a linear operation but that's
+ 
+
+ align:start position:0%
+is it's a linear operation but that's
+obvious because it just inherits all the
+
+ align:start position:0%
+obvious because it just inherits all the
+ 
+
+ align:start position:0%
+obvious because it just inherits all the
+properties from tensors so i'm not going
+
+ align:start position:0%
+properties from tensors so i'm not going
+ 
+
+ align:start position:0%
+properties from tensors so i'm not going
+to go through that if you want to
+
+ align:start position:0%
+to go through that if you want to
+ 
+
+ align:start position:0%
+to go through that if you want to
+double check from the details there in
+
+ align:start position:0%
+double check from the details there in
+ 
+
+ align:start position:0%
+double check from the details there in
+the notes that have been posted
+
+ align:start position:0%
+the notes that have been posted
+ 
+
+ align:start position:0%
+the notes that have been posted
+just like with the tensors i extract
+
+ align:start position:0%
+just like with the tensors i extract
+ 
+
+ align:start position:0%
+just like with the tensors i extract
+components from this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by putting my basis vectors inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i take my one form p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i put in my alpha's basis vector
+
+ align:start position:0%
+and i put in my alpha's basis vector
+ 
+
+ align:start position:0%
+and i put in my alpha's basis vector
+this gives me the alpha component of the
+
+ align:start position:0%
+this gives me the alpha component of the
+ 
+
+ align:start position:0%
+this gives me the alpha component of the
+one form
+
+ align:start position:0%
+one form
+ 
+
+ align:start position:0%
+one form
+notice it's in the downstairs position
+
+ align:start position:0%
+notice it's in the downstairs position
+ 
+
+ align:start position:0%
+notice it's in the downstairs position
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when i uh one of the reasons why i
+
+ align:start position:0%
+when i uh one of the reasons why i
+ 
+
+ align:start position:0%
+when i uh one of the reasons why i
+want to sort of go through this step is
+
+ align:start position:0%
+want to sort of go through this step is
+ 
+
+ align:start position:0%
+want to sort of go through this step is
+it gives me a way to sort of think about
+
+ align:start position:0%
+it gives me a way to sort of think about
+ 
+
+ align:start position:0%
+it gives me a way to sort of think about
+how i get
+
+ align:start position:0%
+how i get
+ 
+
+ align:start position:0%
+how i get
+what this scale what's going on with
+
+ align:start position:0%
+what this scale what's going on with
+ 
+
+ align:start position:0%
+what this scale what's going on with
+this scalar that i wrote down on the top
+
+ align:start position:0%
+this scalar that i wrote down on the top
+ 
+
+ align:start position:0%
+this scalar that i wrote down on the top
+board here so what is the scalar that i
+
+ align:start position:0%
+board here so what is the scalar that i
+ 
+
+ align:start position:0%
+board here so what is the scalar that i
+get by putting a vector into my one form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i take this put my vector in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i use the fact that i can write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my vector my vector using its components
+
+ align:start position:0%
+my vector my vector using its components
+ 
+
+ align:start position:0%
+my vector my vector using its components
+and the basis vector
+
+ align:start position:0%
+and the basis vector
+ 
+
+ align:start position:0%
+and the basis vector
+i use linearity to pull this guy out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the scalar that i get by doing this
+
+ align:start position:0%
+so the scalar that i get by doing this
+ 
+
+ align:start position:0%
+so the scalar that i get by doing this
+is just the scalar that one gets
+
+ align:start position:0%
+is just the scalar that one gets
+ 
+
+ align:start position:0%
+is just the scalar that one gets
+by contracting the upstairs
+
+ align:start position:0%
+by contracting the upstairs
+ 
+
+ align:start position:0%
+by contracting the upstairs
+components that i use to set up my
+
+ align:start position:0%
+components that i use to set up my
+ 
+
+ align:start position:0%
+components that i use to set up my
+vector with the downstairs components i
+
+ align:start position:0%
+vector with the downstairs components i
+ 
+
+ align:start position:0%
+vector with the downstairs components i
+use to set up my one form
+
+ align:start position:0%
+use to set up my one form
+ 
+
+ align:start position:0%
+use to set up my one form
+okay this is an operation that is called
+
+ align:start position:0%
+okay this is an operation that is called
+ 
+
+ align:start position:0%
+okay this is an operation that is called
+contraction
+
+ align:start position:0%
+contraction
+ 
+
+ align:start position:0%
+contraction
+uh for reasons that i hope are fairly
+
+ align:start position:0%
+uh for reasons that i hope are fairly
+ 
+
+ align:start position:0%
+uh for reasons that i hope are fairly
+obvious so let me define a few other
+
+ align:start position:0%
+obvious so let me define a few other
+ 
+
+ align:start position:0%
+obvious so let me define a few other
+characteristics of this thing and in
+
+ align:start position:0%
+characteristics of this thing and in
+ 
+
+ align:start position:0%
+characteristics of this thing and in
+just a few moments
+
+ align:start position:0%
+just a few moments
+ 
+
+ align:start position:0%
+just a few moments
+we'll see what this is good for
+
+ align:start position:0%
+we'll see what this is good for
+ 
+
+ align:start position:0%
+we'll see what this is good for
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+one of the things i'm going to want to
+
+ align:start position:0%
+one of the things i'm going to want to
+ 
+
+ align:start position:0%
+one of the things i'm going to want to
+do is change the representation of this
+
+ align:start position:0%
+do is change the representation of this
+ 
+
+ align:start position:0%
+do is change the representation of this
+thing so i'm going to want to know how
+
+ align:start position:0%
+thing so i'm going to want to know how
+ 
+
+ align:start position:0%
+thing so i'm going to want to know how
+these components transform between
+
+ align:start position:0%
+these components transform between
+ 
+
+ align:start position:0%
+these components transform between
+different frames of reference but we've
+
+ align:start position:0%
+different frames of reference but we've
+ 
+
+ align:start position:0%
+different frames of reference but we've
+already done that okay we did this using
+
+ align:start position:0%
+already done that okay we did this using
+ 
+
+ align:start position:0%
+already done that okay we did this using
+tensors and this is just the tensor
+
+ align:start position:0%
+tensors and this is just the tensor
+ 
+
+ align:start position:0%
+tensors and this is just the tensor
+okay so if i change reference frames if
+
+ align:start position:0%
+okay so if i change reference frames if
+ 
+
+ align:start position:0%
+okay so if i change reference frames if
+i want to know what the components are
+
+ align:start position:0%
+i want to know what the components are
+ 
+
+ align:start position:0%
+i want to know what the components are
+and according to some bard observer you
+
+ align:start position:0%
+and according to some bard observer you
+ 
+
+ align:start position:0%
+and according to some bard observer you
+know i will step through the algebra in
+
+ align:start position:0%
+know i will step through the algebra in
+ 
+
+ align:start position:0%
+know i will step through the algebra in
+my notes
+
+ align:start position:0%
+my notes
+ 
+
+ align:start position:0%
+my notes
+but i think you know where i'm going to
+
+ align:start position:0%
+but i think you know where i'm going to
+ 
+
+ align:start position:0%
+but i think you know where i'm going to
+go with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just take the components uh in the
+
+ align:start position:0%
+you just take the components uh in the
+ 
+
+ align:start position:0%
+you just take the components uh in the
+unbarred frame line it up contract it
+
+ align:start position:0%
+unbarred frame line it up contract it
+ 
+
+ align:start position:0%
+unbarred frame line it up contract it
+with the correct
+
+ align:start position:0%
+with the correct
+ 
+
+ align:start position:0%
+with the correct
+uh setup of my lawrence transformation
+
+ align:start position:0%
+uh setup of my lawrence transformation
+ 
+
+ align:start position:0%
+uh setup of my lawrence transformation
+matrix boom line up the indices
+
+ align:start position:0%
+matrix boom line up the indices
+ 
+
+ align:start position:0%
+matrix boom line up the indices
+and we've got it there so
+
+ align:start position:0%
+and we've got it there so
+ 
+
+ align:start position:0%
+and we've got it there so
+the last thing which i want to do with
+
+ align:start position:0%
+the last thing which i want to do with
+ 
+
+ align:start position:0%
+the last thing which i want to do with
+this before i sort of talk a little bit
+
+ align:start position:0%
+this before i sort of talk a little bit
+ 
+
+ align:start position:0%
+this before i sort of talk a little bit
+about what this is really good for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is say you know i've got these basis
+
+ align:start position:0%
+is say you know i've got these basis
+ 
+
+ align:start position:0%
+is say you know i've got these basis
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+that allow me to kind of relate my
+
+ align:start position:0%
+that allow me to kind of relate my
+ 
+
+ align:start position:0%
+that allow me to kind of relate my
+uh the components of my vectors to the
+
+ align:start position:0%
+uh the components of my vectors to the
+ 
+
+ align:start position:0%
+uh the components of my vectors to the
+geometric object in a way where i don't
+
+ align:start position:0%
+geometric object in a way where i don't
+ 
+
+ align:start position:0%
+geometric object in a way where i don't
+use a represented by symbol i actually
+
+ align:start position:0%
+use a represented by symbol i actually
+ 
+
+ align:start position:0%
+use a represented by symbol i actually
+have an odds to god equals sign
+
+ align:start position:0%
+have an odds to god equals sign
+ 
+
+ align:start position:0%
+have an odds to god equals sign
+can i define a similar set of basis one
+
+ align:start position:0%
+can i define a similar set of basis one
+ 
+
+ align:start position:0%
+can i define a similar set of basis one
+forms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i want to do is define a family of
+
+ align:start position:0%
+what i want to do is define a family of
+ 
+
+ align:start position:0%
+what i want to do is define a family of
+geometric objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i will denote them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with an omega and a tilde
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that any one form
+
+ align:start position:0%
+such that any one form
+ 
+
+ align:start position:0%
+such that any one form
+can be written as its components
+
+ align:start position:0%
+can be written as its components
+ 
+
+ align:start position:0%
+can be written as its components
+attached to these little basis vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the way i'm going to do this is i'm
+
+ align:start position:0%
+well the way i'm going to do this is i'm
+ 
+
+ align:start position:0%
+well the way i'm going to do this is i'm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+exploit the fact that i already know
+
+ align:start position:0%
+exploit the fact that i already know
+ 
+
+ align:start position:0%
+exploit the fact that i already know
+what basis
+
+ align:start position:0%
+what basis
+ 
+
+ align:start position:0%
+what basis
+vectors are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i know for instance that if i take my
+
+ align:start position:0%
+so i know for instance that if i take my
+ 
+
+ align:start position:0%
+so i know for instance that if i take my
+one form
+
+ align:start position:0%
+one form
+ 
+
+ align:start position:0%
+one form
+and i plug in a basis vector i get this
+
+ align:start position:0%
+and i plug in a basis vector i get this
+ 
+
+ align:start position:0%
+and i plug in a basis vector i get this
+and so what i want to do
+
+ align:start position:0%
+and so what i want to do
+ 
+
+ align:start position:0%
+and so what i want to do
+is combine this thing which i would like
+
+ align:start position:0%
+is combine this thing which i would like
+ 
+
+ align:start position:0%
+is combine this thing which i would like
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+with the defining operation of
+
+ align:start position:0%
+with the defining operation of
+ 
+
+ align:start position:0%
+with the defining operation of
+contraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i know p alpha
+
+ align:start position:0%
+okay so i know p alpha
+ 
+
+ align:start position:0%
+okay so i know p alpha
+a alpha is what i get when i've got my
+
+ align:start position:0%
+a alpha is what i get when i've got my
+ 
+
+ align:start position:0%
+a alpha is what i get when i've got my
+one form
+
+ align:start position:0%
+one form
+ 
+
+ align:start position:0%
+one form
+and i plug into its slot the vector a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's insist that when i do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can write this as p beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+omega beta now remember these are the
+
+ align:start position:0%
+omega beta now remember these are the
+ 
+
+ align:start position:0%
+omega beta now remember these are the
+components this is the actual basis one
+
+ align:start position:0%
+components this is the actual basis one
+ 
+
+ align:start position:0%
+components this is the actual basis one
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+so i'm going to stick into my basis one
+
+ align:start position:0%
+so i'm going to stick into my basis one
+ 
+
+ align:start position:0%
+so i'm going to stick into my basis one
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+this form of the vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay i can then use the out bugger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can then use the linearity of the
+
+ align:start position:0%
+i can then use the linearity of the
+ 
+
+ align:start position:0%
+i can then use the linearity of the
+tensor nature
+
+ align:start position:0%
+tensor nature
+ 
+
+ align:start position:0%
+tensor nature
+to pull out that component of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what this tells me is this is exactly
+
+ align:start position:0%
+so what this tells me is this is exactly
+ 
+
+ align:start position:0%
+so what this tells me is this is exactly
+what i want provided
+
+ align:start position:0%
+what i want provided
+ 
+
+ align:start position:0%
+what i want provided
+whatever this geometric object is
+
+ align:start position:0%
+whatever this geometric object is
+ 
+
+ align:start position:0%
+whatever this geometric object is
+it obeys the rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that when i plug basis vectors into it
+
+ align:start position:0%
+that when i plug basis vectors into it
+ 
+
+ align:start position:0%
+that when i plug basis vectors into it
+i get the kronecker delta back okay
+
+ align:start position:0%
+i get the kronecker delta back okay
+ 
+
+ align:start position:0%
+i get the kronecker delta back okay
+now this may all seem really really
+
+ align:start position:0%
+now this may all seem really really
+ 
+
+ align:start position:0%
+now this may all seem really really
+trivial right now and indeed if you
+
+ align:start position:0%
+trivial right now and indeed if you
+ 
+
+ align:start position:0%
+trivial right now and indeed if you
+think about this in terms of just
+
+ align:start position:0%
+think about this in terms of just
+ 
+
+ align:start position:0%
+think about this in terms of just
+writing down mathematical symbols this
+
+ align:start position:0%
+writing down mathematical symbols this
+ 
+
+ align:start position:0%
+writing down mathematical symbols this
+is fairly trivial okay one thing which i
+
+ align:start position:0%
+is fairly trivial okay one thing which i
+ 
+
+ align:start position:0%
+is fairly trivial okay one thing which i
+want to emphasize is that if you go
+
+ align:start position:0%
+want to emphasize is that if you go
+ 
+
+ align:start position:0%
+want to emphasize is that if you go
+through and say well
+
+ align:start position:0%
+through and say well
+ 
+
+ align:start position:0%
+through and say well
+you know if i'm working in a basis where
+
+ align:start position:0%
+you know if i'm working in a basis where
+ 
+
+ align:start position:0%
+you know if i'm working in a basis where
+this has a timeline component that i'll
+
+ align:start position:0%
+this has a timeline component that i'll
+ 
+
+ align:start position:0%
+this has a timeline component that i'll
+say is
+
+ align:start position:0%
+say is
+ 
+
+ align:start position:0%
+say is
+one the timeline direction zero
+
+ align:start position:0%
+one the timeline direction zero
+ 
+
+ align:start position:0%
+one the timeline direction zero
+everywhere else it has an
+
+ align:start position:0%
+everywhere else it has an
+ 
+
+ align:start position:0%
+everywhere else it has an
+x a member of the set that points in the
+
+ align:start position:0%
+x a member of the set that points in the
+ 
+
+ align:start position:0%
+x a member of the set that points in the
+x direction so it's zero
+
+ align:start position:0%
+x direction so it's zero
+ 
+
+ align:start position:0%
+x direction so it's zero
+one along x zero everywhere else this
+
+ align:start position:0%
+one along x zero everywhere else this
+ 
+
+ align:start position:0%
+one along x zero everywhere else this
+then leads to
+
+ align:start position:0%
+then leads to
+ 
+
+ align:start position:0%
+then leads to
+so as an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a set of basis objects that a particular
+
+ align:start position:0%
+a set of basis objects that a particular
+ 
+
+ align:start position:0%
+a set of basis objects that a particular
+observer
+
+ align:start position:0%
+observer
+ 
+
+ align:start position:0%
+observer
+would write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just like so okay and i won't write out
+
+ align:start position:0%
+just like so okay and i won't write out
+ 
+
+ align:start position:0%
+just like so okay and i won't write out
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the two and three components and again
+
+ align:start position:0%
+the two and three components and again
+ 
+
+ align:start position:0%
+the two and three components and again
+you look at this and you think to
+
+ align:start position:0%
+you look at this and you think to
+ 
+
+ align:start position:0%
+you look at this and you think to
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+dude you're just repeating basis vectors
+
+ align:start position:0%
+dude you're just repeating basis vectors
+ 
+
+ align:start position:0%
+dude you're just repeating basis vectors
+what's the big deal here
+
+ align:start position:0%
+what's the big deal here
+ 
+
+ align:start position:0%
+what's the big deal here
+now i'm going to explain the fact these
+
+ align:start position:0%
+now i'm going to explain the fact these
+ 
+
+ align:start position:0%
+now i'm going to explain the fact these
+are sometimes called dual vectors
+
+ align:start position:0%
+are sometimes called dual vectors
+ 
+
+ align:start position:0%
+are sometimes called dual vectors
+so if we want to think about this in a
+
+ align:start position:0%
+so if we want to think about this in a
+ 
+
+ align:start position:0%
+so if we want to think about this in a
+language that is reminiscent of linear
+
+ align:start position:0%
+language that is reminiscent of linear
+ 
+
+ align:start position:0%
+language that is reminiscent of linear
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+if you think of the basis vectors as
+
+ align:start position:0%
+if you think of the basis vectors as
+ 
+
+ align:start position:0%
+if you think of the basis vectors as
+column vectors then my basis
+
+ align:start position:0%
+column vectors then my basis
+ 
+
+ align:start position:0%
+column vectors then my basis
+one forms are essentially row vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so these look a lot like my basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they enter in a dual way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so they end up playing they're
+
+ align:start position:0%
+okay and so they end up playing they're
+ 
+
+ align:start position:0%
+okay and so they end up playing they're
+going to play an important role
+
+ align:start position:0%
+going to play an important role
+ 
+
+ align:start position:0%
+going to play an important role
+in helping us to you know whenever i
+
+ align:start position:0%
+in helping us to you know whenever i
+ 
+
+ align:start position:0%
+in helping us to you know whenever i
+contract two objects together to make
+
+ align:start position:0%
+contract two objects together to make
+ 
+
+ align:start position:0%
+contract two objects together to make
+some kind of a
+
+ align:start position:0%
+some kind of a
+ 
+
+ align:start position:0%
+some kind of a
+lorenzen variant scalar i'm going to
+
+ align:start position:0%
+lorenzen variant scalar i'm going to
+ 
+
+ align:start position:0%
+lorenzen variant scalar i'm going to
+want to only combine objects that have a
+
+ align:start position:0%
+want to only combine objects that have a
+ 
+
+ align:start position:0%
+want to only combine objects that have a
+dual nature like this that's the only
+
+ align:start position:0%
+dual nature like this that's the only
+ 
+
+ align:start position:0%
+dual nature like this that's the only
+way i can get something sensible out of
+
+ align:start position:0%
+way i can get something sensible out of
+ 
+
+ align:start position:0%
+way i can get something sensible out of
+it so let me give you an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an equation that i can write
+
+ align:start position:0%
+this is an equation that i can write
+ 
+
+ align:start position:0%
+this is an equation that i can write
+down okay no question if i'm in a
+
+ align:start position:0%
+down okay no question if i'm in a
+ 
+
+ align:start position:0%
+down okay no question if i'm in a
+particular frame i've got the components
+
+ align:start position:0%
+particular frame i've got the components
+ 
+
+ align:start position:0%
+particular frame i've got the components
+of vector a i've got the components of
+
+ align:start position:0%
+of vector a i've got the components of
+ 
+
+ align:start position:0%
+of vector a i've got the components of
+vector b
+
+ align:start position:0%
+vector b
+ 
+
+ align:start position:0%
+vector b
+i can multiply their components together
+
+ align:start position:0%
+i can multiply their components together
+ 
+
+ align:start position:0%
+i can multiply their components together
+sum them and square them
+
+ align:start position:0%
+sum them and square them
+ 
+
+ align:start position:0%
+sum them and square them
+so this is mathematically well defined
+
+ align:start position:0%
+so this is mathematically well defined
+ 
+
+ align:start position:0%
+so this is mathematically well defined
+but plays no role
+
+ align:start position:0%
+but plays no role
+ 
+
+ align:start position:0%
+but plays no role
+in the physics we are going to talk
+
+ align:start position:0%
+in the physics we are going to talk
+ 
+
+ align:start position:0%
+in the physics we are going to talk
+about this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay because this is not related to the
+
+ align:start position:0%
+okay because this is not related to the
+ 
+
+ align:start position:0%
+okay because this is not related to the
+underlying invariant structure
+
+ align:start position:0%
+underlying invariant structure
+ 
+
+ align:start position:0%
+underlying invariant structure
+of the manifold that we are working with
+
+ align:start position:0%
+of the manifold that we are working with
+ 
+
+ align:start position:0%
+of the manifold that we are working with
+so remember i talked about how a
+
+ align:start position:0%
+so remember i talked about how a
+ 
+
+ align:start position:0%
+so remember i talked about how a
+manifold
+
+ align:start position:0%
+manifold
+ 
+
+ align:start position:0%
+manifold
+is essentially a sufficiently smooth set
+
+ align:start position:0%
+is essentially a sufficiently smooth set
+ 
+
+ align:start position:0%
+is essentially a sufficiently smooth set
+of points endowed with
+
+ align:start position:0%
+of points endowed with
+ 
+
+ align:start position:0%
+of points endowed with
+a metric well the metric is what tells
+
+ align:start position:0%
+a metric well the metric is what tells
+ 
+
+ align:start position:0%
+a metric well the metric is what tells
+us that this
+
+ align:start position:0%
+us that this
+ 
+
+ align:start position:0%
+us that this
+is you know mathematically sure write it
+
+ align:start position:0%
+is you know mathematically sure write it
+ 
+
+ align:start position:0%
+is you know mathematically sure write it
+down but it means nothing
+
+ align:start position:0%
+down but it means nothing
+ 
+
+ align:start position:0%
+down but it means nothing
+by contrast of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this has frame independent meaning this
+
+ align:start position:0%
+this has frame independent meaning this
+ 
+
+ align:start position:0%
+this has frame independent meaning this
+is important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the sense in which these p's
+
+ align:start position:0%
+so that's the sense in which these p's
+ 
+
+ align:start position:0%
+so that's the sense in which these p's
+this is the sense in which these one
+
+ align:start position:0%
+this is the sense in which these one
+ 
+
+ align:start position:0%
+this is the sense in which these one
+forms are often called dual vectors
+
+ align:start position:0%
+forms are often called dual vectors
+ 
+
+ align:start position:0%
+forms are often called dual vectors
+okay it is when they are combined with
+
+ align:start position:0%
+okay it is when they are combined with
+ 
+
+ align:start position:0%
+okay it is when they are combined with
+vectors they are dual to it in the sense
+
+ align:start position:0%
+vectors they are dual to it in the sense
+ 
+
+ align:start position:0%
+vectors they are dual to it in the sense
+that when they are combined in this
+
+ align:start position:0%
+that when they are combined in this
+ 
+
+ align:start position:0%
+that when they are combined in this
+appropriate way
+
+ align:start position:0%
+appropriate way
+ 
+
+ align:start position:0%
+appropriate way
+uh we find that they describe the
+
+ align:start position:0%
+uh we find that they describe the
+ 
+
+ align:start position:0%
+uh we find that they describe the
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+um they they capture the invariant
+
+ align:start position:0%
+um they they capture the invariant
+ 
+
+ align:start position:0%
+um they they capture the invariant
+characteristics of the physics that are
+
+ align:start position:0%
+characteristics of the physics that are
+ 
+
+ align:start position:0%
+characteristics of the physics that are
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+in the theory that we are describing if
+
+ align:start position:0%
+in the theory that we are describing if
+ 
+
+ align:start position:0%
+in the theory that we are describing if
+i may sort of
+
+ align:start position:0%
+i may sort of
+ 
+
+ align:start position:0%
+i may sort of
+uh give one more example that is from a
+
+ align:start position:0%
+uh give one more example that is from a
+ 
+
+ align:start position:0%
+uh give one more example that is from a
+completely different field
+
+ align:start position:0%
+completely different field
+ 
+
+ align:start position:0%
+completely different field
+but i think helps to sort of illustrate
+
+ align:start position:0%
+but i think helps to sort of illustrate
+ 
+
+ align:start position:0%
+but i think helps to sort of illustrate
+a useful analogy to think about these
+
+ align:start position:0%
+a useful analogy to think about these
+ 
+
+ align:start position:0%
+a useful analogy to think about these
+things suppose you are doing quantum
+
+ align:start position:0%
+things suppose you are doing quantum
+ 
+
+ align:start position:0%
+things suppose you are doing quantum
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+and i give you two wave functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose you have a wave function
+
+ align:start position:0%
+so suppose you have a wave function
+ 
+
+ align:start position:0%
+so suppose you have a wave function
+psi of x and another wave function
+
+ align:start position:0%
+psi of x and another wave function
+ 
+
+ align:start position:0%
+psi of x and another wave function
+5x if you wanted to you could multiply
+
+ align:start position:0%
+5x if you wanted to you could multiply
+ 
+
+ align:start position:0%
+5x if you wanted to you could multiply
+them together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and integrate over all space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know what you would do with that
+
+ align:start position:0%
+i don't know what you would do with that
+ 
+
+ align:start position:0%
+i don't know what you would do with that
+but you could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the other hand you could take the
+
+ align:start position:0%
+on the other hand you could take the
+ 
+
+ align:start position:0%
+on the other hand you could take the
+complex conjugate of one of them
+
+ align:start position:0%
+complex conjugate of one of them
+ 
+
+ align:start position:0%
+complex conjugate of one of them
+multiply it by the other one multiply it
+
+ align:start position:0%
+multiply it by the other one multiply it
+ 
+
+ align:start position:0%
+multiply it by the other one multiply it
+over all space
+
+ align:start position:0%
+over all space
+ 
+
+ align:start position:0%
+over all space
+and in the notation that you learn about
+
+ align:start position:0%
+and in the notation that you learn about
+ 
+
+ align:start position:0%
+and in the notation that you learn about
+this is of course just the inner product
+
+ align:start position:0%
+this is of course just the inner product
+ 
+
+ align:start position:0%
+this is of course just the inner product
+of wave function psi with wave function
+
+ align:start position:0%
+of wave function psi with wave function
+ 
+
+ align:start position:0%
+of wave function psi with wave function
+phi okay
+
+ align:start position:0%
+phi okay
+ 
+
+ align:start position:0%
+phi okay
+forming the one form using a one form is
+
+ align:start position:0%
+forming the one form using a one form is
+ 
+
+ align:start position:0%
+forming the one form using a one form is
+akin to
+
+ align:start position:0%
+akin to
+ 
+
+ align:start position:0%
+akin to
+selecting an object that has uh you know
+
+ align:start position:0%
+selecting an object that has uh you know
+ 
+
+ align:start position:0%
+selecting an object that has uh you know
+it allows us to make a mathematical
+
+ align:start position:0%
+it allows us to make a mathematical
+ 
+
+ align:start position:0%
+it allows us to make a mathematical
+construction similar to the quantum
+
+ align:start position:0%
+construction similar to the quantum
+ 
+
+ align:start position:0%
+construction similar to the quantum
+mechanical inner product that we use
+
+ align:start position:0%
+mechanical inner product that we use
+ 
+
+ align:start position:0%
+mechanical inner product that we use
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and as we'll see in just a couple of
+
+ align:start position:0%
+and as we'll see in just a couple of
+ 
+
+ align:start position:0%
+and as we'll see in just a couple of
+minutes it's actually really easy
+
+ align:start position:0%
+minutes it's actually really easy
+ 
+
+ align:start position:0%
+minutes it's actually really easy
+to flip back and forth between one forms
+
+ align:start position:0%
+to flip back and forth between one forms
+ 
+
+ align:start position:0%
+to flip back and forth between one forms
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and vectors okay so
+
+ align:start position:0%
+and vectors okay so
+ 
+
+ align:start position:0%
+and vectors okay so
+better way to sort of move forward with
+
+ align:start position:0%
+better way to sort of move forward with
+ 
+
+ align:start position:0%
+better way to sort of move forward with
+this is rather than talking in terms of
+
+ align:start position:0%
+this is rather than talking in terms of
+ 
+
+ align:start position:0%
+this is rather than talking in terms of
+these more
+
+ align:start position:0%
+these more
+ 
+
+ align:start position:0%
+these more
+abstract things let me give you a good
+
+ align:start position:0%
+abstract things let me give you a good
+ 
+
+ align:start position:0%
+abstract things let me give you a good
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so imagine i have
+
+ align:start position:0%
+so imagine i have
+ 
+
+ align:start position:0%
+so imagine i have
+some trajectory through space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's let the t-axis go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's my x and y axes you all can
+
+ align:start position:0%
+there's my x and y axes you all can
+ 
+
+ align:start position:0%
+there's my x and y axes you all can
+imagine the z-axis
+
+ align:start position:0%
+imagine the z-axis
+ 
+
+ align:start position:0%
+imagine the z-axis
+and some observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves through space-time like so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh last lecture we talked about a couple
+
+ align:start position:0%
+uh last lecture we talked about a couple
+ 
+
+ align:start position:0%
+uh last lecture we talked about a couple
+of important examples of four vectors
+
+ align:start position:0%
+of important examples of four vectors
+ 
+
+ align:start position:0%
+of important examples of four vectors
+and so one which is germane the
+
+ align:start position:0%
+and so one which is germane the
+ 
+
+ align:start position:0%
+and so one which is germane the
+situation is the four velocity of this
+
+ align:start position:0%
+situation is the four velocity of this
+ 
+
+ align:start position:0%
+situation is the four velocity of this
+observer
+
+ align:start position:0%
+observer
+ 
+
+ align:start position:0%
+observer
+that just expresses the rate of change
+
+ align:start position:0%
+that just expresses the rate of change
+ 
+
+ align:start position:0%
+that just expresses the rate of change
+of its position in space
+
+ align:start position:0%
+of its position in space
+ 
+
+ align:start position:0%
+of its position in space
+time per unit proper
+
+ align:start position:0%
+time per unit proper
+ 
+
+ align:start position:0%
+time per unit proper
+time okay i'll remind you tau
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is time as measured
+
+ align:start position:0%
+is time as measured
+ 
+
+ align:start position:0%
+is time as measured
+along this observer's trajectory so
+
+ align:start position:0%
+along this observer's trajectory so
+ 
+
+ align:start position:0%
+along this observer's trajectory so
+roughly speaking not even roughly
+
+ align:start position:0%
+roughly speaking not even roughly
+ 
+
+ align:start position:0%
+roughly speaking not even roughly
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+exactly speaking tau is the time that is
+
+ align:start position:0%
+exactly speaking tau is the time that is
+ 
+
+ align:start position:0%
+exactly speaking tau is the time that is
+measured by the clock
+
+ align:start position:0%
+measured by the clock
+ 
+
+ align:start position:0%
+measured by the clock
+by the watt of the person moving along
+
+ align:start position:0%
+by the watt of the person moving along
+ 
+
+ align:start position:0%
+by the watt of the person moving along
+there okay
+
+ align:start position:0%
+there okay
+ 
+
+ align:start position:0%
+there okay
+so suppose in addition to this person
+
+ align:start position:0%
+so suppose in addition to this person
+ 
+
+ align:start position:0%
+so suppose in addition to this person
+sort of traveling along through space
+
+ align:start position:0%
+sort of traveling along through space
+ 
+
+ align:start position:0%
+sort of traveling along through space
+time here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose space-time is filled with
+
+ align:start position:0%
+suppose space-time is filled with
+ 
+
+ align:start position:0%
+suppose space-time is filled with
+some field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phi which depends on all
+
+ align:start position:0%
+phi which depends on all
+ 
+
+ align:start position:0%
+phi which depends on all
+of my space-time coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question i want to ask is what is the
+
+ align:start position:0%
+question i want to ask is what is the
+ 
+
+ align:start position:0%
+question i want to ask is what is the
+rate of change of phi
+
+ align:start position:0%
+rate of change of phi
+ 
+
+ align:start position:0%
+rate of change of phi
+along this observer's trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you were working in ordinary
+
+ align:start position:0%
+so if you were working in ordinary
+ 
+
+ align:start position:0%
+so if you were working in ordinary
+euclidean space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you would basically say ah this is easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so your three-space intuition you don't
+
+ align:start position:0%
+so your three-space intuition you don't
+ 
+
+ align:start position:0%
+so your three-space intuition you don't
+have this proper time to worry about
+
+ align:start position:0%
+have this proper time to worry about
+ 
+
+ align:start position:0%
+have this proper time to worry about
+so you would just say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defy dt along this trajectory
+
+ align:start position:0%
+defy dt along this trajectory
+ 
+
+ align:start position:0%
+defy dt along this trajectory
+is just what i get when i calculate dx
+
+ align:start position:0%
+is just what i get when i calculate dx
+ 
+
+ align:start position:0%
+is just what i get when i calculate dx
+dt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then look at the x derivative of my
+
+ align:start position:0%
+and then look at the x derivative of my
+ 
+
+ align:start position:0%
+and then look at the x derivative of my
+field phi
+
+ align:start position:0%
+field phi
+ 
+
+ align:start position:0%
+field phi
+plus d y e t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is one of those places where
+
+ align:start position:0%
+this is one of those places where
+ 
+
+ align:start position:0%
+this is one of those places where
+getting the difference between a partial
+
+ align:start position:0%
+getting the difference between a partial
+ 
+
+ align:start position:0%
+getting the difference between a partial
+and a total derivative right is
+
+ align:start position:0%
+and a total derivative right is
+ 
+
+ align:start position:0%
+and a total derivative right is
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+so if you see me do that again if i
+
+ align:start position:0%
+so if you see me do that again if i
+ 
+
+ align:start position:0%
+so if you see me do that again if i
+don't correct it yell at me
+
+ align:start position:0%
+don't correct it yell at me
+ 
+
+ align:start position:0%
+don't correct it yell at me
+okay so you get this then you say ah
+
+ align:start position:0%
+okay so you get this then you say ah
+ 
+
+ align:start position:0%
+okay so you get this then you say ah
+this is nothing more
+
+ align:start position:0%
+this is nothing more
+ 
+
+ align:start position:0%
+this is nothing more
+than that particle's velocity dotted
+
+ align:start position:0%
+than that particle's velocity dotted
+ 
+
+ align:start position:0%
+than that particle's velocity dotted
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+the gradient of the field phi okay the
+
+ align:start position:0%
+the gradient of the field phi okay the
+ 
+
+ align:start position:0%
+the gradient of the field phi okay the
+directional derivative along
+
+ align:start position:0%
+directional derivative along
+ 
+
+ align:start position:0%
+directional derivative along
+the uh the the velocity of this
+
+ align:start position:0%
+the uh the the velocity of this
+ 
+
+ align:start position:0%
+the uh the the velocity of this
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+so generalizing this to space time
+
+ align:start position:0%
+so generalizing this to space time
+ 
+
+ align:start position:0%
+so generalizing this to space time
+you basically have the same thing going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only now time is a coordinate so we
+
+ align:start position:0%
+only now time is a coordinate so we
+ 
+
+ align:start position:0%
+only now time is a coordinate so we
+don't treat time as the independent
+
+ align:start position:0%
+don't treat time as the independent
+ 
+
+ align:start position:0%
+don't treat time as the independent
+parameter that describes ticking of
+
+ align:start position:0%
+parameter that describes ticking of
+ 
+
+ align:start position:0%
+parameter that describes ticking of
+clock as i move along it i use the
+
+ align:start position:0%
+clock as i move along it i use the
+ 
+
+ align:start position:0%
+clock as i move along it i use the
+proper time of the observer
+
+ align:start position:0%
+proper time of the observer
+ 
+
+ align:start position:0%
+proper time of the observer
+as my independent parameter
+
+ align:start position:0%
+as my independent parameter
+ 
+
+ align:start position:0%
+as my independent parameter
+so what i will say is bugger i did it
+
+ align:start position:0%
+so what i will say is bugger i did it
+ 
+
+ align:start position:0%
+so what i will say is bugger i did it
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the rate at which the field changes
+
+ align:start position:0%
+so the rate at which the field changes
+ 
+
+ align:start position:0%
+so the rate at which the field changes
+per unit of this guy's proper time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay every one of these is a component
+
+ align:start position:0%
+okay every one of these is a component
+ 
+
+ align:start position:0%
+okay every one of these is a component
+of the four velocity
+
+ align:start position:0%
+of the four velocity
+ 
+
+ align:start position:0%
+of the four velocity
+so now we introduce a little bit of
+
+ align:start position:0%
+so now we introduce a little bit of
+ 
+
+ align:start position:0%
+so now we introduce a little bit of
+notation so this
+
+ align:start position:0%
+notation so this
+ 
+
+ align:start position:0%
+notation so this
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm very mad at myself here stop doing
+
+ align:start position:0%
+i'm very mad at myself here stop doing
+ 
+
+ align:start position:0%
+i'm very mad at myself here stop doing
+that scott
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's what i get when i contract the four
+
+ align:start position:0%
+it's what i get when i contract the four
+ 
+
+ align:start position:0%
+it's what i get when i contract the four
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+against a quantity that's defined by
+
+ align:start position:0%
+against a quantity that's defined by
+ 
+
+ align:start position:0%
+against a quantity that's defined by
+taking the derivative of this field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to be taking derivatives
+
+ align:start position:0%
+we're going to be taking derivatives
+ 
+
+ align:start position:0%
+we're going to be taking derivatives
+like this a lot so
+
+ align:start position:0%
+like this a lot so
+ 
+
+ align:start position:0%
+like this a lot so
+a little bit of notation being
+
+ align:start position:0%
+a little bit of notation being
+ 
+
+ align:start position:0%
+a little bit of notation being
+introduced to save us some writing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the directional derivative along
+
+ align:start position:0%
+this is the directional derivative along
+ 
+
+ align:start position:0%
+this is the directional derivative along
+the trajectory of this body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is a frame independent scalar
+
+ align:start position:0%
+now this is a frame independent scalar
+ 
+
+ align:start position:0%
+now this is a frame independent scalar
+okay this is a quantity that all
+
+ align:start position:0%
+okay this is a quantity that all
+ 
+
+ align:start position:0%
+okay this is a quantity that all
+observers will agree on
+
+ align:start position:0%
+observers will agree on
+ 
+
+ align:start position:0%
+observers will agree on
+this is a four velocity excuse me we
+
+ align:start position:0%
+this is a four velocity excuse me we
+ 
+
+ align:start position:0%
+this is a four velocity excuse me we
+know this is a four velocity these are
+
+ align:start position:0%
+know this is a four velocity these are
+ 
+
+ align:start position:0%
+know this is a four velocity these are
+the components of a four vector
+
+ align:start position:0%
+the components of a four vector
+ 
+
+ align:start position:0%
+the components of a four vector
+so these are the components of a one
+
+ align:start position:0%
+so these are the components of a one
+ 
+
+ align:start position:0%
+so these are the components of a one
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+okay so the generalization of a gradient
+
+ align:start position:0%
+okay so the generalization of a gradient
+ 
+
+ align:start position:0%
+okay so the generalization of a gradient
+is an example of a one form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so re using that uh abstract notation
+
+ align:start position:0%
+so re using that uh abstract notation
+ 
+
+ align:start position:0%
+so re using that uh abstract notation
+that i gave earlier
+
+ align:start position:0%
+that i gave earlier
+ 
+
+ align:start position:0%
+that i gave earlier
+i can write so what way you will
+
+ align:start position:0%
+i can write so what way you will
+ 
+
+ align:start position:0%
+i can write so what way you will
+sometimes see this
+
+ align:start position:0%
+sometimes see this
+ 
+
+ align:start position:0%
+sometimes see this
+is the abstract gradient one form of the
+
+ align:start position:0%
+is the abstract gradient one form of the
+ 
+
+ align:start position:0%
+is the abstract gradient one form of the
+field phi
+
+ align:start position:0%
+field phi
+ 
+
+ align:start position:0%
+field phi
+is represented by the components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the alpha phi you will also in
+
+ align:start position:0%
+the alpha phi you will also in
+ 
+
+ align:start position:0%
+the alpha phi you will also in
+some cases and i actually have a few
+
+ align:start position:0%
+some cases and i actually have a few
+ 
+
+ align:start position:0%
+some cases and i actually have a few
+notes about
+
+ align:start position:0%
+notes about
+ 
+
+ align:start position:0%
+notes about
+lines about this in my notes sometimes
+
+ align:start position:0%
+lines about this in my notes sometimes
+ 
+
+ align:start position:0%
+lines about this in my notes sometimes
+people will sort of recycle
+
+ align:start position:0%
+people will sort of recycle
+ 
+
+ align:start position:0%
+people will sort of recycle
+the notation of a gradient that you guys
+
+ align:start position:0%
+the notation of a gradient that you guys
+ 
+
+ align:start position:0%
+the notation of a gradient that you guys
+learned about in
+
+ align:start position:0%
+learned about in
+ 
+
+ align:start position:0%
+learned about in
+undergraduate e m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i urge a little bit of caution with this
+
+ align:start position:0%
+i urge a little bit of caution with this
+ 
+
+ align:start position:0%
+i urge a little bit of caution with this
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+okay because we are going to use this
+
+ align:start position:0%
+okay because we are going to use this
+ 
+
+ align:start position:0%
+okay because we are going to use this
+symbol for a derivative to mean
+
+ align:start position:0%
+symbol for a derivative to mean
+ 
+
+ align:start position:0%
+symbol for a derivative to mean
+something a little bit different
+
+ align:start position:0%
+something a little bit different
+ 
+
+ align:start position:0%
+something a little bit different
+uh in just a couple of lectures it turns
+
+ align:start position:0%
+uh in just a couple of lectures it turns
+ 
+
+ align:start position:0%
+uh in just a couple of lectures it turns
+out that the something different reduces
+
+ align:start position:0%
+out that the something different reduces
+ 
+
+ align:start position:0%
+out that the something different reduces
+to this in the special relativity limit
+
+ align:start position:0%
+to this in the special relativity limit
+ 
+
+ align:start position:0%
+to this in the special relativity limit
+so there's no harm being done
+
+ align:start position:0%
+so there's no harm being done
+ 
+
+ align:start position:0%
+so there's no harm being done
+but just bear in mind this particular
+
+ align:start position:0%
+but just bear in mind this particular
+ 
+
+ align:start position:0%
+but just bear in mind this particular
+notion of a derivative here is going to
+
+ align:start position:0%
+notion of a derivative here is going to
+ 
+
+ align:start position:0%
+notion of a derivative here is going to
+sort of change its meaning
+
+ align:start position:0%
+sort of change its meaning
+ 
+
+ align:start position:0%
+sort of change its meaning
+in a little bit another little bit of
+
+ align:start position:0%
+in a little bit another little bit of
+ 
+
+ align:start position:0%
+in a little bit another little bit of
+notation that is sometimes used here
+
+ align:start position:0%
+notation that is sometimes used here
+ 
+
+ align:start position:0%
+notation that is sometimes used here
+and this is one where unfortunately i
+
+ align:start position:0%
+and this is one where unfortunately i
+ 
+
+ align:start position:0%
+and this is one where unfortunately i
+think i'm stuck with this notation
+
+ align:start position:0%
+think i'm stuck with this notation
+ 
+
+ align:start position:0%
+think i'm stuck with this notation
+one often says so this idea of
+
+ align:start position:0%
+one often says so this idea of
+ 
+
+ align:start position:0%
+one often says so this idea of
+taking a derivative along
+
+ align:start position:0%
+taking a derivative along
+ 
+
+ align:start position:0%
+taking a derivative along
+a particular four velocity it comes up a
+
+ align:start position:0%
+a particular four velocity it comes up a
+ 
+
+ align:start position:0%
+a particular four velocity it comes up a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes what people then do is they
+
+ align:start position:0%
+sometimes what people then do is they
+ 
+
+ align:start position:0%
+sometimes what people then do is they
+define it as the directional
+
+ align:start position:0%
+define it as the directional
+ 
+
+ align:start position:0%
+define it as the directional
+gradient along you of the field phi
+
+ align:start position:0%
+gradient along you of the field phi
+ 
+
+ align:start position:0%
+gradient along you of the field phi
+okay so don't worry about this too much
+
+ align:start position:0%
+okay so don't worry about this too much
+ 
+
+ align:start position:0%
+okay so don't worry about this too much
+we'll come back to when it's a little
+
+ align:start position:0%
+we'll come back to when it's a little
+ 
+
+ align:start position:0%
+we'll come back to when it's a little
+bit more appropriate i just want to be
+
+ align:start position:0%
+bit more appropriate i just want to be
+ 
+
+ align:start position:0%
+bit more appropriate i just want to be
+aware especially for those who might be
+
+ align:start position:0%
+aware especially for those who might be
+ 
+
+ align:start position:0%
+aware especially for those who might be
+reading ahead
+
+ align:start position:0%
+reading ahead
+ 
+
+ align:start position:0%
+reading ahead
+when you sort of see this so just think
+
+ align:start position:0%
+when you sort of see this so just think
+ 
+
+ align:start position:0%
+when you sort of see this so just think
+of this as what you get when i am taking
+
+ align:start position:0%
+of this as what you get when i am taking
+ 
+
+ align:start position:0%
+of this as what you get when i am taking
+a gradient along a velocity unit
+
+ align:start position:0%
+a gradient along a velocity unit
+ 
+
+ align:start position:0%
+a gradient along a velocity unit
+basically refers to the
+
+ align:start position:0%
+basically refers to the
+ 
+
+ align:start position:0%
+basically refers to the
+gradient one form contracted with the
+
+ align:start position:0%
+gradient one form contracted with the
+ 
+
+ align:start position:0%
+gradient one form contracted with the
+four vector u
+
+ align:start position:0%
+four vector u
+ 
+
+ align:start position:0%
+four vector u
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coming back to so the last thing i want
+
+ align:start position:0%
+coming back to so the last thing i want
+ 
+
+ align:start position:0%
+coming back to so the last thing i want
+to do as i talk about this
+
+ align:start position:0%
+to do as i talk about this
+ 
+
+ align:start position:0%
+to do as i talk about this
+is uh revisit this notion of one forms
+
+ align:start position:0%
+is uh revisit this notion of one forms
+ 
+
+ align:start position:0%
+is uh revisit this notion of one forms
+as being dual to vectors for just a
+
+ align:start position:0%
+as being dual to vectors for just a
+ 
+
+ align:start position:0%
+as being dual to vectors for just a
+moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've just introduced the gradient as
+
+ align:start position:0%
+so we've just introduced the gradient as
+ 
+
+ align:start position:0%
+so we've just introduced the gradient as
+our first
+
+ align:start position:0%
+our first
+ 
+
+ align:start position:0%
+our first
+example of a one form
+
+ align:start position:0%
+example of a one form
+ 
+
+ align:start position:0%
+example of a one form
+so the notion of the gradient is a one
+
+ align:start position:0%
+so the notion of the gradient is a one
+ 
+
+ align:start position:0%
+so the notion of the gradient is a one
+form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this gives us a nice way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to think about what the basis one forms
+
+ align:start position:0%
+to think about what the basis one forms
+ 
+
+ align:start position:0%
+to think about what the basis one forms
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when i introduced basis one forms a
+
+ align:start position:0%
+so when i introduced basis one forms a
+ 
+
+ align:start position:0%
+so when i introduced basis one forms a
+few moments ago it was a purely
+
+ align:start position:0%
+few moments ago it was a purely
+ 
+
+ align:start position:0%
+few moments ago it was a purely
+mathematical definition i just wanted to
+
+ align:start position:0%
+mathematical definition i just wanted to
+ 
+
+ align:start position:0%
+mathematical definition i just wanted to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+objects such that when i popped in the
+
+ align:start position:0%
+objects such that when i popped in the
+ 
+
+ align:start position:0%
+objects such that when i popped in the
+basis vectors
+
+ align:start position:0%
+basis vectors
+ 
+
+ align:start position:0%
+basis vectors
+i got the chronic delta back and you
+
+ align:start position:0%
+i got the chronic delta back and you
+ 
+
+ align:start position:0%
+i got the chronic delta back and you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+after sort of belaboring the obvious
+
+ align:start position:0%
+after sort of belaboring the obvious
+ 
+
+ align:start position:0%
+after sort of belaboring the obvious
+perhaps for a little bit too long we
+
+ align:start position:0%
+perhaps for a little bit too long we
+ 
+
+ align:start position:0%
+perhaps for a little bit too long we
+essentially got a bunch of ones and
+
+ align:start position:0%
+essentially got a bunch of ones and
+ 
+
+ align:start position:0%
+essentially got a bunch of ones and
+zeros out of it
+
+ align:start position:0%
+zeros out of it
+ 
+
+ align:start position:0%
+zeros out of it
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+putting in math all of those words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i did a lot of junk to get that okay
+
+ align:start position:0%
+i did a lot of junk to get that okay
+ 
+
+ align:start position:0%
+i did a lot of junk to get that okay
+but we also know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i just take the derivative
+
+ align:start position:0%
+if i just take the derivative
+ 
+
+ align:start position:0%
+if i just take the derivative
+of my coordinate with my coordinate
+
+ align:start position:0%
+of my coordinate with my coordinate
+ 
+
+ align:start position:0%
+of my coordinate with my coordinate
+i'm going to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the chronic deltas okay
+
+ align:start position:0%
+the chronic deltas okay
+ 
+
+ align:start position:0%
+the chronic deltas okay
+you know this and this these are the
+
+ align:start position:0%
+you know this and this these are the
+ 
+
+ align:start position:0%
+you know this and this these are the
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+so i can think of this operation here as
+
+ align:start position:0%
+so i can think of this operation here as
+ 
+
+ align:start position:0%
+so i can think of this operation here as
+telling me if i regard
+
+ align:start position:0%
+telling me if i regard
+ 
+
+ align:start position:0%
+telling me if i regard
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as this kind of abstract form
+
+ align:start position:0%
+as this kind of abstract form
+ 
+
+ align:start position:0%
+as this kind of abstract form
+of the gradient applied to the
+
+ align:start position:0%
+of the gradient applied to the
+ 
+
+ align:start position:0%
+of the gradient applied to the
+coordinate itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is nothing more than my basis one
+
+ align:start position:0%
+this is nothing more than my basis one
+ 
+
+ align:start position:0%
+this is nothing more than my basis one
+form so my basis one forms
+
+ align:start position:0%
+form so my basis one forms
+ 
+
+ align:start position:0%
+form so my basis one forms
+are kind of like gradients of my
+
+ align:start position:0%
+are kind of like gradients of my
+ 
+
+ align:start position:0%
+are kind of like gradients of my
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+okay you're sitting here thinking okay
+
+ align:start position:0%
+okay you're sitting here thinking okay
+ 
+
+ align:start position:0%
+okay you're sitting here thinking okay
+what the hell does this have to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me combine set that aside
+
+ align:start position:0%
+so let me combine set that aside
+ 
+
+ align:start position:0%
+so let me combine set that aside
+aside for just a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remind you of some pretty important
+
+ align:start position:0%
+and remind you of some pretty important
+ 
+
+ align:start position:0%
+and remind you of some pretty important
+intuition that you probably learned the
+
+ align:start position:0%
+intuition that you probably learned the
+ 
+
+ align:start position:0%
+intuition that you probably learned the
+very first time you learned about the
+
+ align:start position:0%
+very first time you learned about the
+ 
+
+ align:start position:0%
+very first time you learned about the
+gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so imagine i just draw
+
+ align:start position:0%
+so imagine i just draw
+ 
+
+ align:start position:0%
+so imagine i just draw
+level surfaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some function in let's just do two
+
+ align:start position:0%
+of some function in let's just do two
+ 
+
+ align:start position:0%
+of some function in let's just do two
+dimensional space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i have some function
+
+ align:start position:0%
+okay so i have some function
+ 
+
+ align:start position:0%
+okay so i have some function
+h of x and y okay
+
+ align:start position:0%
+h of x and y okay
+ 
+
+ align:start position:0%
+h of x and y okay
+this represents like for instance a
+
+ align:start position:0%
+this represents like for instance a
+ 
+
+ align:start position:0%
+this represents like for instance a
+height field okay if i'm looking at a
+
+ align:start position:0%
+height field okay if i'm looking at a
+ 
+
+ align:start position:0%
+height field okay if i'm looking at a
+topographic map this might tell me about
+
+ align:start position:0%
+topographic map this might tell me about
+ 
+
+ align:start position:0%
+topographic map this might tell me about
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+things are high and where things are low
+
+ align:start position:0%
+things are high and where things are low
+ 
+
+ align:start position:0%
+things are high and where things are low
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+h of x y there might be level surfaces
+
+ align:start position:0%
+h of x y there might be level surfaces
+ 
+
+ align:start position:0%
+h of x y there might be level surfaces
+on my map
+
+ align:start position:0%
+on my map
+ 
+
+ align:start position:0%
+on my map
+they kind of look like this
+
+ align:start position:0%
+they kind of look like this
+ 
+
+ align:start position:0%
+they kind of look like this
+another one that kind of looks like this
+
+ align:start position:0%
+another one that kind of looks like this
+ 
+
+ align:start position:0%
+another one that kind of looks like this
+and maybe i got something like this
+
+ align:start position:0%
+and maybe i got something like this
+ 
+
+ align:start position:0%
+and maybe i got something like this
+and then something kind of right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we know looking at this thing that
+
+ align:start position:0%
+so we know looking at this thing that
+ 
+
+ align:start position:0%
+so we know looking at this thing that
+the gradient
+
+ align:start position:0%
+the gradient
+ 
+
+ align:start position:0%
+the gradient
+is very low here and very high here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's put this into the language of what
+
+ align:start position:0%
+let's put this into the language of what
+ 
+
+ align:start position:0%
+let's put this into the language of what
+we are looking at right now
+
+ align:start position:0%
+we are looking at right now
+ 
+
+ align:start position:0%
+we are looking at right now
+okay let's let delta x
+
+ align:start position:0%
+okay let's let delta x
+ 
+
+ align:start position:0%
+okay let's let delta x
+be a displacement vector in the x y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and d
+
+ align:start position:0%
+and d
+ 
+
+ align:start position:0%
+and d
+h is going to be my one form of my hud
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how do i get the change in height
+
+ align:start position:0%
+okay how do i get the change in height
+ 
+
+ align:start position:0%
+okay how do i get the change in height
+as i move along my displacement vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+take my one form plop into its slot
+
+ align:start position:0%
+take my one form plop into its slot
+ 
+
+ align:start position:0%
+take my one form plop into its slot
+delta x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i get something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is kind of the thing which i
+
+ align:start position:0%
+but this is kind of the thing which i
+ 
+
+ align:start position:0%
+but this is kind of the thing which i
+kind of want to emphasize here
+
+ align:start position:0%
+kind of want to emphasize here
+ 
+
+ align:start position:0%
+kind of want to emphasize here
+is we have a lot of geometric intuition
+
+ align:start position:0%
+is we have a lot of geometric intuition
+ 
+
+ align:start position:0%
+is we have a lot of geometric intuition
+about vectors right so if i have a delta
+
+ align:start position:0%
+about vectors right so if i have a delta
+ 
+
+ align:start position:0%
+about vectors right so if i have a delta
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+let's say this is my delta x it lasts
+
+ align:start position:0%
+let's say this is my delta x it lasts
+ 
+
+ align:start position:0%
+let's say this is my delta x it lasts
+for about
+
+ align:start position:0%
+for about
+ 
+
+ align:start position:0%
+for about
+this long over here and it lasts it's i
+
+ align:start position:0%
+this long over here and it lasts it's i
+ 
+
+ align:start position:0%
+this long over here and it lasts it's i
+take that exact same delta x and i apply
+
+ align:start position:0%
+take that exact same delta x and i apply
+ 
+
+ align:start position:0%
+take that exact same delta x and i apply
+it over here i get a very different
+
+ align:start position:0%
+it over here i get a very different
+ 
+
+ align:start position:0%
+it over here i get a very different
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+because that goes through many more
+
+ align:start position:0%
+because that goes through many more
+ 
+
+ align:start position:0%
+because that goes through many more
+contours on that
+
+ align:start position:0%
+contours on that
+ 
+
+ align:start position:0%
+contours on that
+on the left side than it does on the
+
+ align:start position:0%
+on the left side than it does on the
+ 
+
+ align:start position:0%
+on the left side than it does on the
+right side
+
+ align:start position:0%
+right side
+ 
+
+ align:start position:0%
+right side
+and the thing this is where this duality
+
+ align:start position:0%
+and the thing this is where this duality
+ 
+
+ align:start position:0%
+and the thing this is where this duality
+kind of comes in
+
+ align:start position:0%
+kind of comes in
+ 
+
+ align:start position:0%
+kind of comes in
+i'm going to put up a couple graphics
+
+ align:start position:0%
+i'm going to put up a couple graphics
+ 
+
+ align:start position:0%
+i'm going to put up a couple graphics
+illustrating this here
+
+ align:start position:0%
+illustrating this here
+ 
+
+ align:start position:0%
+illustrating this here
+is that you should think of the one form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as essentially that set of level
+
+ align:start position:0%
+as essentially that set of level
+ 
+
+ align:start position:0%
+as essentially that set of level
+surfaces
+
+ align:start position:0%
+surfaces
+ 
+
+ align:start position:0%
+surfaces
+okay it's a little confusing i'm not
+
+ align:start position:0%
+okay it's a little confusing i'm not
+ 
+
+ align:start position:0%
+okay it's a little confusing i'm not
+going to i mean i can see a couple blank
+
+ align:start position:0%
+going to i mean i can see a couple blank
+ 
+
+ align:start position:0%
+going to i mean i can see a couple blank
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+maybe even majority of you have kind of
+
+ align:start position:0%
+maybe even majority of you have kind of
+ 
+
+ align:start position:0%
+maybe even majority of you have kind of
+blank looks on your faces here
+
+ align:start position:0%
+blank looks on your faces here
+ 
+
+ align:start position:0%
+blank looks on your faces here
+okay and that's fine okay so what i kind
+
+ align:start position:0%
+okay and that's fine okay so what i kind
+ 
+
+ align:start position:0%
+okay and that's fine okay so what i kind
+of want you to regard is that when i'm
+
+ align:start position:0%
+of want you to regard is that when i'm
+ 
+
+ align:start position:0%
+of want you to regard is that when i'm
+talking about basis one forms and one
+
+ align:start position:0%
+talking about basis one forms and one
+ 
+
+ align:start position:0%
+talking about basis one forms and one
+forms of functions they have a very
+
+ align:start position:0%
+forms of functions they have a very
+ 
+
+ align:start position:0%
+forms of functions they have a very
+different geometric interpretation even
+
+ align:start position:0%
+different geometric interpretation even
+ 
+
+ align:start position:0%
+different geometric interpretation even
+though you're kind of used to gradient
+
+ align:start position:0%
+though you're kind of used to gradient
+ 
+
+ align:start position:0%
+though you're kind of used to gradient
+as telling you something about you know
+
+ align:start position:0%
+as telling you something about you know
+ 
+
+ align:start position:0%
+as telling you something about you know
+the direction along which something is
+
+ align:start position:0%
+the direction along which something is
+ 
+
+ align:start position:0%
+the direction along which something is
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+actually you define that direction the
+
+ align:start position:0%
+actually you define that direction the
+ 
+
+ align:start position:0%
+actually you define that direction the
+thing that you're worried about is sort
+
+ align:start position:0%
+thing that you're worried about is sort
+ 
+
+ align:start position:0%
+thing that you're worried about is sort
+of how close the different level
+
+ align:start position:0%
+of how close the different level
+ 
+
+ align:start position:0%
+of how close the different level
+surfaces are
+
+ align:start position:0%
+surfaces are
+ 
+
+ align:start position:0%
+surfaces are
+of things okay so coming back to this
+
+ align:start position:0%
+of things okay so coming back to this
+ 
+
+ align:start position:0%
+of things okay so coming back to this
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+that uh my basis one form that i use are
+
+ align:start position:0%
+that uh my basis one form that i use are
+ 
+
+ align:start position:0%
+that uh my basis one form that i use are
+essentially just the great gradients of
+
+ align:start position:0%
+essentially just the great gradients of
+ 
+
+ align:start position:0%
+essentially just the great gradients of
+the coordinates
+
+ align:start position:0%
+the coordinates
+ 
+
+ align:start position:0%
+the coordinates
+so i'm going to put some graphics up on
+
+ align:start position:0%
+so i'm going to put some graphics up on
+ 
+
+ align:start position:0%
+so i'm going to put some graphics up on
+the website which i've actually scanned
+
+ align:start position:0%
+the website which i've actually scanned
+ 
+
+ align:start position:0%
+the website which i've actually scanned
+the textbook by misner thorne and
+
+ align:start position:0%
+the textbook by misner thorne and
+ 
+
+ align:start position:0%
+the textbook by misner thorne and
+wheeler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what they basically show is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i let's say this is the time
+
+ align:start position:0%
+if i let's say this is the time
+ 
+
+ align:start position:0%
+if i let's say this is the time
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+let's say this is my x-axis and this is
+
+ align:start position:0%
+let's say this is my x-axis and this is
+ 
+
+ align:start position:0%
+let's say this is my x-axis and this is
+my y-axis
+
+ align:start position:0%
+my y-axis
+ 
+
+ align:start position:0%
+my y-axis
+your intuition is that the x basis
+
+ align:start position:0%
+your intuition is that the x basis
+ 
+
+ align:start position:0%
+your intuition is that the x basis
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+will be a little arrow pointing along x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what your intuition should be like for
+
+ align:start position:0%
+what your intuition should be like for
+ 
+
+ align:start position:0%
+what your intuition should be like for
+the x basis one form
+
+ align:start position:0%
+the x basis one form
+ 
+
+ align:start position:0%
+the x basis one form
+is a series of sheets normal to the
+
+ align:start position:0%
+is a series of sheets normal to the
+ 
+
+ align:start position:0%
+is a series of sheets normal to the
+x-axis
+
+ align:start position:0%
+x-axis
+ 
+
+ align:start position:0%
+x-axis
+that fill all of space okay spaced one
+
+ align:start position:0%
+that fill all of space okay spaced one
+ 
+
+ align:start position:0%
+that fill all of space okay spaced one
+unit apart filling all of space kind of
+
+ align:start position:0%
+unit apart filling all of space kind of
+ 
+
+ align:start position:0%
+unit apart filling all of space kind of
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so here's one example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of one of those sheets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and notice the x-axis pierces every one
+
+ align:start position:0%
+and notice the x-axis pierces every one
+ 
+
+ align:start position:0%
+and notice the x-axis pierces every one
+of those things that's another way in
+
+ align:start position:0%
+of those things that's another way in
+ 
+
+ align:start position:0%
+of those things that's another way in
+which these are sort of a set of dual
+
+ align:start position:0%
+which these are sort of a set of dual
+ 
+
+ align:start position:0%
+which these are sort of a set of dual
+functions to the
+
+ align:start position:0%
+functions to the
+ 
+
+ align:start position:0%
+functions to the
+vectors themselves okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this notion so i'm going to turn to
+
+ align:start position:0%
+this notion so i'm going to turn to
+ 
+
+ align:start position:0%
+this notion so i'm going to turn to
+something which is perhaps a little less
+
+ align:start position:0%
+something which is perhaps a little less
+ 
+
+ align:start position:0%
+something which is perhaps a little less
+uh weird in about 30 seconds
+
+ align:start position:0%
+uh weird in about 30 seconds
+ 
+
+ align:start position:0%
+uh weird in about 30 seconds
+but the one thing which i kind of want
+
+ align:start position:0%
+but the one thing which i kind of want
+ 
+
+ align:start position:0%
+but the one thing which i kind of want
+to emphasize with this and again i'm
+
+ align:start position:0%
+to emphasize with this and again i'm
+ 
+
+ align:start position:0%
+to emphasize with this and again i'm
+going to put a couple graphics up that
+
+ align:start position:0%
+going to put a couple graphics up that
+ 
+
+ align:start position:0%
+going to put a couple graphics up that
+help to illustrate this and there's some
+
+ align:start position:0%
+help to illustrate this and there's some
+ 
+
+ align:start position:0%
+help to illustrate this and there's some
+really nice discussion of this
+
+ align:start position:0%
+really nice discussion of this
+ 
+
+ align:start position:0%
+really nice discussion of this
+mtw is particularly good for for this
+
+ align:start position:0%
+mtw is particularly good for for this
+ 
+
+ align:start position:0%
+mtw is particularly good for for this
+discussion um
+
+ align:start position:0%
+discussion um
+ 
+
+ align:start position:0%
+discussion um
+this ends up being a really useful
+
+ align:start position:0%
+this ends up being a really useful
+ 
+
+ align:start position:0%
+this ends up being a really useful
+notion for capturing how we are going to
+
+ align:start position:0%
+notion for capturing how we are going to
+ 
+
+ align:start position:0%
+notion for capturing how we are going to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+fluxes through particular directions
+
+ align:start position:0%
+fluxes through particular directions
+ 
+
+ align:start position:0%
+fluxes through particular directions
+okay because if i want to know the flux
+
+ align:start position:0%
+okay because if i want to know the flux
+ 
+
+ align:start position:0%
+okay because if i want to know the flux
+of something in the x direction
+
+ align:start position:0%
+of something in the x direction
+ 
+
+ align:start position:0%
+of something in the x direction
+well my x basis one form is actually
+
+ align:start position:0%
+well my x basis one form is actually
+ 
+
+ align:start position:0%
+well my x basis one form is actually
+like a sheet
+
+ align:start position:0%
+like a sheet
+ 
+
+ align:start position:0%
+like a sheet
+that captures everything that flows in
+
+ align:start position:0%
+that captures everything that flows in
+ 
+
+ align:start position:0%
+that captures everything that flows in
+the x direction okay so it's sort of a
+
+ align:start position:0%
+the x direction okay so it's sort of a
+ 
+
+ align:start position:0%
+the x direction okay so it's sort of a
+mathematical object that's designed for
+
+ align:start position:0%
+mathematical object that's designed for
+ 
+
+ align:start position:0%
+mathematical object that's designed for
+catching fluxes
+
+ align:start position:0%
+catching fluxes
+ 
+
+ align:start position:0%
+catching fluxes
+okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if this isn't quite gelling with you
+
+ align:start position:0%
+if this isn't quite gelling with you
+ 
+
+ align:start position:0%
+if this isn't quite gelling with you
+that's fine
+
+ align:start position:0%
+that's fine
+ 
+
+ align:start position:0%
+that's fine
+okay this is without a doubt one of the
+
+ align:start position:0%
+okay this is without a doubt one of the
+ 
+
+ align:start position:0%
+okay this is without a doubt one of the
+goofier things we're going to talk about
+
+ align:start position:0%
+goofier things we're going to talk about
+ 
+
+ align:start position:0%
+goofier things we're going to talk about
+uh in this first introductory period of
+
+ align:start position:0%
+uh in this first introductory period of
+ 
+
+ align:start position:0%
+uh in this first introductory period of
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+this is one of those places where i
+
+ align:start position:0%
+this is one of those places where i
+ 
+
+ align:start position:0%
+this is one of those places where i
+think it's sort of fair to say
+
+ align:start position:0%
+think it's sort of fair to say
+ 
+
+ align:start position:0%
+think it's sort of fair to say
+if you're not quite getting what's going
+
+ align:start position:0%
+if you're not quite getting what's going
+ 
+
+ align:start position:0%
+if you're not quite getting what's going
+on shut up and calculate works well
+
+ align:start position:0%
+on shut up and calculate works well
+ 
+
+ align:start position:0%
+on shut up and calculate works well
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+okay it's kind of like you know
+
+ align:start position:0%
+okay it's kind of like you know
+ 
+
+ align:start position:0%
+okay it's kind of like you know
+fineman's mantra on quantum mechanics
+
+ align:start position:0%
+fineman's mantra on quantum mechanics
+ 
+
+ align:start position:0%
+fineman's mantra on quantum mechanics
+sometimes you just gotta say
+
+ align:start position:0%
+sometimes you just gotta say
+ 
+
+ align:start position:0%
+sometimes you just gotta say
+okay whatever uh learn the way it goes
+
+ align:start position:0%
+okay whatever uh learn the way it goes
+ 
+
+ align:start position:0%
+okay whatever uh learn the way it goes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and it's kind of like playing a musical
+
+ align:start position:0%
+and it's kind of like playing a musical
+ 
+
+ align:start position:0%
+and it's kind of like playing a musical
+instrument you sort of strum it and
+
+ align:start position:0%
+instrument you sort of strum it and
+ 
+
+ align:start position:0%
+instrument you sort of strum it and
+practice it for a while and it becomes
+
+ align:start position:0%
+practice it for a while and it becomes
+ 
+
+ align:start position:0%
+practice it for a while and it becomes
+second nature after a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to wrap this up what i want to do
+
+ align:start position:0%
+so to wrap this up what i want to do
+ 
+
+ align:start position:0%
+so to wrap this up what i want to do
+so the last major thing today is i hope
+
+ align:start position:0%
+so the last major thing today is i hope
+ 
+
+ align:start position:0%
+so the last major thing today is i hope
+i can kind of put a bow
+
+ align:start position:0%
+i can kind of put a bow
+ 
+
+ align:start position:0%
+i can kind of put a bow
+on our discussion of tensors let's come
+
+ align:start position:0%
+on our discussion of tensors let's come
+ 
+
+ align:start position:0%
+on our discussion of tensors let's come
+back to the metric
+
+ align:start position:0%
+back to the metric
+ 
+
+ align:start position:0%
+back to the metric
+as our original example of a tensor here
+
+ align:start position:0%
+as our original example of a tensor here
+ 
+
+ align:start position:0%
+as our original example of a tensor here
+so when i give you the metric
+
+ align:start position:0%
+so when i give you the metric
+ 
+
+ align:start position:0%
+so when i give you the metric
+as an abstract tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i imagine i have filled both slots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i get a lorentz invariant number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a dot b is what i get when i take this
+
+ align:start position:0%
+a dot b is what i get when i take this
+ 
+
+ align:start position:0%
+a dot b is what i get when i take this
+tensor and i put
+
+ align:start position:0%
+tensor and i put
+ 
+
+ align:start position:0%
+tensor and i put
+a and b into its slots suppose i only
+
+ align:start position:0%
+a and b into its slots suppose i only
+ 
+
+ align:start position:0%
+a and b into its slots suppose i only
+fill
+
+ align:start position:0%
+fill
+ 
+
+ align:start position:0%
+fill
+one of its slots
+
+ align:start position:0%
+one of its slots
+ 
+
+ align:start position:0%
+one of its slots
+well if i take this i plug in
+
+ align:start position:0%
+well if i take this i plug in
+ 
+
+ align:start position:0%
+well if i take this i plug in
+the vector a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i leave the other slot blank well
+
+ align:start position:0%
+but i leave the other slot blank well
+ 
+
+ align:start position:0%
+but i leave the other slot blank well
+what i've got is a mathematical object
+
+ align:start position:0%
+what i've got is a mathematical object
+ 
+
+ align:start position:0%
+what i've got is a mathematical object
+that will take a vector
+
+ align:start position:0%
+that will take a vector
+ 
+
+ align:start position:0%
+that will take a vector
+and produce a lorentz invariant number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a one form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do this very carefully
+
+ align:start position:0%
+so let's do this very carefully
+ 
+
+ align:start position:0%
+so let's do this very carefully
+abstractly for a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but at this point we basically have
+
+ align:start position:0%
+but at this point we basically have
+ 
+
+ align:start position:0%
+but at this point we basically have
+almost all the pieces in place
+
+ align:start position:0%
+almost all the pieces in place
+ 
+
+ align:start position:0%
+almost all the pieces in place
+and so i'm going to kind of tone down
+
+ align:start position:0%
+and so i'm going to kind of tone down
+ 
+
+ align:start position:0%
+and so i'm going to kind of tone down
+some of the formality fairly soon
+
+ align:start position:0%
+some of the formality fairly soon
+ 
+
+ align:start position:0%
+some of the formality fairly soon
+so let's define a
+
+ align:start position:0%
+so let's define a
+ 
+
+ align:start position:0%
+so let's define a
+one form an object
+
+ align:start position:0%
+one form an object
+ 
+
+ align:start position:0%
+one form an object
+that takes a single vector inside of it
+
+ align:start position:0%
+that takes a single vector inside of it
+ 
+
+ align:start position:0%
+that takes a single vector inside of it
+as what i get
+
+ align:start position:0%
+as what i get
+ 
+
+ align:start position:0%
+as what i get
+when i take the metric and put that
+
+ align:start position:0%
+when i take the metric and put that
+ 
+
+ align:start position:0%
+when i take the metric and put that
+vector in there if i want to get its
+
+ align:start position:0%
+vector in there if i want to get its
+ 
+
+ align:start position:0%
+vector in there if i want to get its
+components out
+
+ align:start position:0%
+components out
+ 
+
+ align:start position:0%
+components out
+well i know the way i do that is i put
+
+ align:start position:0%
+well i know the way i do that is i put
+ 
+
+ align:start position:0%
+well i know the way i do that is i put
+the basis vector in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this guy is symmetric so i can flip the
+
+ align:start position:0%
+this guy is symmetric so i can flip the
+ 
+
+ align:start position:0%
+this guy is symmetric so i can flip the
+order of the metric is symmetric so i
+
+ align:start position:0%
+order of the metric is symmetric so i
+ 
+
+ align:start position:0%
+order of the metric is symmetric so i
+can flip the order of these guys
+
+ align:start position:0%
+can flip the order of these guys
+ 
+
+ align:start position:0%
+can flip the order of these guys
+and what this tells me is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my one form component of a
+
+ align:start position:0%
+my one form component of a
+ 
+
+ align:start position:0%
+my one form component of a
+is just the vector component of a hit by
+
+ align:start position:0%
+is just the vector component of a hit by
+ 
+
+ align:start position:0%
+is just the vector component of a hit by
+the components of the metric in other
+
+ align:start position:0%
+the components of the metric in other
+ 
+
+ align:start position:0%
+the components of the metric in other
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+the metric
+
+ align:start position:0%
+the metric
+ 
+
+ align:start position:0%
+the metric
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+converts vectors
+
+ align:start position:0%
+converts vectors
+ 
+
+ align:start position:0%
+converts vectors
+into one forms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lowering the indices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is an invertible procedure as
+
+ align:start position:0%
+okay this is an invertible procedure as
+ 
+
+ align:start position:0%
+okay this is an invertible procedure as
+well so this metric
+
+ align:start position:0%
+well so this metric
+ 
+
+ align:start position:0%
+well so this metric
+i can define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ada with indices in the upstairs
+
+ align:start position:0%
+ada with indices in the upstairs
+ 
+
+ align:start position:0%
+ada with indices in the upstairs
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+by requiring that ada
+
+ align:start position:0%
+by requiring that ada
+ 
+
+ align:start position:0%
+by requiring that ada
+alpha beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contracted with it in the downstairs
+
+ align:start position:0%
+contracted with it in the downstairs
+ 
+
+ align:start position:0%
+contracted with it in the downstairs
+position gives me
+
+ align:start position:0%
+position gives me
+ 
+
+ align:start position:0%
+position gives me
+the identity back incidentally when you
+
+ align:start position:0%
+the identity back incidentally when you
+ 
+
+ align:start position:0%
+the identity back incidentally when you
+do this
+
+ align:start position:0%
+do this
+ 
+
+ align:start position:0%
+do this
+you again find it's got exactly the same
+
+ align:start position:0%
+you again find it's got exactly the same
+ 
+
+ align:start position:0%
+you again find it's got exactly the same
+uh matrix representation
+
+ align:start position:0%
+uh matrix representation
+ 
+
+ align:start position:0%
+uh matrix representation
+so this thing with its indices in the
+
+ align:start position:0%
+so this thing with its indices in the
+ 
+
+ align:start position:0%
+so this thing with its indices in the
+upstairs position is just minus one
+
+ align:start position:0%
+upstairs position is just minus one
+ 
+
+ align:start position:0%
+upstairs position is just minus one
+one one one it will not always be that
+
+ align:start position:0%
+one one one it will not always be that
+ 
+
+ align:start position:0%
+one one one it will not always be that
+way so
+
+ align:start position:0%
+way so
+ 
+
+ align:start position:0%
+way so
+okay again this is just because special
+
+ align:start position:0%
+okay again this is just because special
+ 
+
+ align:start position:0%
+okay again this is just because special
+relativity in
+
+ align:start position:0%
+relativity in
+ 
+
+ align:start position:0%
+relativity in
+uh rectilinear coordinates is simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i will often call that the inverse
+
+ align:start position:0%
+so i will often call that the inverse
+ 
+
+ align:start position:0%
+so i will often call that the inverse
+metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you shouldn't have a lot of
+
+ align:start position:0%
+and then you shouldn't have a lot of
+ 
+
+ align:start position:0%
+and then you shouldn't have a lot of
+trouble convincing yourself
+
+ align:start position:0%
+trouble convincing yourself
+ 
+
+ align:start position:0%
+trouble convincing yourself
+that if i've got a one form
+
+ align:start position:0%
+that if i've got a one form
+ 
+
+ align:start position:0%
+that if i've got a one form
+i can make a vector out of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a contraction operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that now tells me
+
+ align:start position:0%
+okay that now tells me
+ 
+
+ align:start position:0%
+okay that now tells me
+that i have about 16 gajillion well
+
+ align:start position:0%
+that i have about 16 gajillion well
+ 
+
+ align:start position:0%
+that i have about 16 gajillion well
+actually it's a countable and finite
+
+ align:start position:0%
+actually it's a countable and finite
+ 
+
+ align:start position:0%
+actually it's a countable and finite
+thing but
+
+ align:start position:0%
+thing but
+ 
+
+ align:start position:0%
+thing but
+i have many ways that i can write down
+
+ align:start position:0%
+i have many ways that i can write down
+ 
+
+ align:start position:0%
+i have many ways that i can write down
+the inner product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two numbers excuse me between two
+
+ align:start position:0%
+two numbers excuse me between two
+ 
+
+ align:start position:0%
+two numbers excuse me between two
+vectors right this guy
+
+ align:start position:0%
+vectors right this guy
+ 
+
+ align:start position:0%
+vectors right this guy
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you like you can now regard a vector
+
+ align:start position:0%
+if you like you can now regard a vector
+ 
+
+ align:start position:0%
+if you like you can now regard a vector
+as being a
+
+ align:start position:0%
+as being a
+ 
+
+ align:start position:0%
+as being a
+sort of a function that you put one
+
+ align:start position:0%
+sort of a function that you put one
+ 
+
+ align:start position:0%
+sort of a function that you put one
+forms into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are all the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are all equivalents to one another
+
+ align:start position:0%
+these are all equivalents to one another
+ 
+
+ align:start position:0%
+these are all equivalents to one another
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+actually making a distinction between
+
+ align:start position:0%
+actually making a distinction between
+ 
+
+ align:start position:0%
+actually making a distinction between
+vector in one form and all that it's
+
+ align:start position:0%
+vector in one form and all that it's
+ 
+
+ align:start position:0%
+vector in one form and all that it's
+just kind of gotten
+
+ align:start position:0%
+just kind of gotten
+ 
+
+ align:start position:0%
+just kind of gotten
+stupid at this point okay so the
+
+ align:start position:0%
+stupid at this point okay so the
+ 
+
+ align:start position:0%
+stupid at this point okay so the
+distinction
+
+ align:start position:0%
+distinction
+ 
+
+ align:start position:0%
+distinction
+among these different objects the
+
+ align:start position:0%
+among these different objects the
+ 
+
+ align:start position:0%
+among these different objects the
+different names kind of doesn't matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and indeed you sort of look at this
+
+ align:start position:0%
+okay and indeed you sort of look at this
+ 
+
+ align:start position:0%
+okay and indeed you sort of look at this
+up till now we've regarded tensors as
+
+ align:start position:0%
+up till now we've regarded tensors as
+ 
+
+ align:start position:0%
+up till now we've regarded tensors as
+being these sort of things that operate
+
+ align:start position:0%
+being these sort of things that operate
+ 
+
+ align:start position:0%
+being these sort of things that operate
+on vectors
+
+ align:start position:0%
+on vectors
+ 
+
+ align:start position:0%
+on vectors
+okay but why not regard vectors as
+
+ align:start position:0%
+okay but why not regard vectors as
+ 
+
+ align:start position:0%
+okay but why not regard vectors as
+things that operate on one forms
+
+ align:start position:0%
+things that operate on one forms
+ 
+
+ align:start position:0%
+things that operate on one forms
+what this sort of tells you is that this
+
+ align:start position:0%
+what this sort of tells you is that this
+ 
+
+ align:start position:0%
+what this sort of tells you is that this
+whole notion
+
+ align:start position:0%
+whole notion
+ 
+
+ align:start position:0%
+whole notion
+of tensors being separate from vectors
+
+ align:start position:0%
+of tensors being separate from vectors
+ 
+
+ align:start position:0%
+of tensors being separate from vectors
+that i talked about before
+
+ align:start position:0%
+that i talked about before
+ 
+
+ align:start position:0%
+that i talked about before
+is kind of silly
+
+ align:start position:0%
+is kind of silly
+ 
+
+ align:start position:0%
+is kind of silly
+so i'm going to revisit the definition
+
+ align:start position:0%
+so i'm going to revisit the definition
+ 
+
+ align:start position:0%
+so i'm going to revisit the definition
+of a tensor that i started the lecture
+
+ align:start position:0%
+of a tensor that i started the lecture
+ 
+
+ align:start position:0%
+of a tensor that i started the lecture
+off with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so so a new
+
+ align:start position:0%
+like so so a new
+ 
+
+ align:start position:0%
+like so so a new
+and more complete definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of type m
+
+ align:start position:0%
+of type m
+ 
+
+ align:start position:0%
+of type m
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a linear mapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of m one forms
+
+ align:start position:0%
+of m one forms
+ 
+
+ align:start position:0%
+of m one forms
+and n vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the lorenz scalars
+
+ align:start position:0%
+to the lorenz scalars
+ 
+
+ align:start position:0%
+to the lorenz scalars
+in this definition so we've already
+
+ align:start position:0%
+in this definition so we've already
+ 
+
+ align:start position:0%
+in this definition so we've already
+introduced zero one tensors
+
+ align:start position:0%
+introduced zero one tensors
+ 
+
+ align:start position:0%
+introduced zero one tensors
+those are one forms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one zero tensors are vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furthermore as i kind of emphasize when
+
+ align:start position:0%
+furthermore as i kind of emphasize when
+ 
+
+ align:start position:0%
+furthermore as i kind of emphasize when
+i wrote this sentence here
+
+ align:start position:0%
+i wrote this sentence here
+ 
+
+ align:start position:0%
+i wrote this sentence here
+the distinction between the slots that
+
+ align:start position:0%
+the distinction between the slots that
+ 
+
+ align:start position:0%
+the distinction between the slots that
+operate on vectors and the slots that
+
+ align:start position:0%
+operate on vectors and the slots that
+ 
+
+ align:start position:0%
+operate on vectors and the slots that
+operate on one forms
+
+ align:start position:0%
+operate on one forms
+ 
+
+ align:start position:0%
+operate on one forms
+it's nice for getting some of the the
+
+ align:start position:0%
+it's nice for getting some of the the
+ 
+
+ align:start position:0%
+it's nice for getting some of the the
+basic foundations laid
+
+ align:start position:0%
+basic foundations laid
+ 
+
+ align:start position:0%
+basic foundations laid
+this is one of those places where now
+
+ align:start position:0%
+this is one of those places where now
+ 
+
+ align:start position:0%
+this is one of those places where now
+that the scaffolding is in place
+
+ align:start position:0%
+that the scaffolding is in place
+ 
+
+ align:start position:0%
+that the scaffolding is in place
+you know we've had the scaffolding in
+
+ align:start position:0%
+you know we've had the scaffolding in
+ 
+
+ align:start position:0%
+you know we've had the scaffolding in
+place for a while but sort of like this
+
+ align:start position:0%
+place for a while but sort of like this
+ 
+
+ align:start position:0%
+place for a while but sort of like this
+wall of our edifest is pretty steady so
+
+ align:start position:0%
+wall of our edifest is pretty steady so
+ 
+
+ align:start position:0%
+wall of our edifest is pretty steady so
+we can kick the scaffolding away
+
+ align:start position:0%
+we can kick the scaffolding away
+ 
+
+ align:start position:0%
+we can kick the scaffolding away
+we can sort of lose this distinction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the metric lets us convert the nature of
+
+ align:start position:0%
+the metric lets us convert the nature of
+ 
+
+ align:start position:0%
+the metric lets us convert the nature of
+the slots
+
+ align:start position:0%
+the slots
+ 
+
+ align:start position:0%
+the slots
+on a tensor so if i have
+
+ align:start position:0%
+on a tensor so if i have
+ 
+
+ align:start position:0%
+on a tensor so if i have
+an m n tensor
+
+ align:start position:0%
+an m n tensor
+ 
+
+ align:start position:0%
+an m n tensor
+and i use the metric to lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means i make it an m minus one
+
+ align:start position:0%
+that means i make it an m minus one
+ 
+
+ align:start position:0%
+that means i make it an m minus one
+and plus one tensor so an example would
+
+ align:start position:0%
+and plus one tensor so an example would
+ 
+
+ align:start position:0%
+and plus one tensor so an example would
+be if i have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think that's where it's a little bit
+
+ align:start position:0%
+i think that's where it's a little bit
+ 
+
+ align:start position:0%
+i think that's where it's a little bit
+easier to read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say i've got a tensor r mu
+
+ align:start position:0%
+let's say i've got a tensor r mu
+ 
+
+ align:start position:0%
+let's say i've got a tensor r mu
+beta gamma delta and i lower
+
+ align:start position:0%
+beta gamma delta and i lower
+ 
+
+ align:start position:0%
+beta gamma delta and i lower
+that first index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this went from something that
+
+ align:start position:0%
+okay so this went from something that
+ 
+
+ align:start position:0%
+okay so this went from something that
+operates on one one form and three
+
+ align:start position:0%
+operates on one one form and three
+ 
+
+ align:start position:0%
+operates on one one form and three
+vectors now it's something that operates
+
+ align:start position:0%
+vectors now it's something that operates
+ 
+
+ align:start position:0%
+vectors now it's something that operates
+on four vectors
+
+ align:start position:0%
+on four vectors
+ 
+
+ align:start position:0%
+on four vectors
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+likewise using the inverse matrix
+
+ align:start position:0%
+likewise using the inverse matrix
+ 
+
+ align:start position:0%
+likewise using the inverse matrix
+assuming the inverse metric
+
+ align:start position:0%
+assuming the inverse metric
+ 
+
+ align:start position:0%
+assuming the inverse metric
+you can raise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just for completeness let's write
+
+ align:start position:0%
+and just for completeness let's write
+ 
+
+ align:start position:0%
+and just for completeness let's write
+that out
+
+ align:start position:0%
+that out
+ 
+
+ align:start position:0%
+that out
+so an example of this would be if i have
+
+ align:start position:0%
+so an example of this would be if i have
+ 
+
+ align:start position:0%
+so an example of this would be if i have
+some tensor s mu beta gamma
+
+ align:start position:0%
+some tensor s mu beta gamma
+ 
+
+ align:start position:0%
+some tensor s mu beta gamma
+and let's say i raise that first index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you get something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's see in my last couple
+
+ align:start position:0%
+okay so let's see in my last couple
+ 
+
+ align:start position:0%
+okay so let's see in my last couple
+minutes recall i do have to leave a
+
+ align:start position:0%
+minutes recall i do have to leave a
+ 
+
+ align:start position:0%
+minutes recall i do have to leave a
+little bit early today because i need to
+
+ align:start position:0%
+little bit early today because i need to
+ 
+
+ align:start position:0%
+little bit early today because i need to
+introduce a speaker but i
+
+ align:start position:0%
+introduce a speaker but i
+ 
+
+ align:start position:0%
+introduce a speaker but i
+just want to wrap up one thing
+
+ align:start position:0%
+just want to wrap up one thing
+ 
+
+ align:start position:0%
+just want to wrap up one thing
+kind of quickly i've spent a bunch of
+
+ align:start position:0%
+kind of quickly i've spent a bunch of
+ 
+
+ align:start position:0%
+kind of quickly i've spent a bunch of
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking about basis objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to go through this fairly
+
+ align:start position:0%
+and i'm going to go through this fairly
+ 
+
+ align:start position:0%
+and i'm going to go through this fairly
+quickly the notes if you want to see a
+
+ align:start position:0%
+quickly the notes if you want to see a
+ 
+
+ align:start position:0%
+quickly the notes if you want to see a
+few more details you're welcome to
+
+ align:start position:0%
+few more details you're welcome to
+ 
+
+ align:start position:0%
+few more details you're welcome to
+download and look at they're not really
+
+ align:start position:0%
+download and look at they're not really
+ 
+
+ align:start position:0%
+download and look at they're not really
+tricky or super
+
+ align:start position:0%
+tricky or super
+ 
+
+ align:start position:0%
+tricky or super
+super critical we know we have basis
+
+ align:start position:0%
+super critical we know we have basis
+ 
+
+ align:start position:0%
+super critical we know we have basis
+objects for vectors which hopefully you
+
+ align:start position:0%
+objects for vectors which hopefully you
+ 
+
+ align:start position:0%
+objects for vectors which hopefully you
+have pretty good intuition about we have
+
+ align:start position:0%
+have pretty good intuition about we have
+ 
+
+ align:start position:0%
+have pretty good intuition about we have
+basis objects for one forms where your
+
+ align:start position:0%
+basis objects for one forms where your
+ 
+
+ align:start position:0%
+basis objects for one forms where your
+intuition is perhaps a little bit more
+
+ align:start position:0%
+intuition is perhaps a little bit more
+ 
+
+ align:start position:0%
+intuition is perhaps a little bit more
+befuddled but it'll come with time
+
+ align:start position:0%
+befuddled but it'll come with time
+ 
+
+ align:start position:0%
+befuddled but it'll come with time
+so you might think uh now i've got two
+
+ align:start position:0%
+so you might think uh now i've got two
+ 
+
+ align:start position:0%
+so you might think uh now i've got two
+index tensors i've got three index
+
+ align:start position:0%
+index tensors i've got three index
+ 
+
+ align:start position:0%
+index tensors i've got three index
+tensors there's a four index tensor on
+
+ align:start position:0%
+tensors there's a four index tensor on
+ 
+
+ align:start position:0%
+tensors there's a four index tensor on
+the board
+
+ align:start position:0%
+the board
+ 
+
+ align:start position:0%
+the board
+scott's probably gonna write a 17 and x
+
+ align:start position:0%
+scott's probably gonna write a 17 and x
+ 
+
+ align:start position:0%
+scott's probably gonna write a 17 and x
+tensor on the board at some point do i
+
+ align:start position:0%
+tensor on the board at some point do i
+ 
+
+ align:start position:0%
+tensor on the board at some point do i
+need a basis object for every one of
+
+ align:start position:0%
+need a basis object for every one of
+ 
+
+ align:start position:0%
+need a basis object for every one of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+so in other words do we need
+
+ align:start position:0%
+so in other words do we need
+ 
+
+ align:start position:0%
+so in other words do we need
+do we do weed do we
+
+ align:start position:0%
+do we do weed do we
+ 
+
+ align:start position:0%
+do we do weed do we
+need lee
+
+ align:start position:0%
+need lee
+ 
+
+ align:start position:0%
+need lee
+glad that's caught on video um
+
+ align:start position:0%
+glad that's caught on video um
+ 
+
+ align:start position:0%
+glad that's caught on video um
+do i need to be able to say something
+
+ align:start position:0%
+do i need to be able to say something
+ 
+
+ align:start position:0%
+do i need to be able to say something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+the abstract metric tensor is these
+
+ align:start position:0%
+the abstract metric tensor is these
+ 
+
+ align:start position:0%
+the abstract metric tensor is these
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+times some kind of a two index
+
+ align:start position:0%
+times some kind of a two index
+ 
+
+ align:start position:0%
+times some kind of a two index
+basis object okay
+
+ align:start position:0%
+basis object okay
+ 
+
+ align:start position:0%
+basis object okay
+okay do i need to do something like this
+
+ align:start position:0%
+okay do i need to do something like this
+ 
+
+ align:start position:0%
+okay do i need to do something like this
+cutting to the chase
+
+ align:start position:0%
+cutting to the chase
+ 
+
+ align:start position:0%
+cutting to the chase
+the answer is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis one forms and vectors are
+
+ align:start position:0%
+basis one forms and vectors are
+ 
+
+ align:start position:0%
+basis one forms and vectors are
+sufficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we're going to do is abstractly
+
+ align:start position:0%
+so what we're going to do is abstractly
+ 
+
+ align:start position:0%
+so what we're going to do is abstractly
+sort of just imagine that if i do have a
+
+ align:start position:0%
+sort of just imagine that if i do have a
+ 
+
+ align:start position:0%
+sort of just imagine that if i do have a
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+i kind of have an outer product okay i
+
+ align:start position:0%
+i kind of have an outer product okay i
+ 
+
+ align:start position:0%
+i kind of have an outer product okay i
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+both of the basis objects attached to
+
+ align:start position:0%
+both of the basis objects attached to
+ 
+
+ align:start position:0%
+both of the basis objects attached to
+this thing
+
+ align:start position:0%
+this thing
+ 
+
+ align:start position:0%
+this thing
+and each one is just attached to those
+
+ align:start position:0%
+and each one is just attached to those
+ 
+
+ align:start position:0%
+and each one is just attached to those
+two slots
+
+ align:start position:0%
+two slots
+ 
+
+ align:start position:0%
+two slots
+okay so in this particular case
+
+ align:start position:0%
+okay so in this particular case
+ 
+
+ align:start position:0%
+okay so in this particular case
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two index basis uh two index basis
+
+ align:start position:0%
+two index basis uh two index basis
+ 
+
+ align:start position:0%
+two index basis uh two index basis
+two form that would go with this thing
+
+ align:start position:0%
+two form that would go with this thing
+ 
+
+ align:start position:0%
+two form that would go with this thing
+here anything with two indices on it
+
+ align:start position:0%
+here anything with two indices on it
+ 
+
+ align:start position:0%
+here anything with two indices on it
+i'm just going to regard this as i'll
+
+ align:start position:0%
+i'm just going to regard this as i'll
+ 
+
+ align:start position:0%
+i'm just going to regard this as i'll
+abstractly
+
+ align:start position:0%
+abstractly
+ 
+
+ align:start position:0%
+abstractly
+write this as just an outer product of
+
+ align:start position:0%
+write this as just an outer product of
+ 
+
+ align:start position:0%
+write this as just an outer product of
+the basis one forms
+
+ align:start position:0%
+the basis one forms
+ 
+
+ align:start position:0%
+the basis one forms
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i whoops if i ever need a basis
+
+ align:start position:0%
+if i whoops if i ever need a basis
+ 
+
+ align:start position:0%
+if i whoops if i ever need a basis
+object for a tensor like this i will
+
+ align:start position:0%
+object for a tensor like this i will
+ 
+
+ align:start position:0%
+object for a tensor like this i will
+just regard this
+
+ align:start position:0%
+just regard this
+ 
+
+ align:start position:0%
+just regard this
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an outer product of these two things so
+
+ align:start position:0%
+an outer product of these two things so
+ 
+
+ align:start position:0%
+an outer product of these two things so
+what's going on with that notation what
+
+ align:start position:0%
+what's going on with that notation what
+ 
+
+ align:start position:0%
+what's going on with that notation what
+does this mean
+
+ align:start position:0%
+does this mean
+ 
+
+ align:start position:0%
+does this mean
+i don't really lose too much sweep about
+
+ align:start position:0%
+i don't really lose too much sweep about
+ 
+
+ align:start position:0%
+i don't really lose too much sweep about
+it it's basically just saying that i
+
+ align:start position:0%
+it it's basically just saying that i
+ 
+
+ align:start position:0%
+it it's basically just saying that i
+have separate objects
+
+ align:start position:0%
+have separate objects
+ 
+
+ align:start position:0%
+have separate objects
+attached to all of my different indices
+
+ align:start position:0%
+attached to all of my different indices
+ 
+
+ align:start position:0%
+attached to all of my different indices
+and they're kind of coming along here
+
+ align:start position:0%
+and they're kind of coming along here
+ 
+
+ align:start position:0%
+and they're kind of coming along here
+and giving a sense of direction to these
+
+ align:start position:0%
+and giving a sense of direction to these
+ 
+
+ align:start position:0%
+and giving a sense of direction to these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so for instance if i have some kind of a
+
+ align:start position:0%
+so for instance if i have some kind of a
+ 
+
+ align:start position:0%
+so for instance if i have some kind of a
+tensor i mean a great one which we're
+
+ align:start position:0%
+tensor i mean a great one which we're
+ 
+
+ align:start position:0%
+tensor i mean a great one which we're
+going to talk about in just a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a quantity known as the stress energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in which i can abstractly think of the
+
+ align:start position:0%
+in which i can abstractly think of the
+ 
+
+ align:start position:0%
+in which i can abstractly think of the
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+as having
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean not to subtract it will have two
+
+ align:start position:0%
+i mean not to subtract it will have two
+ 
+
+ align:start position:0%
+i mean not to subtract it will have two
+components and i can think of it as
+
+ align:start position:0%
+components and i can think of it as
+ 
+
+ align:start position:0%
+components and i can think of it as
+essentially pointing
+
+ align:start position:0%
+essentially pointing
+ 
+
+ align:start position:0%
+essentially pointing
+in two different directions
+
+ align:start position:0%
+in two different directions
+ 
+
+ align:start position:0%
+in two different directions
+at once now we're going to talk about
+
+ align:start position:0%
+at once now we're going to talk about
+ 
+
+ align:start position:0%
+at once now we're going to talk about
+this in a lot more detail
+
+ align:start position:0%
+this in a lot more detail
+ 
+
+ align:start position:0%
+this in a lot more detail
+in a couple of weeks actually not even a
+
+ align:start position:0%
+in a couple of weeks actually not even a
+ 
+
+ align:start position:0%
+in a couple of weeks actually not even a
+couple weeks a couple of lectures
+
+ align:start position:0%
+couple weeks a couple of lectures
+ 
+
+ align:start position:0%
+couple weeks a couple of lectures
+what i'm going to teach you is that the
+
+ align:start position:0%
+what i'm going to teach you is that the
+ 
+
+ align:start position:0%
+what i'm going to teach you is that the
+alpha beta compound of the stress energy
+
+ align:start position:0%
+alpha beta compound of the stress energy
+ 
+
+ align:start position:0%
+alpha beta compound of the stress energy
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+tells me about the flux of
+
+ align:start position:0%
+tells me about the flux of
+ 
+
+ align:start position:0%
+tells me about the flux of
+four momentum component alpha in the
+
+ align:start position:0%
+four momentum component alpha in the
+ 
+
+ align:start position:0%
+four momentum component alpha in the
+beta direction
+
+ align:start position:0%
+beta direction
+ 
+
+ align:start position:0%
+beta direction
+okay and so this is basically the saying
+
+ align:start position:0%
+okay and so this is basically the saying
+ 
+
+ align:start position:0%
+okay and so this is basically the saying
+you know when i think of it as
+
+ align:start position:0%
+you know when i think of it as
+ 
+
+ align:start position:0%
+you know when i think of it as
+the actual object not just the
+
+ align:start position:0%
+the actual object not just the
+ 
+
+ align:start position:0%
+the actual object not just the
+representation according to some
+
+ align:start position:0%
+representation according to some
+ 
+
+ align:start position:0%
+representation according to some
+observer
+
+ align:start position:0%
+observer
+ 
+
+ align:start position:0%
+observer
+here is the thing that gives me the
+
+ align:start position:0%
+here is the thing that gives me the
+ 
+
+ align:start position:0%
+here is the thing that gives me the
+direction of my four velocity
+
+ align:start position:0%
+direction of my four velocity
+ 
+
+ align:start position:0%
+direction of my four velocity
+gives me my four momentum and here is
+
+ align:start position:0%
+gives me my four momentum and here is
+ 
+
+ align:start position:0%
+gives me my four momentum and here is
+the direction in which it is flowing
+
+ align:start position:0%
+the direction in which it is flowing
+ 
+
+ align:start position:0%
+the direction in which it is flowing
+okay and you know sometimes we will make
+
+ align:start position:0%
+okay and you know sometimes we will make
+ 
+
+ align:start position:0%
+okay and you know sometimes we will make
+more complicated objects and so you
+
+ align:start position:0%
+more complicated objects and so you
+ 
+
+ align:start position:0%
+more complicated objects and so you
+might need to
+
+ align:start position:0%
+might need to
+ 
+
+ align:start position:0%
+might need to
+sort of imagine here's one which i
+
+ align:start position:0%
+sort of imagine here's one which i
+ 
+
+ align:start position:0%
+sort of imagine here's one which i
+actually wrote down in my notes here
+
+ align:start position:0%
+actually wrote down in my notes here
+ 
+
+ align:start position:0%
+actually wrote down in my notes here
+there will be times when we're going to
+
+ align:start position:0%
+there will be times when we're going to
+ 
+
+ align:start position:0%
+there will be times when we're going to
+care about a tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which at least abstractly we might need
+
+ align:start position:0%
+which at least abstractly we might need
+ 
+
+ align:start position:0%
+which at least abstractly we might need
+to regard as having this whole
+
+ align:start position:0%
+to regard as having this whole
+ 
+
+ align:start position:0%
+to regard as having this whole
+set of sort of vomitous uh basis vectors
+
+ align:start position:0%
+set of sort of vomitous uh basis vectors
+ 
+
+ align:start position:0%
+set of sort of vomitous uh basis vectors
+coming along for the ride here
+
+ align:start position:0%
+coming along for the ride here
+ 
+
+ align:start position:0%
+coming along for the ride here
+okay and you know it's it is actually
+
+ align:start position:0%
+okay and you know it's it is actually
+ 
+
+ align:start position:0%
+okay and you know it's it is actually
+fairly important to have all these
+
+ align:start position:0%
+fairly important to have all these
+ 
+
+ align:start position:0%
+fairly important to have all these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+that are in place where i will just
+
+ align:start position:0%
+that are in place where i will just
+ 
+
+ align:start position:0%
+that are in place where i will just
+conclude things for today
+
+ align:start position:0%
+conclude things for today
+ 
+
+ align:start position:0%
+conclude things for today
+is that the place where it is
+
+ align:start position:0%
+is that the place where it is
+ 
+
+ align:start position:0%
+is that the place where it is
+particularly important to remember that
+
+ align:start position:0%
+particularly important to remember that
+ 
+
+ align:start position:0%
+particularly important to remember that
+we kind of
+
+ align:start position:0%
+we kind of
+ 
+
+ align:start position:0%
+we kind of
+sometimes almost just implicitly have
+
+ align:start position:0%
+sometimes almost just implicitly have
+ 
+
+ align:start position:0%
+sometimes almost just implicitly have
+these things coming along for the ride
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's important when we calculate
+
+ align:start position:0%
+it's important when we calculate
+ 
+
+ align:start position:0%
+it's important when we calculate
+derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um i gave you guys an example
+
+ align:start position:0%
+so um i gave you guys an example
+ 
+
+ align:start position:0%
+so um i gave you guys an example
+of a sort of a a directional derivative
+
+ align:start position:0%
+of a sort of a a directional derivative
+ 
+
+ align:start position:0%
+of a sort of a a directional derivative
+for a scalar field that filled all space
+
+ align:start position:0%
+for a scalar field that filled all space
+ 
+
+ align:start position:0%
+for a scalar field that filled all space
+on i imagine that there was some
+
+ align:start position:0%
+on i imagine that there was some
+ 
+
+ align:start position:0%
+on i imagine that there was some
+trajectory of an observer moving through
+
+ align:start position:0%
+trajectory of an observer moving through
+ 
+
+ align:start position:0%
+trajectory of an observer moving through
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+now imagine it isn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a scalar field that fills all space time
+
+ align:start position:0%
+a scalar field that fills all space time
+ 
+
+ align:start position:0%
+a scalar field that fills all space time
+but it's a tensor field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's t it's the y direction
+
+ align:start position:0%
+so here's t it's the y direction
+ 
+
+ align:start position:0%
+so here's t it's the y direction
+the x direction here's my observer
+
+ align:start position:0%
+the x direction here's my observer
+ 
+
+ align:start position:0%
+the x direction here's my observer
+moving through all this thing
+
+ align:start position:0%
+moving through all this thing
+ 
+
+ align:start position:0%
+moving through all this thing
+and again i'm going to say that this
+
+ align:start position:0%
+and again i'm going to say that this
+ 
+
+ align:start position:0%
+and again i'm going to say that this
+trajectory is characterized by a floor
+
+ align:start position:0%
+trajectory is characterized by a floor
+ 
+
+ align:start position:0%
+trajectory is characterized by a floor
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+dxd tau and i'm going to imagine that
+
+ align:start position:0%
+dxd tau and i'm going to imagine that
+ 
+
+ align:start position:0%
+dxd tau and i'm going to imagine that
+there is some
+
+ align:start position:0%
+there is some
+ 
+
+ align:start position:0%
+there is some
+tensor field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it fills all of space time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when i go and calculate
+
+ align:start position:0%
+when i go and calculate
+ 
+
+ align:start position:0%
+when i go and calculate
+the derivative of this thing
+
+ align:start position:0%
+the derivative of this thing
+ 
+
+ align:start position:0%
+the derivative of this thing
+when we're working in special relativity
+
+ align:start position:0%
+when we're working in special relativity
+ 
+
+ align:start position:0%
+when we're working in special relativity
+where we are right now
+
+ align:start position:0%
+where we are right now
+ 
+
+ align:start position:0%
+where we are right now
+these guys are going to be constant so
+
+ align:start position:0%
+these guys are going to be constant so
+ 
+
+ align:start position:0%
+these guys are going to be constant so
+it doesn't really matter but soon we're
+
+ align:start position:0%
+it doesn't really matter but soon we're
+ 
+
+ align:start position:0%
+it doesn't really matter but soon we're
+going to generalize to
+
+ align:start position:0%
+going to generalize to
+ 
+
+ align:start position:0%
+going to generalize to
+more complicated geometries more
+
+ align:start position:0%
+more complicated geometries more
+ 
+
+ align:start position:0%
+more complicated geometries more
+complicated space times
+
+ align:start position:0%
+complicated space times
+ 
+
+ align:start position:0%
+complicated space times
+and the basis objects will themselves
+
+ align:start position:0%
+and the basis objects will themselves
+ 
+
+ align:start position:0%
+and the basis objects will themselves
+vary as i move along the trajectory
+
+ align:start position:0%
+vary as i move along the trajectory
+ 
+
+ align:start position:0%
+vary as i move along the trajectory
+and i will need to in order to have
+
+ align:start position:0%
+and i will need to in order to have
+ 
+
+ align:start position:0%
+and i will need to in order to have
+a notion of a derivative that is a
+
+ align:start position:0%
+a notion of a derivative that is a
+ 
+
+ align:start position:0%
+a notion of a derivative that is a
+properly formed geometric object
+
+ align:start position:0%
+properly formed geometric object
+ 
+
+ align:start position:0%
+properly formed geometric object
+i'm gonna have to worry about how the
+
+ align:start position:0%
+i'm gonna have to worry about how the
+ 
+
+ align:start position:0%
+i'm gonna have to worry about how the
+basis objects change as i move along the
+
+ align:start position:0%
+basis objects change as i move along the
+ 
+
+ align:start position:0%
+basis objects change as i move along the
+trajectory as well
+
+ align:start position:0%
+trajectory as well
+ 
+
+ align:start position:0%
+trajectory as well
+okay so that tends to just make the
+
+ align:start position:0%
+okay so that tends to just make the
+ 
+
+ align:start position:0%
+okay so that tends to just make the
+analysis a little bit more complicated
+
+ align:start position:0%
+analysis a little bit more complicated
+ 
+
+ align:start position:0%
+analysis a little bit more complicated
+i have a few notes about this that i
+
+ align:start position:0%
+i have a few notes about this that i
+ 
+
+ align:start position:0%
+i have a few notes about this that i
+will put up onto the web page but
+
+ align:start position:0%
+will put up onto the web page but
+ 
+
+ align:start position:0%
+will put up onto the web page but
+i don't want to go into too much detail
+
+ align:start position:0%
+i don't want to go into too much detail
+ 
+
+ align:start position:0%
+i don't want to go into too much detail
+beyond that until we actually get into
+
+ align:start position:0%
+beyond that until we actually get into
+ 
+
+ align:start position:0%
+beyond that until we actually get into
+some of the details of these derivatives
+
+ align:start position:0%
+some of the details of these derivatives
+ 
+
+ align:start position:0%
+some of the details of these derivatives
+so i'm just going to leave it at that
+
+ align:start position:0%
+so i'm just going to leave it at that
+ 
+
+ align:start position:0%
+so i'm just going to leave it at that
+for now
+
+ align:start position:0%
+for now
+ 
+
+ align:start position:0%
+for now
+so yeah i'll just say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the derivative in principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and quite often in practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will depend on how these guys
+
+ align:start position:0%
+it will depend on how these guys
+ 
+
+ align:start position:0%
+it will depend on how these guys
+vary in space and time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me just say you guys kind of
+
+ align:start position:0%
+and let me just say you guys kind of
+ 
+
+ align:start position:0%
+and let me just say you guys kind of
+already know that because when you
+
+ align:start position:0%
+already know that because when you
+ 
+
+ align:start position:0%
+already know that because when you
+studied e
+
+ align:start position:0%
+studied e
+ 
+
+ align:start position:0%
+studied e
+m you got these somewhat complicated
+
+ align:start position:0%
+m you got these somewhat complicated
+ 
+
+ align:start position:0%
+m you got these somewhat complicated
+formulas for things like the divergence
+
+ align:start position:0%
+formulas for things like the divergence
+ 
+
+ align:start position:0%
+formulas for things like the divergence
+and curl and stuff like that
+
+ align:start position:0%
+and curl and stuff like that
+ 
+
+ align:start position:0%
+and curl and stuff like that
+and those are essentially because those
+
+ align:start position:0%
+and those are essentially because those
+ 
+
+ align:start position:0%
+and those are essentially because those
+are sort of notions of derivative where
+
+ align:start position:0%
+are sort of notions of derivative where
+ 
+
+ align:start position:0%
+are sort of notions of derivative where
+you are taking into account the fact
+
+ align:start position:0%
+you are taking into account the fact
+ 
+
+ align:start position:0%
+you are taking into account the fact
+that when you're in a curvilinear
+
+ align:start position:0%
+that when you're in a curvilinear
+ 
+
+ align:start position:0%
+that when you're in a curvilinear
+coordinate system your basis vectors are
+
+ align:start position:0%
+coordinate system your basis vectors are
+ 
+
+ align:start position:0%
+coordinate system your basis vectors are
+shifting as you move from point to point
+
+ align:start position:0%
+shifting as you move from point to point
+ 
+
+ align:start position:0%
+shifting as you move from point to point
+okay the stuff we're going to get out of
+
+ align:start position:0%
+okay the stuff we're going to get out of
+ 
+
+ align:start position:0%
+okay the stuff we're going to get out of
+this will look a little bit different
+
+ align:start position:0%
+this will look a little bit different
+ 
+
+ align:start position:0%
+this will look a little bit different
+and it comes to the fact as i emphasize
+
+ align:start position:0%
+and it comes to the fact as i emphasize
+ 
+
+ align:start position:0%
+and it comes to the fact as i emphasize
+in my last lecture that we are going to
+
+ align:start position:0%
+in my last lecture that we are going to
+ 
+
+ align:start position:0%
+in my last lecture that we are going to
+tend to use what we call a coordinate
+
+ align:start position:0%
+tend to use what we call a coordinate
+ 
+
+ align:start position:0%
+tend to use what we call a coordinate
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+whereas when you guys learn stuff in e m
+
+ align:start position:0%
+whereas when you guys learn stuff in e m
+ 
+
+ align:start position:0%
+whereas when you guys learn stuff in e m
+you are using what's known as an
+
+ align:start position:0%
+you are using what's known as an
+ 
+
+ align:start position:0%
+you are using what's known as an
+orthonormal basis
+
+ align:start position:0%
+orthonormal basis
+ 
+
+ align:start position:0%
+orthonormal basis
+it does lead to slight differences
+
+ align:start position:0%
+it does lead to slight differences
+ 
+
+ align:start position:0%
+it does lead to slight differences
+there's a mapping between them
+
+ align:start position:0%
+there's a mapping between them
+ 
+
+ align:start position:0%
+there's a mapping between them
+not that hard to figure it out but we
+
+ align:start position:0%
+not that hard to figure it out but we
+ 
+
+ align:start position:0%
+not that hard to figure it out but we
+don't need to get into those weeds just
+
+ align:start position:0%
+don't need to get into those weeds just
+ 
+
+ align:start position:0%
+don't need to get into those weeds just
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+all right so i will pick it up from
+
+ align:start position:0%
+all right so i will pick it up from
+ 
+
+ align:start position:0%
+all right so i will pick it up from
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+on thursday so i'll begin with a brief
+
+ align:start position:0%
+on thursday so i'll begin with a brief
+ 
+
+ align:start position:0%
+on thursday so i'll begin with a brief
+recap of everything we did
+
+ align:start position:0%
+recap of everything we did
+ 
+
+ align:start position:0%
+recap of everything we did
+the primary thing which i really wanted
+
+ align:start position:0%
+the primary thing which i really wanted
+ 
+
+ align:start position:0%
+the primary thing which i really wanted
+to emphasize more than anything
+
+ align:start position:0%
+to emphasize more than anything
+ 
+
+ align:start position:0%
+to emphasize more than anything
+is this board plus this idea that the
+
+ align:start position:0%
+is this board plus this idea that the
+ 
+
+ align:start position:0%
+is this board plus this idea that the
+metric can be used to raise and lower
+
+ align:start position:0%
+metric can be used to raise and lower
+ 
+
+ align:start position:0%
+metric can be used to raise and lower
+the indices of a tensor okay at this
+
+ align:start position:0%
+the indices of a tensor okay at this
+ 
+
+ align:start position:0%
+the indices of a tensor okay at this
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+talking about vectors talking about one
+
+ align:start position:0%
+talking about vectors talking about one
+ 
+
+ align:start position:0%
+talking about vectors talking about one
+forms
+
+ align:start position:0%
+forms
+ 
+
+ align:start position:0%
+forms
+you know many of you in a math class
+
+ align:start position:0%
+you know many of you in a math class
+ 
+
+ align:start position:0%
+you know many of you in a math class
+probably learned about contravarian
+
+ align:start position:0%
+probably learned about contravarian
+ 
+
+ align:start position:0%
+probably learned about contravarian
+vector components and covariant vector
+
+ align:start position:0%
+vector components and covariant vector
+ 
+
+ align:start position:0%
+vector components and covariant vector
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+once you've got a metric it's kind of
+
+ align:start position:0%
+once you've got a metric it's kind of
+ 
+
+ align:start position:0%
+once you've got a metric it's kind of
+like who cares okay you can just go from
+
+ align:start position:0%
+like who cares okay you can just go from
+ 
+
+ align:start position:0%
+like who cares okay you can just go from
+one to the other
+
+ align:start position:0%
+one to the other
+ 
+
+ align:start position:0%
+one to the other
+and that's why i tend to uh almost
+
+ align:start position:0%
+and that's why i tend to uh almost
+ 
+
+ align:start position:0%
+and that's why i tend to uh almost
+religiously
+
+ align:start position:0%
+religiously
+ 
+
+ align:start position:0%
+religiously
+i avoid the terms covariance
+
+ align:start position:0%
+i avoid the terms covariance
+ 
+
+ align:start position:0%
+i avoid the terms covariance
+contravariant and i say upstairs and
+
+ align:start position:0%
+contravariant and i say upstairs and
+ 
+
+ align:start position:0%
+contravariant and i say upstairs and
+downstairs
+
+ align:start position:0%
+downstairs
+ 
+
+ align:start position:0%
+downstairs
+okay because i can flip back and forth
+
+ align:start position:0%
+okay because i can flip back and forth
+ 
+
+ align:start position:0%
+okay because i can flip back and forth
+between them and they're physical
+
+ align:start position:0%
+between them and they're physical
+ 
+
+ align:start position:0%
+between them and they're physical
+there's really no physical meaning in
+
+ align:start position:0%
+there's really no physical meaning in
+ 
+
+ align:start position:0%
+there's really no physical meaning in
+them you have to think carefully about
+
+ align:start position:0%
+them you have to think carefully about
+ 
+
+ align:start position:0%
+them you have to think carefully about
+what is physically measurable and it
+
+ align:start position:0%
+what is physically measurable and it
+ 
+
+ align:start position:0%
+what is physically measurable and it
+kind of has nothing to do with one
+
+ align:start position:0%
+kind of has nothing to do with one
+ 
+
+ align:start position:0%
+kind of has nothing to do with one
+with whether it's covariant or calm
+
+ align:start position:0%
+with whether it's covariant or calm
+ 
+
+ align:start position:0%
+with whether it's covariant or calm
+variant upstairs or downstairs
+
+ align:start position:0%
+variant upstairs or downstairs
+ 
+
+ align:start position:0%
+variant upstairs or downstairs
+all right i will end there since i have
+
+ align:start position:0%
+all right i will end there since i have
+ 
+
+ align:start position:0%
+all right i will end there since i have
+to go and introduce someone
+
+ align:start position:0%
+to go and introduce someone
+ 
+
+ align:start position:0%
+to go and introduce someone
+you
\ No newline at end of file
diff --git a/HTs6Zhc2S1M.txt b/HTs6Zhc2S1M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..643922b8f4482c9e99685a6ba23c19a9c7868d09
--- /dev/null
+++ b/HTs6Zhc2S1M.txt
@@ -0,0 +1,1195 @@
+align:start position:0%
+ 
+the covariance between two random
+
+ align:start position:0%
+the covariance between two random
+ 
+
+ align:start position:0%
+the covariance between two random
+variables tells us something about the
+
+ align:start position:0%
+variables tells us something about the
+ 
+
+ align:start position:0%
+variables tells us something about the
+strength of the dependence between them
+
+ align:start position:0%
+strength of the dependence between them
+ 
+
+ align:start position:0%
+strength of the dependence between them
+but it is not so easy to interpret
+
+ align:start position:0%
+but it is not so easy to interpret
+ 
+
+ align:start position:0%
+but it is not so easy to interpret
+qualitatively for example if I tell you
+
+ align:start position:0%
+qualitatively for example if I tell you
+ 
+
+ align:start position:0%
+qualitatively for example if I tell you
+that the covariance of x and y is equal
+
+ align:start position:0%
+that the covariance of x and y is equal
+ 
+
+ align:start position:0%
+that the covariance of x and y is equal
+to 5 this does not tell you very much
+
+ align:start position:0%
+to 5 this does not tell you very much
+ 
+
+ align:start position:0%
+to 5 this does not tell you very much
+about whether x and y are closely
+
+ align:start position:0%
+about whether x and y are closely
+ 
+
+ align:start position:0%
+about whether x and y are closely
+related or not another difficulty is
+
+ align:start position:0%
+related or not another difficulty is
+ 
+
+ align:start position:0%
+related or not another difficulty is
+that if x and y are in units let's say
+
+ align:start position:0%
+that if x and y are in units let's say
+ 
+
+ align:start position:0%
+that if x and y are in units let's say
+of meters then the covariance will have
+
+ align:start position:0%
+of meters then the covariance will have
+ 
+
+ align:start position:0%
+of meters then the covariance will have
+units of meters squared and this is hard
+
+ align:start position:0%
+units of meters squared and this is hard
+ 
+
+ align:start position:0%
+units of meters squared and this is hard
+to interpret a much more informative
+
+ align:start position:0%
+to interpret a much more informative
+ 
+
+ align:start position:0%
+to interpret a much more informative
+quantity is the so called correlation
+
+ align:start position:0%
+quantity is the so called correlation
+ 
+
+ align:start position:0%
+quantity is the so called correlation
+coefficient which is a dimensionless
+
+ align:start position:0%
+coefficient which is a dimensionless
+ 
+
+ align:start position:0%
+coefficient which is a dimensionless
+version of the covariance it is defined
+
+ align:start position:0%
+version of the covariance it is defined
+ 
+
+ align:start position:0%
+version of the covariance it is defined
+by this formula here we just take the
+
+ align:start position:0%
+by this formula here we just take the
+ 
+
+ align:start position:0%
+by this formula here we just take the
+covariance and divide it by the product
+
+ align:start position:0%
+covariance and divide it by the product
+ 
+
+ align:start position:0%
+covariance and divide it by the product
+of the standard deviations of the two
+
+ align:start position:0%
+of the standard deviations of the two
+ 
+
+ align:start position:0%
+of the standard deviations of the two
+random variables now if X has units of
+
+ align:start position:0%
+random variables now if X has units of
+ 
+
+ align:start position:0%
+random variables now if X has units of
+meters then the standard deviation also
+
+ align:start position:0%
+meters then the standard deviation also
+ 
+
+ align:start position:0%
+meters then the standard deviation also
+has units of meters and so this ratio
+
+ align:start position:0%
+has units of meters and so this ratio
+ 
+
+ align:start position:0%
+has units of meters and so this ratio
+will be dimensionless and it is not
+
+ align:start position:0%
+will be dimensionless and it is not
+ 
+
+ align:start position:0%
+will be dimensionless and it is not
+affected by the units that were using
+
+ align:start position:0%
+affected by the units that were using
+ 
+
+ align:start position:0%
+affected by the units that were using
+the same is true for this ratio here and
+
+ align:start position:0%
+the same is true for this ratio here and
+ 
+
+ align:start position:0%
+the same is true for this ratio here and
+this is why the correlation coefficient
+
+ align:start position:0%
+this is why the correlation coefficient
+ 
+
+ align:start position:0%
+this is why the correlation coefficient
+does not have any units of its own one
+
+ align:start position:0%
+does not have any units of its own one
+ 
+
+ align:start position:0%
+does not have any units of its own one
+remark if we're dealing with the random
+
+ align:start position:0%
+remark if we're dealing with the random
+ 
+
+ align:start position:0%
+remark if we're dealing with the random
+variable whose standard deviation is
+
+ align:start position:0%
+variable whose standard deviation is
+ 
+
+ align:start position:0%
+variable whose standard deviation is
+equal to zero so its variance is also
+
+ align:start position:0%
+equal to zero so its variance is also
+ 
+
+ align:start position:0%
+equal to zero so its variance is also
+equal to zero then we have a random
+
+ align:start position:0%
+equal to zero then we have a random
+ 
+
+ align:start position:0%
+equal to zero then we have a random
+variable which is identically equal to a
+
+ align:start position:0%
+variable which is identically equal to a
+ 
+
+ align:start position:0%
+variable which is identically equal to a
+constant well for such cases of the
+
+ align:start position:0%
+constant well for such cases of the
+ 
+
+ align:start position:0%
+constant well for such cases of the
+general random variables then the
+
+ align:start position:0%
+general random variables then the
+ 
+
+ align:start position:0%
+general random variables then the
+correlation coefficient is not defined
+
+ align:start position:0%
+correlation coefficient is not defined
+ 
+
+ align:start position:0%
+correlation coefficient is not defined
+because it would have involved a
+
+ align:start position:0%
+because it would have involved a
+ 
+
+ align:start position:0%
+because it would have involved a
+division by zero a very important
+
+ align:start position:0%
+division by zero a very important
+ 
+
+ align:start position:0%
+division by zero a very important
+property of the correlation coefficient
+
+ align:start position:0%
+property of the correlation coefficient
+ 
+
+ align:start position:0%
+property of the correlation coefficient
+is the following it turns out that the
+
+ align:start position:0%
+is the following it turns out that the
+ 
+
+ align:start position:0%
+is the following it turns out that the
+correlation coefficient is always
+
+ align:start position:0%
+correlation coefficient is always
+ 
+
+ align:start position:0%
+correlation coefficient is always
+between minus 1 and 1 and this allows us
+
+ align:start position:0%
+between minus 1 and 1 and this allows us
+ 
+
+ align:start position:0%
+between minus 1 and 1 and this allows us
+to judge whether a certain correlation
+
+ align:start position:0%
+to judge whether a certain correlation
+ 
+
+ align:start position:0%
+to judge whether a certain correlation
+coefficient is big or not because we now
+
+ align:start position:0%
+coefficient is big or not because we now
+ 
+
+ align:start position:0%
+coefficient is big or not because we now
+have an absolute scale and so it does
+
+ align:start position:0%
+have an absolute scale and so it does
+ 
+
+ align:start position:0%
+have an absolute scale and so it does
+provide a measure of the degree to which
+
+ align:start position:0%
+provide a measure of the degree to which
+ 
+
+ align:start position:0%
+provide a measure of the degree to which
+two random variables are associated to
+
+ align:start position:0%
+two random variables are associated to
+ 
+
+ align:start position:0%
+two random variables are associated to
+interpret the correlation coefficient
+
+ align:start position:0%
+interpret the correlation coefficient
+ 
+
+ align:start position:0%
+interpret the correlation coefficient
+let us now look at some extreme cases
+
+ align:start position:0%
+let us now look at some extreme cases
+ 
+
+ align:start position:0%
+let us now look at some extreme cases
+suppose that
+
+ align:start position:0%
+suppose that
+ 
+
+ align:start position:0%
+suppose that
+and why are independent in that case we
+
+ align:start position:0%
+and why are independent in that case we
+ 
+
+ align:start position:0%
+and why are independent in that case we
+know that the covariance is going to be
+
+ align:start position:0%
+know that the covariance is going to be
+ 
+
+ align:start position:0%
+know that the covariance is going to be
+equal to zero and therefore the
+
+ align:start position:0%
+equal to zero and therefore the
+ 
+
+ align:start position:0%
+equal to zero and therefore the
+correlation coefficient is also going to
+
+ align:start position:0%
+correlation coefficient is also going to
+ 
+
+ align:start position:0%
+correlation coefficient is also going to
+be equal to zero and in that case we say
+
+ align:start position:0%
+be equal to zero and in that case we say
+ 
+
+ align:start position:0%
+be equal to zero and in that case we say
+that the two random variables are
+
+ align:start position:0%
+that the two random variables are
+ 
+
+ align:start position:0%
+that the two random variables are
+uncorrelated however the converse
+
+ align:start position:0%
+uncorrelated however the converse
+ 
+
+ align:start position:0%
+uncorrelated however the converse
+statement is not true we have seen
+
+ align:start position:0%
+statement is not true we have seen
+ 
+
+ align:start position:0%
+statement is not true we have seen
+already an example in which we have zero
+
+ align:start position:0%
+already an example in which we have zero
+ 
+
+ align:start position:0%
+already an example in which we have zero
+covariance and therefore zero
+
+ align:start position:0%
+covariance and therefore zero
+ 
+
+ align:start position:0%
+covariance and therefore zero
+correlation but yet the two random
+
+ align:start position:0%
+correlation but yet the two random
+ 
+
+ align:start position:0%
+correlation but yet the two random
+variables were dependent let us now look
+
+ align:start position:0%
+variables were dependent let us now look
+ 
+
+ align:start position:0%
+variables were dependent let us now look
+at the other extreme where the two
+
+ align:start position:0%
+at the other extreme where the two
+ 
+
+ align:start position:0%
+at the other extreme where the two
+random variables are as dependent as
+
+ align:start position:0%
+random variables are as dependent as
+ 
+
+ align:start position:0%
+random variables are as dependent as
+they can be so let's look at the
+
+ align:start position:0%
+they can be so let's look at the
+ 
+
+ align:start position:0%
+they can be so let's look at the
+correlation coefficient of one random
+
+ align:start position:0%
+correlation coefficient of one random
+ 
+
+ align:start position:0%
+correlation coefficient of one random
+variable with itself what is it going to
+
+ align:start position:0%
+variable with itself what is it going to
+ 
+
+ align:start position:0%
+variable with itself what is it going to
+be well the covariance of a random
+
+ align:start position:0%
+be well the covariance of a random
+ 
+
+ align:start position:0%
+be well the covariance of a random
+variable with itself is just the
+
+ align:start position:0%
+variable with itself is just the
+ 
+
+ align:start position:0%
+variable with itself is just the
+variance of that random variable now
+
+ align:start position:0%
+variance of that random variable now
+ 
+
+ align:start position:0%
+variance of that random variable now
+Sigma X is going to be the same as Sigma
+
+ align:start position:0%
+Sigma X is going to be the same as Sigma
+ 
+
+ align:start position:0%
+Sigma X is going to be the same as Sigma
+Y because we are taking Y to be the same
+
+ align:start position:0%
+Y because we are taking Y to be the same
+ 
+
+ align:start position:0%
+Y because we are taking Y to be the same
+as X so we're dividing by Sigma x
+
+ align:start position:0%
+as X so we're dividing by Sigma x
+ 
+
+ align:start position:0%
+as X so we're dividing by Sigma x
+squared but the square of the standard
+
+ align:start position:0%
+squared but the square of the standard
+ 
+
+ align:start position:0%
+squared but the square of the standard
+deviation is the variance so we obtain a
+
+ align:start position:0%
+deviation is the variance so we obtain a
+ 
+
+ align:start position:0%
+deviation is the variance so we obtain a
+value of one so a correlation
+
+ align:start position:0%
+value of one so a correlation
+ 
+
+ align:start position:0%
+value of one so a correlation
+coefficient of one shows up in such a
+
+ align:start position:0%
+coefficient of one shows up in such a
+ 
+
+ align:start position:0%
+coefficient of one shows up in such a
+case of an extreme dependence if instead
+
+ align:start position:0%
+case of an extreme dependence if instead
+ 
+
+ align:start position:0%
+case of an extreme dependence if instead
+we had taken the correlation coefficient
+
+ align:start position:0%
+we had taken the correlation coefficient
+ 
+
+ align:start position:0%
+we had taken the correlation coefficient
+of X with the negative of X in that case
+
+ align:start position:0%
+of X with the negative of X in that case
+ 
+
+ align:start position:0%
+of X with the negative of X in that case
+we would have obtained a correlation
+
+ align:start position:0%
+we would have obtained a correlation
+ 
+
+ align:start position:0%
+we would have obtained a correlation
+coefficient of minus one in somewhat
+
+ align:start position:0%
+coefficient of minus one in somewhat
+ 
+
+ align:start position:0%
+coefficient of minus one in somewhat
+more general situation that the one we
+
+ align:start position:0%
+more general situation that the one we
+ 
+
+ align:start position:0%
+more general situation that the one we
+considered here is the following if we
+
+ align:start position:0%
+considered here is the following if we
+ 
+
+ align:start position:0%
+considered here is the following if we
+have two random variables that have a
+
+ align:start position:0%
+have two random variables that have a
+ 
+
+ align:start position:0%
+have two random variables that have a
+linear relation that is if I know why I
+
+ align:start position:0%
+linear relation that is if I know why I
+ 
+
+ align:start position:0%
+linear relation that is if I know why I
+can figure out the value of x with
+
+ align:start position:0%
+can figure out the value of x with
+ 
+
+ align:start position:0%
+can figure out the value of x with
+absolute certainty and they can figure
+
+ align:start position:0%
+absolute certainty and they can figure
+ 
+
+ align:start position:0%
+absolute certainty and they can figure
+it out by using a linear formula in this
+
+ align:start position:0%
+it out by using a linear formula in this
+ 
+
+ align:start position:0%
+it out by using a linear formula in this
+case it turns out that the correlation
+
+ align:start position:0%
+case it turns out that the correlation
+ 
+
+ align:start position:0%
+case it turns out that the correlation
+coefficient is either plus 1 or minus 1
+
+ align:start position:0%
+coefficient is either plus 1 or minus 1
+ 
+
+ align:start position:0%
+coefficient is either plus 1 or minus 1
+and the converse is true if the
+
+ align:start position:0%
+and the converse is true if the
+ 
+
+ align:start position:0%
+and the converse is true if the
+correlation coefficient has absolute
+
+ align:start position:0%
+correlation coefficient has absolute
+ 
+
+ align:start position:0%
+correlation coefficient has absolute
+value of 1 then the two random variables
+
+ align:start position:0%
+value of 1 then the two random variables
+ 
+
+ align:start position:0%
+value of 1 then the two random variables
+obey a deterministic linear relation
+
+ align:start position:0%
+obey a deterministic linear relation
+ 
+
+ align:start position:0%
+obey a deterministic linear relation
+between them so to conclude an extreme
+
+ align:start position:0%
+between them so to conclude an extreme
+ 
+
+ align:start position:0%
+between them so to conclude an extreme
+value for the correlation coefficient of
+
+ align:start position:0%
+value for the correlation coefficient of
+ 
+
+ align:start position:0%
+value for the correlation coefficient of
+plus or minus
+
+ align:start position:0%
+plus or minus
+ 
+
+ align:start position:0%
+plus or minus
+one is equivalent to having a
+
+ align:start position:0%
+one is equivalent to having a
+ 
+
+ align:start position:0%
+one is equivalent to having a
+deterministic relation between the two
+
+ align:start position:0%
+deterministic relation between the two
+ 
+
+ align:start position:0%
+deterministic relation between the two
+random variables involved a final remark
+
+ align:start position:0%
+random variables involved a final remark
+ 
+
+ align:start position:0%
+random variables involved a final remark
+about the algebraic properties of the
+
+ align:start position:0%
+about the algebraic properties of the
+ 
+
+ align:start position:0%
+about the algebraic properties of the
+correlation coefficient what can we say
+
+ align:start position:0%
+correlation coefficient what can we say
+ 
+
+ align:start position:0%
+correlation coefficient what can we say
+about the correlation coefficient of a
+
+ align:start position:0%
+about the correlation coefficient of a
+ 
+
+ align:start position:0%
+about the correlation coefficient of a
+linear function of a random variable
+
+ align:start position:0%
+linear function of a random variable
+ 
+
+ align:start position:0%
+linear function of a random variable
+with another well we already know
+
+ align:start position:0%
+with another well we already know
+ 
+
+ align:start position:0%
+with another well we already know
+something about what happens to the
+
+ align:start position:0%
+something about what happens to the
+ 
+
+ align:start position:0%
+something about what happens to the
+covariance when we form a linear
+
+ align:start position:0%
+covariance when we form a linear
+ 
+
+ align:start position:0%
+covariance when we form a linear
+function and the covariance of AX plus B
+
+ align:start position:0%
+function and the covariance of AX plus B
+ 
+
+ align:start position:0%
+function and the covariance of AX plus B
+with Y is related this way to the
+
+ align:start position:0%
+with Y is related this way to the
+ 
+
+ align:start position:0%
+with Y is related this way to the
+covariance of X with Y now let us use
+
+ align:start position:0%
+covariance of X with Y now let us use
+ 
+
+ align:start position:0%
+covariance of X with Y now let us use
+this property and calculate the
+
+ align:start position:0%
+this property and calculate the
+ 
+
+ align:start position:0%
+this property and calculate the
+correlation coefficient between ax plus
+
+ align:start position:0%
+correlation coefficient between ax plus
+ 
+
+ align:start position:0%
+correlation coefficient between ax plus
+B and Y in the numerator we have the
+
+ align:start position:0%
+B and Y in the numerator we have the
+ 
+
+ align:start position:0%
+B and Y in the numerator we have the
+covariance of AX plus B with Y which is
+
+ align:start position:0%
+covariance of AX plus B with Y which is
+ 
+
+ align:start position:0%
+covariance of AX plus B with Y which is
+equal to a times the covariance of X
+
+ align:start position:0%
+equal to a times the covariance of X
+ 
+
+ align:start position:0%
+equal to a times the covariance of X
+with Y at the denominator we have the
+
+ align:start position:0%
+with Y at the denominator we have the
+ 
+
+ align:start position:0%
+with Y at the denominator we have the
+standard deviation of this random
+
+ align:start position:0%
+standard deviation of this random
+ 
+
+ align:start position:0%
+standard deviation of this random
+variable now the standard deviation of
+
+ align:start position:0%
+variable now the standard deviation of
+ 
+
+ align:start position:0%
+variable now the standard deviation of
+this random variable is equal to a times
+
+ align:start position:0%
+this random variable is equal to a times
+ 
+
+ align:start position:0%
+this random variable is equal to a times
+the standard deviation of X if a is
+
+ align:start position:0%
+the standard deviation of X if a is
+ 
+
+ align:start position:0%
+the standard deviation of X if a is
+positive if a is negative then we need
+
+ align:start position:0%
+positive if a is negative then we need
+ 
+
+ align:start position:0%
+positive if a is negative then we need
+to put a minus sign but in either case
+
+ align:start position:0%
+to put a minus sign but in either case
+ 
+
+ align:start position:0%
+to put a minus sign but in either case
+we will have here the absolute value of
+
+ align:start position:0%
+we will have here the absolute value of
+ 
+
+ align:start position:0%
+we will have here the absolute value of
+a time's the standard deviation of X and
+
+ align:start position:0%
+a time's the standard deviation of X and
+ 
+
+ align:start position:0%
+a time's the standard deviation of X and
+then we divide by the standard deviation
+
+ align:start position:0%
+then we divide by the standard deviation
+ 
+
+ align:start position:0%
+then we divide by the standard deviation
+of the second random variable which is y
+
+ align:start position:0%
+of the second random variable which is y
+ 
+
+ align:start position:0%
+of the second random variable which is y
+and so what we obtain here is this ratio
+
+ align:start position:0%
+and so what we obtain here is this ratio
+ 
+
+ align:start position:0%
+and so what we obtain here is this ratio
+which is a correlation coefficient of x
+
+ align:start position:0%
+which is a correlation coefficient of x
+ 
+
+ align:start position:0%
+which is a correlation coefficient of x
+with y times this quantity which is the
+
+ align:start position:0%
+with y times this quantity which is the
+ 
+
+ align:start position:0%
+with y times this quantity which is the
+sine of a so we have the sine of a
+
+ align:start position:0%
+sine of a so we have the sine of a
+ 
+
+ align:start position:0%
+sine of a so we have the sine of a
+time's the correlation coefficient of X
+
+ align:start position:0%
+time's the correlation coefficient of X
+ 
+
+ align:start position:0%
+time's the correlation coefficient of X
+with Y so in particular the magnitude of
+
+ align:start position:0%
+with Y so in particular the magnitude of
+ 
+
+ align:start position:0%
+with Y so in particular the magnitude of
+the correlation coefficient is not going
+
+ align:start position:0%
+the correlation coefficient is not going
+ 
+
+ align:start position:0%
+the correlation coefficient is not going
+to change when we replace X by ax plus B
+
+ align:start position:0%
+to change when we replace X by ax plus B
+ 
+
+ align:start position:0%
+to change when we replace X by ax plus B
+and this essentially means that if we
+
+ align:start position:0%
+and this essentially means that if we
+ 
+
+ align:start position:0%
+and this essentially means that if we
+change the units of the random variable
+
+ align:start position:0%
+change the units of the random variable
+ 
+
+ align:start position:0%
+change the units of the random variable
+X for example suppose that X was degrees
+
+ align:start position:0%
+X for example suppose that X was degrees
+ 
+
+ align:start position:0%
+X for example suppose that X was degrees
+Celsius and ax plus B is degrees
+
+ align:start position:0%
+Celsius and ax plus B is degrees
+ 
+
+ align:start position:0%
+Celsius and ax plus B is degrees
+Fahrenheit going from one set of units
+
+ align:start position:0%
+Fahrenheit going from one set of units
+ 
+
+ align:start position:0%
+Fahrenheit going from one set of units
+Celsius degrees to another set of units
+
+ align:start position:0%
+Celsius degrees to another set of units
+ 
+
+ align:start position:0%
+Celsius degrees to another set of units
+degrees in Fahrenheit is not going to
+
+ align:start position:0%
+degrees in Fahrenheit is not going to
+ 
+
+ align:start position:0%
+degrees in Fahrenheit is not going to
+change the correlation coefficient of
+
+ align:start position:0%
+change the correlation coefficient of
+ 
+
+ align:start position:0%
+change the correlation coefficient of
+the temperature with some other random
+
+ align:start position:0%
+the temperature with some other random
+ 
+
+ align:start position:0%
+the temperature with some other random
+variable so this is a nice property of
+
+ align:start position:0%
+variable so this is a nice property of
+ 
+
+ align:start position:0%
+variable so this is a nice property of
+the correlation coefficient again which
+
+ align:start position:0%
+the correlation coefficient again which
+ 
+
+ align:start position:0%
+the correlation coefficient again which
+reflects the fact that it's dimensions
+
+ align:start position:0%
+reflects the fact that it's dimensions
+ 
+
+ align:start position:0%
+reflects the fact that it's dimensions
+less it doesn't have any units of its
+
+ align:start position:0%
+less it doesn't have any units of its
+ 
+
+ align:start position:0%
+less it doesn't have any units of its
+own and it doesn't depend on what kinds
+
+ align:start position:0%
+own and it doesn't depend on what kinds
+ 
+
+ align:start position:0%
+own and it doesn't depend on what kinds
+of Units we use for each one of the
+
+ align:start position:0%
+of Units we use for each one of the
+ 
+
+ align:start position:0%
+of Units we use for each one of the
+random variables
\ No newline at end of file
diff --git a/HeM4EzQoGOQ.txt b/HeM4EzQoGOQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..57f92600c2c3edafac468ba6dbe5a02cb043f0ac
--- /dev/null
+++ b/HeM4EzQoGOQ.txt
@@ -0,0 +1,8344 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu good afternoon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody so I'm gonna start this
+
+ align:start position:0%
+everybody so I'm gonna start this
+ 
+
+ align:start position:0%
+everybody so I'm gonna start this
+morning or this afternoon this afternoon
+
+ align:start position:0%
+morning or this afternoon this afternoon
+ 
+
+ align:start position:0%
+morning or this afternoon this afternoon
+with the question we had at the bottom
+
+ align:start position:0%
+with the question we had at the bottom
+ 
+
+ align:start position:0%
+with the question we had at the bottom
+of last uh lecture's handout and but
+
+ align:start position:0%
+of last uh lecture's handout and but
+ 
+
+ align:start position:0%
+of last uh lecture's handout and but
+we're not going to actually answer this
+
+ align:start position:0%
+we're not going to actually answer this
+ 
+
+ align:start position:0%
+we're not going to actually answer this
+question until the end of today's
+
+ align:start position:0%
+question until the end of today's
+ 
+
+ align:start position:0%
+question until the end of today's
+lecture but let's look at what the
+
+ align:start position:0%
+lecture but let's look at what the
+ 
+
+ align:start position:0%
+lecture but let's look at what the
+question is and you can be thinking
+
+ align:start position:0%
+question is and you can be thinking
+ 
+
+ align:start position:0%
+question is and you can be thinking
+about it during today's lecture all
+
+ align:start position:0%
+about it during today's lecture all
+ 
+
+ align:start position:0%
+about it during today's lecture all
+right so the question is that vitamin
+
+ align:start position:0%
+right so the question is that vitamin
+ 
+
+ align:start position:0%
+right so the question is that vitamin
+B12 which we've already mentioned once
+
+ align:start position:0%
+B12 which we've already mentioned once
+ 
+
+ align:start position:0%
+B12 which we've already mentioned once
+uh in in this course it has a large
+
+ align:start position:0%
+uh in in this course it has a large
+ 
+
+ align:start position:0%
+uh in in this course it has a large
+negative Redux potential standard
+
+ align:start position:0%
+negative Redux potential standard
+ 
+
+ align:start position:0%
+negative Redux potential standard
+reduction potential is large
+
+ align:start position:0%
+reduction potential is large
+ 
+
+ align:start position:0%
+reduction potential is large
+negative so how does it get reduced in
+
+ align:start position:0%
+negative so how does it get reduced in
+ 
+
+ align:start position:0%
+negative so how does it get reduced in
+the body so let's think about the the
+
+ align:start position:0%
+the body so let's think about the the
+ 
+
+ align:start position:0%
+the body so let's think about the the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+here as we learned last
+
+ align:start position:0%
+here as we learned last
+ 
+
+ align:start position:0%
+here as we learned last
+time compounds with large negative
+
+ align:start position:0%
+time compounds with large negative
+ 
+
+ align:start position:0%
+time compounds with large negative
+reduction potentials are hard to
+
+ align:start position:0%
+reduction potentials are hard to
+ 
+
+ align:start position:0%
+reduction potentials are hard to
+reduce they're easy to oxidize which
+
+ align:start position:0%
+reduce they're easy to oxidize which
+ 
+
+ align:start position:0%
+reduce they're easy to oxidize which
+makes them good reducing agents but
+
+ align:start position:0%
+makes them good reducing agents but
+ 
+
+ align:start position:0%
+makes them good reducing agents but
+they're hard to reduce and vitamin B12
+
+ align:start position:0%
+they're hard to reduce and vitamin B12
+ 
+
+ align:start position:0%
+they're hard to reduce and vitamin B12
+has a large negative value value so it's
+
+ align:start position:0%
+has a large negative value value so it's
+ 
+
+ align:start position:0%
+has a large negative value value so it's
+hard to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduce but in the body it needs to be
+
+ align:start position:0%
+reduce but in the body it needs to be
+ 
+
+ align:start position:0%
+reduce but in the body it needs to be
+reduced to be active for one particular
+
+ align:start position:0%
+reduced to be active for one particular
+ 
+
+ align:start position:0%
+reduced to be active for one particular
+enzyme so it needs to be reduced but
+
+ align:start position:0%
+enzyme so it needs to be reduced but
+ 
+
+ align:start position:0%
+enzyme so it needs to be reduced but
+it's hard to reduce so what does the
+
+ align:start position:0%
+it's hard to reduce so what does the
+ 
+
+ align:start position:0%
+it's hard to reduce so what does the
+body do to compensate how does this work
+
+ align:start position:0%
+body do to compensate how does this work
+ 
+
+ align:start position:0%
+body do to compensate how does this work
+so I'm going to answer this at the end
+
+ align:start position:0%
+so I'm going to answer this at the end
+ 
+
+ align:start position:0%
+so I'm going to answer this at the end
+of class but let me first tell you in
+
+ align:start position:0%
+of class but let me first tell you in
+ 
+
+ align:start position:0%
+of class but let me first tell you in
+the beginning of class why this is an
+
+ align:start position:0%
+the beginning of class why this is an
+ 
+
+ align:start position:0%
+the beginning of class why this is an
+important question so the proper
+
+ align:start position:0%
+important question so the proper
+ 
+
+ align:start position:0%
+important question so the proper
+functioning of a particular enzyme
+
+ align:start position:0%
+functioning of a particular enzyme
+ 
+
+ align:start position:0%
+functioning of a particular enzyme
+requires red produced B12 and also
+
+ align:start position:0%
+requires red produced B12 and also
+ 
+
+ align:start position:0%
+requires red produced B12 and also
+another B vitamin called folic
+
+ align:start position:0%
+another B vitamin called folic
+ 
+
+ align:start position:0%
+another B vitamin called folic
+acid and this particular enzyme is
+
+ align:start position:0%
+acid and this particular enzyme is
+ 
+
+ align:start position:0%
+acid and this particular enzyme is
+believed to be important in preventing
+
+ align:start position:0%
+believed to be important in preventing
+ 
+
+ align:start position:0%
+believed to be important in preventing
+heart disease and also important in
+
+ align:start position:0%
+heart disease and also important in
+ 
+
+ align:start position:0%
+heart disease and also important in
+preventing birth
+
+ align:start position:0%
+preventing birth
+ 
+
+ align:start position:0%
+preventing birth
+defects and also important for
+
+ align:start position:0%
+defects and also important for
+ 
+
+ align:start position:0%
+defects and also important for
+maintaining mental
+
+ align:start position:0%
+maintaining mental
+ 
+
+ align:start position:0%
+maintaining mental
+health so this September uh Laura
+
+ align:start position:0%
+health so this September uh Laura
+ 
+
+ align:start position:0%
+health so this September uh Laura
+Phillips who's a recitation instructor
+
+ align:start position:0%
+Phillips who's a recitation instructor
+ 
+
+ align:start position:0%
+Phillips who's a recitation instructor
+and I went to Oxford to attend a meeting
+
+ align:start position:0%
+and I went to Oxford to attend a meeting
+ 
+
+ align:start position:0%
+and I went to Oxford to attend a meeting
+on vitamin B12 and it was a very Medical
+
+ align:start position:0%
+on vitamin B12 and it was a very Medical
+ 
+
+ align:start position:0%
+on vitamin B12 and it was a very Medical
+based meeting and a large number of the
+
+ align:start position:0%
+based meeting and a large number of the
+ 
+
+ align:start position:0%
+based meeting and a large number of the
+talks were by physicians talking about
+
+ align:start position:0%
+talks were by physicians talking about
+ 
+
+ align:start position:0%
+talks were by physicians talking about
+treating people with B12 deficiencies
+
+ align:start position:0%
+treating people with B12 deficiencies
+ 
+
+ align:start position:0%
+treating people with B12 deficiencies
+that had mental
+
+ align:start position:0%
+that had mental
+ 
+
+ align:start position:0%
+that had mental
+illnesses and uh they told one story of
+
+ align:start position:0%
+illnesses and uh they told one story of
+ 
+
+ align:start position:0%
+illnesses and uh they told one story of
+a man who uh he was sort of a
+
+ align:start position:0%
+a man who uh he was sort of a
+ 
+
+ align:start position:0%
+a man who uh he was sort of a
+middle-aged man and he couldn't really
+
+ align:start position:0%
+middle-aged man and he couldn't really
+ 
+
+ align:start position:0%
+middle-aged man and he couldn't really
+function at work he couldn't remember
+
+ align:start position:0%
+function at work he couldn't remember
+ 
+
+ align:start position:0%
+function at work he couldn't remember
+what he was supposed to be doing and so
+
+ align:start position:0%
+what he was supposed to be doing and so
+ 
+
+ align:start position:0%
+what he was supposed to be doing and so
+he was having trouble he was having
+
+ align:start position:0%
+he was having trouble he was having
+ 
+
+ align:start position:0%
+he was having trouble he was having
+trouble driving he couldn't remember all
+
+ align:start position:0%
+trouble driving he couldn't remember all
+ 
+
+ align:start position:0%
+trouble driving he couldn't remember all
+the rules of the road uh and of course
+
+ align:start position:0%
+the rules of the road uh and of course
+ 
+
+ align:start position:0%
+the rules of the road uh and of course
+it seems like an Eng land this this guy
+
+ align:start position:0%
+it seems like an Eng land this this guy
+ 
+
+ align:start position:0%
+it seems like an Eng land this this guy
+was in England that was even more
+
+ align:start position:0%
+was in England that was even more
+ 
+
+ align:start position:0%
+was in England that was even more
+complicated uh and he'd leave his house
+
+ align:start position:0%
+complicated uh and he'd leave his house
+ 
+
+ align:start position:0%
+complicated uh and he'd leave his house
+and he couldn't remember where he lived
+
+ align:start position:0%
+and he couldn't remember where he lived
+ 
+
+ align:start position:0%
+and he couldn't remember where he lived
+so he had all these symptoms there were
+
+ align:start position:0%
+so he had all these symptoms there were
+ 
+
+ align:start position:0%
+so he had all these symptoms there were
+sort of Alzheimer's disease but he was a
+
+ align:start position:0%
+sort of Alzheimer's disease but he was a
+ 
+
+ align:start position:0%
+sort of Alzheimer's disease but he was a
+he was not an older man and uh it didn't
+
+ align:start position:0%
+he was not an older man and uh it didn't
+ 
+
+ align:start position:0%
+he was not an older man and uh it didn't
+seem like Alzheimer's was right So
+
+ align:start position:0%
+seem like Alzheimer's was right So
+ 
+
+ align:start position:0%
+seem like Alzheimer's was right So
+eventually he ended up with this
+
+ align:start position:0%
+eventually he ended up with this
+ 
+
+ align:start position:0%
+eventually he ended up with this
+physician who diagnosed that he had a
+
+ align:start position:0%
+physician who diagnosed that he had a
+ 
+
+ align:start position:0%
+physician who diagnosed that he had a
+B12 deficiency and it was great for this
+
+ align:start position:0%
+B12 deficiency and it was great for this
+ 
+
+ align:start position:0%
+B12 deficiency and it was great for this
+particular individual because when they
+
+ align:start position:0%
+particular individual because when they
+ 
+
+ align:start position:0%
+particular individual because when they
+started giving him vitamin B12 uh in
+
+ align:start position:0%
+started giving him vitamin B12 uh in
+ 
+
+ align:start position:0%
+started giving him vitamin B12 uh in
+high doses he actually recovered so he
+
+ align:start position:0%
+high doses he actually recovered so he
+ 
+
+ align:start position:0%
+high doses he actually recovered so he
+got his driver's license back he got his
+
+ align:start position:0%
+got his driver's license back he got his
+ 
+
+ align:start position:0%
+got his driver's license back he got his
+job back and he was able to get back and
+
+ align:start position:0%
+job back and he was able to get back and
+ 
+
+ align:start position:0%
+job back and he was able to get back and
+forth from home uh without any
+
+ align:start position:0%
+forth from home uh without any
+ 
+
+ align:start position:0%
+forth from home uh without any
+challenges so I think a lot of the time
+
+ align:start position:0%
+challenges so I think a lot of the time
+ 
+
+ align:start position:0%
+challenges so I think a lot of the time
+one cannot point to B12 as the source of
+
+ align:start position:0%
+one cannot point to B12 as the source of
+ 
+
+ align:start position:0%
+one cannot point to B12 as the source of
+any uh mental uh
+
+ align:start position:0%
+any uh mental uh
+ 
+
+ align:start position:0%
+any uh mental uh
+forgetfulness but uh and people do ask
+
+ align:start position:0%
+forgetfulness but uh and people do ask
+ 
+
+ align:start position:0%
+forgetfulness but uh and people do ask
+me and people advertise this like in
+
+ align:start position:0%
+me and people advertise this like in
+ 
+
+ align:start position:0%
+me and people advertise this like in
+health food stores you can buy vitamin
+
+ align:start position:0%
+health food stores you can buy vitamin
+ 
+
+ align:start position:0%
+health food stores you can buy vitamin
+B12 and it talks about you know
+
+ align:start position:0%
+B12 and it talks about you know
+ 
+
+ align:start position:0%
+B12 and it talks about you know
+improving one's memory and things like
+
+ align:start position:0%
+improving one's memory and things like
+ 
+
+ align:start position:0%
+improving one's memory and things like
+that I think that if you had a vitamin
+
+ align:start position:0%
+that I think that if you had a vitamin
+ 
+
+ align:start position:0%
+that I think that if you had a vitamin
+B12 deficiency you should be taking B12
+
+ align:start position:0%
+B12 deficiency you should be taking B12
+ 
+
+ align:start position:0%
+B12 deficiency you should be taking B12
+uh but I think if you don't have a B12
+
+ align:start position:0%
+uh but I think if you don't have a B12
+ 
+
+ align:start position:0%
+uh but I think if you don't have a B12
+deficiency taking excess is not going to
+
+ align:start position:0%
+deficiency taking excess is not going to
+ 
+
+ align:start position:0%
+deficiency taking excess is not going to
+help you do better on exams although I
+
+ align:start position:0%
+help you do better on exams although I
+ 
+
+ align:start position:0%
+help you do better on exams although I
+guess they do have squirt B12 you know
+
+ align:start position:0%
+guess they do have squirt B12 you know
+ 
+
+ align:start position:0%
+guess they do have squirt B12 you know
+just a little extra dose squirted in the
+
+ align:start position:0%
+just a little extra dose squirted in the
+ 
+
+ align:start position:0%
+just a little extra dose squirted in the
+nose before the exam just to be on the
+
+ align:start position:0%
+nose before the exam just to be on the
+ 
+
+ align:start position:0%
+nose before the exam just to be on the
+safe side uh in case in case that helps
+
+ align:start position:0%
+safe side uh in case in case that helps
+ 
+
+ align:start position:0%
+safe side uh in case in case that helps
+um so I won't vouch for anything like
+
+ align:start position:0%
+um so I won't vouch for anything like
+ 
+
+ align:start position:0%
+um so I won't vouch for anything like
+that with memory and b12 but um
+
+ align:start position:0%
+that with memory and b12 but um
+ 
+
+ align:start position:0%
+that with memory and b12 but um
+nonetheless these enzymes are important
+
+ align:start position:0%
+nonetheless these enzymes are important
+ 
+
+ align:start position:0%
+nonetheless these enzymes are important
+and it's important to figure out how the
+
+ align:start position:0%
+and it's important to figure out how the
+ 
+
+ align:start position:0%
+and it's important to figure out how the
+B12 gets reduced so the enzyme can
+
+ align:start position:0%
+B12 gets reduced so the enzyme can
+ 
+
+ align:start position:0%
+B12 gets reduced so the enzyme can
+function all right so what is the enzyme
+
+ align:start position:0%
+function all right so what is the enzyme
+ 
+
+ align:start position:0%
+function all right so what is the enzyme
+the enzyme's name is methionine synthes
+
+ align:start position:0%
+the enzyme's name is methionine synthes
+ 
+
+ align:start position:0%
+the enzyme's name is methionine synthes
+and it uses these two B vitamins vitamin
+
+ align:start position:0%
+and it uses these two B vitamins vitamin
+ 
+
+ align:start position:0%
+and it uses these two B vitamins vitamin
+B12 and folic acid it converts an amino
+
+ align:start position:0%
+B12 and folic acid it converts an amino
+ 
+
+ align:start position:0%
+B12 and folic acid it converts an amino
+acid called homocystine to another one
+
+ align:start position:0%
+acid called homocystine to another one
+ 
+
+ align:start position:0%
+acid called homocystine to another one
+called methionine and it also converts
+
+ align:start position:0%
+called methionine and it also converts
+ 
+
+ align:start position:0%
+called methionine and it also converts
+one form of the folic acid to another
+
+ align:start position:0%
+one form of the folic acid to another
+ 
+
+ align:start position:0%
+one form of the folic acid to another
+form of the folic acid and as I said
+
+ align:start position:0%
+form of the folic acid and as I said
+ 
+
+ align:start position:0%
+form of the folic acid and as I said
+inhibition of this enzyme is believed to
+
+ align:start position:0%
+inhibition of this enzyme is believed to
+ 
+
+ align:start position:0%
+inhibition of this enzyme is believed to
+be involved with heart disease uh it's
+
+ align:start position:0%
+be involved with heart disease uh it's
+ 
+
+ align:start position:0%
+be involved with heart disease uh it's
+been linked to birth defects and also
+
+ align:start position:0%
+been linked to birth defects and also
+ 
+
+ align:start position:0%
+been linked to birth defects and also
+anemia and perhaps um a real deficiency
+
+ align:start position:0%
+anemia and perhaps um a real deficiency
+ 
+
+ align:start position:0%
+anemia and perhaps um a real deficiency
+has been linked to uh mental uh issues
+
+ align:start position:0%
+has been linked to uh mental uh issues
+ 
+
+ align:start position:0%
+has been linked to uh mental uh issues
+so um this is a pretty important enzyme
+
+ align:start position:0%
+so um this is a pretty important enzyme
+ 
+
+ align:start position:0%
+so um this is a pretty important enzyme
+there's only two enzymes in humans that
+
+ align:start position:0%
+there's only two enzymes in humans that
+ 
+
+ align:start position:0%
+there's only two enzymes in humans that
+use vitamin B12 uh birth defects and one
+
+ align:start position:0%
+use vitamin B12 uh birth defects and one
+ 
+
+ align:start position:0%
+use vitamin B12 uh birth defects and one
+of those enzymes can lead to this
+
+ align:start position:0%
+of those enzymes can lead to this
+ 
+
+ align:start position:0%
+of those enzymes can lead to this
+problem I talked about with buffering
+
+ align:start position:0%
+problem I talked about with buffering
+ 
+
+ align:start position:0%
+problem I talked about with buffering
+the blood uh and that can lead to death
+
+ align:start position:0%
+the blood uh and that can lead to death
+ 
+
+ align:start position:0%
+the blood uh and that can lead to death
+and infants if it's not corrected if
+
+ align:start position:0%
+and infants if it's not corrected if
+ 
+
+ align:start position:0%
+and infants if it's not corrected if
+it's too severe of a problem because the
+
+ align:start position:0%
+it's too severe of a problem because the
+ 
+
+ align:start position:0%
+it's too severe of a problem because the
+blood can't handle the change in PH and
+
+ align:start position:0%
+blood can't handle the change in PH and
+ 
+
+ align:start position:0%
+blood can't handle the change in PH and
+uh this one is also quite important
+
+ align:start position:0%
+uh this one is also quite important
+ 
+
+ align:start position:0%
+uh this one is also quite important
+medically so at this point I think I may
+
+ align:start position:0%
+medically so at this point I think I may
+ 
+
+ align:start position:0%
+medically so at this point I think I may
+have scared you that you want to know am
+
+ align:start position:0%
+have scared you that you want to know am
+ 
+
+ align:start position:0%
+have scared you that you want to know am
+I getting enough B12 and folic acid in
+
+ align:start position:0%
+I getting enough B12 and folic acid in
+ 
+
+ align:start position:0%
+I getting enough B12 and folic acid in
+my diet so I thought I would uh share
+
+ align:start position:0%
+my diet so I thought I would uh share
+ 
+
+ align:start position:0%
+my diet so I thought I would uh share
+with you where where you get B12 and
+
+ align:start position:0%
+with you where where you get B12 and
+ 
+
+ align:start position:0%
+with you where where you get B12 and
+folic acid in your in your diet in the
+
+ align:start position:0%
+folic acid in your in your diet in the
+ 
+
+ align:start position:0%
+folic acid in your in your diet in the
+end of class we'll talk about how B12 is
+
+ align:start position:0%
+end of class we'll talk about how B12 is
+ 
+
+ align:start position:0%
+end of class we'll talk about how B12 is
+reduced so where do you get these in
+
+ align:start position:0%
+reduced so where do you get these in
+ 
+
+ align:start position:0%
+reduced so where do you get these in
+your diet well for vitamin B12 does
+
+ align:start position:0%
+your diet well for vitamin B12 does
+ 
+
+ align:start position:0%
+your diet well for vitamin B12 does
+anybody know in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diet I've heard spinach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no total yes cereal that's supplemented
+
+ align:start position:0%
+no total yes cereal that's supplemented
+ 
+
+ align:start position:0%
+no total yes cereal that's supplemented
+with vitamins that's a good way to get
+
+ align:start position:0%
+with vitamins that's a good way to get
+ 
+
+ align:start position:0%
+with vitamins that's a good way to get
+it um but naturally
+
+ align:start position:0%
+it um but naturally
+ 
+
+ align:start position:0%
+it um but naturally
+occurring it comes in meat red meat
+
+ align:start position:0%
+occurring it comes in meat red meat
+ 
+
+ align:start position:0%
+occurring it comes in meat red meat
+other forms of
+
+ align:start position:0%
+other forms of
+ 
+
+ align:start position:0%
+other forms of
+meat uh this is the one vitamin that
+
+ align:start position:0%
+meat uh this is the one vitamin that
+ 
+
+ align:start position:0%
+meat uh this is the one vitamin that
+vegetarians say they need to have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+supplemented so uh as it's not a huge
+
+ align:start position:0%
+supplemented so uh as it's not a huge
+ 
+
+ align:start position:0%
+supplemented so uh as it's not a huge
+problem because as I said cereal and
+
+ align:start position:0%
+problem because as I said cereal and
+ 
+
+ align:start position:0%
+problem because as I said cereal and
+other things but in the in the natural
+
+ align:start position:0%
+other things but in the in the natural
+ 
+
+ align:start position:0%
+other things but in the in the natural
+diet it comes uh from meat and uh what
+
+ align:start position:0%
+diet it comes uh from meat and uh what
+ 
+
+ align:start position:0%
+diet it comes uh from meat and uh what
+about folic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid vegetables yeah so folic from
+
+ align:start position:0%
+acid vegetables yeah so folic from
+ 
+
+ align:start position:0%
+acid vegetables yeah so folic from
+foliage so green green leafy things work
+
+ align:start position:0%
+foliage so green green leafy things work
+ 
+
+ align:start position:0%
+foliage so green green leafy things work
+um also I was at another meeting with
+
+ align:start position:0%
+um also I was at another meeting with
+ 
+
+ align:start position:0%
+um also I was at another meeting with
+medical doctors uh talking about vitamin
+
+ align:start position:0%
+medical doctors uh talking about vitamin
+ 
+
+ align:start position:0%
+medical doctors uh talking about vitamin
+B12 and folic acid these were new
+
+ align:start position:0%
+B12 and folic acid these were new
+ 
+
+ align:start position:0%
+B12 and folic acid these were new
+Norwegian Physicians and so they
+
+ align:start position:0%
+Norwegian Physicians and so they
+ 
+
+ align:start position:0%
+Norwegian Physicians and so they
+informed me of another source of folic
+
+ align:start position:0%
+informed me of another source of folic
+ 
+
+ align:start position:0%
+informed me of another source of folic
+acid that I was unaware of uh which is
+
+ align:start position:0%
+acid that I was unaware of uh which is
+ 
+
+ align:start position:0%
+acid that I was unaware of uh which is
+apparently nor and
+
+ align:start position:0%
+apparently nor and
+ 
+
+ align:start position:0%
+apparently nor and
+beer um I can't vouch for this but
+
+ align:start position:0%
+beer um I can't vouch for this but
+ 
+
+ align:start position:0%
+beer um I can't vouch for this but
+that's what they told
+
+ align:start position:0%
+that's what they told
+ 
+
+ align:start position:0%
+that's what they told
+me um but also perhaps a better Source
+
+ align:start position:0%
+me um but also perhaps a better Source
+ 
+
+ align:start position:0%
+me um but also perhaps a better Source
+would be leafy green
+
+ align:start position:0%
+would be leafy green
+ 
+
+ align:start position:0%
+would be leafy green
+vegetables uh and orange juice is
+
+ align:start position:0%
+vegetables uh and orange juice is
+ 
+
+ align:start position:0%
+vegetables uh and orange juice is
+actually quite good so some of you may
+
+ align:start position:0%
+actually quite good so some of you may
+ 
+
+ align:start position:0%
+actually quite good so some of you may
+have seen if You' seen raise your hand
+
+ align:start position:0%
+have seen if You' seen raise your hand
+ 
+
+ align:start position:0%
+have seen if You' seen raise your hand
+if you've seen this commercial with
+
+ align:start position:0%
+if you've seen this commercial with
+ 
+
+ align:start position:0%
+if you've seen this commercial with
+orange juice and it says orange juice
+
+ align:start position:0%
+orange juice and it says orange juice
+ 
+
+ align:start position:0%
+orange juice and it says orange juice
+it's good for your heart have you seen
+
+ align:start position:0%
+it's good for your heart have you seen
+ 
+
+ align:start position:0%
+it's good for your heart have you seen
+that that ad yeah that actually is
+
+ align:start position:0%
+that that ad yeah that actually is
+ 
+
+ align:start position:0%
+that that ad yeah that actually is
+probably true and that's true true
+
+ align:start position:0%
+probably true and that's true true
+ 
+
+ align:start position:0%
+probably true and that's true true
+because you get a lot of folic acid in
+
+ align:start position:0%
+because you get a lot of folic acid in
+ 
+
+ align:start position:0%
+because you get a lot of folic acid in
+orange juice uh so anyway here are some
+
+ align:start position:0%
+orange juice uh so anyway here are some
+ 
+
+ align:start position:0%
+orange juice uh so anyway here are some
+dietary suggestions for
+
+ align:start position:0%
+dietary suggestions for
+ 
+
+ align:start position:0%
+dietary suggestions for
+you all right but you actually don't
+
+ align:start position:0%
+you all right but you actually don't
+ 
+
+ align:start position:0%
+you all right but you actually don't
+have to worry too much about folic acid
+
+ align:start position:0%
+have to worry too much about folic acid
+ 
+
+ align:start position:0%
+have to worry too much about folic acid
+anymore um because now it is fortified
+
+ align:start position:0%
+anymore um because now it is fortified
+ 
+
+ align:start position:0%
+anymore um because now it is fortified
+in bread in addition to breakfast
+
+ align:start position:0%
+in bread in addition to breakfast
+ 
+
+ align:start position:0%
+in bread in addition to breakfast
+cereals all bread is is now has extra
+
+ align:start position:0%
+cereals all bread is is now has extra
+ 
+
+ align:start position:0%
+cereals all bread is is now has extra
+folic acid and this started as a
+
+ align:start position:0%
+folic acid and this started as a
+ 
+
+ align:start position:0%
+folic acid and this started as a
+campaign uh because you need a lot if
+
+ align:start position:0%
+campaign uh because you need a lot if
+ 
+
+ align:start position:0%
+campaign uh because you need a lot if
+you're a woman who's who is uh pregnant
+
+ align:start position:0%
+you're a woman who's who is uh pregnant
+ 
+
+ align:start position:0%
+you're a woman who's who is uh pregnant
+you need a lot of folic acid or the baby
+
+ align:start position:0%
+you need a lot of folic acid or the baby
+ 
+
+ align:start position:0%
+you need a lot of folic acid or the baby
+can be born with birth defects now the
+
+ align:start position:0%
+can be born with birth defects now the
+ 
+
+ align:start position:0%
+can be born with birth defects now the
+problem is that often you need the folic
+
+ align:start position:0%
+problem is that often you need the folic
+ 
+
+ align:start position:0%
+problem is that often you need the folic
+acid before you know that you're
+
+ align:start position:0%
+acid before you know that you're
+ 
+
+ align:start position:0%
+acid before you know that you're
+pregnant so you need the F folic acid
+
+ align:start position:0%
+pregnant so you need the F folic acid
+ 
+
+ align:start position:0%
+pregnant so you need the F folic acid
+from day one and so uh a lot of
+
+ align:start position:0%
+from day one and so uh a lot of
+ 
+
+ align:start position:0%
+from day one and so uh a lot of
+scientists have been campaigning in
+
+ align:start position:0%
+scientists have been campaigning in
+ 
+
+ align:start position:0%
+scientists have been campaigning in
+Washington for a long time saying you
+
+ align:start position:0%
+Washington for a long time saying you
+ 
+
+ align:start position:0%
+Washington for a long time saying you
+need to put the folic acid in bread
+
+ align:start position:0%
+need to put the folic acid in bread
+ 
+
+ align:start position:0%
+need to put the folic acid in bread
+because the women need the folic acid
+
+ align:start position:0%
+because the women need the folic acid
+ 
+
+ align:start position:0%
+because the women need the folic acid
+before they know that they're pregnant
+
+ align:start position:0%
+before they know that they're pregnant
+ 
+
+ align:start position:0%
+before they know that they're pregnant
+this argument did not go very well and
+
+ align:start position:0%
+this argument did not go very well and
+ 
+
+ align:start position:0%
+this argument did not go very well and
+it was years and years and years of this
+
+ align:start position:0%
+it was years and years and years of this
+ 
+
+ align:start position:0%
+it was years and years and years of this
+argument and then all of a sudden some
+
+ align:start position:0%
+argument and then all of a sudden some
+ 
+
+ align:start position:0%
+argument and then all of a sudden some
+studies came out that really linked uh
+
+ align:start position:0%
+studies came out that really linked uh
+ 
+
+ align:start position:0%
+studies came out that really linked uh
+folic acid and heart disease through the
+
+ align:start position:0%
+folic acid and heart disease through the
+ 
+
+ align:start position:0%
+folic acid and heart disease through the
+activity of this B12 dependent enzyme
+
+ align:start position:0%
+activity of this B12 dependent enzyme
+ 
+
+ align:start position:0%
+activity of this B12 dependent enzyme
+and all of a sudden the climate in
+
+ align:start position:0%
+and all of a sudden the climate in
+ 
+
+ align:start position:0%
+and all of a sudden the climate in
+Washington changed and they said oh this
+
+ align:start position:0%
+Washington changed and they said oh this
+ 
+
+ align:start position:0%
+Washington changed and they said oh this
+may prevent heart disease all right
+
+ align:start position:0%
+may prevent heart disease all right
+ 
+
+ align:start position:0%
+may prevent heart disease all right
+let's let's uh fortify bread so uh it's
+
+ align:start position:0%
+let's let's uh fortify bread so uh it's
+ 
+
+ align:start position:0%
+let's let's uh fortify bread so uh it's
+a good example of a sort of Science and
+
+ align:start position:0%
+a good example of a sort of Science and
+ 
+
+ align:start position:0%
+a good example of a sort of Science and
+politics where political decisions that
+
+ align:start position:0%
+politics where political decisions that
+ 
+
+ align:start position:0%
+politics where political decisions that
+are made about science are really based
+
+ align:start position:0%
+are made about science are really based
+ 
+
+ align:start position:0%
+are made about science are really based
+on politics and not on the science so uh
+
+ align:start position:0%
+on politics and not on the science so uh
+ 
+
+ align:start position:0%
+on politics and not on the science so uh
+but at this point things are are looking
+
+ align:start position:0%
+but at this point things are are looking
+ 
+
+ align:start position:0%
+but at this point things are are looking
+better although some recent Studies have
+
+ align:start position:0%
+better although some recent Studies have
+ 
+
+ align:start position:0%
+better although some recent Studies have
+shown that there's still issues for some
+
+ align:start position:0%
+shown that there's still issues for some
+ 
+
+ align:start position:0%
+shown that there's still issues for some
+women in getting enough folic
+
+ align:start position:0%
+women in getting enough folic
+ 
+
+ align:start position:0%
+women in getting enough folic
+acid all right so um then we need to
+
+ align:start position:0%
+acid all right so um then we need to
+ 
+
+ align:start position:0%
+acid all right so um then we need to
+know how it's reduced so we're going to
+
+ align:start position:0%
+know how it's reduced so we're going to
+ 
+
+ align:start position:0%
+know how it's reduced so we're going to
+come back to this at the end of of today
+
+ align:start position:0%
+come back to this at the end of of today
+ 
+
+ align:start position:0%
+come back to this at the end of of today
+and uh and look at how all the things
+
+ align:start position:0%
+and uh and look at how all the things
+ 
+
+ align:start position:0%
+and uh and look at how all the things
+we've been learning about oxidation
+
+ align:start position:0%
+we've been learning about oxidation
+ 
+
+ align:start position:0%
+we've been learning about oxidation
+reduction apply to not only the uh
+
+ align:start position:0%
+reduction apply to not only the uh
+ 
+
+ align:start position:0%
+reduction apply to not only the uh
+batteries that you buy but to the
+
+ align:start position:0%
+batteries that you buy but to the
+ 
+
+ align:start position:0%
+batteries that you buy but to the
+reactions such as the reaction of
+
+ align:start position:0%
+reactions such as the reaction of
+ 
+
+ align:start position:0%
+reactions such as the reaction of
+methine synthes which is actually
+
+ align:start position:0%
+methine synthes which is actually
+ 
+
+ align:start position:0%
+methine synthes which is actually
+happening in your in your body right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so today we're going to talk
+
+ align:start position:0%
+all right so today we're going to talk
+ 
+
+ align:start position:0%
+all right so today we're going to talk
+about this a final uh lecture of
+
+ align:start position:0%
+about this a final uh lecture of
+ 
+
+ align:start position:0%
+about this a final uh lecture of
+oxidation and reduction and we're going
+
+ align:start position:0%
+oxidation and reduction and we're going
+ 
+
+ align:start position:0%
+oxidation and reduction and we're going
+to talk about adding and subtracting
+
+ align:start position:0%
+to talk about adding and subtracting
+ 
+
+ align:start position:0%
+to talk about adding and subtracting
+half cell reactions um this is listed as
+
+ align:start position:0%
+half cell reactions um this is listed as
+ 
+
+ align:start position:0%
+half cell reactions um this is listed as
+a topic but I decided to uh remove this
+
+ align:start position:0%
+a topic but I decided to uh remove this
+ 
+
+ align:start position:0%
+a topic but I decided to uh remove this
+so it's not actually in your handout
+
+ align:start position:0%
+so it's not actually in your handout
+ 
+
+ align:start position:0%
+so it's not actually in your handout
+although it's still listed as being in
+
+ align:start position:0%
+although it's still listed as being in
+ 
+
+ align:start position:0%
+although it's still listed as being in
+your handout so you can cross that out
+
+ align:start position:0%
+your handout so you can cross that out
+ 
+
+ align:start position:0%
+your handout so you can cross that out
+just for interest of time uh and we're
+
+ align:start position:0%
+just for interest of time uh and we're
+ 
+
+ align:start position:0%
+just for interest of time uh and we're
+going to talk about the nerst equation
+
+ align:start position:0%
+going to talk about the nerst equation
+ 
+
+ align:start position:0%
+going to talk about the nerst equation
+which is one of my favorite equation so
+
+ align:start position:0%
+which is one of my favorite equation so
+ 
+
+ align:start position:0%
+which is one of my favorite equation so
+I'm looking forward to
+
+ align:start position:0%
+I'm looking forward to
+ 
+
+ align:start position:0%
+I'm looking forward to
+that all right a couple other
+
+ align:start position:0%
+that all right a couple other
+ 
+
+ align:start position:0%
+that all right a couple other
+announcements before we get into this
+
+ align:start position:0%
+announcements before we get into this
+ 
+
+ align:start position:0%
+announcements before we get into this
+material I want to remind people there's
+
+ align:start position:0%
+material I want to remind people there's
+ 
+
+ align:start position:0%
+material I want to remind people there's
+a forum tonight we had a great Forum
+
+ align:start position:0%
+a forum tonight we had a great Forum
+ 
+
+ align:start position:0%
+a forum tonight we had a great Forum
+last week and so uh I encourage you uh
+
+ align:start position:0%
+last week and so uh I encourage you uh
+ 
+
+ align:start position:0%
+last week and so uh I encourage you uh
+to uh sign up and come to these forums
+
+ align:start position:0%
+to uh sign up and come to these forums
+ 
+
+ align:start position:0%
+to uh sign up and come to these forums
+also uh the problem sets doe F this
+
+ align:start position:0%
+also uh the problem sets doe F this
+ 
+
+ align:start position:0%
+also uh the problem sets doe F this
+Friday as usual and then the next
+
+ align:start position:0%
+Friday as usual and then the next
+ 
+
+ align:start position:0%
+Friday as usual and then the next
+problem set is a really short problem
+
+ align:start position:0%
+problem set is a really short problem
+ 
+
+ align:start position:0%
+problem set is a really short problem
+Set uh that'll be due Wednesday so that
+
+ align:start position:0%
+Set uh that'll be due Wednesday so that
+ 
+
+ align:start position:0%
+Set uh that'll be due Wednesday so that
+problem set just covers material on
+
+ align:start position:0%
+problem set just covers material on
+ 
+
+ align:start position:0%
+problem set just covers material on
+Friday's class and Monday's class so
+
+ align:start position:0%
+Friday's class and Monday's class so
+ 
+
+ align:start position:0%
+Friday's class and Monday's class so
+it's actually really very
+
+ align:start position:0%
+it's actually really very
+ 
+
+ align:start position:0%
+it's actually really very
+short Okay so down to some business all
+
+ align:start position:0%
+short Okay so down to some business all
+ 
+
+ align:start position:0%
+short Okay so down to some business all
+right so adding and subtracting half
+
+ align:start position:0%
+right so adding and subtracting half
+ 
+
+ align:start position:0%
+right so adding and subtracting half
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+reactions so
+
+ align:start position:0%
+reactions so
+ 
+
+ align:start position:0%
+reactions so
+suppose you needed to know something
+
+ align:start position:0%
+suppose you needed to know something
+ 
+
+ align:start position:0%
+suppose you needed to know something
+about this particular equation and the
+
+ align:start position:0%
+about this particular equation and the
+ 
+
+ align:start position:0%
+about this particular equation and the
+standard reduction potential for the
+
+ align:start position:0%
+standard reduction potential for the
+ 
+
+ align:start position:0%
+standard reduction potential for the
+reaction of copper 2 with one electron
+
+ align:start position:0%
+reaction of copper 2 with one electron
+ 
+
+ align:start position:0%
+reaction of copper 2 with one electron
+going to Copper plus one but it wasn't
+
+ align:start position:0%
+going to Copper plus one but it wasn't
+ 
+
+ align:start position:0%
+going to Copper plus one but it wasn't
+given and you're looking in the table
+
+ align:start position:0%
+given and you're looking in the table
+ 
+
+ align:start position:0%
+given and you're looking in the table
+and it's not given however other things
+
+ align:start position:0%
+and it's not given however other things
+ 
+
+ align:start position:0%
+and it's not given however other things
+related are
+
+ align:start position:0%
+related are
+ 
+
+ align:start position:0%
+related are
+given suppose you do find in the table
+
+ align:start position:0%
+given suppose you do find in the table
+ 
+
+ align:start position:0%
+given suppose you do find in the table
+copper plus two with two electrons going
+
+ align:start position:0%
+copper plus two with two electrons going
+ 
+
+ align:start position:0%
+copper plus two with two electrons going
+to Copper zero copper solid and you find
+
+ align:start position:0%
+to Copper zero copper solid and you find
+ 
+
+ align:start position:0%
+to Copper zero copper solid and you find
+Copper solid going to Copper + one plus
+
+ align:start position:0%
+Copper solid going to Copper + one plus
+ 
+
+ align:start position:0%
+Copper solid going to Copper + one plus
+one electron that information about both
+
+ align:start position:0%
+one electron that information about both
+ 
+
+ align:start position:0%
+one electron that information about both
+of those reactions is provided so you
+
+ align:start position:0%
+of those reactions is provided so you
+ 
+
+ align:start position:0%
+of those reactions is provided so you
+see the relationship between these two
+
+ align:start position:0%
+see the relationship between these two
+ 
+
+ align:start position:0%
+see the relationship between these two
+equations so you can use the information
+
+ align:start position:0%
+equations so you can use the information
+ 
+
+ align:start position:0%
+equations so you can use the information
+about these to calculate a standard
+
+ align:start position:0%
+about these to calculate a standard
+ 
+
+ align:start position:0%
+about these to calculate a standard
+reduction potential for this
+
+ align:start position:0%
+reduction potential for this
+ 
+
+ align:start position:0%
+reduction potential for this
+one so if you add these two reactions
+
+ align:start position:0%
+one so if you add these two reactions
+ 
+
+ align:start position:0%
+one so if you add these two reactions
+together together you get the reaction
+
+ align:start position:0%
+together together you get the reaction
+ 
+
+ align:start position:0%
+together together you get the reaction
+of interest you get copper 2 and one
+
+ align:start position:0%
+of interest you get copper 2 and one
+ 
+
+ align:start position:0%
+of interest you get copper 2 and one
+electron going to Copper one one
+
+ align:start position:0%
+electron going to Copper one one
+ 
+
+ align:start position:0%
+electron going to Copper one one
+electron cancels and the copper solid
+
+ align:start position:0%
+electron cancels and the copper solid
+ 
+
+ align:start position:0%
+electron cancels and the copper solid
+cancels and you get the reaction of
+
+ align:start position:0%
+cancels and you get the reaction of
+ 
+
+ align:start position:0%
+cancels and you get the reaction of
+Interest so if you can add together two
+
+ align:start position:0%
+Interest so if you can add together two
+ 
+
+ align:start position:0%
+Interest so if you can add together two
+reactions to get the reaction of
+
+ align:start position:0%
+reactions to get the reaction of
+ 
+
+ align:start position:0%
+reactions to get the reaction of
+Interest what do you do with the
+
+ align:start position:0%
+Interest what do you do with the
+ 
+
+ align:start position:0%
+Interest what do you do with the
+standard reduction potentials to uh to
+
+ align:start position:0%
+standard reduction potentials to uh to
+ 
+
+ align:start position:0%
+standard reduction potentials to uh to
+get the answer for the reduction
+
+ align:start position:0%
+get the answer for the reduction
+ 
+
+ align:start position:0%
+get the answer for the reduction
+potential for this
+
+ align:start position:0%
+potential for this
+ 
+
+ align:start position:0%
+potential for this
+reaction so this all comes back to Delta
+
+ align:start position:0%
+reaction so this all comes back to Delta
+ 
+
+ align:start position:0%
+reaction so this all comes back to Delta
+G everything thing most things are
+
+ align:start position:0%
+G everything thing most things are
+ 
+
+ align:start position:0%
+G everything thing most things are
+related in some ways to Delta G free
+
+ align:start position:0%
+related in some ways to Delta G free
+ 
+
+ align:start position:0%
+related in some ways to Delta G free
+energy so the free energy in the
+
+ align:start position:0%
+energy so the free energy in the
+ 
+
+ align:start position:0%
+energy so the free energy in the
+standard State Delta G KN for that new
+
+ align:start position:0%
+standard State Delta G KN for that new
+ 
+
+ align:start position:0%
+standard State Delta G KN for that new
+reaction that you're interested in is
+
+ align:start position:0%
+reaction that you're interested in is
+ 
+
+ align:start position:0%
+reaction that you're interested in is
+equal to the Delta G KN for the
+
+ align:start position:0%
+equal to the Delta G KN for the
+ 
+
+ align:start position:0%
+equal to the Delta G KN for the
+reduction part reaction that was a
+
+ align:start position:0%
+reduction part reaction that was a
+ 
+
+ align:start position:0%
+reduction part reaction that was a
+reduction in uh in the added equations
+
+ align:start position:0%
+reduction in uh in the added equations
+ 
+
+ align:start position:0%
+reduction in uh in the added equations
+minus the Delta G information for the
+
+ align:start position:0%
+minus the Delta G information for the
+ 
+
+ align:start position:0%
+minus the Delta G information for the
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+reaction you notice we're doing a
+
+ align:start position:0%
+reaction you notice we're doing a
+ 
+
+ align:start position:0%
+reaction you notice we're doing a
+derivation here all right so then we
+
+ align:start position:0%
+derivation here all right so then we
+ 
+
+ align:start position:0%
+derivation here all right so then we
+know something about the relationship
+
+ align:start position:0%
+know something about the relationship
+ 
+
+ align:start position:0%
+know something about the relationship
+between Delta G and standard reduction
+
+ align:start position:0%
+between Delta G and standard reduction
+ 
+
+ align:start position:0%
+between Delta G and standard reduction
+potentials so we talked about this last
+
+ align:start position:0%
+potentials so we talked about this last
+ 
+
+ align:start position:0%
+potentials so we talked about this last
+time that Delta G KN equals minus n
+
+ align:start position:0%
+time that Delta G KN equals minus n
+ 
+
+ align:start position:0%
+time that Delta G KN equals minus n
+which is the moles of electrons uh times
+
+ align:start position:0%
+which is the moles of electrons uh times
+ 
+
+ align:start position:0%
+which is the moles of electrons uh times
+Faraday constant times the standard
+
+ align:start position:0%
+Faraday constant times the standard
+ 
+
+ align:start position:0%
+Faraday constant times the standard
+reduction potential so if we substitute
+
+ align:start position:0%
+reduction potential so if we substitute
+ 
+
+ align:start position:0%
+reduction potential so if we substitute
+that into all of these we get this
+
+ align:start position:0%
+that into all of these we get this
+ 
+
+ align:start position:0%
+that into all of these we get this
+equation and we can cancel out the fadas
+
+ align:start position:0%
+equation and we can cancel out the fadas
+ 
+
+ align:start position:0%
+equation and we can cancel out the fadas
+constant and uh and solve then for the
+
+ align:start position:0%
+constant and uh and solve then for the
+ 
+
+ align:start position:0%
+constant and uh and solve then for the
+standard reduction potential for the new
+
+ align:start position:0%
+standard reduction potential for the new
+ 
+
+ align:start position:0%
+standard reduction potential for the new
+reaction which is what we want so if we
+
+ align:start position:0%
+reaction which is what we want so if we
+ 
+
+ align:start position:0%
+reaction which is what we want so if we
+get rid a fadas constant it cancels out
+
+ align:start position:0%
+get rid a fadas constant it cancels out
+ 
+
+ align:start position:0%
+get rid a fadas constant it cancels out
+bring the number of moles of electrons
+
+ align:start position:0%
+bring the number of moles of electrons
+ 
+
+ align:start position:0%
+bring the number of moles of electrons
+for the new reaction down
+
+ align:start position:0%
+for the new reaction down
+ 
+
+ align:start position:0%
+for the new reaction down
+here we get this equation which tells
+
+ align:start position:0%
+here we get this equation which tells
+ 
+
+ align:start position:0%
+here we get this equation which tells
+you about um you have the number of
+
+ align:start position:0%
+you about um you have the number of
+ 
+
+ align:start position:0%
+you about um you have the number of
+moles of the reaction and the standard
+
+ align:start position:0%
+moles of the reaction and the standard
+ 
+
+ align:start position:0%
+moles of the reaction and the standard
+reduction potential for the reduction
+
+ align:start position:0%
+reduction potential for the reduction
+ 
+
+ align:start position:0%
+reduction potential for the reduction
+reaction number of moles of electron the
+
+ align:start position:0%
+reaction number of moles of electron the
+ 
+
+ align:start position:0%
+reaction number of moles of electron the
+standard reduction potential for the
+
+ align:start position:0%
+standard reduction potential for the
+ 
+
+ align:start position:0%
+standard reduction potential for the
+reaction that's an oxidation that's
+
+ align:start position:0%
+reaction that's an oxidation that's
+ 
+
+ align:start position:0%
+reaction that's an oxidation that's
+added to the reduction to give you
+
+ align:start position:0%
+added to the reduction to give you
+ 
+
+ align:start position:0%
+added to the reduction to give you
+this new reaction and uh that's divided
+
+ align:start position:0%
+this new reaction and uh that's divided
+ 
+
+ align:start position:0%
+this new reaction and uh that's divided
+by the number of moles electrons
+
+ align:start position:0%
+by the number of moles electrons
+ 
+
+ align:start position:0%
+by the number of moles electrons
+involved in that new reaction that
+
+ align:start position:0%
+involved in that new reaction that
+ 
+
+ align:start position:0%
+involved in that new reaction that
+you're interested
+
+ align:start position:0%
+you're interested
+ 
+
+ align:start position:0%
+you're interested
+in so let's use that then so if we uh if
+
+ align:start position:0%
+in so let's use that then so if we uh if
+ 
+
+ align:start position:0%
+in so let's use that then so if we uh if
+we go and we look these were our two
+
+ align:start position:0%
+we go and we look these were our two
+ 
+
+ align:start position:0%
+we go and we look these were our two
+reactions that we're adding together
+
+ align:start position:0%
+reactions that we're adding together
+ 
+
+ align:start position:0%
+reactions that we're adding together
+one's an oxidation one's a reduction and
+
+ align:start position:0%
+one's an oxidation one's a reduction and
+ 
+
+ align:start position:0%
+one's an oxidation one's a reduction and
+we can look up what the standard
+
+ align:start position:0%
+we can look up what the standard
+ 
+
+ align:start position:0%
+we can look up what the standard
+reduction potentials are that are
+
+ align:start position:0%
+reduction potentials are that are
+ 
+
+ align:start position:0%
+reduction potentials are that are
+related to those two equations so the
+
+ align:start position:0%
+related to those two equations so the
+ 
+
+ align:start position:0%
+related to those two equations so the
+standard reduction potential called
+
+ align:start position:0%
+standard reduction potential called
+ 
+
+ align:start position:0%
+standard reduction potential called
+copper 2 to copper copper + one to
+
+ align:start position:0%
+copper 2 to copper copper + one to
+ 
+
+ align:start position:0%
+copper 2 to copper copper + one to
+Copper so again we're looking up
+
+ align:start position:0%
+Copper so again we're looking up
+ 
+
+ align:start position:0%
+Copper so again we're looking up
+reduction potentials and we can find out
+
+ align:start position:0%
+reduction potentials and we can find out
+ 
+
+ align:start position:0%
+reduction potentials and we can find out
+what those are and then we can plug them
+
+ align:start position:0%
+what those are and then we can plug them
+ 
+
+ align:start position:0%
+what those are and then we can plug them
+in so here's our equation
+
+ align:start position:0%
+in so here's our equation
+ 
+
+ align:start position:0%
+in so here's our equation
+again so for the reduction we have two
+
+ align:start position:0%
+again so for the reduction we have two
+ 
+
+ align:start position:0%
+again so for the reduction we have two
+electrons involved in the reduction and
+
+ align:start position:0%
+electrons involved in the reduction and
+ 
+
+ align:start position:0%
+electrons involved in the reduction and
+a standard reduction potential of plus.
+
+ align:start position:0%
+a standard reduction potential of plus.
+ 
+
+ align:start position:0%
+a standard reduction potential of plus.
+34 volts then we put in the information
+
+ align:start position:0%
+34 volts then we put in the information
+ 
+
+ align:start position:0%
+34 volts then we put in the information
+about the reaction that was written as
+
+ align:start position:0%
+about the reaction that was written as
+ 
+
+ align:start position:0%
+about the reaction that was written as
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+oxidation and so that's minus there's
+
+ align:start position:0%
+oxidation and so that's minus there's
+ 
+
+ align:start position:0%
+oxidation and so that's minus there's
+one electron involved in that and a
+
+ align:start position:0%
+one electron involved in that and a
+ 
+
+ align:start position:0%
+one electron involved in that and a
+reduction potential now again it's
+
+ align:start position:0%
+reduction potential now again it's
+ 
+
+ align:start position:0%
+reduction potential now again it's
+entered in as the reduction potential
+
+ align:start position:0%
+entered in as the reduction potential
+ 
+
+ align:start position:0%
+entered in as the reduction potential
+according to the equation this is a
+
+ align:start position:0%
+according to the equation this is a
+ 
+
+ align:start position:0%
+according to the equation this is a
+reduction potential of 0.5 to2 volts and
+
+ align:start position:0%
+reduction potential of 0.5 to2 volts and
+ 
+
+ align:start position:0%
+reduction potential of 0.5 to2 volts and
+then in the final reaction there's one
+
+ align:start position:0%
+then in the final reaction there's one
+ 
+
+ align:start position:0%
+then in the final reaction there's one
+electron involved in that and so we put
+
+ align:start position:0%
+electron involved in that and so we put
+ 
+
+ align:start position:0%
+electron involved in that and so we put
+the one here and we can get out an
+
+ align:start position:0%
+the one here and we can get out an
+ 
+
+ align:start position:0%
+the one here and we can get out an
+answer of
+
+ align:start position:0%
+answer of
+ 
+
+ align:start position:0%
+answer of
+plus1 158 volts and so now we found out
+
+ align:start position:0%
+plus1 158 volts and so now we found out
+ 
+
+ align:start position:0%
+plus1 158 volts and so now we found out
+a new standard reduction potential for
+
+ align:start position:0%
+a new standard reduction potential for
+ 
+
+ align:start position:0%
+a new standard reduction potential for
+this half reaction knowing information
+
+ align:start position:0%
+this half reaction knowing information
+ 
+
+ align:start position:0%
+this half reaction knowing information
+about other half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactions and so this would be then the
+
+ align:start position:0%
+reactions and so this would be then the
+ 
+
+ align:start position:0%
+reactions and so this would be then the
+copper 2 copper 1 reduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential so what about the cells we're
+
+ align:start position:0%
+potential so what about the cells we're
+ 
+
+ align:start position:0%
+potential so what about the cells we're
+talking about before the electrochemical
+
+ align:start position:0%
+talking about before the electrochemical
+ 
+
+ align:start position:0%
+talking about before the electrochemical
+cells with the balanced equations well
+
+ align:start position:0%
+cells with the balanced equations well
+ 
+
+ align:start position:0%
+cells with the balanced equations well
+in that case if you have a that case for
+
+ align:start position:0%
+in that case if you have a that case for
+ 
+
+ align:start position:0%
+in that case if you have a that case for
+an electrochemical cell the number of
+
+ align:start position:0%
+an electrochemical cell the number of
+ 
+
+ align:start position:0%
+an electrochemical cell the number of
+moles of electrons released at the anode
+
+ align:start position:0%
+moles of electrons released at the anode
+ 
+
+ align:start position:0%
+moles of electrons released at the anode
+is going to be equal to the moles taken
+
+ align:start position:0%
+is going to be equal to the moles taken
+ 
+
+ align:start position:0%
+is going to be equal to the moles taken
+up at the cathode which is equal to the
+
+ align:start position:0%
+up at the cathode which is equal to the
+ 
+
+ align:start position:0%
+up at the cathode which is equal to the
+overall moles that get balanced out so
+
+ align:start position:0%
+overall moles that get balanced out so
+ 
+
+ align:start position:0%
+overall moles that get balanced out so
+you balance the equation you always want
+
+ align:start position:0%
+you balance the equation you always want
+ 
+
+ align:start position:0%
+you balance the equation you always want
+to cancel out your electrons and have
+
+ align:start position:0%
+to cancel out your electrons and have
+ 
+
+ align:start position:0%
+to cancel out your electrons and have
+none left in your balanced equation
+
+ align:start position:0%
+none left in your balanced equation
+ 
+
+ align:start position:0%
+none left in your balanced equation
+otherwise it's not balanced so in that
+
+ align:start position:0%
+otherwise it's not balanced so in that
+ 
+
+ align:start position:0%
+otherwise it's not balanced so in that
+case you don't use this it simplifies to
+
+ align:start position:0%
+case you don't use this it simplifies to
+ 
+
+ align:start position:0%
+case you don't use this it simplifies to
+the equation that we talked about before
+
+ align:start position:0%
+the equation that we talked about before
+ 
+
+ align:start position:0%
+the equation that we talked about before
+where the reduction potential for the
+
+ align:start position:0%
+where the reduction potential for the
+ 
+
+ align:start position:0%
+where the reduction potential for the
+cell now it's the cell potential not
+
+ align:start position:0%
+cell now it's the cell potential not
+ 
+
+ align:start position:0%
+cell now it's the cell potential not
+the uh another half potential is equal
+
+ align:start position:0%
+the uh another half potential is equal
+ 
+
+ align:start position:0%
+the uh another half potential is equal
+to the reduction potential for the
+
+ align:start position:0%
+to the reduction potential for the
+ 
+
+ align:start position:0%
+to the reduction potential for the
+reaction at the cathode minus the
+
+ align:start position:0%
+reaction at the cathode minus the
+ 
+
+ align:start position:0%
+reaction at the cathode minus the
+reduction potential for the reaction of
+
+ align:start position:0%
+reduction potential for the reaction of
+ 
+
+ align:start position:0%
+reduction potential for the reaction of
+the anode so you use this for Balan
+
+ align:start position:0%
+the anode so you use this for Balan
+ 
+
+ align:start position:0%
+the anode so you use this for Balan
+cells and you use this for half cell
+
+ align:start position:0%
+cells and you use this for half cell
+ 
+
+ align:start position:0%
+cells and you use this for half cell
+reactions and so again for a half cell
+
+ align:start position:0%
+reactions and so again for a half cell
+ 
+
+ align:start position:0%
+reactions and so again for a half cell
+reaction you must use this otherwise
+
+ align:start position:0%
+reaction you must use this otherwise
+ 
+
+ align:start position:0%
+reaction you must use this otherwise
+it's not going to work out you can
+
+ align:start position:0%
+it's not going to work out you can
+ 
+
+ align:start position:0%
+it's not going to work out you can
+recognize a half cell reaction because
+
+ align:start position:0%
+recognize a half cell reaction because
+ 
+
+ align:start position:0%
+recognize a half cell reaction because
+it's still has electrons in it so that's
+
+ align:start position:0%
+it's still has electrons in it so that's
+ 
+
+ align:start position:0%
+it's still has electrons in it so that's
+a half cell reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's just sort of a little uh
+
+ align:start position:0%
+okay so that's just sort of a little uh
+ 
+
+ align:start position:0%
+okay so that's just sort of a little uh
+a little side thing that will come in
+
+ align:start position:0%
+a little side thing that will come in
+ 
+
+ align:start position:0%
+a little side thing that will come in
+handy in finishing up the problem set
+
+ align:start position:0%
+handy in finishing up the problem set
+ 
+
+ align:start position:0%
+handy in finishing up the problem set
+and on the test and now we can talk
+
+ align:start position:0%
+and on the test and now we can talk
+ 
+
+ align:start position:0%
+and on the test and now we can talk
+about uh one of my more favorite topics
+
+ align:start position:0%
+about uh one of my more favorite topics
+ 
+
+ align:start position:0%
+about uh one of my more favorite topics
+which is the nurs
+
+ align:start position:0%
+which is the nurs
+ 
+
+ align:start position:0%
+which is the nurs
+equation so a lot of you have probably
+
+ align:start position:0%
+equation so a lot of you have probably
+ 
+
+ align:start position:0%
+equation so a lot of you have probably
+experienced the ramifications of the
+
+ align:start position:0%
+experienced the ramifications of the
+ 
+
+ align:start position:0%
+experienced the ramifications of the
+nurs equation without realizing uh
+
+ align:start position:0%
+nurs equation without realizing uh
+ 
+
+ align:start position:0%
+nurs equation without realizing uh
+that's what you've done um I assume that
+
+ align:start position:0%
+that's what you've done um I assume that
+ 
+
+ align:start position:0%
+that's what you've done um I assume that
+pretty much everybody has had an aocc
+
+ align:start position:0%
+pretty much everybody has had an aocc
+ 
+
+ align:start position:0%
+pretty much everybody has had an aocc
+where you go to use your favorite Gadget
+
+ align:start position:0%
+where you go to use your favorite Gadget
+ 
+
+ align:start position:0%
+where you go to use your favorite Gadget
+and discover that the battery is no
+
+ align:start position:0%
+and discover that the battery is no
+ 
+
+ align:start position:0%
+and discover that the battery is no
+longer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functioning a few people say yeah maybe
+
+ align:start position:0%
+functioning a few people say yeah maybe
+ 
+
+ align:start position:0%
+functioning a few people say yeah maybe
+that's happened to me and so then you
+
+ align:start position:0%
+that's happened to me and so then you
+ 
+
+ align:start position:0%
+that's happened to me and so then you
+start doing things like this where you
+
+ align:start position:0%
+start doing things like this where you
+ 
+
+ align:start position:0%
+start doing things like this where you
+uh either get some kind of recharger or
+
+ align:start position:0%
+uh either get some kind of recharger or
+ 
+
+ align:start position:0%
+uh either get some kind of recharger or
+you go out and stockpile batteries which
+
+ align:start position:0%
+you go out and stockpile batteries which
+ 
+
+ align:start position:0%
+you go out and stockpile batteries which
+then if you keep them long enough it
+
+ align:start position:0%
+then if you keep them long enough it
+ 
+
+ align:start position:0%
+then if you keep them long enough it
+seems like they don't work either anyway
+
+ align:start position:0%
+seems like they don't work either anyway
+ 
+
+ align:start position:0%
+seems like they don't work either anyway
+that's all the nerst equation in action
+
+ align:start position:0%
+that's all the nerst equation in action
+ 
+
+ align:start position:0%
+that's all the nerst equation in action
+so um an exhausted uh battery is a sign
+
+ align:start position:0%
+so um an exhausted uh battery is a sign
+ 
+
+ align:start position:0%
+so um an exhausted uh battery is a sign
+that equilibrium has been
+
+ align:start position:0%
+that equilibrium has been
+ 
+
+ align:start position:0%
+that equilibrium has been
+reached so at
+
+ align:start position:0%
+reached so at
+ 
+
+ align:start position:0%
+reached so at
+equilibrium the uh the cell generates
+
+ align:start position:0%
+equilibrium the uh the cell generates
+ 
+
+ align:start position:0%
+equilibrium the uh the cell generates
+zero potential across its electrodes so
+
+ align:start position:0%
+zero potential across its electrodes so
+ 
+
+ align:start position:0%
+zero potential across its electrodes so
+it's not working
+
+ align:start position:0%
+it's not working
+ 
+
+ align:start position:0%
+it's not working
+anymore and so to understand this
+
+ align:start position:0%
+anymore and so to understand this
+ 
+
+ align:start position:0%
+anymore and so to understand this
+problem we need to think about how the
+
+ align:start position:0%
+problem we need to think about how the
+ 
+
+ align:start position:0%
+problem we need to think about how the
+composition of that cell is changing
+
+ align:start position:0%
+composition of that cell is changing
+ 
+
+ align:start position:0%
+composition of that cell is changing
+over time so this gets back to all the
+
+ align:start position:0%
+over time so this gets back to all the
+ 
+
+ align:start position:0%
+over time so this gets back to all the
+other things we've talked about with
+
+ align:start position:0%
+other things we've talked about with
+ 
+
+ align:start position:0%
+other things we've talked about with
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+equilibrium so what do we know about
+
+ align:start position:0%
+equilibrium so what do we know about
+ 
+
+ align:start position:0%
+equilibrium so what do we know about
+this kind kind of stuff what do we know
+
+ align:start position:0%
+this kind kind of stuff what do we know
+ 
+
+ align:start position:0%
+this kind kind of stuff what do we know
+about equilibrium and components of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction so we know that Delta G changes
+
+ align:start position:0%
+reaction so we know that Delta G changes
+ 
+
+ align:start position:0%
+reaction so we know that Delta G changes
+as the composition of the reaction
+
+ align:start position:0%
+as the composition of the reaction
+ 
+
+ align:start position:0%
+as the composition of the reaction
+changes and we know that it changes
+
+ align:start position:0%
+changes and we know that it changes
+ 
+
+ align:start position:0%
+changes and we know that it changes
+until we reach uh at equilibrium Delta g
+
+ align:start position:0%
+until we reach uh at equilibrium Delta g
+ 
+
+ align:start position:0%
+until we reach uh at equilibrium Delta g
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero we know that Delta G at some given
+
+ align:start position:0%
+zero we know that Delta G at some given
+ 
+
+ align:start position:0%
+zero we know that Delta G at some given
+time some different reaction mixture is
+
+ align:start position:0%
+time some different reaction mixture is
+ 
+
+ align:start position:0%
+time some different reaction mixture is
+equal to Delta G KN Delta G at standard
+
+ align:start position:0%
+equal to Delta G KN Delta G at standard
+ 
+
+ align:start position:0%
+equal to Delta G KN Delta G at standard
+conditions plus RT the gas constant
+
+ align:start position:0%
+conditions plus RT the gas constant
+ 
+
+ align:start position:0%
+conditions plus RT the gas constant
+times temperature times the natural log
+
+ align:start position:0%
+times temperature times the natural log
+ 
+
+ align:start position:0%
+times temperature times the natural log
+of Q and Q is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what reaction quotient so the Delta G at
+
+ align:start position:0%
+what reaction quotient so the Delta G at
+ 
+
+ align:start position:0%
+what reaction quotient so the Delta G at
+any particular time depends on the
+
+ align:start position:0%
+any particular time depends on the
+ 
+
+ align:start position:0%
+any particular time depends on the
+composition depends on the reaction
+
+ align:start position:0%
+composition depends on the reaction
+ 
+
+ align:start position:0%
+composition depends on the reaction
+that's going on the components of that
+
+ align:start position:0%
+that's going on the components of that
+ 
+
+ align:start position:0%
+that's going on the components of that
+reaction so we've seen this before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last time we talked about the
+
+ align:start position:0%
+last time we talked about the
+ 
+
+ align:start position:0%
+last time we talked about the
+relationship between Delta G and cell
+
+ align:start position:0%
+relationship between Delta G and cell
+ 
+
+ align:start position:0%
+relationship between Delta G and cell
+potential Delta e so we know something
+
+ align:start position:0%
+potential Delta e so we know something
+ 
+
+ align:start position:0%
+potential Delta e so we know something
+about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationship we know that Delta G is
+
+ align:start position:0%
+relationship we know that Delta G is
+ 
+
+ align:start position:0%
+relationship we know that Delta G is
+equal to the number of moles of
+
+ align:start position:0%
+equal to the number of moles of
+ 
+
+ align:start position:0%
+equal to the number of moles of
+electrons times Faraday constant times
+
+ align:start position:0%
+electrons times Faraday constant times
+ 
+
+ align:start position:0%
+electrons times Faraday constant times
+Delta e KN the change in cell
+
+ align:start position:0%
+Delta e KN the change in cell
+ 
+
+ align:start position:0%
+Delta e KN the change in cell
+potential for the reaction
+
+ align:start position:0%
+potential for the reaction
+ 
+
+ align:start position:0%
+potential for the reaction
+and also this could be applied if this
+
+ align:start position:0%
+and also this could be applied if this
+ 
+
+ align:start position:0%
+and also this could be applied if this
+was Delta G to Delta e so it's it holds
+
+ align:start position:0%
+was Delta G to Delta e so it's it holds
+ 
+
+ align:start position:0%
+was Delta G to Delta e so it's it holds
+if you're under stand standard
+
+ align:start position:0%
+if you're under stand standard
+ 
+
+ align:start position:0%
+if you're under stand standard
+conditions you're both uh Delta G KN
+
+ align:start position:0%
+conditions you're both uh Delta G KN
+ 
+
+ align:start position:0%
+conditions you're both uh Delta G KN
+Delta e KN or under non-standard
+
+ align:start position:0%
+Delta e KN or under non-standard
+ 
+
+ align:start position:0%
+Delta e KN or under non-standard
+conditions so if we combine those things
+
+ align:start position:0%
+conditions so if we combine those things
+ 
+
+ align:start position:0%
+conditions so if we combine those things
+we get the ner
+
+ align:start position:0%
+we get the ner
+ 
+
+ align:start position:0%
+we get the ner
+equation so if we take what we already
+
+ align:start position:0%
+equation so if we take what we already
+ 
+
+ align:start position:0%
+equation so if we take what we already
+knew about Delta G from
+
+ align:start position:0%
+knew about Delta G from
+ 
+
+ align:start position:0%
+knew about Delta G from
+before and now plug in instead of Delta
+
+ align:start position:0%
+before and now plug in instead of Delta
+ 
+
+ align:start position:0%
+before and now plug in instead of Delta
+G KN minus n farad constant time Delta e
+
+ align:start position:0%
+G KN minus n farad constant time Delta e
+ 
+
+ align:start position:0%
+G KN minus n farad constant time Delta e
+KN and also we're going to substitute in
+
+ align:start position:0%
+KN and also we're going to substitute in
+ 
+
+ align:start position:0%
+KN and also we're going to substitute in
+for Delta g u minus n farad constant
+
+ align:start position:0%
+for Delta g u minus n farad constant
+ 
+
+ align:start position:0%
+for Delta g u minus n farad constant
+times Delta e over here and we
+
+ align:start position:0%
+times Delta e over here and we
+ 
+
+ align:start position:0%
+times Delta e over here and we
+substitute over here and we keep this
+
+ align:start position:0%
+substitute over here and we keep this
+ 
+
+ align:start position:0%
+substitute over here and we keep this
+part the same and then if we divide
+
+ align:start position:0%
+part the same and then if we divide
+ 
+
+ align:start position:0%
+part the same and then if we divide
+by n and farad a constant we get the
+
+ align:start position:0%
+by n and farad a constant we get the
+ 
+
+ align:start position:0%
+by n and farad a constant we get the
+nerst equation here so Delta e the Delta
+
+ align:start position:0%
+nerst equation here so Delta e the Delta
+ 
+
+ align:start position:0%
+nerst equation here so Delta e the Delta
+e at some given point for some different
+
+ align:start position:0%
+e at some given point for some different
+ 
+
+ align:start position:0%
+e at some given point for some different
+reaction quotient at some different time
+
+ align:start position:0%
+reaction quotient at some different time
+ 
+
+ align:start position:0%
+reaction quotient at some different time
+in the cell is going to be equal to the
+
+ align:start position:0%
+in the cell is going to be equal to the
+ 
+
+ align:start position:0%
+in the cell is going to be equal to the
+standard cell potential under standard
+
+ align:start position:0%
+standard cell potential under standard
+ 
+
+ align:start position:0%
+standard cell potential under standard
+conditions minus RT gas constant
+
+ align:start position:0%
+conditions minus RT gas constant
+ 
+
+ align:start position:0%
+conditions minus RT gas constant
+temperature over the number of moles of
+
+ align:start position:0%
+temperature over the number of moles of
+ 
+
+ align:start position:0%
+temperature over the number of moles of
+electrons times Faraday constant times
+
+ align:start position:0%
+electrons times Faraday constant times
+ 
+
+ align:start position:0%
+electrons times Faraday constant times
+the natural log of Q the reaction
+
+ align:start position:0%
+the natural log of Q the reaction
+ 
+
+ align:start position:0%
+the natural log of Q the reaction
+quotient so what the cell potential is
+
+ align:start position:0%
+quotient so what the cell potential is
+ 
+
+ align:start position:0%
+quotient so what the cell potential is
+at some given time depends on the re
+
+ align:start position:0%
+at some given time depends on the re
+ 
+
+ align:start position:0%
+at some given time depends on the re
+reaction where you are in the reaction
+
+ align:start position:0%
+reaction where you are in the reaction
+ 
+
+ align:start position:0%
+reaction where you are in the reaction
+what the composition of products to
+
+ align:start position:0%
+what the composition of products to
+ 
+
+ align:start position:0%
+what the composition of products to
+reactants is at that given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so this way we can calculate how
+
+ align:start position:0%
+time so this way we can calculate how
+ 
+
+ align:start position:0%
+time so this way we can calculate how
+close the battery is to being dead uh
+
+ align:start position:0%
+close the battery is to being dead uh
+ 
+
+ align:start position:0%
+close the battery is to being dead uh
+sort of where we are in the trajectory
+
+ align:start position:0%
+sort of where we are in the trajectory
+ 
+
+ align:start position:0%
+sort of where we are in the trajectory
+of things what kind of potential we're
+
+ align:start position:0%
+of things what kind of potential we're
+ 
+
+ align:start position:0%
+of things what kind of potential we're
+getting at that particular given
+
+ align:start position:0%
+getting at that particular given
+ 
+
+ align:start position:0%
+getting at that particular given
+time so let's do an example of using the
+
+ align:start position:0%
+time so let's do an example of using the
+ 
+
+ align:start position:0%
+time so let's do an example of using the
+ner equation
+
+ align:start position:0%
+ner equation
+ 
+
+ align:start position:0%
+ner equation
+so here is a particular
+
+ align:start position:0%
+so here is a particular
+ 
+
+ align:start position:0%
+so here is a particular
+reaction we have copper plus two plus
+
+ align:start position:0%
+reaction we have copper plus two plus
+ 
+
+ align:start position:0%
+reaction we have copper plus two plus
+zinc solid going to zinc plus 2 plus
+
+ align:start position:0%
+zinc solid going to zinc plus 2 plus
+ 
+
+ align:start position:0%
+zinc solid going to zinc plus 2 plus
+copper and we're told that uh the zinc
+
+ align:start position:0%
+copper and we're told that uh the zinc
+ 
+
+ align:start position:0%
+copper and we're told that uh the zinc
+ions concentration is10 molar and copper
+
+ align:start position:0%
+ions concentration is10 molar and copper
+ 
+
+ align:start position:0%
+ions concentration is10 molar and copper
++ 2 is
+
+ align:start position:0%
++ 2 is
+ 
+
+ align:start position:0%
++ 2 is
+.10 molar and so these are not standard
+
+ align:start position:0%
+.10 molar and so these are not standard
+ 
+
+ align:start position:0%
+.10 molar and so these are not standard
+conditions so we know we want to use the
+
+ align:start position:0%
+conditions so we know we want to use the
+ 
+
+ align:start position:0%
+conditions so we know we want to use the
+nerst
+
+ align:start position:0%
+nerst
+ 
+
+ align:start position:0%
+nerst
+equation so the first step in doing this
+
+ align:start position:0%
+equation so the first step in doing this
+ 
+
+ align:start position:0%
+equation so the first step in doing this
+well write down the nerst
+
+ align:start position:0%
+well write down the nerst
+ 
+
+ align:start position:0%
+well write down the nerst
+equation so the cell potential at some
+
+ align:start position:0%
+equation so the cell potential at some
+ 
+
+ align:start position:0%
+equation so the cell potential at some
+given time is equal to the cell standard
+
+ align:start position:0%
+given time is equal to the cell standard
+ 
+
+ align:start position:0%
+given time is equal to the cell standard
+cell potential minus RT over n * feraday
+
+ align:start position:0%
+cell potential minus RT over n * feraday
+ 
+
+ align:start position:0%
+cell potential minus RT over n * feraday
+constant times the natural log of Q
+
+ align:start position:0%
+constant times the natural log of Q
+ 
+
+ align:start position:0%
+constant times the natural log of Q
+we'll have step one being to find the
+
+ align:start position:0%
+we'll have step one being to find the
+ 
+
+ align:start position:0%
+we'll have step one being to find the
+standard cell
+
+ align:start position:0%
+standard cell
+ 
+
+ align:start position:0%
+standard cell
+potential so find Delta e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KN all right so to do this we need to
+
+ align:start position:0%
+KN all right so to do this we need to
+ 
+
+ align:start position:0%
+KN all right so to do this we need to
+know we need to look at both reactions
+
+ align:start position:0%
+know we need to look at both reactions
+ 
+
+ align:start position:0%
+know we need to look at both reactions
+we need to know the standard reduction
+
+ align:start position:0%
+we need to know the standard reduction
+ 
+
+ align:start position:0%
+we need to know the standard reduction
+potential for both reactions all right
+
+ align:start position:0%
+potential for both reactions all right
+ 
+
+ align:start position:0%
+potential for both reactions all right
+so one reaction involves copper plus
+
+ align:start position:0%
+so one reaction involves copper plus
+ 
+
+ align:start position:0%
+so one reaction involves copper plus
+two going to Copper
+
+ align:start position:0%
+two going to Copper
+ 
+
+ align:start position:0%
+two going to Copper
+solid and this reaction involves two
+
+ align:start position:0%
+solid and this reaction involves two
+ 
+
+ align:start position:0%
+solid and this reaction involves two
+electrons the other reaction that's
+
+ align:start position:0%
+electrons the other reaction that's
+ 
+
+ align:start position:0%
+electrons the other reaction that's
+going in the forward direction is is
+
+ align:start position:0%
+going in the forward direction is is
+ 
+
+ align:start position:0%
+going in the forward direction is is
+that zinc
+
+ align:start position:0%
+that zinc
+ 
+
+ align:start position:0%
+that zinc
+solid is going to zinc +
+
+ align:start position:0%
+solid is going to zinc +
+ 
+
+ align:start position:0%
+solid is going to zinc +
+2+ two
+
+ align:start position:0%
+2+ two
+ 
+
+ align:start position:0%
+2+ two
+electrons so we have a reduction and an
+
+ align:start position:0%
+electrons so we have a reduction and an
+ 
+
+ align:start position:0%
+electrons so we have a reduction and an
+oxidation so this reaction would be
+
+ align:start position:0%
+oxidation so this reaction would be
+ 
+
+ align:start position:0%
+oxidation so this reaction would be
+occurring where at the cathode or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anode at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cathode and so that must mean that the
+
+ align:start position:0%
+cathode and so that must mean that the
+ 
+
+ align:start position:0%
+cathode and so that must mean that the
+other one is happening at the
+
+ align:start position:0%
+other one is happening at the
+ 
+
+ align:start position:0%
+other one is happening at the
+anode now we need to know the standard
+
+ align:start position:0%
+anode now we need to know the standard
+ 
+
+ align:start position:0%
+anode now we need to know the standard
+reduction potential for the two couples
+
+ align:start position:0%
+reduction potential for the two couples
+ 
+
+ align:start position:0%
+reduction potential for the two couples
+we need to know the reduction potential
+
+ align:start position:0%
+we need to know the reduction potential
+ 
+
+ align:start position:0%
+we need to know the reduction potential
+of copper 2+ to Copper solid and we need
+
+ align:start position:0%
+of copper 2+ to Copper solid and we need
+ 
+
+ align:start position:0%
+of copper 2+ to Copper solid and we need
+to know the potential for zinc 2+ to
+
+ align:start position:0%
+to know the potential for zinc 2+ to
+ 
+
+ align:start position:0%
+to know the potential for zinc 2+ to
+zinc
+
+ align:start position:0%
+zinc
+ 
+
+ align:start position:0%
+zinc
+solid and we can look those up in a
+
+ align:start position:0%
+solid and we can look those up in a
+ 
+
+ align:start position:0%
+solid and we can look those up in a
+table
+
+ align:start position:0%
+table
+ 
+
+ align:start position:0%
+table
+and they're up here if you can see them
+
+ align:start position:0%
+and they're up here if you can see them
+ 
+
+ align:start position:0%
+and they're up here if you can see them
+I'm actually going to write them down to
+
+ align:start position:0%
+I'm actually going to write them down to
+ 
+
+ align:start position:0%
+I'm actually going to write them down to
+a couple more significant figures and so
+
+ align:start position:0%
+a couple more significant figures and so
+ 
+
+ align:start position:0%
+a couple more significant figures and so
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is340 and the other is
+
+ align:start position:0%
+is340 and the other is
+ 
+
+ align:start position:0%
+is340 and the other is
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7628 and those are in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volts okay so we have that information
+
+ align:start position:0%
+volts okay so we have that information
+ 
+
+ align:start position:0%
+volts okay so we have that information
+and now this is a balanced reaction
+
+ align:start position:0%
+and now this is a balanced reaction
+ 
+
+ align:start position:0%
+and now this is a balanced reaction
+there were no extra electrons floating
+
+ align:start position:0%
+there were no extra electrons floating
+ 
+
+ align:start position:0%
+there were no extra electrons floating
+around so so we can use uh this is a
+
+ align:start position:0%
+around so so we can use uh this is a
+ 
+
+ align:start position:0%
+around so so we can use uh this is a
+cell we're trying to find a cell
+
+ align:start position:0%
+cell we're trying to find a cell
+ 
+
+ align:start position:0%
+cell we're trying to find a cell
+potential here so we can calculate that
+
+ align:start position:0%
+potential here so we can calculate that
+ 
+
+ align:start position:0%
+potential here so we can calculate that
+for the particular cell in question from
+
+ align:start position:0%
+for the particular cell in question from
+ 
+
+ align:start position:0%
+for the particular cell in question from
+the standard reduction potention for the
+
+ align:start position:0%
+the standard reduction potention for the
+ 
+
+ align:start position:0%
+the standard reduction potention for the
+reaction at the
+
+ align:start position:0%
+reaction at the
+ 
+
+ align:start position:0%
+reaction at the
+cathode minus the standard reduction
+
+ align:start position:0%
+cathode minus the standard reduction
+ 
+
+ align:start position:0%
+cathode minus the standard reduction
+potential for the reaction at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anode and so that's going to be equal to
+
+ align:start position:0%
+anode and so that's going to be equal to
+ 
+
+ align:start position:0%
+anode and so that's going to be equal to
+0.0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+.34 minus a
+
+ align:start position:0%
+.34 minus a
+ 
+
+ align:start position:0%
+.34 minus a
+0.76
+
+ align:start position:0%
+0.76
+ 
+
+ align:start position:0%
+0.76
+28 which is going to uh give you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.13
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volts so this is the reaction we use and
+
+ align:start position:0%
+volts so this is the reaction we use and
+ 
+
+ align:start position:0%
+volts so this is the reaction we use and
+again we're not changing the sign
+
+ align:start position:0%
+again we're not changing the sign
+ 
+
+ align:start position:0%
+again we're not changing the sign
+because we're looking up and entering
+
+ align:start position:0%
+because we're looking up and entering
+ 
+
+ align:start position:0%
+because we're looking up and entering
+standard reduction potentials but you
+
+ align:start position:0%
+standard reduction potentials but you
+ 
+
+ align:start position:0%
+standard reduction potentials but you
+need to know which is the reaction at
+
+ align:start position:0%
+need to know which is the reaction at
+ 
+
+ align:start position:0%
+need to know which is the reaction at
+the cathode and which is the reaction
+
+ align:start position:0%
+the cathode and which is the reaction
+ 
+
+ align:start position:0%
+the cathode and which is the reaction
+action at the ano to put them in the
+
+ align:start position:0%
+action at the ano to put them in the
+ 
+
+ align:start position:0%
+action at the ano to put them in the
+right place all right so we have our our
+
+ align:start position:0%
+right place all right so we have our our
+ 
+
+ align:start position:0%
+right place all right so we have our our
+first thing
+
+ align:start position:0%
+first thing
+ 
+
+ align:start position:0%
+first thing
+there now what do we need to know well
+
+ align:start position:0%
+there now what do we need to know well
+ 
+
+ align:start position:0%
+there now what do we need to know well
+we also need to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q so step two let's find
+
+ align:start position:0%
+Q so step two let's find
+ 
+
+ align:start position:0%
+Q so step two let's find
+Q so what's Q going to be equal
+
+ align:start position:0%
+Q so what's Q going to be equal
+ 
+
+ align:start position:0%
+Q so what's Q going to be equal
+to what's on top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+of yeah zinc
+
+ align:start position:0%
+of yeah zinc
+ 
+
+ align:start position:0%
+of yeah zinc
+2+ and nothing else because it's
+
+ align:start position:0%
+2+ and nothing else because it's
+ 
+
+ align:start position:0%
+2+ and nothing else because it's
+products over reactants but we don't
+
+ align:start position:0%
+products over reactants but we don't
+ 
+
+ align:start position:0%
+products over reactants but we don't
+include solids in our equation so it's
+
+ align:start position:0%
+include solids in our equation so it's
+ 
+
+ align:start position:0%
+include solids in our equation so it's
+just zinc 2+ and that's going to be then
+
+ align:start position:0%
+just zinc 2+ and that's going to be then
+ 
+
+ align:start position:0%
+just zinc 2+ and that's going to be then
+over copper 2+ again we're not including
+
+ align:start position:0%
+over copper 2+ again we're not including
+ 
+
+ align:start position:0%
+over copper 2+ again we're not including
+solids uh we're not including the zinc
+
+ align:start position:0%
+solids uh we're not including the zinc
+ 
+
+ align:start position:0%
+solids uh we're not including the zinc
+solids so products over
+
+ align:start position:0%
+solids so products over
+ 
+
+ align:start position:0%
+solids so products over
+reactants and we can plug this
+
+ align:start position:0%
+reactants and we can plug this
+ 
+
+ align:start position:0%
+reactants and we can plug this
+in we have 0
+
+ align:start position:0%
+in we have 0
+ 
+
+ align:start position:0%
+in we have 0
+1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.0010 and that gives us
+
+ align:start position:0%
+0.0010 and that gives us
+ 
+
+ align:start position:0%
+0.0010 and that gives us
+1.0 * 10 to the 2 for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q step three we also need to know
+
+ align:start position:0%
+Q step three we also need to know
+ 
+
+ align:start position:0%
+Q step three we also need to know
+n how many moles of electrons are
+
+ align:start position:0%
+n how many moles of electrons are
+ 
+
+ align:start position:0%
+n how many moles of electrons are
+involved in this
+
+ align:start position:0%
+involved in this
+ 
+
+ align:start position:0%
+involved in this
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+two so n equals 2 so we have from a
+
+ align:start position:0%
+two so n equals 2 so we have from a
+ 
+
+ align:start position:0%
+two so n equals 2 so we have from a
+copper 2+ to Copper solid zinc 2+ to
+
+ align:start position:0%
+copper 2+ to Copper solid zinc 2+ to
+ 
+
+ align:start position:0%
+copper 2+ to Copper solid zinc 2+ to
+zinc solid they're two electrons evolved
+
+ align:start position:0%
+zinc solid they're two electrons evolved
+ 
+
+ align:start position:0%
+zinc solid they're two electrons evolved
+they are not in the equation because
+
+ align:start position:0%
+they are not in the equation because
+ 
+
+ align:start position:0%
+they are not in the equation because
+they canceled out this is one is obvious
+
+ align:start position:0%
+they canceled out this is one is obvious
+ 
+
+ align:start position:0%
+they canceled out this is one is obvious
+sometimes they're harder and you
+
+ align:start position:0%
+sometimes they're harder and you
+ 
+
+ align:start position:0%
+sometimes they're harder and you
+actually really have to think about how
+
+ align:start position:0%
+actually really have to think about how
+ 
+
+ align:start position:0%
+actually really have to think about how
+that equation was balanced to come up
+
+ align:start position:0%
+that equation was balanced to come up
+ 
+
+ align:start position:0%
+that equation was balanced to come up
+with the right answer uh for the number
+
+ align:start position:0%
+with the right answer uh for the number
+ 
+
+ align:start position:0%
+with the right answer uh for the number
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moles all right so now we can plug all
+
+ align:start position:0%
+moles all right so now we can plug all
+ 
+
+ align:start position:0%
+moles all right so now we can plug all
+that information in to the equation so
+
+ align:start position:0%
+that information in to the equation so
+ 
+
+ align:start position:0%
+that information in to the equation so
+we're looking for uh what the cell
+
+ align:start position:0%
+we're looking for uh what the cell
+ 
+
+ align:start position:0%
+we're looking for uh what the cell
+potential is at a particular time so
+
+ align:start position:0%
+potential is at a particular time so
+ 
+
+ align:start position:0%
+potential is at a particular time so
+that will be equal to the standard cell
+
+ align:start position:0%
+that will be equal to the standard cell
+ 
+
+ align:start position:0%
+that will be equal to the standard cell
+potential that we
+
+ align:start position:0%
+potential that we
+ 
+
+ align:start position:0%
+potential that we
+calculated minus um RT and R is the gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant so write the gas constant out
+
+ align:start position:0%
+constant so write the gas constant out
+ 
+
+ align:start position:0%
+constant so write the gas constant out
+times the temperature and the
+
+ align:start position:0%
+times the temperature and the
+ 
+
+ align:start position:0%
+times the temperature and the
+temperature for all the problems you're
+
+ align:start position:0%
+temperature for all the problems you're
+ 
+
+ align:start position:0%
+temperature for all the problems you're
+going to do in this unit is always going
+
+ align:start position:0%
+going to do in this unit is always going
+ 
+
+ align:start position:0%
+going to do in this unit is always going
+to be at room
+
+ align:start position:0%
+to be at room
+ 
+
+ align:start position:0%
+to be at room
+temperature times the natural log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q and that's going to be
+
+ align:start position:0%
+Q and that's going to be
+ 
+
+ align:start position:0%
+Q and that's going to be
+over 2 times Faraday
+
+ align:start position:0%
+over 2 times Faraday
+ 
+
+ align:start position:0%
+over 2 times Faraday
+constant and I'm writing all this out
+
+ align:start position:0%
+constant and I'm writing all this out
+ 
+
+ align:start position:0%
+constant and I'm writing all this out
+because we're going to talk about units
+
+ align:start position:0%
+because we're going to talk about units
+ 
+
+ align:start position:0%
+because we're going to talk about units
+in a minute so times Faraday
+
+ align:start position:0%
+in a minute so times Faraday
+ 
+
+ align:start position:0%
+in a minute so times Faraday
+constant so now we can cancel out we'll
+
+ align:start position:0%
+constant so now we can cancel out we'll
+ 
+
+ align:start position:0%
+constant so now we can cancel out we'll
+cancel moles
+
+ align:start position:0%
+cancel moles
+ 
+
+ align:start position:0%
+cancel moles
+and we're going to cancel
+
+ align:start position:0%
+and we're going to cancel
+ 
+
+ align:start position:0%
+and we're going to cancel
+Kelvin and we're going to be left with
+
+ align:start position:0%
+Kelvin and we're going to be left with
+ 
+
+ align:start position:0%
+Kelvin and we're going to be left with
+jewels per
+
+ align:start position:0%
+jewels per
+ 
+
+ align:start position:0%
+jewels per
+Kum is that a good thing what is Jewels
+
+ align:start position:0%
+Kum is that a good thing what is Jewels
+ 
+
+ align:start position:0%
+Kum is that a good thing what is Jewels
+per Kum equal a volt right so that will
+
+ align:start position:0%
+per Kum equal a volt right so that will
+ 
+
+ align:start position:0%
+per Kum equal a volt right so that will
+do very well because we're going to have
+
+ align:start position:0%
+do very well because we're going to have
+ 
+
+ align:start position:0%
+do very well because we're going to have
+a volt here we're going to subtract
+
+ align:start position:0%
+a volt here we're going to subtract
+ 
+
+ align:start position:0%
+a volt here we're going to subtract
+something in volt so that will leave us
+
+ align:start position:0%
+something in volt so that will leave us
+ 
+
+ align:start position:0%
+something in volt so that will leave us
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+jewels and a volt equals Jews per Kum
+
+ align:start position:0%
+jewels and a volt equals Jews per Kum
+ 
+
+ align:start position:0%
+jewels and a volt equals Jews per Kum
+so that gives us
+
+ align:start position:0%
+so that gives us
+ 
+
+ align:start position:0%
+so that gives us
+1.13 volts minus this calculates out to
+
+ align:start position:0%
+1.13 volts minus this calculates out to
+ 
+
+ align:start position:0%
+1.13 volts minus this calculates out to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+volts and if we worked this out this
+
+ align:start position:0%
+volts and if we worked this out this
+ 
+
+ align:start position:0%
+volts and if we worked this out this
+would give us a number with two
+
+ align:start position:0%
+would give us a number with two
+ 
+
+ align:start position:0%
+would give us a number with two
+significant figures after the decimal
+
+ align:start position:0%
+significant figures after the decimal
+ 
+
+ align:start position:0%
+significant figures after the decimal
+point and so um that leaves us with
+
+ align:start position:0%
+point and so um that leaves us with
+ 
+
+ align:start position:0%
+point and so um that leaves us with
+these significant figures here we're
+
+ align:start position:0%
+these significant figures here we're
+ 
+
+ align:start position:0%
+these significant figures here we're
+actually going to lose one in the
+
+ align:start position:0%
+actually going to lose one in the
+ 
+
+ align:start position:0%
+actually going to lose one in the
+subtraction anyway and we come up with
+
+ align:start position:0%
+subtraction anyway and we come up with
+ 
+
+ align:start position:0%
+subtraction anyway and we come up with
+an answer of zero 1
+
+ align:start position:0%
+an answer of zero 1
+ 
+
+ align:start position:0%
+an answer of zero 1
+044 uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volts so I will mention in terms of
+
+ align:start position:0%
+volts so I will mention in terms of
+ 
+
+ align:start position:0%
+volts so I will mention in terms of
+significant figures this is like the
+
+ align:start position:0%
+significant figures this is like the
+ 
+
+ align:start position:0%
+significant figures this is like the
+nastiest problem yeah you have a
+
+ align:start position:0%
+nastiest problem yeah you have a
+ 
+
+ align:start position:0%
+nastiest problem yeah you have a
+question yeah you said it' be tricky
+
+ align:start position:0%
+question yeah you said it' be tricky
+ 
+
+ align:start position:0%
+question yeah you said it' be tricky
+sometimes to find out the number of
+
+ align:start position:0%
+sometimes to find out the number of
+ 
+
+ align:start position:0%
+sometimes to find out the number of
+moles involved
+
+ align:start position:0%
+moles involved
+ 
+
+ align:start position:0%
+moles involved
+yeah uh sometimes when you look at the
+
+ align:start position:0%
+yeah uh sometimes when you look at the
+ 
+
+ align:start position:0%
+yeah uh sometimes when you look at the
+equation there's a lot of different
+
+ align:start position:0%
+equation there's a lot of different
+ 
+
+ align:start position:0%
+equation there's a lot of different
+things going on and you actually have to
+
+ align:start position:0%
+things going on and you actually have to
+ 
+
+ align:start position:0%
+things going on and you actually have to
+do sort of a step backwards to think all
+
+ align:start position:0%
+do sort of a step backwards to think all
+ 
+
+ align:start position:0%
+do sort of a step backwards to think all
+right what number of what what were the
+
+ align:start position:0%
+right what number of what what were the
+ 
+
+ align:start position:0%
+right what number of what what were the
+half reactions and what was canceled
+
+ align:start position:0%
+half reactions and what was canceled
+ 
+
+ align:start position:0%
+half reactions and what was canceled
+some a lot of times it's very obvious
+
+ align:start position:0%
+some a lot of times it's very obvious
+ 
+
+ align:start position:0%
+some a lot of times it's very obvious
+but some of them are a little bit longer
+
+ align:start position:0%
+but some of them are a little bit longer
+ 
+
+ align:start position:0%
+but some of them are a little bit longer
+there may be one in the problem set I
+
+ align:start position:0%
+there may be one in the problem set I
+ 
+
+ align:start position:0%
+there may be one in the problem set I
+don't remember but you'll know you know
+
+ align:start position:0%
+don't remember but you'll know you know
+ 
+
+ align:start position:0%
+don't remember but you'll know you know
+what I mean when you see it but
+
+ align:start position:0%
+what I mean when you see it but
+ 
+
+ align:start position:0%
+what I mean when you see it but
+sometimes it'll be just very obvious
+
+ align:start position:0%
+sometimes it'll be just very obvious
+ 
+
+ align:start position:0%
+sometimes it'll be just very obvious
+like that that it'll be two other times
+
+ align:start position:0%
+like that that it'll be two other times
+ 
+
+ align:start position:0%
+like that that it'll be two other times
+it's it's a little bit harder to see and
+
+ align:start position:0%
+it's it's a little bit harder to see and
+ 
+
+ align:start position:0%
+it's it's a little bit harder to see and
+you sort of want to think backwards from
+
+ align:start position:0%
+you sort of want to think backwards from
+ 
+
+ align:start position:0%
+you sort of want to think backwards from
+what those half reactions were and how
+
+ align:start position:0%
+what those half reactions were and how
+ 
+
+ align:start position:0%
+what those half reactions were and how
+you would have balanced
+
+ align:start position:0%
+you would have balanced
+ 
+
+ align:start position:0%
+you would have balanced
+them all right so in terms of
+
+ align:start position:0%
+them all right so in terms of
+ 
+
+ align:start position:0%
+them all right so in terms of
+significant figures these problems are
+
+ align:start position:0%
+significant figures these problems are
+ 
+
+ align:start position:0%
+significant figures these problems are
+probably some of the worst in terms of
+
+ align:start position:0%
+probably some of the worst in terms of
+ 
+
+ align:start position:0%
+probably some of the worst in terms of
+significant figures acid base is pretty
+
+ align:start position:0%
+significant figures acid base is pretty
+ 
+
+ align:start position:0%
+significant figures acid base is pretty
+bad too but you notice we started with a
+
+ align:start position:0%
+bad too but you notice we started with a
+ 
+
+ align:start position:0%
+bad too but you notice we started with a
+subtraction and in the subtraction you
+
+ align:start position:0%
+subtraction and in the subtraction you
+ 
+
+ align:start position:0%
+subtraction and in the subtraction you
+often lose significant figures then we
+
+ align:start position:0%
+often lose significant figures then we
+ 
+
+ align:start position:0%
+often lose significant figures then we
+had um we had a division then we have a
+
+ align:start position:0%
+had um we had a division then we have a
+ 
+
+ align:start position:0%
+had um we had a division then we have a
+log and then we have multiplication and
+
+ align:start position:0%
+log and then we have multiplication and
+ 
+
+ align:start position:0%
+log and then we have multiplication and
+division and then another
+
+ align:start position:0%
+division and then another
+ 
+
+ align:start position:0%
+division and then another
+subtraction so the only thing I can say
+
+ align:start position:0%
+subtraction so the only thing I can say
+ 
+
+ align:start position:0%
+subtraction so the only thing I can say
+for these problems is that it helps to
+
+ align:start position:0%
+for these problems is that it helps to
+ 
+
+ align:start position:0%
+for these problems is that it helps to
+really write out every step and to put a
+
+ align:start position:0%
+really write out every step and to put a
+ 
+
+ align:start position:0%
+really write out every step and to put a
+line under where your significant figure
+
+ align:start position:0%
+line under where your significant figure
+ 
+
+ align:start position:0%
+line under where your significant figure
+is after each calculation to make sure
+
+ align:start position:0%
+is after each calculation to make sure
+ 
+
+ align:start position:0%
+is after each calculation to make sure
+that you aren't um getting the wrong
+
+ align:start position:0%
+that you aren't um getting the wrong
+ 
+
+ align:start position:0%
+that you aren't um getting the wrong
+significant figures at the end so you
+
+ align:start position:0%
+significant figures at the end so you
+ 
+
+ align:start position:0%
+significant figures at the end so you
+can't in this case go back and say all
+
+ align:start position:0%
+can't in this case go back and say all
+ 
+
+ align:start position:0%
+can't in this case go back and say all
+right how many significant figures did I
+
+ align:start position:0%
+right how many significant figures did I
+ 
+
+ align:start position:0%
+right how many significant figures did I
+have in the information that was given
+
+ align:start position:0%
+have in the information that was given
+ 
+
+ align:start position:0%
+have in the information that was given
+to me that's how many I have at the end
+
+ align:start position:0%
+to me that's how many I have at the end
+ 
+
+ align:start position:0%
+to me that's how many I have at the end
+that's not going to work for you so
+
+ align:start position:0%
+that's not going to work for you so
+ 
+
+ align:start position:0%
+that's not going to work for you so
+these are a little bit tricky a lot of
+
+ align:start position:0%
+these are a little bit tricky a lot of
+ 
+
+ align:start position:0%
+these are a little bit tricky a lot of
+the time you'll have a break because
+
+ align:start position:0%
+the time you'll have a break because
+ 
+
+ align:start position:0%
+the time you'll have a break because
+there won't be many significant figures
+
+ align:start position:0%
+there won't be many significant figures
+ 
+
+ align:start position:0%
+there won't be many significant figures
+in this answer and so when you do the
+
+ align:start position:0%
+in this answer and so when you do the
+ 
+
+ align:start position:0%
+in this answer and so when you do the
+subtraction you kind of compensate it
+
+ align:start position:0%
+subtraction you kind of compensate it
+ 
+
+ align:start position:0%
+subtraction you kind of compensate it
+doesn't sometimes it doesn't matter how
+
+ align:start position:0%
+doesn't sometimes it doesn't matter how
+ 
+
+ align:start position:0%
+doesn't sometimes it doesn't matter how
+many you really have here because you're
+
+ align:start position:0%
+many you really have here because you're
+ 
+
+ align:start position:0%
+many you really have here because you're
+going to lose them in that subtraction
+
+ align:start position:0%
+going to lose them in that subtraction
+ 
+
+ align:start position:0%
+going to lose them in that subtraction
+step anyway but just to warn you uh this
+
+ align:start position:0%
+step anyway but just to warn you uh this
+ 
+
+ align:start position:0%
+step anyway but just to warn you uh this
+is uh there's a lot of different
+
+ align:start position:0%
+is uh there's a lot of different
+ 
+
+ align:start position:0%
+is uh there's a lot of different
+significant figure stuff this was
+
+ align:start position:0%
+significant figure stuff this was
+ 
+
+ align:start position:0%
+significant figure stuff this was
+actually be a great significant figure
+
+ align:start position:0%
+actually be a great significant figure
+ 
+
+ align:start position:0%
+actually be a great significant figure
+problem that's all your testing because
+
+ align:start position:0%
+problem that's all your testing because
+ 
+
+ align:start position:0%
+problem that's all your testing because
+you have to do every kind of significant
+
+ align:start position:0%
+you have to do every kind of significant
+ 
+
+ align:start position:0%
+you have to do every kind of significant
+figure uh uh situation in this one
+
+ align:start position:0%
+figure uh uh situation in this one
+ 
+
+ align:start position:0%
+figure uh uh situation in this one
+problem but I'm going to make your life
+
+ align:start position:0%
+problem but I'm going to make your life
+ 
+
+ align:start position:0%
+problem but I'm going to make your life
+slightly easier and what I'm going to do
+
+ align:start position:0%
+slightly easier and what I'm going to do
+ 
+
+ align:start position:0%
+slightly easier and what I'm going to do
+is do some of the steps for you so if we
+
+ align:start position:0%
+is do some of the steps for you so if we
+ 
+
+ align:start position:0%
+is do some of the steps for you so if we
+talk about constants for a minute we're
+
+ align:start position:0%
+talk about constants for a minute we're
+ 
+
+ align:start position:0%
+talk about constants for a minute we're
+always going to be at room temperature
+
+ align:start position:0%
+always going to be at room temperature
+ 
+
+ align:start position:0%
+always going to be at room temperature
+in this unit because well that's just
+
+ align:start position:0%
+in this unit because well that's just
+ 
+
+ align:start position:0%
+in this unit because well that's just
+where we are it's going to make it
+
+ align:start position:0%
+where we are it's going to make it
+ 
+
+ align:start position:0%
+where we are it's going to make it
+harder to do anything else so unless
+
+ align:start position:0%
+harder to do anything else so unless
+ 
+
+ align:start position:0%
+harder to do anything else so unless
+specified assume room temperature if you
+
+ align:start position:0%
+specified assume room temperature if you
+ 
+
+ align:start position:0%
+specified assume room temperature if you
+do that you find that this is always
+
+ align:start position:0%
+do that you find that this is always
+ 
+
+ align:start position:0%
+do that you find that this is always
+going to be the same number so you have
+
+ align:start position:0%
+going to be the same number so you have
+ 
+
+ align:start position:0%
+going to be the same number so you have
+the gas constant the temperature and
+
+ align:start position:0%
+the gas constant the temperature and
+ 
+
+ align:start position:0%
+the gas constant the temperature and
+Faraday constant
+
+ align:start position:0%
+Faraday constant
+ 
+
+ align:start position:0%
+Faraday constant
+and so there's all there's one number
+
+ align:start position:0%
+and so there's all there's one number
+ 
+
+ align:start position:0%
+and so there's all there's one number
+that that's equal to and so you can use
+
+ align:start position:0%
+that that's equal to and so you can use
+ 
+
+ align:start position:0%
+that that's equal to and so you can use
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+number or if you prefer to use a log
+
+ align:start position:0%
+number or if you prefer to use a log
+ 
+
+ align:start position:0%
+number or if you prefer to use a log
+base 10 rather than natural log you can
+
+ align:start position:0%
+base 10 rather than natural log you can
+ 
+
+ align:start position:0%
+base 10 rather than natural log you can
+take this number and multiply it by the
+
+ align:start position:0%
+take this number and multiply it by the
+ 
+
+ align:start position:0%
+take this number and multiply it by the
+conversion factor and you have sort of
+
+ align:start position:0%
+conversion factor and you have sort of
+ 
+
+ align:start position:0%
+conversion factor and you have sort of
+another constant which you can use in uh
+
+ align:start position:0%
+another constant which you can use in uh
+ 
+
+ align:start position:0%
+another constant which you can use in uh
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+problem and on the tests I will actually
+
+ align:start position:0%
+problem and on the tests I will actually
+ 
+
+ align:start position:0%
+problem and on the tests I will actually
+give the equations in this format to you
+
+ align:start position:0%
+give the equations in this format to you
+ 
+
+ align:start position:0%
+give the equations in this format to you
+um on on your sheet and so you can pick
+
+ align:start position:0%
+um on on your sheet and so you can pick
+ 
+
+ align:start position:0%
+um on on your sheet and so you can pick
+one of these if there's room I'll give
+
+ align:start position:0%
+one of these if there's room I'll give
+ 
+
+ align:start position:0%
+one of these if there's room I'll give
+both otherwise I'll just give one but
+
+ align:start position:0%
+both otherwise I'll just give one but
+ 
+
+ align:start position:0%
+both otherwise I'll just give one but
+it's the same type of problem you just
+
+ align:start position:0%
+it's the same type of problem you just
+ 
+
+ align:start position:0%
+it's the same type of problem you just
+have to pay attention to which log to
+
+ align:start position:0%
+have to pay attention to which log to
+ 
+
+ align:start position:0%
+have to pay attention to which log to
+use and I'll make sure that the number
+
+ align:start position:0%
+use and I'll make sure that the number
+ 
+
+ align:start position:0%
+use and I'll make sure that the number
+of significant figures here is not
+
+ align:start position:0%
+of significant figures here is not
+ 
+
+ align:start position:0%
+of significant figures here is not
+limiting in the problem so you don't
+
+ align:start position:0%
+limiting in the problem so you don't
+ 
+
+ align:start position:0%
+limiting in the problem so you don't
+have to worry about that so I highly
+
+ align:start position:0%
+have to worry about that so I highly
+ 
+
+ align:start position:0%
+have to worry about that so I highly
+recommend if I provide these to you save
+
+ align:start position:0%
+recommend if I provide these to you save
+ 
+
+ align:start position:0%
+recommend if I provide these to you save
+those extra steps of multiplying things
+
+ align:start position:0%
+those extra steps of multiplying things
+ 
+
+ align:start position:0%
+those extra steps of multiplying things
+out it'll save you some time and uh and
+
+ align:start position:0%
+out it'll save you some time and uh and
+ 
+
+ align:start position:0%
+out it'll save you some time and uh and
+uh maybe a little bit of significant
+
+ align:start position:0%
+uh maybe a little bit of significant
+ 
+
+ align:start position:0%
+uh maybe a little bit of significant
+figure headache so those will be
+
+ align:start position:0%
+figure headache so those will be
+ 
+
+ align:start position:0%
+figure headache so those will be
+available just to simplify these these
+
+ align:start position:0%
+available just to simplify these these
+ 
+
+ align:start position:0%
+available just to simplify these these
+problems I'm sure that you can all
+
+ align:start position:0%
+problems I'm sure that you can all
+ 
+
+ align:start position:0%
+problems I'm sure that you can all
+multiply RT over Faraday constant so I'm
+
+ align:start position:0%
+multiply RT over Faraday constant so I'm
+ 
+
+ align:start position:0%
+multiply RT over Faraday constant so I'm
+just going to provide that for you and
+
+ align:start position:0%
+just going to provide that for you and
+ 
+
+ align:start position:0%
+just going to provide that for you and
+not require you to do it on on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+test okay so what what happens at uh at
+
+ align:start position:0%
+test okay so what what happens at uh at
+ 
+
+ align:start position:0%
+test okay so what what happens at uh at
+equilibrium then at
+
+ align:start position:0%
+equilibrium then at
+ 
+
+ align:start position:0%
+equilibrium then at
+equilibrium what is Q equal
+
+ align:start position:0%
+equilibrium what is Q equal
+ 
+
+ align:start position:0%
+equilibrium what is Q equal
+Q equals k at equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so what about Delta G what is
+
+ align:start position:0%
+right so what about Delta G what is
+ 
+
+ align:start position:0%
+right so what about Delta G what is
+Delta G equal to
+
+ align:start position:0%
+Delta G equal to
+ 
+
+ align:start position:0%
+Delta G equal to
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero do you see where we're going with
+
+ align:start position:0%
+zero do you see where we're going with
+ 
+
+ align:start position:0%
+zero do you see where we're going with
+this you have the hand out you can look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead so we know from
+
+ align:start position:0%
+ahead so we know from
+ 
+
+ align:start position:0%
+ahead so we know from
+before that uh Delta gal Delta G Plus RT
+
+ align:start position:0%
+before that uh Delta gal Delta G Plus RT
+ 
+
+ align:start position:0%
+before that uh Delta gal Delta G Plus RT
+natural law log of Q we also know that
+
+ align:start position:0%
+natural law log of Q we also know that
+ 
+
+ align:start position:0%
+natural law log of Q we also know that
+Delta g equals minus RT natural log of K
+
+ align:start position:0%
+Delta g equals minus RT natural log of K
+ 
+
+ align:start position:0%
+Delta g equals minus RT natural log of K
+because when uh at equilibrium Delta G
+
+ align:start position:0%
+because when uh at equilibrium Delta G
+ 
+
+ align:start position:0%
+because when uh at equilibrium Delta G
+is zero so we drop that out and at
+
+ align:start position:0%
+is zero so we drop that out and at
+ 
+
+ align:start position:0%
+is zero so we drop that out and at
+equilibrium Q equals K so we've seen
+
+ align:start position:0%
+equilibrium Q equals K so we've seen
+ 
+
+ align:start position:0%
+equilibrium Q equals K so we've seen
+this expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before so we know
+
+ align:start position:0%
+before so we know
+ 
+
+ align:start position:0%
+before so we know
+that we also know the relationship
+
+ align:start position:0%
+that we also know the relationship
+ 
+
+ align:start position:0%
+that we also know the relationship
+between Delta G and cell potential we
+
+ align:start position:0%
+between Delta G and cell potential we
+ 
+
+ align:start position:0%
+between Delta G and cell potential we
+know that Delta G equal minus n the
+
+ align:start position:0%
+know that Delta G equal minus n the
+ 
+
+ align:start position:0%
+know that Delta G equal minus n the
+number of moles of electrons Faraday
+
+ align:start position:0%
+number of moles of electrons Faraday
+ 
+
+ align:start position:0%
+number of moles of electrons Faraday
+constant times the standard cell
+
+ align:start position:0%
+constant times the standard cell
+ 
+
+ align:start position:0%
+constant times the standard cell
+potential so now we can rearrange these
+
+ align:start position:0%
+potential so now we can rearrange these
+ 
+
+ align:start position:0%
+potential so now we can rearrange these
+and relate the equilibrium constant to
+
+ align:start position:0%
+and relate the equilibrium constant to
+ 
+
+ align:start position:0%
+and relate the equilibrium constant to
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+potential so combining we get this so we
+
+ align:start position:0%
+potential so combining we get this so we
+ 
+
+ align:start position:0%
+potential so combining we get this so we
+just set those two equal to each other
+
+ align:start position:0%
+just set those two equal to each other
+ 
+
+ align:start position:0%
+just set those two equal to each other
+and we can solve for
+
+ align:start position:0%
+and we can solve for
+ 
+
+ align:start position:0%
+and we can solve for
+k or at least natural log of K a in
+
+ align:start position:0%
+k or at least natural log of K a in
+ 
+
+ align:start position:0%
+k or at least natural log of K a in
+terms of cell
+
+ align:start position:0%
+terms of cell
+ 
+
+ align:start position:0%
+terms of cell
+potential and so you can calculate
+
+ align:start position:0%
+potential and so you can calculate
+ 
+
+ align:start position:0%
+potential and so you can calculate
+equilibrium po the equilibrium constant
+
+ align:start position:0%
+equilibrium po the equilibrium constant
+ 
+
+ align:start position:0%
+equilibrium po the equilibrium constant
+from cell
+
+ align:start position:0%
+from cell
+ 
+
+ align:start position:0%
+from cell
+potentials and of course this is
+
+ align:start position:0%
+potentials and of course this is
+ 
+
+ align:start position:0%
+potentials and of course this is
+important because if you want your cell
+
+ align:start position:0%
+important because if you want your cell
+ 
+
+ align:start position:0%
+important because if you want your cell
+to be uh producing some kind of current
+
+ align:start position:0%
+to be uh producing some kind of current
+ 
+
+ align:start position:0%
+to be uh producing some kind of current
+um creating energy or if you want to
+
+ align:start position:0%
+um creating energy or if you want to
+ 
+
+ align:start position:0%
+um creating energy or if you want to
+apply something to get a non-spontaneous
+
+ align:start position:0%
+apply something to get a non-spontaneous
+ 
+
+ align:start position:0%
+apply something to get a non-spontaneous
+reaction to go you care about what the
+
+ align:start position:0%
+reaction to go you care about what the
+ 
+
+ align:start position:0%
+reaction to go you care about what the
+composition of the reaction is you care
+
+ align:start position:0%
+composition of the reaction is you care
+ 
+
+ align:start position:0%
+composition of the reaction is you care
+about the equilibri ium constant and you
+
+ align:start position:0%
+about the equilibri ium constant and you
+ 
+
+ align:start position:0%
+about the equilibri ium constant and you
+care about these
+
+ align:start position:0%
+care about these
+ 
+
+ align:start position:0%
+care about these
+relationships so if you know about K you
+
+ align:start position:0%
+relationships so if you know about K you
+ 
+
+ align:start position:0%
+relationships so if you know about K you
+can also think about you know if the
+
+ align:start position:0%
+can also think about you know if the
+ 
+
+ align:start position:0%
+can also think about you know if the
+reaction is really favorable in One
+
+ align:start position:0%
+reaction is really favorable in One
+ 
+
+ align:start position:0%
+reaction is really favorable in One
+Direction or in the other directions at
+
+ align:start position:0%
+Direction or in the other directions at
+ 
+
+ align:start position:0%
+Direction or in the other directions at
+equilibrium do you have a lot more
+
+ align:start position:0%
+equilibrium do you have a lot more
+ 
+
+ align:start position:0%
+equilibrium do you have a lot more
+products or a lot more reactants and
+
+ align:start position:0%
+products or a lot more reactants and
+ 
+
+ align:start position:0%
+products or a lot more reactants and
+some of the same questions we've talked
+
+ align:start position:0%
+some of the same questions we've talked
+ 
+
+ align:start position:0%
+some of the same questions we've talked
+about before see how all these units are
+
+ align:start position:0%
+about before see how all these units are
+ 
+
+ align:start position:0%
+about before see how all these units are
+kind of fitting together and how would I
+
+ align:start position:0%
+kind of fitting together and how would I
+ 
+
+ align:start position:0%
+kind of fitting together and how would I
+told you that everything that you
+
+ align:start position:0%
+told you that everything that you
+ 
+
+ align:start position:0%
+told you that everything that you
+learned you have to remember because
+
+ align:start position:0%
+learned you have to remember because
+ 
+
+ align:start position:0%
+learned you have to remember because
+it's going to come back
+
+ align:start position:0%
+it's going to come back
+ 
+
+ align:start position:0%
+it's going to come back
+it's back again so we're back to
+
+ align:start position:0%
+it's back again so we're back to
+ 
+
+ align:start position:0%
+it's back again so we're back to
+thinking about equilibrium constants
+
+ align:start position:0%
+thinking about equilibrium constants
+ 
+
+ align:start position:0%
+thinking about equilibrium constants
+this part this half semester of the
+
+ align:start position:0%
+this part this half semester of the
+ 
+
+ align:start position:0%
+this part this half semester of the
+course is very very connected can't get
+
+ align:start position:0%
+course is very very connected can't get
+ 
+
+ align:start position:0%
+course is very very connected can't get
+away from any of the
+
+ align:start position:0%
+away from any of the
+ 
+
+ align:start position:0%
+away from any of the
+material which is kind of good because
+
+ align:start position:0%
+material which is kind of good because
+ 
+
+ align:start position:0%
+material which is kind of good because
+on the exam it is kind of all related so
+
+ align:start position:0%
+on the exam it is kind of all related so
+ 
+
+ align:start position:0%
+on the exam it is kind of all related so
+um doing the next unit is reviewing the
+
+ align:start position:0%
+um doing the next unit is reviewing the
+ 
+
+ align:start position:0%
+um doing the next unit is reviewing the
+unit that you already did all right so
+
+ align:start position:0%
+unit that you already did all right so
+ 
+
+ align:start position:0%
+unit that you already did all right so
+let's look at an example of an oxidation
+
+ align:start position:0%
+let's look at an example of an oxidation
+ 
+
+ align:start position:0%
+let's look at an example of an oxidation
+reduction reaction and talk about what
+
+ align:start position:0%
+reduction reaction and talk about what
+ 
+
+ align:start position:0%
+reduction reaction and talk about what
+the equilibrium constant is again at
+
+ align:start position:0%
+the equilibrium constant is again at
+ 
+
+ align:start position:0%
+the equilibrium constant is again at
+room temperature
+
+ align:start position:0%
+room temperature
+ 
+
+ align:start position:0%
+room temperature
+temperature so this is going to involve
+
+ align:start position:0%
+temperature so this is going to involve
+ 
+
+ align:start position:0%
+temperature so this is going to involve
+two half
+
+ align:start position:0%
+two half
+ 
+
+ align:start position:0%
+two half
+reactions we have a reaction with zinc
+
+ align:start position:0%
+reactions we have a reaction with zinc
+ 
+
+ align:start position:0%
+reactions we have a reaction with zinc
+in the forward Direction I mean uh with
+
+ align:start position:0%
+in the forward Direction I mean uh with
+ 
+
+ align:start position:0%
+in the forward Direction I mean uh with
+lead lead plus two going to lead solid
+
+ align:start position:0%
+lead lead plus two going to lead solid
+ 
+
+ align:start position:0%
+lead lead plus two going to lead solid
+so lead plus two electrons going to lead
+
+ align:start position:0%
+so lead plus two electrons going to lead
+ 
+
+ align:start position:0%
+so lead plus two electrons going to lead
+solid we also have zinc solid going to
+
+ align:start position:0%
+solid we also have zinc solid going to
+ 
+
+ align:start position:0%
+solid we also have zinc solid going to
+zinc plus two and then two electrons so
+
+ align:start position:0%
+zinc plus two and then two electrons so
+ 
+
+ align:start position:0%
+zinc plus two and then two electrons so
+those are the two half reactions
+
+ align:start position:0%
+those are the two half reactions
+ 
+
+ align:start position:0%
+those are the two half reactions
+involved in this uh cell reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if we're interested in K interested
+
+ align:start position:0%
+now if we're interested in K interested
+ 
+
+ align:start position:0%
+now if we're interested in K interested
+in the magnitude of K we want to think
+
+ align:start position:0%
+in the magnitude of K we want to think
+ 
+
+ align:start position:0%
+in the magnitude of K we want to think
+about if K is big is K greater than one
+
+ align:start position:0%
+about if K is big is K greater than one
+ 
+
+ align:start position:0%
+about if K is big is K greater than one
+for this reaction we can do the math and
+
+ align:start position:0%
+for this reaction we can do the math and
+ 
+
+ align:start position:0%
+for this reaction we can do the math and
+calculate knowing something about the
+
+ align:start position:0%
+calculate knowing something about the
+ 
+
+ align:start position:0%
+calculate knowing something about the
+cell potentials or we can just think
+
+ align:start position:0%
+cell potentials or we can just think
+ 
+
+ align:start position:0%
+cell potentials or we can just think
+about whether this reaction would be
+
+ align:start position:0%
+about whether this reaction would be
+ 
+
+ align:start position:0%
+about whether this reaction would be
+favorable before doing the
+
+ align:start position:0%
+favorable before doing the
+ 
+
+ align:start position:0%
+favorable before doing the
+math so if you think about what's
+
+ align:start position:0%
+math so if you think about what's
+ 
+
+ align:start position:0%
+math so if you think about what's
+happening in the Ford reaction what's
+
+ align:start position:0%
+happening in the Ford reaction what's
+ 
+
+ align:start position:0%
+happening in the Ford reaction what's
+happening well what's happening is that
+
+ align:start position:0%
+happening well what's happening is that
+ 
+
+ align:start position:0%
+happening well what's happening is that
+zinc is reducing lead plus two so lead
+
+ align:start position:0%
+zinc is reducing lead plus two so lead
+ 
+
+ align:start position:0%
+zinc is reducing lead plus two so lead
+plus two is being reduced to lead solid
+
+ align:start position:0%
+plus two is being reduced to lead solid
+ 
+
+ align:start position:0%
+plus two is being reduced to lead solid
+and zinc is being oxidized it's acting
+
+ align:start position:0%
+and zinc is being oxidized it's acting
+ 
+
+ align:start position:0%
+and zinc is being oxidized it's acting
+as a reducing
+
+ align:start position:0%
+as a reducing
+ 
+
+ align:start position:0%
+as a reducing
+agent and in the backward reaction
+
+ align:start position:0%
+agent and in the backward reaction
+ 
+
+ align:start position:0%
+agent and in the backward reaction
+what's happening well in the backward
+
+ align:start position:0%
+what's happening well in the backward
+ 
+
+ align:start position:0%
+what's happening well in the backward
+reaction we have lead solid reducing
+
+ align:start position:0%
+reaction we have lead solid reducing
+ 
+
+ align:start position:0%
+reaction we have lead solid reducing
+zinc plus two to zinc
+
+ align:start position:0%
+zinc plus two to zinc
+ 
+
+ align:start position:0%
+zinc plus two to zinc
+solid so if we think about are there
+
+ align:start position:0%
+solid so if we think about are there
+ 
+
+ align:start position:0%
+solid so if we think about are there
+going to be more products or reactants
+
+ align:start position:0%
+going to be more products or reactants
+ 
+
+ align:start position:0%
+going to be more products or reactants
+really thinking about which of these two
+
+ align:start position:0%
+really thinking about which of these two
+ 
+
+ align:start position:0%
+really thinking about which of these two
+things is a better reducing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agent so if zinc is a better reducing
+
+ align:start position:0%
+agent so if zinc is a better reducing
+ 
+
+ align:start position:0%
+agent so if zinc is a better reducing
+agent than lead it will favor the
+
+ align:start position:0%
+agent than lead it will favor the
+ 
+
+ align:start position:0%
+agent than lead it will favor the
+forward Direction and we'll have a k
+
+ align:start position:0%
+forward Direction and we'll have a k
+ 
+
+ align:start position:0%
+forward Direction and we'll have a k
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+one so is it a better reducing agent so
+
+ align:start position:0%
+one so is it a better reducing agent so
+ 
+
+ align:start position:0%
+one so is it a better reducing agent so
+we talked last time about how to figure
+
+ align:start position:0%
+we talked last time about how to figure
+ 
+
+ align:start position:0%
+we talked last time about how to figure
+this out and we talked last time about
+
+ align:start position:0%
+this out and we talked last time about
+ 
+
+ align:start position:0%
+this out and we talked last time about
+the fact that things with positive
+
+ align:start position:0%
+the fact that things with positive
+ 
+
+ align:start position:0%
+the fact that things with positive
+numbers up here the oxidized uh species
+
+ align:start position:0%
+numbers up here the oxidized uh species
+ 
+
+ align:start position:0%
+numbers up here the oxidized uh species
+of this is a strongly oxidizing and at
+
+ align:start position:0%
+of this is a strongly oxidizing and at
+ 
+
+ align:start position:0%
+of this is a strongly oxidizing and at
+the bottom with these negative numbers
+
+ align:start position:0%
+the bottom with these negative numbers
+ 
+
+ align:start position:0%
+the bottom with these negative numbers
+the reduced form is strongly reducing so
+
+ align:start position:0%
+the reduced form is strongly reducing so
+ 
+
+ align:start position:0%
+the reduced form is strongly reducing so
+we can look at where things are their
+
+ align:start position:0%
+we can look at where things are their
+ 
+
+ align:start position:0%
+we can look at where things are their
+numbers their standard reduction
+
+ align:start position:0%
+numbers their standard reduction
+ 
+
+ align:start position:0%
+numbers their standard reduction
+potentials and figure out which one's a
+
+ align:start position:0%
+potentials and figure out which one's a
+ 
+
+ align:start position:0%
+potentials and figure out which one's a
+better reducing
+
+ align:start position:0%
+better reducing
+ 
+
+ align:start position:0%
+better reducing
+agent so if we look those up we know the
+
+ align:start position:0%
+agent so if we look those up we know the
+ 
+
+ align:start position:0%
+agent so if we look those up we know the
+zinc couple we just talked about that
+
+ align:start position:0%
+zinc couple we just talked about that
+ 
+
+ align:start position:0%
+zinc couple we just talked about that
+one actually minus
+
+ align:start position:0%
+one actually minus
+ 
+
+ align:start position:0%
+one actually minus
+7628 and we can look up the standard
+
+ align:start position:0%
+7628 and we can look up the standard
+ 
+
+ align:start position:0%
+7628 and we can look up the standard
+reduction potential of lead and it's
+
+ align:start position:0%
+reduction potential of lead and it's
+ 
+
+ align:start position:0%
+reduction potential of lead and it's
+also negative but it's a smaller
+
+ align:start position:0%
+also negative but it's a smaller
+ 
+
+ align:start position:0%
+also negative but it's a smaller
+negative number minus1
+
+ align:start position:0%
+negative number minus1
+ 
+
+ align:start position:0%
+negative number minus1
+1263 so this is a big negative number so
+
+ align:start position:0%
+1263 so this is a big negative number so
+ 
+
+ align:start position:0%
+1263 so this is a big negative number so
+is it going to be a good reducing
+
+ align:start position:0%
+is it going to be a good reducing
+ 
+
+ align:start position:0%
+is it going to be a good reducing
+agent what do we know about how
+
+ align:start position:0%
+agent what do we know about how
+ 
+
+ align:start position:0%
+agent what do we know about how
+difficult it is to add electrons to
+
+ align:start position:0%
+difficult it is to add electrons to
+ 
+
+ align:start position:0%
+difficult it is to add electrons to
+this is it hard to add electrons to this
+
+ align:start position:0%
+this is it hard to add electrons to this
+ 
+
+ align:start position:0%
+this is it hard to add electrons to this
+yeah so it's hard hard to reduce that
+
+ align:start position:0%
+yeah so it's hard hard to reduce that
+ 
+
+ align:start position:0%
+yeah so it's hard hard to reduce that
+makes it easier to oxidize so does that
+
+ align:start position:0%
+makes it easier to oxidize so does that
+ 
+
+ align:start position:0%
+makes it easier to oxidize so does that
+make it a good reducing agent yeah it
+
+ align:start position:0%
+make it a good reducing agent yeah it
+ 
+
+ align:start position:0%
+make it a good reducing agent yeah it
+does does because a reducing agent gets
+
+ align:start position:0%
+does does because a reducing agent gets
+ 
+
+ align:start position:0%
+does does because a reducing agent gets
+oxidized itself it reduces other things
+
+ align:start position:0%
+oxidized itself it reduces other things
+ 
+
+ align:start position:0%
+oxidized itself it reduces other things
+so this would be a good reducing agent
+
+ align:start position:0%
+so this would be a good reducing agent
+ 
+
+ align:start position:0%
+so this would be a good reducing agent
+well what about this is it as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good no it's not as good it's probably
+
+ align:start position:0%
+good no it's not as good it's probably
+ 
+
+ align:start position:0%
+good no it's not as good it's probably
+not bad but it's not it's not as good a
+
+ align:start position:0%
+not bad but it's not it's not as good a
+ 
+
+ align:start position:0%
+not bad but it's not it's not as good a
+reducing agent it would be a little bit
+
+ align:start position:0%
+reducing agent it would be a little bit
+ 
+
+ align:start position:0%
+reducing agent it would be a little bit
+easier to reduce than than zinc a little
+
+ align:start position:0%
+easier to reduce than than zinc a little
+ 
+
+ align:start position:0%
+easier to reduce than than zinc a little
+harder to oxidize so it's not as good a
+
+ align:start position:0%
+harder to oxidize so it's not as good a
+ 
+
+ align:start position:0%
+harder to oxidize so it's not as good a
+reducing agent because it's a more
+
+ align:start position:0%
+reducing agent because it's a more
+ 
+
+ align:start position:0%
+reducing agent because it's a more
+positive POS number than this one so
+
+ align:start position:0%
+positive POS number than this one so
+ 
+
+ align:start position:0%
+positive POS number than this one so
+this is the bigger negative number so
+
+ align:start position:0%
+this is the bigger negative number so
+ 
+
+ align:start position:0%
+this is the bigger negative number so
+this is the better reducing agent so if
+
+ align:start position:0%
+this is the better reducing agent so if
+ 
+
+ align:start position:0%
+this is the better reducing agent so if
+that's the better reducing agent then
+
+ align:start position:0%
+that's the better reducing agent then
+ 
+
+ align:start position:0%
+that's the better reducing agent then
+the equilibrium should lie to the right
+
+ align:start position:0%
+the equilibrium should lie to the right
+ 
+
+ align:start position:0%
+the equilibrium should lie to the right
+there should be more products than
+
+ align:start position:0%
+there should be more products than
+ 
+
+ align:start position:0%
+there should be more products than
+reactants at equilibrium because in the
+
+ align:start position:0%
+reactants at equilibrium because in the
+ 
+
+ align:start position:0%
+reactants at equilibrium because in the
+forward Direction zinc is acting as the
+
+ align:start position:0%
+forward Direction zinc is acting as the
+ 
+
+ align:start position:0%
+forward Direction zinc is acting as the
+reducing agent and it's a better
+
+ align:start position:0%
+reducing agent and it's a better
+ 
+
+ align:start position:0%
+reducing agent and it's a better
+reducing agent so it should drive the
+
+ align:start position:0%
+reducing agent so it should drive the
+ 
+
+ align:start position:0%
+reducing agent so it should drive the
+equilibrium such that they're more
+
+ align:start position:0%
+equilibrium such that they're more
+ 
+
+ align:start position:0%
+equilibrium such that they're more
+products than reactants and we can
+
+ align:start position:0%
+products than reactants and we can
+ 
+
+ align:start position:0%
+products than reactants and we can
+actually so K should be greater than
+
+ align:start position:0%
+actually so K should be greater than
+ 
+
+ align:start position:0%
+actually so K should be greater than
+one and we can actually do the math and
+
+ align:start position:0%
+one and we can actually do the math and
+ 
+
+ align:start position:0%
+one and we can actually do the math and
+prove that this is true so this is very
+
+ align:start position:0%
+prove that this is true so this is very
+ 
+
+ align:start position:0%
+prove that this is true so this is very
+much like when we talked in acids and
+
+ align:start position:0%
+much like when we talked in acids and
+ 
+
+ align:start position:0%
+much like when we talked in acids and
+bases about equilibrium and K values and
+
+ align:start position:0%
+bases about equilibrium and K values and
+ 
+
+ align:start position:0%
+bases about equilibrium and K values and
+how if something is a stronger acid one
+
+ align:start position:0%
+how if something is a stronger acid one
+ 
+
+ align:start position:0%
+how if something is a stronger acid one
+way then a stronger acid in the backward
+
+ align:start position:0%
+way then a stronger acid in the backward
+ 
+
+ align:start position:0%
+way then a stronger acid in the backward
+reaction you could predict what K would
+
+ align:start position:0%
+reaction you could predict what K would
+ 
+
+ align:start position:0%
+reaction you could predict what K would
+be or you could do the math it's the
+
+ align:start position:0%
+be or you could do the math it's the
+ 
+
+ align:start position:0%
+be or you could do the math it's the
+same principle
+
+ align:start position:0%
+same principle
+ 
+
+ align:start position:0%
+same principle
+here so if we go through the math we can
+
+ align:start position:0%
+here so if we go through the math we can
+ 
+
+ align:start position:0%
+here so if we go through the math we can
+plug in the standard uh reduction
+
+ align:start position:0%
+plug in the standard uh reduction
+ 
+
+ align:start position:0%
+plug in the standard uh reduction
+potential for the lead couple and the
+
+ align:start position:0%
+potential for the lead couple and the
+ 
+
+ align:start position:0%
+potential for the lead couple and the
+standard reduction potential for the
+
+ align:start position:0%
+standard reduction potential for the
+ 
+
+ align:start position:0%
+standard reduction potential for the
+zinc couple and get an answer for the
+
+ align:start position:0%
+zinc couple and get an answer for the
+ 
+
+ align:start position:0%
+zinc couple and get an answer for the
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential what is n for this this is
+
+ align:start position:0%
+potential what is n for this this is
+ 
+
+ align:start position:0%
+potential what is n for this this is
+also a fairly simple one two so we know
+
+ align:start position:0%
+also a fairly simple one two so we know
+ 
+
+ align:start position:0%
+also a fairly simple one two so we know
+n is two and then we can plug into our
+
+ align:start position:0%
+n is two and then we can plug into our
+ 
+
+ align:start position:0%
+n is two and then we can plug into our
+equations that's all we really needed to
+
+ align:start position:0%
+equations that's all we really needed to
+ 
+
+ align:start position:0%
+equations that's all we really needed to
+know to do this one so we needed to know
+
+ align:start position:0%
+know to do this one so we needed to know
+ 
+
+ align:start position:0%
+know to do this one so we needed to know
+the standard uh potential for the
+
+ align:start position:0%
+the standard uh potential for the
+ 
+
+ align:start position:0%
+the standard uh potential for the
+reaction which we calculated Faraday
+
+ align:start position:0%
+reaction which we calculated Faraday
+ 
+
+ align:start position:0%
+reaction which we calculated Faraday
+constant we need to know n and RT and so
+
+ align:start position:0%
+constant we need to know n and RT and so
+ 
+
+ align:start position:0%
+constant we need to know n and RT and so
+we can put those in and I'll also
+
+ align:start position:0%
+we can put those in and I'll also
+ 
+
+ align:start position:0%
+we can put those in and I'll also
+provide uh this with the math worked out
+
+ align:start position:0%
+provide uh this with the math worked out
+ 
+
+ align:start position:0%
+provide uh this with the math worked out
+for Faraday constant and R and
+
+ align:start position:0%
+for Faraday constant and R and
+ 
+
+ align:start position:0%
+for Faraday constant and R and
+T and so we can plug that in and put in
+
+ align:start position:0%
+T and so we can plug that in and put in
+ 
+
+ align:start position:0%
+T and so we can plug that in and put in
+our two and put in the uh number of
+
+ align:start position:0%
+our two and put in the uh number of
+ 
+
+ align:start position:0%
+our two and put in the uh number of
+volts the standard cell potential that
+
+ align:start position:0%
+volts the standard cell potential that
+ 
+
+ align:start position:0%
+volts the standard cell potential that
+we calculated just before and go back
+
+ align:start position:0%
+we calculated just before and go back
+ 
+
+ align:start position:0%
+we calculated just before and go back
+and calculate for K and so K is 21. five
+
+ align:start position:0%
+and calculate for K and so K is 21. five
+ 
+
+ align:start position:0%
+and calculate for K and so K is 21. five
+that's definitely bigger than one that
+
+ align:start position:0%
+that's definitely bigger than one that
+ 
+
+ align:start position:0%
+that's definitely bigger than one that
+is a very big number uh or k Sorry log
+
+ align:start position:0%
+is a very big number uh or k Sorry log
+ 
+
+ align:start position:0%
+is a very big number uh or k Sorry log
+of K and K turns out to be a very very
+
+ align:start position:0%
+of K and K turns out to be a very very
+ 
+
+ align:start position:0%
+of K and K turns out to be a very very
+big number and uh so the forward
+
+ align:start position:0%
+big number and uh so the forward
+ 
+
+ align:start position:0%
+big number and uh so the forward
+reaction is definitely favored which is
+
+ align:start position:0%
+reaction is definitely favored which is
+ 
+
+ align:start position:0%
+reaction is definitely favored which is
+uh which is what we assumed thinking
+
+ align:start position:0%
+uh which is what we assumed thinking
+ 
+
+ align:start position:0%
+uh which is what we assumed thinking
+about which was a better reducing agent
+
+ align:start position:0%
+about which was a better reducing agent
+ 
+
+ align:start position:0%
+about which was a better reducing agent
+it said that the Ford reaction should be
+
+ align:start position:0%
+it said that the Ford reaction should be
+ 
+
+ align:start position:0%
+it said that the Ford reaction should be
+favored that K should be greater than
+
+ align:start position:0%
+favored that K should be greater than
+ 
+
+ align:start position:0%
+favored that K should be greater than
+one and when you do the math you find
+
+ align:start position:0%
+one and when you do the math you find
+ 
+
+ align:start position:0%
+one and when you do the math you find
+that K is in fact greater than one uh it
+
+ align:start position:0%
+that K is in fact greater than one uh it
+ 
+
+ align:start position:0%
+that K is in fact greater than one uh it
+is favored in that direction more
+
+ align:start position:0%
+is favored in that direction more
+ 
+
+ align:start position:0%
+is favored in that direction more
+products than reactants at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium okay so in the last couple
+
+ align:start position:0%
+equilibrium okay so in the last couple
+ 
+
+ align:start position:0%
+equilibrium okay so in the last couple
+minutes then I want to go back to
+
+ align:start position:0%
+minutes then I want to go back to
+ 
+
+ align:start position:0%
+minutes then I want to go back to
+biological systems and show you that the
+
+ align:start position:0%
+biological systems and show you that the
+ 
+
+ align:start position:0%
+biological systems and show you that the
+same equations apply all the same
+
+ align:start position:0%
+same equations apply all the same
+ 
+
+ align:start position:0%
+same equations apply all the same
+principles apply that you just learned
+
+ align:start position:0%
+principles apply that you just learned
+ 
+
+ align:start position:0%
+principles apply that you just learned
+to a biological system so answering the
+
+ align:start position:0%
+to a biological system so answering the
+ 
+
+ align:start position:0%
+to a biological system so answering the
+question of how B12 is reduced in the
+
+ align:start position:0%
+question of how B12 is reduced in the
+ 
+
+ align:start position:0%
+question of how B12 is reduced in the
+body so B12 is reduced in the body by a
+
+ align:start position:0%
+body so B12 is reduced in the body by a
+ 
+
+ align:start position:0%
+body so B12 is reduced in the body by a
+protein uh called
+
+ align:start position:0%
+protein uh called
+ 
+
+ align:start position:0%
+protein uh called
+flavodoxin um and this contains another
+
+ align:start position:0%
+flavodoxin um and this contains another
+ 
+
+ align:start position:0%
+flavodoxin um and this contains another
+B vitamin A flaven B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vitamin if we look at the standard cell
+
+ align:start position:0%
+vitamin if we look at the standard cell
+ 
+
+ align:start position:0%
+vitamin if we look at the standard cell
+potentials the reduction potentials uh
+
+ align:start position:0%
+potentials the reduction potentials uh
+ 
+
+ align:start position:0%
+potentials the reduction potentials uh
+for these reactions the reduction
+
+ align:start position:0%
+for these reactions the reduction
+ 
+
+ align:start position:0%
+for these reactions the reduction
+potential e not for vitamin B12 is us.
+
+ align:start position:0%
+potential e not for vitamin B12 is us.
+ 
+
+ align:start position:0%
+potential e not for vitamin B12 is us.
+526 volts that's a very low number for a
+
+ align:start position:0%
+526 volts that's a very low number for a
+ 
+
+ align:start position:0%
+526 volts that's a very low number for a
+biological system that's one of the
+
+ align:start position:0%
+biological system that's one of the
+ 
+
+ align:start position:0%
+biological system that's one of the
+lowest standard reduction potentials
+
+ align:start position:0%
+lowest standard reduction potentials
+ 
+
+ align:start position:0%
+lowest standard reduction potentials
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+flavodoxin is is minus. 23
+
+ align:start position:0%
+flavodoxin is is minus. 23
+ 
+
+ align:start position:0%
+flavodoxin is is minus. 23
+volts so let's think about this reaction
+
+ align:start position:0%
+volts so let's think about this reaction
+ 
+
+ align:start position:0%
+volts so let's think about this reaction
+and whether it's favorable or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not so B12 then is a better reducing
+
+ align:start position:0%
+not so B12 then is a better reducing
+ 
+
+ align:start position:0%
+not so B12 then is a better reducing
+agent than flavodoxin it has a more
+
+ align:start position:0%
+agent than flavodoxin it has a more
+ 
+
+ align:start position:0%
+agent than flavodoxin it has a more
+negative number as we just saw in the
+
+ align:start position:0%
+negative number as we just saw in the
+ 
+
+ align:start position:0%
+negative number as we just saw in the
+last example that makes it a better
+
+ align:start position:0%
+last example that makes it a better
+ 
+
+ align:start position:0%
+last example that makes it a better
+reducing agent it's hard to reduce B12
+
+ align:start position:0%
+reducing agent it's hard to reduce B12
+ 
+
+ align:start position:0%
+reducing agent it's hard to reduce B12
+easier to
+
+ align:start position:0%
+easier to
+ 
+
+ align:start position:0%
+easier to
+oxidize flavodoxin has a more positive
+
+ align:start position:0%
+oxidize flavodoxin has a more positive
+ 
+
+ align:start position:0%
+oxidize flavodoxin has a more positive
+number just like we saw in the last one
+
+ align:start position:0%
+number just like we saw in the last one
+ 
+
+ align:start position:0%
+number just like we saw in the last one
+it's not as good a reducing agent so if
+
+ align:start position:0%
+it's not as good a reducing agent so if
+ 
+
+ align:start position:0%
+it's not as good a reducing agent so if
+this reaction occurred
+
+ align:start position:0%
+this reaction occurred
+ 
+
+ align:start position:0%
+this reaction occurred
+spontaneously B12 should be reducing
+
+ align:start position:0%
+spontaneously B12 should be reducing
+ 
+
+ align:start position:0%
+spontaneously B12 should be reducing
+flavodoxin not the other way around so
+
+ align:start position:0%
+flavodoxin not the other way around so
+ 
+
+ align:start position:0%
+flavodoxin not the other way around so
+we just just worked an example where we
+
+ align:start position:0%
+we just just worked an example where we
+ 
+
+ align:start position:0%
+we just just worked an example where we
+saw there was one thing that was a
+
+ align:start position:0%
+saw there was one thing that was a
+ 
+
+ align:start position:0%
+saw there was one thing that was a
+really good reducing agent another
+
+ align:start position:0%
+really good reducing agent another
+ 
+
+ align:start position:0%
+really good reducing agent another
+wasn't as good and we had an enormous K
+
+ align:start position:0%
+wasn't as good and we had an enormous K
+ 
+
+ align:start position:0%
+wasn't as good and we had an enormous K
+so it was very much favored in the other
+
+ align:start position:0%
+so it was very much favored in the other
+ 
+
+ align:start position:0%
+so it was very much favored in the other
+direction so this should not be
+
+ align:start position:0%
+direction so this should not be
+ 
+
+ align:start position:0%
+direction so this should not be
+occurring it doesn't seem possible that
+
+ align:start position:0%
+occurring it doesn't seem possible that
+ 
+
+ align:start position:0%
+occurring it doesn't seem possible that
+this is occurring yet it
+
+ align:start position:0%
+this is occurring yet it
+ 
+
+ align:start position:0%
+this is occurring yet it
+is so is the reduction
+
+ align:start position:0%
+is so is the reduction
+ 
+
+ align:start position:0%
+is so is the reduction
+spontaneous no it wouldn't be let's
+
+ align:start position:0%
+spontaneous no it wouldn't be let's
+ 
+
+ align:start position:0%
+spontaneous no it wouldn't be let's
+actually calculate the numbers and and
+
+ align:start position:0%
+actually calculate the numbers and and
+ 
+
+ align:start position:0%
+actually calculate the numbers and and
+see see how bad it is so again you can
+
+ align:start position:0%
+see see how bad it is so again you can
+ 
+
+ align:start position:0%
+see see how bad it is so again you can
+use this exact same equation instead of
+
+ align:start position:0%
+use this exact same equation instead of
+ 
+
+ align:start position:0%
+use this exact same equation instead of
+calling things cathodes and anodes you
+
+ align:start position:0%
+calling things cathodes and anodes you
+ 
+
+ align:start position:0%
+calling things cathodes and anodes you
+can just consider it in terms of the
+
+ align:start position:0%
+can just consider it in terms of the
+ 
+
+ align:start position:0%
+can just consider it in terms of the
+reduction and the oxidation and we can
+
+ align:start position:0%
+reduction and the oxidation and we can
+ 
+
+ align:start position:0%
+reduction and the oxidation and we can
+plug in in the values so what's being
+
+ align:start position:0%
+plug in in the values so what's being
+ 
+
+ align:start position:0%
+plug in in the values so what's being
+reduced is B12 what's being oxidized is
+
+ align:start position:0%
+reduced is B12 what's being oxidized is
+ 
+
+ align:start position:0%
+reduced is B12 what's being oxidized is
+flavodoxin in the
+
+ align:start position:0%
+flavodoxin in the
+ 
+
+ align:start position:0%
+flavodoxin in the
+body we can put in the numbers minus.
+
+ align:start position:0%
+body we can put in the numbers minus.
+ 
+
+ align:start position:0%
+body we can put in the numbers minus.
+526 volts and then it's minus a negative
+
+ align:start position:0%
+526 volts and then it's minus a negative
+ 
+
+ align:start position:0%
+526 volts and then it's minus a negative
+number of minus .23 volts and we get out
+
+ align:start position:0%
+number of minus .23 volts and we get out
+ 
+
+ align:start position:0%
+number of minus .23 volts and we get out
+that the cell potential
+
+ align:start position:0%
+that the cell potential
+ 
+
+ align:start position:0%
+that the cell potential
+is -. 296
+
+ align:start position:0%
+is -. 296
+ 
+
+ align:start position:0%
+is -. 296
+Vols so that's not going to be
+
+ align:start position:0%
+Vols so that's not going to be
+ 
+
+ align:start position:0%
+Vols so that's not going to be
+spontaneous it's a negative number for
+
+ align:start position:0%
+spontaneous it's a negative number for
+ 
+
+ align:start position:0%
+spontaneous it's a negative number for
+Delta e of the cell which is going to
+
+ align:start position:0%
+Delta e of the cell which is going to
+ 
+
+ align:start position:0%
+Delta e of the cell which is going to
+mean what about Delta
+
+ align:start position:0%
+mean what about Delta
+ 
+
+ align:start position:0%
+mean what about Delta
+G it's going to be
+
+ align:start position:0%
+G it's going to be
+ 
+
+ align:start position:0%
+G it's going to be
+positive so no it's definitely not
+
+ align:start position:0%
+positive so no it's definitely not
+ 
+
+ align:start position:0%
+positive so no it's definitely not
+spontaneous and then we can continue to
+
+ align:start position:0%
+spontaneous and then we can continue to
+ 
+
+ align:start position:0%
+spontaneous and then we can continue to
+go on and plug in these numbers and
+
+ align:start position:0%
+go on and plug in these numbers and
+ 
+
+ align:start position:0%
+go on and plug in these numbers and
+calculate what Delta G knot would be so
+
+ align:start position:0%
+calculate what Delta G knot would be so
+ 
+
+ align:start position:0%
+calculate what Delta G knot would be so
+by this equation that we've seen many
+
+ align:start position:0%
+by this equation that we've seen many
+ 
+
+ align:start position:0%
+by this equation that we've seen many
+many times today there's it's a one
+
+ align:start position:0%
+many times today there's it's a one
+ 
+
+ align:start position:0%
+many times today there's it's a one
+electron reduction so one electron is
+
+ align:start position:0%
+electron reduction so one electron is
+ 
+
+ align:start position:0%
+electron reduction so one electron is
+involved we plug in Faraday constant and
+
+ align:start position:0%
+involved we plug in Faraday constant and
+ 
+
+ align:start position:0%
+involved we plug in Faraday constant and
+we plug in the cell potential and we get
+
+ align:start position:0%
+we plug in the cell potential and we get
+ 
+
+ align:start position:0%
+we plug in the cell potential and we get
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+28.6 K per
+
+ align:start position:0%
+28.6 K per
+ 
+
+ align:start position:0%
+28.6 K per
+mole so that's a very positive number
+
+ align:start position:0%
+mole so that's a very positive number
+ 
+
+ align:start position:0%
+mole so that's a very positive number
+it's a pretty big number for Delta G so
+
+ align:start position:0%
+it's a pretty big number for Delta G so
+ 
+
+ align:start position:0%
+it's a pretty big number for Delta G so
+how does this reaction go so why don't
+
+ align:start position:0%
+how does this reaction go so why don't
+ 
+
+ align:start position:0%
+how does this reaction go so why don't
+we all have heart disease megaloblastic
+
+ align:start position:0%
+we all have heart disease megaloblastic
+ 
+
+ align:start position:0%
+we all have heart disease megaloblastic
+anemia uh problems finding our way home
+
+ align:start position:0%
+anemia uh problems finding our way home
+ 
+
+ align:start position:0%
+anemia uh problems finding our way home
+um what what happens well it the answer
+
+ align:start position:0%
+um what what happens well it the answer
+ 
+
+ align:start position:0%
+um what what happens well it the answer
+is that the body has to apply energy to
+
+ align:start position:0%
+is that the body has to apply energy to
+ 
+
+ align:start position:0%
+is that the body has to apply energy to
+get the reaction to go so in this case
+
+ align:start position:0%
+get the reaction to go so in this case
+ 
+
+ align:start position:0%
+get the reaction to go so in this case
+the energy comes in the form of a
+
+ align:start position:0%
+the energy comes in the form of a
+ 
+
+ align:start position:0%
+the energy comes in the form of a
+molecule called acenil
+
+ align:start position:0%
+molecule called acenil
+ 
+
+ align:start position:0%
+molecule called acenil
+methionine and the cleavage of acenil
+
+ align:start position:0%
+methionine and the cleavage of acenil
+ 
+
+ align:start position:0%
+methionine and the cleavage of acenil
+methionine generates is uh the Delta G
+
+ align:start position:0%
+methionine generates is uh the Delta G
+ 
+
+ align:start position:0%
+methionine generates is uh the Delta G
+for that is minus 37 6 K per mole so
+
+ align:start position:0%
+for that is minus 37 6 K per mole so
+ 
+
+ align:start position:0%
+for that is minus 37 6 K per mole so
+it's very favorable and it's more
+
+ align:start position:0%
+it's very favorable and it's more
+ 
+
+ align:start position:0%
+it's very favorable and it's more
+favorable than this reaction is
+
+ align:start position:0%
+favorable than this reaction is
+ 
+
+ align:start position:0%
+favorable than this reaction is
+unfavorable so when you put those things
+
+ align:start position:0%
+unfavorable so when you put those things
+ 
+
+ align:start position:0%
+unfavorable so when you put those things
+together it
+
+ align:start position:0%
+together it
+ 
+
+ align:start position:0%
+together it
+goes so what do you call it when you
+
+ align:start position:0%
+goes so what do you call it when you
+ 
+
+ align:start position:0%
+goes so what do you call it when you
+have a cell in which an unfavorable
+
+ align:start position:0%
+have a cell in which an unfavorable
+ 
+
+ align:start position:0%
+have a cell in which an unfavorable
+reaction is driven by applying energy
+
+ align:start position:0%
+reaction is driven by applying energy
+ 
+
+ align:start position:0%
+reaction is driven by applying energy
+what was that called that we talked
+
+ align:start position:0%
+what was that called that we talked
+ 
+
+ align:start position:0%
+what was that called that we talked
+about last
+
+ align:start position:0%
+about last
+ 
+
+ align:start position:0%
+about last
+time yeah so it's electrolytic cell so
+
+ align:start position:0%
+time yeah so it's electrolytic cell so
+ 
+
+ align:start position:0%
+time yeah so it's electrolytic cell so
+the body just does the same thing that
+
+ align:start position:0%
+the body just does the same thing that
+ 
+
+ align:start position:0%
+the body just does the same thing that
+you would do to drive any
+
+ align:start position:0%
+you would do to drive any
+ 
+
+ align:start position:0%
+you would do to drive any
+non-spontaneous
+
+ align:start position:0%
+non-spontaneous
+ 
+
+ align:start position:0%
+non-spontaneous
+reaction it comes up with an energy
+
+ align:start position:0%
+reaction it comes up with an energy
+ 
+
+ align:start position:0%
+reaction it comes up with an energy
+source couples the reaction and then the
+
+ align:start position:0%
+source couples the reaction and then the
+ 
+
+ align:start position:0%
+source couples the reaction and then the
+reaction goes again same principles that
+
+ align:start position:0%
+reaction goes again same principles that
+ 
+
+ align:start position:0%
+reaction goes again same principles that
+apply
\ No newline at end of file
diff --git a/I2uSCTUHsUI.txt b/I2uSCTUHsUI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..22598cf3991623b51d0a4155bad63a04a3d86b53
--- /dev/null
+++ b/I2uSCTUHsUI.txt
@@ -0,0 +1,15091 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is your brief overview of women
+
+ align:start position:0%
+this is your brief overview of women
+ 
+
+ align:start position:0%
+this is your brief overview of women
+talk about where you start with the
+
+ align:start position:0%
+talk about where you start with the
+ 
+
+ align:start position:0%
+talk about where you start with the
+quadrotor motivating example we're going
+
+ align:start position:0%
+quadrotor motivating example we're going
+ 
+
+ align:start position:0%
+quadrotor motivating example we're going
+to move into planning with Markov
+
+ align:start position:0%
+to move into planning with Markov
+ 
+
+ align:start position:0%
+to move into planning with Markov
+decision processes give a little bit
+
+ align:start position:0%
+decision processes give a little bit
+ 
+
+ align:start position:0%
+decision processes give a little bit
+about value iteration before discussing
+
+ align:start position:0%
+about value iteration before discussing
+ 
+
+ align:start position:0%
+about value iteration before discussing
+heuristic guided solvers they were going
+
+ align:start position:0%
+heuristic guided solvers they were going
+ 
+
+ align:start position:0%
+heuristic guided solvers they were going
+to go into the more stochastic case
+
+ align:start position:0%
+to go into the more stochastic case
+ 
+
+ align:start position:0%
+to go into the more stochastic case
+partially observable Markov decision
+
+ align:start position:0%
+partially observable Markov decision
+ 
+
+ align:start position:0%
+partially observable Markov decision
+processes in an operating space so we
+
+ align:start position:0%
+processes in an operating space so we
+ 
+
+ align:start position:0%
+processes in an operating space so we
+very often now stand under promotion
+
+ align:start position:0%
+very often now stand under promotion
+ 
+
+ align:start position:0%
+very often now stand under promotion
+planning as a problem given for example
+
+ align:start position:0%
+planning as a problem given for example
+ 
+
+ align:start position:0%
+planning as a problem given for example
+with the Amazon Fulfillment Center we
+
+ align:start position:0%
+with the Amazon Fulfillment Center we
+ 
+
+ align:start position:0%
+with the Amazon Fulfillment Center we
+start with the goal configuration to
+
+ align:start position:0%
+start with the goal configuration to
+ 
+
+ align:start position:0%
+start with the goal configuration to
+start configuration set of actions we
+
+ align:start position:0%
+start configuration set of actions we
+ 
+
+ align:start position:0%
+start configuration set of actions we
+can take and some type of reward
+
+ align:start position:0%
+can take and some type of reward
+ 
+
+ align:start position:0%
+can take and some type of reward
+function or function so for instance it
+
+ align:start position:0%
+function or function so for instance it
+ 
+
+ align:start position:0%
+function or function so for instance it
+would have a big corner starting at the
+
+ align:start position:0%
+would have a big corner starting at the
+ 
+
+ align:start position:0%
+would have a big corner starting at the
+Amazon Fulfillment Center and we want to
+
+ align:start position:0%
+Amazon Fulfillment Center and we want to
+ 
+
+ align:start position:0%
+Amazon Fulfillment Center and we want to
+get it to 77 mascot and let's say we
+
+ align:start position:0%
+get it to 77 mascot and let's say we
+ 
+
+ align:start position:0%
+get it to 77 mascot and let's say we
+want to take the shortstop's to get
+
+ align:start position:0%
+want to take the shortstop's to get
+ 
+
+ align:start position:0%
+want to take the shortstop's to get
+there we would follow the REC dash line
+
+ align:start position:0%
+there we would follow the REC dash line
+ 
+
+ align:start position:0%
+there we would follow the REC dash line
+but as we can see it was very close to
+
+ align:start position:0%
+but as we can see it was very close to
+ 
+
+ align:start position:0%
+but as we can see it was very close to
+these obstacles so including at very
+
+ align:start position:0%
+these obstacles so including at very
+ 
+
+ align:start position:0%
+these obstacles so including at very
+high risk for missions of failure
+
+ align:start position:0%
+high risk for missions of failure
+ 
+
+ align:start position:0%
+high risk for missions of failure
+crashes if there's anything and he had
+
+ align:start position:0%
+crashes if there's anything and he had
+ 
+
+ align:start position:0%
+crashes if there's anything and he had
+started be in this path we're gonna had
+
+ align:start position:0%
+started be in this path we're gonna had
+ 
+
+ align:start position:0%
+started be in this path we're gonna had
+a problem so one of the ways you can
+
+ align:start position:0%
+a problem so one of the ways you can
+ 
+
+ align:start position:0%
+a problem so one of the ways you can
+sort of compensate for that is we have
+
+ align:start position:0%
+sort of compensate for that is we have
+ 
+
+ align:start position:0%
+sort of compensate for that is we have
+follow something about the green path
+
+ align:start position:0%
+follow something about the green path
+ 
+
+ align:start position:0%
+follow something about the green path
+which is adjusted to give us a little
+
+ align:start position:0%
+which is adjusted to give us a little
+ 
+
+ align:start position:0%
+which is adjusted to give us a little
+bit more space under my questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as you can see the level of
+
+ align:start position:0%
+so as you can see the level of
+ 
+
+ align:start position:0%
+so as you can see the level of
+uncertainty it sort of allows us to
+
+ align:start position:0%
+uncertainty it sort of allows us to
+ 
+
+ align:start position:0%
+uncertainty it sort of allows us to
+determine how easy or difficult
+
+ align:start position:0%
+determine how easy or difficult
+ 
+
+ align:start position:0%
+determine how easy or difficult
+containing this all on the India side we
+
+ align:start position:0%
+containing this all on the India side we
+ 
+
+ align:start position:0%
+containing this all on the India side we
+have deterministic dynamics and
+
+ align:start position:0%
+have deterministic dynamics and
+ 
+
+ align:start position:0%
+have deterministic dynamics and
+deterministic sensors in this case our
+
+ align:start position:0%
+deterministic sensors in this case our
+ 
+
+ align:start position:0%
+deterministic sensors in this case our
+actions are going to be executed cus
+
+ align:start position:0%
+actions are going to be executed cus
+ 
+
+ align:start position:0%
+actions are going to be executed cus
+commanding and our sense against us
+
+ align:start position:0%
+commanding and our sense against us
+ 
+
+ align:start position:0%
+commanding and our sense against us
+exactly where we are this would be
+
+ align:start position:0%
+exactly where we are this would be
+ 
+
+ align:start position:0%
+exactly where we are this would be
+something like dead reckoning validated
+
+ align:start position:0%
+something like dead reckoning validated
+ 
+
+ align:start position:0%
+something like dead reckoning validated
+through sensing barrier dominant if we
+
+ align:start position:0%
+through sensing barrier dominant if we
+ 
+
+ align:start position:0%
+through sensing barrier dominant if we
+would know a little bit more difficult
+
+ align:start position:0%
+would know a little bit more difficult
+ 
+
+ align:start position:0%
+would know a little bit more difficult
+case we have deterministic dynamics our
+
+ align:start position:0%
+case we have deterministic dynamics our
+ 
+
+ align:start position:0%
+case we have deterministic dynamics our
+commands are being executed but maybe we
+
+ align:start position:0%
+commands are being executed but maybe we
+ 
+
+ align:start position:0%
+commands are being executed but maybe we
+have a noisy camera so we have some
+
+ align:start position:0%
+have a noisy camera so we have some
+ 
+
+ align:start position:0%
+have a noisy camera so we have some
+uncertainty in the sensors in the cases
+
+ align:start position:0%
+uncertainty in the sensors in the cases
+ 
+
+ align:start position:0%
+uncertainty in the sensors in the cases
+where we would see dead reckoning but we
+
+ align:start position:0%
+where we would see dead reckoning but we
+ 
+
+ align:start position:0%
+where we would see dead reckoning but we
+need contain a common filter and sort of
+
+ align:start position:0%
+need contain a common filter and sort of
+ 
+
+ align:start position:0%
+need contain a common filter and sort of
+get rid of that noise level now down at
+
+ align:start position:0%
+get rid of that noise level now down at
+ 
+
+ align:start position:0%
+get rid of that noise level now down at
+the bottom sorry what is that it's
+
+ align:start position:0%
+the bottom sorry what is that it's
+ 
+
+ align:start position:0%
+the bottom sorry what is that it's
+essentially you are saying I will
+
+ align:start position:0%
+essentially you are saying I will
+ 
+
+ align:start position:0%
+essentially you are saying I will
+execute this action it's gonna execute
+
+ align:start position:0%
+execute this action it's gonna execute
+ 
+
+ align:start position:0%
+execute this action it's gonna execute
+it exactly then 20 bottom we have a
+
+ align:start position:0%
+it exactly then 20 bottom we have a
+ 
+
+ align:start position:0%
+it exactly then 20 bottom we have a
+passive dynamics ensure mystic sensors
+
+ align:start position:0%
+passive dynamics ensure mystic sensors
+ 
+
+ align:start position:0%
+passive dynamics ensure mystic sensors
+so in this case maybe there's some
+
+ align:start position:0%
+so in this case maybe there's some
+ 
+
+ align:start position:0%
+so in this case maybe there's some
+uncertainty in our actions but we can
+
+ align:start position:0%
+uncertainty in our actions but we can
+ 
+
+ align:start position:0%
+uncertainty in our actions but we can
+validate through sensing this is where
+
+ align:start position:0%
+validate through sensing this is where
+ 
+
+ align:start position:0%
+validate through sensing this is where
+we're gonna spend the next section on
+
+ align:start position:0%
+we're gonna spend the next section on
+ 
+
+ align:start position:0%
+we're gonna spend the next section on
+Markov decision processes and then
+
+ align:start position:0%
+Markov decision processes and then
+ 
+
+ align:start position:0%
+Markov decision processes and then
+briefly later in the lecture we're going
+
+ align:start position:0%
+briefly later in the lecture we're going
+ 
+
+ align:start position:0%
+briefly later in the lecture we're going
+to talk about this most difficult case
+
+ align:start position:0%
+to talk about this most difficult case
+ 
+
+ align:start position:0%
+to talk about this most difficult case
+which is the stochastic dynamics in
+
+ align:start position:0%
+which is the stochastic dynamics in
+ 
+
+ align:start position:0%
+which is the stochastic dynamics in
+stochastic sensors our execution may be
+
+ align:start position:0%
+stochastic sensors our execution may be
+ 
+
+ align:start position:0%
+stochastic sensors our execution may be
+may not
+
+ align:start position:0%
+may not
+ 
+
+ align:start position:0%
+may not
+our sensors may be a little bit noisy
+
+ align:start position:0%
+our sensors may be a little bit noisy
+ 
+
+ align:start position:0%
+our sensors may be a little bit noisy
+and this is where we see partially
+
+ align:start position:0%
+and this is where we see partially
+ 
+
+ align:start position:0%
+and this is where we see partially
+observable Markov decision processes
+
+ align:start position:0%
+observable Markov decision processes
+ 
+
+ align:start position:0%
+observable Markov decision processes
+we making this a big clarification on
+
+ align:start position:0%
+we making this a big clarification on
+ 
+
+ align:start position:0%
+we making this a big clarification on
+the other desert answer dead reckoning
+
+ align:start position:0%
+the other desert answer dead reckoning
+ 
+
+ align:start position:0%
+the other desert answer dead reckoning
+is where you estimate your position
+
+ align:start position:0%
+is where you estimate your position
+ 
+
+ align:start position:0%
+is where you estimate your position
+using the publicity model but you don't
+
+ align:start position:0%
+using the publicity model but you don't
+ 
+
+ align:start position:0%
+using the publicity model but you don't
+use any observations about investing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we talked a little bit and
+
+ align:start position:0%
+okay so we talked a little bit and
+ 
+
+ align:start position:0%
+okay so we talked a little bit and
+certainly Morgan focus and this is the
+
+ align:start position:0%
+certainly Morgan focus and this is the
+ 
+
+ align:start position:0%
+certainly Morgan focus and this is the
+case where for instance even if you tell
+
+ align:start position:0%
+case where for instance even if you tell
+ 
+
+ align:start position:0%
+case where for instance even if you tell
+about their quadrotor to stay in its
+
+ align:start position:0%
+about their quadrotor to stay in its
+ 
+
+ align:start position:0%
+about their quadrotor to stay in its
+place and a gust of wind comes by it's
+
+ align:start position:0%
+place and a gust of wind comes by it's
+ 
+
+ align:start position:0%
+place and a gust of wind comes by it's
+not going to stay in that same place
+
+ align:start position:0%
+not going to stay in that same place
+ 
+
+ align:start position:0%
+not going to stay in that same place
+right it's gonna have a little bit of
+
+ align:start position:0%
+right it's gonna have a little bit of
+ 
+
+ align:start position:0%
+right it's gonna have a little bit of
+movement and we can see this causes
+
+ align:start position:0%
+movement and we can see this causes
+ 
+
+ align:start position:0%
+movement and we can see this causes
+things of this disparity where you have
+
+ align:start position:0%
+things of this disparity where you have
+ 
+
+ align:start position:0%
+things of this disparity where you have
+a community up during your actual
+
+ align:start position:0%
+a community up during your actual
+ 
+
+ align:start position:0%
+a community up during your actual
+trajectory and they get direct
+
+ align:start position:0%
+trajectory and they get direct
+ 
+
+ align:start position:0%
+trajectory and they get direct
+associated so in order to compensate
+
+ align:start position:0%
+associated so in order to compensate
+ 
+
+ align:start position:0%
+associated so in order to compensate
+that we want to model things without
+
+ align:start position:0%
+that we want to model things without
+ 
+
+ align:start position:0%
+that we want to model things without
+uncertainty or else we have these higher
+
+ align:start position:0%
+uncertainty or else we have these higher
+ 
+
+ align:start position:0%
+uncertainty or else we have these higher
+situations where you command to follow
+
+ align:start position:0%
+situations where you command to follow
+ 
+
+ align:start position:0%
+situations where you command to follow
+us online we don't cooperate the
+
+ align:start position:0%
+us online we don't cooperate the
+ 
+
+ align:start position:0%
+us online we don't cooperate the
+uncertainty and we see a crash so this
+
+ align:start position:0%
+uncertainty and we see a crash so this
+ 
+
+ align:start position:0%
+uncertainty and we see a crash so this
+allows us to introduce planning with
+
+ align:start position:0%
+allows us to introduce planning with
+ 
+
+ align:start position:0%
+allows us to introduce planning with
+Markov decision processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so NDP's have a substates a sudden
+
+ align:start position:0%
+so NDP's have a substates a sudden
+ 
+
+ align:start position:0%
+so NDP's have a substates a sudden
+actions you can take in transition
+
+ align:start position:0%
+actions you can take in transition
+ 
+
+ align:start position:0%
+actions you can take in transition
+models so essentially what's a
+
+ align:start position:0%
+models so essentially what's a
+ 
+
+ align:start position:0%
+models so essentially what's a
+probability of reaching some state if
+
+ align:start position:0%
+probability of reaching some state if
+ 
+
+ align:start position:0%
+probability of reaching some state if
+you take an action immediate reward
+
+ align:start position:0%
+you take an action immediate reward
+ 
+
+ align:start position:0%
+you take an action immediate reward
+function and a discount factor this
+
+ align:start position:0%
+function and a discount factor this
+ 
+
+ align:start position:0%
+function and a discount factor this
+discount factor is important because it
+
+ align:start position:0%
+discount factor is important because it
+ 
+
+ align:start position:0%
+discount factor is important because it
+allows me to prioritize gain in the Year
+
+ align:start position:0%
+allows me to prioritize gain in the Year
+ 
+
+ align:start position:0%
+allows me to prioritize gain in the Year
+award as opposed to an uncertain future
+
+ align:start position:0%
+award as opposed to an uncertain future
+ 
+
+ align:start position:0%
+award as opposed to an uncertain future
+over it so the concept of burden has
+
+ align:start position:0%
+over it so the concept of burden has
+ 
+
+ align:start position:0%
+over it so the concept of burden has
+been to rush now we want to find an
+
+ align:start position:0%
+been to rush now we want to find an
+ 
+
+ align:start position:0%
+been to rush now we want to find an
+optimal policy level essentially back of
+
+ align:start position:0%
+optimal policy level essentially back of
+ 
+
+ align:start position:0%
+optimal policy level essentially back of
+an action or the best option for each
+
+ align:start position:0%
+an action or the best option for each
+ 
+
+ align:start position:0%
+an action or the best option for each
+state and what we hope to get from this
+
+ align:start position:0%
+state and what we hope to get from this
+ 
+
+ align:start position:0%
+state and what we hope to get from this
+is and maximize expected lifetime reward
+
+ align:start position:0%
+is and maximize expected lifetime reward
+ 
+
+ align:start position:0%
+is and maximize expected lifetime reward
+so we want to maximize B queuing and
+
+ align:start position:0%
+so we want to maximize B queuing and
+ 
+
+ align:start position:0%
+so we want to maximize B queuing and
+reward we get go visit activities so
+
+ align:start position:0%
+reward we get go visit activities so
+ 
+
+ align:start position:0%
+reward we get go visit activities so
+let's go through an example and in this
+
+ align:start position:0%
+let's go through an example and in this
+ 
+
+ align:start position:0%
+let's go through an example and in this
+environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actions maybe yeah up-down left-right in
+
+ align:start position:0%
+actions maybe yeah up-down left-right in
+ 
+
+ align:start position:0%
+actions maybe yeah up-down left-right in
+this case we call them north-south
+
+ align:start position:0%
+this case we call them north-south
+ 
+
+ align:start position:0%
+this case we call them north-south
+east-west or null the next thing we for
+
+ align:start position:0%
+east-west or null the next thing we for
+ 
+
+ align:start position:0%
+east-west or null the next thing we for
+this example arbitrarily gave ourselves
+
+ align:start position:0%
+this example arbitrarily gave ourselves
+ 
+
+ align:start position:0%
+this example arbitrarily gave ourselves
+a transition probability so we said that
+
+ align:start position:0%
+a transition probability so we said that
+ 
+
+ align:start position:0%
+a transition probability so we said that
+you owe a 50% chance of following your
+
+ align:start position:0%
+you owe a 50% chance of following your
+ 
+
+ align:start position:0%
+you owe a 50% chance of following your
+community action with a 25% chance of
+
+ align:start position:0%
+community action with a 25% chance of
+ 
+
+ align:start position:0%
+community action with a 25% chance of
+moving to the left or the right next we
+
+ align:start position:0%
+moving to the left or the right next we
+ 
+
+ align:start position:0%
+moving to the left or the right next we
+have the reward function and again we
+
+ align:start position:0%
+have the reward function and again we
+ 
+
+ align:start position:0%
+have the reward function and again we
+are generally decided that we want it to
+
+ align:start position:0%
+are generally decided that we want it to
+ 
+
+ align:start position:0%
+are generally decided that we want it to
+be a reward if you get to the State 6-5
+
+ align:start position:0%
+be a reward if you get to the State 6-5
+ 
+
+ align:start position:0%
+be a reward if you get to the State 6-5
+that you need for mentored one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like me this week we said clockwise
+
+ align:start position:0%
+like me this week we said clockwise
+ 
+
+ align:start position:0%
+like me this week we said clockwise
+counterclockwise from the attention in
+
+ align:start position:0%
+counterclockwise from the attention in
+ 
+
+ align:start position:0%
+counterclockwise from the attention in
+the direction of action huh and finally
+
+ align:start position:0%
+the direction of action huh and finally
+ 
+
+ align:start position:0%
+the direction of action huh and finally
+ourselves a discount factor of 0.9 so
+
+ align:start position:0%
+ourselves a discount factor of 0.9 so
+ 
+
+ align:start position:0%
+ourselves a discount factor of 0.9 so
+let's assume for a second that we have
+
+ align:start position:0%
+let's assume for a second that we have
+ 
+
+ align:start position:0%
+let's assume for a second that we have
+our optimal policy and let's say that
+
+ align:start position:0%
+our optimal policy and let's say that
+ 
+
+ align:start position:0%
+our optimal policy and let's say that
+our optimal policy says from this game
+
+ align:start position:0%
+our optimal policy says from this game
+ 
+
+ align:start position:0%
+our optimal policy says from this game
+you want to see the actual Moore's right
+
+ align:start position:0%
+you want to see the actual Moore's right
+ 
+
+ align:start position:0%
+you want to see the actual Moore's right
+as we discussed me up some chance of
+
+ align:start position:0%
+as we discussed me up some chance of
+ 
+
+ align:start position:0%
+as we discussed me up some chance of
+going north 25% chance of going to the
+
+ align:start position:0%
+going north 25% chance of going to the
+ 
+
+ align:start position:0%
+going north 25% chance of going to the
+left or right so after that time set
+
+ align:start position:0%
+left or right so after that time set
+ 
+
+ align:start position:0%
+left or right so after that time set
+this these are our possible states of
+
+ align:start position:0%
+this these are our possible states of
+ 
+
+ align:start position:0%
+this these are our possible states of
+meat spend up in right so now let's
+
+ align:start position:0%
+meat spend up in right so now let's
+ 
+
+ align:start position:0%
+meat spend up in right so now let's
+assume for a second that we take our
+
+ align:start position:0%
+assume for a second that we take our
+ 
+
+ align:start position:0%
+assume for a second that we take our
+next action when our next action says go
+
+ align:start position:0%
+next action when our next action says go
+ 
+
+ align:start position:0%
+next action when our next action says go
+north again become the same probability
+
+ align:start position:0%
+north again become the same probability
+ 
+
+ align:start position:0%
+north again become the same probability
+distribution and of these other states
+
+ align:start position:0%
+distribution and of these other states
+ 
+
+ align:start position:0%
+distribution and of these other states
+we could end up and not get to tax types
+
+ align:start position:0%
+we could end up and not get to tax types
+ 
+
+ align:start position:0%
+we could end up and not get to tax types
+we can see this starts getting very
+
+ align:start position:0%
+we can see this starts getting very
+ 
+
+ align:start position:0%
+we can see this starts getting very
+complicated right and there's increasing
+
+ align:start position:0%
+complicated right and there's increasing
+ 
+
+ align:start position:0%
+complicated right and there's increasing
+amounts of uncertainty so does anybody
+
+ align:start position:0%
+amounts of uncertainty so does anybody
+ 
+
+ align:start position:0%
+amounts of uncertainty so does anybody
+have any ideas on how we can start a
+
+ align:start position:0%
+have any ideas on how we can start a
+ 
+
+ align:start position:0%
+have any ideas on how we can start a
+collapse the situation keeping in mind
+
+ align:start position:0%
+collapse the situation keeping in mind
+ 
+
+ align:start position:0%
+collapse the situation keeping in mind
+that our sensors at this point are
+
+ align:start position:0%
+that our sensors at this point are
+ 
+
+ align:start position:0%
+that our sensors at this point are
+deterministic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I to a corner as I can fly to a
+
+ align:start position:0%
+yeah I to a corner as I can fly to a
+ 
+
+ align:start position:0%
+yeah I to a corner as I can fly to a
+corner did you die this will be we've
+
+ align:start position:0%
+corner did you die this will be we've
+ 
+
+ align:start position:0%
+corner did you die this will be we've
+seen the look at you one okay so the
+
+ align:start position:0%
+seen the look at you one okay so the
+ 
+
+ align:start position:0%
+seen the look at you one okay so the
+probabilities you're not at you one yeah
+
+ align:start position:0%
+probabilities you're not at you one yeah
+ 
+
+ align:start position:0%
+probabilities you're not at you one yeah
+the issue is if you what five it
+
+ align:start position:0%
+the issue is if you what five it
+ 
+
+ align:start position:0%
+the issue is if you what five it
+shouldn't do those numbers always that
+
+ align:start position:0%
+shouldn't do those numbers always that
+ 
+
+ align:start position:0%
+shouldn't do those numbers always that
+you want I mean your problem you know
+
+ align:start position:0%
+you want I mean your problem you know
+ 
+
+ align:start position:0%
+you want I mean your problem you know
+accessory yeah so this is just it's a
+
+ align:start position:0%
+accessory yeah so this is just it's a
+ 
+
+ align:start position:0%
+accessory yeah so this is just it's a
+point that's just about surgery we would
+
+ align:start position:0%
+point that's just about surgery we would
+ 
+
+ align:start position:0%
+point that's just about surgery we would
+add another section to the screen it
+
+ align:start position:0%
+add another section to the screen it
+ 
+
+ align:start position:0%
+add another section to the screen it
+just move the great over we just cut it
+
+ align:start position:0%
+just move the great over we just cut it
+ 
+
+ align:start position:0%
+just move the great over we just cut it
+off her graphics yet those are all okay
+
+ align:start position:0%
+off her graphics yet those are all okay
+ 
+
+ align:start position:0%
+off her graphics yet those are all okay
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+the easiest way to do it is just to take
+
+ align:start position:0%
+the easiest way to do it is just to take
+ 
+
+ align:start position:0%
+the easiest way to do it is just to take
+an observation so at this point we say
+
+ align:start position:0%
+an observation so at this point we say
+ 
+
+ align:start position:0%
+an observation so at this point we say
+after our first five time we weren't
+
+ align:start position:0%
+after our first five time we weren't
+ 
+
+ align:start position:0%
+after our first five time we weren't
+sure which of these three states for
+
+ align:start position:0%
+sure which of these three states for
+ 
+
+ align:start position:0%
+sure which of these three states for
+your interest we took an observation and
+
+ align:start position:0%
+your interest we took an observation and
+ 
+
+ align:start position:0%
+your interest we took an observation and
+said we're actually here with the
+
+ align:start position:0%
+said we're actually here with the
+ 
+
+ align:start position:0%
+said we're actually here with the
+complete certainty so sweet this little
+
+ align:start position:0%
+complete certainty so sweet this little
+ 
+
+ align:start position:0%
+complete certainty so sweet this little
+bit earlier we're gonna look at it from
+
+ align:start position:0%
+bit earlier we're gonna look at it from
+ 
+
+ align:start position:0%
+bit earlier we're gonna look at it from
+a tree view right he said that we
+
+ align:start position:0%
+a tree view right he said that we
+ 
+
+ align:start position:0%
+a tree view right he said that we
+started in the state we took an action
+
+ align:start position:0%
+started in the state we took an action
+ 
+
+ align:start position:0%
+started in the state we took an action
+and this is our possible States free
+
+ align:start position:0%
+and this is our possible States free
+ 
+
+ align:start position:0%
+and this is our possible States free
+development arena collapses by taking
+
+ align:start position:0%
+development arena collapses by taking
+ 
+
+ align:start position:0%
+development arena collapses by taking
+this observation and now we have a
+
+ align:start position:0%
+this observation and now we have a
+ 
+
+ align:start position:0%
+this observation and now we have a
+company started here and we take our
+
+ align:start position:0%
+company started here and we take our
+ 
+
+ align:start position:0%
+company started here and we take our
+next action and see that we have moved
+
+ align:start position:0%
+next action and see that we have moved
+ 
+
+ align:start position:0%
+next action and see that we have moved
+out here so this is allows us to
+
+ align:start position:0%
+out here so this is allows us to
+ 
+
+ align:start position:0%
+out here so this is allows us to
+basically ignore the history of states
+
+ align:start position:0%
+basically ignore the history of states
+ 
+
+ align:start position:0%
+basically ignore the history of states
+we have the same percentage probability
+
+ align:start position:0%
+we have the same percentage probability
+ 
+
+ align:start position:0%
+we have the same percentage probability
+from each
+
+ align:start position:0%
+from each
+ 
+
+ align:start position:0%
+from each
+this will be really really useful in
+
+ align:start position:0%
+this will be really really useful in
+ 
+
+ align:start position:0%
+this will be really really useful in
+completely collapsing the distribution
+
+ align:start position:0%
+completely collapsing the distribution
+ 
+
+ align:start position:0%
+completely collapsing the distribution
+every single time you take an
+
+ align:start position:0%
+every single time you take an
+ 
+
+ align:start position:0%
+every single time you take an
+observation anyway having questions
+
+ align:start position:0%
+observation anyway having questions
+ 
+
+ align:start position:0%
+observation anyway having questions
+about them
+
+ align:start position:0%
+about them
+ 
+
+ align:start position:0%
+about them
+okay so let's go back now I can figure
+
+ align:start position:0%
+okay so let's go back now I can figure
+ 
+
+ align:start position:0%
+okay so let's go back now I can figure
+out how we came up with this optimal
+
+ align:start position:0%
+out how we came up with this optimal
+ 
+
+ align:start position:0%
+out how we came up with this optimal
+policy the way we do that is through
+
+ align:start position:0%
+policy the way we do that is through
+ 
+
+ align:start position:0%
+policy the way we do that is through
+dynamic programming your student movies
+
+ align:start position:0%
+dynamic programming your student movies
+ 
+
+ align:start position:0%
+dynamic programming your student movies
+community value iteration or policy
+
+ align:start position:0%
+community value iteration or policy
+ 
+
+ align:start position:0%
+community value iteration or policy
+iteration for this lecture we're going
+
+ align:start position:0%
+iteration for this lecture we're going
+ 
+
+ align:start position:0%
+iteration for this lecture we're going
+to focus on value generation
+
+ align:start position:0%
+to focus on value generation
+ 
+
+ align:start position:0%
+to focus on value generation
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so let's take the same example we had we
+
+ align:start position:0%
+so let's take the same example we had we
+ 
+
+ align:start position:0%
+so let's take the same example we had we
+still want to maximize the expected
+
+ align:start position:0%
+still want to maximize the expected
+ 
+
+ align:start position:0%
+still want to maximize the expected
+reward and so to start we're going to
+
+ align:start position:0%
+reward and so to start we're going to
+ 
+
+ align:start position:0%
+reward and so to start we're going to
+initialize the values of each day to 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's for example start t0 we're going
+
+ align:start position:0%
+let's for example start t0 we're going
+ 
+
+ align:start position:0%
+let's for example start t0 we're going
+to focus on sweet 6 5 and we're going to
+
+ align:start position:0%
+to focus on sweet 6 5 and we're going to
+ 
+
+ align:start position:0%
+to focus on sweet 6 5 and we're going to
+say that we're gonna take the null
+
+ align:start position:0%
+say that we're gonna take the null
+ 
+
+ align:start position:0%
+say that we're gonna take the null
+action was far away with the probability
+
+ align:start position:0%
+action was far away with the probability
+ 
+
+ align:start position:0%
+action was far away with the probability
+distribution for 65 we have a few
+
+ align:start position:0%
+distribution for 65 we have a few
+ 
+
+ align:start position:0%
+distribution for 65 we have a few
+percent of staying we have 20 percent
+
+ align:start position:0%
+percent of staying we have 20 percent
+ 
+
+ align:start position:0%
+percent of staying we have 20 percent
+chance of going to 5 5 and it's 25%
+
+ align:start position:0%
+chance of going to 5 5 and it's 25%
+ 
+
+ align:start position:0%
+chance of going to 5 5 and it's 25%
+chance of going to 75 the next our
+
+ align:start position:0%
+chance of going to 75 the next our
+ 
+
+ align:start position:0%
+chance of going to 75 the next our
+information is values at each of those
+
+ align:start position:0%
+information is values at each of those
+ 
+
+ align:start position:0%
+information is values at each of those
+seeds that we can end up in and
+
+ align:start position:0%
+seeds that we can end up in and
+ 
+
+ align:start position:0%
+seeds that we can end up in and
+currently they're all set to 0 and
+
+ align:start position:0%
+currently they're all set to 0 and
+ 
+
+ align:start position:0%
+currently they're all set to 0 and
+finally the most important part players
+
+ align:start position:0%
+finally the most important part players
+ 
+
+ align:start position:0%
+finally the most important part players
+will be with the reward moving at 65
+
+ align:start position:0%
+will be with the reward moving at 65
+ 
+
+ align:start position:0%
+will be with the reward moving at 65
+taking it all actually regardless of
+
+ align:start position:0%
+taking it all actually regardless of
+ 
+
+ align:start position:0%
+taking it all actually regardless of
+what state the other is going to be 1 as
+
+ align:start position:0%
+what state the other is going to be 1 as
+ 
+
+ align:start position:0%
+what state the other is going to be 1 as
+we defined in our initial setup so let's
+
+ align:start position:0%
+we defined in our initial setup so let's
+ 
+
+ align:start position:0%
+we defined in our initial setup so let's
+see how we would happen the next time
+
+ align:start position:0%
+see how we would happen the next time
+ 
+
+ align:start position:0%
+see how we would happen the next time
+step not able to see we start getting
+
+ align:start position:0%
+step not able to see we start getting
+ 
+
+ align:start position:0%
+step not able to see we start getting
+the probabilities right and from there
+
+ align:start position:0%
+the probabilities right and from there
+ 
+
+ align:start position:0%
+the probabilities right and from there
+we would add the reward and it because
+
+ align:start position:0%
+we would add the reward and it because
+ 
+
+ align:start position:0%
+we would add the reward and it because
+we said that the reward is not dependent
+
+ align:start position:0%
+we said that the reward is not dependent
+ 
+
+ align:start position:0%
+we said that the reward is not dependent
+on this game you end up in fun it should
+
+ align:start position:0%
+on this game you end up in fun it should
+ 
+
+ align:start position:0%
+on this game you end up in fun it should
+be pressed all three probabilities there
+
+ align:start position:0%
+be pressed all three probabilities there
+ 
+
+ align:start position:0%
+be pressed all three probabilities there
+we're gonna add in the discounted value
+
+ align:start position:0%
+we're gonna add in the discounted value
+ 
+
+ align:start position:0%
+we're gonna add in the discounted value
+that we have from before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a way to look at this in a more
+
+ align:start position:0%
+so a way to look at this in a more
+ 
+
+ align:start position:0%
+so a way to look at this in a more
+generalized form is to say that across
+
+ align:start position:0%
+generalized form is to say that across
+ 
+
+ align:start position:0%
+generalized form is to say that across
+all the states that you can end up in
+
+ align:start position:0%
+all the states that you can end up in
+ 
+
+ align:start position:0%
+all the states that you can end up in
+you're going to look at the probability
+
+ align:start position:0%
+you're going to look at the probability
+ 
+
+ align:start position:0%
+you're going to look at the probability
+of ending up in that state you're
+
+ align:start position:0%
+of ending up in that state you're
+ 
+
+ align:start position:0%
+of ending up in that state you're
+multiply that by the sum of the reward
+
+ align:start position:0%
+multiply that by the sum of the reward
+ 
+
+ align:start position:0%
+multiply that by the sum of the reward
+and it just kind of lifetime value
+
+ align:start position:0%
+and it just kind of lifetime value
+ 
+
+ align:start position:0%
+and it just kind of lifetime value
+better present so we want to make sure
+
+ align:start position:0%
+better present so we want to make sure
+ 
+
+ align:start position:0%
+better present so we want to make sure
+that we're getting the best possible
+
+ align:start position:0%
+that we're getting the best possible
+ 
+
+ align:start position:0%
+that we're getting the best possible
+value so we need to incorporate all the
+
+ align:start position:0%
+value so we need to incorporate all the
+ 
+
+ align:start position:0%
+value so we need to incorporate all the
+other actions that we can take for that
+
+ align:start position:0%
+other actions that we can take for that
+ 
+
+ align:start position:0%
+other actions that we can take for that
+state so what's gonna happen is we're
+
+ align:start position:0%
+state so what's gonna happen is we're
+ 
+
+ align:start position:0%
+state so what's gonna happen is we're
+going to take the general formula we're
+
+ align:start position:0%
+going to take the general formula we're
+ 
+
+ align:start position:0%
+going to take the general formula we're
+going to repeat it over all of the
+
+ align:start position:0%
+going to repeat it over all of the
+ 
+
+ align:start position:0%
+going to repeat it over all of the
+possible actions and then we're going to
+
+ align:start position:0%
+possible actions and then we're going to
+ 
+
+ align:start position:0%
+possible actions and then we're going to
+take the maximum so for this example
+
+ align:start position:0%
+take the maximum so for this example
+ 
+
+ align:start position:0%
+take the maximum so for this example
+this state's very easy all of them are
+
+ align:start position:0%
+this state's very easy all of them are
+ 
+
+ align:start position:0%
+this state's very easy all of them are
+the same in this case
+
+ align:start position:0%
+the same in this case
+ 
+
+ align:start position:0%
+the same in this case
+but we go across let me see if we get a
+
+ align:start position:0%
+but we go across let me see if we get a
+ 
+
+ align:start position:0%
+but we go across let me see if we get a
+value of one and we update it every time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this gives us what's called being by the
+
+ align:start position:0%
+this gives us what's called being by the
+ 
+
+ align:start position:0%
+this gives us what's called being by the
+open backup or update equation this will
+
+ align:start position:0%
+open backup or update equation this will
+ 
+
+ align:start position:0%
+open backup or update equation this will
+be really important because it reaches
+
+ align:start position:0%
+be really important because it reaches
+ 
+
+ align:start position:0%
+be really important because it reaches
+across the entire state space and allows
+
+ align:start position:0%
+across the entire state space and allows
+ 
+
+ align:start position:0%
+across the entire state space and allows
+two prior history
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what this will end up looking like
+
+ align:start position:0%
+so what this will end up looking like
+ 
+
+ align:start position:0%
+so what this will end up looking like
+because we're gonna eat early calculate
+
+ align:start position:0%
+because we're gonna eat early calculate
+ 
+
+ align:start position:0%
+because we're gonna eat early calculate
+the values across the entire state space
+
+ align:start position:0%
+the values across the entire state space
+ 
+
+ align:start position:0%
+the values across the entire state space
+so at T zero we determine that all the
+
+ align:start position:0%
+so at T zero we determine that all the
+ 
+
+ align:start position:0%
+so at T zero we determine that all the
+values of zero back to 165 gives a value
+
+ align:start position:0%
+values of zero back to 165 gives a value
+ 
+
+ align:start position:0%
+values of zero back to 165 gives a value
+of one and at T 2 we see that values
+
+ align:start position:0%
+of one and at T 2 we see that values
+ 
+
+ align:start position:0%
+of one and at T 2 we see that values
+start to propagate out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the way it works is you repeat those
+
+ align:start position:0%
+so the way it works is you repeat those
+ 
+
+ align:start position:0%
+so the way it works is you repeat those
+iterations until your changes in value
+
+ align:start position:0%
+iterations until your changes in value
+ 
+
+ align:start position:0%
+iterations until your changes in value
+become what we've is that are small
+
+ align:start position:0%
+become what we've is that are small
+ 
+
+ align:start position:0%
+become what we've is that are small
+enough which would indicate your
+
+ align:start position:0%
+enough which would indicate your
+ 
+
+ align:start position:0%
+enough which would indicate your
+approximation is close enough to the
+
+ align:start position:0%
+approximation is close enough to the
+ 
+
+ align:start position:0%
+approximation is close enough to the
+real value from there you would extract
+
+ align:start position:0%
+real value from there you would extract
+ 
+
+ align:start position:0%
+real value from there you would extract
+the optimal policy from the lifetime
+
+ align:start position:0%
+the optimal policy from the lifetime
+ 
+
+ align:start position:0%
+the optimal policy from the lifetime
+values so you see this in a moment
+
+ align:start position:0%
+values so you see this in a moment
+ 
+
+ align:start position:0%
+values so you see this in a moment
+illusion and you're now just taking the
+
+ align:start position:0%
+illusion and you're now just taking the
+ 
+
+ align:start position:0%
+illusion and you're now just taking the
+action coming and you would map those
+
+ align:start position:0%
+action coming and you would map those
+ 
+
+ align:start position:0%
+action coming and you would map those
+options to your schemes an example of
+
+ align:start position:0%
+options to your schemes an example of
+ 
+
+ align:start position:0%
+options to your schemes an example of
+what this might look like propagating
+
+ align:start position:0%
+what this might look like propagating
+ 
+
+ align:start position:0%
+what this might look like propagating
+out maybe you say blue is the reward and
+
+ align:start position:0%
+out maybe you say blue is the reward and
+ 
+
+ align:start position:0%
+out maybe you say blue is the reward and
+red is an obstacle etc you can see it as
+
+ align:start position:0%
+red is an obstacle etc you can see it as
+ 
+
+ align:start position:0%
+red is an obstacle etc you can see it as
+that probably propagates out and you
+
+ align:start position:0%
+that probably propagates out and you
+ 
+
+ align:start position:0%
+that probably propagates out and you
+start seeing your policy by the arrows
+
+ align:start position:0%
+start seeing your policy by the arrows
+ 
+
+ align:start position:0%
+start seeing your policy by the arrows
+anybody have any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one last thing to mention about this
+
+ align:start position:0%
+so one last thing to mention about this
+ 
+
+ align:start position:0%
+so one last thing to mention about this
+though is that the complexity tree
+
+ align:start position:0%
+though is that the complexity tree
+ 
+
+ align:start position:0%
+though is that the complexity tree
+deterioration is dependent on the size
+
+ align:start position:0%
+deterioration is dependent on the size
+ 
+
+ align:start position:0%
+deterioration is dependent on the size
+of the states P squared and the number
+
+ align:start position:0%
+of the states P squared and the number
+ 
+
+ align:start position:0%
+of the states P squared and the number
+of actions you take so you can imagine
+
+ align:start position:0%
+of actions you take so you can imagine
+ 
+
+ align:start position:0%
+of actions you take so you can imagine
+as your state space expands or you
+
+ align:start position:0%
+as your state space expands or you
+ 
+
+ align:start position:0%
+as your state space expands or you
+gather more actions it starts getting
+
+ align:start position:0%
+gather more actions it starts getting
+ 
+
+ align:start position:0%
+gather more actions it starts getting
+very complex in which case value
+
+ align:start position:0%
+very complex in which case value
+ 
+
+ align:start position:0%
+very complex in which case value
+depiction becomes very time intensive
+
+ align:start position:0%
+depiction becomes very time intensive
+ 
+
+ align:start position:0%
+depiction becomes very time intensive
+and costly so this allows us to move
+
+ align:start position:0%
+and costly so this allows us to move
+ 
+
+ align:start position:0%
+and costly so this allows us to move
+into question so so how do you I just
+
+ align:start position:0%
+into question so so how do you I just
+ 
+
+ align:start position:0%
+into question so so how do you I just
+gonna show him how many of you have
+
+ align:start position:0%
+gonna show him how many of you have
+ 
+
+ align:start position:0%
+gonna show him how many of you have
+learned valuation before versus how many
+
+ align:start position:0%
+learned valuation before versus how many
+ 
+
+ align:start position:0%
+learned valuation before versus how many
+you've seen for the first time so how
+
+ align:start position:0%
+you've seen for the first time so how
+ 
+
+ align:start position:0%
+you've seen for the first time so how
+many have seen it before okay and then
+
+ align:start position:0%
+many have seen it before okay and then
+ 
+
+ align:start position:0%
+many have seen it before okay and then
+how many it assists the first time any
+
+ align:start position:0%
+how many it assists the first time any
+ 
+
+ align:start position:0%
+how many it assists the first time any
+questions on value duration before we
+
+ align:start position:0%
+questions on value duration before we
+ 
+
+ align:start position:0%
+questions on value duration before we
+jump in it's an essential part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the most important thing we said
+
+ align:start position:0%
+so the most important thing we said
+ 
+
+ align:start position:0%
+so the most important thing we said
+about value iteration is that it's super
+
+ align:start position:0%
+about value iteration is that it's super
+ 
+
+ align:start position:0%
+about value iteration is that it's super
+slow it's going to have to go over every
+
+ align:start position:0%
+slow it's going to have to go over every
+ 
+
+ align:start position:0%
+slow it's going to have to go over every
+possible statement and every possible
+
+ align:start position:0%
+possible statement and every possible
+ 
+
+ align:start position:0%
+possible statement and every possible
+actually to take apart a space is
+
+ align:start position:0%
+actually to take apart a space is
+ 
+
+ align:start position:0%
+actually to take apart a space is
+multi-dimensional and take a lot of
+
+ align:start position:0%
+multi-dimensional and take a lot of
+ 
+
+ align:start position:0%
+multi-dimensional and take a lot of
+different actions that's really possibly
+
+ align:start position:0%
+different actions that's really possibly
+ 
+
+ align:start position:0%
+different actions that's really possibly
+so well what the approach worker
+
+ align:start position:0%
+so well what the approach worker
+ 
+
+ align:start position:0%
+so well what the approach worker
+probably gonna want to take is using
+
+ align:start position:0%
+probably gonna want to take is using
+ 
+
+ align:start position:0%
+probably gonna want to take is using
+some sort of best first search company
+
+ align:start position:0%
+some sort of best first search company
+ 
+
+ align:start position:0%
+some sort of best first search company
+who can tell me some example algorithms
+
+ align:start position:0%
+who can tell me some example algorithms
+ 
+
+ align:start position:0%
+who can tell me some example algorithms
+that already be done based on so that's
+
+ align:start position:0%
+that already be done based on so that's
+ 
+
+ align:start position:0%
+that already be done based on so that's
+very good that's exactly fram face head
+
+ align:start position:0%
+very good that's exactly fram face head
+ 
+
+ align:start position:0%
+very good that's exactly fram face head
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+it's pretty terminus that graph search
+
+ align:start position:0%
+it's pretty terminus that graph search
+ 
+
+ align:start position:0%
+it's pretty terminus that graph search
+when you have a draft we can use a
+
+ align:start position:0%
+when you have a draft we can use a
+ 
+
+ align:start position:0%
+when you have a draft we can use a
+heuristic and we walk walk down it and
+
+ align:start position:0%
+heuristic and we walk walk down it and
+ 
+
+ align:start position:0%
+heuristic and we walk walk down it and
+search the space that we're most
+
+ align:start position:0%
+search the space that we're most
+ 
+
+ align:start position:0%
+search the space that we're most
+interested in to the historical very
+
+ align:start position:0%
+interested in to the historical very
+ 
+
+ align:start position:0%
+interested in to the historical very
+good so we're going to introduce two new
+
+ align:start position:0%
+good so we're going to introduce two new
+ 
+
+ align:start position:0%
+good so we're going to introduce two new
+algorithms focusing on the last AO star
+
+ align:start position:0%
+algorithms focusing on the last AO star
+ 
+
+ align:start position:0%
+algorithms focusing on the last AO star
+is another that we can use to search for
+
+ align:start position:0%
+is another that we can use to search for
+ 
+
+ align:start position:0%
+is another that we can use to search for
+graphs that have this sort of a o stands
+
+ align:start position:0%
+graphs that have this sort of a o stands
+ 
+
+ align:start position:0%
+graphs that have this sort of a o stands
+for and or graphs as opposed to the
+
+ align:start position:0%
+for and or graphs as opposed to the
+ 
+
+ align:start position:0%
+for and or graphs as opposed to the
+simple simple simple graphs that we have
+
+ align:start position:0%
+simple simple simple graphs that we have
+ 
+
+ align:start position:0%
+simple simple simple graphs that we have
+used the and is kind of a way to express
+
+ align:start position:0%
+used the and is kind of a way to express
+ 
+
+ align:start position:0%
+used the and is kind of a way to express
+Kabbalistic coupling in teenagers so if
+
+ align:start position:0%
+Kabbalistic coupling in teenagers so if
+ 
+
+ align:start position:0%
+Kabbalistic coupling in teenagers so if
+we explore one thing we might have to
+
+ align:start position:0%
+we explore one thing we might have to
+ 
+
+ align:start position:0%
+we explore one thing we might have to
+explore other we'll discuss that a
+
+ align:start position:0%
+explore other we'll discuss that a
+ 
+
+ align:start position:0%
+explore other we'll discuss that a
+little bit more mimics life elio is a
+
+ align:start position:0%
+little bit more mimics life elio is a
+ 
+
+ align:start position:0%
+little bit more mimics life elio is a
+bit more of a generalization what it
+
+ align:start position:0%
+bit more of a generalization what it
+ 
+
+ align:start position:0%
+bit more of a generalization what it
+does is allows us to search loony graphs
+
+ align:start position:0%
+does is allows us to search loony graphs
+ 
+
+ align:start position:0%
+does is allows us to search loony graphs
+and deal what the problem was to
+
+ align:start position:0%
+and deal what the problem was to
+ 
+
+ align:start position:0%
+and deal what the problem was to
+coupling and a lot
+
+ align:start position:0%
+coupling and a lot
+ 
+
+ align:start position:0%
+coupling and a lot
+to search and find the best path with a
+
+ align:start position:0%
+to search and find the best path with a
+ 
+
+ align:start position:0%
+to search and find the best path with a
+heuristic guided algorithm over him from
+
+ align:start position:0%
+heuristic guided algorithm over him from
+ 
+
+ align:start position:0%
+heuristic guided algorithm over him from
+the time horizon possibly revisiting
+
+ align:start position:0%
+the time horizon possibly revisiting
+ 
+
+ align:start position:0%
+the time horizon possibly revisiting
+states using the tools we just had an
+
+ align:start position:0%
+states using the tools we just had an
+ 
+
+ align:start position:0%
+states using the tools we just had an
+evaluation to understanding what the
+
+ align:start position:0%
+evaluation to understanding what the
+ 
+
+ align:start position:0%
+evaluation to understanding what the
+next interview so we'll talk about
+
+ align:start position:0%
+next interview so we'll talk about
+ 
+
+ align:start position:0%
+next interview so we'll talk about
+exactly how to get R and D keys that we
+
+ align:start position:0%
+exactly how to get R and D keys that we
+ 
+
+ align:start position:0%
+exactly how to get R and D keys that we
+just saw these four arrow examples to
+
+ align:start position:0%
+just saw these four arrow examples to
+ 
+
+ align:start position:0%
+just saw these four arrow examples to
+these sort of hand or graphs we'll talk
+
+ align:start position:0%
+these sort of hand or graphs we'll talk
+ 
+
+ align:start position:0%
+these sort of hand or graphs we'll talk
+about two kids it's one simple one where
+
+ align:start position:0%
+about two kids it's one simple one where
+ 
+
+ align:start position:0%
+about two kids it's one simple one where
+we could apply the and we'll start off
+
+ align:start position:0%
+we could apply the and we'll start off
+ 
+
+ align:start position:0%
+we could apply the and we'll start off
+with is where you have a quadcopter and
+
+ align:start position:0%
+with is where you have a quadcopter and
+ 
+
+ align:start position:0%
+with is where you have a quadcopter and
+in command an action north you have a
+
+ align:start position:0%
+in command an action north you have a
+ 
+
+ align:start position:0%
+in command an action north you have a
+high probability of going north but you
+
+ align:start position:0%
+high probability of going north but you
+ 
+
+ align:start position:0%
+high probability of going north but you
+might go on and vice versa you go east
+
+ align:start position:0%
+might go on and vice versa you go east
+ 
+
+ align:start position:0%
+might go on and vice versa you go east
+you might go no this is expressed here
+
+ align:start position:0%
+you might go no this is expressed here
+ 
+
+ align:start position:0%
+you might go no this is expressed here
+with the growing tree and these and
+
+ align:start position:0%
+with the growing tree and these and
+ 
+
+ align:start position:0%
+with the growing tree and these and
+enters they connect but despite the
+
+ align:start position:0%
+enters they connect but despite the
+ 
+
+ align:start position:0%
+enters they connect but despite the
+action Utley might command from zero
+
+ align:start position:0%
+action Utley might command from zero
+ 
+
+ align:start position:0%
+action Utley might command from zero
+zero we might end up in one zero or zero
+
+ align:start position:0%
+zero we might end up in one zero or zero
+ 
+
+ align:start position:0%
+zero we might end up in one zero or zero
+one right and as we propagate outward
+
+ align:start position:0%
+one right and as we propagate outward
+ 
+
+ align:start position:0%
+one right and as we propagate outward
+you can see how we're never going to
+
+ align:start position:0%
+you can see how we're never going to
+ 
+
+ align:start position:0%
+you can see how we're never going to
+move back to escape into we're gonna be
+
+ align:start position:0%
+move back to escape into we're gonna be
+ 
+
+ align:start position:0%
+move back to escape into we're gonna be
+moving in the northeast are actually
+
+ align:start position:0%
+moving in the northeast are actually
+ 
+
+ align:start position:0%
+moving in the northeast are actually
+constantly our participants and our
+
+ align:start position:0%
+constantly our participants and our
+ 
+
+ align:start position:0%
+constantly our participants and our
+probability distribution across fish to
+
+ align:start position:0%
+probability distribution across fish to
+ 
+
+ align:start position:0%
+probability distribution across fish to
+be able to experience and that's that's
+
+ align:start position:0%
+be able to experience and that's that's
+ 
+
+ align:start position:0%
+be able to experience and that's that's
+the coupling of the edges because as we
+
+ align:start position:0%
+the coupling of the edges because as we
+ 
+
+ align:start position:0%
+the coupling of the edges because as we
+explore down the tree we have to explore
+
+ align:start position:0%
+explore down the tree we have to explore
+ 
+
+ align:start position:0%
+explore down the tree we have to explore
+all the edges together anyone have any
+
+ align:start position:0%
+all the edges together anyone have any
+ 
+
+ align:start position:0%
+all the edges together anyone have any
+questions on just this kind of
+
+ align:start position:0%
+questions on just this kind of
+ 
+
+ align:start position:0%
+questions on just this kind of
+conversion this population
+
+ align:start position:0%
+conversion this population
+ 
+
+ align:start position:0%
+conversion this population
+I have a broader question we mentioned
+
+ align:start position:0%
+I have a broader question we mentioned
+ 
+
+ align:start position:0%
+I have a broader question we mentioned
+the MVPs deal with finite States do we
+
+ align:start position:0%
+the MVPs deal with finite States do we
+ 
+
+ align:start position:0%
+the MVPs deal with finite States do we
+always just discretize this world into a
+
+ align:start position:0%
+always just discretize this world into a
+ 
+
+ align:start position:0%
+always just discretize this world into a
+set of mind things yes that's that's
+
+ align:start position:0%
+set of mind things yes that's that's
+ 
+
+ align:start position:0%
+set of mind things yes that's that's
+kind of a prerequisite for searching
+
+ align:start position:0%
+kind of a prerequisite for searching
+ 
+
+ align:start position:0%
+kind of a prerequisite for searching
+over the state space as finely as
+
+ align:start position:0%
+over the state space as finely as
+ 
+
+ align:start position:0%
+over the state space as finely as
+possible yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's look at this case instead
+
+ align:start position:0%
+so now let's look at this case instead
+ 
+
+ align:start position:0%
+so now let's look at this case instead
+of the Northeast it's not
+
+ align:start position:0%
+of the Northeast it's not
+ 
+
+ align:start position:0%
+of the Northeast it's not
+non-deterministic what every command
+
+ align:start position:0%
+non-deterministic what every command
+ 
+
+ align:start position:0%
+non-deterministic what every command
+action north or south whether we go
+
+ align:start position:0%
+action north or south whether we go
+ 
+
+ align:start position:0%
+action north or south whether we go
+under so here we see this movie
+
+ align:start position:0%
+under so here we see this movie
+ 
+
+ align:start position:0%
+under so here we see this movie
+structure into which we see that we
+
+ align:start position:0%
+structure into which we see that we
+ 
+
+ align:start position:0%
+structure into which we see that we
+might on our first action commanding
+
+ align:start position:0%
+might on our first action commanding
+ 
+
+ align:start position:0%
+might on our first action commanding
+North we might go to a plus one and then
+
+ align:start position:0%
+North we might go to a plus one and then
+ 
+
+ align:start position:0%
+North we might go to a plus one and then
+going to North again but we have our end
+
+ align:start position:0%
+going to North again but we have our end
+ 
+
+ align:start position:0%
+going to North again but we have our end
+engine our probability distribution
+
+ align:start position:0%
+engine our probability distribution
+ 
+
+ align:start position:0%
+engine our probability distribution
+might say goodnight mister what this
+
+ align:start position:0%
+might say goodnight mister what this
+ 
+
+ align:start position:0%
+might say goodnight mister what this
+does it creates this movie structure
+
+ align:start position:0%
+does it creates this movie structure
+ 
+
+ align:start position:0%
+does it creates this movie structure
+this is exactly what we're gonna need to
+
+ align:start position:0%
+this is exactly what we're gonna need to
+ 
+
+ align:start position:0%
+this is exactly what we're gonna need to
+plug this is a very real-world scenario
+
+ align:start position:0%
+plug this is a very real-world scenario
+ 
+
+ align:start position:0%
+plug this is a very real-world scenario
+or it's a very likely you might return
+
+ align:start position:0%
+or it's a very likely you might return
+ 
+
+ align:start position:0%
+or it's a very likely you might return
+to somewhere we we just came from just
+
+ align:start position:0%
+to somewhere we we just came from just
+ 
+
+ align:start position:0%
+to somewhere we we just came from just
+because of the uncertainty and this is
+
+ align:start position:0%
+because of the uncertainty and this is
+ 
+
+ align:start position:0%
+because of the uncertainty and this is
+the type of problems so we're going to
+
+ align:start position:0%
+the type of problems so we're going to
+ 
+
+ align:start position:0%
+the type of problems so we're going to
+use the
+
+ align:start position:0%
+use the
+ 
+
+ align:start position:0%
+use the
+where I talk about the three main things
+
+ align:start position:0%
+where I talk about the three main things
+ 
+
+ align:start position:0%
+where I talk about the three main things
+that its benefit as a heuristic Qaeda
+
+ align:start position:0%
+that its benefit as a heuristic Qaeda
+ 
+
+ align:start position:0%
+that its benefit as a heuristic Qaeda
+Network and what that means is that we
+
+ align:start position:0%
+Network and what that means is that we
+ 
+
+ align:start position:0%
+Network and what that means is that we
+have our large state space here but
+
+ align:start position:0%
+have our large state space here but
+ 
+
+ align:start position:0%
+have our large state space here but
+we're only gonna work that portion of
+
+ align:start position:0%
+we're only gonna work that portion of
+ 
+
+ align:start position:0%
+we're only gonna work that portion of
+this raid out portion we're only at the
+
+ align:start position:0%
+this raid out portion we're only at the
+ 
+
+ align:start position:0%
+this raid out portion we're only at the
+portion that is interesting to us the
+
+ align:start position:0%
+portion that is interesting to us the
+ 
+
+ align:start position:0%
+portion that is interesting to us the
+Porsche and provides us with the biggest
+
+ align:start position:0%
+Porsche and provides us with the biggest
+ 
+
+ align:start position:0%
+Porsche and provides us with the biggest
+rewards of course that's reachable if we
+
+ align:start position:0%
+rewards of course that's reachable if we
+ 
+
+ align:start position:0%
+rewards of course that's reachable if we
+follow an optimal policy we do this out
+
+ align:start position:0%
+follow an optimal policy we do this out
+ 
+
+ align:start position:0%
+follow an optimal policy we do this out
+with some admissible heuristic there's
+
+ align:start position:0%
+with some admissible heuristic there's
+ 
+
+ align:start position:0%
+with some admissible heuristic there's
+many causes over excavator orange just
+
+ align:start position:0%
+many causes over excavator orange just
+ 
+
+ align:start position:0%
+many causes over excavator orange just
+like a sponge the idea will let me keep
+
+ align:start position:0%
+like a sponge the idea will let me keep
+ 
+
+ align:start position:0%
+like a sponge the idea will let me keep
+the problem small so we don't have to
+
+ align:start position:0%
+the problem small so we don't have to
+ 
+
+ align:start position:0%
+the problem small so we don't have to
+search without a relation or a giant
+
+ align:start position:0%
+search without a relation or a giant
+ 
+
+ align:start position:0%
+search without a relation or a giant
+database what we'll do next is at the
+
+ align:start position:0%
+database what we'll do next is at the
+ 
+
+ align:start position:0%
+database what we'll do next is at the
+state space expense we get a bigger
+
+ align:start position:0%
+state space expense we get a bigger
+ 
+
+ align:start position:0%
+state space expense we get a bigger
+barrier about the states we're
+
+ align:start position:0%
+barrier about the states we're
+ 
+
+ align:start position:0%
+barrier about the states we're
+interested a great dude for every
+
+ align:start position:0%
+interested a great dude for every
+ 
+
+ align:start position:0%
+interested a great dude for every
+donation we're going to figure out what
+
+ align:start position:0%
+donation we're going to figure out what
+ 
+
+ align:start position:0%
+donation we're going to figure out what
+the best action is and the night the
+
+ align:start position:0%
+the best action is and the night the
+ 
+
+ align:start position:0%
+the best action is and the night the
+ideal case the actions that we need the
+
+ align:start position:0%
+ideal case the actions that we need the
+ 
+
+ align:start position:0%
+ideal case the actions that we need the
+states that we would never reach using
+
+ align:start position:0%
+states that we would never reach using
+ 
+
+ align:start position:0%
+states that we would never reach using
+an optimal policy are never going to
+
+ align:start position:0%
+an optimal policy are never going to
+ 
+
+ align:start position:0%
+an optimal policy are never going to
+explore because our policy is going to
+
+ align:start position:0%
+explore because our policy is going to
+ 
+
+ align:start position:0%
+explore because our policy is going to
+say no don't go over there that's
+
+ align:start position:0%
+say no don't go over there that's
+ 
+
+ align:start position:0%
+say no don't go over there that's
+or that's getting your partner so we're
+
+ align:start position:0%
+or that's getting your partner so we're
+ 
+
+ align:start position:0%
+or that's getting your partner so we're
+going to be searching in a very specific
+
+ align:start position:0%
+going to be searching in a very specific
+ 
+
+ align:start position:0%
+going to be searching in a very specific
+part of the state's case that is useful
+
+ align:start position:0%
+part of the state's case that is useful
+ 
+
+ align:start position:0%
+part of the state's case that is useful
+to double counts most circle as a high
+
+ align:start position:0%
+to double counts most circle as a high
+ 
+
+ align:start position:0%
+to double counts most circle as a high
+reward so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the what's important here the L
+
+ align:start position:0%
+so the what's important here the L
+ 
+
+ align:start position:0%
+so the what's important here the L
+stands for groups it's an extension of
+
+ align:start position:0%
+stands for groups it's an extension of
+ 
+
+ align:start position:0%
+stands for groups it's an extension of
+the day under the widget itself as an
+
+ align:start position:0%
+the day under the widget itself as an
+ 
+
+ align:start position:0%
+the day under the widget itself as an
+extension they start over we can handle
+
+ align:start position:0%
+extension they start over we can handle
+ 
+
+ align:start position:0%
+extension they start over we can handle
+the infinite horizon problems like the
+
+ align:start position:0%
+the infinite horizon problems like the
+ 
+
+ align:start position:0%
+the infinite horizon problems like the
+transition in different ways really
+
+ align:start position:0%
+transition in different ways really
+ 
+
+ align:start position:0%
+transition in different ways really
+models kind of a real world center
+
+ align:start position:0%
+models kind of a real world center
+ 
+
+ align:start position:0%
+models kind of a real world center
+inspiration
+
+ align:start position:0%
+inspiration
+ 
+
+ align:start position:0%
+inspiration
+any questions so far kind of the broad
+
+ align:start position:0%
+any questions so far kind of the broad
+ 
+
+ align:start position:0%
+any questions so far kind of the broad
+scope of what another stars
+
+ align:start position:0%
+scope of what another stars
+ 
+
+ align:start position:0%
+scope of what another stars
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+sharp d AO stands for and or crafts so
+
+ align:start position:0%
+sharp d AO stands for and or crafts so
+ 
+
+ align:start position:0%
+sharp d AO stands for and or crafts so
+that's graphs that we have here and just
+
+ align:start position:0%
+that's graphs that we have here and just
+ 
+
+ align:start position:0%
+that's graphs that we have here and just
+are coupled that happy to attempt to do
+
+ align:start position:0%
+are coupled that happy to attempt to do
+ 
+
+ align:start position:0%
+are coupled that happy to attempt to do
+transition you might end up here or you
+
+ align:start position:0%
+transition you might end up here or you
+ 
+
+ align:start position:0%
+transition you might end up here or you
+might enough that that's the acid notion
+
+ align:start position:0%
+might enough that that's the acid notion
+ 
+
+ align:start position:0%
+might enough that that's the acid notion
+that of this probabilistic coupling that
+
+ align:start position:0%
+that of this probabilistic coupling that
+ 
+
+ align:start position:0%
+that of this probabilistic coupling that
+we'll see in action as we said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right probably a little we're going
+
+ align:start position:0%
+all right probably a little we're going
+ 
+
+ align:start position:0%
+all right probably a little we're going
+to do we're going to give put this MDP
+
+ align:start position:0%
+to do we're going to give put this MDP
+ 
+
+ align:start position:0%
+to do we're going to give put this MDP
+or a on graph with transition
+
+ align:start position:0%
+or a on graph with transition
+ 
+
+ align:start position:0%
+or a on graph with transition
+probabilities or award function to
+
+ align:start position:0%
+probabilities or award function to
+ 
+
+ align:start position:0%
+probabilities or award function to
+distance these are all things that we
+
+ align:start position:0%
+distance these are all things that we
+ 
+
+ align:start position:0%
+distance these are all things that we
+kind of defined prior to figuring out
+
+ align:start position:0%
+kind of defined prior to figuring out
+ 
+
+ align:start position:0%
+kind of defined prior to figuring out
+but we're going to come out with is an
+
+ align:start position:0%
+but we're going to come out with is an
+ 
+
+ align:start position:0%
+but we're going to come out with is an
+optimal policy for every regionals
+
+ align:start position:0%
+optimal policy for every regionals
+ 
+
+ align:start position:0%
+optimal policy for every regionals
+it's a little different than what a
+
+ align:start position:0%
+it's a little different than what a
+ 
+
+ align:start position:0%
+it's a little different than what a
+Eurasian gives which is an optimal
+
+ align:start position:0%
+Eurasian gives which is an optimal
+ 
+
+ align:start position:0%
+Eurasian gives which is an optimal
+policy every possible state but we argue
+
+ align:start position:0%
+policy every possible state but we argue
+ 
+
+ align:start position:0%
+policy every possible state but we argue
+that that's Auto leaning that if we know
+
+ align:start position:0%
+that that's Auto leaning that if we know
+ 
+
+ align:start position:0%
+that that's Auto leaning that if we know
+where we're starting and we follow our
+
+ align:start position:0%
+where we're starting and we follow our
+ 
+
+ align:start position:0%
+where we're starting and we follow our
+optimal policy were only going to
+
+ align:start position:0%
+optimal policy were only going to
+ 
+
+ align:start position:0%
+optimal policy were only going to
+explore certain portion of assessments
+
+ align:start position:0%
+explore certain portion of assessments
+ 
+
+ align:start position:0%
+explore certain portion of assessments
+and we're going to exploit that to get
+
+ align:start position:0%
+and we're going to exploit that to get
+ 
+
+ align:start position:0%
+and we're going to exploit that to get
+it prefer has a plan a little bit more
+
+ align:start position:0%
+it prefer has a plan a little bit more
+ 
+
+ align:start position:0%
+it prefer has a plan a little bit more
+than during a high dimensional spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll define some terms that we're
+
+ align:start position:0%
+so we'll define some terms that we're
+ 
+
+ align:start position:0%
+so we'll define some terms that we're
+going to use throughout those we've
+
+ align:start position:0%
+going to use throughout those we've
+ 
+
+ align:start position:0%
+going to use throughout those we've
+already talked about our state space
+
+ align:start position:0%
+already talked about our state space
+ 
+
+ align:start position:0%
+already talked about our state space
+this is just a small portion of it that
+
+ align:start position:0%
+this is just a small portion of it that
+ 
+
+ align:start position:0%
+this is just a small portion of it that
+we're gonna work with us we're gonna
+
+ align:start position:0%
+we're gonna work with us we're gonna
+ 
+
+ align:start position:0%
+we're gonna work with us we're gonna
+walk through this example
+
+ align:start position:0%
+walk through this example
+ 
+
+ align:start position:0%
+walk through this example
+next we're gonna define something called
+
+ align:start position:0%
+next we're gonna define something called
+ 
+
+ align:start position:0%
+next we're gonna define something called
+a kangaroo and that's the initialize
+
+ align:start position:0%
+a kangaroo and that's the initialize
+ 
+
+ align:start position:0%
+a kangaroo and that's the initialize
+that to just I see arrows but as we
+
+ align:start position:0%
+that to just I see arrows but as we
+ 
+
+ align:start position:0%
+that to just I see arrows but as we
+progressed in the algorithm it's going
+
+ align:start position:0%
+progressed in the algorithm it's going
+ 
+
+ align:start position:0%
+progressed in the algorithm it's going
+to go it's going to grow only to the
+
+ align:start position:0%
+to go it's going to grow only to the
+ 
+
+ align:start position:0%
+to go it's going to grow only to the
+areas that were interested in a subset
+
+ align:start position:0%
+areas that were interested in a subset
+ 
+
+ align:start position:0%
+areas that were interested in a subset
+of this is the terminals now these
+
+ align:start position:0%
+of this is the terminals now these
+ 
+
+ align:start position:0%
+of this is the terminals now these
+aren't goal States these are just
+
+ align:start position:0%
+aren't goal States these are just
+ 
+
+ align:start position:0%
+aren't goal States these are just
+awareness of our space that we've added
+
+ align:start position:0%
+awareness of our space that we've added
+ 
+
+ align:start position:0%
+awareness of our space that we've added
+two envelopes this is what it would be
+
+ align:start position:0%
+two envelopes this is what it would be
+ 
+
+ align:start position:0%
+two envelopes this is what it would be
+in the it's just a note that haven't
+
+ align:start position:0%
+in the it's just a note that haven't
+ 
+
+ align:start position:0%
+in the it's just a note that haven't
+been expanded yet here my manager on
+
+ align:start position:0%
+been expanded yet here my manager on
+ 
+
+ align:start position:0%
+been expanded yet here my manager on
+anything greater but you can imagine the
+
+ align:start position:0%
+anything greater but you can imagine the
+ 
+
+ align:start position:0%
+anything greater but you can imagine the
+state space comes out further down
+
+ align:start position:0%
+state space comes out further down
+ 
+
+ align:start position:0%
+state space comes out further down
+further and we're keeping track of the
+
+ align:start position:0%
+further and we're keeping track of the
+ 
+
+ align:start position:0%
+further and we're keeping track of the
+notes that you haven't expanded yet
+
+ align:start position:0%
+notes that you haven't expanded yet
+ 
+
+ align:start position:0%
+notes that you haven't expanded yet
+or likewise we show that when an issue
+
+ align:start position:0%
+or likewise we show that when an issue
+ 
+
+ align:start position:0%
+or likewise we show that when an issue
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other the other few things are going
+
+ align:start position:0%
+the other the other few things are going
+ 
+
+ align:start position:0%
+the other the other few things are going
+to find you ready to find the states
+
+ align:start position:0%
+to find you ready to find the states
+ 
+
+ align:start position:0%
+to find you ready to find the states
+that we're going to define Kosta
+
+ align:start position:0%
+that we're going to define Kosta
+ 
+
+ align:start position:0%
+that we're going to define Kosta
+heuristic or the work function RT and
+
+ align:start position:0%
+heuristic or the work function RT and
+ 
+
+ align:start position:0%
+heuristic or the work function RT and
+transition probability matrix this type
+
+ align:start position:0%
+transition probability matrix this type
+ 
+
+ align:start position:0%
+transition probability matrix this type
+of matrices that are we're going to use
+
+ align:start position:0%
+of matrices that are we're going to use
+ 
+
+ align:start position:0%
+of matrices that are we're going to use
+what's important here is that our reward
+
+ align:start position:0%
+what's important here is that our reward
+ 
+
+ align:start position:0%
+what's important here is that our reward
+function our transition probabilities
+
+ align:start position:0%
+function our transition probabilities
+ 
+
+ align:start position:0%
+function our transition probabilities
+are slightly altered to account for the
+
+ align:start position:0%
+are slightly altered to account for the
+ 
+
+ align:start position:0%
+are slightly altered to account for the
+fact that we haven't explored the entire
+
+ align:start position:0%
+fact that we haven't explored the entire
+ 
+
+ align:start position:0%
+fact that we haven't explored the entire
+database then we see here that that node
+
+ align:start position:0%
+database then we see here that that node
+ 
+
+ align:start position:0%
+database then we see here that that node
+is an ST in other words it's one of
+
+ align:start position:0%
+is an ST in other words it's one of
+ 
+
+ align:start position:0%
+is an ST in other words it's one of
+those terminal edges science remotes
+
+ align:start position:0%
+those terminal edges science remotes
+ 
+
+ align:start position:0%
+those terminal edges science remotes
+we're gonna graduate can transition out
+
+ align:start position:0%
+we're gonna graduate can transition out
+ 
+
+ align:start position:0%
+we're gonna graduate can transition out
+of it because we don't know what so far
+
+ align:start position:0%
+of it because we don't know what so far
+ 
+
+ align:start position:0%
+of it because we don't know what so far
+and we're going to send its reward to be
+
+ align:start position:0%
+and we're going to send its reward to be
+ 
+
+ align:start position:0%
+and we're going to send its reward to be
+the houmous whatever we think that the
+
+ align:start position:0%
+the houmous whatever we think that the
+ 
+
+ align:start position:0%
+the houmous whatever we think that the
+reward is going to be when we begin to
+
+ align:start position:0%
+reward is going to be when we begin to
+ 
+
+ align:start position:0%
+reward is going to be when we begin to
+explore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and like I said we're just going to keep
+
+ align:start position:0%
+and like I said we're just going to keep
+ 
+
+ align:start position:0%
+and like I said we're just going to keep
+this into a policy search just like we
+
+ align:start position:0%
+this into a policy search just like we
+ 
+
+ align:start position:0%
+this into a policy search just like we
+discussed the value iteration and I'm
+
+ align:start position:0%
+discussed the value iteration and I'm
+ 
+
+ align:start position:0%
+discussed the value iteration and I'm
+the sub-problem necessary for optimal
+
+ align:start position:0%
+the sub-problem necessary for optimal
+ 
+
+ align:start position:0%
+the sub-problem necessary for optimal
+policy on the side so farsighted
+
+ align:start position:0%
+policy on the side so farsighted
+ 
+
+ align:start position:0%
+policy on the side so farsighted
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the devil steps is very text people
+
+ align:start position:0%
+the devil steps is very text people
+ 
+
+ align:start position:0%
+the devil steps is very text people
+we're going to definitely walk through
+
+ align:start position:0%
+we're going to definitely walk through
+ 
+
+ align:start position:0%
+we're going to definitely walk through
+every single step we're going to do two
+
+ align:start position:0%
+every single step we're going to do two
+ 
+
+ align:start position:0%
+every single step we're going to do two
+full rotations so like I said we're
+
+ align:start position:0%
+full rotations so like I said we're
+ 
+
+ align:start position:0%
+full rotations so like I said we're
+going to create our party continue
+
+ align:start position:0%
+going to create our party continue
+ 
+
+ align:start position:0%
+going to create our party continue
+that's our work function transition
+
+ align:start position:0%
+that's our work function transition
+ 
+
+ align:start position:0%
+that's our work function transition
+probabilities definition to show news
+
+ align:start position:0%
+probabilities definition to show news
+ 
+
+ align:start position:0%
+probabilities definition to show news
+value iteration to find the optimal
+
+ align:start position:0%
+value iteration to find the optimal
+ 
+
+ align:start position:0%
+value iteration to find the optimal
+policy of the sub space that we're
+
+ align:start position:0%
+policy of the sub space that we're
+ 
+
+ align:start position:0%
+policy of the sub space that we're
+living now and then we're going to this
+
+ align:start position:0%
+living now and then we're going to this
+ 
+
+ align:start position:0%
+living now and then we're going to this
+is probably the most important step
+
+ align:start position:0%
+is probably the most important step
+ 
+
+ align:start position:0%
+is probably the most important step
+knowing this optimal policy we take a
+
+ align:start position:0%
+knowing this optimal policy we take a
+ 
+
+ align:start position:0%
+knowing this optimal policy we take a
+look at what new states that are eternal
+
+ align:start position:0%
+look at what new states that are eternal
+ 
+
+ align:start position:0%
+look at what new states that are eternal
+States note that we haven't explored yet
+
+ align:start position:0%
+States note that we haven't explored yet
+ 
+
+ align:start position:0%
+States note that we haven't explored yet
+what new states we might visit now so
+
+ align:start position:0%
+what new states we might visit now so
+ 
+
+ align:start position:0%
+what new states we might visit now so
+let's say we have our policy and
+
+ align:start position:0%
+let's say we have our policy and
+ 
+
+ align:start position:0%
+let's say we have our policy and
+acceleration goes north and we know that
+
+ align:start position:0%
+acceleration goes north and we know that
+ 
+
+ align:start position:0%
+acceleration goes north and we know that
+we haven't explored the North State debt
+
+ align:start position:0%
+we haven't explored the North State debt
+ 
+
+ align:start position:0%
+we haven't explored the North State debt
+we know this is the state that we're
+
+ align:start position:0%
+we know this is the state that we're
+ 
+
+ align:start position:0%
+we know this is the state that we're
+going to reach following what we
+
+ align:start position:0%
+going to reach following what we
+ 
+
+ align:start position:0%
+going to reach following what we
+consider now to be already inaudible
+
+ align:start position:0%
+consider now to be already inaudible
+ 
+
+ align:start position:0%
+consider now to be already inaudible
+that's that's the states we're gonna
+
+ align:start position:0%
+that's that's the states we're gonna
+ 
+
+ align:start position:0%
+that's that's the states we're gonna
+expand next do some bookkeeping and
+
+ align:start position:0%
+expand next do some bookkeeping and
+ 
+
+ align:start position:0%
+expand next do some bookkeeping and
+adding them to an internal state
+
+ align:start position:0%
+adding them to an internal state
+ 
+
+ align:start position:0%
+adding them to an internal state
+settlement than the ones we expanded and
+
+ align:start position:0%
+settlement than the ones we expanded and
+ 
+
+ align:start position:0%
+settlement than the ones we expanded and
+adding them directly what's important
+
+ align:start position:0%
+adding them directly what's important
+ 
+
+ align:start position:0%
+adding them directly what's important
+here is that we're only gonna add space
+
+ align:start position:0%
+here is that we're only gonna add space
+ 
+
+ align:start position:0%
+here is that we're only gonna add space
+that we haven't used them to our
+
+ align:start position:0%
+that we haven't used them to our
+ 
+
+ align:start position:0%
+that we haven't used them to our
+envelope and this is this is basically
+
+ align:start position:0%
+envelope and this is this is basically
+ 
+
+ align:start position:0%
+envelope and this is this is basically
+the whole pack that allows us to deal
+
+ align:start position:0%
+the whole pack that allows us to deal
+ 
+
+ align:start position:0%
+the whole pack that allows us to deal
+with looming drops we're not going to
+
+ align:start position:0%
+with looming drops we're not going to
+ 
+
+ align:start position:0%
+with looming drops we're not going to
+continually explore notes that we might
+
+ align:start position:0%
+continually explore notes that we might
+ 
+
+ align:start position:0%
+continually explore notes that we might
+reach a second time probabilistically
+
+ align:start position:0%
+reach a second time probabilistically
+ 
+
+ align:start position:0%
+reach a second time probabilistically
+we're gonna let value iteration kind of
+
+ align:start position:0%
+we're gonna let value iteration kind of
+ 
+
+ align:start position:0%
+we're gonna let value iteration kind of
+handle up
+
+ align:start position:0%
+handle up
+ 
+
+ align:start position:0%
+handle up
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right sure
+
+ align:start position:0%
+right sure
+ 
+
+ align:start position:0%
+right sure
+so you can imagine what we'll talk about
+
+ align:start position:0%
+so you can imagine what we'll talk about
+ 
+
+ align:start position:0%
+so you can imagine what we'll talk about
+termination and depth as you can imagine
+
+ align:start position:0%
+termination and depth as you can imagine
+ 
+
+ align:start position:0%
+termination and depth as you can imagine
+that as we have these terminal States
+
+ align:start position:0%
+that as we have these terminal States
+ 
+
+ align:start position:0%
+that as we have these terminal States
+but you have a policy that guides you to
+
+ align:start position:0%
+but you have a policy that guides you to
+ 
+
+ align:start position:0%
+but you have a policy that guides you to
+a part of the states makes the greatest
+
+ align:start position:0%
+a part of the states makes the greatest
+ 
+
+ align:start position:0%
+a part of the states makes the greatest
+and actually we've reached your goal
+
+ align:start position:0%
+and actually we've reached your goal
+ 
+
+ align:start position:0%
+and actually we've reached your goal
+your optimal policy to say just a click
+
+ align:start position:0%
+your optimal policy to say just a click
+ 
+
+ align:start position:0%
+your optimal policy to say just a click
+right and it's not gonna say anything
+
+ align:start position:0%
+right and it's not gonna say anything
+ 
+
+ align:start position:0%
+right and it's not gonna say anything
+work again essentially with the ghost
+
+ align:start position:0%
+work again essentially with the ghost
+ 
+
+ align:start position:0%
+work again essentially with the ghost
+days definite or in the market in case
+
+ align:start position:0%
+days definite or in the market in case
+ 
+
+ align:start position:0%
+days definite or in the market in case
+if there's nothing else you can mention
+
+ align:start position:0%
+if there's nothing else you can mention
+ 
+
+ align:start position:0%
+if there's nothing else you can mention
+the idea is that you that your policy on
+
+ align:start position:0%
+the idea is that you that your policy on
+ 
+
+ align:start position:0%
+the idea is that you that your policy on
+your sub space never tells you to go to
+
+ align:start position:0%
+your sub space never tells you to go to
+ 
+
+ align:start position:0%
+your sub space never tells you to go to
+a terminal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+policy is running another generation
+
+ align:start position:0%
+policy is running another generation
+ 
+
+ align:start position:0%
+policy is running another generation
+entirely yes we're going to treat a
+
+ align:start position:0%
+entirely yes we're going to treat a
+ 
+
+ align:start position:0%
+entirely yes we're going to treat a
+section of the black box but the trick
+
+ align:start position:0%
+section of the black box but the trick
+ 
+
+ align:start position:0%
+section of the black box but the trick
+here is that we're doing it on a smaller
+
+ align:start position:0%
+here is that we're doing it on a smaller
+ 
+
+ align:start position:0%
+here is that we're doing it on a smaller
+portion space all right put the specs up
+
+ align:start position:0%
+portion space all right put the specs up
+ 
+
+ align:start position:0%
+portion space all right put the specs up
+there hopefully you can sort of see us
+
+ align:start position:0%
+there hopefully you can sort of see us
+ 
+
+ align:start position:0%
+there hopefully you can sort of see us
+but for now we'll just kind of walk
+
+ align:start position:0%
+but for now we'll just kind of walk
+ 
+
+ align:start position:0%
+but for now we'll just kind of walk
+through from the beginning we said that
+
+ align:start position:0%
+through from the beginning we said that
+ 
+
+ align:start position:0%
+through from the beginning we said that
+our envelope and our terminal notes are
+
+ align:start position:0%
+our envelope and our terminal notes are
+ 
+
+ align:start position:0%
+our envelope and our terminal notes are
+very hard just as 0fficer that was very
+
+ align:start position:0%
+very hard just as 0fficer that was very
+ 
+
+ align:start position:0%
+very hard just as 0fficer that was very
+simply we use these definitions and say
+
+ align:start position:0%
+simply we use these definitions and say
+ 
+
+ align:start position:0%
+simply we use these definitions and say
+ok the transition probability out of s0
+
+ align:start position:0%
+ok the transition probability out of s0
+ 
+
+ align:start position:0%
+ok the transition probability out of s0
+to any note that's just so that we don't
+
+ align:start position:0%
+to any note that's just so that we don't
+ 
+
+ align:start position:0%
+to any note that's just so that we don't
+transition out all the policy based on
+
+ align:start position:0%
+transition out all the policy based on
+ 
+
+ align:start position:0%
+transition out all the policy based on
+holding a portion or spaceman
+
+ align:start position:0%
+holding a portion or spaceman
+ 
+
+ align:start position:0%
+holding a portion or spaceman
+and our work function were just applied
+
+ align:start position:0%
+and our work function were just applied
+ 
+
+ align:start position:0%
+and our work function were just applied
+to be a heuristic and I say that's
+
+ align:start position:0%
+to be a heuristic and I say that's
+ 
+
+ align:start position:0%
+to be a heuristic and I say that's
+plenty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last attitude evaluation on this
+
+ align:start position:0%
+last attitude evaluation on this
+ 
+
+ align:start position:0%
+last attitude evaluation on this
+combination this is a very very basic
+
+ align:start position:0%
+combination this is a very very basic
+ 
+
+ align:start position:0%
+combination this is a very very basic
+case we're just going to reason this to
+
+ align:start position:0%
+case we're just going to reason this to
+ 
+
+ align:start position:0%
+case we're just going to reason this to
+kind of building machinery understand
+
+ align:start position:0%
+kind of building machinery understand
+ 
+
+ align:start position:0%
+kind of building machinery understand
+what we're doing some very basic use for
+
+ align:start position:0%
+what we're doing some very basic use for
+ 
+
+ align:start position:0%
+what we're doing some very basic use for
+it you only know what happens I see
+
+ align:start position:0%
+it you only know what happens I see
+ 
+
+ align:start position:0%
+it you only know what happens I see
+arrow we can transition out of it all we
+
+ align:start position:0%
+arrow we can transition out of it all we
+ 
+
+ align:start position:0%
+arrow we can transition out of it all we
+have is some heuristic so the only thing
+
+ align:start position:0%
+have is some heuristic so the only thing
+ 
+
+ align:start position:0%
+have is some heuristic so the only thing
+we do is not somebody actually I take my
+
+ align:start position:0%
+we do is not somebody actually I take my
+ 
+
+ align:start position:0%
+we do is not somebody actually I take my
+festival is very simple case just to
+
+ align:start position:0%
+festival is very simple case just to
+ 
+
+ align:start position:0%
+festival is very simple case just to
+kind of get us warmed up understand
+
+ align:start position:0%
+kind of get us warmed up understand
+ 
+
+ align:start position:0%
+kind of get us warmed up understand
+what's happening
+
+ align:start position:0%
+what's happening
+ 
+
+ align:start position:0%
+what's happening
+so using this policy and knowing that
+
+ align:start position:0%
+so using this policy and knowing that
+ 
+
+ align:start position:0%
+so using this policy and knowing that
+best zeros in our terminal set we're
+
+ align:start position:0%
+best zeros in our terminal set we're
+ 
+
+ align:start position:0%
+best zeros in our terminal set we're
+going to take the intersection between
+
+ align:start position:0%
+going to take the intersection between
+ 
+
+ align:start position:0%
+going to take the intersection between
+this terminal mode set and the notice
+
+ align:start position:0%
+this terminal mode set and the notice
+ 
+
+ align:start position:0%
+this terminal mode set and the notice
+that we might reach out our policy now
+
+ align:start position:0%
+that we might reach out our policy now
+ 
+
+ align:start position:0%
+that we might reach out our policy now
+we know we're at zero the only actually
+
+ align:start position:0%
+we know we're at zero the only actually
+ 
+
+ align:start position:0%
+we know we're at zero the only actually
+the action that our that our optimal
+
+ align:start position:0%
+the action that our that our optimal
+ 
+
+ align:start position:0%
+the action that our that our optimal
+policy says to take it is not so we know
+
+ align:start position:0%
+policy says to take it is not so we know
+ 
+
+ align:start position:0%
+policy says to take it is not so we know
+we're there we know it's our terminal
+
+ align:start position:0%
+we're there we know it's our terminal
+ 
+
+ align:start position:0%
+we're there we know it's our terminal
+notice that so that's that's the only
+
+ align:start position:0%
+notice that so that's that's the only
+ 
+
+ align:start position:0%
+notice that so that's that's the only
+thing that we can reach so far so far so
+
+ align:start position:0%
+thing that we can reach so far so far so
+ 
+
+ align:start position:0%
+thing that we can reach so far so far so
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's exactly where accidentally
+
+ align:start position:0%
+so that's exactly where accidentally
+ 
+
+ align:start position:0%
+so that's exactly where accidentally
+just pretend xs0 today you can see those
+
+ align:start position:0%
+just pretend xs0 today you can see those
+ 
+
+ align:start position:0%
+just pretend xs0 today you can see those
+two are that's up there just a moment
+
+ align:start position:0%
+two are that's up there just a moment
+ 
+
+ align:start position:0%
+two are that's up there just a moment
+that zero from are several notes and
+
+ align:start position:0%
+that zero from are several notes and
+ 
+
+ align:start position:0%
+that zero from are several notes and
+it's children any other the children
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here we go we're going a little bit
+
+ align:start position:0%
+now here we go we're going a little bit
+ 
+
+ align:start position:0%
+now here we go we're going a little bit
+more the same thing again but I would
+
+ align:start position:0%
+more the same thing again but I would
+ 
+
+ align:start position:0%
+more the same thing again but I would
+obviously have more notes in a bigger
+
+ align:start position:0%
+obviously have more notes in a bigger
+ 
+
+ align:start position:0%
+obviously have more notes in a bigger
+subspace Explorer
+
+ align:start position:0%
+subspace Explorer
+ 
+
+ align:start position:0%
+subspace Explorer
+so using these definitions we see our
+
+ align:start position:0%
+so using these definitions we see our
+ 
+
+ align:start position:0%
+so using these definitions we see our
+work function is there's a tuple that we
+
+ align:start position:0%
+work function is there's a tuple that we
+ 
+
+ align:start position:0%
+work function is there's a tuple that we
+start promptly this is a zero and he's
+
+ align:start position:0%
+start promptly this is a zero and he's
+ 
+
+ align:start position:0%
+start promptly this is a zero and he's
+one of these reactions which they wanted
+
+ align:start position:0%
+one of these reactions which they wanted
+ 
+
+ align:start position:0%
+one of these reactions which they wanted
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+we have our instant nature or functions
+
+ align:start position:0%
+we have our instant nature or functions
+ 
+
+ align:start position:0%
+we have our instant nature or functions
+six more feet bigger rewards from taking
+
+ align:start position:0%
+six more feet bigger rewards from taking
+ 
+
+ align:start position:0%
+six more feet bigger rewards from taking
+those actions from a D&C
+
+ align:start position:0%
+those actions from a D&C
+ 
+
+ align:start position:0%
+those actions from a D&C
+and I actually think it's just the
+
+ align:start position:0%
+and I actually think it's just the
+ 
+
+ align:start position:0%
+and I actually think it's just the
+heuristic and likewise for distribution
+
+ align:start position:0%
+heuristic and likewise for distribution
+ 
+
+ align:start position:0%
+heuristic and likewise for distribution
+probability regions
+
+ align:start position:0%
+probability regions
+ 
+
+ align:start position:0%
+probability regions
+this is transitioning from estate
+
+ align:start position:0%
+this is transitioning from estate
+ 
+
+ align:start position:0%
+this is transitioning from estate
+investor we're saying if we take action
+
+ align:start position:0%
+investor we're saying if we take action
+ 
+
+ align:start position:0%
+investor we're saying if we take action
+a1 a2 and a3 what's the probability look
+
+ align:start position:0%
+a1 a2 and a3 what's the probability look
+ 
+
+ align:start position:0%
+a1 a2 and a3 what's the probability look
+so part here we're gonna look at
+
+ align:start position:0%
+so part here we're gonna look at
+ 
+
+ align:start position:0%
+so part here we're gonna look at
+something to take an action will end up
+
+ align:start position:0%
+something to take an action will end up
+ 
+
+ align:start position:0%
+something to take an action will end up
+our receiver united up and we'll see how
+
+ align:start position:0%
+our receiver united up and we'll see how
+ 
+
+ align:start position:0%
+our receiver united up and we'll see how
+this out that sort of collapses down to
+
+ align:start position:0%
+this out that sort of collapses down to
+ 
+
+ align:start position:0%
+this out that sort of collapses down to
+a star and everything else we're also
+
+ align:start position:0%
+a star and everything else we're also
+ 
+
+ align:start position:0%
+a star and everything else we're also
+obviously gonna look at the publicity is
+
+ align:start position:0%
+obviously gonna look at the publicity is
+ 
+
+ align:start position:0%
+obviously gonna look at the publicity is
+when we say move anyone within a small
+
+ align:start position:0%
+when we say move anyone within a small
+ 
+
+ align:start position:0%
+when we say move anyone within a small
+probability aw that's very necessary
+
+ align:start position:0%
+probability aw that's very necessary
+ 
+
+ align:start position:0%
+probability aw that's very necessary
+that we're gonna look at and expand be
+
+ align:start position:0%
+that we're gonna look at and expand be
+ 
+
+ align:start position:0%
+that we're gonna look at and expand be
+together besides we want to try it
+
+ align:start position:0%
+together besides we want to try it
+ 
+
+ align:start position:0%
+together besides we want to try it
+likewise if we tried to take action III
+
+ align:start position:0%
+likewise if we tried to take action III
+ 
+
+ align:start position:0%
+likewise if we tried to take action III
+we have this venom all three males
+
+ align:start position:0%
+we have this venom all three males
+ 
+
+ align:start position:0%
+we have this venom all three males
+the tighter the problem was the coupling
+
+ align:start position:0%
+the tighter the problem was the coupling
+ 
+
+ align:start position:0%
+the tighter the problem was the coupling
+the more distance perhaps more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just not this assuming that if you
+
+ align:start position:0%
+so just not this assuming that if you
+ 
+
+ align:start position:0%
+so just not this assuming that if you
+take action you want me to
+
+ align:start position:0%
+take action you want me to
+ 
+
+ align:start position:0%
+take action you want me to
+what could someone tell me about the
+
+ align:start position:0%
+what could someone tell me about the
+ 
+
+ align:start position:0%
+what could someone tell me about the
+policies that we have the rewards here
+
+ align:start position:0%
+policies that we have the rewards here
+ 
+
+ align:start position:0%
+policies that we have the rewards here
+range to be in the policy from s0
+
+ align:start position:0%
+range to be in the policy from s0
+ 
+
+ align:start position:0%
+range to be in the policy from s0
+take a minute to take over the rewards
+
+ align:start position:0%
+take a minute to take over the rewards
+ 
+
+ align:start position:0%
+take a minute to take over the rewards
+sort of just judge what the best action
+
+ align:start position:0%
+sort of just judge what the best action
+ 
+
+ align:start position:0%
+sort of just judge what the best action
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have the reward that you have gotten
+
+ align:start position:0%
+you have the reward that you have gotten
+ 
+
+ align:start position:0%
+you have the reward that you have gotten
+so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+does that help you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so the policy that one says from a zero
+
+ align:start position:0%
+so the policy that one says from a zero
+ 
+
+ align:start position:0%
+so the policy that one says from a zero
+take action k1 that's going to state
+
+ align:start position:0%
+take action k1 that's going to state
+ 
+
+ align:start position:0%
+take action k1 that's going to state
+you know just for fun
+
+ align:start position:0%
+you know just for fun
+ 
+
+ align:start position:0%
+you know just for fun
+and you can see there so much in the
+
+ align:start position:0%
+and you can see there so much in the
+ 
+
+ align:start position:0%
+and you can see there so much in the
+picture what that means is that the
+
+ align:start position:0%
+picture what that means is that the
+ 
+
+ align:start position:0%
+picture what that means is that the
+notes that we might reach that are in
+
+ align:start position:0%
+notes that we might reach that are in
+ 
+
+ align:start position:0%
+notes that we might reach that are in
+our terminal state except using our
+
+ align:start position:0%
+our terminal state except using our
+ 
+
+ align:start position:0%
+our terminal state except using our
+policy is no name so that's the note
+
+ align:start position:0%
+policy is no name so that's the note
+ 
+
+ align:start position:0%
+policy is no name so that's the note
+we're gonna expand and this is where you
+
+ align:start position:0%
+we're gonna expand and this is where you
+ 
+
+ align:start position:0%
+we're gonna expand and this is where you
+really really see all we've done is
+
+ align:start position:0%
+really really see all we've done is
+ 
+
+ align:start position:0%
+really really see all we've done is
+collapsed on the a star a star would say
+
+ align:start position:0%
+collapsed on the a star a star would say
+ 
+
+ align:start position:0%
+collapsed on the a star a star would say
+okay let's look at the best node using
+
+ align:start position:0%
+okay let's look at the best node using
+ 
+
+ align:start position:0%
+okay let's look at the best node using
+some heuristic actually one takes us to
+
+ align:start position:0%
+some heuristic actually one takes us to
+ 
+
+ align:start position:0%
+some heuristic actually one takes us to
+that festival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when everything's deterministic
+
+ align:start position:0%
+so when everything's deterministic
+ 
+
+ align:start position:0%
+so when everything's deterministic
+basically this algorithm collapse it
+
+ align:start position:0%
+basically this algorithm collapse it
+ 
+
+ align:start position:0%
+basically this algorithm collapse it
+down to a star and nothing super
+
+ align:start position:0%
+down to a star and nothing super
+ 
+
+ align:start position:0%
+down to a star and nothing super
+interesting the interesting case does
+
+ align:start position:0%
+interesting the interesting case does
+ 
+
+ align:start position:0%
+interesting the interesting case does
+come up to more pelvis and that's where
+
+ align:start position:0%
+come up to more pelvis and that's where
+ 
+
+ align:start position:0%
+come up to more pelvis and that's where
+nodes are publicly coupled in this and
+
+ align:start position:0%
+nodes are publicly coupled in this and
+ 
+
+ align:start position:0%
+nodes are publicly coupled in this and
+practices so now we have our policy
+
+ align:start position:0%
+practices so now we have our policy
+ 
+
+ align:start position:0%
+practices so now we have our policy
+policies reflected never being the same
+
+ align:start position:0%
+policies reflected never being the same
+ 
+
+ align:start position:0%
+policies reflected never being the same
+with edge actually like accidentally
+
+ align:start position:0%
+with edge actually like accidentally
+ 
+
+ align:start position:0%
+with edge actually like accidentally
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so what I want to look at is what birds
+
+ align:start position:0%
+so what I want to look at is what birds
+ 
+
+ align:start position:0%
+so what I want to look at is what birds
+are how reachable all around us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talked about that if we were to
+
+ align:start position:0%
+so we talked about that if we were to
+ 
+
+ align:start position:0%
+so we talked about that if we were to
+take actually we have some probability I
+
+ align:start position:0%
+take actually we have some probability I
+ 
+
+ align:start position:0%
+take actually we have some probability I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+so in 93 snakes
+
+ align:start position:0%
+so in 93 snakes
+ 
+
+ align:start position:0%
+so in 93 snakes
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+what's what's reachable take actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's where we get the notion
+
+ align:start position:0%
+and that's where we get the notion
+ 
+
+ align:start position:0%
+and that's where we get the notion
+this probabilistic company we're gonna
+
+ align:start position:0%
+this probabilistic company we're gonna
+ 
+
+ align:start position:0%
+this probabilistic company we're gonna
+expand things together
+
+ align:start position:0%
+expand things together
+ 
+
+ align:start position:0%
+expand things together
+I explore the part of the state space
+
+ align:start position:0%
+I explore the part of the state space
+ 
+
+ align:start position:0%
+I explore the part of the state space
+that we reach both by our optimal policy
+
+ align:start position:0%
+that we reach both by our optimal policy
+ 
+
+ align:start position:0%
+that we reach both by our optimal policy
+and that we might accidentally end up in
+
+ align:start position:0%
+and that we might accidentally end up in
+ 
+
+ align:start position:0%
+and that we might accidentally end up in
+if this is what guarantees that we'll
+
+ align:start position:0%
+if this is what guarantees that we'll
+ 
+
+ align:start position:0%
+if this is what guarantees that we'll
+have a manager to take from any state
+
+ align:start position:0%
+have a manager to take from any state
+ 
+
+ align:start position:0%
+have a manager to take from any state
+that we intend it to go to
+
+ align:start position:0%
+that we intend it to go to
+ 
+
+ align:start position:0%
+that we intend it to go to
+whether we might end up in probably
+
+ align:start position:0%
+whether we might end up in probably
+ 
+
+ align:start position:0%
+whether we might end up in probably
+that's that's how our state space
+
+ align:start position:0%
+that's that's how our state space
+ 
+
+ align:start position:0%
+that's that's how our state space
+expands our envelope expands to become
+
+ align:start position:0%
+expands our envelope expands to become
+ 
+
+ align:start position:0%
+expands our envelope expands to become
+there's only the reachable and
+
+ align:start position:0%
+there's only the reachable and
+ 
+
+ align:start position:0%
+there's only the reachable and
+interesting statistic it's not as simple
+
+ align:start position:0%
+interesting statistic it's not as simple
+ 
+
+ align:start position:0%
+interesting statistic it's not as simple
+as just expanding kind of the curious
+
+ align:start position:0%
+as just expanding kind of the curious
+ 
+
+ align:start position:0%
+as just expanding kind of the curious
+that like they start because we never
+
+ align:start position:0%
+that like they start because we never
+ 
+
+ align:start position:0%
+that like they start because we never
+table statement and you can see that if
+
+ align:start position:0%
+table statement and you can see that if
+ 
+
+ align:start position:0%
+table statement and you can see that if
+you have a tiger coupling and you're you
+
+ align:start position:0%
+you have a tiger coupling and you're you
+ 
+
+ align:start position:0%
+you have a tiger coupling and you're you
+don't get to exploit this optimization
+
+ align:start position:0%
+don't get to exploit this optimization
+ 
+
+ align:start position:0%
+don't get to exploit this optimization
+aspiration so for example a three we
+
+ align:start position:0%
+aspiration so for example a three we
+ 
+
+ align:start position:0%
+aspiration so for example a three we
+would have had to expand offerings as
+
+ align:start position:0%
+would have had to expand offerings as
+ 
+
+ align:start position:0%
+would have had to expand offerings as
+opposed to a one you can just speak to a
+
+ align:start position:0%
+opposed to a one you can just speak to a
+ 
+
+ align:start position:0%
+opposed to a one you can just speak to a
+more expensive register this is from a
+
+ align:start position:0%
+more expensive register this is from a
+ 
+
+ align:start position:0%
+more expensive register this is from a
+particular case a lot buddy firstly you
+
+ align:start position:0%
+particular case a lot buddy firstly you
+ 
+
+ align:start position:0%
+particular case a lot buddy firstly you
+know when
+
+ align:start position:0%
+know when
+ 
+
+ align:start position:0%
+know when
+the t-statistic mr. president
+
+ align:start position:0%
+the t-statistic mr. president
+ 
+
+ align:start position:0%
+the t-statistic mr. president
+so in this case when you meet Renee she
+
+ align:start position:0%
+so in this case when you meet Renee she
+ 
+
+ align:start position:0%
+so in this case when you meet Renee she
+was looking to be Prophet Ibrahim it's a
+
+ align:start position:0%
+was looking to be Prophet Ibrahim it's a
+ 
+
+ align:start position:0%
+was looking to be Prophet Ibrahim it's a
+good finish never say that we won't put
+
+ align:start position:0%
+good finish never say that we won't put
+ 
+
+ align:start position:0%
+good finish never say that we won't put
+the pistol sir 45 RBIs so in the
+
+ align:start position:0%
+the pistol sir 45 RBIs so in the
+ 
+
+ align:start position:0%
+the pistol sir 45 RBIs so in the
+complete sense of running this algorithm
+
+ align:start position:0%
+complete sense of running this algorithm
+ 
+
+ align:start position:0%
+complete sense of running this algorithm
+shouldn't print it because what if we do
+
+ align:start position:0%
+shouldn't print it because what if we do
+ 
+
+ align:start position:0%
+shouldn't print it because what if we do
+if we don't have that 2% chance to end
+
+ align:start position:0%
+if we don't have that 2% chance to end
+ 
+
+ align:start position:0%
+if we don't have that 2% chance to end
+up we need to have a policy for
+
+ align:start position:0%
+up we need to have a policy for
+ 
+
+ align:start position:0%
+up we need to have a policy for
+corrected
+
+ align:start position:0%
+corrected
+ 
+
+ align:start position:0%
+corrected
+right to the end of it you can imagine
+
+ align:start position:0%
+right to the end of it you can imagine
+ 
+
+ align:start position:0%
+right to the end of it you can imagine
+that these know try to push back
+
+ align:start position:0%
+that these know try to push back
+ 
+
+ align:start position:0%
+that these know try to push back
+whatever happens I suppose that the
+
+ align:start position:0%
+whatever happens I suppose that the
+ 
+
+ align:start position:0%
+whatever happens I suppose that the
+probability is low enough you can have
+
+ align:start position:0%
+probability is low enough you can have
+ 
+
+ align:start position:0%
+probability is low enough you can have
+some sort of cut off so just a quick
+
+ align:start position:0%
+some sort of cut off so just a quick
+ 
+
+ align:start position:0%
+some sort of cut off so just a quick
+point so I think that's an excellent
+
+ align:start position:0%
+point so I think that's an excellent
+ 
+
+ align:start position:0%
+point so I think that's an excellent
+point an excellent answer
+
+ align:start position:0%
+point an excellent answer
+ 
+
+ align:start position:0%
+point an excellent answer
+we're gonna talk about next week exactly
+
+ align:start position:0%
+we're gonna talk about next week exactly
+ 
+
+ align:start position:0%
+we're gonna talk about next week exactly
+what's gonna happen if you can prove
+
+ align:start position:0%
+what's gonna happen if you can prove
+ 
+
+ align:start position:0%
+what's gonna happen if you can prove
+sort of lower power ability events and
+
+ align:start position:0%
+sort of lower power ability events and
+ 
+
+ align:start position:0%
+sort of lower power ability events and
+actually tape it right here will be
+
+ align:start position:0%
+actually tape it right here will be
+ 
+
+ align:start position:0%
+actually tape it right here will be
+lecturing on good question
+
+ align:start position:0%
+lecturing on good question
+ 
+
+ align:start position:0%
+lecturing on good question
+that sort of also gets us into the sense
+
+ align:start position:0%
+that sort of also gets us into the sense
+ 
+
+ align:start position:0%
+that sort of also gets us into the sense
+that if kind of every state in the world
+
+ align:start position:0%
+that if kind of every state in the world
+ 
+
+ align:start position:0%
+that if kind of every state in the world
+were probabilistic ly coupled let's say
+
+ align:start position:0%
+were probabilistic ly coupled let's say
+ 
+
+ align:start position:0%
+were probabilistic ly coupled let's say
+we got some transporter
+
+ align:start position:0%
+we got some transporter
+ 
+
+ align:start position:0%
+we got some transporter
+start represented we if we had this
+
+ align:start position:0%
+start represented we if we had this
+ 
+
+ align:start position:0%
+start represented we if we had this
+transported that non-deterministic we
+
+ align:start position:0%
+transported that non-deterministic we
+ 
+
+ align:start position:0%
+transported that non-deterministic we
+put us in any state in the world we have
+
+ align:start position:0%
+put us in any state in the world we have
+ 
+
+ align:start position:0%
+put us in any state in the world we have
+to explore because
+
+ align:start position:0%
+to explore because
+ 
+
+ align:start position:0%
+to explore because
+so publicly that's not the case yet we
+
+ align:start position:0%
+so publicly that's not the case yet we
+ 
+
+ align:start position:0%
+so publicly that's not the case yet we
+did kind of take advantage of the fact
+
+ align:start position:0%
+did kind of take advantage of the fact
+ 
+
+ align:start position:0%
+did kind of take advantage of the fact
+we might end up or most likely where we
+
+ align:start position:0%
+we might end up or most likely where we
+ 
+
+ align:start position:0%
+we might end up or most likely where we
+commanded with some probability this
+
+ align:start position:0%
+commanded with some probability this
+ 
+
+ align:start position:0%
+commanded with some probability this
+exactly what we just talked about couple
+
+ align:start position:0%
+exactly what we just talked about couple
+ 
+
+ align:start position:0%
+exactly what we just talked about couple
+these big no to this and inch let me
+
+ align:start position:0%
+these big no to this and inch let me
+ 
+
+ align:start position:0%
+these big no to this and inch let me
+expand those two does everyone
+
+ align:start position:0%
+expand those two does everyone
+ 
+
+ align:start position:0%
+expand those two does everyone
+understand people the intuition and the
+
+ align:start position:0%
+understand people the intuition and the
+ 
+
+ align:start position:0%
+understand people the intuition and the
+logic for why both of them happen even
+
+ align:start position:0%
+logic for why both of them happen even
+ 
+
+ align:start position:0%
+logic for why both of them happen even
+if there's only a small problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what we're going to repeat
+
+ align:start position:0%
+so this is what we're going to repeat
+ 
+
+ align:start position:0%
+so this is what we're going to repeat
+until dark spaces now you can imagine
+
+ align:start position:0%
+until dark spaces now you can imagine
+ 
+
+ align:start position:0%
+until dark spaces now you can imagine
+that the next time we brought in our
+
+ align:start position:0%
+that the next time we brought in our
+ 
+
+ align:start position:0%
+that the next time we brought in our
+evaluation we're now running it on all
+
+ align:start position:0%
+evaluation we're now running it on all
+ 
+
+ align:start position:0%
+evaluation we're now running it on all
+of these colored things go back we could
+
+ align:start position:0%
+of these colored things go back we could
+ 
+
+ align:start position:0%
+of these colored things go back we could
+imagine the next time now that we have a
+
+ align:start position:0%
+imagine the next time now that we have a
+ 
+
+ align:start position:0%
+imagine the next time now that we have a
+little bit more information what lies
+
+ align:start position:0%
+little bit more information what lies
+ 
+
+ align:start position:0%
+little bit more information what lies
+beyond a and B that our policy might say
+
+ align:start position:0%
+beyond a and B that our policy might say
+ 
+
+ align:start position:0%
+beyond a and B that our policy might say
+oh you know I actually from s0 see like
+
+ align:start position:0%
+oh you know I actually from s0 see like
+ 
+
+ align:start position:0%
+oh you know I actually from s0 see like
+action a3 was the best today what that
+
+ align:start position:0%
+action a3 was the best today what that
+ 
+
+ align:start position:0%
+action a3 was the best today what that
+does those move into the next part of
+
+ align:start position:0%
+does those move into the next part of
+ 
+
+ align:start position:0%
+does those move into the next part of
+the subspace that as we gain more
+
+ align:start position:0%
+the subspace that as we gain more
+ 
+
+ align:start position:0%
+the subspace that as we gain more
+information about Steve that's a good
+
+ align:start position:0%
+information about Steve that's a good
+ 
+
+ align:start position:0%
+information about Steve that's a good
+question when we did I try run about
+
+ align:start position:0%
+question when we did I try run about
+ 
+
+ align:start position:0%
+question when we did I try run about
+whether there is sort of a way to save
+
+ align:start position:0%
+whether there is sort of a way to save
+ 
+
+ align:start position:0%
+whether there is sort of a way to save
+on the computation you didn't primerica
+
+ align:start position:0%
+on the computation you didn't primerica
+ 
+
+ align:start position:0%
+on the computation you didn't primerica
+value iteration and these locations and
+
+ align:start position:0%
+value iteration and these locations and
+ 
+
+ align:start position:0%
+value iteration and these locations and
+we have we've looked at it a little bit
+
+ align:start position:0%
+we have we've looked at it a little bit
+ 
+
+ align:start position:0%
+we have we've looked at it a little bit
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+I sleep some stuff but not I haven't got
+
+ align:start position:0%
+I sleep some stuff but not I haven't got
+ 
+
+ align:start position:0%
+I sleep some stuff but not I haven't got
+a paper that specifically things but you
+
+ align:start position:0%
+a paper that specifically things but you
+ 
+
+ align:start position:0%
+a paper that specifically things but you
+can imagine how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you already run value duration like a
+
+ align:start position:0%
+you already run value duration like a
+ 
+
+ align:start position:0%
+you already run value duration like a
+previous iteration you add the new
+
+ align:start position:0%
+previous iteration you add the new
+ 
+
+ align:start position:0%
+previous iteration you add the new
+terminal life of such an expanded ID you
+
+ align:start position:0%
+terminal life of such an expanded ID you
+ 
+
+ align:start position:0%
+terminal life of such an expanded ID you
+run it again until it stabilizes now
+
+ align:start position:0%
+run it again until it stabilizes now
+ 
+
+ align:start position:0%
+run it again until it stabilizes now
+when you've saved accommodation having
+
+ align:start position:0%
+when you've saved accommodation having
+ 
+
+ align:start position:0%
+when you've saved accommodation having
+to run valuations and multiple times so
+
+ align:start position:0%
+to run valuations and multiple times so
+ 
+
+ align:start position:0%
+to run valuations and multiple times so
+I'm trying to think of how this is
+
+ align:start position:0%
+I'm trying to think of how this is
+ 
+
+ align:start position:0%
+I'm trying to think of how this is
+different from something like in funding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I don't know enough about that
+
+ align:start position:0%
+I think I don't know enough about that
+ 
+
+ align:start position:0%
+I think I don't know enough about that
+but maybe I kind of basic understanding
+
+ align:start position:0%
+but maybe I kind of basic understanding
+ 
+
+ align:start position:0%
+but maybe I kind of basic understanding
+says that what's what's useful here is
+
+ align:start position:0%
+says that what's what's useful here is
+ 
+
+ align:start position:0%
+says that what's what's useful here is
+kind of the it's this explicit problem I
+
+ align:start position:0%
+kind of the it's this explicit problem I
+ 
+
+ align:start position:0%
+kind of the it's this explicit problem I
+don't know how much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also as long as your jurisdictions
+
+ align:start position:0%
+and also as long as your jurisdictions
+ 
+
+ align:start position:0%
+and also as long as your jurisdictions
+admissible it's guaranteed optimality
+
+ align:start position:0%
+admissible it's guaranteed optimality
+ 
+
+ align:start position:0%
+admissible it's guaranteed optimality
+with not all filled by monoculars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right just like they start as optimal as
+
+ align:start position:0%
+right just like they start as optimal as
+ 
+
+ align:start position:0%
+right just like they start as optimal as
+long as you're consistent right so
+
+ align:start position:0%
+long as you're consistent right so
+ 
+
+ align:start position:0%
+long as you're consistent right so
+that's definitely every couple days and
+
+ align:start position:0%
+that's definitely every couple days and
+ 
+
+ align:start position:0%
+that's definitely every couple days and
+we only explore the portion of the state
+
+ align:start position:0%
+we only explore the portion of the state
+ 
+
+ align:start position:0%
+we only explore the portion of the state
+space that will reach an optimum
+
+ align:start position:0%
+space that will reach an optimum
+ 
+
+ align:start position:0%
+space that will reach an optimum
+possible mm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll talk about quickly determination
+
+ align:start position:0%
+we'll talk about quickly determination
+ 
+
+ align:start position:0%
+we'll talk about quickly determination
+we've touched on most of us so it's most
+
+ align:start position:0%
+we've touched on most of us so it's most
+ 
+
+ align:start position:0%
+we've touched on most of us so it's most
+most likely when there are no more
+
+ align:start position:0%
+most likely when there are no more
+ 
+
+ align:start position:0%
+most likely when there are no more
+states expands when we've reached our
+
+ align:start position:0%
+states expands when we've reached our
+ 
+
+ align:start position:0%
+states expands when we've reached our
+goal it's when our policy that we run on
+
+ align:start position:0%
+goal it's when our policy that we run on
+ 
+
+ align:start position:0%
+goal it's when our policy that we run on
+our entire envelope from value variation
+
+ align:start position:0%
+our entire envelope from value variation
+ 
+
+ align:start position:0%
+our entire envelope from value variation
+it doesn't say that we should go to
+
+ align:start position:0%
+it doesn't say that we should go to
+ 
+
+ align:start position:0%
+it doesn't say that we should go to
+anymore we've said that those are only
+
+ align:start position:0%
+anymore we've said that those are only
+ 
+
+ align:start position:0%
+anymore we've said that those are only
+the things that are reachable and need
+
+ align:start position:0%
+the things that are reachable and need
+ 
+
+ align:start position:0%
+the things that are reachable and need
+both reachable because frivolity not on
+
+ align:start position:0%
+both reachable because frivolity not on
+ 
+
+ align:start position:0%
+both reachable because frivolity not on
+policy and needed own polling if we
+
+ align:start position:0%
+policy and needed own polling if we
+ 
+
+ align:start position:0%
+policy and needed own polling if we
+might accidentally another missus gives
+
+ align:start position:0%
+might accidentally another missus gives
+ 
+
+ align:start position:0%
+might accidentally another missus gives
+us the sense of business policy on the
+
+ align:start position:0%
+us the sense of business policy on the
+ 
+
+ align:start position:0%
+us the sense of business policy on the
+entire state space that we can end up in
+
+ align:start position:0%
+entire state space that we can end up in
+ 
+
+ align:start position:0%
+entire state space that we can end up in
+and following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the third bullet here touches on
+
+ align:start position:0%
+because the third bullet here touches on
+ 
+
+ align:start position:0%
+because the third bullet here touches on
+if you don't expand the states are
+
+ align:start position:0%
+if you don't expand the states are
+ 
+
+ align:start position:0%
+if you don't expand the states are
+probabilistic we coupled and we do
+
+ align:start position:0%
+probabilistic we coupled and we do
+ 
+
+ align:start position:0%
+probabilistic we coupled and we do
+accidentally end up there we risk
+
+ align:start position:0%
+accidentally end up there we risk
+ 
+
+ align:start position:0%
+accidentally end up there we risk
+getting lost they're not happy
+
+ align:start position:0%
+getting lost they're not happy
+ 
+
+ align:start position:0%
+getting lost they're not happy
+impossible we can compute this all
+
+ align:start position:0%
+impossible we can compute this all
+ 
+
+ align:start position:0%
+impossible we can compute this all
+offline and have a plan before we can
+
+ align:start position:0%
+offline and have a plan before we can
+ 
+
+ align:start position:0%
+offline and have a plan before we can
+start applying to know exactly where we
+
+ align:start position:0%
+start applying to know exactly where we
+ 
+
+ align:start position:0%
+start applying to know exactly where we
+want to go even if our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come back to this this was our
+
+ align:start position:0%
+come back to this this was our
+ 
+
+ align:start position:0%
+come back to this this was our
+motivating
+
+ align:start position:0%
+motivating
+ 
+
+ align:start position:0%
+motivating
+and so we show that these drill
+
+ align:start position:0%
+and so we show that these drill
+ 
+
+ align:start position:0%
+and so we show that these drill
+platforms can be models by casting we
+
+ align:start position:0%
+platforms can be models by casting we
+ 
+
+ align:start position:0%
+platforms can be models by casting we
+know we didn't pretty easily deal search
+
+ align:start position:0%
+know we didn't pretty easily deal search
+ 
+
+ align:start position:0%
+know we didn't pretty easily deal search
+our students base and deal with those
+
+ align:start position:0%
+our students base and deal with those
+ 
+
+ align:start position:0%
+our students base and deal with those
+probabilities and expand you know that
+
+ align:start position:0%
+probabilities and expand you know that
+ 
+
+ align:start position:0%
+probabilities and expand you know that
+we might end up and that heuristic
+
+ align:start position:0%
+we might end up and that heuristic
+ 
+
+ align:start position:0%
+we might end up and that heuristic
+allows us to not have to explore an area
+
+ align:start position:0%
+allows us to not have to explore an area
+ 
+
+ align:start position:0%
+allows us to not have to explore an area
+we might never actually end up there
+
+ align:start position:0%
+we might never actually end up there
+ 
+
+ align:start position:0%
+we might never actually end up there
+will always be commanding 477 that's out
+
+ align:start position:0%
+will always be commanding 477 that's out
+ 
+
+ align:start position:0%
+will always be commanding 477 that's out
+we're never going to try to think about
+
+ align:start position:0%
+we're never going to try to think about
+ 
+
+ align:start position:0%
+we're never going to try to think about
+sure if there's a custom
+
+ align:start position:0%
+sure if there's a custom
+ 
+
+ align:start position:0%
+sure if there's a custom
+we have some probability there but you
+
+ align:start position:0%
+we have some probability there but you
+ 
+
+ align:start position:0%
+we have some probability there but you
+can imagine the movies for a small
+
+ align:start position:0%
+can imagine the movies for a small
+ 
+
+ align:start position:0%
+can imagine the movies for a small
+portion of this because we'll always try
+
+ align:start position:0%
+portion of this because we'll always try
+ 
+
+ align:start position:0%
+portion of this because we'll always try
+to be trying to correct to get back to
+
+ align:start position:0%
+to be trying to correct to get back to
+ 
+
+ align:start position:0%
+to be trying to correct to get back to
+the top sometimes and with using our
+
+ align:start position:0%
+the top sometimes and with using our
+ 
+
+ align:start position:0%
+the top sometimes and with using our
+reward function we get to determine
+
+ align:start position:0%
+reward function we get to determine
+ 
+
+ align:start position:0%
+reward function we get to determine
+if you want to buy a quick bath or if
+
+ align:start position:0%
+if you want to buy a quick bath or if
+ 
+
+ align:start position:0%
+if you want to buy a quick bath or if
+you want to fly a safer path for example
+
+ align:start position:0%
+you want to fly a safer path for example
+ 
+
+ align:start position:0%
+you want to fly a safer path for example
+our time times are probably perhaps
+
+ align:start position:0%
+our time times are probably perhaps
+ 
+
+ align:start position:0%
+our time times are probably perhaps
+reduce them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right are there any questions about
+
+ align:start position:0%
+all right are there any questions about
+ 
+
+ align:start position:0%
+all right are there any questions about
+planning with MVPs I love this stuff hi
+
+ align:start position:0%
+planning with MVPs I love this stuff hi
+ 
+
+ align:start position:0%
+planning with MVPs I love this stuff hi
+what I'm going to be talking about for
+
+ align:start position:0%
+what I'm going to be talking about for
+ 
+
+ align:start position:0%
+what I'm going to be talking about for
+the rest of this lecture is extending
+
+ align:start position:0%
+the rest of this lecture is extending
+ 
+
+ align:start position:0%
+the rest of this lecture is extending
+beyond MVPs to a broader climate
+
+ align:start position:0%
+beyond MVPs to a broader climate
+ 
+
+ align:start position:0%
+beyond MVPs to a broader climate
+problems called funky keys partially
+
+ align:start position:0%
+problems called funky keys partially
+ 
+
+ align:start position:0%
+problems called funky keys partially
+observable Markov decision processes I
+
+ align:start position:0%
+observable Markov decision processes I
+ 
+
+ align:start position:0%
+observable Markov decision processes I
+love this stuff I think it's really cool
+
+ align:start position:0%
+love this stuff I think it's really cool
+ 
+
+ align:start position:0%
+love this stuff I think it's really cool
+they're really fun problems we're going
+
+ align:start position:0%
+they're really fun problems we're going
+ 
+
+ align:start position:0%
+they're really fun problems we're going
+to talk about that why there's so much
+
+ align:start position:0%
+to talk about that why there's so much
+ 
+
+ align:start position:0%
+to talk about that why there's so much
+harder to plan with executable but why
+
+ align:start position:0%
+harder to plan with executable but why
+ 
+
+ align:start position:0%
+harder to plan with executable but why
+they're important to at least know about
+
+ align:start position:0%
+they're important to at least know about
+ 
+
+ align:start position:0%
+they're important to at least know about
+it you can model real world problems
+
+ align:start position:0%
+it you can model real world problems
+ 
+
+ align:start position:0%
+it you can model real world problems
+whatever and then we're going to delve
+
+ align:start position:0%
+whatever and then we're going to delve
+ 
+
+ align:start position:0%
+whatever and then we're going to delve
+into a case study of a specific punky
+
+ align:start position:0%
+into a case study of a specific punky
+ 
+
+ align:start position:0%
+into a case study of a specific punky
+peach solver we're not going to go into
+
+ align:start position:0%
+peach solver we're not going to go into
+ 
+
+ align:start position:0%
+peach solver we're not going to go into
+as much detail as we did for MVPs but
+
+ align:start position:0%
+as much detail as we did for MVPs but
+ 
+
+ align:start position:0%
+as much detail as we did for MVPs but
+we're going to look at what powerful
+
+ align:start position:0%
+we're going to look at what powerful
+ 
+
+ align:start position:0%
+we're going to look at what powerful
+results we get by planning with pumpkins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first I want to reframe this in the
+
+ align:start position:0%
+so first I want to reframe this in the
+ 
+
+ align:start position:0%
+so first I want to reframe this in the
+overall job right we have this spectrum
+
+ align:start position:0%
+overall job right we have this spectrum
+ 
+
+ align:start position:0%
+overall job right we have this spectrum
+planner and me and a couple with
+
+ align:start position:0%
+planner and me and a couple with
+ 
+
+ align:start position:0%
+planner and me and a couple with
+uncertainty is difficulty of planning
+
+ align:start position:0%
+uncertainty is difficulty of planning
+ 
+
+ align:start position:0%
+uncertainty is difficulty of planning
+from solving of executed problem I mean
+
+ align:start position:0%
+from solving of executed problem I mean
+ 
+
+ align:start position:0%
+from solving of executed problem I mean
+I even killed these first two days love
+
+ align:start position:0%
+I even killed these first two days love
+ 
+
+ align:start position:0%
+I even killed these first two days love
+is really just discusses the body and
+
+ align:start position:0%
+is really just discusses the body and
+ 
+
+ align:start position:0%
+is really just discusses the body and
+what I'm going to talk about is the case
+
+ align:start position:0%
+what I'm going to talk about is the case
+ 
+
+ align:start position:0%
+what I'm going to talk about is the case
+when both your dynamics and your sensors
+
+ align:start position:0%
+when both your dynamics and your sensors
+ 
+
+ align:start position:0%
+when both your dynamics and your sensors
+are stochastic why is that important
+
+ align:start position:0%
+are stochastic why is that important
+ 
+
+ align:start position:0%
+are stochastic why is that important
+it's because when we first saw this
+
+ align:start position:0%
+it's because when we first saw this
+ 
+
+ align:start position:0%
+it's because when we first saw this
+slide our motivating example slide we
+
+ align:start position:0%
+slide our motivating example slide we
+ 
+
+ align:start position:0%
+slide our motivating example slide we
+only saw the left-hand side we said our
+
+ align:start position:0%
+only saw the left-hand side we said our
+ 
+
+ align:start position:0%
+only saw the left-hand side we said our
+actions aren't certain but good news we
+
+ align:start position:0%
+actions aren't certain but good news we
+ 
+
+ align:start position:0%
+actions aren't certain but good news we
+have a perfect sense of nool imperfect
+
+ align:start position:0%
+have a perfect sense of nool imperfect
+ 
+
+ align:start position:0%
+have a perfect sense of nool imperfect
+in camera but that's unrealistic I think
+
+ align:start position:0%
+in camera but that's unrealistic I think
+ 
+
+ align:start position:0%
+in camera but that's unrealistic I think
+we've all to some extent experience the
+
+ align:start position:0%
+we've all to some extent experience the
+ 
+
+ align:start position:0%
+we've all to some extent experience the
+fact that no sensor is totally perfect
+
+ align:start position:0%
+fact that no sensor is totally perfect
+ 
+
+ align:start position:0%
+fact that no sensor is totally perfect
+your camera might have a fluctuating
+
+ align:start position:0%
+your camera might have a fluctuating
+ 
+
+ align:start position:0%
+your camera might have a fluctuating
+pixel values by your laser range finder
+
+ align:start position:0%
+pixel values by your laser range finder
+ 
+
+ align:start position:0%
+pixel values by your laser range finder
+is gonna never beat out exactly the
+
+ align:start position:0%
+is gonna never beat out exactly the
+ 
+
+ align:start position:0%
+is gonna never beat out exactly the
+right number all the time you can have a
+
+ align:start position:0%
+right number all the time you can have a
+ 
+
+ align:start position:0%
+right number all the time you can have a
+camera different lighting conditions
+
+ align:start position:0%
+camera different lighting conditions
+ 
+
+ align:start position:0%
+camera different lighting conditions
+that would be different you might not be
+
+ align:start position:0%
+that would be different you might not be
+ 
+
+ align:start position:0%
+that would be different you might not be
+able to observe your full state that's
+
+ align:start position:0%
+able to observe your full state that's
+ 
+
+ align:start position:0%
+able to observe your full state that's
+in a way than in perfect sense it right
+
+ align:start position:0%
+in a way than in perfect sense it right
+ 
+
+ align:start position:0%
+in a way than in perfect sense it right
+if I'm in this room I have imperfect
+
+ align:start position:0%
+if I'm in this room I have imperfect
+ 
+
+ align:start position:0%
+if I'm in this room I have imperfect
+eyes idea to map out all of mi t--'s
+
+ align:start position:0%
+eyes idea to map out all of mi t--'s
+ 
+
+ align:start position:0%
+eyes idea to map out all of mi t--'s
+campus because I'm blocked by Wallace
+
+ align:start position:0%
+campus because I'm blocked by Wallace
+ 
+
+ align:start position:0%
+campus because I'm blocked by Wallace
+how do you deal with the fact that you
+
+ align:start position:0%
+how do you deal with the fact that you
+ 
+
+ align:start position:0%
+how do you deal with the fact that you
+can see under obstacles all the time
+
+ align:start position:0%
+can see under obstacles all the time
+ 
+
+ align:start position:0%
+can see under obstacles all the time
+we've already talked about some cases
+
+ align:start position:0%
+we've already talked about some cases
+ 
+
+ align:start position:0%
+we've already talked about some cases
+there are some algorithms that can help
+
+ align:start position:0%
+there are some algorithms that can help
+ 
+
+ align:start position:0%
+there are some algorithms that can help
+us with that mcdee starlight but can you
+
+ align:start position:0%
+us with that mcdee starlight but can you
+ 
+
+ align:start position:0%
+us with that mcdee starlight but can you
+reason about these things probabilistic
+
+ align:start position:0%
+reason about these things probabilistic
+ 
+
+ align:start position:0%
+reason about these things probabilistic
+and then finally you might be in a non
+
+ align:start position:0%
+and then finally you might be in a non
+ 
+
+ align:start position:0%
+and then finally you might be in a non
+unique environment where you cannot
+
+ align:start position:0%
+unique environment where you cannot
+ 
+
+ align:start position:0%
+unique environment where you cannot
+resolve their statement with certainty
+
+ align:start position:0%
+resolve their statement with certainty
+ 
+
+ align:start position:0%
+resolve their statement with certainty
+no matter how good your sensors are
+
+ align:start position:0%
+no matter how good your sensors are
+ 
+
+ align:start position:0%
+no matter how good your sensors are
+imagine you're in a building two
+
+ align:start position:0%
+imagine you're in a building two
+ 
+
+ align:start position:0%
+imagine you're in a building two
+identical hallways you're dropped off in
+
+ align:start position:0%
+identical hallways you're dropped off in
+ 
+
+ align:start position:0%
+identical hallways you're dropped off in
+one of them how can you result how can
+
+ align:start position:0%
+one of them how can you result how can
+ 
+
+ align:start position:0%
+one of them how can you result how can
+you figure out where you are American
+
+ align:start position:0%
+you figure out where you are American
+ 
+
+ align:start position:0%
+you figure out where you are American
+unless you start exploring and so we've
+
+ align:start position:0%
+unless you start exploring and so we've
+ 
+
+ align:start position:0%
+unless you start exploring and so we've
+got to deal with this uncertainty right
+
+ align:start position:0%
+got to deal with this uncertainty right
+ 
+
+ align:start position:0%
+got to deal with this uncertainty right
+it's part of every single problem and
+
+ align:start position:0%
+it's part of every single problem and
+ 
+
+ align:start position:0%
+it's part of every single problem and
+just like when observational uncertainty
+
+ align:start position:0%
+just like when observational uncertainty
+ 
+
+ align:start position:0%
+just like when observational uncertainty
+is small you may be ignore it
+
+ align:start position:0%
+is small you may be ignore it
+ 
+
+ align:start position:0%
+is small you may be ignore it
+but it's there and so we're gonna
+
+ align:start position:0%
+but it's there and so we're gonna
+ 
+
+ align:start position:0%
+but it's there and so we're gonna
+formulate this as a pom DP a partially
+
+ align:start position:0%
+formulate this as a pom DP a partially
+ 
+
+ align:start position:0%
+formulate this as a pom DP a partially
+observable Markov decision process and
+
+ align:start position:0%
+observable Markov decision process and
+ 
+
+ align:start position:0%
+observable Markov decision process and
+this next slide is just like the MVP
+
+ align:start position:0%
+this next slide is just like the MVP
+ 
+
+ align:start position:0%
+this next slide is just like the MVP
+slide parry but importantly right we can
+
+ align:start position:0%
+slide parry but importantly right we can
+ 
+
+ align:start position:0%
+slide parry but importantly right we can
+formulate upon DP with seven elements an
+
+ align:start position:0%
+formulate upon DP with seven elements an
+ 
+
+ align:start position:0%
+formulate upon DP with seven elements an
+MVP to five right most of them or all of
+
+ align:start position:0%
+MVP to five right most of them or all of
+ 
+
+ align:start position:0%
+MVP to five right most of them or all of
+those are carried over here we've got
+
+ align:start position:0%
+those are carried over here we've got
+ 
+
+ align:start position:0%
+those are carried over here we've got
+our set of states where maybe you've got
+
+ align:start position:0%
+our set of states where maybe you've got
+ 
+
+ align:start position:0%
+our set of states where maybe you've got
+a set of actions what we can do we've
+
+ align:start position:0%
+a set of actions what we can do we've
+ 
+
+ align:start position:0%
+a set of actions what we can do we've
+got our transition model which says
+
+ align:start position:0%
+got our transition model which says
+ 
+
+ align:start position:0%
+got our transition model which says
+given that I started in one state and
+
+ align:start position:0%
+given that I started in one state and
+ 
+
+ align:start position:0%
+given that I started in one state and
+then I took an action what's the
+
+ align:start position:0%
+then I took an action what's the
+ 
+
+ align:start position:0%
+then I took an action what's the
+probability I end up somewhere else and
+
+ align:start position:0%
+probability I end up somewhere else and
+ 
+
+ align:start position:0%
+probability I end up somewhere else and
+like David was talking about
+
+ align:start position:0%
+like David was talking about
+ 
+
+ align:start position:0%
+like David was talking about
+hopefully that distribution is pretty
+
+ align:start position:0%
+hopefully that distribution is pretty
+ 
+
+ align:start position:0%
+hopefully that distribution is pretty
+local we're not teleporting all over the
+
+ align:start position:0%
+local we're not teleporting all over the
+ 
+
+ align:start position:0%
+local we're not teleporting all over the
+world we've got a reward function this
+
+ align:start position:0%
+world we've got a reward function this
+ 
+
+ align:start position:0%
+world we've got a reward function this
+is exactly the same for MVPs and you've
+
+ align:start position:0%
+is exactly the same for MVPs and you've
+ 
+
+ align:start position:0%
+is exactly the same for MVPs and you've
+got a discount pack down here is these
+
+ align:start position:0%
+got a discount pack down here is these
+ 
+
+ align:start position:0%
+got a discount pack down here is these
+two elements the set of possible
+
+ align:start position:0%
+two elements the set of possible
+ 
+
+ align:start position:0%
+two elements the set of possible
+observations in a probabilistic model
+
+ align:start position:0%
+observations in a probabilistic model
+ 
+
+ align:start position:0%
+observations in a probabilistic model
+for the probability of making an
+
+ align:start position:0%
+for the probability of making an
+ 
+
+ align:start position:0%
+for the probability of making an
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+given your state than the action you
+
+ align:start position:0%
+given your state than the action you
+ 
+
+ align:start position:0%
+given your state than the action you
+just Tucker and now it's important I
+
+ align:start position:0%
+just Tucker and now it's important I
+ 
+
+ align:start position:0%
+just Tucker and now it's important I
+think it matches up really well with
+
+ align:start position:0%
+think it matches up really well with
+ 
+
+ align:start position:0%
+think it matches up really well with
+real-world sensors having this
+
+ align:start position:0%
+real-world sensors having this
+ 
+
+ align:start position:0%
+real-world sensors having this
+probabilistic model if you have a laser
+
+ align:start position:0%
+probabilistic model if you have a laser
+ 
+
+ align:start position:0%
+probabilistic model if you have a laser
+rangefinder for example and you're
+
+ align:start position:0%
+rangefinder for example and you're
+ 
+
+ align:start position:0%
+rangefinder for example and you're
+standing one foot away from the wall now
+
+ align:start position:0%
+standing one foot away from the wall now
+ 
+
+ align:start position:0%
+standing one foot away from the wall now
+a perfect sensor would always say you're
+
+ align:start position:0%
+a perfect sensor would always say you're
+ 
+
+ align:start position:0%
+a perfect sensor would always say you're
+one foot away from the wall you're one
+
+ align:start position:0%
+one foot away from the wall you're one
+ 
+
+ align:start position:0%
+one foot away from the wall you're one
+foot away from whatever live in the
+
+ align:start position:0%
+foot away from whatever live in the
+ 
+
+ align:start position:0%
+foot away from whatever live in the
+moment every single reading is constant
+
+ align:start position:0%
+moment every single reading is constant
+ 
+
+ align:start position:0%
+moment every single reading is constant
+but realistically they might be Gaussian
+
+ align:start position:0%
+but realistically they might be Gaussian
+ 
+
+ align:start position:0%
+but realistically they might be Gaussian
+noise for example or at a more extreme
+
+ align:start position:0%
+noise for example or at a more extreme
+ 
+
+ align:start position:0%
+noise for example or at a more extreme
+case it says you're one foot away from
+
+ align:start position:0%
+case it says you're one foot away from
+ 
+
+ align:start position:0%
+case it says you're one foot away from
+the wall you're two feet there right
+
+ align:start position:0%
+the wall you're two feet there right
+ 
+
+ align:start position:0%
+the wall you're two feet there right
+there there's this distribution and so
+
+ align:start position:0%
+there there's this distribution and so
+ 
+
+ align:start position:0%
+there there's this distribution and so
+you would ideally characterize that
+
+ align:start position:0%
+you would ideally characterize that
+ 
+
+ align:start position:0%
+you would ideally characterize that
+distribution and you plug that into this
+
+ align:start position:0%
+distribution and you plug that into this
+ 
+
+ align:start position:0%
+distribution and you plug that into this
+model and that formula is your monkey
+
+ align:start position:0%
+model and that formula is your monkey
+ 
+
+ align:start position:0%
+model and that formula is your monkey
+this sounds really hairy but it can work
+
+ align:start position:0%
+this sounds really hairy but it can work
+ 
+
+ align:start position:0%
+this sounds really hairy but it can work
+through just sort of a sample iteration
+
+ align:start position:0%
+through just sort of a sample iteration
+ 
+
+ align:start position:0%
+through just sort of a sample iteration
+of them living in a pom beauty world
+
+ align:start position:0%
+of them living in a pom beauty world
+ 
+
+ align:start position:0%
+of them living in a pom beauty world
+it's not too bad you start at some state
+
+ align:start position:0%
+it's not too bad you start at some state
+ 
+
+ align:start position:0%
+it's not too bad you start at some state
+s take an action a with some probability
+
+ align:start position:0%
+s take an action a with some probability
+ 
+
+ align:start position:0%
+s take an action a with some probability
+you're gonna end up in a bunch of
+
+ align:start position:0%
+you're gonna end up in a bunch of
+ 
+
+ align:start position:0%
+you're gonna end up in a bunch of
+different states based on your
+
+ align:start position:0%
+different states based on your
+ 
+
+ align:start position:0%
+different states based on your
+transition look at that point we can use
+
+ align:start position:0%
+transition look at that point we can use
+ 
+
+ align:start position:0%
+transition look at that point we can use
+the lessons we learned from MVP land
+
+ align:start position:0%
+the lessons we learned from MVP land
+ 
+
+ align:start position:0%
+the lessons we learned from MVP land
+where we said when we make observations
+
+ align:start position:0%
+where we said when we make observations
+ 
+
+ align:start position:0%
+where we said when we make observations
+we reduce our uncertainty to collapse
+
+ align:start position:0%
+we reduce our uncertainty to collapse
+ 
+
+ align:start position:0%
+we reduce our uncertainty to collapse
+into a single state so we say let's save
+
+ align:start position:0%
+into a single state so we say let's save
+ 
+
+ align:start position:0%
+into a single state so we say let's save
+it but this time observations aren't
+
+ align:start position:0%
+it but this time observations aren't
+ 
+
+ align:start position:0%
+it but this time observations aren't
+guaranteed to resolve all our
+
+ align:start position:0%
+guaranteed to resolve all our
+ 
+
+ align:start position:0%
+guaranteed to resolve all our
+uncertainty so we make an observation
+
+ align:start position:0%
+uncertainty so we make an observation
+ 
+
+ align:start position:0%
+uncertainty so we make an observation
+and that observation is probabilistic
+
+ align:start position:0%
+and that observation is probabilistic
+ 
+
+ align:start position:0%
+and that observation is probabilistic
+based on our current state and the
+
+ align:start position:0%
+based on our current state and the
+ 
+
+ align:start position:0%
+based on our current state and the
+actually we've just done and again
+
+ align:start position:0%
+actually we've just done and again
+ 
+
+ align:start position:0%
+actually we've just done and again
+obviously depends on your current state
+
+ align:start position:0%
+obviously depends on your current state
+ 
+
+ align:start position:0%
+obviously depends on your current state
+because if you're one foot away from the
+
+ align:start position:0%
+because if you're one foot away from the
+ 
+
+ align:start position:0%
+because if you're one foot away from the
+wall hopefully you'll get a different
+
+ align:start position:0%
+wall hopefully you'll get a different
+ 
+
+ align:start position:0%
+wall hopefully you'll get a different
+characterization of observations than if
+
+ align:start position:0%
+characterization of observations than if
+ 
+
+ align:start position:0%
+characterization of observations than if
+you're 20 feet away from the wall
+
+ align:start position:0%
+you're 20 feet away from the wall
+ 
+
+ align:start position:0%
+you're 20 feet away from the wall
+otherwise your sensor is totally useless
+
+ align:start position:0%
+otherwise your sensor is totally useless
+ 
+
+ align:start position:0%
+otherwise your sensor is totally useless
+are there any questions about this
+
+ align:start position:0%
+are there any questions about this
+ 
+
+ align:start position:0%
+are there any questions about this
+formulation yet public questions so
+
+ align:start position:0%
+formulation yet public questions so
+ 
+
+ align:start position:0%
+formulation yet public questions so
+we'll take the observationally
+
+ align:start position:0%
+we'll take the observationally
+ 
+
+ align:start position:0%
+we'll take the observationally
+toleration and they affect the infer
+
+ align:start position:0%
+toleration and they affect the infer
+ 
+
+ align:start position:0%
+toleration and they affect the infer
+worse that you're eating is it just kind
+
+ align:start position:0%
+worse that you're eating is it just kind
+ 
+
+ align:start position:0%
+worse that you're eating is it just kind
+of a constant problem France a moment
+
+ align:start position:0%
+of a constant problem France a moment
+ 
+
+ align:start position:0%
+of a constant problem France a moment
+ago the monkey master calls him energy
+
+ align:start position:0%
+ago the monkey master calls him energy
+ 
+
+ align:start position:0%
+ago the monkey master calls him energy
+on that artistry
+
+ align:start position:0%
+on that artistry
+ 
+
+ align:start position:0%
+on that artistry
+so I mean crossfade possibly cause
+
+ align:start position:0%
+so I mean crossfade possibly cause
+ 
+
+ align:start position:0%
+so I mean crossfade possibly cause
+signature state when taking observation
+
+ align:start position:0%
+signature state when taking observation
+ 
+
+ align:start position:0%
+signature state when taking observation
+there's a hyper no means of horses for
+
+ align:start position:0%
+there's a hyper no means of horses for
+ 
+
+ align:start position:0%
+there's a hyper no means of horses for
+each operation review so thank you for
+
+ align:start position:0%
+each operation review so thank you for
+ 
+
+ align:start position:0%
+each operation review so thank you for
+answering so you could I imagine
+
+ align:start position:0%
+answering so you could I imagine
+ 
+
+ align:start position:0%
+answering so you could I imagine
+implement an algorithm where yet every
+
+ align:start position:0%
+implement an algorithm where yet every
+ 
+
+ align:start position:0%
+implement an algorithm where yet every
+time you make an observation then try to
+
+ align:start position:0%
+time you make an observation then try to
+ 
+
+ align:start position:0%
+time you make an observation then try to
+say alright what's my most likely
+
+ align:start position:0%
+say alright what's my most likely
+ 
+
+ align:start position:0%
+say alright what's my most likely
+estimate or maybe my belief and cost
+
+ align:start position:0%
+estimate or maybe my belief and cost
+ 
+
+ align:start position:0%
+estimate or maybe my belief and cost
+estimate but inherent with that is the
+
+ align:start position:0%
+estimate but inherent with that is the
+ 
+
+ align:start position:0%
+estimate but inherent with that is the
+risk that you're discarding a lot of
+
+ align:start position:0%
+risk that you're discarding a lot of
+ 
+
+ align:start position:0%
+risk that you're discarding a lot of
+information right because you're going
+
+ align:start position:0%
+information right because you're going
+ 
+
+ align:start position:0%
+information right because you're going
+to generate a probability distribution
+
+ align:start position:0%
+to generate a probability distribution
+ 
+
+ align:start position:0%
+to generate a probability distribution
+over your state and so yes you can't say
+
+ align:start position:0%
+over your state and so yes you can't say
+ 
+
+ align:start position:0%
+over your state and so yes you can't say
+I'm going to stick with the maximum
+
+ align:start position:0%
+I'm going to stick with the maximum
+ 
+
+ align:start position:0%
+I'm going to stick with the maximum
+likely an estimate but if you can you
+
+ align:start position:0%
+likely an estimate but if you can you
+ 
+
+ align:start position:0%
+likely an estimate but if you can you
+should probably try to maintain that
+
+ align:start position:0%
+should probably try to maintain that
+ 
+
+ align:start position:0%
+should probably try to maintain that
+distribution as long as possible okay
+
+ align:start position:0%
+distribution as long as possible okay
+ 
+
+ align:start position:0%
+distribution as long as possible okay
+and we'll see that this is really
+
+ align:start position:0%
+and we'll see that this is really
+ 
+
+ align:start position:0%
+and we'll see that this is really
+computationally expensive unless you
+
+ align:start position:0%
+computationally expensive unless you
+ 
+
+ align:start position:0%
+computationally expensive unless you
+start making some assumptions and in a
+
+ align:start position:0%
+start making some assumptions and in a
+ 
+
+ align:start position:0%
+start making some assumptions and in a
+few key in the case study we're going to
+
+ align:start position:0%
+few key in the case study we're going to
+ 
+
+ align:start position:0%
+few key in the case study we're going to
+look into that's exactly but I've seen a
+
+ align:start position:0%
+look into that's exactly but I've seen a
+ 
+
+ align:start position:0%
+look into that's exactly but I've seen a
+lot in the literature that as far as as
+
+ align:start position:0%
+lot in the literature that as far as as
+ 
+
+ align:start position:0%
+lot in the literature that as far as as
+much as you can you want to maintain
+
+ align:start position:0%
+much as you can you want to maintain
+ 
+
+ align:start position:0%
+much as you can you want to maintain
+these distributions for
+
+ align:start position:0%
+these distributions for
+ 
+
+ align:start position:0%
+these distributions for
+detectives any other prospects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we're going to compare now the
+
+ align:start position:0%
+what we're going to compare now the
+ 
+
+ align:start position:0%
+what we're going to compare now the
+execution of a Pompey piece to the
+
+ align:start position:0%
+execution of a Pompey piece to the
+ 
+
+ align:start position:0%
+execution of a Pompey piece to the
+execution of an empty start out we're
+
+ align:start position:0%
+execution of an empty start out we're
+ 
+
+ align:start position:0%
+execution of an empty start out we're
+living in the same great world not the
+
+ align:start position:0%
+living in the same great world not the
+ 
+
+ align:start position:0%
+living in the same great world not the
+same transition model that we think
+
+ align:start position:0%
+same transition model that we think
+ 
+
+ align:start position:0%
+same transition model that we think
+steeply we take action one we want to go
+
+ align:start position:0%
+steeply we take action one we want to go
+ 
+
+ align:start position:0%
+steeply we take action one we want to go
+north right we have this distribution
+
+ align:start position:0%
+north right we have this distribution
+ 
+
+ align:start position:0%
+north right we have this distribution
+that we generate and at this point what
+
+ align:start position:0%
+that we generate and at this point what
+ 
+
+ align:start position:0%
+that we generate and at this point what
+did we say we said we hate the fact that
+
+ align:start position:0%
+did we say we said we hate the fact that
+ 
+
+ align:start position:0%
+did we say we said we hate the fact that
+we have to deal with three cases three
+
+ align:start position:0%
+we have to deal with three cases three
+ 
+
+ align:start position:0%
+we have to deal with three cases three
+is two too many
+
+ align:start position:0%
+is two too many
+ 
+
+ align:start position:0%
+is two too many
+so let's make an observation to collapse
+
+ align:start position:0%
+so let's make an observation to collapse
+ 
+
+ align:start position:0%
+so let's make an observation to collapse
+this distribution now I've described a
+
+ align:start position:0%
+this distribution now I've described a
+ 
+
+ align:start position:0%
+this distribution now I've described a
+lot about the new easy sensors right
+
+ align:start position:0%
+lot about the new easy sensors right
+ 
+
+ align:start position:0%
+lot about the new easy sensors right
+we're basically in to true measurements
+
+ align:start position:0%
+we're basically in to true measurements
+ 
+
+ align:start position:0%
+we're basically in to true measurements
+some plus some some noise
+
+ align:start position:0%
+some plus some some noise
+ 
+
+ align:start position:0%
+some plus some some noise
+maybe gotta understand the distribution
+
+ align:start position:0%
+maybe gotta understand the distribution
+ 
+
+ align:start position:0%
+maybe gotta understand the distribution
+there's another sort of partially
+
+ align:start position:0%
+there's another sort of partially
+ 
+
+ align:start position:0%
+there's another sort of partially
+observable sensor you can have in a pump
+
+ align:start position:0%
+observable sensor you can have in a pump
+ 
+
+ align:start position:0%
+observable sensor you can have in a pump
+EP which really feeds it to the named
+
+ align:start position:0%
+EP which really feeds it to the named
+ 
+
+ align:start position:0%
+EP which really feeds it to the named
+person we observe what if you can only
+
+ align:start position:0%
+person we observe what if you can only
+ 
+
+ align:start position:0%
+person we observe what if you can only
+observe a part of your state for example
+
+ align:start position:0%
+observe a part of your state for example
+ 
+
+ align:start position:0%
+observe a part of your state for example
+if you're living in an XY grid maybe you
+
+ align:start position:0%
+if you're living in an XY grid maybe you
+ 
+
+ align:start position:0%
+if you're living in an XY grid maybe you
+can only observe your Y dimension this
+
+ align:start position:0%
+can only observe your Y dimension this
+ 
+
+ align:start position:0%
+can only observe your Y dimension this
+could map it up in a real-world example
+
+ align:start position:0%
+could map it up in a real-world example
+ 
+
+ align:start position:0%
+could map it up in a real-world example
+to a quadrotor flying down a hallway
+
+ align:start position:0%
+to a quadrotor flying down a hallway
+ 
+
+ align:start position:0%
+to a quadrotor flying down a hallway
+Kathleen was working on a project on a
+
+ align:start position:0%
+Kathleen was working on a project on a
+ 
+
+ align:start position:0%
+Kathleen was working on a project on a
+DARPA project with quad rotors playing
+
+ align:start position:0%
+DARPA project with quad rotors playing
+ 
+
+ align:start position:0%
+DARPA project with quad rotors playing
+on hallways if the hallway is too long
+
+ align:start position:0%
+on hallways if the hallway is too long
+ 
+
+ align:start position:0%
+on hallways if the hallway is too long
+your laser rangefinder isn't going to be
+
+ align:start position:0%
+your laser rangefinder isn't going to be
+ 
+
+ align:start position:0%
+your laser rangefinder isn't going to be
+able to determine where you are along
+
+ align:start position:0%
+able to determine where you are along
+ 
+
+ align:start position:0%
+able to determine where you are along
+one axis but it can tell where you are
+
+ align:start position:0%
+one axis but it can tell where you are
+ 
+
+ align:start position:0%
+one axis but it can tell where you are
+along another and so that's what I've
+
+ align:start position:0%
+along another and so that's what I've
+ 
+
+ align:start position:0%
+along another and so that's what I've
+said I've said pretend this quadrotor
+
+ align:start position:0%
+said I've said pretend this quadrotor
+ 
+
+ align:start position:0%
+said I've said pretend this quadrotor
+has that sensor it can only observe its
+
+ align:start position:0%
+has that sensor it can only observe its
+ 
+
+ align:start position:0%
+has that sensor it can only observe its
+y-component and it says my Y component
+
+ align:start position:0%
+y-component and it says my Y component
+ 
+
+ align:start position:0%
+y-component and it says my Y component
+is three no idea what my next component
+
+ align:start position:0%
+is three no idea what my next component
+ 
+
+ align:start position:0%
+is three no idea what my next component
+is well this sucks right because we got
+
+ align:start position:0%
+is well this sucks right because we got
+ 
+
+ align:start position:0%
+is well this sucks right because we got
+rid of this state but then we couldn't
+
+ align:start position:0%
+rid of this state but then we couldn't
+ 
+
+ align:start position:0%
+rid of this state but then we couldn't
+decide are we at state one three
+
+ align:start position:0%
+decide are we at state one three
+ 
+
+ align:start position:0%
+decide are we at state one three
+we're three if there's no way of
+
+ align:start position:0%
+we're three if there's no way of
+ 
+
+ align:start position:0%
+we're three if there's no way of
+resolving this so we can renormalize we
+
+ align:start position:0%
+resolving this so we can renormalize we
+ 
+
+ align:start position:0%
+resolving this so we can renormalize we
+can add in the effects from the
+
+ align:start position:0%
+can add in the effects from the
+ 
+
+ align:start position:0%
+can add in the effects from the
+observation probability is the same
+
+ align:start position:0%
+observation probability is the same
+ 
+
+ align:start position:0%
+observation probability is the same
+maybe in fact I'm far more likely to
+
+ align:start position:0%
+maybe in fact I'm far more likely to
+ 
+
+ align:start position:0%
+maybe in fact I'm far more likely to
+observe state three or a wide component
+
+ align:start position:0%
+observe state three or a wide component
+ 
+
+ align:start position:0%
+observe state three or a wide component
+of three if I'm at one three but in this
+
+ align:start position:0%
+of three if I'm at one three but in this
+ 
+
+ align:start position:0%
+of three if I'm at one three but in this
+case you say it's equally likely to make
+
+ align:start position:0%
+case you say it's equally likely to make
+ 
+
+ align:start position:0%
+case you say it's equally likely to make
+that observation for those two states
+
+ align:start position:0%
+that observation for those two states
+ 
+
+ align:start position:0%
+that observation for those two states
+and so now we've got to deal with these
+
+ align:start position:0%
+and so now we've got to deal with these
+ 
+
+ align:start position:0%
+and so now we've got to deal with these
+two cases and so when we take our next
+
+ align:start position:0%
+two cases and so when we take our next
+ 
+
+ align:start position:0%
+two cases and so when we take our next
+step in instead of reset it into a
+
+ align:start position:0%
+step in instead of reset it into a
+ 
+
+ align:start position:0%
+step in instead of reset it into a
+single state we've got to keep growing
+
+ align:start position:0%
+single state we've got to keep growing
+ 
+
+ align:start position:0%
+single state we've got to keep growing
+this tree and what's the key difference
+
+ align:start position:0%
+this tree and what's the key difference
+ 
+
+ align:start position:0%
+this tree and what's the key difference
+between this and when we were executed
+
+ align:start position:0%
+between this and when we were executed
+ 
+
+ align:start position:0%
+between this and when we were executed
+our MVP it's a we didn't manage to
+
+ align:start position:0%
+our MVP it's a we didn't manage to
+ 
+
+ align:start position:0%
+our MVP it's a we didn't manage to
+collapse back to a single state we
+
+ align:start position:0%
+collapse back to a single state we
+ 
+
+ align:start position:0%
+collapse back to a single state we
+didn't manage to reset the problem and
+
+ align:start position:0%
+didn't manage to reset the problem and
+ 
+
+ align:start position:0%
+didn't manage to reset the problem and
+this is you know annoying because you
+
+ align:start position:0%
+this is you know annoying because you
+ 
+
+ align:start position:0%
+this is you know annoying because you
+can't execute the policy and say I'm
+
+ align:start position:0%
+can't execute the policy and say I'm
+ 
+
+ align:start position:0%
+can't execute the policy and say I'm
+certain but this is my configuration to
+
+ align:start position:0%
+certain but this is my configuration to
+ 
+
+ align:start position:0%
+certain but this is my configuration to
+your policy can't map from exactly
+
+ align:start position:0%
+your policy can't map from exactly
+ 
+
+ align:start position:0%
+your policy can't map from exactly
+States
+
+ align:start position:0%
+States
+ 
+
+ align:start position:0%
+States
+attractive because you never know your
+
+ align:start position:0%
+attractive because you never know your
+ 
+
+ align:start position:0%
+attractive because you never know your
+exact state is this make sense is
+
+ align:start position:0%
+exact state is this make sense is
+ 
+
+ align:start position:0%
+exact state is this make sense is
+everyone lost poop planning right face
+
+ align:start position:0%
+everyone lost poop planning right face
+ 
+
+ align:start position:0%
+everyone lost poop planning right face
+yeah just so you hear because so from
+
+ align:start position:0%
+yeah just so you hear because so from
+ 
+
+ align:start position:0%
+yeah just so you hear because so from
+the left to the right yeah
+
+ align:start position:0%
+the left to the right yeah
+ 
+
+ align:start position:0%
+the left to the right yeah
+you're basically mapping from one belief
+
+ align:start position:0%
+you're basically mapping from one belief
+ 
+
+ align:start position:0%
+you're basically mapping from one belief
+state you're not a glue stick
+
+ align:start position:0%
+state you're not a glue stick
+ 
+
+ align:start position:0%
+state you're not a glue stick
+that's not like a one arrow thing but
+
+ align:start position:0%
+that's not like a one arrow thing but
+ 
+
+ align:start position:0%
+that's not like a one arrow thing but
+yeah and then from that second layer you
+
+ align:start position:0%
+yeah and then from that second layer you
+ 
+
+ align:start position:0%
+yeah and then from that second layer you
+should have two arrows one with
+
+ align:start position:0%
+should have two arrows one with
+ 
+
+ align:start position:0%
+should have two arrows one with
+probability 0.5 that observes 3 and that
+
+ align:start position:0%
+probability 0.5 that observes 3 and that
+ 
+
+ align:start position:0%
+probability 0.5 that observes 3 and that
+gives rise to that loop stated just show
+
+ align:start position:0%
+gives rise to that loop stated just show
+ 
+
+ align:start position:0%
+gives rise to that loop stated just show
+in one with probably 0.5 where the
+
+ align:start position:0%
+in one with probably 0.5 where the
+ 
+
+ align:start position:0%
+in one with probably 0.5 where the
+sensor is reading for because if you
+
+ align:start position:0%
+sensor is reading for because if you
+ 
+
+ align:start position:0%
+sensor is reading for because if you
+have knows you're probably looking at
+
+ align:start position:0%
+have knows you're probably looking at
+ 
+
+ align:start position:0%
+have knows you're probably looking at
+you for you might as well just observe
+
+ align:start position:0%
+you for you might as well just observe
+ 
+
+ align:start position:0%
+you for you might as well just observe
+for as well as your Y so in this case
+
+ align:start position:0%
+for as well as your Y so in this case
+ 
+
+ align:start position:0%
+for as well as your Y so in this case
+honey I'm I'm not sure Q if you were
+
+ align:start position:0%
+honey I'm I'm not sure Q if you were
+ 
+
+ align:start position:0%
+honey I'm I'm not sure Q if you were
+just trying to show one range of your of
+
+ align:start position:0%
+just trying to show one range of your of
+ 
+
+ align:start position:0%
+just trying to show one range of your of
+your public complaining but basically
+
+ align:start position:0%
+your public complaining but basically
+ 
+
+ align:start position:0%
+your public complaining but basically
+what do you have to do you know yeah
+
+ align:start position:0%
+what do you have to do you know yeah
+ 
+
+ align:start position:0%
+what do you have to do you know yeah
+this to the second layer you would have
+
+ align:start position:0%
+this to the second layer you would have
+ 
+
+ align:start position:0%
+this to the second layer you would have
+a branch so this is 0.5 probability on
+
+ align:start position:0%
+a branch so this is 0.5 probability on
+ 
+
+ align:start position:0%
+a branch so this is 0.5 probability on
+either one giving you 3 1 4 for the one
+
+ align:start position:0%
+either one giving you 3 1 4 for the one
+ 
+
+ align:start position:0%
+either one giving you 3 1 4 for the one
+that I showed you guys our belief state
+
+ align:start position:0%
+that I showed you guys our belief state
+ 
+
+ align:start position:0%
+that I showed you guys our belief state
+or the other one you get truth
+
+ align:start position:0%
+or the other one you get truth
+ 
+
+ align:start position:0%
+or the other one you get truth
+- for probably one yeah so you were
+
+ align:start position:0%
+- for probably one yeah so you were
+ 
+
+ align:start position:0%
+- for probably one yeah so you were
+perfectly describing planning right I
+
+ align:start position:0%
+perfectly describing planning right I
+ 
+
+ align:start position:0%
+perfectly describing planning right I
+should have made this more clear this
+
+ align:start position:0%
+should have made this more clear this
+ 
+
+ align:start position:0%
+should have made this more clear this
+isn't complaining
+
+ align:start position:0%
+isn't complaining
+ 
+
+ align:start position:0%
+isn't complaining
+this is executed we have this policy
+
+ align:start position:0%
+this is executed we have this policy
+ 
+
+ align:start position:0%
+this is executed we have this policy
+that we're going to execute and so if we
+
+ align:start position:0%
+that we're going to execute and so if we
+ 
+
+ align:start position:0%
+that we're going to execute and so if we
+were planning we would have to consider
+
+ align:start position:0%
+were planning we would have to consider
+ 
+
+ align:start position:0%
+were planning we would have to consider
+all these branches and say well yeah I
+
+ align:start position:0%
+all these branches and say well yeah I
+ 
+
+ align:start position:0%
+all these branches and say well yeah I
+could take like there's a 50% chance
+
+ align:start position:0%
+could take like there's a 50% chance
+ 
+
+ align:start position:0%
+could take like there's a 50% chance
+I'll end up here if the Y value is going
+
+ align:start position:0%
+I'll end up here if the Y value is going
+ 
+
+ align:start position:0%
+I'll end up here if the Y value is going
+to report you're gonna have to prove
+
+ align:start position:0%
+to report you're gonna have to prove
+ 
+
+ align:start position:0%
+to report you're gonna have to prove
+this whole thing I'm saying no this is
+
+ align:start position:0%
+this whole thing I'm saying no this is
+ 
+
+ align:start position:0%
+this whole thing I'm saying no this is
+real time execution
+
+ align:start position:0%
+real time execution
+ 
+
+ align:start position:0%
+real time execution
+yeah great question any others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this is a great time to transition
+
+ align:start position:0%
+well this is a great time to transition
+ 
+
+ align:start position:0%
+well this is a great time to transition
+- well we can't just magically be handed
+
+ align:start position:0%
+- well we can't just magically be handed
+ 
+
+ align:start position:0%
+- well we can't just magically be handed
+his policies how do we actually generate
+
+ align:start position:0%
+his policies how do we actually generate
+ 
+
+ align:start position:0%
+his policies how do we actually generate
+them how do we start planning in the
+
+ align:start position:0%
+them how do we start planning in the
+ 
+
+ align:start position:0%
+them how do we start planning in the
+belief space the belief space right
+
+ align:start position:0%
+belief space the belief space right
+ 
+
+ align:start position:0%
+belief space the belief space right
+space distributions impossible
+
+ align:start position:0%
+space distributions impossible
+ 
+
+ align:start position:0%
+space distributions impossible
+configurations so I'm going to talk
+
+ align:start position:0%
+configurations so I'm going to talk
+ 
+
+ align:start position:0%
+configurations so I'm going to talk
+about a sort of general class of
+
+ align:start position:0%
+about a sort of general class of
+ 
+
+ align:start position:0%
+about a sort of general class of
+algorithms a lot of planets in tom
+
+ align:start position:0%
+algorithms a lot of planets in tom
+ 
+
+ align:start position:0%
+algorithms a lot of planets in tom
+mcneiland in the belief space plan with
+
+ align:start position:0%
+mcneiland in the belief space plan with
+ 
+
+ align:start position:0%
+mcneiland in the belief space plan with
+probabilistic roadmaps prm's break the
+
+ align:start position:0%
+probabilistic roadmaps prm's break the
+ 
+
+ align:start position:0%
+probabilistic roadmaps prm's break the
+goal to generate a policy then maps from
+
+ align:start position:0%
+goal to generate a policy then maps from
+ 
+
+ align:start position:0%
+goal to generate a policy then maps from
+a belief state to an action and I'm
+
+ align:start position:0%
+a belief state to an action and I'm
+ 
+
+ align:start position:0%
+a belief state to an action and I'm
+gonna go into a little more later
+
+ align:start position:0%
+gonna go into a little more later
+ 
+
+ align:start position:0%
+gonna go into a little more later
+now whatever we've stated is but the
+
+ align:start position:0%
+now whatever we've stated is but the
+ 
+
+ align:start position:0%
+now whatever we've stated is but the
+general algorithm and this graphic
+
+ align:start position:0%
+general algorithm and this graphic
+ 
+
+ align:start position:0%
+general algorithm and this graphic
+illustrates these four steps is we're
+
+ align:start position:0%
+illustrates these four steps is we're
+ 
+
+ align:start position:0%
+illustrates these four steps is we're
+gonna sample points from the
+
+ align:start position:0%
+gonna sample points from the
+ 
+
+ align:start position:0%
+gonna sample points from the
+configuration space right as if
+
+ align:start position:0%
+configuration space right as if
+ 
+
+ align:start position:0%
+configuration space right as if
+everything was deterministic we're gonna
+
+ align:start position:0%
+everything was deterministic we're gonna
+ 
+
+ align:start position:0%
+everything was deterministic we're gonna
+connect those points to nearby points
+
+ align:start position:0%
+connect those points to nearby points
+ 
+
+ align:start position:0%
+connect those points to nearby points
+and define nearby however you want to
+
+ align:start position:0%
+and define nearby however you want to
+ 
+
+ align:start position:0%
+and define nearby however you want to
+leave your closest neighbors all
+
+ align:start position:0%
+leave your closest neighbors all
+ 
+
+ align:start position:0%
+leave your closest neighbors all
+neighbors within a radius whatever as
+
+ align:start position:0%
+neighbors within a radius whatever as
+ 
+
+ align:start position:0%
+neighbors within a radius whatever as
+long as those edges don't collide with
+
+ align:start position:0%
+long as those edges don't collide with
+ 
+
+ align:start position:0%
+long as those edges don't collide with
+obstacles once you've done that somehow
+
+ align:start position:0%
+obstacles once you've done that somehow
+ 
+
+ align:start position:0%
+obstacles once you've done that somehow
+and there's some magic in this you're
+
+ align:start position:0%
+and there's some magic in this you're
+ 
+
+ align:start position:0%
+and there's some magic in this you're
+going to transform your configuration
+
+ align:start position:0%
+going to transform your configuration
+ 
+
+ align:start position:0%
+going to transform your configuration
+space probabilistic roadmap to a
+
+ align:start position:0%
+space probabilistic roadmap to a
+ 
+
+ align:start position:0%
+space probabilistic roadmap to a
+probabilistic roadmap in the belief
+
+ align:start position:0%
+probabilistic roadmap in the belief
+ 
+
+ align:start position:0%
+probabilistic roadmap in the belief
+space great once you've done that you
+
+ align:start position:0%
+space great once you've done that you
+ 
+
+ align:start position:0%
+space great once you've done that you
+can just do shortest paths depending on
+
+ align:start position:0%
+can just do shortest paths depending on
+ 
+
+ align:start position:0%
+can just do shortest paths depending on
+whatever it cost by community news and
+
+ align:start position:0%
+whatever it cost by community news and
+ 
+
+ align:start position:0%
+whatever it cost by community news and
+what's really cool is you get different
+
+ align:start position:0%
+what's really cool is you get different
+ 
+
+ align:start position:0%
+what's really cool is you get different
+shortest paths for when you stay in the
+
+ align:start position:0%
+shortest paths for when you stay in the
+ 
+
+ align:start position:0%
+shortest paths for when you stay in the
+configuration space and when you go to
+
+ align:start position:0%
+configuration space and when you go to
+ 
+
+ align:start position:0%
+configuration space and when you go to
+the belief space so the green path that
+
+ align:start position:0%
+the belief space so the green path that
+ 
+
+ align:start position:0%
+the belief space so the green path that
+bottom right figures seems a lot longer
+
+ align:start position:0%
+bottom right figures seems a lot longer
+ 
+
+ align:start position:0%
+bottom right figures seems a lot longer
+than the right path and the reason is
+
+ align:start position:0%
+than the right path and the reason is
+ 
+
+ align:start position:0%
+than the right path and the reason is
+the green path was planned in the belief
+
+ align:start position:0%
+the green path was planned in the belief
+ 
+
+ align:start position:0%
+the green path was planned in the belief
+space and followed a lot of landmarks
+
+ align:start position:0%
+space and followed a lot of landmarks
+ 
+
+ align:start position:0%
+space and followed a lot of landmarks
+that the quadrotor could take
+
+ align:start position:0%
+that the quadrotor could take
+ 
+
+ align:start position:0%
+that the quadrotor could take
+measurements off
+
+ align:start position:0%
+measurements off
+ 
+
+ align:start position:0%
+measurements off
+it was really confident about its
+
+ align:start position:0%
+it was really confident about its
+ 
+
+ align:start position:0%
+it was really confident about its
+position where's the red Pakistan shorts
+
+ align:start position:0%
+position where's the red Pakistan shorts
+ 
+
+ align:start position:0%
+position where's the red Pakistan shorts
+but had a higher light I'll do a
+
+ align:start position:0%
+but had a higher light I'll do a
+ 
+
+ align:start position:0%
+but had a higher light I'll do a
+different relation we're gonna look into
+
+ align:start position:0%
+different relation we're gonna look into
+ 
+
+ align:start position:0%
+different relation we're gonna look into
+that finger more later I'm going to
+
+ align:start position:0%
+that finger more later I'm going to
+ 
+
+ align:start position:0%
+that finger more later I'm going to
+segment this algorithm into two parts
+
+ align:start position:0%
+segment this algorithm into two parts
+ 
+
+ align:start position:0%
+segment this algorithm into two parts
+the first part these first two steps
+
+ align:start position:0%
+the first part these first two steps
+ 
+
+ align:start position:0%
+the first part these first two steps
+it's just probabilistic roadmaps who
+
+ align:start position:0%
+it's just probabilistic roadmaps who
+ 
+
+ align:start position:0%
+it's just probabilistic roadmaps who
+here has heard about bubble mystic
+
+ align:start position:0%
+here has heard about bubble mystic
+ 
+
+ align:start position:0%
+here has heard about bubble mystic
+roadmaps raise your hand
+
+ align:start position:0%
+roadmaps raise your hand
+ 
+
+ align:start position:0%
+roadmaps raise your hand
+50/50 I'm so excited for the 50% you
+
+ align:start position:0%
+50/50 I'm so excited for the 50% you
+ 
+
+ align:start position:0%
+50/50 I'm so excited for the 50% you
+haven't heard one of the top algorithms
+
+ align:start position:0%
+haven't heard one of the top algorithms
+ 
+
+ align:start position:0%
+haven't heard one of the top algorithms
+in my opinion it's really simple and
+
+ align:start position:0%
+in my opinion it's really simple and
+ 
+
+ align:start position:0%
+in my opinion it's really simple and
+it's really powerful here's basically
+
+ align:start position:0%
+it's really powerful here's basically
+ 
+
+ align:start position:0%
+it's really powerful here's basically
+almost a complete implementation of
+
+ align:start position:0%
+almost a complete implementation of
+ 
+
+ align:start position:0%
+almost a complete implementation of
+probabilistic roadmaps sumo kind of sort
+
+ align:start position:0%
+probabilistic roadmaps sumo kind of sort
+ 
+
+ align:start position:0%
+probabilistic roadmaps sumo kind of sort
+of probably paste but it's almost there
+
+ align:start position:0%
+of probably paste but it's almost there
+ 
+
+ align:start position:0%
+of probably paste but it's almost there
+right you're going to construct the
+
+ align:start position:0%
+right you're going to construct the
+ 
+
+ align:start position:0%
+right you're going to construct the
+graph is empty you're gonna add your
+
+ align:start position:0%
+graph is empty you're gonna add your
+ 
+
+ align:start position:0%
+graph is empty you're gonna add your
+start goal through your start to figure
+
+ align:start position:0%
+start goal through your start to figure
+ 
+
+ align:start position:0%
+start goal through your start to figure
+if it may be the Green Dot and the bulk
+
+ align:start position:0%
+if it may be the Green Dot and the bulk
+ 
+
+ align:start position:0%
+if it may be the Green Dot and the bulk
+of the Vickery from the red dot then
+
+ align:start position:0%
+of the Vickery from the red dot then
+ 
+
+ align:start position:0%
+of the Vickery from the red dot then
+you're just gonna keep sampling nodes
+
+ align:start position:0%
+you're just gonna keep sampling nodes
+ 
+
+ align:start position:0%
+you're just gonna keep sampling nodes
+from the free space you say hello to
+
+ align:start position:0%
+from the free space you say hello to
+ 
+
+ align:start position:0%
+from the free space you say hello to
+three you're gonna add that to your crap
+
+ align:start position:0%
+three you're gonna add that to your crap
+ 
+
+ align:start position:0%
+three you're gonna add that to your crap
+you're gonna connect that node to a
+
+ align:start position:0%
+you're gonna connect that node to a
+ 
+
+ align:start position:0%
+you're gonna connect that node to a
+bunch of other nodes nearby and then
+
+ align:start position:0%
+bunch of other nodes nearby and then
+ 
+
+ align:start position:0%
+bunch of other nodes nearby and then
+you're just gonna keep simple and keep
+
+ align:start position:0%
+you're just gonna keep simple and keep
+ 
+
+ align:start position:0%
+you're just gonna keep simple and keep
+sampling
+
+ align:start position:0%
+sampling
+ 
+
+ align:start position:0%
+sampling
+until maybe you have enough nodes where
+
+ align:start position:0%
+until maybe you have enough nodes where
+ 
+
+ align:start position:0%
+until maybe you have enough nodes where
+maybe until you have your complete path
+
+ align:start position:0%
+maybe until you have your complete path
+ 
+
+ align:start position:0%
+maybe until you have your complete path
+should be nothing there and then once
+
+ align:start position:0%
+should be nothing there and then once
+ 
+
+ align:start position:0%
+should be nothing there and then once
+you've got this whole graph you can just
+
+ align:start position:0%
+you've got this whole graph you can just
+ 
+
+ align:start position:0%
+you've got this whole graph you can just
+find the shortest path along path and
+
+ align:start position:0%
+find the shortest path along path and
+ 
+
+ align:start position:0%
+find the shortest path along path and
+there's some really cool results that if
+
+ align:start position:0%
+there's some really cool results that if
+ 
+
+ align:start position:0%
+there's some really cool results that if
+you sample a good way and so on
+
+ align:start position:0%
+you sample a good way and so on
+ 
+
+ align:start position:0%
+you sample a good way and so on
+asymptotically as you start sampling
+
+ align:start position:0%
+asymptotically as you start sampling
+ 
+
+ align:start position:0%
+asymptotically as you start sampling
+more you're gonna ask you publicly
+
+ align:start position:0%
+more you're gonna ask you publicly
+ 
+
+ align:start position:0%
+more you're gonna ask you publicly
+the best path getting completely that
+
+ align:start position:0%
+the best path getting completely that
+ 
+
+ align:start position:0%
+the best path getting completely that
+continuous space the power problem was
+
+ align:start position:0%
+continuous space the power problem was
+ 
+
+ align:start position:0%
+continuous space the power problem was
+the road madison a bunch of randomized
+
+ align:start position:0%
+the road madison a bunch of randomized
+ 
+
+ align:start position:0%
+the road madison a bunch of randomized
+algorithms though is that they scale
+
+ align:start position:0%
+algorithms though is that they scale
+ 
+
+ align:start position:0%
+algorithms though is that they scale
+pretty well for high dimensions so you
+
+ align:start position:0%
+pretty well for high dimensions so you
+ 
+
+ align:start position:0%
+pretty well for high dimensions so you
+don't actually consider consider
+
+ align:start position:0%
+don't actually consider consider
+ 
+
+ align:start position:0%
+don't actually consider consider
+continuous space you just sample about
+
+ align:start position:0%
+continuous space you just sample about
+ 
+
+ align:start position:0%
+continuous space you just sample about
+two parties are there any questions
+
+ align:start position:0%
+two parties are there any questions
+ 
+
+ align:start position:0%
+two parties are there any questions
+about probabilistic roadmaps they're
+
+ align:start position:0%
+about probabilistic roadmaps they're
+ 
+
+ align:start position:0%
+about probabilistic roadmaps they're
+really cool if you're interested and you
+
+ align:start position:0%
+really cool if you're interested and you
+ 
+
+ align:start position:0%
+really cool if you're interested and you
+just worry about prm's probably heard of
+
+ align:start position:0%
+just worry about prm's probably heard of
+ 
+
+ align:start position:0%
+just worry about prm's probably heard of
+haven't heard about RRTs
+
+ align:start position:0%
+haven't heard about RRTs
+ 
+
+ align:start position:0%
+haven't heard about RRTs
+those are also really efficient yet so
+
+ align:start position:0%
+those are also really efficient yet so
+ 
+
+ align:start position:0%
+those are also really efficient yet so
+for any more volatile sample like this
+
+ align:start position:0%
+for any more volatile sample like this
+ 
+
+ align:start position:0%
+for any more volatile sample like this
+uniform example that notion of them they
+
+ align:start position:0%
+uniform example that notion of them they
+ 
+
+ align:start position:0%
+uniform example that notion of them they
+spend at least one game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry are what you're accusing where to
+
+ align:start position:0%
+sorry are what you're accusing where to
+ 
+
+ align:start position:0%
+sorry are what you're accusing where to
+place the dot board or what lady's
+
+ align:start position:0%
+place the dot board or what lady's
+ 
+
+ align:start position:0%
+place the dot board or what lady's
+message out there isn't on their house
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in general probabilistic romance you
+
+ align:start position:0%
+so in general probabilistic romance you
+ 
+
+ align:start position:0%
+so in general probabilistic romance you
+can through in whatever simpler the way
+
+ align:start position:0%
+can through in whatever simpler the way
+ 
+
+ align:start position:0%
+can through in whatever simpler the way
+this particular one I the way I
+
+ align:start position:0%
+this particular one I the way I
+ 
+
+ align:start position:0%
+this particular one I the way I
+implemented this is use sample points
+
+ align:start position:0%
+implemented this is use sample points
+ 
+
+ align:start position:0%
+implemented this is use sample points
+uniformly from the entire space if it's
+
+ align:start position:0%
+uniformly from the entire space if it's
+ 
+
+ align:start position:0%
+uniformly from the entire space if it's
+inside an obstacle you remove it once
+
+ align:start position:0%
+inside an obstacle you remove it once
+ 
+
+ align:start position:0%
+inside an obstacle you remove it once
+you place it
+
+ align:start position:0%
+you place it
+ 
+
+ align:start position:0%
+you place it
+this was connect to the K closest that
+
+ align:start position:0%
+this was connect to the K closest that
+ 
+
+ align:start position:0%
+this was connect to the K closest that
+concave seven in the space and if
+
+ align:start position:0%
+concave seven in the space and if
+ 
+
+ align:start position:0%
+concave seven in the space and if
+there's an edge that if that makes
+
+ align:start position:0%
+there's an edge that if that makes
+ 
+
+ align:start position:0%
+there's an edge that if that makes
+collides with an obstacle removal I'd be
+
+ align:start position:0%
+collides with an obstacle removal I'd be
+ 
+
+ align:start position:0%
+collides with an obstacle removal I'd be
+happy to go into more detail about pure
+
+ align:start position:0%
+happy to go into more detail about pure
+ 
+
+ align:start position:0%
+happy to go into more detail about pure
+insulator alright but that's not that's
+
+ align:start position:0%
+insulator alright but that's not that's
+ 
+
+ align:start position:0%
+insulator alright but that's not that's
+not enough because when we described as
+
+ align:start position:0%
+not enough because when we described as
+ 
+
+ align:start position:0%
+not enough because when we described as
+prm's in the configuration space but we
+
+ align:start position:0%
+prm's in the configuration space but we
+ 
+
+ align:start position:0%
+prm's in the configuration space but we
+need to do is somehow elevate a PRM from
+
+ align:start position:0%
+need to do is somehow elevate a PRM from
+ 
+
+ align:start position:0%
+need to do is somehow elevate a PRM from
+the configuration space to a belief
+
+ align:start position:0%
+the configuration space to a belief
+ 
+
+ align:start position:0%
+the configuration space to a belief
+space and this is really hard
+
+ align:start position:0%
+space and this is really hard
+ 
+
+ align:start position:0%
+space and this is really hard
+we don't have access right to these
+
+ align:start position:0%
+we don't have access right to these
+ 
+
+ align:start position:0%
+we don't have access right to these
+rocket digger agents let's imagine we
+
+ align:start position:0%
+rocket digger agents let's imagine we
+ 
+
+ align:start position:0%
+rocket digger agents let's imagine we
+were in this really simple world where
+
+ align:start position:0%
+were in this really simple world where
+ 
+
+ align:start position:0%
+were in this really simple world where
+the quadrotor could be in three possible
+
+ align:start position:0%
+the quadrotor could be in three possible
+ 
+
+ align:start position:0%
+the quadrotor could be in three possible
+states one two frite them really easy
+
+ align:start position:0%
+states one two frite them really easy
+ 
+
+ align:start position:0%
+states one two frite them really easy
+right sample about the points they're
+
+ align:start position:0%
+right sample about the points they're
+ 
+
+ align:start position:0%
+right sample about the points they're
+going to end up in one two or three it
+
+ align:start position:0%
+going to end up in one two or three it
+ 
+
+ align:start position:0%
+going to end up in one two or three it
+pretty quickly cover the entire space
+
+ align:start position:0%
+pretty quickly cover the entire space
+ 
+
+ align:start position:0%
+pretty quickly cover the entire space
+but this simple configuration space when
+
+ align:start position:0%
+but this simple configuration space when
+ 
+
+ align:start position:0%
+but this simple configuration space when
+transformed to the belief space
+
+ align:start position:0%
+transformed to the belief space
+ 
+
+ align:start position:0%
+transformed to the belief space
+you have infinite possible distributions
+
+ align:start position:0%
+you have infinite possible distributions
+ 
+
+ align:start position:0%
+you have infinite possible distributions
+to consider
+
+ align:start position:0%
+to consider
+ 
+
+ align:start position:0%
+to consider
+there's the distribution where you have
+
+ align:start position:0%
+there's the distribution where you have
+ 
+
+ align:start position:0%
+there's the distribution where you have
+a 100% chance probability percent
+
+ align:start position:0%
+a 100% chance probability percent
+ 
+
+ align:start position:0%
+a 100% chance probability percent
+probability here you state 100%
+
+ align:start position:0%
+probability here you state 100%
+ 
+
+ align:start position:0%
+probability here you state 100%
+probability that you're in state to 100%
+
+ align:start position:0%
+probability that you're in state to 100%
+ 
+
+ align:start position:0%
+probability that you're in state to 100%
+probability here at state 3 and then
+
+ align:start position:0%
+probability here at state 3 and then
+ 
+
+ align:start position:0%
+probability here at state 3 and then
+everything in between right we went from
+
+ align:start position:0%
+everything in between right we went from
+ 
+
+ align:start position:0%
+everything in between right we went from
+3 to infinity it's not boding well and
+
+ align:start position:0%
+3 to infinity it's not boding well and
+ 
+
+ align:start position:0%
+3 to infinity it's not boding well and
+even if you start saying well I'm not
+
+ align:start position:0%
+even if you start saying well I'm not
+ 
+
+ align:start position:0%
+even if you start saying well I'm not
+going to consider the whole distribution
+
+ align:start position:0%
+going to consider the whole distribution
+ 
+
+ align:start position:0%
+going to consider the whole distribution
+I just care about like the mean of the
+
+ align:start position:0%
+I just care about like the mean of the
+ 
+
+ align:start position:0%
+I just care about like the mean of the
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+it's still not pretty right well this is
+
+ align:start position:0%
+it's still not pretty right well this is
+ 
+
+ align:start position:0%
+it's still not pretty right well this is
+where this is where we have to start
+
+ align:start position:0%
+where this is where we have to start
+ 
+
+ align:start position:0%
+where this is where we have to start
+making approximations and this is where
+
+ align:start position:0%
+making approximations and this is where
+ 
+
+ align:start position:0%
+making approximations and this is where
+you start getting differences in planner
+
+ align:start position:0%
+you start getting differences in planner
+ 
+
+ align:start position:0%
+you start getting differences in planner
+in pungi be planners where they make
+
+ align:start position:0%
+in pungi be planners where they make
+ 
+
+ align:start position:0%
+in pungi be planners where they make
+assumptions where they make
+
+ align:start position:0%
+assumptions where they make
+ 
+
+ align:start position:0%
+assumptions where they make
+approximations so these images are from
+
+ align:start position:0%
+approximations so these images are from
+ 
+
+ align:start position:0%
+approximations so these images are from
+the belief road map paper from the
+
+ align:start position:0%
+the belief road map paper from the
+ 
+
+ align:start position:0%
+the belief road map paper from the
+robust robotics group a couple years ago
+
+ align:start position:0%
+robust robotics group a couple years ago
+ 
+
+ align:start position:0%
+robust robotics group a couple years ago
+but I'm going to talk about a different
+
+ align:start position:0%
+but I'm going to talk about a different
+ 
+
+ align:start position:0%
+but I'm going to talk about a different
+plan soon but the idea behind a lot of
+
+ align:start position:0%
+plan soon but the idea behind a lot of
+ 
+
+ align:start position:0%
+plan soon but the idea behind a lot of
+these planners is maybe we can start
+
+ align:start position:0%
+these planners is maybe we can start
+ 
+
+ align:start position:0%
+these planners is maybe we can start
+saying what these distributions are
+
+ align:start position:0%
+saying what these distributions are
+ 
+
+ align:start position:0%
+saying what these distributions are
+going to look like based on our models
+
+ align:start position:0%
+going to look like based on our models
+ 
+
+ align:start position:0%
+going to look like based on our models
+wait so to our planning problem if we
+
+ align:start position:0%
+wait so to our planning problem if we
+ 
+
+ align:start position:0%
+wait so to our planning problem if we
+know we start to breathe and we know our
+
+ align:start position:0%
+know we start to breathe and we know our
+ 
+
+ align:start position:0%
+know we start to breathe and we know our
+transition distribution we can start
+
+ align:start position:0%
+transition distribution we can start
+ 
+
+ align:start position:0%
+transition distribution we can start
+saying well then this is my probability
+
+ align:start position:0%
+saying well then this is my probability
+ 
+
+ align:start position:0%
+saying well then this is my probability
+distribution and then when I make an
+
+ align:start position:0%
+distribution and then when I make an
+ 
+
+ align:start position:0%
+distribution and then when I make an
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+I can build distributions off that and
+
+ align:start position:0%
+I can build distributions off that and
+ 
+
+ align:start position:0%
+I can build distributions off that and
+so if you could exhaustively just sort
+
+ align:start position:0%
+so if you could exhaustively just sort
+ 
+
+ align:start position:0%
+so if you could exhaustively just sort
+of propagate these distributions forward
+
+ align:start position:0%
+of propagate these distributions forward
+ 
+
+ align:start position:0%
+of propagate these distributions forward
+that'd be great
+
+ align:start position:0%
+that'd be great
+ 
+
+ align:start position:0%
+that'd be great
+it's unrealistic and I just want to
+
+ align:start position:0%
+it's unrealistic and I just want to
+ 
+
+ align:start position:0%
+it's unrealistic and I just want to
+point in terms of a visual the visual
+
+ align:start position:0%
+point in terms of a visual the visual
+ 
+
+ align:start position:0%
+point in terms of a visual the visual
+way to represent these
+
+ align:start position:0%
+way to represent these
+ 
+
+ align:start position:0%
+way to represent these
+it's a really nice way of saying in the
+
+ align:start position:0%
+it's a really nice way of saying in the
+ 
+
+ align:start position:0%
+it's a really nice way of saying in the
+deterministic world right you have these
+
+ align:start position:0%
+deterministic world right you have these
+ 
+
+ align:start position:0%
+deterministic world right you have these
+dots and edges in a probabilistic world
+
+ align:start position:0%
+dots and edges in a probabilistic world
+ 
+
+ align:start position:0%
+dots and edges in a probabilistic world
+these sort of circles these ellipsoids
+
+ align:start position:0%
+these sort of circles these ellipsoids
+ 
+
+ align:start position:0%
+these sort of circles these ellipsoids
+represent uncertainty typically it's one
+
+ align:start position:0%
+represent uncertainty typically it's one
+ 
+
+ align:start position:0%
+represent uncertainty typically it's one
+standard deviation or three standard
+
+ align:start position:0%
+standard deviation or three standard
+ 
+
+ align:start position:0%
+standard deviation or three standard
+deviations away and so you can start you
+
+ align:start position:0%
+deviations away and so you can start you
+ 
+
+ align:start position:0%
+deviations away and so you can start you
+know building into the map these are the
+
+ align:start position:0%
+know building into the map these are the
+ 
+
+ align:start position:0%
+know building into the map these are the
+distributions and the variances I can
+
+ align:start position:0%
+distributions and the variances I can
+ 
+
+ align:start position:0%
+distributions and the variances I can
+see up these notes
+
+ align:start position:0%
+see up these notes
+ 
+
+ align:start position:0%
+see up these notes
+are there any questions about this sort
+
+ align:start position:0%
+are there any questions about this sort
+ 
+
+ align:start position:0%
+are there any questions about this sort
+of stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right well we're going to delve now
+
+ align:start position:0%
+all right well we're going to delve now
+ 
+
+ align:start position:0%
+all right well we're going to delve now
+into a specific case study feedback
+
+ align:start position:0%
+into a specific case study feedback
+ 
+
+ align:start position:0%
+into a specific case study feedback
+based information state roadmaps for an
+
+ align:start position:0%
+based information state roadmaps for an
+ 
+
+ align:start position:0%
+based information state roadmaps for an
+adult only way I'm going to refer to it
+
+ align:start position:0%
+adult only way I'm going to refer to it
+ 
+
+ align:start position:0%
+adult only way I'm going to refer to it
+refer to it
+
+ align:start position:0%
+refer to it
+ 
+
+ align:start position:0%
+refer to it
+the idea behind us is you're going to
+
+ align:start position:0%
+the idea behind us is you're going to
+ 
+
+ align:start position:0%
+the idea behind us is you're going to
+sample mean configurations from your
+
+ align:start position:0%
+sample mean configurations from your
+ 
+
+ align:start position:0%
+sample mean configurations from your
+configuration space then you want to
+
+ align:start position:0%
+configuration space then you want to
+ 
+
+ align:start position:0%
+configuration space then you want to
+build you want to build an lqr that's
+
+ align:start position:0%
+build you want to build an lqr that's
+ 
+
+ align:start position:0%
+build you want to build an lqr that's
+linear quadratic regulator controller
+
+ align:start position:0%
+linear quadratic regulator controller
+ 
+
+ align:start position:0%
+linear quadratic regulator controller
+around these points then that will
+
+ align:start position:0%
+around these points then that will
+ 
+
+ align:start position:0%
+around these points then that will
+generate what Barretts you can tolerate
+
+ align:start position:0%
+generate what Barretts you can tolerate
+ 
+
+ align:start position:0%
+generate what Barretts you can tolerate
+rates of lqr controllers you don't know
+
+ align:start position:0%
+rates of lqr controllers you don't know
+ 
+
+ align:start position:0%
+rates of lqr controllers you don't know
+they're really nice they around being a
+
+ align:start position:0%
+they're really nice they around being a
+ 
+
+ align:start position:0%
+they're really nice they around being a
+small region around a point they can
+
+ align:start position:0%
+small region around a point they can
+ 
+
+ align:start position:0%
+small region around a point they can
+drive a quadrant for example to that
+
+ align:start position:0%
+drive a quadrant for example to that
+ 
+
+ align:start position:0%
+drive a quadrant for example to that
+indicative and so if you build these out
+
+ align:start position:0%
+indicative and so if you build these out
+ 
+
+ align:start position:0%
+indicative and so if you build these out
+you are controllers around points you
+
+ align:start position:0%
+you are controllers around points you
+ 
+
+ align:start position:0%
+you are controllers around points you
+can say all right anytime I end up in
+
+ align:start position:0%
+can say all right anytime I end up in
+ 
+
+ align:start position:0%
+can say all right anytime I end up in
+this cloud right this cloud in the
+
+ align:start position:0%
+this cloud right this cloud in the
+ 
+
+ align:start position:0%
+this cloud right this cloud in the
+belief space to any sort of distribution
+
+ align:start position:0%
+belief space to any sort of distribution
+ 
+
+ align:start position:0%
+belief space to any sort of distribution
+I can bring it back to that mean and so
+
+ align:start position:0%
+I can bring it back to that mean and so
+ 
+
+ align:start position:0%
+I can bring it back to that mean and so
+now what we've done is we've generated
+
+ align:start position:0%
+now what we've done is we've generated
+ 
+
+ align:start position:0%
+now what we've done is we've generated
+every point we just need to connect them
+
+ align:start position:0%
+every point we just need to connect them
+ 
+
+ align:start position:0%
+every point we just need to connect them
+and the idea is if you have a feedback
+
+ align:start position:0%
+and the idea is if you have a feedback
+ 
+
+ align:start position:0%
+and the idea is if you have a feedback
+controller feedback based they can get
+
+ align:start position:0%
+controller feedback based they can get
+ 
+
+ align:start position:0%
+controller feedback based they can get
+to one cloud to another anywhere in the
+
+ align:start position:0%
+to one cloud to another anywhere in the
+ 
+
+ align:start position:0%
+to one cloud to another anywhere in the
+clouds then you can get from point to
+
+ align:start position:0%
+clouds then you can get from point to
+ 
+
+ align:start position:0%
+clouds then you can get from point to
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+all right this is how you generate the
+
+ align:start position:0%
+all right this is how you generate the
+ 
+
+ align:start position:0%
+all right this is how you generate the
+graph and what's cool is the way they
+
+ align:start position:0%
+graph and what's cool is the way they
+ 
+
+ align:start position:0%
+graph and what's cool is the way they
+formulated the problem they said well
+
+ align:start position:0%
+formulated the problem they said well
+ 
+
+ align:start position:0%
+formulated the problem they said well
+setup the cost of executing an egg we
+
+ align:start position:0%
+setup the cost of executing an egg we
+ 
+
+ align:start position:0%
+setup the cost of executing an egg we
+switched from rewards to costs because
+
+ align:start position:0%
+switched from rewards to costs because
+ 
+
+ align:start position:0%
+switched from rewards to costs because
+the pessimist is now okay well the cost
+
+ align:start position:0%
+the pessimist is now okay well the cost
+ 
+
+ align:start position:0%
+the pessimist is now okay well the cost
+is going to be a linear combination
+
+ align:start position:0%
+is going to be a linear combination
+ 
+
+ align:start position:0%
+is going to be a linear combination
+of the expected time to execute that egg
+
+ align:start position:0%
+of the expected time to execute that egg
+ 
+
+ align:start position:0%
+of the expected time to execute that egg
+and the uncertainty along that edge now
+
+ align:start position:0%
+and the uncertainty along that edge now
+ 
+
+ align:start position:0%
+and the uncertainty along that edge now
+this is actually really cool to Playland
+
+ align:start position:0%
+this is actually really cool to Playland
+ 
+
+ align:start position:0%
+this is actually really cool to Playland
+what do you think would happen if I said
+
+ align:start position:0%
+what do you think would happen if I said
+ 
+
+ align:start position:0%
+what do you think would happen if I said
+beta to zero unless like what sort of
+
+ align:start position:0%
+beta to zero unless like what sort of
+ 
+
+ align:start position:0%
+beta to zero unless like what sort of
+material even get a real cool because
+
+ align:start position:0%
+material even get a real cool because
+ 
+
+ align:start position:0%
+material even get a real cool because
+they know the few names
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which I don't let it go also in the make
+
+ align:start position:0%
+which I don't let it go also in the make
+ 
+
+ align:start position:0%
+which I don't let it go also in the make
+room you're gonna get a shorter span
+
+ align:start position:0%
+room you're gonna get a shorter span
+ 
+
+ align:start position:0%
+room you're gonna get a shorter span
+shortest path that's ready right this
+
+ align:start position:0%
+shortest path that's ready right this
+ 
+
+ align:start position:0%
+shortest path that's ready right this
+term goes away the cost is a function of
+
+ align:start position:0%
+term goes away the cost is a function of
+ 
+
+ align:start position:0%
+term goes away the cost is a function of
+the time shortest path now what's cool
+
+ align:start position:0%
+the time shortest path now what's cool
+ 
+
+ align:start position:0%
+the time shortest path now what's cool
+is this one day I was messing around
+
+ align:start position:0%
+is this one day I was messing around
+ 
+
+ align:start position:0%
+is this one day I was messing around
+with this code like I wonder what
+
+ align:start position:0%
+with this code like I wonder what
+ 
+
+ align:start position:0%
+with this code like I wonder what
+happens in mice an outlet is zero right
+
+ align:start position:0%
+happens in mice an outlet is zero right
+ 
+
+ align:start position:0%
+happens in mice an outlet is zero right
+so your cost is purely a function of
+
+ align:start position:0%
+so your cost is purely a function of
+ 
+
+ align:start position:0%
+so your cost is purely a function of
+uncertainty turns out what the quadrotor
+
+ align:start position:0%
+uncertainty turns out what the quadrotor
+ 
+
+ align:start position:0%
+uncertainty turns out what the quadrotor
+does is it just hangs out where it
+
+ align:start position:0%
+does is it just hangs out where it
+ 
+
+ align:start position:0%
+does is it just hangs out where it
+starts
+
+ align:start position:0%
+starts
+ 
+
+ align:start position:0%
+starts
+it says I'm in no hurry I know where I
+
+ align:start position:0%
+it says I'm in no hurry I know where I
+ 
+
+ align:start position:0%
+it says I'm in no hurry I know where I
+am I'm just gonna stay here so you know
+
+ align:start position:0%
+am I'm just gonna stay here so you know
+ 
+
+ align:start position:0%
+am I'm just gonna stay here so you know
+like what but I find this amazing right
+
+ align:start position:0%
+like what but I find this amazing right
+ 
+
+ align:start position:0%
+like what but I find this amazing right
+because this almost models behavior you
+
+ align:start position:0%
+because this almost models behavior you
+ 
+
+ align:start position:0%
+because this almost models behavior you
+can start saying like do I want to be a
+
+ align:start position:0%
+can start saying like do I want to be a
+ 
+
+ align:start position:0%
+can start saying like do I want to be a
+risky quadrotor or a safe one like how
+
+ align:start position:0%
+risky quadrotor or a safe one like how
+ 
+
+ align:start position:0%
+risky quadrotor or a safe one like how
+important is it for me to get some real
+
+ align:start position:0%
+important is it for me to get some real
+ 
+
+ align:start position:0%
+important is it for me to get some real
+time or you know we sing and it's just
+
+ align:start position:0%
+time or you know we sing and it's just
+ 
+
+ align:start position:0%
+time or you know we sing and it's just
+those two parameters or you can even
+
+ align:start position:0%
+those two parameters or you can even
+ 
+
+ align:start position:0%
+those two parameters or you can even
+make it one that out by one minus alpha
+
+ align:start position:0%
+make it one that out by one minus alpha
+ 
+
+ align:start position:0%
+make it one that out by one minus alpha
+I think this stuff is really cool all
+
+ align:start position:0%
+I think this stuff is really cool all
+ 
+
+ align:start position:0%
+I think this stuff is really cool all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+the one detail that I'm really going to
+
+ align:start position:0%
+the one detail that I'm really going to
+ 
+
+ align:start position:0%
+the one detail that I'm really going to
+go into for firm is the cost equipment
+
+ align:start position:0%
+go into for firm is the cost equipment
+ 
+
+ align:start position:0%
+go into for firm is the cost equipment
+which is based on the bellman back-up
+
+ align:start position:0%
+which is based on the bellman back-up
+ 
+
+ align:start position:0%
+which is based on the bellman back-up
+equation that we had the cost to go
+
+ align:start position:0%
+equation that we had the cost to go
+ 
+
+ align:start position:0%
+equation that we had the cost to go
+great expected cost from a belief state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is well you're going to take the best
+
+ align:start position:0%
+is well you're going to take the best
+ 
+
+ align:start position:0%
+is well you're going to take the best
+dungeon so you're going to take the min
+
+ align:start position:0%
+dungeon so you're going to take the min
+ 
+
+ align:start position:0%
+dungeon so you're going to take the min
+of this whole thing you're gonna say
+
+ align:start position:0%
+of this whole thing you're gonna say
+ 
+
+ align:start position:0%
+of this whole thing you're gonna say
+it's the cost of executing a specific
+
+ align:start position:0%
+it's the cost of executing a specific
+ 
+
+ align:start position:0%
+it's the cost of executing a specific
+action plus the cost of colliding with
+
+ align:start position:0%
+action plus the cost of colliding with
+ 
+
+ align:start position:0%
+action plus the cost of colliding with
+something an obstacle times the
+
+ align:start position:0%
+something an obstacle times the
+ 
+
+ align:start position:0%
+something an obstacle times the
+probability of colliding that's this
+
+ align:start position:0%
+probability of colliding that's this
+ 
+
+ align:start position:0%
+probability of colliding that's this
+term and then
+
+ align:start position:0%
+term and then
+ 
+
+ align:start position:0%
+term and then
+you've got to say well okay and then
+
+ align:start position:0%
+you've got to say well okay and then
+ 
+
+ align:start position:0%
+you've got to say well okay and then
+once they reach the state what's the
+
+ align:start position:0%
+once they reach the state what's the
+ 
+
+ align:start position:0%
+once they reach the state what's the
+cost through there and then I could wait
+
+ align:start position:0%
+cost through there and then I could wait
+ 
+
+ align:start position:0%
+cost through there and then I could wait
+that by the probability of ending up
+
+ align:start position:0%
+that by the probability of ending up
+ 
+
+ align:start position:0%
+that by the probability of ending up
+United State does this equation makes
+
+ align:start position:0%
+United State does this equation makes
+ 
+
+ align:start position:0%
+United State does this equation makes
+sense to people like there are a lot of
+
+ align:start position:0%
+sense to people like there are a lot of
+ 
+
+ align:start position:0%
+sense to people like there are a lot of
+symbols and honestly I hate notation but
+
+ align:start position:0%
+symbols and honestly I hate notation but
+ 
+
+ align:start position:0%
+symbols and honestly I hate notation but
+it works you just plug it with the cost
+
+ align:start position:0%
+it works you just plug it with the cost
+ 
+
+ align:start position:0%
+it works you just plug it with the cost
+is I'm going to take the best option
+
+ align:start position:0%
+is I'm going to take the best option
+ 
+
+ align:start position:0%
+is I'm going to take the best option
+it's going to be the constant using that
+
+ align:start position:0%
+it's going to be the constant using that
+ 
+
+ align:start position:0%
+it's going to be the constant using that
+action the cost of colliding times the
+
+ align:start position:0%
+action the cost of colliding times the
+ 
+
+ align:start position:0%
+action the cost of colliding times the
+probability of colliding give them that
+
+ align:start position:0%
+probability of colliding give them that
+ 
+
+ align:start position:0%
+probability of colliding give them that
+I use that action and I started where I
+
+ align:start position:0%
+I use that action and I started where I
+ 
+
+ align:start position:0%
+I use that action and I started where I
+started and then the cost from where I
+
+ align:start position:0%
+started and then the cost from where I
+ 
+
+ align:start position:0%
+started and then the cost from where I
+end up
+
+ align:start position:0%
+end up
+ 
+
+ align:start position:0%
+end up
+and since you end up you know
+
+ align:start position:0%
+and since you end up you know
+ 
+
+ align:start position:0%
+and since you end up you know
+probability distribution ready to
+
+ align:start position:0%
+probability distribution ready to
+ 
+
+ align:start position:0%
+probability distribution ready to
+consider all those pieces yeah when you
+
+ align:start position:0%
+consider all those pieces yeah when you
+ 
+
+ align:start position:0%
+consider all those pieces yeah when you
+define like an action from one place or
+
+ align:start position:0%
+define like an action from one place or
+ 
+
+ align:start position:0%
+define like an action from one place or
+another you have always think of it as
+
+ align:start position:0%
+another you have always think of it as
+ 
+
+ align:start position:0%
+another you have always think of it as
+starting from the example
+
+ align:start position:0%
+starting from the example
+ 
+
+ align:start position:0%
+starting from the example
+so it's from the so formerly it was from
+
+ align:start position:0%
+so it's from the so formerly it was from
+ 
+
+ align:start position:0%
+so it's from the so formerly it was from
+the belief state is the mean plus yeah
+
+ align:start position:0%
+the belief state is the mean plus yeah
+ 
+
+ align:start position:0%
+the belief state is the mean plus yeah
+the variance once it stabilizes to that
+
+ align:start position:0%
+the variance once it stabilizes to that
+ 
+
+ align:start position:0%
+the variance once it stabilizes to that
+point and the way that variance is
+
+ align:start position:0%
+point and the way that variance is
+ 
+
+ align:start position:0%
+point and the way that variance is
+generated I should have said is wait
+
+ align:start position:0%
+generated I should have said is wait
+ 
+
+ align:start position:0%
+generated I should have said is wait
+you're going to have models of these
+
+ align:start position:0%
+you're going to have models of these
+ 
+
+ align:start position:0%
+you're going to have models of these
+quadrotors or and so you can I spent a
+
+ align:start position:0%
+quadrotors or and so you can I spent a
+ 
+
+ align:start position:0%
+quadrotors or and so you can I spent a
+good time in the ACL with John how 4:16
+
+ align:start position:0%
+good time in the ACL with John how 4:16
+ 
+
+ align:start position:0%
+good time in the ACL with John how 4:16
+and you just let the quadrotor hover you
+
+ align:start position:0%
+and you just let the quadrotor hover you
+ 
+
+ align:start position:0%
+and you just let the quadrotor hover you
+measure its position for a lot for a
+
+ align:start position:0%
+measure its position for a lot for a
+ 
+
+ align:start position:0%
+measure its position for a lot for a
+long time and you get by the
+
+ align:start position:0%
+long time and you get by the
+ 
+
+ align:start position:0%
+long time and you get by the
+distribution over where it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the letter M yeah wait so you're
+
+ align:start position:0%
+what is the letter M yeah wait so you're
+ 
+
+ align:start position:0%
+what is the letter M yeah wait so you're
+summing over these are the three states
+
+ align:start position:0%
+summing over these are the three states
+ 
+
+ align:start position:0%
+summing over these are the three states
+that could end up in right so if
+
+ align:start position:0%
+that could end up in right so if
+ 
+
+ align:start position:0%
+that could end up in right so if
+everything we're deterministic this
+
+ align:start position:0%
+everything we're deterministic this
+ 
+
+ align:start position:0%
+everything we're deterministic this
+would just be ignored some it's where
+
+ align:start position:0%
+would just be ignored some it's where
+ 
+
+ align:start position:0%
+would just be ignored some it's where
+you might happen
+
+ align:start position:0%
+you might happen
+ 
+
+ align:start position:0%
+you might happen
+realistically you could end up being
+
+ align:start position:0%
+realistically you could end up being
+ 
+
+ align:start position:0%
+realistically you could end up being
+some of those four operating out of a
+
+ align:start position:0%
+some of those four operating out of a
+ 
+
+ align:start position:0%
+some of those four operating out of a
+genius space and you have Kachinas
+
+ align:start position:0%
+genius space and you have Kachinas
+ 
+
+ align:start position:0%
+genius space and you have Kachinas
+observations so those are some over the
+
+ align:start position:0%
+observations so those are some over the
+ 
+
+ align:start position:0%
+observations so those are some over the
+observation samples that generated when
+
+ align:start position:0%
+observation samples that generated when
+ 
+
+ align:start position:0%
+observation samples that generated when
+so that is a finite sum over the
+
+ align:start position:0%
+so that is a finite sum over the
+ 
+
+ align:start position:0%
+so that is a finite sum over the
+possible anthony observations basically
+
+ align:start position:0%
+possible anthony observations basically
+ 
+
+ align:start position:0%
+possible anthony observations basically
+my cabbage yeah so there's definitely
+
+ align:start position:0%
+my cabbage yeah so there's definitely
+ 
+
+ align:start position:0%
+my cabbage yeah so there's definitely
+food in terms of where you could end up
+
+ align:start position:0%
+food in terms of where you could end up
+ 
+
+ align:start position:0%
+food in terms of where you could end up
+and maybe in space there's a sentiment
+
+ align:start position:0%
+and maybe in space there's a sentiment
+ 
+
+ align:start position:0%
+and maybe in space there's a sentiment
+feedback you're allowed
+
+ align:start position:0%
+feedback you're allowed
+ 
+
+ align:start position:0%
+feedback you're allowed
+I think the observation if you model it
+
+ align:start position:0%
+I think the observation if you model it
+ 
+
+ align:start position:0%
+I think the observation if you model it
+as the Gaussian if you made some nice
+
+ align:start position:0%
+as the Gaussian if you made some nice
+ 
+
+ align:start position:0%
+as the Gaussian if you made some nice
+and some things if you try to bless
+
+ align:start position:0%
+and some things if you try to bless
+ 
+
+ align:start position:0%
+and some things if you try to bless
+potatoes well just what so pretty
+
+ align:start position:0%
+potatoes well just what so pretty
+ 
+
+ align:start position:0%
+potatoes well just what so pretty
+you start so if you start with the ocean
+
+ align:start position:0%
+you start so if you start with the ocean
+ 
+
+ align:start position:0%
+you start so if you start with the ocean
+boys and you have a linear model yet
+
+ align:start position:0%
+boys and you have a linear model yet
+ 
+
+ align:start position:0%
+boys and you have a linear model yet
+then your prediction is going to be
+
+ align:start position:0%
+then your prediction is going to be
+ 
+
+ align:start position:0%
+then your prediction is going to be
+couching yeah but then if you have
+
+ align:start position:0%
+couching yeah but then if you have
+ 
+
+ align:start position:0%
+couching yeah but then if you have
+dodging observations which is great
+
+ align:start position:0%
+dodging observations which is great
+ 
+
+ align:start position:0%
+dodging observations which is great
+because in yet or updated ouches but the
+
+ align:start position:0%
+because in yet or updated ouches but the
+ 
+
+ align:start position:0%
+because in yet or updated ouches but the
+observations bases engineer so basically
+
+ align:start position:0%
+observations bases engineer so basically
+ 
+
+ align:start position:0%
+observations bases engineer so basically
+not only have two simple positions but
+
+ align:start position:0%
+not only have two simple positions but
+ 
+
+ align:start position:0%
+not only have two simple positions but
+you also have two simple with initial
+
+ align:start position:0%
+you also have two simple with initial
+ 
+
+ align:start position:0%
+you also have two simple with initial
+observations that you might get as you
+
+ align:start position:0%
+observations that you might get as you
+ 
+
+ align:start position:0%
+observations that you might get as you
+go along
+
+ align:start position:0%
+go along
+ 
+
+ align:start position:0%
+go along
+yeah so that you can basically would but
+
+ align:start position:0%
+yeah so that you can basically would but
+ 
+
+ align:start position:0%
+yeah so that you can basically would but
+basically it's great but you would be
+
+ align:start position:0%
+basically it's great but you would be
+ 
+
+ align:start position:0%
+basically it's great but you would be
+basically reducing a possibly infinite
+
+ align:start position:0%
+basically reducing a possibly infinite
+ 
+
+ align:start position:0%
+basically reducing a possibly infinite
+branching yeah which is your couch into
+
+ align:start position:0%
+branching yeah which is your couch into
+ 
+
+ align:start position:0%
+branching yeah which is your couch into
+kind of like a mark or the car which
+
+ align:start position:0%
+kind of like a mark or the car which
+ 
+
+ align:start position:0%
+kind of like a mark or the car which
+research something like let me generate
+
+ align:start position:0%
+research something like let me generate
+ 
+
+ align:start position:0%
+research something like let me generate
+a whole bunch of meaningful samples if
+
+ align:start position:0%
+a whole bunch of meaningful samples if
+ 
+
+ align:start position:0%
+a whole bunch of meaningful samples if
+those are doing so is that where that
+
+ align:start position:0%
+those are doing so is that where that
+ 
+
+ align:start position:0%
+those are doing so is that where that
+something yeah
+
+ align:start position:0%
+something yeah
+ 
+
+ align:start position:0%
+something yeah
+and a fun fact theorem that I read
+
+ align:start position:0%
+and a fun fact theorem that I read
+ 
+
+ align:start position:0%
+and a fun fact theorem that I read
+trusted was that if you just sample
+
+ align:start position:0%
+trusted was that if you just sample
+ 
+
+ align:start position:0%
+trusted was that if you just sample
+randomly right from your configuration
+
+ align:start position:0%
+randomly right from your configuration
+ 
+
+ align:start position:0%
+randomly right from your configuration
+space to zero probability of
+
+ align:start position:0%
+space to zero probability of
+ 
+
+ align:start position:0%
+space to zero probability of
+constructing a graph that without any
+
+ align:start position:0%
+constructing a graph that without any
+ 
+
+ align:start position:0%
+constructing a graph that without any
+assumptions will be connected crisper
+
+ align:start position:0%
+assumptions will be connected crisper
+ 
+
+ align:start position:0%
+assumptions will be connected crisper
+prm's right you're sampling up now
+
+ align:start position:0%
+prm's right you're sampling up now
+ 
+
+ align:start position:0%
+prm's right you're sampling up now
+things will turn out nicely not the case
+
+ align:start position:0%
+things will turn out nicely not the case
+ 
+
+ align:start position:0%
+things will turn out nicely not the case
+in the belief state that's why we need
+
+ align:start position:0%
+in the belief state that's why we need
+ 
+
+ align:start position:0%
+in the belief state that's why we need
+to make these assumptions okay we're
+
+ align:start position:0%
+to make these assumptions okay we're
+ 
+
+ align:start position:0%
+to make these assumptions okay we're
+killing it you know funky cheese now we
+
+ align:start position:0%
+killing it you know funky cheese now we
+ 
+
+ align:start position:0%
+killing it you know funky cheese now we
+get to look at some really fun graphics
+
+ align:start position:0%
+get to look at some really fun graphics
+ 
+
+ align:start position:0%
+get to look at some really fun graphics
+generated from real flights using firm
+
+ align:start position:0%
+generated from real flights using firm
+ 
+
+ align:start position:0%
+generated from real flights using firm
+okay the big takeaway is that firm
+
+ align:start position:0%
+okay the big takeaway is that firm
+ 
+
+ align:start position:0%
+okay the big takeaway is that firm
+prefers safer paths we've got two images
+
+ align:start position:0%
+prefers safer paths we've got two images
+ 
+
+ align:start position:0%
+prefers safer paths we've got two images
+that look really similar I'm going to
+
+ align:start position:0%
+that look really similar I'm going to
+ 
+
+ align:start position:0%
+that look really similar I'm going to
+talk about one and then why they're
+
+ align:start position:0%
+talk about one and then why they're
+ 
+
+ align:start position:0%
+talk about one and then why they're
+slightly different the test light that
+
+ align:start position:0%
+slightly different the test light that
+ 
+
+ align:start position:0%
+slightly different the test light that
+we put this quadrotor under was we said
+
+ align:start position:0%
+we put this quadrotor under was we said
+ 
+
+ align:start position:0%
+we put this quadrotor under was we said
+we're going to start at this
+
+ align:start position:0%
+we're going to start at this
+ 
+
+ align:start position:0%
+we're going to start at this
+configuration we're gonna go to this
+
+ align:start position:0%
+configuration we're gonna go to this
+ 
+
+ align:start position:0%
+configuration we're gonna go to this
+configuration and there's this big blue
+
+ align:start position:0%
+configuration and there's this big blue
+ 
+
+ align:start position:0%
+configuration and there's this big blue
+obstacle and there are landmarks that
+
+ align:start position:0%
+obstacle and there are landmarks that
+ 
+
+ align:start position:0%
+obstacle and there are landmarks that
+you can take measurements all books
+
+ align:start position:0%
+you can take measurements all books
+ 
+
+ align:start position:0%
+you can take measurements all books
+those are these red dots we want to
+
+ align:start position:0%
+those are these red dots we want to
+ 
+
+ align:start position:0%
+those are these red dots we want to
+compare two planets right a PRM and a
+
+ align:start position:0%
+compare two planets right a PRM and a
+ 
+
+ align:start position:0%
+compare two planets right a PRM and a
+fermion planner the PRF fan said right I
+
+ align:start position:0%
+fermion planner the PRF fan said right I
+ 
+
+ align:start position:0%
+fermion planner the PRF fan said right I
+just want to minimize time and so they
+
+ align:start position:0%
+just want to minimize time and so they
+ 
+
+ align:start position:0%
+just want to minimize time and so they
+find the shortest path is stay to the
+
+ align:start position:0%
+find the shortest path is stay to the
+ 
+
+ align:start position:0%
+find the shortest path is stay to the
+left of the obstacle but that's actually
+
+ align:start position:0%
+left of the obstacle but that's actually
+ 
+
+ align:start position:0%
+left of the obstacle but that's actually
+a really narrow path between the
+
+ align:start position:0%
+a really narrow path between the
+ 
+
+ align:start position:0%
+a really narrow path between the
+obstacle and the wall on the other hand
+
+ align:start position:0%
+obstacle and the wall on the other hand
+ 
+
+ align:start position:0%
+obstacle and the wall on the other hand
+the firm planner said right I want to
+
+ align:start position:0%
+the firm planner said right I want to
+ 
+
+ align:start position:0%
+the firm planner said right I want to
+minimize the linear combination of time
+
+ align:start position:0%
+minimize the linear combination of time
+ 
+
+ align:start position:0%
+minimize the linear combination of time
+and uncertainty and so if you ramp up
+
+ align:start position:0%
+and uncertainty and so if you ramp up
+ 
+
+ align:start position:0%
+and uncertainty and so if you ramp up
+the term the wait for uncertainty at
+
+ align:start position:0%
+the term the wait for uncertainty at
+ 
+
+ align:start position:0%
+the term the wait for uncertainty at
+some point the path sort of pops over
+
+ align:start position:0%
+some point the path sort of pops over
+ 
+
+ align:start position:0%
+some point the path sort of pops over
+the obstacle really puts
+
+ align:start position:0%
+the obstacle really puts
+ 
+
+ align:start position:0%
+the obstacle really puts
+and then you get this safer path but
+
+ align:start position:0%
+and then you get this safer path but
+ 
+
+ align:start position:0%
+and then you get this safer path but
+that's longer and how do we know it's
+
+ align:start position:0%
+that's longer and how do we know it's
+ 
+
+ align:start position:0%
+that's longer and how do we know it's
+safer because these ellipsoids that
+
+ align:start position:0%
+safer because these ellipsoids that
+ 
+
+ align:start position:0%
+safer because these ellipsoids that
+we've drawn are the 3d versions of what
+
+ align:start position:0%
+we've drawn are the 3d versions of what
+ 
+
+ align:start position:0%
+we've drawn are the 3d versions of what
+we saw for the PRM and not elevated to
+
+ align:start position:0%
+we saw for the PRM and not elevated to
+ 
+
+ align:start position:0%
+we saw for the PRM and not elevated to
+the belief space version it's the
+
+ align:start position:0%
+the belief space version it's the
+ 
+
+ align:start position:0%
+the belief space version it's the
+uncertainty that the quadrotor has for
+
+ align:start position:0%
+uncertainty that the quadrotor has for
+ 
+
+ align:start position:0%
+uncertainty that the quadrotor has for
+its true state why is the PRF plan why
+
+ align:start position:0%
+its true state why is the PRF plan why
+ 
+
+ align:start position:0%
+its true state why is the PRF plan why
+does it have such vague ellipsoids it's
+
+ align:start position:0%
+does it have such vague ellipsoids it's
+ 
+
+ align:start position:0%
+does it have such vague ellipsoids it's
+because when it's behind the obstacle it
+
+ align:start position:0%
+because when it's behind the obstacle it
+ 
+
+ align:start position:0%
+because when it's behind the obstacle it
+can't make any of these measurements
+
+ align:start position:0%
+can't make any of these measurements
+ 
+
+ align:start position:0%
+can't make any of these measurements
+because they can't see the land lines so
+
+ align:start position:0%
+because they can't see the land lines so
+ 
+
+ align:start position:0%
+because they can't see the land lines so
+it's basically using dead reckoning and
+
+ align:start position:0%
+it's basically using dead reckoning and
+ 
+
+ align:start position:0%
+it's basically using dead reckoning and
+the transition model right did not
+
+ align:start position:0%
+the transition model right did not
+ 
+
+ align:start position:0%
+the transition model right did not
+deterministic and service profits
+
+ align:start position:0%
+deterministic and service profits
+ 
+
+ align:start position:0%
+deterministic and service profits
+uncertainty grips and so we can see
+
+ align:start position:0%
+uncertainty grips and so we can see
+ 
+
+ align:start position:0%
+uncertainty grips and so we can see
+these ellipsoids are bigger from PRM
+
+ align:start position:0%
+these ellipsoids are bigger from PRM
+ 
+
+ align:start position:0%
+these ellipsoids are bigger from PRM
+infer and then the reason I have two
+
+ align:start position:0%
+infer and then the reason I have two
+ 
+
+ align:start position:0%
+infer and then the reason I have two
+images is they are slightly different
+
+ align:start position:0%
+images is they are slightly different
+ 
+
+ align:start position:0%
+images is they are slightly different
+it's that these landmarks were
+
+ align:start position:0%
+it's that these landmarks were
+ 
+
+ align:start position:0%
+it's that these landmarks were
+fictitious landmarks that we said you
+
+ align:start position:0%
+fictitious landmarks that we said you
+ 
+
+ align:start position:0%
+fictitious landmarks that we said you
+can and we would generate fake
+
+ align:start position:0%
+can and we would generate fake
+ 
+
+ align:start position:0%
+can and we would generate fake
+measurements off the bank until we could
+
+ align:start position:0%
+measurements off the bank until we could
+ 
+
+ align:start position:0%
+measurements off the bank until we could
+tune the noise of the landmarks maybe a
+
+ align:start position:0%
+tune the noise of the landmarks maybe a
+ 
+
+ align:start position:0%
+tune the noise of the landmarks maybe a
+little bit of kick but it allowed us to
+
+ align:start position:0%
+little bit of kick but it allowed us to
+ 
+
+ align:start position:0%
+little bit of kick but it allowed us to
+say when we increase the noise from some
+
+ align:start position:0%
+say when we increase the noise from some
+ 
+
+ align:start position:0%
+say when we increase the noise from some
+dimension was number of point oh five
+
+ align:start position:0%
+dimension was number of point oh five
+ 
+
+ align:start position:0%
+dimension was number of point oh five
+two point one five you can see the
+
+ align:start position:0%
+two point one five you can see the
+ 
+
+ align:start position:0%
+two point one five you can see the
+uncertainty ellipsoids for pyaara grow
+
+ align:start position:0%
+uncertainty ellipsoids for pyaara grow
+ 
+
+ align:start position:0%
+uncertainty ellipsoids for pyaara grow
+when we increase the noise
+
+ align:start position:0%
+when we increase the noise
+ 
+
+ align:start position:0%
+when we increase the noise
+where's preferring they stay about the
+
+ align:start position:0%
+where's preferring they stay about the
+ 
+
+ align:start position:0%
+where's preferring they stay about the
+same and importantly these ellipsoids
+
+ align:start position:0%
+same and importantly these ellipsoids
+ 
+
+ align:start position:0%
+same and importantly these ellipsoids
+grow enough that they serve overlapping
+
+ align:start position:0%
+grow enough that they serve overlapping
+ 
+
+ align:start position:0%
+grow enough that they serve overlapping
+with the obstacles that represents a
+
+ align:start position:0%
+with the obstacles that represents a
+ 
+
+ align:start position:0%
+with the obstacles that represents a
+very high probability of collision
+
+ align:start position:0%
+very high probability of collision
+ 
+
+ align:start position:0%
+very high probability of collision
+where's confirmed the way it managed to
+
+ align:start position:0%
+where's confirmed the way it managed to
+ 
+
+ align:start position:0%
+where's confirmed the way it managed to
+keep these ellipsoid so small is protect
+
+ align:start position:0%
+keep these ellipsoid so small is protect
+ 
+
+ align:start position:0%
+keep these ellipsoid so small is protect
+the cost function the same right same
+
+ align:start position:0%
+the cost function the same right same
+ 
+
+ align:start position:0%
+the cost function the same right same
+way the footpath certainty same way
+
+ align:start position:0%
+way the footpath certainty same way
+ 
+
+ align:start position:0%
+way the footpath certainty same way
+behind right but the answer think he was
+
+ align:start position:0%
+behind right but the answer think he was
+ 
+
+ align:start position:0%
+behind right but the answer think he was
+so much higher and so it would decide
+
+ align:start position:0%
+so much higher and so it would decide
+ 
+
+ align:start position:0%
+so much higher and so it would decide
+well i can sacrifice a little bit of
+
+ align:start position:0%
+well i can sacrifice a little bit of
+ 
+
+ align:start position:0%
+well i can sacrifice a little bit of
+time I can take the slower path I can
+
+ align:start position:0%
+time I can take the slower path I can
+ 
+
+ align:start position:0%
+time I can take the slower path I can
+just hang out by a landmark really major
+
+ align:start position:0%
+just hang out by a landmark really major
+ 
+
+ align:start position:0%
+just hang out by a landmark really major
+know where I am before continue it's in
+
+ align:start position:0%
+know where I am before continue it's in
+ 
+
+ align:start position:0%
+know where I am before continue it's in
+the path the duration of the flight -
+
+ align:start position:0%
+the path the duration of the flight -
+ 
+
+ align:start position:0%
+the path the duration of the flight -
+it's a lot longer for firm as a tiny
+
+ align:start position:0%
+it's a lot longer for firm as a tiny
+ 
+
+ align:start position:0%
+it's a lot longer for firm as a tiny
+would increase but the uncertainty would
+
+ align:start position:0%
+would increase but the uncertainty would
+ 
+
+ align:start position:0%
+would increase but the uncertainty would
+stay about the constant people
+
+ align:start position:0%
+stay about the constant people
+ 
+
+ align:start position:0%
+stay about the constant people
+understand these graphics great all
+
+ align:start position:0%
+understand these graphics great all
+ 
+
+ align:start position:0%
+understand these graphics great all
+right you've got a graph that just
+
+ align:start position:0%
+right you've got a graph that just
+ 
+
+ align:start position:0%
+right you've got a graph that just
+represents a little more formally that
+
+ align:start position:0%
+represents a little more formally that
+ 
+
+ align:start position:0%
+represents a little more formally that
+growing uncertainty as the noise
+
+ align:start position:0%
+growing uncertainty as the noise
+ 
+
+ align:start position:0%
+growing uncertainty as the noise
+increases the variance along a single
+
+ align:start position:0%
+increases the variance along a single
+ 
+
+ align:start position:0%
+increases the variance along a single
+dimension Z Y and X from PRM which is
+
+ align:start position:0%
+dimension Z Y and X from PRM which is
+ 
+
+ align:start position:0%
+dimension Z Y and X from PRM which is
+that and fern the variance for PRM is
+
+ align:start position:0%
+that and fern the variance for PRM is
+ 
+
+ align:start position:0%
+that and fern the variance for PRM is
+always higher than the growth refer it
+
+ align:start position:0%
+always higher than the growth refer it
+ 
+
+ align:start position:0%
+always higher than the growth refer it
+slower and it stays about constant
+
+ align:start position:0%
+slower and it stays about constant
+ 
+
+ align:start position:0%
+slower and it stays about constant
+that's the big takeaway and from
+
+ align:start position:0%
+that's the big takeaway and from
+ 
+
+ align:start position:0%
+that's the big takeaway and from
+minimizes this uncertainty and then the
+
+ align:start position:0%
+minimizes this uncertainty and then the
+ 
+
+ align:start position:0%
+minimizes this uncertainty and then the
+final image from these results that I
+
+ align:start position:0%
+final image from these results that I
+ 
+
+ align:start position:0%
+final image from these results that I
+want to show is in simulation they said
+
+ align:start position:0%
+want to show is in simulation they said
+ 
+
+ align:start position:0%
+want to show is in simulation they said
+well let's actually make her how often
+
+ align:start position:0%
+well let's actually make her how often
+ 
+
+ align:start position:0%
+well let's actually make her how often
+in practice we didn't want to do this in
+
+ align:start position:0%
+in practice we didn't want to do this in
+ 
+
+ align:start position:0%
+in practice we didn't want to do this in
+the real world because I don't want to
+
+ align:start position:0%
+the real world because I don't want to
+ 
+
+ align:start position:0%
+the real world because I don't want to
+crash with water under that many times
+
+ align:start position:0%
+crash with water under that many times
+ 
+
+ align:start position:0%
+crash with water under that many times
+the kiss debate is comparing a reactive
+
+ align:start position:0%
+the kiss debate is comparing a reactive
+ 
+
+ align:start position:0%
+the kiss debate is comparing a reactive
+manner in the deterministic one cracking
+
+ align:start position:0%
+manner in the deterministic one cracking
+ 
+
+ align:start position:0%
+manner in the deterministic one cracking
+as noise increases noise was simulated
+
+ align:start position:0%
+as noise increases noise was simulated
+ 
+
+ align:start position:0%
+as noise increases noise was simulated
+with wind strength the number of crashes
+
+ align:start position:0%
+with wind strength the number of crashes
+ 
+
+ align:start position:0%
+with wind strength the number of crashes
+increases for PRF basically they prefer
+
+ align:start position:0%
+increases for PRF basically they prefer
+ 
+
+ align:start position:0%
+increases for PRF basically they prefer
+it stays constant and low the reason
+
+ align:start position:0%
+it stays constant and low the reason
+ 
+
+ align:start position:0%
+it stays constant and low the reason
+there are two planners or two lines is
+
+ align:start position:0%
+there are two planners or two lines is
+ 
+
+ align:start position:0%
+there are two planners or two lines is
+there were two claimants with different
+
+ align:start position:0%
+there were two claimants with different
+ 
+
+ align:start position:0%
+there were two claimants with different
+time horizons important thing is birth
+
+ align:start position:0%
+time horizons important thing is birth
+ 
+
+ align:start position:0%
+time horizons important thing is birth
+is low and constant PR empress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've talked now throughout all
+
+ align:start position:0%
+we've talked now throughout all
+ 
+
+ align:start position:0%
+we've talked now throughout all
+probabilistic claim you ever need to
+
+ align:start position:0%
+probabilistic claim you ever need to
+ 
+
+ align:start position:0%
+probabilistic claim you ever need to
+know cranium gunfight but we have
+
+ align:start position:0%
+know cranium gunfight but we have
+ 
+
+ align:start position:0%
+know cranium gunfight but we have
+covered a lot of stuff what are the big
+
+ align:start position:0%
+covered a lot of stuff what are the big
+ 
+
+ align:start position:0%
+covered a lot of stuff what are the big
+table is we've learned the real world
+
+ align:start position:0%
+table is we've learned the real world
+ 
+
+ align:start position:0%
+table is we've learned the real world
+columns are stochastic rate monitors are
+
+ align:start position:0%
+columns are stochastic rate monitors are
+ 
+
+ align:start position:0%
+columns are stochastic rate monitors are
+not these perfect contains of the weekly
+
+ align:start position:0%
+not these perfect contains of the weekly
+ 
+
+ align:start position:0%
+not these perfect contains of the weekly
+but it's important to model them as
+
+ align:start position:0%
+but it's important to model them as
+ 
+
+ align:start position:0%
+but it's important to model them as
+they're constant the problem is once you
+
+ align:start position:0%
+they're constant the problem is once you
+ 
+
+ align:start position:0%
+they're constant the problem is once you
+start modeling them as stochastic it
+
+ align:start position:0%
+start modeling them as stochastic it
+ 
+
+ align:start position:0%
+start modeling them as stochastic it
+becomes a lot harder to solve but if you
+
+ align:start position:0%
+becomes a lot harder to solve but if you
+ 
+
+ align:start position:0%
+becomes a lot harder to solve but if you
+make some assumptions where even if you
+
+ align:start position:0%
+make some assumptions where even if you
+ 
+
+ align:start position:0%
+make some assumptions where even if you
+don't if you're just smart that you use
+
+ align:start position:0%
+don't if you're just smart that you use
+ 
+
+ align:start position:0%
+don't if you're just smart that you use
+heuristics you can resolve this
+
+ align:start position:0%
+heuristics you can resolve this
+ 
+
+ align:start position:0%
+heuristics you can resolve this
+complexity and so I hope you remember
+
+ align:start position:0%
+complexity and so I hope you remember
+ 
+
+ align:start position:0%
+complexity and so I hope you remember
+these three points you remember like
+
+ align:start position:0%
+these three points you remember like
+ 
+
+ align:start position:0%
+these three points you remember like
+this graphic or that graphic the idea
+
+ align:start position:0%
+this graphic or that graphic the idea
+ 
+
+ align:start position:0%
+this graphic or that graphic the idea
+that if you take that certainty into
+
+ align:start position:0%
+that if you take that certainty into
+ 
+
+ align:start position:0%
+that if you take that certainty into
+account you fundamentally different
+
+ align:start position:0%
+account you fundamentally different
+ 
+
+ align:start position:0%
+account you fundamentally different
+paths and move and that can be a good
+
+ align:start position:0%
+paths and move and that can be a good
+ 
+
+ align:start position:0%
+paths and move and that can be a good
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+what questions do that and if you have
+
+ align:start position:0%
+what questions do that and if you have
+ 
+
+ align:start position:0%
+what questions do that and if you have
+yeah preferences so far people have 50%
+
+ align:start position:0%
+yeah preferences so far people have 50%
+ 
+
+ align:start position:0%
+yeah preferences so far people have 50%
+on the IRA problems so how can say you
+
+ align:start position:0%
+on the IRA problems so how can say you
+ 
+
+ align:start position:0%
+on the IRA problems so how can say you
+know that you could hurry
+
+ align:start position:0%
+know that you could hurry
+ 
+
+ align:start position:0%
+know that you could hurry
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I saw that already so I imagine one
+
+ align:start position:0%
+I saw that already so I imagine one
+ 
+
+ align:start position:0%
+I saw that already so I imagine one
+thing that I would like to test is if we
+
+ align:start position:0%
+thing that I would like to test is if we
+ 
+
+ align:start position:0%
+thing that I would like to test is if we
+go back to our right this really crude
+
+ align:start position:0%
+go back to our right this really crude
+ 
+
+ align:start position:0%
+go back to our right this really crude
+version of our cost equation we could
+
+ align:start position:0%
+version of our cost equation we could
+ 
+
+ align:start position:0%
+version of our cost equation we could
+imagine saying if you want to come up
+
+ align:start position:0%
+imagine saying if you want to come up
+ 
+
+ align:start position:0%
+imagine saying if you want to come up
+with a bound for uncertainty that we can
+
+ align:start position:0%
+with a bound for uncertainty that we can
+ 
+
+ align:start position:0%
+with a bound for uncertainty that we can
+tolerate you could imagine maybe like
+
+ align:start position:0%
+tolerate you could imagine maybe like
+ 
+
+ align:start position:0%
+tolerate you could imagine maybe like
+sending the intercept for this to be
+
+ align:start position:0%
+sending the intercept for this to be
+ 
+
+ align:start position:0%
+sending the intercept for this to be
+that bound something like that yeah
+
+ align:start position:0%
+that bound something like that yeah
+ 
+
+ align:start position:0%
+that bound something like that yeah
+exactly so it only comes into effect I
+
+ align:start position:0%
+exactly so it only comes into effect I
+ 
+
+ align:start position:0%
+exactly so it only comes into effect I
+possibly what I chose a terrible idea
+
+ align:start position:0%
+possibly what I chose a terrible idea
+ 
+
+ align:start position:0%
+possibly what I chose a terrible idea
+especially simulation just try it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from again departed institution on the
+
+ align:start position:0%
+from again departed institution on the
+ 
+
+ align:start position:0%
+from again departed institution on the
+networks of heart but I gather the exam
+
+ align:start position:0%
+networks of heart but I gather the exam
+ 
+
+ align:start position:0%
+networks of heart but I gather the exam
+but it's a TCP straight there's more
+
+ align:start position:0%
+but it's a TCP straight there's more
+ 
+
+ align:start position:0%
+but it's a TCP straight there's more
+than mocking :
+
+ align:start position:0%
+than mocking :
+ 
+
+ align:start position:0%
+than mocking :
+so therefore you must see my parents
+
+ align:start position:0%
+so therefore you must see my parents
+ 
+
+ align:start position:0%
+so therefore you must see my parents
+made party and then Eric Acharya and the
+
+ align:start position:0%
+made party and then Eric Acharya and the
+ 
+
+ align:start position:0%
+made party and then Eric Acharya and the
+monument normal distributions are
+
+ align:start position:0%
+monument normal distributions are
+ 
+
+ align:start position:0%
+monument normal distributions are
+conjugate to each other therefore even
+
+ align:start position:0%
+conjugate to each other therefore even
+ 
+
+ align:start position:0%
+conjugate to each other therefore even
+quite happy to help their Asian and
+
+ align:start position:0%
+quite happy to help their Asian and
+ 
+
+ align:start position:0%
+quite happy to help their Asian and
+asian-american posterity
+
+ align:start position:0%
+asian-american posterity
+ 
+
+ align:start position:0%
+asian-american posterity
+sure so I think that might be making
+
+ align:start position:0%
+sure so I think that might be making
+ 
+
+ align:start position:0%
+sure so I think that might be making
+some assumptions that you might not be
+
+ align:start position:0%
+some assumptions that you might not be
+ 
+
+ align:start position:0%
+some assumptions that you might not be
+wanting to make about the nature of the
+
+ align:start position:0%
+wanting to make about the nature of the
+ 
+
+ align:start position:0%
+wanting to make about the nature of the
+distribution that they're trying to
+
+ align:start position:0%
+distribution that they're trying to
+ 
+
+ align:start position:0%
+distribution that they're trying to
+propagate I need to think about this
+
+ align:start position:0%
+propagate I need to think about this
+ 
+
+ align:start position:0%
+propagate I need to think about this
+some more but I think intuitively we can
+
+ align:start position:0%
+some more but I think intuitively we can
+ 
+
+ align:start position:0%
+some more but I think intuitively we can
+understand that any time you're
+
+ align:start position:0%
+understand that any time you're
+ 
+
+ align:start position:0%
+understand that any time you're
+propagating a distribution versus a
+
+ align:start position:0%
+propagating a distribution versus a
+ 
+
+ align:start position:0%
+propagating a distribution versus a
+single discrete value it's definitely
+
+ align:start position:0%
+single discrete value it's definitely
+ 
+
+ align:start position:0%
+single discrete value it's definitely
+not gonna be easier and so as as your
+
+ align:start position:0%
+not gonna be easier and so as as your
+ 
+
+ align:start position:0%
+not gonna be easier and so as as your
+distributions become more complex
+
+ align:start position:0%
+distributions become more complex
+ 
+
+ align:start position:0%
+distributions become more complex
+perhaps if you're modeling of real-world
+
+ align:start position:0%
+perhaps if you're modeling of real-world
+ 
+
+ align:start position:0%
+perhaps if you're modeling of real-world
+stochastic sensor you might not be able
+
+ align:start position:0%
+stochastic sensor you might not be able
+ 
+
+ align:start position:0%
+stochastic sensor you might not be able
+to perform these efficient updates using
+
+ align:start position:0%
+to perform these efficient updates using
+ 
+
+ align:start position:0%
+to perform these efficient updates using
+positive privately any other questions
+
+ align:start position:0%
+positive privately any other questions
+ 
+
+ align:start position:0%
+positive privately any other questions
+otherwise we yeah the soil is a firm
+
+ align:start position:0%
+otherwise we yeah the soil is a firm
+ 
+
+ align:start position:0%
+otherwise we yeah the soil is a firm
+examples are showing this is all fine
+
+ align:start position:0%
+examples are showing this is all fine
+ 
+
+ align:start position:0%
+examples are showing this is all fine
+fat off longer you're spraying it
+
+ align:start position:0%
+fat off longer you're spraying it
+ 
+
+ align:start position:0%
+fat off longer you're spraying it
+offline and have you expand this at all
+
+ align:start position:0%
+offline and have you expand this at all
+ 
+
+ align:start position:0%
+offline and have you expand this at all
+to like an online case that all were
+
+ align:start position:0%
+to like an online case that all were
+ 
+
+ align:start position:0%
+to like an online case that all were
+party planning
+
+ align:start position:0%
+party planning
+ 
+
+ align:start position:0%
+party planning
+right so it's not good I can tell you
+
+ align:start position:0%
+right so it's not good I can tell you
+ 
+
+ align:start position:0%
+right so it's not good I can tell you
+that much but nice is firm generates a
+
+ align:start position:0%
+that much but nice is firm generates a
+ 
+
+ align:start position:0%
+that much but nice is firm generates a
+policy so if you construct your PRM to
+
+ align:start position:0%
+policy so if you construct your PRM to
+ 
+
+ align:start position:0%
+policy so if you construct your PRM to
+say don't just find the word about like
+
+ align:start position:0%
+say don't just find the word about like
+ 
+
+ align:start position:0%
+say don't just find the word about like
+sampling points until you're confident
+
+ align:start position:0%
+sampling points until you're confident
+ 
+
+ align:start position:0%
+sampling points until you're confident
+that you're always going to end up near
+
+ align:start position:0%
+that you're always going to end up near
+ 
+
+ align:start position:0%
+that you're always going to end up near
+some point you can construct a policy
+
+ align:start position:0%
+some point you can construct a policy
+ 
+
+ align:start position:0%
+some point you can construct a policy
+and then just online look up with my
+
+ align:start position:0%
+and then just online look up with my
+ 
+
+ align:start position:0%
+and then just online look up with my
+belief that matters most closely it took
+
+ align:start position:0%
+belief that matters most closely it took
+ 
+
+ align:start position:0%
+belief that matters most closely it took
+for I think we sampled 600 nodes in a
+
+ align:start position:0%
+for I think we sampled 600 nodes in a
+ 
+
+ align:start position:0%
+for I think we sampled 600 nodes in a
+dimensions on this so - it's a three
+
+ align:start position:0%
+dimensions on this so - it's a three
+ 
+
+ align:start position:0%
+dimensions on this so - it's a three
+meter by 8 by 3 meter thing it took
+
+ align:start position:0%
+meter by 8 by 3 meter thing it took
+ 
+
+ align:start position:0%
+meter by 8 by 3 meter thing it took
+about 15 minutes it was really slow
+
+ align:start position:0%
+about 15 minutes it was really slow
+ 
+
+ align:start position:0%
+about 15 minutes it was really slow
+granted it was a virtual machine but
+
+ align:start position:0%
+granted it was a virtual machine but
+ 
+
+ align:start position:0%
+granted it was a virtual machine but
+it's not something run every plant on
+
+ align:start position:0%
+it's not something run every plant on
+ 
+
+ align:start position:0%
+it's not something run every plant on
+the plot with purim typically lasts
+
+ align:start position:0%
+the plot with purim typically lasts
+ 
+
+ align:start position:0%
+the plot with purim typically lasts
+oh it's a lot faster thank you so when
+
+ align:start position:0%
+oh it's a lot faster thank you so when
+ 
+
+ align:start position:0%
+oh it's a lot faster thank you so when
+we just did PRM I think it was one
+
+ align:start position:0%
+we just did PRM I think it was one
+ 
+
+ align:start position:0%
+we just did PRM I think it was one
+minute or something at least an order of
+
+ align:start position:0%
+minute or something at least an order of
+ 
+
+ align:start position:0%
+minute or something at least an order of
+magnitude and you could you could use
+
+ align:start position:0%
+magnitude and you could you could use
+ 
+
+ align:start position:0%
+magnitude and you could you could use
+other planners as well as our RTS and
+
+ align:start position:0%
+other planners as well as our RTS and
+ 
+
+ align:start position:0%
+other planners as well as our RTS and
+there are our environments there are
+
+ align:start position:0%
+there are our environments there are
+ 
+
+ align:start position:0%
+there are our environments there are
+public key versions parties all right
+
+ align:start position:0%
+public key versions parties all right
+ 
+
+ align:start position:0%
+public key versions parties all right
+I'm going to turn it over to Steve so we
+
+ align:start position:0%
+I'm going to turn it over to Steve so we
+ 
+
+ align:start position:0%
+I'm going to turn it over to Steve so we
+can learn about this project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just a few quick words about the grand
+
+ align:start position:0%
+just a few quick words about the grand
+ 
+
+ align:start position:0%
+just a few quick words about the grand
+challenge so the final again the final
+
+ align:start position:0%
+challenge so the final again the final
+ 
+
+ align:start position:0%
+challenge so the final again the final
+assignment will be released tonight for
+
+ align:start position:0%
+assignment will be released tonight for
+ 
+
+ align:start position:0%
+assignment will be released tonight for
+this and as Professor orange mentioned
+
+ align:start position:0%
+this and as Professor orange mentioned
+ 
+
+ align:start position:0%
+this and as Professor orange mentioned
+it's going to be each scope different
+
+ align:start position:0%
+it's going to be each scope different
+ 
+
+ align:start position:0%
+it's going to be each scope different
+from what we originally had in the
+
+ align:start position:0%
+from what we originally had in the
+ 
+
+ align:start position:0%
+from what we originally had in the
+syllabus due to time constraints but
+
+ align:start position:0%
+syllabus due to time constraints but
+ 
+
+ align:start position:0%
+syllabus due to time constraints but
+here's a preview of what you'll be doing
+
+ align:start position:0%
+here's a preview of what you'll be doing
+ 
+
+ align:start position:0%
+here's a preview of what you'll be doing
+so for an overview it will be a
+
+ align:start position:0%
+so for an overview it will be a
+ 
+
+ align:start position:0%
+so for an overview it will be a
+classified collaboration so what we're
+
+ align:start position:0%
+classified collaboration so what we're
+ 
+
+ align:start position:0%
+classified collaboration so what we're
+going to do you guys are going to stay
+
+ align:start position:0%
+going to do you guys are going to stay
+ 
+
+ align:start position:0%
+going to do you guys are going to stay
+in your advanced lecture teams and each
+
+ align:start position:0%
+in your advanced lecture teams and each
+ 
+
+ align:start position:0%
+in your advanced lecture teams and each
+basically up slide which is done the
+
+ align:start position:0%
+basically up slide which is done the
+ 
+
+ align:start position:0%
+basically up slide which is done the
+great work you've done on that I'm Tara
+
+ align:start position:0%
+great work you've done on that I'm Tara
+ 
+
+ align:start position:0%
+great work you've done on that I'm Tara
+Parker a robot that we have so it's not
+
+ align:start position:0%
+Parker a robot that we have so it's not
+ 
+
+ align:start position:0%
+Parker a robot that we have so it's not
+a competition where each team will be
+
+ align:start position:0%
+a competition where each team will be
+ 
+
+ align:start position:0%
+a competition where each team will be
+competing against each other
+
+ align:start position:0%
+competing against each other
+ 
+
+ align:start position:0%
+competing against each other
+all right and so again I'm pretty
+
+ align:start position:0%
+all right and so again I'm pretty
+ 
+
+ align:start position:0%
+all right and so again I'm pretty
+scoping it the syllabus originally said
+
+ align:start position:0%
+scoping it the syllabus originally said
+ 
+
+ align:start position:0%
+scoping it the syllabus originally said
+it with 20% of your grade it's probably
+
+ align:start position:0%
+it with 20% of your grade it's probably
+ 
+
+ align:start position:0%
+it with 20% of your grade it's probably
+gonna be more like 10 or 15% yeah so
+
+ align:start position:0%
+gonna be more like 10 or 15% yeah so
+ 
+
+ align:start position:0%
+gonna be more like 10 or 15% yeah so
+this is the robot you guys are we using
+
+ align:start position:0%
+this is the robot you guys are we using
+ 
+
+ align:start position:0%
+this is the robot you guys are we using
+it's called an X we're robot usually it
+
+ align:start position:0%
+it's called an X we're robot usually it
+ 
+
+ align:start position:0%
+it's called an X we're robot usually it
+has a robotic arm on it but we're
+
+ align:start position:0%
+has a robotic arm on it but we're
+ 
+
+ align:start position:0%
+has a robotic arm on it but we're
+actually not going to be using it for
+
+ align:start position:0%
+actually not going to be using it for
+ 
+
+ align:start position:0%
+actually not going to be using it for
+this front that about this face made by
+
+ align:start position:0%
+this front that about this face made by
+ 
+
+ align:start position:0%
+this front that about this face made by
+a company from Spain its pinnacle robot
+
+ align:start position:0%
+a company from Spain its pinnacle robot
+ 
+
+ align:start position:0%
+a company from Spain its pinnacle robot
+one cool thing about it is that it's
+
+ align:start position:0%
+one cool thing about it is that it's
+ 
+
+ align:start position:0%
+one cool thing about it is that it's
+actually omnidirectional so there are
+
+ align:start position:0%
+actually omnidirectional so there are
+ 
+
+ align:start position:0%
+actually omnidirectional so there are
+wheels on your wheels here what that
+
+ align:start position:0%
+wheels on your wheels here what that
+ 
+
+ align:start position:0%
+wheels on your wheels here what that
+means is that you can drive sideways
+
+ align:start position:0%
+means is that you can drive sideways
+ 
+
+ align:start position:0%
+means is that you can drive sideways
+let's write the big parallel parking our
+
+ align:start position:0%
+let's write the big parallel parking our
+ 
+
+ align:start position:0%
+let's write the big parallel parking our
+car very easy we're not going to be
+
+ align:start position:0%
+car very easy we're not going to be
+ 
+
+ align:start position:0%
+car very easy we're not going to be
+dragging it probably this fast you're
+
+ align:start position:0%
+dragging it probably this fast you're
+ 
+
+ align:start position:0%
+dragging it probably this fast you're
+just super heavy and we don't want
+
+ align:start position:0%
+just super heavy and we don't want
+ 
+
+ align:start position:0%
+just super heavy and we don't want
+anyone to yeah we got to screw in
+
+ align:start position:0%
+anyone to yeah we got to screw in
+ 
+
+ align:start position:0%
+anyone to yeah we got to screw in
+screwed in competition but it's a refund
+
+ align:start position:0%
+screwed in competition but it's a refund
+ 
+
+ align:start position:0%
+screwed in competition but it's a refund
+of our box so you guys be working on
+
+ align:start position:0%
+of our box so you guys be working on
+ 
+
+ align:start position:0%
+of our box so you guys be working on
+this and so the actual challenge itself
+
+ align:start position:0%
+this and so the actual challenge itself
+ 
+
+ align:start position:0%
+this and so the actual challenge itself
+as we've mentioned many times throughout
+
+ align:start position:0%
+as we've mentioned many times throughout
+ 
+
+ align:start position:0%
+as we've mentioned many times throughout
+this class will be a modified
+
+ align:start position:0%
+this class will be a modified
+ 
+
+ align:start position:0%
+this class will be a modified
+orienteering challenge so there's going
+
+ align:start position:0%
+orienteering challenge so there's going
+ 
+
+ align:start position:0%
+orienteering challenge so there's going
+to be a few different challenge stations
+
+ align:start position:0%
+to be a few different challenge stations
+ 
+
+ align:start position:0%
+to be a few different challenge stations
+that you have that prior to and at those
+
+ align:start position:0%
+that you have that prior to and at those
+ 
+
+ align:start position:0%
+that you have that prior to and at those
+stations so be small and computational
+
+ align:start position:0%
+stations so be small and computational
+ 
+
+ align:start position:0%
+stations so be small and computational
+challenges and those cognitive
+
+ align:start position:0%
+challenges and those cognitive
+ 
+
+ align:start position:0%
+challenges and those cognitive
+challenges will be a subset of the
+
+ align:start position:0%
+challenges will be a subset of the
+ 
+
+ align:start position:0%
+challenges will be a subset of the
+advantage lecture teams not all of them
+
+ align:start position:0%
+advantage lecture teams not all of them
+ 
+
+ align:start position:0%
+advantage lecture teams not all of them
+and the goal is to complete as many of
+
+ align:start position:0%
+and the goal is to complete as many of
+ 
+
+ align:start position:0%
+and the goal is to complete as many of
+those as of those as you can and try and
+
+ align:start position:0%
+those as of those as you can and try and
+ 
+
+ align:start position:0%
+those as of those as you can and try and
+sort of do that as quickly as possible
+
+ align:start position:0%
+sort of do that as quickly as possible
+ 
+
+ align:start position:0%
+sort of do that as quickly as possible
+and it's also going to be held indoors
+
+ align:start position:0%
+and it's also going to be held indoors
+ 
+
+ align:start position:0%
+and it's also going to be held indoors
+in our lab space where we just showed
+
+ align:start position:0%
+in our lab space where we just showed
+ 
+
+ align:start position:0%
+in our lab space where we just showed
+you so that way for brains we can still
+
+ align:start position:0%
+you so that way for brains we can still
+ 
+
+ align:start position:0%
+you so that way for brains we can still
+have the Grand Challenge at the end of
+
+ align:start position:0%
+have the Grand Challenge at the end of
+ 
+
+ align:start position:0%
+have the Grand Challenge at the end of
+the semester so this is sort of a power
+
+ align:start position:0%
+the semester so this is sort of a power
+ 
+
+ align:start position:0%
+the semester so this is sort of a power
+it's set up as a last night actually so
+
+ align:start position:0%
+it's set up as a last night actually so
+ 
+
+ align:start position:0%
+it's set up as a last night actually so
+to be able to pack around a small little
+
+ align:start position:0%
+to be able to pack around a small little
+ 
+
+ align:start position:0%
+to be able to pack around a small little
+Lego maze that you set up and there's
+
+ align:start position:0%
+Lego maze that you set up and there's
+ 
+
+ align:start position:0%
+Lego maze that you set up and there's
+going to be sort of different things
+
+ align:start position:0%
+going to be sort of different things
+ 
+
+ align:start position:0%
+going to be sort of different things
+that you have to do with the different
+
+ align:start position:0%
+that you have to do with the different
+ 
+
+ align:start position:0%
+that you have to do with the different
+places so what are you actually going to
+
+ align:start position:0%
+places so what are you actually going to
+ 
+
+ align:start position:0%
+places so what are you actually going to
+be doing what assignment are you guys
+
+ align:start position:0%
+be doing what assignment are you guys
+ 
+
+ align:start position:0%
+be doing what assignment are you guys
+gonna be doing well it's actually a
+
+ align:start position:0%
+gonna be doing well it's actually a
+ 
+
+ align:start position:0%
+gonna be doing well it's actually a
+little flexible since each of you did
+
+ align:start position:0%
+little flexible since each of you did
+ 
+
+ align:start position:0%
+little flexible since each of you did
+different things for your advanced
+
+ align:start position:0%
+different things for your advanced
+ 
+
+ align:start position:0%
+different things for your advanced
+lectures you're all you know each team
+
+ align:start position:0%
+lectures you're all you know each team
+ 
+
+ align:start position:0%
+lectures you're all you know each team
+is going to have a bit of a different
+
+ align:start position:0%
+is going to have a bit of a different
+ 
+
+ align:start position:0%
+is going to have a bit of a different
+assignment applying it to this I have
+
+ align:start position:0%
+assignment applying it to this I have
+ 
+
+ align:start position:0%
+assignment applying it to this I have
+some proposed ideas that I'm going to
+
+ align:start position:0%
+some proposed ideas that I'm going to
+ 
+
+ align:start position:0%
+some proposed ideas that I'm going to
+talk about in the next slide here like
+
+ align:start position:0%
+talk about in the next slide here like
+ 
+
+ align:start position:0%
+talk about in the next slide here like
+the big thing is that these are just
+
+ align:start position:0%
+the big thing is that these are just
+ 
+
+ align:start position:0%
+the big thing is that these are just
+ideas you guys have a lot of flexibility
+
+ align:start position:0%
+ideas you guys have a lot of flexibility
+ 
+
+ align:start position:0%
+ideas you guys have a lot of flexibility
+in this you can talk to you'll be
+
+ align:start position:0%
+in this you can talk to you'll be
+ 
+
+ align:start position:0%
+in this you can talk to you'll be
+probably working with the court that's a
+
+ align:start position:0%
+probably working with the court that's a
+ 
+
+ align:start position:0%
+probably working with the court that's a
+lot to have access to the robot you know
+
+ align:start position:0%
+lot to have access to the robot you know
+ 
+
+ align:start position:0%
+lot to have access to the robot you know
+we can arrange extra office hours to you
+
+ align:start position:0%
+we can arrange extra office hours to you
+ 
+
+ align:start position:0%
+we can arrange extra office hours to you
+guys to some piece of hardware to test
+
+ align:start position:0%
+guys to some piece of hardware to test
+ 
+
+ align:start position:0%
+guys to some piece of hardware to test
+things so we'll be arranging all of that
+
+ align:start position:0%
+things so we'll be arranging all of that
+ 
+
+ align:start position:0%
+things so we'll be arranging all of that
+things as sort of on an as-needed basis
+
+ align:start position:0%
+things as sort of on an as-needed basis
+ 
+
+ align:start position:0%
+things as sort of on an as-needed basis
+if you want it to basically you know
+
+ align:start position:0%
+if you want it to basically you know
+ 
+
+ align:start position:0%
+if you want it to basically you know
+it'll depend on your team
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know you yeah me an anon Tiago who
+
+ align:start position:0%
+you know you yeah me an anon Tiago who
+ 
+
+ align:start position:0%
+you know you yeah me an anon Tiago who
+gave a lecture earlier in the semester
+
+ align:start position:0%
+gave a lecture earlier in the semester
+ 
+
+ align:start position:0%
+gave a lecture earlier in the semester
+and possibly also a few other people
+
+ align:start position:0%
+and possibly also a few other people
+ 
+
+ align:start position:0%
+and possibly also a few other people
+from our lab will be the main contact
+
+ align:start position:0%
+from our lab will be the main contact
+ 
+
+ align:start position:0%
+from our lab will be the main contact
+point spread so of course it should go
+
+ align:start position:0%
+point spread so of course it should go
+ 
+
+ align:start position:0%
+point spread so of course it should go
+without saying but all the team are good
+
+ align:start position:0%
+without saying but all the team are good
+ 
+
+ align:start position:0%
+without saying but all the team are good
+should contribute equally within your
+
+ align:start position:0%
+should contribute equally within your
+ 
+
+ align:start position:0%
+should contribute equally within your
+team so it'll be a little bit you know
+
+ align:start position:0%
+team so it'll be a little bit you know
+ 
+
+ align:start position:0%
+team so it'll be a little bit you know
+maybe less structure than in Vince
+
+ align:start position:0%
+maybe less structure than in Vince
+ 
+
+ align:start position:0%
+maybe less structure than in Vince
+lecture but just make sure that Edward
+
+ align:start position:0%
+lecture but just make sure that Edward
+ 
+
+ align:start position:0%
+lecture but just make sure that Edward
+is contributing equally in the
+
+ align:start position:0%
+is contributing equally in the
+ 
+
+ align:start position:0%
+is contributing equally in the
+assignment and it's trim it involved
+
+ align:start position:0%
+assignment and it's trim it involved
+ 
+
+ align:start position:0%
+assignment and it's trim it involved
+using a thing called the robot operating
+
+ align:start position:0%
+using a thing called the robot operating
+ 
+
+ align:start position:0%
+using a thing called the robot operating
+system or broths which is basically a
+
+ align:start position:0%
+system or broths which is basically a
+ 
+
+ align:start position:0%
+system or broths which is basically a
+stuff or a framework for communicating
+
+ align:start position:0%
+stuff or a framework for communicating
+ 
+
+ align:start position:0%
+stuff or a framework for communicating
+and it's used a lot in robotics just a
+
+ align:start position:0%
+and it's used a lot in robotics just a
+ 
+
+ align:start position:0%
+and it's used a lot in robotics just a
+quick show of hands how many of you have
+
+ align:start position:0%
+quick show of hands how many of you have
+ 
+
+ align:start position:0%
+quick show of hands how many of you have
+huge graphs before oh it's a lot of
+
+ align:start position:0%
+huge graphs before oh it's a lot of
+ 
+
+ align:start position:0%
+huge graphs before oh it's a lot of
+hubris how many of her defrost if not
+
+ align:start position:0%
+hubris how many of her defrost if not
+ 
+
+ align:start position:0%
+hubris how many of her defrost if not
+use it so ok so a lot of people so
+
+ align:start position:0%
+use it so ok so a lot of people so
+ 
+
+ align:start position:0%
+use it so ok so a lot of people so
+that's a good starting point so here are
+
+ align:start position:0%
+that's a good starting point so here are
+ 
+
+ align:start position:0%
+that's a good starting point so here are
+these opposed we proposed the tap speech
+
+ align:start position:0%
+these opposed we proposed the tap speech
+ 
+
+ align:start position:0%
+these opposed we proposed the tap speech
+group and of course all of these are up
+
+ align:start position:0%
+group and of course all of these are up
+ 
+
+ align:start position:0%
+group and of course all of these are up
+to change if you guys wanted to ninjas
+
+ align:start position:0%
+to change if you guys wanted to ninjas
+ 
+
+ align:start position:0%
+to change if you guys wanted to ninjas
+let me know you know basically so some
+
+ align:start position:0%
+let me know you know basically so some
+ 
+
+ align:start position:0%
+let me know you know basically so some
+of the groups it's a very clear how it
+
+ align:start position:0%
+of the groups it's a very clear how it
+ 
+
+ align:start position:0%
+of the groups it's a very clear how it
+would immediately apply to the grand
+
+ align:start position:0%
+would immediately apply to the grand
+ 
+
+ align:start position:0%
+would immediately apply to the grand
+challenge so incremental path planning
+
+ align:start position:0%
+challenge so incremental path planning
+ 
+
+ align:start position:0%
+challenge so incremental path planning
+well we have a mobile robot so maybe we
+
+ align:start position:0%
+well we have a mobile robot so maybe we
+ 
+
+ align:start position:0%
+well we have a mobile robot so maybe we
+can actually put that on the robot and
+
+ align:start position:0%
+can actually put that on the robot and
+ 
+
+ align:start position:0%
+can actually put that on the robot and
+get it to you know change your plan if
+
+ align:start position:0%
+get it to you know change your plan if
+ 
+
+ align:start position:0%
+get it to you know change your plan if
+something gets in the way the semantics
+
+ align:start position:0%
+something gets in the way the semantics
+ 
+
+ align:start position:0%
+something gets in the way the semantics
+localization group obviously very
+
+ align:start position:0%
+localization group obviously very
+ 
+
+ align:start position:0%
+localization group obviously very
+applicable to the grand challenge you
+
+ align:start position:0%
+applicable to the grand challenge you
+ 
+
+ align:start position:0%
+applicable to the grand challenge you
+know you need to know where you are so
+
+ align:start position:0%
+know you need to know where you are so
+ 
+
+ align:start position:0%
+know you need to know where you are so
+the robot that we have now can actually
+
+ align:start position:0%
+the robot that we have now can actually
+ 
+
+ align:start position:0%
+the robot that we have now can actually
+do normal metric localization so we can
+
+ align:start position:0%
+do normal metric localization so we can
+ 
+
+ align:start position:0%
+do normal metric localization so we can
+sort of know where it is
+
+ align:start position:0%
+sort of know where it is
+ 
+
+ align:start position:0%
+sort of know where it is
+but would be interesting to see is
+
+ align:start position:0%
+but would be interesting to see is
+ 
+
+ align:start position:0%
+but would be interesting to see is
+compare the symmetric localization to
+
+ align:start position:0%
+compare the symmetric localization to
+ 
+
+ align:start position:0%
+compare the symmetric localization to
+that one but how would you do submit to
+
+ align:start position:0%
+that one but how would you do submit to
+ 
+
+ align:start position:0%
+that one but how would you do submit to
+globalization
+
+ align:start position:0%
+globalization
+ 
+
+ align:start position:0%
+globalization
+well we can use a Cameron to choose
+
+ align:start position:0%
+well we can use a Cameron to choose
+ 
+
+ align:start position:0%
+well we can use a Cameron to choose
+position with learning to do
+
+ align:start position:0%
+position with learning to do
+ 
+
+ align:start position:0%
+position with learning to do
+classification the visual classification
+
+ align:start position:0%
+classification the visual classification
+ 
+
+ align:start position:0%
+classification the visual classification
+for deep learning group so I think these
+
+ align:start position:0%
+for deep learning group so I think these
+ 
+
+ align:start position:0%
+for deep learning group so I think these
+two groups would have a really nice
+
+ align:start position:0%
+two groups would have a really nice
+ 
+
+ align:start position:0%
+two groups would have a really nice
+synergy and a really cool way to work
+
+ align:start position:0%
+synergy and a really cool way to work
+ 
+
+ align:start position:0%
+synergy and a really cool way to work
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+so the MCTS group very cool but I had a
+
+ align:start position:0%
+so the MCTS group very cool but I had a
+ 
+
+ align:start position:0%
+so the MCTS group very cool but I had a
+little trouble think what exactly about
+
+ align:start position:0%
+little trouble think what exactly about
+ 
+
+ align:start position:0%
+little trouble think what exactly about
+that would apply so maybe you look like
+
+ align:start position:0%
+that would apply so maybe you look like
+ 
+
+ align:start position:0%
+that would apply so maybe you look like
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+yeah say I'm clarifying all these are
+
+ align:start position:0%
+yeah say I'm clarifying all these are
+ 
+
+ align:start position:0%
+yeah say I'm clarifying all these are
+separate runs of the robot so actually
+
+ align:start position:0%
+separate runs of the robot so actually
+ 
+
+ align:start position:0%
+separate runs of the robot so actually
+probably going to rent all of them that
+
+ align:start position:0%
+probably going to rent all of them that
+ 
+
+ align:start position:0%
+probably going to rent all of them that
+like so big reason this would be
+
+ align:start position:0%
+like so big reason this would be
+ 
+
+ align:start position:0%
+like so big reason this would be
+probably one run of the robot we're
+
+ align:start position:0%
+probably one run of the robot we're
+ 
+
+ align:start position:0%
+probably one run of the robot we're
+going to decouple these so that if one
+
+ align:start position:0%
+going to decouple these so that if one
+ 
+
+ align:start position:0%
+going to decouple these so that if one
+or a subset of these don't work super
+
+ align:start position:0%
+or a subset of these don't work super
+ 
+
+ align:start position:0%
+or a subset of these don't work super
+well the other groups will still be able
+
+ align:start position:0%
+well the other groups will still be able
+ 
+
+ align:start position:0%
+well the other groups will still be able
+to run so carefully planning now - so
+
+ align:start position:0%
+to run so carefully planning now - so
+ 
+
+ align:start position:0%
+to run so carefully planning now - so
+the MCTS group I was thinking maybe
+
+ align:start position:0%
+the MCTS group I was thinking maybe
+ 
+
+ align:start position:0%
+the MCTS group I was thinking maybe
+maybe solvent that could be a really
+
+ align:start position:0%
+maybe solvent that could be a really
+ 
+
+ align:start position:0%
+maybe solvent that could be a really
+nice way to one of the one of those
+
+ align:start position:0%
+nice way to one of the one of those
+ 
+
+ align:start position:0%
+nice way to one of the one of those
+computational challenges if you have to
+
+ align:start position:0%
+computational challenges if you have to
+ 
+
+ align:start position:0%
+computational challenges if you have to
+play against a human and you know if it
+
+ align:start position:0%
+play against a human and you know if it
+ 
+
+ align:start position:0%
+play against a human and you know if it
+wins great you can go faster when you
+
+ align:start position:0%
+wins great you can go faster when you
+ 
+
+ align:start position:0%
+wins great you can go faster when you
+get more points so you can implement it
+
+ align:start position:0%
+get more points so you can implement it
+ 
+
+ align:start position:0%
+get more points so you can implement it
+on a on a different game rather than can
+
+ align:start position:0%
+on a on a different game rather than can
+ 
+
+ align:start position:0%
+on a on a different game rather than can
+explore or possibly and sort of wrap it
+
+ align:start position:0%
+explore or possibly and sort of wrap it
+ 
+
+ align:start position:0%
+explore or possibly and sort of wrap it
+around prosthetic I like that the beach
+
+ align:start position:0%
+around prosthetic I like that the beach
+ 
+
+ align:start position:0%
+around prosthetic I like that the beach
+ability group I think would also be a
+
+ align:start position:0%
+ability group I think would also be a
+ 
+
+ align:start position:0%
+ability group I think would also be a
+great place to do and one of these
+
+ align:start position:0%
+great place to do and one of these
+ 
+
+ align:start position:0%
+great place to do and one of these
+challenge stations so it could give you
+
+ align:start position:0%
+challenge stations so it could give you
+ 
+
+ align:start position:0%
+challenge stations so it could give you
+guys different puzzle said maybe sort of
+
+ align:start position:0%
+guys different puzzle said maybe sort of
+ 
+
+ align:start position:0%
+guys different puzzle said maybe sort of
+some sort of maze like state space and
+
+ align:start position:0%
+some sort of maze like state space and
+ 
+
+ align:start position:0%
+some sort of maze like state space and
+you have to see could you even reach the
+
+ align:start position:0%
+you have to see could you even reach the
+ 
+
+ align:start position:0%
+you have to see could you even reach the
+goal there and if you get the answer
+
+ align:start position:0%
+goal there and if you get the answer
+ 
+
+ align:start position:0%
+goal there and if you get the answer
+right or you can move on to the next
+
+ align:start position:0%
+right or you can move on to the next
+ 
+
+ align:start position:0%
+right or you can move on to the next
+stage or get more points or something
+
+ align:start position:0%
+stage or get more points or something
+ 
+
+ align:start position:0%
+stage or get more points or something
+like that but again these are the
+
+ align:start position:0%
+like that but again these are the
+ 
+
+ align:start position:0%
+like that but again these are the
+suggestions so for example they can they
+
+ align:start position:0%
+suggestions so for example they can they
+ 
+
+ align:start position:0%
+suggestions so for example they can they
+do yeah so if you guys have other
+
+ align:start position:0%
+do yeah so if you guys have other
+ 
+
+ align:start position:0%
+do yeah so if you guys have other
+suggestions on how to implement your
+
+ align:start position:0%
+suggestions on how to implement your
+ 
+
+ align:start position:0%
+suggestions on how to implement your
+team stuff into the game challenge
+
+ align:start position:0%
+team stuff into the game challenge
+ 
+
+ align:start position:0%
+team stuff into the game challenge
+definitely send me an e-mail preferably
+
+ align:start position:0%
+definitely send me an e-mail preferably
+ 
+
+ align:start position:0%
+definitely send me an e-mail preferably
+today or a soon of you you know people
+
+ align:start position:0%
+today or a soon of you you know people
+ 
+
+ align:start position:0%
+today or a soon of you you know people
+these things and we need to change these
+
+ align:start position:0%
+these things and we need to change these
+ 
+
+ align:start position:0%
+these things and we need to change these
+service suggestions right now the last
+
+ align:start position:0%
+service suggestions right now the last
+ 
+
+ align:start position:0%
+service suggestions right now the last
+one the last two are sort of more
+
+ align:start position:0%
+one the last two are sort of more
+ 
+
+ align:start position:0%
+one the last two are sort of more
+planning related so playing with
+
+ align:start position:0%
+planning related so playing with
+ 
+
+ align:start position:0%
+planning related so playing with
+temporal logic which was Monday's
+
+ align:start position:0%
+temporal logic which was Monday's
+ 
+
+ align:start position:0%
+temporal logic which was Monday's
+lecture I thought would be a cool a cool
+
+ align:start position:0%
+lecture I thought would be a cool a cool
+ 
+
+ align:start position:0%
+lecture I thought would be a cool a cool
+way to sort of control the robots
+
+ align:start position:0%
+way to sort of control the robots
+ 
+
+ align:start position:0%
+way to sort of control the robots
+high-level action so maybe maybe that's
+
+ align:start position:0%
+high-level action so maybe maybe that's
+ 
+
+ align:start position:0%
+high-level action so maybe maybe that's
+good about modeling our Venn challenge
+
+ align:start position:0%
+good about modeling our Venn challenge
+ 
+
+ align:start position:0%
+good about modeling our Venn challenge
+with P to DL and maybe with linear
+
+ align:start position:0%
+with P to DL and maybe with linear
+ 
+
+ align:start position:0%
+with P to DL and maybe with linear
+temporal logic goals models if you get
+
+ align:start position:0%
+temporal logic goals models if you get
+ 
+
+ align:start position:0%
+temporal logic goals models if you get
+homina then you could compile that and
+
+ align:start position:0%
+homina then you could compile that and
+ 
+
+ align:start position:0%
+homina then you could compile that and
+call a player on it and execute
+
+ align:start position:0%
+call a player on it and execute
+ 
+
+ align:start position:0%
+call a player on it and execute
+plan on the extra robot to holding the
+
+ align:start position:0%
+plan on the extra robot to holding the
+ 
+
+ align:start position:0%
+plan on the extra robot to holding the
+high-level actions of the robot that's a
+
+ align:start position:0%
+high-level actions of the robot that's a
+ 
+
+ align:start position:0%
+high-level actions of the robot that's a
+possibility
+
+ align:start position:0%
+possibility
+ 
+
+ align:start position:0%
+possibility
+and for today's boot the enterprise and
+
+ align:start position:0%
+and for today's boot the enterprise and
+ 
+
+ align:start position:0%
+and for today's boot the enterprise and
+policy planning maybe you know you could
+
+ align:start position:0%
+policy planning maybe you know you could
+ 
+
+ align:start position:0%
+policy planning maybe you know you could
+do something actually sort of similar
+
+ align:start position:0%
+do something actually sort of similar
+ 
+
+ align:start position:0%
+do something actually sort of similar
+but instead of modeling the domain as
+
+ align:start position:0%
+but instead of modeling the domain as
+ 
+
+ align:start position:0%
+but instead of modeling the domain as
+pddl model it as an MVP and solve it
+
+ align:start position:0%
+pddl model it as an MVP and solve it
+ 
+
+ align:start position:0%
+pddl model it as an MVP and solve it
+with lar and instead of a policy on how
+
+ align:start position:0%
+with lar and instead of a policy on how
+ 
+
+ align:start position:0%
+with lar and instead of a policy on how
+to control the robot maybe we can change
+
+ align:start position:0%
+to control the robot maybe we can change
+ 
+
+ align:start position:0%
+to control the robot maybe we can change
+change it a little bit to certain
+
+ align:start position:0%
+change it a little bit to certain
+ 
+
+ align:start position:0%
+change it a little bit to certain
+squares to me you know more risky than
+
+ align:start position:0%
+squares to me you know more risky than
+ 
+
+ align:start position:0%
+squares to me you know more risky than
+others and so on so again there's
+
+ align:start position:0%
+others and so on so again there's
+ 
+
+ align:start position:0%
+others and so on so again there's
+flexibility in all of these here so
+
+ align:start position:0%
+flexibility in all of these here so
+ 
+
+ align:start position:0%
+flexibility in all of these here so
+these are just some of the suggestions
+
+ align:start position:0%
+these are just some of the suggestions
+ 
+
+ align:start position:0%
+these are just some of the suggestions
+to do what comedy questions before we
+
+ align:start position:0%
+to do what comedy questions before we
+ 
+
+ align:start position:0%
+to do what comedy questions before we
+this is all I have so anyone have any
+
+ align:start position:0%
+this is all I have so anyone have any
+ 
+
+ align:start position:0%
+this is all I have so anyone have any
+questions yeah so it's basically you
+
+ align:start position:0%
+questions yeah so it's basically you
+ 
+
+ align:start position:0%
+questions yeah so it's basically you
+guys really divide up the work amongst
+
+ align:start position:0%
+guys really divide up the work amongst
+ 
+
+ align:start position:0%
+guys really divide up the work amongst
+yourselves it's really different for
+
+ align:start position:0%
+yourselves it's really different for
+ 
+
+ align:start position:0%
+yourselves it's really different for
+every team so we're right yeah you
+
+ align:start position:0%
+every team so we're right yeah you
+ 
+
+ align:start position:0%
+every team so we're right yeah you
+should be so meeting their own separate
+
+ align:start position:0%
+should be so meeting their own separate
+ 
+
+ align:start position:0%
+should be so meeting their own separate
+package for for example these two teams
+
+ align:start position:0%
+package for for example these two teams
+ 
+
+ align:start position:0%
+package for for example these two teams
+there's probably going to be a common
+
+ align:start position:0%
+there's probably going to be a common
+ 
+
+ align:start position:0%
+there's probably going to be a common
+interface where the output of this one
+
+ align:start position:0%
+interface where the output of this one
+ 
+
+ align:start position:0%
+interface where the output of this one
+goes to the input of our so for that one
+
+ align:start position:0%
+goes to the input of our so for that one
+ 
+
+ align:start position:0%
+goes to the input of our so for that one
+we're going to give you sort of the
+
+ align:start position:0%
+we're going to give you sort of the
+ 
+
+ align:start position:0%
+we're going to give you sort of the
+interface name interruption message but
+
+ align:start position:0%
+interface name interruption message but
+ 
+
+ align:start position:0%
+interface name interruption message but
+other than that we provide enough to
+
+ align:start position:0%
+other than that we provide enough to
+ 
+
+ align:start position:0%
+other than that we provide enough to
+work if you guys don't really so I think
+
+ align:start position:0%
+work if you guys don't really so I think
+ 
+
+ align:start position:0%
+work if you guys don't really so I think
+your plays will be integration if you're
+
+ align:start position:0%
+your plays will be integration if you're
+ 
+
+ align:start position:0%
+your plays will be integration if you're
+trying to get into it all the pieces
+
+ align:start position:0%
+trying to get into it all the pieces
+ 
+
+ align:start position:0%
+trying to get into it all the pieces
+doing for the hits
+
+ align:start position:0%
+doing for the hits
+ 
+
+ align:start position:0%
+doing for the hits
+God we thank thing that uses sub legend
+
+ align:start position:0%
+God we thank thing that uses sub legend
+ 
+
+ align:start position:0%
+God we thank thing that uses sub legend
+still with that penicillin to do in here
+
+ align:start position:0%
+still with that penicillin to do in here
+ 
+
+ align:start position:0%
+still with that penicillin to do in here
+it can be really unpleasant to do take a
+
+ align:start position:0%
+it can be really unpleasant to do take a
+ 
+
+ align:start position:0%
+it can be really unpleasant to do take a
+lot of time so we don't want you to have
+
+ align:start position:0%
+lot of time so we don't want you to have
+ 
+
+ align:start position:0%
+lot of time so we don't want you to have
+that experience so that's why like even
+
+ align:start position:0%
+that experience so that's why like even
+ 
+
+ align:start position:0%
+that experience so that's why like even
+if not only what we want to do is to be
+
+ align:start position:0%
+if not only what we want to do is to be
+ 
+
+ align:start position:0%
+if not only what we want to do is to be
+able to get your own capability if you
+
+ align:start position:0%
+able to get your own capability if you
+ 
+
+ align:start position:0%
+able to get your own capability if you
+guys choose to integrate with other
+
+ align:start position:0%
+guys choose to integrate with other
+ 
+
+ align:start position:0%
+guys choose to integrate with other
+goals because you are really excited by
+
+ align:start position:0%
+goals because you are really excited by
+ 
+
+ align:start position:0%
+goals because you are really excited by
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and because that's purely
\ No newline at end of file
diff --git a/I5r_4tzl0u4.txt b/I5r_4tzl0u4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d9475a42a754db7463d4332ff836ffca87e1fd8
--- /dev/null
+++ b/I5r_4tzl0u4.txt
@@ -0,0 +1,6067 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hi guys I'm Nancy demash I'm
+
+ align:start position:0%
+ocw.mit.edu hi guys I'm Nancy demash I'm
+ 
+
+ align:start position:0%
+ocw.mit.edu hi guys I'm Nancy demash I'm
+uh presenting today on uh what as you
+
+ align:start position:0%
+uh presenting today on uh what as you
+ 
+
+ align:start position:0%
+uh presenting today on uh what as you
+can see from my title before for the
+
+ align:start position:0%
+can see from my title before for the
+ 
+
+ align:start position:0%
+can see from my title before for the
+Scramble for Africa tracing African
+
+ align:start position:0%
+Scramble for Africa tracing African
+ 
+
+ align:start position:0%
+Scramble for Africa tracing African
+architecture through trade Circa 1200
+
+ align:start position:0%
+architecture through trade Circa 1200
+ 
+
+ align:start position:0%
+architecture through trade Circa 1200
+Common Era um what immediately comes to
+
+ align:start position:0%
+Common Era um what immediately comes to
+ 
+
+ align:start position:0%
+Common Era um what immediately comes to
+mind when you think of Africa anybody
+
+ align:start position:0%
+mind when you think of Africa anybody
+ 
+
+ align:start position:0%
+mind when you think of Africa anybody
+shout out something I won't penalize
+
+ align:start position:0%
+shout out something I won't penalize
+ 
+
+ align:start position:0%
+shout out something I won't penalize
+you something anything at all I don't
+
+ align:start position:0%
+you something anything at all I don't
+ 
+
+ align:start position:0%
+you something anything at all I don't
+conflict diamonds okay diamonds good one
+
+ align:start position:0%
+conflict diamonds okay diamonds good one
+ 
+
+ align:start position:0%
+conflict diamonds okay diamonds good one
+new movie that just came out anybody
+
+ align:start position:0%
+new movie that just came out anybody
+ 
+
+ align:start position:0%
+new movie that just came out anybody
+else black people black people okay even
+
+ align:start position:0%
+else black people black people okay even
+ 
+
+ align:start position:0%
+else black people black people okay even
+even better that that's that's that's
+
+ align:start position:0%
+even better that that's that's that's
+ 
+
+ align:start position:0%
+even better that that's that's that's
+true okay well it's already a given that
+
+ align:start position:0%
+true okay well it's already a given that
+ 
+
+ align:start position:0%
+true okay well it's already a given that
+Africa is represented in the news and
+
+ align:start position:0%
+Africa is represented in the news and
+ 
+
+ align:start position:0%
+Africa is represented in the news and
+media um but the images that we have of
+
+ align:start position:0%
+media um but the images that we have of
+ 
+
+ align:start position:0%
+media um but the images that we have of
+Africa rarely go beyond the ubiquitous
+
+ align:start position:0%
+Africa rarely go beyond the ubiquitous
+ 
+
+ align:start position:0%
+Africa rarely go beyond the ubiquitous
+and um often you know uh very pejorative
+
+ align:start position:0%
+and um often you know uh very pejorative
+ 
+
+ align:start position:0%
+and um often you know uh very pejorative
+misconceptions and cliches of the
+
+ align:start position:0%
+misconceptions and cliches of the
+ 
+
+ align:start position:0%
+misconceptions and cliches of the
+continent uh we're presented with a
+
+ align:start position:0%
+continent uh we're presented with a
+ 
+
+ align:start position:0%
+continent uh we're presented with a
+place that's always in the midst of
+
+ align:start position:0%
+place that's always in the midst of
+ 
+
+ align:start position:0%
+place that's always in the midst of
+disintegration and Chaos so we tend to
+
+ align:start position:0%
+disintegration and Chaos so we tend to
+ 
+
+ align:start position:0%
+disintegration and Chaos so we tend to
+approach Africa with a sense of P pity
+
+ align:start position:0%
+approach Africa with a sense of P pity
+ 
+
+ align:start position:0%
+approach Africa with a sense of P pity
+now um in reality there's much more
+
+ align:start position:0%
+now um in reality there's much more
+ 
+
+ align:start position:0%
+now um in reality there's much more
+going on and that at the public level
+
+ align:start position:0%
+going on and that at the public level
+ 
+
+ align:start position:0%
+going on and that at the public level
+we're not always attuned to um these are
+
+ align:start position:0%
+we're not always attuned to um these are
+ 
+
+ align:start position:0%
+we're not always attuned to um these are
+conventions that have become you know a
+
+ align:start position:0%
+conventions that have become you know a
+ 
+
+ align:start position:0%
+conventions that have become you know a
+sort of cultural and social pathology in
+
+ align:start position:0%
+sort of cultural and social pathology in
+ 
+
+ align:start position:0%
+sort of cultural and social pathology in
+the west and at this pathology at the
+
+ align:start position:0%
+the west and at this pathology at the
+ 
+
+ align:start position:0%
+the west and at this pathology at the
+heart of it um is what curator oan wer
+
+ align:start position:0%
+heart of it um is what curator oan wer
+ 
+
+ align:start position:0%
+heart of it um is what curator oan wer
+calls um AFR pessimism as you'll
+
+ align:start position:0%
+calls um AFR pessimism as you'll
+ 
+
+ align:start position:0%
+calls um AFR pessimism as you'll
+probably read in the in your readings
+
+ align:start position:0%
+probably read in the in your readings
+ 
+
+ align:start position:0%
+probably read in the in your readings
+for this week and um the exhibition book
+
+ align:start position:0%
+for this week and um the exhibition book
+ 
+
+ align:start position:0%
+for this week and um the exhibition book
+snap Jud
+
+ align:start position:0%
+snap Jud
+ 
+
+ align:start position:0%
+snap Jud
+judgments so you know the great thing
+
+ align:start position:0%
+judgments so you know the great thing
+ 
+
+ align:start position:0%
+judgments so you know the great thing
+about the study of African uh of art and
+
+ align:start position:0%
+about the study of African uh of art and
+ 
+
+ align:start position:0%
+about the study of African uh of art and
+architecture um is that it finds ways to
+
+ align:start position:0%
+architecture um is that it finds ways to
+ 
+
+ align:start position:0%
+architecture um is that it finds ways to
+upset these pervasive AFR pesimistic uh
+
+ align:start position:0%
+upset these pervasive AFR pesimistic uh
+ 
+
+ align:start position:0%
+upset these pervasive AFR pesimistic uh
+conventions of
+
+ align:start position:0%
+conventions of
+ 
+
+ align:start position:0%
+conventions of
+Imaging um and that we're both very
+
+ align:start position:0%
+Imaging um and that we're both very
+ 
+
+ align:start position:0%
+Imaging um and that we're both very
+attracted to and dangerously immune to
+
+ align:start position:0%
+attracted to and dangerously immune to
+ 
+
+ align:start position:0%
+attracted to and dangerously immune to
+at the same time um instead what we want
+
+ align:start position:0%
+at the same time um instead what we want
+ 
+
+ align:start position:0%
+at the same time um instead what we want
+to do is raise vital questions on
+
+ align:start position:0%
+to do is raise vital questions on
+ 
+
+ align:start position:0%
+to do is raise vital questions on
+uh and to propose new possibilities for
+
+ align:start position:0%
+uh and to propose new possibilities for
+ 
+
+ align:start position:0%
+uh and to propose new possibilities for
+the meaning of how we understand African
+
+ align:start position:0%
+the meaning of how we understand African
+ 
+
+ align:start position:0%
+the meaning of how we understand African
+culture and
+
+ align:start position:0%
+culture and
+ 
+
+ align:start position:0%
+culture and
+architecture um before European
+
+ align:start position:0%
+architecture um before European
+ 
+
+ align:start position:0%
+architecture um before European
+colonization well before
+
+ align:start position:0%
+colonization well before
+ 
+
+ align:start position:0%
+colonization well before
+1200 um which is the Scramble for Africa
+
+ align:start position:0%
+1200 um which is the Scramble for Africa
+ 
+
+ align:start position:0%
+1200 um which is the Scramble for Africa
+which I'm talking about now um just to
+
+ align:start position:0%
+which I'm talking about now um just to
+ 
+
+ align:start position:0%
+which I'm talking about now um just to
+reiterate the BBC in
+
+ align:start position:0%
+reiterate the BBC in
+ 
+
+ align:start position:0%
+reiterate the BBC in
+2006 issued um this article asking is
+
+ align:start position:0%
+2006 issued um this article asking is
+ 
+
+ align:start position:0%
+2006 issued um this article asking is
+Africa's architecture
+
+ align:start position:0%
+Africa's architecture
+ 
+
+ align:start position:0%
+Africa's architecture
+dying um you know I mean obviously just
+
+ align:start position:0%
+dying um you know I mean obviously just
+ 
+
+ align:start position:0%
+dying um you know I mean obviously just
+the language right right there I mean
+
+ align:start position:0%
+the language right right there I mean
+ 
+
+ align:start position:0%
+the language right right there I mean
+the fact that you know the death and you
+
+ align:start position:0%
+the fact that you know the death and you
+ 
+
+ align:start position:0%
+the fact that you know the death and you
+know um and disintegration is you know
+
+ align:start position:0%
+know um and disintegration is you know
+ 
+
+ align:start position:0%
+know um and disintegration is you know
+entirely evident um we have let's just
+
+ align:start position:0%
+entirely evident um we have let's just
+ 
+
+ align:start position:0%
+entirely evident um we have let's just
+read some of these comments this was an
+
+ align:start position:0%
+read some of these comments this was an
+ 
+
+ align:start position:0%
+read some of these comments this was an
+interview that was conducted um we
+
+ align:start position:0%
+interview that was conducted um we
+ 
+
+ align:start position:0%
+interview that was conducted um we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+Joshua um the architecture that is
+
+ align:start position:0%
+Joshua um the architecture that is
+ 
+
+ align:start position:0%
+Joshua um the architecture that is
+indigenous to Africa is too primitive
+
+ align:start position:0%
+indigenous to Africa is too primitive
+ 
+
+ align:start position:0%
+indigenous to Africa is too primitive
+Africa has to move with recent with
+
+ align:start position:0%
+Africa has to move with recent with
+ 
+
+ align:start position:0%
+Africa has to move with recent with
+recent advances in building construction
+
+ align:start position:0%
+recent advances in building construction
+ 
+
+ align:start position:0%
+recent advances in building construction
+the need of the people in Africa has
+
+ align:start position:0%
+the need of the people in Africa has
+ 
+
+ align:start position:0%
+the need of the people in Africa has
+changed over the time therefore
+
+ align:start position:0%
+changed over the time therefore
+ 
+
+ align:start position:0%
+changed over the time therefore
+buildings should be designed and built
+
+ align:start position:0%
+buildings should be designed and built
+ 
+
+ align:start position:0%
+buildings should be designed and built
+in a way that these needs are met okay
+
+ align:start position:0%
+in a way that these needs are met okay
+ 
+
+ align:start position:0%
+in a way that these needs are met okay
+that's fair enough um but you know is it
+
+ align:start position:0%
+that's fair enough um but you know is it
+ 
+
+ align:start position:0%
+that's fair enough um but you know is it
+primitive you know is it uh is it is it
+
+ align:start position:0%
+primitive you know is it uh is it is it
+ 
+
+ align:start position:0%
+primitive you know is it uh is it is it
+you know on on the decline you know I
+
+ align:start position:0%
+you know on on the decline you know I
+ 
+
+ align:start position:0%
+you know on on the decline you know I
+mean these are you know these are people
+
+ align:start position:0%
+mean these are you know these are people
+ 
+
+ align:start position:0%
+mean these are you know these are people
+living there
+
+ align:start position:0%
+living there
+ 
+
+ align:start position:0%
+living there
+presumably um who espouse these opinions
+
+ align:start position:0%
+presumably um who espouse these opinions
+ 
+
+ align:start position:0%
+presumably um who espouse these opinions
+you know and going on you have um
+
+ align:start position:0%
+you know and going on you have um
+ 
+
+ align:start position:0%
+you know and going on you have um
+somebody like VI Victor Chambers Sierra
+
+ align:start position:0%
+somebody like VI Victor Chambers Sierra
+ 
+
+ align:start position:0%
+somebody like VI Victor Chambers Sierra
+Leon uh uh who someone from Sierra Leon
+
+ align:start position:0%
+Leon uh uh who someone from Sierra Leon
+ 
+
+ align:start position:0%
+Leon uh uh who someone from Sierra Leon
+who lives in Ghana he says is it only n
+
+ align:start position:0%
+who lives in Ghana he says is it only n
+ 
+
+ align:start position:0%
+who lives in Ghana he says is it only n
+in Nigeria Kenya and Uganda buildings
+
+ align:start position:0%
+in Nigeria Kenya and Uganda buildings
+ 
+
+ align:start position:0%
+in Nigeria Kenya and Uganda buildings
+have been collapsing even in Europe and
+
+ align:start position:0%
+have been collapsing even in Europe and
+ 
+
+ align:start position:0%
+have been collapsing even in Europe and
+the United States where perhaps they
+
+ align:start position:0%
+the United States where perhaps they
+ 
+
+ align:start position:0%
+the United States where perhaps they
+have better building structures
+
+ align:start position:0%
+have better building structures
+ 
+
+ align:start position:0%
+have better building structures
+well-built buildings have been
+
+ align:start position:0%
+well-built buildings have been
+ 
+
+ align:start position:0%
+well-built buildings have been
+collapsing anyways while we give the
+
+ align:start position:0%
+collapsing anyways while we give the
+ 
+
+ align:start position:0%
+collapsing anyways while we give the
+modern uh giveway to Modern impressive
+
+ align:start position:0%
+modern uh giveway to Modern impressive
+ 
+
+ align:start position:0%
+modern uh giveway to Modern impressive
+architecture we must not neglect our
+
+ align:start position:0%
+architecture we must not neglect our
+ 
+
+ align:start position:0%
+architecture we must not neglect our
+heritage in style and meaning well but
+
+ align:start position:0%
+heritage in style and meaning well but
+ 
+
+ align:start position:0%
+heritage in style and meaning well but
+you know that's that's that's all well
+
+ align:start position:0%
+you know that's that's that's all well
+ 
+
+ align:start position:0%
+you know that's that's that's all well
+and good too um so you know the language
+
+ align:start position:0%
+and good too um so you know the language
+ 
+
+ align:start position:0%
+and good too um so you know the language
+perpetuates this notion that
+
+ align:start position:0%
+perpetuates this notion that
+ 
+
+ align:start position:0%
+perpetuates this notion that
+architecture is dying and that um and
+
+ align:start position:0%
+architecture is dying and that um and
+ 
+
+ align:start position:0%
+architecture is dying and that um and
+that you know it there's that there's no
+
+ align:start position:0%
+that you know it there's that there's no
+ 
+
+ align:start position:0%
+that you know it there's that there's no
+hope that you know it's a lost cause
+
+ align:start position:0%
+hope that you know it's a lost cause
+ 
+
+ align:start position:0%
+hope that you know it's a lost cause
+which is really something that today I
+
+ align:start position:0%
+which is really something that today I
+ 
+
+ align:start position:0%
+which is really something that today I
+hope that we can combat and um really
+
+ align:start position:0%
+hope that we can combat and um really
+ 
+
+ align:start position:0%
+hope that we can combat and um really
+grapple with so um in this class we're
+
+ align:start position:0%
+grapple with so um in this class we're
+ 
+
+ align:start position:0%
+grapple with so um in this class we're
+going to leave behind the political map
+
+ align:start position:0%
+going to leave behind the political map
+ 
+
+ align:start position:0%
+going to leave behind the political map
+that you guys I'm sure have all seen you
+
+ align:start position:0%
+that you guys I'm sure have all seen you
+ 
+
+ align:start position:0%
+that you guys I'm sure have all seen you
+know dozens and times dozens of times in
+
+ align:start position:0%
+know dozens and times dozens of times in
+ 
+
+ align:start position:0%
+know dozens and times dozens of times in
+your upbringing and schooling um and in
+
+ align:start position:0%
+your upbringing and schooling um and in
+ 
+
+ align:start position:0%
+your upbringing and schooling um and in
+order to do that we're going to travel
+
+ align:start position:0%
+order to do that we're going to travel
+ 
+
+ align:start position:0%
+order to do that we're going to travel
+back um and as I said focus in on the
+
+ align:start position:0%
+back um and as I said focus in on the
+ 
+
+ align:start position:0%
+back um and as I said focus in on the
+year 1200 um and try to understand the
+
+ align:start position:0%
+year 1200 um and try to understand the
+ 
+
+ align:start position:0%
+year 1200 um and try to understand the
+historical development of various
+
+ align:start position:0%
+historical development of various
+ 
+
+ align:start position:0%
+historical development of various
+architectural forms as a function of
+
+ align:start position:0%
+architectural forms as a function of
+ 
+
+ align:start position:0%
+architectural forms as a function of
+natural resources and the complex
+
+ align:start position:0%
+natural resources and the complex
+ 
+
+ align:start position:0%
+natural resources and the complex
+changing societies and trading economies
+
+ align:start position:0%
+changing societies and trading economies
+ 
+
+ align:start position:0%
+changing societies and trading economies
+that depended on these
+
+ align:start position:0%
+that depended on these
+ 
+
+ align:start position:0%
+that depended on these
+resources um in tandem with this we're
+
+ align:start position:0%
+resources um in tandem with this we're
+ 
+
+ align:start position:0%
+resources um in tandem with this we're
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+to see how different architectural
+
+ align:start position:0%
+to see how different architectural
+ 
+
+ align:start position:0%
+to see how different architectural
+typologies evolved and uh were
+
+ align:start position:0%
+typologies evolved and uh were
+ 
+
+ align:start position:0%
+typologies evolved and uh were
+influenced by uh environmental and
+
+ align:start position:0%
+influenced by uh environmental and
+ 
+
+ align:start position:0%
+influenced by uh environmental and
+climatic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changes okay so um first let's let's
+
+ align:start position:0%
+changes okay so um first let's let's
+ 
+
+ align:start position:0%
+changes okay so um first let's let's
+take a look now as as a disclaimer you
+
+ align:start position:0%
+take a look now as as a disclaimer you
+ 
+
+ align:start position:0%
+take a look now as as a disclaimer you
+know and this came up uh over the course
+
+ align:start position:0%
+know and this came up uh over the course
+ 
+
+ align:start position:0%
+know and this came up uh over the course
+of uh the the term you know I've been
+
+ align:start position:0%
+of uh the the term you know I've been
+ 
+
+ align:start position:0%
+of uh the the term you know I've been
+you know I've been grappling with a lot
+
+ align:start position:0%
+you know I've been grappling with a lot
+ 
+
+ align:start position:0%
+you know I've been grappling with a lot
+of these maps and um you know for for
+
+ align:start position:0%
+of these maps and um you know for for
+ 
+
+ align:start position:0%
+of these maps and um you know for for
+their lacks for their absences for you
+
+ align:start position:0%
+their lacks for their absences for you
+ 
+
+ align:start position:0%
+their lacks for their absences for you
+know a lot a whole slew of problems that
+
+ align:start position:0%
+know a lot a whole slew of problems that
+ 
+
+ align:start position:0%
+know a lot a whole slew of problems that
+they present um now you know but um so
+
+ align:start position:0%
+they present um now you know but um so
+ 
+
+ align:start position:0%
+they present um now you know but um so
+you know a lot of the maps that I show
+
+ align:start position:0%
+you know a lot of the maps that I show
+ 
+
+ align:start position:0%
+you know a lot of the maps that I show
+here will not always be be perfect but I
+
+ align:start position:0%
+here will not always be be perfect but I
+ 
+
+ align:start position:0%
+here will not always be be perfect but I
+will you know try to try my best to
+
+ align:start position:0%
+will you know try to try my best to
+ 
+
+ align:start position:0%
+will you know try to try my best to
+illustrate their their flaws um now in
+
+ align:start position:0%
+illustrate their their flaws um now in
+ 
+
+ align:start position:0%
+illustrate their their flaws um now in
+in the maps presented here we have um on
+
+ align:start position:0%
+in the maps presented here we have um on
+ 
+
+ align:start position:0%
+in the maps presented here we have um on
+the one the image on the right we have
+
+ align:start position:0%
+the one the image on the right we have
+ 
+
+ align:start position:0%
+the one the image on the right we have
+four uh vegetation zones okay so we have
+
+ align:start position:0%
+four uh vegetation zones okay so we have
+ 
+
+ align:start position:0%
+four uh vegetation zones okay so we have
+the the Sahara which is this orange
+
+ align:start position:0%
+the the Sahara which is this orange
+ 
+
+ align:start position:0%
+the the Sahara which is this orange
+region um which is primarily desert you
+
+ align:start position:0%
+region um which is primarily desert you
+ 
+
+ align:start position:0%
+region um which is primarily desert you
+know you only find mostly camels maybe a
+
+ align:start position:0%
+know you only find mostly camels maybe a
+ 
+
+ align:start position:0%
+know you only find mostly camels maybe a
+couple of goats here and there um and
+
+ align:start position:0%
+couple of goats here and there um and
+ 
+
+ align:start position:0%
+couple of goats here and there um and
+here you have this uh Sahan semi-desert
+
+ align:start position:0%
+here you have this uh Sahan semi-desert
+ 
+
+ align:start position:0%
+here you have this uh Sahan semi-desert
+which is not quite a savannah but has
+
+ align:start position:0%
+which is not quite a savannah but has
+ 
+
+ align:start position:0%
+which is not quite a savannah but has
+you know P patches of uh of of grass and
+
+ align:start position:0%
+you know P patches of uh of of grass and
+ 
+
+ align:start position:0%
+you know P patches of uh of of grass and
+so on growing intermittently and you'll
+
+ align:start position:0%
+so on growing intermittently and you'll
+ 
+
+ align:start position:0%
+so on growing intermittently and you'll
+find a lot more like goats and
+
+ align:start position:0%
+find a lot more like goats and
+ 
+
+ align:start position:0%
+find a lot more like goats and
+pastoralism basically as you uh proceed
+
+ align:start position:0%
+pastoralism basically as you uh proceed
+ 
+
+ align:start position:0%
+pastoralism basically as you uh proceed
+South you'll find the the greater
+
+ align:start position:0%
+South you'll find the the greater
+ 
+
+ align:start position:0%
+South you'll find the the greater
+incidence of
+
+ align:start position:0%
+incidence of
+ 
+
+ align:start position:0%
+incidence of
+pastoralism um and then you have this
+
+ align:start position:0%
+pastoralism um and then you have this
+ 
+
+ align:start position:0%
+pastoralism um and then you have this
+Savannah region and the rainforest along
+
+ align:start position:0%
+Savannah region and the rainforest along
+ 
+
+ align:start position:0%
+Savannah region and the rainforest along
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coastline um so uh and so some of these
+
+ align:start position:0%
+coastline um so uh and so some of these
+ 
+
+ align:start position:0%
+coastline um so uh and so some of these
+resources um like salt which actually um
+
+ align:start position:0%
+resources um like salt which actually um
+ 
+
+ align:start position:0%
+resources um like salt which actually um
+uh was
+
+ align:start position:0%
+uh was
+ 
+
+ align:start position:0%
+uh was
+extracted uh from the Sahara and gold
+
+ align:start position:0%
+extracted uh from the Sahara and gold
+ 
+
+ align:start position:0%
+extracted uh from the Sahara and gold
+which is mined in um present day uh
+
+ align:start position:0%
+which is mined in um present day uh
+ 
+
+ align:start position:0%
+which is mined in um present day uh
+Ghana Mali kot deoir um Guinea burino
+
+ align:start position:0%
+Ghana Mali kot deoir um Guinea burino
+ 
+
+ align:start position:0%
+Ghana Mali kot deoir um Guinea burino
+Faso um Togo and Benin um you know
+
+ align:start position:0%
+Faso um Togo and Benin um you know
+ 
+
+ align:start position:0%
+Faso um Togo and Benin um you know
+basically this whole chunk of land is
+
+ align:start position:0%
+basically this whole chunk of land is
+ 
+
+ align:start position:0%
+basically this whole chunk of land is
+just uh entirely full of chalk full of
+
+ align:start position:0%
+just uh entirely full of chalk full of
+ 
+
+ align:start position:0%
+just uh entirely full of chalk full of
+gold um and also you'll find iron which
+
+ align:start position:0%
+gold um and also you'll find iron which
+ 
+
+ align:start position:0%
+gold um and also you'll find iron which
+on the um image on the left you'll find
+
+ align:start position:0%
+on the um image on the left you'll find
+ 
+
+ align:start position:0%
+on the um image on the left you'll find
+these black lines um are showing the
+
+ align:start position:0%
+these black lines um are showing the
+ 
+
+ align:start position:0%
+these black lines um are showing the
+spread of iron working throughout the
+
+ align:start position:0%
+spread of iron working throughout the
+ 
+
+ align:start position:0%
+spread of iron working throughout the
+continent um now and and that's
+
+ align:start position:0%
+continent um now and and that's
+ 
+
+ align:start position:0%
+continent um now and and that's
+something I'll get back to uh later on
+
+ align:start position:0%
+something I'll get back to uh later on
+ 
+
+ align:start position:0%
+something I'll get back to uh later on
+as the as the lecture progresses but
+
+ align:start position:0%
+as the as the lecture progresses but
+ 
+
+ align:start position:0%
+as the as the lecture progresses but
+basically what I want you to see is how
+
+ align:start position:0%
+basically what I want you to see is how
+ 
+
+ align:start position:0%
+basically what I want you to see is how
+um the these resources also hold on
+
+ align:start position:0%
+um the these resources also hold on
+ 
+
+ align:start position:0%
+um the these resources also hold on
+before I um close there's uh cattle
+
+ align:start position:0%
+before I um close there's uh cattle
+ 
+
+ align:start position:0%
+before I um close there's uh cattle
+domestication of cattle along this this
+
+ align:start position:0%
+domestication of cattle along this this
+ 
+
+ align:start position:0%
+domestication of cattle along this this
+line right here um and
+
+ align:start position:0%
+line right here um and
+ 
+
+ align:start position:0%
+line right here um and
+also um from what is now Tunisia
+
+ align:start position:0%
+also um from what is now Tunisia
+ 
+
+ align:start position:0%
+also um from what is now Tunisia
+spreading
+
+ align:start position:0%
+spreading
+ 
+
+ align:start position:0%
+spreading
+Southward um but um what I want you to
+
+ align:start position:0%
+Southward um but um what I want you to
+ 
+
+ align:start position:0%
+Southward um but um what I want you to
+see is that these Goods really shape the
+
+ align:start position:0%
+see is that these Goods really shape the
+ 
+
+ align:start position:0%
+see is that these Goods really shape the
+flow um throughout the continent um of
+
+ align:start position:0%
+flow um throughout the continent um of
+ 
+
+ align:start position:0%
+flow um throughout the continent um of
+trade okay so this again shows the major
+
+ align:start position:0%
+trade okay so this again shows the major
+ 
+
+ align:start position:0%
+trade okay so this again shows the major
+trade routes um you know in the yellow
+
+ align:start position:0%
+trade routes um you know in the yellow
+ 
+
+ align:start position:0%
+trade routes um you know in the yellow
+triangles like here um and some of the
+
+ align:start position:0%
+triangles like here um and some of the
+ 
+
+ align:start position:0%
+triangles like here um and some of the
+white ones as well show where
+
+ align:start position:0%
+white ones as well show where
+ 
+
+ align:start position:0%
+white ones as well show where
+salt um was extracted and also you have
+
+ align:start position:0%
+salt um was extracted and also you have
+ 
+
+ align:start position:0%
+salt um was extracted and also you have
+this orange copper source which is um
+
+ align:start position:0%
+this orange copper source which is um
+ 
+
+ align:start position:0%
+this orange copper source which is um
+you know located right here um you know
+
+ align:start position:0%
+you know located right here um you know
+ 
+
+ align:start position:0%
+you know located right here um you know
+the the I mean this map is also
+
+ align:start position:0%
+the the I mean this map is also
+ 
+
+ align:start position:0%
+the the I mean this map is also
+problematic because it shows you know
+
+ align:start position:0%
+problematic because it shows you know
+ 
+
+ align:start position:0%
+problematic because it shows you know
+yes it shows some East West connectivity
+
+ align:start position:0%
+yes it shows some East West connectivity
+ 
+
+ align:start position:0%
+yes it shows some East West connectivity
+but equally there was an important um
+
+ align:start position:0%
+but equally there was an important um
+ 
+
+ align:start position:0%
+but equally there was an important um
+North South axis of uh of dynamic uh
+
+ align:start position:0%
+North South axis of uh of dynamic uh
+ 
+
+ align:start position:0%
+North South axis of uh of dynamic uh
+connection as well um it ignores
+
+ align:start position:0%
+connection as well um it ignores
+ 
+
+ align:start position:0%
+connection as well um it ignores
+blatantly the foundies that um you'd
+
+ align:start position:0%
+blatantly the foundies that um you'd
+ 
+
+ align:start position:0%
+blatantly the foundies that um you'd
+find in axom um metal metal foundaries
+
+ align:start position:0%
+find in axom um metal metal foundaries
+ 
+
+ align:start position:0%
+find in axom um metal metal foundaries
+um and you know as I mentioned you know
+
+ align:start position:0%
+um and you know as I mentioned you know
+ 
+
+ align:start position:0%
+um and you know as I mentioned you know
+this is one of the take-home lessons for
+
+ align:start position:0%
+this is one of the take-home lessons for
+ 
+
+ align:start position:0%
+this is one of the take-home lessons for
+today that you know maps are constructs
+
+ align:start position:0%
+today that you know maps are constructs
+ 
+
+ align:start position:0%
+today that you know maps are constructs
+in the same way that history is a
+
+ align:start position:0%
+in the same way that history is a
+ 
+
+ align:start position:0%
+in the same way that history is a
+construct and we have to be critical of
+
+ align:start position:0%
+construct and we have to be critical of
+ 
+
+ align:start position:0%
+construct and we have to be critical of
+them okay so
+
+ align:start position:0%
+them okay so
+ 
+
+ align:start position:0%
+them okay so
+um moving on to slide five we have just
+
+ align:start position:0%
+um moving on to slide five we have just
+ 
+
+ align:start position:0%
+um moving on to slide five we have just
+this is just an introduction to the some
+
+ align:start position:0%
+this is just an introduction to the some
+ 
+
+ align:start position:0%
+this is just an introduction to the some
+of the great Empires that
+
+ align:start position:0%
+of the great Empires that
+ 
+
+ align:start position:0%
+of the great Empires that
+arose um as a result of these you know
+
+ align:start position:0%
+arose um as a result of these you know
+ 
+
+ align:start position:0%
+arose um as a result of these you know
+complex trading networks um but you know
+
+ align:start position:0%
+complex trading networks um but you know
+ 
+
+ align:start position:0%
+complex trading networks um but you know
+because I'm focusing mainly on the
+
+ align:start position:0%
+because I'm focusing mainly on the
+ 
+
+ align:start position:0%
+because I'm focusing mainly on the
+period of like 1200 we're only going to
+
+ align:start position:0%
+period of like 1200 we're only going to
+ 
+
+ align:start position:0%
+period of like 1200 we're only going to
+be um discussing the Ghana and Molly
+
+ align:start position:0%
+be um discussing the Ghana and Molly
+ 
+
+ align:start position:0%
+be um discussing the Ghana and Molly
+Empires um the image on the on the left
+
+ align:start position:0%
+Empires um the image on the on the left
+ 
+
+ align:start position:0%
+Empires um the image on the on the left
+I adapted sort of um initially the
+
+ align:start position:0%
+I adapted sort of um initially the
+ 
+
+ align:start position:0%
+I adapted sort of um initially the
+Iberian Peninsula in Saudi Arabia was
+
+ align:start position:0%
+Iberian Peninsula in Saudi Arabia was
+ 
+
+ align:start position:0%
+Iberian Peninsula in Saudi Arabia was
+not shaded purple which is supposed to
+
+ align:start position:0%
+not shaded purple which is supposed to
+ 
+
+ align:start position:0%
+not shaded purple which is supposed to
+be the region where is Islam spread um
+
+ align:start position:0%
+be the region where is Islam spread um
+ 
+
+ align:start position:0%
+be the region where is Islam spread um
+but yeah I uh uh appropriated it a bit
+
+ align:start position:0%
+but yeah I uh uh appropriated it a bit
+ 
+
+ align:start position:0%
+but yeah I uh uh appropriated it a bit
+um and you know once again there is this
+
+ align:start position:0%
+um and you know once again there is this
+ 
+
+ align:start position:0%
+um and you know once again there is this
+north south axis which isn't really
+
+ align:start position:0%
+north south axis which isn't really
+ 
+
+ align:start position:0%
+north south axis which isn't really
+being represented and you know this
+
+ align:start position:0%
+being represented and you know this
+ 
+
+ align:start position:0%
+being represented and you know this
+perhaps this map better accounts for the
+
+ align:start position:0%
+perhaps this map better accounts for the
+ 
+
+ align:start position:0%
+perhaps this map better accounts for the
+spread of like iron working and cattle
+
+ align:start position:0%
+spread of like iron working and cattle
+ 
+
+ align:start position:0%
+spread of like iron working and cattle
+and so on that really was um within that
+
+ align:start position:0%
+and so on that really was um within that
+ 
+
+ align:start position:0%
+and so on that really was um within that
+shift or yeah
+
+ align:start position:0%
+shift or yeah
+ 
+
+ align:start position:0%
+shift or yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so you know Prosperity generated
+
+ align:start position:0%
+um okay so you know Prosperity generated
+ 
+
+ align:start position:0%
+um okay so you know Prosperity generated
+through trade led to the growth of
+
+ align:start position:0%
+through trade led to the growth of
+ 
+
+ align:start position:0%
+through trade led to the growth of
+urbanization and certain um settlements
+
+ align:start position:0%
+urbanization and certain um settlements
+ 
+
+ align:start position:0%
+urbanization and certain um settlements
+um cities along these trading routes
+
+ align:start position:0%
+um cities along these trading routes
+ 
+
+ align:start position:0%
+um cities along these trading routes
+which you know you'll see Central nodes
+
+ align:start position:0%
+which you know you'll see Central nodes
+ 
+
+ align:start position:0%
+which you know you'll see Central nodes
+here and there um really were crucibles
+
+ align:start position:0%
+here and there um really were crucibles
+ 
+
+ align:start position:0%
+here and there um really were crucibles
+of ideas and values and
+
+ align:start position:0%
+of ideas and values and
+ 
+
+ align:start position:0%
+of ideas and values and
+practices um you know that uh that were
+
+ align:start position:0%
+practices um you know that uh that were
+ 
+
+ align:start position:0%
+practices um you know that uh that were
+spread and it's pretty remarkable as I
+
+ align:start position:0%
+spread and it's pretty remarkable as I
+ 
+
+ align:start position:0%
+spread and it's pretty remarkable as I
+hope you'll see so where are we going
+
+ align:start position:0%
+hope you'll see so where are we going
+ 
+
+ align:start position:0%
+hope you'll see so where are we going
+today okay um we're going to start out
+
+ align:start position:0%
+today okay um we're going to start out
+ 
+
+ align:start position:0%
+today okay um we're going to start out
+in uh Morocco Southern Morocco um a
+
+ align:start position:0%
+in uh Morocco Southern Morocco um a
+ 
+
+ align:start position:0%
+in uh Morocco Southern Morocco um a
+fortress called um the kba a Ben hadu um
+
+ align:start position:0%
+fortress called um the kba a Ben hadu um
+ 
+
+ align:start position:0%
+fortress called um the kba a Ben hadu um
+we're then going to go down to the great
+
+ align:start position:0%
+we're then going to go down to the great
+ 
+
+ align:start position:0%
+we're then going to go down to the great
+Mosque of Jenny and Molly and then go up
+
+ align:start position:0%
+Mosque of Jenny and Molly and then go up
+ 
+
+ align:start position:0%
+Mosque of Jenny and Molly and then go up
+slightly um Northeast to um the mopti
+
+ align:start position:0%
+slightly um Northeast to um the mopti
+ 
+
+ align:start position:0%
+slightly um Northeast to um the mopti
+region in mly to the to see the dogon
+
+ align:start position:0%
+region in mly to the to see the dogon
+ 
+
+ align:start position:0%
+region in mly to the to see the dogon
+communities we're then going to sweep
+
+ align:start position:0%
+communities we're then going to sweep
+ 
+
+ align:start position:0%
+communities we're then going to sweep
+across um this this uh East West axis of
+
+ align:start position:0%
+across um this this uh East West axis of
+ 
+
+ align:start position:0%
+across um this this uh East West axis of
+trade and we're going to go to lella and
+
+ align:start position:0%
+trade and we're going to go to lella and
+ 
+
+ align:start position:0%
+trade and we're going to go to lella and
+following trade route South along the
+
+ align:start position:0%
+following trade route South along the
+ 
+
+ align:start position:0%
+following trade route South along the
+Swahili Coast um we're going to stop in
+
+ align:start position:0%
+Swahili Coast um we're going to stop in
+ 
+
+ align:start position:0%
+Swahili Coast um we're going to stop in
+uh huni kubba and then we're going to
+
+ align:start position:0%
+uh huni kubba and then we're going to
+ 
+
+ align:start position:0%
+uh huni kubba and then we're going to
+end in Great
+
+ align:start position:0%
+end in Great
+ 
+
+ align:start position:0%
+end in Great
+Zimbabwe
+
+ align:start position:0%
+Zimbabwe
+ 
+
+ align:start position:0%
+Zimbabwe
+um all
+
+ align:start position:0%
+um all
+ 
+
+ align:start position:0%
+um all
+right so uh so let's begin at our site
+
+ align:start position:0%
+right so uh so let's begin at our site
+ 
+
+ align:start position:0%
+right so uh so let's begin at our site
+uh at Aid Ben hadu in southern Morocco
+
+ align:start position:0%
+uh at Aid Ben hadu in southern Morocco
+ 
+
+ align:start position:0%
+uh at Aid Ben hadu in southern Morocco
+it's located right here outside of
+
+ align:start position:0%
+it's located right here outside of
+ 
+
+ align:start position:0%
+it's located right here outside of
+where's zette which I think may or may
+
+ align:start position:0%
+where's zette which I think may or may
+ 
+
+ align:start position:0%
+where's zette which I think may or may
+not be on your sheet um um but before we
+
+ align:start position:0%
+not be on your sheet um um but before we
+ 
+
+ align:start position:0%
+not be on your sheet um um but before we
+do that let's get sort of a a sense of
+
+ align:start position:0%
+do that let's get sort of a a sense of
+ 
+
+ align:start position:0%
+do that let's get sort of a a sense of
+historical
+
+ align:start position:0%
+historical
+ 
+
+ align:start position:0%
+historical
+backdrop um it's the middle of the 8th
+
+ align:start position:0%
+backdrop um it's the middle of the 8th
+ 
+
+ align:start position:0%
+backdrop um it's the middle of the 8th
+century and the Arab conquests under the
+
+ align:start position:0%
+century and the Arab conquests under the
+ 
+
+ align:start position:0%
+century and the Arab conquests under the
+Amaya dynasties based in D Damascus are
+
+ align:start position:0%
+Amaya dynasties based in D Damascus are
+ 
+
+ align:start position:0%
+Amaya dynasties based in D Damascus are
+penetrating full Forest into the MB
+
+ align:start position:0%
+penetrating full Forest into the MB
+ 
+
+ align:start position:0%
+penetrating full Forest into the MB
+which is um the westernmost region where
+
+ align:start position:0%
+which is um the westernmost region where
+ 
+
+ align:start position:0%
+which is um the westernmost region where
+Islam uh spread it's actually the Arabic
+
+ align:start position:0%
+Islam uh spread it's actually the Arabic
+ 
+
+ align:start position:0%
+Islam uh spread it's actually the Arabic
+word for for
+
+ align:start position:0%
+word for for
+ 
+
+ align:start position:0%
+word for for
+West um and uh and so you know you see
+
+ align:start position:0%
+West um and uh and so you know you see
+ 
+
+ align:start position:0%
+West um and uh and so you know you see
+uh right here there's the um there's
+
+ align:start position:0%
+uh right here there's the um there's
+ 
+
+ align:start position:0%
+uh right here there's the um there's
+this uh east to west um line of uh line
+
+ align:start position:0%
+this uh east to west um line of uh line
+ 
+
+ align:start position:0%
+this uh east to west um line of uh line
+of movement going on and um and I I also
+
+ align:start position:0%
+of movement going on and um and I I also
+ 
+
+ align:start position:0%
+of movement going on and um and I I also
+want to want to stress one thing you
+
+ align:start position:0%
+want to want to stress one thing you
+ 
+
+ align:start position:0%
+want to want to stress one thing you
+know typically we always think of um
+
+ align:start position:0%
+know typically we always think of um
+ 
+
+ align:start position:0%
+know typically we always think of um
+people from the MB as berbers but um
+
+ align:start position:0%
+people from the MB as berbers but um
+ 
+
+ align:start position:0%
+people from the MB as berbers but um
+just to um dispel this misconception the
+
+ align:start position:0%
+just to um dispel this misconception the
+ 
+
+ align:start position:0%
+just to um dispel this misconception the
+term Berber is actually derived from um
+
+ align:start position:0%
+term Berber is actually derived from um
+ 
+
+ align:start position:0%
+term Berber is actually derived from um
+the Greek term barbaros which means
+
+ align:start position:0%
+the Greek term barbaros which means
+ 
+
+ align:start position:0%
+the Greek term barbaros which means
+Barbarian um and this you know really we
+
+ align:start position:0%
+Barbarian um and this you know really we
+ 
+
+ align:start position:0%
+Barbarian um and this you know really we
+want to call these people uh what they
+
+ align:start position:0%
+want to call these people uh what they
+ 
+
+ align:start position:0%
+want to call these people uh what they
+call themselves which is Iman which
+
+ align:start position:0%
+call themselves which is Iman which
+ 
+
+ align:start position:0%
+call themselves which is Iman which
+means um free men in their their own
+
+ align:start position:0%
+means um free men in their their own
+ 
+
+ align:start position:0%
+means um free men in their their own
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+um uh and you know the amazan people put
+
+ align:start position:0%
+um uh and you know the amazan people put
+ 
+
+ align:start position:0%
+um uh and you know the amazan people put
+up a a good fight um
+
+ align:start position:0%
+up a a good fight um
+ 
+
+ align:start position:0%
+up a a good fight um
+against Islam
+
+ align:start position:0%
+against Islam
+ 
+
+ align:start position:0%
+against Islam
+um uh and the incoming Muslims in the
+
+ align:start position:0%
+um uh and the incoming Muslims in the
+ 
+
+ align:start position:0%
+um uh and the incoming Muslims in the
+8th Century but the advantages of um
+
+ align:start position:0%
+8th Century but the advantages of um
+ 
+
+ align:start position:0%
+8th Century but the advantages of um
+fully submitting to the religion far
+
+ align:start position:0%
+fully submitting to the religion far
+ 
+
+ align:start position:0%
+fully submitting to the religion far
+outweighed um the disadvantages posed by
+
+ align:start position:0%
+outweighed um the disadvantages posed by
+ 
+
+ align:start position:0%
+outweighed um the disadvantages posed by
+Rebellion so by 1100 um the mebe
+
+ align:start position:0%
+Rebellion so by 1100 um the mebe
+ 
+
+ align:start position:0%
+Rebellion so by 1100 um the mebe
+kingdoms um began to mobilize their
+
+ align:start position:0%
+kingdoms um began to mobilize their
+ 
+
+ align:start position:0%
+kingdoms um began to mobilize their
+power and it's under the El morovids or
+
+ align:start position:0%
+power and it's under the El morovids or
+ 
+
+ align:start position:0%
+power and it's under the El morovids or
+uh as they're called in Arabic the El
+
+ align:start position:0%
+uh as they're called in Arabic the El
+ 
+
+ align:start position:0%
+uh as they're called in Arabic the El
+morab bitun right up here from 1050 to
+
+ align:start position:0%
+morab bitun right up here from 1050 to
+ 
+
+ align:start position:0%
+morab bitun right up here from 1050 to
+114 40 um that they really seized power
+
+ align:start position:0%
+114 40 um that they really seized power
+ 
+
+ align:start position:0%
+114 40 um that they really seized power
+over all of
+
+ align:start position:0%
+over all of
+ 
+
+ align:start position:0%
+over all of
+Algeria Morocco
+
+ align:start position:0%
+Algeria Morocco
+ 
+
+ align:start position:0%
+Algeria Morocco
+Tunisia um and the alberian Iberian uh
+
+ align:start position:0%
+Tunisia um and the alberian Iberian uh
+ 
+
+ align:start position:0%
+Tunisia um and the alberian Iberian uh
+Peninsula as well um but protecting this
+
+ align:start position:0%
+Peninsula as well um but protecting this
+ 
+
+ align:start position:0%
+Peninsula as well um but protecting this
+territory wasn't an easy task for the El
+
+ align:start position:0%
+territory wasn't an easy task for the El
+ 
+
+ align:start position:0%
+territory wasn't an easy task for the El
+morovids um and they had to build
+
+ align:start position:0%
+morovids um and they had to build
+ 
+
+ align:start position:0%
+morovids um and they had to build
+strongholds to sustain their he hegemony
+
+ align:start position:0%
+strongholds to sustain their he hegemony
+ 
+
+ align:start position:0%
+strongholds to sustain their he hegemony
+um a Ben hadu is an example of this type
+
+ align:start position:0%
+um a Ben hadu is an example of this type
+ 
+
+ align:start position:0%
+um a Ben hadu is an example of this type
+of defend defensive
+
+ align:start position:0%
+of defend defensive
+ 
+
+ align:start position:0%
+of defend defensive
+architecture um um and it is essentially
+
+ align:start position:0%
+architecture um um and it is essentially
+ 
+
+ align:start position:0%
+architecture um um and it is essentially
+a casba which I'm sure you know you've
+
+ align:start position:0%
+a casba which I'm sure you know you've
+ 
+
+ align:start position:0%
+a casba which I'm sure you know you've
+all heard from uh The Clash's popular
+
+ align:start position:0%
+all heard from uh The Clash's popular
+ 
+
+ align:start position:0%
+all heard from uh The Clash's popular
+song uh means uh it means uh it's the
+
+ align:start position:0%
+song uh means uh it means uh it's the
+ 
+
+ align:start position:0%
+song uh means uh it means uh it's the
+Arabic word for Fortress um and uh and
+
+ align:start position:0%
+Arabic word for Fortress um and uh and
+ 
+
+ align:start position:0%
+Arabic word for Fortress um and uh and
+these people clearly did not want their
+
+ align:start position:0%
+these people clearly did not want their
+ 
+
+ align:start position:0%
+these people clearly did not want their
+casba rocked so um so to do that to keep
+
+ align:start position:0%
+casba rocked so um so to do that to keep
+ 
+
+ align:start position:0%
+casba rocked so um so to do that to keep
+it from being rocked they they built um
+
+ align:start position:0%
+it from being rocked they they built um
+ 
+
+ align:start position:0%
+it from being rocked they they built um
+High um uh High mud and stone um walls
+
+ align:start position:0%
+High um uh High mud and stone um walls
+ 
+
+ align:start position:0%
+High um uh High mud and stone um walls
+um you know demonstrated uh here
+
+ align:start position:0%
+um you know demonstrated uh here
+ 
+
+ align:start position:0%
+um you know demonstrated uh here
+actually this is um and you'll see these
+
+ align:start position:0%
+actually this is um and you'll see these
+ 
+
+ align:start position:0%
+actually this is um and you'll see these
+these crenellations which are these tiny
+
+ align:start position:0%
+these crenellations which are these tiny
+ 
+
+ align:start position:0%
+these crenellations which are these tiny
+slits actually you know they're not tiny
+
+ align:start position:0%
+slits actually you know they're not tiny
+ 
+
+ align:start position:0%
+slits actually you know they're not tiny
+I mean they're they're slits slit
+
+ align:start position:0%
+I mean they're they're slits slit
+ 
+
+ align:start position:0%
+I mean they're they're slits slit
+Windows um that were used you know to to
+
+ align:start position:0%
+Windows um that were used you know to to
+ 
+
+ align:start position:0%
+Windows um that were used you know to to
+shoot uh arrows and other other weapons
+
+ align:start position:0%
+shoot uh arrows and other other weapons
+ 
+
+ align:start position:0%
+shoot uh arrows and other other weapons
+you know it's I mean it's a defense
+
+ align:start position:0%
+you know it's I mean it's a defense
+ 
+
+ align:start position:0%
+you know it's I mean it's a defense
+mechanism and also you know keeping
+
+ align:start position:0%
+mechanism and also you know keeping
+ 
+
+ align:start position:0%
+mechanism and also you know keeping
+keeping sunlight out keeping um the cool
+
+ align:start position:0%
+keeping sunlight out keeping um the cool
+ 
+
+ align:start position:0%
+keeping sunlight out keeping um the cool
+uh the you know um cool air within the
+
+ align:start position:0%
+uh the you know um cool air within the
+ 
+
+ align:start position:0%
+uh the you know um cool air within the
+the structures
+
+ align:start position:0%
+the structures
+ 
+
+ align:start position:0%
+the structures
+themselves um and the roof
+
+ align:start position:0%
+themselves um and the roof
+ 
+
+ align:start position:0%
+themselves um and the roof
+Terraces um are often um laid with um
+
+ align:start position:0%
+Terraces um are often um laid with um
+ 
+
+ align:start position:0%
+Terraces um are often um laid with um
+beams of the trunks of palm trees also
+
+ align:start position:0%
+beams of the trunks of palm trees also
+ 
+
+ align:start position:0%
+beams of the trunks of palm trees also
+to um
+
+ align:start position:0%
+to um
+ 
+
+ align:start position:0%
+to um
+to sort of in insulate um to some extent
+
+ align:start position:0%
+to sort of in insulate um to some extent
+ 
+
+ align:start position:0%
+to sort of in insulate um to some extent
+um today its inhabitants moved from from
+
+ align:start position:0%
+um today its inhabitants moved from from
+ 
+
+ align:start position:0%
+um today its inhabitants moved from from
+the former um kaser this word kaser in
+
+ align:start position:0%
+the former um kaser this word kaser in
+ 
+
+ align:start position:0%
+the former um kaser this word kaser in
+Arabic is Castle so this former um
+
+ align:start position:0%
+Arabic is Castle so this former um
+ 
+
+ align:start position:0%
+Arabic is Castle so this former um
+Fortress to the new area across this Wy
+
+ align:start position:0%
+Fortress to the new area across this Wy
+ 
+
+ align:start position:0%
+Fortress to the new area across this Wy
+which is a basically a river valley I
+
+ align:start position:0%
+which is a basically a river valley I
+ 
+
+ align:start position:0%
+which is a basically a river valley I
+mean as you saw in the previous
+
+ align:start position:0%
+mean as you saw in the previous
+ 
+
+ align:start position:0%
+mean as you saw in the previous
+um picture right here there is sort of
+
+ align:start position:0%
+um picture right here there is sort of
+ 
+
+ align:start position:0%
+um picture right here there is sort of
+this um
+
+ align:start position:0%
+this um
+ 
+
+ align:start position:0%
+this um
+slight River
+
+ align:start position:0%
+slight River
+ 
+
+ align:start position:0%
+slight River
+um uh and it's you know now a blessed
+
+ align:start position:0%
+um uh and it's you know now a blessed
+ 
+
+ align:start position:0%
+um uh and it's you know now a blessed
+UNESCO world heritage
+
+ align:start position:0%
+UNESCO world heritage
+ 
+
+ align:start position:0%
+UNESCO world heritage
+site um so uh so why is this why is this
+
+ align:start position:0%
+site um so uh so why is this why is this
+ 
+
+ align:start position:0%
+site um so uh so why is this why is this
+so important okay um basically uh in
+
+ align:start position:0%
+so important okay um basically uh in
+ 
+
+ align:start position:0%
+so important okay um basically uh in
+this region of Morocco you have in you
+
+ align:start position:0%
+this region of Morocco you have in you
+ 
+
+ align:start position:0%
+this region of Morocco you have in you
+know this wette region you have more
+
+ align:start position:0%
+know this wette region you have more
+ 
+
+ align:start position:0%
+know this wette region you have more
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+300 um
+
+ align:start position:0%
+300 um
+ 
+
+ align:start position:0%
+300 um
+uh out of the Thousand or so casbas that
+
+ align:start position:0%
+uh out of the Thousand or so casbas that
+ 
+
+ align:start position:0%
+uh out of the Thousand or so casbas that
+have been identified in the whole
+
+ align:start position:0%
+have been identified in the whole
+ 
+
+ align:start position:0%
+have been identified in the whole
+country now that is a huge concentration
+
+ align:start position:0%
+country now that is a huge concentration
+ 
+
+ align:start position:0%
+country now that is a huge concentration
+of casbas in in one region and you know
+
+ align:start position:0%
+of casbas in in one region and you know
+ 
+
+ align:start position:0%
+of casbas in in one region and you know
+it's by it's it's no accident that
+
+ align:start position:0%
+it's by it's it's no accident that
+ 
+
+ align:start position:0%
+it's by it's it's no accident that
+they're all in in that region because
+
+ align:start position:0%
+they're all in in that region because
+ 
+
+ align:start position:0%
+they're all in in that region because
+you know there there's this huge um
+
+ align:start position:0%
+you know there there's this huge um
+ 
+
+ align:start position:0%
+you know there there's this huge um
+monopolization on the trade routes and
+
+ align:start position:0%
+monopolization on the trade routes and
+ 
+
+ align:start position:0%
+monopolization on the trade routes and
+um a Ben hadu is actually on a route um
+
+ align:start position:0%
+um a Ben hadu is actually on a route um
+ 
+
+ align:start position:0%
+um a Ben hadu is actually on a route um
+it it it's has a strategic location on
+
+ align:start position:0%
+it it it's has a strategic location on
+ 
+
+ align:start position:0%
+it it it's has a strategic location on
+the route to moroes and some of the
+
+ align:start position:0%
+the route to moroes and some of the
+ 
+
+ align:start position:0%
+the route to moroes and some of the
+Imperial cities okay so where are we
+
+ align:start position:0%
+Imperial cities okay so where are we
+ 
+
+ align:start position:0%
+Imperial cities okay so where are we
+going next well right now we're going to
+
+ align:start position:0%
+going next well right now we're going to
+ 
+
+ align:start position:0%
+going next well right now we're going to
+um the great mosque in in Jenny in Molly
+
+ align:start position:0%
+um the great mosque in in Jenny in Molly
+ 
+
+ align:start position:0%
+um the great mosque in in Jenny in Molly
+um and you know we're going to follow
+
+ align:start position:0%
+um and you know we're going to follow
+ 
+
+ align:start position:0%
+um and you know we're going to follow
+basically not these two lines
+
+ align:start position:0%
+basically not these two lines
+ 
+
+ align:start position:0%
+basically not these two lines
+specifically but lines that uh of trade
+
+ align:start position:0%
+specifically but lines that uh of trade
+ 
+
+ align:start position:0%
+specifically but lines that uh of trade
+that connected the two regions
+
+ align:start position:0%
+that connected the two regions
+ 
+
+ align:start position:0%
+that connected the two regions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um okay so the rise and exports of uh
+
+ align:start position:0%
+um okay so the rise and exports of uh
+ 
+
+ align:start position:0%
+um okay so the rise and exports of uh
+West West African gold Ivory salt and
+
+ align:start position:0%
+West West African gold Ivory salt and
+ 
+
+ align:start position:0%
+West West African gold Ivory salt and
+slaves uh were major factors in the rise
+
+ align:start position:0%
+slaves uh were major factors in the rise
+ 
+
+ align:start position:0%
+slaves uh were major factors in the rise
+of the grassland kingdoms um but what's
+
+ align:start position:0%
+of the grassland kingdoms um but what's
+ 
+
+ align:start position:0%
+of the grassland kingdoms um but what's
+unique about Jenny is that it as a city
+
+ align:start position:0%
+unique about Jenny is that it as a city
+ 
+
+ align:start position:0%
+unique about Jenny is that it as a city
+it was never subsumed into any Kingdom
+
+ align:start position:0%
+it was never subsumed into any Kingdom
+ 
+
+ align:start position:0%
+it was never subsumed into any Kingdom
+and remained
+
+ align:start position:0%
+and remained
+ 
+
+ align:start position:0%
+and remained
+independent um even though it did
+
+ align:start position:0%
+independent um even though it did
+ 
+
+ align:start position:0%
+independent um even though it did
+benefit from the stability of the Ghana
+
+ align:start position:0%
+benefit from the stability of the Ghana
+ 
+
+ align:start position:0%
+benefit from the stability of the Ghana
+Empire and the gold that it thrived upon
+
+ align:start position:0%
+Empire and the gold that it thrived upon
+ 
+
+ align:start position:0%
+Empire and the gold that it thrived upon
+um in fact uh um most most of the the
+
+ align:start position:0%
+um in fact uh um most most of the the
+ 
+
+ align:start position:0%
+um in fact uh um most most of the the
+first um large scale States um with
+
+ align:start position:0%
+first um large scale States um with
+ 
+
+ align:start position:0%
+first um large scale States um with
+capitals located near the desert Fringe
+
+ align:start position:0%
+capitals located near the desert Fringe
+ 
+
+ align:start position:0%
+capitals located near the desert Fringe
+um also predate Muslim trading contacts
+
+ align:start position:0%
+um also predate Muslim trading contacts
+ 
+
+ align:start position:0%
+um also predate Muslim trading contacts
+and in in genant specifically there have
+
+ align:start position:0%
+and in in genant specifically there have
+ 
+
+ align:start position:0%
+and in in genant specifically there have
+been helenistic beads that have been
+
+ align:start position:0%
+been helenistic beads that have been
+ 
+
+ align:start position:0%
+been helenistic beads that have been
+excavated at the site um which date back
+
+ align:start position:0%
+excavated at the site um which date back
+ 
+
+ align:start position:0%
+excavated at the site um which date back
+to 250 um before the Common Era um by
+
+ align:start position:0%
+to 250 um before the Common Era um by
+ 
+
+ align:start position:0%
+to 250 um before the Common Era um by
+700 uh of the Common Era a solid trading
+
+ align:start position:0%
+700 uh of the Common Era a solid trading
+ 
+
+ align:start position:0%
+700 uh of the Common Era a solid trading
+network was established and taking
+
+ align:start position:0%
+network was established and taking
+ 
+
+ align:start position:0%
+network was established and taking
+shapee in West Africa um as you'll see
+
+ align:start position:0%
+shapee in West Africa um as you'll see
+ 
+
+ align:start position:0%
+shapee in West Africa um as you'll see
+uh in this map in slide 11 um we have
+
+ align:start position:0%
+uh in this map in slide 11 um we have
+ 
+
+ align:start position:0%
+uh in this map in slide 11 um we have
+you know these s's which indicate salt
+
+ align:start position:0%
+you know these s's which indicate salt
+ 
+
+ align:start position:0%
+you know these s's which indicate salt
+um G's which indicate
+
+ align:start position:0%
+um G's which indicate
+ 
+
+ align:start position:0%
+um G's which indicate
+gold um and you know they're they're
+
+ align:start position:0%
+gold um and you know they're they're
+ 
+
+ align:start position:0%
+gold um and you know they're they're
+just they're all over the place and this
+
+ align:start position:0%
+just they're all over the place and this
+ 
+
+ align:start position:0%
+just they're all over the place and this
+this circle right here is the former
+
+ align:start position:0%
+this circle right here is the former
+ 
+
+ align:start position:0%
+this circle right here is the former
+Ghana um Empire and right here is Jenny
+
+ align:start position:0%
+Ghana um Empire and right here is Jenny
+ 
+
+ align:start position:0%
+Ghana um Empire and right here is Jenny
+um just outside of it
+
+ align:start position:0%
+um just outside of it
+ 
+
+ align:start position:0%
+um just outside of it
+okay um and you know even though one
+
+ align:start position:0%
+okay um and you know even though one
+ 
+
+ align:start position:0%
+okay um and you know even though one
+thing to keep in mind even though Molly
+
+ align:start position:0%
+thing to keep in mind even though Molly
+ 
+
+ align:start position:0%
+thing to keep in mind even though Molly
+about 90% of the population now
+
+ align:start position:0%
+about 90% of the population now
+ 
+
+ align:start position:0%
+about 90% of the population now
+practices Islam you have to remember
+
+ align:start position:0%
+practices Islam you have to remember
+ 
+
+ align:start position:0%
+practices Islam you have to remember
+that back in you know the year 1200 or
+
+ align:start position:0%
+that back in you know the year 1200 or
+ 
+
+ align:start position:0%
+that back in you know the year 1200 or
+so you know it was still a site of
+
+ align:start position:0%
+so you know it was still a site of
+ 
+
+ align:start position:0%
+so you know it was still a site of
+religious contestation and um and you
+
+ align:start position:0%
+religious contestation and um and you
+ 
+
+ align:start position:0%
+religious contestation and um and you
+know they I mean you know
+
+ align:start position:0%
+know they I mean you know
+ 
+
+ align:start position:0%
+know they I mean you know
+um uh Native pra religious practices
+
+ align:start position:0%
+um uh Native pra religious practices
+ 
+
+ align:start position:0%
+um uh Native pra religious practices
+were still um sort of you know practiced
+
+ align:start position:0%
+were still um sort of you know practiced
+ 
+
+ align:start position:0%
+were still um sort of you know practiced
+in secret or you know tried to mainly
+
+ align:start position:0%
+in secret or you know tried to mainly
+ 
+
+ align:start position:0%
+in secret or you know tried to mainly
+keep it hidden from the Muslim
+
+ align:start position:0%
+keep it hidden from the Muslim
+ 
+
+ align:start position:0%
+keep it hidden from the Muslim
+population um okay so let's look at the
+
+ align:start position:0%
+population um okay so let's look at the
+ 
+
+ align:start position:0%
+population um okay so let's look at the
+great Mosque of Jenny um although the
+
+ align:start position:0%
+great Mosque of Jenny um although the
+ 
+
+ align:start position:0%
+great Mosque of Jenny um although the
+original structure of the mosque D dates
+
+ align:start position:0%
+original structure of the mosque D dates
+ 
+
+ align:start position:0%
+original structure of the mosque D dates
+back to the 13th century this is a typo
+
+ align:start position:0%
+back to the 13th century this is a typo
+ 
+
+ align:start position:0%
+back to the 13th century this is a typo
+it should say
+
+ align:start position:0%
+it should say
+ 
+
+ align:start position:0%
+it should say
+13th um when it was founded um by by a
+
+ align:start position:0%
+13th um when it was founded um by by a
+ 
+
+ align:start position:0%
+13th um when it was founded um by by a
+local um Jenny uh Chief named
+
+ align:start position:0%
+local um Jenny uh Chief named
+ 
+
+ align:start position:0%
+local um Jenny uh Chief named
+Koro um by the early 19th century it was
+
+ align:start position:0%
+Koro um by the early 19th century it was
+ 
+
+ align:start position:0%
+Koro um by the early 19th century it was
+largely demolished and then uh
+
+ align:start position:0%
+largely demolished and then uh
+ 
+
+ align:start position:0%
+largely demolished and then uh
+reconstructed in similar form um trying
+
+ align:start position:0%
+reconstructed in similar form um trying
+ 
+
+ align:start position:0%
+reconstructed in similar form um trying
+to be true to its original form under
+
+ align:start position:0%
+to be true to its original form under
+ 
+
+ align:start position:0%
+to be true to its original form under
+the French Colonial Direction in
+
+ align:start position:0%
+the French Colonial Direction in
+ 
+
+ align:start position:0%
+the French Colonial Direction in
+1907 um so right here you see the this
+
+ align:start position:0%
+1907 um so right here you see the this
+ 
+
+ align:start position:0%
+1907 um so right here you see the this
+is the kibla wall which um faces Mecca
+
+ align:start position:0%
+is the kibla wall which um faces Mecca
+ 
+
+ align:start position:0%
+is the kibla wall which um faces Mecca
+and the soup which uh I I haven't read
+
+ align:start position:0%
+and the soup which uh I I haven't read
+ 
+
+ align:start position:0%
+and the soup which uh I I haven't read
+anything specifically but my assump
+
+ align:start position:0%
+anything specifically but my assump
+ 
+
+ align:start position:0%
+anything specifically but my assump
+would be that um there was probably some
+
+ align:start position:0%
+would be that um there was probably some
+ 
+
+ align:start position:0%
+would be that um there was probably some
+sort of w or um institution or like a
+
+ align:start position:0%
+sort of w or um institution or like a
+ 
+
+ align:start position:0%
+sort of w or um institution or like a
+charitable endowment that um instituted
+
+ align:start position:0%
+charitable endowment that um instituted
+ 
+
+ align:start position:0%
+charitable endowment that um instituted
+the presence of the marketplace I don't
+
+ align:start position:0%
+the presence of the marketplace I don't
+ 
+
+ align:start position:0%
+the presence of the marketplace I don't
+know if it if it was already there
+
+ align:start position:0%
+know if it if it was already there
+ 
+
+ align:start position:0%
+know if it if it was already there
+before the construction of the mosque
+
+ align:start position:0%
+before the construction of the mosque
+ 
+
+ align:start position:0%
+before the construction of the mosque
+anyways um so let's check out this
+
+ align:start position:0%
+anyways um so let's check out this
+ 
+
+ align:start position:0%
+anyways um so let's check out this
+YouTube click
+
+ align:start position:0%
+YouTube click
+ 
+
+ align:start position:0%
+YouTube click
+clip videos removed due to copyright
+
+ align:start position:0%
+clip videos removed due to copyright
+ 
+
+ align:start position:0%
+clip videos removed due to copyright
+restrictions that's it that's that um so
+
+ align:start position:0%
+restrictions that's it that's that um so
+ 
+
+ align:start position:0%
+restrictions that's it that's that um so
+so to return um we have uh a plan of the
+
+ align:start position:0%
+so to return um we have uh a plan of the
+ 
+
+ align:start position:0%
+so to return um we have uh a plan of the
+mosque which features you know this this
+
+ align:start position:0%
+mosque which features you know this this
+ 
+
+ align:start position:0%
+mosque which features you know this this
+transverse Nave you have the women's
+
+ align:start position:0%
+transverse Nave you have the women's
+ 
+
+ align:start position:0%
+transverse Nave you have the women's
+Gallery in the back um uh hypo style uh
+
+ align:start position:0%
+Gallery in the back um uh hypo style uh
+ 
+
+ align:start position:0%
+Gallery in the back um uh hypo style uh
+hallway or Hall Courtyard um rather and
+
+ align:start position:0%
+hallway or Hall Courtyard um rather and
+ 
+
+ align:start position:0%
+hallway or Hall Courtyard um rather and
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+entrances uh of the mosque are on the
+
+ align:start position:0%
+entrances uh of the mosque are on the
+ 
+
+ align:start position:0%
+entrances uh of the mosque are on the
+North and South South ends um as I
+
+ align:start position:0%
+North and South South ends um as I
+ 
+
+ align:start position:0%
+North and South South ends um as I
+mentioned you know the
+
+ align:start position:0%
+mentioned you know the
+ 
+
+ align:start position:0%
+mentioned you know the
+the um Palm um
+
+ align:start position:0%
+the um Palm um
+ 
+
+ align:start position:0%
+the um Palm um
+uh uh Palm structures they they really
+
+ align:start position:0%
+uh uh Palm structures they they really
+ 
+
+ align:start position:0%
+uh uh Palm structures they they really
+were you know the helped um they still
+
+ align:start position:0%
+were you know the helped um they still
+ 
+
+ align:start position:0%
+were you know the helped um they still
+help um the local masons um with the uh
+
+ align:start position:0%
+help um the local masons um with the uh
+ 
+
+ align:start position:0%
+help um the local masons um with the uh
+perform the reapplication of mud and so
+
+ align:start position:0%
+perform the reapplication of mud and so
+ 
+
+ align:start position:0%
+perform the reapplication of mud and so
+on um and uh to what what's really
+
+ align:start position:0%
+on um and uh to what what's really
+ 
+
+ align:start position:0%
+on um and uh to what what's really
+phenomenal about the mosque in general
+
+ align:start position:0%
+phenomenal about the mosque in general
+ 
+
+ align:start position:0%
+phenomenal about the mosque in general
+is that you know during the day it it
+
+ align:start position:0%
+is that you know during the day it it
+ 
+
+ align:start position:0%
+is that you know during the day it it
+the mud um soaks up all of this heat
+
+ align:start position:0%
+the mud um soaks up all of this heat
+ 
+
+ align:start position:0%
+the mud um soaks up all of this heat
+from the Sun and uh and yet the mosque
+
+ align:start position:0%
+from the Sun and uh and yet the mosque
+ 
+
+ align:start position:0%
+from the Sun and uh and yet the mosque
+stays cool during the day and at night
+
+ align:start position:0%
+stays cool during the day and at night
+ 
+
+ align:start position:0%
+stays cool during the day and at night
+because it has absorbed all of this heat
+
+ align:start position:0%
+because it has absorbed all of this heat
+ 
+
+ align:start position:0%
+because it has absorbed all of this heat
+it then you know provides um warmth um
+
+ align:start position:0%
+it then you know provides um warmth um
+ 
+
+ align:start position:0%
+it then you know provides um warmth um
+in the interior of the mosque um and
+
+ align:start position:0%
+in the interior of the mosque um and
+ 
+
+ align:start position:0%
+in the interior of the mosque um and
+that you I don't have an image here but
+
+ align:start position:0%
+that you I don't have an image here but
+ 
+
+ align:start position:0%
+that you I don't have an image here but
+there actually um ceramic pipes that
+
+ align:start position:0%
+there actually um ceramic pipes that
+ 
+
+ align:start position:0%
+there actually um ceramic pipes that
+were um built to um to lead the drainage
+
+ align:start position:0%
+were um built to um to lead the drainage
+ 
+
+ align:start position:0%
+were um built to um to lead the drainage
+uh away from the mosque and uh the
+
+ align:start position:0%
+uh away from the mosque and uh the
+ 
+
+ align:start position:0%
+uh away from the mosque and uh the
+building itself to prevent um further
+
+ align:start position:0%
+building itself to prevent um further
+ 
+
+ align:start position:0%
+building itself to prevent um further
+deterioration
+
+ align:start position:0%
+deterioration
+ 
+
+ align:start position:0%
+deterioration
+um so that's that's that okay so where
+
+ align:start position:0%
+um so that's that's that okay so where
+ 
+
+ align:start position:0%
+um so that's that's that okay so where
+are we going next we're going to the
+
+ align:start position:0%
+are we going next we're going to the
+ 
+
+ align:start position:0%
+are we going next we're going to the
+doong communities also in Mali in the uh
+
+ align:start position:0%
+doong communities also in Mali in the uh
+ 
+
+ align:start position:0%
+doong communities also in Mali in the uh
+mopti region um and we're following you
+
+ align:start position:0%
+mopti region um and we're following you
+ 
+
+ align:start position:0%
+mopti region um and we're following you
+know more or less the the same trade
+
+ align:start position:0%
+know more or less the the same trade
+ 
+
+ align:start position:0%
+know more or less the the same trade
+route um so these you know at at first
+
+ align:start position:0%
+route um so these you know at at first
+ 
+
+ align:start position:0%
+route um so these you know at at first
+glance they seem chaotic right I mean
+
+ align:start position:0%
+glance they seem chaotic right I mean
+ 
+
+ align:start position:0%
+glance they seem chaotic right I mean
+you have this aerial view um that's
+
+ align:start position:0%
+you have this aerial view um that's
+ 
+
+ align:start position:0%
+you have this aerial view um that's
+that's from a from a high uh High
+
+ align:start position:0%
+that's from a from a high uh High
+ 
+
+ align:start position:0%
+that's from a from a high uh High
+distance above ground you know it's it
+
+ align:start position:0%
+distance above ground you know it's it
+ 
+
+ align:start position:0%
+distance above ground you know it's it
+just it looks it looks like a mess but
+
+ align:start position:0%
+just it looks it looks like a mess but
+ 
+
+ align:start position:0%
+just it looks it looks like a mess but
+it isn't um in the 12th century um these
+
+ align:start position:0%
+it isn't um in the 12th century um these
+ 
+
+ align:start position:0%
+it isn't um in the 12th century um these
+communities started um on the edges on
+
+ align:start position:0%
+communities started um on the edges on
+ 
+
+ align:start position:0%
+communities started um on the edges on
+the edges of this sandstone a scart
+
+ align:start position:0%
+the edges of this sandstone a scart
+ 
+
+ align:start position:0%
+the edges of this sandstone a scart
+which you'll see right right here um
+
+ align:start position:0%
+which you'll see right right here um
+ 
+
+ align:start position:0%
+which you'll see right right here um
+hidden sort of in in this Cliff um
+
+ align:start position:0%
+hidden sort of in in this Cliff um
+ 
+
+ align:start position:0%
+hidden sort of in in this Cliff um
+and um it's believed that you know was
+
+ align:start position:0%
+and um it's believed that you know was
+ 
+
+ align:start position:0%
+and um it's believed that you know was
+started by descendants of an early Iron
+
+ align:start position:0%
+started by descendants of an early Iron
+ 
+
+ align:start position:0%
+started by descendants of an early Iron
+Age Community um their Villages are
+
+ align:start position:0%
+Age Community um their Villages are
+ 
+
+ align:start position:0%
+Age Community um their Villages are
+highly
+
+ align:start position:0%
+highly
+ 
+
+ align:start position:0%
+highly
+organized according to a cosmological
+
+ align:start position:0%
+organized according to a cosmological
+ 
+
+ align:start position:0%
+organized according to a cosmological
+system which is at the core of the Doon
+
+ align:start position:0%
+system which is at the core of the Doon
+ 
+
+ align:start position:0%
+system which is at the core of the Doon
+uh people's belief system um you know
+
+ align:start position:0%
+uh people's belief system um you know
+ 
+
+ align:start position:0%
+uh people's belief system um you know
+right here you see a a a plan of
+
+ align:start position:0%
+right here you see a a a plan of
+ 
+
+ align:start position:0%
+right here you see a a a plan of
+basically what um the people living in
+
+ align:start position:0%
+basically what um the people living in
+ 
+
+ align:start position:0%
+basically what um the people living in
+this region think is uh you that they
+
+ align:start position:0%
+this region think is uh you that they
+ 
+
+ align:start position:0%
+this region think is uh you that they
+structure their homes according to this
+
+ align:start position:0%
+structure their homes according to this
+ 
+
+ align:start position:0%
+structure their homes according to this
+idea of a world egg that the world as we
+
+ align:start position:0%
+idea of a world egg that the world as we
+ 
+
+ align:start position:0%
+idea of a world egg that the world as we
+know it is disseminated um from a
+
+ align:start position:0%
+know it is disseminated um from a
+ 
+
+ align:start position:0%
+know it is disseminated um from a
+Seedling from um from you know this this
+
+ align:start position:0%
+Seedling from um from you know this this
+ 
+
+ align:start position:0%
+Seedling from um from you know this this
+idea of of reproductive reproduction and
+
+ align:start position:0%
+idea of of reproductive reproduction and
+ 
+
+ align:start position:0%
+idea of of reproductive reproduction and
+and fertility um and you see
+
+ align:start position:0%
+and fertility um and you see
+ 
+
+ align:start position:0%
+and fertility um and you see
+interestingly you see the outline of a
+
+ align:start position:0%
+interestingly you see the outline of a
+ 
+
+ align:start position:0%
+interestingly you see the outline of a
+man in a fetal
+
+ align:start position:0%
+man in a fetal
+ 
+
+ align:start position:0%
+man in a fetal
+position um which of course reinforces
+
+ align:start position:0%
+position um which of course reinforces
+ 
+
+ align:start position:0%
+position um which of course reinforces
+this idea that you know the home that
+
+ align:start position:0%
+this idea that you know the home that
+ 
+
+ align:start position:0%
+this idea that you know the home that
+domestic space is a womb it is a a site
+
+ align:start position:0%
+domestic space is a womb it is a a site
+ 
+
+ align:start position:0%
+domestic space is a womb it is a a site
+of uh of birth um a site of generation
+
+ align:start position:0%
+of uh of birth um a site of generation
+ 
+
+ align:start position:0%
+of uh of birth um a site of generation
+or of uh a generative um in its capacity
+
+ align:start position:0%
+or of uh a generative um in its capacity
+ 
+
+ align:start position:0%
+or of uh a generative um in its capacity
+um and right here you have these um this
+
+ align:start position:0%
+um and right here you have these um this
+ 
+
+ align:start position:0%
+um and right here you have these um this
+is just an example of some of the
+
+ align:start position:0%
+is just an example of some of the
+ 
+
+ align:start position:0%
+is just an example of some of the
+artwork um created by the Doon people um
+
+ align:start position:0%
+artwork um created by the Doon people um
+ 
+
+ align:start position:0%
+artwork um created by the Doon people um
+in uh carved um figures carved out of
+
+ align:start position:0%
+in uh carved um figures carved out of
+ 
+
+ align:start position:0%
+in uh carved um figures carved out of
+wood um having apic um value talismanic
+
+ align:start position:0%
+wood um having apic um value talismanic
+ 
+
+ align:start position:0%
+wood um having apic um value talismanic
+value um and uh in the image on the left
+
+ align:start position:0%
+value um and uh in the image on the left
+ 
+
+ align:start position:0%
+value um and uh in the image on the left
+you see um these Grainer which um are
+
+ align:start position:0%
+you see um these Grainer which um are
+ 
+
+ align:start position:0%
+you see um these Grainer which um are
+thought to
+
+ align:start position:0%
+thought to
+ 
+
+ align:start position:0%
+thought to
+um uh have both you know this this this
+
+ align:start position:0%
+um uh have both you know this this this
+ 
+
+ align:start position:0%
+um uh have both you know this this this
+conical phallic shape and a hollow you
+
+ align:start position:0%
+conical phallic shape and a hollow you
+ 
+
+ align:start position:0%
+conical phallic shape and a hollow you
+know vaginal shape which of course
+
+ align:start position:0%
+know vaginal shape which of course
+ 
+
+ align:start position:0%
+know vaginal shape which of course
+reinforces the whole um reproduction
+
+ align:start position:0%
+reinforces the whole um reproduction
+ 
+
+ align:start position:0%
+reinforces the whole um reproduction
+fertility Trope um the houses and the
+
+ align:start position:0%
+fertility Trope um the houses and the
+ 
+
+ align:start position:0%
+fertility Trope um the houses and the
+greeneries are built um out of a
+
+ align:start position:0%
+greeneries are built um out of a
+ 
+
+ align:start position:0%
+greeneries are built um out of a
+combination of mud and stone and uh with
+
+ align:start position:0%
+combination of mud and stone and uh with
+ 
+
+ align:start position:0%
+combination of mud and stone and uh with
+the addition of okay uh with the
+
+ align:start position:0%
+the addition of okay uh with the
+ 
+
+ align:start position:0%
+the addition of okay uh with the
+addition of um the um yes decoration
+
+ align:start position:0%
+addition of um the um yes decoration
+ 
+
+ align:start position:0%
+addition of um the um yes decoration
+decorative um right doors
+
+ align:start position:0%
+decorative um right doors
+ 
+
+ align:start position:0%
+decorative um right doors
+um so we're going to cut across to
+
+ align:start position:0%
+um so we're going to cut across to
+ 
+
+ align:start position:0%
+um so we're going to cut across to
+lella um located in what is now
+
+ align:start position:0%
+lella um located in what is now
+ 
+
+ align:start position:0%
+lella um located in what is now
+Ethiopia um Christianity was first
+
+ align:start position:0%
+Ethiopia um Christianity was first
+ 
+
+ align:start position:0%
+Ethiopia um Christianity was first
+established in Nubia in the 4th Century
+
+ align:start position:0%
+established in Nubia in the 4th Century
+ 
+
+ align:start position:0%
+established in Nubia in the 4th Century
+um and it had a powerful religious
+
+ align:start position:0%
+um and it had a powerful religious
+ 
+
+ align:start position:0%
+um and it had a powerful religious
+presence you know um of course Way
+
+ align:start position:0%
+presence you know um of course Way
+ 
+
+ align:start position:0%
+presence you know um of course Way
+Beyond uh Colonial um uh Colonial
+
+ align:start position:0%
+Beyond uh Colonial um uh Colonial
+ 
+
+ align:start position:0%
+Beyond uh Colonial um uh Colonial
+influence and
+
+ align:start position:0%
+influence and
+ 
+
+ align:start position:0%
+influence and
+propitiation um under the zague Dynasty
+
+ align:start position:0%
+propitiation um under the zague Dynasty
+ 
+
+ align:start position:0%
+propitiation um under the zague Dynasty
+in the 12th century Central Authority in
+
+ align:start position:0%
+in the 12th century Central Authority in
+ 
+
+ align:start position:0%
+in the 12th century Central Authority in
+the north was established and the
+
+ align:start position:0%
+the north was established and the
+ 
+
+ align:start position:0%
+the north was established and the
+capital shift shifted from axum to
+
+ align:start position:0%
+capital shift shifted from axum to
+ 
+
+ align:start position:0%
+capital shift shifted from axum to
+libella so axum is right here to libella
+
+ align:start position:0%
+libella so axum is right here to libella
+ 
+
+ align:start position:0%
+libella so axum is right here to libella
+just south of it um in the losta
+
+ align:start position:0%
+just south of it um in the losta
+ 
+
+ align:start position:0%
+just south of it um in the losta
+mountain range so here the the
+
+ align:start position:0%
+mountain range so here the the
+ 
+
+ align:start position:0%
+mountain range so here the the
+maintenance of a religious economy was
+
+ align:start position:0%
+maintenance of a religious economy was
+ 
+
+ align:start position:0%
+maintenance of a religious economy was
+vital to the actual economy and it comp
+
+ align:start position:0%
+vital to the actual economy and it comp
+ 
+
+ align:start position:0%
+vital to the actual economy and it comp
+composed of the the king um priests and
+
+ align:start position:0%
+composed of the the king um priests and
+ 
+
+ align:start position:0%
+composed of the the king um priests and
+Farmers um now this image right here
+
+ align:start position:0%
+Farmers um now this image right here
+ 
+
+ align:start position:0%
+Farmers um now this image right here
+taking from Professor jar zek's article
+
+ align:start position:0%
+taking from Professor jar zek's article
+ 
+
+ align:start position:0%
+taking from Professor jar zek's article
+is actually of um the Church of uh
+
+ align:start position:0%
+is actually of um the Church of uh
+ 
+
+ align:start position:0%
+is actually of um the Church of uh
+yamahana Christos not of lliella but um
+
+ align:start position:0%
+yamahana Christos not of lliella but um
+ 
+
+ align:start position:0%
+yamahana Christos not of lliella but um
+I included it for the sake of um
+
+ align:start position:0%
+I included it for the sake of um
+ 
+
+ align:start position:0%
+I included it for the sake of um
+conveying this idea that um both
+
+ align:start position:0%
+conveying this idea that um both
+ 
+
+ align:start position:0%
+conveying this idea that um both
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+um uh used this very intricate system of
+
+ align:start position:0%
+um uh used this very intricate system of
+ 
+
+ align:start position:0%
+um uh used this very intricate system of
+uh hydroengineering
+
+ align:start position:0%
+uh hydroengineering
+ 
+
+ align:start position:0%
+uh hydroengineering
+collecting water um from um
+
+ align:start position:0%
+collecting water um from um
+ 
+
+ align:start position:0%
+collecting water um from um
+um from the base of the CH of the church
+
+ align:start position:0%
+um from the base of the CH of the church
+ 
+
+ align:start position:0%
+um from the base of the CH of the church
+from this uh Basin structure um and also
+
+ align:start position:0%
+from this uh Basin structure um and also
+ 
+
+ align:start position:0%
+from this uh Basin structure um and also
+you know um it should be noted that king
+
+ align:start position:0%
+you know um it should be noted that king
+ 
+
+ align:start position:0%
+you know um it should be noted that king
+libella um controlled the water supply
+
+ align:start position:0%
+libella um controlled the water supply
+ 
+
+ align:start position:0%
+libella um controlled the water supply
+and marketed marketed it as such as holy
+
+ align:start position:0%
+and marketed marketed it as such as holy
+ 
+
+ align:start position:0%
+and marketed marketed it as such as holy
+water um to entice pilgrims which in
+
+ align:start position:0%
+water um to entice pilgrims which in
+ 
+
+ align:start position:0%
+water um to entice pilgrims which in
+turn help help the economy um the water
+
+ align:start position:0%
+turn help help the economy um the water
+ 
+
+ align:start position:0%
+turn help help the economy um the water
+basin at the base of uh of this church
+
+ align:start position:0%
+basin at the base of uh of this church
+ 
+
+ align:start position:0%
+basin at the base of uh of this church
+of St George
+
+ align:start position:0%
+of St George
+ 
+
+ align:start position:0%
+of St George
+um leads to its own spring and the man
+
+ align:start position:0%
+um leads to its own spring and the man
+ 
+
+ align:start position:0%
+um leads to its own spring and the man
+who is um supposedly built um this
+
+ align:start position:0%
+who is um supposedly built um this
+ 
+
+ align:start position:0%
+who is um supposedly built um this
+complex system hydroengineering
+
+ align:start position:0%
+complex system hydroengineering
+ 
+
+ align:start position:0%
+complex system hydroengineering
+system um is named ABA libanos um it's
+
+ align:start position:0%
+system um is named ABA libanos um it's
+ 
+
+ align:start position:0%
+system um is named ABA libanos um it's
+contested whether he was from Lebanon or
+
+ align:start position:0%
+contested whether he was from Lebanon or
+ 
+
+ align:start position:0%
+contested whether he was from Lebanon or
+not um but he um was responsible for
+
+ align:start position:0%
+not um but he um was responsible for
+ 
+
+ align:start position:0%
+not um but he um was responsible for
+this um uh building of artisian Wells um
+
+ align:start position:0%
+this um uh building of artisian Wells um
+ 
+
+ align:start position:0%
+this um uh building of artisian Wells um
+to distribute water
+
+ align:start position:0%
+to distribute water
+ 
+
+ align:start position:0%
+to distribute water
+okay so next we're going to move to uh
+
+ align:start position:0%
+okay so next we're going to move to uh
+ 
+
+ align:start position:0%
+okay so next we're going to move to uh
+husi Kuba in Tanzania um current modern
+
+ align:start position:0%
+husi Kuba in Tanzania um current modern
+ 
+
+ align:start position:0%
+husi Kuba in Tanzania um current modern
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+Tanzania um and we need to situate
+
+ align:start position:0%
+Tanzania um and we need to situate
+ 
+
+ align:start position:0%
+Tanzania um and we need to situate
+ourselves historically a bit um the uh
+
+ align:start position:0%
+ourselves historically a bit um the uh
+ 
+
+ align:start position:0%
+ourselves historically a bit um the uh
+the language um Swahili um is a really a
+
+ align:start position:0%
+the language um Swahili um is a really a
+ 
+
+ align:start position:0%
+the language um Swahili um is a really a
+creolized language you know on the on
+
+ align:start position:0%
+creolized language you know on the on
+ 
+
+ align:start position:0%
+creolized language you know on the on
+the swah on the east African Coast um
+
+ align:start position:0%
+the swah on the east African Coast um
+ 
+
+ align:start position:0%
+the swah on the east African Coast um
+but it is bontu in its structure
+
+ align:start position:0%
+but it is bontu in its structure
+ 
+
+ align:start position:0%
+but it is bontu in its structure
+and if you remember from a map I showed
+
+ align:start position:0%
+and if you remember from a map I showed
+ 
+
+ align:start position:0%
+and if you remember from a map I showed
+earlier maybe you don't but the bondu
+
+ align:start position:0%
+earlier maybe you don't but the bondu
+ 
+
+ align:start position:0%
+earlier maybe you don't but the bondu
+bontu peoples really spread um East and
+
+ align:start position:0%
+bontu peoples really spread um East and
+ 
+
+ align:start position:0%
+bontu peoples really spread um East and
+onto the West so I mean it just shows
+
+ align:start position:0%
+onto the West so I mean it just shows
+ 
+
+ align:start position:0%
+onto the West so I mean it just shows
+that the because Swahili as a language
+
+ align:start position:0%
+that the because Swahili as a language
+ 
+
+ align:start position:0%
+that the because Swahili as a language
+is um mainly has bond to gr grammar and
+
+ align:start position:0%
+is um mainly has bond to gr grammar and
+ 
+
+ align:start position:0%
+is um mainly has bond to gr grammar and
+structure um that you know the even
+
+ align:start position:0%
+structure um that you know the even
+ 
+
+ align:start position:0%
+structure um that you know the even
+though there was you know Arab influence
+
+ align:start position:0%
+though there was you know Arab influence
+ 
+
+ align:start position:0%
+though there was you know Arab influence
+Arabic words Hindi words Portuguese
+
+ align:start position:0%
+Arabic words Hindi words Portuguese
+ 
+
+ align:start position:0%
+Arabic words Hindi words Portuguese
+words imported into the language um its
+
+ align:start position:0%
+words imported into the language um its
+ 
+
+ align:start position:0%
+words imported into the language um its
+structure at its core was uh was uh from
+
+ align:start position:0%
+structure at its core was uh was uh from
+ 
+
+ align:start position:0%
+structure at its core was uh was uh from
+another region of Africa altogether so
+
+ align:start position:0%
+another region of Africa altogether so
+ 
+
+ align:start position:0%
+another region of Africa altogether so
+um what was the impetus for um this C
+
+ align:start position:0%
+um what was the impetus for um this C
+ 
+
+ align:start position:0%
+um what was the impetus for um this C
+Coastal trade um sorry well um the
+
+ align:start position:0%
+Coastal trade um sorry well um the
+ 
+
+ align:start position:0%
+Coastal trade um sorry well um the
+Mongol invasions of the 13th century had
+
+ align:start position:0%
+Mongol invasions of the 13th century had
+ 
+
+ align:start position:0%
+Mongol invasions of the 13th century had
+a Hu had huge repercussions on world
+
+ align:start position:0%
+a Hu had huge repercussions on world
+ 
+
+ align:start position:0%
+a Hu had huge repercussions on world
+history and even when gask Khan died in
+
+ align:start position:0%
+history and even when gask Khan died in
+ 
+
+ align:start position:0%
+history and even when gask Khan died in
+1227 his Empire Empire was still growing
+
+ align:start position:0%
+1227 his Empire Empire was still growing
+ 
+
+ align:start position:0%
+1227 his Empire Empire was still growing
+um masses of people in Iran and Central
+
+ align:start position:0%
+um masses of people in Iran and Central
+ 
+
+ align:start position:0%
+um masses of people in Iran and Central
+Asia were wiped out and in
+
+ align:start position:0%
+Asia were wiped out and in
+ 
+
+ align:start position:0%
+Asia were wiped out and in
+1258 uh Baghdad was entirely sacked
+
+ align:start position:0%
+1258 uh Baghdad was entirely sacked
+ 
+
+ align:start position:0%
+1258 uh Baghdad was entirely sacked
+which led to decline of the Abid Empire
+
+ align:start position:0%
+which led to decline of the Abid Empire
+ 
+
+ align:start position:0%
+which led to decline of the Abid Empire
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+cipit um and you know everywhere the
+
+ align:start position:0%
+cipit um and you know everywhere the
+ 
+
+ align:start position:0%
+cipit um and you know everywhere the
+Mongols went they plundered their
+
+ align:start position:0%
+Mongols went they plundered their
+ 
+
+ align:start position:0%
+Mongols went they plundered their
+subjects turned uh them into surfs and
+
+ align:start position:0%
+subjects turned uh them into surfs and
+ 
+
+ align:start position:0%
+subjects turned uh them into surfs and
+you know taxed them
+
+ align:start position:0%
+you know taxed them
+ 
+
+ align:start position:0%
+you know taxed them
+ruinously but uh that said they had
+
+ align:start position:0%
+ruinously but uh that said they had
+ 
+
+ align:start position:0%
+ruinously but uh that said they had
+complete control over this whole vast
+
+ align:start position:0%
+complete control over this whole vast
+ 
+
+ align:start position:0%
+complete control over this whole vast
+expanse of land um the different
+
+ align:start position:0%
+expanse of land um the different
+ 
+
+ align:start position:0%
+expanse of land um the different
+shadings indicate um uh genas Khan's um
+
+ align:start position:0%
+shadings indicate um uh genas Khan's um
+ 
+
+ align:start position:0%
+shadings indicate um uh genas Khan's um
+successors his four sons who uh div
+
+ align:start position:0%
+successors his four sons who uh div
+ 
+
+ align:start position:0%
+successors his four sons who uh div
+mainly you know divided up this this
+
+ align:start position:0%
+mainly you know divided up this this
+ 
+
+ align:start position:0%
+mainly you know divided up this this
+region for administrative purposes and
+
+ align:start position:0%
+region for administrative purposes and
+ 
+
+ align:start position:0%
+region for administrative purposes and
+also purposes of
+
+ align:start position:0%
+also purposes of
+ 
+
+ align:start position:0%
+also purposes of
+rivalry um uh but the the but the
+
+ align:start position:0%
+rivalry um uh but the the but the
+ 
+
+ align:start position:0%
+rivalry um uh but the the but the
+Mongols actually you know uh contribut
+
+ align:start position:0%
+Mongols actually you know uh contribut
+ 
+
+ align:start position:0%
+Mongols actually you know uh contribut
+greatly to the the established trading
+
+ align:start position:0%
+greatly to the the established trading
+ 
+
+ align:start position:0%
+greatly to the the established trading
+networks and through their jam system
+
+ align:start position:0%
+networks and through their jam system
+ 
+
+ align:start position:0%
+networks and through their jam system
+which was a postal system uh which is
+
+ align:start position:0%
+which was a postal system uh which is
+ 
+
+ align:start position:0%
+which was a postal system uh which is
+pretty much you know I mean for its day
+
+ align:start position:0%
+pretty much you know I mean for its day
+ 
+
+ align:start position:0%
+pretty much you know I mean for its day
+it was equivalent to our modern-day
+
+ align:start position:0%
+it was equivalent to our modern-day
+ 
+
+ align:start position:0%
+it was equivalent to our modern-day
+FedEx I mean it was pretty remarkable um
+
+ align:start position:0%
+FedEx I mean it was pretty remarkable um
+ 
+
+ align:start position:0%
+FedEx I mean it was pretty remarkable um
+with the speed that they were able to
+
+ align:start position:0%
+with the speed that they were able to
+ 
+
+ align:start position:0%
+with the speed that they were able to
+get things to and from
+
+ align:start position:0%
+get things to and from
+ 
+
+ align:start position:0%
+get things to and from
+places um so basically I excuse this map
+
+ align:start position:0%
+places um so basically I excuse this map
+ 
+
+ align:start position:0%
+places um so basically I excuse this map
+I know it's a little busy but um uh
+
+ align:start position:0%
+I know it's a little busy but um uh
+ 
+
+ align:start position:0%
+I know it's a little busy but um uh
+basically because of the uh the effect
+
+ align:start position:0%
+basically because of the uh the effect
+ 
+
+ align:start position:0%
+basically because of the uh the effect
+of Mongol conquest everything shifted
+
+ align:start position:0%
+of Mongol conquest everything shifted
+ 
+
+ align:start position:0%
+of Mongol conquest everything shifted
+downward um not everything but you know
+
+ align:start position:0%
+downward um not everything but you know
+ 
+
+ align:start position:0%
+downward um not everything but you know
+there was this shift downward and shibin
+
+ align:start position:0%
+there was this shift downward and shibin
+ 
+
+ align:start position:0%
+there was this shift downward and shibin
+will talk about that somewhat in his
+
+ align:start position:0%
+will talk about that somewhat in his
+ 
+
+ align:start position:0%
+will talk about that somewhat in his
+talk um focusing in on the area of the
+
+ align:start position:0%
+talk um focusing in on the area of the
+ 
+
+ align:start position:0%
+talk um focusing in on the area of the
+Indian Ocean um but to return to our um
+
+ align:start position:0%
+Indian Ocean um but to return to our um
+ 
+
+ align:start position:0%
+Indian Ocean um but to return to our um
+Point um and also Monsoon Cycles
+
+ align:start position:0%
+Point um and also Monsoon Cycles
+ 
+
+ align:start position:0%
+Point um and also Monsoon Cycles
+um uh also regulated Maritime trade too
+
+ align:start position:0%
+um uh also regulated Maritime trade too
+ 
+
+ align:start position:0%
+um uh also regulated Maritime trade too
+had to be um in tune with the
+
+ align:start position:0%
+had to be um in tune with the
+ 
+
+ align:start position:0%
+had to be um in tune with the
+weather
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay this isn't these are just more
+
+ align:start position:0%
+um okay this isn't these are just more
+ 
+
+ align:start position:0%
+um okay this isn't these are just more
+trade
+
+ align:start position:0%
+trade
+ 
+
+ align:start position:0%
+trade
+routes all right so now we turn to hus
+
+ align:start position:0%
+routes all right so now we turn to hus
+ 
+
+ align:start position:0%
+routes all right so now we turn to hus
+Kua which was a palace um it literally
+
+ align:start position:0%
+Kua which was a palace um it literally
+ 
+
+ align:start position:0%
+Kua which was a palace um it literally
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+um uh it literally uh means large Fort
+
+ align:start position:0%
+um uh it literally uh means large Fort
+ 
+
+ align:start position:0%
+um uh it literally uh means large Fort
+um and it was um built at the entrance
+
+ align:start position:0%
+um and it was um built at the entrance
+ 
+
+ align:start position:0%
+um and it was um built at the entrance
+to the harbor of kilwa um it was
+
+ align:start position:0%
+to the harbor of kilwa um it was
+ 
+
+ align:start position:0%
+to the harbor of kilwa um it was
+constructed on a high Sandstone Headland
+
+ align:start position:0%
+constructed on a high Sandstone Headland
+ 
+
+ align:start position:0%
+constructed on a high Sandstone Headland
+and it was actually built out entirely
+
+ align:start position:0%
+and it was actually built out entirely
+ 
+
+ align:start position:0%
+and it was actually built out entirely
+out of coral which is amazing if you
+
+ align:start position:0%
+out of coral which is amazing if you
+ 
+
+ align:start position:0%
+out of coral which is amazing if you
+consider I mean that all of this Coral
+
+ align:start position:0%
+consider I mean that all of this Coral
+ 
+
+ align:start position:0%
+consider I mean that all of this Coral
+from the The Reef just outside of the
+
+ align:start position:0%
+from the The Reef just outside of the
+ 
+
+ align:start position:0%
+from the The Reef just outside of the
+off the
+
+ align:start position:0%
+off the
+ 
+
+ align:start position:0%
+off the
+mainland um built this you know entirely
+
+ align:start position:0%
+mainland um built this you know entirely
+ 
+
+ align:start position:0%
+mainland um built this you know entirely
+intricate structure um here is a digital
+
+ align:start position:0%
+intricate structure um here is a digital
+ 
+
+ align:start position:0%
+intricate structure um here is a digital
+reconstruction of what is now in you
+
+ align:start position:0%
+reconstruction of what is now in you
+ 
+
+ align:start position:0%
+reconstruction of what is now in you
+know unfortunately in Ruins but um just
+
+ align:start position:0%
+know unfortunately in Ruins but um just
+ 
+
+ align:start position:0%
+know unfortunately in Ruins but um just
+to give you a sense of what the building
+
+ align:start position:0%
+to give you a sense of what the building
+ 
+
+ align:start position:0%
+to give you a sense of what the building
+composed here is a reconstructed uh
+
+ align:start position:0%
+composed here is a reconstructed uh
+ 
+
+ align:start position:0%
+composed here is a reconstructed uh
+floor plan we have a stairwell which is
+
+ align:start position:0%
+floor plan we have a stairwell which is
+ 
+
+ align:start position:0%
+floor plan we have a stairwell which is
+located right here that um basically
+
+ align:start position:0%
+located right here that um basically
+ 
+
+ align:start position:0%
+located right here that um basically
+also I think is right here um or
+
+ align:start position:0%
+also I think is right here um or
+ 
+
+ align:start position:0%
+also I think is right here um or
+actually wait no right here excuse me
+
+ align:start position:0%
+actually wait no right here excuse me
+ 
+
+ align:start position:0%
+actually wait no right here excuse me
+stairwell um that would lead into what
+
+ align:start position:0%
+stairwell um that would lead into what
+ 
+
+ align:start position:0%
+stairwell um that would lead into what
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh what were storage rooms all around
+
+ align:start position:0%
+uh what were storage rooms all around
+ 
+
+ align:start position:0%
+uh what were storage rooms all around
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+quadrangle um and uh as goods were being
+
+ align:start position:0%
+quadrangle um and uh as goods were being
+ 
+
+ align:start position:0%
+quadrangle um and uh as goods were being
+um received they were recorded and taxed
+
+ align:start position:0%
+um received they were recorded and taxed
+ 
+
+ align:start position:0%
+um received they were recorded and taxed
+and this this fort um provided great
+
+ align:start position:0%
+and this this fort um provided great
+ 
+
+ align:start position:0%
+and this this fort um provided great
+surveillance uh over what was incoming
+
+ align:start position:0%
+surveillance uh over what was incoming
+ 
+
+ align:start position:0%
+surveillance uh over what was incoming
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+outgoing um
+
+ align:start position:0%
+outgoing um
+ 
+
+ align:start position:0%
+outgoing um
+and uh also you have this this sector is
+
+ align:start position:0%
+and uh also you have this this sector is
+ 
+
+ align:start position:0%
+and uh also you have this this sector is
+sort of the Sultan's um private
+
+ align:start position:0%
+sort of the Sultan's um private
+ 
+
+ align:start position:0%
+sort of the Sultan's um private
+headquarters you have an audience Hall
+
+ align:start position:0%
+headquarters you have an audience Hall
+ 
+
+ align:start position:0%
+headquarters you have an audience Hall
+which is thought to have been the place
+
+ align:start position:0%
+which is thought to have been the place
+ 
+
+ align:start position:0%
+which is thought to have been the place
+where the sultan received his his Min
+
+ align:start position:0%
+where the sultan received his his Min
+ 
+
+ align:start position:0%
+where the sultan received his his Min
+his uh his uh corders um and you also
+
+ align:start position:0%
+his uh his uh corders um and you also
+ 
+
+ align:start position:0%
+his uh his uh corders um and you also
+have a swimming pool that's not a dome
+
+ align:start position:0%
+have a swimming pool that's not a dome
+ 
+
+ align:start position:0%
+have a swimming pool that's not a dome
+it's a swimming
+
+ align:start position:0%
+it's a swimming
+ 
+
+ align:start position:0%
+it's a swimming
+pool um interestingly enough and these
+
+ align:start position:0%
+pool um interestingly enough and these
+ 
+
+ align:start position:0%
+pool um interestingly enough and these
+are all like private rooms for wives and
+
+ align:start position:0%
+are all like private rooms for wives and
+ 
+
+ align:start position:0%
+are all like private rooms for wives and
+children and so on
+
+ align:start position:0%
+children and so on
+ 
+
+ align:start position:0%
+children and so on
+um and uh actually um the uh Dewan which
+
+ align:start position:0%
+um and uh actually um the uh Dewan which
+ 
+
+ align:start position:0%
+um and uh actually um the uh Dewan which
+was featured yeah the Dewan actually was
+
+ align:start position:0%
+was featured yeah the Dewan actually was
+ 
+
+ align:start position:0%
+was featured yeah the Dewan actually was
+right here where he received his
+
+ align:start position:0%
+right here where he received his
+ 
+
+ align:start position:0%
+right here where he received his
+courtiers um a Chinese Yuan Dynasty
+
+ align:start position:0%
+courtiers um a Chinese Yuan Dynasty
+ 
+
+ align:start position:0%
+courtiers um a Chinese Yuan Dynasty
+flask was found on the floor of the
+
+ align:start position:0%
+flask was found on the floor of the
+ 
+
+ align:start position:0%
+flask was found on the floor of the
+private head private quarters dating to
+
+ align:start position:0%
+private head private quarters dating to
+ 
+
+ align:start position:0%
+private head private quarters dating to
+about 13th 1300 so you know there is
+
+ align:start position:0%
+about 13th 1300 so you know there is
+ 
+
+ align:start position:0%
+about 13th 1300 so you know there is
+archaeological evidence that states that
+
+ align:start position:0%
+archaeological evidence that states that
+ 
+
+ align:start position:0%
+archaeological evidence that states that
+um this
+
+ align:start position:0%
+um this
+ 
+
+ align:start position:0%
+um this
+was a site of international
+
+ align:start position:0%
+was a site of international
+ 
+
+ align:start position:0%
+was a site of international
+trade um so now we want to move to our
+
+ align:start position:0%
+trade um so now we want to move to our
+ 
+
+ align:start position:0%
+trade um so now we want to move to our
+last site which is Great
+
+ align:start position:0%
+last site which is Great
+ 
+
+ align:start position:0%
+last site which is Great
+Zimbabwe um and let's uh let's take a a
+
+ align:start position:0%
+Zimbabwe um and let's uh let's take a a
+ 
+
+ align:start position:0%
+Zimbabwe um and let's uh let's take a a
+look at it all right but before we do
+
+ align:start position:0%
+look at it all right but before we do
+ 
+
+ align:start position:0%
+look at it all right but before we do
+that um I just want to reinforce again
+
+ align:start position:0%
+that um I just want to reinforce again
+ 
+
+ align:start position:0%
+that um I just want to reinforce again
+um that iron working uh and iron
+
+ align:start position:0%
+um that iron working uh and iron
+ 
+
+ align:start position:0%
+um that iron working uh and iron
+smelting really spread with um the bonto
+
+ align:start position:0%
+smelting really spread with um the bonto
+ 
+
+ align:start position:0%
+smelting really spread with um the bonto
+spal and which led to um you know where
+
+ align:start position:0%
+spal and which led to um you know where
+ 
+
+ align:start position:0%
+spal and which led to um you know where
+we we're concentrating on Great Zimbabwe
+
+ align:start position:0%
+we we're concentrating on Great Zimbabwe
+ 
+
+ align:start position:0%
+we we're concentrating on Great Zimbabwe
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so okay so what is um Great Zimbabwe
+
+ align:start position:0%
+so okay so what is um Great Zimbabwe
+ 
+
+ align:start position:0%
+so okay so what is um Great Zimbabwe
+okay there's a picture of an Oro bull um
+
+ align:start position:0%
+okay there's a picture of an Oro bull um
+ 
+
+ align:start position:0%
+okay there's a picture of an Oro bull um
+I'll get to that in a little bit um the
+
+ align:start position:0%
+I'll get to that in a little bit um the
+ 
+
+ align:start position:0%
+I'll get to that in a little bit um the
+monomotapa Empire um built an elliptical
+
+ align:start position:0%
+monomotapa Empire um built an elliptical
+ 
+
+ align:start position:0%
+monomotapa Empire um built an elliptical
+Granite Stone uh stone wall with a tall
+
+ align:start position:0%
+Granite Stone uh stone wall with a tall
+ 
+
+ align:start position:0%
+Granite Stone uh stone wall with a tall
+mon Monument uh in the valley which is
+
+ align:start position:0%
+mon Monument uh in the valley which is
+ 
+
+ align:start position:0%
+mon Monument uh in the valley which is
+sort of right here this conical
+
+ align:start position:0%
+sort of right here this conical
+ 
+
+ align:start position:0%
+sort of right here this conical
+structure which is not its purpose is
+
+ align:start position:0%
+structure which is not its purpose is
+ 
+
+ align:start position:0%
+structure which is not its purpose is
+not really known to Scholars it could be
+
+ align:start position:0%
+not really known to Scholars it could be
+ 
+
+ align:start position:0%
+not really known to Scholars it could be
+a Greenery it could have been a treasury
+
+ align:start position:0%
+a Greenery it could have been a treasury
+ 
+
+ align:start position:0%
+a Greenery it could have been a treasury
+it could have been a whole slew of
+
+ align:start position:0%
+it could have been a whole slew of
+ 
+
+ align:start position:0%
+it could have been a whole slew of
+things but nobody's really quite certain
+
+ align:start position:0%
+things but nobody's really quite certain
+ 
+
+ align:start position:0%
+things but nobody's really quite certain
+as to what it was um these walls were
+
+ align:start position:0%
+as to what it was um these walls were
+ 
+
+ align:start position:0%
+as to what it was um these walls were
+key elements to the governments that
+
+ align:start position:0%
+key elements to the governments that
+ 
+
+ align:start position:0%
+key elements to the governments that
+formed in the region between the 11th
+
+ align:start position:0%
+formed in the region between the 11th
+ 
+
+ align:start position:0%
+formed in the region between the 11th
+and 15th centuries um its walls believe
+
+ align:start position:0%
+and 15th centuries um its walls believe
+ 
+
+ align:start position:0%
+and 15th centuries um its walls believe
+it or not are uh 10 meters high and an
+
+ align:start position:0%
+it or not are uh 10 meters high and an
+ 
+
+ align:start position:0%
+it or not are uh 10 meters high and an
+average of 3 meters thick
+
+ align:start position:0%
+average of 3 meters thick
+ 
+
+ align:start position:0%
+average of 3 meters thick
+um and you know I mean this calls into
+
+ align:start position:0%
+um and you know I mean this calls into
+ 
+
+ align:start position:0%
+um and you know I mean this calls into
+question you know to what extent was
+
+ align:start position:0%
+question you know to what extent was
+ 
+
+ align:start position:0%
+question you know to what extent was
+this intended forward defense um some
+
+ align:start position:0%
+this intended forward defense um some
+ 
+
+ align:start position:0%
+this intended forward defense um some
+Scholars have postulated that um that
+
+ align:start position:0%
+Scholars have postulated that um that
+ 
+
+ align:start position:0%
+Scholars have postulated that um that
+because uh the domestication of cattle
+
+ align:start position:0%
+because uh the domestication of cattle
+ 
+
+ align:start position:0%
+because uh the domestication of cattle
+spread Southward you know they needed
+
+ align:start position:0%
+spread Southward you know they needed
+ 
+
+ align:start position:0%
+spread Southward you know they needed
+structures to enclose the cattle um but
+
+ align:start position:0%
+structures to enclose the cattle um but
+ 
+
+ align:start position:0%
+structures to enclose the cattle um but
+having walls 3 m thick I mean rarely I
+
+ align:start position:0%
+having walls 3 m thick I mean rarely I
+ 
+
+ align:start position:0%
+having walls 3 m thick I mean rarely I
+mean it really doesn't explain much in
+
+ align:start position:0%
+mean it really doesn't explain much in
+ 
+
+ align:start position:0%
+mean it really doesn't explain much in
+terms of keeping cat up they not going
+
+ align:start position:0%
+terms of keeping cat up they not going
+ 
+
+ align:start position:0%
+terms of keeping cat up they not going
+to bust through you know three meters of
+
+ align:start position:0%
+to bust through you know three meters of
+ 
+
+ align:start position:0%
+to bust through you know three meters of
+wall um but
+
+ align:start position:0%
+wall um but
+ 
+
+ align:start position:0%
+wall um but
+anyways um you see you know really um
+
+ align:start position:0%
+anyways um you see you know really um
+ 
+
+ align:start position:0%
+anyways um you see you know really um
+hold on uh you see really
+
+ align:start position:0%
+hold on uh you see really
+ 
+
+ align:start position:0%
+hold on uh you see really
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh a lot of Chinese porcelain that's
+
+ align:start position:0%
+um uh a lot of Chinese porcelain that's
+ 
+
+ align:start position:0%
+um uh a lot of Chinese porcelain that's
+been excavated um like in husi Kua um
+
+ align:start position:0%
+been excavated um like in husi Kua um
+ 
+
+ align:start position:0%
+been excavated um like in husi Kua um
+and the luxury these luxuries of course
+
+ align:start position:0%
+and the luxury these luxuries of course
+ 
+
+ align:start position:0%
+and the luxury these luxuries of course
+you know point to the existence of a
+
+ align:start position:0%
+you know point to the existence of a
+ 
+
+ align:start position:0%
+you know point to the existence of a
+social Elite um which you know points to
+
+ align:start position:0%
+social Elite um which you know points to
+ 
+
+ align:start position:0%
+social Elite um which you know points to
+these really complex um s
+
+ align:start position:0%
+these really complex um s
+ 
+
+ align:start position:0%
+these really complex um s
+Society um but eventually the site was
+
+ align:start position:0%
+Society um but eventually the site was
+ 
+
+ align:start position:0%
+Society um but eventually the site was
+abandoned and um Scholars you know think
+
+ align:start position:0%
+abandoned and um Scholars you know think
+ 
+
+ align:start position:0%
+abandoned and um Scholars you know think
+that this is probably due to either
+
+ align:start position:0%
+that this is probably due to either
+ 
+
+ align:start position:0%
+that this is probably due to either
+drought or
+
+ align:start position:0%
+drought or
+ 
+
+ align:start position:0%
+drought or
+disease um but unfort Ely um when the
+
+ align:start position:0%
+disease um but unfort Ely um when the
+ 
+
+ align:start position:0%
+disease um but unfort Ely um when the
+site was uh excavated uh or colonized
+
+ align:start position:0%
+site was uh excavated uh or colonized
+ 
+
+ align:start position:0%
+site was uh excavated uh or colonized
+rather by cesil roads what you know this
+
+ align:start position:0%
+rather by cesil roads what you know this
+ 
+
+ align:start position:0%
+rather by cesil roads what you know this
+area was once called rodesia um much of
+
+ align:start position:0%
+area was once called rodesia um much of
+ 
+
+ align:start position:0%
+area was once called rodesia um much of
+the artifacts are pillaged so that's
+
+ align:start position:0%
+the artifacts are pillaged so that's
+ 
+
+ align:start position:0%
+the artifacts are pillaged so that's
+that's what you get for colonization but
+
+ align:start position:0%
+that's what you get for colonization but
+ 
+
+ align:start position:0%
+that's what you get for colonization but
+um I hope today I've demonstrated that
+
+ align:start position:0%
+um I hope today I've demonstrated that
+ 
+
+ align:start position:0%
+um I hope today I've demonstrated that
+you know architecture African
+
+ align:start position:0%
+you know architecture African
+ 
+
+ align:start position:0%
+you know architecture African
+architecture is neither uniform nor
+
+ align:start position:0%
+architecture is neither uniform nor
+ 
+
+ align:start position:0%
+architecture is neither uniform nor
+simplistic nor dying um as the BBC might
+
+ align:start position:0%
+simplistic nor dying um as the BBC might
+ 
+
+ align:start position:0%
+simplistic nor dying um as the BBC might
+have us believe um rather it's diverse
+
+ align:start position:0%
+have us believe um rather it's diverse
+ 
+
+ align:start position:0%
+have us believe um rather it's diverse
+and Rich and its societies reflect
+
+ align:start position:0%
+and Rich and its societies reflect
+ 
+
+ align:start position:0%
+and Rich and its societies reflect
+neither the chaos nor
+
+ align:start position:0%
+neither the chaos nor
+ 
+
+ align:start position:0%
+neither the chaos nor
+disintegration um that uh
+
+ align:start position:0%
+disintegration um that uh
+ 
+
+ align:start position:0%
+disintegration um that uh
+misconceptions um perpetuate and to
+
+ align:start position:0%
+misconceptions um perpetuate and to
+ 
+
+ align:start position:0%
+misconceptions um perpetuate and to
+appropriate oan weor term that I
+
+ align:start position:0%
+appropriate oan weor term that I
+ 
+
+ align:start position:0%
+appropriate oan weor term that I
+mentioned at the beginning um it's
+
+ align:start position:0%
+mentioned at the beginning um it's
+ 
+
+ align:start position:0%
+mentioned at the beginning um it's
+through this lens of uh afro optimism
+
+ align:start position:0%
+through this lens of uh afro optimism
+ 
+
+ align:start position:0%
+through this lens of uh afro optimism
+rather uh that we might look at Africa
+
+ align:start position:0%
+rather uh that we might look at Africa
+ 
+
+ align:start position:0%
+rather uh that we might look at Africa
+and and its architecture and Global
+
+ align:start position:0%
+and and its architecture and Global
+ 
+
+ align:start position:0%
+and and its architecture and Global
+interactions um with a more positive
+
+ align:start position:0%
+interactions um with a more positive
+ 
+
+ align:start position:0%
+interactions um with a more positive
+outlook thank you
\ No newline at end of file
diff --git a/IAf2m_sLWq4.txt b/IAf2m_sLWq4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52459cacf837b48d95fcd13ef52a266d94f9f1a2
--- /dev/null
+++ b/IAf2m_sLWq4.txt
@@ -0,0 +1,8283 @@
+align:start position:0%
+ 
+okay let's talk a little bit about
+
+ align:start position:0%
+okay let's talk a little bit about
+ 
+
+ align:start position:0%
+okay let's talk a little bit about
+plasma
+
+ align:start position:0%
+plasma
+ 
+
+ align:start position:0%
+plasma
+Diagnostics so this very word
+
+ align:start position:0%
+Diagnostics so this very word
+ 
+
+ align:start position:0%
+Diagnostics so this very word
+diagnostic is pretty interesting um
+
+ align:start position:0%
+diagnostic is pretty interesting um
+ 
+
+ align:start position:0%
+diagnostic is pretty interesting um
+Gnostic here is coming from knowledge
+
+ align:start position:0%
+Gnostic here is coming from knowledge
+ 
+
+ align:start position:0%
+Gnostic here is coming from knowledge
+and D as a word sort of meaning through
+
+ align:start position:0%
+and D as a word sort of meaning through
+ 
+
+ align:start position:0%
+and D as a word sort of meaning through
+so these are objects that we gain
+
+ align:start position:0%
+so these are objects that we gain
+ 
+
+ align:start position:0%
+so these are objects that we gain
+knowledge through we're trying to gain
+
+ align:start position:0%
+knowledge through we're trying to gain
+ 
+
+ align:start position:0%
+knowledge through we're trying to gain
+knowledge about our plasma right this is
+
+ align:start position:0%
+knowledge about our plasma right this is
+ 
+
+ align:start position:0%
+knowledge about our plasma right this is
+the whole purpose of this class we're
+
+ align:start position:0%
+the whole purpose of this class we're
+ 
+
+ align:start position:0%
+the whole purpose of this class we're
+trying to gain knowledge about the
+
+ align:start position:0%
+trying to gain knowledge about the
+ 
+
+ align:start position:0%
+trying to gain knowledge about the
+plasma indirectly we can't directly look
+
+ align:start position:0%
+plasma indirectly we can't directly look
+ 
+
+ align:start position:0%
+plasma indirectly we can't directly look
+at a plasma and measure its density or
+
+ align:start position:0%
+at a plasma and measure its density or
+ 
+
+ align:start position:0%
+at a plasma and measure its density or
+its temperature or its velocity or any
+
+ align:start position:0%
+its temperature or its velocity or any
+ 
+
+ align:start position:0%
+its temperature or its velocity or any
+of the other quantities we're interested
+
+ align:start position:0%
+of the other quantities we're interested
+ 
+
+ align:start position:0%
+of the other quantities we're interested
+in instead we're inferring it from some
+
+ align:start position:0%
+in instead we're inferring it from some
+ 
+
+ align:start position:0%
+in instead we're inferring it from some
+sort of physical effect the plasma has
+
+ align:start position:0%
+sort of physical effect the plasma has
+ 
+
+ align:start position:0%
+sort of physical effect the plasma has
+on something else and we're used to this
+
+ align:start position:0%
+on something else and we're used to this
+ 
+
+ align:start position:0%
+on something else and we're used to this
+kind of uh measurement with more basic
+
+ align:start position:0%
+kind of uh measurement with more basic
+ 
+
+ align:start position:0%
+kind of uh measurement with more basic
+Diagnostics if we think about something
+
+ align:start position:0%
+Diagnostics if we think about something
+ 
+
+ align:start position:0%
+Diagnostics if we think about something
+like a
+
+ align:start position:0%
+like a
+ 
+
+ align:start position:0%
+like a
+thermometer and it's filled with Mercury
+
+ align:start position:0%
+thermometer and it's filled with Mercury
+ 
+
+ align:start position:0%
+thermometer and it's filled with Mercury
+what's the physical principle that
+
+ align:start position:0%
+what's the physical principle that
+ 
+
+ align:start position:0%
+what's the physical principle that
+allows us to measure temperature using a
+
+ align:start position:0%
+allows us to measure temperature using a
+ 
+
+ align:start position:0%
+allows us to measure temperature using a
+thermometer a liquid metal
+
+ align:start position:0%
+thermometer a liquid metal
+ 
+
+ align:start position:0%
+thermometer a liquid metal
+thermometer
+
+ align:start position:0%
+thermometer
+ 
+
+ align:start position:0%
+thermometer
+yeah yeah so the thermal expansion of
+
+ align:start position:0%
+yeah yeah so the thermal expansion of
+ 
+
+ align:start position:0%
+yeah yeah so the thermal expansion of
+this metal which moves it up and down
+
+ align:start position:0%
+this metal which moves it up and down
+ 
+
+ align:start position:0%
+this metal which moves it up and down
+here and we can calibrate this and then
+
+ align:start position:0%
+here and we can calibrate this and then
+ 
+
+ align:start position:0%
+here and we can calibrate this and then
+we can measure temperature so this is an
+
+ align:start position:0%
+we can measure temperature so this is an
+ 
+
+ align:start position:0%
+we can measure temperature so this is an
+example of something that we are
+
+ align:start position:0%
+example of something that we are
+ 
+
+ align:start position:0%
+example of something that we are
+relatively familiar with like thermal
+
+ align:start position:0%
+relatively familiar with like thermal
+ 
+
+ align:start position:0%
+relatively familiar with like thermal
+expansion of metal it's something we can
+
+ align:start position:0%
+expansion of metal it's something we can
+ 
+
+ align:start position:0%
+expansion of metal it's something we can
+see with our eyes we can pick up a
+
+ align:start position:0%
+see with our eyes we can pick up a
+ 
+
+ align:start position:0%
+see with our eyes we can pick up a
+thermometer we can touch it this is
+
+ align:start position:0%
+thermometer we can touch it this is
+ 
+
+ align:start position:0%
+thermometer we can touch it this is
+rarely the case with something like a
+
+ align:start position:0%
+rarely the case with something like a
+ 
+
+ align:start position:0%
+rarely the case with something like a
+plasma right our intuition usually fails
+
+ align:start position:0%
+plasma right our intuition usually fails
+ 
+
+ align:start position:0%
+plasma right our intuition usually fails
+so we have to fall back on mathematics
+
+ align:start position:0%
+so we have to fall back on mathematics
+ 
+
+ align:start position:0%
+so we have to fall back on mathematics
+or we have to build our in intuition for
+
+ align:start position:0%
+or we have to build our in intuition for
+ 
+
+ align:start position:0%
+or we have to build our in intuition for
+plasma in the same way that we built our
+
+ align:start position:0%
+plasma in the same way that we built our
+ 
+
+ align:start position:0%
+plasma in the same way that we built our
+intuition for things like thermometers
+
+ align:start position:0%
+intuition for things like thermometers
+ 
+
+ align:start position:0%
+intuition for things like thermometers
+as we were growing
+
+ align:start position:0%
+as we were growing
+ 
+
+ align:start position:0%
+as we were growing
+up for example here we were talking
+
+ align:start position:0%
+up for example here we were talking
+ 
+
+ align:start position:0%
+up for example here we were talking
+about the expansion of metal but in a
+
+ align:start position:0%
+about the expansion of metal but in a
+ 
+
+ align:start position:0%
+about the expansion of metal but in a
+plasma we may be looking at something as
+
+ align:start position:0%
+plasma we may be looking at something as
+ 
+
+ align:start position:0%
+plasma we may be looking at something as
+obscure as the polarization of a beam of
+
+ align:start position:0%
+obscure as the polarization of a beam of
+ 
+
+ align:start position:0%
+obscure as the polarization of a beam of
+light telling us something about
+
+ align:start position:0%
+light telling us something about
+ 
+
+ align:start position:0%
+light telling us something about
+magnetic fields something that
+
+ align:start position:0%
+magnetic fields something that
+ 
+
+ align:start position:0%
+magnetic fields something that
+immediately it isn't obvious that these
+
+ align:start position:0%
+immediately it isn't obvious that these
+ 
+
+ align:start position:0%
+immediately it isn't obvious that these
+things are linked
+
+ align:start position:0%
+things are linked
+ 
+
+ align:start position:0%
+things are linked
+for we're going to be assuming very good
+
+ align:start position:0%
+for we're going to be assuming very good
+ 
+
+ align:start position:0%
+for we're going to be assuming very good
+plasma physic knowledge in this class so
+
+ align:start position:0%
+plasma physic knowledge in this class so
+ 
+
+ align:start position:0%
+plasma physic knowledge in this class so
+the prerequisite for this class is for
+
+ align:start position:0%
+the prerequisite for this class is for
+ 
+
+ align:start position:0%
+the prerequisite for this class is for
+students who taking 22611 right so
+
+ align:start position:0%
+students who taking 22611 right so
+ 
+
+ align:start position:0%
+students who taking 22611 right so
+that's a class that uses Francis Chen's
+
+ align:start position:0%
+that's a class that uses Francis Chen's
+ 
+
+ align:start position:0%
+that's a class that uses Francis Chen's
+introduction to PL phics textbook and
+
+ align:start position:0%
+introduction to PL phics textbook and
+ 
+
+ align:start position:0%
+introduction to PL phics textbook and
+we'll be drawing extensively from that
+
+ align:start position:0%
+we'll be drawing extensively from that
+ 
+
+ align:start position:0%
+we'll be drawing extensively from that
+without redoing any derivations this is
+
+ align:start position:0%
+without redoing any derivations this is
+ 
+
+ align:start position:0%
+without redoing any derivations this is
+a very hard class to take at the same
+
+ align:start position:0%
+a very hard class to take at the same
+ 
+
+ align:start position:0%
+a very hard class to take at the same
+time as 22611 I recommend you don't try
+
+ align:start position:0%
+time as 22611 I recommend you don't try
+ 
+
+ align:start position:0%
+time as 22611 I recommend you don't try
+but I know that some of you going to and
+
+ align:start position:0%
+but I know that some of you going to and
+ 
+
+ align:start position:0%
+but I know that some of you going to and
+that's fine but just as a warning it's
+
+ align:start position:0%
+that's fine but just as a warning it's
+ 
+
+ align:start position:0%
+that's fine but just as a warning it's
+going to be very very difficult if you
+
+ align:start position:0%
+going to be very very difficult if you
+ 
+
+ align:start position:0%
+going to be very very difficult if you
+uh are a little bit shaky in your plasma
+
+ align:start position:0%
+uh are a little bit shaky in your plasma
+ 
+
+ align:start position:0%
+uh are a little bit shaky in your plasma
+physics I suggest revising your
+
+ align:start position:0%
+physics I suggest revising your
+ 
+
+ align:start position:0%
+physics I suggest revising your
+electromagnetism your waves in plasmas
+
+ align:start position:0%
+electromagnetism your waves in plasmas
+ 
+
+ align:start position:0%
+electromagnetism your waves in plasmas
+and things like landal damping
+
+ align:start position:0%
+and things like landal damping
+ 
+
+ align:start position:0%
+and things like landal damping
+especially later on when we get on to
+
+ align:start position:0%
+especially later on when we get on to
+ 
+
+ align:start position:0%
+especially later on when we get on to
+con
+
+ align:start position:0%
+con
+ 
+
+ align:start position:0%
+con
+any questions on any of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so why do we bother with
+
+ align:start position:0%
+that so why do we bother with
+ 
+
+ align:start position:0%
+that so why do we bother with
+Diagnostics in the first place well
+
+ align:start position:0%
+Diagnostics in the first place well
+ 
+
+ align:start position:0%
+Diagnostics in the first place well
+there's no point making a plasma that
+
+ align:start position:0%
+there's no point making a plasma that
+ 
+
+ align:start position:0%
+there's no point making a plasma that
+you can't actually measure so we could
+
+ align:start position:0%
+you can't actually measure so we could
+ 
+
+ align:start position:0%
+you can't actually measure so we could
+have a a huge toac or a giant laser or a
+
+ align:start position:0%
+have a a huge toac or a giant laser or a
+ 
+
+ align:start position:0%
+have a a huge toac or a giant laser or a
+big pulse power machine and we could
+
+ align:start position:0%
+big pulse power machine and we could
+ 
+
+ align:start position:0%
+big pulse power machine and we could
+make the world's greatest plasma but if
+
+ align:start position:0%
+make the world's greatest plasma but if
+ 
+
+ align:start position:0%
+make the world's greatest plasma but if
+we don't know anything about it it's
+
+ align:start position:0%
+we don't know anything about it it's
+ 
+
+ align:start position:0%
+we don't know anything about it it's
+completely pointless and so plasma
+
+ align:start position:0%
+completely pointless and so plasma
+ 
+
+ align:start position:0%
+completely pointless and so plasma
+experiment really goes hand in hand with
+
+ align:start position:0%
+experiment really goes hand in hand with
+ 
+
+ align:start position:0%
+experiment really goes hand in hand with
+plasma Diagnostics and these Diagnostics
+
+ align:start position:0%
+plasma Diagnostics and these Diagnostics
+ 
+
+ align:start position:0%
+plasma Diagnostics and these Diagnostics
+are extremely important in the history
+
+ align:start position:0%
+are extremely important in the history
+ 
+
+ align:start position:0%
+are extremely important in the history
+of fusion and in the history of plasma
+
+ align:start position:0%
+of fusion and in the history of plasma
+ 
+
+ align:start position:0%
+of fusion and in the history of plasma
+physics so one example that I told the
+
+ align:start position:0%
+physics so one example that I told the
+ 
+
+ align:start position:0%
+physics so one example that I told the
+students about in Fusion Energy last
+
+ align:start position:0%
+students about in Fusion Energy last
+ 
+
+ align:start position:0%
+students about in Fusion Energy last
+semester that they'll probably remember
+
+ align:start position:0%
+semester that they'll probably remember
+ 
+
+ align:start position:0%
+semester that they'll probably remember
+is the Zeta pinch so this was a toroidal
+
+ align:start position:0%
+is the Zeta pinch so this was a toroidal
+ 
+
+ align:start position:0%
+is the Zeta pinch so this was a toroidal
+z pinch type device that was built in
+
+ align:start position:0%
+z pinch type device that was built in
+ 
+
+ align:start position:0%
+z pinch type device that was built in
+the UK in the
+
+ align:start position:0%
+the UK in the
+ 
+
+ align:start position:0%
+the UK in the
+50s and the Brits got very excited
+
+ align:start position:0%
+50s and the Brits got very excited
+ 
+
+ align:start position:0%
+50s and the Brits got very excited
+because when they cranked up the current
+
+ align:start position:0%
+because when they cranked up the current
+ 
+
+ align:start position:0%
+because when they cranked up the current
+on their pidal pinch they started
+
+ align:start position:0%
+on their pidal pinch they started
+ 
+
+ align:start position:0%
+on their pidal pinch they started
+measuring burst of neutrons and they
+
+ align:start position:0%
+measuring burst of neutrons and they
+ 
+
+ align:start position:0%
+measuring burst of neutrons and they
+said aha we see neutrons therefore we're
+
+ align:start position:0%
+said aha we see neutrons therefore we're
+ 
+
+ align:start position:0%
+said aha we see neutrons therefore we're
+getting Fusion now there was a problem
+
+ align:start position:0%
+getting Fusion now there was a problem
+ 
+
+ align:start position:0%
+getting Fusion now there was a problem
+with this because when they looked into
+
+ align:start position:0%
+with this because when they looked into
+ 
+
+ align:start position:0%
+with this because when they looked into
+more detail they realized that the F the
+
+ align:start position:0%
+more detail they realized that the F the
+ 
+
+ align:start position:0%
+more detail they realized that the F the
+neutron burst they were getting was not
+
+ align:start position:0%
+neutron burst they were getting was not
+ 
+
+ align:start position:0%
+neutron burst they were getting was not
+isotropic so it couldn't be
+
+ align:start position:0%
+isotropic so it couldn't be
+ 
+
+ align:start position:0%
+isotropic so it couldn't be
+thermonuclear in origin and also the
+
+ align:start position:0%
+thermonuclear in origin and also the
+ 
+
+ align:start position:0%
+thermonuclear in origin and also the
+temperature of their plasma was far too
+
+ align:start position:0%
+temperature of their plasma was far too
+ 
+
+ align:start position:0%
+temperature of their plasma was far too
+low so they didn't have sufficient
+
+ align:start position:0%
+low so they didn't have sufficient
+ 
+
+ align:start position:0%
+low so they didn't have sufficient
+Diagnostics to realize that these
+
+ align:start position:0%
+Diagnostics to realize that these
+ 
+
+ align:start position:0%
+Diagnostics to realize that these
+neutrons were not coming from a
+
+ align:start position:0%
+neutrons were not coming from a
+ 
+
+ align:start position:0%
+neutrons were not coming from a
+thermonuclear Fusion process but were in
+
+ align:start position:0%
+thermonuclear Fusion process but were in
+ 
+
+ align:start position:0%
+thermonuclear Fusion process but were in
+fact coming from mhd instabilities
+
+ align:start position:0%
+fact coming from mhd instabilities
+ 
+
+ align:start position:0%
+fact coming from mhd instabilities
+within the plasma this was extremely
+
+ align:start position:0%
+within the plasma this was extremely
+ 
+
+ align:start position:0%
+within the plasma this was extremely
+embarrassing uh but the upshot of it was
+
+ align:start position:0%
+embarrassing uh but the upshot of it was
+ 
+
+ align:start position:0%
+embarrassing uh but the upshot of it was
+that this team veloped a technique
+
+ align:start position:0%
+that this team veloped a technique
+ 
+
+ align:start position:0%
+that this team veloped a technique
+called Thompson scattering which uses a
+
+ align:start position:0%
+called Thompson scattering which uses a
+ 
+
+ align:start position:0%
+called Thompson scattering which uses a
+focus laser beam to measure the
+
+ align:start position:0%
+focus laser beam to measure the
+ 
+
+ align:start position:0%
+focus laser beam to measure the
+temperature of a plasma and they
+
+ align:start position:0%
+temperature of a plasma and they
+ 
+
+ align:start position:0%
+temperature of a plasma and they
+developed it just in time for the
+
+ align:start position:0%
+developed it just in time for the
+ 
+
+ align:start position:0%
+developed it just in time for the
+Russians to announced their new device
+
+ align:start position:0%
+Russians to announced their new device
+ 
+
+ align:start position:0%
+Russians to announced their new device
+which they called a fermac uh which they
+
+ align:start position:0%
+which they called a fermac uh which they
+ 
+
+ align:start position:0%
+which they called a fermac uh which they
+claimed had temperatures over a kiler
+
+ align:start position:0%
+claimed had temperatures over a kiler
+ 
+
+ align:start position:0%
+claimed had temperatures over a kiler
+electron volt which is about 10 times
+
+ align:start position:0%
+electron volt which is about 10 times
+ 
+
+ align:start position:0%
+electron volt which is about 10 times
+higher than any other device that anyone
+
+ align:start position:0%
+higher than any other device that anyone
+ 
+
+ align:start position:0%
+higher than any other device that anyone
+had been trying to do fusion with at the
+
+ align:start position:0%
+had been trying to do fusion with at the
+ 
+
+ align:start position:0%
+had been trying to do fusion with at the
+time this again caused a huge Fay
+
+ align:start position:0%
+time this again caused a huge Fay
+ 
+
+ align:start position:0%
+time this again caused a huge Fay
+because lots of groups from around the
+
+ align:start position:0%
+because lots of groups from around the
+ 
+
+ align:start position:0%
+because lots of groups from around the
+world didn't believe it they said how
+
+ align:start position:0%
+world didn't believe it they said how
+ 
+
+ align:start position:0%
+world didn't believe it they said how
+the Russians managed to get such an
+
+ align:start position:0%
+the Russians managed to get such an
+ 
+
+ align:start position:0%
+the Russians managed to get such an
+incredible result from their machine and
+
+ align:start position:0%
+incredible result from their machine and
+ 
+
+ align:start position:0%
+incredible result from their machine and
+so the team from the UK who had worked
+
+ align:start position:0%
+so the team from the UK who had worked
+ 
+
+ align:start position:0%
+so the team from the UK who had worked
+on Zeta and then worked on Thompson
+
+ align:start position:0%
+on Zeta and then worked on Thompson
+ 
+
+ align:start position:0%
+on Zeta and then worked on Thompson
+scattering flew over to Moscow with
+
+ align:start position:0%
+scattering flew over to Moscow with
+ 
+
+ align:start position:0%
+scattering flew over to Moscow with
+their Ruby laser and made the first
+
+ align:start position:0%
+their Ruby laser and made the first
+ 
+
+ align:start position:0%
+their Ruby laser and made the first
+Thompson scattering measurements on a
+
+ align:start position:0%
+Thompson scattering measurements on a
+ 
+
+ align:start position:0%
+Thompson scattering measurements on a
+toac confirming that had temperatures of
+
+ align:start position:0%
+toac confirming that had temperatures of
+ 
+
+ align:start position:0%
+toac confirming that had temperatures of
+a killer electron volt and the rest is
+
+ align:start position:0%
+a killer electron volt and the rest is
+ 
+
+ align:start position:0%
+a killer electron volt and the rest is
+kind of History immediately everywhere
+
+ align:start position:0%
+kind of History immediately everywhere
+ 
+
+ align:start position:0%
+kind of History immediately everywhere
+around the world people started
+
+ align:start position:0%
+around the world people started
+ 
+
+ align:start position:0%
+around the world people started
+converting their other machines into
+
+ align:start position:0%
+converting their other machines into
+ 
+
+ align:start position:0%
+converting their other machines into
+toomax the Princeton model celerator
+
+ align:start position:0%
+toomax the Princeton model celerator
+ 
+
+ align:start position:0%
+toomax the Princeton model celerator
+they cut off all the long loopy bits and
+
+ align:start position:0%
+they cut off all the long loopy bits and
+ 
+
+ align:start position:0%
+they cut off all the long loopy bits and
+just shoved two halves together and it
+
+ align:start position:0%
+just shoved two halves together and it
+ 
+
+ align:start position:0%
+just shoved two halves together and it
+became the princet and model SE toac
+
+ align:start position:0%
+became the princet and model SE toac
+ 
+
+ align:start position:0%
+became the princet and model SE toac
+instead and this happened overnight and
+
+ align:start position:0%
+instead and this happened overnight and
+ 
+
+ align:start position:0%
+instead and this happened overnight and
+we are still living in a post Thompson
+
+ align:start position:0%
+we are still living in a post Thompson
+ 
+
+ align:start position:0%
+we are still living in a post Thompson
+Gathering post toac world because all of
+
+ align:start position:0%
+Gathering post toac world because all of
+ 
+
+ align:start position:0%
+Gathering post toac world because all of
+our major devices now are
+
+ align:start position:0%
+our major devices now are
+ 
+
+ align:start position:0%
+our major devices now are
+toxs another good example is the
+
+ align:start position:0%
+toxs another good example is the
+ 
+
+ align:start position:0%
+toxs another good example is the
+national ignition facility um the
+
+ align:start position:0%
+national ignition facility um the
+ 
+
+ align:start position:0%
+national ignition facility um the
+national inition facility was carefully
+
+ align:start position:0%
+national inition facility was carefully
+ 
+
+ align:start position:0%
+national inition facility was carefully
+designed using the best simulations
+
+ align:start position:0%
+designed using the best simulations
+ 
+
+ align:start position:0%
+designed using the best simulations
+available all these incredible radiation
+
+ align:start position:0%
+available all these incredible radiation
+ 
+
+ align:start position:0%
+available all these incredible radiation
+hydrodynamics multi-group everything you
+
+ align:start position:0%
+hydrodynamics multi-group everything you
+ 
+
+ align:start position:0%
+hydrodynamics multi-group everything you
+can think of all the best physics in the
+
+ align:start position:0%
+can think of all the best physics in the
+ 
+
+ align:start position:0%
+can think of all the best physics in the
+world and they were very confident that
+
+ align:start position:0%
+world and they were very confident that
+ 
+
+ align:start position:0%
+world and they were very confident that
+when they turned on the national
+
+ align:start position:0%
+when they turned on the national
+ 
+
+ align:start position:0%
+when they turned on the national
+ignition facility they were going to get
+
+ align:start position:0%
+ignition facility they were going to get
+ 
+
+ align:start position:0%
+ignition facility they were going to get
+ignition they were so confident they put
+
+ align:start position:0%
+ignition they were so confident they put
+ 
+
+ align:start position:0%
+ignition they were so confident they put
+it in the name of the experiment and so
+
+ align:start position:0%
+it in the name of the experiment and so
+ 
+
+ align:start position:0%
+it in the name of the experiment and so
+back in 2009 or so they started running
+
+ align:start position:0%
+back in 2009 or so they started running
+ 
+
+ align:start position:0%
+back in 2009 or so they started running
+the first experiments and they said we
+
+ align:start position:0%
+the first experiments and they said we
+ 
+
+ align:start position:0%
+the first experiments and they said we
+don't really need any Diagnostics
+
+ align:start position:0%
+don't really need any Diagnostics
+ 
+
+ align:start position:0%
+don't really need any Diagnostics
+because it's going to work it's obvious
+
+ align:start position:0%
+because it's going to work it's obvious
+ 
+
+ align:start position:0%
+because it's going to work it's obvious
+we know exactly what's happening we'll
+
+ align:start position:0%
+we know exactly what's happening we'll
+ 
+
+ align:start position:0%
+we know exactly what's happening we'll
+just have basically some Neutron
+
+ align:start position:0%
+just have basically some Neutron
+ 
+
+ align:start position:0%
+just have basically some Neutron
+counters so that we can go ding we got
+
+ align:start position:0%
+counters so that we can go ding we got
+ 
+
+ align:start position:0%
+counters so that we can go ding we got
+to ignition and take the box and move on
+
+ align:start position:0%
+to ignition and take the box and move on
+ 
+
+ align:start position:0%
+to ignition and take the box and move on
+now this didn't happen when they turned
+
+ align:start position:0%
+now this didn't happen when they turned
+ 
+
+ align:start position:0%
+now this didn't happen when they turned
+on this the signal was barely measurable
+
+ align:start position:0%
+on this the signal was barely measurable
+ 
+
+ align:start position:0%
+on this the signal was barely measurable
+uh there was almost no neutrons at all
+
+ align:start position:0%
+uh there was almost no neutrons at all
+ 
+
+ align:start position:0%
+uh there was almost no neutrons at all
+coming out of it and they had no idea
+
+ align:start position:0%
+coming out of it and they had no idea
+ 
+
+ align:start position:0%
+coming out of it and they had no idea
+why the reason they had no idea why is
+
+ align:start position:0%
+why the reason they had no idea why is
+ 
+
+ align:start position:0%
+why the reason they had no idea why is
+because they didn't have any Diagnostics
+
+ align:start position:0%
+because they didn't have any Diagnostics
+ 
+
+ align:start position:0%
+because they didn't have any Diagnostics
+to tell them what was actually happening
+
+ align:start position:0%
+to tell them what was actually happening
+ 
+
+ align:start position:0%
+to tell them what was actually happening
+they only had Diagnostics to tell them
+
+ align:start position:0%
+they only had Diagnostics to tell them
+ 
+
+ align:start position:0%
+they only had Diagnostics to tell them
+whether they were successful or not and
+
+ align:start position:0%
+whether they were successful or not and
+ 
+
+ align:start position:0%
+whether they were successful or not and
+the answer was they weren't um so no one
+
+ align:start position:0%
+the answer was they weren't um so no one
+ 
+
+ align:start position:0%
+the answer was they weren't um so no one
+knew what was going on but a decade
+
+ align:start position:0%
+knew what was going on but a decade
+ 
+
+ align:start position:0%
+knew what was going on but a decade
+later they now have very good diagnostic
+
+ align:start position:0%
+later they now have very good diagnostic
+ 
+
+ align:start position:0%
+later they now have very good diagnostic
+if and it's no coincidence that of
+
+ align:start position:0%
+if and it's no coincidence that of
+ 
+
+ align:start position:0%
+if and it's no coincidence that of
+course they now have ignition as well
+
+ align:start position:0%
+course they now have ignition as well
+ 
+
+ align:start position:0%
+course they now have ignition as well
+because they understand a great deal
+
+ align:start position:0%
+because they understand a great deal
+ 
+
+ align:start position:0%
+because they understand a great deal
+about physics going on inside this
+
+ align:start position:0%
+about physics going on inside this
+ 
+
+ align:start position:0%
+about physics going on inside this
+experiment so you really need to have
+
+ align:start position:0%
+experiment so you really need to have
+ 
+
+ align:start position:0%
+experiment so you really need to have
+good Diagnostics do good plasma physics
+
+ align:start position:0%
+good Diagnostics do good plasma physics
+ 
+
+ align:start position:0%
+good Diagnostics do good plasma physics
+and to build good Fusion reactors as
+
+ align:start position:0%
+and to build good Fusion reactors as
+ 
+
+ align:start position:0%
+and to build good Fusion reactors as
+well who needs to know about Diagnostics
+
+ align:start position:0%
+well who needs to know about Diagnostics
+ 
+
+ align:start position:0%
+well who needs to know about Diagnostics
+well obviously experimenters we kind of
+
+ align:start position:0%
+well obviously experimenters we kind of
+ 
+
+ align:start position:0%
+well obviously experimenters we kind of
+I imagine many of the people in this
+
+ align:start position:0%
+I imagine many of the people in this
+ 
+
+ align:start position:0%
+I imagine many of the people in this
+room are doing experimental plasma phys
+
+ align:start position:0%
+room are doing experimental plasma phys
+ 
+
+ align:start position:0%
+room are doing experimental plasma phys
+and that's why they're here they want to
+
+ align:start position:0%
+and that's why they're here they want to
+ 
+
+ align:start position:0%
+and that's why they're here they want to
+understand the plasmas that their
+
+ align:start position:0%
+understand the plasmas that their
+ 
+
+ align:start position:0%
+understand the plasmas that their
+machines are producing and they want to
+
+ align:start position:0%
+machines are producing and they want to
+ 
+
+ align:start position:0%
+machines are producing and they want to
+probe the mysteries of the universe and
+
+ align:start position:0%
+probe the mysteries of the universe and
+ 
+
+ align:start position:0%
+probe the mysteries of the universe and
+get unlimited clean renewable energy and
+
+ align:start position:0%
+get unlimited clean renewable energy and
+ 
+
+ align:start position:0%
+get unlimited clean renewable energy and
+all that sort of stuff but they also
+
+ align:start position:0%
+all that sort of stuff but they also
+ 
+
+ align:start position:0%
+all that sort of stuff but they also
+want to understand the uncertainty
+
+ align:start position:0%
+want to understand the uncertainty
+ 
+
+ align:start position:0%
+want to understand the uncertainty
+involved in their measurements when
+
+ align:start position:0%
+involved in their measurements when
+ 
+
+ align:start position:0%
+involved in their measurements when
+someone says you the temperature on this
+
+ align:start position:0%
+someone says you the temperature on this
+ 
+
+ align:start position:0%
+someone says you the temperature on this
+toac is one kilo electron volt what does
+
+ align:start position:0%
+toac is one kilo electron volt what does
+ 
+
+ align:start position:0%
+toac is one kilo electron volt what does
+that mean where is it one Kil electron
+
+ align:start position:0%
+that mean where is it one Kil electron
+ 
+
+ align:start position:0%
+that mean where is it one Kil electron
+volt uh what's the error bars on that is
+
+ align:start position:0%
+volt uh what's the error bars on that is
+ 
+
+ align:start position:0%
+volt uh what's the error bars on that is
+that true for the entire discharge
+
+ align:start position:0%
+that true for the entire discharge
+ 
+
+ align:start position:0%
+that true for the entire discharge
+there's huge limitations in the
+
+ align:start position:0%
+there's huge limitations in the
+ 
+
+ align:start position:0%
+there's huge limitations in the
+Diagnostics we have and we need to
+
+ align:start position:0%
+Diagnostics we have and we need to
+ 
+
+ align:start position:0%
+Diagnostics we have and we need to
+understand those limitations if you're
+
+ align:start position:0%
+understand those limitations if you're
+ 
+
+ align:start position:0%
+understand those limitations if you're
+doing computational uh work if you're
+
+ align:start position:0%
+doing computational uh work if you're
+ 
+
+ align:start position:0%
+doing computational uh work if you're
+doing large simulations you might be
+
+ align:start position:0%
+doing large simulations you might be
+ 
+
+ align:start position:0%
+doing large simulations you might be
+interested in Diagnostics because they
+
+ align:start position:0%
+interested in Diagnostics because they
+ 
+
+ align:start position:0%
+interested in Diagnostics because they
+serve as a primary way of validating
+
+ align:start position:0%
+serve as a primary way of validating
+ 
+
+ align:start position:0%
+serve as a primary way of validating
+your code your code is only really
+
+ align:start position:0%
+your code your code is only really
+ 
+
+ align:start position:0%
+your code your code is only really
+worthwhile if it makes predictions that
+
+ align:start position:0%
+worthwhile if it makes predictions that
+ 
+
+ align:start position:0%
+worthwhile if it makes predictions that
+agree with reality and so you may want
+
+ align:start position:0%
+agree with reality and so you may want
+ 
+
+ align:start position:0%
+agree with reality and so you may want
+to understand how diagnosticians are
+
+ align:start position:0%
+to understand how diagnosticians are
+ 
+
+ align:start position:0%
+to understand how diagnosticians are
+making these measurements so that they
+
+ align:start position:0%
+making these measurements so that they
+ 
+
+ align:start position:0%
+making these measurements so that they
+can understand whether your code is
+
+ align:start position:0%
+can understand whether your code is
+ 
+
+ align:start position:0%
+can understand whether your code is
+right or not and you may also be
+
+ align:start position:0%
+right or not and you may also be
+ 
+
+ align:start position:0%
+right or not and you may also be
+motivated to make useful outputs from a
+
+ align:start position:0%
+motivated to make useful outputs from a
+ 
+
+ align:start position:0%
+motivated to make useful outputs from a
+computer simulation you may get a very
+
+ align:start position:0%
+computer simulation you may get a very
+ 
+
+ align:start position:0%
+computer simulation you may get a very
+large amount of data that's very hard to
+
+ align:start position:0%
+large amount of data that's very hard to
+ 
+
+ align:start position:0%
+large amount of data that's very hard to
+distill down one way to distill that
+
+ align:start position:0%
+distill down one way to distill that
+ 
+
+ align:start position:0%
+distill down one way to distill that
+down is to think about the Diagnostics
+
+ align:start position:0%
+down is to think about the Diagnostics
+ 
+
+ align:start position:0%
+down is to think about the Diagnostics
+that experimentalists use and reduce
+
+ align:start position:0%
+that experimentalists use and reduce
+ 
+
+ align:start position:0%
+that experimentalists use and reduce
+your data set to looks a bit more like
+
+ align:start position:0%
+your data set to looks a bit more like
+ 
+
+ align:start position:0%
+your data set to looks a bit more like
+those Diagnostics that gives you an
+
+ align:start position:0%
+those Diagnostics that gives you an
+ 
+
+ align:start position:0%
+those Diagnostics that gives you an
+easier way of comparing your data with
+
+ align:start position:0%
+easier way of comparing your data with
+ 
+
+ align:start position:0%
+easier way of comparing your data with
+reality um if you're a theorist I think
+
+ align:start position:0%
+reality um if you're a theorist I think
+ 
+
+ align:start position:0%
+reality um if you're a theorist I think
+you should still know about Diagnostics
+
+ align:start position:0%
+you should still know about Diagnostics
+ 
+
+ align:start position:0%
+you should still know about Diagnostics
+I think you should be very skeptical
+
+ align:start position:0%
+I think you should be very skeptical
+ 
+
+ align:start position:0%
+I think you should be very skeptical
+about your experimental colleagues I
+
+ align:start position:0%
+about your experimental colleagues I
+ 
+
+ align:start position:0%
+about your experimental colleagues I
+don't think you should believe them when
+
+ align:start position:0%
+don't think you should believe them when
+ 
+
+ align:start position:0%
+don't think you should believe them when
+they say the temperature is one kiler
+
+ align:start position:0%
+they say the temperature is one kiler
+ 
+
+ align:start position:0%
+they say the temperature is one kiler
+electron fault you should ask where and
+
+ align:start position:0%
+electron fault you should ask where and
+ 
+
+ align:start position:0%
+electron fault you should ask where and
+when you know how sure are you because
+
+ align:start position:0%
+when you know how sure are you because
+ 
+
+ align:start position:0%
+when you know how sure are you because
+these people are trying to tell you
+
+ align:start position:0%
+these people are trying to tell you
+ 
+
+ align:start position:0%
+these people are trying to tell you
+something and you're going to go out and
+
+ align:start position:0%
+something and you're going to go out and
+ 
+
+ align:start position:0%
+something and you're going to go out and
+tell all your colleagues that your
+
+ align:start position:0%
+tell all your colleagues that your
+ 
+
+ align:start position:0%
+tell all your colleagues that your
+theory has been proved and if they were
+
+ align:start position:0%
+theory has been proved and if they were
+ 
+
+ align:start position:0%
+theory has been proved and if they were
+wrong you're going to be very very
+
+ align:start position:0%
+wrong you're going to be very very
+ 
+
+ align:start position:0%
+wrong you're going to be very very
+embarrassed you might also be motivated
+
+ align:start position:0%
+embarrassed you might also be motivated
+ 
+
+ align:start position:0%
+embarrassed you might also be motivated
+to design theories which have testable
+
+ align:start position:0%
+to design theories which have testable
+ 
+
+ align:start position:0%
+to design theories which have testable
+prediction right so a lot of theor iCal
+
+ align:start position:0%
+prediction right so a lot of theor iCal
+ 
+
+ align:start position:0%
+prediction right so a lot of theor iCal
+work is phrased in a language which is
+
+ align:start position:0%
+work is phrased in a language which is
+ 
+
+ align:start position:0%
+work is phrased in a language which is
+very different from the way that
+
+ align:start position:0%
+very different from the way that
+ 
+
+ align:start position:0%
+very different from the way that
+experimentalists speak and that means
+
+ align:start position:0%
+experimentalists speak and that means
+ 
+
+ align:start position:0%
+experimentalists speak and that means
+that when experimentalists read your
+
+ align:start position:0%
+that when experimentalists read your
+ 
+
+ align:start position:0%
+that when experimentalists read your
+papers they don't understand what's
+
+ align:start position:0%
+papers they don't understand what's
+ 
+
+ align:start position:0%
+papers they don't understand what's
+going on and they also don't know um how
+
+ align:start position:0%
+going on and they also don't know um how
+ 
+
+ align:start position:0%
+going on and they also don't know um how
+exactly they can test your predictions
+
+ align:start position:0%
+exactly they can test your predictions
+ 
+
+ align:start position:0%
+exactly they can test your predictions
+if you know how diagnosticians think you
+
+ align:start position:0%
+if you know how diagnosticians think you
+ 
+
+ align:start position:0%
+if you know how diagnosticians think you
+can write papers which are clearer for
+
+ align:start position:0%
+can write papers which are clearer for
+ 
+
+ align:start position:0%
+can write papers which are clearer for
+them they can go test your theory prove
+
+ align:start position:0%
+them they can go test your theory prove
+ 
+
+ align:start position:0%
+them they can go test your theory prove
+it right and then you can go let your
+
+ align:start position:0%
+it right and then you can go let your
+ 
+
+ align:start position:0%
+it right and then you can go let your
+Nobel Prize so it's pretty important to
+
+ align:start position:0%
+Nobel Prize so it's pretty important to
+ 
+
+ align:start position:0%
+Nobel Prize so it's pretty important to
+know how Diagnostics work
+
+ align:start position:0%
+know how Diagnostics work
+ 
+
+ align:start position:0%
+know how Diagnostics work
+there all right I've been talking for a
+
+ align:start position:0%
+there all right I've been talking for a
+ 
+
+ align:start position:0%
+there all right I've been talking for a
+bit so I'll pause and see if there's any
+
+ align:start position:0%
+bit so I'll pause and see if there's any
+ 
+
+ align:start position:0%
+bit so I'll pause and see if there's any
+questions so
+
+ align:start position:0%
+questions so
+ 
+
+ align:start position:0%
+questions so
+far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things what can we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before we get on to what can we measure
+
+ align:start position:0%
+before we get on to what can we measure
+ 
+
+ align:start position:0%
+before we get on to what can we measure
+what would we like to measure you know
+
+ align:start position:0%
+what would we like to measure you know
+ 
+
+ align:start position:0%
+what would we like to measure you know
+what would a theorist like to ask us for
+
+ align:start position:0%
+what would a theorist like to ask us for
+ 
+
+ align:start position:0%
+what would a theorist like to ask us for
+so what can we measure what do
+
+ align:start position:0%
+so what can we measure what do
+ 
+
+ align:start position:0%
+so what can we measure what do
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want well if it's not too much to ask
+
+ align:start position:0%
+want well if it's not too much to ask
+ 
+
+ align:start position:0%
+want well if it's not too much to ask
+we'd like to know the position and
+
+ align:start position:0%
+we'd like to know the position and
+ 
+
+ align:start position:0%
+we'd like to know the position and
+velocity of every single in the plasma
+
+ align:start position:0%
+velocity of every single in the plasma
+ 
+
+ align:start position:0%
+velocity of every single in the plasma
+at every point in space and time right
+
+ align:start position:0%
+at every point in space and time right
+ 
+
+ align:start position:0%
+at every point in space and time right
+so this would be the clich type
+
+ align:start position:0%
+so this would be the clich type
+ 
+
+ align:start position:0%
+so this would be the clich type
+distribution here we'd have sort of f of
+
+ align:start position:0%
+distribution here we'd have sort of f of
+ 
+
+ align:start position:0%
+distribution here we'd have sort of f of
+x as a vector v is a vector time and
+
+ align:start position:0%
+x as a vector v is a vector time and
+ 
+
+ align:start position:0%
+x as a vector v is a vector time and
+this would simply look like the sum of a
+
+ align:start position:0%
+this would simply look like the sum of a
+ 
+
+ align:start position:0%
+this would simply look like the sum of a
+series of Delta functions which are the
+
+ align:start position:0%
+series of Delta functions which are the
+ 
+
+ align:start position:0%
+series of Delta functions which are the
+position of particle I the velocity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle I and both of those should be
+
+ align:start position:0%
+particle I and both of those should be
+ 
+
+ align:start position:0%
+particle I and both of those should be
+functions of time as well and our full
+
+ align:start position:0%
+functions of time as well and our full
+ 
+
+ align:start position:0%
+functions of time as well and our full
+distribution function is just the sum
+
+ align:start position:0%
+distribution function is just the sum
+ 
+
+ align:start position:0%
+distribution function is just the sum
+over all of these particles so this is
+
+ align:start position:0%
+over all of these particles so this is
+ 
+
+ align:start position:0%
+over all of these particles so this is
+threedimensional three velocity vectors
+
+ align:start position:0%
+threedimensional three velocity vectors
+ 
+
+ align:start position:0%
+threedimensional three velocity vectors
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time now of course a theorists might
+
+ align:start position:0%
+time now of course a theorists might
+ 
+
+ align:start position:0%
+time now of course a theorists might
+tell you they want that but they don't
+
+ align:start position:0%
+tell you they want that but they don't
+ 
+
+ align:start position:0%
+tell you they want that but they don't
+really no one wants that it's absolutely
+
+ align:start position:0%
+really no one wants that it's absolutely
+ 
+
+ align:start position:0%
+really no one wants that it's absolutely
+impossible to work with right this is a
+
+ align:start position:0%
+impossible to work with right this is a
+ 
+
+ align:start position:0%
+impossible to work with right this is a
+mess so what theorists really want is
+
+ align:start position:0%
+mess so what theorists really want is
+ 
+
+ align:start position:0%
+mess so what theorists really want is
+they want some sort of moments of this
+
+ align:start position:0%
+they want some sort of moments of this
+ 
+
+ align:start position:0%
+they want some sort of moments of this
+they they would like to have a
+
+ align:start position:0%
+they they would like to have a
+ 
+
+ align:start position:0%
+they they would like to have a
+simplified version of this at best
+
+ align:start position:0%
+simplified version of this at best
+ 
+
+ align:start position:0%
+simplified version of this at best
+they'd like to have a distribution
+
+ align:start position:0%
+they'd like to have a distribution
+ 
+
+ align:start position:0%
+they'd like to have a distribution
+function which is smooth this one is
+
+ align:start position:0%
+function which is smooth this one is
+ 
+
+ align:start position:0%
+function which is smooth this one is
+very very spiky and hard to work with um
+
+ align:start position:0%
+very very spiky and hard to work with um
+ 
+
+ align:start position:0%
+very very spiky and hard to work with um
+but they may may also be willing to get
+
+ align:start position:0%
+but they may may also be willing to get
+ 
+
+ align:start position:0%
+but they may may also be willing to get
+away with letting you give them some
+
+ align:start position:0%
+away with letting you give them some
+ 
+
+ align:start position:0%
+away with letting you give them some
+thermodynamic variables some variables
+
+ align:start position:0%
+thermodynamic variables some variables
+ 
+
+ align:start position:0%
+thermodynamic variables some variables
+where we've taken moments over this so
+
+ align:start position:0%
+where we've taken moments over this so
+ 
+
+ align:start position:0%
+where we've taken moments over this so
+if we look at some of the moments that
+
+ align:start position:0%
+if we look at some of the moments that
+ 
+
+ align:start position:0%
+if we look at some of the moments that
+we can take
+
+ align:start position:0%
+we can take
+ 
+
+ align:start position:0%
+we can take
+here we would have things like the
+
+ align:start position:0%
+here we would have things like the
+ 
+
+ align:start position:0%
+here we would have things like the
+density and this is an integral over
+
+ align:start position:0%
+density and this is an integral over
+ 
+
+ align:start position:0%
+density and this is an integral over
+your the velocity part of your
+
+ align:start position:0%
+your the velocity part of your
+ 
+
+ align:start position:0%
+your the velocity part of your
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d3v that's the den
+
+ align:start position:0%
+d3v that's the den
+ 
+
+ align:start position:0%
+d3v that's the den
+or you might want to know things like
+
+ align:start position:0%
+or you might want to know things like
+ 
+
+ align:start position:0%
+or you might want to know things like
+the average velocity of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles and you can keep going with
+
+ align:start position:0%
+particles and you can keep going with
+ 
+
+ align:start position:0%
+particles and you can keep going with
+this by multiplying your distribution
+
+ align:start position:0%
+this by multiplying your distribution
+ 
+
+ align:start position:0%
+this by multiplying your distribution
+function by larger and larger powers of
+
+ align:start position:0%
+function by larger and larger powers of
+ 
+
+ align:start position:0%
+function by larger and larger powers of
+v and you start getting tensors and all
+
+ align:start position:0%
+v and you start getting tensors and all
+ 
+
+ align:start position:0%
+v and you start getting tensors and all
+sorts of exciting things like that I'm
+
+ align:start position:0%
+sorts of exciting things like that I'm
+ 
+
+ align:start position:0%
+sorts of exciting things like that I'm
+just going to put Etc before we get
+
+ align:start position:0%
+just going to put Etc before we get
+ 
+
+ align:start position:0%
+just going to put Etc before we get
+carried away we get our St um you might
+
+ align:start position:0%
+carried away we get our St um you might
+ 
+
+ align:start position:0%
+carried away we get our St um you might
+also want to know things like magnetic
+
+ align:start position:0%
+also want to know things like magnetic
+ 
+
+ align:start position:0%
+also want to know things like magnetic
+fields
+
+ align:start position:0%
+fields
+ 
+
+ align:start position:0%
+fields
+these are pretty important in plasmas
+
+ align:start position:0%
+these are pretty important in plasmas
+ 
+
+ align:start position:0%
+these are pretty important in plasmas
+because plasmas move in response to
+
+ align:start position:0%
+because plasmas move in response to
+ 
+
+ align:start position:0%
+because plasmas move in response to
+magnetic fields these magnetic fields
+
+ align:start position:0%
+magnetic fields these magnetic fields
+ 
+
+ align:start position:0%
+magnetic fields these magnetic fields
+are caused by currents
+
+ align:start position:0%
+are caused by currents
+ 
+
+ align:start position:0%
+are caused by currents
+fundamentally electric
+
+ align:start position:0%
+fundamentally electric
+ 
+
+ align:start position:0%
+fundamentally electric
+currents and those electric currents can
+
+ align:start position:0%
+currents and those electric currents can
+ 
+
+ align:start position:0%
+currents and those electric currents can
+be external so they could be provided by
+
+ align:start position:0%
+be external so they could be provided by
+ 
+
+ align:start position:0%
+be external so they could be provided by
+a large set of magnets that surround
+
+ align:start position:0%
+a large set of magnets that surround
+ 
+
+ align:start position:0%
+a large set of magnets that surround
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma or they could be internal they
+
+ align:start position:0%
+plasma or they could be internal they
+ 
+
+ align:start position:0%
+plasma or they could be internal they
+could be provided by the plasma motion
+
+ align:start position:0%
+could be provided by the plasma motion
+ 
+
+ align:start position:0%
+could be provided by the plasma motion
+itself probably getting a little bit low
+
+ align:start position:0%
+itself probably getting a little bit low
+ 
+
+ align:start position:0%
+itself probably getting a little bit low
+there go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up they're clearly very very important
+
+ align:start position:0%
+up they're clearly very very important
+ 
+
+ align:start position:0%
+up they're clearly very very important
+now in reality even if we can
+
+ align:start position:0%
+now in reality even if we can
+ 
+
+ align:start position:0%
+now in reality even if we can
+measure density and velocity and
+
+ align:start position:0%
+measure density and velocity and
+ 
+
+ align:start position:0%
+measure density and velocity and
+magnetic fields we're not really going
+
+ align:start position:0%
+magnetic fields we're not really going
+ 
+
+ align:start position:0%
+magnetic fields we're not really going
+to be able to get them at every point in
+
+ align:start position:0%
+to be able to get them at every point in
+ 
+
+ align:start position:0%
+to be able to get them at every point in
+space and time we're quite limited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so diagnostic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limitations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to end up things uh which
+
+ align:start position:0%
+we're going to end up things uh which
+ 
+
+ align:start position:0%
+we're going to end up things uh which
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spas in space I'm just going to use
+
+ align:start position:0%
+spas in space I'm just going to use
+ 
+
+ align:start position:0%
+spas in space I'm just going to use
+Vector X for space and time so we don't
+
+ align:start position:0%
+Vector X for space and time so we don't
+ 
+
+ align:start position:0%
+Vector X for space and time so we don't
+have it all the time this may be because
+
+ align:start position:0%
+have it all the time this may be because
+ 
+
+ align:start position:0%
+have it all the time this may be because
+our diagnostic uh only measures at a
+
+ align:start position:0%
+our diagnostic uh only measures at a
+ 
+
+ align:start position:0%
+our diagnostic uh only measures at a
+single point as a function of time or it
+
+ align:start position:0%
+single point as a function of time or it
+ 
+
+ align:start position:0%
+single point as a function of time or it
+may be a picture which measures spatial
+
+ align:start position:0%
+may be a picture which measures spatial
+ 
+
+ align:start position:0%
+may be a picture which measures spatial
+variation at a single time or may be
+
+ align:start position:0%
+variation at a single time or may be
+ 
+
+ align:start position:0%
+variation at a single time or may be
+some combination of those here
+
+ align:start position:0%
+some combination of those here
+ 
+
+ align:start position:0%
+some combination of those here
+um our diagnostic is often going to be
+
+ align:start position:0%
+um our diagnostic is often going to be
+ 
+
+ align:start position:0%
+um our diagnostic is often going to be
+what we call line
+
+ align:start position:0%
+what we call line
+ 
+
+ align:start position:0%
+what we call line
+integrated this is especially true for
+
+ align:start position:0%
+integrated this is especially true for
+ 
+
+ align:start position:0%
+integrated this is especially true for
+Diagnostics which use light light
+
+ align:start position:0%
+Diagnostics which use light light
+ 
+
+ align:start position:0%
+Diagnostics which use light light
+famously mostly traveling in straight
+
+ align:start position:0%
+famously mostly traveling in straight
+ 
+
+ align:start position:0%
+famously mostly traveling in straight
+lines um means that you don't get to
+
+ align:start position:0%
+lines um means that you don't get to
+ 
+
+ align:start position:0%
+lines um means that you don't get to
+choose where the light comes from that
+
+ align:start position:0%
+choose where the light comes from that
+ 
+
+ align:start position:0%
+choose where the light comes from that
+you're measuring it's going to be along
+
+ align:start position:0%
+you're measuring it's going to be along
+ 
+
+ align:start position:0%
+you're measuring it's going to be along
+some chord so we could say what we're
+
+ align:start position:0%
+some chord so we could say what we're
+ 
+
+ align:start position:0%
+some chord so we could say what we're
+measuring is not the density but the
+
+ align:start position:0%
+measuring is not the density but the
+ 
+
+ align:start position:0%
+measuring is not the density but the
+density along a cord DL here which is
+
+ align:start position:0%
+density along a cord DL here which is
+ 
+
+ align:start position:0%
+density along a cord DL here which is
+the path of our ray of light through the
+
+ align:start position:0%
+the path of our ray of light through the
+ 
+
+ align:start position:0%
+the path of our ray of light through the
+plasma so that means as opposed to
+
+ align:start position:0%
+plasma so that means as opposed to
+ 
+
+ align:start position:0%
+plasma so that means as opposed to
+knowing n of a specific point you know
+
+ align:start position:0%
+knowing n of a specific point you know
+ 
+
+ align:start position:0%
+knowing n of a specific point you know
+the integral of n over some point if you
+
+ align:start position:0%
+the integral of n over some point if you
+ 
+
+ align:start position:0%
+the integral of n over some point if you
+happen to know some symmetry about your
+
+ align:start position:0%
+happen to know some symmetry about your
+ 
+
+ align:start position:0%
+happen to know some symmetry about your
+plasma then maybe you can work out what
+
+ align:start position:0%
+plasma then maybe you can work out what
+ 
+
+ align:start position:0%
+plasma then maybe you can work out what
+n is locally but otherwise you're kind
+
+ align:start position:0%
+n is locally but otherwise you're kind
+ 
+
+ align:start position:0%
+n is locally but otherwise you're kind
+of stuck uh with this measurement
+
+ align:start position:0%
+of stuck uh with this measurement
+ 
+
+ align:start position:0%
+of stuck uh with this measurement
+instead almost certainly your
+
+ align:start position:0%
+instead almost certainly your
+ 
+
+ align:start position:0%
+instead almost certainly your
+measurement is going to be filtered in
+
+ align:start position:0%
+measurement is going to be filtered in
+ 
+
+ align:start position:0%
+measurement is going to be filtered in
+some way I'm using the word filtered
+
+ align:start position:0%
+some way I'm using the word filtered
+ 
+
+ align:start position:0%
+some way I'm using the word filtered
+here very
+
+ align:start position:0%
+here very
+ 
+
+ align:start position:0%
+here very
+broadly uh this is means that your
+
+ align:start position:0%
+broadly uh this is means that your
+ 
+
+ align:start position:0%
+broadly uh this is means that your
+instrument is in some way an imperfect
+
+ align:start position:0%
+instrument is in some way an imperfect
+ 
+
+ align:start position:0%
+instrument is in some way an imperfect
+measurement of the world and so there is
+
+ align:start position:0%
+measurement of the world and so there is
+ 
+
+ align:start position:0%
+measurement of the world and so there is
+some sort of response function that you
+
+ align:start position:0%
+some sort of response function that you
+ 
+
+ align:start position:0%
+some sort of response function that you
+have to convolve or deconvolve from your
+
+ align:start position:0%
+have to convolve or deconvolve from your
+ 
+
+ align:start position:0%
+have to convolve or deconvolve from your
+instrument or convolve your synthetic
+
+ align:start position:0%
+instrument or convolve your synthetic
+ 
+
+ align:start position:0%
+instrument or convolve your synthetic
+data with in order to understand what it
+
+ align:start position:0%
+data with in order to understand what it
+ 
+
+ align:start position:0%
+data with in order to understand what it
+does this could be things like uh
+
+ align:start position:0%
+does this could be things like uh
+ 
+
+ align:start position:0%
+does this could be things like uh
+frequency response if you're measuring
+
+ align:start position:0%
+frequency response if you're measuring
+ 
+
+ align:start position:0%
+frequency response if you're measuring
+voltages this could be things like uh
+
+ align:start position:0%
+voltages this could be things like uh
+ 
+
+ align:start position:0%
+voltages this could be things like uh
+resolution if you're taking images with
+
+ align:start position:0%
+resolution if you're taking images with
+ 
+
+ align:start position:0%
+resolution if you're taking images with
+a camera uh that sort of thing so almost
+
+ align:start position:0%
+a camera uh that sort of thing so almost
+ 
+
+ align:start position:0%
+a camera uh that sort of thing so almost
+everything has some sort of response
+
+ align:start position:0%
+everything has some sort of response
+ 
+
+ align:start position:0%
+everything has some sort of response
+function and it's also probably going to
+
+ align:start position:0%
+function and it's also probably going to
+ 
+
+ align:start position:0%
+function and it's also probably going to
+depend on physics that we just don't
+
+ align:start position:0%
+depend on physics that we just don't
+ 
+
+ align:start position:0%
+depend on physics that we just don't
+understand very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so depend on poorly understood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics a great example of this is
+
+ align:start position:0%
+physics a great example of this is
+ 
+
+ align:start position:0%
+physics a great example of this is
+spectroscopy so Atomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data anyone who's ever done spectroscopy
+
+ align:start position:0%
+data anyone who's ever done spectroscopy
+ 
+
+ align:start position:0%
+data anyone who's ever done spectroscopy
+will know that there's a lot of
+
+ align:start position:0%
+will know that there's a lot of
+ 
+
+ align:start position:0%
+will know that there's a lot of
+electrons there's lots of places they
+
+ align:start position:0%
+electrons there's lots of places they
+ 
+
+ align:start position:0%
+electrons there's lots of places they
+can be they can interact in lots of ways
+
+ align:start position:0%
+can be they can interact in lots of ways
+ 
+
+ align:start position:0%
+can be they can interact in lots of ways
+and so it's very hard to actually make
+
+ align:start position:0%
+and so it's very hard to actually make
+ 
+
+ align:start position:0%
+and so it's very hard to actually make
+predictions for the Spectra of even
+
+ align:start position:0%
+predictions for the Spectra of even
+ 
+
+ align:start position:0%
+predictions for the Spectra of even
+something as simple as helium and so if
+
+ align:start position:0%
+something as simple as helium and so if
+ 
+
+ align:start position:0%
+something as simple as helium and so if
+we're trying to understand spectroscopy
+
+ align:start position:0%
+we're trying to understand spectroscopy
+ 
+
+ align:start position:0%
+we're trying to understand spectroscopy
+we need to use this Atomic data but we
+
+ align:start position:0%
+we need to use this Atomic data but we
+ 
+
+ align:start position:0%
+we need to use this Atomic data but we
+should be cautious of the atomic data
+
+ align:start position:0%
+should be cautious of the atomic data
+ 
+
+ align:start position:0%
+should be cautious of the atomic data
+which is mostly provided by theorists as
+
+ align:start position:0%
+which is mostly provided by theorists as
+ 
+
+ align:start position:0%
+which is mostly provided by theorists as
+well so we should be cautious anyway um
+
+ align:start position:0%
+well so we should be cautious anyway um
+ 
+
+ align:start position:0%
+well so we should be cautious anyway um
+but we should be cautious of this Atomic
+
+ align:start position:0%
+but we should be cautious of this Atomic
+ 
+
+ align:start position:0%
+but we should be cautious of this Atomic
+data because it forms part of our
+
+ align:start position:0%
+data because it forms part of our
+ 
+
+ align:start position:0%
+data because it forms part of our
+interpretation so we may not just have
+
+ align:start position:0%
+interpretation so we may not just have
+ 
+
+ align:start position:0%
+interpretation so we may not just have
+errors due to some of these other things
+
+ align:start position:0%
+errors due to some of these other things
+ 
+
+ align:start position:0%
+errors due to some of these other things
+we may have errors due to how we
+
+ align:start position:0%
+we may have errors due to how we
+ 
+
+ align:start position:0%
+we may have errors due to how we
+interpret this so we should always be on
+
+ align:start position:0%
+interpret this so we should always be on
+ 
+
+ align:start position:0%
+interpret this so we should always be on
+the lookout for like H that looks weird
+
+ align:start position:0%
+the lookout for like H that looks weird
+ 
+
+ align:start position:0%
+the lookout for like H that looks weird
+I wonder why that's going on and see if
+
+ align:start position:0%
+I wonder why that's going on and see if
+ 
+
+ align:start position:0%
+I wonder why that's going on and see if
+we can check whether this is the model
+
+ align:start position:0%
+we can check whether this is the model
+ 
+
+ align:start position:0%
+we can check whether this is the model
+dependent effect or whether it's to do
+
+ align:start position:0%
+dependent effect or whether it's to do
+ 
+
+ align:start position:0%
+dependent effect or whether it's to do
+as our diagnostic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead so in this lecture course we are
+
+ align:start position:0%
+instead so in this lecture course we are
+ 
+
+ align:start position:0%
+instead so in this lecture course we are
+focusing on the principles um Professor
+
+ align:start position:0%
+focusing on the principles um Professor
+ 
+
+ align:start position:0%
+focusing on the principles um Professor
+Hutchinson put this in the title of his
+
+ align:start position:0%
+Hutchinson put this in the title of his
+ 
+
+ align:start position:0%
+Hutchinson put this in the title of his
+book after teaching this course for many
+
+ align:start position:0%
+book after teaching this course for many
+ 
+
+ align:start position:0%
+book after teaching this course for many
+years and he explains what he means by
+
+ align:start position:0%
+years and he explains what he means by
+ 
+
+ align:start position:0%
+years and he explains what he means by
+principles in the introduction and I
+
+ align:start position:0%
+principles in the introduction and I
+ 
+
+ align:start position:0%
+principles in the introduction and I
+think it's very very wise he says that
+
+ align:start position:0%
+think it's very very wise he says that
+ 
+
+ align:start position:0%
+think it's very very wise he says that
+we're not going to focus on the
+
+ align:start position:0%
+we're not going to focus on the
+ 
+
+ align:start position:0%
+we're not going to focus on the
+Practical implementations of Diagnostics
+
+ align:start position:0%
+Practical implementations of Diagnostics
+ 
+
+ align:start position:0%
+Practical implementations of Diagnostics
+those things change over time there's
+
+ align:start position:0%
+those things change over time there's
+ 
+
+ align:start position:0%
+those things change over time there's
+always a new camera that works in a new
+
+ align:start position:0%
+always a new camera that works in a new
+ 
+
+ align:start position:0%
+always a new camera that works in a new
+way that's better um but what doesn't
+
+ align:start position:0%
+way that's better um but what doesn't
+ 
+
+ align:start position:0%
+way that's better um but what doesn't
+change is what a plasma is the equations
+
+ align:start position:0%
+change is what a plasma is the equations
+ 
+
+ align:start position:0%
+change is what a plasma is the equations
+that govern it and some of the
+
+ align:start position:0%
+that govern it and some of the
+ 
+
+ align:start position:0%
+that govern it and some of the
+techniques uh that we can use now
+
+ align:start position:0%
+techniques uh that we can use now
+ 
+
+ align:start position:0%
+techniques uh that we can use now
+there's always new techniques that
+
+ align:start position:0%
+there's always new techniques that
+ 
+
+ align:start position:0%
+there's always new techniques that
+people are coming up with this is a very
+
+ align:start position:0%
+people are coming up with this is a very
+ 
+
+ align:start position:0%
+people are coming up with this is a very
+very Lively field there's a conference
+
+ align:start position:0%
+very Lively field there's a conference
+ 
+
+ align:start position:0%
+very Lively field there's a conference
+every year high temperature plasma
+
+ align:start position:0%
+every year high temperature plasma
+ 
+
+ align:start position:0%
+every year high temperature plasma
+Diagnostics uh which is well worth going
+
+ align:start position:0%
+Diagnostics uh which is well worth going
+ 
+
+ align:start position:0%
+Diagnostics uh which is well worth going
+to where people present new Diagnostics
+
+ align:start position:0%
+to where people present new Diagnostics
+ 
+
+ align:start position:0%
+to where people present new Diagnostics
+new interpretations new ways of
+
+ align:start position:0%
+new interpretations new ways of
+ 
+
+ align:start position:0%
+new interpretations new ways of
+measurement it's very very Dynamic there
+
+ align:start position:0%
+measurement it's very very Dynamic there
+ 
+
+ align:start position:0%
+measurement it's very very Dynamic there
+are lots of different ways to try and
+
+ align:start position:0%
+are lots of different ways to try and
+ 
+
+ align:start position:0%
+are lots of different ways to try and
+measure a plasma there are some
+
+ align:start position:0%
+measure a plasma there are some
+ 
+
+ align:start position:0%
+measure a plasma there are some
+techniques which are very successful but
+
+ align:start position:0%
+techniques which are very successful but
+ 
+
+ align:start position:0%
+techniques which are very successful but
+have only been implemented in one or two
+
+ align:start position:0%
+have only been implemented in one or two
+ 
+
+ align:start position:0%
+have only been implemented in one or two
+institutions just simply because of the
+
+ align:start position:0%
+institutions just simply because of the
+ 
+
+ align:start position:0%
+institutions just simply because of the
+cost that some techniques are very
+
+ align:start position:0%
+cost that some techniques are very
+ 
+
+ align:start position:0%
+cost that some techniques are very
+successful and have only been
+
+ align:start position:0%
+successful and have only been
+ 
+
+ align:start position:0%
+successful and have only been
+implemented because of institutional
+
+ align:start position:0%
+implemented because of institutional
+ 
+
+ align:start position:0%
+implemented because of institutional
+inertia because of the specialized
+
+ align:start position:0%
+inertia because of the specialized
+ 
+
+ align:start position:0%
+inertia because of the specialized
+knowledge to be used so it's always
+
+ align:start position:0%
+knowledge to be used so it's always
+ 
+
+ align:start position:0%
+knowledge to be used so it's always
+worth reading up some papers you never
+
+ align:start position:0%
+worth reading up some papers you never
+ 
+
+ align:start position:0%
+worth reading up some papers you never
+find you'll you'll never know you'll
+
+ align:start position:0%
+find you'll you'll never know you'll
+ 
+
+ align:start position:0%
+find you'll you'll never know you'll
+probably find that the Russians did it
+
+ align:start position:0%
+probably find that the Russians did it
+ 
+
+ align:start position:0%
+probably find that the Russians did it
+back in the 70s is true was almost every
+
+ align:start position:0%
+back in the 70s is true was almost every
+ 
+
+ align:start position:0%
+back in the 70s is true was almost every
+diagnostic you can think of uh and they
+
+ align:start position:0%
+diagnostic you can think of uh and they
+ 
+
+ align:start position:0%
+diagnostic you can think of uh and they
+published it in some obscure Journal so
+
+ align:start position:0%
+published it in some obscure Journal so
+ 
+
+ align:start position:0%
+published it in some obscure Journal so
+it's worth looking out to see whether
+
+ align:start position:0%
+it's worth looking out to see whether
+ 
+
+ align:start position:0%
+it's worth looking out to see whether
+someone's already tried to do what
+
+ align:start position:0%
+someone's already tried to do what
+ 
+
+ align:start position:0%
+someone's already tried to do what
+you're trying to
+
+ align:start position:0%
+you're trying to
+ 
+
+ align:start position:0%
+you're trying to
+do so any questions on this sort of
+
+ align:start position:0%
+do so any questions on this sort of
+ 
+
+ align:start position:0%
+do so any questions on this sort of
+introduction then we're can have an
+
+ align:start position:0%
+introduction then we're can have an
+ 
+
+ align:start position:0%
+introduction then we're can have an
+interactive PA of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah imagine you've got a plasma which
+
+ align:start position:0%
+yeah imagine you've got a plasma which
+ 
+
+ align:start position:0%
+yeah imagine you've got a plasma which
+is glowing right so it's emitting light
+
+ align:start position:0%
+is glowing right so it's emitting light
+ 
+
+ align:start position:0%
+is glowing right so it's emitting light
+and I have a camera and I'm looking at
+
+ align:start position:0%
+and I have a camera and I'm looking at
+ 
+
+ align:start position:0%
+and I have a camera and I'm looking at
+this plasma and the plasma is not
+
+ align:start position:0%
+this plasma and the plasma is not
+ 
+
+ align:start position:0%
+this plasma and the plasma is not
+uniform right maybe the core of it is
+
+ align:start position:0%
+uniform right maybe the core of it is
+ 
+
+ align:start position:0%
+uniform right maybe the core of it is
+very hot like a toac and the edge is
+
+ align:start position:0%
+very hot like a toac and the edge is
+ 
+
+ align:start position:0%
+very hot like a toac and the edge is
+very cold but that means along the line
+
+ align:start position:0%
+very cold but that means along the line
+ 
+
+ align:start position:0%
+very cold but that means along the line
+of sight between the plasma and your
+
+ align:start position:0%
+of sight between the plasma and your
+ 
+
+ align:start position:0%
+of sight between the plasma and your
+camera over there you are adding up the
+
+ align:start position:0%
+camera over there you are adding up the
+ 
+
+ align:start position:0%
+camera over there you are adding up the
+emission from each little blob of plasma
+
+ align:start position:0%
+emission from each little blob of plasma
+ 
+
+ align:start position:0%
+emission from each little blob of plasma
+along your line of sight so you're
+
+ align:start position:0%
+along your line of sight so you're
+ 
+
+ align:start position:0%
+along your line of sight so you're
+adding up emission from some hot bits of
+
+ align:start position:0%
+adding up emission from some hot bits of
+ 
+
+ align:start position:0%
+adding up emission from some hot bits of
+plasma some cold bits of plasma so if
+
+ align:start position:0%
+plasma some cold bits of plasma so if
+ 
+
+ align:start position:0%
+plasma some cold bits of plasma so if
+you look at the Spectrum of that you're
+
+ align:start position:0%
+you look at the Spectrum of that you're
+ 
+
+ align:start position:0%
+you look at the Spectrum of that you're
+going to see lines that correspond to a
+
+ align:start position:0%
+going to see lines that correspond to a
+ 
+
+ align:start position:0%
+going to see lines that correspond to a
+cold plasma and a hot plasma
+
+ align:start position:0%
+cold plasma and a hot plasma
+ 
+
+ align:start position:0%
+cold plasma and a hot plasma
+simultaneously that doesn't make any
+
+ align:start position:0%
+simultaneously that doesn't make any
+ 
+
+ align:start position:0%
+simultaneously that doesn't make any
+sense right so you need to know that
+
+ align:start position:0%
+sense right so you need to know that
+ 
+
+ align:start position:0%
+sense right so you need to know that
+that's happening gets worse than that of
+
+ align:start position:0%
+that's happening gets worse than that of
+ 
+
+ align:start position:0%
+that's happening gets worse than that of
+course different bits of plasma can be
+
+ align:start position:0%
+course different bits of plasma can be
+ 
+
+ align:start position:0%
+course different bits of plasma can be
+absorbing as well and so you may have
+
+ align:start position:0%
+absorbing as well and so you may have
+ 
+
+ align:start position:0%
+absorbing as well and so you may have
+attenuation of some of those lines as it
+
+ align:start position:0%
+attenuation of some of those lines as it
+ 
+
+ align:start position:0%
+attenuation of some of those lines as it
+goes through this becomes radiation
+
+ align:start position:0%
+goes through this becomes radiation
+ 
+
+ align:start position:0%
+goes through this becomes radiation
+transport and it's like a whole mess
+
+ align:start position:0%
+transport and it's like a whole mess
+ 
+
+ align:start position:0%
+transport and it's like a whole mess
+right so that's one simple example there
+
+ align:start position:0%
+right so that's one simple example there
+ 
+
+ align:start position:0%
+right so that's one simple example there
+that just as you look through a plasma
+
+ align:start position:0%
+that just as you look through a plasma
+ 
+
+ align:start position:0%
+that just as you look through a plasma
+you're going to get very different
+
+ align:start position:0%
+you're going to get very different
+ 
+
+ align:start position:0%
+you're going to get very different
+properties all contributing to your
+
+ align:start position:0%
+properties all contributing to your
+ 
+
+ align:start position:0%
+properties all contributing to your
+final measurement this isn't the case of
+
+ align:start position:0%
+final measurement this isn't the case of
+ 
+
+ align:start position:0%
+final measurement this isn't the case of
+something that's very local like a
+
+ align:start position:0%
+something that's very local like a
+ 
+
+ align:start position:0%
+something that's very local like a
+langere probe or a B dot probe or
+
+ align:start position:0%
+langere probe or a B dot probe or
+ 
+
+ align:start position:0%
+langere probe or a B dot probe or
+Thompson scattering but it's very much
+
+ align:start position:0%
+Thompson scattering but it's very much
+ 
+
+ align:start position:0%
+Thompson scattering but it's very much
+the case for I would say about half the
+
+ align:start position:0%
+the case for I would say about half the
+ 
+
+ align:start position:0%
+the case for I would say about half the
+Diagnostics we going to talk about in
+
+ align:start position:0%
+Diagnostics we going to talk about in
+ 
+
+ align:start position:0%
+Diagnostics we going to talk about in
+this course they're going to suffer from
+
+ align:start position:0%
+this course they're going to suffer from
+ 
+
+ align:start position:0%
+this course they're going to suffer from
+light integration and the reason is
+
+ align:start position:0%
+light integration and the reason is
+ 
+
+ align:start position:0%
+light integration and the reason is
+plasma is
+
+ align:start position:0%
+plasma is
+ 
+
+ align:start position:0%
+plasma is
+electromagnetic light is electromagnetic
+
+ align:start position:0%
+electromagnetic light is electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic light is electromagnetic
+so we use light to prob plasmas and
+
+ align:start position:0%
+so we use light to prob plasmas and
+ 
+
+ align:start position:0%
+so we use light to prob plasmas and
+light has this problem of line
+
+ align:start position:0%
+light has this problem of line
+ 
+
+ align:start position:0%
+light has this problem of line
+integration so it almost always comes up
+
+ align:start position:0%
+integration so it almost always comes up
+ 
+
+ align:start position:0%
+integration so it almost always comes up
+no matter what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question how's it going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columbia good thumbs up all right
+
+ align:start position:0%
+Columbia good thumbs up all right
+ 
+
+ align:start position:0%
+Columbia good thumbs up all right
+so what I'd like to do I found when I
+
+ align:start position:0%
+so what I'd like to do I found when I
+ 
+
+ align:start position:0%
+so what I'd like to do I found when I
+taught this class before there's a huge
+
+ align:start position:0%
+taught this class before there's a huge
+ 
+
+ align:start position:0%
+taught this class before there's a huge
+array of people who take it which is
+
+ align:start position:0%
+array of people who take it which is
+ 
+
+ align:start position:0%
+array of people who take it which is
+super exciting and they all work on very
+
+ align:start position:0%
+super exciting and they all work on very
+ 
+
+ align:start position:0%
+super exciting and they all work on very
+different things and this is my
+
+ align:start position:0%
+different things and this is my
+ 
+
+ align:start position:0%
+different things and this is my
+opportunity to find out some of the
+
+ align:start position:0%
+opportunity to find out some of the
+ 
+
+ align:start position:0%
+opportunity to find out some of the
+stuff you work on as we play pin your
+
+ align:start position:0%
+stuff you work on as we play pin your
+ 
+
+ align:start position:0%
+stuff you work on as we play pin your
+plasma to the board so as you can all
+
+ align:start position:0%
+plasma to the board so as you can all
+ 
+
+ align:start position:0%
+plasma to the board so as you can all
+see we have a temperature scale on the
+
+ align:start position:0%
+see we have a temperature scale on the
+ 
+
+ align:start position:0%
+see we have a temperature scale on the
+side here that goes from 0.1 evv and
+
+ align:start position:0%
+side here that goes from 0.1 evv and
+ 
+
+ align:start position:0%
+side here that goes from 0.1 evv and
+yeah you can still get plasmas there up
+
+ align:start position:0%
+yeah you can still get plasmas there up
+ 
+
+ align:start position:0%
+yeah you can still get plasmas there up
+to 10 KV and above you know whatever um
+
+ align:start position:0%
+to 10 KV and above you know whatever um
+ 
+
+ align:start position:0%
+to 10 KV and above you know whatever um
+and then we've got densities here if you
+
+ align:start position:0%
+and then we've got densities here if you
+ 
+
+ align:start position:0%
+and then we've got densities here if you
+thought that was logarithmic they go
+
+ align:start position:0%
+thought that was logarithmic they go
+ 
+
+ align:start position:0%
+thought that was logarithmic they go
+from 10th plus
+
+ align:start position:0%
+from 10th plus
+ 
+
+ align:start position:0%
+from 10th plus
+16 particles per cubic meter to 10th
+
+ align:start position:0%
+16 particles per cubic meter to 10th
+ 
+
+ align:start position:0%
+16 particles per cubic meter to 10th
+plus 32 particles per cubic meter here
+
+ align:start position:0%
+plus 32 particles per cubic meter here
+ 
+
+ align:start position:0%
+plus 32 particles per cubic meter here
+so 16 orders of magnitude and yet we're
+
+ align:start position:0%
+so 16 orders of magnitude and yet we're
+ 
+
+ align:start position:0%
+so 16 orders of magnitude and yet we're
+all sitting in the same room trying to
+
+ align:start position:0%
+all sitting in the same room trying to
+ 
+
+ align:start position:0%
+all sitting in the same room trying to
+learn the same stuff that's one of the
+
+ align:start position:0%
+learn the same stuff that's one of the
+ 
+
+ align:start position:0%
+learn the same stuff that's one of the
+reasons why this topic is very
+
+ align:start position:0%
+reasons why this topic is very
+ 
+
+ align:start position:0%
+reasons why this topic is very
+fascinating and also quite hard to teach
+
+ align:start position:0%
+fascinating and also quite hard to teach
+ 
+
+ align:start position:0%
+fascinating and also quite hard to teach
+at times I've also trying to get the
+
+ align:start position:0%
+at times I've also trying to get the
+ 
+
+ align:start position:0%
+at times I've also trying to get the
+third dimension to you guys uh we're
+
+ align:start position:0%
+third dimension to you guys uh we're
+ 
+
+ align:start position:0%
+third dimension to you guys uh we're
+going to be using Color uh and we're
+
+ align:start position:0%
+going to be using Color uh and we're
+ 
+
+ align:start position:0%
+going to be using Color uh and we're
+looking at the magnetic field here so
+
+ align:start position:0%
+looking at the magnetic field here so
+ 
+
+ align:start position:0%
+looking at the magnetic field here so
+I've got a magnetic field going from 0
+
+ align:start position:0%
+I've got a magnetic field going from 0
+ 
+
+ align:start position:0%
+I've got a magnetic field going from 0
+point not one which I think most of us
+
+ align:start position:0%
+point not one which I think most of us
+ 
+
+ align:start position:0%
+point not one which I think most of us
+agree is basically zero um all the way
+
+ align:start position:0%
+agree is basically zero um all the way
+ 
+
+ align:start position:0%
+agree is basically zero um all the way
+up to like 100 Tesla or so which I know
+
+ align:start position:0%
+up to like 100 Tesla or so which I know
+ 
+
+ align:start position:0%
+up to like 100 Tesla or so which I know
+some places where you get 100 Tesla in
+
+ align:start position:0%
+some places where you get 100 Tesla in
+ 
+
+ align:start position:0%
+some places where you get 100 Tesla in
+pass physics I don't know whether anyone
+
+ align:start position:0%
+pass physics I don't know whether anyone
+ 
+
+ align:start position:0%
+pass physics I don't know whether anyone
+working here uh works on those but the
+
+ align:start position:0%
+working here uh works on those but the
+ 
+
+ align:start position:0%
+working here uh works on those but the
+idea is um uh you're either going to
+
+ align:start position:0%
+idea is um uh you're either going to
+ 
+
+ align:start position:0%
+idea is um uh you're either going to
+volunteer or I'm going to start pointing
+
+ align:start position:0%
+volunteer or I'm going to start pointing
+ 
+
+ align:start position:0%
+volunteer or I'm going to start pointing
+and you're going to come up if you're
+
+ align:start position:0%
+and you're going to come up if you're
+ 
+
+ align:start position:0%
+and you're going to come up if you're
+here in the room or you're going to tell
+
+ align:start position:0%
+here in the room or you're going to tell
+ 
+
+ align:start position:0%
+here in the room or you're going to tell
+me if you're over there in Columbia uh
+
+ align:start position:0%
+me if you're over there in Columbia uh
+ 
+
+ align:start position:0%
+me if you're over there in Columbia uh
+where your plasma falls on this board so
+
+ align:start position:0%
+where your plasma falls on this board so
+ 
+
+ align:start position:0%
+where your plasma falls on this board so
+we'll just draw little circles so say
+
+ align:start position:0%
+we'll just draw little circles so say
+ 
+
+ align:start position:0%
+we'll just draw little circles so say
+you got a plasma that is 100 Tesla and
+
+ align:start position:0%
+you got a plasma that is 100 Tesla and
+ 
+
+ align:start position:0%
+you got a plasma that is 100 Tesla and
+it lives up in this corner here you
+
+ align:start position:0%
+it lives up in this corner here you
+ 
+
+ align:start position:0%
+it lives up in this corner here you
+would just draw a little blob being like
+
+ align:start position:0%
+would just draw a little blob being like
+ 
+
+ align:start position:0%
+would just draw a little blob being like
+that's my plasma you put a number in and
+
+ align:start position:0%
+that's my plasma you put a number in and
+ 
+
+ align:start position:0%
+that's my plasma you put a number in and
+by the side of it you maybe write
+
+ align:start position:0%
+by the side of it you maybe write
+ 
+
+ align:start position:0%
+by the side of it you maybe write
+something about your plasma maybe it's a
+
+ align:start position:0%
+something about your plasma maybe it's a
+ 
+
+ align:start position:0%
+something about your plasma maybe it's a
+magnetized ICF implosion on nith and
+
+ align:start position:0%
+magnetized ICF implosion on nith and
+ 
+
+ align:start position:0%
+magnetized ICF implosion on nith and
+you'd maybe dot down a couple of
+
+ align:start position:0%
+you'd maybe dot down a couple of
+ 
+
+ align:start position:0%
+you'd maybe dot down a couple of
+Diagnostics that you work on if you
+
+ align:start position:0%
+Diagnostics that you work on if you
+ 
+
+ align:start position:0%
+Diagnostics that you work on if you
+don't work on any diagnostics at the
+
+ align:start position:0%
+don't work on any diagnostics at the
+ 
+
+ align:start position:0%
+don't work on any diagnostics at the
+moment that's fine maybe just mention a
+
+ align:start position:0%
+moment that's fine maybe just mention a
+ 
+
+ align:start position:0%
+moment that's fine maybe just mention a
+diagnostic you know is used and you
+
+ align:start position:0%
+diagnostic you know is used and you
+ 
+
+ align:start position:0%
+diagnostic you know is used and you
+don't have to be exhausted if you
+
+ align:start position:0%
+don't have to be exhausted if you
+ 
+
+ align:start position:0%
+don't have to be exhausted if you
+mention the toac you don't have to list
+
+ align:start position:0%
+mention the toac you don't have to list
+ 
+
+ align:start position:0%
+mention the toac you don't have to list
+every diagnostic on the toat just the
+
+ align:start position:0%
+every diagnostic on the toat just the
+ 
+
+ align:start position:0%
+every diagnostic on the toat just the
+one that you work on and let someone
+
+ align:start position:0%
+one that you work on and let someone
+ 
+
+ align:start position:0%
+one that you work on and let someone
+else have a go at mentioning some of the
+
+ align:start position:0%
+else have a go at mentioning some of the
+ 
+
+ align:start position:0%
+else have a go at mentioning some of the
+other on so I'm going to erase that now
+
+ align:start position:0%
+other on so I'm going to erase that now
+ 
+
+ align:start position:0%
+other on so I'm going to erase that now
+because I I think that's slightly
+
+ align:start position:0%
+because I I think that's slightly
+ 
+
+ align:start position:0%
+because I I think that's slightly
+optimistic even for a magnetized ITF
+
+ align:start position:0%
+optimistic even for a magnetized ITF
+ 
+
+ align:start position:0%
+optimistic even for a magnetized ITF
+shot and I now going to turn around and
+
+ align:start position:0%
+shot and I now going to turn around and
+ 
+
+ align:start position:0%
+shot and I now going to turn around and
+see someone with their hand up as the
+
+ align:start position:0%
+see someone with their hand up as the
+ 
+
+ align:start position:0%
+see someone with their hand up as the
+first willing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volunteer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good as you're walking up what's your
+
+ align:start position:0%
+good as you're walking up what's your
+ 
+
+ align:start position:0%
+good as you're walking up what's your
+name and your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+department
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um Can the folks at Columbia hear I'm
+
+ align:start position:0%
+um Can the folks at Columbia hear I'm
+ 
+
+ align:start position:0%
+um Can the folks at Columbia hear I'm
+okay if I sort of stand nearby or is it
+
+ align:start position:0%
+okay if I sort of stand nearby or is it
+ 
+
+ align:start position:0%
+okay if I sort of stand nearby or is it
+very quiet oh de okay you should have
+
+ align:start position:0%
+very quiet oh de okay you should have
+ 
+
+ align:start position:0%
+very quiet oh de okay you should have
+this okay hello everybody I'm Vince I
+
+ align:start position:0%
+this okay hello everybody I'm Vince I
+ 
+
+ align:start position:0%
+this okay hello everybody I'm Vince I
+work with uh Nathan Howard and Pablo
+
+ align:start position:0%
+work with uh Nathan Howard and Pablo
+ 
+
+ align:start position:0%
+work with uh Nathan Howard and Pablo
+Rodriguez Hernandez on modeling uh
+
+ align:start position:0%
+Rodriguez Hernandez on modeling uh
+ 
+
+ align:start position:0%
+Rodriguez Hernandez on modeling uh
+turbulent transport in the spark reactor
+
+ align:start position:0%
+turbulent transport in the spark reactor
+ 
+
+ align:start position:0%
+turbulent transport in the spark reactor
+I don't remember off the top of my head
+
+ align:start position:0%
+I don't remember off the top of my head
+ 
+
+ align:start position:0%
+I don't remember off the top of my head
+the particle density I think it's in
+
+ align:start position:0%
+the particle density I think it's in
+ 
+
+ align:start position:0%
+the particle density I think it's in
+this range um just a circle you said or
+
+ align:start position:0%
+this range um just a circle you said or
+ 
+
+ align:start position:0%
+this range um just a circle you said or
+like yeah where's my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little I have 10 20 10 okay 10 20 yeah
+
+ align:start position:0%
+little I have 10 20 10 okay 10 20 yeah
+ 
+
+ align:start position:0%
+little I have 10 20 10 okay 10 20 yeah
+okay yeah cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh cool I put a little number on it like
+
+ align:start position:0%
+uh cool I put a little number on it like
+ 
+
+ align:start position:0%
+uh cool I put a little number on it like
+one and then just right on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side yeah I should not have made this so
+
+ align:start position:0%
+side yeah I should not have made this so
+ 
+
+ align:start position:0%
+side yeah I should not have made this so
+High um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's see
+
+ align:start position:0%
+uh let's see
+ 
+
+ align:start position:0%
+uh let's see
+I I don't work with any diagnostics at
+
+ align:start position:0%
+I I don't work with any diagnostics at
+ 
+
+ align:start position:0%
+I I don't work with any diagnostics at
+the moment I uh work with um heat flux
+
+ align:start position:0%
+the moment I uh work with um heat flux
+ 
+
+ align:start position:0%
+the moment I uh work with um heat flux
+data okay uh that's generated uh via
+
+ align:start position:0%
+data okay uh that's generated uh via
+ 
+
+ align:start position:0%
+data okay uh that's generated uh via
+um uh via simulation code like tglf and
+
+ align:start position:0%
+um uh via simulation code like tglf and
+ 
+
+ align:start position:0%
+um uh via simulation code like tglf and
+uh and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gyro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and anyone else
+
+ align:start position:0%
+um and anyone else
+ 
+
+ align:start position:0%
+um and anyone else
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't let's go for that like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a how you smell it all right next
+
+ align:start position:0%
+a how you smell it all right next
+ 
+
+ align:start position:0%
+a how you smell it all right next
+volunteer let's have one from Columbia
+
+ align:start position:0%
+volunteer let's have one from Columbia
+ 
+
+ align:start position:0%
+volunteer let's have one from Columbia
+please hey
+
+ align:start position:0%
+please hey
+ 
+
+ align:start position:0%
+please hey
+Nigel hello I work with plasmas that are
+
+ align:start position:0%
+Nigel hello I work with plasmas that are
+ 
+
+ align:start position:0%
+Nigel hello I work with plasmas that are
+10 of the 19 inity about 100 EV
+
+ align:start position:0%
+10 of the 19 inity about 100 EV
+ 
+
+ align:start position:0%
+10 of the 19 inity about 100 EV
+uh with a magnetic field of
+
+ align:start position:0%
+uh with a magnetic field of
+ 
+
+ align:start position:0%
+uh with a magnetic field of
+0.1 on that order of magnitude yeah so
+
+ align:start position:0%
+0.1 on that order of magnitude yeah so
+ 
+
+ align:start position:0%
+0.1 on that order of magnitude yeah so
+what was that t 19 and 100 EV yes so
+
+ align:start position:0%
+what was that t 19 and 100 EV yes so
+ 
+
+ align:start position:0%
+what was that t 19 and 100 EV yes so
+kind of about here
+
+ align:start position:0%
+kind of about here
+ 
+
+ align:start position:0%
+kind of about here
+yeah okay and so what's this plasma this
+
+ align:start position:0%
+yeah okay and so what's this plasma this
+ 
+
+ align:start position:0%
+yeah okay and so what's this plasma this
+is that's the hbt plasma that's the tokc
+
+ align:start position:0%
+is that's the hbt plasma that's the tokc
+ 
+
+ align:start position:0%
+is that's the hbt plasma that's the tokc
+that we have at Columbia cool uh and I
+
+ align:start position:0%
+that we have at Columbia cool uh and I
+ 
+
+ align:start position:0%
+that we have at Columbia cool uh and I
+work with Lang Mir probas mirov coils
+
+ align:start position:0%
+work with Lang Mir probas mirov coils
+ 
+
+ align:start position:0%
+work with Lang Mir probas mirov coils
+and tangential extreme electr U extreme
+
+ align:start position:0%
+and tangential extreme electr U extreme
+ 
+
+ align:start position:0%
+and tangential extreme electr U extreme
+ultraviolet light so TV uh okay
+
+ align:start position:0%
+ultraviolet light so TV uh okay
+ 
+
+ align:start position:0%
+ultraviolet light so TV uh okay
+okay and mov which I'm just going to
+
+ align:start position:0%
+okay and mov which I'm just going to
+ 
+
+ align:start position:0%
+okay and mov which I'm just going to
+write as B dot sort of B dots yeah great
+
+ align:start position:0%
+write as B dot sort of B dots yeah great
+ 
+
+ align:start position:0%
+write as B dot sort of B dots yeah great
+volunteer from in the
+
+ align:start position:0%
+volunteer from in the
+ 
+
+ align:start position:0%
+volunteer from in the
+room come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up I can have both of these working at
+
+ align:start position:0%
+up I can have both of these working at
+ 
+
+ align:start position:0%
+up I can have both of these working at
+the same time I think that's there you
+
+ align:start position:0%
+the same time I think that's there you
+ 
+
+ align:start position:0%
+the same time I think that's there you
+go uh hi my name is Amelia I do some
+
+ align:start position:0%
+go uh hi my name is Amelia I do some
+ 
+
+ align:start position:0%
+go uh hi my name is Amelia I do some
+work with d3d on a linman alpha
+
+ align:start position:0%
+work with d3d on a linman alpha
+ 
+
+ align:start position:0%
+work with d3d on a linman alpha
+diagnostic that's like roughly year is
+
+ align:start position:0%
+diagnostic that's like roughly year is
+ 
+
+ align:start position:0%
+diagnostic that's like roughly year is
+in in operating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space that low I think it's like a
+
+ align:start position:0%
+space that low I think it's like a
+ 
+
+ align:start position:0%
+space that low I think it's like a
+little higher it's like four to five
+
+ align:start position:0%
+little higher it's like four to five
+ 
+
+ align:start position:0%
+little higher it's like four to five
+often was good enough for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me and then linan Alpha is a spectral
+
+ align:start position:0%
+me and then linan Alpha is a spectral
+ 
+
+ align:start position:0%
+me and then linan Alpha is a spectral
+line of hydrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great thank you got a volunteer from
+
+ align:start position:0%
+great thank you got a volunteer from
+ 
+
+ align:start position:0%
+great thank you got a volunteer from
+Columbia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh do I need raise my hand or can I
+
+ align:start position:0%
+yeah oh do I need raise my hand or can I
+ 
+
+ align:start position:0%
+yeah oh do I need raise my hand or can I
+just oh yeah please stop yeah please go
+
+ align:start position:0%
+just oh yeah please stop yeah please go
+ 
+
+ align:start position:0%
+just oh yeah please stop yeah please go
+for it oh hi I'm uh Jacob Reitz I'm at
+
+ align:start position:0%
+for it oh hi I'm uh Jacob Reitz I'm at
+ 
+
+ align:start position:0%
+for it oh hi I'm uh Jacob Reitz I'm at
+Columbia I just got done working with uh
+
+ align:start position:0%
+Columbia I just got done working with uh
+ 
+
+ align:start position:0%
+Columbia I just got done working with uh
+some d3d plasmas as well nice um roughly
+
+ align:start position:0%
+some d3d plasmas as well nice um roughly
+ 
+
+ align:start position:0%
+some d3d plasmas as well nice um roughly
+the same area I'd say yeah uh and I was
+
+ align:start position:0%
+the same area I'd say yeah uh and I was
+ 
+
+ align:start position:0%
+the same area I'd say yeah uh and I was
+working with uh B
+
+ align:start position:0%
+working with uh B
+ 
+
+ align:start position:0%
+working with uh B
+bomet cool what the bomet measure uh
+
+ align:start position:0%
+bomet cool what the bomet measure uh
+ 
+
+ align:start position:0%
+bomet cool what the bomet measure uh
+bomet were measuring radiation fluxes
+
+ align:start position:0%
+bomet were measuring radiation fluxes
+ 
+
+ align:start position:0%
+bomet were measuring radiation fluxes
+most heat loads and uh it's fast bmers
+
+ align:start position:0%
+most heat loads and uh it's fast bmers
+ 
+
+ align:start position:0%
+most heat loads and uh it's fast bmers
+so they're AXS awesome thank you anyone
+
+ align:start position:0%
+so they're AXS awesome thank you anyone
+ 
+
+ align:start position:0%
+so they're AXS awesome thank you anyone
+in the room come on one of the ni people
+
+ align:start position:0%
+in the room come on one of the ni people
+ 
+
+ align:start position:0%
+in the room come on one of the ni people
+come on ICF we need to we need to push
+
+ align:start position:0%
+come on ICF we need to we need to push
+ 
+
+ align:start position:0%
+come on ICF we need to we need to push
+up into this corner is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shocking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi I'm
+
+ align:start position:0%
+hi I'm
+ 
+
+ align:start position:0%
+hi I'm
+Chris um so I'm M uh hdp for confinement
+
+ align:start position:0%
+Chris um so I'm M uh hdp for confinement
+ 
+
+ align:start position:0%
+Chris um so I'm M uh hdp for confinement
+fusion and our temperatures are over
+
+ align:start position:0%
+fusion and our temperatures are over
+ 
+
+ align:start position:0%
+fusion and our temperatures are over
+here three to 10 KV I'm gonna say okay
+
+ align:start position:0%
+here three to 10 KV I'm gonna say okay
+ 
+
+ align:start position:0%
+here three to 10 KV I'm gonna say okay
+and then I work in units of row
+
+ align:start position:0%
+and then I work in units of row
+ 
+
+ align:start position:0%
+and then I work in units of row
+R so 300 to
+
+ align:start position:0%
+R so 300 to
+ 
+
+ align:start position:0%
+R so 300 to
+600 okay okay
+
+ align:start position:0%
+600 okay okay
+ 
+
+ align:start position:0%
+600 okay okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so and that's where I don't operate
+
+ align:start position:0%
+so and that's where I don't operate
+ 
+
+ align:start position:0%
+so and that's where I don't operate
+magnetic fields but I'm gonna say Skyler
+
+ align:start position:0%
+magnetic fields but I'm gonna say Skyler
+ 
+
+ align:start position:0%
+magnetic fields but I'm gonna say Skyler
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+10 100 Tesla
+
+ align:start position:0%
+10 100 Tesla
+ 
+
+ align:start position:0%
+10 100 Tesla
+okay yeah no I know it is you don't stop
+
+ align:start position:0%
+okay yeah no I know it is you don't stop
+ 
+
+ align:start position:0%
+okay yeah no I know it is you don't stop
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+n and then what are we up to four so for
+
+ align:start position:0%
+n and then what are we up to four so for
+ 
+
+ align:start position:0%
+n and then what are we up to four so for
+mine I'll put um Neutron
+
+ align:start position:0%
+mine I'll put um Neutron
+ 
+
+ align:start position:0%
+mine I'll put um Neutron
+spectrometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neon um what about you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys
+
+ align:start position:0%
+guys
+ 
+
+ align:start position:0%
+guys
+no good
+
+ align:start position:0%
+no good
+ 
+
+ align:start position:0%
+no good
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got cool all right we have anyone else
+
+ align:start position:0%
+got cool all right we have anyone else
+ 
+
+ align:start position:0%
+got cool all right we have anyone else
+from Columbia willing to
+
+ align:start position:0%
+from Columbia willing to
+ 
+
+ align:start position:0%
+from Columbia willing to
+volunteer yeah oh I also do oh I hope
+
+ align:start position:0%
+volunteer yeah oh I also do oh I hope
+ 
+
+ align:start position:0%
+volunteer yeah oh I also do oh I hope
+you can hear me I also do d3d
+
+ align:start position:0%
+you can hear me I also do d3d
+ 
+
+ align:start position:0%
+you can hear me I also do d3d
+experiments particularly Runway electron
+
+ align:start position:0%
+experiments particularly Runway electron
+ 
+
+ align:start position:0%
+experiments particularly Runway electron
+experiments and we use a gam imager and
+
+ align:start position:0%
+experiments and we use a gam imager and
+ 
+
+ align:start position:0%
+experiments and we use a gam imager and
+also some hard x-ray
+
+ align:start position:0%
+also some hard x-ray
+ 
+
+ align:start position:0%
+also some hard x-ray
+detectors so their scintillators which
+
+ align:start position:0%
+detectors so their scintillators which
+ 
+
+ align:start position:0%
+detectors so their scintillators which
+register hard xrays incident on cool I'm
+
+ align:start position:0%
+register hard xrays incident on cool I'm
+ 
+
+ align:start position:0%
+register hard xrays incident on cool I'm
+going to put that on gamma rays and hard
+
+ align:start position:0%
+going to put that on gamma rays and hard
+ 
+
+ align:start position:0%
+going to put that on gamma rays and hard
+x-rays that's good stuff all right
+
+ align:start position:0%
+x-rays that's good stuff all right
+ 
+
+ align:start position:0%
+x-rays that's good stuff all right
+anyone in the room yeah go for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I'm Stan I'm in NSE I also work on
+
+ align:start position:0%
+it I'm Stan I'm in NSE I also work on
+ 
+
+ align:start position:0%
+it I'm Stan I'm in NSE I also work on
+spark and I do soft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gray um so the ones I'm working on are
+
+ align:start position:0%
+gray um so the ones I'm working on are
+ 
+
+ align:start position:0%
+gray um so the ones I'm working on are
+diamond based um because specifically
+
+ align:start position:0%
+diamond based um because specifically
+ 
+
+ align:start position:0%
+diamond based um because specifically
+for spark traditional silicone diode
+
+ align:start position:0%
+for spark traditional silicone diode
+ 
+
+ align:start position:0%
+for spark traditional silicone diode
+would die from the neutrons um so we're
+
+ align:start position:0%
+would die from the neutrons um so we're
+ 
+
+ align:start position:0%
+would die from the neutrons um so we're
+using a diamond Bas Tech instead and
+
+ align:start position:0%
+using a diamond Bas Tech instead and
+ 
+
+ align:start position:0%
+using a diamond Bas Tech instead and
+they're in very early stage development
+
+ align:start position:0%
+they're in very early stage development
+ 
+
+ align:start position:0%
+they're in very early stage development
+Although our collaborators in Rome have
+
+ align:start position:0%
+Although our collaborators in Rome have
+ 
+
+ align:start position:0%
+Although our collaborators in Rome have
+had some promising results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah hi I'm niol um I'm working on Arc
+
+ align:start position:0%
+yeah hi I'm niol um I'm working on Arc
+ 
+
+ align:start position:0%
+yeah hi I'm niol um I'm working on Arc
+stuff right now but I wanted to mention
+
+ align:start position:0%
+stuff right now but I wanted to mention
+ 
+
+ align:start position:0%
+stuff right now but I wanted to mention
+what I was working for my master back in
+
+ align:start position:0%
+what I was working for my master back in
+ 
+
+ align:start position:0%
+what I was working for my master back in
+Serbia I was working with sudo spark
+
+ align:start position:0%
+Serbia I was working with sudo spark
+ 
+
+ align:start position:0%
+Serbia I was working with sudo spark
+discharges which were like ionized gases
+
+ align:start position:0%
+discharges which were like ionized gases
+ 
+
+ align:start position:0%
+discharges which were like ionized gases
+more than actual plasmas there were
+
+ align:start position:0%
+more than actual plasmas there were
+ 
+
+ align:start position:0%
+more than actual plasmas there were
+somewhere like this region
+
+ align:start position:0%
+somewhere like this region
+ 
+
+ align:start position:0%
+somewhere like this region
+is here what number is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now and what I was doing with those was
+
+ align:start position:0%
+now and what I was doing with those was
+ 
+
+ align:start position:0%
+now and what I was doing with those was
+vacuum ultraviolet
+
+ align:start position:0%
+vacuum ultraviolet
+ 
+
+ align:start position:0%
+vacuum ultraviolet
+spectroscopy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those were like not M but yeah all
+
+ align:start position:0%
+and those were like not M but yeah all
+ 
+
+ align:start position:0%
+and those were like not M but yeah all
+right thank you anyone from
+
+ align:start position:0%
+right thank you anyone from
+ 
+
+ align:start position:0%
+right thank you anyone from
+Columbia um I can say one uh so CNT is
+
+ align:start position:0%
+Columbia um I can say one uh so CNT is
+ 
+
+ align:start position:0%
+Columbia um I can say one uh so CNT is
+no longer operational uh but I am
+
+ align:start position:0%
+no longer operational uh but I am
+ 
+
+ align:start position:0%
+no longer operational uh but I am
+working on upgrading it and the
+
+ align:start position:0%
+working on upgrading it and the
+ 
+
+ align:start position:0%
+working on upgrading it and the
+operational density was of the order of
+
+ align:start position:0%
+operational density was of the order of
+ 
+
+ align:start position:0%
+operational density was of the order of
+10 to the
+
+ align:start position:0%
+10 to the
+ 
+
+ align:start position:0%
+10 to the
+16th yeah yeah and magnetic field 06
+
+ align:start position:0%
+16th yeah yeah and magnetic field 06
+ 
+
+ align:start position:0%
+16th yeah yeah and magnetic field 06
+Tesla I think temperature order
+
+ align:start position:0%
+Tesla I think temperature order
+ 
+
+ align:start position:0%
+Tesla I think temperature order
+of an EV I'm not too sure okay so kind
+
+ align:start position:0%
+of an EV I'm not too sure okay so kind
+ 
+
+ align:start position:0%
+of an EV I'm not too sure okay so kind
+of like here yeah probably low yeah and
+
+ align:start position:0%
+of like here yeah probably low yeah and
+ 
+
+ align:start position:0%
+of like here yeah probably low yeah and
+you said 06 I'm gonna call that 0.1
+
+ align:start position:0%
+you said 06 I'm gonna call that 0.1
+ 
+
+ align:start position:0%
+you said 06 I'm gonna call that 0.1
+we'll round up yeah sounds good sounds
+
+ align:start position:0%
+we'll round up yeah sounds good sounds
+ 
+
+ align:start position:0%
+we'll round up yeah sounds good sounds
+good cool okay so this is CNT Plus+ or
+
+ align:start position:0%
+good cool okay so this is CNT Plus+ or
+ 
+
+ align:start position:0%
+good cool okay so this is CNT Plus+ or
+whatever the new name will be exactly
+
+ align:start position:0%
+whatever the new name will be exactly
+ 
+
+ align:start position:0%
+whatever the new name will be exactly
+exactly exactly cool and what are you
+
+ align:start position:0%
+exactly exactly cool and what are you
+ 
+
+ align:start position:0%
+exactly exactly cool and what are you
+going to be diagnosing it with um so
+
+ align:start position:0%
+going to be diagnosing it with um so
+ 
+
+ align:start position:0%
+going to be diagnosing it with um so
+they had a Electron Beam that also was
+
+ align:start position:0%
+they had a Electron Beam that also was
+ 
+
+ align:start position:0%
+they had a Electron Beam that also was
+paired with a fluorescent Rod uh to M
+
+ align:start position:0%
+paired with a fluorescent Rod uh to M
+ 
+
+ align:start position:0%
+paired with a fluorescent Rod uh to M
+the to map the magnetic field surfaces
+
+ align:start position:0%
+the to map the magnetic field surfaces
+ 
+
+ align:start position:0%
+the to map the magnetic field surfaces
+nice yeah I saw them doing that
+
+ align:start position:0%
+nice yeah I saw them doing that
+ 
+
+ align:start position:0%
+nice yeah I saw them doing that
+technique on w7x as well it's really
+
+ align:start position:0%
+technique on w7x as well it's really
+ 
+
+ align:start position:0%
+technique on w7x as well it's really
+cool nice
+
+ align:start position:0%
+cool nice
+ 
+
+ align:start position:0%
+cool nice
+yeah all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah hi I'm Lany so I actually work in
+
+ align:start position:0%
+yeah hi I'm Lany so I actually work in
+ 
+
+ align:start position:0%
+yeah hi I'm Lany so I actually work in
+the Aerospace department and I work with
+
+ align:start position:0%
+the Aerospace department and I work with
+ 
+
+ align:start position:0%
+the Aerospace department and I work with
+non-equilibrium plasmas so I actually am
+
+ align:start position:0%
+non-equilibrium plasmas so I actually am
+ 
+
+ align:start position:0%
+non-equilibrium plasmas so I actually am
+in we go from low we work from low
+
+ align:start position:0%
+in we go from low we work from low
+ 
+
+ align:start position:0%
+in we go from low we work from low
+pressure to atmospheric pressure um in
+
+ align:start position:0%
+pressure to atmospheric pressure um in
+ 
+
+ align:start position:0%
+pressure to atmospheric pressure um in
+this general area but in a non-thermal
+
+ align:start position:0%
+this general area but in a non-thermal
+ 
+
+ align:start position:0%
+this general area but in a non-thermal
+plasma our electrons are closer to the
+
+ align:start position:0%
+plasma our electrons are closer to the
+ 
+
+ align:start position:0%
+plasma our electrons are closer to the
+10 e you know anywhere from one to 10 EV
+
+ align:start position:0%
+10 e you know anywhere from one to 10 EV
+ 
+
+ align:start position:0%
+10 e you know anywhere from one to 10 EV
+and our um gas temperature is much lower
+
+ align:start position:0%
+and our um gas temperature is much lower
+ 
+
+ align:start position:0%
+and our um gas temperature is much lower
+so kind of in that region right
+
+ align:start position:0%
+so kind of in that region right
+ 
+
+ align:start position:0%
+so kind of in that region right
+there and then we typically use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+umal we typically use um OES Optical
+
+ align:start position:0%
+umal we typically use um OES Optical
+ 
+
+ align:start position:0%
+umal we typically use um OES Optical
+emission spectroscopy or ftir for a um
+
+ align:start position:0%
+emission spectroscopy or ftir for a um
+ 
+
+ align:start position:0%
+emission spectroscopy or ftir for a um
+transform infrared
+
+ align:start position:0%
+transform infrared
+ 
+
+ align:start position:0%
+transform infrared
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+resonance thank you yeah so I I remember
+
+ align:start position:0%
+resonance thank you yeah so I I remember
+ 
+
+ align:start position:0%
+resonance thank you yeah so I I remember
+doing this class two years ago and there
+
+ align:start position:0%
+doing this class two years ago and there
+ 
+
+ align:start position:0%
+doing this class two years ago and there
+are some folks from arastra as well who
+
+ align:start position:0%
+are some folks from arastra as well who
+ 
+
+ align:start position:0%
+are some folks from arastra as well who
+came and talked about those plasmas
+
+ align:start position:0%
+came and talked about those plasmas
+ 
+
+ align:start position:0%
+came and talked about those plasmas
+which is wider scale now goes down to
+
+ align:start position:0%
+which is wider scale now goes down to
+ 
+
+ align:start position:0%
+which is wider scale now goes down to
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+what I consider to be quite a low
+
+ align:start position:0%
+what I consider to be quite a low
+ 
+
+ align:start position:0%
+what I consider to be quite a low
+density but there we go and that's why
+
+ align:start position:0%
+density but there we go and that's why
+ 
+
+ align:start position:0%
+density but there we go and that's why
+it's kind of fun that we can go all the
+
+ align:start position:0%
+it's kind of fun that we can go all the
+ 
+
+ align:start position:0%
+it's kind of fun that we can go all the
+way up much High densities as well okay
+
+ align:start position:0%
+way up much High densities as well okay
+ 
+
+ align:start position:0%
+way up much High densities as well okay
+any more Volunteers in the room or from
+
+ align:start position:0%
+any more Volunteers in the room or from
+ 
+
+ align:start position:0%
+any more Volunteers in the room or from
+Columbia Ling come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up hello everybody I am laning I work
+
+ align:start position:0%
+up hello everybody I am laning I work
+ 
+
+ align:start position:0%
+up hello everybody I am laning I work
+with Jack um my project is the magnetic
+
+ align:start position:0%
+with Jack um my project is the magnetic
+ 
+
+ align:start position:0%
+with Jack um my project is the magnetic
+reconnection on Z it's a collaboration
+
+ align:start position:0%
+reconnection on Z it's a collaboration
+ 
+
+ align:start position:0%
+reconnection on Z it's a collaboration
+with s National Labs so on the Z machine
+
+ align:start position:0%
+with s National Labs so on the Z machine
+ 
+
+ align:start position:0%
+with s National Labs so on the Z machine
+the largest pulse power machine um
+
+ align:start position:0%
+the largest pulse power machine um
+ 
+
+ align:start position:0%
+the largest pulse power machine um
+I think we're achieving densities around
+
+ align:start position:0%
+I think we're achieving densities around
+ 
+
+ align:start position:0%
+I think we're achieving densities around
+10 24 to 10
+
+ align:start position:0%
+10 24 to 10
+ 
+
+ align:start position:0%
+10 24 to 10
+25 uh electrons per cubic meter in the
+
+ align:start position:0%
+25 uh electrons per cubic meter in the
+ 
+
+ align:start position:0%
+25 uh electrons per cubic meter in the
+reconduction layer and I I believe our
+
+ align:start position:0%
+reconduction layer and I I believe our
+ 
+
+ align:start position:0%
+reconduction layer and I I believe our
+temperature is for for the bulk of the
+
+ align:start position:0%
+temperature is for for the bulk of the
+ 
+
+ align:start position:0%
+temperature is for for the bulk of the
+plasma I think are tens of EV but for
+
+ align:start position:0%
+plasma I think are tens of EV but for
+ 
+
+ align:start position:0%
+plasma I think are tens of EV but for
+plasmoids can get up to a little bit
+
+ align:start position:0%
+plasmoids can get up to a little bit
+ 
+
+ align:start position:0%
+plasmoids can get up to a little bit
+above 100 e so maybe
+
+ align:start position:0%
+above 100 e so maybe
+ 
+
+ align:start position:0%
+above 100 e so maybe
+somewhere somewhere like in this region
+
+ align:start position:0%
+somewhere somewhere like in this region
+ 
+
+ align:start position:0%
+somewhere somewhere like in this region
+is um and then the I believe the
+
+ align:start position:0%
+is um and then the I believe the
+ 
+
+ align:start position:0%
+is um and then the I believe the
+magnetic fields we're achieving are tens
+
+ align:start position:0%
+magnetic fields we're achieving are tens
+ 
+
+ align:start position:0%
+magnetic fields we're achieving are tens
+of Tesla typically so the work I've been
+
+ align:start position:0%
+of Tesla typically so the work I've been
+ 
+
+ align:start position:0%
+of Tesla typically so the work I've been
+focusing
+
+ align:start position:0%
+focusing
+ 
+
+ align:start position:0%
+focusing
+on this a number number
+
+ align:start position:0%
+on this a number number
+ 
+
+ align:start position:0%
+on this a number number
+eight uh lately the diagnostic that I've
+
+ align:start position:0%
+eight uh lately the diagnostic that I've
+ 
+
+ align:start position:0%
+eight uh lately the diagnostic that I've
+been working on it's all been synthetic
+
+ align:start position:0%
+been working on it's all been synthetic
+ 
+
+ align:start position:0%
+been working on it's all been synthetic
+so just modeling but it's preparation
+
+ align:start position:0%
+so just modeling but it's preparation
+ 
+
+ align:start position:0%
+so just modeling but it's preparation
+for upcoming shot it's on cograph so
+
+ align:start position:0%
+for upcoming shot it's on cograph so
+ 
+
+ align:start position:0%
+for upcoming shot it's on cograph so
+using a proving laser beam to try to
+
+ align:start position:0%
+using a proving laser beam to try to
+ 
+
+ align:start position:0%
+using a proving laser beam to try to
+indirectly constrain the electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density thank you all right anyone else
+
+ align:start position:0%
+density thank you all right anyone else
+ 
+
+ align:start position:0%
+density thank you all right anyone else
+yeah going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up so I work with neral elatic
+
+ align:start position:0%
+up so I work with neral elatic
+ 
+
+ align:start position:0%
+up so I work with neral elatic
+confinment Fusion which is a bit
+
+ align:start position:0%
+confinment Fusion which is a bit
+ 
+
+ align:start position:0%
+confinment Fusion which is a bit
+different from this I would assume way
+
+ align:start position:0%
+different from this I would assume way
+ 
+
+ align:start position:0%
+different from this I would assume way
+up here somewhere maybe here um the
+
+ align:start position:0%
+up here somewhere maybe here um the
+ 
+
+ align:start position:0%
+up here somewhere maybe here um the
+range of 40 to 100 KV but the pressure
+
+ align:start position:0%
+range of 40 to 100 KV but the pressure
+ 
+
+ align:start position:0%
+range of 40 to 100 KV but the pressure
+is incredibly low current very
+
+ align:start position:0%
+is incredibly low current very
+ 
+
+ align:start position:0%
+is incredibly low current very
+low oh sorry
+
+ align:start position:0%
+low oh sorry
+ 
+
+ align:start position:0%
+low oh sorry
+so I guess
+
+ align:start position:0%
+so I guess
+ 
+
+ align:start position:0%
+so I guess
+very similar to NF we're only using
+
+ align:start position:0%
+very similar to NF we're only using
+ 
+
+ align:start position:0%
+very similar to NF we're only using
+Neutron
+
+ align:start position:0%
+Neutron
+ 
+
+ align:start position:0%
+Neutron
+detectors kind of like a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h23 yeah welome to up upgrade that soon
+
+ align:start position:0%
+h23 yeah welome to up upgrade that soon
+ 
+
+ align:start position:0%
+h23 yeah welome to up upgrade that soon
+right thank you anyone from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columbia
+
+ align:start position:0%
+Columbia
+ 
+
+ align:start position:0%
+Columbia
+yeah hey I'm Daniel I'm also working on
+
+ align:start position:0%
+yeah hey I'm Daniel I'm also working on
+ 
+
+ align:start position:0%
+yeah hey I'm Daniel I'm also working on
+spark specifically on uh equilibrium
+
+ align:start position:0%
+spark specifically on uh equilibrium
+ 
+
+ align:start position:0%
+spark specifically on uh equilibrium
+Dynamics and for that most of what I'm
+
+ align:start position:0%
+Dynamics and for that most of what I'm
+ 
+
+ align:start position:0%
+Dynamics and for that most of what I'm
+looking at are flux Loops so um
+
+ align:start position:0%
+looking at are flux Loops so um
+ 
+
+ align:start position:0%
+looking at are flux Loops so um
+you know Finding where the plasma
+
+ align:start position:0%
+you know Finding where the plasma
+ 
+
+ align:start position:0%
+you know Finding where the plasma
+boundary actually is inside the vacuum
+
+ align:start position:0%
+boundary actually is inside the vacuum
+ 
+
+ align:start position:0%
+boundary actually is inside the vacuum
+vessel nice good stuff thank you anyone
+
+ align:start position:0%
+vessel nice good stuff thank you anyone
+ 
+
+ align:start position:0%
+vessel nice good stuff thank you anyone
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+room yeah come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up hi I'm Jacob um similar to Amelia I'm
+
+ align:start position:0%
+up hi I'm Jacob um similar to Amelia I'm
+ 
+
+ align:start position:0%
+up hi I'm Jacob um similar to Amelia I'm
+doing azex upgrade in pedestal so I'll
+
+ align:start position:0%
+doing azex upgrade in pedestal so I'll
+ 
+
+ align:start position:0%
+doing azex upgrade in pedestal so I'll
+put that in her same
+
+ align:start position:0%
+put that in her same
+ 
+
+ align:start position:0%
+put that in her same
+bubble
+
+ align:start position:0%
+bubble
+ 
+
+ align:start position:0%
+bubble
+and I work on correlation
+
+ align:start position:0%
+and I work on correlation
+ 
+
+ align:start position:0%
+and I work on correlation
+ECE to look at temperature fluctuations
+
+ align:start position:0%
+ECE to look at temperature fluctuations
+ 
+
+ align:start position:0%
+ECE to look at temperature fluctuations
+e electron cyron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emission we like our AC but we should
+
+ align:start position:0%
+emission we like our AC but we should
+ 
+
+ align:start position:0%
+emission we like our AC but we should
+spell them out at least once cool anyone
+
+ align:start position:0%
+spell them out at least once cool anyone
+ 
+
+ align:start position:0%
+spell them out at least once cool anyone
+else yeah come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up hi I'm Leo I'm working on spark I'm
+
+ align:start position:0%
+up hi I'm Leo I'm working on spark I'm
+ 
+
+ align:start position:0%
+up hi I'm Leo I'm working on spark I'm
+looking at the and the vert areas so
+
+ align:start position:0%
+looking at the and the vert areas so
+ 
+
+ align:start position:0%
+looking at the and the vert areas so
+depending on how detached it is
+
+ align:start position:0%
+depending on how detached it is
+ 
+
+ align:start position:0%
+depending on how detached it is
+somewhere right here
+
+ align:start position:0%
+somewhere right here
+ 
+
+ align:start position:0%
+somewhere right here
+and langar Lang yeah well I mean
+
+ align:start position:0%
+and langar Lang yeah well I mean
+ 
+
+ align:start position:0%
+and langar Lang yeah well I mean
+synthetic SP doesn't exist
+
+ align:start position:0%
+synthetic SP doesn't exist
+ 
+
+ align:start position:0%
+synthetic SP doesn't exist
+yet but at least they're planning to
+
+ align:start position:0%
+yet but at least they're planning to
+ 
+
+ align:start position:0%
+yet but at least they're planning to
+have some Diagnostics nice all right
+
+ align:start position:0%
+have some Diagnostics nice all right
+ 
+
+ align:start position:0%
+have some Diagnostics nice all right
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+else yeah going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up um so I work with plasma but it was
+
+ align:start position:0%
+up um so I work with plasma but it was
+ 
+
+ align:start position:0%
+up um so I work with plasma but it was
+actually simulation for accelerators so
+
+ align:start position:0%
+actually simulation for accelerators so
+ 
+
+ align:start position:0%
+actually simulation for accelerators so
+the magnetic field um for some
+
+ align:start position:0%
+the magnetic field um for some
+ 
+
+ align:start position:0%
+the magnetic field um for some
+simulation for plasma wave acceler it
+
+ align:start position:0%
+simulation for plasma wave acceler it
+ 
+
+ align:start position:0%
+simulation for plasma wave acceler it
+went up to like for some cases because
+
+ align:start position:0%
+went up to like for some cases because
+ 
+
+ align:start position:0%
+went up to like for some cases because
+we were trying to scale up to 15 TV
+
+ align:start position:0%
+we were trying to scale up to 15 TV
+ 
+
+ align:start position:0%
+we were trying to scale up to 15 TV
+scale up to like a few thousand Tesla so
+
+ align:start position:0%
+scale up to like a few thousand Tesla so
+ 
+
+ align:start position:0%
+scale up to like a few thousand Tesla so
+but it's simulations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's but the diagnostic is all from
+
+ align:start position:0%
+that's but the diagnostic is all from
+ 
+
+ align:start position:0%
+that's but the diagnostic is all from
+simulation so it's like um particle um
+
+ align:start position:0%
+simulation so it's like um particle um
+ 
+
+ align:start position:0%
+simulation so it's like um particle um
+histogram and U Photon energy
+
+ align:start position:0%
+histogram and U Photon energy
+ 
+
+ align:start position:0%
+histogram and U Photon energy
+um I well depends on what what Collision
+
+ align:start position:0%
+um I well depends on what what Collision
+ 
+
+ align:start position:0%
+um I well depends on what what Collision
+you want to do you could make them like
+
+ align:start position:0%
+you want to do you could make them like
+ 
+
+ align:start position:0%
+you want to do you could make them like
+really Ultra tight and and would put
+
+ align:start position:0%
+really Ultra tight and and would put
+ 
+
+ align:start position:0%
+really Ultra tight and and would put
+them somewhere that here um for the
+
+ align:start position:0%
+them somewhere that here um for the
+ 
+
+ align:start position:0%
+them somewhere that here um for the
+temperature I'm not so sure but the
+
+ align:start position:0%
+temperature I'm not so sure but the
+ 
+
+ align:start position:0%
+temperature I'm not so sure but the
+ultimate goal is to scale it up to 15 TV
+
+ align:start position:0%
+ultimate goal is to scale it up to 15 TV
+ 
+
+ align:start position:0%
+ultimate goal is to scale it up to 15 TV
+okay yeah yeah would be good if we had a
+
+ align:start position:0%
+okay yeah yeah would be good if we had a
+ 
+
+ align:start position:0%
+okay yeah yeah would be good if we had a
+lock
+
+ align:start position:0%
+lock
+ 
+
+ align:start position:0%
+lock
+scale all right thank you yeah good
+
+ align:start position:0%
+scale all right thank you yeah good
+ 
+
+ align:start position:0%
+scale all right thank you yeah good
+stuff anyone else from Columbia I know
+
+ align:start position:0%
+stuff anyone else from Columbia I know
+ 
+
+ align:start position:0%
+stuff anyone else from Columbia I know
+there's like I think there's like nine
+
+ align:start position:0%
+there's like I think there's like nine
+ 
+
+ align:start position:0%
+there's like I think there's like nine
+of you and there's 30 of us so I've been
+
+ align:start position:0%
+of you and there's 30 of us so I've been
+ 
+
+ align:start position:0%
+of you and there's 30 of us so I've been
+trying to balance it a little bit so I
+
+ align:start position:0%
+trying to balance it a little bit so I
+ 
+
+ align:start position:0%
+trying to balance it a little bit so I
+may have got three all now oh yeah hey I
+
+ align:start position:0%
+may have got three all now oh yeah hey I
+ 
+
+ align:start position:0%
+may have got three all now oh yeah hey I
+see your hand hey yeah um so I've done
+
+ align:start position:0%
+see your hand hey yeah um so I've done
+ 
+
+ align:start position:0%
+see your hand hey yeah um so I've done
+work on c2w which sits kind of in
+
+ align:start position:0%
+work on c2w which sits kind of in
+ 
+
+ align:start position:0%
+work on c2w which sits kind of in
+between numbers two and three blobs so
+
+ align:start position:0%
+between numbers two and three blobs so
+ 
+
+ align:start position:0%
+between numbers two and three blobs so
+10 to the 19 and yeah just under one um
+
+ align:start position:0%
+10 to the 19 and yeah just under one um
+ 
+
+ align:start position:0%
+10 to the 19 and yeah just under one um
+kuv and then the magnetic field is just
+
+ align:start position:0%
+kuv and then the magnetic field is just
+ 
+
+ align:start position:0%
+kuv and then the magnetic field is just
+under um like one Tesla one Tesla okay
+
+ align:start position:0%
+under um like one Tesla one Tesla okay
+ 
+
+ align:start position:0%
+under um like one Tesla one Tesla okay
+so I put it in like
+
+ align:start position:0%
+so I put it in like
+ 
+
+ align:start position:0%
+so I put it in like
+this okay so what are you using on
+
+ align:start position:0%
+this okay so what are you using on
+ 
+
+ align:start position:0%
+this okay so what are you using on
+ctw yeah so um a lot of them have been
+
+ align:start position:0%
+ctw yeah so um a lot of them have been
+ 
+
+ align:start position:0%
+ctw yeah so um a lot of them have been
+mentioned but I don't think um
+
+ align:start position:0%
+mentioned but I don't think um
+ 
+
+ align:start position:0%
+mentioned but I don't think um
+interferometry has been mentioned um or
+
+ align:start position:0%
+interferometry has been mentioned um or
+ 
+
+ align:start position:0%
+interferometry has been mentioned um or
+uh biased Bomer so like energy
+
+ align:start position:0%
+uh biased Bomer so like energy
+ 
+
+ align:start position:0%
+uh biased Bomer so like energy
+analyzers cool I'll put both of those in
+
+ align:start position:0%
+analyzers cool I'll put both of those in
+ 
+
+ align:start position:0%
+analyzers cool I'll put both of those in
+bias pomet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nice all right anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columbia all right looks like we're all
+
+ align:start position:0%
+Columbia all right looks like we're all
+ 
+
+ align:start position:0%
+Columbia all right looks like we're all
+good so I feel like the purpose of this
+
+ align:start position:0%
+good so I feel like the purpose of this
+ 
+
+ align:start position:0%
+good so I feel like the purpose of this
+exercise is just to get a feel for some
+
+ align:start position:0%
+exercise is just to get a feel for some
+ 
+
+ align:start position:0%
+exercise is just to get a feel for some
+of the different things that we might
+
+ align:start position:0%
+of the different things that we might
+ 
+
+ align:start position:0%
+of the different things that we might
+end up talking about um I got a few
+
+ align:start position:0%
+end up talking about um I got a few
+ 
+
+ align:start position:0%
+end up talking about um I got a few
+other things on here to add so we've
+
+ align:start position:0%
+other things on here to add so we've
+ 
+
+ align:start position:0%
+other things on here to add so we've
+already had spark and ni uh there's a
+
+ align:start position:0%
+already had spark and ni uh there's a
+ 
+
+ align:start position:0%
+already had spark and ni uh there's a
+very cool technique for doing Fusion
+
+ align:start position:0%
+very cool technique for doing Fusion
+ 
+
+ align:start position:0%
+very cool technique for doing Fusion
+using pulse power is there to my heart
+
+ align:start position:0%
+using pulse power is there to my heart
+ 
+
+ align:start position:0%
+using pulse power is there to my heart
+which is magnetized liner inertial
+
+ align:start position:0%
+which is magnetized liner inertial
+ 
+
+ align:start position:0%
+which is magnetized liner inertial
+fusion um this is an interesting one
+
+ align:start position:0%
+fusion um this is an interesting one
+ 
+
+ align:start position:0%
+fusion um this is an interesting one
+because it works using magnetic field
+
+ align:start position:0%
+because it works using magnetic field
+ 
+
+ align:start position:0%
+because it works using magnetic field
+compression so we start out with fields
+
+ align:start position:0%
+compression so we start out with fields
+ 
+
+ align:start position:0%
+compression so we start out with fields
+of about 10 Tesla or so and we start out
+
+ align:start position:0%
+of about 10 Tesla or so and we start out
+ 
+
+ align:start position:0%
+of about 10 Tesla or so and we start out
+at densities of about 10 to the 26 which
+
+ align:start position:0%
+at densities of about 10 to the 26 which
+ 
+
+ align:start position:0%
+at densities of about 10 to the 26 which
+is about here and temperatures about 300
+
+ align:start position:0%
+is about here and temperatures about 300
+ 
+
+ align:start position:0%
+is about here and temperatures about 300
+EV but then we as we compress we
+
+ align:start position:0%
+EV but then we as we compress we
+ 
+
+ align:start position:0%
+EV but then we as we compress we
+obviously get to much higher densities
+
+ align:start position:0%
+obviously get to much higher densities
+ 
+
+ align:start position:0%
+obviously get to much higher densities
+much higher temperatures and we're also
+
+ align:start position:0%
+much higher temperatures and we're also
+ 
+
+ align:start position:0%
+much higher temperatures and we're also
+compressing the magnetic field so in
+
+ align:start position:0%
+compressing the magnetic field so in
+ 
+
+ align:start position:0%
+compressing the magnetic field so in
+fact the number I've got written on here
+
+ align:start position:0%
+fact the number I've got written on here
+ 
+
+ align:start position:0%
+fact the number I've got written on here
+means I'm allowed to use the green chalk
+
+ align:start position:0%
+means I'm allowed to use the green chalk
+ 
+
+ align:start position:0%
+means I'm allowed to use the green chalk
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+uh and we're going to go up to 10 to 29
+
+ align:start position:0%
+uh and we're going to go up to 10 to 29
+ 
+
+ align:start position:0%
+uh and we're going to go up to 10 to 29
+uh in density and 8 KV here right so
+
+ align:start position:0%
+uh in density and 8 KV here right so
+ 
+
+ align:start position:0%
+uh in density and 8 KV here right so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+magift and there's lots of cool
+
+ align:start position:0%
+magift and there's lots of cool
+ 
+
+ align:start position:0%
+magift and there's lots of cool
+Diagnostics that they use on magift but
+
+ align:start position:0%
+Diagnostics that they use on magift but
+ 
+
+ align:start position:0%
+Diagnostics that they use on magift but
+one of the ones which I think is rather
+
+ align:start position:0%
+one of the ones which I think is rather
+ 
+
+ align:start position:0%
+one of the ones which I think is rather
+neat is that they have some Neutron
+
+ align:start position:0%
+neat is that they have some Neutron
+ 
+
+ align:start position:0%
+neat is that they have some Neutron
+spectrometers that they can actually use
+
+ align:start position:0%
+spectrometers that they can actually use
+ 
+
+ align:start position:0%
+spectrometers that they can actually use
+to measure the magnetic field because
+
+ align:start position:0%
+to measure the magnetic field because
+ 
+
+ align:start position:0%
+to measure the magnetic field because
+they fill this with dyum and you get
+
+ align:start position:0%
+they fill this with dyum and you get
+ 
+
+ align:start position:0%
+they fill this with dyum and you get
+duum dyum reaction that make tritium and
+
+ align:start position:0%
+duum dyum reaction that make tritium and
+ 
+
+ align:start position:0%
+duum dyum reaction that make tritium and
+then when the tritium reacts it's
+
+ align:start position:0%
+then when the tritium reacts it's
+ 
+
+ align:start position:0%
+then when the tritium reacts it's
+already moved some distance along the
+
+ align:start position:0%
+already moved some distance along the
+ 
+
+ align:start position:0%
+already moved some distance along the
+magnetic field and so you actually get
+
+ align:start position:0%
+magnetic field and so you actually get
+ 
+
+ align:start position:0%
+magnetic field and so you actually get
+an anisotropic Neutron Spectrum from
+
+ align:start position:0%
+an anisotropic Neutron Spectrum from
+ 
+
+ align:start position:0%
+an anisotropic Neutron Spectrum from
+these secondary DT reactions so you're
+
+ align:start position:0%
+these secondary DT reactions so you're
+ 
+
+ align:start position:0%
+these secondary DT reactions so you're
+able to use Neutron
+
+ align:start position:0%
+able to use Neutron
+ 
+
+ align:start position:0%
+able to use Neutron
+spectroscopy to get the B field out
+
+ align:start position:0%
+spectroscopy to get the B field out
+ 
+
+ align:start position:0%
+spectroscopy to get the B field out
+which is not something that you would
+
+ align:start position:0%
+which is not something that you would
+ 
+
+ align:start position:0%
+which is not something that you would
+necessarily expect to be able to
+
+ align:start position:0%
+necessarily expect to be able to
+ 
+
+ align:start position:0%
+necessarily expect to be able to
+do another one I've got on here is a
+
+ align:start position:0%
+do another one I've got on here is a
+ 
+
+ align:start position:0%
+do another one I've got on here is a
+whole froster does anyone work on whole
+
+ align:start position:0%
+whole froster does anyone work on whole
+ 
+
+ align:start position:0%
+whole froster does anyone work on whole
+frosters here this a type of plasma
+
+ align:start position:0%
+frosters here this a type of plasma
+ 
+
+ align:start position:0%
+frosters here this a type of plasma
+froster for satellites um these are
+
+ align:start position:0%
+froster for satellites um these are
+ 
+
+ align:start position:0%
+froster for satellites um these are
+working with relatively low magnetic
+
+ align:start position:0%
+working with relatively low magnetic
+ 
+
+ align:start position:0%
+working with relatively low magnetic
+fields so I got 0.01 Tesla written here
+
+ align:start position:0%
+fields so I got 0.01 Tesla written here
+ 
+
+ align:start position:0%
+fields so I got 0.01 Tesla written here
+tally 18 kind of densities and they're
+
+ align:start position:0%
+tally 18 kind of densities and they're
+ 
+
+ align:start position:0%
+tally 18 kind of densities and they're
+also working at about 30 EV
+
+ align:start position:0%
+also working at about 30 EV
+ 
+
+ align:start position:0%
+also working at about 30 EV
+so here right so whole
+
+ align:start position:0%
+so here right so whole
+ 
+
+ align:start position:0%
+so here right so whole
+Thruster I don't know a huge amount
+
+ align:start position:0%
+Thruster I don't know a huge amount
+ 
+
+ align:start position:0%
+Thruster I don't know a huge amount
+about the Diagnostics used on these but
+
+ align:start position:0%
+about the Diagnostics used on these but
+ 
+
+ align:start position:0%
+about the Diagnostics used on these but
+the sorts of Diagnostics people would
+
+ align:start position:0%
+the sorts of Diagnostics people would
+ 
+
+ align:start position:0%
+the sorts of Diagnostics people would
+probably use are things like Lang again
+
+ align:start position:0%
+probably use are things like Lang again
+ 
+
+ align:start position:0%
+probably use are things like Lang again
+because these are relatively low
+
+ align:start position:0%
+because these are relatively low
+ 
+
+ align:start position:0%
+because these are relatively low
+temperature low density plasmas so you
+
+ align:start position:0%
+temperature low density plasmas so you
+ 
+
+ align:start position:0%
+temperature low density plasmas so you
+can get away with sticking stuff inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um just uh down the road from here in
+
+ align:start position:0%
+um just uh down the road from here in
+ 
+
+ align:start position:0%
+um just uh down the road from here in
+fact not very far from here at all I'm
+
+ align:start position:0%
+fact not very far from here at all I'm
+ 
+
+ align:start position:0%
+fact not very far from here at all I'm
+not sure I can point directly at it
+
+ align:start position:0%
+not sure I can point directly at it
+ 
+
+ align:start position:0%
+not sure I can point directly at it
+right now is a machine called dionysis
+
+ align:start position:0%
+right now is a machine called dionysis
+ 
+
+ align:start position:0%
+right now is a machine called dionysis
+which is a Helicon plasma that's used
+
+ align:start position:0%
+which is a Helicon plasma that's used
+ 
+
+ align:start position:0%
+which is a Helicon plasma that's used
+for plasma material interactions that's
+
+ align:start position:0%
+for plasma material interactions that's
+ 
+
+ align:start position:0%
+for plasma material interactions that's
+got magnetic fields of about 0.1 Tesla
+
+ align:start position:0%
+got magnetic fields of about 0.1 Tesla
+ 
+
+ align:start position:0%
+got magnetic fields of about 0.1 Tesla
+density is around about Tesla 17 and uh
+
+ align:start position:0%
+density is around about Tesla 17 and uh
+ 
+
+ align:start position:0%
+density is around about Tesla 17 and uh
+relatively low temperature about 5 so it
+
+ align:start position:0%
+relatively low temperature about 5 so it
+ 
+
+ align:start position:0%
+relatively low temperature about 5 so it
+also sits around about here so this is a
+
+ align:start position:0%
+also sits around about here so this is a
+ 
+
+ align:start position:0%
+also sits around about here so this is a
+HELOC
+
+ align:start position:0%
+HELOC
+ 
+
+ align:start position:0%
+HELOC
+which is a sort of RF driven
+
+ align:start position:0%
+which is a sort of RF driven
+ 
+
+ align:start position:0%
+which is a sort of RF driven
+plasma and again these the Diagnostics
+
+ align:start position:0%
+plasma and again these the Diagnostics
+ 
+
+ align:start position:0%
+plasma and again these the Diagnostics
+that tend to be used in that are things
+
+ align:start position:0%
+that tend to be used in that are things
+ 
+
+ align:start position:0%
+that tend to be used in that are things
+like Lang pros and then uh the work that
+
+ align:start position:0%
+like Lang pros and then uh the work that
+ 
+
+ align:start position:0%
+like Lang pros and then uh the work that
+I do uh both uh before I came here and
+
+ align:start position:0%
+I do uh both uh before I came here and
+ 
+
+ align:start position:0%
+I do uh both uh before I came here and
+now the machine we're building is using
+
+ align:start position:0%
+now the machine we're building is using
+ 
+
+ align:start position:0%
+now the machine we're building is using
+pulse power so this is similar to the
+
+ align:start position:0%
+pulse power so this is similar to the
+ 
+
+ align:start position:0%
+pulse power so this is similar to the
+stuff that lanting was talking about on
+
+ align:start position:0%
+stuff that lanting was talking about on
+ 
+
+ align:start position:0%
+stuff that lanting was talking about on
+Z and uh what we talking about with
+
+ align:start position:0%
+Z and uh what we talking about with
+ 
+
+ align:start position:0%
+Z and uh what we talking about with
+maglif but on a more modest scale
+
+ align:start position:0%
+maglif but on a more modest scale
+ 
+
+ align:start position:0%
+maglif but on a more modest scale
+because we're only University and so we
+
+ align:start position:0%
+because we're only University and so we
+ 
+
+ align:start position:0%
+because we're only University and so we
+tend to be in a regime when we're
+
+ align:start position:0%
+tend to be in a regime when we're
+ 
+
+ align:start position:0%
+tend to be in a regime when we're
+dealing with fields of up to about a 10
+
+ align:start position:0%
+dealing with fields of up to about a 10
+ 
+
+ align:start position:0%
+dealing with fields of up to about a 10
+10 Tesla or so
+
+ align:start position:0%
+10 Tesla or so
+ 
+
+ align:start position:0%
+10 Tesla or so
+um we've got densities of around have
+
+ align:start position:0%
+um we've got densities of around have
+ 
+
+ align:start position:0%
+um we've got densities of around have
+done this in CC so it's 10 to 23 or so
+
+ align:start position:0%
+done this in CC so it's 10 to 23 or so
+ 
+
+ align:start position:0%
+done this in CC so it's 10 to 23 or so
+and temperature is up to about 100 EV so
+
+ align:start position:0%
+and temperature is up to about 100 EV so
+ 
+
+ align:start position:0%
+and temperature is up to about 100 EV so
+quite similar the
+
+ align:start position:0%
+quite similar the
+ 
+
+ align:start position:0%
+quite similar the
+Magi and the Mars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shots and we use Diagnostics some of
+
+ align:start position:0%
+shots and we use Diagnostics some of
+ 
+
+ align:start position:0%
+shots and we use Diagnostics some of
+which have already been mentioned so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interferometry Faraday rotation Imaging
+
+ align:start position:0%
+interferometry Faraday rotation Imaging
+ 
+
+ align:start position:0%
+interferometry Faraday rotation Imaging
+which is this technique for measuring
+
+ align:start position:0%
+which is this technique for measuring
+ 
+
+ align:start position:0%
+which is this technique for measuring
+magnetic fields using the polariz of
+
+ align:start position:0%
+magnetic fields using the polariz of
+ 
+
+ align:start position:0%
+magnetic fields using the polariz of
+light and my favorite diagnostic which
+
+ align:start position:0%
+light and my favorite diagnostic which
+ 
+
+ align:start position:0%
+light and my favorite diagnostic which
+is why we spend so long talking about it
+
+ align:start position:0%
+is why we spend so long talking about it
+ 
+
+ align:start position:0%
+is why we spend so long talking about it
+Thomson
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scaton but that's kind of where I'm
+
+ align:start position:0%
+scaton but that's kind of where I'm
+ 
+
+ align:start position:0%
+scaton but that's kind of where I'm
+coming from just so you know what my
+
+ align:start position:0%
+coming from just so you know what my
+ 
+
+ align:start position:0%
+coming from just so you know what my
+background is that obviously feeds into
+
+ align:start position:0%
+background is that obviously feeds into
+ 
+
+ align:start position:0%
+background is that obviously feeds into
+my biases about what exactly I spend
+
+ align:start position:0%
+my biases about what exactly I spend
+ 
+
+ align:start position:0%
+my biases about what exactly I spend
+more or less time teaching but I will
+
+ align:start position:0%
+more or less time teaching but I will
+ 
+
+ align:start position:0%
+more or less time teaching but I will
+try and cover as much as I can this
+
+ align:start position:0%
+try and cover as much as I can this
+ 
+
+ align:start position:0%
+try and cover as much as I can this
+parameter space and some of the
+
+ align:start position:0%
+parameter space and some of the
+ 
+
+ align:start position:0%
+parameter space and some of the
+Diagnostics that you've mentioned uh but
+
+ align:start position:0%
+Diagnostics that you've mentioned uh but
+ 
+
+ align:start position:0%
+Diagnostics that you've mentioned uh but
+the thing about teaching a class like
+
+ align:start position:0%
+the thing about teaching a class like
+ 
+
+ align:start position:0%
+the thing about teaching a class like
+this that I always find is whenever I
+
+ align:start position:0%
+this that I always find is whenever I
+ 
+
+ align:start position:0%
+this that I always find is whenever I
+teach on some specific diagnostic
+
+ align:start position:0%
+teach on some specific diagnostic
+ 
+
+ align:start position:0%
+teach on some specific diagnostic
+there'll be someone in the class who's
+
+ align:start position:0%
+there'll be someone in the class who's
+ 
+
+ align:start position:0%
+there'll be someone in the class who's
+doing their PHD on it and they know much
+
+ align:start position:0%
+doing their PHD on it and they know much
+ 
+
+ align:start position:0%
+doing their PHD on it and they know much
+more about it than me right so and I
+
+ align:start position:0%
+more about it than me right so and I
+ 
+
+ align:start position:0%
+more about it than me right so and I
+know much much less about it and that's
+
+ align:start position:0%
+know much much less about it and that's
+ 
+
+ align:start position:0%
+know much much less about it and that's
+great this is what makes this class
+
+ align:start position:0%
+great this is what makes this class
+ 
+
+ align:start position:0%
+great this is what makes this class
+enjoyable so please if I say something
+
+ align:start position:0%
+enjoyable so please if I say something
+ 
+
+ align:start position:0%
+enjoyable so please if I say something
+that's like wrong or if you think you've
+
+ align:start position:0%
+that's like wrong or if you think you've
+ 
+
+ align:start position:0%
+that's like wrong or if you think you've
+got something to add or like oh these
+
+ align:start position:0%
+got something to add or like oh these
+ 
+
+ align:start position:0%
+got something to add or like oh these
+days we do it like that that was 20
+
+ align:start position:0%
+days we do it like that that was 20
+ 
+
+ align:start position:0%
+days we do it like that that was 20
+years ago just shout out and please add
+
+ align:start position:0%
+years ago just shout out and please add
+ 
+
+ align:start position:0%
+years ago just shout out and please add
+the conversation because I know I'm not
+
+ align:start position:0%
+the conversation because I know I'm not
+ 
+
+ align:start position:0%
+the conversation because I know I'm not
+the expert on this stuff most of the
+
+ align:start position:0%
+the expert on this stuff most of the
+ 
+
+ align:start position:0%
+the expert on this stuff most of the
+time I'm using a textbook to try and
+
+ align:start position:0%
+time I'm using a textbook to try and
+ 
+
+ align:start position:0%
+time I'm using a textbook to try and
+learn about it myself there are often
+
+ align:start position:0%
+learn about it myself there are often
+ 
+
+ align:start position:0%
+learn about it myself there are often
+not very many good review papers either
+
+ align:start position:0%
+not very many good review papers either
+ 
+
+ align:start position:0%
+not very many good review papers either
+so if you know a good review paper for a
+
+ align:start position:0%
+so if you know a good review paper for a
+ 
+
+ align:start position:0%
+so if you know a good review paper for a
+diagnostic I've never found a good one
+
+ align:start position:0%
+diagnostic I've never found a good one
+ 
+
+ align:start position:0%
+diagnostic I've never found a good one
+for uh electron cyclotron emission uh
+
+ align:start position:0%
+for uh electron cyclotron emission uh
+ 
+
+ align:start position:0%
+for uh electron cyclotron emission uh
+diagnostics for example um then let me
+
+ align:start position:0%
+diagnostics for example um then let me
+ 
+
+ align:start position:0%
+diagnostics for example um then let me
+know and I can read that and then I can
+
+ align:start position:0%
+know and I can read that and then I can
+ 
+
+ align:start position:0%
+know and I can read that and then I can
+regurgitate the rest of the class and
+
+ align:start position:0%
+regurgitate the rest of the class and
+ 
+
+ align:start position:0%
+regurgitate the rest of the class and
+look very intelligent so that would help
+
+ align:start position:0%
+look very intelligent so that would help
+ 
+
+ align:start position:0%
+look very intelligent so that would help
+me a great deal um but I'll pause here
+
+ align:start position:0%
+me a great deal um but I'll pause here
+ 
+
+ align:start position:0%
+me a great deal um but I'll pause here
+if anyone has any questions uh and then
+
+ align:start position:0%
+if anyone has any questions uh and then
+ 
+
+ align:start position:0%
+if anyone has any questions uh and then
+we'll probably just leave it for today I
+
+ align:start position:0%
+we'll probably just leave it for today I
+ 
+
+ align:start position:0%
+we'll probably just leave it for today I
+know it's a little bit early but I think
+
+ align:start position:0%
+know it's a little bit early but I think
+ 
+
+ align:start position:0%
+know it's a little bit early but I think
+we can all do a little bit of a break in
+
+ align:start position:0%
+we can all do a little bit of a break in
+ 
+
+ align:start position:0%
+we can all do a little bit of a break in
+our first week of the semester so any
+
+ align:start position:0%
+our first week of the semester so any
+ 
+
+ align:start position:0%
+our first week of the semester so any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I I mean I I rushed through this a
+
+ align:start position:0%
+yes I I mean I I rushed through this a
+ 
+
+ align:start position:0%
+yes I I mean I I rushed through this a
+little bit so the the subtlety is that
+
+ align:start position:0%
+little bit so the the subtlety is that
+ 
+
+ align:start position:0%
+little bit so the the subtlety is that
+they were using they weren't looking
+
+ align:start position:0%
+they were using they weren't looking
+ 
+
+ align:start position:0%
+they were using they weren't looking
+they're not looking at the DD neutrons
+
+ align:start position:0%
+they're not looking at the DD neutrons
+ 
+
+ align:start position:0%
+they're not looking at the DD neutrons
+those are isotropic so they fill it with
+
+ align:start position:0%
+those are isotropic so they fill it with
+ 
+
+ align:start position:0%
+those are isotropic so they fill it with
+d deuterium gas only there's no tritium
+
+ align:start position:0%
+d deuterium gas only there's no tritium
+ 
+
+ align:start position:0%
+d deuterium gas only there's no tritium
+in there and they look at the DD
+
+ align:start position:0%
+in there and they look at the DD
+ 
+
+ align:start position:0%
+in there and they look at the DD
+neutrons that's isotropic on magli it
+
+ align:start position:0%
+neutrons that's isotropic on magli it
+ 
+
+ align:start position:0%
+neutrons that's isotropic on magli it
+wasn't on Z so on magli it is the what's
+
+ align:start position:0%
+wasn't on Z so on magli it is the what's
+ 
+
+ align:start position:0%
+wasn't on Z so on magli it is the what's
+cool is that DD reaction can produce a
+
+ align:start position:0%
+cool is that DD reaction can produce a
+ 
+
+ align:start position:0%
+cool is that DD reaction can produce a
+tritium ion that tritium ion is
+
+ align:start position:0%
+tritium ion that tritium ion is
+ 
+
+ align:start position:0%
+tritium ion that tritium ion is
+energetic but these magnetic fields are
+
+ align:start position:0%
+energetic but these magnetic fields are
+ 
+
+ align:start position:0%
+energetic but these magnetic fields are
+huge so it is magnetized so in fact the
+
+ align:start position:0%
+huge so it is magnetized so in fact the
+ 
+
+ align:start position:0%
+huge so it is magnetized so in fact the
+tritium Moves preferentially In One
+
+ align:start position:0%
+tritium Moves preferentially In One
+ 
+
+ align:start position:0%
+tritium Moves preferentially In One
+Direction or in two directions along the
+
+ align:start position:0%
+Direction or in two directions along the
+ 
+
+ align:start position:0%
+Direction or in two directions along the
+field lines so when it collides with the
+
+ align:start position:0%
+field lines so when it collides with the
+ 
+
+ align:start position:0%
+field lines so when it collides with the
+dyum and produces a distinctive Neutron
+
+ align:start position:0%
+dyum and produces a distinctive Neutron
+ 
+
+ align:start position:0%
+dyum and produces a distinctive Neutron
+at you know 14
+
+ align:start position:0%
+at you know 14
+ 
+
+ align:start position:0%
+at you know 14
+me those neutrons are now coming out
+
+ align:start position:0%
+me those neutrons are now coming out
+ 
+
+ align:start position:0%
+me those neutrons are now coming out
+anisotropically and the strength of that
+
+ align:start position:0%
+anisotropically and the strength of that
+ 
+
+ align:start position:0%
+anisotropically and the strength of that
+anisotropy is can be used to measure the
+
+ align:start position:0%
+anisotropy is can be used to measure the
+ 
+
+ align:start position:0%
+anisotropy is can be used to measure the
+magnetic field because it tells you how
+
+ align:start position:0%
+magnetic field because it tells you how
+ 
+
+ align:start position:0%
+magnetic field because it tells you how
+confined the trums are in a certain
+
+ align:start position:0%
+confined the trums are in a certain
+ 
+
+ align:start position:0%
+confined the trums are in a certain
+direction which is pretty neat so yeah
+
+ align:start position:0%
+direction which is pretty neat so yeah
+ 
+
+ align:start position:0%
+direction which is pretty neat so yeah
+so it's not a problem for maget because
+
+ align:start position:0%
+so it's not a problem for maget because
+ 
+
+ align:start position:0%
+so it's not a problem for maget because
+the DD neutrons are isotropic yeah and
+
+ align:start position:0%
+the DD neutrons are isotropic yeah and
+ 
+
+ align:start position:0%
+the DD neutrons are isotropic yeah and
+in a real magift you know if you want to
+
+ align:start position:0%
+in a real magift you know if you want to
+ 
+
+ align:start position:0%
+in a real magift you know if you want to
+do magift as a power plant then you just
+
+ align:start position:0%
+do magift as a power plant then you just
+ 
+
+ align:start position:0%
+do magift as a power plant then you just
+do DTE fusion and you wouldn't see this
+
+ align:start position:0%
+do DTE fusion and you wouldn't see this
+ 
+
+ align:start position:0%
+do DTE fusion and you wouldn't see this
+on isotropy at all because all the
+
+ align:start position:0%
+on isotropy at all because all the
+ 
+
+ align:start position:0%
+on isotropy at all because all the
+fusion would happen
+
+ align:start position:0%
+fusion would happen
+ 
+
+ align:start position:0%
+fusion would happen
+yeah any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right thank you very much
+
+ align:start position:0%
+questions all right thank you very much
+ 
+
+ align:start position:0%
+questions all right thank you very much
+and I'll see you on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tuesday
\ No newline at end of file
diff --git a/IbKCGrVGpco.txt b/IbKCGrVGpco.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47cc307938694b157029acafc128862d3320be2d
--- /dev/null
+++ b/IbKCGrVGpco.txt
@@ -0,0 +1,216 @@
+A conceptual schematic for a multicore processor
+is shown below.
+
+To reduce the average memory access time,
+each of the four cores has its own cache,
+
+which will satisfy most memory requests.
+
+If there's a cache miss, a request is sent
+to the shared main memory.
+
+With a modest number of cores and a good cache
+hit ratio, the number of memory requests that
+
+must access main memory during normal operation
+should be pretty small.
+
+To keep the number of memory accesses to a
+minimum, the caches implement a write-back
+
+strategy,
+where ST instructions update the cache, but
+
+main memory is only updated when a dirty cache
+line is replaced.
+
+Our goal is that each core should share the
+contents of main memory, i.e., changes made
+
+by one core should visible to all the other
+cores.
+
+In the example shown here, core 0 is running
+Thread A and core 1 is running Thread B.
+
+Both threads reference two shared memory locations
+holding the values for the variables X and
+
+Y.
+
+The current values of X and Y are 1 and 2,
+respectively.
+
+Those values are held in main memory as well
+as being cached by each core.
+
+What happens when the threads are executed?
+
+Each thread executes independently, updating
+its cache during stores to X and Y.
+
+For any possible execution order, either concurrent
+or sequential, the result is the same: Thread
+
+A prints "2", Thread B prints "1".
+
+Hardware engineers would point to the consistent
+outcomes and declare victory!
+
+But closer examination of the final system
+state reveals some problems.
+
+After execution is complete, the two cores
+disagree on the values of X and Y.
+
+Threads running on core 0 will see X=3 and
+Y=2.
+
+Threads running on core 1 will see X=1 and
+Y=4.
+
+Because of the caches, the system isn't behaving
+as if there's a single shared memory.
+
+On the other hand, we can't eliminate the
+caches since that would cause the average
+
+memory access time to skyrocket, ruining any
+hoped-for performance improvement from using
+
+multiple cores.
+
+What outcome should we expect?
+
+One plausible standard of correctness is the
+outcome when the threads are run a single
+
+timeshared core.
+
+The argument would be that a multicore implementation
+should produce the same outcome but more quickly,
+
+with parallel execution replacing timesharing.
+
+The table shows the possible results of the
+timesharing experiment, where the outcome
+
+depends on the order in which the statements
+are executed.
+
+Programmers will understand that there is
+more than one possible outcome and know that
+
+they would have to impose additional constraints
+on execution order, say, using semaphores,
+
+if they wanted a specific outcome.
+
+Notice that the multicore outcome of 2,1 doesn't
+appear anywhere on the list of possible outcomes
+
+from sequential timeshared execution.
+
+The notion that executing N threads in parallel
+should correspond to some interleaved execution
+
+of those threads on a single core is called
+"sequential consistency".
+
+If multicore systems implement sequential
+consistency, then programmers can think of
+
+the systems as providing hardware-accelerated
+timesharing.
+
+So, our simple multicore system fails on two
+accounts.
+
+First, it doesn't correctly implement a shared
+memory since, as we've seen, it's possible
+
+for the two cores to disagree about the current
+value of a shared variable.
+
+Second, as a consequence of the first problem,
+the system doesn't implement sequential consistency.
+
+Clearly, we'll need to figure out a fix!
+
+One possible fix is to give up on sequential
+consistency.
+
+An alternative memory semantics is "weak consistency",
+which only requires that the memory operations
+
+from each thread appear to be performed in
+the order issued by that thread.
+
+In other words, in a weakly consistent system,
+if a particular thread writes to X and then
+
+writes to Y, the possible outcomes from reads
+of X and Y by any thread would be one of
+
+(unchanged X, unchanged Y),
+or (changed X, unchanged Y),
+
+or (changed X, changed Y).
+
+But no thread would see changed Y but unchanged
+X.
+
+In a weakly consistent system, memory operations
+from other threads may overlap in arbitrary
+
+ways (not necessarily consistent with any
+sequential interleaving).
+
+Note that our multicore cache system doesn't
+itself guarantee even weak consistency.
+
+A thread that executes "write X; write Y"
+will update its local cache, but later cache
+
+replacements may cause the updated Y value
+to be written to main memory before the updated
+
+X value.
+
+To implement weak consistency, the thread
+should be modified to "write X; communicate
+
+changes to all other processors; write Y".
+
+In the next section, we'll discuss how to
+modify the caches to perform the required
+
+communication automatically.
+
+Out-of-order cores have an extra complication
+since there's no guarantee that successive
+
+ST instructions will complete in the order
+they appeared in the program.
+
+These architectures provide a BARRIER instruction
+that guarantees that memory operations before
+
+the BARRIER are completed before memory operation
+executed after the BARRIER.
+
+There are many types of memory consistency
+- each commercially-available multicore system
+
+has its own particular guarantees about what
+happens when.
+
+So the prudent programmer needs to read the
+ISA manual carefully to ensure that her program
+
+will do what she wants.
+
+See the referenced PDF file for a very readable
+discussion about memory semantics in multicore
+
+systems.
\ No newline at end of file
diff --git a/J23egLCM2tc.txt b/J23egLCM2tc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a10a8dd4f1bb0e974aa690f77e3937e257cae400
--- /dev/null
+++ b/J23egLCM2tc.txt
@@ -0,0 +1,9931 @@
+align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+let's get started and if anybody else
+
+ align:start position:0%
+let's get started and if anybody else
+ 
+
+ align:start position:0%
+let's get started and if anybody else
+shows up then
+
+ align:start position:0%
+shows up then
+ 
+
+ align:start position:0%
+shows up then
+that'll be fine so today we're going to
+
+ align:start position:0%
+that'll be fine so today we're going to
+ 
+
+ align:start position:0%
+that'll be fine so today we're going to
+talk about how to write a lab report
+
+ align:start position:0%
+talk about how to write a lab report
+ 
+
+ align:start position:0%
+talk about how to write a lab report
+which is a pretty important part of this
+
+ align:start position:0%
+which is a pretty important part of this
+ 
+
+ align:start position:0%
+which is a pretty important part of this
+course since it's going to determine a
+
+ align:start position:0%
+course since it's going to determine a
+ 
+
+ align:start position:0%
+course since it's going to determine a
+good portion of your grade
+
+ align:start position:0%
+good portion of your grade
+ 
+
+ align:start position:0%
+good portion of your grade
+and in general it's good to know how to
+
+ align:start position:0%
+and in general it's good to know how to
+ 
+
+ align:start position:0%
+and in general it's good to know how to
+communicate the science that you do
+
+ align:start position:0%
+communicate the science that you do
+ 
+
+ align:start position:0%
+communicate the science that you do
+whether it's in this class
+
+ align:start position:0%
+whether it's in this class
+ 
+
+ align:start position:0%
+whether it's in this class
+or in your research or in any other
+
+ align:start position:0%
+or in your research or in any other
+ 
+
+ align:start position:0%
+or in your research or in any other
+context really
+
+ align:start position:0%
+context really
+ 
+
+ align:start position:0%
+context really
+so i wanted to start just by thinking
+
+ align:start position:0%
+so i wanted to start just by thinking
+ 
+
+ align:start position:0%
+so i wanted to start just by thinking
+about these two questions which is why
+
+ align:start position:0%
+about these two questions which is why
+ 
+
+ align:start position:0%
+about these two questions which is why
+is it important to write up your results
+
+ align:start position:0%
+is it important to write up your results
+ 
+
+ align:start position:0%
+is it important to write up your results
+and then how should you write a lab
+
+ align:start position:0%
+and then how should you write a lab
+ 
+
+ align:start position:0%
+and then how should you write a lab
+report
+
+ align:start position:0%
+report
+ 
+
+ align:start position:0%
+report
+and to help get us thinking about these
+
+ align:start position:0%
+and to help get us thinking about these
+ 
+
+ align:start position:0%
+and to help get us thinking about these
+questions i print it out
+
+ align:start position:0%
+questions i print it out
+ 
+
+ align:start position:0%
+questions i print it out
+on this handout that has a good chunk of
+
+ align:start position:0%
+on this handout that has a good chunk of
+ 
+
+ align:start position:0%
+on this handout that has a good chunk of
+text on it the top part is
+
+ align:start position:0%
+text on it the top part is
+ 
+
+ align:start position:0%
+text on it the top part is
+ira remsen's account of his experiment
+
+ align:start position:0%
+ira remsen's account of his experiment
+ 
+
+ align:start position:0%
+ira remsen's account of his experiment
+with copper and nitric acid if you have
+
+ align:start position:0%
+with copper and nitric acid if you have
+ 
+
+ align:start position:0%
+with copper and nitric acid if you have
+not read it before it's a pretty
+
+ align:start position:0%
+not read it before it's a pretty
+ 
+
+ align:start position:0%
+not read it before it's a pretty
+good read so if you could skim that and
+
+ align:start position:0%
+good read so if you could skim that and
+ 
+
+ align:start position:0%
+good read so if you could skim that and
+then at the bottom there is
+
+ align:start position:0%
+then at the bottom there is
+ 
+
+ align:start position:0%
+then at the bottom there is
+a shorter description of the same
+
+ align:start position:0%
+a shorter description of the same
+ 
+
+ align:start position:0%
+a shorter description of the same
+experiment in a way that you may find it
+
+ align:start position:0%
+experiment in a way that you may find it
+ 
+
+ align:start position:0%
+experiment in a way that you may find it
+written either in a lab report or in a
+
+ align:start position:0%
+written either in a lab report or in a
+ 
+
+ align:start position:0%
+written either in a lab report or in a
+scientific paper if you're going to
+
+ align:start position:0%
+scientific paper if you're going to
+ 
+
+ align:start position:0%
+scientific paper if you're going to
+publish
+
+ align:start position:0%
+publish
+ 
+
+ align:start position:0%
+publish
+these results so if you guys want to
+
+ align:start position:0%
+these results so if you guys want to
+ 
+
+ align:start position:0%
+these results so if you guys want to
+give those a quick skim through and then
+
+ align:start position:0%
+give those a quick skim through and then
+ 
+
+ align:start position:0%
+give those a quick skim through and then
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+use those to sort of talk about these
+
+ align:start position:0%
+use those to sort of talk about these
+ 
+
+ align:start position:0%
+use those to sort of talk about these
+topics of how do you communicate your
+
+ align:start position:0%
+topics of how do you communicate your
+ 
+
+ align:start position:0%
+topics of how do you communicate your
+science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you've never seen this experiment
+
+ align:start position:0%
+and if you've never seen this experiment
+ 
+
+ align:start position:0%
+and if you've never seen this experiment
+done before i have
+
+ align:start position:0%
+done before i have
+ 
+
+ align:start position:0%
+done before i have
+a little bit of a video to show what
+
+ align:start position:0%
+a little bit of a video to show what
+ 
+
+ align:start position:0%
+a little bit of a video to show what
+happens when you put nitric acid on a
+
+ align:start position:0%
+happens when you put nitric acid on a
+ 
+
+ align:start position:0%
+happens when you put nitric acid on a
+penny
+
+ align:start position:0%
+penny
+ 
+
+ align:start position:0%
+penny
+so you can have an even more vivid
+
+ align:start position:0%
+so you can have an even more vivid
+ 
+
+ align:start position:0%
+so you can have an even more vivid
+visual of
+
+ align:start position:0%
+visual of
+ 
+
+ align:start position:0%
+visual of
+what ira empson was going through when
+
+ align:start position:0%
+what ira empson was going through when
+ 
+
+ align:start position:0%
+what ira empson was going through when
+he decided to pick this up and throw it
+
+ align:start position:0%
+he decided to pick this up and throw it
+ 
+
+ align:start position:0%
+he decided to pick this up and throw it
+out a window a few drops of nitric acid
+
+ align:start position:0%
+out a window a few drops of nitric acid
+ 
+
+ align:start position:0%
+out a window a few drops of nitric acid
+are placed on an older copper penny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it goes for a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that should give you a little bit of
+
+ align:start position:0%
+so that should give you a little bit of
+ 
+
+ align:start position:0%
+so that should give you a little bit of
+an idea of kind of the situation that he
+
+ align:start position:0%
+an idea of kind of the situation that he
+ 
+
+ align:start position:0%
+an idea of kind of the situation that he
+was in
+
+ align:start position:0%
+was in
+ 
+
+ align:start position:0%
+was in
+and so having had a chance to skim these
+
+ align:start position:0%
+and so having had a chance to skim these
+ 
+
+ align:start position:0%
+and so having had a chance to skim these
+two things does anyone have any answers
+
+ align:start position:0%
+two things does anyone have any answers
+ 
+
+ align:start position:0%
+two things does anyone have any answers
+to these questions about why is it
+
+ align:start position:0%
+to these questions about why is it
+ 
+
+ align:start position:0%
+to these questions about why is it
+important to write up your results or
+
+ align:start position:0%
+important to write up your results or
+ 
+
+ align:start position:0%
+important to write up your results or
+how should you communicate your results
+
+ align:start position:0%
+how should you communicate your results
+ 
+
+ align:start position:0%
+how should you communicate your results
+to other people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it's like not ambiguous so
+
+ align:start position:0%
+yeah so it's like not ambiguous so
+ 
+
+ align:start position:0%
+yeah so it's like not ambiguous so
+people know what to expect or they know
+
+ align:start position:0%
+people know what to expect or they know
+ 
+
+ align:start position:0%
+people know what to expect or they know
+how to handle the situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah using really clear language so that
+
+ align:start position:0%
+yeah using really clear language so that
+ 
+
+ align:start position:0%
+yeah using really clear language so that
+people know
+
+ align:start position:0%
+people know
+ 
+
+ align:start position:0%
+people know
+what is going to happen like he said the
+
+ align:start position:0%
+what is going to happen like he said the
+ 
+
+ align:start position:0%
+what is going to happen like he said the
+language acts upon
+
+ align:start position:0%
+language acts upon
+ 
+
+ align:start position:0%
+language acts upon
+um is very vague and it led to this
+
+ align:start position:0%
+um is very vague and it led to this
+ 
+
+ align:start position:0%
+um is very vague and it led to this
+experiment happening
+
+ align:start position:0%
+experiment happening
+ 
+
+ align:start position:0%
+experiment happening
+where uh our remsen burned his hands on
+
+ align:start position:0%
+where uh our remsen burned his hands on
+ 
+
+ align:start position:0%
+where uh our remsen burned his hands on
+some nitric acid so
+
+ align:start position:0%
+some nitric acid so
+ 
+
+ align:start position:0%
+some nitric acid so
+instead of acts upon saying things like
+
+ align:start position:0%
+instead of acts upon saying things like
+ 
+
+ align:start position:0%
+instead of acts upon saying things like
+what else could you say instead
+
+ align:start position:0%
+what else could you say instead
+ 
+
+ align:start position:0%
+what else could you say instead
+what are better words you could use to
+
+ align:start position:0%
+what are better words you could use to
+ 
+
+ align:start position:0%
+what are better words you could use to
+warn people of what's going to happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah corrosive those things that
+
+ align:start position:0%
+yeah yeah corrosive those things that
+ 
+
+ align:start position:0%
+yeah yeah corrosive those things that
+scott talked about in his safety lecture
+
+ align:start position:0%
+scott talked about in his safety lecture
+ 
+
+ align:start position:0%
+scott talked about in his safety lecture
+so same some of the general terms that
+
+ align:start position:0%
+so same some of the general terms that
+ 
+
+ align:start position:0%
+so same some of the general terms that
+we use to describe chemicals it's
+
+ align:start position:0%
+we use to describe chemicals it's
+ 
+
+ align:start position:0%
+we use to describe chemicals it's
+corrosive it will burn
+
+ align:start position:0%
+corrosive it will burn
+ 
+
+ align:start position:0%
+corrosive it will burn
+creates toxic gases is carcinogenic
+
+ align:start position:0%
+creates toxic gases is carcinogenic
+ 
+
+ align:start position:0%
+creates toxic gases is carcinogenic
+things like that um
+
+ align:start position:0%
+things like that um
+ 
+
+ align:start position:0%
+things like that um
+what other sort of guidelines should
+
+ align:start position:0%
+what other sort of guidelines should
+ 
+
+ align:start position:0%
+what other sort of guidelines should
+there be for how you want your
+
+ align:start position:0%
+there be for how you want your
+ 
+
+ align:start position:0%
+there be for how you want your
+results written up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah definitely you want to
+
+ align:start position:0%
+yeah yeah definitely you want to
+ 
+
+ align:start position:0%
+yeah yeah definitely you want to
+communicate how much you used so
+
+ align:start position:0%
+communicate how much you used so
+ 
+
+ align:start position:0%
+communicate how much you used so
+in that first experiment he said i put
+
+ align:start position:0%
+in that first experiment he said i put
+ 
+
+ align:start position:0%
+in that first experiment he said i put
+some nitric acid on a penny
+
+ align:start position:0%
+some nitric acid on a penny
+ 
+
+ align:start position:0%
+some nitric acid on a penny
+so you don't know what scale that was on
+
+ align:start position:0%
+so you don't know what scale that was on
+ 
+
+ align:start position:0%
+so you don't know what scale that was on
+or what scale it can be safely done at
+
+ align:start position:0%
+or what scale it can be safely done at
+ 
+
+ align:start position:0%
+or what scale it can be safely done at
+so using
+
+ align:start position:0%
+so using
+ 
+
+ align:start position:0%
+so using
+exact quantities so if somebody is going
+
+ align:start position:0%
+exact quantities so if somebody is going
+ 
+
+ align:start position:0%
+exact quantities so if somebody is going
+to redo the experiment they would know
+
+ align:start position:0%
+to redo the experiment they would know
+ 
+
+ align:start position:0%
+to redo the experiment they would know
+exactly how much you used and what they
+
+ align:start position:0%
+exactly how much you used and what they
+ 
+
+ align:start position:0%
+exactly how much you used and what they
+should expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in terms of the length of these two
+
+ align:start position:0%
+in terms of the length of these two
+ 
+
+ align:start position:0%
+in terms of the length of these two
+pieces of writing which one is easier to
+
+ align:start position:0%
+pieces of writing which one is easier to
+ 
+
+ align:start position:0%
+pieces of writing which one is easier to
+read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bottom one so being clear and concise
+
+ align:start position:0%
+bottom one so being clear and concise
+ 
+
+ align:start position:0%
+bottom one so being clear and concise
+using objective
+
+ align:start position:0%
+using objective
+ 
+
+ align:start position:0%
+using objective
+short sentences so that people can
+
+ align:start position:0%
+short sentences so that people can
+ 
+
+ align:start position:0%
+short sentences so that people can
+follow what you're writing and they
+
+ align:start position:0%
+follow what you're writing and they
+ 
+
+ align:start position:0%
+follow what you're writing and they
+don't have to read this whole huge chunk
+
+ align:start position:0%
+don't have to read this whole huge chunk
+ 
+
+ align:start position:0%
+don't have to read this whole huge chunk
+of text in order to get the gist of
+
+ align:start position:0%
+of text in order to get the gist of
+ 
+
+ align:start position:0%
+of text in order to get the gist of
+what's going on
+
+ align:start position:0%
+what's going on
+ 
+
+ align:start position:0%
+what's going on
+so those are some things to keep in mind
+
+ align:start position:0%
+so those are some things to keep in mind
+ 
+
+ align:start position:0%
+so those are some things to keep in mind
+while writing up your lab report um
+
+ align:start position:0%
+while writing up your lab report um
+ 
+
+ align:start position:0%
+while writing up your lab report um
+there's a picture of aaron remsin he was
+
+ align:start position:0%
+there's a picture of aaron remsin he was
+ 
+
+ align:start position:0%
+there's a picture of aaron remsin he was
+a chemist in the 1800s he was born in
+
+ align:start position:0%
+a chemist in the 1800s he was born in
+ 
+
+ align:start position:0%
+a chemist in the 1800s he was born in
+1846 and he became the president of
+
+ align:start position:0%
+1846 and he became the president of
+ 
+
+ align:start position:0%
+1846 and he became the president of
+johns hopkins university
+
+ align:start position:0%
+johns hopkins university
+ 
+
+ align:start position:0%
+johns hopkins university
+and also is well known for discovering
+
+ align:start position:0%
+and also is well known for discovering
+ 
+
+ align:start position:0%
+and also is well known for discovering
+the sweetener saccharin
+
+ align:start position:0%
+the sweetener saccharin
+ 
+
+ align:start position:0%
+the sweetener saccharin
+which he also discovered by tasting it
+
+ align:start position:0%
+which he also discovered by tasting it
+ 
+
+ align:start position:0%
+which he also discovered by tasting it
+on his hands
+
+ align:start position:0%
+on his hands
+ 
+
+ align:start position:0%
+on his hands
+as a result of some more poor lab
+
+ align:start position:0%
+as a result of some more poor lab
+ 
+
+ align:start position:0%
+as a result of some more poor lab
+technique so
+
+ align:start position:0%
+technique so
+ 
+
+ align:start position:0%
+technique so
+i mean he became pretty famous but don't
+
+ align:start position:0%
+i mean he became pretty famous but don't
+ 
+
+ align:start position:0%
+i mean he became pretty famous but don't
+follow his lead necessarily in that way
+
+ align:start position:0%
+follow his lead necessarily in that way
+ 
+
+ align:start position:0%
+follow his lead necessarily in that way
+so a good lab report starts before the
+
+ align:start position:0%
+so a good lab report starts before the
+ 
+
+ align:start position:0%
+so a good lab report starts before the
+lab even begins and so here are some
+
+ align:start position:0%
+lab even begins and so here are some
+ 
+
+ align:start position:0%
+lab even begins and so here are some
+things that you should be keeping in
+
+ align:start position:0%
+things that you should be keeping in
+ 
+
+ align:start position:0%
+things that you should be keeping in
+mind before you even come into the lab
+
+ align:start position:0%
+mind before you even come into the lab
+ 
+
+ align:start position:0%
+mind before you even come into the lab
+to help set you up to be able to do the
+
+ align:start position:0%
+to help set you up to be able to do the
+ 
+
+ align:start position:0%
+to help set you up to be able to do the
+experiment successfully
+
+ align:start position:0%
+experiment successfully
+ 
+
+ align:start position:0%
+experiment successfully
+and to be able to have the data that you
+
+ align:start position:0%
+and to be able to have the data that you
+ 
+
+ align:start position:0%
+and to be able to have the data that you
+need to write a lab report so you want
+
+ align:start position:0%
+need to write a lab report so you want
+ 
+
+ align:start position:0%
+need to write a lab report so you want
+to know
+
+ align:start position:0%
+to know
+ 
+
+ align:start position:0%
+to know
+planning your procedures ahead of time
+
+ align:start position:0%
+planning your procedures ahead of time
+ 
+
+ align:start position:0%
+planning your procedures ahead of time
+things that can influence your results
+
+ align:start position:0%
+things that can influence your results
+ 
+
+ align:start position:0%
+things that can influence your results
+what quantities you need to measure and
+
+ align:start position:0%
+what quantities you need to measure and
+ 
+
+ align:start position:0%
+what quantities you need to measure and
+what data and results you'll need to
+
+ align:start position:0%
+what data and results you'll need to
+ 
+
+ align:start position:0%
+what data and results you'll need to
+collect
+
+ align:start position:0%
+collect
+ 
+
+ align:start position:0%
+collect
+that you can have all of this in your
+
+ align:start position:0%
+that you can have all of this in your
+ 
+
+ align:start position:0%
+that you can have all of this in your
+notebook so that when you go to write up
+
+ align:start position:0%
+notebook so that when you go to write up
+ 
+
+ align:start position:0%
+notebook so that when you go to write up
+your report
+
+ align:start position:0%
+your report
+ 
+
+ align:start position:0%
+your report
+you know you have all of the information
+
+ align:start position:0%
+you know you have all of the information
+ 
+
+ align:start position:0%
+you know you have all of the information
+that you need
+
+ align:start position:0%
+that you need
+ 
+
+ align:start position:0%
+that you need
+it's very hard to go back into the lab
+
+ align:start position:0%
+it's very hard to go back into the lab
+ 
+
+ align:start position:0%
+it's very hard to go back into the lab
+and write something down that you forgot
+
+ align:start position:0%
+and write something down that you forgot
+ 
+
+ align:start position:0%
+and write something down that you forgot
+after you're in your dorm room at 10 pm
+
+ align:start position:0%
+after you're in your dorm room at 10 pm
+ 
+
+ align:start position:0%
+after you're in your dorm room at 10 pm
+the night before the lab's due going oh
+
+ align:start position:0%
+the night before the lab's due going oh
+ 
+
+ align:start position:0%
+the night before the lab's due going oh
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+how much did this weigh so you want to
+
+ align:start position:0%
+how much did this weigh so you want to
+ 
+
+ align:start position:0%
+how much did this weigh so you want to
+plan out ahead of time what you're going
+
+ align:start position:0%
+plan out ahead of time what you're going
+ 
+
+ align:start position:0%
+plan out ahead of time what you're going
+to need to collect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are a bunch of parts of the lab
+
+ align:start position:0%
+there are a bunch of parts of the lab
+ 
+
+ align:start position:0%
+there are a bunch of parts of the lab
+report and this looks slightly
+
+ align:start position:0%
+report and this looks slightly
+ 
+
+ align:start position:0%
+report and this looks slightly
+overwhelming but it's actually there to
+
+ align:start position:0%
+overwhelming but it's actually there to
+ 
+
+ align:start position:0%
+overwhelming but it's actually there to
+help you
+
+ align:start position:0%
+help you
+ 
+
+ align:start position:0%
+help you
+kind of organize your thoughts and
+
+ align:start position:0%
+kind of organize your thoughts and
+ 
+
+ align:start position:0%
+kind of organize your thoughts and
+present things in a format that other
+
+ align:start position:0%
+present things in a format that other
+ 
+
+ align:start position:0%
+present things in a format that other
+people can recognize so if you've
+
+ align:start position:0%
+people can recognize so if you've
+ 
+
+ align:start position:0%
+people can recognize so if you've
+ever written a report for another course
+
+ align:start position:0%
+ever written a report for another course
+ 
+
+ align:start position:0%
+ever written a report for another course
+or if you've read scientific articles in
+
+ align:start position:0%
+or if you've read scientific articles in
+ 
+
+ align:start position:0%
+or if you've read scientific articles in
+the literature these
+
+ align:start position:0%
+the literature these
+ 
+
+ align:start position:0%
+the literature these
+titles may seem pretty familiar to you
+
+ align:start position:0%
+titles may seem pretty familiar to you
+ 
+
+ align:start position:0%
+titles may seem pretty familiar to you
+you guys
+
+ align:start position:0%
+you guys
+ 
+
+ align:start position:0%
+you guys
+written live reports for other classes
+
+ align:start position:0%
+written live reports for other classes
+ 
+
+ align:start position:0%
+written live reports for other classes
+before yes read articles most of you
+
+ align:start position:0%
+before yes read articles most of you
+ 
+
+ align:start position:0%
+before yes read articles most of you
+maybe okay so we're going to go through
+
+ align:start position:0%
+maybe okay so we're going to go through
+ 
+
+ align:start position:0%
+maybe okay so we're going to go through
+these parts of the lab report
+
+ align:start position:0%
+these parts of the lab report
+ 
+
+ align:start position:0%
+these parts of the lab report
+and talk about in detail what belongs in
+
+ align:start position:0%
+and talk about in detail what belongs in
+ 
+
+ align:start position:0%
+and talk about in detail what belongs in
+each section
+
+ align:start position:0%
+each section
+ 
+
+ align:start position:0%
+each section
+and we're going to try to do that in the
+
+ align:start position:0%
+and we're going to try to do that in the
+ 
+
+ align:start position:0%
+and we're going to try to do that in the
+context of the ferrocene experiment to
+
+ align:start position:0%
+context of the ferrocene experiment to
+ 
+
+ align:start position:0%
+context of the ferrocene experiment to
+help you guys sort of plan out your
+
+ align:start position:0%
+help you guys sort of plan out your
+ 
+
+ align:start position:0%
+help you guys sort of plan out your
+report
+
+ align:start position:0%
+report
+ 
+
+ align:start position:0%
+report
+for the one that you're going to have to
+
+ align:start position:0%
+for the one that you're going to have to
+ 
+
+ align:start position:0%
+for the one that you're going to have to
+write starting next week
+
+ align:start position:0%
+write starting next week
+ 
+
+ align:start position:0%
+write starting next week
+hopefully you've already started the
+
+ align:start position:0%
+hopefully you've already started the
+ 
+
+ align:start position:0%
+hopefully you've already started the
+little pieces of it
+
+ align:start position:0%
+little pieces of it
+ 
+
+ align:start position:0%
+little pieces of it
+so the first thing is the title that's
+
+ align:start position:0%
+so the first thing is the title that's
+ 
+
+ align:start position:0%
+so the first thing is the title that's
+usually pretty boring keep it straight
+
+ align:start position:0%
+usually pretty boring keep it straight
+ 
+
+ align:start position:0%
+usually pretty boring keep it straight
+to the point
+
+ align:start position:0%
+to the point
+ 
+
+ align:start position:0%
+to the point
+have it have something to do with what
+
+ align:start position:0%
+have it have something to do with what
+ 
+
+ align:start position:0%
+have it have something to do with what
+the experiment that you did is
+
+ align:start position:0%
+the experiment that you did is
+ 
+
+ align:start position:0%
+the experiment that you did is
+and then the first thing that you're
+
+ align:start position:0%
+and then the first thing that you're
+ 
+
+ align:start position:0%
+and then the first thing that you're
+going to write after the title is the
+
+ align:start position:0%
+going to write after the title is the
+ 
+
+ align:start position:0%
+going to write after the title is the
+abstract and the abstract that you guys
+
+ align:start position:0%
+abstract and the abstract that you guys
+ 
+
+ align:start position:0%
+abstract and the abstract that you guys
+are probably pretty familiar with
+
+ align:start position:0%
+are probably pretty familiar with
+ 
+
+ align:start position:0%
+are probably pretty familiar with
+is very short it's three to four
+
+ align:start position:0%
+is very short it's three to four
+ 
+
+ align:start position:0%
+is very short it's three to four
+sentences keep it in complete sentences
+
+ align:start position:0%
+sentences keep it in complete sentences
+ 
+
+ align:start position:0%
+sentences keep it in complete sentences
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+and then you discuss the point of the
+
+ align:start position:0%
+and then you discuss the point of the
+ 
+
+ align:start position:0%
+and then you discuss the point of the
+experiment you briefly tell what you did
+
+ align:start position:0%
+experiment you briefly tell what you did
+ 
+
+ align:start position:0%
+experiment you briefly tell what you did
+and what you found you can talk about
+
+ align:start position:0%
+and what you found you can talk about
+ 
+
+ align:start position:0%
+and what you found you can talk about
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+results if you have any yields melting
+
+ align:start position:0%
+results if you have any yields melting
+ 
+
+ align:start position:0%
+results if you have any yields melting
+points easily
+
+ align:start position:0%
+points easily
+ 
+
+ align:start position:0%
+points easily
+digestible results that you can put at
+
+ align:start position:0%
+digestible results that you can put at
+ 
+
+ align:start position:0%
+digestible results that you can put at
+the end so for your ferrocene you would
+
+ align:start position:0%
+the end so for your ferrocene you would
+ 
+
+ align:start position:0%
+the end so for your ferrocene you would
+say i
+
+ align:start position:0%
+say i
+ 
+
+ align:start position:0%
+say i
+synthesized ferrocene this many grams
+
+ align:start position:0%
+synthesized ferrocene this many grams
+ 
+
+ align:start position:0%
+synthesized ferrocene this many grams
+this was its melting point
+
+ align:start position:0%
+this was its melting point
+ 
+
+ align:start position:0%
+this was its melting point
+something like that and the abstract is
+
+ align:start position:0%
+something like that and the abstract is
+ 
+
+ align:start position:0%
+something like that and the abstract is
+best written at the end of your report
+
+ align:start position:0%
+best written at the end of your report
+ 
+
+ align:start position:0%
+best written at the end of your report
+so after you've done
+
+ align:start position:0%
+so after you've done
+ 
+
+ align:start position:0%
+so after you've done
+everything else then you can go back and
+
+ align:start position:0%
+everything else then you can go back and
+ 
+
+ align:start position:0%
+everything else then you can go back and
+write the abstract because the abstract
+
+ align:start position:0%
+write the abstract because the abstract
+ 
+
+ align:start position:0%
+write the abstract because the abstract
+is essentially just a short summary of
+
+ align:start position:0%
+is essentially just a short summary of
+ 
+
+ align:start position:0%
+is essentially just a short summary of
+everything else you've written
+
+ align:start position:0%
+everything else you've written
+ 
+
+ align:start position:0%
+everything else you've written
+so if all the other stuff is there then
+
+ align:start position:0%
+so if all the other stuff is there then
+ 
+
+ align:start position:0%
+so if all the other stuff is there then
+you can look at each section
+
+ align:start position:0%
+you can look at each section
+ 
+
+ align:start position:0%
+you can look at each section
+take a sentence out of it smush it all
+
+ align:start position:0%
+take a sentence out of it smush it all
+ 
+
+ align:start position:0%
+take a sentence out of it smush it all
+together and then you have your abstract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then after you're abstract on the
+
+ align:start position:0%
+so then after you're abstract on the
+ 
+
+ align:start position:0%
+so then after you're abstract on the
+start and the guidelines for how to
+
+ align:start position:0%
+start and the guidelines for how to
+ 
+
+ align:start position:0%
+start and the guidelines for how to
+format this and how to write everything
+
+ align:start position:0%
+format this and how to write everything
+ 
+
+ align:start position:0%
+format this and how to write everything
+are in your lab manual so you should
+
+ align:start position:0%
+are in your lab manual so you should
+ 
+
+ align:start position:0%
+are in your lab manual so you should
+definitely look at those
+
+ align:start position:0%
+definitely look at those
+ 
+
+ align:start position:0%
+definitely look at those
+while you are preparing your lab report
+
+ align:start position:0%
+while you are preparing your lab report
+ 
+
+ align:start position:0%
+while you are preparing your lab report
+and it'll tell you that
+
+ align:start position:0%
+and it'll tell you that
+ 
+
+ align:start position:0%
+and it'll tell you that
+after the abstract that goes on your
+
+ align:start position:0%
+after the abstract that goes on your
+ 
+
+ align:start position:0%
+after the abstract that goes on your
+first page the start of the second page
+
+ align:start position:0%
+first page the start of the second page
+ 
+
+ align:start position:0%
+first page the start of the second page
+of the lab report is going to be your
+
+ align:start position:0%
+of the lab report is going to be your
+ 
+
+ align:start position:0%
+of the lab report is going to be your
+introduction
+
+ align:start position:0%
+introduction
+ 
+
+ align:start position:0%
+introduction
+the introduction should probably be
+
+ align:start position:0%
+the introduction should probably be
+ 
+
+ align:start position:0%
+the introduction should probably be
+about a page or two long give or take
+
+ align:start position:0%
+about a page or two long give or take
+ 
+
+ align:start position:0%
+about a page or two long give or take
+depending on the experiment and how much
+
+ align:start position:0%
+depending on the experiment and how much
+ 
+
+ align:start position:0%
+depending on the experiment and how much
+you need to introduce ahead of time
+
+ align:start position:0%
+you need to introduce ahead of time
+ 
+
+ align:start position:0%
+you need to introduce ahead of time
+and you're going to tell the reader what
+
+ align:start position:0%
+and you're going to tell the reader what
+ 
+
+ align:start position:0%
+and you're going to tell the reader what
+you plan to do and why
+
+ align:start position:0%
+you plan to do and why
+ 
+
+ align:start position:0%
+you plan to do and why
+they should care about it give any
+
+ align:start position:0%
+they should care about it give any
+ 
+
+ align:start position:0%
+they should care about it give any
+background that is necessary so any
+
+ align:start position:0%
+background that is necessary so any
+ 
+
+ align:start position:0%
+background that is necessary so any
+historic background any scientific
+
+ align:start position:0%
+historic background any scientific
+ 
+
+ align:start position:0%
+historic background any scientific
+background experiments that have come
+
+ align:start position:0%
+background experiments that have come
+ 
+
+ align:start position:0%
+background experiments that have come
+before this one that influenced your
+
+ align:start position:0%
+before this one that influenced your
+ 
+
+ align:start position:0%
+before this one that influenced your
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+include balanced chemical equations of
+
+ align:start position:0%
+include balanced chemical equations of
+ 
+
+ align:start position:0%
+include balanced chemical equations of
+important reactions this is very
+
+ align:start position:0%
+important reactions this is very
+ 
+
+ align:start position:0%
+important reactions this is very
+important so if you're going to be doing
+
+ align:start position:0%
+important so if you're going to be doing
+ 
+
+ align:start position:0%
+important so if you're going to be doing
+some sort of chemical reaction which in
+
+ align:start position:0%
+some sort of chemical reaction which in
+ 
+
+ align:start position:0%
+some sort of chemical reaction which in
+this lab
+
+ align:start position:0%
+this lab
+ 
+
+ align:start position:0%
+this lab
+we did we did two then you should
+
+ align:start position:0%
+we did we did two then you should
+ 
+
+ align:start position:0%
+we did we did two then you should
+include
+
+ align:start position:0%
+include
+ 
+
+ align:start position:0%
+include
+the balanced chemical equation for what
+
+ align:start position:0%
+the balanced chemical equation for what
+ 
+
+ align:start position:0%
+the balanced chemical equation for what
+the work that you're planning to do
+
+ align:start position:0%
+the work that you're planning to do
+ 
+
+ align:start position:0%
+the work that you're planning to do
+and then also any fundamental
+
+ align:start position:0%
+and then also any fundamental
+ 
+
+ align:start position:0%
+and then also any fundamental
+mathematical equations that you plan to
+
+ align:start position:0%
+mathematical equations that you plan to
+ 
+
+ align:start position:0%
+mathematical equations that you plan to
+use to analyze your data in this case we
+
+ align:start position:0%
+use to analyze your data in this case we
+ 
+
+ align:start position:0%
+use to analyze your data in this case we
+don't have so many in this lab but in
+
+ align:start position:0%
+don't have so many in this lab but in
+ 
+
+ align:start position:0%
+don't have so many in this lab but in
+future labs
+
+ align:start position:0%
+future labs
+ 
+
+ align:start position:0%
+future labs
+like the catalase lab when you're doing
+
+ align:start position:0%
+like the catalase lab when you're doing
+ 
+
+ align:start position:0%
+like the catalase lab when you're doing
+kinetics you'll be have
+
+ align:start position:0%
+kinetics you'll be have
+ 
+
+ align:start position:0%
+kinetics you'll be have
+you'll have a lot more mathematical
+
+ align:start position:0%
+you'll have a lot more mathematical
+ 
+
+ align:start position:0%
+you'll have a lot more mathematical
+equations that you're going to need to
+
+ align:start position:0%
+equations that you're going to need to
+ 
+
+ align:start position:0%
+equations that you're going to need to
+use and explain
+
+ align:start position:0%
+use and explain
+ 
+
+ align:start position:0%
+use and explain
+to your reader at the beginning so that
+
+ align:start position:0%
+to your reader at the beginning so that
+ 
+
+ align:start position:0%
+to your reader at the beginning so that
+they know what's coming and then you
+
+ align:start position:0%
+they know what's coming and then you
+ 
+
+ align:start position:0%
+they know what's coming and then you
+want to discuss any important techniques
+
+ align:start position:0%
+want to discuss any important techniques
+ 
+
+ align:start position:0%
+want to discuss any important techniques
+and why you need to use them in the lab
+
+ align:start position:0%
+and why you need to use them in the lab
+ 
+
+ align:start position:0%
+and why you need to use them in the lab
+sort of their relevance to the
+
+ align:start position:0%
+sort of their relevance to the
+ 
+
+ align:start position:0%
+sort of their relevance to the
+experiment that you are
+
+ align:start position:0%
+experiment that you are
+ 
+
+ align:start position:0%
+experiment that you are
+planning to do so with this in mind
+
+ align:start position:0%
+planning to do so with this in mind
+ 
+
+ align:start position:0%
+planning to do so with this in mind
+let's brainstorm what might go in the
+
+ align:start position:0%
+let's brainstorm what might go in the
+ 
+
+ align:start position:0%
+let's brainstorm what might go in the
+introduction of your ferris scene
+
+ align:start position:0%
+introduction of your ferris scene
+ 
+
+ align:start position:0%
+introduction of your ferris scene
+reports
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can think about the ferrocene
+
+ align:start position:0%
+so you can think about the ferrocene
+ 
+
+ align:start position:0%
+so you can think about the ferrocene
+lecture from tuesday
+
+ align:start position:0%
+lecture from tuesday
+ 
+
+ align:start position:0%
+lecture from tuesday
+stuff you've done in the lab so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah like how it was discovered and how
+
+ align:start position:0%
+yeah like how it was discovered and how
+ 
+
+ align:start position:0%
+yeah like how it was discovered and how
+it launched
+
+ align:start position:0%
+it launched
+ 
+
+ align:start position:0%
+it launched
+like transition metal chemistry yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the discovery in history
+
+ align:start position:0%
+the discovery in history
+ 
+
+ align:start position:0%
+the discovery in history
+of ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and other organometallic chemistry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um relevant this is a parasite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uses a ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you guys perform the acetylation of
+
+ align:start position:0%
+you guys perform the acetylation of
+ 
+
+ align:start position:0%
+you guys perform the acetylation of
+ferrous scene so why do we care that you
+
+ align:start position:0%
+ferrous scene so why do we care that you
+ 
+
+ align:start position:0%
+ferrous scene so why do we care that you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+add different groups to the pharisee
+
+ align:start position:0%
+add different groups to the pharisee
+ 
+
+ align:start position:0%
+add different groups to the pharisee
+rings that's a good thing to mention
+
+ align:start position:0%
+rings that's a good thing to mention
+ 
+
+ align:start position:0%
+rings that's a good thing to mention
+so we've got some historic and
+
+ align:start position:0%
+so we've got some historic and
+ 
+
+ align:start position:0%
+so we've got some historic and
+scientific background what else can we
+
+ align:start position:0%
+scientific background what else can we
+ 
+
+ align:start position:0%
+scientific background what else can we
+put in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um like synthesis of ferrocene so like
+
+ align:start position:0%
+um like synthesis of ferrocene so like
+ 
+
+ align:start position:0%
+um like synthesis of ferrocene so like
+the equations the equations with the
+
+ align:start position:0%
+the equations the equations with the
+ 
+
+ align:start position:0%
+the equations the equations with the
+organic molecules yeah
+
+ align:start position:0%
+organic molecules yeah
+ 
+
+ align:start position:0%
+organic molecules yeah
+yep chemical equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and acetyl ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we've got our balance chemical
+
+ align:start position:0%
+all right we've got our balance chemical
+ 
+
+ align:start position:0%
+all right we've got our balance chemical
+equations do we have any mathematical
+
+ align:start position:0%
+equations do we have any mathematical
+ 
+
+ align:start position:0%
+equations do we have any mathematical
+equations that we need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no then what techniques might you talk
+
+ align:start position:0%
+no then what techniques might you talk
+ 
+
+ align:start position:0%
+no then what techniques might you talk
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah sublimation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah inert air free technique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you want to talk about that and
+
+ align:start position:0%
+yeah so you want to talk about that and
+ 
+
+ align:start position:0%
+yeah so you want to talk about that and
+why we care about that in relation to
+
+ align:start position:0%
+why we care about that in relation to
+ 
+
+ align:start position:0%
+why we care about that in relation to
+what could happen to the different
+
+ align:start position:0%
+what could happen to the different
+ 
+
+ align:start position:0%
+what could happen to the different
+components of our ferrocene synthesis
+
+ align:start position:0%
+components of our ferrocene synthesis
+ 
+
+ align:start position:0%
+components of our ferrocene synthesis
+what other techniques um then layer from
+
+ align:start position:0%
+what other techniques um then layer from
+ 
+
+ align:start position:0%
+what other techniques um then layer from
+yeah tlc
+
+ align:start position:0%
+yeah tlc
+ 
+
+ align:start position:0%
+yeah tlc
+and and the column
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+running out of room yeah tlc
+
+ align:start position:0%
+running out of room yeah tlc
+ 
+
+ align:start position:0%
+running out of room yeah tlc
+and column chromatography so how you're
+
+ align:start position:0%
+and column chromatography so how you're
+ 
+
+ align:start position:0%
+and column chromatography so how you're
+going to purify your products when
+
+ align:start position:0%
+going to purify your products when
+ 
+
+ align:start position:0%
+going to purify your products when
+you're done
+
+ align:start position:0%
+you're done
+ 
+
+ align:start position:0%
+you're done
+yes anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we can talk about filtration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how you're going to isolate your
+
+ align:start position:0%
+how you're going to isolate your
+ 
+
+ align:start position:0%
+how you're going to isolate your
+products from
+
+ align:start position:0%
+products from
+ 
+
+ align:start position:0%
+products from
+during the synthesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah melting point melting point and how
+
+ align:start position:0%
+yeah melting point melting point and how
+ 
+
+ align:start position:0%
+yeah melting point melting point and how
+you can use the analysis the melting
+
+ align:start position:0%
+you can use the analysis the melting
+ 
+
+ align:start position:0%
+you can use the analysis the melting
+point analysis so what
+
+ align:start position:0%
+point analysis so what
+ 
+
+ align:start position:0%
+point analysis so what
+does the melting point tell you what
+
+ align:start position:0%
+does the melting point tell you what
+ 
+
+ align:start position:0%
+does the melting point tell you what
+information are we getting from that why
+
+ align:start position:0%
+information are we getting from that why
+ 
+
+ align:start position:0%
+information are we getting from that why
+are we taking melting points
+
+ align:start position:0%
+are we taking melting points
+ 
+
+ align:start position:0%
+are we taking melting points
+yeah still tell you the purity yeah so
+
+ align:start position:0%
+yeah still tell you the purity yeah so
+ 
+
+ align:start position:0%
+yeah still tell you the purity yeah so
+you can compare it to the literature
+
+ align:start position:0%
+you can compare it to the literature
+ 
+
+ align:start position:0%
+you can compare it to the literature
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+and you can look at the width of the
+
+ align:start position:0%
+and you can look at the width of the
+ 
+
+ align:start position:0%
+and you can look at the width of the
+melting range to see how pure your
+
+ align:start position:0%
+melting range to see how pure your
+ 
+
+ align:start position:0%
+melting range to see how pure your
+compound is
+
+ align:start position:0%
+compound is
+ 
+
+ align:start position:0%
+compound is
+so all of these things are good things
+
+ align:start position:0%
+so all of these things are good things
+ 
+
+ align:start position:0%
+so all of these things are good things
+that you can discuss
+
+ align:start position:0%
+that you can discuss
+ 
+
+ align:start position:0%
+that you can discuss
+in your introduction and you don't need
+
+ align:start position:0%
+in your introduction and you don't need
+ 
+
+ align:start position:0%
+in your introduction and you don't need
+to go into crazy amounts of detail
+
+ align:start position:0%
+to go into crazy amounts of detail
+ 
+
+ align:start position:0%
+to go into crazy amounts of detail
+but you want to give enough detail that
+
+ align:start position:0%
+but you want to give enough detail that
+ 
+
+ align:start position:0%
+but you want to give enough detail that
+the reader will know why
+
+ align:start position:0%
+the reader will know why
+ 
+
+ align:start position:0%
+the reader will know why
+those are important for your particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a note on including equations in the
+
+ align:start position:0%
+so a note on including equations in the
+ 
+
+ align:start position:0%
+so a note on including equations in the
+lab report we said that you need to
+
+ align:start position:0%
+lab report we said that you need to
+ 
+
+ align:start position:0%
+lab report we said that you need to
+include any mathematic or chemical
+
+ align:start position:0%
+include any mathematic or chemical
+ 
+
+ align:start position:0%
+include any mathematic or chemical
+equations that you're going to be used
+
+ align:start position:0%
+equations that you're going to be used
+ 
+
+ align:start position:0%
+equations that you're going to be used
+in the introduction and the way that you
+
+ align:start position:0%
+in the introduction and the way that you
+ 
+
+ align:start position:0%
+in the introduction and the way that you
+do this is you give each equation a
+
+ align:start position:0%
+do this is you give each equation a
+ 
+
+ align:start position:0%
+do this is you give each equation a
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+and when you write it in your report
+
+ align:start position:0%
+and when you write it in your report
+ 
+
+ align:start position:0%
+and when you write it in your report
+you'll write either the chemical
+
+ align:start position:0%
+you'll write either the chemical
+ 
+
+ align:start position:0%
+you'll write either the chemical
+equation or a mathematical equation and
+
+ align:start position:0%
+equation or a mathematical equation and
+ 
+
+ align:start position:0%
+equation or a mathematical equation and
+then over to the right in parentheses
+
+ align:start position:0%
+then over to the right in parentheses
+ 
+
+ align:start position:0%
+then over to the right in parentheses
+you'll number them and you'll number
+
+ align:start position:0%
+you'll number them and you'll number
+ 
+
+ align:start position:0%
+you'll number them and you'll number
+them in order
+
+ align:start position:0%
+them in order
+ 
+
+ align:start position:0%
+them in order
+and you can either number them both the
+
+ align:start position:0%
+and you can either number them both the
+ 
+
+ align:start position:0%
+and you can either number them both the
+chemical and the mathematical equations
+
+ align:start position:0%
+chemical and the mathematical equations
+ 
+
+ align:start position:0%
+chemical and the mathematical equations
+sequentially so you can just any
+
+ align:start position:0%
+sequentially so you can just any
+ 
+
+ align:start position:0%
+sequentially so you can just any
+equation no matter what kind it is just
+
+ align:start position:0%
+equation no matter what kind it is just
+ 
+
+ align:start position:0%
+equation no matter what kind it is just
+go 1 2 3 all the way down
+
+ align:start position:0%
+go 1 2 3 all the way down
+ 
+
+ align:start position:0%
+go 1 2 3 all the way down
+or if you want you can separate and have
+
+ align:start position:0%
+or if you want you can separate and have
+ 
+
+ align:start position:0%
+or if you want you can separate and have
+one of the types of equations be in just
+
+ align:start position:0%
+one of the types of equations be in just
+ 
+
+ align:start position:0%
+one of the types of equations be in just
+regular numbers and then the other one
+
+ align:start position:0%
+regular numbers and then the other one
+ 
+
+ align:start position:0%
+regular numbers and then the other one
+in roman numerals
+
+ align:start position:0%
+in roman numerals
+ 
+
+ align:start position:0%
+in roman numerals
+both formats are acceptable and if you
+
+ align:start position:0%
+both formats are acceptable and if you
+ 
+
+ align:start position:0%
+both formats are acceptable and if you
+have any questions about how to do any
+
+ align:start position:0%
+have any questions about how to do any
+ 
+
+ align:start position:0%
+have any questions about how to do any
+of the formatting things i'm going to
+
+ align:start position:0%
+of the formatting things i'm going to
+ 
+
+ align:start position:0%
+of the formatting things i'm going to
+talk to you about it's all from the acs
+
+ align:start position:0%
+talk to you about it's all from the acs
+ 
+
+ align:start position:0%
+talk to you about it's all from the acs
+style guide
+
+ align:start position:0%
+style guide
+ 
+
+ align:start position:0%
+style guide
+so we have these books in the lab if you
+
+ align:start position:0%
+so we have these books in the lab if you
+ 
+
+ align:start position:0%
+so we have these books in the lab if you
+want to borrow one
+
+ align:start position:0%
+want to borrow one
+ 
+
+ align:start position:0%
+want to borrow one
+there's some information online as well
+
+ align:start position:0%
+there's some information online as well
+ 
+
+ align:start position:0%
+there's some information online as well
+or you can talk to
+
+ align:start position:0%
+or you can talk to
+ 
+
+ align:start position:0%
+or you can talk to
+me or john or the tas if you have
+
+ align:start position:0%
+me or john or the tas if you have
+ 
+
+ align:start position:0%
+me or john or the tas if you have
+questions and can't find anything but
+
+ align:start position:0%
+questions and can't find anything but
+ 
+
+ align:start position:0%
+questions and can't find anything but
+that's where all of the information for
+
+ align:start position:0%
+that's where all of the information for
+ 
+
+ align:start position:0%
+that's where all of the information for
+how to format things from this
+
+ align:start position:0%
+how to format things from this
+ 
+
+ align:start position:0%
+how to format things from this
+presentation are coming from so we're
+
+ align:start position:0%
+presentation are coming from so we're
+ 
+
+ align:start position:0%
+presentation are coming from so we're
+going to use acs formatting for
+
+ align:start position:0%
+going to use acs formatting for
+ 
+
+ align:start position:0%
+going to use acs formatting for
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+and then the important thing is that
+
+ align:start position:0%
+and then the important thing is that
+ 
+
+ align:start position:0%
+and then the important thing is that
+equations and anything else that you add
+
+ align:start position:0%
+equations and anything else that you add
+ 
+
+ align:start position:0%
+equations and anything else that you add
+like tables and figures and we'll talk
+
+ align:start position:0%
+like tables and figures and we'll talk
+ 
+
+ align:start position:0%
+like tables and figures and we'll talk
+about those in a little bit they can't
+
+ align:start position:0%
+about those in a little bit they can't
+ 
+
+ align:start position:0%
+about those in a little bit they can't
+stand on their own you must reference
+
+ align:start position:0%
+stand on their own you must reference
+ 
+
+ align:start position:0%
+stand on their own you must reference
+them in the text
+
+ align:start position:0%
+them in the text
+ 
+
+ align:start position:0%
+them in the text
+so you can't just throw an equation up
+
+ align:start position:0%
+so you can't just throw an equation up
+ 
+
+ align:start position:0%
+so you can't just throw an equation up
+here and not talk about it you'll have
+
+ align:start position:0%
+here and not talk about it you'll have
+ 
+
+ align:start position:0%
+here and not talk about it you'll have
+to throw in a sentence that says the
+
+ align:start position:0%
+to throw in a sentence that says the
+ 
+
+ align:start position:0%
+to throw in a sentence that says the
+reaction of copper and nitric acid as
+
+ align:start position:0%
+reaction of copper and nitric acid as
+ 
+
+ align:start position:0%
+reaction of copper and nitric acid as
+shown in equation one
+
+ align:start position:0%
+shown in equation one
+ 
+
+ align:start position:0%
+shown in equation one
+so the next part is procedures and
+
+ align:start position:0%
+so the next part is procedures and
+ 
+
+ align:start position:0%
+so the next part is procedures and
+observations
+
+ align:start position:0%
+observations
+ 
+
+ align:start position:0%
+observations
+so this includes what you actually did
+
+ align:start position:0%
+so this includes what you actually did
+ 
+
+ align:start position:0%
+so this includes what you actually did
+in the lab and the really important
+
+ align:start position:0%
+in the lab and the really important
+ 
+
+ align:start position:0%
+in the lab and the really important
+thing about this is that it has to match
+
+ align:start position:0%
+thing about this is that it has to match
+ 
+
+ align:start position:0%
+thing about this is that it has to match
+what is in your lab notebook
+
+ align:start position:0%
+what is in your lab notebook
+ 
+
+ align:start position:0%
+what is in your lab notebook
+so we already gave you an idealized
+
+ align:start position:0%
+so we already gave you an idealized
+ 
+
+ align:start position:0%
+so we already gave you an idealized
+version of the procedure of
+
+ align:start position:0%
+version of the procedure of
+ 
+
+ align:start position:0%
+version of the procedure of
+kind of an idea of how you're supposed
+
+ align:start position:0%
+kind of an idea of how you're supposed
+ 
+
+ align:start position:0%
+kind of an idea of how you're supposed
+to be doing it but we want to know what
+
+ align:start position:0%
+to be doing it but we want to know what
+ 
+
+ align:start position:0%
+to be doing it but we want to know what
+actually happened when you did the
+
+ align:start position:0%
+actually happened when you did the
+ 
+
+ align:start position:0%
+actually happened when you did the
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+so if you accidentally added twice as
+
+ align:start position:0%
+so if you accidentally added twice as
+ 
+
+ align:start position:0%
+so if you accidentally added twice as
+much cyclopentadiene as you were
+
+ align:start position:0%
+much cyclopentadiene as you were
+ 
+
+ align:start position:0%
+much cyclopentadiene as you were
+supposed to
+
+ align:start position:0%
+supposed to
+ 
+
+ align:start position:0%
+supposed to
+write that in your procedure
+
+ align:start position:0%
+write that in your procedure
+ 
+
+ align:start position:0%
+write that in your procedure
+don't just recopy what is in the lab
+
+ align:start position:0%
+don't just recopy what is in the lab
+ 
+
+ align:start position:0%
+don't just recopy what is in the lab
+notebook
+
+ align:start position:0%
+notebook
+ 
+
+ align:start position:0%
+notebook
+draw a diagram of any specialty
+
+ align:start position:0%
+draw a diagram of any specialty
+ 
+
+ align:start position:0%
+draw a diagram of any specialty
+glassware that you use so you don't need
+
+ align:start position:0%
+glassware that you use so you don't need
+ 
+
+ align:start position:0%
+glassware that you use so you don't need
+to tell us piece by piece how you
+
+ align:start position:0%
+to tell us piece by piece how you
+ 
+
+ align:start position:0%
+to tell us piece by piece how you
+assembled your glassware you can just
+
+ align:start position:0%
+assembled your glassware you can just
+ 
+
+ align:start position:0%
+assembled your glassware you can just
+draw a picture and say i set up a
+
+ align:start position:0%
+draw a picture and say i set up a
+ 
+
+ align:start position:0%
+draw a picture and say i set up a
+distillation as shown in figure one
+
+ align:start position:0%
+distillation as shown in figure one
+ 
+
+ align:start position:0%
+distillation as shown in figure one
+and that's all you need to do then you
+
+ align:start position:0%
+and that's all you need to do then you
+ 
+
+ align:start position:0%
+and that's all you need to do then you
+need to give enough
+
+ align:start position:0%
+need to give enough
+ 
+
+ align:start position:0%
+need to give enough
+information for one of your classmates
+
+ align:start position:0%
+information for one of your classmates
+ 
+
+ align:start position:0%
+information for one of your classmates
+to recreate the procedure so again you
+
+ align:start position:0%
+to recreate the procedure so again you
+ 
+
+ align:start position:0%
+to recreate the procedure so again you
+don't need to go into excruciating
+
+ align:start position:0%
+don't need to go into excruciating
+ 
+
+ align:start position:0%
+don't need to go into excruciating
+detail about how you
+
+ align:start position:0%
+detail about how you
+ 
+
+ align:start position:0%
+detail about how you
+injected things out of a syringe assume
+
+ align:start position:0%
+injected things out of a syringe assume
+ 
+
+ align:start position:0%
+injected things out of a syringe assume
+that one of your classmates is reading
+
+ align:start position:0%
+that one of your classmates is reading
+ 
+
+ align:start position:0%
+that one of your classmates is reading
+this and they have the same knowledge
+
+ align:start position:0%
+this and they have the same knowledge
+ 
+
+ align:start position:0%
+this and they have the same knowledge
+that you do so if you say i used a
+
+ align:start position:0%
+that you do so if you say i used a
+ 
+
+ align:start position:0%
+that you do so if you say i used a
+syringe to measure this or a syringe was
+
+ align:start position:0%
+syringe to measure this or a syringe was
+ 
+
+ align:start position:0%
+syringe to measure this or a syringe was
+used because you're not supposed to use
+
+ align:start position:0%
+used because you're not supposed to use
+ 
+
+ align:start position:0%
+used because you're not supposed to use
+pronouns then
+
+ align:start position:0%
+pronouns then
+ 
+
+ align:start position:0%
+pronouns then
+that will be enough information for one
+
+ align:start position:0%
+that will be enough information for one
+ 
+
+ align:start position:0%
+that will be enough information for one
+of us to recreate the experiment
+
+ align:start position:0%
+of us to recreate the experiment
+ 
+
+ align:start position:0%
+of us to recreate the experiment
+include all the information about a
+
+ align:start position:0%
+include all the information about a
+ 
+
+ align:start position:0%
+include all the information about a
+chemical with the correct precision
+
+ align:start position:0%
+chemical with the correct precision
+ 
+
+ align:start position:0%
+chemical with the correct precision
+so you want to if you know when you're
+
+ align:start position:0%
+so you want to if you know when you're
+ 
+
+ align:start position:0%
+so you want to if you know when you're
+measuring and we'll talk about this next
+
+ align:start position:0%
+measuring and we'll talk about this next
+ 
+
+ align:start position:0%
+measuring and we'll talk about this next
+week in our lecture
+
+ align:start position:0%
+week in our lecture
+ 
+
+ align:start position:0%
+week in our lecture
+about the different precision of
+
+ align:start position:0%
+about the different precision of
+ 
+
+ align:start position:0%
+about the different precision of
+glassware you want to
+
+ align:start position:0%
+glassware you want to
+ 
+
+ align:start position:0%
+glassware you want to
+include all relevant significant figures
+
+ align:start position:0%
+include all relevant significant figures
+ 
+
+ align:start position:0%
+include all relevant significant figures
+so if you're measuring something
+
+ align:start position:0%
+so if you're measuring something
+ 
+
+ align:start position:0%
+so if you're measuring something
+that has more than one decimal place
+
+ align:start position:0%
+that has more than one decimal place
+ 
+
+ align:start position:0%
+that has more than one decimal place
+include all of the decimal places so 5.2
+
+ align:start position:0%
+include all of the decimal places so 5.2
+ 
+
+ align:start position:0%
+include all of the decimal places so 5.2
+milliliters of eight molar
+
+ align:start position:0%
+milliliters of eight molar
+ 
+
+ align:start position:0%
+milliliters of eight molar
+nitric acid was added not just five
+
+ align:start position:0%
+nitric acid was added not just five
+ 
+
+ align:start position:0%
+nitric acid was added not just five
+milliliters of added and
+
+ align:start position:0%
+milliliters of added and
+ 
+
+ align:start position:0%
+milliliters of added and
+if there's any specific way that you
+
+ align:start position:0%
+if there's any specific way that you
+ 
+
+ align:start position:0%
+if there's any specific way that you
+added things like when you guys added
+
+ align:start position:0%
+added things like when you guys added
+ 
+
+ align:start position:0%
+added things like when you guys added
+your aliquots you did 0.25 milliliters
+
+ align:start position:0%
+your aliquots you did 0.25 milliliters
+ 
+
+ align:start position:0%
+your aliquots you did 0.25 milliliters
+at a time you want to include that
+
+ align:start position:0%
+at a time you want to include that
+ 
+
+ align:start position:0%
+at a time you want to include that
+so that people don't add it all at once
+
+ align:start position:0%
+so that people don't add it all at once
+ 
+
+ align:start position:0%
+so that people don't add it all at once
+something like that or if you add
+
+ align:start position:0%
+something like that or if you add
+ 
+
+ align:start position:0%
+something like that or if you add
+something dropwise
+
+ align:start position:0%
+something dropwise
+ 
+
+ align:start position:0%
+something dropwise
+make sure that's included and then you
+
+ align:start position:0%
+make sure that's included and then you
+ 
+
+ align:start position:0%
+make sure that's included and then you
+want to give brief observations about
+
+ align:start position:0%
+want to give brief observations about
+ 
+
+ align:start position:0%
+want to give brief observations about
+color texture and state of matter of
+
+ align:start position:0%
+color texture and state of matter of
+ 
+
+ align:start position:0%
+color texture and state of matter of
+your product so
+
+ align:start position:0%
+your product so
+ 
+
+ align:start position:0%
+your product so
+you can say i formed five grams of a
+
+ align:start position:0%
+you can say i formed five grams of a
+ 
+
+ align:start position:0%
+you can say i formed five grams of a
+white powder
+
+ align:start position:0%
+white powder
+ 
+
+ align:start position:0%
+white powder
+something like that just so that again
+
+ align:start position:0%
+something like that just so that again
+ 
+
+ align:start position:0%
+something like that just so that again
+when the reader's doing the lab if they
+
+ align:start position:0%
+when the reader's doing the lab if they
+ 
+
+ align:start position:0%
+when the reader's doing the lab if they
+get a white powder they want to know oh
+
+ align:start position:0%
+get a white powder they want to know oh
+ 
+
+ align:start position:0%
+get a white powder they want to know oh
+is this is this correct yes and then if
+
+ align:start position:0%
+is this is this correct yes and then if
+ 
+
+ align:start position:0%
+is this is this correct yes and then if
+there are any safety concerns that are
+
+ align:start position:0%
+there are any safety concerns that are
+ 
+
+ align:start position:0%
+there are any safety concerns that are
+relevant or unusual
+
+ align:start position:0%
+relevant or unusual
+ 
+
+ align:start position:0%
+relevant or unusual
+those can also go in your procedure and
+
+ align:start position:0%
+those can also go in your procedure and
+ 
+
+ align:start position:0%
+those can also go in your procedure and
+observation section
+
+ align:start position:0%
+observation section
+ 
+
+ align:start position:0%
+observation section
+so again thinking about ferrocene what
+
+ align:start position:0%
+so again thinking about ferrocene what
+ 
+
+ align:start position:0%
+so again thinking about ferrocene what
+are you going to write out the
+
+ align:start position:0%
+are you going to write out the
+ 
+
+ align:start position:0%
+are you going to write out the
+procedures of
+
+ align:start position:0%
+procedures of
+ 
+
+ align:start position:0%
+procedures of
+what was the first thing that we did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess not even that you guys did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cracking the cyclopentadiene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so even though you guys didn't do that
+
+ align:start position:0%
+so even though you guys didn't do that
+ 
+
+ align:start position:0%
+so even though you guys didn't do that
+necessarily yourselves that was an
+
+ align:start position:0%
+necessarily yourselves that was an
+ 
+
+ align:start position:0%
+necessarily yourselves that was an
+important part of the procedure so you
+
+ align:start position:0%
+important part of the procedure so you
+ 
+
+ align:start position:0%
+important part of the procedure so you
+should include
+
+ align:start position:0%
+should include
+ 
+
+ align:start position:0%
+should include
+cracking the cyclopentadiene monomer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so your other question yeah um like was
+
+ align:start position:0%
+so your other question yeah um like was
+ 
+
+ align:start position:0%
+so your other question yeah um like was
+this not absolutely dry
+
+ align:start position:0%
+this not absolutely dry
+ 
+
+ align:start position:0%
+this not absolutely dry
+so if we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so if you're going to be drawing
+
+ align:start position:0%
+yeah so if you're going to be drawing
+ 
+
+ align:start position:0%
+yeah so if you're going to be drawing
+any pictures of glassware or
+
+ align:start position:0%
+any pictures of glassware or
+ 
+
+ align:start position:0%
+any pictures of glassware or
+chemical equations you can handwrite
+
+ align:start position:0%
+chemical equations you can handwrite
+ 
+
+ align:start position:0%
+chemical equations you can handwrite
+them and scan them in and insert them as
+
+ align:start position:0%
+them and scan them in and insert them as
+ 
+
+ align:start position:0%
+them and scan them in and insert them as
+pictures into your lab report if that's
+
+ align:start position:0%
+pictures into your lab report if that's
+ 
+
+ align:start position:0%
+pictures into your lab report if that's
+easier
+
+ align:start position:0%
+easier
+ 
+
+ align:start position:0%
+easier
+you can also use for chemical equations
+
+ align:start position:0%
+you can also use for chemical equations
+ 
+
+ align:start position:0%
+you can also use for chemical equations
+especially chemdraw if you have access
+
+ align:start position:0%
+especially chemdraw if you have access
+ 
+
+ align:start position:0%
+especially chemdraw if you have access
+to that on a
+
+ align:start position:0%
+to that on a
+ 
+
+ align:start position:0%
+to that on a
+lab computer or there's some free
+
+ align:start position:0%
+lab computer or there's some free
+ 
+
+ align:start position:0%
+lab computer or there's some free
+versions like marvinsketch or chemdoodle
+
+ align:start position:0%
+versions like marvinsketch or chemdoodle
+ 
+
+ align:start position:0%
+versions like marvinsketch or chemdoodle
+that you can find online
+
+ align:start position:0%
+that you can find online
+ 
+
+ align:start position:0%
+that you can find online
+that'll give you the actual chemical
+
+ align:start position:0%
+that'll give you the actual chemical
+ 
+
+ align:start position:0%
+that'll give you the actual chemical
+structures that you can draw and then
+
+ align:start position:0%
+structures that you can draw and then
+ 
+
+ align:start position:0%
+structures that you can draw and then
+you can just copy and paste those into
+
+ align:start position:0%
+you can just copy and paste those into
+ 
+
+ align:start position:0%
+you can just copy and paste those into
+your lab report
+
+ align:start position:0%
+your lab report
+ 
+
+ align:start position:0%
+your lab report
+and also if you have chem draw it has a
+
+ align:start position:0%
+and also if you have chem draw it has a
+ 
+
+ align:start position:0%
+and also if you have chem draw it has a
+glassware feature where you can actually
+
+ align:start position:0%
+glassware feature where you can actually
+ 
+
+ align:start position:0%
+glassware feature where you can actually
+build different glassware setups you can
+
+ align:start position:0%
+build different glassware setups you can
+ 
+
+ align:start position:0%
+build different glassware setups you can
+build the distillation in there if you
+
+ align:start position:0%
+build the distillation in there if you
+ 
+
+ align:start position:0%
+build the distillation in there if you
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+but yeah if you hand write anything like
+
+ align:start position:0%
+but yeah if you hand write anything like
+ 
+
+ align:start position:0%
+but yeah if you hand write anything like
+equations or pictures you can scan those
+
+ align:start position:0%
+equations or pictures you can scan those
+ 
+
+ align:start position:0%
+equations or pictures you can scan those
+in and insert them as a picture
+
+ align:start position:0%
+in and insert them as a picture
+ 
+
+ align:start position:0%
+in and insert them as a picture
+so once you crack the cp what was the
+
+ align:start position:0%
+so once you crack the cp what was the
+ 
+
+ align:start position:0%
+so once you crack the cp what was the
+next big part of the procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first thing you made
+
+ align:start position:0%
+first thing you made
+ 
+
+ align:start position:0%
+first thing you made
+we'll just call it synthesis of
+
+ align:start position:0%
+we'll just call it synthesis of
+ 
+
+ align:start position:0%
+we'll just call it synthesis of
+ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that would be yeah preparing the koh
+
+ align:start position:0%
+so that would be yeah preparing the koh
+ 
+
+ align:start position:0%
+so that would be yeah preparing the koh
+preparing the iron chloride mixing them
+
+ align:start position:0%
+preparing the iron chloride mixing them
+ 
+
+ align:start position:0%
+preparing the iron chloride mixing them
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+shaking for who knows how long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then your filtration and your
+
+ align:start position:0%
+and then your filtration and your
+ 
+
+ align:start position:0%
+and then your filtration and your
+isolation of the ferrocene
+
+ align:start position:0%
+isolation of the ferrocene
+ 
+
+ align:start position:0%
+isolation of the ferrocene
+then the next thing was the synthesis of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acetyl ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which some of you have done and some of
+
+ align:start position:0%
+which some of you have done and some of
+ 
+
+ align:start position:0%
+which some of you have done and some of
+you will do today and then
+
+ align:start position:0%
+you will do today and then
+ 
+
+ align:start position:0%
+you will do today and then
+what are we doing next week the last day
+
+ align:start position:0%
+what are we doing next week the last day
+ 
+
+ align:start position:0%
+what are we doing next week the last day
+tlc the important parts of that are
+
+ align:start position:0%
+tlc the important parts of that are
+ 
+
+ align:start position:0%
+tlc the important parts of that are
+running the tlc and also choosing your
+
+ align:start position:0%
+running the tlc and also choosing your
+ 
+
+ align:start position:0%
+running the tlc and also choosing your
+solvent so you want to make sure that
+
+ align:start position:0%
+solvent so you want to make sure that
+ 
+
+ align:start position:0%
+solvent so you want to make sure that
+you include both of those things in
+
+ align:start position:0%
+you include both of those things in
+ 
+
+ align:start position:0%
+you include both of those things in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and then what's the last thing we're
+
+ align:start position:0%
+and then what's the last thing we're
+ 
+
+ align:start position:0%
+and then what's the last thing we're
+going to do to purify the product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+column chromatography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you'll have a bunch of different
+
+ align:start position:0%
+so you'll have a bunch of different
+ 
+
+ align:start position:0%
+so you'll have a bunch of different
+parts to the procedure for this lab and
+
+ align:start position:0%
+parts to the procedure for this lab and
+ 
+
+ align:start position:0%
+parts to the procedure for this lab and
+for most of the labs that we do
+
+ align:start position:0%
+for most of the labs that we do
+ 
+
+ align:start position:0%
+for most of the labs that we do
+especially since they're all multiple
+
+ align:start position:0%
+especially since they're all multiple
+ 
+
+ align:start position:0%
+especially since they're all multiple
+day labs so you will have
+
+ align:start position:0%
+day labs so you will have
+ 
+
+ align:start position:0%
+day labs so you will have
+a lot of things to write about in the
+
+ align:start position:0%
+a lot of things to write about in the
+ 
+
+ align:start position:0%
+a lot of things to write about in the
+procedure and so you want to keep those
+
+ align:start position:0%
+procedure and so you want to keep those
+ 
+
+ align:start position:0%
+procedure and so you want to keep those
+straight between your days and this is
+
+ align:start position:0%
+straight between your days and this is
+ 
+
+ align:start position:0%
+straight between your days and this is
+where your lab notebook and the notes
+
+ align:start position:0%
+where your lab notebook and the notes
+ 
+
+ align:start position:0%
+where your lab notebook and the notes
+that you take in the lab are going to be
+
+ align:start position:0%
+that you take in the lab are going to be
+ 
+
+ align:start position:0%
+that you take in the lab are going to be
+super
+
+ align:start position:0%
+super
+ 
+
+ align:start position:0%
+super
+important and helpful in writing up what
+
+ align:start position:0%
+important and helpful in writing up what
+ 
+
+ align:start position:0%
+important and helpful in writing up what
+is happening in this section of the lab
+
+ align:start position:0%
+is happening in this section of the lab
+ 
+
+ align:start position:0%
+is happening in this section of the lab
+the way that you
+
+ align:start position:0%
+the way that you
+ 
+
+ align:start position:0%
+the way that you
+write especially the whole out report
+
+ align:start position:0%
+write especially the whole out report
+ 
+
+ align:start position:0%
+write especially the whole out report
+but especially the procedure and
+
+ align:start position:0%
+but especially the procedure and
+ 
+
+ align:start position:0%
+but especially the procedure and
+observation section is in the third
+
+ align:start position:0%
+observation section is in the third
+ 
+
+ align:start position:0%
+observation section is in the third
+person passive voice and this kind of
+
+ align:start position:0%
+person passive voice and this kind of
+ 
+
+ align:start position:0%
+person passive voice and this kind of
+feels awkward for a lot of people
+
+ align:start position:0%
+feels awkward for a lot of people
+ 
+
+ align:start position:0%
+feels awkward for a lot of people
+at first but instead of writing
+
+ align:start position:0%
+at first but instead of writing
+ 
+
+ align:start position:0%
+at first but instead of writing
+something like i added five milliliters
+
+ align:start position:0%
+something like i added five milliliters
+ 
+
+ align:start position:0%
+something like i added five milliliters
+of nitric acid to the copper it took
+
+ align:start position:0%
+of nitric acid to the copper it took
+ 
+
+ align:start position:0%
+of nitric acid to the copper it took
+this long and i used
+
+ align:start position:0%
+this long and i used
+ 
+
+ align:start position:0%
+this long and i used
+6.2 molar nitric acid and copper
+
+ align:start position:0%
+6.2 molar nitric acid and copper
+ 
+
+ align:start position:0%
+6.2 molar nitric acid and copper
+shavings
+
+ align:start position:0%
+shavings
+ 
+
+ align:start position:0%
+shavings
+you would write it in the passive voice
+
+ align:start position:0%
+you would write it in the passive voice
+ 
+
+ align:start position:0%
+you would write it in the passive voice
+so two around bottom flask containing
+
+ align:start position:0%
+so two around bottom flask containing
+ 
+
+ align:start position:0%
+so two around bottom flask containing
+copper
+
+ align:start position:0%
+copper
+ 
+
+ align:start position:0%
+copper
+metal shavings was added five
+
+ align:start position:0%
+metal shavings was added five
+ 
+
+ align:start position:0%
+metal shavings was added five
+milliliters of nitric acid the acid was
+
+ align:start position:0%
+milliliters of nitric acid the acid was
+ 
+
+ align:start position:0%
+milliliters of nitric acid the acid was
+added drop-wise over the course of 15
+
+ align:start position:0%
+added drop-wise over the course of 15
+ 
+
+ align:start position:0%
+added drop-wise over the course of 15
+minutes
+
+ align:start position:0%
+minutes
+ 
+
+ align:start position:0%
+minutes
+so there are no real actors in your lab
+
+ align:start position:0%
+so there are no real actors in your lab
+ 
+
+ align:start position:0%
+so there are no real actors in your lab
+report except for
+
+ align:start position:0%
+report except for
+ 
+
+ align:start position:0%
+report except for
+the chemicals themselves so the chemical
+
+ align:start position:0%
+the chemicals themselves so the chemical
+ 
+
+ align:start position:0%
+the chemicals themselves so the chemical
+was added by who we don't care
+
+ align:start position:0%
+was added by who we don't care
+ 
+
+ align:start position:0%
+was added by who we don't care
+you want to write in the passive voice
+
+ align:start position:0%
+you want to write in the passive voice
+ 
+
+ align:start position:0%
+you want to write in the passive voice
+and as an example here is an article
+
+ align:start position:0%
+and as an example here is an article
+ 
+
+ align:start position:0%
+and as an example here is an article
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it was recently published in jax the
+
+ align:start position:0%
+it was recently published in jax the
+ 
+
+ align:start position:0%
+it was recently published in jax the
+journal journal of the american chemical
+
+ align:start position:0%
+journal journal of the american chemical
+ 
+
+ align:start position:0%
+journal journal of the american chemical
+society and you can see that this is how
+
+ align:start position:0%
+society and you can see that this is how
+ 
+
+ align:start position:0%
+society and you can see that this is how
+a procedural section is written for
+
+ align:start position:0%
+a procedural section is written for
+ 
+
+ align:start position:0%
+a procedural section is written for
+something that's going to be published
+
+ align:start position:0%
+something that's going to be published
+ 
+
+ align:start position:0%
+something that's going to be published
+and one of the ways that you can do it
+
+ align:start position:0%
+and one of the ways that you can do it
+ 
+
+ align:start position:0%
+and one of the ways that you can do it
+you can either say in the sentences
+
+ align:start position:0%
+you can either say in the sentences
+ 
+
+ align:start position:0%
+you can either say in the sentences
+like 10 millimoles of 2 4-dibromobutyl
+
+ align:start position:0%
+like 10 millimoles of 2 4-dibromobutyl
+ 
+
+ align:start position:0%
+like 10 millimoles of 2 4-dibromobutyl
+chloride was added
+
+ align:start position:0%
+chloride was added
+ 
+
+ align:start position:0%
+chloride was added
+or you can put the quantities in
+
+ align:start position:0%
+or you can put the quantities in
+ 
+
+ align:start position:0%
+or you can put the quantities in
+parentheses and in this case they've
+
+ align:start position:0%
+parentheses and in this case they've
+ 
+
+ align:start position:0%
+parentheses and in this case they've
+chosen to do it in millimolar
+
+ align:start position:0%
+chosen to do it in millimolar
+ 
+
+ align:start position:0%
+chosen to do it in millimolar
+in your lab report you can use whatever
+
+ align:start position:0%
+in your lab report you can use whatever
+ 
+
+ align:start position:0%
+in your lab report you can use whatever
+quantity you measured so if you measured
+
+ align:start position:0%
+quantity you measured so if you measured
+ 
+
+ align:start position:0%
+quantity you measured so if you measured
+it out in grams or milliliters then
+
+ align:start position:0%
+it out in grams or milliliters then
+ 
+
+ align:start position:0%
+it out in grams or milliliters then
+that's what you should write in your
+
+ align:start position:0%
+that's what you should write in your
+ 
+
+ align:start position:0%
+that's what you should write in your
+report here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's an example a thing and
+
+ align:start position:0%
+so that's an example a thing and
+ 
+
+ align:start position:0%
+so that's an example a thing and
+something to note
+
+ align:start position:0%
+something to note
+ 
+
+ align:start position:0%
+something to note
+this didn't copy over well when i copy
+
+ align:start position:0%
+this didn't copy over well when i copy
+ 
+
+ align:start position:0%
+this didn't copy over well when i copy
+and pasted it but you should definitely
+
+ align:start position:0%
+and pasted it but you should definitely
+ 
+
+ align:start position:0%
+and pasted it but you should definitely
+always make sure to superscript and
+
+ align:start position:0%
+always make sure to superscript and
+ 
+
+ align:start position:0%
+always make sure to superscript and
+subscript things as appropriate
+
+ align:start position:0%
+subscript things as appropriate
+ 
+
+ align:start position:0%
+subscript things as appropriate
+take the time and do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that should go without saying and
+
+ align:start position:0%
+yeah that should go without saying and
+ 
+
+ align:start position:0%
+yeah that should go without saying and
+one of the handouts that i gave you is
+
+ align:start position:0%
+one of the handouts that i gave you is
+ 
+
+ align:start position:0%
+one of the handouts that i gave you is
+also another example
+
+ align:start position:0%
+also another example
+ 
+
+ align:start position:0%
+also another example
+of a procedural section that has been
+
+ align:start position:0%
+of a procedural section that has been
+ 
+
+ align:start position:0%
+of a procedural section that has been
+written for a lab that you guys
+
+ align:start position:0%
+written for a lab that you guys
+ 
+
+ align:start position:0%
+written for a lab that you guys
+are not going to do but it's another
+
+ align:start position:0%
+are not going to do but it's another
+ 
+
+ align:start position:0%
+are not going to do but it's another
+example of how the language can go
+
+ align:start position:0%
+example of how the language can go
+ 
+
+ align:start position:0%
+example of how the language can go
+and what it looks like when it's all
+
+ align:start position:0%
+and what it looks like when it's all
+ 
+
+ align:start position:0%
+and what it looks like when it's all
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+the next section is the results
+
+ align:start position:0%
+the next section is the results
+ 
+
+ align:start position:0%
+the next section is the results
+so the results that you collected are
+
+ align:start position:0%
+so the results that you collected are
+ 
+
+ align:start position:0%
+so the results that you collected are
+going to be summarized in
+
+ align:start position:0%
+going to be summarized in
+ 
+
+ align:start position:0%
+going to be summarized in
+your results section obviously this is
+
+ align:start position:0%
+your results section obviously this is
+ 
+
+ align:start position:0%
+your results section obviously this is
+best done using tables or graphs if you
+
+ align:start position:0%
+best done using tables or graphs if you
+ 
+
+ align:start position:0%
+best done using tables or graphs if you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+and this is not the place to analyze
+
+ align:start position:0%
+and this is not the place to analyze
+ 
+
+ align:start position:0%
+and this is not the place to analyze
+your data so you don't want to be making
+
+ align:start position:0%
+your data so you don't want to be making
+ 
+
+ align:start position:0%
+your data so you don't want to be making
+any comments about it saying oh i got
+
+ align:start position:0%
+any comments about it saying oh i got
+ 
+
+ align:start position:0%
+any comments about it saying oh i got
+this terrible yield of 22
+
+ align:start position:0%
+this terrible yield of 22
+ 
+
+ align:start position:0%
+this terrible yield of 22
+or whatever you don't really want to
+
+ align:start position:0%
+or whatever you don't really want to
+ 
+
+ align:start position:0%
+or whatever you don't really want to
+write that anywhere but
+
+ align:start position:0%
+write that anywhere but
+ 
+
+ align:start position:0%
+write that anywhere but
+here you're just presenting the results
+
+ align:start position:0%
+here you're just presenting the results
+ 
+
+ align:start position:0%
+here you're just presenting the results
+and then you will talk about them and
+
+ align:start position:0%
+and then you will talk about them and
+ 
+
+ align:start position:0%
+and then you will talk about them and
+what they mean
+
+ align:start position:0%
+what they mean
+ 
+
+ align:start position:0%
+what they mean
+in your discussion section so
+
+ align:start position:0%
+in your discussion section so
+ 
+
+ align:start position:0%
+in your discussion section so
+what sort of results are you going to
+
+ align:start position:0%
+what sort of results are you going to
+ 
+
+ align:start position:0%
+what sort of results are you going to
+have for your ferris scene lab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you're going to put them in a
+
+ align:start position:0%
+and if you're going to put them in a
+ 
+
+ align:start position:0%
+and if you're going to put them in a
+table what would our table look like
+
+ align:start position:0%
+table what would our table look like
+ 
+
+ align:start position:0%
+table what would our table look like
+what are some good headings for the data
+
+ align:start position:0%
+what are some good headings for the data
+ 
+
+ align:start position:0%
+what are some good headings for the data
+that we will have from ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yield
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what units grams sure
+
+ align:start position:0%
+what units grams sure
+ 
+
+ align:start position:0%
+what units grams sure
+you can do grams you can do milligrams
+
+ align:start position:0%
+you can do grams you can do milligrams
+ 
+
+ align:start position:0%
+you can do grams you can do milligrams
+depending on
+
+ align:start position:0%
+depending on
+ 
+
+ align:start position:0%
+depending on
+how successful your synthesis was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first column should be like name
+
+ align:start position:0%
+the first column should be like name
+ 
+
+ align:start position:0%
+the first column should be like name
+yeah compound name
+
+ align:start position:0%
+yeah compound name
+ 
+
+ align:start position:0%
+yeah compound name
+what other data can we talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no all the way left melting point yeah
+
+ align:start position:0%
+no all the way left melting point yeah
+ 
+
+ align:start position:0%
+no all the way left melting point yeah
+we'll throw that over here because it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecular weight's not necessarily a
+
+ align:start position:0%
+molecular weight's not necessarily a
+ 
+
+ align:start position:0%
+molecular weight's not necessarily a
+result so that would be something that
+
+ align:start position:0%
+result so that would be something that
+ 
+
+ align:start position:0%
+result so that would be something that
+you could include in your calculations
+
+ align:start position:0%
+you could include in your calculations
+ 
+
+ align:start position:0%
+you could include in your calculations
+when you're doing your
+
+ align:start position:0%
+when you're doing your
+ 
+
+ align:start position:0%
+when you're doing your
+theoretical yield calculation something
+
+ align:start position:0%
+theoretical yield calculation something
+ 
+
+ align:start position:0%
+theoretical yield calculation something
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what rs rf
+
+ align:start position:0%
+what rs rf
+ 
+
+ align:start position:0%
+what rs rf
+so you could include that in a table but
+
+ align:start position:0%
+so you could include that in a table but
+ 
+
+ align:start position:0%
+so you could include that in a table but
+it may be smart to do a separate table
+
+ align:start position:0%
+it may be smart to do a separate table
+ 
+
+ align:start position:0%
+it may be smart to do a separate table
+for your rf values but that definitely
+
+ align:start position:0%
+for your rf values but that definitely
+ 
+
+ align:start position:0%
+for your rf values but that definitely
+should be in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i mean you could include like
+
+ align:start position:0%
+yeah i mean you could include like
+ 
+
+ align:start position:0%
+yeah i mean you could include like
+qualitative
+
+ align:start position:0%
+qualitative
+ 
+
+ align:start position:0%
+qualitative
+like appearance color yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color appearance so you can say it was
+
+ align:start position:0%
+color appearance so you can say it was
+ 
+
+ align:start position:0%
+color appearance so you can say it was
+light orange
+
+ align:start position:0%
+light orange
+ 
+
+ align:start position:0%
+light orange
+dark orange red it was a powder it was
+
+ align:start position:0%
+dark orange red it was a powder it was
+ 
+
+ align:start position:0%
+dark orange red it was a powder it was
+clumpy
+
+ align:start position:0%
+clumpy
+ 
+
+ align:start position:0%
+clumpy
+you got big giant crystals of it
+
+ align:start position:0%
+you got big giant crystals of it
+ 
+
+ align:start position:0%
+you got big giant crystals of it
+whatever you got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what other information are we gonna get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+related to yield but what's another way
+
+ align:start position:0%
+related to yield but what's another way
+ 
+
+ align:start position:0%
+related to yield but what's another way
+to report yield
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+percent yield yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent so this would be a really
+
+ align:start position:0%
+excellent so this would be a really
+ 
+
+ align:start position:0%
+excellent so this would be a really
+great table to include
+
+ align:start position:0%
+great table to include
+ 
+
+ align:start position:0%
+great table to include
+in your ferris scene report with all of
+
+ align:start position:0%
+in your ferris scene report with all of
+ 
+
+ align:start position:0%
+in your ferris scene report with all of
+this data in it and then what compounds
+
+ align:start position:0%
+this data in it and then what compounds
+ 
+
+ align:start position:0%
+this data in it and then what compounds
+are we going to have all of this
+
+ align:start position:0%
+are we going to have all of this
+ 
+
+ align:start position:0%
+are we going to have all of this
+information for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pharisee ferrocene what kind of
+
+ align:start position:0%
+pharisee ferrocene what kind of
+ 
+
+ align:start position:0%
+pharisee ferrocene what kind of
+ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crude ferrocene
+
+ align:start position:0%
+crude ferrocene
+ 
+
+ align:start position:0%
+crude ferrocene
+what purified ferrocene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and acetyl ferrocene both crude and pure
+
+ align:start position:0%
+and acetyl ferrocene both crude and pure
+ 
+
+ align:start position:0%
+and acetyl ferrocene both crude and pure
+of that as well
+
+ align:start position:0%
+of that as well
+ 
+
+ align:start position:0%
+of that as well
+yes pre and post column
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may not have all of this data for
+
+ align:start position:0%
+you may not have all of this data for
+ 
+
+ align:start position:0%
+you may not have all of this data for
+all of these compounds but you should
+
+ align:start position:0%
+all of these compounds but you should
+ 
+
+ align:start position:0%
+all of these compounds but you should
+be pretty close and if you made any
+
+ align:start position:0%
+be pretty close and if you made any
+ 
+
+ align:start position:0%
+be pretty close and if you made any
+diacetyl ferrocene you can put that in
+
+ align:start position:0%
+diacetyl ferrocene you can put that in
+ 
+
+ align:start position:0%
+diacetyl ferrocene you can put that in
+here too
+
+ align:start position:0%
+here too
+ 
+
+ align:start position:0%
+here too
+if you have enough to collect off of
+
+ align:start position:0%
+if you have enough to collect off of
+ 
+
+ align:start position:0%
+if you have enough to collect off of
+your column and you'll find out next
+
+ align:start position:0%
+your column and you'll find out next
+ 
+
+ align:start position:0%
+your column and you'll find out next
+week if you have enough of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so those are your results
+
+ align:start position:0%
+so yeah so those are your results
+ 
+
+ align:start position:0%
+so yeah so those are your results
+anything else that we're missing in
+
+ align:start position:0%
+anything else that we're missing in
+ 
+
+ align:start position:0%
+anything else that we're missing in
+terms of results for this lab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no that looks pretty good so
+
+ align:start position:0%
+no that looks pretty good so
+ 
+
+ align:start position:0%
+no that looks pretty good so
+if you wanted to insert a graph which in
+
+ align:start position:0%
+if you wanted to insert a graph which in
+ 
+
+ align:start position:0%
+if you wanted to insert a graph which in
+this case we don't really have any
+
+ align:start position:0%
+this case we don't really have any
+ 
+
+ align:start position:0%
+this case we don't really have any
+graphs necessarily that would go into
+
+ align:start position:0%
+graphs necessarily that would go into
+ 
+
+ align:start position:0%
+graphs necessarily that would go into
+your lab report yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what a great question so you guys are
+
+ align:start position:0%
+what a great question so you guys are
+ 
+
+ align:start position:0%
+what a great question so you guys are
+making the calibration curve for your
+
+ align:start position:0%
+making the calibration curve for your
+ 
+
+ align:start position:0%
+making the calibration curve for your
+melting points right
+
+ align:start position:0%
+melting points right
+ 
+
+ align:start position:0%
+melting points right
+where would you put that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have one vote for calculations one
+
+ align:start position:0%
+we have one vote for calculations one
+ 
+
+ align:start position:0%
+we have one vote for calculations one
+vote for appendix
+
+ align:start position:0%
+vote for appendix
+ 
+
+ align:start position:0%
+vote for appendix
+any thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the things that get inserted into
+
+ align:start position:0%
+so the things that get inserted into
+ 
+
+ align:start position:0%
+so the things that get inserted into
+your results section
+
+ align:start position:0%
+your results section
+ 
+
+ align:start position:0%
+your results section
+or your calculation section are things
+
+ align:start position:0%
+or your calculation section are things
+ 
+
+ align:start position:0%
+or your calculation section are things
+that are very directly related to the
+
+ align:start position:0%
+that are very directly related to the
+ 
+
+ align:start position:0%
+that are very directly related to the
+goals of the lab
+
+ align:start position:0%
+goals of the lab
+ 
+
+ align:start position:0%
+goals of the lab
+so if you need something to
+
+ align:start position:0%
+so if you need something to
+ 
+
+ align:start position:0%
+so if you need something to
+get whatever data that you care about so
+
+ align:start position:0%
+get whatever data that you care about so
+ 
+
+ align:start position:0%
+get whatever data that you care about so
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+like in the catalase lab that you guys
+
+ align:start position:0%
+like in the catalase lab that you guys
+ 
+
+ align:start position:0%
+like in the catalase lab that you guys
+are going to be doing you'll need to
+
+ align:start position:0%
+are going to be doing you'll need to
+ 
+
+ align:start position:0%
+are going to be doing you'll need to
+make graphs in order to get
+
+ align:start position:0%
+make graphs in order to get
+ 
+
+ align:start position:0%
+make graphs in order to get
+some rate constant data so those graphs
+
+ align:start position:0%
+some rate constant data so those graphs
+ 
+
+ align:start position:0%
+some rate constant data so those graphs
+are super important to the goal of the
+
+ align:start position:0%
+are super important to the goal of the
+ 
+
+ align:start position:0%
+are super important to the goal of the
+lab
+
+ align:start position:0%
+lab
+ 
+
+ align:start position:0%
+lab
+is a melting point calibration curve
+
+ align:start position:0%
+is a melting point calibration curve
+ 
+
+ align:start position:0%
+is a melting point calibration curve
+very important to our stated goal of
+
+ align:start position:0%
+very important to our stated goal of
+ 
+
+ align:start position:0%
+very important to our stated goal of
+this lab
+
+ align:start position:0%
+this lab
+ 
+
+ align:start position:0%
+this lab
+not necessarily but we need it in order
+
+ align:start position:0%
+not necessarily but we need it in order
+ 
+
+ align:start position:0%
+not necessarily but we need it in order
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+the data that we care about so that's
+
+ align:start position:0%
+the data that we care about so that's
+ 
+
+ align:start position:0%
+the data that we care about so that's
+something that can go in an appendix
+
+ align:start position:0%
+something that can go in an appendix
+ 
+
+ align:start position:0%
+something that can go in an appendix
+and that would be an excellent spot for
+
+ align:start position:0%
+and that would be an excellent spot for
+ 
+
+ align:start position:0%
+and that would be an excellent spot for
+your melting point calibration curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because just like anything else if you
+
+ align:start position:0%
+because just like anything else if you
+ 
+
+ align:start position:0%
+because just like anything else if you
+put something in an appendix you need to
+
+ align:start position:0%
+put something in an appendix you need to
+ 
+
+ align:start position:0%
+put something in an appendix you need to
+reference it in your lab because why
+
+ align:start position:0%
+reference it in your lab because why
+ 
+
+ align:start position:0%
+reference it in your lab because why
+would you include it anywhere if it
+
+ align:start position:0%
+would you include it anywhere if it
+ 
+
+ align:start position:0%
+would you include it anywhere if it
+doesn't matter for your lab might
+
+ align:start position:0%
+doesn't matter for your lab might
+ 
+
+ align:start position:0%
+doesn't matter for your lab might
+so why
+
+ align:start position:0%
+so why
+ 
+
+ align:start position:0%
+so why
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the procedure for making the melting
+
+ align:start position:0%
+the procedure for making the melting
+ 
+
+ align:start position:0%
+the procedure for making the melting
+point calibration curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+any thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put it in the appendix yeah so again
+
+ align:start position:0%
+put it in the appendix yeah so again
+ 
+
+ align:start position:0%
+put it in the appendix yeah so again
+that's something that can probably go in
+
+ align:start position:0%
+that's something that can probably go in
+ 
+
+ align:start position:0%
+that's something that can probably go in
+the appendix because it's not super
+
+ align:start position:0%
+the appendix because it's not super
+ 
+
+ align:start position:0%
+the appendix because it's not super
+important to
+
+ align:start position:0%
+important to
+ 
+
+ align:start position:0%
+important to
+your actual lab but in a procedure
+
+ align:start position:0%
+your actual lab but in a procedure
+ 
+
+ align:start position:0%
+your actual lab but in a procedure
+section like a list of every
+
+ align:start position:0%
+section like a list of every
+ 
+
+ align:start position:0%
+section like a list of every
+instrumentation you use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's that's also a good way to
+
+ align:start position:0%
+yeah so that's that's also a good way to
+ 
+
+ align:start position:0%
+yeah so that's that's also a good way to
+do it so there's a couple ways
+
+ align:start position:0%
+do it so there's a couple ways
+ 
+
+ align:start position:0%
+do it so there's a couple ways
+so one would be to put the procedure in
+
+ align:start position:0%
+so one would be to put the procedure in
+ 
+
+ align:start position:0%
+so one would be to put the procedure in
+the appendix with the melting point
+
+ align:start position:0%
+the appendix with the melting point
+ 
+
+ align:start position:0%
+the appendix with the melting point
+calibration curve and have a note in
+
+ align:start position:0%
+calibration curve and have a note in
+ 
+
+ align:start position:0%
+calibration curve and have a note in
+your procedure saying c appendix for
+
+ align:start position:0%
+your procedure saying c appendix for
+ 
+
+ align:start position:0%
+your procedure saying c appendix for
+calibration curve and the procedure for
+
+ align:start position:0%
+calibration curve and the procedure for
+ 
+
+ align:start position:0%
+calibration curve and the procedure for
+generating it or when you are making
+
+ align:start position:0%
+generating it or when you are making
+ 
+
+ align:start position:0%
+generating it or when you are making
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+procedure section you can have different
+
+ align:start position:0%
+procedure section you can have different
+ 
+
+ align:start position:0%
+procedure section you can have different
+sections for
+
+ align:start position:0%
+sections for
+ 
+
+ align:start position:0%
+sections for
+all of the different things that we did
+
+ align:start position:0%
+all of the different things that we did
+ 
+
+ align:start position:0%
+all of the different things that we did
+so you would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sections of the procedure for the
+
+ align:start position:0%
+sections of the procedure for the
+ 
+
+ align:start position:0%
+sections of the procedure for the
+synthesis pieces and then
+
+ align:start position:0%
+synthesis pieces and then
+ 
+
+ align:start position:0%
+synthesis pieces and then
+sections of the procedure for the
+
+ align:start position:0%
+sections of the procedure for the
+ 
+
+ align:start position:0%
+sections of the procedure for the
+techniques that you used and if you
+
+ align:start position:0%
+techniques that you used and if you
+ 
+
+ align:start position:0%
+techniques that you used and if you
+wanted to put a
+
+ align:start position:0%
+wanted to put a
+ 
+
+ align:start position:0%
+wanted to put a
+technique section for the melting point
+
+ align:start position:0%
+technique section for the melting point
+ 
+
+ align:start position:0%
+technique section for the melting point
+then you could say melting point was
+
+ align:start position:0%
+then you could say melting point was
+ 
+
+ align:start position:0%
+then you could say melting point was
+determined
+
+ align:start position:0%
+determined
+ 
+
+ align:start position:0%
+determined
+this way and then talk about how you
+
+ align:start position:0%
+this way and then talk about how you
+ 
+
+ align:start position:0%
+this way and then talk about how you
+made the calibration curve there
+
+ align:start position:0%
+made the calibration curve there
+ 
+
+ align:start position:0%
+made the calibration curve there
+so there's a couple ways to do it as
+
+ align:start position:0%
+so there's a couple ways to do it as
+ 
+
+ align:start position:0%
+so there's a couple ways to do it as
+long as the information is there
+
+ align:start position:0%
+long as the information is there
+ 
+
+ align:start position:0%
+long as the information is there
+and referenced well then that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceptable
+
+ align:start position:0%
+acceptable
+ 
+
+ align:start position:0%
+acceptable
+so if you are planning to insert a graph
+
+ align:start position:0%
+so if you are planning to insert a graph
+ 
+
+ align:start position:0%
+so if you are planning to insert a graph
+into your lab report if you want to put
+
+ align:start position:0%
+into your lab report if you want to put
+ 
+
+ align:start position:0%
+into your lab report if you want to put
+the calibration curve or any other graph
+
+ align:start position:0%
+the calibration curve or any other graph
+ 
+
+ align:start position:0%
+the calibration curve or any other graph
+that you make throughout the semester
+
+ align:start position:0%
+that you make throughout the semester
+ 
+
+ align:start position:0%
+that you make throughout the semester
+into your lab report you will insert it
+
+ align:start position:0%
+into your lab report you will insert it
+ 
+
+ align:start position:0%
+into your lab report you will insert it
+as a figure and the way that you
+
+ align:start position:0%
+as a figure and the way that you
+ 
+
+ align:start position:0%
+as a figure and the way that you
+reference your figures is that you
+
+ align:start position:0%
+reference your figures is that you
+ 
+
+ align:start position:0%
+reference your figures is that you
+insert the figure or the graph or
+
+ align:start position:0%
+insert the figure or the graph or
+ 
+
+ align:start position:0%
+insert the figure or the graph or
+whatever it may be and then you need to
+
+ align:start position:0%
+whatever it may be and then you need to
+ 
+
+ align:start position:0%
+whatever it may be and then you need to
+put a caption which goes
+
+ align:start position:0%
+put a caption which goes
+ 
+
+ align:start position:0%
+put a caption which goes
+underneath the figure or the graph and
+
+ align:start position:0%
+underneath the figure or the graph and
+ 
+
+ align:start position:0%
+underneath the figure or the graph and
+even though this is a graphic it's
+
+ align:start position:0%
+even though this is a graphic it's
+ 
+
+ align:start position:0%
+even though this is a graphic it's
+labeled as figure one
+
+ align:start position:0%
+labeled as figure one
+ 
+
+ align:start position:0%
+labeled as figure one
+and then you get number your figures one
+
+ align:start position:0%
+and then you get number your figures one
+ 
+
+ align:start position:0%
+and then you get number your figures one
+two three four five as many as you have
+
+ align:start position:0%
+two three four five as many as you have
+ 
+
+ align:start position:0%
+two three four five as many as you have
+throughout your lab report
+
+ align:start position:0%
+throughout your lab report
+ 
+
+ align:start position:0%
+throughout your lab report
+and then you need some sort of
+
+ align:start position:0%
+and then you need some sort of
+ 
+
+ align:start position:0%
+and then you need some sort of
+description of
+
+ align:start position:0%
+description of
+ 
+
+ align:start position:0%
+description of
+what the figure is or what the graph is
+
+ align:start position:0%
+what the figure is or what the graph is
+ 
+
+ align:start position:0%
+what the figure is or what the graph is
+showing and if it's a graph then you
+
+ align:start position:0%
+showing and if it's a graph then you
+ 
+
+ align:start position:0%
+showing and if it's a graph then you
+need to make sure that the graph itself
+
+ align:start position:0%
+need to make sure that the graph itself
+ 
+
+ align:start position:0%
+need to make sure that the graph itself
+has a title and axes that are labeled
+
+ align:start position:0%
+has a title and axes that are labeled
+ 
+
+ align:start position:0%
+has a title and axes that are labeled
+with units
+
+ align:start position:0%
+with units
+ 
+
+ align:start position:0%
+with units
+that kind of goes without saying and a
+
+ align:start position:0%
+that kind of goes without saying and a
+ 
+
+ align:start position:0%
+that kind of goes without saying and a
+legend if you need one
+
+ align:start position:0%
+legend if you need one
+ 
+
+ align:start position:0%
+legend if you need one
+and then all of that information also
+
+ align:start position:0%
+and then all of that information also
+ 
+
+ align:start position:0%
+and then all of that information also
+gets reiterated in the caption
+
+ align:start position:0%
+gets reiterated in the caption
+ 
+
+ align:start position:0%
+gets reiterated in the caption
+the caption goes below the graph which
+
+ align:start position:0%
+the caption goes below the graph which
+ 
+
+ align:start position:0%
+the caption goes below the graph which
+is important because
+
+ align:start position:0%
+is important because
+ 
+
+ align:start position:0%
+is important because
+if you're going to insert a table then
+
+ align:start position:0%
+if you're going to insert a table then
+ 
+
+ align:start position:0%
+if you're going to insert a table then
+the tables
+
+ align:start position:0%
+the tables
+ 
+
+ align:start position:0%
+the tables
+also get inserted however they are
+
+ align:start position:0%
+also get inserted however they are
+ 
+
+ align:start position:0%
+also get inserted however they are
+called tables and
+
+ align:start position:0%
+called tables and
+ 
+
+ align:start position:0%
+called tables and
+the caption goes above the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you want to make sure when you have
+
+ align:start position:0%
+so you want to make sure when you have
+ 
+
+ align:start position:0%
+so you want to make sure when you have
+your table that you have all of your
+
+ align:start position:0%
+your table that you have all of your
+ 
+
+ align:start position:0%
+your table that you have all of your
+columns with headings and with
+
+ align:start position:0%
+columns with headings and with
+ 
+
+ align:start position:0%
+columns with headings and with
+appropriate units and if you choose a
+
+ align:start position:0%
+appropriate units and if you choose a
+ 
+
+ align:start position:0%
+appropriate units and if you choose a
+unit that
+
+ align:start position:0%
+unit that
+ 
+
+ align:start position:0%
+unit that
+gives you a reasonable number of digits
+
+ align:start position:0%
+gives you a reasonable number of digits
+ 
+
+ align:start position:0%
+gives you a reasonable number of digits
+in your data and if something is getting
+
+ align:start position:0%
+in your data and if something is getting
+ 
+
+ align:start position:0%
+in your data and if something is getting
+out of hand or if you have one
+
+ align:start position:0%
+out of hand or if you have one
+ 
+
+ align:start position:0%
+out of hand or if you have one
+measurement that's on a different scale
+
+ align:start position:0%
+measurement that's on a different scale
+ 
+
+ align:start position:0%
+measurement that's on a different scale
+than the others use scientific notation
+
+ align:start position:0%
+than the others use scientific notation
+ 
+
+ align:start position:0%
+than the others use scientific notation
+or you can change the units for one
+
+ align:start position:0%
+or you can change the units for one
+ 
+
+ align:start position:0%
+or you can change the units for one
+column but
+
+ align:start position:0%
+column but
+ 
+
+ align:start position:0%
+column but
+try to avoid that so yeah that's how you
+
+ align:start position:0%
+try to avoid that so yeah that's how you
+ 
+
+ align:start position:0%
+try to avoid that so yeah that's how you
+insert
+
+ align:start position:0%
+insert
+ 
+
+ align:start position:0%
+insert
+a table into your lab report
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculations so any time that you
+
+ align:start position:0%
+calculations so any time that you
+ 
+
+ align:start position:0%
+calculations so any time that you
+present data that was not directly
+
+ align:start position:0%
+present data that was not directly
+ 
+
+ align:start position:0%
+present data that was not directly
+measured you need to show how it was
+
+ align:start position:0%
+measured you need to show how it was
+ 
+
+ align:start position:0%
+measured you need to show how it was
+calculated with
+
+ align:start position:0%
+calculated with
+ 
+
+ align:start position:0%
+calculated with
+appropriate units so when the data is
+
+ align:start position:0%
+appropriate units so when the data is
+ 
+
+ align:start position:0%
+appropriate units so when the data is
+presented you should show an equation
+
+ align:start position:0%
+presented you should show an equation
+ 
+
+ align:start position:0%
+presented you should show an equation
+so the general form of the equation that
+
+ align:start position:0%
+so the general form of the equation that
+ 
+
+ align:start position:0%
+so the general form of the equation that
+you're using
+
+ align:start position:0%
+you're using
+ 
+
+ align:start position:0%
+you're using
+a sample calculation with one set of
+
+ align:start position:0%
+a sample calculation with one set of
+ 
+
+ align:start position:0%
+a sample calculation with one set of
+your data and then the final answer
+
+ align:start position:0%
+your data and then the final answer
+ 
+
+ align:start position:0%
+your data and then the final answer
+so if you're going to be doing a
+
+ align:start position:0%
+so if you're going to be doing a
+ 
+
+ align:start position:0%
+so if you're going to be doing a
+calculation repeatedly
+
+ align:start position:0%
+calculation repeatedly
+ 
+
+ align:start position:0%
+calculation repeatedly
+like percent yield you're going to
+
+ align:start position:0%
+like percent yield you're going to
+ 
+
+ align:start position:0%
+like percent yield you're going to
+calculate percent yields for a whole
+
+ align:start position:0%
+calculate percent yields for a whole
+ 
+
+ align:start position:0%
+calculate percent yields for a whole
+bunch of different compounds
+
+ align:start position:0%
+bunch of different compounds
+ 
+
+ align:start position:0%
+bunch of different compounds
+you just need to show the calculation
+
+ align:start position:0%
+you just need to show the calculation
+ 
+
+ align:start position:0%
+you just need to show the calculation
+once and then just show the percent
+
+ align:start position:0%
+once and then just show the percent
+ 
+
+ align:start position:0%
+once and then just show the percent
+yields for
+
+ align:start position:0%
+yields for
+ 
+
+ align:start position:0%
+yields for
+the other three compounds that you're
+
+ align:start position:0%
+the other three compounds that you're
+ 
+
+ align:start position:0%
+the other three compounds that you're
+calculating it for
+
+ align:start position:0%
+calculating it for
+ 
+
+ align:start position:0%
+calculating it for
+there are lengthy calculations that you
+
+ align:start position:0%
+there are lengthy calculations that you
+ 
+
+ align:start position:0%
+there are lengthy calculations that you
+can do in an excel spreadsheet then you
+
+ align:start position:0%
+can do in an excel spreadsheet then you
+ 
+
+ align:start position:0%
+can do in an excel spreadsheet then you
+can include the excel spreadsheet in an
+
+ align:start position:0%
+can include the excel spreadsheet in an
+ 
+
+ align:start position:0%
+can include the excel spreadsheet in an
+appendix as long as in your report
+
+ align:start position:0%
+appendix as long as in your report
+ 
+
+ align:start position:0%
+appendix as long as in your report
+you have shown a sample calculation and
+
+ align:start position:0%
+you have shown a sample calculation and
+ 
+
+ align:start position:0%
+you have shown a sample calculation and
+the equations that you're using to
+
+ align:start position:0%
+the equations that you're using to
+ 
+
+ align:start position:0%
+the equations that you're using to
+get all of the data in that excel
+
+ align:start position:0%
+get all of the data in that excel
+ 
+
+ align:start position:0%
+get all of the data in that excel
+spreadsheet
+
+ align:start position:0%
+spreadsheet
+ 
+
+ align:start position:0%
+spreadsheet
+you can also include a lot if you have a
+
+ align:start position:0%
+you can also include a lot if you have a
+ 
+
+ align:start position:0%
+you can also include a lot if you have a
+lot of calculations you can include them
+
+ align:start position:0%
+lot of calculations you can include them
+ 
+
+ align:start position:0%
+lot of calculations you can include them
+in an appendix as long as the data is
+
+ align:start position:0%
+in an appendix as long as the data is
+ 
+
+ align:start position:0%
+in an appendix as long as the data is
+well labeled
+
+ align:start position:0%
+well labeled
+ 
+
+ align:start position:0%
+well labeled
+and the sample calculations and
+
+ align:start position:0%
+and the sample calculations and
+ 
+
+ align:start position:0%
+and the sample calculations and
+equations have been shown and again all
+
+ align:start position:0%
+equations have been shown and again all
+ 
+
+ align:start position:0%
+equations have been shown and again all
+of this should be in your report
+
+ align:start position:0%
+of this should be in your report
+ 
+
+ align:start position:0%
+of this should be in your report
+somewhere and then if you need to add
+
+ align:start position:0%
+somewhere and then if you need to add
+ 
+
+ align:start position:0%
+somewhere and then if you need to add
+more in an appendix you can if your
+
+ align:start position:0%
+more in an appendix you can if your
+ 
+
+ align:start position:0%
+more in an appendix you can if your
+report's getting really long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the discussion this is where you
+
+ align:start position:0%
+so the discussion this is where you
+ 
+
+ align:start position:0%
+so the discussion this is where you
+finally get to talk about
+
+ align:start position:0%
+finally get to talk about
+ 
+
+ align:start position:0%
+finally get to talk about
+your data and what it means
+
+ align:start position:0%
+your data and what it means
+ 
+
+ align:start position:0%
+your data and what it means
+so you will summarize your key results
+
+ align:start position:0%
+so you will summarize your key results
+ 
+
+ align:start position:0%
+so you will summarize your key results
+explain any difficulties or errors that
+
+ align:start position:0%
+explain any difficulties or errors that
+ 
+
+ align:start position:0%
+explain any difficulties or errors that
+led to erroneous results
+
+ align:start position:0%
+led to erroneous results
+ 
+
+ align:start position:0%
+led to erroneous results
+so if you accidentally spilled some of
+
+ align:start position:0%
+so if you accidentally spilled some of
+ 
+
+ align:start position:0%
+so if you accidentally spilled some of
+your ferrocene solution
+
+ align:start position:0%
+your ferrocene solution
+ 
+
+ align:start position:0%
+your ferrocene solution
+then you might talk about how that
+
+ align:start position:0%
+then you might talk about how that
+ 
+
+ align:start position:0%
+then you might talk about how that
+impacted your yield
+
+ align:start position:0%
+impacted your yield
+ 
+
+ align:start position:0%
+impacted your yield
+offer suggestions to improve the
+
+ align:start position:0%
+offer suggestions to improve the
+ 
+
+ align:start position:0%
+offer suggestions to improve the
+experiment so
+
+ align:start position:0%
+experiment so
+ 
+
+ align:start position:0%
+experiment so
+one of them could be maybe change the
+
+ align:start position:0%
+one of them could be maybe change the
+ 
+
+ align:start position:0%
+one of them could be maybe change the
+glassware that you're using if
+
+ align:start position:0%
+glassware that you're using if
+ 
+
+ align:start position:0%
+glassware that you're using if
+you're spilling a lot of chemicals or if
+
+ align:start position:0%
+you're spilling a lot of chemicals or if
+ 
+
+ align:start position:0%
+you're spilling a lot of chemicals or if
+you have an idea for different chemicals
+
+ align:start position:0%
+you have an idea for different chemicals
+ 
+
+ align:start position:0%
+you have an idea for different chemicals
+that we could use that would be better
+
+ align:start position:0%
+that we could use that would be better
+ 
+
+ align:start position:0%
+that we could use that would be better
+for this similar procedure
+
+ align:start position:0%
+for this similar procedure
+ 
+
+ align:start position:0%
+for this similar procedure
+that would be a good time to talk about
+
+ align:start position:0%
+that would be a good time to talk about
+ 
+
+ align:start position:0%
+that would be a good time to talk about
+it or
+
+ align:start position:0%
+it or
+ 
+
+ align:start position:0%
+it or
+adjustments to the length of time that
+
+ align:start position:0%
+adjustments to the length of time that
+ 
+
+ align:start position:0%
+adjustments to the length of time that
+you do something
+
+ align:start position:0%
+you do something
+ 
+
+ align:start position:0%
+you do something
+anything that you can think of that may
+
+ align:start position:0%
+anything that you can think of that may
+ 
+
+ align:start position:0%
+anything that you can think of that may
+improve the lab this would be a nice
+
+ align:start position:0%
+improve the lab this would be a nice
+ 
+
+ align:start position:0%
+improve the lab this would be a nice
+spot to put it and then answer any
+
+ align:start position:0%
+spot to put it and then answer any
+ 
+
+ align:start position:0%
+spot to put it and then answer any
+questions that are posed in the lab
+
+ align:start position:0%
+questions that are posed in the lab
+ 
+
+ align:start position:0%
+questions that are posed in the lab
+manual
+
+ align:start position:0%
+manual
+ 
+
+ align:start position:0%
+manual
+there are no questions in the lab manual
+
+ align:start position:0%
+there are no questions in the lab manual
+ 
+
+ align:start position:0%
+there are no questions in the lab manual
+for the ferrocene experiment but you'll
+
+ align:start position:0%
+for the ferrocene experiment but you'll
+ 
+
+ align:start position:0%
+for the ferrocene experiment but you'll
+notice if you look at the other
+
+ align:start position:0%
+notice if you look at the other
+ 
+
+ align:start position:0%
+notice if you look at the other
+labs throughout later in the semester at
+
+ align:start position:0%
+labs throughout later in the semester at
+ 
+
+ align:start position:0%
+labs throughout later in the semester at
+the end of the lab there are a set of
+
+ align:start position:0%
+the end of the lab there are a set of
+ 
+
+ align:start position:0%
+the end of the lab there are a set of
+discussion questions
+
+ align:start position:0%
+discussion questions
+ 
+
+ align:start position:0%
+discussion questions
+that relate to the procedures and the
+
+ align:start position:0%
+that relate to the procedures and the
+ 
+
+ align:start position:0%
+that relate to the procedures and the
+data that you will collect in the lab
+
+ align:start position:0%
+data that you will collect in the lab
+ 
+
+ align:start position:0%
+data that you will collect in the lab
+do not just answer those questions in a
+
+ align:start position:0%
+do not just answer those questions in a
+ 
+
+ align:start position:0%
+do not just answer those questions in a
+list a lot of them are numbered don't go
+
+ align:start position:0%
+list a lot of them are numbered don't go
+ 
+
+ align:start position:0%
+list a lot of them are numbered don't go
+through and make your discussion a
+
+ align:start position:0%
+through and make your discussion a
+ 
+
+ align:start position:0%
+through and make your discussion a
+bulleted or numbered list of answers to
+
+ align:start position:0%
+bulleted or numbered list of answers to
+ 
+
+ align:start position:0%
+bulleted or numbered list of answers to
+these questions and don't just write one
+
+ align:start position:0%
+these questions and don't just write one
+ 
+
+ align:start position:0%
+these questions and don't just write one
+sentence after the other that's very
+
+ align:start position:0%
+sentence after the other that's very
+ 
+
+ align:start position:0%
+sentence after the other that's very
+obviously just
+
+ align:start position:0%
+obviously just
+ 
+
+ align:start position:0%
+obviously just
+answers to the questions your discussion
+
+ align:start position:0%
+answers to the questions your discussion
+ 
+
+ align:start position:0%
+answers to the questions your discussion
+section should flow nicely this will be
+
+ align:start position:0%
+section should flow nicely this will be
+ 
+
+ align:start position:0%
+section should flow nicely this will be
+the longest
+
+ align:start position:0%
+the longest
+ 
+
+ align:start position:0%
+the longest
+section of your lab report and it should
+
+ align:start position:0%
+section of your lab report and it should
+ 
+
+ align:start position:0%
+section of your lab report and it should
+be the one with the most thought put
+
+ align:start position:0%
+be the one with the most thought put
+ 
+
+ align:start position:0%
+be the one with the most thought put
+into it so make it
+
+ align:start position:0%
+into it so make it
+ 
+
+ align:start position:0%
+into it so make it
+flow like a nice piece of writing your
+
+ align:start position:0%
+flow like a nice piece of writing your
+ 
+
+ align:start position:0%
+flow like a nice piece of writing your
+tas have to read these they will
+
+ align:start position:0%
+tas have to read these they will
+ 
+
+ align:start position:0%
+tas have to read these they will
+appreciate them
+
+ align:start position:0%
+appreciate them
+ 
+
+ align:start position:0%
+appreciate them
+much more if you write with good grammar
+
+ align:start position:0%
+much more if you write with good grammar
+ 
+
+ align:start position:0%
+much more if you write with good grammar
+and in a way that is intelligent and
+
+ align:start position:0%
+and in a way that is intelligent and
+ 
+
+ align:start position:0%
+and in a way that is intelligent and
+easy to follow
+
+ align:start position:0%
+easy to follow
+ 
+
+ align:start position:0%
+easy to follow
+the answer should tell a coherent story
+
+ align:start position:0%
+the answer should tell a coherent story
+ 
+
+ align:start position:0%
+the answer should tell a coherent story
+throughout all of your
+
+ align:start position:0%
+throughout all of your
+ 
+
+ align:start position:0%
+throughout all of your
+discussion you can talk about sources of
+
+ align:start position:0%
+discussion you can talk about sources of
+ 
+
+ align:start position:0%
+discussion you can talk about sources of
+error that either came from
+
+ align:start position:0%
+error that either came from
+ 
+
+ align:start position:0%
+error that either came from
+you or random errors and we'll talk
+
+ align:start position:0%
+you or random errors and we'll talk
+ 
+
+ align:start position:0%
+you or random errors and we'll talk
+about different types of error again
+
+ align:start position:0%
+about different types of error again
+ 
+
+ align:start position:0%
+about different types of error again
+next week
+
+ align:start position:0%
+next week
+ 
+
+ align:start position:0%
+next week
+and then analyze your data and your
+
+ align:start position:0%
+and then analyze your data and your
+ 
+
+ align:start position:0%
+and then analyze your data and your
+errors so your calculations should have
+
+ align:start position:0%
+errors so your calculations should have
+ 
+
+ align:start position:0%
+errors so your calculations should have
+already been done
+
+ align:start position:0%
+already been done
+ 
+
+ align:start position:0%
+already been done
+so do not include more calculations in
+
+ align:start position:0%
+so do not include more calculations in
+ 
+
+ align:start position:0%
+so do not include more calculations in
+your discussion if you need to calculate
+
+ align:start position:0%
+your discussion if you need to calculate
+ 
+
+ align:start position:0%
+your discussion if you need to calculate
+something go back and do it
+
+ align:start position:0%
+something go back and do it
+ 
+
+ align:start position:0%
+something go back and do it
+in the results section but now you want
+
+ align:start position:0%
+in the results section but now you want
+ 
+
+ align:start position:0%
+in the results section but now you want
+to analyze the data
+
+ align:start position:0%
+to analyze the data
+ 
+
+ align:start position:0%
+to analyze the data
+and talk about what it means so you've
+
+ align:start position:0%
+and talk about what it means so you've
+ 
+
+ align:start position:0%
+and talk about what it means so you've
+reported your melting point you've
+
+ align:start position:0%
+reported your melting point you've
+ 
+
+ align:start position:0%
+reported your melting point you've
+reported all of your yields you've
+
+ align:start position:0%
+reported all of your yields you've
+ 
+
+ align:start position:0%
+reported all of your yields you've
+reported your rf values what does it
+
+ align:start position:0%
+reported your rf values what does it
+ 
+
+ align:start position:0%
+reported your rf values what does it
+mean what does it say about the success
+
+ align:start position:0%
+mean what does it say about the success
+ 
+
+ align:start position:0%
+mean what does it say about the success
+of the experiment go back to your intro
+
+ align:start position:0%
+of the experiment go back to your intro
+ 
+
+ align:start position:0%
+of the experiment go back to your intro
+and say hey
+
+ align:start position:0%
+and say hey
+ 
+
+ align:start position:0%
+and say hey
+this is what i said i was going to do
+
+ align:start position:0%
+this is what i said i was going to do
+ 
+
+ align:start position:0%
+this is what i said i was going to do
+did i do it and here is my data to
+
+ align:start position:0%
+did i do it and here is my data to
+ 
+
+ align:start position:0%
+did i do it and here is my data to
+explain why
+
+ align:start position:0%
+explain why
+ 
+
+ align:start position:0%
+explain why
+so what can we talk about in the
+
+ align:start position:0%
+so what can we talk about in the
+ 
+
+ align:start position:0%
+so what can we talk about in the
+ferrocene discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you can discuss how like um
+
+ align:start position:0%
+um you can discuss how like um
+ 
+
+ align:start position:0%
+um you can discuss how like um
+our percent yield isn't 100
+
+ align:start position:0%
+our percent yield isn't 100
+ 
+
+ align:start position:0%
+our percent yield isn't 100
+because of errors potentially like
+
+ align:start position:0%
+because of errors potentially like
+ 
+
+ align:start position:0%
+because of errors potentially like
+because it doesn't scrape all the
+
+ align:start position:0%
+because it doesn't scrape all the
+ 
+
+ align:start position:0%
+because it doesn't scrape all the
+terrorists
+
+ align:start position:0%
+terrorists
+ 
+
+ align:start position:0%
+terrorists
+off the uh
+
+ align:start position:0%
+off the uh
+ 
+
+ align:start position:0%
+off the uh
+yeah yeah different so you can talk
+
+ align:start position:0%
+yeah yeah different so you can talk
+ 
+
+ align:start position:0%
+yeah yeah different so you can talk
+about your percent yield it's
+
+ align:start position:0%
+about your percent yield it's
+ 
+
+ align:start position:0%
+about your percent yield it's
+not going to be 100 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why might that be so different parts of
+
+ align:start position:0%
+why might that be so different parts of
+ 
+
+ align:start position:0%
+why might that be so different parts of
+the procedure where did you lose product
+
+ align:start position:0%
+the procedure where did you lose product
+ 
+
+ align:start position:0%
+the procedure where did you lose product
+scraping it out of the round bottom that
+
+ align:start position:0%
+scraping it out of the round bottom that
+ 
+
+ align:start position:0%
+scraping it out of the round bottom that
+was really hard a lot of people were
+
+ align:start position:0%
+was really hard a lot of people were
+ 
+
+ align:start position:0%
+was really hard a lot of people were
+struggling to get all of their acetyl
+
+ align:start position:0%
+struggling to get all of their acetyl
+ 
+
+ align:start position:0%
+struggling to get all of their acetyl
+ferrocene out of the round bottom
+
+ align:start position:0%
+ferrocene out of the round bottom
+ 
+
+ align:start position:0%
+ferrocene out of the round bottom
+yesterday
+
+ align:start position:0%
+yesterday
+ 
+
+ align:start position:0%
+yesterday
+or scraping stuff off of the with ferris
+
+ align:start position:0%
+or scraping stuff off of the with ferris
+ 
+
+ align:start position:0%
+or scraping stuff off of the with ferris
+scene when you sublimed it
+
+ align:start position:0%
+scene when you sublimed it
+ 
+
+ align:start position:0%
+scene when you sublimed it
+different pieces so you can go back
+
+ align:start position:0%
+different pieces so you can go back
+ 
+
+ align:start position:0%
+different pieces so you can go back
+again and this is a good spot when your
+
+ align:start position:0%
+again and this is a good spot when your
+ 
+
+ align:start position:0%
+again and this is a good spot when your
+notebook
+
+ align:start position:0%
+notebook
+ 
+
+ align:start position:0%
+notebook
+is going to help you a lot if you take
+
+ align:start position:0%
+is going to help you a lot if you take
+ 
+
+ align:start position:0%
+is going to help you a lot if you take
+good notes in the lab then you'll know
+
+ align:start position:0%
+good notes in the lab then you'll know
+ 
+
+ align:start position:0%
+good notes in the lab then you'll know
+oh yep that's where my product went
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else can we talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so after we do photography experiments
+
+ align:start position:0%
+so after we do photography experiments
+ 
+
+ align:start position:0%
+so after we do photography experiments
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+percentage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so after you do your tlc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll have uh one way to tell how pure
+
+ align:start position:0%
+you'll have uh one way to tell how pure
+ 
+
+ align:start position:0%
+you'll have uh one way to tell how pure
+your um your final mixture was did you
+
+ align:start position:0%
+your um your final mixture was did you
+ 
+
+ align:start position:0%
+your um your final mixture was did you
+still have ferrocene left when you
+
+ align:start position:0%
+still have ferrocene left when you
+ 
+
+ align:start position:0%
+still have ferrocene left when you
+thought you only had made acetyl
+
+ align:start position:0%
+thought you only had made acetyl
+ 
+
+ align:start position:0%
+thought you only had made acetyl
+ferrocene
+
+ align:start position:0%
+ferrocene
+ 
+
+ align:start position:0%
+ferrocene
+so amounts of compounds left over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you'll have that information from tlc
+
+ align:start position:0%
+so you'll have that information from tlc
+ 
+
+ align:start position:0%
+so you'll have that information from tlc
+and from your column when you run your
+
+ align:start position:0%
+and from your column when you run your
+ 
+
+ align:start position:0%
+and from your column when you run your
+column and you separate out your
+
+ align:start position:0%
+column and you separate out your
+ 
+
+ align:start position:0%
+column and you separate out your
+ferrocene and your acetyl ferris scene
+
+ align:start position:0%
+ferrocene and your acetyl ferris scene
+ 
+
+ align:start position:0%
+ferrocene and your acetyl ferris scene
+you'll see how
+
+ align:start position:0%
+you'll see how
+ 
+
+ align:start position:0%
+you'll see how
+pure your product was and you can talk
+
+ align:start position:0%
+pure your product was and you can talk
+ 
+
+ align:start position:0%
+pure your product was and you can talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that and why you may not have had a
+
+ align:start position:0%
+that and why you may not have had a
+ 
+
+ align:start position:0%
+that and why you may not have had a
+completely pure product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what else is in our in our results
+
+ align:start position:0%
+so what else is in our in our results
+ 
+
+ align:start position:0%
+so what else is in our in our results
+chart that we have not discussed over
+
+ align:start position:0%
+chart that we have not discussed over
+ 
+
+ align:start position:0%
+chart that we have not discussed over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+melting ranges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+melting point and what does that tell us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same thing you can get purity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so was your melting point too low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or a wide range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else can your melting point help
+
+ align:start position:0%
+what else can your melting point help
+ 
+
+ align:start position:0%
+what else can your melting point help
+you tell to some extent
+
+ align:start position:0%
+you tell to some extent
+ 
+
+ align:start position:0%
+you tell to some extent
+in our case we're kind of using it to
+
+ align:start position:0%
+in our case we're kind of using it to
+ 
+
+ align:start position:0%
+in our case we're kind of using it to
+determine the identity of our products
+
+ align:start position:0%
+determine the identity of our products
+ 
+
+ align:start position:0%
+determine the identity of our products
+right because we don't have a lot of
+
+ align:start position:0%
+right because we don't have a lot of
+ 
+
+ align:start position:0%
+right because we don't have a lot of
+really spectroscopic ways of
+
+ align:start position:0%
+really spectroscopic ways of
+ 
+
+ align:start position:0%
+really spectroscopic ways of
+characterizing this product so
+
+ align:start position:0%
+characterizing this product so
+ 
+
+ align:start position:0%
+characterizing this product so
+we are going to use it
+
+ align:start position:0%
+we are going to use it
+ 
+
+ align:start position:0%
+we are going to use it
+to identify your products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can tell us how pure your product
+
+ align:start position:0%
+so you can tell us how pure your product
+ 
+
+ align:start position:0%
+so you can tell us how pure your product
+was and then compared to the literature
+
+ align:start position:0%
+was and then compared to the literature
+ 
+
+ align:start position:0%
+was and then compared to the literature
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um see what the identity is and
+
+ align:start position:0%
+um see what the identity is and
+ 
+
+ align:start position:0%
+um see what the identity is and
+hopefully your melting points of
+
+ align:start position:0%
+hopefully your melting points of
+ 
+
+ align:start position:0%
+hopefully your melting points of
+ferrocene and acetyl ferricine are not
+
+ align:start position:0%
+ferrocene and acetyl ferricine are not
+ 
+
+ align:start position:0%
+ferrocene and acetyl ferricine are not
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+so that you did in fact have some
+
+ align:start position:0%
+so that you did in fact have some
+ 
+
+ align:start position:0%
+so that you did in fact have some
+evidence that you made a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound
+
+ align:start position:0%
+compound
+ 
+
+ align:start position:0%
+compound
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can again bring in some more of
+
+ align:start position:0%
+so you can again bring in some more of
+ 
+
+ align:start position:0%
+so you can again bring in some more of
+your results talk about the color
+
+ align:start position:0%
+your results talk about the color
+ 
+
+ align:start position:0%
+your results talk about the color
+and the appearance of things so your
+
+ align:start position:0%
+and the appearance of things so your
+ 
+
+ align:start position:0%
+and the appearance of things so your
+ferricine and your acetyl ferrocene are
+
+ align:start position:0%
+ferricine and your acetyl ferrocene are
+ 
+
+ align:start position:0%
+ferricine and your acetyl ferrocene are
+different colors you can talk about why
+
+ align:start position:0%
+different colors you can talk about why
+ 
+
+ align:start position:0%
+different colors you can talk about why
+that might be
+
+ align:start position:0%
+that might be
+ 
+
+ align:start position:0%
+that might be
+and how you can use that to identify
+
+ align:start position:0%
+and how you can use that to identify
+ 
+
+ align:start position:0%
+and how you can use that to identify
+different your
+
+ align:start position:0%
+different your
+ 
+
+ align:start position:0%
+different your
+different compounds especially on your
+
+ align:start position:0%
+different compounds especially on your
+ 
+
+ align:start position:0%
+different compounds especially on your
+tlc plate so when you run your tlc and
+
+ align:start position:0%
+tlc plate so when you run your tlc and
+ 
+
+ align:start position:0%
+tlc plate so when you run your tlc and
+in your column you'll be able to
+
+ align:start position:0%
+in your column you'll be able to
+ 
+
+ align:start position:0%
+in your column you'll be able to
+tell your compounds apart by color
+
+ align:start position:0%
+tell your compounds apart by color
+ 
+
+ align:start position:0%
+tell your compounds apart by color
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+so yeah and then again if you had any
+
+ align:start position:0%
+so yeah and then again if you had any
+ 
+
+ align:start position:0%
+so yeah and then again if you had any
+suggestions for how to improve the
+
+ align:start position:0%
+suggestions for how to improve the
+ 
+
+ align:start position:0%
+suggestions for how to improve the
+procedure those can also go in your
+
+ align:start position:0%
+procedure those can also go in your
+ 
+
+ align:start position:0%
+procedure those can also go in your
+discussion if you were doing something
+
+ align:start position:0%
+discussion if you were doing something
+ 
+
+ align:start position:0%
+discussion if you were doing something
+and said oh this would be much better if
+
+ align:start position:0%
+and said oh this would be much better if
+ 
+
+ align:start position:0%
+and said oh this would be much better if
+we did it this way or you know the
+
+ align:start position:0%
+we did it this way or you know the
+ 
+
+ align:start position:0%
+we did it this way or you know the
+sublimation
+
+ align:start position:0%
+sublimation
+ 
+
+ align:start position:0%
+sublimation
+i found this cool trick for it please
+
+ align:start position:0%
+i found this cool trick for it please
+ 
+
+ align:start position:0%
+i found this cool trick for it please
+tell us
+
+ align:start position:0%
+tell us
+ 
+
+ align:start position:0%
+tell us
+and perhaps your
+
+ align:start position:0%
+and perhaps your
+ 
+
+ align:start position:0%
+and perhaps your
+genius idea will help us improve the lab
+
+ align:start position:0%
+genius idea will help us improve the lab
+ 
+
+ align:start position:0%
+genius idea will help us improve the lab
+for future semesters of students
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then at the end there's a conclusion so
+
+ align:start position:0%
+then at the end there's a conclusion so
+ 
+
+ align:start position:0%
+then at the end there's a conclusion so
+you briefly summarize your results this
+
+ align:start position:0%
+you briefly summarize your results this
+ 
+
+ align:start position:0%
+you briefly summarize your results this
+again is pretty similar to the abstract
+
+ align:start position:0%
+again is pretty similar to the abstract
+ 
+
+ align:start position:0%
+again is pretty similar to the abstract
+it'll just be about a paragraph
+
+ align:start position:0%
+it'll just be about a paragraph
+ 
+
+ align:start position:0%
+it'll just be about a paragraph
+maybe a little bit longer a statement
+
+ align:start position:0%
+maybe a little bit longer a statement
+ 
+
+ align:start position:0%
+maybe a little bit longer a statement
+about whether you achieve the goals for
+
+ align:start position:0%
+about whether you achieve the goals for
+ 
+
+ align:start position:0%
+about whether you achieve the goals for
+the lab then wrap up your discussion
+
+ align:start position:0%
+the lab then wrap up your discussion
+ 
+
+ align:start position:0%
+the lab then wrap up your discussion
+section
+
+ align:start position:0%
+section
+ 
+
+ align:start position:0%
+section
+and kind of tie everything together
+
+ align:start position:0%
+and kind of tie everything together
+ 
+
+ align:start position:0%
+and kind of tie everything together
+based on the abstract and the conclusion
+
+ align:start position:0%
+based on the abstract and the conclusion
+ 
+
+ align:start position:0%
+based on the abstract and the conclusion
+if people read those two parts they
+
+ align:start position:0%
+if people read those two parts they
+ 
+
+ align:start position:0%
+if people read those two parts they
+should have a
+
+ align:start position:0%
+should have a
+ 
+
+ align:start position:0%
+should have a
+generally pretty good idea about what
+
+ align:start position:0%
+generally pretty good idea about what
+ 
+
+ align:start position:0%
+generally pretty good idea about what
+happened in the lab and if they want
+
+ align:start position:0%
+happened in the lab and if they want
+ 
+
+ align:start position:0%
+happened in the lab and if they want
+details then they can read
+
+ align:start position:0%
+details then they can read
+ 
+
+ align:start position:0%
+details then they can read
+the rest of it so conclusion again wrap
+
+ align:start position:0%
+the rest of it so conclusion again wrap
+ 
+
+ align:start position:0%
+the rest of it so conclusion again wrap
+it all up and then once you're done with
+
+ align:start position:0%
+it all up and then once you're done with
+ 
+
+ align:start position:0%
+it all up and then once you're done with
+all of this go back and write your
+
+ align:start position:0%
+all of this go back and write your
+ 
+
+ align:start position:0%
+all of this go back and write your
+abstract because now we have all of the
+
+ align:start position:0%
+abstract because now we have all of the
+ 
+
+ align:start position:0%
+abstract because now we have all of the
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+that needs to be neatly summarized in
+
+ align:start position:0%
+that needs to be neatly summarized in
+ 
+
+ align:start position:0%
+that needs to be neatly summarized in
+our abstract
+
+ align:start position:0%
+our abstract
+ 
+
+ align:start position:0%
+our abstract
+the very last thing that we need to talk
+
+ align:start position:0%
+the very last thing that we need to talk
+ 
+
+ align:start position:0%
+the very last thing that we need to talk
+about is references
+
+ align:start position:0%
+about is references
+ 
+
+ align:start position:0%
+about is references
+so you're at the end of your report you
+
+ align:start position:0%
+so you're at the end of your report you
+ 
+
+ align:start position:0%
+so you're at the end of your report you
+need to list all the sources that you
+
+ align:start position:0%
+need to list all the sources that you
+ 
+
+ align:start position:0%
+need to list all the sources that you
+use but you also need to cite them in
+
+ align:start position:0%
+use but you also need to cite them in
+ 
+
+ align:start position:0%
+use but you also need to cite them in
+the text and this should not be anything
+
+ align:start position:0%
+the text and this should not be anything
+ 
+
+ align:start position:0%
+the text and this should not be anything
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+do not use wikipedia as a reference
+
+ align:start position:0%
+do not use wikipedia as a reference
+ 
+
+ align:start position:0%
+do not use wikipedia as a reference
+you can cite the lab manual in the
+
+ align:start position:0%
+you can cite the lab manual in the
+ 
+
+ align:start position:0%
+you can cite the lab manual in the
+lectures that's a good idea
+
+ align:start position:0%
+lectures that's a good idea
+ 
+
+ align:start position:0%
+lectures that's a good idea
+and then there's also a handout that i
+
+ align:start position:0%
+and then there's also a handout that i
+ 
+
+ align:start position:0%
+and then there's also a handout that i
+gave you as to the format of how to
+
+ align:start position:0%
+gave you as to the format of how to
+ 
+
+ align:start position:0%
+gave you as to the format of how to
+cite different commonly referenced
+
+ align:start position:0%
+cite different commonly referenced
+ 
+
+ align:start position:0%
+cite different commonly referenced
+sources like books
+
+ align:start position:0%
+sources like books
+ 
+
+ align:start position:0%
+sources like books
+articles things like that the acs style
+
+ align:start position:0%
+articles things like that the acs style
+ 
+
+ align:start position:0%
+articles things like that the acs style
+guide
+
+ align:start position:0%
+guide
+ 
+
+ align:start position:0%
+guide
+also has information about how to cite
+
+ align:start position:0%
+also has information about how to cite
+ 
+
+ align:start position:0%
+also has information about how to cite
+any type of reference that you could
+
+ align:start position:0%
+any type of reference that you could
+ 
+
+ align:start position:0%
+any type of reference that you could
+ever need to cite
+
+ align:start position:0%
+ever need to cite
+ 
+
+ align:start position:0%
+ever need to cite
+the in-text citations there are three
+
+ align:start position:0%
+the in-text citations there are three
+ 
+
+ align:start position:0%
+the in-text citations there are three
+ways that you can do them so if you're
+
+ align:start position:0%
+ways that you can do them so if you're
+ 
+
+ align:start position:0%
+ways that you can do them so if you're
+planning to cite this
+
+ align:start position:0%
+planning to cite this
+ 
+
+ align:start position:0%
+planning to cite this
+article in your lab report for some
+
+ align:start position:0%
+article in your lab report for some
+ 
+
+ align:start position:0%
+article in your lab report for some
+reason then
+
+ align:start position:0%
+reason then
+ 
+
+ align:start position:0%
+reason then
+you would have a sentence and then the
+
+ align:start position:0%
+you would have a sentence and then the
+ 
+
+ align:start position:0%
+you would have a sentence and then the
+first way to do it is to include the
+
+ align:start position:0%
+first way to do it is to include the
+ 
+
+ align:start position:0%
+first way to do it is to include the
+author's name
+
+ align:start position:0%
+author's name
+ 
+
+ align:start position:0%
+author's name
+and then the year you can also
+
+ align:start position:0%
+and then the year you can also
+ 
+
+ align:start position:0%
+and then the year you can also
+have a numbered list and use sub
+
+ align:start position:0%
+have a numbered list and use sub
+ 
+
+ align:start position:0%
+have a numbered list and use sub
+or superscripts at the end of the
+
+ align:start position:0%
+or superscripts at the end of the
+ 
+
+ align:start position:0%
+or superscripts at the end of the
+sentence or the last way is to put the
+
+ align:start position:0%
+sentence or the last way is to put the
+ 
+
+ align:start position:0%
+sentence or the last way is to put the
+number of the reference in parentheses
+
+ align:start position:0%
+number of the reference in parentheses
+ 
+
+ align:start position:0%
+number of the reference in parentheses
+in italics at the end of the sentence
+
+ align:start position:0%
+in italics at the end of the sentence
+ 
+
+ align:start position:0%
+in italics at the end of the sentence
+so up to you all three ways are acs
+
+ align:start position:0%
+so up to you all three ways are acs
+ 
+
+ align:start position:0%
+so up to you all three ways are acs
+approved
+
+ align:start position:0%
+approved
+ 
+
+ align:start position:0%
+approved
+whichever one you find the easiest or
+
+ align:start position:0%
+whichever one you find the easiest or
+ 
+
+ align:start position:0%
+whichever one you find the easiest or
+most familiar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appendices we already talked about this
+
+ align:start position:0%
+appendices we already talked about this
+ 
+
+ align:start position:0%
+appendices we already talked about this
+a little bit it's a really good way to
+
+ align:start position:0%
+a little bit it's a really good way to
+ 
+
+ align:start position:0%
+a little bit it's a really good way to
+include relevant information that
+
+ align:start position:0%
+include relevant information that
+ 
+
+ align:start position:0%
+include relevant information that
+doesn't fit well into the body of the
+
+ align:start position:0%
+doesn't fit well into the body of the
+ 
+
+ align:start position:0%
+doesn't fit well into the body of the
+lab report or maybe isn't
+
+ align:start position:0%
+lab report or maybe isn't
+ 
+
+ align:start position:0%
+lab report or maybe isn't
+the most important thing in to the
+
+ align:start position:0%
+the most important thing in to the
+ 
+
+ align:start position:0%
+the most important thing in to the
+goal that you're trying to achieve they
+
+ align:start position:0%
+goal that you're trying to achieve they
+ 
+
+ align:start position:0%
+goal that you're trying to achieve they
+don't count towards your page limit so
+
+ align:start position:0%
+don't count towards your page limit so
+ 
+
+ align:start position:0%
+don't count towards your page limit so
+if your lab report is getting long and
+
+ align:start position:0%
+if your lab report is getting long and
+ 
+
+ align:start position:0%
+if your lab report is getting long and
+you can find things that
+
+ align:start position:0%
+you can find things that
+ 
+
+ align:start position:0%
+you can find things that
+would go in the appendix that's not a
+
+ align:start position:0%
+would go in the appendix that's not a
+ 
+
+ align:start position:0%
+would go in the appendix that's not a
+bad thing
+
+ align:start position:0%
+bad thing
+ 
+
+ align:start position:0%
+bad thing
+don't put stuff that should be in the
+
+ align:start position:0%
+don't put stuff that should be in the
+ 
+
+ align:start position:0%
+don't put stuff that should be in the
+lab report in the appendix just for the
+
+ align:start position:0%
+lab report in the appendix just for the
+ 
+
+ align:start position:0%
+lab report in the appendix just for the
+sake of giving yourself extra space in
+
+ align:start position:0%
+sake of giving yourself extra space in
+ 
+
+ align:start position:0%
+sake of giving yourself extra space in
+the lab report we will take points off
+
+ align:start position:0%
+the lab report we will take points off
+ 
+
+ align:start position:0%
+the lab report we will take points off
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+appendices have a number and a title so
+
+ align:start position:0%
+appendices have a number and a title so
+ 
+
+ align:start position:0%
+appendices have a number and a title so
+appendix one and then you would say
+
+ align:start position:0%
+appendix one and then you would say
+ 
+
+ align:start position:0%
+appendix one and then you would say
+what's in appendix one
+
+ align:start position:0%
+what's in appendix one
+ 
+
+ align:start position:0%
+what's in appendix one
+refer to them in the text of the report
+
+ align:start position:0%
+refer to them in the text of the report
+ 
+
+ align:start position:0%
+refer to them in the text of the report
+like anything else
+
+ align:start position:0%
+like anything else
+ 
+
+ align:start position:0%
+like anything else
+the format this is probably the most
+
+ align:start position:0%
+the format this is probably the most
+ 
+
+ align:start position:0%
+the format this is probably the most
+important thing that you guys care about
+
+ align:start position:0%
+important thing that you guys care about
+ 
+
+ align:start position:0%
+important thing that you guys care about
+there's a 10 page limit
+
+ align:start position:0%
+there's a 10 page limit
+ 
+
+ align:start position:0%
+there's a 10 page limit
+plus or minus two pages so if yours is
+
+ align:start position:0%
+plus or minus two pages so if yours is
+ 
+
+ align:start position:0%
+plus or minus two pages so if yours is
+significantly shorter than 10 pages or
+
+ align:start position:0%
+significantly shorter than 10 pages or
+ 
+
+ align:start position:0%
+significantly shorter than 10 pages or
+significantly longer
+
+ align:start position:0%
+significantly longer
+ 
+
+ align:start position:0%
+significantly longer
+then you will start to lose points
+
+ align:start position:0%
+then you will start to lose points
+ 
+
+ align:start position:0%
+then you will start to lose points
+10 pages should be the right amount of
+
+ align:start position:0%
+10 pages should be the right amount of
+ 
+
+ align:start position:0%
+10 pages should be the right amount of
+space to talk about all of the results
+
+ align:start position:0%
+space to talk about all of the results
+ 
+
+ align:start position:0%
+space to talk about all of the results
+in all of these labs
+
+ align:start position:0%
+in all of these labs
+ 
+
+ align:start position:0%
+in all of these labs
+one and a half line spacing in word one
+
+ align:start position:0%
+one and a half line spacing in word one
+ 
+
+ align:start position:0%
+one and a half line spacing in word one
+inch margins
+
+ align:start position:0%
+inch margins
+ 
+
+ align:start position:0%
+inch margins
+12 point times new roman font pretty
+
+ align:start position:0%
+12 point times new roman font pretty
+ 
+
+ align:start position:0%
+12 point times new roman font pretty
+standard stuff and then print it out
+
+ align:start position:0%
+standard stuff and then print it out
+ 
+
+ align:start position:0%
+standard stuff and then print it out
+if we want an electronic version we will
+
+ align:start position:0%
+if we want an electronic version we will
+ 
+
+ align:start position:0%
+if we want an electronic version we will
+request it but most of the
+
+ align:start position:0%
+request it but most of the
+ 
+
+ align:start position:0%
+request it but most of the
+grading is done by hand so
+
+ align:start position:0%
+grading is done by hand so
+ 
+
+ align:start position:0%
+grading is done by hand so
+we print it out and we will give you
+
+ align:start position:0%
+we print it out and we will give you
+ 
+
+ align:start position:0%
+we print it out and we will give you
+back the hard copy the following week
+
+ align:start position:0%
+back the hard copy the following week
+ 
+
+ align:start position:0%
+back the hard copy the following week
+ethics we've talked about this before
+
+ align:start position:0%
+ethics we've talked about this before
+ 
+
+ align:start position:0%
+ethics we've talked about this before
+already but do your own work
+
+ align:start position:0%
+already but do your own work
+ 
+
+ align:start position:0%
+already but do your own work
+don't use lab reports from prior
+
+ align:start position:0%
+don't use lab reports from prior
+ 
+
+ align:start position:0%
+don't use lab reports from prior
+students do not copy and paste anything
+
+ align:start position:0%
+students do not copy and paste anything
+ 
+
+ align:start position:0%
+students do not copy and paste anything
+that you did not write yourself
+
+ align:start position:0%
+that you did not write yourself
+ 
+
+ align:start position:0%
+that you did not write yourself
+cite your sources and do not go looking
+
+ align:start position:0%
+cite your sources and do not go looking
+ 
+
+ align:start position:0%
+cite your sources and do not go looking
+for similar reports on the internet some
+
+ align:start position:0%
+for similar reports on the internet some
+ 
+
+ align:start position:0%
+for similar reports on the internet some
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+labs that we do here are similar to labs
+
+ align:start position:0%
+labs that we do here are similar to labs
+ 
+
+ align:start position:0%
+labs that we do here are similar to labs
+that they do other places some of them
+
+ align:start position:0%
+that they do other places some of them
+ 
+
+ align:start position:0%
+that they do other places some of them
+are wildly different so you won't find
+
+ align:start position:0%
+are wildly different so you won't find
+ 
+
+ align:start position:0%
+are wildly different so you won't find
+anything anyway
+
+ align:start position:0%
+anything anyway
+ 
+
+ align:start position:0%
+anything anyway
+the tas and instructors are here to help
+
+ align:start position:0%
+the tas and instructors are here to help
+ 
+
+ align:start position:0%
+the tas and instructors are here to help
+you succeed so we are the ones who are
+
+ align:start position:0%
+you succeed so we are the ones who are
+ 
+
+ align:start position:0%
+you succeed so we are the ones who are
+grading your lab reports so instead of
+
+ align:start position:0%
+grading your lab reports so instead of
+ 
+
+ align:start position:0%
+grading your lab reports so instead of
+going looking up some random
+
+ align:start position:0%
+going looking up some random
+ 
+
+ align:start position:0%
+going looking up some random
+report from some other person at a
+
+ align:start position:0%
+report from some other person at a
+ 
+
+ align:start position:0%
+report from some other person at a
+different institution on the internet
+
+ align:start position:0%
+different institution on the internet
+ 
+
+ align:start position:0%
+different institution on the internet
+come talk to us we are the ones who know
+
+ align:start position:0%
+come talk to us we are the ones who know
+ 
+
+ align:start position:0%
+come talk to us we are the ones who know
+how we will be grading it what we are
+
+ align:start position:0%
+how we will be grading it what we are
+ 
+
+ align:start position:0%
+how we will be grading it what we are
+looking for and what you did
+
+ align:start position:0%
+looking for and what you did
+ 
+
+ align:start position:0%
+looking for and what you did
+specifically so we can help you
+
+ align:start position:0%
+specifically so we can help you
+ 
+
+ align:start position:0%
+specifically so we can help you
+write your lab report the best way
+
+ align:start position:0%
+write your lab report the best way
+ 
+
+ align:start position:0%
+write your lab report the best way
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+here is the point breakdown for how most
+
+ align:start position:0%
+here is the point breakdown for how most
+ 
+
+ align:start position:0%
+here is the point breakdown for how most
+of the lab reports are graded
+
+ align:start position:0%
+of the lab reports are graded
+ 
+
+ align:start position:0%
+of the lab reports are graded
+you can see that the discussion and the
+
+ align:start position:0%
+you can see that the discussion and the
+ 
+
+ align:start position:0%
+you can see that the discussion and the
+results portion are
+
+ align:start position:0%
+results portion are
+ 
+
+ align:start position:0%
+results portion are
+weighted more heavily than the rest of
+
+ align:start position:0%
+weighted more heavily than the rest of
+ 
+
+ align:start position:0%
+weighted more heavily than the rest of
+it um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the ester lab you will be un
+
+ align:start position:0%
+in the ester lab you will be un
+ 
+
+ align:start position:0%
+in the ester lab you will be un
+identifying an unknown
+
+ align:start position:0%
+identifying an unknown
+ 
+
+ align:start position:0%
+identifying an unknown
+and so that's only for one lab which is
+
+ align:start position:0%
+and so that's only for one lab which is
+ 
+
+ align:start position:0%
+and so that's only for one lab which is
+why there are ranges on here it kind of
+
+ align:start position:0%
+why there are ranges on here it kind of
+ 
+
+ align:start position:0%
+why there are ranges on here it kind of
+varies from lab to lab based on
+
+ align:start position:0%
+varies from lab to lab based on
+ 
+
+ align:start position:0%
+varies from lab to lab based on
+how much time and effort you're going to
+
+ align:start position:0%
+how much time and effort you're going to
+ 
+
+ align:start position:0%
+how much time and effort you're going to
+be putting into each of the sections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+submission and grading so labs are due
+
+ align:start position:0%
+submission and grading so labs are due
+ 
+
+ align:start position:0%
+submission and grading so labs are due
+at the start of lab on the dates listed
+
+ align:start position:0%
+at the start of lab on the dates listed
+ 
+
+ align:start position:0%
+at the start of lab on the dates listed
+in the lab manual there is a locked box
+
+ align:start position:0%
+in the lab manual there is a locked box
+ 
+
+ align:start position:0%
+in the lab manual there is a locked box
+outside of the stock room in the lab and
+
+ align:start position:0%
+outside of the stock room in the lab and
+ 
+
+ align:start position:0%
+outside of the stock room in the lab and
+that's where you will turn your lab in
+
+ align:start position:0%
+that's where you will turn your lab in
+ 
+
+ align:start position:0%
+that's where you will turn your lab in
+do not
+
+ align:start position:0%
+do not
+ 
+
+ align:start position:0%
+do not
+turn your lab into your ta's mailbox or
+
+ align:start position:0%
+turn your lab into your ta's mailbox or
+ 
+
+ align:start position:0%
+turn your lab into your ta's mailbox or
+to my mailbox or to john's mailbox
+
+ align:start position:0%
+to my mailbox or to john's mailbox
+ 
+
+ align:start position:0%
+to my mailbox or to john's mailbox
+it goes into the lock box then the tas
+
+ align:start position:0%
+it goes into the lock box then the tas
+ 
+
+ align:start position:0%
+it goes into the lock box then the tas
+will collect them
+
+ align:start position:0%
+will collect them
+ 
+
+ align:start position:0%
+will collect them
+they will grade them and they will be
+
+ align:start position:0%
+they will grade them and they will be
+ 
+
+ align:start position:0%
+they will grade them and they will be
+returned one week from when you turned
+
+ align:start position:0%
+returned one week from when you turned
+ 
+
+ align:start position:0%
+returned one week from when you turned
+it in so if you have a monday wednesday
+
+ align:start position:0%
+it in so if you have a monday wednesday
+ 
+
+ align:start position:0%
+it in so if you have a monday wednesday
+lab if you turn your lab in on monday
+
+ align:start position:0%
+lab if you turn your lab in on monday
+ 
+
+ align:start position:0%
+lab if you turn your lab in on monday
+you will be graded the following monday
+
+ align:start position:0%
+you will be graded the following monday
+ 
+
+ align:start position:0%
+you will be graded the following monday
+when you get it back on that following
+
+ align:start position:0%
+when you get it back on that following
+ 
+
+ align:start position:0%
+when you get it back on that following
+monday you have one week to dispute any
+
+ align:start position:0%
+monday you have one week to dispute any
+ 
+
+ align:start position:0%
+monday you have one week to dispute any
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+with your ta so they'll give you back
+
+ align:start position:0%
+with your ta so they'll give you back
+ 
+
+ align:start position:0%
+with your ta so they'll give you back
+the lab report with their comments on it
+
+ align:start position:0%
+the lab report with their comments on it
+ 
+
+ align:start position:0%
+the lab report with their comments on it
+and if you disagree with something
+
+ align:start position:0%
+and if you disagree with something
+ 
+
+ align:start position:0%
+and if you disagree with something
+talk to your ta try to figure out what
+
+ align:start position:0%
+talk to your ta try to figure out what
+ 
+
+ align:start position:0%
+talk to your ta try to figure out what
+why they graded it the way they did if
+
+ align:start position:0%
+why they graded it the way they did if
+ 
+
+ align:start position:0%
+why they graded it the way they did if
+you guys could resolve
+
+ align:start position:0%
+you guys could resolve
+ 
+
+ align:start position:0%
+you guys could resolve
+whatever point conflict do you think
+
+ align:start position:0%
+whatever point conflict do you think
+ 
+
+ align:start position:0%
+whatever point conflict do you think
+that you're having if the ta made a
+
+ align:start position:0%
+that you're having if the ta made a
+ 
+
+ align:start position:0%
+that you're having if the ta made a
+mistake if you made a mistake and didn't
+
+ align:start position:0%
+mistake if you made a mistake and didn't
+ 
+
+ align:start position:0%
+mistake if you made a mistake and didn't
+realize it
+
+ align:start position:0%
+realize it
+ 
+
+ align:start position:0%
+realize it
+figure it out if you can't figure it out
+
+ align:start position:0%
+figure it out if you can't figure it out
+ 
+
+ align:start position:0%
+figure it out if you can't figure it out
+then you can submit your report to me
+
+ align:start position:0%
+then you can submit your report to me
+ 
+
+ align:start position:0%
+then you can submit your report to me
+and i will regrade the entire thing
+
+ align:start position:0%
+and i will regrade the entire thing
+ 
+
+ align:start position:0%
+and i will regrade the entire thing
+for either more or less points depending
+
+ align:start position:0%
+for either more or less points depending
+ 
+
+ align:start position:0%
+for either more or less points depending
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+how well you wrote your live report so
+
+ align:start position:0%
+how well you wrote your live report so
+ 
+
+ align:start position:0%
+how well you wrote your live report so
+that's the last resort is giving it to
+
+ align:start position:0%
+that's the last resort is giving it to
+ 
+
+ align:start position:0%
+that's the last resort is giving it to
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+um and then grades will be posted on
+
+ align:start position:0%
+um and then grades will be posted on
+ 
+
+ align:start position:0%
+um and then grades will be posted on
+stellar one week after the reports are
+
+ align:start position:0%
+stellar one week after the reports are
+ 
+
+ align:start position:0%
+stellar one week after the reports are
+returned once
+
+ align:start position:0%
+returned once
+ 
+
+ align:start position:0%
+returned once
+any point disputes have been resolved so
+
+ align:start position:0%
+any point disputes have been resolved so
+ 
+
+ align:start position:0%
+any point disputes have been resolved so
+that you'll be able to keep track of
+
+ align:start position:0%
+that you'll be able to keep track of
+ 
+
+ align:start position:0%
+that you'll be able to keep track of
+your scores
+
+ align:start position:0%
+your scores
+ 
+
+ align:start position:0%
+your scores
+ahead the final report is an oral report
+
+ align:start position:0%
+ahead the final report is an oral report
+ 
+
+ align:start position:0%
+ahead the final report is an oral report
+it'll be a chalk talk so
+
+ align:start position:0%
+it'll be a chalk talk so
+ 
+
+ align:start position:0%
+it'll be a chalk talk so
+no power points you'll get a chalkboard
+
+ align:start position:0%
+no power points you'll get a chalkboard
+ 
+
+ align:start position:0%
+no power points you'll get a chalkboard
+and any handouts that you want to bring
+
+ align:start position:0%
+and any handouts that you want to bring
+ 
+
+ align:start position:0%
+and any handouts that you want to bring
+it'll be you and your tas and you have
+
+ align:start position:0%
+it'll be you and your tas and you have
+ 
+
+ align:start position:0%
+it'll be you and your tas and you have
+to convince them that you
+
+ align:start position:0%
+to convince them that you
+ 
+
+ align:start position:0%
+to convince them that you
+understand the experiment and your data
+
+ align:start position:0%
+understand the experiment and your data
+ 
+
+ align:start position:0%
+understand the experiment and your data
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+so this will be for the final report of
+
+ align:start position:0%
+so this will be for the final report of
+ 
+
+ align:start position:0%
+so this will be for the final report of
+the semester so it's a long ways off but
+
+ align:start position:0%
+the semester so it's a long ways off but
+ 
+
+ align:start position:0%
+the semester so it's a long ways off but
+i wanted to give you a heads up just
+
+ align:start position:0%
+i wanted to give you a heads up just
+ 
+
+ align:start position:0%
+i wanted to give you a heads up just
+something to be thinking about it's the
+
+ align:start position:0%
+something to be thinking about it's the
+ 
+
+ align:start position:0%
+something to be thinking about it's the
+same information that's in a written
+
+ align:start position:0%
+same information that's in a written
+ 
+
+ align:start position:0%
+same information that's in a written
+report it's just a different way of
+
+ align:start position:0%
+report it's just a different way of
+ 
+
+ align:start position:0%
+report it's just a different way of
+presenting it and it should not be scary
+
+ align:start position:0%
+presenting it and it should not be scary
+ 
+
+ align:start position:0%
+presenting it and it should not be scary
+you guys know what you're doing and by
+
+ align:start position:0%
+you guys know what you're doing and by
+ 
+
+ align:start position:0%
+you guys know what you're doing and by
+that point you'll definitely know what
+
+ align:start position:0%
+that point you'll definitely know what
+ 
+
+ align:start position:0%
+that point you'll definitely know what
+you're doing
+
+ align:start position:0%
+you're doing
+ 
+
+ align:start position:0%
+you're doing
+and the tas are obviously here to help
+
+ align:start position:0%
+and the tas are obviously here to help
+ 
+
+ align:start position:0%
+and the tas are obviously here to help
+you guys
+
+ align:start position:0%
+you guys
+ 
+
+ align:start position:0%
+you guys
+with anything that you need and there
+
+ align:start position:0%
+with anything that you need and there
+ 
+
+ align:start position:0%
+with anything that you need and there
+will be a couple of
+
+ align:start position:0%
+will be a couple of
+ 
+
+ align:start position:0%
+will be a couple of
+courses or class lectures later in the
+
+ align:start position:0%
+courses or class lectures later in the
+ 
+
+ align:start position:0%
+courses or class lectures later in the
+semester where the tas will
+
+ align:start position:0%
+semester where the tas will
+ 
+
+ align:start position:0%
+semester where the tas will
+give you beautiful examples of good
+
+ align:start position:0%
+give you beautiful examples of good
+ 
+
+ align:start position:0%
+give you beautiful examples of good
+oral reports and bad oral reports so if
+
+ align:start position:0%
+oral reports and bad oral reports so if
+ 
+
+ align:start position:0%
+oral reports and bad oral reports so if
+you want to come see your tas
+
+ align:start position:0%
+you want to come see your tas
+ 
+
+ align:start position:0%
+you want to come see your tas
+acting skills put that on your calendar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anyone have any questions about
+
+ align:start position:0%
+does anyone have any questions about
+ 
+
+ align:start position:0%
+does anyone have any questions about
+anything that we have talked about today
+
+ align:start position:0%
+anything that we have talked about today
+ 
+
+ align:start position:0%
+anything that we have talked about today
+um you should scan them in and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put them in your lab report and print it
+
+ align:start position:0%
+put them in your lab report and print it
+ 
+
+ align:start position:0%
+put them in your lab report and print it
+out all together try not to write
+
+ align:start position:0%
+out all together try not to write
+ 
+
+ align:start position:0%
+out all together try not to write
+extra notes on the end um afterwards
+
+ align:start position:0%
+extra notes on the end um afterwards
+ 
+
+ align:start position:0%
+extra notes on the end um afterwards
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+we won't have everything printed so that
+
+ align:start position:0%
+we won't have everything printed so that
+ 
+
+ align:start position:0%
+we won't have everything printed so that
+it doesn't get confused with the tas
+
+ align:start position:0%
+it doesn't get confused with the tas
+ 
+
+ align:start position:0%
+it doesn't get confused with the tas
+notes and
+
+ align:start position:0%
+notes and
+ 
+
+ align:start position:0%
+notes and
+people adding things um after they've
+
+ align:start position:0%
+people adding things um after they've
+ 
+
+ align:start position:0%
+people adding things um after they've
+been graded
+
+ align:start position:0%
+been graded
+ 
+
+ align:start position:0%
+been graded
+yeah um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes are those they will be so yeah there
+
+ align:start position:0%
+yes are those they will be so yeah there
+ 
+
+ align:start position:0%
+yes are those they will be so yeah there
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+office hours before every lab report is
+
+ align:start position:0%
+office hours before every lab report is
+ 
+
+ align:start position:0%
+office hours before every lab report is
+turned in
+
+ align:start position:0%
+turned in
+ 
+
+ align:start position:0%
+turned in
+and the tas uh are going to
+
+ align:start position:0%
+and the tas uh are going to
+ 
+
+ align:start position:0%
+and the tas uh are going to
+they'll be posted on stellar next week
+
+ align:start position:0%
+they'll be posted on stellar next week
+ 
+
+ align:start position:0%
+they'll be posted on stellar next week
+once we schedule it with all the task
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
\ No newline at end of file
diff --git a/JPyuH4qXLZ0.txt b/JPyuH4qXLZ0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..abf23277c30c969f7b7b1b8192419cc7329db885
--- /dev/null
+++ b/JPyuH4qXLZ0.txt
@@ -0,0 +1,13245 @@
+align:start position:0%
+ 
+we're going to get started handouts are
+
+ align:start position:0%
+we're going to get started handouts are
+ 
+
+ align:start position:0%
+we're going to get started handouts are
+by the door if anybody didn't pick one
+
+ align:start position:0%
+by the door if anybody didn't pick one
+ 
+
+ align:start position:0%
+by the door if anybody didn't pick one
+up uh my name is Charles lerson I'll be
+
+ align:start position:0%
+up uh my name is Charles lerson I'll be
+ 
+
+ align:start position:0%
+up uh my name is Charles lerson I'll be
+lecturing this course uh this term
+
+ align:start position:0%
+lecturing this course uh this term
+ 
+
+ align:start position:0%
+lecturing this course uh this term
+introduction to algorithms with Eric
+
+ align:start position:0%
+introduction to algorithms with Eric
+ 
+
+ align:start position:0%
+introduction to algorithms with Eric
+Dain so uh in addition this is an SMA
+
+ align:start position:0%
+Dain so uh in addition this is an SMA
+ 
+
+ align:start position:0%
+Dain so uh in addition this is an SMA
+course a Singapore MIT Alliance course
+
+ align:start position:0%
+course a Singapore MIT Alliance course
+ 
+
+ align:start position:0%
+course a Singapore MIT Alliance course
+which will be uh run in Singapore by
+
+ align:start position:0%
+which will be uh run in Singapore by
+ 
+
+ align:start position:0%
+which will be uh run in Singapore by
+David Shu and so all the uh lectures
+
+ align:start position:0%
+David Shu and so all the uh lectures
+ 
+
+ align:start position:0%
+David Shu and so all the uh lectures
+will be videotaped and made available on
+
+ align:start position:0%
+will be videotaped and made available on
+ 
+
+ align:start position:0%
+will be videotaped and made available on
+the web uh for the Singapore students as
+
+ align:start position:0%
+the web uh for the Singapore students as
+ 
+
+ align:start position:0%
+the web uh for the Singapore students as
+well as for MIT students who choose to
+
+ align:start position:0%
+well as for MIT students who choose to
+ 
+
+ align:start position:0%
+well as for MIT students who choose to
+watch them on the
+
+ align:start position:0%
+watch them on the
+ 
+
+ align:start position:0%
+watch them on the
+web um if you uh have an issue of not
+
+ align:start position:0%
+web um if you uh have an issue of not
+ 
+
+ align:start position:0%
+web um if you uh have an issue of not
+wanting to be on the
+
+ align:start position:0%
+wanting to be on the
+ 
+
+ align:start position:0%
+wanting to be on the
+videotape uh you should sit in the back
+
+ align:start position:0%
+videotape uh you should sit in the back
+ 
+
+ align:start position:0%
+videotape uh you should sit in the back
+row okay uh otherwise uh you will be on
+
+ align:start position:0%
+row okay uh otherwise uh you will be on
+ 
+
+ align:start position:0%
+row okay uh otherwise uh you will be on
+it there is a video recording policy but
+
+ align:start position:0%
+it there is a video recording policy but
+ 
+
+ align:start position:0%
+it there is a video recording policy but
+it seems like they ran out so if anybody
+
+ align:start position:0%
+it seems like they ran out so if anybody
+ 
+
+ align:start position:0%
+it seems like they ran out so if anybody
+wants to see it uh people if they could
+
+ align:start position:0%
+wants to see it uh people if they could
+ 
+
+ align:start position:0%
+wants to see it uh people if they could
+just sort of pass them around maybe a
+
+ align:start position:0%
+just sort of pass them around maybe a
+ 
+
+ align:start position:0%
+just sort of pass them around maybe a
+little bit or or uh once you've done
+
+ align:start position:0%
+little bit or or uh once you've done
+ 
+
+ align:start position:0%
+little bit or or uh once you've done
+reading it or um you can come up and I I
+
+ align:start position:0%
+reading it or um you can come up and I I
+ 
+
+ align:start position:0%
+reading it or um you can come up and I I
+did secure one uh copy uh let's uh
+
+ align:start position:0%
+did secure one uh copy uh let's uh
+ 
+
+ align:start position:0%
+did secure one uh copy uh let's uh
+before we get into the content of the
+
+ align:start position:0%
+before we get into the content of the
+ 
+
+ align:start position:0%
+before we get into the content of the
+course let's briefly go over uh the
+
+ align:start position:0%
+course let's briefly go over uh the
+ 
+
+ align:start position:0%
+course let's briefly go over uh the
+course information because there's some
+
+ align:start position:0%
+course information because there's some
+ 
+
+ align:start position:0%
+course information because there's some
+uh administrative things that we sort of
+
+ align:start position:0%
+uh administrative things that we sort of
+ 
+
+ align:start position:0%
+uh administrative things that we sort of
+have to do as you can see this term we
+
+ align:start position:0%
+have to do as you can see this term we
+ 
+
+ align:start position:0%
+have to do as you can see this term we
+have a big
+
+ align:start position:0%
+have a big
+ 
+
+ align:start position:0%
+have a big
+staff so take a look at the uh handout
+
+ align:start position:0%
+staff so take a look at the uh handout
+ 
+
+ align:start position:0%
+staff so take a look at the uh handout
+here um including this term six Tas
+
+ align:start position:0%
+here um including this term six Tas
+ 
+
+ align:start position:0%
+here um including this term six Tas
+which is which is two more Tas than we
+
+ align:start position:0%
+which is which is two more Tas than we
+ 
+
+ align:start position:0%
+which is which is two more Tas than we
+normally get for this course so that
+
+ align:start position:0%
+normally get for this course so that
+ 
+
+ align:start position:0%
+normally get for this course so that
+means recitations will be particularly
+
+ align:start position:0%
+means recitations will be particularly
+ 
+
+ align:start position:0%
+means recitations will be particularly
+small uh there is a worldwide web uh
+
+ align:start position:0%
+small uh there is a worldwide web uh
+ 
+
+ align:start position:0%
+small uh there is a worldwide web uh
+page and uh you should bookmark that and
+
+ align:start position:0%
+page and uh you should bookmark that and
+ 
+
+ align:start position:0%
+page and uh you should bookmark that and
+go there regularly because that's where
+
+ align:start position:0%
+go there regularly because that's where
+ 
+
+ align:start position:0%
+go there regularly because that's where
+everything will be
+
+ align:start position:0%
+everything will be
+ 
+
+ align:start position:0%
+everything will be
+distributed uh email you should not be
+
+ align:start position:0%
+distributed uh email you should not be
+ 
+
+ align:start position:0%
+distributed uh email you should not be
+emailing directly to the uh even though
+
+ align:start position:0%
+emailing directly to the uh even though
+ 
+
+ align:start position:0%
+emailing directly to the uh even though
+we give you our email addresses directly
+
+ align:start position:0%
+we give you our email addresses directly
+ 
+
+ align:start position:0%
+we give you our email addresses directly
+to the staff in general to the
+
+ align:start position:0%
+to the staff in general to the
+ 
+
+ align:start position:0%
+to the staff in general to the
+individual members of the staff you
+
+ align:start position:0%
+individual members of the staff you
+ 
+
+ align:start position:0%
+individual members of the staff you
+should uh email us generally and the
+
+ align:start position:0%
+should uh email us generally and the
+ 
+
+ align:start position:0%
+should uh email us generally and the
+reason is you'll get much faster
+
+ align:start position:0%
+reason is you'll get much faster
+ 
+
+ align:start position:0%
+reason is you'll get much faster
+response and also uh for any
+
+ align:start position:0%
+response and also uh for any
+ 
+
+ align:start position:0%
+response and also uh for any
+Communications generally we like to
+
+ align:start position:0%
+Communications generally we like to
+ 
+
+ align:start position:0%
+Communications generally we like to
+monitor what the communications are so
+
+ align:start position:0%
+monitor what the communications are so
+ 
+
+ align:start position:0%
+monitor what the communications are so
+it's helpful to have emails coming to
+
+ align:start position:0%
+it's helpful to have emails coming to
+ 
+
+ align:start position:0%
+it's helpful to have emails coming to
+everybody on the course staff as I
+
+ align:start position:0%
+everybody on the course staff as I
+ 
+
+ align:start position:0%
+everybody on the course staff as I
+mentioned we'll be doing distance
+
+ align:start position:0%
+mentioned we'll be doing distance
+ 
+
+ align:start position:0%
+mentioned we'll be doing distance
+learning this term uh and so you can
+
+ align:start position:0%
+learning this term uh and so you can
+ 
+
+ align:start position:0%
+learning this term uh and so you can
+watch lectures uh online if you choose
+
+ align:start position:0%
+watch lectures uh online if you choose
+ 
+
+ align:start position:0%
+watch lectures uh online if you choose
+to do do that uh I would recommend for
+
+ align:start position:0%
+to do do that uh I would recommend for
+ 
+
+ align:start position:0%
+to do do that uh I would recommend for
+people of the opportunity to uh to watch
+
+ align:start position:0%
+people of the opportunity to uh to watch
+ 
+
+ align:start position:0%
+people of the opportunity to uh to watch
+uh to to come live it's better live you
+
+ align:start position:0%
+uh to to come live it's better live you
+ 
+
+ align:start position:0%
+uh to to come live it's better live you
+get to interact uh there's an intangible
+
+ align:start position:0%
+get to interact uh there's an intangible
+ 
+
+ align:start position:0%
+get to interact uh there's an intangible
+that comes with having it live in fact
+
+ align:start position:0%
+that comes with having it live in fact
+ 
+
+ align:start position:0%
+that comes with having it live in fact
+uh in addition to the videos uh I meet
+
+ align:start position:0%
+uh in addition to the videos uh I meet
+ 
+
+ align:start position:0%
+uh in addition to the videos uh I meet
+uh weekly with the Singapore students uh
+
+ align:start position:0%
+uh weekly with the Singapore students uh
+ 
+
+ align:start position:0%
+uh weekly with the Singapore students uh
+so that they have a live session as
+
+ align:start position:0%
+so that they have a live session as
+ 
+
+ align:start position:0%
+so that they have a live session as
+well uh prerequisites um the uh
+
+ align:start position:0%
+well uh prerequisites um the uh
+ 
+
+ align:start position:0%
+well uh prerequisites um the uh
+prerequisites for this course is uh are
+
+ align:start position:0%
+prerequisites for this course is uh are
+ 
+
+ align:start position:0%
+prerequisites for this course is uh are
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+6042 which is math for computer science
+
+ align:start position:0%
+6042 which is math for computer science
+ 
+
+ align:start position:0%
+6042 which is math for computer science
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+61 uh you basically need discrete
+
+ align:start position:0%
+61 uh you basically need discrete
+ 
+
+ align:start position:0%
+61 uh you basically need discrete
+mathematics and probability as well as
+
+ align:start position:0%
+mathematics and probability as well as
+ 
+
+ align:start position:0%
+mathematics and probability as well as
+programming experience to take this
+
+ align:start position:0%
+programming experience to take this
+ 
+
+ align:start position:0%
+programming experience to take this
+course successfully people who do not
+
+ align:start position:0%
+course successfully people who do not
+ 
+
+ align:start position:0%
+course successfully people who do not
+have that background should not be in
+
+ align:start position:0%
+have that background should not be in
+ 
+
+ align:start position:0%
+have that background should not be in
+the class we will be checking
+
+ align:start position:0%
+the class we will be checking
+ 
+
+ align:start position:0%
+the class we will be checking
+prerequisites if you have any questions
+
+ align:start position:0%
+prerequisites if you have any questions
+ 
+
+ align:start position:0%
+prerequisites if you have any questions
+please come to talk to us after
+
+ align:start position:0%
+please come to talk to us after
+ 
+
+ align:start position:0%
+please come to talk to us after
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+um let's see lectures are here okay for
+
+ align:start position:0%
+um let's see lectures are here okay for
+ 
+
+ align:start position:0%
+um let's see lectures are here okay for
+students they have the videotapes and
+
+ align:start position:0%
+students they have the videotapes and
+ 
+
+ align:start position:0%
+students they have the videotapes and
+they'll also be in um uh and they also
+
+ align:start position:0%
+they'll also be in um uh and they also
+ 
+
+ align:start position:0%
+they'll also be in um uh and they also
+will have a uh weekly meeting uh
+
+ align:start position:0%
+will have a uh weekly meeting uh
+ 
+
+ align:start position:0%
+will have a uh weekly meeting uh
+students must attend a 1-hour recitation
+
+ align:start position:0%
+students must attend a 1-hour recitation
+ 
+
+ align:start position:0%
+students must attend a 1-hour recitation
+session each week there will be new
+
+ align:start position:0%
+session each week there will be new
+ 
+
+ align:start position:0%
+session each week there will be new
+material presented in the recitation
+
+ align:start position:0%
+material presented in the recitation
+ 
+
+ align:start position:0%
+material presented in the recitation
+unlike the lectures they will not be
+
+ align:start position:0%
+unlike the lectures they will not be
+ 
+
+ align:start position:0%
+unlike the lectures they will not be
+online unlike the lectures there will
+
+ align:start position:0%
+online unlike the lectures there will
+ 
+
+ align:start position:0%
+online unlike the lectures there will
+not be lecture notes distributed for the
+
+ align:start position:0%
+not be lecture notes distributed for the
+ 
+
+ align:start position:0%
+not be lecture notes distributed for the
+recitations in general okay and yet
+
+ align:start position:0%
+recitations in general okay and yet
+ 
+
+ align:start position:0%
+recitations in general okay and yet
+there will be material there uh that is
+
+ align:start position:0%
+there will be material there uh that is
+ 
+
+ align:start position:0%
+there will be material there uh that is
+uh Direct ly uh on the exams and so
+
+ align:start position:0%
+uh Direct ly uh on the exams and so
+ 
+
+ align:start position:0%
+uh Direct ly uh on the exams and so
+every term we say oh when do when did
+
+ align:start position:0%
+every term we say oh when do when did
+ 
+
+ align:start position:0%
+every term we say oh when do when did
+you cover that that was in recitation
+
+ align:start position:0%
+you cover that that was in recitation
+ 
+
+ align:start position:0%
+you cover that that was in recitation
+you missed that one so recitations are
+
+ align:start position:0%
+you missed that one so recitations are
+ 
+
+ align:start position:0%
+you missed that one so recitations are
+mandatory um and in particular also let
+
+ align:start position:0%
+mandatory um and in particular also let
+ 
+
+ align:start position:0%
+mandatory um and in particular also let
+me just mention your recitation
+
+ align:start position:0%
+me just mention your recitation
+ 
+
+ align:start position:0%
+me just mention your recitation
+instructor is the one who assigns your
+
+ align:start position:0%
+instructor is the one who assigns your
+ 
+
+ align:start position:0%
+instructor is the one who assigns your
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+grade okay so we have a grades meeting
+
+ align:start position:0%
+grade okay so we have a grades meeting
+ 
+
+ align:start position:0%
+grade okay so we have a grades meeting
+and we keep everybody normal but your
+
+ align:start position:0%
+and we keep everybody normal but your
+ 
+
+ align:start position:0%
+and we keep everybody normal but your
+recitation has the final say on your
+
+ align:start position:0%
+recitation has the final say on your
+ 
+
+ align:start position:0%
+recitation has the final say on your
+grade
+
+ align:start position:0%
+grade
+ 
+
+ align:start position:0%
+grade
+um handouts handouts are available on
+
+ align:start position:0%
+um handouts handouts are available on
+ 
+
+ align:start position:0%
+um handouts handouts are available on
+the course web page we will not
+
+ align:start position:0%
+the course web page we will not
+ 
+
+ align:start position:0%
+the course web page we will not
+generally except for this one first
+
+ align:start position:0%
+generally except for this one first
+ 
+
+ align:start position:0%
+generally except for this one first
+handout we will not generly be bringing
+
+ align:start position:0%
+handout we will not generly be bringing
+ 
+
+ align:start position:0%
+handout we will not generly be bringing
+handouts to class textbook is the is
+
+ align:start position:0%
+handouts to class textbook is the is
+ 
+
+ align:start position:0%
+handouts to class textbook is the is
+this book introduction to
+
+ align:start position:0%
+this book introduction to
+ 
+
+ align:start position:0%
+this book introduction to
+algorithms okay uh MIT students can get
+
+ align:start position:0%
+algorithms okay uh MIT students can get
+ 
+
+ align:start position:0%
+algorithms okay uh MIT students can get
+it at any of the local bookstores
+
+ align:start position:0%
+it at any of the local bookstores
+ 
+
+ align:start position:0%
+it at any of the local bookstores
+including the MIT Coupe there's also a
+
+ align:start position:0%
+including the MIT Coupe there's also a
+ 
+
+ align:start position:0%
+including the MIT Coupe there's also a
+new online service that uh that provides
+
+ align:start position:0%
+new online service that uh that provides
+ 
+
+ align:start position:0%
+new online service that uh that provides
+uh uh uh textbooks you can also get a
+
+ align:start position:0%
+uh uh uh textbooks you can also get a
+ 
+
+ align:start position:0%
+uh uh uh textbooks you can also get a
+discount if you buy it at the
+
+ align:start position:0%
+discount if you buy it at the
+ 
+
+ align:start position:0%
+discount if you buy it at the
+MIT uh press bookstore uh there's a
+
+ align:start position:0%
+MIT uh press bookstore uh there's a
+ 
+
+ align:start position:0%
+MIT uh press bookstore uh there's a
+coupon in the uh MIT student telephone
+
+ align:start position:0%
+coupon in the uh MIT student telephone
+ 
+
+ align:start position:0%
+coupon in the uh MIT student telephone
+directory for discount on MIT press
+
+ align:start position:0%
+directory for discount on MIT press
+ 
+
+ align:start position:0%
+directory for discount on MIT press
+books and you can use that to purchase
+
+ align:start position:0%
+books and you can use that to purchase
+ 
+
+ align:start position:0%
+books and you can use that to purchase
+this book at a
+
+ align:start position:0%
+this book at a
+ 
+
+ align:start position:0%
+this book at a
+discount
+
+ align:start position:0%
+discount
+ 
+
+ align:start position:0%
+discount
+um uh yep course website uh this is the
+
+ align:start position:0%
+um uh yep course website uh this is the
+ 
+
+ align:start position:0%
+um uh yep course website uh this is the
+uh course website it links to the
+
+ align:start position:0%
+uh course website it links to the
+ 
+
+ align:start position:0%
+uh course website it links to the
+Stellar website which is where actually
+
+ align:start position:0%
+Stellar website which is where actually
+ 
+
+ align:start position:0%
+Stellar website which is where actually
+everything will be
+
+ align:start position:0%
+everything will be
+ 
+
+ align:start position:0%
+everything will be
+kept um and uh SMA students have their
+
+ align:start position:0%
+kept um and uh SMA students have their
+ 
+
+ align:start position:0%
+kept um and uh SMA students have their
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+website uh a lot some students find this
+
+ align:start position:0%
+website uh a lot some students find this
+ 
+
+ align:start position:0%
+website uh a lot some students find this
+course particularly
+
+ align:start position:0%
+course particularly
+ 
+
+ align:start position:0%
+course particularly
+challenging uh so each we will have
+
+ align:start position:0%
+challenging uh so each we will have
+ 
+
+ align:start position:0%
+challenging uh so each we will have
+extra help we will H uh post uh weekly
+
+ align:start position:0%
+extra help we will H uh post uh weekly
+ 
+
+ align:start position:0%
+extra help we will H uh post uh weekly
+office hours on the course website for
+
+ align:start position:0%
+office hours on the course website for
+ 
+
+ align:start position:0%
+office hours on the course website for
+the Tas and then as an experiment this
+
+ align:start position:0%
+the Tas and then as an experiment this
+ 
+
+ align:start position:0%
+the Tas and then as an experiment this
+term we're going to offer homework labs
+
+ align:start position:0%
+term we're going to offer homework labs
+ 
+
+ align:start position:0%
+term we're going to offer homework labs
+for this class so what a homework lab is
+
+ align:start position:0%
+for this class so what a homework lab is
+ 
+
+ align:start position:0%
+for this class so what a homework lab is
+is it's a place and a time you can go
+
+ align:start position:0%
+is it's a place and a time you can go
+ 
+
+ align:start position:0%
+is it's a place and a time you can go
+where other people in the course will go
+
+ align:start position:0%
+where other people in the course will go
+ 
+
+ align:start position:0%
+where other people in the course will go
+to do do homework and there will be uh
+
+ align:start position:0%
+to do do homework and there will be uh
+ 
+
+ align:start position:0%
+to do do homework and there will be uh
+uh typically two Tas who staff the lab
+
+ align:start position:0%
+uh typically two Tas who staff the lab
+ 
+
+ align:start position:0%
+uh typically two Tas who staff the lab
+and so as you're working on your
+
+ align:start position:0%
+and so as you're working on your
+ 
+
+ align:start position:0%
+and so as you're working on your
+homework you can get help from the Tas
+
+ align:start position:0%
+homework you can get help from the Tas
+ 
+
+ align:start position:0%
+homework you can get help from the Tas
+if you need it and it's a generally a
+
+ align:start position:0%
+if you need it and it's a generally a
+ 
+
+ align:start position:0%
+if you need it and it's a generally a
+place and we we're going to schedule
+
+ align:start position:0%
+place and we we're going to schedule
+ 
+
+ align:start position:0%
+place and we we're going to schedule
+those and they'll be on the um uh course
+
+ align:start position:0%
+those and they'll be on the um uh course
+ 
+
+ align:start position:0%
+those and they'll be on the um uh course
+calendar for where it is and when it is
+
+ align:start position:0%
+calendar for where it is and when it is
+ 
+
+ align:start position:0%
+calendar for where it is and when it is
+that the uh that they'll be held but
+
+ align:start position:0%
+that the uh that they'll be held but
+ 
+
+ align:start position:0%
+that the uh that they'll be held but
+usually Sundays 2: to 4:00 p.m. uh or
+
+ align:start position:0%
+usually Sundays 2: to 4:00 p.m. uh or
+ 
+
+ align:start position:0%
+usually Sundays 2: to 4:00 p.m. uh or
+else it'll be in uh some evening I think
+
+ align:start position:0%
+else it'll be in uh some evening I think
+ 
+
+ align:start position:0%
+else it'll be in uh some evening I think
+the first one is an evening right um uh
+
+ align:start position:0%
+the first one is an evening right um uh
+ 
+
+ align:start position:0%
+the first one is an evening right um uh
+near to when the homework is due your
+
+ align:start position:0%
+near to when the homework is due your
+ 
+
+ align:start position:0%
+near to when the homework is due your
+best bet is try to do the homework in
+
+ align:start position:0%
+best bet is try to do the homework in
+ 
+
+ align:start position:0%
+best bet is try to do the homework in
+advance of the homework lab but then if
+
+ align:start position:0%
+advance of the homework lab but then if
+ 
+
+ align:start position:0%
+advance of the homework lab but then if
+you want extra help if you want to talk
+
+ align:start position:0%
+you want extra help if you want to talk
+ 
+
+ align:start position:0%
+you want extra help if you want to talk
+over your Solutions with people because
+
+ align:start position:0%
+over your Solutions with people because
+ 
+
+ align:start position:0%
+over your Solutions with people because
+as we'll talk about problem sets you can
+
+ align:start position:0%
+as we'll talk about problem sets you can
+ 
+
+ align:start position:0%
+as we'll talk about problem sets you can
+solve and collaboration with other
+
+ align:start position:0%
+solve and collaboration with other
+ 
+
+ align:start position:0%
+solve and collaboration with other
+people in the class
+
+ align:start position:0%
+people in the class
+ 
+
+ align:start position:0%
+people in the class
+okay um in addition there are several uh
+
+ align:start position:0%
+okay um in addition there are several uh
+ 
+
+ align:start position:0%
+okay um in addition there are several uh
+peer Assistance
+
+ align:start position:0%
+peer Assistance
+ 
+
+ align:start position:0%
+peer Assistance
+programs uh and uh those usually get Al
+
+ align:start position:0%
+programs uh and uh those usually get Al
+ 
+
+ align:start position:0%
+programs uh and uh those usually get Al
+also the office of um minority education
+
+ align:start position:0%
+also the office of um minority education
+ 
+
+ align:start position:0%
+also the office of um minority education
+has a an assistance program and those
+
+ align:start position:0%
+has a an assistance program and those
+ 
+
+ align:start position:0%
+has a an assistance program and those
+usually get booked up pretty quickly so
+
+ align:start position:0%
+usually get booked up pretty quickly so
+ 
+
+ align:start position:0%
+usually get booked up pretty quickly so
+if you're interested in those good idea
+
+ align:start position:0%
+if you're interested in those good idea
+ 
+
+ align:start position:0%
+if you're interested in those good idea
+to make uh an appointment to get there
+
+ align:start position:0%
+to make uh an appointment to get there
+ 
+
+ align:start position:0%
+to make uh an appointment to get there
+and get
+
+ align:start position:0%
+and get
+ 
+
+ align:start position:0%
+and get
+um uh get help soon okay so the homework
+
+ align:start position:0%
+um uh get help soon okay so the homework
+ 
+
+ align:start position:0%
+um uh get help soon okay so the homework
+Labs I hope a lot of people will try
+
+ align:start position:0%
+Labs I hope a lot of people will try
+ 
+
+ align:start position:0%
+Labs I hope a lot of people will try
+that out we've never done this I don't
+
+ align:start position:0%
+that out we've never done this I don't
+ 
+
+ align:start position:0%
+that out we've never done this I don't
+know if any other course do other people
+
+ align:start position:0%
+know if any other course do other people
+ 
+
+ align:start position:0%
+know if any other course do other people
+have know of courses at MIT that have
+
+ align:start position:0%
+have know of courses at MIT that have
+ 
+
+ align:start position:0%
+have know of courses at MIT that have
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+this yeah 6011 did it last 6011 did it
+
+ align:start position:0%
+this yeah 6011 did it last 6011 did it
+ 
+
+ align:start position:0%
+this yeah 6011 did it last 6011 did it
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so um uh and was it successful in that
+
+ align:start position:0%
+so um uh and was it successful in that
+ 
+
+ align:start position:0%
+so um uh and was it successful in that
+class never went
+
+ align:start position:0%
+class never went
+ 
+
+ align:start position:0%
+class never went
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good so we'll see we'll see okay if it
+
+ align:start position:0%
+good so we'll see we'll see okay if it
+ 
+
+ align:start position:0%
+good so we'll see we'll see okay if it
+if it's not paying off then we'll just
+
+ align:start position:0%
+if it's not paying off then we'll just
+ 
+
+ align:start position:0%
+if it's not paying off then we'll just
+return to ordinary office hours for
+
+ align:start position:0%
+return to ordinary office hours for
+ 
+
+ align:start position:0%
+return to ordinary office hours for
+those Tas but um uh but I think that uh
+
+ align:start position:0%
+those Tas but um uh but I think that uh
+ 
+
+ align:start position:0%
+those Tas but um uh but I think that uh
+for some students I think that's a
+
+ align:start position:0%
+for some students I think that's a
+ 
+
+ align:start position:0%
+for some students I think that's a
+that's a good
+
+ align:start position:0%
+that's a good
+ 
+
+ align:start position:0%
+that's a good
+opportunity uh if you wish to be
+
+ align:start position:0%
+opportunity uh if you wish to be
+ 
+
+ align:start position:0%
+opportunity uh if you wish to be
+registered in this course you must sign
+
+ align:start position:0%
+registered in this course you must sign
+ 
+
+ align:start position:0%
+registered in this course you must sign
+up on the course web page so that's
+
+ align:start position:0%
+up on the course web page so that's
+ 
+
+ align:start position:0%
+up on the course web page so that's
+requirement one must be done
+
+ align:start position:0%
+requirement one must be done
+ 
+
+ align:start position:0%
+requirement one must be done
+today um uh we will uh uh you'll find it
+
+ align:start position:0%
+today um uh we will uh uh you'll find it
+ 
+
+ align:start position:0%
+today um uh we will uh uh you'll find it
+difficult to pass the course if you're
+
+ align:start position:0%
+difficult to pass the course if you're
+ 
+
+ align:start position:0%
+difficult to pass the course if you're
+not in the
+
+ align:start position:0%
+not in the
+ 
+
+ align:start position:0%
+not in the
+class okay uh and uh you should notify
+
+ align:start position:0%
+class okay uh and uh you should notify
+ 
+
+ align:start position:0%
+class okay uh and uh you should notify
+your ta if you decide to drop so that we
+
+ align:start position:0%
+your ta if you decide to drop so that we
+ 
+
+ align:start position:0%
+your ta if you decide to drop so that we
+can get you off and stop the mailings
+
+ align:start position:0%
+can get you off and stop the mailings
+ 
+
+ align:start position:0%
+can get you off and stop the mailings
+stop the spam okay um and uh you should
+
+ align:start position:0%
+stop the spam okay um and uh you should
+ 
+
+ align:start position:0%
+stop the spam okay um and uh you should
+register today before 700 p.m. and then
+
+ align:start position:0%
+register today before 700 p.m. and then
+ 
+
+ align:start position:0%
+register today before 700 p.m. and then
+we're going to email your recitation
+
+ align:start position:0%
+we're going to email your recitation
+ 
+
+ align:start position:0%
+we're going to email your recitation
+assignment to you before noon
+
+ align:start position:0%
+assignment to you before noon
+ 
+
+ align:start position:0%
+assignment to you before noon
+tomorrow okay and if you don't in
+
+ align:start position:0%
+tomorrow okay and if you don't in
+ 
+
+ align:start position:0%
+tomorrow okay and if you don't in
+receive this information by Thursday
+
+ align:start position:0%
+receive this information by Thursday
+ 
+
+ align:start position:0%
+receive this information by Thursday
+noon please send us
+
+ align:start position:0%
+noon please send us
+ 
+
+ align:start position:0%
+noon please send us
+email okay saying to the course staff
+
+ align:start position:0%
+email okay saying to the course staff
+ 
+
+ align:start position:0%
+email okay saying to the course staff
+generally not to me individually um
+
+ align:start position:0%
+generally not to me individually um
+ 
+
+ align:start position:0%
+generally not to me individually um
+saying that you didn't receive your
+
+ align:start position:0%
+saying that you didn't receive your
+ 
+
+ align:start position:0%
+saying that you didn't receive your
+recitation assignment and uh so if you
+
+ align:start position:0%
+recitation assignment and uh so if you
+ 
+
+ align:start position:0%
+recitation assignment and uh so if you
+haven't received it by Thursday noon you
+
+ align:start position:0%
+haven't received it by Thursday noon you
+ 
+
+ align:start position:0%
+haven't received it by Thursday noon you
+know you want to um I think that
+
+ align:start position:0%
+know you want to um I think that
+ 
+
+ align:start position:0%
+know you want to um I think that
+generally I think you're going to try to
+
+ align:start position:0%
+generally I think you're going to try to
+ 
+
+ align:start position:0%
+generally I think you're going to try to
+send them out tonight right or at least
+
+ align:start position:0%
+send them out tonight right or at least
+ 
+
+ align:start position:0%
+send them out tonight right or at least
+by tomorrow morning yep okay uh SMA
+
+ align:start position:0%
+by tomorrow morning yep okay uh SMA
+ 
+
+ align:start position:0%
+by tomorrow morning yep okay uh SMA
+students don't have to worry about
+
+ align:start position:0%
+students don't have to worry about
+ 
+
+ align:start position:0%
+students don't have to worry about
+this uh problem sets we have nine
+
+ align:start position:0%
+this uh problem sets we have nine
+ 
+
+ align:start position:0%
+this uh problem sets we have nine
+problem sets that we project will be
+
+ align:start position:0%
+problem sets that we project will be
+ 
+
+ align:start position:0%
+problem sets that we project will be
+assigned during the
+
+ align:start position:0%
+assigned during the
+ 
+
+ align:start position:0%
+assigned during the
+semester uh a couple things about
+
+ align:start position:0%
+semester uh a couple things about
+ 
+
+ align:start position:0%
+semester uh a couple things about
+problem sets homeworks won't generally
+
+ align:start position:0%
+problem sets homeworks won't generally
+ 
+
+ align:start position:0%
+problem sets homeworks won't generally
+be accepted uh if you are extenda St
+
+ align:start position:0%
+be accepted uh if you are extenda St
+ 
+
+ align:start position:0%
+be accepted uh if you are extenda St
+circumstances you should make prior
+
+ align:start position:0%
+circumstances you should make prior
+ 
+
+ align:start position:0%
+circumstances you should make prior
+arrangements with your recitation
+
+ align:start position:0%
+arrangements with your recitation
+ 
+
+ align:start position:0%
+arrangements with your recitation
+instructor in fact almost all the
+
+ align:start position:0%
+instructor in fact almost all the
+ 
+
+ align:start position:0%
+instructor in fact almost all the
+administrative stuff you shouldn't come
+
+ align:start position:0%
+administrative stuff you shouldn't come
+ 
+
+ align:start position:0%
+administrative stuff you shouldn't come
+to me to ask say can I hand in something
+
+ align:start position:0%
+to me to ask say can I hand in something
+ 
+
+ align:start position:0%
+to me to ask say can I hand in something
+let you should be talking to your
+
+ align:start position:0%
+let you should be talking to your
+ 
+
+ align:start position:0%
+let you should be talking to your
+recitation
+
+ align:start position:0%
+recitation
+ 
+
+ align:start position:0%
+recitation
+instructor okay um
+
+ align:start position:0%
+instructor okay um
+ 
+
+ align:start position:0%
+instructor okay um
+you can read the other things about the
+
+ align:start position:0%
+you can read the other things about the
+ 
+
+ align:start position:0%
+you can read the other things about the
+uh the form uh there are both uh but let
+
+ align:start position:0%
+uh the form uh there are both uh but let
+ 
+
+ align:start position:0%
+uh the form uh there are both uh but let
+me just mention that they're exercises
+
+ align:start position:0%
+me just mention that they're exercises
+ 
+
+ align:start position:0%
+me just mention that they're exercises
+that should be solved but not handed in
+
+ align:start position:0%
+that should be solved but not handed in
+ 
+
+ align:start position:0%
+that should be solved but not handed in
+as well uh to give you drill on the
+
+ align:start position:0%
+as well uh to give you drill on the
+ 
+
+ align:start position:0%
+as well uh to give you drill on the
+material I highly recommend you doing
+
+ align:start position:0%
+material I highly recommend you doing
+ 
+
+ align:start position:0%
+material I highly recommend you doing
+the exercises they both test your
+
+ align:start position:0%
+the exercises they both test your
+ 
+
+ align:start position:0%
+the exercises they both test your
+understanding of the material and
+
+ align:start position:0%
+understanding of the material and
+ 
+
+ align:start position:0%
+understanding of the material and
+exercises have this way of finding
+
+ align:start position:0%
+exercises have this way of finding
+ 
+
+ align:start position:0%
+exercises have this way of finding
+themselves on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quizzes um you're often asked to
+
+ align:start position:0%
+quizzes um you're often asked to
+ 
+
+ align:start position:0%
+quizzes um you're often asked to
+describe algorithms and here's a little
+
+ align:start position:0%
+describe algorithms and here's a little
+ 
+
+ align:start position:0%
+describe algorithms and here's a little
+outline of what you can use to describe
+
+ align:start position:0%
+outline of what you can use to describe
+ 
+
+ align:start position:0%
+outline of what you can use to describe
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+algorithm okay uh the grading policy is
+
+ align:start position:0%
+algorithm okay uh the grading policy is
+ 
+
+ align:start position:0%
+algorithm okay uh the grading policy is
+something that somehow I cover and
+
+ align:start position:0%
+something that somehow I cover and
+ 
+
+ align:start position:0%
+something that somehow I cover and
+always every term there's at least a
+
+ align:start position:0%
+always every term there's at least a
+ 
+
+ align:start position:0%
+always every term there's at least a
+couple of students who pretend like I
+
+ align:start position:0%
+couple of students who pretend like I
+ 
+
+ align:start position:0%
+couple of students who pretend like I
+never showed them this okay
+
+ align:start position:0%
+never showed them this okay
+ 
+
+ align:start position:0%
+never showed them this okay
+so uh if you skip problems it has a
+
+ align:start position:0%
+so uh if you skip problems it has a
+ 
+
+ align:start position:0%
+so uh if you skip problems it has a
+nonlinear effect on your
+
+ align:start position:0%
+nonlinear effect on your
+ 
+
+ align:start position:0%
+nonlinear effect on your
+grade okay nonlinear okay so if you
+
+ align:start position:0%
+grade okay nonlinear okay so if you
+ 
+
+ align:start position:0%
+grade okay nonlinear okay so if you
+don't skip any any problems no effect on
+
+ align:start position:0%
+don't skip any any problems no effect on
+ 
+
+ align:start position:0%
+don't skip any any problems no effect on
+your grade okay uh if you skip one
+
+ align:start position:0%
+your grade okay uh if you skip one
+ 
+
+ align:start position:0%
+your grade okay uh if you skip one
+problem eh 100th of a letter grade we
+
+ align:start position:0%
+problem eh 100th of a letter grade we
+ 
+
+ align:start position:0%
+problem eh 100th of a letter grade we
+can handle that okay but two problems
+
+ align:start position:0%
+can handle that okay but two problems
+ 
+
+ align:start position:0%
+can handle that okay but two problems
+it's a tenth and as you see by the time
+
+ align:start position:0%
+it's a tenth and as you see by the time
+ 
+
+ align:start position:0%
+it's a tenth and as you see by the time
+you've skipped uh like five letter
+
+ align:start position:0%
+you've skipped uh like five letter
+ 
+
+ align:start position:0%
+you've skipped uh like five letter
+grades it's already a third of five
+
+ align:start position:0%
+grades it's already a third of five
+ 
+
+ align:start position:0%
+grades it's already a third of five
+problems this is not problem sets by the
+
+ align:start position:0%
+problems this is not problem sets by the
+ 
+
+ align:start position:0%
+problems this is not problem sets by the
+way this is problems okay uh you're down
+
+ align:start position:0%
+way this is problems okay uh you're down
+ 
+
+ align:start position:0%
+way this is problems okay uh you're down
+a third of a letter
+
+ align:start position:0%
+a third of a letter
+ 
+
+ align:start position:0%
+a third of a letter
+grade okay and if you uh don't do nine
+
+ align:start position:0%
+grade okay and if you uh don't do nine
+ 
+
+ align:start position:0%
+grade okay and if you uh don't do nine
+or more so that's typically about uh
+
+ align:start position:0%
+or more so that's typically about uh
+ 
+
+ align:start position:0%
+or more so that's typically about uh
+three to four problem sets okay you
+
+ align:start position:0%
+three to four problem sets okay you
+ 
+
+ align:start position:0%
+three to four problem sets okay you
+don't pass the
+
+ align:start position:0%
+don't pass the
+ 
+
+ align:start position:0%
+don't pass the
+class okay so I always have some
+
+ align:start position:0%
+class okay so I always have some
+ 
+
+ align:start position:0%
+class okay so I always have some
+students coming at the end of the year
+
+ align:start position:0%
+students coming at the end of the year
+ 
+
+ align:start position:0%
+students coming at the end of the year
+saying I didn't do any of my problems
+
+ align:start position:0%
+saying I didn't do any of my problems
+ 
+
+ align:start position:0%
+saying I didn't do any of my problems
+can you just pass me because I did okay
+
+ align:start position:0%
+can you just pass me because I did okay
+ 
+
+ align:start position:0%
+can you just pass me because I did okay
+on the exams answer
+
+ align:start position:0%
+on the exams answer
+ 
+
+ align:start position:0%
+on the exams answer
+no okay very simple answer because we've
+
+ align:start position:0%
+no okay very simple answer because we've
+ 
+
+ align:start position:0%
+no okay very simple answer because we've
+set it up front Okay so the problem sets
+
+ align:start position:0%
+set it up front Okay so the problem sets
+ 
+
+ align:start position:0%
+set it up front Okay so the problem sets
+are an integral part of the uh the
+
+ align:start position:0%
+are an integral part of the uh the
+ 
+
+ align:start position:0%
+are an integral part of the uh the
+course collaboration policy this is
+
+ align:start position:0%
+course collaboration policy this is
+ 
+
+ align:start position:0%
+course collaboration policy this is
+extremely important so everybody pay
+
+ align:start position:0%
+extremely important so everybody pay
+ 
+
+ align:start position:0%
+extremely important so everybody pay
+attention if you're sleep now wake up
+
+ align:start position:0%
+attention if you're sleep now wake up
+ 
+
+ align:start position:0%
+attention if you're sleep now wake up
+okay um yeah like that's going to wake
+
+ align:start position:0%
+okay um yeah like that's going to wake
+ 
+
+ align:start position:0%
+okay um yeah like that's going to wake
+anybody up
+
+ align:start position:0%
+anybody up
+ 
+
+ align:start position:0%
+anybody up
+right okay um so the goal of homework uh
+
+ align:start position:0%
+right okay um so the goal of homework uh
+ 
+
+ align:start position:0%
+right okay um so the goal of homework uh
+professor demaines in My Philosophy is
+
+ align:start position:0%
+professor demaines in My Philosophy is
+ 
+
+ align:start position:0%
+professor demaines in My Philosophy is
+that the goal of homework is to help you
+
+ align:start position:0%
+that the goal of homework is to help you
+ 
+
+ align:start position:0%
+that the goal of homework is to help you
+learn the material and one way of
+
+ align:start position:0%
+learn the material and one way of
+ 
+
+ align:start position:0%
+learn the material and one way of
+helping to learn is not to just be stuck
+
+ align:start position:0%
+helping to learn is not to just be stuck
+ 
+
+ align:start position:0%
+helping to learn is not to just be stuck
+and unable to solve something because
+
+ align:start position:0%
+and unable to solve something because
+ 
+
+ align:start position:0%
+and unable to solve something because
+then you're in no better shape when the
+
+ align:start position:0%
+then you're in no better shape when the
+ 
+
+ align:start position:0%
+then you're in no better shape when the
+exam rolls around okay which is where
+
+ align:start position:0%
+exam rolls around okay which is where
+ 
+
+ align:start position:0%
+exam rolls around okay which is where
+we're actually evaluating you
+
+ align:start position:0%
+we're actually evaluating you
+ 
+
+ align:start position:0%
+we're actually evaluating you
+okay so you're encouraged to collaborate
+
+ align:start position:0%
+okay so you're encouraged to collaborate
+ 
+
+ align:start position:0%
+okay so you're encouraged to collaborate
+but there are uh there are some uh
+
+ align:start position:0%
+but there are uh there are some uh
+ 
+
+ align:start position:0%
+but there are uh there are some uh
+Common Sense things about collaboration
+
+ align:start position:0%
+Common Sense things about collaboration
+ 
+
+ align:start position:0%
+Common Sense things about collaboration
+if you go and you collaborate to the
+
+ align:start position:0%
+if you go and you collaborate to the
+ 
+
+ align:start position:0%
+if you go and you collaborate to the
+extent that all you're doing is getting
+
+ align:start position:0%
+extent that all you're doing is getting
+ 
+
+ align:start position:0%
+extent that all you're doing is getting
+the information from some somebody else
+
+ align:start position:0%
+the information from some somebody else
+ 
+
+ align:start position:0%
+the information from some somebody else
+you're not learning the material okay
+
+ align:start position:0%
+you're not learning the material okay
+ 
+
+ align:start position:0%
+you're not learning the material okay
+and you're not going to do well on the
+
+ align:start position:0%
+and you're not going to do well on the
+ 
+
+ align:start position:0%
+and you're not going to do well on the
+exams um so in our experience students
+
+ align:start position:0%
+exams um so in our experience students
+ 
+
+ align:start position:0%
+exams um so in our experience students
+who collaborate generally do better than
+
+ align:start position:0%
+who collaborate generally do better than
+ 
+
+ align:start position:0%
+who collaborate generally do better than
+students who work
+
+ align:start position:0%
+students who work
+ 
+
+ align:start position:0%
+students who work
+alone okay uh but you owe it to yourself
+
+ align:start position:0%
+alone okay uh but you owe it to yourself
+ 
+
+ align:start position:0%
+alone okay uh but you owe it to yourself
+if you're going to work in a study group
+
+ align:start position:0%
+if you're going to work in a study group
+ 
+
+ align:start position:0%
+if you're going to work in a study group
+uh to be prepared for your study group
+
+ align:start position:0%
+uh to be prepared for your study group
+ 
+
+ align:start position:0%
+uh to be prepared for your study group
+meeting and specifically you should
+
+ align:start position:0%
+meeting and specifically you should
+ 
+
+ align:start position:0%
+meeting and specifically you should
+spend a half an hour to 45 minutes uh on
+
+ align:start position:0%
+spend a half an hour to 45 minutes uh on
+ 
+
+ align:start position:0%
+spend a half an hour to 45 minutes uh on
+each problem before you go to your group
+
+ align:start position:0%
+each problem before you go to your group
+ 
+
+ align:start position:0%
+each problem before you go to your group
+so you're up to speed and you've tried
+
+ align:start position:0%
+so you're up to speed and you've tried
+ 
+
+ align:start position:0%
+so you're up to speed and you've tried
+out your
+
+ align:start position:0%
+out your
+ 
+
+ align:start position:0%
+out your
+ideas okay and you may have solutions to
+
+ align:start position:0%
+ideas okay and you may have solutions to
+ 
+
+ align:start position:0%
+ideas okay and you may have solutions to
+some you may be stuck on some other ones
+
+ align:start position:0%
+some you may be stuck on some other ones
+ 
+
+ align:start position:0%
+some you may be stuck on some other ones
+but at least you've applied yourself to
+
+ align:start position:0%
+but at least you've applied yourself to
+ 
+
+ align:start position:0%
+but at least you've applied yourself to
+it okay after 35 30 to 45 minutes if you
+
+ align:start position:0%
+it okay after 35 30 to 45 minutes if you
+ 
+
+ align:start position:0%
+it okay after 35 30 to 45 minutes if you
+can't get the problem just sitting there
+
+ align:start position:0%
+can't get the problem just sitting there
+ 
+
+ align:start position:0%
+can't get the problem just sitting there
+and banging your head against it makes
+
+ align:start position:0%
+and banging your head against it makes
+ 
+
+ align:start position:0%
+and banging your head against it makes
+no sense okay it's not a productive use
+
+ align:start position:0%
+no sense okay it's not a productive use
+ 
+
+ align:start position:0%
+no sense okay it's not a productive use
+of your time and I know most of you uh
+
+ align:start position:0%
+of your time and I know most of you uh
+ 
+
+ align:start position:0%
+of your time and I know most of you uh
+have uh issues with having time on your
+
+ align:start position:0%
+have uh issues with having time on your
+ 
+
+ align:start position:0%
+have uh issues with having time on your
+hands
+
+ align:start position:0%
+hands
+ 
+
+ align:start position:0%
+hands
+right okay like it's not there okay so
+
+ align:start position:0%
+right okay like it's not there okay so
+ 
+
+ align:start position:0%
+right okay like it's not there okay so
+don't go banging your head against
+
+ align:start position:0%
+don't go banging your head against
+ 
+
+ align:start position:0%
+don't go banging your head against
+problems that are that are too hard okay
+
+ align:start position:0%
+problems that are that are too hard okay
+ 
+
+ align:start position:0%
+problems that are that are too hard okay
+or where you don't understand what's
+
+ align:start position:0%
+or where you don't understand what's
+ 
+
+ align:start position:0%
+or where you don't understand what's
+going on or whatever so that's when the
+
+ align:start position:0%
+going on or whatever so that's when the
+ 
+
+ align:start position:0%
+going on or whatever so that's when the
+study group can can help out and as I
+
+ align:start position:0%
+study group can can help out and as I
+ 
+
+ align:start position:0%
+study group can can help out and as I
+mentioned we'll have homework Labs which
+
+ align:start position:0%
+mentioned we'll have homework Labs which
+ 
+
+ align:start position:0%
+mentioned we'll have homework Labs which
+will give you an opportunity to go and
+
+ align:start position:0%
+will give you an opportunity to go and
+ 
+
+ align:start position:0%
+will give you an opportunity to go and
+do that and coordinate with other other
+
+ align:start position:0%
+do that and coordinate with other other
+ 
+
+ align:start position:0%
+do that and coordinate with other other
+students rather than necessarily having
+
+ align:start position:0%
+students rather than necessarily having
+ 
+
+ align:start position:0%
+students rather than necessarily having
+to form your own group and the Tas will
+
+ align:start position:0%
+to form your own group and the Tas will
+ 
+
+ align:start position:0%
+to form your own group and the Tas will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+there um uh so if your group is unable
+
+ align:start position:0%
+there um uh so if your group is unable
+ 
+
+ align:start position:0%
+there um uh so if your group is unable
+to solve the problem then talk to other
+
+ align:start position:0%
+to solve the problem then talk to other
+ 
+
+ align:start position:0%
+to solve the problem then talk to other
+groups or ask your recitation instructor
+
+ align:start position:0%
+groups or ask your recitation instructor
+ 
+
+ align:start position:0%
+groups or ask your recitation instructor
+now that's how you go about solving them
+
+ align:start position:0%
+now that's how you go about solving them
+ 
+
+ align:start position:0%
+now that's how you go about solving them
+okay writing up the problem sets however
+
+ align:start position:0%
+okay writing up the problem sets however
+ 
+
+ align:start position:0%
+okay writing up the problem sets however
+is your individual responsibility and
+
+ align:start position:0%
+is your individual responsibility and
+ 
+
+ align:start position:0%
+is your individual responsibility and
+should be done alone you don't write up
+
+ align:start position:0%
+should be done alone you don't write up
+ 
+
+ align:start position:0%
+should be done alone you don't write up
+your problems solutions with other
+
+ align:start position:0%
+your problems solutions with other
+ 
+
+ align:start position:0%
+your problems solutions with other
+students you write them up on their own
+
+ align:start position:0%
+students you write them up on their own
+ 
+
+ align:start position:0%
+students you write them up on their own
+on your own okay and uh you should uh on
+
+ align:start position:0%
+on your own okay and uh you should uh on
+ 
+
+ align:start position:0%
+on your own okay and uh you should uh on
+your problem sets because this is an
+
+ align:start position:0%
+your problem sets because this is an
+ 
+
+ align:start position:0%
+your problem sets because this is an
+academic place we understand that the
+
+ align:start position:0%
+academic place we understand that the
+ 
+
+ align:start position:0%
+academic place we understand that the
+source of academic information is very
+
+ align:start position:0%
+source of academic information is very
+ 
+
+ align:start position:0%
+source of academic information is very
+important if you collaborated on
+
+ align:start position:0%
+important if you collaborated on
+ 
+
+ align:start position:0%
+important if you collaborated on
+Solutions you should write a list of the
+
+ align:start position:0%
+Solutions you should write a list of the
+ 
+
+ align:start position:0%
+Solutions you should write a list of the
+collaborators say I I work with so and
+
+ align:start position:0%
+collaborators say I I work with so and
+ 
+
+ align:start position:0%
+collaborators say I I work with so and
+so on the uh on this solution okay it
+
+ align:start position:0%
+so on the uh on this solution okay it
+ 
+
+ align:start position:0%
+so on the uh on this solution okay it
+does not affect your grade it's just a
+
+ align:start position:0%
+does not affect your grade it's just a
+ 
+
+ align:start position:0%
+does not affect your grade it's just a
+question of being
+
+ align:start position:0%
+question of being
+ 
+
+ align:start position:0%
+question of being
+scholarly
+
+ align:start position:0%
+scholarly
+ 
+
+ align:start position:0%
+scholarly
+okay um it is a a violation of this
+
+ align:start position:0%
+okay um it is a a violation of this
+ 
+
+ align:start position:0%
+okay um it is a a violation of this
+policy to submit a problem solution that
+
+ align:start position:0%
+policy to submit a problem solution that
+ 
+
+ align:start position:0%
+policy to submit a problem solution that
+you cannot orally explain to a member of
+
+ align:start position:0%
+you cannot orally explain to a member of
+ 
+
+ align:start position:0%
+you cannot orally explain to a member of
+the course
+
+ align:start position:0%
+the course
+ 
+
+ align:start position:0%
+the course
+staff so you say oh well my write up is
+
+ align:start position:0%
+staff so you say oh well my write up is
+ 
+
+ align:start position:0%
+staff so you say oh well my write up is
+similar to that other person's because
+
+ align:start position:0%
+similar to that other person's because
+ 
+
+ align:start position:0%
+similar to that other person's because
+you know we uh I didn't copy them you
+
+ align:start position:0%
+you know we uh I didn't copy them you
+ 
+
+ align:start position:0%
+you know we uh I didn't copy them you
+know we're we may ask you to orally
+
+ align:start position:0%
+know we're we may ask you to orally
+ 
+
+ align:start position:0%
+know we're we may ask you to orally
+explain your solution if you're unable
+
+ align:start position:0%
+explain your solution if you're unable
+ 
+
+ align:start position:0%
+explain your solution if you're unable
+the presumption is according to this
+
+ align:start position:0%
+the presumption is according to this
+ 
+
+ align:start position:0%
+the presumption is according to this
+policy presumption is that you
+
+ align:start position:0%
+policy presumption is that you
+ 
+
+ align:start position:0%
+policy presumption is that you
+cheated so do not write up stuff that
+
+ align:start position:0%
+cheated so do not write up stuff that
+ 
+
+ align:start position:0%
+cheated so do not write up stuff that
+you don't understand
+
+ align:start position:0%
+you don't understand
+ 
+
+ align:start position:0%
+you don't understand
+understand okay so you should be able to
+
+ align:start position:0%
+understand okay so you should be able to
+ 
+
+ align:start position:0%
+understand okay so you should be able to
+write up the stuff that you understand
+
+ align:start position:0%
+write up the stuff that you understand
+ 
+
+ align:start position:0%
+write up the stuff that you understand
+understand how you you know why you're
+
+ align:start position:0%
+understand how you you know why you're
+ 
+
+ align:start position:0%
+understand how you you know why you're
+putting down what you're putting
+
+ align:start position:0%
+putting down what you're putting
+ 
+
+ align:start position:0%
+putting down what you're putting
+down if it isn't obvious no
+
+ align:start position:0%
+down if it isn't obvious no
+ 
+
+ align:start position:0%
+down if it isn't obvious no
+collaboration whatsoever is permitted on
+
+ align:start position:0%
+collaboration whatsoever is permitted on
+ 
+
+ align:start position:0%
+collaboration whatsoever is permitted on
+exams exams is when we evaluate you okay
+
+ align:start position:0%
+exams exams is when we evaluate you okay
+ 
+
+ align:start position:0%
+exams exams is when we evaluate you okay
+and now we're not interested in
+
+ align:start position:0%
+and now we're not interested in
+ 
+
+ align:start position:0%
+and now we're not interested in
+evaluating other people interested in
+
+ align:start position:0%
+evaluating other people interested in
+ 
+
+ align:start position:0%
+evaluating other people interested in
+evaluating you okay so no collaboration
+
+ align:start position:0%
+evaluating you okay so no collaboration
+ 
+
+ align:start position:0%
+evaluating you okay so no collaboration
+on exams we will have a take-home exam
+
+ align:start position:0%
+on exams we will have a take-home exam
+ 
+
+ align:start position:0%
+on exams we will have a take-home exam
+for the second quiz
+
+ align:start position:0%
+for the second quiz
+ 
+
+ align:start position:0%
+for the second quiz
+so you should look at the schedule if
+
+ align:start position:0%
+so you should look at the schedule if
+ 
+
+ align:start position:0%
+so you should look at the schedule if
+there are problems with the schedule of
+
+ align:start position:0%
+there are problems with the schedule of
+ 
+
+ align:start position:0%
+there are problems with the schedule of
+that we want to know early okay um and
+
+ align:start position:0%
+that we want to know early okay um and
+ 
+
+ align:start position:0%
+that we want to know early okay um and
+we'll give you more details about the
+
+ align:start position:0%
+we'll give you more details about the
+ 
+
+ align:start position:0%
+we'll give you more details about the
+collaboration in the lecture on Monday
+
+ align:start position:0%
+collaboration in the lecture on Monday
+ 
+
+ align:start position:0%
+collaboration in the lecture on Monday
+November 28th now generally the lectures
+
+ align:start position:0%
+November 28th now generally the lectures
+ 
+
+ align:start position:0%
+November 28th now generally the lectures
+here okay are they're mandatory and that
+
+ align:start position:0%
+here okay are they're mandatory and that
+ 
+
+ align:start position:0%
+here okay are they're mandatory and that
+you have to know them but I know that
+
+ align:start position:0%
+you have to know them but I know that
+ 
+
+ align:start position:0%
+you have to know them but I know that
+some people say gee 9:30 is kind of
+
+ align:start position:0%
+some people say gee 9:30 is kind of
+ 
+
+ align:start position:0%
+some people say gee 9:30 is kind of
+early especially on a Monday you know or
+
+ align:start position:0%
+early especially on a Monday you know or
+ 
+
+ align:start position:0%
+early especially on a Monday you know or
+whatever okay it can be kind of early to
+
+ align:start position:0%
+whatever okay it can be kind of early to
+ 
+
+ align:start position:0%
+whatever okay it can be kind of early to
+get up okay um however on Monday
+
+ align:start position:0%
+get up okay um however on Monday
+ 
+
+ align:start position:0%
+get up okay um however on Monday
+November
+
+ align:start position:0%
+November
+ 
+
+ align:start position:0%
+November
+28th okay you fail the exam if you do
+
+ align:start position:0%
+28th okay you fail the exam if you do
+ 
+
+ align:start position:0%
+28th okay you fail the exam if you do
+not show up to lecture on
+
+ align:start position:0%
+not show up to lecture on
+ 
+
+ align:start position:0%
+not show up to lecture on
+time okay that one day you must show up
+
+ align:start position:0%
+time okay that one day you must show up
+ 
+
+ align:start position:0%
+time okay that one day you must show up
+any questions about that okay that one
+
+ align:start position:0%
+any questions about that okay that one
+ 
+
+ align:start position:0%
+any questions about that okay that one
+day you must show up here okay even if
+
+ align:start position:0%
+day you must show up here okay even if
+ 
+
+ align:start position:0%
+day you must show up here okay even if
+you've been watching them on the
+
+ align:start position:0%
+you've been watching them on the
+ 
+
+ align:start position:0%
+you've been watching them on the
+web
+
+ align:start position:0%
+web
+ 
+
+ align:start position:0%
+web
+okay um and um generally if you think
+
+ align:start position:0%
+okay um and um generally if you think
+ 
+
+ align:start position:0%
+okay um and um generally if you think
+you've
+
+ align:start position:0%
+you've
+ 
+
+ align:start position:0%
+you've
+transgressed best is to come to us to
+
+ align:start position:0%
+transgressed best is to come to us to
+ 
+
+ align:start position:0%
+transgressed best is to come to us to
+talk about it we can usually work
+
+ align:start position:0%
+talk about it we can usually work
+ 
+
+ align:start position:0%
+talk about it we can usually work
+something out it's when we find somebody
+
+ align:start position:0%
+something out it's when we find somebody
+ 
+
+ align:start position:0%
+something out it's when we find somebody
+is transgressed from a third party or
+
+ align:start position:0%
+is transgressed from a third party or
+ 
+
+ align:start position:0%
+is transgressed from a third party or
+from obvious analyses that we do of
+
+ align:start position:0%
+from obvious analyses that we do of
+ 
+
+ align:start position:0%
+from obvious analyses that we do of
+homeworks that's when um uh that's when
+
+ align:start position:0%
+homeworks that's when um uh that's when
+ 
+
+ align:start position:0%
+homeworks that's when um uh that's when
+things get messy okay so if you think
+
+ align:start position:0%
+things get messy okay so if you think
+ 
+
+ align:start position:0%
+things get messy okay so if you think
+you for some reason or other you think
+
+ align:start position:0%
+you for some reason or other you think
+ 
+
+ align:start position:0%
+you for some reason or other you think
+oh I may have done something wrong
+
+ align:start position:0%
+oh I may have done something wrong
+ 
+
+ align:start position:0%
+oh I may have done something wrong
+please come and talk to us okay we're
+
+ align:start position:0%
+please come and talk to us okay we're
+ 
+
+ align:start position:0%
+please come and talk to us okay we're
+actually we were students once too I'll
+
+ align:start position:0%
+actually we were students once too I'll
+ 
+
+ align:start position:0%
+actually we were students once too I'll
+be it many years
+
+ align:start position:0%
+be it many years
+ 
+
+ align:start position:0%
+be it many years
+ago okay any
+
+ align:start position:0%
+ago okay any
+ 
+
+ align:start position:0%
+ago okay any
+questions so this class has great
+
+ align:start position:0%
+questions so this class has great
+ 
+
+ align:start position:0%
+questions so this class has great
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+fabulous material okay and uh it's uh
+
+ align:start position:0%
+fabulous material okay and uh it's uh
+ 
+
+ align:start position:0%
+fabulous material okay and uh it's uh
+it's really um it's really fun uh but
+
+ align:start position:0%
+it's really um it's really fun uh but
+ 
+
+ align:start position:0%
+it's really um it's really fun uh but
+you do have to work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard okay so let's talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+content okay this is the topic of the
+
+ align:start position:0%
+content okay this is the topic of the
+ 
+
+ align:start position:0%
+content okay this is the topic of the
+first first part of the course the first
+
+ align:start position:0%
+first first part of the course the first
+ 
+
+ align:start position:0%
+first first part of the course the first
+part of the course is focused on
+
+ align:start position:0%
+part of the course is focused on
+ 
+
+ align:start position:0%
+part of the course is focused on
+analysis the second part of the course
+
+ align:start position:0%
+analysis the second part of the course
+ 
+
+ align:start position:0%
+analysis the second part of the course
+is focused on
+
+ align:start position:0%
+is focused on
+ 
+
+ align:start position:0%
+is focused on
+design okay before you can do design you
+
+ align:start position:0%
+design okay before you can do design you
+ 
+
+ align:start position:0%
+design okay before you can do design you
+have to master a bunch of uh techniques
+
+ align:start position:0%
+have to master a bunch of uh techniques
+ 
+
+ align:start position:0%
+have to master a bunch of uh techniques
+for analyzing algorithms okay and then
+
+ align:start position:0%
+for analyzing algorithms okay and then
+ 
+
+ align:start position:0%
+for analyzing algorithms okay and then
+you'll be in a position to design
+
+ align:start position:0%
+you'll be in a position to design
+ 
+
+ align:start position:0%
+you'll be in a position to design
+algorithms that you can analyze and that
+
+ align:start position:0%
+algorithms that you can analyze and that
+ 
+
+ align:start position:0%
+algorithms that you can analyze and that
+which are efficient so analysis of
+
+ align:start position:0%
+which are efficient so analysis of
+ 
+
+ align:start position:0%
+which are efficient so analysis of
+algorithm is the theoretical study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of computer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+performance and resource
+
+ align:start position:0%
+performance and resource
+ 
+
+ align:start position:0%
+performance and resource
+usage and in particular focuses on
+
+ align:start position:0%
+usage and in particular focuses on
+ 
+
+ align:start position:0%
+usage and in particular focuses on
+performance okay we're studying how to
+
+ align:start position:0%
+performance okay we're studying how to
+ 
+
+ align:start position:0%
+performance okay we're studying how to
+make things fast okay particular
+
+ align:start position:0%
+make things fast okay particular
+ 
+
+ align:start position:0%
+make things fast okay particular
+computer programs we also will discover
+
+ align:start position:0%
+computer programs we also will discover
+ 
+
+ align:start position:0%
+computer programs we also will discover
+o talk about other resources such as
+
+ align:start position:0%
+o talk about other resources such as
+ 
+
+ align:start position:0%
+o talk about other resources such as
+communication such as memory whether RAM
+
+ align:start position:0%
+communication such as memory whether RAM
+ 
+
+ align:start position:0%
+communication such as memory whether RAM
+memory or disk
+
+ align:start position:0%
+memory or disk
+ 
+
+ align:start position:0%
+memory or disk
+memory okay so there are other resources
+
+ align:start position:0%
+memory okay so there are other resources
+ 
+
+ align:start position:0%
+memory okay so there are other resources
+that we may care about okay but
+
+ align:start position:0%
+that we may care about okay but
+ 
+
+ align:start position:0%
+that we may care about okay but
+predominantly we focus on performance
+
+ align:start position:0%
+predominantly we focus on performance
+ 
+
+ align:start position:0%
+predominantly we focus on performance
+okay so because this is a course about
+
+ align:start position:0%
+okay so because this is a course about
+ 
+
+ align:start position:0%
+okay so because this is a course about
+performance I like to put things in
+
+ align:start position:0%
+performance I like to put things in
+ 
+
+ align:start position:0%
+performance I like to put things in
+perspective a little bit by starting out
+
+ align:start position:0%
+perspective a little bit by starting out
+ 
+
+ align:start position:0%
+perspective a little bit by starting out
+and asking
+
+ align:start position:0%
+and asking
+ 
+
+ align:start position:0%
+and asking
+in programming what's
+
+ align:start position:0%
+in programming what's
+ 
+
+ align:start position:0%
+in programming what's
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important than
+
+ align:start position:0%
+important than
+ 
+
+ align:start position:0%
+important than
+performance if you're in an engineering
+
+ align:start position:0%
+performance if you're in an engineering
+ 
+
+ align:start position:0%
+performance if you're in an engineering
+situation and writing code okay writing
+
+ align:start position:0%
+situation and writing code okay writing
+ 
+
+ align:start position:0%
+situation and writing code okay writing
+software what's more important than
+
+ align:start position:0%
+software what's more important than
+ 
+
+ align:start position:0%
+software what's more important than
+performance correctness good okay what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else Simplicity Simplicity can be
+
+ align:start position:0%
+else Simplicity Simplicity can be
+ 
+
+ align:start position:0%
+else Simplicity Simplicity can be
+very good
+
+ align:start position:0%
+very good
+ 
+
+ align:start position:0%
+very good
+yep yeah maintainability maintainability
+
+ align:start position:0%
+yep yeah maintainability maintainability
+ 
+
+ align:start position:0%
+yep yeah maintainability maintainability
+okay often much more important than
+
+ align:start position:0%
+okay often much more important than
+ 
+
+ align:start position:0%
+okay often much more important than
+performance cost cost okay and what type
+
+ align:start position:0%
+performance cost cost okay and what type
+ 
+
+ align:start position:0%
+performance cost cost okay and what type
+of cost are you thinking M no but I mean
+
+ align:start position:0%
+of cost are you thinking M no but I mean
+ 
+
+ align:start position:0%
+of cost are you thinking M no but I mean
+cost of what like Hardware comput I
+
+ align:start position:0%
+cost of what like Hardware comput I
+ 
+
+ align:start position:0%
+cost of what like Hardware comput I
+guess computation we're talking software
+
+ align:start position:0%
+guess computation we're talking software
+ 
+
+ align:start position:0%
+guess computation we're talking software
+here right okay so so what type of cost
+
+ align:start position:0%
+here right okay so so what type of cost
+ 
+
+ align:start position:0%
+here right okay so so what type of cost
+do you have in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mind okay yeah so so then you're sort of
+
+ align:start position:0%
+mind okay yeah so so then you're sort of
+ 
+
+ align:start position:0%
+mind okay yeah so so then you're sort of
+okay there are some costs that are
+
+ align:start position:0%
+okay there are some costs that are
+ 
+
+ align:start position:0%
+okay there are some costs that are
+involved when programming
+
+ align:start position:0%
+involved when programming
+ 
+
+ align:start position:0%
+involved when programming
+like programmer time okay so programmer
+
+ align:start position:0%
+like programmer time okay so programmer
+ 
+
+ align:start position:0%
+like programmer time okay so programmer
+time is another thing also that might be
+
+ align:start position:0%
+time is another thing also that might be
+ 
+
+ align:start position:0%
+time is another thing also that might be
+stability stability okay robustness of
+
+ align:start position:0%
+stability stability okay robustness of
+ 
+
+ align:start position:0%
+stability stability okay robustness of
+the software okay does it break all the
+
+ align:start position:0%
+the software okay does it break all the
+ 
+
+ align:start position:0%
+the software okay does it break all the
+time what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else come on we got a bunch of Engineers
+
+ align:start position:0%
+else come on we got a bunch of Engineers
+ 
+
+ align:start position:0%
+else come on we got a bunch of Engineers
+here a lot of things
+
+ align:start position:0%
+here a lot of things
+ 
+
+ align:start position:0%
+here a lot of things
+how about features features can be more
+
+ align:start position:0%
+how about features features can be more
+ 
+
+ align:start position:0%
+how about features features can be more
+important having a a wider collection of
+
+ align:start position:0%
+important having a a wider collection of
+ 
+
+ align:start position:0%
+important having a a wider collection of
+features than your competitors
+
+ align:start position:0%
+features than your competitors
+ 
+
+ align:start position:0%
+features than your competitors
+functionality
+
+ align:start position:0%
+functionality
+ 
+
+ align:start position:0%
+functionality
+modularity okay is it designed in a way
+
+ align:start position:0%
+modularity okay is it designed in a way
+ 
+
+ align:start position:0%
+modularity okay is it designed in a way
+where you can make changes in a local
+
+ align:start position:0%
+where you can make changes in a local
+ 
+
+ align:start position:0%
+where you can make changes in a local
+part of the code and it doesn't you
+
+ align:start position:0%
+part of the code and it doesn't you
+ 
+
+ align:start position:0%
+part of the code and it doesn't you
+don't have to make changes across the
+
+ align:start position:0%
+don't have to make changes across the
+ 
+
+ align:start position:0%
+don't have to make changes across the
+code in order to affect a a simple
+
+ align:start position:0%
+code in order to affect a a simple
+ 
+
+ align:start position:0%
+code in order to affect a a simple
+change in the
+
+ align:start position:0%
+change in the
+ 
+
+ align:start position:0%
+change in the
+functionality
+
+ align:start position:0%
+functionality
+ 
+
+ align:start position:0%
+functionality
+okay okay there's one big one which is
+
+ align:start position:0%
+okay okay there's one big one which is
+ 
+
+ align:start position:0%
+okay okay there's one big one which is
+definitely especially in the 9s was like
+
+ align:start position:0%
+definitely especially in the 9s was like
+ 
+
+ align:start position:0%
+definitely especially in the 9s was like
+the big thing
+
+ align:start position:0%
+the big thing
+ 
+
+ align:start position:0%
+the big thing
+computers the big
+
+ align:start position:0%
+computers the big
+ 
+
+ align:start position:0%
+computers the big
+thing well security actually good I
+
+ align:start position:0%
+thing well security actually good I
+ 
+
+ align:start position:0%
+thing well security actually good I
+don't even have that down security is
+
+ align:start position:0%
+don't even have that down security is
+ 
+
+ align:start position:0%
+don't even have that down security is
+excellent okay that's actually been more
+
+ align:start position:0%
+excellent okay that's actually been more
+ 
+
+ align:start position:0%
+excellent okay that's actually been more
+in the 2000 okay security has been been
+
+ align:start position:0%
+in the 2000 okay security has been been
+ 
+
+ align:start position:0%
+in the 2000 okay security has been been
+far more important often than uh
+
+ align:start position:0%
+far more important often than uh
+ 
+
+ align:start position:0%
+far more important often than uh
+performance scalability scalability has
+
+ align:start position:0%
+performance scalability scalability has
+ 
+
+ align:start position:0%
+performance scalability scalability has
+been important although scalability in
+
+ align:start position:0%
+been important although scalability in
+ 
+
+ align:start position:0%
+been important although scalability in
+some sense is uh is performance related
+
+ align:start position:0%
+some sense is uh is performance related
+ 
+
+ align:start position:0%
+some sense is uh is performance related
+but yes scalability is good so what was
+
+ align:start position:0%
+but yes scalability is good so what was
+ 
+
+ align:start position:0%
+but yes scalability is good so what was
+the big breakthrough in the I why do
+
+ align:start position:0%
+the big breakthrough in the I why do
+ 
+
+ align:start position:0%
+the big breakthrough in the I why do
+people use macintoshes rather than uh
+
+ align:start position:0%
+people use macintoshes rather than uh
+ 
+
+ align:start position:0%
+people use macintoshes rather than uh
+than Windows those people who are of
+
+ align:start position:0%
+than Windows those people who are of
+ 
+
+ align:start position:0%
+than Windows those people who are of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+religion user user
+
+ align:start position:0%
+religion user user
+ 
+
+ align:start position:0%
+religion user user
+friendliness wow if you look at the
+
+ align:start position:0%
+friendliness wow if you look at the
+ 
+
+ align:start position:0%
+friendliness wow if you look at the
+number of cycles of computers that went
+
+ align:start position:0%
+number of cycles of computers that went
+ 
+
+ align:start position:0%
+number of cycles of computers that went
+into user friendliness in the '90s it
+
+ align:start position:0%
+into user friendliness in the '90s it
+ 
+
+ align:start position:0%
+into user friendliness in the '90s it
+grew from almost nothing to where it's
+
+ align:start position:0%
+grew from almost nothing to where it's
+ 
+
+ align:start position:0%
+grew from almost nothing to where it's
+now the vast part of the uh computation
+
+ align:start position:0%
+now the vast part of the uh computation
+ 
+
+ align:start position:0%
+now the vast part of the uh computation
+goes into user friendly so all those
+
+ align:start position:0%
+goes into user friendly so all those
+ 
+
+ align:start position:0%
+goes into user friendly so all those
+things are more important than
+
+ align:start position:0%
+things are more important than
+ 
+
+ align:start position:0%
+things are more important than
+performance so this is a course on
+
+ align:start position:0%
+performance so this is a course on
+ 
+
+ align:start position:0%
+performance so this is a course on
+performance okay so then you can say
+
+ align:start position:0%
+performance okay so then you can say
+ 
+
+ align:start position:0%
+performance okay so then you can say
+okay well so why do we bother then why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+algorithms and
+
+ align:start position:0%
+algorithms and
+ 
+
+ align:start position:0%
+algorithms and
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+performance okay if it's at the bottom
+
+ align:start position:0%
+performance okay if it's at the bottom
+ 
+
+ align:start position:0%
+performance okay if it's at the bottom
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+Heap almost always people would rather
+
+ align:start position:0%
+Heap almost always people would rather
+ 
+
+ align:start position:0%
+Heap almost always people would rather
+have these other
+
+ align:start position:0%
+have these other
+ 
+
+ align:start position:0%
+have these other
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+than than performance you go off and you
+
+ align:start position:0%
+than than performance you go off and you
+ 
+
+ align:start position:0%
+than than performance you go off and you
+say to to somebody would I rather have
+
+ align:start position:0%
+say to to somebody would I rather have
+ 
+
+ align:start position:0%
+say to to somebody would I rather have
+performance or more user more user
+
+ align:start position:0%
+performance or more user more user
+ 
+
+ align:start position:0%
+performance or more user more user
+friendliness it's almost always you know
+
+ align:start position:0%
+friendliness it's almost always you know
+ 
+
+ align:start position:0%
+friendliness it's almost always you know
+more important than performance why do
+
+ align:start position:0%
+more important than performance why do
+ 
+
+ align:start position:0%
+more important than performance why do
+we care
+
+ align:start position:0%
+we care
+ 
+
+ align:start position:0%
+we care
+then yeah you have to come back after
+
+ align:start position:0%
+then yeah you have to come back after
+ 
+
+ align:start position:0%
+then yeah you have to come back after
+two hours to get the right answer that
+
+ align:start position:0%
+two hours to get the right answer that
+ 
+
+ align:start position:0%
+two hours to get the right answer that
+wasn't user friendly that wasn't user
+
+ align:start position:0%
+wasn't user friendly that wasn't user
+ 
+
+ align:start position:0%
+wasn't user friendly that wasn't user
+friendly so sometimes performance is
+
+ align:start position:0%
+friendly so sometimes performance is
+ 
+
+ align:start position:0%
+friendly so sometimes performance is
+correlated with user friendliness
+
+ align:start position:0%
+correlated with user friendliness
+ 
+
+ align:start position:0%
+correlated with user friendliness
+absolutely okay you know nothing is more
+
+ align:start position:0%
+absolutely okay you know nothing is more
+ 
+
+ align:start position:0%
+absolutely okay you know nothing is more
+frustrating than sitting there waiting
+
+ align:start position:0%
+frustrating than sitting there waiting
+ 
+
+ align:start position:0%
+frustrating than sitting there waiting
+right okay so that's that's a good
+
+ align:start position:0%
+right okay so that's that's a good
+ 
+
+ align:start position:0%
+right okay so that's that's a good
+reason what are some other reasons why
+
+ align:start position:0%
+reason what are some other reasons why
+ 
+
+ align:start position:0%
+reason what are some other reasons why
+we some applications uh real time
+
+ align:start position:0%
+we some applications uh real time
+ 
+
+ align:start position:0%
+we some applications uh real time
+constraints sometimes they have realtime
+
+ align:start position:0%
+constraints sometimes they have realtime
+ 
+
+ align:start position:0%
+constraints sometimes they have realtime
+constraints so they don't actually work
+
+ align:start position:0%
+constraints so they don't actually work
+ 
+
+ align:start position:0%
+constraints so they don't actually work
+unless they perform adequately
+
+ align:start position:0%
+unless they perform adequately
+ 
+
+ align:start position:0%
+unless they perform adequately
+yep it's really hard to get exponential
+
+ align:start position:0%
+yep it's really hard to get exponential
+ 
+
+ align:start position:0%
+yep it's really hard to get exponential
+improvements in user
+
+ align:start position:0%
+improvements in user
+ 
+
+ align:start position:0%
+improvements in user
+friendliness um hard to get well we
+
+ align:start position:0%
+friendliness um hard to get well we
+ 
+
+ align:start position:0%
+friendliness um hard to get well we
+don't measure user we don't usually
+
+ align:start position:0%
+don't measure user we don't usually
+ 
+
+ align:start position:0%
+don't measure user we don't usually
+quantify user friendliness so I'm not
+
+ align:start position:0%
+quantify user friendliness so I'm not
+ 
+
+ align:start position:0%
+quantify user friendliness so I'm not
+sure that's a but I understand what
+
+ align:start position:0%
+sure that's a but I understand what
+ 
+
+ align:start position:0%
+sure that's a but I understand what
+you're saying yeah so we don't get he
+
+ align:start position:0%
+you're saying yeah so we don't get he
+ 
+
+ align:start position:0%
+you're saying yeah so we don't get he
+says get don't get
+
+ align:start position:0%
+says get don't get
+ 
+
+ align:start position:0%
+says get don't get
+exponential uh uh performance
+
+ align:start position:0%
+exponential uh uh performance
+ 
+
+ align:start position:0%
+exponential uh uh performance
+improvements in user friendliness we
+
+ align:start position:0%
+improvements in user friendliness we
+ 
+
+ align:start position:0%
+improvements in user friendliness we
+often don't get that in performance
+
+ align:start position:0%
+often don't get that in performance
+ 
+
+ align:start position:0%
+often don't get that in performance
+either by the way okay sometimes we do
+
+ align:start position:0%
+either by the way okay sometimes we do
+ 
+
+ align:start position:0%
+either by the way okay sometimes we do
+but okay but that's good
+
+ align:start position:0%
+but okay but that's good
+ 
+
+ align:start position:0%
+but okay but that's good
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so there's several reasons that um
+
+ align:start position:0%
+so so there's several reasons that um
+ 
+
+ align:start position:0%
+so so there's several reasons that um
+that I think are important one is that
+
+ align:start position:0%
+that I think are important one is that
+ 
+
+ align:start position:0%
+that I think are important one is that
+often performance measures the line
+
+ align:start position:0%
+often performance measures the line
+ 
+
+ align:start position:0%
+often performance measures the line
+between the feasible and the infeasible
+
+ align:start position:0%
+between the feasible and the infeasible
+ 
+
+ align:start position:0%
+between the feasible and the infeasible
+okay so we heard some of these things
+
+ align:start position:0%
+okay so we heard some of these things
+ 
+
+ align:start position:0%
+okay so we heard some of these things
+for example in real time when there are
+
+ align:start position:0%
+for example in real time when there are
+ 
+
+ align:start position:0%
+for example in real time when there are
+real time requirements if it's not fast
+
+ align:start position:0%
+real time requirements if it's not fast
+ 
+
+ align:start position:0%
+real time requirements if it's not fast
+enough it's simply not
+
+ align:start position:0%
+enough it's simply not
+ 
+
+ align:start position:0%
+enough it's simply not
+functional okay or if it uses too much
+
+ align:start position:0%
+functional okay or if it uses too much
+ 
+
+ align:start position:0%
+functional okay or if it uses too much
+memory it's simply not going to work for
+
+ align:start position:0%
+memory it's simply not going to work for
+ 
+
+ align:start position:0%
+memory it's simply not going to work for
+you okay and as a consequence what you
+
+ align:start position:0%
+you okay and as a consequence what you
+ 
+
+ align:start position:0%
+you okay and as a consequence what you
+find is algorithms are on The Cutting
+
+ align:start position:0%
+find is algorithms are on The Cutting
+ 
+
+ align:start position:0%
+find is algorithms are on The Cutting
+Edge of
+
+ align:start position:0%
+Edge of
+ 
+
+ align:start position:0%
+Edge of
+Entrepreneurship if you're talking about
+
+ align:start position:0%
+Entrepreneurship if you're talking about
+ 
+
+ align:start position:0%
+Entrepreneurship if you're talking about
+just reimplementing stuff that people
+
+ align:start position:0%
+just reimplementing stuff that people
+ 
+
+ align:start position:0%
+just reimplementing stuff that people
+did 10 years ago performance isn't that
+
+ align:start position:0%
+did 10 years ago performance isn't that
+ 
+
+ align:start position:0%
+did 10 years ago performance isn't that
+important at some level but if you're
+
+ align:start position:0%
+important at some level but if you're
+ 
+
+ align:start position:0%
+important at some level but if you're
+talking about doing stuff that nobody's
+
+ align:start position:0%
+talking about doing stuff that nobody's
+ 
+
+ align:start position:0%
+talking about doing stuff that nobody's
+done before one of the reasons often
+
+ align:start position:0%
+done before one of the reasons often
+ 
+
+ align:start position:0%
+done before one of the reasons often
+that they haven't done it is because
+
+ align:start position:0%
+that they haven't done it is because
+ 
+
+ align:start position:0%
+that they haven't done it is because
+it's too time consuming it's too uh you
+
+ align:start position:0%
+it's too time consuming it's too uh you
+ 
+
+ align:start position:0%
+it's too time consuming it's too uh you
+know things don't scale and so forth so
+
+ align:start position:0%
+know things don't scale and so forth so
+ 
+
+ align:start position:0%
+know things don't scale and so forth so
+that's one reason okay is the feasible
+
+ align:start position:0%
+that's one reason okay is the feasible
+ 
+
+ align:start position:0%
+that's one reason okay is the feasible
+versus infeasible another thing is that
+
+ align:start position:0%
+versus infeasible another thing is that
+ 
+
+ align:start position:0%
+versus infeasible another thing is that
+uh algorithms give you an a language for
+
+ align:start position:0%
+uh algorithms give you an a language for
+ 
+
+ align:start position:0%
+uh algorithms give you an a language for
+talking about program
+
+ align:start position:0%
+talking about program
+ 
+
+ align:start position:0%
+talking about program
+Behavior okay and that turns out to be
+
+ align:start position:0%
+Behavior okay and that turns out to be
+ 
+
+ align:start position:0%
+Behavior okay and that turns out to be
+is a language that has uh been pervasive
+
+ align:start position:0%
+is a language that has uh been pervasive
+ 
+
+ align:start position:0%
+is a language that has uh been pervasive
+through computer science is that the
+
+ align:start position:0%
+through computer science is that the
+ 
+
+ align:start position:0%
+through computer science is that the
+theoretical language is what gets
+
+ align:start position:0%
+theoretical language is what gets
+ 
+
+ align:start position:0%
+theoretical language is what gets
+adopted by all the practitioners because
+
+ align:start position:0%
+adopted by all the practitioners because
+ 
+
+ align:start position:0%
+adopted by all the practitioners because
+it's clean way of thinking about things
+
+ align:start position:0%
+it's clean way of thinking about things
+ 
+
+ align:start position:0%
+it's clean way of thinking about things
+I think a a good way I think about
+
+ align:start position:0%
+I think a a good way I think about
+ 
+
+ align:start position:0%
+I think a a good way I think about
+performance and the reason it's on the
+
+ align:start position:0%
+performance and the reason it's on the
+ 
+
+ align:start position:0%
+performance and the reason it's on the
+bottom of the Heap is sort of like
+
+ align:start position:0%
+bottom of the Heap is sort of like
+ 
+
+ align:start position:0%
+bottom of the Heap is sort of like
+um performance is like money it's like
+
+ align:start position:0%
+um performance is like money it's like
+ 
+
+ align:start position:0%
+um performance is like money it's like
+currency okay so you say what good does
+
+ align:start position:0%
+currency okay so you say what good does
+ 
+
+ align:start position:0%
+currency okay so you say what good does
+a stack of $100 bills do for you okay
+
+ align:start position:0%
+a stack of $100 bills do for you okay
+ 
+
+ align:start position:0%
+a stack of $100 bills do for you okay
+wouldn't you rather have food or water
+
+ align:start position:0%
+wouldn't you rather have food or water
+ 
+
+ align:start position:0%
+wouldn't you rather have food or water
+or shelter or whatever and you're
+
+ align:start position:0%
+or shelter or whatever and you're
+ 
+
+ align:start position:0%
+or shelter or whatever and you're
+willing to pay those
+
+ align:start position:0%
+willing to pay those
+ 
+
+ align:start position:0%
+willing to pay those
+$100 bills for if you have $100 bills
+
+ align:start position:0%
+$100 bills for if you have $100 bills
+ 
+
+ align:start position:0%
+$100 bills for if you have $100 bills
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh for uh for that
+
+ align:start position:0%
+uh for uh for that
+ 
+
+ align:start position:0%
+uh for uh for that
+commodity okay even though water is far
+
+ align:start position:0%
+commodity okay even though water is far
+ 
+
+ align:start position:0%
+commodity okay even though water is far
+more important to your living okay well
+
+ align:start position:0%
+more important to your living okay well
+ 
+
+ align:start position:0%
+more important to your living okay well
+similarly performance is what you use to
+
+ align:start position:0%
+similarly performance is what you use to
+ 
+
+ align:start position:0%
+similarly performance is what you use to
+pay for user friendliness it's what you
+
+ align:start position:0%
+pay for user friendliness it's what you
+ 
+
+ align:start position:0%
+pay for user friendliness it's what you
+pay for security and you hear people say
+
+ align:start position:0%
+pay for security and you hear people say
+ 
+
+ align:start position:0%
+pay for security and you hear people say
+for example that um you know I want
+
+ align:start position:0%
+for example that um you know I want
+ 
+
+ align:start position:0%
+for example that um you know I want
+greater functionality so people will
+
+ align:start position:0%
+greater functionality so people will
+ 
+
+ align:start position:0%
+greater functionality so people will
+program in Java even though it's much
+
+ align:start position:0%
+program in Java even though it's much
+ 
+
+ align:start position:0%
+program in Java even though it's much
+slower than C because it has and they'll
+
+ align:start position:0%
+slower than C because it has and they'll
+ 
+
+ align:start position:0%
+slower than C because it has and they'll
+say it cost me maybe a factor of three
+
+ align:start position:0%
+say it cost me maybe a factor of three
+ 
+
+ align:start position:0%
+say it cost me maybe a factor of three
+or something in performance to program
+
+ align:start position:0%
+or something in performance to program
+ 
+
+ align:start position:0%
+or something in performance to program
+in Java but it's but Java is worth it
+
+ align:start position:0%
+in Java but it's but Java is worth it
+ 
+
+ align:start position:0%
+in Java but it's but Java is worth it
+because it's got all these
+
+ align:start position:0%
+because it's got all these
+ 
+
+ align:start position:0%
+because it's got all these
+objectoriented features and so forth
+
+ align:start position:0%
+objectoriented features and so forth
+ 
+
+ align:start position:0%
+objectoriented features and so forth
+exception mechanisms and so on and so
+
+ align:start position:0%
+exception mechanisms and so on and so
+ 
+
+ align:start position:0%
+exception mechanisms and so on and so
+people are willing to pay a factor of
+
+ align:start position:0%
+people are willing to pay a factor of
+ 
+
+ align:start position:0%
+people are willing to pay a factor of
+three in performance so that's why you
+
+ align:start position:0%
+three in performance so that's why you
+ 
+
+ align:start position:0%
+three in performance so that's why you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+performance okay because you can use it
+
+ align:start position:0%
+performance okay because you can use it
+ 
+
+ align:start position:0%
+performance okay because you can use it
+to pay for these other things that you
+
+ align:start position:0%
+to pay for these other things that you
+ 
+
+ align:start position:0%
+to pay for these other things that you
+want okay and that's why in some sense
+
+ align:start position:0%
+want okay and that's why in some sense
+ 
+
+ align:start position:0%
+want okay and that's why in some sense
+it's on the bottom of the Heap okay
+
+ align:start position:0%
+it's on the bottom of the Heap okay
+ 
+
+ align:start position:0%
+it's on the bottom of the Heap okay
+because it's the universal that
+
+ align:start position:0%
+because it's the universal that
+ 
+
+ align:start position:0%
+because it's the universal that
+everybody is that that you Quantified do
+
+ align:start position:0%
+everybody is that that you Quantified do
+ 
+
+ align:start position:0%
+everybody is that that you Quantified do
+you want to spend a factor of two on
+
+ align:start position:0%
+you want to spend a factor of two on
+ 
+
+ align:start position:0%
+you want to spend a factor of two on
+this or spend a factor of three on
+
+ align:start position:0%
+this or spend a factor of three on
+ 
+
+ align:start position:0%
+this or spend a factor of three on
+security Etc okay and in addition the
+
+ align:start position:0%
+security Etc okay and in addition the
+ 
+
+ align:start position:0%
+security Etc okay and in addition the
+lessons generalized to other resource
+
+ align:start position:0%
+lessons generalized to other resource
+ 
+
+ align:start position:0%
+lessons generalized to other resource
+measures like communication like memory
+
+ align:start position:0%
+measures like communication like memory
+ 
+
+ align:start position:0%
+measures like communication like memory
+and so forth and the last reason we
+
+ align:start position:0%
+and so forth and the last reason we
+ 
+
+ align:start position:0%
+and so forth and the last reason we
+study algorithms performance is it's
+
+ align:start position:0%
+study algorithms performance is it's
+ 
+
+ align:start position:0%
+study algorithms performance is it's
+tons of fun okay you know speed is
+
+ align:start position:0%
+tons of fun okay you know speed is
+ 
+
+ align:start position:0%
+tons of fun okay you know speed is
+always fun right like why do people you
+
+ align:start position:0%
+always fun right like why do people you
+ 
+
+ align:start position:0%
+always fun right like why do people you
+know drive fast cars race race horses
+
+ align:start position:0%
+know drive fast cars race race horses
+ 
+
+ align:start position:0%
+know drive fast cars race race horses
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+you know whatever okay you know Rockets
+
+ align:start position:0%
+you know whatever okay you know Rockets
+ 
+
+ align:start position:0%
+you know whatever okay you know Rockets
+Etc why do we do that because speed is
+
+ align:start position:0%
+Etc why do we do that because speed is
+ 
+
+ align:start position:0%
+Etc why do we do that because speed is
+fun okay ski who likes to ski I love to
+
+ align:start position:0%
+fun okay ski who likes to ski I love to
+ 
+
+ align:start position:0%
+fun okay ski who likes to ski I love to
+ski okay I like going fast on those skis
+
+ align:start position:0%
+ski okay I like going fast on those skis
+ 
+
+ align:start position:0%
+ski okay I like going fast on those skis
+okay it's fun okay hockey fast sports
+
+ align:start position:0%
+okay it's fun okay hockey fast sports
+ 
+
+ align:start position:0%
+okay it's fun okay hockey fast sports
+right okay we all like the fast Sports
+
+ align:start position:0%
+right okay we all like the fast Sports
+ 
+
+ align:start position:0%
+right okay we all like the fast Sports
+okay not all of us I mean some people
+
+ align:start position:0%
+okay not all of us I mean some people
+ 
+
+ align:start position:0%
+okay not all of us I mean some people
+say ah he's not talking to
+
+ align:start position:0%
+say ah he's not talking to
+ 
+
+ align:start position:0%
+say ah he's not talking to
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+okay so let's move on so that's sort of
+
+ align:start position:0%
+okay so let's move on so that's sort of
+ 
+
+ align:start position:0%
+okay so let's move on so that's sort of
+a little bit of a a notion as to why we
+
+ align:start position:0%
+a little bit of a a notion as to why we
+ 
+
+ align:start position:0%
+a little bit of a a notion as to why we
+study this is that it does in some sense
+
+ align:start position:0%
+study this is that it does in some sense
+ 
+
+ align:start position:0%
+study this is that it does in some sense
+form common basis for all these other
+
+ align:start position:0%
+form common basis for all these other
+ 
+
+ align:start position:0%
+form common basis for all these other
+things we care about and so we want to
+
+ align:start position:0%
+things we care about and so we want to
+ 
+
+ align:start position:0%
+things we care about and so we want to
+understand how can we generate money for
+
+ align:start position:0%
+understand how can we generate money for
+ 
+
+ align:start position:0%
+understand how can we generate money for
+ourselves in
+
+ align:start position:0%
+ourselves in
+ 
+
+ align:start position:0%
+ourselves in
+computation okay so we're going to start
+
+ align:start position:0%
+computation okay so we're going to start
+ 
+
+ align:start position:0%
+computation okay so we're going to start
+out with a very simple
+
+ align:start position:0%
+out with a very simple
+ 
+
+ align:start position:0%
+out with a very simple
+problem it's one of the oldest problems
+
+ align:start position:0%
+problem it's one of the oldest problems
+ 
+
+ align:start position:0%
+problem it's one of the oldest problems
+that has been studied in
+
+ align:start position:0%
+that has been studied in
+ 
+
+ align:start position:0%
+that has been studied in
+algorithms as the problem of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorting okay and we're going to actually
+
+ align:start position:0%
+sorting okay and we're going to actually
+ 
+
+ align:start position:0%
+sorting okay and we're going to actually
+study this for several lectures okay so
+
+ align:start position:0%
+study this for several lectures okay so
+ 
+
+ align:start position:0%
+study this for several lectures okay so
+we're we're going to uh because sorting
+
+ align:start position:0%
+we're we're going to uh because sorting
+ 
+
+ align:start position:0%
+we're we're going to uh because sorting
+contains many algorithmic
+
+ align:start position:0%
+contains many algorithmic
+ 
+
+ align:start position:0%
+contains many algorithmic
+techniques so the Sorting problem is the
+
+ align:start position:0%
+techniques so the Sorting problem is the
+ 
+
+ align:start position:0%
+techniques so the Sorting problem is the
+following we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence A1
+
+ align:start position:0%
+sequence A1
+ 
+
+ align:start position:0%
+sequence A1
+A2 up to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input and our output
+
+ align:start position:0%
+input and our output
+ 
+
+ align:start position:0%
+input and our output
+is a permutation of those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers okay a permutation is a
+
+ align:start position:0%
+numbers okay a permutation is a
+ 
+
+ align:start position:0%
+numbers okay a permutation is a
+rearrangement of the numbers okay every
+
+ align:start position:0%
+rearrangement of the numbers okay every
+ 
+
+ align:start position:0%
+rearrangement of the numbers okay every
+number appears exactly once in the
+
+ align:start position:0%
+number appears exactly once in the
+ 
+
+ align:start position:0%
+number appears exactly once in the
+rearrangement such that so I sometimes
+
+ align:start position:0%
+rearrangement such that so I sometimes
+ 
+
+ align:start position:0%
+rearrangement such that so I sometimes
+use a dollar sign to mean such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay such that
+
+ align:start position:0%
+that okay such that
+ 
+
+ align:start position:0%
+that okay such that
+A1 is less than or equal to A2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime such that they're monotonically
+
+ align:start position:0%
+Prime such that they're monotonically
+ 
+
+ align:start position:0%
+Prime such that they're monotonically
+increasing in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size okay so take a bunch of numbers put
+
+ align:start position:0%
+size okay so take a bunch of numbers put
+ 
+
+ align:start position:0%
+size okay so take a bunch of numbers put
+them in
+
+ align:start position:0%
+them in
+ 
+
+ align:start position:0%
+them in
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+okay so here's an algorithm to do it
+
+ align:start position:0%
+okay so here's an algorithm to do it
+ 
+
+ align:start position:0%
+okay so here's an algorithm to do it
+it's called insertion sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to write this algorithm
+
+ align:start position:0%
+and I'm going to write this algorithm
+ 
+
+ align:start position:0%
+and I'm going to write this algorithm
+in uh what we call pseudo code so it's
+
+ align:start position:0%
+in uh what we call pseudo code so it's
+ 
+
+ align:start position:0%
+in uh what we call pseudo code so it's
+sort of a programming language except
+
+ align:start position:0%
+sort of a programming language except
+ 
+
+ align:start position:0%
+sort of a programming language except
+it's got English in there often okay and
+
+ align:start position:0%
+it's got English in there often okay and
+ 
+
+ align:start position:0%
+it's got English in there often okay and
+it's just a shorthand for writing uh be
+
+ align:start position:0%
+it's just a shorthand for writing uh be
+ 
+
+ align:start position:0%
+it's just a shorthand for writing uh be
+for being precise okay so this
+
+ align:start position:0%
+for being precise okay so this
+ 
+
+ align:start position:0%
+for being precise okay so this
+sorts a from one to
+
+ align:start position:0%
+sorts a from one to
+ 
+
+ align:start position:0%
+sorts a from one to
+n and here's the code for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what we call pseudo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code
+
+ align:start position:0%
+code
+ 
+
+ align:start position:0%
+code
+okay and uh if you don't understand the
+
+ align:start position:0%
+okay and uh if you don't understand the
+ 
+
+ align:start position:0%
+okay and uh if you don't understand the
+pseudo code then um you should ask
+
+ align:start position:0%
+pseudo code then um you should ask
+ 
+
+ align:start position:0%
+pseudo code then um you should ask
+questions about any of the notations
+
+ align:start position:0%
+questions about any of the notations
+ 
+
+ align:start position:0%
+questions about any of the notations
+you'll start to get used to it as we go
+
+ align:start position:0%
+you'll start to get used to it as we go
+ 
+
+ align:start position:0%
+you'll start to get used to it as we go
+on one thing is that in the pseudo code
+
+ align:start position:0%
+on one thing is that in the pseudo code
+ 
+
+ align:start position:0%
+on one thing is that in the pseudo code
+we use indentation where in most
+
+ align:start position:0%
+we use indentation where in most
+ 
+
+ align:start position:0%
+we use indentation where in most
+languages they have some kind of begin
+
+ align:start position:0%
+languages they have some kind of begin
+ 
+
+ align:start position:0%
+languages they have some kind of begin
+end delimiters like Curly braces or
+
+ align:start position:0%
+end delimiters like Curly braces or
+ 
+
+ align:start position:0%
+end delimiters like Curly braces or
+something in Java or c for example okay
+
+ align:start position:0%
+something in Java or c for example okay
+ 
+
+ align:start position:0%
+something in Java or c for example okay
+we just use indentation the whole idea
+
+ align:start position:0%
+we just use indentation the whole idea
+ 
+
+ align:start position:0%
+we just use indentation the whole idea
+of the pseudo code is to try to get the
+
+ align:start position:0%
+of the pseudo code is to try to get the
+ 
+
+ align:start position:0%
+of the pseudo code is to try to get the
+algorithms as short as possible while
+
+ align:start position:0%
+algorithms as short as possible while
+ 
+
+ align:start position:0%
+algorithms as short as possible while
+still understanding what the individual
+
+ align:start position:0%
+still understanding what the individual
+ 
+
+ align:start position:0%
+still understanding what the individual
+steps are okay um in practice there
+
+ align:start position:0%
+steps are okay um in practice there
+ 
+
+ align:start position:0%
+steps are okay um in practice there
+actually have been languages that use
+
+ align:start position:0%
+actually have been languages that use
+ 
+
+ align:start position:0%
+actually have been languages that use
+indentation as a means of showing uh the
+
+ align:start position:0%
+indentation as a means of showing uh the
+ 
+
+ align:start position:0%
+indentation as a means of showing uh the
+nesting of things it's generally a bad
+
+ align:start position:0%
+nesting of things it's generally a bad
+ 
+
+ align:start position:0%
+nesting of things it's generally a bad
+idea because when you page from one if
+
+ align:start position:0%
+idea because when you page from one if
+ 
+
+ align:start position:0%
+idea because when you page from one if
+things go over one page to another for
+
+ align:start position:0%
+things go over one page to another for
+ 
+
+ align:start position:0%
+things go over one page to another for
+example okay you can't tell what level
+
+ align:start position:0%
+example okay you can't tell what level
+ 
+
+ align:start position:0%
+example okay you can't tell what level
+of nesting it is whereas with uh with
+
+ align:start position:0%
+of nesting it is whereas with uh with
+ 
+
+ align:start position:0%
+of nesting it is whereas with uh with
+explicit braces it's much easier to tell
+
+ align:start position:0%
+explicit braces it's much easier to tell
+ 
+
+ align:start position:0%
+explicit braces it's much easier to tell
+so there there reasons why this is a bad
+
+ align:start position:0%
+so there there reasons why this is a bad
+ 
+
+ align:start position:0%
+so there there reasons why this is a bad
+notation okay if you were writing uh if
+
+ align:start position:0%
+notation okay if you were writing uh if
+ 
+
+ align:start position:0%
+notation okay if you were writing uh if
+you were doing software engineering but
+
+ align:start position:0%
+you were doing software engineering but
+ 
+
+ align:start position:0%
+you were doing software engineering but
+it's a good one for us because it just
+
+ align:start position:0%
+it's a good one for us because it just
+ 
+
+ align:start position:0%
+it's a good one for us because it just
+keeps things short makes fewer uh fewer
+
+ align:start position:0%
+keeps things short makes fewer uh fewer
+ 
+
+ align:start position:0%
+keeps things short makes fewer uh fewer
+things to write down so um this is
+
+ align:start position:0%
+things to write down so um this is
+ 
+
+ align:start position:0%
+things to write down so um this is
+insertion sord let's try to figure out a
+
+ align:start position:0%
+insertion sord let's try to figure out a
+ 
+
+ align:start position:0%
+insertion sord let's try to figure out a
+little bit what this does okay so
+
+ align:start position:0%
+little bit what this does okay so
+ 
+
+ align:start position:0%
+little bit what this does okay so
+um so it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it basically takes an array
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um at any point the thing to understand
+
+ align:start position:0%
+um at any point the thing to understand
+ 
+
+ align:start position:0%
+um at any point the thing to understand
+is so we're going to we're setting
+
+ align:start position:0%
+is so we're going to we're setting
+ 
+
+ align:start position:0%
+is so we're going to we're setting
+basically we're running the outer loop
+
+ align:start position:0%
+basically we're running the outer loop
+ 
+
+ align:start position:0%
+basically we're running the outer loop
+from J is 2 to n and the inner loop that
+
+ align:start position:0%
+from J is 2 to n and the inner loop that
+ 
+
+ align:start position:0%
+from J is 2 to n and the inner loop that
+starts at um uh at J minus one and then
+
+ align:start position:0%
+starts at um uh at J minus one and then
+ 
+
+ align:start position:0%
+starts at um uh at J minus one and then
+goes down until it's uh until it's uh
+
+ align:start position:0%
+goes down until it's uh until it's uh
+ 
+
+ align:start position:0%
+goes down until it's uh until it's uh
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay so basically so if we look at any
+
+ align:start position:0%
+okay so basically so if we look at any
+ 
+
+ align:start position:0%
+okay so basically so if we look at any
+point in the algorithm we essentially
+
+ align:start position:0%
+point in the algorithm we essentially
+ 
+
+ align:start position:0%
+point in the algorithm we essentially
+are looking at some element here
+
+ align:start position:0%
+are looking at some element here
+ 
+
+ align:start position:0%
+are looking at some element here
+J A of J the jth
+
+ align:start position:0%
+J A of J the jth
+ 
+
+ align:start position:0%
+J A of J the jth
+element okay and what we do is
+
+ align:start position:0%
+element okay and what we do is
+ 
+
+ align:start position:0%
+element okay and what we do is
+essentially is we pull a value out here
+
+ align:start position:0%
+essentially is we pull a value out here
+ 
+
+ align:start position:0%
+essentially is we pull a value out here
+that we call the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+okay and at this point the important
+
+ align:start position:0%
+okay and at this point the important
+ 
+
+ align:start position:0%
+okay and at this point the important
+thing to understand is and we'll talk
+
+ align:start position:0%
+thing to understand is and we'll talk
+ 
+
+ align:start position:0%
+thing to understand is and we'll talk
+more about this in recitation on Friday
+
+ align:start position:0%
+more about this in recitation on Friday
+ 
+
+ align:start position:0%
+more about this in recitation on Friday
+is that there is an invariant that's
+
+ align:start position:0%
+is that there is an invariant that's
+ 
+
+ align:start position:0%
+is that there is an invariant that's
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+maintained by this Loop each time
+
+ align:start position:0%
+maintained by this Loop each time
+ 
+
+ align:start position:0%
+maintained by this Loop each time
+through the invariant is that this part
+
+ align:start position:0%
+through the invariant is that this part
+ 
+
+ align:start position:0%
+through the invariant is that this part
+of the array is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorted and the goal each time through
+
+ align:start position:0%
+sorted and the goal each time through
+ 
+
+ align:start position:0%
+sorted and the goal each time through
+the loop is to increase is to increase
+
+ align:start position:0%
+the loop is to increase is to increase
+ 
+
+ align:start position:0%
+the loop is to increase is to increase
+is to add one to the length of the
+
+ align:start position:0%
+is to add one to the length of the
+ 
+
+ align:start position:0%
+is to add one to the length of the
+things that are
+
+ align:start position:0%
+things that are
+ 
+
+ align:start position:0%
+things that are
+sorted and the way we do that is we pull
+
+ align:start position:0%
+sorted and the way we do that is we pull
+ 
+
+ align:start position:0%
+sorted and the way we do that is we pull
+out the key and then we just copy values
+
+ align:start position:0%
+out the key and then we just copy values
+ 
+
+ align:start position:0%
+out the key and then we just copy values
+up like this
+
+ align:start position:0%
+up like this
+ 
+
+ align:start position:0%
+up like this
+we keep copying up okay until we find
+
+ align:start position:0%
+we keep copying up okay until we find
+ 
+
+ align:start position:0%
+we keep copying up okay until we find
+the place where this key goes and then
+
+ align:start position:0%
+the place where this key goes and then
+ 
+
+ align:start position:0%
+the place where this key goes and then
+we insert it in that place and that's
+
+ align:start position:0%
+we insert it in that place and that's
+ 
+
+ align:start position:0%
+we insert it in that place and that's
+why it's called insertion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort okay so we just sort of move the
+
+ align:start position:0%
+sort okay so we just sort of move the
+ 
+
+ align:start position:0%
+sort okay so we just sort of move the
+things copy the things up until we find
+
+ align:start position:0%
+things copy the things up until we find
+ 
+
+ align:start position:0%
+things copy the things up until we find
+where it goes and then we put it into
+
+ align:start position:0%
+where it goes and then we put it into
+ 
+
+ align:start position:0%
+where it goes and then we put it into
+place and then we now we have that from
+
+ align:start position:0%
+place and then we now we have that from
+ 
+
+ align:start position:0%
+place and then we now we have that from
+a from one to J is sorted and now we can
+
+ align:start position:0%
+a from one to J is sorted and now we can
+ 
+
+ align:start position:0%
+a from one to J is sorted and now we can
+work on J +
+
+ align:start position:0%
+work on J +
+ 
+
+ align:start position:0%
+work on J +
+one okay so let's give an example of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that imagine we're doing
+
+ align:start position:0%
+that imagine we're doing
+ 
+
+ align:start position:0%
+that imagine we're doing
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+936 so we start out with 2 JAL 2 and we
+
+ align:start position:0%
+936 so we start out with 2 JAL 2 and we
+ 
+
+ align:start position:0%
+936 so we start out with 2 JAL 2 and we
+figure out that we want to insert it
+
+ align:start position:0%
+figure out that we want to insert it
+ 
+
+ align:start position:0%
+figure out that we want to insert it
+there so now we have 28 4 9 3
+
+ align:start position:0%
+there so now we have 28 4 9 3
+ 
+
+ align:start position:0%
+there so now we have 28 4 9 3
+6 okay then we look at the
+
+ align:start position:0%
+6 okay then we look at the
+ 
+
+ align:start position:0%
+6 okay then we look at the
+four and we say oh well that goes over
+
+ align:start position:0%
+four and we say oh well that goes over
+ 
+
+ align:start position:0%
+four and we say oh well that goes over
+here so we get 2
+
+ align:start position:0%
+here so we get 2
+ 
+
+ align:start position:0%
+here so we get 2
+48 93
+
+ align:start position:0%
+48 93
+ 
+
+ align:start position:0%
+48 93
+6 okay after the second iteration of the
+
+ align:start position:0%
+6 okay after the second iteration of the
+ 
+
+ align:start position:0%
+6 okay after the second iteration of the
+outer
+
+ align:start position:0%
+outer
+ 
+
+ align:start position:0%
+outer
+loop then we look at
+
+ align:start position:0%
+loop then we look at
+ 
+
+ align:start position:0%
+loop then we look at
+nine and we discover immediately it just
+
+ align:start position:0%
+nine and we discover immediately it just
+ 
+
+ align:start position:0%
+nine and we discover immediately it just
+goes right there very little work to do
+
+ align:start position:0%
+goes right there very little work to do
+ 
+
+ align:start position:0%
+goes right there very little work to do
+on that step okay so we have exactly the
+
+ align:start position:0%
+on that step okay so we have exactly the
+ 
+
+ align:start position:0%
+on that step okay so we have exactly the
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+output after that iteration then we look
+
+ align:start position:0%
+output after that iteration then we look
+ 
+
+ align:start position:0%
+output after that iteration then we look
+at the three that's going to be inserted
+
+ align:start position:0%
+at the three that's going to be inserted
+ 
+
+ align:start position:0%
+at the three that's going to be inserted
+over there 2 3 4 8 9 six and finally we
+
+ align:start position:0%
+over there 2 3 4 8 9 six and finally we
+ 
+
+ align:start position:0%
+over there 2 3 4 8 9 six and finally we
+look at the six that goes in there 2 3 4
+
+ align:start position:0%
+look at the six that goes in there 2 3 4
+ 
+
+ align:start position:0%
+look at the six that goes in there 2 3 4
+6 8 9 and at that point we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um The Rance here starts at one yes yes
+
+ align:start position:0%
+um The Rance here starts at one yes yes
+ 
+
+ align:start position:0%
+um The Rance here starts at one yes yes
+okay a one to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so this is the insertion sort
+
+ align:start position:0%
+okay okay so this is the insertion sort
+ 
+
+ align:start position:0%
+okay okay so this is the insertion sort
+algorithm and it's the first Al
+
+ align:start position:0%
+algorithm and it's the first Al
+ 
+
+ align:start position:0%
+algorithm and it's the first Al
+algorithm that we're going to analyze
+
+ align:start position:0%
+algorithm that we're going to analyze
+ 
+
+ align:start position:0%
+algorithm that we're going to analyze
+okay we're going to pick out pull out
+
+ align:start position:0%
+okay we're going to pick out pull out
+ 
+
+ align:start position:0%
+okay we're going to pick out pull out
+some tools that we have from our math
+
+ align:start position:0%
+some tools that we have from our math
+ 
+
+ align:start position:0%
+some tools that we have from our math
+background to to help to analyze it so
+
+ align:start position:0%
+background to to help to analyze it so
+ 
+
+ align:start position:0%
+background to to help to analyze it so
+first of all let's to take a look at the
+
+ align:start position:0%
+first of all let's to take a look at the
+ 
+
+ align:start position:0%
+first of all let's to take a look at the
+issue of running
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so the running time depends of this
+
+ align:start position:0%
+okay so the running time depends of this
+ 
+
+ align:start position:0%
+okay so the running time depends of this
+algorithm depends on a lot of
+
+ align:start position:0%
+algorithm depends on a lot of
+ 
+
+ align:start position:0%
+algorithm depends on a lot of
+things okay so one thing it depends on
+
+ align:start position:0%
+things okay so one thing it depends on
+ 
+
+ align:start position:0%
+things okay so one thing it depends on
+is the input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself okay so for example if the input
+
+ align:start position:0%
+itself okay so for example if the input
+ 
+
+ align:start position:0%
+itself okay so for example if the input
+is already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorted okay then insertion sort has very
+
+ align:start position:0%
+sorted okay then insertion sort has very
+ 
+
+ align:start position:0%
+sorted okay then insertion sort has very
+little work to do
+
+ align:start position:0%
+little work to do
+ 
+
+ align:start position:0%
+little work to do
+okay because every time through it's
+
+ align:start position:0%
+okay because every time through it's
+ 
+
+ align:start position:0%
+okay because every time through it's
+going to be like this case doesn't have
+
+ align:start position:0%
+going to be like this case doesn't have
+ 
+
+ align:start position:0%
+going to be like this case doesn't have
+to shuffle too many guys over because
+
+ align:start position:0%
+to shuffle too many guys over because
+ 
+
+ align:start position:0%
+to shuffle too many guys over because
+they're already in
+
+ align:start position:0%
+they're already in
+ 
+
+ align:start position:0%
+they're already in
+place okay whereas in some sense what's
+
+ align:start position:0%
+place okay whereas in some sense what's
+ 
+
+ align:start position:0%
+place okay whereas in some sense what's
+the worst case for insertion
+
+ align:start position:0%
+the worst case for insertion
+ 
+
+ align:start position:0%
+the worst case for insertion
+sort yeah if it's reverse
+
+ align:start position:0%
+sort yeah if it's reverse
+ 
+
+ align:start position:0%
+sort yeah if it's reverse
+sorted then it's going to have to do a
+
+ align:start position:0%
+sorted then it's going to have to do a
+ 
+
+ align:start position:0%
+sorted then it's going to have to do a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+work because it's going to have to
+
+ align:start position:0%
+work because it's going to have to
+ 
+
+ align:start position:0%
+work because it's going to have to
+shuffle everything over on each
+
+ align:start position:0%
+shuffle everything over on each
+ 
+
+ align:start position:0%
+shuffle everything over on each
+step okay of the outer
+
+ align:start position:0%
+step okay of the outer
+ 
+
+ align:start position:0%
+step okay of the outer
+loop in addition to the actual input it
+
+ align:start position:0%
+loop in addition to the actual input it
+ 
+
+ align:start position:0%
+loop in addition to the actual input it
+depends of course on the input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size so here for example we did six
+
+ align:start position:0%
+size so here for example we did six
+ 
+
+ align:start position:0%
+size so here for example we did six
+elements it's going to take
+
+ align:start position:0%
+elements it's going to take
+ 
+
+ align:start position:0%
+elements it's going to take
+longer if we for example do 6 * 10 to
+
+ align:start position:0%
+longer if we for example do 6 * 10 to
+ 
+
+ align:start position:0%
+longer if we for example do 6 * 10 to
+the 9th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements okay so if we're sorting a lot
+
+ align:start position:0%
+elements okay so if we're sorting a lot
+ 
+
+ align:start position:0%
+elements okay so if we're sorting a lot
+more stuff it's going to take us a lot
+
+ align:start position:0%
+more stuff it's going to take us a lot
+ 
+
+ align:start position:0%
+more stuff it's going to take us a lot
+longer so typically the way we handle
+
+ align:start position:0%
+longer so typically the way we handle
+ 
+
+ align:start position:0%
+longer so typically the way we handle
+that is we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameterize things in the input
+
+ align:start position:0%
+parameterize things in the input
+ 
+
+ align:start position:0%
+parameterize things in the input
+size so we're going to talk about time
+
+ align:start position:0%
+size so we're going to talk about time
+ 
+
+ align:start position:0%
+size so we're going to talk about time
+as a function of the size of things that
+
+ align:start position:0%
+as a function of the size of things that
+ 
+
+ align:start position:0%
+as a function of the size of things that
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+sorting so we can look at what is the
+
+ align:start position:0%
+sorting so we can look at what is the
+ 
+
+ align:start position:0%
+sorting so we can look at what is the
+behavior of
+
+ align:start position:0%
+behavior of
+ 
+
+ align:start position:0%
+behavior of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay and the last thing I want to say
+
+ align:start position:0%
+okay and the last thing I want to say
+ 
+
+ align:start position:0%
+okay and the last thing I want to say
+about running time is generally we want
+
+ align:start position:0%
+about running time is generally we want
+ 
+
+ align:start position:0%
+about running time is generally we want
+upper bounds on the running time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to know that the time is no more
+
+ align:start position:0%
+we want to know that the time is no more
+ 
+
+ align:start position:0%
+we want to know that the time is no more
+than a certain amount and the reason is
+
+ align:start position:0%
+than a certain amount and the reason is
+ 
+
+ align:start position:0%
+than a certain amount and the reason is
+because that represents a guarantee to
+
+ align:start position:0%
+because that represents a guarantee to
+ 
+
+ align:start position:0%
+because that represents a guarantee to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+user okay so if I say it's not going to
+
+ align:start position:0%
+user okay so if I say it's not going to
+ 
+
+ align:start position:0%
+user okay so if I say it's not going to
+run for example I tell you here's a
+
+ align:start position:0%
+run for example I tell you here's a
+ 
+
+ align:start position:0%
+run for example I tell you here's a
+program and it won't run more than 3
+
+ align:start position:0%
+program and it won't run more than 3
+ 
+
+ align:start position:0%
+program and it won't run more than 3
+seconds okay that gives you real
+
+ align:start position:0%
+seconds okay that gives you real
+ 
+
+ align:start position:0%
+seconds okay that gives you real
+information about how you could use it
+
+ align:start position:0%
+information about how you could use it
+ 
+
+ align:start position:0%
+information about how you could use it
+for example in a real-time
+
+ align:start position:0%
+for example in a real-time
+ 
+
+ align:start position:0%
+for example in a real-time
+setting okay whereas if I said here's a
+
+ align:start position:0%
+setting okay whereas if I said here's a
+ 
+
+ align:start position:0%
+setting okay whereas if I said here's a
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+and you know goes at least 3 seconds you
+
+ align:start position:0%
+and you know goes at least 3 seconds you
+ 
+
+ align:start position:0%
+and you know goes at least 3 seconds you
+don't know if it's going to go you know
+
+ align:start position:0%
+don't know if it's going to go you know
+ 
+
+ align:start position:0%
+don't know if it's going to go you know
+for three years doesn't give you that
+
+ align:start position:0%
+for three years doesn't give you that
+ 
+
+ align:start position:0%
+for three years doesn't give you that
+much guarantee if you're a user of it so
+
+ align:start position:0%
+much guarantee if you're a user of it so
+ 
+
+ align:start position:0%
+much guarantee if you're a user of it so
+generally we want upper bounds because
+
+ align:start position:0%
+generally we want upper bounds because
+ 
+
+ align:start position:0%
+generally we want upper bounds because
+it represents a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guarantee to the
+
+ align:start position:0%
+guarantee to the
+ 
+
+ align:start position:0%
+guarantee to the
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+user so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are different kinds of analyses
+
+ align:start position:0%
+there are different kinds of analyses
+ 
+
+ align:start position:0%
+there are different kinds of analyses
+that people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do the one we're mostly going to focus
+
+ align:start position:0%
+do the one we're mostly going to focus
+ 
+
+ align:start position:0%
+do the one we're mostly going to focus
+on is what's called worst
+
+ align:start position:0%
+on is what's called worst
+ 
+
+ align:start position:0%
+on is what's called worst
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+analysis okay and this is what we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually where we Define t of n
+
+ align:start position:0%
+usually where we Define t of n
+ 
+
+ align:start position:0%
+usually where we Define t of n
+to be the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time on
+
+ align:start position:0%
+time on
+ 
+
+ align:start position:0%
+time on
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+input of size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay so it's the maximum input the
+
+ align:start position:0%
+n okay so it's the maximum input the
+ 
+
+ align:start position:0%
+n okay so it's the maximum input the
+maximum it could possibly cost us on an
+
+ align:start position:0%
+maximum it could possibly cost us on an
+ 
+
+ align:start position:0%
+maximum it could possibly cost us on an
+input of size
+
+ align:start position:0%
+input of size
+ 
+
+ align:start position:0%
+input of size
+n okay so what that does is if you look
+
+ align:start position:0%
+n okay so what that does is if you look
+ 
+
+ align:start position:0%
+n okay so what that does is if you look
+at the fact that sometimes the inputs
+
+ align:start position:0%
+at the fact that sometimes the inputs
+ 
+
+ align:start position:0%
+at the fact that sometimes the inputs
+are better and sometimes they're worse
+
+ align:start position:0%
+are better and sometimes they're worse
+ 
+
+ align:start position:0%
+are better and sometimes they're worse
+we're looking at the worst case of those
+
+ align:start position:0%
+we're looking at the worst case of those
+ 
+
+ align:start position:0%
+we're looking at the worst case of those
+because that's the way we're going to be
+
+ align:start position:0%
+because that's the way we're going to be
+ 
+
+ align:start position:0%
+because that's the way we're going to be
+able to make a guarantee it always does
+
+ align:start position:0%
+able to make a guarantee it always does
+ 
+
+ align:start position:0%
+able to make a guarantee it always does
+something rather than just sometimes
+
+ align:start position:0%
+something rather than just sometimes
+ 
+
+ align:start position:0%
+something rather than just sometimes
+does something okay so we're looking at
+
+ align:start position:0%
+does something okay so we're looking at
+ 
+
+ align:start position:0%
+does something okay so we're looking at
+the maximum notice that if I didn't have
+
+ align:start position:0%
+the maximum notice that if I didn't have
+ 
+
+ align:start position:0%
+the maximum notice that if I didn't have
+maximum then T of n in some sense is a
+
+ align:start position:0%
+maximum then T of n in some sense is a
+ 
+
+ align:start position:0%
+maximum then T of n in some sense is a
+relation not a
+
+ align:start position:0%
+relation not a
+ 
+
+ align:start position:0%
+relation not a
+function because the time on an input of
+
+ align:start position:0%
+function because the time on an input of
+ 
+
+ align:start position:0%
+function because the time on an input of
+size n well depends upon which input of
+
+ align:start position:0%
+size n well depends upon which input of
+ 
+
+ align:start position:0%
+size n well depends upon which input of
+size in I could have many different
+
+ align:start position:0%
+size in I could have many different
+ 
+
+ align:start position:0%
+size in I could have many different
+times but by putting the maximum at it
+
+ align:start position:0%
+times but by putting the maximum at it
+ 
+
+ align:start position:0%
+times but by putting the maximum at it
+it turns that relation into a function
+
+ align:start position:0%
+it turns that relation into a function
+ 
+
+ align:start position:0%
+it turns that relation into a function
+because there's only one maximum time
+
+ align:start position:0%
+because there's only one maximum time
+ 
+
+ align:start position:0%
+because there's only one maximum time
+that it will take
+
+ align:start position:0%
+that it will take
+ 
+
+ align:start position:0%
+that it will take
+okay sometimes we'll talk about average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so sometimes we'll do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here T of n is then the expected
+
+ align:start position:0%
+this here T of n is then the expected
+ 
+
+ align:start position:0%
+this here T of n is then the expected
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs of size
+
+ align:start position:0%
+inputs of size
+ 
+
+ align:start position:0%
+inputs of size
+n okay so it's the expected time now if
+
+ align:start position:0%
+n okay so it's the expected time now if
+ 
+
+ align:start position:0%
+n okay so it's the expected time now if
+I talk about expected time what else do
+
+ align:start position:0%
+I talk about expected time what else do
+ 
+
+ align:start position:0%
+I talk about expected time what else do
+I need to say here what does that mean
+
+ align:start position:0%
+I need to say here what does that mean
+ 
+
+ align:start position:0%
+I need to say here what does that mean
+expected
+
+ align:start position:0%
+expected
+ 
+
+ align:start position:0%
+expected
+time I'm sorry raise your hand so I can
+
+ align:start position:0%
+time I'm sorry raise your hand so I can
+ 
+
+ align:start position:0%
+time I'm sorry raise your hand so I can
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+who's expected inputs what does that
+
+ align:start position:0%
+who's expected inputs what does that
+ 
+
+ align:start position:0%
+who's expected inputs what does that
+mean expected
+
+ align:start position:0%
+mean expected
+ 
+
+ align:start position:0%
+mean expected
+inputs so you expect the AL for certain
+
+ align:start position:0%
+inputs so you expect the AL for certain
+ 
+
+ align:start position:0%
+inputs so you expect the AL for certain
+time and you're assuming you receive a
+
+ align:start position:0%
+time and you're assuming you receive a
+ 
+
+ align:start position:0%
+time and you're assuming you receive a
+certain
+
+ align:start position:0%
+certain
+ 
+
+ align:start position:0%
+certain
+type okay I need I need more math what I
+
+ align:start position:0%
+type okay I need I need more math what I
+ 
+
+ align:start position:0%
+type okay I need I need more math what I
+mean by expected time here math over
+
+ align:start position:0%
+mean by expected time here math over
+ 
+
+ align:start position:0%
+mean by expected time here math over
+here you have to take the time of
+
+ align:start position:0%
+here you have to take the time of
+ 
+
+ align:start position:0%
+here you have to take the time of
+every you have to take the time of every
+
+ align:start position:0%
+every you have to take the time of every
+ 
+
+ align:start position:0%
+every you have to take the time of every
+input and then average
+
+ align:start position:0%
+input and then average
+ 
+
+ align:start position:0%
+input and then average
+them okay that's kind of what we mean by
+
+ align:start position:0%
+them okay that's kind of what we mean by
+ 
+
+ align:start position:0%
+them okay that's kind of what we mean by
+expected time good not
+
+ align:start position:0%
+expected time good not
+ 
+
+ align:start position:0%
+expected time good not
+quite okay that I mean you what you say
+
+ align:start position:0%
+quite okay that I mean you what you say
+ 
+
+ align:start position:0%
+quite okay that I mean you what you say
+is completely correct except it's not
+
+ align:start position:0%
+is completely correct except it's not
+ 
+
+ align:start position:0%
+is completely correct except it's not
+enough not quite enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's the time of every input times
+
+ align:start position:0%
+yeah it's the time of every input times
+ 
+
+ align:start position:0%
+yeah it's the time of every input times
+the probability that'll be that in which
+
+ align:start position:0%
+the probability that'll be that in which
+ 
+
+ align:start position:0%
+the probability that'll be that in which
+is a way of taking a weighted average
+
+ align:start position:0%
+is a way of taking a weighted average
+ 
+
+ align:start position:0%
+is a way of taking a weighted average
+exactly right so how do I know what the
+
+ align:start position:0%
+exactly right so how do I know what the
+ 
+
+ align:start position:0%
+exactly right so how do I know what the
+probability of every input is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's how do I know what the
+
+ align:start position:0%
+what's how do I know what the
+ 
+
+ align:start position:0%
+what's how do I know what the
+probability of particular input occurs
+
+ align:start position:0%
+probability of particular input occurs
+ 
+
+ align:start position:0%
+probability of particular input occurs
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a given
+
+ align:start position:0%
+in a given
+ 
+
+ align:start position:0%
+in a given
+situation I
+
+ align:start position:0%
+situation I
+ 
+
+ align:start position:0%
+situation I
+don't okay I have to make an assumption
+
+ align:start position:0%
+don't okay I have to make an assumption
+ 
+
+ align:start position:0%
+don't okay I have to make an assumption
+what's that assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called what what kind of assumption do I
+
+ align:start position:0%
+called what what kind of assumption do I
+ 
+
+ align:start position:0%
+called what what kind of assumption do I
+have to meet I need an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assumption of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right of the statistical
+
+ align:start position:0%
+right of the statistical
+ 
+
+ align:start position:0%
+right of the statistical
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+okay of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs otherwise expected time doesn't
+
+ align:start position:0%
+inputs otherwise expected time doesn't
+ 
+
+ align:start position:0%
+inputs otherwise expected time doesn't
+mean anything because I don't know what
+
+ align:start position:0%
+mean anything because I don't know what
+ 
+
+ align:start position:0%
+mean anything because I don't know what
+the probability of something is in order
+
+ align:start position:0%
+the probability of something is in order
+ 
+
+ align:start position:0%
+the probability of something is in order
+to do probability you need some
+
+ align:start position:0%
+to do probability you need some
+ 
+
+ align:start position:0%
+to do probability you need some
+assumptions okay you got to State those
+
+ align:start position:0%
+assumptions okay you got to State those
+ 
+
+ align:start position:0%
+assumptions okay you got to State those
+assumptions clearly so one of the most
+
+ align:start position:0%
+assumptions clearly so one of the most
+ 
+
+ align:start position:0%
+assumptions clearly so one of the most
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+assumptions is that all inputs are
+
+ align:start position:0%
+assumptions is that all inputs are
+ 
+
+ align:start position:0%
+assumptions is that all inputs are
+equally likely that's called the uniform
+
+ align:start position:0%
+equally likely that's called the uniform
+ 
+
+ align:start position:0%
+equally likely that's called the uniform
+distribution okay every input of size n
+
+ align:start position:0%
+distribution okay every input of size n
+ 
+
+ align:start position:0%
+distribution okay every input of size n
+is equally likely that kind of
+
+ align:start position:0%
+is equally likely that kind of
+ 
+
+ align:start position:0%
+is equally likely that kind of
+uh uh thing but there are other ways
+
+ align:start position:0%
+uh uh thing but there are other ways
+ 
+
+ align:start position:0%
+uh uh thing but there are other ways
+that you could make that assumption and
+
+ align:start position:0%
+that you could make that assumption and
+ 
+
+ align:start position:0%
+that you could make that assumption and
+they may not all be uh be true so this
+
+ align:start position:0%
+they may not all be uh be true so this
+ 
+
+ align:start position:0%
+they may not all be uh be true so this
+is much more complicated as you can see
+
+ align:start position:0%
+is much more complicated as you can see
+ 
+
+ align:start position:0%
+is much more complicated as you can see
+fortunately all of you have a strong
+
+ align:start position:0%
+fortunately all of you have a strong
+ 
+
+ align:start position:0%
+fortunately all of you have a strong
+probability background and so so we will
+
+ align:start position:0%
+probability background and so so we will
+ 
+
+ align:start position:0%
+probability background and so so we will
+not have any trouble addressing these uh
+
+ align:start position:0%
+not have any trouble addressing these uh
+ 
+
+ align:start position:0%
+not have any trouble addressing these uh
+uh probabilistic issues of dealing with
+
+ align:start position:0%
+uh probabilistic issues of dealing with
+ 
+
+ align:start position:0%
+uh probabilistic issues of dealing with
+expectations and stuff okay
+
+ align:start position:0%
+expectations and stuff okay
+ 
+
+ align:start position:0%
+expectations and stuff okay
+so if you don't time to go and say gee
+
+ align:start position:0%
+so if you don't time to go and say gee
+ 
+
+ align:start position:0%
+so if you don't time to go and say gee
+maybe I should take that probability
+
+ align:start position:0%
+maybe I should take that probability
+ 
+
+ align:start position:0%
+maybe I should take that probability
+class that's a prerequisite for this
+
+ align:start position:0%
+class that's a prerequisite for this
+ 
+
+ align:start position:0%
+class that's a prerequisite for this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+okay last one I want to mention is best
+
+ align:start position:0%
+okay last one I want to mention is best
+ 
+
+ align:start position:0%
+okay last one I want to mention is best
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+analysis and this
+
+ align:start position:0%
+analysis and this
+ 
+
+ align:start position:0%
+analysis and this
+I claim is bogus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bogus no
+
+ align:start position:0%
+bogus no
+ 
+
+ align:start position:0%
+bogus no
+good why is best case analysis bogus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably doesn't everen the best case
+
+ align:start position:0%
+probably doesn't everen the best case
+ 
+
+ align:start position:0%
+probably doesn't everen the best case
+probably doesn't ever
+
+ align:start position:0%
+probably doesn't ever
+ 
+
+ align:start position:0%
+probably doesn't ever
+happen uh actually it's interesting
+
+ align:start position:0%
+happen uh actually it's interesting
+ 
+
+ align:start position:0%
+happen uh actually it's interesting
+because for the Sorting problem the most
+
+ align:start position:0%
+because for the Sorting problem the most
+ 
+
+ align:start position:0%
+because for the Sorting problem the most
+common thing that gets sorted are things
+
+ align:start position:0%
+common thing that gets sorted are things
+ 
+
+ align:start position:0%
+common thing that gets sorted are things
+that are already
+
+ align:start position:0%
+that are already
+ 
+
+ align:start position:0%
+that are already
+sorted interestingly okay so for example
+
+ align:start position:0%
+sorted interestingly okay so for example
+ 
+
+ align:start position:0%
+sorted interestingly okay so for example
+or at least almost sorted okay so for
+
+ align:start position:0%
+or at least almost sorted okay so for
+ 
+
+ align:start position:0%
+or at least almost sorted okay so for
+example one of the most common things
+
+ align:start position:0%
+example one of the most common things
+ 
+
+ align:start position:0%
+example one of the most common things
+that sorted is check numbers by Banks
+
+ align:start position:0%
+that sorted is check numbers by Banks
+ 
+
+ align:start position:0%
+that sorted is check numbers by Banks
+they tend to come in in the same order
+
+ align:start position:0%
+they tend to come in in the same order
+ 
+
+ align:start position:0%
+they tend to come in in the same order
+that they're
+
+ align:start position:0%
+that they're
+ 
+
+ align:start position:0%
+that they're
+written okay so that they're sorting
+
+ align:start position:0%
+written okay so that they're sorting
+ 
+
+ align:start position:0%
+written okay so that they're sorting
+things that are almost always sorted
+
+ align:start position:0%
+things that are almost always sorted
+ 
+
+ align:start position:0%
+things that are almost always sorted
+okay I mean it's good but okay you want
+
+ align:start position:0%
+okay I mean it's good but okay you want
+ 
+
+ align:start position:0%
+okay I mean it's good but okay you want
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah an upper bound not a lower
+
+ align:start position:0%
+yeah an upper bound not a lower
+ 
+
+ align:start position:0%
+yeah an upper bound not a lower
+bound yeah you want to make a guarantee
+
+ align:start position:0%
+bound yeah you want to make a guarantee
+ 
+
+ align:start position:0%
+bound yeah you want to make a guarantee
+and so why is this not a guarantee it's
+
+ align:start position:0%
+and so why is this not a guarantee it's
+ 
+
+ align:start position:0%
+and so why is this not a guarantee it's
+not guaranteed that you're get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+um okay so I mean you're on to something
+
+ align:start position:0%
+um okay so I mean you're on to something
+ 
+
+ align:start position:0%
+um okay so I mean you're on to something
+there you're on to something something
+
+ align:start position:0%
+there you're on to something something
+ 
+
+ align:start position:0%
+there you're on to something something
+but we need a little more Precision here
+
+ align:start position:0%
+but we need a little more Precision here
+ 
+
+ align:start position:0%
+but we need a little more Precision here
+okay how can I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cheat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah you can
+
+ align:start position:0%
+yeah yeah yeah you can
+ 
+
+ align:start position:0%
+yeah yeah yeah you can
+cheat okay you know you cheat with a you
+
+ align:start position:0%
+cheat okay you know you cheat with a you
+ 
+
+ align:start position:0%
+cheat okay you know you cheat with a you
+take a any slow algorithm you
+
+ align:start position:0%
+take a any slow algorithm you
+ 
+
+ align:start position:0%
+take a any slow algorithm you
+want and just check for some particular
+
+ align:start position:0%
+want and just check for some particular
+ 
+
+ align:start position:0%
+want and just check for some particular
+input and if it's that input you say
+
+ align:start position:0%
+input and if it's that input you say
+ 
+
+ align:start position:0%
+input and if it's that input you say
+immediately yeah okay here's the
+
+ align:start position:0%
+immediately yeah okay here's the
+ 
+
+ align:start position:0%
+immediately yeah okay here's the
+answer and it's got a good
+
+ align:start position:0%
+answer and it's got a good
+ 
+
+ align:start position:0%
+answer and it's got a good
+best case but it doesn't tell you
+
+ align:start position:0%
+best case but it doesn't tell you
+ 
+
+ align:start position:0%
+best case but it doesn't tell you
+anything about the vast majority of
+
+ align:start position:0%
+anything about the vast majority of
+ 
+
+ align:start position:0%
+anything about the vast majority of
+what's going
+
+ align:start position:0%
+what's going
+ 
+
+ align:start position:0%
+what's going
+on okay so you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cheat okay with a slow algorithm that
+
+ align:start position:0%
+cheat okay with a slow algorithm that
+ 
+
+ align:start position:0%
+cheat okay with a slow algorithm that
+works fast on some input doesn't really
+
+ align:start position:0%
+works fast on some input doesn't really
+ 
+
+ align:start position:0%
+works fast on some input doesn't really
+do much for you okay so we normally
+
+ align:start position:0%
+do much for you okay so we normally
+ 
+
+ align:start position:0%
+do much for you okay so we normally
+don't worry about
+
+ align:start position:0%
+don't worry about
+ 
+
+ align:start position:0%
+don't worry about
+that okay so let's see what is
+
+ align:start position:0%
+that okay so let's see what is
+ 
+
+ align:start position:0%
+that okay so let's see what is
+insertion
+
+ align:start position:0%
+insertion
+ 
+
+ align:start position:0%
+insertion
+sorts where case
+
+ align:start position:0%
+sorts where case
+ 
+
+ align:start position:0%
+sorts where case
+time okay
+
+ align:start position:0%
+time okay
+ 
+
+ align:start position:0%
+time okay
+so now we get into some sort of funny
+
+ align:start position:0%
+so now we get into some sort of funny
+ 
+
+ align:start position:0%
+so now we get into some sort of funny
+issues first of all it it sort of it
+
+ align:start position:0%
+issues first of all it it sort of it
+ 
+
+ align:start position:0%
+issues first of all it it sort of it
+depends on the computer you're running
+
+ align:start position:0%
+depends on the computer you're running
+ 
+
+ align:start position:0%
+depends on the computer you're running
+on whose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computer right you know is it is it
+
+ align:start position:0%
+computer right you know is it is it
+ 
+
+ align:start position:0%
+computer right you know is it is it
+a big super computer or is it uh your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wristwatch okay you know that different
+
+ align:start position:0%
+wristwatch okay you know that different
+ 
+
+ align:start position:0%
+wristwatch okay you know that different
+computational
+
+ align:start position:0%
+computational
+ 
+
+ align:start position:0%
+computational
+abilities okay and when we compare
+
+ align:start position:0%
+abilities okay and when we compare
+ 
+
+ align:start position:0%
+abilities okay and when we compare
+algorithms We compare them typically for
+
+ align:start position:0%
+algorithms We compare them typically for
+ 
+
+ align:start position:0%
+algorithms We compare them typically for
+relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speed okay this is if you compared two
+
+ align:start position:0%
+speed okay this is if you compared two
+ 
+
+ align:start position:0%
+speed okay this is if you compared two
+algorithms on the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine You could argue well it doesn't
+
+ align:start position:0%
+machine You could argue well it doesn't
+ 
+
+ align:start position:0%
+machine You could argue well it doesn't
+really matter what the machine is
+
+ align:start position:0%
+really matter what the machine is
+ 
+
+ align:start position:0%
+really matter what the machine is
+because I'll just look at their relative
+
+ align:start position:0%
+because I'll just look at their relative
+ 
+
+ align:start position:0%
+because I'll just look at their relative
+speed but of course I may also be
+
+ align:start position:0%
+speed but of course I may also be
+ 
+
+ align:start position:0%
+speed but of course I may also be
+interested in absolute
+
+ align:start position:0%
+interested in absolute
+ 
+
+ align:start position:0%
+interested in absolute
+speed is one algorithm actually better
+
+ align:start position:0%
+speed is one algorithm actually better
+ 
+
+ align:start position:0%
+speed is one algorithm actually better
+no matter what machine it's run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on and so this kind of gets sort of
+
+ align:start position:0%
+on and so this kind of gets sort of
+ 
+
+ align:start position:0%
+on and so this kind of gets sort of
+confusing as to how I can talk about the
+
+ align:start position:0%
+confusing as to how I can talk about the
+ 
+
+ align:start position:0%
+confusing as to how I can talk about the
+worst case time of an algorithm a piece
+
+ align:start position:0%
+worst case time of an algorithm a piece
+ 
+
+ align:start position:0%
+worst case time of an algorithm a piece
+of software when I'm not talking about
+
+ align:start position:0%
+of software when I'm not talking about
+ 
+
+ align:start position:0%
+of software when I'm not talking about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hardware okay because clearly if I run
+
+ align:start position:0%
+hardware okay because clearly if I run
+ 
+
+ align:start position:0%
+hardware okay because clearly if I run
+on a faster machine my algorithms are
+
+ align:start position:0%
+on a faster machine my algorithms are
+ 
+
+ align:start position:0%
+on a faster machine my algorithms are
+going to go
+
+ align:start position:0%
+going to go
+ 
+
+ align:start position:0%
+going to go
+faster so this is where you get the big
+
+ align:start position:0%
+faster so this is where you get the big
+ 
+
+ align:start position:0%
+faster so this is where you get the big
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+um algorithms which is why algorithms is
+
+ align:start position:0%
+um algorithms which is why algorithms is
+ 
+
+ align:start position:0%
+um algorithms which is why algorithms is
+such a huge field why it spawns
+
+ align:start position:0%
+such a huge field why it spawns
+ 
+
+ align:start position:0%
+such a huge field why it spawns
+companies like Google like aamai like
+
+ align:start position:0%
+companies like Google like aamai like
+ 
+
+ align:start position:0%
+companies like Google like aamai like
+Amazon okay why algorithmic analysis has
+
+ align:start position:0%
+Amazon okay why algorithmic analysis has
+ 
+
+ align:start position:0%
+Amazon okay why algorithmic analysis has
+been such throughout the history of
+
+ align:start position:0%
+been such throughout the history of
+ 
+
+ align:start position:0%
+been such throughout the history of
+computing has been such a huge success
+
+ align:start position:0%
+computing has been such a huge success
+ 
+
+ align:start position:0%
+computing has been such a huge success
+is our ability to master and to be able
+
+ align:start position:0%
+is our ability to master and to be able
+ 
+
+ align:start position:0%
+is our ability to master and to be able
+to take what's a apparently a really
+
+ align:start position:0%
+to take what's a apparently a really
+ 
+
+ align:start position:0%
+to take what's a apparently a really
+messy complicated situation and reduce
+
+ align:start position:0%
+messy complicated situation and reduce
+ 
+
+ align:start position:0%
+messy complicated situation and reduce
+it to do being able to do some
+
+ align:start position:0%
+it to do being able to do some
+ 
+
+ align:start position:0%
+it to do being able to do some
+mathematics okay and that idea is called
+
+ align:start position:0%
+mathematics okay and that idea is called
+ 
+
+ align:start position:0%
+mathematics okay and that idea is called
+ASM totic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis and the basic idea of Astic
+
+ align:start position:0%
+analysis and the basic idea of Astic
+ 
+
+ align:start position:0%
+analysis and the basic idea of Astic
+analysis is to
+
+ align:start position:0%
+analysis is to
+ 
+
+ align:start position:0%
+analysis is to
+ignore machine dependent constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+look instead of at the actual running
+
+ align:start position:0%
+look instead of at the actual running
+ 
+
+ align:start position:0%
+look instead of at the actual running
+time look at the growth of the running
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we don't look at the actual
+
+ align:start position:0%
+okay so we don't look at the actual
+ 
+
+ align:start position:0%
+okay so we don't look at the actual
+running time we look at the
+
+ align:start position:0%
+running time we look at the
+ 
+
+ align:start position:0%
+running time we look at the
+growth okay so let's see what we mean by
+
+ align:start position:0%
+growth okay so let's see what we mean by
+ 
+
+ align:start position:0%
+growth okay so let's see what we mean by
+that so this is a huge idea it's not a
+
+ align:start position:0%
+that so this is a huge idea it's not a
+ 
+
+ align:start position:0%
+that so this is a huge idea it's not a
+hard not a not a hard idea otherwise I
+
+ align:start position:0%
+hard not a not a hard idea otherwise I
+ 
+
+ align:start position:0%
+hard not a not a hard idea otherwise I
+won't be able to teach it in the first
+
+ align:start position:0%
+won't be able to teach it in the first
+ 
+
+ align:start position:0%
+won't be able to teach it in the first
+lecture but it's a huge idea we're going
+
+ align:start position:0%
+lecture but it's a huge idea we're going
+ 
+
+ align:start position:0%
+lecture but it's a huge idea we're going
+to spend a couple of lectures
+
+ align:start position:0%
+to spend a couple of lectures
+ 
+
+ align:start position:0%
+to spend a couple of lectures
+understanding the implications of that
+
+ align:start position:0%
+understanding the implications of that
+ 
+
+ align:start position:0%
+understanding the implications of that
+and we'll basically be doing it
+
+ align:start position:0%
+and we'll basically be doing it
+ 
+
+ align:start position:0%
+and we'll basically be doing it
+throughout the the term and you will if
+
+ align:start position:0%
+throughout the the term and you will if
+ 
+
+ align:start position:0%
+throughout the the term and you will if
+you go on to be practicing Engineers
+
+ align:start position:0%
+you go on to be practicing Engineers
+ 
+
+ align:start position:0%
+you go on to be practicing Engineers
+you'll be doing it all the
+
+ align:start position:0%
+you'll be doing it all the
+ 
+
+ align:start position:0%
+you'll be doing it all the
+time in order to that we adopt some
+
+ align:start position:0%
+time in order to that we adopt some
+ 
+
+ align:start position:0%
+time in order to that we adopt some
+notations that are going to help
+
+ align:start position:0%
+notations that are going to help
+ 
+
+ align:start position:0%
+notations that are going to help
+us and in particular we adapt asmic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation okay so most of you have seen
+
+ align:start position:0%
+notation okay so most of you have seen
+ 
+
+ align:start position:0%
+notation okay so most of you have seen
+some kind of ASM totic notation maybe a
+
+ align:start position:0%
+some kind of ASM totic notation maybe a
+ 
+
+ align:start position:0%
+some kind of ASM totic notation maybe a
+few of you haven't but mostly uh you
+
+ align:start position:0%
+few of you haven't but mostly uh you
+ 
+
+ align:start position:0%
+few of you haven't but mostly uh you
+should have seen a little bit the one
+
+ align:start position:0%
+should have seen a little bit the one
+ 
+
+ align:start position:0%
+should have seen a little bit the one
+we're going to be using in this class
+
+ align:start position:0%
+we're going to be using in this class
+ 
+
+ align:start position:0%
+we're going to be using in this class
+predominantly is Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation okay and Theta notation is
+
+ align:start position:0%
+notation okay and Theta notation is
+ 
+
+ align:start position:0%
+notation okay and Theta notation is
+pretty easy notation to master because
+
+ align:start position:0%
+pretty easy notation to master because
+ 
+
+ align:start position:0%
+pretty easy notation to master because
+all you do is you just from a formula
+
+ align:start position:0%
+all you do is you just from a formula
+ 
+
+ align:start position:0%
+all you do is you just from a formula
+you just drop low order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms and
+
+ align:start position:0%
+terms and
+ 
+
+ align:start position:0%
+terms and
+ignore leading constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for
+
+ align:start position:0%
+okay so for
+ 
+
+ align:start position:0%
+okay so for
+example if I have a formula like 3 n
+
+ align:start position:0%
+example if I have a formula like 3 n
+ 
+
+ align:start position:0%
+example if I have a formula like 3 n
+cubed
+
+ align:start position:0%
+cubed
+ 
+
+ align:start position:0%
+cubed
+plus 90 n^ 2 - 5 n +
+
+ align:start position:0%
+plus 90 n^ 2 - 5 n +
+ 
+
+ align:start position:0%
+plus 90 n^ 2 - 5 n +
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+6046 I say well what's
+
+ align:start position:0%
+6046 I say well what's
+ 
+
+ align:start position:0%
+6046 I say well what's
+the what are the what low order terms do
+
+ align:start position:0%
+the what are the what low order terms do
+ 
+
+ align:start position:0%
+the what are the what low order terms do
+I drop well n cubed is a bigger term
+
+ align:start position:0%
+I drop well n cubed is a bigger term
+ 
+
+ align:start position:0%
+I drop well n cubed is a bigger term
+than N2 so I'm going to drop all these
+
+ align:start position:0%
+than N2 so I'm going to drop all these
+ 
+
+ align:start position:0%
+than N2 so I'm going to drop all these
+terms and I'm ignore the leading
+
+ align:start position:0%
+terms and I'm ignore the leading
+ 
+
+ align:start position:0%
+terms and I'm ignore the leading
+constant so I say that's Theta of n
+
+ align:start position:0%
+constant so I say that's Theta of n
+ 
+
+ align:start position:0%
+constant so I say that's Theta of n
+Cub that's pretty
+
+ align:start position:0%
+Cub that's pretty
+ 
+
+ align:start position:0%
+Cub that's pretty
+easy okay so that's as that's Theta
+
+ align:start position:0%
+easy okay so that's as that's Theta
+ 
+
+ align:start position:0%
+easy okay so that's as that's Theta
+notation now this is an
+
+ align:start position:0%
+notation now this is an
+ 
+
+ align:start position:0%
+notation now this is an
+engineering way of manipulating Theta
+
+ align:start position:0%
+engineering way of manipulating Theta
+ 
+
+ align:start position:0%
+engineering way of manipulating Theta
+notation there's actually a mathematical
+
+ align:start position:0%
+notation there's actually a mathematical
+ 
+
+ align:start position:0%
+notation there's actually a mathematical
+definition for this which we're going to
+
+ align:start position:0%
+definition for this which we're going to
+ 
+
+ align:start position:0%
+definition for this which we're going to
+talk about next time okay which is a
+
+ align:start position:0%
+talk about next time okay which is a
+ 
+
+ align:start position:0%
+talk about next time okay which is a
+definition in terms of sets of functions
+
+ align:start position:0%
+definition in terms of sets of functions
+ 
+
+ align:start position:0%
+definition in terms of sets of functions
+and you are going to be responsible in
+
+ align:start position:0%
+and you are going to be responsible in
+ 
+
+ align:start position:0%
+and you are going to be responsible in
+this class this is both both a math and
+
+ align:start position:0%
+this class this is both both a math and
+ 
+
+ align:start position:0%
+this class this is both both a math and
+an engineering computer science
+
+ align:start position:0%
+an engineering computer science
+ 
+
+ align:start position:0%
+an engineering computer science
+engineering class so throughout the
+
+ align:start position:0%
+engineering class so throughout the
+ 
+
+ align:start position:0%
+engineering class so throughout the
+course you're going to be responsible
+
+ align:start position:0%
+course you're going to be responsible
+ 
+
+ align:start position:0%
+course you're going to be responsible
+both for mathematical rigor as if it
+
+ align:start position:0%
+both for mathematical rigor as if it
+ 
+
+ align:start position:0%
+both for mathematical rigor as if it
+were a math course and Engineering
+
+ align:start position:0%
+were a math course and Engineering
+ 
+
+ align:start position:0%
+were a math course and Engineering
+common sense because it's an engineering
+
+ align:start position:0%
+common sense because it's an engineering
+ 
+
+ align:start position:0%
+common sense because it's an engineering
+course okay we're going to be doing both
+
+ align:start position:0%
+course okay we're going to be doing both
+ 
+
+ align:start position:0%
+course okay we're going to be doing both
+okay so this is the engineering way of
+
+ align:start position:0%
+okay so this is the engineering way of
+ 
+
+ align:start position:0%
+okay so this is the engineering way of
+understanding what you do so you're
+
+ align:start position:0%
+understanding what you do so you're
+ 
+
+ align:start position:0%
+understanding what you do so you're
+responsible for being able to do these
+
+ align:start position:0%
+responsible for being able to do these
+ 
+
+ align:start position:0%
+responsible for being able to do these
+manipulations you're also going to be
+
+ align:start position:0%
+manipulations you're also going to be
+ 
+
+ align:start position:0%
+manipulations you're also going to be
+responsible for understanding the
+
+ align:start position:0%
+responsible for understanding the
+ 
+
+ align:start position:0%
+responsible for understanding the
+mathematical definition of theta
+
+ align:start position:0%
+mathematical definition of theta
+ 
+
+ align:start position:0%
+mathematical definition of theta
+notation and of its related uh O
+
+ align:start position:0%
+notation and of its related uh O
+ 
+
+ align:start position:0%
+notation and of its related uh O
+notation and Omega
+
+ align:start position:0%
+notation and Omega
+ 
+
+ align:start position:0%
+notation and Omega
+notation okay
+
+ align:start position:0%
+notation okay
+ 
+
+ align:start position:0%
+notation okay
+so if I take a look as n approaches
+
+ align:start position:0%
+so if I take a look as n approaches
+ 
+
+ align:start position:0%
+so if I take a look as n approaches
+Infinity a Theta n 2
+
+ align:start position:0%
+Infinity a Theta n 2
+ 
+
+ align:start position:0%
+Infinity a Theta n 2
+algorithm always beats
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eventually a Theta of n cubed algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as n gets bigger doesn't matter what
+
+ align:start position:0%
+as n gets bigger doesn't matter what
+ 
+
+ align:start position:0%
+as n gets bigger doesn't matter what
+these other terms were if I were
+
+ align:start position:0%
+these other terms were if I were
+ 
+
+ align:start position:0%
+these other terms were if I were
+describing the absolute precise behavior
+
+ align:start position:0%
+describing the absolute precise behavior
+ 
+
+ align:start position:0%
+describing the absolute precise behavior
+in terms of a
+
+ align:start position:0%
+in terms of a
+ 
+
+ align:start position:0%
+in terms of a
+formula okay if I had a Theta n^2
+
+ align:start position:0%
+formula okay if I had a Theta n^2
+ 
+
+ align:start position:0%
+formula okay if I had a Theta n^2
+algorithm it would always be faster for
+
+ align:start position:0%
+algorithm it would always be faster for
+ 
+
+ align:start position:0%
+algorithm it would always be faster for
+sufficiently large n than a Theta n
+
+ align:start position:0%
+sufficiently large n than a Theta n
+ 
+
+ align:start position:0%
+sufficiently large n than a Theta n
+cubed algorithm wouldn't matter what
+
+ align:start position:0%
+cubed algorithm wouldn't matter what
+ 
+
+ align:start position:0%
+cubed algorithm wouldn't matter what
+those lower terms were wouldn't matter
+
+ align:start position:0%
+those lower terms were wouldn't matter
+ 
+
+ align:start position:0%
+those lower terms were wouldn't matter
+what the leading constant
+
+ align:start position:0%
+what the leading constant
+ 
+
+ align:start position:0%
+what the leading constant
+was okay this one will always be faster
+
+ align:start position:0%
+was okay this one will always be faster
+ 
+
+ align:start position:0%
+was okay this one will always be faster
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+ran the Theta n^2 algorithm on a slow
+
+ align:start position:0%
+ran the Theta n^2 algorithm on a slow
+ 
+
+ align:start position:0%
+ran the Theta n^2 algorithm on a slow
+computer and the Theta n cubed algorithm
+
+ align:start position:0%
+computer and the Theta n cubed algorithm
+ 
+
+ align:start position:0%
+computer and the Theta n cubed algorithm
+on a fast
+
+ align:start position:0%
+on a fast
+ 
+
+ align:start position:0%
+on a fast
+computer so the great thing about ASM
+
+ align:start position:0%
+computer so the great thing about ASM
+ 
+
+ align:start position:0%
+computer so the great thing about ASM
+totic notation is it satisfies our issue
+
+ align:start position:0%
+totic notation is it satisfies our issue
+ 
+
+ align:start position:0%
+totic notation is it satisfies our issue
+of being able to compare both relative
+
+ align:start position:0%
+of being able to compare both relative
+ 
+
+ align:start position:0%
+of being able to compare both relative
+and absolute
+
+ align:start position:0%
+and absolute
+ 
+
+ align:start position:0%
+and absolute
+speed okay because we're able to do this
+
+ align:start position:0%
+speed okay because we're able to do this
+ 
+
+ align:start position:0%
+speed okay because we're able to do this
+no matter what the computer no matter
+
+ align:start position:0%
+no matter what the computer no matter
+ 
+
+ align:start position:0%
+no matter what the computer no matter
+what the platform
+
+ align:start position:0%
+what the platform
+ 
+
+ align:start position:0%
+what the platform
+so on different platforms we may get
+
+ align:start position:0%
+so on different platforms we may get
+ 
+
+ align:start position:0%
+so on different platforms we may get
+different constants here machine
+
+ align:start position:0%
+different constants here machine
+ 
+
+ align:start position:0%
+different constants here machine
+dependent constants for the actual
+
+ align:start position:0%
+dependent constants for the actual
+ 
+
+ align:start position:0%
+dependent constants for the actual
+running time but if I look at the growth
+
+ align:start position:0%
+running time but if I look at the growth
+ 
+
+ align:start position:0%
+running time but if I look at the growth
+as the size of the input gets larger the
+
+ align:start position:0%
+as the size of the input gets larger the
+ 
+
+ align:start position:0%
+as the size of the input gets larger the
+astics generally won't
+
+ align:start position:0%
+astics generally won't
+ 
+
+ align:start position:0%
+astics generally won't
+change okay so for
+
+ align:start position:0%
+change okay so for
+ 
+
+ align:start position:0%
+change okay so for
+example I just draw that as a
+
+ align:start position:0%
+example I just draw that as a
+ 
+
+ align:start position:0%
+example I just draw that as a
+picture so if I have n on this axis and
+
+ align:start position:0%
+picture so if I have n on this axis and
+ 
+
+ align:start position:0%
+picture so if I have n on this axis and
+T of n on this
+
+ align:start position:0%
+T of n on this
+ 
+
+ align:start position:0%
+T of n on this
+axis then this may be a
+
+ align:start position:0%
+axis then this may be a
+ 
+
+ align:start position:0%
+axis then this may be a
+uh this may be for example a Theta n
+
+ align:start position:0%
+uh this may be for example a Theta n
+ 
+
+ align:start position:0%
+uh this may be for example a Theta n
+cubed algorithm and this may be a Theta
+
+ align:start position:0%
+cubed algorithm and this may be a Theta
+ 
+
+ align:start position:0%
+cubed algorithm and this may be a Theta
+n squar
+
+ align:start position:0%
+n squar
+ 
+
+ align:start position:0%
+n squar
+algorithm there's always going to be
+
+ align:start position:0%
+algorithm there's always going to be
+ 
+
+ align:start position:0%
+algorithm there's always going to be
+some point n
+
+ align:start position:0%
+some point n
+ 
+
+ align:start position:0%
+some point n
+not where if you go for everything
+
+ align:start position:0%
+not where if you go for everything
+ 
+
+ align:start position:0%
+not where if you go for everything
+larger the Theta n^2 algorithm is going
+
+ align:start position:0%
+larger the Theta n^2 algorithm is going
+ 
+
+ align:start position:0%
+larger the Theta n^2 algorithm is going
+to be cheaper than the Theta n cubed
+
+ align:start position:0%
+to be cheaper than the Theta n cubed
+ 
+
+ align:start position:0%
+to be cheaper than the Theta n cubed
+algorithm no matter how much Advantage
+
+ align:start position:0%
+algorithm no matter how much Advantage
+ 
+
+ align:start position:0%
+algorithm no matter how much Advantage
+you give it at the beginning in terms of
+
+ align:start position:0%
+you give it at the beginning in terms of
+ 
+
+ align:start position:0%
+you give it at the beginning in terms of
+the speed of the computer you're running
+
+ align:start position:0%
+the speed of the computer you're running
+ 
+
+ align:start position:0%
+the speed of the computer you're running
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+now from an engineering point of view
+
+ align:start position:0%
+now from an engineering point of view
+ 
+
+ align:start position:0%
+now from an engineering point of view
+there's some issues we have to deal with
+
+ align:start position:0%
+there's some issues we have to deal with
+ 
+
+ align:start position:0%
+there's some issues we have to deal with
+because sometimes it could be that that
+
+ align:start position:0%
+because sometimes it could be that that
+ 
+
+ align:start position:0%
+because sometimes it could be that that
+n0o is so
+
+ align:start position:0%
+n0o is so
+ 
+
+ align:start position:0%
+n0o is so
+large that you know the computers aren't
+
+ align:start position:0%
+large that you know the computers aren't
+ 
+
+ align:start position:0%
+large that you know the computers aren't
+big enough to run the
+
+ align:start position:0%
+big enough to run the
+ 
+
+ align:start position:0%
+big enough to run the
+problem so that's why we nevertheless
+
+ align:start position:0%
+problem so that's why we nevertheless
+ 
+
+ align:start position:0%
+problem so that's why we nevertheless
+are interested in some of the slower
+
+ align:start position:0%
+are interested in some of the slower
+ 
+
+ align:start position:0%
+are interested in some of the slower
+algorithms okay because some of the
+
+ align:start position:0%
+algorithms okay because some of the
+ 
+
+ align:start position:0%
+algorithms okay because some of the
+slower algorithms even though they may
+
+ align:start position:0%
+slower algorithms even though they may
+ 
+
+ align:start position:0%
+slower algorithms even though they may
+not ASM
+
+ align:start position:0%
+not ASM
+ 
+
+ align:start position:0%
+not ASM
+totically be slower I mean ASM totically
+
+ align:start position:0%
+totically be slower I mean ASM totically
+ 
+
+ align:start position:0%
+totically be slower I mean ASM totically
+the be slower they may still be faster
+
+ align:start position:0%
+the be slower they may still be faster
+ 
+
+ align:start position:0%
+the be slower they may still be faster
+on reasonable sizes of things and so we
+
+ align:start position:0%
+on reasonable sizes of things and so we
+ 
+
+ align:start position:0%
+on reasonable sizes of things and so we
+have to both balance our mathematical
+
+ align:start position:0%
+have to both balance our mathematical
+ 
+
+ align:start position:0%
+have to both balance our mathematical
+understanding with our engineering
+
+ align:start position:0%
+understanding with our engineering
+ 
+
+ align:start position:0%
+understanding with our engineering
+common sense in order to do good
+
+ align:start position:0%
+common sense in order to do good
+ 
+
+ align:start position:0%
+common sense in order to do good
+programming so just having done analysis
+
+ align:start position:0%
+programming so just having done analysis
+ 
+
+ align:start position:0%
+programming so just having done analysis
+of algorithms doesn't automatically make
+
+ align:start position:0%
+of algorithms doesn't automatically make
+ 
+
+ align:start position:0%
+of algorithms doesn't automatically make
+you a good
+
+ align:start position:0%
+you a good
+ 
+
+ align:start position:0%
+you a good
+programmer okay you also need to learn
+
+ align:start position:0%
+programmer okay you also need to learn
+ 
+
+ align:start position:0%
+programmer okay you also need to learn
+how to program and lead to use these
+
+ align:start position:0%
+how to program and lead to use these
+ 
+
+ align:start position:0%
+how to program and lead to use these
+tools in practice to understand when
+
+ align:start position:0%
+tools in practice to understand when
+ 
+
+ align:start position:0%
+tools in practice to understand when
+they're relevant and when they're not
+
+ align:start position:0%
+they're relevant and when they're not
+ 
+
+ align:start position:0%
+they're relevant and when they're not
+relevant okay so there's a there's a
+
+ align:start position:0%
+relevant okay so there's a there's a
+ 
+
+ align:start position:0%
+relevant okay so there's a there's a
+saying that um
+
+ align:start position:0%
+saying that um
+ 
+
+ align:start position:0%
+saying that um
+if you want to be a good programmer you
+
+ align:start position:0%
+if you want to be a good programmer you
+ 
+
+ align:start position:0%
+if you want to be a good programmer you
+just program every day for two years
+
+ align:start position:0%
+just program every day for two years
+ 
+
+ align:start position:0%
+just program every day for two years
+you'll be an excellent
+
+ align:start position:0%
+you'll be an excellent
+ 
+
+ align:start position:0%
+you'll be an excellent
+programmer okay if you want to be a
+
+ align:start position:0%
+programmer okay if you want to be a
+ 
+
+ align:start position:0%
+programmer okay if you want to be a
+worldclass programmer you can program
+
+ align:start position:0%
+worldclass programmer you can program
+ 
+
+ align:start position:0%
+worldclass programmer you can program
+every day for 10 years or you can
+
+ align:start position:0%
+every day for 10 years or you can
+ 
+
+ align:start position:0%
+every day for 10 years or you can
+program every day for two years and take
+
+ align:start position:0%
+program every day for two years and take
+ 
+
+ align:start position:0%
+program every day for two years and take
+an algorithms
+
+ align:start position:0%
+an algorithms
+ 
+
+ align:start position:0%
+an algorithms
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+so let's get back to what we were doing
+
+ align:start position:0%
+so let's get back to what we were doing
+ 
+
+ align:start position:0%
+so let's get back to what we were doing
+which is analyzing insertion sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to look at the worst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case which as we mentioned before is
+
+ align:start position:0%
+case which as we mentioned before is
+ 
+
+ align:start position:0%
+case which as we mentioned before is
+when the
+
+ align:start position:0%
+when the
+ 
+
+ align:start position:0%
+when the
+input is reverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorted so the biggest element comes
+
+ align:start position:0%
+sorted so the biggest element comes
+ 
+
+ align:start position:0%
+sorted so the biggest element comes
+first and the smallest
+
+ align:start position:0%
+first and the smallest
+ 
+
+ align:start position:0%
+first and the smallest
+last because now every time you do the
+
+ align:start position:0%
+last because now every time you do the
+ 
+
+ align:start position:0%
+last because now every time you do the
+insertion you got to shuffle everything
+
+ align:start position:0%
+insertion you got to shuffle everything
+ 
+
+ align:start position:0%
+insertion you got to shuffle everything
+over okay so you can write down the
+
+ align:start position:0%
+over okay so you can write down the
+ 
+
+ align:start position:0%
+over okay so you can write down the
+running time by looking at the nesting
+
+ align:start position:0%
+running time by looking at the nesting
+ 
+
+ align:start position:0%
+running time by looking at the nesting
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Loops so we do is we sum up so we what
+
+ align:start position:0%
+Loops so we do is we sum up so we what
+ 
+
+ align:start position:0%
+Loops so we do is we sum up so we what
+we assume is that every operation every
+
+ align:start position:0%
+we assume is that every operation every
+ 
+
+ align:start position:0%
+we assume is that every operation every
+Elemental operation is going to take
+
+ align:start position:0%
+Elemental operation is going to take
+ 
+
+ align:start position:0%
+Elemental operation is going to take
+some constant amount of time but we
+
+ align:start position:0%
+some constant amount of time but we
+ 
+
+ align:start position:0%
+some constant amount of time but we
+don't have to worry about what that
+
+ align:start position:0%
+don't have to worry about what that
+ 
+
+ align:start position:0%
+don't have to worry about what that
+constant is because we're going to be
+
+ align:start position:0%
+constant is because we're going to be
+ 
+
+ align:start position:0%
+constant is because we're going to be
+doing ASM totic analysis as I say it's
+
+ align:start position:0%
+doing ASM totic analysis as I say it's
+ 
+
+ align:start position:0%
+doing ASM totic analysis as I say it's
+the beauty of the method is that it
+
+ align:start position:0%
+the beauty of the method is that it
+ 
+
+ align:start position:0%
+the beauty of the method is that it
+causes all these things that are real
+
+ align:start position:0%
+causes all these things that are real
+ 
+
+ align:start position:0%
+causes all these things that are real
+distinctions to sort of vanish we sort
+
+ align:start position:0%
+distinctions to sort of vanish we sort
+ 
+
+ align:start position:0%
+distinctions to sort of vanish we sort
+of look at them from from 30,000 ft
+
+ align:start position:0%
+of look at them from from 30,000 ft
+ 
+
+ align:start position:0%
+of look at them from from 30,000 ft
+rather than from uh from you know uh you
+
+ align:start position:0%
+rather than from uh from you know uh you
+ 
+
+ align:start position:0%
+rather than from uh from you know uh you
+know 3 millimeters or something okay so
+
+ align:start position:0%
+know 3 millimeters or something okay so
+ 
+
+ align:start position:0%
+know 3 millimeters or something okay so
+each of these operations is going to
+
+ align:start position:0%
+each of these operations is going to
+ 
+
+ align:start position:0%
+each of these operations is going to
+sort of be a basic operation one way to
+
+ align:start position:0%
+sort of be a basic operation one way to
+ 
+
+ align:start position:0%
+sort of be a basic operation one way to
+think about this in terms of counting
+
+ align:start position:0%
+think about this in terms of counting
+ 
+
+ align:start position:0%
+think about this in terms of counting
+operations is counting memory references
+
+ align:start position:0%
+operations is counting memory references
+ 
+
+ align:start position:0%
+operations is counting memory references
+how many times do you actually access
+
+ align:start position:0%
+how many times do you actually access
+ 
+
+ align:start position:0%
+how many times do you actually access
+some variable okay that's another way of
+
+ align:start position:0%
+some variable okay that's another way of
+ 
+
+ align:start position:0%
+some variable okay that's another way of
+sort of thinking about this model
+
+ align:start position:0%
+sort of thinking about this model
+ 
+
+ align:start position:0%
+sort of thinking about this model
+so when we do that well we're going to
+
+ align:start position:0%
+so when we do that well we're going to
+ 
+
+ align:start position:0%
+so when we do that well we're going to
+go through this
+
+ align:start position:0%
+go through this
+ 
+
+ align:start position:0%
+go through this
+Loop J is going from 2 to
+
+ align:start position:0%
+Loop J is going from 2 to
+ 
+
+ align:start position:0%
+Loop J is going from 2 to
+n okay and then we're going to add up
+
+ align:start position:0%
+n okay and then we're going to add up
+ 
+
+ align:start position:0%
+n okay and then we're going to add up
+the work that we do within the loop so
+
+ align:start position:0%
+the work that we do within the loop so
+ 
+
+ align:start position:0%
+the work that we do within the loop so
+we can sort of write that in math as
+
+ align:start position:0%
+we can sort of write that in math as
+ 
+
+ align:start position:0%
+we can sort of write that in math as
+summation of J = 2 to
+
+ align:start position:0%
+summation of J = 2 to
+ 
+
+ align:start position:0%
+summation of J = 2 to
+n okay and then what is the work that's
+
+ align:start position:0%
+n okay and then what is the work that's
+ 
+
+ align:start position:0%
+n okay and then what is the work that's
+going on in this in this
+
+ align:start position:0%
+going on in this in this
+ 
+
+ align:start position:0%
+going on in this in this
+Loop well the work that's going on in
+
+ align:start position:0%
+Loop well the work that's going on in
+ 
+
+ align:start position:0%
+Loop well the work that's going on in
+this Loop varies
+
+ align:start position:0%
+this Loop varies
+ 
+
+ align:start position:0%
+this Loop varies
+but in the worst
+
+ align:start position:0%
+but in the worst
+ 
+
+ align:start position:0%
+but in the worst
+case how much how many operations are
+
+ align:start position:0%
+case how much how many operations are
+ 
+
+ align:start position:0%
+case how much how many operations are
+going on
+
+ align:start position:0%
+going on
+ 
+
+ align:start position:0%
+going on
+here for each value of J so for given
+
+ align:start position:0%
+here for each value of J so for given
+ 
+
+ align:start position:0%
+here for each value of J so for given
+value of J how much work goes on in this
+
+ align:start position:0%
+value of J how much work goes on in this
+ 
+
+ align:start position:0%
+value of J how much work goes on in this
+Loop somebody tell me ASM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+totically yeah asymptotically
+
+ align:start position:0%
+totically yeah asymptotically
+ 
+
+ align:start position:0%
+totically yeah asymptotically
+is so it's j time some constant so it's
+
+ align:start position:0%
+is so it's j time some constant so it's
+ 
+
+ align:start position:0%
+is so it's j time some constant so it's
+Theta J okay so there's Theta J work
+
+ align:start position:0%
+Theta J okay so there's Theta J work
+ 
+
+ align:start position:0%
+Theta J okay so there's Theta J work
+going on here because this Loop okay
+
+ align:start position:0%
+going on here because this Loop okay
+ 
+
+ align:start position:0%
+going on here because this Loop okay
+starts out with I being J minus one and
+
+ align:start position:0%
+starts out with I being J minus one and
+ 
+
+ align:start position:0%
+starts out with I being J minus one and
+then it's doing just a constant amount
+
+ align:start position:0%
+then it's doing just a constant amount
+ 
+
+ align:start position:0%
+then it's doing just a constant amount
+of stuff for each step of the value of I
+
+ align:start position:0%
+of stuff for each step of the value of I
+ 
+
+ align:start position:0%
+of stuff for each step of the value of I
+and I is running from from uh uh J minus
+
+ align:start position:0%
+and I is running from from uh uh J minus
+ 
+
+ align:start position:0%
+and I is running from from uh uh J minus
+one down to uh down to zero so we can
+
+ align:start position:0%
+one down to uh down to zero so we can
+ 
+
+ align:start position:0%
+one down to uh down to zero so we can
+say that that's Theta J work that's
+
+ align:start position:0%
+say that that's Theta J work that's
+ 
+
+ align:start position:0%
+say that that's Theta J work that's
+going on
+
+ align:start position:0%
+going on
+ 
+
+ align:start position:0%
+going on
+people follow
+
+ align:start position:0%
+people follow
+ 
+
+ align:start position:0%
+people follow
+that okay and now we have a formula we
+
+ align:start position:0%
+that okay and now we have a formula we
+ 
+
+ align:start position:0%
+that okay and now we have a formula we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+evaluate so what is the evaluation if I
+
+ align:start position:0%
+evaluate so what is the evaluation if I
+ 
+
+ align:start position:0%
+evaluate so what is the evaluation if I
+want to simplify this formula what's
+
+ align:start position:0%
+want to simplify this formula what's
+ 
+
+ align:start position:0%
+want to simplify this formula what's
+that equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to sorry in the back there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+okay so that's just Theta n 2
+
+ align:start position:0%
+okay so that's just Theta n 2
+ 
+
+ align:start position:0%
+okay so that's just Theta n 2
+good okay because this when you're
+
+ align:start position:0%
+good okay because this when you're
+ 
+
+ align:start position:0%
+good okay because this when you're
+saying it's the sum of consecutive
+
+ align:start position:0%
+saying it's the sum of consecutive
+ 
+
+ align:start position:0%
+saying it's the sum of consecutive
+numbers you mean what what's the
+
+ align:start position:0%
+numbers you mean what what's the
+ 
+
+ align:start position:0%
+numbers you mean what what's the
+mathematical term we have for that so we
+
+ align:start position:0%
+mathematical term we have for that so we
+ 
+
+ align:start position:0%
+mathematical term we have for that so we
+can communicate got to know these things
+
+ align:start position:0%
+can communicate got to know these things
+ 
+
+ align:start position:0%
+can communicate got to know these things
+so you
+
+ align:start position:0%
+so you
+ 
+
+ align:start position:0%
+so you
+communicate it's called what type of
+
+ align:start position:0%
+communicate it's called what type of
+ 
+
+ align:start position:0%
+communicate it's called what type of
+sequence it's actually a series but
+
+ align:start position:0%
+sequence it's actually a series but
+ 
+
+ align:start position:0%
+sequence it's actually a series but
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+okay what type of series is this
+
+ align:start position:0%
+okay what type of series is this
+ 
+
+ align:start position:0%
+okay what type of series is this
+called arithmetic series
+
+ align:start position:0%
+called arithmetic series
+ 
+
+ align:start position:0%
+called arithmetic series
+good wow got some sharp people who can
+
+ align:start position:0%
+good wow got some sharp people who can
+ 
+
+ align:start position:0%
+good wow got some sharp people who can
+communicate okay this is an arithmetic
+
+ align:start position:0%
+communicate okay this is an arithmetic
+ 
+
+ align:start position:0%
+communicate okay this is an arithmetic
+the series you're basically summing 1 +
+
+ align:start position:0%
+the series you're basically summing 1 +
+ 
+
+ align:start position:0%
+the series you're basically summing 1 +
+2 + 3 + 4 some constants in there but
+
+ align:start position:0%
+2 + 3 + 4 some constants in there but
+ 
+
+ align:start position:0%
+2 + 3 + 4 some constants in there but
+basically it's 1 + 2 + 3 + 4 + 5 + 6 up
+
+ align:start position:0%
+basically it's 1 + 2 + 3 + 4 + 5 + 6 up
+ 
+
+ align:start position:0%
+basically it's 1 + 2 + 3 + 4 + 5 + 6 up
+to n that's Theta of n^2 okay so if you
+
+ align:start position:0%
+to n that's Theta of n^2 okay so if you
+ 
+
+ align:start position:0%
+to n that's Theta of n^2 okay so if you
+don't know this math there's a chapter
+
+ align:start position:0%
+don't know this math there's a chapter
+ 
+
+ align:start position:0%
+don't know this math there's a chapter
+in the book or you could have taken the
+
+ align:start position:0%
+in the book or you could have taken the
+ 
+
+ align:start position:0%
+in the book or you could have taken the
+prerequisite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right arithmetic series people have
+
+ align:start position:0%
+okay right arithmetic series people have
+ 
+
+ align:start position:0%
+okay right arithmetic series people have
+this vague recollection oh
+
+ align:start position:0%
+this vague recollection oh
+ 
+
+ align:start position:0%
+this vague recollection oh
+yeah okay good now you have to learn
+
+ align:start position:0%
+yeah okay good now you have to learn
+ 
+
+ align:start position:0%
+yeah okay good now you have to learn
+these manipulations we'll talk about it
+
+ align:start position:0%
+these manipulations we'll talk about it
+ 
+
+ align:start position:0%
+these manipulations we'll talk about it
+a bit next time okay but you have to
+
+ align:start position:0%
+a bit next time okay but you have to
+ 
+
+ align:start position:0%
+a bit next time okay but you have to
+learn your Theta manipulations for what
+
+ align:start position:0%
+learn your Theta manipulations for what
+ 
+
+ align:start position:0%
+learn your Theta manipulations for what
+works with Theta you have to be very
+
+ align:start position:0%
+works with Theta you have to be very
+ 
+
+ align:start position:0%
+works with Theta you have to be very
+careful because Theta is a weak
+
+ align:start position:0%
+careful because Theta is a weak
+ 
+
+ align:start position:0%
+careful because Theta is a weak
+notation okay so strong notation is
+
+ align:start position:0%
+notation okay so strong notation is
+ 
+
+ align:start position:0%
+notation okay so strong notation is
+something like Li nits notation from
+
+ align:start position:0%
+something like Li nits notation from
+ 
+
+ align:start position:0%
+something like Li nits notation from
+calculus where you the chain rule is
+
+ align:start position:0%
+calculus where you the chain rule is
+ 
+
+ align:start position:0%
+calculus where you the chain rule is
+just canceling two things and just it's
+
+ align:start position:0%
+just canceling two things and just it's
+ 
+
+ align:start position:0%
+just canceling two things and just it's
+fabulous that you can cancel in the
+
+ align:start position:0%
+fabulous that you can cancel in the
+ 
+
+ align:start position:0%
+fabulous that you can cancel in the
+chain rule okay just okay and Li nits
+
+ align:start position:0%
+chain rule okay just okay and Li nits
+ 
+
+ align:start position:0%
+chain rule okay just okay and Li nits
+notation just expresses that so directly
+
+ align:start position:0%
+notation just expresses that so directly
+ 
+
+ align:start position:0%
+notation just expresses that so directly
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+manipulate Theta notation isn't like
+
+ align:start position:0%
+manipulate Theta notation isn't like
+ 
+
+ align:start position:0%
+manipulate Theta notation isn't like
+that if you think it's like that you're
+
+ align:start position:0%
+that if you think it's like that you're
+ 
+
+ align:start position:0%
+that if you think it's like that you're
+in trouble you really have to think of
+
+ align:start position:0%
+in trouble you really have to think of
+ 
+
+ align:start position:0%
+in trouble you really have to think of
+what's going on under the Theta notation
+
+ align:start position:0%
+what's going on under the Theta notation
+ 
+
+ align:start position:0%
+what's going on under the Theta notation
+and it's more of a descriptive notation
+
+ align:start position:0%
+and it's more of a descriptive notation
+ 
+
+ align:start position:0%
+and it's more of a descriptive notation
+than it is a manipulative notation there
+
+ align:start position:0%
+than it is a manipulative notation there
+ 
+
+ align:start position:0%
+than it is a manipulative notation there
+are manipulations you can do with it but
+
+ align:start position:0%
+are manipulations you can do with it but
+ 
+
+ align:start position:0%
+are manipulations you can do with it but
+unless you understand what's really
+
+ align:start position:0%
+unless you understand what's really
+ 
+
+ align:start position:0%
+unless you understand what's really
+going on under the Thea notation you
+
+ align:start position:0%
+going on under the Thea notation you
+ 
+
+ align:start position:0%
+going on under the Thea notation you
+will find yourself in trouble okay and
+
+ align:start position:0%
+will find yourself in trouble okay and
+ 
+
+ align:start position:0%
+will find yourself in trouble okay and
+next time we'll talk a little bit more
+
+ align:start position:0%
+next time we'll talk a little bit more
+ 
+
+ align:start position:0%
+next time we'll talk a little bit more
+about Theta
+
+ align:start position:0%
+about Theta
+ 
+
+ align:start position:0%
+about Theta
+notation so is in insertions sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast well it turns out for small n it's
+
+ align:start position:0%
+fast well it turns out for small n it's
+ 
+
+ align:start position:0%
+fast well it turns out for small n it's
+moderately fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but it is not at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all for large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm going to give you an
+
+ align:start position:0%
+okay so I'm going to give you an
+ 
+
+ align:start position:0%
+okay so I'm going to give you an
+algorithm that's faster it's called
+
+ align:start position:0%
+algorithm that's faster it's called
+ 
+
+ align:start position:0%
+algorithm that's faster it's called
+merge
+
+ align:start position:0%
+merge
+ 
+
+ align:start position:0%
+merge
+sort wonder if I should leave insertion
+
+ align:start position:0%
+sort wonder if I should leave insertion
+ 
+
+ align:start position:0%
+sort wonder if I should leave insertion
+sort up why not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm going to write on this
+
+ align:start position:0%
+okay I'm going to write on this
+ 
+
+ align:start position:0%
+okay I'm going to write on this
+later okay so if you're taking notes
+
+ align:start position:0%
+later okay so if you're taking notes
+ 
+
+ align:start position:0%
+later okay so if you're taking notes
+leave some space on the left here's
+
+ align:start position:0%
+leave some space on the left here's
+ 
+
+ align:start position:0%
+leave some space on the left here's
+merge
+
+ align:start position:0%
+merge
+ 
+
+ align:start position:0%
+merge
+sort of an array a from one up to
+
+ align:start position:0%
+sort of an array a from one up to
+ 
+
+ align:start position:0%
+sort of an array a from one up to
+n and it's basically three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps if n equal 1 we're
+
+ align:start position:0%
+steps if n equal 1 we're
+ 
+
+ align:start position:0%
+steps if n equal 1 we're
+done sorting one element it's already
+
+ align:start position:0%
+done sorting one element it's already
+ 
+
+ align:start position:0%
+done sorting one element it's already
+sorted all right okay so recursive
+
+ align:start position:0%
+sorted all right okay so recursive
+ 
+
+ align:start position:0%
+sorted all right okay so recursive
+algorithm otherwise what we do is we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recursively
+
+ align:start position:0%
+recursively
+ 
+
+ align:start position:0%
+recursively
+sort a from
+
+ align:start position:0%
+sort a from
+ 
+
+ align:start position:0%
+sort a from
+one up to the ceiling of n /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and the array a of the ceiling of n / 2
+
+ align:start position:0%
+and the array a of the ceiling of n / 2
+ 
+
+ align:start position:0%
+and the array a of the ceiling of n / 2
++
+
+ align:start position:0%
++
+ 
+
+ align:start position:0%
++
+1 up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay so we sort two halves of the of
+
+ align:start position:0%
+n okay so we sort two halves of the of
+ 
+
+ align:start position:0%
+n okay so we sort two halves of the of
+the uh input and then three we take
+
+ align:start position:0%
+the uh input and then three we take
+ 
+
+ align:start position:0%
+the uh input and then three we take
+those two lists that we've done and we
+
+ align:start position:0%
+those two lists that we've done and we
+ 
+
+ align:start position:0%
+those two lists that we've done and we
+merge them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to do that we use a merge sub rutine
+
+ align:start position:0%
+and to do that we use a merge sub rutine
+ 
+
+ align:start position:0%
+and to do that we use a merge sub rutine
+which I'll show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you so the key sub rutine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+merge and it works like this I have two
+
+ align:start position:0%
+merge and it works like this I have two
+ 
+
+ align:start position:0%
+merge and it works like this I have two
+lists let's say one of them is 20 I'm
+
+ align:start position:0%
+lists let's say one of them is 20 I'm
+ 
+
+ align:start position:0%
+lists let's say one of them is 20 I'm
+doing this in Reverse ERS 72 so I've
+
+ align:start position:0%
+doing this in Reverse ERS 72 so I've
+ 
+
+ align:start position:0%
+doing this in Reverse ERS 72 so I've
+sorted this like this and then I sort
+
+ align:start position:0%
+sorted this like this and then I sort
+ 
+
+ align:start position:0%
+sorted this like this and then I sort
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+one I don't know why I do it this order
+
+ align:start position:0%
+one I don't know why I do it this order
+ 
+
+ align:start position:0%
+one I don't know why I do it this order
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+anyway okay and here's my other list I
+
+ align:start position:0%
+anyway okay and here's my other list I
+ 
+
+ align:start position:0%
+anyway okay and here's my other list I
+have my two list that I've sorted so
+
+ align:start position:0%
+have my two list that I've sorted so
+ 
+
+ align:start position:0%
+have my two list that I've sorted so
+this is A1 up to a ceiling of N /2 and
+
+ align:start position:0%
+this is A1 up to a ceiling of N /2 and
+ 
+
+ align:start position:0%
+this is A1 up to a ceiling of N /2 and
+ceiling of n/2 + 1 up to a n for the way
+
+ align:start position:0%
+ceiling of n/2 + 1 up to a n for the way
+ 
+
+ align:start position:0%
+ceiling of n/2 + 1 up to a n for the way
+it will be called in this program okay
+
+ align:start position:0%
+it will be called in this program okay
+ 
+
+ align:start position:0%
+it will be called in this program okay
+and now to to merge these two what I
+
+ align:start position:0%
+and now to to merge these two what I
+ 
+
+ align:start position:0%
+and now to to merge these two what I
+want to do is produce a sorted list out
+
+ align:start position:0%
+want to do is produce a sorted list out
+ 
+
+ align:start position:0%
+want to do is produce a sorted list out
+of both of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so what I do is first observe where
+
+ align:start position:0%
+them so what I do is first observe where
+ 
+
+ align:start position:0%
+them so what I do is first observe where
+is the smallest
+
+ align:start position:0%
+is the smallest
+ 
+
+ align:start position:0%
+is the smallest
+element of any two lists that are
+
+ align:start position:0%
+element of any two lists that are
+ 
+
+ align:start position:0%
+element of any two lists that are
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+sorted it's in one of two places the
+
+ align:start position:0%
+sorted it's in one of two places the
+ 
+
+ align:start position:0%
+sorted it's in one of two places the
+head of the first list or the head of
+
+ align:start position:0%
+head of the first list or the head of
+ 
+
+ align:start position:0%
+head of the first list or the head of
+the second list so I look at those two
+
+ align:start position:0%
+the second list so I look at those two
+ 
+
+ align:start position:0%
+the second list so I look at those two
+elements and I say which one is
+
+ align:start position:0%
+elements and I say which one is
+ 
+
+ align:start position:0%
+elements and I say which one is
+smaller this one is smaller so then what
+
+ align:start position:0%
+smaller this one is smaller so then what
+ 
+
+ align:start position:0%
+smaller this one is smaller so then what
+I do is I output into my output
+
+ align:start position:0%
+I do is I output into my output
+ 
+
+ align:start position:0%
+I do is I output into my output
+array the smaller of the two and I cross
+
+ align:start position:0%
+array the smaller of the two and I cross
+ 
+
+ align:start position:0%
+array the smaller of the two and I cross
+it off and now where's the next smallest
+
+ align:start position:0%
+it off and now where's the next smallest
+ 
+
+ align:start position:0%
+it off and now where's the next smallest
+element and the answer is it's going to
+
+ align:start position:0%
+element and the answer is it's going to
+ 
+
+ align:start position:0%
+element and the answer is it's going to
+be the head of one of these two
+
+ align:start position:0%
+be the head of one of these two
+ 
+
+ align:start position:0%
+be the head of one of these two
+lists so then I cross out this guy put
+
+ align:start position:0%
+lists so then I cross out this guy put
+ 
+
+ align:start position:0%
+lists so then I cross out this guy put
+him here and circle this
+
+ align:start position:0%
+him here and circle this
+ 
+
+ align:start position:0%
+him here and circle this
+one and now I look at these two guys
+
+ align:start position:0%
+one and now I look at these two guys
+ 
+
+ align:start position:0%
+one and now I look at these two guys
+this one's smaller so I output
+
+ align:start position:0%
+this one's smaller so I output
+ 
+
+ align:start position:0%
+this one's smaller so I output
+that and circle that one now we look at
+
+ align:start position:0%
+that and circle that one now we look at
+ 
+
+ align:start position:0%
+that and circle that one now we look at
+these two guys output nine so every step
+
+ align:start position:0%
+these two guys output nine so every step
+ 
+
+ align:start position:0%
+these two guys output nine so every step
+here is some fixed number of of
+
+ align:start position:0%
+here is some fixed number of of
+ 
+
+ align:start position:0%
+here is some fixed number of of
+operations that's independent of the
+
+ align:start position:0%
+operations that's independent of the
+ 
+
+ align:start position:0%
+operations that's independent of the
+size of the arrays at each
+
+ align:start position:0%
+size of the arrays at each
+ 
+
+ align:start position:0%
+size of the arrays at each
+step okay each individual step is just
+
+ align:start position:0%
+step okay each individual step is just
+ 
+
+ align:start position:0%
+step okay each individual step is just
+me looking at two elements and picking
+
+ align:start position:0%
+me looking at two elements and picking
+ 
+
+ align:start position:0%
+me looking at two elements and picking
+out the smallest and advancing some
+
+ align:start position:0%
+out the smallest and advancing some
+ 
+
+ align:start position:0%
+out the smallest and advancing some
+pointers into the into the array so I
+
+ align:start position:0%
+pointers into the into the array so I
+ 
+
+ align:start position:0%
+pointers into the into the array so I
+know where the current head of that of
+
+ align:start position:0%
+know where the current head of that of
+ 
+
+ align:start position:0%
+know where the current head of that of
+that list is okay and so therefore the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time is order
+
+ align:start position:0%
+time is order
+ 
+
+ align:start position:0%
+time is order
+n on N total elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the time to actually go through this
+
+ align:start position:0%
+so the time to actually go through this
+ 
+
+ align:start position:0%
+so the time to actually go through this
+and merge two lists is order n we
+
+ align:start position:0%
+and merge two lists is order n we
+ 
+
+ align:start position:0%
+and merge two lists is order n we
+sometimes call this linear
+
+ align:start position:0%
+sometimes call this linear
+ 
+
+ align:start position:0%
+sometimes call this linear
+time okay because it's not quadratic
+
+ align:start position:0%
+time okay because it's not quadratic
+ 
+
+ align:start position:0%
+time okay because it's not quadratic
+or whatever it's proportional to n okay
+
+ align:start position:0%
+or whatever it's proportional to n okay
+ 
+
+ align:start position:0%
+or whatever it's proportional to n okay
+proportional to the input size so it's
+
+ align:start position:0%
+proportional to the input size so it's
+ 
+
+ align:start position:0%
+proportional to the input size so it's
+linear time I go through and I just do
+
+ align:start position:0%
+linear time I go through and I just do
+ 
+
+ align:start position:0%
+linear time I go through and I just do
+this simple operation just working up
+
+ align:start position:0%
+this simple operation just working up
+ 
+
+ align:start position:0%
+this simple operation just working up
+these lists and in the end I've done ENT
+
+ align:start position:0%
+these lists and in the end I've done ENT
+ 
+
+ align:start position:0%
+these lists and in the end I've done ENT
+n operations order n operations Each of
+
+ align:start position:0%
+n operations order n operations Each of
+ 
+
+ align:start position:0%
+n operations order n operations Each of
+which cost constant time that's a total
+
+ align:start position:0%
+which cost constant time that's a total
+ 
+
+ align:start position:0%
+which cost constant time that's a total
+of order n
+
+ align:start position:0%
+of order n
+ 
+
+ align:start position:0%
+of order n
+time okay everybody with
+
+ align:start position:0%
+time okay everybody with
+ 
+
+ align:start position:0%
+time okay everybody with
+me okay
+
+ align:start position:0%
+me okay
+ 
+
+ align:start position:0%
+me okay
+so about that so this is a recursive
+
+ align:start position:0%
+so about that so this is a recursive
+ 
+
+ align:start position:0%
+so about that so this is a recursive
+program we can actually now write what's
+
+ align:start position:0%
+program we can actually now write what's
+ 
+
+ align:start position:0%
+program we can actually now write what's
+called a recurrence for this program and
+
+ align:start position:0%
+called a recurrence for this program and
+ 
+
+ align:start position:0%
+called a recurrence for this program and
+the way we do that is we say let's let
+
+ align:start position:0%
+the way we do that is we say let's let
+ 
+
+ align:start position:0%
+the way we do that is we say let's let
+the time to sort ele n elements be T of
+
+ align:start position:0%
+the time to sort ele n elements be T of
+ 
+
+ align:start position:0%
+the time to sort ele n elements be T of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+then how long does it take to do step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that's just constant
+
+ align:start position:0%
+one that's just constant
+ 
+
+ align:start position:0%
+one that's just constant
+time okay we just check to see if n is
+
+ align:start position:0%
+time okay we just check to see if n is
+ 
+
+ align:start position:0%
+time okay we just check to see if n is
+one and if it is we return so that's
+
+ align:start position:0%
+one and if it is we return so that's
+ 
+
+ align:start position:0%
+one and if it is we return so that's
+independent of the size of what anything
+
+ align:start position:0%
+independent of the size of what anything
+ 
+
+ align:start position:0%
+independent of the size of what anything
+that we're doing it's just takes a
+
+ align:start position:0%
+that we're doing it's just takes a
+ 
+
+ align:start position:0%
+that we're doing it's just takes a
+certain number of machine instructions
+
+ align:start position:0%
+certain number of machine instructions
+ 
+
+ align:start position:0%
+certain number of machine instructions
+on whatever machine okay and we say it's
+
+ align:start position:0%
+on whatever machine okay and we say it's
+ 
+
+ align:start position:0%
+on whatever machine okay and we say it's
+constant time we call that Theta 1 this
+
+ align:start position:0%
+constant time we call that Theta 1 this
+ 
+
+ align:start position:0%
+constant time we call that Theta 1 this
+is actually a little bit of an
+
+ align:start position:0%
+is actually a little bit of an
+ 
+
+ align:start position:0%
+is actually a little bit of an
+abuse okay which if you get into it then
+
+ align:start position:0%
+abuse okay which if you get into it then
+ 
+
+ align:start position:0%
+abuse okay which if you get into it then
+the reason is because typically in order
+
+ align:start position:0%
+the reason is because typically in order
+ 
+
+ align:start position:0%
+the reason is because typically in order
+to say it you need to say what it's
+
+ align:start position:0%
+to say it you need to say what it's
+ 
+
+ align:start position:0%
+to say it you need to say what it's
+growing with and nevertheless we use
+
+ align:start position:0%
+growing with and nevertheless we use
+ 
+
+ align:start position:0%
+growing with and nevertheless we use
+this as an abuse of the notation just
+
+ align:start position:0%
+this as an abuse of the notation just
+ 
+
+ align:start position:0%
+this as an abuse of the notation just
+mean it's a
+
+ align:start position:0%
+mean it's a
+ 
+
+ align:start position:0%
+mean it's a
+constant okay so that's an
+
+ align:start position:0%
+constant okay so that's an
+ 
+
+ align:start position:0%
+constant okay so that's an
+abuse just so people know okay but it
+
+ align:start position:0%
+abuse just so people know okay but it
+ 
+
+ align:start position:0%
+abuse just so people know okay but it
+simplifies things if I can just write
+
+ align:start position:0%
+simplifies things if I can just write
+ 
+
+ align:start position:0%
+simplifies things if I can just write
+Theta 1 and it basically means the same
+
+ align:start position:0%
+Theta 1 and it basically means the same
+ 
+
+ align:start position:0%
+Theta 1 and it basically means the same
+thing okay now we recursively sort these
+
+ align:start position:0%
+thing okay now we recursively sort these
+ 
+
+ align:start position:0%
+thing okay now we recursively sort these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+things so so how can I describe that if
+
+ align:start position:0%
+things so so how can I describe that if
+ 
+
+ align:start position:0%
+things so so how can I describe that if
+I'm going to recur the time to do
+
+ align:start position:0%
+I'm going to recur the time to do
+ 
+
+ align:start position:0%
+I'm going to recur the time to do
+this I can describe as
+
+ align:start position:0%
+this I can describe as
+ 
+
+ align:start position:0%
+this I can describe as
+recursively as T of ceiling of n
+
+ align:start position:0%
+recursively as T of ceiling of n
+ 
+
+ align:start position:0%
+recursively as T of ceiling of n
+/2 plus T
+
+ align:start position:0%
+/2 plus T
+ 
+
+ align:start position:0%
+/2 plus T
+of n minus ceiling of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2 that's actually kind of messy so what
+
+ align:start position:0%
+/2 that's actually kind of messy so what
+ 
+
+ align:start position:0%
+/2 that's actually kind of messy so what
+we'll do is we'll just be
+
+ align:start position:0%
+we'll do is we'll just be
+ 
+
+ align:start position:0%
+we'll do is we'll just be
+sloppy write T of n / 2 2 T of n/2
+
+ align:start position:0%
+sloppy write T of n / 2 2 T of n/2
+ 
+
+ align:start position:0%
+sloppy write T of n / 2 2 T of n/2
+okay so this is just us being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sloppy and we'll see on Friday in
+
+ align:start position:0%
+sloppy and we'll see on Friday in
+ 
+
+ align:start position:0%
+sloppy and we'll see on Friday in
+recitation it's okay to be
+
+ align:start position:0%
+recitation it's okay to be
+ 
+
+ align:start position:0%
+recitation it's okay to be
+sloppy okay that's the great thing about
+
+ align:start position:0%
+sloppy okay that's the great thing about
+ 
+
+ align:start position:0%
+sloppy okay that's the great thing about
+algorithms is you can as long as you're
+
+ align:start position:0%
+algorithms is you can as long as you're
+ 
+
+ align:start position:0%
+algorithms is you can as long as you're
+rigorous and precise you can be as
+
+ align:start position:0%
+rigorous and precise you can be as
+ 
+
+ align:start position:0%
+rigorous and precise you can be as
+sloppy as you
+
+ align:start position:0%
+sloppy as you
+ 
+
+ align:start position:0%
+sloppy as you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+okay okay so this is sloppy because I
+
+ align:start position:0%
+okay okay so this is sloppy because I
+ 
+
+ align:start position:0%
+okay okay so this is sloppy because I
+didn't worry about what was going on
+
+ align:start position:0%
+didn't worry about what was going on
+ 
+
+ align:start position:0%
+didn't worry about what was going on
+because it turns out it doesn't make any
+
+ align:start position:0%
+because it turns out it doesn't make any
+ 
+
+ align:start position:0%
+because it turns out it doesn't make any
+difference and we're going to actually
+
+ align:start position:0%
+difference and we're going to actually
+ 
+
+ align:start position:0%
+difference and we're going to actually
+see that that's the
+
+ align:start position:0%
+see that that's the
+ 
+
+ align:start position:0%
+see that that's the
+case and finally I have to merge the two
+
+ align:start position:0%
+case and finally I have to merge the two
+ 
+
+ align:start position:0%
+case and finally I have to merge the two
+sorted lists which have a total of n
+
+ align:start position:0%
+sorted lists which have a total of n
+ 
+
+ align:start position:0%
+sorted lists which have a total of n
+elements and we just Analyze That using
+
+ align:start position:0%
+elements and we just Analyze That using
+ 
+
+ align:start position:0%
+elements and we just Analyze That using
+the merge sub routine that takes us
+
+ align:start position:0%
+the merge sub routine that takes us
+ 
+
+ align:start position:0%
+the merge sub routine that takes us
+Theta n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so that allows us now to write a
+
+ align:start position:0%
+time so that allows us now to write a
+ 
+
+ align:start position:0%
+time so that allows us now to write a
+recurrence for the performance of merge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort is just say that t of n is equal
+
+ align:start position:0%
+sort is just say that t of n is equal
+ 
+
+ align:start position:0%
+sort is just say that t of n is equal
+to Theta
+
+ align:start position:0%
+to Theta
+ 
+
+ align:start position:0%
+to Theta
+1 if n =
+
+ align:start position:0%
+1 if n =
+ 
+
+ align:start position:0%
+1 if n =
+1 and 2 T of n /
+
+ align:start position:0%
+1 and 2 T of n /
+ 
+
+ align:start position:0%
+1 and 2 T of n /
+2 plus Theta of
+
+ align:start position:0%
+2 plus Theta of
+ 
+
+ align:start position:0%
+2 plus Theta of
+n if n is bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay because either I'm doing step
+
+ align:start position:0%
+one okay because either I'm doing step
+ 
+
+ align:start position:0%
+one okay because either I'm doing step
+one or I'm doing all steps 1 2 and three
+
+ align:start position:0%
+one or I'm doing all steps 1 2 and three
+ 
+
+ align:start position:0%
+one or I'm doing all steps 1 2 and three
+I'm doing step one and I return and I'm
+
+ align:start position:0%
+I'm doing step one and I return and I'm
+ 
+
+ align:start position:0%
+I'm doing step one and I return and I'm
+done or else I'm doing step one I don't
+
+ align:start position:0%
+done or else I'm doing step one I don't
+ 
+
+ align:start position:0%
+done or else I'm doing step one I don't
+return and then I also do steps two and
+
+ align:start position:0%
+return and then I also do steps two and
+ 
+
+ align:start position:0%
+return and then I also do steps two and
+three so I add those together I could
+
+ align:start position:0%
+three so I add those together I could
+ 
+
+ align:start position:0%
+three so I add those together I could
+say Theta n plus Theta 1 but Theta n
+
+ align:start position:0%
+say Theta n plus Theta 1 but Theta n
+ 
+
+ align:start position:0%
+say Theta n plus Theta 1 but Theta n
+plus Theta 1 is just Theta n because
+
+ align:start position:0%
+plus Theta 1 is just Theta n because
+ 
+
+ align:start position:0%
+plus Theta 1 is just Theta n because
+Theta 1 is a lower order term than Theta
+
+ align:start position:0%
+Theta 1 is a lower order term than Theta
+ 
+
+ align:start position:0%
+Theta 1 is a lower order term than Theta
+N I can throw it
+
+ align:start position:0%
+N I can throw it
+ 
+
+ align:start position:0%
+N I can throw it
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+okay so it's either Theta 1 or it's 2 T
+
+ align:start position:0%
+okay so it's either Theta 1 or it's 2 T
+ 
+
+ align:start position:0%
+okay so it's either Theta 1 or it's 2 T
+of n / 2 + Theta
+
+ align:start position:0%
+of n / 2 + Theta
+ 
+
+ align:start position:0%
+of n / 2 + Theta
+n okay now typically we won't be writing
+
+ align:start position:0%
+n okay now typically we won't be writing
+ 
+
+ align:start position:0%
+n okay now typically we won't be writing
+this usually we omit
+
+ align:start position:0%
+this usually we omit
+ 
+
+ align:start position:0%
+this usually we omit
+this if it makes no difference to the
+
+ align:start position:0%
+this if it makes no difference to the
+ 
+
+ align:start position:0%
+this if it makes no difference to the
+solution of the recurrence we'll usually
+
+ align:start position:0%
+solution of the recurrence we'll usually
+ 
+
+ align:start position:0%
+solution of the recurrence we'll usually
+omit constant base cases because in
+
+ align:start position:0%
+omit constant base cases because in
+ 
+
+ align:start position:0%
+omit constant base cases because in
+algorithms it's not true generally in
+
+ align:start position:0%
+algorithms it's not true generally in
+ 
+
+ align:start position:0%
+algorithms it's not true generally in
+mathematics but in
+
+ align:start position:0%
+mathematics but in
+ 
+
+ align:start position:0%
+mathematics but in
+algorithms if you're running something
+
+ align:start position:0%
+algorithms if you're running something
+ 
+
+ align:start position:0%
+algorithms if you're running something
+on a constant size input it takes
+
+ align:start position:0%
+on a constant size input it takes
+ 
+
+ align:start position:0%
+on a constant size input it takes
+constant time always okay so we don't
+
+ align:start position:0%
+constant time always okay so we don't
+ 
+
+ align:start position:0%
+constant time always okay so we don't
+worry about what this value is and it
+
+ align:start position:0%
+worry about what this value is and it
+ 
+
+ align:start position:0%
+worry about what this value is and it
+turns out it has no real impact on the
+
+ align:start position:0%
+turns out it has no real impact on the
+ 
+
+ align:start position:0%
+turns out it has no real impact on the
+ASM totic solution of the recurrence
+
+ align:start position:0%
+ASM totic solution of the recurrence
+ 
+
+ align:start position:0%
+ASM totic solution of the recurrence
+so how do we solve a recurrence like
+
+ align:start position:0%
+so how do we solve a recurrence like
+ 
+
+ align:start position:0%
+so how do we solve a recurrence like
+this I now have t of n expressed in
+
+ align:start position:0%
+this I now have t of n expressed in
+ 
+
+ align:start position:0%
+this I now have t of n expressed in
+terms of T of n /
+
+ align:start position:0%
+terms of T of n /
+ 
+
+ align:start position:0%
+terms of T of n /
+2 okay so that's what we're going to do
+
+ align:start position:0%
+2 okay so that's what we're going to do
+ 
+
+ align:start position:0%
+2 okay so that's what we're going to do
+in so that's in the book and it's also
+
+ align:start position:0%
+in so that's in the book and it's also
+ 
+
+ align:start position:0%
+in so that's in the book and it's also
+in lecture
+
+ align:start position:0%
+in lecture
+ 
+
+ align:start position:0%
+in lecture
+two so we're going to do lecture two
+
+ align:start position:0%
+two so we're going to do lecture two
+ 
+
+ align:start position:0%
+two so we're going to do lecture two
+okay to solve that but in the meantime
+
+ align:start position:0%
+okay to solve that but in the meantime
+ 
+
+ align:start position:0%
+okay to solve that but in the meantime
+what I'm going to do is give you a uh a
+
+ align:start position:0%
+what I'm going to do is give you a uh a
+ 
+
+ align:start position:0%
+what I'm going to do is give you a uh a
+visual way of understanding what this
+
+ align:start position:0%
+visual way of understanding what this
+ 
+
+ align:start position:0%
+visual way of understanding what this
+costs which is one of the techniques
+
+ align:start position:0%
+costs which is one of the techniques
+ 
+
+ align:start position:0%
+costs which is one of the techniques
+we'll elaborate on next time is it's
+
+ align:start position:0%
+we'll elaborate on next time is it's
+ 
+
+ align:start position:0%
+we'll elaborate on next time is it's
+called a recursion
+
+ align:start position:0%
+called a recursion
+ 
+
+ align:start position:0%
+called a recursion
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+technique and I'll use it for the actual
+
+ align:start position:0%
+technique and I'll use it for the actual
+ 
+
+ align:start position:0%
+technique and I'll use it for the actual
+for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence that's almost the same 2 T of
+
+ align:start position:0%
+recurrence that's almost the same 2 T of
+ 
+
+ align:start position:0%
+recurrence that's almost the same 2 T of
+n / 2 but I'm going to actually
+
+ align:start position:0%
+n / 2 but I'm going to actually
+ 
+
+ align:start position:0%
+n / 2 but I'm going to actually
+explicitly because I want you to see
+
+ align:start position:0%
+explicitly because I want you to see
+ 
+
+ align:start position:0%
+explicitly because I want you to see
+where it hap where it
+
+ align:start position:0%
+where it hap where it
+ 
+
+ align:start position:0%
+where it hap where it
+occurs plus some constant times n
+
+ align:start position:0%
+occurs plus some constant times n
+ 
+
+ align:start position:0%
+occurs plus some constant times n
+where C is a constant greater than zero
+
+ align:start position:0%
+where C is a constant greater than zero
+ 
+
+ align:start position:0%
+where C is a constant greater than zero
+so we're going to look at at this
+
+ align:start position:0%
+so we're going to look at at this
+ 
+
+ align:start position:0%
+so we're going to look at at this
+recurrence okay with a base case of
+
+ align:start position:0%
+recurrence okay with a base case of
+ 
+
+ align:start position:0%
+recurrence okay with a base case of
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+one okay so I'm just making the constant
+
+ align:start position:0%
+one okay so I'm just making the constant
+ 
+
+ align:start position:0%
+one okay so I'm just making the constant
+in here at the upper bound on the
+
+ align:start position:0%
+in here at the upper bound on the
+ 
+
+ align:start position:0%
+in here at the upper bound on the
+constant be explicit rather than
+
+ align:start position:0%
+constant be explicit rather than
+ 
+
+ align:start position:0%
+constant be explicit rather than
+implicit okay and the way you do a
+
+ align:start position:0%
+implicit okay and the way you do a
+ 
+
+ align:start position:0%
+implicit okay and the way you do a
+recursion tree is the following you
+
+ align:start position:0%
+recursion tree is the following you
+ 
+
+ align:start position:0%
+recursion tree is the following you
+start out by writing
+
+ align:start position:0%
+start out by writing
+ 
+
+ align:start position:0%
+start out by writing
+down the the left hand side of the
+
+ align:start position:0%
+down the the left hand side of the
+ 
+
+ align:start position:0%
+down the the left hand side of the
+currence and then what you do is you say
+
+ align:start position:0%
+currence and then what you do is you say
+ 
+
+ align:start position:0%
+currence and then what you do is you say
+well that's equal to and now let's write
+
+ align:start position:0%
+well that's equal to and now let's write
+ 
+
+ align:start position:0%
+well that's equal to and now let's write
+it as a tree I do c of n work plus now
+
+ align:start position:0%
+it as a tree I do c of n work plus now
+ 
+
+ align:start position:0%
+it as a tree I do c of n work plus now
+I'm going to have to do work on each of
+
+ align:start position:0%
+I'm going to have to do work on each of
+ 
+
+ align:start position:0%
+I'm going to have to do work on each of
+the My Two children T of N /2 and T of n
+
+ align:start position:0%
+the My Two children T of N /2 and T of n
+ 
+
+ align:start position:0%
+the My Two children T of N /2 and T of n
+/2 so if I sum up what's in here I get
+
+ align:start position:0%
+/2 so if I sum up what's in here I get
+ 
+
+ align:start position:0%
+/2 so if I sum up what's in here I get
+this because that's what the recurrence
+
+ align:start position:0%
+this because that's what the recurrence
+ 
+
+ align:start position:0%
+this because that's what the recurrence
+says T of n is 2 T of n/ 2 plus CN I
+
+ align:start position:0%
+says T of n is 2 T of n/ 2 plus CN I
+ 
+
+ align:start position:0%
+says T of n is 2 T of n/ 2 plus CN I
+have 2T of n /2 plus a
+
+ align:start position:0%
+have 2T of n /2 plus a
+ 
+
+ align:start position:0%
+have 2T of n /2 plus a
+CN then I do it again I say you have CN
+
+ align:start position:0%
+CN then I do it again I say you have CN
+ 
+
+ align:start position:0%
+CN then I do it again I say you have CN
+here I now have here CN /2 and here's CN
+
+ align:start position:0%
+here I now have here CN /2 and here's CN
+ 
+
+ align:start position:0%
+here I now have here CN /2 and here's CN
+over2
+
+ align:start position:0%
+over2
+ 
+
+ align:start position:0%
+over2
+and each of these now has a t of N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over4 and these each have a t of n over4
+
+ align:start position:0%
+over4 and these each have a t of n over4
+ 
+
+ align:start position:0%
+over4 and these each have a t of n over4
+this has a t of N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over4 and I keep doing
+
+ align:start position:0%
+over4 and I keep doing
+ 
+
+ align:start position:0%
+over4 and I keep doing
+that the dangerous dot dot
+
+ align:start position:0%
+that the dangerous dot dot
+ 
+
+ align:start position:0%
+that the dangerous dot dot
+dots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if I keep doing that I end up
+
+ align:start position:0%
+okay and if I keep doing that I end up
+ 
+
+ align:start position:0%
+okay and if I keep doing that I end up
+with it looking like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and I keep going down till I get to
+
+ align:start position:0%
+this and I keep going down till I get to
+ 
+
+ align:start position:0%
+this and I keep going down till I get to
+a leaf and a leaf I have essentially a t
+
+ align:start position:0%
+a leaf and a leaf I have essentially a t
+ 
+
+ align:start position:0%
+a leaf and a leaf I have essentially a t
+of one that's Theta 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay or t of and so the first question I
+
+ align:start position:0%
+okay or t of and so the first question I
+ 
+
+ align:start position:0%
+okay or t of and so the first question I
+ask here is what is the
+
+ align:start position:0%
+ask here is what is the
+ 
+
+ align:start position:0%
+ask here is what is the
+height of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree yeah L yeah it's log in it's
+
+ align:start position:0%
+tree yeah L yeah it's log in it's
+ 
+
+ align:start position:0%
+tree yeah L yeah it's log in it's
+actually um very close to exactly log in
+
+ align:start position:0%
+actually um very close to exactly log in
+ 
+
+ align:start position:0%
+actually um very close to exactly log in
+because I'm starting out with at the top
+
+ align:start position:0%
+because I'm starting out with at the top
+ 
+
+ align:start position:0%
+because I'm starting out with at the top
+with n and then I go to n/2 and n over4
+
+ align:start position:0%
+with n and then I go to n/2 and n over4
+ 
+
+ align:start position:0%
+with n and then I go to n/2 and n over4
+and all the way down till I get
+
+ align:start position:0%
+and all the way down till I get
+ 
+
+ align:start position:0%
+and all the way down till I get
+to one so the number of having of n till
+
+ align:start position:0%
+to one so the number of having of n till
+ 
+
+ align:start position:0%
+to one so the number of having of n till
+I get to one is log n so the height here
+
+ align:start position:0%
+I get to one is log n so the height here
+ 
+
+ align:start position:0%
+I get to one is log n so the height here
+is log
+
+ align:start position:0%
+is log
+ 
+
+ align:start position:0%
+is log
+n okay it's okay if it's constant times
+
+ align:start position:0%
+n okay it's okay if it's constant times
+ 
+
+ align:start position:0%
+n okay it's okay if it's constant times
+log n but it doesn't matter okay how
+
+ align:start position:0%
+log n but it doesn't matter okay how
+ 
+
+ align:start position:0%
+log n but it doesn't matter okay how
+many leaves are in this tree by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way how many leaves does this tree have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so the number of leaves is
+
+ align:start position:0%
+yeah yeah so the number of leaves is
+ 
+
+ align:start position:0%
+yeah yeah so the number of leaves is
+actually once again is actually pretty
+
+ align:start position:0%
+actually once again is actually pretty
+ 
+
+ align:start position:0%
+actually once again is actually pretty
+close it's actually
+
+ align:start position:0%
+close it's actually
+ 
+
+ align:start position:0%
+close it's actually
+n okay if you took it all the way down
+
+ align:start position:0%
+n okay if you took it all the way down
+ 
+
+ align:start position:0%
+n okay if you took it all the way down
+if you've made simple let's make some
+
+ align:start position:0%
+if you've made simple let's make some
+ 
+
+ align:start position:0%
+if you've made simple let's make some
+simplifying assumption N is a perfect
+
+ align:start position:0%
+simplifying assumption N is a perfect
+ 
+
+ align:start position:0%
+simplifying assumption N is a perfect
+power of
+
+ align:start position:0%
+power of
+ 
+
+ align:start position:0%
+power of
+two okay so it's an integer power of two
+
+ align:start position:0%
+two okay so it's an integer power of two
+ 
+
+ align:start position:0%
+two okay so it's an integer power of two
+then this is exactly log n to get down
+
+ align:start position:0%
+then this is exactly log n to get down
+ 
+
+ align:start position:0%
+then this is exactly log n to get down
+to T of one and then they're exactly n
+
+ align:start position:0%
+to T of one and then they're exactly n
+ 
+
+ align:start position:0%
+to T of one and then they're exactly n
+leaves okay because the number of leaves
+
+ align:start position:0%
+leaves okay because the number of leaves
+ 
+
+ align:start position:0%
+leaves okay because the number of leaves
+at the first here
+
+ align:start position:0%
+at the first here
+ 
+
+ align:start position:0%
+at the first here
+is number of nodes at this level is 1 2
+
+ align:start position:0%
+is number of nodes at this level is 1 2
+ 
+
+ align:start position:0%
+is number of nodes at this level is 1 2
+4 8 and if I in general go down height H
+
+ align:start position:0%
+4 8 and if I in general go down height H
+ 
+
+ align:start position:0%
+4 8 and if I in general go down height H
+I have two to the H leaves two to the
+
+ align:start position:0%
+I have two to the H leaves two to the
+ 
+
+ align:start position:0%
+I have two to the H leaves two to the
+log n that's just
+
+ align:start position:0%
+log n that's just
+ 
+
+ align:start position:0%
+log n that's just
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay okay so we're doing math here
+
+ align:start position:0%
+okay okay so we're doing math here
+ 
+
+ align:start position:0%
+okay okay so we're doing math here
+right okay so now let's do the figure
+
+ align:start position:0%
+right okay so now let's do the figure
+ 
+
+ align:start position:0%
+right okay so now let's do the figure
+out how much work if I look at adding up
+
+ align:start position:0%
+out how much work if I look at adding up
+ 
+
+ align:start position:0%
+out how much work if I look at adding up
+every everything in this tree I'm going
+
+ align:start position:0%
+every everything in this tree I'm going
+ 
+
+ align:start position:0%
+every everything in this tree I'm going
+to get T of
+
+ align:start position:0%
+to get T of
+ 
+
+ align:start position:0%
+to get T of
+n so let's add that up well let's add it
+
+ align:start position:0%
+n so let's add that up well let's add it
+ 
+
+ align:start position:0%
+n so let's add that up well let's add it
+up level by level how much do we have in
+
+ align:start position:0%
+up level by level how much do we have in
+ 
+
+ align:start position:0%
+up level by level how much do we have in
+the first level just
+
+ align:start position:0%
+the first level just
+ 
+
+ align:start position:0%
+the first level just
+CN if I add up the second level how much
+
+ align:start position:0%
+CN if I add up the second level how much
+ 
+
+ align:start position:0%
+CN if I add up the second level how much
+do I
+
+ align:start position:0%
+do I
+ 
+
+ align:start position:0%
+do I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+CN how about if I add up the third
+
+ align:start position:0%
+CN how about if I add up the third
+ 
+
+ align:start position:0%
+CN how about if I add up the third
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+CN how about if I add up all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leaves it's Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay it's actually not necessarily CN
+
+ align:start position:0%
+n okay it's actually not necessarily CN
+ 
+
+ align:start position:0%
+n okay it's actually not necessarily CN
+because the boundary case may have a
+
+ align:start position:0%
+because the boundary case may have a
+ 
+
+ align:start position:0%
+because the boundary case may have a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+okay so it's actually Theta n but CN all
+
+ align:start position:0%
+okay so it's actually Theta n but CN all
+ 
+
+ align:start position:0%
+okay so it's actually Theta n but CN all
+the way here so if I add up the total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amount that's equal to CN * log n cuz
+
+ align:start position:0%
+amount that's equal to CN * log n cuz
+ 
+
+ align:start position:0%
+amount that's equal to CN * log n cuz
+that's the height that's how many cn's I
+
+ align:start position:0%
+that's the height that's how many cn's I
+ 
+
+ align:start position:0%
+that's the height that's how many cn's I
+have here
+
+ align:start position:0%
+have here
+ 
+
+ align:start position:0%
+have here
+plus Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and this is a higher order term than
+
+ align:start position:0%
+n and this is a higher order term than
+ 
+
+ align:start position:0%
+n and this is a higher order term than
+this so This goes away get rid of the
+
+ align:start position:0%
+this so This goes away get rid of the
+ 
+
+ align:start position:0%
+this so This goes away get rid of the
+constants that's equal to Theta of n log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay and Theta of n log
+
+ align:start position:0%
+n okay and Theta of n log
+ 
+
+ align:start position:0%
+n okay and Theta of n log
+n is is ASM totically
+
+ align:start position:0%
+n is is ASM totically
+ 
+
+ align:start position:0%
+n is is ASM totically
+faster than Theta n
+
+ align:start position:0%
+faster than Theta n
+ 
+
+ align:start position:0%
+faster than Theta n
+2 so merge sort on a large enough input
+
+ align:start position:0%
+2 so merge sort on a large enough input
+ 
+
+ align:start position:0%
+2 so merge sort on a large enough input
+size is going to beat insertion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort okay merge sort is going to be a
+
+ align:start position:0%
+sort okay merge sort is going to be a
+ 
+
+ align:start position:0%
+sort okay merge sort is going to be a
+faster algorithm sorry you guys I didn't
+
+ align:start position:0%
+faster algorithm sorry you guys I didn't
+ 
+
+ align:start position:0%
+faster algorithm sorry you guys I didn't
+realize you couldn't see over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay should speak up can't see okay so
+
+ align:start position:0%
+okay should speak up can't see okay so
+ 
+
+ align:start position:0%
+okay should speak up can't see okay so
+this is a faster algorithm because Theta
+
+ align:start position:0%
+this is a faster algorithm because Theta
+ 
+
+ align:start position:0%
+this is a faster algorithm because Theta
+n log n grows more slowly than Theta n 2
+
+ align:start position:0%
+n log n grows more slowly than Theta n 2
+ 
+
+ align:start position:0%
+n log n grows more slowly than Theta n 2
+and merge sword asymptotically beats
+
+ align:start position:0%
+and merge sword asymptotically beats
+ 
+
+ align:start position:0%
+and merge sword asymptotically beats
+insertion sord so even if you ran
+
+ align:start position:0%
+insertion sord so even if you ran
+ 
+
+ align:start position:0%
+insertion sord so even if you ran
+insertion sword on a supercomputer
+
+ align:start position:0%
+insertion sword on a supercomputer
+ 
+
+ align:start position:0%
+insertion sword on a supercomputer
+somebody running on a
+
+ align:start position:0%
+somebody running on a
+ 
+
+ align:start position:0%
+somebody running on a
+PC with merge sort for a sufficiently
+
+ align:start position:0%
+PC with merge sort for a sufficiently
+ 
+
+ align:start position:0%
+PC with merge sort for a sufficiently
+large input clobber
+
+ align:start position:0%
+large input clobber
+ 
+
+ align:start position:0%
+large input clobber
+them okay cuz actually n squ is way
+
+ align:start position:0%
+them okay cuz actually n squ is way
+ 
+
+ align:start position:0%
+them okay cuz actually n squ is way
+bigger than n log n once you get the n's
+
+ align:start position:0%
+bigger than n log n once you get the n's
+ 
+
+ align:start position:0%
+bigger than n log n once you get the n's
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+okay and in practice merge sort tends to
+
+ align:start position:0%
+okay and in practice merge sort tends to
+ 
+
+ align:start position:0%
+okay and in practice merge sort tends to
+win here for n bigger than say 30 or so
+
+ align:start position:0%
+win here for n bigger than say 30 or so
+ 
+
+ align:start position:0%
+win here for n bigger than say 30 or so
+so if you have a very small input like
+
+ align:start position:0%
+so if you have a very small input like
+ 
+
+ align:start position:0%
+so if you have a very small input like
+30 elements insertion sort is a
+
+ align:start position:0%
+30 elements insertion sort is a
+ 
+
+ align:start position:0%
+30 elements insertion sort is a
+perfectly decent sort to use okay but
+
+ align:start position:0%
+perfectly decent sort to use okay but
+ 
+
+ align:start position:0%
+perfectly decent sort to use okay but
+merge sword is going to be a lot
+
+ align:start position:0%
+merge sword is going to be a lot
+ 
+
+ align:start position:0%
+merge sword is going to be a lot
+faster for even for something that's you
+
+ align:start position:0%
+faster for even for something that's you
+ 
+
+ align:start position:0%
+faster for even for something that's you
+know only a few dozen
+
+ align:start position:0%
+know only a few dozen
+ 
+
+ align:start position:0%
+know only a few dozen
+elements okay it's going to actually be
+
+ align:start position:0%
+elements okay it's going to actually be
+ 
+
+ align:start position:0%
+elements okay it's going to actually be
+a faster
+
+ align:start position:0%
+a faster
+ 
+
+ align:start position:0%
+a faster
+algorithm okay so that's sort of the
+
+ align:start position:0%
+algorithm okay so that's sort of the
+ 
+
+ align:start position:0%
+algorithm okay so that's sort of the
+lessons Okay so remember that uh to get
+
+ align:start position:0%
+lessons Okay so remember that uh to get
+ 
+
+ align:start position:0%
+lessons Okay so remember that uh to get
+your resit assignments and attend
+
+ align:start position:0%
+your resit assignments and attend
+ 
+
+ align:start position:0%
+your resit assignments and attend
+recitation on Friday cuz we're going to
+
+ align:start position:0%
+recitation on Friday cuz we're going to
+ 
+
+ align:start position:0%
+recitation on Friday cuz we're going to
+be going through a bunch of the things
+
+ align:start position:0%
+be going through a bunch of the things
+ 
+
+ align:start position:0%
+be going through a bunch of the things
+that I've left on the table here and see
+
+ align:start position:0%
+that I've left on the table here and see
+ 
+
+ align:start position:0%
+that I've left on the table here and see
+you next Monday
\ No newline at end of file
diff --git a/JZRusgbh-lA.txt b/JZRusgbh-lA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b3d0573ce96a4df348c8252dd344745cbfb6cb17
--- /dev/null
+++ b/JZRusgbh-lA.txt
@@ -0,0 +1,6627 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hi thanks for inviting me
+
+ align:start position:0%
+ocw.mit.edu hi thanks for inviting me
+ 
+
+ align:start position:0%
+ocw.mit.edu hi thanks for inviting me
+uh well uh it's been 20 years since I've
+
+ align:start position:0%
+uh well uh it's been 20 years since I've
+ 
+
+ align:start position:0%
+uh well uh it's been 20 years since I've
+been on the campus and and I mean I I
+
+ align:start position:0%
+been on the campus and and I mean I I
+ 
+
+ align:start position:0%
+been on the campus and and I mean I I
+see I would have been in your place I
+
+ align:start position:0%
+see I would have been in your place I
+ 
+
+ align:start position:0%
+see I would have been in your place I
+mean just 20 years back and I know the
+
+ align:start position:0%
+mean just 20 years back and I know the
+ 
+
+ align:start position:0%
+mean just 20 years back and I know the
+the problems that that that history
+
+ align:start position:0%
+the problems that that that history
+ 
+
+ align:start position:0%
+the problems that that that history
+teachers actually face when teaching
+
+ align:start position:0%
+teachers actually face when teaching
+ 
+
+ align:start position:0%
+teachers actually face when teaching
+history to undergrads you know like you
+
+ align:start position:0%
+history to undergrads you know like you
+ 
+
+ align:start position:0%
+history to undergrads you know like you
+all and uh I thought um I'd I'd uh I'd
+
+ align:start position:0%
+all and uh I thought um I'd I'd uh I'd
+ 
+
+ align:start position:0%
+all and uh I thought um I'd I'd uh I'd
+propose a lecture a special lecture for
+
+ align:start position:0%
+propose a lecture a special lecture for
+ 
+
+ align:start position:0%
+propose a lecture a special lecture for
+you all just to kind of give a global
+
+ align:start position:0%
+you all just to kind of give a global
+ 
+
+ align:start position:0%
+you all just to kind of give a global
+perspective on things uh usually you're
+
+ align:start position:0%
+perspective on things uh usually you're
+ 
+
+ align:start position:0%
+perspective on things uh usually you're
+taught history as
+
+ align:start position:0%
+taught history as
+ 
+
+ align:start position:0%
+taught history as
+uh some people some buildings some
+
+ align:start position:0%
+uh some people some buildings some
+ 
+
+ align:start position:0%
+uh some people some buildings some
+places and and uh somehow the
+
+ align:start position:0%
+places and and uh somehow the
+ 
+
+ align:start position:0%
+places and and uh somehow the
+interconnections are just lost and uh
+
+ align:start position:0%
+interconnections are just lost and uh
+ 
+
+ align:start position:0%
+interconnections are just lost and uh
+um I can tell you how some of the maps
+
+ align:start position:0%
+um I can tell you how some of the maps
+ 
+
+ align:start position:0%
+um I can tell you how some of the maps
+would look is uh to your left is a map
+
+ align:start position:0%
+would look is uh to your left is a map
+ 
+
+ align:start position:0%
+would look is uh to your left is a map
+of Iran and these are how National
+
+ align:start position:0%
+of Iran and these are how National
+ 
+
+ align:start position:0%
+of Iran and these are how National
+History is actually written what is
+
+ align:start position:0%
+History is actually written what is
+ 
+
+ align:start position:0%
+History is actually written what is
+outside of the borders is a complete
+
+ align:start position:0%
+outside of the borders is a complete
+ 
+
+ align:start position:0%
+outside of the borders is a complete
+abys it's black and uh to your right is
+
+ align:start position:0%
+abys it's black and uh to your right is
+ 
+
+ align:start position:0%
+abys it's black and uh to your right is
+is what you would call like Rel
+
+ align:start position:0%
+is what you would call like Rel
+ 
+
+ align:start position:0%
+is what you would call like Rel
+religious history is like an expansion
+
+ align:start position:0%
+religious history is like an expansion
+ 
+
+ align:start position:0%
+religious history is like an expansion
+of of domains um political domains and
+
+ align:start position:0%
+of of domains um political domains and
+ 
+
+ align:start position:0%
+of of domains um political domains and
+uh you have no idea of what is happening
+
+ align:start position:0%
+uh you have no idea of what is happening
+ 
+
+ align:start position:0%
+uh you have no idea of what is happening
+outside of this again it's it's black um
+
+ align:start position:0%
+outside of this again it's it's black um
+ 
+
+ align:start position:0%
+outside of this again it's it's black um
+we get some clues in in um in a book by
+
+ align:start position:0%
+we get some clues in in um in a book by
+ 
+
+ align:start position:0%
+we get some clues in in um in a book by
+U Mark kuransky called salt world
+
+ align:start position:0%
+U Mark kuransky called salt world
+ 
+
+ align:start position:0%
+U Mark kuransky called salt world
+history it is a book as the name
+
+ align:start position:0%
+history it is a book as the name
+ 
+
+ align:start position:0%
+history it is a book as the name
+suggests completely about salt from the
+
+ align:start position:0%
+suggests completely about salt from the
+ 
+
+ align:start position:0%
+suggests completely about salt from the
+preservation of mummies and the pickling
+
+ align:start position:0%
+preservation of mummies and the pickling
+ 
+
+ align:start position:0%
+preservation of mummies and the pickling
+of vegetables in ancient Egypt to
+
+ align:start position:0%
+of vegetables in ancient Egypt to
+ 
+
+ align:start position:0%
+of vegetables in ancient Egypt to
+Gandhi's Salt March in
+
+ align:start position:0%
+Gandhi's Salt March in
+ 
+
+ align:start position:0%
+Gandhi's Salt March in
+Gujarat as a demonstration against
+
+ align:start position:0%
+Gujarat as a demonstration against
+ 
+
+ align:start position:0%
+Gujarat as a demonstration against
+Colonial taxes it is only about Salt the
+
+ align:start position:0%
+Colonial taxes it is only about Salt the
+ 
+
+ align:start position:0%
+Colonial taxes it is only about Salt the
+anecdotes are fun to read and it
+
+ align:start position:0%
+anecdotes are fun to read and it
+ 
+
+ align:start position:0%
+anecdotes are fun to read and it
+successfully makes connections across
+
+ align:start position:0%
+successfully makes connections across
+ 
+
+ align:start position:0%
+successfully makes connections across
+cultures just by telling stories about
+
+ align:start position:0%
+cultures just by telling stories about
+ 
+
+ align:start position:0%
+cultures just by telling stories about
+salt uh the world seems a much smaller
+
+ align:start position:0%
+salt uh the world seems a much smaller
+ 
+
+ align:start position:0%
+salt uh the world seems a much smaller
+space uh people seem more alike um their
+
+ align:start position:0%
+space uh people seem more alike um their
+ 
+
+ align:start position:0%
+space uh people seem more alike um their
+physiological and transcendental
+
+ align:start position:0%
+physiological and transcendental
+ 
+
+ align:start position:0%
+physiological and transcendental
+connections with salt are no longer
+
+ align:start position:0%
+connections with salt are no longer
+ 
+
+ align:start position:0%
+connections with salt are no longer
+local but enmeshed in the economic
+
+ align:start position:0%
+local but enmeshed in the economic
+ 
+
+ align:start position:0%
+local but enmeshed in the economic
+scientific political religious and
+
+ align:start position:0%
+scientific political religious and
+ 
+
+ align:start position:0%
+scientific political religious and
+culinary occupations of the world in
+
+ align:start position:0%
+culinary occupations of the world in
+ 
+
+ align:start position:0%
+culinary occupations of the world in
+short uh it's making connections through
+
+ align:start position:0%
+short uh it's making connections through
+ 
+
+ align:start position:0%
+short uh it's making connections through
+anecdotes maybe but it's making
+
+ align:start position:0%
+anecdotes maybe but it's making
+ 
+
+ align:start position:0%
+anecdotes maybe but it's making
+connections um to the right is a global
+
+ align:start position:0%
+connections um to the right is a global
+ 
+
+ align:start position:0%
+connections um to the right is a global
+history of architecture by ching jazbeck
+
+ align:start position:0%
+history of architecture by ching jazbeck
+ 
+
+ align:start position:0%
+history of architecture by ching jazbeck
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+prakash uh which also focuses on on
+
+ align:start position:0%
+prakash uh which also focuses on on
+ 
+
+ align:start position:0%
+prakash uh which also focuses on on
+seeing connections tensions and
+
+ align:start position:0%
+seeing connections tensions and
+ 
+
+ align:start position:0%
+seeing connections tensions and
+associations in a similar way
+
+ align:start position:0%
+associations in a similar way
+ 
+
+ align:start position:0%
+associations in a similar way
+uh they they call it synchrony so when
+
+ align:start position:0%
+uh they they call it synchrony so when
+ 
+
+ align:start position:0%
+uh they they call it synchrony so when
+things actually happen simultaneously
+
+ align:start position:0%
+things actually happen simultaneously
+ 
+
+ align:start position:0%
+things actually happen simultaneously
+around the world uh it's not just a
+
+ align:start position:0%
+around the world uh it's not just a
+ 
+
+ align:start position:0%
+around the world uh it's not just a
+matter of coincidence it's part of a a
+
+ align:start position:0%
+matter of coincidence it's part of a a
+ 
+
+ align:start position:0%
+matter of coincidence it's part of a a
+larger scheme of architectural
+
+ align:start position:0%
+larger scheme of architectural
+ 
+
+ align:start position:0%
+larger scheme of architectural
+development um and um that that somehow
+
+ align:start position:0%
+development um and um that that somehow
+ 
+
+ align:start position:0%
+development um and um that that somehow
+U hints towards a much a a better way of
+
+ align:start position:0%
+U hints towards a much a a better way of
+ 
+
+ align:start position:0%
+U hints towards a much a a better way of
+looking at history uh beyond the
+
+ align:start position:0%
+looking at history uh beyond the
+ 
+
+ align:start position:0%
+looking at history uh beyond the
+stigmatizing uh uh discourses on on on
+
+ align:start position:0%
+stigmatizing uh uh discourses on on on
+ 
+
+ align:start position:0%
+stigmatizing uh uh discourses on on on
+on Nations and things like
+
+ align:start position:0%
+on Nations and things like
+ 
+
+ align:start position:0%
+on Nations and things like
+that um so yeah you'll be wondering I
+
+ align:start position:0%
+that um so yeah you'll be wondering I
+ 
+
+ align:start position:0%
+that um so yeah you'll be wondering I
+mean I'm going to spend 40 minutes
+
+ align:start position:0%
+mean I'm going to spend 40 minutes
+ 
+
+ align:start position:0%
+mean I'm going to spend 40 minutes
+talking about breaks and uh well I'll
+
+ align:start position:0%
+talking about breaks and uh well I'll
+ 
+
+ align:start position:0%
+talking about breaks and uh well I'll
+just like to justify that uh the the
+
+ align:start position:0%
+just like to justify that uh the the
+ 
+
+ align:start position:0%
+just like to justify that uh the the
+break is a global thing uh it's surely
+
+ align:start position:0%
+break is a global thing uh it's surely
+ 
+
+ align:start position:0%
+break is a global thing uh it's surely
+the most common Building Material in the
+
+ align:start position:0%
+the most common Building Material in the
+ 
+
+ align:start position:0%
+the most common Building Material in the
+world and since almost every
+
+ align:start position:0%
+world and since almost every
+ 
+
+ align:start position:0%
+world and since almost every
+geographical region in the world has
+
+ align:start position:0%
+geographical region in the world has
+ 
+
+ align:start position:0%
+geographical region in the world has
+adopted it during some phase in history
+
+ align:start position:0%
+adopted it during some phase in history
+ 
+
+ align:start position:0%
+adopted it during some phase in history
+uh it promises to make a great global
+
+ align:start position:0%
+uh it promises to make a great global
+ 
+
+ align:start position:0%
+uh it promises to make a great global
+history uh so just like salt it it has a
+
+ align:start position:0%
+history uh so just like salt it it has a
+ 
+
+ align:start position:0%
+history uh so just like salt it it has a
+kind of a universal use and uh I will
+
+ align:start position:0%
+kind of a universal use and uh I will
+ 
+
+ align:start position:0%
+kind of a universal use and uh I will
+talk about bricks and if other things
+
+ align:start position:0%
+talk about bricks and if other things
+ 
+
+ align:start position:0%
+talk about bricks and if other things
+come up we can talk about those
+
+ align:start position:0%
+come up we can talk about those
+ 
+
+ align:start position:0%
+come up we can talk about those
+so H obviously I'm not the first um
+
+ align:start position:0%
+so H obviously I'm not the first um
+ 
+
+ align:start position:0%
+so H obviously I'm not the first um
+brick of world history by James WP
+
+ align:start position:0%
+brick of world history by James WP
+ 
+
+ align:start position:0%
+brick of world history by James WP
+Campbell provides great insights into
+
+ align:start position:0%
+Campbell provides great insights into
+ 
+
+ align:start position:0%
+Campbell provides great insights into
+the use of brick in all its forms mud
+
+ align:start position:0%
+the use of brick in all its forms mud
+ 
+
+ align:start position:0%
+the use of brick in all its forms mud
+bricks baked bricks glazed bricks
+
+ align:start position:0%
+bricks baked bricks glazed bricks
+ 
+
+ align:start position:0%
+bricks baked bricks glazed bricks
+terracotta shape bricks as well as brick
+
+ align:start position:0%
+terracotta shape bricks as well as brick
+ 
+
+ align:start position:0%
+terracotta shape bricks as well as brick
+laying techniques and brick production
+
+ align:start position:0%
+laying techniques and brick production
+ 
+
+ align:start position:0%
+laying techniques and brick production
+throughout history of course uh he's an
+
+ align:start position:0%
+throughout history of course uh he's an
+ 
+
+ align:start position:0%
+throughout history of course uh he's an
+Englishman and he he kind of climaxes on
+
+ align:start position:0%
+Englishman and he he kind of climaxes on
+ 
+
+ align:start position:0%
+Englishman and he he kind of climaxes on
+the Renaissance so uh in some way I'd
+
+ align:start position:0%
+the Renaissance so uh in some way I'd
+ 
+
+ align:start position:0%
+the Renaissance so uh in some way I'd
+like to extend his study to to kind of
+
+ align:start position:0%
+like to extend his study to to kind of
+ 
+
+ align:start position:0%
+like to extend his study to to kind of
+incorporate things that happen maybe in
+
+ align:start position:0%
+incorporate things that happen maybe in
+ 
+
+ align:start position:0%
+incorporate things that happen maybe in
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+China
+
+ align:start position:0%
+China
+ 
+
+ align:start position:0%
+China
+um well I kind of needed some Authority
+
+ align:start position:0%
+um well I kind of needed some Authority
+ 
+
+ align:start position:0%
+um well I kind of needed some Authority
+on my introduction and uh who better
+
+ align:start position:0%
+on my introduction and uh who better
+ 
+
+ align:start position:0%
+on my introduction and uh who better
+than Lin um he's well known for uh um
+
+ align:start position:0%
+than Lin um he's well known for uh um
+ 
+
+ align:start position:0%
+than Lin um he's well known for uh um
+building amazing brick houses in in in
+
+ align:start position:0%
+building amazing brick houses in in in
+ 
+
+ align:start position:0%
+building amazing brick houses in in in
+England and he also happened to build
+
+ align:start position:0%
+England and he also happened to build
+ 
+
+ align:start position:0%
+England and he also happened to build
+the the imperial capital complex in
+
+ align:start position:0%
+the the imperial capital complex in
+ 
+
+ align:start position:0%
+the the imperial capital complex in
+Delhi uh a short walk around massav
+
+ align:start position:0%
+Delhi uh a short walk around massav
+ 
+
+ align:start position:0%
+Delhi uh a short walk around massav
+would uh would kind of kind of start you
+
+ align:start position:0%
+would uh would kind of kind of start you
+ 
+
+ align:start position:0%
+would uh would kind of kind of start you
+off on this journey and uh I think
+
+ align:start position:0%
+off on this journey and uh I think
+ 
+
+ align:start position:0%
+off on this journey and uh I think
+uh I I don't want to I don't want to
+
+ align:start position:0%
+uh I I don't want to I don't want to
+ 
+
+ align:start position:0%
+uh I I don't want to I don't want to
+point out the details right now but if
+
+ align:start position:0%
+point out the details right now but if
+ 
+
+ align:start position:0%
+point out the details right now but if
+you can just start keeping some details
+
+ align:start position:0%
+you can just start keeping some details
+ 
+
+ align:start position:0%
+you can just start keeping some details
+in mind you'll you'll start making
+
+ align:start position:0%
+in mind you'll you'll start making
+ 
+
+ align:start position:0%
+in mind you'll you'll start making
+connections through the lecture
+
+ align:start position:0%
+connections through the lecture
+ 
+
+ align:start position:0%
+connections through the lecture
+so uh this is the ashown house and it's
+
+ align:start position:0%
+so uh this is the ashown house and it's
+ 
+
+ align:start position:0%
+so uh this is the ashown house and it's
+the lobby
+
+ align:start position:0%
+the lobby
+ 
+
+ align:start position:0%
+the lobby
+um uh I remember 20 years back I used to
+
+ align:start position:0%
+um uh I remember 20 years back I used to
+ 
+
+ align:start position:0%
+um uh I remember 20 years back I used to
+uh practice my mountain climbing on this
+
+ align:start position:0%
+uh practice my mountain climbing on this
+ 
+
+ align:start position:0%
+uh practice my mountain climbing on this
+wall and uh these are basically these
+
+ align:start position:0%
+wall and uh these are basically these
+ 
+
+ align:start position:0%
+wall and uh these are basically these
+deformed bricks that are kind of
+
+ align:start position:0%
+deformed bricks that are kind of
+ 
+
+ align:start position:0%
+deformed bricks that are kind of
+embedded into this wall and uh um of
+
+ align:start position:0%
+embedded into this wall and uh um of
+ 
+
+ align:start position:0%
+embedded into this wall and uh um of
+course the inside two are is extremely
+
+ align:start position:0%
+course the inside two are is extremely
+ 
+
+ align:start position:0%
+course the inside two are is extremely
+beautiful um this is byos
+
+ align:start position:0%
+beautiful um this is byos
+ 
+
+ align:start position:0%
+beautiful um this is byos
+rnan
+
+ align:start position:0%
+rnan
+ 
+
+ align:start position:0%
+rnan
+uh so you can start
+
+ align:start position:0%
+uh so you can start
+ 
+
+ align:start position:0%
+uh so you can start
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+patterns and of course this requires
+
+ align:start position:0%
+patterns and of course this requires
+ 
+
+ align:start position:0%
+patterns and of course this requires
+this is called the hering bone pattern
+
+ align:start position:0%
+this is called the hering bone pattern
+ 
+
+ align:start position:0%
+this is called the hering bone pattern
+and this requires a lot of skill
+
+ align:start position:0%
+and this requires a lot of skill
+ 
+
+ align:start position:0%
+and this requires a lot of skill
+obviously this one has kind of caved in
+
+ align:start position:0%
+obviously this one has kind of caved in
+ 
+
+ align:start position:0%
+obviously this one has kind of caved in
+in some way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh this is Hi-Fi Pizza you wouldn't
+
+ align:start position:0%
+um uh this is Hi-Fi Pizza you wouldn't
+ 
+
+ align:start position:0%
+um uh this is Hi-Fi Pizza you wouldn't
+have noticed the building above but it's
+
+ align:start position:0%
+have noticed the building above but it's
+ 
+
+ align:start position:0%
+have noticed the building above but it's
+it's quite remarkable it's got some
+
+ align:start position:0%
+it's quite remarkable it's got some
+ 
+
+ align:start position:0%
+it's quite remarkable it's got some
+pretty beautiful details there and
+
+ align:start position:0%
+pretty beautiful details there and
+ 
+
+ align:start position:0%
+pretty beautiful details there and
+uh keep these in mind for sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is this is Terra Cotta uh I'm
+
+ align:start position:0%
+so this is this is Terra Cotta uh I'm
+ 
+
+ align:start position:0%
+so this is this is Terra Cotta uh I'm
+I'm wondering uh if if you can start
+
+ align:start position:0%
+I'm wondering uh if if you can start
+ 
+
+ align:start position:0%
+I'm wondering uh if if you can start
+writing back I mean writing a history
+
+ align:start position:0%
+writing back I mean writing a history
+ 
+
+ align:start position:0%
+writing back I mean writing a history
+for this I mean how how did things get
+
+ align:start position:0%
+for this I mean how how did things get
+ 
+
+ align:start position:0%
+for this I mean how how did things get
+here U some kind of a movement of
+
+ align:start position:0%
+here U some kind of a movement of
+ 
+
+ align:start position:0%
+here U some kind of a movement of
+technology and I think that's what
+
+ align:start position:0%
+technology and I think that's what
+ 
+
+ align:start position:0%
+technology and I think that's what
+that's what I'm more interested in in in
+
+ align:start position:0%
+that's what I'm more interested in in in
+ 
+
+ align:start position:0%
+that's what I'm more interested in in in
+kind of sharing this kind of a global
+
+ align:start position:0%
+kind of sharing this kind of a global
+ 
+
+ align:start position:0%
+kind of sharing this kind of a global
+history with you so
+
+ align:start position:0%
+history with you so
+ 
+
+ align:start position:0%
+history with you so
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so what I'll what I'll start with
+
+ align:start position:0%
+um so what I'll what I'll start with
+ 
+
+ align:start position:0%
+um so what I'll what I'll start with
+is the first brick uh these were
+
+ align:start position:0%
+is the first brick uh these were
+ 
+
+ align:start position:0%
+is the first brick uh these were
+essentially hand molded and uh they were
+
+ align:start position:0%
+essentially hand molded and uh they were
+ 
+
+ align:start position:0%
+essentially hand molded and uh they were
+just mud and water and uh they kind of
+
+ align:start position:0%
+just mud and water and uh they kind of
+ 
+
+ align:start position:0%
+just mud and water and uh they kind of
+resemble these U pieces of dough and U
+
+ align:start position:0%
+resemble these U pieces of dough and U
+ 
+
+ align:start position:0%
+resemble these U pieces of dough and U
+the the ones at the at the bottom
+
+ align:start position:0%
+the the ones at the at the bottom
+ 
+
+ align:start position:0%
+the the ones at the at the bottom
+actually have some finger Impressions U
+
+ align:start position:0%
+actually have some finger Impressions U
+ 
+
+ align:start position:0%
+actually have some finger Impressions U
+marked in it um
+
+ align:start position:0%
+marked in it um
+ 
+
+ align:start position:0%
+marked in it um
+why why do you make bricks why not just
+
+ align:start position:0%
+why why do you make bricks why not just
+ 
+
+ align:start position:0%
+why why do you make bricks why not just
+uh construct in mud uh there's there are
+
+ align:start position:0%
+uh construct in mud uh there's there are
+ 
+
+ align:start position:0%
+uh construct in mud uh there's there are
+some reasons uh the first reason and
+
+ align:start position:0%
+some reasons uh the first reason and
+ 
+
+ align:start position:0%
+some reasons uh the first reason and
+probably the most important one would be
+
+ align:start position:0%
+probably the most important one would be
+ 
+
+ align:start position:0%
+probably the most important one would be
+transport is that it's tougher to
+
+ align:start position:0%
+transport is that it's tougher to
+ 
+
+ align:start position:0%
+transport is that it's tougher to
+transport mud than transport brick uh in
+
+ align:start position:0%
+transport mud than transport brick uh in
+ 
+
+ align:start position:0%
+transport mud than transport brick uh in
+uh as far as uh you need some kind of
+
+ align:start position:0%
+uh as far as uh you need some kind of
+ 
+
+ align:start position:0%
+uh as far as uh you need some kind of
+formwork to actually fill mud in and
+
+ align:start position:0%
+formwork to actually fill mud in and
+ 
+
+ align:start position:0%
+formwork to actually fill mud in and
+then compacted brick of course s kind of
+
+ align:start position:0%
+then compacted brick of course s kind of
+ 
+
+ align:start position:0%
+then compacted brick of course s kind of
+made if especially like this uh the
+
+ align:start position:0%
+made if especially like this uh the
+ 
+
+ align:start position:0%
+made if especially like this uh the
+first bricks were actually found in
+
+ align:start position:0%
+first bricks were actually found in
+ 
+
+ align:start position:0%
+first bricks were actually found in
+neolithic Jericho 8,300 BC so this is
+
+ align:start position:0%
+neolithic Jericho 8,300 BC so this is
+ 
+
+ align:start position:0%
+neolithic Jericho 8,300 BC so this is
+old um I moved to the river valley
+
+ align:start position:0%
+old um I moved to the river valley
+ 
+
+ align:start position:0%
+old um I moved to the river valley
+civilizations and uh their use of of
+
+ align:start position:0%
+civilizations and uh their use of of
+ 
+
+ align:start position:0%
+civilizations and uh their use of of
+brick I I would Define brick in its
+
+ align:start position:0%
+brick I I would Define brick in its
+ 
+
+ align:start position:0%
+brick I I would Define brick in its
+widest sense
+
+ align:start position:0%
+widest sense
+ 
+
+ align:start position:0%
+widest sense
+incorporating pottery and Terra Cotta
+
+ align:start position:0%
+incorporating pottery and Terra Cotta
+ 
+
+ align:start position:0%
+incorporating pottery and Terra Cotta
+and I mean taking in as much as things
+
+ align:start position:0%
+and I mean taking in as much as things
+ 
+
+ align:start position:0%
+and I mean taking in as much as things
+that are made of mud and then baked or
+
+ align:start position:0%
+that are made of mud and then baked or
+ 
+
+ align:start position:0%
+that are made of mud and then baked or
+sundried or or just molded in hand
+
+ align:start position:0%
+sundried or or just molded in hand
+ 
+
+ align:start position:0%
+sundried or or just molded in hand
+uh these yellow patches are
+
+ align:start position:0%
+uh these yellow patches are
+ 
+
+ align:start position:0%
+uh these yellow patches are
+uh I I don't they didn't settle here to
+
+ align:start position:0%
+uh I I don't they didn't settle here to
+ 
+
+ align:start position:0%
+uh I I don't they didn't settle here to
+make bricks I want to make that very
+
+ align:start position:0%
+make bricks I want to make that very
+ 
+
+ align:start position:0%
+make bricks I want to make that very
+clear so the river valley had other
+
+ align:start position:0%
+clear so the river valley had other
+ 
+
+ align:start position:0%
+clear so the river valley had other
+things to offer it wasn't the bricks and
+
+ align:start position:0%
+things to offer it wasn't the bricks and
+ 
+
+ align:start position:0%
+things to offer it wasn't the bricks and
+of course uh the banpo is uh I'm sure
+
+ align:start position:0%
+of course uh the banpo is uh I'm sure
+ 
+
+ align:start position:0%
+of course uh the banpo is uh I'm sure
+kind of surprising it normally doesn't
+
+ align:start position:0%
+kind of surprising it normally doesn't
+ 
+
+ align:start position:0%
+kind of surprising it normally doesn't
+come under the the the Genesis of brick
+
+ align:start position:0%
+come under the the the Genesis of brick
+ 
+
+ align:start position:0%
+come under the the the Genesis of brick
+and uh this was interesting and uh it it
+
+ align:start position:0%
+and uh this was interesting and uh it it
+ 
+
+ align:start position:0%
+and uh this was interesting and uh it it
+it had one of the most advanced skills
+
+ align:start position:0%
+it had one of the most advanced skills
+ 
+
+ align:start position:0%
+it had one of the most advanced skills
+at for the time and uh I I'd like you
+
+ align:start position:0%
+at for the time and uh I I'd like you
+ 
+
+ align:start position:0%
+at for the time and uh I I'd like you
+all to keep that in mind for the rest of
+
+ align:start position:0%
+all to keep that in mind for the rest of
+ 
+
+ align:start position:0%
+all to keep that in mind for the rest of
+the lecture because somehow uh China
+
+ align:start position:0%
+the lecture because somehow uh China
+ 
+
+ align:start position:0%
+the lecture because somehow uh China
+keeps producing um very interesting
+
+ align:start position:0%
+keeps producing um very interesting
+ 
+
+ align:start position:0%
+keeps producing um very interesting
+baked products uh
+
+ align:start position:0%
+baked products uh
+ 
+
+ align:start position:0%
+baked products uh
+well fired uh throughout history U and
+
+ align:start position:0%
+well fired uh throughout history U and
+ 
+
+ align:start position:0%
+well fired uh throughout history U and
+it kind of stays a little aloof from
+
+ align:start position:0%
+it kind of stays a little aloof from
+ 
+
+ align:start position:0%
+it kind of stays a little aloof from
+from this kind of a mass that will keep
+
+ align:start position:0%
+from this kind of a mass that will keep
+ 
+
+ align:start position:0%
+from this kind of a mass that will keep
+growing throughout the
+
+ align:start position:0%
+growing throughout the
+ 
+
+ align:start position:0%
+growing throughout the
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+um 1500 BC uh uh the the image on top is
+
+ align:start position:0%
+um 1500 BC uh uh the the image on top is
+ 
+
+ align:start position:0%
+um 1500 BC uh uh the the image on top is
+is of a wall painting and uh it shows
+
+ align:start position:0%
+is of a wall painting and uh it shows
+ 
+
+ align:start position:0%
+is of a wall painting and uh it shows
+the process of the brick making and uh
+
+ align:start position:0%
+the process of the brick making and uh
+ 
+
+ align:start position:0%
+the process of the brick making and uh
+they obviously used U they kind of
+
+ align:start position:0%
+they obviously used U they kind of
+ 
+
+ align:start position:0%
+they obviously used U they kind of
+evolved into using molds for uh for
+
+ align:start position:0%
+evolved into using molds for uh for
+ 
+
+ align:start position:0%
+evolved into using molds for uh for
+their uh for the bricks and these were
+
+ align:start position:0%
+their uh for the bricks and these were
+ 
+
+ align:start position:0%
+their uh for the bricks and these were
+sunr so they had mud water and grass and
+
+ align:start position:0%
+sunr so they had mud water and grass and
+ 
+
+ align:start position:0%
+sunr so they had mud water and grass and
+they kind of mix them up and
+
+ align:start position:0%
+they kind of mix them up and
+ 
+
+ align:start position:0%
+they kind of mix them up and
+uh and and uh set them in in what you
+
+ align:start position:0%
+uh and and uh set them in in what you
+ 
+
+ align:start position:0%
+uh and and uh set them in in what you
+see as as the mold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is uh so
+
+ align:start position:0%
+um this is uh so
+ 
+
+ align:start position:0%
+um this is uh so
+why don't I just look at this this would
+
+ align:start position:0%
+why don't I just look at this this would
+ 
+
+ align:start position:0%
+why don't I just look at this this would
+be the Mesopotamian angle
+
+ align:start position:0%
+be the Mesopotamian angle
+ 
+
+ align:start position:0%
+be the Mesopotamian angle
+so uh they had they developed four
+
+ align:start position:0%
+so uh they had they developed four
+ 
+
+ align:start position:0%
+so uh they had they developed four
+different kinds of bricks in this time
+
+ align:start position:0%
+different kinds of bricks in this time
+ 
+
+ align:start position:0%
+different kinds of bricks in this time
+and uh they
+
+ align:start position:0%
+and uh they
+ 
+
+ align:start position:0%
+and uh they
+were this is a zigurat so they were
+
+ align:start position:0%
+were this is a zigurat so they were
+ 
+
+ align:start position:0%
+were this is a zigurat so they were
+basically mounds of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bricks but they also managed to develop
+
+ align:start position:0%
+bricks but they also managed to develop
+ 
+
+ align:start position:0%
+bricks but they also managed to develop
+molded braks now these these would
+
+ align:start position:0%
+molded braks now these these would
+ 
+
+ align:start position:0%
+molded braks now these these would
+actually be be
+
+ align:start position:0%
+actually be be
+ 
+
+ align:start position:0%
+actually be be
+uh um constructed on on a large scale
+
+ align:start position:0%
+uh um constructed on on a large scale
+ 
+
+ align:start position:0%
+uh um constructed on on a large scale
+there' be set up um on on on the floor
+
+ align:start position:0%
+there' be set up um on on on the floor
+ 
+
+ align:start position:0%
+there' be set up um on on on the floor
+they actually designed as as a complete
+
+ align:start position:0%
+they actually designed as as a complete
+ 
+
+ align:start position:0%
+they actually designed as as a complete
+as a complete uh panel and then fired
+
+ align:start position:0%
+as a complete uh panel and then fired
+ 
+
+ align:start position:0%
+as a complete uh panel and then fired
+separately so it it is quite an
+
+ align:start position:0%
+separately so it it is quite an
+ 
+
+ align:start position:0%
+separately so it it is quite an
+elaborate uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method um this is again another
+
+ align:start position:0%
+method um this is again another
+ 
+
+ align:start position:0%
+method um this is again another
+settlement between Iran and
+
+ align:start position:0%
+settlement between Iran and
+ 
+
+ align:start position:0%
+settlement between Iran and
+Afghanistan uh
+
+ align:start position:0%
+Afghanistan uh
+ 
+
+ align:start position:0%
+Afghanistan uh
+uh there can also be patterns made in in
+
+ align:start position:0%
+uh there can also be patterns made in in
+ 
+
+ align:start position:0%
+uh there can also be patterns made in in
+mud bricks and uh this one of course is
+
+ align:start position:0%
+mud bricks and uh this one of course is
+ 
+
+ align:start position:0%
+mud bricks and uh this one of course is
+uh is something related to the palm tree
+
+ align:start position:0%
+uh is something related to the palm tree
+ 
+
+ align:start position:0%
+uh is something related to the palm tree
+they probably uh had some kind of an
+
+ align:start position:0%
+they probably uh had some kind of an
+ 
+
+ align:start position:0%
+they probably uh had some kind of an
+icon iconic kind of connection there um
+
+ align:start position:0%
+icon iconic kind of connection there um
+ 
+
+ align:start position:0%
+icon iconic kind of connection there um
+and it has a very uh a stock elevation
+
+ align:start position:0%
+and it has a very uh a stock elevation
+ 
+
+ align:start position:0%
+and it has a very uh a stock elevation
+this is the Great temple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rema and we come to the indari
+
+ align:start position:0%
+Rema and we come to the indari
+ 
+
+ align:start position:0%
+Rema and we come to the indari
+civilization um this is a pick of Moen
+
+ align:start position:0%
+civilization um this is a pick of Moen
+ 
+
+ align:start position:0%
+civilization um this is a pick of Moen
+jadaro um what what actually remains in
+
+ align:start position:0%
+jadaro um what what actually remains in
+ 
+
+ align:start position:0%
+jadaro um what what actually remains in
+in these ruins are uh actually bake
+
+ align:start position:0%
+in these ruins are uh actually bake
+ 
+
+ align:start position:0%
+in these ruins are uh actually bake
+bricks and just heaps of of mud bricks
+
+ align:start position:0%
+bricks and just heaps of of mud bricks
+ 
+
+ align:start position:0%
+bricks and just heaps of of mud bricks
+uh what what you find is
+
+ align:start position:0%
+uh what what you find is
+ 
+
+ align:start position:0%
+uh what what you find is
+bathrooms uh uh
+
+ align:start position:0%
+bathrooms uh uh
+ 
+
+ align:start position:0%
+bathrooms uh uh
+gutters public baths uh Graves uh things
+
+ align:start position:0%
+gutters public baths uh Graves uh things
+ 
+
+ align:start position:0%
+gutters public baths uh Graves uh things
+that uh that uh that you would build in
+
+ align:start position:0%
+that uh that uh that you would build in
+ 
+
+ align:start position:0%
+that uh that uh that you would build in
+in bake break so there's a certain
+
+ align:start position:0%
+in bake break so there's a certain
+ 
+
+ align:start position:0%
+in bake break so there's a certain
+importance assigned to Big brick in this
+
+ align:start position:0%
+importance assigned to Big brick in this
+ 
+
+ align:start position:0%
+importance assigned to Big brick in this
+time um which is uh which kind of tells
+
+ align:start position:0%
+time um which is uh which kind of tells
+ 
+
+ align:start position:0%
+time um which is uh which kind of tells
+on on on how much effort was actually
+
+ align:start position:0%
+on on on how much effort was actually
+ 
+
+ align:start position:0%
+on on on how much effort was actually
+involved in making the braks so uh there
+
+ align:start position:0%
+involved in making the braks so uh there
+ 
+
+ align:start position:0%
+involved in making the braks so uh there
+was at at some point in in 3000 BC it
+
+ align:start position:0%
+was at at some point in in 3000 BC it
+ 
+
+ align:start position:0%
+was at at some point in in 3000 BC it
+big brick was was 30 times more
+
+ align:start position:0%
+big brick was was 30 times more
+ 
+
+ align:start position:0%
+big brick was was 30 times more
+expensive than mud brick
+
+ align:start position:0%
+expensive than mud brick
+ 
+
+ align:start position:0%
+expensive than mud brick
+so and uh there have also been studies
+
+ align:start position:0%
+so and uh there have also been studies
+ 
+
+ align:start position:0%
+so and uh there have also been studies
+involving
+
+ align:start position:0%
+involving
+ 
+
+ align:start position:0%
+involving
+uh uh the indas where uh they actually
+
+ align:start position:0%
+uh uh the indas where uh they actually
+ 
+
+ align:start position:0%
+uh uh the indas where uh they actually
+said that fired briak was a product of
+
+ align:start position:0%
+said that fired briak was a product of
+ 
+
+ align:start position:0%
+said that fired briak was a product of
+urban Specialists so this was already
+
+ align:start position:0%
+urban Specialists so this was already
+ 
+
+ align:start position:0%
+urban Specialists so this was already
+some kind of um an industry building up
+
+ align:start position:0%
+some kind of um an industry building up
+ 
+
+ align:start position:0%
+some kind of um an industry building up
+here and uh it it kind of required
+
+ align:start position:0%
+here and uh it it kind of required
+ 
+
+ align:start position:0%
+here and uh it it kind of required
+certain political economies that that
+
+ align:start position:0%
+certain political economies that that
+ 
+
+ align:start position:0%
+certain political economies that that
+uh that can that produce these
+
+ align:start position:0%
+uh that can that produce these
+ 
+
+ align:start position:0%
+uh that can that produce these
+breaks um
+
+ align:start position:0%
+breaks um
+ 
+
+ align:start position:0%
+breaks um
+when we come to thousand BC uh there's a
+
+ align:start position:0%
+when we come to thousand BC uh there's a
+ 
+
+ align:start position:0%
+when we come to thousand BC uh there's a
+kind of a surge in Mesopotamia and uh
+
+ align:start position:0%
+kind of a surge in Mesopotamia and uh
+ 
+
+ align:start position:0%
+kind of a surge in Mesopotamia and uh
+the Arian uh kind of descent into the
+
+ align:start position:0%
+the Arian uh kind of descent into the
+ 
+
+ align:start position:0%
+the Arian uh kind of descent into the
+Ganges Valley um again this is still
+
+ align:start position:0%
+Ganges Valley um again this is still
+ 
+
+ align:start position:0%
+Ganges Valley um again this is still
+restricted to river valleys and
+
+ align:start position:0%
+restricted to river valleys and
+ 
+
+ align:start position:0%
+restricted to river valleys and
+uh though not too much remains of uh of
+
+ align:start position:0%
+uh though not too much remains of uh of
+ 
+
+ align:start position:0%
+uh though not too much remains of uh of
+uh the Ganges uh of the of the Arian
+
+ align:start position:0%
+uh the Ganges uh of the of the Arian
+ 
+
+ align:start position:0%
+uh the Ganges uh of the of the Arian
+temp
+
+ align:start position:0%
+temp
+ 
+
+ align:start position:0%
+temp
+built uh at in this
+
+ align:start position:0%
+built uh at in this
+ 
+
+ align:start position:0%
+built uh at in this
+period um I I just wanted to briefly
+
+ align:start position:0%
+period um I I just wanted to briefly
+ 
+
+ align:start position:0%
+period um I I just wanted to briefly
+indicate
+
+ align:start position:0%
+indicate
+ 
+
+ align:start position:0%
+indicate
+uh uh the Greek Empire and uh its
+
+ align:start position:0%
+uh uh the Greek Empire and uh its
+ 
+
+ align:start position:0%
+uh uh the Greek Empire and uh its
+contribution to this study is uh
+
+ align:start position:0%
+contribution to this study is uh
+ 
+
+ align:start position:0%
+contribution to this study is uh
+basically the the roof tiles and
+
+ align:start position:0%
+basically the the roof tiles and
+ 
+
+ align:start position:0%
+basically the the roof tiles and
+uh uh apart from that uh it doesn't
+
+ align:start position:0%
+uh uh apart from that uh it doesn't
+ 
+
+ align:start position:0%
+uh uh apart from that uh it doesn't
+really expand this this these yellow
+
+ align:start position:0%
+really expand this this these yellow
+ 
+
+ align:start position:0%
+really expand this this these yellow
+patches basically for for the study so
+
+ align:start position:0%
+patches basically for for the study so
+ 
+
+ align:start position:0%
+patches basically for for the study so
+uh in a way U studies that are that are
+
+ align:start position:0%
+uh in a way U studies that are that are
+ 
+
+ align:start position:0%
+uh in a way U studies that are that are
+focused um primarily on on some kind of
+
+ align:start position:0%
+focused um primarily on on some kind of
+ 
+
+ align:start position:0%
+focused um primarily on on some kind of
+material aspects um kind of
+
+ align:start position:0%
+material aspects um kind of
+ 
+
+ align:start position:0%
+material aspects um kind of
+Overlook uh certain other histories and
+
+ align:start position:0%
+Overlook uh certain other histories and
+ 
+
+ align:start position:0%
+Overlook uh certain other histories and
+uh um yeah so some some civilizations
+
+ align:start position:0%
+uh um yeah so some some civilizations
+ 
+
+ align:start position:0%
+uh um yeah so some some civilizations
+just don't don't appeal in their
+
+ align:start position:0%
+just don't don't appeal in their
+ 
+
+ align:start position:0%
+just don't don't appeal in their
+breckness
+
+ align:start position:0%
+breckness
+ 
+
+ align:start position:0%
+breckness
+um this is Babylon uh the first signs of
+
+ align:start position:0%
+um this is Babylon uh the first signs of
+ 
+
+ align:start position:0%
+um this is Babylon uh the first signs of
+of glaze brick of course used very
+
+ align:start position:0%
+of glaze brick of course used very
+ 
+
+ align:start position:0%
+of glaze brick of course used very
+extensively this is also
+
+ align:start position:0%
+extensively this is also
+ 
+
+ align:start position:0%
+extensively this is also
+um U laid out on as a panel and then
+
+ align:start position:0%
+um U laid out on as a panel and then
+ 
+
+ align:start position:0%
+um U laid out on as a panel and then
+glazed and then baked
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separately uh now uh in this period
+
+ align:start position:0%
+separately uh now uh in this period
+ 
+
+ align:start position:0%
+separately uh now uh in this period
+there's a little um this is 400 BC and
+
+ align:start position:0%
+there's a little um this is 400 BC and
+ 
+
+ align:start position:0%
+there's a little um this is 400 BC and
+this would be when Buddhism just gave a
+
+ align:start position:0%
+this would be when Buddhism just gave a
+ 
+
+ align:start position:0%
+this would be when Buddhism just gave a
+little push to to break work in East
+
+ align:start position:0%
+little push to to break work in East
+ 
+
+ align:start position:0%
+little push to to break work in East
+India and uh and of course uh China in
+
+ align:start position:0%
+India and uh and of course uh China in
+ 
+
+ align:start position:0%
+India and uh and of course uh China in
+this time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh oh okay so
+
+ align:start position:0%
+uh oh okay so
+ 
+
+ align:start position:0%
+uh oh okay so
+uh we move into uh 200 BC which was uh
+
+ align:start position:0%
+uh we move into uh 200 BC which was uh
+ 
+
+ align:start position:0%
+uh we move into uh 200 BC which was uh
+which is uh the the the expansion of the
+
+ align:start position:0%
+which is uh the the the expansion of the
+ 
+
+ align:start position:0%
+which is uh the the the expansion of the
+Roman Empire and uh in China we see the
+
+ align:start position:0%
+Roman Empire and uh in China we see the
+ 
+
+ align:start position:0%
+Roman Empire and uh in China we see the
+dynasty actually starting to break to
+
+ align:start position:0%
+dynasty actually starting to break to
+ 
+
+ align:start position:0%
+dynasty actually starting to break to
+build the Bri the the Great Wall of
+
+ align:start position:0%
+build the Bri the the Great Wall of
+ 
+
+ align:start position:0%
+build the Bri the the Great Wall of
+China and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so this is this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rome technology is taken to to a whole
+
+ align:start position:0%
+Rome technology is taken to to a whole
+ 
+
+ align:start position:0%
+Rome technology is taken to to a whole
+other limit uh the the use of of uh the
+
+ align:start position:0%
+other limit uh the the use of of uh the
+ 
+
+ align:start position:0%
+other limit uh the the use of of uh the
+concreted wall um and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh here in Rome uh
+
+ align:start position:0%
+uh here in Rome uh
+ 
+
+ align:start position:0%
+uh here in Rome uh
+the the the industry actually builds up
+
+ align:start position:0%
+the the the industry actually builds up
+ 
+
+ align:start position:0%
+the the the industry actually builds up
+to the point that it can it can Mass
+
+ align:start position:0%
+to the point that it can it can Mass
+ 
+
+ align:start position:0%
+to the point that it can it can Mass
+manufacture for an Empire this large I
+
+ align:start position:0%
+manufacture for an Empire this large I
+ 
+
+ align:start position:0%
+manufacture for an Empire this large I
+mean it's expanding right north of of
+
+ align:start position:0%
+mean it's expanding right north of of
+ 
+
+ align:start position:0%
+mean it's expanding right north of of
+the entire Africa and you have most of
+
+ align:start position:0%
+the entire Africa and you have most of
+ 
+
+ align:start position:0%
+the entire Africa and you have most of
+Europe taken in and U of course it gets
+
+ align:start position:0%
+Europe taken in and U of course it gets
+ 
+
+ align:start position:0%
+Europe taken in and U of course it gets
+all the way to England
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we see the transference of of
+
+ align:start position:0%
+and we see the transference of of
+ 
+
+ align:start position:0%
+and we see the transference of of
+certain Greek details into into terra
+
+ align:start position:0%
+certain Greek details into into terra
+ 
+
+ align:start position:0%
+certain Greek details into into terra
+cotta into brick into kind of cut Breck
+
+ align:start position:0%
+cotta into brick into kind of cut Breck
+ 
+
+ align:start position:0%
+cotta into brick into kind of cut Breck
+and this is an an interesting
+
+ align:start position:0%
+and this is an an interesting
+ 
+
+ align:start position:0%
+and this is an an interesting
+interesting point where you can actually
+
+ align:start position:0%
+interesting point where you can actually
+ 
+
+ align:start position:0%
+interesting point where you can actually
+see certain Technologies being invented
+
+ align:start position:0%
+see certain Technologies being invented
+ 
+
+ align:start position:0%
+see certain Technologies being invented
+to to suit uh transition in some way and
+
+ align:start position:0%
+to to suit uh transition in some way and
+ 
+
+ align:start position:0%
+to to suit uh transition in some way and
+uh here again U I'd just like to bring
+
+ align:start position:0%
+uh here again U I'd just like to bring
+ 
+
+ align:start position:0%
+uh here again U I'd just like to bring
+to your notice that uh the Cornus
+
+ align:start position:0%
+to your notice that uh the Cornus
+ 
+
+ align:start position:0%
+to your notice that uh the Cornus
+actually as in in Greek architecture the
+
+ align:start position:0%
+actually as in in Greek architecture the
+ 
+
+ align:start position:0%
+actually as in in Greek architecture the
+Cornus is again extremely important for
+
+ align:start position:0%
+Cornus is again extremely important for
+ 
+
+ align:start position:0%
+Cornus is again extremely important for
+for the brick work in Rome as well and
+
+ align:start position:0%
+for the brick work in Rome as well and
+ 
+
+ align:start position:0%
+for the brick work in Rome as well and
+uh the the use of of
+
+ align:start position:0%
+uh the the use of of
+ 
+
+ align:start position:0%
+uh the the use of of
+celling uh is
+
+ align:start position:0%
+celling uh is
+ 
+
+ align:start position:0%
+celling uh is
+uh is is is
+
+ align:start position:0%
+uh is is is
+ 
+
+ align:start position:0%
+uh is is is
+used uh this is a this is an example of
+
+ align:start position:0%
+used uh this is a this is an example of
+ 
+
+ align:start position:0%
+used uh this is a this is an example of
+a brick K in in Rome they say that there
+
+ align:start position:0%
+a brick K in in Rome they say that there
+ 
+
+ align:start position:0%
+a brick K in in Rome they say that there
+were uh even coal Coal kills I mean that
+
+ align:start position:0%
+were uh even coal Coal kills I mean that
+ 
+
+ align:start position:0%
+were uh even coal Coal kills I mean that
+would kind of uh uh justify their their
+
+ align:start position:0%
+would kind of uh uh justify their their
+ 
+
+ align:start position:0%
+would kind of uh uh justify their their
+rapid expansion and their production of
+
+ align:start position:0%
+rapid expansion and their production of
+ 
+
+ align:start position:0%
+rapid expansion and their production of
+of brick at such in such large scales um
+
+ align:start position:0%
+of brick at such in such large scales um
+ 
+
+ align:start position:0%
+of brick at such in such large scales um
+their their standard types were uh the
+
+ align:start position:0%
+their their standard types were uh the
+ 
+
+ align:start position:0%
+their their standard types were uh the
+one right at the bottom is uh was
+
+ align:start position:0%
+one right at the bottom is uh was
+ 
+
+ align:start position:0%
+one right at the bottom is uh was
+actually 2 ft by 2 ft and that was their
+
+ align:start position:0%
+actually 2 ft by 2 ft and that was their
+ 
+
+ align:start position:0%
+actually 2 ft by 2 ft and that was their
+Standard Tile that they Ed this was the
+
+ align:start position:0%
+Standard Tile that they Ed this was the
+ 
+
+ align:start position:0%
+Standard Tile that they Ed this was the
+the Roman brick and the ones above are
+
+ align:start position:0%
+the Roman brick and the ones above are
+ 
+
+ align:start position:0%
+the Roman brick and the ones above are
+actually special braks use for other
+
+ align:start position:0%
+actually special braks use for other
+ 
+
+ align:start position:0%
+actually special braks use for other
+reasons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this is this is the Great Wall of
+
+ align:start position:0%
+uh this is this is the Great Wall of
+ 
+
+ align:start position:0%
+uh this is this is the Great Wall of
+China
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+um this is uh this is a Time the black
+
+ align:start position:0%
+um this is uh this is a Time the black
+ 
+
+ align:start position:0%
+um this is uh this is a Time the black
+outline in this in this map actually
+
+ align:start position:0%
+outline in this in this map actually
+ 
+
+ align:start position:0%
+outline in this in this map actually
+indicates uh how far the Buddhist Empire
+
+ align:start position:0%
+indicates uh how far the Buddhist Empire
+ 
+
+ align:start position:0%
+indicates uh how far the Buddhist Empire
+actually did go uh at this time and uh
+
+ align:start position:0%
+actually did go uh at this time and uh
+ 
+
+ align:start position:0%
+actually did go uh at this time and uh
+but it again does not really affect uh
+
+ align:start position:0%
+but it again does not really affect uh
+ 
+
+ align:start position:0%
+but it again does not really affect uh
+the the Brick history as yet so China
+
+ align:start position:0%
+the the Brick history as yet so China
+ 
+
+ align:start position:0%
+the the Brick history as yet so China
+Still Remains uh a little U kind of uh
+
+ align:start position:0%
+Still Remains uh a little U kind of uh
+ 
+
+ align:start position:0%
+Still Remains uh a little U kind of uh
+producing uh terra cotta Soldiers the
+
+ align:start position:0%
+producing uh terra cotta Soldiers the
+ 
+
+ align:start position:0%
+producing uh terra cotta Soldiers the
+Terra Cotta Army and and uh this kind of
+
+ align:start position:0%
+Terra Cotta Army and and uh this kind of
+ 
+
+ align:start position:0%
+Terra Cotta Army and and uh this kind of
+a whole different um um brick work while
+
+ align:start position:0%
+a whole different um um brick work while
+ 
+
+ align:start position:0%
+a whole different um um brick work while
+uh the sasanians actually take on this
+
+ align:start position:0%
+uh the sasanians actually take on this
+ 
+
+ align:start position:0%
+uh the sasanians actually take on this
+uh uh a whole new kind a new style for
+
+ align:start position:0%
+uh uh a whole new kind a new style for
+ 
+
+ align:start position:0%
+uh uh a whole new kind a new style for
+brick work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is an example of a fire temple
+
+ align:start position:0%
+um this is an example of a fire temple
+ 
+
+ align:start position:0%
+um this is an example of a fire temple
+and this is just the extents of of the
+
+ align:start position:0%
+and this is just the extents of of the
+ 
+
+ align:start position:0%
+and this is just the extents of of the
+sanan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Empire um there's a there's a
+
+ align:start position:0%
+Empire um there's a there's a
+ 
+
+ align:start position:0%
+Empire um there's a there's a
+flamboyance in in
+
+ align:start position:0%
+flamboyance in in
+ 
+
+ align:start position:0%
+flamboyance in in
+structural uh use of brick and uh of
+
+ align:start position:0%
+structural uh use of brick and uh of
+ 
+
+ align:start position:0%
+structural uh use of brick and uh of
+course as as ornament as to its
+
+ align:start position:0%
+course as as ornament as to its
+ 
+
+ align:start position:0%
+course as as ornament as to its
+um it's it's used
+
+ align:start position:0%
+um it's it's used
+ 
+
+ align:start position:0%
+um it's it's used
+extensively uh these are the
+
+ align:start position:0%
+extensively uh these are the
+ 
+
+ align:start position:0%
+extensively uh these are the
+Warriors in in in China and I mean these
+
+ align:start position:0%
+Warriors in in in China and I mean these
+ 
+
+ align:start position:0%
+Warriors in in in China and I mean these
+are these are thousands and thousands of
+
+ align:start position:0%
+are these are thousands and thousands of
+ 
+
+ align:start position:0%
+are these are thousands and thousands of
+them so uh this is
+
+ align:start position:0%
+them so uh this is
+ 
+
+ align:start position:0%
+them so uh this is
+actually it's like a they're actually
+
+ align:start position:0%
+actually it's like a they're actually
+ 
+
+ align:start position:0%
+actually it's like a they're actually
+working on kind of a parallel technology
+
+ align:start position:0%
+working on kind of a parallel technology
+ 
+
+ align:start position:0%
+working on kind of a parallel technology
+in some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way um this uh 600 uh C is when we
+
+ align:start position:0%
+way um this uh 600 uh C is when we
+ 
+
+ align:start position:0%
+way um this uh 600 uh C is when we
+actually um we start seeing the SE the
+
+ align:start position:0%
+actually um we start seeing the SE the
+ 
+
+ align:start position:0%
+actually um we start seeing the SE the
+the the fragmentation of of the Roman
+
+ align:start position:0%
+the the fragmentation of of the Roman
+ 
+
+ align:start position:0%
+the the fragmentation of of the Roman
+Empire and it's its two arms one the
+
+ align:start position:0%
+Empire and it's its two arms one the
+ 
+
+ align:start position:0%
+Empire and it's its two arms one the
+bantine and the other the raava and uh
+
+ align:start position:0%
+bantine and the other the raava and uh
+ 
+
+ align:start position:0%
+bantine and the other the raava and uh
+there's also then a surge in in Bengal
+
+ align:start position:0%
+there's also then a surge in in Bengal
+ 
+
+ align:start position:0%
+there's also then a surge in in Bengal
+at this time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I I put this map here just to kind of
+
+ align:start position:0%
+um I I put this map here just to kind of
+ 
+
+ align:start position:0%
+um I I put this map here just to kind of
+um clarify certain things is that what
+
+ align:start position:0%
+um clarify certain things is that what
+ 
+
+ align:start position:0%
+um clarify certain things is that what
+actually is missing in this
+
+ align:start position:0%
+actually is missing in this
+ 
+
+ align:start position:0%
+actually is missing in this
+one uh
+
+ align:start position:0%
+one uh
+ 
+
+ align:start position:0%
+one uh
+and uh so I actually place this in in
+
+ align:start position:0%
+and uh so I actually place this in in
+ 
+
+ align:start position:0%
+and uh so I actually place this in in
+just to kind of give you all a reference
+
+ align:start position:0%
+just to kind of give you all a reference
+ 
+
+ align:start position:0%
+just to kind of give you all a reference
+in some way of of where all the empires
+
+ align:start position:0%
+in some way of of where all the empires
+ 
+
+ align:start position:0%
+in some way of of where all the empires
+actually had extended in some way and
+
+ align:start position:0%
+actually had extended in some way and
+ 
+
+ align:start position:0%
+actually had extended in some way and
+uh you see the Europe is completely
+
+ align:start position:0%
+uh you see the Europe is completely
+ 
+
+ align:start position:0%
+uh you see the Europe is completely
+fragmented there and and of course the
+
+ align:start position:0%
+fragmented there and and of course the
+ 
+
+ align:start position:0%
+fragmented there and and of course the
+the ummayads is have have taken over the
+
+ align:start position:0%
+the ummayads is have have taken over the
+ 
+
+ align:start position:0%
+the ummayads is have have taken over the
+the enti I mean the the first expansion
+
+ align:start position:0%
+the enti I mean the the first expansion
+ 
+
+ align:start position:0%
+the enti I mean the the first expansion
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Islam and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we see a a the the complete
+
+ align:start position:0%
+and we see a a the the complete
+ 
+
+ align:start position:0%
+and we see a a the the complete
+difference uh between between the two
+
+ align:start position:0%
+difference uh between between the two
+ 
+
+ align:start position:0%
+difference uh between between the two
+Styles actually in uh in to the left is
+
+ align:start position:0%
+Styles actually in uh in to the left is
+ 
+
+ align:start position:0%
+Styles actually in uh in to the left is
+actually the bantine and to the right is
+
+ align:start position:0%
+actually the bantine and to the right is
+ 
+
+ align:start position:0%
+actually the bantine and to the right is
+is the Ravena style and uh there's a
+
+ align:start position:0%
+is the Ravena style and uh there's a
+ 
+
+ align:start position:0%
+is the Ravena style and uh there's a
+certain solidity that is that is
+
+ align:start position:0%
+certain solidity that is that is
+ 
+
+ align:start position:0%
+certain solidity that is that is
+associated with the Ravena style which
+
+ align:start position:0%
+associated with the Ravena style which
+ 
+
+ align:start position:0%
+associated with the Ravena style which
+actually continues through uh in Italy
+
+ align:start position:0%
+actually continues through uh in Italy
+ 
+
+ align:start position:0%
+actually continues through uh in Italy
+and while while uh the use of of more
+
+ align:start position:0%
+and while while uh the use of of more
+ 
+
+ align:start position:0%
+and while while uh the use of of more
+flamboyant more slender arches actually
+
+ align:start position:0%
+flamboyant more slender arches actually
+ 
+
+ align:start position:0%
+flamboyant more slender arches actually
+are uh are actually used in the in the
+
+ align:start position:0%
+are uh are actually used in the in the
+ 
+
+ align:start position:0%
+are uh are actually used in the in the
+bisen and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Empire yeah and uh we see the the first
+
+ align:start position:0%
+Empire yeah and uh we see the the first
+ 
+
+ align:start position:0%
+Empire yeah and uh we see the the first
+the emergence of the do tooth pattern
+
+ align:start position:0%
+the emergence of the do tooth pattern
+ 
+
+ align:start position:0%
+the emergence of the do tooth pattern
+here uh you can see it in the top left
+
+ align:start position:0%
+here uh you can see it in the top left
+ 
+
+ align:start position:0%
+here uh you can see it in the top left
+photograph and you can see the towards
+
+ align:start position:0%
+photograph and you can see the towards
+ 
+
+ align:start position:0%
+photograph and you can see the towards
+the roof it's actually lined with the do
+
+ align:start position:0%
+the roof it's actually lined with the do
+ 
+
+ align:start position:0%
+the roof it's actually lined with the do
+too uh pattern and uh that would be the
+
+ align:start position:0%
+too uh pattern and uh that would be the
+ 
+
+ align:start position:0%
+too uh pattern and uh that would be the
+one on the left here uh left bottom and
+
+ align:start position:0%
+one on the left here uh left bottom and
+ 
+
+ align:start position:0%
+one on the left here uh left bottom and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+to as a as a comparison Just Between the
+
+ align:start position:0%
+to as a as a comparison Just Between the
+ 
+
+ align:start position:0%
+to as a as a comparison Just Between the
+left and the right you can actually see
+
+ align:start position:0%
+left and the right you can actually see
+ 
+
+ align:start position:0%
+left and the right you can actually see
+the the the kind of differences between
+
+ align:start position:0%
+the the the kind of differences between
+ 
+
+ align:start position:0%
+the the the kind of differences between
+two Styles one much more solid and uh
+
+ align:start position:0%
+two Styles one much more solid and uh
+ 
+
+ align:start position:0%
+two Styles one much more solid and uh
+the one on the left actually more more
+
+ align:start position:0%
+the one on the left actually more more
+ 
+
+ align:start position:0%
+the one on the left actually more more
+more flamboyant in that way um there's
+
+ align:start position:0%
+more flamboyant in that way um there's
+ 
+
+ align:start position:0%
+more flamboyant in that way um there's
+also a a kind of creation of of Terra
+
+ align:start position:0%
+also a a kind of creation of of Terra
+ 
+
+ align:start position:0%
+also a a kind of creation of of Terra
+Cotta as as a facade
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material this uh is actually the the
+
+ align:start position:0%
+material this uh is actually the the
+ 
+
+ align:start position:0%
+material this uh is actually the the
+little Splurge of when Buddhism and
+
+ align:start position:0%
+little Splurge of when Buddhism and
+ 
+
+ align:start position:0%
+little Splurge of when Buddhism and
+Hinduism actually found some kind of a
+
+ align:start position:0%
+Hinduism actually found some kind of a
+ 
+
+ align:start position:0%
+Hinduism actually found some kind of a
+Confluence in in uh in eastern central
+
+ align:start position:0%
+Confluence in in uh in eastern central
+ 
+
+ align:start position:0%
+Confluence in in uh in eastern central
+India and uh these are the these are the
+
+ align:start position:0%
+India and uh these are the these are the
+ 
+
+ align:start position:0%
+India and uh these are the these are the
+few uh surviving brick temples uh in the
+
+ align:start position:0%
+few uh surviving brick temples uh in the
+ 
+
+ align:start position:0%
+few uh surviving brick temples uh in the
+region and uh these are of course the
+
+ align:start position:0%
+region and uh these are of course the
+ 
+
+ align:start position:0%
+region and uh these are of course the
+they are they are completely cut brick
+
+ align:start position:0%
+they are they are completely cut brick
+ 
+
+ align:start position:0%
+they are they are completely cut brick
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and when we come to uh 900 CE
+
+ align:start position:0%
+uh and when we come to uh 900 CE
+ 
+
+ align:start position:0%
+uh and when we come to uh 900 CE
+uh the the abbasids have kind of uh have
+
+ align:start position:0%
+uh the the abbasids have kind of uh have
+ 
+
+ align:start position:0%
+uh the the abbasids have kind of uh have
+already lost their their empire which is
+
+ align:start position:0%
+already lost their their empire which is
+ 
+
+ align:start position:0%
+already lost their their empire which is
+uh which was actually which extended all
+
+ align:start position:0%
+uh which was actually which extended all
+ 
+
+ align:start position:0%
+uh which was actually which extended all
+of that green
+
+ align:start position:0%
+of that green
+ 
+
+ align:start position:0%
+of that green
+and uh and the samanids actually are are
+
+ align:start position:0%
+and uh and the samanids actually are are
+ 
+
+ align:start position:0%
+and uh and the samanids actually are are
+are a group close to the Caspian which
+
+ align:start position:0%
+are a group close to the Caspian which
+ 
+
+ align:start position:0%
+are a group close to the Caspian which
+which are actually developing this U
+
+ align:start position:0%
+which are actually developing this U
+ 
+
+ align:start position:0%
+which are actually developing this U
+very uh very intense technology on on
+
+ align:start position:0%
+very uh very intense technology on on
+ 
+
+ align:start position:0%
+very uh very intense technology on on
+decorative brick work and uh we see this
+
+ align:start position:0%
+decorative brick work and uh we see this
+ 
+
+ align:start position:0%
+decorative brick work and uh we see this
+the Ganges Valley again dotted with
+
+ align:start position:0%
+the Ganges Valley again dotted with
+ 
+
+ align:start position:0%
+the Ganges Valley again dotted with
+these brick temples at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time um this is actually just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an enamel kind of
+
+ align:start position:0%
+an enamel kind of
+ 
+
+ align:start position:0%
+an enamel kind of
+a u on an enamel decoration on a chest
+
+ align:start position:0%
+a u on an enamel decoration on a chest
+ 
+
+ align:start position:0%
+a u on an enamel decoration on a chest
+which actually shows some kind of a
+
+ align:start position:0%
+which actually shows some kind of a
+ 
+
+ align:start position:0%
+which actually shows some kind of a
+Confluence between uh um
+
+ align:start position:0%
+Confluence between uh um
+ 
+
+ align:start position:0%
+Confluence between uh um
+the the the Roman and
+
+ align:start position:0%
+the the the Roman and
+ 
+
+ align:start position:0%
+the the the Roman and
+the and the Islamic so actually what
+
+ align:start position:0%
+the and the Islamic so actually what
+ 
+
+ align:start position:0%
+the and the Islamic so actually what
+what uh what I want to want to talk
+
+ align:start position:0%
+what uh what I want to want to talk
+ 
+
+ align:start position:0%
+what uh what I want to want to talk
+about is is the is the smooth transition
+
+ align:start position:0%
+about is is the is the smooth transition
+ 
+
+ align:start position:0%
+about is is the is the smooth transition
+between from from the Roman to the
+
+ align:start position:0%
+between from from the Roman to the
+ 
+
+ align:start position:0%
+between from from the Roman to the
+Islamic and uh this whole uh um and and
+
+ align:start position:0%
+Islamic and uh this whole uh um and and
+ 
+
+ align:start position:0%
+Islamic and uh this whole uh um and and
+we'll see it how it's actually played
+
+ align:start position:0%
+we'll see it how it's actually played
+ 
+
+ align:start position:0%
+we'll see it how it's actually played
+out in in these different buildings
+
+ align:start position:0%
+out in in these different buildings
+ 
+
+ align:start position:0%
+out in in these different buildings
+around uh around the Islamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+empire so these are actually the early
+
+ align:start position:0%
+empire so these are actually the early
+ 
+
+ align:start position:0%
+empire so these are actually the early
+the Early mosques built by the
+
+ align:start position:0%
+the Early mosques built by the
+ 
+
+ align:start position:0%
+the Early mosques built by the
+abbasids and
+
+ align:start position:0%
+abbasids and
+ 
+
+ align:start position:0%
+abbasids and
+uh and we see as as it come uh we see it
+
+ align:start position:0%
+uh and we see as as it come uh we see it
+ 
+
+ align:start position:0%
+uh and we see as as it come uh we see it
+in uh in seia where uh a certain
+
+ align:start position:0%
+in uh in seia where uh a certain
+ 
+
+ align:start position:0%
+in uh in seia where uh a certain
+adaptation of of those of the slightly
+
+ align:start position:0%
+adaptation of of those of the slightly
+ 
+
+ align:start position:0%
+adaptation of of those of the slightly
+more flamboyant style is actually is
+
+ align:start position:0%
+more flamboyant style is actually is
+ 
+
+ align:start position:0%
+more flamboyant style is actually is
+actually made out and uh you see it in
+
+ align:start position:0%
+actually made out and uh you see it in
+ 
+
+ align:start position:0%
+actually made out and uh you see it in
+in caravan as well um the the Dome is
+
+ align:start position:0%
+in caravan as well um the the Dome is
+ 
+
+ align:start position:0%
+in caravan as well um the the Dome is
+actually created by by eight archers so
+
+ align:start position:0%
+actually created by by eight archers so
+ 
+
+ align:start position:0%
+actually created by by eight archers so
+uh that in a in a kind of a
+
+ align:start position:0%
+uh that in a in a kind of a
+ 
+
+ align:start position:0%
+uh that in a in a kind of a
+Roman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method uh this is I think the one of the
+
+ align:start position:0%
+method uh this is I think the one of the
+ 
+
+ align:start position:0%
+method uh this is I think the one of the
+most blatant examples of of the transfer
+
+ align:start position:0%
+most blatant examples of of the transfer
+ 
+
+ align:start position:0%
+most blatant examples of of the transfer
+of of the most smooth transfer from the
+
+ align:start position:0%
+of of the most smooth transfer from the
+ 
+
+ align:start position:0%
+of of the most smooth transfer from the
+Roman to to the Islamic and this would
+
+ align:start position:0%
+Roman to to the Islamic and this would
+ 
+
+ align:start position:0%
+Roman to to the Islamic and this would
+be this is in Toledo in Spain and uh we
+
+ align:start position:0%
+be this is in Toledo in Spain and uh we
+ 
+
+ align:start position:0%
+be this is in Toledo in Spain and uh we
+see the Arches which are again uh
+
+ align:start position:0%
+see the Arches which are again uh
+ 
+
+ align:start position:0%
+see the Arches which are again uh
+they're Dum arches in some way and uh
+
+ align:start position:0%
+they're Dum arches in some way and uh
+ 
+
+ align:start position:0%
+they're Dum arches in some way and uh
+it's it's uh it's something that will
+
+ align:start position:0%
+it's it's uh it's something that will
+ 
+
+ align:start position:0%
+it's it's uh it's something that will
+keep repeating in uh in uh in Islamic
+
+ align:start position:0%
+keep repeating in uh in uh in Islamic
+ 
+
+ align:start position:0%
+keep repeating in uh in uh in Islamic
+architecture of this time especially
+
+ align:start position:0%
+architecture of this time especially
+ 
+
+ align:start position:0%
+architecture of this time especially
+that which overlaps with the Roman
+
+ align:start position:0%
+that which overlaps with the Roman
+ 
+
+ align:start position:0%
+that which overlaps with the Roman
+Empire
+
+ align:start position:0%
+Empire
+ 
+
+ align:start position:0%
+Empire
+so uh in some way there's there's this
+
+ align:start position:0%
+so uh in some way there's there's this
+ 
+
+ align:start position:0%
+so uh in some way there's there's this
+whole uh kind of no apprehension to uh
+
+ align:start position:0%
+whole uh kind of no apprehension to uh
+ 
+
+ align:start position:0%
+whole uh kind of no apprehension to uh
+to adapting to uh
+
+ align:start position:0%
+to adapting to uh
+ 
+
+ align:start position:0%
+to adapting to uh
+appropriating this the transition just
+
+ align:start position:0%
+appropriating this the transition just
+ 
+
+ align:start position:0%
+appropriating this the transition just
+seems to be extremely smooth in that
+
+ align:start position:0%
+seems to be extremely smooth in that
+ 
+
+ align:start position:0%
+seems to be extremely smooth in that
+way and this of course is is the Tomb of
+
+ align:start position:0%
+way and this of course is is the Tomb of
+ 
+
+ align:start position:0%
+way and this of course is is the Tomb of
+the samanids it's a beautiful building
+
+ align:start position:0%
+the samanids it's a beautiful building
+ 
+
+ align:start position:0%
+the samanids it's a beautiful building
+uh this was this is the the area near
+
+ align:start position:0%
+uh this was this is the the area near
+ 
+
+ align:start position:0%
+uh this was this is the the area near
+the Caspian actually which I was talking
+
+ align:start position:0%
+the Caspian actually which I was talking
+ 
+
+ align:start position:0%
+the Caspian actually which I was talking
+about which actually develops its own
+
+ align:start position:0%
+about which actually develops its own
+ 
+
+ align:start position:0%
+about which actually develops its own
+its own way of of decorative masonry in
+
+ align:start position:0%
+its own way of of decorative masonry in
+ 
+
+ align:start position:0%
+its own way of of decorative masonry in
+in this building
+
+ align:start position:0%
+in this building
+ 
+
+ align:start position:0%
+in this building
+uh the the bricks are not really special
+
+ align:start position:0%
+uh the the bricks are not really special
+ 
+
+ align:start position:0%
+uh the the bricks are not really special
+bricks they are they are your they
+
+ align:start position:0%
+bricks they are they are your they
+ 
+
+ align:start position:0%
+bricks they are they are your they
+almost the same cuboidal bricks that you
+
+ align:start position:0%
+almost the same cuboidal bricks that you
+ 
+
+ align:start position:0%
+almost the same cuboidal bricks that you
+get today uh it is it is purely in the
+
+ align:start position:0%
+get today uh it is it is purely in the
+ 
+
+ align:start position:0%
+get today uh it is it is purely in the
+brick laying that uh that you find the
+
+ align:start position:0%
+brick laying that uh that you find the
+ 
+
+ align:start position:0%
+brick laying that uh that you find the
+decorative uh brick masonry as a as a
+
+ align:start position:0%
+decorative uh brick masonry as a as a
+ 
+
+ align:start position:0%
+decorative uh brick masonry as a as a
+craft um and of course there are uh
+
+ align:start position:0%
+craft um and of course there are uh
+ 
+
+ align:start position:0%
+craft um and of course there are uh
+there are the same kind of signs uh for
+
+ align:start position:0%
+there are the same kind of signs uh for
+ 
+
+ align:start position:0%
+there are the same kind of signs uh for
+for some kind of a development from
+
+ align:start position:0%
+for some kind of a development from
+ 
+
+ align:start position:0%
+for some kind of a development from
+sasanian and Roman so there's there's a
+
+ align:start position:0%
+sasanian and Roman so there's there's a
+ 
+
+ align:start position:0%
+sasanian and Roman so there's there's a
+kind of combination here in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region these are some of the bonds which
+
+ align:start position:0%
+region these are some of the bonds which
+ 
+
+ align:start position:0%
+region these are some of the bonds which
+which are actually uh are just beautiful
+
+ align:start position:0%
+which are actually uh are just beautiful
+ 
+
+ align:start position:0%
+which are actually uh are just beautiful
+I mean just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and and then of course they that
+
+ align:start position:0%
+this and and then of course they that
+ 
+
+ align:start position:0%
+this and and then of course they that
+that entire area develops its Style from
+
+ align:start position:0%
+that entire area develops its Style from
+ 
+
+ align:start position:0%
+that entire area develops its Style from
+from here this is uh this is a minate
+
+ align:start position:0%
+from here this is uh this is a minate
+ 
+
+ align:start position:0%
+from here this is uh this is a minate
+built in almost the same kind of a
+
+ align:start position:0%
+built in almost the same kind of a
+ 
+
+ align:start position:0%
+built in almost the same kind of a
+pattern and and Technology also so you
+
+ align:start position:0%
+pattern and and Technology also so you
+ 
+
+ align:start position:0%
+pattern and and Technology also so you
+see the same uh fourth band from the
+
+ align:start position:0%
+see the same uh fourth band from the
+ 
+
+ align:start position:0%
+see the same uh fourth band from the
+bottom actually has those circles and uh
+
+ align:start position:0%
+bottom actually has those circles and uh
+ 
+
+ align:start position:0%
+bottom actually has those circles and uh
+you can you can find those those similar
+
+ align:start position:0%
+you can you can find those those similar
+ 
+
+ align:start position:0%
+you can you can find those those similar
+Circle circular special braks in in this
+
+ align:start position:0%
+Circle circular special braks in in this
+ 
+
+ align:start position:0%
+Circle circular special braks in in this
+mosque in this tomb as well at at the
+
+ align:start position:0%
+mosque in this tomb as well at at the
+ 
+
+ align:start position:0%
+mosque in this tomb as well at at the
+top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and this was the the little flourish
+
+ align:start position:0%
+uh and this was the the little flourish
+ 
+
+ align:start position:0%
+uh and this was the the little flourish
+between uh in in Central and Eastern
+
+ align:start position:0%
+between uh in in Central and Eastern
+ 
+
+ align:start position:0%
+between uh in in Central and Eastern
+India this is nalanda
+
+ align:start position:0%
+India this is nalanda
+ 
+
+ align:start position:0%
+India this is nalanda
+University
+
+ align:start position:0%
+University
+ 
+
+ align:start position:0%
+University
+uh again made of break and uh there at
+
+ align:start position:0%
+uh again made of break and uh there at
+ 
+
+ align:start position:0%
+uh again made of break and uh there at
+this time there's a proliferation of of
+
+ align:start position:0%
+this time there's a proliferation of of
+ 
+
+ align:start position:0%
+this time there's a proliferation of of
+supas that actually go out uh made of
+
+ align:start position:0%
+supas that actually go out uh made of
+ 
+
+ align:start position:0%
+supas that actually go out uh made of
+break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is uh this is now getting to
+
+ align:start position:0%
+um this is uh this is now getting to
+ 
+
+ align:start position:0%
+um this is uh this is now getting to
+where I would be more interested in the
+
+ align:start position:0%
+where I would be more interested in the
+ 
+
+ align:start position:0%
+where I would be more interested in the
+study is uh the the emergence of pagan
+
+ align:start position:0%
+study is uh the the emergence of pagan
+ 
+
+ align:start position:0%
+study is uh the the emergence of pagan
+in in Burma and
+
+ align:start position:0%
+in in Burma and
+ 
+
+ align:start position:0%
+in in Burma and
+uh and some kind of a parallel uh
+
+ align:start position:0%
+uh and some kind of a parallel uh
+ 
+
+ align:start position:0%
+uh and some kind of a parallel uh
+similar decorative masonry in in
+
+ align:start position:0%
+similar decorative masonry in in
+ 
+
+ align:start position:0%
+similar decorative masonry in in
+the by the sjuk uh Turks and uh this is
+
+ align:start position:0%
+the by the sjuk uh Turks and uh this is
+ 
+
+ align:start position:0%
+the by the sjuk uh Turks and uh this is
+an an interesting time because uh the
+
+ align:start position:0%
+an an interesting time because uh the
+ 
+
+ align:start position:0%
+an an interesting time because uh the
+central region between them is actually
+
+ align:start position:0%
+central region between them is actually
+ 
+
+ align:start position:0%
+central region between them is actually
+occupied by uh by other
+
+ align:start position:0%
+occupied by uh by other
+ 
+
+ align:start position:0%
+occupied by uh by other
+political uh by other political parties
+
+ align:start position:0%
+political uh by other political parties
+ 
+
+ align:start position:0%
+political uh by other political parties
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh this this actually I mean this would
+
+ align:start position:0%
+uh this this actually I mean this would
+ 
+
+ align:start position:0%
+uh this this actually I mean this would
+be a little hypothetical but it is it is
+
+ align:start position:0%
+be a little hypothetical but it is it is
+ 
+
+ align:start position:0%
+be a little hypothetical but it is it is
+worth proposing in the sense of uh when
+
+ align:start position:0%
+worth proposing in the sense of uh when
+ 
+
+ align:start position:0%
+worth proposing in the sense of uh when
+we actually see uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we see uh some kind of a a Terra
+
+ align:start position:0%
+uh we see uh some kind of a a Terra
+ 
+
+ align:start position:0%
+uh we see uh some kind of a a Terra
+Cotta uh facing which is which is
+
+ align:start position:0%
+Cotta uh facing which is which is
+ 
+
+ align:start position:0%
+Cotta uh facing which is which is
+adapted in some way to uh uh to the
+
+ align:start position:0%
+adapted in some way to uh uh to the
+ 
+
+ align:start position:0%
+adapted in some way to uh uh to the
+Islamic Motif and things like that and
+
+ align:start position:0%
+Islamic Motif and things like that and
+ 
+
+ align:start position:0%
+Islamic Motif and things like that and
+and this is of course
+
+ align:start position:0%
+and this is of course
+ 
+
+ align:start position:0%
+and this is of course
+proliferated uh through the use of of
+
+ align:start position:0%
+proliferated uh through the use of of
+ 
+
+ align:start position:0%
+proliferated uh through the use of of
+certain forms um Robert hillenbrand a an
+
+ align:start position:0%
+certain forms um Robert hillenbrand a an
+ 
+
+ align:start position:0%
+certain forms um Robert hillenbrand a an
+Islamic scholar actually uh uh theorizes
+
+ align:start position:0%
+Islamic scholar actually uh uh theorizes
+ 
+
+ align:start position:0%
+Islamic scholar actually uh uh theorizes
+this in the sense that he
+
+ align:start position:0%
+this in the sense that he
+ 
+
+ align:start position:0%
+this in the sense that he
+uh he talks about it in the sense of
+
+ align:start position:0%
+uh he talks about it in the sense of
+ 
+
+ align:start position:0%
+uh he talks about it in the sense of
+that a certain amount of mosqu were
+
+ align:start position:0%
+that a certain amount of mosqu were
+ 
+
+ align:start position:0%
+that a certain amount of mosqu were
+already built in this in these regions
+
+ align:start position:0%
+already built in this in these regions
+ 
+
+ align:start position:0%
+already built in this in these regions
+and the idea of of of spreading identity
+
+ align:start position:0%
+and the idea of of of spreading identity
+ 
+
+ align:start position:0%
+and the idea of of of spreading identity
+in some way religious identity was
+
+ align:start position:0%
+in some way religious identity was
+ 
+
+ align:start position:0%
+in some way religious identity was
+actually uh ad adopted by these other
+
+ align:start position:0%
+actually uh ad adopted by these other
+ 
+
+ align:start position:0%
+actually uh ad adopted by these other
+buildings which were the minet and uh
+
+ align:start position:0%
+buildings which were the minet and uh
+ 
+
+ align:start position:0%
+buildings which were the minet and uh
+the tomb and uh these are tombs that
+
+ align:start position:0%
+the tomb and uh these are tombs that
+ 
+
+ align:start position:0%
+the tomb and uh these are tombs that
+actually proliferate from uh from Iran
+
+ align:start position:0%
+actually proliferate from uh from Iran
+ 
+
+ align:start position:0%
+actually proliferate from uh from Iran
+uh during the sjuk T Turks and uh they
+
+ align:start position:0%
+uh during the sjuk T Turks and uh they
+ 
+
+ align:start position:0%
+uh during the sjuk T Turks and uh they
+reach all the way to Swan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Egypt and of course this these tombs are
+
+ align:start position:0%
+Egypt and of course this these tombs are
+ 
+
+ align:start position:0%
+Egypt and of course this these tombs are
+uh they they they carry the same kind of
+
+ align:start position:0%
+uh they they they carry the same kind of
+ 
+
+ align:start position:0%
+uh they they they carry the same kind of
+patterns that that were persistent in in
+
+ align:start position:0%
+patterns that that were persistent in in
+ 
+
+ align:start position:0%
+patterns that that were persistent in in
+the Caspian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area uh this is Isfahan this is the
+
+ align:start position:0%
+area uh this is Isfahan this is the
+ 
+
+ align:start position:0%
+area uh this is Isfahan this is the
+great mosque tahan and uh this the
+
+ align:start position:0%
+great mosque tahan and uh this the
+ 
+
+ align:start position:0%
+great mosque tahan and uh this the
+entire Le
+
+ align:start position:0%
+entire Le
+ 
+
+ align:start position:0%
+entire Le
+route um that that that leads to the to
+
+ align:start position:0%
+route um that that that leads to the to
+ 
+
+ align:start position:0%
+route um that that that leads to the to
+the main mosque is is the Market Street
+
+ align:start position:0%
+the main mosque is is the Market Street
+ 
+
+ align:start position:0%
+the main mosque is is the Market Street
+and uh each of each of the domes is
+
+ align:start position:0%
+and uh each of each of the domes is
+ 
+
+ align:start position:0%
+and uh each of each of the domes is
+actually built in in a different pattern
+
+ align:start position:0%
+actually built in in a different pattern
+ 
+
+ align:start position:0%
+actually built in in a different pattern
+so you have uh a complete and and I'm
+
+ align:start position:0%
+so you have uh a complete and and I'm
+ 
+
+ align:start position:0%
+so you have uh a complete and and I'm
+just showing an example at the right
+
+ align:start position:0%
+just showing an example at the right
+ 
+
+ align:start position:0%
+just showing an example at the right
+hand bottom here uh of of how these
+
+ align:start position:0%
+hand bottom here uh of of how these
+ 
+
+ align:start position:0%
+hand bottom here uh of of how these
+patterns actually uh were used in in
+
+ align:start position:0%
+patterns actually uh were used in in
+ 
+
+ align:start position:0%
+patterns actually uh were used in in
+this Dome construction You by walting of
+
+ align:start position:0%
+this Dome construction You by walting of
+ 
+
+ align:start position:0%
+this Dome construction You by walting of
+course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is in aristan this again the sjuk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Turks in in England
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in this is a little later sorry
+
+ align:start position:0%
+in this is a little later sorry
+ 
+
+ align:start position:0%
+in this is a little later sorry
+uh in uh in Burma uh I was talking about
+
+ align:start position:0%
+uh in uh in Burma uh I was talking about
+ 
+
+ align:start position:0%
+uh in uh in Burma uh I was talking about
+the the Pagan Empire and and this
+
+ align:start position:0%
+the the Pagan Empire and and this
+ 
+
+ align:start position:0%
+the the Pagan Empire and and this
+actually stretched the entire height of
+
+ align:start position:0%
+actually stretched the entire height of
+ 
+
+ align:start position:0%
+actually stretched the entire height of
+of of uh Burma and this was along the
+
+ align:start position:0%
+of of uh Burma and this was along the
+ 
+
+ align:start position:0%
+of of uh Burma and this was along the
+river irawadi and uh this the the the
+
+ align:start position:0%
+river irawadi and uh this the the the
+ 
+
+ align:start position:0%
+river irawadi and uh this the the the
+Empire is is about 400 years old but it
+
+ align:start position:0%
+Empire is is about 400 years old but it
+ 
+
+ align:start position:0%
+Empire is is about 400 years old but it
+it sees us some kind of a PR
+
+ align:start position:0%
+it sees us some kind of a PR
+ 
+
+ align:start position:0%
+it sees us some kind of a PR
+proliferation of of decorative brick
+
+ align:start position:0%
+proliferation of of decorative brick
+ 
+
+ align:start position:0%
+proliferation of of decorative brick
+work at this time and uh it's
+
+ align:start position:0%
+work at this time and uh it's
+ 
+
+ align:start position:0%
+work at this time and uh it's
+interesting to to kind of see uh the
+
+ align:start position:0%
+interesting to to kind of see uh the
+ 
+
+ align:start position:0%
+interesting to to kind of see uh the
+references of this Empire of pagan with
+
+ align:start position:0%
+references of this Empire of pagan with
+ 
+
+ align:start position:0%
+references of this Empire of pagan with
+respect to the sjuk Turks as well as
+
+ align:start position:0%
+respect to the sjuk Turks as well as
+ 
+
+ align:start position:0%
+respect to the sjuk Turks as well as
+China in the sense that it actually
+
+ align:start position:0%
+China in the sense that it actually
+ 
+
+ align:start position:0%
+China in the sense that it actually
+adopts uh uh the Terra Cotta kind of a
+
+ align:start position:0%
+adopts uh uh the Terra Cotta kind of a
+ 
+
+ align:start position:0%
+adopts uh uh the Terra Cotta kind of a
+the Terracotta wees that are that are
+
+ align:start position:0%
+the Terracotta wees that are that are
+ 
+
+ align:start position:0%
+the Terracotta wees that are that are
+that make some kind of reference to both
+
+ align:start position:0%
+that make some kind of reference to both
+ 
+
+ align:start position:0%
+that make some kind of reference to both
+to both regions and uh this is of course
+
+ align:start position:0%
+to both regions and uh this is of course
+ 
+
+ align:start position:0%
+to both regions and uh this is of course
+a time when
+
+ align:start position:0%
+a time when
+ 
+
+ align:start position:0%
+a time when
+when the entire area is global and uh
+
+ align:start position:0%
+when the entire area is global and uh
+ 
+
+ align:start position:0%
+when the entire area is global and uh
+the whole uh and and these these
+
+ align:start position:0%
+the whole uh and and these these
+ 
+
+ align:start position:0%
+the whole uh and and these these
+connections are very possible of of this
+
+ align:start position:0%
+connections are very possible of of this
+ 
+
+ align:start position:0%
+connections are very possible of of this
+kind of a transfer of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Technology um 1 1200 uh we see uh the
+
+ align:start position:0%
+Technology um 1 1200 uh we see uh the
+ 
+
+ align:start position:0%
+Technology um 1 1200 uh we see uh the
+lower uh kind of the the the the African
+
+ align:start position:0%
+lower uh kind of the the the the African
+ 
+
+ align:start position:0%
+lower uh kind of the the the the African
+rout actually connecting back to to the
+
+ align:start position:0%
+rout actually connecting back to to the
+ 
+
+ align:start position:0%
+rout actually connecting back to to the
+Nile and and uh Italy
+
+ align:start position:0%
+Nile and and uh Italy
+ 
+
+ align:start position:0%
+Nile and and uh Italy
+producing maintaining its production of
+
+ align:start position:0%
+producing maintaining its production of
+ 
+
+ align:start position:0%
+producing maintaining its production of
+of decorative brick work and and England
+
+ align:start position:0%
+of decorative brick work and and England
+ 
+
+ align:start position:0%
+of decorative brick work and and England
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so uh we see the first the first
+
+ align:start position:0%
+um so uh we see the first the first
+ 
+
+ align:start position:0%
+um so uh we see the first the first
+U building built out of Roman bricks and
+
+ align:start position:0%
+U building built out of Roman bricks and
+ 
+
+ align:start position:0%
+U building built out of Roman bricks and
+uh this one is again this is uh this is
+
+ align:start position:0%
+uh this one is again this is uh this is
+ 
+
+ align:start position:0%
+uh this one is again this is uh this is
+a kind of a just a continuation of some
+
+ align:start position:0%
+a kind of a just a continuation of some
+ 
+
+ align:start position:0%
+a kind of a just a continuation of some
+kind of a tradition or kind of a
+
+ align:start position:0%
+kind of a tradition or kind of a
+ 
+
+ align:start position:0%
+kind of a tradition or kind of a
+technology of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+construction so this is this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Italy so
+
+ align:start position:0%
+Italy so
+ 
+
+ align:start position:0%
+Italy so
+Sienna um
+
+ align:start position:0%
+Sienna um
+ 
+
+ align:start position:0%
+Sienna um
+the the the idea of of the guild is
+
+ align:start position:0%
+the the the idea of of the guild is
+ 
+
+ align:start position:0%
+the the the idea of of the guild is
+actually building up at this time when
+
+ align:start position:0%
+actually building up at this time when
+ 
+
+ align:start position:0%
+actually building up at this time when
+uh um certain groups of of Masons were
+
+ align:start position:0%
+uh um certain groups of of Masons were
+ 
+
+ align:start position:0%
+uh um certain groups of of Masons were
+actually getting together and and
+
+ align:start position:0%
+actually getting together and and
+ 
+
+ align:start position:0%
+actually getting together and and
+producing and making buildings
+
+ align:start position:0%
+producing and making buildings
+ 
+
+ align:start position:0%
+producing and making buildings
+completely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is uh in in Multan close to
+
+ align:start position:0%
+so this is uh in in Multan close to
+ 
+
+ align:start position:0%
+so this is uh in in Multan close to
+Pakistan now in Pakistan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is all uh again the same
+
+ align:start position:0%
+so this is all uh again the same
+ 
+
+ align:start position:0%
+so this is all uh again the same
+Iranian uh Technologies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extended um I kind of end at at
+
+ align:start position:0%
+extended um I kind of end at at
+ 
+
+ align:start position:0%
+extended um I kind of end at at
+uh at at the at the 1450 when when I
+
+ align:start position:0%
+uh at at the at the 1450 when when I
+ 
+
+ align:start position:0%
+uh at at the at the 1450 when when I
+think uh tracking brick uh loses I mean
+
+ align:start position:0%
+think uh tracking brick uh loses I mean
+ 
+
+ align:start position:0%
+think uh tracking brick uh loses I mean
+I lost complete control of of tracking
+
+ align:start position:0%
+I lost complete control of of tracking
+ 
+
+ align:start position:0%
+I lost complete control of of tracking
+brick at this time it's when all
+
+ align:start position:0%
+brick at this time it's when all
+ 
+
+ align:start position:0%
+brick at this time it's when all
+medieval cities were being built and and
+
+ align:start position:0%
+medieval cities were being built and and
+ 
+
+ align:start position:0%
+medieval cities were being built and and
+every medieval city was built out of
+
+ align:start position:0%
+every medieval city was built out of
+ 
+
+ align:start position:0%
+every medieval city was built out of
+brick and uh and uh it it's uh I I kind
+
+ align:start position:0%
+brick and uh and uh it it's uh I I kind
+ 
+
+ align:start position:0%
+brick and uh and uh it it's uh I I kind
+of uh with the black outline I just uh
+
+ align:start position:0%
+of uh with the black outline I just uh
+ 
+
+ align:start position:0%
+of uh with the black outline I just uh
+give a rough impression of where where
+
+ align:start position:0%
+give a rough impression of where where
+ 
+
+ align:start position:0%
+give a rough impression of where where
+uh these these cities actually were
+
+ align:start position:0%
+uh these these cities actually were
+ 
+
+ align:start position:0%
+uh these these cities actually were
+being built in some way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we see
+
+ align:start position:0%
+um we see
+ 
+
+ align:start position:0%
+um we see
+fortification and of course these are
+
+ align:start position:0%
+fortification and of course these are
+ 
+
+ align:start position:0%
+fortification and of course these are
+now details that you can start seeing
+
+ align:start position:0%
+now details that you can start seeing
+ 
+
+ align:start position:0%
+now details that you can start seeing
+here as well in in the real estate
+
+ align:start position:0%
+here as well in in the real estate
+ 
+
+ align:start position:0%
+here as well in in the real estate
+building and things like that so this is
+
+ align:start position:0%
+building and things like that so this is
+ 
+
+ align:start position:0%
+building and things like that so this is
+where actually certain medieval for
+
+ align:start position:0%
+where actually certain medieval for
+ 
+
+ align:start position:0%
+where actually certain medieval for
+likee constructions were uh propagated
+
+ align:start position:0%
+likee constructions were uh propagated
+ 
+
+ align:start position:0%
+likee constructions were uh propagated
+some kind of a decorated brick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masonry this is uh in England these are
+
+ align:start position:0%
+masonry this is uh in England these are
+ 
+
+ align:start position:0%
+masonry this is uh in England these are
+uh these are again special bricks they
+
+ align:start position:0%
+uh these are again special bricks they
+ 
+
+ align:start position:0%
+uh these are again special bricks they
+are uh the the complete design is is is
+
+ align:start position:0%
+are uh the the complete design is is is
+ 
+
+ align:start position:0%
+are uh the the complete design is is is
+seen first and then uh and then the the
+
+ align:start position:0%
+seen first and then uh and then the the
+ 
+
+ align:start position:0%
+seen first and then uh and then the the
+bricks actually molded and then uh
+
+ align:start position:0%
+bricks actually molded and then uh
+ 
+
+ align:start position:0%
+bricks actually molded and then uh
+placed to to form this this kind of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pattern uh around the 1600s we also see
+
+ align:start position:0%
+pattern uh around the 1600s we also see
+ 
+
+ align:start position:0%
+pattern uh around the 1600s we also see
+uh a a propagation of of this of of the
+
+ align:start position:0%
+uh a a propagation of of this of of the
+ 
+
+ align:start position:0%
+uh a a propagation of of this of of the
+pigeon Tower or the Dove Court uh as
+
+ align:start position:0%
+pigeon Tower or the Dove Court uh as
+ 
+
+ align:start position:0%
+pigeon Tower or the Dove Court uh as
+carrying decorative brick masonry on it
+
+ align:start position:0%
+carrying decorative brick masonry on it
+ 
+
+ align:start position:0%
+carrying decorative brick masonry on it
+and uh this this goes all the way to
+
+ align:start position:0%
+and uh this this goes all the way to
+ 
+
+ align:start position:0%
+and uh this this goes all the way to
+England North North of France Germany
+
+ align:start position:0%
+England North North of France Germany
+ 
+
+ align:start position:0%
+England North North of France Germany
+completely uh it fills up all of Iran uh
+
+ align:start position:0%
+completely uh it fills up all of Iran uh
+ 
+
+ align:start position:0%
+completely uh it fills up all of Iran uh
+so so this kind of a form which is
+
+ align:start position:0%
+so so this kind of a form which is
+ 
+
+ align:start position:0%
+so so this kind of a form which is
+actually carrying uh a very secular form
+
+ align:start position:0%
+actually carrying uh a very secular form
+ 
+
+ align:start position:0%
+actually carrying uh a very secular form
+carrying uh the the pattern brick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masonry uh I I I keep this one in the
+
+ align:start position:0%
+masonry uh I I I keep this one in the
+ 
+
+ align:start position:0%
+masonry uh I I I keep this one in the
+sense that uh I'd like to talk about
+
+ align:start position:0%
+sense that uh I'd like to talk about
+ 
+
+ align:start position:0%
+sense that uh I'd like to talk about
+pattern brick masonry as some kind of a
+
+ align:start position:0%
+pattern brick masonry as some kind of a
+ 
+
+ align:start position:0%
+pattern brick masonry as some kind of a
+branding
+
+ align:start position:0%
+branding
+ 
+
+ align:start position:0%
+branding
+uh in the sense of of branding of Empire
+
+ align:start position:0%
+uh in the sense of of branding of Empire
+ 
+
+ align:start position:0%
+uh in the sense of of branding of Empire
+if that's possible in the sense that uh
+
+ align:start position:0%
+if that's possible in the sense that uh
+ 
+
+ align:start position:0%
+if that's possible in the sense that uh
+a complete set of public institutions
+
+ align:start position:0%
+a complete set of public institutions
+ 
+
+ align:start position:0%
+a complete set of public institutions
+are actually built in in pattern brick
+
+ align:start position:0%
+are actually built in in pattern brick
+ 
+
+ align:start position:0%
+are actually built in in pattern brick
+masonry so how you can actually
+
+ align:start position:0%
+masonry so how you can actually
+ 
+
+ align:start position:0%
+masonry so how you can actually
+recognize uh an architect's work uh
+
+ align:start position:0%
+recognize uh an architect's work uh
+ 
+
+ align:start position:0%
+recognize uh an architect's work uh
+maybe in the city you can actually point
+
+ align:start position:0%
+maybe in the city you can actually point
+ 
+
+ align:start position:0%
+maybe in the city you can actually point
+out to a Gary building or something like
+
+ align:start position:0%
+out to a Gary building or something like
+ 
+
+ align:start position:0%
+out to a Gary building or something like
+that in that sense this actually has a
+
+ align:start position:0%
+that in that sense this actually has a
+ 
+
+ align:start position:0%
+that in that sense this actually has a
+kind of a sense of branding in that in
+
+ align:start position:0%
+kind of a sense of branding in that in
+ 
+
+ align:start position:0%
+kind of a sense of branding in that in
+in the way that it's extremely
+
+ align:start position:0%
+in the way that it's extremely
+ 
+
+ align:start position:0%
+in the way that it's extremely
+recognizable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I I see four regions actually in the
+
+ align:start position:0%
+um I I see four regions actually in the
+ 
+
+ align:start position:0%
+um I I see four regions actually in the
+1600s as as developing their their
+
+ align:start position:0%
+1600s as as developing their their
+ 
+
+ align:start position:0%
+1600s as as developing their their
+characteristic decorative brick masonry
+
+ align:start position:0%
+characteristic decorative brick masonry
+ 
+
+ align:start position:0%
+characteristic decorative brick masonry
+uh one is
+
+ align:start position:0%
+uh one is
+ 
+
+ align:start position:0%
+uh one is
+Bengal the other is Italy England and
+
+ align:start position:0%
+Bengal the other is Italy England and
+ 
+
+ align:start position:0%
+Bengal the other is Italy England and
+Iran so these are kind of four Pockets
+
+ align:start position:0%
+Iran so these are kind of four Pockets
+ 
+
+ align:start position:0%
+Iran so these are kind of four Pockets
+which are actually extremely connected
+
+ align:start position:0%
+which are actually extremely connected
+ 
+
+ align:start position:0%
+which are actually extremely connected
+through the buildings that I've just
+
+ align:start position:0%
+through the buildings that I've just
+ 
+
+ align:start position:0%
+through the buildings that I've just
+shown you uh and and and I'd like to
+
+ align:start position:0%
+shown you uh and and and I'd like to
+ 
+
+ align:start position:0%
+shown you uh and and and I'd like to
+take take one thread through and and
+
+ align:start position:0%
+take take one thread through and and
+ 
+
+ align:start position:0%
+take take one thread through and and
+that would be Bengal uh these are preal
+
+ align:start position:0%
+that would be Bengal uh these are preal
+ 
+
+ align:start position:0%
+that would be Bengal uh these are preal
+Empire this is the preal Salan in Bengal
+
+ align:start position:0%
+Empire this is the preal Salan in Bengal
+ 
+
+ align:start position:0%
+Empire this is the preal Salan in Bengal
+uh of God and hazzat pandwa and uh you
+
+ align:start position:0%
+uh of God and hazzat pandwa and uh you
+ 
+
+ align:start position:0%
+uh of God and hazzat pandwa and uh you
+can see these are of course completely
+
+ align:start position:0%
+can see these are of course completely
+ 
+
+ align:start position:0%
+can see these are of course completely
+ruined uh this is you can just see the
+
+ align:start position:0%
+ruined uh this is you can just see the
+ 
+
+ align:start position:0%
+ruined uh this is you can just see the
+the few patterns and the Terra Cotta
+
+ align:start position:0%
+the few patterns and the Terra Cotta
+ 
+
+ align:start position:0%
+the few patterns and the Terra Cotta
+Works uh in in in this
+
+ align:start position:0%
+Works uh in in in this
+ 
+
+ align:start position:0%
+Works uh in in in this
+picture uh the
+
+ align:start position:0%
+picture uh the
+ 
+
+ align:start position:0%
+picture uh the
+mosques uh this is uh the UI molum again
+
+ align:start position:0%
+mosques uh this is uh the UI molum again
+ 
+
+ align:start position:0%
+mosques uh this is uh the UI molum again
+it's it's the proliferation of the Tomb
+
+ align:start position:0%
+it's it's the proliferation of the Tomb
+ 
+
+ align:start position:0%
+it's it's the proliferation of the Tomb
+as the as the carrier of and and these
+
+ align:start position:0%
+as the as the carrier of and and these
+ 
+
+ align:start position:0%
+as the as the carrier of and and these
+images are actually reminiscent of the
+
+ align:start position:0%
+images are actually reminiscent of the
+ 
+
+ align:start position:0%
+images are actually reminiscent of the
+Aswan tombs and and uh it's it's and the
+
+ align:start position:0%
+Aswan tombs and and uh it's it's and the
+ 
+
+ align:start position:0%
+Aswan tombs and and uh it's it's and the
+Pagan and and this this kind of a the
+
+ align:start position:0%
+Pagan and and this this kind of a the
+ 
+
+ align:start position:0%
+Pagan and and this this kind of a the
+plan is is a chamber and it's a very
+
+ align:start position:0%
+plan is is a chamber and it's a very
+ 
+
+ align:start position:0%
+plan is is a chamber and it's a very
+solid structure uh decorated brick brick
+
+ align:start position:0%
+solid structure uh decorated brick brick
+ 
+
+ align:start position:0%
+solid structure uh decorated brick brick
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+and uh this is a very high level of
+
+ align:start position:0%
+and uh this is a very high level of
+ 
+
+ align:start position:0%
+and uh this is a very high level of
+terracotta facing in in these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works and and these
+
+ align:start position:0%
+works and and these
+ 
+
+ align:start position:0%
+works and and these
+mosques
+
+ align:start position:0%
+mosques
+ 
+
+ align:start position:0%
+mosques
+uh well there are two stories for these
+
+ align:start position:0%
+uh well there are two stories for these
+ 
+
+ align:start position:0%
+uh well there are two stories for these
+mosques one is that
+
+ align:start position:0%
+mosques one is that
+ 
+
+ align:start position:0%
+mosques one is that
+uh uh they they actually plundered the
+
+ align:start position:0%
+uh uh they they actually plundered the
+ 
+
+ align:start position:0%
+uh uh they they actually plundered the
+Pagan temples and the Buddhist temples
+
+ align:start position:0%
+Pagan temples and the Buddhist temples
+ 
+
+ align:start position:0%
+Pagan temples and the Buddhist temples
+in the area and actually used the Terra
+
+ align:start position:0%
+in the area and actually used the Terra
+ 
+
+ align:start position:0%
+in the area and actually used the Terra
+Cotta for the
+
+ align:start position:0%
+Cotta for the
+ 
+
+ align:start position:0%
+Cotta for the
+mosques uh or of course it a more Global
+
+ align:start position:0%
+mosques uh or of course it a more Global
+ 
+
+ align:start position:0%
+mosques uh or of course it a more Global
+explanation would be that the Craftsmen
+
+ align:start position:0%
+explanation would be that the Craftsmen
+ 
+
+ align:start position:0%
+explanation would be that the Craftsmen
+were just just there and uh this kind of
+
+ align:start position:0%
+were just just there and uh this kind of
+ 
+
+ align:start position:0%
+were just just there and uh this kind of
+a uh just a blurring of boundaries and
+
+ align:start position:0%
+a uh just a blurring of boundaries and
+ 
+
+ align:start position:0%
+a uh just a blurring of boundaries and
+the movement of Craftsman can actually
+
+ align:start position:0%
+the movement of Craftsman can actually
+ 
+
+ align:start position:0%
+the movement of Craftsman can actually
+facilitate architecture like this and
+
+ align:start position:0%
+facilitate architecture like this and
+ 
+
+ align:start position:0%
+facilitate architecture like this and
+this moves very smoothly into these are
+
+ align:start position:0%
+this moves very smoothly into these are
+ 
+
+ align:start position:0%
+this moves very smoothly into these are
+these are temples these are Hindu
+
+ align:start position:0%
+these are temples these are Hindu
+ 
+
+ align:start position:0%
+these are temples these are Hindu
+temples and uh in vishnupur again Bengal
+
+ align:start position:0%
+temples and uh in vishnupur again Bengal
+ 
+
+ align:start position:0%
+temples and uh in vishnupur again Bengal
+and again they have the same uh kind of
+
+ align:start position:0%
+and again they have the same uh kind of
+ 
+
+ align:start position:0%
+and again they have the same uh kind of
+a Tom like uh character to them and uh
+
+ align:start position:0%
+a Tom like uh character to them and uh
+ 
+
+ align:start position:0%
+a Tom like uh character to them and uh
+uh you can see the whole the the
+
+ align:start position:0%
+uh you can see the whole the the
+ 
+
+ align:start position:0%
+uh you can see the whole the the
+transference of from Buddhist to Islamic
+
+ align:start position:0%
+transference of from Buddhist to Islamic
+ 
+
+ align:start position:0%
+transference of from Buddhist to Islamic
+and to Hindu and uh kind of
+
+ align:start position:0%
+and to Hindu and uh kind of
+ 
+
+ align:start position:0%
+and to Hindu and uh kind of
+a religious
+
+ align:start position:0%
+a religious
+ 
+
+ align:start position:0%
+a religious
+integration and uh we end up with a 19th
+
+ align:start position:0%
+integration and uh we end up with a 19th
+ 
+
+ align:start position:0%
+integration and uh we end up with a 19th
+century uh settlement in Bengal which is
+
+ align:start position:0%
+century uh settlement in Bengal which is
+ 
+
+ align:start position:0%
+century uh settlement in Bengal which is
+again built and break this is just one
+
+ align:start position:0%
+again built and break this is just one
+ 
+
+ align:start position:0%
+again built and break this is just one
+settlement and and then the um there are
+
+ align:start position:0%
+settlement and and then the um there are
+ 
+
+ align:start position:0%
+settlement and and then the um there are
+there are accounts of the river changing
+
+ align:start position:0%
+there are accounts of the river changing
+ 
+
+ align:start position:0%
+there are accounts of the river changing
+course and this is actually the entire
+
+ align:start position:0%
+course and this is actually the entire
+ 
+
+ align:start position:0%
+course and this is actually the entire
+Delta region of the Ganges so the the
+
+ align:start position:0%
+Delta region of the Ganges so the the
+ 
+
+ align:start position:0%
+Delta region of the Ganges so the the
+the keeps changing course in that
+
+ align:start position:0%
+the keeps changing course in that
+ 
+
+ align:start position:0%
+the keeps changing course in that
+sense um the importance of cities also
+
+ align:start position:0%
+sense um the importance of cities also
+ 
+
+ align:start position:0%
+sense um the importance of cities also
+kind of depends on
+
+ align:start position:0%
+kind of depends on
+ 
+
+ align:start position:0%
+kind of depends on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh later in the 19th century decorative
+
+ align:start position:0%
+uh later in the 19th century decorative
+ 
+
+ align:start position:0%
+uh later in the 19th century decorative
+brick masonry actually gets into uh
+
+ align:start position:0%
+brick masonry actually gets into uh
+ 
+
+ align:start position:0%
+brick masonry actually gets into uh
+International expositions as
+
+ align:start position:0%
+International expositions as
+ 
+
+ align:start position:0%
+International expositions as
+representative of some kind of identity
+
+ align:start position:0%
+representative of some kind of identity
+ 
+
+ align:start position:0%
+representative of some kind of identity
+uh it it
+
+ align:start position:0%
+uh it it
+ 
+
+ align:start position:0%
+uh it it
+uh it it it is uh put into manuals into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are some of the first houses built
+
+ align:start position:0%
+these are some of the first houses built
+ 
+
+ align:start position:0%
+these are some of the first houses built
+not on the left is actually the one of
+
+ align:start position:0%
+not on the left is actually the one of
+ 
+
+ align:start position:0%
+not on the left is actually the one of
+the first houses built in in America and
+
+ align:start position:0%
+the first houses built in in America and
+ 
+
+ align:start position:0%
+the first houses built in in America and
+uh this would be of course the the New
+
+ align:start position:0%
+uh this would be of course the the New
+ 
+
+ align:start position:0%
+uh this would be of course the the New
+England kind of a house and these these
+
+ align:start position:0%
+England kind of a house and these these
+ 
+
+ align:start position:0%
+England kind of a house and these these
+the one on the right is uh in
+
+ align:start position:0%
+the one on the right is uh in
+ 
+
+ align:start position:0%
+the one on the right is uh in
+DC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um these are again carry forward of of
+
+ align:start position:0%
+um these are again carry forward of of
+ 
+
+ align:start position:0%
+um these are again carry forward of of
+some kind of pattern brick masonry which
+
+ align:start position:0%
+some kind of pattern brick masonry which
+ 
+
+ align:start position:0%
+some kind of pattern brick masonry which
+is which which finds a complex route
+
+ align:start position:0%
+is which which finds a complex route
+ 
+
+ align:start position:0%
+is which which finds a complex route
+through uh through England and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh more more recent uh we have
+
+ align:start position:0%
+uh uh more more recent uh we have
+ 
+
+ align:start position:0%
+uh uh more more recent uh we have
+Antonio godi who uh kind of worked with
+
+ align:start position:0%
+Antonio godi who uh kind of worked with
+ 
+
+ align:start position:0%
+Antonio godi who uh kind of worked with
+all kinds of decorative brick work in
+
+ align:start position:0%
+all kinds of decorative brick work in
+ 
+
+ align:start position:0%
+all kinds of decorative brick work in
+the sense of special breaks and Terra
+
+ align:start position:0%
+the sense of special breaks and Terra
+ 
+
+ align:start position:0%
+the sense of special breaks and Terra
+Cotta um
+
+ align:start position:0%
+Cotta um
+ 
+
+ align:start position:0%
+Cotta um
+uh deformed bricks tiles uh in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense uh even more recent Frank Lloyd
+
+ align:start position:0%
+sense uh even more recent Frank Lloyd
+ 
+
+ align:start position:0%
+sense uh even more recent Frank Lloyd
+Wright uh and Lou khah and we also have
+
+ align:start position:0%
+Wright uh and Lou khah and we also have
+ 
+
+ align:start position:0%
+Wright uh and Lou khah and we also have
+the monad KN building in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chicago and uh certain uh sensibility
+
+ align:start position:0%
+Chicago and uh certain uh sensibility
+ 
+
+ align:start position:0%
+Chicago and uh certain uh sensibility
+about about making the plint carries
+
+ align:start position:0%
+about about making the plint carries
+ 
+
+ align:start position:0%
+about about making the plint carries
+forward uh through
+
+ align:start position:0%
+forward uh through
+ 
+
+ align:start position:0%
+forward uh through
+through uh through certain examples
+
+ align:start position:0%
+through uh through certain examples
+ 
+
+ align:start position:0%
+through uh through certain examples
+which I did not show you all uh is uh
+
+ align:start position:0%
+which I did not show you all uh is uh
+ 
+
+ align:start position:0%
+which I did not show you all uh is uh
+Frankl right kind of
+
+ align:start position:0%
+Frankl right kind of
+ 
+
+ align:start position:0%
+Frankl right kind of
+emphasizes uh the horizontal in some way
+
+ align:start position:0%
+emphasizes uh the horizontal in some way
+ 
+
+ align:start position:0%
+emphasizes uh the horizontal in some way
+and you can see his his vertical joints
+
+ align:start position:0%
+and you can see his his vertical joints
+ 
+
+ align:start position:0%
+and you can see his his vertical joints
+are are flush with the brick and uh his
+
+ align:start position:0%
+are are flush with the brick and uh his
+ 
+
+ align:start position:0%
+are are flush with the brick and uh his
+his horizontal actually recessed in some
+
+ align:start position:0%
+his horizontal actually recessed in some
+ 
+
+ align:start position:0%
+his horizontal actually recessed in some
+way so you actually catch horizontal
+
+ align:start position:0%
+way so you actually catch horizontal
+ 
+
+ align:start position:0%
+way so you actually catch horizontal
+lines as
+
+ align:start position:0%
+lines as
+ 
+
+ align:start position:0%
+lines as
+Shadows um these were also used in in
+
+ align:start position:0%
+Shadows um these were also used in in
+ 
+
+ align:start position:0%
+Shadows um these were also used in in
+Roman brick work
+
+ align:start position:0%
+Roman brick work
+ 
+
+ align:start position:0%
+Roman brick work
+uh long
+
+ align:start position:0%
+uh long
+ 
+
+ align:start position:0%
+uh long
+before um Iran of course uh this is
+
+ align:start position:0%
+before um Iran of course uh this is
+ 
+
+ align:start position:0%
+before um Iran of course uh this is
+recent work an aak Khan winner aak Khan
+
+ align:start position:0%
+recent work an aak Khan winner aak Khan
+ 
+
+ align:start position:0%
+recent work an aak Khan winner aak Khan
+Award winner and uh it actually kind of
+
+ align:start position:0%
+Award winner and uh it actually kind of
+ 
+
+ align:start position:0%
+Award winner and uh it actually kind of
+uses decorative brick masonry as as an
+
+ align:start position:0%
+uses decorative brick masonry as as an
+ 
+
+ align:start position:0%
+uses decorative brick masonry as as an
+identity uh as a national identity now
+
+ align:start position:0%
+identity uh as a national identity now
+ 
+
+ align:start position:0%
+identity uh as a national identity now
+it it reflects in Miniatures it reflects
+
+ align:start position:0%
+it it reflects in Miniatures it reflects
+ 
+
+ align:start position:0%
+it it reflects in Miniatures it reflects
+in in the architecture as
+
+ align:start position:0%
+in in the architecture as
+ 
+
+ align:start position:0%
+in in the architecture as
+well um I'll I'll just end with the
+
+ align:start position:0%
+well um I'll I'll just end with the
+ 
+
+ align:start position:0%
+well um I'll I'll just end with the
+works of Lori Baker in Kerala India and
+
+ align:start position:0%
+works of Lori Baker in Kerala India and
+ 
+
+ align:start position:0%
+works of Lori Baker in Kerala India and
+uh his his he being called the poor
+
+ align:start position:0%
+uh his his he being called the poor
+ 
+
+ align:start position:0%
+uh his his he being called the poor
+man's architect so the actually brick
+
+ align:start position:0%
+man's architect so the actually brick
+ 
+
+ align:start position:0%
+man's architect so the actually brick
+work starts uh in in in the developing
+
+ align:start position:0%
+work starts uh in in in the developing
+ 
+
+ align:start position:0%
+work starts uh in in in the developing
+nations uh starts to kind of respond to
+
+ align:start position:0%
+nations uh starts to kind of respond to
+ 
+
+ align:start position:0%
+nations uh starts to kind of respond to
+um uh the financial conditions and and
+
+ align:start position:0%
+um uh the financial conditions and and
+ 
+
+ align:start position:0%
+um uh the financial conditions and and
+basically the general economy of of the
+
+ align:start position:0%
+basically the general economy of of the
+ 
+
+ align:start position:0%
+basically the general economy of of the
+the and of course making beautiful
+
+ align:start position:0%
+the and of course making beautiful
+ 
+
+ align:start position:0%
+the and of course making beautiful
+buildings within a a certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+economy
+
+ align:start position:0%
+economy
+ 
+
+ align:start position:0%
+economy
+um he uses the the thinnest wall
+
+ align:start position:0%
+um he uses the the thinnest wall
+ 
+
+ align:start position:0%
+um he uses the the thinnest wall
+possible which is just uh half of the
+
+ align:start position:0%
+possible which is just uh half of the
+ 
+
+ align:start position:0%
+possible which is just uh half of the
+brick size and of course the stability
+
+ align:start position:0%
+brick size and of course the stability
+ 
+
+ align:start position:0%
+brick size and of course the stability
+is got through certain geometries of of
+
+ align:start position:0%
+is got through certain geometries of of
+ 
+
+ align:start position:0%
+is got through certain geometries of of
+of arches and plan and things like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is a girls hostel just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll just end on on some on a note
+
+ align:start position:0%
+and I'll just end on on some on a note
+ 
+
+ align:start position:0%
+and I'll just end on on some on a note
+on which is slightly more Technology
+
+ align:start position:0%
+on which is slightly more Technology
+ 
+
+ align:start position:0%
+on which is slightly more Technology
+based in the sense that we've we've kind
+
+ align:start position:0%
+based in the sense that we've we've kind
+ 
+
+ align:start position:0%
+based in the sense that we've we've kind
+of passed the the stage of of uh of
+
+ align:start position:0%
+of passed the the stage of of uh of
+ 
+
+ align:start position:0%
+of passed the the stage of of uh of
+doing this and
+
+ align:start position:0%
+doing this and
+ 
+
+ align:start position:0%
+doing this and
+uh and our kills have definitely kind of
+
+ align:start position:0%
+uh and our kills have definitely kind of
+ 
+
+ align:start position:0%
+uh and our kills have definitely kind of
+evolved into
+
+ align:start position:0%
+evolved into
+ 
+
+ align:start position:0%
+evolved into
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um into this at the right hand bottom is
+
+ align:start position:0%
+um into this at the right hand bottom is
+ 
+
+ align:start position:0%
+um into this at the right hand bottom is
+actually what our modern brick making
+
+ align:start position:0%
+actually what our modern brick making
+ 
+
+ align:start position:0%
+actually what our modern brick making
+factory would look like and and the
+
+ align:start position:0%
+factory would look like and and the
+ 
+
+ align:start position:0%
+factory would look like and and the
+possibilities of of creating any kind of
+
+ align:start position:0%
+possibilities of of creating any kind of
+ 
+
+ align:start position:0%
+possibilities of of creating any kind of
+brick of any color and any size and any
+
+ align:start position:0%
+brick of any color and any size and any
+ 
+
+ align:start position:0%
+brick of any color and any size and any
+uh any
+
+ align:start position:0%
+uh any
+ 
+
+ align:start position:0%
+uh any
+consistency um and just the fact that uh
+
+ align:start position:0%
+consistency um and just the fact that uh
+ 
+
+ align:start position:0%
+consistency um and just the fact that uh
+the potential of decorative brick
+
+ align:start position:0%
+the potential of decorative brick
+ 
+
+ align:start position:0%
+the potential of decorative brick
+masonry even
+
+ align:start position:0%
+masonry even
+ 
+
+ align:start position:0%
+masonry even
+today thank you
\ No newline at end of file
diff --git a/KkSr0SvXfNY.txt b/KkSr0SvXfNY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a9835e85b7f36bfa5d15b1b8910726e2d713bfe
--- /dev/null
+++ b/KkSr0SvXfNY.txt
@@ -0,0 +1,1715 @@
+align:start position:0%
+ 
+here is the answer answer it's easier
+
+ align:start position:0%
+here is the answer answer it's easier
+ 
+
+ align:start position:0%
+here is the answer answer it's easier
+apparently to write one over T and one
+
+ align:start position:0%
+apparently to write one over T and one
+ 
+
+ align:start position:0%
+apparently to write one over T and one
+over T is equal to one plus one over
+
+ align:start position:0%
+over T is equal to one plus one over
+ 
+
+ align:start position:0%
+over T is equal to one plus one over
+four V naught squared over e times E
+
+ align:start position:0%
+four V naught squared over e times E
+ 
+
+ align:start position:0%
+four V naught squared over e times E
+Plus V naught times sine squared of two
+
+ align:start position:0%
+Plus V naught times sine squared of two
+ 
+
+ align:start position:0%
+Plus V naught times sine squared of two
+K to a so the one thing to notice in
+
+ align:start position:0%
+K to a so the one thing to notice in
+ 
+
+ align:start position:0%
+K to a so the one thing to notice in
+this formula it's a little complicated
+
+ align:start position:0%
+this formula it's a little complicated
+ 
+
+ align:start position:0%
+this formula it's a little complicated
+is that the second term is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because V naught squared is positive if
+
+ align:start position:0%
+because V naught squared is positive if
+ 
+
+ align:start position:0%
+because V naught squared is positive if
+the energy is positive a sine squared is
+
+ align:start position:0%
+the energy is positive a sine squared is
+ 
+
+ align:start position:0%
+the energy is positive a sine squared is
+positive so if this is positive if the
+
+ align:start position:0%
+positive so if this is positive if the
+ 
+
+ align:start position:0%
+positive so if this is positive if the
+right hand side is greater than 1 and
+
+ align:start position:0%
+right hand side is greater than 1 and
+ 
+
+ align:start position:0%
+right hand side is greater than 1 and
+therefore the T is less than 1 so this
+
+ align:start position:0%
+therefore the T is less than 1 so this
+ 
+
+ align:start position:0%
+therefore the T is less than 1 so this
+implies P less than or equal to 1 and
+
+ align:start position:0%
+implies P less than or equal to 1 and
+ 
+
+ align:start position:0%
+implies P less than or equal to 1 and
+there seems to be a possibility of T
+
+ align:start position:0%
+there seems to be a possibility of T
+ 
+
+ align:start position:0%
+there seems to be a possibility of T
+being equal to 1 exactly if the sine
+
+ align:start position:0%
+being equal to 1 exactly if the sine
+ 
+
+ align:start position:0%
+being equal to 1 exactly if the sine
+squared of this quantity or the sine of
+
+ align:start position:0%
+squared of this quantity or the sine of
+ 
+
+ align:start position:0%
+squared of this quantity or the sine of
+this one did he vanishes so there is a
+
+ align:start position:0%
+this one did he vanishes so there is a
+ 
+
+ align:start position:0%
+this one did he vanishes so there is a
+possibility of very interesting
+
+ align:start position:0%
+possibility of very interesting
+ 
+
+ align:start position:0%
+possibility of very interesting
+saturation in which the transmission is
+
+ align:start position:0%
+saturation in which the transmission is
+ 
+
+ align:start position:0%
+saturation in which the transmission is
+really equal to 1 so we'll we'll see it
+
+ align:start position:0%
+really equal to 1 so we'll we'll see it
+ 
+
+ align:start position:0%
+really equal to 1 so we'll we'll see it
+the other thing you can notice is that
+
+ align:start position:0%
+the other thing you can notice is that
+ 
+
+ align:start position:0%
+the other thing you can notice is that
+as he goes to 0 this is infinite and
+
+ align:start position:0%
+as he goes to 0 this is infinite and
+ 
+
+ align:start position:0%
+as he goes to 0 this is infinite and
+therefore T is going to 0 no
+
+ align:start position:0%
+therefore T is going to 0 no
+ 
+
+ align:start position:0%
+therefore T is going to 0 no
+transmission as some the energy goes to
+
+ align:start position:0%
+transmission as some the energy goes to
+ 
+
+ align:start position:0%
+transmission as some the energy goes to
+0 as the energy goes to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this term goes to 0 and you get
+
+ align:start position:0%
+well this term goes to 0 and you get
+ 
+
+ align:start position:0%
+well this term goes to 0 and you get
+transmission P equals to 1 so these are
+
+ align:start position:0%
+transmission P equals to 1 so these are
+ 
+
+ align:start position:0%
+transmission P equals to 1 so these are
+interesting limits now to appreciate
+
+ align:start position:0%
+interesting limits now to appreciate
+ 
+
+ align:start position:0%
+interesting limits now to appreciate
+this better we can write it with unit
+
+ align:start position:0%
+this better we can write it with unit
+ 
+
+ align:start position:0%
+this better we can write it with unit
+free language so for that I'll do the
+
+ align:start position:0%
+free language so for that I'll do the
+ 
+
+ align:start position:0%
+free language so for that I'll do the
+following I'll it's a little rewriting
+
+ align:start position:0%
+following I'll it's a little rewriting
+ 
+
+ align:start position:0%
+following I'll it's a little rewriting
+but it helps a bit so think of 2 K 2
+
+ align:start position:0%
+but it helps a bit so think of 2 K 2
+ 
+
+ align:start position:0%
+but it helps a bit so think of 2 K 2
+times a this factor as the argument of
+
+ align:start position:0%
+times a this factor as the argument of
+ 
+
+ align:start position:0%
+times a this factor as the argument of
+the sine function well it's 2 K 2 was
+
+ align:start position:0%
+the sine function well it's 2 K 2 was
+ 
+
+ align:start position:0%
+the sine function well it's 2 K 2 was
+define up there so it's two M ay squared
+
+ align:start position:0%
+define up there so it's two M ay squared
+ 
+
+ align:start position:0%
+define up there so it's two M ay squared
+e plus V naught over H squared and now I
+
+ align:start position:0%
+e plus V naught over H squared and now I
+ 
+
+ align:start position:0%
+e plus V naught over H squared and now I
+put the a inside the square root so what
+
+ align:start position:0%
+put the a inside the square root so what
+ 
+
+ align:start position:0%
+put the a inside the square root so what
+do we have here 2 times square root of
+
+ align:start position:0%
+do we have here 2 times square root of
+ 
+
+ align:start position:0%
+do we have here 2 times square root of
+2m a squared let's factor a V naught so
+
+ align:start position:0%
+2m a squared let's factor a V naught so
+ 
+
+ align:start position:0%
+2m a squared let's factor a V naught so
+you have 1 plus e over V naught and have
+
+ align:start position:0%
+you have 1 plus e over V naught and have
+ 
+
+ align:start position:0%
+you have 1 plus e over V naught and have
+H squared here so this is ok there's
+
+ align:start position:0%
+H squared here so this is ok there's
+ 
+
+ align:start position:0%
+H squared here so this is ok there's
+clearly two things you can do first
+
+ align:start position:0%
+clearly two things you can do first
+ 
+
+ align:start position:0%
+clearly two things you can do first
+define a unit free energy so the energy
+
+ align:start position:0%
+define a unit free energy so the energy
+ 
+
+ align:start position:0%
+define a unit free energy so the energy
+is now described by this little e
+
+ align:start position:0%
+is now described by this little e
+ 
+
+ align:start position:0%
+is now described by this little e
+without units that compares the energy
+
+ align:start position:0%
+without units that compares the energy
+ 
+
+ align:start position:0%
+without units that compares the energy
+of your energy eigenstate to the depth
+
+ align:start position:0%
+of your energy eigenstate to the depth
+ 
+
+ align:start position:0%
+of your energy eigenstate to the depth
+of the potential so it should be over V
+
+ align:start position:0%
+of the potential so it should be over V
+ 
+
+ align:start position:0%
+of the potential so it should be over V
+naught so this is nice you don't have to
+
+ align:start position:0%
+naught so this is nice you don't have to
+ 
+
+ align:start position:0%
+naught so this is nice you don't have to
+talk about Eevee
+
+ align:start position:0%
+talk about Eevee
+ 
+
+ align:start position:0%
+talk about Eevee
+or some quantity just a pure number and
+
+ align:start position:0%
+or some quantity just a pure number and
+ 
+
+ align:start position:0%
+or some quantity just a pure number and
+here there is another number that is
+
+ align:start position:0%
+here there is another number that is
+ 
+
+ align:start position:0%
+here there is another number that is
+famous this is the number Z naught
+
+ align:start position:0%
+famous this is the number Z naught
+ 
+
+ align:start position:0%
+famous this is the number Z naught
+squared of potential well this is the
+
+ align:start position:0%
+squared of potential well this is the
+ 
+
+ align:start position:0%
+squared of potential well this is the
+unit free number that tells you how deep
+
+ align:start position:0%
+unit free number that tells you how deep
+ 
+
+ align:start position:0%
+unit free number that tells you how deep
+or profound is your potential and
+
+ align:start position:0%
+or profound is your potential and
+ 
+
+ align:start position:0%
+or profound is your potential and
+controls the number of zeros so at this
+
+ align:start position:0%
+controls the number of zeros so at this
+ 
+
+ align:start position:0%
+controls the number of zeros so at this
+moment this is simply to Z naught
+
+ align:start position:0%
+moment this is simply to Z naught
+ 
+
+ align:start position:0%
+moment this is simply to Z naught
+because the square root is there and
+
+ align:start position:0%
+because the square root is there and
+ 
+
+ align:start position:0%
+because the square root is there and
+takes the Z naught squared out the Z
+
+ align:start position:0%
+takes the Z naught squared out the Z
+ 
+
+ align:start position:0%
+takes the Z naught squared out the Z
+naught square root of 1 plus e just kind
+
+ align:start position:0%
+naught square root of 1 plus e just kind
+ 
+
+ align:start position:0%
+naught square root of 1 plus e just kind
+of nice so of here you can divide by V
+
+ align:start position:0%
+of nice so of here you can divide by V
+ 
+
+ align:start position:0%
+of nice so of here you can divide by V
+naught squared numerator and denominator
+
+ align:start position:0%
+naught squared numerator and denominator
+ 
+
+ align:start position:0%
+naught squared numerator and denominator
+so you have an e over V naught and a 1
+
+ align:start position:0%
+so you have an e over V naught and a 1
+ 
+
+ align:start position:0%
+so you have an e over V naught and a 1
+plus an e over V naught so the end
+
+ align:start position:0%
+plus an e over V naught so the end
+ 
+
+ align:start position:0%
+plus an e over V naught so the end
+result is that 1 over T is now 1 plus 1
+
+ align:start position:0%
+result is that 1 over T is now 1 plus 1
+ 
+
+ align:start position:0%
+result is that 1 over T is now 1 plus 1
+over 4 e 1 plus e sine squared of 2 Z
+
+ align:start position:0%
+over 4 e 1 plus e sine squared of 2 Z
+ 
+
+ align:start position:0%
+over 4 e 1 plus e sine squared of 2 Z
+naught square root of 1 plus e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's ready for numerical calculation
+
+ align:start position:0%
+so it's ready for numerical calculation
+ 
+
+ align:start position:0%
+so it's ready for numerical calculation
+for plotting and doing all kinds of
+
+ align:start position:0%
+for plotting and doing all kinds of
+ 
+
+ align:start position:0%
+for plotting and doing all kinds of
+things with it but what we want to
+
+ align:start position:0%
+things with it but what we want to
+ 
+
+ align:start position:0%
+things with it but what we want to
+understand is this phenomenon that you
+
+ align:start position:0%
+understand is this phenomenon that you
+ 
+
+ align:start position:0%
+understand is this phenomenon that you
+would expect in general some reflection
+
+ align:start position:0%
+would expect in general some reflection
+ 
+
+ align:start position:0%
+would expect in general some reflection
+and some transmission but there is a
+
+ align:start position:0%
+and some transmission but there is a
+ 
+
+ align:start position:0%
+and some transmission but there is a
+possibility when T is equal to one and
+
+ align:start position:0%
+possibility when T is equal to one and
+ 
+
+ align:start position:0%
+possibility when T is equal to one and
+in particular when this sine squared
+
+ align:start position:0%
+in particular when this sine squared
+ 
+
+ align:start position:0%
+in particular when this sine squared
+function is equal to zero and that will
+
+ align:start position:0%
+function is equal to zero and that will
+ 
+
+ align:start position:0%
+function is equal to zero and that will
+make T equals to one then you have a
+
+ align:start position:0%
+make T equals to one then you have a
+ 
+
+ align:start position:0%
+make T equals to one then you have a
+perfect transmission so let's see why it
+
+ align:start position:0%
+perfect transmission so let's see why it
+ 
+
+ align:start position:0%
+perfect transmission so let's see why it
+is happening or under what circumstances
+
+ align:start position:0%
+is happening or under what circumstances
+ 
+
+ align:start position:0%
+is happening or under what circumstances
+it happens so for what energies will we
+
+ align:start position:0%
+it happens so for what energies will we
+ 
+
+ align:start position:0%
+it happens so for what energies will we
+have for what energies energies is P
+
+ align:start position:0%
+have for what energies energies is P
+ 
+
+ align:start position:0%
+have for what energies energies is P
+equal to 1 it's perfect transmission no
+
+ align:start position:0%
+equal to 1 it's perfect transmission no
+ 
+
+ align:start position:0%
+equal to 1 it's perfect transmission no
+reflection whatsoever so we need then
+
+ align:start position:0%
+reflection whatsoever so we need then
+ 
+
+ align:start position:0%
+reflection whatsoever so we need then
+that the argument of this sine function
+
+ align:start position:0%
+that the argument of this sine function
+ 
+
+ align:start position:0%
+that the argument of this sine function
+be equal to multiple of Pi to Z naught
+
+ align:start position:0%
+be equal to multiple of Pi to Z naught
+ 
+
+ align:start position:0%
+be equal to multiple of Pi to Z naught
+square root of 1 plus e is equal a
+
+ align:start position:0%
+square root of 1 plus e is equal a
+ 
+
+ align:start position:0%
+square root of 1 plus e is equal a
+multiple of Pi now we will say what
+
+ align:start position:0%
+multiple of Pi now we will say what
+ 
+
+ align:start position:0%
+multiple of Pi now we will say what
+multiple of Pi well will be 0 1 2 3 not
+
+ align:start position:0%
+multiple of Pi well will be 0 1 2 3 not
+ 
+
+ align:start position:0%
+multiple of Pi well will be 0 1 2 3 not
+obvious because the only thing you have
+
+ align:start position:0%
+obvious because the only thing you have
+ 
+
+ align:start position:0%
+obvious because the only thing you have
+here to adjust is the energy the energy
+
+ align:start position:0%
+here to adjust is the energy the energy
+ 
+
+ align:start position:0%
+here to adjust is the energy the energy
+is positive and that's that little e
+
+ align:start position:0%
+is positive and that's that little e
+ 
+
+ align:start position:0%
+is positive and that's that little e
+here so this number n must exceed some
+
+ align:start position:0%
+here so this number n must exceed some
+ 
+
+ align:start position:0%
+here so this number n must exceed some
+number because this left hand side never
+
+ align:start position:0%
+number because this left hand side never
+ 
+
+ align:start position:0%
+number because this left hand side never
+becomes very small the small
+
+ align:start position:0%
+becomes very small the small
+ 
+
+ align:start position:0%
+becomes very small the small
+it can be is to Z not so n must be
+
+ align:start position:0%
+it can be is to Z not so n must be
+ 
+
+ align:start position:0%
+it can be is to Z not so n must be
+greater than or equal to to Z naught
+
+ align:start position:0%
+greater than or equal to to Z naught
+ 
+
+ align:start position:0%
+greater than or equal to to Z naught
+over PI this is because e since e is
+
+ align:start position:0%
+over PI this is because e since e is
+ 
+
+ align:start position:0%
+over PI this is because e since e is
+greater than zero so the left-hand side
+
+ align:start position:0%
+greater than zero so the left-hand side
+ 
+
+ align:start position:0%
+greater than zero so the left-hand side
+is it's a number that is greater than to
+
+ align:start position:0%
+is it's a number that is greater than to
+ 
+
+ align:start position:0%
+is it's a number that is greater than to
+Z naught and the right-hand side must
+
+ align:start position:0%
+Z naught and the right-hand side must
+ 
+
+ align:start position:0%
+Z naught and the right-hand side must
+therefore be that way so all right so
+
+ align:start position:0%
+therefore be that way so all right so
+ 
+
+ align:start position:0%
+therefore be that way so all right so
+this is a possibility but then let's
+
+ align:start position:0%
+this is a possibility but then let's
+ 
+
+ align:start position:0%
+this is a possibility but then let's
+calculate those values of the energies
+
+ align:start position:0%
+calculate those values of the energies
+ 
+
+ align:start position:0%
+calculate those values of the energies
+calculate those e-m-s so what do we have
+
+ align:start position:0%
+calculate those e-m-s so what do we have
+ 
+
+ align:start position:0%
+calculate those e-m-s so what do we have
+we square the left hand side for Z
+
+ align:start position:0%
+we square the left hand side for Z
+ 
+
+ align:start position:0%
+we square the left hand side for Z
+naught squared times 1 plus e n is equal
+
+ align:start position:0%
+naught squared times 1 plus e n is equal
+ 
+
+ align:start position:0%
+naught squared times 1 plus e n is equal
+to PI squared and square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and en is equal to minus one plus N
+
+ align:start position:0%
+and en is equal to minus one plus N
+ 
+
+ align:start position:0%
+and en is equal to minus one plus N
+squared PI squared over four Z naught
+
+ align:start position:0%
+squared PI squared over four Z naught
+ 
+
+ align:start position:0%
+squared PI squared over four Z naught
+square okay this is quantitatively nice
+
+ align:start position:0%
+square okay this is quantitatively nice
+ 
+
+ align:start position:0%
+square okay this is quantitatively nice
+but probably still doesn't give us much
+
+ align:start position:0%
+but probably still doesn't give us much
+ 
+
+ align:start position:0%
+but probably still doesn't give us much
+intuition about what's going on so let
+
+ align:start position:0%
+intuition about what's going on so let
+ 
+
+ align:start position:0%
+intuition about what's going on so let
+me go back to the total energy so
+
+ align:start position:0%
+me go back to the total energy so
+ 
+
+ align:start position:0%
+me go back to the total energy so
+multiply e n remember was energy divided
+
+ align:start position:0%
+multiply e n remember was energy divided
+ 
+
+ align:start position:0%
+multiply e n remember was energy divided
+by V naught so multiply all terms by V
+
+ align:start position:0%
+by V naught so multiply all terms by V
+ 
+
+ align:start position:0%
+by V naught so multiply all terms by V
+naught e equals minus V naught plus N
+
+ align:start position:0%
+naught e equals minus V naught plus N
+ 
+
+ align:start position:0%
+naught e equals minus V naught plus N
+squared PI squared on V naught over for
+
+ align:start position:0%
+squared PI squared on V naught over for
+ 
+
+ align:start position:0%
+squared PI squared on V naught over for
+Z naught squared now I'm going to go all
+
+ align:start position:0%
+Z naught squared now I'm going to go all
+ 
+
+ align:start position:0%
+Z naught squared now I'm going to go all
+the way back to conventional language
+
+ align:start position:0%
+the way back to conventional language
+ 
+
+ align:start position:0%
+the way back to conventional language
+now n to 4 times Z naught squared which
+
+ align:start position:0%
+now n to 4 times Z naught squared which
+ 
+
+ align:start position:0%
+now n to 4 times Z naught squared which
+is 2m a squared V naught over H bar
+
+ align:start position:0%
+is 2m a squared V naught over H bar
+ 
+
+ align:start position:0%
+is 2m a squared V naught over H bar
+squared so E is minus V naught plus N
+
+ align:start position:0%
+squared so E is minus V naught plus N
+ 
+
+ align:start position:0%
+squared so E is minus V naught plus N
+squared PI squared the V naught scans on
+
+ align:start position:0%
+squared PI squared the V naught scans on
+ 
+
+ align:start position:0%
+squared PI squared the V naught scans on
+H squared over 2m times 2a squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think they got every term right so
+
+ align:start position:0%
+I think they got every term right so
+ 
+
+ align:start position:0%
+I think they got every term right so
+what does this say well think of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential in this region there's an e
+
+ align:start position:0%
+potential in this region there's an e
+ 
+
+ align:start position:0%
+potential in this region there's an e
+here and there's minus V not there so it
+
+ align:start position:0%
+here and there's minus V not there so it
+ 
+
+ align:start position:0%
+here and there's minus V not there so it
+says E is minus V not plus this quantity
+
+ align:start position:0%
+says E is minus V not plus this quantity
+ 
+
+ align:start position:0%
+says E is minus V not plus this quantity
+so minus V not plus this quantity which
+
+ align:start position:0%
+so minus V not plus this quantity which
+ 
+
+ align:start position:0%
+so minus V not plus this quantity which
+is N squared PI squared H squared over
+
+ align:start position:0%
+is N squared PI squared H squared over
+ 
+
+ align:start position:0%
+is N squared PI squared H squared over
+2m and 2a squared so the resonance
+
+ align:start position:0%
+2m and 2a squared so the resonance
+ 
+
+ align:start position:0%
+2m and 2a squared so the resonance
+happens if the energy is a distance
+
+ align:start position:0%
+happens if the energy is a distance
+ 
+
+ align:start position:0%
+happens if the energy is a distance
+above the bottom of the potential which
+
+ align:start position:0%
+above the bottom of the potential which
+ 
+
+ align:start position:0%
+above the bottom of the potential which
+is equal to this quantity and now you
+
+ align:start position:0%
+is equal to this quantity and now you
+ 
+
+ align:start position:0%
+is equal to this quantity and now you
+see something that we could have seen
+
+ align:start position:0%
+see something that we could have seen
+ 
+
+ align:start position:0%
+see something that we could have seen
+maybe some other way
+
+ align:start position:0%
+maybe some other way
+ 
+
+ align:start position:0%
+maybe some other way
+that what's happening here is a little
+
+ align:start position:0%
+that what's happening here is a little
+ 
+
+ align:start position:0%
+that what's happening here is a little
+strange at first sight of this are the
+
+ align:start position:0%
+strange at first sight of this are the
+ 
+
+ align:start position:0%
+strange at first sight of this are the
+energy levels of an infinite square well
+
+ align:start position:0%
+energy levels of an infinite square well
+ 
+
+ align:start position:0%
+energy levels of an infinite square well
+of width to a you remember the energy
+
+ align:start position:0%
+of width to a you remember the energy
+ 
+
+ align:start position:0%
+of width to a you remember the energy
+levels of an infinite square well our m
+
+ align:start position:0%
+levels of an infinite square well our m
+ 
+
+ align:start position:0%
+levels of an infinite square well our m
+squared pi squared H squared over 2m
+
+ align:start position:0%
+squared pi squared H squared over 2m
+ 
+
+ align:start position:0%
+squared pi squared H squared over 2m
+times the width squared and those are
+
+ align:start position:0%
+times the width squared and those are
+ 
+
+ align:start position:0%
+times the width squared and those are
+exactly it so the energies at which you
+
+ align:start position:0%
+exactly it so the energies at which you
+ 
+
+ align:start position:0%
+exactly it so the energies at which you
+find a transmission and it's the name is
+
+ align:start position:0%
+find a transmission and it's the name is
+ 
+
+ align:start position:0%
+find a transmission and it's the name is
+going to become obvious in a second
+
+ align:start position:0%
+going to become obvious in a second
+ 
+
+ align:start position:0%
+going to become obvious in a second
+it's called the resonant transition are
+
+ align:start position:0%
+it's called the resonant transition are
+ 
+
+ align:start position:0%
+it's called the resonant transition are
+those in which the energy e coincides
+
+ align:start position:0%
+those in which the energy e coincides
+ 
+
+ align:start position:0%
+those in which the energy e coincides
+with some hypothetical energy of the
+
+ align:start position:0%
+with some hypothetical energy of the
+ 
+
+ align:start position:0%
+with some hypothetical energy of the
+infinite square well that you would put
+
+ align:start position:0%
+infinite square well that you would put
+ 
+
+ align:start position:0%
+infinite square well that you would put
+here if this is if you would have put an
+
+ align:start position:0%
+here if this is if you would have put an
+ 
+
+ align:start position:0%
+here if this is if you would have put an
+infinite square well in the middle
+
+ align:start position:0%
+infinite square well in the middle
+ 
+
+ align:start position:0%
+infinite square well in the middle
+and look at where are the energies of
+
+ align:start position:0%
+and look at where are the energies of
+ 
+
+ align:start position:0%
+and look at where are the energies of
+bound states that are bigger than zero
+
+ align:start position:0%
+bound states that are bigger than zero
+ 
+
+ align:start position:0%
+bound states that are bigger than zero
+you know there might be bound state
+
+ align:start position:0%
+you know there might be bound state
+ 
+
+ align:start position:0%
+you know there might be bound state
+energies here but those that are not
+
+ align:start position:0%
+energies here but those that are not
+ 
+
+ align:start position:0%
+energies here but those that are not
+relevant because you only consider
+
+ align:start position:0%
+relevant because you only consider
+ 
+
+ align:start position:0%
+relevant because you only consider
+energy is positive so if you find an
+
+ align:start position:0%
+energy is positive so if you find an
+ 
+
+ align:start position:0%
+energy is positive so if you find an
+energy that this positive that
+
+ align:start position:0%
+energy that this positive that
+ 
+
+ align:start position:0%
+energy that this positive that
+corresponds to a would be infinite bound
+
+ align:start position:0%
+corresponds to a would be infinite bound
+ 
+
+ align:start position:0%
+corresponds to a would be infinite bound
+of infinite square well that's it that's
+
+ align:start position:0%
+of infinite square well that's it that's
+ 
+
+ align:start position:0%
+of infinite square well that's it that's
+an energy for which you will have
+
+ align:start position:0%
+an energy for which you will have
+ 
+
+ align:start position:0%
+an energy for which you will have
+transmission and in fact if we think
+
+ align:start position:0%
+transmission and in fact if we think
+ 
+
+ align:start position:0%
+transmission and in fact if we think
+about this from the viewpoint of the
+
+ align:start position:0%
+about this from the viewpoint of the
+ 
+
+ align:start position:0%
+about this from the viewpoint of the
+wavefunction um this this factor over
+
+ align:start position:0%
+wavefunction um this this factor over
+ 
+
+ align:start position:0%
+wavefunction um this this factor over
+here look at this this property over
+
+ align:start position:0%
+here look at this this property over
+ 
+
+ align:start position:0%
+here look at this this property over
+here so what do we have the the
+
+ align:start position:0%
+here so what do we have the the
+ 
+
+ align:start position:0%
+here so what do we have the the
+condition was that k2 times 2a the
+
+ align:start position:0%
+condition was that k2 times 2a the
+ 
+
+ align:start position:0%
+condition was that k2 times 2a the
+argument of the sine function would be a
+
+ align:start position:0%
+argument of the sine function would be a
+ 
+
+ align:start position:0%
+argument of the sine function would be a
+multiple of pi but k2 is 2pi over the
+
+ align:start position:0%
+multiple of pi but k2 is 2pi over the
+ 
+
+ align:start position:0%
+multiple of pi but k2 is 2pi over the
+wavelength of the wave that you have in
+
+ align:start position:0%
+wavelength of the wave that you have in
+ 
+
+ align:start position:0%
+wavelength of the wave that you have in
+this range over 2a is equal to n pi so
+
+ align:start position:0%
+this range over 2a is equal to n pi so
+ 
+
+ align:start position:0%
+this range over 2a is equal to n pi so
+we can cancel the PI's and the tools and
+
+ align:start position:0%
+we can cancel the PI's and the tools and
+ 
+
+ align:start position:0%
+we can cancel the PI's and the tools and
+you get 2a over lambda is equal to n
+
+ align:start position:0%
+you get 2a over lambda is equal to n
+ 
+
+ align:start position:0%
+you get 2a over lambda is equal to n
+over 2 and what does that say it says
+
+ align:start position:0%
+over 2 and what does that say it says
+ 
+
+ align:start position:0%
+over 2 and what does that say it says
+that the de Broglie wavelength that you
+
+ align:start position:0%
+that the de Broglie wavelength that you
+ 
+
+ align:start position:0%
+that the de Broglie wavelength that you
+have in this region is such that it fits
+
+ align:start position:0%
+have in this region is such that it fits
+ 
+
+ align:start position:0%
+have in this region is such that it fits
+into 2a let me write it yet in another
+
+ align:start position:0%
+into 2a let me write it yet in another
+ 
+
+ align:start position:0%
+into 2a let me write it yet in another
+way let me write this a as um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I won't write like that leave it like
+
+ align:start position:0%
+I won't write like that leave it like
+ 
+
+ align:start position:0%
+I won't write like that leave it like
+that the wavelength lambda fit into to a
+
+ align:start position:0%
+that the wavelength lambda fit into to a
+ 
+
+ align:start position:0%
+that the wavelength lambda fit into to a
+1/2 integer number of times and that's
+
+ align:start position:0%
+1/2 integer number of times and that's
+ 
+
+ align:start position:0%
+1/2 integer number of times and that's
+exactly what you have in a infinite
+
+ align:start position:0%
+exactly what you have in a infinite
+ 
+
+ align:start position:0%
+exactly what you have in a infinite
+square well if you have width well you
+
+ align:start position:0%
+square well if you have width well you
+ 
+
+ align:start position:0%
+square well if you have width well you
+could have half a wavelength there for n
+
+ align:start position:0%
+could have half a wavelength there for n
+ 
+
+ align:start position:0%
+could have half a wavelength there for n
+equal 1 a full thing for m equal to 3
+
+ align:start position:0%
+equal 1 a full thing for m equal to 3
+ 
+
+ align:start position:0%
+equal 1 a full thing for m equal to 3
+halves for n equal 3 you always get 1/2
+
+ align:start position:0%
+halves for n equal 3 you always get 1/2
+ 
+
+ align:start position:0%
+halves for n equal 3 you always get 1/2
+and 1/2 sum halves increasing and
+
+ align:start position:0%
+and 1/2 sum halves increasing and
+ 
+
+ align:start position:0%
+and 1/2 sum halves increasing and
+increasing all the time so yeah um so
+
+ align:start position:0%
+increasing all the time so yeah um so
+ 
+
+ align:start position:0%
+increasing all the time so yeah um so
+the way I think I wanted to do it is
+
+ align:start position:0%
+the way I think I wanted to do it is
+ 
+
+ align:start position:0%
+the way I think I wanted to do it is
+this this equation can be written as n
+
+ align:start position:0%
+this this equation can be written as n
+ 
+
+ align:start position:0%
+this this equation can be written as n
+is equal to 2ei over lambda over 2
+
+ align:start position:0%
+is equal to 2ei over lambda over 2
+ 
+
+ align:start position:0%
+is equal to 2ei over lambda over 2
+that's the same equation so in this way
+
+ align:start position:0%
+that's the same equation so in this way
+ 
+
+ align:start position:0%
+that's the same equation so in this way
+you say an integer number of times is
+
+ align:start position:0%
+you say an integer number of times is
+ 
+
+ align:start position:0%
+you say an integer number of times is
+the is to a divided by lambda over 2
+
+ align:start position:0%
+the is to a divided by lambda over 2
+ 
+
+ align:start position:0%
+the is to a divided by lambda over 2
+which is precisely the condition for a
+
+ align:start position:0%
+which is precisely the condition for a
+ 
+
+ align:start position:0%
+which is precisely the condition for a
+infinite square well energy eigenstate
+
+ align:start position:0%
+infinite square well energy eigenstate
+ 
+
+ align:start position:0%
+infinite square well energy eigenstate
+so there's no infinite square well
+
+ align:start position:0%
+so there's no infinite square well
+ 
+
+ align:start position:0%
+so there's no infinite square well
+anywhere in this problem but somehow
+
+ align:start position:0%
+anywhere in this problem but somehow
+ 
+
+ align:start position:0%
+anywhere in this problem but somehow
+when the wavelength of the de Broglie
+
+ align:start position:0%
+when the wavelength of the de Broglie
+ 
+
+ align:start position:0%
+when the wavelength of the de Broglie
+representation of the particle in this
+
+ align:start position:0%
+representation of the particle in this
+ 
+
+ align:start position:0%
+representation of the particle in this
+region is an exact number of 1/2 waves
+
+ align:start position:0%
+region is an exact number of 1/2 waves
+ 
+
+ align:start position:0%
+region is an exact number of 1/2 waves
+there's resonance and this resonance is
+
+ align:start position:0%
+there's resonance and this resonance is
+ 
+
+ align:start position:0%
+there's resonance and this resonance is
+such it allows the wave to go completely
+
+ align:start position:0%
+such it allows the wave to go completely
+ 
+
+ align:start position:0%
+such it allows the wave to go completely
+through it's a pretty remarkable
+
+ align:start position:0%
+through it's a pretty remarkable
+ 
+
+ align:start position:0%
+through it's a pretty remarkable
+phenomenon so the infinite square well
+
+ align:start position:0%
+phenomenon so the infinite square well
+ 
+
+ align:start position:0%
+phenomenon so the infinite square well
+appears just as a way to think of what
+
+ align:start position:0%
+appears just as a way to think of what
+ 
+
+ align:start position:0%
+appears just as a way to think of what
+are the energies at which you will
+
+ align:start position:0%
+are the energies at which you will
+ 
+
+ align:start position:0%
+are the energies at which you will
+observe the resonances but the resonance
+
+ align:start position:0%
+observe the resonances but the resonance
+ 
+
+ align:start position:0%
+observe the resonances but the resonance
+is simply due to having a an exact
+
+ align:start position:0%
+is simply due to having a an exact
+ 
+
+ align:start position:0%
+is simply due to having a an exact
+number of half waves in this region so
+
+ align:start position:0%
+number of half waves in this region so
+ 
+
+ align:start position:0%
+number of half waves in this region so
+we can do an a little number
+
+ align:start position:0%
+we can do an a little number
+ 
+
+ align:start position:0%
+we can do an a little number
+a good example to show how that works
\ No newline at end of file
diff --git a/L-P7WhWkKrM.txt b/L-P7WhWkKrM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e07c832cb496ef809fe2d88f720338cfa6aadf74
--- /dev/null
+++ b/L-P7WhWkKrM.txt
@@ -0,0 +1,339 @@
+align:start position:0%
+ 
+for ocw this has been another year of
+
+ align:start position:0%
+for ocw this has been another year of
+ 
+
+ align:start position:0%
+for ocw this has been another year of
+great growth and learning
+
+ align:start position:0%
+great growth and learning
+ 
+
+ align:start position:0%
+great growth and learning
+we're honing our publishing processes so
+
+ align:start position:0%
+we're honing our publishing processes so
+ 
+
+ align:start position:0%
+we're honing our publishing processes so
+that courses can be posted on the ocw
+
+ align:start position:0%
+that courses can be posted on the ocw
+ 
+
+ align:start position:0%
+that courses can be posted on the ocw
+site more rapidly
+
+ align:start position:0%
+site more rapidly
+ 
+
+ align:start position:0%
+site more rapidly
+as we focus on enriching course content
+
+ align:start position:0%
+as we focus on enriching course content
+ 
+
+ align:start position:0%
+as we focus on enriching course content
+Learners have more in-depth resources to
+
+ align:start position:0%
+Learners have more in-depth resources to
+ 
+
+ align:start position:0%
+Learners have more in-depth resources to
+pick and choose what they learn in a
+
+ align:start position:0%
+pick and choose what they learn in a
+ 
+
+ align:start position:0%
+pick and choose what they learn in a
+given course
+
+ align:start position:0%
+given course
+ 
+
+ align:start position:0%
+given course
+as we continue to produce more courses
+
+ align:start position:0%
+as we continue to produce more courses
+ 
+
+ align:start position:0%
+as we continue to produce more courses
+and resources some of the questions on
+
+ align:start position:0%
+and resources some of the questions on
+ 
+
+ align:start position:0%
+and resources some of the questions on
+our minds are
+
+ align:start position:0%
+our minds are
+ 
+
+ align:start position:0%
+our minds are
+how do we make ocw more accessible and
+
+ align:start position:0%
+how do we make ocw more accessible and
+ 
+
+ align:start position:0%
+how do we make ocw more accessible and
+more useful for educators and students
+
+ align:start position:0%
+more useful for educators and students
+ 
+
+ align:start position:0%
+more useful for educators and students
+how can we Elevate our efforts to serve
+
+ align:start position:0%
+how can we Elevate our efforts to serve
+ 
+
+ align:start position:0%
+how can we Elevate our efforts to serve
+anyone interested in expanding their
+
+ align:start position:0%
+anyone interested in expanding their
+ 
+
+ align:start position:0%
+anyone interested in expanding their
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+supporting their livelihood or their
+
+ align:start position:0%
+supporting their livelihood or their
+ 
+
+ align:start position:0%
+supporting their livelihood or their
+community
+
+ align:start position:0%
+community
+ 
+
+ align:start position:0%
+community
+we've started toward the right direction
+
+ align:start position:0%
+we've started toward the right direction
+ 
+
+ align:start position:0%
+we've started toward the right direction
+by improving the portability of our
+
+ align:start position:0%
+by improving the portability of our
+ 
+
+ align:start position:0%
+by improving the portability of our
+content
+
+ align:start position:0%
+content
+ 
+
+ align:start position:0%
+content
+we're already seeing an uptick in
+
+ align:start position:0%
+we're already seeing an uptick in
+ 
+
+ align:start position:0%
+we're already seeing an uptick in
+Learners coming to ocw on their mobile
+
+ align:start position:0%
+Learners coming to ocw on their mobile
+ 
+
+ align:start position:0%
+Learners coming to ocw on their mobile
+devices
+
+ align:start position:0%
+devices
+ 
+
+ align:start position:0%
+devices
+we want to be even more available where
+
+ align:start position:0%
+we want to be even more available where
+ 
+
+ align:start position:0%
+we want to be even more available where
+people are learning and that includes
+
+ align:start position:0%
+people are learning and that includes
+ 
+
+ align:start position:0%
+people are learning and that includes
+YouTube and other social media channels
+
+ align:start position:0%
+YouTube and other social media channels
+ 
+
+ align:start position:0%
+YouTube and other social media channels
+we're also making strides and
+
+ align:start position:0%
+we're also making strides and
+ 
+
+ align:start position:0%
+we're also making strides and
+collaborating with like-minded
+
+ align:start position:0%
+collaborating with like-minded
+ 
+
+ align:start position:0%
+collaborating with like-minded
+organizations
+
+ align:start position:0%
+organizations
+ 
+
+ align:start position:0%
+organizations
+because we know we really can't do this
+
+ align:start position:0%
+because we know we really can't do this
+ 
+
+ align:start position:0%
+because we know we really can't do this
+alone especially if we want to affect
+
+ align:start position:0%
+alone especially if we want to affect
+ 
+
+ align:start position:0%
+alone especially if we want to affect
+significant change and it's really our
+
+ align:start position:0%
+significant change and it's really our
+ 
+
+ align:start position:0%
+significant change and it's really our
+MIT faculty the ocw staff and our
+
+ align:start position:0%
+MIT faculty the ocw staff and our
+ 
+
+ align:start position:0%
+MIT faculty the ocw staff and our
+amazing supporters who are helping us
+
+ align:start position:0%
+amazing supporters who are helping us
+ 
+
+ align:start position:0%
+amazing supporters who are helping us
+all along the way
+
+ align:start position:0%
+all along the way
+ 
+
+ align:start position:0%
+all along the way
+we're grateful to all of you
+
+ align:start position:0%
+we're grateful to all of you
+ 
+
+ align:start position:0%
+we're grateful to all of you
+thank you for trusting us to be part of
+
+ align:start position:0%
+thank you for trusting us to be part of
+ 
+
+ align:start position:0%
+thank you for trusting us to be part of
+your Learning Journey
+
+ align:start position:0%
+your Learning Journey
+ 
+
+ align:start position:0%
+your Learning Journey
+and thank you for believing in our
+
+ align:start position:0%
+and thank you for believing in our
+ 
+
+ align:start position:0%
+and thank you for believing in our
+efforts to open learning together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/Liy6fEbv8OU.txt b/Liy6fEbv8OU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8bbe88b74313a09a18a6c59a23f126a648c1a380
--- /dev/null
+++ b/Liy6fEbv8OU.txt
@@ -0,0 +1,16859 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tests of the basic household models
+
+ align:start position:0%
+the tests of the basic household models
+ 
+
+ align:start position:0%
+the tests of the basic household models
+in particular the efficient household
+
+ align:start position:0%
+in particular the efficient household
+ 
+
+ align:start position:0%
+in particular the efficient household
+models uh basically fail both in the
+
+ align:start position:0%
+models uh basically fail both in the
+ 
+
+ align:start position:0%
+models uh basically fail both in the
+production space and the consumption
+
+ align:start position:0%
+production space and the consumption
+ 
+
+ align:start position:0%
+production space and the consumption
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+so we better think about something else
+
+ align:start position:0%
+so we better think about something else
+ 
+
+ align:start position:0%
+so we better think about something else
+in order to try to understand the family
+
+ align:start position:0%
+in order to try to understand the family
+ 
+
+ align:start position:0%
+in order to try to understand the family
+and this is what a lot of the recent
+
+ align:start position:0%
+and this is what a lot of the recent
+ 
+
+ align:start position:0%
+and this is what a lot of the recent
+literature has tried to to do
+
+ align:start position:0%
+literature has tried to to do
+ 
+
+ align:start position:0%
+literature has tried to to do
+without yet getting to another framework
+
+ align:start position:0%
+without yet getting to another framework
+ 
+
+ align:start position:0%
+without yet getting to another framework
+that would be a satisfactory alternative
+
+ align:start position:0%
+that would be a satisfactory alternative
+ 
+
+ align:start position:0%
+that would be a satisfactory alternative
+framework but at least we have some you
+
+ align:start position:0%
+framework but at least we have some you
+ 
+
+ align:start position:0%
+framework but at least we have some you
+know some some Clues
+
+ align:start position:0%
+know some some Clues
+ 
+
+ align:start position:0%
+know some some Clues
+so I'll talk about some of these people
+
+ align:start position:0%
+so I'll talk about some of these people
+ 
+
+ align:start position:0%
+so I'll talk about some of these people
+first and then I'll I'll do a unit on a
+
+ align:start position:0%
+first and then I'll I'll do a unit on a
+ 
+
+ align:start position:0%
+first and then I'll I'll do a unit on a
+female labor for participation gender
+
+ align:start position:0%
+female labor for participation gender
+ 
+
+ align:start position:0%
+female labor for participation gender
+and the labor market to to complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so one first set of topic that of issue
+
+ align:start position:0%
+so one first set of topic that of issue
+ 
+
+ align:start position:0%
+so one first set of topic that of issue
+that people have looked at is the
+
+ align:start position:0%
+that people have looked at is the
+ 
+
+ align:start position:0%
+that people have looked at is the
+information flows that basically one of
+
+ align:start position:0%
+information flows that basically one of
+ 
+
+ align:start position:0%
+information flows that basically one of
+the Assumption of the efficient
+
+ align:start position:0%
+the Assumption of the efficient
+ 
+
+ align:start position:0%
+the Assumption of the efficient
+household model is that people who are
+
+ align:start position:0%
+household model is that people who are
+ 
+
+ align:start position:0%
+household model is that people who are
+part of a family should do better than
+
+ align:start position:0%
+part of a family should do better than
+ 
+
+ align:start position:0%
+part of a family should do better than
+any random people playing some games
+
+ align:start position:0%
+any random people playing some games
+ 
+
+ align:start position:0%
+any random people playing some games
+simply because they know each other and
+
+ align:start position:0%
+simply because they know each other and
+ 
+
+ align:start position:0%
+simply because they know each other and
+they have the ability to communicate
+
+ align:start position:0%
+they have the ability to communicate
+ 
+
+ align:start position:0%
+they have the ability to communicate
+easily and this is something that has
+
+ align:start position:0%
+easily and this is something that has
+ 
+
+ align:start position:0%
+easily and this is something that has
+been put to the test most recently by a
+
+ align:start position:0%
+been put to the test most recently by a
+ 
+
+ align:start position:0%
+been put to the test most recently by a
+nice paper by gottem Rao Matthew Ridley
+
+ align:start position:0%
+nice paper by gottem Rao Matthew Ridley
+ 
+
+ align:start position:0%
+nice paper by gottem Rao Matthew Ridley
+who is a student in the program who is
+
+ align:start position:0%
+who is a student in the program who is
+ 
+
+ align:start position:0%
+who is a student in the program who is
+in the jail market this year and Frank
+
+ align:start position:0%
+in the jail market this year and Frank
+ 
+
+ align:start position:0%
+in the jail market this year and Frank
+sinbach whom you know very well
+
+ align:start position:0%
+sinbach whom you know very well
+ 
+
+ align:start position:0%
+sinbach whom you know very well
+which looks at whether people share
+
+ align:start position:0%
+which looks at whether people share
+ 
+
+ align:start position:0%
+which looks at whether people share
+information that they both transparently
+
+ align:start position:0%
+information that they both transparently
+ 
+
+ align:start position:0%
+information that they both transparently
+know that they have
+
+ align:start position:0%
+know that they have
+ 
+
+ align:start position:0%
+know that they have
+um and what they show will I show you in
+
+ align:start position:0%
+um and what they show will I show you in
+ 
+
+ align:start position:0%
+um and what they show will I show you in
+a minute is that people do not share
+
+ align:start position:0%
+a minute is that people do not share
+ 
+
+ align:start position:0%
+a minute is that people do not share
+information in particular husbands pay
+
+ align:start position:0%
+information in particular husbands pay
+ 
+
+ align:start position:0%
+information in particular husbands pay
+no attention to the of a little
+
+ align:start position:0%
+no attention to the of a little
+ 
+
+ align:start position:0%
+no attention to the of a little
+attention to the information that they
+
+ align:start position:0%
+attention to the information that they
+ 
+
+ align:start position:0%
+attention to the information that they
+know their wife has for a simple simple
+
+ align:start position:0%
+know their wife has for a simple simple
+ 
+
+ align:start position:0%
+know their wife has for a simple simple
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so the experiment is the following it's
+
+ align:start position:0%
+so the experiment is the following it's
+ 
+
+ align:start position:0%
+so the experiment is the following it's
+a social learning experiment with format
+
+ align:start position:0%
+a social learning experiment with format
+ 
+
+ align:start position:0%
+a social learning experiment with format
+couples and 500 strangers
+
+ align:start position:0%
+couples and 500 strangers
+ 
+
+ align:start position:0%
+couples and 500 strangers
+which is trying to ask whether people
+
+ align:start position:0%
+which is trying to ask whether people
+ 
+
+ align:start position:0%
+which is trying to ask whether people
+respond similarly to info that was given
+
+ align:start position:0%
+respond similarly to info that was given
+ 
+
+ align:start position:0%
+respond similarly to info that was given
+to them
+
+ align:start position:0%
+to them
+ 
+
+ align:start position:0%
+to them
+always given to their spouse whether
+
+ align:start position:0%
+always given to their spouse whether
+ 
+
+ align:start position:0%
+always given to their spouse whether
+that's different from men and women
+
+ align:start position:0%
+that's different from men and women
+ 
+
+ align:start position:0%
+that's different from men and women
+whether this is due to a lack of
+
+ align:start position:0%
+whether this is due to a lack of
+ 
+
+ align:start position:0%
+whether this is due to a lack of
+communication or whether the information
+
+ align:start position:0%
+communication or whether the information
+ 
+
+ align:start position:0%
+communication or whether the information
+is not weighed appropriately even if you
+
+ align:start position:0%
+is not weighed appropriately even if you
+ 
+
+ align:start position:0%
+is not weighed appropriately even if you
+know that it exists and whether couples
+
+ align:start position:0%
+know that it exists and whether couples
+ 
+
+ align:start position:0%
+know that it exists and whether couples
+are behaving in any ways differently
+
+ align:start position:0%
+are behaving in any ways differently
+ 
+
+ align:start position:0%
+are behaving in any ways differently
+from any condom strangers on this on
+
+ align:start position:0%
+from any condom strangers on this on
+ 
+
+ align:start position:0%
+from any condom strangers on this on
+this dimensions
+
+ align:start position:0%
+this dimensions
+ 
+
+ align:start position:0%
+this dimensions
+so what they did is that the the they
+
+ align:start position:0%
+so what they did is that the the they
+ 
+
+ align:start position:0%
+so what they did is that the the they
+gave people one of these games where you
+
+ align:start position:0%
+gave people one of these games where you
+ 
+
+ align:start position:0%
+gave people one of these games where you
+are trying to to guess the share of Red
+
+ align:start position:0%
+are trying to to guess the share of Red
+ 
+
+ align:start position:0%
+are trying to to guess the share of Red
+Bulls in a noun and then you making more
+
+ align:start position:0%
+Bulls in a noun and then you making more
+ 
+
+ align:start position:0%
+Bulls in a noun and then you making more
+money if you get closer
+
+ align:start position:0%
+money if you get closer
+ 
+
+ align:start position:0%
+money if you get closer
+people then are given signals on what
+
+ align:start position:0%
+people then are given signals on what
+ 
+
+ align:start position:0%
+people then are given signals on what
+the share might be
+
+ align:start position:0%
+the share might be
+ 
+
+ align:start position:0%
+the share might be
+either by them for themselves uh their
+
+ align:start position:0%
+either by them for themselves uh their
+ 
+
+ align:start position:0%
+either by them for themselves uh their
+spouse in the spouse treatment their
+
+ align:start position:0%
+spouse in the spouse treatment their
+ 
+
+ align:start position:0%
+spouse in the spouse treatment their
+spouse can get a signal and then they
+
+ align:start position:0%
+spouse can get a signal and then they
+ 
+
+ align:start position:0%
+spouse can get a signal and then they
+can discuss to find out whatever signal
+
+ align:start position:0%
+can discuss to find out whatever signal
+ 
+
+ align:start position:0%
+can discuss to find out whatever signal
+their spouse got
+
+ align:start position:0%
+their spouse got
+ 
+
+ align:start position:0%
+their spouse got
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+the uh there is a third treatment where
+
+ align:start position:0%
+the uh there is a third treatment where
+ 
+
+ align:start position:0%
+the uh there is a third treatment where
+the spouse gets a signal they don't even
+
+ align:start position:0%
+the spouse gets a signal they don't even
+ 
+
+ align:start position:0%
+the spouse gets a signal they don't even
+need to discuss Frank or Frank's area is
+
+ align:start position:0%
+need to discuss Frank or Frank's area is
+ 
+
+ align:start position:0%
+need to discuss Frank or Frank's area is
+telling them hey uh you know for would
+
+ align:start position:0%
+telling them hey uh you know for would
+ 
+
+ align:start position:0%
+telling them hey uh you know for would
+be for example telling me a budget has
+
+ align:start position:0%
+be for example telling me a budget has
+ 
+
+ align:start position:0%
+be for example telling me a budget has
+gotten you know uh the signal that there
+
+ align:start position:0%
+gotten you know uh the signal that there
+ 
+
+ align:start position:0%
+gotten you know uh the signal that there
+are two-thirds of blue uh on in the
+
+ align:start position:0%
+are two-thirds of blue uh on in the
+ 
+
+ align:start position:0%
+are two-thirds of blue uh on in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+in his own draw he he drew mostly blue
+
+ align:start position:0%
+in his own draw he he drew mostly blue
+ 
+
+ align:start position:0%
+in his own draw he he drew mostly blue
+balls
+
+ align:start position:0%
+balls
+ 
+
+ align:start position:0%
+balls
+so the key out outcome of interest is
+
+ align:start position:0%
+so the key out outcome of interest is
+ 
+
+ align:start position:0%
+so the key out outcome of interest is
+the by Asian in the by Asian of dating
+
+ align:start position:0%
+the by Asian in the by Asian of dating
+ 
+
+ align:start position:0%
+the by Asian in the by Asian of dating
+as a function of your signal how much
+
+ align:start position:0%
+as a function of your signal how much
+ 
+
+ align:start position:0%
+as a function of your signal how much
+weight do you put on your own signals
+
+ align:start position:0%
+weight do you put on your own signals
+ 
+
+ align:start position:0%
+weight do you put on your own signals
+depending on who uncovered them
+
+ align:start position:0%
+depending on who uncovered them
+ 
+
+ align:start position:0%
+depending on who uncovered them
+so clearly if there is information
+
+ align:start position:0%
+so clearly if there is information
+ 
+
+ align:start position:0%
+so clearly if there is information
+pulling in a household there is nothing
+
+ align:start position:0%
+pulling in a household there is nothing
+ 
+
+ align:start position:0%
+pulling in a household there is nothing
+very tricky here you should weigh your
+
+ align:start position:0%
+very tricky here you should weigh your
+ 
+
+ align:start position:0%
+very tricky here you should weigh your
+information your own and your spouse
+
+ align:start position:0%
+information your own and your spouse
+ 
+
+ align:start position:0%
+information your own and your spouse
+information equally
+
+ align:start position:0%
+information equally
+ 
+
+ align:start position:0%
+information equally
+uh so in the third treatment you should
+
+ align:start position:0%
+uh so in the third treatment you should
+ 
+
+ align:start position:0%
+uh so in the third treatment you should
+clearly with information of the spouse
+
+ align:start position:0%
+clearly with information of the spouse
+ 
+
+ align:start position:0%
+clearly with information of the spouse
+equally and then maybe in the second
+
+ align:start position:0%
+equally and then maybe in the second
+ 
+
+ align:start position:0%
+equally and then maybe in the second
+treatment if people find it difficult to
+
+ align:start position:0%
+treatment if people find it difficult to
+ 
+
+ align:start position:0%
+treatment if people find it difficult to
+communicate they will they will uh you
+
+ align:start position:0%
+communicate they will they will uh you
+ 
+
+ align:start position:0%
+communicate they will they will uh you
+will lose something a little bit note
+
+ align:start position:0%
+will lose something a little bit note
+ 
+
+ align:start position:0%
+will lose something a little bit note
+that here there is nothing like the
+
+ align:start position:0%
+that here there is nothing like the
+ 
+
+ align:start position:0%
+that here there is nothing like the
+there is nothing strategic the the the
+
+ align:start position:0%
+there is nothing strategic the the the
+ 
+
+ align:start position:0%
+there is nothing strategic the the the
+the the earnings the proceeds of the
+
+ align:start position:0%
+the the earnings the proceeds of the
+ 
+
+ align:start position:0%
+the the earnings the proceeds of the
+experiments are shared between the
+
+ align:start position:0%
+experiments are shared between the
+ 
+
+ align:start position:0%
+experiments are shared between the
+husbands and their wife so their the
+
+ align:start position:0%
+husbands and their wife so their the
+ 
+
+ align:start position:0%
+husbands and their wife so their the
+dominant strategy is clearly to do as
+
+ align:start position:0%
+dominant strategy is clearly to do as
+ 
+
+ align:start position:0%
+dominant strategy is clearly to do as
+well as possible is no nothing that you
+
+ align:start position:0%
+well as possible is no nothing that you
+ 
+
+ align:start position:0%
+well as possible is no nothing that you
+can gain by not paying attention to the
+
+ align:start position:0%
+can gain by not paying attention to the
+ 
+
+ align:start position:0%
+can gain by not paying attention to the
+full signal so it's really focusing on
+
+ align:start position:0%
+full signal so it's really focusing on
+ 
+
+ align:start position:0%
+full signal so it's really focusing on
+this are you even able to communicate or
+
+ align:start position:0%
+this are you even able to communicate or
+ 
+
+ align:start position:0%
+this are you even able to communicate or
+to pay attention to what the other has
+
+ align:start position:0%
+to pay attention to what the other has
+ 
+
+ align:start position:0%
+to pay attention to what the other has
+to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the uh the bottom line and I guess
+
+ align:start position:0%
+so the uh the bottom line and I guess
+ 
+
+ align:start position:0%
+so the uh the bottom line and I guess
+that's the key results is that uh
+
+ align:start position:0%
+that's the key results is that uh
+ 
+
+ align:start position:0%
+that's the key results is that uh
+husbands uh heavily discount the weight
+
+ align:start position:0%
+husbands uh heavily discount the weight
+ 
+
+ align:start position:0%
+husbands uh heavily discount the weight
+information uh even when it's perfectly
+
+ align:start position:0%
+information uh even when it's perfectly
+ 
+
+ align:start position:0%
+information uh even when it's perfectly
+communicated
+
+ align:start position:0%
+communicated
+ 
+
+ align:start position:0%
+communicated
+so you can see as a function of what
+
+ align:start position:0%
+so you can see as a function of what
+ 
+
+ align:start position:0%
+so you can see as a function of what
+people eventually yes you can backward
+
+ align:start position:0%
+people eventually yes you can backward
+ 
+
+ align:start position:0%
+people eventually yes you can backward
+in induct what is the weight that they
+
+ align:start position:0%
+in induct what is the weight that they
+ 
+
+ align:start position:0%
+in induct what is the weight that they
+give to their own information to the
+
+ align:start position:0%
+give to their own information to the
+ 
+
+ align:start position:0%
+give to their own information to the
+information given to the spouse or
+
+ align:start position:0%
+information given to the spouse or
+ 
+
+ align:start position:0%
+information given to the spouse or
+either transmitted directly or by by by
+
+ align:start position:0%
+either transmitted directly or by by by
+ 
+
+ align:start position:0%
+either transmitted directly or by by by
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+and basically what they find is people
+
+ align:start position:0%
+and basically what they find is people
+ 
+
+ align:start position:0%
+and basically what they find is people
+put a lot of uh weight on their on any
+
+ align:start position:0%
+put a lot of uh weight on their on any
+ 
+
+ align:start position:0%
+put a lot of uh weight on their on any
+new information they get by signal which
+
+ align:start position:0%
+new information they get by signal which
+ 
+
+ align:start position:0%
+new information they get by signal which
+suggest that their own priors on the is
+
+ align:start position:0%
+suggest that their own priors on the is
+ 
+
+ align:start position:0%
+suggest that their own priors on the is
+quite flat as it should be because how
+
+ align:start position:0%
+quite flat as it should be because how
+ 
+
+ align:start position:0%
+quite flat as it should be because how
+would you know
+
+ align:start position:0%
+would you know
+ 
+
+ align:start position:0%
+would you know
+so people put a lot of information on
+
+ align:start position:0%
+so people put a lot of information on
+ 
+
+ align:start position:0%
+so people put a lot of information on
+their own signal but they put less
+
+ align:start position:0%
+their own signal but they put less
+ 
+
+ align:start position:0%
+their own signal but they put less
+information much less information on a
+
+ align:start position:0%
+information much less information on a
+ 
+
+ align:start position:0%
+information much less information on a
+signal that's given to their wife and
+
+ align:start position:0%
+signal that's given to their wife and
+ 
+
+ align:start position:0%
+signal that's given to their wife and
+that they could discuss about and
+
+ align:start position:0%
+that they could discuss about and
+ 
+
+ align:start position:0%
+that they could discuss about and
+strangely enough when they are told
+
+ align:start position:0%
+strangely enough when they are told
+ 
+
+ align:start position:0%
+strangely enough when they are told
+instead of here's your signal little
+
+ align:start position:0%
+instead of here's your signal little
+ 
+
+ align:start position:0%
+instead of here's your signal little
+here is your spouse's signal where it
+
+ align:start position:0%
+here is your spouse's signal where it
+ 
+
+ align:start position:0%
+here is your spouse's signal where it
+really should be exactly the same there
+
+ align:start position:0%
+really should be exactly the same there
+ 
+
+ align:start position:0%
+really should be exactly the same there
+is no discussion issue they pay zero
+
+ align:start position:0%
+is no discussion issue they pay zero
+ 
+
+ align:start position:0%
+is no discussion issue they pay zero
+information attention to this
+
+ align:start position:0%
+information attention to this
+ 
+
+ align:start position:0%
+information attention to this
+so so that's pretty striking in the
+
+ align:start position:0%
+so so that's pretty striking in the
+ 
+
+ align:start position:0%
+so so that's pretty striking in the
+sense of it's not even about lack of
+
+ align:start position:0%
+sense of it's not even about lack of
+ 
+
+ align:start position:0%
+sense of it's not even about lack of
+communication it's just you know they're
+
+ align:start position:0%
+communication it's just you know they're
+ 
+
+ align:start position:0%
+communication it's just you know they're
+maybe so used to not paying attention to
+
+ align:start position:0%
+maybe so used to not paying attention to
+ 
+
+ align:start position:0%
+maybe so used to not paying attention to
+anything coming from their wife that uh
+
+ align:start position:0%
+anything coming from their wife that uh
+ 
+
+ align:start position:0%
+anything coming from their wife that uh
+even in this case where it signals about
+
+ align:start position:0%
+even in this case where it signals about
+ 
+
+ align:start position:0%
+even in this case where it signals about
+how many urns there is in a
+
+ align:start position:0%
+how many urns there is in a
+ 
+
+ align:start position:0%
+how many urns there is in a
+bowl there is in ons there they don't
+
+ align:start position:0%
+bowl there is in ons there they don't
+ 
+
+ align:start position:0%
+bowl there is in ons there they don't
+pay attention for the wife that's not
+
+ align:start position:0%
+pay attention for the wife that's not
+ 
+
+ align:start position:0%
+pay attention for the wife that's not
+the same thing the wife I used to pay
+
+ align:start position:0%
+the same thing the wife I used to pay
+ 
+
+ align:start position:0%
+the same thing the wife I used to pay
+you know the wise actually pay just as
+
+ align:start position:0%
+you know the wise actually pay just as
+ 
+
+ align:start position:0%
+you know the wise actually pay just as
+much attention to the information given
+
+ align:start position:0%
+much attention to the information given
+ 
+
+ align:start position:0%
+much attention to the information given
+to the husband and to the information
+
+ align:start position:0%
+to the husband and to the information
+ 
+
+ align:start position:0%
+to the husband and to the information
+that they get themselves which is the
+
+ align:start position:0%
+that they get themselves which is the
+ 
+
+ align:start position:0%
+that they get themselves which is the
+rational thing to do so you might wonder
+
+ align:start position:0%
+rational thing to do so you might wonder
+ 
+
+ align:start position:0%
+rational thing to do so you might wonder
+whether it's about gender in general or
+
+ align:start position:0%
+whether it's about gender in general or
+ 
+
+ align:start position:0%
+whether it's about gender in general or
+just simply woman being more you know
+
+ align:start position:0%
+just simply woman being more you know
+ 
+
+ align:start position:0%
+just simply woman being more you know
+smarter or more open-minded or more
+
+ align:start position:0%
+smarter or more open-minded or more
+ 
+
+ align:start position:0%
+smarter or more open-minded or more
+paying more information to more
+
+ align:start position:0%
+paying more information to more
+ 
+
+ align:start position:0%
+paying more information to more
+attention to the information of others
+
+ align:start position:0%
+attention to the information of others
+ 
+
+ align:start position:0%
+attention to the information of others
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+but in fact when you do the information
+
+ align:start position:0%
+but in fact when you do the information
+ 
+
+ align:start position:0%
+but in fact when you do the information
+with Stanger so you can do the same
+
+ align:start position:0%
+with Stanger so you can do the same
+ 
+
+ align:start position:0%
+with Stanger so you can do the same
+thing instead of pairing you with your
+
+ align:start position:0%
+thing instead of pairing you with your
+ 
+
+ align:start position:0%
+thing instead of pairing you with your
+spouse I pair you with a perfect
+
+ align:start position:0%
+spouse I pair you with a perfect
+ 
+
+ align:start position:0%
+spouse I pair you with a perfect
+stranger similarly with a perfect
+
+ align:start position:0%
+stranger similarly with a perfect
+ 
+
+ align:start position:0%
+stranger similarly with a perfect
+stranger you should be able to discuss
+
+ align:start position:0%
+stranger you should be able to discuss
+ 
+
+ align:start position:0%
+stranger you should be able to discuss
+um if they have the signal and you have
+
+ align:start position:0%
+um if they have the signal and you have
+ 
+
+ align:start position:0%
+um if they have the signal and you have
+to elicit from them or if I give
+
+ align:start position:0%
+to elicit from them or if I give
+ 
+
+ align:start position:0%
+to elicit from them or if I give
+directly this is the signal that
+
+ align:start position:0%
+directly this is the signal that
+ 
+
+ align:start position:0%
+directly this is the signal that
+Wrecking got you should you should just
+
+ align:start position:0%
+Wrecking got you should you should just
+ 
+
+ align:start position:0%
+Wrecking got you should you should just
+read this exactly as your own and there
+
+ align:start position:0%
+read this exactly as your own and there
+ 
+
+ align:start position:0%
+read this exactly as your own and there
+I didn't put back the graphs uh I think
+
+ align:start position:0%
+I didn't put back the graphs uh I think
+ 
+
+ align:start position:0%
+I didn't put back the graphs uh I think
+yeah I didn't put back the graphs but uh
+
+ align:start position:0%
+yeah I didn't put back the graphs but uh
+ 
+
+ align:start position:0%
+yeah I didn't put back the graphs but uh
+the the finding is that uh people pay
+
+ align:start position:0%
+the the finding is that uh people pay
+ 
+
+ align:start position:0%
+the the finding is that uh people pay
+little information to little attention
+
+ align:start position:0%
+little information to little attention
+ 
+
+ align:start position:0%
+little information to little attention
+to the information given to strangers
+
+ align:start position:0%
+to the information given to strangers
+ 
+
+ align:start position:0%
+to the information given to strangers
+and their woman do the same thing as men
+
+ align:start position:0%
+and their woman do the same thing as men
+ 
+
+ align:start position:0%
+and their woman do the same thing as men
+so the fact that we see women paying
+
+ align:start position:0%
+so the fact that we see women paying
+ 
+
+ align:start position:0%
+so the fact that we see women paying
+more paying attention to their husband
+
+ align:start position:0%
+more paying attention to their husband
+ 
+
+ align:start position:0%
+more paying attention to their husband
+is not due to the fact that women in
+
+ align:start position:0%
+is not due to the fact that women in
+ 
+
+ align:start position:0%
+is not due to the fact that women in
+general pay more information to
+
+ align:start position:0%
+general pay more information to
+ 
+
+ align:start position:0%
+general pay more information to
+attention that cons is transmitted by
+
+ align:start position:0%
+attention that cons is transmitted by
+ 
+
+ align:start position:0%
+attention that cons is transmitted by
+other people
+
+ align:start position:0%
+other people
+ 
+
+ align:start position:0%
+other people
+but it's something about the household
+
+ align:start position:0%
+but it's something about the household
+ 
+
+ align:start position:0%
+but it's something about the household
+that the women are used to listen to
+
+ align:start position:0%
+that the women are used to listen to
+ 
+
+ align:start position:0%
+that the women are used to listen to
+their husband and husbands are used to
+
+ align:start position:0%
+their husband and husbands are used to
+ 
+
+ align:start position:0%
+their husband and husbands are used to
+not to listen to their wife and nobody
+
+ align:start position:0%
+not to listen to their wife and nobody
+ 
+
+ align:start position:0%
+not to listen to their wife and nobody
+listens to strangers
+
+ align:start position:0%
+listens to strangers
+ 
+
+ align:start position:0%
+listens to strangers
+so irrespective of the of of the
+
+ align:start position:0%
+so irrespective of the of of the
+ 
+
+ align:start position:0%
+so irrespective of the of of the
+household context is a pretty
+
+ align:start position:0%
+household context is a pretty
+ 
+
+ align:start position:0%
+household context is a pretty
+interesting for social learning because
+
+ align:start position:0%
+interesting for social learning because
+ 
+
+ align:start position:0%
+interesting for social learning because
+that's gonna limit a lot social learning
+
+ align:start position:0%
+that's gonna limit a lot social learning
+ 
+
+ align:start position:0%
+that's gonna limit a lot social learning
+if nobody pays any attention to anything
+
+ align:start position:0%
+if nobody pays any attention to anything
+ 
+
+ align:start position:0%
+if nobody pays any attention to anything
+that someone else tells them uh but for
+
+ align:start position:0%
+that someone else tells them uh but for
+ 
+
+ align:start position:0%
+that someone else tells them uh but for
+the point of view of the household this
+
+ align:start position:0%
+the point of view of the household this
+ 
+
+ align:start position:0%
+the point of view of the household this
+kind of really puts a clear wrench in
+
+ align:start position:0%
+kind of really puts a clear wrench in
+ 
+
+ align:start position:0%
+kind of really puts a clear wrench in
+the theory that the information
+
+ align:start position:0%
+the theory that the information
+ 
+
+ align:start position:0%
+the theory that the information
+communication is perfect in a household
+
+ align:start position:0%
+communication is perfect in a household
+ 
+
+ align:start position:0%
+communication is perfect in a household
+which should explain why which would you
+
+ align:start position:0%
+which should explain why which would you
+ 
+
+ align:start position:0%
+which should explain why which would you
+know go to our deficiency so that might
+
+ align:start position:0%
+know go to our deficiency so that might
+ 
+
+ align:start position:0%
+know go to our deficiency so that might
+be one reason why efficiency is not
+
+ align:start position:0%
+be one reason why efficiency is not
+ 
+
+ align:start position:0%
+be one reason why efficiency is not
+achieved within the household any
+
+ align:start position:0%
+achieved within the household any
+ 
+
+ align:start position:0%
+achieved within the household any
+question on this study yeah
+
+ align:start position:0%
+question on this study yeah
+ 
+
+ align:start position:0%
+question on this study yeah
+interpretation for why the
+
+ align:start position:0%
+interpretation for why the
+ 
+
+ align:start position:0%
+interpretation for why the
+perfectly communicated I mean you would
+
+ align:start position:0%
+perfectly communicated I mean you would
+ 
+
+ align:start position:0%
+perfectly communicated I mean you would
+you would think that the perfectly
+
+ align:start position:0%
+you would think that the perfectly
+ 
+
+ align:start position:0%
+you would think that the perfectly
+communicated and the discussion should
+
+ align:start position:0%
+communicated and the discussion should
+ 
+
+ align:start position:0%
+communicated and the discussion should
+yes yeah this is the
+
+ align:start position:0%
+yes yeah this is the
+ 
+
+ align:start position:0%
+yes yeah this is the
+this is quite surprising in that because
+
+ align:start position:0%
+this is quite surprising in that because
+ 
+
+ align:start position:0%
+this is quite surprising in that because
+it's not about the inability to
+
+ align:start position:0%
+it's not about the inability to
+ 
+
+ align:start position:0%
+it's not about the inability to
+communicate it's just basically you
+
+ align:start position:0%
+communicate it's just basically you
+ 
+
+ align:start position:0%
+communicate it's just basically you
+don't trust the information that comes
+
+ align:start position:0%
+don't trust the information that comes
+ 
+
+ align:start position:0%
+don't trust the information that comes
+from someone else
+
+ align:start position:0%
+from someone else
+ 
+
+ align:start position:0%
+from someone else
+even though it's information even though
+
+ align:start position:0%
+even though it's information even though
+ 
+
+ align:start position:0%
+even though it's information even though
+you're perfectly there's no agency of
+
+ align:start position:0%
+you're perfectly there's no agency of
+ 
+
+ align:start position:0%
+you're perfectly there's no agency of
+that other person
+
+ align:start position:0%
+that other person
+ 
+
+ align:start position:0%
+that other person
+but why does the discussion have like a
+
+ align:start position:0%
+but why does the discussion have like a
+ 
+
+ align:start position:0%
+but why does the discussion have like a
+better treatment there then the then the
+
+ align:start position:0%
+better treatment there then the then the
+ 
+
+ align:start position:0%
+better treatment there then the then the
+direct that's that's I don't know that's
+
+ align:start position:0%
+direct that's that's I don't know that's
+ 
+
+ align:start position:0%
+direct that's that's I don't know that's
+that's surprising and interesting
+
+ align:start position:0%
+that's surprising and interesting
+ 
+
+ align:start position:0%
+that's surprising and interesting
+I don't think that we have a good answer
+
+ align:start position:0%
+I don't think that we have a good answer
+ 
+
+ align:start position:0%
+I don't think that we have a good answer
+I don't think that they have necessarily
+
+ align:start position:0%
+I don't think that they have necessarily
+ 
+
+ align:start position:0%
+I don't think that they have necessarily
+a good one so yeah okay does uh the
+
+ align:start position:0%
+a good one so yeah okay does uh the
+ 
+
+ align:start position:0%
+a good one so yeah okay does uh the
+graph for uh when people have stranger
+
+ align:start position:0%
+graph for uh when people have stranger
+ 
+
+ align:start position:0%
+graph for uh when people have stranger
+when people are speaking with strangers
+
+ align:start position:0%
+when people are speaking with strangers
+ 
+
+ align:start position:0%
+when people are speaking with strangers
+look the same in terms of yeah it looks
+
+ align:start position:0%
+look the same in terms of yeah it looks
+ 
+
+ align:start position:0%
+look the same in terms of yeah it looks
+like the husband's craft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm pretty sure I suddenly have a doubt
+
+ align:start position:0%
+I'm pretty sure I suddenly have a doubt
+ 
+
+ align:start position:0%
+I'm pretty sure I suddenly have a doubt
+of whether there is the the order is the
+
+ align:start position:0%
+of whether there is the the order is the
+ 
+
+ align:start position:0%
+of whether there is the the order is the
+same I don't know whether the jump is
+
+ align:start position:0%
+same I don't know whether the jump is
+ 
+
+ align:start position:0%
+same I don't know whether the jump is
+that big between directly communicated
+
+ align:start position:0%
+that big between directly communicated
+ 
+
+ align:start position:0%
+that big between directly communicated
+versus versus communication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can probably check it by the end of this
+
+ align:start position:0%
+can probably check it by the end of this
+ 
+
+ align:start position:0%
+can probably check it by the end of this
+lecture I have it somewhere sort of
+
+ align:start position:0%
+lecture I have it somewhere sort of
+ 
+
+ align:start position:0%
+lecture I have it somewhere sort of
+interesting if the spouse is sitting by
+
+ align:start position:0%
+interesting if the spouse is sitting by
+ 
+
+ align:start position:0%
+interesting if the spouse is sitting by
+a discussion is better than the perfect
+
+ align:start position:0%
+a discussion is better than the perfect
+ 
+
+ align:start position:0%
+a discussion is better than the perfect
+stranger or if it's exactly the same
+
+ align:start position:0%
+stranger or if it's exactly the same
+ 
+
+ align:start position:0%
+stranger or if it's exactly the same
+thing I'll check that for my phone I I'm
+
+ align:start position:0%
+thing I'll check that for my phone I I'm
+ 
+
+ align:start position:0%
+thing I'll check that for my phone I I'm
+very scared of moving my computer
+
+ align:start position:0%
+very scared of moving my computer
+ 
+
+ align:start position:0%
+very scared of moving my computer
+yeah and again I have the slide
+
+ align:start position:0%
+yeah and again I have the slide
+ 
+
+ align:start position:0%
+yeah and again I have the slide
+somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's the same uh except this
+
+ align:start position:0%
+yeah that's the same uh except this
+ 
+
+ align:start position:0%
+yeah that's the same uh except this
+thunder discussion is uh a little bit
+
+ align:start position:0%
+thunder discussion is uh a little bit
+ 
+
+ align:start position:0%
+thunder discussion is uh a little bit
+closer to the perfectly communicated
+
+ align:start position:0%
+closer to the perfectly communicated
+ 
+
+ align:start position:0%
+closer to the perfectly communicated
+signal but the order is the same
+
+ align:start position:0%
+signal but the order is the same
+ 
+
+ align:start position:0%
+signal but the order is the same
+and for women it's again the the order
+
+ align:start position:0%
+and for women it's again the the order
+ 
+
+ align:start position:0%
+and for women it's again the the order
+is the same
+
+ align:start position:0%
+is the same
+ 
+
+ align:start position:0%
+is the same
+and the the Boost bars are a little bit
+
+ align:start position:0%
+and the the Boost bars are a little bit
+ 
+
+ align:start position:0%
+and the the Boost bars are a little bit
+higher so women are don't apply zero
+
+ align:start position:0%
+higher so women are don't apply zero
+ 
+
+ align:start position:0%
+higher so women are don't apply zero
+information to the signals of others but
+
+ align:start position:0%
+information to the signals of others but
+ 
+
+ align:start position:0%
+information to the signals of others but
+almost you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a cool paper
+
+ align:start position:0%
+so that's a cool paper
+ 
+
+ align:start position:0%
+so that's a cool paper
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+very creative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in this case we found the woman
+
+ align:start position:0%
+so in this case we found the woman
+ 
+
+ align:start position:0%
+so in this case we found the woman
+paying attention to uh to what their
+
+ align:start position:0%
+paying attention to uh to what their
+ 
+
+ align:start position:0%
+paying attention to uh to what their
+husband uh
+
+ align:start position:0%
+husband uh
+ 
+
+ align:start position:0%
+husband uh
+tell them we find husband not paying
+
+ align:start position:0%
+tell them we find husband not paying
+ 
+
+ align:start position:0%
+tell them we find husband not paying
+attention to what their wife tell them
+
+ align:start position:0%
+attention to what their wife tell them
+ 
+
+ align:start position:0%
+attention to what their wife tell them
+and then there is sort of one more
+
+ align:start position:0%
+and then there is sort of one more
+ 
+
+ align:start position:0%
+and then there is sort of one more
+possible step which is are you going to
+
+ align:start position:0%
+possible step which is are you going to
+ 
+
+ align:start position:0%
+possible step which is are you going to
+try and manipulate information when it's
+
+ align:start position:0%
+try and manipulate information when it's
+ 
+
+ align:start position:0%
+try and manipulate information when it's
+inconvenient for you
+
+ align:start position:0%
+inconvenient for you
+ 
+
+ align:start position:0%
+inconvenient for you
+so in a paper by nabash Erica fields and
+
+ align:start position:0%
+so in a paper by nabash Erica fields and
+ 
+
+ align:start position:0%
+so in a paper by nabash Erica fields and
+I think she's Jennifer Lee a woman are
+
+ align:start position:0%
+I think she's Jennifer Lee a woman are
+ 
+
+ align:start position:0%
+I think she's Jennifer Lee a woman are
+proposed to
+
+ align:start position:0%
+proposed to
+ 
+
+ align:start position:0%
+proposed to
+jump the queue to get an injectable
+
+ align:start position:0%
+jump the queue to get an injectable
+ 
+
+ align:start position:0%
+jump the queue to get an injectable
+contraceptive that's valid for three
+
+ align:start position:0%
+contraceptive that's valid for three
+ 
+
+ align:start position:0%
+contraceptive that's valid for three
+months
+
+ align:start position:0%
+months
+ 
+
+ align:start position:0%
+months
+now this is in in
+
+ align:start position:0%
+now this is in in
+ 
+
+ align:start position:0%
+now this is in in
+Zambia
+
+ align:start position:0%
+Zambia
+ 
+
+ align:start position:0%
+Zambia
+where like in many African countries
+
+ align:start position:0%
+where like in many African countries
+ 
+
+ align:start position:0%
+where like in many African countries
+women and men have different views on
+
+ align:start position:0%
+women and men have different views on
+ 
+
+ align:start position:0%
+women and men have different views on
+how many children they would like to
+
+ align:start position:0%
+how many children they would like to
+ 
+
+ align:start position:0%
+how many children they would like to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+with men wanting to have more children
+
+ align:start position:0%
+with men wanting to have more children
+ 
+
+ align:start position:0%
+with men wanting to have more children
+than women partly because probably they
+
+ align:start position:0%
+than women partly because probably they
+ 
+
+ align:start position:0%
+than women partly because probably they
+are not internalizing the fact that the
+
+ align:start position:0%
+are not internalizing the fact that the
+ 
+
+ align:start position:0%
+are not internalizing the fact that the
+chance of dying in childbirth is not at
+
+ align:start position:0%
+chance of dying in childbirth is not at
+ 
+
+ align:start position:0%
+chance of dying in childbirth is not at
+all zero
+
+ align:start position:0%
+all zero
+ 
+
+ align:start position:0%
+all zero
+so that's they have these different
+
+ align:start position:0%
+so that's they have these different
+ 
+
+ align:start position:0%
+so that's they have these different
+performances that's well established in
+
+ align:start position:0%
+performances that's well established in
+ 
+
+ align:start position:0%
+performances that's well established in
+this context
+
+ align:start position:0%
+this context
+ 
+
+ align:start position:0%
+this context
+so what they do in this experiment is
+
+ align:start position:0%
+so what they do in this experiment is
+ 
+
+ align:start position:0%
+so what they do in this experiment is
+that they are giving people so there is
+
+ align:start position:0%
+that they are giving people so there is
+ 
+
+ align:start position:0%
+that they are giving people so there is
+injectable contraceptive existing Zambia
+
+ align:start position:0%
+injectable contraceptive existing Zambia
+ 
+
+ align:start position:0%
+injectable contraceptive existing Zambia
+but there is a long queue to to get it
+
+ align:start position:0%
+but there is a long queue to to get it
+ 
+
+ align:start position:0%
+but there is a long queue to to get it
+they give people a voucher to jump the
+
+ align:start position:0%
+they give people a voucher to jump the
+ 
+
+ align:start position:0%
+they give people a voucher to jump the
+queue and there are two treatments
+
+ align:start position:0%
+queue and there are two treatments
+ 
+
+ align:start position:0%
+queue and there are two treatments
+either it's the individual who get the
+
+ align:start position:0%
+either it's the individual who get the
+ 
+
+ align:start position:0%
+either it's the individual who get the
+the individual woman who gets the
+
+ align:start position:0%
+the individual woman who gets the
+ 
+
+ align:start position:0%
+the individual woman who gets the
+voucher
+
+ align:start position:0%
+voucher
+ 
+
+ align:start position:0%
+voucher
+or it's the couple who gets it together
+
+ align:start position:0%
+or it's the couple who gets it together
+ 
+
+ align:start position:0%
+or it's the couple who gets it together
+and you don't goes to discuss it
+
+ align:start position:0%
+and you don't goes to discuss it
+ 
+
+ align:start position:0%
+and you don't goes to discuss it
+and in fact in many uh of the discussion
+
+ align:start position:0%
+and in fact in many uh of the discussion
+ 
+
+ align:start position:0%
+and in fact in many uh of the discussion
+in population population Council Etc
+
+ align:start position:0%
+in population population Council Etc
+ 
+
+ align:start position:0%
+in population population Council Etc
+people who are discussing contraception
+
+ align:start position:0%
+people who are discussing contraception
+ 
+
+ align:start position:0%
+people who are discussing contraception
+there is that view that involving the
+
+ align:start position:0%
+there is that view that involving the
+ 
+
+ align:start position:0%
+there is that view that involving the
+husbands having a discussion with the
+
+ align:start position:0%
+husbands having a discussion with the
+ 
+
+ align:start position:0%
+husbands having a discussion with the
+husband on contraception is a good thing
+
+ align:start position:0%
+husband on contraception is a good thing
+ 
+
+ align:start position:0%
+husband on contraception is a good thing
+because you need their go-ahead so the
+
+ align:start position:0%
+because you need their go-ahead so the
+ 
+
+ align:start position:0%
+because you need their go-ahead so the
+in the policy world the prior on this
+
+ align:start position:0%
+in the policy world the prior on this
+ 
+
+ align:start position:0%
+in the policy world the prior on this
+would be that the effects on in terms of
+
+ align:start position:0%
+would be that the effects on in terms of
+ 
+
+ align:start position:0%
+would be that the effects on in terms of
+taking an appointment and ultimately
+
+ align:start position:0%
+taking an appointment and ultimately
+ 
+
+ align:start position:0%
+taking an appointment and ultimately
+getting the shot would be larger if
+
+ align:start position:0%
+getting the shot would be larger if
+ 
+
+ align:start position:0%
+getting the shot would be larger if
+there is a couple discussion then it's
+
+ align:start position:0%
+there is a couple discussion then it's
+ 
+
+ align:start position:0%
+there is a couple discussion then it's
+given straight to the individual but of
+
+ align:start position:0%
+given straight to the individual but of
+ 
+
+ align:start position:0%
+given straight to the individual but of
+course it omits the fact that the woman
+
+ align:start position:0%
+course it omits the fact that the woman
+ 
+
+ align:start position:0%
+course it omits the fact that the woman
+could just decide to go get it done and
+
+ align:start position:0%
+could just decide to go get it done and
+ 
+
+ align:start position:0%
+could just decide to go get it done and
+nobody would be any wider so if she
+
+ align:start position:0%
+nobody would be any wider so if she
+ 
+
+ align:start position:0%
+nobody would be any wider so if she
+anticipated a difference in opinion she
+
+ align:start position:0%
+anticipated a difference in opinion she
+ 
+
+ align:start position:0%
+anticipated a difference in opinion she
+might just suppress the information and
+
+ align:start position:0%
+might just suppress the information and
+ 
+
+ align:start position:0%
+might just suppress the information and
+not and not tell anybody and get it done
+
+ align:start position:0%
+not and not tell anybody and get it done
+ 
+
+ align:start position:0%
+not and not tell anybody and get it done
+so that's basically a nice setup where
+
+ align:start position:0%
+so that's basically a nice setup where
+ 
+
+ align:start position:0%
+so that's basically a nice setup where
+you're running an experiment and you you
+
+ align:start position:0%
+you're running an experiment and you you
+ 
+
+ align:start position:0%
+you're running an experiment and you you
+might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might do you don't know what the
+
+ align:start position:0%
+you might do you don't know what the
+ 
+
+ align:start position:0%
+you might do you don't know what the
+result might be
+
+ align:start position:0%
+result might be
+ 
+
+ align:start position:0%
+result might be
+and what they find here very clearly is
+
+ align:start position:0%
+and what they find here very clearly is
+ 
+
+ align:start position:0%
+and what they find here very clearly is
+that so you are now comparing the the
+
+ align:start position:0%
+that so you are now comparing the the
+ 
+
+ align:start position:0%
+that so you are now comparing the the
+individual versus a couple
+
+ align:start position:0%
+individual versus a couple
+ 
+
+ align:start position:0%
+individual versus a couple
+and people who were assigned to the
+
+ align:start position:0%
+and people who were assigned to the
+ 
+
+ align:start position:0%
+and people who were assigned to the
+couple treatment are less likely to to
+
+ align:start position:0%
+couple treatment are less likely to to
+ 
+
+ align:start position:0%
+couple treatment are less likely to to
+redeem the voucher
+
+ align:start position:0%
+redeem the voucher
+ 
+
+ align:start position:0%
+redeem the voucher
+uh and ultimately less likely to uh to
+
+ align:start position:0%
+uh and ultimately less likely to uh to
+ 
+
+ align:start position:0%
+uh and ultimately less likely to uh to
+receive the injectable
+
+ align:start position:0%
+receive the injectable
+ 
+
+ align:start position:0%
+receive the injectable
+so that's not quite significant when we
+
+ align:start position:0%
+so that's not quite significant when we
+ 
+
+ align:start position:0%
+so that's not quite significant when we
+take all of the women but some woman it
+
+ align:start position:0%
+take all of the women but some woman it
+ 
+
+ align:start position:0%
+take all of the women but some woman it
+involves a lot of zero because many
+
+ align:start position:0%
+involves a lot of zero because many
+ 
+
+ align:start position:0%
+involves a lot of zero because many
+women never you know kind of got never
+
+ align:start position:0%
+women never you know kind of got never
+ 
+
+ align:start position:0%
+women never you know kind of got never
+replied if you look at the people who
+
+ align:start position:0%
+replied if you look at the people who
+ 
+
+ align:start position:0%
+replied if you look at the people who
+responded to the survey uh there is a 26
+
+ align:start position:0%
+responded to the survey uh there is a 26
+ 
+
+ align:start position:0%
+responded to the survey uh there is a 26
+percentage Point decline in getting uh
+
+ align:start position:0%
+percentage Point decline in getting uh
+ 
+
+ align:start position:0%
+percentage Point decline in getting uh
+in in actually Redeeming the voucher on
+
+ align:start position:0%
+in in actually Redeeming the voucher on
+ 
+
+ align:start position:0%
+in in actually Redeeming the voucher on
+a 65 busy so it's something that people
+
+ align:start position:0%
+a 65 busy so it's something that people
+ 
+
+ align:start position:0%
+a 65 busy so it's something that people
+are interesting interested in 65 of the
+
+ align:start position:0%
+are interesting interested in 65 of the
+ 
+
+ align:start position:0%
+are interesting interested in 65 of the
+woman do it
+
+ align:start position:0%
+woman do it
+ 
+
+ align:start position:0%
+woman do it
+uh but this gets done by you know 26
+
+ align:start position:0%
+uh but this gets done by you know 26
+ 
+
+ align:start position:0%
+uh but this gets done by you know 26
+percent percentage point if the men are
+
+ align:start position:0%
+percent percentage point if the men are
+ 
+
+ align:start position:0%
+percent percentage point if the men are
+involved uh for Redeeming the voucher in
+
+ align:start position:0%
+involved uh for Redeeming the voucher in
+ 
+
+ align:start position:0%
+involved uh for Redeeming the voucher in
+terms of receiving the actually
+
+ align:start position:0%
+terms of receiving the actually
+ 
+
+ align:start position:0%
+terms of receiving the actually
+receiving the injectable 30 of women
+
+ align:start position:0%
+receiving the injectable 30 of women
+ 
+
+ align:start position:0%
+receiving the injectable 30 of women
+actually receive the injectable in the
+
+ align:start position:0%
+actually receive the injectable in the
+ 
+
+ align:start position:0%
+actually receive the injectable in the
+individual treatment but it goes down to
+
+ align:start position:0%
+individual treatment but it goes down to
+ 
+
+ align:start position:0%
+individual treatment but it goes down to
+like seven percent in the couple
+
+ align:start position:0%
+like seven percent in the couple
+ 
+
+ align:start position:0%
+like seven percent in the couple
+treatment
+
+ align:start position:0%
+treatment
+ 
+
+ align:start position:0%
+treatment
+so here uh it's clearly a a case where
+
+ align:start position:0%
+so here uh it's clearly a a case where
+ 
+
+ align:start position:0%
+so here uh it's clearly a a case where
+the woman just didn't tell her husband
+
+ align:start position:0%
+the woman just didn't tell her husband
+ 
+
+ align:start position:0%
+the woman just didn't tell her husband
+and got it done yeah why if the voucher
+
+ align:start position:0%
+and got it done yeah why if the voucher
+ 
+
+ align:start position:0%
+and got it done yeah why if the voucher
+is for skipping the uh or like moving
+
+ align:start position:0%
+is for skipping the uh or like moving
+ 
+
+ align:start position:0%
+is for skipping the uh or like moving
+forward in the queue why would we expect
+
+ align:start position:0%
+forward in the queue why would we expect
+ 
+
+ align:start position:0%
+forward in the queue why would we expect
+there to be a different outcome for
+
+ align:start position:0%
+there to be a different outcome for
+ 
+
+ align:start position:0%
+there to be a different outcome for
+redeeming a voucher and receiving agenda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have your consultation and then once
+
+ align:start position:0%
+you have your consultation and then once
+ 
+
+ align:start position:0%
+you have your consultation and then once
+you have your consultation you discuss
+
+ align:start position:0%
+you have your consultation you discuss
+ 
+
+ align:start position:0%
+you have your consultation you discuss
+it and then they might decide that they
+
+ align:start position:0%
+it and then they might decide that they
+ 
+
+ align:start position:0%
+it and then they might decide that they
+don't want to do it because it's three
+
+ align:start position:0%
+don't want to do it because it's three
+ 
+
+ align:start position:0%
+don't want to do it because it's three
+months and there are side effects and so
+
+ align:start position:0%
+months and there are side effects and so
+ 
+
+ align:start position:0%
+months and there are side effects and so
+the voucher is for the for the
+
+ align:start position:0%
+the voucher is for the for the
+ 
+
+ align:start position:0%
+the voucher is for the for the
+consultation
+
+ align:start position:0%
+consultation
+ 
+
+ align:start position:0%
+consultation
+so of people who get the consultation
+
+ align:start position:0%
+so of people who get the consultation
+ 
+
+ align:start position:0%
+so of people who get the consultation
+some people might get cool fit
+
+ align:start position:0%
+some people might get cool fit
+ 
+
+ align:start position:0%
+some people might get cool fit
+in the process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the that's that's the
+
+ align:start position:0%
+so that's the that's that's the
+ 
+
+ align:start position:0%
+so that's the that's that's the
+difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so this is a setting where uh the
+
+ align:start position:0%
+um so this is a setting where uh the
+ 
+
+ align:start position:0%
+um so this is a setting where uh the
+most likely explanation is that the
+
+ align:start position:0%
+most likely explanation is that the
+ 
+
+ align:start position:0%
+most likely explanation is that the
+woman who got it to loan never disgusted
+
+ align:start position:0%
+woman who got it to loan never disgusted
+ 
+
+ align:start position:0%
+woman who got it to loan never disgusted
+and then just got it done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so it's not necessarily the fact that
+
+ align:start position:0%
+so it's not necessarily the fact that
+ 
+
+ align:start position:0%
+so it's not necessarily the fact that
+households are so this is women
+
+ align:start position:0%
+households are so this is women
+ 
+
+ align:start position:0%
+households are so this is women
+suppressing information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who are both students here when they
+
+ align:start position:0%
+who are both students here when they
+ 
+
+ align:start position:0%
+who are both students here when they
+were students here they run the opposite
+
+ align:start position:0%
+were students here they run the opposite
+ 
+
+ align:start position:0%
+were students here they run the opposite
+experiment and in fact I wrote not the
+
+ align:start position:0%
+experiment and in fact I wrote not the
+ 
+
+ align:start position:0%
+experiment and in fact I wrote not the
+generalizable result but now that I
+
+ align:start position:0%
+generalizable result but now that I
+ 
+
+ align:start position:0%
+generalizable result but now that I
+think about it I should have written
+
+ align:start position:0%
+think about it I should have written
+ 
+
+ align:start position:0%
+think about it I should have written
+this is that was a information given to
+
+ align:start position:0%
+this is that was a information given to
+ 
+
+ align:start position:0%
+this is that was a information given to
+women
+
+ align:start position:0%
+women
+ 
+
+ align:start position:0%
+women
+and then hidden by women and now this is
+
+ align:start position:0%
+and then hidden by women and now this is
+ 
+
+ align:start position:0%
+and then hidden by women and now this is
+information given to men
+
+ align:start position:0%
+information given to men
+ 
+
+ align:start position:0%
+information given to men
+on a different topic so it's different
+
+ align:start position:0%
+on a different topic so it's different
+ 
+
+ align:start position:0%
+on a different topic so it's different
+context different topic but one of the
+
+ align:start position:0%
+context different topic but one of the
+ 
+
+ align:start position:0%
+context different topic but one of the
+things that changes is the information
+
+ align:start position:0%
+things that changes is the information
+ 
+
+ align:start position:0%
+things that changes is the information
+is given to men
+
+ align:start position:0%
+is given to men
+ 
+
+ align:start position:0%
+is given to men
+um they give this is this is kind of
+
+ align:start position:0%
+um they give this is this is kind of
+ 
+
+ align:start position:0%
+um they give this is this is kind of
+previewing our labor woman and the
+
+ align:start position:0%
+previewing our labor woman and the
+ 
+
+ align:start position:0%
+previewing our labor woman and the
+liberal markets they gave
+
+ align:start position:0%
+liberal markets they gave
+ 
+
+ align:start position:0%
+liberal markets they gave
+either man a woman a voucher for access
+
+ align:start position:0%
+either man a woman a voucher for access
+ 
+
+ align:start position:0%
+either man a woman a voucher for access
+to a training program for women
+
+ align:start position:0%
+to a training program for women
+ 
+
+ align:start position:0%
+to a training program for women
+so if they gave the voucher for the to
+
+ align:start position:0%
+so if they gave the voucher for the to
+ 
+
+ align:start position:0%
+so if they gave the voucher for the to
+the man it was
+
+ align:start position:0%
+the man it was
+ 
+
+ align:start position:0%
+the man it was
+for her wife to access this training
+
+ align:start position:0%
+for her wife to access this training
+ 
+
+ align:start position:0%
+for her wife to access this training
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+so they either had it given to the man
+
+ align:start position:0%
+so they either had it given to the man
+ 
+
+ align:start position:0%
+so they either had it given to the man
+privately
+
+ align:start position:0%
+privately
+ 
+
+ align:start position:0%
+privately
+so if he was not interested he could
+
+ align:start position:0%
+so if he was not interested he could
+ 
+
+ align:start position:0%
+so if he was not interested he could
+just eat up the information and never
+
+ align:start position:0%
+just eat up the information and never
+ 
+
+ align:start position:0%
+just eat up the information and never
+discuss it or they gave it to the woman
+
+ align:start position:0%
+discuss it or they gave it to the woman
+ 
+
+ align:start position:0%
+discuss it or they gave it to the woman
+privately or they gave it to them
+
+ align:start position:0%
+privately or they gave it to them
+ 
+
+ align:start position:0%
+privately or they gave it to them
+forcing a discussion
+
+ align:start position:0%
+forcing a discussion
+ 
+
+ align:start position:0%
+forcing a discussion
+so there again the idea here in this
+
+ align:start position:0%
+so there again the idea here in this
+ 
+
+ align:start position:0%
+so there again the idea here in this
+case the difference in opinion as we
+
+ align:start position:0%
+case the difference in opinion as we
+ 
+
+ align:start position:0%
+case the difference in opinion as we
+will see is that a lot of women would
+
+ align:start position:0%
+will see is that a lot of women would
+ 
+
+ align:start position:0%
+will see is that a lot of women would
+like to work and most men prefer if
+
+ align:start position:0%
+like to work and most men prefer if
+ 
+
+ align:start position:0%
+like to work and most men prefer if
+their wives don't work
+
+ align:start position:0%
+their wives don't work
+ 
+
+ align:start position:0%
+their wives don't work
+so the easiest thing for the husband
+
+ align:start position:0%
+so the easiest thing for the husband
+ 
+
+ align:start position:0%
+so the easiest thing for the husband
+would have been to just not even share
+
+ align:start position:0%
+would have been to just not even share
+ 
+
+ align:start position:0%
+would have been to just not even share
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+in that case the initial the final take
+
+ align:start position:0%
+in that case the initial the final take
+ 
+
+ align:start position:0%
+in that case the initial the final take
+up of the experiment might have been
+
+ align:start position:0%
+up of the experiment might have been
+ 
+
+ align:start position:0%
+up of the experiment might have been
+lower in the case where the voucher is
+
+ align:start position:0%
+lower in the case where the voucher is
+ 
+
+ align:start position:0%
+lower in the case where the voucher is
+given to the man only
+
+ align:start position:0%
+given to the man only
+ 
+
+ align:start position:0%
+given to the man only
+in fact what defined in terms of final
+
+ align:start position:0%
+in fact what defined in terms of final
+ 
+
+ align:start position:0%
+in fact what defined in terms of final
+annulments
+
+ align:start position:0%
+annulments
+ 
+
+ align:start position:0%
+annulments
+is that uh the the the the final
+
+ align:start position:0%
+is that uh the the the the final
+ 
+
+ align:start position:0%
+is that uh the the the the final
+enrollment of the woman if the husband
+
+ align:start position:0%
+enrollment of the woman if the husband
+ 
+
+ align:start position:0%
+enrollment of the woman if the husband
+gets the ticket is as large uh when the
+
+ align:start position:0%
+gets the ticket is as large uh when the
+ 
+
+ align:start position:0%
+gets the ticket is as large uh when the
+woman doesn't isn't even informed that
+
+ align:start position:0%
+woman doesn't isn't even informed that
+ 
+
+ align:start position:0%
+woman doesn't isn't even informed that
+the ticket exists as when she's informed
+
+ align:start position:0%
+the ticket exists as when she's informed
+ 
+
+ align:start position:0%
+the ticket exists as when she's informed
+in fact if anything slightly larger if
+
+ align:start position:0%
+in fact if anything slightly larger if
+ 
+
+ align:start position:0%
+in fact if anything slightly larger if
+the woman is not informed
+
+ align:start position:0%
+the woman is not informed
+ 
+
+ align:start position:0%
+the woman is not informed
+but let's say these two are the same so
+
+ align:start position:0%
+but let's say these two are the same so
+ 
+
+ align:start position:0%
+but let's say these two are the same so
+it means that uh the
+
+ align:start position:0%
+it means that uh the
+ 
+
+ align:start position:0%
+it means that uh the
+there is no additional there's no loss
+
+ align:start position:0%
+there is no additional there's no loss
+ 
+
+ align:start position:0%
+there is no additional there's no loss
+in allowing the husband to never
+
+ align:start position:0%
+in allowing the husband to never
+ 
+
+ align:start position:0%
+in allowing the husband to never
+discuss it with your wife or never
+
+ align:start position:0%
+discuss it with your wife or never
+ 
+
+ align:start position:0%
+discuss it with your wife or never
+because our wife is not even aware of
+
+ align:start position:0%
+because our wife is not even aware of
+ 
+
+ align:start position:0%
+because our wife is not even aware of
+the information
+
+ align:start position:0%
+the information
+ 
+
+ align:start position:0%
+the information
+so even if a wife is aware of the
+
+ align:start position:0%
+so even if a wife is aware of the
+ 
+
+ align:start position:0%
+so even if a wife is aware of the
+information uh finally the outcome is
+
+ align:start position:0%
+information uh finally the outcome is
+ 
+
+ align:start position:0%
+information uh finally the outcome is
+the same maybe because there is zero
+
+ align:start position:0%
+the same maybe because there is zero
+ 
+
+ align:start position:0%
+the same maybe because there is zero
+bargaining power that she has anyways
+
+ align:start position:0%
+bargaining power that she has anyways
+ 
+
+ align:start position:0%
+bargaining power that she has anyways
+we're going back to the mat to the Frank
+
+ align:start position:0%
+we're going back to the mat to the Frank
+ 
+
+ align:start position:0%
+we're going back to the mat to the Frank
+and Matthew and gotamp thing if you pay
+
+ align:start position:0%
+and Matthew and gotamp thing if you pay
+ 
+
+ align:start position:0%
+and Matthew and gotamp thing if you pay
+no attention to what he's gonna say you
+
+ align:start position:0%
+no attention to what he's gonna say you
+ 
+
+ align:start position:0%
+no attention to what he's gonna say you
+can let her know or you cannot let her
+
+ align:start position:0%
+can let her know or you cannot let her
+ 
+
+ align:start position:0%
+can let her know or you cannot let her
+know doesn't matter you're making the
+
+ align:start position:0%
+know doesn't matter you're making the
+ 
+
+ align:start position:0%
+know doesn't matter you're making the
+same decision eventually
+
+ align:start position:0%
+same decision eventually
+ 
+
+ align:start position:0%
+same decision eventually
+uh but she doesn't seem to be hiding
+
+ align:start position:0%
+uh but she doesn't seem to be hiding
+ 
+
+ align:start position:0%
+uh but she doesn't seem to be hiding
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+and then interestingly in the discussion
+
+ align:start position:0%
+and then interestingly in the discussion
+ 
+
+ align:start position:0%
+and then interestingly in the discussion
+group uh the final checkup actually goes
+
+ align:start position:0%
+group uh the final checkup actually goes
+ 
+
+ align:start position:0%
+group uh the final checkup actually goes
+down so fasting a discussion on the
+
+ align:start position:0%
+down so fasting a discussion on the
+ 
+
+ align:start position:0%
+down so fasting a discussion on the
+issue uh which their intuition was it's
+
+ align:start position:0%
+issue uh which their intuition was it's
+ 
+
+ align:start position:0%
+issue uh which their intuition was it's
+going to increase the take up because
+
+ align:start position:0%
+going to increase the take up because
+ 
+
+ align:start position:0%
+going to increase the take up because
+you know it's going to give a chance to
+
+ align:start position:0%
+you know it's going to give a chance to
+ 
+
+ align:start position:0%
+you know it's going to give a chance to
+the wife to say so it's a discussion
+
+ align:start position:0%
+the wife to say so it's a discussion
+ 
+
+ align:start position:0%
+the wife to say so it's a discussion
+with someone like a facilitator
+
+ align:start position:0%
+with someone like a facilitator
+ 
+
+ align:start position:0%
+with someone like a facilitator
+basically being present in the
+
+ align:start position:0%
+basically being present in the
+ 
+
+ align:start position:0%
+basically being present in the
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+and according to the transcript of the
+
+ align:start position:0%
+and according to the transcript of the
+ 
+
+ align:start position:0%
+and according to the transcript of the
+facilitator they are very you know
+
+ align:start position:0%
+facilitator they are very you know
+ 
+
+ align:start position:0%
+facilitator they are very you know
+polite and discussed the opportunity and
+
+ align:start position:0%
+polite and discussed the opportunity and
+ 
+
+ align:start position:0%
+polite and discussed the opportunity and
+so on and so the the prior here that it
+
+ align:start position:0%
+so on and so the the prior here that it
+ 
+
+ align:start position:0%
+so on and so the the prior here that it
+would make the thing go up because your
+
+ align:start position:0%
+would make the thing go up because your
+ 
+
+ align:start position:0%
+would make the thing go up because your
+husband could you know learn
+
+ align:start position:0%
+husband could you know learn
+ 
+
+ align:start position:0%
+husband could you know learn
+the wife would have a chance to express
+
+ align:start position:0%
+the wife would have a chance to express
+ 
+
+ align:start position:0%
+the wife would have a chance to express
+her preferences also to address maybe
+
+ align:start position:0%
+her preferences also to address maybe
+ 
+
+ align:start position:0%
+her preferences also to address maybe
+some of the concerns of the husband and
+
+ align:start position:0%
+some of the concerns of the husband and
+ 
+
+ align:start position:0%
+some of the concerns of the husband and
+so on and so forth but uh in fact the
+
+ align:start position:0%
+so on and so forth but uh in fact the
+ 
+
+ align:start position:0%
+so on and so forth but uh in fact the
+opposite happened and when they
+
+ align:start position:0%
+opposite happened and when they
+ 
+
+ align:start position:0%
+opposite happened and when they
+discussed the it it crashes
+
+ align:start position:0%
+discussed the it it crashes
+ 
+
+ align:start position:0%
+discussed the it it crashes
+so we don't have a good you know model
+
+ align:start position:0%
+so we don't have a good you know model
+ 
+
+ align:start position:0%
+so we don't have a good you know model
+for that they propose something where
+
+ align:start position:0%
+for that they propose something where
+ 
+
+ align:start position:0%
+for that they propose something where
+just discussing as you know having
+
+ align:start position:0%
+just discussing as you know having
+ 
+
+ align:start position:0%
+just discussing as you know having
+arguments is too costly
+
+ align:start position:0%
+arguments is too costly
+ 
+
+ align:start position:0%
+arguments is too costly
+and people hate
+
+ align:start position:0%
+and people hate
+ 
+
+ align:start position:0%
+and people hate
+fighting about things so if you force
+
+ align:start position:0%
+fighting about things so if you force
+ 
+
+ align:start position:0%
+fighting about things so if you force
+them to discuss they actually shut down
+
+ align:start position:0%
+them to discuss they actually shut down
+ 
+
+ align:start position:0%
+them to discuss they actually shut down
+their mind and they're like don't even
+
+ align:start position:0%
+their mind and they're like don't even
+ 
+
+ align:start position:0%
+their mind and they're like don't even
+want to hear about it
+
+ align:start position:0%
+want to hear about it
+ 
+
+ align:start position:0%
+want to hear about it
+um when the wife get the ticket
+
+ align:start position:0%
+um when the wife get the ticket
+ 
+
+ align:start position:0%
+um when the wife get the ticket
+the husband has to approve at the end of
+
+ align:start position:0%
+the husband has to approve at the end of
+ 
+
+ align:start position:0%
+the husband has to approve at the end of
+the day so the wife doesn't get the it
+
+ align:start position:0%
+the day so the wife doesn't get the it
+ 
+
+ align:start position:0%
+the day so the wife doesn't get the it
+is asymmetric here the wife doesn't get
+
+ align:start position:0%
+is asymmetric here the wife doesn't get
+ 
+
+ align:start position:0%
+is asymmetric here the wife doesn't get
+to enroll in uh in the program without
+
+ align:start position:0%
+to enroll in uh in the program without
+ 
+
+ align:start position:0%
+to enroll in uh in the program without
+her husband knowing so here we would
+
+ align:start position:0%
+her husband knowing so here we would
+ 
+
+ align:start position:0%
+her husband knowing so here we would
+expect that with or without information
+
+ align:start position:0%
+expect that with or without information
+ 
+
+ align:start position:0%
+expect that with or without information
+would be a similar similar enrollment
+
+ align:start position:0%
+would be a similar similar enrollment
+ 
+
+ align:start position:0%
+would be a similar similar enrollment
+and that's
+
+ align:start position:0%
+and that's
+ 
+
+ align:start position:0%
+and that's
+more or less what we find the discussion
+
+ align:start position:0%
+more or less what we find the discussion
+ 
+
+ align:start position:0%
+more or less what we find the discussion
+effect is lower in this case it's really
+
+ align:start position:0%
+effect is lower in this case it's really
+ 
+
+ align:start position:0%
+effect is lower in this case it's really
+in the case of the husband the fact that
+
+ align:start position:0%
+in the case of the husband the fact that
+ 
+
+ align:start position:0%
+in the case of the husband the fact that
+the discussion is
+
+ align:start position:0%
+the discussion is
+ 
+
+ align:start position:0%
+the discussion is
+discussion effect is lower and uh
+
+ align:start position:0%
+discussion effect is lower and uh
+ 
+
+ align:start position:0%
+discussion effect is lower and uh
+interestingly the the overall take up
+
+ align:start position:0%
+interestingly the the overall take up
+ 
+
+ align:start position:0%
+interestingly the the overall take up
+from the wife getting the ticket from
+
+ align:start position:0%
+from the wife getting the ticket from
+ 
+
+ align:start position:0%
+from the wife getting the ticket from
+the husband getting the ticket is more
+
+ align:start position:0%
+the husband getting the ticket is more
+ 
+
+ align:start position:0%
+the husband getting the ticket is more
+or less similar
+
+ align:start position:0%
+or less similar
+ 
+
+ align:start position:0%
+or less similar
+so maybe it's a little different than
+
+ align:start position:0%
+so maybe it's a little different than
+ 
+
+ align:start position:0%
+so maybe it's a little different than
+the than what we found in arms where if
+
+ align:start position:0%
+the than what we found in arms where if
+ 
+
+ align:start position:0%
+the than what we found in arms where if
+the information gets from the husband
+
+ align:start position:0%
+the information gets from the husband
+ 
+
+ align:start position:0%
+the information gets from the husband
+the wife is entirely discounted if it
+
+ align:start position:0%
+the wife is entirely discounted if it
+ 
+
+ align:start position:0%
+the wife is entirely discounted if it
+seems that you know the
+
+ align:start position:0%
+seems that you know the
+ 
+
+ align:start position:0%
+seems that you know the
+the source of the information and the
+
+ align:start position:0%
+the source of the information and the
+ 
+
+ align:start position:0%
+the source of the information and the
+ticket doesn't seem to matter much for
+
+ align:start position:0%
+ticket doesn't seem to matter much for
+ 
+
+ align:start position:0%
+ticket doesn't seem to matter much for
+the final outcome
+
+ align:start position:0%
+the final outcome
+ 
+
+ align:start position:0%
+the final outcome
+so just to say that these things are
+
+ align:start position:0%
+so just to say that these things are
+ 
+
+ align:start position:0%
+so just to say that these things are
+still I can't say that we have yet
+
+ align:start position:0%
+still I can't say that we have yet
+ 
+
+ align:start position:0%
+still I can't say that we have yet
+stylized patterns but very interesting
+
+ align:start position:0%
+stylized patterns but very interesting
+ 
+
+ align:start position:0%
+stylized patterns but very interesting
+uh very interesting set of facts
+
+ align:start position:0%
+uh very interesting set of facts
+ 
+
+ align:start position:0%
+uh very interesting set of facts
+so let me stop here for uh sort of
+
+ align:start position:0%
+so let me stop here for uh sort of
+ 
+
+ align:start position:0%
+so let me stop here for uh sort of
+General yeah to what extent has kind of
+
+ align:start position:0%
+General yeah to what extent has kind of
+ 
+
+ align:start position:0%
+General yeah to what extent has kind of
+like this literature on like uh gender
+
+ align:start position:0%
+like this literature on like uh gender
+ 
+
+ align:start position:0%
+like this literature on like uh gender
+norms and information sharing being
+
+ align:start position:0%
+norms and information sharing being
+ 
+
+ align:start position:0%
+norms and information sharing being
+replicated in other countries other
+
+ align:start position:0%
+replicated in other countries other
+ 
+
+ align:start position:0%
+replicated in other countries other
+cultures and things like that I think
+
+ align:start position:0%
+cultures and things like that I think
+ 
+
+ align:start position:0%
+cultures and things like that I think
+all these papers we looked at were India
+
+ align:start position:0%
+all these papers we looked at were India
+ 
+
+ align:start position:0%
+all these papers we looked at were India
+uh no the uh in Zambia
+
+ align:start position:0%
+uh no the uh in Zambia
+ 
+
+ align:start position:0%
+uh no the uh in Zambia
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is some work in the U.S which I'm
+
+ align:start position:0%
+there is some work in the U.S which I'm
+ 
+
+ align:start position:0%
+there is some work in the U.S which I'm
+going to discuss in a minute on a woman
+
+ align:start position:0%
+going to discuss in a minute on a woman
+ 
+
+ align:start position:0%
+going to discuss in a minute on a woman
+in the labor Supply
+
+ align:start position:0%
+in the labor Supply
+ 
+
+ align:start position:0%
+in the labor Supply
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I can't say the entire Globe has been
+
+ align:start position:0%
+so I can't say the entire Globe has been
+ 
+
+ align:start position:0%
+so I can't say the entire Globe has been
+covered but it's not just in there
+
+ align:start position:0%
+covered but it's not just in there
+ 
+
+ align:start position:0%
+covered but it's not just in there
+India has a particularly
+
+ align:start position:0%
+India has a particularly
+ 
+
+ align:start position:0%
+India has a particularly
+anti-female Libra first participation it
+
+ align:start position:0%
+anti-female Libra first participation it
+ 
+
+ align:start position:0%
+anti-female Libra first participation it
+was the labor force participation is
+
+ align:start position:0%
+was the labor force participation is
+ 
+
+ align:start position:0%
+was the labor force participation is
+lowest in the world in India lowest and
+
+ align:start position:0%
+lowest in the world in India lowest and
+ 
+
+ align:start position:0%
+lowest in the world in India lowest and
+lower in Saudi Arabia or other places
+
+ align:start position:0%
+lower in Saudi Arabia or other places
+ 
+
+ align:start position:0%
+lower in Saudi Arabia or other places
+that you would consider to be pretty
+
+ align:start position:0%
+that you would consider to be pretty
+ 
+
+ align:start position:0%
+that you would consider to be pretty
+anti-woman's work so I think that's a
+
+ align:start position:0%
+anti-woman's work so I think that's a
+ 
+
+ align:start position:0%
+anti-woman's work so I think that's a
+good question that you know all of the
+
+ align:start position:0%
+good question that you know all of the
+ 
+
+ align:start position:0%
+good question that you know all of the
+work that is in India might be tainted
+
+ align:start position:0%
+work that is in India might be tainted
+ 
+
+ align:start position:0%
+work that is in India might be tainted
+by this particularly strong social Norm
+
+ align:start position:0%
+by this particularly strong social Norm
+ 
+
+ align:start position:0%
+by this particularly strong social Norm
+against women working but
+
+ align:start position:0%
+against women working but
+ 
+
+ align:start position:0%
+against women working but
+for example with a lot of the work that
+
+ align:start position:0%
+for example with a lot of the work that
+ 
+
+ align:start position:0%
+for example with a lot of the work that
+we've seen on the household actually was
+
+ align:start position:0%
+we've seen on the household actually was
+ 
+
+ align:start position:0%
+we've seen on the household actually was
+not from India for example
+
+ align:start position:0%
+not from India for example
+ 
+
+ align:start position:0%
+not from India for example
+my paper was Chris Judo is from Cote
+
+ align:start position:0%
+my paper was Chris Judo is from Cote
+ 
+
+ align:start position:0%
+my paper was Chris Judo is from Cote
+d'Ivoire the ud paper is from Burkina
+
+ align:start position:0%
+d'Ivoire the ud paper is from Burkina
+ 
+
+ align:start position:0%
+d'Ivoire the ud paper is from Burkina
+Faso
+
+ align:start position:0%
+Faso
+ 
+
+ align:start position:0%
+Faso
+um so I actually do think there is a
+
+ align:start position:0%
+um so I actually do think there is a
+ 
+
+ align:start position:0%
+um so I actually do think there is a
+fair amount of things on the households
+
+ align:start position:0%
+fair amount of things on the households
+ 
+
+ align:start position:0%
+fair amount of things on the households
+that's not on that's not on India the
+
+ align:start position:0%
+that's not on that's not on India the
+ 
+
+ align:start position:0%
+that's not on that's not on India the
+and I think you absolutely right that
+
+ align:start position:0%
+and I think you absolutely right that
+ 
+
+ align:start position:0%
+and I think you absolutely right that
+the culture setup matters a lot in terms
+
+ align:start position:0%
+the culture setup matters a lot in terms
+ 
+
+ align:start position:0%
+the culture setup matters a lot in terms
+of women labor for partition a lot quite
+
+ align:start position:0%
+of women labor for partition a lot quite
+ 
+
+ align:start position:0%
+of women labor for partition a lot quite
+a bit of the work is on India perhaps
+
+ align:start position:0%
+a bit of the work is on India perhaps
+ 
+
+ align:start position:0%
+a bit of the work is on India perhaps
+because this is such a surprising
+
+ align:start position:0%
+because this is such a surprising
+ 
+
+ align:start position:0%
+because this is such a surprising
+surprisingly anti-woman work setup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me continue talking about very
+
+ align:start position:0%
+okay let me continue talking about very
+ 
+
+ align:start position:0%
+okay let me continue talking about very
+relevant I just put them in a different
+
+ align:start position:0%
+relevant I just put them in a different
+ 
+
+ align:start position:0%
+relevant I just put them in a different
+set of slide for having uh
+
+ align:start position:0%
+set of slide for having uh
+ 
+
+ align:start position:0%
+set of slide for having uh
+for logical consistency
+
+ align:start position:0%
+for logical consistency
+ 
+
+ align:start position:0%
+for logical consistency
+but it's very much the the continuation
+
+ align:start position:0%
+but it's very much the the continuation
+ 
+
+ align:start position:0%
+but it's very much the the continuation
+of talking about the family with the
+
+ align:start position:0%
+of talking about the family with the
+ 
+
+ align:start position:0%
+of talking about the family with the
+angle of talking about women in the
+
+ align:start position:0%
+angle of talking about women in the
+ 
+
+ align:start position:0%
+angle of talking about women in the
+labor markets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a very active area of work
+
+ align:start position:0%
+so this is a very active area of work
+ 
+
+ align:start position:0%
+so this is a very active area of work
+right now a lot of exciting stuff are
+
+ align:start position:0%
+right now a lot of exciting stuff are
+ 
+
+ align:start position:0%
+right now a lot of exciting stuff are
+being done there's still more stuff to
+
+ align:start position:0%
+being done there's still more stuff to
+ 
+
+ align:start position:0%
+being done there's still more stuff to
+be done but this is one of the one of
+
+ align:start position:0%
+be done but this is one of the one of
+ 
+
+ align:start position:0%
+be done but this is one of the one of
+the place where there is a lot of recent
+
+ align:start position:0%
+the place where there is a lot of recent
+ 
+
+ align:start position:0%
+the place where there is a lot of recent
+people so I thought it made a chance to
+
+ align:start position:0%
+people so I thought it made a chance to
+ 
+
+ align:start position:0%
+people so I thought it made a chance to
+have a whole a whole lecture about that
+
+ align:start position:0%
+have a whole a whole lecture about that
+ 
+
+ align:start position:0%
+have a whole a whole lecture about that
+so interestingly if you read uh papers
+
+ align:start position:0%
+so interestingly if you read uh papers
+ 
+
+ align:start position:0%
+so interestingly if you read uh papers
+on a bargaining power and a household in
+
+ align:start position:0%
+on a bargaining power and a household in
+ 
+
+ align:start position:0%
+on a bargaining power and a household in
+the U.S
+
+ align:start position:0%
+the U.S
+ 
+
+ align:start position:0%
+the U.S
+the outcome that they show to show that
+
+ align:start position:0%
+the outcome that they show to show that
+ 
+
+ align:start position:0%
+the outcome that they show to show that
+women have more bargaining power is
+
+ align:start position:0%
+women have more bargaining power is
+ 
+
+ align:start position:0%
+women have more bargaining power is
+Leisure that is female liberal Supply
+
+ align:start position:0%
+Leisure that is female liberal Supply
+ 
+
+ align:start position:0%
+Leisure that is female liberal Supply
+which is seen as a sign of law if women
+
+ align:start position:0%
+which is seen as a sign of law if women
+ 
+
+ align:start position:0%
+which is seen as a sign of law if women
+have to work is seen as a sign of lowly
+
+ align:start position:0%
+have to work is seen as a sign of lowly
+ 
+
+ align:start position:0%
+have to work is seen as a sign of lowly
+low bargaining power in the U.S so for
+
+ align:start position:0%
+low bargaining power in the U.S so for
+ 
+
+ align:start position:0%
+low bargaining power in the U.S so for
+example if you read a Josh younggrist
+
+ align:start position:0%
+example if you read a Josh younggrist
+ 
+
+ align:start position:0%
+example if you read a Josh younggrist
+paper looking at the marriage market and
+
+ align:start position:0%
+paper looking at the marriage market and
+ 
+
+ align:start position:0%
+paper looking at the marriage market and
+showing that women who have who are from
+
+ align:start position:0%
+showing that women who have who are from
+ 
+
+ align:start position:0%
+showing that women who have who are from
+ethnic communities where there are more
+
+ align:start position:0%
+ethnic communities where there are more
+ 
+
+ align:start position:0%
+ethnic communities where there are more
+men relative to women have more
+
+ align:start position:0%
+men relative to women have more
+ 
+
+ align:start position:0%
+men relative to women have more
+bargaining power
+
+ align:start position:0%
+bargaining power
+ 
+
+ align:start position:0%
+bargaining power
+the idea being that if the union breaks
+
+ align:start position:0%
+the idea being that if the union breaks
+ 
+
+ align:start position:0%
+the idea being that if the union breaks
+they it would be easier for them to uh
+
+ align:start position:0%
+they it would be easier for them to uh
+ 
+
+ align:start position:0%
+they it would be easier for them to uh
+to remarry well in that paper the
+
+ align:start position:0%
+to remarry well in that paper the
+ 
+
+ align:start position:0%
+to remarry well in that paper the
+outcome is female labor force
+
+ align:start position:0%
+outcome is female labor force
+ 
+
+ align:start position:0%
+outcome is female labor force
+participation what he shows is female
+
+ align:start position:0%
+participation what he shows is female
+ 
+
+ align:start position:0%
+participation what he shows is female
+love of the series is lower and these
+
+ align:start position:0%
+love of the series is lower and these
+ 
+
+ align:start position:0%
+love of the series is lower and these
+groups where ethnic groups where women
+
+ align:start position:0%
+groups where ethnic groups where women
+ 
+
+ align:start position:0%
+groups where ethnic groups where women
+of higher bargain power
+
+ align:start position:0%
+of higher bargain power
+ 
+
+ align:start position:0%
+of higher bargain power
+so and in the capori papers from the U.S
+
+ align:start position:0%
+so and in the capori papers from the U.S
+ 
+
+ align:start position:0%
+so and in the capori papers from the U.S
+as well this is pretty much always women
+
+ align:start position:0%
+as well this is pretty much always women
+ 
+
+ align:start position:0%
+as well this is pretty much always women
+liberal Supply they like that outcome
+
+ align:start position:0%
+liberal Supply they like that outcome
+ 
+
+ align:start position:0%
+liberal Supply they like that outcome
+because Leisure is a good that is
+
+ align:start position:0%
+because Leisure is a good that is
+ 
+
+ align:start position:0%
+because Leisure is a good that is
+privately consumed and is a bit harder
+
+ align:start position:0%
+privately consumed and is a bit harder
+ 
+
+ align:start position:0%
+privately consumed and is a bit harder
+to share so that makes sense but of
+
+ align:start position:0%
+to share so that makes sense but of
+ 
+
+ align:start position:0%
+to share so that makes sense but of
+course in most developing countries that
+
+ align:start position:0%
+course in most developing countries that
+ 
+
+ align:start position:0%
+course in most developing countries that
+would that would be a silly outcome
+
+ align:start position:0%
+would that would be a silly outcome
+ 
+
+ align:start position:0%
+would that would be a silly outcome
+because a female labor Supply is
+
+ align:start position:0%
+because a female labor Supply is
+ 
+
+ align:start position:0%
+because a female labor Supply is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+considered to be on the contrary
+
+ align:start position:0%
+considered to be on the contrary
+ 
+
+ align:start position:0%
+considered to be on the contrary
+something that women wants to do and
+
+ align:start position:0%
+something that women wants to do and
+ 
+
+ align:start position:0%
+something that women wants to do and
+their husbands don't want them to do so
+
+ align:start position:0%
+their husbands don't want them to do so
+ 
+
+ align:start position:0%
+their husbands don't want them to do so
+there is a nice review paper by rohini
+
+ align:start position:0%
+there is a nice review paper by rohini
+ 
+
+ align:start position:0%
+there is a nice review paper by rohini
+Pandey and co-authors
+
+ align:start position:0%
+Pandey and co-authors
+ 
+
+ align:start position:0%
+Pandey and co-authors
+which looks at uh which is basically
+
+ align:start position:0%
+which looks at uh which is basically
+ 
+
+ align:start position:0%
+which looks at uh which is basically
+descriptive evidence of what women want
+
+ align:start position:0%
+descriptive evidence of what women want
+ 
+
+ align:start position:0%
+descriptive evidence of what women want
+to do and what men want to do and what
+
+ align:start position:0%
+to do and what men want to do and what
+ 
+
+ align:start position:0%
+to do and what men want to do and what
+it shows is that most women in most
+
+ align:start position:0%
+it shows is that most women in most
+ 
+
+ align:start position:0%
+it shows is that most women in most
+developing countries particularly in
+
+ align:start position:0%
+developing countries particularly in
+ 
+
+ align:start position:0%
+developing countries particularly in
+South Asia but not only women would like
+
+ align:start position:0%
+South Asia but not only women would like
+ 
+
+ align:start position:0%
+South Asia but not only women would like
+to work and their husband don't want
+
+ align:start position:0%
+to work and their husband don't want
+ 
+
+ align:start position:0%
+to work and their husband don't want
+them to work
+
+ align:start position:0%
+them to work
+ 
+
+ align:start position:0%
+them to work
+and in fact they are less likely to work
+
+ align:start position:0%
+and in fact they are less likely to work
+ 
+
+ align:start position:0%
+and in fact they are less likely to work
+just in term of back one this is a bit
+
+ align:start position:0%
+just in term of back one this is a bit
+ 
+
+ align:start position:0%
+just in term of back one this is a bit
+anticipating what we are going to what
+
+ align:start position:0%
+anticipating what we are going to what
+ 
+
+ align:start position:0%
+anticipating what we are going to what
+we're going to do in 772 but there is a
+
+ align:start position:0%
+we're going to do in 772 but there is a
+ 
+
+ align:start position:0%
+we're going to do in 772 but there is a
+recent paper by Sheikh publishing
+
+ align:start position:0%
+recent paper by Sheikh publishing
+ 
+
+ align:start position:0%
+recent paper by Sheikh publishing
+econometrica
+
+ align:start position:0%
+econometrica
+ 
+
+ align:start position:0%
+econometrica
+chain others she and Chiang taishi and a
+
+ align:start position:0%
+chain others she and Chiang taishi and a
+ 
+
+ align:start position:0%
+chain others she and Chiang taishi and a
+bunch of other people which which extend
+
+ align:start position:0%
+bunch of other people which which extend
+ 
+
+ align:start position:0%
+bunch of other people which which extend
+their framework which you're gonna
+
+ align:start position:0%
+their framework which you're gonna
+ 
+
+ align:start position:0%
+their framework which you're gonna
+become painfully familiar with in 772 on
+
+ align:start position:0%
+become painfully familiar with in 772 on
+ 
+
+ align:start position:0%
+become painfully familiar with in 772 on
+misallocation of resources to show that
+
+ align:start position:0%
+misallocation of resources to show that
+ 
+
+ align:start position:0%
+misallocation of resources to show that
+uh in the US the entry of black people
+
+ align:start position:0%
+uh in the US the entry of black people
+ 
+
+ align:start position:0%
+uh in the US the entry of black people
+and women in bit better paid occupations
+
+ align:start position:0%
+and women in bit better paid occupations
+ 
+
+ align:start position:0%
+and women in bit better paid occupations
+have led to a large increase in labor
+
+ align:start position:0%
+have led to a large increase in labor
+ 
+
+ align:start position:0%
+have led to a large increase in labor
+for productivity simply by allocating
+
+ align:start position:0%
+for productivity simply by allocating
+ 
+
+ align:start position:0%
+for productivity simply by allocating
+talent to where it should be going
+
+ align:start position:0%
+talent to where it should be going
+ 
+
+ align:start position:0%
+talent to where it should be going
+and in particular for students in the
+
+ align:start position:0%
+and in particular for students in the
+ 
+
+ align:start position:0%
+and in particular for students in the
+second year who are thinking about their
+
+ align:start position:0%
+second year who are thinking about their
+ 
+
+ align:start position:0%
+second year who are thinking about their
+people somehow I absolutely love the
+
+ align:start position:0%
+people somehow I absolutely love the
+ 
+
+ align:start position:0%
+people somehow I absolutely love the
+first sentence of their abstract it says
+
+ align:start position:0%
+first sentence of their abstract it says
+ 
+
+ align:start position:0%
+first sentence of their abstract it says
+in 1960 94 of doctors and lawyers were
+
+ align:start position:0%
+in 1960 94 of doctors and lawyers were
+ 
+
+ align:start position:0%
+in 1960 94 of doctors and lawyers were
+white men by 2010 the fraction was just
+
+ align:start position:0%
+white men by 2010 the fraction was just
+ 
+
+ align:start position:0%
+white men by 2010 the fraction was just
+62 percent
+
+ align:start position:0%
+62 percent
+ 
+
+ align:start position:0%
+62 percent
+so why do I love this way of writing the
+
+ align:start position:0%
+so why do I love this way of writing the
+ 
+
+ align:start position:0%
+so why do I love this way of writing the
+abstract it gives you a very concrete
+
+ align:start position:0%
+abstract it gives you a very concrete
+ 
+
+ align:start position:0%
+abstract it gives you a very concrete
+fact that you might have known
+
+ align:start position:0%
+fact that you might have known
+ 
+
+ align:start position:0%
+fact that you might have known
+qualitatively but not maybe
+
+ align:start position:0%
+qualitatively but not maybe
+ 
+
+ align:start position:0%
+qualitatively but not maybe
+quantitatively and it sets the stage for
+
+ align:start position:0%
+quantitatively and it sets the stage for
+ 
+
+ align:start position:0%
+quantitatively and it sets the stage for
+their next question which is uh
+
+ align:start position:0%
+their next question which is uh
+ 
+
+ align:start position:0%
+their next question which is uh
+presumably it's not because they have
+
+ align:start position:0%
+presumably it's not because they have
+ 
+
+ align:start position:0%
+presumably it's not because they have
+become more talented at becoming lawyers
+
+ align:start position:0%
+become more talented at becoming lawyers
+ 
+
+ align:start position:0%
+become more talented at becoming lawyers
+so this is related in part two barriers
+
+ align:start position:0%
+so this is related in part two barriers
+ 
+
+ align:start position:0%
+so this is related in part two barriers
+institutional cultural and social norms
+
+ align:start position:0%
+institutional cultural and social norms
+ 
+
+ align:start position:0%
+institutional cultural and social norms
+Etc that have made that made it harder
+
+ align:start position:0%
+Etc that have made that made it harder
+ 
+
+ align:start position:0%
+Etc that have made that made it harder
+for them to access these jobs in the
+
+ align:start position:0%
+for them to access these jobs in the
+ 
+
+ align:start position:0%
+for them to access these jobs in the
+first place and therefore it should lead
+
+ align:start position:0%
+first place and therefore it should lead
+ 
+
+ align:start position:0%
+first place and therefore it should lead
+to a better allocation of talent and
+
+ align:start position:0%
+to a better allocation of talent and
+ 
+
+ align:start position:0%
+to a better allocation of talent and
+more productivity
+
+ align:start position:0%
+more productivity
+ 
+
+ align:start position:0%
+more productivity
+uh so that's what that's what the people
+
+ align:start position:0%
+uh so that's what that's what the people
+ 
+
+ align:start position:0%
+uh so that's what that's what the people
+went on doing and by and so they
+
+ align:start position:0%
+went on doing and by and so they
+ 
+
+ align:start position:0%
+went on doing and by and so they
+calibrate that 20 to 40 percent of
+
+ align:start position:0%
+calibrate that 20 to 40 percent of
+ 
+
+ align:start position:0%
+calibrate that 20 to 40 percent of
+outcome goals in the US can be explained
+
+ align:start position:0%
+outcome goals in the US can be explained
+ 
+
+ align:start position:0%
+outcome goals in the US can be explained
+by this so given that it's a period
+
+ align:start position:0%
+by this so given that it's a period
+ 
+
+ align:start position:0%
+by this so given that it's a period
+where outward ghost was in general a
+
+ align:start position:0%
+where outward ghost was in general a
+ 
+
+ align:start position:0%
+where outward ghost was in general a
+slower uh this is uh I think it would
+
+ align:start position:0%
+slower uh this is uh I think it would
+ 
+
+ align:start position:0%
+slower uh this is uh I think it would
+have been even slower if women and and
+
+ align:start position:0%
+have been even slower if women and and
+ 
+
+ align:start position:0%
+have been even slower if women and and
+black people had not been uh able to
+
+ align:start position:0%
+black people had not been uh able to
+ 
+
+ align:start position:0%
+black people had not been uh able to
+access in larger numbers those those
+
+ align:start position:0%
+access in larger numbers those those
+ 
+
+ align:start position:0%
+access in larger numbers those those
+occupations
+
+ align:start position:0%
+occupations
+ 
+
+ align:start position:0%
+occupations
+uh so this first sentence of the
+
+ align:start position:0%
+uh so this first sentence of the
+ 
+
+ align:start position:0%
+uh so this first sentence of the
+abstract it's it kind of you it's pretty
+
+ align:start position:0%
+abstract it's it kind of you it's pretty
+ 
+
+ align:start position:0%
+abstract it's it kind of you it's pretty
+it's like it's rap
+
+ align:start position:0%
+it's like it's rap
+ 
+
+ align:start position:0%
+it's like it's rap
+in one in one sentence it just sits at
+
+ align:start position:0%
+in one in one sentence it just sits at
+ 
+
+ align:start position:0%
+in one in one sentence it just sits at
+the stage very nicely and so this is an
+
+ align:start position:0%
+the stage very nicely and so this is an
+ 
+
+ align:start position:0%
+the stage very nicely and so this is an
+important question and of course from
+
+ align:start position:0%
+important question and of course from
+ 
+
+ align:start position:0%
+important question and of course from
+there you could have gone I'm going to
+
+ align:start position:0%
+there you could have gone I'm going to
+ 
+
+ align:start position:0%
+there you could have gone I'm going to
+explain why and in fact that's not what
+
+ align:start position:0%
+explain why and in fact that's not what
+ 
+
+ align:start position:0%
+explain why and in fact that's not what
+they are interested in is explaining the
+
+ align:start position:0%
+they are interested in is explaining the
+ 
+
+ align:start position:0%
+they are interested in is explaining the
+consequences but it sets up immediately
+
+ align:start position:0%
+consequences but it sets up immediately
+ 
+
+ align:start position:0%
+consequences but it sets up immediately
+why we should care yeah so just just to
+
+ align:start position:0%
+why we should care yeah so just just to
+ 
+
+ align:start position:0%
+why we should care yeah so just just to
+understand it's like the
+
+ align:start position:0%
+understand it's like the
+ 
+
+ align:start position:0%
+understand it's like the
+just the Striking quantity like I put a
+
+ align:start position:0%
+just the Striking quantity like I put a
+ 
+
+ align:start position:0%
+just the Striking quantity like I put a
+lot of abstract start with the very
+
+ align:start position:0%
+lot of abstract start with the very
+ 
+
+ align:start position:0%
+lot of abstract start with the very
+concrete sentences
+
+ align:start position:0%
+concrete sentences
+ 
+
+ align:start position:0%
+concrete sentences
+but maybe not as concrete as this I
+
+ align:start position:0%
+but maybe not as concrete as this I
+ 
+
+ align:start position:0%
+but maybe not as concrete as this I
+think it's a very concrete fact somewhat
+
+ align:start position:0%
+think it's a very concrete fact somewhat
+ 
+
+ align:start position:0%
+think it's a very concrete fact somewhat
+unexpected in terms of the quantitative
+
+ align:start position:0%
+unexpected in terms of the quantitative
+ 
+
+ align:start position:0%
+unexpected in terms of the quantitative
+aspect and that immediate issue I'm
+
+ align:start position:0%
+aspect and that immediate issue I'm
+ 
+
+ align:start position:0%
+aspect and that immediate issue I'm
+going to show you the impact of the next
+
+ align:start position:0%
+going to show you the impact of the next
+ 
+
+ align:start position:0%
+going to show you the impact of the next
+sentence because I'm going to show you
+
+ align:start position:0%
+sentence because I'm going to show you
+ 
+
+ align:start position:0%
+sentence because I'm going to show you
+the impact of this transition
+
+ align:start position:0%
+the impact of this transition
+ 
+
+ align:start position:0%
+the impact of this transition
+and this is likely going to be large
+
+ align:start position:0%
+and this is likely going to be large
+ 
+
+ align:start position:0%
+and this is likely going to be large
+because that is a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other people from the US which uh
+
+ align:start position:0%
+other people from the US which uh
+ 
+
+ align:start position:0%
+other people from the US which uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+shows which is related to this idea of
+
+ align:start position:0%
+shows which is related to this idea of
+ 
+
+ align:start position:0%
+shows which is related to this idea of
+of women labor Supply as uh actually
+
+ align:start position:0%
+of women labor Supply as uh actually
+ 
+
+ align:start position:0%
+of women labor Supply as uh actually
+something that they would like and that
+
+ align:start position:0%
+something that they would like and that
+ 
+
+ align:start position:0%
+something that they would like and that
+is constrained by the husband in the U.S
+
+ align:start position:0%
+is constrained by the husband in the U.S
+ 
+
+ align:start position:0%
+is constrained by the husband in the U.S
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+people by Leo Boston to mafujiwara and
+
+ align:start position:0%
+people by Leo Boston to mafujiwara and
+ 
+
+ align:start position:0%
+people by Leo Boston to mafujiwara and
+Mandy Palace in MBA at the top business
+
+ align:start position:0%
+Mandy Palace in MBA at the top business
+ 
+
+ align:start position:0%
+Mandy Palace in MBA at the top business
+school that's not very far from here
+
+ align:start position:0%
+school that's not very far from here
+ 
+
+ align:start position:0%
+school that's not very far from here
+there are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they had them work in their orientation
+
+ align:start position:0%
+they had them work in their orientation
+ 
+
+ align:start position:0%
+they had them work in their orientation
+session
+
+ align:start position:0%
+session
+ 
+
+ align:start position:0%
+session
+is there a mixed group mixed gender
+
+ align:start position:0%
+is there a mixed group mixed gender
+ 
+
+ align:start position:0%
+is there a mixed group mixed gender
+group or in a single sex gender group
+
+ align:start position:0%
+group or in a single sex gender group
+ 
+
+ align:start position:0%
+group or in a single sex gender group
+and then they had them say what type of
+
+ align:start position:0%
+and then they had them say what type of
+ 
+
+ align:start position:0%
+and then they had them say what type of
+job they want to apply to
+
+ align:start position:0%
+job they want to apply to
+ 
+
+ align:start position:0%
+job they want to apply to
+either in a way that the way that they
+
+ align:start position:0%
+either in a way that the way that they
+ 
+
+ align:start position:0%
+either in a way that the way that they
+were supposed to say it either it was
+
+ align:start position:0%
+were supposed to say it either it was
+ 
+
+ align:start position:0%
+were supposed to say it either it was
+said this is going to be discussed in
+
+ align:start position:0%
+said this is going to be discussed in
+ 
+
+ align:start position:0%
+said this is going to be discussed in
+your entire group
+
+ align:start position:0%
+your entire group
+ 
+
+ align:start position:0%
+your entire group
+or destroys this this survey is going to
+
+ align:start position:0%
+or destroys this this survey is going to
+ 
+
+ align:start position:0%
+or destroys this this survey is going to
+remain private so this is a typical Leo
+
+ align:start position:0%
+remain private so this is a typical Leo
+ 
+
+ align:start position:0%
+remain private so this is a typical Leo
+Bernstein
+
+ align:start position:0%
+Bernstein
+ 
+
+ align:start position:0%
+Bernstein
+kind of trick that you also have in
+
+ align:start position:0%
+kind of trick that you also have in
+ 
+
+ align:start position:0%
+kind of trick that you also have in
+their uh in their education paper on
+
+ align:start position:0%
+their uh in their education paper on
+ 
+
+ align:start position:0%
+their uh in their education paper on
+basically threatening to make uh
+
+ align:start position:0%
+basically threatening to make uh
+ 
+
+ align:start position:0%
+basically threatening to make uh
+threatening to make a
+
+ align:start position:0%
+threatening to make a
+ 
+
+ align:start position:0%
+threatening to make a
+an affirmation of value public or not
+
+ align:start position:0%
+an affirmation of value public or not
+ 
+
+ align:start position:0%
+an affirmation of value public or not
+which therefore makes it social and
+
+ align:start position:0%
+which therefore makes it social and
+ 
+
+ align:start position:0%
+which therefore makes it social and
+potentially have as it hit the social
+
+ align:start position:0%
+potentially have as it hit the social
+ 
+
+ align:start position:0%
+potentially have as it hit the social
+norms or not
+
+ align:start position:0%
+norms or not
+ 
+
+ align:start position:0%
+norms or not
+but this is perhaps my my favorite
+
+ align:start position:0%
+but this is perhaps my my favorite
+ 
+
+ align:start position:0%
+but this is perhaps my my favorite
+application of this trick because it
+
+ align:start position:0%
+application of this trick because it
+ 
+
+ align:start position:0%
+application of this trick because it
+seems
+
+ align:start position:0%
+seems
+ 
+
+ align:start position:0%
+seems
+in summer it seems very natural that you
+
+ align:start position:0%
+in summer it seems very natural that you
+ 
+
+ align:start position:0%
+in summer it seems very natural that you
+would either fill this survey privately
+
+ align:start position:0%
+would either fill this survey privately
+ 
+
+ align:start position:0%
+would either fill this survey privately
+or discuss it with the group
+
+ align:start position:0%
+or discuss it with the group
+ 
+
+ align:start position:0%
+or discuss it with the group
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+either and and it seems to be a large
+
+ align:start position:0%
+either and and it seems to be a large
+ 
+
+ align:start position:0%
+either and and it seems to be a large
+enough manipulation that people would be
+
+ align:start position:0%
+enough manipulation that people would be
+ 
+
+ align:start position:0%
+enough manipulation that people would be
+sensitive to it
+
+ align:start position:0%
+sensitive to it
+ 
+
+ align:start position:0%
+sensitive to it
+anyway what they find is that when women
+
+ align:start position:0%
+anyway what they find is that when women
+ 
+
+ align:start position:0%
+anyway what they find is that when women
+are are doing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+choice of you know are listing their
+
+ align:start position:0%
+choice of you know are listing their
+ 
+
+ align:start position:0%
+choice of you know are listing their
+choice of preferred careers this is very
+
+ align:start position:0%
+choice of preferred careers this is very
+ 
+
+ align:start position:0%
+choice of preferred careers this is very
+high stakes because it's uh information
+
+ align:start position:0%
+high stakes because it's uh information
+ 
+
+ align:start position:0%
+high stakes because it's uh information
+about careers this is in career fair so
+
+ align:start position:0%
+about careers this is in career fair so
+ 
+
+ align:start position:0%
+about careers this is in career fair so
+what the report is what you know artists
+
+ align:start position:0%
+what the report is what you know artists
+ 
+
+ align:start position:0%
+what the report is what you know artists
+they would have believed at that time
+
+ align:start position:0%
+they would have believed at that time
+ 
+
+ align:start position:0%
+they would have believed at that time
+subsequently I assumed they had another
+
+ align:start position:0%
+subsequently I assumed they had another
+ 
+
+ align:start position:0%
+subsequently I assumed they had another
+chance to report is going to be what the
+
+ align:start position:0%
+chance to report is going to be what the
+ 
+
+ align:start position:0%
+chance to report is going to be what the
+concealers are going to use to find them
+
+ align:start position:0%
+concealers are going to use to find them
+ 
+
+ align:start position:0%
+concealers are going to use to find them
+internship which in turn which turns
+
+ align:start position:0%
+internship which in turn which turns
+ 
+
+ align:start position:0%
+internship which in turn which turns
+into job so this is a very high stake
+
+ align:start position:0%
+into job so this is a very high stake
+ 
+
+ align:start position:0%
+into job so this is a very high stake
+decision
+
+ align:start position:0%
+decision
+ 
+
+ align:start position:0%
+decision
+and when one in in gender uh
+
+ align:start position:0%
+and when one in in gender uh
+ 
+
+ align:start position:0%
+and when one in in gender uh
+in gender reunified group single gender
+
+ align:start position:0%
+in gender reunified group single gender
+ 
+
+ align:start position:0%
+in gender reunified group single gender
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+it makes no difference uh to do it
+
+ align:start position:0%
+it makes no difference uh to do it
+ 
+
+ align:start position:0%
+it makes no difference uh to do it
+publicly or privately
+
+ align:start position:0%
+publicly or privately
+ 
+
+ align:start position:0%
+publicly or privately
+but in groups where they are both men
+
+ align:start position:0%
+but in groups where they are both men
+ 
+
+ align:start position:0%
+but in groups where they are both men
+and women
+
+ align:start position:0%
+and women
+ 
+
+ align:start position:0%
+and women
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+are less ambition if they think that
+
+ align:start position:0%
+are less ambition if they think that
+ 
+
+ align:start position:0%
+are less ambition if they think that
+their choice is going to be publicly
+
+ align:start position:0%
+their choice is going to be publicly
+ 
+
+ align:start position:0%
+their choice is going to be publicly
+revealed the display less ambitious in
+
+ align:start position:0%
+revealed the display less ambitious in
+ 
+
+ align:start position:0%
+revealed the display less ambitious in
+the treatment where they are made to
+
+ align:start position:0%
+the treatment where they are made to
+ 
+
+ align:start position:0%
+the treatment where they are made to
+believe that their choice is going to be
+
+ align:start position:0%
+believe that their choice is going to be
+ 
+
+ align:start position:0%
+believe that their choice is going to be
+publicly revealed
+
+ align:start position:0%
+publicly revealed
+ 
+
+ align:start position:0%
+publicly revealed
+so that's why they call it active acting
+
+ align:start position:0%
+so that's why they call it active acting
+ 
+
+ align:start position:0%
+so that's why they call it active acting
+wife because they think that the wife
+
+ align:start position:0%
+wife because they think that the wife
+ 
+
+ align:start position:0%
+wife because they think that the wife
+doesn't want to be the future wife
+
+ align:start position:0%
+doesn't want to be the future wife
+ 
+
+ align:start position:0%
+doesn't want to be the future wife
+sorry let me finish
+
+ align:start position:0%
+sorry let me finish
+ 
+
+ align:start position:0%
+sorry let me finish
+that is true only for a single women but
+
+ align:start position:0%
+that is true only for a single women but
+ 
+
+ align:start position:0%
+that is true only for a single women but
+not for married women
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for a single woman
+
+ align:start position:0%
+so for a single woman
+ 
+
+ align:start position:0%
+so for a single woman
+in mixed group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you they are much less they are they are
+
+ align:start position:0%
+you they are much less they are they are
+ 
+
+ align:start position:0%
+you they are much less they are they are
+revealing less ambitious choices if
+
+ align:start position:0%
+revealing less ambitious choices if
+ 
+
+ align:start position:0%
+revealing less ambitious choices if
+those choices are going to be public
+
+ align:start position:0%
+those choices are going to be public
+ 
+
+ align:start position:0%
+those choices are going to be public
+then if they are going to be private
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the so they they relate that to the the
+
+ align:start position:0%
+the so they they relate that to the the
+ 
+
+ align:start position:0%
+the so they they relate that to the the
+thing that if you you don't want to
+
+ align:start position:0%
+thing that if you you don't want to
+ 
+
+ align:start position:0%
+thing that if you you don't want to
+appear to be an over-ambitious woman if
+
+ align:start position:0%
+appear to be an over-ambitious woman if
+ 
+
+ align:start position:0%
+appear to be an over-ambitious woman if
+you're single that makes you less my
+
+ align:start position:0%
+you're single that makes you less my
+ 
+
+ align:start position:0%
+you're single that makes you less my
+marriageable less attractive on the
+
+ align:start position:0%
+marriageable less attractive on the
+ 
+
+ align:start position:0%
+marriageable less attractive on the
+marriage market and presumably the the
+
+ align:start position:0%
+marriage market and presumably the the
+ 
+
+ align:start position:0%
+marriage market and presumably the the
+the the men uh around you in your MBA
+
+ align:start position:0%
+the the men uh around you in your MBA
+ 
+
+ align:start position:0%
+the the men uh around you in your MBA
+program are potential needs
+
+ align:start position:0%
+program are potential needs
+ 
+
+ align:start position:0%
+program are potential needs
+so that's to show that this this uh um
+
+ align:start position:0%
+so that's to show that this this uh um
+ 
+
+ align:start position:0%
+so that's to show that this this uh um
+this kind of phenomenon of maybe a woman
+
+ align:start position:0%
+this kind of phenomenon of maybe a woman
+ 
+
+ align:start position:0%
+this kind of phenomenon of maybe a woman
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+anticipating
+
+ align:start position:0%
+anticipating
+ 
+
+ align:start position:0%
+anticipating
+the desire of their husbands or
+
+ align:start position:0%
+the desire of their husbands or
+ 
+
+ align:start position:0%
+the desire of their husbands or
+potential husbands that they shouldn't
+
+ align:start position:0%
+potential husbands that they shouldn't
+ 
+
+ align:start position:0%
+potential husbands that they shouldn't
+work or they should not be ambitious on
+
+ align:start position:0%
+work or they should not be ambitious on
+ 
+
+ align:start position:0%
+work or they should not be ambitious on
+their work is is pervasive
+
+ align:start position:0%
+their work is is pervasive
+ 
+
+ align:start position:0%
+their work is is pervasive
+so this last fact it's consistent with
+
+ align:start position:0%
+so this last fact it's consistent with
+ 
+
+ align:start position:0%
+so this last fact it's consistent with
+an efficient household model with
+
+ align:start position:0%
+an efficient household model with
+ 
+
+ align:start position:0%
+an efficient household model with
+limited commitment that is one where
+
+ align:start position:0%
+limited commitment that is one where
+ 
+
+ align:start position:0%
+limited commitment that is one where
+the person who has you know people are
+
+ align:start position:0%
+the person who has you know people are
+ 
+
+ align:start position:0%
+the person who has you know people are
+bargaining efficiency but based on how
+
+ align:start position:0%
+bargaining efficiency but based on how
+ 
+
+ align:start position:0%
+bargaining efficiency but based on how
+much money they they bring to the
+
+ align:start position:0%
+much money they they bring to the
+ 
+
+ align:start position:0%
+much money they they bring to the
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+so that's but then if for some reason
+
+ align:start position:0%
+so that's but then if for some reason
+ 
+
+ align:start position:0%
+so that's but then if for some reason
+you have an exogenous shock and suddenly
+
+ align:start position:0%
+you have an exogenous shock and suddenly
+ 
+
+ align:start position:0%
+you have an exogenous shock and suddenly
+your bargaining power increases uh you
+
+ align:start position:0%
+your bargaining power increases uh you
+ 
+
+ align:start position:0%
+your bargaining power increases uh you
+certainly you share to the your outside
+
+ align:start position:0%
+certainly you share to the your outside
+ 
+
+ align:start position:0%
+certainly you share to the your outside
+option increases then the bargaining
+
+ align:start position:0%
+option increases then the bargaining
+ 
+
+ align:start position:0%
+option increases then the bargaining
+power is renegotiated so in a fully
+
+ align:start position:0%
+power is renegotiated so in a fully
+ 
+
+ align:start position:0%
+power is renegotiated so in a fully
+efficient household model there would be
+
+ align:start position:0%
+efficient household model there would be
+ 
+
+ align:start position:0%
+efficient household model there would be
+no negotiation every time someone gets
+
+ align:start position:0%
+no negotiation every time someone gets
+ 
+
+ align:start position:0%
+no negotiation every time someone gets
+more money but a more
+
+ align:start position:0%
+more money but a more
+ 
+
+ align:start position:0%
+more money but a more
+a model with limited commitment which by
+
+ align:start position:0%
+a model with limited commitment which by
+ 
+
+ align:start position:0%
+a model with limited commitment which by
+the way has become the Workhorse model
+
+ align:start position:0%
+the way has become the Workhorse model
+ 
+
+ align:start position:0%
+the way has become the Workhorse model
+of insurance both in developing
+
+ align:start position:0%
+of insurance both in developing
+ 
+
+ align:start position:0%
+of insurance both in developing
+countries and in developed countries
+
+ align:start position:0%
+countries and in developed countries
+ 
+
+ align:start position:0%
+countries and in developed countries
+where bargaining power is affected by
+
+ align:start position:0%
+where bargaining power is affected by
+ 
+
+ align:start position:0%
+where bargaining power is affected by
+people's outside option means that a
+
+ align:start position:0%
+people's outside option means that a
+ 
+
+ align:start position:0%
+people's outside option means that a
+woman who he who worked more who wants
+
+ align:start position:0%
+woman who he who worked more who wants
+ 
+
+ align:start position:0%
+woman who he who worked more who wants
+more as more
+
+ align:start position:0%
+more as more
+ 
+
+ align:start position:0%
+more as more
+bargaining power in the household so she
+
+ align:start position:0%
+bargaining power in the household so she
+ 
+
+ align:start position:0%
+bargaining power in the household so she
+cannot this this young woman finishing
+
+ align:start position:0%
+cannot this this young woman finishing
+ 
+
+ align:start position:0%
+cannot this this young woman finishing
+their MBA cannot say
+
+ align:start position:0%
+their MBA cannot say
+ 
+
+ align:start position:0%
+their MBA cannot say
+okay I'm committing to not be power to
+
+ align:start position:0%
+okay I'm committing to not be power to
+ 
+
+ align:start position:0%
+okay I'm committing to not be power to
+not Bargain Hunt I'm committing to a low
+
+ align:start position:0%
+not Bargain Hunt I'm committing to a low
+ 
+
+ align:start position:0%
+not Bargain Hunt I'm committing to a low
+bargaining power and a household but let
+
+ align:start position:0%
+bargaining power and a household but let
+ 
+
+ align:start position:0%
+bargaining power and a household but let
+me you know earn more money it's going
+
+ align:start position:0%
+me you know earn more money it's going
+ 
+
+ align:start position:0%
+me you know earn more money it's going
+to be good it's going to be more money
+
+ align:start position:0%
+to be good it's going to be more money
+ 
+
+ align:start position:0%
+to be good it's going to be more money
+for you to spend after all right they
+
+ align:start position:0%
+for you to spend after all right they
+ 
+
+ align:start position:0%
+for you to spend after all right they
+can't do that because once they have the
+
+ align:start position:0%
+can't do that because once they have the
+ 
+
+ align:start position:0%
+can't do that because once they have the
+money they'll be in a position to say
+
+ align:start position:0%
+money they'll be in a position to say
+ 
+
+ align:start position:0%
+money they'll be in a position to say
+ you if we are not bargaining the
+
+ align:start position:0%
+ you if we are not bargaining the
+ 
+
+ align:start position:0%
+ you if we are not bargaining the
+way that I would want to bang and I'm
+
+ align:start position:0%
+way that I would want to bang and I'm
+ 
+
+ align:start position:0%
+way that I would want to bang and I'm
+just leaving this household
+
+ align:start position:0%
+just leaving this household
+ 
+
+ align:start position:0%
+just leaving this household
+so that's consistent with that
+
+ align:start position:0%
+so that's consistent with that
+ 
+
+ align:start position:0%
+so that's consistent with that
+and then maybe that's why uh they would
+
+ align:start position:0%
+and then maybe that's why uh they would
+ 
+
+ align:start position:0%
+and then maybe that's why uh they would
+they don't want to display that they
+
+ align:start position:0%
+they don't want to display that they
+ 
+
+ align:start position:0%
+they don't want to display that they
+might they have this kind of foundation
+
+ align:start position:0%
+might they have this kind of foundation
+ 
+
+ align:start position:0%
+might they have this kind of foundation
+it is also consistent with a more
+
+ align:start position:0%
+it is also consistent with a more
+ 
+
+ align:start position:0%
+it is also consistent with a more
+General social norms that women
+
+ align:start position:0%
+General social norms that women
+ 
+
+ align:start position:0%
+General social norms that women
+shouldn't be working or that I was we
+
+ align:start position:0%
+shouldn't be working or that I was we
+ 
+
+ align:start position:0%
+shouldn't be working or that I was we
+see more in a minute they should not
+
+ align:start position:0%
+see more in a minute they should not
+ 
+
+ align:start position:0%
+see more in a minute they should not
+earn more than their more than their
+
+ align:start position:0%
+earn more than their more than their
+ 
+
+ align:start position:0%
+earn more than their more than their
+husbands
+
+ align:start position:0%
+husbands
+ 
+
+ align:start position:0%
+husbands
+so let's spend some time talking about
+
+ align:start position:0%
+so let's spend some time talking about
+ 
+
+ align:start position:0%
+so let's spend some time talking about
+these social norms about women working
+
+ align:start position:0%
+these social norms about women working
+ 
+
+ align:start position:0%
+these social norms about women working
+even before the social norms it's there
+
+ align:start position:0%
+even before the social norms it's there
+ 
+
+ align:start position:0%
+even before the social norms it's there
+is a legal framework and often we tend
+
+ align:start position:0%
+is a legal framework and often we tend
+ 
+
+ align:start position:0%
+is a legal framework and often we tend
+to forget as economists we are too
+
+ align:start position:0%
+to forget as economists we are too
+ 
+
+ align:start position:0%
+to forget as economists we are too
+cogent we consider that the legal
+
+ align:start position:0%
+cogent we consider that the legal
+ 
+
+ align:start position:0%
+cogent we consider that the legal
+framework is irrelevant any negotiation
+
+ align:start position:0%
+framework is irrelevant any negotiation
+ 
+
+ align:start position:0%
+framework is irrelevant any negotiation
+can happen anyways but in reality the
+
+ align:start position:0%
+can happen anyways but in reality the
+ 
+
+ align:start position:0%
+can happen anyways but in reality the
+legal framework what is legal what is
+
+ align:start position:0%
+legal framework what is legal what is
+ 
+
+ align:start position:0%
+legal framework what is legal what is
+not what other rights do determine what
+
+ align:start position:0%
+not what other rights do determine what
+ 
+
+ align:start position:0%
+not what other rights do determine what
+you know the the context in which this
+
+ align:start position:0%
+you know the the context in which this
+ 
+
+ align:start position:0%
+you know the the context in which this
+negotiation are happening
+
+ align:start position:0%
+negotiation are happening
+ 
+
+ align:start position:0%
+negotiation are happening
+and Penny Goldberg when she was Chief
+
+ align:start position:0%
+and Penny Goldberg when she was Chief
+ 
+
+ align:start position:0%
+and Penny Goldberg when she was Chief
+Economist at the bank led a project
+
+ align:start position:0%
+Economist at the bank led a project
+ 
+
+ align:start position:0%
+Economist at the bank led a project
+where they put together a new exciting
+
+ align:start position:0%
+where they put together a new exciting
+ 
+
+ align:start position:0%
+where they put together a new exciting
+database on gender rights
+
+ align:start position:0%
+database on gender rights
+ 
+
+ align:start position:0%
+database on gender rights
+uh which is which they have uh they have
+
+ align:start position:0%
+uh which is which they have uh they have
+ 
+
+ align:start position:0%
+uh which is which they have uh they have
+rights in in Liberal Market in property
+
+ align:start position:0%
+rights in in Liberal Market in property
+ 
+
+ align:start position:0%
+rights in in Liberal Market in property
+anti-discrimination
+
+ align:start position:0%
+anti-discrimination
+ 
+
+ align:start position:0%
+anti-discrimination
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um that database is public you can use
+
+ align:start position:0%
+um that database is public you can use
+ 
+
+ align:start position:0%
+um that database is public you can use
+it to do whatever you want and it's
+
+ align:start position:0%
+it to do whatever you want and it's
+ 
+
+ align:start position:0%
+it to do whatever you want and it's
+updated every year and they have a short
+
+ align:start position:0%
+updated every year and they have a short
+ 
+
+ align:start position:0%
+updated every year and they have a short
+paper in area inside where the the they
+
+ align:start position:0%
+paper in area inside where the the they
+ 
+
+ align:start position:0%
+paper in area inside where the the they
+are just putting together some
+
+ align:start position:0%
+are just putting together some
+ 
+
+ align:start position:0%
+are just putting together some
+descriptive data facts about this
+
+ align:start position:0%
+descriptive data facts about this
+ 
+
+ align:start position:0%
+descriptive data facts about this
+database
+
+ align:start position:0%
+database
+ 
+
+ align:start position:0%
+database
+and just a few things first of all the
+
+ align:start position:0%
+and just a few things first of all the
+ 
+
+ align:start position:0%
+and just a few things first of all the
+average is 75 out of 100 that is for
+
+ align:start position:0%
+average is 75 out of 100 that is for
+ 
+
+ align:start position:0%
+average is 75 out of 100 that is for
+every four rights that the husband had
+
+ align:start position:0%
+every four rights that the husband had
+ 
+
+ align:start position:0%
+every four rights that the husband had
+that the men have awareness tree it's
+
+ align:start position:0%
+that the men have awareness tree it's
+ 
+
+ align:start position:0%
+that the men have awareness tree it's
+particularly low in Middle Eastern North
+
+ align:start position:0%
+particularly low in Middle Eastern North
+ 
+
+ align:start position:0%
+particularly low in Middle Eastern North
+Africa and South Asia it's not gonna
+
+ align:start position:0%
+Africa and South Asia it's not gonna
+ 
+
+ align:start position:0%
+Africa and South Asia it's not gonna
+surprise you 40 percent in Mina so women
+
+ align:start position:0%
+surprise you 40 percent in Mina so women
+ 
+
+ align:start position:0%
+surprise you 40 percent in Mina so women
+have 40 percent of the right of men and
+
+ align:start position:0%
+have 40 percent of the right of men and
+ 
+
+ align:start position:0%
+have 40 percent of the right of men and
+60 in South Asia so it's not just about
+
+ align:start position:0%
+60 in South Asia so it's not just about
+ 
+
+ align:start position:0%
+60 in South Asia so it's not just about
+social Norm in India Pakistan Bangladesh
+
+ align:start position:0%
+social Norm in India Pakistan Bangladesh
+ 
+
+ align:start position:0%
+social Norm in India Pakistan Bangladesh
+it's also the law
+
+ align:start position:0%
+it's also the law
+ 
+
+ align:start position:0%
+it's also the law
+and they also show a strong Coalition
+
+ align:start position:0%
+and they also show a strong Coalition
+ 
+
+ align:start position:0%
+and they also show a strong Coalition
+between legal rights and female labor
+
+ align:start position:0%
+between legal rights and female labor
+ 
+
+ align:start position:0%
+between legal rights and female labor
+force participation and the gender gap
+
+ align:start position:0%
+force participation and the gender gap
+ 
+
+ align:start position:0%
+force participation and the gender gap
+so it is not cool that the laws on that
+
+ align:start position:0%
+so it is not cool that the laws on that
+ 
+
+ align:start position:0%
+so it is not cool that the laws on that
+Sams are irrelevant except perhaps you
+
+ align:start position:0%
+Sams are irrelevant except perhaps you
+ 
+
+ align:start position:0%
+Sams are irrelevant except perhaps you
+could say well this is just all
+
+ align:start position:0%
+could say well this is just all
+ 
+
+ align:start position:0%
+could say well this is just all
+correlation so in places where they are
+
+ align:start position:0%
+correlation so in places where they are
+ 
+
+ align:start position:0%
+correlation so in places where they are
+not interested in giving women access to
+
+ align:start position:0%
+not interested in giving women access to
+ 
+
+ align:start position:0%
+not interested in giving women access to
+the labor force anywhere it's also the
+
+ align:start position:0%
+the labor force anywhere it's also the
+ 
+
+ align:start position:0%
+the labor force anywhere it's also the
+places where the laws are less are less
+
+ align:start position:0%
+places where the laws are less are less
+ 
+
+ align:start position:0%
+places where the laws are less are less
+General so that's at this point it's
+
+ align:start position:0%
+General so that's at this point it's
+ 
+
+ align:start position:0%
+General so that's at this point it's
+just a correlation
+
+ align:start position:0%
+just a correlation
+ 
+
+ align:start position:0%
+just a correlation
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so all of this is super
+
+ align:start position:0%
+yeah yeah so all of this is super
+ 
+
+ align:start position:0%
+yeah yeah so all of this is super
+endogenous yeah yeah absolutely all of
+
+ align:start position:0%
+endogenous yeah yeah absolutely all of
+ 
+
+ align:start position:0%
+endogenous yeah yeah absolutely all of
+this super on the dreams in fact one of
+
+ align:start position:0%
+this super on the dreams in fact one of
+ 
+
+ align:start position:0%
+this super on the dreams in fact one of
+the things that they also showed which I
+
+ align:start position:0%
+the things that they also showed which I
+ 
+
+ align:start position:0%
+the things that they also showed which I
+have not put it's got it's gotten better
+
+ align:start position:0%
+have not put it's got it's gotten better
+ 
+
+ align:start position:0%
+have not put it's got it's gotten better
+uh so not just in Saudi Arabia not just
+
+ align:start position:0%
+uh so not just in Saudi Arabia not just
+ 
+
+ align:start position:0%
+uh so not just in Saudi Arabia not just
+in Mina but all over the world there
+
+ align:start position:0%
+in Mina but all over the world there
+ 
+
+ align:start position:0%
+in Mina but all over the world there
+have been a num they're basically
+
+ align:start position:0%
+have been a num they're basically
+ 
+
+ align:start position:0%
+have been a num they're basically
+documenting the reform that have
+
+ align:start position:0%
+documenting the reform that have
+ 
+
+ align:start position:0%
+documenting the reform that have
+happened over the last several decades
+
+ align:start position:0%
+happened over the last several decades
+ 
+
+ align:start position:0%
+happened over the last several decades
+and it has gotten better everywhere and
+
+ align:start position:0%
+and it has gotten better everywhere and
+ 
+
+ align:start position:0%
+and it has gotten better everywhere and
+you're right the fact that it gets
+
+ align:start position:0%
+you're right the fact that it gets
+ 
+
+ align:start position:0%
+you're right the fact that it gets
+better might rely it might be a product
+
+ align:start position:0%
+better might rely it might be a product
+ 
+
+ align:start position:0%
+better might rely it might be a product
+in some extent of labor market nightness
+
+ align:start position:0%
+in some extent of labor market nightness
+ 
+
+ align:start position:0%
+in some extent of labor market nightness
+like uh in Saudi Arabia that's not
+
+ align:start position:0%
+like uh in Saudi Arabia that's not
+ 
+
+ align:start position:0%
+like uh in Saudi Arabia that's not
+something that to my extent to my
+
+ align:start position:0%
+something that to my extent to my
+ 
+
+ align:start position:0%
+something that to my extent to my
+knowledge they discuss in the paper
+
+ align:start position:0%
+knowledge they discuss in the paper
+ 
+
+ align:start position:0%
+knowledge they discuss in the paper
+whether someone something someone could
+
+ align:start position:0%
+whether someone something someone could
+ 
+
+ align:start position:0%
+whether someone something someone could
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+do we expect
+
+ align:start position:0%
+do we expect
+ 
+
+ align:start position:0%
+do we expect
+labor market tightness to necessarily
+
+ align:start position:0%
+labor market tightness to necessarily
+ 
+
+ align:start position:0%
+labor market tightness to necessarily
+reduce gender wage gaps or you might
+
+ align:start position:0%
+reduce gender wage gaps or you might
+ 
+
+ align:start position:0%
+reduce gender wage gaps or you might
+expect maybe more like interesting
+
+ align:start position:0%
+expect maybe more like interesting
+ 
+
+ align:start position:0%
+expect maybe more like interesting
+College
+
+ align:start position:0%
+College
+ 
+
+ align:start position:0%
+College
+I don't think they would be I don't
+
+ align:start position:0%
+I don't think they would be I don't
+ 
+
+ align:start position:0%
+I don't think they would be I don't
+think there is a there is a I think it's
+
+ align:start position:0%
+think there is a there is a I think it's
+ 
+
+ align:start position:0%
+think there is a there is a I think it's
+going to depend a bit on the mother
+
+ align:start position:0%
+going to depend a bit on the mother
+ 
+
+ align:start position:0%
+going to depend a bit on the mother
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+in general yes you would expect I
+
+ align:start position:0%
+in general yes you would expect I
+ 
+
+ align:start position:0%
+in general yes you would expect I
+assumed you would expect that but it
+
+ align:start position:0%
+assumed you would expect that but it
+ 
+
+ align:start position:0%
+assumed you would expect that but it
+depends on whether there are also
+
+ align:start position:0%
+depends on whether there are also
+ 
+
+ align:start position:0%
+depends on whether there are also
+restriction on on what women can and
+
+ align:start position:0%
+restriction on on what women can and
+ 
+
+ align:start position:0%
+restriction on on what women can and
+which Market women can is related to
+
+ align:start position:0%
+which Market women can is related to
+ 
+
+ align:start position:0%
+which Market women can is related to
+this allocation point that is made by
+
+ align:start position:0%
+this allocation point that is made by
+ 
+
+ align:start position:0%
+this allocation point that is made by
+the share and others people suppose that
+
+ align:start position:0%
+the share and others people suppose that
+ 
+
+ align:start position:0%
+the share and others people suppose that
+woman can only work in textile
+
+ align:start position:0%
+woman can only work in textile
+ 
+
+ align:start position:0%
+woman can only work in textile
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+labor market
+
+ align:start position:0%
+labor market
+ 
+
+ align:start position:0%
+labor market
+tightness might not do much to the to
+
+ align:start position:0%
+tightness might not do much to the to
+ 
+
+ align:start position:0%
+tightness might not do much to the to
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+to the gender gap
+
+ align:start position:0%
+to the gender gap
+ 
+
+ align:start position:0%
+to the gender gap
+uh because what you're going to see is
+
+ align:start position:0%
+uh because what you're going to see is
+ 
+
+ align:start position:0%
+uh because what you're going to see is
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+more women employed in textile and then
+
+ align:start position:0%
+more women employed in textile and then
+ 
+
+ align:start position:0%
+more women employed in textile and then
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+all the men that are freed from textile
+
+ align:start position:0%
+all the men that are freed from textile
+ 
+
+ align:start position:0%
+all the men that are freed from textile
+moving to the other sectors and uh and
+
+ align:start position:0%
+moving to the other sectors and uh and
+ 
+
+ align:start position:0%
+moving to the other sectors and uh and
+and and getting increased wages there
+
+ align:start position:0%
+and and getting increased wages there
+ 
+
+ align:start position:0%
+and and getting increased wages there
+it's also related to uh something that
+
+ align:start position:0%
+it's also related to uh something that
+ 
+
+ align:start position:0%
+it's also related to uh something that
+I'm not going to talk about today but uh
+
+ align:start position:0%
+I'm not going to talk about today but uh
+ 
+
+ align:start position:0%
+I'm not going to talk about today but uh
+um that there is starting to be some
+
+ align:start position:0%
+um that there is starting to be some
+ 
+
+ align:start position:0%
+um that there is starting to be some
+work on is uh and I think you might do
+
+ align:start position:0%
+work on is uh and I think you might do
+ 
+
+ align:start position:0%
+work on is uh and I think you might do
+more with Ben is monopson is in the
+
+ align:start position:0%
+more with Ben is monopson is in the
+ 
+
+ align:start position:0%
+more with Ben is monopson is in the
+labor market
+
+ align:start position:0%
+labor market
+ 
+
+ align:start position:0%
+labor market
+so the woman both women and men might be
+
+ align:start position:0%
+so the woman both women and men might be
+ 
+
+ align:start position:0%
+so the woman both women and men might be
+subject to uh
+
+ align:start position:0%
+subject to uh
+ 
+
+ align:start position:0%
+subject to uh
+non-competitive or imperfect competition
+
+ align:start position:0%
+non-competitive or imperfect competition
+ 
+
+ align:start position:0%
+non-competitive or imperfect competition
+in the labor market
+
+ align:start position:0%
+in the labor market
+ 
+
+ align:start position:0%
+in the labor market
+because it's hard to find another job
+
+ align:start position:0%
+because it's hard to find another job
+ 
+
+ align:start position:0%
+because it's hard to find another job
+once you have one or and this imperfect
+
+ align:start position:0%
+once you have one or and this imperfect
+ 
+
+ align:start position:0%
+once you have one or and this imperfect
+competition might be stronger for for a
+
+ align:start position:0%
+competition might be stronger for for a
+ 
+
+ align:start position:0%
+competition might be stronger for for a
+woman because they are more restricted
+
+ align:start position:0%
+woman because they are more restricted
+ 
+
+ align:start position:0%
+woman because they are more restricted
+in the type of job that they can they
+
+ align:start position:0%
+in the type of job that they can they
+ 
+
+ align:start position:0%
+in the type of job that they can they
+they can access to for example they
+
+ align:start position:0%
+they can access to for example they
+ 
+
+ align:start position:0%
+they can access to for example they
+cannot move because they cannot move
+
+ align:start position:0%
+cannot move because they cannot move
+ 
+
+ align:start position:0%
+cannot move because they cannot move
+their family they cannot travel far
+
+ align:start position:0%
+their family they cannot travel far
+ 
+
+ align:start position:0%
+their family they cannot travel far
+because they cannot go on buses they
+
+ align:start position:0%
+because they cannot go on buses they
+ 
+
+ align:start position:0%
+because they cannot go on buses they
+have limitation on the sectors in which
+
+ align:start position:0%
+have limitation on the sectors in which
+ 
+
+ align:start position:0%
+have limitation on the sectors in which
+they work so in this kind of a model we
+
+ align:start position:0%
+they work so in this kind of a model we
+ 
+
+ align:start position:0%
+they work so in this kind of a model we
+said you might expect that the
+
+ align:start position:0%
+said you might expect that the
+ 
+
+ align:start position:0%
+said you might expect that the
+the an increase in the labor market
+
+ align:start position:0%
+the an increase in the labor market
+ 
+
+ align:start position:0%
+the an increase in the labor market
+tightness in general is not going to
+
+ align:start position:0%
+tightness in general is not going to
+ 
+
+ align:start position:0%
+tightness in general is not going to
+lead too much of an improvement for the
+
+ align:start position:0%
+lead too much of an improvement for the
+ 
+
+ align:start position:0%
+lead too much of an improvement for the
+women's situation so I think it's it's
+
+ align:start position:0%
+women's situation so I think it's it's
+ 
+
+ align:start position:0%
+women's situation so I think it's it's
+gonna depend on the mother and on the on
+
+ align:start position:0%
+gonna depend on the mother and on the on
+ 
+
+ align:start position:0%
+gonna depend on the mother and on the on
+the setting obviously
+
+ align:start position:0%
+the setting obviously
+ 
+
+ align:start position:0%
+the setting obviously
+so let's let's talk let's let's take it
+
+ align:start position:0%
+so let's let's talk let's let's take it
+ 
+
+ align:start position:0%
+so let's let's talk let's let's take it
+side step two to think about culture and
+
+ align:start position:0%
+side step two to think about culture and
+ 
+
+ align:start position:0%
+side step two to think about culture and
+social norms and then in particular
+
+ align:start position:0%
+social norms and then in particular
+ 
+
+ align:start position:0%
+social norms and then in particular
+culture and social norms in the liberal
+
+ align:start position:0%
+culture and social norms in the liberal
+ 
+
+ align:start position:0%
+culture and social norms in the liberal
+Market
+
+ align:start position:0%
+Market
+ 
+
+ align:start position:0%
+Market
+so um at Nissan at Harvard is someone
+
+ align:start position:0%
+so um at Nissan at Harvard is someone
+ 
+
+ align:start position:0%
+so um at Nissan at Harvard is someone
+who has done a lot to to to bring back
+
+ align:start position:0%
+who has done a lot to to to bring back
+ 
+
+ align:start position:0%
+who has done a lot to to to bring back
+sort of the study of culture and social
+
+ align:start position:0%
+sort of the study of culture and social
+ 
+
+ align:start position:0%
+sort of the study of culture and social
+norms as a legitimate object of study in
+
+ align:start position:0%
+norms as a legitimate object of study in
+ 
+
+ align:start position:0%
+norms as a legitimate object of study in
+economics uh in saying that it still has
+
+ align:start position:0%
+economics uh in saying that it still has
+ 
+
+ align:start position:0%
+economics uh in saying that it still has
+a lot of impact on on the way that
+
+ align:start position:0%
+a lot of impact on on the way that
+ 
+
+ align:start position:0%
+a lot of impact on on the way that
+people live their lives and economic
+
+ align:start position:0%
+people live their lives and economic
+ 
+
+ align:start position:0%
+people live their lives and economic
+outcomes Etc
+
+ align:start position:0%
+outcomes Etc
+ 
+
+ align:start position:0%
+outcomes Etc
+um one recent paper is uh one recent
+
+ align:start position:0%
+um one recent paper is uh one recent
+ 
+
+ align:start position:0%
+um one recent paper is uh one recent
+study is a not the people is from a few
+
+ align:start position:0%
+study is a not the people is from a few
+ 
+
+ align:start position:0%
+study is a not the people is from a few
+years ago but it's a
+
+ align:start position:0%
+years ago but it's a
+ 
+
+ align:start position:0%
+years ago but it's a
+one of the great example of his work uh
+
+ align:start position:0%
+one of the great example of his work uh
+ 
+
+ align:start position:0%
+one of the great example of his work uh
+this is joined by the by the way with
+
+ align:start position:0%
+this is joined by the by the way with
+ 
+
+ align:start position:0%
+this is joined by the by the way with
+Alberto alizina and Paula Juliano
+
+ align:start position:0%
+Alberto alizina and Paula Juliano
+ 
+
+ align:start position:0%
+Alberto alizina and Paula Juliano
+what they do is to read and to test an
+
+ align:start position:0%
+what they do is to read and to test an
+ 
+
+ align:start position:0%
+what they do is to read and to test an
+old hypothesis of esterbus group which
+
+ align:start position:0%
+old hypothesis of esterbus group which
+ 
+
+ align:start position:0%
+old hypothesis of esterbus group which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+which is in regions where the plow was
+
+ align:start position:0%
+which is in regions where the plow was
+ 
+
+ align:start position:0%
+which is in regions where the plow was
+dominant males were more involved in
+
+ align:start position:0%
+dominant males were more involved in
+ 
+
+ align:start position:0%
+dominant males were more involved in
+walking up the field and women were more
+
+ align:start position:0%
+walking up the field and women were more
+ 
+
+ align:start position:0%
+walking up the field and women were more
+evaluated valued will women were less
+
+ align:start position:0%
+evaluated valued will women were less
+ 
+
+ align:start position:0%
+evaluated valued will women were less
+evaluated valued valued
+
+ align:start position:0%
+evaluated valued valued
+ 
+
+ align:start position:0%
+evaluated valued valued
+so for example if you look at India
+
+ align:start position:0%
+so for example if you look at India
+ 
+
+ align:start position:0%
+so for example if you look at India
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+and you look at North India versus South
+
+ align:start position:0%
+and you look at North India versus South
+ 
+
+ align:start position:0%
+and you look at North India versus South
+India a cliche which is correct is that
+
+ align:start position:0%
+India a cliche which is correct is that
+ 
+
+ align:start position:0%
+India a cliche which is correct is that
+women are better treated in the south of
+
+ align:start position:0%
+women are better treated in the south of
+ 
+
+ align:start position:0%
+women are better treated in the south of
+India
+
+ align:start position:0%
+India
+ 
+
+ align:start position:0%
+India
+and the south of India is a culture of
+
+ align:start position:0%
+and the south of India is a culture of
+ 
+
+ align:start position:0%
+and the south of India is a culture of
+rice where traditionally it's done by
+
+ align:start position:0%
+rice where traditionally it's done by
+ 
+
+ align:start position:0%
+rice where traditionally it's done by
+hand in fact today it's still done by
+
+ align:start position:0%
+hand in fact today it's still done by
+ 
+
+ align:start position:0%
+hand in fact today it's still done by
+hand it's always been done by hand it's
+
+ align:start position:0%
+hand it's always been done by hand it's
+ 
+
+ align:start position:0%
+hand it's always been done by hand it's
+labor intensive but not in a
+
+ align:start position:0%
+labor intensive but not in a
+ 
+
+ align:start position:0%
+labor intensive but not in a
+particularly
+
+ align:start position:0%
+particularly
+ 
+
+ align:start position:0%
+particularly
+you don't need to be super strong you
+
+ align:start position:0%
+you don't need to be super strong you
+ 
+
+ align:start position:0%
+you don't need to be super strong you
+need to be patient and just you know get
+
+ align:start position:0%
+need to be patient and just you know get
+ 
+
+ align:start position:0%
+need to be patient and just you know get
+it done whereas the north of India
+
+ align:start position:0%
+it done whereas the north of India
+ 
+
+ align:start position:0%
+it done whereas the north of India
+traditionally was not the right place
+
+ align:start position:0%
+traditionally was not the right place
+ 
+
+ align:start position:0%
+traditionally was not the right place
+also now they are doing right there but
+
+ align:start position:0%
+also now they are doing right there but
+ 
+
+ align:start position:0%
+also now they are doing right there but
+it's not a place which is suitable to
+
+ align:start position:0%
+it's not a place which is suitable to
+ 
+
+ align:start position:0%
+it's not a place which is suitable to
+ice originally so it was more of a plow
+
+ align:start position:0%
+ice originally so it was more of a plow
+ 
+
+ align:start position:0%
+ice originally so it was more of a plow
+culture and then wind culture and the uh
+
+ align:start position:0%
+culture and then wind culture and the uh
+ 
+
+ align:start position:0%
+culture and then wind culture and the uh
+where the labor Supply where Muslim men
+
+ align:start position:0%
+where the labor Supply where Muslim men
+ 
+
+ align:start position:0%
+where the labor Supply where Muslim men
+were involved traditionally in
+
+ align:start position:0%
+were involved traditionally in
+ 
+
+ align:start position:0%
+were involved traditionally in
+agriculture and in fact you'd still see
+
+ align:start position:0%
+agriculture and in fact you'd still see
+ 
+
+ align:start position:0%
+agriculture and in fact you'd still see
+this Coalition today where any dimension
+
+ align:start position:0%
+this Coalition today where any dimension
+ 
+
+ align:start position:0%
+this Coalition today where any dimension
+of women empowerment is worse in the
+
+ align:start position:0%
+of women empowerment is worse in the
+ 
+
+ align:start position:0%
+of women empowerment is worse in the
+nursing yourself so the Ester was
+
+ align:start position:0%
+nursing yourself so the Ester was
+ 
+
+ align:start position:0%
+nursing yourself so the Ester was
+hypothesis is that that's a general fact
+
+ align:start position:0%
+hypothesis is that that's a general fact
+ 
+
+ align:start position:0%
+hypothesis is that that's a general fact
+so what they do here to test the idea is
+
+ align:start position:0%
+so what they do here to test the idea is
+ 
+
+ align:start position:0%
+so what they do here to test the idea is
+that they use an FAO database on Corp
+
+ align:start position:0%
+that they use an FAO database on Corp
+ 
+
+ align:start position:0%
+that they use an FAO database on Corp
+suitability to build an index of where
+
+ align:start position:0%
+suitability to build an index of where
+ 
+
+ align:start position:0%
+suitability to build an index of where
+the plow was more likely to be used in
+
+ align:start position:0%
+the plow was more likely to be used in
+ 
+
+ align:start position:0%
+the plow was more likely to be used in
+ancient time and then they correlated
+
+ align:start position:0%
+ancient time and then they correlated
+ 
+
+ align:start position:0%
+ancient time and then they correlated
+with today's social norm and then they
+
+ align:start position:0%
+with today's social norm and then they
+ 
+
+ align:start position:0%
+with today's social norm and then they
+put fixed effect and some such to try
+
+ align:start position:0%
+put fixed effect and some such to try
+ 
+
+ align:start position:0%
+put fixed effect and some such to try
+and and test it so I'll just show you
+
+ align:start position:0%
+and and test it so I'll just show you
+ 
+
+ align:start position:0%
+and and test it so I'll just show you
+one graph which kind of makes it clear
+
+ align:start position:0%
+one graph which kind of makes it clear
+ 
+
+ align:start position:0%
+one graph which kind of makes it clear
+conditional plow use
+
+ align:start position:0%
+conditional plow use
+ 
+
+ align:start position:0%
+conditional plow use
+and female labor force participation so
+
+ align:start position:0%
+and female labor force participation so
+ 
+
+ align:start position:0%
+and female labor force participation so
+this is not real you this is a kind of
+
+ align:start position:0%
+this is not real you this is a kind of
+ 
+
+ align:start position:0%
+this is not real you this is a kind of
+expected use based on the cup
+
+ align:start position:0%
+expected use based on the cup
+ 
+
+ align:start position:0%
+expected use based on the cup
+suitability for the cup mix and you can
+
+ align:start position:0%
+suitability for the cup mix and you can
+ 
+
+ align:start position:0%
+suitability for the cup mix and you can
+see that the labor first participation
+
+ align:start position:0%
+see that the labor first participation
+ 
+
+ align:start position:0%
+see that the labor first participation
+is higher in places that were less
+
+ align:start position:0%
+is higher in places that were less
+ 
+
+ align:start position:0%
+is higher in places that were less
+likely to use the plan so that's the
+
+ align:start position:0%
+likely to use the plan so that's the
+ 
+
+ align:start position:0%
+likely to use the plan so that's the
+cost country interpretation
+
+ align:start position:0%
+cost country interpretation
+ 
+
+ align:start position:0%
+cost country interpretation
+I I find
+
+ align:start position:0%
+I I find
+ 
+
+ align:start position:0%
+I I find
+the the people are quite convincing in
+
+ align:start position:0%
+the the people are quite convincing in
+ 
+
+ align:start position:0%
+the the people are quite convincing in
+terms of the very many tests they do Etc
+
+ align:start position:0%
+terms of the very many tests they do Etc
+ 
+
+ align:start position:0%
+terms of the very many tests they do Etc
+it's cross-country so it's never you
+
+ align:start position:0%
+it's cross-country so it's never you
+ 
+
+ align:start position:0%
+it's cross-country so it's never you
+know going to be completely completely
+
+ align:start position:0%
+know going to be completely completely
+ 
+
+ align:start position:0%
+know going to be completely completely
+watertight and the other one is the
+
+ align:start position:0%
+watertight and the other one is the
+ 
+
+ align:start position:0%
+watertight and the other one is the
+entire world and so there is some some
+
+ align:start position:0%
+entire world and so there is some some
+ 
+
+ align:start position:0%
+entire world and so there is some some
+benefits to that as well so I I strongly
+
+ align:start position:0%
+benefits to that as well so I I strongly
+ 
+
+ align:start position:0%
+benefits to that as well so I I strongly
+uh suggest you you have a look at these
+
+ align:start position:0%
+uh suggest you you have a look at these
+ 
+
+ align:start position:0%
+uh suggest you you have a look at these
+people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now one more problem with the social
+
+ align:start position:0%
+now one more problem with the social
+ 
+
+ align:start position:0%
+now one more problem with the social
+norms is that uh and one reason why they
+
+ align:start position:0%
+norms is that uh and one reason why they
+ 
+
+ align:start position:0%
+norms is that uh and one reason why they
+might be very persistent
+
+ align:start position:0%
+might be very persistent
+ 
+
+ align:start position:0%
+might be very persistent
+is that even when the change you might
+
+ align:start position:0%
+is that even when the change you might
+ 
+
+ align:start position:0%
+is that even when the change you might
+not know that the change in particular
+
+ align:start position:0%
+not know that the change in particular
+ 
+
+ align:start position:0%
+not know that the change in particular
+if as we've seen in our first paper we
+
+ align:start position:0%
+if as we've seen in our first paper we
+ 
+
+ align:start position:0%
+if as we've seen in our first paper we
+discussed today the discussions are
+
+ align:start position:0%
+discussed today the discussions are
+ 
+
+ align:start position:0%
+discussed today the discussions are
+you're not very good at discussing
+
+ align:start position:0%
+you're not very good at discussing
+ 
+
+ align:start position:0%
+you're not very good at discussing
+things with
+
+ align:start position:0%
+things with
+ 
+
+ align:start position:0%
+things with
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+so if you if you find it difficult to
+
+ align:start position:0%
+so if you if you find it difficult to
+ 
+
+ align:start position:0%
+so if you if you find it difficult to
+learn about from others about how many
+
+ align:start position:0%
+learn about from others about how many
+ 
+
+ align:start position:0%
+learn about from others about how many
+blue urns there is in a jar you might
+
+ align:start position:0%
+blue urns there is in a jar you might
+ 
+
+ align:start position:0%
+blue urns there is in a jar you might
+find it even more difficult to discuss
+
+ align:start position:0%
+find it even more difficult to discuss
+ 
+
+ align:start position:0%
+find it even more difficult to discuss
+whether it's okay for your wife to work
+
+ align:start position:0%
+whether it's okay for your wife to work
+ 
+
+ align:start position:0%
+whether it's okay for your wife to work
+or it's not okay for your wife to work
+
+ align:start position:0%
+or it's not okay for your wife to work
+ 
+
+ align:start position:0%
+or it's not okay for your wife to work
+which might lead to a misperception of
+
+ align:start position:0%
+which might lead to a misperception of
+ 
+
+ align:start position:0%
+which might lead to a misperception of
+social Norm
+
+ align:start position:0%
+social Norm
+ 
+
+ align:start position:0%
+social Norm
+and hence sort of the second or
+
+ align:start position:0%
+and hence sort of the second or
+ 
+
+ align:start position:0%
+and hence sort of the second or
+birthday trick which is uh basically we
+
+ align:start position:0%
+birthday trick which is uh basically we
+ 
+
+ align:start position:0%
+birthday trick which is uh basically we
+see as performed in several people which
+
+ align:start position:0%
+see as performed in several people which
+ 
+
+ align:start position:0%
+see as performed in several people which
+is trying to uh see if there is a bias
+
+ align:start position:0%
+is trying to uh see if there is a bias
+ 
+
+ align:start position:0%
+is trying to uh see if there is a bias
+in the perception of social norm and if
+
+ align:start position:0%
+in the perception of social norm and if
+ 
+
+ align:start position:0%
+in the perception of social norm and if
+there is one to dbias people
+
+ align:start position:0%
+there is one to dbias people
+ 
+
+ align:start position:0%
+there is one to dbias people
+so this particular experiment which we
+
+ align:start position:0%
+so this particular experiment which we
+ 
+
+ align:start position:0%
+so this particular experiment which we
+presented in this very room I remember
+
+ align:start position:0%
+presented in this very room I remember
+ 
+
+ align:start position:0%
+presented in this very room I remember
+so he was there presenting it from this
+
+ align:start position:0%
+so he was there presenting it from this
+ 
+
+ align:start position:0%
+so he was there presenting it from this
+space from where I took was with 500
+
+ align:start position:0%
+space from where I took was with 500
+ 
+
+ align:start position:0%
+space from where I took was with 500
+young men in Saudi Arabia
+
+ align:start position:0%
+young men in Saudi Arabia
+ 
+
+ align:start position:0%
+young men in Saudi Arabia
+and they put them in a room or by by
+
+ align:start position:0%
+and they put them in a room or by by
+ 
+
+ align:start position:0%
+and they put them in a room or by by
+groups of about 30
+
+ align:start position:0%
+groups of about 30
+ 
+
+ align:start position:0%
+groups of about 30
+and then they asked them first their
+
+ align:start position:0%
+and then they asked them first their
+ 
+
+ align:start position:0%
+and then they asked them first their
+opinion on whether women should be
+
+ align:start position:0%
+opinion on whether women should be
+ 
+
+ align:start position:0%
+opinion on whether women should be
+allowed to work outside the home
+
+ align:start position:0%
+allowed to work outside the home
+ 
+
+ align:start position:0%
+allowed to work outside the home
+and surprisingly in this younger group
+
+ align:start position:0%
+and surprisingly in this younger group
+ 
+
+ align:start position:0%
+and surprisingly in this younger group
+there is actually a fair number of
+
+ align:start position:0%
+there is actually a fair number of
+ 
+
+ align:start position:0%
+there is actually a fair number of
+people who thinks it would be okay 87
+
+ align:start position:0%
+people who thinks it would be okay 87
+ 
+
+ align:start position:0%
+people who thinks it would be okay 87
+percent of men agree with the statement
+
+ align:start position:0%
+percent of men agree with the statement
+ 
+
+ align:start position:0%
+percent of men agree with the statement
+in my opinion women should be allowed to
+
+ align:start position:0%
+in my opinion women should be allowed to
+ 
+
+ align:start position:0%
+in my opinion women should be allowed to
+work outside the home
+
+ align:start position:0%
+work outside the home
+ 
+
+ align:start position:0%
+work outside the home
+but when asked then they asked take
+
+ align:start position:0%
+but when asked then they asked take
+ 
+
+ align:start position:0%
+but when asked then they asked take
+consider these other men in this room
+
+ align:start position:0%
+consider these other men in this room
+ 
+
+ align:start position:0%
+consider these other men in this room
+who are with you uh how many do you
+
+ align:start position:0%
+who are with you uh how many do you
+ 
+
+ align:start position:0%
+who are with you uh how many do you
+think will answer yes to that same
+
+ align:start position:0%
+think will answer yes to that same
+ 
+
+ align:start position:0%
+think will answer yes to that same
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+and there the the three-quarter
+
+ align:start position:0%
+and there the the three-quarter
+ 
+
+ align:start position:0%
+and there the the three-quarter
+underestimate the numbers
+
+ align:start position:0%
+underestimate the numbers
+ 
+
+ align:start position:0%
+underestimate the numbers
+uh so the most of them even though so
+
+ align:start position:0%
+uh so the most of them even though so
+ 
+
+ align:start position:0%
+uh so the most of them even though so
+most of them say a number that is lower
+
+ align:start position:0%
+most of them say a number that is lower
+ 
+
+ align:start position:0%
+most of them say a number that is lower
+than 80 percent
+
+ align:start position:0%
+than 80 percent
+ 
+
+ align:start position:0%
+than 80 percent
+80 percent
+
+ align:start position:0%
+80 percent
+ 
+
+ align:start position:0%
+80 percent
+most of them say a lower number
+
+ align:start position:0%
+most of them say a lower number
+ 
+
+ align:start position:0%
+most of them say a lower number
+sometimes much lower number
+
+ align:start position:0%
+sometimes much lower number
+ 
+
+ align:start position:0%
+sometimes much lower number
+so what they do in the experiment is
+
+ align:start position:0%
+so what they do in the experiment is
+ 
+
+ align:start position:0%
+so what they do in the experiment is
+that then for half of these men after
+
+ align:start position:0%
+that then for half of these men after
+ 
+
+ align:start position:0%
+that then for half of these men after
+eliciting their own norm and their own
+
+ align:start position:0%
+eliciting their own norm and their own
+ 
+
+ align:start position:0%
+eliciting their own norm and their own
+view as well as their view of other
+
+ align:start position:0%
+view as well as their view of other
+ 
+
+ align:start position:0%
+view as well as their view of other
+people's View
+
+ align:start position:0%
+people's View
+ 
+
+ align:start position:0%
+people's View
+to give them the right number about
+
+ align:start position:0%
+to give them the right number about
+ 
+
+ align:start position:0%
+to give them the right number about
+other people's View
+
+ align:start position:0%
+other people's View
+ 
+
+ align:start position:0%
+other people's View
+obviously the answer is not yes it is
+
+ align:start position:0%
+obviously the answer is not yes it is
+ 
+
+ align:start position:0%
+obviously the answer is not yes it is
+okay or it's not okay that's not but the
+
+ align:start position:0%
+okay or it's not okay that's not but the
+ 
+
+ align:start position:0%
+okay or it's not okay that's not but the
+answer is you know by the way it is
+
+ align:start position:0%
+answer is you know by the way it is
+ 
+
+ align:start position:0%
+answer is you know by the way it is
+seven percent of of people we
+
+ align:start position:0%
+seven percent of of people we
+ 
+
+ align:start position:0%
+seven percent of of people we
+interviewed think that uh it's fine
+
+ align:start position:0%
+interviewed think that uh it's fine
+ 
+
+ align:start position:0%
+interviewed think that uh it's fine
+and then the uh they are given the
+
+ align:start position:0%
+and then the uh they are given the
+ 
+
+ align:start position:0%
+and then the uh they are given the
+choice between a five dollars Amazon
+
+ align:start position:0%
+choice between a five dollars Amazon
+ 
+
+ align:start position:0%
+choice between a five dollars Amazon
+certificate and the opportunity to sign
+
+ align:start position:0%
+certificate and the opportunity to sign
+ 
+
+ align:start position:0%
+certificate and the opportunity to sign
+up their wife for a platform on the job
+
+ align:start position:0%
+up their wife for a platform on the job
+ 
+
+ align:start position:0%
+up their wife for a platform on the job
+and then they follow up they give them
+
+ align:start position:0%
+and then they follow up they give them
+ 
+
+ align:start position:0%
+and then they follow up they give them
+follow-up calls to try to look at longer
+
+ align:start position:0%
+follow-up calls to try to look at longer
+ 
+
+ align:start position:0%
+follow-up calls to try to look at longer
+term outcomes
+
+ align:start position:0%
+term outcomes
+ 
+
+ align:start position:0%
+term outcomes
+and then that's what and then after that
+
+ align:start position:0%
+and then that's what and then after that
+ 
+
+ align:start position:0%
+and then that's what and then after that
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+uh they do even better than that they
+
+ align:start position:0%
+uh they do even better than that they
+ 
+
+ align:start position:0%
+uh they do even better than that they
+they do another experiment where they
+
+ align:start position:0%
+they do another experiment where they
+ 
+
+ align:start position:0%
+they do another experiment where they
+are doing the same thing but in the
+
+ align:start position:0%
+are doing the same thing but in the
+ 
+
+ align:start position:0%
+are doing the same thing but in the
+context where people are women are given
+
+ align:start position:0%
+context where people are women are given
+ 
+
+ align:start position:0%
+context where people are women are given
+a job
+
+ align:start position:0%
+a job
+ 
+
+ align:start position:0%
+a job
+uh in a real job many women are they
+
+ align:start position:0%
+uh in a real job many women are they
+ 
+
+ align:start position:0%
+uh in a real job many women are they
+have a large number of people who are
+
+ align:start position:0%
+have a large number of people who are
+ 
+
+ align:start position:0%
+have a large number of people who are
+given a real job
+
+ align:start position:0%
+given a real job
+ 
+
+ align:start position:0%
+given a real job
+and this is a marketing phone marketing
+
+ align:start position:0%
+and this is a marketing phone marketing
+ 
+
+ align:start position:0%
+and this is a marketing phone marketing
+and then they are given the opportunity
+
+ align:start position:0%
+and then they are given the opportunity
+ 
+
+ align:start position:0%
+and then they are given the opportunity
+to do it either from home or from uh
+
+ align:start position:0%
+to do it either from home or from uh
+ 
+
+ align:start position:0%
+to do it either from home or from uh
+from office
+
+ align:start position:0%
+from office
+ 
+
+ align:start position:0%
+from office
+and the office job is more
+
+ align:start position:0%
+and the office job is more
+ 
+
+ align:start position:0%
+and the office job is more
+and the question is how many people take
+
+ align:start position:0%
+and the question is how many people take
+ 
+
+ align:start position:0%
+and the question is how many people take
+the office job so that's the second
+
+ align:start position:0%
+the office job so that's the second
+ 
+
+ align:start position:0%
+the office job so that's the second
+experiment which I'm not going to show
+
+ align:start position:0%
+experiment which I'm not going to show
+ 
+
+ align:start position:0%
+experiment which I'm not going to show
+you today but has exactly the same type
+
+ align:start position:0%
+you today but has exactly the same type
+ 
+
+ align:start position:0%
+you today but has exactly the same type
+of the same type of results and is a
+
+ align:start position:0%
+of the same type of results and is a
+ 
+
+ align:start position:0%
+of the same type of results and is a
+stronger you know more high-stick thing
+
+ align:start position:0%
+stronger you know more high-stick thing
+ 
+
+ align:start position:0%
+stronger you know more high-stick thing
+here this is a little bit you know this
+
+ align:start position:0%
+here this is a little bit you know this
+ 
+
+ align:start position:0%
+here this is a little bit you know this
+is just signing off for a job that's not
+
+ align:start position:0%
+is just signing off for a job that's not
+ 
+
+ align:start position:0%
+is just signing off for a job that's not
+so much
+
+ align:start position:0%
+so much
+ 
+
+ align:start position:0%
+so much
+but for what they find here on average
+
+ align:start position:0%
+but for what they find here on average
+ 
+
+ align:start position:0%
+but for what they find here on average
+the people who are the best
+
+ align:start position:0%
+the people who are the best
+ 
+
+ align:start position:0%
+the people who are the best
+um are more likely to to sign up for the
+
+ align:start position:0%
+um are more likely to to sign up for the
+ 
+
+ align:start position:0%
+um are more likely to to sign up for the
+to sign their wife up for the job
+
+ align:start position:0%
+to sign their wife up for the job
+ 
+
+ align:start position:0%
+to sign their wife up for the job
+platform 32 percent versus 23 and of
+
+ align:start position:0%
+platform 32 percent versus 23 and of
+ 
+
+ align:start position:0%
+platform 32 percent versus 23 and of
+course where it becomes more interesting
+
+ align:start position:0%
+course where it becomes more interesting
+ 
+
+ align:start position:0%
+course where it becomes more interesting
+so then we can look also sorry we can
+
+ align:start position:0%
+so then we can look also sorry we can
+ 
+
+ align:start position:0%
+so then we can look also sorry we can
+look at whether the in fact
+
+ align:start position:0%
+look at whether the in fact
+ 
+
+ align:start position:0%
+look at whether the in fact
+applied for the job and you find a
+
+ align:start position:0%
+applied for the job and you find a
+ 
+
+ align:start position:0%
+applied for the job and you find a
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+you can look at whether they are
+
+ align:start position:0%
+you can look at whether they are
+ 
+
+ align:start position:0%
+you can look at whether they are
+interviewed for the job and you still
+
+ align:start position:0%
+interviewed for the job and you still
+ 
+
+ align:start position:0%
+interviewed for the job and you still
+find a difference and then you can you
+
+ align:start position:0%
+find a difference and then you can you
+ 
+
+ align:start position:0%
+find a difference and then you can you
+can look at whether they are employed uh
+
+ align:start position:0%
+can look at whether they are employed uh
+ 
+
+ align:start position:0%
+can look at whether they are employed uh
+or driving lessons and there you don't
+
+ align:start position:0%
+or driving lessons and there you don't
+ 
+
+ align:start position:0%
+or driving lessons and there you don't
+find a difference in this lower outcomes
+
+ align:start position:0%
+find a difference in this lower outcomes
+ 
+
+ align:start position:0%
+find a difference in this lower outcomes
+uh party so this is why
+
+ align:start position:0%
+uh party so this is why
+ 
+
+ align:start position:0%
+uh party so this is why
+actually I was editing the paper and I
+
+ align:start position:0%
+actually I was editing the paper and I
+ 
+
+ align:start position:0%
+actually I was editing the paper and I
+got this
+
+ align:start position:0%
+got this
+ 
+
+ align:start position:0%
+got this
+I was editing the paper at the AR and I
+
+ align:start position:0%
+I was editing the paper at the AR and I
+ 
+
+ align:start position:0%
+I was editing the paper at the AR and I
+got this is what they sent
+
+ align:start position:0%
+got this is what they sent
+ 
+
+ align:start position:0%
+got this is what they sent
+and I was like I don't know at the end
+
+ align:start position:0%
+and I was like I don't know at the end
+ 
+
+ align:start position:0%
+and I was like I don't know at the end
+of the day I don't know if this is
+
+ align:start position:0%
+of the day I don't know if this is
+ 
+
+ align:start position:0%
+of the day I don't know if this is
+employed I like the proof is the
+
+ align:start position:0%
+employed I like the proof is the
+ 
+
+ align:start position:0%
+employed I like the proof is the
+bullying is whether they are employed
+
+ align:start position:0%
+bullying is whether they are employed
+ 
+
+ align:start position:0%
+bullying is whether they are employed
+and maybe there is an effect but maybe
+
+ align:start position:0%
+and maybe there is an effect but maybe
+ 
+
+ align:start position:0%
+and maybe there is an effect but maybe
+not it's the CP value of
+
+ align:start position:0%
+not it's the CP value of
+ 
+
+ align:start position:0%
+not it's the CP value of
+0.24 I don't know what to think like at
+
+ align:start position:0%
+0.24 I don't know what to think like at
+ 
+
+ align:start position:0%
+0.24 I don't know what to think like at
+the end of the day does it matter does
+
+ align:start position:0%
+the end of the day does it matter does
+ 
+
+ align:start position:0%
+the end of the day does it matter does
+it not matter I need a real outcome
+
+ align:start position:0%
+it not matter I need a real outcome
+ 
+
+ align:start position:0%
+it not matter I need a real outcome
+which is why they went and did this
+
+ align:start position:0%
+which is why they went and did this
+ 
+
+ align:start position:0%
+which is why they went and did this
+second experiment
+
+ align:start position:0%
+second experiment
+ 
+
+ align:start position:0%
+second experiment
+where the which is you know
+
+ align:start position:0%
+where the which is you know
+ 
+
+ align:start position:0%
+where the which is you know
+where basically they were thinking the
+
+ align:start position:0%
+where basically they were thinking the
+ 
+
+ align:start position:0%
+where basically they were thinking the
+poem with this one is that eventually
+
+ align:start position:0%
+poem with this one is that eventually
+ 
+
+ align:start position:0%
+poem with this one is that eventually
+it's not very powered because there are
+
+ align:start position:0%
+it's not very powered because there are
+ 
+
+ align:start position:0%
+it's not very powered because there are
+so many steps between signing up for a
+
+ align:start position:0%
+so many steps between signing up for a
+ 
+
+ align:start position:0%
+so many steps between signing up for a
+job platform and actually getting the
+
+ align:start position:0%
+job platform and actually getting the
+ 
+
+ align:start position:0%
+job platform and actually getting the
+job that they were never going to be
+
+ align:start position:0%
+job that they were never going to be
+ 
+
+ align:start position:0%
+job that they were never going to be
+power so my my objection here as an
+
+ align:start position:0%
+power so my my objection here as an
+ 
+
+ align:start position:0%
+power so my my objection here as an
+editor that is a kind of a point about
+
+ align:start position:0%
+editor that is a kind of a point about
+ 
+
+ align:start position:0%
+editor that is a kind of a point about
+how you want to think about designing
+
+ align:start position:0%
+how you want to think about designing
+ 
+
+ align:start position:0%
+how you want to think about designing
+your research project as well my
+
+ align:start position:0%
+your research project as well my
+ 
+
+ align:start position:0%
+your research project as well my
+objection here as an editor was that
+
+ align:start position:0%
+objection here as an editor was that
+ 
+
+ align:start position:0%
+objection here as an editor was that
+this particular project was not powered
+
+ align:start position:0%
+this particular project was not powered
+ 
+
+ align:start position:0%
+this particular project was not powered
+to find employment effects
+
+ align:start position:0%
+to find employment effects
+ 
+
+ align:start position:0%
+to find employment effects
+because given the number of things that
+
+ align:start position:0%
+because given the number of things that
+ 
+
+ align:start position:0%
+because given the number of things that
+have been given the few people who are
+
+ align:start position:0%
+have been given the few people who are
+ 
+
+ align:start position:0%
+have been given the few people who are
+employed about seven percent it would
+
+ align:start position:0%
+employed about seven percent it would
+ 
+
+ align:start position:0%
+employed about seven percent it would
+have taken a much larger sample to be
+
+ align:start position:0%
+have taken a much larger sample to be
+ 
+
+ align:start position:0%
+have taken a much larger sample to be
+able to detect any effect that is not
+
+ align:start position:0%
+able to detect any effect that is not
+ 
+
+ align:start position:0%
+able to detect any effect that is not
+diagonomous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I was like you know I don't it's fine
+
+ align:start position:0%
+so I was like you know I don't it's fine
+ 
+
+ align:start position:0%
+so I was like you know I don't it's fine
+to find zero I have no issue with zero
+
+ align:start position:0%
+to find zero I have no issue with zero
+ 
+
+ align:start position:0%
+to find zero I have no issue with zero
+but I
+
+ align:start position:0%
+but I
+ 
+
+ align:start position:0%
+but I
+your paper is not power to find an
+
+ align:start position:0%
+your paper is not power to find an
+ 
+
+ align:start position:0%
+your paper is not power to find an
+impact on the outcome that you want to
+
+ align:start position:0%
+impact on the outcome that you want to
+ 
+
+ align:start position:0%
+impact on the outcome that you want to
+find an impact on it's only power to
+
+ align:start position:0%
+find an impact on it's only power to
+ 
+
+ align:start position:0%
+find an impact on it's only power to
+find an impact on this intermediate
+
+ align:start position:0%
+find an impact on this intermediate
+ 
+
+ align:start position:0%
+find an impact on this intermediate
+outcomes where we have it so it's
+
+ align:start position:0%
+outcomes where we have it so it's
+ 
+
+ align:start position:0%
+outcomes where we have it so it's
+promising but it's not enough for the
+
+ align:start position:0%
+promising but it's not enough for the
+ 
+
+ align:start position:0%
+promising but it's not enough for the
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+so at this point they could have said
+
+ align:start position:0%
+so at this point they could have said
+ 
+
+ align:start position:0%
+so at this point they could have said
+fine we're just going to go one level
+
+ align:start position:0%
+fine we're just going to go one level
+ 
+
+ align:start position:0%
+fine we're just going to go one level
+down and publish without intermediate
+
+ align:start position:0%
+down and publish without intermediate
+ 
+
+ align:start position:0%
+down and publish without intermediate
+outcome
+
+ align:start position:0%
+outcome
+ 
+
+ align:start position:0%
+outcome
+all they could have done what they did
+
+ align:start position:0%
+all they could have done what they did
+ 
+
+ align:start position:0%
+all they could have done what they did
+which was the right move in my opinion
+
+ align:start position:0%
+which was the right move in my opinion
+ 
+
+ align:start position:0%
+which was the right move in my opinion
+which is to design a better power
+
+ align:start position:0%
+which is to design a better power
+ 
+
+ align:start position:0%
+which is to design a better power
+outcome and to find a better powered
+
+ align:start position:0%
+outcome and to find a better powered
+ 
+
+ align:start position:0%
+outcome and to find a better powered
+outcome basically that's why the second
+
+ align:start position:0%
+outcome basically that's why the second
+ 
+
+ align:start position:0%
+outcome basically that's why the second
+experiment by setting themselves in a
+
+ align:start position:0%
+experiment by setting themselves in a
+ 
+
+ align:start position:0%
+experiment by setting themselves in a
+context where already people were
+
+ align:start position:0%
+context where already people were
+ 
+
+ align:start position:0%
+context where already people were
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+and the decision was from home versus
+
+ align:start position:0%
+and the decision was from home versus
+ 
+
+ align:start position:0%
+and the decision was from home versus
+outside the home for more money so
+
+ align:start position:0%
+outside the home for more money so
+ 
+
+ align:start position:0%
+outside the home for more money so
+that's super powerful and if they had
+
+ align:start position:0%
+that's super powerful and if they had
+ 
+
+ align:start position:0%
+that's super powerful and if they had
+fun in fact the in my detail later I
+
+ align:start position:0%
+fun in fact the in my detail later I
+ 
+
+ align:start position:0%
+fun in fact the in my detail later I
+said could post me your design before
+
+ align:start position:0%
+said could post me your design before
+ 
+
+ align:start position:0%
+said could post me your design before
+you run it I'm going to tell you whether
+
+ align:start position:0%
+you run it I'm going to tell you whether
+ 
+
+ align:start position:0%
+you run it I'm going to tell you whether
+I'm going to sign up you know whether
+
+ align:start position:0%
+I'm going to sign up you know whether
+ 
+
+ align:start position:0%
+I'm going to sign up you know whether
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+satisfactory whatever you find
+
+ align:start position:0%
+satisfactory whatever you find
+ 
+
+ align:start position:0%
+satisfactory whatever you find
+and so when you propose the second
+
+ align:start position:0%
+and so when you propose the second
+ 
+
+ align:start position:0%
+and so when you propose the second
+designer I was like that's great because
+
+ align:start position:0%
+designer I was like that's great because
+ 
+
+ align:start position:0%
+designer I was like that's great because
+if you find nothing it's like this is
+
+ align:start position:0%
+if you find nothing it's like this is
+ 
+
+ align:start position:0%
+if you find nothing it's like this is
+powerful this is going to be a real zero
+
+ align:start position:0%
+powerful this is going to be a real zero
+ 
+
+ align:start position:0%
+powerful this is going to be a real zero
+if you find an effect then there's an
+
+ align:start position:0%
+if you find an effect then there's an
+ 
+
+ align:start position:0%
+if you find an effect then there's an
+effect so go ahead and run it and
+
+ align:start position:0%
+effect so go ahead and run it and
+ 
+
+ align:start position:0%
+effect so go ahead and run it and
+basically I told him that I would
+
+ align:start position:0%
+basically I told him that I would
+ 
+
+ align:start position:0%
+basically I told him that I would
+publish no matter what innocent no
+
+ align:start position:0%
+publish no matter what innocent no
+ 
+
+ align:start position:0%
+publish no matter what innocent no
+matter what he found in this second
+
+ align:start position:0%
+matter what he found in this second
+ 
+
+ align:start position:0%
+matter what he found in this second
+experiment because that was well that
+
+ align:start position:0%
+experiment because that was well that
+ 
+
+ align:start position:0%
+experiment because that was well that
+was well powered for the outcome we
+
+ align:start position:0%
+was well powered for the outcome we
+ 
+
+ align:start position:0%
+was well powered for the outcome we
+cared about
+
+ align:start position:0%
+cared about
+ 
+
+ align:start position:0%
+cared about
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we can do a little better than that
+
+ align:start position:0%
+we can do a little better than that
+ 
+
+ align:start position:0%
+we can do a little better than that
+already more interesting than that is
+
+ align:start position:0%
+already more interesting than that is
+ 
+
+ align:start position:0%
+already more interesting than that is
+you have one more prediction on the the
+
+ align:start position:0%
+you have one more prediction on the the
+ 
+
+ align:start position:0%
+you have one more prediction on the the
+sign up which is the sign up should come
+
+ align:start position:0%
+sign up which is the sign up should come
+ 
+
+ align:start position:0%
+sign up which is the sign up should come
+from the fact who are originally biased
+
+ align:start position:0%
+from the fact who are originally biased
+ 
+
+ align:start position:0%
+from the fact who are originally biased
+about the in underestimating the
+
+ align:start position:0%
+about the in underestimating the
+ 
+
+ align:start position:0%
+about the in underestimating the
+fraction of people so some people were
+
+ align:start position:0%
+fraction of people so some people were
+ 
+
+ align:start position:0%
+fraction of people so some people were
+underestimating the fraction of of
+
+ align:start position:0%
+underestimating the fraction of of
+ 
+
+ align:start position:0%
+underestimating the fraction of of
+people a lot of them and some people
+
+ align:start position:0%
+people a lot of them and some people
+ 
+
+ align:start position:0%
+people a lot of them and some people
+were over but there are still some
+
+ align:start position:0%
+were over but there are still some
+ 
+
+ align:start position:0%
+were over but there are still some
+people who are estimating the fraction
+
+ align:start position:0%
+people who are estimating the fraction
+ 
+
+ align:start position:0%
+people who are estimating the fraction
+of people who found the working for a
+
+ align:start position:0%
+of people who found the working for a
+ 
+
+ align:start position:0%
+of people who found the working for a
+job acceptable and so the finding is
+
+ align:start position:0%
+job acceptable and so the finding is
+ 
+
+ align:start position:0%
+job acceptable and so the finding is
+that these guys if anything the control
+
+ align:start position:0%
+that these guys if anything the control
+ 
+
+ align:start position:0%
+that these guys if anything the control
+is slightly larger so they they were not
+
+ align:start position:0%
+is slightly larger so they they were not
+ 
+
+ align:start position:0%
+is slightly larger so they they were not
+it's not the the opinion didn't really
+
+ align:start position:0%
+it's not the the opinion didn't really
+ 
+
+ align:start position:0%
+it's not the the opinion didn't really
+change or if anything it changed in the
+
+ align:start position:0%
+change or if anything it changed in the
+ 
+
+ align:start position:0%
+change or if anything it changed in the
+open Direction you expect and so the
+
+ align:start position:0%
+open Direction you expect and so the
+ 
+
+ align:start position:0%
+open Direction you expect and so the
+effect on sign up comes from the people
+
+ align:start position:0%
+effect on sign up comes from the people
+ 
+
+ align:start position:0%
+effect on sign up comes from the people
+who who have um who were initially
+
+ align:start position:0%
+who who have um who were initially
+ 
+
+ align:start position:0%
+who who have um who were initially
+underestimating the social Norm so any
+
+ align:start position:0%
+underestimating the social Norm so any
+ 
+
+ align:start position:0%
+underestimating the social Norm so any
+experiments if you want to run this type
+
+ align:start position:0%
+experiments if you want to run this type
+ 
+
+ align:start position:0%
+experiments if you want to run this type
+of experiment where you're debiasing
+
+ align:start position:0%
+of experiment where you're debiasing
+ 
+
+ align:start position:0%
+of experiment where you're debiasing
+it's really important to have the
+
+ align:start position:0%
+it's really important to have the
+ 
+
+ align:start position:0%
+it's really important to have the
+Baseline value so that you can because
+
+ align:start position:0%
+Baseline value so that you can because
+ 
+
+ align:start position:0%
+Baseline value so that you can because
+the prediction is really not just about
+
+ align:start position:0%
+the prediction is really not just about
+ 
+
+ align:start position:0%
+the prediction is really not just about
+the effect of the treatment but how the
+
+ align:start position:0%
+the effect of the treatment but how the
+ 
+
+ align:start position:0%
+the effect of the treatment but how the
+effect of the treatment uh vary as a
+
+ align:start position:0%
+effect of the treatment uh vary as a
+ 
+
+ align:start position:0%
+effect of the treatment uh vary as a
+function of what whether you're moving
+
+ align:start position:0%
+function of what whether you're moving
+ 
+
+ align:start position:0%
+function of what whether you're moving
+people up or down with your information
+
+ align:start position:0%
+people up or down with your information
+ 
+
+ align:start position:0%
+people up or down with your information
+so that's that's important
+
+ align:start position:0%
+so that's that's important
+ 
+
+ align:start position:0%
+so that's that's important
+keep in mind
+
+ align:start position:0%
+keep in mind
+ 
+
+ align:start position:0%
+keep in mind
+because that's you know this type of
+
+ align:start position:0%
+because that's you know this type of
+ 
+
+ align:start position:0%
+because that's you know this type of
+idea of I'm going to debias in something
+
+ align:start position:0%
+idea of I'm going to debias in something
+ 
+
+ align:start position:0%
+idea of I'm going to debias in something
+or the other it could be the social Norm
+
+ align:start position:0%
+or the other it could be the social Norm
+ 
+
+ align:start position:0%
+or the other it could be the social Norm
+the weather in California or uh you know
+
+ align:start position:0%
+the weather in California or uh you know
+ 
+
+ align:start position:0%
+the weather in California or uh you know
+you people's own ability in math I don't
+
+ align:start position:0%
+you people's own ability in math I don't
+ 
+
+ align:start position:0%
+you people's own ability in math I don't
+know all of these things
+
+ align:start position:0%
+know all of these things
+ 
+
+ align:start position:0%
+know all of these things
+you expect different results depending
+
+ align:start position:0%
+you expect different results depending
+ 
+
+ align:start position:0%
+you expect different results depending
+on what you're given so you need to
+
+ align:start position:0%
+on what you're given so you need to
+ 
+
+ align:start position:0%
+on what you're given so you need to
+estimate the Baseline
+
+ align:start position:0%
+estimate the Baseline
+ 
+
+ align:start position:0%
+estimate the Baseline
+so that's the idea so that's a social
+
+ align:start position:0%
+so that's the idea so that's a social
+ 
+
+ align:start position:0%
+so that's the idea so that's a social
+Norm about women working outside the the
+
+ align:start position:0%
+Norm about women working outside the the
+ 
+
+ align:start position:0%
+Norm about women working outside the the
+house there are other social norms
+
+ align:start position:0%
+house there are other social norms
+ 
+
+ align:start position:0%
+house there are other social norms
+standing in the way of women's success
+
+ align:start position:0%
+standing in the way of women's success
+ 
+
+ align:start position:0%
+standing in the way of women's success
+uh so a Marian Bertrand uh
+
+ align:start position:0%
+uh so a Marian Bertrand uh
+ 
+
+ align:start position:0%
+uh so a Marian Bertrand uh
+Jennifer
+
+ align:start position:0%
+Jennifer
+ 
+
+ align:start position:0%
+Jennifer
+have this paper showing you know looking
+
+ align:start position:0%
+have this paper showing you know looking
+ 
+
+ align:start position:0%
+have this paper showing you know looking
+at the norm that a woman must earn less
+
+ align:start position:0%
+at the norm that a woman must earn less
+ 
+
+ align:start position:0%
+at the norm that a woman must earn less
+than their husband and what they show is
+
+ align:start position:0%
+than their husband and what they show is
+ 
+
+ align:start position:0%
+than their husband and what they show is
+that when women is that there is a
+
+ align:start position:0%
+that when women is that there is a
+ 
+
+ align:start position:0%
+that when women is that there is a
+discontinuity in women's in in the
+
+ align:start position:0%
+discontinuity in women's in in the
+ 
+
+ align:start position:0%
+discontinuity in women's in in the
+faction of people that you're finding
+
+ align:start position:0%
+faction of people that you're finding
+ 
+
+ align:start position:0%
+faction of people that you're finding
+precisely at the place where women and
+
+ align:start position:0%
+precisely at the place where women and
+ 
+
+ align:start position:0%
+precisely at the place where women and
+men would be earning the same in the
+
+ align:start position:0%
+men would be earning the same in the
+ 
+
+ align:start position:0%
+men would be earning the same in the
+household so basically you have a big
+
+ align:start position:0%
+household so basically you have a big
+ 
+
+ align:start position:0%
+household so basically you have a big
+hole of of women who aren't just above
+
+ align:start position:0%
+hole of of women who aren't just above
+ 
+
+ align:start position:0%
+hole of of women who aren't just above
+the household their husband
+
+ align:start position:0%
+the household their husband
+ 
+
+ align:start position:0%
+the household their husband
+and the kailash is trying to uh do his
+
+ align:start position:0%
+and the kailash is trying to uh do his
+ 
+
+ align:start position:0%
+and the kailash is trying to uh do his
+Sonia people on on this topic trying to
+
+ align:start position:0%
+Sonia people on on this topic trying to
+ 
+
+ align:start position:0%
+Sonia people on on this topic trying to
+see whether this can be replicated in an
+
+ align:start position:0%
+see whether this can be replicated in an
+ 
+
+ align:start position:0%
+see whether this can be replicated in an
+experimental way
+
+ align:start position:0%
+experimental way
+ 
+
+ align:start position:0%
+experimental way
+so that's one the social Norm of women
+
+ align:start position:0%
+so that's one the social Norm of women
+ 
+
+ align:start position:0%
+so that's one the social Norm of women
+cannot earn more than her husband which
+
+ align:start position:0%
+cannot earn more than her husband which
+ 
+
+ align:start position:0%
+cannot earn more than her husband which
+you find in the U.S there is good reason
+
+ align:start position:0%
+you find in the U.S there is good reason
+ 
+
+ align:start position:0%
+you find in the U.S there is good reason
+to think that you're finding in other
+
+ align:start position:0%
+to think that you're finding in other
+ 
+
+ align:start position:0%
+to think that you're finding in other
+places that are even more conservative
+
+ align:start position:0%
+places that are even more conservative
+ 
+
+ align:start position:0%
+places that are even more conservative
+but we'll we'll find out maybe soon and
+
+ align:start position:0%
+but we'll we'll find out maybe soon and
+ 
+
+ align:start position:0%
+but we'll we'll find out maybe soon and
+then there is uh Claudia golzin
+
+ align:start position:0%
+then there is uh Claudia golzin
+ 
+
+ align:start position:0%
+then there is uh Claudia golzin
+which is who has of course made a career
+
+ align:start position:0%
+which is who has of course made a career
+ 
+
+ align:start position:0%
+which is who has of course made a career
+looking at women in the labor market and
+
+ align:start position:0%
+looking at women in the labor market and
+ 
+
+ align:start position:0%
+looking at women in the labor market and
+is now saying that for example in in a
+
+ align:start position:0%
+is now saying that for example in in a
+ 
+
+ align:start position:0%
+is now saying that for example in in a
+recent
+
+ align:start position:0%
+recent
+ 
+
+ align:start position:0%
+recent
+uh recent work that the norm of the full
+
+ align:start position:0%
+uh recent work that the norm of the full
+ 
+
+ align:start position:0%
+uh recent work that the norm of the full
+rigid full-time full-week many hours
+
+ align:start position:0%
+rigid full-time full-week many hours
+ 
+
+ align:start position:0%
+rigid full-time full-week many hours
+maybe the last thing that's holding
+
+ align:start position:0%
+maybe the last thing that's holding
+ 
+
+ align:start position:0%
+maybe the last thing that's holding
+women now in the U.S labor markets so
+
+ align:start position:0%
+women now in the U.S labor markets so
+ 
+
+ align:start position:0%
+women now in the U.S labor markets so
+for example when you look at the lawyers
+
+ align:start position:0%
+for example when you look at the lawyers
+ 
+
+ align:start position:0%
+for example when you look at the lawyers
+work very very long hours and women
+
+ align:start position:0%
+work very very long hours and women
+ 
+
+ align:start position:0%
+work very very long hours and women
+eventually don't go into this profession
+
+ align:start position:0%
+eventually don't go into this profession
+ 
+
+ align:start position:0%
+eventually don't go into this profession
+or they quit them early or they choose
+
+ align:start position:0%
+or they quit them early or they choose
+ 
+
+ align:start position:0%
+or they quit them early or they choose
+mummy tracks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here there are two social norms he
+
+ align:start position:0%
+so here there are two social norms he
+ 
+
+ align:start position:0%
+so here there are two social norms he
+could that some some sense could could
+
+ align:start position:0%
+could that some some sense could could
+ 
+
+ align:start position:0%
+could that some some sense could could
+fight could conspire to keep women
+
+ align:start position:0%
+fight could conspire to keep women
+ 
+
+ align:start position:0%
+fight could conspire to keep women
+to hold women back in this situation the
+
+ align:start position:0%
+to hold women back in this situation the
+ 
+
+ align:start position:0%
+to hold women back in this situation the
+one is that you're a good employee if
+
+ align:start position:0%
+one is that you're a good employee if
+ 
+
+ align:start position:0%
+one is that you're a good employee if
+you work
+
+ align:start position:0%
+you work
+ 
+
+ align:start position:0%
+you work
+all the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have super super long hours and
+
+ align:start position:0%
+if you have super super long hours and
+ 
+
+ align:start position:0%
+if you have super super long hours and
+two is that if there is one person in
+
+ align:start position:0%
+two is that if there is one person in
+ 
+
+ align:start position:0%
+two is that if there is one person in
+the household that has to comply with
+
+ align:start position:0%
+the household that has to comply with
+ 
+
+ align:start position:0%
+the household that has to comply with
+that it has to be the husband because
+
+ align:start position:0%
+that it has to be the husband because
+ 
+
+ align:start position:0%
+that it has to be the husband because
+the wife has to take care of the
+
+ align:start position:0%
+the wife has to take care of the
+ 
+
+ align:start position:0%
+the wife has to take care of the
+children
+
+ align:start position:0%
+children
+ 
+
+ align:start position:0%
+children
+so that idea of that women are
+
+ align:start position:0%
+so that idea of that women are
+ 
+
+ align:start position:0%
+so that idea of that women are
+multitasking is when I'm going to come
+
+ align:start position:0%
+multitasking is when I'm going to come
+ 
+
+ align:start position:0%
+multitasking is when I'm going to come
+back to because I think that's for
+
+ align:start position:0%
+back to because I think that's for
+ 
+
+ align:start position:0%
+back to because I think that's for
+developing countries that's a pretty
+
+ align:start position:0%
+developing countries that's a pretty
+ 
+
+ align:start position:0%
+developing countries that's a pretty
+essential one that that sphere of women
+
+ align:start position:0%
+essential one that that sphere of women
+ 
+
+ align:start position:0%
+essential one that that sphere of women
+being in charge of of of children pretty
+
+ align:start position:0%
+being in charge of of of children pretty
+ 
+
+ align:start position:0%
+being in charge of of of children pretty
+much exclusively or as the residual
+
+ align:start position:0%
+much exclusively or as the residual
+ 
+
+ align:start position:0%
+much exclusively or as the residual
+claimant is actually the one the one
+
+ align:start position:0%
+claimant is actually the one the one
+ 
+
+ align:start position:0%
+claimant is actually the one the one
+thing that you kind of refining
+
+ align:start position:0%
+thing that you kind of refining
+ 
+
+ align:start position:0%
+thing that you kind of refining
+interacting with other parts of the
+
+ align:start position:0%
+interacting with other parts of the
+ 
+
+ align:start position:0%
+interacting with other parts of the
+labor market to hold a woman back
+
+ align:start position:0%
+labor market to hold a woman back
+ 
+
+ align:start position:0%
+labor market to hold a woman back
+so we'll go back to that towards the end
+
+ align:start position:0%
+so we'll go back to that towards the end
+ 
+
+ align:start position:0%
+so we'll go back to that towards the end
+of this lecture so one question then is
+
+ align:start position:0%
+of this lecture so one question then is
+ 
+
+ align:start position:0%
+of this lecture so one question then is
+that okay you have these social norms
+
+ align:start position:0%
+that okay you have these social norms
+ 
+
+ align:start position:0%
+that okay you have these social norms
+they are very persistent uh it's uh
+
+ align:start position:0%
+they are very persistent uh it's uh
+ 
+
+ align:start position:0%
+they are very persistent uh it's uh
+people might be to some extent misguided
+
+ align:start position:0%
+people might be to some extent misguided
+ 
+
+ align:start position:0%
+people might be to some extent misguided
+about them but
+
+ align:start position:0%
+about them but
+ 
+
+ align:start position:0%
+about them but
+um an interesting question is whether
+
+ align:start position:0%
+um an interesting question is whether
+ 
+
+ align:start position:0%
+um an interesting question is whether
+these Norms can be changed by teaching
+
+ align:start position:0%
+these Norms can be changed by teaching
+ 
+
+ align:start position:0%
+these Norms can be changed by teaching
+that's not a very economics way of
+
+ align:start position:0%
+that's not a very economics way of
+ 
+
+ align:start position:0%
+that's not a very economics way of
+thinking you know we tend to follow the
+
+ align:start position:0%
+thinking you know we tend to follow the
+ 
+
+ align:start position:0%
+thinking you know we tend to follow the
+Becker Stigler or the Gusty boost known
+
+ align:start position:0%
+Becker Stigler or the Gusty boost known
+ 
+
+ align:start position:0%
+Becker Stigler or the Gusty boost known
+as disputandu media it's like whatever
+
+ align:start position:0%
+as disputandu media it's like whatever
+ 
+
+ align:start position:0%
+as disputandu media it's like whatever
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+
+ align:start position:0%
+preferences are what they have what they
+ 
+
+ align:start position:0%
+preferences are what they have what they
+are and you know indeed you can tell
+
+ align:start position:0%
+are and you know indeed you can tell
+ 
+
+ align:start position:0%
+are and you know indeed you can tell
+people what the preferences of others
+
+ align:start position:0%
+people what the preferences of others
+ 
+
+ align:start position:0%
+people what the preferences of others
+are and inform them about that but you
+
+ align:start position:0%
+are and inform them about that but you
+ 
+
+ align:start position:0%
+are and inform them about that but you
+can't really affect people's own view so
+
+ align:start position:0%
+can't really affect people's own view so
+ 
+
+ align:start position:0%
+can't really affect people's own view so
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+but so that's a traditional economics
+
+ align:start position:0%
+but so that's a traditional economics
+ 
+
+ align:start position:0%
+but so that's a traditional economics
+way of thinking uh
+
+ align:start position:0%
+way of thinking uh
+ 
+
+ align:start position:0%
+way of thinking uh
+I already remember reminded you of the
+
+ align:start position:0%
+I already remember reminded you of the
+ 
+
+ align:start position:0%
+I already remember reminded you of the
+course theorem
+
+ align:start position:0%
+course theorem
+ 
+
+ align:start position:0%
+course theorem
+that would think that lose doesn't
+
+ align:start position:0%
+that would think that lose doesn't
+ 
+
+ align:start position:0%
+that would think that lose doesn't
+matter because people bargain their way
+
+ align:start position:0%
+matter because people bargain their way
+ 
+
+ align:start position:0%
+matter because people bargain their way
+out of them anyways and then that's the
+
+ align:start position:0%
+out of them anyways and then that's the
+ 
+
+ align:start position:0%
+out of them anyways and then that's the
+second one second Trope for the day is
+
+ align:start position:0%
+second one second Trope for the day is
+ 
+
+ align:start position:0%
+second one second Trope for the day is
+preferences cannot be changed
+
+ align:start position:0%
+preferences cannot be changed
+ 
+
+ align:start position:0%
+preferences cannot be changed
+but we are learning that that's not the
+
+ align:start position:0%
+but we are learning that that's not the
+ 
+
+ align:start position:0%
+but we are learning that that's not the
+case because on many things people's own
+
+ align:start position:0%
+case because on many things people's own
+ 
+
+ align:start position:0%
+case because on many things people's own
+sense of what their preferences are is
+
+ align:start position:0%
+sense of what their preferences are is
+ 
+
+ align:start position:0%
+sense of what their preferences are is
+super big anyways
+
+ align:start position:0%
+super big anyways
+ 
+
+ align:start position:0%
+super big anyways
+so they are these interesting
+
+ align:start position:0%
+so they are these interesting
+ 
+
+ align:start position:0%
+so they are these interesting
+experiments about trying to make people
+
+ align:start position:0%
+experiments about trying to make people
+ 
+
+ align:start position:0%
+experiments about trying to make people
+value things like mugs or Butters of
+
+ align:start position:0%
+value things like mugs or Butters of
+ 
+
+ align:start position:0%
+value things like mugs or Butters of
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+
+ align:start position:0%
+wines and their judgment being
+ 
+
+ align:start position:0%
+wines and their judgment being
+influenced by the last digit of their
+
+ align:start position:0%
+influenced by the last digit of their
+ 
+
+ align:start position:0%
+influenced by the last digit of their
+social security number or if they just
+
+ align:start position:0%
+social security number or if they just
+ 
+
+ align:start position:0%
+social security number or if they just
+had to write it down so people are
+
+ align:start position:0%
+had to write it down so people are
+ 
+
+ align:start position:0%
+had to write it down so people are
+forced us to write down their social MBA
+
+ align:start position:0%
+forced us to write down their social MBA
+ 
+
+ align:start position:0%
+forced us to write down their social MBA
+students are first asked to write down
+
+ align:start position:0%
+students are first asked to write down
+ 
+
+ align:start position:0%
+students are first asked to write down
+their the last two digits of their
+
+ align:start position:0%
+their the last two digits of their
+ 
+
+ align:start position:0%
+their the last two digits of their
+social security number
+
+ align:start position:0%
+social security number
+ 
+
+ align:start position:0%
+social security number
+and then they are given a bottle of wine
+
+ align:start position:0%
+and then they are given a bottle of wine
+ 
+
+ align:start position:0%
+and then they are given a bottle of wine
+and they're asked to bid for the butter
+
+ align:start position:0%
+and they're asked to bid for the butter
+ 
+
+ align:start position:0%
+and they're asked to bid for the butter
+of wine and people will have a higher
+
+ align:start position:0%
+of wine and people will have a higher
+ 
+
+ align:start position:0%
+of wine and people will have a higher
+Social Security number pay more for the
+
+ align:start position:0%
+Social Security number pay more for the
+ 
+
+ align:start position:0%
+Social Security number pay more for the
+battle than people who don't
+
+ align:start position:0%
+battle than people who don't
+ 
+
+ align:start position:0%
+battle than people who don't
+so that's an example of saying people
+
+ align:start position:0%
+so that's an example of saying people
+ 
+
+ align:start position:0%
+so that's an example of saying people
+have on many things we just don't know
+
+ align:start position:0%
+have on many things we just don't know
+ 
+
+ align:start position:0%
+have on many things we just don't know
+but you know we have two weeks you know
+
+ align:start position:0%
+but you know we have two weeks you know
+ 
+
+ align:start position:0%
+but you know we have two weeks you know
+we have to express an opinion we express
+
+ align:start position:0%
+we have to express an opinion we express
+ 
+
+ align:start position:0%
+we have to express an opinion we express
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+
+ align:start position:0%
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+
+ align:start position:0%
+an opinion and that might be true for
+for things you know deeper than butter
+
+ align:start position:0%
+for things you know deeper than butter
+ 
+
+ align:start position:0%
+for things you know deeper than butter
+of wines but for things like values and
+
+ align:start position:0%
+of wines but for things like values and
+ 
+
+ align:start position:0%
+of wines but for things like values and
+things like that and if that's the case
+
+ align:start position:0%
+things like that and if that's the case
+ 
+
+ align:start position:0%
+things like that and if that's the case
+then that means that perhaps Norms are
+
+ align:start position:0%
+then that means that perhaps Norms are
+ 
+
+ align:start position:0%
+then that means that perhaps Norms are
+not a fatality perhaps it's possible to
+
+ align:start position:0%
+not a fatality perhaps it's possible to
+ 
+
+ align:start position:0%
+not a fatality perhaps it's possible to
+to change social norms
+
+ align:start position:0%
+to change social norms
+ 
+
+ align:start position:0%
+to change social norms
+and in fact there is a literature on a
+
+ align:start position:0%
+and in fact there is a literature on a
+ 
+
+ align:start position:0%
+and in fact there is a literature on a
+on TV
+
+ align:start position:0%
+on TV
+ 
+
+ align:start position:0%
+on TV
+showing that you can
+
+ align:start position:0%
+showing that you can
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+
+ align:start position:0%
+showing that you can
+that TV entertainment can change
+
+ align:start position:0%
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+
+ align:start position:0%
+that TV entertainment can change
+people's social norms so a great paper
+
+ align:start position:0%
+people's social norms so a great paper
+ 
+
+ align:start position:0%
+people's social norms so a great paper
+by Eliana laferrara on soap opera in
+
+ align:start position:0%
+by Eliana laferrara on soap opera in
+ 
+
+ align:start position:0%
+by Eliana laferrara on soap opera in
+Brazil to show that to the super so in
+
+ align:start position:0%
+Brazil to show that to the super so in
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+
+ align:start position:0%
+Brazil to show that to the super so in
+Brazil during the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before the Democracy came back
+
+ align:start position:0%
+before the Democracy came back
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+
+ align:start position:0%
+before the Democracy came back
+a lot of the TV a lot of the film cinema
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+people move to TV
+because this was less dangerous
+
+ align:start position:0%
+because this was less dangerous
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+
+ align:start position:0%
+because this was less dangerous
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+
+ align:start position:0%
+politically than doing films and they
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+
+ align:start position:0%
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+were doing this soap opera
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+and the model of the soap opera was
+ 
+
+ align:start position:0%
+and the model of the soap opera was
+usually a woman with no children or very
+
+ align:start position:0%
+usually a woman with no children or very
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+
+ align:start position:0%
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+few children living his Modern Life and
+
+ align:start position:0%
+few children living his Modern Life and
+ 
+
+ align:start position:0%
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+an attractive in an attractive setup
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+and what she does is that she looks at
+ 
+
+ align:start position:0%
+and what she does is that she looks at
+the houses so popular diffused via cable
+
+ align:start position:0%
+the houses so popular diffused via cable
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+
+ align:start position:0%
+the houses so popular diffused via cable
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+
+ align:start position:0%
+TV all over the all over Brazil with the
+ 
+
+ align:start position:0%
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+introduction of of cable
+
+ align:start position:0%
+introduction of of cable
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+
+ align:start position:0%
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+
+ align:start position:0%
+and and does a different diff to show
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+
+ align:start position:0%
+and and does a different diff to show
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+
+ align:start position:0%
+that in places which as places get
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+
+ align:start position:0%
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+ align:start position:0%
+access to to the soap opera the number
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+
+ align:start position:0%
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+ align:start position:0%
+of kids declines in those places
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+
+ align:start position:0%
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+
+ align:start position:0%
+and one kind of interesting supporting
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+
+ align:start position:0%
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+
+ align:start position:0%
+piece of evidence which shows that that
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+
+ align:start position:0%
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+
+ align:start position:0%
+might be in fact be related to that is
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+
+ align:start position:0%
+might be in fact be related to that is
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+
+ align:start position:0%
+that the the name given to the kids are
+ 
+
+ align:start position:0%
+that the the name given to the kids are
+increasingly the names of the people in
+
+ align:start position:0%
+increasingly the names of the people in
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+
+ align:start position:0%
+increasingly the names of the people in
+the super world so whoever so that's
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+ align:start position:0%
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+
+ align:start position:0%
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+that suggests that indeed people are
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+ align:start position:0%
+that suggests that indeed people are
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+
+ align:start position:0%
+that suggests that indeed people are
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+ align:start position:0%
+paying attention and something as
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+
+ align:start position:0%
+paying attention and something as
+important as fertility is affected by by
+
+ align:start position:0%
+important as fertility is affected by by
+ 
+
+ align:start position:0%
+important as fertility is affected by by
+TV Abhijit have another recent people
+
+ align:start position:0%
+TV Abhijit have another recent people
+ 
+
+ align:start position:0%
+TV Abhijit have another recent people
+are doing a randomized experiment of an
+
+ align:start position:0%
+are doing a randomized experiment of an
+ 
+
+ align:start position:0%
+are doing a randomized experiment of an
+MTV program in Nigeria looking at uh
+
+ align:start position:0%
+MTV program in Nigeria looking at uh
+ 
+
+ align:start position:0%
+MTV program in Nigeria looking at uh
+basically a risky sexual behavior or
+
+ align:start position:0%
+basically a risky sexual behavior or
+ 
+
+ align:start position:0%
+basically a risky sexual behavior or
+respectful attitude of boys with a
+
+ align:start position:0%
+respectful attitude of boys with a
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+ align:start position:0%
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+girlfriend and this type of things which
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+ align:start position:0%
+girlfriend and this type of things which
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+ align:start position:0%
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+also show an impact of this of TV so TV
+
+ align:start position:0%
+also show an impact of this of TV so TV
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+
+ align:start position:0%
+also show an impact of this of TV so TV
+is one
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+ align:start position:0%
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+
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+ align:start position:0%
+another thing that is changed by by you
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+um we um I have a paper with Laurie
+
+ align:start position:0%
+um we um I have a paper with Laurie
+ 
+
+ align:start position:0%
+um we um I have a paper with Laurie
+biman rohini Pandey and raghetts looking
+
+ align:start position:0%
+biman rohini Pandey and raghetts looking
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+
+ align:start position:0%
+biman rohini Pandey and raghetts looking
+at a woman leader in India
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+and and what we find is that exposure to
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+
+ align:start position:0%
+and and what we find is that exposure to
+a woman that is imposed On You by uh
+
+ align:start position:0%
+a woman that is imposed On You by uh
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+
+ align:start position:0%
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+quotas makes people more willing to
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
+change the social Norm when when
+ 
+
+ align:start position:0%
+change the social Norm when when
+children are younger and therefore uh
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+ align:start position:0%
+children are younger and therefore uh
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+
+ align:start position:0%
+children are younger and therefore uh
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+ align:start position:0%
+there is uh in education would be a good
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+ align:start position:0%
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+
+ align:start position:0%
+it so Seema jayachandra and um
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+
+ align:start position:0%
+it so Seema jayachandra and um
+do this I've done this paper in
+
+ align:start position:0%
+do this I've done this paper in
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+
+ align:start position:0%
+do this I've done this paper in
+collaboration with the NGO in North
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+ align:start position:0%
+collaboration with the NGO in North
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+
+ align:start position:0%
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+India called brechtu to try to affect
+
+ align:start position:0%
+India called brechtu to try to affect
+ 
+
+ align:start position:0%
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+adolescent view of women and girls
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
+three weeks for two years
+ 
+
+ align:start position:0%
+three weeks for two years
+and they did an RCT in 314 screen high
+
+ align:start position:0%
+and they did an RCT in 314 screen high
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+ 
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+ align:start position:0%
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+the gender Norms huge
+
+ align:start position:0%
+the gender Norms huge
+ 
+
+ align:start position:0%
+the gender Norms huge
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discrepancy in the number of boys who
+
+ align:start position:0%
+discrepancy in the number of boys who
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+
+ align:start position:0%
+discrepancy in the number of boys who
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+
+ align:start position:0%
+are born versus girls any any way you
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+
+ align:start position:0%
+are born versus girls any any way you
+like her you know it's a pretty horrible
+
+ align:start position:0%
+like her you know it's a pretty horrible
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+
+ align:start position:0%
+like her you know it's a pretty horrible
+place for a woman
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+ align:start position:0%
+place for a woman
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+
+ align:start position:0%
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+
+ align:start position:0%
+so if you find an effect there that's
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+
+ align:start position:0%
+so if you find an effect there that's
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+
+ align:start position:0%
+encouraging and what they find overall
+ 
+
+ align:start position:0%
+encouraging and what they find overall
+is some effect 25 standard 0.25 standard
+
+ align:start position:0%
+is some effect 25 standard 0.25 standard
+ 
+
+ align:start position:0%
+is some effect 25 standard 0.25 standard
+deviation Improvement on self-reported
+
+ align:start position:0%
+deviation Improvement on self-reported
+ 
+
+ align:start position:0%
+deviation Improvement on self-reported
+gender Norms so whether it's okay for
+
+ align:start position:0%
+gender Norms so whether it's okay for
+ 
+
+ align:start position:0%
+gender Norms so whether it's okay for
+women to work whether it's okay for with
+
+ align:start position:0%
+women to work whether it's okay for with
+ 
+
+ align:start position:0%
+women to work whether it's okay for with
+our boys need to leave enough space for
+
+ align:start position:0%
+our boys need to leave enough space for
+ 
+
+ align:start position:0%
+our boys need to leave enough space for
+women whether
+
+ align:start position:0%
+women whether
+ 
+
+ align:start position:0%
+women whether
+if there is not enough job it's men who
+
+ align:start position:0%
+if there is not enough job it's men who
+ 
+
+ align:start position:0%
+if there is not enough job it's men who
+should have the first job and so on and
+
+ align:start position:0%
+should have the first job and so on and
+ 
+
+ align:start position:0%
+should have the first job and so on and
+so forth and some some effect on
+
+ align:start position:0%
+so forth and some some effect on
+ 
+
+ align:start position:0%
+so forth and some some effect on
+Behavior even among in particular among
+
+ align:start position:0%
+Behavior even among in particular among
+ 
+
+ align:start position:0%
+Behavior even among in particular among
+boys
+
+ align:start position:0%
+boys
+ 
+
+ align:start position:0%
+boys
+so this is kind of the summary looking
+
+ align:start position:0%
+so this is kind of the summary looking
+ 
+
+ align:start position:0%
+so this is kind of the summary looking
+at their index you should look at the
+
+ align:start position:0%
+at their index you should look at the
+ 
+
+ align:start position:0%
+at their index you should look at the
+paper to look at what goes into each of
+
+ align:start position:0%
+paper to look at what goes into each of
+ 
+
+ align:start position:0%
+paper to look at what goes into each of
+the index
+
+ align:start position:0%
+the index
+ 
+
+ align:start position:0%
+the index
+but to the general attitude I summarize
+
+ align:start position:0%
+but to the general attitude I summarize
+ 
+
+ align:start position:0%
+but to the general attitude I summarize
+the aspiration as you know what you want
+
+ align:start position:0%
+the aspiration as you know what you want
+ 
+
+ align:start position:0%
+the aspiration as you know what you want
+to do with your career uh the behavior
+
+ align:start position:0%
+to do with your career uh the behavior
+ 
+
+ align:start position:0%
+to do with your career uh the behavior
+is you know what to do in terms of
+
+ align:start position:0%
+is you know what to do in terms of
+ 
+
+ align:start position:0%
+is you know what to do in terms of
+chores and stuff like that both for
+
+ align:start position:0%
+chores and stuff like that both for
+ 
+
+ align:start position:0%
+chores and stuff like that both for
+girls and for and for boys
+
+ align:start position:0%
+girls and for and for boys
+ 
+
+ align:start position:0%
+girls and for and for boys
+and so they find this effect they find
+
+ align:start position:0%
+and so they find this effect they find
+ 
+
+ align:start position:0%
+and so they find this effect they find
+that it persists over uh several years
+
+ align:start position:0%
+that it persists over uh several years
+ 
+
+ align:start position:0%
+that it persists over uh several years
+after the intervention so they are now
+
+ align:start position:0%
+after the intervention so they are now
+ 
+
+ align:start position:0%
+after the intervention so they are now
+trying to to scale it up uh
+
+ align:start position:0%
+trying to to scale it up uh
+ 
+
+ align:start position:0%
+trying to to scale it up uh
+in in the rest of the state
+
+ align:start position:0%
+in in the rest of the state
+ 
+
+ align:start position:0%
+in in the rest of the state
+so that's very encouraging in the sense
+
+ align:start position:0%
+so that's very encouraging in the sense
+ 
+
+ align:start position:0%
+so that's very encouraging in the sense
+that it suggests that it might be
+
+ align:start position:0%
+that it suggests that it might be
+ 
+
+ align:start position:0%
+that it suggests that it might be
+possible to
+
+ align:start position:0%
+possible to
+ 
+
+ align:start position:0%
+possible to
+to teach directly teach social norms
+
+ align:start position:0%
+to teach directly teach social norms
+ 
+
+ align:start position:0%
+to teach directly teach social norms
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+for a study like this like
+
+ align:start position:0%
+for a study like this like
+ 
+
+ align:start position:0%
+for a study like this like
+how important is it to have like
+
+ align:start position:0%
+how important is it to have like
+ 
+
+ align:start position:0%
+how important is it to have like
+behavioral measures like could someone
+
+ align:start position:0%
+behavioral measures like could someone
+ 
+
+ align:start position:0%
+behavioral measures like could someone
+say what's demand effects yeah yeah
+
+ align:start position:0%
+say what's demand effects yeah yeah
+ 
+
+ align:start position:0%
+say what's demand effects yeah yeah
+because someone could say that and
+
+ align:start position:0%
+because someone could say that and
+ 
+
+ align:start position:0%
+because someone could say that and
+someone has said that that
+
+ align:start position:0%
+someone has said that that
+ 
+
+ align:start position:0%
+someone has said that that
+is also a paper edited at the at the AR
+
+ align:start position:0%
+is also a paper edited at the at the AR
+ 
+
+ align:start position:0%
+is also a paper edited at the at the AR
+and I've decided to publish because I
+
+ align:start position:0%
+and I've decided to publish because I
+ 
+
+ align:start position:0%
+and I've decided to publish because I
+think the result is so important but
+
+ align:start position:0%
+think the result is so important but
+ 
+
+ align:start position:0%
+think the result is so important but
+it's clearly come up in all of the
+
+ align:start position:0%
+it's clearly come up in all of the
+ 
+
+ align:start position:0%
+it's clearly come up in all of the
+referee reports saying well you know the
+
+ align:start position:0%
+referee reports saying well you know the
+ 
+
+ align:start position:0%
+referee reports saying well you know the
+you know you just told the kids like for
+
+ align:start position:0%
+you know you just told the kids like for
+ 
+
+ align:start position:0%
+you know you just told the kids like for
+two years that they have to be nice to
+
+ align:start position:0%
+two years that they have to be nice to
+ 
+
+ align:start position:0%
+two years that they have to be nice to
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+to their
+
+ align:start position:0%
+to their
+ 
+
+ align:start position:0%
+to their
+to to women so they are parting that
+
+ align:start position:0%
+to to women so they are parting that
+ 
+
+ align:start position:0%
+to to women so they are parting that
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+so there there is an interesting
+
+ align:start position:0%
+so there there is an interesting
+ 
+
+ align:start position:0%
+so there there is an interesting
+there is an interesting
+
+ align:start position:0%
+there is an interesting
+ 
+
+ align:start position:0%
+there is an interesting
+twist in the paper where they are they
+
+ align:start position:0%
+twist in the paper where they are they
+ 
+
+ align:start position:0%
+twist in the paper where they are they
+develop a test or they they use
+
+ align:start position:0%
+develop a test or they they use
+ 
+
+ align:start position:0%
+develop a test or they they use
+a test for testing for social
+
+ align:start position:0%
+a test for testing for social
+ 
+
+ align:start position:0%
+a test for testing for social
+desirability
+
+ align:start position:0%
+desirability
+ 
+
+ align:start position:0%
+desirability
+kind of trying to catch social
+
+ align:start position:0%
+kind of trying to catch social
+ 
+
+ align:start position:0%
+kind of trying to catch social
+desirability bias that they implement
+
+ align:start position:0%
+desirability bias that they implement
+ 
+
+ align:start position:0%
+desirability bias that they implement
+it also helps that they are looking for
+
+ align:start position:0%
+it also helps that they are looking for
+ 
+
+ align:start position:0%
+it also helps that they are looking for
+long-term outcomes so a lot a long time
+
+ align:start position:0%
+long-term outcomes so a lot a long time
+ 
+
+ align:start position:0%
+long-term outcomes so a lot a long time
+after the intervention itself was
+
+ align:start position:0%
+after the intervention itself was
+ 
+
+ align:start position:0%
+after the intervention itself was
+stopped
+
+ align:start position:0%
+stopped
+ 
+
+ align:start position:0%
+stopped
+so if people still remember one year
+
+ align:start position:0%
+so if people still remember one year
+ 
+
+ align:start position:0%
+so if people still remember one year
+after the fact that you want them to say
+
+ align:start position:0%
+after the fact that you want them to say
+ 
+
+ align:start position:0%
+after the fact that you want them to say
+that one has to be nice to women you
+
+ align:start position:0%
+that one has to be nice to women you
+ 
+
+ align:start position:0%
+that one has to be nice to women you
+know maybe that
+
+ align:start position:0%
+know maybe that
+ 
+
+ align:start position:0%
+know maybe that
+maybe maybe there is no difference
+
+ align:start position:0%
+maybe maybe there is no difference
+ 
+
+ align:start position:0%
+maybe maybe there is no difference
+anymore between people wanting to say
+
+ align:start position:0%
+anymore between people wanting to say
+ 
+
+ align:start position:0%
+anymore between people wanting to say
+that and people actually believe in it
+
+ align:start position:0%
+that and people actually believe in it
+ 
+
+ align:start position:0%
+that and people actually believe in it
+and then of course there is a
+
+ align:start position:0%
+and then of course there is a
+ 
+
+ align:start position:0%
+and then of course there is a
+self-reported behavior that's again
+
+ align:start position:0%
+self-reported behavior that's again
+ 
+
+ align:start position:0%
+self-reported behavior that's again
+self-reported so it could be demand
+
+ align:start position:0%
+self-reported so it could be demand
+ 
+
+ align:start position:0%
+self-reported so it could be demand
+effect but that's uh
+
+ align:start position:0%
+effect but that's uh
+ 
+
+ align:start position:0%
+effect but that's uh
+you know it's like whether you help at
+
+ align:start position:0%
+you know it's like whether you help at
+ 
+
+ align:start position:0%
+you know it's like whether you help at
+home and that type of things could be uh
+
+ align:start position:0%
+home and that type of things could be uh
+ 
+
+ align:start position:0%
+home and that type of things could be uh
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+it would be lying if the if which they
+
+ align:start position:0%
+it would be lying if the if which they
+ 
+
+ align:start position:0%
+it would be lying if the if which they
+might also do just to be nice so this
+
+ align:start position:0%
+might also do just to be nice so this
+ 
+
+ align:start position:0%
+might also do just to be nice so this
+but that remains that
+
+ align:start position:0%
+but that remains that
+ 
+
+ align:start position:0%
+but that remains that
+finding a
+
+ align:start position:0%
+finding a
+ 
+
+ align:start position:0%
+finding a
+kind of hard measure of
+
+ align:start position:0%
+kind of hard measure of
+ 
+
+ align:start position:0%
+kind of hard measure of
+of uh impact on Behavior would be the
+
+ align:start position:0%
+of uh impact on Behavior would be the
+ 
+
+ align:start position:0%
+of uh impact on Behavior would be the
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+cool thing to do there
+
+ align:start position:0%
+cool thing to do there
+ 
+
+ align:start position:0%
+cool thing to do there
+I've got this adolescence so you could
+
+ align:start position:0%
+I've got this adolescence so you could
+ 
+
+ align:start position:0%
+I've got this adolescence so you could
+try and Trust Trace them until they get
+
+ align:start position:0%
+try and Trust Trace them until they get
+ 
+
+ align:start position:0%
+try and Trust Trace them until they get
+married and uh like Allah like in our
+
+ align:start position:0%
+married and uh like Allah like in our
+ 
+
+ align:start position:0%
+married and uh like Allah like in our
+paper or Indiana where we trust people
+
+ align:start position:0%
+paper or Indiana where we trust people
+ 
+
+ align:start position:0%
+paper or Indiana where we trust people
+forever but it's it's it's a pretty
+
+ align:start position:0%
+forever but it's it's it's a pretty
+ 
+
+ align:start position:0%
+forever but it's it's it's a pretty
+it's a pretty commitment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now getting women to given the
+
+ align:start position:0%
+so now getting women to given the
+ 
+
+ align:start position:0%
+so now getting women to given the
+disagreement
+
+ align:start position:0%
+disagreement
+ 
+
+ align:start position:0%
+disagreement
+taking now the the the the social Norm
+
+ align:start position:0%
+taking now the the the the social Norm
+ 
+
+ align:start position:0%
+taking now the the the the social Norm
+is given for a moment
+
+ align:start position:0%
+is given for a moment
+ 
+
+ align:start position:0%
+is given for a moment
+to get women to participate in the in
+
+ align:start position:0%
+to get women to participate in the in
+ 
+
+ align:start position:0%
+to get women to participate in the in
+the labor force you could you could
+
+ align:start position:0%
+the labor force you could you could
+ 
+
+ align:start position:0%
+the labor force you could you could
+either change husband's opinion or
+
+ align:start position:0%
+either change husband's opinion or
+ 
+
+ align:start position:0%
+either change husband's opinion or
+change the wife ability to advocate for
+
+ align:start position:0%
+change the wife ability to advocate for
+ 
+
+ align:start position:0%
+change the wife ability to advocate for
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+if there is this you know as long as
+
+ align:start position:0%
+if there is this you know as long as
+ 
+
+ align:start position:0%
+if there is this you know as long as
+people still have this differential
+
+ align:start position:0%
+people still have this differential
+ 
+
+ align:start position:0%
+people still have this differential
+opinion
+
+ align:start position:0%
+opinion
+ 
+
+ align:start position:0%
+opinion
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so people by Maddie McElroy looks at
+
+ align:start position:0%
+so people by Maddie McElroy looks at
+ 
+
+ align:start position:0%
+so people by Maddie McElroy looks at
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+she that's like that's actually was our
+
+ align:start position:0%
+she that's like that's actually was our
+ 
+
+ align:start position:0%
+she that's like that's actually was our
+job market paper so in an experiment she
+
+ align:start position:0%
+job market paper so in an experiment she
+ 
+
+ align:start position:0%
+job market paper so in an experiment she
+conducted on her own on the shoestring
+
+ align:start position:0%
+conducted on her own on the shoestring
+ 
+
+ align:start position:0%
+conducted on her own on the shoestring
+budget in up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you know she hails from Virginia so
+
+ align:start position:0%
+um you know she hails from Virginia so
+ 
+
+ align:start position:0%
+um you know she hails from Virginia so
+up was
+
+ align:start position:0%
+up was
+ 
+
+ align:start position:0%
+up was
+quite a different setup
+
+ align:start position:0%
+quite a different setup
+ 
+
+ align:start position:0%
+quite a different setup
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so it's well worth reading first of all
+
+ align:start position:0%
+so it's well worth reading first of all
+ 
+
+ align:start position:0%
+so it's well worth reading first of all
+it's a very good people also going awful
+
+ align:start position:0%
+it's a very good people also going awful
+ 
+
+ align:start position:0%
+it's a very good people also going awful
+just to have a sense of you know what
+
+ align:start position:0%
+just to have a sense of you know what
+ 
+
+ align:start position:0%
+just to have a sense of you know what
+you can do as a graduate student if
+
+ align:start position:0%
+you can do as a graduate student if
+ 
+
+ align:start position:0%
+you can do as a graduate student if
+that's what you decide to do
+
+ align:start position:0%
+that's what you decide to do
+ 
+
+ align:start position:0%
+that's what you decide to do
+uh she teamed up with a large carpet
+
+ align:start position:0%
+uh she teamed up with a large carpet
+ 
+
+ align:start position:0%
+uh she teamed up with a large carpet
+manufacturer in India the largest carpet
+
+ align:start position:0%
+manufacturer in India the largest carpet
+ 
+
+ align:start position:0%
+manufacturer in India the largest carpet
+manufacturer in India
+
+ align:start position:0%
+manufacturer in India
+ 
+
+ align:start position:0%
+manufacturer in India
+and they wanted to record women uh in
+
+ align:start position:0%
+and they wanted to record women uh in
+ 
+
+ align:start position:0%
+and they wanted to record women uh in
+part and probably mostly because of
+
+ align:start position:0%
+part and probably mostly because of
+ 
+
+ align:start position:0%
+part and probably mostly because of
+tightness in the liberal Market they
+
+ align:start position:0%
+tightness in the liberal Market they
+ 
+
+ align:start position:0%
+tightness in the liberal Market they
+just can't hire enough Weaver anymore
+
+ align:start position:0%
+just can't hire enough Weaver anymore
+ 
+
+ align:start position:0%
+just can't hire enough Weaver anymore
+and weaving is traditionally actually a
+
+ align:start position:0%
+and weaving is traditionally actually a
+ 
+
+ align:start position:0%
+and weaving is traditionally actually a
+male occupation in up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's funny because in the 192 class I
+
+ align:start position:0%
+it's funny because in the 192 class I
+ 
+
+ align:start position:0%
+it's funny because in the 192 class I
+think it's Arthur who mentioned this as
+
+ align:start position:0%
+think it's Arthur who mentioned this as
+ 
+
+ align:start position:0%
+think it's Arthur who mentioned this as
+an archetypal female occupation well it
+
+ align:start position:0%
+an archetypal female occupation well it
+ 
+
+ align:start position:0%
+an archetypal female occupation well it
+turns out in in up it's a male
+
+ align:start position:0%
+turns out in in up it's a male
+ 
+
+ align:start position:0%
+turns out in in up it's a male
+occupation and they are trying to get
+
+ align:start position:0%
+occupation and they are trying to get
+ 
+
+ align:start position:0%
+occupation and they are trying to get
+women in it
+
+ align:start position:0%
+women in it
+ 
+
+ align:start position:0%
+women in it
+uh because there are no reason why women
+
+ align:start position:0%
+uh because there are no reason why women
+ 
+
+ align:start position:0%
+uh because there are no reason why women
+couldn't do weaving
+
+ align:start position:0%
+couldn't do weaving
+ 
+
+ align:start position:0%
+couldn't do weaving
+and so in fact it's with the same
+
+ align:start position:0%
+and so in fact it's with the same
+ 
+
+ align:start position:0%
+and so in fact it's with the same
+partner that Matt and Maddie did the
+
+ align:start position:0%
+partner that Matt and Maddie did the
+ 
+
+ align:start position:0%
+partner that Matt and Maddie did the
+first experiment that I mentioned before
+
+ align:start position:0%
+first experiment that I mentioned before
+ 
+
+ align:start position:0%
+first experiment that I mentioned before
+where they gave the voucher for the
+
+ align:start position:0%
+where they gave the voucher for the
+ 
+
+ align:start position:0%
+where they gave the voucher for the
+training and so it's a second experiment
+
+ align:start position:0%
+training and so it's a second experiment
+ 
+
+ align:start position:0%
+training and so it's a second experiment
+with the same same partner
+
+ align:start position:0%
+with the same same partner
+ 
+
+ align:start position:0%
+with the same same partner
+and then they did two things
+
+ align:start position:0%
+and then they did two things
+ 
+
+ align:start position:0%
+and then they did two things
+um they oh she did two things she did
+
+ align:start position:0%
+um they oh she did two things she did
+ 
+
+ align:start position:0%
+um they oh she did two things she did
+she did a psychosocial intervention uh
+
+ align:start position:0%
+she did a psychosocial intervention uh
+ 
+
+ align:start position:0%
+she did a psychosocial intervention uh
+called generalized self-efficacy
+
+ align:start position:0%
+called generalized self-efficacy
+ 
+
+ align:start position:0%
+called generalized self-efficacy
+training um
+
+ align:start position:0%
+training um
+ 
+
+ align:start position:0%
+training um
+over several weeks
+
+ align:start position:0%
+over several weeks
+ 
+
+ align:start position:0%
+over several weeks
+that's one intervention and the other is
+
+ align:start position:0%
+that's one intervention and the other is
+ 
+
+ align:start position:0%
+that's one intervention and the other is
+a promotion of the job to the husband
+
+ align:start position:0%
+a promotion of the job to the husband
+ 
+
+ align:start position:0%
+a promotion of the job to the husband
+and the in-laws which is a six minutes
+
+ align:start position:0%
+and the in-laws which is a six minutes
+ 
+
+ align:start position:0%
+and the in-laws which is a six minutes
+video that was meant to address some of
+
+ align:start position:0%
+video that was meant to address some of
+ 
+
+ align:start position:0%
+video that was meant to address some of
+the concern that uh husbands might have
+
+ align:start position:0%
+the concern that uh husbands might have
+ 
+
+ align:start position:0%
+the concern that uh husbands might have
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+
+ align:start position:0%
+might have had so that kind of did some
+ 
+
+ align:start position:0%
+might have had so that kind of did some
+focus group to figure out what people
+
+ align:start position:0%
+focus group to figure out what people
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+
+ align:start position:0%
+focus group to figure out what people
+were worried about and then they did
+
+ align:start position:0%
+were worried about and then they did
+ 
+
+ align:start position:0%
+were worried about and then they did
+this video and then they showed the
+
+ align:start position:0%
+this video and then they showed the
+ 
+
+ align:start position:0%
+this video and then they showed the
+video in you know in on the iPad
+
+ align:start position:0%
+video in you know in on the iPad
+ 
+
+ align:start position:0%
+video in you know in on the iPad
+when going from house to house so the
+
+ align:start position:0%
+when going from house to house so the
+ 
+
+ align:start position:0%
+when going from house to house so the
+video had explained that it was woman
+
+ align:start position:0%
+video had explained that it was woman
+ 
+
+ align:start position:0%
+video had explained that it was woman
+only workplaces and
+
+ align:start position:0%
+only workplaces and
+ 
+
+ align:start position:0%
+only workplaces and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+what people would be doing there and the
+
+ align:start position:0%
+what people would be doing there and the
+ 
+
+ align:start position:0%
+what people would be doing there and the
+money they could make and and all of
+
+ align:start position:0%
+money they could make and and all of
+ 
+
+ align:start position:0%
+money they could make and and all of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and then of course so you have two
+
+ align:start position:0%
+and then of course so you have two
+ 
+
+ align:start position:0%
+and then of course so you have two
+treatment and the interaction
+
+ align:start position:0%
+treatment and the interaction
+ 
+
+ align:start position:0%
+treatment and the interaction
+because you might expect that the
+
+ align:start position:0%
+because you might expect that the
+ 
+
+ align:start position:0%
+because you might expect that the
+self-efficacy intervention would have
+
+ align:start position:0%
+self-efficacy intervention would have
+ 
+
+ align:start position:0%
+self-efficacy intervention would have
+different in Impact uh when the husband
+
+ align:start position:0%
+different in Impact uh when the husband
+ 
+
+ align:start position:0%
+different in Impact uh when the husband
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+might be predisposed to be interested in
+
+ align:start position:0%
+might be predisposed to be interested in
+ 
+
+ align:start position:0%
+might be predisposed to be interested in
+the job versus when the when they when
+
+ align:start position:0%
+the job versus when the when they when
+ 
+
+ align:start position:0%
+the job versus when the when they when
+they are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the design self-efficacy training so
+
+ align:start position:0%
+so the design self-efficacy training so
+ 
+
+ align:start position:0%
+so the design self-efficacy training so
+this is an old concept by bandura from
+
+ align:start position:0%
+this is an old concept by bandura from
+ 
+
+ align:start position:0%
+this is an old concept by bandura from
+the 77 which is actually very very
+
+ align:start position:0%
+the 77 which is actually very very
+ 
+
+ align:start position:0%
+the 77 which is actually very very
+classic in Psychology but it's one of
+
+ align:start position:0%
+classic in Psychology but it's one of
+ 
+
+ align:start position:0%
+classic in Psychology but it's one of
+the concepts that has not yet made its
+
+ align:start position:0%
+the concepts that has not yet made its
+ 
+
+ align:start position:0%
+the concepts that has not yet made its
+way into economics and behavioral
+
+ align:start position:0%
+way into economics and behavioral
+ 
+
+ align:start position:0%
+way into economics and behavioral
+economics in a large in a large way
+
+ align:start position:0%
+economics in a large in a large way
+ 
+
+ align:start position:0%
+economics in a large in a large way
+maybe after my newspaper it will
+
+ align:start position:0%
+maybe after my newspaper it will
+ 
+
+ align:start position:0%
+maybe after my newspaper it will
+and it's the idea that you can affect
+
+ align:start position:0%
+and it's the idea that you can affect
+ 
+
+ align:start position:0%
+and it's the idea that you can affect
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the outcomes you can affect your
+
+ align:start position:0%
+the outcomes you can affect your
+ 
+
+ align:start position:0%
+the outcomes you can affect your
+outcomes by doing by your agency you
+
+ align:start position:0%
+outcomes by doing by your agency you
+ 
+
+ align:start position:0%
+outcomes by doing by your agency you
+have Agency on the outcomes that around
+
+ align:start position:0%
+have Agency on the outcomes that around
+ 
+
+ align:start position:0%
+have Agency on the outcomes that around
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+so uh they're taking basically going
+
+ align:start position:0%
+so uh they're taking basically going
+ 
+
+ align:start position:0%
+so uh they're taking basically going
+from case studies and on the uh
+
+ align:start position:0%
+from case studies and on the uh
+ 
+
+ align:start position:0%
+from case studies and on the uh
+discussing through situation or problems
+
+ align:start position:0%
+discussing through situation or problems
+ 
+
+ align:start position:0%
+discussing through situation or problems
+that the women might might have and then
+
+ align:start position:0%
+that the women might might have and then
+ 
+
+ align:start position:0%
+that the women might might have and then
+how she can you know how she can address
+
+ align:start position:0%
+how she can you know how she can address
+ 
+
+ align:start position:0%
+how she can you know how she can address
+it and there is a sort of standard
+
+ align:start position:0%
+it and there is a sort of standard
+ 
+
+ align:start position:0%
+it and there is a sort of standard
+skill for for General selfie efficacy so
+
+ align:start position:0%
+skill for for General selfie efficacy so
+ 
+
+ align:start position:0%
+skill for for General selfie efficacy so
+generalizes as opposed to in any
+
+ align:start position:0%
+generalizes as opposed to in any
+ 
+
+ align:start position:0%
+generalizes as opposed to in any
+particular era you could have
+
+ align:start position:0%
+particular era you could have
+ 
+
+ align:start position:0%
+particular era you could have
+self-efficacy for children and no for
+
+ align:start position:0%
+self-efficacy for children and no for
+ 
+
+ align:start position:0%
+self-efficacy for children and no for
+not self-empsey foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so there is a scale for it so she
+
+ align:start position:0%
+uh so there is a scale for it so she
+ 
+
+ align:start position:0%
+uh so there is a scale for it so she
+measured she measured at the end and
+
+ align:start position:0%
+measured she measured at the end and
+ 
+
+ align:start position:0%
+measured she measured at the end and
+then at the beginning and then the
+
+ align:start position:0%
+then at the beginning and then the
+ 
+
+ align:start position:0%
+then at the beginning and then the
+training uh took place in in importantly
+
+ align:start position:0%
+training uh took place in in importantly
+ 
+
+ align:start position:0%
+training uh took place in in importantly
+in the training she she was sure to pick
+
+ align:start position:0%
+in the training she she was sure to pick
+ 
+
+ align:start position:0%
+in the training she she was sure to pick
+so she took an exit she worked with an
+
+ align:start position:0%
+so she took an exit she worked with an
+ 
+
+ align:start position:0%
+so she took an exit she worked with an
+organization that was with psychologists
+
+ align:start position:0%
+organization that was with psychologists
+ 
+
+ align:start position:0%
+organization that was with psychologists
+who were specialist in that and she went
+
+ align:start position:0%
+who were specialist in that and she went
+ 
+
+ align:start position:0%
+who were specialist in that and she went
+she changed a little bit the curriculum
+
+ align:start position:0%
+she changed a little bit the curriculum
+ 
+
+ align:start position:0%
+she changed a little bit the curriculum
+to make sure that there was no examples
+
+ align:start position:0%
+to make sure that there was no examples
+ 
+
+ align:start position:0%
+to make sure that there was no examples
+that had anything to do with labor
+
+ align:start position:0%
+that had anything to do with labor
+ 
+
+ align:start position:0%
+that had anything to do with labor
+markets because she didn't want to
+
+ align:start position:0%
+markets because she didn't want to
+ 
+
+ align:start position:0%
+markets because she didn't want to
+directly uh kind of lead in this
+
+ align:start position:0%
+directly uh kind of lead in this
+ 
+
+ align:start position:0%
+directly uh kind of lead in this
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+uh but so in terms of the the
+
+ align:start position:0%
+uh but so in terms of the the
+ 
+
+ align:start position:0%
+uh but so in terms of the the
+so the GSE questions of the firm you
+
+ align:start position:0%
+so the GSE questions of the firm you
+ 
+
+ align:start position:0%
+so the GSE questions of the firm you
+know can you affect this outcome can you
+
+ align:start position:0%
+know can you affect this outcome can you
+ 
+
+ align:start position:0%
+know can you affect this outcome can you
+affect that outcome generally you would
+
+ align:start position:0%
+affect that outcome generally you would
+ 
+
+ align:start position:0%
+affect that outcome generally you would
+say that if a child is sick you are able
+
+ align:start position:0%
+say that if a child is sick you are able
+ 
+
+ align:start position:0%
+say that if a child is sick you are able
+to kind of do what it takes to to to
+
+ align:start position:0%
+to kind of do what it takes to to to
+ 
+
+ align:start position:0%
+to kind of do what it takes to to to
+help them
+
+ align:start position:0%
+help them
+ 
+
+ align:start position:0%
+help them
+Etc
+
+ align:start position:0%
+Etc
+ 
+
+ align:start position:0%
+Etc
+um so they look she looks at the impact
+
+ align:start position:0%
+um so they look she looks at the impact
+ 
+
+ align:start position:0%
+um so they look she looks at the impact
+of the treatment and the promotion you
+
+ align:start position:0%
+of the treatment and the promotion you
+ 
+
+ align:start position:0%
+of the treatment and the promotion you
+can look at the impact of the treatment
+
+ align:start position:0%
+can look at the impact of the treatment
+ 
+
+ align:start position:0%
+can look at the impact of the treatment
+the promotion or the two interacted
+
+ align:start position:0%
+the promotion or the two interacted
+ 
+
+ align:start position:0%
+the promotion or the two interacted
+given what we discussed about
+
+ align:start position:0%
+given what we discussed about
+ 
+
+ align:start position:0%
+given what we discussed about
+interaction let's focus on the
+
+ align:start position:0%
+interaction let's focus on the
+ 
+
+ align:start position:0%
+interaction let's focus on the
+interactive specification immediately
+
+ align:start position:0%
+interactive specification immediately
+ 
+
+ align:start position:0%
+interactive specification immediately
+and you can see that um
+
+ align:start position:0%
+and you can see that um
+ 
+
+ align:start position:0%
+and you can see that um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+you can look at the the impact of of the
+
+ align:start position:0%
+you can look at the the impact of of the
+ 
+
+ align:start position:0%
+you can look at the the impact of of the
+intervention after several weeks
+
+ align:start position:0%
+intervention after several weeks
+ 
+
+ align:start position:0%
+intervention after several weeks
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+you know starting towards the at the end
+
+ align:start position:0%
+you know starting towards the at the end
+ 
+
+ align:start position:0%
+you know starting towards the at the end
+of the program
+
+ align:start position:0%
+of the program
+ 
+
+ align:start position:0%
+of the program
+the GSE leads to
+
+ align:start position:0%
+the GSE leads to
+ 
+
+ align:start position:0%
+the GSE leads to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the two GSC specification lead to a more
+
+ align:start position:0%
+the two GSC specification lead to a more
+ 
+
+ align:start position:0%
+the two GSC specification lead to a more
+more GSE
+
+ align:start position:0%
+more GSE
+ 
+
+ align:start position:0%
+more GSE
+and the the
+
+ align:start position:0%
+and the the
+ 
+
+ align:start position:0%
+and the the
+the promotion itself doesn't lead to
+
+ align:start position:0%
+the promotion itself doesn't lead to
+ 
+
+ align:start position:0%
+the promotion itself doesn't lead to
+more to more GSE
+
+ align:start position:0%
+more to more GSE
+ 
+
+ align:start position:0%
+more to more GSE
+it's not perhaps powered very much so
+
+ align:start position:0%
+it's not perhaps powered very much so
+ 
+
+ align:start position:0%
+it's not perhaps powered very much so
+it's difficult to show that these things
+
+ align:start position:0%
+it's difficult to show that these things
+ 
+
+ align:start position:0%
+it's difficult to show that these things
+are significantly different
+
+ align:start position:0%
+are significantly different
+ 
+
+ align:start position:0%
+are significantly different
+which is something she has been
+
+ align:start position:0%
+which is something she has been
+ 
+
+ align:start position:0%
+which is something she has been
+struggling with the sample size is not
+
+ align:start position:0%
+struggling with the sample size is not
+ 
+
+ align:start position:0%
+struggling with the sample size is not
+like enormous
+
+ align:start position:0%
+like enormous
+ 
+
+ align:start position:0%
+like enormous
+but you do find that in an over time it
+
+ align:start position:0%
+but you do find that in an over time it
+ 
+
+ align:start position:0%
+but you do find that in an over time it
+seems relatively stable that the GSE
+
+ align:start position:0%
+seems relatively stable that the GSE
+ 
+
+ align:start position:0%
+seems relatively stable that the GSE
+treatment seems to increase GSE but you
+
+ align:start position:0%
+treatment seems to increase GSE but you
+ 
+
+ align:start position:0%
+treatment seems to increase GSE but you
+can see why she preferred to look at the
+
+ align:start position:0%
+can see why she preferred to look at the
+ 
+
+ align:start position:0%
+can see why she preferred to look at the
+uninteracted specification because then
+
+ align:start position:0%
+uninteracted specification because then
+ 
+
+ align:start position:0%
+uninteracted specification because then
+it looked like it's pulling these two so
+
+ align:start position:0%
+it looked like it's pulling these two so
+ 
+
+ align:start position:0%
+it looked like it's pulling these two so
+you get some extra precision and you're
+
+ align:start position:0%
+you get some extra precision and you're
+ 
+
+ align:start position:0%
+you get some extra precision and you're
+finding then across the ball that the G
+
+ align:start position:0%
+finding then across the ball that the G
+ 
+
+ align:start position:0%
+finding then across the ball that the G
+is being treated with GSE increase your
+
+ align:start position:0%
+is being treated with GSE increase your
+ 
+
+ align:start position:0%
+is being treated with GSE increase your
+GSE
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then when we look at of uh of a
+
+ align:start position:0%
+then when we look at of uh of a
+ 
+
+ align:start position:0%
+then when we look at of uh of a
+participation in the in the firm program
+
+ align:start position:0%
+participation in the in the firm program
+ 
+
+ align:start position:0%
+participation in the in the firm program
+so this is the the main outcome was
+
+ align:start position:0%
+so this is the the main outcome was
+ 
+
+ align:start position:0%
+so this is the the main outcome was
+either participation in The Firm program
+
+ align:start position:0%
+either participation in The Firm program
+ 
+
+ align:start position:0%
+either participation in The Firm program
+or working or working outside of the
+
+ align:start position:0%
+or working or working outside of the
+ 
+
+ align:start position:0%
+or working or working outside of the
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+you find that the promotion at the
+
+ align:start position:0%
+you find that the promotion at the
+ 
+
+ align:start position:0%
+you find that the promotion at the
+robust increase and signing up for the
+
+ align:start position:0%
+robust increase and signing up for the
+ 
+
+ align:start position:0%
+robust increase and signing up for the
+from firm program and for doing any work
+
+ align:start position:0%
+from firm program and for doing any work
+ 
+
+ align:start position:0%
+from firm program and for doing any work
+including this one at least in uh in the
+
+ align:start position:0%
+including this one at least in uh in the
+ 
+
+ align:start position:0%
+including this one at least in uh in the
+first five months though it was not
+
+ align:start position:0%
+first five months though it was not
+ 
+
+ align:start position:0%
+first five months though it was not
+durable over time
+
+ align:start position:0%
+durable over time
+ 
+
+ align:start position:0%
+durable over time
+the GSE had impact uh that's not
+
+ align:start position:0%
+the GSE had impact uh that's not
+ 
+
+ align:start position:0%
+the GSE had impact uh that's not
+significant on for signing up on the
+
+ align:start position:0%
+significant on for signing up on the
+ 
+
+ align:start position:0%
+significant on for signing up on the
+first on the firm's program it's
+
+ align:start position:0%
+first on the firm's program it's
+ 
+
+ align:start position:0%
+first on the firm's program it's
+significant for working of farm in
+
+ align:start position:0%
+significant for working of farm in
+ 
+
+ align:start position:0%
+significant for working of farm in
+general and not remember that the GSE
+
+ align:start position:0%
+general and not remember that the GSE
+ 
+
+ align:start position:0%
+general and not remember that the GSE
+was not about was not the GSE
+
+ align:start position:0%
+was not about was not the GSE
+ 
+
+ align:start position:0%
+was not about was not the GSE
+intervention had nothing to do with the
+
+ align:start position:0%
+intervention had nothing to do with the
+ 
+
+ align:start position:0%
+intervention had nothing to do with the
+program so it was not particularly
+
+ align:start position:0%
+program so it was not particularly
+ 
+
+ align:start position:0%
+program so it was not particularly
+promoting the program it was just giving
+
+ align:start position:0%
+promoting the program it was just giving
+ 
+
+ align:start position:0%
+promoting the program it was just giving
+people women agency to do whatever they
+
+ align:start position:0%
+people women agency to do whatever they
+ 
+
+ align:start position:0%
+people women agency to do whatever they
+want in their life it was not even about
+
+ align:start position:0%
+want in their life it was not even about
+ 
+
+ align:start position:0%
+want in their life it was not even about
+work so that's probably a better outcome
+
+ align:start position:0%
+work so that's probably a better outcome
+ 
+
+ align:start position:0%
+work so that's probably a better outcome
+so GSC alone uh increase a female labor
+
+ align:start position:0%
+so GSC alone uh increase a female labor
+ 
+
+ align:start position:0%
+so GSC alone uh increase a female labor
+force participation so this is something
+
+ align:start position:0%
+force participation so this is something
+ 
+
+ align:start position:0%
+force participation so this is something
+that women tend to want to do and in
+
+ align:start position:0%
+that women tend to want to do and in
+ 
+
+ align:start position:0%
+that women tend to want to do and in
+fact you think that they want to do
+
+ align:start position:0%
+fact you think that they want to do
+ 
+
+ align:start position:0%
+fact you think that they want to do
+about as much as the promotion treatment
+
+ align:start position:0%
+about as much as the promotion treatment
+ 
+
+ align:start position:0%
+about as much as the promotion treatment
+directly to the husband
+
+ align:start position:0%
+directly to the husband
+ 
+
+ align:start position:0%
+directly to the husband
+but when you combine the two instead of
+
+ align:start position:0%
+but when you combine the two instead of
+ 
+
+ align:start position:0%
+but when you combine the two instead of
+having a larger effect which is what I
+
+ align:start position:0%
+having a larger effect which is what I
+ 
+
+ align:start position:0%
+having a larger effect which is what I
+would have expected you find
+
+ align:start position:0%
+would have expected you find
+ 
+
+ align:start position:0%
+would have expected you find
+no significant effect or a smaller
+
+ align:start position:0%
+no significant effect or a smaller
+ 
+
+ align:start position:0%
+no significant effect or a smaller
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+and in fact at six weeks the effective
+
+ align:start position:0%
+and in fact at six weeks the effective
+ 
+
+ align:start position:0%
+and in fact at six weeks the effective
+is even significantly different
+
+ align:start position:0%
+is even significantly different
+ 
+
+ align:start position:0%
+is even significantly different
+uh from having just a promo if you add
+
+ align:start position:0%
+uh from having just a promo if you add
+ 
+
+ align:start position:0%
+uh from having just a promo if you add
+the GST to the promotion you have the
+
+ align:start position:0%
+the GST to the promotion you have the
+ 
+
+ align:start position:0%
+the GST to the promotion you have the
+effect crushing
+
+ align:start position:0%
+effect crushing
+ 
+
+ align:start position:0%
+effect crushing
+so that's a bit surprising
+
+ align:start position:0%
+so that's a bit surprising
+ 
+
+ align:start position:0%
+so that's a bit surprising
+uh and and maybe a bit reminiscent of
+
+ align:start position:0%
+uh and and maybe a bit reminiscent of
+ 
+
+ align:start position:0%
+uh and and maybe a bit reminiscent of
+this discussion treatment that led to
+
+ align:start position:0%
+this discussion treatment that led to
+ 
+
+ align:start position:0%
+this discussion treatment that led to
+actually less take up than when is the
+
+ align:start position:0%
+actually less take up than when is the
+ 
+
+ align:start position:0%
+actually less take up than when is the
+other wife alone or the husband alone
+
+ align:start position:0%
+other wife alone or the husband alone
+ 
+
+ align:start position:0%
+other wife alone or the husband alone
+was given the ticket
+
+ align:start position:0%
+was given the ticket
+ 
+
+ align:start position:0%
+was given the ticket
+and again suggest that there is
+
+ align:start position:0%
+and again suggest that there is
+ 
+
+ align:start position:0%
+and again suggest that there is
+something about
+
+ align:start position:0%
+something about
+ 
+
+ align:start position:0%
+something about
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+basically women
+
+ align:start position:0%
+basically women
+ 
+
+ align:start position:0%
+basically women
+in one possible interpretation I'm not
+
+ align:start position:0%
+in one possible interpretation I'm not
+ 
+
+ align:start position:0%
+in one possible interpretation I'm not
+saying it's the right one but one
+
+ align:start position:0%
+saying it's the right one but one
+ 
+
+ align:start position:0%
+saying it's the right one but one
+possible interpretation of this result
+
+ align:start position:0%
+possible interpretation of this result
+ 
+
+ align:start position:0%
+possible interpretation of this result
+is that women want to work
+
+ align:start position:0%
+is that women want to work
+ 
+
+ align:start position:0%
+is that women want to work
+with the the GSC treatment they are
+
+ align:start position:0%
+with the the GSC treatment they are
+ 
+
+ align:start position:0%
+with the the GSC treatment they are
+given they are given the power to
+
+ align:start position:0%
+given they are given the power to
+ 
+
+ align:start position:0%
+given they are given the power to
+advocate for what they want
+
+ align:start position:0%
+advocate for what they want
+ 
+
+ align:start position:0%
+advocate for what they want
+and then they they do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh husband that's in the GSE treatment
+
+ align:start position:0%
+oh husband that's in the GSE treatment
+ 
+
+ align:start position:0%
+oh husband that's in the GSE treatment
+alone or husband find out that actually
+
+ align:start position:0%
+alone or husband find out that actually
+ 
+
+ align:start position:0%
+alone or husband find out that actually
+if you can make money and it's not a bad
+
+ align:start position:0%
+if you can make money and it's not a bad
+ 
+
+ align:start position:0%
+if you can make money and it's not a bad
+thing let's let's give this a try
+
+ align:start position:0%
+thing let's let's give this a try
+ 
+
+ align:start position:0%
+thing let's let's give this a try
+and push them to work
+
+ align:start position:0%
+and push them to work
+ 
+
+ align:start position:0%
+and push them to work
+but when she has self-efficacy to argue
+
+ align:start position:0%
+but when she has self-efficacy to argue
+ 
+
+ align:start position:0%
+but when she has self-efficacy to argue
+for herself she's like I'm not going to
+
+ align:start position:0%
+for herself she's like I'm not going to
+ 
+
+ align:start position:0%
+for herself she's like I'm not going to
+take this new job that you are just
+
+ align:start position:0%
+take this new job that you are just
+ 
+
+ align:start position:0%
+take this new job that you are just
+decided is interesting
+
+ align:start position:0%
+decided is interesting
+ 
+
+ align:start position:0%
+decided is interesting
+or something like that like cheese
+
+ align:start position:0%
+or something like that like cheese
+ 
+
+ align:start position:0%
+or something like that like cheese
+sufficiently she's kind of less
+
+ align:start position:0%
+sufficiently she's kind of less
+ 
+
+ align:start position:0%
+sufficiently she's kind of less
+she's resistant to the idea that's
+
+ align:start position:0%
+she's resistant to the idea that's
+ 
+
+ align:start position:0%
+she's resistant to the idea that's
+imposed this new idea that has been
+
+ align:start position:0%
+imposed this new idea that has been
+ 
+
+ align:start position:0%
+imposed this new idea that has been
+imposed imposed to her
+
+ align:start position:0%
+imposed imposed to her
+ 
+
+ align:start position:0%
+imposed imposed to her
+that's just an interpretation uh which
+
+ align:start position:0%
+that's just an interpretation uh which
+ 
+
+ align:start position:0%
+that's just an interpretation uh which
+is hard to prove
+
+ align:start position:0%
+is hard to prove
+ 
+
+ align:start position:0%
+is hard to prove
+but again shows how the things are
+
+ align:start position:0%
+but again shows how the things are
+ 
+
+ align:start position:0%
+but again shows how the things are
+complicated because the again my my
+
+ align:start position:0%
+complicated because the again my my
+ 
+
+ align:start position:0%
+complicated because the again my my
+prior would have been that combining the
+
+ align:start position:0%
+prior would have been that combining the
+ 
+
+ align:start position:0%
+prior would have been that combining the
+two would have a larger effect than
+
+ align:start position:0%
+two would have a larger effect than
+ 
+
+ align:start position:0%
+two would have a larger effect than
+doing either individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of the reason why a woman might
+
+ align:start position:0%
+so one of the reason why a woman might
+ 
+
+ align:start position:0%
+so one of the reason why a woman might
+well men might be reluctant to see their
+
+ align:start position:0%
+well men might be reluctant to see their
+ 
+
+ align:start position:0%
+well men might be reluctant to see their
+wives walking is because it might
+
+ align:start position:0%
+wives walking is because it might
+ 
+
+ align:start position:0%
+wives walking is because it might
+increase bargaining power
+
+ align:start position:0%
+increase bargaining power
+ 
+
+ align:start position:0%
+increase bargaining power
+debugging power and in The Limited uh in
+
+ align:start position:0%
+debugging power and in The Limited uh in
+ 
+
+ align:start position:0%
+debugging power and in The Limited uh in
+a limited commitment uh mother you don't
+
+ align:start position:0%
+a limited commitment uh mother you don't
+ 
+
+ align:start position:0%
+a limited commitment uh mother you don't
+want to do that you want to keep your
+
+ align:start position:0%
+want to do that you want to keep your
+ 
+
+ align:start position:0%
+want to do that you want to keep your
+woman men might want to keep a woman
+
+ align:start position:0%
+woman men might want to keep a woman
+ 
+
+ align:start position:0%
+woman men might want to keep a woman
+home in order to make sure that they
+
+ align:start position:0%
+home in order to make sure that they
+ 
+
+ align:start position:0%
+home in order to make sure that they
+remain they don't you know they don't
+
+ align:start position:0%
+remain they don't you know they don't
+ 
+
+ align:start position:0%
+remain they don't you know they don't
+become snooty and they Remain the the
+
+ align:start position:0%
+become snooty and they Remain the the
+ 
+
+ align:start position:0%
+become snooty and they Remain the the
+the man Remains the boss of the house
+
+ align:start position:0%
+the man Remains the boss of the house
+ 
+
+ align:start position:0%
+the man Remains the boss of the house
+um so there is a an experiment by a
+
+ align:start position:0%
+um so there is a an experiment by a
+ 
+
+ align:start position:0%
+um so there is a an experiment by a
+project a vicious project by rohini
+
+ align:start position:0%
+project a vicious project by rohini
+ 
+
+ align:start position:0%
+project a vicious project by rohini
+Pandey Natalia Regal Simon Channel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is in madhya Pradesh
+
+ align:start position:0%
+which is in madhya Pradesh
+ 
+
+ align:start position:0%
+which is in madhya Pradesh
+where they um
+
+ align:start position:0%
+where they um
+ 
+
+ align:start position:0%
+where they um
+they didn't increase access to work
+
+ align:start position:0%
+they didn't increase access to work
+ 
+
+ align:start position:0%
+they didn't increase access to work
+but they increased the control of the
+
+ align:start position:0%
+but they increased the control of the
+ 
+
+ align:start position:0%
+but they increased the control of the
+woman
+
+ align:start position:0%
+woman
+ 
+
+ align:start position:0%
+woman
+to the money coming from work that they
+
+ align:start position:0%
+to the money coming from work that they
+ 
+
+ align:start position:0%
+to the money coming from work that they
+were doing anyways so this is in the
+
+ align:start position:0%
+were doing anyways so this is in the
+ 
+
+ align:start position:0%
+were doing anyways so this is in the
+context of the energy program the energy
+
+ align:start position:0%
+context of the energy program the energy
+ 
+
+ align:start position:0%
+context of the energy program the energy
+is a workfair program in India
+
+ align:start position:0%
+is a workfair program in India
+ 
+
+ align:start position:0%
+is a workfair program in India
+whereby women have women and men
+
+ align:start position:0%
+whereby women have women and men
+ 
+
+ align:start position:0%
+whereby women have women and men
+everyone has access to a certain number
+
+ align:start position:0%
+everyone has access to a certain number
+ 
+
+ align:start position:0%
+everyone has access to a certain number
+of of labored every every year so this
+
+ align:start position:0%
+of of labored every every year so this
+ 
+
+ align:start position:0%
+of of labored every every year so this
+is quite well paid because it's at the
+
+ align:start position:0%
+is quite well paid because it's at the
+ 
+
+ align:start position:0%
+is quite well paid because it's at the
+official minimum wage for and and in
+
+ align:start position:0%
+official minimum wage for and and in
+ 
+
+ align:start position:0%
+official minimum wage for and and in
+some states actually extreme a part of
+
+ align:start position:0%
+some states actually extreme a part of
+ 
+
+ align:start position:0%
+some states actually extreme a part of
+the household sustenance
+
+ align:start position:0%
+the household sustenance
+ 
+
+ align:start position:0%
+the household sustenance
+uh so what they look at here is a
+
+ align:start position:0%
+uh so what they look at here is a
+ 
+
+ align:start position:0%
+uh so what they look at here is a
+program where
+
+ align:start position:0%
+program where
+ 
+
+ align:start position:0%
+program where
+people women the government gave access
+
+ align:start position:0%
+people women the government gave access
+ 
+
+ align:start position:0%
+people women the government gave access
+to bank accounts in randomly selected
+
+ align:start position:0%
+to bank accounts in randomly selected
+ 
+
+ align:start position:0%
+to bank accounts in randomly selected
+GPS
+
+ align:start position:0%
+GPS
+ 
+
+ align:start position:0%
+GPS
+and in one treatment the energy a
+
+ align:start position:0%
+and in one treatment the energy a
+ 
+
+ align:start position:0%
+and in one treatment the energy a
+payment of the woman was directly sent
+
+ align:start position:0%
+payment of the woman was directly sent
+ 
+
+ align:start position:0%
+payment of the woman was directly sent
+to the bank account of the woman
+
+ align:start position:0%
+to the bank account of the woman
+ 
+
+ align:start position:0%
+to the bank account of the woman
+so it doesn't change uh access to job
+
+ align:start position:0%
+so it doesn't change uh access to job
+ 
+
+ align:start position:0%
+so it doesn't change uh access to job
+which in a sense they already have but
+
+ align:start position:0%
+which in a sense they already have but
+ 
+
+ align:start position:0%
+which in a sense they already have but
+it makes sure that they control their
+
+ align:start position:0%
+it makes sure that they control their
+ 
+
+ align:start position:0%
+it makes sure that they control their
+their own job
+
+ align:start position:0%
+their own job
+ 
+
+ align:start position:0%
+their own job
+and what they find in terms of impacts
+
+ align:start position:0%
+and what they find in terms of impacts
+ 
+
+ align:start position:0%
+and what they find in terms of impacts
+is that it increases a labor Supply
+
+ align:start position:0%
+is that it increases a labor Supply
+ 
+
+ align:start position:0%
+is that it increases a labor Supply
+it's a woman who have no access to who
+
+ align:start position:0%
+it's a woman who have no access to who
+ 
+
+ align:start position:0%
+it's a woman who have no access to who
+can now retain their earnings are more
+
+ align:start position:0%
+can now retain their earnings are more
+ 
+
+ align:start position:0%
+can now retain their earnings are more
+likely to to work in the short run
+
+ align:start position:0%
+likely to to work in the short run
+ 
+
+ align:start position:0%
+likely to to work in the short run
+although not in the long run
+
+ align:start position:0%
+although not in the long run
+ 
+
+ align:start position:0%
+although not in the long run
+and so this is just when this is
+
+ align:start position:0%
+and so this is just when this is
+ 
+
+ align:start position:0%
+and so this is just when this is
+happening because in the at some point
+
+ align:start position:0%
+happening because in the at some point
+ 
+
+ align:start position:0%
+happening because in the at some point
+it stopped so this is while it's
+
+ align:start position:0%
+it stopped so this is while it's
+ 
+
+ align:start position:0%
+it stopped so this is while it's
+happening they have they have more
+
+ align:start position:0%
+happening they have they have more
+ 
+
+ align:start position:0%
+happening they have they have more
+access to the to the program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the this is true both in the nraga
+
+ align:start position:0%
+um the this is true both in the nraga
+ 
+
+ align:start position:0%
+um the this is true both in the nraga
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+and in other form of work which is not
+
+ align:start position:0%
+and in other form of work which is not
+ 
+
+ align:start position:0%
+and in other form of work which is not
+directly deposited to this account
+
+ align:start position:0%
+directly deposited to this account
+ 
+
+ align:start position:0%
+directly deposited to this account
+so their interpretation is that women
+
+ align:start position:0%
+so their interpretation is that women
+ 
+
+ align:start position:0%
+so their interpretation is that women
+were women found out about this that now
+
+ align:start position:0%
+were women found out about this that now
+ 
+
+ align:start position:0%
+were women found out about this that now
+they would be able to retain their
+
+ align:start position:0%
+they would be able to retain their
+ 
+
+ align:start position:0%
+they would be able to retain their
+earnings they started working that
+
+ align:start position:0%
+earnings they started working that
+ 
+
+ align:start position:0%
+earnings they started working that
+increases their mining power and gave
+
+ align:start position:0%
+increases their mining power and gave
+ 
+
+ align:start position:0%
+increases their mining power and gave
+them the possibility to work even more
+
+ align:start position:0%
+them the possibility to work even more
+ 
+
+ align:start position:0%
+them the possibility to work even more
+and so that's why you go you have an
+
+ align:start position:0%
+and so that's why you go you have an
+ 
+
+ align:start position:0%
+and so that's why you go you have an
+increase in labor Supply in energy and
+
+ align:start position:0%
+increase in labor Supply in energy and
+ 
+
+ align:start position:0%
+increase in labor Supply in energy and
+in a non-linear energy program as well
+
+ align:start position:0%
+in a non-linear energy program as well
+ 
+
+ align:start position:0%
+in a non-linear energy program as well
+and they show some evidence for that
+
+ align:start position:0%
+and they show some evidence for that
+ 
+
+ align:start position:0%
+and they show some evidence for that
+which is that um
+
+ align:start position:0%
+which is that um
+ 
+
+ align:start position:0%
+which is that um
+if you look at other dimension of women
+
+ align:start position:0%
+if you look at other dimension of women
+ 
+
+ align:start position:0%
+if you look at other dimension of women
+empowerment like for example Mobility
+
+ align:start position:0%
+empowerment like for example Mobility
+ 
+
+ align:start position:0%
+empowerment like for example Mobility
+Etc among the women who were the most
+
+ align:start position:0%
+Etc among the women who were the most
+ 
+
+ align:start position:0%
+Etc among the women who were the most
+constraints among the women who were the
+
+ align:start position:0%
+constraints among the women who were the
+ 
+
+ align:start position:0%
+constraints among the women who were the
+least empowered at the beginning
+
+ align:start position:0%
+least empowered at the beginning
+ 
+
+ align:start position:0%
+least empowered at the beginning
+you find some evidence that other
+
+ align:start position:0%
+you find some evidence that other
+ 
+
+ align:start position:0%
+you find some evidence that other
+measures of empowerment like how much
+
+ align:start position:0%
+measures of empowerment like how much
+ 
+
+ align:start position:0%
+measures of empowerment like how much
+they they can purchase they have a say
+
+ align:start position:0%
+they they can purchase they have a say
+ 
+
+ align:start position:0%
+they they can purchase they have a say
+on decision making uh they they can move
+
+ align:start position:0%
+on decision making uh they they can move
+ 
+
+ align:start position:0%
+on decision making uh they they can move
+to visit their parents or stuff like
+
+ align:start position:0%
+to visit their parents or stuff like
+ 
+
+ align:start position:0%
+to visit their parents or stuff like
+that can and then this is an aggregator
+
+ align:start position:0%
+that can and then this is an aggregator
+ 
+
+ align:start position:0%
+that can and then this is an aggregator
+full of the measures that they have is
+
+ align:start position:0%
+full of the measures that they have is
+ 
+
+ align:start position:0%
+full of the measures that they have is
+affected by the program
+
+ align:start position:0%
+affected by the program
+ 
+
+ align:start position:0%
+affected by the program
+so this is the idea that indeed the the
+
+ align:start position:0%
+so this is the idea that indeed the the
+ 
+
+ align:start position:0%
+so this is the idea that indeed the the
+bargaining power might be an impact of
+
+ align:start position:0%
+bargaining power might be an impact of
+ 
+
+ align:start position:0%
+bargaining power might be an impact of
+how much you're working so here is like
+
+ align:start position:0%
+how much you're working so here is like
+ 
+
+ align:start position:0%
+how much you're working so here is like
+you're walking
+
+ align:start position:0%
+you're walking
+ 
+
+ align:start position:0%
+you're walking
+you can you keep more of your earnings
+
+ align:start position:0%
+you can you keep more of your earnings
+ 
+
+ align:start position:0%
+you can you keep more of your earnings
+therefore and therefore you work more
+
+ align:start position:0%
+therefore and therefore you work more
+ 
+
+ align:start position:0%
+therefore and therefore you work more
+the two combined gives you more
+
+ align:start position:0%
+the two combined gives you more
+ 
+
+ align:start position:0%
+the two combined gives you more
+bargaining power you work even more and
+
+ align:start position:0%
+bargaining power you work even more and
+ 
+
+ align:start position:0%
+bargaining power you work even more and
+that also increases you know your your
+
+ align:start position:0%
+that also increases you know your your
+ 
+
+ align:start position:0%
+that also increases you know your your
+uh your decision power in other sphere
+
+ align:start position:0%
+uh your decision power in other sphere
+ 
+
+ align:start position:0%
+uh your decision power in other sphere
+of the family
+
+ align:start position:0%
+of the family
+ 
+
+ align:start position:0%
+of the family
+so that's the optimistic take
+
+ align:start position:0%
+so that's the optimistic take
+ 
+
+ align:start position:0%
+so that's the optimistic take
+uh this is the the
+
+ align:start position:0%
+uh this is the the
+ 
+
+ align:start position:0%
+uh this is the the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the Norms of uh uh you know how the
+
+ align:start position:0%
+the Norms of uh uh you know how the
+ 
+
+ align:start position:0%
+the Norms of uh uh you know how the
+Norms uh you know male male and female
+
+ align:start position:0%
+Norms uh you know male male and female
+ 
+
+ align:start position:0%
+Norms uh you know male male and female
+reports of various things that are
+
+ align:start position:0%
+reports of various things that are
+ 
+
+ align:start position:0%
+reports of various things that are
+affected
+
+ align:start position:0%
+affected
+ 
+
+ align:start position:0%
+affected
+uh and again showing some impact on on
+
+ align:start position:0%
+uh and again showing some impact on on
+ 
+
+ align:start position:0%
+uh and again showing some impact on on
+the social Norm so that's the optimistic
+
+ align:start position:0%
+the social Norm so that's the optimistic
+ 
+
+ align:start position:0%
+the social Norm so that's the optimistic
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+uh the the less optimistic take is from
+
+ align:start position:0%
+uh the the less optimistic take is from
+ 
+
+ align:start position:0%
+uh the the less optimistic take is from
+uh some people by Maddie which looks at
+
+ align:start position:0%
+uh some people by Maddie which looks at
+ 
+
+ align:start position:0%
+uh some people by Maddie which looks at
+the long run effect of the access to
+
+ align:start position:0%
+the long run effect of the access to
+ 
+
+ align:start position:0%
+the long run effect of the access to
+this employment opportunity due to the
+
+ align:start position:0%
+this employment opportunity due to the
+ 
+
+ align:start position:0%
+this employment opportunity due to the
+exactly exogenously due to the promotion
+
+ align:start position:0%
+exactly exogenously due to the promotion
+ 
+
+ align:start position:0%
+exactly exogenously due to the promotion
+sample
+
+ align:start position:0%
+sample
+ 
+
+ align:start position:0%
+sample
+so now forgetting the the generalized
+
+ align:start position:0%
+so now forgetting the the generalized
+ 
+
+ align:start position:0%
+so now forgetting the the generalized
+self-efficient efficacy which itself
+
+ align:start position:0%
+self-efficient efficacy which itself
+ 
+
+ align:start position:0%
+self-efficient efficacy which itself
+would have changed bargaining power
+
+ align:start position:0%
+would have changed bargaining power
+ 
+
+ align:start position:0%
+would have changed bargaining power
+um and in fact she does find some impact
+
+ align:start position:0%
+um and in fact she does find some impact
+ 
+
+ align:start position:0%
+um and in fact she does find some impact
+on savings and some impact on own
+
+ align:start position:0%
+on savings and some impact on own
+ 
+
+ align:start position:0%
+on savings and some impact on own
+decisions
+
+ align:start position:0%
+decisions
+ 
+
+ align:start position:0%
+decisions
+the promotion gave access to women to
+
+ align:start position:0%
+the promotion gave access to women to
+ 
+
+ align:start position:0%
+the promotion gave access to women to
+this outside employment opportunity so a
+
+ align:start position:0%
+this outside employment opportunity so a
+ 
+
+ align:start position:0%
+this outside employment opportunity so a
+natural question is whether that there
+
+ align:start position:0%
+natural question is whether that there
+ 
+
+ align:start position:0%
+natural question is whether that there
+is an impact of that over time of this
+
+ align:start position:0%
+is an impact of that over time of this
+ 
+
+ align:start position:0%
+is an impact of that over time of this
+new work that they have on their uh on
+
+ align:start position:0%
+new work that they have on their uh on
+ 
+
+ align:start position:0%
+new work that they have on their uh on
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+decision making so she follows decision
+
+ align:start position:0%
+decision making so she follows decision
+ 
+
+ align:start position:0%
+decision making so she follows decision
+making in households we are given where
+
+ align:start position:0%
+making in households we are given where
+ 
+
+ align:start position:0%
+making in households we are given where
+husbands were given the promotion
+
+ align:start position:0%
+husbands were given the promotion
+ 
+
+ align:start position:0%
+husbands were given the promotion
+compared to the control group
+
+ align:start position:0%
+compared to the control group
+ 
+
+ align:start position:0%
+compared to the control group
+forgetting the GSE
+
+ align:start position:0%
+forgetting the GSE
+ 
+
+ align:start position:0%
+forgetting the GSE
+and what she finds is that in the short
+
+ align:start position:0%
+and what she finds is that in the short
+ 
+
+ align:start position:0%
+and what she finds is that in the short
+run women spend more time working but
+
+ align:start position:0%
+run women spend more time working but
+ 
+
+ align:start position:0%
+run women spend more time working but
+just as much time on doing chores so
+
+ align:start position:0%
+just as much time on doing chores so
+ 
+
+ align:start position:0%
+just as much time on doing chores so
+that they in fact have less leisure
+
+ align:start position:0%
+that they in fact have less leisure
+ 
+
+ align:start position:0%
+that they in fact have less leisure
+at four months they think that they have
+
+ align:start position:0%
+at four months they think that they have
+ 
+
+ align:start position:0%
+at four months they think that they have
+more decision making power but their
+
+ align:start position:0%
+more decision making power but their
+ 
+
+ align:start position:0%
+more decision making power but their
+family does not
+
+ align:start position:0%
+family does not
+ 
+
+ align:start position:0%
+family does not
+and then quickly they just drop out of
+
+ align:start position:0%
+and then quickly they just drop out of
+ 
+
+ align:start position:0%
+and then quickly they just drop out of
+the job
+
+ align:start position:0%
+the job
+ 
+
+ align:start position:0%
+the job
+because they have uh but it is there
+
+ align:start position:0%
+because they have uh but it is there
+ 
+
+ align:start position:0%
+because they have uh but it is there
+because they it's incompatible with
+
+ align:start position:0%
+because they it's incompatible with
+ 
+
+ align:start position:0%
+because they it's incompatible with
+their other responsibilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that shows that
+
+ align:start position:0%
+so that shows that
+ 
+
+ align:start position:0%
+so that shows that
+you know this this this expected effect
+
+ align:start position:0%
+you know this this this expected effect
+ 
+
+ align:start position:0%
+you know this this this expected effect
+on this hoped for effect on of working
+
+ align:start position:0%
+on this hoped for effect on of working
+ 
+
+ align:start position:0%
+on this hoped for effect on of working
+on increasing your bargaining power it's
+
+ align:start position:0%
+on increasing your bargaining power it's
+ 
+
+ align:start position:0%
+on increasing your bargaining power it's
+not doesn't always happen it didn't
+
+ align:start position:0%
+not doesn't always happen it didn't
+ 
+
+ align:start position:0%
+not doesn't always happen it didn't
+happen in our people
+
+ align:start position:0%
+happen in our people
+ 
+
+ align:start position:0%
+happen in our people
+so interestingly they dropped out uh
+
+ align:start position:0%
+so interestingly they dropped out uh
+ 
+
+ align:start position:0%
+so interestingly they dropped out uh
+because that's incompatible with their
+
+ align:start position:0%
+because that's incompatible with their
+ 
+
+ align:start position:0%
+because that's incompatible with their
+responsibility that linked to what we
+
+ align:start position:0%
+responsibility that linked to what we
+ 
+
+ align:start position:0%
+responsibility that linked to what we
+were seeing at the very beginning of the
+
+ align:start position:0%
+were seeing at the very beginning of the
+ 
+
+ align:start position:0%
+were seeing at the very beginning of the
+of the lecture which is a woman uh often
+
+ align:start position:0%
+of the lecture which is a woman uh often
+ 
+
+ align:start position:0%
+of the lecture which is a woman uh often
+reported they would like to work but
+
+ align:start position:0%
+reported they would like to work but
+ 
+
+ align:start position:0%
+reported they would like to work but
+they cannot because their husbands don't
+
+ align:start position:0%
+they cannot because their husbands don't
+ 
+
+ align:start position:0%
+they cannot because their husbands don't
+want or they cannot because it's
+
+ align:start position:0%
+want or they cannot because it's
+ 
+
+ align:start position:0%
+want or they cannot because it's
+incompatible with their child care
+
+ align:start position:0%
+incompatible with their child care
+ 
+
+ align:start position:0%
+incompatible with their child care
+responsibility and they would like a
+
+ align:start position:0%
+responsibility and they would like a
+ 
+
+ align:start position:0%
+responsibility and they would like a
+part-time job
+
+ align:start position:0%
+part-time job
+ 
+
+ align:start position:0%
+part-time job
+so that's relates to this Claudia golden
+
+ align:start position:0%
+so that's relates to this Claudia golden
+ 
+
+ align:start position:0%
+so that's relates to this Claudia golden
+idea that the problem is is mainly that
+
+ align:start position:0%
+idea that the problem is is mainly that
+ 
+
+ align:start position:0%
+idea that the problem is is mainly that
+the job don't have to be all be
+
+ align:start position:0%
+the job don't have to be all be
+ 
+
+ align:start position:0%
+the job don't have to be all be
+structured full time
+
+ align:start position:0%
+structured full time
+ 
+
+ align:start position:0%
+structured full time
+that's the that's the
+
+ align:start position:0%
+that's the that's the
+ 
+
+ align:start position:0%
+that's the that's the
+so perhaps uh the the strongest Norm is
+
+ align:start position:0%
+so perhaps uh the the strongest Norm is
+ 
+
+ align:start position:0%
+so perhaps uh the the strongest Norm is
+that women must take care social Norm
+
+ align:start position:0%
+that women must take care social Norm
+ 
+
+ align:start position:0%
+that women must take care social Norm
+that hold women back that's kind of you
+
+ align:start position:0%
+that hold women back that's kind of you
+ 
+
+ align:start position:0%
+that hold women back that's kind of you
+will find everywhere and sort of help
+
+ align:start position:0%
+will find everywhere and sort of help
+ 
+
+ align:start position:0%
+will find everywhere and sort of help
+staying to a lot of these things that it
+
+ align:start position:0%
+staying to a lot of these things that it
+ 
+
+ align:start position:0%
+staying to a lot of these things that it
+is women who must take care of children
+
+ align:start position:0%
+is women who must take care of children
+ 
+
+ align:start position:0%
+is women who must take care of children
+we saw it in Cote d'Ivoire where it's
+
+ align:start position:0%
+we saw it in Cote d'Ivoire where it's
+ 
+
+ align:start position:0%
+we saw it in Cote d'Ivoire where it's
+women who you know when woman income
+
+ align:start position:0%
+women who you know when woman income
+ 
+
+ align:start position:0%
+women who you know when woman income
+goes up there is more food on the table
+
+ align:start position:0%
+goes up there is more food on the table
+ 
+
+ align:start position:0%
+goes up there is more food on the table
+which seems a bit absurd from the
+
+ align:start position:0%
+which seems a bit absurd from the
+ 
+
+ align:start position:0%
+which seems a bit absurd from the
+efficiency of the household point of
+
+ align:start position:0%
+efficiency of the household point of
+ 
+
+ align:start position:0%
+efficiency of the household point of
+view but is related to this idea that
+
+ align:start position:0%
+view but is related to this idea that
+ 
+
+ align:start position:0%
+view but is related to this idea that
+it's women who have to feed kids
+
+ align:start position:0%
+it's women who have to feed kids
+ 
+
+ align:start position:0%
+it's women who have to feed kids
+and this might explain another stylus
+
+ align:start position:0%
+and this might explain another stylus
+ 
+
+ align:start position:0%
+and this might explain another stylus
+fact which was first established by the
+
+ align:start position:0%
+fact which was first established by the
+ 
+
+ align:start position:0%
+fact which was first established by the
+melee McKenzie and Woodruff
+
+ align:start position:0%
+melee McKenzie and Woodruff
+ 
+
+ align:start position:0%
+melee McKenzie and Woodruff
+they show that when you give the same
+
+ align:start position:0%
+they show that when you give the same
+ 
+
+ align:start position:0%
+they show that when you give the same
+sized Grant randomly assigned to female
+
+ align:start position:0%
+sized Grant randomly assigned to female
+ 
+
+ align:start position:0%
+sized Grant randomly assigned to female
+business
+
+ align:start position:0%
+business
+ 
+
+ align:start position:0%
+business
+there's no impact on the profitability
+
+ align:start position:0%
+there's no impact on the profitability
+ 
+
+ align:start position:0%
+there's no impact on the profitability
+of female business
+
+ align:start position:0%
+of female business
+ 
+
+ align:start position:0%
+of female business
+the same Grant to male business and
+
+ align:start position:0%
+the same Grant to male business and
+ 
+
+ align:start position:0%
+the same Grant to male business and
+there are large effects
+
+ align:start position:0%
+there are large effects
+ 
+
+ align:start position:0%
+there are large effects
+so basically it seems that the
+
+ align:start position:0%
+so basically it seems that the
+ 
+
+ align:start position:0%
+so basically it seems that the
+profitability the marginal impact on
+
+ align:start position:0%
+profitability the marginal impact on
+ 
+
+ align:start position:0%
+profitability the marginal impact on
+money on female businesses zero one is
+
+ align:start position:0%
+money on female businesses zero one is
+ 
+
+ align:start position:0%
+money on female businesses zero one is
+very high on male businesses so this
+
+ align:start position:0%
+very high on male businesses so this
+ 
+
+ align:start position:0%
+very high on male businesses so this
+kind of this fact of maybe female
+
+ align:start position:0%
+kind of this fact of maybe female
+ 
+
+ align:start position:0%
+kind of this fact of maybe female
+businesses are less profitable than male
+
+ align:start position:0%
+businesses are less profitable than male
+ 
+
+ align:start position:0%
+businesses are less profitable than male
+male businesses
+
+ align:start position:0%
+male businesses
+ 
+
+ align:start position:0%
+male businesses
+so why is that and I'll finish on that
+
+ align:start position:0%
+so why is that and I'll finish on that
+ 
+
+ align:start position:0%
+so why is that and I'll finish on that
+I'm mindful of the time
+
+ align:start position:0%
+I'm mindful of the time
+ 
+
+ align:start position:0%
+I'm mindful of the time
+another paper by rohini Pandey Natalia
+
+ align:start position:0%
+another paper by rohini Pandey Natalia
+ 
+
+ align:start position:0%
+another paper by rohini Pandey Natalia
+ringgoldenerica field this is Trio plus
+
+ align:start position:0%
+ringgoldenerica field this is Trio plus
+ 
+
+ align:start position:0%
+ringgoldenerica field this is Trio plus
+another quarter
+
+ align:start position:0%
+another quarter
+ 
+
+ align:start position:0%
+another quarter
+argue by revisiting the same data plus
+
+ align:start position:0%
+argue by revisiting the same data plus
+ 
+
+ align:start position:0%
+argue by revisiting the same data plus
+other data that they bring to the table
+
+ align:start position:0%
+other data that they bring to the table
+ 
+
+ align:start position:0%
+other data that they bring to the table
+that it's not the business female
+
+ align:start position:0%
+that it's not the business female
+ 
+
+ align:start position:0%
+that it's not the business female
+business that is in productive is that
+
+ align:start position:0%
+business that is in productive is that
+ 
+
+ align:start position:0%
+business that is in productive is that
+the money is never invested in the
+
+ align:start position:0%
+the money is never invested in the
+ 
+
+ align:start position:0%
+the money is never invested in the
+female business
+
+ align:start position:0%
+female business
+ 
+
+ align:start position:0%
+female business
+but in fact if you looked on at a single
+
+ align:start position:0%
+but in fact if you looked on at a single
+ 
+
+ align:start position:0%
+but in fact if you looked on at a single
+woman
+
+ align:start position:0%
+woman
+ 
+
+ align:start position:0%
+woman
+and you give them fellowship if it's
+
+ align:start position:0%
+and you give them fellowship if it's
+ 
+
+ align:start position:0%
+and you give them fellowship if it's
+called um money grant money the effect
+
+ align:start position:0%
+called um money grant money the effect
+ 
+
+ align:start position:0%
+called um money grant money the effect
+would be the same in fact they don't
+
+ align:start position:0%
+would be the same in fact they don't
+ 
+
+ align:start position:0%
+would be the same in fact they don't
+really have very many single women to
+
+ align:start position:0%
+really have very many single women to
+ 
+
+ align:start position:0%
+really have very many single women to
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+but what happens to show is that the the
+
+ align:start position:0%
+but what happens to show is that the the
+ 
+
+ align:start position:0%
+but what happens to show is that the the
+the family income increases just as much
+
+ align:start position:0%
+the family income increases just as much
+ 
+
+ align:start position:0%
+the family income increases just as much
+if you give the money to the female
+
+ align:start position:0%
+if you give the money to the female
+ 
+
+ align:start position:0%
+if you give the money to the female
+business versus money to the male
+
+ align:start position:0%
+business versus money to the male
+ 
+
+ align:start position:0%
+business versus money to the male
+business it's just that
+
+ align:start position:0%
+business it's just that
+ 
+
+ align:start position:0%
+business it's just that
+when you give money to the female
+
+ align:start position:0%
+when you give money to the female
+ 
+
+ align:start position:0%
+when you give money to the female
+business it's invested in the mail
+
+ align:start position:0%
+business it's invested in the mail
+ 
+
+ align:start position:0%
+business it's invested in the mail
+business
+
+ align:start position:0%
+business
+ 
+
+ align:start position:0%
+business
+so it looks like
+
+ align:start position:0%
+so it looks like
+ 
+
+ align:start position:0%
+so it looks like
+the female business is not productive
+
+ align:start position:0%
+the female business is not productive
+ 
+
+ align:start position:0%
+the female business is not productive
+but it's because the money was never
+
+ align:start position:0%
+but it's because the money was never
+ 
+
+ align:start position:0%
+but it's because the money was never
+invested there in the first place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a paper where and whether they're on
+
+ align:start position:0%
+has a paper where and whether they're on
+ 
+
+ align:start position:0%
+has a paper where and whether they're on
+an experiment with vegetable vendors
+
+ align:start position:0%
+an experiment with vegetable vendors
+ 
+
+ align:start position:0%
+an experiment with vegetable vendors
+uh also in India and they show that if
+
+ align:start position:0%
+uh also in India and they show that if
+ 
+
+ align:start position:0%
+uh also in India and they show that if
+you give them the same input so they
+
+ align:start position:0%
+you give them the same input so they
+ 
+
+ align:start position:0%
+you give them the same input so they
+they replicate that fact that women own
+
+ align:start position:0%
+they replicate that fact that women own
+ 
+
+ align:start position:0%
+they replicate that fact that women own
+vegetable stores appear to be less
+
+ align:start position:0%
+vegetable stores appear to be less
+ 
+
+ align:start position:0%
+vegetable stores appear to be less
+productive than female than male owned
+
+ align:start position:0%
+productive than female than male owned
+ 
+
+ align:start position:0%
+productive than female than male owned
+vegetable stools
+
+ align:start position:0%
+vegetable stools
+ 
+
+ align:start position:0%
+vegetable stools
+but then what they do is this fun
+
+ align:start position:0%
+but then what they do is this fun
+ 
+
+ align:start position:0%
+but then what they do is this fun
+experiment where they give
+
+ align:start position:0%
+experiment where they give
+ 
+
+ align:start position:0%
+experiment where they give
+Traders they give them vegetables to
+
+ align:start position:0%
+Traders they give them vegetables to
+ 
+
+ align:start position:0%
+Traders they give them vegetables to
+sell
+
+ align:start position:0%
+sell
+ 
+
+ align:start position:0%
+sell
+and they observe they they sell for one
+
+ align:start position:0%
+and they observe they they sell for one
+ 
+
+ align:start position:0%
+and they observe they they sell for one
+day and
+
+ align:start position:0%
+day and
+ 
+
+ align:start position:0%
+day and
+after several days and then they
+
+ align:start position:0%
+after several days and then they
+ 
+
+ align:start position:0%
+after several days and then they
+calculate how much money they're making
+
+ align:start position:0%
+calculate how much money they're making
+ 
+
+ align:start position:0%
+calculate how much money they're making
+and they show that starting with the
+
+ align:start position:0%
+and they show that starting with the
+ 
+
+ align:start position:0%
+and they show that starting with the
+same endowment women make the same
+
+ align:start position:0%
+same endowment women make the same
+ 
+
+ align:start position:0%
+same endowment women make the same
+amount of money as men
+
+ align:start position:0%
+amount of money as men
+ 
+
+ align:start position:0%
+amount of money as men
+so it's not that women are less good
+
+ align:start position:0%
+so it's not that women are less good
+ 
+
+ align:start position:0%
+so it's not that women are less good
+Trader or it's not that customers
+
+ align:start position:0%
+Trader or it's not that customers
+ 
+
+ align:start position:0%
+Trader or it's not that customers
+discriminate against women it's just
+
+ align:start position:0%
+discriminate against women it's just
+ 
+
+ align:start position:0%
+discriminate against women it's just
+that they probably start with a much
+
+ align:start position:0%
+that they probably start with a much
+ 
+
+ align:start position:0%
+that they probably start with a much
+lower endowment and that's very
+
+ align:start position:0%
+lower endowment and that's very
+ 
+
+ align:start position:0%
+lower endowment and that's very
+consistent with this idea of in the
+
+ align:start position:0%
+consistent with this idea of in the
+ 
+
+ align:start position:0%
+consistent with this idea of in the
+wrinkle uh Pandey fin paper that's all
+
+ align:start position:0%
+wrinkle uh Pandey fin paper that's all
+ 
+
+ align:start position:0%
+wrinkle uh Pandey fin paper that's all
+the the money was not productive because
+
+ align:start position:0%
+the the money was not productive because
+ 
+
+ align:start position:0%
+the the money was not productive because
+it was never invested in the first place
+
+ align:start position:0%
+it was never invested in the first place
+ 
+
+ align:start position:0%
+it was never invested in the first place
+so then the question is why is it that
+
+ align:start position:0%
+so then the question is why is it that
+ 
+
+ align:start position:0%
+so then the question is why is it that
+so the lower investment in the female
+
+ align:start position:0%
+so the lower investment in the female
+ 
+
+ align:start position:0%
+so the lower investment in the female
+business is not in turn endogenously
+
+ align:start position:0%
+business is not in turn endogenously
+ 
+
+ align:start position:0%
+business is not in turn endogenously
+relating to the fact that the female
+
+ align:start position:0%
+relating to the fact that the female
+ 
+
+ align:start position:0%
+relating to the fact that the female
+business isn't productive because you
+
+ align:start position:0%
+business isn't productive because you
+ 
+
+ align:start position:0%
+business isn't productive because you
+could say of course you don't invest in
+
+ align:start position:0%
+could say of course you don't invest in
+ 
+
+ align:start position:0%
+could say of course you don't invest in
+women female business and productive
+
+ align:start position:0%
+women female business and productive
+ 
+
+ align:start position:0%
+women female business and productive
+that's why you don't invest
+
+ align:start position:0%
+that's why you don't invest
+ 
+
+ align:start position:0%
+that's why you don't invest
+paper suggests that's not that because
+
+ align:start position:0%
+paper suggests that's not that because
+ 
+
+ align:start position:0%
+paper suggests that's not that because
+if we invest the same we get the same
+
+ align:start position:0%
+if we invest the same we get the same
+ 
+
+ align:start position:0%
+if we invest the same we get the same
+uh so maybe another reason why people
+
+ align:start position:0%
+uh so maybe another reason why people
+ 
+
+ align:start position:0%
+uh so maybe another reason why people
+are not investing in the in the female
+
+ align:start position:0%
+are not investing in the in the female
+ 
+
+ align:start position:0%
+are not investing in the in the female
+businesses that the female business is
+
+ align:start position:0%
+businesses that the female business is
+ 
+
+ align:start position:0%
+businesses that the female business is
+never made to make much money in the
+
+ align:start position:0%
+never made to make much money in the
+ 
+
+ align:start position:0%
+never made to make much money in the
+first place it meant to kind of be
+
+ align:start position:0%
+first place it meant to kind of be
+ 
+
+ align:start position:0%
+first place it meant to kind of be
+something that women can do while
+
+ align:start position:0%
+something that women can do while
+ 
+
+ align:start position:0%
+something that women can do while
+minding the kids near them
+
+ align:start position:0%
+minding the kids near them
+ 
+
+ align:start position:0%
+minding the kids near them
+and it's something so therefore you
+
+ align:start position:0%
+and it's something so therefore you
+ 
+
+ align:start position:0%
+and it's something so therefore you
+can't you don't you can't really grow it
+
+ align:start position:0%
+can't you don't you can't really grow it
+ 
+
+ align:start position:0%
+can't you don't you can't really grow it
+because then you would be able to take
+
+ align:start position:0%
+because then you would be able to take
+ 
+
+ align:start position:0%
+because then you would be able to take
+care of the kids and the same constraint
+
+ align:start position:0%
+care of the kids and the same constraint
+ 
+
+ align:start position:0%
+care of the kids and the same constraint
+is precisely what makes it difficult for
+
+ align:start position:0%
+is precisely what makes it difficult for
+ 
+
+ align:start position:0%
+is precisely what makes it difficult for
+them to get or keep jobs and also the
+
+ align:start position:0%
+them to get or keep jobs and also the
+ 
+
+ align:start position:0%
+them to get or keep jobs and also the
+reason why promotions are constrained so
+
+ align:start position:0%
+reason why promotions are constrained so
+ 
+
+ align:start position:0%
+reason why promotions are constrained so
+there is another paper by Woodruff and
+
+ align:start position:0%
+there is another paper by Woodruff and
+ 
+
+ align:start position:0%
+there is another paper by Woodruff and
+others in Bangladesh showing that even
+
+ align:start position:0%
+others in Bangladesh showing that even
+ 
+
+ align:start position:0%
+others in Bangladesh showing that even
+in factories the perfectly good
+
+ align:start position:0%
+in factories the perfectly good
+ 
+
+ align:start position:0%
+in factories the perfectly good
+tailors are not promoted at the same
+
+ align:start position:0%
+tailors are not promoted at the same
+ 
+
+ align:start position:0%
+tailors are not promoted at the same
+rate as men even though if they are
+
+ align:start position:0%
+rate as men even though if they are
+ 
+
+ align:start position:0%
+rate as men even though if they are
+promoted they are just as productive
+
+ align:start position:0%
+promoted they are just as productive
+ 
+
+ align:start position:0%
+promoted they are just as productive
+and there are many reasons for that but
+
+ align:start position:0%
+and there are many reasons for that but
+ 
+
+ align:start position:0%
+and there are many reasons for that but
+one of the reason could be that there is
+
+ align:start position:0%
+one of the reason could be that there is
+ 
+
+ align:start position:0%
+one of the reason could be that there is
+an anticipation that they will not stay
+
+ align:start position:0%
+an anticipation that they will not stay
+ 
+
+ align:start position:0%
+an anticipation that they will not stay
+there is in fact much larger turnover
+
+ align:start position:0%
+there is in fact much larger turnover
+ 
+
+ align:start position:0%
+there is in fact much larger turnover
+for women than for men as a paper on
+
+ align:start position:0%
+for women than for men as a paper on
+ 
+
+ align:start position:0%
+for women than for men as a paper on
+that also for women Enterprises and that
+
+ align:start position:0%
+that also for women Enterprises and that
+ 
+
+ align:start position:0%
+that also for women Enterprises and that
+may all be related to this child care
+
+ align:start position:0%
+may all be related to this child care
+ 
+
+ align:start position:0%
+may all be related to this child care
+Child Care Norm
+
+ align:start position:0%
+Child Care Norm
+ 
+
+ align:start position:0%
+Child Care Norm
+so let me stop there which uh I think is
+
+ align:start position:0%
+so let me stop there which uh I think is
+ 
+
+ align:start position:0%
+so let me stop there which uh I think is
+a good place to step there is a very
+
+ align:start position:0%
+a good place to step there is a very
+ 
+
+ align:start position:0%
+a good place to step there is a very
+active agenda on on gender liberal
+
+ align:start position:0%
+active agenda on on gender liberal
+ 
+
+ align:start position:0%
+active agenda on on gender liberal
+Market just catch the surface but it's a
+
+ align:start position:0%
+Market just catch the surface but it's a
+ 
+
+ align:start position:0%
+Market just catch the surface but it's a
+good place to to do because it kind of
+
+ align:start position:0%
+good place to to do because it kind of
+ 
+
+ align:start position:0%
+good place to to do because it kind of
+has you have everything a little bit
+
+ align:start position:0%
+has you have everything a little bit
+ 
+
+ align:start position:0%
+has you have everything a little bit
+coming there the the Norms the uh the
+
+ align:start position:0%
+coming there the the Norms the uh the
+ 
+
+ align:start position:0%
+coming there the the Norms the uh the
+family situation Etc
\ No newline at end of file
diff --git a/LzGIpm5UFCg.txt b/LzGIpm5UFCg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..feb0c74adfa98c8266f13792aec2173dd0791f67
--- /dev/null
+++ b/LzGIpm5UFCg.txt
@@ -0,0 +1,15043 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+opencourseware under a Creative Commons
+
+ align:start position:0%
+opencourseware under a Creative Commons
+ 
+
+ align:start position:0%
+opencourseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the topic for lecture for the next
+
+ align:start position:0%
+the the topic for lecture for the next
+ 
+
+ align:start position:0%
+the the topic for lecture for the next
+couple of days
+
+ align:start position:0%
+couple of days
+ 
+
+ align:start position:0%
+couple of days
+um is going to be
+
+ align:start position:0%
+um is going to be
+ 
+
+ align:start position:0%
+um is going to be
+romantic love or or mating behavior or
+
+ align:start position:0%
+romantic love or or mating behavior or
+ 
+
+ align:start position:0%
+romantic love or or mating behavior or
+the interaction thereof or something
+
+ align:start position:0%
+the interaction thereof or something
+ 
+
+ align:start position:0%
+the interaction thereof or something
+like that and I just learned that the
+
+ align:start position:0%
+like that and I just learned that the
+ 
+
+ align:start position:0%
+like that and I just learned that the
+Shakespeare Ensemble is doing uh doing
+
+ align:start position:0%
+Shakespeare Ensemble is doing uh doing
+ 
+
+ align:start position:0%
+Shakespeare Ensemble is doing uh doing
+Taming of the Shrew uh when
+
+ align:start position:0%
+Taming of the Shrew uh when
+ 
+
+ align:start position:0%
+Taming of the Shrew uh when
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh tonight tomorrow night and Saturday
+
+ align:start position:0%
+uh tonight tomorrow night and Saturday
+ 
+
+ align:start position:0%
+uh tonight tomorrow night and Saturday
+at eight o'clock where little crazy
+
+ align:start position:0%
+at eight o'clock where little crazy
+ 
+
+ align:start position:0%
+at eight o'clock where little crazy
+theater we should probably assign it you
+
+ align:start position:0%
+theater we should probably assign it you
+ 
+
+ align:start position:0%
+theater we should probably assign it you
+know like as homework or something like
+
+ align:start position:0%
+know like as homework or something like
+ 
+
+ align:start position:0%
+know like as homework or something like
+that but uh but you can go after today's
+
+ align:start position:0%
+that but uh but you can go after today's
+ 
+
+ align:start position:0%
+that but uh but you can go after today's
+lecture you can go and try to apply
+
+ align:start position:0%
+lecture you can go and try to apply
+ 
+
+ align:start position:0%
+lecture you can go and try to apply
+evolutionary psychological theory to
+
+ align:start position:0%
+evolutionary psychological theory to
+ 
+
+ align:start position:0%
+evolutionary psychological theory to
+Taming of the Shrew if you like and you
+
+ align:start position:0%
+Taming of the Shrew if you like and you
+ 
+
+ align:start position:0%
+Taming of the Shrew if you like and you
+can tell Bianca how you liked it
+
+ align:start position:0%
+can tell Bianca how you liked it
+ 
+
+ align:start position:0%
+can tell Bianca how you liked it
+um all right
+
+ align:start position:0%
+um all right
+ 
+
+ align:start position:0%
+um all right
+enough Shakespeare Shakespeare shows up
+
+ align:start position:0%
+enough Shakespeare Shakespeare shows up
+ 
+
+ align:start position:0%
+enough Shakespeare Shakespeare shows up
+again maybe later today
+
+ align:start position:0%
+again maybe later today
+ 
+
+ align:start position:0%
+again maybe later today
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh let me let me tell you
+
+ align:start position:0%
+uh let me let me tell you
+ 
+
+ align:start position:0%
+uh let me let me tell you
+a um
+
+ align:start position:0%
+a um
+ 
+
+ align:start position:0%
+a um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+let me tell you about Chris and Terry
+
+ align:start position:0%
+let me tell you about Chris and Terry
+ 
+
+ align:start position:0%
+let me tell you about Chris and Terry
+here who are having an argument
+
+ align:start position:0%
+here who are having an argument
+ 
+
+ align:start position:0%
+here who are having an argument
+um I realize this is sort of a working
+
+ align:start position:0%
+um I realize this is sort of a working
+ 
+
+ align:start position:0%
+um I realize this is sort of a working
+memory exercise too so you have to pay
+
+ align:start position:0%
+memory exercise too so you have to pay
+ 
+
+ align:start position:0%
+memory exercise too so you have to pay
+attention uh to the particular details
+
+ align:start position:0%
+attention uh to the particular details
+ 
+
+ align:start position:0%
+attention uh to the particular details
+here so Chris and Terry are having an
+
+ align:start position:0%
+here so Chris and Terry are having an
+ 
+
+ align:start position:0%
+here so Chris and Terry are having an
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+um they they've been going together for
+
+ align:start position:0%
+um they they've been going together for
+ 
+
+ align:start position:0%
+um they they've been going together for
+about a year
+
+ align:start position:0%
+about a year
+ 
+
+ align:start position:0%
+about a year
+um they don't live together they do
+
+ align:start position:0%
+um they don't live together they do
+ 
+
+ align:start position:0%
+um they don't live together they do
+sleep together
+
+ align:start position:0%
+sleep together
+ 
+
+ align:start position:0%
+sleep together
+Chris accuses Terry so Chris accuses
+
+ align:start position:0%
+Chris accuses Terry so Chris accuses
+ 
+
+ align:start position:0%
+Chris accuses Terry so Chris accuses
+Terry of seeing someone else on the side
+
+ align:start position:0%
+Terry of seeing someone else on the side
+ 
+
+ align:start position:0%
+Terry of seeing someone else on the side
+Terry doesn't want to talk about it
+
+ align:start position:0%
+Terry doesn't want to talk about it
+ 
+
+ align:start position:0%
+Terry doesn't want to talk about it
+Chris says that Terry never wants to
+
+ align:start position:0%
+Chris says that Terry never wants to
+ 
+
+ align:start position:0%
+Chris says that Terry never wants to
+talk about anything
+
+ align:start position:0%
+talk about anything
+ 
+
+ align:start position:0%
+talk about anything
+um Terry shouts that well maybe there is
+
+ align:start position:0%
+um Terry shouts that well maybe there is
+ 
+
+ align:start position:0%
+um Terry shouts that well maybe there is
+somebody else on the side and says well
+
+ align:start position:0%
+somebody else on the side and says well
+ 
+
+ align:start position:0%
+somebody else on the side and says well
+it's not like there's been much activity
+
+ align:start position:0%
+it's not like there's been much activity
+ 
+
+ align:start position:0%
+it's not like there's been much activity
+in this relationship lately anyway
+
+ align:start position:0%
+in this relationship lately anyway
+ 
+
+ align:start position:0%
+in this relationship lately anyway
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Chris snorts that there's more to a
+
+ align:start position:0%
+Chris snorts that there's more to a
+ 
+
+ align:start position:0%
+Chris snorts that there's more to a
+relationship than just sex
+
+ align:start position:0%
+relationship than just sex
+ 
+
+ align:start position:0%
+relationship than just sex
+all right you got that
+
+ align:start position:0%
+all right you got that
+ 
+
+ align:start position:0%
+all right you got that
+and you will have noticed
+
+ align:start position:0%
+and you will have noticed
+ 
+
+ align:start position:0%
+and you will have noticed
+even Kristen who stayed up all night
+
+ align:start position:0%
+even Kristen who stayed up all night
+ 
+
+ align:start position:0%
+even Kristen who stayed up all night
+cheering the Red Sox will have noticed
+
+ align:start position:0%
+cheering the Red Sox will have noticed
+ 
+
+ align:start position:0%
+cheering the Red Sox will have noticed
+that Chris and Terry are deliberately
+
+ align:start position:0%
+that Chris and Terry are deliberately
+ 
+
+ align:start position:0%
+that Chris and Terry are deliberately
+um ambiguous as to the sex of of who's
+
+ align:start position:0%
+um ambiguous as to the sex of of who's
+ 
+
+ align:start position:0%
+um ambiguous as to the sex of of who's
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+um they could of course be the same sex
+
+ align:start position:0%
+um they could of course be the same sex
+ 
+
+ align:start position:0%
+um they could of course be the same sex
+um and that reminds me to say ahead of
+
+ align:start position:0%
+um and that reminds me to say ahead of
+ 
+
+ align:start position:0%
+um and that reminds me to say ahead of
+time I'm going to talk almost
+
+ align:start position:0%
+time I'm going to talk almost
+ 
+
+ align:start position:0%
+time I'm going to talk almost
+exclusively for the next two days uh
+
+ align:start position:0%
+exclusively for the next two days uh
+ 
+
+ align:start position:0%
+exclusively for the next two days uh
+next to lectures about heterosexual
+
+ align:start position:0%
+next to lectures about heterosexual
+ 
+
+ align:start position:0%
+next to lectures about heterosexual
+relationships
+
+ align:start position:0%
+relationships
+ 
+
+ align:start position:0%
+relationships
+lots of fascinating stuff to say about
+
+ align:start position:0%
+lots of fascinating stuff to say about
+ 
+
+ align:start position:0%
+lots of fascinating stuff to say about
+same-sex relationships like so many
+
+ align:start position:0%
+same-sex relationships like so many
+ 
+
+ align:start position:0%
+same-sex relationships like so many
+topics in the introductory psych it's
+
+ align:start position:0%
+topics in the introductory psych it's
+ 
+
+ align:start position:0%
+topics in the introductory psych it's
+just one I'm not going to get to so if
+
+ align:start position:0%
+just one I'm not going to get to so if
+ 
+
+ align:start position:0%
+just one I'm not going to get to so if
+we assume that Chris and Terry are
+
+ align:start position:0%
+we assume that Chris and Terry are
+ 
+
+ align:start position:0%
+we assume that Chris and Terry are
+um uh are are male and female one of
+
+ align:start position:0%
+um uh are are male and female one of
+ 
+
+ align:start position:0%
+um uh are are male and female one of
+them is male and one of them is female
+
+ align:start position:0%
+them is male and one of them is female
+ 
+
+ align:start position:0%
+them is male and one of them is female
+um and I don't remember which side I was
+
+ align:start position:0%
+um and I don't remember which side I was
+ 
+
+ align:start position:0%
+um and I don't remember which side I was
+gesturing to so I don't remember was
+
+ align:start position:0%
+gesturing to so I don't remember was
+ 
+
+ align:start position:0%
+gesturing to so I don't remember was
+this Chris or Terry
+
+ align:start position:0%
+this Chris or Terry
+ 
+
+ align:start position:0%
+this Chris or Terry
+that was Terry this was Chris okay so
+
+ align:start position:0%
+that was Terry this was Chris okay so
+ 
+
+ align:start position:0%
+that was Terry this was Chris okay so
+um how many people vote that Terry is uh
+
+ align:start position:0%
+um how many people vote that Terry is uh
+ 
+
+ align:start position:0%
+um how many people vote that Terry is uh
+the male person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many votes Chris is the male person
+
+ align:start position:0%
+how many votes Chris is the male person
+ 
+
+ align:start position:0%
+how many votes Chris is the male person
+how many vote that I got lost within the
+
+ align:start position:0%
+how many vote that I got lost within the
+ 
+
+ align:start position:0%
+how many vote that I got lost within the
+details I can't remember who's who
+
+ align:start position:0%
+details I can't remember who's who
+ 
+
+ align:start position:0%
+details I can't remember who's who
+anymore all right quick quick review uh
+
+ align:start position:0%
+anymore all right quick quick review uh
+ 
+
+ align:start position:0%
+anymore all right quick quick review uh
+Chris accuses Terry of seeing someone on
+
+ align:start position:0%
+Chris accuses Terry of seeing someone on
+ 
+
+ align:start position:0%
+Chris accuses Terry of seeing someone on
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sansa talk Terry shouts that there may
+
+ align:start position:0%
+Sansa talk Terry shouts that there may
+ 
+
+ align:start position:0%
+Sansa talk Terry shouts that there may
+be somebody on the side and there hasn't
+
+ align:start position:0%
+be somebody on the side and there hasn't
+ 
+
+ align:start position:0%
+be somebody on the side and there hasn't
+been much activity and Chris says
+
+ align:start position:0%
+been much activity and Chris says
+ 
+
+ align:start position:0%
+been much activity and Chris says
+there's more to a relationship than sex
+
+ align:start position:0%
+there's more to a relationship than sex
+ 
+
+ align:start position:0%
+there's more to a relationship than sex
+um how many vote Terry's mail
+
+ align:start position:0%
+um how many vote Terry's mail
+ 
+
+ align:start position:0%
+um how many vote Terry's mail
+how many vote Chris's mail
+
+ align:start position:0%
+how many vote Chris's mail
+ 
+
+ align:start position:0%
+how many vote Chris's mail
+uh gee there seems to be a fairly strong
+
+ align:start position:0%
+uh gee there seems to be a fairly strong
+ 
+
+ align:start position:0%
+uh gee there seems to be a fairly strong
+asymmetry there which is capturing
+
+ align:start position:0%
+asymmetry there which is capturing
+ 
+
+ align:start position:0%
+asymmetry there which is capturing
+something of the the cliche that
+
+ align:start position:0%
+something of the the cliche that
+ 
+
+ align:start position:0%
+something of the the cliche that
+um you know men are just interested in
+
+ align:start position:0%
+um you know men are just interested in
+ 
+
+ align:start position:0%
+um you know men are just interested in
+sex and women are interested in
+
+ align:start position:0%
+sex and women are interested in
+ 
+
+ align:start position:0%
+sex and women are interested in
+commitment or something like that this
+
+ align:start position:0%
+commitment or something like that this
+ 
+
+ align:start position:0%
+commitment or something like that this
+is a sort of a cartoon version
+
+ align:start position:0%
+is a sort of a cartoon version
+ 
+
+ align:start position:0%
+is a sort of a cartoon version
+recognizing
+
+ align:start position:0%
+recognizing
+ 
+
+ align:start position:0%
+recognizing
+that actually was sort of backed off
+
+ align:start position:0%
+that actually was sort of backed off
+ 
+
+ align:start position:0%
+that actually was sort of backed off
+what I was saying last time about
+
+ align:start position:0%
+what I was saying last time about
+ 
+
+ align:start position:0%
+what I was saying last time about
+talking about individual differences and
+
+ align:start position:0%
+talking about individual differences and
+ 
+
+ align:start position:0%
+talking about individual differences and
+now we're talking about on average again
+
+ align:start position:0%
+now we're talking about on average again
+ 
+
+ align:start position:0%
+now we're talking about on average again
+recognizing that this vast variations in
+
+ align:start position:0%
+recognizing that this vast variations in
+ 
+
+ align:start position:0%
+recognizing that this vast variations in
+um uh in in relationships between men
+
+ align:start position:0%
+um uh in in relationships between men
+ 
+
+ align:start position:0%
+um uh in in relationships between men
+and women is there any truth to this
+
+ align:start position:0%
+and women is there any truth to this
+ 
+
+ align:start position:0%
+and women is there any truth to this
+sort of asymmetry if there is
+
+ align:start position:0%
+sort of asymmetry if there is
+ 
+
+ align:start position:0%
+sort of asymmetry if there is
+how in the world would you explain it
+
+ align:start position:0%
+how in the world would you explain it
+ 
+
+ align:start position:0%
+how in the world would you explain it
+um that's that's the job for uh today's
+
+ align:start position:0%
+um that's that's the job for uh today's
+ 
+
+ align:start position:0%
+um that's that's the job for uh today's
+lecture well I mean there's lots of
+
+ align:start position:0%
+lecture well I mean there's lots of
+ 
+
+ align:start position:0%
+lecture well I mean there's lots of
+anecdotal evidence how about a little
+
+ align:start position:0%
+anecdotal evidence how about a little
+ 
+
+ align:start position:0%
+anecdotal evidence how about a little
+bit of of data evidence from um
+
+ align:start position:0%
+bit of of data evidence from um
+ 
+
+ align:start position:0%
+bit of of data evidence from um
+from one of my favorite experiments in
+
+ align:start position:0%
+from one of my favorite experiments in
+ 
+
+ align:start position:0%
+from one of my favorite experiments in
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+um in the annals of experiments that you
+
+ align:start position:0%
+um in the annals of experiments that you
+ 
+
+ align:start position:0%
+um in the annals of experiments that you
+can't see how they ever got it past does
+
+ align:start position:0%
+can't see how they ever got it past does
+ 
+
+ align:start position:0%
+can't see how they ever got it past does
+it say IRB on the handout IRB stands for
+
+ align:start position:0%
+it say IRB on the handout IRB stands for
+ 
+
+ align:start position:0%
+it say IRB on the handout IRB stands for
+institutional review board
+
+ align:start position:0%
+institutional review board
+ 
+
+ align:start position:0%
+institutional review board
+um do you don't have to worry about that
+
+ align:start position:0%
+um do you don't have to worry about that
+ 
+
+ align:start position:0%
+um do you don't have to worry about that
+bit of jargon but those are the people
+
+ align:start position:0%
+bit of jargon but those are the people
+ 
+
+ align:start position:0%
+bit of jargon but those are the people
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+um look at experimental protocols and
+
+ align:start position:0%
+um look at experimental protocols and
+ 
+
+ align:start position:0%
+um look at experimental protocols and
+decide whether it's uh permissible to do
+
+ align:start position:0%
+decide whether it's uh permissible to do
+ 
+
+ align:start position:0%
+decide whether it's uh permissible to do
+this so you know if if you volunteer to
+
+ align:start position:0%
+this so you know if if you volunteer to
+ 
+
+ align:start position:0%
+this so you know if if you volunteer to
+be a subject in our lab please do we
+
+ align:start position:0%
+be a subject in our lab please do we
+ 
+
+ align:start position:0%
+be a subject in our lab please do we
+need subjects talk to Kristen
+
+ align:start position:0%
+need subjects talk to Kristen
+ 
+
+ align:start position:0%
+need subjects talk to Kristen
+um anyway if you do we'll have you sign
+
+ align:start position:0%
+um anyway if you do we'll have you sign
+ 
+
+ align:start position:0%
+um anyway if you do we'll have you sign
+a seven page consent form
+
+ align:start position:0%
+a seven page consent form
+ 
+
+ align:start position:0%
+a seven page consent form
+um because they're really worried about
+
+ align:start position:0%
+um because they're really worried about
+ 
+
+ align:start position:0%
+um because they're really worried about
+the damage we can do to you looking at
+
+ align:start position:0%
+the damage we can do to you looking at
+ 
+
+ align:start position:0%
+the damage we can do to you looking at
+little red and green bars on a computer
+
+ align:start position:0%
+little red and green bars on a computer
+ 
+
+ align:start position:0%
+little red and green bars on a computer
+screen so you have to imagine how this
+
+ align:start position:0%
+screen so you have to imagine how this
+ 
+
+ align:start position:0%
+screen so you have to imagine how this
+experiment ever got passed uh
+
+ align:start position:0%
+experiment ever got passed uh
+ 
+
+ align:start position:0%
+experiment ever got passed uh
+the IRB though it does seem like a good
+
+ align:start position:0%
+the IRB though it does seem like a good
+ 
+
+ align:start position:0%
+the IRB though it does seem like a good
+one for reality TV perhaps anyway so
+
+ align:start position:0%
+one for reality TV perhaps anyway so
+ 
+
+ align:start position:0%
+one for reality TV perhaps anyway so
+here you are you're wandering around on
+
+ align:start position:0%
+here you are you're wandering around on
+ 
+
+ align:start position:0%
+here you are you're wandering around on
+campus and an attractive member of the
+
+ align:start position:0%
+campus and an attractive member of the
+ 
+
+ align:start position:0%
+campus and an attractive member of the
+opposite sex approaches you and asks you
+
+ align:start position:0%
+opposite sex approaches you and asks you
+ 
+
+ align:start position:0%
+opposite sex approaches you and asks you
+one of these three questions I should
+
+ align:start position:0%
+one of these three questions I should
+ 
+
+ align:start position:0%
+one of these three questions I should
+note that I was explaining this to my
+
+ align:start position:0%
+note that I was explaining this to my
+ 
+
+ align:start position:0%
+note that I was explaining this to my
+wife this morning and she got confused
+
+ align:start position:0%
+wife this morning and she got confused
+ 
+
+ align:start position:0%
+wife this morning and she got confused
+and thought this was a multiple choice
+
+ align:start position:0%
+and thought this was a multiple choice
+ 
+
+ align:start position:0%
+and thought this was a multiple choice
+test it's not a multiple choice test
+
+ align:start position:0%
+test it's not a multiple choice test
+ 
+
+ align:start position:0%
+test it's not a multiple choice test
+which would be even weirder
+
+ align:start position:0%
+which would be even weirder
+ 
+
+ align:start position:0%
+which would be even weirder
+um but it's it's a so the the the
+
+ align:start position:0%
+um but it's it's a so the the the
+ 
+
+ align:start position:0%
+um but it's it's a so the the the
+percentages don't need to add up to a
+
+ align:start position:0%
+percentages don't need to add up to a
+ 
+
+ align:start position:0%
+percentages don't need to add up to a
+hundred that that's important but this
+
+ align:start position:0%
+hundred that that's important but this
+ 
+
+ align:start position:0%
+hundred that that's important but this
+person comes up to you and asks you
+
+ align:start position:0%
+person comes up to you and asks you
+ 
+
+ align:start position:0%
+person comes up to you and asks you
+either oh so it says something effective
+
+ align:start position:0%
+either oh so it says something effective
+ 
+
+ align:start position:0%
+either oh so it says something effective
+you know I've seen you around campus and
+
+ align:start position:0%
+you know I've seen you around campus and
+ 
+
+ align:start position:0%
+you know I've seen you around campus and
+and and you you're you're really an
+
+ align:start position:0%
+and and you you're you're really an
+ 
+
+ align:start position:0%
+and and you you're you're really an
+attractive person
+
+ align:start position:0%
+attractive person
+ 
+
+ align:start position:0%
+attractive person
+um would you go on a date with me that's
+
+ align:start position:0%
+um would you go on a date with me that's
+ 
+
+ align:start position:0%
+um would you go on a date with me that's
+question one would you come back to my
+
+ align:start position:0%
+question one would you come back to my
+ 
+
+ align:start position:0%
+question one would you come back to my
+uh apartment with me or would you have
+
+ align:start position:0%
+uh apartment with me or would you have
+ 
+
+ align:start position:0%
+uh apartment with me or would you have
+sex with me and
+
+ align:start position:0%
+sex with me and
+ 
+
+ align:start position:0%
+sex with me and
+um what
+
+ align:start position:0%
+um what
+ 
+
+ align:start position:0%
+um what
+what I can't find out
+
+ align:start position:0%
+what I can't find out
+ 
+
+ align:start position:0%
+what I can't find out
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the second what happens after the
+
+ align:start position:0%
+the second what happens after the
+ 
+
+ align:start position:0%
+the second what happens after the
+subject gives an answer
+
+ align:start position:0%
+subject gives an answer
+ 
+
+ align:start position:0%
+subject gives an answer
+right you know it's uh
+
+ align:start position:0%
+right you know it's uh
+ 
+
+ align:start position:0%
+right you know it's uh
+this is this is a quite famous
+
+ align:start position:0%
+this is this is a quite famous
+ 
+
+ align:start position:0%
+this is this is a quite famous
+experiment but the original experiment
+
+ align:start position:0%
+experiment but the original experiment
+ 
+
+ align:start position:0%
+experiment but the original experiment
+is published in a very obscure journal
+
+ align:start position:0%
+is published in a very obscure journal
+ 
+
+ align:start position:0%
+is published in a very obscure journal
+and I don't actually have a copy of the
+
+ align:start position:0%
+and I don't actually have a copy of the
+ 
+
+ align:start position:0%
+and I don't actually have a copy of the
+of the um article uh so we've got um
+
+ align:start position:0%
+of the um article uh so we've got um
+ 
+
+ align:start position:0%
+of the um article uh so we've got um
+these three questions there's the date
+
+ align:start position:0%
+these three questions there's the date
+ 
+
+ align:start position:0%
+these three questions there's the date
+question the apartment question and the
+
+ align:start position:0%
+question the apartment question and the
+ 
+
+ align:start position:0%
+question the apartment question and the
+uh and and the sex question
+
+ align:start position:0%
+uh and and the sex question
+ 
+
+ align:start position:0%
+uh and and the sex question
+um and uh so we'll plot percent yes here
+
+ align:start position:0%
+um and uh so we'll plot percent yes here
+ 
+
+ align:start position:0%
+um and uh so we'll plot percent yes here
+okay if you are a woman person
+
+ align:start position:0%
+okay if you are a woman person
+ 
+
+ align:start position:0%
+okay if you are a woman person
+um what do you think what what
+
+ align:start position:0%
+um what do you think what what
+ 
+
+ align:start position:0%
+um what do you think what what
+percentage of women said yes I'll go on
+
+ align:start position:0%
+percentage of women said yes I'll go on
+ 
+
+ align:start position:0%
+percentage of women said yes I'll go on
+a date with you would you think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's something
+
+ align:start position:0%
+that's something
+ 
+
+ align:start position:0%
+that's something
+you read it but it's not Enlightenment
+
+ align:start position:0%
+you read it but it's not Enlightenment
+ 
+
+ align:start position:0%
+you read it but it's not Enlightenment
+is it yeah
+
+ align:start position:0%
+is it yeah
+ 
+
+ align:start position:0%
+is it yeah
+it's on the website it's on the website
+
+ align:start position:0%
+it's on the website it's on the website
+ 
+
+ align:start position:0%
+it's on the website it's on the website
+oh the articles on the website yeah did
+
+ align:start position:0%
+oh the articles on the website yeah did
+ 
+
+ align:start position:0%
+oh the articles on the website yeah did
+I wait a second I thought I didn't find
+
+ align:start position:0%
+I wait a second I thought I didn't find
+ 
+
+ align:start position:0%
+I wait a second I thought I didn't find
+the original article
+
+ align:start position:0%
+the original article
+ 
+
+ align:start position:0%
+the original article
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+oh okay well 50 thank you
+
+ align:start position:0%
+oh okay well 50 thank you
+ 
+
+ align:start position:0%
+oh okay well 50 thank you
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+this whoops 50 doesn't go all the way up
+
+ align:start position:0%
+this whoops 50 doesn't go all the way up
+ 
+
+ align:start position:0%
+this whoops 50 doesn't go all the way up
+to yeah okay 50 this kind of takes the
+
+ align:start position:0%
+to yeah okay 50 this kind of takes the
+ 
+
+ align:start position:0%
+to yeah okay 50 this kind of takes the
+uh the guesswork out of it a bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I was kind of guy I thought we'd find
+
+ align:start position:0%
+oh I was kind of guy I thought we'd find
+ 
+
+ align:start position:0%
+oh I was kind of guy I thought we'd find
+out if you memorized all the percentages
+
+ align:start position:0%
+out if you memorized all the percentages
+ 
+
+ align:start position:0%
+out if you memorized all the percentages
+or so all right if you're not if you're
+
+ align:start position:0%
+or so all right if you're not if you're
+ 
+
+ align:start position:0%
+or so all right if you're not if you're
+not the good person who went and read
+
+ align:start position:0%
+not the good person who went and read
+ 
+
+ align:start position:0%
+not the good person who went and read
+everything on the website
+
+ align:start position:0%
+everything on the website
+ 
+
+ align:start position:0%
+everything on the website
+all right how many how many women do you
+
+ align:start position:0%
+all right how many how many women do you
+ 
+
+ align:start position:0%
+all right how many how many women do you
+think were willing to go back to the
+
+ align:start position:0%
+think were willing to go back to the
+ 
+
+ align:start position:0%
+think were willing to go back to the
+guy's apartment
+
+ align:start position:0%
+guy's apartment
+ 
+
+ align:start position:0%
+guy's apartment
+two nine sounds great the average is
+
+ align:start position:0%
+two nine sounds great the average is
+ 
+
+ align:start position:0%
+two nine sounds great the average is
+about six
+
+ align:start position:0%
+about six
+ 
+
+ align:start position:0%
+about six
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+fifty six number percentage of women who
+
+ align:start position:0%
+fifty six number percentage of women who
+ 
+
+ align:start position:0%
+fifty six number percentage of women who
+said sure I will have sex with you
+
+ align:start position:0%
+said sure I will have sex with you
+ 
+
+ align:start position:0%
+said sure I will have sex with you
+zero would be a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sequel issue here that you'd love to
+
+ align:start position:0%
+the sequel issue here that you'd love to
+ 
+
+ align:start position:0%
+the sequel issue here that you'd love to
+know the answer to Is how many times the
+
+ align:start position:0%
+know the answer to Is how many times the
+ 
+
+ align:start position:0%
+know the answer to Is how many times the
+guy got like punched or reported to the
+
+ align:start position:0%
+guy got like punched or reported to the
+ 
+
+ align:start position:0%
+guy got like punched or reported to the
+campus police or something but now look
+
+ align:start position:0%
+campus police or something but now look
+ 
+
+ align:start position:0%
+campus police or something but now look
+do I have any color chalk no we'll just
+
+ align:start position:0%
+do I have any color chalk no we'll just
+ 
+
+ align:start position:0%
+do I have any color chalk no we'll just
+have to go for hatched bars today so
+
+ align:start position:0%
+have to go for hatched bars today so
+ 
+
+ align:start position:0%
+have to go for hatched bars today so
+that's the female data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's let's start at the other end here
+
+ align:start position:0%
+let's let's start at the other end here
+ 
+
+ align:start position:0%
+let's let's start at the other end here
+what percentage of guides approached by
+
+ align:start position:0%
+what percentage of guides approached by
+ 
+
+ align:start position:0%
+what percentage of guides approached by
+a woman who said I think you're
+
+ align:start position:0%
+a woman who said I think you're
+ 
+
+ align:start position:0%
+a woman who said I think you're
+attractive would you like to have sex he
+
+ align:start position:0%
+attractive would you like to have sex he
+ 
+
+ align:start position:0%
+attractive would you like to have sex he
+said yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she said she wasn't going to be
+
+ align:start position:0%
+she said she wasn't going to be
+ 
+
+ align:start position:0%
+she said she wasn't going to be
+answering anymore yeah yeah okay it's 75
+
+ align:start position:0%
+answering anymore yeah yeah okay it's 75
+ 
+
+ align:start position:0%
+answering anymore yeah yeah okay it's 75
+percent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it's also interesting
+
+ align:start position:0%
+now it's also interesting
+ 
+
+ align:start position:0%
+now it's also interesting
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+also interesting to see what happens
+
+ align:start position:0%
+also interesting to see what happens
+ 
+
+ align:start position:0%
+also interesting to see what happens
+with the rest of the questions if you
+
+ align:start position:0%
+with the rest of the questions if you
+ 
+
+ align:start position:0%
+with the rest of the questions if you
+ask would you go back to the apartment
+
+ align:start position:0%
+ask would you go back to the apartment
+ 
+
+ align:start position:0%
+ask would you go back to the apartment
+with me that drops to about I think 67
+
+ align:start position:0%
+with me that drops to about I think 67
+ 
+
+ align:start position:0%
+with me that drops to about I think 67
+and if you ask
+
+ align:start position:0%
+and if you ask
+ 
+
+ align:start position:0%
+and if you ask
+um you know would you go on a date with
+
+ align:start position:0%
+um you know would you go on a date with
+ 
+
+ align:start position:0%
+um you know would you go on a date with
+me it drops to 50. so not only now look
+
+ align:start position:0%
+me it drops to 50. so not only now look
+ 
+
+ align:start position:0%
+me it drops to 50. so not only now look
+the world is full of interesting
+
+ align:start position:0%
+the world is full of interesting
+ 
+
+ align:start position:0%
+the world is full of interesting
+asymmetries in data and and even even
+
+ align:start position:0%
+asymmetries in data and and even even
+ 
+
+ align:start position:0%
+asymmetries in data and and even even
+sex differences you know sex differences
+
+ align:start position:0%
+sex differences you know sex differences
+ 
+
+ align:start position:0%
+sex differences you know sex differences
+and say you know mathematical ability or
+
+ align:start position:0%
+and say you know mathematical ability or
+ 
+
+ align:start position:0%
+and say you know mathematical ability or
+something like that sex differences in
+
+ align:start position:0%
+something like that sex differences in
+ 
+
+ align:start position:0%
+something like that sex differences in
+most stuff look like this you know
+
+ align:start position:0%
+most stuff look like this you know
+ 
+
+ align:start position:0%
+most stuff look like this you know
+there's a data point with an error bar
+
+ align:start position:0%
+there's a data point with an error bar
+ 
+
+ align:start position:0%
+there's a data point with an error bar
+and there's another data point with an
+
+ align:start position:0%
+and there's another data point with an
+ 
+
+ align:start position:0%
+and there's another data point with an
+error bar and you say oh yeah look
+
+ align:start position:0%
+error bar and you say oh yeah look
+ 
+
+ align:start position:0%
+error bar and you say oh yeah look
+there's a significant sex difference if
+
+ align:start position:0%
+there's a significant sex difference if
+ 
+
+ align:start position:0%
+there's a significant sex difference if
+we run eight and a half million subjects
+
+ align:start position:0%
+we run eight and a half million subjects
+ 
+
+ align:start position:0%
+we run eight and a half million subjects
+you don't get data like this most the
+
+ align:start position:0%
+you don't get data like this most the
+ 
+
+ align:start position:0%
+you don't get data like this most the
+time this is like a huge asymmetry so
+
+ align:start position:0%
+time this is like a huge asymmetry so
+ 
+
+ align:start position:0%
+time this is like a huge asymmetry so
+one interesting question is why is this
+
+ align:start position:0%
+one interesting question is why is this
+ 
+
+ align:start position:0%
+one interesting question is why is this
+huge and another interesting question is
+
+ align:start position:0%
+huge and another interesting question is
+ 
+
+ align:start position:0%
+huge and another interesting question is
+this um apparently counter-intuitive
+
+ align:start position:0%
+this um apparently counter-intuitive
+ 
+
+ align:start position:0%
+this um apparently counter-intuitive
+slope to the male data where you're more
+
+ align:start position:0%
+slope to the male data where you're more
+ 
+
+ align:start position:0%
+slope to the male data where you're more
+likely if you're a guy to say oh sure
+
+ align:start position:0%
+likely if you're a guy to say oh sure
+ 
+
+ align:start position:0%
+likely if you're a guy to say oh sure
+I'll have sex with you right now
+
+ align:start position:0%
+I'll have sex with you right now
+ 
+
+ align:start position:0%
+I'll have sex with you right now
+um but I don't actually want to go on a
+
+ align:start position:0%
+um but I don't actually want to go on a
+ 
+
+ align:start position:0%
+um but I don't actually want to go on a
+date with you
+
+ align:start position:0%
+date with you
+ 
+
+ align:start position:0%
+date with you
+um which is
+
+ align:start position:0%
+um which is
+ 
+
+ align:start position:0%
+um which is
+on the face of it perhaps a little odd
+
+ align:start position:0%
+on the face of it perhaps a little odd
+ 
+
+ align:start position:0%
+on the face of it perhaps a little odd
+but we'll come back to try to explain
+
+ align:start position:0%
+but we'll come back to try to explain
+ 
+
+ align:start position:0%
+but we'll come back to try to explain
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um there are multiple ways
+
+ align:start position:0%
+um there are multiple ways
+ 
+
+ align:start position:0%
+um there are multiple ways
+this is not some weird isolated data
+
+ align:start position:0%
+this is not some weird isolated data
+ 
+
+ align:start position:0%
+this is not some weird isolated data
+point where where people just did a very
+
+ align:start position:0%
+point where where people just did a very
+ 
+
+ align:start position:0%
+point where where people just did a very
+odd it's an odd experiment here this is
+
+ align:start position:0%
+odd it's an odd experiment here this is
+ 
+
+ align:start position:0%
+odd it's an odd experiment here this is
+the one that you really wonder about
+
+ align:start position:0%
+the one that you really wonder about
+ 
+
+ align:start position:0%
+the one that you really wonder about
+what the next sentence was you know hi
+
+ align:start position:0%
+what the next sentence was you know hi
+ 
+
+ align:start position:0%
+what the next sentence was you know hi
+you're very attractive would you have
+
+ align:start position:0%
+you're very attractive would you have
+ 
+
+ align:start position:0%
+you're very attractive would you have
+sex with me oh yes sure just kidding
+
+ align:start position:0%
+sex with me oh yes sure just kidding
+ 
+
+ align:start position:0%
+sex with me oh yes sure just kidding
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+it's a very odd experiment but a very
+
+ align:start position:0%
+it's a very odd experiment but a very
+ 
+
+ align:start position:0%
+it's a very odd experiment but a very
+interesting one yeah
+
+ align:start position:0%
+interesting one yeah
+ 
+
+ align:start position:0%
+interesting one yeah
+Mara knows the answer to the rest of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my expert witness can probably tell me
+
+ align:start position:0%
+my expert witness can probably tell me
+ 
+
+ align:start position:0%
+my expert witness can probably tell me
+better because she's read this more
+
+ align:start position:0%
+better because she's read this more
+ 
+
+ align:start position:0%
+better because she's read this more
+recently apparently the description I
+
+ align:start position:0%
+recently apparently the description I
+ 
+
+ align:start position:0%
+recently apparently the description I
+think is simply that the the uh the
+
+ align:start position:0%
+think is simply that the the uh the
+ 
+
+ align:start position:0%
+think is simply that the the uh the
+experimenter this experimenters
+
+ align:start position:0%
+experimenter this experimenters
+ 
+
+ align:start position:0%
+experimenter this experimenters
+Confederate is described as being
+
+ align:start position:0%
+Confederate is described as being
+ 
+
+ align:start position:0%
+Confederate is described as being
+attractive but but look do the intuition
+
+ align:start position:0%
+attractive but but look do the intuition
+ 
+
+ align:start position:0%
+attractive but but look do the intuition
+you can only do the real intuition for
+
+ align:start position:0%
+you can only do the real intuition for
+ 
+
+ align:start position:0%
+you can only do the real intuition for
+the sex that you happen to belong to but
+
+ align:start position:0%
+the sex that you happen to belong to but
+ 
+
+ align:start position:0%
+the sex that you happen to belong to but
+ask yourself you know really attractive
+
+ align:start position:0%
+ask yourself you know really attractive
+ 
+
+ align:start position:0%
+ask yourself you know really attractive
+guy comes up and says would you like to
+
+ align:start position:0%
+guy comes up and says would you like to
+ 
+
+ align:start position:0%
+guy comes up and says would you like to
+have sex with me right now do you think
+
+ align:start position:0%
+have sex with me right now do you think
+ 
+
+ align:start position:0%
+have sex with me right now do you think
+the point moves a lot off zero and and
+
+ align:start position:0%
+the point moves a lot off zero and and
+ 
+
+ align:start position:0%
+the point moves a lot off zero and and
+short of
+
+ align:start position:0%
+short of
+ 
+
+ align:start position:0%
+short of
+um you know I don't know
+
+ align:start position:0%
+um you know I don't know
+ 
+
+ align:start position:0%
+um you know I don't know
+non-human woman
+
+ align:start position:0%
+non-human woman
+ 
+
+ align:start position:0%
+non-human woman
+it's not clear how much that point moves
+
+ align:start position:0%
+it's not clear how much that point moves
+ 
+
+ align:start position:0%
+it's not clear how much that point moves
+either the
+
+ align:start position:0%
+either the
+ 
+
+ align:start position:0%
+either the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I I don't know and it's not one of these
+
+ align:start position:0%
+I I don't know and it's not one of these
+ 
+
+ align:start position:0%
+I I don't know and it's not one of these
+things I I also by the way
+
+ align:start position:0%
+things I I also by the way
+ 
+
+ align:start position:0%
+things I I also by the way
+I do not recommend
+
+ align:start position:0%
+I do not recommend
+ 
+
+ align:start position:0%
+I do not recommend
+um you know when you go off into course
+
+ align:start position:0%
+um you know when you go off into course
+ 
+
+ align:start position:0%
+um you know when you go off into course
+15 seems to be the place where they like
+
+ align:start position:0%
+15 seems to be the place where they like
+ 
+
+ align:start position:0%
+15 seems to be the place where they like
+to do you know survey experiments and
+
+ align:start position:0%
+to do you know survey experiments and
+ 
+
+ align:start position:0%
+to do you know survey experiments and
+stuff like that I don't recommend this
+
+ align:start position:0%
+stuff like that I don't recommend this
+ 
+
+ align:start position:0%
+stuff like that I don't recommend this
+one as one to try because I really do
+
+ align:start position:0%
+one as one to try because I really do
+ 
+
+ align:start position:0%
+one as one to try because I really do
+think that it's hard to imagine how to
+
+ align:start position:0%
+think that it's hard to imagine how to
+ 
+
+ align:start position:0%
+think that it's hard to imagine how to
+do this without getting into serious
+
+ align:start position:0%
+do this without getting into serious
+ 
+
+ align:start position:0%
+do this without getting into serious
+trouble fascinating fascinating as the
+
+ align:start position:0%
+trouble fascinating fascinating as the
+ 
+
+ align:start position:0%
+trouble fascinating fascinating as the
+experiment is
+
+ align:start position:0%
+experiment is
+ 
+
+ align:start position:0%
+experiment is
+um other efforts for it to get at the
+
+ align:start position:0%
+um other efforts for it to get at the
+ 
+
+ align:start position:0%
+um other efforts for it to get at the
+same point have been done
+
+ align:start position:0%
+same point have been done
+ 
+
+ align:start position:0%
+same point have been done
+um in sort of more indirect fashion so
+
+ align:start position:0%
+um in sort of more indirect fashion so
+ 
+
+ align:start position:0%
+um in sort of more indirect fashion so
+you can you can be your subject in this
+
+ align:start position:0%
+you can you can be your subject in this
+ 
+
+ align:start position:0%
+you can you can be your subject in this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um which was one where you were asked to
+
+ align:start position:0%
+um which was one where you were asked to
+ 
+
+ align:start position:0%
+um which was one where you were asked to
+rate a variety of um
+
+ align:start position:0%
+rate a variety of um
+ 
+
+ align:start position:0%
+rate a variety of um
+uh events as being uh positive or
+
+ align:start position:0%
+uh events as being uh positive or
+ 
+
+ align:start position:0%
+uh events as being uh positive or
+negative affectively positive or
+
+ align:start position:0%
+negative affectively positive or
+ 
+
+ align:start position:0%
+negative affectively positive or
+negative if this happened and and and
+
+ align:start position:0%
+negative if this happened and and and
+ 
+
+ align:start position:0%
+negative if this happened and and and
+the uh the most Salient one seems to me
+
+ align:start position:0%
+the uh the most Salient one seems to me
+ 
+
+ align:start position:0%
+the uh the most Salient one seems to me
+to be one where uh the description was
+
+ align:start position:0%
+to be one where uh the description was
+ 
+
+ align:start position:0%
+to be one where uh the description was
+you're on a crowded subway car
+
+ align:start position:0%
+you're on a crowded subway car
+ 
+
+ align:start position:0%
+you're on a crowded subway car
+uh an attractive member of the sex to
+
+ align:start position:0%
+uh an attractive member of the sex to
+ 
+
+ align:start position:0%
+uh an attractive member of the sex to
+which you are attracted
+
+ align:start position:0%
+which you are attracted
+ 
+
+ align:start position:0%
+which you are attracted
+um begins to surreptitiously touch you
+
+ align:start position:0%
+um begins to surreptitiously touch you
+ 
+
+ align:start position:0%
+um begins to surreptitiously touch you
+on the subway car
+
+ align:start position:0%
+on the subway car
+ 
+
+ align:start position:0%
+on the subway car
+is this a positive or A negative event
+
+ align:start position:0%
+is this a positive or A negative event
+ 
+
+ align:start position:0%
+is this a positive or A negative event
+the answer in in the data is women
+
+ align:start position:0%
+the answer in in the data is women
+ 
+
+ align:start position:0%
+the answer in in the data is women
+overwhelmingly say ooh you know that's
+
+ align:start position:0%
+overwhelmingly say ooh you know that's
+ 
+
+ align:start position:0%
+overwhelmingly say ooh you know that's
+kind of creepy and and negative this is
+
+ align:start position:0%
+kind of creepy and and negative this is
+ 
+
+ align:start position:0%
+kind of creepy and and negative this is
+not good and guys fairly overwhelmingly
+
+ align:start position:0%
+not good and guys fairly overwhelmingly
+ 
+
+ align:start position:0%
+not good and guys fairly overwhelmingly
+say yeah
+
+ align:start position:0%
+say yeah
+ 
+
+ align:start position:0%
+say yeah
+what's up to them here the um this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this asymmetrical
+
+ align:start position:0%
+this asymmetrical
+ 
+
+ align:start position:0%
+this asymmetrical
+um result and and what we want to do is
+
+ align:start position:0%
+um result and and what we want to do is
+ 
+
+ align:start position:0%
+um result and and what we want to do is
+try to account for that asymmetry now
+
+ align:start position:0%
+try to account for that asymmetry now
+ 
+
+ align:start position:0%
+try to account for that asymmetry now
+um assuming that you have not been
+
+ align:start position:0%
+um assuming that you have not been
+ 
+
+ align:start position:0%
+um assuming that you have not been
+entirely comatose for the first half of
+
+ align:start position:0%
+entirely comatose for the first half of
+ 
+
+ align:start position:0%
+entirely comatose for the first half of
+the course you will recognize that the
+
+ align:start position:0%
+the course you will recognize that the
+ 
+
+ align:start position:0%
+the course you will recognize that the
+broad classes of explanation are going
+
+ align:start position:0%
+broad classes of explanation are going
+ 
+
+ align:start position:0%
+broad classes of explanation are going
+to be nature nurture kinds of things and
+
+ align:start position:0%
+to be nature nurture kinds of things and
+ 
+
+ align:start position:0%
+to be nature nurture kinds of things and
+and of course it's always a combination
+
+ align:start position:0%
+and of course it's always a combination
+ 
+
+ align:start position:0%
+and of course it's always a combination
+in particular today what I'm going to
+
+ align:start position:0%
+in particular today what I'm going to
+ 
+
+ align:start position:0%
+in particular today what I'm going to
+talk about is
+
+ align:start position:0%
+talk about is
+ 
+
+ align:start position:0%
+talk about is
+um a biological account in and and
+
+ align:start position:0%
+um a biological account in and and
+ 
+
+ align:start position:0%
+um a biological account in and and
+that's the account coming out of
+
+ align:start position:0%
+that's the account coming out of
+ 
+
+ align:start position:0%
+that's the account coming out of
+evolutionary psychology evolutionary
+
+ align:start position:0%
+evolutionary psychology evolutionary
+ 
+
+ align:start position:0%
+evolutionary psychology evolutionary
+ecology the application of evolutionary
+
+ align:start position:0%
+ecology the application of evolutionary
+ 
+
+ align:start position:0%
+ecology the application of evolutionary
+theory two topics in Psychology is very
+
+ align:start position:0%
+theory two topics in Psychology is very
+ 
+
+ align:start position:0%
+theory two topics in Psychology is very
+uh prevalent very important these days
+
+ align:start position:0%
+uh prevalent very important these days
+ 
+
+ align:start position:0%
+uh prevalent very important these days
+it gets applied to a huge range of
+
+ align:start position:0%
+it gets applied to a huge range of
+ 
+
+ align:start position:0%
+it gets applied to a huge range of
+topics some of which it probably doesn't
+
+ align:start position:0%
+topics some of which it probably doesn't
+ 
+
+ align:start position:0%
+topics some of which it probably doesn't
+have much to say about but if there's
+
+ align:start position:0%
+have much to say about but if there's
+ 
+
+ align:start position:0%
+have much to say about but if there's
+anything that it's got a lot to say
+
+ align:start position:0%
+anything that it's got a lot to say
+ 
+
+ align:start position:0%
+anything that it's got a lot to say
+about it's probably human mating
+
+ align:start position:0%
+about it's probably human mating
+ 
+
+ align:start position:0%
+about it's probably human mating
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+um and um and so that's why I'll talk
+
+ align:start position:0%
+um and um and so that's why I'll talk
+ 
+
+ align:start position:0%
+um and um and so that's why I'll talk
+about evolutionary psychology in this
+
+ align:start position:0%
+about evolutionary psychology in this
+ 
+
+ align:start position:0%
+about evolutionary psychology in this
+particular this particular context this
+
+ align:start position:0%
+particular this particular context this
+ 
+
+ align:start position:0%
+particular this particular context this
+is not to say it's the only way of
+
+ align:start position:0%
+is not to say it's the only way of
+ 
+
+ align:start position:0%
+is not to say it's the only way of
+accounting for mating behavior but it's
+
+ align:start position:0%
+accounting for mating behavior but it's
+ 
+
+ align:start position:0%
+accounting for mating behavior but it's
+a particularly I think it's very hard to
+
+ align:start position:0%
+a particularly I think it's very hard to
+ 
+
+ align:start position:0%
+a particularly I think it's very hard to
+argue that that these sort of biological
+
+ align:start position:0%
+argue that that these sort of biological
+ 
+
+ align:start position:0%
+argue that that these sort of biological
+forces don't have some shaping influence
+
+ align:start position:0%
+forces don't have some shaping influence
+ 
+
+ align:start position:0%
+forces don't have some shaping influence
+on um on the way that we select mates
+
+ align:start position:0%
+on um on the way that we select mates
+ 
+
+ align:start position:0%
+on um on the way that we select mates
+and I and and I want to try cashing out
+
+ align:start position:0%
+and I and and I want to try cashing out
+ 
+
+ align:start position:0%
+and I and and I want to try cashing out
+that argument today if you want to read
+
+ align:start position:0%
+that argument today if you want to read
+ 
+
+ align:start position:0%
+that argument today if you want to read
+more about it
+
+ align:start position:0%
+more about it
+ 
+
+ align:start position:0%
+more about it
+um there are
+
+ align:start position:0%
+um there are
+ 
+
+ align:start position:0%
+um there are
+several uh I I put reference to several
+
+ align:start position:0%
+several uh I I put reference to several
+ 
+
+ align:start position:0%
+several uh I I put reference to several
+books on the on the handout all of which
+
+ align:start position:0%
+books on the on the handout all of which
+ 
+
+ align:start position:0%
+books on the on the handout all of which
+I put on there because they're both uh
+
+ align:start position:0%
+I put on there because they're both uh
+ 
+
+ align:start position:0%
+I put on there because they're both uh
+yeah they they talk about the topic but
+
+ align:start position:0%
+yeah they they talk about the topic but
+ 
+
+ align:start position:0%
+yeah they they talk about the topic but
+they're all good reads my current
+
+ align:start position:0%
+they're all good reads my current
+ 
+
+ align:start position:0%
+they're all good reads my current
+favorite actually is the bow meister and
+
+ align:start position:0%
+favorite actually is the bow meister and
+ 
+
+ align:start position:0%
+favorite actually is the bow meister and
+uh Tice one it's less of one of the ones
+
+ align:start position:0%
+uh Tice one it's less of one of the ones
+ 
+
+ align:start position:0%
+uh Tice one it's less of one of the ones
+that's sort of been on the best seller
+
+ align:start position:0%
+that's sort of been on the best seller
+ 
+
+ align:start position:0%
+that's sort of been on the best seller
+list but it's a beautifully written uh
+
+ align:start position:0%
+list but it's a beautifully written uh
+ 
+
+ align:start position:0%
+list but it's a beautifully written uh
+book on this topic if you're if you are
+
+ align:start position:0%
+book on this topic if you're if you are
+ 
+
+ align:start position:0%
+book on this topic if you're if you are
+if you're interested
+
+ align:start position:0%
+if you're interested
+ 
+
+ align:start position:0%
+if you're interested
+um all right so let's run down the basic
+
+ align:start position:0%
+um all right so let's run down the basic
+ 
+
+ align:start position:0%
+um all right so let's run down the basic
+um evolutionary psych argument and then
+
+ align:start position:0%
+um evolutionary psych argument and then
+ 
+
+ align:start position:0%
+um evolutionary psych argument and then
+attempt to see
+
+ align:start position:0%
+attempt to see
+ 
+
+ align:start position:0%
+attempt to see
+um how it might account for the sort of
+
+ align:start position:0%
+um how it might account for the sort of
+ 
+
+ align:start position:0%
+um how it might account for the sort of
+data that we see in this um this area
+
+ align:start position:0%
+data that we see in this um this area
+ 
+
+ align:start position:0%
+data that we see in this um this area
+um if you are
+
+ align:start position:0%
+um if you are
+ 
+
+ align:start position:0%
+um if you are
+operating within uh this sort of
+
+ align:start position:0%
+operating within uh this sort of
+ 
+
+ align:start position:0%
+operating within uh this sort of
+evolutionary framework your goal as an
+
+ align:start position:0%
+evolutionary framework your goal as an
+ 
+
+ align:start position:0%
+evolutionary framework your goal as an
+organism is to do what
+
+ align:start position:0%
+organism is to do what
+ 
+
+ align:start position:0%
+organism is to do what
+pass on your genes you got to propagate
+
+ align:start position:0%
+pass on your genes you got to propagate
+ 
+
+ align:start position:0%
+pass on your genes you got to propagate
+your genes in some fashion
+
+ align:start position:0%
+your genes in some fashion
+ 
+
+ align:start position:0%
+your genes in some fashion
+um you gotta um yeah yeah you you want
+
+ align:start position:0%
+um you gotta um yeah yeah you you want
+ 
+
+ align:start position:0%
+um you gotta um yeah yeah you you want
+to get that genetic material into future
+
+ align:start position:0%
+to get that genetic material into future
+ 
+
+ align:start position:0%
+to get that genetic material into future
+generations and and how are you gonna do
+
+ align:start position:0%
+generations and and how are you gonna do
+ 
+
+ align:start position:0%
+generations and and how are you gonna do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weren't you paying attention in high
+
+ align:start position:0%
+weren't you paying attention in high
+ 
+
+ align:start position:0%
+weren't you paying attention in high
+school
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are several ways but the but
+
+ align:start position:0%
+there are several ways but the but
+ 
+
+ align:start position:0%
+there are several ways but the but
+sexual reproduction is considered
+
+ align:start position:0%
+sexual reproduction is considered
+ 
+
+ align:start position:0%
+sexual reproduction is considered
+perhaps the most direct of these it's
+
+ align:start position:0%
+perhaps the most direct of these it's
+ 
+
+ align:start position:0%
+perhaps the most direct of these it's
+not the only one by the way it's
+
+ align:start position:0%
+not the only one by the way it's
+ 
+
+ align:start position:0%
+not the only one by the way it's
+important to point out
+
+ align:start position:0%
+important to point out
+ 
+
+ align:start position:0%
+important to point out
+um that uh it's not the if you think
+
+ align:start position:0%
+um that uh it's not the if you think
+ 
+
+ align:start position:0%
+um that uh it's not the if you think
+that again by the way all of this stuff
+
+ align:start position:0%
+that again by the way all of this stuff
+ 
+
+ align:start position:0%
+that again by the way all of this stuff
+is presumably operating at a very
+
+ align:start position:0%
+is presumably operating at a very
+ 
+
+ align:start position:0%
+is presumably operating at a very
+unconscious implicit kind of level
+
+ align:start position:0%
+unconscious implicit kind of level
+ 
+
+ align:start position:0%
+unconscious implicit kind of level
+nobody assumes that people are wandering
+
+ align:start position:0%
+nobody assumes that people are wandering
+ 
+
+ align:start position:0%
+nobody assumes that people are wandering
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+um you know the the dating scene saying
+
+ align:start position:0%
+um you know the the dating scene saying
+ 
+
+ align:start position:0%
+um you know the the dating scene saying
+gotta pass on by genes how am I going to
+
+ align:start position:0%
+gotta pass on by genes how am I going to
+ 
+
+ align:start position:0%
+gotta pass on by genes how am I going to
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+um but the forces the forces that are
+
+ align:start position:0%
+um but the forces the forces that are
+ 
+
+ align:start position:0%
+um but the forces the forces that are
+are shaping that behavior
+
+ align:start position:0%
+are shaping that behavior
+ 
+
+ align:start position:0%
+are shaping that behavior
+our pres are within this Viewpoint
+
+ align:start position:0%
+our pres are within this Viewpoint
+ 
+
+ align:start position:0%
+our pres are within this Viewpoint
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+by this this drive to pass on genetic
+
+ align:start position:0%
+by this this drive to pass on genetic
+ 
+
+ align:start position:0%
+by this this drive to pass on genetic
+material into into the Next Generation
+
+ align:start position:0%
+material into into the Next Generation
+ 
+
+ align:start position:0%
+material into into the Next Generation
+you can also
+
+ align:start position:0%
+you can also
+ 
+
+ align:start position:0%
+you can also
+um propagate your genes by taking care
+
+ align:start position:0%
+um propagate your genes by taking care
+ 
+
+ align:start position:0%
+um propagate your genes by taking care
+of um your relations so if you are uh if
+
+ align:start position:0%
+of um your relations so if you are uh if
+ 
+
+ align:start position:0%
+of um your relations so if you are uh if
+you've got a a brother or sister with
+
+ align:start position:0%
+you've got a a brother or sister with
+ 
+
+ align:start position:0%
+you've got a a brother or sister with
+kids those kids are genetically related
+
+ align:start position:0%
+kids those kids are genetically related
+ 
+
+ align:start position:0%
+kids those kids are genetically related
+to you and if you nurture them if you
+
+ align:start position:0%
+to you and if you nurture them if you
+ 
+
+ align:start position:0%
+to you and if you nurture them if you
+pay for their college education or
+
+ align:start position:0%
+pay for their college education or
+ 
+
+ align:start position:0%
+pay for their college education or
+something they're not as genetically
+
+ align:start position:0%
+something they're not as genetically
+ 
+
+ align:start position:0%
+something they're not as genetically
+related to you as your own children but
+
+ align:start position:0%
+related to you as your own children but
+ 
+
+ align:start position:0%
+related to you as your own children but
+they're genetically related to you and
+
+ align:start position:0%
+they're genetically related to you and
+ 
+
+ align:start position:0%
+they're genetically related to you and
+so you can do the propagation thing
+
+ align:start position:0%
+so you can do the propagation thing
+ 
+
+ align:start position:0%
+so you can do the propagation thing
+indirectly rather than through uh just
+
+ align:start position:0%
+indirectly rather than through uh just
+ 
+
+ align:start position:0%
+indirectly rather than through uh just
+uh you know regular old-fashioned uh
+
+ align:start position:0%
+uh you know regular old-fashioned uh
+ 
+
+ align:start position:0%
+uh you know regular old-fashioned uh
+sexual reproduction this by the way
+
+ align:start position:0%
+sexual reproduction this by the way
+ 
+
+ align:start position:0%
+sexual reproduction this by the way
+um is one of the uh arguments offered by
+
+ align:start position:0%
+um is one of the uh arguments offered by
+ 
+
+ align:start position:0%
+um is one of the uh arguments offered by
+evolutionary psychologists
+
+ align:start position:0%
+evolutionary psychologists
+ 
+
+ align:start position:0%
+evolutionary psychologists
+um for the Persistence of same-sex
+
+ align:start position:0%
+um for the Persistence of same-sex
+ 
+
+ align:start position:0%
+um for the Persistence of same-sex
+relations same-sex relationships are a
+
+ align:start position:0%
+relations same-sex relationships are a
+ 
+
+ align:start position:0%
+relations same-sex relationships are a
+problem from this evolutionary point of
+
+ align:start position:0%
+problem from this evolutionary point of
+ 
+
+ align:start position:0%
+problem from this evolutionary point of
+view because they don't lead to
+
+ align:start position:0%
+view because they don't lead to
+ 
+
+ align:start position:0%
+view because they don't lead to
+offspring right whatever else is going
+
+ align:start position:0%
+offspring right whatever else is going
+ 
+
+ align:start position:0%
+offspring right whatever else is going
+going on they don't lead
+
+ align:start position:0%
+going on they don't lead
+ 
+
+ align:start position:0%
+going on they don't lead
+um they don't lead to offspring and so
+
+ align:start position:0%
+um they don't lead to offspring and so
+ 
+
+ align:start position:0%
+um they don't lead to offspring and so
+one of the I don't know if there's any
+
+ align:start position:0%
+one of the I don't know if there's any
+ 
+
+ align:start position:0%
+one of the I don't know if there's any
+data for it I've never perhaps because I
+
+ align:start position:0%
+data for it I've never perhaps because I
+ 
+
+ align:start position:0%
+data for it I've never perhaps because I
+haven't looked
+
+ align:start position:0%
+haven't looked
+ 
+
+ align:start position:0%
+haven't looked
+um but one of the arguments that has
+
+ align:start position:0%
+um but one of the arguments that has
+ 
+
+ align:start position:0%
+um but one of the arguments that has
+been uh put forward uh from time to time
+
+ align:start position:0%
+been uh put forward uh from time to time
+ 
+
+ align:start position:0%
+been uh put forward uh from time to time
+are things like oh gay men make great
+
+ align:start position:0%
+are things like oh gay men make great
+ 
+
+ align:start position:0%
+are things like oh gay men make great
+uncles
+
+ align:start position:0%
+uncles
+ 
+
+ align:start position:0%
+uncles
+they're not going to have kids of their
+
+ align:start position:0%
+they're not going to have kids of their
+ 
+
+ align:start position:0%
+they're not going to have kids of their
+own but they take care of their sister's
+
+ align:start position:0%
+own but they take care of their sister's
+ 
+
+ align:start position:0%
+own but they take care of their sister's
+kids and that's why it's uh it's it's
+
+ align:start position:0%
+kids and that's why it's uh it's it's
+ 
+
+ align:start position:0%
+kids and that's why it's uh it's it's
+not selected out it's not selected
+
+ align:start position:0%
+not selected out it's not selected
+ 
+
+ align:start position:0%
+not selected out it's not selected
+against
+
+ align:start position:0%
+against
+ 
+
+ align:start position:0%
+against
+um by uh by Evolution
+
+ align:start position:0%
+um by uh by Evolution
+ 
+
+ align:start position:0%
+um by uh by Evolution
+um in any case
+
+ align:start position:0%
+um in any case
+ 
+
+ align:start position:0%
+um in any case
+sticking with this sort of uh Mainline
+
+ align:start position:0%
+sticking with this sort of uh Mainline
+ 
+
+ align:start position:0%
+sticking with this sort of uh Mainline
+tale you want to propagate your genes
+
+ align:start position:0%
+tale you want to propagate your genes
+ 
+
+ align:start position:0%
+tale you want to propagate your genes
+sexual reproduction is a is a good way
+
+ align:start position:0%
+sexual reproduction is a is a good way
+ 
+
+ align:start position:0%
+sexual reproduction is a is a good way
+to do it
+
+ align:start position:0%
+to do it
+ 
+
+ align:start position:0%
+to do it
+um now uh the thing about sex is uh you
+
+ align:start position:0%
+um now uh the thing about sex is uh you
+ 
+
+ align:start position:0%
+um now uh the thing about sex is uh you
+get pregnant
+
+ align:start position:0%
+get pregnant
+ 
+
+ align:start position:0%
+get pregnant
+actually only half of you get pregnant
+
+ align:start position:0%
+actually only half of you get pregnant
+ 
+
+ align:start position:0%
+actually only half of you get pregnant
+um it was sort of an ambiguous sentence
+
+ align:start position:0%
+um it was sort of an ambiguous sentence
+ 
+
+ align:start position:0%
+um it was sort of an ambiguous sentence
+uh this is half of you plural get
+
+ align:start position:0%
+uh this is half of you plural get
+ 
+
+ align:start position:0%
+uh this is half of you plural get
+pregnant not half of you as an
+
+ align:start position:0%
+pregnant not half of you as an
+ 
+
+ align:start position:0%
+pregnant not half of you as an
+individual get pregnant if you you never
+
+ align:start position:0%
+individual get pregnant if you you never
+ 
+
+ align:start position:0%
+individual get pregnant if you you never
+know what people learn in high school
+
+ align:start position:0%
+know what people learn in high school
+ 
+
+ align:start position:0%
+know what people learn in high school
+um in any case
+
+ align:start position:0%
+um in any case
+ 
+
+ align:start position:0%
+um in any case
+it is that fact that's the key fact in
+
+ align:start position:0%
+it is that fact that's the key fact in
+ 
+
+ align:start position:0%
+it is that fact that's the key fact in
+this story
+
+ align:start position:0%
+this story
+ 
+
+ align:start position:0%
+this story
+um that produces the asymmetry women get
+
+ align:start position:0%
+um that produces the asymmetry women get
+ 
+
+ align:start position:0%
+um that produces the asymmetry women get
+pregnant men don't get pregnant why is
+
+ align:start position:0%
+pregnant men don't get pregnant why is
+ 
+
+ align:start position:0%
+pregnant men don't get pregnant why is
+that important well that's important
+
+ align:start position:0%
+that important well that's important
+ 
+
+ align:start position:0%
+that important well that's important
+because being pregnant
+
+ align:start position:0%
+because being pregnant
+ 
+
+ align:start position:0%
+because being pregnant
+ties you up for nine months being
+
+ align:start position:0%
+ties you up for nine months being
+ 
+
+ align:start position:0%
+ties you up for nine months being
+pregnant for nine months at a time
+
+ align:start position:0%
+pregnant for nine months at a time
+ 
+
+ align:start position:0%
+pregnant for nine months at a time
+greatly is is is a profound rate
+
+ align:start position:0%
+greatly is is is a profound rate
+ 
+
+ align:start position:0%
+greatly is is is a profound rate
+limiting step on how many kids you can
+
+ align:start position:0%
+limiting step on how many kids you can
+ 
+
+ align:start position:0%
+limiting step on how many kids you can
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+and then if you're a a human and and uh
+
+ align:start position:0%
+and then if you're a a human and and uh
+ 
+
+ align:start position:0%
+and then if you're a a human and and uh
+not not a spider or something like that
+
+ align:start position:0%
+not not a spider or something like that
+ 
+
+ align:start position:0%
+not not a spider or something like that
+once the kid is born or hatched or
+
+ align:start position:0%
+once the kid is born or hatched or
+ 
+
+ align:start position:0%
+once the kid is born or hatched or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+you still got a problem here you want
+
+ align:start position:0%
+you still got a problem here you want
+ 
+
+ align:start position:0%
+you still got a problem here you want
+this little bundle of jeans to do
+
+ align:start position:0%
+this little bundle of jeans to do
+ 
+
+ align:start position:0%
+this little bundle of jeans to do
+something for you in evolutionary terms
+
+ align:start position:0%
+something for you in evolutionary terms
+ 
+
+ align:start position:0%
+something for you in evolutionary terms
+you got to keep it alive so it's not
+
+ align:start position:0%
+you got to keep it alive so it's not
+ 
+
+ align:start position:0%
+you got to keep it alive so it's not
+just the nine months there's a long time
+
+ align:start position:0%
+just the nine months there's a long time
+ 
+
+ align:start position:0%
+just the nine months there's a long time
+long-term commitment to this little
+
+ align:start position:0%
+long-term commitment to this little
+ 
+
+ align:start position:0%
+long-term commitment to this little
+evolutionary project that you've gotten
+
+ align:start position:0%
+evolutionary project that you've gotten
+ 
+
+ align:start position:0%
+evolutionary project that you've gotten
+into the same constraints do not
+
+ align:start position:0%
+into the same constraints do not
+ 
+
+ align:start position:0%
+into the same constraints do not
+necessarily apply to men certainly the
+
+ align:start position:0%
+necessarily apply to men certainly the
+ 
+
+ align:start position:0%
+necessarily apply to men certainly the
+rate limiting step does not apply
+
+ align:start position:0%
+rate limiting step does not apply
+ 
+
+ align:start position:0%
+rate limiting step does not apply
+because in principle guys can go off and
+
+ align:start position:0%
+because in principle guys can go off and
+ 
+
+ align:start position:0%
+because in principle guys can go off and
+have a gazillion babies that's a
+
+ align:start position:0%
+have a gazillion babies that's a
+ 
+
+ align:start position:0%
+have a gazillion babies that's a
+technical term
+
+ align:start position:0%
+technical term
+ 
+
+ align:start position:0%
+technical term
+um as long as they can find the
+
+ align:start position:0%
+um as long as they can find the
+ 
+
+ align:start position:0%
+um as long as they can find the
+requisite gazillion women
+
+ align:start position:0%
+requisite gazillion women
+ 
+
+ align:start position:0%
+requisite gazillion women
+right that's the rate limiting step for
+
+ align:start position:0%
+right that's the rate limiting step for
+ 
+
+ align:start position:0%
+right that's the rate limiting step for
+men is just how many women can you
+
+ align:start position:0%
+men is just how many women can you
+ 
+
+ align:start position:0%
+men is just how many women can you
+successfully impregnate
+
+ align:start position:0%
+successfully impregnate
+ 
+
+ align:start position:0%
+successfully impregnate
+um now we're talking in we're not
+
+ align:start position:0%
+um now we're talking in we're not
+ 
+
+ align:start position:0%
+um now we're talking in we're not
+talking in what is right in in
+
+ align:start position:0%
+talking in what is right in in
+ 
+
+ align:start position:0%
+talking in what is right in in
+social civilized world or something like
+
+ align:start position:0%
+social civilized world or something like
+ 
+
+ align:start position:0%
+social civilized world or something like
+that right but we're just talking about
+
+ align:start position:0%
+that right but we're just talking about
+ 
+
+ align:start position:0%
+that right but we're just talking about
+the biology of the situation here the
+
+ align:start position:0%
+the biology of the situation here the
+ 
+
+ align:start position:0%
+the biology of the situation here the
+men don't get pregnant if if uh you get
+
+ align:start position:0%
+men don't get pregnant if if uh you get
+ 
+
+ align:start position:0%
+men don't get pregnant if if uh you get
+woman one pregnant today you can get
+
+ align:start position:0%
+woman one pregnant today you can get
+ 
+
+ align:start position:0%
+woman one pregnant today you can get
+woman two pregnant tomorrow in principle
+
+ align:start position:0%
+woman two pregnant tomorrow in principle
+ 
+
+ align:start position:0%
+woman two pregnant tomorrow in principle
+that's not true for the woman if you are
+
+ align:start position:0%
+that's not true for the woman if you are
+ 
+
+ align:start position:0%
+that's not true for the woman if you are
+a woman and you get pregnant today you
+
+ align:start position:0%
+a woman and you get pregnant today you
+ 
+
+ align:start position:0%
+a woman and you get pregnant today you
+don't get to get pregnant again tomorrow
+
+ align:start position:0%
+don't get to get pregnant again tomorrow
+ 
+
+ align:start position:0%
+don't get to get pregnant again tomorrow
+right that doesn't work so fundamental
+
+ align:start position:0%
+right that doesn't work so fundamental
+ 
+
+ align:start position:0%
+right that doesn't work so fundamental
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+The evolutionary psych argument is that
+
+ align:start position:0%
+The evolutionary psych argument is that
+ 
+
+ align:start position:0%
+The evolutionary psych argument is that
+this should produce fundamental
+
+ align:start position:0%
+this should produce fundamental
+ 
+
+ align:start position:0%
+this should produce fundamental
+differences in behavior in particular if
+
+ align:start position:0%
+differences in behavior in particular if
+ 
+
+ align:start position:0%
+differences in behavior in particular if
+your goal is to get as many successful
+
+ align:start position:0%
+your goal is to get as many successful
+ 
+
+ align:start position:0%
+your goal is to get as many successful
+bundles of genes into the Next
+
+ align:start position:0%
+bundles of genes into the Next
+ 
+
+ align:start position:0%
+bundles of genes into the Next
+Generation as possible guys should be
+
+ align:start position:0%
+Generation as possible guys should be
+ 
+
+ align:start position:0%
+Generation as possible guys should be
+inclined to have sex early and often
+
+ align:start position:0%
+inclined to have sex early and often
+ 
+
+ align:start position:0%
+inclined to have sex early and often
+with as many partners as possible
+
+ align:start position:0%
+with as many partners as possible
+ 
+
+ align:start position:0%
+with as many partners as possible
+because that's going to produce lots and
+
+ align:start position:0%
+because that's going to produce lots and
+ 
+
+ align:start position:0%
+because that's going to produce lots and
+lots of babies women should be looking
+
+ align:start position:0%
+lots of babies women should be looking
+ 
+
+ align:start position:0%
+lots of babies women should be looking
+for something more like commitment
+
+ align:start position:0%
+for something more like commitment
+ 
+
+ align:start position:0%
+for something more like commitment
+because it's a lot easier to take care
+
+ align:start position:0%
+because it's a lot easier to take care
+ 
+
+ align:start position:0%
+because it's a lot easier to take care
+of this little bundle of joy if somebody
+
+ align:start position:0%
+of this little bundle of joy if somebody
+ 
+
+ align:start position:0%
+of this little bundle of joy if somebody
+else is helping out either helping take
+
+ align:start position:0%
+else is helping out either helping take
+ 
+
+ align:start position:0%
+else is helping out either helping take
+care of the uh the kid or at the very
+
+ align:start position:0%
+care of the uh the kid or at the very
+ 
+
+ align:start position:0%
+care of the uh the kid or at the very
+least providing resources for this right
+
+ align:start position:0%
+least providing resources for this right
+ 
+
+ align:start position:0%
+least providing resources for this right
+it's an expensive business raising a kid
+
+ align:start position:0%
+it's an expensive business raising a kid
+ 
+
+ align:start position:0%
+it's an expensive business raising a kid
+not just an expensive business if you
+
+ align:start position:0%
+not just an expensive business if you
+ 
+
+ align:start position:0%
+not just an expensive business if you
+you know in your nice middle class kid
+
+ align:start position:0%
+you know in your nice middle class kid
+ 
+
+ align:start position:0%
+you know in your nice middle class kid
+and you're expecting to go to MIT or
+
+ align:start position:0%
+and you're expecting to go to MIT or
+ 
+
+ align:start position:0%
+and you're expecting to go to MIT or
+something like that it's an expensive
+
+ align:start position:0%
+something like that it's an expensive
+ 
+
+ align:start position:0%
+something like that it's an expensive
+business period you gotta feed the kid
+
+ align:start position:0%
+business period you gotta feed the kid
+ 
+
+ align:start position:0%
+business period you gotta feed the kid
+you gotta keep it warm and so on
+
+ align:start position:0%
+you gotta keep it warm and so on
+ 
+
+ align:start position:0%
+you gotta keep it warm and so on
+resources are required and you it is in
+
+ align:start position:0%
+resources are required and you it is in
+ 
+
+ align:start position:0%
+resources are required and you it is in
+your interest as as the woman to have
+
+ align:start position:0%
+your interest as as the woman to have
+ 
+
+ align:start position:0%
+your interest as as the woman to have
+um to have guys around at least a guy
+
+ align:start position:0%
+um to have guys around at least a guy
+ 
+
+ align:start position:0%
+um to have guys around at least a guy
+around who's going to provide resources
+
+ align:start position:0%
+around who's going to provide resources
+ 
+
+ align:start position:0%
+around who's going to provide resources
+now you can make up other stories you
+
+ align:start position:0%
+now you can make up other stories you
+ 
+
+ align:start position:0%
+now you can make up other stories you
+could make up a story that says it would
+
+ align:start position:0%
+could make up a story that says it would
+ 
+
+ align:start position:0%
+could make up a story that says it would
+be in the woman's interest to have
+
+ align:start position:0%
+be in the woman's interest to have
+ 
+
+ align:start position:0%
+be in the woman's interest to have
+multiple mates
+
+ align:start position:0%
+multiple mates
+ 
+
+ align:start position:0%
+multiple mates
+who are kept in some doubt about who the
+
+ align:start position:0%
+who are kept in some doubt about who the
+ 
+
+ align:start position:0%
+who are kept in some doubt about who the
+father is so that they all provide
+
+ align:start position:0%
+father is so that they all provide
+ 
+
+ align:start position:0%
+father is so that they all provide
+resource
+
+ align:start position:0%
+resource
+ 
+
+ align:start position:0%
+resource
+now it sounds funny but there's no
+
+ align:start position:0%
+now it sounds funny but there's no
+ 
+
+ align:start position:0%
+now it sounds funny but there's no
+reason why that story and there are
+
+ align:start position:0%
+reason why that story and there are
+ 
+
+ align:start position:0%
+reason why that story and there are
+species where that seems to
+
+ align:start position:0%
+species where that seems to
+ 
+
+ align:start position:0%
+species where that seems to
+um you know where that you can almost
+
+ align:start position:0%
+um you know where that you can almost
+ 
+
+ align:start position:0%
+um you know where that you can almost
+always find an animal where it works out
+
+ align:start position:0%
+always find an animal where it works out
+ 
+
+ align:start position:0%
+always find an animal where it works out
+if if humans were a polyandrous species
+
+ align:start position:0%
+if if humans were a polyandrous species
+ 
+
+ align:start position:0%
+if if humans were a polyandrous species
+a species where females had
+
+ align:start position:0%
+a species where females had
+ 
+
+ align:start position:0%
+a species where females had
+um multiple mates at the same time that
+
+ align:start position:0%
+um multiple mates at the same time that
+ 
+
+ align:start position:0%
+um multiple mates at the same time that
+that would require explanation and you
+
+ align:start position:0%
+that would require explanation and you
+ 
+
+ align:start position:0%
+that would require explanation and you
+could try explaining it in the same
+
+ align:start position:0%
+could try explaining it in the same
+ 
+
+ align:start position:0%
+could try explaining it in the same
+terms as it turns out
+
+ align:start position:0%
+terms as it turns out
+ 
+
+ align:start position:0%
+terms as it turns out
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in you know across cultures the pattern
+
+ align:start position:0%
+in you know across cultures the pattern
+ 
+
+ align:start position:0%
+in you know across cultures the pattern
+is either one male one female or
+
+ align:start position:0%
+is either one male one female or
+ 
+
+ align:start position:0%
+is either one male one female or
+um uh one male several females that
+
+ align:start position:0%
+um uh one male several females that
+ 
+
+ align:start position:0%
+um uh one male several females that
+there are much rarer instances of one
+
+ align:start position:0%
+there are much rarer instances of one
+ 
+
+ align:start position:0%
+there are much rarer instances of one
+female
+
+ align:start position:0%
+female
+ 
+
+ align:start position:0%
+female
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+many males in in human populations
+
+ align:start position:0%
+many males in in human populations
+ 
+
+ align:start position:0%
+many males in in human populations
+um so the mainline story is that the the
+
+ align:start position:0%
+um so the mainline story is that the the
+ 
+
+ align:start position:0%
+um so the mainline story is that the the
+the constraints of biology are going to
+
+ align:start position:0%
+the constraints of biology are going to
+ 
+
+ align:start position:0%
+the constraints of biology are going to
+Incline uh the population to a
+
+ align:start position:0%
+Incline uh the population to a
+ 
+
+ align:start position:0%
+Incline uh the population to a
+population of males who are interested
+
+ align:start position:0%
+population of males who are interested
+ 
+
+ align:start position:0%
+population of males who are interested
+um in
+
+ align:start position:0%
+um in
+ 
+
+ align:start position:0%
+um in
+frequent sex and uh and and you know
+
+ align:start position:0%
+frequent sex and uh and and you know
+ 
+
+ align:start position:0%
+frequent sex and uh and and you know
+whenever and women who are going to be
+
+ align:start position:0%
+whenever and women who are going to be
+ 
+
+ align:start position:0%
+whenever and women who are going to be
+looking for uh a mate who's gonna who's
+
+ align:start position:0%
+looking for uh a mate who's gonna who's
+ 
+
+ align:start position:0%
+looking for uh a mate who's gonna who's
+willing to make some sort of commitment
+
+ align:start position:0%
+willing to make some sort of commitment
+ 
+
+ align:start position:0%
+willing to make some sort of commitment
+now is there any evidence for
+
+ align:start position:0%
+now is there any evidence for
+ 
+
+ align:start position:0%
+now is there any evidence for
+um evolutionary forces biological
+
+ align:start position:0%
+um evolutionary forces biological
+ 
+
+ align:start position:0%
+um evolutionary forces biological
+constraints on mate selection in humans
+
+ align:start position:0%
+constraints on mate selection in humans
+ 
+
+ align:start position:0%
+constraints on mate selection in humans
+quite apart from these questions about
+
+ align:start position:0%
+quite apart from these questions about
+ 
+
+ align:start position:0%
+quite apart from these questions about
+uh you know who wants sex and when are
+
+ align:start position:0%
+uh you know who wants sex and when are
+ 
+
+ align:start position:0%
+uh you know who wants sex and when are
+there any is there any evidence for this
+
+ align:start position:0%
+there any is there any evidence for this
+ 
+
+ align:start position:0%
+there any is there any evidence for this
+um at all uh the answer is yes and and
+
+ align:start position:0%
+um at all uh the answer is yes and and
+ 
+
+ align:start position:0%
+um at all uh the answer is yes and and
+and in if I give some examples it's sort
+
+ align:start position:0%
+and in if I give some examples it's sort
+ 
+
+ align:start position:0%
+and in if I give some examples it's sort
+of surprising that this was ever
+
+ align:start position:0%
+of surprising that this was ever
+ 
+
+ align:start position:0%
+of surprising that this was ever
+controversial
+
+ align:start position:0%
+controversial
+ 
+
+ align:start position:0%
+controversial
+um so well let's give an example for
+
+ align:start position:0%
+um so well let's give an example for
+ 
+
+ align:start position:0%
+um so well let's give an example for
+example if you're looking for evidence
+
+ align:start position:0%
+example if you're looking for evidence
+ 
+
+ align:start position:0%
+example if you're looking for evidence
+that something has these sort of
+
+ align:start position:0%
+that something has these sort of
+ 
+
+ align:start position:0%
+that something has these sort of
+biological evolutionary Roots what
+
+ align:start position:0%
+biological evolutionary Roots what
+ 
+
+ align:start position:0%
+biological evolutionary Roots what
+you're looking for is something that is
+
+ align:start position:0%
+you're looking for is something that is
+ 
+
+ align:start position:0%
+you're looking for is something that is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+ubiquitous in human societies you don't
+
+ align:start position:0%
+ubiquitous in human societies you don't
+ 
+
+ align:start position:0%
+ubiquitous in human societies you don't
+want something where
+
+ align:start position:0%
+want something where
+ 
+
+ align:start position:0%
+want something where
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh you know it's deemed attractive in
+
+ align:start position:0%
+uh you know it's deemed attractive in
+ 
+
+ align:start position:0%
+uh you know it's deemed attractive in
+one population or the desirable in one
+
+ align:start position:0%
+one population or the desirable in one
+ 
+
+ align:start position:0%
+one population or the desirable in one
+population and not in another population
+
+ align:start position:0%
+population and not in another population
+ 
+
+ align:start position:0%
+population and not in another population
+that could be very culturally determined
+
+ align:start position:0%
+that could be very culturally determined
+ 
+
+ align:start position:0%
+that could be very culturally determined
+so I I don't know of much in the way of
+
+ align:start position:0%
+so I I don't know of much in the way of
+ 
+
+ align:start position:0%
+so I I don't know of much in the way of
+great evolutionary psych arguments in
+
+ align:start position:0%
+great evolutionary psych arguments in
+ 
+
+ align:start position:0%
+great evolutionary psych arguments in
+favor of which bits of your body should
+
+ align:start position:0%
+favor of which bits of your body should
+ 
+
+ align:start position:0%
+favor of which bits of your body should
+be pierced right that that's that that
+
+ align:start position:0%
+be pierced right that that's that that
+ 
+
+ align:start position:0%
+be pierced right that that's that that
+seems to be the sort of thing that some
+
+ align:start position:0%
+seems to be the sort of thing that some
+ 
+
+ align:start position:0%
+seems to be the sort of thing that some
+some groups think this is attractive and
+
+ align:start position:0%
+some groups think this is attractive and
+ 
+
+ align:start position:0%
+some groups think this is attractive and
+some groups think that is attractive and
+
+ align:start position:0%
+some groups think that is attractive and
+ 
+
+ align:start position:0%
+some groups think that is attractive and
+yeah but across humans cultures
+
+ align:start position:0%
+yeah but across humans cultures
+ 
+
+ align:start position:0%
+yeah but across humans cultures
+a consistent preference for mates who
+
+ align:start position:0%
+a consistent preference for mates who
+ 
+
+ align:start position:0%
+a consistent preference for mates who
+are young and healthy as opposed to
+
+ align:start position:0%
+are young and healthy as opposed to
+ 
+
+ align:start position:0%
+are young and healthy as opposed to
+mates who are old and sick
+
+ align:start position:0%
+mates who are old and sick
+ 
+
+ align:start position:0%
+mates who are old and sick
+there is no place where
+
+ align:start position:0%
+there is no place where
+ 
+
+ align:start position:0%
+there is no place where
+um the the ideal of attractiveness is
+
+ align:start position:0%
+um the the ideal of attractiveness is
+ 
+
+ align:start position:0%
+um the the ideal of attractiveness is
+um is an old person with a disease it
+
+ align:start position:0%
+um is an old person with a disease it
+ 
+
+ align:start position:0%
+um is an old person with a disease it
+just isn't the case now it almost sounds
+
+ align:start position:0%
+just isn't the case now it almost sounds
+ 
+
+ align:start position:0%
+just isn't the case now it almost sounds
+funny but
+
+ align:start position:0%
+funny but
+ 
+
+ align:start position:0%
+funny but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+well you know
+
+ align:start position:0%
+well you know
+ 
+
+ align:start position:0%
+well you know
+I got a house full of books I like to
+
+ align:start position:0%
+I got a house full of books I like to
+ 
+
+ align:start position:0%
+I got a house full of books I like to
+collect books it turns out that the
+
+ align:start position:0%
+collect books it turns out that the
+ 
+
+ align:start position:0%
+collect books it turns out that the
+books I like best are pretty old and
+
+ align:start position:0%
+books I like best are pretty old and
+ 
+
+ align:start position:0%
+books I like best are pretty old and
+diseased
+
+ align:start position:0%
+diseased
+ 
+
+ align:start position:0%
+diseased
+and and that's not weird right that that
+
+ align:start position:0%
+and and that's not weird right that that
+ 
+
+ align:start position:0%
+and and that's not weird right that that
+doesn't strike people as as odd
+
+ align:start position:0%
+doesn't strike people as as odd
+ 
+
+ align:start position:0%
+doesn't strike people as as odd
+um there you do need to explain it
+
+ align:start position:0%
+um there you do need to explain it
+ 
+
+ align:start position:0%
+um there you do need to explain it
+doesn't take much work to explain why
+
+ align:start position:0%
+doesn't take much work to explain why
+ 
+
+ align:start position:0%
+doesn't take much work to explain why
+there's a preference for young healthy
+
+ align:start position:0%
+there's a preference for young healthy
+ 
+
+ align:start position:0%
+there's a preference for young healthy
+mates over old disease mates if you
+
+ align:start position:0%
+mates over old disease mates if you
+ 
+
+ align:start position:0%
+mates over old disease mates if you
+think that this had something to do with
+
+ align:start position:0%
+think that this had something to do with
+ 
+
+ align:start position:0%
+think that this had something to do with
+a drive towards reproduction you're much
+
+ align:start position:0%
+a drive towards reproduction you're much
+ 
+
+ align:start position:0%
+a drive towards reproduction you're much
+more likely to reproduce successfully
+
+ align:start position:0%
+more likely to reproduce successfully
+ 
+
+ align:start position:0%
+more likely to reproduce successfully
+with a young healthy mate
+
+ align:start position:0%
+with a young healthy mate
+ 
+
+ align:start position:0%
+with a young healthy mate
+um the Contra the reason that these
+
+ align:start position:0%
+um the Contra the reason that these
+ 
+
+ align:start position:0%
+um the Contra the reason that these
+topics have been
+
+ align:start position:0%
+topics have been
+ 
+
+ align:start position:0%
+topics have been
+controversial has less to do with the
+
+ align:start position:0%
+controversial has less to do with the
+ 
+
+ align:start position:0%
+controversial has less to do with the
+science of the situation or has had less
+
+ align:start position:0%
+science of the situation or has had less
+ 
+
+ align:start position:0%
+science of the situation or has had less
+to do with the science of the situation
+
+ align:start position:0%
+to do with the science of the situation
+ 
+
+ align:start position:0%
+to do with the science of the situation
+than with the politics of the situation
+
+ align:start position:0%
+than with the politics of the situation
+ 
+
+ align:start position:0%
+than with the politics of the situation
+it is possible as in the IQ case to go
+
+ align:start position:0%
+it is possible as in the IQ case to go
+ 
+
+ align:start position:0%
+it is possible as in the IQ case to go
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+uncontroversial or or fairly
+
+ align:start position:0%
+uncontroversial or or fairly
+ 
+
+ align:start position:0%
+uncontroversial or or fairly
+straightforward bits of science to um to
+
+ align:start position:0%
+straightforward bits of science to um to
+ 
+
+ align:start position:0%
+straightforward bits of science to um to
+undesirable or at least controversial
+
+ align:start position:0%
+undesirable or at least controversial
+ 
+
+ align:start position:0%
+undesirable or at least controversial
+conclusions in in a more political realm
+
+ align:start position:0%
+conclusions in in a more political realm
+ 
+
+ align:start position:0%
+conclusions in in a more political realm
+so the sorts of things if you agree you
+
+ align:start position:0%
+so the sorts of things if you agree you
+ 
+
+ align:start position:0%
+so the sorts of things if you agree you
+know if if you are forced by the data to
+
+ align:start position:0%
+know if if you are forced by the data to
+ 
+
+ align:start position:0%
+know if if you are forced by the data to
+say look there's a whopping asymmetry
+
+ align:start position:0%
+say look there's a whopping asymmetry
+ 
+
+ align:start position:0%
+say look there's a whopping asymmetry
+between males and females in in this
+
+ align:start position:0%
+between males and females in in this
+ 
+
+ align:start position:0%
+between males and females in in this
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+it is perhaps the concern is that it's a
+
+ align:start position:0%
+it is perhaps the concern is that it's a
+ 
+
+ align:start position:0%
+it is perhaps the concern is that it's a
+slippery slope from you know here to
+
+ align:start position:0%
+slippery slope from you know here to
+ 
+
+ align:start position:0%
+slippery slope from you know here to
+saying well it's okay to pay women less
+
+ align:start position:0%
+saying well it's okay to pay women less
+ 
+
+ align:start position:0%
+saying well it's okay to pay women less
+than men the actual causal chain between
+
+ align:start position:0%
+than men the actual causal chain between
+ 
+
+ align:start position:0%
+than men the actual causal chain between
+this particular factoid and paying women
+
+ align:start position:0%
+this particular factoid and paying women
+ 
+
+ align:start position:0%
+this particular factoid and paying women
+less than men is not immediately obvious
+
+ align:start position:0%
+less than men is not immediately obvious
+ 
+
+ align:start position:0%
+less than men is not immediately obvious
+to me as I'm saying it right here but
+
+ align:start position:0%
+to me as I'm saying it right here but
+ 
+
+ align:start position:0%
+to me as I'm saying it right here but
+the the reason that this was politically
+
+ align:start position:0%
+the the reason that this was politically
+ 
+
+ align:start position:0%
+the the reason that this was politically
+it is politically controversial is
+
+ align:start position:0%
+it is politically controversial is
+ 
+
+ align:start position:0%
+it is politically controversial is
+because anything that acknowledges a
+
+ align:start position:0%
+because anything that acknowledges a
+ 
+
+ align:start position:0%
+because anything that acknowledges a
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+some sort of biological difference
+
+ align:start position:0%
+some sort of biological difference
+ 
+
+ align:start position:0%
+some sort of biological difference
+between say men and women
+
+ align:start position:0%
+between say men and women
+ 
+
+ align:start position:0%
+between say men and women
+and in principle be used as a defense
+
+ align:start position:0%
+and in principle be used as a defense
+ 
+
+ align:start position:0%
+and in principle be used as a defense
+for social inequalities that you may
+
+ align:start position:0%
+for social inequalities that you may
+ 
+
+ align:start position:0%
+for social inequalities that you may
+want you that you may not find desirable
+
+ align:start position:0%
+want you that you may not find desirable
+ 
+
+ align:start position:0%
+want you that you may not find desirable
+but that's really a separate question
+
+ align:start position:0%
+but that's really a separate question
+ 
+
+ align:start position:0%
+but that's really a separate question
+the the scientific question or the
+
+ align:start position:0%
+the the scientific question or the
+ 
+
+ align:start position:0%
+the the scientific question or the
+psychological question is are there
+
+ align:start position:0%
+psychological question is are there
+ 
+
+ align:start position:0%
+psychological question is are there
+differences there certainly seem to be
+
+ align:start position:0%
+differences there certainly seem to be
+ 
+
+ align:start position:0%
+differences there certainly seem to be
+data differences and and and and where
+
+ align:start position:0%
+data differences and and and and where
+ 
+
+ align:start position:0%
+data differences and and and and where
+do they
+
+ align:start position:0%
+do they
+ 
+
+ align:start position:0%
+do they
+where do they come from
+
+ align:start position:0%
+where do they come from
+ 
+
+ align:start position:0%
+where do they come from
+um so uh
+
+ align:start position:0%
+um so uh
+ 
+
+ align:start position:0%
+um so uh
+if you ask that there are other there
+
+ align:start position:0%
+if you ask that there are other there
+ 
+
+ align:start position:0%
+if you ask that there are other there
+are other sort of universal preferences
+
+ align:start position:0%
+are other sort of universal preferences
+ 
+
+ align:start position:0%
+are other sort of universal preferences
+that seem to reflect this desire for a
+
+ align:start position:0%
+that seem to reflect this desire for a
+ 
+
+ align:start position:0%
+that seem to reflect this desire for a
+mate who is likely to be
+
+ align:start position:0%
+mate who is likely to be
+ 
+
+ align:start position:0%
+mate who is likely to be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a a good partner in reproduction so
+
+ align:start position:0%
+a a good partner in reproduction so
+ 
+
+ align:start position:0%
+a a good partner in reproduction so
+there is a what is it that makes a face
+
+ align:start position:0%
+there is a what is it that makes a face
+ 
+
+ align:start position:0%
+there is a what is it that makes a face
+attractive well one of the things that
+
+ align:start position:0%
+attractive well one of the things that
+ 
+
+ align:start position:0%
+attractive well one of the things that
+is attractive is facial symmetry that
+
+ align:start position:0%
+is attractive is facial symmetry that
+ 
+
+ align:start position:0%
+is attractive is facial symmetry that
+all all else being equal
+
+ align:start position:0%
+all all else being equal
+ 
+
+ align:start position:0%
+all all else being equal
+um it's considered to be better and
+
+ align:start position:0%
+um it's considered to be better and
+ 
+
+ align:start position:0%
+um it's considered to be better and
+you're considered to be more attractive
+
+ align:start position:0%
+you're considered to be more attractive
+ 
+
+ align:start position:0%
+you're considered to be more attractive
+a face is rated as more attractive it's
+
+ align:start position:0%
+a face is rated as more attractive it's
+ 
+
+ align:start position:0%
+a face is rated as more attractive it's
+some if it's symmetrical then if it's
+
+ align:start position:0%
+some if it's symmetrical then if it's
+ 
+
+ align:start position:0%
+some if it's symmetrical then if it's
+asymmetrical why is that most of the
+
+ align:start position:0%
+asymmetrical why is that most of the
+ 
+
+ align:start position:0%
+asymmetrical why is that most of the
+things that are likely likely to produce
+
+ align:start position:0%
+things that are likely likely to produce
+ 
+
+ align:start position:0%
+things that are likely likely to produce
+noticeable asymmetries in um in the face
+
+ align:start position:0%
+noticeable asymmetries in um in the face
+ 
+
+ align:start position:0%
+noticeable asymmetries in um in the face
+are um are things that suggest either
+
+ align:start position:0%
+are um are things that suggest either
+ 
+
+ align:start position:0%
+are um are things that suggest either
+um a genetic deformity of some sort or
+
+ align:start position:0%
+um a genetic deformity of some sort or
+ 
+
+ align:start position:0%
+um a genetic deformity of some sort or
+or an accident neither of which are
+
+ align:start position:0%
+or an accident neither of which are
+ 
+
+ align:start position:0%
+or an accident neither of which are
+strong uh you know the the neither are
+
+ align:start position:0%
+strong uh you know the the neither are
+ 
+
+ align:start position:0%
+strong uh you know the the neither are
+going to be great advertisements for
+
+ align:start position:0%
+going to be great advertisements for
+ 
+
+ align:start position:0%
+going to be great advertisements for
+um reproductive success
+
+ align:start position:0%
+um reproductive success
+ 
+
+ align:start position:0%
+um reproductive success
+right imagine somebody with half a face
+
+ align:start position:0%
+right imagine somebody with half a face
+ 
+
+ align:start position:0%
+right imagine somebody with half a face
+there's some you you know intuitively
+
+ align:start position:0%
+there's some you you know intuitively
+ 
+
+ align:start position:0%
+there's some you you know intuitively
+that either you're watching a sci-fi
+
+ align:start position:0%
+that either you're watching a sci-fi
+ 
+
+ align:start position:0%
+that either you're watching a sci-fi
+movie or it is something fundamentally
+
+ align:start position:0%
+movie or it is something fundamentally
+ 
+
+ align:start position:0%
+movie or it is something fundamentally
+um fundamentally wrong here oh what is
+
+ align:start position:0%
+um fundamentally wrong here oh what is
+ 
+
+ align:start position:0%
+um fundamentally wrong here oh what is
+an attractive face in general is is a in
+
+ align:start position:0%
+an attractive face in general is is a in
+ 
+
+ align:start position:0%
+an attractive face in general is is a in
+is an interesting I didn't put all those
+
+ align:start position:0%
+is an interesting I didn't put all those
+ 
+
+ align:start position:0%
+is an interesting I didn't put all those
+references on the handout
+
+ align:start position:0%
+references on the handout
+ 
+
+ align:start position:0%
+references on the handout
+um there's an interesting literature on
+
+ align:start position:0%
+um there's an interesting literature on
+ 
+
+ align:start position:0%
+um there's an interesting literature on
+what makes an attractive face that that
+
+ align:start position:0%
+what makes an attractive face that that
+ 
+
+ align:start position:0%
+what makes an attractive face that that
+uh um is worth a little side note uh
+
+ align:start position:0%
+uh um is worth a little side note uh
+ 
+
+ align:start position:0%
+uh um is worth a little side note uh
+this uh one theory is that what is
+
+ align:start position:0%
+this uh one theory is that what is
+ 
+
+ align:start position:0%
+this uh one theory is that what is
+attractive
+
+ align:start position:0%
+attractive
+ 
+
+ align:start position:0%
+attractive
+um is not you you could have two
+
+ align:start position:0%
+um is not you you could have two
+ 
+
+ align:start position:0%
+um is not you you could have two
+theories one Theory would be attractive
+
+ align:start position:0%
+theories one Theory would be attractive
+ 
+
+ align:start position:0%
+theories one Theory would be attractive
+is one end of a scale that runs from
+
+ align:start position:0%
+is one end of a scale that runs from
+ 
+
+ align:start position:0%
+is one end of a scale that runs from
+ugly to gorgeous right and that all
+
+ align:start position:0%
+ugly to gorgeous right and that all
+ 
+
+ align:start position:0%
+ugly to gorgeous right and that all
+those Hollywood actors and actresses are
+
+ align:start position:0%
+those Hollywood actors and actresses are
+ 
+
+ align:start position:0%
+those Hollywood actors and actresses are
+pegged out here on the gorgeous end of
+
+ align:start position:0%
+pegged out here on the gorgeous end of
+ 
+
+ align:start position:0%
+pegged out here on the gorgeous end of
+some some scale
+
+ align:start position:0%
+some some scale
+ 
+
+ align:start position:0%
+some some scale
+um what um
+
+ align:start position:0%
+um what um
+ 
+
+ align:start position:0%
+um what um
+the alternative theory is that it is
+
+ align:start position:0%
+the alternative theory is that it is
+ 
+
+ align:start position:0%
+the alternative theory is that it is
+um average
+
+ align:start position:0%
+um average
+ 
+
+ align:start position:0%
+um average
+faces and that an average face is what's
+
+ align:start position:0%
+faces and that an average face is what's
+ 
+
+ align:start position:0%
+faces and that an average face is what's
+normal is what's deemed attractive and
+
+ align:start position:0%
+normal is what's deemed attractive and
+ 
+
+ align:start position:0%
+normal is what's deemed attractive and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um the evidence for this the original
+
+ align:start position:0%
+um the evidence for this the original
+ 
+
+ align:start position:0%
+um the evidence for this the original
+evidence for this comes from a
+
+ align:start position:0%
+evidence for this comes from a
+ 
+
+ align:start position:0%
+evidence for this comes from a
+photographic technique where what you
+
+ align:start position:0%
+photographic technique where what you
+ 
+
+ align:start position:0%
+photographic technique where what you
+did was you took a whole bunch of
+
+ align:start position:0%
+did was you took a whole bunch of
+ 
+
+ align:start position:0%
+did was you took a whole bunch of
+photographs and superimposed them to
+
+ align:start position:0%
+photographs and superimposed them to
+ 
+
+ align:start position:0%
+photographs and superimposed them to
+make a composite face
+
+ align:start position:0%
+make a composite face
+ 
+
+ align:start position:0%
+make a composite face
+and you found that those were rated as
+
+ align:start position:0%
+and you found that those were rated as
+ 
+
+ align:start position:0%
+and you found that those were rated as
+more attractive than individual faces
+
+ align:start position:0%
+more attractive than individual faces
+ 
+
+ align:start position:0%
+more attractive than individual faces
+um as as a whole and this this was being
+
+ align:start position:0%
+um as as a whole and this this was being
+ 
+
+ align:start position:0%
+um as as a whole and this this was being
+done by clever techniques back oh I
+
+ align:start position:0%
+done by clever techniques back oh I
+ 
+
+ align:start position:0%
+done by clever techniques back oh I
+think you know in early part of the 20th
+
+ align:start position:0%
+think you know in early part of the 20th
+ 
+
+ align:start position:0%
+think you know in early part of the 20th
+century
+
+ align:start position:0%
+century
+ 
+
+ align:start position:0%
+century
+um and it's it's gotten a lot easier now
+
+ align:start position:0%
+um and it's it's gotten a lot easier now
+ 
+
+ align:start position:0%
+um and it's it's gotten a lot easier now
+that we've got computers to to to do
+
+ align:start position:0%
+that we've got computers to to to do
+ 
+
+ align:start position:0%
+that we've got computers to to to do
+these sort of things the difficulty
+
+ align:start position:0%
+these sort of things the difficulty
+ 
+
+ align:start position:0%
+these sort of things the difficulty
+one of the things that made this uh
+
+ align:start position:0%
+one of the things that made this uh
+ 
+
+ align:start position:0%
+one of the things that made this uh
+research a little tricky is that one
+
+ align:start position:0%
+research a little tricky is that one
+ 
+
+ align:start position:0%
+research a little tricky is that one
+thing that averaging faces does is it
+
+ align:start position:0%
+thing that averaging faces does is it
+ 
+
+ align:start position:0%
+thing that averaging faces does is it
+does wonders for your complexion
+
+ align:start position:0%
+does wonders for your complexion
+ 
+
+ align:start position:0%
+does wonders for your complexion
+nobody you know there are just not uh
+
+ align:start position:0%
+nobody you know there are just not uh
+ 
+
+ align:start position:0%
+nobody you know there are just not uh
+you know you know everybody's knows it's
+
+ align:start position:0%
+you know you know everybody's knows it's
+ 
+
+ align:start position:0%
+you know you know everybody's knows it's
+in more or less the same place but
+
+ align:start position:0%
+in more or less the same place but
+ 
+
+ align:start position:0%
+in more or less the same place but
+everybody's zit is not and so if you
+
+ align:start position:0%
+everybody's zit is not and so if you
+ 
+
+ align:start position:0%
+everybody's zit is not and so if you
+average a hundred faces you get people
+
+ align:start position:0%
+average a hundred faces you get people
+ 
+
+ align:start position:0%
+average a hundred faces you get people
+with gorgeous complexions and there's
+
+ align:start position:0%
+with gorgeous complexions and there's
+ 
+
+ align:start position:0%
+with gorgeous complexions and there's
+some part of that effect that just comes
+
+ align:start position:0%
+some part of that effect that just comes
+ 
+
+ align:start position:0%
+some part of that effect that just comes
+from the fact that um they look like
+
+ align:start position:0%
+from the fact that um they look like
+ 
+
+ align:start position:0%
+from the fact that um they look like
+they had really healthy skin
+
+ align:start position:0%
+they had really healthy skin
+ 
+
+ align:start position:0%
+they had really healthy skin
+um that it's a debate that jumps back
+
+ align:start position:0%
+um that it's a debate that jumps back
+ 
+
+ align:start position:0%
+um that it's a debate that jumps back
+and forth if you turn out to be deeply
+
+ align:start position:0%
+and forth if you turn out to be deeply
+ 
+
+ align:start position:0%
+and forth if you turn out to be deeply
+interested in what makes a face
+
+ align:start position:0%
+interested in what makes a face
+ 
+
+ align:start position:0%
+interested in what makes a face
+attractive send me a note I'll send you
+
+ align:start position:0%
+attractive send me a note I'll send you
+ 
+
+ align:start position:0%
+attractive send me a note I'll send you
+the uh the references since I see I
+
+ align:start position:0%
+the uh the references since I see I
+ 
+
+ align:start position:0%
+the uh the references since I see I
+didn't put them on the uh on the handout
+
+ align:start position:0%
+didn't put them on the uh on the handout
+ 
+
+ align:start position:0%
+didn't put them on the uh on the handout
+um we can ask for a couple other things
+
+ align:start position:0%
+um we can ask for a couple other things
+ 
+
+ align:start position:0%
+um we can ask for a couple other things
+that that suggest these universals
+
+ align:start position:0%
+that that suggest these universals
+ 
+
+ align:start position:0%
+that that suggest these universals
+across human populations
+
+ align:start position:0%
+across human populations
+ 
+
+ align:start position:0%
+across human populations
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on average
+
+ align:start position:0%
+on average
+ 
+
+ align:start position:0%
+on average
+if uh uh
+
+ align:start position:0%
+if uh uh
+ 
+
+ align:start position:0%
+if uh uh
+what What's what what's more desirable
+
+ align:start position:0%
+what What's what what's more desirable
+ 
+
+ align:start position:0%
+what What's what what's more desirable
+in a mate uh richer or poorer
+
+ align:start position:0%
+in a mate uh richer or poorer
+ 
+
+ align:start position:0%
+in a mate uh richer or poorer
+richer that's easy enough
+
+ align:start position:0%
+richer that's easy enough
+ 
+
+ align:start position:0%
+richer that's easy enough
+um is that preference the same for men
+
+ align:start position:0%
+um is that preference the same for men
+ 
+
+ align:start position:0%
+um is that preference the same for men
+and women who want who's more interested
+
+ align:start position:0%
+and women who want who's more interested
+ 
+
+ align:start position:0%
+and women who want who's more interested
+in finding I'll tell you the answer uh
+
+ align:start position:0%
+in finding I'll tell you the answer uh
+ 
+
+ align:start position:0%
+in finding I'll tell you the answer uh
+it's not the same how many vote that uh
+
+ align:start position:0%
+it's not the same how many vote that uh
+ 
+
+ align:start position:0%
+it's not the same how many vote that uh
+that it's men who are more interested in
+
+ align:start position:0%
+that it's men who are more interested in
+ 
+
+ align:start position:0%
+that it's men who are more interested in
+finding a wealthy mate
+
+ align:start position:0%
+finding a wealthy mate
+ 
+
+ align:start position:0%
+finding a wealthy mate
+how many vote that it's women
+
+ align:start position:0%
+how many vote that it's women
+ 
+
+ align:start position:0%
+how many vote that it's women
+you got the right intuition and The
+
+ align:start position:0%
+you got the right intuition and The
+ 
+
+ align:start position:0%
+you got the right intuition and The
+evolutionary psych story there is the
+
+ align:start position:0%
+evolutionary psych story there is the
+ 
+
+ align:start position:0%
+evolutionary psych story there is the
+resource story that what you're looking
+
+ align:start position:0%
+resource story that what you're looking
+ 
+
+ align:start position:0%
+resource story that what you're looking
+for is evidence of of uh resource you
+
+ align:start position:0%
+for is evidence of of uh resource you
+ 
+
+ align:start position:0%
+for is evidence of of uh resource you
+know does this guy is this guy going to
+
+ align:start position:0%
+know does this guy is this guy going to
+ 
+
+ align:start position:0%
+know does this guy is this guy going to
+help me uh feed all those hundreds of
+
+ align:start position:0%
+help me uh feed all those hundreds of
+ 
+
+ align:start position:0%
+help me uh feed all those hundreds of
+babies that he thinks we're going to
+
+ align:start position:0%
+babies that he thinks we're going to
+ 
+
+ align:start position:0%
+babies that he thinks we're going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+um the uh and and this is also presumed
+
+ align:start position:0%
+um the uh and and this is also presumed
+ 
+
+ align:start position:0%
+um the uh and and this is also presumed
+to be uh the
+
+ align:start position:0%
+to be uh the
+ 
+
+ align:start position:0%
+to be uh the
+you know why why is it that driving you
+
+ align:start position:0%
+you know why why is it that driving you
+ 
+
+ align:start position:0%
+you know why why is it that driving you
+know cruising around town in the fancy
+
+ align:start position:0%
+know cruising around town in the fancy
+ 
+
+ align:start position:0%
+know cruising around town in the fancy
+car you know what's that about that's a
+
+ align:start position:0%
+car you know what's that about that's a
+ 
+
+ align:start position:0%
+car you know what's that about that's a
+peacock tail effect I think I already
+
+ align:start position:0%
+peacock tail effect I think I already
+ 
+
+ align:start position:0%
+peacock tail effect I think I already
+described the peacock tail effect uh
+
+ align:start position:0%
+described the peacock tail effect uh
+ 
+
+ align:start position:0%
+described the peacock tail effect uh
+earlier in the course the idea is you
+
+ align:start position:0%
+earlier in the course the idea is you
+ 
+
+ align:start position:0%
+earlier in the course the idea is you
+know I'm showing off my resources I've
+
+ align:start position:0%
+know I'm showing off my resources I've
+ 
+
+ align:start position:0%
+know I'm showing off my resources I've
+got so much money that I can buy this
+
+ align:start position:0%
+got so much money that I can buy this
+ 
+
+ align:start position:0%
+got so much money that I can buy this
+stupid car my hubcaps cost more than
+
+ align:start position:0%
+stupid car my hubcaps cost more than
+ 
+
+ align:start position:0%
+stupid car my hubcaps cost more than
+your house
+
+ align:start position:0%
+your house
+ 
+
+ align:start position:0%
+your house
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which is why you want to mate with me
+
+ align:start position:0%
+which is why you want to mate with me
+ 
+
+ align:start position:0%
+which is why you want to mate with me
+yeah this is this is this is presumed to
+
+ align:start position:0%
+yeah this is this is this is presumed to
+ 
+
+ align:start position:0%
+yeah this is this is this is presumed to
+be the way that the okay
+
+ align:start position:0%
+be the way that the okay
+ 
+
+ align:start position:0%
+be the way that the okay
+um how about age of uh of spouse or age
+
+ align:start position:0%
+um how about age of uh of spouse or age
+ 
+
+ align:start position:0%
+um how about age of uh of spouse or age
+age of age of mate
+
+ align:start position:0%
+age of age of mate
+ 
+
+ align:start position:0%
+age of age of mate
+um on average if you are a male you want
+
+ align:start position:0%
+um on average if you are a male you want
+ 
+
+ align:start position:0%
+um on average if you are a male you want
+a uh this is this is very importantly on
+
+ align:start position:0%
+a uh this is this is very importantly on
+ 
+
+ align:start position:0%
+a uh this is this is very importantly on
+average because it's not to say you're
+
+ align:start position:0%
+average because it's not to say you're
+ 
+
+ align:start position:0%
+average because it's not to say you're
+sitting there well let's get the data
+
+ align:start position:0%
+sitting there well let's get the data
+ 
+
+ align:start position:0%
+sitting there well let's get the data
+point first
+
+ align:start position:0%
+point first
+ 
+
+ align:start position:0%
+point first
+um if if you're a male on average how
+
+ align:start position:0%
+um if if you're a male on average how
+ 
+
+ align:start position:0%
+um if if you're a male on average how
+many people vote that you are looking
+
+ align:start position:0%
+many people vote that you are looking
+ 
+
+ align:start position:0%
+many people vote that you are looking
+for a mate who is uh whether this is a
+
+ align:start position:0%
+for a mate who is uh whether this is a
+ 
+
+ align:start position:0%
+for a mate who is uh whether this is a
+three alternative Force choice you gotta
+
+ align:start position:0%
+three alternative Force choice you gotta
+ 
+
+ align:start position:0%
+three alternative Force choice you gotta
+vote for one of them a little older
+
+ align:start position:0%
+vote for one of them a little older
+ 
+
+ align:start position:0%
+vote for one of them a little older
+exactly the same age little younger how
+
+ align:start position:0%
+exactly the same age little younger how
+ 
+
+ align:start position:0%
+exactly the same age little younger how
+many vote for a little older
+
+ align:start position:0%
+many vote for a little older
+ 
+
+ align:start position:0%
+many vote for a little older
+how many vote for just the same age
+
+ align:start position:0%
+how many vote for just the same age
+ 
+
+ align:start position:0%
+how many vote for just the same age
+how many vote for a little younger okay
+
+ align:start position:0%
+how many vote for a little younger okay
+ 
+
+ align:start position:0%
+how many vote for a little younger okay
+you got that intuition right
+
+ align:start position:0%
+you got that intuition right
+ 
+
+ align:start position:0%
+you got that intuition right
+um the uh so males uh on average in
+
+ align:start position:0%
+um the uh so males uh on average in
+ 
+
+ align:start position:0%
+um the uh so males uh on average in
+culture after culture seek mates who are
+
+ align:start position:0%
+culture after culture seek mates who are
+ 
+
+ align:start position:0%
+culture after culture seek mates who are
+a little younger they amount varies
+
+ align:start position:0%
+a little younger they amount varies
+ 
+
+ align:start position:0%
+a little younger they amount varies
+culturally In some cultures it's
+
+ align:start position:0%
+culturally In some cultures it's
+ 
+
+ align:start position:0%
+culturally In some cultures it's
+significantly younger In some cultures
+
+ align:start position:0%
+significantly younger In some cultures
+ 
+
+ align:start position:0%
+significantly younger In some cultures
+it's it's only a couple of years but it
+
+ align:start position:0%
+it's it's only a couple of years but it
+ 
+
+ align:start position:0%
+it's it's only a couple of years but it
+is a cross-cultured uh
+
+ align:start position:0%
+is a cross-cultured uh
+ 
+
+ align:start position:0%
+is a cross-cultured uh
+um younger
+
+ align:start position:0%
+um younger
+ 
+
+ align:start position:0%
+um younger
+um oh and okay so the point I was going
+
+ align:start position:0%
+um oh and okay so the point I was going
+ 
+
+ align:start position:0%
+um oh and okay so the point I was going
+to make before is you're sitting there
+
+ align:start position:0%
+to make before is you're sitting there
+ 
+
+ align:start position:0%
+to make before is you're sitting there
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+my girlfriend is like two years older
+
+ align:start position:0%
+my girlfriend is like two years older
+ 
+
+ align:start position:0%
+my girlfriend is like two years older
+than me
+
+ align:start position:0%
+than me
+ 
+
+ align:start position:0%
+than me
+this does not mean that you are some
+
+ align:start position:0%
+this does not mean that you are some
+ 
+
+ align:start position:0%
+this does not mean that you are some
+sort of genetic Misfit
+
+ align:start position:0%
+sort of genetic Misfit
+ 
+
+ align:start position:0%
+sort of genetic Misfit
+it means that we're back to talking
+
+ align:start position:0%
+it means that we're back to talking
+ 
+
+ align:start position:0%
+it means that we're back to talking
+about the mean value and all of these
+
+ align:start position:0%
+about the mean value and all of these
+ 
+
+ align:start position:0%
+about the mean value and all of these
+things have a distribution around them
+
+ align:start position:0%
+things have a distribution around them
+ 
+
+ align:start position:0%
+things have a distribution around them
+um it would be considered odd if your
+
+ align:start position:0%
+um it would be considered odd if your
+ 
+
+ align:start position:0%
+um it would be considered odd if your
+choice in um uh inmates was I only date
+
+ align:start position:0%
+choice in um uh inmates was I only date
+ 
+
+ align:start position:0%
+choice in um uh inmates was I only date
+women who are 60 years older than me now
+
+ align:start position:0%
+women who are 60 years older than me now
+ 
+
+ align:start position:0%
+women who are 60 years older than me now
+that would be considered unusual
+
+ align:start position:0%
+that would be considered unusual
+ 
+
+ align:start position:0%
+that would be considered unusual
+um but you know that should be way way
+
+ align:start position:0%
+um but you know that should be way way
+ 
+
+ align:start position:0%
+um but you know that should be way way
+out on one tale of it but but typically
+
+ align:start position:0%
+out on one tale of it but but typically
+ 
+
+ align:start position:0%
+out on one tale of it but but typically
+the mean of that that distribution lies
+
+ align:start position:0%
+the mean of that that distribution lies
+ 
+
+ align:start position:0%
+the mean of that that distribution lies
+a little younger okay let's ask okay why
+
+ align:start position:0%
+a little younger okay let's ask okay why
+ 
+
+ align:start position:0%
+a little younger okay let's ask okay why
+is that the case
+
+ align:start position:0%
+is that the case
+ 
+
+ align:start position:0%
+is that the case
+if you're following this evolutionary
+
+ align:start position:0%
+if you're following this evolutionary
+ 
+
+ align:start position:0%
+if you're following this evolutionary
+psych story why do males seek females
+
+ align:start position:0%
+psych story why do males seek females
+ 
+
+ align:start position:0%
+psych story why do males seek females
+who are slightly younger
+
+ align:start position:0%
+who are slightly younger
+ 
+
+ align:start position:0%
+who are slightly younger
+more babies right this is uh there's
+
+ align:start position:0%
+more babies right this is uh there's
+ 
+
+ align:start position:0%
+more babies right this is uh there's
+this the the males may not be limited in
+
+ align:start position:0%
+this the the males may not be limited in
+ 
+
+ align:start position:0%
+this the the males may not be limited in
+principle by the same rate limiting step
+
+ align:start position:0%
+principle by the same rate limiting step
+ 
+
+ align:start position:0%
+principle by the same rate limiting step
+but if you're in a culture that's going
+
+ align:start position:0%
+but if you're in a culture that's going
+ 
+
+ align:start position:0%
+but if you're in a culture that's going
+to limit you to one woman yeah better
+
+ align:start position:0%
+to limit you to one woman yeah better
+ 
+
+ align:start position:0%
+to limit you to one woman yeah better
+get one woman who's gonna produce the
+
+ align:start position:0%
+get one woman who's gonna produce the
+ 
+
+ align:start position:0%
+get one woman who's gonna produce the
+maximum number of babies
+
+ align:start position:0%
+maximum number of babies
+ 
+
+ align:start position:0%
+maximum number of babies
+um so you better start young and and
+
+ align:start position:0%
+um so you better start young and and
+ 
+
+ align:start position:0%
+um so you better start young and and
+okay so if you are a woman same multiple
+
+ align:start position:0%
+okay so if you are a woman same multiple
+ 
+
+ align:start position:0%
+okay so if you are a woman same multiple
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+um if you are a woman the average
+
+ align:start position:0%
+um if you are a woman the average
+ 
+
+ align:start position:0%
+um if you are a woman the average
+across cultures women prefer
+
+ align:start position:0%
+across cultures women prefer
+ 
+
+ align:start position:0%
+across cultures women prefer
+um how many vote that women prefer males
+
+ align:start position:0%
+um how many vote that women prefer males
+ 
+
+ align:start position:0%
+um how many vote that women prefer males
+who are slightly older
+
+ align:start position:0%
+who are slightly older
+ 
+
+ align:start position:0%
+who are slightly older
+exactly the same age
+
+ align:start position:0%
+exactly the same age
+ 
+
+ align:start position:0%
+exactly the same age
+slightly younger you got the right
+
+ align:start position:0%
+slightly younger you got the right
+ 
+
+ align:start position:0%
+slightly younger you got the right
+intuition again it's very convenient
+
+ align:start position:0%
+intuition again it's very convenient
+ 
+
+ align:start position:0%
+intuition again it's very convenient
+that this is the way it works out it's
+
+ align:start position:0%
+that this is the way it works out it's
+ 
+
+ align:start position:0%
+that this is the way it works out it's
+really bad news if everybody wants
+
+ align:start position:0%
+really bad news if everybody wants
+ 
+
+ align:start position:0%
+really bad news if everybody wants
+younger mates right there's going to be
+
+ align:start position:0%
+younger mates right there's going to be
+ 
+
+ align:start position:0%
+younger mates right there's going to be
+a that doesn't work well
+
+ align:start position:0%
+a that doesn't work well
+ 
+
+ align:start position:0%
+a that doesn't work well
+um but actually we'll come back to that
+
+ align:start position:0%
+um but actually we'll come back to that
+ 
+
+ align:start position:0%
+um but actually we'll come back to that
+in in uh in the next lecture I'll just
+
+ align:start position:0%
+in in uh in the next lecture I'll just
+ 
+
+ align:start position:0%
+in in uh in the next lecture I'll just
+put that out there uh as a problem to
+
+ align:start position:0%
+put that out there uh as a problem to
+ 
+
+ align:start position:0%
+put that out there uh as a problem to
+solve everybody does want
+
+ align:start position:0%
+solve everybody does want
+ 
+
+ align:start position:0%
+solve everybody does want
+um to to max out you know on the
+
+ align:start position:0%
+um to to max out you know on the
+ 
+
+ align:start position:0%
+um to to max out you know on the
+attractive attractive Rich gorgeous
+
+ align:start position:0%
+attractive attractive Rich gorgeous
+ 
+
+ align:start position:0%
+attractive attractive Rich gorgeous
+thing but most of us aren't going to get
+
+ align:start position:0%
+thing but most of us aren't going to get
+ 
+
+ align:start position:0%
+thing but most of us aren't going to get
+that right there's got to be some so if
+
+ align:start position:0%
+that right there's got to be some so if
+ 
+
+ align:start position:0%
+that right there's got to be some so if
+it's one male to one female roughly
+
+ align:start position:0%
+it's one male to one female roughly
+ 
+
+ align:start position:0%
+it's one male to one female roughly
+speaking we can't all have that person
+
+ align:start position:0%
+speaking we can't all have that person
+ 
+
+ align:start position:0%
+speaking we can't all have that person
+it just isn't going to work well so
+
+ align:start position:0%
+it just isn't going to work well so
+ 
+
+ align:start position:0%
+it just isn't going to work well so
+we'll we'll try we'll have to solve that
+
+ align:start position:0%
+we'll we'll try we'll have to solve that
+ 
+
+ align:start position:0%
+we'll we'll try we'll have to solve that
+next week
+
+ align:start position:0%
+next week
+ 
+
+ align:start position:0%
+next week
+um okay why do why do females want males
+
+ align:start position:0%
+um okay why do why do females want males
+ 
+
+ align:start position:0%
+um okay why do why do females want males
+who are slightly older
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maturity good luck
+
+ align:start position:0%
+maturity good luck
+ 
+
+ align:start position:0%
+maturity good luck
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evolutionary The evolutionary psych
+
+ align:start position:0%
+evolutionary The evolutionary psych
+ 
+
+ align:start position:0%
+evolutionary The evolutionary psych
+argument is is is is the resource
+
+ align:start position:0%
+argument is is is is the resource
+ 
+
+ align:start position:0%
+argument is is is is the resource
+argument I'm sure maturity doesn't hurt
+
+ align:start position:0%
+argument I'm sure maturity doesn't hurt
+ 
+
+ align:start position:0%
+argument I'm sure maturity doesn't hurt
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+um but uh but it's it's the it's the
+
+ align:start position:0%
+um but uh but it's it's the it's the
+ 
+
+ align:start position:0%
+um but uh but it's it's the it's the
+resource argument a guy has more has had
+
+ align:start position:0%
+resource argument a guy has more has had
+ 
+
+ align:start position:0%
+resource argument a guy has more has had
+a chance to accumulate more resource if
+
+ align:start position:0%
+a chance to accumulate more resource if
+ 
+
+ align:start position:0%
+a chance to accumulate more resource if
+he's a little older and and so you've
+
+ align:start position:0%
+he's a little older and and so you've
+ 
+
+ align:start position:0%
+he's a little older and and so you've
+got these endless
+
+ align:start position:0%
+got these endless
+ 
+
+ align:start position:0%
+got these endless
+um sometimes literally endless big thick
+
+ align:start position:0%
+um sometimes literally endless big thick
+ 
+
+ align:start position:0%
+um sometimes literally endless big thick
+19th century romance uh you know novels
+
+ align:start position:0%
+19th century romance uh you know novels
+ 
+
+ align:start position:0%
+19th century romance uh you know novels
+that you read in English Lit at some
+
+ align:start position:0%
+that you read in English Lit at some
+ 
+
+ align:start position:0%
+that you read in English Lit at some
+point where
+
+ align:start position:0%
+point where
+ 
+
+ align:start position:0%
+point where
+um you know he loves her but they can't
+
+ align:start position:0%
+um you know he loves her but they can't
+ 
+
+ align:start position:0%
+um you know he loves her but they can't
+get together for 800 Pages because he's
+
+ align:start position:0%
+get together for 800 Pages because he's
+ 
+
+ align:start position:0%
+get together for 800 Pages because he's
+got to go out and collect resource in
+
+ align:start position:0%
+got to go out and collect resource in
+ 
+
+ align:start position:0%
+got to go out and collect resource in
+some fashion until he can come back and
+
+ align:start position:0%
+some fashion until he can come back and
+ 
+
+ align:start position:0%
+some fashion until he can come back and
+tell uh you know Show daddy that that he
+
+ align:start position:0%
+tell uh you know Show daddy that that he
+ 
+
+ align:start position:0%
+tell uh you know Show daddy that that he
+can support the the daughter the
+
+ align:start position:0%
+can support the the daughter the
+ 
+
+ align:start position:0%
+can support the the daughter the
+alternative version of the 19th century
+
+ align:start position:0%
+alternative version of the 19th century
+ 
+
+ align:start position:0%
+alternative version of the 19th century
+romance is the interview where daddy
+
+ align:start position:0%
+romance is the interview where daddy
+ 
+
+ align:start position:0%
+romance is the interview where daddy
+asks
+
+ align:start position:0%
+asks
+ 
+
+ align:start position:0%
+asks
+um how much money your daddy left you
+
+ align:start position:0%
+um how much money your daddy left you
+ 
+
+ align:start position:0%
+um how much money your daddy left you
+right oh yes I have a hundred thousand
+
+ align:start position:0%
+right oh yes I have a hundred thousand
+ 
+
+ align:start position:0%
+right oh yes I have a hundred thousand
+no no a thousand dollar a thousand
+
+ align:start position:0%
+no no a thousand dollar a thousand
+ 
+
+ align:start position:0%
+no no a thousand dollar a thousand
+pounds they're all English novels a
+
+ align:start position:0%
+pounds they're all English novels a
+ 
+
+ align:start position:0%
+pounds they're all English novels a
+thousand pounds a year in the funds or
+
+ align:start position:0%
+thousand pounds a year in the funds or
+ 
+
+ align:start position:0%
+thousand pounds a year in the funds or
+something like that that's resource
+
+ align:start position:0%
+something like that that's resource
+ 
+
+ align:start position:0%
+something like that that's resource
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+um anyway
+
+ align:start position:0%
+um anyway
+ 
+
+ align:start position:0%
+um anyway
+uh oh there's one exception there is a
+
+ align:start position:0%
+uh oh there's one exception there is a
+ 
+
+ align:start position:0%
+uh oh there's one exception there is a
+population of males
+
+ align:start position:0%
+population of males
+ 
+
+ align:start position:0%
+population of males
+who seek slightly older women
+
+ align:start position:0%
+who seek slightly older women
+ 
+
+ align:start position:0%
+who seek slightly older women
+who is that population
+
+ align:start position:0%
+who is that population
+ 
+
+ align:start position:0%
+who is that population
+exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's this cruel sick turtle that I
+
+ align:start position:0%
+there's this cruel sick turtle that I
+ 
+
+ align:start position:0%
+there's this cruel sick turtle that I
+just we just got from that from all the
+
+ align:start position:0%
+just we just got from that from all the
+ 
+
+ align:start position:0%
+just we just got from that from all the
+answers given to that were by women all
+
+ align:start position:0%
+answers given to that were by women all
+ 
+
+ align:start position:0%
+answers given to that were by women all
+of whom were were snickering about it
+
+ align:start position:0%
+of whom were were snickering about it
+ 
+
+ align:start position:0%
+of whom were were snickering about it
+um which is Harsh
+
+ align:start position:0%
+um which is Harsh
+ 
+
+ align:start position:0%
+um which is Harsh
+um but it is it's teenage males
+
+ align:start position:0%
+um but it is it's teenage males
+ 
+
+ align:start position:0%
+um but it is it's teenage males
+particularly young teenage males who
+
+ align:start position:0%
+particularly young teenage males who
+ 
+
+ align:start position:0%
+particularly young teenage males who
+develop
+
+ align:start position:0%
+develop
+ 
+
+ align:start position:0%
+develop
+um crushes on slightly older or maybe
+
+ align:start position:0%
+um crushes on slightly older or maybe
+ 
+
+ align:start position:0%
+um crushes on slightly older or maybe
+quite a bit older women why
+
+ align:start position:0%
+quite a bit older women why
+ 
+
+ align:start position:0%
+quite a bit older women why
+what's that about
+
+ align:start position:0%
+what's that about
+ 
+
+ align:start position:0%
+what's that about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+they're fertile exactly now I mean the
+
+ align:start position:0%
+they're fertile exactly now I mean the
+ 
+
+ align:start position:0%
+they're fertile exactly now I mean the
+kid doesn't know this right again this
+
+ align:start position:0%
+kid doesn't know this right again this
+ 
+
+ align:start position:0%
+kid doesn't know this right again this
+is yeah oh I think I'd better fall in
+
+ align:start position:0%
+is yeah oh I think I'd better fall in
+ 
+
+ align:start position:0%
+is yeah oh I think I'd better fall in
+love with somebody who's fertile you
+
+ align:start position:0%
+love with somebody who's fertile you
+ 
+
+ align:start position:0%
+love with somebody who's fertile you
+know it's
+
+ align:start position:0%
+know it's
+ 
+
+ align:start position:0%
+know it's
+that's presumably not what's operating
+
+ align:start position:0%
+that's presumably not what's operating
+ 
+
+ align:start position:0%
+that's presumably not what's operating
+at any sort of conscious level here but
+
+ align:start position:0%
+at any sort of conscious level here but
+ 
+
+ align:start position:0%
+at any sort of conscious level here but
+if your goal is you know if if if
+
+ align:start position:0%
+if your goal is you know if if if
+ 
+
+ align:start position:0%
+if your goal is you know if if if
+evolutionary forces are driving you to
+
+ align:start position:0%
+evolutionary forces are driving you to
+ 
+
+ align:start position:0%
+evolutionary forces are driving you to
+look for a mate who's going to be
+
+ align:start position:0%
+look for a mate who's going to be
+ 
+
+ align:start position:0%
+look for a mate who's going to be
+fertile and you're you know
+
+ align:start position:0%
+fertile and you're you know
+ 
+
+ align:start position:0%
+fertile and you're you know
+an early adolescent male
+
+ align:start position:0%
+an early adolescent male
+ 
+
+ align:start position:0%
+an early adolescent male
+nine-year-old girls are not the
+
+ align:start position:0%
+nine-year-old girls are not the
+ 
+
+ align:start position:0%
+nine-year-old girls are not the
+population of choice
+
+ align:start position:0%
+population of choice
+ 
+
+ align:start position:0%
+population of choice
+um and and and you will notice you may
+
+ align:start position:0%
+um and and and you will notice you may
+ 
+
+ align:start position:0%
+um and and and you will notice you may
+notice that that that that even the
+
+ align:start position:0%
+notice that that that that even the
+ 
+
+ align:start position:0%
+notice that that that that even the
+example gives you a sort of a ooh kind
+
+ align:start position:0%
+example gives you a sort of a ooh kind
+ 
+
+ align:start position:0%
+example gives you a sort of a ooh kind
+of feeling we have a sort of a gut
+
+ align:start position:0%
+of feeling we have a sort of a gut
+ 
+
+ align:start position:0%
+of feeling we have a sort of a gut
+built-in reaction that there are some
+
+ align:start position:0%
+built-in reaction that there are some
+ 
+
+ align:start position:0%
+built-in reaction that there are some
+relationships that are okay and some
+
+ align:start position:0%
+relationships that are okay and some
+ 
+
+ align:start position:0%
+relationships that are okay and some
+relationships that are odd and and so
+
+ align:start position:0%
+relationships that are odd and and so
+ 
+
+ align:start position:0%
+relationships that are odd and and so
+relationships and and in particular
+
+ align:start position:0%
+relationships and and in particular
+ 
+
+ align:start position:0%
+relationships and and in particular
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+relationships uh guys can go and pursue
+
+ align:start position:0%
+relationships uh guys can go and pursue
+ 
+
+ align:start position:0%
+relationships uh guys can go and pursue
+fertile females that's okay that can be
+
+ align:start position:0%
+fertile females that's okay that can be
+ 
+
+ align:start position:0%
+fertile females that's okay that can be
+shown in an airline movie right and
+
+ align:start position:0%
+shown in an airline movie right and
+ 
+
+ align:start position:0%
+shown in an airline movie right and
+again we don't have the airline moving
+
+ align:start position:0%
+again we don't have the airline moving
+ 
+
+ align:start position:0%
+again we don't have the airline moving
+in the headline comes up the search for
+
+ align:start position:0%
+in the headline comes up the search for
+ 
+
+ align:start position:0%
+in the headline comes up the search for
+the fertile woman
+
+ align:start position:0%
+the fertile woman
+ 
+
+ align:start position:0%
+the fertile woman
+um but you know ask yourself who it is
+
+ align:start position:0%
+um but you know ask yourself who it is
+ 
+
+ align:start position:0%
+um but you know ask yourself who it is
+who romantic comedies are about you
+
+ align:start position:0%
+who romantic comedies are about you
+ 
+
+ align:start position:0%
+who romantic comedies are about you
+wouldn't put a movie on on on the
+
+ align:start position:0%
+wouldn't put a movie on on on the
+ 
+
+ align:start position:0%
+wouldn't put a movie on on on the
+airline for family consumption about
+
+ align:start position:0%
+airline for family consumption about
+ 
+
+ align:start position:0%
+airline for family consumption about
+some guys uh unrequited passion for a
+
+ align:start position:0%
+some guys uh unrequited passion for a
+ 
+
+ align:start position:0%
+some guys uh unrequited passion for a
+nine-year-old girl it would seem icky
+
+ align:start position:0%
+nine-year-old girl it would seem icky
+ 
+
+ align:start position:0%
+nine-year-old girl it would seem icky
+right that there's something wrong there
+
+ align:start position:0%
+right that there's something wrong there
+ 
+
+ align:start position:0%
+right that there's something wrong there
+um and um
+
+ align:start position:0%
+um and um
+ 
+
+ align:start position:0%
+um and um
+why presumably this has something to do
+
+ align:start position:0%
+why presumably this has something to do
+ 
+
+ align:start position:0%
+why presumably this has something to do
+with these the same sort of uh
+
+ align:start position:0%
+with these the same sort of uh
+ 
+
+ align:start position:0%
+with these the same sort of uh
+the same sort of forces
+
+ align:start position:0%
+the same sort of forces
+ 
+
+ align:start position:0%
+the same sort of forces
+um Okay so
+
+ align:start position:0%
+um Okay so
+ 
+
+ align:start position:0%
+um Okay so
+Let's uh let's move on a bit uh to this
+
+ align:start position:0%
+Let's uh let's move on a bit uh to this
+ 
+
+ align:start position:0%
+Let's uh let's move on a bit uh to this
+uh elaborate on this issue a bit who
+
+ align:start position:0%
+uh elaborate on this issue a bit who
+ 
+
+ align:start position:0%
+uh elaborate on this issue a bit who
+should be faithful in relations who
+
+ align:start position:0%
+should be faithful in relations who
+ 
+
+ align:start position:0%
+should be faithful in relations who
+should cheat
+
+ align:start position:0%
+should cheat
+ 
+
+ align:start position:0%
+should cheat
+um so let's start with guys now now
+
+ align:start position:0%
+um so let's start with guys now now
+ 
+
+ align:start position:0%
+um so let's start with guys now now
+recognize here by the way that we are
+
+ align:start position:0%
+recognize here by the way that we are
+ 
+
+ align:start position:0%
+recognize here by the way that we are
+talking again
+
+ align:start position:0%
+talking again
+ 
+
+ align:start position:0%
+talking again
+within the context of this evolutionary
+
+ align:start position:0%
+within the context of this evolutionary
+ 
+
+ align:start position:0%
+within the context of this evolutionary
+psych uh Viewpoint we are not saying who
+
+ align:start position:0%
+psych uh Viewpoint we are not saying who
+ 
+
+ align:start position:0%
+psych uh Viewpoint we are not saying who
+should cheat in your relationship right
+
+ align:start position:0%
+should cheat in your relationship right
+ 
+
+ align:start position:0%
+should cheat in your relationship right
+now with the person sitting next to you
+
+ align:start position:0%
+now with the person sitting next to you
+ 
+
+ align:start position:0%
+now with the person sitting next to you
+or something like that or who does
+
+ align:start position:0%
+or something like that or who does
+ 
+
+ align:start position:0%
+or something like that or who does
+society say it's okay to cheat with but
+
+ align:start position:0%
+society say it's okay to cheat with but
+ 
+
+ align:start position:0%
+society say it's okay to cheat with but
+in terms of this theory about
+
+ align:start position:0%
+in terms of this theory about
+ 
+
+ align:start position:0%
+in terms of this theory about
+evolutionary forces working on mate
+
+ align:start position:0%
+evolutionary forces working on mate
+ 
+
+ align:start position:0%
+evolutionary forces working on mate
+selection who should have an
+
+ align:start position:0%
+selection who should have an
+ 
+
+ align:start position:0%
+selection who should have an
+evolutionary drive to Cheat should guys
+
+ align:start position:0%
+evolutionary drive to Cheat should guys
+ 
+
+ align:start position:0%
+evolutionary drive to Cheat should guys
+yeah right that's a pretty
+
+ align:start position:0%
+yeah right that's a pretty
+ 
+
+ align:start position:0%
+yeah right that's a pretty
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+um argument that that if you can get
+
+ align:start position:0%
+um argument that that if you can get
+ 
+
+ align:start position:0%
+um argument that that if you can get
+away with it
+
+ align:start position:0%
+away with it
+ 
+
+ align:start position:0%
+away with it
+if you can have a few no-cost babies
+
+ align:start position:0%
+if you can have a few no-cost babies
+ 
+
+ align:start position:0%
+if you can have a few no-cost babies
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+great you've done your evolutionary work
+
+ align:start position:0%
+great you've done your evolutionary work
+ 
+
+ align:start position:0%
+great you've done your evolutionary work
+you may be yeah look if we switch to a
+
+ align:start position:0%
+you may be yeah look if we switch to a
+ 
+
+ align:start position:0%
+you may be yeah look if we switch to a
+different context of sort of uh cultural
+
+ align:start position:0%
+different context of sort of uh cultural
+ 
+
+ align:start position:0%
+different context of sort of uh cultural
+civilized World kind of you may be a
+
+ align:start position:0%
+civilized World kind of you may be a
+ 
+
+ align:start position:0%
+civilized World kind of you may be a
+jerk but you're you're an evolutionary
+
+ align:start position:0%
+jerk but you're you're an evolutionary
+ 
+
+ align:start position:0%
+jerk but you're you're an evolutionary
+evolutionarily successful jerk I suppose
+
+ align:start position:0%
+evolutionarily successful jerk I suppose
+ 
+
+ align:start position:0%
+evolutionarily successful jerk I suppose
+would be okay how about women
+
+ align:start position:0%
+would be okay how about women
+ 
+
+ align:start position:0%
+would be okay how about women
+should women should women
+
+ align:start position:0%
+should women should women
+ 
+
+ align:start position:0%
+should women should women
+be unfaithful and and and play around
+
+ align:start position:0%
+be unfaithful and and and play around
+ 
+
+ align:start position:0%
+be unfaithful and and and play around
+yes what's what okay the yes argument
+
+ align:start position:0%
+yes what's what okay the yes argument
+ 
+
+ align:start position:0%
+yes what's what okay the yes argument
+why what what's the yes argument again
+
+ align:start position:0%
+why what what's the yes argument again
+ 
+
+ align:start position:0%
+why what what's the yes argument again
+from an evolutionary point of view
+
+ align:start position:0%
+from an evolutionary point of view
+ 
+
+ align:start position:0%
+from an evolutionary point of view
+yeah yeah you might get a stronger mate
+
+ align:start position:0%
+yeah yeah you might get a stronger mate
+ 
+
+ align:start position:0%
+yeah yeah you might get a stronger mate
+you're hedging your genetic bets right
+
+ align:start position:0%
+you're hedging your genetic bets right
+ 
+
+ align:start position:0%
+you're hedging your genetic bets right
+if you are going to be if you yeah yeah
+
+ align:start position:0%
+if you are going to be if you yeah yeah
+ 
+
+ align:start position:0%
+if you are going to be if you yeah yeah
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+um link up with this this guy
+
+ align:start position:0%
+um link up with this this guy
+ 
+
+ align:start position:0%
+um link up with this this guy
+maybe he turns out to be a genetic dud
+
+ align:start position:0%
+maybe he turns out to be a genetic dud
+ 
+
+ align:start position:0%
+maybe he turns out to be a genetic dud
+if you just have your 18 babies with him
+
+ align:start position:0%
+if you just have your 18 babies with him
+ 
+
+ align:start position:0%
+if you just have your 18 babies with him
+you know how good is that
+
+ align:start position:0%
+you know how good is that
+ 
+
+ align:start position:0%
+you know how good is that
+um but if you spread it around a bit you
+
+ align:start position:0%
+um but if you spread it around a bit you
+ 
+
+ align:start position:0%
+um but if you spread it around a bit you
+know your genes are the same in all
+
+ align:start position:0%
+know your genes are the same in all
+ 
+
+ align:start position:0%
+know your genes are the same in all
+cases who cares right you're always
+
+ align:start position:0%
+cases who cares right you're always
+ 
+
+ align:start position:0%
+cases who cares right you're always
+getting your half of the package and so
+
+ align:start position:0%
+getting your half of the package and so
+ 
+
+ align:start position:0%
+getting your half of the package and so
+you might as well mix it up a bit and
+
+ align:start position:0%
+you might as well mix it up a bit and
+ 
+
+ align:start position:0%
+you might as well mix it up a bit and
+and and so that's the that's the that's
+
+ align:start position:0%
+and and so that's the that's the that's
+ 
+
+ align:start position:0%
+and and so that's the that's the that's
+the yes argument or that's a a
+
+ align:start position:0%
+the yes argument or that's a a
+ 
+
+ align:start position:0%
+the yes argument or that's a a
+um yes argument
+
+ align:start position:0%
+um yes argument
+ 
+
+ align:start position:0%
+um yes argument
+um what about a uh what a oh any other
+
+ align:start position:0%
+um what about a uh what a oh any other
+ 
+
+ align:start position:0%
+um what about a uh what a oh any other
+yes arguments there are yep
+
+ align:start position:0%
+yes arguments there are yep
+ 
+
+ align:start position:0%
+yes arguments there are yep
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you remain more faithful to have more
+
+ align:start position:0%
+you remain more faithful to have more
+ 
+
+ align:start position:0%
+you remain more faithful to have more
+resources ah yes okay so this is a a
+
+ align:start position:0%
+resources ah yes okay so this is a a
+ 
+
+ align:start position:0%
+resources ah yes okay so this is a a
+particular version of the more General
+
+ align:start position:0%
+particular version of the more General
+ 
+
+ align:start position:0%
+particular version of the more General
+argument there's a resource argument
+
+ align:start position:0%
+argument there's a resource argument
+ 
+
+ align:start position:0%
+argument there's a resource argument
+here he's giving a particular version
+
+ align:start position:0%
+here he's giving a particular version
+ 
+
+ align:start position:0%
+here he's giving a particular version
+which is go
+
+ align:start position:0%
+which is go
+ 
+
+ align:start position:0%
+which is go
+x with the guy with the good genes and
+
+ align:start position:0%
+x with the guy with the good genes and
+ 
+
+ align:start position:0%
+x with the guy with the good genes and
+snooker the guy with the good resources
+
+ align:start position:0%
+snooker the guy with the good resources
+ 
+
+ align:start position:0%
+snooker the guy with the good resources
+right and and convince him that it's his
+
+ align:start position:0%
+right and and convince him that it's his
+ 
+
+ align:start position:0%
+right and and convince him that it's his
+kid so he devotes the resources to raise
+
+ align:start position:0%
+kid so he devotes the resources to raise
+ 
+
+ align:start position:0%
+kid so he devotes the resources to raise
+his genes right that's uh more generally
+
+ align:start position:0%
+his genes right that's uh more generally
+ 
+
+ align:start position:0%
+his genes right that's uh more generally
+you might
+
+ align:start position:0%
+you might
+ 
+
+ align:start position:0%
+you might
+um yeah you might just play around uh to
+
+ align:start position:0%
+um yeah you might just play around uh to
+ 
+
+ align:start position:0%
+um yeah you might just play around uh to
+shop around because you get more
+
+ align:start position:0%
+shop around because you get more
+ 
+
+ align:start position:0%
+shop around because you get more
+resources in general
+
+ align:start position:0%
+resources in general
+ 
+
+ align:start position:0%
+resources in general
+right there guys will give you stuff in
+
+ align:start position:0%
+right there guys will give you stuff in
+ 
+
+ align:start position:0%
+right there guys will give you stuff in
+some fashion or other so there might be
+
+ align:start position:0%
+some fashion or other so there might be
+ 
+
+ align:start position:0%
+some fashion or other so there might be
+a sort of a quasi-economic go out and
+
+ align:start position:0%
+a sort of a quasi-economic go out and
+ 
+
+ align:start position:0%
+a sort of a quasi-economic go out and
+get the goodies kind of uh uh kind of
+
+ align:start position:0%
+get the goodies kind of uh uh kind of
+ 
+
+ align:start position:0%
+get the goodies kind of uh uh kind of
+argument okay those are those are good
+
+ align:start position:0%
+argument okay those are those are good
+ 
+
+ align:start position:0%
+argument okay those are those are good
+yes arguments how about no arguments
+
+ align:start position:0%
+yes arguments how about no arguments
+ 
+
+ align:start position:0%
+yes arguments how about no arguments
+um against the notion of of uh yeah
+
+ align:start position:0%
+um against the notion of of uh yeah
+ 
+
+ align:start position:0%
+um against the notion of of uh yeah
+you could lose the resources why would
+
+ align:start position:0%
+you could lose the resources why would
+ 
+
+ align:start position:0%
+you could lose the resources why would
+you lose the resources what's the guy's
+
+ align:start position:0%
+you lose the resources what's the guy's
+ 
+
+ align:start position:0%
+you lose the resources what's the guy's
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+it's not his kid and this is a crucial
+
+ align:start position:0%
+it's not his kid and this is a crucial
+ 
+
+ align:start position:0%
+it's not his kid and this is a crucial
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+um it again it's a another part of this
+
+ align:start position:0%
+um it again it's a another part of this
+ 
+
+ align:start position:0%
+um it again it's a another part of this
+fundamental asymmetry because it's the
+
+ align:start position:0%
+fundamental asymmetry because it's the
+ 
+
+ align:start position:0%
+fundamental asymmetry because it's the
+woman who gets present a president right
+
+ align:start position:0%
+woman who gets present a president right
+ 
+
+ align:start position:0%
+woman who gets present a president right
+the woman who gets pregnant
+
+ align:start position:0%
+the woman who gets pregnant
+ 
+
+ align:start position:0%
+the woman who gets pregnant
+she always knows who the mother is
+
+ align:start position:0%
+she always knows who the mother is
+ 
+
+ align:start position:0%
+she always knows who the mother is
+actually he knows who the mother is too
+
+ align:start position:0%
+actually he knows who the mother is too
+ 
+
+ align:start position:0%
+actually he knows who the mother is too
+there's no doubt about who the mother is
+
+ align:start position:0%
+there's no doubt about who the mother is
+ 
+
+ align:start position:0%
+there's no doubt about who the mother is
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the maternal the maternal genes are not
+
+ align:start position:0%
+the maternal the maternal genes are not
+ 
+
+ align:start position:0%
+the maternal the maternal genes are not
+an issue here paternal genes are an
+
+ align:start position:0%
+an issue here paternal genes are an
+ 
+
+ align:start position:0%
+an issue here paternal genes are an
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um and doubts about paternity have a
+
+ align:start position:0%
+um and doubts about paternity have a
+ 
+
+ align:start position:0%
+um and doubts about paternity have a
+variety of uh of consequences
+
+ align:start position:0%
+variety of uh of consequences
+ 
+
+ align:start position:0%
+variety of uh of consequences
+um male sexual jealousy is a a real and
+
+ align:start position:0%
+um male sexual jealousy is a a real and
+ 
+
+ align:start position:0%
+um male sexual jealousy is a a real and
+and potentially dangerous phenomenon in
+
+ align:start position:0%
+and potentially dangerous phenomenon in
+ 
+
+ align:start position:0%
+and potentially dangerous phenomenon in
+fact it it it's uh I don't think there
+
+ align:start position:0%
+fact it it it's uh I don't think there
+ 
+
+ align:start position:0%
+fact it it it's uh I don't think there
+are any states where it's still the case
+
+ align:start position:0%
+are any states where it's still the case
+ 
+
+ align:start position:0%
+are any states where it's still the case
+um for in there were states where it was
+
+ align:start position:0%
+um for in there were states where it was
+ 
+
+ align:start position:0%
+um for in there were states where it was
+the case that killing an Unfaithful wife
+
+ align:start position:0%
+the case that killing an Unfaithful wife
+ 
+
+ align:start position:0%
+the case that killing an Unfaithful wife
+was not murder
+
+ align:start position:0%
+was not murder
+ 
+
+ align:start position:0%
+was not murder
+um it was never the I don't think it was
+
+ align:start position:0%
+um it was never the I don't think it was
+ 
+
+ align:start position:0%
+um it was never the I don't think it was
+ever the other way around you couldn't
+
+ align:start position:0%
+ever the other way around you couldn't
+ 
+
+ align:start position:0%
+ever the other way around you couldn't
+kill your Unfaithful husband but killing
+
+ align:start position:0%
+kill your Unfaithful husband but killing
+ 
+
+ align:start position:0%
+kill your Unfaithful husband but killing
+the Unfaithful wife
+
+ align:start position:0%
+the Unfaithful wife
+ 
+
+ align:start position:0%
+the Unfaithful wife
+um was you know it wasn't necessarily A
+
+ align:start position:0%
+um was you know it wasn't necessarily A
+ 
+
+ align:start position:0%
+um was you know it wasn't necessarily A
+laudable act but it wasn't murder in the
+
+ align:start position:0%
+laudable act but it wasn't murder in the
+ 
+
+ align:start position:0%
+laudable act but it wasn't murder in the
+way that killing somebody else
+
+ align:start position:0%
+way that killing somebody else
+ 
+
+ align:start position:0%
+way that killing somebody else
+um was I don't believe that anybody
+
+ align:start position:0%
+um was I don't believe that anybody
+ 
+
+ align:start position:0%
+um was I don't believe that anybody
+happen to know that they come from a
+
+ align:start position:0%
+happen to know that they come from a
+ 
+
+ align:start position:0%
+happen to know that they come from a
+state where you can still do that with
+
+ align:start position:0%
+state where you can still do that with
+ 
+
+ align:start position:0%
+state where you can still do that with
+impunity
+
+ align:start position:0%
+impunity
+ 
+
+ align:start position:0%
+impunity
+I think Louisiana I think Louisiana was
+
+ align:start position:0%
+I think Louisiana I think Louisiana was
+ 
+
+ align:start position:0%
+I think Louisiana I think Louisiana was
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but in any case
+
+ align:start position:0%
+but in any case
+ 
+
+ align:start position:0%
+but in any case
+um oh and they're they're interesting
+
+ align:start position:0%
+um oh and they're they're interesting
+ 
+
+ align:start position:0%
+um oh and they're they're interesting
+wrinkles there are interesting wrinkles
+
+ align:start position:0%
+wrinkles there are interesting wrinkles
+ 
+
+ align:start position:0%
+wrinkles there are interesting wrinkles
+on this if you um
+
+ align:start position:0%
+on this if you um
+ 
+
+ align:start position:0%
+on this if you um
+when a baby is born
+
+ align:start position:0%
+when a baby is born
+ 
+
+ align:start position:0%
+when a baby is born
+the first question anybody asks is is it
+
+ align:start position:0%
+the first question anybody asks is is it
+ 
+
+ align:start position:0%
+the first question anybody asks is is it
+a boy or a girl which is an interesting
+
+ align:start position:0%
+a boy or a girl which is an interesting
+ 
+
+ align:start position:0%
+a boy or a girl which is an interesting
+factoid in its own right but the sort of
+
+ align:start position:0%
+factoid in its own right but the sort of
+ 
+
+ align:start position:0%
+factoid in its own right but the sort of
+the second topic of conversation is who
+
+ align:start position:0%
+the second topic of conversation is who
+ 
+
+ align:start position:0%
+the second topic of conversation is who
+does the kid look like
+
+ align:start position:0%
+does the kid look like
+ 
+
+ align:start position:0%
+does the kid look like
+and what's the answer
+
+ align:start position:0%
+and what's the answer
+ 
+
+ align:start position:0%
+and what's the answer
+the answer is
+
+ align:start position:0%
+the answer is
+ 
+
+ align:start position:0%
+the answer is
+um a bias towards saying that the kid
+
+ align:start position:0%
+um a bias towards saying that the kid
+ 
+
+ align:start position:0%
+um a bias towards saying that the kid
+looks like the father
+
+ align:start position:0%
+looks like the father
+ 
+
+ align:start position:0%
+looks like the father
+now why should that be the case and it
+
+ align:start position:0%
+now why should that be the case and it
+ 
+
+ align:start position:0%
+now why should that be the case and it
+turns out that the bias is strong if it
+
+ align:start position:0%
+turns out that the bias is strong if it
+ 
+
+ align:start position:0%
+turns out that the bias is strong if it
+depends who's giving the answer the
+
+ align:start position:0%
+depends who's giving the answer the
+ 
+
+ align:start position:0%
+depends who's giving the answer the
+answer by the wife's family by the
+
+ align:start position:0%
+answer by the wife's family by the
+ 
+
+ align:start position:0%
+answer by the wife's family by the
+mother's family
+
+ align:start position:0%
+mother's family
+ 
+
+ align:start position:0%
+mother's family
+is more skewed towards saying it looks
+
+ align:start position:0%
+is more skewed towards saying it looks
+ 
+
+ align:start position:0%
+is more skewed towards saying it looks
+like the father
+
+ align:start position:0%
+like the father
+ 
+
+ align:start position:0%
+like the father
+um and there are at least two reasons
+
+ align:start position:0%
+um and there are at least two reasons
+ 
+
+ align:start position:0%
+um and there are at least two reasons
+why this is the case one of them seems
+
+ align:start position:0%
+why this is the case one of them seems
+ 
+
+ align:start position:0%
+why this is the case one of them seems
+to be an effort again quite unconscious
+
+ align:start position:0%
+to be an effort again quite unconscious
+ 
+
+ align:start position:0%
+to be an effort again quite unconscious
+to prove to the dad you don't have to
+
+ align:start position:0%
+to prove to the dad you don't have to
+ 
+
+ align:start position:0%
+to prove to the dad you don't have to
+say it looks like the mother we know who
+
+ align:start position:0%
+say it looks like the mother we know who
+ 
+
+ align:start position:0%
+say it looks like the mother we know who
+the mother is saying it looks like the
+
+ align:start position:0%
+the mother is saying it looks like the
+ 
+
+ align:start position:0%
+the mother is saying it looks like the
+father is reassuring to the father who
+
+ align:start position:0%
+father is reassuring to the father who
+ 
+
+ align:start position:0%
+father is reassuring to the father who
+might otherwise deny resource to this
+
+ align:start position:0%
+might otherwise deny resource to this
+ 
+
+ align:start position:0%
+might otherwise deny resource to this
+kid
+
+ align:start position:0%
+kid
+ 
+
+ align:start position:0%
+kid
+or go out and kill the mother or
+
+ align:start position:0%
+or go out and kill the mother or
+ 
+
+ align:start position:0%
+or go out and kill the mother or
+something inconvenient like that right
+
+ align:start position:0%
+something inconvenient like that right
+ 
+
+ align:start position:0%
+something inconvenient like that right
+so it's important to believe that this
+
+ align:start position:0%
+so it's important to believe that this
+ 
+
+ align:start position:0%
+so it's important to believe that this
+is your bundle of genes the guy is in in
+
+ align:start position:0%
+is your bundle of genes the guy is in in
+ 
+
+ align:start position:0%
+is your bundle of genes the guy is in in
+theoretical doubt the woman is not in
+
+ align:start position:0%
+theoretical doubt the woman is not in
+ 
+
+ align:start position:0%
+theoretical doubt the woman is not in
+doubt the other reason why it may be
+
+ align:start position:0%
+doubt the other reason why it may be
+ 
+
+ align:start position:0%
+doubt the other reason why it may be
+true is there is some evidence that um
+
+ align:start position:0%
+true is there is some evidence that um
+ 
+
+ align:start position:0%
+true is there is some evidence that um
+babies actually look more like their
+
+ align:start position:0%
+babies actually look more like their
+ 
+
+ align:start position:0%
+babies actually look more like their
+fathers when they're young and that this
+
+ align:start position:0%
+fathers when they're young and that this
+ 
+
+ align:start position:0%
+fathers when they're young and that this
+wears off with age
+
+ align:start position:0%
+wears off with age
+ 
+
+ align:start position:0%
+wears off with age
+um this if this is true it would be an
+
+ align:start position:0%
+um this if this is true it would be an
+ 
+
+ align:start position:0%
+um this if this is true it would be an
+interesting argument for this
+
+ align:start position:0%
+interesting argument for this
+ 
+
+ align:start position:0%
+interesting argument for this
+evolutionary pressure because babies who
+
+ align:start position:0%
+evolutionary pressure because babies who
+ 
+
+ align:start position:0%
+evolutionary pressure because babies who
+looked clearly like Dad probably had a
+
+ align:start position:0%
+looked clearly like Dad probably had a
+ 
+
+ align:start position:0%
+looked clearly like Dad probably had a
+little Edge because dad looked at this
+
+ align:start position:0%
+little Edge because dad looked at this
+ 
+
+ align:start position:0%
+little Edge because dad looked at this
+little bundle of joy and said it's mine
+
+ align:start position:0%
+little bundle of joy and said it's mine
+ 
+
+ align:start position:0%
+little bundle of joy and said it's mine
+and if the you know the kid looked like
+
+ align:start position:0%
+and if the you know the kid looked like
+ 
+
+ align:start position:0%
+and if the you know the kid looked like
+the Milkman or something
+
+ align:start position:0%
+the Milkman or something
+ 
+
+ align:start position:0%
+the Milkman or something
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know the kid may not have you
+
+ align:start position:0%
+you know the kid may not have you
+ 
+
+ align:start position:0%
+you know the kid may not have you
+actually I don't even use that as an
+
+ align:start position:0%
+actually I don't even use that as an
+ 
+
+ align:start position:0%
+actually I don't even use that as an
+example anymore are there still Milkmen
+
+ align:start position:0%
+example anymore are there still Milkmen
+ 
+
+ align:start position:0%
+example anymore are there still Milkmen
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+it used to be
+
+ align:start position:0%
+it used to be
+ 
+
+ align:start position:0%
+it used to be
+it's it's an inaccurate it's a sort of
+
+ align:start position:0%
+it's it's an inaccurate it's a sort of
+ 
+
+ align:start position:0%
+it's it's an inaccurate it's a sort of
+an anachronism like talking about
+
+ align:start position:0%
+an anachronism like talking about
+ 
+
+ align:start position:0%
+an anachronism like talking about
+dialing the phone it's a the the the
+
+ align:start position:0%
+dialing the phone it's a the the the
+ 
+
+ align:start position:0%
+dialing the phone it's a the the the
+this is a this is a very mid-50s kind of
+
+ align:start position:0%
+this is a this is a very mid-50s kind of
+ 
+
+ align:start position:0%
+this is a this is a very mid-50s kind of
+anachronistic sort of cliche about you
+
+ align:start position:0%
+anachronistic sort of cliche about you
+ 
+
+ align:start position:0%
+anachronistic sort of cliche about you
+know the woman who would be at home the
+
+ align:start position:0%
+know the woman who would be at home the
+ 
+
+ align:start position:0%
+know the woman who would be at home the
+Milkman who would be the man who
+
+ align:start position:0%
+Milkman who would be the man who
+ 
+
+ align:start position:0%
+Milkman who would be the man who
+delivered the milk
+
+ align:start position:0%
+delivered the milk
+ 
+
+ align:start position:0%
+delivered the milk
+um since you didn't go to the
+
+ align:start position:0%
+um since you didn't go to the
+ 
+
+ align:start position:0%
+um since you didn't go to the
+supermarket to buy milk it came to your
+
+ align:start position:0%
+supermarket to buy milk it came to your
+ 
+
+ align:start position:0%
+supermarket to buy milk it came to your
+house
+
+ align:start position:0%
+house
+ 
+
+ align:start position:0%
+house
+um and then various other things
+
+ align:start position:0%
+um and then various other things
+ 
+
+ align:start position:0%
+um and then various other things
+happened and you know anyway
+
+ align:start position:0%
+happened and you know anyway
+ 
+
+ align:start position:0%
+happened and you know anyway
+so much for for for cultural
+
+ align:start position:0%
+so much for for for cultural
+ 
+
+ align:start position:0%
+so much for for for cultural
+Enlightenment here
+
+ align:start position:0%
+Enlightenment here
+ 
+
+ align:start position:0%
+Enlightenment here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in any case
+
+ align:start position:0%
+so in any case
+ 
+
+ align:start position:0%
+so in any case
+there's a pressure for women to be
+
+ align:start position:0%
+there's a pressure for women to be
+ 
+
+ align:start position:0%
+there's a pressure for women to be
+faithful
+
+ align:start position:0%
+faithful
+ 
+
+ align:start position:0%
+faithful
+um because of the uh basically in some
+
+ align:start position:0%
+um because of the uh basically in some
+ 
+
+ align:start position:0%
+um because of the uh basically in some
+fashion because of the danger of
+
+ align:start position:0%
+fashion because of the danger of
+ 
+
+ align:start position:0%
+fashion because of the danger of
+alienating the male in in uh
+
+ align:start position:0%
+alienating the male in in uh
+ 
+
+ align:start position:0%
+alienating the male in in uh
+in some way or um in some way or other
+
+ align:start position:0%
+in some way or um in some way or other
+ 
+
+ align:start position:0%
+in some way or um in some way or other
+um the uh there's a problem here it's
+
+ align:start position:0%
+um the uh there's a problem here it's
+ 
+
+ align:start position:0%
+um the uh there's a problem here it's
+sort of a problem there's a a potential
+
+ align:start position:0%
+sort of a problem there's a a potential
+ 
+
+ align:start position:0%
+sort of a problem there's a a potential
+problem with this if you think about it
+
+ align:start position:0%
+problem with this if you think about it
+ 
+
+ align:start position:0%
+problem with this if you think about it
+we've just come up with a theory that
+
+ align:start position:0%
+we've just come up with a theory that
+ 
+
+ align:start position:0%
+we've just come up with a theory that
+explains why women should be faithful or
+
+ align:start position:0%
+explains why women should be faithful or
+ 
+
+ align:start position:0%
+explains why women should be faithful or
+and shouldn't be faithful and in fact we
+
+ align:start position:0%
+and shouldn't be faithful and in fact we
+ 
+
+ align:start position:0%
+and shouldn't be faithful and in fact we
+could elaborate on this and and
+
+ align:start position:0%
+could elaborate on this and and
+ 
+
+ align:start position:0%
+could elaborate on this and and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+say that the evolutionary pressures
+
+ align:start position:0%
+say that the evolutionary pressures
+ 
+
+ align:start position:0%
+say that the evolutionary pressures
+should cause the you know you you could
+
+ align:start position:0%
+should cause the you know you you could
+ 
+
+ align:start position:0%
+should cause the you know you you could
+argue that the evolutionary pressures
+
+ align:start position:0%
+argue that the evolutionary pressures
+ 
+
+ align:start position:0%
+argue that the evolutionary pressures
+could push women to have less of a sex
+
+ align:start position:0%
+could push women to have less of a sex
+ 
+
+ align:start position:0%
+could push women to have less of a sex
+drive therefore making them more likely
+
+ align:start position:0%
+drive therefore making them more likely
+ 
+
+ align:start position:0%
+drive therefore making them more likely
+to remain faithful or you could have it
+
+ align:start position:0%
+to remain faithful or you could have it
+ 
+
+ align:start position:0%
+to remain faithful or you could have it
+explained that they have just the same
+
+ align:start position:0%
+explained that they have just the same
+ 
+
+ align:start position:0%
+explained that they have just the same
+sex drive but they're supposed to deny
+
+ align:start position:0%
+sex drive but they're supposed to deny
+ 
+
+ align:start position:0%
+sex drive but they're supposed to deny
+the existence that you can have a lot of
+
+ align:start position:0%
+the existence that you can have a lot of
+ 
+
+ align:start position:0%
+the existence that you can have a lot of
+different explanations
+
+ align:start position:0%
+different explanations
+ 
+
+ align:start position:0%
+different explanations
+and this is a problem if this is a
+
+ align:start position:0%
+and this is a problem if this is a
+ 
+
+ align:start position:0%
+and this is a problem if this is a
+problem with a theory a theory that
+
+ align:start position:0%
+problem with a theory a theory that
+ 
+
+ align:start position:0%
+problem with a theory a theory that
+explains all possible outcomes
+
+ align:start position:0%
+explains all possible outcomes
+ 
+
+ align:start position:0%
+explains all possible outcomes
+um isn't a great theory on the other
+
+ align:start position:0%
+um isn't a great theory on the other
+ 
+
+ align:start position:0%
+um isn't a great theory on the other
+hand in human being in Human mating
+
+ align:start position:0%
+hand in human being in Human mating
+ 
+
+ align:start position:0%
+hand in human being in Human mating
+behavior all the possible outcomes are
+
+ align:start position:0%
+behavior all the possible outcomes are
+ 
+
+ align:start position:0%
+behavior all the possible outcomes are
+out there so you don't want to have a
+
+ align:start position:0%
+out there so you don't want to have a
+ 
+
+ align:start position:0%
+out there so you don't want to have a
+theory that just explains one thing
+
+ align:start position:0%
+theory that just explains one thing
+ 
+
+ align:start position:0%
+theory that just explains one thing
+because that wouldn't be an adequate
+
+ align:start position:0%
+because that wouldn't be an adequate
+ 
+
+ align:start position:0%
+because that wouldn't be an adequate
+Theory here either I think the fairer
+
+ align:start position:0%
+Theory here either I think the fairer
+ 
+
+ align:start position:0%
+Theory here either I think the fairer
+thing to say about evolutionary theory
+
+ align:start position:0%
+thing to say about evolutionary theory
+ 
+
+ align:start position:0%
+thing to say about evolutionary theory
+is that it hasn't reached a degree of
+
+ align:start position:0%
+is that it hasn't reached a degree of
+ 
+
+ align:start position:0%
+is that it hasn't reached a degree of
+sophistication where it can explain in
+
+ align:start position:0%
+sophistication where it can explain in
+ 
+
+ align:start position:0%
+sophistication where it can explain in
+detail
+
+ align:start position:0%
+detail
+ 
+
+ align:start position:0%
+detail
+when a woman should or should not be
+
+ align:start position:0%
+when a woman should or should not be
+ 
+
+ align:start position:0%
+when a woman should or should not be
+faithful there are examples elsewhere of
+
+ align:start position:0%
+faithful there are examples elsewhere of
+ 
+
+ align:start position:0%
+faithful there are examples elsewhere of
+these sort of trade-off situations that
+
+ align:start position:0%
+these sort of trade-off situations that
+ 
+
+ align:start position:0%
+these sort of trade-off situations that
+that uh evolutionary sorts of theories
+
+ align:start position:0%
+that uh evolutionary sorts of theories
+ 
+
+ align:start position:0%
+that uh evolutionary sorts of theories
+explain rather well so a an example
+
+ align:start position:0%
+explain rather well so a an example
+ 
+
+ align:start position:0%
+explain rather well so a an example
+um sort of in the same ballpark comes
+
+ align:start position:0%
+um sort of in the same ballpark comes
+ 
+
+ align:start position:0%
+um sort of in the same ballpark comes
+from Cuckoos you know about cuckoos
+
+ align:start position:0%
+from Cuckoos you know about cuckoos
+ 
+
+ align:start position:0%
+from Cuckoos you know about cuckoos
+Cuckoos are nasty Birds
+
+ align:start position:0%
+Cuckoos are nasty Birds
+ 
+
+ align:start position:0%
+Cuckoos are nasty Birds
+Cuckoos like to lay their eggs in
+
+ align:start position:0%
+Cuckoos like to lay their eggs in
+ 
+
+ align:start position:0%
+Cuckoos like to lay their eggs in
+somebody else's nest
+
+ align:start position:0%
+somebody else's nest
+ 
+
+ align:start position:0%
+somebody else's nest
+because this business of raising kids is
+
+ align:start position:0%
+because this business of raising kids is
+ 
+
+ align:start position:0%
+because this business of raising kids is
+resource intensive and if you can get
+
+ align:start position:0%
+resource intensive and if you can get
+ 
+
+ align:start position:0%
+resource intensive and if you can get
+somebody else to do it great so Cuckoos
+
+ align:start position:0%
+somebody else to do it great so Cuckoos
+ 
+
+ align:start position:0%
+somebody else to do it great so Cuckoos
+lay their eggs in somebody else's next
+
+ align:start position:0%
+lay their eggs in somebody else's next
+ 
+
+ align:start position:0%
+lay their eggs in somebody else's next
+nest and it gets better from there
+
+ align:start position:0%
+nest and it gets better from there
+ 
+
+ align:start position:0%
+nest and it gets better from there
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the cuckoo egg hatches early
+
+ align:start position:0%
+the cuckoo egg hatches early
+ 
+
+ align:start position:0%
+the cuckoo egg hatches early
+and the cuckoo chick has this lovely
+
+ align:start position:0%
+and the cuckoo chick has this lovely
+ 
+
+ align:start position:0%
+and the cuckoo chick has this lovely
+reflex where what it does is it arches
+
+ align:start position:0%
+reflex where what it does is it arches
+ 
+
+ align:start position:0%
+reflex where what it does is it arches
+its little cuckoo back and kicks the
+
+ align:start position:0%
+its little cuckoo back and kicks the
+ 
+
+ align:start position:0%
+its little cuckoo back and kicks the
+other eggs out so it kills off its um
+
+ align:start position:0%
+other eggs out so it kills off its um
+ 
+
+ align:start position:0%
+other eggs out so it kills off its um
+its adopted siblings and and then it
+
+ align:start position:0%
+its adopted siblings and and then it
+ 
+
+ align:start position:0%
+its adopted siblings and and then it
+sits there making I'm hungry noises and
+
+ align:start position:0%
+sits there making I'm hungry noises and
+ 
+
+ align:start position:0%
+sits there making I'm hungry noises and
+gets fed by genetically unrelated Birds
+
+ align:start position:0%
+gets fed by genetically unrelated Birds
+ 
+
+ align:start position:0%
+gets fed by genetically unrelated Birds
+um now this is the there's an obvious
+
+ align:start position:0%
+um now this is the there's an obvious
+ 
+
+ align:start position:0%
+um now this is the there's an obvious
+problem here it's in the Cuckoo's
+
+ align:start position:0%
+problem here it's in the Cuckoo's
+ 
+
+ align:start position:0%
+problem here it's in the Cuckoo's
+interest to do this but you can't have
+
+ align:start position:0%
+interest to do this but you can't have
+ 
+
+ align:start position:0%
+interest to do this but you can't have
+too many Cuckoos if Cuckoos do this to
+
+ align:start position:0%
+too many Cuckoos if Cuckoos do this to
+ 
+
+ align:start position:0%
+too many Cuckoos if Cuckoos do this to
+every Nest then there's no Next
+
+ align:start position:0%
+every Nest then there's no Next
+ 
+
+ align:start position:0%
+every Nest then there's no Next
+Generation right because there's nobody
+
+ align:start position:0%
+Generation right because there's nobody
+ 
+
+ align:start position:0%
+Generation right because there's nobody
+left dumb enough to raise your kids in
+
+ align:start position:0%
+left dumb enough to raise your kids in
+ 
+
+ align:start position:0%
+left dumb enough to raise your kids in
+the Next Generation
+
+ align:start position:0%
+the Next Generation
+ 
+
+ align:start position:0%
+the Next Generation
+so there's an equilibrium that you you
+
+ align:start position:0%
+so there's an equilibrium that you you
+ 
+
+ align:start position:0%
+so there's an equilibrium that you you
+can write down equations for this that
+
+ align:start position:0%
+can write down equations for this that
+ 
+
+ align:start position:0%
+can write down equations for this that
+say a a healthy population can tolerate
+
+ align:start position:0%
+say a a healthy population can tolerate
+ 
+
+ align:start position:0%
+say a a healthy population can tolerate
+this many cuckoos
+
+ align:start position:0%
+this many cuckoos
+ 
+
+ align:start position:0%
+this many cuckoos
+this many cheaters you might ask by the
+
+ align:start position:0%
+this many cheaters you might ask by the
+ 
+
+ align:start position:0%
+this many cheaters you might ask by the
+way why the the that stupid bird the
+
+ align:start position:0%
+way why the the that stupid bird the
+ 
+
+ align:start position:0%
+way why the the that stupid bird the
+stupid Sparrow or whatever who's got a
+
+ align:start position:0%
+stupid Sparrow or whatever who's got a
+ 
+
+ align:start position:0%
+stupid Sparrow or whatever who's got a
+cuckoo in his nest her nest
+
+ align:start position:0%
+cuckoo in his nest her nest
+ 
+
+ align:start position:0%
+cuckoo in his nest her nest
+doesn't say get out of here
+
+ align:start position:0%
+doesn't say get out of here
+ 
+
+ align:start position:0%
+doesn't say get out of here
+um and the problem seems to be
+
+ align:start position:0%
+um and the problem seems to be
+ 
+
+ align:start position:0%
+um and the problem seems to be
+um that uh that the
+
+ align:start position:0%
+um that uh that the
+ 
+
+ align:start position:0%
+um that uh that the
+cuckoo behaves as a sort of a super
+
+ align:start position:0%
+cuckoo behaves as a sort of a super
+ 
+
+ align:start position:0%
+cuckoo behaves as a sort of a super
+normal baby stimulus
+
+ align:start position:0%
+normal baby stimulus
+ 
+
+ align:start position:0%
+normal baby stimulus
+that you know you you as a a mommy
+
+ align:start position:0%
+that you know you you as a a mommy
+ 
+
+ align:start position:0%
+that you know you you as a a mommy
+Sparrow or Daddy's Sparrow you are built
+
+ align:start position:0%
+Sparrow or Daddy's Sparrow you are built
+ 
+
+ align:start position:0%
+Sparrow or Daddy's Sparrow you are built
+to say oh look at that it's cute it's a
+
+ align:start position:0%
+to say oh look at that it's cute it's a
+ 
+
+ align:start position:0%
+to say oh look at that it's cute it's a
+baby I want to feed it and and and your
+
+ align:start position:0%
+baby I want to feed it and and and your
+ 
+
+ align:start position:0%
+baby I want to feed it and and and your
+success is whether this thing is growing
+
+ align:start position:0%
+success is whether this thing is growing
+ 
+
+ align:start position:0%
+success is whether this thing is growing
+and here's this honking huge cuckoo baby
+
+ align:start position:0%
+and here's this honking huge cuckoo baby
+ 
+
+ align:start position:0%
+and here's this honking huge cuckoo baby
+wow I hit the jackpot I got the greatest
+
+ align:start position:0%
+wow I hit the jackpot I got the greatest
+ 
+
+ align:start position:0%
+wow I hit the jackpot I got the greatest
+baby in the world doesn't happen to be
+
+ align:start position:0%
+baby in the world doesn't happen to be
+ 
+
+ align:start position:0%
+baby in the world doesn't happen to be
+genetically related to me
+
+ align:start position:0%
+genetically related to me
+ 
+
+ align:start position:0%
+genetically related to me
+um but it's a great baby and so I stuff
+
+ align:start position:0%
+um but it's a great baby and so I stuff
+ 
+
+ align:start position:0%
+um but it's a great baby and so I stuff
+it full of worms
+
+ align:start position:0%
+it full of worms
+ 
+
+ align:start position:0%
+it full of worms
+um the last year there was an article
+
+ align:start position:0%
+um the last year there was an article
+ 
+
+ align:start position:0%
+um the last year there was an article
+about a species of I don't remember what
+
+ align:start position:0%
+about a species of I don't remember what
+ 
+
+ align:start position:0%
+about a species of I don't remember what
+but some other non-coo bird that has
+
+ align:start position:0%
+but some other non-coo bird that has
+ 
+
+ align:start position:0%
+but some other non-coo bird that has
+learned now how to recognize or you know
+
+ align:start position:0%
+learned now how to recognize or you know
+ 
+
+ align:start position:0%
+learned now how to recognize or you know
+it has evolved the ability to recognize
+
+ align:start position:0%
+it has evolved the ability to recognize
+ 
+
+ align:start position:0%
+it has evolved the ability to recognize
+um the uh the Cuckoos and you can't lay
+
+ align:start position:0%
+um the uh the Cuckoos and you can't lay
+ 
+
+ align:start position:0%
+um the uh the Cuckoos and you can't lay
+your cuckoo eggs in those nests because
+
+ align:start position:0%
+your cuckoo eggs in those nests because
+ 
+
+ align:start position:0%
+your cuckoo eggs in those nests because
+that uh species will get rid of you and
+
+ align:start position:0%
+that uh species will get rid of you and
+ 
+
+ align:start position:0%
+that uh species will get rid of you and
+and preserve their own but anyway you've
+
+ align:start position:0%
+and preserve their own but anyway you've
+ 
+
+ align:start position:0%
+and preserve their own but anyway you've
+got to have it there's an equilibrium
+
+ align:start position:0%
+got to have it there's an equilibrium
+ 
+
+ align:start position:0%
+got to have it there's an equilibrium
+State here you have a balance that
+
+ align:start position:0%
+State here you have a balance that
+ 
+
+ align:start position:0%
+State here you have a balance that
+tolerates a certain amount of cheating
+
+ align:start position:0%
+tolerates a certain amount of cheating
+ 
+
+ align:start position:0%
+tolerates a certain amount of cheating
+and not the same thing happens in human
+
+ align:start position:0%
+and not the same thing happens in human
+ 
+
+ align:start position:0%
+and not the same thing happens in human
+um Human Relationships
+
+ align:start position:0%
+um Human Relationships
+ 
+
+ align:start position:0%
+um Human Relationships
+um though the the uh the details are
+
+ align:start position:0%
+um though the the uh the details are
+ 
+
+ align:start position:0%
+um though the the uh the details are
+much more complicated to work out but
+
+ align:start position:0%
+much more complicated to work out but
+ 
+
+ align:start position:0%
+much more complicated to work out but
+um do people lie
+
+ align:start position:0%
+um do people lie
+ 
+
+ align:start position:0%
+um do people lie
+yeah sure right do people lie all the
+
+ align:start position:0%
+yeah sure right do people lie all the
+ 
+
+ align:start position:0%
+yeah sure right do people lie all the
+time no you can't do that you can't have
+
+ align:start position:0%
+time no you can't do that you can't have
+ 
+
+ align:start position:0%
+time no you can't do that you can't have
+an arbitrary relationship between truth
+
+ align:start position:0%
+an arbitrary relationship between truth
+ 
+
+ align:start position:0%
+an arbitrary relationship between truth
+and utterances cannot have arbitrary
+
+ align:start position:0%
+and utterances cannot have arbitrary
+ 
+
+ align:start position:0%
+and utterances cannot have arbitrary
+truth value because then there wouldn't
+
+ align:start position:0%
+truth value because then there wouldn't
+ 
+
+ align:start position:0%
+truth value because then there wouldn't
+be any point to communication
+
+ align:start position:0%
+be any point to communication
+ 
+
+ align:start position:0%
+be any point to communication
+so on average
+
+ align:start position:0%
+so on average
+ 
+
+ align:start position:0%
+so on average
+people as a whole have to tell the truth
+
+ align:start position:0%
+people as a whole have to tell the truth
+ 
+
+ align:start position:0%
+people as a whole have to tell the truth
+does everybody have to tell the same
+
+ align:start position:0%
+does everybody have to tell the same
+ 
+
+ align:start position:0%
+does everybody have to tell the same
+amount of Truth No the population can
+
+ align:start position:0%
+amount of Truth No the population can
+ 
+
+ align:start position:0%
+amount of Truth No the population can
+tolerate
+
+ align:start position:0%
+tolerate
+ 
+
+ align:start position:0%
+tolerate
+some amount of real Liars right
+
+ align:start position:0%
+some amount of real Liars right
+ 
+
+ align:start position:0%
+some amount of real Liars right
+pathological lying through their teeth
+
+ align:start position:0%
+pathological lying through their teeth
+ 
+
+ align:start position:0%
+pathological lying through their teeth
+all the time oh yes I love you baby I
+
+ align:start position:0%
+all the time oh yes I love you baby I
+ 
+
+ align:start position:0%
+all the time oh yes I love you baby I
+will devote all my resources to you
+
+ align:start position:0%
+will devote all my resources to you
+ 
+
+ align:start position:0%
+will devote all my resources to you
+Liars
+
+ align:start position:0%
+Liars
+ 
+
+ align:start position:0%
+Liars
+um or whatever whatever realm it is but
+
+ align:start position:0%
+um or whatever whatever realm it is but
+ 
+
+ align:start position:0%
+um or whatever whatever realm it is but
+again there's going to be an equilibrium
+
+ align:start position:0%
+again there's going to be an equilibrium
+ 
+
+ align:start position:0%
+again there's going to be an equilibrium
+equation there somewhere not as well
+
+ align:start position:0%
+equation there somewhere not as well
+ 
+
+ align:start position:0%
+equation there somewhere not as well
+worked out as with Cuckoos that says we
+
+ align:start position:0%
+worked out as with Cuckoos that says we
+ 
+
+ align:start position:0%
+worked out as with Cuckoos that says we
+can only tolerate so many liars if every
+
+ align:start position:0%
+can only tolerate so many liars if every
+ 
+
+ align:start position:0%
+can only tolerate so many liars if every
+so you could ask the question is there
+
+ align:start position:0%
+so you could ask the question is there
+ 
+
+ align:start position:0%
+so you could ask the question is there
+motivation for guys to lie in
+
+ align:start position:0%
+motivation for guys to lie in
+ 
+
+ align:start position:0%
+motivation for guys to lie in
+relationships
+
+ align:start position:0%
+relationships
+ 
+
+ align:start position:0%
+relationships
+right are you seeing anybody else oh no
+
+ align:start position:0%
+right are you seeing anybody else oh no
+ 
+
+ align:start position:0%
+right are you seeing anybody else oh no
+not me
+
+ align:start position:0%
+not me
+ 
+
+ align:start position:0%
+not me
+um if everybody lies about that the game
+
+ align:start position:0%
+um if everybody lies about that the game
+ 
+
+ align:start position:0%
+um if everybody lies about that the game
+falls apart
+
+ align:start position:0%
+falls apart
+ 
+
+ align:start position:0%
+falls apart
+if some people lie about it they get
+
+ align:start position:0%
+if some people lie about it they get
+ 
+
+ align:start position:0%
+if some people lie about it they get
+away with it so the population as a
+
+ align:start position:0%
+away with it so the population as a
+ 
+
+ align:start position:0%
+away with it so the population as a
+whole will tolerate some subset of
+
+ align:start position:0%
+whole will tolerate some subset of
+ 
+
+ align:start position:0%
+whole will tolerate some subset of
+cheaters
+
+ align:start position:0%
+cheaters
+ 
+
+ align:start position:0%
+cheaters
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and you know one can have the hope the
+
+ align:start position:0%
+and you know one can have the hope the
+ 
+
+ align:start position:0%
+and you know one can have the hope the
+theoretical hope that uh that you know
+
+ align:start position:0%
+theoretical hope that uh that you know
+ 
+
+ align:start position:0%
+theoretical hope that uh that you know
+another few generations of work in the
+
+ align:start position:0%
+another few generations of work in the
+ 
+
+ align:start position:0%
+another few generations of work in the
+area and you'd be able to write the
+
+ align:start position:0%
+area and you'd be able to write the
+ 
+
+ align:start position:0%
+area and you'd be able to write the
+equation you'll be able to say look a
+
+ align:start position:0%
+equation you'll be able to say look a
+ 
+
+ align:start position:0%
+equation you'll be able to say look a
+population like
+
+ align:start position:0%
+population like
+ 
+
+ align:start position:0%
+population like
+uh you know an undergraduate population
+
+ align:start position:0%
+uh you know an undergraduate population
+ 
+
+ align:start position:0%
+uh you know an undergraduate population
+can tolerate
+
+ align:start position:0%
+can tolerate
+ 
+
+ align:start position:0%
+can tolerate
+10 cheaters
+
+ align:start position:0%
+10 cheaters
+ 
+
+ align:start position:0%
+10 cheaters
+if we've got 11 cheaters we have to
+
+ align:start position:0%
+if we've got 11 cheaters we have to
+ 
+
+ align:start position:0%
+if we've got 11 cheaters we have to
+invoke you know the Dean's office or
+
+ align:start position:0%
+invoke you know the Dean's office or
+ 
+
+ align:start position:0%
+invoke you know the Dean's office or
+something and and throw them out because
+
+ align:start position:0%
+something and and throw them out because
+ 
+
+ align:start position:0%
+something and and throw them out because
+the population will crash otherwise
+
+ align:start position:0%
+the population will crash otherwise
+ 
+
+ align:start position:0%
+the population will crash otherwise
+there's something anyway we're nowhere
+
+ align:start position:0%
+there's something anyway we're nowhere
+ 
+
+ align:start position:0%
+there's something anyway we're nowhere
+near that point at this point we can't
+
+ align:start position:0%
+near that point at this point we can't
+ 
+
+ align:start position:0%
+near that point at this point we can't
+write the equations
+
+ align:start position:0%
+write the equations
+ 
+
+ align:start position:0%
+write the equations
+um but that seems to be the way you get
+
+ align:start position:0%
+um but that seems to be the way you get
+ 
+
+ align:start position:0%
+um but that seems to be the way you get
+to the solution to um
+
+ align:start position:0%
+to the solution to um
+ 
+
+ align:start position:0%
+to the solution to um
+to the problem that the theory at the
+
+ align:start position:0%
+to the problem that the theory at the
+ 
+
+ align:start position:0%
+to the problem that the theory at the
+moment predicts kind of everything
+
+ align:start position:0%
+moment predicts kind of everything
+ 
+
+ align:start position:0%
+moment predicts kind of everything
+um the theory also doesn't predict the
+
+ align:start position:0%
+um the theory also doesn't predict the
+ 
+
+ align:start position:0%
+um the theory also doesn't predict the
+full range of behavior I see I've got
+
+ align:start position:0%
+full range of behavior I see I've got
+ 
+
+ align:start position:0%
+full range of behavior I see I've got
+these problems listed on the handout
+
+ align:start position:0%
+these problems listed on the handout
+ 
+
+ align:start position:0%
+these problems listed on the handout
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in particular it's
+
+ align:start position:0%
+in particular it's
+ 
+
+ align:start position:0%
+in particular it's
+explaining group Behavior explaining the
+
+ align:start position:0%
+explaining group Behavior explaining the
+ 
+
+ align:start position:0%
+explaining group Behavior explaining the
+behavior of individuals is something
+
+ align:start position:0%
+behavior of individuals is something
+ 
+
+ align:start position:0%
+behavior of individuals is something
+that I'll get to in the next lecture
+
+ align:start position:0%
+that I'll get to in the next lecture
+ 
+
+ align:start position:0%
+that I'll get to in the next lecture
+actually I'll get to some of it later in
+
+ align:start position:0%
+actually I'll get to some of it later in
+ 
+
+ align:start position:0%
+actually I'll get to some of it later in
+the in the present lecture
+
+ align:start position:0%
+the in the present lecture
+ 
+
+ align:start position:0%
+the in the present lecture
+um and the third problem let me say a
+
+ align:start position:0%
+um and the third problem let me say a
+ 
+
+ align:start position:0%
+um and the third problem let me say a
+bit about that before we take a a Break
+
+ align:start position:0%
+bit about that before we take a a Break
+ 
+
+ align:start position:0%
+bit about that before we take a a Break
+um is that Civilization may have changed
+
+ align:start position:0%
+um is that Civilization may have changed
+ 
+
+ align:start position:0%
+um is that Civilization may have changed
+the rules one of the most uh striking uh
+
+ align:start position:0%
+the rules one of the most uh striking uh
+ 
+
+ align:start position:0%
+the rules one of the most uh striking uh
+there's several examples of this one of
+
+ align:start position:0%
+there's several examples of this one of
+ 
+
+ align:start position:0%
+there's several examples of this one of
+them is
+
+ align:start position:0%
+them is
+ 
+
+ align:start position:0%
+them is
+um you know if you were operating in a
+
+ align:start position:0%
+um you know if you were operating in a
+ 
+
+ align:start position:0%
+um you know if you were operating in a
+sort of a purely darwinian kind of a
+
+ align:start position:0%
+sort of a purely darwinian kind of a
+ 
+
+ align:start position:0%
+sort of a purely darwinian kind of a
+world that would be very difficult very
+
+ align:start position:0%
+world that would be very difficult very
+ 
+
+ align:start position:0%
+world that would be very difficult very
+very difficult probably but very
+
+ align:start position:0%
+very difficult probably but very
+ 
+
+ align:start position:0%
+very difficult probably but very
+different than operating in a world
+
+ align:start position:0%
+different than operating in a world
+ 
+
+ align:start position:0%
+different than operating in a world
+where you are being told explicitly what
+
+ align:start position:0%
+where you are being told explicitly what
+ 
+
+ align:start position:0%
+where you are being told explicitly what
+is and is not appropriate sexual
+
+ align:start position:0%
+is and is not appropriate sexual
+ 
+
+ align:start position:0%
+is and is not appropriate sexual
+behavior you're being told explicitly
+
+ align:start position:0%
+behavior you're being told explicitly
+ 
+
+ align:start position:0%
+behavior you're being told explicitly
+um if uh that that you know your genes
+
+ align:start position:0%
+um if uh that that you know your genes
+ 
+
+ align:start position:0%
+um if uh that that you know your genes
+your evolutionary history if you're a
+
+ align:start position:0%
+your evolutionary history if you're a
+ 
+
+ align:start position:0%
+your evolutionary history if you're a
+male may be saying go off and mate with
+
+ align:start position:0%
+male may be saying go off and mate with
+ 
+
+ align:start position:0%
+male may be saying go off and mate with
+everybody Under the Sun but there are
+
+ align:start position:0%
+everybody Under the Sun but there are
+ 
+
+ align:start position:0%
+everybody Under the Sun but there are
+societal strictures that say not really
+
+ align:start position:0%
+societal strictures that say not really
+ 
+
+ align:start position:0%
+societal strictures that say not really
+you know that's just not quite really
+
+ align:start position:0%
+you know that's just not quite really
+ 
+
+ align:start position:0%
+you know that's just not quite really
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um so that complicates things but a more
+
+ align:start position:0%
+um so that complicates things but a more
+ 
+
+ align:start position:0%
+um so that complicates things but a more
+interesting complication
+
+ align:start position:0%
+interesting complication
+ 
+
+ align:start position:0%
+interesting complication
+um arises more recently in in history
+
+ align:start position:0%
+um arises more recently in in history
+ 
+
+ align:start position:0%
+um arises more recently in in history
+with the Advent of um artificial
+
+ align:start position:0%
+with the Advent of um artificial
+ 
+
+ align:start position:0%
+with the Advent of um artificial
+contraception
+
+ align:start position:0%
+contraception
+ 
+
+ align:start position:0%
+contraception
+that if if the fundamental
+
+ align:start position:0%
+that if if the fundamental
+ 
+
+ align:start position:0%
+that if if the fundamental
+route to these asymmetries is that women
+
+ align:start position:0%
+route to these asymmetries is that women
+ 
+
+ align:start position:0%
+route to these asymmetries is that women
+get pregnant
+
+ align:start position:0%
+get pregnant
+ 
+
+ align:start position:0%
+get pregnant
+you know that sex makes you pregnant and
+
+ align:start position:0%
+you know that sex makes you pregnant and
+ 
+
+ align:start position:0%
+you know that sex makes you pregnant and
+it's only women that get pregnant what
+
+ align:start position:0%
+it's only women that get pregnant what
+ 
+
+ align:start position:0%
+it's only women that get pregnant what
+happens if you decouple sex from
+
+ align:start position:0%
+happens if you decouple sex from
+ 
+
+ align:start position:0%
+happens if you decouple sex from
+pregnancy does it change the game
+
+ align:start position:0%
+pregnancy does it change the game
+ 
+
+ align:start position:0%
+pregnancy does it change the game
+well potentially yes
+
+ align:start position:0%
+well potentially yes
+ 
+
+ align:start position:0%
+well potentially yes
+it has not made these asymmetries
+
+ align:start position:0%
+it has not made these asymmetries
+ 
+
+ align:start position:0%
+it has not made these asymmetries
+disappear
+
+ align:start position:0%
+disappear
+ 
+
+ align:start position:0%
+disappear
+um that's a a a topic that I will
+
+ align:start position:0%
+um that's a a a topic that I will
+ 
+
+ align:start position:0%
+um that's a a a topic that I will
+actually return to in a later lecture
+
+ align:start position:0%
+actually return to in a later lecture
+ 
+
+ align:start position:0%
+actually return to in a later lecture
+um it's not made these asymmetries
+
+ align:start position:0%
+um it's not made these asymmetries
+ 
+
+ align:start position:0%
+um it's not made these asymmetries
+disappear and that suggests that the the
+
+ align:start position:0%
+disappear and that suggests that the the
+ 
+
+ align:start position:0%
+disappear and that suggests that the the
+forces that that shaped our our brains
+
+ align:start position:0%
+forces that that shaped our our brains
+ 
+
+ align:start position:0%
+forces that that shaped our our brains
+The evolutionary forces that shaped our
+
+ align:start position:0%
+The evolutionary forces that shaped our
+ 
+
+ align:start position:0%
+The evolutionary forces that shaped our
+brains over long periods of time
+
+ align:start position:0%
+brains over long periods of time
+ 
+
+ align:start position:0%
+brains over long periods of time
+um still operate
+
+ align:start position:0%
+um still operate
+ 
+
+ align:start position:0%
+um still operate
+even though the rules of the game have
+
+ align:start position:0%
+even though the rules of the game have
+ 
+
+ align:start position:0%
+even though the rules of the game have
+changed somewhat you can you can get an
+
+ align:start position:0%
+changed somewhat you can you can get an
+ 
+
+ align:start position:0%
+changed somewhat you can you can get an
+intuitive feeling for this if you if we
+
+ align:start position:0%
+intuitive feeling for this if you if we
+ 
+
+ align:start position:0%
+intuitive feeling for this if you if we
+let's return to the question of female
+
+ align:start position:0%
+let's return to the question of female
+ 
+
+ align:start position:0%
+let's return to the question of female
+fidelity
+
+ align:start position:0%
+fidelity
+ 
+
+ align:start position:0%
+fidelity
+should a woman cheat well part of the
+
+ align:start position:0%
+should a woman cheat well part of the
+ 
+
+ align:start position:0%
+should a woman cheat well part of the
+answer to why a female should might be
+
+ align:start position:0%
+answer to why a female should might be
+ 
+
+ align:start position:0%
+answer to why a female should might be
+inclined not to cheat in a relationship
+
+ align:start position:0%
+inclined not to cheat in a relationship
+ 
+
+ align:start position:0%
+inclined not to cheat in a relationship
+was that the male might be jealous and
+
+ align:start position:0%
+was that the male might be jealous and
+ 
+
+ align:start position:0%
+was that the male might be jealous and
+that would have a variety of possible
+
+ align:start position:0%
+that would have a variety of possible
+ 
+
+ align:start position:0%
+that would have a variety of possible
+bad consequences withdrawal of resources
+
+ align:start position:0%
+bad consequences withdrawal of resources
+ 
+
+ align:start position:0%
+bad consequences withdrawal of resources
+or potentially violence
+
+ align:start position:0%
+or potentially violence
+ 
+
+ align:start position:0%
+or potentially violence
+um in some fashion something bad might
+
+ align:start position:0%
+um in some fashion something bad might
+ 
+
+ align:start position:0%
+um in some fashion something bad might
+happen Okay how much do you think that
+
+ align:start position:0%
+happen Okay how much do you think that
+ 
+
+ align:start position:0%
+happen Okay how much do you think that
+those bad consequences are ameliorated
+
+ align:start position:0%
+those bad consequences are ameliorated
+ 
+
+ align:start position:0%
+those bad consequences are ameliorated
+if when she's confronted yo did you
+
+ align:start position:0%
+if when she's confronted yo did you
+ 
+
+ align:start position:0%
+if when she's confronted yo did you
+cheat on me yes I cheated on you but
+
+ align:start position:0%
+cheat on me yes I cheated on you but
+ 
+
+ align:start position:0%
+cheat on me yes I cheated on you but
+it's okay because we took precautions
+
+ align:start position:0%
+it's okay because we took precautions
+ 
+
+ align:start position:0%
+it's okay because we took precautions
+do you think that makes a difference in
+
+ align:start position:0%
+do you think that makes a difference in
+ 
+
+ align:start position:0%
+do you think that makes a difference in
+the argument
+
+ align:start position:0%
+the argument
+ 
+
+ align:start position:0%
+the argument
+no it doesn't intuitively it doesn't
+
+ align:start position:0%
+no it doesn't intuitively it doesn't
+ 
+
+ align:start position:0%
+no it doesn't intuitively it doesn't
+seem likely that it makes a difference
+
+ align:start position:0%
+seem likely that it makes a difference
+ 
+
+ align:start position:0%
+seem likely that it makes a difference
+suggesting that the the
+
+ align:start position:0%
+suggesting that the the
+ 
+
+ align:start position:0%
+suggesting that the the
+forces that are driving
+
+ align:start position:0%
+forces that are driving
+ 
+
+ align:start position:0%
+forces that are driving
+um these questions of who should cheat
+
+ align:start position:0%
+um these questions of who should cheat
+ 
+
+ align:start position:0%
+um these questions of who should cheat
+and who shouldn't cheat
+
+ align:start position:0%
+and who shouldn't cheat
+ 
+
+ align:start position:0%
+and who shouldn't cheat
+Are Walled off from knowledge about
+
+ align:start position:0%
+Are Walled off from knowledge about
+ 
+
+ align:start position:0%
+Are Walled off from knowledge about
+modern contraception in sort of the way
+
+ align:start position:0%
+modern contraception in sort of the way
+ 
+
+ align:start position:0%
+modern contraception in sort of the way
+that um that the forces that are driving
+
+ align:start position:0%
+that um that the forces that are driving
+ 
+
+ align:start position:0%
+that um that the forces that are driving
+taste diversions Are Walled off from
+
+ align:start position:0%
+taste diversions Are Walled off from
+ 
+
+ align:start position:0%
+taste diversions Are Walled off from
+what you know about what it is that made
+
+ align:start position:0%
+what you know about what it is that made
+ 
+
+ align:start position:0%
+what you know about what it is that made
+you sick remember from earlier in the
+
+ align:start position:0%
+you sick remember from earlier in the
+ 
+
+ align:start position:0%
+you sick remember from earlier in the
+course you got sick because you got the
+
+ align:start position:0%
+course you got sick because you got the
+ 
+
+ align:start position:0%
+course you got sick because you got the
+flu but you ate a tuna fish sandwich the
+
+ align:start position:0%
+flu but you ate a tuna fish sandwich the
+ 
+
+ align:start position:0%
+flu but you ate a tuna fish sandwich the
+day before you got the flu and now you
+
+ align:start position:0%
+day before you got the flu and now you
+ 
+
+ align:start position:0%
+day before you got the flu and now you
+can't eat tuna fish anymore because this
+
+ align:start position:0%
+can't eat tuna fish anymore because this
+ 
+
+ align:start position:0%
+can't eat tuna fish anymore because this
+little chunk of brain said tuna fish
+
+ align:start position:0%
+little chunk of brain said tuna fish
+ 
+
+ align:start position:0%
+little chunk of brain said tuna fish
+poisoned us we never eat it again right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know in a chunk of guy brain that is
+
+ align:start position:0%
+you know in a chunk of guy brain that is
+ 
+
+ align:start position:0%
+you know in a chunk of guy brain that is
+saying need to know woman is faithful
+
+ align:start position:0%
+saying need to know woman is faithful
+ 
+
+ align:start position:0%
+saying need to know woman is faithful
+why well because I need to know whose
+
+ align:start position:0%
+why well because I need to know whose
+ 
+
+ align:start position:0%
+why well because I need to know whose
+genes they are
+
+ align:start position:0%
+genes they are
+ 
+
+ align:start position:0%
+genes they are
+um the woman isn't pregnant I don't care
+
+ align:start position:0%
+um the woman isn't pregnant I don't care
+ 
+
+ align:start position:0%
+um the woman isn't pregnant I don't care
+I you know this is I'm a very simple
+
+ align:start position:0%
+I you know this is I'm a very simple
+ 
+
+ align:start position:0%
+I you know this is I'm a very simple
+little chunk of brain I just need to
+
+ align:start position:0%
+little chunk of brain I just need to
+ 
+
+ align:start position:0%
+little chunk of brain I just need to
+know woman is faithful or I get you know
+
+ align:start position:0%
+know woman is faithful or I get you know
+ 
+
+ align:start position:0%
+know woman is faithful or I get you know
+I have unhappy things happen in me yeah
+
+ align:start position:0%
+I have unhappy things happen in me yeah
+ 
+
+ align:start position:0%
+I have unhappy things happen in me yeah
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+so the the persist
+
+ align:start position:0%
+so the the persist
+ 
+
+ align:start position:0%
+so the the persist
+s of these sorts of asymmetries and
+
+ align:start position:0%
+s of these sorts of asymmetries and
+ 
+
+ align:start position:0%
+s of these sorts of asymmetries and
+these sorts of behaviors is another
+
+ align:start position:0%
+these sorts of behaviors is another
+ 
+
+ align:start position:0%
+these sorts of behaviors is another
+argument that can be used to argue that
+
+ align:start position:0%
+argument that can be used to argue that
+ 
+
+ align:start position:0%
+argument that can be used to argue that
+these are deep-seated
+
+ align:start position:0%
+these are deep-seated
+ 
+
+ align:start position:0%
+these are deep-seated
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+behaviors with with Evolution oh I
+
+ align:start position:0%
+behaviors with with Evolution oh I
+ 
+
+ align:start position:0%
+behaviors with with Evolution oh I
+should say by the way that these are
+
+ align:start position:0%
+should say by the way that these are
+ 
+
+ align:start position:0%
+should say by the way that these are
+explanations not excuses in any way
+
+ align:start position:0%
+explanations not excuses in any way
+ 
+
+ align:start position:0%
+explanations not excuses in any way
+shape or form right coming home and
+
+ align:start position:0%
+shape or form right coming home and
+ 
+
+ align:start position:0%
+shape or form right coming home and
+flipping to the other side of this right
+
+ align:start position:0%
+flipping to the other side of this right
+ 
+
+ align:start position:0%
+flipping to the other side of this right
+you're the guy this time did you cheat
+
+ align:start position:0%
+you're the guy this time did you cheat
+ 
+
+ align:start position:0%
+you're the guy this time did you cheat
+yes but that's okay because I have
+
+ align:start position:0%
+yes but that's okay because I have
+ 
+
+ align:start position:0%
+yes but that's okay because I have
+deep-seated evolutionary forces within
+
+ align:start position:0%
+deep-seated evolutionary forces within
+ 
+
+ align:start position:0%
+deep-seated evolutionary forces within
+me that make it necessary for me to
+
+ align:start position:0%
+me that make it necessary for me to
+ 
+
+ align:start position:0%
+me that make it necessary for me to
+cheat you know that that's an
+
+ align:start position:0%
+cheat you know that that's an
+ 
+
+ align:start position:0%
+cheat you know that that's an
+interesting explanation but it's not an
+
+ align:start position:0%
+interesting explanation but it's not an
+ 
+
+ align:start position:0%
+interesting explanation but it's not an
+excuse in a relationship any more than
+
+ align:start position:0%
+excuse in a relationship any more than
+ 
+
+ align:start position:0%
+excuse in a relationship any more than
+it's an excuse you know uh you know yes
+
+ align:start position:0%
+it's an excuse you know uh you know yes
+ 
+
+ align:start position:0%
+it's an excuse you know uh you know yes
+I I I uh
+
+ align:start position:0%
+I I I uh
+ 
+
+ align:start position:0%
+I I I uh
+hit my girlfriend because I was jealous
+
+ align:start position:0%
+hit my girlfriend because I was jealous
+ 
+
+ align:start position:0%
+hit my girlfriend because I was jealous
+you know great lovely we have these
+
+ align:start position:0%
+you know great lovely we have these
+ 
+
+ align:start position:0%
+you know great lovely we have these
+great evolutionary Arguments for it
+
+ align:start position:0%
+great evolutionary Arguments for it
+ 
+
+ align:start position:0%
+great evolutionary Arguments for it
+that's not an excuse that's where you
+
+ align:start position:0%
+that's not an excuse that's where you
+ 
+
+ align:start position:0%
+that's not an excuse that's where you
+get into again why these things are
+
+ align:start position:0%
+get into again why these things are
+ 
+
+ align:start position:0%
+get into again why these things are
+politically controversial is the
+
+ align:start position:0%
+politically controversial is the
+ 
+
+ align:start position:0%
+politically controversial is the
+possibility of turning
+
+ align:start position:0%
+possibility of turning
+ 
+
+ align:start position:0%
+possibility of turning
+um explanation into excuse you can
+
+ align:start position:0%
+um explanation into excuse you can
+ 
+
+ align:start position:0%
+um explanation into excuse you can
+decide well to use an example that I
+
+ align:start position:0%
+decide well to use an example that I
+ 
+
+ align:start position:0%
+decide well to use an example that I
+will probably use uh again
+
+ align:start position:0%
+will probably use uh again
+ 
+
+ align:start position:0%
+will probably use uh again
+um it's a little like saying look
+
+ align:start position:0%
+um it's a little like saying look
+ 
+
+ align:start position:0%
+um it's a little like saying look
+gravity is a force you can't thwart
+
+ align:start position:0%
+gravity is a force you can't thwart
+ 
+
+ align:start position:0%
+gravity is a force you can't thwart
+gravity so I'm just gonna lie here
+
+ align:start position:0%
+gravity so I'm just gonna lie here
+ 
+
+ align:start position:0%
+gravity so I'm just gonna lie here
+forever right it opens lost the glasses
+
+ align:start position:0%
+forever right it opens lost the glasses
+ 
+
+ align:start position:0%
+forever right it opens lost the glasses
+where the glasses go all right yeah
+
+ align:start position:0%
+where the glasses go all right yeah
+ 
+
+ align:start position:0%
+where the glasses go all right yeah
+that's a really stupid argument
+
+ align:start position:0%
+that's a really stupid argument
+ 
+
+ align:start position:0%
+that's a really stupid argument
+um and it's similarly stupid to say
+
+ align:start position:0%
+um and it's similarly stupid to say
+ 
+
+ align:start position:0%
+um and it's similarly stupid to say
+biology is a powerful force therefore I
+
+ align:start position:0%
+biology is a powerful force therefore I
+ 
+
+ align:start position:0%
+biology is a powerful force therefore I
+had to do whatever
+
+ align:start position:0%
+had to do whatever
+ 
+
+ align:start position:0%
+had to do whatever
+yeah there are other powerful forces out
+
+ align:start position:0%
+yeah there are other powerful forces out
+ 
+
+ align:start position:0%
+yeah there are other powerful forces out
+there and civilization morality culture
+
+ align:start position:0%
+there and civilization morality culture
+ 
+
+ align:start position:0%
+there and civilization morality culture
+whatever are powerful forces and if they
+
+ align:start position:0%
+whatever are powerful forces and if they
+ 
+
+ align:start position:0%
+whatever are powerful forces and if they
+say don't do it it may be hard work not
+
+ align:start position:0%
+say don't do it it may be hard work not
+ 
+
+ align:start position:0%
+say don't do it it may be hard work not
+to do it but that doesn't mean you
+
+ align:start position:0%
+to do it but that doesn't mean you
+ 
+
+ align:start position:0%
+to do it but that doesn't mean you
+shouldn't do it or you should do
+
+ align:start position:0%
+shouldn't do it or you should do
+ 
+
+ align:start position:0%
+shouldn't do it or you should do
+whatever you've got the basic idea
+
+ align:start position:0%
+whatever you've got the basic idea
+ 
+
+ align:start position:0%
+whatever you've got the basic idea
+um well on that sentence with way too
+
+ align:start position:0%
+um well on that sentence with way too
+ 
+
+ align:start position:0%
+um well on that sentence with way too
+many double negatives in it
+
+ align:start position:0%
+many double negatives in it
+ 
+
+ align:start position:0%
+many double negatives in it
+let us take a brief break and then I'll
+
+ align:start position:0%
+let us take a brief break and then I'll
+ 
+
+ align:start position:0%
+let us take a brief break and then I'll
+turn to the question of individual
+
+ align:start position:0%
+turn to the question of individual
+ 
+
+ align:start position:0%
+turn to the question of individual
+Behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before they I mean after they come back
+
+ align:start position:0%
+before they I mean after they come back
+ 
+
+ align:start position:0%
+before they I mean after they come back
+from the break maybe
+
+ align:start position:0%
+from the break maybe
+ 
+
+ align:start position:0%
+from the break maybe
+would you prefer at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+I'll do my best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slow down will it be funny because we
+
+ align:start position:0%
+slow down will it be funny because we
+ 
+
+ align:start position:0%
+slow down will it be funny because we
+want the answer okay good quick funny
+
+ align:start position:0%
+want the answer okay good quick funny
+ 
+
+ align:start position:0%
+want the answer okay good quick funny
+announcement that'll keep them all right
+
+ align:start position:0%
+announcement that'll keep them all right
+ 
+
+ align:start position:0%
+announcement that'll keep them all right
+so be here in about 20 minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me let me elaborate I realized
+
+ align:start position:0%
+let me let me elaborate I realized
+ 
+
+ align:start position:0%
+let me let me elaborate I realized
+looking at the handout that I didn't
+
+ align:start position:0%
+looking at the handout that I didn't
+ 
+
+ align:start position:0%
+looking at the handout that I didn't
+elaborate particularly well on this
+
+ align:start position:0%
+elaborate particularly well on this
+ 
+
+ align:start position:0%
+elaborate particularly well on this
+problem two part
+
+ align:start position:0%
+problem two part
+ 
+
+ align:start position:0%
+problem two part
+about it not uh about these evolutionary
+
+ align:start position:0%
+about it not uh about these evolutionary
+ 
+
+ align:start position:0%
+about it not uh about these evolutionary
+theories not explaining the uh the full
+
+ align:start position:0%
+theories not explaining the uh the full
+ 
+
+ align:start position:0%
+theories not explaining the uh the full
+range of behavior uh well so
+
+ align:start position:0%
+range of behavior uh well so
+ 
+
+ align:start position:0%
+range of behavior uh well so
+you know it explains you know perhaps
+
+ align:start position:0%
+you know it explains you know perhaps
+ 
+
+ align:start position:0%
+you know it explains you know perhaps
+the uh the theory as as elaborate thus
+
+ align:start position:0%
+the uh the theory as as elaborate thus
+ 
+
+ align:start position:0%
+the uh the theory as as elaborate thus
+far explains for instance why you might
+
+ align:start position:0%
+far explains for instance why you might
+ 
+
+ align:start position:0%
+far explains for instance why you might
+be attracted to one person or another
+
+ align:start position:0%
+be attracted to one person or another
+ 
+
+ align:start position:0%
+be attracted to one person or another
+but it doesn't explain what you do
+
+ align:start position:0%
+but it doesn't explain what you do
+ 
+
+ align:start position:0%
+but it doesn't explain what you do
+in any particular way so you know you
+
+ align:start position:0%
+in any particular way so you know you
+ 
+
+ align:start position:0%
+in any particular way so you know you
+see an attractive uh potential mate you
+
+ align:start position:0%
+see an attractive uh potential mate you
+ 
+
+ align:start position:0%
+see an attractive uh potential mate you
+know if your bird you might do some sort
+
+ align:start position:0%
+know if your bird you might do some sort
+ 
+
+ align:start position:0%
+know if your bird you might do some sort
+of weird mating dance or something like
+
+ align:start position:0%
+of weird mating dance or something like
+ 
+
+ align:start position:0%
+of weird mating dance or something like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um if you're yeah if you're a human you
+
+ align:start position:0%
+um if you're yeah if you're a human you
+ 
+
+ align:start position:0%
+um if you're yeah if you're a human you
+might do some weird mating dance or
+
+ align:start position:0%
+might do some weird mating dance or
+ 
+
+ align:start position:0%
+might do some weird mating dance or
+something like that or you know you can
+
+ align:start position:0%
+something like that or you know you can
+ 
+
+ align:start position:0%
+something like that or you know you can
+ask yourself about the rain what do you
+
+ align:start position:0%
+ask yourself about the rain what do you
+ 
+
+ align:start position:0%
+ask yourself about the rain what do you
+do if there's an attractive mate
+
+ align:start position:0%
+do if there's an attractive mate
+ 
+
+ align:start position:0%
+do if there's an attractive mate
+possibility you could uh you know you
+
+ align:start position:0%
+possibility you could uh you know you
+ 
+
+ align:start position:0%
+possibility you could uh you know you
+could you could dance you could hang
+
+ align:start position:0%
+could you could dance you could hang
+ 
+
+ align:start position:0%
+could you could dance you could hang
+around you could act pathetic
+
+ align:start position:0%
+around you could act pathetic
+ 
+
+ align:start position:0%
+around you could act pathetic
+um you could ask non-pathetic you could
+
+ align:start position:0%
+um you could ask non-pathetic you could
+ 
+
+ align:start position:0%
+um you could ask non-pathetic you could
+get person a to talk to person B and and
+
+ align:start position:0%
+get person a to talk to person B and and
+ 
+
+ align:start position:0%
+get person a to talk to person B and and
+who knows C who's the uncle of D or
+
+ align:start position:0%
+who knows C who's the uncle of D or
+ 
+
+ align:start position:0%
+who knows C who's the uncle of D or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+just knowing that there was evolutionary
+
+ align:start position:0%
+just knowing that there was evolutionary
+ 
+
+ align:start position:0%
+just knowing that there was evolutionary
+pressure here isn't really a a full
+
+ align:start position:0%
+pressure here isn't really a a full
+ 
+
+ align:start position:0%
+pressure here isn't really a a full
+story about human mating behavior by any
+
+ align:start position:0%
+story about human mating behavior by any
+ 
+
+ align:start position:0%
+story about human mating behavior by any
+stretch of the imagination
+
+ align:start position:0%
+stretch of the imagination
+ 
+
+ align:start position:0%
+stretch of the imagination
+um what's going to elaborate it on it on
+
+ align:start position:0%
+um what's going to elaborate it on it on
+ 
+
+ align:start position:0%
+um what's going to elaborate it on it on
+it you can probably get a good piece of
+
+ align:start position:0%
+it you can probably get a good piece of
+ 
+
+ align:start position:0%
+it you can probably get a good piece of
+mileage from uh asking about law of
+
+ align:start position:0%
+mileage from uh asking about law of
+ 
+
+ align:start position:0%
+mileage from uh asking about law of
+effect kinds of things what you do in
+
+ align:start position:0%
+effect kinds of things what you do in
+ 
+
+ align:start position:0%
+effect kinds of things what you do in
+mating situations or a courtship
+
+ align:start position:0%
+mating situations or a courtship
+ 
+
+ align:start position:0%
+mating situations or a courtship
+situations is going to be shaped
+
+ align:start position:0%
+situations is going to be shaped
+ 
+
+ align:start position:0%
+situations is going to be shaped
+um at least in part by the schedule of
+
+ align:start position:0%
+um at least in part by the schedule of
+ 
+
+ align:start position:0%
+um at least in part by the schedule of
+reinforcement
+
+ align:start position:0%
+reinforcement
+ 
+
+ align:start position:0%
+reinforcement
+right if something you know you do a
+
+ align:start position:0%
+right if something you know you do a
+ 
+
+ align:start position:0%
+right if something you know you do a
+mating dance and and and uh the
+
+ align:start position:0%
+mating dance and and and uh the
+ 
+
+ align:start position:0%
+mating dance and and and uh the
+potential mate your response
+
+ align:start position:0%
+potential mate your response
+ 
+
+ align:start position:0%
+potential mate your response
+you're gonna be inclined to do that
+
+ align:start position:0%
+you're gonna be inclined to do that
+ 
+
+ align:start position:0%
+you're gonna be inclined to do that
+dance more it's not why birds do it
+
+ align:start position:0%
+dance more it's not why birds do it
+ 
+
+ align:start position:0%
+dance more it's not why birds do it
+birds are wired typically to do the
+
+ align:start position:0%
+birds are wired typically to do the
+ 
+
+ align:start position:0%
+birds are wired typically to do the
+dance but you know if you go off and do
+
+ align:start position:0%
+dance but you know if you go off and do
+ 
+
+ align:start position:0%
+dance but you know if you go off and do
+some weird dance and and he or she says
+
+ align:start position:0%
+some weird dance and and he or she says
+ 
+
+ align:start position:0%
+some weird dance and and he or she says
+hey this is good
+
+ align:start position:0%
+hey this is good
+ 
+
+ align:start position:0%
+hey this is good
+um you know you do it again uh it at the
+
+ align:start position:0%
+um you know you do it again uh it at the
+ 
+
+ align:start position:0%
+um you know you do it again uh it at the
+uh the whole
+
+ align:start position:0%
+uh the whole
+ 
+
+ align:start position:0%
+uh the whole
+uh I don't know a ritual I don't know
+
+ align:start position:0%
+uh I don't know a ritual I don't know
+ 
+
+ align:start position:0%
+uh I don't know a ritual I don't know
+what you want to call who touches who
+
+ align:start position:0%
+what you want to call who touches who
+ 
+
+ align:start position:0%
+what you want to call who touches who
+when where and how is also heavily
+
+ align:start position:0%
+when where and how is also heavily
+ 
+
+ align:start position:0%
+when where and how is also heavily
+shaped by law of effect sorts of things
+
+ align:start position:0%
+shaped by law of effect sorts of things
+ 
+
+ align:start position:0%
+shaped by law of effect sorts of things
+you know if it's rewarded it happens
+
+ align:start position:0%
+you know if it's rewarded it happens
+ 
+
+ align:start position:0%
+you know if it's rewarded it happens
+again if it's if if it's if it's not
+
+ align:start position:0%
+again if it's if if it's if it's not
+ 
+
+ align:start position:0%
+again if it's if if it's if it's not
+rewarded it doesn't happen again
+
+ align:start position:0%
+rewarded it doesn't happen again
+ 
+
+ align:start position:0%
+rewarded it doesn't happen again
+um more on this later but I did want to
+
+ align:start position:0%
+um more on this later but I did want to
+ 
+
+ align:start position:0%
+um more on this later but I did want to
+just say that what that there's nothing
+
+ align:start position:0%
+just say that what that there's nothing
+ 
+
+ align:start position:0%
+just say that what that there's nothing
+in these sort of evolutionary psych
+
+ align:start position:0%
+in these sort of evolutionary psych
+ 
+
+ align:start position:0%
+in these sort of evolutionary psych
+theory that really talks to that
+
+ align:start position:0%
+theory that really talks to that
+ 
+
+ align:start position:0%
+theory that really talks to that
+um now let me
+
+ align:start position:0%
+um now let me
+ 
+
+ align:start position:0%
+um now let me
+um go on to try to say what does talk
+
+ align:start position:0%
+um go on to try to say what does talk
+ 
+
+ align:start position:0%
+um go on to try to say what does talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+behavior in in romantic uh romantic
+
+ align:start position:0%
+behavior in in romantic uh romantic
+ 
+
+ align:start position:0%
+behavior in in romantic uh romantic
+relationships
+
+ align:start position:0%
+relationships
+ 
+
+ align:start position:0%
+relationships
+um you know to get Beyond this notion of
+
+ align:start position:0%
+um you know to get Beyond this notion of
+ 
+
+ align:start position:0%
+um you know to get Beyond this notion of
+what what average population's uh what
+
+ align:start position:0%
+what what average population's uh what
+ 
+
+ align:start position:0%
+what what average population's uh what
+average populations do in a world full
+
+ align:start position:0%
+average populations do in a world full
+ 
+
+ align:start position:0%
+average populations do in a world full
+of potential mates why are you attracted
+
+ align:start position:0%
+of potential mates why are you attracted
+ 
+
+ align:start position:0%
+of potential mates why are you attracted
+to this one now you know what's what can
+
+ align:start position:0%
+to this one now you know what's what can
+ 
+
+ align:start position:0%
+to this one now you know what's what can
+we say about that
+
+ align:start position:0%
+we say about that
+ 
+
+ align:start position:0%
+we say about that
+um there there certainly seems to be
+
+ align:start position:0%
+um there there certainly seems to be
+ 
+
+ align:start position:0%
+um there there certainly seems to be
+something to explain there are a variety
+
+ align:start position:0%
+something to explain there are a variety
+ 
+
+ align:start position:0%
+something to explain there are a variety
+of candidate sorts of theories out there
+
+ align:start position:0%
+of candidate sorts of theories out there
+ 
+
+ align:start position:0%
+of candidate sorts of theories out there
+one of them is nicely encapsulated in
+
+ align:start position:0%
+one of them is nicely encapsulated in
+ 
+
+ align:start position:0%
+one of them is nicely encapsulated in
+um uh in shakes oh I realized I didn't
+
+ align:start position:0%
+um uh in shakes oh I realized I didn't
+ 
+
+ align:start position:0%
+um uh in shakes oh I realized I didn't
+put the most clear-cut piece of uh
+
+ align:start position:0%
+put the most clear-cut piece of uh
+ 
+
+ align:start position:0%
+put the most clear-cut piece of uh
+citation on that quote at the bottom of
+
+ align:start position:0%
+citation on that quote at the bottom of
+ 
+
+ align:start position:0%
+citation on that quote at the bottom of
+page three that's Midsummer Night's
+
+ align:start position:0%
+page three that's Midsummer Night's
+ 
+
+ align:start position:0%
+page three that's Midsummer Night's
+Dream Shakespeare's Midsummer Night
+
+ align:start position:0%
+Dream Shakespeare's Midsummer Night
+ 
+
+ align:start position:0%
+Dream Shakespeare's Midsummer Night
+stream and Shakespeare has Theseus Duke
+
+ align:start position:0%
+stream and Shakespeare has Theseus Duke
+ 
+
+ align:start position:0%
+stream and Shakespeare has Theseus Duke
+of Athens say that lovers and mad men
+
+ align:start position:0%
+of Athens say that lovers and mad men
+ 
+
+ align:start position:0%
+of Athens say that lovers and mad men
+have such seething brains such shaping
+
+ align:start position:0%
+have such seething brains such shaping
+ 
+
+ align:start position:0%
+have such seething brains such shaping
+fans fantasies that apprehend more than
+
+ align:start position:0%
+fans fantasies that apprehend more than
+ 
+
+ align:start position:0%
+fans fantasies that apprehend more than
+cool reason ever comprehends The Lunatic
+
+ align:start position:0%
+cool reason ever comprehends The Lunatic
+ 
+
+ align:start position:0%
+cool reason ever comprehends The Lunatic
+the lover and the poet are of
+
+ align:start position:0%
+the lover and the poet are of
+ 
+
+ align:start position:0%
+the lover and the poet are of
+imagination all compact this is a theory
+
+ align:start position:0%
+imagination all compact this is a theory
+ 
+
+ align:start position:0%
+imagination all compact this is a theory
+of romantic behavior that says you're
+
+ align:start position:0%
+of romantic behavior that says you're
+ 
+
+ align:start position:0%
+of romantic behavior that says you're
+attracted to whom you're attracted to at
+
+ align:start position:0%
+attracted to whom you're attracted to at
+ 
+
+ align:start position:0%
+attracted to whom you're attracted to at
+the moment and you're doing what you're
+
+ align:start position:0%
+the moment and you're doing what you're
+ 
+
+ align:start position:0%
+the moment and you're doing what you're
+doing in response to that now because
+
+ align:start position:0%
+doing in response to that now because
+ 
+
+ align:start position:0%
+doing in response to that now because
+you're nuts
+
+ align:start position:0%
+you're nuts
+ 
+
+ align:start position:0%
+you're nuts
+I mean it basically it's a form of
+
+ align:start position:0%
+I mean it basically it's a form of
+ 
+
+ align:start position:0%
+I mean it basically it's a form of
+insanity
+
+ align:start position:0%
+insanity
+ 
+
+ align:start position:0%
+insanity
+um and not uncommon uh theory in in
+
+ align:start position:0%
+um and not uncommon uh theory in in
+ 
+
+ align:start position:0%
+um and not uncommon uh theory in in
+literary that shows up in literary
+
+ align:start position:0%
+literary that shows up in literary
+ 
+
+ align:start position:0%
+literary that shows up in literary
+circles and you may have
+
+ align:start position:0%
+circles and you may have
+ 
+
+ align:start position:0%
+circles and you may have
+um the the place to get some intuitive
+
+ align:start position:0%
+um the the place to get some intuitive
+ 
+
+ align:start position:0%
+um the the place to get some intuitive
+uh feeling for that is to remember what
+
+ align:start position:0%
+uh feeling for that is to remember what
+ 
+
+ align:start position:0%
+uh feeling for that is to remember what
+it felt like
+
+ align:start position:0%
+it felt like
+ 
+
+ align:start position:0%
+it felt like
+um if you were ever completely
+
+ align:start position:0%
+um if you were ever completely
+ 
+
+ align:start position:0%
+um if you were ever completely
+infatuated with somebody
+
+ align:start position:0%
+infatuated with somebody
+ 
+
+ align:start position:0%
+infatuated with somebody
+preferably somebody who didn't know you
+
+ align:start position:0%
+preferably somebody who didn't know you
+ 
+
+ align:start position:0%
+preferably somebody who didn't know you
+were infatuated with them right
+
+ align:start position:0%
+were infatuated with them right
+ 
+
+ align:start position:0%
+were infatuated with them right
+some random other person in across the
+
+ align:start position:0%
+some random other person in across the
+ 
+
+ align:start position:0%
+some random other person in across the
+you know crowded room kind of thing
+
+ align:start position:0%
+you know crowded room kind of thing
+ 
+
+ align:start position:0%
+you know crowded room kind of thing
+um you know that has the feeling of
+
+ align:start position:0%
+um you know that has the feeling of
+ 
+
+ align:start position:0%
+um you know that has the feeling of
+being more or less out of your mind
+
+ align:start position:0%
+being more or less out of your mind
+ 
+
+ align:start position:0%
+being more or less out of your mind
+but you don't realize at the time
+
+ align:start position:0%
+but you don't realize at the time
+ 
+
+ align:start position:0%
+but you don't realize at the time
+um and reams of bad High School poetry
+
+ align:start position:0%
+um and reams of bad High School poetry
+ 
+
+ align:start position:0%
+um and reams of bad High School poetry
+are written under those
+
+ align:start position:0%
+are written under those
+ 
+
+ align:start position:0%
+are written under those
+conditions and if you're very lucky uh
+
+ align:start position:0%
+conditions and if you're very lucky uh
+ 
+
+ align:start position:0%
+conditions and if you're very lucky uh
+nobody else gets to see that stuff
+
+ align:start position:0%
+nobody else gets to see that stuff
+ 
+
+ align:start position:0%
+nobody else gets to see that stuff
+mostly
+
+ align:start position:0%
+mostly
+ 
+
+ align:start position:0%
+mostly
+um they in in my in my experience so
+
+ align:start position:0%
+um they in in my in my experience so
+ 
+
+ align:start position:0%
+um they in in my in my experience so
+back when I was in high school how many
+
+ align:start position:0%
+back when I was in high school how many
+ 
+
+ align:start position:0%
+back when I was in high school how many
+people have ever seen a book called
+
+ align:start position:0%
+people have ever seen a book called
+ 
+
+ align:start position:0%
+people have ever seen a book called
+Jonathan Livingston Seagull
+
+ align:start position:0%
+Jonathan Livingston Seagull
+ 
+
+ align:start position:0%
+Jonathan Livingston Seagull
+oh it's still out there it's it's it's
+
+ align:start position:0%
+oh it's still out there it's it's it's
+ 
+
+ align:start position:0%
+oh it's still out there it's it's it's
+very sappy
+
+ align:start position:0%
+very sappy
+ 
+
+ align:start position:0%
+very sappy
+um and it was the sort of thing you gave
+
+ align:start position:0%
+um and it was the sort of thing you gave
+ 
+
+ align:start position:0%
+um and it was the sort of thing you gave
+to somebody who you were deeply in love
+
+ align:start position:0%
+to somebody who you were deeply in love
+ 
+
+ align:start position:0%
+to somebody who you were deeply in love
+with properly in high school
+
+ align:start position:0%
+with properly in high school
+ 
+
+ align:start position:0%
+with properly in high school
+um and it turns out that both my wife
+
+ align:start position:0%
+um and it turns out that both my wife
+ 
+
+ align:start position:0%
+um and it turns out that both my wife
+and I have copies of this book
+
+ align:start position:0%
+and I have copies of this book
+ 
+
+ align:start position:0%
+and I have copies of this book
+given to us by people other than each
+
+ align:start position:0%
+given to us by people other than each
+ 
+
+ align:start position:0%
+given to us by people other than each
+other because we didn't know each other
+
+ align:start position:0%
+other because we didn't know each other
+ 
+
+ align:start position:0%
+other because we didn't know each other
+in high school both with inscriptions so
+
+ align:start position:0%
+in high school both with inscriptions so
+ 
+
+ align:start position:0%
+in high school both with inscriptions so
+florid that you know you just can't read
+
+ align:start position:0%
+florid that you know you just can't read
+ 
+
+ align:start position:0%
+florid that you know you just can't read
+them they're they're they're quite a bit
+
+ align:start position:0%
+them they're they're they're quite a bit
+ 
+
+ align:start position:0%
+them they're they're they're quite a bit
+one of these why haven't we destroyed
+
+ align:start position:0%
+one of these why haven't we destroyed
+ 
+
+ align:start position:0%
+one of these why haven't we destroyed
+them well and there's a certain
+
+ align:start position:0%
+them well and there's a certain
+ 
+
+ align:start position:0%
+them well and there's a certain
+Nostalgia there of some sort and all you
+
+ align:start position:0%
+Nostalgia there of some sort and all you
+ 
+
+ align:start position:0%
+Nostalgia there of some sort and all you
+you gotta save these things for your
+
+ align:start position:0%
+you gotta save these things for your
+ 
+
+ align:start position:0%
+you gotta save these things for your
+children one day you know you're my one
+
+ align:start position:0%
+children one day you know you're my one
+ 
+
+ align:start position:0%
+children one day you know you're my one
+of my kids is going to be up in the
+
+ align:start position:0%
+of my kids is going to be up in the
+ 
+
+ align:start position:0%
+of my kids is going to be up in the
+attic and find this thing and read it
+
+ align:start position:0%
+attic and find this thing and read it
+ 
+
+ align:start position:0%
+attic and find this thing and read it
+and and fall down dead laughing
+
+ align:start position:0%
+and and fall down dead laughing
+ 
+
+ align:start position:0%
+and and fall down dead laughing
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+um all right but the the relevant
+
+ align:start position:0%
+um all right but the the relevant
+ 
+
+ align:start position:0%
+um all right but the the relevant
+question here is
+
+ align:start position:0%
+question here is
+ 
+
+ align:start position:0%
+question here is
+that's not a bad Theory
+
+ align:start position:0%
+that's not a bad Theory
+ 
+
+ align:start position:0%
+that's not a bad Theory
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+why don't we why isn't this the abnormal
+
+ align:start position:0%
+why don't we why isn't this the abnormal
+ 
+
+ align:start position:0%
+why don't we why isn't this the abnormal
+psych part of the course why aren't we
+
+ align:start position:0%
+psych part of the course why aren't we
+ 
+
+ align:start position:0%
+psych part of the course why aren't we
+talking about love in the context of
+
+ align:start position:0%
+talking about love in the context of
+ 
+
+ align:start position:0%
+talking about love in the context of
+psychopathology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the answer
+
+ align:start position:0%
+what's the answer
+ 
+
+ align:start position:0%
+what's the answer
+nobody knows what the answer is how do
+
+ align:start position:0%
+nobody knows what the answer is how do
+ 
+
+ align:start position:0%
+nobody knows what the answer is how do
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's a reason it's called
+
+ align:start position:0%
+yeah there's a reason it's called
+ 
+
+ align:start position:0%
+yeah there's a reason it's called
+abnormal psychology as as a possible now
+
+ align:start position:0%
+abnormal psychology as as a possible now
+ 
+
+ align:start position:0%
+abnormal psychology as as a possible now
+look if if I don't know quite what would
+
+ align:start position:0%
+look if if I don't know quite what would
+ 
+
+ align:start position:0%
+look if if I don't know quite what would
+happen if um you know if bad people
+
+ align:start position:0%
+happen if um you know if bad people
+ 
+
+ align:start position:0%
+happen if um you know if bad people
+found a way to put something in the
+
+ align:start position:0%
+found a way to put something in the
+ 
+
+ align:start position:0%
+found a way to put something in the
+water that made us all uh flooredly
+
+ align:start position:0%
+water that made us all uh flooredly
+ 
+
+ align:start position:0%
+water that made us all uh flooredly
+schizophrenic if it became the majority
+
+ align:start position:0%
+schizophrenic if it became the majority
+ 
+
+ align:start position:0%
+schizophrenic if it became the majority
+state it would still be
+
+ align:start position:0%
+state it would still be
+ 
+
+ align:start position:0%
+state it would still be
+um psychopathological probably but by
+
+ align:start position:0%
+um psychopathological probably but by
+ 
+
+ align:start position:0%
+um psychopathological probably but by
+and large what we talk about in abnormal
+
+ align:start position:0%
+and large what we talk about in abnormal
+ 
+
+ align:start position:0%
+and large what we talk about in abnormal
+psychology is abnormal and uh
+
+ align:start position:0%
+psychology is abnormal and uh
+ 
+
+ align:start position:0%
+psychology is abnormal and uh
+being loved may be a sort of insanity
+
+ align:start position:0%
+being loved may be a sort of insanity
+ 
+
+ align:start position:0%
+being loved may be a sort of insanity
+but it's a very well look Shakespeare
+
+ align:start position:0%
+but it's a very well look Shakespeare
+ 
+
+ align:start position:0%
+but it's a very well look Shakespeare
+knew this too so if we borrow from as
+
+ align:start position:0%
+knew this too so if we borrow from as
+ 
+
+ align:start position:0%
+knew this too so if we borrow from as
+you like it we have the explanation of
+
+ align:start position:0%
+you like it we have the explanation of
+ 
+
+ align:start position:0%
+you like it we have the explanation of
+uh this given in this case by Rosalind
+
+ align:start position:0%
+uh this given in this case by Rosalind
+ 
+
+ align:start position:0%
+uh this given in this case by Rosalind
+roslyndon in in uh and as you like it
+
+ align:start position:0%
+roslyndon in in uh and as you like it
+ 
+
+ align:start position:0%
+roslyndon in in uh and as you like it
+saying that that love is merely Madness
+
+ align:start position:0%
+saying that that love is merely Madness
+ 
+
+ align:start position:0%
+saying that that love is merely Madness
+merely a Madness and I tell you deserves
+
+ align:start position:0%
+merely a Madness and I tell you deserves
+ 
+
+ align:start position:0%
+merely a Madness and I tell you deserves
+a dark house and a whip as Mad Men do
+
+ align:start position:0%
+a dark house and a whip as Mad Men do
+ 
+
+ align:start position:0%
+a dark house and a whip as Mad Men do
+which tells you something about it
+
+ align:start position:0%
+which tells you something about it
+ 
+
+ align:start position:0%
+which tells you something about it
+Elizabethan psychotherapy
+
+ align:start position:0%
+Elizabethan psychotherapy
+ 
+
+ align:start position:0%
+Elizabethan psychotherapy
+um the reason they are not so punished
+
+ align:start position:0%
+um the reason they are not so punished
+ 
+
+ align:start position:0%
+um the reason they are not so punished
+and cured which also tells you something
+
+ align:start position:0%
+and cured which also tells you something
+ 
+
+ align:start position:0%
+and cured which also tells you something
+about Elizabethan Psychotherapy the
+
+ align:start position:0%
+about Elizabethan Psychotherapy the
+ 
+
+ align:start position:0%
+about Elizabethan Psychotherapy the
+notion was not that you were just being
+
+ align:start position:0%
+notion was not that you were just being
+ 
+
+ align:start position:0%
+notion was not that you were just being
+nasty to crazy people but that being
+
+ align:start position:0%
+nasty to crazy people but that being
+ 
+
+ align:start position:0%
+nasty to crazy people but that being
+nasty was Curative
+
+ align:start position:0%
+nasty was Curative
+ 
+
+ align:start position:0%
+nasty was Curative
+um the reason they are not so punished
+
+ align:start position:0%
+um the reason they are not so punished
+ 
+
+ align:start position:0%
+um the reason they are not so punished
+and cured is that the lunacy is so
+
+ align:start position:0%
+and cured is that the lunacy is so
+ 
+
+ align:start position:0%
+and cured is that the lunacy is so
+ordinary that the whippers are in love
+
+ align:start position:0%
+ordinary that the whippers are in love
+ 
+
+ align:start position:0%
+ordinary that the whippers are in love
+too it doesn't make any real sense it's
+
+ align:start position:0%
+too it doesn't make any real sense it's
+ 
+
+ align:start position:0%
+too it doesn't make any real sense it's
+not a useful Theory to say that that
+
+ align:start position:0%
+not a useful Theory to say that that
+ 
+
+ align:start position:0%
+not a useful Theory to say that that
+being in love is is a form of insanity
+
+ align:start position:0%
+being in love is is a form of insanity
+ 
+
+ align:start position:0%
+being in love is is a form of insanity
+because it's essentially a universal
+
+ align:start position:0%
+because it's essentially a universal
+ 
+
+ align:start position:0%
+because it's essentially a universal
+form of insanity
+
+ align:start position:0%
+form of insanity
+ 
+
+ align:start position:0%
+form of insanity
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you might think
+
+ align:start position:0%
+you might think
+ 
+
+ align:start position:0%
+you might think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there's nothing much to say in an intro
+
+ align:start position:0%
+there's nothing much to say in an intro
+ 
+
+ align:start position:0%
+there's nothing much to say in an intro
+psych class about this at all and that
+
+ align:start position:0%
+psych class about this at all and that
+ 
+
+ align:start position:0%
+psych class about this at all and that
+the whole topic is kind of best left to
+
+ align:start position:0%
+the whole topic is kind of best left to
+ 
+
+ align:start position:0%
+the whole topic is kind of best left to
+Shakespeare and and and other literary
+
+ align:start position:0%
+Shakespeare and and and other literary
+ 
+
+ align:start position:0%
+Shakespeare and and and other literary
+sources and that's an ox not a bad
+
+ align:start position:0%
+sources and that's an ox not a bad
+ 
+
+ align:start position:0%
+sources and that's an ox not a bad
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+um but I think there is something uh
+
+ align:start position:0%
+um but I think there is something uh
+ 
+
+ align:start position:0%
+um but I think there is something uh
+useful to be said in the context of
+
+ align:start position:0%
+useful to be said in the context of
+ 
+
+ align:start position:0%
+useful to be said in the context of
+psychology
+
+ align:start position:0%
+psychology
+ 
+
+ align:start position:0%
+psychology
+um you could we can switch back to
+
+ align:start position:0%
+um you could we can switch back to
+ 
+
+ align:start position:0%
+um you could we can switch back to
+Shakespeare and ask uh how are I wait
+
+ align:start position:0%
+Shakespeare and ask uh how are I wait
+ 
+
+ align:start position:0%
+Shakespeare and ask uh how are I wait
+wait first we have to check on how high
+
+ align:start position:0%
+wait first we have to check on how high
+ 
+
+ align:start position:0%
+wait first we have to check on how high
+school education is going these days how
+
+ align:start position:0%
+school education is going these days how
+ 
+
+ align:start position:0%
+school education is going these days how
+many people had to read Romeo and Juliet
+
+ align:start position:0%
+many people had to read Romeo and Juliet
+ 
+
+ align:start position:0%
+many people had to read Romeo and Juliet
+in high school somewhere oh okay good
+
+ align:start position:0%
+in high school somewhere oh okay good
+ 
+
+ align:start position:0%
+in high school somewhere oh okay good
+just checking
+
+ align:start position:0%
+just checking
+ 
+
+ align:start position:0%
+just checking
+um so uh you know Romeo is looking
+
+ align:start position:0%
+um so uh you know Romeo is looking
+ 
+
+ align:start position:0%
+um so uh you know Romeo is looking
+across a crowded uh a dance hall here
+
+ align:start position:0%
+across a crowded uh a dance hall here
+ 
+
+ align:start position:0%
+across a crowded uh a dance hall here
+um and he sees um he sees Juliet and
+
+ align:start position:0%
+um and he sees um he sees Juliet and
+ 
+
+ align:start position:0%
+um and he sees um he sees Juliet and
+he's supposed to be in love with
+
+ align:start position:0%
+he's supposed to be in love with
+ 
+
+ align:start position:0%
+he's supposed to be in love with
+Boss line good you got that question
+
+ align:start position:0%
+Boss line good you got that question
+ 
+
+ align:start position:0%
+Boss line good you got that question
+right on the test
+
+ align:start position:0%
+right on the test
+ 
+
+ align:start position:0%
+right on the test
+um right he's he's been mooning around
+
+ align:start position:0%
+um right he's he's been mooning around
+ 
+
+ align:start position:0%
+um right he's he's been mooning around
+about this woman Roslyn he walks in he
+
+ align:start position:0%
+about this woman Roslyn he walks in he
+ 
+
+ align:start position:0%
+about this woman Roslyn he walks in he
+sees Juliet and it's you know oh she
+
+ align:start position:0%
+sees Juliet and it's you know oh she
+ 
+
+ align:start position:0%
+sees Juliet and it's you know oh she
+does make the toy teach the teachers
+
+ align:start position:0%
+does make the toy teach the teachers
+ 
+
+ align:start position:0%
+does make the toy teach the teachers
+you can see why I'm not a Shakespearean
+
+ align:start position:0%
+you can see why I'm not a Shakespearean
+ 
+
+ align:start position:0%
+you can see why I'm not a Shakespearean
+actor she does teach the Torches to burn
+
+ align:start position:0%
+actor she does teach the Torches to burn
+ 
+
+ align:start position:0%
+actor she does teach the Torches to burn
+bright and and and all that good stuff
+
+ align:start position:0%
+bright and and and all that good stuff
+ 
+
+ align:start position:0%
+bright and and and all that good stuff
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+why what can what can you uh what can
+
+ align:start position:0%
+why what can what can you uh what can
+ 
+
+ align:start position:0%
+why what can what can you uh what can
+you say about it there are a variety of
+
+ align:start position:0%
+you say about it there are a variety of
+ 
+
+ align:start position:0%
+you say about it there are a variety of
+things well we could we could develop
+
+ align:start position:0%
+things well we could we could develop
+ 
+
+ align:start position:0%
+things well we could we could develop
+what we could call the chemical theory
+
+ align:start position:0%
+what we could call the chemical theory
+ 
+
+ align:start position:0%
+what we could call the chemical theory
+of Love here we've passed through the
+
+ align:start position:0%
+of Love here we've passed through the
+ 
+
+ align:start position:0%
+of Love here we've passed through the
+insanity Theory let's work on the
+
+ align:start position:0%
+insanity Theory let's work on the
+ 
+
+ align:start position:0%
+insanity Theory let's work on the
+chemical Theory a little bit
+
+ align:start position:0%
+chemical Theory a little bit
+ 
+
+ align:start position:0%
+chemical Theory a little bit
+um chemical Theory gets you a a certain
+
+ align:start position:0%
+um chemical Theory gets you a a certain
+ 
+
+ align:start position:0%
+um chemical Theory gets you a a certain
+uh distance oh I didn't put this on the
+
+ align:start position:0%
+uh distance oh I didn't put this on the
+ 
+
+ align:start position:0%
+uh distance oh I didn't put this on the
+handout yet because I wasn't convinced I
+
+ align:start position:0%
+handout yet because I wasn't convinced I
+ 
+
+ align:start position:0%
+handout yet because I wasn't convinced I
+was going to get here so the the I'll
+
+ align:start position:0%
+was going to get here so the the I'll
+ 
+
+ align:start position:0%
+was going to get here so the the I'll
+put a few of these terms on there next
+
+ align:start position:0%
+put a few of these terms on there next
+ 
+
+ align:start position:0%
+put a few of these terms on there next
+time but you can you can write on the
+
+ align:start position:0%
+time but you can you can write on the
+ 
+
+ align:start position:0%
+time but you can you can write on the
+back of the handout so uh
+
+ align:start position:0%
+back of the handout so uh
+ 
+
+ align:start position:0%
+back of the handout so uh
+chemical aspects one thing that's uh
+
+ align:start position:0%
+chemical aspects one thing that's uh
+ 
+
+ align:start position:0%
+chemical aspects one thing that's uh
+related to chemical aspects is is the
+
+ align:start position:0%
+related to chemical aspects is is the
+ 
+
+ align:start position:0%
+related to chemical aspects is is the
+proximity Factor you want to get two
+
+ align:start position:0%
+proximity Factor you want to get two
+ 
+
+ align:start position:0%
+proximity Factor you want to get two
+things to uh to yeah to interact and
+
+ align:start position:0%
+things to uh to yeah to interact and
+ 
+
+ align:start position:0%
+things to uh to yeah to interact and
+make make heat you got to bring them
+
+ align:start position:0%
+make make heat you got to bring them
+ 
+
+ align:start position:0%
+make make heat you got to bring them
+together right it sounds trivial but
+
+ align:start position:0%
+together right it sounds trivial but
+ 
+
+ align:start position:0%
+together right it sounds trivial but
+um well the scary version of this is
+
+ align:start position:0%
+um well the scary version of this is
+ 
+
+ align:start position:0%
+um well the scary version of this is
+that a a a not uh insignificant number
+
+ align:start position:0%
+that a a a not uh insignificant number
+ 
+
+ align:start position:0%
+that a a a not uh insignificant number
+of you will meet your uh eventual mate
+
+ align:start position:0%
+of you will meet your uh eventual mate
+ 
+
+ align:start position:0%
+of you will meet your uh eventual mate
+here not here like in 10 to 50 right now
+
+ align:start position:0%
+here not here like in 10 to 50 right now
+ 
+
+ align:start position:0%
+here not here like in 10 to 50 right now
+but but
+
+ align:start position:0%
+but but
+ 
+
+ align:start position:0%
+but but
+um during your undergraduate years
+
+ align:start position:0%
+um during your undergraduate years
+ 
+
+ align:start position:0%
+um during your undergraduate years
+um at uh at MIT and so you know somebody
+
+ align:start position:0%
+um at uh at MIT and so you know somebody
+ 
+
+ align:start position:0%
+um at uh at MIT and so you know somebody
+somebody in this room may be that person
+
+ align:start position:0%
+somebody in this room may be that person
+ 
+
+ align:start position:0%
+somebody in this room may be that person
+or something like that one of the
+
+ align:start position:0%
+or something like that one of the
+ 
+
+ align:start position:0%
+or something like that one of the
+reasons is it's a great deal easier to
+
+ align:start position:0%
+reasons is it's a great deal easier to
+ 
+
+ align:start position:0%
+reasons is it's a great deal easier to
+fall in love with somebody you actually
+
+ align:start position:0%
+fall in love with somebody you actually
+ 
+
+ align:start position:0%
+fall in love with somebody you actually
+interact with there are lovely people at
+
+ align:start position:0%
+interact with there are lovely people at
+ 
+
+ align:start position:0%
+interact with there are lovely people at
+Caltech I'm told
+
+ align:start position:0%
+Caltech I'm told
+ 
+
+ align:start position:0%
+Caltech I'm told
+um but mostly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+there are bitter jealous disappointed
+
+ align:start position:0%
+there are bitter jealous disappointed
+ 
+
+ align:start position:0%
+there are bitter jealous disappointed
+people at Caltech I'm told all of whom
+
+ align:start position:0%
+people at Caltech I'm told all of whom
+ 
+
+ align:start position:0%
+people at Caltech I'm told all of whom
+actually wanted to go to MIT
+
+ align:start position:0%
+actually wanted to go to MIT
+ 
+
+ align:start position:0%
+actually wanted to go to MIT
+um but anyway
+
+ align:start position:0%
+um but anyway
+ 
+
+ align:start position:0%
+um but anyway
+you see the point
+
+ align:start position:0%
+you see the point
+ 
+
+ align:start position:0%
+you see the point
+um the other so proximity helps now
+
+ align:start position:0%
+um the other so proximity helps now
+ 
+
+ align:start position:0%
+um the other so proximity helps now
+another another chemical aspect of of um
+
+ align:start position:0%
+another another chemical aspect of of um
+ 
+
+ align:start position:0%
+another another chemical aspect of of um
+the the this romantic love business
+
+ align:start position:0%
+the the this romantic love business
+ 
+
+ align:start position:0%
+the the this romantic love business
+um is that if you want a chemical
+
+ align:start position:0%
+um is that if you want a chemical
+ 
+
+ align:start position:0%
+um is that if you want a chemical
+reaction to speed up
+
+ align:start position:0%
+reaction to speed up
+ 
+
+ align:start position:0%
+reaction to speed up
+um one of the things that's useful to do
+
+ align:start position:0%
+um one of the things that's useful to do
+ 
+
+ align:start position:0%
+um one of the things that's useful to do
+is to add heat right
+
+ align:start position:0%
+is to add heat right
+ 
+
+ align:start position:0%
+is to add heat right
+um that that works that works too
+
+ align:start position:0%
+um that that works that works too
+ 
+
+ align:start position:0%
+um that that works that works too
+um and it works in um not not just like
+
+ align:start position:0%
+um and it works in um not not just like
+ 
+
+ align:start position:0%
+um and it works in um not not just like
+turning up the thermostat but
+
+ align:start position:0%
+turning up the thermostat but
+ 
+
+ align:start position:0%
+turning up the thermostat but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you are more likely
+
+ align:start position:0%
+you are more likely
+ 
+
+ align:start position:0%
+you are more likely
+to fall in love with somebody
+
+ align:start position:0%
+to fall in love with somebody
+ 
+
+ align:start position:0%
+to fall in love with somebody
+um uh if your arousal level is up that
+
+ align:start position:0%
+um uh if your arousal level is up that
+ 
+
+ align:start position:0%
+um uh if your arousal level is up that
+seems pretty obvious the non-obvious
+
+ align:start position:0%
+seems pretty obvious the non-obvious
+ 
+
+ align:start position:0%
+seems pretty obvious the non-obvious
+piece of it is that you're pretty stupid
+
+ align:start position:0%
+piece of it is that you're pretty stupid
+ 
+
+ align:start position:0%
+piece of it is that you're pretty stupid
+about this and you don't care too much
+
+ align:start position:0%
+about this and you don't care too much
+ 
+
+ align:start position:0%
+about this and you don't care too much
+where the arousal comes from the Romeo
+
+ align:start position:0%
+where the arousal comes from the Romeo
+ 
+
+ align:start position:0%
+where the arousal comes from the Romeo
+and Juliet thing is not a bad example
+
+ align:start position:0%
+and Juliet thing is not a bad example
+ 
+
+ align:start position:0%
+and Juliet thing is not a bad example
+uh Romeo is which family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Montague Montague that sounds right yeah
+
+ align:start position:0%
+Montague Montague that sounds right yeah
+ 
+
+ align:start position:0%
+Montague Montague that sounds right yeah
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+Romeo is at whose party
+
+ align:start position:0%
+Romeo is at whose party
+ 
+
+ align:start position:0%
+Romeo is at whose party
+do they want him at this party what are
+
+ align:start position:0%
+do they want him at this party what are
+ 
+
+ align:start position:0%
+do they want him at this party what are
+they going to do if they find him yeah
+
+ align:start position:0%
+they going to do if they find him yeah
+ 
+
+ align:start position:0%
+they going to do if they find him yeah
+so how does that make him feel
+
+ align:start position:0%
+so how does that make him feel
+ 
+
+ align:start position:0%
+so how does that make him feel
+his level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+his little heart is going Pitter Pat
+
+ align:start position:0%
+his little heart is going Pitter Pat
+ 
+
+ align:start position:0%
+his little heart is going Pitter Pat
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+there is some sense in which
+
+ align:start position:0%
+there is some sense in which
+ 
+
+ align:start position:0%
+there is some sense in which
+that contributes
+
+ align:start position:0%
+that contributes
+ 
+
+ align:start position:0%
+that contributes
+to uh that that modulates how attractive
+
+ align:start position:0%
+to uh that that modulates how attractive
+ 
+
+ align:start position:0%
+to uh that that modulates how attractive
+you think somebody else is
+
+ align:start position:0%
+you think somebody else is
+ 
+
+ align:start position:0%
+you think somebody else is
+um the the the example in the the
+
+ align:start position:0%
+um the the the example in the the
+ 
+
+ align:start position:0%
+um the the the example in the the
+clearest pop culture example of this is
+
+ align:start position:0%
+clearest pop culture example of this is
+ 
+
+ align:start position:0%
+clearest pop culture example of this is
+ask yourself about the standard
+
+ align:start position:0%
+ask yourself about the standard
+ 
+
+ align:start position:0%
+ask yourself about the standard
+Adventure movie Paradigm it's got a guy
+
+ align:start position:0%
+Adventure movie Paradigm it's got a guy
+ 
+
+ align:start position:0%
+Adventure movie Paradigm it's got a guy
+it's got a girl right do they like each
+
+ align:start position:0%
+it's got a girl right do they like each
+ 
+
+ align:start position:0%
+it's got a girl right do they like each
+other at the beginning of the movie no
+
+ align:start position:0%
+other at the beginning of the movie no
+ 
+
+ align:start position:0%
+other at the beginning of the movie no
+what do they do for the duration of the
+
+ align:start position:0%
+what do they do for the duration of the
+ 
+
+ align:start position:0%
+what do they do for the duration of the
+movie they find themselves in disastrous
+
+ align:start position:0%
+movie they find themselves in disastrous
+ 
+
+ align:start position:0%
+movie they find themselves in disastrous
+situations after after disaster
+
+ align:start position:0%
+situations after after disaster
+ 
+
+ align:start position:0%
+situations after after disaster
+situation what do they like each other
+
+ align:start position:0%
+situation what do they like each other
+ 
+
+ align:start position:0%
+situation what do they like each other
+during the no no they spend the whole
+
+ align:start position:0%
+during the no no they spend the whole
+ 
+
+ align:start position:0%
+during the no no they spend the whole
+movie sniping each other and and double
+
+ align:start position:0%
+movie sniping each other and and double
+ 
+
+ align:start position:0%
+movie sniping each other and and double
+crossing each other and stuff like that
+
+ align:start position:0%
+crossing each other and stuff like that
+ 
+
+ align:start position:0%
+crossing each other and stuff like that
+the end of the movie they're both
+
+ align:start position:0%
+the end of the movie they're both
+ 
+
+ align:start position:0%
+the end of the movie they're both
+hanging by one fingernail from the
+
+ align:start position:0%
+hanging by one fingernail from the
+ 
+
+ align:start position:0%
+hanging by one fingernail from the
+helicopter over the volcano or something
+
+ align:start position:0%
+helicopter over the volcano or something
+ 
+
+ align:start position:0%
+helicopter over the volcano or something
+like that and what do they realize
+
+ align:start position:0%
+like that and what do they realize
+ 
+
+ align:start position:0%
+like that and what do they realize
+you know this is great
+
+ align:start position:0%
+you know this is great
+ 
+
+ align:start position:0%
+you know this is great
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it sounds silly but the fact that we
+
+ align:start position:0%
+it sounds silly but the fact that we
+ 
+
+ align:start position:0%
+it sounds silly but the fact that we
+have been willing to tolerate that plot
+
+ align:start position:0%
+have been willing to tolerate that plot
+ 
+
+ align:start position:0%
+have been willing to tolerate that plot
+line forever suggests that there's
+
+ align:start position:0%
+line forever suggests that there's
+ 
+
+ align:start position:0%
+line forever suggests that there's
+there's something to it there is even
+
+ align:start position:0%
+there's something to it there is even
+ 
+
+ align:start position:0%
+there's something to it there is even
+exp okay I got enough time to tell you
+
+ align:start position:0%
+exp okay I got enough time to tell you
+ 
+
+ align:start position:0%
+exp okay I got enough time to tell you
+about what is arguably one of the great
+
+ align:start position:0%
+about what is arguably one of the great
+ 
+
+ align:start position:0%
+about what is arguably one of the great
+experiments in in in uh experimental
+
+ align:start position:0%
+experiments in in in uh experimental
+ 
+
+ align:start position:0%
+experiments in in in uh experimental
+psychology did I already tell you about
+
+ align:start position:0%
+psychology did I already tell you about
+ 
+
+ align:start position:0%
+psychology did I already tell you about
+the shaky Bridge experiment no good
+
+ align:start position:0%
+the shaky Bridge experiment no good
+ 
+
+ align:start position:0%
+the shaky Bridge experiment no good
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the uh it's this is an experiment so
+
+ align:start position:0%
+the uh it's this is an experiment so
+ 
+
+ align:start position:0%
+the uh it's this is an experiment so
+good that I did a pilgrimage to the
+
+ align:start position:0%
+good that I did a pilgrimage to the
+ 
+
+ align:start position:0%
+good that I did a pilgrimage to the
+place where it was done
+
+ align:start position:0%
+place where it was done
+ 
+
+ align:start position:0%
+place where it was done
+um which turns out to be in Vancouver
+
+ align:start position:0%
+um which turns out to be in Vancouver
+ 
+
+ align:start position:0%
+um which turns out to be in Vancouver
+Vancouver has
+
+ align:start position:0%
+Vancouver has
+ 
+
+ align:start position:0%
+Vancouver has
+um a a park with a deep gorge and and a
+
+ align:start position:0%
+um a a park with a deep gorge and and a
+ 
+
+ align:start position:0%
+um a a park with a deep gorge and and a
+Raiders of the Lost Ark style suspension
+
+ align:start position:0%
+Raiders of the Lost Ark style suspension
+ 
+
+ align:start position:0%
+Raiders of the Lost Ark style suspension
+bridge going across it or Shrek you know
+
+ align:start position:0%
+bridge going across it or Shrek you know
+ 
+
+ align:start position:0%
+bridge going across it or Shrek you know
+what not trees the donkey going across
+
+ align:start position:0%
+what not trees the donkey going across
+ 
+
+ align:start position:0%
+what not trees the donkey going across
+you know you know the bridge no
+
+ align:start position:0%
+you know you know the bridge no
+ 
+
+ align:start position:0%
+you know you know the bridge no
+volcanoes and Dragons or anything but
+
+ align:start position:0%
+volcanoes and Dragons or anything but
+ 
+
+ align:start position:0%
+volcanoes and Dragons or anything but
+it's a shaky Bridge here's what they did
+
+ align:start position:0%
+it's a shaky Bridge here's what they did
+ 
+
+ align:start position:0%
+it's a shaky Bridge here's what they did
+you're a guy for this experiment you're
+
+ align:start position:0%
+you're a guy for this experiment you're
+ 
+
+ align:start position:0%
+you're a guy for this experiment you're
+a guy and
+
+ align:start position:0%
+a guy and
+ 
+
+ align:start position:0%
+a guy and
+um you are walking across this shaky
+
+ align:start position:0%
+um you are walking across this shaky
+ 
+
+ align:start position:0%
+um you are walking across this shaky
+bridge and in the middle of the bridge
+
+ align:start position:0%
+bridge and in the middle of the bridge
+ 
+
+ align:start position:0%
+bridge and in the middle of the bridge
+you meet a woman
+
+ align:start position:0%
+you meet a woman
+ 
+
+ align:start position:0%
+you meet a woman
+um and she says I'm doing a study for
+
+ align:start position:0%
+um and she says I'm doing a study for
+ 
+
+ align:start position:0%
+um and she says I'm doing a study for
+psychology would you fill out my little
+
+ align:start position:0%
+psychology would you fill out my little
+ 
+
+ align:start position:0%
+psychology would you fill out my little
+questionnaire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you know as part of the process
+
+ align:start position:0%
+okay you know as part of the process
+ 
+
+ align:start position:0%
+okay you know as part of the process
+he's obvious if you want to know more
+
+ align:start position:0%
+he's obvious if you want to know more
+ 
+
+ align:start position:0%
+he's obvious if you want to know more
+about this experiment
+
+ align:start position:0%
+about this experiment
+ 
+
+ align:start position:0%
+about this experiment
+um once we've collected the data
+
+ align:start position:0%
+um once we've collected the data
+ 
+
+ align:start position:0%
+um once we've collected the data
+um you can phone me at this number at
+
+ align:start position:0%
+um you can phone me at this number at
+ 
+
+ align:start position:0%
+um you can phone me at this number at
+the lab my name is uh Sarah
+
+ align:start position:0%
+the lab my name is uh Sarah
+ 
+
+ align:start position:0%
+the lab my name is uh Sarah
+okay so that's group one group two turns
+
+ align:start position:0%
+okay so that's group one group two turns
+ 
+
+ align:start position:0%
+okay so that's group one group two turns
+out round the corner from this shaky
+
+ align:start position:0%
+out round the corner from this shaky
+ 
+
+ align:start position:0%
+out round the corner from this shaky
+Bridge there's another bridge over the
+
+ align:start position:0%
+Bridge there's another bridge over the
+ 
+
+ align:start position:0%
+Bridge there's another bridge over the
+same river it's a big concrete slab it
+
+ align:start position:0%
+same river it's a big concrete slab it
+ 
+
+ align:start position:0%
+same river it's a big concrete slab it
+don't shake at all
+
+ align:start position:0%
+don't shake at all
+ 
+
+ align:start position:0%
+don't shake at all
+you're a different white guy a d white
+
+ align:start position:0%
+you're a different white guy a d white
+ 
+
+ align:start position:0%
+you're a different white guy a d white
+guy I don't remember if you're a white
+
+ align:start position:0%
+guy I don't remember if you're a white
+ 
+
+ align:start position:0%
+guy I don't remember if you're a white
+guy you're a guy
+
+ align:start position:0%
+guy you're a guy
+ 
+
+ align:start position:0%
+guy you're a guy
+um you're walking across the bridge and
+
+ align:start position:0%
+um you're walking across the bridge and
+ 
+
+ align:start position:0%
+um you're walking across the bridge and
+and you meet uh a woman and same story
+
+ align:start position:0%
+and you meet uh a woman and same story
+ 
+
+ align:start position:0%
+and you meet uh a woman and same story
+um if you're interested in the results
+
+ align:start position:0%
+um if you're interested in the results
+ 
+
+ align:start position:0%
+um if you're interested in the results
+of this experiment
+
+ align:start position:0%
+of this experiment
+ 
+
+ align:start position:0%
+of this experiment
+um uh phone this number and ask for
+
+ align:start position:0%
+um uh phone this number and ask for
+ 
+
+ align:start position:0%
+um uh phone this number and ask for
+Rebecca needless to say Rebecca and
+
+ align:start position:0%
+Rebecca needless to say Rebecca and
+ 
+
+ align:start position:0%
+Rebecca needless to say Rebecca and
+Sarah are the same person the only thing
+
+ align:start position:0%
+Sarah are the same person the only thing
+ 
+
+ align:start position:0%
+Sarah are the same person the only thing
+that differs is whether you met her on a
+
+ align:start position:0%
+that differs is whether you met her on a
+ 
+
+ align:start position:0%
+that differs is whether you met her on a
+um the shaky Bridge or on the non-shaky
+
+ align:start position:0%
+um the shaky Bridge or on the non-shaky
+ 
+
+ align:start position:0%
+um the shaky Bridge or on the non-shaky
+bridge the data are who calls
+
+ align:start position:0%
+bridge the data are who calls
+ 
+
+ align:start position:0%
+bridge the data are who calls
+right so you call up the number
+
+ align:start position:0%
+right so you call up the number
+ 
+
+ align:start position:0%
+right so you call up the number
+some guy answers you know he says uh
+
+ align:start position:0%
+some guy answers you know he says uh
+ 
+
+ align:start position:0%
+some guy answers you know he says uh
+Rebecca there and uh he says no no I'll
+
+ align:start position:0%
+Rebecca there and uh he says no no I'll
+ 
+
+ align:start position:0%
+Rebecca there and uh he says no no I'll
+take a message and hangs up the phone
+
+ align:start position:0%
+take a message and hangs up the phone
+ 
+
+ align:start position:0%
+take a message and hangs up the phone
+another one for Rebecca
+
+ align:start position:0%
+another one for Rebecca
+ 
+
+ align:start position:0%
+another one for Rebecca
+um it turns out that more guys who met
+
+ align:start position:0%
+um it turns out that more guys who met
+ 
+
+ align:start position:0%
+um it turns out that more guys who met
+Sarah on the shaky Bridge thrown in then
+
+ align:start position:0%
+Sarah on the shaky Bridge thrown in then
+ 
+
+ align:start position:0%
+Sarah on the shaky Bridge thrown in then
+who met Rebecca on the solid Bridge
+
+ align:start position:0%
+who met Rebecca on the solid Bridge
+ 
+
+ align:start position:0%
+who met Rebecca on the solid Bridge
+why is that the argument the the this
+
+ align:start position:0%
+why is that the argument the the this
+ 
+
+ align:start position:0%
+why is that the argument the the this
+this arousal heat argument is it's known
+
+ align:start position:0%
+this arousal heat argument is it's known
+ 
+
+ align:start position:0%
+this arousal heat argument is it's known
+in the trade as misattribution of
+
+ align:start position:0%
+in the trade as misattribution of
+ 
+
+ align:start position:0%
+in the trade as misattribution of
+arousal you walk across the bridge you
+
+ align:start position:0%
+arousal you walk across the bridge you
+ 
+
+ align:start position:0%
+arousal you walk across the bridge you
+meet a woman person
+
+ align:start position:0%
+meet a woman person
+ 
+
+ align:start position:0%
+meet a woman person
+um you ask yourself
+
+ align:start position:0%
+um you ask yourself
+ 
+
+ align:start position:0%
+um you ask yourself
+how do I feel my heart is beating
+
+ align:start position:0%
+how do I feel my heart is beating
+ 
+
+ align:start position:0%
+how do I feel my heart is beating
+my palms are sweaty
+
+ align:start position:0%
+my palms are sweaty
+ 
+
+ align:start position:0%
+my palms are sweaty
+it must be love
+
+ align:start position:0%
+it must be love
+ 
+
+ align:start position:0%
+it must be love
+um and it's enough of an effect to
+
+ align:start position:0%
+um and it's enough of an effect to
+ 
+
+ align:start position:0%
+um and it's enough of an effect to
+change whether or not you'll phone up to
+
+ align:start position:0%
+change whether or not you'll phone up to
+ 
+
+ align:start position:0%
+change whether or not you'll phone up to
+get the results of the uh um to get the
+
+ align:start position:0%
+get the results of the uh um to get the
+ 
+
+ align:start position:0%
+get the results of the uh um to get the
+results of the experiment look you
+
+ align:start position:0%
+results of the experiment look you
+ 
+
+ align:start position:0%
+results of the experiment look you
+shouldn't over stress the result
+
+ align:start position:0%
+shouldn't over stress the result
+ 
+
+ align:start position:0%
+shouldn't over stress the result
+um nobody's done this particular
+
+ align:start position:0%
+um nobody's done this particular
+ 
+
+ align:start position:0%
+um nobody's done this particular
+experiment but if you meet a chicken in
+
+ align:start position:0%
+experiment but if you meet a chicken in
+ 
+
+ align:start position:0%
+experiment but if you meet a chicken in
+the middle of the bridge you don't say
+
+ align:start position:0%
+the middle of the bridge you don't say
+ 
+
+ align:start position:0%
+the middle of the bridge you don't say
+my heart is beating my palms are sweaty
+
+ align:start position:0%
+my heart is beating my palms are sweaty
+ 
+
+ align:start position:0%
+my heart is beating my palms are sweaty
+I love the chicken it it but it does
+
+ align:start position:0%
+I love the chicken it it but it does
+ 
+
+ align:start position:0%
+I love the chicken it it but it does
+modulate things now
\ No newline at end of file
diff --git a/M2d4HsBsu8Y.txt b/M2d4HsBsu8Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9c9cef3e8cdccc3f2839fe2f9af43233fe974870
--- /dev/null
+++ b/M2d4HsBsu8Y.txt
@@ -0,0 +1,13507 @@
+align:start position:0%
+ 
+last time so we're talking about a set
+
+ align:start position:0%
+last time so we're talking about a set
+ 
+
+ align:start position:0%
+last time so we're talking about a set
+of real numbers and last time i stated
+
+ align:start position:0%
+of real numbers and last time i stated
+ 
+
+ align:start position:0%
+of real numbers and last time i stated
+the following theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the existence and
+
+ align:start position:0%
+about the existence and
+ 
+
+ align:start position:0%
+about the existence and
+properties of r that make it special
+
+ align:start position:0%
+properties of r that make it special
+ 
+
+ align:start position:0%
+properties of r that make it special
+so the theorem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a unique ordered field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the least upper bound property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing the rational numbers so
+
+ align:start position:0%
+containing the rational numbers so
+ 
+
+ align:start position:0%
+containing the rational numbers so
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+a field was
+
+ align:start position:0%
+a field was
+ 
+
+ align:start position:0%
+a field was
+a set that had
+
+ align:start position:0%
+a set that had
+ 
+
+ align:start position:0%
+a set that had
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+operations plus and multiplication
+
+ align:start position:0%
+operations plus and multiplication
+ 
+
+ align:start position:0%
+operations plus and multiplication
+an ordered field
+
+ align:start position:0%
+an ordered field
+ 
+
+ align:start position:0%
+an ordered field
+also this set has an order on it
+
+ align:start position:0%
+also this set has an order on it
+ 
+
+ align:start position:0%
+also this set has an order on it
+and this order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interacts with
+
+ align:start position:0%
+interacts with
+ 
+
+ align:start position:0%
+interacts with
+the operations of addition and
+
+ align:start position:0%
+the operations of addition and
+ 
+
+ align:start position:0%
+the operations of addition and
+multiplication in natural ways and the
+
+ align:start position:0%
+multiplication in natural ways and the
+ 
+
+ align:start position:0%
+multiplication in natural ways and the
+least upper bound property means
+
+ align:start position:0%
+least upper bound property means
+ 
+
+ align:start position:0%
+least upper bound property means
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+non-empty subset which is bounded above
+
+ align:start position:0%
+non-empty subset which is bounded above
+ 
+
+ align:start position:0%
+non-empty subset which is bounded above
+has a supremum in
+
+ align:start position:0%
+has a supremum in
+ 
+
+ align:start position:0%
+has a supremum in
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in the set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the least upper bound property
+
+ align:start position:0%
+so the least upper bound property
+ 
+
+ align:start position:0%
+so the least upper bound property
+meaning the supremum belongs in r not
+
+ align:start position:0%
+meaning the supremum belongs in r not
+ 
+
+ align:start position:0%
+meaning the supremum belongs in r not
+necessarily in the non-empty set which
+
+ align:start position:0%
+necessarily in the non-empty set which
+ 
+
+ align:start position:0%
+necessarily in the non-empty set which
+is bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we saw last time that q the rational
+
+ align:start position:0%
+and we saw last time that q the rational
+ 
+
+ align:start position:0%
+and we saw last time that q the rational
+numbers does not have this property but
+
+ align:start position:0%
+numbers does not have this property but
+ 
+
+ align:start position:0%
+numbers does not have this property but
+looking at that set uh q positive
+
+ align:start position:0%
+looking at that set uh q positive
+ 
+
+ align:start position:0%
+looking at that set uh q positive
+rational q squared less than two
+
+ align:start position:0%
+rational q squared less than two
+ 
+
+ align:start position:0%
+rational q squared less than two
+that set was bounded above but didn't
+
+ align:start position:0%
+that set was bounded above but didn't
+ 
+
+ align:start position:0%
+that set was bounded above but didn't
+have a supremum in irrational numbers
+
+ align:start position:0%
+have a supremum in irrational numbers
+ 
+
+ align:start position:0%
+have a supremum in irrational numbers
+because the square root of 2
+
+ align:start position:0%
+because the square root of 2
+ 
+
+ align:start position:0%
+because the square root of 2
+essentially is not a rational number
+
+ align:start position:0%
+essentially is not a rational number
+ 
+
+ align:start position:0%
+essentially is not a rational number
+and the square root of 2 would be the
+
+ align:start position:0%
+and the square root of 2 would be the
+ 
+
+ align:start position:0%
+and the square root of 2 would be the
+supreme
+
+ align:start position:0%
+supreme
+ 
+
+ align:start position:0%
+supreme
+okay so just based on this theorem which
+
+ align:start position:0%
+okay so just based on this theorem which
+ 
+
+ align:start position:0%
+okay so just based on this theorem which
+characterizes
+
+ align:start position:0%
+characterizes
+ 
+
+ align:start position:0%
+characterizes
+and constructs r the set of real numbers
+
+ align:start position:0%
+and constructs r the set of real numbers
+ 
+
+ align:start position:0%
+and constructs r the set of real numbers
+we're now going to prove
+
+ align:start position:0%
+we're now going to prove
+ 
+
+ align:start position:0%
+we're now going to prove
+facts about real numbers
+
+ align:start position:0%
+facts about real numbers
+ 
+
+ align:start position:0%
+facts about real numbers
+and soon turn to limits
+
+ align:start position:0%
+and soon turn to limits
+ 
+
+ align:start position:0%
+and soon turn to limits
+so as i said in the beginning limits is
+
+ align:start position:0%
+so as i said in the beginning limits is
+ 
+
+ align:start position:0%
+so as i said in the beginning limits is
+are are the central object of study
+
+ align:start position:0%
+are are the central object of study
+ 
+
+ align:start position:0%
+are are the central object of study
+in analysis that's what analysis is the
+
+ align:start position:0%
+in analysis that's what analysis is the
+ 
+
+ align:start position:0%
+in analysis that's what analysis is the
+study of limits the real
+
+ align:start position:0%
+study of limits the real
+ 
+
+ align:start position:0%
+study of limits the real
+analysis part or the real and that is
+
+ align:start position:0%
+analysis part or the real and that is
+ 
+
+ align:start position:0%
+analysis part or the real and that is
+that we're doing this within the setting
+
+ align:start position:0%
+that we're doing this within the setting
+ 
+
+ align:start position:0%
+that we're doing this within the setting
+of the real numbers
+
+ align:start position:0%
+of the real numbers
+ 
+
+ align:start position:0%
+of the real numbers
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now let me just point out something kind
+
+ align:start position:0%
+now let me just point out something kind
+ 
+
+ align:start position:0%
+now let me just point out something kind
+of simple about the real numbers
+
+ align:start position:0%
+of simple about the real numbers
+ 
+
+ align:start position:0%
+of simple about the real numbers
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean extremely simple fact about the
+
+ align:start position:0%
+i mean extremely simple fact about the
+ 
+
+ align:start position:0%
+i mean extremely simple fact about the
+real numbers is
+
+ align:start position:0%
+real numbers is
+ 
+
+ align:start position:0%
+real numbers is
+it's not discrete like the integers are
+
+ align:start position:0%
+it's not discrete like the integers are
+ 
+
+ align:start position:0%
+it's not discrete like the integers are
+so for the integers if i take one
+
+ align:start position:0%
+so for the integers if i take one
+ 
+
+ align:start position:0%
+so for the integers if i take one
+integer and another it's not necessarily
+
+ align:start position:0%
+integer and another it's not necessarily
+ 
+
+ align:start position:0%
+integer and another it's not necessarily
+the case that there's an integer
+
+ align:start position:0%
+the case that there's an integer
+ 
+
+ align:start position:0%
+the case that there's an integer
+strictly in between them there's not an
+
+ align:start position:0%
+strictly in between them there's not an
+ 
+
+ align:start position:0%
+strictly in between them there's not an
+integer between 0 and 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but r does satisfy this property
+
+ align:start position:0%
+but r does satisfy this property
+ 
+
+ align:start position:0%
+but r does satisfy this property
+essentially because
+
+ align:start position:0%
+essentially because
+ 
+
+ align:start position:0%
+essentially because
+it's a field so
+
+ align:start position:0%
+it's a field so
+ 
+
+ align:start position:0%
+it's a field so
+and it's an ordered field so
+
+ align:start position:0%
+and it's an ordered field so
+ 
+
+ align:start position:0%
+and it's an ordered field so
+what's the simple fact
+
+ align:start position:0%
+what's the simple fact
+ 
+
+ align:start position:0%
+what's the simple fact
+if x
+
+ align:start position:0%
+if x
+ 
+
+ align:start position:0%
+if x
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+are real numbers
+
+ align:start position:0%
+are real numbers
+ 
+
+ align:start position:0%
+are real numbers
+and x is less than y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists a real number r little
+
+ align:start position:0%
+then there exists a real number r little
+ 
+
+ align:start position:0%
+then there exists a real number r little
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is less than r
+
+ align:start position:0%
+x is less than r
+ 
+
+ align:start position:0%
+x is less than r
+is less than y
+
+ align:start position:0%
+is less than y
+ 
+
+ align:start position:0%
+is less than y
+and i can give you r explicitly r is
+
+ align:start position:0%
+and i can give you r explicitly r is
+ 
+
+ align:start position:0%
+and i can give you r explicitly r is
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus y over 2.
+
+ align:start position:0%
+x plus y over 2.
+ 
+
+ align:start position:0%
+x plus y over 2.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right that's not so surprising
+
+ align:start position:0%
+all right that's not so surprising
+ 
+
+ align:start position:0%
+all right that's not so surprising
+now this
+
+ align:start position:0%
+now this
+ 
+
+ align:start position:0%
+now this
+statement here is also true if i replace
+
+ align:start position:0%
+statement here is also true if i replace
+ 
+
+ align:start position:0%
+statement here is also true if i replace
+r with rational numbers namely if
+
+ align:start position:0%
+r with rational numbers namely if
+ 
+
+ align:start position:0%
+r with rational numbers namely if
+i have two rational numbers one less
+
+ align:start position:0%
+i have two rational numbers one less
+ 
+
+ align:start position:0%
+i have two rational numbers one less
+than the other then there's just a
+
+ align:start position:0%
+than the other then there's just a
+ 
+
+ align:start position:0%
+than the other then there's just a
+rational number in between
+
+ align:start position:0%
+rational number in between
+ 
+
+ align:start position:0%
+rational number in between
+uh that's between x and y right i just
+
+ align:start position:0%
+uh that's between x and y right i just
+ 
+
+ align:start position:0%
+uh that's between x and y right i just
+again define r in this way now a natural
+
+ align:start position:0%
+again define r in this way now a natural
+ 
+
+ align:start position:0%
+again define r in this way now a natural
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the following
+
+ align:start position:0%
+is the following
+ 
+
+ align:start position:0%
+is the following
+is that if x and y
+
+ align:start position:0%
+is that if x and y
+ 
+
+ align:start position:0%
+is that if x and y
+are in r
+
+ align:start position:0%
+are in r
+ 
+
+ align:start position:0%
+are in r
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x is less than y
+
+ align:start position:0%
+x is less than y
+ 
+
+ align:start position:0%
+x is less than y
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+does there i'll put a question mark over
+
+ align:start position:0%
+does there i'll put a question mark over
+ 
+
+ align:start position:0%
+does there i'll put a question mark over
+that does there exist
+
+ align:start position:0%
+that does there exist
+ 
+
+ align:start position:0%
+that does there exist
+an r and q
+
+ align:start position:0%
+an r and q
+ 
+
+ align:start position:0%
+an r and q
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+x is less than r is less than y
+
+ align:start position:0%
+x is less than r is less than y
+ 
+
+ align:start position:0%
+x is less than r is less than y
+okay i can't necessarily define r by
+
+ align:start position:0%
+okay i can't necessarily define r by
+ 
+
+ align:start position:0%
+okay i can't necessarily define r by
+this formula here and guarantee that
+
+ align:start position:0%
+this formula here and guarantee that
+ 
+
+ align:start position:0%
+this formula here and guarantee that
+r will
+
+ align:start position:0%
+r will
+ 
+
+ align:start position:0%
+r will
+be rational so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x equals root 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+say y equals 2 root 2
+
+ align:start position:0%
+say y equals 2 root 2
+ 
+
+ align:start position:0%
+say y equals 2 root 2
+then x plus y over 2
+
+ align:start position:0%
+then x plus y over 2
+ 
+
+ align:start position:0%
+then x plus y over 2
+equals 3 halves
+
+ align:start position:0%
+equals 3 halves
+ 
+
+ align:start position:0%
+equals 3 halves
+root 2
+
+ align:start position:0%
+root 2
+ 
+
+ align:start position:0%
+root 2
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+not a rational number because if it were
+
+ align:start position:0%
+not a rational number because if it were
+ 
+
+ align:start position:0%
+not a rational number because if it were
+a rational number then i could multiply
+
+ align:start position:0%
+a rational number then i could multiply
+ 
+
+ align:start position:0%
+a rational number then i could multiply
+2 through by 2 3 and say square root of
+
+ align:start position:0%
+2 through by 2 3 and say square root of
+ 
+
+ align:start position:0%
+2 through by 2 3 and say square root of
+2 is a rational number so
+
+ align:start position:0%
+2 is a rational number so
+ 
+
+ align:start position:0%
+2 is a rational number so
+all of that to say
+
+ align:start position:0%
+all of that to say
+ 
+
+ align:start position:0%
+all of that to say
+that simply by doing this trick of just
+
+ align:start position:0%
+that simply by doing this trick of just
+ 
+
+ align:start position:0%
+that simply by doing this trick of just
+taking the average does not necessarily
+
+ align:start position:0%
+taking the average does not necessarily
+ 
+
+ align:start position:0%
+taking the average does not necessarily
+mean that if i take two real numbers one
+
+ align:start position:0%
+mean that if i take two real numbers one
+ 
+
+ align:start position:0%
+mean that if i take two real numbers one
+less than the other then there exists a
+
+ align:start position:0%
+less than the other then there exists a
+ 
+
+ align:start position:0%
+less than the other then there exists a
+rational in between them
+
+ align:start position:0%
+rational in between them
+ 
+
+ align:start position:0%
+rational in between them
+um that's not so clear to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is one of the most
+
+ align:start position:0%
+but this is one of the most
+ 
+
+ align:start position:0%
+but this is one of the most
+this is one of the basic facts about r
+
+ align:start position:0%
+this is one of the basic facts about r
+ 
+
+ align:start position:0%
+this is one of the basic facts about r
+is that the answer to this question is
+
+ align:start position:0%
+is that the answer to this question is
+ 
+
+ align:start position:0%
+is that the answer to this question is
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+and that the in some sense the rational
+
+ align:start position:0%
+and that the in some sense the rational
+ 
+
+ align:start position:0%
+and that the in some sense the rational
+numbers are
+
+ align:start position:0%
+numbers are
+ 
+
+ align:start position:0%
+numbers are
+dense in the real numbers for any two
+
+ align:start position:0%
+dense in the real numbers for any two
+ 
+
+ align:start position:0%
+dense in the real numbers for any two
+real numbers i can find a rational in
+
+ align:start position:0%
+real numbers i can find a rational in
+ 
+
+ align:start position:0%
+real numbers i can find a rational in
+between them okay
+
+ align:start position:0%
+between them okay
+ 
+
+ align:start position:0%
+between them okay
+it's uh the first
+
+ align:start position:0%
+it's uh the first
+ 
+
+ align:start position:0%
+it's uh the first
+main property of the rational of the
+
+ align:start position:0%
+main property of the rational of the
+ 
+
+ align:start position:0%
+main property of the rational of the
+real numbers will prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it'll be a consequence of
+
+ align:start position:0%
+and it'll be a consequence of
+ 
+
+ align:start position:0%
+and it'll be a consequence of
+a second property we'll prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is called the archamidian property
+
+ align:start position:0%
+which is called the archamidian property
+ 
+
+ align:start position:0%
+which is called the archamidian property
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+theorems has two parts this first is
+
+ align:start position:0%
+theorems has two parts this first is
+ 
+
+ align:start position:0%
+theorems has two parts this first is
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+archimedean property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of r
+
+ align:start position:0%
+of r
+ 
+
+ align:start position:0%
+of r
+and the statement of this is
+
+ align:start position:0%
+and the statement of this is
+ 
+
+ align:start position:0%
+and the statement of this is
+if x and y
+
+ align:start position:0%
+if x and y
+ 
+
+ align:start position:0%
+if x and y
+are in r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+then there exists
+ 
+
+ align:start position:0%
+then there exists
+a natural number n
+
+ align:start position:0%
+a natural number n
+ 
+
+ align:start position:0%
+a natural number n
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+n x
+
+ align:start position:0%
+n x
+ 
+
+ align:start position:0%
+n x
+is bigger than y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then the second part of this
+
+ align:start position:0%
+okay and then the second part of this
+ 
+
+ align:start position:0%
+okay and then the second part of this
+theorem is the statement that
+
+ align:start position:0%
+theorem is the statement that
+ 
+
+ align:start position:0%
+theorem is the statement that
+the rationals are dense that the answer
+
+ align:start position:0%
+the rationals are dense that the answer
+ 
+
+ align:start position:0%
+the rationals are dense that the answer
+to this question is yes
+
+ align:start position:0%
+to this question is yes
+ 
+
+ align:start position:0%
+to this question is yes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this usually goes by the name of the
+
+ align:start position:0%
+this usually goes by the name of the
+ 
+
+ align:start position:0%
+this usually goes by the name of the
+density of the rationals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it states that if
+
+ align:start position:0%
+so it states that if
+ 
+
+ align:start position:0%
+so it states that if
+x and y are in r
+
+ align:start position:0%
+x and y are in r
+ 
+
+ align:start position:0%
+x and y are in r
+and x is less than y
+
+ align:start position:0%
+and x is less than y
+ 
+
+ align:start position:0%
+and x is less than y
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+rational number little r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that x is less than r is less than
+
+ align:start position:0%
+such that x is less than r is less than
+ 
+
+ align:start position:0%
+such that x is less than r is less than
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's prove the first theorem
+
+ align:start position:0%
+so let's prove the first theorem
+ 
+
+ align:start position:0%
+so let's prove the first theorem
+the first part of this theorem the
+
+ align:start position:0%
+the first part of this theorem the
+ 
+
+ align:start position:0%
+the first part of this theorem the
+archimedean property
+
+ align:start position:0%
+archimedean property
+ 
+
+ align:start position:0%
+archimedean property
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what do we have to use
+
+ align:start position:0%
+what do we have to use
+ 
+
+ align:start position:0%
+what do we have to use
+to prove this theorem
+
+ align:start position:0%
+to prove this theorem
+ 
+
+ align:start position:0%
+to prove this theorem
+just what we know about the real numbers
+
+ align:start position:0%
+just what we know about the real numbers
+ 
+
+ align:start position:0%
+just what we know about the real numbers
+the fact that it's an ordered field with
+
+ align:start position:0%
+the fact that it's an ordered field with
+ 
+
+ align:start position:0%
+the fact that it's an ordered field with
+the least upper bound property you'll
+
+ align:start position:0%
+the least upper bound property you'll
+ 
+
+ align:start position:0%
+the least upper bound property you'll
+see how this least upper bound property
+
+ align:start position:0%
+see how this least upper bound property
+ 
+
+ align:start position:0%
+see how this least upper bound property
+plays a major role in
+
+ align:start position:0%
+plays a major role in
+ 
+
+ align:start position:0%
+plays a major role in
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+all of these elementary things we prove
+
+ align:start position:0%
+all of these elementary things we prove
+ 
+
+ align:start position:0%
+all of these elementary things we prove
+about r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+restate our hypothesis so suppose x and
+
+ align:start position:0%
+restate our hypothesis so suppose x and
+ 
+
+ align:start position:0%
+restate our hypothesis so suppose x and
+y are in
+
+ align:start position:0%
+y are in
+ 
+
+ align:start position:0%
+y are in
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x is less than
+
+ align:start position:0%
+and x is less than
+ 
+
+ align:start position:0%
+and x is less than
+x is bigger than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we wish to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just restating this inequality here
+
+ align:start position:0%
+so just restating this inequality here
+ 
+
+ align:start position:0%
+so just restating this inequality here
+we wish to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show the word show you you should read
+
+ align:start position:0%
+show the word show you you should read
+ 
+
+ align:start position:0%
+show the word show you you should read
+as synonymous with proof
+
+ align:start position:0%
+as synonymous with proof
+ 
+
+ align:start position:0%
+as synonymous with proof
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+there exists a natural number n
+
+ align:start position:0%
+there exists a natural number n
+ 
+
+ align:start position:0%
+there exists a natural number n
+such that n is bigger than
+
+ align:start position:0%
+such that n is bigger than
+ 
+
+ align:start position:0%
+such that n is bigger than
+y over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's just restating that so we're
+
+ align:start position:0%
+okay that's just restating that so we're
+ 
+
+ align:start position:0%
+okay that's just restating that so we're
+going to prove this by contradiction um
+
+ align:start position:0%
+going to prove this by contradiction um
+ 
+
+ align:start position:0%
+going to prove this by contradiction um
+so the proof will go by
+
+ align:start position:0%
+so the proof will go by
+ 
+
+ align:start position:0%
+so the proof will go by
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is again this is our hypothesis
+
+ align:start position:0%
+this is again this is our hypothesis
+ 
+
+ align:start position:0%
+this is again this is our hypothesis
+which we will assume throughout the
+
+ align:start position:0%
+which we will assume throughout the
+ 
+
+ align:start position:0%
+which we will assume throughout the
+proof the thing we're trying to prove is
+
+ align:start position:0%
+proof the thing we're trying to prove is
+ 
+
+ align:start position:0%
+proof the thing we're trying to prove is
+this statement here the second sentence
+
+ align:start position:0%
+this statement here the second sentence
+ 
+
+ align:start position:0%
+this statement here the second sentence
+so this is the thing that we will
+
+ align:start position:0%
+so this is the thing that we will
+ 
+
+ align:start position:0%
+so this is the thing that we will
+negate we will not negate uh the
+
+ align:start position:0%
+negate we will not negate uh the
+ 
+
+ align:start position:0%
+negate we will not negate uh the
+hypothesis we're negating what we want
+
+ align:start position:0%
+hypothesis we're negating what we want
+ 
+
+ align:start position:0%
+hypothesis we're negating what we want
+to prove in the end and then uh arriving
+
+ align:start position:0%
+to prove in the end and then uh arriving
+ 
+
+ align:start position:0%
+to prove in the end and then uh arriving
+at a false statement therefore showing
+
+ align:start position:0%
+at a false statement therefore showing
+ 
+
+ align:start position:0%
+at a false statement therefore showing
+um our conclusion
+
+ align:start position:0%
+um our conclusion
+ 
+
+ align:start position:0%
+um our conclusion
+is true so
+
+ align:start position:0%
+is true so
+ 
+
+ align:start position:0%
+is true so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so we assume that the second
+
+ align:start position:0%
+okay so we assume that the second
+ 
+
+ align:start position:0%
+okay so we assume that the second
+statement is false
+
+ align:start position:0%
+statement is false
+ 
+
+ align:start position:0%
+statement is false
+again we're assuming the first statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose not ie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're all in a natural number
+
+ align:start position:0%
+we're all in a natural number
+ 
+
+ align:start position:0%
+we're all in a natural number
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and is less than or equal to
+
+ align:start position:0%
+and is less than or equal to
+ 
+
+ align:start position:0%
+and is less than or equal to
+y over x right that's the negation of
+
+ align:start position:0%
+y over x right that's the negation of
+ 
+
+ align:start position:0%
+y over x right that's the negation of
+uh the f of there exists a integer
+
+ align:start position:0%
+uh the f of there exists a integer
+ 
+
+ align:start position:0%
+uh the f of there exists a integer
+that's bigger than y over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the natural numbers as a subset
+
+ align:start position:0%
+then the natural numbers as a subset
+ 
+
+ align:start position:0%
+then the natural numbers as a subset
+of the real numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the set of natural numbers is a
+
+ align:start position:0%
+the set of natural numbers is a
+ 
+
+ align:start position:0%
+the set of natural numbers is a
+non-empty subset of r which is bounded
+
+ align:start position:0%
+non-empty subset of r which is bounded
+ 
+
+ align:start position:0%
+non-empty subset of r which is bounded
+above therefore it has a supremum
+
+ align:start position:0%
+above therefore it has a supremum
+ 
+
+ align:start position:0%
+above therefore it has a supremum
+so by
+
+ align:start position:0%
+so by
+ 
+
+ align:start position:0%
+so by
+the least upper bound property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and has
+
+ align:start position:0%
+and has
+ 
+
+ align:start position:0%
+and has
+a supremum
+
+ align:start position:0%
+a supremum
+ 
+
+ align:start position:0%
+a supremum
+call it a
+
+ align:start position:0%
+call it a
+ 
+
+ align:start position:0%
+call it a
+in r
+
+ align:start position:0%
+in r
+ 
+
+ align:start position:0%
+in r
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since a
+
+ align:start position:0%
+since a
+ 
+
+ align:start position:0%
+since a
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the supremum of n
+
+ align:start position:0%
+the supremum of n
+ 
+
+ align:start position:0%
+the supremum of n
+anything smaller than a cannot be an
+
+ align:start position:0%
+anything smaller than a cannot be an
+ 
+
+ align:start position:0%
+anything smaller than a cannot be an
+upper bound for the natural numbers okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because remember a is supposed to be the
+
+ align:start position:0%
+because remember a is supposed to be the
+ 
+
+ align:start position:0%
+because remember a is supposed to be the
+least upper bound anything smaller than
+
+ align:start position:0%
+least upper bound anything smaller than
+ 
+
+ align:start position:0%
+least upper bound anything smaller than
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+cannot be an upper bound for the natural
+
+ align:start position:0%
+cannot be an upper bound for the natural
+ 
+
+ align:start position:0%
+cannot be an upper bound for the natural
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+is not
+
+ align:start position:0%
+is not
+ 
+
+ align:start position:0%
+is not
+an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upper bound
+
+ align:start position:0%
+upper bound
+ 
+
+ align:start position:0%
+upper bound
+for n
+
+ align:start position:0%
+for n
+ 
+
+ align:start position:0%
+for n
+but what does that mean
+
+ align:start position:0%
+but what does that mean
+ 
+
+ align:start position:0%
+but what does that mean
+so if a minus 1 is not an upper bound
+
+ align:start position:0%
+so if a minus 1 is not an upper bound
+ 
+
+ align:start position:0%
+so if a minus 1 is not an upper bound
+for n that means there must exist some
+
+ align:start position:0%
+for n that means there must exist some
+ 
+
+ align:start position:0%
+for n that means there must exist some
+integer in n which is strictly bigger
+
+ align:start position:0%
+integer in n which is strictly bigger
+ 
+
+ align:start position:0%
+integer in n which is strictly bigger
+than a minus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a natural number i'll call
+
+ align:start position:0%
+there exists a natural number i'll call
+ 
+
+ align:start position:0%
+there exists a natural number i'll call
+it m
+
+ align:start position:0%
+it m
+ 
+
+ align:start position:0%
+it m
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+a minus 1
+
+ align:start position:0%
+a minus 1
+ 
+
+ align:start position:0%
+a minus 1
+is less than m
+
+ align:start position:0%
+is less than m
+ 
+
+ align:start position:0%
+is less than m
+but then this implies
+
+ align:start position:0%
+but then this implies
+ 
+
+ align:start position:0%
+but then this implies
+that a
+
+ align:start position:0%
+that a
+ 
+
+ align:start position:0%
+that a
+is less than m plus 1
+
+ align:start position:0%
+is less than m plus 1
+ 
+
+ align:start position:0%
+is less than m plus 1
+which implies that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not an upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the natural numbers because n plus 1
+
+ align:start position:0%
+for the natural numbers because n plus 1
+ 
+
+ align:start position:0%
+for the natural numbers because n plus 1
+m's an integer a natural number so n
+
+ align:start position:0%
+m's an integer a natural number so n
+ 
+
+ align:start position:0%
+m's an integer a natural number so n
+plus 1 is a natural number and i've just
+
+ align:start position:0%
+plus 1 is a natural number and i've just
+ 
+
+ align:start position:0%
+plus 1 is a natural number and i've just
+found a natural number bigger than a
+
+ align:start position:0%
+found a natural number bigger than a
+ 
+
+ align:start position:0%
+found a natural number bigger than a
+that means a can't be an upper bound for
+
+ align:start position:0%
+that means a can't be an upper bound for
+ 
+
+ align:start position:0%
+that means a can't be an upper bound for
+the natural numbers but
+
+ align:start position:0%
+the natural numbers but
+ 
+
+ align:start position:0%
+the natural numbers but
+and therefore a does not equal
+
+ align:start position:0%
+and therefore a does not equal
+ 
+
+ align:start position:0%
+and therefore a does not equal
+the soup of n and this is
+
+ align:start position:0%
+the soup of n and this is
+ 
+
+ align:start position:0%
+the soup of n and this is
+a contradiction because we
+
+ align:start position:0%
+a contradiction because we
+ 
+
+ align:start position:0%
+a contradiction because we
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because a is defined as a soup of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from the assumption just to recap
+
+ align:start position:0%
+so from the assumption just to recap
+ 
+
+ align:start position:0%
+so from the assumption just to recap
+just from the assumption that
+
+ align:start position:0%
+just from the assumption that
+ 
+
+ align:start position:0%
+just from the assumption that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for all natural numbers n n is less than
+
+ align:start position:0%
+for all natural numbers n n is less than
+ 
+
+ align:start position:0%
+for all natural numbers n n is less than
+or equal to y over x
+
+ align:start position:0%
+or equal to y over x
+ 
+
+ align:start position:0%
+or equal to y over x
+uh we concluded that it has a supremum
+
+ align:start position:0%
+uh we concluded that it has a supremum
+ 
+
+ align:start position:0%
+uh we concluded that it has a supremum
+that's not its suprema okay so that's a
+
+ align:start position:0%
+that's not its suprema okay so that's a
+ 
+
+ align:start position:0%
+that's not its suprema okay so that's a
+false statement and therefore our
+
+ align:start position:0%
+false statement and therefore our
+ 
+
+ align:start position:0%
+false statement and therefore our
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+assumption
+
+ align:start position:0%
+assumption
+ 
+
+ align:start position:0%
+assumption
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+for all natural numbers in
+
+ align:start position:0%
+for all natural numbers in
+ 
+
+ align:start position:0%
+for all natural numbers in
+n is less than or equal to y over x that
+
+ align:start position:0%
+n is less than or equal to y over x that
+ 
+
+ align:start position:0%
+n is less than or equal to y over x that
+must be false and therefore there exists
+
+ align:start position:0%
+must be false and therefore there exists
+ 
+
+ align:start position:0%
+must be false and therefore there exists
+an n
+
+ align:start position:0%
+an n
+ 
+
+ align:start position:0%
+an n
+which is bigger than y over x
+
+ align:start position:0%
+which is bigger than y over x
+ 
+
+ align:start position:0%
+which is bigger than y over x
+which is what we wanted to prove
+
+ align:start position:0%
+which is what we wanted to prove
+ 
+
+ align:start position:0%
+which is what we wanted to prove
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the second
+
+ align:start position:0%
+for the second
+ 
+
+ align:start position:0%
+for the second
+proof of the second theorem the density
+
+ align:start position:0%
+proof of the second theorem the density
+ 
+
+ align:start position:0%
+proof of the second theorem the density
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+rational numbers we'll do
+
+ align:start position:0%
+rational numbers we'll do
+ 
+
+ align:start position:0%
+rational numbers we'll do
+so we have three cases to consider
+
+ align:start position:0%
+so we have three cases to consider
+ 
+
+ align:start position:0%
+so we have three cases to consider
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+x and y are real numbers
+
+ align:start position:0%
+x and y are real numbers
+ 
+
+ align:start position:0%
+x and y are real numbers
+x is less than y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call it a
+
+ align:start position:0%
+call it a
+ 
+
+ align:start position:0%
+call it a
+x is less than 0 is less than y
+
+ align:start position:0%
+x is less than 0 is less than y
+ 
+
+ align:start position:0%
+x is less than 0 is less than y
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+0 is bigger than or equal to x is less
+
+ align:start position:0%
+0 is bigger than or equal to x is less
+ 
+
+ align:start position:0%
+0 is bigger than or equal to x is less
+than y
+
+ align:start position:0%
+than y
+ 
+
+ align:start position:0%
+than y
+you can see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is less than y is less than or equal
+
+ align:start position:0%
+x is less than y is less than or equal
+ 
+
+ align:start position:0%
+x is less than y is less than or equal
+to 0. okay
+
+ align:start position:0%
+to 0. okay
+ 
+
+ align:start position:0%
+to 0. okay
+so we want to find a rational number
+
+ align:start position:0%
+so we want to find a rational number
+ 
+
+ align:start position:0%
+so we want to find a rational number
+between x and y so for this case this is
+
+ align:start position:0%
+between x and y so for this case this is
+ 
+
+ align:start position:0%
+between x and y so for this case this is
+pretty simple we just take r to be zero
+
+ align:start position:0%
+pretty simple we just take r to be zero
+ 
+
+ align:start position:0%
+pretty simple we just take r to be zero
+so i'm not going to say anything about
+
+ align:start position:0%
+so i'm not going to say anything about
+ 
+
+ align:start position:0%
+so i'm not going to say anything about
+case a
+
+ align:start position:0%
+case a
+ 
+
+ align:start position:0%
+case a
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+i'm just going to move on to case b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case b
+
+ align:start position:0%
+case b
+ 
+
+ align:start position:0%
+case b
+so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is bigger than or equal to zero and
+
+ align:start position:0%
+x is bigger than or equal to zero and
+ 
+
+ align:start position:0%
+x is bigger than or equal to zero and
+less than y
+
+ align:start position:0%
+less than y
+ 
+
+ align:start position:0%
+less than y
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ap i'll refer to
+
+ align:start position:0%
+ap i'll refer to
+ 
+
+ align:start position:0%
+ap i'll refer to
+so that'll that'll
+
+ align:start position:0%
+so that'll that'll
+ 
+
+ align:start position:0%
+so that'll that'll
+be shorthand notation for the
+
+ align:start position:0%
+be shorthand notation for the
+ 
+
+ align:start position:0%
+be shorthand notation for the
+archimedean property so part one which
+
+ align:start position:0%
+archimedean property so part one which
+ 
+
+ align:start position:0%
+archimedean property so part one which
+we've already proven is true
+
+ align:start position:0%
+we've already proven is true
+ 
+
+ align:start position:0%
+we've already proven is true
+by the archimedean property
+
+ align:start position:0%
+by the archimedean property
+ 
+
+ align:start position:0%
+by the archimedean property
+there exists a natural number in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that n times y minus x
+
+ align:start position:0%
+such that n times y minus x
+ 
+
+ align:start position:0%
+such that n times y minus x
+is bigger than one
+
+ align:start position:0%
+is bigger than one
+ 
+
+ align:start position:0%
+is bigger than one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to use the archimedean
+
+ align:start position:0%
+we're going to use the archimedean
+ 
+
+ align:start position:0%
+we're going to use the archimedean
+property again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists an integer l
+
+ align:start position:0%
+there exists an integer l
+ 
+
+ align:start position:0%
+there exists an integer l
+and a natural number l
+
+ align:start position:0%
+and a natural number l
+ 
+
+ align:start position:0%
+and a natural number l
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l is bigger than n times x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+the set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of all integers of natural numbers k
+
+ align:start position:0%
+of all integers of natural numbers k
+ 
+
+ align:start position:0%
+of all integers of natural numbers k
+such that k is bigger than
+
+ align:start position:0%
+such that k is bigger than
+ 
+
+ align:start position:0%
+such that k is bigger than
+an x
+
+ align:start position:0%
+an x
+ 
+
+ align:start position:0%
+an x
+is non-empty
+
+ align:start position:0%
+is non-empty
+ 
+
+ align:start position:0%
+is non-empty
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a subset of the natural
+
+ align:start position:0%
+so this is a subset of the natural
+ 
+
+ align:start position:0%
+so this is a subset of the natural
+numbers so it has a least element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the well ordering property
+
+ align:start position:0%
+by the well ordering property
+ 
+
+ align:start position:0%
+by the well ordering property
+of the natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the least element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what does this mean
+
+ align:start position:0%
+okay now what does this mean
+ 
+
+ align:start position:0%
+okay now what does this mean
+what does m have to satisfy what we're
+
+ align:start position:0%
+what does m have to satisfy what we're
+ 
+
+ align:start position:0%
+what does m have to satisfy what we're
+going to show
+
+ align:start position:0%
+going to show
+ 
+
+ align:start position:0%
+going to show
+is that m over n
+
+ align:start position:0%
+is that m over n
+ 
+
+ align:start position:0%
+is that m over n
+is in fact um a rational number
+
+ align:start position:0%
+is in fact um a rational number
+ 
+
+ align:start position:0%
+is in fact um a rational number
+that is between x and y
+
+ align:start position:0%
+that is between x and y
+ 
+
+ align:start position:0%
+that is between x and y
+okay so the goal is i guess
+
+ align:start position:0%
+okay so the goal is i guess
+ 
+
+ align:start position:0%
+okay so the goal is i guess
+so let me just uh
+
+ align:start position:0%
+so let me just uh
+ 
+
+ align:start position:0%
+so let me just uh
+make a comment here
+
+ align:start position:0%
+make a comment here
+ 
+
+ align:start position:0%
+make a comment here
+so once we've made uh once we found this
+
+ align:start position:0%
+so once we've made uh once we found this
+ 
+
+ align:start position:0%
+so once we've made uh once we found this
+natural number little n
+
+ align:start position:0%
+natural number little n
+ 
+
+ align:start position:0%
+natural number little n
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that n times y minus x is bigger than
+
+ align:start position:0%
+so that n times y minus x is bigger than
+ 
+
+ align:start position:0%
+so that n times y minus x is bigger than
+one what does this mean this means n
+
+ align:start position:0%
+one what does this mean this means n
+ 
+
+ align:start position:0%
+one what does this mean this means n
+times y
+
+ align:start position:0%
+times y
+ 
+
+ align:start position:0%
+times y
+is bigger than
+
+ align:start position:0%
+is bigger than
+ 
+
+ align:start position:0%
+is bigger than
+n x plus one
+
+ align:start position:0%
+n x plus one
+ 
+
+ align:start position:0%
+n x plus one
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+our goal is then to find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this stuff in in brackets you should
+
+ align:start position:0%
+so this stuff in in brackets you should
+ 
+
+ align:start position:0%
+so this stuff in in brackets you should
+not consider as part of the proof this
+
+ align:start position:0%
+not consider as part of the proof this
+ 
+
+ align:start position:0%
+not consider as part of the proof this
+is me trying to explain to you um
+
+ align:start position:0%
+is me trying to explain to you um
+ 
+
+ align:start position:0%
+is me trying to explain to you um
+you know where
+
+ align:start position:0%
+you know where
+ 
+
+ align:start position:0%
+you know where
+from here we would like to go to
+
+ align:start position:0%
+from here we would like to go to
+ 
+
+ align:start position:0%
+from here we would like to go to
+conclude the proof that there exists a
+
+ align:start position:0%
+conclude the proof that there exists a
+ 
+
+ align:start position:0%
+conclude the proof that there exists a
+rational number between y and x
+
+ align:start position:0%
+rational number between y and x
+ 
+
+ align:start position:0%
+rational number between y and x
+so we have this inequality the
+
+ align:start position:0%
+so we have this inequality the
+ 
+
+ align:start position:0%
+so we have this inequality the
+archamidian property tells us there's a
+
+ align:start position:0%
+archamidian property tells us there's a
+ 
+
+ align:start position:0%
+archamidian property tells us there's a
+natural number that satisfies this
+
+ align:start position:0%
+natural number that satisfies this
+ 
+
+ align:start position:0%
+natural number that satisfies this
+so what we would like to do is find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another natural number and i'm
+
+ align:start position:0%
+another natural number and i'm
+ 
+
+ align:start position:0%
+another natural number and i'm
+foreshadowing what's to come
+
+ align:start position:0%
+foreshadowing what's to come
+ 
+
+ align:start position:0%
+foreshadowing what's to come
+a natural number m well let's not uh i
+
+ align:start position:0%
+a natural number m well let's not uh i
+ 
+
+ align:start position:0%
+a natural number m well let's not uh i
+don't want you to give you any false
+
+ align:start position:0%
+don't want you to give you any false
+ 
+
+ align:start position:0%
+don't want you to give you any false
+hopes i mean they're not false it'll
+
+ align:start position:0%
+hopes i mean they're not false it'll
+ 
+
+ align:start position:0%
+hopes i mean they're not false it'll
+happen in a minute but let's
+
+ align:start position:0%
+happen in a minute but let's
+ 
+
+ align:start position:0%
+happen in a minute but let's
+call this j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that two things happen um
+
+ align:start position:0%
+so that two things happen um
+ 
+
+ align:start position:0%
+so that two things happen um
+n times x is less than
+
+ align:start position:0%
+n times x is less than
+ 
+
+ align:start position:0%
+n times x is less than
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or equal to
+
+ align:start position:0%
+or equal to
+ 
+
+ align:start position:0%
+or equal to
+and x plus 1. so if we're able to find
+
+ align:start position:0%
+and x plus 1. so if we're able to find
+ 
+
+ align:start position:0%
+and x plus 1. so if we're able to find
+such an integer j satisfying this
+
+ align:start position:0%
+such an integer j satisfying this
+ 
+
+ align:start position:0%
+such an integer j satisfying this
+these two inequalities then
+
+ align:start position:0%
+these two inequalities then
+ 
+
+ align:start position:0%
+these two inequalities then
+from this inequality we would get that
+
+ align:start position:0%
+from this inequality we would get that
+ 
+
+ align:start position:0%
+from this inequality we would get that
+n y is bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+this is bigger than n x
+
+ align:start position:0%
+this is bigger than n x
+ 
+
+ align:start position:0%
+this is bigger than n x
+plus one which is bigger than or equal
+
+ align:start position:0%
+plus one which is bigger than or equal
+ 
+
+ align:start position:0%
+plus one which is bigger than or equal
+to j
+
+ align:start position:0%
+to j
+ 
+
+ align:start position:0%
+to j
+which is bigger than
+
+ align:start position:0%
+which is bigger than
+ 
+
+ align:start position:0%
+which is bigger than
+nx
+
+ align:start position:0%
+nx
+ 
+
+ align:start position:0%
+nx
+ie so let me just rewrite this in x is
+
+ align:start position:0%
+ie so let me just rewrite this in x is
+ 
+
+ align:start position:0%
+ie so let me just rewrite this in x is
+less than j is less than
+
+ align:start position:0%
+less than j is less than
+ 
+
+ align:start position:0%
+less than j is less than
+n times y or in other words
+
+ align:start position:0%
+n times y or in other words
+ 
+
+ align:start position:0%
+n times y or in other words
+x is less than j over n
+
+ align:start position:0%
+x is less than j over n
+ 
+
+ align:start position:0%
+x is less than j over n
+is less than y and here's our rational
+
+ align:start position:0%
+is less than y and here's our rational
+ 
+
+ align:start position:0%
+is less than y and here's our rational
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+which we would choose
+
+ align:start position:0%
+which we would choose
+ 
+
+ align:start position:0%
+which we would choose
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's the game plan which maybe i
+
+ align:start position:0%
+that's the game plan which maybe i
+ 
+
+ align:start position:0%
+that's the game plan which maybe i
+should have said
+
+ align:start position:0%
+should have said
+ 
+
+ align:start position:0%
+should have said
+right after i came up with this integer
+
+ align:start position:0%
+right after i came up with this integer
+ 
+
+ align:start position:0%
+right after i came up with this integer
+little n
+
+ align:start position:0%
+little n
+ 
+
+ align:start position:0%
+little n
+you may be asking why come up with this
+
+ align:start position:0%
+you may be asking why come up with this
+ 
+
+ align:start position:0%
+you may be asking why come up with this
+integer little n well
+
+ align:start position:0%
+integer little n well
+ 
+
+ align:start position:0%
+integer little n well
+we have to start somewhere in the
+
+ align:start position:0%
+we have to start somewhere in the
+ 
+
+ align:start position:0%
+we have to start somewhere in the
+archmedian property gives us this and
+
+ align:start position:0%
+archmedian property gives us this and
+ 
+
+ align:start position:0%
+archmedian property gives us this and
+this somehow gives us a scale to
+
+ align:start position:0%
+this somehow gives us a scale to
+ 
+
+ align:start position:0%
+this somehow gives us a scale to
+at least a
+
+ align:start position:0%
+at least a
+ 
+
+ align:start position:0%
+at least a
+scale one over n to kind of work on
+
+ align:start position:0%
+scale one over n to kind of work on
+ 
+
+ align:start position:0%
+scale one over n to kind of work on
+um but anyway so going back to the proof
+
+ align:start position:0%
+um but anyway so going back to the proof
+ 
+
+ align:start position:0%
+um but anyway so going back to the proof
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we have by the well ordering property
+
+ align:start position:0%
+so we have by the well ordering property
+ 
+
+ align:start position:0%
+so we have by the well ordering property
+of the natural numbers this set s
+
+ align:start position:0%
+of the natural numbers this set s
+ 
+
+ align:start position:0%
+of the natural numbers this set s
+which is the set of all natural numbers
+
+ align:start position:0%
+which is the set of all natural numbers
+ 
+
+ align:start position:0%
+which is the set of all natural numbers
+so that k is bigger than n x
+
+ align:start position:0%
+so that k is bigger than n x
+ 
+
+ align:start position:0%
+so that k is bigger than n x
+has a least element little m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so s has a least element m means m is in
+
+ align:start position:0%
+so s has a least element m means m is in
+ 
+
+ align:start position:0%
+so s has a least element m means m is in
+s so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since m is an s
+
+ align:start position:0%
+since m is an s
+ 
+
+ align:start position:0%
+since m is an s
+this means simply by the definition of
+
+ align:start position:0%
+this means simply by the definition of
+ 
+
+ align:start position:0%
+this means simply by the definition of
+what s is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in x is less than m
+
+ align:start position:0%
+in x is less than m
+ 
+
+ align:start position:0%
+in x is less than m
+that's very good
+
+ align:start position:0%
+that's very good
+ 
+
+ align:start position:0%
+that's very good
+that's one of the properties we wanted i
+
+ align:start position:0%
+that's one of the properties we wanted i
+ 
+
+ align:start position:0%
+that's one of the properties we wanted i
+wrote it as j but we wanted an integer
+
+ align:start position:0%
+wrote it as j but we wanted an integer
+ 
+
+ align:start position:0%
+wrote it as j but we wanted an integer
+to satisfy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since m is
+
+ align:start position:0%
+since m is
+ 
+
+ align:start position:0%
+since m is
+the least element of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m minus 1 is not an s
+
+ align:start position:0%
+m minus 1 is not an s
+ 
+
+ align:start position:0%
+m minus 1 is not an s
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that implies that n minus 1 not in x
+
+ align:start position:0%
+so that implies that n minus 1 not in x
+ 
+
+ align:start position:0%
+so that implies that n minus 1 not in x
+means in s means
+
+ align:start position:0%
+means in s means
+ 
+
+ align:start position:0%
+means in s means
+m minus 1 is less than or equal to n
+
+ align:start position:0%
+m minus 1 is less than or equal to n
+ 
+
+ align:start position:0%
+m minus 1 is less than or equal to n
+times x
+
+ align:start position:0%
+times x
+ 
+
+ align:start position:0%
+times x
+i e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m is less than or equal to n times x
+
+ align:start position:0%
+m is less than or equal to n times x
+ 
+
+ align:start position:0%
+m is less than or equal to n times x
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+now we'll combine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these two inequalities along with the
+
+ align:start position:0%
+these two inequalities along with the
+ 
+
+ align:start position:0%
+these two inequalities along with the
+first one involving n times one uh times
+
+ align:start position:0%
+first one involving n times one uh times
+ 
+
+ align:start position:0%
+first one involving n times one uh times
+y minus x so i'm just basically
+
+ align:start position:0%
+y minus x so i'm just basically
+ 
+
+ align:start position:0%
+y minus x so i'm just basically
+rewriting what i told you our goal was
+
+ align:start position:0%
+rewriting what i told you our goal was
+ 
+
+ align:start position:0%
+rewriting what i told you our goal was
+here in this uh bracket
+
+ align:start position:0%
+here in this uh bracket
+ 
+
+ align:start position:0%
+here in this uh bracket
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+n times x is less than m
+
+ align:start position:0%
+n times x is less than m
+ 
+
+ align:start position:0%
+n times x is less than m
+and this is less than or equal to n
+
+ align:start position:0%
+and this is less than or equal to n
+ 
+
+ align:start position:0%
+and this is less than or equal to n
+times x plus 1
+
+ align:start position:0%
+times x plus 1
+ 
+
+ align:start position:0%
+times x plus 1
+which by our definition of n
+
+ align:start position:0%
+which by our definition of n
+ 
+
+ align:start position:0%
+which by our definition of n
+and the first inequality we have up
+
+ align:start position:0%
+and the first inequality we have up
+ 
+
+ align:start position:0%
+and the first inequality we have up
+there involving y is less than n times y
+
+ align:start position:0%
+there involving y is less than n times y
+ 
+
+ align:start position:0%
+there involving y is less than n times y
+so we have nx is less than m is less
+
+ align:start position:0%
+so we have nx is less than m is less
+ 
+
+ align:start position:0%
+so we have nx is less than m is less
+than ny
+
+ align:start position:0%
+than ny
+ 
+
+ align:start position:0%
+than ny
+so that means x is less than
+
+ align:start position:0%
+so that means x is less than
+ 
+
+ align:start position:0%
+so that means x is less than
+m over n is less than y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+r equals m over n
+
+ align:start position:0%
+r equals m over n
+ 
+
+ align:start position:0%
+r equals m over n
+which is a
+
+ align:start position:0%
+which is a
+ 
+
+ align:start position:0%
+which is a
+proportion of
+
+ align:start position:0%
+proportion of
+ 
+
+ align:start position:0%
+proportion of
+natural numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our choice that's an awkward way to
+
+ align:start position:0%
+our choice that's an awkward way to
+ 
+
+ align:start position:0%
+our choice that's an awkward way to
+finish the sentence but um my mind went
+
+ align:start position:0%
+finish the sentence but um my mind went
+ 
+
+ align:start position:0%
+finish the sentence but um my mind went
+blank anyways so okay that handles the
+
+ align:start position:0%
+blank anyways so okay that handles the
+ 
+
+ align:start position:0%
+blank anyways so okay that handles the
+case b
+
+ align:start position:0%
+case b
+ 
+
+ align:start position:0%
+case b
+right that x is bigger than or equal to
+
+ align:start position:0%
+right that x is bigger than or equal to
+ 
+
+ align:start position:0%
+right that x is bigger than or equal to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so one small uh
+
+ align:start position:0%
+um so one small uh
+ 
+
+ align:start position:0%
+um so one small uh
+thing that i
+
+ align:start position:0%
+thing that i
+ 
+
+ align:start position:0%
+thing that i
+just a very minor comment if you've got
+
+ align:start position:0%
+just a very minor comment if you've got
+ 
+
+ align:start position:0%
+just a very minor comment if you've got
+all this and and you understand it
+
+ align:start position:0%
+all this and and you understand it
+ 
+
+ align:start position:0%
+all this and and you understand it
+that's fine but you may be asking since
+
+ align:start position:0%
+that's fine but you may be asking since
+ 
+
+ align:start position:0%
+that's fine but you may be asking since
+i never actually said it out loud where
+
+ align:start position:0%
+i never actually said it out loud where
+ 
+
+ align:start position:0%
+i never actually said it out loud where
+did i use the fact that x is bigger than
+
+ align:start position:0%
+did i use the fact that x is bigger than
+ 
+
+ align:start position:0%
+did i use the fact that x is bigger than
+or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so where i use that so let's just assume
+
+ align:start position:0%
+so where i use that so let's just assume
+ 
+
+ align:start position:0%
+so where i use that so let's just assume
+x is bigger than zero so what
+
+ align:start position:0%
+x is bigger than zero so what
+ 
+
+ align:start position:0%
+x is bigger than zero so what
+where did i use um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+really write um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this place here so i don't want to
+
+ align:start position:0%
+in this place here so i don't want to
+ 
+
+ align:start position:0%
+in this place here so i don't want to
+spend too much time on that but um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by being able to claim that m minus 1 is
+
+ align:start position:0%
+by being able to claim that m minus 1 is
+ 
+
+ align:start position:0%
+by being able to claim that m minus 1 is
+not an s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so what about case
+
+ align:start position:0%
+all right so what about case
+ 
+
+ align:start position:0%
+all right so what about case
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+so in case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c will just reduce to case b
+
+ align:start position:0%
+c will just reduce to case b
+ 
+
+ align:start position:0%
+c will just reduce to case b
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+x is less than y which is less than or
+
+ align:start position:0%
+x is less than y which is less than or
+ 
+
+ align:start position:0%
+x is less than y which is less than or
+equal to 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 is bigger than or equal to minus y
+
+ align:start position:0%
+0 is bigger than or equal to minus y
+ 
+
+ align:start position:0%
+0 is bigger than or equal to minus y
+which is bigger than minus x
+
+ align:start position:0%
+which is bigger than minus x
+ 
+
+ align:start position:0%
+which is bigger than minus x
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by case
+
+ align:start position:0%
+by case
+ 
+
+ align:start position:0%
+by case
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+a rational number
+
+ align:start position:0%
+a rational number
+ 
+
+ align:start position:0%
+a rational number
+our tilde
+
+ align:start position:0%
+our tilde
+ 
+
+ align:start position:0%
+our tilde
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus y is less than our tilde is less
+
+ align:start position:0%
+minus y is less than our tilde is less
+ 
+
+ align:start position:0%
+minus y is less than our tilde is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that
+
+ align:start position:0%
+this implies that
+ 
+
+ align:start position:0%
+this implies that
+x is less than minus r tilde is less
+
+ align:start position:0%
+x is less than minus r tilde is less
+ 
+
+ align:start position:0%
+x is less than minus r tilde is less
+than y
+
+ align:start position:0%
+than y
+ 
+
+ align:start position:0%
+than y
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+r equal to minus r tilde
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does the job
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that proves the theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll use this in just a minute to
+
+ align:start position:0%
+so we'll use this in just a minute to
+ 
+
+ align:start position:0%
+so we'll use this in just a minute to
+prove a simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement about
+
+ align:start position:0%
+statement about
+ 
+
+ align:start position:0%
+statement about
+soups about
+
+ align:start position:0%
+soups about
+ 
+
+ align:start position:0%
+soups about
+soups and imps
+
+ align:start position:0%
+soups and imps
+ 
+
+ align:start position:0%
+soups and imps
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before i use it let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go on and what i'd like to do is state
+
+ align:start position:0%
+go on and what i'd like to do is state
+ 
+
+ align:start position:0%
+go on and what i'd like to do is state
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a different way
+
+ align:start position:0%
+a different way
+ 
+
+ align:start position:0%
+a different way
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+verify that
+
+ align:start position:0%
+verify that
+ 
+
+ align:start position:0%
+verify that
+a number is the soup of a set or the m
+
+ align:start position:0%
+a number is the soup of a set or the m
+ 
+
+ align:start position:0%
+a number is the soup of a set or the m
+of a set so i'm just going to state it
+
+ align:start position:0%
+of a set so i'm just going to state it
+ 
+
+ align:start position:0%
+of a set so i'm just going to state it
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+soups and there's an analogous statement
+
+ align:start position:0%
+soups and there's an analogous statement
+ 
+
+ align:start position:0%
+soups and there's an analogous statement
+for imps so the theorem is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this will actually be on the
+
+ align:start position:0%
+and this will actually be on the
+ 
+
+ align:start position:0%
+and this will actually be on the
+assignment so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume s is a subset of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and bound it above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so s has the supremum
+
+ align:start position:0%
+so s has the supremum
+ 
+
+ align:start position:0%
+so s has the supremum
+so i'm going to tell you what the
+
+ align:start position:0%
+so i'm going to tell you what the
+ 
+
+ align:start position:0%
+so i'm going to tell you what the
+supremum satisfies and it's an if and
+
+ align:start position:0%
+supremum satisfies and it's an if and
+ 
+
+ align:start position:0%
+supremum satisfies and it's an if and
+only if statement
+
+ align:start position:0%
+only if statement
+ 
+
+ align:start position:0%
+only if statement
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some number x equals a soup of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if so either i'll do a
+
+ align:start position:0%
+if and only if so either i'll do a
+ 
+
+ align:start position:0%
+if and only if so either i'll do a
+double arrow or i'll write if and only
+
+ align:start position:0%
+double arrow or i'll write if and only
+ 
+
+ align:start position:0%
+double arrow or i'll write if and only
+if iff
+
+ align:start position:0%
+if iff
+ 
+
+ align:start position:0%
+if iff
+two conditions are satisfied the first
+
+ align:start position:0%
+two conditions are satisfied the first
+ 
+
+ align:start position:0%
+two conditions are satisfied the first
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+x is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an upper bound for s
+
+ align:start position:0%
+an upper bound for s
+ 
+
+ align:start position:0%
+an upper bound for s
+and the second
+
+ align:start position:0%
+and the second
+ 
+
+ align:start position:0%
+and the second
+so at one point or very in the very near
+
+ align:start position:0%
+so at one point or very in the very near
+ 
+
+ align:start position:0%
+so at one point or very in the very near
+future we're going to be seeing epsilons
+
+ align:start position:0%
+future we're going to be seeing epsilons
+ 
+
+ align:start position:0%
+future we're going to be seeing epsilons
+and deltas so i'll state it this way
+
+ align:start position:0%
+and deltas so i'll state it this way
+ 
+
+ align:start position:0%
+and deltas so i'll state it this way
+so you should
+
+ align:start position:0%
+so you should
+ 
+
+ align:start position:0%
+so you should
+start seeing them now for every epsilon
+
+ align:start position:0%
+start seeing them now for every epsilon
+ 
+
+ align:start position:0%
+start seeing them now for every epsilon
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+an element y in s
+
+ align:start position:0%
+an element y in s
+ 
+
+ align:start position:0%
+an element y in s
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+x minus epsilon is less than y
+
+ align:start position:0%
+x minus epsilon is less than y
+ 
+
+ align:start position:0%
+x minus epsilon is less than y
+is less than or equal to x
+
+ align:start position:0%
+is less than or equal to x
+ 
+
+ align:start position:0%
+is less than or equal to x
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know why why
+
+ align:start position:0%
+you know why why
+ 
+
+ align:start position:0%
+you know why why
+why should this be the case well
+
+ align:start position:0%
+why should this be the case well
+ 
+
+ align:start position:0%
+why should this be the case well
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+s is
+
+ align:start position:0%
+s is
+ 
+
+ align:start position:0%
+s is
+all over here to the left of x
+
+ align:start position:0%
+all over here to the left of x
+ 
+
+ align:start position:0%
+all over here to the left of x
+then and if i take something smaller
+
+ align:start position:0%
+then and if i take something smaller
+ 
+
+ align:start position:0%
+then and if i take something smaller
+so i'm actually kind of giving you a
+
+ align:start position:0%
+so i'm actually kind of giving you a
+ 
+
+ align:start position:0%
+so i'm actually kind of giving you a
+picture proof of one direction
+
+ align:start position:0%
+picture proof of one direction
+ 
+
+ align:start position:0%
+picture proof of one direction
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so if i take something smaller x minus
+
+ align:start position:0%
+so if i take something smaller x minus
+ 
+
+ align:start position:0%
+so if i take something smaller x minus
+epsilon then this cannot be an upper
+
+ align:start position:0%
+epsilon then this cannot be an upper
+ 
+
+ align:start position:0%
+epsilon then this cannot be an upper
+bound for s
+
+ align:start position:0%
+bound for s
+ 
+
+ align:start position:0%
+bound for s
+so therefore there must exist
+
+ align:start position:0%
+so therefore there must exist
+ 
+
+ align:start position:0%
+so therefore there must exist
+some y and s bigger than x minus epsilon
+
+ align:start position:0%
+some y and s bigger than x minus epsilon
+ 
+
+ align:start position:0%
+some y and s bigger than x minus epsilon
+and it's less than or equal to x because
+
+ align:start position:0%
+and it's less than or equal to x because
+ 
+
+ align:start position:0%
+and it's less than or equal to x because
+x is an upper bound for s so
+
+ align:start position:0%
+x is an upper bound for s so
+ 
+
+ align:start position:0%
+x is an upper bound for s so
+in fact this picture
+
+ align:start position:0%
+in fact this picture
+ 
+
+ align:start position:0%
+in fact this picture
+is a proof of this direction namely if x
+
+ align:start position:0%
+is a proof of this direction namely if x
+ 
+
+ align:start position:0%
+is a proof of this direction namely if x
+is a the supremum of s
+
+ align:start position:0%
+is a the supremum of s
+ 
+
+ align:start position:0%
+is a the supremum of s
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh these two conditions are satisfied
+
+ align:start position:0%
+uh these two conditions are satisfied
+ 
+
+ align:start position:0%
+uh these two conditions are satisfied
+and then on the assignment i'll have you
+
+ align:start position:0%
+and then on the assignment i'll have you
+ 
+
+ align:start position:0%
+and then on the assignment i'll have you
+prove the other direction basically
+
+ align:start position:0%
+prove the other direction basically
+ 
+
+ align:start position:0%
+prove the other direction basically
+that these two conditions imply that a
+
+ align:start position:0%
+that these two conditions imply that a
+ 
+
+ align:start position:0%
+that these two conditions imply that a
+real number is
+
+ align:start position:0%
+real number is
+ 
+
+ align:start position:0%
+real number is
+the supremum of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+let's use the serum
+
+ align:start position:0%
+let's use the serum
+ 
+
+ align:start position:0%
+let's use the serum
+and our comedian property to prove a
+
+ align:start position:0%
+and our comedian property to prove a
+ 
+
+ align:start position:0%
+and our comedian property to prove a
+simple statement about
+
+ align:start position:0%
+simple statement about
+ 
+
+ align:start position:0%
+simple statement about
+the soup of a simple set
+
+ align:start position:0%
+the soup of a simple set
+ 
+
+ align:start position:0%
+the soup of a simple set
+so i should so let me also write here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i'm not going to state it as a
+
+ align:start position:0%
+that i'm not going to state it as a
+ 
+
+ align:start position:0%
+that i'm not going to state it as a
+theorem but i'll just this is a remark
+
+ align:start position:0%
+theorem but i'll just this is a remark
+ 
+
+ align:start position:0%
+theorem but i'll just this is a remark
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'm being a little bit loose with what
+
+ align:start position:0%
+i'm being a little bit loose with what
+ 
+
+ align:start position:0%
+i'm being a little bit loose with what
+i'm writing down but it's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x equals m s
+
+ align:start position:0%
+x equals m s
+ 
+
+ align:start position:0%
+x equals m s
+so for s a non-empty
+
+ align:start position:0%
+so for s a non-empty
+ 
+
+ align:start position:0%
+so for s a non-empty
+subset which is bounded below
+
+ align:start position:0%
+subset which is bounded below
+ 
+
+ align:start position:0%
+subset which is bounded below
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+an analogous characterization as
+
+ align:start position:0%
+an analogous characterization as
+ 
+
+ align:start position:0%
+an analogous characterization as
+x is a
+
+ align:start position:0%
+x is a
+ 
+
+ align:start position:0%
+x is a
+lower bound for s
+
+ align:start position:0%
+lower bound for s
+ 
+
+ align:start position:0%
+lower bound for s
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're all epsilon positive
+
+ align:start position:0%
+we're all epsilon positive
+ 
+
+ align:start position:0%
+we're all epsilon positive
+there exists a y in s
+
+ align:start position:0%
+there exists a y in s
+ 
+
+ align:start position:0%
+there exists a y in s
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+x is less than or equal to y is less
+
+ align:start position:0%
+x is less than or equal to y is less
+ 
+
+ align:start position:0%
+x is less than or equal to y is less
+than x plus epsilon
+
+ align:start position:0%
+than x plus epsilon
+ 
+
+ align:start position:0%
+than x plus epsilon
+okay so this is the analogous statement
+
+ align:start position:0%
+okay so this is the analogous statement
+ 
+
+ align:start position:0%
+okay so this is the analogous statement
+for the m
+
+ align:start position:0%
+for the m
+ 
+
+ align:start position:0%
+for the m
+for something to be the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um okay so this is a i guess you could
+
+ align:start position:0%
+um okay so this is a i guess you could
+ 
+
+ align:start position:0%
+um okay so this is a i guess you could
+call it a theorem it's not a very
+
+ align:start position:0%
+call it a theorem it's not a very
+ 
+
+ align:start position:0%
+call it a theorem it's not a very
+spectacular theorem but
+
+ align:start position:0%
+spectacular theorem but
+ 
+
+ align:start position:0%
+spectacular theorem but
+if i look at the set 1 minus 1 over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a natural number and i take its soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to one
+
+ align:start position:0%
+this is equal to one
+ 
+
+ align:start position:0%
+this is equal to one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this shouldn't surprise you too much
+
+ align:start position:0%
+so this shouldn't surprise you too much
+ 
+
+ align:start position:0%
+so this shouldn't surprise you too much
+because what is this set um
+
+ align:start position:0%
+because what is this set um
+ 
+
+ align:start position:0%
+because what is this set um
+this is the set
+
+ align:start position:0%
+this is the set
+ 
+
+ align:start position:0%
+this is the set
+zero one-half
+
+ align:start position:0%
+zero one-half
+ 
+
+ align:start position:0%
+zero one-half
+two-thirds
+
+ align:start position:0%
+two-thirds
+ 
+
+ align:start position:0%
+two-thirds
+three-fourths
+
+ align:start position:0%
+three-fourths
+ 
+
+ align:start position:0%
+three-fourths
+four-fifths
+
+ align:start position:0%
+four-fifths
+ 
+
+ align:start position:0%
+four-fifths
+and so on so you see one is always
+
+ align:start position:0%
+and so on so you see one is always
+ 
+
+ align:start position:0%
+and so on so you see one is always
+bigger than or equal to everything in
+
+ align:start position:0%
+bigger than or equal to everything in
+ 
+
+ align:start position:0%
+bigger than or equal to everything in
+here so it's certainly an upper bound
+
+ align:start position:0%
+here so it's certainly an upper bound
+ 
+
+ align:start position:0%
+here so it's certainly an upper bound
+and everything is kind of progressively
+
+ align:start position:0%
+and everything is kind of progressively
+ 
+
+ align:start position:0%
+and everything is kind of progressively
+getting closer to one so it should
+
+ align:start position:0%
+getting closer to one so it should
+ 
+
+ align:start position:0%
+getting closer to one so it should
+satisfy the second property namely if i
+
+ align:start position:0%
+satisfy the second property namely if i
+ 
+
+ align:start position:0%
+satisfy the second property namely if i
+go a little bit to the left of one then
+
+ align:start position:0%
+go a little bit to the left of one then
+ 
+
+ align:start position:0%
+go a little bit to the left of one then
+i'll be able to find
+
+ align:start position:0%
+i'll be able to find
+ 
+
+ align:start position:0%
+i'll be able to find
+something less than or equal to one and
+
+ align:start position:0%
+something less than or equal to one and
+ 
+
+ align:start position:0%
+something less than or equal to one and
+bigger than that thing
+
+ align:start position:0%
+bigger than that thing
+ 
+
+ align:start position:0%
+bigger than that thing
+to the left of one and that'll be how we
+
+ align:start position:0%
+to the left of one and that'll be how we
+ 
+
+ align:start position:0%
+to the left of one and that'll be how we
+prove
+
+ align:start position:0%
+prove
+ 
+
+ align:start position:0%
+prove
+this theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+first off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since 1 minus 1 over n is less than 1
+
+ align:start position:0%
+since 1 minus 1 over n is less than 1
+ 
+
+ align:start position:0%
+since 1 minus 1 over n is less than 1
+for all natural numbers in
+
+ align:start position:0%
+for all natural numbers in
+ 
+
+ align:start position:0%
+for all natural numbers in
+this implies
+
+ align:start position:0%
+this implies
+ 
+
+ align:start position:0%
+this implies
+one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an upper bound for this set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we're going to uh verify
+
+ align:start position:0%
+now we're going to uh verify
+ 
+
+ align:start position:0%
+now we're going to uh verify
+that 1 satisfies that second property of
+
+ align:start position:0%
+that 1 satisfies that second property of
+ 
+
+ align:start position:0%
+that 1 satisfies that second property of
+the theorem that for every epsilon
+
+ align:start position:0%
+the theorem that for every epsilon
+ 
+
+ align:start position:0%
+the theorem that for every epsilon
+positive i can find a natural number
+
+ align:start position:0%
+positive i can find a natural number
+ 
+
+ align:start position:0%
+positive i can find a natural number
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+little n so that 1 minus 1 over n
+
+ align:start position:0%
+little n so that 1 minus 1 over n
+ 
+
+ align:start position:0%
+little n so that 1 minus 1 over n
+is bigger than 1 minus epsilon
+
+ align:start position:0%
+is bigger than 1 minus epsilon
+ 
+
+ align:start position:0%
+is bigger than 1 minus epsilon
+okay and we'll use archimedean property
+
+ align:start position:0%
+okay and we'll use archimedean property
+ 
+
+ align:start position:0%
+okay and we'll use archimedean property
+for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you're ever supposed to show
+
+ align:start position:0%
+so if you're ever supposed to show
+ 
+
+ align:start position:0%
+so if you're ever supposed to show
+something for every epsilon positive
+
+ align:start position:0%
+something for every epsilon positive
+ 
+
+ align:start position:0%
+something for every epsilon positive
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+every proof should start off with let
+
+ align:start position:0%
+every proof should start off with let
+ 
+
+ align:start position:0%
+every proof should start off with let
+epsilon be positive in fact i'll give
+
+ align:start position:0%
+epsilon be positive in fact i'll give
+ 
+
+ align:start position:0%
+epsilon be positive in fact i'll give
+you a couple of points on the exam if
+
+ align:start position:0%
+you a couple of points on the exam if
+ 
+
+ align:start position:0%
+you a couple of points on the exam if
+there's epsilon
+
+ align:start position:0%
+there's epsilon
+ 
+
+ align:start position:0%
+there's epsilon
+delta m's whatever proofs
+
+ align:start position:0%
+delta m's whatever proofs
+ 
+
+ align:start position:0%
+delta m's whatever proofs
+which means you should prove something
+
+ align:start position:0%
+which means you should prove something
+ 
+
+ align:start position:0%
+which means you should prove something
+for all epsilon i'll give you a couple
+
+ align:start position:0%
+for all epsilon i'll give you a couple
+ 
+
+ align:start position:0%
+for all epsilon i'll give you a couple
+of points on the exam
+
+ align:start position:0%
+of points on the exam
+ 
+
+ align:start position:0%
+of points on the exam
+if you just at least state let epsilon
+
+ align:start position:0%
+if you just at least state let epsilon
+ 
+
+ align:start position:0%
+if you just at least state let epsilon
+be positive so
+
+ align:start position:0%
+be positive so
+ 
+
+ align:start position:0%
+be positive so
+let epsilon be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist
+
+ align:start position:0%
+there exist
+ 
+
+ align:start position:0%
+there exist
+so by the archimedean property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a natural number in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over epsilon is less than n
+
+ align:start position:0%
+1 over epsilon is less than n
+ 
+
+ align:start position:0%
+1 over epsilon is less than n
+okay this is taking for example in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the statement of the archimedean
+
+ align:start position:0%
+the statement of the archimedean
+ 
+
+ align:start position:0%
+the statement of the archimedean
+property if you'd like it's taking x to
+
+ align:start position:0%
+property if you'd like it's taking x to
+ 
+
+ align:start position:0%
+property if you'd like it's taking x to
+be 1
+
+ align:start position:0%
+be 1
+ 
+
+ align:start position:0%
+be 1
+and y to be one over epsilon
+
+ align:start position:0%
+and y to be one over epsilon
+ 
+
+ align:start position:0%
+and y to be one over epsilon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one minus
+
+ align:start position:0%
+one minus
+ 
+
+ align:start position:0%
+one minus
+one over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go
+
+ align:start position:0%
+let's go
+ 
+
+ align:start position:0%
+let's go
+let's do it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one minus epsilon
+
+ align:start position:0%
+and one minus epsilon
+ 
+
+ align:start position:0%
+and one minus epsilon
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+so since
+
+ align:start position:0%
+so since
+ 
+
+ align:start position:0%
+so since
+epsilon is less than
+
+ align:start position:0%
+epsilon is less than
+ 
+
+ align:start position:0%
+epsilon is less than
+one over epsilon is less than n
+
+ align:start position:0%
+one over epsilon is less than n
+ 
+
+ align:start position:0%
+one over epsilon is less than n
+this is equivalent to saying one over n
+
+ align:start position:0%
+this is equivalent to saying one over n
+ 
+
+ align:start position:0%
+this is equivalent to saying one over n
+is less than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+minus epsilon is less than minus 1 over
+
+ align:start position:0%
+minus epsilon is less than minus 1 over
+ 
+
+ align:start position:0%
+minus epsilon is less than minus 1 over
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+so then 1 minus epsilon is less than 1
+
+ align:start position:0%
+so then 1 minus epsilon is less than 1
+ 
+
+ align:start position:0%
+so then 1 minus epsilon is less than 1
+minus 1 over n which is
+
+ align:start position:0%
+minus 1 over n which is
+ 
+
+ align:start position:0%
+minus 1 over n which is
+as we have up here is less than 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus there exists a natural number in
+
+ align:start position:0%
+thus there exists a natural number in
+ 
+
+ align:start position:0%
+thus there exists a natural number in
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay that went kind of quick so what i
+
+ align:start position:0%
+okay that went kind of quick so what i
+ 
+
+ align:start position:0%
+okay that went kind of quick so what i
+did was i found a natural number n which
+
+ align:start position:0%
+did was i found a natural number n which
+ 
+
+ align:start position:0%
+did was i found a natural number n which
+is bigger than one over epsilon and from
+
+ align:start position:0%
+is bigger than one over epsilon and from
+ 
+
+ align:start position:0%
+is bigger than one over epsilon and from
+now on typically i won't state it like
+
+ align:start position:0%
+now on typically i won't state it like
+ 
+
+ align:start position:0%
+now on typically i won't state it like
+this i'll state it more like this
+
+ align:start position:0%
+this i'll state it more like this
+ 
+
+ align:start position:0%
+this i'll state it more like this
+um which you know this
+
+ align:start position:0%
+um which you know this
+ 
+
+ align:start position:0%
+um which you know this
+follows from this
+
+ align:start position:0%
+follows from this
+ 
+
+ align:start position:0%
+follows from this
+um so when i make a statement like
+
+ align:start position:0%
+um so when i make a statement like
+ 
+
+ align:start position:0%
+um so when i make a statement like
+choose a natural number so that one over
+
+ align:start position:0%
+choose a natural number so that one over
+ 
+
+ align:start position:0%
+choose a natural number so that one over
+n is less than epsilon um
+
+ align:start position:0%
+n is less than epsilon um
+ 
+
+ align:start position:0%
+n is less than epsilon um
+that follows from the archimedean
+
+ align:start position:0%
+that follows from the archimedean
+ 
+
+ align:start position:0%
+that follows from the archimedean
+property just by taking one over this
+
+ align:start position:0%
+property just by taking one over this
+ 
+
+ align:start position:0%
+property just by taking one over this
+inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so from there we concluded that
+
+ align:start position:0%
+okay and so from there we concluded that
+ 
+
+ align:start position:0%
+okay and so from there we concluded that
+one minus epsilon is less than one minus
+
+ align:start position:0%
+one minus epsilon is less than one minus
+ 
+
+ align:start position:0%
+one minus epsilon is less than one minus
+one over n which is still less than one
+
+ align:start position:0%
+one over n which is still less than one
+ 
+
+ align:start position:0%
+one over n which is still less than one
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we have proven the second number two
+
+ align:start position:0%
+we have proven the second number two
+ 
+
+ align:start position:0%
+we have proven the second number two
+property of
+
+ align:start position:0%
+property of
+ 
+
+ align:start position:0%
+property of
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and thus by the theorem one is equal to
+
+ align:start position:0%
+and thus by the theorem one is equal to
+ 
+
+ align:start position:0%
+and thus by the theorem one is equal to
+the supremum of this set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's get a little more
+
+ align:start position:0%
+so let's get a little more
+ 
+
+ align:start position:0%
+so let's get a little more
+familiarity with uh
+
+ align:start position:0%
+familiarity with uh
+ 
+
+ align:start position:0%
+familiarity with uh
+using this uh using soups and imps and
+
+ align:start position:0%
+using this uh using soups and imps and
+ 
+
+ align:start position:0%
+using this uh using soups and imps and
+in particular using that theorem which i
+
+ align:start position:0%
+in particular using that theorem which i
+ 
+
+ align:start position:0%
+in particular using that theorem which i
+stated right there about uh this
+
+ align:start position:0%
+stated right there about uh this
+ 
+
+ align:start position:0%
+stated right there about uh this
+characterization of the soup as being an
+
+ align:start position:0%
+characterization of the soup as being an
+ 
+
+ align:start position:0%
+characterization of the soup as being an
+upper bound and satisfying the second
+
+ align:start position:0%
+upper bound and satisfying the second
+ 
+
+ align:start position:0%
+upper bound and satisfying the second
+property that for
+
+ align:start position:0%
+property that for
+ 
+
+ align:start position:0%
+property that for
+every epsilon positive you can find
+
+ align:start position:0%
+every epsilon positive you can find
+ 
+
+ align:start position:0%
+every epsilon positive you can find
+something in the set which is bigger
+
+ align:start position:0%
+something in the set which is bigger
+ 
+
+ align:start position:0%
+something in the set which is bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+x minus epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to do that let's look at a couple of
+
+ align:start position:0%
+so to do that let's look at a couple of
+ 
+
+ align:start position:0%
+so to do that let's look at a couple of
+different sets
+
+ align:start position:0%
+different sets
+ 
+
+ align:start position:0%
+different sets
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types of subsets of real numbers so for
+
+ align:start position:0%
+types of subsets of real numbers so for
+ 
+
+ align:start position:0%
+types of subsets of real numbers so for
+x uh
+
+ align:start position:0%
+x uh
+ 
+
+ align:start position:0%
+x uh
+a real number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a a subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we define
+
+ align:start position:0%
+we define
+ 
+
+ align:start position:0%
+we define
+two sets
+
+ align:start position:0%
+two sets
+ 
+
+ align:start position:0%
+two sets
+x plus a this is just the shift of a by
+
+ align:start position:0%
+x plus a this is just the shift of a by
+ 
+
+ align:start position:0%
+x plus a this is just the shift of a by
+x so this is the set of all elements of
+
+ align:start position:0%
+x so this is the set of all elements of
+ 
+
+ align:start position:0%
+x so this is the set of all elements of
+the form
+
+ align:start position:0%
+the form
+ 
+
+ align:start position:0%
+the form
+x plus little a
+
+ align:start position:0%
+x plus little a
+ 
+
+ align:start position:0%
+x plus little a
+where little a's and capital a
+
+ align:start position:0%
+where little a's and capital a
+ 
+
+ align:start position:0%
+where little a's and capital a
+and x times a this is the set of all
+
+ align:start position:0%
+and x times a this is the set of all
+ 
+
+ align:start position:0%
+and x times a this is the set of all
+elements of the form
+
+ align:start position:0%
+elements of the form
+ 
+
+ align:start position:0%
+elements of the form
+x times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where a is in
+
+ align:start position:0%
+where a is in
+ 
+
+ align:start position:0%
+where a is in
+capital a so from now on basically
+
+ align:start position:0%
+capital a so from now on basically
+ 
+
+ align:start position:0%
+capital a so from now on basically
+towards the end until almost the end of
+
+ align:start position:0%
+towards the end until almost the end of
+ 
+
+ align:start position:0%
+towards the end until almost the end of
+the course we're working as in subsets
+
+ align:start position:0%
+the course we're working as in subsets
+ 
+
+ align:start position:0%
+the course we're working as in subsets
+of the real numbers okay so these things
+
+ align:start position:0%
+of the real numbers okay so these things
+ 
+
+ align:start position:0%
+of the real numbers okay so these things
+are meaningful
+
+ align:start position:0%
+are meaningful
+ 
+
+ align:start position:0%
+are meaningful
+plus and multiplication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the following theorem
+
+ align:start position:0%
+we have the following theorem
+ 
+
+ align:start position:0%
+we have the following theorem
+so let's let's uh
+
+ align:start position:0%
+so let's let's uh
+ 
+
+ align:start position:0%
+so let's let's uh
+let me state the assumptions and then
+
+ align:start position:0%
+let me state the assumptions and then
+ 
+
+ align:start position:0%
+let me state the assumptions and then
+we'll probably guess the conclusions
+
+ align:start position:0%
+we'll probably guess the conclusions
+ 
+
+ align:start position:0%
+we'll probably guess the conclusions
+if x is a real number
+
+ align:start position:0%
+if x is a real number
+ 
+
+ align:start position:0%
+if x is a real number
+and a is
+
+ align:start position:0%
+and a is
+ 
+
+ align:start position:0%
+and a is
+bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the conclusion is
+
+ align:start position:0%
+then the conclusion is
+ 
+
+ align:start position:0%
+then the conclusion is
+x plus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded above
+
+ align:start position:0%
+is bounded above
+ 
+
+ align:start position:0%
+is bounded above
+and the supremum of this set
+
+ align:start position:0%
+and the supremum of this set
+ 
+
+ align:start position:0%
+and the supremum of this set
+x plus a is equal to x plus
+
+ align:start position:0%
+x plus a is equal to x plus
+ 
+
+ align:start position:0%
+x plus a is equal to x plus
+the supremum of a
+
+ align:start position:0%
+the supremum of a
+ 
+
+ align:start position:0%
+the supremum of a
+you know we should be able to kind of
+
+ align:start position:0%
+you know we should be able to kind of
+ 
+
+ align:start position:0%
+you know we should be able to kind of
+guess this because let's assume
+
+ align:start position:0%
+guess this because let's assume
+ 
+
+ align:start position:0%
+guess this because let's assume
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+this interval here
+
+ align:start position:0%
+this interval here
+ 
+
+ align:start position:0%
+this interval here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that would make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the soup a
+
+ align:start position:0%
+the soup a
+ 
+
+ align:start position:0%
+the soup a
+this let's say right endpoint of this
+
+ align:start position:0%
+this let's say right endpoint of this
+ 
+
+ align:start position:0%
+this let's say right endpoint of this
+interval then when i shift everything by
+
+ align:start position:0%
+interval then when i shift everything by
+ 
+
+ align:start position:0%
+interval then when i shift everything by
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this point soup a shifts to x plus soup
+
+ align:start position:0%
+this point soup a shifts to x plus soup
+ 
+
+ align:start position:0%
+this point soup a shifts to x plus soup
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+which should be the supremum of x plus
+
+ align:start position:0%
+which should be the supremum of x plus
+ 
+
+ align:start position:0%
+which should be the supremum of x plus
+capital a
+
+ align:start position:0%
+capital a
+ 
+
+ align:start position:0%
+capital a
+okay so this is not too
+
+ align:start position:0%
+okay so this is not too
+ 
+
+ align:start position:0%
+okay so this is not too
+surprising
+
+ align:start position:0%
+surprising
+ 
+
+ align:start position:0%
+surprising
+you know there are surprising theorems
+
+ align:start position:0%
+you know there are surprising theorems
+ 
+
+ align:start position:0%
+you know there are surprising theorems
+in analysis we already saw one um
+
+ align:start position:0%
+in analysis we already saw one um
+ 
+
+ align:start position:0%
+in analysis we already saw one um
+at least
+
+ align:start position:0%
+at least
+ 
+
+ align:start position:0%
+at least
+i thought it was surprising hopefully
+
+ align:start position:0%
+i thought it was surprising hopefully
+ 
+
+ align:start position:0%
+i thought it was surprising hopefully
+you found it surprising um
+
+ align:start position:0%
+you found it surprising um
+ 
+
+ align:start position:0%
+you found it surprising um
+about the cardinality of the power set
+
+ align:start position:0%
+about the cardinality of the power set
+ 
+
+ align:start position:0%
+about the cardinality of the power set
+compared to the cardinality of the
+
+ align:start position:0%
+compared to the cardinality of the
+ 
+
+ align:start position:0%
+compared to the cardinality of the
+original set
+
+ align:start position:0%
+original set
+ 
+
+ align:start position:0%
+original set
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you come up with this strange looking
+
+ align:start position:0%
+you come up with this strange looking
+ 
+
+ align:start position:0%
+you come up with this strange looking
+or the proof of that
+
+ align:start position:0%
+or the proof of that
+ 
+
+ align:start position:0%
+or the proof of that
+remember you came up with this strange
+
+ align:start position:0%
+remember you came up with this strange
+ 
+
+ align:start position:0%
+remember you came up with this strange
+looking set which you kind of had to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which in the end basically referenced
+
+ align:start position:0%
+which in the end basically referenced
+ 
+
+ align:start position:0%
+which in the end basically referenced
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in its definition
+
+ align:start position:0%
+in its definition
+ 
+
+ align:start position:0%
+in its definition
+which led to
+
+ align:start position:0%
+which led to
+ 
+
+ align:start position:0%
+which led to
+you know the conclusion we wanted
+
+ align:start position:0%
+you know the conclusion we wanted
+ 
+
+ align:start position:0%
+you know the conclusion we wanted
+okay but this one is not so scary this
+
+ align:start position:0%
+okay but this one is not so scary this
+ 
+
+ align:start position:0%
+okay but this one is not so scary this
+this one you should be able this theorem
+
+ align:start position:0%
+this one you should be able this theorem
+ 
+
+ align:start position:0%
+this one you should be able this theorem
+you should be able to believe
+
+ align:start position:0%
+you should be able to believe
+ 
+
+ align:start position:0%
+you should be able to believe
+and maybe even prove without me telling
+
+ align:start position:0%
+and maybe even prove without me telling
+ 
+
+ align:start position:0%
+and maybe even prove without me telling
+you how to
+
+ align:start position:0%
+you how to
+ 
+
+ align:start position:0%
+you how to
+if not that's fine too
+
+ align:start position:0%
+if not that's fine too
+ 
+
+ align:start position:0%
+if not that's fine too
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+statement is that if x is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus a or x times a sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup of x times a
+
+ align:start position:0%
+soup of x times a
+ 
+
+ align:start position:0%
+soup of x times a
+equals x times
+
+ align:start position:0%
+equals x times
+ 
+
+ align:start position:0%
+equals x times
+the soup of a
+
+ align:start position:0%
+the soup of a
+ 
+
+ align:start position:0%
+the soup of a
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again so if i were to draw a picture
+
+ align:start position:0%
+and again so if i were to draw a picture
+ 
+
+ align:start position:0%
+and again so if i were to draw a picture
+and let's say
+
+ align:start position:0%
+and let's say
+ 
+
+ align:start position:0%
+and let's say
+a is kind of symmetric with respect to 0
+
+ align:start position:0%
+a is kind of symmetric with respect to 0
+ 
+
+ align:start position:0%
+a is kind of symmetric with respect to 0
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's a
+
+ align:start position:0%
+here's a
+ 
+
+ align:start position:0%
+here's a
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+soup of a and i multiply it by x
+
+ align:start position:0%
+soup of a and i multiply it by x
+ 
+
+ align:start position:0%
+soup of a and i multiply it by x
+then this kind of either fattens the
+
+ align:start position:0%
+then this kind of either fattens the
+ 
+
+ align:start position:0%
+then this kind of either fattens the
+interval or makes it smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say i made it smaller now to x
+
+ align:start position:0%
+so let's say i made it smaller now to x
+ 
+
+ align:start position:0%
+so let's say i made it smaller now to x
+times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+x times soup of a would be the supremum
+
+ align:start position:0%
+x times soup of a would be the supremum
+ 
+
+ align:start position:0%
+x times soup of a would be the supremum
+of this set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why x positive well
+
+ align:start position:0%
+why x positive well
+ 
+
+ align:start position:0%
+why x positive well
+the reason is because if i multiply by x
+
+ align:start position:0%
+the reason is because if i multiply by x
+ 
+
+ align:start position:0%
+the reason is because if i multiply by x
+negative this not only shrinks it but it
+
+ align:start position:0%
+negative this not only shrinks it but it
+ 
+
+ align:start position:0%
+negative this not only shrinks it but it
+flips things so in fact there's a
+
+ align:start position:0%
+flips things so in fact there's a
+ 
+
+ align:start position:0%
+flips things so in fact there's a
+statement in the book about if x is
+
+ align:start position:0%
+statement in the book about if x is
+ 
+
+ align:start position:0%
+statement in the book about if x is
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+here you would need to assume a is
+
+ align:start position:0%
+here you would need to assume a is
+ 
+
+ align:start position:0%
+here you would need to assume a is
+bounded below
+
+ align:start position:0%
+bounded below
+ 
+
+ align:start position:0%
+bounded below
+so the corresponding statement for x
+
+ align:start position:0%
+so the corresponding statement for x
+ 
+
+ align:start position:0%
+so the corresponding statement for x
+negative is if x is less than 0 and a is
+
+ align:start position:0%
+negative is if x is less than 0 and a is
+ 
+
+ align:start position:0%
+negative is if x is less than 0 and a is
+bounded below
+
+ align:start position:0%
+bounded below
+ 
+
+ align:start position:0%
+bounded below
+then x times a is bounded above
+
+ align:start position:0%
+then x times a is bounded above
+ 
+
+ align:start position:0%
+then x times a is bounded above
+because multiplying by something
+
+ align:start position:0%
+because multiplying by something
+ 
+
+ align:start position:0%
+because multiplying by something
+negative flips inequalities
+
+ align:start position:0%
+negative flips inequalities
+ 
+
+ align:start position:0%
+negative flips inequalities
+and the soup of x times a
+
+ align:start position:0%
+and the soup of x times a
+ 
+
+ align:start position:0%
+and the soup of x times a
+is equal to minus
+
+ align:start position:0%
+is equal to minus
+ 
+
+ align:start position:0%
+is equal to minus
+x times the inf of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or there's no minus this should be soup
+
+ align:start position:0%
+or there's no minus this should be soup
+ 
+
+ align:start position:0%
+or there's no minus this should be soup
+of x times a is equal to x times the imp
+
+ align:start position:0%
+of x times a is equal to x times the imp
+ 
+
+ align:start position:0%
+of x times a is equal to x times the imp
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's prove um
+
+ align:start position:0%
+all right so let's prove um
+ 
+
+ align:start position:0%
+all right so let's prove um
+these two theorems
+
+ align:start position:0%
+these two theorems
+ 
+
+ align:start position:0%
+these two theorems
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+using um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using this previous theorem that i
+
+ align:start position:0%
+using this previous theorem that i
+ 
+
+ align:start position:0%
+using this previous theorem that i
+stated without proof but you'll prove in
+
+ align:start position:0%
+stated without proof but you'll prove in
+ 
+
+ align:start position:0%
+stated without proof but you'll prove in
+the assignment about how to characterize
+
+ align:start position:0%
+the assignment about how to characterize
+ 
+
+ align:start position:0%
+the assignment about how to characterize
+supes of sets as upper bounds and
+
+ align:start position:0%
+supes of sets as upper bounds and
+ 
+
+ align:start position:0%
+supes of sets as upper bounds and
+satisfying this epsilon property
+
+ align:start position:0%
+satisfying this epsilon property
+ 
+
+ align:start position:0%
+satisfying this epsilon property
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just restate our assumptions
+
+ align:start position:0%
+so let me just restate our assumptions
+ 
+
+ align:start position:0%
+so let me just restate our assumptions
+so suppose x is r
+
+ align:start position:0%
+so suppose x is r
+ 
+
+ align:start position:0%
+so suppose x is r
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is bounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the number super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist in r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because r has the least upper bound
+
+ align:start position:0%
+because r has the least upper bound
+ 
+
+ align:start position:0%
+because r has the least upper bound
+property a is a non-empty subset
+
+ align:start position:0%
+property a is a non-empty subset
+ 
+
+ align:start position:0%
+property a is a non-empty subset
+uh so i should have said that in the so
+
+ align:start position:0%
+uh so i should have said that in the so
+ 
+
+ align:start position:0%
+uh so i should have said that in the so
+all of this is
+
+ align:start position:0%
+all of this is
+ 
+
+ align:start position:0%
+all of this is
+for a non-empty subset of a so that i'm
+
+ align:start position:0%
+for a non-empty subset of a so that i'm
+ 
+
+ align:start position:0%
+for a non-empty subset of a so that i'm
+talking about something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i have a non-empty subset which is
+
+ align:start position:0%
+so i have a non-empty subset which is
+ 
+
+ align:start position:0%
+so i have a non-empty subset which is
+bounded above by the least upper bound
+
+ align:start position:0%
+bounded above by the least upper bound
+ 
+
+ align:start position:0%
+bounded above by the least upper bound
+property the supremum of a exists in r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now i'm going to show that
+
+ align:start position:0%
+so now i'm going to show that
+ 
+
+ align:start position:0%
+so now i'm going to show that
+x times the soup of a satisfies that's
+
+ align:start position:0%
+x times the soup of a satisfies that's
+ 
+
+ align:start position:0%
+x times the soup of a satisfies that's
+an it's an upper bound for x times a
+
+ align:start position:0%
+an it's an upper bound for x times a
+ 
+
+ align:start position:0%
+an it's an upper bound for x times a
+then for all
+
+ align:start position:0%
+then for all
+ 
+
+ align:start position:0%
+then for all
+a in a since
+
+ align:start position:0%
+a in a since
+ 
+
+ align:start position:0%
+a in a since
+soup a is an upper bound for capital a
+
+ align:start position:0%
+soup a is an upper bound for capital a
+ 
+
+ align:start position:0%
+soup a is an upper bound for capital a
+little a is less than or equal to
+
+ align:start position:0%
+little a is less than or equal to
+ 
+
+ align:start position:0%
+little a is less than or equal to
+soup a
+
+ align:start position:0%
+soup a
+ 
+
+ align:start position:0%
+soup a
+which implies that
+
+ align:start position:0%
+which implies that
+ 
+
+ align:start position:0%
+which implies that
+for all a and capital a if i multiply
+
+ align:start position:0%
+for all a and capital a if i multiply
+ 
+
+ align:start position:0%
+for all a and capital a if i multiply
+through by x
+
+ align:start position:0%
+through by x
+ 
+
+ align:start position:0%
+through by x
+i mean if i add x to both sides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+little a is less than or equal to x plus
+
+ align:start position:0%
+little a is less than or equal to x plus
+ 
+
+ align:start position:0%
+little a is less than or equal to x plus
+soup of a
+
+ align:start position:0%
+soup of a
+ 
+
+ align:start position:0%
+soup of a
+which implies that x plus
+
+ align:start position:0%
+which implies that x plus
+ 
+
+ align:start position:0%
+which implies that x plus
+super of a
+
+ align:start position:0%
+super of a
+ 
+
+ align:start position:0%
+super of a
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+an upper bound
+
+ align:start position:0%
+an upper bound
+ 
+
+ align:start position:0%
+an upper bound
+for the set
+
+ align:start position:0%
+for the set
+ 
+
+ align:start position:0%
+for the set
+x plus a
+
+ align:start position:0%
+x plus a
+ 
+
+ align:start position:0%
+x plus a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the first property we wanted
+
+ align:start position:0%
+so that's the first property we wanted
+ 
+
+ align:start position:0%
+so that's the first property we wanted
+to prove of x plus soup a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we'll prove the second property
+
+ align:start position:0%
+now we'll prove the second property
+ 
+
+ align:start position:0%
+now we'll prove the second property
+this epsilon property let epsilon be
+
+ align:start position:0%
+this epsilon property let epsilon be
+ 
+
+ align:start position:0%
+this epsilon property let epsilon be
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the previous theorem
+
+ align:start position:0%
+by the previous theorem
+ 
+
+ align:start position:0%
+by the previous theorem
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+a y in a
+
+ align:start position:0%
+a y in a
+ 
+
+ align:start position:0%
+a y in a
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suit minus a is less than epsilon is
+
+ align:start position:0%
+suit minus a is less than epsilon is
+ 
+
+ align:start position:0%
+suit minus a is less than epsilon is
+less than y is less than or equal to
+
+ align:start position:0%
+less than y is less than or equal to
+ 
+
+ align:start position:0%
+less than y is less than or equal to
+soup a
+
+ align:start position:0%
+soup a
+ 
+
+ align:start position:0%
+soup a
+right this is just
+
+ align:start position:0%
+right this is just
+ 
+
+ align:start position:0%
+right this is just
+from the fact that the supremum of a
+
+ align:start position:0%
+from the fact that the supremum of a
+ 
+
+ align:start position:0%
+from the fact that the supremum of a
+satisfies those two conditions up there
+
+ align:start position:0%
+satisfies those two conditions up there
+ 
+
+ align:start position:0%
+satisfies those two conditions up there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i just add x through all of these
+
+ align:start position:0%
+now i just add x through all of these
+ 
+
+ align:start position:0%
+now i just add x through all of these
+inequalities
+
+ align:start position:0%
+inequalities
+ 
+
+ align:start position:0%
+inequalities
+which implies there exists a y
+
+ align:start position:0%
+which implies there exists a y
+ 
+
+ align:start position:0%
+which implies there exists a y
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus super a
+
+ align:start position:0%
+x plus super a
+ 
+
+ align:start position:0%
+x plus super a
+minus epsilon is less than
+
+ align:start position:0%
+minus epsilon is less than
+ 
+
+ align:start position:0%
+minus epsilon is less than
+x plus y which is less than
+
+ align:start position:0%
+x plus y which is less than
+ 
+
+ align:start position:0%
+x plus y which is less than
+or equal to x plus
+
+ align:start position:0%
+or equal to x plus
+ 
+
+ align:start position:0%
+or equal to x plus
+soup of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that proves the second property because
+
+ align:start position:0%
+that proves the second property because
+ 
+
+ align:start position:0%
+that proves the second property because
+what have i done i found
+
+ align:start position:0%
+what have i done i found
+ 
+
+ align:start position:0%
+what have i done i found
+for every epsilon positive an element of
+
+ align:start position:0%
+for every epsilon positive an element of
+ 
+
+ align:start position:0%
+for every epsilon positive an element of
+the set x plus a
+
+ align:start position:0%
+the set x plus a
+ 
+
+ align:start position:0%
+the set x plus a
+so i'll even i'll restate this
+
+ align:start position:0%
+so i'll even i'll restate this
+ 
+
+ align:start position:0%
+so i'll even i'll restate this
+which implies there exists
+
+ align:start position:0%
+which implies there exists
+ 
+
+ align:start position:0%
+which implies there exists
+an element z in the set x plus capital a
+
+ align:start position:0%
+an element z in the set x plus capital a
+ 
+
+ align:start position:0%
+an element z in the set x plus capital a
+namely x plus y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus soup a
+
+ align:start position:0%
+x plus soup a
+ 
+
+ align:start position:0%
+x plus soup a
+minus epsilon is less than z is less
+
+ align:start position:0%
+minus epsilon is less than z is less
+ 
+
+ align:start position:0%
+minus epsilon is less than z is less
+than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus
+
+ align:start position:0%
+x plus
+ 
+
+ align:start position:0%
+x plus
+soup a
+
+ align:start position:0%
+soup a
+ 
+
+ align:start position:0%
+soup a
+all right and that's the second uh
+
+ align:start position:0%
+all right and that's the second uh
+ 
+
+ align:start position:0%
+all right and that's the second uh
+property which we wanted to prove this
+
+ align:start position:0%
+property which we wanted to prove this
+ 
+
+ align:start position:0%
+property which we wanted to prove this
+epsilon property uh now we've proven it
+
+ align:start position:0%
+epsilon property uh now we've proven it
+ 
+
+ align:start position:0%
+epsilon property uh now we've proven it
+for x plus soup a
+
+ align:start position:0%
+for x plus soup a
+ 
+
+ align:start position:0%
+for x plus soup a
+uh for the set x plus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+soup of x plus a
+
+ align:start position:0%
+soup of x plus a
+ 
+
+ align:start position:0%
+soup of x plus a
+equals x plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we proved that x plus soup a is the
+
+ align:start position:0%
+uh we proved that x plus soup a is the
+ 
+
+ align:start position:0%
+uh we proved that x plus soup a is the
+supremum of x plus a by showing it was
+
+ align:start position:0%
+supremum of x plus a by showing it was
+ 
+
+ align:start position:0%
+supremum of x plus a by showing it was
+an upper bound and it satisfied uh this
+
+ align:start position:0%
+an upper bound and it satisfied uh this
+ 
+
+ align:start position:0%
+an upper bound and it satisfied uh this
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean it's essentially the same proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x times capital a
+
+ align:start position:0%
+x times capital a
+ 
+
+ align:start position:0%
+x times capital a
+you just replace
+
+ align:start position:0%
+you just replace
+ 
+
+ align:start position:0%
+you just replace
+pluses with multiplication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in fact
+
+ align:start position:0%
+so in fact
+ 
+
+ align:start position:0%
+so in fact
+i'm running a little short on time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it gets a little slow moving today
+
+ align:start position:0%
+it gets a little slow moving today
+ 
+
+ align:start position:0%
+it gets a little slow moving today
+so i will not
+
+ align:start position:0%
+so i will not
+ 
+
+ align:start position:0%
+so i will not
+go through
+
+ align:start position:0%
+go through
+ 
+
+ align:start position:0%
+go through
+actually write the proof of
+
+ align:start position:0%
+actually write the proof of
+ 
+
+ align:start position:0%
+actually write the proof of
+the second part simply because
+
+ align:start position:0%
+the second part simply because
+ 
+
+ align:start position:0%
+the second part simply because
+the same logic works
+
+ align:start position:0%
+the same logic works
+ 
+
+ align:start position:0%
+the same logic works
+only now i replace everything by
+
+ align:start position:0%
+only now i replace everything by
+ 
+
+ align:start position:0%
+only now i replace everything by
+multiplication by x instead of addition
+
+ align:start position:0%
+multiplication by x instead of addition
+ 
+
+ align:start position:0%
+multiplication by x instead of addition
+by x
+
+ align:start position:0%
+by x
+ 
+
+ align:start position:0%
+by x
+well almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why not let's go through the proof
+
+ align:start position:0%
+okay why not let's go through the proof
+ 
+
+ align:start position:0%
+okay why not let's go through the proof
+real quick
+
+ align:start position:0%
+real quick
+ 
+
+ align:start position:0%
+real quick
+i just won't spend as much time
+
+ align:start position:0%
+i just won't spend as much time
+ 
+
+ align:start position:0%
+i just won't spend as much time
+explaining
+
+ align:start position:0%
+explaining
+ 
+
+ align:start position:0%
+explaining
+uh stuff so now we want to do
+
+ align:start position:0%
+uh stuff so now we want to do
+ 
+
+ align:start position:0%
+uh stuff so now we want to do
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we want to show x times
+
+ align:start position:0%
+we want to show x times
+ 
+
+ align:start position:0%
+we want to show x times
+um soup a is the supremum of x times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose x is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+soup a again exists in r because a is
+
+ align:start position:0%
+soup a again exists in r because a is
+ 
+
+ align:start position:0%
+soup a again exists in r because a is
+bounded above
+
+ align:start position:0%
+bounded above
+ 
+
+ align:start position:0%
+bounded above
+and because soup a is an upper bound for
+
+ align:start position:0%
+and because soup a is an upper bound for
+ 
+
+ align:start position:0%
+and because soup a is an upper bound for
+capital a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for all a and capital a
+
+ align:start position:0%
+then for all a and capital a
+ 
+
+ align:start position:0%
+then for all a and capital a
+a is less than or equal to
+
+ align:start position:0%
+a is less than or equal to
+ 
+
+ align:start position:0%
+a is less than or equal to
+soup a which implies that
+
+ align:start position:0%
+soup a which implies that
+ 
+
+ align:start position:0%
+soup a which implies that
+for all a and capital a
+
+ align:start position:0%
+for all a and capital a
+ 
+
+ align:start position:0%
+for all a and capital a
+x times little a is less than or equal
+
+ align:start position:0%
+x times little a is less than or equal
+ 
+
+ align:start position:0%
+x times little a is less than or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+x times soup a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies that x times soup a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+an upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for x times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we've proven that x times soup a
+
+ align:start position:0%
+okay so we've proven that x times soup a
+ 
+
+ align:start position:0%
+okay so we've proven that x times soup a
+is an upper bound for the set x times a
+
+ align:start position:0%
+is an upper bound for the set x times a
+ 
+
+ align:start position:0%
+is an upper bound for the set x times a
+we now want to verify this epsilon
+
+ align:start position:0%
+we now want to verify this epsilon
+ 
+
+ align:start position:0%
+we now want to verify this epsilon
+property for x times soup a with respect
+
+ align:start position:0%
+property for x times soup a with respect
+ 
+
+ align:start position:0%
+property for x times soup a with respect
+to the set x times a
+
+ align:start position:0%
+to the set x times a
+ 
+
+ align:start position:0%
+to the set x times a
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let epsilon be positive
+
+ align:start position:0%
+let epsilon be positive
+ 
+
+ align:start position:0%
+let epsilon be positive
+and i'm going to put in brackets again
+
+ align:start position:0%
+and i'm going to put in brackets again
+ 
+
+ align:start position:0%
+and i'm going to put in brackets again
+what we want to do what we want to
+
+ align:start position:0%
+what we want to do what we want to
+ 
+
+ align:start position:0%
+what we want to do what we want to
+define
+
+ align:start position:0%
+define
+ 
+
+ align:start position:0%
+define
+we want to show
+
+ align:start position:0%
+we want to show
+ 
+
+ align:start position:0%
+we want to show
+there exists a z in x times a
+
+ align:start position:0%
+there exists a z in x times a
+ 
+
+ align:start position:0%
+there exists a z in x times a
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+times soup a
+
+ align:start position:0%
+times soup a
+ 
+
+ align:start position:0%
+times soup a
+minus epsilon is less than z
+
+ align:start position:0%
+minus epsilon is less than z
+ 
+
+ align:start position:0%
+minus epsilon is less than z
+c is always less than or equal to x
+
+ align:start position:0%
+c is always less than or equal to x
+ 
+
+ align:start position:0%
+c is always less than or equal to x
+times soup a since we've proven x times
+
+ align:start position:0%
+times soup a since we've proven x times
+ 
+
+ align:start position:0%
+times soup a since we've proven x times
+soup as an upper bound for this set so
+
+ align:start position:0%
+soup as an upper bound for this set so
+ 
+
+ align:start position:0%
+soup as an upper bound for this set so
+i'm not going to
+
+ align:start position:0%
+i'm not going to
+ 
+
+ align:start position:0%
+i'm not going to
+keep writing the second inequality
+
+ align:start position:0%
+keep writing the second inequality
+ 
+
+ align:start position:0%
+keep writing the second inequality
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is what we want to prove
+
+ align:start position:0%
+so this is what we want to prove
+ 
+
+ align:start position:0%
+so this is what we want to prove
+we haven't proven it yet so let epsilon
+
+ align:start position:0%
+we haven't proven it yet so let epsilon
+ 
+
+ align:start position:0%
+we haven't proven it yet so let epsilon
+be positive then
+
+ align:start position:0%
+be positive then
+ 
+
+ align:start position:0%
+be positive then
+just as
+
+ align:start position:0%
+just as
+ 
+
+ align:start position:0%
+just as
+we did in the plus case
+
+ align:start position:0%
+we did in the plus case
+ 
+
+ align:start position:0%
+we did in the plus case
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there exists an element y in a
+
+ align:start position:0%
+there exists an element y in a
+ 
+
+ align:start position:0%
+there exists an element y in a
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+soup a minus
+
+ align:start position:0%
+soup a minus
+ 
+
+ align:start position:0%
+soup a minus
+now here we're going to choose y not
+
+ align:start position:0%
+now here we're going to choose y not
+ 
+
+ align:start position:0%
+now here we're going to choose y not
+exactly for epsilon here
+
+ align:start position:0%
+exactly for epsilon here
+ 
+
+ align:start position:0%
+exactly for epsilon here
+remember the statement for number 2
+
+ align:start position:0%
+remember the statement for number 2
+ 
+
+ align:start position:0%
+remember the statement for number 2
+holds
+
+ align:start position:0%
+holds
+ 
+
+ align:start position:0%
+holds
+for soup a for every epsilon in
+
+ align:start position:0%
+for soup a for every epsilon in
+ 
+
+ align:start position:0%
+for soup a for every epsilon in
+particular i can choose
+
+ align:start position:0%
+particular i can choose
+ 
+
+ align:start position:0%
+particular i can choose
+anything i want here
+
+ align:start position:0%
+anything i want here
+ 
+
+ align:start position:0%
+anything i want here
+and find a y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in between soup a minus whatever i want
+
+ align:start position:0%
+in between soup a minus whatever i want
+ 
+
+ align:start position:0%
+in between soup a minus whatever i want
+here which is positive in soup a
+
+ align:start position:0%
+here which is positive in soup a
+ 
+
+ align:start position:0%
+here which is positive in soup a
+so instead of putting epsilon here like
+
+ align:start position:0%
+so instead of putting epsilon here like
+ 
+
+ align:start position:0%
+so instead of putting epsilon here like
+i did before
+
+ align:start position:0%
+i did before
+ 
+
+ align:start position:0%
+i did before
+i'm going to put epsilon over x which i
+
+ align:start position:0%
+i'm going to put epsilon over x which i
+ 
+
+ align:start position:0%
+i'm going to put epsilon over x which i
+can do because x is positive
+
+ align:start position:0%
+can do because x is positive
+ 
+
+ align:start position:0%
+can do because x is positive
+which means epsilon over x is some
+
+ align:start position:0%
+which means epsilon over x is some
+ 
+
+ align:start position:0%
+which means epsilon over x is some
+positive number
+
+ align:start position:0%
+positive number
+ 
+
+ align:start position:0%
+positive number
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+why did i choose epsilon over x
+
+ align:start position:0%
+why did i choose epsilon over x
+ 
+
+ align:start position:0%
+why did i choose epsilon over x
+because magic happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+that means there exists a y in a
+
+ align:start position:0%
+that means there exists a y in a
+ 
+
+ align:start position:0%
+that means there exists a y in a
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if i multiply
+
+ align:start position:0%
+if i multiply
+ 
+
+ align:start position:0%
+if i multiply
+through by x
+
+ align:start position:0%
+through by x
+ 
+
+ align:start position:0%
+through by x
+i get x times soup
+
+ align:start position:0%
+i get x times soup
+ 
+
+ align:start position:0%
+i get x times soup
+a minus epsilon is less than x times y
+
+ align:start position:0%
+a minus epsilon is less than x times y
+ 
+
+ align:start position:0%
+a minus epsilon is less than x times y
+is less than so i'm going to stop
+
+ align:start position:0%
+is less than so i'm going to stop
+ 
+
+ align:start position:0%
+is less than so i'm going to stop
+writing this inequality because this is
+
+ align:start position:0%
+writing this inequality because this is
+ 
+
+ align:start position:0%
+writing this inequality because this is
+always true because x times soup a is
+
+ align:start position:0%
+always true because x times soup a is
+ 
+
+ align:start position:0%
+always true because x times soup a is
+bigger than or equal to x times y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies there exists a z
+
+ align:start position:0%
+which implies there exists a z
+ 
+
+ align:start position:0%
+which implies there exists a z
+in x times a
+
+ align:start position:0%
+in x times a
+ 
+
+ align:start position:0%
+in x times a
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+z equals x times y where y is from here
+
+ align:start position:0%
+z equals x times y where y is from here
+ 
+
+ align:start position:0%
+z equals x times y where y is from here
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+x times soup a
+
+ align:start position:0%
+x times soup a
+ 
+
+ align:start position:0%
+x times soup a
+minus epsilon is less than z
+
+ align:start position:0%
+minus epsilon is less than z
+ 
+
+ align:start position:0%
+minus epsilon is less than z
+and therefore x times
+
+ align:start position:0%
+and therefore x times
+ 
+
+ align:start position:0%
+and therefore x times
+soup a
+
+ align:start position:0%
+soup a
+ 
+
+ align:start position:0%
+soup a
+satisfies the second epsilon property
+
+ align:start position:0%
+satisfies the second epsilon property
+ 
+
+ align:start position:0%
+satisfies the second epsilon property
+with respect to s given by x times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the end okay
+
+ align:start position:0%
+and that's the end okay
+ 
+
+ align:start position:0%
+and that's the end okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you see that uh
+
+ align:start position:0%
+you see that uh
+ 
+
+ align:start position:0%
+you see that uh
+i wanted this in the end so i chose y to
+
+ align:start position:0%
+i wanted this in the end so i chose y to
+ 
+
+ align:start position:0%
+i wanted this in the end so i chose y to
+give me this slightly
+
+ align:start position:0%
+give me this slightly
+ 
+
+ align:start position:0%
+give me this slightly
+different thing for epsilon over x
+
+ align:start position:0%
+different thing for epsilon over x
+ 
+
+ align:start position:0%
+different thing for epsilon over x
+because in the end i would multiply
+
+ align:start position:0%
+because in the end i would multiply
+ 
+
+ align:start position:0%
+because in the end i would multiply
+through by x
+
+ align:start position:0%
+through by x
+ 
+
+ align:start position:0%
+through by x
+and i wanted this
+
+ align:start position:0%
+and i wanted this
+ 
+
+ align:start position:0%
+and i wanted this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we do proofs for
+
+ align:start position:0%
+we do proofs for
+ 
+
+ align:start position:0%
+we do proofs for
+limits
+
+ align:start position:0%
+limits
+ 
+
+ align:start position:0%
+limits
+uh you'll see we we're always trying to
+
+ align:start position:0%
+uh you'll see we we're always trying to
+ 
+
+ align:start position:0%
+uh you'll see we we're always trying to
+make something less than epsilon so
+
+ align:start position:0%
+make something less than epsilon so
+ 
+
+ align:start position:0%
+make something less than epsilon so
+quite often we'll have to choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something to be less than epsilon over 5
+
+ align:start position:0%
+something to be less than epsilon over 5
+ 
+
+ align:start position:0%
+something to be less than epsilon over 5
+or epsilon over some number
+
+ align:start position:0%
+or epsilon over some number
+ 
+
+ align:start position:0%
+or epsilon over some number
+for everything to work out in the end
+
+ align:start position:0%
+for everything to work out in the end
+ 
+
+ align:start position:0%
+for everything to work out in the end
+just like we did here so that's kind of
+
+ align:start position:0%
+just like we did here so that's kind of
+ 
+
+ align:start position:0%
+just like we did here so that's kind of
+a preview of things to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one last
+
+ align:start position:0%
+and one last
+ 
+
+ align:start position:0%
+and one last
+kind of simple theorem about soups and
+
+ align:start position:0%
+kind of simple theorem about soups and
+ 
+
+ align:start position:0%
+kind of simple theorem about soups and
+imps this really doesn't use that
+
+ align:start position:0%
+imps this really doesn't use that
+ 
+
+ align:start position:0%
+imps this really doesn't use that
+theorem but just basically what the
+
+ align:start position:0%
+theorem but just basically what the
+ 
+
+ align:start position:0%
+theorem but just basically what the
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+soups and imps are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+namely that
+
+ align:start position:0%
+namely that
+ 
+
+ align:start position:0%
+namely that
+if a
+
+ align:start position:0%
+if a
+ 
+
+ align:start position:0%
+if a
+and b
+
+ align:start position:0%
+and b
+ 
+
+ align:start position:0%
+and b
+are subsets of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for all
+
+ align:start position:0%
+and for all
+ 
+
+ align:start position:0%
+and for all
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+rounded above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found it below
+
+ align:start position:0%
+found it below
+ 
+
+ align:start position:0%
+found it below
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for all x y
+
+ align:start position:0%
+for all x y
+ 
+
+ align:start position:0%
+for all x y
+so for all x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and for all y
+
+ align:start position:0%
+and for all y
+ 
+
+ align:start position:0%
+and for all y
+and b
+
+ align:start position:0%
+and b
+ 
+
+ align:start position:0%
+and b
+x is less than or equal to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup of a is less than or equal to
+
+ align:start position:0%
+soup of a is less than or equal to
+ 
+
+ align:start position:0%
+soup of a is less than or equal to
+the infant b okay so picture wise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a everything here sits below
+
+ align:start position:0%
+here's a everything here sits below
+ 
+
+ align:start position:0%
+here's a everything here sits below
+everything in b so b has to be over here
+
+ align:start position:0%
+everything in b so b has to be over here
+ 
+
+ align:start position:0%
+everything in b so b has to be over here
+and therefore the soup of a which is
+
+ align:start position:0%
+and therefore the soup of a which is
+ 
+
+ align:start position:0%
+and therefore the soup of a which is
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+has to be less than or equal to the inf
+
+ align:start position:0%
+has to be less than or equal to the inf
+ 
+
+ align:start position:0%
+has to be less than or equal to the inf
+b which is there that's the picture that
+
+ align:start position:0%
+b which is there that's the picture that
+ 
+
+ align:start position:0%
+b which is there that's the picture that
+goes along with this all right but how
+
+ align:start position:0%
+goes along with this all right but how
+ 
+
+ align:start position:0%
+goes along with this all right but how
+do we actually prove this i mean we have
+
+ align:start position:0%
+do we actually prove this i mean we have
+ 
+
+ align:start position:0%
+do we actually prove this i mean we have
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+the definitions pictures do not suffice
+
+ align:start position:0%
+the definitions pictures do not suffice
+ 
+
+ align:start position:0%
+the definitions pictures do not suffice
+although they inform us they they don't
+
+ align:start position:0%
+although they inform us they they don't
+ 
+
+ align:start position:0%
+although they inform us they they don't
+suffice
+
+ align:start position:0%
+suffice
+ 
+
+ align:start position:0%
+suffice
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is quite simple
+
+ align:start position:0%
+this is quite simple
+ 
+
+ align:start position:0%
+this is quite simple
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm not gonna rewrite the hypotheses
+
+ align:start position:0%
+so i'm not gonna rewrite the hypotheses
+ 
+
+ align:start position:0%
+so i'm not gonna rewrite the hypotheses
+now because uh
+
+ align:start position:0%
+now because uh
+ 
+
+ align:start position:0%
+now because uh
+take a little bit but
+
+ align:start position:0%
+take a little bit but
+ 
+
+ align:start position:0%
+take a little bit but
+um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all x and
+
+ align:start position:0%
+all x and
+ 
+
+ align:start position:0%
+all x and
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+basically what we're going to do is
+
+ align:start position:0%
+basically what we're going to do is
+ 
+
+ align:start position:0%
+basically what we're going to do is
+we're going to take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a soup and then an imph all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at y being b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and a
+
+ align:start position:0%
+for all x and a
+ 
+
+ align:start position:0%
+for all x and a
+x is less than or equal to y
+
+ align:start position:0%
+x is less than or equal to y
+ 
+
+ align:start position:0%
+x is less than or equal to y
+which implies y
+
+ align:start position:0%
+which implies y
+ 
+
+ align:start position:0%
+which implies y
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is an upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or a
+
+ align:start position:0%
+or a
+ 
+
+ align:start position:0%
+or a
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+uh the soup a the
+
+ align:start position:0%
+uh the soup a the
+ 
+
+ align:start position:0%
+uh the soup a the
+supremum of a which is the least upper
+
+ align:start position:0%
+supremum of a which is the least upper
+ 
+
+ align:start position:0%
+supremum of a which is the least upper
+bound has to be
+
+ align:start position:0%
+bound has to be
+ 
+
+ align:start position:0%
+bound has to be
+smaller than or equal to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus we've proven
+
+ align:start position:0%
+thus we've proven
+ 
+
+ align:start position:0%
+thus we've proven
+for all y
+
+ align:start position:0%
+for all y
+ 
+
+ align:start position:0%
+for all y
+and b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup a is less than or equal to y
+
+ align:start position:0%
+soup a is less than or equal to y
+ 
+
+ align:start position:0%
+soup a is less than or equal to y
+which implies that
+
+ align:start position:0%
+which implies that
+ 
+
+ align:start position:0%
+which implies that
+soup a
+
+ align:start position:0%
+soup a
+ 
+
+ align:start position:0%
+soup a
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lower bound
+
+ align:start position:0%
+a lower bound
+ 
+
+ align:start position:0%
+a lower bound
+for b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by that same logic a minute ago so
+
+ align:start position:0%
+and by that same logic a minute ago so
+ 
+
+ align:start position:0%
+and by that same logic a minute ago so
+remember the the infimum of b is the
+
+ align:start position:0%
+remember the the infimum of b is the
+ 
+
+ align:start position:0%
+remember the the infimum of b is the
+greatest lower bound so if i take any
+
+ align:start position:0%
+greatest lower bound so if i take any
+ 
+
+ align:start position:0%
+greatest lower bound so if i take any
+lower bound of b
+
+ align:start position:0%
+lower bound of b
+ 
+
+ align:start position:0%
+lower bound of b
+it has to be less than or equal to the m
+
+ align:start position:0%
+it has to be less than or equal to the m
+ 
+
+ align:start position:0%
+it has to be less than or equal to the m
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+so which implies soup a is less than or
+
+ align:start position:0%
+so which implies soup a is less than or
+ 
+
+ align:start position:0%
+so which implies soup a is less than or
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh we're starting to close out here our
+
+ align:start position:0%
+uh we're starting to close out here our
+ 
+
+ align:start position:0%
+uh we're starting to close out here our
+discussion of or at least our
+
+ align:start position:0%
+discussion of or at least our
+ 
+
+ align:start position:0%
+discussion of or at least our
+discussion of the elementary properties
+
+ align:start position:0%
+discussion of the elementary properties
+ 
+
+ align:start position:0%
+discussion of the elementary properties
+of the real numbers so let me say just a
+
+ align:start position:0%
+of the real numbers so let me say just a
+ 
+
+ align:start position:0%
+of the real numbers so let me say just a
+couple of things about the absolute
+
+ align:start position:0%
+couple of things about the absolute
+ 
+
+ align:start position:0%
+couple of things about the absolute
+value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and let me recall how this is
+
+ align:start position:0%
+okay and let me recall how this is
+ 
+
+ align:start position:0%
+okay and let me recall how this is
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+at least this is how it should have been
+
+ align:start position:0%
+at least this is how it should have been
+ 
+
+ align:start position:0%
+at least this is how it should have been
+defined from your calculus class
+
+ align:start position:0%
+defined from your calculus class
+ 
+
+ align:start position:0%
+defined from your calculus class
+if x is in r we define the absolute
+
+ align:start position:0%
+if x is in r we define the absolute
+ 
+
+ align:start position:0%
+if x is in r we define the absolute
+value of x this is either
+
+ align:start position:0%
+value of x this is either
+ 
+
+ align:start position:0%
+value of x this is either
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+if x is bigger than or equal to 0
+
+ align:start position:0%
+if x is bigger than or equal to 0
+ 
+
+ align:start position:0%
+if x is bigger than or equal to 0
+or minus x
+
+ align:start position:0%
+or minus x
+ 
+
+ align:start position:0%
+or minus x
+if x is less than or equal to 0
+
+ align:start position:0%
+if x is less than or equal to 0
+ 
+
+ align:start position:0%
+if x is less than or equal to 0
+note that these two things agree when x
+
+ align:start position:0%
+note that these two things agree when x
+ 
+
+ align:start position:0%
+note that these two things agree when x
+is zero so that i'm not defining the
+
+ align:start position:0%
+is zero so that i'm not defining the
+ 
+
+ align:start position:0%
+is zero so that i'm not defining the
+absolute value of x to be
+
+ align:start position:0%
+absolute value of x to be
+ 
+
+ align:start position:0%
+absolute value of x to be
+two different things when x equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and you know what is this
+
+ align:start position:0%
+and you know what is this
+ 
+
+ align:start position:0%
+and you know what is this
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+really kind of meant to
+
+ align:start position:0%
+really kind of meant to
+ 
+
+ align:start position:0%
+really kind of meant to
+be it's supposed to be
+
+ align:start position:0%
+be it's supposed to be
+ 
+
+ align:start position:0%
+be it's supposed to be
+kind of it's supposed to measure the
+
+ align:start position:0%
+kind of it's supposed to measure the
+ 
+
+ align:start position:0%
+kind of it's supposed to measure the
+distance from
+
+ align:start position:0%
+distance from
+ 
+
+ align:start position:0%
+distance from
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or it's supposed to
+
+ align:start position:0%
+or it's supposed to
+ 
+
+ align:start position:0%
+or it's supposed to
+represent i shouldn't say uh
+
+ align:start position:0%
+represent i shouldn't say uh
+ 
+
+ align:start position:0%
+represent i shouldn't say uh
+you know is the distance because i
+
+ align:start position:0%
+you know is the distance because i
+ 
+
+ align:start position:0%
+you know is the distance because i
+haven't told you what a distance means
+
+ align:start position:0%
+haven't told you what a distance means
+ 
+
+ align:start position:0%
+haven't told you what a distance means
+but what is what is it supposed to
+
+ align:start position:0%
+but what is what is it supposed to
+ 
+
+ align:start position:0%
+but what is what is it supposed to
+represent it's supposed to represent the
+
+ align:start position:0%
+represent it's supposed to represent the
+ 
+
+ align:start position:0%
+represent it's supposed to represent the
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+uh from x to zero
+
+ align:start position:0%
+uh from x to zero
+ 
+
+ align:start position:0%
+uh from x to zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know why it's always non-negative i
+
+ align:start position:0%
+you know why it's always non-negative i
+ 
+
+ align:start position:0%
+you know why it's always non-negative i
+mean if i have
+
+ align:start position:0%
+mean if i have
+ 
+
+ align:start position:0%
+mean if i have
+x was over here
+
+ align:start position:0%
+x was over here
+ 
+
+ align:start position:0%
+x was over here
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this distance is meant to be absolute
+
+ align:start position:0%
+this distance is meant to be absolute
+ 
+
+ align:start position:0%
+this distance is meant to be absolute
+value of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in fact that's the first thing that
+
+ align:start position:0%
+so in fact that's the first thing that
+ 
+
+ align:start position:0%
+so in fact that's the first thing that
+uh so i'm just gonna prove uh some very
+
+ align:start position:0%
+uh so i'm just gonna prove uh some very
+ 
+
+ align:start position:0%
+uh so i'm just gonna prove uh some very
+simple properties of the absolute value
+
+ align:start position:0%
+simple properties of the absolute value
+ 
+
+ align:start position:0%
+simple properties of the absolute value
+i mean again these properties should not
+
+ align:start position:0%
+i mean again these properties should not
+ 
+
+ align:start position:0%
+i mean again these properties should not
+be surprising to you you should know all
+
+ align:start position:0%
+be surprising to you you should know all
+ 
+
+ align:start position:0%
+be surprising to you you should know all
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but we're trying to get familiar uh
+
+ align:start position:0%
+but we're trying to get familiar uh
+ 
+
+ align:start position:0%
+but we're trying to get familiar uh
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+that's a tough word to say
+
+ align:start position:0%
+that's a tough word to say
+ 
+
+ align:start position:0%
+that's a tough word to say
+familiarities
+
+ align:start position:0%
+familiarities
+ 
+
+ align:start position:0%
+familiarities
+or familiarity with proofs
+
+ align:start position:0%
+or familiarity with proofs
+ 
+
+ align:start position:0%
+or familiarity with proofs
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i'm gonna do as many proofs uh as i
+
+ align:start position:0%
+so i'm gonna do as many proofs uh as i
+ 
+
+ align:start position:0%
+so i'm gonna do as many proofs uh as i
+can for you so
+
+ align:start position:0%
+can for you so
+ 
+
+ align:start position:0%
+can for you so
+the first statement is
+
+ align:start position:0%
+the first statement is
+ 
+
+ align:start position:0%
+the first statement is
+for all x and r
+
+ align:start position:0%
+for all x and r
+ 
+
+ align:start position:0%
+for all x and r
+absolute value of x is bigger than zero
+
+ align:start position:0%
+absolute value of x is bigger than zero
+ 
+
+ align:start position:0%
+absolute value of x is bigger than zero
+bigger than or equal to zero
+
+ align:start position:0%
+bigger than or equal to zero
+ 
+
+ align:start position:0%
+bigger than or equal to zero
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absolute value equals 0
+
+ align:start position:0%
+the absolute value equals 0
+ 
+
+ align:start position:0%
+the absolute value equals 0
+if and only if x equals 0.
+
+ align:start position:0%
+if and only if x equals 0.
+ 
+
+ align:start position:0%
+if and only if x equals 0.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second property is that for all
+
+ align:start position:0%
+the second property is that for all
+ 
+
+ align:start position:0%
+the second property is that for all
+x and r
+
+ align:start position:0%
+x and r
+ 
+
+ align:start position:0%
+x and r
+the absolute value of x equals the
+
+ align:start position:0%
+the absolute value of x equals the
+ 
+
+ align:start position:0%
+the absolute value of x equals the
+absolute value of minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x y and r
+
+ align:start position:0%
+for all x y and r
+ 
+
+ align:start position:0%
+for all x y and r
+if i
+
+ align:start position:0%
+if i
+ 
+
+ align:start position:0%
+if i
+take the
+
+ align:start position:0%
+take the
+ 
+
+ align:start position:0%
+take the
+absolute value of the product this is
+
+ align:start position:0%
+absolute value of the product this is
+ 
+
+ align:start position:0%
+absolute value of the product this is
+equal to the product of the absolute
+
+ align:start position:0%
+equal to the product of the absolute
+ 
+
+ align:start position:0%
+equal to the product of the absolute
+values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and r the absolute value of x
+
+ align:start position:0%
+for all x and r the absolute value of x
+ 
+
+ align:start position:0%
+for all x and r the absolute value of x
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+absolute value of x
+
+ align:start position:0%
+absolute value of x
+ 
+
+ align:start position:0%
+absolute value of x
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fifth property is if x and y is in
+
+ align:start position:0%
+the fifth property is if x and y is in
+ 
+
+ align:start position:0%
+the fifth property is if x and y is in
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is less than or equal to y
+
+ align:start position:0%
+x is less than or equal to y
+ 
+
+ align:start position:0%
+x is less than or equal to y
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+and only if
+
+ align:start position:0%
+and only if
+ 
+
+ align:start position:0%
+and only if
+minus y is less than or equal to x is
+
+ align:start position:0%
+minus y is less than or equal to x is
+ 
+
+ align:start position:0%
+minus y is less than or equal to x is
+less than or equal to y
+
+ align:start position:0%
+less than or equal to y
+ 
+
+ align:start position:0%
+less than or equal to y
+and the sixth property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we'll prove
+
+ align:start position:0%
+that we'll prove
+ 
+
+ align:start position:0%
+that we'll prove
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and r
+
+ align:start position:0%
+for all x and r
+ 
+
+ align:start position:0%
+for all x and r
+x is less than or equal to its absolute
+
+ align:start position:0%
+x is less than or equal to its absolute
+ 
+
+ align:start position:0%
+x is less than or equal to its absolute
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again these are not too surprising
+
+ align:start position:0%
+so again these are not too surprising
+ 
+
+ align:start position:0%
+so again these are not too surprising
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but we'll go through the proofs
+
+ align:start position:0%
+but we'll go through the proofs
+ 
+
+ align:start position:0%
+but we'll go through the proofs
+because that's the point of this class
+
+ align:start position:0%
+because that's the point of this class
+ 
+
+ align:start position:0%
+because that's the point of this class
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later on in life you'll come across some
+
+ align:start position:0%
+later on in life you'll come across some
+ 
+
+ align:start position:0%
+later on in life you'll come across some
+more interesting theorems and then
+
+ align:start position:0%
+more interesting theorems and then
+ 
+
+ align:start position:0%
+more interesting theorems and then
+definitely this one um
+
+ align:start position:0%
+definitely this one um
+ 
+
+ align:start position:0%
+definitely this one um
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if so we're going to prove this first
+
+ align:start position:0%
+if so we're going to prove this first
+ 
+
+ align:start position:0%
+if so we're going to prove this first
+statement that if x is in r the absolute
+
+ align:start position:0%
+statement that if x is in r the absolute
+ 
+
+ align:start position:0%
+statement that if x is in r the absolute
+value of x is bigger than or equal to 0.
+
+ align:start position:0%
+value of x is bigger than or equal to 0.
+ 
+
+ align:start position:0%
+value of x is bigger than or equal to 0.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if x is bigger than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the absolute value of x is by
+
+ align:start position:0%
+then the absolute value of x is by
+ 
+
+ align:start position:0%
+then the absolute value of x is by
+definition equal to x which is bigger
+
+ align:start position:0%
+definition equal to x which is bigger
+ 
+
+ align:start position:0%
+definition equal to x which is bigger
+than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is less than or equal to zero
+
+ align:start position:0%
+if x is less than or equal to zero
+ 
+
+ align:start position:0%
+if x is less than or equal to zero
+then the absolute then
+
+ align:start position:0%
+then the absolute then
+ 
+
+ align:start position:0%
+then the absolute then
+minus x is bigger than or equal to zero
+
+ align:start position:0%
+minus x is bigger than or equal to zero
+ 
+
+ align:start position:0%
+minus x is bigger than or equal to zero
+and by the definition of the absolute
+
+ align:start position:0%
+and by the definition of the absolute
+ 
+
+ align:start position:0%
+and by the definition of the absolute
+value the absolute value of x is equal
+
+ align:start position:0%
+value the absolute value of x is equal
+ 
+
+ align:start position:0%
+value the absolute value of x is equal
+to minus x
+
+ align:start position:0%
+to minus x
+ 
+
+ align:start position:0%
+to minus x
+which is bigger than or equal to zero so
+
+ align:start position:0%
+which is bigger than or equal to zero so
+ 
+
+ align:start position:0%
+which is bigger than or equal to zero so
+that's proven that the absolute value of
+
+ align:start position:0%
+that's proven that the absolute value of
+ 
+
+ align:start position:0%
+that's proven that the absolute value of
+x is always bigger than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's prove this statement
+
+ align:start position:0%
+so now let's prove this statement
+ 
+
+ align:start position:0%
+so now let's prove this statement
+absolute value of x equals zero if and
+
+ align:start position:0%
+absolute value of x equals zero if and
+ 
+
+ align:start position:0%
+absolute value of x equals zero if and
+only if x equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you see an if and only if or two
+
+ align:start position:0%
+so when you see an if and only if or two
+ 
+
+ align:start position:0%
+so when you see an if and only if or two
+arrows here that means there's two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statements you need to prove that this
+
+ align:start position:0%
+statements you need to prove that this
+ 
+
+ align:start position:0%
+statements you need to prove that this
+implies this and this implies this
+
+ align:start position:0%
+implies this and this implies this
+ 
+
+ align:start position:0%
+implies this and this implies this
+so let's start with
+
+ align:start position:0%
+so let's start with
+ 
+
+ align:start position:0%
+so let's start with
+this direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually if and only if there's an easy
+
+ align:start position:0%
+usually if and only if there's an easy
+ 
+
+ align:start position:0%
+usually if and only if there's an easy
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+if x equals 0 then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is clear simply from the definition
+
+ align:start position:0%
+this is clear simply from the definition
+ 
+
+ align:start position:0%
+this is clear simply from the definition
+right then absolute value of x equals x
+
+ align:start position:0%
+right then absolute value of x equals x
+ 
+
+ align:start position:0%
+right then absolute value of x equals x
+equals 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go with
+
+ align:start position:0%
+let's go with
+ 
+
+ align:start position:0%
+let's go with
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other direction so
+
+ align:start position:0%
+other direction so
+ 
+
+ align:start position:0%
+other direction so
+suppose the absolute value of x
+
+ align:start position:0%
+suppose the absolute value of x
+ 
+
+ align:start position:0%
+suppose the absolute value of x
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if x is bigger than or equal to zero
+
+ align:start position:0%
+and if x is bigger than or equal to zero
+ 
+
+ align:start position:0%
+and if x is bigger than or equal to zero
+we get that x is equal to its absolute
+
+ align:start position:0%
+we get that x is equal to its absolute
+ 
+
+ align:start position:0%
+we get that x is equal to its absolute
+value of x is equal to 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is less than or equal to 0
+
+ align:start position:0%
+if x is less than or equal to 0
+ 
+
+ align:start position:0%
+if x is less than or equal to 0
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus x is equal to
+
+ align:start position:0%
+minus x is equal to
+ 
+
+ align:start position:0%
+minus x is equal to
+its absolute value of x
+
+ align:start position:0%
+its absolute value of x
+ 
+
+ align:start position:0%
+its absolute value of x
+which equals to zero or
+
+ align:start position:0%
+which equals to zero or
+ 
+
+ align:start position:0%
+which equals to zero or
+x equals zero so
+
+ align:start position:0%
+x equals zero so
+ 
+
+ align:start position:0%
+x equals zero so
+assuming the absolute value of x is zero
+
+ align:start position:0%
+assuming the absolute value of x is zero
+ 
+
+ align:start position:0%
+assuming the absolute value of x is zero
+we've proven that x equals zero in both
+
+ align:start position:0%
+we've proven that x equals zero in both
+ 
+
+ align:start position:0%
+we've proven that x equals zero in both
+cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that proves the the first
+
+ align:start position:0%
+all right so that proves the the first
+ 
+
+ align:start position:0%
+all right so that proves the the first
+property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we're on to proving uh
+
+ align:start position:0%
+okay so now we're on to proving uh
+ 
+
+ align:start position:0%
+okay so now we're on to proving uh
+number two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number two
+
+ align:start position:0%
+number two
+ 
+
+ align:start position:0%
+number two
+for all x and r the absolute value of x
+
+ align:start position:0%
+for all x and r the absolute value of x
+ 
+
+ align:start position:0%
+for all x and r the absolute value of x
+equals minus x so
+
+ align:start position:0%
+equals minus x so
+ 
+
+ align:start position:0%
+equals minus x so
+we'll do that by again we have to
+
+ align:start position:0%
+we'll do that by again we have to
+ 
+
+ align:start position:0%
+we'll do that by again we have to
+consider two cases x is non-negative or
+
+ align:start position:0%
+consider two cases x is non-negative or
+ 
+
+ align:start position:0%
+consider two cases x is non-negative or
+x is
+
+ align:start position:0%
+x is
+ 
+
+ align:start position:0%
+x is
+non-positive so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is bigger than or equal to zero
+
+ align:start position:0%
+if x is bigger than or equal to zero
+ 
+
+ align:start position:0%
+if x is bigger than or equal to zero
+then minus x is less than or equal to
+
+ align:start position:0%
+then minus x is less than or equal to
+ 
+
+ align:start position:0%
+then minus x is less than or equal to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+which implies that the absolute value of
+
+ align:start position:0%
+which implies that the absolute value of
+ 
+
+ align:start position:0%
+which implies that the absolute value of
+minus x equals minus
+
+ align:start position:0%
+minus x equals minus
+ 
+
+ align:start position:0%
+minus x equals minus
+minus x which equals x which equals
+
+ align:start position:0%
+minus x which equals x which equals
+ 
+
+ align:start position:0%
+minus x which equals x which equals
+the absolute value of x since we're in
+
+ align:start position:0%
+the absolute value of x since we're in
+ 
+
+ align:start position:0%
+the absolute value of x since we're in
+the case that x is not negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is less than or equal to 0
+
+ align:start position:0%
+if x is less than or equal to 0
+ 
+
+ align:start position:0%
+if x is less than or equal to 0
+and minus x is bigger than or equal to 0
+
+ align:start position:0%
+and minus x is bigger than or equal to 0
+ 
+
+ align:start position:0%
+and minus x is bigger than or equal to 0
+which implies that
+
+ align:start position:0%
+which implies that
+ 
+
+ align:start position:0%
+which implies that
+the absolute value of minus x
+
+ align:start position:0%
+the absolute value of minus x
+ 
+
+ align:start position:0%
+the absolute value of minus x
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+minus x which is
+
+ align:start position:0%
+minus x which is
+ 
+
+ align:start position:0%
+minus x which is
+since x is less than or equal to 0 and
+
+ align:start position:0%
+since x is less than or equal to 0 and
+ 
+
+ align:start position:0%
+since x is less than or equal to 0 and
+by the definition of the absolute value
+
+ align:start position:0%
+by the definition of the absolute value
+ 
+
+ align:start position:0%
+by the definition of the absolute value
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+the absolute value of x so that proves
+
+ align:start position:0%
+the absolute value of x so that proves
+ 
+
+ align:start position:0%
+the absolute value of x so that proves
+2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for all x y uh real number x the
+
+ align:start position:0%
+okay so for all x y uh real number x the
+ 
+
+ align:start position:0%
+okay so for all x y uh real number x the
+absolute value of x times y
+
+ align:start position:0%
+absolute value of x times y
+ 
+
+ align:start position:0%
+absolute value of x times y
+is equal to the absolute value of x
+
+ align:start position:0%
+is equal to the absolute value of x
+ 
+
+ align:start position:0%
+is equal to the absolute value of x
+times absolute value of y
+
+ align:start position:0%
+times absolute value of y
+ 
+
+ align:start position:0%
+times absolute value of y
+so we need to consider two cases one of
+
+ align:start position:0%
+so we need to consider two cases one of
+ 
+
+ align:start position:0%
+so we need to consider two cases one of
+them is
+
+ align:start position:0%
+them is
+ 
+
+ align:start position:0%
+them is
+both of them are non-negative
+
+ align:start position:0%
+both of them are non-negative
+ 
+
+ align:start position:0%
+both of them are non-negative
+both of them are non-positive
+
+ align:start position:0%
+both of them are non-positive
+ 
+
+ align:start position:0%
+both of them are non-positive
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+both of them are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or one of them is positive one is one of
+
+ align:start position:0%
+or one of them is positive one is one of
+ 
+
+ align:start position:0%
+or one of them is positive one is one of
+them is
+
+ align:start position:0%
+them is
+ 
+
+ align:start position:0%
+them is
+non-negative
+
+ align:start position:0%
+non-negative
+ 
+
+ align:start position:0%
+non-negative
+or one of them is non-negative one of
+
+ align:start position:0%
+or one of them is non-negative one of
+ 
+
+ align:start position:0%
+or one of them is non-negative one of
+them is non-positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if x is bigger than or equal to zero
+
+ align:start position:0%
+if x is bigger than or equal to zero
+ 
+
+ align:start position:0%
+if x is bigger than or equal to zero
+and y is bigger than or equal to 0
+
+ align:start position:0%
+and y is bigger than or equal to 0
+ 
+
+ align:start position:0%
+and y is bigger than or equal to 0
+and x times y is bigger than or equal to
+
+ align:start position:0%
+and x times y is bigger than or equal to
+ 
+
+ align:start position:0%
+and x times y is bigger than or equal to
+0 which implies x
+
+ align:start position:0%
+0 which implies x
+ 
+
+ align:start position:0%
+0 which implies x
+the absolute value of x
+
+ align:start position:0%
+the absolute value of x
+ 
+
+ align:start position:0%
+the absolute value of x
+times y is equal to x times y
+
+ align:start position:0%
+times y is equal to x times y
+ 
+
+ align:start position:0%
+times y is equal to x times y
+and since x is non-negative that's equal
+
+ align:start position:0%
+and since x is non-negative that's equal
+ 
+
+ align:start position:0%
+and since x is non-negative that's equal
+to its absolute value since y is
+
+ align:start position:0%
+to its absolute value since y is
+ 
+
+ align:start position:0%
+to its absolute value since y is
+non-negative that's equal to its
+
+ align:start position:0%
+non-negative that's equal to its
+ 
+
+ align:start position:0%
+non-negative that's equal to its
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is
+
+ align:start position:0%
+if x is
+ 
+
+ align:start position:0%
+if x is
+bigger than or equal to zero
+
+ align:start position:0%
+bigger than or equal to zero
+ 
+
+ align:start position:0%
+bigger than or equal to zero
+y is less than or equal to zero
+
+ align:start position:0%
+y is less than or equal to zero
+ 
+
+ align:start position:0%
+y is less than or equal to zero
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+minus x times y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bigger than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies that the absolute value of x
+
+ align:start position:0%
+implies that the absolute value of x
+ 
+
+ align:start position:0%
+implies that the absolute value of x
+times y
+
+ align:start position:0%
+times y
+ 
+
+ align:start position:0%
+times y
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's write it this way
+
+ align:start position:0%
+let's write it this way
+ 
+
+ align:start position:0%
+let's write it this way
+this is equal to minus x
+
+ align:start position:0%
+this is equal to minus x
+ 
+
+ align:start position:0%
+this is equal to minus x
+y which is equal to x times
+
+ align:start position:0%
+y which is equal to x times
+ 
+
+ align:start position:0%
+y which is equal to x times
+minus y and since y is negative minus y
+
+ align:start position:0%
+minus y and since y is negative minus y
+ 
+
+ align:start position:0%
+minus y and since y is negative minus y
+is equal to its absolute value and since
+
+ align:start position:0%
+is equal to its absolute value and since
+ 
+
+ align:start position:0%
+is equal to its absolute value and since
+x is non-negative x is equal to its
+
+ align:start position:0%
+x is non-negative x is equal to its
+ 
+
+ align:start position:0%
+x is non-negative x is equal to its
+absolute value so this is equal to
+
+ align:start position:0%
+absolute value so this is equal to
+ 
+
+ align:start position:0%
+absolute value so this is equal to
+that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another piece of chalk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the case that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you might be thinking about what about x
+
+ align:start position:0%
+you might be thinking about what about x
+ 
+
+ align:start position:0%
+you might be thinking about what about x
+negative and y non-negative so y y
+
+ align:start position:0%
+negative and y non-negative so y y
+ 
+
+ align:start position:0%
+negative and y non-negative so y y
+bigger than or equal to 0 x less than or
+
+ align:start position:0%
+bigger than or equal to 0 x less than or
+ 
+
+ align:start position:0%
+bigger than or equal to 0 x less than or
+equal to 0 it's the same proof just
+
+ align:start position:0%
+equal to 0 it's the same proof just
+ 
+
+ align:start position:0%
+equal to 0 it's the same proof just
+exchange x and y so i'm not going to do
+
+ align:start position:0%
+exchange x and y so i'm not going to do
+ 
+
+ align:start position:0%
+exchange x and y so i'm not going to do
+that case
+
+ align:start position:0%
+that case
+ 
+
+ align:start position:0%
+that case
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if x is less than or equal to zero
+
+ align:start position:0%
+if x is less than or equal to zero
+ 
+
+ align:start position:0%
+if x is less than or equal to zero
+y is less than or equal to zero
+
+ align:start position:0%
+y is less than or equal to zero
+ 
+
+ align:start position:0%
+y is less than or equal to zero
+and this implies that
+
+ align:start position:0%
+and this implies that
+ 
+
+ align:start position:0%
+and this implies that
+minus x is bigger than or equal to zero
+
+ align:start position:0%
+minus x is bigger than or equal to zero
+ 
+
+ align:start position:0%
+minus x is bigger than or equal to zero
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+minus y is bigger than or equal to zero
+
+ align:start position:0%
+minus y is bigger than or equal to zero
+ 
+
+ align:start position:0%
+minus y is bigger than or equal to zero
+which by this first case which we've
+
+ align:start position:0%
+which by this first case which we've
+ 
+
+ align:start position:0%
+which by this first case which we've
+proven now apply to minus x and minus y
+
+ align:start position:0%
+proven now apply to minus x and minus y
+ 
+
+ align:start position:0%
+proven now apply to minus x and minus y
+i get that the absolute value of minus x
+
+ align:start position:0%
+i get that the absolute value of minus x
+ 
+
+ align:start position:0%
+i get that the absolute value of minus x
+times minus y
+
+ align:start position:0%
+times minus y
+ 
+
+ align:start position:0%
+times minus y
+which is equal to x times y
+
+ align:start position:0%
+which is equal to x times y
+ 
+
+ align:start position:0%
+which is equal to x times y
+so minus x times minus y is equal to x
+
+ align:start position:0%
+so minus x times minus y is equal to x
+ 
+
+ align:start position:0%
+so minus x times minus y is equal to x
+times y this is equal to the absolute
+
+ align:start position:0%
+times y this is equal to the absolute
+ 
+
+ align:start position:0%
+times y this is equal to the absolute
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+minus x times the absolute value of
+
+ align:start position:0%
+minus x times the absolute value of
+ 
+
+ align:start position:0%
+minus x times the absolute value of
+minus y
+
+ align:start position:0%
+minus y
+ 
+
+ align:start position:0%
+minus y
+and by number two
+
+ align:start position:0%
+and by number two
+ 
+
+ align:start position:0%
+and by number two
+which we've already proven which is that
+
+ align:start position:0%
+which we've already proven which is that
+ 
+
+ align:start position:0%
+which we've already proven which is that
+the absolute value of minus a number is
+
+ align:start position:0%
+the absolute value of minus a number is
+ 
+
+ align:start position:0%
+the absolute value of minus a number is
+equal to the absolute value of the
+
+ align:start position:0%
+equal to the absolute value of the
+ 
+
+ align:start position:0%
+equal to the absolute value of the
+number again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get that
+
+ align:start position:0%
+we get that
+ 
+
+ align:start position:0%
+we get that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for four this is just a special case
+
+ align:start position:0%
+and for four this is just a special case
+ 
+
+ align:start position:0%
+and for four this is just a special case
+of three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take y equals x
+
+ align:start position:0%
+take y equals x
+ 
+
+ align:start position:0%
+take y equals x
+and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for number five
+
+ align:start position:0%
+now for number five
+ 
+
+ align:start position:0%
+now for number five
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's an if and only if so we need to
+
+ align:start position:0%
+it's an if and only if so we need to
+ 
+
+ align:start position:0%
+it's an if and only if so we need to
+prove
+
+ align:start position:0%
+prove
+ 
+
+ align:start position:0%
+prove
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+uh directions namely willow soup
+
+ align:start position:0%
+uh directions namely willow soup
+ 
+
+ align:start position:0%
+uh directions namely willow soup
+we'll assume this and then prove this
+
+ align:start position:0%
+we'll assume this and then prove this
+ 
+
+ align:start position:0%
+we'll assume this and then prove this
+and then assume this and then prove that
+
+ align:start position:0%
+and then assume this and then prove that
+ 
+
+ align:start position:0%
+and then assume this and then prove that
+so suppose so this is the
+
+ align:start position:0%
+so suppose so this is the
+ 
+
+ align:start position:0%
+so suppose so this is the
+this direction meaning suppose our
+
+ align:start position:0%
+this direction meaning suppose our
+ 
+
+ align:start position:0%
+this direction meaning suppose our
+assumption is going to be suppose the
+
+ align:start position:0%
+assumption is going to be suppose the
+ 
+
+ align:start position:0%
+assumption is going to be suppose the
+absolute value of x
+
+ align:start position:0%
+absolute value of x
+ 
+
+ align:start position:0%
+absolute value of x
+is less than or equal to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is bigger than or equal to 0
+
+ align:start position:0%
+x is bigger than or equal to 0
+ 
+
+ align:start position:0%
+x is bigger than or equal to 0
+then this means that
+
+ align:start position:0%
+then this means that
+ 
+
+ align:start position:0%
+then this means that
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if the absolute value of x is less than
+
+ align:start position:0%
+if the absolute value of x is less than
+ 
+
+ align:start position:0%
+if the absolute value of x is less than
+or equal to y that automatically tells
+
+ align:start position:0%
+or equal to y that automatically tells
+ 
+
+ align:start position:0%
+or equal to y that automatically tells
+you y is not negative
+
+ align:start position:0%
+you y is not negative
+ 
+
+ align:start position:0%
+you y is not negative
+so therefore
+
+ align:start position:0%
+so therefore
+ 
+
+ align:start position:0%
+so therefore
+minus y is less than or equal to 0
+
+ align:start position:0%
+minus y is less than or equal to 0
+ 
+
+ align:start position:0%
+minus y is less than or equal to 0
+which is less than or equal to x which
+
+ align:start position:0%
+which is less than or equal to x which
+ 
+
+ align:start position:0%
+which is less than or equal to x which
+equals the absolute value of x which is
+
+ align:start position:0%
+equals the absolute value of x which is
+ 
+
+ align:start position:0%
+equals the absolute value of x which is
+less than or equal to y
+
+ align:start position:0%
+less than or equal to y
+ 
+
+ align:start position:0%
+less than or equal to y
+ie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus y is less than or equal to x is
+
+ align:start position:0%
+minus y is less than or equal to x is
+ 
+
+ align:start position:0%
+minus y is less than or equal to x is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the other case that x is less than
+
+ align:start position:0%
+so in the other case that x is less than
+ 
+
+ align:start position:0%
+so in the other case that x is less than
+or equal to 0.
+
+ align:start position:0%
+or equal to 0.
+ 
+
+ align:start position:0%
+or equal to 0.
+i can apply
+
+ align:start position:0%
+i can apply
+ 
+
+ align:start position:0%
+i can apply
+basically this part which i've already
+
+ align:start position:0%
+basically this part which i've already
+ 
+
+ align:start position:0%
+basically this part which i've already
+proven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and minus x is bigger than or equal to 0
+
+ align:start position:0%
+and minus x is bigger than or equal to 0
+ 
+
+ align:start position:0%
+and minus x is bigger than or equal to 0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the absolute value of minus x which is
+
+ align:start position:0%
+the absolute value of minus x which is
+ 
+
+ align:start position:0%
+the absolute value of minus x which is
+equal to the absolute value of x
+
+ align:start position:0%
+equal to the absolute value of x
+ 
+
+ align:start position:0%
+equal to the absolute value of x
+is less than or equal to y
+
+ align:start position:0%
+is less than or equal to y
+ 
+
+ align:start position:0%
+is less than or equal to y
+which implies by this first case i've
+
+ align:start position:0%
+which implies by this first case i've
+ 
+
+ align:start position:0%
+which implies by this first case i've
+proven applied now to minus x
+
+ align:start position:0%
+proven applied now to minus x
+ 
+
+ align:start position:0%
+proven applied now to minus x
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+that minus y is less than or equal to
+
+ align:start position:0%
+that minus y is less than or equal to
+ 
+
+ align:start position:0%
+that minus y is less than or equal to
+minus x is less than or equal to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+multiplying through by -1 flips all the
+
+ align:start position:0%
+multiplying through by -1 flips all the
+ 
+
+ align:start position:0%
+multiplying through by -1 flips all the
+inequalities
+
+ align:start position:0%
+inequalities
+ 
+
+ align:start position:0%
+inequalities
+uh and also flips the sign which
+
+ align:start position:0%
+uh and also flips the sign which
+ 
+
+ align:start position:0%
+uh and also flips the sign which
+basically means it leaves this
+
+ align:start position:0%
+basically means it leaves this
+ 
+
+ align:start position:0%
+basically means it leaves this
+inequality unchanged if i
+
+ align:start position:0%
+inequality unchanged if i
+ 
+
+ align:start position:0%
+inequality unchanged if i
+replace this by x so multiply through by
+
+ align:start position:0%
+replace this by x so multiply through by
+ 
+
+ align:start position:0%
+replace this by x so multiply through by
+-1 flips the inequalities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and proves what we want to do um so
+
+ align:start position:0%
+and proves what we want to do um so
+ 
+
+ align:start position:0%
+and proves what we want to do um so
+in either case so for the first case we
+
+ align:start position:0%
+in either case so for the first case we
+ 
+
+ align:start position:0%
+in either case so for the first case we
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+wrote down a proof and we reduced the
+
+ align:start position:0%
+wrote down a proof and we reduced the
+ 
+
+ align:start position:0%
+wrote down a proof and we reduced the
+second case x negative
+
+ align:start position:0%
+second case x negative
+ 
+
+ align:start position:0%
+second case x negative
+uh to the first case that we've already
+
+ align:start position:0%
+uh to the first case that we've already
+ 
+
+ align:start position:0%
+uh to the first case that we've already
+proven okay so we've proven that this
+
+ align:start position:0%
+proven okay so we've proven that this
+ 
+
+ align:start position:0%
+proven okay so we've proven that this
+uh inequality the absolute value of x
+
+ align:start position:0%
+uh inequality the absolute value of x
+ 
+
+ align:start position:0%
+uh inequality the absolute value of x
+less than or equal to y
+
+ align:start position:0%
+less than or equal to y
+ 
+
+ align:start position:0%
+less than or equal to y
+implies that um
+
+ align:start position:0%
+implies that um
+ 
+
+ align:start position:0%
+implies that um
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+so now we need to prove the converse
+
+ align:start position:0%
+so now we need to prove the converse
+ 
+
+ align:start position:0%
+so now we need to prove the converse
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the converse direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose minus y is less than or
+
+ align:start position:0%
+suppose minus y is less than or
+ 
+
+ align:start position:0%
+suppose minus y is less than or
+less than or equal to x is less than or
+
+ align:start position:0%
+less than or equal to x is less than or
+ 
+
+ align:start position:0%
+less than or equal to x is less than or
+equal to y and i want to prove the
+
+ align:start position:0%
+equal to y and i want to prove the
+ 
+
+ align:start position:0%
+equal to y and i want to prove the
+absolute value of x is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is bigger than or equal to 0
+
+ align:start position:0%
+if x is bigger than or equal to 0
+ 
+
+ align:start position:0%
+if x is bigger than or equal to 0
+then the absolute value of x is equal to
+
+ align:start position:0%
+then the absolute value of x is equal to
+ 
+
+ align:start position:0%
+then the absolute value of x is equal to
+x which by this inequality
+
+ align:start position:0%
+x which by this inequality
+ 
+
+ align:start position:0%
+x which by this inequality
+is less than or equal to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x is less than or equal to 0
+
+ align:start position:0%
+if x is less than or equal to 0
+ 
+
+ align:start position:0%
+if x is less than or equal to 0
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+minus y is less than or equal to x
+
+ align:start position:0%
+minus y is less than or equal to x
+ 
+
+ align:start position:0%
+minus y is less than or equal to x
+implies that
+
+ align:start position:0%
+implies that
+ 
+
+ align:start position:0%
+implies that
+minus x is less than or equal to y
+
+ align:start position:0%
+minus x is less than or equal to y
+ 
+
+ align:start position:0%
+minus x is less than or equal to y
+and because
+
+ align:start position:0%
+and because
+ 
+
+ align:start position:0%
+and because
+x is negative
+
+ align:start position:0%
+x is negative
+ 
+
+ align:start position:0%
+x is negative
+minus x is equal to its absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore we've proven the absolute
+
+ align:start position:0%
+and therefore we've proven the absolute
+ 
+
+ align:start position:0%
+and therefore we've proven the absolute
+value of x is less than or equal to y
+
+ align:start position:0%
+value of x is less than or equal to y
+ 
+
+ align:start position:0%
+value of x is less than or equal to y
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh we've proven number five
+
+ align:start position:0%
+uh we've proven number five
+ 
+
+ align:start position:0%
+uh we've proven number five
+and number six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh for number six what do we do we just
+
+ align:start position:0%
+uh for number six what do we do we just
+ 
+
+ align:start position:0%
+uh for number six what do we do we just
+take y equals the absolute value of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5 to conclude that
+
+ align:start position:0%
+5 to conclude that
+ 
+
+ align:start position:0%
+5 to conclude that
+x is less than or equal to the absolute
+
+ align:start position:0%
+x is less than or equal to the absolute
+ 
+
+ align:start position:0%
+x is less than or equal to the absolute
+value of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and bigger than or equal to minus the
+
+ align:start position:0%
+and bigger than or equal to minus the
+ 
+
+ align:start position:0%
+and bigger than or equal to minus the
+absolute value of x okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+i'm going to prove one last theorem so
+
+ align:start position:0%
+i'm going to prove one last theorem so
+ 
+
+ align:start position:0%
+i'm going to prove one last theorem so
+this one is actually very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the absolute value it's probably
+
+ align:start position:0%
+about the absolute value it's probably
+ 
+
+ align:start position:0%
+about the absolute value it's probably
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this inequality is is one of the one
+
+ align:start position:0%
+so this inequality is is one of the one
+ 
+
+ align:start position:0%
+so this inequality is is one of the one
+of the most important
+
+ align:start position:0%
+of the most important
+ 
+
+ align:start position:0%
+of the most important
+tools in all of analysis and you get to
+
+ align:start position:0%
+tools in all of analysis and you get to
+ 
+
+ align:start position:0%
+tools in all of analysis and you get to
+see it right here in your first analysis
+
+ align:start position:0%
+see it right here in your first analysis
+ 
+
+ align:start position:0%
+see it right here in your first analysis
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+there's two
+
+ align:start position:0%
+there's two
+ 
+
+ align:start position:0%
+there's two
+basically two other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things will prove at some at one point
+
+ align:start position:0%
+things will prove at some at one point
+ 
+
+ align:start position:0%
+things will prove at some at one point
+which i don't know
+
+ align:start position:0%
+which i don't know
+ 
+
+ align:start position:0%
+which i don't know
+are the two other most important things
+
+ align:start position:0%
+are the two other most important things
+ 
+
+ align:start position:0%
+are the two other most important things
+in analysis this is the triangle
+
+ align:start position:0%
+in analysis this is the triangle
+ 
+
+ align:start position:0%
+in analysis this is the triangle
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+and the other two are
+
+ align:start position:0%
+and the other two are
+ 
+
+ align:start position:0%
+and the other two are
+integration by parts
+
+ align:start position:0%
+integration by parts
+ 
+
+ align:start position:0%
+integration by parts
+and change of variables those three
+
+ align:start position:0%
+and change of variables those three
+ 
+
+ align:start position:0%
+and change of variables those three
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+fuel
+
+ align:start position:0%
+fuel
+ 
+
+ align:start position:0%
+fuel
+the analysis machine so this theorem so
+
+ align:start position:0%
+the analysis machine so this theorem so
+ 
+
+ align:start position:0%
+the analysis machine so this theorem so
+this is the triangle inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it states for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x y and r
+
+ align:start position:0%
+x y and r
+ 
+
+ align:start position:0%
+x y and r
+the absolute value of x plus y is less
+
+ align:start position:0%
+the absolute value of x plus y is less
+ 
+
+ align:start position:0%
+the absolute value of x plus y is less
+than or equal to the absolute value of x
+
+ align:start position:0%
+than or equal to the absolute value of x
+ 
+
+ align:start position:0%
+than or equal to the absolute value of x
+plus the absolute value of y why is it
+
+ align:start position:0%
+plus the absolute value of y why is it
+ 
+
+ align:start position:0%
+plus the absolute value of y why is it
+called the triangle inequality well
+
+ align:start position:0%
+called the triangle inequality well
+ 
+
+ align:start position:0%
+called the triangle inequality well
+let's try to think so although x and y
+
+ align:start position:0%
+let's try to think so although x and y
+ 
+
+ align:start position:0%
+let's try to think so although x and y
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+elements of
+
+ align:start position:0%
+elements of
+ 
+
+ align:start position:0%
+elements of
+the real number line let's instead try
+
+ align:start position:0%
+the real number line let's instead try
+ 
+
+ align:start position:0%
+the real number line let's instead try
+and think of these as two
+
+ align:start position:0%
+and think of these as two
+ 
+
+ align:start position:0%
+and think of these as two
+vectors instead
+
+ align:start position:0%
+vectors instead
+ 
+
+ align:start position:0%
+vectors instead
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's the vector x and then
+
+ align:start position:0%
+so here's the vector x and then
+ 
+
+ align:start position:0%
+so here's the vector x and then
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+actually i'm running out of time so
+
+ align:start position:0%
+actually i'm running out of time so
+ 
+
+ align:start position:0%
+actually i'm running out of time so
+okay so i think we'll we'll stop
+
+ align:start position:0%
+okay so i think we'll we'll stop
+ 
+
+ align:start position:0%
+okay so i think we'll we'll stop
+stop here
\ No newline at end of file
diff --git a/NSHizBK9JD8.txt b/NSHizBK9JD8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d191a1f1400d337efed45e0865684c8fb1278065
--- /dev/null
+++ b/NSHizBK9JD8.txt
@@ -0,0 +1,11469 @@
+align:start position:0%
+ 
+good morning everyone welcome to the
+
+ align:start position:0%
+good morning everyone welcome to the
+ 
+
+ align:start position:0%
+good morning everyone welcome to the
+13th lecture of 606
+
+ align:start position:0%
+13th lecture of 606
+ 
+
+ align:start position:0%
+13th lecture of 606
+just to recap from uh
+
+ align:start position:0%
+just to recap from uh
+ 
+
+ align:start position:0%
+just to recap from uh
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+we've been talking about shortest single
+
+ align:start position:0%
+we've been talking about shortest single
+ 
+
+ align:start position:0%
+we've been talking about shortest single
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+shortest paths on weighted graphs for
+
+ align:start position:0%
+shortest paths on weighted graphs for
+ 
+
+ align:start position:0%
+shortest paths on weighted graphs for
+the past
+
+ align:start position:0%
+the past
+ 
+
+ align:start position:0%
+the past
+two lectures
+
+ align:start position:0%
+two lectures
+ 
+
+ align:start position:0%
+two lectures
+previously we were only talking about
+
+ align:start position:0%
+previously we were only talking about
+ 
+
+ align:start position:0%
+previously we were only talking about
+unweighted graphs
+
+ align:start position:0%
+unweighted graphs
+ 
+
+ align:start position:0%
+unweighted graphs
+and so far up until today
+
+ align:start position:0%
+and so far up until today
+ 
+
+ align:start position:0%
+and so far up until today
+we've talked about three ways to solve
+
+ align:start position:0%
+we've talked about three ways to solve
+ 
+
+ align:start position:0%
+we've talked about three ways to solve
+single source shortest paths
+
+ align:start position:0%
+single source shortest paths
+ 
+
+ align:start position:0%
+single source shortest paths
+on weighted graphs
+
+ align:start position:0%
+on weighted graphs
+ 
+
+ align:start position:0%
+on weighted graphs
+namely the first one use bfs if you can
+
+ align:start position:0%
+namely the first one use bfs if you can
+ 
+
+ align:start position:0%
+namely the first one use bfs if you can
+kind of transform your graph into a
+
+ align:start position:0%
+kind of transform your graph into a
+ 
+
+ align:start position:0%
+kind of transform your graph into a
+linear size graph with
+
+ align:start position:0%
+linear size graph with
+ 
+
+ align:start position:0%
+linear size graph with
+that's unweighted that corresponds to
+
+ align:start position:0%
+that's unweighted that corresponds to
+ 
+
+ align:start position:0%
+that's unweighted that corresponds to
+your weighted problem
+
+ align:start position:0%
+your weighted problem
+ 
+
+ align:start position:0%
+your weighted problem
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+replacing each weighted edge with
+
+ align:start position:0%
+replacing each weighted edge with
+ 
+
+ align:start position:0%
+replacing each weighted edge with
+of weights w with w
+
+ align:start position:0%
+of weights w with w
+ 
+
+ align:start position:0%
+of weights w with w
+single edges now that's only good for
+
+ align:start position:0%
+single edges now that's only good for
+ 
+
+ align:start position:0%
+single edges now that's only good for
+positive weight things
+
+ align:start position:0%
+positive weight things
+ 
+
+ align:start position:0%
+positive weight things
+and if the sum of your weights are small
+
+ align:start position:0%
+and if the sum of your weights are small
+ 
+
+ align:start position:0%
+and if the sum of your weights are small
+right but if the sum of your weights is
+
+ align:start position:0%
+right but if the sum of your weights is
+ 
+
+ align:start position:0%
+right but if the sum of your weights is
+linear in the combinatorial size of your
+
+ align:start position:0%
+linear in the combinatorial size of your
+ 
+
+ align:start position:0%
+linear in the combinatorial size of your
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+v plus e then we can get a linear time
+
+ align:start position:0%
+v plus e then we can get a linear time
+ 
+
+ align:start position:0%
+v plus e then we can get a linear time
+algorithm to solve
+
+ align:start position:0%
+algorithm to solve
+ 
+
+ align:start position:0%
+algorithm to solve
+weighted shortest paths using breadth
+
+ align:start position:0%
+weighted shortest paths using breadth
+ 
+
+ align:start position:0%
+weighted shortest paths using breadth
+first search
+
+ align:start position:0%
+first search
+ 
+
+ align:start position:0%
+first search
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we talked about
+
+ align:start position:0%
+we talked about
+ 
+
+ align:start position:0%
+we talked about
+how we could if we if we
+
+ align:start position:0%
+how we could if we if we
+ 
+
+ align:start position:0%
+how we could if we if we
+the the problem with weighted shortest
+
+ align:start position:0%
+the the problem with weighted shortest
+ 
+
+ align:start position:0%
+the the problem with weighted shortest
+paths is if our weights were negative
+
+ align:start position:0%
+paths is if our weights were negative
+ 
+
+ align:start position:0%
+paths is if our weights were negative
+and there could exist cycles then we
+
+ align:start position:0%
+and there could exist cycles then we
+ 
+
+ align:start position:0%
+and there could exist cycles then we
+could have negative weight cycles and
+
+ align:start position:0%
+could have negative weight cycles and
+ 
+
+ align:start position:0%
+could have negative weight cycles and
+that would be
+
+ align:start position:0%
+that would be
+ 
+
+ align:start position:0%
+that would be
+more difficult to handle because then
+
+ align:start position:0%
+more difficult to handle because then
+ 
+
+ align:start position:0%
+more difficult to handle because then
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+vertices where you have an unbounded
+
+ align:start position:0%
+vertices where you have an unbounded
+ 
+
+ align:start position:0%
+vertices where you have an unbounded
+number of edges you might have to go
+
+ align:start position:0%
+number of edges you might have to go
+ 
+
+ align:start position:0%
+number of edges you might have to go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+for a shortest path there might not be a
+
+ align:start position:0%
+for a shortest path there might not be a
+ 
+
+ align:start position:0%
+for a shortest path there might not be a
+finite length shortest path so
+
+ align:start position:0%
+finite length shortest path so
+ 
+
+ align:start position:0%
+finite length shortest path so
+but in the in the condition where we
+
+ align:start position:0%
+but in the in the condition where we
+ 
+
+ align:start position:0%
+but in the in the condition where we
+didn't have cycles in the graph of
+
+ align:start position:0%
+didn't have cycles in the graph of
+ 
+
+ align:start position:0%
+didn't have cycles in the graph of
+course we couldn't have negative weight
+
+ align:start position:0%
+course we couldn't have negative weight
+ 
+
+ align:start position:0%
+course we couldn't have negative weight
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+so we are also able to do uh
+
+ align:start position:0%
+so we are also able to do uh
+ 
+
+ align:start position:0%
+so we are also able to do uh
+that in linear time by exploiting the
+
+ align:start position:0%
+that in linear time by exploiting the
+ 
+
+ align:start position:0%
+that in linear time by exploiting the
+fact that our vertices could be ordered
+
+ align:start position:0%
+fact that our vertices could be ordered
+ 
+
+ align:start position:0%
+fact that our vertices could be ordered
+in a topological order and that we could
+
+ align:start position:0%
+in a topological order and that we could
+ 
+
+ align:start position:0%
+in a topological order and that we could
+kind of push
+
+ align:start position:0%
+kind of push
+ 
+
+ align:start position:0%
+kind of push
+shortest path information from the
+
+ align:start position:0%
+shortest path information from the
+ 
+
+ align:start position:0%
+shortest path information from the
+furthest one back to the ones forward
+
+ align:start position:0%
+furthest one back to the ones forward
+ 
+
+ align:start position:0%
+furthest one back to the ones forward
+right by relaxing edges forward by
+
+ align:start position:0%
+right by relaxing edges forward by
+ 
+
+ align:start position:0%
+right by relaxing edges forward by
+maintaining this invariant
+
+ align:start position:0%
+maintaining this invariant
+ 
+
+ align:start position:0%
+maintaining this invariant
+that we had shortest paths
+
+ align:start position:0%
+that we had shortest paths
+ 
+
+ align:start position:0%
+that we had shortest paths
+as we were processing these things in
+
+ align:start position:0%
+as we were processing these things in
+ 
+
+ align:start position:0%
+as we were processing these things in
+topological
+
+ align:start position:0%
+topological
+ 
+
+ align:start position:0%
+topological
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+then last time
+
+ align:start position:0%
+then last time
+ 
+
+ align:start position:0%
+then last time
+we were talking about general graphs
+
+ align:start position:0%
+we were talking about general graphs
+ 
+
+ align:start position:0%
+we were talking about general graphs
+graphs that could contain cycles and
+
+ align:start position:0%
+graphs that could contain cycles and
+ 
+
+ align:start position:0%
+graphs that could contain cycles and
+this is our most general algorithm
+
+ align:start position:0%
+this is our most general algorithm
+ 
+
+ align:start position:0%
+this is our most general algorithm
+because if there are negative weight
+
+ align:start position:0%
+because if there are negative weight
+ 
+
+ align:start position:0%
+because if there are negative weight
+cycles bellman ford which we talked
+
+ align:start position:0%
+cycles bellman ford which we talked
+ 
+
+ align:start position:0%
+cycles bellman ford which we talked
+about last time can detect them and in
+
+ align:start position:0%
+about last time can detect them and in
+ 
+
+ align:start position:0%
+about last time can detect them and in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+for any vertex that had a finite weight
+
+ align:start position:0%
+for any vertex that had a finite weight
+ 
+
+ align:start position:0%
+for any vertex that had a finite weight
+shortest path
+
+ align:start position:0%
+shortest path
+ 
+
+ align:start position:0%
+shortest path
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+we could compute that a shortest path
+
+ align:start position:0%
+we could compute that a shortest path
+ 
+
+ align:start position:0%
+we could compute that a shortest path
+for it
+
+ align:start position:0%
+for it
+ 
+
+ align:start position:0%
+for it
+computed systems and for anyone that is
+
+ align:start position:0%
+computed systems and for anyone that is
+ 
+
+ align:start position:0%
+computed systems and for anyone that is
+reachable from a negative weight cycle
+
+ align:start position:0%
+reachable from a negative weight cycle
+ 
+
+ align:start position:0%
+reachable from a negative weight cycle
+not only could we
+
+ align:start position:0%
+not only could we
+ 
+
+ align:start position:0%
+not only could we
+mark it as
+
+ align:start position:0%
+mark it as
+ 
+
+ align:start position:0%
+mark it as
+minus infinity distance but we could
+
+ align:start position:0%
+minus infinity distance but we could
+ 
+
+ align:start position:0%
+minus infinity distance but we could
+also find a negative weight cycle
+
+ align:start position:0%
+also find a negative weight cycle
+ 
+
+ align:start position:0%
+also find a negative weight cycle
+essentially by duplicating our graph to
+
+ align:start position:0%
+essentially by duplicating our graph to
+ 
+
+ align:start position:0%
+essentially by duplicating our graph to
+make it a dag and being able to follow
+
+ align:start position:0%
+make it a dag and being able to follow
+ 
+
+ align:start position:0%
+make it a dag and being able to follow
+pointers back
+
+ align:start position:0%
+pointers back
+ 
+
+ align:start position:0%
+pointers back
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+expanded dag that had multiple layers
+
+ align:start position:0%
+expanded dag that had multiple layers
+ 
+
+ align:start position:0%
+expanded dag that had multiple layers
+okay so that's what we've done up until
+
+ align:start position:0%
+okay so that's what we've done up until
+ 
+
+ align:start position:0%
+okay so that's what we've done up until
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we've gotten linear for some types of
+
+ align:start position:0%
+we've gotten linear for some types of
+ 
+
+ align:start position:0%
+we've gotten linear for some types of
+graphs
+
+ align:start position:0%
+graphs
+ 
+
+ align:start position:0%
+graphs
+and we've gotten kind of quadratic v
+
+ align:start position:0%
+and we've gotten kind of quadratic v
+ 
+
+ align:start position:0%
+and we've gotten kind of quadratic v
+times e
+
+ align:start position:0%
+times e
+ 
+
+ align:start position:0%
+times e
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+general graphs ones that could contain
+
+ align:start position:0%
+general graphs ones that could contain
+ 
+
+ align:start position:0%
+general graphs ones that could contain
+negative cycles now
+
+ align:start position:0%
+negative cycles now
+ 
+
+ align:start position:0%
+negative cycles now
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+bad is this well if the graph is sparse
+
+ align:start position:0%
+bad is this well if the graph is sparse
+ 
+
+ align:start position:0%
+bad is this well if the graph is sparse
+right if if the number of edges in our
+
+ align:start position:0%
+right if if the number of edges in our
+ 
+
+ align:start position:0%
+right if if the number of edges in our
+graph is on the order of v
+
+ align:start position:0%
+graph is on the order of v
+ 
+
+ align:start position:0%
+graph is on the order of v
+then this is quadratic time and v right
+
+ align:start position:0%
+then this is quadratic time and v right
+ 
+
+ align:start position:0%
+then this is quadratic time and v right
+v squared but if this is
+
+ align:start position:0%
+v squared but if this is
+ 
+
+ align:start position:0%
+v squared but if this is
+if it's the graph is dense where we have
+
+ align:start position:0%
+if it's the graph is dense where we have
+ 
+
+ align:start position:0%
+if it's the graph is dense where we have
+quadratic limit like the complete graph
+
+ align:start position:0%
+quadratic limit like the complete graph
+ 
+
+ align:start position:0%
+quadratic limit like the complete graph
+where every edge is present then we have
+
+ align:start position:0%
+where every edge is present then we have
+ 
+
+ align:start position:0%
+where every edge is present then we have
+quadratically many
+
+ align:start position:0%
+quadratically many
+ 
+
+ align:start position:0%
+quadratically many
+edges in our graph in v and so this
+
+ align:start position:0%
+edges in our graph in v and so this
+ 
+
+ align:start position:0%
+edges in our graph in v and so this
+running time is v cubed
+
+ align:start position:0%
+running time is v cubed
+ 
+
+ align:start position:0%
+running time is v cubed
+v cube's not great in terms of its
+
+ align:start position:0%
+v cube's not great in terms of its
+ 
+
+ align:start position:0%
+v cube's not great in terms of its
+running time we would like something
+
+ align:start position:0%
+running time we would like something
+ 
+
+ align:start position:0%
+running time we would like something
+closer to linear
+
+ align:start position:0%
+closer to linear
+ 
+
+ align:start position:0%
+closer to linear
+right and so that's what we're going to
+
+ align:start position:0%
+right and so that's what we're going to
+ 
+
+ align:start position:0%
+right and so that's what we're going to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+if we have uh this restriction where we
+
+ align:start position:0%
+if we have uh this restriction where we
+ 
+
+ align:start position:0%
+if we have uh this restriction where we
+have non-negative weights we can't have
+
+ align:start position:0%
+have non-negative weights we can't have
+ 
+
+ align:start position:0%
+have non-negative weights we can't have
+negative weight cycles
+
+ align:start position:0%
+negative weight cycles
+ 
+
+ align:start position:0%
+negative weight cycles
+right and this is a restriction that
+
+ align:start position:0%
+right and this is a restriction that
+ 
+
+ align:start position:0%
+right and this is a restriction that
+comes up a lot
+
+ align:start position:0%
+comes up a lot
+ 
+
+ align:start position:0%
+comes up a lot
+for many gra graphs you might encounter
+
+ align:start position:0%
+for many gra graphs you might encounter
+ 
+
+ align:start position:0%
+for many gra graphs you might encounter
+right a lot of times you're uh you don't
+
+ align:start position:0%
+right a lot of times you're uh you don't
+ 
+
+ align:start position:0%
+right a lot of times you're uh you don't
+have both positive and negative weights
+
+ align:start position:0%
+have both positive and negative weights
+ 
+
+ align:start position:0%
+have both positive and negative weights
+right i don't have a negative distance
+
+ align:start position:0%
+right i don't have a negative distance
+ 
+
+ align:start position:0%
+right i don't have a negative distance
+to my house right
+
+ align:start position:0%
+to my house right
+ 
+
+ align:start position:0%
+to my house right
+in any metric we have non-negative
+
+ align:start position:0%
+in any metric we have non-negative
+ 
+
+ align:start position:0%
+in any metric we have non-negative
+weights
+
+ align:start position:0%
+weights
+ 
+
+ align:start position:0%
+weights
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+the these things come up a lot and we
+
+ align:start position:0%
+the these things come up a lot and we
+ 
+
+ align:start position:0%
+the these things come up a lot and we
+can actually do quite a bit better since
+
+ align:start position:0%
+can actually do quite a bit better since
+ 
+
+ align:start position:0%
+can actually do quite a bit better since
+there are no negative weight cycles we
+
+ align:start position:0%
+there are no negative weight cycles we
+ 
+
+ align:start position:0%
+there are no negative weight cycles we
+can get almost linear
+
+ align:start position:0%
+can get almost linear
+ 
+
+ align:start position:0%
+can get almost linear
+right it's not going to be quite
+
+ align:start position:0%
+right it's not going to be quite
+ 
+
+ align:start position:0%
+right it's not going to be quite
+v plus e
+
+ align:start position:0%
+v plus e
+ 
+
+ align:start position:0%
+v plus e
+as you see up here
+
+ align:start position:0%
+as you see up here
+ 
+
+ align:start position:0%
+as you see up here
+on the slide we're going to get
+
+ align:start position:0%
+on the slide we're going to get
+ 
+
+ align:start position:0%
+on the slide we're going to get
+something very close
+
+ align:start position:0%
+something very close
+ 
+
+ align:start position:0%
+something very close
+it's v plus e but on the v term we have
+
+ align:start position:0%
+it's v plus e but on the v term we have
+ 
+
+ align:start position:0%
+it's v plus e but on the v term we have
+this logarithmic factor in v which
+
+ align:start position:0%
+this logarithmic factor in v which
+ 
+
+ align:start position:0%
+this logarithmic factor in v which
+remember for all intents and purposes
+
+ align:start position:0%
+remember for all intents and purposes
+ 
+
+ align:start position:0%
+remember for all intents and purposes
+this log of that thing in real life is
+
+ align:start position:0%
+this log of that thing in real life is
+ 
+
+ align:start position:0%
+this log of that thing in real life is
+not going to be bigger than like a
+
+ align:start position:0%
+not going to be bigger than like a
+ 
+
+ align:start position:0%
+not going to be bigger than like a
+factor of 30 or something like that
+
+ align:start position:0%
+factor of 30 or something like that
+ 
+
+ align:start position:0%
+factor of 30 or something like that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+maybe 60 but it's a it's a small number
+
+ align:start position:0%
+maybe 60 but it's a it's a small number
+ 
+
+ align:start position:0%
+maybe 60 but it's a it's a small number
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+this is actually pretty good performance
+
+ align:start position:0%
+this is actually pretty good performance
+ 
+
+ align:start position:0%
+this is actually pretty good performance
+it's almost linear that's what i'm
+
+ align:start position:0%
+it's almost linear that's what i'm
+ 
+
+ align:start position:0%
+it's almost linear that's what i'm
+saying almost linear here and that's
+
+ align:start position:0%
+saying almost linear here and that's
+ 
+
+ align:start position:0%
+saying almost linear here and that's
+what we're going to try to do today
+
+ align:start position:0%
+what we're going to try to do today
+ 
+
+ align:start position:0%
+what we're going to try to do today
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how do we do this well i'm going to make
+
+ align:start position:0%
+how do we do this well i'm going to make
+ 
+
+ align:start position:0%
+how do we do this well i'm going to make
+two observations here first off
+
+ align:start position:0%
+two observations here first off
+ 
+
+ align:start position:0%
+two observations here first off
+our idea
+
+ align:start position:0%
+our idea
+ 
+
+ align:start position:0%
+our idea
+is going to be to generalize the notion
+
+ align:start position:0%
+is going to be to generalize the notion
+ 
+
+ align:start position:0%
+is going to be to generalize the notion
+of bfs right when we had bfs we split up
+
+ align:start position:0%
+of bfs right when we had bfs we split up
+ 
+
+ align:start position:0%
+of bfs right when we had bfs we split up
+our graph
+
+ align:start position:0%
+our graph
+ 
+
+ align:start position:0%
+our graph
+to solve unweighted short uh solve
+
+ align:start position:0%
+to solve unweighted short uh solve
+ 
+
+ align:start position:0%
+to solve unweighted short uh solve
+weighted shortest paths with bfs we
+
+ align:start position:0%
+weighted shortest paths with bfs we
+ 
+
+ align:start position:0%
+weighted shortest paths with bfs we
+could take our positive edge weights
+
+ align:start position:0%
+could take our positive edge weights
+ 
+
+ align:start position:0%
+could take our positive edge weights
+break them up into individual
+
+ align:start position:0%
+break them up into individual
+ 
+
+ align:start position:0%
+break them up into individual
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+but if the the total weight of our edges
+
+ align:start position:0%
+but if the the total weight of our edges
+ 
+
+ align:start position:0%
+but if the the total weight of our edges
+was large
+
+ align:start position:0%
+was large
+ 
+
+ align:start position:0%
+was large
+then we'd have a problem because now
+
+ align:start position:0%
+then we'd have a problem because now
+ 
+
+ align:start position:0%
+then we'd have a problem because now
+we've expanded the size of our graph
+
+ align:start position:0%
+we've expanded the size of our graph
+ 
+
+ align:start position:0%
+we've expanded the size of our graph
+right this is the same issue that we had
+
+ align:start position:0%
+right this is the same issue that we had
+ 
+
+ align:start position:0%
+right this is the same issue that we had
+with something like radix sort where
+
+ align:start position:0%
+with something like radix sort where
+ 
+
+ align:start position:0%
+with something like radix sort where
+we don't want our algorithm to run in
+
+ align:start position:0%
+we don't want our algorithm to run in
+ 
+
+ align:start position:0%
+we don't want our algorithm to run in
+the size of the numbers in our input
+
+ align:start position:0%
+the size of the numbers in our input
+ 
+
+ align:start position:0%
+the size of the numbers in our input
+we want our algorithm to run in the
+
+ align:start position:0%
+we want our algorithm to run in the
+ 
+
+ align:start position:0%
+we want our algorithm to run in the
+number of numbers in our input right
+
+ align:start position:0%
+number of numbers in our input right
+ 
+
+ align:start position:0%
+number of numbers in our input right
+this is the difference between n and u
+
+ align:start position:0%
+this is the difference between n and u
+ 
+
+ align:start position:0%
+this is the difference between n and u
+right uh back when we were talking about
+
+ align:start position:0%
+right uh back when we were talking about
+ 
+
+ align:start position:0%
+right uh back when we were talking about
+data structures here
+
+ align:start position:0%
+data structures here
+ 
+
+ align:start position:0%
+data structures here
+if the size of our weights are large
+
+ align:start position:0%
+if the size of our weights are large
+ 
+
+ align:start position:0%
+if the size of our weights are large
+compared to v and e
+
+ align:start position:0%
+compared to v and e
+ 
+
+ align:start position:0%
+compared to v and e
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we can't doing this expansion is going
+
+ align:start position:0%
+we can't doing this expansion is going
+ 
+
+ align:start position:0%
+we can't doing this expansion is going
+to be difficult but if we had
+
+ align:start position:0%
+to be difficult but if we had
+ 
+
+ align:start position:0%
+to be difficult but if we had
+say some graph
+
+ align:start position:0%
+say some graph
+ 
+
+ align:start position:0%
+say some graph
+this is my graph g
+
+ align:start position:0%
+this is my graph g
+ 
+
+ align:start position:0%
+this is my graph g
+and we had a source vertex s
+
+ align:start position:0%
+and we had a source vertex s
+ 
+
+ align:start position:0%
+and we had a source vertex s
+the idea here
+
+ align:start position:0%
+the idea here
+ 
+
+ align:start position:0%
+the idea here
+is going to still be to try to grow
+
+ align:start position:0%
+is going to still be to try to grow
+ 
+
+ align:start position:0%
+is going to still be to try to grow
+you know a frontier of increasing
+
+ align:start position:0%
+you know a frontier of increasing
+ 
+
+ align:start position:0%
+you know a frontier of increasing
+distance from my source
+
+ align:start position:0%
+distance from my source
+ 
+
+ align:start position:0%
+distance from my source
+and try to maintain all of the things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+within a certain distance from my source
+
+ align:start position:0%
+within a certain distance from my source
+ 
+
+ align:start position:0%
+within a certain distance from my source
+so that's the idea grow a sphere
+
+ align:start position:0%
+so that's the idea grow a sphere
+ 
+
+ align:start position:0%
+so that's the idea grow a sphere
+centered at my source repeatedly explore
+
+ align:start position:0%
+centered at my source repeatedly explore
+ 
+
+ align:start position:0%
+centered at my source repeatedly explore
+closer vertices
+
+ align:start position:0%
+closer vertices
+ 
+
+ align:start position:0%
+closer vertices
+before i get to further ones but
+
+ align:start position:0%
+before i get to further ones but
+ 
+
+ align:start position:0%
+before i get to further ones but
+how can i explore closer vertices
+
+ align:start position:0%
+how can i explore closer vertices
+ 
+
+ align:start position:0%
+how can i explore closer vertices
+if i don't know the distances beforehand
+
+ align:start position:0%
+if i don't know the distances beforehand
+ 
+
+ align:start position:0%
+if i don't know the distances beforehand
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is kind of seems like a circular
+
+ align:start position:0%
+this is kind of seems like a circular
+ 
+
+ align:start position:0%
+this is kind of seems like a circular
+logic right i'm going to use the
+
+ align:start position:0%
+logic right i'm going to use the
+ 
+
+ align:start position:0%
+logic right i'm going to use the
+distance to my things to compute the
+
+ align:start position:0%
+distance to my things to compute the
+ 
+
+ align:start position:0%
+distance to my things to compute the
+distances to my things that doesn't work
+
+ align:start position:0%
+distances to my things that doesn't work
+ 
+
+ align:start position:0%
+distances to my things that doesn't work
+so well right
+
+ align:start position:0%
+so well right
+ 
+
+ align:start position:0%
+so well right
+so how do we do this well the idea here
+
+ align:start position:0%
+so how do we do this well the idea here
+ 
+
+ align:start position:0%
+so how do we do this well the idea here
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+gradually compute the distances compute
+
+ align:start position:0%
+gradually compute the distances compute
+ 
+
+ align:start position:0%
+gradually compute the distances compute
+the distances as we go
+
+ align:start position:0%
+the distances as we go
+ 
+
+ align:start position:0%
+the distances as we go
+so that we maintain this property now
+
+ align:start position:0%
+so that we maintain this property now
+ 
+
+ align:start position:0%
+so that we maintain this property now
+this property this idea
+
+ align:start position:0%
+this property this idea
+ 
+
+ align:start position:0%
+this property this idea
+wouldn't work
+
+ align:start position:0%
+wouldn't work
+ 
+
+ align:start position:0%
+wouldn't work
+necessarily in the context of negative
+
+ align:start position:0%
+necessarily in the context of negative
+ 
+
+ align:start position:0%
+necessarily in the context of negative
+edge weights
+
+ align:start position:0%
+edge weights
+ 
+
+ align:start position:0%
+edge weights
+right here we have this
+
+ align:start position:0%
+right here we have this
+ 
+
+ align:start position:0%
+right here we have this
+growing frontier this ball around my
+
+ align:start position:0%
+growing frontier this ball around my
+ 
+
+ align:start position:0%
+growing frontier this ball around my
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+as i grow my thing
+
+ align:start position:0%
+as i grow my thing
+ 
+
+ align:start position:0%
+as i grow my thing
+these things are at further and further
+
+ align:start position:0%
+these things are at further and further
+ 
+
+ align:start position:0%
+these things are at further and further
+distance right because any edge from
+
+ align:start position:0%
+distance right because any edge from
+ 
+
+ align:start position:0%
+distance right because any edge from
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+back here as i'm growing my ball of
+
+ align:start position:0%
+back here as i'm growing my ball of
+ 
+
+ align:start position:0%
+back here as i'm growing my ball of
+certain distance these things are
+
+ align:start position:0%
+certain distance these things are
+ 
+
+ align:start position:0%
+certain distance these things are
+outside that distance right we're kind
+
+ align:start position:0%
+outside that distance right we're kind
+ 
+
+ align:start position:0%
+outside that distance right we're kind
+of using
+
+ align:start position:0%
+of using
+ 
+
+ align:start position:0%
+of using
+a key observation here here's my
+
+ align:start position:0%
+a key observation here here's my
+ 
+
+ align:start position:0%
+a key observation here here's my
+observation one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+weights
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh greater than or equal to zero
+
+ align:start position:0%
+uh greater than or equal to zero
+ 
+
+ align:start position:0%
+uh greater than or equal to zero
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shortest paths
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe maybe weakly monotonically
+
+ align:start position:0%
+maybe maybe weakly monotonically
+ 
+
+ align:start position:0%
+maybe maybe weakly monotonically
+increase right
+
+ align:start position:0%
+increase right
+ 
+
+ align:start position:0%
+increase right
+if there are zero weight edges but in
+
+ align:start position:0%
+if there are zero weight edges but in
+ 
+
+ align:start position:0%
+if there are zero weight edges but in
+general if i had a path going from s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to some v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's going through some
+
+ align:start position:0%
+and it's going through some
+ 
+
+ align:start position:0%
+and it's going through some
+vertex u
+
+ align:start position:0%
+vertex u
+ 
+
+ align:start position:0%
+vertex u
+right i have some shortest path this is
+
+ align:start position:0%
+right i have some shortest path this is
+ 
+
+ align:start position:0%
+right i have some shortest path this is
+the shortest path from s to v
+
+ align:start position:0%
+the shortest path from s to v
+ 
+
+ align:start position:0%
+the shortest path from s to v
+and it goes through some point u some
+
+ align:start position:0%
+and it goes through some point u some
+ 
+
+ align:start position:0%
+and it goes through some point u some
+vertex u
+
+ align:start position:0%
+vertex u
+ 
+
+ align:start position:0%
+vertex u
+then this monotonicity more specifically
+
+ align:start position:0%
+then this monotonicity more specifically
+ 
+
+ align:start position:0%
+then this monotonicity more specifically
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+the shortest path from
+
+ align:start position:0%
+the shortest path from
+ 
+
+ align:start position:0%
+the shortest path from
+s to u
+
+ align:start position:0%
+s to u
+ 
+
+ align:start position:0%
+s to u
+and the shortest path from s to v
+
+ align:start position:0%
+and the shortest path from s to v
+ 
+
+ align:start position:0%
+and the shortest path from s to v
+which is this whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+how do these relate to each other
+
+ align:start position:0%
+how do these relate to each other
+ 
+
+ align:start position:0%
+how do these relate to each other
+if this is along that path
+
+ align:start position:0%
+if this is along that path
+ 
+
+ align:start position:0%
+if this is along that path
+then this has to be at least as large
+
+ align:start position:0%
+then this has to be at least as large
+ 
+
+ align:start position:0%
+then this has to be at least as large
+as the sub-path right because all of
+
+ align:start position:0%
+as the sub-path right because all of
+ 
+
+ align:start position:0%
+as the sub-path right because all of
+these the weight of this path cannot be
+
+ align:start position:0%
+these the weight of this path cannot be
+ 
+
+ align:start position:0%
+these the weight of this path cannot be
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+so that's the thing that dijkstra is
+
+ align:start position:0%
+so that's the thing that dijkstra is
+ 
+
+ align:start position:0%
+so that's the thing that dijkstra is
+going to exploit
+
+ align:start position:0%
+going to exploit
+ 
+
+ align:start position:0%
+going to exploit
+it essentially means that when i'm
+
+ align:start position:0%
+it essentially means that when i'm
+ 
+
+ align:start position:0%
+it essentially means that when i'm
+expanding this frontier
+
+ align:start position:0%
+expanding this frontier
+ 
+
+ align:start position:0%
+expanding this frontier
+of distance away from x
+
+ align:start position:0%
+of distance away from x
+ 
+
+ align:start position:0%
+of distance away from x
+it's possible if i had negative weight
+
+ align:start position:0%
+it's possible if i had negative weight
+ 
+
+ align:start position:0%
+it's possible if i had negative weight
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this line
+
+ align:start position:0%
+this line
+ 
+
+ align:start position:0%
+this line
+if i had some very negative weight going
+
+ align:start position:0%
+if i had some very negative weight going
+ 
+
+ align:start position:0%
+if i had some very negative weight going
+from a vertex here to a vertex here
+
+ align:start position:0%
+from a vertex here to a vertex here
+ 
+
+ align:start position:0%
+from a vertex here to a vertex here
+this vertex
+
+ align:start position:0%
+this vertex
+ 
+
+ align:start position:0%
+this vertex
+could be within
+
+ align:start position:0%
+could be within
+ 
+
+ align:start position:0%
+could be within
+this boundary
+
+ align:start position:0%
+this boundary
+ 
+
+ align:start position:0%
+this boundary
+maybe maybe if this distance is x this
+
+ align:start position:0%
+maybe maybe if this distance is x this
+ 
+
+ align:start position:0%
+maybe maybe if this distance is x this
+guy could be within x right my my
+
+ align:start position:0%
+guy could be within x right my my
+ 
+
+ align:start position:0%
+guy could be within x right my my
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the things that are within distance x of
+
+ align:start position:0%
+the things that are within distance x of
+ 
+
+ align:start position:0%
+the things that are within distance x of
+s might not be all contained there could
+
+ align:start position:0%
+s might not be all contained there could
+ 
+
+ align:start position:0%
+s might not be all contained there could
+be a path from
+
+ align:start position:0%
+be a path from
+ 
+
+ align:start position:0%
+be a path from
+here to this
+
+ align:start position:0%
+here to this
+ 
+
+ align:start position:0%
+here to this
+other vertex with distance x
+
+ align:start position:0%
+other vertex with distance x
+ 
+
+ align:start position:0%
+other vertex with distance x
+that doesn't have this property because
+
+ align:start position:0%
+that doesn't have this property because
+ 
+
+ align:start position:0%
+that doesn't have this property because
+i could decrease in distance along the
+
+ align:start position:0%
+i could decrease in distance along the
+ 
+
+ align:start position:0%
+i could decrease in distance along the
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+okay so that's the first observation
+
+ align:start position:0%
+okay so that's the first observation
+ 
+
+ align:start position:0%
+okay so that's the first observation
+second observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's see if we can piggyback on
+
+ align:start position:0%
+well let's see if we can piggyback on
+ 
+
+ align:start position:0%
+well let's see if we can piggyback on
+dag
+
+ align:start position:0%
+dag
+ 
+
+ align:start position:0%
+dag
+relaxation right
+
+ align:start position:0%
+relaxation right
+ 
+
+ align:start position:0%
+relaxation right
+i claim to you that
+
+ align:start position:0%
+i claim to you that
+ 
+
+ align:start position:0%
+i claim to you that
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+single source shortest paths faster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we're given
+
+ align:start position:0%
+if we're given
+ 
+
+ align:start position:0%
+if we're given
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance beforehand
+
+ align:start position:0%
+distance beforehand
+ 
+
+ align:start position:0%
+distance beforehand
+distance from s
+
+ align:start position:0%
+distance from s
+ 
+
+ align:start position:0%
+distance from s
+right so here's the idea i'm not going
+
+ align:start position:0%
+right so here's the idea i'm not going
+ 
+
+ align:start position:0%
+right so here's the idea i'm not going
+to give you the distances to all these
+
+ align:start position:0%
+to give you the distances to all these
+ 
+
+ align:start position:0%
+to give you the distances to all these
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead i'm going to give you the
+
+ align:start position:0%
+instead i'm going to give you the
+ 
+
+ align:start position:0%
+instead i'm going to give you the
+order of the vertices in some increasing
+
+ align:start position:0%
+order of the vertices in some increasing
+ 
+
+ align:start position:0%
+order of the vertices in some increasing
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+from s
+
+ align:start position:0%
+from s
+ 
+
+ align:start position:0%
+from s
+okay so basically i'm saying if i had
+
+ align:start position:0%
+okay so basically i'm saying if i had
+ 
+
+ align:start position:0%
+okay so basically i'm saying if i had
+some i don't know here's a graph uh
+
+ align:start position:0%
+some i don't know here's a graph uh
+ 
+
+ align:start position:0%
+some i don't know here's a graph uh
+let's see if i can remember
+
+ align:start position:0%
+let's see if i can remember
+ 
+
+ align:start position:0%
+let's see if i can remember
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and i'm gonna put some edges on
+
+ align:start position:0%
+okay and i'm gonna put some edges on
+ 
+
+ align:start position:0%
+okay and i'm gonna put some edges on
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and i'm going to call these
+
+ align:start position:0%
+okay and i'm going to call these
+ 
+
+ align:start position:0%
+okay and i'm going to call these
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+0 1 2
+
+ align:start position:0%
+0 1 2
+ 
+
+ align:start position:0%
+0 1 2
+3 and 4. okay so here's a graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe i put some edge weights on here
+
+ align:start position:0%
+maybe i put some edge weights on here
+ 
+
+ align:start position:0%
+maybe i put some edge weights on here
+i'm going to say this one is
+
+ align:start position:0%
+i'm going to say this one is
+ 
+
+ align:start position:0%
+i'm going to say this one is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+this one is 2
+
+ align:start position:0%
+this one is 2
+ 
+
+ align:start position:0%
+this one is 2
+this one is 3 this is
+
+ align:start position:0%
+this one is 3 this is
+ 
+
+ align:start position:0%
+this one is 3 this is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+this is 1 this is 0 and this is 0.
+
+ align:start position:0%
+this is 1 this is 0 and this is 0.
+ 
+
+ align:start position:0%
+this is 1 this is 0 and this is 0.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+from vertex one two
+
+ align:start position:0%
+from vertex one two
+ 
+
+ align:start position:0%
+from vertex one two
+two uh that was a two for
+
+ align:start position:0%
+two uh that was a two for
+ 
+
+ align:start position:0%
+two uh that was a two for
+the labeling of that vertex
+
+ align:start position:0%
+the labeling of that vertex
+ 
+
+ align:start position:0%
+the labeling of that vertex
+that edge is zero weight okay so here's
+
+ align:start position:0%
+that edge is zero weight okay so here's
+ 
+
+ align:start position:0%
+that edge is zero weight okay so here's
+a weighted graph
+
+ align:start position:0%
+a weighted graph
+ 
+
+ align:start position:0%
+a weighted graph
+okay and i don't necessarily know
+
+ align:start position:0%
+okay and i don't necessarily know
+ 
+
+ align:start position:0%
+okay and i don't necessarily know
+i could use bellman ford to find
+
+ align:start position:0%
+i could use bellman ford to find
+ 
+
+ align:start position:0%
+i could use bellman ford to find
+shortest paths from this vertex
+
+ align:start position:0%
+shortest paths from this vertex
+ 
+
+ align:start position:0%
+shortest paths from this vertex
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the idea here is i'm not going to
+
+ align:start position:0%
+but the idea here is i'm not going to
+ 
+
+ align:start position:0%
+but the idea here is i'm not going to
+give you shortest paths i'm going to try
+
+ align:start position:0%
+give you shortest paths i'm going to try
+ 
+
+ align:start position:0%
+give you shortest paths i'm going to try
+to compute shortest paths but i'm going
+
+ align:start position:0%
+to compute shortest paths but i'm going
+ 
+
+ align:start position:0%
+to compute shortest paths but i'm going
+to give you some additional information
+
+ align:start position:0%
+to give you some additional information
+ 
+
+ align:start position:0%
+to give you some additional information
+i'm going to give you the order of their
+
+ align:start position:0%
+i'm going to give you the order of their
+ 
+
+ align:start position:0%
+i'm going to give you the order of their
+shortest path distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the source
+
+ align:start position:0%
+from the source
+ 
+
+ align:start position:0%
+from the source
+and i can just i'm going to eyeball this
+
+ align:start position:0%
+and i can just i'm going to eyeball this
+ 
+
+ align:start position:0%
+and i can just i'm going to eyeball this
+and say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to change this slightly to
+
+ align:start position:0%
+i'm going to change this slightly to
+ 
+
+ align:start position:0%
+i'm going to change this slightly to
+make it a little bit more interesting
+
+ align:start position:0%
+make it a little bit more interesting
+ 
+
+ align:start position:0%
+make it a little bit more interesting
+i'm going to say this
+
+ align:start position:0%
+i'm going to say this
+ 
+
+ align:start position:0%
+i'm going to say this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+distance 4
+
+ align:start position:0%
+distance 4
+ 
+
+ align:start position:0%
+distance 4
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so now what we have is
+
+ align:start position:0%
+all right so now what we have is
+ 
+
+ align:start position:0%
+all right so now what we have is
+the shortest path distance i'm just
+
+ align:start position:0%
+the shortest path distance i'm just
+ 
+
+ align:start position:0%
+the shortest path distance i'm just
+eyeballing this the shortest path
+
+ align:start position:0%
+eyeballing this the shortest path
+ 
+
+ align:start position:0%
+eyeballing this the shortest path
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah bad example
+
+ align:start position:0%
+ah bad example
+ 
+
+ align:start position:0%
+ah bad example
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+these are the weights
+
+ align:start position:0%
+these are the weights
+ 
+
+ align:start position:0%
+these are the weights
+shortest path distance to 3 is going to
+
+ align:start position:0%
+shortest path distance to 3 is going to
+ 
+
+ align:start position:0%
+shortest path distance to 3 is going to
+be 2 i'm going to say
+
+ align:start position:0%
+be 2 i'm going to say
+ 
+
+ align:start position:0%
+be 2 i'm going to say
+through there
+
+ align:start position:0%
+through there
+ 
+
+ align:start position:0%
+through there
+shortest path distance here is two also
+
+ align:start position:0%
+shortest path distance here is two also
+ 
+
+ align:start position:0%
+shortest path distance here is two also
+shortest path distance here is also two
+
+ align:start position:0%
+shortest path distance here is also two
+ 
+
+ align:start position:0%
+shortest path distance here is also two
+because i can go through both of these
+
+ align:start position:0%
+because i can go through both of these
+ 
+
+ align:start position:0%
+because i can go through both of these
+zeros and
+
+ align:start position:0%
+zeros and
+ 
+
+ align:start position:0%
+zeros and
+it's not a problem and then the shortest
+
+ align:start position:0%
+it's not a problem and then the shortest
+ 
+
+ align:start position:0%
+it's not a problem and then the shortest
+path distance here is two to here and a
+
+ align:start position:0%
+path distance here is two to here and a
+ 
+
+ align:start position:0%
+path distance here is two to here and a
+third to there okay so these are
+
+ align:start position:0%
+third to there okay so these are
+ 
+
+ align:start position:0%
+third to there okay so these are
+listed in increasing distance
+
+ align:start position:0%
+listed in increasing distance
+ 
+
+ align:start position:0%
+listed in increasing distance
+from my source
+
+ align:start position:0%
+from my source
+ 
+
+ align:start position:0%
+from my source
+okay i
+
+ align:start position:0%
+okay i
+ 
+
+ align:start position:0%
+okay i
+i had to compute those deltas to
+
+ align:start position:0%
+i had to compute those deltas to
+ 
+
+ align:start position:0%
+i had to compute those deltas to
+kind of convince you that this is the
+
+ align:start position:0%
+kind of convince you that this is the
+ 
+
+ align:start position:0%
+kind of convince you that this is the
+right ordering but this is a right
+
+ align:start position:0%
+right ordering but this is a right
+ 
+
+ align:start position:0%
+right ordering but this is a right
+ordering of these things now it's not
+
+ align:start position:0%
+ordering of these things now it's not
+ 
+
+ align:start position:0%
+ordering of these things now it's not
+the only right ordering
+
+ align:start position:0%
+the only right ordering
+ 
+
+ align:start position:0%
+the only right ordering
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but it is a right order okay so i'm told
+
+ align:start position:0%
+but it is a right order okay so i'm told
+ 
+
+ align:start position:0%
+but it is a right order okay so i'm told
+i'm i'm arguing to you that i could
+
+ align:start position:0%
+i'm i'm arguing to you that i could
+ 
+
+ align:start position:0%
+i'm i'm arguing to you that i could
+solve single source shortest paths
+
+ align:start position:0%
+solve single source shortest paths
+ 
+
+ align:start position:0%
+solve single source shortest paths
+in linear time
+
+ align:start position:0%
+in linear time
+ 
+
+ align:start position:0%
+in linear time
+if i were to give you the vertices in
+
+ align:start position:0%
+if i were to give you the vertices in
+ 
+
+ align:start position:0%
+if i were to give you the vertices in
+increasing distance how could i do that
+
+ align:start position:0%
+increasing distance how could i do that
+ 
+
+ align:start position:0%
+increasing distance how could i do that
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it because of this first observation
+
+ align:start position:0%
+it because of this first observation
+ 
+
+ align:start position:0%
+it because of this first observation
+i know that if these are increasing in
+
+ align:start position:0%
+i know that if these are increasing in
+ 
+
+ align:start position:0%
+i know that if these are increasing in
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+any edge going backwards with respect to
+
+ align:start position:0%
+any edge going backwards with respect to
+ 
+
+ align:start position:0%
+any edge going backwards with respect to
+this ordering
+
+ align:start position:0%
+this ordering
+ 
+
+ align:start position:0%
+this ordering
+can't participate in shortest paths with
+
+ align:start position:0%
+can't participate in shortest paths with
+ 
+
+ align:start position:0%
+can't participate in shortest paths with
+one exception
+
+ align:start position:0%
+one exception
+ 
+
+ align:start position:0%
+one exception
+anyone know what that exception is no no
+
+ align:start position:0%
+anyone know what that exception is no no
+ 
+
+ align:start position:0%
+anyone know what that exception is no no
+edge can go backwards in this ordering
+
+ align:start position:0%
+edge can go backwards in this ordering
+ 
+
+ align:start position:0%
+edge can go backwards in this ordering
+based on this observation
+
+ align:start position:0%
+based on this observation
+ 
+
+ align:start position:0%
+based on this observation
+except under what condition
+
+ align:start position:0%
+except under what condition
+ 
+
+ align:start position:0%
+except under what condition
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+if the weight is zero yeah so if the
+
+ align:start position:0%
+if the weight is zero yeah so if the
+ 
+
+ align:start position:0%
+if the weight is zero yeah so if the
+weight is zero just just like this
+
+ align:start position:0%
+weight is zero just just like this
+ 
+
+ align:start position:0%
+weight is zero just just like this
+situation here
+
+ align:start position:0%
+situation here
+ 
+
+ align:start position:0%
+situation here
+then i could go backwards in the
+
+ align:start position:0%
+then i could go backwards in the
+ 
+
+ align:start position:0%
+then i could go backwards in the
+ordering
+
+ align:start position:0%
+ordering
+ 
+
+ align:start position:0%
+ordering
+seems problematic right the idea is i'm
+
+ align:start position:0%
+seems problematic right the idea is i'm
+ 
+
+ align:start position:0%
+seems problematic right the idea is i'm
+going to want to construct a dag
+
+ align:start position:0%
+going to want to construct a dag
+ 
+
+ align:start position:0%
+going to want to construct a dag
+so that i can run dag relaxation
+
+ align:start position:0%
+so that i can run dag relaxation
+ 
+
+ align:start position:0%
+so that i can run dag relaxation
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if i have a
+
+ align:start position:0%
+if i have a
+ 
+
+ align:start position:0%
+if i have a
+component here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has zero weights
+
+ align:start position:0%
+that has zero weights
+ 
+
+ align:start position:0%
+that has zero weights
+i can kind of
+
+ align:start position:0%
+i can kind of
+ 
+
+ align:start position:0%
+i can kind of
+coalesce this thing down
+
+ align:start position:0%
+coalesce this thing down
+ 
+
+ align:start position:0%
+coalesce this thing down
+i can i can deal with this this this
+
+ align:start position:0%
+i can i can deal with this this this
+ 
+
+ align:start position:0%
+i can i can deal with this this this
+component separately
+
+ align:start position:0%
+component separately
+ 
+
+ align:start position:0%
+component separately
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+let's let's worry about that separately
+
+ align:start position:0%
+let's let's worry about that separately
+ 
+
+ align:start position:0%
+let's let's worry about that separately
+if we do
+
+ align:start position:0%
+if we do
+ 
+
+ align:start position:0%
+if we do
+we can kind of collapse this edge down
+
+ align:start position:0%
+we can kind of collapse this edge down
+ 
+
+ align:start position:0%
+we can kind of collapse this edge down
+into a single vertex
+
+ align:start position:0%
+into a single vertex
+ 
+
+ align:start position:0%
+into a single vertex
+and transform this graph so it does
+
+ align:start position:0%
+and transform this graph so it does
+ 
+
+ align:start position:0%
+and transform this graph so it does
+respect the ordering okay so i'm going
+
+ align:start position:0%
+respect the ordering okay so i'm going
+ 
+
+ align:start position:0%
+respect the ordering okay so i'm going
+to transform this
+
+ align:start position:0%
+to transform this
+ 
+
+ align:start position:0%
+to transform this
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+a new graph
+
+ align:start position:0%
+a new graph
+ 
+
+ align:start position:0%
+a new graph
+this is a graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contains vertex 2 and vertex 0
+
+ align:start position:0%
+contains vertex 2 and vertex 0
+ 
+
+ align:start position:0%
+contains vertex 2 and vertex 0
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+1 and 3 here
+
+ align:start position:0%
+1 and 3 here
+ 
+
+ align:start position:0%
+1 and 3 here
+and vertex 4.
+
+ align:start position:0%
+and vertex 4.
+ 
+
+ align:start position:0%
+and vertex 4.
+okay now we have
+
+ align:start position:0%
+okay now we have
+ 
+
+ align:start position:0%
+okay now we have
+uh and i'm only going to keep edges
+
+ align:start position:0%
+uh and i'm only going to keep edges
+ 
+
+ align:start position:0%
+uh and i'm only going to keep edges
+going forward in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+i'm going to need to collapse this
+
+ align:start position:0%
+i'm going to need to collapse this
+ 
+
+ align:start position:0%
+i'm going to need to collapse this
+entire section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this entire section
+
+ align:start position:0%
+right this entire section
+ 
+
+ align:start position:0%
+right this entire section
+down into one vertex this doesn't quite
+
+ align:start position:0%
+down into one vertex this doesn't quite
+ 
+
+ align:start position:0%
+down into one vertex this doesn't quite
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+let's let's ignore uh
+
+ align:start position:0%
+let's let's ignore uh
+ 
+
+ align:start position:0%
+let's let's ignore uh
+zero weight edges for now let's assume
+
+ align:start position:0%
+zero weight edges for now let's assume
+ 
+
+ align:start position:0%
+zero weight edges for now let's assume
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right there's something broken here
+
+ align:start position:0%
+all right there's something broken here
+ 
+
+ align:start position:0%
+all right there's something broken here
+if i have a cycle here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+right now i don't have a cycle of zero
+
+ align:start position:0%
+right now i don't have a cycle of zero
+ 
+
+ align:start position:0%
+right now i don't have a cycle of zero
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+right so what i could do is i could take
+
+ align:start position:0%
+right so what i could do is i could take
+ 
+
+ align:start position:0%
+right so what i could do is i could take
+this vertex
+
+ align:start position:0%
+this vertex
+ 
+
+ align:start position:0%
+this vertex
+and put it after both of these vertices
+
+ align:start position:0%
+and put it after both of these vertices
+ 
+
+ align:start position:0%
+and put it after both of these vertices
+and now i would or
+
+ align:start position:0%
+and now i would or
+ 
+
+ align:start position:0%
+and now i would or
+i could rearrange the order of these
+
+ align:start position:0%
+i could rearrange the order of these
+ 
+
+ align:start position:0%
+i could rearrange the order of these
+three vertices where there's a path of
+
+ align:start position:0%
+three vertices where there's a path of
+ 
+
+ align:start position:0%
+three vertices where there's a path of
+length zero
+
+ align:start position:0%
+length zero
+ 
+
+ align:start position:0%
+length zero
+and get a new ordering that still
+
+ align:start position:0%
+and get a new ordering that still
+ 
+
+ align:start position:0%
+and get a new ordering that still
+satisfies the property
+
+ align:start position:0%
+satisfies the property
+ 
+
+ align:start position:0%
+satisfies the property
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's always the case
+
+ align:start position:0%
+and that's always the case
+ 
+
+ align:start position:0%
+and that's always the case
+because uh paths
+
+ align:start position:0%
+because uh paths
+ 
+
+ align:start position:0%
+because uh paths
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+can't increase
+
+ align:start position:0%
+can't increase
+ 
+
+ align:start position:0%
+can't increase
+path can't decrease in in weight i can
+
+ align:start position:0%
+path can't decrease in in weight i can
+ 
+
+ align:start position:0%
+path can't decrease in in weight i can
+rearrange the ordering of these things
+
+ align:start position:0%
+rearrange the ordering of these things
+ 
+
+ align:start position:0%
+rearrange the ordering of these things
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+three comes first
+
+ align:start position:0%
+three comes first
+ 
+
+ align:start position:0%
+three comes first
+one comes second and two comes third
+
+ align:start position:0%
+one comes second and two comes third
+ 
+
+ align:start position:0%
+one comes second and two comes third
+of those three vertices okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so for for every set of
+
+ align:start position:0%
+yeah so for for every set of
+ 
+
+ align:start position:0%
+yeah so for for every set of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+zero edges i can just
+
+ align:start position:0%
+zero edges i can just
+ 
+
+ align:start position:0%
+zero edges i can just
+flip the relationship if they have the
+
+ align:start position:0%
+flip the relationship if they have the
+ 
+
+ align:start position:0%
+flip the relationship if they have the
+same distance okay in my input
+
+ align:start position:0%
+same distance okay in my input
+ 
+
+ align:start position:0%
+same distance okay in my input
+i'm given vertices that have the same
+
+ align:start position:0%
+i'm given vertices that have the same
+ 
+
+ align:start position:0%
+i'm given vertices that have the same
+distance from the source and so if those
+
+ align:start position:0%
+distance from the source and so if those
+ 
+
+ align:start position:0%
+distance from the source and so if those
+are the same distance from the source
+
+ align:start position:0%
+are the same distance from the source
+ 
+
+ align:start position:0%
+are the same distance from the source
+and they're connected by zero eight edge
+
+ align:start position:0%
+and they're connected by zero eight edge
+ 
+
+ align:start position:0%
+and they're connected by zero eight edge
+it doesn't hurt me to flip their
+
+ align:start position:0%
+it doesn't hurt me to flip their
+ 
+
+ align:start position:0%
+it doesn't hurt me to flip their
+ordering so i'm gonna do that okay
+
+ align:start position:0%
+ordering so i'm gonna do that okay
+ 
+
+ align:start position:0%
+ordering so i'm gonna do that okay
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+convert that into a graph with a
+
+ align:start position:0%
+convert that into a graph with a
+ 
+
+ align:start position:0%
+convert that into a graph with a
+different ordering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+three now one
+
+ align:start position:0%
+three now one
+ 
+
+ align:start position:0%
+three now one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay and i have this distance this edge
+
+ align:start position:0%
+okay and i have this distance this edge
+ 
+
+ align:start position:0%
+okay and i have this distance this edge
+this edge this edge this edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what am i missing two to three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+i think i have all of those edges
+
+ align:start position:0%
+i think i have all of those edges
+ 
+
+ align:start position:0%
+i think i have all of those edges
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now i have the property that
+
+ align:start position:0%
+now i have the property that
+ 
+
+ align:start position:0%
+now i have the property that
+every edge that could participate in the
+
+ align:start position:0%
+every edge that could participate in the
+ 
+
+ align:start position:0%
+every edge that could participate in the
+shortest path are going forward in the
+
+ align:start position:0%
+shortest path are going forward in the
+ 
+
+ align:start position:0%
+shortest path are going forward in the
+ordering
+
+ align:start position:0%
+ordering
+ 
+
+ align:start position:0%
+ordering
+right because
+
+ align:start position:0%
+right because
+ 
+
+ align:start position:0%
+right because
+all of these
+
+ align:start position:0%
+all of these
+ 
+
+ align:start position:0%
+all of these
+are zero weight
+
+ align:start position:0%
+are zero weight
+ 
+
+ align:start position:0%
+are zero weight
+so we flip those around so they're going
+
+ align:start position:0%
+so we flip those around so they're going
+ 
+
+ align:start position:0%
+so we flip those around so they're going
+correct with respect to the ordering
+
+ align:start position:0%
+correct with respect to the ordering
+ 
+
+ align:start position:0%
+correct with respect to the ordering
+and any
+
+ align:start position:0%
+and any
+ 
+
+ align:start position:0%
+and any
+edge going backwards that is positive
+
+ align:start position:0%
+edge going backwards that is positive
+ 
+
+ align:start position:0%
+edge going backwards that is positive
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+certainly can't be used in any shortest
+
+ align:start position:0%
+certainly can't be used in any shortest
+ 
+
+ align:start position:0%
+certainly can't be used in any shortest
+path so i'm just going to get rid of
+
+ align:start position:0%
+path so i'm just going to get rid of
+ 
+
+ align:start position:0%
+path so i'm just going to get rid of
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what do i do if there's a zero
+
+ align:start position:0%
+yeah what do i do if there's a zero
+ 
+
+ align:start position:0%
+yeah what do i do if there's a zero
+weight cycle
+
+ align:start position:0%
+weight cycle
+ 
+
+ align:start position:0%
+weight cycle
+if there's a zero weight cycle i can
+
+ align:start position:0%
+if there's a zero weight cycle i can
+ 
+
+ align:start position:0%
+if there's a zero weight cycle i can
+just coalesce them all together down to
+
+ align:start position:0%
+just coalesce them all together down to
+ 
+
+ align:start position:0%
+just coalesce them all together down to
+a single vertex because if i reach one
+
+ align:start position:0%
+a single vertex because if i reach one
+ 
+
+ align:start position:0%
+a single vertex because if i reach one
+of them i can reach all of them
+
+ align:start position:0%
+of them i can reach all of them
+ 
+
+ align:start position:0%
+of them i can reach all of them
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly i'm computing a topological so
+
+ align:start position:0%
+exactly i'm computing a topological so
+ 
+
+ align:start position:0%
+exactly i'm computing a topological so
+the idea here is we're trying to
+
+ align:start position:0%
+the idea here is we're trying to
+ 
+
+ align:start position:0%
+the idea here is we're trying to
+construct a dag
+
+ align:start position:0%
+construct a dag
+ 
+
+ align:start position:0%
+construct a dag
+i can construct this dag in linear time
+
+ align:start position:0%
+i can construct this dag in linear time
+ 
+
+ align:start position:0%
+i can construct this dag in linear time
+and then i can run
+
+ align:start position:0%
+and then i can run
+ 
+
+ align:start position:0%
+and then i can run
+dag relaxation on this graph
+
+ align:start position:0%
+dag relaxation on this graph
+ 
+
+ align:start position:0%
+dag relaxation on this graph
+in linear time to get shortest paths
+
+ align:start position:0%
+in linear time to get shortest paths
+ 
+
+ align:start position:0%
+in linear time to get shortest paths
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+that's an approach if i knew the
+
+ align:start position:0%
+that's an approach if i knew the
+ 
+
+ align:start position:0%
+that's an approach if i knew the
+ordering of the vertices in increasing
+
+ align:start position:0%
+ordering of the vertices in increasing
+ 
+
+ align:start position:0%
+ordering of the vertices in increasing
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+then i could use dag relaxation so we're
+
+ align:start position:0%
+then i could use dag relaxation so we're
+ 
+
+ align:start position:0%
+then i could use dag relaxation so we're
+going to use both of these observations
+
+ align:start position:0%
+going to use both of these observations
+ 
+
+ align:start position:0%
+going to use both of these observations
+that's how we're going to solve this uh
+
+ align:start position:0%
+that's how we're going to solve this uh
+ 
+
+ align:start position:0%
+that's how we're going to solve this uh
+single source shortest problem
+
+ align:start position:0%
+single source shortest problem
+ 
+
+ align:start position:0%
+single source shortest problem
+with non-negative weights using dijkstra
+
+ align:start position:0%
+with non-negative weights using dijkstra
+ 
+
+ align:start position:0%
+with non-negative weights using dijkstra
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+finally now where we're coming to
+
+ align:start position:0%
+finally now where we're coming to
+ 
+
+ align:start position:0%
+finally now where we're coming to
+sorry i missed a case here when i was
+
+ align:start position:0%
+sorry i missed a case here when i was
+ 
+
+ align:start position:0%
+sorry i missed a case here when i was
+writing up my notes and i'm trying i
+
+ align:start position:0%
+writing up my notes and i'm trying i
+ 
+
+ align:start position:0%
+writing up my notes and i'm trying i
+tried to fix it live and hopefully you
+
+ align:start position:0%
+tried to fix it live and hopefully you
+ 
+
+ align:start position:0%
+tried to fix it live and hopefully you
+guys followed me
+
+ align:start position:0%
+guys followed me
+ 
+
+ align:start position:0%
+guys followed me
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dijkstra's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did i spell that right
+
+ align:start position:0%
+did i spell that right
+ 
+
+ align:start position:0%
+did i spell that right
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+dix
+
+ align:start position:0%
+dix
+ 
+
+ align:start position:0%
+dix
+styx
+
+ align:start position:0%
+styx
+ 
+
+ align:start position:0%
+styx
+draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now dykstra
+
+ align:start position:0%
+now dykstra
+ 
+
+ align:start position:0%
+now dykstra
+was this dutch computer scientist
+
+ align:start position:0%
+was this dutch computer scientist
+ 
+
+ align:start position:0%
+was this dutch computer scientist
+okay this is him
+
+ align:start position:0%
+okay this is him
+ 
+
+ align:start position:0%
+okay this is him
+pretty famous he he wrote a monograph on
+
+ align:start position:0%
+pretty famous he he wrote a monograph on
+ 
+
+ align:start position:0%
+pretty famous he he wrote a monograph on
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+uh programming languages should uh start
+
+ align:start position:0%
+uh programming languages should uh start
+ 
+
+ align:start position:0%
+uh programming languages should uh start
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+zero indexing as opposed to one indexing
+
+ align:start position:0%
+zero indexing as opposed to one indexing
+ 
+
+ align:start position:0%
+zero indexing as opposed to one indexing
+so i like him but uh in particular he
+
+ align:start position:0%
+so i like him but uh in particular he
+ 
+
+ align:start position:0%
+so i like him but uh in particular he
+designed this very nice generalization
+
+ align:start position:0%
+designed this very nice generalization
+ 
+
+ align:start position:0%
+designed this very nice generalization
+of bfs for weighted graphs
+
+ align:start position:0%
+of bfs for weighted graphs
+ 
+
+ align:start position:0%
+of bfs for weighted graphs
+uh but maybe i didn't spell this right
+
+ align:start position:0%
+uh but maybe i didn't spell this right
+ 
+
+ align:start position:0%
+uh but maybe i didn't spell this right
+because when he writes his name he
+
+ align:start position:0%
+because when he writes his name he
+ 
+
+ align:start position:0%
+because when he writes his name he
+writes it with a y with a dash over it
+
+ align:start position:0%
+writes it with a y with a dash over it
+ 
+
+ align:start position:0%
+writes it with a y with a dash over it
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in re in reality
+
+ align:start position:0%
+in re in reality
+ 
+
+ align:start position:0%
+in re in reality
+on a dutch typewriter
+
+ align:start position:0%
+on a dutch typewriter
+ 
+
+ align:start position:0%
+on a dutch typewriter
+you might have a a character that looks
+
+ align:start position:0%
+you might have a a character that looks
+ 
+
+ align:start position:0%
+you might have a a character that looks
+like this y
+
+ align:start position:0%
+like this y
+ 
+
+ align:start position:0%
+like this y
+with a new loud on top of it
+
+ align:start position:0%
+with a new loud on top of it
+ 
+
+ align:start position:0%
+with a new loud on top of it
+but on a modern
+
+ align:start position:0%
+but on a modern
+ 
+
+ align:start position:0%
+but on a modern
+on a on a english keyboard
+
+ align:start position:0%
+on a on a english keyboard
+ 
+
+ align:start position:0%
+on a on a english keyboard
+this looks
+
+ align:start position:0%
+this looks
+ 
+
+ align:start position:0%
+this looks
+pretty similar to an ij
+
+ align:start position:0%
+pretty similar to an ij
+ 
+
+ align:start position:0%
+pretty similar to an ij
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a lot of manuscripts
+
+ align:start position:0%
+in a lot of manuscripts
+ 
+
+ align:start position:0%
+in a lot of manuscripts
+we write it as
+
+ align:start position:0%
+we write it as
+ 
+
+ align:start position:0%
+we write it as
+d i j there's no j sound in dijkstra
+
+ align:start position:0%
+d i j there's no j sound in dijkstra
+ 
+
+ align:start position:0%
+d i j there's no j sound in dijkstra
+it's coming from this this y here okay
+
+ align:start position:0%
+it's coming from this this y here okay
+ 
+
+ align:start position:0%
+it's coming from this this y here okay
+so that's a interesting way to remember
+
+ align:start position:0%
+so that's a interesting way to remember
+ 
+
+ align:start position:0%
+so that's a interesting way to remember
+how to spell dijkstra
+
+ align:start position:0%
+how to spell dijkstra
+ 
+
+ align:start position:0%
+how to spell dijkstra
+but the basic idea behind dijkstra is
+
+ align:start position:0%
+but the basic idea behind dijkstra is
+ 
+
+ align:start position:0%
+but the basic idea behind dijkstra is
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relax
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+source okay this is the same kind of
+
+ align:start position:0%
+source okay this is the same kind of
+ 
+
+ align:start position:0%
+source okay this is the same kind of
+difficulty we had before when we were
+
+ align:start position:0%
+difficulty we had before when we were
+ 
+
+ align:start position:0%
+difficulty we had before when we were
+trying to you know
+
+ align:start position:0%
+trying to you know
+ 
+
+ align:start position:0%
+trying to you know
+generalize bfs
+
+ align:start position:0%
+generalize bfs
+ 
+
+ align:start position:0%
+generalize bfs
+so how do we know
+
+ align:start position:0%
+so how do we know
+ 
+
+ align:start position:0%
+so how do we know
+what the
+
+ align:start position:0%
+what the
+ 
+
+ align:start position:0%
+what the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+vertex is with increasing distance to s
+
+ align:start position:0%
+vertex is with increasing distance to s
+ 
+
+ align:start position:0%
+vertex is with increasing distance to s
+well the second idea is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+efficiently
+
+ align:start position:0%
+efficiently
+ 
+
+ align:start position:0%
+efficiently
+using a data structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the data structure we're going
+
+ align:start position:0%
+okay and the data structure we're going
+ 
+
+ align:start position:0%
+okay and the data structure we're going
+to use is something i like to call
+
+ align:start position:0%
+to use is something i like to call
+ 
+
+ align:start position:0%
+to use is something i like to call
+a changeable priority cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a little different than
+
+ align:start position:0%
+okay so this is a little different than
+ 
+
+ align:start position:0%
+okay so this is a little different than
+a normal priority queue
+
+ align:start position:0%
+a normal priority queue
+ 
+
+ align:start position:0%
+a normal priority queue
+that we had
+
+ align:start position:0%
+that we had
+ 
+
+ align:start position:0%
+that we had
+uh at the end of our data structures
+
+ align:start position:0%
+uh at the end of our data structures
+ 
+
+ align:start position:0%
+uh at the end of our data structures
+uh unit
+
+ align:start position:0%
+uh unit
+ 
+
+ align:start position:0%
+uh unit
+this changeable priority queue has three
+
+ align:start position:0%
+this changeable priority queue has three
+ 
+
+ align:start position:0%
+this changeable priority queue has three
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+we're going to say it's a
+
+ align:start position:0%
+we're going to say it's a
+ 
+
+ align:start position:0%
+we're going to say it's a
+queue
+
+ align:start position:0%
+queue
+ 
+
+ align:start position:0%
+queue
+we can build it
+
+ align:start position:0%
+we can build it
+ 
+
+ align:start position:0%
+we can build it
+on an iterable set
+
+ align:start position:0%
+on an iterable set
+ 
+
+ align:start position:0%
+on an iterable set
+of items just
+
+ align:start position:0%
+of items just
+ 
+
+ align:start position:0%
+of items just
+stick
+
+ align:start position:0%
+stick
+ 
+
+ align:start position:0%
+stick
+x uh like n items in there
+
+ align:start position:0%
+x uh like n items in there
+ 
+
+ align:start position:0%
+x uh like n items in there
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+delete min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the queue
+
+ align:start position:0%
+from the queue
+ 
+
+ align:start position:0%
+from the queue
+okay this is the same now as the
+
+ align:start position:0%
+okay this is the same now as the
+ 
+
+ align:start position:0%
+okay this is the same now as the
+priority queue it's this third operation
+
+ align:start position:0%
+priority queue it's this third operation
+ 
+
+ align:start position:0%
+priority queue it's this third operation
+that's going to be different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decrease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the key
+
+ align:start position:0%
+the key
+ 
+
+ align:start position:0%
+the key
+of an item that has id id
+
+ align:start position:0%
+of an item that has id id
+ 
+
+ align:start position:0%
+of an item that has id id
+okay so this is a little strange
+
+ align:start position:0%
+okay so this is a little strange
+ 
+
+ align:start position:0%
+okay so this is a little strange
+what the heck is this id
+
+ align:start position:0%
+what the heck is this id
+ 
+
+ align:start position:0%
+what the heck is this id
+all right with the changeable priority
+
+ align:start position:0%
+all right with the changeable priority
+ 
+
+ align:start position:0%
+all right with the changeable priority
+queue
+
+ align:start position:0%
+queue
+ 
+
+ align:start position:0%
+queue
+each of our items has two values instead
+
+ align:start position:0%
+each of our items has two values instead
+ 
+
+ align:start position:0%
+each of our items has two values instead
+of one value it has a key
+
+ align:start position:0%
+of one value it has a key
+ 
+
+ align:start position:0%
+of one value it has a key
+but it also on which the priority queue
+
+ align:start position:0%
+but it also on which the priority queue
+ 
+
+ align:start position:0%
+but it also on which the priority queue
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+deleting the min
+
+ align:start position:0%
+deleting the min
+ 
+
+ align:start position:0%
+deleting the min
+item
+
+ align:start position:0%
+item
+ 
+
+ align:start position:0%
+item
+with the minimum key
+
+ align:start position:0%
+with the minimum key
+ 
+
+ align:start position:0%
+with the minimum key
+but also each item has an id associated
+
+ align:start position:0%
+but also each item has an id associated
+ 
+
+ align:start position:0%
+but also each item has an id associated
+with it a unique integer
+
+ align:start position:0%
+with it a unique integer
+ 
+
+ align:start position:0%
+with it a unique integer
+okay so that
+
+ align:start position:0%
+okay so that
+ 
+
+ align:start position:0%
+okay so that
+when we perform this operation decrease
+
+ align:start position:0%
+when we perform this operation decrease
+ 
+
+ align:start position:0%
+when we perform this operation decrease
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+it can find some
+
+ align:start position:0%
+it can find some
+ 
+
+ align:start position:0%
+it can find some
+item in our data structure with a given
+
+ align:start position:0%
+item in our data structure with a given
+ 
+
+ align:start position:0%
+item in our data structure with a given
+id
+
+ align:start position:0%
+id
+ 
+
+ align:start position:0%
+id
+and if it's contained there it's going
+
+ align:start position:0%
+and if it's contained there it's going
+ 
+
+ align:start position:0%
+and if it's contained there it's going
+to change its
+
+ align:start position:0%
+to change its
+ 
+
+ align:start position:0%
+to change its
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+to some smaller value okay
+
+ align:start position:0%
+to some smaller value okay
+ 
+
+ align:start position:0%
+to some smaller value okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+don't worry about the edge cases here
+
+ align:start position:0%
+don't worry about the edge cases here
+ 
+
+ align:start position:0%
+don't worry about the edge cases here
+we're always going to make sure this k
+
+ align:start position:0%
+we're always going to make sure this k
+ 
+
+ align:start position:0%
+we're always going to make sure this k
+is going to be smaller than whatever
+
+ align:start position:0%
+is going to be smaller than whatever
+ 
+
+ align:start position:0%
+is going to be smaller than whatever
+that key was to begin with all right so
+
+ align:start position:0%
+that key was to begin with all right so
+ 
+
+ align:start position:0%
+that key was to begin with all right so
+this is a really a kind of a funky
+
+ align:start position:0%
+this is a really a kind of a funky
+ 
+
+ align:start position:0%
+this is a really a kind of a funky
+operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i had a priority queue
+
+ align:start position:0%
+if i had a priority queue
+ 
+
+ align:start position:0%
+if i had a priority queue
+not a changeable priority queue but i
+
+ align:start position:0%
+not a changeable priority queue but i
+ 
+
+ align:start position:0%
+not a changeable priority queue but i
+had a priority queue and i wanted to
+
+ align:start position:0%
+had a priority queue and i wanted to
+ 
+
+ align:start position:0%
+had a priority queue and i wanted to
+implement a changeable priority queue
+
+ align:start position:0%
+implement a changeable priority queue
+ 
+
+ align:start position:0%
+implement a changeable priority queue
+how could i do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+a regular priority queue is already
+
+ align:start position:0%
+a regular priority queue is already
+ 
+
+ align:start position:0%
+a regular priority queue is already
+going to get me these two operations
+
+ align:start position:0%
+going to get me these two operations
+ 
+
+ align:start position:0%
+going to get me these two operations
+it's just this one i essentially need to
+
+ align:start position:0%
+it's just this one i essentially need to
+ 
+
+ align:start position:0%
+it's just this one i essentially need to
+find something by a id
+
+ align:start position:0%
+find something by a id
+ 
+
+ align:start position:0%
+find something by a id
+and then update its key
+
+ align:start position:0%
+and then update its key
+ 
+
+ align:start position:0%
+and then update its key
+okay so the idea how to implement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is going to be to use a regular
+
+ align:start position:0%
+this is going to be to use a regular
+ 
+
+ align:start position:0%
+this is going to be to use a regular
+priority queue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to call it q prime
+
+ align:start position:0%
+i'm going to call it q prime
+ 
+
+ align:start position:0%
+i'm going to call it q prime
+and i'm going to cross link it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a dictionary d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is just a regular priority queue
+
+ align:start position:0%
+so this is just a regular priority queue
+ 
+
+ align:start position:0%
+so this is just a regular priority queue
+on my items that has the key as defined
+
+ align:start position:0%
+on my items that has the key as defined
+ 
+
+ align:start position:0%
+on my items that has the key as defined
+above right
+
+ align:start position:0%
+above right
+ 
+
+ align:start position:0%
+above right
+but i'm going to cross-link it with a
+
+ align:start position:0%
+but i'm going to cross-link it with a
+ 
+
+ align:start position:0%
+but i'm going to cross-link it with a
+dictionary a dictionary that maps ids
+
+ align:start position:0%
+dictionary a dictionary that maps ids
+ 
+
+ align:start position:0%
+dictionary a dictionary that maps ids
+to their location in the priority queue
+
+ align:start position:0%
+to their location in the priority queue
+ 
+
+ align:start position:0%
+to their location in the priority queue
+we've done this many times in the data
+
+ align:start position:0%
+we've done this many times in the data
+ 
+
+ align:start position:0%
+we've done this many times in the data
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+section we're trying to cross-link to
+
+ align:start position:0%
+section we're trying to cross-link to
+ 
+
+ align:start position:0%
+section we're trying to cross-link to
+data structures to make
+
+ align:start position:0%
+data structures to make
+ 
+
+ align:start position:0%
+data structures to make
+a query on a different type of key
+
+ align:start position:0%
+a query on a different type of key
+ 
+
+ align:start position:0%
+a query on a different type of key
+to find its place in another data
+
+ align:start position:0%
+to find its place in another data
+ 
+
+ align:start position:0%
+to find its place in another data
+structure okay
+
+ align:start position:0%
+structure okay
+ 
+
+ align:start position:0%
+structure okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if we had a priority queue in a
+
+ align:start position:0%
+if we had a priority queue in a
+ 
+
+ align:start position:0%
+if we had a priority queue in a
+dictionary
+
+ align:start position:0%
+dictionary
+ 
+
+ align:start position:0%
+dictionary
+we could do this stuff
+
+ align:start position:0%
+we could do this stuff
+ 
+
+ align:start position:0%
+we could do this stuff
+pretty fast
+
+ align:start position:0%
+pretty fast
+ 
+
+ align:start position:0%
+pretty fast
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in particular i'm going to assume that
+
+ align:start position:0%
+in particular i'm going to assume that
+ 
+
+ align:start position:0%
+in particular i'm going to assume that
+our ids of our vertices
+
+ align:start position:0%
+our ids of our vertices
+ 
+
+ align:start position:0%
+our ids of our vertices
+are the integers between zero and v
+
+ align:start position:0%
+are the integers between zero and v
+ 
+
+ align:start position:0%
+are the integers between zero and v
+minus one and so for my dictionary
+
+ align:start position:0%
+minus one and so for my dictionary
+ 
+
+ align:start position:0%
+minus one and so for my dictionary
+i could get constant time looking up of
+
+ align:start position:0%
+i could get constant time looking up of
+ 
+
+ align:start position:0%
+i could get constant time looking up of
+that id
+
+ align:start position:0%
+that id
+ 
+
+ align:start position:0%
+that id
+by using what data structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we could get okay so we could get
+
+ align:start position:0%
+we could get okay so we could get
+ 
+
+ align:start position:0%
+we could get okay so we could get
+expected constant time
+
+ align:start position:0%
+expected constant time
+ 
+
+ align:start position:0%
+expected constant time
+if we used a hash table
+
+ align:start position:0%
+if we used a hash table
+ 
+
+ align:start position:0%
+if we used a hash table
+but if we knew that our
+
+ align:start position:0%
+but if we knew that our
+ 
+
+ align:start position:0%
+but if we knew that our
+vertex ids were just the numbers from 0
+
+ align:start position:0%
+vertex ids were just the numbers from 0
+ 
+
+ align:start position:0%
+vertex ids were just the numbers from 0
+to v minus 1
+
+ align:start position:0%
+to v minus 1
+ 
+
+ align:start position:0%
+to v minus 1
+we could get a rid of that expected time
+
+ align:start position:0%
+we could get a rid of that expected time
+ 
+
+ align:start position:0%
+we could get a rid of that expected time
+by using
+
+ align:start position:0%
+by using
+ 
+
+ align:start position:0%
+by using
+a direct access array
+
+ align:start position:0%
+a direct access array
+ 
+
+ align:start position:0%
+a direct access array
+great okay so that's what the assumption
+
+ align:start position:0%
+great okay so that's what the assumption
+ 
+
+ align:start position:0%
+great okay so that's what the assumption
+and so really the name of the game here
+
+ align:start position:0%
+and so really the name of the game here
+ 
+
+ align:start position:0%
+and so really the name of the game here
+is to choose a priority queue here
+
+ align:start position:0%
+is to choose a priority queue here
+ 
+
+ align:start position:0%
+is to choose a priority queue here
+that's going to make these things fast
+
+ align:start position:0%
+that's going to make these things fast
+ 
+
+ align:start position:0%
+that's going to make these things fast
+when we start to look at dijkstra okay
+
+ align:start position:0%
+when we start to look at dijkstra okay
+ 
+
+ align:start position:0%
+when we start to look at dijkstra okay
+so we're going to use this
+
+ align:start position:0%
+so we're going to use this
+ 
+
+ align:start position:0%
+so we're going to use this
+data structure
+
+ align:start position:0%
+data structure
+ 
+
+ align:start position:0%
+data structure
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+keep track of
+
+ align:start position:0%
+keep track of
+ 
+
+ align:start position:0%
+keep track of
+our distance estimates to all of the
+
+ align:start position:0%
+our distance estimates to all of the
+ 
+
+ align:start position:0%
+our distance estimates to all of the
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+away from s okay so this is dijkstra's
+
+ align:start position:0%
+away from s okay so this is dijkstra's
+ 
+
+ align:start position:0%
+away from s okay so this is dijkstra's
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+okay set
+
+ align:start position:0%
+okay set
+ 
+
+ align:start position:0%
+okay set
+so same initialization step
+
+ align:start position:0%
+so same initialization step
+ 
+
+ align:start position:0%
+so same initialization step
+we're going to set our this is a
+
+ align:start position:0%
+we're going to set our this is a
+ 
+
+ align:start position:0%
+we're going to set our this is a
+estimate d not delta
+
+ align:start position:0%
+estimate d not delta
+ 
+
+ align:start position:0%
+estimate d not delta
+we're going to want the d's to be our
+
+ align:start position:0%
+we're going to want the d's to be our
+ 
+
+ align:start position:0%
+we're going to want the d's to be our
+deltas at the end of the algorithm
+
+ align:start position:0%
+deltas at the end of the algorithm
+ 
+
+ align:start position:0%
+deltas at the end of the algorithm
+that's what we're going to have to prove
+
+ align:start position:0%
+that's what we're going to have to prove
+ 
+
+ align:start position:0%
+that's what we're going to have to prove
+so we first set all of them to infinity
+
+ align:start position:0%
+so we first set all of them to infinity
+ 
+
+ align:start position:0%
+so we first set all of them to infinity
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+d of ss
+
+ align:start position:0%
+d of ss
+ 
+
+ align:start position:0%
+d of ss
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and here we're never going to update it
+
+ align:start position:0%
+and here we're never going to update it
+ 
+
+ align:start position:0%
+and here we're never going to update it
+again right because
+
+ align:start position:0%
+again right because
+ 
+
+ align:start position:0%
+again right because
+our shortest distances in a graph with
+
+ align:start position:0%
+our shortest distances in a graph with
+ 
+
+ align:start position:0%
+our shortest distances in a graph with
+non-negative edge weights
+
+ align:start position:0%
+non-negative edge weights
+ 
+
+ align:start position:0%
+non-negative edge weights
+certainly can't go below zero okay
+
+ align:start position:0%
+certainly can't go below zero okay
+ 
+
+ align:start position:0%
+certainly can't go below zero okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now we build
+
+ align:start position:0%
+now we build
+ 
+
+ align:start position:0%
+now we build
+our build our changeable priority queue
+
+ align:start position:0%
+our build our changeable priority queue
+ 
+
+ align:start position:0%
+our build our changeable priority queue
+queue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+an item
+
+ align:start position:0%
+an item
+ 
+
+ align:start position:0%
+an item
+i'm gonna say an item
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+x is represented by a tuple of its id
+
+ align:start position:0%
+x is represented by a tuple of its id
+ 
+
+ align:start position:0%
+x is represented by a tuple of its id
+and then it's key
+
+ align:start position:0%
+and then it's key
+ 
+
+ align:start position:0%
+and then it's key
+just for brevity here
+
+ align:start position:0%
+just for brevity here
+ 
+
+ align:start position:0%
+just for brevity here
+okay with an item
+
+ align:start position:0%
+okay with an item
+ 
+
+ align:start position:0%
+okay with an item
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+d of sv so i'm going to be storing in my
+
+ align:start position:0%
+d of sv so i'm going to be storing in my
+ 
+
+ align:start position:0%
+d of sv so i'm going to be storing in my
+changeable priority queue the vertex
+
+ align:start position:0%
+changeable priority queue the vertex
+ 
+
+ align:start position:0%
+changeable priority queue the vertex
+label
+
+ align:start position:0%
+label
+ 
+
+ align:start position:0%
+label
+and its shortest path distance estimate
+
+ align:start position:0%
+and its shortest path distance estimate
+ 
+
+ align:start position:0%
+and its shortest path distance estimate
+d right and that's going to be the key
+
+ align:start position:0%
+d right and that's going to be the key
+ 
+
+ align:start position:0%
+d right and that's going to be the key
+the minimum that i'm trying to going to
+
+ align:start position:0%
+the minimum that i'm trying to going to
+ 
+
+ align:start position:0%
+the minimum that i'm trying to going to
+be querying on
+
+ align:start position:0%
+be querying on
+ 
+
+ align:start position:0%
+be querying on
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+v and v
+
+ align:start position:0%
+v and v
+ 
+
+ align:start position:0%
+v and v
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i'm going to build that thing it's
+
+ align:start position:0%
+so i'm going to build that thing it's
+ 
+
+ align:start position:0%
+so i'm going to build that thing it's
+going to then have all of my vertices in
+
+ align:start position:0%
+going to then have all of my vertices in
+ 
+
+ align:start position:0%
+going to then have all of my vertices in
+my graph
+
+ align:start position:0%
+my graph
+ 
+
+ align:start position:0%
+my graph
+then while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my changeable
+
+ align:start position:0%
+my changeable
+ 
+
+ align:start position:0%
+my changeable
+priority queue still has items
+
+ align:start position:0%
+priority queue still has items
+ 
+
+ align:start position:0%
+priority queue still has items
+not empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+s u
+
+ align:start position:0%
+s u
+ 
+
+ align:start position:0%
+s u
+so some item
+
+ align:start position:0%
+so some item
+ 
+
+ align:start position:0%
+so some item
+such that its
+
+ align:start position:0%
+such that its
+ 
+
+ align:start position:0%
+such that its
+distance is minimized right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+minimum distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i'm going to remove i'm going to
+
+ align:start position:0%
+okay so i'm going to remove i'm going to
+ 
+
+ align:start position:0%
+okay so i'm going to remove i'm going to
+look at all the things in my priority
+
+ align:start position:0%
+look at all the things in my priority
+ 
+
+ align:start position:0%
+look at all the things in my priority
+queue at the start it's just going to be
+
+ align:start position:0%
+queue at the start it's just going to be
+ 
+
+ align:start position:0%
+queue at the start it's just going to be
+s right because everything has shortest
+
+ align:start position:0%
+s right because everything has shortest
+ 
+
+ align:start position:0%
+s right because everything has shortest
+path distance estimate infinite except
+
+ align:start position:0%
+path distance estimate infinite except
+ 
+
+ align:start position:0%
+path distance estimate infinite except
+for s and so that's clearly the smallest
+
+ align:start position:0%
+for s and so that's clearly the smallest
+ 
+
+ align:start position:0%
+for s and so that's clearly the smallest
+okay so i'm going to remove that from my
+
+ align:start position:0%
+okay so i'm going to remove that from my
+ 
+
+ align:start position:0%
+okay so i'm going to remove that from my
+queue and then i'm going to process it
+
+ align:start position:0%
+queue and then i'm going to process it
+ 
+
+ align:start position:0%
+queue and then i'm going to process it
+okay how am i going to process it
+
+ align:start position:0%
+okay how am i going to process it
+ 
+
+ align:start position:0%
+okay how am i going to process it
+it's the exact same kind of thing as dag
+
+ align:start position:0%
+it's the exact same kind of thing as dag
+ 
+
+ align:start position:0%
+it's the exact same kind of thing as dag
+relaxation i'm going to relax all its
+
+ align:start position:0%
+relaxation i'm going to relax all its
+ 
+
+ align:start position:0%
+relaxation i'm going to relax all its
+outgoing edges right so
+
+ align:start position:0%
+outgoing edges right so
+ 
+
+ align:start position:0%
+outgoing edges right so
+just for completeness for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the outgoing adjacencies
+
+ align:start position:0%
+the outgoing adjacencies
+ 
+
+ align:start position:0%
+the outgoing adjacencies
+of u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to
+
+ align:start position:0%
+i'm going to
+ 
+
+ align:start position:0%
+i'm going to
+relax
+
+ align:start position:0%
+relax
+ 
+
+ align:start position:0%
+relax
+oh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to check whether
+
+ align:start position:0%
+we have to check whether
+ 
+
+ align:start position:0%
+we have to check whether
+whether we can relax it right
+
+ align:start position:0%
+whether we can relax it right
+ 
+
+ align:start position:0%
+whether we can relax it right
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+d the shortest path distance estimate to
+
+ align:start position:0%
+d the shortest path distance estimate to
+ 
+
+ align:start position:0%
+d the shortest path distance estimate to
+v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+u first and then
+
+ align:start position:0%
+u first and then
+ 
+
+ align:start position:0%
+u first and then
+crossing that edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if going through that is better this
+
+ align:start position:0%
+if going through that is better this
+ 
+
+ align:start position:0%
+if going through that is better this
+this is violating our triangle
+
+ align:start position:0%
+this is violating our triangle
+ 
+
+ align:start position:0%
+this is violating our triangle
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+and so we relax
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edge
+
+ align:start position:0%
+edge
+ 
+
+ align:start position:0%
+edge
+u v
+
+ align:start position:0%
+u v
+ 
+
+ align:start position:0%
+u v
+and by that we mean
+
+ align:start position:0%
+and by that we mean
+ 
+
+ align:start position:0%
+and by that we mean
+sets this thing to be equal to that
+
+ align:start position:0%
+sets this thing to be equal to that
+ 
+
+ align:start position:0%
+sets this thing to be equal to that
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+right that's what we meant by relax and
+
+ align:start position:0%
+right that's what we meant by relax and
+ 
+
+ align:start position:0%
+right that's what we meant by relax and
+then we have one other thing to do we've
+
+ align:start position:0%
+then we have one other thing to do we've
+ 
+
+ align:start position:0%
+then we have one other thing to do we've
+changed these
+
+ align:start position:0%
+changed these
+ 
+
+ align:start position:0%
+changed these
+distance estimates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but our q doesn't know that we change
+
+ align:start position:0%
+but our q doesn't know that we change
+ 
+
+ align:start position:0%
+but our q doesn't know that we change
+these things right we added these items
+
+ align:start position:0%
+these things right we added these items
+ 
+
+ align:start position:0%
+these things right we added these items
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but it doesn't know that my distances
+
+ align:start position:0%
+but it doesn't know that my distances
+ 
+
+ align:start position:0%
+but it doesn't know that my distances
+has changed right so we have to tell the
+
+ align:start position:0%
+has changed right so we have to tell the
+ 
+
+ align:start position:0%
+has changed right so we have to tell the
+queue to remember
+
+ align:start position:0%
+queue to remember
+ 
+
+ align:start position:0%
+queue to remember
+we uh to change its
+
+ align:start position:0%
+we uh to change its
+ 
+
+ align:start position:0%
+we uh to change its
+key value
+
+ align:start position:0%
+key value
+ 
+
+ align:start position:0%
+key value
+associated with the item v
+
+ align:start position:0%
+associated with the item v
+ 
+
+ align:start position:0%
+associated with the item v
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+decrease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it decrease
+
+ align:start position:0%
+what is it decrease
+ 
+
+ align:start position:0%
+what is it decrease
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+vertex v
+
+ align:start position:0%
+vertex v
+ 
+
+ align:start position:0%
+vertex v
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the new
+
+ align:start position:0%
+the new
+ 
+
+ align:start position:0%
+the new
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+v the one that i just decreased here
+
+ align:start position:0%
+v the one that i just decreased here
+ 
+
+ align:start position:0%
+v the one that i just decreased here
+right and i know that i decreased it
+
+ align:start position:0%
+right and i know that i decreased it
+ 
+
+ align:start position:0%
+right and i know that i decreased it
+because i set it to a smaller value that
+
+ align:start position:0%
+because i set it to a smaller value that
+ 
+
+ align:start position:0%
+because i set it to a smaller value that
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+all right so that's
+
+ align:start position:0%
+all right so that's
+ 
+
+ align:start position:0%
+all right so that's
+dijkstra
+
+ align:start position:0%
+dijkstra
+ 
+
+ align:start position:0%
+dijkstra
+let's run it on
+
+ align:start position:0%
+let's run it on
+ 
+
+ align:start position:0%
+let's run it on
+an example
+
+ align:start position:0%
+an example
+ 
+
+ align:start position:0%
+an example
+okay so here's an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have a
+
+ align:start position:0%
+i have a
+ 
+
+ align:start position:0%
+i have a
+directed graph it does contain cycles in
+
+ align:start position:0%
+directed graph it does contain cycles in
+ 
+
+ align:start position:0%
+directed graph it does contain cycles in
+particular here are some cycles
+
+ align:start position:0%
+particular here are some cycles
+ 
+
+ align:start position:0%
+particular here are some cycles
+i think those are the the main ones
+
+ align:start position:0%
+i think those are the the main ones
+ 
+
+ align:start position:0%
+i think those are the the main ones
+okay there are definitely cycles in this
+
+ align:start position:0%
+okay there are definitely cycles in this
+ 
+
+ align:start position:0%
+okay there are definitely cycles in this
+graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and but as you see all of the weights
+
+ align:start position:0%
+and but as you see all of the weights
+ 
+
+ align:start position:0%
+and but as you see all of the weights
+are non-negative in particular they're
+
+ align:start position:0%
+are non-negative in particular they're
+ 
+
+ align:start position:0%
+are non-negative in particular they're
+positive actually it's going to be just
+
+ align:start position:0%
+positive actually it's going to be just
+ 
+
+ align:start position:0%
+positive actually it's going to be just
+helpful in
+
+ align:start position:0%
+helpful in
+ 
+
+ align:start position:0%
+helpful in
+in writing out this example so let's run
+
+ align:start position:0%
+in writing out this example so let's run
+ 
+
+ align:start position:0%
+in writing out this example so let's run
+dijkstra on this
+
+ align:start position:0%
+dijkstra on this
+ 
+
+ align:start position:0%
+dijkstra on this
+graph okay first we initialize and we
+
+ align:start position:0%
+graph okay first we initialize and we
+ 
+
+ align:start position:0%
+graph okay first we initialize and we
+set the shortest path distance i'm going
+
+ align:start position:0%
+set the shortest path distance i'm going
+ 
+
+ align:start position:0%
+set the shortest path distance i'm going
+to label it in white here
+
+ align:start position:0%
+to label it in white here
+ 
+
+ align:start position:0%
+to label it in white here
+to all of the things and i'm going to as
+
+ align:start position:0%
+to all of the things and i'm going to as
+ 
+
+ align:start position:0%
+to all of the things and i'm going to as
+i update it i'm just going to cross them
+
+ align:start position:0%
+i update it i'm just going to cross them
+ 
+
+ align:start position:0%
+i update it i'm just going to cross them
+out and write a new number okay
+
+ align:start position:0%
+out and write a new number okay
+ 
+
+ align:start position:0%
+out and write a new number okay
+so that's what it is at the start right
+
+ align:start position:0%
+so that's what it is at the start right
+ 
+
+ align:start position:0%
+so that's what it is at the start right
+that's initialization that's after step
+
+ align:start position:0%
+that's initialization that's after step
+ 
+
+ align:start position:0%
+that's initialization that's after step
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and then i stick things into my queue
+
+ align:start position:0%
+and then i stick things into my queue
+ 
+
+ align:start position:0%
+and then i stick things into my queue
+what's in my queue here's my q
+
+ align:start position:0%
+what's in my queue here's my q
+ 
+
+ align:start position:0%
+what's in my queue here's my q
+right it's everything
+
+ align:start position:0%
+right it's everything
+ 
+
+ align:start position:0%
+right it's everything
+right it's vertices
+
+ align:start position:0%
+right it's vertices
+ 
+
+ align:start position:0%
+right it's vertices
+s a b
+
+ align:start position:0%
+s a b
+ 
+
+ align:start position:0%
+s a b
+c d
+
+ align:start position:0%
+c d
+ 
+
+ align:start position:0%
+c d
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i got five items
+
+ align:start position:0%
+i got five items
+ 
+
+ align:start position:0%
+i got five items
+in my queue
+
+ align:start position:0%
+in my queue
+ 
+
+ align:start position:0%
+in my queue
+really it's the item pair with its
+
+ align:start position:0%
+really it's the item pair with its
+ 
+
+ align:start position:0%
+really it's the item pair with its
+shortest distance estimate i'm just not
+
+ align:start position:0%
+shortest distance estimate i'm just not
+ 
+
+ align:start position:0%
+shortest distance estimate i'm just not
+going to rewrite that here okay
+
+ align:start position:0%
+going to rewrite that here okay
+ 
+
+ align:start position:0%
+going to rewrite that here okay
+so the idea here is what's the the while
+
+ align:start position:0%
+so the idea here is what's the the while
+ 
+
+ align:start position:0%
+so the idea here is what's the the while
+loop okay q is not empty great
+
+ align:start position:0%
+loop okay q is not empty great
+ 
+
+ align:start position:0%
+loop okay q is not empty great
+we're gonna delete
+
+ align:start position:0%
+we're gonna delete
+ 
+
+ align:start position:0%
+we're gonna delete
+the one with the smallest distance
+
+ align:start position:0%
+the one with the smallest distance
+ 
+
+ align:start position:0%
+the one with the smallest distance
+estimate which is
+
+ align:start position:0%
+estimate which is
+ 
+
+ align:start position:0%
+estimate which is
+s right yeah
+
+ align:start position:0%
+s right yeah
+ 
+
+ align:start position:0%
+s right yeah
+so i remove that
+
+ align:start position:0%
+so i remove that
+ 
+
+ align:start position:0%
+so i remove that
+and then i relax edges out of s right so
+
+ align:start position:0%
+and then i relax edges out of s right so
+ 
+
+ align:start position:0%
+and then i relax edges out of s right so
+i relax edge
+
+ align:start position:0%
+i relax edge
+ 
+
+ align:start position:0%
+i relax edge
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+that's better than the distance estimate
+
+ align:start position:0%
+that's better than the distance estimate
+ 
+
+ align:start position:0%
+that's better than the distance estimate
+10 is better than the distance estimate
+
+ align:start position:0%
+10 is better than the distance estimate
+ 
+
+ align:start position:0%
+10 is better than the distance estimate
+infinite so i'm going to
+
+ align:start position:0%
+infinite so i'm going to
+ 
+
+ align:start position:0%
+infinite so i'm going to
+change this to 10.
+
+ align:start position:0%
+change this to 10.
+ 
+
+ align:start position:0%
+change this to 10.
+and then here's another outgoing edge
+
+ align:start position:0%
+and then here's another outgoing edge
+ 
+
+ align:start position:0%
+and then here's another outgoing edge
+3 is better than
+
+ align:start position:0%
+3 is better than
+ 
+
+ align:start position:0%
+3 is better than
+infinite so
+
+ align:start position:0%
+infinite so
+ 
+
+ align:start position:0%
+infinite so
+i'm going to change its delta to 3.
+
+ align:start position:0%
+i'm going to change its delta to 3.
+ 
+
+ align:start position:0%
+i'm going to change its delta to 3.
+okay so now i go back in here
+
+ align:start position:0%
+okay so now i go back in here
+ 
+
+ align:start position:0%
+okay so now i go back in here
+and i change the distance estimates
+
+ align:start position:0%
+and i change the distance estimates
+ 
+
+ align:start position:0%
+and i change the distance estimates
+associated with my q
+
+ align:start position:0%
+associated with my q
+ 
+
+ align:start position:0%
+associated with my q
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now next step of the algorithm
+
+ align:start position:0%
+now next step of the algorithm
+ 
+
+ align:start position:0%
+now next step of the algorithm
+s is done
+
+ align:start position:0%
+s is done
+ 
+
+ align:start position:0%
+s is done
+right i've processed everything
+
+ align:start position:0%
+right i've processed everything
+ 
+
+ align:start position:0%
+right i've processed everything
+distance 0 away
+
+ align:start position:0%
+distance 0 away
+ 
+
+ align:start position:0%
+distance 0 away
+but i'm now going to use my priority
+
+ align:start position:0%
+but i'm now going to use my priority
+ 
+
+ align:start position:0%
+but i'm now going to use my priority
+queue to say
+
+ align:start position:0%
+queue to say
+ 
+
+ align:start position:0%
+queue to say
+which of my vertices has the shortest
+
+ align:start position:0%
+which of my vertices has the shortest
+ 
+
+ align:start position:0%
+which of my vertices has the shortest
+distance estimate now
+
+ align:start position:0%
+distance estimate now
+ 
+
+ align:start position:0%
+distance estimate now
+so which one is it
+
+ align:start position:0%
+so which one is it
+ 
+
+ align:start position:0%
+so which one is it
+a b or c or d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's three c right three is smaller
+
+ align:start position:0%
+yeah it's three c right three is smaller
+ 
+
+ align:start position:0%
+yeah it's three c right three is smaller
+than 10. so
+
+ align:start position:0%
+than 10. so
+ 
+
+ align:start position:0%
+than 10. so
+q is going to magically delete c for me
+
+ align:start position:0%
+q is going to magically delete c for me
+ 
+
+ align:start position:0%
+q is going to magically delete c for me
+tell me what that is and now i'm going
+
+ align:start position:0%
+tell me what that is and now i'm going
+ 
+
+ align:start position:0%
+tell me what that is and now i'm going
+to process that right i've now changed
+
+ align:start position:0%
+to process that right i've now changed
+ 
+
+ align:start position:0%
+to process that right i've now changed
+my boundary
+
+ align:start position:0%
+my boundary
+ 
+
+ align:start position:0%
+my boundary
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+okay and now i relax edges
+
+ align:start position:0%
+okay and now i relax edges
+ 
+
+ align:start position:0%
+okay and now i relax edges
+out of c
+
+ align:start position:0%
+out of c
+ 
+
+ align:start position:0%
+out of c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's an edge out of c that's a 4
+
+ align:start position:0%
+here's an edge out of c that's a 4
+ 
+
+ align:start position:0%
+here's an edge out of c that's a 4
+a 4 plus the 3 is smaller than 10
+
+ align:start position:0%
+a 4 plus the 3 is smaller than 10
+ 
+
+ align:start position:0%
+a 4 plus the 3 is smaller than 10
+so i update it
+
+ align:start position:0%
+so i update it
+ 
+
+ align:start position:0%
+so i update it
+3 plus 8 is 11. that's smaller than
+
+ align:start position:0%
+3 plus 8 is 11. that's smaller than
+ 
+
+ align:start position:0%
+3 plus 8 is 11. that's smaller than
+infinite so i update it i relax
+
+ align:start position:0%
+infinite so i update it i relax
+ 
+
+ align:start position:0%
+infinite so i update it i relax
+3 plus 2 is smaller than infinite so i
+
+ align:start position:0%
+3 plus 2 is smaller than infinite so i
+ 
+
+ align:start position:0%
+3 plus 2 is smaller than infinite so i
+relax that as well
+
+ align:start position:0%
+relax that as well
+ 
+
+ align:start position:0%
+relax that as well
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now of the things still left in my queue
+
+ align:start position:0%
+now of the things still left in my queue
+ 
+
+ align:start position:0%
+now of the things still left in my queue
+i'm actually going to
+
+ align:start position:0%
+i'm actually going to
+ 
+
+ align:start position:0%
+i'm actually going to
+remove it from my queue instead of
+
+ align:start position:0%
+remove it from my queue instead of
+ 
+
+ align:start position:0%
+remove it from my queue instead of
+crossing it out maybe that's better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the vertices still left in my queue
+
+ align:start position:0%
+of the vertices still left in my queue
+ 
+
+ align:start position:0%
+of the vertices still left in my queue
+which has smallest distance
+
+ align:start position:0%
+which has smallest distance
+ 
+
+ align:start position:0%
+which has smallest distance
+yeah d
+
+ align:start position:0%
+yeah d
+ 
+
+ align:start position:0%
+yeah d
+d has five seven or eleven five is the
+
+ align:start position:0%
+d has five seven or eleven five is the
+ 
+
+ align:start position:0%
+d has five seven or eleven five is the
+smallest so i remove d from my q and i
+
+ align:start position:0%
+smallest so i remove d from my q and i
+ 
+
+ align:start position:0%
+smallest so i remove d from my q and i
+relax edges from it
+
+ align:start position:0%
+relax edges from it
+ 
+
+ align:start position:0%
+relax edges from it
+and now my
+
+ align:start position:0%
+and now my
+ 
+
+ align:start position:0%
+and now my
+boundary looks something like this
+
+ align:start position:0%
+boundary looks something like this
+ 
+
+ align:start position:0%
+boundary looks something like this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i relax edges out of it five plus five
+
+ align:start position:0%
+i relax edges out of it five plus five
+ 
+
+ align:start position:0%
+i relax edges out of it five plus five
+that's ten ten is smaller than eleven so
+
+ align:start position:0%
+that's ten ten is smaller than eleven so
+ 
+
+ align:start position:0%
+that's ten ten is smaller than eleven so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+a ten
+
+ align:start position:0%
+a ten
+ 
+
+ align:start position:0%
+a ten
+and that's the only outgoing edge from d
+
+ align:start position:0%
+and that's the only outgoing edge from d
+ 
+
+ align:start position:0%
+and that's the only outgoing edge from d
+so i'm done okay and then the last seven
+
+ align:start position:0%
+so i'm done okay and then the last seven
+ 
+
+ align:start position:0%
+so i'm done okay and then the last seven
+is smaller than 10.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i relax edges out of a
+
+ align:start position:0%
+i relax edges out of a
+ 
+
+ align:start position:0%
+i relax edges out of a
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+to b
+
+ align:start position:0%
+to b
+ 
+
+ align:start position:0%
+to b
+seven plus two is smaller than ten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i'm done so what i did every
+
+ align:start position:0%
+and now i'm done so what i did every
+ 
+
+ align:start position:0%
+and now i'm done so what i did every
+time i
+
+ align:start position:0%
+time i
+ 
+
+ align:start position:0%
+time i
+removed s or i removed a vertex i set
+
+ align:start position:0%
+removed s or i removed a vertex i set
+ 
+
+ align:start position:0%
+removed s or i removed a vertex i set
+its shortest path distance to the
+
+ align:start position:0%
+its shortest path distance to the
+ 
+
+ align:start position:0%
+its shortest path distance to the
+small the the last value i assigned to
+
+ align:start position:0%
+small the the last value i assigned to
+ 
+
+ align:start position:0%
+small the the last value i assigned to
+it so this was then three
+
+ align:start position:0%
+it so this was then three
+ 
+
+ align:start position:0%
+it so this was then three
+and then a was seven
+
+ align:start position:0%
+and then a was seven
+ 
+
+ align:start position:0%
+and then a was seven
+b was nine
+
+ align:start position:0%
+b was nine
+ 
+
+ align:start position:0%
+b was nine
+and then d was five
+
+ align:start position:0%
+and then d was five
+ 
+
+ align:start position:0%
+and then d was five
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's dijkstra in action
+
+ align:start position:0%
+so that's dijkstra in action
+ 
+
+ align:start position:0%
+so that's dijkstra in action
+it seems like
+
+ align:start position:0%
+it seems like
+ 
+
+ align:start position:0%
+it seems like
+these are the shortest path distances
+
+ align:start position:0%
+these are the shortest path distances
+ 
+
+ align:start position:0%
+these are the shortest path distances
+but how do we prove that did it do the
+
+ align:start position:0%
+but how do we prove that did it do the
+ 
+
+ align:start position:0%
+but how do we prove that did it do the
+right thing
+
+ align:start position:0%
+right thing
+ 
+
+ align:start position:0%
+right thing
+well let's find out
+
+ align:start position:0%
+well let's find out
+ 
+
+ align:start position:0%
+well let's find out
+so that's what we're going to spend
+
+ align:start position:0%
+so that's what we're going to spend
+ 
+
+ align:start position:0%
+so that's what we're going to spend
+some time on right now is talking about
+
+ align:start position:0%
+some time on right now is talking about
+ 
+
+ align:start position:0%
+some time on right now is talking about
+the correctness of dijkstra's algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay correctness follows from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+two main observations
+
+ align:start position:0%
+two main observations
+ 
+
+ align:start position:0%
+two main observations
+okay so the the claim here that we're
+
+ align:start position:0%
+okay so the the claim here that we're
+ 
+
+ align:start position:0%
+okay so the the claim here that we're
+trying to prove is that
+
+ align:start position:0%
+trying to prove is that
+ 
+
+ align:start position:0%
+trying to prove is that
+d of s
+
+ align:start position:0%
+d of s
+ 
+
+ align:start position:0%
+d of s
+equals the delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s so the estimates
+
+ align:start position:0%
+s so the estimates
+ 
+
+ align:start position:0%
+s so the estimates
+equal the shortest path distances
+
+ align:start position:0%
+equal the shortest path distances
+ 
+
+ align:start position:0%
+equal the shortest path distances
+at the end of dijkstra
+
+ align:start position:0%
+at the end of dijkstra
+ 
+
+ align:start position:0%
+at the end of dijkstra
+for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v and v
+
+ align:start position:0%
+v and v
+ 
+
+ align:start position:0%
+v and v
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+ant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and this is going to follow from two
+
+ align:start position:0%
+and this is going to follow from two
+ 
+
+ align:start position:0%
+and this is going to follow from two
+observations so the proof
+
+ align:start position:0%
+observations so the proof
+ 
+
+ align:start position:0%
+observations so the proof
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if ever relaxation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+d of s of v it sets the estimate equal
+
+ align:start position:0%
+d of s of v it sets the estimate equal
+ 
+
+ align:start position:0%
+d of s of v it sets the estimate equal
+to the shortest path distance
+
+ align:start position:0%
+to the shortest path distance
+ 
+
+ align:start position:0%
+to the shortest path distance
+if it ever does that
+
+ align:start position:0%
+if it ever does that
+ 
+
+ align:start position:0%
+if it ever does that
+i argue to you
+
+ align:start position:0%
+i argue to you
+ 
+
+ align:start position:0%
+i argue to you
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's not a very strong statement
+
+ align:start position:0%
+okay that's not a very strong statement
+ 
+
+ align:start position:0%
+okay that's not a very strong statement
+right this is saying if i ever set the
+
+ align:start position:0%
+right this is saying if i ever set the
+ 
+
+ align:start position:0%
+right this is saying if i ever set the
+the distance estimate
+
+ align:start position:0%
+the distance estimate
+ 
+
+ align:start position:0%
+the distance estimate
+to the true distance
+
+ align:start position:0%
+to the true distance
+ 
+
+ align:start position:0%
+to the true distance
+i'm never going to set it to a different
+
+ align:start position:0%
+i'm never going to set it to a different
+ 
+
+ align:start position:0%
+i'm never going to set it to a different
+value later on
+
+ align:start position:0%
+value later on
+ 
+
+ align:start position:0%
+value later on
+and why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+relaxation
+
+ align:start position:0%
+relaxation
+ 
+
+ align:start position:0%
+relaxation
+only ever decreases the distance right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relaxation
+
+ align:start position:0%
+relaxation
+ 
+
+ align:start position:0%
+relaxation
+only decreases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dsv
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we proved in lecture 11 so two lectures
+
+ align:start position:0%
+we proved in lecture 11 so two lectures
+ 
+
+ align:start position:0%
+we proved in lecture 11 so two lectures
+ago that relaxation is safe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what is safe mean
+
+ align:start position:0%
+and what is safe mean
+ 
+
+ align:start position:0%
+and what is safe mean
+safe means that
+
+ align:start position:0%
+safe means that
+ 
+
+ align:start position:0%
+safe means that
+relaxation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that these relaxation will only ever
+
+ align:start position:0%
+that these relaxation will only ever
+ 
+
+ align:start position:0%
+that these relaxation will only ever
+change these distance estimates
+
+ align:start position:0%
+change these distance estimates
+ 
+
+ align:start position:0%
+change these distance estimates
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+be either
+
+ align:start position:0%
+be either
+ 
+
+ align:start position:0%
+be either
+infinite right it was never there was
+
+ align:start position:0%
+infinite right it was never there was
+ 
+
+ align:start position:0%
+infinite right it was never there was
+never a path
+
+ align:start position:0%
+never a path
+ 
+
+ align:start position:0%
+never a path
+to my
+
+ align:start position:0%
+to my
+ 
+
+ align:start position:0%
+to my
+my vertex or
+
+ align:start position:0%
+my vertex or
+ 
+
+ align:start position:0%
+my vertex or
+it was the length of some path to v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length
+
+ align:start position:0%
+length
+ 
+
+ align:start position:0%
+length
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what does that mean
+
+ align:start position:0%
+okay so what does that mean
+ 
+
+ align:start position:0%
+okay so what does that mean
+it only decreases
+
+ align:start position:0%
+it only decreases
+ 
+
+ align:start position:0%
+it only decreases
+but it's always the length of some path
+
+ align:start position:0%
+but it's always the length of some path
+ 
+
+ align:start position:0%
+but it's always the length of some path
+to v right so if this is the length of
+
+ align:start position:0%
+to v right so if this is the length of
+ 
+
+ align:start position:0%
+to v right so if this is the length of
+the shortest path to v i could never set
+
+ align:start position:0%
+the shortest path to v i could never set
+ 
+
+ align:start position:0%
+the shortest path to v i could never set
+it to a smaller length
+
+ align:start position:0%
+it to a smaller length
+ 
+
+ align:start position:0%
+it to a smaller length
+right because there are no paths with
+
+ align:start position:0%
+right because there are no paths with
+ 
+
+ align:start position:0%
+right because there are no paths with
+shorter distance that's the kind of
+
+ align:start position:0%
+shorter distance that's the kind of
+ 
+
+ align:start position:0%
+shorter distance that's the kind of
+little point okay so with this
+
+ align:start position:0%
+little point okay so with this
+ 
+
+ align:start position:0%
+little point okay so with this
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+i i'm gonna argue this final claim
+
+ align:start position:0%
+i i'm gonna argue this final claim
+ 
+
+ align:start position:0%
+i i'm gonna argue this final claim
+it suffices to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my estimate
+
+ align:start position:0%
+my estimate
+ 
+
+ align:start position:0%
+my estimate
+equals the shortest distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v is removed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+the queue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and since i remove every vertex from the
+
+ align:start position:0%
+and since i remove every vertex from the
+ 
+
+ align:start position:0%
+and since i remove every vertex from the
+queue
+
+ align:start position:0%
+queue
+ 
+
+ align:start position:0%
+queue
+in this while loop
+
+ align:start position:0%
+in this while loop
+ 
+
+ align:start position:0%
+in this while loop
+i will have eventually set all of the
+
+ align:start position:0%
+i will have eventually set all of the
+ 
+
+ align:start position:0%
+i will have eventually set all of the
+distance estimates to the real distance
+
+ align:start position:0%
+distance estimates to the real distance
+ 
+
+ align:start position:0%
+distance estimates to the real distance
+and will be golden
+
+ align:start position:0%
+and will be golden
+ 
+
+ align:start position:0%
+and will be golden
+happy days all right so we'll be done
+
+ align:start position:0%
+happy days all right so we'll be done
+ 
+
+ align:start position:0%
+happy days all right so we'll be done
+if we can prove that statement all right
+
+ align:start position:0%
+if we can prove that statement all right
+ 
+
+ align:start position:0%
+if we can prove that statement all right
+so we're gonna prove this by induction
+
+ align:start position:0%
+so we're gonna prove this by induction
+ 
+
+ align:start position:0%
+so we're gonna prove this by induction
+obviously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+production
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+removed
+
+ align:start position:0%
+removed
+ 
+
+ align:start position:0%
+removed
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+the queue
+
+ align:start position:0%
+the queue
+ 
+
+ align:start position:0%
+the queue
+all right so the q
+
+ align:start position:0%
+all right so the q
+ 
+
+ align:start position:0%
+all right so the q
+we're we're popping vertices from this q
+
+ align:start position:0%
+we're we're popping vertices from this q
+ 
+
+ align:start position:0%
+we're we're popping vertices from this q
+in some order
+
+ align:start position:0%
+in some order
+ 
+
+ align:start position:0%
+in some order
+so i'm going to just argue that this
+
+ align:start position:0%
+so i'm going to just argue that this
+ 
+
+ align:start position:0%
+so i'm going to just argue that this
+claim is true for the first k
+
+ align:start position:0%
+claim is true for the first k
+ 
+
+ align:start position:0%
+claim is true for the first k
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+clearly that's true for k equals 1
+
+ align:start position:0%
+clearly that's true for k equals 1
+ 
+
+ align:start position:0%
+clearly that's true for k equals 1
+base case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k equals 1
+
+ align:start position:0%
+k equals 1
+ 
+
+ align:start position:0%
+k equals 1
+right what is k equals 1 that means the
+
+ align:start position:0%
+right what is k equals 1 that means the
+ 
+
+ align:start position:0%
+right what is k equals 1 that means the
+first vertex that i pop has this
+
+ align:start position:0%
+first vertex that i pop has this
+ 
+
+ align:start position:0%
+first vertex that i pop has this
+property which is definitely true
+
+ align:start position:0%
+property which is definitely true
+ 
+
+ align:start position:0%
+property which is definitely true
+because we set
+
+ align:start position:0%
+because we set
+ 
+
+ align:start position:0%
+because we set
+the shortest path distance to s to be
+
+ align:start position:0%
+the shortest path distance to s to be
+ 
+
+ align:start position:0%
+the shortest path distance to s to be
+zero that's all good
+
+ align:start position:0%
+zero that's all good
+ 
+
+ align:start position:0%
+zero that's all good
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we have our inductive step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+assume it's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+k prime
+
+ align:start position:0%
+k prime
+ 
+
+ align:start position:0%
+k prime
+sorry k less than
+
+ align:start position:0%
+sorry k less than
+ 
+
+ align:start position:0%
+sorry k less than
+k prime okay
+
+ align:start position:0%
+k prime okay
+ 
+
+ align:start position:0%
+k prime okay
+and let's let
+
+ align:start position:0%
+and let's let
+ 
+
+ align:start position:0%
+and let's let
+v prime
+
+ align:start position:0%
+v prime
+ 
+
+ align:start position:0%
+v prime
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+k prime
+
+ align:start position:0%
+k prime
+ 
+
+ align:start position:0%
+k prime
+vertex pot
+
+ align:start position:0%
+vertex pot
+ 
+
+ align:start position:0%
+vertex pot
+okay v prime
+
+ align:start position:0%
+okay v prime
+ 
+
+ align:start position:0%
+okay v prime
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now let's look at some
+
+ align:start position:0%
+and now let's look at some
+ 
+
+ align:start position:0%
+and now let's look at some
+shortest path
+
+ align:start position:0%
+shortest path
+ 
+
+ align:start position:0%
+shortest path
+from s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to v prime
+
+ align:start position:0%
+to v prime
+ 
+
+ align:start position:0%
+to v prime
+so we got the shortest path
+
+ align:start position:0%
+so we got the shortest path
+ 
+
+ align:start position:0%
+so we got the shortest path
+from s to v prime
+
+ align:start position:0%
+from s to v prime
+ 
+
+ align:start position:0%
+from s to v prime
+it exists v prime is
+
+ align:start position:0%
+it exists v prime is
+ 
+
+ align:start position:0%
+it exists v prime is
+accessible let's say we pruned our graph
+
+ align:start position:0%
+accessible let's say we pruned our graph
+ 
+
+ align:start position:0%
+accessible let's say we pruned our graph
+to be only the things accessible from s
+
+ align:start position:0%
+to be only the things accessible from s
+ 
+
+ align:start position:0%
+to be only the things accessible from s
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+yeah there exists a shortest path
+
+ align:start position:0%
+yeah there exists a shortest path
+ 
+
+ align:start position:0%
+yeah there exists a shortest path
+to v prime okay
+
+ align:start position:0%
+to v prime okay
+ 
+
+ align:start position:0%
+to v prime okay
+and now let's think about
+
+ align:start position:0%
+and now let's think about
+ 
+
+ align:start position:0%
+and now let's think about
+these vertices
+
+ align:start position:0%
+these vertices
+ 
+
+ align:start position:0%
+these vertices
+some of them
+
+ align:start position:0%
+some of them
+ 
+
+ align:start position:0%
+some of them
+were removed from the queue
+
+ align:start position:0%
+were removed from the queue
+ 
+
+ align:start position:0%
+were removed from the queue
+and some of them were not right s was
+
+ align:start position:0%
+and some of them were not right s was
+ 
+
+ align:start position:0%
+and some of them were not right s was
+definitely removed from the queue
+
+ align:start position:0%
+definitely removed from the queue
+ 
+
+ align:start position:0%
+definitely removed from the queue
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+some of these other vertices might not
+
+ align:start position:0%
+some of these other vertices might not
+ 
+
+ align:start position:0%
+some of these other vertices might not
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+right i want to be able to induct on
+
+ align:start position:0%
+right i want to be able to induct on
+ 
+
+ align:start position:0%
+right i want to be able to induct on
+this path in particular
+
+ align:start position:0%
+this path in particular
+ 
+
+ align:start position:0%
+this path in particular
+the vertex before me
+
+ align:start position:0%
+the vertex before me
+ 
+
+ align:start position:0%
+the vertex before me
+so that i can say that when i removed it
+
+ align:start position:0%
+so that i can say that when i removed it
+ 
+
+ align:start position:0%
+so that i can say that when i removed it
+and i relax the edge to v prime
+
+ align:start position:0%
+and i relax the edge to v prime
+ 
+
+ align:start position:0%
+and i relax the edge to v prime
+then we're all golden right
+
+ align:start position:0%
+then we're all golden right
+ 
+
+ align:start position:0%
+then we're all golden right
+but that might not be the case there
+
+ align:start position:0%
+but that might not be the case there
+ 
+
+ align:start position:0%
+but that might not be the case there
+could be a vertex the vertex preceding
+
+ align:start position:0%
+could be a vertex the vertex preceding
+ 
+
+ align:start position:0%
+could be a vertex the vertex preceding
+me in the graph in this shortest path
+
+ align:start position:0%
+me in the graph in this shortest path
+ 
+
+ align:start position:0%
+me in the graph in this shortest path
+it was not popped from q i need to argue
+
+ align:start position:0%
+it was not popped from q i need to argue
+ 
+
+ align:start position:0%
+it was not popped from q i need to argue
+that it was or some other thing okay so
+
+ align:start position:0%
+that it was or some other thing okay so
+ 
+
+ align:start position:0%
+that it was or some other thing okay so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+in this path from s to v
+
+ align:start position:0%
+in this path from s to v
+ 
+
+ align:start position:0%
+in this path from s to v
+i'm going to call it
+
+ align:start position:0%
+i'm going to call it
+ 
+
+ align:start position:0%
+i'm going to call it
+y i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a vertex y
+
+ align:start position:0%
+a vertex y
+ 
+
+ align:start position:0%
+a vertex y
+that is not in q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+after i pop v prime this is the first or
+
+ align:start position:0%
+after i pop v prime this is the first or
+ 
+
+ align:start position:0%
+after i pop v prime this is the first or
+before i pop v prime
+
+ align:start position:0%
+before i pop v prime
+ 
+
+ align:start position:0%
+before i pop v prime
+y is not in the queue now these might be
+
+ align:start position:0%
+y is not in the queue now these might be
+ 
+
+ align:start position:0%
+y is not in the queue now these might be
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+vertex right if all of the preceding
+
+ align:start position:0%
+vertex right if all of the preceding
+ 
+
+ align:start position:0%
+vertex right if all of the preceding
+ones on this path
+
+ align:start position:0%
+ones on this path
+ 
+
+ align:start position:0%
+ones on this path
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+were in the queue
+
+ align:start position:0%
+were in the queue
+ 
+
+ align:start position:0%
+were in the queue
+but in particular
+
+ align:start position:0%
+but in particular
+ 
+
+ align:start position:0%
+but in particular
+we're going to look at this guy okay and
+
+ align:start position:0%
+we're going to look at this guy okay and
+ 
+
+ align:start position:0%
+we're going to look at this guy okay and
+say its predecessor's x in the path
+
+ align:start position:0%
+say its predecessor's x in the path
+ 
+
+ align:start position:0%
+say its predecessor's x in the path
+well what do i know
+
+ align:start position:0%
+well what do i know
+ 
+
+ align:start position:0%
+well what do i know
+i know that x is in the queue right
+
+ align:start position:0%
+i know that x is in the queue right
+ 
+
+ align:start position:0%
+i know that x is in the queue right
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+was popped from the queue
+
+ align:start position:0%
+was popped from the queue
+ 
+
+ align:start position:0%
+was popped from the queue
+not in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+which means that by induction
+
+ align:start position:0%
+which means that by induction
+ 
+
+ align:start position:0%
+which means that by induction
+the shortest path
+
+ align:start position:0%
+the shortest path
+ 
+
+ align:start position:0%
+the shortest path
+distance was set here correctly
+
+ align:start position:0%
+distance was set here correctly
+ 
+
+ align:start position:0%
+distance was set here correctly
+so that the
+
+ align:start position:0%
+so that the
+ 
+
+ align:start position:0%
+so that the
+the distance estimate at y
+
+ align:start position:0%
+the distance estimate at y
+ 
+
+ align:start position:0%
+the distance estimate at y
+can't be bigger than
+
+ align:start position:0%
+can't be bigger than
+ 
+
+ align:start position:0%
+can't be bigger than
+the shortest path to x
+
+ align:start position:0%
+the shortest path to x
+ 
+
+ align:start position:0%
+the shortest path to x
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+x y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but this is on the shortest path to y
+
+ align:start position:0%
+but this is on the shortest path to y
+ 
+
+ align:start position:0%
+but this is on the shortest path to y
+right because sub paths of
+
+ align:start position:0%
+right because sub paths of
+ 
+
+ align:start position:0%
+right because sub paths of
+shortest paths are shortest paths so
+
+ align:start position:0%
+shortest paths are shortest paths so
+ 
+
+ align:start position:0%
+shortest paths are shortest paths so
+this has to equal
+
+ align:start position:0%
+this has to equal
+ 
+
+ align:start position:0%
+this has to equal
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+s y right the distance to y so actually
+
+ align:start position:0%
+s y right the distance to y so actually
+ 
+
+ align:start position:0%
+s y right the distance to y so actually
+y is all good here right and so if v
+
+ align:start position:0%
+y is all good here right and so if v
+ 
+
+ align:start position:0%
+y is all good here right and so if v
+prime were y we'd be done
+
+ align:start position:0%
+prime were y we'd be done
+ 
+
+ align:start position:0%
+prime were y we'd be done
+right that's the same argument as dag
+
+ align:start position:0%
+right that's the same argument as dag
+ 
+
+ align:start position:0%
+right that's the same argument as dag
+relaxation
+
+ align:start position:0%
+relaxation
+ 
+
+ align:start position:0%
+relaxation
+but we need to prove something about v
+
+ align:start position:0%
+but we need to prove something about v
+ 
+
+ align:start position:0%
+but we need to prove something about v
+prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well because we have non-negative
+
+ align:start position:0%
+well because we have non-negative
+ 
+
+ align:start position:0%
+well because we have non-negative
+weights the distance to v prime
+
+ align:start position:0%
+weights the distance to v prime
+ 
+
+ align:start position:0%
+weights the distance to v prime
+has to be at least as big as this
+
+ align:start position:0%
+has to be at least as big as this
+ 
+
+ align:start position:0%
+has to be at least as big as this
+distance right because it's a sub-path
+
+ align:start position:0%
+distance right because it's a sub-path
+ 
+
+ align:start position:0%
+distance right because it's a sub-path
+right so this has to be less than or
+
+ align:start position:0%
+right so this has to be less than or
+ 
+
+ align:start position:0%
+right so this has to be less than or
+equal to the true distance
+
+ align:start position:0%
+equal to the true distance
+ 
+
+ align:start position:0%
+equal to the true distance
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the prime
+
+ align:start position:0%
+the prime
+ 
+
+ align:start position:0%
+the prime
+right because
+
+ align:start position:0%
+right because
+ 
+
+ align:start position:0%
+right because
+of negative uh non-negative weights
+
+ align:start position:0%
+of negative uh non-negative weights
+ 
+
+ align:start position:0%
+of negative uh non-negative weights
+right because the weights are
+
+ align:start position:0%
+right because the weights are
+ 
+
+ align:start position:0%
+right because the weights are
+non-negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but because relaxation is safe
+
+ align:start position:0%
+but because relaxation is safe
+ 
+
+ align:start position:0%
+but because relaxation is safe
+we know that our distance estimate for v
+
+ align:start position:0%
+we know that our distance estimate for v
+ 
+
+ align:start position:0%
+we know that our distance estimate for v
+prime has to be at least the shortest
+
+ align:start position:0%
+prime has to be at least the shortest
+ 
+
+ align:start position:0%
+prime has to be at least the shortest
+path distance right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is because it's safe
+
+ align:start position:0%
+right this is because it's safe
+ 
+
+ align:start position:0%
+right this is because it's safe
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+weights are
+
+ align:start position:0%
+weights are
+ 
+
+ align:start position:0%
+weights are
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+greater than or equal to zero
+
+ align:start position:0%
+greater than or equal to zero
+ 
+
+ align:start position:0%
+greater than or equal to zero
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the last step here
+
+ align:start position:0%
+the last step here
+ 
+
+ align:start position:0%
+the last step here
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+because we're popping the minimum from
+
+ align:start position:0%
+because we're popping the minimum from
+ 
+
+ align:start position:0%
+because we're popping the minimum from
+our priority queue
+
+ align:start position:0%
+our priority queue
+ 
+
+ align:start position:0%
+our priority queue
+right the thing with the smallest
+
+ align:start position:0%
+right the thing with the smallest
+ 
+
+ align:start position:0%
+right the thing with the smallest
+shortest path distance
+
+ align:start position:0%
+shortest path distance
+ 
+
+ align:start position:0%
+shortest path distance
+this has to be less than or equal to
+
+ align:start position:0%
+this has to be less than or equal to
+ 
+
+ align:start position:0%
+this has to be less than or equal to
+the shortest path distance estimate to y
+
+ align:start position:0%
+the shortest path distance estimate to y
+ 
+
+ align:start position:0%
+the shortest path distance estimate to y
+right because this is the smallest among
+
+ align:start position:0%
+right because this is the smallest among
+ 
+
+ align:start position:0%
+right because this is the smallest among
+all such vertices in my queue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but these are the same value
+
+ align:start position:0%
+but these are the same value
+ 
+
+ align:start position:0%
+but these are the same value
+so everything between here is the same
+
+ align:start position:0%
+so everything between here is the same
+ 
+
+ align:start position:0%
+so everything between here is the same
+value in particular
+
+ align:start position:0%
+value in particular
+ 
+
+ align:start position:0%
+value in particular
+the estimate here
+
+ align:start position:0%
+the estimate here
+ 
+
+ align:start position:0%
+the estimate here
+is equal to my true shortest path
+
+ align:start position:0%
+is equal to my true shortest path
+ 
+
+ align:start position:0%
+is equal to my true shortest path
+distance which is exactly what we're
+
+ align:start position:0%
+distance which is exactly what we're
+ 
+
+ align:start position:0%
+distance which is exactly what we're
+trying to prove okay so that's why
+
+ align:start position:0%
+trying to prove okay so that's why
+ 
+
+ align:start position:0%
+trying to prove okay so that's why
+dijkstra is correct
+
+ align:start position:0%
+dijkstra is correct
+ 
+
+ align:start position:0%
+dijkstra is correct
+and spend the last five minutes on
+
+ align:start position:0%
+and spend the last five minutes on
+ 
+
+ align:start position:0%
+and spend the last five minutes on
+the running time of dykstra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we set this up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that we did everything in terms of
+
+ align:start position:0%
+so that we did everything in terms of
+ 
+
+ align:start position:0%
+so that we did everything in terms of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+these q operations
+
+ align:start position:0%
+these q operations
+ 
+
+ align:start position:0%
+these q operations
+right so we have these q operations we
+
+ align:start position:0%
+right so we have these q operations we
+ 
+
+ align:start position:0%
+right so we have these q operations we
+have three of them
+
+ align:start position:0%
+have three of them
+ 
+
+ align:start position:0%
+have three of them
+i'm going to say if i have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a build operation let's say it takes b
+
+ align:start position:0%
+a build operation let's say it takes b
+ 
+
+ align:start position:0%
+a build operation let's say it takes b
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+delete min i'm going to say it takes m
+
+ align:start position:0%
+delete min i'm going to say it takes m
+ 
+
+ align:start position:0%
+delete min i'm going to say it takes m
+time and this decreased key i'm going to
+
+ align:start position:0%
+time and this decreased key i'm going to
+ 
+
+ align:start position:0%
+time and this decreased key i'm going to
+say it takes d time
+
+ align:start position:0%
+say it takes d time
+ 
+
+ align:start position:0%
+say it takes d time
+okay so what's the running time of
+
+ align:start position:0%
+okay so what's the running time of
+ 
+
+ align:start position:0%
+okay so what's the running time of
+dijkstra if i take a look at that
+
+ align:start position:0%
+dijkstra if i take a look at that
+ 
+
+ align:start position:0%
+dijkstra if i take a look at that
+algorithm over there
+
+ align:start position:0%
+algorithm over there
+ 
+
+ align:start position:0%
+algorithm over there
+well i guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's switch these back up again
+
+ align:start position:0%
+let's switch these back up again
+ 
+
+ align:start position:0%
+let's switch these back up again
+okay so what does this do we build once
+
+ align:start position:0%
+okay so what does this do we build once
+ 
+
+ align:start position:0%
+okay so what does this do we build once
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+then we delete
+
+ align:start position:0%
+then we delete
+ 
+
+ align:start position:0%
+then we delete
+the minimum from the queue how many
+
+ align:start position:0%
+the minimum from the queue how many
+ 
+
+ align:start position:0%
+the minimum from the queue how many
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+v times right we remove every vertex
+
+ align:start position:0%
+v times right we remove every vertex
+ 
+
+ align:start position:0%
+v times right we remove every vertex
+from our q
+
+ align:start position:0%
+from our q
+ 
+
+ align:start position:0%
+from our q
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+for every possible edge
+
+ align:start position:0%
+for every possible edge
+ 
+
+ align:start position:0%
+for every possible edge
+we may need to relax
+
+ align:start position:0%
+we may need to relax
+ 
+
+ align:start position:0%
+we may need to relax
+and decrease the key in our queue
+
+ align:start position:0%
+and decrease the key in our queue
+ 
+
+ align:start position:0%
+and decrease the key in our queue
+once for every outgoing edge
+
+ align:start position:0%
+once for every outgoing edge
+ 
+
+ align:start position:0%
+once for every outgoing edge
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the running time is
+
+ align:start position:0%
+so the running time is
+ 
+
+ align:start position:0%
+so the running time is
+b plus
+
+ align:start position:0%
+b plus
+ 
+
+ align:start position:0%
+b plus
+v times
+
+ align:start position:0%
+v times
+ 
+
+ align:start position:0%
+v times
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how could we implement this priority
+
+ align:start position:0%
+so how could we implement this priority
+ 
+
+ align:start position:0%
+so how could we implement this priority
+queue well
+
+ align:start position:0%
+queue well
+ 
+
+ align:start position:0%
+queue well
+if we use the stupidest priority in the
+
+ align:start position:0%
+if we use the stupidest priority in the
+ 
+
+ align:start position:0%
+if we use the stupidest priority in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+here's here's a list of different
+
+ align:start position:0%
+here's here's a list of different
+ 
+
+ align:start position:0%
+here's here's a list of different
+implementations we could have for our
+
+ align:start position:0%
+implementations we could have for our
+ 
+
+ align:start position:0%
+implementations we could have for our
+priority queues
+
+ align:start position:0%
+priority queues
+ 
+
+ align:start position:0%
+priority queues
+and when i say priority queue i mean
+
+ align:start position:0%
+and when i say priority queue i mean
+ 
+
+ align:start position:0%
+and when i say priority queue i mean
+this priority queue
+
+ align:start position:0%
+this priority queue
+ 
+
+ align:start position:0%
+this priority queue
+we're already implementing the
+
+ align:start position:0%
+we're already implementing the
+ 
+
+ align:start position:0%
+we're already implementing the
+changeable priority queue by linking it
+
+ align:start position:0%
+changeable priority queue by linking it
+ 
+
+ align:start position:0%
+changeable priority queue by linking it
+with a dictionary that's efficient okay
+
+ align:start position:0%
+with a dictionary that's efficient okay
+ 
+
+ align:start position:0%
+with a dictionary that's efficient okay
+if i just use an array
+
+ align:start position:0%
+if i just use an array
+ 
+
+ align:start position:0%
+if i just use an array
+i can find the min in linear time sure
+
+ align:start position:0%
+i can find the min in linear time sure
+ 
+
+ align:start position:0%
+i can find the min in linear time sure
+and i don't have to update that array in
+
+ align:start position:0%
+and i don't have to update that array in
+ 
+
+ align:start position:0%
+and i don't have to update that array in
+any way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean i can just keep the distances in
+
+ align:start position:0%
+i mean i can just keep the distances in
+ 
+
+ align:start position:0%
+i mean i can just keep the distances in
+my direct access array i don't have to
+
+ align:start position:0%
+my direct access array i don't have to
+ 
+
+ align:start position:0%
+my direct access array i don't have to
+store a separate data structure i just
+
+ align:start position:0%
+store a separate data structure i just
+ 
+
+ align:start position:0%
+store a separate data structure i just
+store the distances in my direct access
+
+ align:start position:0%
+store the distances in my direct access
+ 
+
+ align:start position:0%
+store the distances in my direct access
+array d
+
+ align:start position:0%
+array d
+ 
+
+ align:start position:0%
+array d
+and so i can find it in constant time
+
+ align:start position:0%
+and so i can find it in constant time
+ 
+
+ align:start position:0%
+and so i can find it in constant time
+and i can update the values stored there
+
+ align:start position:0%
+and i can update the values stored there
+ 
+
+ align:start position:0%
+and i can update the values stored there
+and then whenever i want the minimum i
+
+ align:start position:0%
+and then whenever i want the minimum i
+ 
+
+ align:start position:0%
+and then whenever i want the minimum i
+can just loop through the whole thing
+
+ align:start position:0%
+can just loop through the whole thing
+ 
+
+ align:start position:0%
+can just loop through the whole thing
+right so that gives me a really fast
+
+ align:start position:0%
+right so that gives me a really fast
+ 
+
+ align:start position:0%
+right so that gives me a really fast
+decreased key
+
+ align:start position:0%
+decreased key
+ 
+
+ align:start position:0%
+decreased key
+but slow delete min but if we take a
+
+ align:start position:0%
+but slow delete min but if we take a
+ 
+
+ align:start position:0%
+but slow delete min but if we take a
+look at the running time bound here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get something if we replace n with v
+
+ align:start position:0%
+we get something if we replace n with v
+ 
+
+ align:start position:0%
+we get something if we replace n with v
+we get a quadratic time algorithm
+
+ align:start position:0%
+we get a quadratic time algorithm
+ 
+
+ align:start position:0%
+we get a quadratic time algorithm
+in the number of vertices which
+
+ align:start position:0%
+in the number of vertices which
+ 
+
+ align:start position:0%
+in the number of vertices which
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+dense graph this is in linear time
+
+ align:start position:0%
+dense graph this is in linear time
+ 
+
+ align:start position:0%
+dense graph this is in linear time
+that's actually pretty good dense
+
+ align:start position:0%
+that's actually pretty good dense
+ 
+
+ align:start position:0%
+that's actually pretty good dense
+meaning that i have at least a quadratic
+
+ align:start position:0%
+meaning that i have at least a quadratic
+ 
+
+ align:start position:0%
+meaning that i have at least a quadratic
+number of vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's actually really good and it's
+
+ align:start position:0%
+so that's actually really good and it's
+ 
+
+ align:start position:0%
+so that's actually really good and it's
+the stupidest possible
+
+ align:start position:0%
+the stupidest possible
+ 
+
+ align:start position:0%
+the stupidest possible
+data structure we could use for this
+
+ align:start position:0%
+data structure we could use for this
+ 
+
+ align:start position:0%
+data structure we could use for this
+priority queue
+
+ align:start position:0%
+priority queue
+ 
+
+ align:start position:0%
+priority queue
+now we can do a little better
+
+ align:start position:0%
+now we can do a little better
+ 
+
+ align:start position:0%
+now we can do a little better
+actually for not dense i mean for sparse
+
+ align:start position:0%
+actually for not dense i mean for sparse
+ 
+
+ align:start position:0%
+actually for not dense i mean for sparse
+graphs where the number of edges is at
+
+ align:start position:0%
+graphs where the number of edges is at
+ 
+
+ align:start position:0%
+graphs where the number of edges is at
+most v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this is pretty bad it's quadratic right
+
+ align:start position:0%
+this is pretty bad it's quadratic right
+ 
+
+ align:start position:0%
+this is pretty bad it's quadratic right
+we want to do something a little better
+
+ align:start position:0%
+we want to do something a little better
+ 
+
+ align:start position:0%
+we want to do something a little better
+now if we're sparse a binary heap
+
+ align:start position:0%
+now if we're sparse a binary heap
+ 
+
+ align:start position:0%
+now if we're sparse a binary heap
+can delete min
+
+ align:start position:0%
+can delete min
+ 
+
+ align:start position:0%
+can delete min
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+logarithmic time but it can actually if
+
+ align:start position:0%
+logarithmic time but it can actually if
+ 
+
+ align:start position:0%
+logarithmic time but it can actually if
+i know where i am in the heap
+
+ align:start position:0%
+i know where i am in the heap
+ 
+
+ align:start position:0%
+i know where i am in the heap
+and i decrease the key
+
+ align:start position:0%
+and i decrease the key
+ 
+
+ align:start position:0%
+and i decrease the key
+and i'm in a min heap
+
+ align:start position:0%
+and i'm in a min heap
+ 
+
+ align:start position:0%
+and i'm in a min heap
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+i can just swap with my parent upwards
+
+ align:start position:0%
+i can just swap with my parent upwards
+ 
+
+ align:start position:0%
+i can just swap with my parent upwards
+in the tree in log n time and free
+
+ align:start position:0%
+in the tree in log n time and free
+ 
+
+ align:start position:0%
+in the tree in log n time and free
+rebalance the refix the binary heap
+
+ align:start position:0%
+rebalance the refix the binary heap
+ 
+
+ align:start position:0%
+rebalance the refix the binary heap
+property and so i can do that in
+
+ align:start position:0%
+property and so i can do that in
+ 
+
+ align:start position:0%
+property and so i can do that in
+logarithmic time
+
+ align:start position:0%
+logarithmic time
+ 
+
+ align:start position:0%
+logarithmic time
+okay and if i do that and i put it into
+
+ align:start position:0%
+okay and if i do that and i put it into
+ 
+
+ align:start position:0%
+okay and if i do that and i put it into
+this formula
+
+ align:start position:0%
+this formula
+ 
+
+ align:start position:0%
+this formula
+i actually get n
+
+ align:start position:0%
+i actually get n
+ 
+
+ align:start position:0%
+i actually get n
+or v
+
+ align:start position:0%
+or v
+ 
+
+ align:start position:0%
+or v
+plus v times log v
+
+ align:start position:0%
+plus v times log v
+ 
+
+ align:start position:0%
+plus v times log v
+plus e times log v
+
+ align:start position:0%
+plus e times log v
+ 
+
+ align:start position:0%
+plus e times log v
+right and so that's going to give me
+
+ align:start position:0%
+right and so that's going to give me
+ 
+
+ align:start position:0%
+right and so that's going to give me
+e log v if i'm assuming that i'm first
+
+ align:start position:0%
+e log v if i'm assuming that i'm first
+ 
+
+ align:start position:0%
+e log v if i'm assuming that i'm first
+you know pruning out all of the things
+
+ align:start position:0%
+you know pruning out all of the things
+ 
+
+ align:start position:0%
+you know pruning out all of the things
+not connected to me then e
+
+ align:start position:0%
+not connected to me then e
+ 
+
+ align:start position:0%
+not connected to me then e
+asymptotically upper bounds v and i get
+
+ align:start position:0%
+asymptotically upper bounds v and i get
+ 
+
+ align:start position:0%
+asymptotically upper bounds v and i get
+this e log v
+
+ align:start position:0%
+this e log v
+ 
+
+ align:start position:0%
+this e log v
+running time which is pretty good
+
+ align:start position:0%
+running time which is pretty good
+ 
+
+ align:start position:0%
+running time which is pretty good
+right that's just an extra log factor on
+
+ align:start position:0%
+right that's just an extra log factor on
+ 
+
+ align:start position:0%
+right that's just an extra log factor on
+linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's a even better well better is
+
+ align:start position:0%
+now there's a even better well better is
+ 
+
+ align:start position:0%
+now there's a even better well better is
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+is hard to say
+
+ align:start position:0%
+is hard to say
+ 
+
+ align:start position:0%
+is hard to say
+really there's a different data
+
+ align:start position:0%
+really there's a different data
+ 
+
+ align:start position:0%
+really there's a different data
+structure that achieves
+
+ align:start position:0%
+structure that achieves
+ 
+
+ align:start position:0%
+structure that achieves
+kind of both bounds for sparse and
+
+ align:start position:0%
+kind of both bounds for sparse and
+ 
+
+ align:start position:0%
+kind of both bounds for sparse and
+dense graphs and everything in between
+
+ align:start position:0%
+dense graphs and everything in between
+ 
+
+ align:start position:0%
+dense graphs and everything in between
+it gives us an e plus v log v running
+
+ align:start position:0%
+it gives us an e plus v log v running
+ 
+
+ align:start position:0%
+it gives us an e plus v log v running
+time bound this data structure is called
+
+ align:start position:0%
+time bound this data structure is called
+ 
+
+ align:start position:0%
+time bound this data structure is called
+the fibonacci heap we're not going to
+
+ align:start position:0%
+the fibonacci heap we're not going to
+ 
+
+ align:start position:0%
+the fibonacci heap we're not going to
+talk about it in 6.06
+
+ align:start position:0%
+talk about it in 6.06
+ 
+
+ align:start position:0%
+talk about it in 6.06
+they talk about it you can look at
+
+ align:start position:0%
+they talk about it you can look at
+ 
+
+ align:start position:0%
+they talk about it you can look at
+chapter 19 in clrs or you can look at i
+
+ align:start position:0%
+chapter 19 in clrs or you can look at i
+ 
+
+ align:start position:0%
+chapter 19 in clrs or you can look at i
+think they talk about it in 6854
+
+ align:start position:0%
+think they talk about it in 6854
+ 
+
+ align:start position:0%
+think they talk about it in 6854
+if you're interested in learning about
+
+ align:start position:0%
+if you're interested in learning about
+ 
+
+ align:start position:0%
+if you're interested in learning about
+fibonacci heaps but these are almost nev
+
+ align:start position:0%
+fibonacci heaps but these are almost nev
+ 
+
+ align:start position:0%
+fibonacci heaps but these are almost nev
+i mean they get good theoretical
+
+ align:start position:0%
+i mean they get good theoretical
+ 
+
+ align:start position:0%
+i mean they get good theoretical
+uh bounds so what you want to say
+
+ align:start position:0%
+uh bounds so what you want to say
+ 
+
+ align:start position:0%
+uh bounds so what you want to say
+is whenever we give you a theory problem
+
+ align:start position:0%
+is whenever we give you a theory problem
+ 
+
+ align:start position:0%
+is whenever we give you a theory problem
+where you might want to use dijkstra
+
+ align:start position:0%
+where you might want to use dijkstra
+ 
+
+ align:start position:0%
+where you might want to use dijkstra
+you want to use this theoretical
+
+ align:start position:0%
+you want to use this theoretical
+ 
+
+ align:start position:0%
+you want to use this theoretical
+running time bound
+
+ align:start position:0%
+running time bound
+ 
+
+ align:start position:0%
+running time bound
+for your problem
+
+ align:start position:0%
+for your problem
+ 
+
+ align:start position:0%
+for your problem
+a plus
+
+ align:start position:0%
+a plus
+ 
+
+ align:start position:0%
+a plus
+v log v but if you happen to know that
+
+ align:start position:0%
+v log v but if you happen to know that
+ 
+
+ align:start position:0%
+v log v but if you happen to know that
+your graph is sparse or dense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just using an array or a heap is going
+
+ align:start position:0%
+just using an array or a heap is going
+ 
+
+ align:start position:0%
+just using an array or a heap is going
+to get you just as good of a running
+
+ align:start position:0%
+to get you just as good of a running
+ 
+
+ align:start position:0%
+to get you just as good of a running
+time very close to linear
+
+ align:start position:0%
+time very close to linear
+ 
+
+ align:start position:0%
+time very close to linear
+right and so in practice
+
+ align:start position:0%
+right and so in practice
+ 
+
+ align:start position:0%
+right and so in practice
+most people when they're implementing a
+
+ align:start position:0%
+most people when they're implementing a
+ 
+
+ align:start position:0%
+most people when they're implementing a
+graph search algorithm they know
+
+ align:start position:0%
+graph search algorithm they know
+ 
+
+ align:start position:0%
+graph search algorithm they know
+if their graph is sparse or dense and so
+
+ align:start position:0%
+if their graph is sparse or dense and so
+ 
+
+ align:start position:0%
+if their graph is sparse or dense and so
+they never bother implementing a
+
+ align:start position:0%
+they never bother implementing a
+ 
+
+ align:start position:0%
+they never bother implementing a
+fibonacci heap which is a little
+
+ align:start position:0%
+fibonacci heap which is a little
+ 
+
+ align:start position:0%
+fibonacci heap which is a little
+complicated okay so they are usually
+
+ align:start position:0%
+complicated okay so they are usually
+ 
+
+ align:start position:0%
+complicated okay so they are usually
+either in one of these first two cases
+
+ align:start position:0%
+either in one of these first two cases
+ 
+
+ align:start position:0%
+either in one of these first two cases
+where v squared is linear because when
+
+ align:start position:0%
+where v squared is linear because when
+ 
+
+ align:start position:0%
+where v squared is linear because when
+your graph is dense
+
+ align:start position:0%
+your graph is dense
+ 
+
+ align:start position:0%
+your graph is dense
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+you know we're very close to linear e
+
+ align:start position:0%
+you know we're very close to linear e
+ 
+
+ align:start position:0%
+you know we're very close to linear e
+times log v
+
+ align:start position:0%
+times log v
+ 
+
+ align:start position:0%
+times log v
+which is v log v if your graph is sparse
+
+ align:start position:0%
+which is v log v if your graph is sparse
+ 
+
+ align:start position:0%
+which is v log v if your graph is sparse
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the running time of dykstra
+
+ align:start position:0%
+the running time of dykstra
+ 
+
+ align:start position:0%
+the running time of dykstra
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far
+
+ align:start position:0%
+so far
+ 
+
+ align:start position:0%
+so far
+we've gotten all of these nice bounds
+
+ align:start position:0%
+we've gotten all of these nice bounds
+ 
+
+ align:start position:0%
+we've gotten all of these nice bounds
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+some special cases where we're
+
+ align:start position:0%
+some special cases where we're
+ 
+
+ align:start position:0%
+some special cases where we're
+i mean special cases where we're linear
+
+ align:start position:0%
+i mean special cases where we're linear
+ 
+
+ align:start position:0%
+i mean special cases where we're linear
+dijkstra where we're close to linear
+
+ align:start position:0%
+dijkstra where we're close to linear
+ 
+
+ align:start position:0%
+dijkstra where we're close to linear
+and bellman ford you know if we throw
+
+ align:start position:0%
+and bellman ford you know if we throw
+ 
+
+ align:start position:0%
+and bellman ford you know if we throw
+our hands up in the air
+
+ align:start position:0%
+our hands up in the air
+ 
+
+ align:start position:0%
+our hands up in the air
+there might be negative cycles in our
+
+ align:start position:0%
+there might be negative cycles in our
+ 
+
+ align:start position:0%
+there might be negative cycles in our
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+we got to spend that quadratic running
+
+ align:start position:0%
+we got to spend that quadratic running
+ 
+
+ align:start position:0%
+we got to spend that quadratic running
+time bound now there are faster
+
+ align:start position:0%
+time bound now there are faster
+ 
+
+ align:start position:0%
+time bound now there are faster
+algorithms but this is the fastest we're
+
+ align:start position:0%
+algorithms but this is the fastest we're
+ 
+
+ align:start position:0%
+algorithms but this is the fastest we're
+going to teach you in this class now
+
+ align:start position:0%
+going to teach you in this class now
+ 
+
+ align:start position:0%
+going to teach you in this class now
+in the next lecture we're going to be
+
+ align:start position:0%
+in the next lecture we're going to be
+ 
+
+ align:start position:0%
+in the next lecture we're going to be
+talking about all pairs shortest paths
+
+ align:start position:0%
+talking about all pairs shortest paths
+ 
+
+ align:start position:0%
+talking about all pairs shortest paths
+and we'll pick it up
+
+ align:start position:0%
+and we'll pick it up
+ 
+
+ align:start position:0%
+and we'll pick it up
+next time
\ No newline at end of file
diff --git a/NVQWWXhbUvs.txt b/NVQWWXhbUvs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d46c57307876894e93f36c1c4d2a81161854b1df
--- /dev/null
+++ b/NVQWWXhbUvs.txt
@@ -0,0 +1,10219 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+and and in some cases we just kind of
+
+ align:start position:0%
+and and in some cases we just kind of
+ 
+
+ align:start position:0%
+and and in some cases we just kind of
+have to guess
+
+ align:start position:0%
+have to guess
+ 
+
+ align:start position:0%
+have to guess
+um but in some cases we have uh for
+
+ align:start position:0%
+um but in some cases we have uh for
+ 
+
+ align:start position:0%
+um but in some cases we have uh for
+especially for languages like Greek and
+
+ align:start position:0%
+especially for languages like Greek and
+ 
+
+ align:start position:0%
+especially for languages like Greek and
+Latin we have descriptions by people who
+
+ align:start position:0%
+Latin we have descriptions by people who
+ 
+
+ align:start position:0%
+Latin we have descriptions by people who
+attempted to describe their own sounds
+
+ align:start position:0%
+attempted to describe their own sounds
+ 
+
+ align:start position:0%
+attempted to describe their own sounds
+that's a that's the kind of thing that
+
+ align:start position:0%
+that's a that's the kind of thing that
+ 
+
+ align:start position:0%
+that's a that's the kind of thing that
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+um we can infer things from mistakes
+
+ align:start position:0%
+um we can infer things from mistakes
+ 
+
+ align:start position:0%
+um we can infer things from mistakes
+that people made at various points so uh
+
+ align:start position:0%
+that people made at various points so uh
+ 
+
+ align:start position:0%
+that people made at various points so uh
+people who were learning how to spell or
+
+ align:start position:0%
+people who were learning how to spell or
+ 
+
+ align:start position:0%
+people who were learning how to spell or
+you know say children or people who who
+
+ align:start position:0%
+you know say children or people who who
+ 
+
+ align:start position:0%
+you know say children or people who who
+weren't uh Highly Educated when they
+
+ align:start position:0%
+weren't uh Highly Educated when they
+ 
+
+ align:start position:0%
+weren't uh Highly Educated when they
+misspelled words uh in say Greek or
+
+ align:start position:0%
+misspelled words uh in say Greek or
+ 
+
+ align:start position:0%
+misspelled words uh in say Greek or
+Latin you can infer things so if you're
+
+ align:start position:0%
+Latin you can infer things so if you're
+ 
+
+ align:start position:0%
+Latin you can infer things so if you're
+making a certain kind of misspelling is
+
+ align:start position:0%
+making a certain kind of misspelling is
+ 
+
+ align:start position:0%
+making a certain kind of misspelling is
+common you get to infer that those
+
+ align:start position:0%
+common you get to infer that those
+ 
+
+ align:start position:0%
+common you get to infer that those
+sounds were kind of common so in the
+
+ align:start position:0%
+sounds were kind of common so in the
+ 
+
+ align:start position:0%
+sounds were kind of common so in the
+case of ancient Greek
+
+ align:start position:0%
+case of ancient Greek
+ 
+
+ align:start position:0%
+case of ancient Greek
+um we think that there was an U partly
+
+ align:start position:0%
+um we think that there was an U partly
+ 
+
+ align:start position:0%
+um we think that there was an U partly
+because there was a period where people
+
+ align:start position:0%
+because there was a period where people
+ 
+
+ align:start position:0%
+because there was a period where people
+were when people misspelled it they
+
+ align:start position:0%
+were when people misspelled it they
+ 
+
+ align:start position:0%
+were when people misspelled it they
+either misspelled it as oo or as e and
+
+ align:start position:0%
+either misspelled it as oo or as e and
+ 
+
+ align:start position:0%
+either misspelled it as oo or as e and
+then later there was a period where
+
+ align:start position:0%
+then later there was a period where
+ 
+
+ align:start position:0%
+then later there was a period where
+people reliably misspelled it as e uh
+
+ align:start position:0%
+people reliably misspelled it as e uh
+ 
+
+ align:start position:0%
+people reliably misspelled it as e uh
+leading us to think that it had shifted
+
+ align:start position:0%
+leading us to think that it had shifted
+ 
+
+ align:start position:0%
+leading us to think that it had shifted
+to what it is in modern Greek which is
+
+ align:start position:0%
+to what it is in modern Greek which is
+ 
+
+ align:start position:0%
+to what it is in modern Greek which is
+an e
+
+ align:start position:0%
+an e
+ 
+
+ align:start position:0%
+an e
+um that's the that's one of the kinds of
+
+ align:start position:0%
+um that's the that's one of the kinds of
+ 
+
+ align:start position:0%
+um that's the that's one of the kinds of
+things people do
+
+ align:start position:0%
+things people do
+ 
+
+ align:start position:0%
+things people do
+um you also get to look at what happens
+
+ align:start position:0%
+um you also get to look at what happens
+ 
+
+ align:start position:0%
+um you also get to look at what happens
+to these words when they get borrowed
+
+ align:start position:0%
+to these words when they get borrowed
+ 
+
+ align:start position:0%
+to these words when they get borrowed
+into other languages
+
+ align:start position:0%
+into other languages
+ 
+
+ align:start position:0%
+into other languages
+um uh so languages that have richer or
+
+ align:start position:0%
+um uh so languages that have richer or
+ 
+
+ align:start position:0%
+um uh so languages that have richer or
+poorer uh uh systems
+
+ align:start position:0%
+poorer uh uh systems
+ 
+
+ align:start position:0%
+poorer uh uh systems
+um there's one classic example from from
+
+ align:start position:0%
+um there's one classic example from from
+ 
+
+ align:start position:0%
+um there's one classic example from from
+Greek and from Latin we know that Greek
+
+ align:start position:0%
+Greek and from Latin we know that Greek
+ 
+
+ align:start position:0%
+Greek and from Latin we know that Greek
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+see I'm sorry Raquel you were right this
+
+ align:start position:0%
+see I'm sorry Raquel you were right this
+ 
+
+ align:start position:0%
+see I'm sorry Raquel you were right this
+is going to be a long a long answer we
+
+ align:start position:0%
+is going to be a long a long answer we
+ 
+
+ align:start position:0%
+is going to be a long a long answer we
+know that the Greek letter this Greek
+
+ align:start position:0%
+know that the Greek letter this Greek
+ 
+
+ align:start position:0%
+know that the Greek letter this Greek
+letter
+
+ align:start position:0%
+letter
+ 
+
+ align:start position:0%
+letter
+um used to be pronounced uh as a P with
+
+ align:start position:0%
+um used to be pronounced uh as a P with
+ 
+
+ align:start position:0%
+um used to be pronounced uh as a P with
+a with an extra puff of air it used to
+
+ align:start position:0%
+a with an extra puff of air it used to
+ 
+
+ align:start position:0%
+a with an extra puff of air it used to
+be Pi or P
+
+ align:start position:0%
+be Pi or P
+ 
+
+ align:start position:0%
+be Pi or P
+um so just an especially emphatic P they
+
+ align:start position:0%
+um so just an especially emphatic P they
+ 
+
+ align:start position:0%
+um so just an especially emphatic P they
+also had another letter
+
+ align:start position:0%
+also had another letter
+ 
+
+ align:start position:0%
+also had another letter
+which was a p without the extra puff of
+
+ align:start position:0%
+which was a p without the extra puff of
+ 
+
+ align:start position:0%
+which was a p without the extra puff of
+air uh B and then this one shifted to
+
+ align:start position:0%
+air uh B and then this one shifted to
+ 
+
+ align:start position:0%
+air uh B and then this one shifted to
+well actually the the modern this is the
+
+ align:start position:0%
+well actually the the modern this is the
+ 
+
+ align:start position:0%
+well actually the the modern this is the
+symbol for it in IPA the the bilabial uh
+
+ align:start position:0%
+symbol for it in IPA the the bilabial uh
+ 
+
+ align:start position:0%
+symbol for it in IPA the the bilabial uh
+fricative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and the the way that we know we can
+
+ align:start position:0%
+um and the the way that we know we can
+ 
+
+ align:start position:0%
+um and the the way that we know we can
+actually date pretty precisely when this
+
+ align:start position:0%
+actually date pretty precisely when this
+ 
+
+ align:start position:0%
+actually date pretty precisely when this
+shift happened
+
+ align:start position:0%
+shift happened
+ 
+
+ align:start position:0%
+shift happened
+um and that's because uh Greek was uh
+
+ align:start position:0%
+um and that's because uh Greek was uh
+ 
+
+ align:start position:0%
+um and that's because uh Greek was uh
+loaning lots of words into Latin Latin
+
+ align:start position:0%
+loaning lots of words into Latin Latin
+ 
+
+ align:start position:0%
+loaning lots of words into Latin Latin
+was borrowing words from Greek including
+
+ align:start position:0%
+was borrowing words from Greek including
+ 
+
+ align:start position:0%
+was borrowing words from Greek including
+a word that they spelled like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the fact that they spelled it like
+
+ align:start position:0%
+and the fact that they spelled it like
+ 
+
+ align:start position:0%
+and the fact that they spelled it like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um first of all suggests that it was a P
+
+ align:start position:0%
+um first of all suggests that it was a P
+ 
+
+ align:start position:0%
+um first of all suggests that it was a P
+with an a a p with an H sound and not
+
+ align:start position:0%
+with an a a p with an H sound and not
+ 
+
+ align:start position:0%
+with an a a p with an H sound and not
+something more like an F because Latin
+
+ align:start position:0%
+something more like an F because Latin
+ 
+
+ align:start position:0%
+something more like an F because Latin
+had an F uh and they would have used an
+
+ align:start position:0%
+had an F uh and they would have used an
+ 
+
+ align:start position:0%
+had an F uh and they would have used an
+F if they if they had thought that this
+
+ align:start position:0%
+F if they if they had thought that this
+ 
+
+ align:start position:0%
+F if they if they had thought that this
+was an F also because people who were
+
+ align:start position:0%
+was an F also because people who were
+ 
+
+ align:start position:0%
+was an F also because people who were
+bad at spelling children and you know
+
+ align:start position:0%
+bad at spelling children and you know
+ 
+
+ align:start position:0%
+bad at spelling children and you know
+people writing graffiti and stuff like
+
+ align:start position:0%
+people writing graffiti and stuff like
+ 
+
+ align:start position:0%
+people writing graffiti and stuff like
+that uh when they misspelled this word
+
+ align:start position:0%
+that uh when they misspelled this word
+ 
+
+ align:start position:0%
+that uh when they misspelled this word
+you know when they were writing graffiti
+
+ align:start position:0%
+you know when they were writing graffiti
+ 
+
+ align:start position:0%
+you know when they were writing graffiti
+about philosophy
+
+ align:start position:0%
+about philosophy
+ 
+
+ align:start position:0%
+about philosophy
+um they would misspell it by leaving out
+
+ align:start position:0%
+um they would misspell it by leaving out
+ 
+
+ align:start position:0%
+um they would misspell it by leaving out
+the age so they would spell it just with
+
+ align:start position:0%
+the age so they would spell it just with
+ 
+
+ align:start position:0%
+the age so they would spell it just with
+a p and then later there was a period
+
+ align:start position:0%
+a p and then later there was a period
+ 
+
+ align:start position:0%
+a p and then later there was a period
+where people who were misspelling this
+
+ align:start position:0%
+where people who were misspelling this
+ 
+
+ align:start position:0%
+where people who were misspelling this
+word would misspell it by writing it
+
+ align:start position:0%
+word would misspell it by writing it
+ 
+
+ align:start position:0%
+word would misspell it by writing it
+with an f and that's how you know that
+
+ align:start position:0%
+with an f and that's how you know that
+ 
+
+ align:start position:0%
+with an f and that's how you know that
+you know the word had changed its
+
+ align:start position:0%
+you know the word had changed its
+ 
+
+ align:start position:0%
+you know the word had changed its
+pronunciation right then you know at
+
+ align:start position:0%
+pronunciation right then you know at
+ 
+
+ align:start position:0%
+pronunciation right then you know at
+that point from uh from an aspirated p a
+
+ align:start position:0%
+that point from uh from an aspirated p a
+ 
+
+ align:start position:0%
+that point from uh from an aspirated p a
+p with an H sound to a to an F
+
+ align:start position:0%
+p with an H sound to a to an F
+ 
+
+ align:start position:0%
+p with an H sound to a to an F
+that's actually benefiting future you
+
+ align:start position:0%
+that's actually benefiting future you
+ 
+
+ align:start position:0%
+that's actually benefiting future you
+were you were being providing valuable
+
+ align:start position:0%
+were you were being providing valuable
+ 
+
+ align:start position:0%
+were you were being providing valuable
+data for for uh for future future
+
+ align:start position:0%
+data for for uh for future future
+ 
+
+ align:start position:0%
+data for for uh for future future
+historical linguists absolutely that's
+
+ align:start position:0%
+historical linguists absolutely that's
+ 
+
+ align:start position:0%
+historical linguists absolutely that's
+absolutely true now please engrave your
+
+ align:start position:0%
+absolutely true now please engrave your
+ 
+
+ align:start position:0%
+absolutely true now please engrave your
+misspellings in stone that will make
+
+ align:start position:0%
+misspellings in stone that will make
+ 
+
+ align:start position:0%
+misspellings in stone that will make
+them a lot easier for people to handle
+
+ align:start position:0%
+them a lot easier for people to handle
+ 
+
+ align:start position:0%
+them a lot easier for people to handle
+any other questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where was I going with all that oh right
+
+ align:start position:0%
+where was I going with all that oh right
+ 
+
+ align:start position:0%
+where was I going with all that oh right
+so uh I was saying I was telling you
+
+ align:start position:0%
+so uh I was saying I was telling you
+ 
+
+ align:start position:0%
+so uh I was saying I was telling you
+some things about uh typology there are
+
+ align:start position:0%
+some things about uh typology there are
+ 
+
+ align:start position:0%
+some things about uh typology there are
+languages that have uh poorer and richer
+
+ align:start position:0%
+languages that have uh poorer and richer
+ 
+
+ align:start position:0%
+languages that have uh poorer and richer
+vowel systems English has a particularly
+
+ align:start position:0%
+vowel systems English has a particularly
+ 
+
+ align:start position:0%
+vowel systems English has a particularly
+Rich system of vowels we have a fairly
+
+ align:start position:0%
+Rich system of vowels we have a fairly
+ 
+
+ align:start position:0%
+Rich system of vowels we have a fairly
+large number of L's or plenty of
+
+ align:start position:0%
+large number of L's or plenty of
+ 
+
+ align:start position:0%
+large number of L's or plenty of
+languages out there that have languages
+
+ align:start position:0%
+languages out there that have languages
+ 
+
+ align:start position:0%
+languages out there that have languages
+like that have fewer that have like five
+
+ align:start position:0%
+like that have fewer that have like five
+ 
+
+ align:start position:0%
+like that have fewer that have like five
+there are plenty of languages that have
+
+ align:start position:0%
+there are plenty of languages that have
+ 
+
+ align:start position:0%
+there are plenty of languages that have
+three if you have three vowels your
+
+ align:start position:0%
+three if you have three vowels your
+ 
+
+ align:start position:0%
+three if you have three vowels your
+three vowels are pretty invariably ah e
+
+ align:start position:0%
+three vowels are pretty invariably ah e
+ 
+
+ align:start position:0%
+three vowels are pretty invariably ah e
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+that is they're the vowels that are kind
+
+ align:start position:0%
+that is they're the vowels that are kind
+ 
+
+ align:start position:0%
+that is they're the vowels that are kind
+of in the corners of this system they're
+
+ align:start position:0%
+of in the corners of this system they're
+ 
+
+ align:start position:0%
+of in the corners of this system they're
+you know at the bottom right and the top
+
+ align:start position:0%
+you know at the bottom right and the top
+ 
+
+ align:start position:0%
+you know at the bottom right and the top
+right and the top left yeah
+
+ align:start position:0%
+right and the top left yeah
+ 
+
+ align:start position:0%
+right and the top left yeah
+there aren't languages out there that
+
+ align:start position:0%
+there aren't languages out there that
+ 
+
+ align:start position:0%
+there aren't languages out there that
+have three vowels and the three vowels
+
+ align:start position:0%
+have three vowels and the three vowels
+ 
+
+ align:start position:0%
+have three vowels and the three vowels
+are you know a a and ah right that's not
+
+ align:start position:0%
+are you know a a and ah right that's not
+ 
+
+ align:start position:0%
+are you know a a and ah right that's not
+a that's not a kind of language that we
+
+ align:start position:0%
+a that's not a kind of language that we
+ 
+
+ align:start position:0%
+a that's not a kind of language that we
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+um and uh there's some work on this uh
+
+ align:start position:0%
+um and uh there's some work on this uh
+ 
+
+ align:start position:0%
+um and uh there's some work on this uh
+including classic work by my colleague
+
+ align:start position:0%
+including classic work by my colleague
+ 
+
+ align:start position:0%
+including classic work by my colleague
+uh Edward Fleming
+
+ align:start position:0%
+uh Edward Fleming
+ 
+
+ align:start position:0%
+uh Edward Fleming
+um uh talking about sort of optimal
+
+ align:start position:0%
+um uh talking about sort of optimal
+ 
+
+ align:start position:0%
+um uh talking about sort of optimal
+distributions of vowels in vowel space
+
+ align:start position:0%
+distributions of vowels in vowel space
+ 
+
+ align:start position:0%
+distributions of vowels in vowel space
+where the idea is sort of you have this
+
+ align:start position:0%
+where the idea is sort of you have this
+ 
+
+ align:start position:0%
+where the idea is sort of you have this
+space in your mouth you want to you want
+
+ align:start position:0%
+space in your mouth you want to you want
+ 
+
+ align:start position:0%
+space in your mouth you want to you want
+your vowels to be sort of maximally
+
+ align:start position:0%
+your vowels to be sort of maximally
+ 
+
+ align:start position:0%
+your vowels to be sort of maximally
+contrastive so you want people to always
+
+ align:start position:0%
+contrastive so you want people to always
+ 
+
+ align:start position:0%
+contrastive so you want people to always
+be able to hear the difference between
+
+ align:start position:0%
+be able to hear the difference between
+ 
+
+ align:start position:0%
+be able to hear the difference between
+different vowels and the best way to do
+
+ align:start position:0%
+different vowels and the best way to do
+ 
+
+ align:start position:0%
+different vowels and the best way to do
+that is to have your valances far apart
+
+ align:start position:0%
+that is to have your valances far apart
+ 
+
+ align:start position:0%
+that is to have your valances far apart
+from each other as possible
+
+ align:start position:0%
+from each other as possible
+ 
+
+ align:start position:0%
+from each other as possible
+um as a theory about why we get the
+
+ align:start position:0%
+um as a theory about why we get the
+ 
+
+ align:start position:0%
+um as a theory about why we get the
+kinds of vowel systems that we get and
+
+ align:start position:0%
+kinds of vowel systems that we get and
+ 
+
+ align:start position:0%
+kinds of vowel systems that we get and
+not others
+
+ align:start position:0%
+not others
+ 
+
+ align:start position:0%
+not others
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh oh right and then there are languages
+
+ align:start position:0%
+uh oh right and then there are languages
+ 
+
+ align:start position:0%
+uh oh right and then there are languages
+that have like French that have
+
+ align:start position:0%
+that have like French that have
+ 
+
+ align:start position:0%
+that have like French that have
+nasalized vowels uh so French has words
+
+ align:start position:0%
+nasalized vowels uh so French has words
+ 
+
+ align:start position:0%
+nasalized vowels uh so French has words
+like meh which is hand and meh which is
+
+ align:start position:0%
+like meh which is hand and meh which is
+ 
+
+ align:start position:0%
+like meh which is hand and meh which is
+dish uh so that's another option that
+
+ align:start position:0%
+dish uh so that's another option that
+ 
+
+ align:start position:0%
+dish uh so that's another option that
+some languages take you can lower your
+
+ align:start position:0%
+some languages take you can lower your
+ 
+
+ align:start position:0%
+some languages take you can lower your
+volume and allow some error to flow
+
+ align:start position:0%
+volume and allow some error to flow
+ 
+
+ align:start position:0%
+volume and allow some error to flow
+through your nasal cavity as you're as
+
+ align:start position:0%
+through your nasal cavity as you're as
+ 
+
+ align:start position:0%
+through your nasal cavity as you're as
+you're making sounds uh French
+
+ align:start position:0%
+you're making sounds uh French
+ 
+
+ align:start position:0%
+you're making sounds uh French
+Portuguese lots of languages do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I said we're classifying vowels
+
+ align:start position:0%
+okay so I said we're classifying vowels
+ 
+
+ align:start position:0%
+okay so I said we're classifying vowels
+why are we classifying vowels partly
+
+ align:start position:0%
+why are we classifying vowels partly
+ 
+
+ align:start position:0%
+why are we classifying vowels partly
+because it's fun but also because it
+
+ align:start position:0%
+because it's fun but also because it
+ 
+
+ align:start position:0%
+because it's fun but also because it
+enables us to sort of realize that we
+
+ align:start position:0%
+enables us to sort of realize that we
+ 
+
+ align:start position:0%
+enables us to sort of realize that we
+wonder about kinds of vowel spaces uh
+
+ align:start position:0%
+wonder about kinds of vowel spaces uh
+ 
+
+ align:start position:0%
+wonder about kinds of vowel spaces uh
+why are all the English vowels in the
+
+ align:start position:0%
+why are all the English vowels in the
+ 
+
+ align:start position:0%
+why are all the English vowels in the
+upper right hand corner do they have to
+
+ align:start position:0%
+upper right hand corner do they have to
+ 
+
+ align:start position:0%
+upper right hand corner do they have to
+be if you had a rounded vowel that was
+
+ align:start position:0%
+be if you had a rounded vowel that was
+ 
+
+ align:start position:0%
+be if you had a rounded vowel that was
+somewhere else what would it sound like
+
+ align:start position:0%
+somewhere else what would it sound like
+ 
+
+ align:start position:0%
+somewhere else what would it sound like
+all that good stuff there another thing
+
+ align:start position:0%
+all that good stuff there another thing
+ 
+
+ align:start position:0%
+all that good stuff there another thing
+that it does is help us to develop uh
+
+ align:start position:0%
+that it does is help us to develop uh
+ 
+
+ align:start position:0%
+that it does is help us to develop uh
+theories of phonologically natural sound
+
+ align:start position:0%
+theories of phonologically natural sound
+ 
+
+ align:start position:0%
+theories of phonologically natural sound
+changes so here are some Turkish nouns
+
+ align:start position:0%
+changes so here are some Turkish nouns
+ 
+
+ align:start position:0%
+changes so here are some Turkish nouns
+uh I'm sorry I'm I'm going to use your
+
+ align:start position:0%
+uh I'm sorry I'm I'm going to use your
+ 
+
+ align:start position:0%
+uh I'm sorry I'm I'm going to use your
+native language uh and uh I'll just ask
+
+ align:start position:0%
+native language uh and uh I'll just ask
+ 
+
+ align:start position:0%
+native language uh and uh I'll just ask
+you to be quiet for the next little
+
+ align:start position:0%
+you to be quiet for the next little
+ 
+
+ align:start position:0%
+you to be quiet for the next little
+while uh here are some Turkish nouns
+
+ align:start position:0%
+while uh here are some Turkish nouns
+ 
+
+ align:start position:0%
+while uh here are some Turkish nouns
+um some of you if you've ever read C.S
+
+ align:start position:0%
+um some of you if you've ever read C.S
+ 
+
+ align:start position:0%
+um some of you if you've ever read C.S
+Lewis you might recognize the first one
+
+ align:start position:0%
+Lewis you might recognize the first one
+ 
+
+ align:start position:0%
+Lewis you might recognize the first one
+um uh and here are the plurals of these
+
+ align:start position:0%
+um uh and here are the plurals of these
+ 
+
+ align:start position:0%
+um uh and here are the plurals of these
+nouns
+
+ align:start position:0%
+nouns
+ 
+
+ align:start position:0%
+nouns
+what's the plural suffix in Turkish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so it's l-a-r
+
+ align:start position:0%
+so it's l-a-r
+ 
+
+ align:start position:0%
+so it's l-a-r
+get loud like in the word for Lions and
+
+ align:start position:0%
+get loud like in the word for Lions and
+ 
+
+ align:start position:0%
+get loud like in the word for Lions and
+the word for arms and the word for
+
+ align:start position:0%
+the word for arms and the word for
+ 
+
+ align:start position:0%
+the word for arms and the word for
+slaves and the word for daughters oh but
+
+ align:start position:0%
+slaves and the word for daughters oh but
+ 
+
+ align:start position:0%
+slaves and the word for daughters oh but
+not in the words for winds teeth and
+
+ align:start position:0%
+not in the words for winds teeth and
+ 
+
+ align:start position:0%
+not in the words for winds teeth and
+Roses right
+
+ align:start position:0%
+Roses right
+ 
+
+ align:start position:0%
+Roses right
+where we seem to get ler
+
+ align:start position:0%
+where we seem to get ler
+ 
+
+ align:start position:0%
+where we seem to get ler
+yeah so we get l-e-r uh for those three
+
+ align:start position:0%
+yeah so we get l-e-r uh for those three
+ 
+
+ align:start position:0%
+yeah so we get l-e-r uh for those three
+uh I'll write them down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Youth
+
+ align:start position:0%
+and Youth
+ 
+
+ align:start position:0%
+and Youth
+and we get a lot for these uh Aslan
+
+ align:start position:0%
+and we get a lot for these uh Aslan
+ 
+
+ align:start position:0%
+and we get a lot for these uh Aslan
+coal
+
+ align:start position:0%
+coal
+ 
+
+ align:start position:0%
+coal
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay having done that I'm now going to
+
+ align:start position:0%
+okay having done that I'm now going to
+ 
+
+ align:start position:0%
+okay having done that I'm now going to
+go back to the last slide
+
+ align:start position:0%
+go back to the last slide
+ 
+
+ align:start position:0%
+go back to the last slide
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what do you think why are we getting LED
+
+ align:start position:0%
+what do you think why are we getting LED
+ 
+
+ align:start position:0%
+what do you think why are we getting LED
+with these and lar with those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Joseph what do you think is happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think this is an example of what's
+
+ align:start position:0%
+I think this is an example of what's
+ 
+
+ align:start position:0%
+I think this is an example of what's
+called vowel Harmony
+
+ align:start position:0%
+called vowel Harmony
+ 
+
+ align:start position:0%
+called vowel Harmony
+um what do you mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you attach it to another word
+
+ align:start position:0%
+you attach it to another word
+ 
+
+ align:start position:0%
+you attach it to another word
+the primary vowels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with whatever
+
+ align:start position:0%
+with whatever
+ 
+
+ align:start position:0%
+with whatever
+some vowel than the other one is yeah
+
+ align:start position:0%
+some vowel than the other one is yeah
+ 
+
+ align:start position:0%
+some vowel than the other one is yeah
+so you're that's that's well said so uh
+
+ align:start position:0%
+so you're that's that's well said so uh
+ 
+
+ align:start position:0%
+so you're that's that's well said so uh
+what does this vowel have in common with
+
+ align:start position:0%
+what does this vowel have in common with
+ 
+
+ align:start position:0%
+what does this vowel have in common with
+these vowels
+
+ align:start position:0%
+these vowels
+ 
+
+ align:start position:0%
+these vowels
+and what does this vowel have in common
+
+ align:start position:0%
+and what does this vowel have in common
+ 
+
+ align:start position:0%
+and what does this vowel have in common
+with these vowels bear in mind that is a
+
+ align:start position:0%
+with these vowels bear in mind that is a
+ 
+
+ align:start position:0%
+with these vowels bear in mind that is a
+front
+
+ align:start position:0%
+front
+ 
+
+ align:start position:0%
+front
+High
+
+ align:start position:0%
+High
+ 
+
+ align:start position:0%
+High
+grounded vowel
+
+ align:start position:0%
+grounded vowel
+ 
+
+ align:start position:0%
+grounded vowel
+and U is a back
+
+ align:start position:0%
+and U is a back
+ 
+
+ align:start position:0%
+and U is a back
+High unrounded buff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do these vowels a e and e
+
+ align:start position:0%
+what do these vowels a e and e
+ 
+
+ align:start position:0%
+what do these vowels a e and e
+all have in common yes
+
+ align:start position:0%
+all have in common yes
+ 
+
+ align:start position:0%
+all have in common yes
+they're all front
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what do these vowels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have in common well they're all back
+
+ align:start position:0%
+have in common well they're all back
+ 
+
+ align:start position:0%
+have in common well they're all back
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and uh the vowel in lar is back and the
+
+ align:start position:0%
+and uh the vowel in lar is back and the
+ 
+
+ align:start position:0%
+and uh the vowel in lar is back and the
+vowel in lair
+
+ align:start position:0%
+vowel in lair
+ 
+
+ align:start position:0%
+vowel in lair
+is front
+
+ align:start position:0%
+is front
+ 
+
+ align:start position:0%
+is front
+so just as Joseph said this is vowel
+
+ align:start position:0%
+so just as Joseph said this is vowel
+ 
+
+ align:start position:0%
+so just as Joseph said this is vowel
+Harmony it's the the vowel of this
+
+ align:start position:0%
+Harmony it's the the vowel of this
+ 
+
+ align:start position:0%
+Harmony it's the the vowel of this
+suffix is having its properties
+
+ align:start position:0%
+suffix is having its properties
+ 
+
+ align:start position:0%
+suffix is having its properties
+determined by the vowel of the
+
+ align:start position:0%
+determined by the vowel of the
+ 
+
+ align:start position:0%
+determined by the vowel of the
+uh of the thing it's being attached to
+
+ align:start position:0%
+uh of the thing it's being attached to
+ 
+
+ align:start position:0%
+uh of the thing it's being attached to
+the noun is being attached to whether
+
+ align:start position:0%
+the noun is being attached to whether
+ 
+
+ align:start position:0%
+the noun is being attached to whether
+it's front or back
+
+ align:start position:0%
+it's front or back
+ 
+
+ align:start position:0%
+it's front or back
+um is determined by the vowel of the of
+
+ align:start position:0%
+um is determined by the vowel of the of
+ 
+
+ align:start position:0%
+um is determined by the vowel of the of
+the noun it's attached to so this is uh
+
+ align:start position:0%
+the noun it's attached to so this is uh
+ 
+
+ align:start position:0%
+the noun it's attached to so this is uh
+front back Harmony there's also rounding
+
+ align:start position:0%
+front back Harmony there's also rounding
+ 
+
+ align:start position:0%
+front back Harmony there's also rounding
+Harmony so cases where you have a suffix
+
+ align:start position:0%
+Harmony so cases where you have a suffix
+ 
+
+ align:start position:0%
+Harmony so cases where you have a suffix
+whose roundedness is determined by the
+
+ align:start position:0%
+whose roundedness is determined by the
+ 
+
+ align:start position:0%
+whose roundedness is determined by the
+roundedness of the vowel that's
+
+ align:start position:0%
+roundedness of the vowel that's
+ 
+
+ align:start position:0%
+roundedness of the vowel that's
+attaching to uh there are other kinds of
+
+ align:start position:0%
+attaching to uh there are other kinds of
+ 
+
+ align:start position:0%
+attaching to uh there are other kinds of
+Harmony but those are things that happen
+
+ align:start position:0%
+Harmony but those are things that happen
+ 
+
+ align:start position:0%
+Harmony but those are things that happen
+and categorizing vowels you know looking
+
+ align:start position:0%
+and categorizing vowels you know looking
+ 
+
+ align:start position:0%
+and categorizing vowels you know looking
+at vowels and thinking oh yeah some of
+
+ align:start position:0%
+at vowels and thinking oh yeah some of
+ 
+
+ align:start position:0%
+at vowels and thinking oh yeah some of
+these are friends and others are back
+
+ align:start position:0%
+these are friends and others are back
+ 
+
+ align:start position:0%
+these are friends and others are back
+um it's not just a fun thing to do that
+
+ align:start position:0%
+um it's not just a fun thing to do that
+ 
+
+ align:start position:0%
+um it's not just a fun thing to do that
+allows us to think about the insides of
+
+ align:start position:0%
+allows us to think about the insides of
+ 
+
+ align:start position:0%
+allows us to think about the insides of
+our mouths it allows us to understand
+
+ align:start position:0%
+our mouths it allows us to understand
+ 
+
+ align:start position:0%
+our mouths it allows us to understand
+Turkish better right what the heck is
+
+ align:start position:0%
+Turkish better right what the heck is
+ 
+
+ align:start position:0%
+Turkish better right what the heck is
+going on in Turkish well it's Harmony
+
+ align:start position:0%
+going on in Turkish well it's Harmony
+ 
+
+ align:start position:0%
+going on in Turkish well it's Harmony
+for front versus back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I think when I was first introducing you
+
+ align:start position:0%
+I think when I was first introducing you
+ 
+
+ align:start position:0%
+I think when I was first introducing you
+to consonants I said uh consonants they
+
+ align:start position:0%
+to consonants I said uh consonants they
+ 
+
+ align:start position:0%
+to consonants I said uh consonants they
+involve uh disturbing the flow of error
+
+ align:start position:0%
+involve uh disturbing the flow of error
+ 
+
+ align:start position:0%
+involve uh disturbing the flow of error
+and the flow of air is usually going
+
+ align:start position:0%
+and the flow of air is usually going
+ 
+
+ align:start position:0%
+and the flow of air is usually going
+outward from your lungs
+
+ align:start position:0%
+outward from your lungs
+ 
+
+ align:start position:0%
+outward from your lungs
+but there are some other options I said
+
+ align:start position:0%
+but there are some other options I said
+ 
+
+ align:start position:0%
+but there are some other options I said
+and and chuckled mysteriously and so I
+
+ align:start position:0%
+and and chuckled mysteriously and so I
+ 
+
+ align:start position:0%
+and and chuckled mysteriously and so I
+want to just show you why I was doing
+
+ align:start position:0%
+want to just show you why I was doing
+ 
+
+ align:start position:0%
+want to just show you why I was doing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um there are other kinds of sounds out
+
+ align:start position:0%
+um there are other kinds of sounds out
+ 
+
+ align:start position:0%
+um there are other kinds of sounds out
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+uh so the first kind of sound that I
+
+ align:start position:0%
+uh so the first kind of sound that I
+ 
+
+ align:start position:0%
+uh so the first kind of sound that I
+wanted to talk about are what are called
+
+ align:start position:0%
+wanted to talk about are what are called
+ 
+
+ align:start position:0%
+wanted to talk about are what are called
+ejectives uh and I have some sound files
+
+ align:start position:0%
+ejectives uh and I have some sound files
+ 
+
+ align:start position:0%
+ejectives uh and I have some sound files
+uh that I'll play for you these were all
+
+ align:start position:0%
+uh that I'll play for you these were all
+ 
+
+ align:start position:0%
+uh that I'll play for you these were all
+compiled and put online by uh uh the the
+
+ align:start position:0%
+compiled and put online by uh uh the the
+ 
+
+ align:start position:0%
+compiled and put online by uh uh the the
+great uh uh phoneticist Peter latifogin
+
+ align:start position:0%
+great uh uh phoneticist Peter latifogin
+ 
+
+ align:start position:0%
+great uh uh phoneticist Peter latifogin
+who used to teach at UCLA he's no longer
+
+ align:start position:0%
+who used to teach at UCLA he's no longer
+ 
+
+ align:start position:0%
+who used to teach at UCLA he's no longer
+with us
+
+ align:start position:0%
+with us
+ 
+
+ align:start position:0%
+with us
+um uh I'll put a link on the website
+
+ align:start position:0%
+um uh I'll put a link on the website
+ 
+
+ align:start position:0%
+um uh I'll put a link on the website
+both to the particular uh classes of
+
+ align:start position:0%
+both to the particular uh classes of
+ 
+
+ align:start position:0%
+both to the particular uh classes of
+sounds that I'm going to show you and to
+
+ align:start position:0%
+sounds that I'm going to show you and to
+ 
+
+ align:start position:0%
+sounds that I'm going to show you and to
+the larger UCLA website which has all
+
+ align:start position:0%
+the larger UCLA website which has all
+ 
+
+ align:start position:0%
+the larger UCLA website which has all
+kinds of cool sound files on it that you
+
+ align:start position:0%
+kinds of cool sound files on it that you
+ 
+
+ align:start position:0%
+kinds of cool sound files on it that you
+can listen to and amaze and annoy your
+
+ align:start position:0%
+can listen to and amaze and annoy your
+ 
+
+ align:start position:0%
+can listen to and amaze and annoy your
+friends with
+
+ align:start position:0%
+friends with
+ 
+
+ align:start position:0%
+friends with
+um so the first type of sound that I
+
+ align:start position:0%
+um so the first type of sound that I
+ 
+
+ align:start position:0%
+um so the first type of sound that I
+want to talk about are what are called
+
+ align:start position:0%
+want to talk about are what are called
+ 
+
+ align:start position:0%
+want to talk about are what are called
+ejectives uh there aren't languages of
+
+ align:start position:0%
+ejectives uh there aren't languages of
+ 
+
+ align:start position:0%
+ejectives uh there aren't languages of
+Europe that have ejectives but they're
+
+ align:start position:0%
+Europe that have ejectives but they're
+ 
+
+ align:start position:0%
+Europe that have ejectives but they're
+quite popular in the languages of North
+
+ align:start position:0%
+quite popular in the languages of North
+ 
+
+ align:start position:0%
+quite popular in the languages of North
+and South America
+
+ align:start position:0%
+and South America
+ 
+
+ align:start position:0%
+and South America
+um and uh so it's worth learning how to
+
+ align:start position:0%
+um and uh so it's worth learning how to
+ 
+
+ align:start position:0%
+um and uh so it's worth learning how to
+do them
+
+ align:start position:0%
+do them
+ 
+
+ align:start position:0%
+do them
+um let's start by making an ejective uh
+
+ align:start position:0%
+um let's start by making an ejective uh
+ 
+
+ align:start position:0%
+um let's start by making an ejective uh
+uh T this is how you make an injective T
+
+ align:start position:0%
+uh T this is how you make an injective T
+ 
+
+ align:start position:0%
+uh T this is how you make an injective T
+you uh so first we'll practice like this
+
+ align:start position:0%
+you uh so first we'll practice like this
+ 
+
+ align:start position:0%
+you uh so first we'll practice like this
+you'll hold your breath
+
+ align:start position:0%
+you'll hold your breath
+ 
+
+ align:start position:0%
+you'll hold your breath
+don't do it now because I have other
+
+ align:start position:0%
+don't do it now because I have other
+ 
+
+ align:start position:0%
+don't do it now because I have other
+things to talk about what you're going
+
+ align:start position:0%
+things to talk about what you're going
+ 
+
+ align:start position:0%
+things to talk about what you're going
+to do is you're going to hold your
+
+ align:start position:0%
+to do is you're going to hold your
+ 
+
+ align:start position:0%
+to do is you're going to hold your
+breath and try to make an audible T
+
+ align:start position:0%
+breath and try to make an audible T
+ 
+
+ align:start position:0%
+breath and try to make an audible T
+sound so go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+and then you know if you were actually
+
+ align:start position:0%
+and then you know if you were actually
+ 
+
+ align:start position:0%
+and then you know if you were actually
+doing this in speech you're not allowed
+
+ align:start position:0%
+doing this in speech you're not allowed
+ 
+
+ align:start position:0%
+doing this in speech you're not allowed
+to stop and hold your breath
+
+ align:start position:0%
+to stop and hold your breath
+ 
+
+ align:start position:0%
+to stop and hold your breath
+um the idea is to uh uh get well so hold
+
+ align:start position:0%
+um the idea is to uh uh get well so hold
+ 
+
+ align:start position:0%
+um the idea is to uh uh get well so hold
+your breath make your ejective tea and
+
+ align:start position:0%
+your breath make your ejective tea and
+ 
+
+ align:start position:0%
+your breath make your ejective tea and
+then release into a vowel so go ah
+
+ align:start position:0%
+then release into a vowel so go ah
+ 
+
+ align:start position:0%
+then release into a vowel so go ah
+at uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool you guys sound very ejective
+
+ align:start position:0%
+cool you guys sound very ejective
+ 
+
+ align:start position:0%
+cool you guys sound very ejective
+um and similarly you can do this with
+
+ align:start position:0%
+um and similarly you can do this with
+ 
+
+ align:start position:0%
+um and similarly you can do this with
+bilabial there are bilabial ejective
+
+ align:start position:0%
+bilabial there are bilabial ejective
+ 
+
+ align:start position:0%
+bilabial there are bilabial ejective
+stops uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or Velar ejective stops like ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+excellent
+
+ align:start position:0%
+excellent
+ 
+
+ align:start position:0%
+excellent
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um we're all amateurs at this but the
+
+ align:start position:0%
+um we're all amateurs at this but the
+ 
+
+ align:start position:0%
+um we're all amateurs at this but the
+Lakota are professionals so let's listen
+
+ align:start position:0%
+Lakota are professionals so let's listen
+ 
+
+ align:start position:0%
+Lakota are professionals so let's listen
+to a Lakota speaker do this
+
+ align:start position:0%
+to a Lakota speaker do this
+ 
+
+ align:start position:0%
+to a Lakota speaker do this
+crew that's an objective dealer
+
+ align:start position:0%
+crew that's an objective dealer
+ 
+
+ align:start position:0%
+crew that's an objective dealer
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+as opposed to here's her her regular
+
+ align:start position:0%
+as opposed to here's her her regular
+ 
+
+ align:start position:0%
+as opposed to here's her her regular
+dealer stop God
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um here's a bilabial one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what that's what adjectives
+
+ align:start position:0%
+so that's what that's what adjectives
+ 
+
+ align:start position:0%
+so that's what that's what adjectives
+sound like in the wild this is Lakota
+
+ align:start position:0%
+sound like in the wild this is Lakota
+ 
+
+ align:start position:0%
+sound like in the wild this is Lakota
+it's a language uh still spoken uh in uh
+
+ align:start position:0%
+it's a language uh still spoken uh in uh
+ 
+
+ align:start position:0%
+it's a language uh still spoken uh in uh
+well near North and South Dakota so
+
+ align:start position:0%
+well near North and South Dakota so
+ 
+
+ align:start position:0%
+well near North and South Dakota so
+there are the lakotas and the nakota's
+
+ align:start position:0%
+there are the lakotas and the nakota's
+ 
+
+ align:start position:0%
+there are the lakotas and the nakota's
+and the Dakotas they all live in that
+
+ align:start position:0%
+and the Dakotas they all live in that
+ 
+
+ align:start position:0%
+and the Dakotas they all live in that
+area they're suing languages yeah oh
+
+ align:start position:0%
+area they're suing languages yeah oh
+ 
+
+ align:start position:0%
+area they're suing languages yeah oh
+Raquel what's
+
+ align:start position:0%
+Raquel what's
+ 
+
+ align:start position:0%
+Raquel what's
+between that and just the norm like
+
+ align:start position:0%
+between that and just the norm like
+ 
+
+ align:start position:0%
+between that and just the norm like
+today's sound followed by the gelato
+
+ align:start position:0%
+today's sound followed by the gelato
+ 
+
+ align:start position:0%
+today's sound followed by the gelato
+stuff uh so it's very similar you're
+
+ align:start position:0%
+stuff uh so it's very similar you're
+ 
+
+ align:start position:0%
+stuff uh so it's very similar you're
+engaging your glove so what you're doing
+
+ align:start position:0%
+engaging your glove so what you're doing
+ 
+
+ align:start position:0%
+engaging your glove so what you're doing
+when you make these sounds
+
+ align:start position:0%
+when you make these sounds
+ 
+
+ align:start position:0%
+when you make these sounds
+um is you are uh making a Velar closure
+
+ align:start position:0%
+um is you are uh making a Velar closure
+ 
+
+ align:start position:0%
+um is you are uh making a Velar closure
+um and then you are also making a
+
+ align:start position:0%
+um and then you are also making a
+ 
+
+ align:start position:0%
+um and then you are also making a
+glottal stop
+
+ align:start position:0%
+glottal stop
+ 
+
+ align:start position:0%
+glottal stop
+and then you are sort of pushing with
+
+ align:start position:0%
+and then you are sort of pushing with
+ 
+
+ align:start position:0%
+and then you are sort of pushing with
+your glottis to make the Velar closure
+
+ align:start position:0%
+your glottis to make the Velar closure
+ 
+
+ align:start position:0%
+your glottis to make the Velar closure
+open so you make your you you move your
+
+ align:start position:0%
+open so you make your you you move your
+ 
+
+ align:start position:0%
+open so you make your you you move your
+larynx in order to get the the closure
+
+ align:start position:0%
+larynx in order to get the the closure
+ 
+
+ align:start position:0%
+larynx in order to get the the closure
+to open and that's what gives it this
+
+ align:start position:0%
+to open and that's what gives it this
+ 
+
+ align:start position:0%
+to open and that's what gives it this
+sort of unique burst so you're right
+
+ align:start position:0%
+sort of unique burst so you're right
+ 
+
+ align:start position:0%
+sort of unique burst so you're right
+there is a global stop involved when
+
+ align:start position:0%
+there is a global stop involved when
+ 
+
+ align:start position:0%
+there is a global stop involved when
+you're doing that uh or at uh
+
+ align:start position:0%
+you're doing that uh or at uh
+ 
+
+ align:start position:0%
+you're doing that uh or at uh
+so when I said that the flow of air is
+
+ align:start position:0%
+so when I said that the flow of air is
+ 
+
+ align:start position:0%
+so when I said that the flow of air is
+usually from your lungs uh here's a
+
+ align:start position:0%
+usually from your lungs uh here's a
+ 
+
+ align:start position:0%
+usually from your lungs uh here's a
+place where it isn't exactly
+
+ align:start position:0%
+place where it isn't exactly
+ 
+
+ align:start position:0%
+place where it isn't exactly
+um the air originally came from your
+
+ align:start position:0%
+um the air originally came from your
+ 
+
+ align:start position:0%
+um the air originally came from your
+lungs well it originally came from you
+
+ align:start position:0%
+lungs well it originally came from you
+ 
+
+ align:start position:0%
+lungs well it originally came from you
+know the world uh it spent some time in
+
+ align:start position:0%
+know the world uh it spent some time in
+ 
+
+ align:start position:0%
+know the world uh it spent some time in
+your lungs and then uh it got trapped
+
+ align:start position:0%
+your lungs and then uh it got trapped
+ 
+
+ align:start position:0%
+your lungs and then uh it got trapped
+between this glutal stop at your larynx
+
+ align:start position:0%
+between this glutal stop at your larynx
+ 
+
+ align:start position:0%
+between this glutal stop at your larynx
+and the closure that you're making in
+
+ align:start position:0%
+and the closure that you're making in
+ 
+
+ align:start position:0%
+and the closure that you're making in
+your mouth and the the flow of air that
+
+ align:start position:0%
+your mouth and the the flow of air that
+ 
+
+ align:start position:0%
+your mouth and the the flow of air that
+caused that's present as you're opening
+
+ align:start position:0%
+caused that's present as you're opening
+ 
+
+ align:start position:0%
+caused that's present as you're opening
+the stop is actually from your larynx
+
+ align:start position:0%
+the stop is actually from your larynx
+ 
+
+ align:start position:0%
+the stop is actually from your larynx
+it's not from your it's not from your
+
+ align:start position:0%
+it's not from your it's not from your
+ 
+
+ align:start position:0%
+it's not from your it's not from your
+lungs right
+
+ align:start position:0%
+lungs right
+ 
+
+ align:start position:0%
+lungs right
+it's not originally from your lungs that
+
+ align:start position:0%
+it's not originally from your lungs that
+ 
+
+ align:start position:0%
+it's not originally from your lungs that
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+those are ejectives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clicks uh I'll I have some recordings of
+
+ align:start position:0%
+clicks uh I'll I have some recordings of
+ 
+
+ align:start position:0%
+clicks uh I'll I have some recordings of
+Clicks in here somewhere yeah there they
+
+ align:start position:0%
+Clicks in here somewhere yeah there they
+ 
+
+ align:start position:0%
+Clicks in here somewhere yeah there they
+are these are Zulu clicks
+
+ align:start position:0%
+are these are Zulu clicks
+ 
+
+ align:start position:0%
+are these are Zulu clicks
+um there are three main kinds of clicks
+
+ align:start position:0%
+um there are three main kinds of clicks
+ 
+
+ align:start position:0%
+um there are three main kinds of clicks
+to think about and clicks again involve
+
+ align:start position:0%
+to think about and clicks again involve
+ 
+
+ align:start position:0%
+to think about and clicks again involve
+a strange
+
+ align:start position:0%
+a strange
+ 
+
+ align:start position:0%
+a strange
+typologically unusual kind of airflow so
+
+ align:start position:0%
+typologically unusual kind of airflow so
+ 
+
+ align:start position:0%
+typologically unusual kind of airflow so
+clicks are found in
+
+ align:start position:0%
+clicks are found in
+ 
+
+ align:start position:0%
+clicks are found in
+um uh so the the languages with the
+
+ align:start position:0%
+um uh so the the languages with the
+ 
+
+ align:start position:0%
+um uh so the the languages with the
+richest click inventories are the koisan
+
+ align:start position:0%
+richest click inventories are the koisan
+ 
+
+ align:start position:0%
+richest click inventories are the koisan
+languages of places like um Namibia uh
+
+ align:start position:0%
+languages of places like um Namibia uh
+ 
+
+ align:start position:0%
+languages of places like um Namibia uh
+uh and then there are a bunch of Bantu
+
+ align:start position:0%
+uh and then there are a bunch of Bantu
+ 
+
+ align:start position:0%
+uh and then there are a bunch of Bantu
+languages that also have clicks
+
+ align:start position:0%
+languages that also have clicks
+ 
+
+ align:start position:0%
+languages that also have clicks
+um uh also in Africa uh uh in theory
+
+ align:start position:0%
+um uh also in Africa uh uh in theory
+ 
+
+ align:start position:0%
+um uh also in Africa uh uh in theory
+because they've been in contact with the
+
+ align:start position:0%
+because they've been in contact with the
+ 
+
+ align:start position:0%
+because they've been in contact with the
+koisan languages so clicks are really
+
+ align:start position:0%
+koisan languages so clicks are really
+ 
+
+ align:start position:0%
+koisan languages so clicks are really
+cross-linguistically not terribly
+
+ align:start position:0%
+cross-linguistically not terribly
+ 
+
+ align:start position:0%
+cross-linguistically not terribly
+popular they're they're only found in in
+
+ align:start position:0%
+popular they're they're only found in in
+ 
+
+ align:start position:0%
+popular they're they're only found in in
+that area and in one um
+
+ align:start position:0%
+that area and in one um
+ 
+
+ align:start position:0%
+that area and in one um
+uh culturally restricted language spoken
+
+ align:start position:0%
+uh culturally restricted language spoken
+ 
+
+ align:start position:0%
+uh culturally restricted language spoken
+by the lardel so the lairdel have a it's
+
+ align:start position:0%
+by the lardel so the lairdel have a it's
+ 
+
+ align:start position:0%
+by the lardel so the lairdel have a it's
+almost a language game it's called demin
+
+ align:start position:0%
+almost a language game it's called demin
+ 
+
+ align:start position:0%
+almost a language game it's called demin
+Uh which is used uh after a certain
+
+ align:start position:0%
+Uh which is used uh after a certain
+ 
+
+ align:start position:0%
+Uh which is used uh after a certain
+initiation ceremony so there's a period
+
+ align:start position:0%
+initiation ceremony so there's a period
+ 
+
+ align:start position:0%
+initiation ceremony so there's a period
+where you're not supposed to speak
+
+ align:start position:0%
+where you're not supposed to speak
+ 
+
+ align:start position:0%
+where you're not supposed to speak
+normal Lardo and so you speak this other
+
+ align:start position:0%
+normal Lardo and so you speak this other
+ 
+
+ align:start position:0%
+normal Lardo and so you speak this other
+thing instead which has all kinds of
+
+ align:start position:0%
+thing instead which has all kinds of
+ 
+
+ align:start position:0%
+thing instead which has all kinds of
+strange sounds in it including clicks
+
+ align:start position:0%
+strange sounds in it including clicks
+ 
+
+ align:start position:0%
+strange sounds in it including clicks
+it's called denim we may get a chance to
+
+ align:start position:0%
+it's called denim we may get a chance to
+ 
+
+ align:start position:0%
+it's called denim we may get a chance to
+talk more about it later but for
+
+ align:start position:0%
+talk more about it later but for
+ 
+
+ align:start position:0%
+talk more about it later but for
+languages that are not spoken under you
+
+ align:start position:0%
+languages that are not spoken under you
+ 
+
+ align:start position:0%
+languages that are not spoken under you
+know special cultural circumstances uh
+
+ align:start position:0%
+know special cultural circumstances uh
+ 
+
+ align:start position:0%
+know special cultural circumstances uh
+these African languages the khoisan
+
+ align:start position:0%
+these African languages the khoisan
+ 
+
+ align:start position:0%
+these African languages the khoisan
+languages and the Bantu languages that
+
+ align:start position:0%
+languages and the Bantu languages that
+ 
+
+ align:start position:0%
+languages and the Bantu languages that
+have been in contact with them are the
+
+ align:start position:0%
+have been in contact with them are the
+ 
+
+ align:start position:0%
+have been in contact with them are the
+only ones that have clicks
+
+ align:start position:0%
+only ones that have clicks
+ 
+
+ align:start position:0%
+only ones that have clicks
+um and I'm talking about clicks now
+
+ align:start position:0%
+um and I'm talking about clicks now
+ 
+
+ align:start position:0%
+um and I'm talking about clicks now
+because they do involve an unusual
+
+ align:start position:0%
+because they do involve an unusual
+ 
+
+ align:start position:0%
+because they do involve an unusual
+airflow they involve making a stop uh
+
+ align:start position:0%
+airflow they involve making a stop uh
+ 
+
+ align:start position:0%
+airflow they involve making a stop uh
+Velar stop and then uh using your tongue
+
+ align:start position:0%
+Velar stop and then uh using your tongue
+ 
+
+ align:start position:0%
+Velar stop and then uh using your tongue
+to sort of sharply draw air into your
+
+ align:start position:0%
+to sort of sharply draw air into your
+ 
+
+ align:start position:0%
+to sort of sharply draw air into your
+mouth uh
+
+ align:start position:0%
+mouth uh
+ 
+
+ align:start position:0%
+mouth uh
+uh for for a moment so what's a click
+
+ align:start position:0%
+uh for for a moment so what's a click
+ 
+
+ align:start position:0%
+uh for for a moment so what's a click
+um One Click is the dental click uh it's
+
+ align:start position:0%
+um One Click is the dental click uh it's
+ 
+
+ align:start position:0%
+um One Click is the dental click uh it's
+the kind of sound you make uh to
+
+ align:start position:0%
+the kind of sound you make uh to
+ 
+
+ align:start position:0%
+the kind of sound you make uh to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh criticize someone uh
+
+ align:start position:0%
+uh criticize someone uh
+ 
+
+ align:start position:0%
+uh criticize someone uh
+kind of thing that you're sometimes see
+
+ align:start position:0%
+kind of thing that you're sometimes see
+ 
+
+ align:start position:0%
+kind of thing that you're sometimes see
+spelled tsk tsk yeah
+
+ align:start position:0%
+spelled tsk tsk yeah
+ 
+
+ align:start position:0%
+spelled tsk tsk yeah
+um there is a lateral click whenever I
+
+ align:start position:0%
+um there is a lateral click whenever I
+ 
+
+ align:start position:0%
+um there is a lateral click whenever I
+read about lateral clicks uh the the
+
+ align:start position:0%
+read about lateral clicks uh the the
+ 
+
+ align:start position:0%
+read about lateral clicks uh the the
+description of them is always that it's
+
+ align:start position:0%
+description of them is always that it's
+ 
+
+ align:start position:0%
+description of them is always that it's
+the sound you make to encourage a horse
+
+ align:start position:0%
+the sound you make to encourage a horse
+ 
+
+ align:start position:0%
+the sound you make to encourage a horse
+I have never had to encourage a horse uh
+
+ align:start position:0%
+I have never had to encourage a horse uh
+ 
+
+ align:start position:0%
+I have never had to encourage a horse uh
+or discourage a I've never I
+
+ align:start position:0%
+or discourage a I've never I
+ 
+
+ align:start position:0%
+or discourage a I've never I
+haven't interacted much with horses so
+
+ align:start position:0%
+haven't interacted much with horses so
+ 
+
+ align:start position:0%
+haven't interacted much with horses so
+uh so I'm not I that that description
+
+ align:start position:0%
+uh so I'm not I that that description
+ 
+
+ align:start position:0%
+uh so I'm not I that that description
+doesn't help me a whole lot I gather it
+
+ align:start position:0%
+doesn't help me a whole lot I gather it
+ 
+
+ align:start position:0%
+doesn't help me a whole lot I gather it
+involves uh sucking the sides of your
+
+ align:start position:0%
+involves uh sucking the sides of your
+ 
+
+ align:start position:0%
+involves uh sucking the sides of your
+tongue in from uh the sides of your
+
+ align:start position:0%
+tongue in from uh the sides of your
+ 
+
+ align:start position:0%
+tongue in from uh the sides of your
+mouth so you're going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I think I hear some lateral clicks
+
+ align:start position:0%
+yes I think I hear some lateral clicks
+ 
+
+ align:start position:0%
+yes I think I hear some lateral clicks
+and then there's another click
+
+ align:start position:0%
+and then there's another click
+ 
+
+ align:start position:0%
+and then there's another click
+um which uh sometimes called a palpable
+
+ align:start position:0%
+um which uh sometimes called a palpable
+ 
+
+ align:start position:0%
+um which uh sometimes called a palpable
+click which goes
+
+ align:start position:0%
+click which goes
+ 
+
+ align:start position:0%
+click which goes
+so you're
+
+ align:start position:0%
+so you're
+ 
+
+ align:start position:0%
+so you're
+oh you guys are really good at that one
+
+ align:start position:0%
+oh you guys are really good at that one
+ 
+
+ align:start position:0%
+oh you guys are really good at that one
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um so uh all three of these clicks are
+
+ align:start position:0%
+um so uh all three of these clicks are
+ 
+
+ align:start position:0%
+um so uh all three of these clicks are
+present for example in Zulu and in
+
+ align:start position:0%
+present for example in Zulu and in
+ 
+
+ align:start position:0%
+present for example in Zulu and in
+closer which is the native language of
+
+ align:start position:0%
+closer which is the native language of
+ 
+
+ align:start position:0%
+closer which is the native language of
+Nelson Mandela
+
+ align:start position:0%
+Nelson Mandela
+ 
+
+ align:start position:0%
+Nelson Mandela
+um and here are some Zulu ones that you
+
+ align:start position:0%
+um and here are some Zulu ones that you
+ 
+
+ align:start position:0%
+um and here are some Zulu ones that you
+can listen to uh so we've got the dental
+
+ align:start position:0%
+can listen to uh so we've got the dental
+ 
+
+ align:start position:0%
+can listen to uh so we've got the dental
+one first uh
+
+ align:start position:0%
+one first uh
+ 
+
+ align:start position:0%
+one first uh
+and here's the lateral one
+
+ align:start position:0%
+and here's the lateral one
+ 
+
+ align:start position:0%
+and here's the lateral one
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and the I'll be a tolerable one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and as you can see from this Zulu uh uh
+
+ align:start position:0%
+and as you can see from this Zulu uh uh
+ 
+
+ align:start position:0%
+and as you can see from this Zulu uh uh
+draws distinctions um depending on
+
+ align:start position:0%
+draws distinctions um depending on
+ 
+
+ align:start position:0%
+draws distinctions um depending on
+basically how you release the stop so uh
+
+ align:start position:0%
+basically how you release the stop so uh
+ 
+
+ align:start position:0%
+basically how you release the stop so uh
+there are clicks those clicks the ones I
+
+ align:start position:0%
+there are clicks those clicks the ones I
+ 
+
+ align:start position:0%
+there are clicks those clicks the ones I
+just played for you involve a voiceless
+
+ align:start position:0%
+just played for you involve a voiceless
+ 
+
+ align:start position:0%
+just played for you involve a voiceless
+stop uh that's not aspirated that
+
+ align:start position:0%
+stop uh that's not aspirated that
+ 
+
+ align:start position:0%
+stop uh that's not aspirated that
+doesn't have this puff of air that I was
+
+ align:start position:0%
+doesn't have this puff of air that I was
+ 
+
+ align:start position:0%
+doesn't have this puff of air that I was
+talking about and that we will talk
+
+ align:start position:0%
+talking about and that we will talk
+ 
+
+ align:start position:0%
+talking about and that we will talk
+about more uh I was talking about when I
+
+ align:start position:0%
+about more uh I was talking about when I
+ 
+
+ align:start position:0%
+about more uh I was talking about when I
+was talking about philosophy in Greek
+
+ align:start position:0%
+was talking about philosophy in Greek
+ 
+
+ align:start position:0%
+was talking about philosophy in Greek
+but you can also build them on aspirated
+
+ align:start position:0%
+but you can also build them on aspirated
+ 
+
+ align:start position:0%
+but you can also build them on aspirated
+stops or on voiced stops or even on
+
+ align:start position:0%
+stops or on voiced stops or even on
+ 
+
+ align:start position:0%
+stops or on voiced stops or even on
+nasals um so maybe I'll just run through
+
+ align:start position:0%
+nasals um so maybe I'll just run through
+ 
+
+ align:start position:0%
+nasals um so maybe I'll just run through
+all the dental clicks here's the
+
+ align:start position:0%
+all the dental clicks here's the
+ 
+
+ align:start position:0%
+all the dental clicks here's the
+voiceless one again
+
+ align:start position:0%
+voiceless one again
+ 
+
+ align:start position:0%
+voiceless one again
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+but here it is aspirated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's sort of air coming out as you
+
+ align:start position:0%
+so there's sort of air coming out as you
+ 
+
+ align:start position:0%
+so there's sort of air coming out as you
+do this and here it is voiced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here it is nasal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh that'll hardly sounded like a click
+
+ align:start position:0%
+oh that'll hardly sounded like a click
+ 
+
+ align:start position:0%
+oh that'll hardly sounded like a click
+at all here let me try to find another
+
+ align:start position:0%
+at all here let me try to find another
+ 
+
+ align:start position:0%
+at all here let me try to find another
+nasal one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep that was clicky and uh here it is as
+
+ align:start position:0%
+yep that was clicky and uh here it is as
+ 
+
+ align:start position:0%
+yep that was clicky and uh here it is as
+a lateral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+baby
+
+ align:start position:0%
+baby
+ 
+
+ align:start position:0%
+baby
+Zulu uh Zulu really does sound like that
+
+ align:start position:0%
+Zulu uh Zulu really does sound like that
+ 
+
+ align:start position:0%
+Zulu uh Zulu really does sound like that
+we did we did a field methods class on
+
+ align:start position:0%
+we did we did a field methods class on
+ 
+
+ align:start position:0%
+we did we did a field methods class on
+Zulu it has this beautiful because it's
+
+ align:start position:0%
+Zulu it has this beautiful because it's
+ 
+
+ align:start position:0%
+Zulu it has this beautiful because it's
+tonal uh so it has all this the
+
+ align:start position:0%
+tonal uh so it has all this the
+ 
+
+ align:start position:0%
+tonal uh so it has all this the
+intonation is just really pretty to
+
+ align:start position:0%
+intonation is just really pretty to
+ 
+
+ align:start position:0%
+intonation is just really pretty to
+listen to
+
+ align:start position:0%
+listen to
+ 
+
+ align:start position:0%
+listen to
+um okay so clicks there's another kind
+
+ align:start position:0%
+um okay so clicks there's another kind
+ 
+
+ align:start position:0%
+um okay so clicks there's another kind
+of thing not all that popular across
+
+ align:start position:0%
+of thing not all that popular across
+ 
+
+ align:start position:0%
+of thing not all that popular across
+linguistically but it happens and uh and
+
+ align:start position:0%
+linguistically but it happens and uh and
+ 
+
+ align:start position:0%
+linguistically but it happens and uh and
+they're Magnificent the koisan languages
+
+ align:start position:0%
+they're Magnificent the koisan languages
+ 
+
+ align:start position:0%
+they're Magnificent the koisan languages
+have even richer uh arrays of Click
+
+ align:start position:0%
+have even richer uh arrays of Click
+ 
+
+ align:start position:0%
+have even richer uh arrays of Click
+inventories than this uh in particular
+
+ align:start position:0%
+inventories than this uh in particular
+ 
+
+ align:start position:0%
+inventories than this uh in particular
+they also have uh bilabial clicks
+
+ align:start position:0%
+they also have uh bilabial clicks
+ 
+
+ align:start position:0%
+they also have uh bilabial clicks
+so they have as a sound
+
+ align:start position:0%
+so they have as a sound
+ 
+
+ align:start position:0%
+so they have as a sound
+um that kind of a sound and uh and they
+
+ align:start position:0%
+um that kind of a sound and uh and they
+ 
+
+ align:start position:0%
+um that kind of a sound and uh and they
+make all of these distinctions among
+
+ align:start position:0%
+make all of these distinctions among
+ 
+
+ align:start position:0%
+make all of these distinctions among
+their clicks uh the result ends up being
+
+ align:start position:0%
+their clicks uh the result ends up being
+ 
+
+ align:start position:0%
+their clicks uh the result ends up being
+that the koisan languages if you count
+
+ align:start position:0%
+that the koisan languages if you count
+ 
+
+ align:start position:0%
+that the koisan languages if you count
+all of these clicks as different
+
+ align:start position:0%
+all of these clicks as different
+ 
+
+ align:start position:0%
+all of these clicks as different
+consonants uh the koi sign languages
+
+ align:start position:0%
+consonants uh the koi sign languages
+ 
+
+ align:start position:0%
+consonants uh the koi sign languages
+have just huge inventories of consonants
+
+ align:start position:0%
+have just huge inventories of consonants
+ 
+
+ align:start position:0%
+have just huge inventories of consonants
+because they have all these different
+
+ align:start position:0%
+because they have all these different
+ 
+
+ align:start position:0%
+because they have all these different
+clicks
+
+ align:start position:0%
+clicks
+ 
+
+ align:start position:0%
+clicks
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indicative of like the
+
+ align:start position:0%
+indicative of like the
+ 
+
+ align:start position:0%
+indicative of like the
+yeah those are tone marks yeah so uh the
+
+ align:start position:0%
+yeah those are tone marks yeah so uh the
+ 
+
+ align:start position:0%
+yeah those are tone marks yeah so uh the
+the um the accents that point down to
+
+ align:start position:0%
+the um the accents that point down to
+ 
+
+ align:start position:0%
+the um the accents that point down to
+the right are low tones and the accents
+
+ align:start position:0%
+the right are low tones and the accents
+ 
+
+ align:start position:0%
+the right are low tones and the accents
+that point up to the right are high
+
+ align:start position:0%
+that point up to the right are high
+ 
+
+ align:start position:0%
+that point up to the right are high
+tones and uh that's all Zulu's got it's
+
+ align:start position:0%
+tones and uh that's all Zulu's got it's
+ 
+
+ align:start position:0%
+tones and uh that's all Zulu's got it's
+got high tones and low tones uh and then
+
+ align:start position:0%
+got high tones and low tones uh and then
+ 
+
+ align:start position:0%
+got high tones and low tones uh and then
+you know you can have long vowels that
+
+ align:start position:0%
+you know you can have long vowels that
+ 
+
+ align:start position:0%
+you know you can have long vowels that
+transition from a high tone to a low
+
+ align:start position:0%
+transition from a high tone to a low
+ 
+
+ align:start position:0%
+transition from a high tone to a low
+tone or vice versa
+
+ align:start position:0%
+tone or vice versa
+ 
+
+ align:start position:0%
+tone or vice versa
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+okay clicks
+
+ align:start position:0%
+okay clicks
+ 
+
+ align:start position:0%
+okay clicks
+uh implosives let me find you some
+
+ align:start position:0%
+uh implosives let me find you some
+ 
+
+ align:start position:0%
+uh implosives let me find you some
+implicits go around here somewhere where
+
+ align:start position:0%
+implicits go around here somewhere where
+ 
+
+ align:start position:0%
+implicits go around here somewhere where
+were they these are implicitous
+
+ align:start position:0%
+were they these are implicitous
+ 
+
+ align:start position:0%
+were they these are implicitous
+um implosives uh what implosives are are
+
+ align:start position:0%
+um implosives uh what implosives are are
+ 
+
+ align:start position:0%
+um implosives uh what implosives are are
+sounds where
+
+ align:start position:0%
+sounds where
+ 
+
+ align:start position:0%
+sounds where
+um so what you should do if you want to
+
+ align:start position:0%
+um so what you should do if you want to
+ 
+
+ align:start position:0%
+um so what you should do if you want to
+make an implosive uh uh B for example is
+
+ align:start position:0%
+make an implosive uh uh B for example is
+ 
+
+ align:start position:0%
+make an implosive uh uh B for example is
+you should make your bilabial closure
+
+ align:start position:0%
+you should make your bilabial closure
+ 
+
+ align:start position:0%
+you should make your bilabial closure
+and then you should try to inhale
+
+ align:start position:0%
+and then you should try to inhale
+ 
+
+ align:start position:0%
+and then you should try to inhale
+so it's like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly so don't hurt yourself but
+
+ align:start position:0%
+and similarly so don't hurt yourself but
+ 
+
+ align:start position:0%
+and similarly so don't hurt yourself but
+that's what you're trying to do
+
+ align:start position:0%
+that's what you're trying to do
+ 
+
+ align:start position:0%
+that's what you're trying to do
+and there are also Villar implosives
+
+ align:start position:0%
+and there are also Villar implosives
+ 
+
+ align:start position:0%
+and there are also Villar implosives
+which you should really be careful with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's here's a here's a native
+
+ align:start position:0%
+so here's here's a here's a native
+ 
+
+ align:start position:0%
+so here's here's a here's a native
+speaker so these are
+
+ align:start position:0%
+speaker so these are
+ 
+
+ align:start position:0%
+speaker so these are
+um not all that uncommon in languages of
+
+ align:start position:0%
+um not all that uncommon in languages of
+ 
+
+ align:start position:0%
+um not all that uncommon in languages of
+India there are a bunch of them in uh
+
+ align:start position:0%
+India there are a bunch of them in uh
+ 
+
+ align:start position:0%
+India there are a bunch of them in uh
+Indonesia uh here are some
+
+ align:start position:0%
+Indonesia uh here are some
+ 
+
+ align:start position:0%
+Indonesia uh here are some
+money that's a bilabial one uh here's a
+
+ align:start position:0%
+money that's a bilabial one uh here's a
+ 
+
+ align:start position:0%
+money that's a bilabial one uh here's a
+retroflex one
+
+ align:start position:0%
+retroflex one
+ 
+
+ align:start position:0%
+retroflex one
+do you know so we could compare his uh
+
+ align:start position:0%
+do you know so we could compare his uh
+ 
+
+ align:start position:0%
+do you know so we could compare his uh
+implicit one with the regular voiced one
+
+ align:start position:0%
+implicit one with the regular voiced one
+ 
+
+ align:start position:0%
+implicit one with the regular voiced one
+so here's the implicit one again bunny
+
+ align:start position:0%
+so here's the implicit one again bunny
+ 
+
+ align:start position:0%
+so here's the implicit one again bunny
+yeah and then here it is not inclusive
+
+ align:start position:0%
+yeah and then here it is not inclusive
+ 
+
+ align:start position:0%
+yeah and then here it is not inclusive
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+uh and here's what it sounds like when
+
+ align:start position:0%
+uh and here's what it sounds like when
+ 
+
+ align:start position:0%
+uh and here's what it sounds like when
+it's feeler then as opposed to the
+
+ align:start position:0%
+it's feeler then as opposed to the
+ 
+
+ align:start position:0%
+it's feeler then as opposed to the
+regular one
+
+ align:start position:0%
+regular one
+ 
+
+ align:start position:0%
+regular one
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so uh again I'll put these sound files
+
+ align:start position:0%
+so uh again I'll put these sound files
+ 
+
+ align:start position:0%
+so uh again I'll put these sound files
+up you can play with them uh at home uh
+
+ align:start position:0%
+up you can play with them uh at home uh
+ 
+
+ align:start position:0%
+up you can play with them uh at home uh
+uh amazing to know your friends
+
+ align:start position:0%
+uh amazing to know your friends
+ 
+
+ align:start position:0%
+uh amazing to know your friends
+no questions about any of that so again
+
+ align:start position:0%
+no questions about any of that so again
+ 
+
+ align:start position:0%
+no questions about any of that so again
+this has all been about sort of uh
+
+ align:start position:0%
+this has all been about sort of uh
+ 
+
+ align:start position:0%
+this has all been about sort of uh
+interesting airflows so here's one where
+
+ align:start position:0%
+interesting airflows so here's one where
+ 
+
+ align:start position:0%
+interesting airflows so here's one where
+the flow of air is not outward at all
+
+ align:start position:0%
+the flow of air is not outward at all
+ 
+
+ align:start position:0%
+the flow of air is not outward at all
+it's uh it's going inward for just a
+
+ align:start position:0%
+it's uh it's going inward for just a
+ 
+
+ align:start position:0%
+it's uh it's going inward for just a
+millisecond I'm trying to suck air into
+
+ align:start position:0%
+millisecond I'm trying to suck air into
+ 
+
+ align:start position:0%
+millisecond I'm trying to suck air into
+your body instead of getting it out as
+
+ align:start position:0%
+your body instead of getting it out as
+ 
+
+ align:start position:0%
+your body instead of getting it out as
+you speak
+
+ align:start position:0%
+you speak
+ 
+
+ align:start position:0%
+you speak
+um there are
+
+ align:start position:0%
+um there are
+ 
+
+ align:start position:0%
+um there are
+so I don't know of any languages that
+
+ align:start position:0%
+so I don't know of any languages that
+ 
+
+ align:start position:0%
+so I don't know of any languages that
+have for example uh a class of vowels
+
+ align:start position:0%
+have for example uh a class of vowels
+ 
+
+ align:start position:0%
+have for example uh a class of vowels
+that you must make while inhaling
+
+ align:start position:0%
+that you must make while inhaling
+ 
+
+ align:start position:0%
+that you must make while inhaling
+so these are are consonants that you
+
+ align:start position:0%
+so these are are consonants that you
+ 
+
+ align:start position:0%
+so these are are consonants that you
+make while attempting to inhale that's a
+
+ align:start position:0%
+make while attempting to inhale that's a
+ 
+
+ align:start position:0%
+make while attempting to inhale that's a
+sense in which the flow of error is
+
+ align:start position:0%
+sense in which the flow of error is
+ 
+
+ align:start position:0%
+sense in which the flow of error is
+different you could imagine a language
+
+ align:start position:0%
+different you could imagine a language
+ 
+
+ align:start position:0%
+different you could imagine a language
+that had you know the vowel ah and also
+
+ align:start position:0%
+that had you know the vowel ah and also
+ 
+
+ align:start position:0%
+that had you know the vowel ah and also
+the vowel right
+
+ align:start position:0%
+the vowel right
+ 
+
+ align:start position:0%
+the vowel right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um I've never heard of a language like
+
+ align:start position:0%
+um I've never heard of a language like
+ 
+
+ align:start position:0%
+um I've never heard of a language like
+that there are languages that will uh
+
+ align:start position:0%
+that there are languages that will uh
+ 
+
+ align:start position:0%
+that there are languages that will uh
+inhale for for particular words or
+
+ align:start position:0%
+inhale for for particular words or
+ 
+
+ align:start position:0%
+inhale for for particular words or
+classes of words so like I'm told that
+
+ align:start position:0%
+classes of words so like I'm told that
+ 
+
+ align:start position:0%
+classes of words so like I'm told that
+um uh in Finland there's an expression
+
+ align:start position:0%
+um uh in Finland there's an expression
+ 
+
+ align:start position:0%
+um uh in Finland there's an expression
+that basically means yes
+
+ align:start position:0%
+that basically means yes
+ 
+
+ align:start position:0%
+that basically means yes
+but it's used only by sort of
+
+ align:start position:0%
+but it's used only by sort of
+ 
+
+ align:start position:0%
+but it's used only by sort of
+middle-aged women and it involves
+
+ align:start position:0%
+middle-aged women and it involves
+ 
+
+ align:start position:0%
+middle-aged women and it involves
+inhaling you say
+
+ align:start position:0%
+inhaling you say
+ 
+
+ align:start position:0%
+inhaling you say
+and that sort of marks you as a
+
+ align:start position:0%
+and that sort of marks you as a
+ 
+
+ align:start position:0%
+and that sort of marks you as a
+middle-aged Finnish woman so if you're
+
+ align:start position:0%
+middle-aged Finnish woman so if you're
+ 
+
+ align:start position:0%
+middle-aged Finnish woman so if you're
+ever attempting to sound like a
+
+ align:start position:0%
+ever attempting to sound like a
+ 
+
+ align:start position:0%
+ever attempting to sound like a
+middle-aged Finnish woman you should do
+
+ align:start position:0%
+middle-aged Finnish woman you should do
+ 
+
+ align:start position:0%
+middle-aged Finnish woman you should do
+that a lot you know
+
+ align:start position:0%
+that a lot you know
+ 
+
+ align:start position:0%
+that a lot you know
+um but I've never heard of a language
+
+ align:start position:0%
+um but I've never heard of a language
+ 
+
+ align:start position:0%
+um but I've never heard of a language
+that had you know they're languages that
+
+ align:start position:0%
+that had you know they're languages that
+ 
+
+ align:start position:0%
+that had you know they're languages that
+have a series of nasal vowels for
+
+ align:start position:0%
+have a series of nasal vowels for
+ 
+
+ align:start position:0%
+have a series of nasal vowels for
+example but there aren't languages that
+
+ align:start position:0%
+example but there aren't languages that
+ 
+
+ align:start position:0%
+example but there aren't languages that
+have a series of inhaled vowels that
+
+ align:start position:0%
+have a series of inhaled vowels that
+ 
+
+ align:start position:0%
+have a series of inhaled vowels that
+doesn't happen
+
+ align:start position:0%
+doesn't happen
+ 
+
+ align:start position:0%
+doesn't happen
+as far as I know
+
+ align:start position:0%
+as far as I know
+ 
+
+ align:start position:0%
+as far as I know
+uh okay
+
+ align:start position:0%
+uh okay
+ 
+
+ align:start position:0%
+uh okay
+um and then drills these don't involve a
+
+ align:start position:0%
+um and then drills these don't involve a
+ 
+
+ align:start position:0%
+um and then drills these don't involve a
+special airflow but I wanted to talk
+
+ align:start position:0%
+special airflow but I wanted to talk
+ 
+
+ align:start position:0%
+special airflow but I wanted to talk
+about them partly because they came up
+
+ align:start position:0%
+about them partly because they came up
+ 
+
+ align:start position:0%
+about them partly because they came up
+uh in class yeah like that
+
+ align:start position:0%
+uh in class yeah like that
+ 
+
+ align:start position:0%
+uh in class yeah like that
+um so trills involve getting some type
+
+ align:start position:0%
+um so trills involve getting some type
+ 
+
+ align:start position:0%
+um so trills involve getting some type
+of uh some part of your vocal tract to
+
+ align:start position:0%
+of uh some part of your vocal tract to
+ 
+
+ align:start position:0%
+of uh some part of your vocal tract to
+flutter uh
+
+ align:start position:0%
+flutter uh
+ 
+
+ align:start position:0%
+flutter uh
+um and there are uh ones that are
+
+ align:start position:0%
+um and there are uh ones that are
+ 
+
+ align:start position:0%
+um and there are uh ones that are
+comparatively famous like the the
+
+ align:start position:0%
+comparatively famous like the the
+ 
+
+ align:start position:0%
+comparatively famous like the the
+so-called rolled R
+
+ align:start position:0%
+so-called rolled R
+ 
+
+ align:start position:0%
+so-called rolled R
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh uh these are some examples that are
+
+ align:start position:0%
+uh uh these are some examples that are
+ 
+
+ align:start position:0%
+uh uh these are some examples that are
+going to sound sort of like that this is
+
+ align:start position:0%
+going to sound sort of like that this is
+ 
+
+ align:start position:0%
+going to sound sort of like that this is
+a language it's a dravidian language uh
+
+ align:start position:0%
+a language it's a dravidian language uh
+ 
+
+ align:start position:0%
+a language it's a dravidian language uh
+called Toda
+
+ align:start position:0%
+called Toda
+ 
+
+ align:start position:0%
+called Toda
+um that has dental trills and also post
+
+ align:start position:0%
+um that has dental trills and also post
+ 
+
+ align:start position:0%
+um that has dental trills and also post
+alveolar Trails so you can listen to
+
+ align:start position:0%
+alveolar Trails so you can listen to
+ 
+
+ align:start position:0%
+alveolar Trails so you can listen to
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+sure we can come on
+
+ align:start position:0%
+sure we can come on
+ 
+
+ align:start position:0%
+sure we can come on
+wake up website
+
+ align:start position:0%
+wake up website
+ 
+
+ align:start position:0%
+wake up website
+okay I take it back we can't listen to
+
+ align:start position:0%
+okay I take it back we can't listen to
+ 
+
+ align:start position:0%
+okay I take it back we can't listen to
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+why can't we listen to those I was
+
+ align:start position:0%
+why can't we listen to those I was
+ 
+
+ align:start position:0%
+why can't we listen to those I was
+listening to them just now
+
+ align:start position:0%
+listening to them just now
+ 
+
+ align:start position:0%
+listening to them just now
+what is your deal okay never mind we'll
+
+ align:start position:0%
+what is your deal okay never mind we'll
+ 
+
+ align:start position:0%
+what is your deal okay never mind we'll
+go to this other one
+
+ align:start position:0%
+go to this other one
+ 
+
+ align:start position:0%
+go to this other one
+um the so okay so the the
+
+ align:start position:0%
+um the so okay so the the
+ 
+
+ align:start position:0%
+um the so okay so the the
+um the world are the sound that's the
+
+ align:start position:0%
+um the world are the sound that's the
+ 
+
+ align:start position:0%
+um the world are the sound that's the
+alveolar Trill uh where you're holding
+
+ align:start position:0%
+alveolar Trill uh where you're holding
+ 
+
+ align:start position:0%
+alveolar Trill uh where you're holding
+your tongue fairly close to your other
+
+ align:start position:0%
+your tongue fairly close to your other
+ 
+
+ align:start position:0%
+your tongue fairly close to your other
+Ridge and uh getting the air to flow and
+
+ align:start position:0%
+Ridge and uh getting the air to flow and
+ 
+
+ align:start position:0%
+Ridge and uh getting the air to flow and
+holding your tongue in such a way that
+
+ align:start position:0%
+holding your tongue in such a way that
+ 
+
+ align:start position:0%
+holding your tongue in such a way that
+your tongue flutters in in the breeze as
+
+ align:start position:0%
+your tongue flutters in in the breeze as
+ 
+
+ align:start position:0%
+your tongue flutters in in the breeze as
+it goes by uh English doesn't have that
+
+ align:start position:0%
+it goes by uh English doesn't have that
+ 
+
+ align:start position:0%
+it goes by uh English doesn't have that
+but uh if you want to learn to speak
+
+ align:start position:0%
+but uh if you want to learn to speak
+ 
+
+ align:start position:0%
+but uh if you want to learn to speak
+Italian or Spanish or a variety of
+
+ align:start position:0%
+Italian or Spanish or a variety of
+ 
+
+ align:start position:0%
+Italian or Spanish or a variety of
+languages of Australia uh you need to
+
+ align:start position:0%
+languages of Australia uh you need to
+ 
+
+ align:start position:0%
+languages of Australia uh you need to
+learn how to roll your r's
+
+ align:start position:0%
+learn how to roll your r's
+ 
+
+ align:start position:0%
+learn how to roll your r's
+um uh it's possible to be physically
+
+ align:start position:0%
+um uh it's possible to be physically
+ 
+
+ align:start position:0%
+um uh it's possible to be physically
+incapable of doing that uh in fact there
+
+ align:start position:0%
+incapable of doing that uh in fact there
+ 
+
+ align:start position:0%
+incapable of doing that uh in fact there
+so for example there are Italians who
+
+ align:start position:0%
+so for example there are Italians who
+ 
+
+ align:start position:0%
+so for example there are Italians who
+cannot roll their ass uh
+
+ align:start position:0%
+cannot roll their ass uh
+ 
+
+ align:start position:0%
+cannot roll their ass uh
+um but it's it's not all that common
+
+ align:start position:0%
+um but it's it's not all that common
+ 
+
+ align:start position:0%
+um but it's it's not all that common
+yeah it's the kind of thing that is a
+
+ align:start position:0%
+yeah it's the kind of thing that is a
+ 
+
+ align:start position:0%
+yeah it's the kind of thing that is a
+speech impediment if your native
+
+ align:start position:0%
+speech impediment if your native
+ 
+
+ align:start position:0%
+speech impediment if your native
+language has rolled ours uh if your
+
+ align:start position:0%
+language has rolled ours uh if your
+ 
+
+ align:start position:0%
+language has rolled ours uh if your
+native language is English then you're
+
+ align:start position:0%
+native language is English then you're
+ 
+
+ align:start position:0%
+native language is English then you're
+off the hook
+
+ align:start position:0%
+off the hook
+ 
+
+ align:start position:0%
+off the hook
+um there are also languages that have
+
+ align:start position:0%
+um there are also languages that have
+ 
+
+ align:start position:0%
+um there are also languages that have
+uvular trills uh that's one possible
+
+ align:start position:0%
+uvular trills uh that's one possible
+ 
+
+ align:start position:0%
+uvular trills uh that's one possible
+pronunciation of the French are the
+
+ align:start position:0%
+pronunciation of the French are the
+ 
+
+ align:start position:0%
+pronunciation of the French are the
+German R uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can only do a uvular Trill with my
+
+ align:start position:0%
+I can only do a uvular Trill with my
+ 
+
+ align:start position:0%
+I can only do a uvular Trill with my
+head tilted back slightly
+
+ align:start position:0%
+head tilted back slightly
+ 
+
+ align:start position:0%
+head tilted back slightly
+um uh so yeah that's again getting your
+
+ align:start position:0%
+um uh so yeah that's again getting your
+ 
+
+ align:start position:0%
+um uh so yeah that's again getting your
+uvula to to move into please
+
+ align:start position:0%
+uvula to to move into please
+ 
+
+ align:start position:0%
+uvula to to move into please
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+I like gargling
+
+ align:start position:0%
+I like gargling
+ 
+
+ align:start position:0%
+I like gargling
+um and then there are languages that
+
+ align:start position:0%
+um and then there are languages that
+ 
+
+ align:start position:0%
+um and then there are languages that
+have bilibial trills which is what
+
+ align:start position:0%
+have bilibial trills which is what
+ 
+
+ align:start position:0%
+have bilibial trills which is what
+Raquel was doing for us uh let me see if
+
+ align:start position:0%
+Raquel was doing for us uh let me see if
+ 
+
+ align:start position:0%
+Raquel was doing for us uh let me see if
+I can get these to come out
+
+ align:start position:0%
+I can get these to come out
+ 
+
+ align:start position:0%
+I can get these to come out
+ah come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right do you see on the website
+
+ align:start position:0%
+all right do you see on the website
+ 
+
+ align:start position:0%
+all right do you see on the website
+there we go
+
+ align:start position:0%
+there we go
+ 
+
+ align:start position:0%
+there we go
+so that's a sound that begins with a
+
+ align:start position:0%
+so that's a sound that begins with a
+ 
+
+ align:start position:0%
+so that's a sound that begins with a
+bilabial trope
+
+ align:start position:0%
+bilabial trope
+ 
+
+ align:start position:0%
+bilabial trope
+yeah you're better at it than me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um or here's another one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this is uh kele it's a language
+
+ align:start position:0%
+yeah so this is uh kele it's a language
+ 
+
+ align:start position:0%
+yeah so this is uh kele it's a language
+spoken in Gabon
+
+ align:start position:0%
+spoken in Gabon
+ 
+
+ align:start position:0%
+spoken in Gabon
+um and Titan which is uh I believe a
+
+ align:start position:0%
+um and Titan which is uh I believe a
+ 
+
+ align:start position:0%
+um and Titan which is uh I believe a
+Polynesian language uh these are
+
+ align:start position:0%
+Polynesian language uh these are
+ 
+
+ align:start position:0%
+Polynesian language uh these are
+languages that have bilabial drills is
+
+ align:start position:0%
+languages that have bilabial drills is
+ 
+
+ align:start position:0%
+languages that have bilabial drills is
+that a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that's the so in linguistics they
+
+ align:start position:0%
+uh that's the so in linguistics they
+ 
+
+ align:start position:0%
+uh that's the so in linguistics they
+aren't usually called that they're
+
+ align:start position:0%
+aren't usually called that they're
+ 
+
+ align:start position:0%
+aren't usually called that they're
+called alveolar trills
+
+ align:start position:0%
+called alveolar trills
+ 
+
+ align:start position:0%
+called alveolar trills
+um we called them rolled ours I think
+
+ align:start position:0%
+um we called them rolled ours I think
+ 
+
+ align:start position:0%
+um we called them rolled ours I think
+because they sound a little bit like a
+
+ align:start position:0%
+because they sound a little bit like a
+ 
+
+ align:start position:0%
+because they sound a little bit like a
+drum roll uh you know it's like there's
+
+ align:start position:0%
+drum roll uh you know it's like there's
+ 
+
+ align:start position:0%
+drum roll uh you know it's like there's
+a repetitive uh sound
+
+ align:start position:0%
+a repetitive uh sound
+ 
+
+ align:start position:0%
+a repetitive uh sound
+you're repeatedly striking the roof of
+
+ align:start position:0%
+you're repeatedly striking the roof of
+ 
+
+ align:start position:0%
+you're repeatedly striking the roof of
+your mouth
+
+ align:start position:0%
+your mouth
+ 
+
+ align:start position:0%
+your mouth
+that's what I always thought that that
+
+ align:start position:0%
+that's what I always thought that that
+ 
+
+ align:start position:0%
+that's what I always thought that that
+term referred to but as I say it's not a
+
+ align:start position:0%
+term referred to but as I say it's not a
+ 
+
+ align:start position:0%
+term referred to but as I say it's not a
+linguistic term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+well because they sound like rolled ours
+
+ align:start position:0%
+well because they sound like rolled ours
+ 
+
+ align:start position:0%
+well because they sound like rolled ours
+um uh I mean I guess they sound sort of
+
+ align:start position:0%
+um uh I mean I guess they sound sort of
+ 
+
+ align:start position:0%
+um uh I mean I guess they sound sort of
+like something is rolling and repeatedly
+
+ align:start position:0%
+like something is rolling and repeatedly
+ 
+
+ align:start position:0%
+like something is rolling and repeatedly
+so they involve a repeated strike of
+
+ align:start position:0%
+so they involve a repeated strike of
+ 
+
+ align:start position:0%
+so they involve a repeated strike of
+something right so if you have something
+
+ align:start position:0%
+something right so if you have something
+ 
+
+ align:start position:0%
+something right so if you have something
+rolling bumping down uh down in a
+
+ align:start position:0%
+rolling bumping down uh down in a
+ 
+
+ align:start position:0%
+rolling bumping down uh down in a
+staircase or something then uh then it
+
+ align:start position:0%
+staircase or something then uh then it
+ 
+
+ align:start position:0%
+staircase or something then uh then it
+might sound a little bit like that I
+
+ align:start position:0%
+might sound a little bit like that I
+ 
+
+ align:start position:0%
+might sound a little bit like that I
+don't know I am now making things up I
+
+ align:start position:0%
+don't know I am now making things up I
+ 
+
+ align:start position:0%
+don't know I am now making things up I
+will uh I will try to flag it when I'm
+
+ align:start position:0%
+will uh I will try to flag it when I'm
+ 
+
+ align:start position:0%
+will uh I will try to flag it when I'm
+making things up but uh uh yes I I don't
+
+ align:start position:0%
+making things up but uh uh yes I I don't
+ 
+
+ align:start position:0%
+making things up but uh uh yes I I don't
+know that's a good question you should
+
+ align:start position:0%
+know that's a good question you should
+ 
+
+ align:start position:0%
+know that's a good question you should
+go look it up in the OED or something
+
+ align:start position:0%
+go look it up in the OED or something
+ 
+
+ align:start position:0%
+go look it up in the OED or something
+maybe they'll have a theory yeah other
+
+ align:start position:0%
+maybe they'll have a theory yeah other
+ 
+
+ align:start position:0%
+maybe they'll have a theory yeah other
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so enough of the bilabial trolls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay and so yeah as I say I'll put
+
+ align:start position:0%
+um okay and so yeah as I say I'll put
+ 
+
+ align:start position:0%
+um okay and so yeah as I say I'll put
+the uh the UCL UCLA sound files up there
+
+ align:start position:0%
+the uh the UCL UCLA sound files up there
+ 
+
+ align:start position:0%
+the uh the UCL UCLA sound files up there
+um so that you can play around with them
+
+ align:start position:0%
+um so that you can play around with them
+ 
+
+ align:start position:0%
+um so that you can play around with them
+okay oh sorry
+
+ align:start position:0%
+okay oh sorry
+ 
+
+ align:start position:0%
+okay oh sorry
+I spoke too soon
+
+ align:start position:0%
+I spoke too soon
+ 
+
+ align:start position:0%
+I spoke too soon
+um so we've been talking about sounds
+
+ align:start position:0%
+um so we've been talking about sounds
+ 
+
+ align:start position:0%
+um so we've been talking about sounds
+for a little while and uh I've been uh
+
+ align:start position:0%
+for a little while and uh I've been uh
+ 
+
+ align:start position:0%
+for a little while and uh I've been uh
+encouraging you to try to make the
+
+ align:start position:0%
+encouraging you to try to make the
+ 
+
+ align:start position:0%
+encouraging you to try to make the
+strange sounds you've all been sort of
+
+ align:start position:0%
+strange sounds you've all been sort of
+ 
+
+ align:start position:0%
+strange sounds you've all been sort of
+clicking at me and uh trilling at me
+
+ align:start position:0%
+clicking at me and uh trilling at me
+ 
+
+ align:start position:0%
+clicking at me and uh trilling at me
+it's been great
+
+ align:start position:0%
+it's been great
+ 
+
+ align:start position:0%
+it's been great
+um but uh there there is another way to
+
+ align:start position:0%
+um but uh there there is another way to
+ 
+
+ align:start position:0%
+um but uh there there is another way to
+study speech sounds and I just wanted to
+
+ align:start position:0%
+study speech sounds and I just wanted to
+ 
+
+ align:start position:0%
+study speech sounds and I just wanted to
+show you how it works
+
+ align:start position:0%
+show you how it works
+ 
+
+ align:start position:0%
+show you how it works
+um uh I hope this works we'll see
+
+ align:start position:0%
+um uh I hope this works we'll see
+ 
+
+ align:start position:0%
+um uh I hope this works we'll see
+um it's possible to make what are called
+
+ align:start position:0%
+um it's possible to make what are called
+ 
+
+ align:start position:0%
+um it's possible to make what are called
+spectrograms and maybe what I'll do is
+
+ align:start position:0%
+spectrograms and maybe what I'll do is
+ 
+
+ align:start position:0%
+spectrograms and maybe what I'll do is
+just show you one and that'll make it
+
+ align:start position:0%
+just show you one and that'll make it
+ 
+
+ align:start position:0%
+just show you one and that'll make it
+easier to talk about what they are let's
+
+ align:start position:0%
+easier to talk about what they are let's
+ 
+
+ align:start position:0%
+easier to talk about what they are let's
+see if I can get this to work
+
+ align:start position:0%
+see if I can get this to work
+ 
+
+ align:start position:0%
+see if I can get this to work
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's see if we can see that
+
+ align:start position:0%
+okay let's see if we can see that
+ 
+
+ align:start position:0%
+okay let's see if we can see that
+there that's a spectrogram
+
+ align:start position:0%
+there that's a spectrogram
+ 
+
+ align:start position:0%
+there that's a spectrogram
+um let's let me zoom in on it
+
+ align:start position:0%
+um let's let me zoom in on it
+ 
+
+ align:start position:0%
+um let's let me zoom in on it
+yeah there we go okay so
+
+ align:start position:0%
+yeah there we go okay so
+ 
+
+ align:start position:0%
+yeah there we go okay so
+um I can zoom in on a little further it
+
+ align:start position:0%
+um I can zoom in on a little further it
+ 
+
+ align:start position:0%
+um I can zoom in on a little further it
+isn't all the holes is it
+
+ align:start position:0%
+isn't all the holes is it
+ 
+
+ align:start position:0%
+isn't all the holes is it
+Okay so this is a program called Pratt
+
+ align:start position:0%
+Okay so this is a program called Pratt
+ 
+
+ align:start position:0%
+Okay so this is a program called Pratt
+it's a freeware program I'll put it up
+
+ align:start position:0%
+it's a freeware program I'll put it up
+ 
+
+ align:start position:0%
+it's a freeware program I'll put it up
+uh online it's something that allows you
+
+ align:start position:0%
+uh online it's something that allows you
+ 
+
+ align:start position:0%
+uh online it's something that allows you
+to make spectrograms as you can see it's
+
+ align:start position:0%
+to make spectrograms as you can see it's
+ 
+
+ align:start position:0%
+to make spectrograms as you can see it's
+very easy it's a pretty easy program to
+
+ align:start position:0%
+very easy it's a pretty easy program to
+ 
+
+ align:start position:0%
+very easy it's a pretty easy program to
+use I'll put up um it's a it's a program
+
+ align:start position:0%
+use I'll put up um it's a it's a program
+ 
+
+ align:start position:0%
+use I'll put up um it's a it's a program
+that's been around for a long time it
+
+ align:start position:0%
+that's been around for a long time it
+ 
+
+ align:start position:0%
+that's been around for a long time it
+was developed by linguists and not by
+
+ align:start position:0%
+was developed by linguists and not by
+ 
+
+ align:start position:0%
+was developed by linguists and not by
+software engineers and you can kind of
+
+ align:start position:0%
+software engineers and you can kind of
+ 
+
+ align:start position:0%
+software engineers and you can kind of
+tell you know so it's uh it's a little
+
+ align:start position:0%
+tell you know so it's uh it's a little
+ 
+
+ align:start position:0%
+tell you know so it's uh it's a little
+bit the interface is a little bit clunky
+
+ align:start position:0%
+bit the interface is a little bit clunky
+ 
+
+ align:start position:0%
+bit the interface is a little bit clunky
+but uh I'll put up some suggestions
+
+ align:start position:0%
+but uh I'll put up some suggestions
+ 
+
+ align:start position:0%
+but uh I'll put up some suggestions
+about how to use it and I encourage you
+
+ align:start position:0%
+about how to use it and I encourage you
+ 
+
+ align:start position:0%
+about how to use it and I encourage you
+to download it and play around with it
+
+ align:start position:0%
+to download it and play around with it
+ 
+
+ align:start position:0%
+to download it and play around with it
+it's fun
+
+ align:start position:0%
+it's fun
+ 
+
+ align:start position:0%
+it's fun
+um what's going on here the thing on the
+
+ align:start position:0%
+um what's going on here the thing on the
+ 
+
+ align:start position:0%
+um what's going on here the thing on the
+bottom of this window is the is the
+
+ align:start position:0%
+bottom of this window is the is the
+ 
+
+ align:start position:0%
+bottom of this window is the is the
+spectrogram
+
+ align:start position:0%
+spectrogram
+ 
+
+ align:start position:0%
+spectrogram
+um and it's a spectrogram showing me
+
+ align:start position:0%
+um and it's a spectrogram showing me
+ 
+
+ align:start position:0%
+um and it's a spectrogram showing me
+making those vowel sounds
+
+ align:start position:0%
+making those vowel sounds
+ 
+
+ align:start position:0%
+making those vowel sounds
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um uh transitioning between them I think
+
+ align:start position:0%
+um uh transitioning between them I think
+ 
+
+ align:start position:0%
+um uh transitioning between them I think
+I might be able to play what we're
+
+ align:start position:0%
+I might be able to play what we're
+ 
+
+ align:start position:0%
+I might be able to play what we're
+looking at here
+
+ align:start position:0%
+looking at here
+ 
+
+ align:start position:0%
+looking at here
+yeah uh so I didn't keep very much of
+
+ align:start position:0%
+yeah uh so I didn't keep very much of
+ 
+
+ align:start position:0%
+yeah uh so I didn't keep very much of
+the the ooh that we can think just about
+
+ align:start position:0%
+the the ooh that we can think just about
+ 
+
+ align:start position:0%
+the the ooh that we can think just about
+the ah and the e
+
+ align:start position:0%
+the ah and the e
+ 
+
+ align:start position:0%
+the ah and the e
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what you're doing when you are making
+
+ align:start position:0%
+what you're doing when you are making
+ 
+
+ align:start position:0%
+what you're doing when you are making
+vowels especially but actually when
+
+ align:start position:0%
+vowels especially but actually when
+ 
+
+ align:start position:0%
+vowels especially but actually when
+you're speaking kind of generally is
+
+ align:start position:0%
+you're speaking kind of generally is
+ 
+
+ align:start position:0%
+you're speaking kind of generally is
+your uh your vocal chords in this case
+
+ align:start position:0%
+your uh your vocal chords in this case
+ 
+
+ align:start position:0%
+your uh your vocal chords in this case
+my vocal cords were vibrating uh they
+
+ align:start position:0%
+my vocal cords were vibrating uh they
+ 
+
+ align:start position:0%
+my vocal cords were vibrating uh they
+were making the uh air vibrate there's
+
+ align:start position:0%
+were making the uh air vibrate there's
+ 
+
+ align:start position:0%
+were making the uh air vibrate there's
+this column of air that comes up through
+
+ align:start position:0%
+this column of air that comes up through
+ 
+
+ align:start position:0%
+this column of air that comes up through
+my vocal tract
+
+ align:start position:0%
+my vocal tract
+ 
+
+ align:start position:0%
+my vocal tract
+um they're making that air vibrate and
+
+ align:start position:0%
+um they're making that air vibrate and
+ 
+
+ align:start position:0%
+um they're making that air vibrate and
+then those vibrations are interacting
+
+ align:start position:0%
+then those vibrations are interacting
+ 
+
+ align:start position:0%
+then those vibrations are interacting
+with other things I'm doing with my
+
+ align:start position:0%
+with other things I'm doing with my
+ 
+
+ align:start position:0%
+with other things I'm doing with my
+vocal tract uh they're bouncing off the
+
+ align:start position:0%
+vocal tract uh they're bouncing off the
+ 
+
+ align:start position:0%
+vocal tract uh they're bouncing off the
+sides of my vocal tract and as I change
+
+ align:start position:0%
+sides of my vocal tract and as I change
+ 
+
+ align:start position:0%
+sides of my vocal tract and as I change
+the shape of my vocal tract I change
+
+ align:start position:0%
+the shape of my vocal tract I change
+ 
+
+ align:start position:0%
+the shape of my vocal tract I change
+what the what those vibrations are doing
+
+ align:start position:0%
+what the what those vibrations are doing
+ 
+
+ align:start position:0%
+what the what those vibrations are doing
+yeah it's a complicated uh phenomenon
+
+ align:start position:0%
+yeah it's a complicated uh phenomenon
+ 
+
+ align:start position:0%
+yeah it's a complicated uh phenomenon
+you end up creating this complicated
+
+ align:start position:0%
+you end up creating this complicated
+ 
+
+ align:start position:0%
+you end up creating this complicated
+waveform
+
+ align:start position:0%
+waveform
+ 
+
+ align:start position:0%
+waveform
+um which you can do a Fourier analysis
+
+ align:start position:0%
+um which you can do a Fourier analysis
+ 
+
+ align:start position:0%
+um which you can do a Fourier analysis
+of and sort of analyze it as a waveform
+
+ align:start position:0%
+of and sort of analyze it as a waveform
+ 
+
+ align:start position:0%
+of and sort of analyze it as a waveform
+that has a bunch of regular sort of sine
+
+ align:start position:0%
+that has a bunch of regular sort of sine
+ 
+
+ align:start position:0%
+that has a bunch of regular sort of sine
+waves of various you know frequencies
+
+ align:start position:0%
+waves of various you know frequencies
+ 
+
+ align:start position:0%
+waves of various you know frequencies
+and amplitudes that are contributing to
+
+ align:start position:0%
+and amplitudes that are contributing to
+ 
+
+ align:start position:0%
+and amplitudes that are contributing to
+it yeah and this is what you do when you
+
+ align:start position:0%
+it yeah and this is what you do when you
+ 
+
+ align:start position:0%
+it yeah and this is what you do when you
+do a Fourier analysis yeah
+
+ align:start position:0%
+do a Fourier analysis yeah
+ 
+
+ align:start position:0%
+do a Fourier analysis yeah
+and what the spectrogram does is sort of
+
+ align:start position:0%
+and what the spectrogram does is sort of
+ 
+
+ align:start position:0%
+and what the spectrogram does is sort of
+Mark for you the frequencies that are
+
+ align:start position:0%
+Mark for you the frequencies that are
+ 
+
+ align:start position:0%
+Mark for you the frequencies that are
+making the greatest contribution to the
+
+ align:start position:0%
+making the greatest contribution to the
+ 
+
+ align:start position:0%
+making the greatest contribution to the
+general complicated error waveform
+
+ align:start position:0%
+general complicated error waveform
+ 
+
+ align:start position:0%
+general complicated error waveform
+um they're the darker parts
+
+ align:start position:0%
+um they're the darker parts
+ 
+
+ align:start position:0%
+um they're the darker parts
+um so these dark bands that you're
+
+ align:start position:0%
+um so these dark bands that you're
+ 
+
+ align:start position:0%
+um so these dark bands that you're
+seeing are what are called formants and
+
+ align:start position:0%
+seeing are what are called formants and
+ 
+
+ align:start position:0%
+seeing are what are called formants and
+they are the the things that are
+
+ align:start position:0%
+they are the the things that are
+ 
+
+ align:start position:0%
+they are the the things that are
+contributing the most to um to the to
+
+ align:start position:0%
+contributing the most to um to the to
+ 
+
+ align:start position:0%
+contributing the most to um to the to
+the sound as you can see they're
+
+ align:start position:0%
+the sound as you can see they're
+ 
+
+ align:start position:0%
+the sound as you can see they're
+shifting as I shift from ah to e so this
+
+ align:start position:0%
+shifting as I shift from ah to e so this
+ 
+
+ align:start position:0%
+shifting as I shift from ah to e so this
+uh this formant down here now see can
+
+ align:start position:0%
+uh this formant down here now see can
+ 
+
+ align:start position:0%
+uh this formant down here now see can
+you see my my
+
+ align:start position:0%
+you see my my
+ 
+
+ align:start position:0%
+you see my my
+can we see my cursor on this yes this
+
+ align:start position:0%
+can we see my cursor on this yes this
+ 
+
+ align:start position:0%
+can we see my cursor on this yes this
+format right here uh you can see as I
+
+ align:start position:0%
+format right here uh you can see as I
+ 
+
+ align:start position:0%
+format right here uh you can see as I
+shift from ah to e it goes up yeah and
+
+ align:start position:0%
+shift from ah to e it goes up yeah and
+ 
+
+ align:start position:0%
+shift from ah to e it goes up yeah and
+this form and up here as I shift from
+
+ align:start position:0%
+this form and up here as I shift from
+ 
+
+ align:start position:0%
+this form and up here as I shift from
+all the e it kind of It kind of dips
+
+ align:start position:0%
+all the e it kind of It kind of dips
+ 
+
+ align:start position:0%
+all the e it kind of It kind of dips
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so how far apart the the the foremans
+
+ align:start position:0%
+so how far apart the the the foremans
+ 
+
+ align:start position:0%
+so how far apart the the the foremans
+are from each other is uh is what
+
+ align:start position:0%
+are from each other is uh is what
+ 
+
+ align:start position:0%
+are from each other is uh is what
+distinguishes the vowels from each other
+
+ align:start position:0%
+distinguishes the vowels from each other
+ 
+
+ align:start position:0%
+distinguishes the vowels from each other
+you're hearing this difference in
+
+ align:start position:0%
+you're hearing this difference in
+ 
+
+ align:start position:0%
+you're hearing this difference in
+informants you can kind of do this for
+
+ align:start position:0%
+informants you can kind of do this for
+ 
+
+ align:start position:0%
+informants you can kind of do this for
+yourself here I'm going to do another
+
+ align:start position:0%
+yourself here I'm going to do another
+ 
+
+ align:start position:0%
+yourself here I'm going to do another
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hang on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so here's another one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I didn't get a very good recording of
+
+ align:start position:0%
+I didn't get a very good recording of
+ 
+
+ align:start position:0%
+I didn't get a very good recording of
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+try that again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm
+
+ align:start position:0%
+hmm
+ 
+
+ align:start position:0%
+hmm
+well whoa
+
+ align:start position:0%
+well whoa
+ 
+
+ align:start position:0%
+well whoa
+hmm that's not doing what I'm expecting
+
+ align:start position:0%
+hmm that's not doing what I'm expecting
+ 
+
+ align:start position:0%
+hmm that's not doing what I'm expecting
+it to oh oh I think I see what it what's
+
+ align:start position:0%
+it to oh oh I think I see what it what's
+ 
+
+ align:start position:0%
+it to oh oh I think I see what it what's
+what it's doing
+
+ align:start position:0%
+what it's doing
+ 
+
+ align:start position:0%
+what it's doing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it has to do with the fact that the
+
+ align:start position:0%
+it has to do with the fact that the
+ 
+
+ align:start position:0%
+it has to do with the fact that the
+microphone in my computer is lousy
+
+ align:start position:0%
+microphone in my computer is lousy
+ 
+
+ align:start position:0%
+microphone in my computer is lousy
+um you can see the the the foramen
+
+ align:start position:0%
+um you can see the the the foramen
+ 
+
+ align:start position:0%
+um you can see the the the foramen
+shifting for this one actually you can't
+
+ align:start position:0%
+shifting for this one actually you can't
+ 
+
+ align:start position:0%
+shifting for this one actually you can't
+see them shifting all that much but you
+
+ align:start position:0%
+see them shifting all that much but you
+ 
+
+ align:start position:0%
+see them shifting all that much but you
+can kind of hear a format shifting if
+
+ align:start position:0%
+can kind of hear a format shifting if
+ 
+
+ align:start position:0%
+can kind of hear a format shifting if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+um do the shift
+
+ align:start position:0%
+um do the shift
+ 
+
+ align:start position:0%
+um do the shift
+oh no wait I think I can think of
+
+ align:start position:0%
+oh no wait I think I can think of
+ 
+
+ align:start position:0%
+oh no wait I think I can think of
+something that will show this better
+
+ align:start position:0%
+something that will show this better
+ 
+
+ align:start position:0%
+something that will show this better
+hang on just a sec one more thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stop stop stop let's try again
+
+ align:start position:0%
+stop stop stop let's try again
+ 
+
+ align:start position:0%
+stop stop stop let's try again
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we go that's better
+
+ align:start position:0%
+there we go that's better
+ 
+
+ align:start position:0%
+there we go that's better
+um so here you can clearly see a formant
+
+ align:start position:0%
+um so here you can clearly see a formant
+ 
+
+ align:start position:0%
+um so here you can clearly see a formant
+going from up here to down here as I
+
+ align:start position:0%
+going from up here to down here as I
+ 
+
+ align:start position:0%
+going from up here to down here as I
+transition from E to is everybody seeing
+
+ align:start position:0%
+transition from E to is everybody seeing
+ 
+
+ align:start position:0%
+transition from E to is everybody seeing
+that I'll play it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+I sound like a dolphin or something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but as as I switch from the e to the ooh
+
+ align:start position:0%
+but as as I switch from the e to the ooh
+ 
+
+ align:start position:0%
+but as as I switch from the e to the ooh
+you can see a a form of descending yeah
+
+ align:start position:0%
+you can see a a form of descending yeah
+ 
+
+ align:start position:0%
+you can see a a form of descending yeah
+um and you can kind of hear that if you
+
+ align:start position:0%
+um and you can kind of hear that if you
+ 
+
+ align:start position:0%
+um and you can kind of hear that if you
+do the so this is something that we were
+
+ align:start position:0%
+do the so this is something that we were
+ 
+
+ align:start position:0%
+do the so this is something that we were
+doing back when I was trying to convince
+
+ align:start position:0%
+doing back when I was trying to convince
+ 
+
+ align:start position:0%
+doing back when I was trying to convince
+you that vowels were worth categorizing
+
+ align:start position:0%
+you that vowels were worth categorizing
+ 
+
+ align:start position:0%
+you that vowels were worth categorizing
+that the the switch from E to ooh
+
+ align:start position:0%
+that the the switch from E to ooh
+ 
+
+ align:start position:0%
+that the the switch from E to ooh
+involves your tongue going from being
+
+ align:start position:0%
+involves your tongue going from being
+ 
+
+ align:start position:0%
+involves your tongue going from being
+front to being back and also your lips
+
+ align:start position:0%
+front to being back and also your lips
+ 
+
+ align:start position:0%
+front to being back and also your lips
+going from being not rounded to being
+
+ align:start position:0%
+going from being not rounded to being
+ 
+
+ align:start position:0%
+going from being not rounded to being
+rounded yeah and if you whisper that to
+
+ align:start position:0%
+rounded yeah and if you whisper that to
+ 
+
+ align:start position:0%
+rounded yeah and if you whisper that to
+yourself so go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might be hearing something
+
+ align:start position:0%
+you might be hearing something
+ 
+
+ align:start position:0%
+you might be hearing something
+descending in Pitch
+
+ align:start position:0%
+descending in Pitch
+ 
+
+ align:start position:0%
+descending in Pitch
+are you hearing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what you're hearing it's that
+
+ align:start position:0%
+and that's what you're hearing it's that
+ 
+
+ align:start position:0%
+and that's what you're hearing it's that
+formant yeah uh you're kind of by
+
+ align:start position:0%
+formant yeah uh you're kind of by
+ 
+
+ align:start position:0%
+formant yeah uh you're kind of by
+Whispering you're you're getting that to
+
+ align:start position:0%
+Whispering you're you're getting that to
+ 
+
+ align:start position:0%
+Whispering you're you're getting that to
+LEAP out at you and you can hear it
+
+ align:start position:0%
+LEAP out at you and you can hear it
+ 
+
+ align:start position:0%
+LEAP out at you and you can hear it
+descending in Pitch why is it descending
+
+ align:start position:0%
+descending in Pitch why is it descending
+ 
+
+ align:start position:0%
+descending in Pitch why is it descending
+in Pitch if you think about what you're
+
+ align:start position:0%
+in Pitch if you think about what you're
+ 
+
+ align:start position:0%
+in Pitch if you think about what you're
+doing think about the inside of your
+
+ align:start position:0%
+doing think about the inside of your
+ 
+
+ align:start position:0%
+doing think about the inside of your
+Vocal Track
+
+ align:start position:0%
+Vocal Track
+ 
+
+ align:start position:0%
+Vocal Track
+as you go from E to ooh let's talk first
+
+ align:start position:0%
+as you go from E to ooh let's talk first
+ 
+
+ align:start position:0%
+as you go from E to ooh let's talk first
+about oh
+
+ align:start position:0%
+about oh
+ 
+
+ align:start position:0%
+about oh
+so ooh is a high back rounded vowel
+
+ align:start position:0%
+so ooh is a high back rounded vowel
+ 
+
+ align:start position:0%
+so ooh is a high back rounded vowel
+was any of that surprising yeah
+
+ align:start position:0%
+was any of that surprising yeah
+ 
+
+ align:start position:0%
+was any of that surprising yeah
+so your tongue is high and bunched up in
+
+ align:start position:0%
+so your tongue is high and bunched up in
+ 
+
+ align:start position:0%
+so your tongue is high and bunched up in
+the back of your mouth and your lips are
+
+ align:start position:0%
+the back of your mouth and your lips are
+ 
+
+ align:start position:0%
+the back of your mouth and your lips are
+rounded ooh
+
+ align:start position:0%
+rounded ooh
+ 
+
+ align:start position:0%
+rounded ooh
+that means that so what you're doing
+
+ align:start position:0%
+that means that so what you're doing
+ 
+
+ align:start position:0%
+that means that so what you're doing
+when you're making vowels right is
+
+ align:start position:0%
+when you're making vowels right is
+ 
+
+ align:start position:0%
+when you're making vowels right is
+you're taking uh this column there
+
+ align:start position:0%
+you're taking uh this column there
+ 
+
+ align:start position:0%
+you're taking uh this column there
+that's in your vocal tract and you're
+
+ align:start position:0%
+that's in your vocal tract and you're
+ 
+
+ align:start position:0%
+that's in your vocal tract and you're
+depending on the vowel making a
+
+ align:start position:0%
+depending on the vowel making a
+ 
+
+ align:start position:0%
+depending on the vowel making a
+partition somewhere uh that isn't
+
+ align:start position:0%
+partition somewhere uh that isn't
+ 
+
+ align:start position:0%
+partition somewhere uh that isn't
+complete you're not blocking off part of
+
+ align:start position:0%
+complete you're not blocking off part of
+ 
+
+ align:start position:0%
+complete you're not blocking off part of
+the track but you're putting your tongue
+
+ align:start position:0%
+the track but you're putting your tongue
+ 
+
+ align:start position:0%
+the track but you're putting your tongue
+kind of in the way so you're making part
+
+ align:start position:0%
+kind of in the way so you're making part
+ 
+
+ align:start position:0%
+kind of in the way so you're making part
+of that that column of air narrower does
+
+ align:start position:0%
+of that that column of air narrower does
+ 
+
+ align:start position:0%
+of that that column of air narrower does
+that make sense uh so for a high back
+
+ align:start position:0%
+that make sense uh so for a high back
+ 
+
+ align:start position:0%
+that make sense uh so for a high back
+rounded vowel by bunching your tongue up
+
+ align:start position:0%
+rounded vowel by bunching your tongue up
+ 
+
+ align:start position:0%
+rounded vowel by bunching your tongue up
+toward the back of your mouth you're
+
+ align:start position:0%
+toward the back of your mouth you're
+ 
+
+ align:start position:0%
+toward the back of your mouth you're
+making sort of not a complete
+
+ align:start position:0%
+making sort of not a complete
+ 
+
+ align:start position:0%
+making sort of not a complete
+obstruction of the flow of air there's
+
+ align:start position:0%
+obstruction of the flow of air there's
+ 
+
+ align:start position:0%
+obstruction of the flow of air there's
+still space for the air to flow past it
+
+ align:start position:0%
+still space for the air to flow past it
+ 
+
+ align:start position:0%
+still space for the air to flow past it
+but you're making it narrower back there
+
+ align:start position:0%
+but you're making it narrower back there
+ 
+
+ align:start position:0%
+but you're making it narrower back there
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and when you make an ooh by making a
+
+ align:start position:0%
+and when you make an ooh by making a
+ 
+
+ align:start position:0%
+and when you make an ooh by making a
+high back gesture with your tongue and
+
+ align:start position:0%
+high back gesture with your tongue and
+ 
+
+ align:start position:0%
+high back gesture with your tongue and
+by rounding your lips you're creating a
+
+ align:start position:0%
+by rounding your lips you're creating a
+ 
+
+ align:start position:0%
+by rounding your lips you're creating a
+compartment uh for uh uh for your vocal
+
+ align:start position:0%
+compartment uh for uh uh for your vocal
+ 
+
+ align:start position:0%
+compartment uh for uh uh for your vocal
+tract which is as large as you can make
+
+ align:start position:0%
+tract which is as large as you can make
+ 
+
+ align:start position:0%
+tract which is as large as you can make
+it right your lips are out there in
+
+ align:start position:0%
+it right your lips are out there in
+ 
+
+ align:start position:0%
+it right your lips are out there in
+front and your tongue is as far back as
+
+ align:start position:0%
+front and your tongue is as far back as
+ 
+
+ align:start position:0%
+front and your tongue is as far back as
+it goes yeah yeah does that make sense
+
+ align:start position:0%
+it goes yeah yeah does that make sense
+ 
+
+ align:start position:0%
+it goes yeah yeah does that make sense
+you're sort of uh compartmentalizing off
+
+ align:start position:0%
+you're sort of uh compartmentalizing off
+ 
+
+ align:start position:0%
+you're sort of uh compartmentalizing off
+that top space of your of your uh of
+
+ align:start position:0%
+that top space of your of your uh of
+ 
+
+ align:start position:0%
+that top space of your of your uh of
+your your vocal tract and you're making
+
+ align:start position:0%
+your your vocal tract and you're making
+ 
+
+ align:start position:0%
+your your vocal tract and you're making
+that space as large as it can be
+
+ align:start position:0%
+that space as large as it can be
+ 
+
+ align:start position:0%
+that space as large as it can be
+as opposed to E where your lips are not
+
+ align:start position:0%
+as opposed to E where your lips are not
+ 
+
+ align:start position:0%
+as opposed to E where your lips are not
+rounded and your tongue is toward the
+
+ align:start position:0%
+rounded and your tongue is toward the
+ 
+
+ align:start position:0%
+rounded and your tongue is toward the
+front of your mouth
+
+ align:start position:0%
+front of your mouth
+ 
+
+ align:start position:0%
+front of your mouth
+so that makes that space that you
+
+ align:start position:0%
+so that makes that space that you
+ 
+
+ align:start position:0%
+so that makes that space that you
+created for oh that makes that space
+
+ align:start position:0%
+created for oh that makes that space
+ 
+
+ align:start position:0%
+created for oh that makes that space
+sort of collapse it makes that space as
+
+ align:start position:0%
+sort of collapse it makes that space as
+ 
+
+ align:start position:0%
+sort of collapse it makes that space as
+small as it can possibly be because now
+
+ align:start position:0%
+small as it can possibly be because now
+ 
+
+ align:start position:0%
+small as it can possibly be because now
+your tongue is shoved up toward the
+
+ align:start position:0%
+your tongue is shoved up toward the
+ 
+
+ align:start position:0%
+your tongue is shoved up toward the
+front of your mouth and your lips are
+
+ align:start position:0%
+front of your mouth and your lips are
+ 
+
+ align:start position:0%
+front of your mouth and your lips are
+not rounded the space between your
+
+ align:start position:0%
+not rounded the space between your
+ 
+
+ align:start position:0%
+not rounded the space between your
+tongue and your lips is now as small as
+
+ align:start position:0%
+tongue and your lips is now as small as
+ 
+
+ align:start position:0%
+tongue and your lips is now as small as
+it gets yeah and that's why the
+
+ align:start position:0%
+it gets yeah and that's why the
+ 
+
+ align:start position:0%
+it gets yeah and that's why the
+transition from E to ooh involves
+
+ align:start position:0%
+transition from E to ooh involves
+ 
+
+ align:start position:0%
+transition from E to ooh involves
+something descending in Pitch it's
+
+ align:start position:0%
+something descending in Pitch it's
+ 
+
+ align:start position:0%
+something descending in Pitch it's
+because you're going from a very small
+
+ align:start position:0%
+because you're going from a very small
+ 
+
+ align:start position:0%
+because you're going from a very small
+compartment with a little bit of
+
+ align:start position:0%
+compartment with a little bit of
+ 
+
+ align:start position:0%
+compartment with a little bit of
+vibration inside it to a large
+
+ align:start position:0%
+vibration inside it to a large
+ 
+
+ align:start position:0%
+vibration inside it to a large
+compartment with a with the same amount
+
+ align:start position:0%
+compartment with a with the same amount
+ 
+
+ align:start position:0%
+compartment with a with the same amount
+of vibration inside it right because
+
+ align:start position:0%
+of vibration inside it right because
+ 
+
+ align:start position:0%
+of vibration inside it right because
+your your vocal cords are vibrating at a
+
+ align:start position:0%
+your your vocal cords are vibrating at a
+ 
+
+ align:start position:0%
+your your vocal cords are vibrating at a
+at a constant rate we're not you're not
+
+ align:start position:0%
+at a constant rate we're not you're not
+ 
+
+ align:start position:0%
+at a constant rate we're not you're not
+fooling around with pitch does that make
+
+ align:start position:0%
+fooling around with pitch does that make
+ 
+
+ align:start position:0%
+fooling around with pitch does that make
+sense so you know as you switch from a
+
+ align:start position:0%
+sense so you know as you switch from a
+ 
+
+ align:start position:0%
+sense so you know as you switch from a
+small compartment to a large one uh one
+
+ align:start position:0%
+small compartment to a large one uh one
+ 
+
+ align:start position:0%
+small compartment to a large one uh one
+component of the very complicated things
+
+ align:start position:0%
+component of the very complicated things
+ 
+
+ align:start position:0%
+component of the very complicated things
+that make up this complicated waveform
+
+ align:start position:0%
+that make up this complicated waveform
+ 
+
+ align:start position:0%
+that make up this complicated waveform
+is uh descending in Pitch because you're
+
+ align:start position:0%
+is uh descending in Pitch because you're
+ 
+
+ align:start position:0%
+is uh descending in Pitch because you're
+you're creating this little space that's
+
+ align:start position:0%
+you're creating this little space that's
+ 
+
+ align:start position:0%
+you're creating this little space that's
+uh that's getting larger and by putting
+
+ align:start position:0%
+uh that's getting larger and by putting
+ 
+
+ align:start position:0%
+uh that's getting larger and by putting
+the same amount of energy to it the
+
+ align:start position:0%
+the same amount of energy to it the
+ 
+
+ align:start position:0%
+the same amount of energy to it the
+molecules there are not moving as fast
+
+ align:start position:0%
+molecules there are not moving as fast
+ 
+
+ align:start position:0%
+molecules there are not moving as fast
+that's what we hear is a lower pitch
+
+ align:start position:0%
+that's what we hear is a lower pitch
+ 
+
+ align:start position:0%
+that's what we hear is a lower pitch
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+it's a way of talking about it anyway
+
+ align:start position:0%
+it's a way of talking about it anyway
+ 
+
+ align:start position:0%
+it's a way of talking about it anyway
+so encourage you to fool around with
+
+ align:start position:0%
+so encourage you to fool around with
+ 
+
+ align:start position:0%
+so encourage you to fool around with
+prot
+
+ align:start position:0%
+prot
+ 
+
+ align:start position:0%
+prot
+um let me just show you some consonants
+
+ align:start position:0%
+um let me just show you some consonants
+ 
+
+ align:start position:0%
+um let me just show you some consonants
+so that you can see what else you can do
+
+ align:start position:0%
+so that you can see what else you can do
+ 
+
+ align:start position:0%
+so that you can see what else you can do
+with props
+
+ align:start position:0%
+with props
+ 
+
+ align:start position:0%
+with props
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+we'll try another one here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bab dad gag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here I've got the same vowel all
+
+ align:start position:0%
+so here I've got the same vowel all
+ 
+
+ align:start position:0%
+so here I've got the same vowel all
+three times and you can see uh these
+
+ align:start position:0%
+three times and you can see uh these
+ 
+
+ align:start position:0%
+three times and you can see uh these
+nice clear bars uh in the middle the
+
+ align:start position:0%
+nice clear bars uh in the middle the
+ 
+
+ align:start position:0%
+nice clear bars uh in the middle the
+difference has to do with what the
+
+ align:start position:0%
+difference has to do with what the
+ 
+
+ align:start position:0%
+difference has to do with what the
+consonants are on either side of the
+
+ align:start position:0%
+consonants are on either side of the
+ 
+
+ align:start position:0%
+consonants are on either side of the
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+one of the things that this
+
+ align:start position:0%
+one of the things that this
+ 
+
+ align:start position:0%
+one of the things that this
+um this
+
+ align:start position:0%
+um this
+ 
+
+ align:start position:0%
+um this
+representation the spectrogram allows us
+
+ align:start position:0%
+representation the spectrogram allows us
+ 
+
+ align:start position:0%
+representation the spectrogram allows us
+to sort of concentrate on if you think
+
+ align:start position:0%
+to sort of concentrate on if you think
+ 
+
+ align:start position:0%
+to sort of concentrate on if you think
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+how do you tell the difference between
+
+ align:start position:0%
+how do you tell the difference between
+ 
+
+ align:start position:0%
+how do you tell the difference between
+bab and gag
+
+ align:start position:0%
+bab and gag
+ 
+
+ align:start position:0%
+bab and gag
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+you know we know articulatory what the
+
+ align:start position:0%
+you know we know articulatory what the
+ 
+
+ align:start position:0%
+you know we know articulatory what the
+difference is the difference is that for
+
+ align:start position:0%
+difference is the difference is that for
+ 
+
+ align:start position:0%
+difference is the difference is that for
+bab you're making a bilabial stop and
+
+ align:start position:0%
+bab you're making a bilabial stop and
+ 
+
+ align:start position:0%
+bab you're making a bilabial stop and
+for gag you're making a Velar stop
+
+ align:start position:0%
+for gag you're making a Velar stop
+ 
+
+ align:start position:0%
+for gag you're making a Velar stop
+but when you're hearing people make
+
+ align:start position:0%
+but when you're hearing people make
+ 
+
+ align:start position:0%
+but when you're hearing people make
+those sounds how are you hearing what
+
+ align:start position:0%
+those sounds how are you hearing what
+ 
+
+ align:start position:0%
+those sounds how are you hearing what
+the difference is between a b and a g
+
+ align:start position:0%
+the difference is between a b and a g
+ 
+
+ align:start position:0%
+the difference is between a b and a g
+bear in mind that B and G are both stops
+
+ align:start position:0%
+bear in mind that B and G are both stops
+ 
+
+ align:start position:0%
+bear in mind that B and G are both stops
+the flow of error is stopped yeah while
+
+ align:start position:0%
+the flow of error is stopped yeah while
+ 
+
+ align:start position:0%
+the flow of error is stopped yeah while
+you're making the sound so while you're
+
+ align:start position:0%
+you're making the sound so while you're
+ 
+
+ align:start position:0%
+you're making the sound so while you're
+making the sound you're not hearing
+
+ align:start position:0%
+making the sound you're not hearing
+ 
+
+ align:start position:0%
+making the sound you're not hearing
+things yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way you distinguish bab from gag
+
+ align:start position:0%
+the way you distinguish bab from gag
+ 
+
+ align:start position:0%
+the way you distinguish bab from gag
+is by looking at what it does to the
+
+ align:start position:0%
+is by looking at what it does to the
+ 
+
+ align:start position:0%
+is by looking at what it does to the
+vowel that's in between right you can
+
+ align:start position:0%
+vowel that's in between right you can
+ 
+
+ align:start position:0%
+vowel that's in between right you can
+see that these formants for the ah vowel
+
+ align:start position:0%
+see that these formants for the ah vowel
+ 
+
+ align:start position:0%
+see that these formants for the ah vowel
+and remember that the vowel was the same
+
+ align:start position:0%
+and remember that the vowel was the same
+ 
+
+ align:start position:0%
+and remember that the vowel was the same
+in all three cases it's especially clear
+
+ align:start position:0%
+in all three cases it's especially clear
+ 
+
+ align:start position:0%
+in all three cases it's especially clear
+for this last one here's gag and you can
+
+ align:start position:0%
+for this last one here's gag and you can
+ 
+
+ align:start position:0%
+for this last one here's gag and you can
+see that uh the formants you know this
+
+ align:start position:0%
+see that uh the formants you know this
+ 
+
+ align:start position:0%
+see that uh the formants you know this
+formant is sort of smile shaped and this
+
+ align:start position:0%
+formant is sort of smile shaped and this
+ 
+
+ align:start position:0%
+formant is sort of smile shaped and this
+formant is frown shaped right this one
+
+ align:start position:0%
+formant is frown shaped right this one
+ 
+
+ align:start position:0%
+formant is frown shaped right this one
+goes down as it goes close to the uh
+
+ align:start position:0%
+goes down as it goes close to the uh
+ 
+
+ align:start position:0%
+goes down as it goes close to the uh
+close to the stop and this one goes up
+
+ align:start position:0%
+close to the stop and this one goes up
+ 
+
+ align:start position:0%
+close to the stop and this one goes up
+as it goes close to the stop as opposed
+
+ align:start position:0%
+as it goes close to the stop as opposed
+ 
+
+ align:start position:0%
+as it goes close to the stop as opposed
+to the bilabial which is you know if
+
+ align:start position:0%
+to the bilabial which is you know if
+ 
+
+ align:start position:0%
+to the bilabial which is you know if
+anything slightly down on both sides
+
+ align:start position:0%
+anything slightly down on both sides
+ 
+
+ align:start position:0%
+anything slightly down on both sides
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is one of the things that makes
+
+ align:start position:0%
+this is one of the things that makes
+ 
+
+ align:start position:0%
+this is one of the things that makes
+speech perception so hard and it makes
+
+ align:start position:0%
+speech perception so hard and it makes
+ 
+
+ align:start position:0%
+speech perception so hard and it makes
+it so hard to like get machines to
+
+ align:start position:0%
+it so hard to like get machines to
+ 
+
+ align:start position:0%
+it so hard to like get machines to
+understand speech it's it's a problem
+
+ align:start position:0%
+understand speech it's it's a problem
+ 
+
+ align:start position:0%
+understand speech it's it's a problem
+that's more or less solved but it's uh
+
+ align:start position:0%
+that's more or less solved but it's uh
+ 
+
+ align:start position:0%
+that's more or less solved but it's uh
+it's a hard problem because it's not
+
+ align:start position:0%
+it's a hard problem because it's not
+ 
+
+ align:start position:0%
+it's a hard problem because it's not
+your your speech is not just a a
+
+ align:start position:0%
+your your speech is not just a a
+ 
+
+ align:start position:0%
+your your speech is not just a a
+sequence of sounds right it's a sequence
+
+ align:start position:0%
+sequence of sounds right it's a sequence
+ 
+
+ align:start position:0%
+sequence of sounds right it's a sequence
+of sounds that all influence each other
+
+ align:start position:0%
+of sounds that all influence each other
+ 
+
+ align:start position:0%
+of sounds that all influence each other
+it's a mess in other words yeah
+
+ align:start position:0%
+it's a mess in other words yeah
+ 
+
+ align:start position:0%
+it's a mess in other words yeah
+um and the best cues for what sound you
+
+ align:start position:0%
+um and the best cues for what sound you
+ 
+
+ align:start position:0%
+um and the best cues for what sound you
+made at a particular Point might not be
+
+ align:start position:0%
+made at a particular Point might not be
+ 
+
+ align:start position:0%
+made at a particular Point might not be
+at that point at all they might be on
+
+ align:start position:0%
+at that point at all they might be on
+ 
+
+ align:start position:0%
+at that point at all they might be on
+neighboring points right that's how you
+
+ align:start position:0%
+neighboring points right that's how you
+ 
+
+ align:start position:0%
+neighboring points right that's how you
+find out what sound you're looking at
+
+ align:start position:0%
+find out what sound you're looking at
+ 
+
+ align:start position:0%
+find out what sound you're looking at
+um and that's what makes speech
+
+ align:start position:0%
+um and that's what makes speech
+ 
+
+ align:start position:0%
+um and that's what makes speech
+perception hard it's uh it's also part
+
+ align:start position:0%
+perception hard it's uh it's also part
+ 
+
+ align:start position:0%
+perception hard it's uh it's also part
+of why
+
+ align:start position:0%
+of why
+ 
+
+ align:start position:0%
+of why
+um so there are
+
+ align:start position:0%
+um so there are
+ 
+
+ align:start position:0%
+um so there are
+generalizations about the kinds of
+
+ align:start position:0%
+generalizations about the kinds of
+ 
+
+ align:start position:0%
+generalizations about the kinds of
+syllables that we find in the in the
+
+ align:start position:0%
+syllables that we find in the in the
+ 
+
+ align:start position:0%
+syllables that we find in the in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+um there are plenty of languages out
+
+ align:start position:0%
+um there are plenty of languages out
+ 
+
+ align:start position:0%
+um there are plenty of languages out
+there in which it's okay for a syllable
+
+ align:start position:0%
+there in which it's okay for a syllable
+ 
+
+ align:start position:0%
+there in which it's okay for a syllable
+to start with a stop let's say you can
+
+ align:start position:0%
+to start with a stop let's say you can
+ 
+
+ align:start position:0%
+to start with a stop let's say you can
+have a syllable like PA like that's an
+
+ align:start position:0%
+have a syllable like PA like that's an
+ 
+
+ align:start position:0%
+have a syllable like PA like that's an
+English word more or less it's a word
+
+ align:start position:0%
+English word more or less it's a word
+ 
+
+ align:start position:0%
+English word more or less it's a word
+for uh for father right paw
+
+ align:start position:0%
+for uh for father right paw
+ 
+
+ align:start position:0%
+for uh for father right paw
+um but in which it's not okay to have a
+
+ align:start position:0%
+um but in which it's not okay to have a
+ 
+
+ align:start position:0%
+um but in which it's not okay to have a
+p followed by a fricative uh and then uh
+
+ align:start position:0%
+p followed by a fricative uh and then uh
+ 
+
+ align:start position:0%
+p followed by a fricative uh and then uh
+and then uh vowel right so you don't
+
+ align:start position:0%
+and then uh vowel right so you don't
+ 
+
+ align:start position:0%
+and then uh vowel right so you don't
+have syllables like sa in English or PHA
+
+ align:start position:0%
+have syllables like sa in English or PHA
+ 
+
+ align:start position:0%
+have syllables like sa in English or PHA
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+uh you can imagine that there are
+
+ align:start position:0%
+uh you can imagine that there are
+ 
+
+ align:start position:0%
+uh you can imagine that there are
+languages that allow syllables like that
+
+ align:start position:0%
+languages that allow syllables like that
+ 
+
+ align:start position:0%
+languages that allow syllables like that
+but if a language is going to restrict
+
+ align:start position:0%
+but if a language is going to restrict
+ 
+
+ align:start position:0%
+but if a language is going to restrict
+its syllables if it's only going to have
+
+ align:start position:0%
+its syllables if it's only going to have
+ 
+
+ align:start position:0%
+its syllables if it's only going to have
+one of these kinds it's only going to
+
+ align:start position:0%
+one of these kinds it's only going to
+ 
+
+ align:start position:0%
+one of these kinds it's only going to
+have this kind or to put it another way
+
+ align:start position:0%
+have this kind or to put it another way
+ 
+
+ align:start position:0%
+have this kind or to put it another way
+there are languages that have both of
+
+ align:start position:0%
+there are languages that have both of
+ 
+
+ align:start position:0%
+there are languages that have both of
+these and there are languages that only
+
+ align:start position:0%
+these and there are languages that only
+ 
+
+ align:start position:0%
+these and there are languages that only
+have this there aren't any languages
+
+ align:start position:0%
+have this there aren't any languages
+ 
+
+ align:start position:0%
+have this there aren't any languages
+that only have this
+
+ align:start position:0%
+that only have this
+ 
+
+ align:start position:0%
+that only have this
+and we can kind of see why the The
+
+ align:start position:0%
+and we can kind of see why the The
+ 
+
+ align:start position:0%
+and we can kind of see why the The
+crucial cue to what kind of stop you're
+
+ align:start position:0%
+crucial cue to what kind of stop you're
+ 
+
+ align:start position:0%
+crucial cue to what kind of stop you're
+hearing it comes from the vowel right so
+
+ align:start position:0%
+hearing it comes from the vowel right so
+ 
+
+ align:start position:0%
+hearing it comes from the vowel right so
+if you put a fricative in between the
+
+ align:start position:0%
+if you put a fricative in between the
+ 
+
+ align:start position:0%
+if you put a fricative in between the
+Stop and the vowel you sort of deprive
+
+ align:start position:0%
+Stop and the vowel you sort of deprive
+ 
+
+ align:start position:0%
+Stop and the vowel you sort of deprive
+yourself of one of the big cues for
+
+ align:start position:0%
+yourself of one of the big cues for
+ 
+
+ align:start position:0%
+yourself of one of the big cues for
+figuring out what kind of stops you're
+
+ align:start position:0%
+figuring out what kind of stops you're
+ 
+
+ align:start position:0%
+figuring out what kind of stops you're
+listening to and so it kind of makes
+
+ align:start position:0%
+listening to and so it kind of makes
+ 
+
+ align:start position:0%
+listening to and so it kind of makes
+sense that we get
+
+ align:start position:0%
+sense that we get
+ 
+
+ align:start position:0%
+sense that we get
+this type of syllable everywhere and the
+
+ align:start position:0%
+this type of syllable everywhere and the
+ 
+
+ align:start position:0%
+this type of syllable everywhere and the
+other type of syllable is only has a
+
+ align:start position:0%
+other type of syllable is only has a
+ 
+
+ align:start position:0%
+other type of syllable is only has a
+higher degree of difficulty basically as
+
+ align:start position:0%
+higher degree of difficulty basically as
+ 
+
+ align:start position:0%
+higher degree of difficulty basically as
+far as perception goes yeah Joseph
+
+ align:start position:0%
+far as perception goes yeah Joseph
+ 
+
+ align:start position:0%
+far as perception goes yeah Joseph
+what effect does that have online
+
+ align:start position:0%
+what effect does that have online
+ 
+
+ align:start position:0%
+what effect does that have online
+is the special yeah
+
+ align:start position:0%
+is the special yeah
+ 
+
+ align:start position:0%
+is the special yeah
+it's perfectly okay to stream three
+
+ align:start position:0%
+it's perfectly okay to stream three
+ 
+
+ align:start position:0%
+it's perfectly okay to stream three
+stops in a row yep
+
+ align:start position:0%
+stops in a row yep
+ 
+
+ align:start position:0%
+stops in a row yep
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I've shown you the easiest way
+
+ align:start position:0%
+right so I've shown you the easiest way
+ 
+
+ align:start position:0%
+right so I've shown you the easiest way
+to figure out what a stop is which is by
+
+ align:start position:0%
+to figure out what a stop is which is by
+ 
+
+ align:start position:0%
+to figure out what a stop is which is by
+looking at its effect on the nearby
+
+ align:start position:0%
+looking at its effect on the nearby
+ 
+
+ align:start position:0%
+looking at its effect on the nearby
+vowel but you're absolutely right there
+
+ align:start position:0%
+vowel but you're absolutely right there
+ 
+
+ align:start position:0%
+vowel but you're absolutely right there
+are languages out there that have
+
+ align:start position:0%
+are languages out there that have
+ 
+
+ align:start position:0%
+are languages out there that have
+strings of strings of stops strings of
+
+ align:start position:0%
+strings of strings of stops strings of
+ 
+
+ align:start position:0%
+strings of strings of stops strings of
+stops and fricatives absolutely happens
+
+ align:start position:0%
+stops and fricatives absolutely happens
+ 
+
+ align:start position:0%
+stops and fricatives absolutely happens
+Russian has words like stretique you
+
+ align:start position:0%
+Russian has words like stretique you
+ 
+
+ align:start position:0%
+Russian has words like stretique you
+know instead of a whole string of stops
+
+ align:start position:0%
+know instead of a whole string of stops
+ 
+
+ align:start position:0%
+know instead of a whole string of stops
+and figuratives at the beginning of a
+
+ align:start position:0%
+and figuratives at the beginning of a
+ 
+
+ align:start position:0%
+and figuratives at the beginning of a
+beginning of a a word a beginning of a
+
+ align:start position:0%
+beginning of a a word a beginning of a
+ 
+
+ align:start position:0%
+beginning of a a word a beginning of a
+syllable the most famous examples of
+
+ align:start position:0%
+syllable the most famous examples of
+ 
+
+ align:start position:0%
+syllable the most famous examples of
+this are languages there are two kinds
+
+ align:start position:0%
+this are languages there are two kinds
+ 
+
+ align:start position:0%
+this are languages there are two kinds
+of languages that are especially famous
+
+ align:start position:0%
+of languages that are especially famous
+ 
+
+ align:start position:0%
+of languages that are especially famous
+for this there's a Salish language
+
+ align:start position:0%
+for this there's a Salish language
+ 
+
+ align:start position:0%
+for this there's a Salish language
+called delacula
+
+ align:start position:0%
+called delacula
+ 
+
+ align:start position:0%
+called delacula
+the Salish languages are spoken in the
+
+ align:start position:0%
+the Salish languages are spoken in the
+ 
+
+ align:start position:0%
+the Salish languages are spoken in the
+Pacific Northwest uh belakula there's
+
+ align:start position:0%
+Pacific Northwest uh belakula there's
+ 
+
+ align:start position:0%
+Pacific Northwest uh belakula there's
+only one word of belakula that I know
+
+ align:start position:0%
+only one word of belakula that I know
+ 
+
+ align:start position:0%
+only one word of belakula that I know
+and it's this so this is a uvular
+
+ align:start position:0%
+and it's this so this is a uvular
+ 
+
+ align:start position:0%
+and it's this so this is a uvular
+fricative a voiceless uvulificative
+
+ align:start position:0%
+fricative a voiceless uvulificative
+ 
+
+ align:start position:0%
+fricative a voiceless uvulificative
+um anybody want to try to pronounce that
+
+ align:start position:0%
+um anybody want to try to pronounce that
+ 
+
+ align:start position:0%
+um anybody want to try to pronounce that
+it's something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only thing I know how to say in
+
+ align:start position:0%
+the only thing I know how to say in
+ 
+
+ align:start position:0%
+the only thing I know how to say in
+Bella cool if I ever meet a Bella coola
+
+ align:start position:0%
+Bella cool if I ever meet a Bella coola
+ 
+
+ align:start position:0%
+Bella cool if I ever meet a Bella coola
+we'll have a very simple conversation
+
+ align:start position:0%
+we'll have a very simple conversation
+ 
+
+ align:start position:0%
+we'll have a very simple conversation
+um I mean steel fat uh and um so here's
+
+ align:start position:0%
+um I mean steel fat uh and um so here's
+ 
+
+ align:start position:0%
+um I mean steel fat uh and um so here's
+a place where you sort of Hope there are
+
+ align:start position:0%
+a place where you sort of Hope there are
+ 
+
+ align:start position:0%
+a place where you sort of Hope there are
+other cues besides effects on vowels
+
+ align:start position:0%
+other cues besides effects on vowels
+ 
+
+ align:start position:0%
+other cues besides effects on vowels
+because there are no vowels uh in this
+
+ align:start position:0%
+because there are no vowels uh in this
+ 
+
+ align:start position:0%
+because there are no vowels uh in this
+word right or uh the Berber languages of
+
+ align:start position:0%
+word right or uh the Berber languages of
+ 
+
+ align:start position:0%
+word right or uh the Berber languages of
+Northern Africa are famous for having
+
+ align:start position:0%
+Northern Africa are famous for having
+ 
+
+ align:start position:0%
+Northern Africa are famous for having
+sounds like this here's the only word I
+
+ align:start position:0%
+sounds like this here's the only word I
+ 
+
+ align:start position:0%
+sounds like this here's the only word I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+the only word I know in England Berber
+
+ align:start position:0%
+the only word I know in England Berber
+ 
+
+ align:start position:0%
+the only word I know in England Berber
+which is spoken in Morocco it means you
+
+ align:start position:0%
+which is spoken in Morocco it means you
+ 
+
+ align:start position:0%
+which is spoken in Morocco it means you
+feminine sprained it
+
+ align:start position:0%
+feminine sprained it
+ 
+
+ align:start position:0%
+feminine sprained it
+um and it's something like
+
+ align:start position:0%
+um and it's something like
+ 
+
+ align:start position:0%
+um and it's something like
+phenologists get really interested in
+
+ align:start position:0%
+phenologists get really interested in
+ 
+
+ align:start position:0%
+phenologists get really interested in
+these languages for lots of reasons one
+
+ align:start position:0%
+these languages for lots of reasons one
+ 
+
+ align:start position:0%
+these languages for lots of reasons one
+is the kind of thing Joseph is asking
+
+ align:start position:0%
+is the kind of thing Joseph is asking
+ 
+
+ align:start position:0%
+is the kind of thing Joseph is asking
+about how do these people figure out
+
+ align:start position:0%
+about how do these people figure out
+ 
+
+ align:start position:0%
+about how do these people figure out
+what sounds they are hearing and the
+
+ align:start position:0%
+what sounds they are hearing and the
+ 
+
+ align:start position:0%
+what sounds they are hearing and the
+answer has to be something like yeah
+
+ align:start position:0%
+answer has to be something like yeah
+ 
+
+ align:start position:0%
+answer has to be something like yeah
+there are lots of good cues on vowels
+
+ align:start position:0%
+there are lots of good cues on vowels
+ 
+
+ align:start position:0%
+there are lots of good cues on vowels
+but there are also cues on other kinds
+
+ align:start position:0%
+but there are also cues on other kinds
+ 
+
+ align:start position:0%
+but there are also cues on other kinds
+of things and we have to figure out what
+
+ align:start position:0%
+of things and we have to figure out what
+ 
+
+ align:start position:0%
+of things and we have to figure out what
+they are you know how what people are
+
+ align:start position:0%
+they are you know how what people are
+ 
+
+ align:start position:0%
+they are you know how what people are
+queuing in on
+
+ align:start position:0%
+queuing in on
+ 
+
+ align:start position:0%
+queuing in on
+um uh there are other questions too like
+
+ align:start position:0%
+um uh there are other questions too like
+ 
+
+ align:start position:0%
+um uh there are other questions too like
+I was just talking about syllables which
+
+ align:start position:0%
+I was just talking about syllables which
+ 
+
+ align:start position:0%
+I was just talking about syllables which
+is something we'll talk about as we get
+
+ align:start position:0%
+is something we'll talk about as we get
+ 
+
+ align:start position:0%
+is something we'll talk about as we get
+further into phenology and the question
+
+ align:start position:0%
+further into phenology and the question
+ 
+
+ align:start position:0%
+further into phenology and the question
+is are there any syllables in this word
+
+ align:start position:0%
+is are there any syllables in this word
+ 
+
+ align:start position:0%
+is are there any syllables in this word
+you know to which the answer turns out
+
+ align:start position:0%
+you know to which the answer turns out
+ 
+
+ align:start position:0%
+you know to which the answer turns out
+to be yes uh so if you look at the if
+
+ align:start position:0%
+to be yes uh so if you look at the if
+ 
+
+ align:start position:0%
+to be yes uh so if you look at the if
+you look carefully at these languages
+
+ align:start position:0%
+you look carefully at these languages
+ 
+
+ align:start position:0%
+you look carefully at these languages
+you can convince yourself that they uh
+
+ align:start position:0%
+you can convince yourself that they uh
+ 
+
+ align:start position:0%
+you can convince yourself that they uh
+that they have syllables
+
+ align:start position:0%
+that they have syllables
+ 
+
+ align:start position:0%
+that they have syllables
+sorry very long answer to Joseph's
+
+ align:start position:0%
+sorry very long answer to Joseph's
+ 
+
+ align:start position:0%
+sorry very long answer to Joseph's
+question to which the short version of
+
+ align:start position:0%
+question to which the short version of
+ 
+
+ align:start position:0%
+question to which the short version of
+the answer would be the best cues are on
+
+ align:start position:0%
+the answer would be the best cues are on
+ 
+
+ align:start position:0%
+the answer would be the best cues are on
+vowels but there must be cues on other
+
+ align:start position:0%
+vowels but there must be cues on other
+ 
+
+ align:start position:0%
+vowels but there must be cues on other
+kinds of things as well which are not as
+
+ align:start position:0%
+kinds of things as well which are not as
+ 
+
+ align:start position:0%
+kinds of things as well which are not as
+not as clear
+
+ align:start position:0%
+not as clear
+ 
+
+ align:start position:0%
+not as clear
+and it's sort of a question for of your
+
+ align:start position:0%
+and it's sort of a question for of your
+ 
+
+ align:start position:0%
+and it's sort of a question for of your
+your level of tolerance for unclarity
+
+ align:start position:0%
+your level of tolerance for unclarity
+ 
+
+ align:start position:0%
+your level of tolerance for unclarity
+or how good you are at picking up on
+
+ align:start position:0%
+or how good you are at picking up on
+ 
+
+ align:start position:0%
+or how good you are at picking up on
+those cues
+
+ align:start position:0%
+those cues
+ 
+
+ align:start position:0%
+those cues
+Okay cool so uh Pratt was I going to do
+
+ align:start position:0%
+Okay cool so uh Pratt was I going to do
+ 
+
+ align:start position:0%
+Okay cool so uh Pratt was I going to do
+anything else with Pratt
+
+ align:start position:0%
+anything else with Pratt
+ 
+
+ align:start position:0%
+anything else with Pratt
+um no those were the things I was going
+
+ align:start position:0%
+um no those were the things I was going
+ 
+
+ align:start position:0%
+um no those were the things I was going
+to do with prop I will leave prod up uh
+
+ align:start position:0%
+to do with prop I will leave prod up uh
+ 
+
+ align:start position:0%
+to do with prop I will leave prod up uh
+I think actually we may be seeing proud
+
+ align:start position:0%
+I think actually we may be seeing proud
+ 
+
+ align:start position:0%
+I think actually we may be seeing proud
+again pretty shortly uh but I'll leave
+
+ align:start position:0%
+again pretty shortly uh but I'll leave
+ 
+
+ align:start position:0%
+again pretty shortly uh but I'll leave
+prod on the on the website so you can uh
+
+ align:start position:0%
+prod on the on the website so you can uh
+ 
+
+ align:start position:0%
+prod on the on the website so you can uh
+you can play around with it at home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I'm going to full screen mode okay
+
+ align:start position:0%
+um I'm going to full screen mode okay
+ 
+
+ align:start position:0%
+um I'm going to full screen mode okay
+oh sorry go back out of screen mode
+
+ align:start position:0%
+oh sorry go back out of screen mode
+ 
+
+ align:start position:0%
+oh sorry go back out of screen mode
+um so we've just been talking about how
+
+ align:start position:0%
+um so we've just been talking about how
+ 
+
+ align:start position:0%
+um so we've just been talking about how
+you know what sounds it is that you are
+
+ align:start position:0%
+you know what sounds it is that you are
+ 
+
+ align:start position:0%
+you know what sounds it is that you are
+hearing uh and some of the cues come
+
+ align:start position:0%
+hearing uh and some of the cues come
+ 
+
+ align:start position:0%
+hearing uh and some of the cues come
+from what's happening during the sound
+
+ align:start position:0%
+from what's happening during the sound
+ 
+
+ align:start position:0%
+from what's happening during the sound
+and some of the cues come from
+
+ align:start position:0%
+and some of the cues come from
+ 
+
+ align:start position:0%
+and some of the cues come from
+neighboring sounds and uh sort of the
+
+ align:start position:0%
+neighboring sounds and uh sort of the
+ 
+
+ align:start position:0%
+neighboring sounds and uh sort of the
+study of this is one of the the central
+
+ align:start position:0%
+study of this is one of the the central
+ 
+
+ align:start position:0%
+study of this is one of the the central
+studies of uh of phenology and of
+
+ align:start position:0%
+studies of uh of phenology and of
+ 
+
+ align:start position:0%
+studies of uh of phenology and of
+phonetics I want to show you about
+
+ align:start position:0%
+phonetics I want to show you about
+ 
+
+ align:start position:0%
+phonetics I want to show you about
+another kind of information that we have
+
+ align:start position:0%
+another kind of information that we have
+ 
+
+ align:start position:0%
+another kind of information that we have
+though it's something called the mcgurk
+
+ align:start position:0%
+though it's something called the mcgurk
+ 
+
+ align:start position:0%
+though it's something called the mcgurk
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+uh and I'll just demonstrate it to you
+
+ align:start position:0%
+uh and I'll just demonstrate it to you
+ 
+
+ align:start position:0%
+uh and I'll just demonstrate it to you
+and then we'll talk about it this guy is
+
+ align:start position:0%
+and then we'll talk about it this guy is
+ 
+
+ align:start position:0%
+and then we'll talk about it this guy is
+going to repeat a syllable
+
+ align:start position:0%
+going to repeat a syllable
+ 
+
+ align:start position:0%
+going to repeat a syllable
+um a couple of times and then when he's
+
+ align:start position:0%
+um a couple of times and then when he's
+ 
+
+ align:start position:0%
+um a couple of times and then when he's
+done I'm going to ask you what syllable
+
+ align:start position:0%
+done I'm going to ask you what syllable
+ 
+
+ align:start position:0%
+done I'm going to ask you what syllable
+you heard okay
+
+ align:start position:0%
+you heard okay
+ 
+
+ align:start position:0%
+you heard okay
+so here's the guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to turn up the volume and do
+
+ align:start position:0%
+I'm going to turn up the volume and do
+ 
+
+ align:start position:0%
+I'm going to turn up the volume and do
+that again so you can hear it better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how many of you heard uh a bar
+
+ align:start position:0%
+okay how many of you heard uh a bar
+ 
+
+ align:start position:0%
+okay how many of you heard uh a bar
+how many of you heard a da
+
+ align:start position:0%
+how many of you heard a da
+ 
+
+ align:start position:0%
+how many of you heard a da
+how many of you heard a ga
+
+ align:start position:0%
+how many of you heard a ga
+ 
+
+ align:start position:0%
+how many of you heard a ga
+okay several of you are raising your
+
+ align:start position:0%
+okay several of you are raising your
+ 
+
+ align:start position:0%
+okay several of you are raising your
+hand several times you're just not sure
+
+ align:start position:0%
+hand several times you're just not sure
+ 
+
+ align:start position:0%
+hand several times you're just not sure
+what you heard or you thought you heard
+
+ align:start position:0%
+what you heard or you thought you heard
+ 
+
+ align:start position:0%
+what you heard or you thought you heard
+several things at once yeah you thought
+
+ align:start position:0%
+several things at once yeah you thought
+ 
+
+ align:start position:0%
+several things at once yeah you thought
+you heard several things at once so
+
+ align:start position:0%
+you heard several things at once so
+ 
+
+ align:start position:0%
+you heard several things at once so
+there's something very confusing going
+
+ align:start position:0%
+there's something very confusing going
+ 
+
+ align:start position:0%
+there's something very confusing going
+on I'm gonna play it again and I want
+
+ align:start position:0%
+on I'm gonna play it again and I want
+ 
+
+ align:start position:0%
+on I'm gonna play it again and I want
+you to close your eyes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody got your eyes closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'll put the link so that you can
+
+ align:start position:0%
+okay I'll put the link so that you can
+ 
+
+ align:start position:0%
+okay I'll put the link so that you can
+play with this at home but here's what's
+
+ align:start position:0%
+play with this at home but here's what's
+ 
+
+ align:start position:0%
+play with this at home but here's what's
+happening you're hearing a recording of
+
+ align:start position:0%
+happening you're hearing a recording of
+ 
+
+ align:start position:0%
+happening you're hearing a recording of
+ba that's what he's doing he's saying ba
+
+ align:start position:0%
+ba that's what he's doing he's saying ba
+ 
+
+ align:start position:0%
+ba that's what he's doing he's saying ba
+but the ba is being carefully timed
+
+ align:start position:0%
+but the ba is being carefully timed
+ 
+
+ align:start position:0%
+but the ba is being carefully timed
+together with a video of him saying ga
+
+ align:start position:0%
+together with a video of him saying ga
+ 
+
+ align:start position:0%
+together with a video of him saying ga
+right and so you can only tell that it's
+
+ align:start position:0%
+right and so you can only tell that it's
+ 
+
+ align:start position:0%
+right and so you can only tell that it's
+ba if you don't look at him right so if
+
+ align:start position:0%
+ba if you don't look at him right so if
+ 
+
+ align:start position:0%
+ba if you don't look at him right so if
+your eyes are closed you hear it as ba
+
+ align:start position:0%
+your eyes are closed you hear it as ba
+ 
+
+ align:start position:0%
+your eyes are closed you hear it as ba
+you know but if your eyes are not closed
+
+ align:start position:0%
+you know but if your eyes are not closed
+ 
+
+ align:start position:0%
+you know but if your eyes are not closed
+if you look at him you should try this
+
+ align:start position:0%
+if you look at him you should try this
+ 
+
+ align:start position:0%
+if you look at him you should try this
+at home maybe if you're on better
+
+ align:start position:0%
+at home maybe if you're on better
+ 
+
+ align:start position:0%
+at home maybe if you're on better
+quality screen the the illusion becomes
+
+ align:start position:0%
+quality screen the the illusion becomes
+ 
+
+ align:start position:0%
+quality screen the the illusion becomes
+fairly clear people generally report
+
+ align:start position:0%
+fairly clear people generally report
+ 
+
+ align:start position:0%
+fairly clear people generally report
+that they're hearing da which is neither
+
+ align:start position:0%
+that they're hearing da which is neither
+ 
+
+ align:start position:0%
+that they're hearing da which is neither
+what they are seeing or what they are
+
+ align:start position:0%
+what they are seeing or what they are
+ 
+
+ align:start position:0%
+what they are seeing or what they are
+hearing
+
+ align:start position:0%
+hearing
+ 
+
+ align:start position:0%
+hearing
+um so what this is teaching us is that
+
+ align:start position:0%
+um so what this is teaching us is that
+ 
+
+ align:start position:0%
+um so what this is teaching us is that
+although there's all this complicated
+
+ align:start position:0%
+although there's all this complicated
+ 
+
+ align:start position:0%
+although there's all this complicated
+phonology going on all of these things
+
+ align:start position:0%
+phonology going on all of these things
+ 
+
+ align:start position:0%
+phonology going on all of these things
+that you're you do to try to figure out
+
+ align:start position:0%
+that you're you do to try to figure out
+ 
+
+ align:start position:0%
+that you're you do to try to figure out
+the speech signal you are also paying
+
+ align:start position:0%
+the speech signal you are also paying
+ 
+
+ align:start position:0%
+the speech signal you are also paying
+attention to what you see uh so
+
+ align:start position:0%
+attention to what you see uh so
+ 
+
+ align:start position:0%
+attention to what you see uh so
+apparently what's going on here again
+
+ align:start position:0%
+apparently what's going on here again
+ 
+
+ align:start position:0%
+apparently what's going on here again
+the recording is of ba right but you're
+
+ align:start position:0%
+the recording is of ba right but you're
+ 
+
+ align:start position:0%
+the recording is of ba right but you're
+looking at this guy and he's clearly not
+
+ align:start position:0%
+looking at this guy and he's clearly not
+ 
+
+ align:start position:0%
+looking at this guy and he's clearly not
+saying ba right because his lips are not
+
+ align:start position:0%
+saying ba right because his lips are not
+ 
+
+ align:start position:0%
+saying ba right because his lips are not
+closing and apparently the evidence of
+
+ align:start position:0%
+closing and apparently the evidence of
+ 
+
+ align:start position:0%
+closing and apparently the evidence of
+your eyes is enough to convince your
+
+ align:start position:0%
+your eyes is enough to convince your
+ 
+
+ align:start position:0%
+your eyes is enough to convince your
+brain to ignore your ears uh when it's
+
+ align:start position:0%
+brain to ignore your ears uh when it's
+ 
+
+ align:start position:0%
+brain to ignore your ears uh when it's
+trying to figure out what you're hearing
+
+ align:start position:0%
+trying to figure out what you're hearing
+ 
+
+ align:start position:0%
+trying to figure out what you're hearing
+yeah so the the cause of the illusion is
+
+ align:start position:0%
+yeah so the the cause of the illusion is
+ 
+
+ align:start position:0%
+yeah so the the cause of the illusion is
+that because you can see that he's not
+
+ align:start position:0%
+that because you can see that he's not
+ 
+
+ align:start position:0%
+that because you can see that he's not
+making a bilabial closure your your
+
+ align:start position:0%
+making a bilabial closure your your
+ 
+
+ align:start position:0%
+making a bilabial closure your your
+brain is like rejecting the hypothesis
+
+ align:start position:0%
+brain is like rejecting the hypothesis
+ 
+
+ align:start position:0%
+brain is like rejecting the hypothesis
+that it's a bilabial closure and trying
+
+ align:start position:0%
+that it's a bilabial closure and trying
+ 
+
+ align:start position:0%
+that it's a bilabial closure and trying
+to come up with the closest sound that
+
+ align:start position:0%
+to come up with the closest sound that
+ 
+
+ align:start position:0%
+to come up with the closest sound that
+it can and you end up with confusion
+
+ align:start position:0%
+it can and you end up with confusion
+ 
+
+ align:start position:0%
+it can and you end up with confusion
+yeah than what would language
+
+ align:start position:0%
+yeah than what would language
+ 
+
+ align:start position:0%
+yeah than what would language
+acquisition look like in individuals
+
+ align:start position:0%
+acquisition look like in individuals
+ 
+
+ align:start position:0%
+acquisition look like in individuals
+were born
+
+ align:start position:0%
+were born
+ 
+
+ align:start position:0%
+were born
+yeah so that's a really good question I
+
+ align:start position:0%
+yeah so that's a really good question I
+ 
+
+ align:start position:0%
+yeah so that's a really good question I
+don't know whether there's any work on
+
+ align:start position:0%
+don't know whether there's any work on
+ 
+
+ align:start position:0%
+don't know whether there's any work on
+that that that question of uh whether
+
+ align:start position:0%
+that that that question of uh whether
+ 
+
+ align:start position:0%
+that that that question of uh whether
+the mcgurk effect has anything to say
+
+ align:start position:0%
+the mcgurk effect has anything to say
+ 
+
+ align:start position:0%
+the mcgurk effect has anything to say
+about that we obviously can get along
+
+ align:start position:0%
+about that we obviously can get along
+ 
+
+ align:start position:0%
+about that we obviously can get along
+just fine without seeing the people that
+
+ align:start position:0%
+just fine without seeing the people that
+ 
+
+ align:start position:0%
+just fine without seeing the people that
+we're talking to we can talk to people
+
+ align:start position:0%
+we're talking to we can talk to people
+ 
+
+ align:start position:0%
+we're talking to we can talk to people
+on the phone right and all kinds of
+
+ align:start position:0%
+on the phone right and all kinds of
+ 
+
+ align:start position:0%
+on the phone right and all kinds of
+things but we are apparently geared to
+
+ align:start position:0%
+things but we are apparently geared to
+ 
+
+ align:start position:0%
+things but we are apparently geared to
+pay so much attention to visual input
+
+ align:start position:0%
+pay so much attention to visual input
+ 
+
+ align:start position:0%
+pay so much attention to visual input
+that it actually overrides uh the
+
+ align:start position:0%
+that it actually overrides uh the
+ 
+
+ align:start position:0%
+that it actually overrides uh the
+evidence of our ears it's a very
+
+ align:start position:0%
+evidence of our ears it's a very
+ 
+
+ align:start position:0%
+evidence of our ears it's a very
+powerful effect I know what's going on
+
+ align:start position:0%
+powerful effect I know what's going on
+ 
+
+ align:start position:0%
+powerful effect I know what's going on
+it happens to me you know what's going
+
+ align:start position:0%
+it happens to me you know what's going
+ 
+
+ align:start position:0%
+it happens to me you know what's going
+on now Ben and will happen to you if you
+
+ align:start position:0%
+on now Ben and will happen to you if you
+ 
+
+ align:start position:0%
+on now Ben and will happen to you if you
+watch this again again I'll put the link
+
+ align:start position:0%
+watch this again again I'll put the link
+ 
+
+ align:start position:0%
+watch this again again I'll put the link
+up and uh you can you can a major
+
+ align:start position:0%
+up and uh you can you can a major
+ 
+
+ align:start position:0%
+up and uh you can you can a major
+friends with it it's a very robust
+
+ align:start position:0%
+friends with it it's a very robust
+ 
+
+ align:start position:0%
+friends with it it's a very robust
+phenomenon it's been demonstrated for a
+
+ align:start position:0%
+phenomenon it's been demonstrated for a
+ 
+
+ align:start position:0%
+phenomenon it's been demonstrated for a
+bunch of different sounds and in a bunch
+
+ align:start position:0%
+bunch of different sounds and in a bunch
+ 
+
+ align:start position:0%
+bunch of different sounds and in a bunch
+of different languages it's not just an
+
+ align:start position:0%
+of different languages it's not just an
+ 
+
+ align:start position:0%
+of different languages it's not just an
+English thing
+
+ align:start position:0%
+English thing
+ 
+
+ align:start position:0%
+English thing
+it's all over the place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now am I done with other things
+
+ align:start position:0%
+now am I done with other things
+ 
+
+ align:start position:0%
+now am I done with other things
+well now I am about to start talking
+
+ align:start position:0%
+well now I am about to start talking
+ 
+
+ align:start position:0%
+well now I am about to start talking
+about something which is pretty
+
+ align:start position:0%
+about something which is pretty
+ 
+
+ align:start position:0%
+about something which is pretty
+complicated and so I'll just give you
+
+ align:start position:0%
+complicated and so I'll just give you
+ 
+
+ align:start position:0%
+complicated and so I'll just give you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah uh so I'll tell you briefly what
+
+ align:start position:0%
+yeah uh so I'll tell you briefly what
+ 
+
+ align:start position:0%
+yeah uh so I'll tell you briefly what
+I'm going to talk about next time and
+
+ align:start position:0%
+I'm going to talk about next time and
+ 
+
+ align:start position:0%
+I'm going to talk about next time and
+we'll just start with this next time
+
+ align:start position:0%
+we'll just start with this next time
+ 
+
+ align:start position:0%
+we'll just start with this next time
+because I don't think we have time to
+
+ align:start position:0%
+because I don't think we have time to
+ 
+
+ align:start position:0%
+because I don't think we have time to
+talk about this in any detail
+
+ align:start position:0%
+talk about this in any detail
+ 
+
+ align:start position:0%
+talk about this in any detail
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh we've been talking well here let me
+
+ align:start position:0%
+uh we've been talking well here let me
+ 
+
+ align:start position:0%
+uh we've been talking well here let me
+show you something and then we'll talk
+
+ align:start position:0%
+show you something and then we'll talk
+ 
+
+ align:start position:0%
+show you something and then we'll talk
+more about it next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back to Pratt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi by spy
+
+ align:start position:0%
+Pi by spy
+ 
+
+ align:start position:0%
+Pi by spy
+ah darn I failed to save that hang on
+
+ align:start position:0%
+ah darn I failed to save that hang on
+ 
+
+ align:start position:0%
+ah darn I failed to save that hang on
+just a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi bye spy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's me saying Pi by spy
+
+ align:start position:0%
+that's me saying Pi by spy
+ 
+
+ align:start position:0%
+that's me saying Pi by spy
+Pi by spy I'm sorry the the um
+
+ align:start position:0%
+Pi by spy I'm sorry the the um
+ 
+
+ align:start position:0%
+Pi by spy I'm sorry the the um
+uh everything's up again okay so uh
+
+ align:start position:0%
+uh everything's up again okay so uh
+ 
+
+ align:start position:0%
+uh everything's up again okay so uh
+here's let's just listen to Pi
+
+ align:start position:0%
+here's let's just listen to Pi
+ 
+
+ align:start position:0%
+here's let's just listen to Pi
+actually let's just look at pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me do that come on you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi Pi okay so that's that's the
+
+ align:start position:0%
+Pi Pi okay so that's that's the
+ 
+
+ align:start position:0%
+Pi Pi okay so that's that's the
+spectrogram of me saying pi and you can
+
+ align:start position:0%
+spectrogram of me saying pi and you can
+ 
+
+ align:start position:0%
+spectrogram of me saying pi and you can
+see here I'll use my cursor instead uh
+
+ align:start position:0%
+see here I'll use my cursor instead uh
+ 
+
+ align:start position:0%
+see here I'll use my cursor instead uh
+what's going on here you know my here's
+
+ align:start position:0%
+what's going on here you know my here's
+ 
+
+ align:start position:0%
+what's going on here you know my here's
+the stop and then this little burst is
+
+ align:start position:0%
+the stop and then this little burst is
+ 
+
+ align:start position:0%
+the stop and then this little burst is
+is my lips opening and then there's a
+
+ align:start position:0%
+is my lips opening and then there's a
+ 
+
+ align:start position:0%
+is my lips opening and then there's a
+little burst of white noise uh and then
+
+ align:start position:0%
+little burst of white noise uh and then
+ 
+
+ align:start position:0%
+little burst of white noise uh and then
+we start in on the vowel you can see the
+
+ align:start position:0%
+we start in on the vowel you can see the
+ 
+
+ align:start position:0%
+we start in on the vowel you can see the
+the bar the four months uh the the black
+
+ align:start position:0%
+the bar the four months uh the the black
+ 
+
+ align:start position:0%
+the bar the four months uh the the black
+bars that indicate that we're doing a
+
+ align:start position:0%
+bars that indicate that we're doing a
+ 
+
+ align:start position:0%
+bars that indicate that we're doing a
+vowel this little burst of white noise
+
+ align:start position:0%
+vowel this little burst of white noise
+ 
+
+ align:start position:0%
+vowel this little burst of white noise
+is the period that elapses in between my
+
+ align:start position:0%
+is the period that elapses in between my
+ 
+
+ align:start position:0%
+is the period that elapses in between my
+lips opening and my vocal cords
+
+ align:start position:0%
+lips opening and my vocal cords
+ 
+
+ align:start position:0%
+lips opening and my vocal cords
+beginning to engage right so there's
+
+ align:start position:0%
+beginning to engage right so there's
+ 
+
+ align:start position:0%
+beginning to engage right so there's
+this period where there's nothing coming
+
+ align:start position:0%
+this period where there's nothing coming
+ 
+
+ align:start position:0%
+this period where there's nothing coming
+out of my lungs but air
+
+ align:start position:0%
+out of my lungs but air
+ 
+
+ align:start position:0%
+out of my lungs but air
+there's always air coming out of my
+
+ align:start position:0%
+there's always air coming out of my
+ 
+
+ align:start position:0%
+there's always air coming out of my
+lungs let me try that again there's
+
+ align:start position:0%
+lungs let me try that again there's
+ 
+
+ align:start position:0%
+lungs let me try that again there's
+nothing coming out of my vocal tract but
+
+ align:start position:0%
+nothing coming out of my vocal tract but
+ 
+
+ align:start position:0%
+nothing coming out of my vocal tract but
+air yeah uh my vocal cords aren't
+
+ align:start position:0%
+air yeah uh my vocal cords aren't
+ 
+
+ align:start position:0%
+air yeah uh my vocal cords aren't
+vibrating yet and it's not long you know
+
+ align:start position:0%
+vibrating yet and it's not long you know
+ 
+
+ align:start position:0%
+vibrating yet and it's not long you know
+it lasts uh some fraction of a second
+
+ align:start position:0%
+it lasts uh some fraction of a second
+ 
+
+ align:start position:0%
+it lasts uh some fraction of a second
+how long does it last it lasts
+
+ align:start position:0%
+how long does it last it lasts
+ 
+
+ align:start position:0%
+how long does it last it lasts
+um who cares how long it lasts
+
+ align:start position:0%
+um who cares how long it lasts
+ 
+
+ align:start position:0%
+um who cares how long it lasts
+do I care do I care long enough to find
+
+ align:start position:0%
+do I care do I care long enough to find
+ 
+
+ align:start position:0%
+do I care do I care long enough to find
+out it lasts less time than that it
+
+ align:start position:0%
+out it lasts less time than that it
+ 
+
+ align:start position:0%
+out it lasts less time than that it
+lasts .06 seconds yeah there we go
+
+ align:start position:0%
+lasts .06 seconds yeah there we go
+ 
+
+ align:start position:0%
+lasts .06 seconds yeah there we go
+um so so that's that's what's going on
+
+ align:start position:0%
+um so so that's that's what's going on
+ 
+
+ align:start position:0%
+um so so that's that's what's going on
+in pi now let's look at spy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spy Spy
+
+ align:start position:0%
+spy Spy
+ 
+
+ align:start position:0%
+spy Spy
+and you can see and actually allow me to
+
+ align:start position:0%
+and you can see and actually allow me to
+ 
+
+ align:start position:0%
+and you can see and actually allow me to
+let you to hear so here's here's the S
+
+ align:start position:0%
+let you to hear so here's here's the S
+ 
+
+ align:start position:0%
+let you to hear so here's here's the S
+this is what fricatives look like these
+
+ align:start position:0%
+this is what fricatives look like these
+ 
+
+ align:start position:0%
+this is what fricatives look like these
+sort of verses of white noise lots more
+
+ align:start position:0%
+sort of verses of white noise lots more
+ 
+
+ align:start position:0%
+sort of verses of white noise lots more
+energy up here uh for the S uh here's
+
+ align:start position:0%
+energy up here uh for the S uh here's
+ 
+
+ align:start position:0%
+energy up here uh for the S uh here's
+the stop you can see what stops look
+
+ align:start position:0%
+the stop you can see what stops look
+ 
+
+ align:start position:0%
+the stop you can see what stops look
+like it's kind of blank here are my lips
+
+ align:start position:0%
+like it's kind of blank here are my lips
+ 
+
+ align:start position:0%
+like it's kind of blank here are my lips
+opening for the end of the stop
+
+ align:start position:0%
+opening for the end of the stop
+ 
+
+ align:start position:0%
+opening for the end of the stop
+and let's just play it starting with the
+
+ align:start position:0%
+and let's just play it starting with the
+ 
+
+ align:start position:0%
+and let's just play it starting with the
+stop bye bye bye
+
+ align:start position:0%
+stop bye bye bye
+ 
+
+ align:start position:0%
+stop bye bye bye
+how many of you hear that as Pi
+
+ align:start position:0%
+how many of you hear that as Pi
+ 
+
+ align:start position:0%
+how many of you hear that as Pi
+how many of you hear it is bi yeah so
+
+ align:start position:0%
+how many of you hear it is bi yeah so
+ 
+
+ align:start position:0%
+how many of you hear it is bi yeah so
+this is an unaspirated voiceless stop
+
+ align:start position:0%
+this is an unaspirated voiceless stop
+ 
+
+ align:start position:0%
+this is an unaspirated voiceless stop
+you know so my lips are opening and then
+
+ align:start position:0%
+you know so my lips are opening and then
+ 
+
+ align:start position:0%
+you know so my lips are opening and then
+my vocal cords get busy right away you
+
+ align:start position:0%
+my vocal cords get busy right away you
+ 
+
+ align:start position:0%
+my vocal cords get busy right away you
+can see there isn't a big gap right in
+
+ align:start position:0%
+can see there isn't a big gap right in
+ 
+
+ align:start position:0%
+can see there isn't a big gap right in
+between the the P and the and what's
+
+ align:start position:0%
+between the the P and the and what's
+ 
+
+ align:start position:0%
+between the the P and the and what's
+happening after it so we will talk more
+
+ align:start position:0%
+happening after it so we will talk more
+ 
+
+ align:start position:0%
+happening after it so we will talk more
+about this next time but this is what's
+
+ align:start position:0%
+about this next time but this is what's
+ 
+
+ align:start position:0%
+about this next time but this is what's
+called aspiration uh English has
+
+ align:start position:0%
+called aspiration uh English has
+ 
+
+ align:start position:0%
+called aspiration uh English has
+aspiration in some places but not in
+
+ align:start position:0%
+aspiration in some places but not in
+ 
+
+ align:start position:0%
+aspiration in some places but not in
+others so we'll do this demonstration
+
+ align:start position:0%
+others so we'll do this demonstration
+ 
+
+ align:start position:0%
+others so we'll do this demonstration
+again next time and then we'll talk
+
+ align:start position:0%
+again next time and then we'll talk
+ 
+
+ align:start position:0%
+again next time and then we'll talk
+about what it means so for now I think
+
+ align:start position:0%
+about what it means so for now I think
+ 
+
+ align:start position:0%
+about what it means so for now I think
+we're done unless anybody has any
+
+ align:start position:0%
+we're done unless anybody has any
+ 
+
+ align:start position:0%
+we're done unless anybody has any
+questions about any of this
+
+ align:start position:0%
+questions about any of this
+ 
+
+ align:start position:0%
+questions about any of this
+all right uh see you not on Tuesday but
+
+ align:start position:0%
+all right uh see you not on Tuesday but
+ 
+
+ align:start position:0%
+all right uh see you not on Tuesday but
+on Thursday right so we don't have class
+
+ align:start position:0%
+on Thursday right so we don't have class
+ 
+
+ align:start position:0%
+on Thursday right so we don't have class
+on Tuesday
\ No newline at end of file
diff --git a/NfD6QNY6Zzg.txt b/NfD6QNY6Zzg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..708bc58819d1445eb29a4dcfa75d36965d52a412
--- /dev/null
+++ b/NfD6QNY6Zzg.txt
@@ -0,0 +1,13443 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so welcome to day two of morphology
+
+ align:start position:0%
+so welcome to day two of morphology
+ 
+
+ align:start position:0%
+so welcome to day two of morphology
+um last time I was trying to get you to
+
+ align:start position:0%
+um last time I was trying to get you to
+ 
+
+ align:start position:0%
+um last time I was trying to get you to
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+that it's worth you know for trying to
+
+ align:start position:0%
+that it's worth you know for trying to
+ 
+
+ align:start position:0%
+that it's worth you know for trying to
+think about what you have in your mind
+
+ align:start position:0%
+think about what you have in your mind
+ 
+
+ align:start position:0%
+think about what you have in your mind
+uh the representations you have in your
+
+ align:start position:0%
+uh the representations you have in your
+ 
+
+ align:start position:0%
+uh the representations you have in your
+mind of what you you can do with your
+
+ align:start position:0%
+mind of what you you can do with your
+ 
+
+ align:start position:0%
+mind of what you you can do with your
+native language if we're trying to think
+
+ align:start position:0%
+native language if we're trying to think
+ 
+
+ align:start position:0%
+native language if we're trying to think
+about that but it's useful to think yeah
+
+ align:start position:0%
+about that but it's useful to think yeah
+ 
+
+ align:start position:0%
+about that but it's useful to think yeah
+your your mental list of elements of
+
+ align:start position:0%
+your your mental list of elements of
+ 
+
+ align:start position:0%
+your your mental list of elements of
+your basic elements of your language
+
+ align:start position:0%
+your basic elements of your language
+ 
+
+ align:start position:0%
+your basic elements of your language
+consists maybe of a list of morphemes
+
+ align:start position:0%
+consists maybe of a list of morphemes
+ 
+
+ align:start position:0%
+consists maybe of a list of morphemes
+where morphemes are these units that can
+
+ align:start position:0%
+where morphemes are these units that can
+ 
+
+ align:start position:0%
+where morphemes are these units that can
+combine in various ways as we've seen
+
+ align:start position:0%
+combine in various ways as we've seen
+ 
+
+ align:start position:0%
+combine in various ways as we've seen
+um each morpheme we're going to need to
+
+ align:start position:0%
+um each morpheme we're going to need to
+ 
+
+ align:start position:0%
+um each morpheme we're going to need to
+tag with information about uh its sound
+
+ align:start position:0%
+tag with information about uh its sound
+ 
+
+ align:start position:0%
+tag with information about uh its sound
+uh it's so how it's pronounced its
+
+ align:start position:0%
+uh it's so how it's pronounced its
+ 
+
+ align:start position:0%
+uh it's so how it's pronounced its
+meaning uh and then information like is
+
+ align:start position:0%
+meaning uh and then information like is
+ 
+
+ align:start position:0%
+meaning uh and then information like is
+it a bound morpheme or a free morpheme
+
+ align:start position:0%
+it a bound morpheme or a free morpheme
+ 
+
+ align:start position:0%
+it a bound morpheme or a free morpheme
+that is is it the kind of morpheme that
+
+ align:start position:0%
+that is is it the kind of morpheme that
+ 
+
+ align:start position:0%
+that is is it the kind of morpheme that
+needs to combine with another morpheme
+
+ align:start position:0%
+needs to combine with another morpheme
+ 
+
+ align:start position:0%
+needs to combine with another morpheme
+or not right so there are free morphemes
+
+ align:start position:0%
+or not right so there are free morphemes
+ 
+
+ align:start position:0%
+or not right so there are free morphemes
+like cat right where
+
+ align:start position:0%
+like cat right where
+ 
+
+ align:start position:0%
+like cat right where
+when we're listing it sound we'll
+
+ align:start position:0%
+when we're listing it sound we'll
+ 
+
+ align:start position:0%
+when we're listing it sound we'll
+represent the fact that it's pronounced
+
+ align:start position:0%
+represent the fact that it's pronounced
+ 
+
+ align:start position:0%
+represent the fact that it's pronounced
+cat and we're listing its meaning we'll
+
+ align:start position:0%
+cat and we're listing its meaning we'll
+ 
+
+ align:start position:0%
+cat and we're listing its meaning we'll
+represent the fact that it refers to a
+
+ align:start position:0%
+represent the fact that it refers to a
+ 
+
+ align:start position:0%
+represent the fact that it refers to a
+certain type of small mammal and uh when
+
+ align:start position:0%
+certain type of small mammal and uh when
+ 
+
+ align:start position:0%
+certain type of small mammal and uh when
+we're listing whether it's bound or free
+
+ align:start position:0%
+we're listing whether it's bound or free
+ 
+
+ align:start position:0%
+we're listing whether it's bound or free
+we'll say that it's free because cat is
+
+ align:start position:0%
+we'll say that it's free because cat is
+ 
+
+ align:start position:0%
+we'll say that it's free because cat is
+a word you can say it by itself as
+
+ align:start position:0%
+a word you can say it by itself as
+ 
+
+ align:start position:0%
+a word you can say it by itself as
+opposed to the S at the end of a word
+
+ align:start position:0%
+opposed to the S at the end of a word
+ 
+
+ align:start position:0%
+opposed to the S at the end of a word
+like cats
+
+ align:start position:0%
+like cats
+ 
+
+ align:start position:0%
+like cats
+um we'll say that's a bound morpheme
+
+ align:start position:0%
+um we'll say that's a bound morpheme
+ 
+
+ align:start position:0%
+um we'll say that's a bound morpheme
+because it's not a a word on its own
+
+ align:start position:0%
+because it's not a a word on its own
+ 
+
+ align:start position:0%
+because it's not a a word on its own
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and if we're talking about bound
+
+ align:start position:0%
+and if we're talking about bound
+ 
+
+ align:start position:0%
+and if we're talking about bound
+morphemes we sort of ran through bound
+
+ align:start position:0%
+morphemes we sort of ran through bound
+ 
+
+ align:start position:0%
+morphemes we sort of ran through bound
+morphemes from a bunch of different
+
+ align:start position:0%
+morphemes from a bunch of different
+ 
+
+ align:start position:0%
+morphemes from a bunch of different
+languages we saw there are prefixes out
+
+ align:start position:0%
+languages we saw there are prefixes out
+ 
+
+ align:start position:0%
+languages we saw there are prefixes out
+there there are suffixes and there are
+
+ align:start position:0%
+there there are suffixes and there are
+ 
+
+ align:start position:0%
+there there are suffixes and there are
+other things we talked about infixes
+
+ align:start position:0%
+other things we talked about infixes
+ 
+
+ align:start position:0%
+other things we talked about infixes
+various other kinds of things there are
+
+ align:start position:0%
+various other kinds of things there are
+ 
+
+ align:start position:0%
+various other kinds of things there are
+other kinds of morphemes to talk about
+
+ align:start position:0%
+other kinds of morphemes to talk about
+ 
+
+ align:start position:0%
+other kinds of morphemes to talk about
+we eventually will
+
+ align:start position:0%
+we eventually will
+ 
+
+ align:start position:0%
+we eventually will
+um but first so what I said here was
+
+ align:start position:0%
+um but first so what I said here was
+ 
+
+ align:start position:0%
+um but first so what I said here was
+first another kind of information we're
+
+ align:start position:0%
+first another kind of information we're
+ 
+
+ align:start position:0%
+first another kind of information we're
+going to have to list but actually
+
+ align:start position:0%
+going to have to list but actually
+ 
+
+ align:start position:0%
+going to have to list but actually
+before that is any of that unclear does
+
+ align:start position:0%
+before that is any of that unclear does
+ 
+
+ align:start position:0%
+before that is any of that unclear does
+that all make sense
+
+ align:start position:0%
+that all make sense
+ 
+
+ align:start position:0%
+that all make sense
+yeah is any is everyone convinced of the
+
+ align:start position:0%
+yeah is any is everyone convinced of the
+ 
+
+ align:start position:0%
+yeah is any is everyone convinced of the
+existence of morphemes are you willing
+
+ align:start position:0%
+existence of morphemes are you willing
+ 
+
+ align:start position:0%
+existence of morphemes are you willing
+to at least assume that they exist okay
+
+ align:start position:0%
+to at least assume that they exist okay
+ 
+
+ align:start position:0%
+to at least assume that they exist okay
+um so you're used to looking words up in
+
+ align:start position:0%
+um so you're used to looking words up in
+ 
+
+ align:start position:0%
+um so you're used to looking words up in
+the dictionary but in your mental
+
+ align:start position:0%
+the dictionary but in your mental
+ 
+
+ align:start position:0%
+the dictionary but in your mental
+dictionary maybe what you have are not
+
+ align:start position:0%
+dictionary maybe what you have are not
+ 
+
+ align:start position:0%
+dictionary maybe what you have are not
+words but morphemes things that are at
+
+ align:start position:0%
+words but morphemes things that are at
+ 
+
+ align:start position:0%
+words but morphemes things that are at
+least sometimes smaller than words
+
+ align:start position:0%
+least sometimes smaller than words
+ 
+
+ align:start position:0%
+least sometimes smaller than words
+um okay so another kind of information
+
+ align:start position:0%
+um okay so another kind of information
+ 
+
+ align:start position:0%
+um okay so another kind of information
+we're gonna have to list
+
+ align:start position:0%
+we're gonna have to list
+ 
+
+ align:start position:0%
+we're gonna have to list
+think about the bound morpheme o that
+
+ align:start position:0%
+think about the bound morpheme o that
+ 
+
+ align:start position:0%
+think about the bound morpheme o that
+shows up at the end of industrial or
+
+ align:start position:0%
+shows up at the end of industrial or
+ 
+
+ align:start position:0%
+shows up at the end of industrial or
+national or autumnal
+
+ align:start position:0%
+national or autumnal
+ 
+
+ align:start position:0%
+national or autumnal
+um that's Limited in where it can go so
+
+ align:start position:0%
+um that's Limited in where it can go so
+ 
+
+ align:start position:0%
+um that's Limited in where it can go so
+there aren't words like assertile or
+
+ align:start position:0%
+there aren't words like assertile or
+ 
+
+ align:start position:0%
+there aren't words like assertile or
+impressel or industrializel
+
+ align:start position:0%
+impressel or industrializel
+ 
+
+ align:start position:0%
+impressel or industrializel
+yeah again let me pause and make sure
+
+ align:start position:0%
+yeah again let me pause and make sure
+ 
+
+ align:start position:0%
+yeah again let me pause and make sure
+that I'm not saying things that are just
+
+ align:start position:0%
+that I'm not saying things that are just
+ 
+
+ align:start position:0%
+that I'm not saying things that are just
+false I think I told you there's a
+
+ align:start position:0%
+false I think I told you there's a
+ 
+
+ align:start position:0%
+false I think I told you there's a
+danger when you're a linguist you
+
+ align:start position:0%
+danger when you're a linguist you
+ 
+
+ align:start position:0%
+danger when you're a linguist you
+gradually get out of touch with your
+
+ align:start position:0%
+gradually get out of touch with your
+ 
+
+ align:start position:0%
+gradually get out of touch with your
+native language but I'm pretty sure this
+
+ align:start position:0%
+native language but I'm pretty sure this
+ 
+
+ align:start position:0%
+native language but I'm pretty sure this
+is true
+
+ align:start position:0%
+is true
+ 
+
+ align:start position:0%
+is true
+yeah uh
+
+ align:start position:0%
+yeah uh
+ 
+
+ align:start position:0%
+yeah uh
+is there a generalization about the
+
+ align:start position:0%
+is there a generalization about the
+ 
+
+ align:start position:0%
+is there a generalization about the
+kinds of things you can add all
+
+ align:start position:0%
+kinds of things you can add all
+ 
+
+ align:start position:0%
+kinds of things you can add all
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+what are they
+
+ align:start position:0%
+what are they
+ 
+
+ align:start position:0%
+what are they
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+nouns yeah so industry and nation and
+
+ align:start position:0%
+nouns yeah so industry and nation and
+ 
+
+ align:start position:0%
+nouns yeah so industry and nation and
+Autumn are all nouns as opposed to
+
+ align:start position:0%
+Autumn are all nouns as opposed to
+ 
+
+ align:start position:0%
+Autumn are all nouns as opposed to
+assert and impress and industrialize
+
+ align:start position:0%
+assert and impress and industrialize
+ 
+
+ align:start position:0%
+assert and impress and industrialize
+which are not nouns what are they
+
+ align:start position:0%
+which are not nouns what are they
+ 
+
+ align:start position:0%
+which are not nouns what are they
+verbs yep okay and if anybody is
+
+ align:start position:0%
+verbs yep okay and if anybody is
+ 
+
+ align:start position:0%
+verbs yep okay and if anybody is
+listening to this and thinking nouns
+
+ align:start position:0%
+listening to this and thinking nouns
+ 
+
+ align:start position:0%
+listening to this and thinking nouns
+verbs what the heck uh don't worry we
+
+ align:start position:0%
+verbs what the heck uh don't worry we
+ 
+
+ align:start position:0%
+verbs what the heck uh don't worry we
+will talk more about this eventually
+
+ align:start position:0%
+will talk more about this eventually
+ 
+
+ align:start position:0%
+will talk more about this eventually
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we just said there is a word
+
+ align:start position:0%
+okay so we just said there is a word
+ 
+
+ align:start position:0%
+okay so we just said there is a word
+industrial because oh maybe I should
+
+ align:start position:0%
+industrial because oh maybe I should
+ 
+
+ align:start position:0%
+industrial because oh maybe I should
+write this on the word or it would if I
+
+ align:start position:0%
+write this on the word or it would if I
+ 
+
+ align:start position:0%
+write this on the word or it would if I
+thought there was chalk anywhere
+
+ align:start position:0%
+thought there was chalk anywhere
+ 
+
+ align:start position:0%
+thought there was chalk anywhere
+anywhere at all ah here we go I'll write
+
+ align:start position:0%
+anywhere at all ah here we go I'll write
+ 
+
+ align:start position:0%
+anywhere at all ah here we go I'll write
+it on the board right here that will be
+
+ align:start position:0%
+it on the board right here that will be
+ 
+
+ align:start position:0%
+it on the board right here that will be
+helpful
+
+ align:start position:0%
+helpful
+ 
+
+ align:start position:0%
+helpful
+now I won't I'll put it over here
+
+ align:start position:0%
+now I won't I'll put it over here
+ 
+
+ align:start position:0%
+now I won't I'll put it over here
+um we've just said all attaches to nouns
+
+ align:start position:0%
+um we've just said all attaches to nouns
+ 
+
+ align:start position:0%
+um we've just said all attaches to nouns
+and can't attach to verbs that's what's
+
+ align:start position:0%
+and can't attach to verbs that's what's
+ 
+
+ align:start position:0%
+and can't attach to verbs that's what's
+going on in the first little list there
+
+ align:start position:0%
+going on in the first little list there
+ 
+
+ align:start position:0%
+going on in the first little list there
+so a noun
+
+ align:start position:0%
+so a noun
+ 
+
+ align:start position:0%
+so a noun
+can have o on it
+
+ align:start position:0%
+can have o on it
+ 
+
+ align:start position:0%
+can have o on it
+write that again over there
+
+ align:start position:0%
+write that again over there
+ 
+
+ align:start position:0%
+write that again over there
+uh this is surely not the most efficient
+
+ align:start position:0%
+uh this is surely not the most efficient
+ 
+
+ align:start position:0%
+uh this is surely not the most efficient
+way to use the Blackboard uh is it
+
+ align:start position:0%
+way to use the Blackboard uh is it
+ 
+
+ align:start position:0%
+way to use the Blackboard uh is it
+necessary does it work can everybody see
+
+ align:start position:0%
+necessary does it work can everybody see
+ 
+
+ align:start position:0%
+necessary does it work can everybody see
+one or another of the things that I
+
+ align:start position:0%
+one or another of the things that I
+ 
+
+ align:start position:0%
+one or another of the things that I
+wrote is there anybody who can only see
+
+ align:start position:0%
+wrote is there anybody who can only see
+ 
+
+ align:start position:0%
+wrote is there anybody who can only see
+one of the things that I wrote
+
+ align:start position:0%
+one of the things that I wrote
+ 
+
+ align:start position:0%
+one of the things that I wrote
+yeah okay so it's worth it to write it
+
+ align:start position:0%
+yeah okay so it's worth it to write it
+ 
+
+ align:start position:0%
+yeah okay so it's worth it to write it
+twice okay so all attaches to nouns yeah
+
+ align:start position:0%
+twice okay so all attaches to nouns yeah
+ 
+
+ align:start position:0%
+twice okay so all attaches to nouns yeah
+and doesn't detect verbs that's why you
+
+ align:start position:0%
+and doesn't detect verbs that's why you
+ 
+
+ align:start position:0%
+and doesn't detect verbs that's why you
+can say industrial it's why you can't
+
+ align:start position:0%
+can say industrial it's why you can't
+ 
+
+ align:start position:0%
+can say industrial it's why you can't
+say industrializel yeah uh why can you
+
+ align:start position:0%
+say industrializel yeah uh why can you
+ 
+
+ align:start position:0%
+say industrializel yeah uh why can you
+say industrializational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a word
+
+ align:start position:0%
+that's a word
+ 
+
+ align:start position:0%
+that's a word
+it's kind of a long word
+
+ align:start position:0%
+it's kind of a long word
+ 
+
+ align:start position:0%
+it's kind of a long word
+industrializational I guess means having
+
+ align:start position:0%
+industrializational I guess means having
+ 
+
+ align:start position:0%
+industrializational I guess means having
+to do with industrialization
+
+ align:start position:0%
+to do with industrialization
+ 
+
+ align:start position:0%
+to do with industrialization
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+industrialization is a noun so Asian is
+
+ align:start position:0%
+industrialization is a noun so Asian is
+ 
+
+ align:start position:0%
+industrialization is a noun so Asian is
+attaching to industrialize and it is
+
+ align:start position:0%
+attaching to industrialize and it is
+ 
+
+ align:start position:0%
+attaching to industrialize and it is
+apparently creating a noun
+
+ align:start position:0%
+apparently creating a noun
+ 
+
+ align:start position:0%
+apparently creating a noun
+so at least for some kinds of morphemes
+
+ align:start position:0%
+so at least for some kinds of morphemes
+ 
+
+ align:start position:0%
+so at least for some kinds of morphemes
+we're going to want to list the kinds of
+
+ align:start position:0%
+we're going to want to list the kinds of
+ 
+
+ align:start position:0%
+we're going to want to list the kinds of
+things they attach to their input and
+
+ align:start position:0%
+things they attach to their input and
+ 
+
+ align:start position:0%
+things they attach to their input and
+then their output yeah so Asian can
+
+ align:start position:0%
+then their output yeah so Asian can
+ 
+
+ align:start position:0%
+then their output yeah so Asian can
+attach to a verb like industrialize and
+
+ align:start position:0%
+attach to a verb like industrialize and
+ 
+
+ align:start position:0%
+attach to a verb like industrialize and
+it can create a noun
+
+ align:start position:0%
+it can create a noun
+ 
+
+ align:start position:0%
+it can create a noun
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+Asian attaches to a verb and then what
+
+ align:start position:0%
+Asian attaches to a verb and then what
+ 
+
+ align:start position:0%
+Asian attaches to a verb and then what
+you get is a noun say that again if you
+
+ align:start position:0%
+you get is a noun say that again if you
+ 
+
+ align:start position:0%
+you get is a noun say that again if you
+take a verb an addition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you end up with is a noun and you
+
+ align:start position:0%
+what you end up with is a noun and you
+ 
+
+ align:start position:0%
+what you end up with is a noun and you
+know that sort of
+
+ align:start position:0%
+know that sort of
+ 
+
+ align:start position:0%
+know that sort of
+if we have intuitions about which things
+
+ align:start position:0%
+if we have intuitions about which things
+ 
+
+ align:start position:0%
+if we have intuitions about which things
+are nouns and which things aren't we
+
+ align:start position:0%
+are nouns and which things aren't we
+ 
+
+ align:start position:0%
+are nouns and which things aren't we
+have the intuition that
+
+ align:start position:0%
+have the intuition that
+ 
+
+ align:start position:0%
+have the intuition that
+industrialization is a noun but now we
+
+ align:start position:0%
+industrialization is a noun but now we
+ 
+
+ align:start position:0%
+industrialization is a noun but now we
+can sort of check our intuition by
+
+ align:start position:0%
+can sort of check our intuition by
+ 
+
+ align:start position:0%
+can sort of check our intuition by
+asking ourselves well we know that all
+
+ align:start position:0%
+asking ourselves well we know that all
+ 
+
+ align:start position:0%
+asking ourselves well we know that all
+attaches to nouns can we attach old to
+
+ align:start position:0%
+attaches to nouns can we attach old to
+ 
+
+ align:start position:0%
+attaches to nouns can we attach old to
+industrialization yes
+
+ align:start position:0%
+industrialization yes
+ 
+
+ align:start position:0%
+industrialization yes
+so our intuition is right that's a noun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay cool so there are at least some
+
+ align:start position:0%
+Okay cool so there are at least some
+ 
+
+ align:start position:0%
+Okay cool so there are at least some
+kinds of morpheme switch uh sort of
+
+ align:start position:0%
+kinds of morpheme switch uh sort of
+ 
+
+ align:start position:0%
+kinds of morpheme switch uh sort of
+convert words into other types of words
+
+ align:start position:0%
+convert words into other types of words
+ 
+
+ align:start position:0%
+convert words into other types of words
+convert nouns into verbs or in the case
+
+ align:start position:0%
+convert nouns into verbs or in the case
+ 
+
+ align:start position:0%
+convert nouns into verbs or in the case
+of all uh yeah verbs and adjectives
+
+ align:start position:0%
+of all uh yeah verbs and adjectives
+ 
+
+ align:start position:0%
+of all uh yeah verbs and adjectives
+sorry nouns into adjectives
+
+ align:start position:0%
+sorry nouns into adjectives
+ 
+
+ align:start position:0%
+sorry nouns into adjectives
+Okay so uh
+
+ align:start position:0%
+Okay so uh
+ 
+
+ align:start position:0%
+Okay so uh
+adding some things to the list I showed
+
+ align:start position:0%
+adding some things to the list I showed
+ 
+
+ align:start position:0%
+adding some things to the list I showed
+you before lexicon has morphemes in it
+
+ align:start position:0%
+you before lexicon has morphemes in it
+ 
+
+ align:start position:0%
+you before lexicon has morphemes in it
+the morphemes uh all contain information
+
+ align:start position:0%
+the morphemes uh all contain information
+ 
+
+ align:start position:0%
+the morphemes uh all contain information
+about sound and meaning and whether it's
+
+ align:start position:0%
+about sound and meaning and whether it's
+ 
+
+ align:start position:0%
+about sound and meaning and whether it's
+bound or free and if it's bound what
+
+ align:start position:0%
+bound or free and if it's bound what
+ 
+
+ align:start position:0%
+bound or free and if it's bound what
+kind of bound morpheme it is prefix or a
+
+ align:start position:0%
+kind of bound morpheme it is prefix or a
+ 
+
+ align:start position:0%
+kind of bound morpheme it is prefix or a
+suffix or a tone or a
+
+ align:start position:0%
+suffix or a tone or a
+ 
+
+ align:start position:0%
+suffix or a tone or a
+an infix or whatever
+
+ align:start position:0%
+an infix or whatever
+ 
+
+ align:start position:0%
+an infix or whatever
+and also what kind of morpheme they can
+
+ align:start position:0%
+and also what kind of morpheme they can
+ 
+
+ align:start position:0%
+and also what kind of morpheme they can
+attach to do they attach to nouns or
+
+ align:start position:0%
+attach to do they attach to nouns or
+ 
+
+ align:start position:0%
+attach to do they attach to nouns or
+verbs or what and at least for some
+
+ align:start position:0%
+verbs or what and at least for some
+ 
+
+ align:start position:0%
+verbs or what and at least for some
+kinds of morphemes what the result is
+
+ align:start position:0%
+kinds of morphemes what the result is
+ 
+
+ align:start position:0%
+kinds of morphemes what the result is
+whether you create a noun or a verb or
+
+ align:start position:0%
+whether you create a noun or a verb or
+ 
+
+ align:start position:0%
+whether you create a noun or a verb or
+an adjective or whatever yeah it's a
+
+ align:start position:0%
+an adjective or whatever yeah it's a
+ 
+
+ align:start position:0%
+an adjective or whatever yeah it's a
+little sound okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+actually sometimes we'll have to say
+
+ align:start position:0%
+actually sometimes we'll have to say
+ 
+
+ align:start position:0%
+actually sometimes we'll have to say
+more than that
+
+ align:start position:0%
+more than that
+ 
+
+ align:start position:0%
+more than that
+so sincere chaste scarce curious deep
+
+ align:start position:0%
+so sincere chaste scarce curious deep
+ 
+
+ align:start position:0%
+so sincere chaste scarce curious deep
+wide and warm what are those
+
+ align:start position:0%
+wide and warm what are those
+ 
+
+ align:start position:0%
+wide and warm what are those
+they're adjectives
+
+ align:start position:0%
+they're adjectives
+ 
+
+ align:start position:0%
+they're adjectives
+and when you add IDI to sincere you get
+
+ align:start position:0%
+and when you add IDI to sincere you get
+ 
+
+ align:start position:0%
+and when you add IDI to sincere you get
+sincerity or when you add idiot to
+
+ align:start position:0%
+sincerity or when you add idiot to
+ 
+
+ align:start position:0%
+sincerity or when you add idiot to
+chaste you get Chastity and what our
+
+ align:start position:0%
+chaste you get Chastity and what our
+ 
+
+ align:start position:0%
+chaste you get Chastity and what our
+sincerity in chastity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're nouns okay so idiot is attaching
+
+ align:start position:0%
+they're nouns okay so idiot is attaching
+ 
+
+ align:start position:0%
+they're nouns okay so idiot is attaching
+to an adjective and it's making a noun
+
+ align:start position:0%
+to an adjective and it's making a noun
+ 
+
+ align:start position:0%
+to an adjective and it's making a noun
+when you add
+
+ align:start position:0%
+when you add
+ 
+
+ align:start position:0%
+when you add
+to Deep
+
+ align:start position:0%
+to Deep
+ 
+
+ align:start position:0%
+to Deep
+you get depth yeah or when you have the
+
+ align:start position:0%
+you get depth yeah or when you have the
+ 
+
+ align:start position:0%
+you get depth yeah or when you have the
+wide you get width uh so is attaching to
+
+ align:start position:0%
+wide you get width uh so is attaching to
+ 
+
+ align:start position:0%
+wide you get width uh so is attaching to
+an adjective and what is it creating
+
+ align:start position:0%
+an adjective and what is it creating
+ 
+
+ align:start position:0%
+an adjective and what is it creating
+a noun yeah so here we have two suffixes
+
+ align:start position:0%
+a noun yeah so here we have two suffixes
+ 
+
+ align:start position:0%
+a noun yeah so here we have two suffixes
+they both seem to do the same thing they
+
+ align:start position:0%
+they both seem to do the same thing they
+ 
+
+ align:start position:0%
+they both seem to do the same thing they
+both attach to adjectives and create
+
+ align:start position:0%
+both attach to adjectives and create
+ 
+
+ align:start position:0%
+both attach to adjectives and create
+nouns
+
+ align:start position:0%
+nouns
+ 
+
+ align:start position:0%
+nouns
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but we're going to have to say something
+
+ align:start position:0%
+but we're going to have to say something
+ 
+
+ align:start position:0%
+but we're going to have to say something
+else right because you cannot say deputy
+
+ align:start position:0%
+else right because you cannot say deputy
+ 
+
+ align:start position:0%
+else right because you cannot say deputy
+right or sincereth yeah those are not
+
+ align:start position:0%
+right or sincereth yeah those are not
+ 
+
+ align:start position:0%
+right or sincereth yeah those are not
+words yeah so you can't add the to the
+
+ align:start position:0%
+words yeah so you can't add the to the
+ 
+
+ align:start position:0%
+words yeah so you can't add the to the
+adjectives at the top and you can't add
+
+ align:start position:0%
+adjectives at the top and you can't add
+ 
+
+ align:start position:0%
+adjectives at the top and you can't add
+80 to the adjectives at the bottom
+
+ align:start position:0%
+80 to the adjectives at the bottom
+ 
+
+ align:start position:0%
+80 to the adjectives at the bottom
+so sometimes it's not enough to say this
+
+ align:start position:0%
+so sometimes it's not enough to say this
+ 
+
+ align:start position:0%
+so sometimes it's not enough to say this
+attaches to adjectives you have to say
+
+ align:start position:0%
+attaches to adjectives you have to say
+ 
+
+ align:start position:0%
+attaches to adjectives you have to say
+it attaches to adjectives in this list
+
+ align:start position:0%
+it attaches to adjectives in this list
+ 
+
+ align:start position:0%
+it attaches to adjectives in this list
+yeah or we have to understand something
+
+ align:start position:0%
+yeah or we have to understand something
+ 
+
+ align:start position:0%
+yeah or we have to understand something
+more about the adjectives
+
+ align:start position:0%
+more about the adjectives
+ 
+
+ align:start position:0%
+more about the adjectives
+anybody have a guess about why there are
+
+ align:start position:0%
+anybody have a guess about why there are
+ 
+
+ align:start position:0%
+anybody have a guess about why there are
+two kinds of adjectives in English
+
+ align:start position:0%
+two kinds of adjectives in English
+ 
+
+ align:start position:0%
+two kinds of adjectives in English
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think you were going to be right but
+
+ align:start position:0%
+I think you were going to be right but
+ 
+
+ align:start position:0%
+I think you were going to be right but
+did you convince yourself not to say
+
+ align:start position:0%
+did you convince yourself not to say
+ 
+
+ align:start position:0%
+did you convince yourself not to say
+that because
+
+ align:start position:0%
+that because
+ 
+
+ align:start position:0%
+that because
+because yeah but it should have yeah
+
+ align:start position:0%
+because yeah but it should have yeah
+ 
+
+ align:start position:0%
+because yeah but it should have yeah
+yeah so the ones the ones at the top yes
+
+ align:start position:0%
+yeah so the ones the ones at the top yes
+ 
+
+ align:start position:0%
+yeah so the ones the ones at the top yes
+look sort of latinate you're absolutely
+
+ align:start position:0%
+look sort of latinate you're absolutely
+ 
+
+ align:start position:0%
+look sort of latinate you're absolutely
+right and the ones at the bottom uh look
+
+ align:start position:0%
+right and the ones at the bottom uh look
+ 
+
+ align:start position:0%
+right and the ones at the bottom uh look
+sort of dramatic yeah
+
+ align:start position:0%
+sort of dramatic yeah
+ 
+
+ align:start position:0%
+sort of dramatic yeah
+that's right yeah so there there are a
+
+ align:start position:0%
+that's right yeah so there there are a
+ 
+
+ align:start position:0%
+that's right yeah so there there are a
+few things like this where it's a result
+
+ align:start position:0%
+few things like this where it's a result
+ 
+
+ align:start position:0%
+few things like this where it's a result
+of English History that we have suffixes
+
+ align:start position:0%
+of English History that we have suffixes
+ 
+
+ align:start position:0%
+of English History that we have suffixes
+that we got from IDI is something that
+
+ align:start position:0%
+that we got from IDI is something that
+ 
+
+ align:start position:0%
+that we got from IDI is something that
+we got from from French and is something
+
+ align:start position:0%
+we got from from French and is something
+ 
+
+ align:start position:0%
+we got from from French and is something
+we got from Germanic uh and so yeah
+
+ align:start position:0%
+we got from Germanic uh and so yeah
+ 
+
+ align:start position:0%
+we got from Germanic uh and so yeah
+these suffixes are sort of maintaining
+
+ align:start position:0%
+these suffixes are sort of maintaining
+ 
+
+ align:start position:0%
+these suffixes are sort of maintaining
+their their history to a certain extent
+
+ align:start position:0%
+their their history to a certain extent
+ 
+
+ align:start position:0%
+their their history to a certain extent
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is related to that yes yep yep score
+
+ align:start position:0%
+it is related to that yes yep yep score
+ 
+
+ align:start position:0%
+it is related to that yes yep yep score
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+good point yep okay so I mean uh you can
+
+ align:start position:0%
+good point yep okay so I mean uh you can
+ 
+
+ align:start position:0%
+good point yep okay so I mean uh you can
+be a native speaker of English and not
+
+ align:start position:0%
+be a native speaker of English and not
+ 
+
+ align:start position:0%
+be a native speaker of English and not
+know this it's not like we're all you
+
+ align:start position:0%
+know this it's not like we're all you
+ 
+
+ align:start position:0%
+know this it's not like we're all you
+know remembering oh yeah those are the
+
+ align:start position:0%
+know remembering oh yeah those are the
+ 
+
+ align:start position:0%
+know remembering oh yeah those are the
+Germanic adjectives those are the
+
+ align:start position:0%
+Germanic adjectives those are the
+ 
+
+ align:start position:0%
+Germanic adjectives those are the
+latinate adjectives so I'll be sure to
+
+ align:start position:0%
+latinate adjectives so I'll be sure to
+ 
+
+ align:start position:0%
+latinate adjectives so I'll be sure to
+add 80 to that one and to that one but
+
+ align:start position:0%
+add 80 to that one and to that one but
+ 
+
+ align:start position:0%
+add 80 to that one and to that one but
+uh you know on some level we have to say
+
+ align:start position:0%
+uh you know on some level we have to say
+ 
+
+ align:start position:0%
+uh you know on some level we have to say
+yeah there are adjectives of class one
+
+ align:start position:0%
+yeah there are adjectives of class one
+ 
+
+ align:start position:0%
+yeah there are adjectives of class one
+and adjectives of class two or something
+
+ align:start position:0%
+and adjectives of class two or something
+ 
+
+ align:start position:0%
+and adjectives of class two or something
+there are purple adjectives and green
+
+ align:start position:0%
+there are purple adjectives and green
+ 
+
+ align:start position:0%
+there are purple adjectives and green
+adjectives something you know we have to
+
+ align:start position:0%
+adjectives something you know we have to
+ 
+
+ align:start position:0%
+adjectives something you know we have to
+distinguish these from each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very I mean this I'm giving you English
+
+ align:start position:0%
+very I mean this I'm giving you English
+ 
+
+ align:start position:0%
+very I mean this I'm giving you English
+examples this is a very common situation
+
+ align:start position:0%
+examples this is a very common situation
+ 
+
+ align:start position:0%
+examples this is a very common situation
+lots of languages have been in intense
+
+ align:start position:0%
+lots of languages have been in intense
+ 
+
+ align:start position:0%
+lots of languages have been in intense
+burrowing uh situations at some point in
+
+ align:start position:0%
+burrowing uh situations at some point in
+ 
+
+ align:start position:0%
+burrowing uh situations at some point in
+their history with uh weird results like
+
+ align:start position:0%
+their history with uh weird results like
+ 
+
+ align:start position:0%
+their history with uh weird results like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we've talked about this a little bit uh
+
+ align:start position:0%
+we've talked about this a little bit uh
+ 
+
+ align:start position:0%
+we've talked about this a little bit uh
+so uh I said when you add the plural
+
+ align:start position:0%
+so uh I said when you add the plural
+ 
+
+ align:start position:0%
+so uh I said when you add the plural
+suffix to cats and dogs so one of the
+
+ align:start position:0%
+suffix to cats and dogs so one of the
+ 
+
+ align:start position:0%
+suffix to cats and dogs so one of the
+first things I said to you uh it's
+
+ align:start position:0%
+first things I said to you uh it's
+ 
+
+ align:start position:0%
+first things I said to you uh it's
+pronounced differently on cats than it
+
+ align:start position:0%
+pronounced differently on cats than it
+ 
+
+ align:start position:0%
+pronounced differently on cats than it
+is on dogs yeah
+
+ align:start position:0%
+is on dogs yeah
+ 
+
+ align:start position:0%
+is on dogs yeah
+um and we talked about why and we're
+
+ align:start position:0%
+um and we talked about why and we're
+ 
+
+ align:start position:0%
+um and we talked about why and we're
+going to talk more about why later uh
+
+ align:start position:0%
+going to talk more about why later uh
+ 
+
+ align:start position:0%
+going to talk more about why later uh
+this is the kind of thing that happens
+
+ align:start position:0%
+this is the kind of thing that happens
+ 
+
+ align:start position:0%
+this is the kind of thing that happens
+sometimes when you add one morpheme to
+
+ align:start position:0%
+sometimes when you add one morpheme to
+ 
+
+ align:start position:0%
+sometimes when you add one morpheme to
+another morpheme one or another or both
+
+ align:start position:0%
+another morpheme one or another or both
+ 
+
+ align:start position:0%
+another morpheme one or another or both
+of the morphemes changes a little bit
+
+ align:start position:0%
+of the morphemes changes a little bit
+ 
+
+ align:start position:0%
+of the morphemes changes a little bit
+we'll talk a lot about this as we start
+
+ align:start position:0%
+we'll talk a lot about this as we start
+ 
+
+ align:start position:0%
+we'll talk a lot about this as we start
+talking about sound change uh phonology
+
+ align:start position:0%
+talking about sound change uh phonology
+ 
+
+ align:start position:0%
+talking about sound change uh phonology
+yeah which is our next topic
+
+ align:start position:0%
+yeah which is our next topic
+ 
+
+ align:start position:0%
+yeah which is our next topic
+but for now we can just pause and notice
+
+ align:start position:0%
+but for now we can just pause and notice
+ 
+
+ align:start position:0%
+but for now we can just pause and notice
+yeah uh if you add o to Electric you get
+
+ align:start position:0%
+yeah uh if you add o to Electric you get
+ 
+
+ align:start position:0%
+yeah uh if you add o to Electric you get
+electrical but if you add any to
+
+ align:start position:0%
+electrical but if you add any to
+ 
+
+ align:start position:0%
+electrical but if you add any to
+Electric you don't get electricity
+
+ align:start position:0%
+Electric you don't get electricity
+ 
+
+ align:start position:0%
+Electric you don't get electricity
+uh you get electricity
+
+ align:start position:0%
+uh you get electricity
+ 
+
+ align:start position:0%
+uh you get electricity
+yeah it's not because electricity would
+
+ align:start position:0%
+yeah it's not because electricity would
+ 
+
+ align:start position:0%
+yeah it's not because electricity would
+be hard to say yeah it's uh just you
+
+ align:start position:0%
+be hard to say yeah it's uh just you
+ 
+
+ align:start position:0%
+be hard to say yeah it's uh just you
+know we have this idiosyncratic sound
+
+ align:start position:0%
+know we have this idiosyncratic sound
+ 
+
+ align:start position:0%
+know we have this idiosyncratic sound
+change which we inherited again from
+
+ align:start position:0%
+change which we inherited again from
+ 
+
+ align:start position:0%
+change which we inherited again from
+from French uh that softens the K2 and S
+
+ align:start position:0%
+from French uh that softens the K2 and S
+ 
+
+ align:start position:0%
+from French uh that softens the K2 and S
+there yeah
+
+ align:start position:0%
+there yeah
+ 
+
+ align:start position:0%
+there yeah
+I'm sorry say it again
+
+ align:start position:0%
+I'm sorry say it again
+ 
+
+ align:start position:0%
+I'm sorry say it again
+oh ideation credit means
+
+ align:start position:0%
+oh ideation credit means
+ 
+
+ align:start position:0%
+oh ideation credit means
+what does it mean what do I mean when I
+
+ align:start position:0%
+what does it mean what do I mean when I
+ 
+
+ align:start position:0%
+what does it mean what do I mean when I
+say you do syncretic it means you
+
+ align:start position:0%
+say you do syncretic it means you
+ 
+
+ align:start position:0%
+say you do syncretic it means you
+sometimes have to say this particular
+
+ align:start position:0%
+sometimes have to say this particular
+ 
+
+ align:start position:0%
+sometimes have to say this particular
+morpheme has two different forms
+
+ align:start position:0%
+morpheme has two different forms
+ 
+
+ align:start position:0%
+morpheme has two different forms
+depending on what it combines with so
+
+ align:start position:0%
+depending on what it combines with so
+ 
+
+ align:start position:0%
+depending on what it combines with so
+you have to say more about that so
+
+ align:start position:0%
+you have to say more about that so
+ 
+
+ align:start position:0%
+you have to say more about that so
+idiosyncratic means special having to do
+
+ align:start position:0%
+idiosyncratic means special having to do
+ 
+
+ align:start position:0%
+idiosyncratic means special having to do
+something special to do with that right
+
+ align:start position:0%
+something special to do with that right
+ 
+
+ align:start position:0%
+something special to do with that right
+so the suffix ick at the end of electric
+
+ align:start position:0%
+so the suffix ick at the end of electric
+ 
+
+ align:start position:0%
+so the suffix ick at the end of electric
+chain will change to is before IDI yeah
+
+ align:start position:0%
+chain will change to is before IDI yeah
+ 
+
+ align:start position:0%
+chain will change to is before IDI yeah
+yeah and there's more to say than that
+
+ align:start position:0%
+yeah and there's more to say than that
+ 
+
+ align:start position:0%
+yeah and there's more to say than that
+but you have to say something that has
+
+ align:start position:0%
+but you have to say something that has
+ 
+
+ align:start position:0%
+but you have to say something that has
+that consequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarly the past tense uh it's like
+
+ align:start position:0%
+similarly the past tense uh it's like
+ 
+
+ align:start position:0%
+similarly the past tense uh it's like
+the plural suffix which can be either Z
+
+ align:start position:0%
+the plural suffix which can be either Z
+ 
+
+ align:start position:0%
+the plural suffix which can be either Z
+or S like in cats and dogs uh has a
+
+ align:start position:0%
+or S like in cats and dogs uh has a
+ 
+
+ align:start position:0%
+or S like in cats and dogs uh has a
+bunch of different forms
+
+ align:start position:0%
+bunch of different forms
+ 
+
+ align:start position:0%
+bunch of different forms
+um sometimes it can be more of a D sound
+
+ align:start position:0%
+um sometimes it can be more of a D sound
+ 
+
+ align:start position:0%
+um sometimes it can be more of a D sound
+like in hand sometimes it can be more of
+
+ align:start position:0%
+like in hand sometimes it can be more of
+ 
+
+ align:start position:0%
+like in hand sometimes it can be more of
+a t sound like in lept
+
+ align:start position:0%
+a t sound like in lept
+ 
+
+ align:start position:0%
+a t sound like in lept
+and the verb itself can undergo changes
+
+ align:start position:0%
+and the verb itself can undergo changes
+ 
+
+ align:start position:0%
+and the verb itself can undergo changes
+when you add the suffix to it right so
+
+ align:start position:0%
+when you add the suffix to it right so
+ 
+
+ align:start position:0%
+when you add the suffix to it right so
+the past tense of hum is hummed that's
+
+ align:start position:0%
+the past tense of hum is hummed that's
+ 
+
+ align:start position:0%
+the past tense of hum is hummed that's
+all fairly peaceful uh but the past
+
+ align:start position:0%
+all fairly peaceful uh but the past
+ 
+
+ align:start position:0%
+all fairly peaceful uh but the past
+tense of leap is not leaped it's leapt
+
+ align:start position:0%
+tense of leap is not leaped it's leapt
+ 
+
+ align:start position:0%
+tense of leap is not leaped it's leapt
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+the past tense of go is not goad it's
+
+ align:start position:0%
+the past tense of go is not goad it's
+ 
+
+ align:start position:0%
+the past tense of go is not goad it's
+went
+
+ align:start position:0%
+went
+ 
+
+ align:start position:0%
+went
+case where we it's what's called
+
+ align:start position:0%
+case where we it's what's called
+ 
+
+ align:start position:0%
+case where we it's what's called
+depletion so uh English speakers at some
+
+ align:start position:0%
+depletion so uh English speakers at some
+ 
+
+ align:start position:0%
+depletion so uh English speakers at some
+point in the history of English for
+
+ align:start position:0%
+point in the history of English for
+ 
+
+ align:start position:0%
+point in the history of English for
+mysterious reasons of their own decided
+
+ align:start position:0%
+mysterious reasons of their own decided
+ 
+
+ align:start position:0%
+mysterious reasons of their own decided
+that the past tense of go should borrow
+
+ align:start position:0%
+that the past tense of go should borrow
+ 
+
+ align:start position:0%
+that the past tense of go should borrow
+that to go should borrow its past tense
+
+ align:start position:0%
+that to go should borrow its past tense
+ 
+
+ align:start position:0%
+that to go should borrow its past tense
+from another verb so for the past tense
+
+ align:start position:0%
+from another verb so for the past tense
+ 
+
+ align:start position:0%
+from another verb so for the past tense
+of go we use the past tense of another
+
+ align:start position:0%
+of go we use the past tense of another
+ 
+
+ align:start position:0%
+of go we use the past tense of another
+verb wend as in to end your way and so
+
+ align:start position:0%
+verb wend as in to end your way and so
+ 
+
+ align:start position:0%
+verb wend as in to end your way and so
+and so the result of the past tense of
+
+ align:start position:0%
+and so the result of the past tense of
+ 
+
+ align:start position:0%
+and so the result of the past tense of
+go it's no longer goad it's now went
+
+ align:start position:0%
+go it's no longer goad it's now went
+ 
+
+ align:start position:0%
+go it's no longer goad it's now went
+languages do things like this be
+
+ align:start position:0%
+languages do things like this be
+ 
+
+ align:start position:0%
+languages do things like this be
+interesting to try to understand why or
+
+ align:start position:0%
+interesting to try to understand why or
+ 
+
+ align:start position:0%
+interesting to try to understand why or
+similarly sing in sang past tense of
+
+ align:start position:0%
+similarly sing in sang past tense of
+ 
+
+ align:start position:0%
+similarly sing in sang past tense of
+sing there's no D or t or anything you
+
+ align:start position:0%
+sing there's no D or t or anything you
+ 
+
+ align:start position:0%
+sing there's no D or t or anything you
+just change the vowel so there are cases
+
+ align:start position:0%
+just change the vowel so there are cases
+ 
+
+ align:start position:0%
+just change the vowel so there are cases
+where a morpheme will have different
+
+ align:start position:0%
+where a morpheme will have different
+ 
+
+ align:start position:0%
+where a morpheme will have different
+forms depending on what it's combining
+
+ align:start position:0%
+forms depending on what it's combining
+ 
+
+ align:start position:0%
+forms depending on what it's combining
+with that's the quick and dirty way of
+
+ align:start position:0%
+with that's the quick and dirty way of
+ 
+
+ align:start position:0%
+with that's the quick and dirty way of
+describing everything that's on the
+
+ align:start position:0%
+describing everything that's on the
+ 
+
+ align:start position:0%
+describing everything that's on the
+screen here yeah
+
+ align:start position:0%
+screen here yeah
+ 
+
+ align:start position:0%
+screen here yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um the technical term for what's going
+
+ align:start position:0%
+um the technical term for what's going
+ 
+
+ align:start position:0%
+um the technical term for what's going
+on here we say that when you have a
+
+ align:start position:0%
+on here we say that when you have a
+ 
+
+ align:start position:0%
+on here we say that when you have a
+morpheme that has two different forms
+
+ align:start position:0%
+morpheme that has two different forms
+ 
+
+ align:start position:0%
+morpheme that has two different forms
+the two different forms or multiple
+
+ align:start position:0%
+the two different forms or multiple
+ 
+
+ align:start position:0%
+the two different forms or multiple
+different forms sometimes it's more than
+
+ align:start position:0%
+different forms sometimes it's more than
+ 
+
+ align:start position:0%
+different forms sometimes it's more than
+two uh the different forms of a morpheme
+
+ align:start position:0%
+two uh the different forms of a morpheme
+ 
+
+ align:start position:0%
+two uh the different forms of a morpheme
+that it takes under different
+
+ align:start position:0%
+that it takes under different
+ 
+
+ align:start position:0%
+that it takes under different
+morphological circumstances those things
+
+ align:start position:0%
+morphological circumstances those things
+ 
+
+ align:start position:0%
+morphological circumstances those things
+are called allomorphs so we say that uh
+
+ align:start position:0%
+are called allomorphs so we say that uh
+ 
+
+ align:start position:0%
+are called allomorphs so we say that uh
+for example the D and the T past tenses
+
+ align:start position:0%
+for example the D and the T past tenses
+ 
+
+ align:start position:0%
+for example the D and the T past tenses
+are two alomorphs of the past tense or
+
+ align:start position:0%
+are two alomorphs of the past tense or
+ 
+
+ align:start position:0%
+are two alomorphs of the past tense or
+that leap and LEP are the Allen morphs
+
+ align:start position:0%
+that leap and LEP are the Allen morphs
+ 
+
+ align:start position:0%
+that leap and LEP are the Allen morphs
+of the verb leap the verb means jump
+
+ align:start position:0%
+of the verb leap the verb means jump
+ 
+
+ align:start position:0%
+of the verb leap the verb means jump
+yeah yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I'm just trying to call your
+
+ align:start position:0%
+oh I'm just trying to call your
+ 
+
+ align:start position:0%
+oh I'm just trying to call your
+attention to the fact that it's
+
+ align:start position:0%
+attention to the fact that it's
+ 
+
+ align:start position:0%
+attention to the fact that it's
+pronounced differently eventually those
+
+ align:start position:0%
+pronounced differently eventually those
+ 
+
+ align:start position:0%
+pronounced differently eventually those
+brackets will mean something but we
+
+ align:start position:0%
+brackets will mean something but we
+ 
+
+ align:start position:0%
+brackets will mean something but we
+haven't gotten far enough yet to get
+
+ align:start position:0%
+haven't gotten far enough yet to get
+ 
+
+ align:start position:0%
+haven't gotten far enough yet to get
+them to mean anything yeah so right now
+
+ align:start position:0%
+them to mean anything yeah so right now
+ 
+
+ align:start position:0%
+them to mean anything yeah so right now
+all I'm doing is calling if I had said
+
+ align:start position:0%
+all I'm doing is calling if I had said
+ 
+
+ align:start position:0%
+all I'm doing is calling if I had said
+leap leapt uh I would have spelled lept
+
+ align:start position:0%
+leap leapt uh I would have spelled lept
+ 
+
+ align:start position:0%
+leap leapt uh I would have spelled lept
+the same way I'm spelling leap we would
+
+ align:start position:0%
+the same way I'm spelling leap we would
+ 
+
+ align:start position:0%
+the same way I'm spelling leap we would
+just pronounce it differently because
+
+ align:start position:0%
+just pronounce it differently because
+ 
+
+ align:start position:0%
+just pronounce it differently because
+English spelling is insane
+
+ align:start position:0%
+English spelling is insane
+ 
+
+ align:start position:0%
+English spelling is insane
+um and so I'm just putting the brackets
+
+ align:start position:0%
+um and so I'm just putting the brackets
+ 
+
+ align:start position:0%
+um and so I'm just putting the brackets
+there to to as a warning sign yeah
+
+ align:start position:0%
+there to to as a warning sign yeah
+ 
+
+ align:start position:0%
+there to to as a warning sign yeah
+here's a place where the spelling is
+
+ align:start position:0%
+here's a place where the spelling is
+ 
+
+ align:start position:0%
+here's a place where the spelling is
+unreliable yeah
+
+ align:start position:0%
+unreliable yeah
+ 
+
+ align:start position:0%
+unreliable yeah
+good question eventually we'll figure
+
+ align:start position:0%
+good question eventually we'll figure
+ 
+
+ align:start position:0%
+good question eventually we'll figure
+out what how to talk about that yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so right so I called it D and T because
+
+ align:start position:0%
+so right so I called it D and T because
+ 
+
+ align:start position:0%
+so right so I called it D and T because
+hummed the past tense of hum
+
+ align:start position:0%
+hummed the past tense of hum
+ 
+
+ align:start position:0%
+hummed the past tense of hum
+although we spell it with an E before
+
+ align:start position:0%
+although we spell it with an E before
+ 
+
+ align:start position:0%
+although we spell it with an E before
+the D if you say it
+
+ align:start position:0%
+the D if you say it
+ 
+
+ align:start position:0%
+the D if you say it
+I think there's only one vowel in that
+
+ align:start position:0%
+I think there's only one vowel in that
+ 
+
+ align:start position:0%
+I think there's only one vowel in that
+word it's hummed right we're not saying
+
+ align:start position:0%
+word it's hummed right we're not saying
+ 
+
+ align:start position:0%
+word it's hummed right we're not saying
+Hamid
+
+ align:start position:0%
+Hamid
+ 
+
+ align:start position:0%
+Hamid
+that's not the past tense of humid
+
+ align:start position:0%
+that's not the past tense of humid
+ 
+
+ align:start position:0%
+that's not the past tense of humid
+yeah yeah so I'm trying to just spell it
+
+ align:start position:0%
+yeah yeah so I'm trying to just spell it
+ 
+
+ align:start position:0%
+yeah yeah so I'm trying to just spell it
+sound which is hard because we haven't
+
+ align:start position:0%
+sound which is hard because we haven't
+ 
+
+ align:start position:0%
+sound which is hard because we haven't
+done phonology yet yeah but uh so but
+
+ align:start position:0%
+done phonology yet yeah but uh so but
+ 
+
+ align:start position:0%
+done phonology yet yeah but uh so but
+that's a really good question
+
+ align:start position:0%
+that's a really good question
+ 
+
+ align:start position:0%
+that's a really good question
+um this is one of many places where
+
+ align:start position:0%
+um this is one of many places where
+ 
+
+ align:start position:0%
+um this is one of many places where
+English spelling will get you in trouble
+
+ align:start position:0%
+English spelling will get you in trouble
+ 
+
+ align:start position:0%
+English spelling will get you in trouble
+uh because English is spelled uh
+
+ align:start position:0%
+uh because English is spelled uh
+ 
+
+ align:start position:0%
+uh because English is spelled uh
+according to rules that are designed to
+
+ align:start position:0%
+according to rules that are designed to
+ 
+
+ align:start position:0%
+according to rules that are designed to
+repel Invaders yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah any questions about any of this
+
+ align:start position:0%
+yeah any questions about any of this
+ 
+
+ align:start position:0%
+yeah any questions about any of this
+these are really good questions you guys
+
+ align:start position:0%
+these are really good questions you guys
+ 
+
+ align:start position:0%
+these are really good questions you guys
+are asking
+
+ align:start position:0%
+are asking
+ 
+
+ align:start position:0%
+are asking
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes so uh sometimes so you know we will
+
+ align:start position:0%
+yes so uh sometimes so you know we will
+ 
+
+ align:start position:0%
+yes so uh sometimes so you know we will
+we will get a chance to talk more in
+
+ align:start position:0%
+we will get a chance to talk more in
+ 
+
+ align:start position:0%
+we will get a chance to talk more in
+fact we'll talk more very soon about how
+
+ align:start position:0%
+fact we'll talk more very soon about how
+ 
+
+ align:start position:0%
+fact we'll talk more very soon about how
+exactly to talk about alamorphy this
+
+ align:start position:0%
+exactly to talk about alamorphy this
+ 
+
+ align:start position:0%
+exactly to talk about alamorphy this
+property of morphemes of having more
+
+ align:start position:0%
+property of morphemes of having more
+ 
+
+ align:start position:0%
+property of morphemes of having more
+than one form of having allomorphs
+
+ align:start position:0%
+than one form of having allomorphs
+ 
+
+ align:start position:0%
+than one form of having allomorphs
+um all we've said so far is sometimes
+
+ align:start position:0%
+um all we've said so far is sometimes
+ 
+
+ align:start position:0%
+um all we've said so far is sometimes
+morphemes have alomorphs yeah so
+
+ align:start position:0%
+morphemes have alomorphs yeah so
+ 
+
+ align:start position:0%
+morphemes have alomorphs yeah so
+depending on what they combine with they
+
+ align:start position:0%
+depending on what they combine with they
+ 
+
+ align:start position:0%
+depending on what they combine with they
+take different forms
+
+ align:start position:0%
+take different forms
+ 
+
+ align:start position:0%
+take different forms
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's often what's called a default
+
+ align:start position:0%
+there's often what's called a default
+ 
+
+ align:start position:0%
+there's often what's called a default
+allomorph that is uh there's a morpheme
+
+ align:start position:0%
+allomorph that is uh there's a morpheme
+ 
+
+ align:start position:0%
+allomorph that is uh there's a morpheme
+that is the basic one that shows up most
+
+ align:start position:0%
+that is the basic one that shows up most
+ 
+
+ align:start position:0%
+that is the basic one that shows up most
+of the time and when we're making our
+
+ align:start position:0%
+of the time and when we're making our
+ 
+
+ align:start position:0%
+of the time and when we're making our
+special statements about other forms uh
+
+ align:start position:0%
+special statements about other forms uh
+ 
+
+ align:start position:0%
+special statements about other forms uh
+well they're going to be about the other
+
+ align:start position:0%
+well they're going to be about the other
+ 
+
+ align:start position:0%
+well they're going to be about the other
+forms so there's going to be the form of
+
+ align:start position:0%
+forms so there's going to be the form of
+ 
+
+ align:start position:0%
+forms so there's going to be the form of
+the morpheme that you start off with and
+
+ align:start position:0%
+the morpheme that you start off with and
+ 
+
+ align:start position:0%
+the morpheme that you start off with and
+then you will do things to it to create
+
+ align:start position:0%
+then you will do things to it to create
+ 
+
+ align:start position:0%
+then you will do things to it to create
+the other allomorphs
+
+ align:start position:0%
+the other allomorphs
+ 
+
+ align:start position:0%
+the other allomorphs
+um so for example uh the default
+
+ align:start position:0%
+um so for example uh the default
+ 
+
+ align:start position:0%
+um so for example uh the default
+assumption if I'm telling you about a
+
+ align:start position:0%
+assumption if I'm telling you about a
+ 
+
+ align:start position:0%
+assumption if I'm telling you about a
+verb I've made up a verb it's flip to
+
+ align:start position:0%
+verb I've made up a verb it's flip to
+ 
+
+ align:start position:0%
+verb I've made up a verb it's flip to
+Fleep it's a special move in soccer in
+
+ align:start position:0%
+Fleep it's a special move in soccer in
+ 
+
+ align:start position:0%
+Fleep it's a special move in soccer in
+which you do a headstand and kick with
+
+ align:start position:0%
+which you do a headstand and kick with
+ 
+
+ align:start position:0%
+which you do a headstand and kick with
+your feet over your head uh I just made
+
+ align:start position:0%
+your feet over your head uh I just made
+ 
+
+ align:start position:0%
+your feet over your head uh I just made
+that up the the past tense of leap
+
+ align:start position:0%
+that up the the past tense of leap
+ 
+
+ align:start position:0%
+that up the the past tense of leap
+you're going to assume that it's flipped
+
+ align:start position:0%
+you're going to assume that it's flipped
+ 
+
+ align:start position:0%
+you're going to assume that it's flipped
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um it could be flipped yeah uh it could
+
+ align:start position:0%
+um it could be flipped yeah uh it could
+ 
+
+ align:start position:0%
+um it could be flipped yeah uh it could
+be like leap but you're going to assume
+
+ align:start position:0%
+be like leap but you're going to assume
+ 
+
+ align:start position:0%
+be like leap but you're going to assume
+that it's flipped that is the default
+
+ align:start position:0%
+that it's flipped that is the default
+ 
+
+ align:start position:0%
+that it's flipped that is the default
+you assume uh that morphemes don't have
+
+ align:start position:0%
+you assume uh that morphemes don't have
+ 
+
+ align:start position:0%
+you assume uh that morphemes don't have
+uh allomorphs other than the one in this
+
+ align:start position:0%
+uh allomorphs other than the one in this
+ 
+
+ align:start position:0%
+uh allomorphs other than the one in this
+case that shows up in sort of ordinary
+
+ align:start position:0%
+case that shows up in sort of ordinary
+ 
+
+ align:start position:0%
+case that shows up in sort of ordinary
+present tense circumstances
+
+ align:start position:0%
+present tense circumstances
+ 
+
+ align:start position:0%
+present tense circumstances
+when they're not combining
+
+ align:start position:0%
+when they're not combining
+ 
+
+ align:start position:0%
+when they're not combining
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah is this any of this surprising or
+
+ align:start position:0%
+yeah is this any of this surprising or
+ 
+
+ align:start position:0%
+yeah is this any of this surprising or
+weird yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I made it up that way to make you think
+
+ align:start position:0%
+I made it up that way to make you think
+ 
+
+ align:start position:0%
+I made it up that way to make you think
+that uh so she asked does that have
+
+ align:start position:0%
+that uh so she asked does that have
+ 
+
+ align:start position:0%
+that uh so she asked does that have
+anything to do with the fact that it
+
+ align:start position:0%
+anything to do with the fact that it
+ 
+
+ align:start position:0%
+anything to do with the fact that it
+looks like the verb leap I guess the
+
+ align:start position:0%
+looks like the verb leap I guess the
+ 
+
+ align:start position:0%
+looks like the verb leap I guess the
+point I was making is we can't have a
+
+ align:start position:0%
+point I was making is we can't have a
+ 
+
+ align:start position:0%
+point I was making is we can't have a
+general rule that if you're making the
+
+ align:start position:0%
+general rule that if you're making the
+ 
+
+ align:start position:0%
+general rule that if you're making the
+past tense of a verb that ends in Eep
+
+ align:start position:0%
+past tense of a verb that ends in Eep
+ 
+
+ align:start position:0%
+past tense of a verb that ends in Eep
+that it's going to change to app that
+
+ align:start position:0%
+that it's going to change to app that
+ 
+
+ align:start position:0%
+that it's going to change to app that
+can when we're trying to figure out
+
+ align:start position:0%
+can when we're trying to figure out
+ 
+
+ align:start position:0%
+can when we're trying to figure out
+what's going on with leap that can't be
+
+ align:start position:0%
+what's going on with leap that can't be
+ 
+
+ align:start position:0%
+what's going on with leap that can't be
+what's going on I guess I could have
+
+ align:start position:0%
+what's going on I guess I could have
+ 
+
+ align:start position:0%
+what's going on I guess I could have
+made that point in other ways we have
+
+ align:start position:0%
+made that point in other ways we have
+ 
+
+ align:start position:0%
+made that point in other ways we have
+verbs like Heap like to Heap up sand and
+
+ align:start position:0%
+verbs like Heap like to Heap up sand and
+ 
+
+ align:start position:0%
+verbs like Heap like to Heap up sand and
+the past tense of Heap is not hept right
+
+ align:start position:0%
+the past tense of Heap is not hept right
+ 
+
+ align:start position:0%
+the past tense of Heap is not hept right
+it's heaped
+
+ align:start position:0%
+it's heaped
+ 
+
+ align:start position:0%
+it's heaped
+but similarly if I make up a new verb
+
+ align:start position:0%
+but similarly if I make up a new verb
+ 
+
+ align:start position:0%
+but similarly if I make up a new verb
+you're not gonna apply what happens in
+
+ align:start position:0%
+you're not gonna apply what happens in
+ 
+
+ align:start position:0%
+you're not gonna apply what happens in
+leap to the new verb yeah yes are there
+
+ align:start position:0%
+leap to the new verb yeah yes are there
+ 
+
+ align:start position:0%
+leap to the new verb yeah yes are there
+any like specific characteristics that
+
+ align:start position:0%
+any like specific characteristics that
+ 
+
+ align:start position:0%
+any like specific characteristics that
+would prefer someone from going towards
+
+ align:start position:0%
+would prefer someone from going towards
+ 
+
+ align:start position:0%
+would prefer someone from going towards
+the default Eleanor like if you made up
+
+ align:start position:0%
+the default Eleanor like if you made up
+ 
+
+ align:start position:0%
+the default Eleanor like if you made up
+another made-up War would there be any
+
+ align:start position:0%
+another made-up War would there be any
+ 
+
+ align:start position:0%
+another made-up War would there be any
+characteristics about that word that
+
+ align:start position:0%
+characteristics about that word that
+ 
+
+ align:start position:0%
+characteristics about that word that
+would happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I see
+
+ align:start position:0%
+oh I see
+ 
+
+ align:start position:0%
+oh I see
+hmm
+
+ align:start position:0%
+hmm
+ 
+
+ align:start position:0%
+hmm
+I don't think there's any way for me to
+
+ align:start position:0%
+I don't think there's any way for me to
+ 
+
+ align:start position:0%
+I don't think there's any way for me to
+induce you
+
+ align:start position:0%
+induce you
+ 
+
+ align:start position:0%
+induce you
+to to to uh to do the leap left thing
+
+ align:start position:0%
+to to to uh to do the leap left thing
+ 
+
+ align:start position:0%
+to to to uh to do the leap left thing
+other than by telling you you know oh by
+
+ align:start position:0%
+other than by telling you you know oh by
+ 
+
+ align:start position:0%
+other than by telling you you know oh by
+the way the past tense of sleep is
+
+ align:start position:0%
+the way the past tense of sleep is
+ 
+
+ align:start position:0%
+the way the past tense of sleep is
+fluffed
+
+ align:start position:0%
+fluffed
+ 
+
+ align:start position:0%
+fluffed
+um but it's interesting to think about
+
+ align:start position:0%
+um but it's interesting to think about
+ 
+
+ align:start position:0%
+um but it's interesting to think about
+sorry recall you were about to comment
+
+ align:start position:0%
+sorry recall you were about to comment
+ 
+
+ align:start position:0%
+sorry recall you were about to comment
+on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thinking thing that's viewed as a
+
+ align:start position:0%
+thinking thing that's viewed as a
+ 
+
+ align:start position:0%
+thinking thing that's viewed as a
+regular compared to the average thing
+
+ align:start position:0%
+regular compared to the average thing
+ 
+
+ align:start position:0%
+regular compared to the average thing
+like if you had like AE to mean the
+
+ align:start position:0%
+like if you had like AE to mean the
+ 
+
+ align:start position:0%
+like if you had like AE to mean the
+plural and like you normally don't do
+
+ align:start position:0%
+plural and like you normally don't do
+ 
+
+ align:start position:0%
+plural and like you normally don't do
+that for all words so like you might do
+
+ align:start position:0%
+that for all words so like you might do
+ 
+
+ align:start position:0%
+that for all words so like you might do
+it for just like I don't know weird
+
+ align:start position:0%
+it for just like I don't know weird
+ 
+
+ align:start position:0%
+it for just like I don't know weird
+plants or something yeah
+
+ align:start position:0%
+plants or something yeah
+ 
+
+ align:start position:0%
+plants or something yeah
+I see I see what you mean and their
+
+ align:start position:0%
+I see I see what you mean and their
+ 
+
+ align:start position:0%
+I see I see what you mean and their
+their language is certainly in which it
+
+ align:start position:0%
+their language is certainly in which it
+ 
+
+ align:start position:0%
+their language is certainly in which it
+might be easier to make a point like
+
+ align:start position:0%
+might be easier to make a point like
+ 
+
+ align:start position:0%
+might be easier to make a point like
+that I guess the other thing to say
+
+ align:start position:0%
+that I guess the other thing to say
+ 
+
+ align:start position:0%
+that I guess the other thing to say
+you're the point you're raising sort of
+
+ align:start position:0%
+you're the point you're raising sort of
+ 
+
+ align:start position:0%
+you're the point you're raising sort of
+brings this up
+
+ align:start position:0%
+brings this up
+ 
+
+ align:start position:0%
+brings this up
+um people sometimes claim anyway that
+
+ align:start position:0%
+um people sometimes claim anyway that
+ 
+
+ align:start position:0%
+um people sometimes claim anyway that
+these kinds of uh irregular alamorphy
+
+ align:start position:0%
+these kinds of uh irregular alamorphy
+ 
+
+ align:start position:0%
+these kinds of uh irregular alamorphy
+these these things you just have to
+
+ align:start position:0%
+these these things you just have to
+ 
+
+ align:start position:0%
+these these things you just have to
+memorize about how things combine
+
+ align:start position:0%
+memorize about how things combine
+ 
+
+ align:start position:0%
+memorize about how things combine
+they'll they'll go away if you they'll
+
+ align:start position:0%
+they'll they'll go away if you they'll
+ 
+
+ align:start position:0%
+they'll they'll go away if you they'll
+sometimes go away if you combine a
+
+ align:start position:0%
+sometimes go away if you combine a
+ 
+
+ align:start position:0%
+sometimes go away if you combine a
+morpheme with something else so the the
+
+ align:start position:0%
+morpheme with something else so the the
+ 
+
+ align:start position:0%
+morpheme with something else so the the
+classic example for some reason the the
+
+ align:start position:0%
+classic example for some reason the the
+ 
+
+ align:start position:0%
+classic example for some reason the the
+plural of leaf
+
+ align:start position:0%
+plural of leaf
+ 
+
+ align:start position:0%
+plural of leaf
+you know the things on trees
+
+ align:start position:0%
+you know the things on trees
+ 
+
+ align:start position:0%
+you know the things on trees
+is leaves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and hero
+
+ align:start position:0%
+and hero
+ 
+
+ align:start position:0%
+and hero
+put it over here too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but I've heard it claimed anyway that
+
+ align:start position:0%
+um but I've heard it claimed anyway that
+ 
+
+ align:start position:0%
+um but I've heard it claimed anyway that
+if you're talking about the athletic
+
+ align:start position:0%
+if you're talking about the athletic
+ 
+
+ align:start position:0%
+if you're talking about the athletic
+team the Toronto Maple Leaf so the
+
+ align:start position:0%
+team the Toronto Maple Leaf so the
+ 
+
+ align:start position:0%
+team the Toronto Maple Leaf so the
+singular would be the Toronto Maple Leaf
+
+ align:start position:0%
+singular would be the Toronto Maple Leaf
+ 
+
+ align:start position:0%
+singular would be the Toronto Maple Leaf
+but the plural is the Toronto Maple
+
+ align:start position:0%
+but the plural is the Toronto Maple
+ 
+
+ align:start position:0%
+but the plural is the Toronto Maple
+Leafs
+
+ align:start position:0%
+Leafs
+ 
+
+ align:start position:0%
+Leafs
+and not the Toronto Maple Leaves
+
+ align:start position:0%
+and not the Toronto Maple Leaves
+ 
+
+ align:start position:0%
+and not the Toronto Maple Leaves
+I'm going to pause I'm not enough of a
+
+ align:start position:0%
+I'm going to pause I'm not enough of a
+ 
+
+ align:start position:0%
+I'm going to pause I'm not enough of a
+sports fan to know whether this is true
+
+ align:start position:0%
+sports fan to know whether this is true
+ 
+
+ align:start position:0%
+sports fan to know whether this is true
+so I'm getting a thumbs up anyway
+
+ align:start position:0%
+so I'm getting a thumbs up anyway
+ 
+
+ align:start position:0%
+so I'm getting a thumbs up anyway
+anybody here from Toronto or is anybody
+
+ align:start position:0%
+anybody here from Toronto or is anybody
+ 
+
+ align:start position:0%
+anybody here from Toronto or is anybody
+a Maple Leafs fan
+
+ align:start position:0%
+a Maple Leafs fan
+ 
+
+ align:start position:0%
+a Maple Leafs fan
+I want to know whether this is true
+
+ align:start position:0%
+I want to know whether this is true
+ 
+
+ align:start position:0%
+I want to know whether this is true
+presumably this is the kind of thing you
+
+ align:start position:0%
+presumably this is the kind of thing you
+ 
+
+ align:start position:0%
+presumably this is the kind of thing you
+could find out by looking at their
+
+ align:start position:0%
+could find out by looking at their
+ 
+
+ align:start position:0%
+could find out by looking at their
+website you know what does it say on
+
+ align:start position:0%
+website you know what does it say on
+ 
+
+ align:start position:0%
+website you know what does it say on
+their t-shirts you know but uh this is a
+
+ align:start position:0%
+their t-shirts you know but uh this is a
+ 
+
+ align:start position:0%
+their t-shirts you know but uh this is a
+claim that I've heard anyway
+
+ align:start position:0%
+claim that I've heard anyway
+ 
+
+ align:start position:0%
+claim that I've heard anyway
+so there are some cases where this Weird
+
+ align:start position:0%
+so there are some cases where this Weird
+ 
+
+ align:start position:0%
+so there are some cases where this Weird
+Al amorphy goes away because you've made
+
+ align:start position:0%
+Al amorphy goes away because you've made
+ 
+
+ align:start position:0%
+Al amorphy goes away because you've made
+it part of this compound or you've made
+
+ align:start position:0%
+it part of this compound or you've made
+ 
+
+ align:start position:0%
+it part of this compound or you've made
+it part of a name right so because it
+
+ align:start position:0%
+it part of a name right so because it
+ 
+
+ align:start position:0%
+it part of a name right so because it
+isn't just about me if you're talking
+
+ align:start position:0%
+isn't just about me if you're talking
+ 
+
+ align:start position:0%
+isn't just about me if you're talking
+about actual maple leaves like tree
+
+ align:start position:0%
+about actual maple leaves like tree
+ 
+
+ align:start position:0%
+about actual maple leaves like tree
+leaves leaves on a tree then those are
+
+ align:start position:0%
+leaves leaves on a tree then those are
+ 
+
+ align:start position:0%
+leaves leaves on a tree then those are
+definitely maple leaves and something
+
+ align:start position:0%
+definitely maple leaves and something
+ 
+
+ align:start position:0%
+definitely maple leaves and something
+about them being the name of an athletic
+
+ align:start position:0%
+about them being the name of an athletic
+ 
+
+ align:start position:0%
+about them being the name of an athletic
+team
+
+ align:start position:0%
+team
+ 
+
+ align:start position:0%
+team
+somebody else had a hand that I
+
+ align:start position:0%
+somebody else had a hand that I
+ 
+
+ align:start position:0%
+somebody else had a hand that I
+ruthlessly ignored oh Joseph
+
+ align:start position:0%
+ruthlessly ignored oh Joseph
+ 
+
+ align:start position:0%
+ruthlessly ignored oh Joseph
+oh they do you you checked yes this is
+
+ align:start position:0%
+oh they do you you checked yes this is
+ 
+
+ align:start position:0%
+oh they do you you checked yes this is
+the kind of thing
+
+ align:start position:0%
+the kind of thing
+ 
+
+ align:start position:0%
+the kind of thing
+I can't tell sometimes that I I was born
+
+ align:start position:0%
+I can't tell sometimes that I I was born
+ 
+
+ align:start position:0%
+I can't tell sometimes that I I was born
+in a different uh Century uh there are
+
+ align:start position:0%
+in a different uh Century uh there are
+ 
+
+ align:start position:0%
+in a different uh Century uh there are
+all kinds of things where I raise
+
+ align:start position:0%
+all kinds of things where I raise
+ 
+
+ align:start position:0%
+all kinds of things where I raise
+interesting questions and then in class
+
+ align:start position:0%
+interesting questions and then in class
+ 
+
+ align:start position:0%
+interesting questions and then in class
+someone will be like yes and here is the
+
+ align:start position:0%
+someone will be like yes and here is the
+ 
+
+ align:start position:0%
+someone will be like yes and here is the
+answer it's like oh right yeah we have
+
+ align:start position:0%
+answer it's like oh right yeah we have
+ 
+
+ align:start position:0%
+answer it's like oh right yeah we have
+the ability to do that now
+
+ align:start position:0%
+the ability to do that now
+ 
+
+ align:start position:0%
+the ability to do that now
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a slings chocolate and slingshot
+
+ align:start position:0%
+with a slings chocolate and slingshot
+ 
+
+ align:start position:0%
+with a slings chocolate and slingshot
+both feel wrong
+
+ align:start position:0%
+both feel wrong
+ 
+
+ align:start position:0%
+both feel wrong
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+sir swing shoots
+
+ align:start position:0%
+sir swing shoots
+ 
+
+ align:start position:0%
+sir swing shoots
+so question was what's the past tense of
+
+ align:start position:0%
+so question was what's the past tense of
+ 
+
+ align:start position:0%
+so question was what's the past tense of
+slingshot two possibilities slingshotted
+
+ align:start position:0%
+slingshot two possibilities slingshotted
+ 
+
+ align:start position:0%
+slingshot two possibilities slingshotted
+and slingshot and there was another
+
+ align:start position:0%
+and slingshot and there was another
+ 
+
+ align:start position:0%
+and slingshot and there was another
+possibility which we will ignore for
+
+ align:start position:0%
+possibility which we will ignore for
+ 
+
+ align:start position:0%
+possibility which we will ignore for
+reasons
+
+ align:start position:0%
+reasons
+ 
+
+ align:start position:0%
+reasons
+who thinks the past tense of slingshot
+
+ align:start position:0%
+who thinks the past tense of slingshot
+ 
+
+ align:start position:0%
+who thinks the past tense of slingshot
+is slingshotted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who thinks it's slingshot
+
+ align:start position:0%
+who thinks it's slingshot
+ 
+
+ align:start position:0%
+who thinks it's slingshot
+interesting there are some examples uh
+
+ align:start position:0%
+interesting there are some examples uh
+ 
+
+ align:start position:0%
+interesting there are some examples uh
+does anybody have another alternative
+
+ align:start position:0%
+does anybody have another alternative
+ 
+
+ align:start position:0%
+does anybody have another alternative
+slingshot no
+
+ align:start position:0%
+slingshot no
+ 
+
+ align:start position:0%
+slingshot no
+shame for shame
+
+ align:start position:0%
+shame for shame
+ 
+
+ align:start position:0%
+shame for shame
+slung slung shoot no
+
+ align:start position:0%
+slung slung shoot no
+ 
+
+ align:start position:0%
+slung slung shoot no
+also no there are some examples of verbs
+
+ align:start position:0%
+also no there are some examples of verbs
+ 
+
+ align:start position:0%
+also no there are some examples of verbs
+or morphemes that if you combine them
+
+ align:start position:0%
+or morphemes that if you combine them
+ 
+
+ align:start position:0%
+or morphemes that if you combine them
+sorry if you if you combine them with
+
+ align:start position:0%
+sorry if you if you combine them with
+ 
+
+ align:start position:0%
+sorry if you if you combine them with
+other morphemes that no one knows this
+
+ align:start position:0%
+other morphemes that no one knows this
+ 
+
+ align:start position:0%
+other morphemes that no one knows this
+is kind of like slingshot
+
+ align:start position:0%
+is kind of like slingshot
+ 
+
+ align:start position:0%
+is kind of like slingshot
+um so take the verb to stride
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the past tense is Strode
+
+ align:start position:0%
+so the past tense is Strode
+ 
+
+ align:start position:0%
+so the past tense is Strode
+and then the participle was you know he
+
+ align:start position:0%
+and then the participle was you know he
+ 
+
+ align:start position:0%
+and then the participle was you know he
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+strident
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+droed strod
+
+ align:start position:0%
+droed strod
+ 
+
+ align:start position:0%
+droed strod
+who thinks it
+
+ align:start position:0%
+who thinks it
+ 
+
+ align:start position:0%
+who thinks it
+who thinks it's strident
+
+ align:start position:0%
+who thinks it's strident
+ 
+
+ align:start position:0%
+who thinks it's strident
+who thinks it's Strode
+
+ align:start position:0%
+who thinks it's Strode
+ 
+
+ align:start position:0%
+who thinks it's Strode
+who has something else they'd like it to
+
+ align:start position:0%
+who has something else they'd like it to
+ 
+
+ align:start position:0%
+who has something else they'd like it to
+be strud any votes for strud
+
+ align:start position:0%
+be strud any votes for strud
+ 
+
+ align:start position:0%
+be strud any votes for strud
+no you're all alone I'm sorry
+
+ align:start position:0%
+no you're all alone I'm sorry
+ 
+
+ align:start position:0%
+no you're all alone I'm sorry
+so this is a classic example of a verb
+
+ align:start position:0%
+so this is a classic example of a verb
+ 
+
+ align:start position:0%
+so this is a classic example of a verb
+where you know English speakers just are
+
+ align:start position:0%
+where you know English speakers just are
+ 
+
+ align:start position:0%
+where you know English speakers just are
+not sure what what the participle of
+
+ align:start position:0%
+not sure what what the participle of
+ 
+
+ align:start position:0%
+not sure what what the participle of
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+sorry Smite is another good example yes
+
+ align:start position:0%
+sorry Smite is another good example yes
+ 
+
+ align:start position:0%
+sorry Smite is another good example yes
+that one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one yeah so for me so smitten has
+
+ align:start position:0%
+that one yeah so for me so smitten has
+ 
+
+ align:start position:0%
+that one yeah so for me so smitten has
+this other other
+
+ align:start position:0%
+this other other
+ 
+
+ align:start position:0%
+this other other
+um use right you can be smitten with
+
+ align:start position:0%
+um use right you can be smitten with
+ 
+
+ align:start position:0%
+um use right you can be smitten with
+someone uh which I think is interfering
+
+ align:start position:0%
+someone uh which I think is interfering
+ 
+
+ align:start position:0%
+someone uh which I think is interfering
+yep okay so lots of fun things to think
+
+ align:start position:0%
+yep okay so lots of fun things to think
+ 
+
+ align:start position:0%
+yep okay so lots of fun things to think
+about about uh about alamorphy
+
+ align:start position:0%
+about about uh about alamorphy
+ 
+
+ align:start position:0%
+about about uh about alamorphy
+uh okay so I'm I'm going through all
+
+ align:start position:0%
+uh okay so I'm I'm going through all
+ 
+
+ align:start position:0%
+uh okay so I'm I'm going through all
+this partly so I want to go back to the
+
+ align:start position:0%
+this partly so I want to go back to the
+ 
+
+ align:start position:0%
+this partly so I want to go back to the
+stuff about uh morphemes combining with
+
+ align:start position:0%
+stuff about uh morphemes combining with
+ 
+
+ align:start position:0%
+stuff about uh morphemes combining with
+things and creating other things
+
+ align:start position:0%
+things and creating other things
+ 
+
+ align:start position:0%
+things and creating other things
+um because uh so far we have talked
+
+ align:start position:0%
+um because uh so far we have talked
+ 
+
+ align:start position:0%
+um because uh so far we have talked
+about various sort of cases where
+
+ align:start position:0%
+about various sort of cases where
+ 
+
+ align:start position:0%
+about various sort of cases where
+morphemes combine with other morphemes
+
+ align:start position:0%
+morphemes combine with other morphemes
+ 
+
+ align:start position:0%
+morphemes combine with other morphemes
+and we've also talked about cases where
+
+ align:start position:0%
+and we've also talked about cases where
+ 
+
+ align:start position:0%
+and we've also talked about cases where
+morphemes combine with more than one
+
+ align:start position:0%
+morphemes combine with more than one
+ 
+
+ align:start position:0%
+morphemes combine with more than one
+morpheme and I kind of want to talk
+
+ align:start position:0%
+morpheme and I kind of want to talk
+ 
+
+ align:start position:0%
+morpheme and I kind of want to talk
+about that a little bit carefully
+
+ align:start position:0%
+about that a little bit carefully
+ 
+
+ align:start position:0%
+about that a little bit carefully
+because it's going to be something it's
+
+ align:start position:0%
+because it's going to be something it's
+ 
+
+ align:start position:0%
+because it's going to be something it's
+going to be useful uh as we we go
+
+ align:start position:0%
+going to be useful uh as we we go
+ 
+
+ align:start position:0%
+going to be useful uh as we we go
+forward in the class so let's talk about
+
+ align:start position:0%
+forward in the class so let's talk about
+ 
+
+ align:start position:0%
+forward in the class so let's talk about
+these particular morphemes think about
+
+ align:start position:0%
+these particular morphemes think about
+ 
+
+ align:start position:0%
+these particular morphemes think about
+the suffix mint uh what does mint attach
+
+ align:start position:0%
+the suffix mint uh what does mint attach
+ 
+
+ align:start position:0%
+the suffix mint uh what does mint attach
+to and what does it create so you can
+
+ align:start position:0%
+to and what does it create so you can
+ 
+
+ align:start position:0%
+to and what does it create so you can
+say things like government and treatment
+
+ align:start position:0%
+say things like government and treatment
+ 
+
+ align:start position:0%
+say things like government and treatment
+you cannot say things like body
+
+ align:start position:0%
+you cannot say things like body
+ 
+
+ align:start position:0%
+you cannot say things like body
+mentorpowerment
+
+ align:start position:0%
+mentorpowerment
+ 
+
+ align:start position:0%
+mentorpowerment
+what does mint attach to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are govern and treat
+
+ align:start position:0%
+what are govern and treat
+ 
+
+ align:start position:0%
+what are govern and treat
+verbs okay so meant erase some stuff
+
+ align:start position:0%
+verbs okay so meant erase some stuff
+ 
+
+ align:start position:0%
+verbs okay so meant erase some stuff
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk about mint
+
+ align:start position:0%
+talk about mint
+ 
+
+ align:start position:0%
+talk about mint
+it attaches to a verb
+
+ align:start position:0%
+it attaches to a verb
+ 
+
+ align:start position:0%
+it attaches to a verb
+and it creates what
+
+ align:start position:0%
+and it creates what
+ 
+
+ align:start position:0%
+and it creates what
+a noun yeah treatment and government are
+
+ align:start position:0%
+a noun yeah treatment and government are
+ 
+
+ align:start position:0%
+a noun yeah treatment and government are
+both nouns and I'll put that again over
+
+ align:start position:0%
+both nouns and I'll put that again over
+ 
+
+ align:start position:0%
+both nouns and I'll put that again over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+mint
+
+ align:start position:0%
+mint
+ 
+
+ align:start position:0%
+mint
+patches the verbs and creates nouns okay
+
+ align:start position:0%
+patches the verbs and creates nouns okay
+ 
+
+ align:start position:0%
+patches the verbs and creates nouns okay
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+um now how about the prefix m as in m
+
+ align:start position:0%
+um now how about the prefix m as in m
+ 
+
+ align:start position:0%
+um now how about the prefix m as in m
+body and M Power uh what does m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attached to and what does it create
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+touches of nouns and makes them into
+
+ align:start position:0%
+touches of nouns and makes them into
+ 
+
+ align:start position:0%
+touches of nouns and makes them into
+verbs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aha
+
+ align:start position:0%
+aha
+ 
+
+ align:start position:0%
+aha
+I'll just say that again
+
+ align:start position:0%
+I'll just say that again
+ 
+
+ align:start position:0%
+I'll just say that again
+over here got to be a better way to do
+
+ align:start position:0%
+over here got to be a better way to do
+ 
+
+ align:start position:0%
+over here got to be a better way to do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+attaches to nouns and makes them into
+
+ align:start position:0%
+attaches to nouns and makes them into
+ 
+
+ align:start position:0%
+attaches to nouns and makes them into
+verbs
+
+ align:start position:0%
+verbs
+ 
+
+ align:start position:0%
+verbs
+okay cool
+
+ align:start position:0%
+okay cool
+ 
+
+ align:start position:0%
+okay cool
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we just said we know why you can't say
+
+ align:start position:0%
+we just said we know why you can't say
+ 
+
+ align:start position:0%
+we just said we know why you can't say
+bodiment or empowerment it's because
+
+ align:start position:0%
+bodiment or empowerment it's because
+ 
+
+ align:start position:0%
+bodiment or empowerment it's because
+mint attaches to verbs and body and
+
+ align:start position:0%
+mint attaches to verbs and body and
+ 
+
+ align:start position:0%
+mint attaches to verbs and body and
+power are not verbs
+
+ align:start position:0%
+power are not verbs
+ 
+
+ align:start position:0%
+power are not verbs
+how come you can say embodiment and
+
+ align:start position:0%
+how come you can say embodiment and
+ 
+
+ align:start position:0%
+how come you can say embodiment and
+empowerment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of you are saying the right thing
+
+ align:start position:0%
+all of you are saying the right thing
+ 
+
+ align:start position:0%
+all of you are saying the right thing
+sort of in chorus as the semester goes
+
+ align:start position:0%
+sort of in chorus as the semester goes
+ 
+
+ align:start position:0%
+sort of in chorus as the semester goes
+along eventually you'll start saying
+
+ align:start position:0%
+along eventually you'll start saying
+ 
+
+ align:start position:0%
+along eventually you'll start saying
+these things in unison this would be
+
+ align:start position:0%
+these things in unison this would be
+ 
+
+ align:start position:0%
+these things in unison this would be
+really cool
+
+ align:start position:0%
+really cool
+ 
+
+ align:start position:0%
+really cool
+um maybe maybe with Harmony so yeah uh
+
+ align:start position:0%
+um maybe maybe with Harmony so yeah uh
+ 
+
+ align:start position:0%
+um maybe maybe with Harmony so yeah uh
+yeah but you can't attachment to body
+
+ align:start position:0%
+yeah but you can't attachment to body
+ 
+
+ align:start position:0%
+yeah but you can't attachment to body
+because body is a noun but you can
+
+ align:start position:0%
+because body is a noun but you can
+ 
+
+ align:start position:0%
+because body is a noun but you can
+attach mint to M body so M body is a
+
+ align:start position:0%
+attach mint to M body so M body is a
+ 
+
+ align:start position:0%
+attach mint to M body so M body is a
+verb Empower is a verb M attaches to the
+
+ align:start position:0%
+verb Empower is a verb M attaches to the
+ 
+
+ align:start position:0%
+verb Empower is a verb M attaches to the
+noun body or the noun power and makes it
+
+ align:start position:0%
+noun body or the noun power and makes it
+ 
+
+ align:start position:0%
+noun body or the noun power and makes it
+into a verb
+
+ align:start position:0%
+into a verb
+ 
+
+ align:start position:0%
+into a verb
+and then mint attaches to the resulting
+
+ align:start position:0%
+and then mint attaches to the resulting
+ 
+
+ align:start position:0%
+and then mint attaches to the resulting
+verb and makes it into a noun again
+
+ align:start position:0%
+verb and makes it into a noun again
+ 
+
+ align:start position:0%
+verb and makes it into a noun again
+so it's useful to think of these
+
+ align:start position:0%
+so it's useful to think of these
+ 
+
+ align:start position:0%
+so it's useful to think of these
+morphemes so words like embodiment and
+
+ align:start position:0%
+morphemes so words like embodiment and
+ 
+
+ align:start position:0%
+morphemes so words like embodiment and
+empowerment not just as consisting of
+
+ align:start position:0%
+empowerment not just as consisting of
+ 
+
+ align:start position:0%
+empowerment not just as consisting of
+three morphemes although they do right a
+
+ align:start position:0%
+three morphemes although they do right a
+ 
+
+ align:start position:0%
+three morphemes although they do right a
+prefix stem and then a suffix but it's
+
+ align:start position:0%
+prefix stem and then a suffix but it's
+ 
+
+ align:start position:0%
+prefix stem and then a suffix but it's
+consisting in three morphemes that are
+
+ align:start position:0%
+consisting in three morphemes that are
+ 
+
+ align:start position:0%
+consisting in three morphemes that are
+assembled in a particular order
+
+ align:start position:0%
+assembled in a particular order
+ 
+
+ align:start position:0%
+assembled in a particular order
+you first attach the prefix and then you
+
+ align:start position:0%
+you first attach the prefix and then you
+ 
+
+ align:start position:0%
+you first attach the prefix and then you
+attach the suffix
+
+ align:start position:0%
+attach the suffix
+ 
+
+ align:start position:0%
+attach the suffix
+people see why I'm saying it that way
+
+ align:start position:0%
+people see why I'm saying it that way
+ 
+
+ align:start position:0%
+people see why I'm saying it that way
+that makes sense
+
+ align:start position:0%
+that makes sense
+ 
+
+ align:start position:0%
+that makes sense
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a way of representing that fact
+
+ align:start position:0%
+here's a way of representing that fact
+ 
+
+ align:start position:0%
+here's a way of representing that fact
+which is going to come in handy as we go
+
+ align:start position:0%
+which is going to come in handy as we go
+ 
+
+ align:start position:0%
+which is going to come in handy as we go
+forward we're going to want to say yeah
+
+ align:start position:0%
+forward we're going to want to say yeah
+ 
+
+ align:start position:0%
+forward we're going to want to say yeah
+you start with power and you glom power
+
+ align:start position:0%
+you start with power and you glom power
+ 
+
+ align:start position:0%
+you start with power and you glom power
+together with this prefix I've given
+
+ align:start position:0%
+together with this prefix I've given
+ 
+
+ align:start position:0%
+together with this prefix I've given
+that the label F which is just supposed
+
+ align:start position:0%
+that the label F which is just supposed
+ 
+
+ align:start position:0%
+that the label F which is just supposed
+to stand for affix yeah so the affix M
+
+ align:start position:0%
+to stand for affix yeah so the affix M
+ 
+
+ align:start position:0%
+to stand for affix yeah so the affix M
+the prefix m attaches to the noun power
+
+ align:start position:0%
+the prefix m attaches to the noun power
+ 
+
+ align:start position:0%
+the prefix m attaches to the noun power
+and creates a verb that's what the sort
+
+ align:start position:0%
+and creates a verb that's what the sort
+ 
+
+ align:start position:0%
+and creates a verb that's what the sort
+of lower left hand side of that tree is
+
+ align:start position:0%
+of lower left hand side of that tree is
+ 
+
+ align:start position:0%
+of lower left hand side of that tree is
+meant to show you does that make sense
+
+ align:start position:0%
+meant to show you does that make sense
+ 
+
+ align:start position:0%
+meant to show you does that make sense
+and then that verb is combined with this
+
+ align:start position:0%
+and then that verb is combined with this
+ 
+
+ align:start position:0%
+and then that verb is combined with this
+other affix meant and the result is a
+
+ align:start position:0%
+other affix meant and the result is a
+ 
+
+ align:start position:0%
+other affix meant and the result is a
+noun
+
+ align:start position:0%
+noun
+ 
+
+ align:start position:0%
+noun
+and power meant
+
+ align:start position:0%
+and power meant
+ 
+
+ align:start position:0%
+and power meant
+does that make sense so this tree is
+
+ align:start position:0%
+does that make sense so this tree is
+ 
+
+ align:start position:0%
+does that make sense so this tree is
+just a way of representing what I just
+
+ align:start position:0%
+just a way of representing what I just
+ 
+
+ align:start position:0%
+just a way of representing what I just
+said which is it's useful to think of
+
+ align:start position:0%
+said which is it's useful to think of
+ 
+
+ align:start position:0%
+said which is it's useful to think of
+this as not just a word consisting of
+
+ align:start position:0%
+this as not just a word consisting of
+ 
+
+ align:start position:0%
+this as not just a word consisting of
+three morphemes but a word consisting of
+
+ align:start position:0%
+three morphemes but a word consisting of
+ 
+
+ align:start position:0%
+three morphemes but a word consisting of
+three morphemes which are attached in
+
+ align:start position:0%
+three morphemes which are attached in
+ 
+
+ align:start position:0%
+three morphemes which are attached in
+pairs that is you attach M to power and
+
+ align:start position:0%
+pairs that is you attach M to power and
+ 
+
+ align:start position:0%
+pairs that is you attach M to power and
+then you attachment to empower
+
+ align:start position:0%
+then you attachment to empower
+ 
+
+ align:start position:0%
+then you attachment to empower
+yeah Replacements of the offices on the
+
+ align:start position:0%
+yeah Replacements of the offices on the
+ 
+
+ align:start position:0%
+yeah Replacements of the offices on the
+stream because of whatever their
+
+ align:start position:0%
+stream because of whatever their
+ 
+
+ align:start position:0%
+stream because of whatever their
+feelings
+
+ align:start position:0%
+feelings
+ 
+
+ align:start position:0%
+feelings
+yes yeah so you're asking why do they
+
+ align:start position:0%
+yes yeah so you're asking why do they
+ 
+
+ align:start position:0%
+yes yeah so you're asking why do they
+put M before power and why do they put
+
+ align:start position:0%
+put M before power and why do they put
+ 
+
+ align:start position:0%
+put M before power and why do they put
+mint after Empower and yes it's just
+
+ align:start position:0%
+mint after Empower and yes it's just
+ 
+
+ align:start position:0%
+mint after Empower and yes it's just
+whether they're prefixes or something
+
+ align:start position:0%
+whether they're prefixes or something
+ 
+
+ align:start position:0%
+whether they're prefixes or something
+that's all I was trying to do
+
+ align:start position:0%
+that's all I was trying to do
+ 
+
+ align:start position:0%
+that's all I was trying to do
+okay so the tree is just a way of
+
+ align:start position:0%
+okay so the tree is just a way of
+ 
+
+ align:start position:0%
+okay so the tree is just a way of
+representing that kind of
+
+ align:start position:0%
+representing that kind of
+ 
+
+ align:start position:0%
+representing that kind of
+derivational history of this word right
+
+ align:start position:0%
+derivational history of this word right
+ 
+
+ align:start position:0%
+derivational history of this word right
+so what's the order of operations that
+
+ align:start position:0%
+so what's the order of operations that
+ 
+
+ align:start position:0%
+so what's the order of operations that
+you use to create this word yeah
+
+ align:start position:0%
+you use to create this word yeah
+ 
+
+ align:start position:0%
+you use to create this word yeah
+yes that's a way to talk about it
+
+ align:start position:0%
+yes that's a way to talk about it
+ 
+
+ align:start position:0%
+yes that's a way to talk about it
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh well uh infixes would be where I
+
+ align:start position:0%
+oh well uh infixes would be where I
+ 
+
+ align:start position:0%
+oh well uh infixes would be where I
+would fail at what I'm trying to do this
+
+ align:start position:0%
+would fail at what I'm trying to do this
+ 
+
+ align:start position:0%
+would fail at what I'm trying to do this
+was your point from just now you know
+
+ align:start position:0%
+was your point from just now you know
+ 
+
+ align:start position:0%
+was your point from just now you know
+I'm trying to represent whether things
+
+ align:start position:0%
+I'm trying to represent whether things
+ 
+
+ align:start position:0%
+I'm trying to represent whether things
+are prefixes or suffixes by using using
+
+ align:start position:0%
+are prefixes or suffixes by using using
+ 
+
+ align:start position:0%
+are prefixes or suffixes by using using
+the tree if we were doing Tagalog and
+
+ align:start position:0%
+the tree if we were doing Tagalog and
+ 
+
+ align:start position:0%
+the tree if we were doing Tagalog and
+you know I wanted to do the past tense
+
+ align:start position:0%
+you know I wanted to do the past tense
+ 
+
+ align:start position:0%
+you know I wanted to do the past tense
+of the verb which involves an infix um
+
+ align:start position:0%
+of the verb which involves an infix um
+ 
+
+ align:start position:0%
+of the verb which involves an infix um
+I'd probably you know
+
+ align:start position:0%
+I'd probably you know
+ 
+
+ align:start position:0%
+I'd probably you know
+put together you know here's the affix
+
+ align:start position:0%
+put together you know here's the affix
+ 
+
+ align:start position:0%
+put together you know here's the affix
+this was a verb and I'm going to put
+
+ align:start position:0%
+this was a verb and I'm going to put
+ 
+
+ align:start position:0%
+this was a verb and I'm going to put
+these two things together as a single
+
+ align:start position:0%
+these two things together as a single
+ 
+
+ align:start position:0%
+these two things together as a single
+thing yeah and then yes somewhere else I
+
+ align:start position:0%
+thing yeah and then yes somewhere else I
+ 
+
+ align:start position:0%
+thing yeah and then yes somewhere else I
+would have to say oh by the way this is
+
+ align:start position:0%
+would have to say oh by the way this is
+ 
+
+ align:start position:0%
+would have to say oh by the way this is
+an infix yeah so try not to take too
+
+ align:start position:0%
+an infix yeah so try not to take too
+ 
+
+ align:start position:0%
+an infix yeah so try not to take too
+seriously which things are to the left
+
+ align:start position:0%
+seriously which things are to the left
+ 
+
+ align:start position:0%
+seriously which things are to the left
+and right of which other things what I'm
+
+ align:start position:0%
+and right of which other things what I'm
+ 
+
+ align:start position:0%
+and right of which other things what I'm
+really trying to get across with these
+
+ align:start position:0%
+really trying to get across with these
+ 
+
+ align:start position:0%
+really trying to get across with these
+trees is the order in which you are
+
+ align:start position:0%
+trees is the order in which you are
+ 
+
+ align:start position:0%
+trees is the order in which you are
+putting things together
+
+ align:start position:0%
+putting things together
+ 
+
+ align:start position:0%
+putting things together
+the fact that some things are prefixes
+
+ align:start position:0%
+the fact that some things are prefixes
+ 
+
+ align:start position:0%
+the fact that some things are prefixes
+and others are suffixes and others are
+
+ align:start position:0%
+and others are suffixes and others are
+ 
+
+ align:start position:0%
+and others are suffixes and others are
+infixes or tones or whatever all else
+
+ align:start position:0%
+infixes or tones or whatever all else
+ 
+
+ align:start position:0%
+infixes or tones or whatever all else
+that's somebody else's job for today
+
+ align:start position:0%
+that's somebody else's job for today
+ 
+
+ align:start position:0%
+that's somebody else's job for today
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's a standard way of talking about
+
+ align:start position:0%
+there's a standard way of talking about
+ 
+
+ align:start position:0%
+there's a standard way of talking about
+trees like this trees like this are very
+
+ align:start position:0%
+trees like this trees like this are very
+ 
+
+ align:start position:0%
+trees like this trees like this are very
+popular we will spend a lot try to get
+
+ align:start position:0%
+popular we will spend a lot try to get
+ 
+
+ align:start position:0%
+popular we will spend a lot try to get
+comfortable with them we will spend lots
+
+ align:start position:0%
+comfortable with them we will spend lots
+ 
+
+ align:start position:0%
+comfortable with them we will spend lots
+of time looking at trees as the semester
+
+ align:start position:0%
+of time looking at trees as the semester
+ 
+
+ align:start position:0%
+of time looking at trees as the semester
+goes along
+
+ align:start position:0%
+goes along
+ 
+
+ align:start position:0%
+goes along
+um there's a standard way of talking
+
+ align:start position:0%
+um there's a standard way of talking
+ 
+
+ align:start position:0%
+um there's a standard way of talking
+about them which involves feminine
+
+ align:start position:0%
+about them which involves feminine
+ 
+
+ align:start position:0%
+about them which involves feminine
+kinship terms uh so we'll say that the
+
+ align:start position:0%
+kinship terms uh so we'll say that the
+ 
+
+ align:start position:0%
+kinship terms uh so we'll say that the
+sister of M is a noun
+
+ align:start position:0%
+sister of M is a noun
+ 
+
+ align:start position:0%
+sister of M is a noun
+because those two things are next to
+
+ align:start position:0%
+because those two things are next to
+ 
+
+ align:start position:0%
+because those two things are next to
+each other on the tree there are two
+
+ align:start position:0%
+each other on the tree there are two
+ 
+
+ align:start position:0%
+each other on the tree there are two
+daughters of the same thing that verb
+
+ align:start position:0%
+daughters of the same thing that verb
+ 
+
+ align:start position:0%
+daughters of the same thing that verb
+node that's above them both
+
+ align:start position:0%
+node that's above them both
+ 
+
+ align:start position:0%
+node that's above them both
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh or another way to say it is that that
+
+ align:start position:0%
+uh or another way to say it is that that
+ 
+
+ align:start position:0%
+uh or another way to say it is that that
+verb is the mother of both M and power
+
+ align:start position:0%
+verb is the mother of both M and power
+ 
+
+ align:start position:0%
+verb is the mother of both M and power
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+I think that's as far as people go with
+
+ align:start position:0%
+I think that's as far as people go with
+ 
+
+ align:start position:0%
+I think that's as far as people go with
+the feminine kinship terms people don't
+
+ align:start position:0%
+the feminine kinship terms people don't
+ 
+
+ align:start position:0%
+the feminine kinship terms people don't
+talk about like ants you know or
+
+ align:start position:0%
+talk about like ants you know or
+ 
+
+ align:start position:0%
+talk about like ants you know or
+whatever so it's uh sisters and
+
+ align:start position:0%
+whatever so it's uh sisters and
+ 
+
+ align:start position:0%
+whatever so it's uh sisters and
+daughters and mothers
+
+ align:start position:0%
+daughters and mothers
+ 
+
+ align:start position:0%
+daughters and mothers
+nobody even talks about grandmothers
+
+ align:start position:0%
+nobody even talks about grandmothers
+ 
+
+ align:start position:0%
+nobody even talks about grandmothers
+it's nuclear families yeah yeah
+
+ align:start position:0%
+it's nuclear families yeah yeah
+ 
+
+ align:start position:0%
+it's nuclear families yeah yeah
+okay so those are just terminology for
+
+ align:start position:0%
+okay so those are just terminology for
+ 
+
+ align:start position:0%
+okay so those are just terminology for
+talking about this so mint has a verb as
+
+ align:start position:0%
+talking about this so mint has a verb as
+ 
+
+ align:start position:0%
+talking about this so mint has a verb as
+a sister and its mother is an and when
+
+ align:start position:0%
+a sister and its mother is an and when
+ 
+
+ align:start position:0%
+a sister and its mother is an and when
+we say mint has a verb as its sister and
+
+ align:start position:0%
+we say mint has a verb as its sister and
+ 
+
+ align:start position:0%
+we say mint has a verb as its sister and
+a noun as its mother that's a way of
+
+ align:start position:0%
+a noun as its mother that's a way of
+ 
+
+ align:start position:0%
+a noun as its mother that's a way of
+saying things like what I have on the
+
+ align:start position:0%
+saying things like what I have on the
+ 
+
+ align:start position:0%
+saying things like what I have on the
+board here twice uh that meant to
+
+ align:start position:0%
+board here twice uh that meant to
+ 
+
+ align:start position:0%
+board here twice uh that meant to
+something that takes a verb and converts
+
+ align:start position:0%
+something that takes a verb and converts
+ 
+
+ align:start position:0%
+something that takes a verb and converts
+it into a noun right that's how that
+
+ align:start position:0%
+it into a noun right that's how that
+ 
+
+ align:start position:0%
+it into a noun right that's how that
+kind of fact is represented in these
+
+ align:start position:0%
+kind of fact is represented in these
+ 
+
+ align:start position:0%
+kind of fact is represented in these
+trees
+
+ align:start position:0%
+trees
+ 
+
+ align:start position:0%
+trees
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there will be times you know
+
+ align:start position:0%
+there will be times you know
+ 
+
+ align:start position:0%
+there will be times you know
+a big surprise this is like day three
+
+ align:start position:0%
+a big surprise this is like day three
+ 
+
+ align:start position:0%
+a big surprise this is like day three
+I'm looking at comparatively simple
+
+ align:start position:0%
+I'm looking at comparatively simple
+ 
+
+ align:start position:0%
+I'm looking at comparatively simple
+cases they're going to be examples where
+
+ align:start position:0%
+cases they're going to be examples where
+ 
+
+ align:start position:0%
+cases they're going to be examples where
+we'll want to distinguish multiple
+
+ align:start position:0%
+we'll want to distinguish multiple
+ 
+
+ align:start position:0%
+we'll want to distinguish multiple
+affixes that are maybe similar to each
+
+ align:start position:0%
+affixes that are maybe similar to each
+ 
+
+ align:start position:0%
+affixes that are maybe similar to each
+other so think about the prefix on
+
+ align:start position:0%
+other so think about the prefix on
+ 
+
+ align:start position:0%
+other so think about the prefix on
+the prefixon shows up in words like
+
+ align:start position:0%
+the prefixon shows up in words like
+ 
+
+ align:start position:0%
+the prefixon shows up in words like
+unwrap and untie
+
+ align:start position:0%
+unwrap and untie
+ 
+
+ align:start position:0%
+unwrap and untie
+and also in words like unlikely and
+
+ align:start position:0%
+and also in words like unlikely and
+ 
+
+ align:start position:0%
+and also in words like unlikely and
+unhappy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um these two ones
+
+ align:start position:0%
+um these two ones
+ 
+
+ align:start position:0%
+um these two ones
+arguably mean different things
+
+ align:start position:0%
+arguably mean different things
+ 
+
+ align:start position:0%
+arguably mean different things
+and they're attaching to different
+
+ align:start position:0%
+and they're attaching to different
+ 
+
+ align:start position:0%
+and they're attaching to different
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so somebody helped me be less vague
+
+ align:start position:0%
+so somebody helped me be less vague
+ 
+
+ align:start position:0%
+so somebody helped me be less vague
+what's the first undoing what does it
+
+ align:start position:0%
+what's the first undoing what does it
+ 
+
+ align:start position:0%
+what's the first undoing what does it
+attach to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verbs okay so there's none that attaches
+
+ align:start position:0%
+verbs okay so there's none that attaches
+ 
+
+ align:start position:0%
+verbs okay so there's none that attaches
+to verbs what does the UN that attaches
+
+ align:start position:0%
+to verbs what does the UN that attaches
+ 
+
+ align:start position:0%
+to verbs what does the UN that attaches
+to verbs mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you undo wait I just used the yeah
+
+ align:start position:0%
+yeah you undo wait I just used the yeah
+ 
+
+ align:start position:0%
+yeah you undo wait I just used the yeah
+you you reverse there we go you you you
+
+ align:start position:0%
+you you reverse there we go you you you
+ 
+
+ align:start position:0%
+you you reverse there we go you you you
+take the result state of the verb and
+
+ align:start position:0%
+take the result state of the verb and
+ 
+
+ align:start position:0%
+take the result state of the verb and
+you cause it to go back to the way it
+
+ align:start position:0%
+you cause it to go back to the way it
+ 
+
+ align:start position:0%
+you cause it to go back to the way it
+was before the verb was done or
+
+ align:start position:0%
+was before the verb was done or
+ 
+
+ align:start position:0%
+was before the verb was done or
+something like that yeah so if you
+
+ align:start position:0%
+something like that yeah so if you
+ 
+
+ align:start position:0%
+something like that yeah so if you
+unwrap something you take something
+
+ align:start position:0%
+unwrap something you take something
+ 
+
+ align:start position:0%
+unwrap something you take something
+which is wrapped and you cause it to not
+
+ align:start position:0%
+which is wrapped and you cause it to not
+ 
+
+ align:start position:0%
+which is wrapped and you cause it to not
+be wrapped anymore
+
+ align:start position:0%
+be wrapped anymore
+ 
+
+ align:start position:0%
+be wrapped anymore
+something like that same with untie so
+
+ align:start position:0%
+something like that same with untie so
+ 
+
+ align:start position:0%
+something like that same with untie so
+there's an on
+
+ align:start position:0%
+there's an on
+ 
+
+ align:start position:0%
+there's an on
+that attaches to verbs
+
+ align:start position:0%
+that attaches to verbs
+ 
+
+ align:start position:0%
+that attaches to verbs
+and means something like reverse
+
+ align:start position:0%
+and means something like reverse
+ 
+
+ align:start position:0%
+and means something like reverse
+or to put it another way
+
+ align:start position:0%
+or to put it another way
+ 
+
+ align:start position:0%
+or to put it another way
+there's none
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that attaches to verbs
+
+ align:start position:0%
+that attaches to verbs
+ 
+
+ align:start position:0%
+that attaches to verbs
+and means something like reverse
+
+ align:start position:0%
+and means something like reverse
+ 
+
+ align:start position:0%
+and means something like reverse
+that's actually putting it the same way
+
+ align:start position:0%
+that's actually putting it the same way
+ 
+
+ align:start position:0%
+that's actually putting it the same way
+but in a different place yeah okay and
+
+ align:start position:0%
+but in a different place yeah okay and
+ 
+
+ align:start position:0%
+but in a different place yeah okay and
+then there's another on that attaches to
+
+ align:start position:0%
+then there's another on that attaches to
+ 
+
+ align:start position:0%
+then there's another on that attaches to
+what what's the other run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it attach to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjectives and what does it mean
+
+ align:start position:0%
+adjectives and what does it mean
+ 
+
+ align:start position:0%
+adjectives and what does it mean
+yeah like not you know or something like
+
+ align:start position:0%
+yeah like not you know or something like
+ 
+
+ align:start position:0%
+yeah like not you know or something like
+that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess get into debates about whether
+
+ align:start position:0%
+I guess get into debates about whether
+ 
+
+ align:start position:0%
+I guess get into debates about whether
+unhappy and sad mean the same thing
+
+ align:start position:0%
+unhappy and sad mean the same thing
+ 
+
+ align:start position:0%
+unhappy and sad mean the same thing
+uh or you know
+
+ align:start position:0%
+uh or you know
+ 
+
+ align:start position:0%
+uh or you know
+unlikely and whatever the opposite of
+
+ align:start position:0%
+unlikely and whatever the opposite of
+ 
+
+ align:start position:0%
+unlikely and whatever the opposite of
+likely is
+
+ align:start position:0%
+likely is
+ 
+
+ align:start position:0%
+likely is
+uh what am I putting here adjectives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not okay okay so two UNS yes
+
+ align:start position:0%
+not okay okay so two UNS yes
+ 
+
+ align:start position:0%
+not okay okay so two UNS yes
+we're like unwrapping uh-huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really good question what kind of tree
+
+ align:start position:0%
+really good question what kind of tree
+ 
+
+ align:start position:0%
+really good question what kind of tree
+should we draw should we draw a tree so
+
+ align:start position:0%
+should we draw should we draw a tree so
+ 
+
+ align:start position:0%
+should we draw should we draw a tree so
+the question was for unwrapping are we
+
+ align:start position:0%
+the question was for unwrapping are we
+ 
+
+ align:start position:0%
+the question was for unwrapping are we
+going to attach un to wrap giving a verb
+
+ align:start position:0%
+going to attach un to wrap giving a verb
+ 
+
+ align:start position:0%
+going to attach un to wrap giving a verb
+unwrap and adding to that or are we
+
+ align:start position:0%
+unwrap and adding to that or are we
+ 
+
+ align:start position:0%
+unwrap and adding to that or are we
+going to add ing to wrap giving you
+
+ align:start position:0%
+going to add ing to wrap giving you
+ 
+
+ align:start position:0%
+going to add ing to wrap giving you
+wrapping
+
+ align:start position:0%
+wrapping
+ 
+
+ align:start position:0%
+wrapping
+and then add on to that a third on
+
+ align:start position:0%
+and then add on to that a third on
+ 
+
+ align:start position:0%
+and then add on to that a third on
+what do people think what should we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you would
+
+ align:start position:0%
+then you would
+ 
+
+ align:start position:0%
+then you would
+you would first where you attach the ink
+
+ align:start position:0%
+you would first where you attach the ink
+ 
+
+ align:start position:0%
+you would first where you attach the ink
+to wrap
+
+ align:start position:0%
+to wrap
+ 
+
+ align:start position:0%
+to wrap
+undo
+
+ align:start position:0%
+undo
+ 
+
+ align:start position:0%
+undo
+yeah so well we have it on maybe this is
+
+ align:start position:0%
+yeah so well we have it on maybe this is
+ 
+
+ align:start position:0%
+yeah so well we have it on maybe this is
+a way to think about it we have an on
+
+ align:start position:0%
+a way to think about it we have an on
+ 
+
+ align:start position:0%
+a way to think about it we have an on
+that we can attach to verbs
+
+ align:start position:0%
+that we can attach to verbs
+ 
+
+ align:start position:0%
+that we can attach to verbs
+and so in the case of unwrapping I guess
+
+ align:start position:0%
+and so in the case of unwrapping I guess
+ 
+
+ align:start position:0%
+and so in the case of unwrapping I guess
+we could hope that we can survive with
+
+ align:start position:0%
+we could hope that we can survive with
+ 
+
+ align:start position:0%
+we could hope that we can survive with
+just that on until something forces us
+
+ align:start position:0%
+just that on until something forces us
+ 
+
+ align:start position:0%
+just that on until something forces us
+to do something else but you have an
+
+ align:start position:0%
+to do something else but you have an
+ 
+
+ align:start position:0%
+to do something else but you have an
+idea too
+
+ align:start position:0%
+idea too
+ 
+
+ align:start position:0%
+idea too
+subscribe to me
+
+ align:start position:0%
+subscribe to me
+ 
+
+ align:start position:0%
+subscribe to me
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I guess there are two words
+
+ align:start position:0%
+right so I guess there are two words
+ 
+
+ align:start position:0%
+right so I guess there are two words
+unwrapping this was your point too there
+
+ align:start position:0%
+unwrapping this was your point too there
+ 
+
+ align:start position:0%
+unwrapping this was your point too there
+are two two words unwrapping that we
+
+ align:start position:0%
+are two two words unwrapping that we
+ 
+
+ align:start position:0%
+are two two words unwrapping that we
+should think about one is uh he is
+
+ align:start position:0%
+should think about one is uh he is
+ 
+
+ align:start position:0%
+should think about one is uh he is
+unwrapping the presence and the other is
+
+ align:start position:0%
+unwrapping the presence and the other is
+ 
+
+ align:start position:0%
+unwrapping the presence and the other is
+unwrapping presence is fun yeah uh where
+
+ align:start position:0%
+unwrapping presence is fun yeah uh where
+ 
+
+ align:start position:0%
+unwrapping presence is fun yeah uh where
+unwrapping presence is fun hopefully
+
+ align:start position:0%
+unwrapping presence is fun hopefully
+ 
+
+ align:start position:0%
+unwrapping presence is fun hopefully
+unwrapping is some kind of noun that's
+
+ align:start position:0%
+unwrapping is some kind of noun that's
+ 
+
+ align:start position:0%
+unwrapping is some kind of noun that's
+what people sometimes call it gerund
+
+ align:start position:0%
+what people sometimes call it gerund
+ 
+
+ align:start position:0%
+what people sometimes call it gerund
+yeah where you convert a noun a verb
+
+ align:start position:0%
+yeah where you convert a noun a verb
+ 
+
+ align:start position:0%
+yeah where you convert a noun a verb
+into a noun that means the process of
+
+ align:start position:0%
+into a noun that means the process of
+ 
+
+ align:start position:0%
+into a noun that means the process of
+doing the verb or something like that
+
+ align:start position:0%
+doing the verb or something like that
+ 
+
+ align:start position:0%
+doing the verb or something like that
+maybe in both cases we would hope yeah
+
+ align:start position:0%
+maybe in both cases we would hope yeah
+ 
+
+ align:start position:0%
+maybe in both cases we would hope yeah
+that you would first create the unverb
+
+ align:start position:0%
+that you would first create the unverb
+ 
+
+ align:start position:0%
+that you would first create the unverb
+right and then you would add ing to it
+
+ align:start position:0%
+right and then you would add ing to it
+ 
+
+ align:start position:0%
+right and then you would add ing to it
+because attaches to verbs and does other
+
+ align:start position:0%
+because attaches to verbs and does other
+ 
+
+ align:start position:0%
+because attaches to verbs and does other
+things with them sometimes they're still
+
+ align:start position:0%
+things with them sometimes they're still
+ 
+
+ align:start position:0%
+things with them sometimes they're still
+verbs sometimes they're nouns no
+
+ align:start position:0%
+verbs sometimes they're nouns no
+ 
+
+ align:start position:0%
+verbs sometimes they're nouns no
+um that would be my first hope until
+
+ align:start position:0%
+um that would be my first hope until
+ 
+
+ align:start position:0%
+um that would be my first hope until
+somebody made me hope for something else
+
+ align:start position:0%
+somebody made me hope for something else
+ 
+
+ align:start position:0%
+somebody made me hope for something else
+maybe one way to say this is uh
+
+ align:start position:0%
+maybe one way to say this is uh
+ 
+
+ align:start position:0%
+maybe one way to say this is uh
+these are cases where we know uh that
+
+ align:start position:0%
+these are cases where we know uh that
+ 
+
+ align:start position:0%
+these are cases where we know uh that
+there have to be two UNS
+
+ align:start position:0%
+there have to be two UNS
+ 
+
+ align:start position:0%
+there have to be two UNS
+yeah both because these two ones seem to
+
+ align:start position:0%
+yeah both because these two ones seem to
+ 
+
+ align:start position:0%
+yeah both because these two ones seem to
+mean slightly different things and
+
+ align:start position:0%
+mean slightly different things and
+ 
+
+ align:start position:0%
+mean slightly different things and
+because well they're just they are
+
+ align:start position:0%
+because well they're just they are
+ 
+
+ align:start position:0%
+because well they're just they are
+attaching to things of different kinds
+
+ align:start position:0%
+attaching to things of different kinds
+ 
+
+ align:start position:0%
+attaching to things of different kinds
+you know verbs and verbs and adjectives
+
+ align:start position:0%
+you know verbs and verbs and adjectives
+ 
+
+ align:start position:0%
+you know verbs and verbs and adjectives
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh your example where we're adding on to
+
+ align:start position:0%
+uh your example where we're adding on to
+ 
+
+ align:start position:0%
+uh your example where we're adding on to
+so suppose we were thinking about the
+
+ align:start position:0%
+so suppose we were thinking about the
+ 
+
+ align:start position:0%
+so suppose we were thinking about the
+the uh unwrapping is fun case the gerund
+
+ align:start position:0%
+the uh unwrapping is fun case the gerund
+ 
+
+ align:start position:0%
+the uh unwrapping is fun case the gerund
+case uh if you wanted to add on after
+
+ align:start position:0%
+case uh if you wanted to add on after
+ 
+
+ align:start position:0%
+case uh if you wanted to add on after
+you added ing after you made it into a
+
+ align:start position:0%
+you added ing after you made it into a
+ 
+
+ align:start position:0%
+you added ing after you made it into a
+noun you'd be invoking an un that
+
+ align:start position:0%
+noun you'd be invoking an un that
+ 
+
+ align:start position:0%
+noun you'd be invoking an un that
+attaches to nouns
+
+ align:start position:0%
+attaches to nouns
+ 
+
+ align:start position:0%
+attaches to nouns
+and then the question the the next
+
+ align:start position:0%
+and then the question the the next
+ 
+
+ align:start position:0%
+and then the question the the next
+question people would ask you would be
+
+ align:start position:0%
+question people would ask you would be
+ 
+
+ align:start position:0%
+question people would ask you would be
+okay so can you show me an example of
+
+ align:start position:0%
+okay so can you show me an example of
+ 
+
+ align:start position:0%
+okay so can you show me an example of
+unattaching to a noun where the noun
+
+ align:start position:0%
+unattaching to a noun where the noun
+ 
+
+ align:start position:0%
+unattaching to a noun where the noun
+isn't created from a verb within you
+
+ align:start position:0%
+isn't created from a verb within you
+ 
+
+ align:start position:0%
+isn't created from a verb within you
+know just a plain noun that would be the
+
+ align:start position:0%
+know just a plain noun that would be the
+ 
+
+ align:start position:0%
+know just a plain noun that would be the
+strongest kind of evidence that we
+
+ align:start position:0%
+strongest kind of evidence that we
+ 
+
+ align:start position:0%
+strongest kind of evidence that we
+needed a third on does that make any
+
+ align:start position:0%
+needed a third on does that make any
+ 
+
+ align:start position:0%
+needed a third on does that make any
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+good question other questions
+
+ align:start position:0%
+good question other questions
+ 
+
+ align:start position:0%
+good question other questions
+okay all right so
+
+ align:start position:0%
+okay all right so
+ 
+
+ align:start position:0%
+okay all right so
+uh so we need what does it go out to
+
+ align:start position:0%
+uh so we need what does it go out to
+ 
+
+ align:start position:0%
+uh so we need what does it go out to
+what does it create Okay cool so we need
+
+ align:start position:0%
+what does it create Okay cool so we need
+ 
+
+ align:start position:0%
+what does it create Okay cool so we need
+two ones uh here's another affix to
+
+ align:start position:0%
+two ones uh here's another affix to
+ 
+
+ align:start position:0%
+two ones uh here's another affix to
+think about Bubble drinkable breakable
+
+ align:start position:0%
+think about Bubble drinkable breakable
+ 
+
+ align:start position:0%
+think about Bubble drinkable breakable
+watchable what's this bubble attached to
+
+ align:start position:0%
+watchable what's this bubble attached to
+ 
+
+ align:start position:0%
+watchable what's this bubble attached to
+verbs and what do you get
+
+ align:start position:0%
+verbs and what do you get
+ 
+
+ align:start position:0%
+verbs and what do you get
+adjectives yeah so Apple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converts verbs
+
+ align:start position:0%
+converts verbs
+ 
+
+ align:start position:0%
+converts verbs
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+two adjectives
+
+ align:start position:0%
+two adjectives
+ 
+
+ align:start position:0%
+two adjectives
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and it also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converts verbs
+
+ align:start position:0%
+converts verbs
+ 
+
+ align:start position:0%
+converts verbs
+into adjectives
+
+ align:start position:0%
+into adjectives
+ 
+
+ align:start position:0%
+into adjectives
+on doesn't convert the things that
+
+ align:start position:0%
+on doesn't convert the things that
+ 
+
+ align:start position:0%
+on doesn't convert the things that
+attaches to at all so far yeah so on
+
+ align:start position:0%
+attaches to at all so far yeah so on
+ 
+
+ align:start position:0%
+attaches to at all so far yeah so on
+we'll go back to on uh sure we will
+
+ align:start position:0%
+we'll go back to on uh sure we will
+ 
+
+ align:start position:0%
+we'll go back to on uh sure we will
+there we go uh on attaches to verbs and
+
+ align:start position:0%
+there we go uh on attaches to verbs and
+ 
+
+ align:start position:0%
+there we go uh on attaches to verbs and
+what you get is a verb unattached
+
+ align:start position:0%
+what you get is a verb unattached
+ 
+
+ align:start position:0%
+what you get is a verb unattached
+adjectives and what you get is an
+
+ align:start position:0%
+adjectives and what you get is an
+ 
+
+ align:start position:0%
+adjectives and what you get is an
+adjective so it changes the meaning but
+
+ align:start position:0%
+adjective so it changes the meaning but
+ 
+
+ align:start position:0%
+adjective so it changes the meaning but
+it doesn't change the category of the
+
+ align:start position:0%
+it doesn't change the category of the
+ 
+
+ align:start position:0%
+it doesn't change the category of the
+word the thing is still the same yeah
+
+ align:start position:0%
+word the thing is still the same yeah
+ 
+
+ align:start position:0%
+word the thing is still the same yeah
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have two UNS one that attaches to
+
+ align:start position:0%
+so we have two UNS one that attaches to
+ 
+
+ align:start position:0%
+so we have two UNS one that attaches to
+verbs and makes new verbs yes thank you
+
+ align:start position:0%
+verbs and makes new verbs yes thank you
+ 
+
+ align:start position:0%
+verbs and makes new verbs yes thank you
+I just said that uh
+
+ align:start position:0%
+I just said that uh
+ 
+
+ align:start position:0%
+I just said that uh
+and then another on that attaches to
+
+ align:start position:0%
+and then another on that attaches to
+ 
+
+ align:start position:0%
+and then another on that attaches to
+adjectives and makes new adjectives
+
+ align:start position:0%
+adjectives and makes new adjectives
+ 
+
+ align:start position:0%
+adjectives and makes new adjectives
+and then we have a novel that attaches
+
+ align:start position:0%
+and then we have a novel that attaches
+ 
+
+ align:start position:0%
+and then we have a novel that attaches
+to verbs and makes adjectives
+
+ align:start position:0%
+to verbs and makes adjectives
+ 
+
+ align:start position:0%
+to verbs and makes adjectives
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+let's think about a case where we're
+
+ align:start position:0%
+let's think about a case where we're
+ 
+
+ align:start position:0%
+let's think about a case where we're
+adding on
+
+ align:start position:0%
+adding on
+ 
+
+ align:start position:0%
+adding on
+and also able a word like unlockable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what should that be able to mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it's the answer
+
+ align:start position:0%
+yes it's the answer
+ 
+
+ align:start position:0%
+yes it's the answer
+so if we're going to start with lock
+
+ align:start position:0%
+so if we're going to start with lock
+ 
+
+ align:start position:0%
+so if we're going to start with lock
+ah you find an eraser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we'll do this over here first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to start with lock
+
+ align:start position:0%
+we're going to start with lock
+ 
+
+ align:start position:0%
+we're going to start with lock
+uh what shall we add first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on let's say okay so lock is a verb
+
+ align:start position:0%
+on let's say okay so lock is a verb
+ 
+
+ align:start position:0%
+on let's say okay so lock is a verb
+we'll add on we'll get so here's an
+
+ align:start position:0%
+we'll add on we'll get so here's an
+ 
+
+ align:start position:0%
+we'll add on we'll get so here's an
+affix
+
+ align:start position:0%
+affix
+ 
+
+ align:start position:0%
+affix
+put these two things together what will
+
+ align:start position:0%
+put these two things together what will
+ 
+
+ align:start position:0%
+put these two things together what will
+the result of adding on to lock be
+
+ align:start position:0%
+the result of adding on to lock be
+ 
+
+ align:start position:0%
+the result of adding on to lock be
+another verb yep
+
+ align:start position:0%
+another verb yep
+ 
+
+ align:start position:0%
+another verb yep
+and then we'll take Abel which we know
+
+ align:start position:0%
+and then we'll take Abel which we know
+ 
+
+ align:start position:0%
+and then we'll take Abel which we know
+attaches to verbs and creates adjectives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um so we'll take that FX we'll take
+
+ align:start position:0%
+um so we'll take that FX we'll take
+ 
+
+ align:start position:0%
+um so we'll take that FX we'll take
+attention to that verb and what we'll
+
+ align:start position:0%
+attention to that verb and what we'll
+ 
+
+ align:start position:0%
+attention to that verb and what we'll
+get will be
+
+ align:start position:0%
+get will be
+ 
+
+ align:start position:0%
+get will be
+an adjective right
+
+ align:start position:0%
+an adjective right
+ 
+
+ align:start position:0%
+an adjective right
+so we'll have an adjective which we
+
+ align:start position:0%
+so we'll have an adjective which we
+ 
+
+ align:start position:0%
+so we'll have an adjective which we
+created by first putting on unlock and
+
+ align:start position:0%
+created by first putting on unlock and
+ 
+
+ align:start position:0%
+created by first putting on unlock and
+then putting a bull on unlock yeah
+
+ align:start position:0%
+then putting a bull on unlock yeah
+ 
+
+ align:start position:0%
+then putting a bull on unlock yeah
+now I'm going to draw the other option
+
+ align:start position:0%
+now I'm going to draw the other option
+ 
+
+ align:start position:0%
+now I'm going to draw the other option
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+uh and where am I going to put it
+
+ align:start position:0%
+uh and where am I going to put it
+ 
+
+ align:start position:0%
+uh and where am I going to put it
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+so over there we attached unfirst so
+
+ align:start position:0%
+so over there we attached unfirst so
+ 
+
+ align:start position:0%
+so over there we attached unfirst so
+this time we're going to take the verb
+
+ align:start position:0%
+this time we're going to take the verb
+ 
+
+ align:start position:0%
+this time we're going to take the verb
+lock
+
+ align:start position:0%
+lock
+ 
+
+ align:start position:0%
+lock
+and we're going to add a bowl to it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's uh the result going to be when we
+
+ align:start position:0%
+what's uh the result going to be when we
+ 
+
+ align:start position:0%
+what's uh the result going to be when we
+add the affix bubble to the verb lock
+
+ align:start position:0%
+add the affix bubble to the verb lock
+ 
+
+ align:start position:0%
+add the affix bubble to the verb lock
+an adjective
+
+ align:start position:0%
+an adjective
+ 
+
+ align:start position:0%
+an adjective
+and we're going to add the affix on to
+
+ align:start position:0%
+and we're going to add the affix on to
+ 
+
+ align:start position:0%
+and we're going to add the affix on to
+that adjective and the result of that
+
+ align:start position:0%
+that adjective and the result of that
+ 
+
+ align:start position:0%
+that adjective and the result of that
+will be an adjective both of these will
+
+ align:start position:0%
+will be an adjective both of these will
+ 
+
+ align:start position:0%
+will be an adjective both of these will
+be pronounced unlockable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what will they mean
+
+ align:start position:0%
+but what will they mean
+ 
+
+ align:start position:0%
+but what will they mean
+what will that one mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it cannot be locked yeah so this is a
+
+ align:start position:0%
+it cannot be locked yeah so this is a
+ 
+
+ align:start position:0%
+it cannot be locked yeah so this is a
+broken lock yeah it is unlockable yeah
+
+ align:start position:0%
+broken lock yeah it is unlockable yeah
+ 
+
+ align:start position:0%
+broken lock yeah it is unlockable yeah
+right because when you add double to
+
+ align:start position:0%
+right because when you add double to
+ 
+
+ align:start position:0%
+right because when you add double to
+lock you get an adjective
+
+ align:start position:0%
+lock you get an adjective
+ 
+
+ align:start position:0%
+lock you get an adjective
+possible to lock
+
+ align:start position:0%
+possible to lock
+ 
+
+ align:start position:0%
+possible to lock
+and then when you add on to it you say
+
+ align:start position:0%
+and then when you add on to it you say
+ 
+
+ align:start position:0%
+and then when you add on to it you say
+not possible to lock this thing
+
+ align:start position:0%
+not possible to lock this thing
+ 
+
+ align:start position:0%
+not possible to lock this thing
+how about that one over that unlockable
+
+ align:start position:0%
+how about that one over that unlockable
+ 
+
+ align:start position:0%
+how about that one over that unlockable
+over there the one where we first added
+
+ align:start position:0%
+over there the one where we first added
+ 
+
+ align:start position:0%
+over there the one where we first added
+on to lock and then we add a double what
+
+ align:start position:0%
+on to lock and then we add a double what
+ 
+
+ align:start position:0%
+on to lock and then we add a double what
+does this one mean
+
+ align:start position:0%
+does this one mean
+ 
+
+ align:start position:0%
+does this one mean
+can be unlocked
+
+ align:start position:0%
+can be unlocked
+ 
+
+ align:start position:0%
+can be unlocked
+this is not a broken lock that's working
+
+ align:start position:0%
+this is not a broken lock that's working
+ 
+
+ align:start position:0%
+this is not a broken lock that's working
+properly
+
+ align:start position:0%
+properly
+ 
+
+ align:start position:0%
+properly
+yeah and that's our intuition about the
+
+ align:start position:0%
+yeah and that's our intuition about the
+ 
+
+ align:start position:0%
+yeah and that's our intuition about the
+word unlockable it is ambiguous
+
+ align:start position:0%
+word unlockable it is ambiguous
+ 
+
+ align:start position:0%
+word unlockable it is ambiguous
+if you say this story is unlockable
+
+ align:start position:0%
+if you say this story is unlockable
+ 
+
+ align:start position:0%
+if you say this story is unlockable
+because I have the key
+
+ align:start position:0%
+because I have the key
+ 
+
+ align:start position:0%
+because I have the key
+or this story is unlockable somebody
+
+ align:start position:0%
+or this story is unlockable somebody
+ 
+
+ align:start position:0%
+or this story is unlockable somebody
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+somebody calls a locksmith
+
+ align:start position:0%
+somebody calls a locksmith
+ 
+
+ align:start position:0%
+somebody calls a locksmith
+does that sound right
+
+ align:start position:0%
+does that sound right
+ 
+
+ align:start position:0%
+does that sound right
+can mean either of those things yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I don't have to you're Unsinkable right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you think do you think there is a
+
+ align:start position:0%
+do you think do you think there is a
+ 
+
+ align:start position:0%
+do you think do you think there is a
+verb unsync
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so actually you're raising oh yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can sink a ship right
+
+ align:start position:0%
+you can sink a ship right
+ 
+
+ align:start position:0%
+you can sink a ship right
+so the verbs transitive
+
+ align:start position:0%
+so the verbs transitive
+ 
+
+ align:start position:0%
+so the verbs transitive
+and the ship can also sink so it can be
+
+ align:start position:0%
+and the ship can also sink so it can be
+ 
+
+ align:start position:0%
+and the ship can also sink so it can be
+intransitive
+
+ align:start position:0%
+intransitive
+ 
+
+ align:start position:0%
+intransitive
+you can lock a door and a door can lock
+
+ align:start position:0%
+you can lock a door and a door can lock
+ 
+
+ align:start position:0%
+you can lock a door and a door can lock
+so we have a bunch of verbs that can go
+
+ align:start position:0%
+so we have a bunch of verbs that can go
+ 
+
+ align:start position:0%
+so we have a bunch of verbs that can go
+back and forth between being transitive
+
+ align:start position:0%
+back and forth between being transitive
+ 
+
+ align:start position:0%
+back and forth between being transitive
+and intransitive we'll talk more about
+
+ align:start position:0%
+and intransitive we'll talk more about
+ 
+
+ align:start position:0%
+and intransitive we'll talk more about
+transitivity later but for people who
+
+ align:start position:0%
+transitivity later but for people who
+ 
+
+ align:start position:0%
+transitivity later but for people who
+are wondering what the heck we're
+
+ align:start position:0%
+are wondering what the heck we're
+ 
+
+ align:start position:0%
+are wondering what the heck we're
+talking about verbs are said to be
+
+ align:start position:0%
+talking about verbs are said to be
+ 
+
+ align:start position:0%
+talking about verbs are said to be
+transitive if they have both the subject
+
+ align:start position:0%
+transitive if they have both the subject
+ 
+
+ align:start position:0%
+transitive if they have both the subject
+and an object so if you sync a ship I
+
+ align:start position:0%
+and an object so if you sync a ship I
+ 
+
+ align:start position:0%
+and an object so if you sync a ship I
+sank the ship then the verb is
+
+ align:start position:0%
+sank the ship then the verb is
+ 
+
+ align:start position:0%
+sank the ship then the verb is
+transitive uh you say the ship sank and
+
+ align:start position:0%
+transitive uh you say the ship sank and
+ 
+
+ align:start position:0%
+transitive uh you say the ship sank and
+there's only a subject There's No Object
+
+ align:start position:0%
+there's only a subject There's No Object
+ 
+
+ align:start position:0%
+there's only a subject There's No Object
+so the verb is intransitive English has
+
+ align:start position:0%
+so the verb is intransitive English has
+ 
+
+ align:start position:0%
+so the verb is intransitive English has
+a lot of verbs that can be either
+
+ align:start position:0%
+a lot of verbs that can be either
+ 
+
+ align:start position:0%
+a lot of verbs that can be either
+and a lot of the verbs that are up here
+
+ align:start position:0%
+and a lot of the verbs that are up here
+ 
+
+ align:start position:0%
+and a lot of the verbs that are up here
+can be either your question raises a
+
+ align:start position:0%
+can be either your question raises a
+ 
+
+ align:start position:0%
+can be either your question raises a
+really good point though which is I just
+
+ align:start position:0%
+really good point though which is I just
+ 
+
+ align:start position:0%
+really good point though which is I just
+sort of casually said you can add on to
+
+ align:start position:0%
+sort of casually said you can add on to
+ 
+
+ align:start position:0%
+sort of casually said you can add on to
+verbs and it means undo the effect of
+
+ align:start position:0%
+verbs and it means undo the effect of
+ 
+
+ align:start position:0%
+verbs and it means undo the effect of
+the verb
+
+ align:start position:0%
+the verb
+ 
+
+ align:start position:0%
+the verb
+look unwrap untie
+
+ align:start position:0%
+look unwrap untie
+ 
+
+ align:start position:0%
+look unwrap untie
+but you can't unsink a ship
+
+ align:start position:0%
+but you can't unsink a ship
+ 
+
+ align:start position:0%
+but you can't unsink a ship
+even if you you know
+
+ align:start position:0%
+even if you you know
+ 
+
+ align:start position:0%
+even if you you know
+go down with divers and find the ship
+
+ align:start position:0%
+go down with divers and find the ship
+ 
+
+ align:start position:0%
+go down with divers and find the ship
+and bring it back to the surface and you
+
+ align:start position:0%
+and bring it back to the surface and you
+ 
+
+ align:start position:0%
+and bring it back to the surface and you
+know you're still not unsinking the ship
+
+ align:start position:0%
+know you're still not unsinking the ship
+ 
+
+ align:start position:0%
+know you're still not unsinking the ship
+I don't think right it doesn't matter
+
+ align:start position:0%
+I don't think right it doesn't matter
+ 
+
+ align:start position:0%
+I don't think right it doesn't matter
+how good you are at
+
+ align:start position:0%
+how good you are at
+ 
+
+ align:start position:0%
+how good you are at
+this yeah so there we have to say some
+
+ align:start position:0%
+this yeah so there we have to say some
+ 
+
+ align:start position:0%
+this yeah so there we have to say some
+other things about that on you're
+
+ align:start position:0%
+other things about that on you're
+ 
+
+ align:start position:0%
+other things about that on you're
+raising a good point there are some
+
+ align:start position:0%
+raising a good point there are some
+ 
+
+ align:start position:0%
+raising a good point there are some
+verbs that cannot be reversed and sync
+
+ align:start position:0%
+verbs that cannot be reversed and sync
+ 
+
+ align:start position:0%
+verbs that cannot be reversed and sync
+maybe is one of them
+
+ align:start position:0%
+maybe is one of them
+ 
+
+ align:start position:0%
+maybe is one of them
+Joseph yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I feel like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it cannot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the other one yeah yeah that's if
+
+ align:start position:0%
+it's the other one yeah yeah that's if
+ 
+
+ align:start position:0%
+it's the other one yeah yeah that's if
+your brain is like my brain then it then
+
+ align:start position:0%
+your brain is like my brain then it then
+ 
+
+ align:start position:0%
+your brain is like my brain then it then
+it really likes that one the one you
+
+ align:start position:0%
+it really likes that one the one you
+ 
+
+ align:start position:0%
+it really likes that one the one you
+can't see it's not your fault yeah it's
+
+ align:start position:0%
+can't see it's not your fault yeah it's
+ 
+
+ align:start position:0%
+can't see it's not your fault yeah it's
+over there under the under the slot yep
+
+ align:start position:0%
+over there under the under the slot yep
+ 
+
+ align:start position:0%
+over there under the under the slot yep
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah it's unlockable the door
+
+ align:start position:0%
+yeah yeah yeah it's unlockable the door
+ 
+
+ align:start position:0%
+yeah yeah yeah it's unlockable the door
+is unlockable versus like
+
+ align:start position:0%
+is unlockable versus like
+ 
+
+ align:start position:0%
+is unlockable versus like
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah I might be more likely to say
+
+ align:start position:0%
+yeah yeah I might be more likely to say
+ 
+
+ align:start position:0%
+yeah yeah I might be more likely to say
+that I I think you're right I have that
+
+ align:start position:0%
+that I I think you're right I have that
+ 
+
+ align:start position:0%
+that I I think you're right I have that
+feeling too and actually I sort of
+
+ align:start position:0%
+feeling too and actually I sort of
+ 
+
+ align:start position:0%
+feeling too and actually I sort of
+cheated a second ago when I said you
+
+ align:start position:0%
+cheated a second ago when I said you
+ 
+
+ align:start position:0%
+cheated a second ago when I said you
+know unlockable it's ambiguous you can
+
+ align:start position:0%
+know unlockable it's ambiguous you can
+ 
+
+ align:start position:0%
+know unlockable it's ambiguous you can
+say either one but for me at least if I
+
+ align:start position:0%
+say either one but for me at least if I
+ 
+
+ align:start position:0%
+say either one but for me at least if I
+want to mean
+
+ align:start position:0%
+want to mean
+ 
+
+ align:start position:0%
+want to mean
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+the one that means it's broken you can't
+
+ align:start position:0%
+the one that means it's broken you can't
+ 
+
+ align:start position:0%
+the one that means it's broken you can't
+lock it I kind of have to say it's
+
+ align:start position:0%
+lock it I kind of have to say it's
+ 
+
+ align:start position:0%
+lock it I kind of have to say it's
+unlockable
+
+ align:start position:0%
+unlockable
+ 
+
+ align:start position:0%
+unlockable
+like as opposed to this one which you
+
+ align:start position:0%
+like as opposed to this one which you
+ 
+
+ align:start position:0%
+like as opposed to this one which you
+say it's unlockable
+
+ align:start position:0%
+say it's unlockable
+ 
+
+ align:start position:0%
+say it's unlockable
+I kind of have to put another stress on
+
+ align:start position:0%
+I kind of have to put another stress on
+ 
+
+ align:start position:0%
+I kind of have to put another stress on
+on or something like that that's my
+
+ align:start position:0%
+on or something like that that's my
+ 
+
+ align:start position:0%
+on or something like that that's my
+feeling but maybe some of you are
+
+ align:start position:0%
+feeling but maybe some of you are
+ 
+
+ align:start position:0%
+feeling but maybe some of you are
+looking at me as though I've grown two
+
+ align:start position:0%
+looking at me as though I've grown two
+ 
+
+ align:start position:0%
+looking at me as though I've grown two
+heads which is a kind of look that I get
+
+ align:start position:0%
+heads which is a kind of look that I get
+ 
+
+ align:start position:0%
+heads which is a kind of look that I get
+a lot just kind of walking around so you
+
+ align:start position:0%
+a lot just kind of walking around so you
+ 
+
+ align:start position:0%
+a lot just kind of walking around so you
+know I'm used to it does anybody else
+
+ align:start position:0%
+know I'm used to it does anybody else
+ 
+
+ align:start position:0%
+know I'm used to it does anybody else
+have that feeling I don't think I
+
+ align:start position:0%
+have that feeling I don't think I
+ 
+
+ align:start position:0%
+have that feeling I don't think I
+pronounced these two verbs the same way
+
+ align:start position:0%
+pronounced these two verbs the same way
+ 
+
+ align:start position:0%
+pronounced these two verbs the same way
+adjectives these two adjectives the same
+
+ align:start position:0%
+adjectives these two adjectives the same
+ 
+
+ align:start position:0%
+adjectives these two adjectives the same
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law yes now uh this is 24 900. we will
+
+ align:start position:0%
+law yes now uh this is 24 900. we will
+ 
+
+ align:start position:0%
+law yes now uh this is 24 900. we will
+surely not get to the bottom of this but
+
+ align:start position:0%
+surely not get to the bottom of this but
+ 
+
+ align:start position:0%
+surely not get to the bottom of this but
+this is a really interesting sort of
+
+ align:start position:0%
+this is a really interesting sort of
+ 
+
+ align:start position:0%
+this is a really interesting sort of
+question and maybe one of the things
+
+ align:start position:0%
+question and maybe one of the things
+ 
+
+ align:start position:0%
+question and maybe one of the things
+we're learning is that if we want to
+
+ align:start position:0%
+we're learning is that if we want to
+ 
+
+ align:start position:0%
+we're learning is that if we want to
+have a full understanding of how stress
+
+ align:start position:0%
+have a full understanding of how stress
+ 
+
+ align:start position:0%
+have a full understanding of how stress
+works we need to be willing to think
+
+ align:start position:0%
+works we need to be willing to think
+ 
+
+ align:start position:0%
+works we need to be willing to think
+about these structures you know these
+
+ align:start position:0%
+about these structures you know these
+ 
+
+ align:start position:0%
+about these structures you know these
+structures are apparently informing our
+
+ align:start position:0%
+structures are apparently informing our
+ 
+
+ align:start position:0%
+structures are apparently informing our
+intuitions about where stress goes and
+
+ align:start position:0%
+intuitions about where stress goes and
+ 
+
+ align:start position:0%
+intuitions about where stress goes and
+how it's treated which is kind of
+
+ align:start position:0%
+how it's treated which is kind of
+ 
+
+ align:start position:0%
+how it's treated which is kind of
+interesting you had to hand up a while
+
+ align:start position:0%
+interesting you had to hand up a while
+ 
+
+ align:start position:0%
+interesting you had to hand up a while
+ago and I never got to I'm sorry yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct oh
+
+ align:start position:0%
+correct oh
+ 
+
+ align:start position:0%
+correct oh
+you can't you can't unsync a ship
+
+ align:start position:0%
+you can't you can't unsync a ship
+ 
+
+ align:start position:0%
+you can't you can't unsync a ship
+huh boy
+
+ align:start position:0%
+huh boy
+ 
+
+ align:start position:0%
+huh boy
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you know in general you can't unsync a
+
+ align:start position:0%
+you know in general you can't unsync a
+ 
+
+ align:start position:0%
+you know in general you can't unsync a
+ship but I think this ship might be
+
+ align:start position:0%
+ship but I think this ship might be
+ 
+
+ align:start position:0%
+ship but I think this ship might be
+Unsinkable
+
+ align:start position:0%
+Unsinkable
+ 
+
+ align:start position:0%
+Unsinkable
+maybe I don't know I don't know
+
+ align:start position:0%
+maybe I don't know I don't know
+ 
+
+ align:start position:0%
+maybe I don't know I don't know
+you can't you can't you can't unburn a
+
+ align:start position:0%
+you can't you can't you can't unburn a
+ 
+
+ align:start position:0%
+you can't you can't you can't unburn a
+letter
+
+ align:start position:0%
+letter
+ 
+
+ align:start position:0%
+letter
+you can't Unbreak a teapot
+
+ align:start position:0%
+you can't Unbreak a teapot
+ 
+
+ align:start position:0%
+you can't Unbreak a teapot
+yeah so so so maybe maybe uh maybe maybe
+
+ align:start position:0%
+yeah so so so maybe maybe uh maybe maybe
+ 
+
+ align:start position:0%
+yeah so so so maybe maybe uh maybe maybe
+I was too fast to say there are verbs
+
+ align:start position:0%
+I was too fast to say there are verbs
+ 
+
+ align:start position:0%
+I was too fast to say there are verbs
+that can't be reversed and to the extent
+
+ align:start position:0%
+that can't be reversed and to the extent
+ 
+
+ align:start position:0%
+that can't be reversed and to the extent
+that you can reverse them I think you
+
+ align:start position:0%
+that you can reverse them I think you
+ 
+
+ align:start position:0%
+that you can reverse them I think you
+then get both of these adjectives you
+
+ align:start position:0%
+then get both of these adjectives you
+ 
+
+ align:start position:0%
+then get both of these adjectives you
+know so
+
+ align:start position:0%
+know so
+ 
+
+ align:start position:0%
+know so
+yeah yeah yeah oh these are deep Waters
+
+ align:start position:0%
+yeah yeah yeah oh these are deep Waters
+ 
+
+ align:start position:0%
+yeah yeah yeah oh these are deep Waters
+fortunately for me other people are
+
+ align:start position:0%
+fortunately for me other people are
+ 
+
+ align:start position:0%
+fortunately for me other people are
+raising their hands let me see what they
+
+ align:start position:0%
+raising their hands let me see what they
+ 
+
+ align:start position:0%
+raising their hands let me see what they
+have to say yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh that's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we have this crazy scientist at MIT he's
+
+ align:start position:0%
+we have this crazy scientist at MIT he's
+ 
+
+ align:start position:0%
+we have this crazy scientist at MIT he's
+been he's doing this weird diving
+
+ align:start position:0%
+been he's doing this weird diving
+ 
+
+ align:start position:0%
+been he's doing this weird diving
+research he's spending all his time
+
+ align:start position:0%
+research he's spending all his time
+ 
+
+ align:start position:0%
+research he's spending all his time
+trying to unsink ships
+
+ align:start position:0%
+trying to unsink ships
+ 
+
+ align:start position:0%
+trying to unsink ships
+I don't know maybe it's just a matter of
+
+ align:start position:0%
+I don't know maybe it's just a matter of
+ 
+
+ align:start position:0%
+I don't know maybe it's just a matter of
+the number of times you say it so that
+
+ align:start position:0%
+the number of times you say it so that
+ 
+
+ align:start position:0%
+the number of times you say it so that
+eventually you know it's just the you
+
+ align:start position:0%
+eventually you know it's just the you
+ 
+
+ align:start position:0%
+eventually you know it's just the you
+know unlocking a door this is the kind
+
+ align:start position:0%
+know unlocking a door this is the kind
+ 
+
+ align:start position:0%
+know unlocking a door this is the kind
+of thing that happens all the time
+
+ align:start position:0%
+of thing that happens all the time
+ 
+
+ align:start position:0%
+of thing that happens all the time
+whereas uh unwrapping your present
+
+ align:start position:0%
+whereas uh unwrapping your present
+ 
+
+ align:start position:0%
+whereas uh unwrapping your present
+whereas unsinking a ship you know people
+
+ align:start position:0%
+whereas unsinking a ship you know people
+ 
+
+ align:start position:0%
+whereas unsinking a ship you know people
+generally don't so yeah maybe that's all
+
+ align:start position:0%
+generally don't so yeah maybe that's all
+ 
+
+ align:start position:0%
+generally don't so yeah maybe that's all
+that's happening did you have a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+uh-huh so uh if you unlock a door you
+
+ align:start position:0%
+uh-huh so uh if you unlock a door you
+ 
+
+ align:start position:0%
+uh-huh so uh if you unlock a door you
+can lock it again
+
+ align:start position:0%
+can lock it again
+ 
+
+ align:start position:0%
+can lock it again
+of course if you can unsync ships you
+
+ align:start position:0%
+of course if you can unsync ships you
+ 
+
+ align:start position:0%
+of course if you can unsync ships you
+can probably sync them again right
+
+ align:start position:0%
+can probably sync them again right
+ 
+
+ align:start position:0%
+can probably sync them again right
+this is going to get expensive and wet
+
+ align:start position:0%
+this is going to get expensive and wet
+ 
+
+ align:start position:0%
+this is going to get expensive and wet
+but yeah so there it's there's only
+
+ align:start position:0%
+but yeah so there it's there's only
+ 
+
+ align:start position:0%
+but yeah so there it's there's only
+something you can do Raquel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+specific word
+
+ align:start position:0%
+specific word
+ 
+
+ align:start position:0%
+specific word
+I guess that is an unbearable that
+
+ align:start position:0%
+I guess that is an unbearable that
+ 
+
+ align:start position:0%
+I guess that is an unbearable that
+breaks this because we don't think
+
+ align:start position:0%
+breaks this because we don't think
+ 
+
+ align:start position:0%
+breaks this because we don't think
+unfair oh that's a very that's that's
+
+ align:start position:0%
+unfair oh that's a very that's that's
+ 
+
+ align:start position:0%
+unfair oh that's a very that's that's
+well yeah so but okay let's those are
+
+ align:start position:0%
+well yeah so but okay let's those are
+ 
+
+ align:start position:0%
+well yeah so but okay let's those are
+both really interesting thoughts I mean
+
+ align:start position:0%
+both really interesting thoughts I mean
+ 
+
+ align:start position:0%
+both really interesting thoughts I mean
+the first thought is sort of what we're
+
+ align:start position:0%
+the first thought is sort of what we're
+ 
+
+ align:start position:0%
+the first thought is sort of what we're
+arguing about is whether unsync is a
+
+ align:start position:0%
+arguing about is whether unsync is a
+ 
+
+ align:start position:0%
+arguing about is whether unsync is a
+word or not and I guess the answer
+
+ align:start position:0%
+word or not and I guess the answer
+ 
+
+ align:start position:0%
+word or not and I guess the answer
+that's sort of emerging is sort of you
+
+ align:start position:0%
+that's sort of emerging is sort of you
+ 
+
+ align:start position:0%
+that's sort of emerging is sort of you
+know it's just not something you do all
+
+ align:start position:0%
+know it's just not something you do all
+ 
+
+ align:start position:0%
+know it's just not something you do all
+the time and so so we're our intuitions
+
+ align:start position:0%
+the time and so so we're our intuitions
+ 
+
+ align:start position:0%
+the time and so so we're our intuitions
+about it are kind of fuzzy unbearable is
+
+ align:start position:0%
+about it are kind of fuzzy unbearable is
+ 
+
+ align:start position:0%
+about it are kind of fuzzy unbearable is
+a really nice example
+
+ align:start position:0%
+a really nice example
+ 
+
+ align:start position:0%
+a really nice example
+um uh basically what that's telling us
+
+ align:start position:0%
+um uh basically what that's telling us
+ 
+
+ align:start position:0%
+um uh basically what that's telling us
+is that uh what the heck is it telling
+
+ align:start position:0%
+is that uh what the heck is it telling
+ 
+
+ align:start position:0%
+is that uh what the heck is it telling
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+unbearable so the bearable right the
+
+ align:start position:0%
+unbearable so the bearable right the
+ 
+
+ align:start position:0%
+unbearable so the bearable right the
+adjective variable right uh has a couple
+
+ align:start position:0%
+adjective variable right uh has a couple
+ 
+
+ align:start position:0%
+adjective variable right uh has a couple
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a couple of meanings
+
+ align:start position:0%
+a couple of meanings
+ 
+
+ align:start position:0%
+a couple of meanings
+um the meaning that you have in mind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the meaning that you have in mind let
+
+ align:start position:0%
+uh the meaning that you have in mind let
+ 
+
+ align:start position:0%
+uh the meaning that you have in mind let
+me remind my computer not to do that
+
+ align:start position:0%
+me remind my computer not to do that
+ 
+
+ align:start position:0%
+me remind my computer not to do that
+sorry the meaning that you have in mind
+
+ align:start position:0%
+sorry the meaning that you have in mind
+ 
+
+ align:start position:0%
+sorry the meaning that you have in mind
+is one where bearable it doesn't just
+
+ align:start position:0%
+is one where bearable it doesn't just
+ 
+
+ align:start position:0%
+is one where bearable it doesn't just
+mean can be carried right it means
+
+ align:start position:0%
+mean can be carried right it means
+ 
+
+ align:start position:0%
+mean can be carried right it means
+something more emotional than that right
+
+ align:start position:0%
+something more emotional than that right
+ 
+
+ align:start position:0%
+something more emotional than that right
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+no but it can have that kind of
+
+ align:start position:0%
+no but it can have that kind of
+ 
+
+ align:start position:0%
+no but it can have that kind of
+emotional meaning when you're bare you
+
+ align:start position:0%
+emotional meaning when you're bare you
+ 
+
+ align:start position:0%
+emotional meaning when you're bare you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+what she she bore the loss of hers of
+
+ align:start position:0%
+what she she bore the loss of hers of
+ 
+
+ align:start position:0%
+what she she bore the loss of hers of
+her stockholdings well yeah so yeah I
+
+ align:start position:0%
+her stockholdings well yeah so yeah I
+ 
+
+ align:start position:0%
+her stockholdings well yeah so yeah I
+know so maybe maybe okay
+
+ align:start position:0%
+know so maybe maybe okay
+ 
+
+ align:start position:0%
+know so maybe maybe okay
+um so so I guess what we're what we're
+
+ align:start position:0%
+um so so I guess what we're what we're
+ 
+
+ align:start position:0%
+um so so I guess what we're what we're
+learning is that although you cannot
+
+ align:start position:0%
+learning is that although you cannot
+ 
+
+ align:start position:0%
+learning is that although you cannot
+unbear something
+
+ align:start position:0%
+unbear something
+ 
+
+ align:start position:0%
+unbear something
+um maybe because there's no sense in
+
+ align:start position:0%
+um maybe because there's no sense in
+ 
+
+ align:start position:0%
+um maybe because there's no sense in
+which you can reverse the bearing of
+
+ align:start position:0%
+which you can reverse the bearing of
+ 
+
+ align:start position:0%
+which you can reverse the bearing of
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+uh there is an adjective variable and
+
+ align:start position:0%
+uh there is an adjective variable and
+ 
+
+ align:start position:0%
+uh there is an adjective variable and
+you can add the other end to that the UN
+
+ align:start position:0%
+you can add the other end to that the UN
+ 
+
+ align:start position:0%
+you can add the other end to that the UN
+that attaches to bearable to adjectives
+
+ align:start position:0%
+that attaches to bearable to adjectives
+ 
+
+ align:start position:0%
+that attaches to bearable to adjectives
+uh it means not bearable there yes okay
+
+ align:start position:0%
+uh it means not bearable there yes okay
+ 
+
+ align:start position:0%
+uh it means not bearable there yes okay
+good that's that's what I got distracted
+
+ align:start position:0%
+good that's that's what I got distracted
+ 
+
+ align:start position:0%
+good that's that's what I got distracted
+by emotions as so often but uh um yeah
+
+ align:start position:0%
+by emotions as so often but uh um yeah
+ 
+
+ align:start position:0%
+by emotions as so often but uh um yeah
+that just has to do with the fact that
+
+ align:start position:0%
+that just has to do with the fact that
+ 
+
+ align:start position:0%
+that just has to do with the fact that
+on you know people you're now debating
+
+ align:start position:0%
+on you know people you're now debating
+ 
+
+ align:start position:0%
+on you know people you're now debating
+about whether you can unsync a ship but
+
+ align:start position:0%
+about whether you can unsync a ship but
+ 
+
+ align:start position:0%
+about whether you can unsync a ship but
+you you surely can't uh unbear a loss I
+
+ align:start position:0%
+you you surely can't uh unbear a loss I
+ 
+
+ align:start position:0%
+you you surely can't uh unbear a loss I
+don't even know what that would mean
+
+ align:start position:0%
+don't even know what that would mean
+ 
+
+ align:start position:0%
+don't even know what that would mean
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um wow lots of questions yes
+
+ align:start position:0%
+um wow lots of questions yes
+ 
+
+ align:start position:0%
+um wow lots of questions yes
+I I think this is about the number like
+
+ align:start position:0%
+I I think this is about the number like
+ 
+
+ align:start position:0%
+I I think this is about the number like
+we used to say Apollo I know you can say
+
+ align:start position:0%
+we used to say Apollo I know you can say
+ 
+
+ align:start position:0%
+we used to say Apollo I know you can say
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+yeah yeah yeah
+
+ align:start position:0%
+yeah yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah yeah
+follow and unfollow is a really good
+
+ align:start position:0%
+follow and unfollow is a really good
+ 
+
+ align:start position:0%
+follow and unfollow is a really good
+example actually yeah so it used to not
+
+ align:start position:0%
+example actually yeah so it used to not
+ 
+
+ align:start position:0%
+example actually yeah so it used to not
+be possible to to unfollow things you
+
+ align:start position:0%
+be possible to to unfollow things you
+ 
+
+ align:start position:0%
+be possible to to unfollow things you
+know one crucial difference I guess is
+
+ align:start position:0%
+know one crucial difference I guess is
+ 
+
+ align:start position:0%
+know one crucial difference I guess is
+that if you wrap something or tie
+
+ align:start position:0%
+that if you wrap something or tie
+ 
+
+ align:start position:0%
+that if you wrap something or tie
+something you change it right so that
+
+ align:start position:0%
+something you change it right so that
+ 
+
+ align:start position:0%
+something you change it right so that
+it's different now as a result of what
+
+ align:start position:0%
+it's different now as a result of what
+ 
+
+ align:start position:0%
+it's different now as a result of what
+you've done so if you tie something it
+
+ align:start position:0%
+you've done so if you tie something it
+ 
+
+ align:start position:0%
+you've done so if you tie something it
+used to be just a string and now it's a
+
+ align:start position:0%
+used to be just a string and now it's a
+ 
+
+ align:start position:0%
+used to be just a string and now it's a
+knot you know or if you wrap something
+
+ align:start position:0%
+knot you know or if you wrap something
+ 
+
+ align:start position:0%
+knot you know or if you wrap something
+it used to be a thing and now it's a
+
+ align:start position:0%
+it used to be a thing and now it's a
+ 
+
+ align:start position:0%
+it used to be a thing and now it's a
+present you know if you sink a ship this
+
+ align:start position:0%
+present you know if you sink a ship this
+ 
+
+ align:start position:0%
+present you know if you sink a ship this
+is what we've all been talking about you
+
+ align:start position:0%
+is what we've all been talking about you
+ 
+
+ align:start position:0%
+is what we've all been talking about you
+know it goes from being on top of the
+
+ align:start position:0%
+know it goes from being on top of the
+ 
+
+ align:start position:0%
+know it goes from being on top of the
+water to being underneath it
+
+ align:start position:0%
+water to being underneath it
+ 
+
+ align:start position:0%
+water to being underneath it
+um as opposed to follow
+
+ align:start position:0%
+um as opposed to follow
+ 
+
+ align:start position:0%
+um as opposed to follow
+if you follow someone in real life uh
+
+ align:start position:0%
+if you follow someone in real life uh
+ 
+
+ align:start position:0%
+if you follow someone in real life uh
+you don't do anything to them right
+
+ align:start position:0%
+you don't do anything to them right
+ 
+
+ align:start position:0%
+you don't do anything to them right
+they're still the same as they were we
+
+ align:start position:0%
+they're still the same as they were we
+ 
+
+ align:start position:0%
+they're still the same as they were we
+kind of have this intuition the follow
+
+ align:start position:0%
+kind of have this intuition the follow
+ 
+
+ align:start position:0%
+kind of have this intuition the follow
+that you can unfollow someone is
+
+ align:start position:0%
+that you can unfollow someone is
+ 
+
+ align:start position:0%
+that you can unfollow someone is
+something that changes them from a
+
+ align:start position:0%
+something that changes them from a
+ 
+
+ align:start position:0%
+something that changes them from a
+person who has you know n number of
+
+ align:start position:0%
+person who has you know n number of
+ 
+
+ align:start position:0%
+person who has you know n number of
+followers to a person who has n plus one
+
+ align:start position:0%
+followers to a person who has n plus one
+ 
+
+ align:start position:0%
+followers to a person who has n plus one
+number of followers so there's something
+
+ align:start position:0%
+number of followers so there's something
+ 
+
+ align:start position:0%
+number of followers so there's something
+about whether the verb changes the state
+
+ align:start position:0%
+about whether the verb changes the state
+ 
+
+ align:start position:0%
+about whether the verb changes the state
+of the object I think that's got
+
+ align:start position:0%
+of the object I think that's got
+ 
+
+ align:start position:0%
+of the object I think that's got
+something to do with all this which is
+
+ align:start position:0%
+something to do with all this which is
+ 
+
+ align:start position:0%
+something to do with all this which is
+why these examples about unsinking ships
+
+ align:start position:0%
+why these examples about unsinking ships
+ 
+
+ align:start position:0%
+why these examples about unsinking ships
+and Unbreaking pots are kind of
+
+ align:start position:0%
+and Unbreaking pots are kind of
+ 
+
+ align:start position:0%
+and Unbreaking pots are kind of
+interesting to think about
+
+ align:start position:0%
+interesting to think about
+ 
+
+ align:start position:0%
+interesting to think about
+no uh yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well Scrabble thinks it's not a word so
+
+ align:start position:0%
+well Scrabble thinks it's not a word so
+ 
+
+ align:start position:0%
+well Scrabble thinks it's not a word so
+I mean Scrabble you know they have to
+
+ align:start position:0%
+I mean Scrabble you know they have to
+ 
+
+ align:start position:0%
+I mean Scrabble you know they have to
+have rules they have to draw a line
+
+ align:start position:0%
+have rules they have to draw a line
+ 
+
+ align:start position:0%
+have rules they have to draw a line
+somewhere yeah
+
+ align:start position:0%
+somewhere yeah
+ 
+
+ align:start position:0%
+somewhere yeah
+um yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Scrabble we should have a like a
+
+ align:start position:0%
+Scrabble we should have a like a
+ 
+
+ align:start position:0%
+Scrabble we should have a like a
+Scrabble version of 24.900 where we try
+
+ align:start position:0%
+Scrabble version of 24.900 where we try
+ 
+
+ align:start position:0%
+Scrabble version of 24.900 where we try
+to figure out what's going on but
+
+ align:start position:0%
+to figure out what's going on but
+ 
+
+ align:start position:0%
+to figure out what's going on but
+Scrabble is not is not English right
+
+ align:start position:0%
+Scrabble is not is not English right
+ 
+
+ align:start position:0%
+Scrabble is not is not English right
+it's something related to English but
+
+ align:start position:0%
+it's something related to English but
+ 
+
+ align:start position:0%
+it's something related to English but
+not the same yeah we're allowed to have
+
+ align:start position:0%
+not the same yeah we're allowed to have
+ 
+
+ align:start position:0%
+not the same yeah we're allowed to have
+our own intuitions about about what
+
+ align:start position:0%
+our own intuitions about about what
+ 
+
+ align:start position:0%
+our own intuitions about about what
+things are words and what things aren't
+
+ align:start position:0%
+things are words and what things aren't
+ 
+
+ align:start position:0%
+things are words and what things aren't
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+after Not Afraid this question but it's
+
+ align:start position:0%
+after Not Afraid this question but it's
+ 
+
+ align:start position:0%
+after Not Afraid this question but it's
+like you started off lecture by saying
+
+ align:start position:0%
+like you started off lecture by saying
+ 
+
+ align:start position:0%
+like you started off lecture by saying
+that media can come from the morphology
+
+ align:start position:0%
+that media can come from the morphology
+ 
+
+ align:start position:0%
+that media can come from the morphology
+yes and now we're trying to I guess
+
+ align:start position:0%
+yes and now we're trying to I guess
+ 
+
+ align:start position:0%
+yes and now we're trying to I guess
+figure out
+
+ align:start position:0%
+figure out
+ 
+
+ align:start position:0%
+figure out
+well so one way to think about it right
+
+ align:start position:0%
+well so one way to think about it right
+ 
+
+ align:start position:0%
+well so one way to think about it right
+would be to think uh so this this stuff
+
+ align:start position:0%
+would be to think uh so this this stuff
+ 
+
+ align:start position:0%
+would be to think uh so this this stuff
+about which verbs can you attach unto
+
+ align:start position:0%
+about which verbs can you attach unto
+ 
+
+ align:start position:0%
+about which verbs can you attach unto
+where I just said uh well so we started
+
+ align:start position:0%
+where I just said uh well so we started
+ 
+
+ align:start position:0%
+where I just said uh well so we started
+by saying uncontattach to verbs and it
+
+ align:start position:0%
+by saying uncontattach to verbs and it
+ 
+
+ align:start position:0%
+by saying uncontattach to verbs and it
+gives you uh a new verb that means
+
+ align:start position:0%
+gives you uh a new verb that means
+ 
+
+ align:start position:0%
+gives you uh a new verb that means
+um take the thing that is in the state
+
+ align:start position:0%
+um take the thing that is in the state
+ 
+
+ align:start position:0%
+um take the thing that is in the state
+resulting from the action of the verb
+
+ align:start position:0%
+resulting from the action of the verb
+ 
+
+ align:start position:0%
+resulting from the action of the verb
+and put it back in the state that it was
+
+ align:start position:0%
+and put it back in the state that it was
+ 
+
+ align:start position:0%
+and put it back in the state that it was
+in before you did the verb that's one
+
+ align:start position:0%
+in before you did the verb that's one
+ 
+
+ align:start position:0%
+in before you did the verb that's one
+way of defining what un means yeah
+
+ align:start position:0%
+way of defining what un means yeah
+ 
+
+ align:start position:0%
+way of defining what un means yeah
+um and then if did that make sense yeah
+
+ align:start position:0%
+um and then if did that make sense yeah
+ 
+
+ align:start position:0%
+um and then if did that make sense yeah
+so if you untie something what does that
+
+ align:start position:0%
+so if you untie something what does that
+ 
+
+ align:start position:0%
+so if you untie something what does that
+do it takes something which is tied
+
+ align:start position:0%
+do it takes something which is tied
+ 
+
+ align:start position:0%
+do it takes something which is tied
+which is in the state that you're in as
+
+ align:start position:0%
+which is in the state that you're in as
+ 
+
+ align:start position:0%
+which is in the state that you're in as
+a result of the verb to tie and converts
+
+ align:start position:0%
+a result of the verb to tie and converts
+ 
+
+ align:start position:0%
+a result of the verb to tie and converts
+it into something which is not tied
+
+ align:start position:0%
+it into something which is not tied
+ 
+
+ align:start position:0%
+it into something which is not tied
+anymore yeah that's what it is to untie
+
+ align:start position:0%
+anymore yeah that's what it is to untie
+ 
+
+ align:start position:0%
+anymore yeah that's what it is to untie
+something yeah so if that's what un
+
+ align:start position:0%
+something yeah so if that's what un
+ 
+
+ align:start position:0%
+something yeah so if that's what un
+means then yes you should be able to
+
+ align:start position:0%
+means then yes you should be able to
+ 
+
+ align:start position:0%
+means then yes you should be able to
+attach it to verbs but you should only
+
+ align:start position:0%
+attach it to verbs but you should only
+ 
+
+ align:start position:0%
+attach it to verbs but you should only
+be able to attach it to verbs that
+
+ align:start position:0%
+be able to attach it to verbs that
+ 
+
+ align:start position:0%
+be able to attach it to verbs that
+change the state of their objects
+
+ align:start position:0%
+change the state of their objects
+ 
+
+ align:start position:0%
+change the state of their objects
+because it it makes reference to this
+
+ align:start position:0%
+because it it makes reference to this
+ 
+
+ align:start position:0%
+because it it makes reference to this
+sort of change of the state of the
+
+ align:start position:0%
+sort of change of the state of the
+ 
+
+ align:start position:0%
+sort of change of the state of the
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+this is me making stuff up right you
+
+ align:start position:0%
+this is me making stuff up right you
+ 
+
+ align:start position:0%
+this is me making stuff up right you
+know here in front of all of you but
+
+ align:start position:0%
+know here in front of all of you but
+ 
+
+ align:start position:0%
+know here in front of all of you but
+this seems reasonable to me I think it
+
+ align:start position:0%
+this seems reasonable to me I think it
+ 
+
+ align:start position:0%
+this seems reasonable to me I think it
+might it might be something like that
+
+ align:start position:0%
+might it might be something like that
+ 
+
+ align:start position:0%
+might it might be something like that
+um yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it should well so it should be valid yes
+
+ align:start position:0%
+it should well so it should be valid yes
+ 
+
+ align:start position:0%
+it should well so it should be valid yes
+it certainly does change the state yes
+
+ align:start position:0%
+it certainly does change the state yes
+ 
+
+ align:start position:0%
+it certainly does change the state yes
+um gosh is that the time yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I I look this is so for me at least
+
+ align:start position:0%
+so I I look this is so for me at least
+ 
+
+ align:start position:0%
+so I I look this is so for me at least
+this is what is cool and fun about
+
+ align:start position:0%
+this is what is cool and fun about
+ 
+
+ align:start position:0%
+this is what is cool and fun about
+Linguistics we're here it is day three
+
+ align:start position:0%
+Linguistics we're here it is day three
+ 
+
+ align:start position:0%
+Linguistics we're here it is day three
+and we are right on the edge I'm a
+
+ align:start position:0%
+and we are right on the edge I'm a
+ 
+
+ align:start position:0%
+and we are right on the edge I'm a
+professional linguist this is what I do
+
+ align:start position:0%
+professional linguist this is what I do
+ 
+
+ align:start position:0%
+professional linguist this is what I do
+for a living and I'm not quite sure what
+
+ align:start position:0%
+for a living and I'm not quite sure what
+ 
+
+ align:start position:0%
+for a living and I'm not quite sure what
+the answer to this question is so you
+
+ align:start position:0%
+the answer to this question is so you
+ 
+
+ align:start position:0%
+the answer to this question is so you
+know you you guys could be the ones who
+
+ align:start position:0%
+know you you guys could be the ones who
+ 
+
+ align:start position:0%
+know you you guys could be the ones who
+figure out what the heck is going on
+
+ align:start position:0%
+figure out what the heck is going on
+ 
+
+ align:start position:0%
+figure out what the heck is going on
+with unsync right to which the answer
+
+ align:start position:0%
+with unsync right to which the answer
+ 
+
+ align:start position:0%
+with unsync right to which the answer
+could be um yeah unsync is more or less
+
+ align:start position:0%
+could be um yeah unsync is more or less
+ 
+
+ align:start position:0%
+could be um yeah unsync is more or less
+okay right it's just not something
+
+ align:start position:0%
+okay right it's just not something
+ 
+
+ align:start position:0%
+okay right it's just not something
+people do all the time and so we're not
+
+ align:start position:0%
+people do all the time and so we're not
+ 
+
+ align:start position:0%
+people do all the time and so we're not
+used to hearing it maybe that's the the
+
+ align:start position:0%
+used to hearing it maybe that's the the
+ 
+
+ align:start position:0%
+used to hearing it maybe that's the the
+easy way of getting out of where I am or
+
+ align:start position:0%
+easy way of getting out of where I am or
+ 
+
+ align:start position:0%
+easy way of getting out of where I am or
+maybe there's more to say about what
+
+ align:start position:0%
+maybe there's more to say about what
+ 
+
+ align:start position:0%
+maybe there's more to say about what
+exactly undoes to the meaning of the
+
+ align:start position:0%
+exactly undoes to the meaning of the
+ 
+
+ align:start position:0%
+exactly undoes to the meaning of the
+verb but that's the kind of answer to
+
+ align:start position:0%
+verb but that's the kind of answer to
+ 
+
+ align:start position:0%
+verb but that's the kind of answer to
+your question that we would get that if
+
+ align:start position:0%
+your question that we would get that if
+ 
+
+ align:start position:0%
+your question that we would get that if
+we if we Define everything about the
+
+ align:start position:0%
+we if we Define everything about the
+ 
+
+ align:start position:0%
+we if we Define everything about the
+meaning of un that that will help us
+
+ align:start position:0%
+meaning of un that that will help us
+ 
+
+ align:start position:0%
+meaning of un that that will help us
+understand why it can attach to some
+
+ align:start position:0%
+understand why it can attach to some
+ 
+
+ align:start position:0%
+understand why it can attach to some
+verbs but not others yeah and as you can
+
+ align:start position:0%
+verbs but not others yeah and as you can
+ 
+
+ align:start position:0%
+verbs but not others yeah and as you can
+see we're not quite there maybe
+
+ align:start position:0%
+see we're not quite there maybe
+ 
+
+ align:start position:0%
+see we're not quite there maybe
+Joseph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you can be unhelpful oh god
+
+ align:start position:0%
+well you can be unhelpful oh god
+ 
+
+ align:start position:0%
+well you can be unhelpful oh god
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+um but there you're adding it to an
+
+ align:start position:0%
+um but there you're adding it to an
+ 
+
+ align:start position:0%
+um but there you're adding it to an
+adjective yeah yeah yeah uh so you
+
+ align:start position:0%
+adjective yeah yeah yeah uh so you
+ 
+
+ align:start position:0%
+adjective yeah yeah yeah uh so you
+cannot unhelp someone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I mean this is a good example of
+
+ align:start position:0%
+so I mean this is a good example of
+ 
+
+ align:start position:0%
+so I mean this is a good example of
+something somebody should have said to
+
+ align:start position:0%
+something somebody should have said to
+ 
+
+ align:start position:0%
+something somebody should have said to
+me when I first said well you know some
+
+ align:start position:0%
+me when I first said well you know some
+ 
+
+ align:start position:0%
+me when I first said well you know some
+verbs change the state of the object and
+
+ align:start position:0%
+verbs change the state of the object and
+ 
+
+ align:start position:0%
+verbs change the state of the object and
+others don't right so if I burn
+
+ align:start position:0%
+others don't right so if I burn
+ 
+
+ align:start position:0%
+others don't right so if I burn
+something you know it goes from being a
+
+ align:start position:0%
+something you know it goes from being a
+ 
+
+ align:start position:0%
+something you know it goes from being a
+thing to being a pile of carbon and uh
+
+ align:start position:0%
+thing to being a pile of carbon and uh
+ 
+
+ align:start position:0%
+thing to being a pile of carbon and uh
+if I break something it goes from
+
+ align:start position:0%
+if I break something it goes from
+ 
+
+ align:start position:0%
+if I break something it goes from
+reading the thing to being if I sink a
+
+ align:start position:0%
+reading the thing to being if I sink a
+ 
+
+ align:start position:0%
+reading the thing to being if I sink a
+ship it goes from being on top of the
+
+ align:start position:0%
+ship it goes from being on top of the
+ 
+
+ align:start position:0%
+ship it goes from being on top of the
+water being under the water if I help
+
+ align:start position:0%
+water being under the water if I help
+ 
+
+ align:start position:0%
+water being under the water if I help
+someone
+
+ align:start position:0%
+someone
+ 
+
+ align:start position:0%
+someone
+maybe they're the same as they were
+
+ align:start position:0%
+maybe they're the same as they were
+ 
+
+ align:start position:0%
+maybe they're the same as they were
+before just in a better position
+
+ align:start position:0%
+before just in a better position
+ 
+
+ align:start position:0%
+before just in a better position
+this is a place where you you're
+
+ align:start position:0%
+this is a place where you you're
+ 
+
+ align:start position:0%
+this is a place where you you're
+entitled to ask what do you mean by
+
+ align:start position:0%
+entitled to ask what do you mean by
+ 
+
+ align:start position:0%
+entitled to ask what do you mean by
+changing the state what counts as the
+
+ align:start position:0%
+changing the state what counts as the
+ 
+
+ align:start position:0%
+changing the state what counts as the
+state and we really must go on yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess yeah maybe that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know I mean look suppose I write
+
+ align:start position:0%
+I don't know I mean look suppose I write
+ 
+
+ align:start position:0%
+I don't know I mean look suppose I write
+you a recommendation letter for a job
+
+ align:start position:0%
+you a recommendation letter for a job
+ 
+
+ align:start position:0%
+you a recommendation letter for a job
+right that's helpful to you I helped him
+
+ align:start position:0%
+right that's helpful to you I helped him
+ 
+
+ align:start position:0%
+right that's helpful to you I helped him
+and then suppose I write another letter
+
+ align:start position:0%
+and then suppose I write another letter
+ 
+
+ align:start position:0%
+and then suppose I write another letter
+saying you know what I take it all back
+
+ align:start position:0%
+saying you know what I take it all back
+ 
+
+ align:start position:0%
+saying you know what I take it all back
+uh you know in fact it's the opposite of
+
+ align:start position:0%
+uh you know in fact it's the opposite of
+ 
+
+ align:start position:0%
+uh you know in fact it's the opposite of
+everything I just said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold on guys yeah yeah no I I see what
+
+ align:start position:0%
+hold on guys yeah yeah no I I see what
+ 
+
+ align:start position:0%
+hold on guys yeah yeah no I I see what
+you mean
+
+ align:start position:0%
+you mean
+ 
+
+ align:start position:0%
+you mean
+all right so moving on then uh from this
+
+ align:start position:0%
+all right so moving on then uh from this
+ 
+
+ align:start position:0%
+all right so moving on then uh from this
+slide uh which has generated so much
+
+ align:start position:0%
+slide uh which has generated so much
+ 
+
+ align:start position:0%
+slide uh which has generated so much
+cool discussion this is great
+
+ align:start position:0%
+cool discussion this is great
+ 
+
+ align:start position:0%
+cool discussion this is great
+okay so trees yeah there uh why is
+
+ align:start position:0%
+okay so trees yeah there uh why is
+ 
+
+ align:start position:0%
+okay so trees yeah there uh why is
+unlockable ambiguous because it has two
+
+ align:start position:0%
+unlockable ambiguous because it has two
+ 
+
+ align:start position:0%
+unlockable ambiguous because it has two
+trees or to put it another way there are
+
+ align:start position:0%
+trees or to put it another way there are
+ 
+
+ align:start position:0%
+trees or to put it another way there are
+these two morphemes you're adding to
+
+ align:start position:0%
+these two morphemes you're adding to
+ 
+
+ align:start position:0%
+these two morphemes you're adding to
+lock and you can add them in either
+
+ align:start position:0%
+lock and you can add them in either
+ 
+
+ align:start position:0%
+lock and you can add them in either
+order yeah with the result that the word
+
+ align:start position:0%
+order yeah with the result that the word
+ 
+
+ align:start position:0%
+order yeah with the result that the word
+is ambiguous in the way that we assist
+
+ align:start position:0%
+is ambiguous in the way that we assist
+ 
+
+ align:start position:0%
+is ambiguous in the way that we assist
+we suspect we we expect yeah uh so you
+
+ align:start position:0%
+we suspect we we expect yeah uh so you
+ 
+
+ align:start position:0%
+we suspect we we expect yeah uh so you
+know here's a model for how we're going
+
+ align:start position:0%
+know here's a model for how we're going
+ 
+
+ align:start position:0%
+know here's a model for how we're going
+to make words we're going to take
+
+ align:start position:0%
+to make words we're going to take
+ 
+
+ align:start position:0%
+to make words we're going to take
+morphemes pairs of morphemes and we're
+
+ align:start position:0%
+morphemes pairs of morphemes and we're
+ 
+
+ align:start position:0%
+morphemes pairs of morphemes and we're
+going to glom them together and we feel
+
+ align:start position:0%
+going to glom them together and we feel
+ 
+
+ align:start position:0%
+going to glom them together and we feel
+silly saying the word glom over and over
+
+ align:start position:0%
+silly saying the word glom over and over
+ 
+
+ align:start position:0%
+silly saying the word glom over and over
+again so we've made up another word for
+
+ align:start position:0%
+again so we've made up another word for
+ 
+
+ align:start position:0%
+again so we've made up another word for
+that we call it merge so merge is this
+
+ align:start position:0%
+that we call it merge so merge is this
+ 
+
+ align:start position:0%
+that we call it merge so merge is this
+process that allows you to take two
+
+ align:start position:0%
+process that allows you to take two
+ 
+
+ align:start position:0%
+process that allows you to take two
+things and put them together and make a
+
+ align:start position:0%
+things and put them together and make a
+ 
+
+ align:start position:0%
+things and put them together and make a
+new thing
+
+ align:start position:0%
+new thing
+ 
+
+ align:start position:0%
+new thing
+so you know you take on and lock and you
+
+ align:start position:0%
+so you know you take on and lock and you
+ 
+
+ align:start position:0%
+so you know you take on and lock and you
+merge them together to make unlock
+
+ align:start position:0%
+merge them together to make unlock
+ 
+
+ align:start position:0%
+merge them together to make unlock
+uh merge is recursive which means only
+
+ align:start position:0%
+uh merge is recursive which means only
+ 
+
+ align:start position:0%
+uh merge is recursive which means only
+that it can reapply to its own output so
+
+ align:start position:0%
+that it can reapply to its own output so
+ 
+
+ align:start position:0%
+that it can reapply to its own output so
+you take on and lock and merge them to
+
+ align:start position:0%
+you take on and lock and merge them to
+ 
+
+ align:start position:0%
+you take on and lock and merge them to
+make unlock and now you have a new thing
+
+ align:start position:0%
+make unlock and now you have a new thing
+ 
+
+ align:start position:0%
+make unlock and now you have a new thing
+unlock and that can also undergo merge
+
+ align:start position:0%
+unlock and that can also undergo merge
+ 
+
+ align:start position:0%
+unlock and that can also undergo merge
+so you can take unlock and merge it with
+
+ align:start position:0%
+so you can take unlock and merge it with
+ 
+
+ align:start position:0%
+so you can take unlock and merge it with
+Abu to get you unlockable that's what's
+
+ align:start position:0%
+Abu to get you unlockable that's what's
+ 
+
+ align:start position:0%
+Abu to get you unlockable that's what's
+going on in the tree on the left
+
+ align:start position:0%
+going on in the tree on the left
+ 
+
+ align:start position:0%
+going on in the tree on the left
+that's all linguists mean when we say
+
+ align:start position:0%
+that's all linguists mean when we say
+ 
+
+ align:start position:0%
+that's all linguists mean when we say
+that merge is recursive
+
+ align:start position:0%
+that merge is recursive
+ 
+
+ align:start position:0%
+that merge is recursive
+May sometimes hear people have arguments
+
+ align:start position:0%
+May sometimes hear people have arguments
+ 
+
+ align:start position:0%
+May sometimes hear people have arguments
+about what it means that's what it means
+
+ align:start position:0%
+about what it means that's what it means
+ 
+
+ align:start position:0%
+about what it means that's what it means
+so it means once you've merged two
+
+ align:start position:0%
+so it means once you've merged two
+ 
+
+ align:start position:0%
+so it means once you've merged two
+things to create a new thing you can
+
+ align:start position:0%
+things to create a new thing you can
+ 
+
+ align:start position:0%
+things to create a new thing you can
+take that new thing and apply merge to
+
+ align:start position:0%
+take that new thing and apply merge to
+ 
+
+ align:start position:0%
+take that new thing and apply merge to
+it as well and make new things that way
+
+ align:start position:0%
+it as well and make new things that way
+ 
+
+ align:start position:0%
+it as well and make new things that way
+yeah that's all it needs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and then there are statements which
+
+ align:start position:0%
+um and then there are statements which
+ 
+
+ align:start position:0%
+um and then there are statements which
+we have to put somewhere like uh Abel
+
+ align:start position:0%
+we have to put somewhere like uh Abel
+ 
+
+ align:start position:0%
+we have to put somewhere like uh Abel
+needs to merge with a verb and the
+
+ align:start position:0%
+needs to merge with a verb and the
+ 
+
+ align:start position:0%
+needs to merge with a verb and the
+result is an adjective things like that
+
+ align:start position:0%
+result is an adjective things like that
+ 
+
+ align:start position:0%
+result is an adjective things like that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes there's a three-half of your binary
+
+ align:start position:0%
+yes there's a three-half of your binary
+ 
+
+ align:start position:0%
+yes there's a three-half of your binary
+ah so I said we're going to take two
+
+ align:start position:0%
+ah so I said we're going to take two
+ 
+
+ align:start position:0%
+ah so I said we're going to take two
+things and we're going to merge them and
+
+ align:start position:0%
+things and we're going to merge them and
+ 
+
+ align:start position:0%
+things and we're going to merge them and
+make a new thing
+
+ align:start position:0%
+make a new thing
+ 
+
+ align:start position:0%
+make a new thing
+um uh really good question about which
+
+ align:start position:0%
+um uh really good question about which
+ 
+
+ align:start position:0%
+um uh really good question about which
+people have arguments yeah
+
+ align:start position:0%
+people have arguments yeah
+ 
+
+ align:start position:0%
+people have arguments yeah
+um actually seems to be the case that
+
+ align:start position:0%
+um actually seems to be the case that
+ 
+
+ align:start position:0%
+um actually seems to be the case that
+the trees are binary
+
+ align:start position:0%
+the trees are binary
+ 
+
+ align:start position:0%
+the trees are binary
+um which is interesting so do it another
+
+ align:start position:0%
+um which is interesting so do it another
+ 
+
+ align:start position:0%
+um which is interesting so do it another
+way there are lots of places where you
+
+ align:start position:0%
+way there are lots of places where you
+ 
+
+ align:start position:0%
+way there are lots of places where you
+can't tell whether the tree is binary or
+
+ align:start position:0%
+can't tell whether the tree is binary or
+ 
+
+ align:start position:0%
+can't tell whether the tree is binary or
+ternary or whatever but in every place
+
+ align:start position:0%
+ternary or whatever but in every place
+ 
+
+ align:start position:0%
+ternary or whatever but in every place
+where you can tell nobody has come up
+
+ align:start position:0%
+where you can tell nobody has come up
+ 
+
+ align:start position:0%
+where you can tell nobody has come up
+with a convincing example of a tree that
+
+ align:start position:0%
+with a convincing example of a tree that
+ 
+
+ align:start position:0%
+with a convincing example of a tree that
+is anything other than binary which is
+
+ align:start position:0%
+is anything other than binary which is
+ 
+
+ align:start position:0%
+is anything other than binary which is
+itself kind of interesting
+
+ align:start position:0%
+itself kind of interesting
+ 
+
+ align:start position:0%
+itself kind of interesting
+try to understand why that is
+
+ align:start position:0%
+try to understand why that is
+ 
+
+ align:start position:0%
+try to understand why that is
+we're going to be doing lots of merging
+
+ align:start position:0%
+we're going to be doing lots of merging
+ 
+
+ align:start position:0%
+we're going to be doing lots of merging
+in morphology and then not so much in
+
+ align:start position:0%
+in morphology and then not so much in
+ 
+
+ align:start position:0%
+in morphology and then not so much in
+phonology and then when we get to syntax
+
+ align:start position:0%
+phonology and then when we get to syntax
+ 
+
+ align:start position:0%
+phonology and then when we get to syntax
+there will be much merging many mergings
+
+ align:start position:0%
+there will be much merging many mergings
+ 
+
+ align:start position:0%
+there will be much merging many mergings
+of things words putting them together to
+
+ align:start position:0%
+of things words putting them together to
+ 
+
+ align:start position:0%
+of things words putting them together to
+make phrases of various kinds okay so
+
+ align:start position:0%
+make phrases of various kinds okay so
+ 
+
+ align:start position:0%
+make phrases of various kinds okay so
+try to get comfortable with the concept
+
+ align:start position:0%
+try to get comfortable with the concept
+ 
+
+ align:start position:0%
+try to get comfortable with the concept
+of merge
+
+ align:start position:0%
+of merge
+ 
+
+ align:start position:0%
+of merge
+should be easy it's not a hard concept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um this is great uh I just want to talk
+
+ align:start position:0%
+um this is great uh I just want to talk
+ 
+
+ align:start position:0%
+um this is great uh I just want to talk
+I want to talk a little more
+
+ align:start position:0%
+I want to talk a little more
+ 
+
+ align:start position:0%
+I want to talk a little more
+systematically about alamorph so
+
+ align:start position:0%
+systematically about alamorph so
+ 
+
+ align:start position:0%
+systematically about alamorph so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh mentioned before you take morphemes
+
+ align:start position:0%
+uh mentioned before you take morphemes
+ 
+
+ align:start position:0%
+uh mentioned before you take morphemes
+you merge them together you create new
+
+ align:start position:0%
+you merge them together you create new
+ 
+
+ align:start position:0%
+you merge them together you create new
+things and what often happens is that
+
+ align:start position:0%
+things and what often happens is that
+ 
+
+ align:start position:0%
+things and what often happens is that
+one or another or both of the morphemes
+
+ align:start position:0%
+one or another or both of the morphemes
+ 
+
+ align:start position:0%
+one or another or both of the morphemes
+will change its form right so the past
+
+ align:start position:0%
+will change its form right so the past
+ 
+
+ align:start position:0%
+will change its form right so the past
+tense of leap is lept the verb changes
+
+ align:start position:0%
+tense of leap is lept the verb changes
+ 
+
+ align:start position:0%
+tense of leap is lept the verb changes
+from leap to LEP yeah the past tense
+
+ align:start position:0%
+from leap to LEP yeah the past tense
+ 
+
+ align:start position:0%
+from leap to LEP yeah the past tense
+suffix can either be t or d or some
+
+ align:start position:0%
+suffix can either be t or d or some
+ 
+
+ align:start position:0%
+suffix can either be t or d or some
+other things yeah so I want to talk a
+
+ align:start position:0%
+other things yeah so I want to talk a
+ 
+
+ align:start position:0%
+other things yeah so I want to talk a
+little bit systematically about these
+
+ align:start position:0%
+little bit systematically about these
+ 
+
+ align:start position:0%
+little bit systematically about these
+allomorphs
+
+ align:start position:0%
+allomorphs
+ 
+
+ align:start position:0%
+allomorphs
+um I'll start by saying that there are
+
+ align:start position:0%
+um I'll start by saying that there are
+ 
+
+ align:start position:0%
+um I'll start by saying that there are
+cases where there just isn't anything
+
+ align:start position:0%
+cases where there just isn't anything
+ 
+
+ align:start position:0%
+cases where there just isn't anything
+interesting no there isn't anything
+
+ align:start position:0%
+interesting no there isn't anything
+ 
+
+ align:start position:0%
+interesting no there isn't anything
+helpful to say past tense of go is went
+
+ align:start position:0%
+helpful to say past tense of go is went
+ 
+
+ align:start position:0%
+helpful to say past tense of go is went
+right and it just is you know if you
+
+ align:start position:0%
+right and it just is you know if you
+ 
+
+ align:start position:0%
+right and it just is you know if you
+want to learn English you got to learn
+
+ align:start position:0%
+want to learn English you got to learn
+ 
+
+ align:start position:0%
+want to learn English you got to learn
+that there's nothing else to say
+
+ align:start position:0%
+that there's nothing else to say
+ 
+
+ align:start position:0%
+that there's nothing else to say
+um but there are other places where
+
+ align:start position:0%
+um but there are other places where
+ 
+
+ align:start position:0%
+um but there are other places where
+there are sort of general laws about
+
+ align:start position:0%
+there are sort of general laws about
+ 
+
+ align:start position:0%
+there are sort of general laws about
+which Elementor if you're going to get
+
+ align:start position:0%
+which Elementor if you're going to get
+ 
+
+ align:start position:0%
+which Elementor if you're going to get
+into Rich circumstance we sort of
+
+ align:start position:0%
+into Rich circumstance we sort of
+ 
+
+ align:start position:0%
+into Rich circumstance we sort of
+alluded to that a little bit when we
+
+ align:start position:0%
+alluded to that a little bit when we
+ 
+
+ align:start position:0%
+alluded to that a little bit when we
+were talking about cats and dogs right
+
+ align:start position:0%
+were talking about cats and dogs right
+ 
+
+ align:start position:0%
+were talking about cats and dogs right
+that s and Z those allomorphs of the
+
+ align:start position:0%
+that s and Z those allomorphs of the
+ 
+
+ align:start position:0%
+that s and Z those allomorphs of the
+plural are sort of conditioned by the
+
+ align:start position:0%
+plural are sort of conditioned by the
+ 
+
+ align:start position:0%
+plural are sort of conditioned by the
+sound that's before them and we'll talk
+
+ align:start position:0%
+sound that's before them and we'll talk
+ 
+
+ align:start position:0%
+sound that's before them and we'll talk
+more about that so I'm going to give you
+
+ align:start position:0%
+more about that so I'm going to give you
+ 
+
+ align:start position:0%
+more about that so I'm going to give you
+an example where there's more to say
+
+ align:start position:0%
+an example where there's more to say
+ 
+
+ align:start position:0%
+an example where there's more to say
+about the alamorphs this is an example
+
+ align:start position:0%
+about the alamorphs this is an example
+ 
+
+ align:start position:0%
+about the alamorphs this is an example
+from polish
+
+ align:start position:0%
+from polish
+ 
+
+ align:start position:0%
+from polish
+I should say I've spelled polish here in
+
+ align:start position:0%
+I should say I've spelled polish here in
+ 
+
+ align:start position:0%
+I should say I've spelled polish here in
+a strange way if anybody here speaks
+
+ align:start position:0%
+a strange way if anybody here speaks
+ 
+
+ align:start position:0%
+a strange way if anybody here speaks
+Polish this isn't the way you're used to
+
+ align:start position:0%
+Polish this isn't the way you're used to
+ 
+
+ align:start position:0%
+Polish this isn't the way you're used to
+seeing polish spelled so I've spelled it
+
+ align:start position:0%
+seeing polish spelled so I've spelled it
+ 
+
+ align:start position:0%
+seeing polish spelled so I've spelled it
+in a way that makes it easier for people
+
+ align:start position:0%
+in a way that makes it easier for people
+ 
+
+ align:start position:0%
+in a way that makes it easier for people
+who don't speak Polish to see what the
+
+ align:start position:0%
+who don't speak Polish to see what the
+ 
+
+ align:start position:0%
+who don't speak Polish to see what the
+words how the words are pronounced more
+
+ align:start position:0%
+words how the words are pronounced more
+ 
+
+ align:start position:0%
+words how the words are pronounced more
+or less
+
+ align:start position:0%
+or less
+ 
+
+ align:start position:0%
+or less
+so here are some Polish words uh they
+
+ align:start position:0%
+so here are some Polish words uh they
+ 
+
+ align:start position:0%
+so here are some Polish words uh they
+mean language pot juice and bow and
+
+ align:start position:0%
+mean language pot juice and bow and
+ 
+
+ align:start position:0%
+mean language pot juice and bow and
+you've got some plurals there does
+
+ align:start position:0%
+you've got some plurals there does
+ 
+
+ align:start position:0%
+you've got some plurals there does
+anybody here speak Polish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can just make anything up that I want
+
+ align:start position:0%
+I can just make anything up that I want
+ 
+
+ align:start position:0%
+I can just make anything up that I want
+believe me this is how polish works it
+
+ align:start position:0%
+believe me this is how polish works it
+ 
+
+ align:start position:0%
+believe me this is how polish works it
+is really I'm not making things up uh
+
+ align:start position:0%
+is really I'm not making things up uh
+ 
+
+ align:start position:0%
+is really I'm not making things up uh
+does anybody find any morphemes in here
+
+ align:start position:0%
+does anybody find any morphemes in here
+ 
+
+ align:start position:0%
+does anybody find any morphemes in here
+I mean there's morphemes that mean
+
+ align:start position:0%
+I mean there's morphemes that mean
+ 
+
+ align:start position:0%
+I mean there's morphemes that mean
+language pot juice and bow what's the
+
+ align:start position:0%
+language pot juice and bow what's the
+ 
+
+ align:start position:0%
+language pot juice and bow what's the
+plural morpheme
+
+ align:start position:0%
+plural morpheme
+ 
+
+ align:start position:0%
+plural morpheme
+E Yeah so this suffix spelled with the
+
+ align:start position:0%
+E Yeah so this suffix spelled with the
+ 
+
+ align:start position:0%
+E Yeah so this suffix spelled with the
+letter i it's pronounced e okay no Allen
+
+ align:start position:0%
+letter i it's pronounced e okay no Allen
+ 
+
+ align:start position:0%
+letter i it's pronounced e okay no Allen
+Murphy here so far
+
+ align:start position:0%
+Murphy here so far
+ 
+
+ align:start position:0%
+Murphy here so far
+here are some more words
+
+ align:start position:0%
+here are some more words
+ 
+
+ align:start position:0%
+here are some more words
+Bank of a river debt and lie
+
+ align:start position:0%
+Bank of a river debt and lie
+ 
+
+ align:start position:0%
+Bank of a river debt and lie
+which have plurals the idea of a plural
+
+ align:start position:0%
+which have plurals the idea of a plural
+ 
+
+ align:start position:0%
+which have plurals the idea of a plural
+of lie is a little strange if you ask me
+
+ align:start position:0%
+of lie is a little strange if you ask me
+ 
+
+ align:start position:0%
+of lie is a little strange if you ask me
+but nobody asked me
+
+ align:start position:0%
+but nobody asked me
+ 
+
+ align:start position:0%
+but nobody asked me
+um if you had the plural morpheme plural
+
+ align:start position:0%
+um if you had the plural morpheme plural
+ 
+
+ align:start position:0%
+um if you had the plural morpheme plural
+morpheme there is e and you get those
+
+ align:start position:0%
+morpheme there is e and you get those
+ 
+
+ align:start position:0%
+morpheme there is e and you get those
+plurals
+
+ align:start position:0%
+plurals
+ 
+
+ align:start position:0%
+plurals
+anybody are you seeing any alamorphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the plural suffix is still the same
+
+ align:start position:0%
+so the plural suffix is still the same
+ 
+
+ align:start position:0%
+so the plural suffix is still the same
+but uh debt for example has two
+
+ align:start position:0%
+but uh debt for example has two
+ 
+
+ align:start position:0%
+but uh debt for example has two
+allomorphs what are they
+
+ align:start position:0%
+allomorphs what are they
+ 
+
+ align:start position:0%
+allomorphs what are they
+somebody attempt to pronounce them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's okay none of us speak Polish
+
+ align:start position:0%
+it's okay none of us speak Polish
+ 
+
+ align:start position:0%
+it's okay none of us speak Polish
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah we've got Duke and dug yeah so debt
+
+ align:start position:0%
+yeah we've got Duke and dug yeah so debt
+ 
+
+ align:start position:0%
+yeah we've got Duke and dug yeah so debt
+has one Elementor if it ends in a k and
+
+ align:start position:0%
+has one Elementor if it ends in a k and
+ 
+
+ align:start position:0%
+has one Elementor if it ends in a k and
+another element that ends in a g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what's the rule do you think that
+
+ align:start position:0%
+what's the rule do you think that
+ 
+
+ align:start position:0%
+what's the rule do you think that
+determines when you get K and when you
+
+ align:start position:0%
+determines when you get K and when you
+ 
+
+ align:start position:0%
+determines when you get K and when you
+get G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I see that's a that's a neat idea so
+
+ align:start position:0%
+oh I see that's a that's a neat idea so
+ 
+
+ align:start position:0%
+oh I see that's a that's a neat idea so
+maybe we could work out a way so all of
+
+ align:start position:0%
+maybe we could work out a way so all of
+ 
+
+ align:start position:0%
+maybe we could work out a way so all of
+you are realizing the problem the
+
+ align:start position:0%
+you are realizing the problem the
+ 
+
+ align:start position:0%
+you are realizing the problem the
+problem is there are the words we
+
+ align:start position:0%
+problem is there are the words we
+ 
+
+ align:start position:0%
+problem is there are the words we
+started with where we have all these
+
+ align:start position:0%
+started with where we have all these
+ 
+
+ align:start position:0%
+started with where we have all these
+words that end in K and when you make
+
+ align:start position:0%
+words that end in K and when you make
+ 
+
+ align:start position:0%
+words that end in K and when you make
+the plural there's still a k before the
+
+ align:start position:0%
+the plural there's still a k before the
+ 
+
+ align:start position:0%
+the plural there's still a k before the
+E and then we have these other words
+
+ align:start position:0%
+E and then we have these other words
+ 
+
+ align:start position:0%
+E and then we have these other words
+where the word ends in K and then when
+
+ align:start position:0%
+where the word ends in K and then when
+ 
+
+ align:start position:0%
+where the word ends in K and then when
+you add plural you get a g yeah
+
+ align:start position:0%
+you add plural you get a g yeah
+ 
+
+ align:start position:0%
+you add plural you get a g yeah
+information because even if you look at
+
+ align:start position:0%
+information because even if you look at
+ 
+
+ align:start position:0%
+information because even if you look at
+the word for bow and lie yeah
+
+ align:start position:0%
+the word for bow and lie yeah
+ 
+
+ align:start position:0%
+the word for bow and lie yeah
+very nice point so uh this slide was
+
+ align:start position:0%
+very nice point so uh this slide was
+ 
+
+ align:start position:0%
+very nice point so uh this slide was
+carefully constructed to have what's
+
+ align:start position:0%
+carefully constructed to have what's
+ 
+
+ align:start position:0%
+carefully constructed to have what's
+called a minimal pair yeah Bo and lie
+
+ align:start position:0%
+called a minimal pair yeah Bo and lie
+ 
+
+ align:start position:0%
+called a minimal pair yeah Bo and lie
+are both pronounced wook in the singular
+
+ align:start position:0%
+are both pronounced wook in the singular
+ 
+
+ align:start position:0%
+are both pronounced wook in the singular
+but in plural
+
+ align:start position:0%
+but in plural
+ 
+
+ align:start position:0%
+but in plural
+the plural of bow is wookie
+
+ align:start position:0%
+the plural of bow is wookie
+ 
+
+ align:start position:0%
+the plural of bow is wookie
+and the plural of lie is Woogie yeah
+
+ align:start position:0%
+and the plural of lie is Woogie yeah
+ 
+
+ align:start position:0%
+and the plural of lie is Woogie yeah
+this is meant to make us despair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the option that you were raising
+
+ align:start position:0%
+about the option that you were raising
+ 
+
+ align:start position:0%
+about the option that you were raising
+right which was maybe if we look at
+
+ align:start position:0%
+right which was maybe if we look at
+ 
+
+ align:start position:0%
+right which was maybe if we look at
+everything about the word we'll be able
+
+ align:start position:0%
+everything about the word we'll be able
+ 
+
+ align:start position:0%
+everything about the word we'll be able
+to predict which K's become G's in which
+
+ align:start position:0%
+to predict which K's become G's in which
+ 
+
+ align:start position:0%
+to predict which K's become G's in which
+case steak Hayes no give up despair yeah
+
+ align:start position:0%
+case steak Hayes no give up despair yeah
+ 
+
+ align:start position:0%
+case steak Hayes no give up despair yeah
+cannot be done we cannot if we start
+
+ align:start position:0%
+cannot be done we cannot if we start
+ 
+
+ align:start position:0%
+cannot be done we cannot if we start
+with a k we cannot predict which K's
+
+ align:start position:0%
+with a k we cannot predict which K's
+ 
+
+ align:start position:0%
+with a k we cannot predict which K's
+will become G's and which ones will not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that's a neat idea so can you
+
+ align:start position:0%
+I think that's a neat idea so can you
+ 
+
+ align:start position:0%
+I think that's a neat idea so can you
+say more about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+might just be that if you end in uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I'll just say again what you
+
+ align:start position:0%
+yeah so I'll just say again what you
+ 
+
+ align:start position:0%
+yeah so I'll just say again what you
+just said just to make sure everybody
+
+ align:start position:0%
+just said just to make sure everybody
+ 
+
+ align:start position:0%
+just said just to make sure everybody
+heard it I framed the problem as which
+
+ align:start position:0%
+heard it I framed the problem as which
+ 
+
+ align:start position:0%
+heard it I framed the problem as which
+case change into G is in which case
+
+ align:start position:0%
+case change into G is in which case
+ 
+
+ align:start position:0%
+case change into G is in which case
+don't change into G's and then we
+
+ align:start position:0%
+don't change into G's and then we
+ 
+
+ align:start position:0%
+don't change into G's and then we
+convinced ourselves thanks to your point
+
+ align:start position:0%
+convinced ourselves thanks to your point
+ 
+
+ align:start position:0%
+convinced ourselves thanks to your point
+that problem is impossible we will just
+
+ align:start position:0%
+that problem is impossible we will just
+ 
+
+ align:start position:0%
+that problem is impossible we will just
+have to list well sometimes K becomes G
+
+ align:start position:0%
+have to list well sometimes K becomes G
+ 
+
+ align:start position:0%
+have to list well sometimes K becomes G
+sometimes K doesn't become G but that's
+
+ align:start position:0%
+sometimes K doesn't become G but that's
+ 
+
+ align:start position:0%
+sometimes K doesn't become G but that's
+because I phrase the problem is which K
+
+ align:start position:0%
+because I phrase the problem is which K
+ 
+
+ align:start position:0%
+because I phrase the problem is which K
+becomes G and which one doesn't if we
+
+ align:start position:0%
+becomes G and which one doesn't if we
+ 
+
+ align:start position:0%
+becomes G and which one doesn't if we
+do if we look at this problem in the
+
+ align:start position:0%
+do if we look at this problem in the
+ 
+
+ align:start position:0%
+do if we look at this problem in the
+other direction this is your suggestion
+
+ align:start position:0%
+other direction this is your suggestion
+ 
+
+ align:start position:0%
+other direction this is your suggestion
+if we start with the plural and think
+
+ align:start position:0%
+if we start with the plural and think
+ 
+
+ align:start position:0%
+if we start with the plural and think
+about the singular
+
+ align:start position:0%
+about the singular
+ 
+
+ align:start position:0%
+about the singular
+then we can say to ourselves okay there
+
+ align:start position:0%
+then we can say to ourselves okay there
+ 
+
+ align:start position:0%
+then we can say to ourselves okay there
+are some nouns that end in K and some
+
+ align:start position:0%
+are some nouns that end in K and some
+ 
+
+ align:start position:0%
+are some nouns that end in K and some
+nouns that end in g
+
+ align:start position:0%
+nouns that end in g
+ 
+
+ align:start position:0%
+nouns that end in g
+and in the singular what's the rule in
+
+ align:start position:0%
+and in the singular what's the rule in
+ 
+
+ align:start position:0%
+and in the singular what's the rule in
+the singular do you get K or do you get
+
+ align:start position:0%
+the singular do you get K or do you get
+ 
+
+ align:start position:0%
+the singular do you get K or do you get
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+K always yeah so what we need for for
+
+ align:start position:0%
+K always yeah so what we need for for
+ 
+
+ align:start position:0%
+K always yeah so what we need for for
+Polish is the willingness to say
+
+ align:start position:0%
+Polish is the willingness to say
+ 
+
+ align:start position:0%
+Polish is the willingness to say
+um uh yeah there are nouns that end in K
+
+ align:start position:0%
+um uh yeah there are nouns that end in K
+ 
+
+ align:start position:0%
+um uh yeah there are nouns that end in K
+announced that end in g the plural
+
+ align:start position:0%
+announced that end in g the plural
+ 
+
+ align:start position:0%
+announced that end in g the plural
+suffix is this letter I this e
+
+ align:start position:0%
+suffix is this letter I this e
+ 
+
+ align:start position:0%
+suffix is this letter I this e
+and there's a very general rule if you
+
+ align:start position:0%
+and there's a very general rule if you
+ 
+
+ align:start position:0%
+and there's a very general rule if you
+have a g at the end of a word turn it
+
+ align:start position:0%
+have a g at the end of a word turn it
+ 
+
+ align:start position:0%
+have a g at the end of a word turn it
+into a k
+
+ align:start position:0%
+into a k
+ 
+
+ align:start position:0%
+into a k
+yeah so if we're making the the Lexicon
+
+ align:start position:0%
+yeah so if we're making the the Lexicon
+ 
+
+ align:start position:0%
+yeah so if we're making the the Lexicon
+for Polish
+
+ align:start position:0%
+for Polish
+ 
+
+ align:start position:0%
+for Polish
+um uh what we want is for the word for
+
+ align:start position:0%
+um uh what we want is for the word for
+ 
+
+ align:start position:0%
+um uh what we want is for the word for
+though to be in the Lexicon book
+
+ align:start position:0%
+though to be in the Lexicon book
+ 
+
+ align:start position:0%
+though to be in the Lexicon book
+and for the word for lie to be in the
+
+ align:start position:0%
+and for the word for lie to be in the
+ 
+
+ align:start position:0%
+and for the word for lie to be in the
+Lexicon Vogue
+
+ align:start position:0%
+Lexicon Vogue
+ 
+
+ align:start position:0%
+Lexicon Vogue
+yeah and then the plural suffix is e
+
+ align:start position:0%
+yeah and then the plural suffix is e
+ 
+
+ align:start position:0%
+yeah and then the plural suffix is e
+and there's a general rule g at the end
+
+ align:start position:0%
+and there's a general rule g at the end
+ 
+
+ align:start position:0%
+and there's a general rule g at the end
+of a word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+becomes k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this means the Lexicon is a little bit
+
+ align:start position:0%
+this means the Lexicon is a little bit
+ 
+
+ align:start position:0%
+this means the Lexicon is a little bit
+abstract right if you ask a Polish
+
+ align:start position:0%
+abstract right if you ask a Polish
+ 
+
+ align:start position:0%
+abstract right if you ask a Polish
+speaker what's the word for lie they're
+
+ align:start position:0%
+speaker what's the word for lie they're
+ 
+
+ align:start position:0%
+speaker what's the word for lie they're
+going to say look
+
+ align:start position:0%
+going to say look
+ 
+
+ align:start position:0%
+going to say look
+and if you say no it's not it's woog
+
+ align:start position:0%
+and if you say no it's not it's woog
+ 
+
+ align:start position:0%
+and if you say no it's not it's woog
+they're going to be like who's the
+
+ align:start position:0%
+they're going to be like who's the
+ 
+
+ align:start position:0%
+they're going to be like who's the
+Polish speaker around here is it you or
+
+ align:start position:0%
+Polish speaker around here is it you or
+ 
+
+ align:start position:0%
+Polish speaker around here is it you or
+me but in fact you are right and the
+
+ align:start position:0%
+me but in fact you are right and the
+ 
+
+ align:start position:0%
+me but in fact you are right and the
+Polish speaker is wrong yeah the word
+
+ align:start position:0%
+Polish speaker is wrong yeah the word
+ 
+
+ align:start position:0%
+Polish speaker is wrong yeah the word
+for lie is yeah and then there's this
+
+ align:start position:0%
+for lie is yeah and then there's this
+ 
+
+ align:start position:0%
+for lie is yeah and then there's this
+rule yeah g becomes k at the ends of
+
+ align:start position:0%
+rule yeah g becomes k at the ends of
+ 
+
+ align:start position:0%
+rule yeah g becomes k at the ends of
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+what that means is that the morpheme for
+
+ align:start position:0%
+what that means is that the morpheme for
+ 
+
+ align:start position:0%
+what that means is that the morpheme for
+lye if we want to know what's the
+
+ align:start position:0%
+lye if we want to know what's the
+ 
+
+ align:start position:0%
+lye if we want to know what's the
+morpheme for lie well it isn't what the
+
+ align:start position:0%
+morpheme for lie well it isn't what the
+ 
+
+ align:start position:0%
+morpheme for lie well it isn't what the
+speaker would say it is necessarily it
+
+ align:start position:0%
+speaker would say it is necessarily it
+ 
+
+ align:start position:0%
+speaker would say it is necessarily it
+doesn't have to be a morpheme that you
+
+ align:start position:0%
+doesn't have to be a morpheme that you
+ 
+
+ align:start position:0%
+doesn't have to be a morpheme that you
+ever hear by itself
+
+ align:start position:0%
+ever hear by itself
+ 
+
+ align:start position:0%
+ever hear by itself
+it only shows up in the plural not in
+
+ align:start position:0%
+it only shows up in the plural not in
+ 
+
+ align:start position:0%
+it only shows up in the plural not in
+the singular
+
+ align:start position:0%
+the singular
+ 
+
+ align:start position:0%
+the singular
+that's the most economical way of
+
+ align:start position:0%
+that's the most economical way of
+ 
+
+ align:start position:0%
+that's the most economical way of
+talking about polish because the fact is
+
+ align:start position:0%
+talking about polish because the fact is
+ 
+
+ align:start position:0%
+talking about polish because the fact is
+I can tell you this from my vast
+
+ align:start position:0%
+I can tell you this from my vast
+ 
+
+ align:start position:0%
+I can tell you this from my vast
+knowledge of Polish ha uh you will never
+
+ align:start position:0%
+knowledge of Polish ha uh you will never
+ 
+
+ align:start position:0%
+knowledge of Polish ha uh you will never
+no matter how many polish words you look
+
+ align:start position:0%
+no matter how many polish words you look
+ 
+
+ align:start position:0%
+no matter how many polish words you look
+at find one that ends with a G they
+
+ align:start position:0%
+at find one that ends with a G they
+ 
+
+ align:start position:0%
+at find one that ends with a G they
+never do
+
+ align:start position:0%
+never do
+ 
+
+ align:start position:0%
+never do
+plenty that end in K but they never end
+
+ align:start position:0%
+plenty that end in K but they never end
+ 
+
+ align:start position:0%
+plenty that end in K but they never end
+with a G so this rule is one that we can
+
+ align:start position:0%
+with a G so this rule is one that we can
+ 
+
+ align:start position:0%
+with a G so this rule is one that we can
+rely on
+
+ align:start position:0%
+rely on
+ 
+
+ align:start position:0%
+rely on
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+this morpheme
+
+ align:start position:0%
+this morpheme
+ 
+
+ align:start position:0%
+this morpheme
+is a free morpheme because it doesn't
+
+ align:start position:0%
+is a free morpheme because it doesn't
+ 
+
+ align:start position:0%
+is a free morpheme because it doesn't
+need to combine with anything
+
+ align:start position:0%
+need to combine with anything
+ 
+
+ align:start position:0%
+need to combine with anything
+it has an allomorph
+
+ align:start position:0%
+it has an allomorph
+ 
+
+ align:start position:0%
+it has an allomorph
+uh which is the result of this General
+
+ align:start position:0%
+uh which is the result of this General
+ 
+
+ align:start position:0%
+uh which is the result of this General
+sound change the G becomes k at the ends
+
+ align:start position:0%
+sound change the G becomes k at the ends
+ 
+
+ align:start position:0%
+sound change the G becomes k at the ends
+of words I guess that's the easiest way
+
+ align:start position:0%
+of words I guess that's the easiest way
+ 
+
+ align:start position:0%
+of words I guess that's the easiest way
+to say it
+
+ align:start position:0%
+to say it
+ 
+
+ align:start position:0%
+to say it
+that's a good point
+
+ align:start position:0%
+that's a good point
+ 
+
+ align:start position:0%
+that's a good point
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a place I told you you know
+
+ align:start position:0%
+so this is a place I told you you know
+ 
+
+ align:start position:0%
+so this is a place I told you you know
+go has the past tense went and you know
+
+ align:start position:0%
+go has the past tense went and you know
+ 
+
+ align:start position:0%
+go has the past tense went and you know
+give up on coming with sound chair up
+
+ align:start position:0%
+give up on coming with sound chair up
+ 
+
+ align:start position:0%
+give up on coming with sound chair up
+with sound changes that will get you
+
+ align:start position:0%
+with sound changes that will get you
+ 
+
+ align:start position:0%
+with sound changes that will get you
+that that's just you know uh our
+
+ align:start position:0%
+that that's just you know uh our
+ 
+
+ align:start position:0%
+that that's just you know uh our
+ancestors being quite peculiar yeah but
+
+ align:start position:0%
+ancestors being quite peculiar yeah but
+ 
+
+ align:start position:0%
+ancestors being quite peculiar yeah but
+uh polish has this general rule that
+
+ align:start position:0%
+uh polish has this general rule that
+ 
+
+ align:start position:0%
+uh polish has this general rule that
+changes final g Decay and so for Polish
+
+ align:start position:0%
+changes final g Decay and so for Polish
+ 
+
+ align:start position:0%
+changes final g Decay and so for Polish
+we don't in the end need to list alamor
+
+ align:start position:0%
+we don't in the end need to list alamor
+ 
+
+ align:start position:0%
+we don't in the end need to list alamor
+if you know lie has Alan works we can if
+
+ align:start position:0%
+if you know lie has Alan works we can if
+ 
+
+ align:start position:0%
+if you know lie has Alan works we can if
+we want we need a hubby it'll keep us
+
+ align:start position:0%
+we want we need a hubby it'll keep us
+ 
+
+ align:start position:0%
+we want we need a hubby it'll keep us
+off the streets but it's okay to just
+
+ align:start position:0%
+off the streets but it's okay to just
+ 
+
+ align:start position:0%
+off the streets but it's okay to just
+say no there's the word realize and then
+
+ align:start position:0%
+say no there's the word realize and then
+ 
+
+ align:start position:0%
+say no there's the word realize and then
+there's this General sound change law
+
+ align:start position:0%
+there's this General sound change law
+ 
+
+ align:start position:0%
+there's this General sound change law
+that changes the K the G to a k yes
+
+ align:start position:0%
+that changes the K the G to a k yes
+ 
+
+ align:start position:0%
+that changes the K the G to a k yes
+concentration or is it actually so this
+
+ align:start position:0%
+concentration or is it actually so this
+ 
+
+ align:start position:0%
+concentration or is it actually so this
+is not polish orthography yeah so uh
+
+ align:start position:0%
+is not polish orthography yeah so uh
+ 
+
+ align:start position:0%
+is not polish orthography yeah so uh
+there's not ordinary polish spelling I
+
+ align:start position:0%
+there's not ordinary polish spelling I
+ 
+
+ align:start position:0%
+there's not ordinary polish spelling I
+think I started by saying that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no that's lie yeah
+
+ align:start position:0%
+no that's lie yeah
+ 
+
+ align:start position:0%
+no that's lie yeah
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes so I think I started this by by
+
+ align:start position:0%
+yes so I think I started this by by
+ 
+
+ align:start position:0%
+yes so I think I started this by by
+saying um I'm going to spell these
+
+ align:start position:0%
+saying um I'm going to spell these
+ 
+
+ align:start position:0%
+saying um I'm going to spell these
+polish words in an unusual way and I
+
+ align:start position:0%
+polish words in an unusual way and I
+ 
+
+ align:start position:0%
+polish words in an unusual way and I
+tried to make it sound like that was for
+
+ align:start position:0%
+tried to make it sound like that was for
+ 
+
+ align:start position:0%
+tried to make it sound like that was for
+your benefits it was so that you would
+
+ align:start position:0%
+your benefits it was so that you would
+ 
+
+ align:start position:0%
+your benefits it was so that you would
+know how the words were pronounced but I
+
+ align:start position:0%
+know how the words were pronounced but I
+ 
+
+ align:start position:0%
+know how the words were pronounced but I
+was actually obscuring the fact which
+
+ align:start position:0%
+was actually obscuring the fact which
+ 
+
+ align:start position:0%
+was actually obscuring the fact which
+you were bringing up which is the Pole's
+
+ align:start position:0%
+you were bringing up which is the Pole's
+ 
+
+ align:start position:0%
+you were bringing up which is the Pole's
+spell as though this rule had not
+
+ align:start position:0%
+spell as though this rule had not
+ 
+
+ align:start position:0%
+spell as though this rule had not
+happened yeah so they pronounced the
+
+ align:start position:0%
+happened yeah so they pronounced the
+ 
+
+ align:start position:0%
+happened yeah so they pronounced the
+word for lie and the word for bow the
+
+ align:start position:0%
+word for lie and the word for bow the
+ 
+
+ align:start position:0%
+word for lie and the word for bow the
+same way uh but you're right they spell
+
+ align:start position:0%
+same way uh but you're right they spell
+ 
+
+ align:start position:0%
+same way uh but you're right they spell
+the word for lie ending with a G they
+
+ align:start position:0%
+the word for lie ending with a G they
+ 
+
+ align:start position:0%
+the word for lie ending with a G they
+also don't use the letter W this is
+
+ align:start position:0%
+also don't use the letter W this is
+ 
+
+ align:start position:0%
+also don't use the letter W this is
+their bardell yeah
+
+ align:start position:0%
+their bardell yeah
+ 
+
+ align:start position:0%
+their bardell yeah
+yeah yes so I don't know
+
+ align:start position:0%
+yeah yes so I don't know
+ 
+
+ align:start position:0%
+yeah yes so I don't know
+been studied in Polish because it would
+
+ align:start position:0%
+been studied in Polish because it would
+ 
+
+ align:start position:0%
+been studied in Polish because it would
+almost seem like
+
+ align:start position:0%
+almost seem like
+ 
+
+ align:start position:0%
+almost seem like
+like speakers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I see what you mean
+
+ align:start position:0%
+oh I see what you mean
+ 
+
+ align:start position:0%
+oh I see what you mean
+um there's a lot of work on the
+
+ align:start position:0%
+um there's a lot of work on the
+ 
+
+ align:start position:0%
+um there's a lot of work on the
+acquisition of morphological and
+
+ align:start position:0%
+acquisition of morphological and
+ 
+
+ align:start position:0%
+acquisition of morphological and
+phonological rules like this I don't
+
+ align:start position:0%
+phonological rules like this I don't
+ 
+
+ align:start position:0%
+phonological rules like this I don't
+know I can't swear that people have
+
+ align:start position:0%
+know I can't swear that people have
+ 
+
+ align:start position:0%
+know I can't swear that people have
+worked on this in Polish my
+
+ align:start position:0%
+worked on this in Polish my
+ 
+
+ align:start position:0%
+worked on this in Polish my
+understanding is that children this is a
+
+ align:start position:0%
+understanding is that children this is a
+ 
+
+ align:start position:0%
+understanding is that children this is a
+very common kind of sound change and
+
+ align:start position:0%
+very common kind of sound change and
+ 
+
+ align:start position:0%
+very common kind of sound change and
+we'll talk more about it as the class
+
+ align:start position:0%
+we'll talk more about it as the class
+ 
+
+ align:start position:0%
+we'll talk more about it as the class
+goes along and my understanding is that
+
+ align:start position:0%
+goes along and my understanding is that
+ 
+
+ align:start position:0%
+goes along and my understanding is that
+children who are learning languages that
+
+ align:start position:0%
+children who are learning languages that
+ 
+
+ align:start position:0%
+children who are learning languages that
+have this kind of sound change it's
+
+ align:start position:0%
+have this kind of sound change it's
+ 
+
+ align:start position:0%
+have this kind of sound change it's
+called final devoicing uh acquire it
+
+ align:start position:0%
+called final devoicing uh acquire it
+ 
+
+ align:start position:0%
+called final devoicing uh acquire it
+kind of immediately it's not it's not
+
+ align:start position:0%
+kind of immediately it's not it's not
+ 
+
+ align:start position:0%
+kind of immediately it's not it's not
+something that takes them a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+children are very smart this is one of
+
+ align:start position:0%
+children are very smart this is one of
+ 
+
+ align:start position:0%
+children are very smart this is one of
+the big results of language acquisition
+
+ align:start position:0%
+the big results of language acquisition
+ 
+
+ align:start position:0%
+the big results of language acquisition
+research they know things before you
+
+ align:start position:0%
+research they know things before you
+ 
+
+ align:start position:0%
+research they know things before you
+would think they do
+
+ align:start position:0%
+would think they do
+ 
+
+ align:start position:0%
+would think they do
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+see where we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's where we are
+
+ align:start position:0%
+yeah that's where we are
+ 
+
+ align:start position:0%
+yeah that's where we are
+yep so we'll never be able to predict
+
+ align:start position:0%
+yep so we'll never be able to predict
+ 
+
+ align:start position:0%
+yep so we'll never be able to predict
+which case change to G in the plural so
+
+ align:start position:0%
+which case change to G in the plural so
+ 
+
+ align:start position:0%
+which case change to G in the plural so
+what we'll do is posit these underlying
+
+ align:start position:0%
+what we'll do is posit these underlying
+ 
+
+ align:start position:0%
+what we'll do is posit these underlying
+forms over there on the right some
+
+ align:start position:0%
+forms over there on the right some
+ 
+
+ align:start position:0%
+forms over there on the right some
+ending in k others ending in g and then
+
+ align:start position:0%
+ending in k others ending in g and then
+ 
+
+ align:start position:0%
+ending in k others ending in g and then
+we'll have a rule G becomes k at the end
+
+ align:start position:0%
+we'll have a rule G becomes k at the end
+ 
+
+ align:start position:0%
+we'll have a rule G becomes k at the end
+of a word
+
+ align:start position:0%
+of a word
+ 
+
+ align:start position:0%
+of a word
+um and given the time I think this is a
+
+ align:start position:0%
+um and given the time I think this is a
+ 
+
+ align:start position:0%
+um and given the time I think this is a
+good place to stop are there any
+
+ align:start position:0%
+good place to stop are there any
+ 
+
+ align:start position:0%
+good place to stop are there any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what let's let's talk about
+
+ align:start position:0%
+you know what let's let's talk about
+ 
+
+ align:start position:0%
+you know what let's let's talk about
+that when we do phonology a little more
+
+ align:start position:0%
+that when we do phonology a little more
+ 
+
+ align:start position:0%
+that when we do phonology a little more
+carefully because yes this this change
+
+ align:start position:0%
+carefully because yes this this change
+ 
+
+ align:start position:0%
+carefully because yes this this change
+from G to K you're right it's part of a
+
+ align:start position:0%
+from G to K you're right it's part of a
+ 
+
+ align:start position:0%
+from G to K you're right it's part of a
+more General change there are lots of
+
+ align:start position:0%
+more General change there are lots of
+ 
+
+ align:start position:0%
+more General change there are lots of
+things like this that happen and it's a
+
+ align:start position:0%
+things like this that happen and it's a
+ 
+
+ align:start position:0%
+things like this that happen and it's a
+very common change so we'll try to talk
+
+ align:start position:0%
+very common change so we'll try to talk
+ 
+
+ align:start position:0%
+very common change so we'll try to talk
+more about it as we get closer to that
+
+ align:start position:0%
+more about it as we get closer to that
+ 
+
+ align:start position:0%
+more about it as we get closer to that
+good good question okay so again
+
+ align:start position:0%
+good good question okay so again
+ 
+
+ align:start position:0%
+good good question okay so again
+problems that do today interpreted
+
+ align:start position:0%
+problems that do today interpreted
+ 
+
+ align:start position:0%
+problems that do today interpreted
+generously it's due by Dawn and I'll try
+
+ align:start position:0%
+generously it's due by Dawn and I'll try
+ 
+
+ align:start position:0%
+generously it's due by Dawn and I'll try
+to put up a new problem set before today
+
+ align:start position:0%
+to put up a new problem set before today
+ 
+
+ align:start position:0%
+to put up a new problem set before today
+is over
\ No newline at end of file
diff --git a/NoOYvZvH_FU.txt b/NoOYvZvH_FU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d71c7b4d3d1469e288c42f1593dd4143171255e
--- /dev/null
+++ b/NoOYvZvH_FU.txt
@@ -0,0 +1,14336 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right welcome back to
+
+ align:start position:0%
+ocw.mit.edu all right welcome back to
+ 
+
+ align:start position:0%
+ocw.mit.edu all right welcome back to
+Dynamic optimality this is a second of
+
+ align:start position:0%
+Dynamic optimality this is a second of
+ 
+
+ align:start position:0%
+Dynamic optimality this is a second of
+two lectures and today we're going to
+
+ align:start position:0%
+two lectures and today we're going to
+ 
+
+ align:start position:0%
+two lectures and today we're going to
+focus mainly on Lower bounds so last
+
+ align:start position:0%
+focus mainly on Lower bounds so last
+ 
+
+ align:start position:0%
+focus mainly on Lower bounds so last
+time we saw this geometric connection to
+
+ align:start position:0%
+time we saw this geometric connection to
+ 
+
+ align:start position:0%
+time we saw this geometric connection to
+binary search trees so again this about
+
+ align:start position:0%
+binary search trees so again this about
+ 
+
+ align:start position:0%
+binary search trees so again this about
+is there one best binary search tree and
+
+ align:start position:0%
+is there one best binary search tree and
+ 
+
+ align:start position:0%
+is there one best binary search tree and
+we represented binary search trees or at
+
+ align:start position:0%
+we represented binary search trees or at
+ 
+
+ align:start position:0%
+we represented binary search trees or at
+least the execution of those algorithms
+
+ align:start position:0%
+least the execution of those algorithms
+ 
+
+ align:start position:0%
+least the execution of those algorithms
+as Point sets in time
+
+ align:start position:0%
+as Point sets in time
+ 
+
+ align:start position:0%
+as Point sets in time
+space and uh it course a point set
+
+ align:start position:0%
+space and uh it course a point set
+ 
+
+ align:start position:0%
+space and uh it course a point set
+corresponded to a valid execution of a
+
+ align:start position:0%
+corresponded to a valid execution of a
+ 
+
+ align:start position:0%
+corresponded to a valid execution of a
+BST tree where each of these points
+
+ align:start position:0%
+BST tree where each of these points
+ 
+
+ align:start position:0%
+BST tree where each of these points
+represented which nodes got touched
+
+ align:start position:0%
+represented which nodes got touched
+ 
+
+ align:start position:0%
+represented which nodes got touched
+during an access if and only if uh the
+
+ align:start position:0%
+during an access if and only if uh the
+ 
+
+ align:start position:0%
+during an access if and only if uh the
+point set was arly satisfied meaning you
+
+ align:start position:0%
+point set was arly satisfied meaning you
+ 
+
+ align:start position:0%
+point set was arly satisfied meaning you
+take any two points in the point set if
+
+ align:start position:0%
+take any two points in the point set if
+ 
+
+ align:start position:0%
+take any two points in the point set if
+they span a rectangle that is not just a
+
+ align:start position:0%
+they span a rectangle that is not just a
+ 
+
+ align:start position:0%
+they span a rectangle that is not just a
+horizontal or vertical line segment
+
+ align:start position:0%
+horizontal or vertical line segment
+ 
+
+ align:start position:0%
+horizontal or vertical line segment
+there must be a third Point somewhere
+
+ align:start position:0%
+there must be a third Point somewhere
+ 
+
+ align:start position:0%
+there must be a third Point somewhere
+inside that rectangle which in the end
+
+ align:start position:0%
+inside that rectangle which in the end
+ 
+
+ align:start position:0%
+inside that rectangle which in the end
+implies that there's a monotone path
+
+ align:start position:0%
+implies that there's a monotone path
+ 
+
+ align:start position:0%
+implies that there's a monotone path
+between those two
+
+ align:start position:0%
+between those two
+ 
+
+ align:start position:0%
+between those two
+points uh and then we saw on the upper
+
+ align:start position:0%
+points uh and then we saw on the upper
+ 
+
+ align:start position:0%
+points uh and then we saw on the upper
+bound side we saw a greedy algorithm
+
+ align:start position:0%
+bound side we saw a greedy algorithm
+ 
+
+ align:start position:0%
+bound side we saw a greedy algorithm
+which was the obvious offline thing to
+
+ align:start position:0%
+which was the obvious offline thing to
+ 
+
+ align:start position:0%
+which was the obvious offline thing to
+do which is as these points come along
+
+ align:start position:0%
+do which is as these points come along
+ 
+
+ align:start position:0%
+do which is as these points come along
+as you do the axises the white dots you
+
+ align:start position:0%
+as you do the axises the white dots you
+ 
+
+ align:start position:0%
+as you do the axises the white dots you
+add the necessary red dots in order to
+
+ align:start position:0%
+add the necessary red dots in order to
+ 
+
+ align:start position:0%
+add the necessary red dots in order to
+make it arly satisfied row by row
+
+ align:start position:0%
+make it arly satisfied row by row
+ 
+
+ align:start position:0%
+make it arly satisfied row by row
+and so that seemed like the obvious
+
+ align:start position:0%
+and so that seemed like the obvious
+ 
+
+ align:start position:0%
+and so that seemed like the obvious
+offline thing to do turns out it could
+
+ align:start position:0%
+offline thing to do turns out it could
+ 
+
+ align:start position:0%
+offline thing to do turns out it could
+be done online up to constant factors I
+
+ align:start position:0%
+be done online up to constant factors I
+ 
+
+ align:start position:0%
+be done online up to constant factors I
+sketched that last time and this is
+
+ align:start position:0%
+sketched that last time and this is
+ 
+
+ align:start position:0%
+sketched that last time and this is
+conjectured to be within a constant
+
+ align:start position:0%
+conjectured to be within a constant
+ 
+
+ align:start position:0%
+conjectured to be within a constant
+factor of optimal we can't prove it what
+
+ align:start position:0%
+factor of optimal we can't prove it what
+ 
+
+ align:start position:0%
+factor of optimal we can't prove it what
+I'm going to show today is our best
+
+ align:start position:0%
+I'm going to show today is our best
+ 
+
+ align:start position:0%
+I'm going to show today is our best
+attempts at proving this is optimal in
+
+ align:start position:0%
+attempts at proving this is optimal in
+ 
+
+ align:start position:0%
+attempts at proving this is optimal in
+particular there's something called ass
+
+ align:start position:0%
+particular there's something called ass
+ 
+
+ align:start position:0%
+particular there's something called ass
+signed greedy algorithm which is almost
+
+ align:start position:0%
+signed greedy algorithm which is almost
+ 
+
+ align:start position:0%
+signed greedy algorithm which is almost
+the same as greedy but it's a lower
+
+ align:start position:0%
+the same as greedy but it's a lower
+ 
+
+ align:start position:0%
+the same as greedy but it's a lower
+bound and greedy is an upper bound so
+
+ align:start position:0%
+bound and greedy is an upper bound so
+ 
+
+ align:start position:0%
+bound and greedy is an upper bound so
+all you need to do is show these two
+
+ align:start position:0%
+all you need to do is show these two
+ 
+
+ align:start position:0%
+all you need to do is show these two
+things are within a constant factor of
+
+ align:start position:0%
+things are within a constant factor of
+ 
+
+ align:start position:0%
+things are within a constant factor of
+each other and we're done um we're not
+
+ align:start position:0%
+each other and we're done um we're not
+ 
+
+ align:start position:0%
+each other and we're done um we're not
+going to get there obviously cuz we
+
+ align:start position:0%
+going to get there obviously cuz we
+ 
+
+ align:start position:0%
+going to get there obviously cuz we
+haven't solved that yet but uh along the
+
+ align:start position:0%
+haven't solved that yet but uh along the
+ 
+
+ align:start position:0%
+haven't solved that yet but uh along the
+way we're going to see Tango trees uh
+
+ align:start position:0%
+way we're going to see Tango trees uh
+ 
+
+ align:start position:0%
+way we're going to see Tango trees uh
+which achieve this log Logan competitive
+
+ align:start position:0%
+which achieve this log Logan competitive
+ 
+
+ align:start position:0%
+which achieve this log Logan competitive
+bound so we think greedy is constant
+
+ align:start position:0%
+bound so we think greedy is constant
+ 
+
+ align:start position:0%
+bound so we think greedy is constant
+competitive the best we know right now
+
+ align:start position:0%
+competitive the best we know right now
+ 
+
+ align:start position:0%
+competitive the best we know right now
+is log Logan this is an improvement over
+
+ align:start position:0%
+is log Logan this is an improvement over
+ 
+
+ align:start position:0%
+is log Logan this is an improvement over
+red black trees which achieve log in any
+
+ align:start position:0%
+red black trees which achieve log in any
+ 
+
+ align:start position:0%
+red black trees which achieve log in any
+balance B your search Tre is within a
+
+ align:start position:0%
+balance B your search Tre is within a
+ 
+
+ align:start position:0%
+balance B your search Tre is within a
+log n factor of optimal because it's all
+
+ align:start position:0%
+log n factor of optimal because it's all
+ 
+
+ align:start position:0%
+log n factor of optimal because it's all
+between constant and log n that we're
+
+ align:start position:0%
+between constant and log n that we're
+ 
+
+ align:start position:0%
+between constant and log n that we're
+trying to do uh another fun consequence
+
+ align:start position:0%
+trying to do uh another fun consequence
+ 
+
+ align:start position:0%
+trying to do uh another fun consequence
+of lower bounds is a particular sense in
+
+ align:start position:0%
+of lower bounds is a particular sense in
+ 
+
+ align:start position:0%
+of lower bounds is a particular sense in
+which log in is is necessary for some
+
+ align:start position:0%
+which log in is is necessary for some
+ 
+
+ align:start position:0%
+which log in is is necessary for some
+access sequences so I argued last time
+
+ align:start position:0%
+access sequences so I argued last time
+ 
+
+ align:start position:0%
+access sequences so I argued last time
+that if you take like a random access
+
+ align:start position:0%
+that if you take like a random access
+ 
+
+ align:start position:0%
+that if you take like a random access
+sequence or uh for example if if you
+
+ align:start position:0%
+sequence or uh for example if if you
+ 
+
+ align:start position:0%
+sequence or uh for example if if you
+look at a binary search tree and you say
+
+ align:start position:0%
+look at a binary search tree and you say
+ 
+
+ align:start position:0%
+look at a binary search tree and you say
+oh I'll just access the thing that's
+
+ align:start position:0%
+oh I'll just access the thing that's
+ 
+
+ align:start position:0%
+oh I'll just access the thing that's
+deepest in the tree there's always
+
+ align:start position:0%
+deepest in the tree there's always
+ 
+
+ align:start position:0%
+deepest in the tree there's always
+something that's deep in the tree of
+
+ align:start position:0%
+something that's deep in the tree of
+ 
+
+ align:start position:0%
+something that's deep in the tree of
+depth at least log in and so for any
+
+ align:start position:0%
+depth at least log in and so for any
+ 
+
+ align:start position:0%
+depth at least log in and so for any
+binary search tree there is an access
+
+ align:start position:0%
+binary search tree there is an access
+ 
+
+ align:start position:0%
+binary search tree there is an access
+sequence no matter what that binary
+
+ align:start position:0%
+sequence no matter what that binary
+ 
+
+ align:start position:0%
+sequence no matter what that binary
+search tree does I can choose the next
+
+ align:start position:0%
+search tree does I can choose the next
+ 
+
+ align:start position:0%
+search tree does I can choose the next
+access to force you to take log n per
+
+ align:start position:0%
+access to force you to take log n per
+ 
+
+ align:start position:0%
+access to force you to take log n per
+operation what we're going to see today
+
+ align:start position:0%
+operation what we're going to see today
+ 
+
+ align:start position:0%
+operation what we're going to see today
+in these lower bounds is one access
+
+ align:start position:0%
+in these lower bounds is one access
+ 
+
+ align:start position:0%
+in these lower bounds is one access
+sequence that for all binary search
+
+ align:start position:0%
+sequence that for all binary search
+ 
+
+ align:start position:0%
+sequence that for all binary search
+trees they must spend log end time just
+
+ align:start position:0%
+trees they must spend log end time just
+ 
+
+ align:start position:0%
+trees they must spend log end time just
+changing the quantifiers around so
+
+ align:start position:0%
+changing the quantifiers around so
+ 
+
+ align:start position:0%
+changing the quantifiers around so
+instead of uh for every binary search
+
+ align:start position:0%
+instead of uh for every binary search
+ 
+
+ align:start position:0%
+instead of uh for every binary search
+tree there is an access sequence there's
+
+ align:start position:0%
+tree there is an access sequence there's
+ 
+
+ align:start position:0%
+tree there is an access sequence there's
+going to be there is an access sequence
+
+ align:start position:0%
+going to be there is an access sequence
+ 
+
+ align:start position:0%
+going to be there is an access sequence
+such that for every binary search tree
+
+ align:start position:0%
+such that for every binary search tree
+ 
+
+ align:start position:0%
+such that for every binary search tree
+you need log end time that's something
+
+ align:start position:0%
+you need log end time that's something
+ 
+
+ align:start position:0%
+you need log end time that's something
+we'll get easily out of these lower
+
+ align:start position:0%
+we'll get easily out of these lower
+ 
+
+ align:start position:0%
+we'll get easily out of these lower
+bounds so let's jump into the lower
+
+ align:start position:0%
+bounds so let's jump into the lower
+ 
+
+ align:start position:0%
+bounds so let's jump into the lower
+bounds and we're going to cover you
+
+ align:start position:0%
+bounds and we're going to cover you
+ 
+
+ align:start position:0%
+bounds and we're going to cover you
+could say three different lower BS BS
+
+ align:start position:0%
+could say three different lower BS BS
+ 
+
+ align:start position:0%
+could say three different lower BS BS
+the independent rectangles is kind of a
+
+ align:start position:0%
+the independent rectangles is kind of a
+ 
+
+ align:start position:0%
+the independent rectangles is kind of a
+generic class of lower bounds then we're
+
+ align:start position:0%
+generic class of lower bounds then we're
+ 
+
+ align:start position:0%
+generic class of lower bounds then we're
+going to see two specific choices of
+
+ align:start position:0%
+going to see two specific choices of
+ 
+
+ align:start position:0%
+going to see two specific choices of
+these independent rectangles which are
+
+ align:start position:0%
+these independent rectangles which are
+ 
+
+ align:start position:0%
+these independent rectangles which are
+actually older than this result so this
+
+ align:start position:0%
+actually older than this result so this
+ 
+
+ align:start position:0%
+actually older than this result so this
+is sort of a modern interpretation of
+
+ align:start position:0%
+is sort of a modern interpretation of
+ 
+
+ align:start position:0%
+is sort of a modern interpretation of
+two older results and a more General
+
+ align:start position:0%
+two older results and a more General
+ 
+
+ align:start position:0%
+two older results and a more General
+result uh sign greedy is going to turn
+
+ align:start position:0%
+result uh sign greedy is going to turn
+ 
+
+ align:start position:0%
+result uh sign greedy is going to turn
+out to be the best lower bound of it's
+
+ align:start position:0%
+out to be the best lower bound of it's
+ 
+
+ align:start position:0%
+out to be the best lower bound of it's
+better than all the ones that we will
+
+ align:start position:0%
+better than all the ones that we will
+ 
+
+ align:start position:0%
+better than all the ones that we will
+cover but each of them has their own
+
+ align:start position:0%
+cover but each of them has their own
+ 
+
+ align:start position:0%
+cover but each of them has their own
+uses for an analysis each of them is
+
+ align:start position:0%
+uses for an analysis each of them is
+ 
+
+ align:start position:0%
+uses for an analysis each of them is
+going to let us analyze an algorithm
+
+ align:start position:0%
+going to let us analyze an algorithm
+ 
+
+ align:start position:0%
+going to let us analyze an algorithm
+that we couldn't or that we don't
+
+ align:start position:0%
+that we couldn't or that we don't
+ 
+
+ align:start position:0%
+that we couldn't or that we don't
+otherwise know how to
+
+ align:start position:0%
+otherwise know how to
+ 
+
+ align:start position:0%
+otherwise know how to
+analyze
+
+ align:start position:0%
+analyze
+ 
+
+ align:start position:0%
+analyze
+so let's do the independent rectangle
+
+ align:start position:0%
+so let's do the independent rectangle
+ 
+
+ align:start position:0%
+so let's do the independent rectangle
+lower bound this s generic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so uh these lower bounds are all
+
+ align:start position:0%
+one so uh these lower bounds are all
+ 
+
+ align:start position:0%
+one so uh these lower bounds are all
+going to refer to The Original Point set
+
+ align:start position:0%
+going to refer to The Original Point set
+ 
+
+ align:start position:0%
+going to refer to The Original Point set
+the white dots the accesses the idea is
+
+ align:start position:0%
+the white dots the accesses the idea is
+ 
+
+ align:start position:0%
+the white dots the accesses the idea is
+you're given an access sequence a
+
+ align:start position:0%
+you're given an access sequence a
+ 
+
+ align:start position:0%
+you're given an access sequence a
+sequence XI X1 up to xn and you want to
+
+ align:start position:0%
+sequence XI X1 up to xn and you want to
+ 
+
+ align:start position:0%
+sequence XI X1 up to xn and you want to
+know some lower bound that every binary
+
+ align:start position:0%
+know some lower bound that every binary
+ 
+
+ align:start position:0%
+know some lower bound that every binary
+search tree requires a certain number of
+
+ align:start position:0%
+search tree requires a certain number of
+ 
+
+ align:start position:0%
+search tree requires a certain number of
+axises a certain number of node Touches
+
+ align:start position:0%
+axises a certain number of node Touches
+ 
+
+ align:start position:0%
+axises a certain number of node Touches
+for that axis sequence you know it's at
+
+ align:start position:0%
+for that axis sequence you know it's at
+ 
+
+ align:start position:0%
+for that axis sequence you know it's at
+least n you want something bigger than n
+
+ align:start position:0%
+least n you want something bigger than n
+ 
+
+ align:start position:0%
+least n you want something bigger than n
+we got to at least touch the nodes that
+
+ align:start position:0%
+we got to at least touch the nodes that
+ 
+
+ align:start position:0%
+we got to at least touch the nodes that
+are that are being
+
+ align:start position:0%
+are that are being
+ 
+
+ align:start position:0%
+are that are being
+accessed um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so uh I want the notion of
+
+ align:start position:0%
+this so uh I want the notion of
+ 
+
+ align:start position:0%
+this so uh I want the notion of
+independent rectangles and general idea
+
+ align:start position:0%
+independent rectangles and general idea
+ 
+
+ align:start position:0%
+independent rectangles and general idea
+is that of dependent rectangles would be
+
+ align:start position:0%
+is that of dependent rectangles would be
+ 
+
+ align:start position:0%
+is that of dependent rectangles would be
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+uh so here's these are two rectangles I
+
+ align:start position:0%
+uh so here's these are two rectangles I
+ 
+
+ align:start position:0%
+uh so here's these are two rectangles I
+consider them dependent because one of
+
+ align:start position:0%
+consider them dependent because one of
+ 
+
+ align:start position:0%
+consider them dependent because one of
+the corners is inside the other
+
+ align:start position:0%
+the corners is inside the other
+ 
+
+ align:start position:0%
+the corners is inside the other
+rectangle but this is true no matter
+
+ align:start position:0%
+rectangle but this is true no matter
+ 
+
+ align:start position:0%
+rectangle but this is true no matter
+where the points are so for example if I
+
+ align:start position:0%
+where the points are so for example if I
+ 
+
+ align:start position:0%
+where the points are so for example if I
+have sorry I take two points they span a
+
+ align:start position:0%
+have sorry I take two points they span a
+ 
+
+ align:start position:0%
+have sorry I take two points they span a
+rectangle uh if I take these two points
+
+ align:start position:0%
+rectangle uh if I take these two points
+ 
+
+ align:start position:0%
+rectangle uh if I take these two points
+for example they span a rectangle this
+
+ align:start position:0%
+for example they span a rectangle this
+ 
+
+ align:start position:0%
+for example they span a rectangle this
+corner is inside that one so these are
+
+ align:start position:0%
+corner is inside that one so these are
+ 
+
+ align:start position:0%
+corner is inside that one so these are
+considered dependent rectangles in
+
+ align:start position:0%
+considered dependent rectangles in
+ 
+
+ align:start position:0%
+considered dependent rectangles in
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+case so corner here does not necessarily
+
+ align:start position:0%
+case so corner here does not necessarily
+ 
+
+ align:start position:0%
+case so corner here does not necessarily
+mean a point any of the Four Corners
+
+ align:start position:0%
+mean a point any of the Four Corners
+ 
+
+ align:start position:0%
+mean a point any of the Four Corners
+rectangles defined by two points but it
+
+ align:start position:0%
+rectangles defined by two points but it
+ 
+
+ align:start position:0%
+rectangles defined by two points but it
+has all four
+
+ align:start position:0%
+has all four
+ 
+
+ align:start position:0%
+has all four
+corners um and so in particular
+
+ align:start position:0%
+corners um and so in particular
+ 
+
+ align:start position:0%
+corners um and so in particular
+independent rectangles well for example
+
+ align:start position:0%
+independent rectangles well for example
+ 
+
+ align:start position:0%
+independent rectangles well for example
+they might be completely disjoint those
+
+ align:start position:0%
+they might be completely disjoint those
+ 
+
+ align:start position:0%
+they might be completely disjoint those
+are going to be
+
+ align:start position:0%
+are going to be
+ 
+
+ align:start position:0%
+are going to be
+independent something like that
+
+ align:start position:0%
+independent something like that
+ 
+
+ align:start position:0%
+independent something like that
+it's independent uh but there's some
+
+ align:start position:0%
+it's independent uh but there's some
+ 
+
+ align:start position:0%
+it's independent uh but there's some
+other cases you can have rectangles that
+
+ align:start position:0%
+other cases you can have rectangles that
+ 
+
+ align:start position:0%
+other cases you can have rectangles that
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+this okay so and it doesn't matter where
+
+ align:start position:0%
+this okay so and it doesn't matter where
+ 
+
+ align:start position:0%
+this okay so and it doesn't matter where
+the points are maybe here here here and
+
+ align:start position:0%
+the points are maybe here here here and
+ 
+
+ align:start position:0%
+the points are maybe here here here and
+here or the other way uh these are
+
+ align:start position:0%
+here or the other way uh these are
+ 
+
+ align:start position:0%
+here or the other way uh these are
+independent and there's one other kind
+
+ align:start position:0%
+independent and there's one other kind
+ 
+
+ align:start position:0%
+independent and there's one other kind
+of special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case which maybe I'll use color draw the
+
+ align:start position:0%
+case which maybe I'll use color draw the
+ 
+
+ align:start position:0%
+case which maybe I'll use color draw the
+other one cuz they're right on top of
+
+ align:start position:0%
+other one cuz they're right on top of
+ 
+
+ align:start position:0%
+other one cuz they're right on top of
+each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I got a point here Point here and a
+
+ align:start position:0%
+so I got a point here Point here and a
+ 
+
+ align:start position:0%
+so I got a point here Point here and a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+here okay these are two two rectangles
+
+ align:start position:0%
+here okay these are two two rectangles
+ 
+
+ align:start position:0%
+here okay these are two two rectangles
+defined on three points so they both are
+
+ align:start position:0%
+defined on three points so they both are
+ 
+
+ align:start position:0%
+defined on three points so they both are
+used this
+
+ align:start position:0%
+used this
+ 
+
+ align:start position:0%
+used this
+point uh and if you check it does
+
+ align:start position:0%
+point uh and if you check it does
+ 
+
+ align:start position:0%
+point uh and if you check it does
+satisfy this condition so no corners
+
+ align:start position:0%
+satisfy this condition so no corners
+ 
+
+ align:start position:0%
+satisfy this condition so no corners
+strictly inside the other uh but we also
+
+ align:start position:0%
+strictly inside the other uh but we also
+ 
+
+ align:start position:0%
+strictly inside the other uh but we also
+need that the rectangles are unsatisfied
+
+ align:start position:0%
+need that the rectangles are unsatisfied
+ 
+
+ align:start position:0%
+need that the rectangles are unsatisfied
+so this is saying that uh there's no
+
+ align:start position:0%
+so this is saying that uh there's no
+ 
+
+ align:start position:0%
+so this is saying that uh there's no
+other point even on the boundary of the
+
+ align:start position:0%
+other point even on the boundary of the
+ 
+
+ align:start position:0%
+other point even on the boundary of the
+rectangle rectangle so this part says
+
+ align:start position:0%
+rectangle rectangle so this part says
+ 
+
+ align:start position:0%
+rectangle rectangle so this part says
+okay there's nothing strictly inside but
+
+ align:start position:0%
+okay there's nothing strictly inside but
+ 
+
+ align:start position:0%
+okay there's nothing strictly inside but
+we also need that on the boundary
+
+ align:start position:0%
+we also need that on the boundary
+ 
+
+ align:start position:0%
+we also need that on the boundary
+there's no other points so this is the
+
+ align:start position:0%
+there's no other points so this is the
+ 
+
+ align:start position:0%
+there's no other points so this is the
+only sort of situation other than
+
+ align:start position:0%
+only sort of situation other than
+ 
+
+ align:start position:0%
+only sort of situation other than
+Reflections where you get uh get this
+
+ align:start position:0%
+Reflections where you get uh get this
+ 
+
+ align:start position:0%
+Reflections where you get uh get this
+working out as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent last case is independent
+
+ align:start position:0%
+independent last case is independent
+ 
+
+ align:start position:0%
+independent last case is independent
+last case is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent all right so this is a
+
+ align:start position:0%
+independent all right so this is a
+ 
+
+ align:start position:0%
+independent all right so this is a
+definition if I give you a set of
+
+ align:start position:0%
+definition if I give you a set of
+ 
+
+ align:start position:0%
+definition if I give you a set of
+rectangles they're
+
+ align:start position:0%
+rectangles they're
+ 
+
+ align:start position:0%
+rectangles they're
+independent if I mean if I was looking
+
+ align:start position:0%
+independent if I mean if I was looking
+ 
+
+ align:start position:0%
+independent if I mean if I was looking
+at pairwise but if if they're pairwise
+
+ align:start position:0%
+at pairwise but if if they're pairwise
+ 
+
+ align:start position:0%
+at pairwise but if if they're pairwise
+independent they will be independent no
+
+ align:start position:0%
+independent they will be independent no
+ 
+
+ align:start position:0%
+independent they will be independent no
+corner of any rectangle strictly inside
+
+ align:start position:0%
+corner of any rectangle strictly inside
+ 
+
+ align:start position:0%
+corner of any rectangle strictly inside
+any other rectangle and there there's no
+
+ align:start position:0%
+any other rectangle and there there's no
+ 
+
+ align:start position:0%
+any other rectangle and there there's no
+points uh of those rectangles that are
+
+ align:start position:0%
+points uh of those rectangles that are
+ 
+
+ align:start position:0%
+points uh of those rectangles that are
+you know inside
+
+ align:start position:0%
+you know inside
+ 
+
+ align:start position:0%
+you know inside
+others Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower bound
+
+ align:start position:0%
+lower bound
+ 
+
+ align:start position:0%
+lower bound
+says the optimal offline binary search
+
+ align:start position:0%
+says the optimal offline binary search
+ 
+
+ align:start position:0%
+says the optimal offline binary search
+tree or the optimal way to add dots to
+
+ align:start position:0%
+tree or the optimal way to add dots to
+ 
+
+ align:start position:0%
+tree or the optimal way to add dots to
+satisfy your point set is going to be at
+
+ align:start position:0%
+satisfy your point set is going to be at
+ 
+
+ align:start position:0%
+satisfy your point set is going to be at
+least the size of the input meaning the
+
+ align:start position:0%
+least the size of the input meaning the
+ 
+
+ align:start position:0%
+least the size of the input meaning the
+number of initial points you have plus
+
+ align:start position:0%
+number of initial points you have plus
+ 
+
+ align:start position:0%
+number of initial points you have plus
+half the maximum number of independent
+
+ align:start position:0%
+half the maximum number of independent
+ 
+
+ align:start position:0%
+half the maximum number of independent
+rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a Max independent set
+
+ align:start position:0%
+okay so this is a Max independent set
+ 
+
+ align:start position:0%
+okay so this is a Max independent set
+problem in general that's MP complete
+
+ align:start position:0%
+problem in general that's MP complete
+ 
+
+ align:start position:0%
+problem in general that's MP complete
+turns out we'll be able to at least
+
+ align:start position:0%
+turns out we'll be able to at least
+ 
+
+ align:start position:0%
+turns out we'll be able to at least
+approximate the number of independent
+
+ align:start position:0%
+approximate the number of independent
+ 
+
+ align:start position:0%
+approximate the number of independent
+rectangles within a constant Factor by
+
+ align:start position:0%
+rectangles within a constant Factor by
+ 
+
+ align:start position:0%
+rectangles within a constant Factor by
+the end of class that's going to be
+
+ align:start position:0%
+the end of class that's going to be
+ 
+
+ align:start position:0%
+the end of class that's going to be
+signed greedy so sign greedy is going to
+
+ align:start position:0%
+signed greedy so sign greedy is going to
+ 
+
+ align:start position:0%
+signed greedy so sign greedy is going to
+be the best way up to constant factors
+
+ align:start position:0%
+be the best way up to constant factors
+ 
+
+ align:start position:0%
+be the best way up to constant factors
+to choose independent rectangles for now
+
+ align:start position:0%
+to choose independent rectangles for now
+ 
+
+ align:start position:0%
+to choose independent rectangles for now
+someone magically tells you what's the
+
+ align:start position:0%
+someone magically tells you what's the
+ 
+
+ align:start position:0%
+someone magically tells you what's the
+best way or you just choose some
+
+ align:start position:0%
+best way or you just choose some
+ 
+
+ align:start position:0%
+best way or you just choose some
+reasonable any choice of independent
+
+ align:start position:0%
+reasonable any choice of independent
+ 
+
+ align:start position:0%
+reasonable any choice of independent
+rectangles will be a lower bound but you
+
+ align:start position:0%
+rectangles will be a lower bound but you
+ 
+
+ align:start position:0%
+rectangles will be a lower bound but you
+get the best lower Bound by choosing the
+
+ align:start position:0%
+get the best lower Bound by choosing the
+ 
+
+ align:start position:0%
+get the best lower Bound by choosing the
+max okay so uh we're going to prove this
+
+ align:start position:0%
+max okay so uh we're going to prove this
+ 
+
+ align:start position:0%
+max okay so uh we're going to prove this
+theorem and then we're going to see two
+
+ align:start position:0%
+theorem and then we're going to see two
+ 
+
+ align:start position:0%
+theorem and then we're going to see two
+we're going to see three different ways
+
+ align:start position:0%
+we're going to see three different ways
+ 
+
+ align:start position:0%
+we're going to see three different ways
+to uh choose those independent
+
+ align:start position:0%
+to uh choose those independent
+ 
+
+ align:start position:0%
+to uh choose those independent
+rectangles and we'll use them for
+
+ align:start position:0%
+rectangles and we'll use them for
+ 
+
+ align:start position:0%
+rectangles and we'll use them for
+various things Wilbur one Wilbur 2 and S
+
+ align:start position:0%
+various things Wilbur one Wilbur 2 and S
+ 
+
+ align:start position:0%
+various things Wilbur one Wilbur 2 and S
+greedy are the going to be the three
+
+ align:start position:0%
+greedy are the going to be the three
+ 
+
+ align:start position:0%
+greedy are the going to be the three
+choices for independent
+
+ align:start position:0%
+choices for independent
+ 
+
+ align:start position:0%
+choices for independent
+rectangles all right to prove this
+
+ align:start position:0%
+rectangles all right to prove this
+ 
+
+ align:start position:0%
+rectangles all right to prove this
+theorem we're going to change it a
+
+ align:start position:0%
+theorem we're going to change it a
+ 
+
+ align:start position:0%
+theorem we're going to change it a
+little bit first
+
+ align:start position:0%
+little bit first
+ 
+
+ align:start position:0%
+little bit first
+and this is kind of the focus of today
+
+ align:start position:0%
+and this is kind of the focus of today
+ 
+
+ align:start position:0%
+and this is kind of the focus of today
+is the idea of signed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangles if you look at the rectangles
+
+ align:start position:0%
+rectangles if you look at the rectangles
+ 
+
+ align:start position:0%
+rectangles if you look at the rectangles
+in the world Spann by two points there
+
+ align:start position:0%
+in the world Spann by two points there
+ 
+
+ align:start position:0%
+in the world Spann by two points there
+are two different kinds there's ones
+
+ align:start position:0%
+are two different kinds there's ones
+ 
+
+ align:start position:0%
+are two different kinds there's ones
+where uh there's the top right lower
+
+ align:start position:0%
+where uh there's the top right lower
+ 
+
+ align:start position:0%
+where uh there's the top right lower
+left kind and then there's the top left
+
+ align:start position:0%
+left kind and then there's the top left
+ 
+
+ align:start position:0%
+left kind and then there's the top left
+lower right kind these are positive
+
+ align:start position:0%
+lower right kind these are positive
+ 
+
+ align:start position:0%
+lower right kind these are positive
+slope or negative
+
+ align:start position:0%
+slope or negative
+ 
+
+ align:start position:0%
+slope or negative
+slope okay those are the two kinds of
+
+ align:start position:0%
+slope okay those are the two kinds of
+ 
+
+ align:start position:0%
+slope okay those are the two kinds of
+rectangles and it's helpful to think
+
+ align:start position:0%
+rectangles and it's helpful to think
+ 
+
+ align:start position:0%
+rectangles and it's helpful to think
+about just the positive rectangles and
+
+ align:start position:0%
+about just the positive rectangles and
+ 
+
+ align:start position:0%
+about just the positive rectangles and
+just the or the slash rectangles and
+
+ align:start position:0%
+just the or the slash rectangles and
+ 
+
+ align:start position:0%
+just the or the slash rectangles and
+just the backs slash rectangles
+
+ align:start position:0%
+just the backs slash rectangles
+ 
+
+ align:start position:0%
+just the backs slash rectangles
+separately so we're going to call a
+
+ align:start position:0%
+separately so we're going to call a
+ 
+
+ align:start position:0%
+separately so we're going to call a
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set it's a little hard to
+
+ align:start position:0%
+set it's a little hard to
+ 
+
+ align:start position:0%
+set it's a little hard to
+pronounce we used to call this plus
+
+ align:start position:0%
+pronounce we used to call this plus
+ 
+
+ align:start position:0%
+pronounce we used to call this plus
+satisfied uh so maybe easiest to
+
+ align:start position:0%
+satisfied uh so maybe easiest to
+ 
+
+ align:start position:0%
+satisfied uh so maybe easiest to
+pronounce it that way the symbol
+
+ align:start position:0%
+pronounce it that way the symbol
+ 
+
+ align:start position:0%
+pronounce it that way the symbol
+formerly known as plus satisfied
+
+ align:start position:0%
+formerly known as plus satisfied
+ 
+
+ align:start position:0%
+formerly known as plus satisfied
+uh if
+
+ align:start position:0%
+uh if
+ 
+
+ align:start position:0%
+uh if
+all uh plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangles that are not on a horizontal
+
+ align:start position:0%
+rectangles that are not on a horizontal
+ 
+
+ align:start position:0%
+rectangles that are not on a horizontal
+or vertical line uh contain another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Point okay so a point set is arbily
+
+ align:start position:0%
+Point okay so a point set is arbily
+ 
+
+ align:start position:0%
+Point okay so a point set is arbily
+satisfied if and only if it is plus
+
+ align:start position:0%
+satisfied if and only if it is plus
+ 
+
+ align:start position:0%
+satisfied if and only if it is plus
+satisfied and minus satisfied okay just
+
+ align:start position:0%
+satisfied and minus satisfied okay just
+ 
+
+ align:start position:0%
+satisfied and minus satisfied okay just
+breaking apart that definition into two
+
+ align:start position:0%
+breaking apart that definition into two
+ 
+
+ align:start position:0%
+breaking apart that definition into two
+parts but now we're going to look at
+
+ align:start position:0%
+parts but now we're going to look at
+ 
+
+ align:start position:0%
+parts but now we're going to look at
+Point sets that are just plus satisfied
+
+ align:start position:0%
+Point sets that are just plus satisfied
+ 
+
+ align:start position:0%
+Point sets that are just plus satisfied
+or Point sets that are just minus
+
+ align:start position:0%
+or Point sets that are just minus
+ 
+
+ align:start position:0%
+or Point sets that are just minus
+satisfied and then we can look at the
+
+ align:start position:0%
+satisfied and then we can look at the
+ 
+
+ align:start position:0%
+satisfied and then we can look at the
+optimal solution if you only care about
+
+ align:start position:0%
+optimal solution if you only care about
+ 
+
+ align:start position:0%
+optimal solution if you only care about
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+rectangles so this is
+
+ align:start position:0%
+rectangles so this is
+ 
+
+ align:start position:0%
+rectangles so this is
+the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smallest plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfied uh
+
+ align:start position:0%
+satisfied uh
+ 
+
+ align:start position:0%
+satisfied uh
+Point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set containing all the access points all
+
+ align:start position:0%
+set containing all the access points all
+ 
+
+ align:start position:0%
+set containing all the access points all
+the given
+
+ align:start position:0%
+the given
+ 
+
+ align:start position:0%
+the given
+points so we call that the
+
+ align:start position:0%
+points so we call that the
+ 
+
+ align:start position:0%
+points so we call that the
+input okay opt was the smallest arly
+
+ align:start position:0%
+input okay opt was the smallest arly
+ 
+
+ align:start position:0%
+input okay opt was the smallest arly
+satisfied opt plus is the you just look
+
+ align:start position:0%
+satisfied opt plus is the you just look
+ 
+
+ align:start position:0%
+satisfied opt plus is the you just look
+at plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+rectangles okay why are we doing this
+
+ align:start position:0%
+rectangles okay why are we doing this
+ 
+
+ align:start position:0%
+rectangles okay why are we doing this
+well for now we're going to do it to
+
+ align:start position:0%
+well for now we're going to do it to
+ 
+
+ align:start position:0%
+well for now we're going to do it to
+prove this theorem so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LMA which is what we're actually going
+
+ align:start position:0%
+LMA which is what we're actually going
+ 
+
+ align:start position:0%
+LMA which is what we're actually going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+prove is if you look at this opt plus
+
+ align:start position:0%
+prove is if you look at this opt plus
+ 
+
+ align:start position:0%
+prove is if you look at this opt plus
+thing it's got to be at least the size
+
+ align:start position:0%
+thing it's got to be at least the size
+ 
+
+ align:start position:0%
+thing it's got to be at least the size
+of the input everything has to be at
+
+ align:start position:0%
+of the input everything has to be at
+ 
+
+ align:start position:0%
+of the input everything has to be at
+least has to at least contain the
+
+ align:start position:0%
+least has to at least contain the
+ 
+
+ align:start position:0%
+least has to at least contain the
+input plus uh
+
+ align:start position:0%
+input plus uh
+ 
+
+ align:start position:0%
+input plus uh
+maximum number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent plus rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is what we're actually
+
+ align:start position:0%
+okay so this is what we're actually
+ 
+
+ align:start position:0%
+okay so this is what we're actually
+going to prove if you want to get plus
+
+ align:start position:0%
+going to prove if you want to get plus
+ 
+
+ align:start position:0%
+going to prove if you want to get plus
+satisfied and you've got K independent
+
+ align:start position:0%
+satisfied and you've got K independent
+ 
+
+ align:start position:0%
+satisfied and you've got K independent
+plus rectangles you need to add at least
+
+ align:start position:0%
+plus rectangles you need to add at least
+ 
+
+ align:start position:0%
+plus rectangles you need to add at least
+that many points so at least one point
+
+ align:start position:0%
+that many points so at least one point
+ 
+
+ align:start position:0%
+that many points so at least one point
+per plus rectangle if you can prove this
+
+ align:start position:0%
+per plus rectangle if you can prove this
+ 
+
+ align:start position:0%
+per plus rectangle if you can prove this
+you prove the theorem because you this
+
+ align:start position:0%
+you prove the theorem because you this
+ 
+
+ align:start position:0%
+you prove the theorem because you this
+holds for minus just as well as plus by
+
+ align:start position:0%
+holds for minus just as well as plus by
+ 
+
+ align:start position:0%
+holds for minus just as well as plus by
+Symmetry and so you take the you take
+
+ align:start position:0%
+Symmetry and so you take the you take
+ 
+
+ align:start position:0%
+Symmetry and so you take the you take
+your maximum independent set of
+
+ align:start position:0%
+your maximum independent set of
+ 
+
+ align:start position:0%
+your maximum independent set of
+rectangles at least half of them are
+
+ align:start position:0%
+rectangles at least half of them are
+ 
+
+ align:start position:0%
+rectangles at least half of them are
+Plus or at least half of them are minus
+
+ align:start position:0%
+Plus or at least half of them are minus
+ 
+
+ align:start position:0%
+Plus or at least half of them are minus
+you apply this bound and that's where
+
+ align:start position:0%
+you apply this bound and that's where
+ 
+
+ align:start position:0%
+you apply this bound and that's where
+you get the 1/2
+
+ align:start position:0%
+you get the 1/2
+ 
+
+ align:start position:0%
+you get the 1/2
+here okay so this is stronger I guess
+
+ align:start position:0%
+here okay so this is stronger I guess
+ 
+
+ align:start position:0%
+here okay so this is stronger I guess
+than the theorem and this is what we're
+
+ align:start position:0%
+than the theorem and this is what we're
+ 
+
+ align:start position:0%
+than the theorem and this is what we're
+actually going to prove and so in this
+
+ align:start position:0%
+actually going to prove and so in this
+ 
+
+ align:start position:0%
+actually going to prove and so in this
+world we just are thinking about plus
+
+ align:start position:0%
+world we just are thinking about plus
+ 
+
+ align:start position:0%
+world we just are thinking about plus
+rectangles which a little weird
+
+ align:start position:0%
+rectangles which a little weird
+ 
+
+ align:start position:0%
+rectangles which a little weird
+but it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works and the proof is going to be in
+
+ align:start position:0%
+works and the proof is going to be in
+ 
+
+ align:start position:0%
+works and the proof is going to be in
+three steps uh I'm first going to give
+
+ align:start position:0%
+three steps uh I'm first going to give
+ 
+
+ align:start position:0%
+three steps uh I'm first going to give
+you overview of the steps and then we'll
+
+ align:start position:0%
+you overview of the steps and then we'll
+ 
+
+ align:start position:0%
+you overview of the steps and then we'll
+actually do them so this is like a two
+
+ align:start position:0%
+actually do them so this is like a two
+ 
+
+ align:start position:0%
+actually do them so this is like a two
+Lev twole proof um first level first
+
+ align:start position:0%
+Lev twole proof um first level first
+ 
+
+ align:start position:0%
+Lev twole proof um first level first
+thing we do the top level is we're going
+
+ align:start position:0%
+thing we do the top level is we're going
+ 
+
+ align:start position:0%
+thing we do the top level is we're going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+find a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangle uh in the independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set and we're going to find a vertical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line that hits only that rectangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're going to have some
+
+ align:start position:0%
+okay so we're going to have some
+ 
+
+ align:start position:0%
+okay so we're going to have some
+rectangle in the independent set and we
+
+ align:start position:0%
+rectangle in the independent set and we
+ 
+
+ align:start position:0%
+rectangle in the independent set and we
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+a vertical line stabbing
+
+ align:start position:0%
+a vertical line stabbing
+ 
+
+ align:start position:0%
+a vertical line stabbing
+it such that no other rectangle stabed
+
+ align:start position:0%
+it such that no other rectangle stabed
+ 
+
+ align:start position:0%
+it such that no other rectangle stabed
+by this vertical line so all the
+
+ align:start position:0%
+by this vertical line so all the
+ 
+
+ align:start position:0%
+by this vertical line so all the
+rectangles it's independent so maybe
+
+ align:start position:0%
+rectangles it's independent so maybe
+ 
+
+ align:start position:0%
+rectangles it's independent so maybe
+they look something like this uh can't
+
+ align:start position:0%
+they look something like this uh can't
+ 
+
+ align:start position:0%
+they look something like this uh can't
+can't nothing like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not obvious that such a thing exists but
+
+ align:start position:0%
+not obvious that such a thing exists but
+ 
+
+ align:start position:0%
+not obvious that such a thing exists but
+it does actually not that hard to find
+
+ align:start position:0%
+it does actually not that hard to find
+ 
+
+ align:start position:0%
+it does actually not that hard to find
+uh we just need some rectangle with some
+
+ align:start position:0%
+uh we just need some rectangle with some
+ 
+
+ align:start position:0%
+uh we just need some rectangle with some
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+okay then um using that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property we're going to be able to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find some points in that re angle that
+
+ align:start position:0%
+find some points in that re angle that
+ 
+
+ align:start position:0%
+find some points in that re angle that
+are also in the optimal Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Solution
+
+ align:start position:0%
+Solution
+ 
+
+ align:start position:0%
+Solution
+uh in the
+
+ align:start position:0%
+uh in the
+ 
+
+ align:start position:0%
+uh in the
+rectangle crossing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line okay me get another color so we're
+
+ align:start position:0%
+line okay me get another color so we're
+ 
+
+ align:start position:0%
+line okay me get another color so we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+find a point on the left of the line and
+
+ align:start position:0%
+find a point on the left of the line and
+ 
+
+ align:start position:0%
+find a point on the left of the line and
+a point on the right of the line
+
+ align:start position:0%
+a point on the right of the line
+ 
+
+ align:start position:0%
+a point on the right of the line
+and they're horizontally adjacent
+
+ align:start position:0%
+and they're horizontally adjacent
+ 
+
+ align:start position:0%
+and they're horizontally adjacent
+meaning there's no other points between
+
+ align:start position:0%
+meaning there's no other points between
+ 
+
+ align:start position:0%
+meaning there's no other points between
+them so that's we know there's some
+
+ align:start position:0%
+them so that's we know there's some
+ 
+
+ align:start position:0%
+them so that's we know there's some
+point in this box and the because this
+
+ align:start position:0%
+point in this box and the because this
+ 
+
+ align:start position:0%
+point in this box and the because this
+is a plus box it's got to be satisfied
+
+ align:start position:0%
+is a plus box it's got to be satisfied
+ 
+
+ align:start position:0%
+is a plus box it's got to be satisfied
+somehow and I claim there's actually two
+
+ align:start position:0%
+somehow and I claim there's actually two
+ 
+
+ align:start position:0%
+somehow and I claim there's actually two
+points on either side of the line one of
+
+ align:start position:0%
+points on either side of the line one of
+ 
+
+ align:start position:0%
+points on either side of the line one of
+them could be equal to this or this but
+
+ align:start position:0%
+them could be equal to this or this but
+ 
+
+ align:start position:0%
+them could be equal to this or this but
+not both obviously because they're
+
+ align:start position:0%
+not both obviously because they're
+ 
+
+ align:start position:0%
+not both obviously because they're
+horizontally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aligned
+
+ align:start position:0%
+aligned
+ 
+
+ align:start position:0%
+aligned
+okay and then what we're going to do is
+
+ align:start position:0%
+okay and then what we're going to do is
+ 
+
+ align:start position:0%
+okay and then what we're going to do is
+charge the rectangle
+
+ align:start position:0%
+charge the rectangle
+ 
+
+ align:start position:0%
+charge the rectangle
+to those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points okay and then basically we're
+
+ align:start position:0%
+points okay and then basically we're
+ 
+
+ align:start position:0%
+points okay and then basically we're
+going to remove that rectangle and
+
+ align:start position:0%
+going to remove that rectangle and
+ 
+
+ align:start position:0%
+going to remove that rectangle and
+repeat and the claim is this charging
+
+ align:start position:0%
+repeat and the claim is this charging
+ 
+
+ align:start position:0%
+repeat and the claim is this charging
+sort of only happens once per point and
+
+ align:start position:0%
+sort of only happens once per point and
+ 
+
+ align:start position:0%
+sort of only happens once per point and
+therefore the number of points in the
+
+ align:start position:0%
+therefore the number of points in the
+ 
+
+ align:start position:0%
+therefore the number of points in the
+optimal solution has to be at least the
+
+ align:start position:0%
+optimal solution has to be at least the
+ 
+
+ align:start position:0%
+optimal solution has to be at least the
+number of rectangles number of plus
+
+ align:start position:0%
+number of rectangles number of plus
+ 
+
+ align:start position:0%
+number of rectangles number of plus
+rectangles in the independent set so
+
+ align:start position:0%
+rectangles in the independent set so
+ 
+
+ align:start position:0%
+rectangles in the independent set so
+basically this is a way of ordering the
+
+ align:start position:0%
+basically this is a way of ordering the
+ 
+
+ align:start position:0%
+basically this is a way of ordering the
+rectangles we're going to take one that
+
+ align:start position:0%
+rectangles we're going to take one that
+ 
+
+ align:start position:0%
+rectangles we're going to take one that
+has one of these vertical lines find two
+
+ align:start position:0%
+has one of these vertical lines find two
+ 
+
+ align:start position:0%
+has one of these vertical lines find two
+points that pay for that rectangle and
+
+ align:start position:0%
+points that pay for that rectangle and
+ 
+
+ align:start position:0%
+points that pay for that rectangle and
+therefore argue that opt has to be at
+
+ align:start position:0%
+therefore argue that opt has to be at
+ 
+
+ align:start position:0%
+therefore argue that opt has to be at
+least the number of rectangles so we
+
+ align:start position:0%
+least the number of rectangles so we
+ 
+
+ align:start position:0%
+least the number of rectangles so we
+have to argue that uh at least one of
+
+ align:start position:0%
+have to argue that uh at least one of
+ 
+
+ align:start position:0%
+have to argue that uh at least one of
+these points is not one of the original
+
+ align:start position:0%
+these points is not one of the original
+ 
+
+ align:start position:0%
+these points is not one of the original
+points right uh and that's where that's
+
+ align:start position:0%
+points right uh and that's where that's
+ 
+
+ align:start position:0%
+points right uh and that's where that's
+where we're getting the input plus
+
+ align:start position:0%
+where we're getting the input plus
+ 
+
+ align:start position:0%
+where we're getting the input plus
+this uh so there's lots of things to
+
+ align:start position:0%
+this uh so there's lots of things to
+ 
+
+ align:start position:0%
+this uh so there's lots of things to
+check here let's do them one at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and throughout I'm going to assume
+
+ align:start position:0%
+time and throughout I'm going to assume
+ 
+
+ align:start position:0%
+time and throughout I'm going to assume
+write that at the
+
+ align:start position:0%
+write that at the
+ 
+
+ align:start position:0%
+write that at the
+bottom assume all X and Y coordinates
+
+ align:start position:0%
+bottom assume all X and Y coordinates
+ 
+
+ align:start position:0%
+bottom assume all X and Y coordinates
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique this is a an idea I mentioned
+
+ align:start position:0%
+unique this is a an idea I mentioned
+ 
+
+ align:start position:0%
+unique this is a an idea I mentioned
+last time as well if you have lots of
+
+ align:start position:0%
+last time as well if you have lots of
+ 
+
+ align:start position:0%
+last time as well if you have lots of
+accesses to the same key imagine them
+
+ align:start position:0%
+accesses to the same key imagine them
+ 
+
+ align:start position:0%
+accesses to the same key imagine them
+being accesses to slightly different
+
+ align:start position:0%
+being accesses to slightly different
+ 
+
+ align:start position:0%
+being accesses to slightly different
+Keys just skew them a little bit and it
+
+ align:start position:0%
+Keys just skew them a little bit and it
+ 
+
+ align:start position:0%
+Keys just skew them a little bit and it
+doesn't change any of the bounds
+
+ align:start position:0%
+doesn't change any of the bounds
+ 
+
+ align:start position:0%
+doesn't change any of the bounds
+much I won't argue that here but at at
+
+ align:start position:0%
+much I won't argue that here but at at
+ 
+
+ align:start position:0%
+much I won't argue that here but at at
+the least think of this as just a
+
+ align:start position:0%
+the least think of this as just a
+ 
+
+ align:start position:0%
+the least think of this as just a
+simplifying assumption for to make the
+
+ align:start position:0%
+simplifying assumption for to make the
+ 
+
+ align:start position:0%
+simplifying assumption for to make the
+proofs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cleaner okay so how we going to do step
+
+ align:start position:0%
+cleaner okay so how we going to do step
+ 
+
+ align:start position:0%
+cleaner okay so how we going to do step
+one I need to find some rectangle and
+
+ align:start position:0%
+one I need to find some rectangle and
+ 
+
+ align:start position:0%
+one I need to find some rectangle and
+some vertical line that only stabs that
+
+ align:start position:0%
+some vertical line that only stabs that
+ 
+
+ align:start position:0%
+some vertical line that only stabs that
+rectangle uh and the way we're going to
+
+ align:start position:0%
+rectangle uh and the way we're going to
+ 
+
+ align:start position:0%
+rectangle uh and the way we're going to
+do that is just take the widest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangle that just has the maximum X
+
+ align:start position:0%
+rectangle that just has the maximum X
+ 
+
+ align:start position:0%
+rectangle that just has the maximum X
+extent might be more than one but just
+
+ align:start position:0%
+extent might be more than one but just
+ 
+
+ align:start position:0%
+extent might be more than one but just
+take one of
+
+ align:start position:0%
+take one of
+ 
+
+ align:start position:0%
+take one of
+them okay so it's very
+
+ align:start position:0%
+them okay so it's very
+ 
+
+ align:start position:0%
+them okay so it's very
+wide what this tells us is that there's
+
+ align:start position:0%
+wide what this tells us is that there's
+ 
+
+ align:start position:0%
+wide what this tells us is that there's
+no other rectangle like this okay this
+
+ align:start position:0%
+no other rectangle like this okay this
+ 
+
+ align:start position:0%
+no other rectangle like this okay this
+would be independent but it would be
+
+ align:start position:0%
+would be independent but it would be
+ 
+
+ align:start position:0%
+would be independent but it would be
+wider so that's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allowed now we have to think about all
+
+ align:start position:0%
+allowed now we have to think about all
+ 
+
+ align:start position:0%
+allowed now we have to think about all
+sorts of scenario so we've got a point
+
+ align:start position:0%
+sorts of scenario so we've got a point
+ 
+
+ align:start position:0%
+sorts of scenario so we've got a point
+here and a point here could still be
+
+ align:start position:0%
+here and a point here could still be
+ 
+
+ align:start position:0%
+here and a point here could still be
+that we have rectangles like this they
+
+ align:start position:0%
+that we have rectangles like this they
+ 
+
+ align:start position:0%
+that we have rectangles like this they
+just can't go farther to the right could
+
+ align:start position:0%
+just can't go farther to the right could
+ 
+
+ align:start position:0%
+just can't go farther to the right could
+be we have rectangles that go like this
+
+ align:start position:0%
+be we have rectangles that go like this
+ 
+
+ align:start position:0%
+be we have rectangles that go like this
+just can't go too far to the left they
+
+ align:start position:0%
+just can't go too far to the left they
+ 
+
+ align:start position:0%
+just can't go too far to the left they
+also can't the these rectangles that are
+
+ align:start position:0%
+also can't the these rectangles that are
+ 
+
+ align:start position:0%
+also can't the these rectangles that are
+anchored in the lower left and these
+
+ align:start position:0%
+anchored in the lower left and these
+ 
+
+ align:start position:0%
+anchored in the lower left and these
+rectangles that are anchored in the
+
+ align:start position:0%
+rectangles that are anchored in the
+ 
+
+ align:start position:0%
+rectangles that are anchored in the
+upper right can't touch each other
+
+ align:start position:0%
+upper right can't touch each other
+ 
+
+ align:start position:0%
+upper right can't touch each other
+because then uh one of them would be
+
+ align:start position:0%
+because then uh one of them would be
+ 
+
+ align:start position:0%
+because then uh one of them would be
+satisfied right this one's going to have
+
+ align:start position:0%
+satisfied right this one's going to have
+ 
+
+ align:start position:0%
+satisfied right this one's going to have
+a point down here this one's going to
+
+ align:start position:0%
+a point down here this one's going to
+ 
+
+ align:start position:0%
+a point down here this one's going to
+have a point here uh I
+
+ align:start position:0%
+have a point here uh I
+ 
+
+ align:start position:0%
+have a point here uh I
+guess yeah let's see how would it go if
+
+ align:start position:0%
+guess yeah let's see how would it go if
+ 
+
+ align:start position:0%
+guess yeah let's see how would it go if
+they were touching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we'd have a
+
+ align:start position:0%
+uh we'd have a
+ 
+
+ align:start position:0%
+uh we'd have a
+corner touching is a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weird ah I see good this can't happen
+
+ align:start position:0%
+weird ah I see good this can't happen
+ 
+
+ align:start position:0%
+weird ah I see good this can't happen
+because we assume the x coordinates are
+
+ align:start position:0%
+because we assume the x coordinates are
+ 
+
+ align:start position:0%
+because we assume the x coordinates are
+distinct okay so that's why I did this
+
+ align:start position:0%
+distinct okay so that's why I did this
+ 
+
+ align:start position:0%
+distinct okay so that's why I did this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+reason um so this can't happen and I
+
+ align:start position:0%
+reason um so this can't happen and I
+ 
+
+ align:start position:0%
+reason um so this can't happen and I
+also can't have them go like this
+
+ align:start position:0%
+also can't have them go like this
+ 
+
+ align:start position:0%
+also can't have them go like this
+because then there's a corner in the
+
+ align:start position:0%
+because then there's a corner in the
+ 
+
+ align:start position:0%
+because then there's a corner in the
+strict interior of the other rectangle
+
+ align:start position:0%
+strict interior of the other rectangle
+ 
+
+ align:start position:0%
+strict interior of the other rectangle
+okay is that clear this rectangle can't
+
+ align:start position:0%
+okay is that clear this rectangle can't
+ 
+
+ align:start position:0%
+okay is that clear this rectangle can't
+come over here because then it that
+
+ align:start position:0%
+come over here because then it that
+ 
+
+ align:start position:0%
+come over here because then it that
+would be uh not independent rectangle
+
+ align:start position:0%
+would be uh not independent rectangle
+ 
+
+ align:start position:0%
+would be uh not independent rectangle
+can't come right to the same spot
+
+ align:start position:0%
+can't come right to the same spot
+ 
+
+ align:start position:0%
+can't come right to the same spot
+because there is no same spot that would
+
+ align:start position:0%
+because there is no same spot that would
+ 
+
+ align:start position:0%
+because there is no same spot that would
+be two points on the same vertical line
+
+ align:start position:0%
+be two points on the same vertical line
+ 
+
+ align:start position:0%
+be two points on the same vertical line
+and so what we must have is a picture
+
+ align:start position:0%
+and so what we must have is a picture
+ 
+
+ align:start position:0%
+and so what we must have is a picture
+more like this where there's a there's
+
+ align:start position:0%
+more like this where there's a there's
+ 
+
+ align:start position:0%
+more like this where there's a there's
+an empty region in between that's not
+
+ align:start position:0%
+an empty region in between that's not
+ 
+
+ align:start position:0%
+an empty region in between that's not
+hit by there can be many of these
+
+ align:start position:0%
+hit by there can be many of these
+ 
+
+ align:start position:0%
+hit by there can be many of these
+rectangles many of these rectangles
+
+ align:start position:0%
+rectangles many of these rectangles
+ 
+
+ align:start position:0%
+rectangles many of these rectangles
+they're independent from each other
+
+ align:start position:0%
+they're independent from each other
+ 
+
+ align:start position:0%
+they're independent from each other
+that's like this case here okay there
+
+ align:start position:0%
+that's like this case here okay there
+ 
+
+ align:start position:0%
+that's like this case here okay there
+can also be some rectangles like this
+
+ align:start position:0%
+can also be some rectangles like this
+ 
+
+ align:start position:0%
+can also be some rectangles like this
+but by the same argument these guys
+
+ align:start position:0%
+but by the same argument these guys
+ 
+
+ align:start position:0%
+but by the same argument these guys
+can't touch each other and they can't
+
+ align:start position:0%
+can't touch each other and they can't
+ 
+
+ align:start position:0%
+can't touch each other and they can't
+overlap horizontally because then one of
+
+ align:start position:0%
+overlap horizontally because then one of
+ 
+
+ align:start position:0%
+overlap horizontally because then one of
+the corners would be inside the other
+
+ align:start position:0%
+the corners would be inside the other
+ 
+
+ align:start position:0%
+the corners would be inside the other
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one or this one that one yeah this
+
+ align:start position:0%
+this one or this one that one yeah this
+ 
+
+ align:start position:0%
+this one or this one that one yeah this
+one cannot happen or that that's what we
+
+ align:start position:0%
+one cannot happen or that that's what we
+ 
+
+ align:start position:0%
+one cannot happen or that that's what we
+claim uhuh right so let's uh you're
+
+ align:start position:0%
+claim uhuh right so let's uh you're
+ 
+
+ align:start position:0%
+claim uhuh right so let's uh you're
+right so we worry
+
+ align:start position:0%
+right so we worry
+ 
+
+ align:start position:0%
+right so we worry
+about uh interesting we worry about
+
+ align:start position:0%
+about uh interesting we worry about
+ 
+
+ align:start position:0%
+about uh interesting we worry about
+something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this sorry why can't that ah um yeah
+
+ align:start position:0%
+this sorry why can't that ah um yeah
+ 
+
+ align:start position:0%
+this sorry why can't that ah um yeah
+you're right I actually drew the wrong
+
+ align:start position:0%
+you're right I actually drew the wrong
+ 
+
+ align:start position:0%
+you're right I actually drew the wrong
+picture sorry kidding um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I really meant line segment here
+
+ align:start position:0%
+yeah I really meant line segment here
+ 
+
+ align:start position:0%
+yeah I really meant line segment here
+I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry poor choice of
+
+ align:start position:0%
+sorry poor choice of
+ 
+
+ align:start position:0%
+sorry poor choice of
+wording so vertical line is actually
+
+ align:start position:0%
+wording so vertical line is actually
+ 
+
+ align:start position:0%
+wording so vertical line is actually
+just going to go the extent of the
+
+ align:start position:0%
+just going to go the extent of the
+ 
+
+ align:start position:0%
+just going to go the extent of the
+rectangle something like this sorry we
+
+ align:start position:0%
+rectangle something like this sorry we
+ 
+
+ align:start position:0%
+rectangle something like this sorry we
+can't forbid rectangles like this uh
+
+ align:start position:0%
+can't forbid rectangles like this uh
+ 
+
+ align:start position:0%
+can't forbid rectangles like this uh
+what we can forbid are rectangles like
+
+ align:start position:0%
+what we can forbid are rectangles like
+ 
+
+ align:start position:0%
+what we can forbid are rectangles like
+this that also try to acoss that
+
+ align:start position:0%
+this that also try to acoss that
+ 
+
+ align:start position:0%
+this that also try to acoss that
+segment okay uh we'll see why this is
+
+ align:start position:0%
+segment okay uh we'll see why this is
+ 
+
+ align:start position:0%
+segment okay uh we'll see why this is
+enough in a moment sorry about that uh
+
+ align:start position:0%
+enough in a moment sorry about that uh
+ 
+
+ align:start position:0%
+enough in a moment sorry about that uh
+okay so what I I really only care about
+
+ align:start position:0%
+okay so what I I really only care about
+ 
+
+ align:start position:0%
+okay so what I I really only care about
+the interior of this
+
+ align:start position:0%
+the interior of this
+ 
+
+ align:start position:0%
+the interior of this
+rectangle I'm trying to get a vertical
+
+ align:start position:0%
+rectangle I'm trying to get a vertical
+ 
+
+ align:start position:0%
+rectangle I'm trying to get a vertical
+line that only stabs this rectangle
+
+ align:start position:0%
+line that only stabs this rectangle
+ 
+
+ align:start position:0%
+line that only stabs this rectangle
+nothing else inside the rectangle sorry
+
+ align:start position:0%
+nothing else inside the rectangle sorry
+ 
+
+ align:start position:0%
+nothing else inside the rectangle sorry
+poor wording I don't care about these
+
+ align:start position:0%
+poor wording I don't care about these
+ 
+
+ align:start position:0%
+poor wording I don't care about these
+guys outside because I can't say
+
+ align:start position:0%
+guys outside because I can't say
+ 
+
+ align:start position:0%
+guys outside because I can't say
+anything about them they could be all
+
+ align:start position:0%
+anything about them they could be all
+ 
+
+ align:start position:0%
+anything about them they could be all
+over the place in an independent set
+
+ align:start position:0%
+over the place in an independent set
+ 
+
+ align:start position:0%
+over the place in an independent set
+claim that that with it I mean relative
+
+ align:start position:0%
+claim that that with it I mean relative
+ 
+
+ align:start position:0%
+claim that that with it I mean relative
+to what hits this rectangle there's
+
+ align:start position:0%
+to what hits this rectangle there's
+ 
+
+ align:start position:0%
+to what hits this rectangle there's
+stuff on the left there's stuff on the
+
+ align:start position:0%
+stuff on the left there's stuff on the
+ 
+
+ align:start position:0%
+stuff on the left there's stuff on the
+right they're these guys there can also
+
+ align:start position:0%
+right they're these guys there can also
+ 
+
+ align:start position:0%
+right they're these guys there can also
+be things like
+
+ align:start position:0%
+be things like
+ 
+
+ align:start position:0%
+be things like
+this okay but still remaining are these
+
+ align:start position:0%
+this okay but still remaining are these
+ 
+
+ align:start position:0%
+this okay but still remaining are these
+regions which are not hit by any
+
+ align:start position:0%
+regions which are not hit by any
+ 
+
+ align:start position:0%
+regions which are not hit by any
+rectangles and that's because what I was
+
+ align:start position:0%
+rectangles and that's because what I was
+ 
+
+ align:start position:0%
+rectangles and that's because what I was
+saying these guys can't touch each other
+
+ align:start position:0%
+saying these guys can't touch each other
+ 
+
+ align:start position:0%
+saying these guys can't touch each other
+because then there' be equal x
+
+ align:start position:0%
+because then there' be equal x
+ 
+
+ align:start position:0%
+because then there' be equal x
+coordinates they can't overlap because
+
+ align:start position:0%
+coordinates they can't overlap because
+ 
+
+ align:start position:0%
+coordinates they can't overlap because
+then one of them would not be
+
+ align:start position:0%
+then one of them would not be
+ 
+
+ align:start position:0%
+then one of them would not be
+independent from the other so I
+
+ align:start position:0%
+independent from the other so I
+ 
+
+ align:start position:0%
+independent from the other so I
+get uh my vertical
+
+ align:start position:0%
+get uh my vertical
+ 
+
+ align:start position:0%
+get uh my vertical
+lines I just need one but it could be
+
+ align:start position:0%
+lines I just need one but it could be
+ 
+
+ align:start position:0%
+lines I just need one but it could be
+any of these in general if you take all
+
+ align:start position:0%
+any of these in general if you take all
+ 
+
+ align:start position:0%
+any of these in general if you take all
+for example if you take all of these uh
+
+ align:start position:0%
+for example if you take all of these uh
+ 
+
+ align:start position:0%
+for example if you take all of these uh
+lower left anchored rectangles and take
+
+ align:start position:0%
+lower left anchored rectangles and take
+ 
+
+ align:start position:0%
+lower left anchored rectangles and take
+just to the right of the rightmost one
+
+ align:start position:0%
+just to the right of the rightmost one
+ 
+
+ align:start position:0%
+just to the right of the rightmost one
+that will be a valid choice for your
+
+ align:start position:0%
+that will be a valid choice for your
+ 
+
+ align:start position:0%
+that will be a valid choice for your
+line because you can argue none of these
+
+ align:start position:0%
+line because you can argue none of these
+ 
+
+ align:start position:0%
+line because you can argue none of these
+can overlap it okay so that's step one
+
+ align:start position:0%
+can overlap it okay so that's step one
+ 
+
+ align:start position:0%
+can overlap it okay so that's step one
+we just take a widest rectangle the one
+
+ align:start position:0%
+we just take a widest rectangle the one
+ 
+
+ align:start position:0%
+we just take a widest rectangle the one
+thing we needed to forbid was some
+
+ align:start position:0%
+thing we needed to forbid was some
+ 
+
+ align:start position:0%
+thing we needed to forbid was some
+something going like this all the way
+
+ align:start position:0%
+something going like this all the way
+ 
+
+ align:start position:0%
+something going like this all the way
+across okay step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two uh step two is actually pretty easy
+
+ align:start position:0%
+two uh step two is actually pretty easy
+ 
+
+ align:start position:0%
+two uh step two is actually pretty easy
+once you've identified this red line you
+
+ align:start position:0%
+once you've identified this red line you
+ 
+
+ align:start position:0%
+once you've identified this red line you
+basically in inside the rectangle you
+
+ align:start position:0%
+basically in inside the rectangle you
+ 
+
+ align:start position:0%
+basically in inside the rectangle you
+know there are some points and I'm going
+
+ align:start position:0%
+know there are some points and I'm going
+ 
+
+ align:start position:0%
+know there are some points and I'm going
+to take the
+
+ align:start position:0%
+to take the
+ 
+
+ align:start position:0%
+to take the
+rightmost and then among all the
+
+ align:start position:0%
+rightmost and then among all the
+ 
+
+ align:start position:0%
+rightmost and then among all the
+rightmost points I'm going to take the
+
+ align:start position:0%
+rightmost points I'm going to take the
+ 
+
+ align:start position:0%
+rightmost points I'm going to take the
+topmost point that is to the left of the
+
+ align:start position:0%
+topmost point that is to the left of the
+ 
+
+ align:start position:0%
+topmost point that is to the left of the
+line and inside the rectangle so let P
+
+ align:start position:0%
+line and inside the rectangle so let P
+ 
+
+ align:start position:0%
+line and inside the rectangle so let P
+be the
+
+ align:start position:0%
+be the
+ 
+
+ align:start position:0%
+be the
+topmost leftmost point
+
+ align:start position:0%
+topmost leftmost point
+ 
+
+ align:start position:0%
+topmost leftmost point
+sorry right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most uh that is both in the
+
+ align:start position:0%
+most uh that is both in the
+ 
+
+ align:start position:0%
+most uh that is both in the
+rectangle and left of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line so this is going to be let me erase
+
+ align:start position:0%
+line so this is going to be let me erase
+ 
+
+ align:start position:0%
+line so this is going to be let me erase
+this one make for a little bit more
+
+ align:start position:0%
+this one make for a little bit more
+ 
+
+ align:start position:0%
+this one make for a little bit more
+room uh so I'm looking at all of this
+
+ align:start position:0%
+room uh so I'm looking at all of this
+ 
+
+ align:start position:0%
+room uh so I'm looking at all of this
+region to the left of the line in the
+
+ align:start position:0%
+region to the left of the line in the
+ 
+
+ align:start position:0%
+region to the left of the line in the
+rectangle I want to take uh
+
+ align:start position:0%
+rectangle I want to take uh
+ 
+
+ align:start position:0%
+rectangle I want to take uh
+the rightmost and then topmost point
+
+ align:start position:0%
+the rightmost and then topmost point
+ 
+
+ align:start position:0%
+the rightmost and then topmost point
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this uh how do I know such a point
+
+ align:start position:0%
+this uh how do I know such a point
+ 
+
+ align:start position:0%
+this uh how do I know such a point
+exists because this point is such a
+
+ align:start position:0%
+exists because this point is such a
+ 
+
+ align:start position:0%
+exists because this point is such a
+point and this point is to the left of
+
+ align:start position:0%
+point and this point is to the left of
+ 
+
+ align:start position:0%
+point and this point is to the left of
+the line so I mean if there's nothing
+
+ align:start position:0%
+the line so I mean if there's nothing
+ 
+
+ align:start position:0%
+the line so I mean if there's nothing
+else in here that is a valid choice but
+
+ align:start position:0%
+else in here that is a valid choice but
+ 
+
+ align:start position:0%
+else in here that is a valid choice but
+in general we go to the right as much as
+
+ align:start position:0%
+in general we go to the right as much as
+ 
+
+ align:start position:0%
+in general we go to the right as much as
+possible then we go up as much as
+
+ align:start position:0%
+possible then we go up as much as
+ 
+
+ align:start position:0%
+possible then we go up as much as
+possible so that's a point which we will
+
+ align:start position:0%
+possible so that's a point which we will
+ 
+
+ align:start position:0%
+possible so that's a point which we will
+call P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectang uh it could be on the border it
+
+ align:start position:0%
+rectang uh it could be on the border it
+ 
+
+ align:start position:0%
+rectang uh it could be on the border it
+could be interior we don't know when you
+
+ align:start position:0%
+could be interior we don't know when you
+ 
+
+ align:start position:0%
+could be interior we don't know when you
+say top so when you said top what is
+
+ align:start position:0%
+say top so when you said top what is
+ 
+
+ align:start position:0%
+say top so when you said top what is
+your top top topmost means a maximum y
+
+ align:start position:0%
+your top top topmost means a maximum y
+ 
+
+ align:start position:0%
+your top top topmost means a maximum y
+coordinate oh okay got s so it could be
+
+ align:start position:0%
+coordinate oh okay got s so it could be
+ 
+
+ align:start position:0%
+coordinate oh okay got s so it could be
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+here we we don't know yeah first we go
+
+ align:start position:0%
+here we we don't know yeah first we go
+ 
+
+ align:start position:0%
+here we we don't know yeah first we go
+rightmost then we among all the things
+
+ align:start position:0%
+rightmost then we among all the things
+ 
+
+ align:start position:0%
+rightmost then we among all the things
+in that column we go to the topmost one
+
+ align:start position:0%
+in that column we go to the topmost one
+ 
+
+ align:start position:0%
+in that column we go to the topmost one
+so it might be on the top it might not
+
+ align:start position:0%
+so it might be on the top it might not
+ 
+
+ align:start position:0%
+so it might be on the top it might not
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+yeah these are points sorry this is a
+
+ align:start position:0%
+yeah these are points sorry this is a
+ 
+
+ align:start position:0%
+yeah these are points sorry this is a
+point uh in opt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus okay and then Q is going to be a
+
+ align:start position:0%
+plus okay and then Q is going to be a
+ 
+
+ align:start position:0%
+plus okay and then Q is going to be a
+similar thing it's going to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bottommost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leftmost point
+
+ align:start position:0%
+leftmost point
+ 
+
+ align:start position:0%
+leftmost point
+in opt
+
+ align:start position:0%
+in opt
+ 
+
+ align:start position:0%
+in opt
+plus uh uh that is in the
+
+ align:start position:0%
+plus uh uh that is in the
+ 
+
+ align:start position:0%
+plus uh uh that is in the
+rectangle and right of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line not totally symmetric though we're
+
+ align:start position:0%
+line not totally symmetric though we're
+ 
+
+ align:start position:0%
+line not totally symmetric though we're
+also going to say and not below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P okay so now we're looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this upper region
+
+ align:start position:0%
+at this upper region
+ 
+
+ align:start position:0%
+at this upper region
+here among all the things that are not
+
+ align:start position:0%
+here among all the things that are not
+ 
+
+ align:start position:0%
+here among all the things that are not
+below P should draun this more
+
+ align:start position:0%
+below P should draun this more
+ 
+
+ align:start position:0%
+below P should draun this more
+horizontal
+
+ align:start position:0%
+horizontal
+ 
+
+ align:start position:0%
+horizontal
+uh and to the right of the red line so
+
+ align:start position:0%
+uh and to the right of the red line so
+ 
+
+ align:start position:0%
+uh and to the right of the red line so
+it's up to here I guess I want to take
+
+ align:start position:0%
+it's up to here I guess I want to take
+ 
+
+ align:start position:0%
+it's up to here I guess I want to take
+the leftmost column that has any points
+
+ align:start position:0%
+the leftmost column that has any points
+ 
+
+ align:start position:0%
+the leftmost column that has any points
+in it and then among those take the
+
+ align:start position:0%
+in it and then among those take the
+ 
+
+ align:start position:0%
+in it and then among those take the
+bottommost point in the
+
+ align:start position:0%
+bottommost point in the
+ 
+
+ align:start position:0%
+bottommost point in the
+column I claim that's actually going to
+
+ align:start position:0%
+column I claim that's actually going to
+ 
+
+ align:start position:0%
+column I claim that's actually going to
+be on this
+
+ align:start position:0%
+be on this
+ 
+
+ align:start position:0%
+be on this
+line okay first thing to check is that
+
+ align:start position:0%
+line okay first thing to check is that
+ 
+
+ align:start position:0%
+line okay first thing to check is that
+such a point exists such a point exists
+
+ align:start position:0%
+such a point exists such a point exists
+ 
+
+ align:start position:0%
+such a point exists such a point exists
+because in particular this is such a
+
+ align:start position:0%
+because in particular this is such a
+ 
+
+ align:start position:0%
+because in particular this is such a
+point it is to the right of the line
+
+ align:start position:0%
+point it is to the right of the line
+ 
+
+ align:start position:0%
+point it is to the right of the line
+it's above the blue line right of the
+
+ align:start position:0%
+it's above the blue line right of the
+ 
+
+ align:start position:0%
+it's above the blue line right of the
+red line in the rectangle okay but I
+
+ align:start position:0%
+red line in the rectangle okay but I
+ 
+
+ align:start position:0%
+red line in the rectangle okay but I
+claim if we take the left most
+
+ align:start position:0%
+claim if we take the left most
+ 
+
+ align:start position:0%
+claim if we take the left most
+bottommost one then they must actually
+
+ align:start position:0%
+bottommost one then they must actually
+ 
+
+ align:start position:0%
+bottommost one then they must actually
+be aligned why if it was somewhere else
+
+ align:start position:0%
+be aligned why if it was somewhere else
+ 
+
+ align:start position:0%
+be aligned why if it was somewhere else
+like up here or like this point then I
+
+ align:start position:0%
+like up here or like this point then I
+ 
+
+ align:start position:0%
+like up here or like this point then I
+claim that is an unsatisfied
+
+ align:start position:0%
+claim that is an unsatisfied
+ 
+
+ align:start position:0%
+claim that is an unsatisfied
+box okay let me uh
+
+ align:start position:0%
+box okay let me uh
+ 
+
+ align:start position:0%
+box okay let me uh
+draw that
+
+ align:start position:0%
+draw that
+ 
+
+ align:start position:0%
+draw that
+picture make it a little
+
+ align:start position:0%
+picture make it a little
+ 
+
+ align:start position:0%
+picture make it a little
+clearer
+
+ align:start position:0%
+clearer
+ 
+
+ align:start position:0%
+clearer
+so something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've got our red
+
+ align:start position:0%
+so we've got our red
+ 
+
+ align:start position:0%
+so we've got our red
+line and we've got
+
+ align:start position:0%
+line and we've got
+ 
+
+ align:start position:0%
+line and we've got
+uh this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture this is
+
+ align:start position:0%
+picture this is
+ 
+
+ align:start position:0%
+picture this is
+p and then we've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got actually we don't know anything
+
+ align:start position:0%
+got actually we don't know anything
+ 
+
+ align:start position:0%
+got actually we don't know anything
+about down here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is Q okay I claim that these black
+
+ align:start position:0%
+this is Q okay I claim that these black
+ 
+
+ align:start position:0%
+this is Q okay I claim that these black
+regions cannot have any points in them
+
+ align:start position:0%
+regions cannot have any points in them
+ 
+
+ align:start position:0%
+regions cannot have any points in them
+because by definition P was in the
+
+ align:start position:0%
+because by definition P was in the
+ 
+
+ align:start position:0%
+because by definition P was in the
+rightmost column so there's nothing in
+
+ align:start position:0%
+rightmost column so there's nothing in
+ 
+
+ align:start position:0%
+rightmost column so there's nothing in
+this strip in between p and the red line
+
+ align:start position:0%
+this strip in between p and the red line
+ 
+
+ align:start position:0%
+this strip in between p and the red line
+and it was the topmost within the column
+
+ align:start position:0%
+and it was the topmost within the column
+ 
+
+ align:start position:0%
+and it was the topmost within the column
+which means there's nothing above p in
+
+ align:start position:0%
+which means there's nothing above p in
+ 
+
+ align:start position:0%
+which means there's nothing above p in
+the column so that's why all the points
+
+ align:start position:0%
+the column so that's why all the points
+ 
+
+ align:start position:0%
+the column so that's why all the points
+are confined to this region over here
+
+ align:start position:0%
+are confined to this region over here
+ 
+
+ align:start position:0%
+are confined to this region over here
+similarly for Q if you look at the
+
+ align:start position:0%
+similarly for Q if you look at the
+ 
+
+ align:start position:0%
+similarly for Q if you look at the
+things that are above or on this
+
+ align:start position:0%
+things that are above or on this
+ 
+
+ align:start position:0%
+things that are above or on this
+horizontal line which was the blue line
+
+ align:start position:0%
+horizontal line which was the blue line
+ 
+
+ align:start position:0%
+horizontal line which was the blue line
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+there then then we know that uh Q is the
+
+ align:start position:0%
+there then then we know that uh Q is the
+ 
+
+ align:start position:0%
+there then then we know that uh Q is the
+there's nothing in in this strip in
+
+ align:start position:0%
+there's nothing in in this strip in
+ 
+
+ align:start position:0%
+there's nothing in in this strip in
+between because Q was leftmost and then
+
+ align:start position:0%
+between because Q was leftmost and then
+ 
+
+ align:start position:0%
+between because Q was leftmost and then
+among leftmost it was bottommost so
+
+ align:start position:0%
+among leftmost it was bottommost so
+ 
+
+ align:start position:0%
+among leftmost it was bottommost so
+there's nothing down here so that means
+
+ align:start position:0%
+there's nothing down here so that means
+ 
+
+ align:start position:0%
+there's nothing down here so that means
+if these guys are not horizontally
+
+ align:start position:0%
+if these guys are not horizontally
+ 
+
+ align:start position:0%
+if these guys are not horizontally
+aligned there is an unsatisfied box here
+
+ align:start position:0%
+aligned there is an unsatisfied box here
+ 
+
+ align:start position:0%
+aligned there is an unsatisfied box here
+contradiction it's a plus box so in opt
+
+ align:start position:0%
+contradiction it's a plus box so in opt
+ 
+
+ align:start position:0%
+contradiction it's a plus box so in opt
+plus there's got to be another point
+
+ align:start position:0%
+plus there's got to be another point
+ 
+
+ align:start position:0%
+plus there's got to be another point
+which is a contradiction so in fact p
+
+ align:start position:0%
+which is a contradiction so in fact p
+ 
+
+ align:start position:0%
+which is a contradiction so in fact p
+and Q must be horizontally aligned so
+
+ align:start position:0%
+and Q must be horizontally aligned so
+ 
+
+ align:start position:0%
+and Q must be horizontally aligned so
+that was step
+
+ align:start position:0%
+that was step
+ 
+
+ align:start position:0%
+that was step
+two finally we get to step three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea with step three I mean now
+
+ align:start position:0%
+so the idea with step three I mean now
+ 
+
+ align:start position:0%
+so the idea with step three I mean now
+we're going to do a charging argument we
+
+ align:start position:0%
+we're going to do a charging argument we
+ 
+
+ align:start position:0%
+we're going to do a charging argument we
+want to say okay uh we want to find
+
+ align:start position:0%
+want to say okay uh we want to find
+ 
+
+ align:start position:0%
+want to say okay uh we want to find
+basically for every independent
+
+ align:start position:0%
+basically for every independent
+ 
+
+ align:start position:0%
+basically for every independent
+rectangle we want to find a point that's
+
+ align:start position:0%
+rectangle we want to find a point that's
+ 
+
+ align:start position:0%
+rectangle we want to find a point that's
+in opt and therefore uh that was not in
+
+ align:start position:0%
+in opt and therefore uh that was not in
+ 
+
+ align:start position:0%
+in opt and therefore uh that was not in
+the original input and therefore the
+
+ align:start position:0%
+the original input and therefore the
+ 
+
+ align:start position:0%
+the original input and therefore the
+orig then opt plus has to be at least
+
+ align:start position:0%
+orig then opt plus has to be at least
+ 
+
+ align:start position:0%
+orig then opt plus has to be at least
+size of the input plus one per each of
+
+ align:start position:0%
+size of the input plus one per each of
+ 
+
+ align:start position:0%
+size of the input plus one per each of
+these plus rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea is the
+
+ align:start position:0%
+so the idea is the
+ 
+
+ align:start position:0%
+so the idea is the
+following because of all this setup
+
+ align:start position:0%
+following because of all this setup
+ 
+
+ align:start position:0%
+following because of all this setup
+because we made
+
+ align:start position:0%
+because we made
+ 
+
+ align:start position:0%
+because we made
+PQ uh horizontally lined we we we put
+
+ align:start position:0%
+PQ uh horizontally lined we we we put
+ 
+
+ align:start position:0%
+PQ uh horizontally lined we we we put
+them in they're inside the rectangle and
+
+ align:start position:0%
+them in they're inside the rectangle and
+ 
+
+ align:start position:0%
+them in they're inside the rectangle and
+furthermore they they're adjacent and
+
+ align:start position:0%
+furthermore they they're adjacent and
+ 
+
+ align:start position:0%
+furthermore they they're adjacent and
+they cross this vertical line and that
+
+ align:start position:0%
+they cross this vertical line and that
+ 
+
+ align:start position:0%
+they cross this vertical line and that
+vertical line is not crossed by any
+
+ align:start position:0%
+vertical line is not crossed by any
+ 
+
+ align:start position:0%
+vertical line is not crossed by any
+other rectangle when I say line I mean
+
+ align:start position:0%
+other rectangle when I say line I mean
+ 
+
+ align:start position:0%
+other rectangle when I say line I mean
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+segment there's no other rectangle that
+
+ align:start position:0%
+segment there's no other rectangle that
+ 
+
+ align:start position:0%
+segment there's no other rectangle that
+hits this red thing therefore these two
+
+ align:start position:0%
+hits this red thing therefore these two
+ 
+
+ align:start position:0%
+hits this red thing therefore these two
+points are not going to get charged as a
+
+ align:start position:0%
+points are not going to get charged as a
+ 
+
+ align:start position:0%
+points are not going to get charged as a
+pair
+
+ align:start position:0%
+pair
+ 
+
+ align:start position:0%
+pair
+ever
+
+ align:start position:0%
+ever
+ 
+
+ align:start position:0%
+ever
+again if you remove this
+
+ align:start position:0%
+again if you remove this
+ 
+
+ align:start position:0%
+again if you remove this
+rectangle repeat this
+
+ align:start position:0%
+rectangle repeat this
+ 
+
+ align:start position:0%
+rectangle repeat this
+process PQ is never going to get uh
+
+ align:start position:0%
+process PQ is never going to get uh
+ 
+
+ align:start position:0%
+process PQ is never going to get uh
+charged again so we charge to PQ and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pair Q never charged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again never be charged by another
+
+ align:start position:0%
+again never be charged by another
+ 
+
+ align:start position:0%
+again never be charged by another
+rectangle uh
+
+ align:start position:0%
+rectangle uh
+ 
+
+ align:start position:0%
+rectangle uh
+because no
+
+ align:start position:0%
+because no
+ 
+
+ align:start position:0%
+because no
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+hits
+
+ align:start position:0%
+hits
+ 
+
+ align:start position:0%
+hits
+uh well he hits the red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing so no
+
+ align:start position:0%
+thing so no
+ 
+
+ align:start position:0%
+thing so no
+rectangle uh contains P the segment
+
+ align:start position:0%
+rectangle uh contains P the segment
+ 
+
+ align:start position:0%
+rectangle uh contains P the segment
+PQ the horizontal segment
+
+ align:start position:0%
+PQ the horizontal segment
+ 
+
+ align:start position:0%
+PQ the horizontal segment
+PQ okay so this is almost what we want
+
+ align:start position:0%
+PQ okay so this is almost what we want
+ 
+
+ align:start position:0%
+PQ okay so this is almost what we want
+we really want a single point which is
+
+ align:start position:0%
+we really want a single point which is
+ 
+
+ align:start position:0%
+we really want a single point which is
+not in the input so we have p and Q
+
+ align:start position:0%
+not in the input so we have p and Q
+ 
+
+ align:start position:0%
+not in the input so we have p and Q
+they're horizontally aligned now if
+
+ align:start position:0%
+they're horizontally aligned now if
+ 
+
+ align:start position:0%
+they're horizontally aligned now if
+they're horizontally aligned we know
+
+ align:start position:0%
+they're horizontally aligned we know
+ 
+
+ align:start position:0%
+they're horizontally aligned we know
+that not both of them are in the
+
+ align:start position:0%
+that not both of them are in the
+ 
+
+ align:start position:0%
+that not both of them are in the
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+input because all Y coordinates are
+
+ align:start position:0%
+input because all Y coordinates are
+ 
+
+ align:start position:0%
+input because all Y coordinates are
+distinct this is usually true because
+
+ align:start position:0%
+distinct this is usually true because
+ 
+
+ align:start position:0%
+distinct this is usually true because
+you're only accessing one point per row
+
+ align:start position:0%
+you're only accessing one point per row
+ 
+
+ align:start position:0%
+you're only accessing one point per row
+per time step so um one of these might
+
+ align:start position:0%
+per time step so um one of these might
+ 
+
+ align:start position:0%
+per time step so um one of these might
+be in the input but the other one is not
+
+ align:start position:0%
+be in the input but the other one is not
+ 
+
+ align:start position:0%
+be in the input but the other one is not
+so that's the one I want to hold on to
+
+ align:start position:0%
+so that's the one I want to hold on to
+ 
+
+ align:start position:0%
+so that's the one I want to hold on to
+and say okay that's a a point added to
+
+ align:start position:0%
+and say okay that's a a point added to
+ 
+
+ align:start position:0%
+and say okay that's a a point added to
+opt
+
+ align:start position:0%
+opt
+ 
+
+ align:start position:0%
+opt
+plus uh that pays for this rectangle uh
+
+ align:start position:0%
+plus uh that pays for this rectangle uh
+ 
+
+ align:start position:0%
+plus uh that pays for this rectangle uh
+it's not quite so simple though because
+
+ align:start position:0%
+it's not quite so simple though because
+ 
+
+ align:start position:0%
+it's not quite so simple though because
+we might have a whole bunch of
+
+ align:start position:0%
+we might have a whole bunch of
+ 
+
+ align:start position:0%
+we might have a whole bunch of
+horizontally aligned things and one
+
+ align:start position:0%
+horizontally aligned things and one
+ 
+
+ align:start position:0%
+horizontally aligned things and one
+rectangle charges to this one one
+
+ align:start position:0%
+rectangle charges to this one one
+ 
+
+ align:start position:0%
+rectangle charges to this one one
+rectangle charges to this one one
+
+ align:start position:0%
+rectangle charges to this one one
+ 
+
+ align:start position:0%
+rectangle charges to this one one
+rectangle charges to this
+
+ align:start position:0%
+rectangle charges to this
+ 
+
+ align:start position:0%
+rectangle charges to this
+pair uh that's okay though because here
+
+ align:start position:0%
+pair uh that's okay though because here
+ 
+
+ align:start position:0%
+pair uh that's okay though because here
+we have four points again one of them
+
+ align:start position:0%
+we have four points again one of them
+ 
+
+ align:start position:0%
+we have four points again one of them
+could be in the input the other three
+
+ align:start position:0%
+could be in the input the other three
+ 
+
+ align:start position:0%
+could be in the input the other three
+have to be added and so you've got three
+
+ align:start position:0%
+have to be added and so you've got three
+ 
+
+ align:start position:0%
+have to be added and so you've got three
+rectangles three added points and we're
+
+ align:start position:0%
+rectangles three added points and we're
+ 
+
+ align:start position:0%
+rectangles three added points and we're
+happy question um just to make argument
+
+ align:start position:0%
+happy question um just to make argument
+ 
+
+ align:start position:0%
+happy question um just to make argument
+formal wouldn't you want to like say
+
+ align:start position:0%
+formal wouldn't you want to like say
+ 
+
+ align:start position:0%
+formal wouldn't you want to like say
+that only like I mean when you're saying
+
+ align:start position:0%
+that only like I mean when you're saying
+ 
+
+ align:start position:0%
+that only like I mean when you're saying
+assume that X and Y are always distinct
+
+ align:start position:0%
+assume that X and Y are always distinct
+ 
+
+ align:start position:0%
+assume that X and Y are always distinct
+but then have the same either X or Y ah
+
+ align:start position:0%
+but then have the same either X or Y ah
+ 
+
+ align:start position:0%
+but then have the same either X or Y ah
+right good point so this is distinct in
+
+ align:start position:0%
+right good point so this is distinct in
+ 
+
+ align:start position:0%
+right good point so this is distinct in
+the input is what I
+
+ align:start position:0%
+the input is what I
+ 
+
+ align:start position:0%
+the input is what I
+meant obviously an opt any satisfied set
+
+ align:start position:0%
+meant obviously an opt any satisfied set
+ 
+
+ align:start position:0%
+meant obviously an opt any satisfied set
+is not going to have this property yeah
+
+ align:start position:0%
+is not going to have this property yeah
+ 
+
+ align:start position:0%
+is not going to have this property yeah
+good so I I want to assume X and Y
+
+ align:start position:0%
+good so I I want to assume X and Y
+ 
+
+ align:start position:0%
+good so I I want to assume X and Y
+coordinates are only distinct in the
+
+ align:start position:0%
+coordinates are only distinct in the
+ 
+
+ align:start position:0%
+coordinates are only distinct in the
+input opt will not have that property
+
+ align:start position:0%
+input opt will not have that property
+ 
+
+ align:start position:0%
+input opt will not have that property
+and that's why p and Q can exist and
+
+ align:start position:0%
+and that's why p and Q can exist and
+ 
+
+ align:start position:0%
+and that's why p and Q can exist and
+have the same y-coordinate another
+
+ align:start position:0%
+have the same y-coordinate another
+ 
+
+ align:start position:0%
+have the same y-coordinate another
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um does this still cover the special
+
+ align:start position:0%
+um does this still cover the special
+ 
+
+ align:start position:0%
+um does this still cover the special
+case where your two points are the
+
+ align:start position:0%
+case where your two points are the
+ 
+
+ align:start position:0%
+case where your two points are the
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+rectangle okay so uh question is can p
+
+ align:start position:0%
+rectangle okay so uh question is can p
+ 
+
+ align:start position:0%
+rectangle okay so uh question is can p
+and Q be the points of the rectangle one
+
+ align:start position:0%
+and Q be the points of the rectangle one
+ 
+
+ align:start position:0%
+and Q be the points of the rectangle one
+of them can be like P could be here and
+
+ align:start position:0%
+of them can be like P could be here and
+ 
+
+ align:start position:0%
+of them can be like P could be here and
+then another point is over here so then
+
+ align:start position:0%
+then another point is over here so then
+ 
+
+ align:start position:0%
+then another point is over here so then
+that will be the segment that you're
+
+ align:start position:0%
+that will be the segment that you're
+ 
+
+ align:start position:0%
+that will be the segment that you're
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+between p and Q uh or it could be Q is
+
+ align:start position:0%
+between p and Q uh or it could be Q is
+ 
+
+ align:start position:0%
+between p and Q uh or it could be Q is
+here and P is over here then that's the
+
+ align:start position:0%
+here and P is over here then that's the
+ 
+
+ align:start position:0%
+here and P is over here then that's the
+segment you can't have them both equal
+
+ align:start position:0%
+segment you can't have them both equal
+ 
+
+ align:start position:0%
+segment you can't have them both equal
+because p and Q have to be horizontally
+
+ align:start position:0%
+because p and Q have to be horizontally
+ 
+
+ align:start position:0%
+because p and Q have to be horizontally
+aligned and also because there's got to
+
+ align:start position:0%
+aligned and also because there's got to
+ 
+
+ align:start position:0%
+aligned and also because there's got to
+be another point in
+
+ align:start position:0%
+be another point in
+ 
+
+ align:start position:0%
+be another point in
+there yeah so that should work you have
+
+ align:start position:0%
+there yeah so that should work you have
+ 
+
+ align:start position:0%
+there yeah so that should work you have
+to check that this this boundary case is
+
+ align:start position:0%
+to check that this this boundary case is
+ 
+
+ align:start position:0%
+to check that this this boundary case is
+still okay but it claim is no other
+
+ align:start position:0%
+still okay but it claim is no other
+ 
+
+ align:start position:0%
+still okay but it claim is no other
+rectangle uh no other rectangle touches
+
+ align:start position:0%
+rectangle uh no other rectangle touches
+ 
+
+ align:start position:0%
+rectangle uh no other rectangle touches
+this red line even on the end point and
+
+ align:start position:0%
+this red line even on the end point and
+ 
+
+ align:start position:0%
+this red line even on the end point and
+therefore no other rectangle will wholly
+
+ align:start position:0%
+therefore no other rectangle will wholly
+ 
+
+ align:start position:0%
+therefore no other rectangle will wholly
+contain p and Q
+
+ align:start position:0%
+contain p and Q
+ 
+
+ align:start position:0%
+contain p and Q
+and so that means uh you're only
+
+ align:start position:0%
+and so that means uh you're only
+ 
+
+ align:start position:0%
+and so that means uh you're only
+charging to this pair once and then this
+
+ align:start position:0%
+charging to this pair once and then this
+ 
+
+ align:start position:0%
+charging to this pair once and then this
+pair charging is okay BEC luckily
+
+ align:start position:0%
+pair charging is okay BEC luckily
+ 
+
+ align:start position:0%
+pair charging is okay BEC luckily
+there's three edges here for vertices
+
+ align:start position:0%
+there's three edges here for vertices
+ 
+
+ align:start position:0%
+there's three edges here for vertices
+one of the vertices we can't charge to
+
+ align:start position:0%
+one of the vertices we can't charge to
+ 
+
+ align:start position:0%
+one of the vertices we can't charge to
+so there's exactly the right number of
+
+ align:start position:0%
+so there's exactly the right number of
+ 
+
+ align:start position:0%
+so there's exactly the right number of
+things for the
+
+ align:start position:0%
+things for the
+ 
+
+ align:start position:0%
+things for the
+edges and we're okay have yeah this can
+
+ align:start position:0%
+edges and we're okay have yeah this can
+ 
+
+ align:start position:0%
+edges and we're okay have yeah this can
+really happen in fact our favorite
+
+ align:start position:0%
+really happen in fact our favorite
+ 
+
+ align:start position:0%
+really happen in fact our favorite
+example of the pin wheel If instead of
+
+ align:start position:0%
+example of the pin wheel If instead of
+ 
+
+ align:start position:0%
+example of the pin wheel If instead of
+doing the greedy addition we do uh this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edition
+
+ align:start position:0%
+Edition
+ 
+
+ align:start position:0%
+Edition
+oops ex these are supposed to be
+
+ align:start position:0%
+oops ex these are supposed to be
+ 
+
+ align:start position:0%
+oops ex these are supposed to be
+horizontally
+
+ align:start position:0%
+horizontally
+ 
+
+ align:start position:0%
+horizontally
+aligned a little hard without a grid
+
+ align:start position:0%
+aligned a little hard without a grid
+ 
+
+ align:start position:0%
+aligned a little hard without a grid
+don't have graph graph Blackboard be
+
+ align:start position:0%
+don't have graph graph Blackboard be
+ 
+
+ align:start position:0%
+don't have graph graph Blackboard be
+great so this should this is not quite
+
+ align:start position:0%
+great so this should this is not quite
+ 
+
+ align:start position:0%
+great so this should this is not quite
+satisfied okay I've got to add some more
+
+ align:start position:0%
+satisfied okay I've got to add some more
+ 
+
+ align:start position:0%
+satisfied okay I've got to add some more
+points uh maybe here or something but it
+
+ align:start position:0%
+points uh maybe here or something but it
+ 
+
+ align:start position:0%
+points uh maybe here or something but it
+has the feature that uh here's an
+
+ align:start position:0%
+has the feature that uh here's an
+ 
+
+ align:start position:0%
+has the feature that uh here's an
+independent set of rectangles I can do
+
+ align:start position:0%
+independent set of rectangles I can do
+ 
+
+ align:start position:0%
+independent set of rectangles I can do
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+one and this
+
+ align:start position:0%
+one and this
+ 
+
+ align:start position:0%
+one and this
+one so this is three independent
+
+ align:start position:0%
+one so this is three independent
+ 
+
+ align:start position:0%
+one so this is three independent
+rectangle as far as the white points go
+
+ align:start position:0%
+rectangle as far as the white points go
+ 
+
+ align:start position:0%
+rectangle as far as the white points go
+they're independent
+
+ align:start position:0%
+they're independent
+ 
+
+ align:start position:0%
+they're independent
+rectangles um you know the corners are
+
+ align:start position:0%
+rectangles um you know the corners are
+ 
+
+ align:start position:0%
+rectangles um you know the corners are
+not strictly inside each other and none
+
+ align:start position:0%
+not strictly inside each other and none
+ 
+
+ align:start position:0%
+not strictly inside each other and none
+of the white points satisfies any of the
+
+ align:start position:0%
+of the white points satisfies any of the
+ 
+
+ align:start position:0%
+of the white points satisfies any of the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+rectangles um and and indeed if you did
+
+ align:start position:0%
+rectangles um and and indeed if you did
+ 
+
+ align:start position:0%
+rectangles um and and indeed if you did
+it if you applied this argument first
+
+ align:start position:0%
+it if you applied this argument first
+ 
+
+ align:start position:0%
+it if you applied this argument first
+you take the widest rectangle you say
+
+ align:start position:0%
+you take the widest rectangle you say
+ 
+
+ align:start position:0%
+you take the widest rectangle you say
+okay here's my vertical red segment uh
+
+ align:start position:0%
+okay here's my vertical red segment uh
+ 
+
+ align:start position:0%
+okay here's my vertical red segment uh
+I'm going to charge to these two guys
+
+ align:start position:0%
+I'm going to charge to these two guys
+ 
+
+ align:start position:0%
+I'm going to charge to these two guys
+this segment and then eventually this
+
+ align:start position:0%
+this segment and then eventually this
+ 
+
+ align:start position:0%
+this segment and then eventually this
+guy will charge to this segment and this
+
+ align:start position:0%
+guy will charge to this segment and this
+ 
+
+ align:start position:0%
+guy will charge to this segment and this
+guy will charge to this segment and
+
+ align:start position:0%
+guy will charge to this segment and
+ 
+
+ align:start position:0%
+guy will charge to this segment and
+luckily there are three added points for
+
+ align:start position:0%
+luckily there are three added points for
+ 
+
+ align:start position:0%
+luckily there are three added points for
+exactly the three segments for the three
+
+ align:start position:0%
+exactly the three segments for the three
+ 
+
+ align:start position:0%
+exactly the three segments for the three
+rectangles okay there had to be another
+
+ align:start position:0%
+rectangles okay there had to be another
+ 
+
+ align:start position:0%
+rectangles okay there had to be another
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+but so that's the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+uh a lot of work but in the end it says
+
+ align:start position:0%
+uh a lot of work but in the end it says
+ 
+
+ align:start position:0%
+uh a lot of work but in the end it says
+look just find an independent set of
+
+ align:start position:0%
+look just find an independent set of
+ 
+
+ align:start position:0%
+look just find an independent set of
+plus boxes plus rectangles that's a
+
+ align:start position:0%
+plus boxes plus rectangles that's a
+ 
+
+ align:start position:0%
+plus boxes plus rectangles that's a
+lower bound on opt so now question
+
+ align:start position:0%
+lower bound on opt so now question
+ 
+
+ align:start position:0%
+lower bound on opt so now question
+remains how do we find a good
+
+ align:start position:0%
+remains how do we find a good
+ 
+
+ align:start position:0%
+remains how do we find a good
+independent set of plus boxes and now
+
+ align:start position:0%
+independent set of plus boxes and now
+ 
+
+ align:start position:0%
+independent set of plus boxes and now
+we'll go through the three different
+
+ align:start position:0%
+we'll go through the three different
+ 
+
+ align:start position:0%
+we'll go through the three different
+ways we know how to do it we'll start
+
+ align:start position:0%
+ways we know how to do it we'll start
+ 
+
+ align:start position:0%
+ways we know how to do it we'll start
+actually with Wilbur 2 it's called
+
+ align:start position:0%
+actually with Wilbur 2 it's called
+ 
+
+ align:start position:0%
+actually with Wilbur 2 it's called
+Wilbur 2 because it was in a paper by
+
+ align:start position:0%
+Wilbur 2 because it was in a paper by
+ 
+
+ align:start position:0%
+Wilbur 2 because it was in a paper by
+Wilbur and he has lower I think he
+
+ align:start position:0%
+Wilbur and he has lower I think he
+ 
+
+ align:start position:0%
+Wilbur and he has lower I think he
+called it lower bound number one and
+
+ align:start position:0%
+called it lower bound number one and
+ 
+
+ align:start position:0%
+called it lower bound number one and
+lower bound number two uh but for
+
+ align:start position:0%
+lower bound number two uh but for
+ 
+
+ align:start position:0%
+lower bound number two uh but for
+pragmatic Reasons I'm going to start
+
+ align:start position:0%
+pragmatic Reasons I'm going to start
+ 
+
+ align:start position:0%
+pragmatic Reasons I'm going to start
+with number two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's from 1989 so it's actually an old
+
+ align:start position:0%
+it's from 1989 so it's actually an old
+ 
+
+ align:start position:0%
+it's from 1989 so it's actually an old
+paper and it was sort of lost for a long
+
+ align:start position:0%
+paper and it was sort of lost for a long
+ 
+
+ align:start position:0%
+paper and it was sort of lost for a long
+time I don't think Wilbur wrote any
+
+ align:start position:0%
+time I don't think Wilbur wrote any
+ 
+
+ align:start position:0%
+time I don't think Wilbur wrote any
+other papers uh and was in scy comp in a
+
+ align:start position:0%
+other papers uh and was in scy comp in a
+ 
+
+ align:start position:0%
+other papers uh and was in scy comp in a
+big Journal but no one uh so it's a few
+
+ align:start position:0%
+big Journal but no one uh so it's a few
+ 
+
+ align:start position:0%
+big Journal but no one uh so it's a few
+years after spit trees um and then sort
+
+ align:start position:0%
+years after spit trees um and then sort
+ 
+
+ align:start position:0%
+years after spit trees um and then sort
+of rediscovered in the like early 2000s
+
+ align:start position:0%
+of rediscovered in the like early 2000s
+ 
+
+ align:start position:0%
+of rediscovered in the like early 2000s
+and turns out to be really useful for a
+
+ align:start position:0%
+and turns out to be really useful for a
+ 
+
+ align:start position:0%
+and turns out to be really useful for a
+lot of a lot of theorems so here's the
+
+ align:start position:0%
+lot of a lot of theorems so here's the
+ 
+
+ align:start position:0%
+lot of a lot of theorems so here's the
+lower bound
+
+ align:start position:0%
+lower bound
+ 
+
+ align:start position:0%
+lower bound
+again we're looking at the input Point
+
+ align:start position:0%
+again we're looking at the input Point
+ 
+
+ align:start position:0%
+again we're looking at the input Point
+set no added points just the original
+
+ align:start position:0%
+set no added points just the original
+ 
+
+ align:start position:0%
+set no added points just the original
+points look at every point and look at
+
+ align:start position:0%
+points look at every point and look at
+ 
+
+ align:start position:0%
+points look at every point and look at
+all the points that you can see from
+
+ align:start position:0%
+all the points that you can see from
+ 
+
+ align:start position:0%
+all the points that you can see from
+this point downward what does c mean I'm
+
+ align:start position:0%
+this point downward what does c mean I'm
+ 
+
+ align:start position:0%
+this point downward what does c mean I'm
+interested in points that when I below P
+
+ align:start position:0%
+interested in points that when I below P
+ 
+
+ align:start position:0%
+interested in points that when I below P
+that when I draw the rectangle contain
+
+ align:start position:0%
+that when I draw the rectangle contain
+ 
+
+ align:start position:0%
+that when I draw the rectangle contain
+no other
+
+ align:start position:0%
+no other
+ 
+
+ align:start position:0%
+no other
+points okay so this is
+
+ align:start position:0%
+points okay so this is
+ 
+
+ align:start position:0%
+points okay so this is
+like uh it's sort of like a lower
+
+ align:start position:0%
+like uh it's sort of like a lower
+ 
+
+ align:start position:0%
+like uh it's sort of like a lower
+envelope it's going to look something
+
+ align:start position:0%
+envelope it's going to look something
+ 
+
+ align:start position:0%
+envelope it's going to look something
+like this uh and I don't know maybe some
+
+ align:start position:0%
+like this uh and I don't know maybe some
+ 
+
+ align:start position:0%
+like this uh and I don't know maybe some
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+like this so all of these
+
+ align:start position:0%
+like this so all of these
+ 
+
+ align:start position:0%
+like this so all of these
+rectangles have to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+empty okay so th these are the uh
+
+ align:start position:0%
+empty okay so th these are the uh
+ 
+
+ align:start position:0%
+empty okay so th these are the uh
+downward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+visible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and now among these points you can
+
+ align:start position:0%
+p and now among these points you can
+ 
+
+ align:start position:0%
+p and now among these points you can
+sort them by
+
+ align:start position:0%
+sort them by
+ 
+
+ align:start position:0%
+sort them by
+y-coordinate and I want to see how many
+
+ align:start position:0%
+y-coordinate and I want to see how many
+ 
+
+ align:start position:0%
+y-coordinate and I want to see how many
+times do they cross this vertical line
+
+ align:start position:0%
+times do they cross this vertical line
+ 
+
+ align:start position:0%
+times do they cross this vertical line
+so if I order them by y-coordinate so
+
+ align:start position:0%
+so if I order them by y-coordinate so
+ 
+
+ align:start position:0%
+so if I order them by y-coordinate so
+let me add some
+
+ align:start position:0%
+let me add some
+ 
+
+ align:start position:0%
+let me add some
+red so I start here maybe I go to here
+
+ align:start position:0%
+red so I start here maybe I go to here
+ 
+
+ align:start position:0%
+red so I start here maybe I go to here
+then next one is over here so that's a
+
+ align:start position:0%
+then next one is over here so that's a
+ 
+
+ align:start position:0%
+then next one is over here so that's a
+cross uh then I go over here then I
+
+ align:start position:0%
+cross uh then I go over here then I
+ 
+
+ align:start position:0%
+cross uh then I go over here then I
+cross then I go here then I cross go
+
+ align:start position:0%
+cross then I go here then I cross go
+ 
+
+ align:start position:0%
+cross then I go here then I cross go
+here here cross so if I visit them in
+
+ align:start position:0%
+here here cross so if I visit them in
+ 
+
+ align:start position:0%
+here here cross so if I visit them in
+order I want to know how many times do I
+
+ align:start position:0%
+order I want to know how many times do I
+ 
+
+ align:start position:0%
+order I want to know how many times do I
+cross this vertical
+
+ align:start position:0%
+cross this vertical
+ 
+
+ align:start position:0%
+cross this vertical
+line this is what we call you think of
+
+ align:start position:0%
+line this is what we call you think of
+ 
+
+ align:start position:0%
+line this is what we call you think of
+this so this is the past of P right all
+
+ align:start position:0%
+this so this is the past of P right all
+ 
+
+ align:start position:0%
+this so this is the past of P right all
+the axises before P think of this as how
+
+ align:start position:0%
+the axises before P think of this as how
+ 
+
+ align:start position:0%
+the axises before P think of this as how
+many times you alternate between uh axis
+
+ align:start position:0%
+many times you alternate between uh axis
+ 
+
+ align:start position:0%
+many times you alternate between uh axis
+on the left of the line and X thing on
+
+ align:start position:0%
+on the left of the line and X thing on
+ 
+
+ align:start position:0%
+on the left of the line and X thing on
+the right of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line so
+
+ align:start position:0%
+line so
+ 
+
+ align:start position:0%
+line so
+count number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alternations uh left or right of p and
+
+ align:start position:0%
+alternations uh left or right of p and
+ 
+
+ align:start position:0%
+alternations uh left or right of p and
+again if we assume that no key is ever
+
+ align:start position:0%
+again if we assume that no key is ever
+ 
+
+ align:start position:0%
+again if we assume that no key is ever
+accessed more than once then there'll
+
+ align:start position:0%
+accessed more than once then there'll
+ 
+
+ align:start position:0%
+accessed more than once then there'll
+always be left or right never exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on uh and then I want to sum over all
+
+ align:start position:0%
+on uh and then I want to sum over all
+ 
+
+ align:start position:0%
+on uh and then I want to sum over all
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I claim this is a lower
+
+ align:start position:0%
+and I claim this is a lower
+ 
+
+ align:start position:0%
+and I claim this is a lower
+bound okay why is it a lower bound
+
+ align:start position:0%
+bound okay why is it a lower bound
+ 
+
+ align:start position:0%
+bound okay why is it a lower bound
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+essentially I take each of these red
+
+ align:start position:0%
+essentially I take each of these red
+ 
+
+ align:start position:0%
+essentially I take each of these red
+lines that cross the P vertical line and
+
+ align:start position:0%
+lines that cross the P vertical line and
+ 
+
+ align:start position:0%
+lines that cross the P vertical line and
+I turn them into a
+
+ align:start position:0%
+I turn them into a
+ 
+
+ align:start position:0%
+I turn them into a
+box so there's one there one
+
+ align:start position:0%
+box so there's one there one
+ 
+
+ align:start position:0%
+box so there's one there one
+there one there and one there
+
+ align:start position:0%
+there one there and one there
+ 
+
+ align:start position:0%
+there one there and one there
+claim if I do this for all
+
+ align:start position:0%
+claim if I do this for all
+ 
+
+ align:start position:0%
+claim if I do this for all
+P none of those all those boxes will be
+
+ align:start position:0%
+P none of those all those boxes will be
+ 
+
+ align:start position:0%
+P none of those all those boxes will be
+independent all those rectangles will be
+
+ align:start position:0%
+independent all those rectangles will be
+ 
+
+ align:start position:0%
+independent all those rectangles will be
+independent from each other I won't
+
+ align:start position:0%
+independent from each other I won't
+ 
+
+ align:start position:0%
+independent from each other I won't
+prove that formally here but you can
+
+ align:start position:0%
+prove that formally here but you can
+ 
+
+ align:start position:0%
+prove that formally here but you can
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+it uh so it's obvious for one p because
+
+ align:start position:0%
+it uh so it's obvious for one p because
+ 
+
+ align:start position:0%
+it uh so it's obvious for one p because
+each of these has a different vertical
+
+ align:start position:0%
+each of these has a different vertical
+ 
+
+ align:start position:0%
+each of these has a different vertical
+span if you do it for all P all the
+
+ align:start position:0%
+span if you do it for all P all the
+ 
+
+ align:start position:0%
+span if you do it for all P all the
+points p uh these won't
+
+ align:start position:0%
+points p uh these won't
+ 
+
+ align:start position:0%
+points p uh these won't
+conflict so by the independent rectangle
+
+ align:start position:0%
+conflict so by the independent rectangle
+ 
+
+ align:start position:0%
+conflict so by the independent rectangle
+lower bound uh this is a lower bound on
+
+ align:start position:0%
+lower bound uh this is a lower bound on
+ 
+
+ align:start position:0%
+lower bound uh this is a lower bound on
+opt
+
+ align:start position:0%
+opt
+ 
+
+ align:start position:0%
+opt
+up up to a factor of
+
+ align:start position:0%
+up up to a factor of
+ 
+
+ align:start position:0%
+up up to a factor of
+two okay so what um Wilber 2 is quite
+
+ align:start position:0%
+two okay so what um Wilber 2 is quite
+ 
+
+ align:start position:0%
+two okay so what um Wilber 2 is quite
+interesting for a long time we've
+
+ align:start position:0%
+interesting for a long time we've
+ 
+
+ align:start position:0%
+interesting for a long time we've
+conjectured that it is the right answer
+
+ align:start position:0%
+conjectured that it is the right answer
+ 
+
+ align:start position:0%
+conjectured that it is the right answer
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conjecture I know it's a weird lower
+
+ align:start position:0%
+conjecture I know it's a weird lower
+ 
+
+ align:start position:0%
+conjecture I know it's a weird lower
+bound to even think of is a very hard
+
+ align:start position:0%
+bound to even think of is a very hard
+ 
+
+ align:start position:0%
+bound to even think of is a very hard
+paper to read uh without the geometric
+
+ align:start position:0%
+paper to read uh without the geometric
+ 
+
+ align:start position:0%
+paper to read uh without the geometric
+view it's it's even harder to imagine
+
+ align:start position:0%
+view it's it's even harder to imagine
+ 
+
+ align:start position:0%
+view it's it's even harder to imagine
+the definition of this bound but uh so
+
+ align:start position:0%
+the definition of this bound but uh so
+ 
+
+ align:start position:0%
+the definition of this bound but uh so
+it's sort of an algorithm it's a way to
+
+ align:start position:0%
+it's sort of an algorithm it's a way to
+ 
+
+ align:start position:0%
+it's sort of an algorithm it's a way to
+assign boxes gives you lower balance a
+
+ align:start position:0%
+assign boxes gives you lower balance a
+ 
+
+ align:start position:0%
+assign boxes gives you lower balance a
+little weird uh we conjecture that it's
+
+ align:start position:0%
+little weird uh we conjecture that it's
+ 
+
+ align:start position:0%
+little weird uh we conjecture that it's
+proportional to the optimal
+
+ align:start position:0%
+proportional to the optimal
+ 
+
+ align:start position:0%
+proportional to the optimal
+solution we can't prove it tried many
+
+ align:start position:0%
+solution we can't prove it tried many
+ 
+
+ align:start position:0%
+solution we can't prove it tried many
+times it's a pain to work with uh but it
+
+ align:start position:0%
+times it's a pain to work with uh but it
+ 
+
+ align:start position:0%
+times it's a pain to work with uh but it
+is what it
+
+ align:start position:0%
+is what it
+ 
+
+ align:start position:0%
+is what it
+is there's one theorem that uses it so I
+
+ align:start position:0%
+is there's one theorem that uses it so I
+ 
+
+ align:start position:0%
+is there's one theorem that uses it so I
+want to tell you about that theorem but
+
+ align:start position:0%
+want to tell you about that theorem but
+ 
+
+ align:start position:0%
+want to tell you about that theorem but
+I don't want to go into it in too much
+
+ align:start position:0%
+I don't want to go into it in too much
+ 
+
+ align:start position:0%
+I don't want to go into it in too much
+detail it's a neat
+
+ align:start position:0%
+detail it's a neat
+ 
+
+ align:start position:0%
+detail it's a neat
+theorem and this is it's in a paper by
+
+ align:start position:0%
+theorem and this is it's in a paper by
+ 
+
+ align:start position:0%
+theorem and this is it's in a paper by
+iono uh 2002 and it was the first paper
+
+ align:start position:0%
+iono uh 2002 and it was the first paper
+ 
+
+ align:start position:0%
+iono uh 2002 and it was the first paper
+to revitalize the Wilber stuff so it's
+
+ align:start position:0%
+to revitalize the Wilber stuff so it's
+ 
+
+ align:start position:0%
+to revitalize the Wilber stuff so it's
+like hey there's this Wilbur 2 bound we
+
+ align:start position:0%
+like hey there's this Wilbur 2 bound we
+ 
+
+ align:start position:0%
+like hey there's this Wilbur 2 bound we
+can use it to solve a new problem which
+
+ align:start position:0%
+can use it to solve a new problem which
+ 
+
+ align:start position:0%
+can use it to solve a new problem which
+is called key independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimality briefly the idea with key key
+
+ align:start position:0%
+optimality briefly the idea with key key
+ 
+
+ align:start position:0%
+optimality briefly the idea with key key
+independent optimality is suppose you've
+
+ align:start position:0%
+independent optimality is suppose you've
+ 
+
+ align:start position:0%
+independent optimality is suppose you've
+heard about Dynamic optimality you know
+
+ align:start position:0%
+heard about Dynamic optimality you know
+ 
+
+ align:start position:0%
+heard about Dynamic optimality you know
+it's really cool because playay trees
+
+ align:start position:0%
+it's really cool because playay trees
+ 
+
+ align:start position:0%
+it's really cool because playay trees
+and whatnot seem to really adapt to
+
+ align:start position:0%
+and whatnot seem to really adapt to
+ 
+
+ align:start position:0%
+and whatnot seem to really adapt to
+whatever your inputs are but suppose
+
+ align:start position:0%
+whatever your inputs are but suppose
+ 
+
+ align:start position:0%
+whatever your inputs are but suppose
+your inputs really don't have keys
+
+ align:start position:0%
+your inputs really don't have keys
+ 
+
+ align:start position:0%
+your inputs really don't have keys
+they're just arbitrary objects labeled
+
+ align:start position:0%
+they're just arbitrary objects labeled
+ 
+
+ align:start position:0%
+they're just arbitrary objects labeled
+however just randomly uh in fact let's
+
+ align:start position:0%
+however just randomly uh in fact let's
+ 
+
+ align:start position:0%
+however just randomly uh in fact let's
+assume that they are labeled randomly
+
+ align:start position:0%
+assume that they are labeled randomly
+ 
+
+ align:start position:0%
+assume that they are labeled randomly
+suppose the keys are generated randomly
+
+ align:start position:0%
+suppose the keys are generated randomly
+ 
+
+ align:start position:0%
+suppose the keys are generated randomly
+because they're meaningless they're just
+
+ align:start position:0%
+because they're meaningless they're just
+ 
+
+ align:start position:0%
+because they're meaningless they're just
+arbitrary things so you figure oh maybe
+
+ align:start position:0%
+arbitrary things so you figure oh maybe
+ 
+
+ align:start position:0%
+arbitrary things so you figure oh maybe
+I'll make it better and just randomize
+
+ align:start position:0%
+I'll make it better and just randomize
+ 
+
+ align:start position:0%
+I'll make it better and just randomize
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+completely uh if
+
+ align:start position:0%
+completely uh if
+ 
+
+ align:start position:0%
+completely uh if
+keys are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random then opt Dynamic opt is the same
+
+ align:start position:0%
+random then opt Dynamic opt is the same
+ 
+
+ align:start position:0%
+random then opt Dynamic opt is the same
+thing up to constant factors as the
+
+ align:start position:0%
+thing up to constant factors as the
+ 
+
+ align:start position:0%
+thing up to constant factors as the
+working set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound that's the theorem so this is cool
+
+ align:start position:0%
+bound that's the theorem so this is cool
+ 
+
+ align:start position:0%
+bound that's the theorem so this is cool
+because it means spay trees are actually
+
+ align:start position:0%
+because it means spay trees are actually
+ 
+
+ align:start position:0%
+because it means spay trees are actually
+optimal in this setting where keys are
+
+ align:start position:0%
+optimal in this setting where keys are
+ 
+
+ align:start position:0%
+optimal in this setting where keys are
+random uh so this is you know in
+
+ align:start position:0%
+random uh so this is you know in
+ 
+
+ align:start position:0%
+random uh so this is you know in
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+over the the randomized keys and the way
+
+ align:start position:0%
+over the the randomized keys and the way
+ 
+
+ align:start position:0%
+over the the randomized keys and the way
+this theorem is proved is basically you
+
+ align:start position:0%
+this theorem is proved is basically you
+ 
+
+ align:start position:0%
+this theorem is proved is basically you
+you take so what this is saying is if we
+
+ align:start position:0%
+you take so what this is saying is if we
+ 
+
+ align:start position:0%
+you take so what this is saying is if we
+take a point set arbitrary Point set but
+
+ align:start position:0%
+take a point set arbitrary Point set but
+ 
+
+ align:start position:0%
+take a point set arbitrary Point set but
+then we Rand randomize the x coordinates
+
+ align:start position:0%
+then we Rand randomize the x coordinates
+ 
+
+ align:start position:0%
+then we Rand randomize the x coordinates
+leave the y-coordinates as they
+
+ align:start position:0%
+leave the y-coordinates as they
+ 
+
+ align:start position:0%
+leave the y-coordinates as they
+are then you can compute how Wilbur 2
+
+ align:start position:0%
+are then you can compute how Wilbur 2
+ 
+
+ align:start position:0%
+are then you can compute how Wilbur 2
+behaves right because now you have a
+
+ align:start position:0%
+behaves right because now you have a
+ 
+
+ align:start position:0%
+behaves right because now you have a
+bunch of points and it's you're randomly
+
+ align:start position:0%
+bunch of points and it's you're randomly
+ 
+
+ align:start position:0%
+bunch of points and it's you're randomly
+shifting their x coordinate so it's like
+
+ align:start position:0%
+shifting their x coordinate so it's like
+ 
+
+ align:start position:0%
+shifting their x coordinate so it's like
+if you're randomly bouncing around an X
+
+ align:start position:0%
+if you're randomly bouncing around an X
+ 
+
+ align:start position:0%
+if you're randomly bouncing around an X
+uh and you're interested in this
+
+ align:start position:0%
+uh and you're interested in this
+ 
+
+ align:start position:0%
+uh and you're interested in this
+envelope on the left and the right you
+
+ align:start position:0%
+envelope on the left and the right you
+ 
+
+ align:start position:0%
+envelope on the left and the right you
+want to know basically how many times
+
+ align:start position:0%
+want to know basically how many times
+ 
+
+ align:start position:0%
+want to know basically how many times
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+uh let's see I guess since I last
+
+ align:start position:0%
+uh let's see I guess since I last
+ 
+
+ align:start position:0%
+uh let's see I guess since I last
+accessed p is here we didn't do that
+
+ align:start position:0%
+accessed p is here we didn't do that
+ 
+
+ align:start position:0%
+accessed p is here we didn't do that
+here but in the working set bound that's
+
+ align:start position:0%
+here but in the working set bound that's
+ 
+
+ align:start position:0%
+here but in the working set bound that's
+part of the deal um how many uh let's
+
+ align:start position:0%
+part of the deal um how many uh let's
+ 
+
+ align:start position:0%
+part of the deal um how many uh let's
+see it's sort of if you look on the left
+
+ align:start position:0%
+see it's sort of if you look on the left
+ 
+
+ align:start position:0%
+see it's sort of if you look on the left
+side it's like how many times does the
+
+ align:start position:0%
+side it's like how many times does the
+ 
+
+ align:start position:0%
+side it's like how many times does the
+max change and you may know if you have
+
+ align:start position:0%
+max change and you may know if you have
+ 
+
+ align:start position:0%
+max change and you may know if you have
+n random numbers and you're
+
+ align:start position:0%
+n random numbers and you're
+ 
+
+ align:start position:0%
+n random numbers and you're
+uh you want to know how many times do
+
+ align:start position:0%
+uh you want to know how many times do
+ 
+
+ align:start position:0%
+uh you want to know how many times do
+the max change as I go left to right as
+
+ align:start position:0%
+the max change as I go left to right as
+ 
+
+ align:start position:0%
+the max change as I go left to right as
+I take larger and larger prefixes of
+
+ align:start position:0%
+I take larger and larger prefixes of
+ 
+
+ align:start position:0%
+I take larger and larger prefixes of
+those n numbers the answer is log n in
+
+ align:start position:0%
+those n numbers the answer is log n in
+ 
+
+ align:start position:0%
+those n numbers the answer is log n in
+expectation because the the more points
+
+ align:start position:0%
+expectation because the the more points
+ 
+
+ align:start position:0%
+expectation because the the more points
+you have the less and less likely it is
+
+ align:start position:0%
+you have the less and less likely it is
+ 
+
+ align:start position:0%
+you have the less and less likely it is
+for the max to
+
+ align:start position:0%
+for the max to
+ 
+
+ align:start position:0%
+for the max to
+change so uh basically you show the
+
+ align:start position:0%
+change so uh basically you show the
+ 
+
+ align:start position:0%
+change so uh basically you show the
+expected Wilbur
+
+ align:start position:0%
+expected Wilbur
+ 
+
+ align:start position:0%
+expected Wilbur
+2 of a point over this randomization is
+
+ align:start position:0%
+2 of a point over this randomization is
+ 
+
+ align:start position:0%
+2 of a point over this randomization is
+Theta log TI where TI is the working set
+
+ align:start position:0%
+Theta log TI where TI is the working set
+ 
+
+ align:start position:0%
+Theta log TI where TI is the working set
+bound and so uh that gives you the
+
+ align:start position:0%
+bound and so uh that gives you the
+ 
+
+ align:start position:0%
+bound and so uh that gives you the
+theorem this is the this is gives you a
+
+ align:start position:0%
+theorem this is the this is gives you a
+ 
+
+ align:start position:0%
+theorem this is the this is gives you a
+lower bound of the working set bound we
+
+ align:start position:0%
+lower bound of the working set bound we
+ 
+
+ align:start position:0%
+lower bound of the working set bound we
+have upper bounds of the working set
+
+ align:start position:0%
+have upper bounds of the working set
+ 
+
+ align:start position:0%
+have upper bounds of the working set
+bound and therefore that's opt okay so
+
+ align:start position:0%
+bound and therefore that's opt okay so
+ 
+
+ align:start position:0%
+bound and therefore that's opt okay so
+that's just a very quick sketch if if
+
+ align:start position:0%
+that's just a very quick sketch if if
+ 
+
+ align:start position:0%
+that's just a very quick sketch if if
+you're interested check out the
+
+ align:start position:0%
+you're interested check out the
+ 
+
+ align:start position:0%
+you're interested check out the
+paper uh that's unfortunately all we
+
+ align:start position:0%
+paper uh that's unfortunately all we
+ 
+
+ align:start position:0%
+paper uh that's unfortunately all we
+know what to do with Wilbur 2 but
+
+ align:start position:0%
+know what to do with Wilbur 2 but
+ 
+
+ align:start position:0%
+know what to do with Wilbur 2 but
+there's this other bound one which seems
+
+ align:start position:0%
+there's this other bound one which seems
+ 
+
+ align:start position:0%
+there's this other bound one which seems
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+good yet we can do a lot more with it so
+
+ align:start position:0%
+good yet we can do a lot more with it so
+ 
+
+ align:start position:0%
+good yet we can do a lot more with it so
+let me go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a lot easier to analyze algorithms
+
+ align:start position:0%
+that a lot easier to analyze algorithms
+ 
+
+ align:start position:0%
+that a lot easier to analyze algorithms
+with respect ECT to Wilbur
+
+ align:start position:0%
+with respect ECT to Wilbur
+ 
+
+ align:start position:0%
+with respect ECT to Wilbur
+one what's Wilbur
+
+ align:start position:0%
+one what's Wilbur
+ 
+
+ align:start position:0%
+one what's Wilbur
+one we're going to fix something called
+
+ align:start position:0%
+one we're going to fix something called
+ 
+
+ align:start position:0%
+one we're going to fix something called
+a lower bound
+
+ align:start position:0%
+a lower bound
+ 
+
+ align:start position:0%
+a lower bound
+tree I'm going to call it P because it's
+
+ align:start position:0%
+tree I'm going to call it P because it's
+ 
+
+ align:start position:0%
+tree I'm going to call it P because it's
+basically going to be a perfect binary
+
+ align:start position:0%
+basically going to be a perfect binary
+ 
+
+ align:start position:0%
+basically going to be a perfect binary
+tree on my
+
+ align:start position:0%
+tree on my
+ 
+
+ align:start position:0%
+tree on my
+keys this tree never changes that's why
+
+ align:start position:0%
+keys this tree never changes that's why
+ 
+
+ align:start position:0%
+keys this tree never changes that's why
+I say fix it is not the binary search
+
+ align:start position:0%
+I say fix it is not the binary search
+ 
+
+ align:start position:0%
+I say fix it is not the binary search
+tree you're looking for it is not the
+
+ align:start position:0%
+tree you're looking for it is not the
+ 
+
+ align:start position:0%
+tree you're looking for it is not the
+binary search tree that you're
+
+ align:start position:0%
+binary search tree that you're
+ 
+
+ align:start position:0%
+binary search tree that you're
+interested in is just a thing to think
+
+ align:start position:0%
+interested in is just a thing to think
+ 
+
+ align:start position:0%
+interested in is just a thing to think
+about okay now for each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node of that tree like let's look at
+
+ align:start position:0%
+node of that tree like let's look at
+ 
+
+ align:start position:0%
+node of that tree like let's look at
+this node and give the node a name
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y so here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y there's the left sub tree of Y and
+
+ align:start position:0%
+y there's the left sub tree of Y and
+ 
+
+ align:start position:0%
+y there's the left sub tree of Y and
+there's the right sub tree of Y okay
+
+ align:start position:0%
+there's the right sub tree of Y okay
+ 
+
+ align:start position:0%
+there's the right sub tree of Y okay
+these are a bunch of keys there's keys
+
+ align:start position:0%
+these are a bunch of keys there's keys
+ 
+
+ align:start position:0%
+these are a bunch of keys there's keys
+that are to the left of Y there's keys
+
+ align:start position:0%
+that are to the left of Y there's keys
+ 
+
+ align:start position:0%
+that are to the left of Y there's keys
+to the right of Y there's keys outside
+
+ align:start position:0%
+to the right of Y there's keys outside
+ 
+
+ align:start position:0%
+to the right of Y there's keys outside
+the sub tree we're going to ignore those
+
+ align:start position:0%
+the sub tree we're going to ignore those
+ 
+
+ align:start position:0%
+the sub tree we're going to ignore those
+I want to look at the accesses to these
+
+ align:start position:0%
+I want to look at the accesses to these
+ 
+
+ align:start position:0%
+I want to look at the accesses to these
+keys and access to these keys and see
+
+ align:start position:0%
+keys and access to these keys and see
+ 
+
+ align:start position:0%
+keys and access to these keys and see
+how many times do I switch between left
+
+ align:start position:0%
+how many times do I switch between left
+ 
+
+ align:start position:0%
+how many times do I switch between left
+and right okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+count number of
+
+ align:start position:0%
+count number of
+ 
+
+ align:start position:0%
+count number of
+alternations so very similar in spirit
+
+ align:start position:0%
+alternations so very similar in spirit
+ 
+
+ align:start position:0%
+alternations so very similar in spirit
+to Wilbur 2 is just relative to this
+
+ align:start position:0%
+to Wilbur 2 is just relative to this
+ 
+
+ align:start position:0%
+to Wilbur 2 is just relative to this
+weird tree which is kind of
+
+ align:start position:0%
+weird tree which is kind of
+ 
+
+ align:start position:0%
+weird tree which is kind of
+arbitrary uh
+
+ align:start position:0%
+arbitrary uh
+ 
+
+ align:start position:0%
+arbitrary uh
+let's see in the axis sequence which is
+
+ align:start position:0%
+let's see in the axis sequence which is
+ 
+
+ align:start position:0%
+let's see in the axis sequence which is
+X1 up to
+
+ align:start position:0%
+X1 up to
+ 
+
+ align:start position:0%
+X1 up to
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+between uh
+
+ align:start position:0%
+between uh
+ 
+
+ align:start position:0%
+between uh
+left and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees of Y so we're going to ignore
+
+ align:start position:0%
+trees of Y so we're going to ignore
+ 
+
+ align:start position:0%
+trees of Y so we're going to ignore
+axises to Y itself we're going to ignore
+
+ align:start position:0%
+axises to Y itself we're going to ignore
+ 
+
+ align:start position:0%
+axises to Y itself we're going to ignore
+aises to keys outside of Y just look at
+
+ align:start position:0%
+aises to keys outside of Y just look at
+ 
+
+ align:start position:0%
+aises to keys outside of Y just look at
+how many times do I switch between X and
+
+ align:start position:0%
+how many times do I switch between X and
+ 
+
+ align:start position:0%
+how many times do I switch between X and
+Y okay that's a lower bound that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim it's a lower Bound for the same
+
+ align:start position:0%
+claim it's a lower Bound for the same
+ 
+
+ align:start position:0%
+claim it's a lower Bound for the same
+reason we use the independent rectangle
+
+ align:start position:0%
+reason we use the independent rectangle
+ 
+
+ align:start position:0%
+reason we use the independent rectangle
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+bound and the claim is if you look at
+
+ align:start position:0%
+bound and the claim is if you look at
+ 
+
+ align:start position:0%
+bound and the claim is if you look at
+these alternations draw the
+
+ align:start position:0%
+these alternations draw the
+ 
+
+ align:start position:0%
+these alternations draw the
+corresponding rectangles basically
+
+ align:start position:0%
+corresponding rectangles basically
+ 
+
+ align:start position:0%
+corresponding rectangles basically
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah so over here we had a vertical line
+
+ align:start position:0%
+yeah so over here we had a vertical line
+ 
+
+ align:start position:0%
+yeah so over here we had a vertical line
+which corresponded to the key and we see
+
+ align:start position:0%
+which corresponded to the key and we see
+ 
+
+ align:start position:0%
+which corresponded to the key and we see
+how many times do we cross the line
+
+ align:start position:0%
+how many times do we cross the line
+ 
+
+ align:start position:0%
+how many times do we cross the line
+basically the same thing over here uh
+
+ align:start position:0%
+basically the same thing over here uh
+ 
+
+ align:start position:0%
+basically the same thing over here uh
+so except now the vertical line there's
+
+ align:start position:0%
+so except now the vertical line there's
+ 
+
+ align:start position:0%
+so except now the vertical line there's
+one big vertical line that corresponds
+
+ align:start position:0%
+one big vertical line that corresponds
+ 
+
+ align:start position:0%
+one big vertical line that corresponds
+to the root node then there's some
+
+ align:start position:0%
+to the root node then there's some
+ 
+
+ align:start position:0%
+to the root node then there's some
+vertical lines that correspond to this
+
+ align:start position:0%
+vertical lines that correspond to this
+ 
+
+ align:start position:0%
+vertical lines that correspond to this
+node and this node and you're interested
+
+ align:start position:0%
+node and this node and you're interested
+ 
+
+ align:start position:0%
+node and this node and you're interested
+in the access sequence how many times
+
+ align:start position:0%
+in the access sequence how many times
+ 
+
+ align:start position:0%
+in the access sequence how many times
+let's do some kind of access sequence
+
+ align:start position:0%
+let's do some kind of access sequence
+ 
+
+ align:start position:0%
+let's do some kind of access sequence
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this whatever these are our points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point and you just look at what is the
+
+ align:start position:0%
+point and you just look at what is the
+ 
+
+ align:start position:0%
+point and you just look at what is the
+what lines are you
+
+ align:start position:0%
+what lines are you
+ 
+
+ align:start position:0%
+what lines are you
+Crossing so like this crosses the big
+
+ align:start position:0%
+Crossing so like this crosses the big
+ 
+
+ align:start position:0%
+Crossing so like this crosses the big
+line so that's going to be one
+
+ align:start position:0%
+line so that's going to be one
+ 
+
+ align:start position:0%
+line so that's going to be one
+alternation between left and right here
+
+ align:start position:0%
+alternation between left and right here
+ 
+
+ align:start position:0%
+alternation between left and right here
+uh here's another alternation between
+
+ align:start position:0%
+uh here's another alternation between
+ 
+
+ align:start position:0%
+uh here's another alternation between
+left and right here's another
+
+ align:start position:0%
+left and right here's another
+ 
+
+ align:start position:0%
+left and right here's another
+alternation between left and right
+
+ align:start position:0%
+alternation between left and right
+ 
+
+ align:start position:0%
+alternation between left and right
+here's another alternation between left
+
+ align:start position:0%
+here's another alternation between left
+ 
+
+ align:start position:0%
+here's another alternation between left
+and right uh and one
+
+ align:start position:0%
+and right uh and one
+ 
+
+ align:start position:0%
+and right uh and one
+more okay so for the big line for the
+
+ align:start position:0%
+more okay so for the big line for the
+ 
+
+ align:start position:0%
+more okay so for the big line for the
+root not that's how many times you cross
+
+ align:start position:0%
+root not that's how many times you cross
+ 
+
+ align:start position:0%
+root not that's how many times you cross
+between left and right relative to the
+
+ align:start position:0%
+between left and right relative to the
+ 
+
+ align:start position:0%
+between left and right relative to the
+root um then for the left sub tree of
+
+ align:start position:0%
+root um then for the left sub tree of
+ 
+
+ align:start position:0%
+root um then for the left sub tree of
+the root there's one crossing here
+
+ align:start position:0%
+the root there's one crossing here
+ 
+
+ align:start position:0%
+the root there's one crossing here
+there's one crossing here one crossing
+
+ align:start position:0%
+there's one crossing here one crossing
+ 
+
+ align:start position:0%
+there's one crossing here one crossing
+here uh these are touching but they're
+
+ align:start position:0%
+here uh these are touching but they're
+ 
+
+ align:start position:0%
+here uh these are touching but they're
+not satisfied so it's okay these are
+
+ align:start position:0%
+not satisfied so it's okay these are
+ 
+
+ align:start position:0%
+not satisfied so it's okay these are
+claim is all these rectangles will be
+
+ align:start position:0%
+claim is all these rectangles will be
+ 
+
+ align:start position:0%
+claim is all these rectangles will be
+independent again I won't prove that
+
+ align:start position:0%
+independent again I won't prove that
+ 
+
+ align:start position:0%
+independent again I won't prove that
+formally but it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true okay rough sketch
+
+ align:start position:0%
+true okay rough sketch
+ 
+
+ align:start position:0%
+true okay rough sketch
+so that's Wilbur one it's again an
+
+ align:start position:0%
+so that's Wilbur one it's again an
+ 
+
+ align:start position:0%
+so that's Wilbur one it's again an
+independent rectangle lower bound it's a
+
+ align:start position:0%
+independent rectangle lower bound it's a
+ 
+
+ align:start position:0%
+independent rectangle lower bound it's a
+little weird because it depends on this
+
+ align:start position:0%
+little weird because it depends on this
+ 
+
+ align:start position:0%
+little weird because it depends on this
+tree you could choose it to be a nice
+
+ align:start position:0%
+tree you could choose it to be a nice
+ 
+
+ align:start position:0%
+tree you could choose it to be a nice
+Perfect Tree you could choose it to be a
+
+ align:start position:0%
+Perfect Tree you could choose it to be a
+ 
+
+ align:start position:0%
+Perfect Tree you could choose it to be a
+different tree you'll get a different
+
+ align:start position:0%
+different tree you'll get a different
+ 
+
+ align:start position:0%
+different tree you'll get a different
+lower bound each time so of course you
+
+ align:start position:0%
+lower bound each time so of course you
+ 
+
+ align:start position:0%
+lower bound each time so of course you
+take the max overall trees that will
+
+ align:start position:0%
+take the max overall trees that will
+ 
+
+ align:start position:0%
+take the max overall trees that will
+give you the biggest Wilbur one lower
+
+ align:start position:0%
+give you the biggest Wilbur one lower
+ 
+
+ align:start position:0%
+give you the biggest Wilbur one lower
+bound we don't know much about that
+
+ align:start position:0%
+bound we don't know much about that
+ 
+
+ align:start position:0%
+bound we don't know much about that
+biggest Wilbur one lower bound uh I
+
+ align:start position:0%
+biggest Wilbur one lower bound uh I
+ 
+
+ align:start position:0%
+biggest Wilbur one lower bound uh I
+guess you could ask the
+
+ align:start position:0%
+guess you could ask the
+ 
+
+ align:start position:0%
+guess you could ask the
+following um open question is it true
+
+ align:start position:0%
+following um open question is it true
+ 
+
+ align:start position:0%
+following um open question is it true
+that for every access
+
+ align:start position:0%
+that for every access
+ 
+
+ align:start position:0%
+that for every access
+sequence there exists a tree
+
+ align:start position:0%
+sequence there exists a tree
+ 
+
+ align:start position:0%
+sequence there exists a tree
+P such that uh Wilbur one is Theta opt
+
+ align:start position:0%
+P such that uh Wilbur one is Theta opt
+ 
+
+ align:start position:0%
+P such that uh Wilbur one is Theta opt
+or is Theta Wilbur 2 or something Wilbur
+
+ align:start position:0%
+or is Theta Wilbur 2 or something Wilbur
+ 
+
+ align:start position:0%
+or is Theta Wilbur 2 or something Wilbur
+2 is is a single quantity you compute it
+
+ align:start position:0%
+2 is is a single quantity you compute it
+ 
+
+ align:start position:0%
+2 is is a single quantity you compute it
+it gives you a bound W one it depends on
+
+ align:start position:0%
+it gives you a bound W one it depends on
+ 
+
+ align:start position:0%
+it gives you a bound W one it depends on
+this P maybe if you choose the best P
+
+ align:start position:0%
+this P maybe if you choose the best P
+ 
+
+ align:start position:0%
+this P maybe if you choose the best P
+for your sequence you get the right
+
+ align:start position:0%
+for your sequence you get the right
+ 
+
+ align:start position:0%
+for your sequence you get the right
+answer but it's definitely the case that
+
+ align:start position:0%
+answer but it's definitely the case that
+ 
+
+ align:start position:0%
+answer but it's definitely the case that
+uh Wilbur one for a fixed p is not the
+
+ align:start position:0%
+uh Wilbur one for a fixed p is not the
+ 
+
+ align:start position:0%
+uh Wilbur one for a fixed p is not the
+right answer
+
+ align:start position:0%
+right answer
+ 
+
+ align:start position:0%
+right answer
+um recall that's easy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove uh well maybe we'll come back to
+
+ align:start position:0%
+prove uh well maybe we'll come back to
+ 
+
+ align:start position:0%
+prove uh well maybe we'll come back to
+that yeah question um so how do you like
+
+ align:start position:0%
+that yeah question um so how do you like
+ 
+
+ align:start position:0%
+that yeah question um so how do you like
+construct this low like is it uh I'll
+
+ align:start position:0%
+construct this low like is it uh I'll
+ 
+
+ align:start position:0%
+construct this low like is it uh I'll
+tell you what we're going to use for the
+
+ align:start position:0%
+tell you what we're going to use for the
+ 
+
+ align:start position:0%
+tell you what we're going to use for the
+question was how do we construct P you
+
+ align:start position:0%
+question was how do we construct P you
+ 
+
+ align:start position:0%
+question was how do we construct P you
+can make it whatever you want what we're
+
+ align:start position:0%
+can make it whatever you want what we're
+ 
+
+ align:start position:0%
+can make it whatever you want what we're
+going to use is the perfect tree which
+
+ align:start position:0%
+going to use is the perfect tree which
+ 
+
+ align:start position:0%
+going to use is the perfect tree which
+is sort of unique uh it's kind of
+
+ align:start position:0%
+is sort of unique uh it's kind of
+ 
+
+ align:start position:0%
+is sort of unique uh it's kind of
+arbitrary but it works it has the fact
+
+ align:start position:0%
+arbitrary but it works it has the fact
+ 
+
+ align:start position:0%
+arbitrary but it works it has the fact
+it has the property that its height is
+
+ align:start position:0%
+it has the property that its height is
+ 
+
+ align:start position:0%
+it has the property that its height is
+log n that's all we'll need we're going
+
+ align:start position:0%
+log n that's all we'll need we're going
+ 
+
+ align:start position:0%
+log n that's all we'll need we're going
+to use that to get tango trees other
+
+ align:start position:0%
+to use that to get tango trees other
+ 
+
+ align:start position:0%
+to use that to get tango trees other
+questions all right
+
+ align:start position:0%
+questions all right
+ 
+
+ align:start position:0%
+questions all right
+let's let me briefly mention a fun
+
+ align:start position:0%
+let's let me briefly mention a fun
+ 
+
+ align:start position:0%
+let's let me briefly mention a fun
+access
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence you may recognize this
+
+ align:start position:0%
+sequence you may recognize this
+ 
+
+ align:start position:0%
+sequence you may recognize this
+sequence this would be in order
+
+ align:start position:0%
+sequence this would be in order
+ 
+
+ align:start position:0%
+sequence this would be in order
+traversal in binary but if I take these
+
+ align:start position:0%
+traversal in binary but if I take these
+ 
+
+ align:start position:0%
+traversal in binary but if I take these
+bit sequences and read them backwards
+
+ align:start position:0%
+bit sequences and read them backwards
+ 
+
+ align:start position:0%
+bit sequences and read them backwards
+then I get zero
+
+ align:start position:0%
+then I get zero
+ 
+
+ align:start position:0%
+then I get zero
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+2 6 1
+
+ align:start position:0%
+2 6 1
+ 
+
+ align:start position:0%
+2 6 1
+5 3
+
+ align:start position:0%
+5 3
+ 
+
+ align:start position:0%
+5 3
+7 this is the number 0 through 7 in a
+
+ align:start position:0%
+7 this is the number 0 through 7 in a
+ 
+
+ align:start position:0%
+7 this is the number 0 through 7 in a
+funny order it's called the bit reversal
+
+ align:start position:0%
+funny order it's called the bit reversal
+ 
+
+ align:start position:0%
+funny order it's called the bit reversal
+sequence if you access 0 4 2 6 1 53 7 in
+
+ align:start position:0%
+sequence if you access 0 4 2 6 1 53 7 in
+ 
+
+ align:start position:0%
+sequence if you access 0 4 2 6 1 53 7 in
+a perfect binary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree it maximizes Wilbur one so in order
+
+ align:start position:0%
+tree it maximizes Wilbur one so in order
+ 
+
+ align:start position:0%
+tree it maximizes Wilbur one so in order
+traversal 0 1 2 3 4
+
+ align:start position:0%
+traversal 0 1 2 3 4
+ 
+
+ align:start position:0%
+traversal 0 1 2 3 4
+5 oops no
+
+ align:start position:0%
+5 oops no
+ 
+
+ align:start position:0%
+5 oops no
+zero six all right ignore seven there's
+
+ align:start position:0%
+zero six all right ignore seven there's
+ 
+
+ align:start position:0%
+zero six all right ignore seven there's
+no seven in this
+
+ align:start position:0%
+no seven in this
+ 
+
+ align:start position:0%
+no seven in this
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+um I do
+
+ align:start position:0%
+um I do
+ 
+
+ align:start position:0%
+um I do
+zero four if you look at the root I
+
+ align:start position:0%
+zero four if you look at the root I
+ 
+
+ align:start position:0%
+zero four if you look at the root I
+alternate left right left right left
+
+ align:start position:0%
+alternate left right left right left
+ 
+
+ align:start position:0%
+alternate left right left right left
+right because the high order bid is
+
+ align:start position:0%
+right because the high order bid is
+ 
+
+ align:start position:0%
+right because the high order bid is
+switching every time and so whether I go
+
+ align:start position:0%
+switching every time and so whether I go
+ 
+
+ align:start position:0%
+switching every time and so whether I go
+to the left of the tree here or the
+
+ align:start position:0%
+to the left of the tree here or the
+ 
+
+ align:start position:0%
+to the left of the tree here or the
+right of the tree is switching every
+
+ align:start position:0%
+right of the tree is switching every
+ 
+
+ align:start position:0%
+right of the tree is switching every
+time and also if you look at any sub
+
+ align:start position:0%
+time and also if you look at any sub
+ 
+
+ align:start position:0%
+time and also if you look at any sub
+tree like when I'm accessing things
+
+ align:start position:0%
+tree like when I'm accessing things
+ 
+
+ align:start position:0%
+tree like when I'm accessing things
+within the sub tree of one it alternates
+
+ align:start position:0%
+within the sub tree of one it alternates
+ 
+
+ align:start position:0%
+within the sub tree of one it alternates
+0er to okay it's too small a tree to
+
+ align:start position:0%
+0er to okay it's too small a tree to
+ 
+
+ align:start position:0%
+0er to okay it's too small a tree to
+really see that happening but it's true
+
+ align:start position:0%
+really see that happening but it's true
+ 
+
+ align:start position:0%
+really see that happening but it's true
+and so if you do this for n Bits you get
+
+ align:start position:0%
+and so if you do this for n Bits you get
+ 
+
+ align:start position:0%
+and so if you do this for n Bits you get
+a two to the a sequence on or k Bits n
+
+ align:start position:0%
+a two to the a sequence on or k Bits n
+ 
+
+ align:start position:0%
+a two to the a sequence on or k Bits n
+equals 2 to the K roughly uh and Wilbur
+
+ align:start position:0%
+equals 2 to the K roughly uh and Wilbur
+ 
+
+ align:start position:0%
+equals 2 to the K roughly uh and Wilbur
+2 Wilbur one the lower bound is log n
+
+ align:start position:0%
+2 Wilbur one the lower bound is log n
+ 
+
+ align:start position:0%
+2 Wilbur one the lower bound is log n
+per guy because the number of
+
+ align:start position:0%
+per guy because the number of
+ 
+
+ align:start position:0%
+per guy because the number of
+alternation every every aess alternate
+
+ align:start position:0%
+alternation every every aess alternate
+ 
+
+ align:start position:0%
+alternation every every aess alternate
+so if you look at a sub tree whatever
+
+ align:start position:0%
+so if you look at a sub tree whatever
+ 
+
+ align:start position:0%
+so if you look at a sub tree whatever
+the size of that sub tree is that's how
+
+ align:start position:0%
+the size of that sub tree is that's how
+ 
+
+ align:start position:0%
+the size of that sub tree is that's how
+many alternations there are and so
+
+ align:start position:0%
+many alternations there are and so
+ 
+
+ align:start position:0%
+many alternations there are and so
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+alternations is Theta and log n because
+
+ align:start position:0%
+alternations is Theta and log n because
+ 
+
+ align:start position:0%
+alternations is Theta and log n because
+it's the sum over all nodes of their
+
+ align:start position:0%
+it's the sum over all nodes of their
+ 
+
+ align:start position:0%
+it's the sum over all nodes of their
+subtree sizes and so
+
+ align:start position:0%
+subtree sizes and so
+ 
+
+ align:start position:0%
+subtree sizes and so
+opt is Theta n log
+
+ align:start position:0%
+opt is Theta n log
+ 
+
+ align:start position:0%
+opt is Theta n log
+n we know we can achieve n log n this is
+
+ align:start position:0%
+n we know we can achieve n log n this is
+ 
+
+ align:start position:0%
+n we know we can achieve n log n this is
+to do n
+
+ align:start position:0%
+to do n
+ 
+
+ align:start position:0%
+to do n
+aises um we know we can achieve n log n
+
+ align:start position:0%
+aises um we know we can achieve n log n
+ 
+
+ align:start position:0%
+aises um we know we can achieve n log n
+with a red black tree or whatever but
+
+ align:start position:0%
+with a red black tree or whatever but
+ 
+
+ align:start position:0%
+with a red black tree or whatever but
+there's actually lower bound of nlog n
+
+ align:start position:0%
+there's actually lower bound of nlog n
+ 
+
+ align:start position:0%
+there's actually lower bound of nlog n
+meaning all binary search trees if
+
+ align:start position:0%
+meaning all binary search trees if
+ 
+
+ align:start position:0%
+meaning all binary search trees if
+you're if you're given this access
+
+ align:start position:0%
+you're if you're given this access
+ 
+
+ align:start position:0%
+you're if you're given this access
+sequence doesn't matter what you're
+
+ align:start position:0%
+sequence doesn't matter what you're
+ 
+
+ align:start position:0%
+sequence doesn't matter what you're
+doing you have to pay nlog n which is
+
+ align:start position:0%
+doing you have to pay nlog n which is
+ 
+
+ align:start position:0%
+doing you have to pay nlog n which is
+kind of cool got little side effect and
+
+ align:start position:0%
+kind of cool got little side effect and
+ 
+
+ align:start position:0%
+kind of cool got little side effect and
+this is that's where Wilbur Wilbur's
+
+ align:start position:0%
+this is that's where Wilbur Wilbur's
+ 
+
+ align:start position:0%
+this is that's where Wilbur Wilbur's
+paper end is like hey cool can find one
+
+ align:start position:0%
+paper end is like hey cool can find one
+ 
+
+ align:start position:0%
+paper end is like hey cool can find one
+AIS sequence that is bad for
+
+ align:start position:0%
+AIS sequence that is bad for
+ 
+
+ align:start position:0%
+AIS sequence that is bad for
+everybody but now we're going to use
+
+ align:start position:0%
+everybody but now we're going to use
+ 
+
+ align:start position:0%
+everybody but now we're going to use
+Wilbur
+
+ align:start position:0%
+Wilbur
+ 
+
+ align:start position:0%
+Wilbur
+one to get one binary search tree that's
+
+ align:start position:0%
+one to get one binary search tree that's
+ 
+
+ align:start position:0%
+one to get one binary search tree that's
+pretty good for all access sequences
+
+ align:start position:0%
+pretty good for all access sequences
+ 
+
+ align:start position:0%
+pretty good for all access sequences
+pretty good meaning within a log log n
+
+ align:start position:0%
+pretty good meaning within a log log n
+ 
+
+ align:start position:0%
+pretty good meaning within a log log n
+factor of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimal and this is Tango trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would be log log and competitive online
+
+ align:start position:0%
+would be log log and competitive online
+ 
+
+ align:start position:0%
+would be log log and competitive online
+binary search
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees why are they called Tango trees
+
+ align:start position:0%
+trees why are they called Tango trees
+ 
+
+ align:start position:0%
+trees why are they called Tango trees
+people made up all sorts of reasons but
+
+ align:start position:0%
+people made up all sorts of reasons but
+ 
+
+ align:start position:0%
+people made up all sorts of reasons but
+I can tell you because I was there uh
+
+ align:start position:0%
+I can tell you because I was there uh
+ 
+
+ align:start position:0%
+I can tell you because I was there uh
+they were invented mostly on a flight
+
+ align:start position:0%
+they were invented mostly on a flight
+ 
+
+ align:start position:0%
+they were invented mostly on a flight
+from New York to buades which is the
+
+ align:start position:0%
+from New York to buades which is the
+ 
+
+ align:start position:0%
+from New York to buades which is the
+center of Tango I bought this t-shirt I
+
+ align:start position:0%
+center of Tango I bought this t-shirt I
+ 
+
+ align:start position:0%
+center of Tango I bought this t-shirt I
+think the day after
+
+ align:start position:0%
+think the day after
+ 
+
+ align:start position:0%
+think the day after
+and uh then that week we wrote the paper
+
+ align:start position:0%
+and uh then that week we wrote the paper
+ 
+
+ align:start position:0%
+and uh then that week we wrote the paper
+and that was Tango trees
+
+ align:start position:0%
+and that was Tango trees
+ 
+
+ align:start position:0%
+and that was Tango trees
+so no particular reason but it sounds
+
+ align:start position:0%
+so no particular reason but it sounds
+ 
+
+ align:start position:0%
+so no particular reason but it sounds
+good and always good to have a cool name
+
+ align:start position:0%
+good and always good to have a cool name
+ 
+
+ align:start position:0%
+good and always good to have a cool name
+so secret is revealed true meaning of
+
+ align:start position:0%
+so secret is revealed true meaning of
+ 
+
+ align:start position:0%
+so secret is revealed true meaning of
+Tango trees is nothing uh so but they
+
+ align:start position:0%
+Tango trees is nothing uh so but they
+ 
+
+ align:start position:0%
+Tango trees is nothing uh so but they
+yeah we'll see um so how did they work
+
+ align:start position:0%
+yeah we'll see um so how did they work
+ 
+
+ align:start position:0%
+yeah we'll see um so how did they work
+it's very simple basically we take
+
+ align:start position:0%
+it's very simple basically we take
+ 
+
+ align:start position:0%
+it's very simple basically we take
+Wilbur one and we simulate
+
+ align:start position:0%
+Wilbur one and we simulate
+ 
+
+ align:start position:0%
+Wilbur one and we simulate
+it so uh
+
+ align:start position:0%
+it so uh
+ 
+
+ align:start position:0%
+it so uh
+uh let me be more precise there's one
+
+ align:start position:0%
+uh let me be more precise there's one
+ 
+
+ align:start position:0%
+uh let me be more precise there's one
+key idea which is to look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preferred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+child of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node uh I'm going to say the preferred
+
+ align:start position:0%
+node uh I'm going to say the preferred
+ 
+
+ align:start position:0%
+node uh I'm going to say the preferred
+child is
+
+ align:start position:0%
+child is
+ 
+
+ align:start position:0%
+child is
+left let's see node y and
+
+ align:start position:0%
+left let's see node y and
+ 
+
+ align:start position:0%
+left let's see node y and
+p it's left if uh
+
+ align:start position:0%
+p it's left if uh
+ 
+
+ align:start position:0%
+p it's left if uh
+uh we
+
+ align:start position:0%
+uh we
+ 
+
+ align:start position:0%
+uh we
+accessed uh the left sub some node in
+
+ align:start position:0%
+accessed uh the left sub some node in
+ 
+
+ align:start position:0%
+accessed uh the left sub some node in
+the left sub tree of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recently it's uh the right child if we
+
+ align:start position:0%
+recently it's uh the right child if we
+ 
+
+ align:start position:0%
+recently it's uh the right child if we
+access something in the right sub tree
+
+ align:start position:0%
+access something in the right sub tree
+ 
+
+ align:start position:0%
+access something in the right sub tree
+most recently so we're just looking at
+
+ align:start position:0%
+most recently so we're just looking at
+ 
+
+ align:start position:0%
+most recently so we're just looking at
+left and right subt tree
+
+ align:start position:0%
+left and right subt tree
+ 
+
+ align:start position:0%
+left and right subt tree
+axises uh what was most recent there's a
+
+ align:start position:0%
+axises uh what was most recent there's a
+ 
+
+ align:start position:0%
+axises uh what was most recent there's a
+special case in the beginning which is
+
+ align:start position:0%
+special case in the beginning which is
+ 
+
+ align:start position:0%
+special case in the beginning which is
+you don't have a preferred child because
+
+ align:start position:0%
+you don't have a preferred child because
+ 
+
+ align:start position:0%
+you don't have a preferred child because
+you haven't accessed either left or
+
+ align:start position:0%
+you haven't accessed either left or
+ 
+
+ align:start position:0%
+you haven't accessed either left or
+right yet so this is if there's if no
+
+ align:start position:0%
+right yet so this is if there's if no
+ 
+
+ align:start position:0%
+right yet so this is if there's if no
+access uh
+
+ align:start position:0%
+access uh
+ 
+
+ align:start position:0%
+access uh
+to left or
+
+ align:start position:0%
+to left or
+ 
+
+ align:start position:0%
+to left or
+right yet so that just happens in the
+
+ align:start position:0%
+right yet so that just happens in the
+ 
+
+ align:start position:0%
+right yet so that just happens in the
+beginning once you've touched everything
+
+ align:start position:0%
+beginning once you've touched everything
+ 
+
+ align:start position:0%
+beginning once you've touched everything
+uh everybody will have a left or right
+
+ align:start position:0%
+uh everybody will have a left or right
+ 
+
+ align:start position:0%
+uh everybody will have a left or right
+preferred child so this is just what was
+
+ align:start position:0%
+preferred child so this is just what was
+ 
+
+ align:start position:0%
+preferred child so this is just what was
+your most recent child this is a a this
+
+ align:start position:0%
+your most recent child this is a a this
+ 
+
+ align:start position:0%
+your most recent child this is a a this
+is like a parent with a very short
+
+ align:start position:0%
+is like a parent with a very short
+ 
+
+ align:start position:0%
+is like a parent with a very short
+memory
+
+ align:start position:0%
+memory
+ 
+
+ align:start position:0%
+memory
+just whichever child I most recently
+
+ align:start position:0%
+just whichever child I most recently
+ 
+
+ align:start position:0%
+just whichever child I most recently
+talk to that is my preferred child at
+
+ align:start position:0%
+talk to that is my preferred child at
+ 
+
+ align:start position:0%
+talk to that is my preferred child at
+the moment okay it's kind of like I
+
+ align:start position:0%
+the moment okay it's kind of like I
+ 
+
+ align:start position:0%
+the moment okay it's kind of like I
+don't know when you're going to uh job
+
+ align:start position:0%
+don't know when you're going to uh job
+ 
+
+ align:start position:0%
+don't know when you're going to uh job
+interviews you know the most recent
+
+ align:start position:0%
+interviews you know the most recent
+ 
+
+ align:start position:0%
+interviews you know the most recent
+interview is the one you remember most
+
+ align:start position:0%
+interview is the one you remember most
+ 
+
+ align:start position:0%
+interview is the one you remember most
+fondly and so oh you like that one the
+
+ align:start position:0%
+fondly and so oh you like that one the
+ 
+
+ align:start position:0%
+fondly and so oh you like that one the
+best independent of which is the coolest
+
+ align:start position:0%
+best independent of which is the coolest
+ 
+
+ align:start position:0%
+best independent of which is the coolest
+okay so uh let me draw a picture and I
+
+ align:start position:0%
+okay so uh let me draw a picture and I
+ 
+
+ align:start position:0%
+okay so uh let me draw a picture and I
+guess I'm going to
+
+ align:start position:0%
+guess I'm going to
+ 
+
+ align:start position:0%
+guess I'm going to
+draw big picture my
+
+ align:start position:0%
+draw big picture my
+ 
+
+ align:start position:0%
+draw big picture my
+favorite P perfectly balanced binary
+
+ align:start position:0%
+favorite P perfectly balanced binary
+ 
+
+ align:start position:0%
+favorite P perfectly balanced binary
+resarch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree eight
+
+ align:start position:0%
+tree eight
+ 
+
+ align:start position:0%
+tree eight
+leaves uh and so now suppose that
+
+ align:start position:0%
+leaves uh and so now suppose that
+ 
+
+ align:start position:0%
+leaves uh and so now suppose that
+every uh node has a preferred
+
+ align:start position:0%
+every uh node has a preferred
+ 
+
+ align:start position:0%
+every uh node has a preferred
+child let's say they all do just because
+
+ align:start position:0%
+child let's say they all do just because
+ 
+
+ align:start position:0%
+child let's say they all do just because
+it makes a more interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture going to draw that with a big
+
+ align:start position:0%
+picture going to draw that with a big
+ 
+
+ align:start position:0%
+picture going to draw that with a big
+fat
+
+ align:start position:0%
+fat
+ 
+
+ align:start position:0%
+fat
+arrow and now uh what does that do it
+
+ align:start position:0%
+arrow and now uh what does that do it
+ 
+
+ align:start position:0%
+arrow and now uh what does that do it
+decomposes our tree this is the perfect
+
+ align:start position:0%
+decomposes our tree this is the perfect
+ 
+
+ align:start position:0%
+decomposes our tree this is the perfect
+tree p is going to be perfectly balanced
+
+ align:start position:0%
+tree p is going to be perfectly balanced
+ 
+
+ align:start position:0%
+tree p is going to be perfectly balanced
+log n height could be any log n height
+
+ align:start position:0%
+log n height could be any log n height
+ 
+
+ align:start position:0%
+log n height could be any log n height
+tree but we'll make it
+
+ align:start position:0%
+tree but we'll make it
+ 
+
+ align:start position:0%
+tree but we'll make it
+perfect uh and it decomposes that tree
+
+ align:start position:0%
+perfect uh and it decomposes that tree
+ 
+
+ align:start position:0%
+perfect uh and it decomposes that tree
+into paths and there's a path here you
+
+ align:start position:0%
+into paths and there's a path here you
+ 
+
+ align:start position:0%
+into paths and there's a path here you
+just keep following parent pointers you
+
+ align:start position:0%
+just keep following parent pointers you
+ 
+
+ align:start position:0%
+just keep following parent pointers you
+get a path not parent pointers preferred
+
+ align:start position:0%
+get a path not parent pointers preferred
+ 
+
+ align:start position:0%
+get a path not parent pointers preferred
+pointers it's also true if you follow
+
+ align:start position:0%
+pointers it's also true if you follow
+ 
+
+ align:start position:0%
+pointers it's also true if you follow
+parent pointers you get a path but
+
+ align:start position:0%
+parent pointers you get a path but
+ 
+
+ align:start position:0%
+parent pointers you get a path but
+they'll overlap each other you follow
+
+ align:start position:0%
+they'll overlap each other you follow
+ 
+
+ align:start position:0%
+they'll overlap each other you follow
+preferred child pointers you get
+
+ align:start position:0%
+preferred child pointers you get
+ 
+
+ align:start position:0%
+preferred child pointers you get
+non-overlapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths there they are we also get these
+
+ align:start position:0%
+paths there they are we also get these
+ 
+
+ align:start position:0%
+paths there they are we also get these
+Singleton paths at the leaves some of
+
+ align:start position:0%
+Singleton paths at the leaves some of
+ 
+
+ align:start position:0%
+Singleton paths at the leaves some of
+the leaves are in Singleton paths these
+
+ align:start position:0%
+the leaves are in Singleton paths these
+ 
+
+ align:start position:0%
+the leaves are in Singleton paths these
+are called preferred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths why do I care because so this
+
+ align:start position:0%
+paths why do I care because so this
+ 
+
+ align:start position:0%
+paths why do I care because so this
+tells me uh the most recently accessed
+
+ align:start position:0%
+tells me uh the most recently accessed
+ 
+
+ align:start position:0%
+tells me uh the most recently accessed
+element was was somebody on this path
+
+ align:start position:0%
+element was was somebody on this path
+ 
+
+ align:start position:0%
+element was was somebody on this path
+right I don't quite know who could have
+
+ align:start position:0%
+right I don't quite know who could have
+ 
+
+ align:start position:0%
+right I don't quite know who could have
+been this one and that would say okay
+
+ align:start position:0%
+been this one and that would say okay
+ 
+
+ align:start position:0%
+been this one and that would say okay
+this is the most recent direction we
+
+ align:start position:0%
+this is the most recent direction we
+ 
+
+ align:start position:0%
+this is the most recent direction we
+went for all of them let's say it's that
+
+ align:start position:0%
+went for all of them let's say it's that
+ 
+
+ align:start position:0%
+went for all of them let's say it's that
+one now suppose I access this node what
+
+ align:start position:0%
+one now suppose I access this node what
+ 
+
+ align:start position:0%
+one now suppose I access this node what
+does that tell me Well if I if I most
+
+ align:start position:0%
+does that tell me Well if I if I most
+ 
+
+ align:start position:0%
+does that tell me Well if I if I most
+recently accessed left here and now I'm
+
+ align:start position:0%
+recently accessed left here and now I'm
+ 
+
+ align:start position:0%
+recently accessed left here and now I'm
+accessing the right if you look at this
+
+ align:start position:0%
+accessing the right if you look at this
+ 
+
+ align:start position:0%
+accessing the right if you look at this
+node The Wilbur one bound goes up by one
+
+ align:start position:0%
+node The Wilbur one bound goes up by one
+ 
+
+ align:start position:0%
+node The Wilbur one bound goes up by one
+because I just accessed left now I
+
+ align:start position:0%
+because I just accessed left now I
+ 
+
+ align:start position:0%
+because I just accessed left now I
+accessed right also if I access this
+
+ align:start position:0%
+accessed right also if I access this
+ 
+
+ align:start position:0%
+accessed right also if I access this
+node this guy is Wilbur one bound goes
+
+ align:start position:0%
+node this guy is Wilbur one bound goes
+ 
+
+ align:start position:0%
+node this guy is Wilbur one bound goes
+up by one because now he's going to the
+
+ align:start position:0%
+up by one because now he's going to the
+ 
+
+ align:start position:0%
+up by one because now he's going to the
+right where his last time he went to the
+
+ align:start position:0%
+right where his last time he went to the
+ 
+
+ align:start position:0%
+right where his last time he went to the
+left also this node previously went to
+
+ align:start position:0%
+left also this node previously went to
+ 
+
+ align:start position:0%
+left also this node previously went to
+the right and went to the left so uh I
+
+ align:start position:0%
+the right and went to the left so uh I
+ 
+
+ align:start position:0%
+the right and went to the left so uh I
+get a Wilbur one went up because of this
+
+ align:start position:0%
+get a Wilbur one went up because of this
+ 
+
+ align:start position:0%
+get a Wilbur one went up because of this
+Edge and it went up because of this Edge
+
+ align:start position:0%
+Edge and it went up because of this Edge
+ 
+
+ align:start position:0%
+Edge and it went up because of this Edge
+in general following nonpreferred
+
+ align:start position:0%
+in general following nonpreferred
+ 
+
+ align:start position:0%
+in general following nonpreferred
+edges I can pay for because Wilbur one
+
+ align:start position:0%
+edges I can pay for because Wilbur one
+ 
+
+ align:start position:0%
+edges I can pay for because Wilbur one
+goes up by one every time I use a
+
+ align:start position:0%
+goes up by one every time I use a
+ 
+
+ align:start position:0%
+goes up by one every time I use a
+non-preferred edge this is another way
+
+ align:start position:0%
+non-preferred edge this is another way
+ 
+
+ align:start position:0%
+non-preferred edge this is another way
+to State The Wilbur one bound this is
+
+ align:start position:0%
+to State The Wilbur one bound this is
+ 
+
+ align:start position:0%
+to State The Wilbur one bound this is
+the cool thing as long as I can run jump
+
+ align:start position:0%
+the cool thing as long as I can run jump
+ 
+
+ align:start position:0%
+the cool thing as long as I can run jump
+go through a path
+
+ align:start position:0%
+go through a path
+ 
+
+ align:start position:0%
+go through a path
+quickly uh ideally if I could do it in
+
+ align:start position:0%
+quickly uh ideally if I could do it in
+ 
+
+ align:start position:0%
+quickly uh ideally if I could do it in
+constant time this would be dynamic
+
+ align:start position:0%
+constant time this would be dynamic
+ 
+
+ align:start position:0%
+constant time this would be dynamic
+optimal binary search tree if I can
+
+ align:start position:0%
+optimal binary search tree if I can
+ 
+
+ align:start position:0%
+optimal binary search tree if I can
+instantly transport to where I need to
+
+ align:start position:0%
+instantly transport to where I need to
+ 
+
+ align:start position:0%
+instantly transport to where I need to
+go on a path and then jump off the path
+
+ align:start position:0%
+go on a path and then jump off the path
+ 
+
+ align:start position:0%
+go on a path and then jump off the path
+to the next path that I can pay
+
+ align:start position:0%
+to the next path that I can pay
+ 
+
+ align:start position:0%
+to the next path that I can pay
+for well constant I can spend constant
+
+ align:start position:0%
+for well constant I can spend constant
+ 
+
+ align:start position:0%
+for well constant I can spend constant
+time to do that uh then I'd be okay I'm
+
+ align:start position:0%
+time to do that uh then I'd be okay I'm
+ 
+
+ align:start position:0%
+time to do that uh then I'd be okay I'm
+not going to be able to do it in
+
+ align:start position:0%
+not going to be able to do it in
+ 
+
+ align:start position:0%
+not going to be able to do it in
+constant time but I'm going to be able
+
+ align:start position:0%
+constant time but I'm going to be able
+ 
+
+ align:start position:0%
+constant time but I'm going to be able
+to do it in log log n time I'm going to
+
+ align:start position:0%
+to do it in log log n time I'm going to
+ 
+
+ align:start position:0%
+to do it in log log n time I'm going to
+be able to jump through a path in log
+
+ align:start position:0%
+be able to jump through a path in log
+ 
+
+ align:start position:0%
+be able to jump through a path in log
+log n time and then jump figure out
+
+ align:start position:0%
+log n time and then jump figure out
+ 
+
+ align:start position:0%
+log n time and then jump figure out
+where I need to diverge From the Path
+
+ align:start position:0%
+where I need to diverge From the Path
+ 
+
+ align:start position:0%
+where I need to diverge From the Path
+because maybe I'm accessing this guy
+
+ align:start position:0%
+because maybe I'm accessing this guy
+ 
+
+ align:start position:0%
+because maybe I'm accessing this guy
+jump to the next PATH do that in log log
+
+ align:start position:0%
+jump to the next PATH do that in log log
+ 
+
+ align:start position:0%
+jump to the next PATH do that in log log
+end time I've got to update the path
+
+ align:start position:0%
+end time I've got to update the path
+ 
+
+ align:start position:0%
+end time I've got to update the path
+structure because now the preferred
+
+ align:start position:0%
+structure because now the preferred
+ 
+
+ align:start position:0%
+structure because now the preferred
+child is to the right it used to be to
+
+ align:start position:0%
+child is to the right it used to be to
+ 
+
+ align:start position:0%
+child is to the right it used to be to
+the left so I've got to do something
+
+ align:start position:0%
+the left so I've got to do something
+ 
+
+ align:start position:0%
+the left so I've got to do something
+that will only pay that will only cost
+
+ align:start position:0%
+that will only pay that will only cost
+ 
+
+ align:start position:0%
+that will only pay that will only cost
+log log n time if I can do that the
+
+ align:start position:0%
+log log n time if I can do that the
+ 
+
+ align:start position:0%
+log log n time if I can do that the
+lower bound is the number of edges the
+
+ align:start position:0%
+lower bound is the number of edges the
+ 
+
+ align:start position:0%
+lower bound is the number of edges the
+upper bound is number of edges number of
+
+ align:start position:0%
+upper bound is number of edges number of
+ 
+
+ align:start position:0%
+upper bound is number of edges number of
+non-preferred edges Times log log in so
+
+ align:start position:0%
+non-preferred edges Times log log in so
+ 
+
+ align:start position:0%
+non-preferred edges Times log log in so
+we get a lower bound uh Wilbur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one which is going to be equal to the
+
+ align:start position:0%
+one which is going to be equal to the
+ 
+
+ align:start position:0%
+one which is going to be equal to the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+non-preferred edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to get an upper bound
+
+ align:start position:0%
+and we're going to get an upper bound
+ 
+
+ align:start position:0%
+and we're going to get an upper bound
+through Tango
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees which is going to be order number
+
+ align:start position:0%
+trees which is going to be order number
+ 
+
+ align:start position:0%
+trees which is going to be order number
+of non-preferred edges Times log log
+
+ align:start position:0%
+of non-preferred edges Times log log
+ 
+
+ align:start position:0%
+of non-preferred edges Times log log
+n okay why is it log log n because each
+
+ align:start position:0%
+n okay why is it log log n because each
+ 
+
+ align:start position:0%
+n okay why is it log log n because each
+of these paths has length Only log n so
+
+ align:start position:0%
+of these paths has length Only log n so
+ 
+
+ align:start position:0%
+of these paths has length Only log n so
+I put them in a b balance binary search
+
+ align:start position:0%
+I put them in a b balance binary search
+ 
+
+ align:start position:0%
+I put them in a b balance binary search
+tree and it has height log log
+
+ align:start position:0%
+tree and it has height log log
+ 
+
+ align:start position:0%
+tree and it has height log log
+in so I take these paths squish them
+
+ align:start position:0%
+in so I take these paths squish them
+ 
+
+ align:start position:0%
+in so I take these paths squish them
+into a tree it's hard to I don't know
+
+ align:start position:0%
+into a tree it's hard to I don't know
+ 
+
+ align:start position:0%
+into a tree it's hard to I don't know
+which way you're squishing but uh it
+
+ align:start position:0%
+which way you're squishing but uh it
+ 
+
+ align:start position:0%
+which way you're squishing but uh it
+says log and depth it's a path I'm going
+
+ align:start position:0%
+says log and depth it's a path I'm going
+ 
+
+ align:start position:0%
+says log and depth it's a path I'm going
+to fold it into a tree so it has height
+
+ align:start position:0%
+to fold it into a tree so it has height
+ 
+
+ align:start position:0%
+to fold it into a tree so it has height
+Only log log end then I can jump around
+
+ align:start position:0%
+Only log log end then I can jump around
+ 
+
+ align:start position:0%
+Only log log end then I can jump around
+it in log log end time that's the idea
+
+ align:start position:0%
+it in log log end time that's the idea
+ 
+
+ align:start position:0%
+it in log log end time that's the idea
+with Tango trees basically done uh few
+
+ align:start position:0%
+with Tango trees basically done uh few
+ 
+
+ align:start position:0%
+with Tango trees basically done uh few
+details and how they
+
+ align:start position:0%
+details and how they
+ 
+
+ align:start position:0%
+details and how they
+work uh I don't want to spend too much
+
+ align:start position:0%
+work uh I don't want to spend too much
+ 
+
+ align:start position:0%
+work uh I don't want to spend too much
+time on them but let's go through some
+
+ align:start position:0%
+time on them but let's go through some
+ 
+
+ align:start position:0%
+time on them but let's go through some
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to store each preferred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path uh as an auxil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree which is just I don't know red
+
+ align:start position:0%
+tree which is just I don't know red
+ 
+
+ align:start position:0%
+tree which is just I don't know red
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+tree let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say what is the red black tree sorted by
+
+ align:start position:0%
+say what is the red black tree sorted by
+ 
+
+ align:start position:0%
+say what is the red black tree sorted by
+I don't have a choice whatever I do has
+
+ align:start position:0%
+I don't have a choice whatever I do has
+ 
+
+ align:start position:0%
+I don't have a choice whatever I do has
+to be a binary search tree among the
+
+ align:start position:0%
+to be a binary search tree among the
+ 
+
+ align:start position:0%
+to be a binary search tree among the
+original keys so if I take these items
+
+ align:start position:0%
+original keys so if I take these items
+ 
+
+ align:start position:0%
+original keys so if I take these items
+and just throw them into a red black
+
+ align:start position:0%
+and just throw them into a red black
+ 
+
+ align:start position:0%
+and just throw them into a red black
+tree I mean they will be sorted by
+
+ align:start position:0%
+tree I mean they will be sorted by
+ 
+
+ align:start position:0%
+tree I mean they will be sorted by
+whatever their x coordinates so this is
+
+ align:start position:0%
+whatever their x coordinates so this is
+ 
+
+ align:start position:0%
+whatever their x coordinates so this is
+the max this is the Min this is
+
+ align:start position:0%
+the max this is the Min this is
+ 
+
+ align:start position:0%
+the max this is the Min this is
+somewhere in between
+
+ align:start position:0%
+somewhere in between
+ 
+
+ align:start position:0%
+somewhere in between
+this is to the left of that so the order
+
+ align:start position:0%
+this is to the left of that so the order
+ 
+
+ align:start position:0%
+this is to the left of that so the order
+is a little weird I'd really like to
+
+ align:start position:0%
+is a little weird I'd really like to
+ 
+
+ align:start position:0%
+is a little weird I'd really like to
+store them sorted by depth but I can't
+
+ align:start position:0%
+store them sorted by depth but I can't
+ 
+
+ align:start position:0%
+store them sorted by depth but I can't
+do that they are sorted by their key
+
+ align:start position:0%
+do that they are sorted by their key
+ 
+
+ align:start position:0%
+do that they are sorted by their key
+values um now what do I need to do with
+
+ align:start position:0%
+values um now what do I need to do with
+ 
+
+ align:start position:0%
+values um now what do I need to do with
+these auxiliary
+
+ align:start position:0%
+these auxiliary
+ 
+
+ align:start position:0%
+these auxiliary
+trees I mean uh the basic thing I do is
+
+ align:start position:0%
+trees I mean uh the basic thing I do is
+ 
+
+ align:start position:0%
+trees I mean uh the basic thing I do is
+a search right I'm searching for a key
+
+ align:start position:0%
+a search right I'm searching for a key
+ 
+
+ align:start position:0%
+a search right I'm searching for a key
+it's a binary search tree so I can still
+
+ align:start position:0%
+it's a binary search tree so I can still
+ 
+
+ align:start position:0%
+it's a binary search tree so I can still
+do a search I can figure out you know
+
+ align:start position:0%
+do a search I can figure out you know
+ 
+
+ align:start position:0%
+do a search I can figure out you know
+this this tree gets represented as
+
+ align:start position:0%
+this this tree gets represented as
+ 
+
+ align:start position:0%
+this this tree gets represented as
+something more like this that would be a
+
+ align:start position:0%
+something more like this that would be a
+ 
+
+ align:start position:0%
+something more like this that would be a
+nicely balanced version of these four
+
+ align:start position:0%
+nicely balanced version of these four
+ 
+
+ align:start position:0%
+nicely balanced version of these four
+nodes so if I called them I don't know a
+
+ align:start position:0%
+nodes so if I called them I don't know a
+ 
+
+ align:start position:0%
+nodes so if I called them I don't know a
+b c d that's their sorted order it's
+
+ align:start position:0%
+b c d that's their sorted order it's
+ 
+
+ align:start position:0%
+b c d that's their sorted order it's
+going to be a b c d that's also their
+
+ align:start position:0%
+going to be a b c d that's also their
+ 
+
+ align:start position:0%
+going to be a b c d that's also their
+sorted order over here so if I search
+
+ align:start position:0%
+sorted order over here so if I search
+ 
+
+ align:start position:0%
+sorted order over here so if I search
+for my key I'll figure out oh do I fall
+
+ align:start position:0%
+for my key I'll figure out oh do I fall
+ 
+
+ align:start position:0%
+for my key I'll figure out oh do I fall
+off here here here here or here now each
+
+ align:start position:0%
+off here here here here or here now each
+ 
+
+ align:start position:0%
+off here here here here or here now each
+of those corresponds to another path I
+
+ align:start position:0%
+of those corresponds to another path I
+ 
+
+ align:start position:0%
+of those corresponds to another path I
+need to visit so if I fall off the left
+
+ align:start position:0%
+need to visit so if I fall off the left
+ 
+
+ align:start position:0%
+need to visit so if I fall off the left
+side of a then I should have a pointer
+
+ align:start position:0%
+side of a then I should have a pointer
+ 
+
+ align:start position:0%
+side of a then I should have a pointer
+to this structure if I fall off
+
+ align:start position:0%
+to this structure if I fall off
+ 
+
+ align:start position:0%
+to this structure if I fall off
+the I guess these two are
+
+ align:start position:0%
+the I guess these two are
+ 
+
+ align:start position:0%
+the I guess these two are
+empty those correspond to these two
+
+ align:start position:0%
+empty those correspond to these two
+ 
+
+ align:start position:0%
+empty those correspond to these two
+places if I fall off here the right side
+
+ align:start position:0%
+places if I fall off here the right side
+ 
+
+ align:start position:0%
+places if I fall off here the right side
+of C which is now here this is going to
+
+ align:start position:0%
+of C which is now here this is going to
+ 
+
+ align:start position:0%
+of C which is now here this is going to
+be a pointer to my new structure which
+
+ align:start position:0%
+be a pointer to my new structure which
+ 
+
+ align:start position:0%
+be a pointer to my new structure which
+corresponds to this
+
+ align:start position:0%
+corresponds to this
+ 
+
+ align:start position:0%
+corresponds to this
+one okay and then this one is going to
+
+ align:start position:0%
+one okay and then this one is going to
+ 
+
+ align:start position:0%
+one okay and then this one is going to
+correspond to all this stuff well in
+
+ align:start position:0%
+correspond to all this stuff well in
+ 
+
+ align:start position:0%
+correspond to all this stuff well in
+particular this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so it's a little hard to draw this
+
+ align:start position:0%
+one so it's a little hard to draw this
+ 
+
+ align:start position:0%
+one so it's a little hard to draw this
+picture but uh you get the idea you just
+
+ align:start position:0%
+picture but uh you get the idea you just
+ 
+
+ align:start position:0%
+picture but uh you get the idea you just
+rebalance each of these things keep the
+
+ align:start position:0%
+rebalance each of these things keep the
+ 
+
+ align:start position:0%
+rebalance each of these things keep the
+the pointers between the preferred paths
+
+ align:start position:0%
+the pointers between the preferred paths
+ 
+
+ align:start position:0%
+the pointers between the preferred paths
+just as they were this is uniquely
+
+ align:start position:0%
+just as they were this is uniquely
+ 
+
+ align:start position:0%
+just as they were this is uniquely
+defined how to do this because it's a
+
+ align:start position:0%
+defined how to do this because it's a
+ 
+
+ align:start position:0%
+defined how to do this because it's a
+binary search
+
+ align:start position:0%
+binary search
+ 
+
+ align:start position:0%
+binary search
+tree okay so uh
+
+ align:start position:0%
+tree okay so uh
+ 
+
+ align:start position:0%
+tree okay so uh
+leaves
+
+ align:start position:0%
+leaves
+ 
+
+ align:start position:0%
+leaves
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+other or let's call them child auxiliary
+
+ align:start position:0%
+other or let's call them child auxiliary
+ 
+
+ align:start position:0%
+other or let's call them child auxiliary
+trees it's uniquely which ones they have
+
+ align:start position:0%
+trees it's uniquely which ones they have
+ 
+
+ align:start position:0%
+trees it's uniquely which ones they have
+to point to in order to still navigate
+
+ align:start position:0%
+to point to in order to still navigate
+ 
+
+ align:start position:0%
+to point to in order to still navigate
+the whole structure so it's a weird way
+
+ align:start position:0%
+the whole structure so it's a weird way
+ 
+
+ align:start position:0%
+the whole structure so it's a weird way
+of rebalancing your
+
+ align:start position:0%
+of rebalancing your
+ 
+
+ align:start position:0%
+of rebalancing your
+tree and the point is each of these red
+
+ align:start position:0%
+tree and the point is each of these red
+ 
+
+ align:start position:0%
+tree and the point is each of these red
+black trees has height log log n because
+
+ align:start position:0%
+black trees has height log log n because
+ 
+
+ align:start position:0%
+black trees has height log log n because
+the number of nodes in it is only log n
+
+ align:start position:0%
+the number of nodes in it is only log n
+ 
+
+ align:start position:0%
+the number of nodes in it is only log n
+and that gives us the
+
+ align:start position:0%
+and that gives us the
+ 
+
+ align:start position:0%
+and that gives us the
+bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um now now key thing to think about is
+
+ align:start position:0%
+um now now key thing to think about is
+ 
+
+ align:start position:0%
+um now now key thing to think about is
+what happens when you change uh I said I
+
+ align:start position:0%
+what happens when you change uh I said I
+ 
+
+ align:start position:0%
+what happens when you change uh I said I
+have to be able to achieve number of
+
+ align:start position:0%
+have to be able to achieve number of
+ 
+
+ align:start position:0%
+have to be able to achieve number of
+non-preferred edges Times log log n so
+
+ align:start position:0%
+non-preferred edges Times log log n so
+ 
+
+ align:start position:0%
+non-preferred edges Times log log n so
+fine I do a log log n search in here
+
+ align:start position:0%
+fine I do a log log n search in here
+ 
+
+ align:start position:0%
+fine I do a log log n search in here
+maybe I decide I have to go off here
+
+ align:start position:0%
+maybe I decide I have to go off here
+ 
+
+ align:start position:0%
+maybe I decide I have to go off here
+then I do a log log n search in here
+
+ align:start position:0%
+then I do a log log n search in here
+ 
+
+ align:start position:0%
+then I do a log log n search in here
+okay then maybe I have to go this way so
+
+ align:start position:0%
+okay then maybe I have to go this way so
+ 
+
+ align:start position:0%
+okay then maybe I have to go this way so
+number of non-preferred edges was two I
+
+ align:start position:0%
+number of non-preferred edges was two I
+ 
+
+ align:start position:0%
+number of non-preferred edges was two I
+did two maybe three searches fine uh
+
+ align:start position:0%
+did two maybe three searches fine uh
+ 
+
+ align:start position:0%
+did two maybe three searches fine uh
+it's going to be number of non-preferred
+
+ align:start position:0%
+it's going to be number of non-preferred
+ 
+
+ align:start position:0%
+it's going to be number of non-preferred
+edges plus one time log log n no big
+
+ align:start position:0%
+edges plus one time log log n no big
+ 
+
+ align:start position:0%
+edges plus one time log log n no big
+deal okay but
+
+ align:start position:0%
+deal okay but
+ 
+
+ align:start position:0%
+deal okay but
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+what now I have to update now this is
+
+ align:start position:0%
+what now I have to update now this is
+ 
+
+ align:start position:0%
+what now I have to update now this is
+the preferred Edge from the root and
+
+ align:start position:0%
+the preferred Edge from the root and
+ 
+
+ align:start position:0%
+the preferred Edge from the root and
+this is the preferred Edge from this
+
+ align:start position:0%
+this is the preferred Edge from this
+ 
+
+ align:start position:0%
+this is the preferred Edge from this
+node how do I update preferred edges
+
+ align:start position:0%
+node how do I update preferred edges
+ 
+
+ align:start position:0%
+node how do I update preferred edges
+that's something to think about so I've
+
+ align:start position:0%
+that's something to think about so I've
+ 
+
+ align:start position:0%
+that's something to think about so I've
+got a path represented by a red black
+
+ align:start position:0%
+got a path represented by a red black
+ 
+
+ align:start position:0%
+got a path represented by a red black
+tree and now I fall off here and there's
+
+ align:start position:0%
+tree and now I fall off here and there's
+ 
+
+ align:start position:0%
+tree and now I fall off here and there's
+another path here I need to convert this
+
+ align:start position:0%
+another path here I need to convert this
+ 
+
+ align:start position:0%
+another path here I need to convert this
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+to uh path that goes like this and then
+
+ align:start position:0%
+to uh path that goes like this and then
+ 
+
+ align:start position:0%
+to uh path that goes like this and then
+does this and separately a path that
+
+ align:start position:0%
+does this and separately a path that
+ 
+
+ align:start position:0%
+does this and separately a path that
+does this okay that's the new version
+
+ align:start position:0%
+does this okay that's the new version
+ 
+
+ align:start position:0%
+does this okay that's the new version
+how do I do that conceptually it's
+
+ align:start position:0%
+how do I do that conceptually it's
+ 
+
+ align:start position:0%
+how do I do that conceptually it's
+pretty simple
+
+ align:start position:0%
+pretty simple
+ 
+
+ align:start position:0%
+pretty simple
+I I want to cut the path here and then
+
+ align:start position:0%
+I I want to cut the path here and then
+ 
+
+ align:start position:0%
+I I want to cut the path here and then
+rejoin along there like
+
+ align:start position:0%
+rejoin along there like
+ 
+
+ align:start position:0%
+rejoin along there like
+that so conceptually if things were
+
+ align:start position:0%
+that so conceptually if things were
+ 
+
+ align:start position:0%
+that so conceptually if things were
+stored by depth this is what we call a
+
+ align:start position:0%
+stored by depth this is what we call a
+ 
+
+ align:start position:0%
+stored by depth this is what we call a
+split and a concat you should know this
+
+ align:start position:0%
+split and a concat you should know this
+ 
+
+ align:start position:0%
+split and a concat you should know this
+from regular bin stretch trees it's like
+
+ align:start position:0%
+from regular bin stretch trees it's like
+ 
+
+ align:start position:0%
+from regular bin stretch trees it's like
+standard exercise for like red black
+
+ align:start position:0%
+standard exercise for like red black
+ 
+
+ align:start position:0%
+standard exercise for like red black
+trees given a query X you can cut this
+
+ align:start position:0%
+trees given a query X you can cut this
+ 
+
+ align:start position:0%
+trees given a query X you can cut this
+tree into two halves and get two red
+
+ align:start position:0%
+tree into two halves and get two red
+ 
+
+ align:start position:0%
+tree into two halves and get two red
+black trees which represent everything
+
+ align:start position:0%
+black trees which represent everything
+ 
+
+ align:start position:0%
+black trees which represent everything
+to the left of X and everything to the
+
+ align:start position:0%
+to the left of X and everything to the
+ 
+
+ align:start position:0%
+to the left of X and everything to the
+right of X similarly given two trees
+
+ align:start position:0%
+right of X similarly given two trees
+ 
+
+ align:start position:0%
+right of X similarly given two trees
+that are sorted like this where all the
+
+ align:start position:0%
+that are sorted like this where all the
+ 
+
+ align:start position:0%
+that are sorted like this where all the
+elements are less than all the elements
+
+ align:start position:0%
+elements are less than all the elements
+ 
+
+ align:start position:0%
+elements are less than all the elements
+over here I can concatenate them into
+
+ align:start position:0%
+over here I can concatenate them into
+ 
+
+ align:start position:0%
+over here I can concatenate them into
+one red black tree and all these take
+
+ align:start position:0%
+one red black tree and all these take
+ 
+
+ align:start position:0%
+one red black tree and all these take
+log n time where N is a number of nodes
+
+ align:start position:0%
+log n time where N is a number of nodes
+ 
+
+ align:start position:0%
+log n time where N is a number of nodes
+here that would be log log n time
+
+ align:start position:0%
+here that would be log log n time
+ 
+
+ align:start position:0%
+here that would be log log n time
+in this world it's not quite so simple
+
+ align:start position:0%
+in this world it's not quite so simple
+ 
+
+ align:start position:0%
+in this world it's not quite so simple
+because things are not sorted by depth
+
+ align:start position:0%
+because things are not sorted by depth
+ 
+
+ align:start position:0%
+because things are not sorted by depth
+they're sorted by key value but it's not
+
+ align:start position:0%
+they're sorted by key value but it's not
+ 
+
+ align:start position:0%
+they're sorted by key value but it's not
+so bad um because I don't know if you
+
+ align:start position:0%
+so bad um because I don't know if you
+ 
+
+ align:start position:0%
+so bad um because I don't know if you
+you look at some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path and you want to say okay
+
+ align:start position:0%
+path and you want to say okay
+ 
+
+ align:start position:0%
+path and you want to say okay
+um I want everything that's
+
+ align:start position:0%
+um I want everything that's
+ 
+
+ align:start position:0%
+um I want everything that's
+below uh I don't know this key value or
+
+ align:start position:0%
+below uh I don't know this key value or
+ 
+
+ align:start position:0%
+below uh I don't know this key value or
+something then that's the same as saying
+
+ align:start position:0%
+something then that's the same as saying
+ 
+
+ align:start position:0%
+something then that's the same as saying
+we take everything that is within in
+
+ align:start position:0%
+we take everything that is within in
+ 
+
+ align:start position:0%
+we take everything that is within in
+this interval of keys so it's strictly
+
+ align:start position:0%
+this interval of keys so it's strictly
+ 
+
+ align:start position:0%
+this interval of keys so it's strictly
+between here and
+
+ align:start position:0%
+between here and
+ 
+
+ align:start position:0%
+between here and
+here let me drw this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slightly so if you look at the
+
+ align:start position:0%
+slightly so if you look at the
+ 
+
+ align:start position:0%
+slightly so if you look at the
+nodes of
+
+ align:start position:0%
+nodes of
+ 
+
+ align:start position:0%
+nodes of
+depth greater than
+
+ align:start position:0%
+depth greater than
+ 
+
+ align:start position:0%
+depth greater than
+d right I want to cut off everybody
+
+ align:start position:0%
+d right I want to cut off everybody
+ 
+
+ align:start position:0%
+d right I want to cut off everybody
+that's deeper than a particular spot in
+
+ align:start position:0%
+that's deeper than a particular spot in
+ 
+
+ align:start position:0%
+that's deeper than a particular spot in
+order to do this kind of
+
+ align:start position:0%
+order to do this kind of
+ 
+
+ align:start position:0%
+order to do this kind of
+change uh these are equal to
+
+ align:start position:0%
+change uh these are equal to
+ 
+
+ align:start position:0%
+change uh these are equal to
+nodes uh in the sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+of that uh so got to give it a
+
+ align:start position:0%
+of that uh so got to give it a
+ 
+
+ align:start position:0%
+of that uh so got to give it a
+name let's say I want to cut here so I'm
+
+ align:start position:0%
+name let's say I want to cut here so I'm
+ 
+
+ align:start position:0%
+name let's say I want to cut here so I'm
+going to look at this node
+
+ align:start position:0%
+going to look at this node
+ 
+
+ align:start position:0%
+going to look at this node
+y this is nodes in the subtree of Y all
+
+ align:start position:0%
+y this is nodes in the subtree of Y all
+ 
+
+ align:start position:0%
+y this is nodes in the subtree of Y all
+of the nodes that are below y are
+
+ align:start position:0%
+of the nodes that are below y are
+ 
+
+ align:start position:0%
+of the nodes that are below y are
+obviously going to have smaller depth in
+
+ align:start position:0%
+obviously going to have smaller depth in
+ 
+
+ align:start position:0%
+obviously going to have smaller depth in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+path this is nodes in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path and uh nodes in a sub tree are
+
+ align:start position:0%
+path and uh nodes in a sub tree are
+ 
+
+ align:start position:0%
+path and uh nodes in a sub tree are
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+nodes with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keys uh in the Min of that sub tree to
+
+ align:start position:0%
+keys uh in the Min of that sub tree to
+ 
+
+ align:start position:0%
+keys uh in the Min of that sub tree to
+the max of that sub Tre it's an
+
+ align:start position:0%
+the max of that sub Tre it's an
+ 
+
+ align:start position:0%
+the max of that sub Tre it's an
+interval so what do I do I split split
+
+ align:start position:0%
+interval so what do I do I split split
+ 
+
+ align:start position:0%
+interval so what do I do I split split
+at Min of Y I split at Max of Y that
+
+ align:start position:0%
+at Min of Y I split at Max of Y that
+ 
+
+ align:start position:0%
+at Min of Y I split at Max of Y that
+gives me the interval so here's the
+
+ align:start position:0%
+gives me the interval so here's the
+ 
+
+ align:start position:0%
+gives me the interval so here's the
+picture I have a tree I want to cut out
+
+ align:start position:0%
+picture I have a tree I want to cut out
+ 
+
+ align:start position:0%
+picture I have a tree I want to cut out
+this interval of nodes this is like
+
+ align:start position:0%
+this interval of nodes this is like
+ 
+
+ align:start position:0%
+this interval of nodes this is like
+range queries kind of in 1D so I split
+
+ align:start position:0%
+range queries kind of in 1D so I split
+ 
+
+ align:start position:0%
+range queries kind of in 1D so I split
+here I split here what I will have are
+
+ align:start position:0%
+here I split here what I will have are
+ 
+
+ align:start position:0%
+here I split here what I will have are
+the things I care about the things to
+
+ align:start position:0%
+the things I care about the things to
+ 
+
+ align:start position:0%
+the things I care about the things to
+the left of it and the things to the
+
+ align:start position:0%
+the left of it and the things to the
+ 
+
+ align:start position:0%
+the left of it and the things to the
+right of it what I wanted was this and
+
+ align:start position:0%
+right of it what I wanted was this and
+ 
+
+ align:start position:0%
+right of it what I wanted was this and
+everything else how do I do that I
+
+ align:start position:0%
+everything else how do I do that I
+ 
+
+ align:start position:0%
+everything else how do I do that I
+concatenate maybe I should uh this is
+
+ align:start position:0%
+concatenate maybe I should uh this is
+ 
+
+ align:start position:0%
+concatenate maybe I should uh this is
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+y this is uh in the
+
+ align:start position:0%
+y this is uh in the
+ 
+
+ align:start position:0%
+y this is uh in the
+interval Min of
+
+ align:start position:0%
+interval Min of
+ 
+
+ align:start position:0%
+interval Min of
+Y to Max of
+
+ align:start position:0%
+Y to Max of
+ 
+
+ align:start position:0%
+Y to Max of
+Y so I wanted those guys those are the
+
+ align:start position:0%
+Y so I wanted those guys those are the
+ 
+
+ align:start position:0%
+Y so I wanted those guys those are the
+nodes that are deeper than D I also want
+
+ align:start position:0%
+nodes that are deeper than D I also want
+ 
+
+ align:start position:0%
+nodes that are deeper than D I also want
+the nodes Al together that are less deep
+
+ align:start position:0%
+the nodes Al together that are less deep
+ 
+
+ align:start position:0%
+the nodes Al together that are less deep
+than d That's these nodes and these
+
+ align:start position:0%
+than d That's these nodes and these
+ 
+
+ align:start position:0%
+than d That's these nodes and these
+nodes so I can Cate these together get
+
+ align:start position:0%
+nodes so I can Cate these together get
+ 
+
+ align:start position:0%
+nodes so I can Cate these together get
+one big tree that represents things with
+
+ align:start position:0%
+one big tree that represents things with
+ 
+
+ align:start position:0%
+one big tree that represents things with
+depth less than D these are the things
+
+ align:start position:0%
+depth less than D these are the things
+ 
+
+ align:start position:0%
+depth less than D these are the things
+with depth greater than
+
+ align:start position:0%
+with depth greater than
+ 
+
+ align:start position:0%
+with depth greater than
+D okay so I do two splits one
+
+ align:start position:0%
+D okay so I do two splits one
+ 
+
+ align:start position:0%
+D okay so I do two splits one
+concatenate and that simulates this kind
+
+ align:start position:0%
+concatenate and that simulates this kind
+ 
+
+ align:start position:0%
+concatenate and that simulates this kind
+of cut operation
+
+ align:start position:0%
+of cut operation
+ 
+
+ align:start position:0%
+of cut operation
+similarly if I want to do a joint
+
+ align:start position:0%
+similarly if I want to do a joint
+ 
+
+ align:start position:0%
+similarly if I want to do a joint
+operation it's a constant number of
+
+ align:start position:0%
+operation it's a constant number of
+ 
+
+ align:start position:0%
+operation it's a constant number of
+splits and concatenates and I'm done
+
+ align:start position:0%
+splits and concatenates and I'm done
+ 
+
+ align:start position:0%
+splits and concatenates and I'm done
+just dealing with the fact that things
+
+ align:start position:0%
+just dealing with the fact that things
+ 
+
+ align:start position:0%
+just dealing with the fact that things
+are in the wrong order here but it's not
+
+ align:start position:0%
+are in the wrong order here but it's not
+ 
+
+ align:start position:0%
+are in the wrong order here but it's not
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bad um one more
+
+ align:start position:0%
+bad um one more
+ 
+
+ align:start position:0%
+bad um one more
+thing which
+
+ align:start position:0%
+thing which
+ 
+
+ align:start position:0%
+thing which
+is I basically describe the overall
+
+ align:start position:0%
+is I basically describe the overall
+ 
+
+ align:start position:0%
+is I basically describe the overall
+structure as a tree of auxiliary trees
+
+ align:start position:0%
+structure as a tree of auxiliary trees
+ 
+
+ align:start position:0%
+structure as a tree of auxiliary trees
+in reality we're in the binary search
+
+ align:start position:0%
+in reality we're in the binary search
+ 
+
+ align:start position:0%
+in reality we're in the binary search
+tree model we can only have one tree
+
+ align:start position:0%
+tree model we can only have one tree
+ 
+
+ align:start position:0%
+tree model we can only have one tree
+not so hard though I mean basically you
+
+ align:start position:0%
+not so hard though I mean basically you
+ 
+
+ align:start position:0%
+not so hard though I mean basically you
+want one tree that represents lots of
+
+ align:start position:0%
+want one tree that represents lots of
+ 
+
+ align:start position:0%
+want one tree that represents lots of
+trees that are kind of pasted together
+
+ align:start position:0%
+trees that are kind of pasted together
+ 
+
+ align:start position:0%
+trees that are kind of pasted together
+so to do that you just Mark each node
+
+ align:start position:0%
+so to do that you just Mark each node
+ 
+
+ align:start position:0%
+so to do that you just Mark each node
+that that transitions from One Tree to
+
+ align:start position:0%
+that that transitions from One Tree to
+ 
+
+ align:start position:0%
+that that transitions from One Tree to
+the next so each node will say I'm the
+
+ align:start position:0%
+the next so each node will say I'm the
+ 
+
+ align:start position:0%
+the next so each node will say I'm the
+root of a new auxiliary tree or just say
+
+ align:start position:0%
+root of a new auxiliary tree or just say
+ 
+
+ align:start position:0%
+root of a new auxiliary tree or just say
+no I'm I'm part of the same auxiliary
+
+ align:start position:0%
+no I'm I'm part of the same auxiliary
+ 
+
+ align:start position:0%
+no I'm I'm part of the same auxiliary
+tree as my
+
+ align:start position:0%
+tree as my
+ 
+
+ align:start position:0%
+tree as my
+parent and when you and then you have to
+
+ align:start position:0%
+parent and when you and then you have to
+ 
+
+ align:start position:0%
+parent and when you and then you have to
+Define these kinds of split and
+
+ align:start position:0%
+Define these kinds of split and
+ 
+
+ align:start position:0%
+Define these kinds of split and
+concatenate operations in this setting
+
+ align:start position:0%
+concatenate operations in this setting
+ 
+
+ align:start position:0%
+concatenate operations in this setting
+where you have a tree embedded inside a
+
+ align:start position:0%
+where you have a tree embedded inside a
+ 
+
+ align:start position:0%
+where you have a tree embedded inside a
+tree but you just ignore all the nodes
+
+ align:start position:0%
+tree but you just ignore all the nodes
+ 
+
+ align:start position:0%
+tree but you just ignore all the nodes
+that are claimed to be part of another
+
+ align:start position:0%
+that are claimed to be part of another
+ 
+
+ align:start position:0%
+that are claimed to be part of another
+tree just pretend they weren't there and
+
+ align:start position:0%
+tree just pretend they weren't there and
+ 
+
+ align:start position:0%
+tree just pretend they weren't there and
+it works so little hand wavy there but
+
+ align:start position:0%
+it works so little hand wavy there but
+ 
+
+ align:start position:0%
+it works so little hand wavy there but
+uh it's kind of a tedious detail you can
+
+ align:start position:0%
+uh it's kind of a tedious detail you can
+ 
+
+ align:start position:0%
+uh it's kind of a tedious detail you can
+stick all these trees into one tree just
+
+ align:start position:0%
+stick all these trees into one tree just
+ 
+
+ align:start position:0%
+stick all these trees into one tree just
+by marking these
+
+ align:start position:0%
+by marking these
+ 
+
+ align:start position:0%
+by marking these
+roots and that's Tango
+
+ align:start position:0%
+roots and that's Tango
+ 
+
+ align:start position:0%
+roots and that's Tango
+trees I already spoiled the climax which
+
+ align:start position:0%
+trees I already spoiled the climax which
+ 
+
+ align:start position:0%
+trees I already spoiled the climax which
+was this log log log in thing but it's
+
+ align:start position:0%
+was this log log log in thing but it's
+ 
+
+ align:start position:0%
+was this log log log in thing but it's
+pretty obvious how to get there there's
+
+ align:start position:0%
+pretty obvious how to get there there's
+ 
+
+ align:start position:0%
+pretty obvious how to get there there's
+just a lot of details to actually do it
+
+ align:start position:0%
+just a lot of details to actually do it
+ 
+
+ align:start position:0%
+just a lot of details to actually do it
+we're just taking the wellber one bound
+
+ align:start position:0%
+we're just taking the wellber one bound
+ 
+
+ align:start position:0%
+we're just taking the wellber one bound
+recasting it in terms of this preferred
+
+ align:start position:0%
+recasting it in terms of this preferred
+ 
+
+ align:start position:0%
+recasting it in terms of this preferred
+path thing where we just it's just the
+
+ align:start position:0%
+path thing where we just it's just the
+ 
+
+ align:start position:0%
+path thing where we just it's just the
+non-preferred edges or the non-preferred
+
+ align:start position:0%
+non-preferred edges or the non-preferred
+ 
+
+ align:start position:0%
+non-preferred edges or the non-preferred
+edges are what Wilbur one counts and so
+
+ align:start position:0%
+edges are what Wilbur one counts and so
+ 
+
+ align:start position:0%
+edges are what Wilbur one counts and so
+we can afford to spend log log n time
+
+ align:start position:0%
+we can afford to spend log log n time
+ 
+
+ align:start position:0%
+we can afford to spend log log n time
+for each of them and the paths
+
+ align:start position:0%
+for each of them and the paths
+ 
+
+ align:start position:0%
+for each of them and the paths
+themselves only have log n NES so you
+
+ align:start position:0%
+themselves only have log n NES so you
+ 
+
+ align:start position:0%
+themselves only have log n NES so you
+can search through them in log log and
+
+ align:start position:0%
+can search through them in log log and
+ 
+
+ align:start position:0%
+can search through them in log log and
+time pretty
+
+ align:start position:0%
+time pretty
+ 
+
+ align:start position:0%
+time pretty
+easy uh this also shows you why Wilbur
+
+ align:start position:0%
+easy uh this also shows you why Wilbur
+ 
+
+ align:start position:0%
+easy uh this also shows you why Wilbur
+one is not a good
+
+ align:start position:0%
+one is not a good
+ 
+
+ align:start position:0%
+one is not a good
+bound with a fixed tree because here are
+
+ align:start position:0%
+bound with a fixed tree because here are
+ 
+
+ align:start position:0%
+bound with a fixed tree because here are
+log n nodes I could just sit there all
+
+ align:start position:0%
+log n nodes I could just sit there all
+ 
+
+ align:start position:0%
+log n nodes I could just sit there all
+day bouncing around all of them in
+
+ align:start position:0%
+day bouncing around all of them in
+ 
+
+ align:start position:0%
+day bouncing around all of them in
+random order I'm definitely going to
+
+ align:start position:0%
+random order I'm definitely going to
+ 
+
+ align:start position:0%
+random order I'm definitely going to
+need log log in time to access them but
+
+ align:start position:0%
+need log log in time to access them but
+ 
+
+ align:start position:0%
+need log log in time to access them but
+Wilbur one is not changing at all so
+
+ align:start position:0%
+Wilbur one is not changing at all so
+ 
+
+ align:start position:0%
+Wilbur one is not changing at all so
+wber one stays constant like zero and I
+
+ align:start position:0%
+wber one stays constant like zero and I
+ 
+
+ align:start position:0%
+wber one stays constant like zero and I
+just all you know I had to warm it up
+
+ align:start position:0%
+just all you know I had to warm it up
+ 
+
+ align:start position:0%
+just all you know I had to warm it up
+but after I've touched everything I can
+
+ align:start position:0%
+but after I've touched everything I can
+ 
+
+ align:start position:0%
+but after I've touched everything I can
+just sit there and bounce around these
+
+ align:start position:0%
+just sit there and bounce around these
+ 
+
+ align:start position:0%
+just sit there and bounce around these
+guys randomly I've got to spend log l
+
+ align:start position:0%
+guys randomly I've got to spend log l
+ 
+
+ align:start position:0%
+guys randomly I've got to spend log l
+and time to do that but Wilbur one
+
+ align:start position:0%
+and time to do that but Wilbur one
+ 
+
+ align:start position:0%
+and time to do that but Wilbur one
+doesn't justify it for me Wilber two
+
+ align:start position:0%
+doesn't justify it for me Wilber two
+ 
+
+ align:start position:0%
+doesn't justify it for me Wilber two
+will go up but Wilbur one with this tree
+
+ align:start position:0%
+will go up but Wilbur one with this tree
+ 
+
+ align:start position:0%
+will go up but Wilbur one with this tree
+it's kind of lame so this is the best
+
+ align:start position:0%
+it's kind of lame so this is the best
+ 
+
+ align:start position:0%
+it's kind of lame so this is the best
+Tango trees could hope to
+
+ align:start position:0%
+Tango trees could hope to
+ 
+
+ align:start position:0%
+Tango trees could hope to
+do using wber one
+
+ align:start position:0%
+do using wber one
+ 
+
+ align:start position:0%
+do using wber one
+uh I would guess that Tango trees are a
+
+ align:start position:0%
+uh I would guess that Tango trees are a
+ 
+
+ align:start position:0%
+uh I would guess that Tango trees are a
+log log Factor away from optimal though
+
+ align:start position:0%
+log log Factor away from optimal though
+ 
+
+ align:start position:0%
+log log Factor away from optimal though
+we don't know that for
+
+ align:start position:0%
+we don't know that for
+ 
+
+ align:start position:0%
+we don't know that for
+sure but greedy we're still pretty sure
+
+ align:start position:0%
+sure but greedy we're still pretty sure
+ 
+
+ align:start position:0%
+sure but greedy we're still pretty sure
+is good it should be constant Factor
+
+ align:start position:0%
+is good it should be constant Factor
+ 
+
+ align:start position:0%
+is good it should be constant Factor
+away from optimal so I want to talk a
+
+ align:start position:0%
+away from optimal so I want to talk a
+ 
+
+ align:start position:0%
+away from optimal so I want to talk a
+little bit about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that there's one one thing on this
+
+ align:start position:0%
+that there's one one thing on this
+ 
+
+ align:start position:0%
+that there's one one thing on this
+outline we haven't talked about we did
+
+ align:start position:0%
+outline we haven't talked about we did
+ 
+
+ align:start position:0%
+outline we haven't talked about we did
+independent rectangles we did Wilbur 1
+
+ align:start position:0%
+independent rectangles we did Wilbur 1
+ 
+
+ align:start position:0%
+independent rectangles we did Wilbur 1
+and two we saw applications of them in
+
+ align:start position:0%
+and two we saw applications of them in
+ 
+
+ align:start position:0%
+and two we saw applications of them in
+particular t trees one thing we haven't
+
+ align:start position:0%
+particular t trees one thing we haven't
+ 
+
+ align:start position:0%
+particular t trees one thing we haven't
+done is sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greedy so let's do sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greedy the still left here is uh we have
+
+ align:start position:0%
+greedy the still left here is uh we have
+ 
+
+ align:start position:0%
+greedy the still left here is uh we have
+two ways to choose rectangles
+
+ align:start position:0%
+two ways to choose rectangles
+ 
+
+ align:start position:0%
+two ways to choose rectangles
+independent rectangles they're different
+
+ align:start position:0%
+independent rectangles they're different
+ 
+
+ align:start position:0%
+independent rectangles they're different
+it'd be kind of nice to know what the
+
+ align:start position:0%
+it'd be kind of nice to know what the
+ 
+
+ align:start position:0%
+it'd be kind of nice to know what the
+best way to choose rectangles is and we
+
+ align:start position:0%
+best way to choose rectangles is and we
+ 
+
+ align:start position:0%
+best way to choose rectangles is and we
+actually know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s greedy so for there's two kinds of s
+
+ align:start position:0%
+s greedy so for there's two kinds of s
+ 
+
+ align:start position:0%
+s greedy so for there's two kinds of s
+greedy there's the plus sign greedy and
+
+ align:start position:0%
+greedy there's the plus sign greedy and
+ 
+
+ align:start position:0%
+greedy there's the plus sign greedy and
+there's the minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greedy okay how does plus greedy work
+
+ align:start position:0%
+greedy okay how does plus greedy work
+ 
+
+ align:start position:0%
+greedy okay how does plus greedy work
+it's the same as greedy you just only
+
+ align:start position:0%
+it's the same as greedy you just only
+ 
+
+ align:start position:0%
+it's the same as greedy you just only
+look at plus rectangles okay remember
+
+ align:start position:0%
+look at plus rectangles okay remember
+ 
+
+ align:start position:0%
+look at plus rectangles okay remember
+plus rectangles and minus rectangles so
+
+ align:start position:0%
+plus rectangles and minus rectangles so
+ 
+
+ align:start position:0%
+plus rectangles and minus rectangles so
+let's look at our favorite
+
+ align:start position:0%
+let's look at our favorite
+ 
+
+ align:start position:0%
+let's look at our favorite
+example here with greedy I would sweep
+
+ align:start position:0%
+example here with greedy I would sweep
+ 
+
+ align:start position:0%
+example here with greedy I would sweep
+up and every rectangle that was
+
+ align:start position:0%
+up and every rectangle that was
+ 
+
+ align:start position:0%
+up and every rectangle that was
+unsatisfied I would satisfy it now I'm
+
+ align:start position:0%
+unsatisfied I would satisfy it now I'm
+ 
+
+ align:start position:0%
+unsatisfied I would satisfy it now I'm
+going to ignore minus rectangles only
+
+ align:start position:0%
+going to ignore minus rectangles only
+ 
+
+ align:start position:0%
+going to ignore minus rectangles only
+look at plus
+
+ align:start position:0%
+look at plus
+ 
+
+ align:start position:0%
+look at plus
+rectangles so I see this rectangle I say
+
+ align:start position:0%
+rectangles so I see this rectangle I say
+ 
+
+ align:start position:0%
+rectangles so I see this rectangle I say
+oh I don't care because that's a minus
+
+ align:start position:0%
+oh I don't care because that's a minus
+ 
+
+ align:start position:0%
+oh I don't care because that's a minus
+rectangle then I see this
+
+ align:start position:0%
+rectangle then I see this
+ 
+
+ align:start position:0%
+rectangle then I see this
+one and this
+
+ align:start position:0%
+one and this
+ 
+
+ align:start position:0%
+one and this
+one okay I say oh those are plus
+
+ align:start position:0%
+one okay I say oh those are plus
+ 
+
+ align:start position:0%
+one okay I say oh those are plus
+rectangles so I'm going to add a point
+
+ align:start position:0%
+rectangles so I'm going to add a point
+ 
+
+ align:start position:0%
+rectangles so I'm going to add a point
+here and to add a point here then I
+
+ align:start position:0%
+here and to add a point here then I
+ 
+
+ align:start position:0%
+here and to add a point here then I
+go uh up to here I see this rectangle
+
+ align:start position:0%
+go uh up to here I see this rectangle
+ 
+
+ align:start position:0%
+go uh up to here I see this rectangle
+which is a plus rectangle that's bad so
+
+ align:start position:0%
+which is a plus rectangle that's bad so
+ 
+
+ align:start position:0%
+which is a plus rectangle that's bad so
+I've got to add a point I see these uh
+
+ align:start position:0%
+I've got to add a point I see these uh
+ 
+
+ align:start position:0%
+I've got to add a point I see these uh
+this minus rectangle I don't care
+
+ align:start position:0%
+this minus rectangle I don't care
+ 
+
+ align:start position:0%
+this minus rectangle I don't care
+about okay this is plus greedy it does
+
+ align:start position:0%
+about okay this is plus greedy it does
+ 
+
+ align:start position:0%
+about okay this is plus greedy it does
+not satisfy the set right this rectangle
+
+ align:start position:0%
+not satisfy the set right this rectangle
+ 
+
+ align:start position:0%
+not satisfy the set right this rectangle
+never got satisfied but it plus
+
+ align:start position:0%
+never got satisfied but it plus
+ 
+
+ align:start position:0%
+never got satisfied but it plus
+satisfies the set if I do plus greedy it
+
+ align:start position:0%
+satisfies the set if I do plus greedy it
+ 
+
+ align:start position:0%
+satisfies the set if I do plus greedy it
+will be plus
+
+ align:start position:0%
+will be plus
+ 
+
+ align:start position:0%
+will be plus
+satisfied uh there's every rectangle you
+
+ align:start position:0%
+satisfied uh there's every rectangle you
+ 
+
+ align:start position:0%
+satisfied uh there's every rectangle you
+draw here if it's plus rectangle it's
+
+ align:start position:0%
+draw here if it's plus rectangle it's
+ 
+
+ align:start position:0%
+draw here if it's plus rectangle it's
+got another point in
+
+ align:start position:0%
+got another point in
+ 
+
+ align:start position:0%
+got another point in
+it what's kind of nice also is you if
+
+ align:start position:0%
+it what's kind of nice also is you if
+ 
+
+ align:start position:0%
+it what's kind of nice also is you if
+you actually draw the rectangles you
+
+ align:start position:0%
+you actually draw the rectangles you
+ 
+
+ align:start position:0%
+you actually draw the rectangles you
+were satisfying so here was uh maybe
+
+ align:start position:0%
+were satisfying so here was uh maybe
+ 
+
+ align:start position:0%
+were satisfying so here was uh maybe
+I'll use another
+
+ align:start position:0%
+I'll use another
+ 
+
+ align:start position:0%
+I'll use another
+color there was one rectangle here there
+
+ align:start position:0%
+color there was one rectangle here there
+ 
+
+ align:start position:0%
+color there was one rectangle here there
+was one rectangle
+
+ align:start position:0%
+was one rectangle
+ 
+
+ align:start position:0%
+was one rectangle
+here uh and there was one rectangle
+
+ align:start position:0%
+here uh and there was one rectangle
+ 
+
+ align:start position:0%
+here uh and there was one rectangle
+here that's a little awkward because
+
+ align:start position:0%
+here that's a little awkward because
+ 
+
+ align:start position:0%
+here that's a little awkward because
+they're not on the original
+
+ align:start position:0%
+they're not on the original
+ 
+
+ align:start position:0%
+they're not on the original
+points so I can change them a little bit
+
+ align:start position:0%
+points so I can change them a little bit
+ 
+
+ align:start position:0%
+points so I can change them a little bit
+maybe move this one down to here and
+
+ align:start position:0%
+maybe move this one down to here and
+ 
+
+ align:start position:0%
+maybe move this one down to here and
+move this one over to
+
+ align:start position:0%
+move this one over to
+ 
+
+ align:start position:0%
+move this one over to
+here okay you could say that those
+
+ align:start position:0%
+here okay you could say that those
+ 
+
+ align:start position:0%
+here okay you could say that those
+rectangles came from those points then
+
+ align:start position:0%
+rectangles came from those points then
+ 
+
+ align:start position:0%
+rectangles came from those points then
+this is a set of independent rectangles
+
+ align:start position:0%
+this is a set of independent rectangles
+ 
+
+ align:start position:0%
+this is a set of independent rectangles
+on the original
+
+ align:start position:0%
+on the original
+ 
+
+ align:start position:0%
+on the original
+points maybe not totally obvious but
+
+ align:start position:0%
+points maybe not totally obvious but
+ 
+
+ align:start position:0%
+points maybe not totally obvious but
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+GD uh will always give
+
+ align:start position:0%
+GD uh will always give
+ 
+
+ align:start position:0%
+GD uh will always give
+you or
+
+ align:start position:0%
+you or
+ 
+
+ align:start position:0%
+you or
+gives an independent set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of plus rectangles so it's a lower
+
+ align:start position:0%
+of of plus rectangles so it's a lower
+ 
+
+ align:start position:0%
+of of plus rectangles so it's a lower
+bound it's not an upper bound because
+
+ align:start position:0%
+bound it's not an upper bound because
+ 
+
+ align:start position:0%
+bound it's not an upper bound because
+it's not satisfying the point set but
+
+ align:start position:0%
+it's not satisfying the point set but
+ 
+
+ align:start position:0%
+it's not satisfying the point set but
+it's a lower bound
+
+ align:start position:0%
+it's a lower bound
+ 
+
+ align:start position:0%
+it's a lower bound
+I claim it's a very good lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound okay it by itself might not be
+
+ align:start position:0%
+bound okay it by itself might not be
+ 
+
+ align:start position:0%
+bound okay it by itself might not be
+great but you have to consider both of
+
+ align:start position:0%
+great but you have to consider both of
+ 
+
+ align:start position:0%
+great but you have to consider both of
+them so theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is if I take the
+
+ align:start position:0%
+is if I take the
+ 
+
+ align:start position:0%
+is if I take the
+max of plus greedy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greedy each of them is lower bound so
+
+ align:start position:0%
+greedy each of them is lower bound so
+ 
+
+ align:start position:0%
+greedy each of them is lower bound so
+the max is a lower bound on
+
+ align:start position:0%
+the max is a lower bound on
+ 
+
+ align:start position:0%
+the max is a lower bound on
+optimal then this is within a constant
+
+ align:start position:0%
+optimal then this is within a constant
+ 
+
+ align:start position:0%
+optimal then this is within a constant
+factor of the biggest possible
+
+ align:start position:0%
+factor of the biggest possible
+ 
+
+ align:start position:0%
+factor of the biggest possible
+independent rectangle lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound and so this is the way you should
+
+ align:start position:0%
+bound and so this is the way you should
+ 
+
+ align:start position:0%
+bound and so this is the way you should
+choose independent rectangles run plus
+
+ align:start position:0%
+choose independent rectangles run plus
+ 
+
+ align:start position:0%
+choose independent rectangles run plus
+GD run minus GD take the best of the two
+
+ align:start position:0%
+GD run minus GD take the best of the two
+ 
+
+ align:start position:0%
+GD run minus GD take the best of the two
+that will always be within a constant
+
+ align:start position:0%
+that will always be within a constant
+ 
+
+ align:start position:0%
+that will always be within a constant
+factor of the best independent set of
+
+ align:start position:0%
+factor of the best independent set of
+ 
+
+ align:start position:0%
+factor of the best independent set of
+rectangles factors like four or
+
+ align:start position:0%
+rectangles factors like four or
+ 
+
+ align:start position:0%
+rectangles factors like four or
+something in the worst case so let me
+
+ align:start position:0%
+something in the worst case so let me
+ 
+
+ align:start position:0%
+something in the worst case so let me
+prove this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you it's kind of a weird
+
+ align:start position:0%
+you it's kind of a weird
+ 
+
+ align:start position:0%
+you it's kind of a weird
+argument uh I'm going to define a new
+
+ align:start position:0%
+argument uh I'm going to define a new
+ 
+
+ align:start position:0%
+argument uh I'm going to define a new
+quantity uh let's call this opt X I
+
+ align:start position:0%
+quantity uh let's call this opt X I
+ 
+
+ align:start position:0%
+quantity uh let's call this opt X I
+guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's sort of like if you consider plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangles separately from minus
+
+ align:start position:0%
+rectangles separately from minus
+ 
+
+ align:start position:0%
+rectangles separately from minus
+rectangles which is what we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doing so I I would like a point set
+
+ align:start position:0%
+doing so I I would like a point set
+ 
+
+ align:start position:0%
+doing so I I would like a point set
+first I'd like a plus satisfying Point
+
+ align:start position:0%
+first I'd like a plus satisfying Point
+ 
+
+ align:start position:0%
+first I'd like a plus satisfying Point
+set and then I'd also like a minus s
+
+ align:start position:0%
+set and then I'd also like a minus s
+ 
+
+ align:start position:0%
+set and then I'd also like a minus s
+minus satisfying Point set then I take
+
+ align:start position:0%
+minus satisfying Point set then I take
+ 
+
+ align:start position:0%
+minus satisfying Point set then I take
+their Union and I say the cost of that
+
+ align:start position:0%
+their Union and I say the cost of that
+ 
+
+ align:start position:0%
+their Union and I say the cost of that
+of the overall of that pair of plus
+
+ align:start position:0%
+of the overall of that pair of plus
+ 
+
+ align:start position:0%
+of the overall of that pair of plus
+satisfying and minus satisfying is the
+
+ align:start position:0%
+satisfying and minus satisfying is the
+ 
+
+ align:start position:0%
+satisfying and minus satisfying is the
+size of the Union so I get a little I
+
+ align:start position:0%
+size of the Union so I get a little I
+ 
+
+ align:start position:0%
+size of the Union so I get a little I
+get a bonus point if they happen to
+
+ align:start position:0%
+get a bonus point if they happen to
+ 
+
+ align:start position:0%
+get a bonus point if they happen to
+overlap not a big deal just a factor of
+
+ align:start position:0%
+overlap not a big deal just a factor of
+ 
+
+ align:start position:0%
+overlap not a big deal just a factor of
+two okay so this is not a core concept
+
+ align:start position:0%
+two okay so this is not a core concept
+ 
+
+ align:start position:0%
+two okay so this is not a core concept
+but it turns out to be basically what
+
+ align:start position:0%
+but it turns out to be basically what
+ 
+
+ align:start position:0%
+but it turns out to be basically what
+we're doing over
+
+ align:start position:0%
+we're doing over
+ 
+
+ align:start position:0%
+we're doing over
+here okay uh let me give you a sequence
+
+ align:start position:0%
+here okay uh let me give you a sequence
+ 
+
+ align:start position:0%
+here okay uh let me give you a sequence
+of crazy
+
+ align:start position:0%
+of crazy
+ 
+
+ align:start position:0%
+of crazy
+inequalities first one is that this opt
+
+ align:start position:0%
+inequalities first one is that this opt
+ 
+
+ align:start position:0%
+inequalities first one is that this opt
+thing is greater than or equal to size
+
+ align:start position:0%
+thing is greater than or equal to size
+ 
+
+ align:start position:0%
+thing is greater than or equal to size
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+input each of these inequalities is
+
+ align:start position:0%
+input each of these inequalities is
+ 
+
+ align:start position:0%
+input each of these inequalities is
+totally obvious but the conclusion is
+
+ align:start position:0%
+totally obvious but the conclusion is
+ 
+
+ align:start position:0%
+totally obvious but the conclusion is
+kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crazy okay the independent rectangle
+
+ align:start position:0%
+crazy okay the independent rectangle
+ 
+
+ align:start position:0%
+crazy okay the independent rectangle
+lower bound which we proved says that if
+
+ align:start position:0%
+lower bound which we proved says that if
+ 
+
+ align:start position:0%
+lower bound which we proved says that if
+you look at plus satisfying things
+
+ align:start position:0%
+you look at plus satisfying things
+ 
+
+ align:start position:0%
+you look at plus satisfying things
+that's going to be at least size of the
+
+ align:start position:0%
+that's going to be at least size of the
+ 
+
+ align:start position:0%
+that's going to be at least size of the
+input plus the max number of independent
+
+ align:start position:0%
+input plus the max number of independent
+ 
+
+ align:start position:0%
+input plus the max number of independent
+rectangles if you look at the minus
+
+ align:start position:0%
+rectangles if you look at the minus
+ 
+
+ align:start position:0%
+rectangles if you look at the minus
+satisfying things that it's also going
+
+ align:start position:0%
+satisfying things that it's also going
+ 
+
+ align:start position:0%
+satisfying things that it's also going
+to be at least size the input plus
+
+ align:start position:0%
+to be at least size the input plus
+ 
+
+ align:start position:0%
+to be at least size the input plus
+maximum number of minus s minus
+
+ align:start position:0%
+maximum number of minus s minus
+ 
+
+ align:start position:0%
+maximum number of minus s minus
+independent rectangles so we already
+
+ align:start position:0%
+independent rectangles so we already
+ 
+
+ align:start position:0%
+independent rectangles so we already
+proved this that you look at this Union
+
+ align:start position:0%
+proved this that you look at this Union
+ 
+
+ align:start position:0%
+proved this that you look at this Union
+it's going to be at least size of the
+
+ align:start position:0%
+it's going to be at least size of the
+ 
+
+ align:start position:0%
+it's going to be at least size of the
+input plus half the overall
+
+ align:start position:0%
+input plus half the overall
+ 
+
+ align:start position:0%
+input plus half the overall
+Max okay so that's that's what we proved
+
+ align:start position:0%
+Max okay so that's that's what we proved
+ 
+
+ align:start position:0%
+Max okay so that's that's what we proved
+at the beginning of
+
+ align:start position:0%
+at the beginning of
+ 
+
+ align:start position:0%
+at the beginning of
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+now this is the best way to choose
+
+ align:start position:0%
+now this is the best way to choose
+ 
+
+ align:start position:0%
+now this is the best way to choose
+independent rectangles greedy this this
+
+ align:start position:0%
+independent rectangles greedy this this
+ 
+
+ align:start position:0%
+independent rectangles greedy this this
+kind of sign greedy which is the max of
+
+ align:start position:0%
+kind of sign greedy which is the max of
+ 
+
+ align:start position:0%
+kind of sign greedy which is the max of
+the two signs is a way to find
+
+ align:start position:0%
+the two signs is a way to find
+ 
+
+ align:start position:0%
+the two signs is a way to find
+independent rectangle so it's only going
+
+ align:start position:0%
+independent rectangle so it's only going
+ 
+
+ align:start position:0%
+independent rectangle so it's only going
+to be worse it's going to be
+
+ align:start position:0%
+to be worse it's going to be
+ 
+
+ align:start position:0%
+to be worse it's going to be
+smaller so we can say uh is greater than
+
+ align:start position:0%
+smaller so we can say uh is greater than
+ 
+
+ align:start position:0%
+smaller so we can say uh is greater than
+or equal to half the max of plus
+
+ align:start position:0%
+or equal to half the max of plus
+ 
+
+ align:start position:0%
+or equal to half the max of plus
+grey and minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grey right this was the max so this is
+
+ align:start position:0%
+grey right this was the max so this is
+ 
+
+ align:start position:0%
+grey right this was the max so this is
+another way to do it so it must be
+
+ align:start position:0%
+another way to do it so it must be
+ 
+
+ align:start position:0%
+another way to do it so it must be
+smaller okay now
+
+ align:start position:0%
+smaller okay now
+ 
+
+ align:start position:0%
+smaller okay now
+greedy greedy computes a satis a plus
+
+ align:start position:0%
+greedy greedy computes a satis a plus
+ 
+
+ align:start position:0%
+greedy greedy computes a satis a plus
+satisfying assignment so I could say
+
+ align:start position:0%
+satisfying assignment so I could say
+ 
+
+ align:start position:0%
+satisfying assignment so I could say
+well if you looked at the optimal plus
+
+ align:start position:0%
+well if you looked at the optimal plus
+ 
+
+ align:start position:0%
+well if you looked at the optimal plus
+satisfying assignment this is something
+
+ align:start position:0%
+satisfying assignment this is something
+ 
+
+ align:start position:0%
+satisfying assignment this is something
+we defined at the beginning of lecture
+
+ align:start position:0%
+we defined at the beginning of lecture
+ 
+
+ align:start position:0%
+we defined at the beginning of lecture
+and the optimal minus satisfying
+
+ align:start position:0%
+and the optimal minus satisfying
+ 
+
+ align:start position:0%
+and the optimal minus satisfying
+assignment that's only going to be
+
+ align:start position:0%
+assignment that's only going to be
+ 
+
+ align:start position:0%
+assignment that's only going to be
+smaller than greedy because greedy is an
+
+ align:start position:0%
+smaller than greedy because greedy is an
+ 
+
+ align:start position:0%
+smaller than greedy because greedy is an
+algorithm for solving opt plus it's uh
+
+ align:start position:0%
+algorithm for solving opt plus it's uh
+ 
+
+ align:start position:0%
+algorithm for solving opt plus it's uh
+can can't be better than the optimum
+
+ align:start position:0%
+can can't be better than the optimum
+ 
+
+ align:start position:0%
+can can't be better than the optimum
+okay greedy again has to be bigger than
+
+ align:start position:0%
+okay greedy again has to be bigger than
+ 
+
+ align:start position:0%
+okay greedy again has to be bigger than
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+optimum uh good now I just want to turn
+
+ align:start position:0%
+optimum uh good now I just want to turn
+ 
+
+ align:start position:0%
+optimum uh good now I just want to turn
+this Max into a plus so this uh because
+
+ align:start position:0%
+this Max into a plus so this uh because
+ 
+
+ align:start position:0%
+this Max into a plus so this uh because
+the max is always at least the average
+
+ align:start position:0%
+the max is always at least the average
+ 
+
+ align:start position:0%
+the max is always at least the average
+so if I take the average which turns it
+
+ align:start position:0%
+so if I take the average which turns it
+ 
+
+ align:start position:0%
+so if I take the average which turns it
+into one quarter opt
+
+ align:start position:0%
+into one quarter opt
+ 
+
+ align:start position:0%
+into one quarter opt
+plus plus opt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus okay then that holds to turn the
+
+ align:start position:0%
+minus okay then that holds to turn the
+ 
+
+ align:start position:0%
+minus okay then that holds to turn the
+max into a plus if I look at the optimal
+
+ align:start position:0%
+max into a plus if I look at the optimal
+ 
+
+ align:start position:0%
+max into a plus if I look at the optimal
+plus satisfying plus the optimal minus
+
+ align:start position:0%
+plus satisfying plus the optimal minus
+ 
+
+ align:start position:0%
+plus satisfying plus the optimal minus
+satisfying that's only going to be
+
+ align:start position:0%
+satisfying that's only going to be
+ 
+
+ align:start position:0%
+satisfying that's only going to be
+bigger than this thing
+
+ align:start position:0%
+bigger than this thing
+ 
+
+ align:start position:0%
+bigger than this thing
+because this can only save like a factor
+
+ align:start position:0%
+because this can only save like a factor
+ 
+
+ align:start position:0%
+because this can only save like a factor
+of two or whatever over just adding them
+
+ align:start position:0%
+of two or whatever over just adding them
+ 
+
+ align:start position:0%
+of two or whatever over just adding them
+up but I I don't even need the factor of
+
+ align:start position:0%
+up but I I don't even need the factor of
+ 
+
+ align:start position:0%
+up but I I don't even need the factor of
+two thing I just
+
+ align:start position:0%
+two thing I just
+ 
+
+ align:start position:0%
+two thing I just
+need uh that if you add them up that's
+
+ align:start position:0%
+need uh that if you add them up that's
+ 
+
+ align:start position:0%
+need uh that if you add them up that's
+only going to be worse than just
+
+ align:start position:0%
+only going to be worse than just
+ 
+
+ align:start position:0%
+only going to be worse than just
+counting them as the
+
+ align:start position:0%
+counting them as the
+ 
+
+ align:start position:0%
+counting them as the
+union so we get I call a sandwich on the
+
+ align:start position:0%
+union so we get I call a sandwich on the
+ 
+
+ align:start position:0%
+union so we get I call a sandwich on the
+one side we have opt of opt X and the
+
+ align:start position:0%
+one side we have opt of opt X and the
+ 
+
+ align:start position:0%
+one side we have opt of opt X and the
+other side we have a quarter optex I
+
+ align:start position:0%
+other side we have a quarter optex I
+ 
+
+ align:start position:0%
+other side we have a quarter optex I
+really don't care about optex personally
+
+ align:start position:0%
+really don't care about optex personally
+ 
+
+ align:start position:0%
+really don't care about optex personally
+I mean it's kind of interesting to see
+
+ align:start position:0%
+I mean it's kind of interesting to see
+ 
+
+ align:start position:0%
+I mean it's kind of interesting to see
+that it's here but the point is these
+
+ align:start position:0%
+that it's here but the point is these
+ 
+
+ align:start position:0%
+that it's here but the point is these
+are within a constant factor of each
+
+ align:start position:0%
+are within a constant factor of each
+ 
+
+ align:start position:0%
+are within a constant factor of each
+other therefore all of these things in
+
+ align:start position:0%
+other therefore all of these things in
+ 
+
+ align:start position:0%
+other therefore all of these things in
+between are within a constant factor of
+
+ align:start position:0%
+between are within a constant factor of
+ 
+
+ align:start position:0%
+between are within a constant factor of
+each other so in particular this thing
+
+ align:start position:0%
+each other so in particular this thing
+ 
+
+ align:start position:0%
+each other so in particular this thing
+Max of the two greedies is within a
+
+ align:start position:0%
+Max of the two greedies is within a
+ 
+
+ align:start position:0%
+Max of the two greedies is within a
+constant factor of of this thing this is
+
+ align:start position:0%
+constant factor of of this thing this is
+ 
+
+ align:start position:0%
+constant factor of of this thing this is
+the independent rectangle lower bound
+
+ align:start position:0%
+the independent rectangle lower bound
+ 
+
+ align:start position:0%
+the independent rectangle lower bound
+the best one it also tells you that Opex
+
+ align:start position:0%
+the best one it also tells you that Opex
+ 
+
+ align:start position:0%
+the best one it also tells you that Opex
+is basically what we're Computing
+
+ align:start position:0%
+is basically what we're Computing
+ 
+
+ align:start position:0%
+is basically what we're Computing
+here so this is weird I'm going to draw
+
+ align:start position:0%
+here so this is weird I'm going to draw
+ 
+
+ align:start position:0%
+here so this is weird I'm going to draw
+one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture which is
+
+ align:start position:0%
+picture which is
+ 
+
+ align:start position:0%
+picture which is
+greedy versus signed greedy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember greedy from last lecture greedy
+
+ align:start position:0%
+remember greedy from last lecture greedy
+ 
+
+ align:start position:0%
+remember greedy from last lecture greedy
+says look I'm going to fix plus boxes
+
+ align:start position:0%
+says look I'm going to fix plus boxes
+ 
+
+ align:start position:0%
+says look I'm going to fix plus boxes
+plus rectangles and I'm going to fix
+
+ align:start position:0%
+plus rectangles and I'm going to fix
+ 
+
+ align:start position:0%
+plus rectangles and I'm going to fix
+minus rectangles it does them both at
+
+ align:start position:0%
+minus rectangles it does them both at
+ 
+
+ align:start position:0%
+minus rectangles it does them both at
+the same time s greedy says look I'm
+
+ align:start position:0%
+the same time s greedy says look I'm
+ 
+
+ align:start position:0%
+the same time s greedy says look I'm
+going to do the plus rectangles
+
+ align:start position:0%
+going to do the plus rectangles
+ 
+
+ align:start position:0%
+going to do the plus rectangles
+separately and then I'm going to do the
+
+ align:start position:0%
+separately and then I'm going to do the
+ 
+
+ align:start position:0%
+separately and then I'm going to do the
+minus rectangles separately and then add
+
+ align:start position:0%
+minus rectangles separately and then add
+ 
+
+ align:start position:0%
+minus rectangles separately and then add
+them up or take the union or take the
+
+ align:start position:0%
+them up or take the union or take the
+ 
+
+ align:start position:0%
+them up or take the union or take the
+max doesn't matter constant Factor okay
+
+ align:start position:0%
+max doesn't matter constant Factor okay
+ 
+
+ align:start position:0%
+max doesn't matter constant Factor okay
+just add them
+
+ align:start position:0%
+just add them
+ 
+
+ align:start position:0%
+just add them
+separately this one is an upper bound it
+
+ align:start position:0%
+separately this one is an upper bound it
+ 
+
+ align:start position:0%
+separately this one is an upper bound it
+is a binary search
+
+ align:start position:0%
+is a binary search
+ 
+
+ align:start position:0%
+is a binary search
+tree this thing is a lower bound all
+
+ align:start position:0%
+tree this thing is a lower bound all
+ 
+
+ align:start position:0%
+tree this thing is a lower bound all
+binary search trees must take at least
+
+ align:start position:0%
+binary search trees must take at least
+ 
+
+ align:start position:0%
+binary search trees must take at least
+this are they equal up to constant
+
+ align:start position:0%
+this are they equal up to constant
+ 
+
+ align:start position:0%
+this are they equal up to constant
+factors we don't know that's the big
+
+ align:start position:0%
+factors we don't know that's the big
+ 
+
+ align:start position:0%
+factors we don't know that's the big
+question they look almost identical but
+
+ align:start position:0%
+question they look almost identical but
+ 
+
+ align:start position:0%
+question they look almost identical but
+what greedy has to deal with is sort of
+
+ align:start position:0%
+what greedy has to deal with is sort of
+ 
+
+ align:start position:0%
+what greedy has to deal with is sort of
+the interrelations when I fix some plus
+
+ align:start position:0%
+the interrelations when I fix some plus
+ 
+
+ align:start position:0%
+the interrelations when I fix some plus
+rectangles I might get new minus
+
+ align:start position:0%
+rectangles I might get new minus
+ 
+
+ align:start position:0%
+rectangles I might get new minus
+rectangles that I have to fix with
+
+ align:start position:0%
+rectangles that I have to fix with
+ 
+
+ align:start position:0%
+rectangles that I have to fix with
+greedy s greedy doesn't have to deal
+
+ align:start position:0%
+greedy s greedy doesn't have to deal
+ 
+
+ align:start position:0%
+greedy s greedy doesn't have to deal
+with that it's just the plus rectangles
+
+ align:start position:0%
+with that it's just the plus rectangles
+ 
+
+ align:start position:0%
+with that it's just the plus rectangles
+they might make more plus rectangles but
+
+ align:start position:0%
+they might make more plus rectangles but
+ 
+
+ align:start position:0%
+they might make more plus rectangles but
+that's all I have to deal with it
+
+ align:start position:0%
+that's all I have to deal with it
+ 
+
+ align:start position:0%
+that's all I have to deal with it
+doesn't deal with the interaction
+
+ align:start position:0%
+doesn't deal with the interaction
+ 
+
+ align:start position:0%
+doesn't deal with the interaction
+between plus and minus rectangles seems
+
+ align:start position:0%
+between plus and minus rectangles seems
+ 
+
+ align:start position:0%
+between plus and minus rectangles seems
+like the interaction kind of Fades away
+
+ align:start position:0%
+like the interaction kind of Fades away
+ 
+
+ align:start position:0%
+like the interaction kind of Fades away
+as a geometric series and therefore
+
+ align:start position:0%
+as a geometric series and therefore
+ 
+
+ align:start position:0%
+as a geometric series and therefore
+these things are the same up to constant
+
+ align:start position:0%
+these things are the same up to constant
+ 
+
+ align:start position:0%
+these things are the same up to constant
+factors but we have no way to prove that
+
+ align:start position:0%
+factors but we have no way to prove that
+ 
+
+ align:start position:0%
+factors but we have no way to prove that
+could be the interaction blows you blows
+
+ align:start position:0%
+could be the interaction blows you blows
+ 
+
+ align:start position:0%
+could be the interaction blows you blows
+you out of the water
+
+ align:start position:0%
+you out of the water
+ 
+
+ align:start position:0%
+you out of the water
+somehow that's the best we know for
+
+ align:start position:0%
+somehow that's the best we know for
+ 
+
+ align:start position:0%
+somehow that's the best we know for
+dynamic optimality um maybe next time I
+
+ align:start position:0%
+dynamic optimality um maybe next time I
+ 
+
+ align:start position:0%
+dynamic optimality um maybe next time I
+teach this class we'll have a final
+
+ align:start position:0%
+teach this class we'll have a final
+ 
+
+ align:start position:0%
+teach this class we'll have a final
+answer and it'll be constant but that's
+
+ align:start position:0%
+answer and it'll be constant but that's
+ 
+
+ align:start position:0%
+answer and it'll be constant but that's
+where we are to today
\ No newline at end of file
diff --git a/OF2sr5e7PrY.txt b/OF2sr5e7PrY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..018af0172bd3bb6a377f996604f9e9b10aa256e4
--- /dev/null
+++ b/OF2sr5e7PrY.txt
@@ -0,0 +1,8707 @@
+align:start position:0%
+ 
+okay so let's get
+
+ align:start position:0%
+okay so let's get
+ 
+
+ align:start position:0%
+okay so let's get
+started um today's lecture we're going
+
+ align:start position:0%
+started um today's lecture we're going
+ 
+
+ align:start position:0%
+started um today's lecture we're going
+to do a little bit of a recap of the
+
+ align:start position:0%
+to do a little bit of a recap of the
+ 
+
+ align:start position:0%
+to do a little bit of a recap of the
+last lecture uh we had begun talking
+
+ align:start position:0%
+last lecture uh we had begun talking
+ 
+
+ align:start position:0%
+last lecture uh we had begun talking
+about binary numbers and then we're
+
+ align:start position:0%
+about binary numbers and then we're
+ 
+
+ align:start position:0%
+about binary numbers and then we're
+going to dive into our second algorithm
+
+ align:start position:0%
+going to dive into our second algorithm
+ 
+
+ align:start position:0%
+going to dive into our second algorithm
+of the class then approx the
+
+ align:start position:0%
+of the class then approx the
+ 
+
+ align:start position:0%
+of the class then approx the
+approximation method algorithm
+
+ align:start position:0%
+approximation method algorithm
+ 
+
+ align:start position:0%
+approximation method algorithm
+so let's remember the motivation we had
+
+ align:start position:0%
+so let's remember the motivation we had
+ 
+
+ align:start position:0%
+so let's remember the motivation we had
+for even talking about binary numbers
+
+ align:start position:0%
+for even talking about binary numbers
+ 
+
+ align:start position:0%
+for even talking about binary numbers
+and how numbers are represented in the
+
+ align:start position:0%
+and how numbers are represented in the
+ 
+
+ align:start position:0%
+and how numbers are represented in the
+computer in the first place and the
+
+ align:start position:0%
+computer in the first place and the
+ 
+
+ align:start position:0%
+computer in the first place and the
+motivation was this piece of code so
+
+ align:start position:0%
+motivation was this piece of code so
+ 
+
+ align:start position:0%
+motivation was this piece of code so
+it's very simple we have an initial X is
+
+ align:start position:0%
+it's very simple we have an initial X is
+ 
+
+ align:start position:0%
+it's very simple we have an initial X is
+zero and then we have a loop that just
+
+ align:start position:0%
+zero and then we have a loop that just
+ 
+
+ align:start position:0%
+zero and then we have a loop that just
+adds 0.1 to itself 10
+
+ align:start position:0%
+adds 0.1 to itself 10
+ 
+
+ align:start position:0%
+adds 0.1 to itself 10
+times and then we printed whether that
+
+ align:start position:0%
+times and then we printed whether that
+ 
+
+ align:start position:0%
+times and then we printed whether that
+sum equals one and what we saw was that
+
+ align:start position:0%
+sum equals one and what we saw was that
+ 
+
+ align:start position:0%
+sum equals one and what we saw was that
+it was false false printing X equivalent
+
+ align:start position:0%
+it was false false printing X equivalent
+ 
+
+ align:start position:0%
+it was false false printing X equivalent
+to one was false so then we printed what
+
+ align:start position:0%
+to one was false so then we printed what
+ 
+
+ align:start position:0%
+to one was false so then we printed what
+the actual value of x was after adding
+
+ align:start position:0%
+the actual value of x was after adding
+ 
+
+ align:start position:0%
+the actual value of x was after adding
+point1 to itself many uh 10 times and we
+
+ align:start position:0%
+point1 to itself many uh 10 times and we
+ 
+
+ align:start position:0%
+point1 to itself many uh 10 times and we
+saw that that summation was actually
+
+ align:start position:0%
+saw that that summation was actually
+ 
+
+ align:start position:0%
+saw that that summation was actually
+9999999 and of course to python 9999 is
+
+ align:start position:0%
+9999999 and of course to python 9999 is
+ 
+
+ align:start position:0%
+9999999 and of course to python 9999 is
+not equal to one so that's why we had
+
+ align:start position:0%
+not equal to one so that's why we had
+ 
+
+ align:start position:0%
+not equal to one so that's why we had
+printed uh false for X equivalent to one
+
+ align:start position:0%
+printed uh false for X equivalent to one
+ 
+
+ align:start position:0%
+printed uh false for X equivalent to one
+right that that
+
+ align:start position:0%
+right that that
+ 
+
+ align:start position:0%
+right that that
+expression and so this is our motivation
+
+ align:start position:0%
+expression and so this is our motivation
+ 
+
+ align:start position:0%
+expression and so this is our motivation
+why in the world does this happen in uh
+
+ align:start position:0%
+why in the world does this happen in uh
+ 
+
+ align:start position:0%
+why in the world does this happen in uh
+in programming and Python and something
+
+ align:start position:0%
+in programming and Python and something
+ 
+
+ align:start position:0%
+in programming and Python and something
+like this could really screw us up right
+
+ align:start position:0%
+like this could really screw us up right
+ 
+
+ align:start position:0%
+like this could really screw us up right
+if we're not even able to compare
+
+ align:start position:0%
+if we're not even able to compare
+ 
+
+ align:start position:0%
+if we're not even able to compare
+floating Point numbers so last lecture
+
+ align:start position:0%
+floating Point numbers so last lecture
+ 
+
+ align:start position:0%
+floating Point numbers so last lecture
+we ended with this piece of code um it
+
+ align:start position:0%
+we ended with this piece of code um it
+ 
+
+ align:start position:0%
+we ended with this piece of code um it
+was a way for us to uh to uh get the
+
+ align:start position:0%
+was a way for us to uh to uh get the
+ 
+
+ align:start position:0%
+was a way for us to uh to uh get the
+binary representation of a number in
+
+ align:start position:0%
+binary representation of a number in
+ 
+
+ align:start position:0%
+binary representation of a number in
+base 10 right so given some number we
+
+ align:start position:0%
+base 10 right so given some number we
+ 
+
+ align:start position:0%
+base 10 right so given some number we
+followed a really simple recipe a really
+
+ align:start position:0%
+followed a really simple recipe a really
+ 
+
+ align:start position:0%
+followed a really simple recipe a really
+simple algorithm to convert that number
+
+ align:start position:0%
+simple algorithm to convert that number
+ 
+
+ align:start position:0%
+simple algorithm to convert that number
+into base
+
+ align:start position:0%
+into base
+ 
+
+ align:start position:0%
+into base
+two the stuff that's in Bo in boxes
+
+ align:start position:0%
+two the stuff that's in Bo in boxes
+ 
+
+ align:start position:0%
+two the stuff that's in Bo in boxes
+let's not wor about it for now but let's
+
+ align:start position:0%
+let's not wor about it for now but let's
+ 
+
+ align:start position:0%
+let's not wor about it for now but let's
+look at just this part right here so the
+
+ align:start position:0%
+look at just this part right here so the
+ 
+
+ align:start position:0%
+look at just this part right here so the
+stuff that's in between the two boxes
+
+ align:start position:0%
+stuff that's in between the two boxes
+ 
+
+ align:start position:0%
+stuff that's in between the two boxes
+and this is the part that does most of
+
+ align:start position:0%
+and this is the part that does most of
+ 
+
+ align:start position:0%
+and this is the part that does most of
+the work for us or all of the work even
+
+ align:start position:0%
+the work for us or all of the work even
+ 
+
+ align:start position:0%
+the work for us or all of the work even
+for us it basically creates a
+
+ align:start position:0%
+for us it basically creates a
+ 
+
+ align:start position:0%
+for us it basically creates a
+string uh initially empty and the idea
+
+ align:start position:0%
+string uh initially empty and the idea
+ 
+
+ align:start position:0%
+string uh initially empty and the idea
+was that we were going to
+
+ align:start position:0%
+was that we were going to
+ 
+
+ align:start position:0%
+was that we were going to
+prepend um either zero or one to that
+
+ align:start position:0%
+prepend um either zero or one to that
+ 
+
+ align:start position:0%
+prepend um either zero or one to that
+string depending on whether the number
+
+ align:start position:0%
+string depending on whether the number
+ 
+
+ align:start position:0%
+string depending on whether the number
+we had was odd or even so for a number
+
+ align:start position:0%
+we had was odd or even so for a number
+ 
+
+ align:start position:0%
+we had was odd or even so for a number
+like 19 if we wanted to convert 19 base
+
+ align:start position:0%
+like 19 if we wanted to convert 19 base
+ 
+
+ align:start position:0%
+like 19 if we wanted to convert 19 base
+10 into base 2 what the algorithm was
+
+ align:start position:0%
+10 into base 2 what the algorithm was
+ 
+
+ align:start position:0%
+10 into base 2 what the algorithm was
+doing is over here in the loop it says
+
+ align:start position:0%
+doing is over here in the loop it says
+ 
+
+ align:start position:0%
+doing is over here in the loop it says
+while the num this num whatever it is
+
+ align:start position:0%
+while the num this num whatever it is
+ 
+
+ align:start position:0%
+while the num this num whatever it is
+initially 19 is still greater than zero
+
+ align:start position:0%
+initially 19 is still greater than zero
+ 
+
+ align:start position:0%
+initially 19 is still greater than zero
+let's get the remainder when we divide
+
+ align:start position:0%
+let's get the remainder when we divide
+ 
+
+ align:start position:0%
+let's get the remainder when we divide
+the number by two so that's what this
+
+ align:start position:0%
+the number by two so that's what this
+ 
+
+ align:start position:0%
+the number by two so that's what this
+num percent two is doing it's either
+
+ align:start position:0%
+num percent two is doing it's either
+ 
+
+ align:start position:0%
+num percent two is doing it's either
+getting a zero or one so 19 the
+
+ align:start position:0%
+getting a zero or one so 19 the
+ 
+
+ align:start position:0%
+getting a zero or one so 19 the
+remainder when we divide 19 by two is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and we're going to pre pend so we're
+
+ align:start position:0%
+one and we're going to pre pend so we're
+ 
+
+ align:start position:0%
+one and we're going to pre pend so we're
+casting this one integer to a string and
+
+ align:start position:0%
+casting this one integer to a string and
+ 
+
+ align:start position:0%
+casting this one integer to a string and
+prepending it to this result which is
+
+ align:start position:0%
+prepending it to this result which is
+ 
+
+ align:start position:0%
+prepending it to this result which is
+initially
+
+ align:start position:0%
+initially
+ 
+
+ align:start position:0%
+initially
+empty so that's what this line is doing
+
+ align:start position:0%
+empty so that's what this line is doing
+ 
+
+ align:start position:0%
+empty so that's what this line is doing
+result equals this thing here and then
+
+ align:start position:0%
+result equals this thing here and then
+ 
+
+ align:start position:0%
+result equals this thing here and then
+we're going to take our number and
+
+ align:start position:0%
+we're going to take our number and
+ 
+
+ align:start position:0%
+we're going to take our number and
+integer divide it by two so we're going
+
+ align:start position:0%
+integer divide it by two so we're going
+ 
+
+ align:start position:0%
+integer divide it by two so we're going
+to take the number 19 and divide it by
+
+ align:start position:0%
+to take the number 19 and divide it by
+ 
+
+ align:start position:0%
+to take the number 19 and divide it by
+two right so that's going to be 9.5 but
+
+ align:start position:0%
+two right so that's going to be 9.5 but
+ 
+
+ align:start position:0%
+two right so that's going to be 9.5 but
+we're only interested in the integer
+
+ align:start position:0%
+we're only interested in the integer
+ 
+
+ align:start position:0%
+we're only interested in the integer
+portion of it so nine and then the
+
+ align:start position:0%
+portion of it so nine and then the
+ 
+
+ align:start position:0%
+portion of it so nine and then the
+loop does the check again is 9 still
+
+ align:start position:0%
+loop does the check again is 9 still
+ 
+
+ align:start position:0%
+loop does the check again is 9 still
+greater than Z Z it is so then we're
+
+ align:start position:0%
+greater than Z Z it is so then we're
+ 
+
+ align:start position:0%
+greater than Z Z it is so then we're
+going to say what's the remainder when
+
+ align:start position:0%
+going to say what's the remainder when
+ 
+
+ align:start position:0%
+going to say what's the remainder when
+we divide 9 by two it's another one so
+
+ align:start position:0%
+we divide 9 by two it's another one so
+ 
+
+ align:start position:0%
+we divide 9 by two it's another one so
+we're going to prepend it that remainder
+
+ align:start position:0%
+we're going to prepend it that remainder
+ 
+
+ align:start position:0%
+we're going to prepend it that remainder
+to the string that we're building up
+
+ align:start position:0%
+to the string that we're building up
+ 
+
+ align:start position:0%
+to the string that we're building up
+okay and again we're going to divide
+
+ align:start position:0%
+okay and again we're going to divide
+ 
+
+ align:start position:0%
+okay and again we're going to divide
+this number by two so now we have 4.5
+
+ align:start position:0%
+this number by two so now we have 4.5
+ 
+
+ align:start position:0%
+this number by two so now we have 4.5
+when we only grab the integer portion of
+
+ align:start position:0%
+when we only grab the integer portion of
+ 
+
+ align:start position:0%
+when we only grab the integer portion of
+it four and again we ask what is the
+
+ align:start position:0%
+it four and again we ask what is the
+ 
+
+ align:start position:0%
+it four and again we ask what is the
+remainder when we divide 4 by two it's a
+
+ align:start position:0%
+remainder when we divide 4 by two it's a
+ 
+
+ align:start position:0%
+remainder when we divide 4 by two it's a
+zero so we prepend the zero to our uh
+
+ align:start position:0%
+zero so we prepend the zero to our uh
+ 
+
+ align:start position:0%
+zero so we prepend the zero to our uh
+sort of this binary string we're
+
+ align:start position:0%
+sort of this binary string we're
+ 
+
+ align:start position:0%
+sort of this binary string we're
+building up again we divide it by two
+
+ align:start position:0%
+building up again we divide it by two
+ 
+
+ align:start position:0%
+building up again we divide it by two
+it's a two the remainder when we divide
+
+ align:start position:0%
+it's a two the remainder when we divide
+ 
+
+ align:start position:0%
+it's a two the remainder when we divide
+two by two is zero it's an even number
+
+ align:start position:0%
+two by two is zero it's an even number
+ 
+
+ align:start position:0%
+two by two is zero it's an even number
+again we divide two by two it's a one
+
+ align:start position:0%
+again we divide two by two it's a one
+ 
+
+ align:start position:0%
+again we divide two by two it's a one
+and the remainder we get when we divide
+
+ align:start position:0%
+and the remainder we get when we divide
+ 
+
+ align:start position:0%
+and the remainder we get when we divide
+one by uh uh or sorry and yeah when we
+
+ align:start position:0%
+one by uh uh or sorry and yeah when we
+ 
+
+ align:start position:0%
+one by uh uh or sorry and yeah when we
+divide one by two is a
+
+ align:start position:0%
+divide one by two is a
+ 
+
+ align:start position:0%
+divide one by two is a
+one and so this is the string that we
+
+ align:start position:0%
+one and so this is the string that we
+ 
+
+ align:start position:0%
+one and so this is the string that we
+had eventually sort of systematically
+
+ align:start position:0%
+had eventually sort of systematically
+ 
+
+ align:start position:0%
+had eventually sort of systematically
+right iteratively built up with this
+
+ align:start position:0%
+right iteratively built up with this
+ 
+
+ align:start position:0%
+right iteratively built up with this
+Loop here and num after we divide this
+
+ align:start position:0%
+Loop here and num after we divide this
+ 
+
+ align:start position:0%
+Loop here and num after we divide this
+is going to be zero and then we break
+
+ align:start position:0%
+is going to be zero and then we break
+ 
+
+ align:start position:0%
+is going to be zero and then we break
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+loop right so the binary representation
+
+ align:start position:0%
+loop right so the binary representation
+ 
+
+ align:start position:0%
+loop right so the binary representation
+of 19 was 1 0011 base two we just kept
+
+ align:start position:0%
+of 19 was 1 0011 base two we just kept
+ 
+
+ align:start position:0%
+of 19 was 1 0011 base two we just kept
+it in a as a
+
+ align:start position:0%
+it in a as a
+ 
+
+ align:start position:0%
+it in a as a
+string the parts that are in red boxes
+
+ align:start position:0%
+string the parts that are in red boxes
+ 
+
+ align:start position:0%
+string the parts that are in red boxes
+is US dealing with uh in case with a
+
+ align:start position:0%
+is US dealing with uh in case with a
+ 
+
+ align:start position:0%
+is US dealing with uh in case with a
+negative number so if the user wanted to
+
+ align:start position:0%
+negative number so if the user wanted to
+ 
+
+ align:start position:0%
+negative number so if the user wanted to
+convert negative 19 to a binary
+
+ align:start position:0%
+convert negative 19 to a binary
+ 
+
+ align:start position:0%
+convert negative 19 to a binary
+representation this if else up here says
+
+ align:start position:0%
+representation this if else up here says
+ 
+
+ align:start position:0%
+representation this if else up here says
+is the number number less than zero if
+
+ align:start position:0%
+is the number number less than zero if
+ 
+
+ align:start position:0%
+is the number number less than zero if
+yes let's set a negative flag to true
+
+ align:start position:0%
+yes let's set a negative flag to true
+ 
+
+ align:start position:0%
+yes let's set a negative flag to true
+and let's just assume the user gave us a
+
+ align:start position:0%
+and let's just assume the user gave us a
+ 
+
+ align:start position:0%
+and let's just assume the user gave us a
+positive number so we convert that
+
+ align:start position:0%
+positive number so we convert that
+ 
+
+ align:start position:0%
+positive number so we convert that
+negative 19 to the absolute value of
+
+ align:start position:0%
+negative 19 to the absolute value of
+ 
+
+ align:start position:0%
+negative 19 to the absolute value of
+itself positive 19 this code goes
+
+ align:start position:0%
+itself positive 19 this code goes
+ 
+
+ align:start position:0%
+itself positive 19 this code goes
+through as if the user had given us a
+
+ align:start position:0%
+through as if the user had given us a
+ 
+
+ align:start position:0%
+through as if the user had given us a
+positive number and then at the end we
+
+ align:start position:0%
+positive number and then at the end we
+ 
+
+ align:start position:0%
+positive number and then at the end we
+would get get the same number as before
+
+ align:start position:0%
+would get get the same number as before
+ 
+
+ align:start position:0%
+would get get the same number as before
+except that we're going to prepend a
+
+ align:start position:0%
+except that we're going to prepend a
+ 
+
+ align:start position:0%
+except that we're going to prepend a
+negative sign so the negative uh so the
+
+ align:start position:0%
+negative sign so the negative uh so the
+ 
+
+ align:start position:0%
+negative sign so the negative uh so the
+binary representation of negative 19 is
+
+ align:start position:0%
+binary representation of negative 19 is
+ 
+
+ align:start position:0%
+binary representation of negative 19 is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing okay so that's that was where we
+
+ align:start position:0%
+thing okay so that's that was where we
+ 
+
+ align:start position:0%
+thing okay so that's that was where we
+ended up we talked about these integers
+
+ align:start position:0%
+ended up we talked about these integers
+ 
+
+ align:start position:0%
+ended up we talked about these integers
+um but now what about fractions right
+
+ align:start position:0%
+um but now what about fractions right
+ 
+
+ align:start position:0%
+um but now what about fractions right
+integers seems really easy there's a
+
+ align:start position:0%
+integers seems really easy there's a
+ 
+
+ align:start position:0%
+integers seems really easy there's a
+really easy simple procedure algorithm
+
+ align:start position:0%
+really easy simple procedure algorithm
+ 
+
+ align:start position:0%
+really easy simple procedure algorithm
+right recipe for us to follow to get the
+
+ align:start position:0%
+right recipe for us to follow to get the
+ 
+
+ align:start position:0%
+right recipe for us to follow to get the
+binary representation but what about
+
+ align:start position:0%
+binary representation but what about
+ 
+
+ align:start position:0%
+binary representation but what about
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+fractions oh yeah sorry so how does the
+
+ align:start position:0%
+fractions oh yeah sorry so how does the
+ 
+
+ align:start position:0%
+fractions oh yeah sorry so how does the
+negative right everything's going to be
+
+ align:start position:0%
+negative right everything's going to be
+ 
+
+ align:start position:0%
+negative right everything's going to be
+Zer or one so how does it read
+
+ align:start position:0%
+Zer or one so how does it read
+ 
+
+ align:start position:0%
+Zer or one so how does it read
+negative um here here here oh we just um
+
+ align:start position:0%
+negative um here here here oh we just um
+ 
+
+ align:start position:0%
+negative um here here here oh we just um
+it doesn't read it we just pretend like
+
+ align:start position:0%
+it doesn't read it we just pretend like
+ 
+
+ align:start position:0%
+it doesn't read it we just pretend like
+we were given a positive number and then
+
+ align:start position:0%
+we were given a positive number and then
+ 
+
+ align:start position:0%
+we were given a positive number and then
+we just do the same process over and
+
+ align:start position:0%
+we just do the same process over and
+ 
+
+ align:start position:0%
+we just do the same process over and
+over again okay so the
+
+ align:start position:0%
+over again okay so the
+ 
+
+ align:start position:0%
+over again okay so the
+computer I mean it for the purposes of
+
+ align:start position:0%
+computer I mean it for the purposes of
+ 
+
+ align:start position:0%
+computer I mean it for the purposes of
+the algorithm it doesn't need to know
+
+ align:start position:0%
+the algorithm it doesn't need to know
+ 
+
+ align:start position:0%
+the algorithm it doesn't need to know
+because the number will come out the
+
+ align:start position:0%
+because the number will come out the
+ 
+
+ align:start position:0%
+because the number will come out the
+same we just flag it as being a negative
+
+ align:start position:0%
+same we just flag it as being a negative
+ 
+
+ align:start position:0%
+same we just flag it as being a negative
+number and then at the end we say Hey
+
+ align:start position:0%
+number and then at the end we say Hey
+ 
+
+ align:start position:0%
+number and then at the end we say Hey
+you we were actually given a negative
+
+ align:start position:0%
+you we were actually given a negative
+ 
+
+ align:start position:0%
+you we were actually given a negative
+number so let's just pop this negative
+
+ align:start position:0%
+number so let's just pop this negative
+ 
+
+ align:start position:0%
+number so let's just pop this negative
+sign right in front of it okay and then
+
+ align:start position:0%
+sign right in front of it okay and then
+ 
+
+ align:start position:0%
+sign right in front of it okay and then
+talk about like the the powers that like
+
+ align:start position:0%
+talk about like the the powers that like
+ 
+
+ align:start position:0%
+talk about like the the powers that like
+two is put to like are we like going
+
+ align:start position:0%
+two is put to like are we like going
+ 
+
+ align:start position:0%
+two is put to like are we like going
+left to right like descending powers or
+
+ align:start position:0%
+left to right like descending powers or
+ 
+
+ align:start position:0%
+left to right like descending powers or
+ascending um we are actually doing
+
+ align:start position:0%
+ascending um we are actually doing
+ 
+
+ align:start position:0%
+ascending um we are actually doing
+ascending when we're building up the
+
+ align:start position:0%
+ascending when we're building up the
+ 
+
+ align:start position:0%
+ascending when we're building up the
+string because we're going right to left
+
+ align:start position:0%
+string because we're going right to left
+ 
+
+ align:start position:0%
+string because we're going right to left
+so yeah yeah exactly so this is two to
+
+ align:start position:0%
+so yeah yeah exactly so this is two to
+ 
+
+ align:start position:0%
+so yeah yeah exactly so this is two to
+the zero and this is two to the
+
+ align:start position:0%
+the zero and this is two to the
+ 
+
+ align:start position:0%
+the zero and this is two to the
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+yeah so in terms of fractions if we're
+
+ align:start position:0%
+yeah so in terms of fractions if we're
+ 
+
+ align:start position:0%
+yeah so in terms of fractions if we're
+thinking about what it means to talk
+
+ align:start position:0%
+thinking about what it means to talk
+ 
+
+ align:start position:0%
+thinking about what it means to talk
+about a fraction action in in human
+
+ align:start position:0%
+about a fraction action in in human
+ 
+
+ align:start position:0%
+about a fraction action in in human
+readable base 10 right so numbers 0
+
+ align:start position:0%
+readable base 10 right so numbers 0
+ 
+
+ align:start position:0%
+readable base 10 right so numbers 0
+through 9 when we have 0. ABC we're
+
+ align:start position:0%
+through 9 when we have 0. ABC we're
+ 
+
+ align:start position:0%
+through 9 when we have 0. ABC we're
+basically saying that's a divided 10
+
+ align:start position:0%
+basically saying that's a divided 10
+ 
+
+ align:start position:0%
+basically saying that's a divided 10
+plus b divided 100 plus C divided by a
+
+ align:start position:0%
+plus b divided 100 plus C divided by a
+ 
+
+ align:start position:0%
+plus b divided 100 plus C divided by a
+th000 and so on and in base two we're
+
+ align:start position:0%
+th000 and so on and in base two we're
+ 
+
+ align:start position:0%
+th000 and so on and in base two we're
+going to have the same sort of thing
+
+ align:start position:0%
+going to have the same sort of thing
+ 
+
+ align:start position:0%
+going to have the same sort of thing
+going on if we're talking about a base
+
+ align:start position:0%
+going on if we're talking about a base
+ 
+
+ align:start position:0%
+going on if we're talking about a base
+two representation of a number 0. a BC
+
+ align:start position:0%
+two representation of a number 0. a BC
+ 
+
+ align:start position:0%
+two representation of a number 0. a BC
+where now a A or C is just zero or one
+
+ align:start position:0%
+where now a A or C is just zero or one
+ 
+
+ align:start position:0%
+where now a A or C is just zero or one
+instead of 0 through n it's going to be
+
+ align:start position:0%
+instead of 0 through n it's going to be
+ 
+
+ align:start position:0%
+instead of 0 through n it's going to be
+the same thing so we would have a ided 2
+
+ align:start position:0%
+the same thing so we would have a ided 2
+ 
+
+ align:start position:0%
+the same thing so we would have a ided 2
+plus b / 4 plus C ID 8 and so on so now
+
+ align:start position:0%
+plus b / 4 plus C ID 8 and so on so now
+ 
+
+ align:start position:0%
+plus b / 4 plus C ID 8 and so on so now
+we're dealing with powers of two instead
+
+ align:start position:0%
+we're dealing with powers of two instead
+ 
+
+ align:start position:0%
+we're dealing with powers of two instead
+of powers of 10 right because our base
+
+ align:start position:0%
+of powers of 10 right because our base
+ 
+
+ align:start position:0%
+of powers of 10 right because our base
+our base is now two instead of
+
+ align:start position:0%
+our base is now two instead of
+ 
+
+ align:start position:0%
+our base is now two instead of
+10 so that means the binary
+
+ align:start position:0%
+10 so that means the binary
+ 
+
+ align:start position:0%
+10 so that means the binary
+representation of a decimal fraction
+
+ align:start position:0%
+representation of a decimal fraction
+ 
+
+ align:start position:0%
+representation of a decimal fraction
+basically means can we find some sort of
+
+ align:start position:0%
+basically means can we find some sort of
+ 
+
+ align:start position:0%
+basically means can we find some sort of
+combination of these values 0.5 time a z
+
+ align:start position:0%
+combination of these values 0.5 time a z
+ 
+
+ align:start position:0%
+combination of these values 0.5 time a z
+or 1 plus 0.25 * a 01 plus .125 * 01 and
+
+ align:start position:0%
+or 1 plus 0.25 * a 01 plus .125 * 01 and
+ 
+
+ align:start position:0%
+or 1 plus 0.25 * a 01 plus .125 * 01 and
+so on and so on so these are all the
+
+ align:start position:0%
+so on and so on so these are all the
+ 
+
+ align:start position:0%
+so on and so on so these are all the
+powers of two to so I'll give you the
+
+ align:start position:0%
+powers of two to so I'll give you the
+ 
+
+ align:start position:0%
+powers of two to so I'll give you the
+recipe for how we can actually find the
+
+ align:start position:0%
+recipe for how we can actually find the
+ 
+
+ align:start position:0%
+recipe for how we can actually find the
+uh the uh the representation of a
+
+ align:start position:0%
+uh the uh the representation of a
+ 
+
+ align:start position:0%
+uh the uh the representation of a
+fraction and this is not something that
+
+ align:start position:0%
+fraction and this is not something that
+ 
+
+ align:start position:0%
+fraction and this is not something that
+we expect you to come up just like the
+
+ align:start position:0%
+we expect you to come up just like the
+ 
+
+ align:start position:0%
+we expect you to come up just like the
+recipe for this is not something we
+
+ align:start position:0%
+recipe for this is not something we
+ 
+
+ align:start position:0%
+recipe for this is not something we
+expect you to come up with but given the
+
+ align:start position:0%
+expect you to come up with but given the
+ 
+
+ align:start position:0%
+expect you to come up with but given the
+recipe you should be able to sort of
+
+ align:start position:0%
+recipe you should be able to sort of
+ 
+
+ align:start position:0%
+recipe you should be able to sort of
+intuitively figure out what is the code
+
+ align:start position:0%
+intuitively figure out what is the code
+ 
+
+ align:start position:0%
+intuitively figure out what is the code
+that actually you know performs this
+
+ align:start position:0%
+that actually you know performs this
+ 
+
+ align:start position:0%
+that actually you know performs this
+this uh this action right that does this
+
+ align:start position:0%
+this uh this action right that does this
+ 
+
+ align:start position:0%
+this uh this action right that does this
+recipe so the idea to convert a decimal
+
+ align:start position:0%
+recipe so the idea to convert a decimal
+ 
+
+ align:start position:0%
+recipe so the idea to convert a decimal
+number to to a uh a decimal fraction in
+
+ align:start position:0%
+number to to a uh a decimal fraction in
+ 
+
+ align:start position:0%
+number to to a uh a decimal fraction in
+base 10 to a fraction uh sorry to a
+
+ align:start position:0%
+base 10 to a fraction uh sorry to a
+ 
+
+ align:start position:0%
+base 10 to a fraction uh sorry to a
+binary fraction right in base two is as
+
+ align:start position:0%
+binary fraction right in base two is as
+ 
+
+ align:start position:0%
+binary fraction right in base two is as
+follows so let's look at the decimal
+
+ align:start position:0%
+follows so let's look at the decimal
+ 
+
+ align:start position:0%
+follows so let's look at the decimal
+number 3 divided 8 just as an example so
+
+ align:start position:0%
+number 3 divided 8 just as an example so
+ 
+
+ align:start position:0%
+number 3 divided 8 just as an example so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+0.375 right but we know it's 3
+
+ align:start position:0%
+0.375 right but we know it's 3
+ 
+
+ align:start position:0%
+0.375 right but we know it's 3
+over8 in base 10 so using numbers uh
+
+ align:start position:0%
+over8 in base 10 so using numbers uh
+ 
+
+ align:start position:0%
+over8 in base 10 so using numbers uh
+know uh numbers 0 through 9 we end up
+
+ align:start position:0%
+know uh numbers 0 through 9 we end up
+ 
+
+ align:start position:0%
+know uh numbers 0 through 9 we end up
+saying it's 3 over 10 plus 7 over 100
+
+ align:start position:0%
+saying it's 3 over 10 plus 7 over 100
+ 
+
+ align:start position:0%
+saying it's 3 over 10 plus 7 over 100
+plus 5 th000 right that's just base 10
+
+ align:start position:0%
+plus 5 th000 right that's just base 10
+ 
+
+ align:start position:0%
+plus 5 th000 right that's just base 10
+but we need to come up with a way to
+
+ align:start position:0%
+but we need to come up with a way to
+ 
+
+ align:start position:0%
+but we need to come up with a way to
+convert this into base 2 and so the
+
+ align:start position:0%
+convert this into base 2 and so the
+ 
+
+ align:start position:0%
+convert this into base 2 and so the
+trick here is to basically say what is
+
+ align:start position:0%
+trick here is to basically say what is
+ 
+
+ align:start position:0%
+trick here is to basically say what is
+the biggest multiple of two that I can
+
+ align:start position:0%
+the biggest multiple of two that I can
+ 
+
+ align:start position:0%
+the biggest multiple of two that I can
+multiply my number my decimal
+
+ align:start position:0%
+multiply my number my decimal
+ 
+
+ align:start position:0%
+multiply my number my decimal
+number with such that I end up getting a
+
+ align:start position:0%
+number with such that I end up getting a
+ 
+
+ align:start position:0%
+number with such that I end up getting a
+whole number an
+
+ align:start position:0%
+whole number an
+ 
+
+ align:start position:0%
+whole number an
+integer that's sort of the trick to this
+
+ align:start position:0%
+integer that's sort of the trick to this
+ 
+
+ align:start position:0%
+integer that's sort of the trick to this
+whole thing can I multiply my 375 or
+
+ align:start position:0%
+whole thing can I multiply my 375 or
+ 
+
+ align:start position:0%
+whole thing can I multiply my 375 or
+what whatever fraction I'm interested in
+
+ align:start position:0%
+what whatever fraction I'm interested in
+ 
+
+ align:start position:0%
+what whatever fraction I'm interested in
+calculate in in changing to base two by
+
+ align:start position:0%
+calculate in in changing to base two by
+ 
+
+ align:start position:0%
+calculate in in changing to base two by
+some power of two big enough such that
+
+ align:start position:0%
+some power of two big enough such that
+ 
+
+ align:start position:0%
+some power of two big enough such that
+I'm going to get a whole number out of
+
+ align:start position:0%
+I'm going to get a whole number out of
+ 
+
+ align:start position:0%
+I'm going to get a whole number out of
+this out of the multiplication and it
+
+ align:start position:0%
+this out of the multiplication and it
+ 
+
+ align:start position:0%
+this out of the multiplication and it
+has to be a power of two because we're
+
+ align:start position:0%
+has to be a power of two because we're
+ 
+
+ align:start position:0%
+has to be a power of two because we're
+converting it to Binary right zeros and
+
+ align:start position:0%
+converting it to Binary right zeros and
+ 
+
+ align:start position:0%
+converting it to Binary right zeros and
+ones so in this simple example 375 is 3
+
+ align:start position:0%
+ones so in this simple example 375 is 3
+ 
+
+ align:start position:0%
+ones so in this simple example 375 is 3
+divided 8 so that means that the biggest
+
+ align:start position:0%
+divided 8 so that means that the biggest
+ 
+
+ align:start position:0%
+divided 8 so that means that the biggest
+power of or the the the smallest power
+
+ align:start position:0%
+power of or the the the smallest power
+ 
+
+ align:start position:0%
+power of or the the the smallest power
+of two I can multiply uh 3 over8 by to
+
+ align:start position:0%
+of two I can multiply uh 3 over8 by to
+ 
+
+ align:start position:0%
+of two I can multiply uh 3 over8 by to
+give me a whole number is eight right
+
+ align:start position:0%
+give me a whole number is eight right
+ 
+
+ align:start position:0%
+give me a whole number is eight right
+that's 2 to the^ of three so if I
+
+ align:start position:0%
+that's 2 to the^ of three so if I
+ 
+
+ align:start position:0%
+that's 2 to the^ of three so if I
+multiply 375 by 8 3 over 8 * 8 gives me
+
+ align:start position:0%
+multiply 375 by 8 3 over 8 * 8 gives me
+ 
+
+ align:start position:0%
+multiply 375 by 8 3 over 8 * 8 gives me
+three in base
+
+ align:start position:0%
+three in base
+ 
+
+ align:start position:0%
+three in base
+10 and now this whole number I know how
+
+ align:start position:0%
+10 and now this whole number I know how
+ 
+
+ align:start position:0%
+10 and now this whole number I know how
+to convert to Binary I have a recipe
+
+ align:start position:0%
+to convert to Binary I have a recipe
+ 
+
+ align:start position:0%
+to convert to Binary I have a recipe
+right we've done it on the board here we
+
+ align:start position:0%
+right we've done it on the board here we
+ 
+
+ align:start position:0%
+right we've done it on the board here we
+have the code on the previous slide so
+
+ align:start position:0%
+have the code on the previous slide so
+ 
+
+ align:start position:0%
+have the code on the previous slide so
+all we have to do now is convert the
+
+ align:start position:0%
+all we have to do now is convert the
+ 
+
+ align:start position:0%
+all we have to do now is convert the
+number three to Binary which is just one
+
+ align:start position:0%
+number three to Binary which is just one
+ 
+
+ align:start position:0%
+number three to Binary which is just one
+one base
+
+ align:start position:0%
+one base
+ 
+
+ align:start position:0%
+one base
+two but this one one is a representation
+
+ align:start position:0%
+two but this one one is a representation
+ 
+
+ align:start position:0%
+two but this one one is a representation
+of the number three so in order to get
+
+ align:start position:0%
+of the number three so in order to get
+ 
+
+ align:start position:0%
+of the number three so in order to get
+back to 375 I need to divide my three by
+
+ align:start position:0%
+back to 375 I need to divide my three by
+ 
+
+ align:start position:0%
+back to 375 I need to divide my three by
+2 to the^ of 3 so I need to divide my 1
+
+ align:start position:0%
+2 to the^ of 3 so I need to divide my 1
+ 
+
+ align:start position:0%
+2 to the^ of 3 so I need to divide my 1
+one by 2 to the^ of 3 and in binary
+
+ align:start position:0%
+one by 2 to the^ of 3 and in binary
+ 
+
+ align:start position:0%
+one by 2 to the^ of 3 and in binary
+dividing by some power of two just means
+
+ align:start position:0%
+dividing by some power of two just means
+ 
+
+ align:start position:0%
+dividing by some power of two just means
+Shifting the decimal point over just
+
+ align:start position:0%
+Shifting the decimal point over just
+ 
+
+ align:start position:0%
+Shifting the decimal point over just
+like in base 10 dividing by 10 means
+
+ align:start position:0%
+like in base 10 dividing by 10 means
+ 
+
+ align:start position:0%
+like in base 10 dividing by 10 means
+Shifting the decimal point over so if
+
+ align:start position:0%
+Shifting the decimal point over so if
+ 
+
+ align:start position:0%
+Shifting the decimal point over so if
+number three is 1 one and and I
+
+ align:start position:0%
+number three is 1 one and and I
+ 
+
+ align:start position:0%
+number three is 1 one and and I
+multiplied by 2 to the 3 to get this
+
+ align:start position:0%
+multiplied by 2 to the 3 to get this
+ 
+
+ align:start position:0%
+multiplied by 2 to the 3 to get this
+value to divide by 2 to the 3 I just
+
+ align:start position:0%
+value to divide by 2 to the 3 I just
+ 
+
+ align:start position:0%
+value to divide by 2 to the 3 I just
+need to move the decimal point from just
+
+ align:start position:0%
+need to move the decimal point from just
+ 
+
+ align:start position:0%
+need to move the decimal point from just
+after the 1 one over one two and then it
+
+ align:start position:0%
+after the 1 one over one two and then it
+ 
+
+ align:start position:0%
+after the 1 one over one two and then it
+add another zero so the representation
+
+ align:start position:0%
+add another zero so the representation
+ 
+
+ align:start position:0%
+add another zero so the representation
+of the 375 becomes
+
+ align:start position:0%
+of the 375 becomes
+ 
+
+ align:start position:0%
+of the 375 becomes
+011 right I just shifted this decimal
+
+ align:start position:0%
+011 right I just shifted this decimal
+ 
+
+ align:start position:0%
+011 right I just shifted this decimal
+point over by three because now we're
+
+ align:start position:0%
+point over by three because now we're
+ 
+
+ align:start position:0%
+point over by three because now we're
+dealing in base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay so that's this that's the
+
+ align:start position:0%
+two okay so that's this that's the
+ 
+
+ align:start position:0%
+two okay so that's this that's the
+system like that's the recipe for
+
+ align:start position:0%
+system like that's the recipe for
+ 
+
+ align:start position:0%
+system like that's the recipe for
+getting this uh decimal uh this binary
+
+ align:start position:0%
+getting this uh decimal uh this binary
+ 
+
+ align:start position:0%
+getting this uh decimal uh this binary
+representation out of a decimal number
+
+ align:start position:0%
+representation out of a decimal number
+ 
+
+ align:start position:0%
+representation out of a decimal number
+but there's a problem right this is all
+
+ align:start position:0%
+but there's a problem right this is all
+ 
+
+ align:start position:0%
+but there's a problem right this is all
+relying on the fact that I can find this
+
+ align:start position:0%
+relying on the fact that I can find this
+ 
+
+ align:start position:0%
+relying on the fact that I can find this
+magical power of two right that if it's
+
+ align:start position:0%
+magical power of two right that if it's
+ 
+
+ align:start position:0%
+magical power of two right that if it's
+big enough right I can find such a power
+
+ align:start position:0%
+big enough right I can find such a power
+ 
+
+ align:start position:0%
+big enough right I can find such a power
+of two that when I multiply with my
+
+ align:start position:0%
+of two that when I multiply with my
+ 
+
+ align:start position:0%
+of two that when I multiply with my
+decimal number I get a whole number out
+
+ align:start position:0%
+decimal number I get a whole number out
+ 
+
+ align:start position:0%
+decimal number I get a whole number out
+of it and that's not always the case
+
+ align:start position:0%
+of it and that's not always the case
+ 
+
+ align:start position:0%
+of it and that's not always the case
+sometimes that power of two is going to
+
+ align:start position:0%
+sometimes that power of two is going to
+ 
+
+ align:start position:0%
+sometimes that power of two is going to
+be really really big or it might not
+
+ align:start position:0%
+be really really big or it might not
+ 
+
+ align:start position:0%
+be really really big or it might not
+even exist okay and so if it's really
+
+ align:start position:0%
+even exist okay and so if it's really
+ 
+
+ align:start position:0%
+even exist okay and so if it's really
+big or if it doesn't exist that's where
+
+ align:start position:0%
+big or if it doesn't exist that's where
+ 
+
+ align:start position:0%
+big or if it doesn't exist that's where
+we run into problems as we're going to
+
+ align:start position:0%
+we run into problems as we're going to
+ 
+
+ align:start position:0%
+we run into problems as we're going to
+see in a little bit okay so this is all
+
+ align:start position:0%
+see in a little bit okay so this is all
+ 
+
+ align:start position:0%
+see in a little bit okay so this is all
+relying on the fact that I can find this
+
+ align:start position:0%
+relying on the fact that I can find this
+ 
+
+ align:start position:0%
+relying on the fact that I can find this
+power of two so here's the code to
+
+ align:start position:0%
+power of two so here's the code to
+ 
+
+ align:start position:0%
+power of two so here's the code to
+actually do this recipe that I had on
+
+ align:start position:0%
+actually do this recipe that I had on
+ 
+
+ align:start position:0%
+actually do this recipe that I had on
+the previous slide finding the power of
+
+ align:start position:0%
+the previous slide finding the power of
+ 
+
+ align:start position:0%
+the previous slide finding the power of
+two doing the conversion and then
+
+ align:start position:0%
+two doing the conversion and then
+ 
+
+ align:start position:0%
+two doing the conversion and then
+Shifting the decimal point over so I'm
+
+ align:start position:0%
+Shifting the decimal point over so I'm
+ 
+
+ align:start position:0%
+Shifting the decimal point over so I'm
+going to do a quick sort of overview of
+
+ align:start position:0%
+going to do a quick sort of overview of
+ 
+
+ align:start position:0%
+going to do a quick sort of overview of
+the pieces and then we can run the
+
+ align:start position:0%
+the pieces and then we can run the
+ 
+
+ align:start position:0%
+the pieces and then we can run the
+python tutor just to show you exactly
+
+ align:start position:0%
+python tutor just to show you exactly
+ 
+
+ align:start position:0%
+python tutor just to show you exactly
+step by step what's going on so let's
+
+ align:start position:0%
+step by step what's going on so let's
+ 
+
+ align:start position:0%
+step by step what's going on so let's
+say I want to do 625 and convert that to
+
+ align:start position:0%
+say I want to do 625 and convert that to
+ 
+
+ align:start position:0%
+say I want to do 625 and convert that to
+a^ of two so I've got my X initialized
+
+ align:start position:0%
+a^ of two so I've got my X initialized
+ 
+
+ align:start position:0%
+a^ of two so I've got my X initialized
+up there this bit here so this big box
+
+ align:start position:0%
+up there this bit here so this big box
+ 
+
+ align:start position:0%
+up there this bit here so this big box
+here is the part that finds this magical
+
+ align:start position:0%
+here is the part that finds this magical
+ 
+
+ align:start position:0%
+here is the part that finds this magical
+power of two for me okay it's just a
+
+ align:start position:0%
+power of two for me okay it's just a
+ 
+
+ align:start position:0%
+power of two for me okay it's just a
+loop that keeps incrementing the P the
+
+ align:start position:0%
+loop that keeps incrementing the P the
+ 
+
+ align:start position:0%
+loop that keeps incrementing the P the
+power such that 2 to the power of P
+
+ align:start position:0%
+power such that 2 to the power of P
+ 
+
+ align:start position:0%
+power such that 2 to the power of P
+multiplied X this percent one just gives
+
+ align:start position:0%
+multiplied X this percent one just gives
+ 
+
+ align:start position:0%
+multiplied X this percent one just gives
+me the decimals bit out of that
+
+ align:start position:0%
+me the decimals bit out of that
+ 
+
+ align:start position:0%
+me the decimals bit out of that
+multiplication is zero so I'm going to
+
+ align:start position:0%
+multiplication is zero so I'm going to
+ 
+
+ align:start position:0%
+multiplication is zero so I'm going to
+keep multiplying two to some power of P
+
+ align:start position:0%
+keep multiplying two to some power of P
+ 
+
+ align:start position:0%
+keep multiplying two to some power of P
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+X as long as I still have a decimal
+
+ align:start position:0%
+X as long as I still have a decimal
+ 
+
+ align:start position:0%
+X as long as I still have a decimal
+piece to my number as soon as this
+
+ align:start position:0%
+piece to my number as soon as this
+ 
+
+ align:start position:0%
+piece to my number as soon as this
+percentage be percent one becomes zero
+
+ align:start position:0%
+percentage be percent one becomes zero
+ 
+
+ align:start position:0%
+percentage be percent one becomes zero
+that means that the number I'm I end up
+
+ align:start position:0%
+that means that the number I'm I end up
+ 
+
+ align:start position:0%
+that means that the number I'm I end up
+with is some number do zero right there
+
+ align:start position:0%
+with is some number do zero right there
+ 
+
+ align:start position:0%
+with is some number do zero right there
+is no more decimal part to
+
+ align:start position:0%
+is no more decimal part to
+ 
+
+ align:start position:0%
+is no more decimal part to
+it at that point I break out of the loop
+
+ align:start position:0%
+it at that point I break out of the loop
+ 
+
+ align:start position:0%
+it at that point I break out of the loop
+and I found my power of P or my power
+
+ align:start position:0%
+and I found my power of P or my power
+ 
+
+ align:start position:0%
+and I found my power of P or my power
+P this is going to be the integer so I'm
+
+ align:start position:0%
+P this is going to be the integer so I'm
+ 
+
+ align:start position:0%
+P this is going to be the integer so I'm
+multiplying X by that special Power by
+
+ align:start position:0%
+multiplying X by that special Power by
+ 
+
+ align:start position:0%
+multiplying X by that special Power by
+two to the power of uh that's by two to
+
+ align:start position:0%
+two to the power of uh that's by two to
+ 
+
+ align:start position:0%
+two to the power of uh that's by two to
+the power of that special power and now
+
+ align:start position:0%
+the power of that special power and now
+ 
+
+ align:start position:0%
+the power of that special power and now
+I have this number so on the previous
+
+ align:start position:0%
+I have this number so on the previous
+ 
+
+ align:start position:0%
+I have this number so on the previous
+slide right it's the number three in
+
+ align:start position:0%
+slide right it's the number three in
+ 
+
+ align:start position:0%
+slide right it's the number three in
+base 10 and then this box here is
+
+ align:start position:0%
+base 10 and then this box here is
+ 
+
+ align:start position:0%
+base 10 and then this box here is
+exactly the same as two slides ago it's
+
+ align:start position:0%
+exactly the same as two slides ago it's
+ 
+
+ align:start position:0%
+exactly the same as two slides ago it's
+this procedure here it's taking my
+
+ align:start position:0%
+this procedure here it's taking my
+ 
+
+ align:start position:0%
+this procedure here it's taking my
+number whatever it may be and getting
+
+ align:start position:0%
+number whatever it may be and getting
+ 
+
+ align:start position:0%
+number whatever it may be and getting
+the binary representation of
+
+ align:start position:0%
+the binary representation of
+ 
+
+ align:start position:0%
+the binary representation of
+it and after that we need to figure out
+
+ align:start position:0%
+it and after that we need to figure out
+ 
+
+ align:start position:0%
+it and after that we need to figure out
+how many spaces to move the decimal
+
+ align:start position:0%
+how many spaces to move the decimal
+ 
+
+ align:start position:0%
+how many spaces to move the decimal
+point backward so so what is the power
+
+ align:start position:0%
+point backward so so what is the power
+ 
+
+ align:start position:0%
+point backward so so what is the power
+of P we multiplied that number by and
+
+ align:start position:0%
+of P we multiplied that number by and
+ 
+
+ align:start position:0%
+of P we multiplied that number by and
+now we need to work our way backward and
+
+ align:start position:0%
+now we need to work our way backward and
+ 
+
+ align:start position:0%
+now we need to work our way backward and
+say well that dot is here let me move
+
+ align:start position:0%
+say well that dot is here let me move
+ 
+
+ align:start position:0%
+say well that dot is here let me move
+the dot back P
+
+ align:start position:0%
+the dot back P
+ 
+
+ align:start position:0%
+the dot back P
+steps and that's what this is doing so
+
+ align:start position:0%
+steps and that's what this is doing so
+ 
+
+ align:start position:0%
+steps and that's what this is doing so
+it's iterating through P minus however
+
+ align:start position:0%
+it's iterating through P minus however
+ 
+
+ align:start position:0%
+it's iterating through P minus however
+long this thing is to pad the front with
+
+ align:start position:0%
+long this thing is to pad the front with
+ 
+
+ align:start position:0%
+long this thing is to pad the front with
+zeros okay because if because sometimes
+
+ align:start position:0%
+zeros okay because if because sometimes
+ 
+
+ align:start position:0%
+zeros okay because if because sometimes
+this is going to be a really small
+
+ align:start position:0%
+this is going to be a really small
+ 
+
+ align:start position:0%
+this is going to be a really small
+number so I need to add some leading
+
+ align:start position:0%
+number so I need to add some leading
+ 
+
+ align:start position:0%
+number so I need to add some leading
+zeros before I put my decimal point and
+
+ align:start position:0%
+zeros before I put my decimal point and
+ 
+
+ align:start position:0%
+zeros before I put my decimal point and
+then I put my decimal point and that's
+
+ align:start position:0%
+then I put my decimal point and that's
+ 
+
+ align:start position:0%
+then I put my decimal point and that's
+all this line is doing and then I and
+
+ align:start position:0%
+all this line is doing and then I and
+ 
+
+ align:start position:0%
+all this line is doing and then I and
+then I print my
+
+ align:start position:0%
+then I print my
+ 
+
+ align:start position:0%
+then I print my
+result so python
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tutor all right so step through so this
+
+ align:start position:0%
+tutor all right so step through so this
+ 
+
+ align:start position:0%
+tutor all right so step through so this
+is 625 just like in the slides p is
+
+ align:start position:0%
+is 625 just like in the slides p is
+ 
+
+ align:start position:0%
+is 625 just like in the slides p is
+initially zero so now this Loop is just
+
+ align:start position:0%
+initially zero so now this Loop is just
+ 
+
+ align:start position:0%
+initially zero so now this Loop is just
+incrementing P1 by one to find uh the
+
+ align:start position:0%
+incrementing P1 by one to find uh the
+ 
+
+ align:start position:0%
+incrementing P1 by one to find uh the
+the point where I have a remainder of
+
+ align:start position:0%
+the point where I have a remainder of
+ 
+
+ align:start position:0%
+the point where I have a remainder of
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+so here I'm actually also printing the
+
+ align:start position:0%
+so here I'm actually also printing the
+ 
+
+ align:start position:0%
+so here I'm actually also printing the
+remainder so here we still have a
+
+ align:start position:0%
+remainder so here we still have a
+ 
+
+ align:start position:0%
+remainder so here we still have a
+nonzero remainder right so it's 625 as a
+
+ align:start position:0%
+nonzero remainder right so it's 625 as a
+ 
+
+ align:start position:0%
+nonzero remainder right so it's 625 as a
+remainder 0.25 as a remainder 0.5 as a
+
+ align:start position:0%
+remainder 0.25 as a remainder 0.5 as a
+ 
+
+ align:start position:0%
+remainder 0.25 as a remainder 0.5 as a
+remainder and then at some point I had
+
+ align:start position:0%
+remainder and then at some point I had
+ 
+
+ align:start position:0%
+remainder and then at some point I had
+multiplied it by 2 to the^ of three
+
+ align:start position:0%
+multiplied it by 2 to the^ of three
+ 
+
+ align:start position:0%
+multiplied it by 2 to the^ of three
+because p is three and I had a zero
+
+ align:start position:0%
+because p is three and I had a zero
+ 
+
+ align:start position:0%
+because p is three and I had a zero
+remainder so now I've broken out of that
+
+ align:start position:0%
+remainder so now I've broken out of that
+ 
+
+ align:start position:0%
+remainder so now I've broken out of that
+Loop and I know num is equal to five I
+
+ align:start position:0%
+Loop and I know num is equal to five I
+ 
+
+ align:start position:0%
+Loop and I know num is equal to five I
+multiplied by 2 ^ 3 time 6 to 5 to give
+
+ align:start position:0%
+multiplied by 2 ^ 3 time 6 to 5 to give
+ 
+
+ align:start position:0%
+multiplied by 2 ^ 3 time 6 to 5 to give
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+five so now I need to convert num which
+
+ align:start position:0%
+five so now I need to convert num which
+ 
+
+ align:start position:0%
+five so now I need to convert num which
+is five using this process we did here
+
+ align:start position:0%
+is five using this process we did here
+ 
+
+ align:start position:0%
+is five using this process we did here
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+binary that's what this code is doing
+
+ align:start position:0%
+binary that's what this code is doing
+ 
+
+ align:start position:0%
+binary that's what this code is doing
+and this is exactly this process we had
+
+ align:start position:0%
+and this is exactly this process we had
+ 
+
+ align:start position:0%
+and this is exactly this process we had
+here so I'm creating this result string
+
+ align:start position:0%
+here so I'm creating this result string
+ 
+
+ align:start position:0%
+here so I'm creating this result string
+and then prepending a zero or one
+
+ align:start position:0%
+and then prepending a zero or one
+ 
+
+ align:start position:0%
+and then prepending a zero or one
+whether the number is uh divisible by
+
+ align:start position:0%
+whether the number is uh divisible by
+ 
+
+ align:start position:0%
+whether the number is uh divisible by
+two or
+
+ align:start position:0%
+two or
+ 
+
+ align:start position:0%
+two or
+not so the number five in binary is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one1 okay so that means I have one Z One
+
+ align:start position:0%
+one1 okay so that means I have one Z One
+ 
+
+ align:start position:0%
+one1 okay so that means I have one Z One
+Dot as my binary representation of five
+
+ align:start position:0%
+Dot as my binary representation of five
+ 
+
+ align:start position:0%
+Dot as my binary representation of five
+and now the code is going to go through
+
+ align:start position:0%
+and now the code is going to go through
+ 
+
+ align:start position:0%
+and now the code is going to go through
+this Loop which means it's going to move
+
+ align:start position:0%
+this Loop which means it's going to move
+ 
+
+ align:start position:0%
+this Loop which means it's going to move
+the decimal point to the left three
+
+ align:start position:0%
+the decimal point to the left three
+ 
+
+ align:start position:0%
+the decimal point to the left three
+slots right because I mult because I
+
+ align:start position:0%
+slots right because I mult because I
+ 
+
+ align:start position:0%
+slots right because I mult because I
+have to multiply by two to the^ of three
+
+ align:start position:0%
+have to multiply by two to the^ of three
+ 
+
+ align:start position:0%
+have to multiply by two to the^ of three
+to get the
+
+ align:start position:0%
+to get the
+ 
+
+ align:start position:0%
+to get the
+five so you can see it's going to go
+
+ align:start position:0%
+five so you can see it's going to go
+ 
+
+ align:start position:0%
+five so you can see it's going to go
+Loop
+
+ align:start position:0%
+Loop
+ 
+
+ align:start position:0%
+Loop
+through uh three slots right so here it
+
+ align:start position:0%
+through uh three slots right so here it
+ 
+
+ align:start position:0%
+through uh three slots right so here it
+is it made the0
+
+ align:start position:0%
+is it made the0
+ 
+
+ align:start position:0%
+is it made the0
+one1 and then sorry this bit which I
+
+ align:start position:0%
+one1 and then sorry this bit which I
+ 
+
+ align:start position:0%
+one1 and then sorry this bit which I
+skipped over applies the dot right so it
+
+ align:start position:0%
+skipped over applies the dot right so it
+ 
+
+ align:start position:0%
+skipped over applies the dot right so it
+puts the dot in front of it and then the
+
+ align:start position:0%
+puts the dot in front of it and then the
+ 
+
+ align:start position:0%
+puts the dot in front of it and then the
+last step is to just print the
+
+ align:start position:0%
+last step is to just print the
+ 
+
+ align:start position:0%
+last step is to just print the
+representation so the binary
+
+ align:start position:0%
+representation so the binary
+ 
+
+ align:start position:0%
+representation so the binary
+representation of 6 to5 is 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+101 so here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code and we can run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so
+
+ align:start position:0%
+it so
+ 
+
+ align:start position:0%
+it so
+0.5 the representation is 0.1 0.625
+
+ align:start position:0%
+0.5 the representation is 0.1 0.625
+ 
+
+ align:start position:0%
+0.5 the representation is 0.1 0.625
+which is what we had just done the
+
+ align:start position:0%
+which is what we had just done the
+ 
+
+ align:start position:0%
+which is what we had just done the
+representation is 0. 101 right and we
+
+ align:start position:0%
+representation is 0. 101 right and we
+ 
+
+ align:start position:0%
+representation is 0. 101 right and we
+can play around with a bunch of these
+
+ align:start position:0%
+can play around with a bunch of these
+ 
+
+ align:start position:0%
+can play around with a bunch of these
+values but then when we do something
+
+ align:start position:0%
+values but then when we do something
+ 
+
+ align:start position:0%
+values but then when we do something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+0.1 what is the representation of 0.1
+
+ align:start position:0%
+0.1 what is the representation of 0.1
+ 
+
+ align:start position:0%
+0.1 what is the representation of 0.1
+going to be right because now we can use
+
+ align:start position:0%
+going to be right because now we can use
+ 
+
+ align:start position:0%
+going to be right because now we can use
+this code to get the representation of
+
+ align:start position:0%
+this code to get the representation of
+ 
+
+ align:start position:0%
+this code to get the representation of
+whatever decimal we'd like point one was
+
+ align:start position:0%
+whatever decimal we'd like point one was
+ 
+
+ align:start position:0%
+whatever decimal we'd like point one was
+this Troublesome decimal so let's see
+
+ align:start position:0%
+this Troublesome decimal so let's see
+ 
+
+ align:start position:0%
+this Troublesome decimal so let's see
+exactly what
+
+ align:start position:0%
+exactly what
+ 
+
+ align:start position:0%
+exactly what
+happened well it had to do a whole lot
+
+ align:start position:0%
+happened well it had to do a whole lot
+ 
+
+ align:start position:0%
+happened well it had to do a whole lot
+of Divisions right um it had to test a
+
+ align:start position:0%
+of Divisions right um it had to test a
+ 
+
+ align:start position:0%
+of Divisions right um it had to test a
+whole bunch of powers of two before
+
+ align:start position:0%
+whole bunch of powers of two before
+ 
+
+ align:start position:0%
+whole bunch of powers of two before
+actually got to a a whole number right
+
+ align:start position:0%
+actually got to a a whole number right
+ 
+
+ align:start position:0%
+actually got to a a whole number right
+in fact about 50 of them and we know
+
+ align:start position:0%
+in fact about 50 of them and we know
+ 
+
+ align:start position:0%
+in fact about 50 of them and we know
+that because there's about 50 of these
+
+ align:start position:0%
+that because there's about 50 of these
+ 
+
+ align:start position:0%
+that because there's about 50 of these
+zeros and ones here right so it was
+
+ align:start position:0%
+zeros and ones here right so it was
+ 
+
+ align:start position:0%
+zeros and ones here right so it was
+approximately two to the^ 50 that it had
+
+ align:start position:0%
+approximately two to the^ 50 that it had
+ 
+
+ align:start position:0%
+approximately two to the^ 50 that it had
+to multiply 0.1 by before it got to a
+
+ align:start position:0%
+to multiply 0.1 by before it got to a
+ 
+
+ align:start position:0%
+to multiply 0.1 by before it got to a
+whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number so what that means for us is a
+
+ align:start position:0%
+number so what that means for us is a
+ 
+
+ align:start position:0%
+number so what that means for us is a
+number that's kind of a a a a linear
+
+ align:start position:0%
+number that's kind of a a a a linear
+ 
+
+ align:start position:0%
+number that's kind of a a a a linear
+combination of powers of two is really
+
+ align:start position:0%
+combination of powers of two is really
+ 
+
+ align:start position:0%
+combination of powers of two is really
+easy and fast to compute right something
+
+ align:start position:0%
+easy and fast to compute right something
+ 
+
+ align:start position:0%
+easy and fast to compute right something
+like you know this one here 1 * 23 is
+
+ align:start position:0%
+like you know this one here 1 * 23 is
+ 
+
+ align:start position:0%
+like you know this one here 1 * 23 is
+01 but something like 0.1 which isn't as
+
+ align:start position:0%
+01 but something like 0.1 which isn't as
+ 
+
+ align:start position:0%
+01 but something like 0.1 which isn't as
+as easy to see what the linear
+
+ align:start position:0%
+as easy to see what the linear
+ 
+
+ align:start position:0%
+as easy to see what the linear
+combination of all these powers of two
+
+ align:start position:0%
+combination of all these powers of two
+ 
+
+ align:start position:0%
+combination of all these powers of two
+are is not so easy to compute right and
+
+ align:start position:0%
+are is not so easy to compute right and
+ 
+
+ align:start position:0%
+are is not so easy to compute right and
+in fact we had to use our program to
+
+ align:start position:0%
+in fact we had to use our program to
+ 
+
+ align:start position:0%
+in fact we had to use our program to
+figure out exactly what it is and it for
+
+ align:start position:0%
+figure out exactly what it is and it for
+ 
+
+ align:start position:0%
+figure out exactly what it is and it for
+us it was about 50 these digits long
+
+ align:start position:0%
+us it was about 50 these digits long
+ 
+
+ align:start position:0%
+us it was about 50 these digits long
+which was pretty long right and some of
+
+ align:start position:0%
+which was pretty long right and some of
+ 
+
+ align:start position:0%
+which was pretty long right and some of
+these numbers could be even longer
+
+ align:start position:0%
+these numbers could be even longer
+ 
+
+ align:start position:0%
+these numbers could be even longer
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+infinite so the point here is that
+
+ align:start position:0%
+infinite so the point here is that
+ 
+
+ align:start position:0%
+infinite so the point here is that
+everything in computer memory is
+
+ align:start position:0%
+everything in computer memory is
+ 
+
+ align:start position:0%
+everything in computer memory is
+represented in terms of bits right zeros
+
+ align:start position:0%
+represented in terms of bits right zeros
+ 
+
+ align:start position:0%
+represented in terms of bits right zeros
+and ones the reason we went through this
+
+ align:start position:0%
+and ones the reason we went through this
+ 
+
+ align:start position:0%
+and ones the reason we went through this
+whole computation is because there are
+
+ align:start position:0%
+whole computation is because there are
+ 
+
+ align:start position:0%
+whole computation is because there are
+some numbers that are just going to be
+
+ align:start position:0%
+some numbers that are just going to be
+ 
+
+ align:start position:0%
+some numbers that are just going to be
+way too big to fit inside these inside
+
+ align:start position:0%
+way too big to fit inside these inside
+ 
+
+ align:start position:0%
+way too big to fit inside these inside
+the computer hardware inside these
+
+ align:start position:0%
+the computer hardware inside these
+ 
+
+ align:start position:0%
+the computer hardware inside these
+representations okay so for integers
+
+ align:start position:0%
+representations okay so for integers
+ 
+
+ align:start position:0%
+representations okay so for integers
+it's straightforward to deal with we had
+
+ align:start position:0%
+it's straightforward to deal with we had
+ 
+
+ align:start position:0%
+it's straightforward to deal with we had
+a really fast way to compute the uh the
+
+ align:start position:0%
+a really fast way to compute the uh the
+ 
+
+ align:start position:0%
+a really fast way to compute the uh the
+the base the base to
+
+ align:start position:0%
+the base the base to
+ 
+
+ align:start position:0%
+the base the base to
+representation but for fractions it's a
+
+ align:start position:0%
+representation but for fractions it's a
+ 
+
+ align:start position:0%
+representation but for fractions it's a
+lot harder and those numbers can be
+
+ align:start position:0%
+lot harder and those numbers can be
+ 
+
+ align:start position:0%
+lot harder and those numbers can be
+really really
+
+ align:start position:0%
+really really
+ 
+
+ align:start position:0%
+really really
+big so now how are these numbers
+
+ align:start position:0%
+big so now how are these numbers
+ 
+
+ align:start position:0%
+big so now how are these numbers
+actually represented inside computer
+
+ align:start position:0%
+actually represented inside computer
+ 
+
+ align:start position:0%
+actually represented inside computer
+memory so they're actually being
+
+ align:start position:0%
+memory so they're actually being
+ 
+
+ align:start position:0%
+memory so they're actually being
+represented in two
+
+ align:start position:0%
+represented in two
+ 
+
+ align:start position:0%
+represented in two
+pieces one is uh one piece is the
+
+ align:start position:0%
+pieces one is uh one piece is the
+ 
+
+ align:start position:0%
+pieces one is uh one piece is the
+significant digit and the other piece is
+
+ align:start position:0%
+significant digit and the other piece is
+ 
+
+ align:start position:0%
+significant digit and the other piece is
+the power of two Okay so
+
+ align:start position:0%
+the power of two Okay so
+ 
+
+ align:start position:0%
+the power of two Okay so
+if we had the representation one comma
+
+ align:start position:0%
+if we had the representation one comma
+ 
+
+ align:start position:0%
+if we had the representation one comma
+one inside computer memory basically the
+
+ align:start position:0%
+one inside computer memory basically the
+ 
+
+ align:start position:0%
+one inside computer memory basically the
+significant digit is one and the Power
+
+ align:start position:0%
+significant digit is one and the Power
+ 
+
+ align:start position:0%
+significant digit is one and the Power
+of Two is one so that means we're going
+
+ align:start position:0%
+of Two is one so that means we're going
+ 
+
+ align:start position:0%
+of Two is one so that means we're going
+to take this one dot and give it the
+
+ align:start position:0%
+to take this one dot and give it the
+ 
+
+ align:start position:0%
+to take this one dot and give it the
+power of two so we're going to add a
+
+ align:start position:0%
+power of two so we're going to add a
+ 
+
+ align:start position:0%
+power of two so we're going to add a
+zero after it so this is the binary 2
+
+ align:start position:0%
+zero after it so this is the binary 2
+ 
+
+ align:start position:0%
+zero after it so this is the binary 2
+representation we basically just move
+
+ align:start position:0%
+representation we basically just move
+ 
+
+ align:start position:0%
+representation we basically just move
+the Dot from here to here and then the
+
+ align:start position:0%
+the Dot from here to here and then the
+ 
+
+ align:start position:0%
+the Dot from here to here and then the
+number one zero and base two is 2.0
+
+ align:start position:0%
+number one zero and base two is 2.0
+ 
+
+ align:start position:0%
+number one zero and base two is 2.0
+right that's what we have on the first
+
+ align:start position:0%
+right that's what we have on the first
+ 
+
+ align:start position:0%
+right that's what we have on the first
+line one comma negative 1 that repres
+
+ align:start position:0%
+line one comma negative 1 that repres
+ 
+
+ align:start position:0%
+line one comma negative 1 that repres
+representation means I'm going to take
+
+ align:start position:0%
+representation means I'm going to take
+ 
+
+ align:start position:0%
+representation means I'm going to take
+the significant digit one and the Power
+
+ align:start position:0%
+the significant digit one and the Power
+ 
+
+ align:start position:0%
+the significant digit one and the Power
+of Two is negative - 1 so I'm going to
+
+ align:start position:0%
+of Two is negative - 1 so I'm going to
+ 
+
+ align:start position:0%
+of Two is negative - 1 so I'm going to
+take this decimal point and move it to
+
+ align:start position:0%
+take this decimal point and move it to
+ 
+
+ align:start position:0%
+take this decimal point and move it to
+the left one so this is going to
+
+ align:start position:0%
+the left one so this is going to
+ 
+
+ align:start position:0%
+the left one so this is going to
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+0.1 right that's the this number 0.1
+
+ align:start position:0%
+0.1 right that's the this number 0.1
+ 
+
+ align:start position:0%
+0.1 right that's the this number 0.1
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+0.5 this is base two this is base 10 and
+
+ align:start position:0%
+0.5 this is base two this is base 10 and
+ 
+
+ align:start position:0%
+0.5 this is base two this is base 10 and
+just to bring the point home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+125 okay is going to be 125 as
+
+ align:start position:0%
+125 okay is going to be 125 as
+ 
+
+ align:start position:0%
+125 okay is going to be 125 as
+significant digit and 2 to the
+
+ align:start position:0%
+significant digit and 2 to the
+ 
+
+ align:start position:0%
+significant digit and 2 to the
+-2 how is this going to work well we're
+
+ align:start position:0%
+-2 how is this going to work well we're
+ 
+
+ align:start position:0%
+-2 how is this going to work well we're
+going to take the 125 and convert it to
+
+ align:start position:0%
+going to take the 125 and convert it to
+ 
+
+ align:start position:0%
+going to take the 125 and convert it to
+a power of two so it's what is this I'm
+
+ align:start position:0%
+a power of two so it's what is this I'm
+ 
+
+ align:start position:0%
+a power of two so it's what is this I'm
+not going to remember what it is one one
+
+ align:start position:0%
+not going to remember what it is one one
+ 
+
+ align:start position:0%
+not going to remember what it is one one
+one one
+
+ align:start position:0%
+one one
+ 
+
+ align:start position:0%
+one one
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+zero one this is what 125 is in base two
+
+ align:start position:0%
+zero one this is what 125 is in base two
+ 
+
+ align:start position:0%
+zero one this is what 125 is in base two
+but the signif but the uh the exponent
+
+ align:start position:0%
+but the signif but the uh the exponent
+ 
+
+ align:start position:0%
+but the signif but the uh the exponent
+here tells me it's -2 so instead of
+
+ align:start position:0%
+here tells me it's -2 so instead of
+ 
+
+ align:start position:0%
+here tells me it's -2 so instead of
+putting the dot here I'm going to move
+
+ align:start position:0%
+putting the dot here I'm going to move
+ 
+
+ align:start position:0%
+putting the dot here I'm going to move
+it one two over so this is the actual
+
+ align:start position:0%
+it one two over so this is the actual
+ 
+
+ align:start position:0%
+it one two over so this is the actual
+number I'm representing in memory and
+
+ align:start position:0%
+number I'm representing in memory and
+ 
+
+ align:start position:0%
+number I'm representing in memory and
+now I can just convert the two pieces
+
+ align:start position:0%
+now I can just convert the two pieces
+ 
+
+ align:start position:0%
+now I can just convert the two pieces
+separately so this is going to be
+
+ align:start position:0%
+separately so this is going to be
+ 
+
+ align:start position:0%
+separately so this is going to be
+31 dot uh what is this 25 right
+
+ align:start position:0%
+31 dot uh what is this 25 right
+ 
+
+ align:start position:0%
+31 dot uh what is this 25 right
+yeah okay so this is how computers
+
+ align:start position:0%
+yeah okay so this is how computers
+ 
+
+ align:start position:0%
+yeah okay so this is how computers
+actually represent numbers inside
+
+ align:start position:0%
+actually represent numbers inside
+ 
+
+ align:start position:0%
+actually represent numbers inside
+memory okay and we call this uh the
+
+ align:start position:0%
+memory okay and we call this uh the
+ 
+
+ align:start position:0%
+memory okay and we call this uh the
+object type which is you know decimal or
+
+ align:start position:0%
+object type which is you know decimal or
+ 
+
+ align:start position:0%
+object type which is you know decimal or
+real number uh a float because this
+
+ align:start position:0%
+real number uh a float because this
+ 
+
+ align:start position:0%
+real number uh a float because this
+decimal point kind of floats around
+
+ align:start position:0%
+decimal point kind of floats around
+ 
+
+ align:start position:0%
+decimal point kind of floats around
+okay or 31.25 for
+
+ align:start position:0%
+okay or 31.25 for
+ 
+
+ align:start position:0%
+okay or 31.25 for
+number uh base 10 base 10 is
+
+ align:start position:0%
+number uh base 10 base 10 is
+ 
+
+ align:start position:0%
+number uh base 10 base 10 is
+31.25 and 125 is how it's represented
+
+ align:start position:0%
+31.25 and 125 is how it's represented
+ 
+
+ align:start position:0%
+31.25 and 125 is how it's represented
+inside memory so it's a base 10 sort of
+
+ align:start position:0%
+inside memory so it's a base 10 sort of
+ 
+
+ align:start position:0%
+inside memory so it's a base 10 sort of
+thing and then what is the power of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two yeah so there's a couple conversions
+
+ align:start position:0%
+two yeah so there's a couple conversions
+ 
+
+ align:start position:0%
+two yeah so there's a couple conversions
+being done here we're representing the
+
+ align:start position:0%
+being done here we're representing the
+ 
+
+ align:start position:0%
+being done here we're representing the
+the the Bas 125 is base 10 and and how
+
+ align:start position:0%
+the the Bas 125 is base 10 and and how
+ 
+
+ align:start position:0%
+the the Bas 125 is base 10 and and how
+much we need to move the decimal point
+
+ align:start position:0%
+much we need to move the decimal point
+ 
+
+ align:start position:0%
+much we need to move the decimal point
+but first we need to make the conversion
+
+ align:start position:0%
+but first we need to make the conversion
+ 
+
+ align:start position:0%
+but first we need to make the conversion
+of 125 to Binary which is this long
+
+ align:start position:0%
+of 125 to Binary which is this long
+ 
+
+ align:start position:0%
+of 125 to Binary which is this long
+thing here not counting this decimal
+
+ align:start position:0%
+thing here not counting this decimal
+ 
+
+ align:start position:0%
+thing here not counting this decimal
+point the Nega -2 dos us we need to move
+
+ align:start position:0%
+point the Nega -2 dos us we need to move
+ 
+
+ align:start position:0%
+point the Nega -2 dos us we need to move
+the decimal point over and then we have
+
+ align:start position:0%
+the decimal point over and then we have
+ 
+
+ align:start position:0%
+the decimal point over and then we have
+the actual number we're trying to store
+
+ align:start position:0%
+the actual number we're trying to store
+ 
+
+ align:start position:0%
+the actual number we're trying to store
+right and the reason we're doing this is
+
+ align:start position:0%
+right and the reason we're doing this is
+ 
+
+ align:start position:0%
+right and the reason we're doing this is
+because we're mostly just storing
+
+ align:start position:0%
+because we're mostly just storing
+ 
+
+ align:start position:0%
+because we're mostly just storing
+numbers as whole numbers inside the
+
+ align:start position:0%
+numbers as whole numbers inside the
+ 
+
+ align:start position:0%
+numbers as whole numbers inside the
+memory we're not storing
+
+ align:start position:0%
+memory we're not storing
+ 
+
+ align:start position:0%
+memory we're not storing
+fractions right yeah I'm just a little
+
+ align:start position:0%
+fractions right yeah I'm just a little
+ 
+
+ align:start position:0%
+fractions right yeah I'm just a little
+confused because you went to all that
+
+ align:start position:0%
+confused because you went to all that
+ 
+
+ align:start position:0%
+confused because you went to all that
+trouble to convert the
+
+ align:start position:0%
+trouble to convert the
+ 
+
+ align:start position:0%
+trouble to convert the
+oh know but that was for fraction that
+
+ align:start position:0%
+oh know but that was for fraction that
+ 
+
+ align:start position:0%
+oh know but that was for fraction that
+was for fractions exactly yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so in the end we did all that
+
+ align:start position:0%
+yeah okay so in the end we did all that
+ 
+
+ align:start position:0%
+yeah okay so in the end we did all that
+because we're trying to figure out the
+
+ align:start position:0%
+because we're trying to figure out the
+ 
+
+ align:start position:0%
+because we're trying to figure out the
+error right why do we get this error
+
+ align:start position:0%
+error right why do we get this error
+ 
+
+ align:start position:0%
+error right why do we get this error
+inside our
+
+ align:start position:0%
+inside our
+ 
+
+ align:start position:0%
+inside our
+programs well in the end it's because
+
+ align:start position:0%
+programs well in the end it's because
+ 
+
+ align:start position:0%
+programs well in the end it's because
+computers have a finite number of bits
+
+ align:start position:0%
+computers have a finite number of bits
+ 
+
+ align:start position:0%
+computers have a finite number of bits
+to store data most modern computers
+
+ align:start position:0%
+to store data most modern computers
+ 
+
+ align:start position:0%
+to store data most modern computers
+maybe have 32 maybe 64 bits to represent
+
+ align:start position:0%
+maybe have 32 maybe 64 bits to represent
+ 
+
+ align:start position:0%
+maybe have 32 maybe 64 bits to represent
+significant ific digits right so if we
+
+ align:start position:0%
+significant ific digits right so if we
+ 
+
+ align:start position:0%
+significant ific digits right so if we
+have 32 slots in order to put these
+
+ align:start position:0%
+have 32 slots in order to put these
+ 
+
+ align:start position:0%
+have 32 slots in order to put these
+significant digits if our number base
+
+ align:start position:0%
+significant digits if our number base
+ 
+
+ align:start position:0%
+significant digits if our number base
+two representation was 50 digits long
+
+ align:start position:0%
+two representation was 50 digits long
+ 
+
+ align:start position:0%
+two representation was 50 digits long
+then we're going to truncate at 32 we
+
+ align:start position:0%
+then we're going to truncate at 32 we
+ 
+
+ align:start position:0%
+then we're going to truncate at 32 we
+can't store those extra bits right and
+
+ align:start position:0%
+can't store those extra bits right and
+ 
+
+ align:start position:0%
+can't store those extra bits right and
+so a number like 0.1 ends up actually
+
+ align:start position:0%
+so a number like 0.1 ends up actually
+ 
+
+ align:start position:0%
+so a number like 0.1 ends up actually
+being an approximation in base two
+
+ align:start position:0%
+being an approximation in base two
+ 
+
+ align:start position:0%
+being an approximation in base two
+inside computer memory we're not able to
+
+ align:start position:0%
+inside computer memory we're not able to
+ 
+
+ align:start position:0%
+inside computer memory we're not able to
+store that number exactly perfectly so
+
+ align:start position:0%
+store that number exactly perfectly so
+ 
+
+ align:start position:0%
+store that number exactly perfectly so
+it becomes an approximation
+
+ align:start position:0%
+it becomes an approximation
+ 
+
+ align:start position:0%
+it becomes an approximation
+right and the approximation actually
+
+ align:start position:0%
+right and the approximation actually
+ 
+
+ align:start position:0%
+right and the approximation actually
+ends up being at the 30C bit right that
+
+ align:start position:0%
+ends up being at the 30C bit right that
+ 
+
+ align:start position:0%
+ends up being at the 30C bit right that
+either will be zero or one you know
+
+ align:start position:0%
+either will be zero or one you know
+ 
+
+ align:start position:0%
+either will be zero or one you know
+depending on how we decide to truncate
+
+ align:start position:0%
+depending on how we decide to truncate
+ 
+
+ align:start position:0%
+depending on how we decide to truncate
+and so the error is actually two to the
+
+ align:start position:0%
+and so the error is actually two to the
+ 
+
+ align:start position:0%
+and so the error is actually two to the
+2 to the - 32 right which is on the
+
+ align:start position:0%
+2 to the - 32 right which is on the
+ 
+
+ align:start position:0%
+2 to the - 32 right which is on the
+order of 2 * 10 the -10 which seems
+
+ align:start position:0%
+order of 2 * 10 the -10 which seems
+ 
+
+ align:start position:0%
+order of 2 * 10 the -10 which seems
+pretty small right it's it's a very
+
+ align:start position:0%
+pretty small right it's it's a very
+ 
+
+ align:start position:0%
+pretty small right it's it's a very
+small error but we just saw that that
+
+ align:start position:0%
+small error but we just saw that that
+ 
+
+ align:start position:0%
+small error but we just saw that that
+error accumulates really really quickly
+
+ align:start position:0%
+error accumulates really really quickly
+ 
+
+ align:start position:0%
+error accumulates really really quickly
+right so while 0.1 has an error at the 2
+
+ align:start position:0%
+right so while 0.1 has an error at the 2
+ 
+
+ align:start position:0%
+right so while 0.1 has an error at the 2
+to the3 2 slot if we take that error and
+
+ align:start position:0%
+to the3 2 slot if we take that error and
+ 
+
+ align:start position:0%
+to the3 2 slot if we take that error and
+we just kind of accumulate it over 10
+
+ align:start position:0%
+we just kind of accumulate it over 10
+ 
+
+ align:start position:0%
+we just kind of accumulate it over 10
+increments as we had this Loop that went
+
+ align:start position:0%
+increments as we had this Loop that went
+ 
+
+ align:start position:0%
+increments as we had this Loop that went
+through 10 times we see that that error
+
+ align:start position:0%
+through 10 times we see that that error
+ 
+
+ align:start position:0%
+through 10 times we see that that error
+ends up becoming a big problem right we
+
+ align:start position:0%
+ends up becoming a big problem right we
+ 
+
+ align:start position:0%
+ends up becoming a big problem right we
+see that it actually at the negative
+
+ align:start position:0%
+see that it actually at the negative
+ 
+
+ align:start position:0%
+see that it actually at the negative
+16th slot or something like that it you
+
+ align:start position:0%
+16th slot or something like that it you
+ 
+
+ align:start position:0%
+16th slot or something like that it you
+know it starts to uh to round to the
+
+ align:start position:0%
+know it starts to uh to round to the
+ 
+
+ align:start position:0%
+know it starts to uh to round to the
+wrong to the wrong thing and so we see
+
+ align:start position:0%
+wrong to the wrong thing and so we see
+ 
+
+ align:start position:0%
+wrong to the wrong thing and so we see
+things like this right we expect it to
+
+ align:start position:0%
+things like this right we expect it to
+ 
+
+ align:start position:0%
+things like this right we expect it to
+be one but it's not one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the moral of the story is we
+
+ align:start position:0%
+okay so the moral of the story is we
+ 
+
+ align:start position:0%
+okay so the moral of the story is we
+don't want to use equivalents right the
+
+ align:start position:0%
+don't want to use equivalents right the
+ 
+
+ align:start position:0%
+don't want to use equivalents right the
+the equivalent operator the equ equal
+
+ align:start position:0%
+the equivalent operator the equ equal
+ 
+
+ align:start position:0%
+the equivalent operator the equ equal
+operator when we're comparing uh
+
+ align:start position:0%
+operator when we're comparing uh
+ 
+
+ align:start position:0%
+operator when we're comparing uh
+comparing floats because of Errors like
+
+ align:start position:0%
+comparing floats because of Errors like
+ 
+
+ align:start position:0%
+comparing floats because of Errors like
+this the errors can accumulate and then
+
+ align:start position:0%
+this the errors can accumulate and then
+ 
+
+ align:start position:0%
+this the errors can accumulate and then
+we start getting the wrong answer and
+
+ align:start position:0%
+we start getting the wrong answer and
+ 
+
+ align:start position:0%
+we start getting the wrong answer and
+then your programs end up not doing what
+
+ align:start position:0%
+then your programs end up not doing what
+ 
+
+ align:start position:0%
+then your programs end up not doing what
+you expect them to do okay so we always
+
+ align:start position:0%
+you expect them to do okay so we always
+ 
+
+ align:start position:0%
+you expect them to do okay so we always
+want to test whether some float is
+
+ align:start position:0%
+want to test whether some float is
+ 
+
+ align:start position:0%
+want to test whether some float is
+within some Epsilon of another
+
+ align:start position:0%
+within some Epsilon of another
+ 
+
+ align:start position:0%
+within some Epsilon of another
+float and so that brings us to
+
+ align:start position:0%
+float and so that brings us to
+ 
+
+ align:start position:0%
+float and so that brings us to
+approximation method last lecture we saw
+
+ align:start position:0%
+approximation method last lecture we saw
+ 
+
+ align:start position:0%
+approximation method last lecture we saw
+the guess and check method as a really
+
+ align:start position:0%
+the guess and check method as a really
+ 
+
+ align:start position:0%
+the guess and check method as a really
+simple algorithm for solving problems we
+
+ align:start position:0%
+simple algorithm for solving problems we
+ 
+
+ align:start position:0%
+simple algorithm for solving problems we
+have a set number of solutions that we
+
+ align:start position:0%
+have a set number of solutions that we
+ 
+
+ align:start position:0%
+have a set number of solutions that we
+can check and then we check each one by
+
+ align:start position:0%
+can check and then we check each one by
+ 
+
+ align:start position:0%
+can check and then we check each one by
+one and then at some point we either
+
+ align:start position:0%
+one and then at some point we either
+ 
+
+ align:start position:0%
+one and then at some point we either
+find the solution or we've checked all
+
+ align:start position:0%
+find the solution or we've checked all
+ 
+
+ align:start position:0%
+find the solution or we've checked all
+that we can check and we haven't found
+
+ align:start position:0%
+that we can check and we haven't found
+ 
+
+ align:start position:0%
+that we can check and we haven't found
+the solution right it's usually an
+
+ align:start position:0%
+the solution right it's usually an
+ 
+
+ align:start position:0%
+the solution right it's usually an
+integer what we're kind of the things
+
+ align:start position:0%
+integer what we're kind of the things
+ 
+
+ align:start position:0%
+integer what we're kind of the things
+that we're checking but as long as you
+
+ align:start position:0%
+that we're checking but as long as you
+ 
+
+ align:start position:0%
+that we're checking but as long as you
+have some finite set of values you can
+
+ align:start position:0%
+have some finite set of values you can
+ 
+
+ align:start position:0%
+have some finite set of values you can
+check for a solution
+
+ align:start position:0%
+check for a solution
+ 
+
+ align:start position:0%
+check for a solution
+through guess and check is totally
+
+ align:start position:0%
+through guess and check is totally
+ 
+
+ align:start position:0%
+through guess and check is totally
+applicable
+
+ align:start position:0%
+applicable
+ 
+
+ align:start position:0%
+applicable
+okay but the problem is it's a little
+
+ align:start position:0%
+okay but the problem is it's a little
+ 
+
+ align:start position:0%
+okay but the problem is it's a little
+bit limiting right it doesn't give us an
+
+ align:start position:0%
+bit limiting right it doesn't give us an
+ 
+
+ align:start position:0%
+bit limiting right it doesn't give us an
+actual approximation to the square root
+
+ align:start position:0%
+actual approximation to the square root
+ 
+
+ align:start position:0%
+actual approximation to the square root
+if you remember the code we wrote last
+
+ align:start position:0%
+if you remember the code we wrote last
+ 
+
+ align:start position:0%
+if you remember the code we wrote last
+time it didn't actually say I'm
+
+ align:start position:0%
+time it didn't actually say I'm
+ 
+
+ align:start position:0%
+time it didn't actually say I'm
+approximating the square root uh of you
+
+ align:start position:0%
+approximating the square root uh of you
+ 
+
+ align:start position:0%
+approximating the square root uh of you
+know five to be 1.4 something or
+
+ align:start position:0%
+know five to be 1.4 something or
+ 
+
+ align:start position:0%
+know five to be 1.4 something or
+whatever it is or 2 point something
+
+ align:start position:0%
+whatever it is or 2 point something
+ 
+
+ align:start position:0%
+whatever it is or 2 point something
+right it was just able to tell me the
+
+ align:start position:0%
+right it was just able to tell me the
+ 
+
+ align:start position:0%
+right it was just able to tell me the
+square root of a perfect square or that
+
+ align:start position:0%
+square root of a perfect square or that
+ 
+
+ align:start position:0%
+square root of a perfect square or that
+the number you gave me is not a perfect
+
+ align:start position:0%
+the number you gave me is not a perfect
+ 
+
+ align:start position:0%
+the number you gave me is not a perfect
+square and so it's a really limiting
+
+ align:start position:0%
+square and so it's a really limiting
+ 
+
+ align:start position:0%
+square and so it's a really limiting
+algorithm but the approximation method
+
+ align:start position:0%
+algorithm but the approximation method
+ 
+
+ align:start position:0%
+algorithm but the approximation method
+the one we're going to see today
+
+ align:start position:0%
+the one we're going to see today
+ 
+
+ align:start position:0%
+the one we're going to see today
+actually is going to be able to give us
+
+ align:start position:0%
+actually is going to be able to give us
+ 
+
+ align:start position:0%
+actually is going to be able to give us
+an approximation to the square root of
+
+ align:start position:0%
+an approximation to the square root of
+ 
+
+ align:start position:0%
+an approximation to the square root of
+any number okay so it's better than
+
+ align:start position:0%
+any number okay so it's better than
+ 
+
+ align:start position:0%
+any number okay so it's better than
+guess and check because we don't just
+
+ align:start position:0%
+guess and check because we don't just
+ 
+
+ align:start position:0%
+guess and check because we don't just
+want the correct answer or nothing it's
+
+ align:start position:0%
+want the correct answer or nothing it's
+ 
+
+ align:start position:0%
+want the correct answer or nothing it's
+not an All or Nothing kind of situation
+
+ align:start position:0%
+not an All or Nothing kind of situation
+ 
+
+ align:start position:0%
+not an All or Nothing kind of situation
+it's that we can approximate the answer
+
+ align:start position:0%
+it's that we can approximate the answer
+ 
+
+ align:start position:0%
+it's that we can approximate the answer
+to some
+
+ align:start position:0%
+to some
+ 
+
+ align:start position:0%
+to some
+degree so we're going to use guess and
+
+ align:start position:0%
+degree so we're going to use guess and
+ 
+
+ align:start position:0%
+degree so we're going to use guess and
+check when the exact answer that we want
+
+ align:start position:0%
+check when the exact answer that we want
+ 
+
+ align:start position:0%
+check when the exact answer that we want
+might not be accessible right we need
+
+ align:start position:0%
+might not be accessible right we need
+ 
+
+ align:start position:0%
+might not be accessible right we need
+some way to find an answer that's just
+
+ align:start position:0%
+some way to find an answer that's just
+ 
+
+ align:start position:0%
+some way to find an answer that's just
+good enough and approximation methods
+
+ align:start position:0%
+good enough and approximation methods
+ 
+
+ align:start position:0%
+good enough and approximation methods
+will not always and not usually actually
+
+ align:start position:0%
+will not always and not usually actually
+ 
+
+ align:start position:0%
+will not always and not usually actually
+most of the time will not give us the
+
+ align:start position:0%
+most of the time will not give us the
+ 
+
+ align:start position:0%
+most of the time will not give us the
+right answer they'll usually give us an
+
+ align:start position:0%
+right answer they'll usually give us an
+ 
+
+ align:start position:0%
+right answer they'll usually give us an
+approximation that's good enough okay
+
+ align:start position:0%
+approximation that's good enough okay
+ 
+
+ align:start position:0%
+approximation that's good enough okay
+and approximation methods these they
+
+ align:start position:0%
+and approximation methods these they
+ 
+
+ align:start position:0%
+and approximation methods these they
+came about because of the exhaustive
+
+ align:start position:0%
+came about because of the exhaustive
+ 
+
+ align:start position:0%
+came about because of the exhaustive
+enumeration limitation right we're not
+
+ align:start position:0%
+enumeration limitation right we're not
+ 
+
+ align:start position:0%
+enumeration limitation right we're not
+able to test all the possible values to
+
+ align:start position:0%
+able to test all the possible values to
+ 
+
+ align:start position:0%
+able to test all the possible values to
+find the exact square root of a number
+
+ align:start position:0%
+find the exact square root of a number
+ 
+
+ align:start position:0%
+find the exact square root of a number
+right because those values are all
+
+ align:start position:0%
+right because those values are all
+ 
+
+ align:start position:0%
+right because those values are all
+infinite so floating points come into
+
+ align:start position:0%
+infinite so floating points come into
+ 
+
+ align:start position:0%
+infinite so floating points come into
+play here the whole thing we've been
+
+ align:start position:0%
+play here the whole thing we've been
+ 
+
+ align:start position:0%
+play here the whole thing we've been
+talking about at the beginning of this
+
+ align:start position:0%
+talking about at the beginning of this
+ 
+
+ align:start position:0%
+talking about at the beginning of this
+lecture and last of last and last last
+
+ align:start position:0%
+lecture and last of last and last last
+ 
+
+ align:start position:0%
+lecture and last of last and last last
+time floating points come into play here
+
+ align:start position:0%
+time floating points come into play here
+ 
+
+ align:start position:0%
+time floating points come into play here
+because they're very important to this
+
+ align:start position:0%
+because they're very important to this
+ 
+
+ align:start position:0%
+because they're very important to this
+method now that we're comparing floats
+
+ align:start position:0%
+method now that we're comparing floats
+ 
+
+ align:start position:0%
+method now that we're comparing floats
+we're have to we're going to have to be
+
+ align:start position:0%
+we're have to we're going to have to be
+ 
+
+ align:start position:0%
+we're have to we're going to have to be
+careful about how we actually do the
+
+ align:start position:0%
+careful about how we actually do the
+ 
+
+ align:start position:0%
+careful about how we actually do the
+comparison so how can we approximate the
+
+ align:start position:0%
+comparison so how can we approximate the
+ 
+
+ align:start position:0%
+comparison so how can we approximate the
+square root well instead of looking at
+
+ align:start position:0%
+square root well instead of looking at
+ 
+
+ align:start position:0%
+square root well instead of looking at
+just whole numbers and saying whether we
+
+ align:start position:0%
+just whole numbers and saying whether we
+ 
+
+ align:start position:0%
+just whole numbers and saying whether we
+found the root or not what we're going
+
+ align:start position:0%
+found the root or not what we're going
+ 
+
+ align:start position:0%
+found the root or not what we're going
+to do is have smaller increments so no
+
+ align:start position:0%
+to do is have smaller increments so no
+ 
+
+ align:start position:0%
+to do is have smaller increments so no
+longer are we doing just integer guess
+
+ align:start position:0%
+longer are we doing just integer guess
+ 
+
+ align:start position:0%
+longer are we doing just integer guess
+and check we're can do 0.1 2 3 point 4
+
+ align:start position:0%
+and check we're can do 0.1 2 3 point 4
+ 
+
+ align:start position:0%
+and check we're can do 0.1 2 3 point 4
+and so on until we get to a guess that's
+
+ align:start position:0%
+and so on until we get to a guess that's
+ 
+
+ align:start position:0%
+and so on until we get to a guess that's
+close enough to X right so we say that
+
+ align:start position:0%
+close enough to X right so we say that
+ 
+
+ align:start position:0%
+close enough to X right so we say that
+2.1 or whatever is good enough to the
+
+ align:start position:0%
+2.1 or whatever is good enough to the
+ 
+
+ align:start position:0%
+2.1 or whatever is good enough to the
+square root of
+
+ align:start position:0%
+square root of
+ 
+
+ align:start position:0%
+square root of
+five what does it mean to be good enough
+
+ align:start position:0%
+five what does it mean to be good enough
+ 
+
+ align:start position:0%
+five what does it mean to be good enough
+right suppose we wanted to find this
+
+ align:start position:0%
+right suppose we wanted to find this
+ 
+
+ align:start position:0%
+right suppose we wanted to find this
+approximation to the square root right
+
+ align:start position:0%
+approximation to the square root right
+ 
+
+ align:start position:0%
+approximation to the square root right
+the guess and check was not able to do
+
+ align:start position:0%
+the guess and check was not able to do
+ 
+
+ align:start position:0%
+the guess and check was not able to do
+this for us but the approximation method
+
+ align:start position:0%
+this for us but the approximation method
+ 
+
+ align:start position:0%
+this for us but the approximation method
+can so what we're asking for can we find
+
+ align:start position:0%
+can so what we're asking for can we find
+ 
+
+ align:start position:0%
+can so what we're asking for can we find
+a root such that that root times that
+
+ align:start position:0%
+a root such that that root times that
+ 
+
+ align:start position:0%
+a root such that that root times that
+root times itself is equal to X right
+
+ align:start position:0%
+root times itself is equal to X right
+ 
+
+ align:start position:0%
+root times itself is equal to X right
+and we're going to do this such that we
+
+ align:start position:0%
+and we're going to do this such that we
+ 
+
+ align:start position:0%
+and we're going to do this such that we
+have a good enough
+
+ align:start position:0%
+have a good enough
+ 
+
+ align:start position:0%
+have a good enough
+approximation so that means that root
+
+ align:start position:0%
+approximation so that means that root
+ 
+
+ align:start position:0%
+approximation so that means that root
+that we're going to find minus
+
+ align:start position:0%
+that we're going to find minus
+ 
+
+ align:start position:0%
+that we're going to find minus
+X is going to be less than some Epsilon
+
+ align:start position:0%
+X is going to be less than some Epsilon
+ 
+
+ align:start position:0%
+X is going to be less than some Epsilon
+or the absolute value of that
+
+ align:start position:0%
+or the absolute value of that
+ 
+
+ align:start position:0%
+or the absolute value of that
+subtraction is going to be less than
+
+ align:start position:0%
+subtraction is going to be less than
+ 
+
+ align:start position:0%
+subtraction is going to be less than
+Epsilon right so in where we did
+
+ align:start position:0%
+Epsilon right so in where we did
+ 
+
+ align:start position:0%
+Epsilon right so in where we did
+incremental step by step we're going to
+
+ align:start position:0%
+incremental step by step we're going to
+ 
+
+ align:start position:0%
+incremental step by step we're going to
+go through as long as we are within or
+
+ align:start position:0%
+go through as long as we are within or
+ 
+
+ align:start position:0%
+go through as long as we are within or
+until we are within some Epsilon of
+
+ align:start position:0%
+until we are within some Epsilon of
+ 
+
+ align:start position:0%
+until we are within some Epsilon of
+X okay so the algorithm will be as
+
+ align:start position:0%
+X okay so the algorithm will be as
+ 
+
+ align:start position:0%
+X okay so the algorithm will be as
+follows we're going to start with a
+
+ align:start position:0%
+follows we're going to start with a
+ 
+
+ align:start position:0%
+follows we're going to start with a
+guess that we know is too small so for
+
+ align:start position:0%
+guess that we know is too small so for
+ 
+
+ align:start position:0%
+guess that we know is too small so for
+the square root of a number we let's
+
+ align:start position:0%
+the square root of a number we let's
+ 
+
+ align:start position:0%
+the square root of a number we let's
+start with zero and then we're going to
+
+ align:start position:0%
+start with zero and then we're going to
+ 
+
+ align:start position:0%
+start with zero and then we're going to
+increment it by a really small value
+
+ align:start position:0%
+increment it by a really small value
+ 
+
+ align:start position:0%
+increment it by a really small value
+with guess and check we incremented it
+
+ align:start position:0%
+with guess and check we incremented it
+ 
+
+ align:start position:0%
+with guess and check we incremented it
+by integers with this uh particular
+
+ align:start position:0%
+by integers with this uh particular
+ 
+
+ align:start position:0%
+by integers with this uh particular
+method we can increment it by 05s or 0.
+
+ align:start position:0%
+method we can increment it by 05s or 0.
+ 
+
+ align:start position:0%
+method we can increment it by 05s or 0.
+ones or 0.001 whatever we'd like okay
+
+ align:start position:0%
+ones or 0.001 whatever we'd like okay
+ 
+
+ align:start position:0%
+ones or 0.001 whatever we'd like okay
+that new increment gives us a new guess
+
+ align:start position:0%
+that new increment gives us a new guess
+ 
+
+ align:start position:0%
+that new increment gives us a new guess
+we're going to check whether this new
+
+ align:start position:0%
+we're going to check whether this new
+ 
+
+ align:start position:0%
+we're going to check whether this new
+guess is now close enough to X if it is
+
+ align:start position:0%
+guess is now close enough to X if it is
+ 
+
+ align:start position:0%
+guess is now close enough to X if it is
+we're good and if it's not we're just
+
+ align:start position:0%
+we're good and if it's not we're just
+ 
+
+ align:start position:0%
+we're good and if it's not we're just
+going to keep incrementing the guess
+
+ align:start position:0%
+going to keep incrementing the guess
+ 
+
+ align:start position:0%
+going to keep incrementing the guess
+until we get close enough to the actual
+
+ align:start position:0%
+until we get close enough to the actual
+ 
+
+ align:start position:0%
+until we get close enough to the actual
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+okay so we are we have two parameters we
+
+ align:start position:0%
+okay so we are we have two parameters we
+ 
+
+ align:start position:0%
+okay so we are we have two parameters we
+actually need to set in the
+
+ align:start position:0%
+actually need to set in the
+ 
+
+ align:start position:0%
+actually need to set in the
+approximation algorithm the first is an
+
+ align:start position:0%
+approximation algorithm the first is an
+ 
+
+ align:start position:0%
+approximation algorithm the first is an
+Epsilon so this is down here how close
+
+ align:start position:0%
+Epsilon so this is down here how close
+ 
+
+ align:start position:0%
+Epsilon so this is down here how close
+do we want to be to the final answer
+
+ align:start position:0%
+do we want to be to the final answer
+ 
+
+ align:start position:0%
+do we want to be to the final answer
+what's the leeway we're going to allow
+
+ align:start position:0%
+what's the leeway we're going to allow
+ 
+
+ align:start position:0%
+what's the leeway we're going to allow
+and second is the increment so how uh
+
+ align:start position:0%
+and second is the increment so how uh
+ 
+
+ align:start position:0%
+and second is the increment so how uh
+much do we want to change our guess
+
+ align:start position:0%
+much do we want to change our guess
+ 
+
+ align:start position:0%
+much do we want to change our guess
+by the way the algorithm performs
+
+ align:start position:0%
+by the way the algorithm performs
+ 
+
+ align:start position:0%
+by the way the algorithm performs
+depends on the values we choose for
+
+ align:start position:0%
+depends on the values we choose for
+ 
+
+ align:start position:0%
+depends on the values we choose for
+these obviously if our guess is smaller
+
+ align:start position:0%
+these obviously if our guess is smaller
+ 
+
+ align:start position:0%
+these obviously if our guess is smaller
+right if we decrease the increment we're
+
+ align:start position:0%
+right if we decrease the increment we're
+ 
+
+ align:start position:0%
+right if we decrease the increment we're
+going to get a much more accurate uh
+
+ align:start position:0%
+going to get a much more accurate uh
+ 
+
+ align:start position:0%
+going to get a much more accurate uh
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+right if we increase the Epsilon how you
+
+ align:start position:0%
+right if we increase the Epsilon how you
+ 
+
+ align:start position:0%
+right if we increase the Epsilon how you
+know how close we want to be to X our
+
+ align:start position:0%
+know how close we want to be to X our
+ 
+
+ align:start position:0%
+know how close we want to be to X our
+program is going to be a faster because
+
+ align:start position:0%
+program is going to be a faster because
+ 
+
+ align:start position:0%
+program is going to be a faster because
+we're going to enter that plus minus
+
+ align:start position:0%
+we're going to enter that plus minus
+ 
+
+ align:start position:0%
+we're going to enter that plus minus
+Epsilon boundary
+
+ align:start position:0%
+Epsilon boundary
+ 
+
+ align:start position:0%
+Epsilon boundary
+faster but it's going to be less
+
+ align:start position:0%
+faster but it's going to be less
+ 
+
+ align:start position:0%
+faster but it's going to be less
+accurate because at some point we're
+
+ align:start position:0%
+accurate because at some point we're
+ 
+
+ align:start position:0%
+accurate because at some point we're
+going to enter the boundary and we're
+
+ align:start position:0%
+going to enter the boundary and we're
+ 
+
+ align:start position:0%
+going to enter the boundary and we're
+going to say good enough I'm not going
+
+ align:start position:0%
+going to say good enough I'm not going
+ 
+
+ align:start position:0%
+going to say good enough I'm not going
+to get any closer to X because there's
+
+ align:start position:0%
+to get any closer to X because there's
+ 
+
+ align:start position:0%
+to get any closer to X because there's
+no need to I'm already with an Epsilon
+
+ align:start position:0%
+no need to I'm already with an Epsilon
+ 
+
+ align:start position:0%
+no need to I'm already with an Epsilon
+so here the guess you know good enough
+
+ align:start position:0%
+so here the guess you know good enough
+ 
+
+ align:start position:0%
+so here the guess you know good enough
+guess was to the square Ro of five was 1
+
+ align:start position:0%
+guess was to the square Ro of five was 1
+ 
+
+ align:start position:0%
+guess was to the square Ro of five was 1
+point something but on the previous
+
+ align:start position:0%
+point something but on the previous
+ 
+
+ align:start position:0%
+point something but on the previous
+slide right when we had a smaller
+
+ align:start position:0%
+slide right when we had a smaller
+ 
+
+ align:start position:0%
+slide right when we had a smaller
+Epsilon the good enough guess was 2
+
+ align:start position:0%
+Epsilon the good enough guess was 2
+ 
+
+ align:start position:0%
+Epsilon the good enough guess was 2
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something so the approximation algorithm
+
+ align:start position:0%
+something so the approximation algorithm
+ 
+
+ align:start position:0%
+something so the approximation algorithm
+is like guess and check except that we
+
+ align:start position:0%
+is like guess and check except that we
+ 
+
+ align:start position:0%
+is like guess and check except that we
+have some small increment we change by a
+
+ align:start position:0%
+have some small increment we change by a
+ 
+
+ align:start position:0%
+have some small increment we change by a
+small amount and we stop when we're
+
+ align:start position:0%
+small amount and we stop when we're
+ 
+
+ align:start position:0%
+small amount and we stop when we're
+close enough so we're going to check
+
+ align:start position:0%
+close enough so we're going to check
+ 
+
+ align:start position:0%
+close enough so we're going to check
+that the absolute value of this solution
+
+ align:start position:0%
+that the absolute value of this solution
+ 
+
+ align:start position:0%
+that the absolute value of this solution
+minus the solution minus the actual
+
+ align:start position:0%
+minus the solution minus the actual
+ 
+
+ align:start position:0%
+minus the solution minus the actual
+answer is within Epsilon so here's some
+
+ align:start position:0%
+answer is within Epsilon so here's some
+ 
+
+ align:start position:0%
+answer is within Epsilon so here's some
+code where we can Implement what ex uh
+
+ align:start position:0%
+code where we can Implement what ex uh
+ 
+
+ align:start position:0%
+code where we can Implement what ex uh
+uh uh finding the square root of a
+
+ align:start position:0%
+uh uh finding the square root of a
+ 
+
+ align:start position:0%
+uh uh finding the square root of a
+number with approximation
+
+ align:start position:0%
+number with approximation
+ 
+
+ align:start position:0%
+number with approximation
+method we have some uh stuff here that
+
+ align:start position:0%
+method we have some uh stuff here that
+ 
+
+ align:start position:0%
+method we have some uh stuff here that
+we're initializing so this is the FI
+
+ align:start position:0%
+we're initializing so this is the FI
+ 
+
+ align:start position:0%
+we're initializing so this is the FI
+thing you want to find the square root
+
+ align:start position:0%
+thing you want to find the square root
+ 
+
+ align:start position:0%
+thing you want to find the square root
+of this is how close we want to be to
+
+ align:start position:0%
+of this is how close we want to be to
+ 
+
+ align:start position:0%
+of this is how close we want to be to
+the final answer
+
+ align:start position:0%
+the final answer
+ 
+
+ align:start position:0%
+the final answer
+and this is our increment numb guesses
+
+ align:start position:0%
+and this is our increment numb guesses
+ 
+
+ align:start position:0%
+and this is our increment numb guesses
+is just to keep track of how many actual
+
+ align:start position:0%
+is just to keep track of how many actual
+ 
+
+ align:start position:0%
+is just to keep track of how many actual
+guesses we're doing and we're going to
+
+ align:start position:0%
+guesses we're doing and we're going to
+ 
+
+ align:start position:0%
+guesses we're doing and we're going to
+start with a guess that we know is too
+
+ align:start position:0%
+start with a guess that we know is too
+ 
+
+ align:start position:0%
+start with a guess that we know is too
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+zero this is the loop that does all of
+
+ align:start position:0%
+zero this is the loop that does all of
+ 
+
+ align:start position:0%
+zero this is the loop that does all of
+the work for
+
+ align:start position:0%
+the work for
+ 
+
+ align:start position:0%
+the work for
+us so the way we would say it in English
+
+ align:start position:0%
+us so the way we would say it in English
+ 
+
+ align:start position:0%
+us so the way we would say it in English
+it says basically while our guess is not
+
+ align:start position:0%
+it says basically while our guess is not
+ 
+
+ align:start position:0%
+it says basically while our guess is not
+with an Epsilon keep making new
+
+ align:start position:0%
+with an Epsilon keep making new
+ 
+
+ align:start position:0%
+with an Epsilon keep making new
+guesses so while what does it mean for
+
+ align:start position:0%
+guesses so while what does it mean for
+ 
+
+ align:start position:0%
+guesses so while what does it mean for
+the guest to not be within Plus or -
+
+ align:start position:0%
+the guest to not be within Plus or -
+ 
+
+ align:start position:0%
+the guest to not be within Plus or -
+Epsilon well the absolute value of Our
+
+ align:start position:0%
+Epsilon well the absolute value of Our
+ 
+
+ align:start position:0%
+Epsilon well the absolute value of Our
+Guest squar -
+
+ align:start position:0%
+Guest squar -
+ 
+
+ align:start position:0%
+Guest squar -
+x is greater or equal to Epsilon so
+
+ align:start position:0%
+x is greater or equal to Epsilon so
+ 
+
+ align:start position:0%
+x is greater or equal to Epsilon so
+while we're still too far
+
+ align:start position:0%
+while we're still too far
+ 
+
+ align:start position:0%
+while we're still too far
+away let's make a new guess so we
+
+ align:start position:0%
+away let's make a new guess so we
+ 
+
+ align:start position:0%
+away let's make a new guess so we
+increment our guess by the increment
+
+ align:start position:0%
+increment our guess by the increment
+ 
+
+ align:start position:0%
+increment our guess by the increment
+value so originally we were zero then
+
+ align:start position:0%
+value so originally we were zero then
+ 
+
+ align:start position:0%
+value so originally we were zero then
+we're 0.1 01 then we're going to be
+
+ align:start position:0%
+we're 0.1 01 then we're going to be
+ 
+
+ align:start position:0%
+we're 0.1 01 then we're going to be
+02 and so on this num guesses again is
+
+ align:start position:0%
+02 and so on this num guesses again is
+ 
+
+ align:start position:0%
+02 and so on this num guesses again is
+just for us to keep track of how many
+
+ align:start position:0%
+just for us to keep track of how many
+ 
+
+ align:start position:0%
+just for us to keep track of how many
+times we've actually gone through this
+
+ align:start position:0%
+times we've actually gone through this
+ 
+
+ align:start position:0%
+times we've actually gone through this
+Loop and at the end we can print how
+
+ align:start position:0%
+Loop and at the end we can print how
+ 
+
+ align:start position:0%
+Loop and at the end we can print how
+many guesses we've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done okay so here's the
+
+ align:start position:0%
+done okay so here's the
+ 
+
+ align:start position:0%
+done okay so here's the
+code and 36 so we can run it what do we
+
+ align:start position:0%
+code and 36 so we can run it what do we
+ 
+
+ align:start position:0%
+code and 36 so we can run it what do we
+see here's our approximation to the
+
+ align:start position:0%
+see here's our approximation to the
+ 
+
+ align:start position:0%
+see here's our approximation to the
+square root of 36 now we know it's
+
+ align:start position:0%
+square root of 36 now we know it's
+ 
+
+ align:start position:0%
+square root of 36 now we know it's
+six and of course if we kept going we
+
+ align:start position:0%
+six and of course if we kept going we
+ 
+
+ align:start position:0%
+six and of course if we kept going we
+could have found probably exactly six
+
+ align:start position:0%
+could have found probably exactly six
+ 
+
+ align:start position:0%
+could have found probably exactly six
+but notice this approximation algorithm
+
+ align:start position:0%
+but notice this approximation algorithm
+ 
+
+ align:start position:0%
+but notice this approximation algorithm
+stops as soon as you enter that plus
+
+ align:start position:0%
+stops as soon as you enter that plus
+ 
+
+ align:start position:0%
+stops as soon as you enter that plus
+minus Epsilon
+
+ align:start position:0%
+minus Epsilon
+ 
+
+ align:start position:0%
+minus Epsilon
+boundary yes um do for Loops always
+
+ align:start position:0%
+boundary yes um do for Loops always
+ 
+
+ align:start position:0%
+boundary yes um do for Loops always
+increase in integer amounts do for Loops
+
+ align:start position:0%
+increase in integer amounts do for Loops
+ 
+
+ align:start position:0%
+increase in integer amounts do for Loops
+always increase in integer amounts yes
+
+ align:start position:0%
+always increase in integer amounts yes
+ 
+
+ align:start position:0%
+always increase in integer amounts yes
+the step has to be an integer positive
+
+ align:start position:0%
+the step has to be an integer positive
+ 
+
+ align:start position:0%
+the step has to be an integer positive
+or negative yeah so exactly a for Loop
+
+ align:start position:0%
+or negative yeah so exactly a for Loop
+ 
+
+ align:start position:0%
+or negative yeah so exactly a for Loop
+would not have worked here right
+
+ align:start position:0%
+would not have worked here right
+ 
+
+ align:start position:0%
+would not have worked here right
+yeah right so here we stopped this
+
+ align:start position:0%
+yeah right so here we stopped this
+ 
+
+ align:start position:0%
+yeah right so here we stopped this
+algorithm as soon as we entered that
+
+ align:start position:0%
+algorithm as soon as we entered that
+ 
+
+ align:start position:0%
+algorithm as soon as we entered that
+plus minus uh boundary of Epsilon right
+
+ align:start position:0%
+plus minus uh boundary of Epsilon right
+ 
+
+ align:start position:0%
+plus minus uh boundary of Epsilon right
+and so five 9991 is close enough to squ
+
+ align:start position:0%
+and so five 9991 is close enough to squ
+ 
+
+ align:start position:0%
+and so five 9991 is close enough to squ
+root of 6 and that's what we're
+
+ align:start position:0%
+root of 6 and that's what we're
+ 
+
+ align:start position:0%
+root of 6 and that's what we're
+reporting the number of guesses here was
+
+ align:start position:0%
+reporting the number of guesses here was
+ 
+
+ align:start position:0%
+reporting the number of guesses here was
+about 5999
+
+ align:start position:0%
+about 5999
+ 
+
+ align:start position:0%
+about 5999
+2,000 and that's makes sense because our
+
+ align:start position:0%
+2,000 and that's makes sense because our
+ 
+
+ align:start position:0%
+2,000 and that's makes sense because our
+increment is
+
+ align:start position:0%
+increment is
+ 
+
+ align:start position:0%
+increment is
+0.001 and we went all the way up to 5.99
+
+ align:start position:0%
+0.001 and we went all the way up to 5.99
+ 
+
+ align:start position:0%
+0.001 and we went all the way up to 5.99
+right so with each time through the loop
+
+ align:start position:0%
+right so with each time through the loop
+ 
+
+ align:start position:0%
+right so with each time through the loop
+we incremented pi1 so that's just this
+
+ align:start position:0%
+we incremented pi1 so that's just this
+ 
+
+ align:start position:0%
+we incremented pi1 so that's just this
+times 10,000 okay that makes sense so
+
+ align:start position:0%
+times 10,000 okay that makes sense so
+ 
+
+ align:start position:0%
+times 10,000 okay that makes sense so
+let's try it with a couple other values
+
+ align:start position:0%
+let's try it with a couple other values
+ 
+
+ align:start position:0%
+let's try it with a couple other values
+so here it is with 24
+
+ align:start position:0%
+so here it is with 24
+ 
+
+ align:start position:0%
+so here it is with 24
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+4.89 again we're seeing these U floating
+
+ align:start position:0%
+4.89 again we're seeing these U floating
+ 
+
+ align:start position:0%
+4.89 again we're seeing these U floating
+Point errors pop into play right
+
+ align:start position:0%
+Point errors pop into play right
+ 
+
+ align:start position:0%
+Point errors pop into play right
+whenever we see this weird like 0 Z and
+
+ align:start position:0%
+whenever we see this weird like 0 Z and
+ 
+
+ align:start position:0%
+whenever we see this weird like 0 Z and
+then some small amount at the end that's
+
+ align:start position:0%
+then some small amount at the end that's
+ 
+
+ align:start position:0%
+then some small amount at the end that's
+these floating Point errors just given
+
+ align:start position:0%
+these floating Point errors just given
+ 
+
+ align:start position:0%
+these floating Point errors just given
+the numbers we're working with adding up
+
+ align:start position:0%
+the numbers we're working with adding up
+ 
+
+ align:start position:0%
+the numbers we're working with adding up
+um here's the square root of two right
+
+ align:start position:0%
+um here's the square root of two right
+ 
+
+ align:start position:0%
+um here's the square root of two right
+1.41 again floating Point Air but this
+
+ align:start position:0%
+1.41 again floating Point Air but this
+ 
+
+ align:start position:0%
+1.41 again floating Point Air but this
+time on the other side 0.9
+
+ align:start position:0%
+time on the other side 0.9
+ 
+
+ align:start position:0%
+time on the other side 0.9
+and9 uh 1 2 3 4 five run
+
+ align:start position:0%
+and9 uh 1 2 3 4 five run
+ 
+
+ align:start position:0%
+and9 uh 1 2 3 4 five run
+it it took a second right there was a
+
+ align:start position:0%
+it it took a second right there was a
+ 
+
+ align:start position:0%
+it it took a second right there was a
+little pause and then it gave us the
+
+ align:start position:0%
+little pause and then it gave us the
+ 
+
+ align:start position:0%
+little pause and then it gave us the
+answer just because it has to Loop
+
+ align:start position:0%
+answer just because it has to Loop
+ 
+
+ align:start position:0%
+answer just because it has to Loop
+through about what is this 100 1 two
+
+ align:start position:0%
+through about what is this 100 1 two
+ 
+
+ align:start position:0%
+through about what is this 100 1 two
+three 1 million times right so did that
+
+ align:start position:0%
+three 1 million times right so did that
+ 
+
+ align:start position:0%
+three 1 million times right so did that
+Loop one million times to get us get us
+
+ align:start position:0%
+Loop one million times to get us get us
+ 
+
+ align:start position:0%
+Loop one million times to get us get us
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+answer and
+
+ align:start position:0%
+answer and
+ 
+
+ align:start position:0%
+answer and
+then we can try one more 54 3 2 1 this
+
+ align:start position:0%
+then we can try one more 54 3 2 1 this
+ 
+
+ align:start position:0%
+then we can try one more 54 3 2 1 this
+should take about five times as long
+
+ align:start position:0%
+should take about five times as long
+ 
+
+ align:start position:0%
+should take about five times as long
+right because
+
+ align:start position:0%
+right because
+ 
+
+ align:start position:0%
+right because
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+1,2003
+
+ align:start position:0%
+1,2003
+ 
+
+ align:start position:0%
+1,2003
+12,345 took about 1 second this one
+
+ align:start position:0%
+12,345 took about 1 second this one
+ 
+
+ align:start position:0%
+12,345 took about 1 second this one
+should take about 5 seconds but it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not I'm pretty sure I was talking for
+
+ align:start position:0%
+not I'm pretty sure I was talking for
+ 
+
+ align:start position:0%
+not I'm pretty sure I was talking for
+more than 5 seconds and this program is
+
+ align:start position:0%
+more than 5 seconds and this program is
+ 
+
+ align:start position:0%
+more than 5 seconds and this program is
+not ending so something's gone wrong I'm
+
+ align:start position:0%
+not ending so something's gone wrong I'm
+ 
+
+ align:start position:0%
+not ending so something's gone wrong I'm
+going to stop it remember you can stop
+
+ align:start position:0%
+going to stop it remember you can stop
+ 
+
+ align:start position:0%
+going to stop it remember you can stop
+it by clicking the shell hitting contrl
+
+ align:start position:0%
+it by clicking the shell hitting contrl
+ 
+
+ align:start position:0%
+it by clicking the shell hitting contrl
+C or the little square here in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corner so what went
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong oh yes my question is will this
+
+ align:start position:0%
+wrong oh yes my question is will this
+ 
+
+ align:start position:0%
+wrong oh yes my question is will this
+Loop always terminate and 54321 was an
+
+ align:start position:0%
+Loop always terminate and 54321 was an
+ 
+
+ align:start position:0%
+Loop always terminate and 54321 was an
+example of the loop not
+
+ align:start position:0%
+example of the loop not
+ 
+
+ align:start position:0%
+example of the loop not
+terminating so what happened right we
+
+ align:start position:0%
+terminating so what happened right we
+ 
+
+ align:start position:0%
+terminating so what happened right we
+did all this let's try to debug what
+
+ align:start position:0%
+did all this let's try to debug what
+ 
+
+ align:start position:0%
+did all this let's try to debug what
+exactly happened because clearly what we
+
+ align:start position:0%
+exactly happened because clearly what we
+ 
+
+ align:start position:0%
+exactly happened because clearly what we
+have in code right now is not really
+
+ align:start position:0%
+have in code right now is not really
+ 
+
+ align:start position:0%
+have in code right now is not really
+giving us much information so let's add
+
+ align:start position:0%
+giving us much information so let's add
+ 
+
+ align:start position:0%
+giving us much information so let's add
+some print
+
+ align:start position:0%
+some print
+ 
+
+ align:start position:0%
+some print
+statements the print statements I'm
+
+ align:start position:0%
+statements the print statements I'm
+ 
+
+ align:start position:0%
+statements the print statements I'm
+adding is just in here so everything
+
+ align:start position:0%
+adding is just in here so everything
+ 
+
+ align:start position:0%
+adding is just in here so everything
+else that's not boxed is the same as on
+
+ align:start position:0%
+else that's not boxed is the same as on
+ 
+
+ align:start position:0%
+else that's not boxed is the same as on
+the previous Slide the only thing I'm
+
+ align:start position:0%
+the previous Slide the only thing I'm
+ 
+
+ align:start position:0%
+the previous Slide the only thing I'm
+adding new is this if statement here so
+
+ align:start position:0%
+adding new is this if statement here so
+ 
+
+ align:start position:0%
+adding new is this if statement here so
+every every 1,000 uh sorry every 100,000
+
+ align:start position:0%
+every every 1,000 uh sorry every 100,000
+ 
+
+ align:start position:0%
+every every 1,000 uh sorry every 100,000
+guesses so every time I've gone through
+
+ align:start position:0%
+guesses so every time I've gone through
+ 
+
+ align:start position:0%
+guesses so every time I've gone through
+this Loop a 100,000 times I'm going to
+
+ align:start position:0%
+this Loop a 100,000 times I'm going to
+ 
+
+ align:start position:0%
+this Loop a 100,000 times I'm going to
+print what the current guess is and what
+
+ align:start position:0%
+print what the current guess is and what
+ 
+
+ align:start position:0%
+print what the current guess is and what
+the guess squ minus X is so how far away
+
+ align:start position:0%
+the guess squ minus X is so how far away
+ 
+
+ align:start position:0%
+the guess squ minus X is so how far away
+I am from X the Epsilon or yeah not the
+
+ align:start position:0%
+I am from X the Epsilon or yeah not the
+ 
+
+ align:start position:0%
+I am from X the Epsilon or yeah not the
+Epsilon but how far away I am from
+
+ align:start position:0%
+Epsilon but how far away I am from
+ 
+
+ align:start position:0%
+Epsilon but how far away I am from
+X so let's run that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code it's down here I added a little bit
+
+ align:start position:0%
+code it's down here I added a little bit
+ 
+
+ align:start position:0%
+code it's down here I added a little bit
+of extra thing which is just it's not
+
+ align:start position:0%
+of extra thing which is just it's not
+ 
+
+ align:start position:0%
+of extra thing which is just it's not
+printing the whole time it's just going
+
+ align:start position:0%
+printing the whole time it's just going
+ 
+
+ align:start position:0%
+printing the whole time it's just going
+to pause for me just to talk about
+
+ align:start position:0%
+to pause for me just to talk about
+ 
+
+ align:start position:0%
+to pause for me just to talk about
+what's going on so here I have the code
+
+ align:start position:0%
+what's going on so here I have the code
+ 
+
+ align:start position:0%
+what's going on so here I have the code
+run has run so my first 100,000 times
+
+ align:start position:0%
+run has run so my first 100,000 times
+ 
+
+ align:start position:0%
+run has run so my first 100,000 times
+through the loop I have my guess being
+
+ align:start position:0%
+through the loop I have my guess being
+ 
+
+ align:start position:0%
+through the loop I have my guess being
+about 10 and how far I am from X is
+
+ align:start position:0%
+about 10 and how far I am from X is
+ 
+
+ align:start position:0%
+about 10 and how far I am from X is
+about 54,000 so I want to be 01 away
+
+ align:start position:0%
+about 54,000 so I want to be 01 away
+ 
+
+ align:start position:0%
+about 54,000 so I want to be 01 away
+from the from X right because that's
+
+ align:start position:0%
+from the from X right because that's
+ 
+
+ align:start position:0%
+from the from X right because that's
+what my Epsilon is and so here I'm
+
+ align:start position:0%
+what my Epsilon is and so here I'm
+ 
+
+ align:start position:0%
+what my Epsilon is and so here I'm
+54,000 away from X so clearly that's too
+
+ align:start position:0%
+54,000 away from X so clearly that's too
+ 
+
+ align:start position:0%
+54,000 away from X so clearly that's too
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+okay um let's continue so then we make
+
+ align:start position:0%
+okay um let's continue so then we make
+ 
+
+ align:start position:0%
+okay um let's continue so then we make
+more guesses and then here when my guess
+
+ align:start position:0%
+more guesses and then here when my guess
+ 
+
+ align:start position:0%
+more guesses and then here when my guess
+is a 100 I am about 44,000 away from X
+
+ align:start position:0%
+is a 100 I am about 44,000 away from X
+ 
+
+ align:start position:0%
+is a 100 I am about 44,000 away from X
+from 54 so looking good let's continue
+
+ align:start position:0%
+from 54 so looking good let's continue
+ 
+
+ align:start position:0%
+from 54 so looking good let's continue
+so with 120 I'm 39,000 away from X with
+
+ align:start position:0%
+so with 120 I'm 39,000 away from X with
+ 
+
+ align:start position:0%
+so with 120 I'm 39,000 away from X with
+200 I'm 14,000 away from X so it's
+
+ align:start position:0%
+200 I'm 14,000 away from X so it's
+ 
+
+ align:start position:0%
+200 I'm 14,000 away from X so it's
+looking much better right I'm getting
+
+ align:start position:0%
+looking much better right I'm getting
+ 
+
+ align:start position:0%
+looking much better right I'm getting
+closer and closer to uh to getting that
+
+ align:start position:0%
+closer and closer to uh to getting that
+ 
+
+ align:start position:0%
+closer and closer to uh to getting that
+difference uh you you know being Zer or
+
+ align:start position:0%
+difference uh you you know being Zer or
+ 
+
+ align:start position:0%
+difference uh you you know being Zer or
+01 continue with 210 I'm 10,000 away
+
+ align:start position:0%
+01 continue with 210 I'm 10,000 away
+ 
+
+ align:start position:0%
+01 continue with 210 I'm 10,000 away
+from X and then I'm almost 6,000 away
+
+ align:start position:0%
+from X and then I'm almost 6,000 away
+ 
+
+ align:start position:0%
+from X and then I'm almost 6,000 away
+from X and then I'm 1,000 away from
+
+ align:start position:0%
+from X and then I'm 1,000 away from
+ 
+
+ align:start position:0%
+from X and then I'm 1,000 away from
+X and then from
+
+ align:start position:0%
+X and then from
+ 
+
+ align:start position:0%
+X and then from
+230 as my guess which brought me 1,400
+
+ align:start position:0%
+230 as my guess which brought me 1,400
+ 
+
+ align:start position:0%
+230 as my guess which brought me 1,400
+away from X the next time I have 240
+
+ align:start position:0%
+away from X the next time I have 240
+ 
+
+ align:start position:0%
+away from X the next time I have 240
+right the next print out I have brings
+
+ align:start position:0%
+right the next print out I have brings
+ 
+
+ align:start position:0%
+right the next print out I have brings
+me to 3,000 away from X so I was 1,000
+
+ align:start position:0%
+me to 3,000 away from X so I was 1,000
+ 
+
+ align:start position:0%
+me to 3,000 away from X so I was 1,000
+but now I'm 3,000
+
+ align:start position:0%
+but now I'm 3,000
+ 
+
+ align:start position:0%
+but now I'm 3,000
+and then from there on things break down
+
+ align:start position:0%
+and then from there on things break down
+ 
+
+ align:start position:0%
+and then from there on things break down
+really quickly because I just get now
+
+ align:start position:0%
+really quickly because I just get now
+ 
+
+ align:start position:0%
+really quickly because I just get now
+farther and farther away from X right so
+
+ align:start position:0%
+farther and farther away from X right so
+ 
+
+ align:start position:0%
+farther and farther away from X right so
+here I am continuing the program for a
+
+ align:start position:0%
+here I am continuing the program for a
+ 
+
+ align:start position:0%
+here I am continuing the program for a
+little bit and then I just keep making
+
+ align:start position:0%
+little bit and then I just keep making
+ 
+
+ align:start position:0%
+little bit and then I just keep making
+guesses right because I was never within
+
+ align:start position:0%
+guesses right because I was never within
+ 
+
+ align:start position:0%
+guesses right because I was never within
+that Epsilon so here's 500 and now I'm
+
+ align:start position:0%
+that Epsilon so here's 500 and now I'm
+ 
+
+ align:start position:0%
+that Epsilon so here's 500 and now I'm
+almost 200,000 away from X and so now
+
+ align:start position:0%
+almost 200,000 away from X and so now
+ 
+
+ align:start position:0%
+almost 200,000 away from X and so now
+you see what's happening this program is
+
+ align:start position:0%
+you see what's happening this program is
+ 
+
+ align:start position:0%
+you see what's happening this program is
+just going to keep getting further and
+
+ align:start position:0%
+just going to keep getting further and
+ 
+
+ align:start position:0%
+just going to keep getting further and
+further away from where I need to
+
+ align:start position:0%
+further away from where I need to
+ 
+
+ align:start position:0%
+further away from where I need to
+be so let's visualize what what exactly
+
+ align:start position:0%
+be so let's visualize what what exactly
+ 
+
+ align:start position:0%
+be so let's visualize what what exactly
+happened this is our X
+
+ align:start position:0%
+happened this is our X
+ 
+
+ align:start position:0%
+happened this is our X
+5,400 uh
+
+ align:start position:0%
+5,400 uh
+ 
+
+ align:start position:0%
+5,400 uh
+54321 and this is our Epsilon let's say
+
+ align:start position:0%
+54321 and this is our Epsilon let's say
+ 
+
+ align:start position:0%
+54321 and this is our Epsilon let's say
+it's you know 01 obviously not to scale
+
+ align:start position:0%
+it's you know 01 obviously not to scale
+ 
+
+ align:start position:0%
+it's you know 01 obviously not to scale
+blue is going to be representing one
+
+ align:start position:0%
+blue is going to be representing one
+ 
+
+ align:start position:0%
+blue is going to be representing one
+guess so here's a guess and then we have
+
+ align:start position:0%
+guess so here's a guess and then we have
+ 
+
+ align:start position:0%
+guess so here's a guess and then we have
+the guess squared a green so let's just
+
+ align:start position:0%
+the guess squared a green so let's just
+ 
+
+ align:start position:0%
+the guess squared a green so let's just
+for visualization purposes let's say
+
+ align:start position:0%
+for visualization purposes let's say
+ 
+
+ align:start position:0%
+for visualization purposes let's say
+this is our guess and this is our guess
+
+ align:start position:0%
+this is our guess and this is our guess
+ 
+
+ align:start position:0%
+this is our guess and this is our guess
+squared okay we're far away from from X
+
+ align:start position:0%
+squared okay we're far away from from X
+ 
+
+ align:start position:0%
+squared okay we're far away from from X
+we're definitely outside the Epsilon
+
+ align:start position:0%
+we're definitely outside the Epsilon
+ 
+
+ align:start position:0%
+we're definitely outside the Epsilon
+boundary we make another guess by
+
+ align:start position:0%
+boundary we make another guess by
+ 
+
+ align:start position:0%
+boundary we make another guess by
+incrementing it a little bit this is the
+
+ align:start position:0%
+incrementing it a little bit this is the
+ 
+
+ align:start position:0%
+incrementing it a little bit this is the
+guess squared we make another guess by
+
+ align:start position:0%
+guess squared we make another guess by
+ 
+
+ align:start position:0%
+guess squared we make another guess by
+incrementing it a little bit because
+
+ align:start position:0%
+incrementing it a little bit because
+ 
+
+ align:start position:0%
+incrementing it a little bit because
+we're still far away from that plus
+
+ align:start position:0%
+we're still far away from that plus
+ 
+
+ align:start position:0%
+we're still far away from that plus
+minus Epsilon this is our guess
+
+ align:start position:0%
+minus Epsilon this is our guess
+ 
+
+ align:start position:0%
+minus Epsilon this is our guess
+squared we make another guess this is
+
+ align:start position:0%
+squared we make another guess this is
+ 
+
+ align:start position:0%
+squared we make another guess this is
+our guess squared we're pretty darn
+
+ align:start position:0%
+our guess squared we're pretty darn
+ 
+
+ align:start position:0%
+our guess squared we're pretty darn
+close to that plusus Epsilon boundary
+
+ align:start position:0%
+close to that plusus Epsilon boundary
+ 
+
+ align:start position:0%
+close to that plusus Epsilon boundary
+right we want to be within that plusus
+
+ align:start position:0%
+right we want to be within that plusus
+ 
+
+ align:start position:0%
+right we want to be within that plusus
+Epsilon so one more guess should make it
+
+ align:start position:0%
+Epsilon so one more guess should make it
+ 
+
+ align:start position:0%
+Epsilon so one more guess should make it
+right this is our next guess but now the
+
+ align:start position:0%
+right this is our next guess but now the
+ 
+
+ align:start position:0%
+right this is our next guess but now the
+guess Square squ is on the other
+
+ align:start position:0%
+guess Square squ is on the other
+ 
+
+ align:start position:0%
+guess Square squ is on the other
+side okay this is the big reveal you
+
+ align:start position:0%
+side okay this is the big reveal you
+ 
+
+ align:start position:0%
+side okay this is the big reveal you
+guys so what happened what happens now
+
+ align:start position:0%
+guys so what happened what happens now
+ 
+
+ align:start position:0%
+guys so what happened what happens now
+the program says keep guessing because
+
+ align:start position:0%
+the program says keep guessing because
+ 
+
+ align:start position:0%
+the program says keep guessing because
+we're not with an Epsilon so it's going
+
+ align:start position:0%
+we're not with an Epsilon so it's going
+ 
+
+ align:start position:0%
+we're not with an Epsilon so it's going
+to make another
+
+ align:start position:0%
+to make another
+ 
+
+ align:start position:0%
+to make another
+guess guess squared and it's just going
+
+ align:start position:0%
+guess guess squared and it's just going
+ 
+
+ align:start position:0%
+guess guess squared and it's just going
+to keep
+
+ align:start position:0%
+to keep
+ 
+
+ align:start position:0%
+to keep
+guessing and then our guess squared is
+
+ align:start position:0%
+guessing and then our guess squared is
+ 
+
+ align:start position:0%
+guessing and then our guess squared is
+just going to keep getting bigger and
+
+ align:start position:0%
+just going to keep getting bigger and
+ 
+
+ align:start position:0%
+just going to keep getting bigger and
+bigger so we basically overshot the
+
+ align:start position:0%
+bigger so we basically overshot the
+ 
+
+ align:start position:0%
+bigger so we basically overshot the
+Epsilon right we've overshot our little
+
+ align:start position:0%
+Epsilon right we've overshot our little
+ 
+
+ align:start position:0%
+Epsilon right we've overshot our little
+plus minus boundary we were interested
+
+ align:start position:0%
+plus minus boundary we were interested
+ 
+
+ align:start position:0%
+plus minus boundary we were interested
+in being
+
+ align:start position:0%
+in being
+ 
+
+ align:start position:0%
+in being
+within
+
+ align:start position:0%
+within
+ 
+
+ align:start position:0%
+within
+right we didn't account for that when we
+
+ align:start position:0%
+right we didn't account for that when we
+ 
+
+ align:start position:0%
+right we didn't account for that when we
+wrote The Loop right all we wanted to do
+
+ align:start position:0%
+wrote The Loop right all we wanted to do
+ 
+
+ align:start position:0%
+wrote The Loop right all we wanted to do
+was be within Epsilon and our program
+
+ align:start position:0%
+was be within Epsilon and our program
+ 
+
+ align:start position:0%
+was be within Epsilon and our program
+would end so let's fix
+
+ align:start position:0%
+would end so let's fix
+ 
+
+ align:start position:0%
+would end so let's fix
+that one addition will fix that and it's
+
+ align:start position:0%
+that one addition will fix that and it's
+ 
+
+ align:start position:0%
+that one addition will fix that and it's
+something that we had been doing in
+
+ align:start position:0%
+something that we had been doing in
+ 
+
+ align:start position:0%
+something that we had been doing in
+guess and check anyway right in guess
+
+ align:start position:0%
+guess and check anyway right in guess
+ 
+
+ align:start position:0%
+guess and check anyway right in guess
+and check we would say something like if
+
+ align:start position:0%
+and check we would say something like if
+ 
+
+ align:start position:0%
+and check we would say something like if
+we've passed the reasonable guess right
+
+ align:start position:0%
+we've passed the reasonable guess right
+ 
+
+ align:start position:0%
+we've passed the reasonable guess right
+when we we know that guess squared from
+
+ align:start position:0%
+when we we know that guess squared from
+ 
+
+ align:start position:0%
+when we we know that guess squared from
+here on out is definitely too big just
+
+ align:start position:0%
+here on out is definitely too big just
+ 
+
+ align:start position:0%
+here on out is definitely too big just
+stop stop guessing right just just stop
+
+ align:start position:0%
+stop stop guessing right just just stop
+ 
+
+ align:start position:0%
+stop stop guessing right just just stop
+and so we can add that same thing here
+
+ align:start position:0%
+and so we can add that same thing here
+ 
+
+ align:start position:0%
+and so we can add that same thing here
+as just another ending condition so
+
+ align:start position:0%
+as just another ending condition so
+ 
+
+ align:start position:0%
+as just another ending condition so
+everything in this code is the same as
+
+ align:start position:0%
+everything in this code is the same as
+ 
+
+ align:start position:0%
+everything in this code is the same as
+before except for this red
+
+ align:start position:0%
+before except for this red
+ 
+
+ align:start position:0%
+before except for this red
+box we're adding another stopping
+
+ align:start position:0%
+box we're adding another stopping
+ 
+
+ align:start position:0%
+box we're adding another stopping
+condition that basically says keep
+
+ align:start position:0%
+condition that basically says keep
+ 
+
+ align:start position:0%
+condition that basically says keep
+guessing while we're we we're while
+
+ align:start position:0%
+guessing while we're we we're while
+ 
+
+ align:start position:0%
+guessing while we're we we're while
+we're still guessing something
+
+ align:start position:0%
+we're still guessing something
+ 
+
+ align:start position:0%
+we're still guessing something
+reasonable right but when we've guessed
+
+ align:start position:0%
+reasonable right but when we've guessed
+ 
+
+ align:start position:0%
+reasonable right but when we've guessed
+something that's not reasonable right
+
+ align:start position:0%
+something that's not reasonable right
+ 
+
+ align:start position:0%
+something that's not reasonable right
+which is when the guess squared is
+
+ align:start position:0%
+which is when the guess squared is
+ 
+
+ align:start position:0%
+which is when the guess squared is
+greater than x right we've we're way
+
+ align:start position:0%
+greater than x right we've we're way
+ 
+
+ align:start position:0%
+greater than x right we've we're way
+past it stop guessing as well so
+
+ align:start position:0%
+past it stop guessing as well so
+ 
+
+ align:start position:0%
+past it stop guessing as well so
+whichever one of these conditions either
+
+ align:start position:0%
+whichever one of these conditions either
+ 
+
+ align:start position:0%
+whichever one of these conditions either
+this one or this one being with an
+
+ align:start position:0%
+this one or this one being with an
+ 
+
+ align:start position:0%
+this one or this one being with an
+Epsilon is true we break out of the
+
+ align:start position:0%
+Epsilon is true we break out of the
+ 
+
+ align:start position:0%
+Epsilon is true we break out of the
+loop and then we have an if else kind of
+
+ align:start position:0%
+loop and then we have an if else kind of
+ 
+
+ align:start position:0%
+loop and then we have an if else kind of
+the same sort of thing we've been doing
+
+ align:start position:0%
+the same sort of thing we've been doing
+ 
+
+ align:start position:0%
+the same sort of thing we've been doing
+so far in the guess and check why did we
+
+ align:start position:0%
+so far in the guess and check why did we
+ 
+
+ align:start position:0%
+so far in the guess and check why did we
+break the loop did we break it because
+
+ align:start position:0%
+break the loop did we break it because
+ 
+
+ align:start position:0%
+break the loop did we break it because
+we were with an
+
+ align:start position:0%
+we were with an
+ 
+
+ align:start position:0%
+we were with an
+Epsilon that is the else Clause here
+
+ align:start position:0%
+Epsilon that is the else Clause here
+ 
+
+ align:start position:0%
+Epsilon that is the else Clause here
+right if we did then we say this is
+
+ align:start position:0%
+right if we did then we say this is
+ 
+
+ align:start position:0%
+right if we did then we say this is
+close to square root of x but if we
+
+ align:start position:0%
+close to square root of x but if we
+ 
+
+ align:start position:0%
+close to square root of x but if we
+broke it because we've passed reasonable
+
+ align:start position:0%
+broke it because we've passed reasonable
+ 
+
+ align:start position:0%
+broke it because we've passed reasonable
+number of guesses then we know we failed
+
+ align:start position:0%
+number of guesses then we know we failed
+ 
+
+ align:start position:0%
+number of guesses then we know we failed
+to find the square root right because of
+
+ align:start position:0%
+to find the square root right because of
+ 
+
+ align:start position:0%
+to find the square root right because of
+We overshot The Mark or
+
+ align:start position:0%
+We overshot The Mark or
+ 
+
+ align:start position:0%
+We overshot The Mark or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+so here is the code with
+
+ align:start position:0%
+so here is the code with
+ 
+
+ align:start position:0%
+so here is the code with
+54321 but now we have that extra
+
+ align:start position:0%
+54321 but now we have that extra
+ 
+
+ align:start position:0%
+54321 but now we have that extra
+condition here guess squared less than
+
+ align:start position:0%
+condition here guess squared less than
+ 
+
+ align:start position:0%
+condition here guess squared less than
+uh less than
+
+ align:start position:0%
+uh less than
+ 
+
+ align:start position:0%
+uh less than
+x so we see that we've done some number
+
+ align:start position:0%
+x so we see that we've done some number
+ 
+
+ align:start position:0%
+x so we see that we've done some number
+of guesses right
+
+ align:start position:0%
+of guesses right
+ 
+
+ align:start position:0%
+of guesses right
+2,300,000
+
+ align:start position:0%
+2,300,000
+ 
+
+ align:start position:0%
+2,300,000
+and the message we get is we F fail to
+
+ align:start position:0%
+and the message we get is we F fail to
+ 
+
+ align:start position:0%
+and the message we get is we F fail to
+find the square root makes sense right
+
+ align:start position:0%
+find the square root makes sense right
+ 
+
+ align:start position:0%
+find the square root makes sense right
+because we knew we would fail and we're
+
+ align:start position:0%
+because we knew we would fail and we're
+ 
+
+ align:start position:0%
+because we knew we would fail and we're
+also reporting what the last guess was
+
+ align:start position:0%
+also reporting what the last guess was
+ 
+
+ align:start position:0%
+also reporting what the last guess was
+and the last guess squared just in case
+
+ align:start position:0%
+and the last guess squared just in case
+ 
+
+ align:start position:0%
+and the last guess squared just in case
+the user wants to use that information
+
+ align:start position:0%
+the user wants to use that information
+ 
+
+ align:start position:0%
+the user wants to use that information
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+anything what are some solutions to fix
+
+ align:start position:0%
+anything what are some solutions to fix
+ 
+
+ align:start position:0%
+anything what are some solutions to fix
+this right if we don't want to fail what
+
+ align:start position:0%
+this right if we don't want to fail what
+ 
+
+ align:start position:0%
+this right if we don't want to fail what
+what can we
+
+ align:start position:0%
+what can we
+ 
+
+ align:start position:0%
+what can we
+do well I gave you a hint right here we
+
+ align:start position:0%
+do well I gave you a hint right here we
+ 
+
+ align:start position:0%
+do well I gave you a hint right here we
+can decrement our increment or we can
+
+ align:start position:0%
+can decrement our increment or we can
+ 
+
+ align:start position:0%
+can decrement our increment or we can
+decrease our increment If instead of uh
+
+ align:start position:0%
+decrease our increment If instead of uh
+ 
+
+ align:start position:0%
+decrease our increment If instead of uh
+adding uh
+
+ align:start position:0%
+adding uh
+ 
+
+ align:start position:0%
+adding uh
+0.00001 every time through the loop
+
+ align:start position:0%
+0.00001 every time through the loop
+ 
+
+ align:start position:0%
+0.00001 every time through the loop
+let's add
+
+ align:start position:0%
+let's add
+ 
+
+ align:start position:0%
+let's add
+0.0000001 so let's make it uh make a
+
+ align:start position:0%
+0.0000001 so let's make it uh make a
+ 
+
+ align:start position:0%
+0.0000001 so let's make it uh make a
+guess 10 times as many guesses we're
+
+ align:start position:0%
+guess 10 times as many guesses we're
+ 
+
+ align:start position:0%
+guess 10 times as many guesses we're
+going to have to wait a little bit maybe
+
+ align:start position:0%
+going to have to wait a little bit maybe
+ 
+
+ align:start position:0%
+going to have to wait a little bit maybe
+about 10 seconds but the program will
+
+ align:start position:0%
+about 10 seconds but the program will
+ 
+
+ align:start position:0%
+about 10 seconds but the program will
+end it's taking this long obviously
+
+ align:start position:0%
+end it's taking this long obviously
+ 
+
+ align:start position:0%
+end it's taking this long obviously
+because it's making all of these extra
+
+ align:start position:0%
+because it's making all of these extra
+ 
+
+ align:start position:0%
+because it's making all of these extra
+guesses right for every one guess we had
+
+ align:start position:0%
+guesses right for every one guess we had
+ 
+
+ align:start position:0%
+guesses right for every one guess we had
+with the program that failed we're now
+
+ align:start position:0%
+with the program that failed we're now
+ 
+
+ align:start position:0%
+with the program that failed we're now
+making 10 guesses right because we
+
+ align:start position:0%
+making 10 guesses right because we
+ 
+
+ align:start position:0%
+making 10 guesses right because we
+decreased our increment
+
+ align:start position:0%
+decreased our increment
+ 
+
+ align:start position:0%
+decreased our increment
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+10 okay so it ended and we see exactly
+
+ align:start position:0%
+10 okay so it ended and we see exactly
+ 
+
+ align:start position:0%
+10 okay so it ended and we see exactly
+that idea and the number of guesses so
+
+ align:start position:0%
+that idea and the number of guesses so
+ 
+
+ align:start position:0%
+that idea and the number of guesses so
+here we had 2.3 million guesses when our
+
+ align:start position:0%
+here we had 2.3 million guesses when our
+ 
+
+ align:start position:0%
+here we had 2.3 million guesses when our
+increment was
+
+ align:start position:0%
+increment was
+ 
+
+ align:start position:0%
+increment was
+0.1 but when our increment was
+
+ align:start position:0%
+0.1 but when our increment was
+ 
+
+ align:start position:0%
+0.1 but when our increment was
+0.1 right four zeros we had 23 million
+
+ align:start position:0%
+0.1 right four zeros we had 23 million
+ 
+
+ align:start position:0%
+0.1 right four zeros we had 23 million
+guesses so obviously we had 10 times as
+
+ align:start position:0%
+guesses so obviously we had 10 times as
+ 
+
+ align:start position:0%
+guesses so obviously we had 10 times as
+many guesses which made our program be
+
+ align:start position:0%
+many guesses which made our program be
+ 
+
+ align:start position:0%
+many guesses which made our program be
+10 times as slow but now we didn't fail
+
+ align:start position:0%
+10 times as slow but now we didn't fail
+ 
+
+ align:start position:0%
+10 times as slow but now we didn't fail
+because we were able to go within that
+
+ align:start position:0%
+because we were able to go within that
+ 
+
+ align:start position:0%
+because we were able to go within that
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+right so we found that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+233.356 Epsilon and how else can we you
+
+ align:start position:0%
+233.356 Epsilon and how else can we you
+ 
+
+ align:start position:0%
+233.356 Epsilon and how else can we you
+know stop the program without it running
+
+ align:start position:0%
+know stop the program without it running
+ 
+
+ align:start position:0%
+know stop the program without it running
+into an infinite Loop right that would
+
+ align:start position:0%
+into an infinite Loop right that would
+ 
+
+ align:start position:0%
+into an infinite Loop right that would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+bad so I think I already went over this
+
+ align:start position:0%
+bad so I think I already went over this
+ 
+
+ align:start position:0%
+bad so I think I already went over this
+right what are some observations about
+
+ align:start position:0%
+right what are some observations about
+ 
+
+ align:start position:0%
+right what are some observations about
+running it uh yes it reported failure so
+
+ align:start position:0%
+running it uh yes it reported failure so
+ 
+
+ align:start position:0%
+running it uh yes it reported failure so
+we reset the increment down to uh 10
+
+ align:start position:0%
+we reset the increment down to uh 10
+ 
+
+ align:start position:0%
+we reset the increment down to uh 10
+times smaller than what it was before
+
+ align:start position:0%
+times smaller than what it was before
+ 
+
+ align:start position:0%
+times smaller than what it was before
+the program was small was slower because
+
+ align:start position:0%
+the program was small was slower because
+ 
+
+ align:start position:0%
+the program was small was slower because
+we had more values to check through okay
+
+ align:start position:0%
+we had more values to check through okay
+ 
+
+ align:start position:0%
+we had more values to check through okay
+so the big idea here is we want to be
+
+ align:start position:0%
+so the big idea here is we want to be
+ 
+
+ align:start position:0%
+so the big idea here is we want to be
+careful When comparing floats if we we
+
+ align:start position:0%
+careful When comparing floats if we we
+ 
+
+ align:start position:0%
+careful When comparing floats if we we
+were using something like equal equal
+
+ align:start position:0%
+were using something like equal equal
+ 
+
+ align:start position:0%
+were using something like equal equal
+sign right that would have been a
+
+ align:start position:0%
+sign right that would have been a
+ 
+
+ align:start position:0%
+sign right that would have been a
+complete disaster that we would might
+
+ align:start position:0%
+complete disaster that we would might
+ 
+
+ align:start position:0%
+complete disaster that we would might
+have never been with an Epsilon or
+
+ align:start position:0%
+have never been with an Epsilon or
+ 
+
+ align:start position:0%
+have never been with an Epsilon or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um yeah so what are some lessons we
+
+ align:start position:0%
+um yeah so what are some lessons we
+ 
+
+ align:start position:0%
+um yeah so what are some lessons we
+learned in
+
+ align:start position:0%
+learned in
+ 
+
+ align:start position:0%
+learned in
+approximation right so we can't use
+
+ align:start position:0%
+approximation right so we can't use
+ 
+
+ align:start position:0%
+approximation right so we can't use
+double equal sign to check for exit
+
+ align:start position:0%
+double equal sign to check for exit
+ 
+
+ align:start position:0%
+double equal sign to check for exit
+conditions we always have to check
+
+ align:start position:0%
+conditions we always have to check
+ 
+
+ align:start position:0%
+conditions we always have to check
+whether we are within plus or minus some
+
+ align:start position:0%
+whether we are within plus or minus some
+ 
+
+ align:start position:0%
+whether we are within plus or minus some
+Epsilon of the actual
+
+ align:start position:0%
+Epsilon of the actual
+ 
+
+ align:start position:0%
+Epsilon of the actual
+answer we have to be careful that we
+
+ align:start position:0%
+answer we have to be careful that we
+ 
+
+ align:start position:0%
+answer we have to be careful that we
+have that the um the exit condition
+
+ align:start position:0%
+have that the um the exit condition
+ 
+
+ align:start position:0%
+have that the um the exit condition
+being plus or minus within some Epsilon
+
+ align:start position:0%
+being plus or minus within some Epsilon
+ 
+
+ align:start position:0%
+being plus or minus within some Epsilon
+doesn't jump over our exit test as we
+
+ align:start position:0%
+doesn't jump over our exit test as we
+ 
+
+ align:start position:0%
+doesn't jump over our exit test as we
+just saw right in that case we add some
+
+ align:start position:0%
+just saw right in that case we add some
+ 
+
+ align:start position:0%
+just saw right in that case we add some
+extra condition and then we saw that we
+
+ align:start position:0%
+extra condition and then we saw that we
+ 
+
+ align:start position:0%
+extra condition and then we saw that we
+actually have a trade-off right we can
+
+ align:start position:0%
+actually have a trade-off right we can
+ 
+
+ align:start position:0%
+actually have a trade-off right we can
+have a program that does terminate and
+
+ align:start position:0%
+have a program that does terminate and
+ 
+
+ align:start position:0%
+have a program that does terminate and
+reports a correct answer right it
+
+ align:start position:0%
+reports a correct answer right it
+ 
+
+ align:start position:0%
+reports a correct answer right it
+doesn't say we failed but it does report
+
+ align:start position:0%
+doesn't say we failed but it does report
+ 
+
+ align:start position:0%
+doesn't say we failed but it does report
+a correct answer but that could be a a
+
+ align:start position:0%
+a correct answer but that could be a a
+ 
+
+ align:start position:0%
+a correct answer but that could be a a
+program that's a lot slower right it's a
+
+ align:start position:0%
+program that's a lot slower right it's a
+ 
+
+ align:start position:0%
+program that's a lot slower right it's a
+lot slower because we had to decrease
+
+ align:start position:0%
+lot slower because we had to decrease
+ 
+
+ align:start position:0%
+lot slower because we had to decrease
+the uh our increment alternatively we
+
+ align:start position:0%
+the uh our increment alternatively we
+ 
+
+ align:start position:0%
+the uh our increment alternatively we
+could have increased our Epsilon
+
+ align:start position:0%
+could have increased our Epsilon
+ 
+
+ align:start position:0%
+could have increased our Epsilon
+boundary right our plus minus Epsilon
+
+ align:start position:0%
+boundary right our plus minus Epsilon
+ 
+
+ align:start position:0%
+boundary right our plus minus Epsilon
+that we allowed to be within could have
+
+ align:start position:0%
+that we allowed to be within could have
+ 
+
+ align:start position:0%
+that we allowed to be within could have
+been bigger but then we would give up on
+
+ align:start position:0%
+been bigger but then we would give up on
+ 
+
+ align:start position:0%
+been bigger but then we would give up on
+some accuracy as well so there's always
+
+ align:start position:0%
+some accuracy as well so there's always
+ 
+
+ align:start position:0%
+some accuracy as well so there's always
+this trade-off of speed versus accuracy
+
+ align:start position:0%
+this trade-off of speed versus accuracy
+ 
+
+ align:start position:0%
+this trade-off of speed versus accuracy
+to get um the program to do to actually
+
+ align:start position:0%
+to get um the program to do to actually
+ 
+
+ align:start position:0%
+to get um the program to do to actually
+give you an answer or to do what you'd
+
+ align:start position:0%
+give you an answer or to do what you'd
+ 
+
+ align:start position:0%
+give you an answer or to do what you'd
+like right and depending on the
+
+ align:start position:0%
+like right and depending on the
+ 
+
+ align:start position:0%
+like right and depending on the
+application you might want accuracy
+
+ align:start position:0%
+application you might want accuracy
+ 
+
+ align:start position:0%
+application you might want accuracy
+versus speed or vice
+
+ align:start position:0%
+versus speed or vice
+ 
+
+ align:start position:0%
+versus speed or vice
+versa
+
+ align:start position:0%
+versa
+ 
+
+ align:start position:0%
+versa
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this approximation algorithm is is
+
+ align:start position:0%
+so this approximation algorithm is is
+ 
+
+ align:start position:0%
+so this approximation algorithm is is
+really slow right to to get an answer
+
+ align:start position:0%
+really slow right to to get an answer
+ 
+
+ align:start position:0%
+really slow right to to get an answer
+for the Square < t of
+
+ align:start position:0%
+for the Square < t of
+ 
+
+ align:start position:0%
+for the Square < t of
+54321 we had to decrease our increment
+
+ align:start position:0%
+54321 we had to decrease our increment
+ 
+
+ align:start position:0%
+54321 we had to decrease our increment
+to something like
+
+ align:start position:0%
+to something like
+ 
+
+ align:start position:0%
+to something like
+0.0000001 and we ran it and that program
+
+ align:start position:0%
+0.0000001 and we ran it and that program
+ 
+
+ align:start position:0%
+0.0000001 and we ran it and that program
+took maybe 10 seconds to run right on my
+
+ align:start position:0%
+took maybe 10 seconds to run right on my
+ 
+
+ align:start position:0%
+took maybe 10 seconds to run right on my
+computer because we started from zero
+
+ align:start position:0%
+computer because we started from zero
+ 
+
+ align:start position:0%
+computer because we started from zero
+and we were just painfully incrementing
+
+ align:start position:0%
+and we were just painfully incrementing
+ 
+
+ align:start position:0%
+and we were just painfully incrementing
+that increment one at a time even though
+
+ align:start position:0%
+that increment one at a time even though
+ 
+
+ align:start position:0%
+that increment one at a time even though
+we knew sort of from what the number
+
+ align:start position:0%
+we knew sort of from what the number
+ 
+
+ align:start position:0%
+we knew sort of from what the number
+actually was 54,000 that that the square
+
+ align:start position:0%
+actually was 54,000 that that the square
+ 
+
+ align:start position:0%
+actually was 54,000 that that the square
+root of it could not really be that low
+
+ align:start position:0%
+root of it could not really be that low
+ 
+
+ align:start position:0%
+root of it could not really be that low
+but that's just the algorithm we had
+
+ align:start position:0%
+but that's just the algorithm we had
+ 
+
+ align:start position:0%
+but that's just the algorithm we had
+right we had to start from something
+
+ align:start position:0%
+right we had to start from something
+ 
+
+ align:start position:0%
+right we had to start from something
+zero just in case the user gave it other
+
+ align:start position:0%
+zero just in case the user gave it other
+ 
+
+ align:start position:0%
+zero just in case the user gave it other
+numbers which you know didn't make sense
+
+ align:start position:0%
+numbers which you know didn't make sense
+ 
+
+ align:start position:0%
+numbers which you know didn't make sense
+to start higher than that and so the
+
+ align:start position:0%
+to start higher than that and so the
+ 
+
+ align:start position:0%
+to start higher than that and so the
+approximation algorithm as you saw can
+
+ align:start position:0%
+approximation algorithm as you saw can
+ 
+
+ align:start position:0%
+approximation algorithm as you saw can
+be really slow the question I have is is
+
+ align:start position:0%
+be really slow the question I have is is
+ 
+
+ align:start position:0%
+be really slow the question I have is is
+there a faster way that still gets good
+
+ align:start position:0%
+there a faster way that still gets good
+ 
+
+ align:start position:0%
+there a faster way that still gets good
+answers and the answer of course is yes
+
+ align:start position:0%
+answers and the answer of course is yes
+ 
+
+ align:start position:0%
+answers and the answer of course is yes
+and we're going to see this uh this uh
+
+ align:start position:0%
+and we're going to see this uh this uh
+ 
+
+ align:start position:0%
+and we're going to see this uh this uh
+particular this algorithm in the next
+
+ align:start position:0%
+particular this algorithm in the next
+ 
+
+ align:start position:0%
+particular this algorithm in the next
+lecture okay so in quick summary we saw
+
+ align:start position:0%
+lecture okay so in quick summary we saw
+ 
+
+ align:start position:0%
+lecture okay so in quick summary we saw
+floating points uh we did a lot of
+
+ align:start position:0%
+floating points uh we did a lot of
+ 
+
+ align:start position:0%
+floating points uh we did a lot of
+calculations with binary numbers you
+
+ align:start position:0%
+calculations with binary numbers you
+ 
+
+ align:start position:0%
+calculations with binary numbers you
+don't need to know how to do those
+
+ align:start position:0%
+don't need to know how to do those
+ 
+
+ align:start position:0%
+don't need to know how to do those
+calculations but again given a recipe or
+
+ align:start position:0%
+calculations but again given a recipe or
+ 
+
+ align:start position:0%
+calculations but again given a recipe or
+an algorithm can you take that and put
+
+ align:start position:0%
+an algorithm can you take that and put
+ 
+
+ align:start position:0%
+an algorithm can you take that and put
+it into code right floating Point
+
+ align:start position:0%
+it into code right floating Point
+ 
+
+ align:start position:0%
+it into code right floating Point
+numbers introduced a little bit of
+
+ align:start position:0%
+numbers introduced a little bit of
+ 
+
+ align:start position:0%
+numbers introduced a little bit of
+challenge for us in comparing them
+
+ align:start position:0%
+challenge for us in comparing them
+ 
+
+ align:start position:0%
+challenge for us in comparing them
+because of the way they're stored in
+
+ align:start position:0%
+because of the way they're stored in
+ 
+
+ align:start position:0%
+because of the way they're stored in
+memory we can't represent some of these
+
+ align:start position:0%
+memory we can't represent some of these
+ 
+
+ align:start position:0%
+memory we can't represent some of these
+numbers exactly in memory so that's a
+
+ align:start position:0%
+numbers exactly in memory so that's a
+ 
+
+ align:start position:0%
+numbers exactly in memory so that's a
+problem because they're not represented
+
+ align:start position:0%
+problem because they're not represented
+ 
+
+ align:start position:0%
+problem because they're not represented
+exactly in memory we might magnify some
+
+ align:start position:0%
+exactly in memory we might magnify some
+ 
+
+ align:start position:0%
+exactly in memory we might magnify some
+errors right as we saw with that Loop
+
+ align:start position:0%
+errors right as we saw with that Loop
+ 
+
+ align:start position:0%
+errors right as we saw with that Loop
+and the approximation methods use floats
+
+ align:start position:0%
+and the approximation methods use floats
+ 
+
+ align:start position:0%
+and the approximation methods use floats
+unfortunately or fortunately right they
+
+ align:start position:0%
+unfortunately or fortunately right they
+ 
+
+ align:start position:0%
+unfortunately or fortunately right they
+need to use floats because we need to
+
+ align:start position:0%
+need to use floats because we need to
+ 
+
+ align:start position:0%
+need to use floats because we need to
+have a small increment and we have to be
+
+ align:start position:0%
+have a small increment and we have to be
+ 
+
+ align:start position:0%
+have a small increment and we have to be
+mindful of these issues uh when using
+
+ align:start position:0%
+mindful of these issues uh when using
+ 
+
+ align:start position:0%
+mindful of these issues uh when using
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/OQq7qH74T5E.txt b/OQq7qH74T5E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..af783d7728cf6ceb40a672c9a0e433cc63c24692
--- /dev/null
+++ b/OQq7qH74T5E.txt
@@ -0,0 +1,8557 @@
+align:start position:0%
+ 
+good morning everyone and
+
+ align:start position:0%
+good morning everyone and
+ 
+
+ align:start position:0%
+good morning everyone and
+welcome or good afternoon welcome to the
+
+ align:start position:0%
+welcome or good afternoon welcome to the
+ 
+
+ align:start position:0%
+welcome or good afternoon welcome to the
+ellen swallow richards
+
+ align:start position:0%
+ellen swallow richards
+ 
+
+ align:start position:0%
+ellen swallow richards
+lecture series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is our beloved charles river this
+
+ align:start position:0%
+this is our beloved charles river this
+ 
+
+ align:start position:0%
+this is our beloved charles river this
+is the river you're going to be testing
+
+ align:start position:0%
+is the river you're going to be testing
+ 
+
+ align:start position:0%
+is the river you're going to be testing
+once you've tested this river
+
+ align:start position:0%
+once you've tested this river
+ 
+
+ align:start position:0%
+once you've tested this river
+you can actually take this testing and
+
+ align:start position:0%
+you can actually take this testing and
+ 
+
+ align:start position:0%
+you can actually take this testing and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+apply it to any body of water
+
+ align:start position:0%
+apply it to any body of water
+ 
+
+ align:start position:0%
+apply it to any body of water
+why should we be concerned about this
+
+ align:start position:0%
+why should we be concerned about this
+ 
+
+ align:start position:0%
+why should we be concerned about this
+charles river
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes because we live that's a good reason
+
+ align:start position:0%
+yes because we live that's a good reason
+ 
+
+ align:start position:0%
+yes because we live that's a good reason
+because we live next to it anyone else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i should you care about your environment
+
+ align:start position:0%
+i should you care about your environment
+ 
+
+ align:start position:0%
+i should you care about your environment
+and speaking of caring about your
+
+ align:start position:0%
+and speaking of caring about your
+ 
+
+ align:start position:0%
+and speaking of caring about your
+environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've got some problems with phosphate
+
+ align:start position:0%
+we've got some problems with phosphate
+ 
+
+ align:start position:0%
+we've got some problems with phosphate
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+we've got a high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phosphorus
+
+ align:start position:0%
+phosphorus
+ 
+
+ align:start position:0%
+phosphorus
+concentrations and those high phosphorus
+
+ align:start position:0%
+concentrations and those high phosphorus
+ 
+
+ align:start position:0%
+concentrations and those high phosphorus
+concentrations lead to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algal blooms
+
+ align:start position:0%
+algal blooms
+ 
+
+ align:start position:0%
+algal blooms
+and those algal blooms produce
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+toxic chemicals
+
+ align:start position:0%
+toxic chemicals
+ 
+
+ align:start position:0%
+toxic chemicals
+and odors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when all this this algae dies
+
+ align:start position:0%
+and when all this this algae dies
+ 
+
+ align:start position:0%
+and when all this this algae dies
+it heads down to the bottom and breaks
+
+ align:start position:0%
+it heads down to the bottom and breaks
+ 
+
+ align:start position:0%
+it heads down to the bottom and breaks
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+and it's acted on by decomposers
+
+ align:start position:0%
+and it's acted on by decomposers
+ 
+
+ align:start position:0%
+and it's acted on by decomposers
+they these microbes start to chew it
+
+ align:start position:0%
+they these microbes start to chew it
+ 
+
+ align:start position:0%
+they these microbes start to chew it
+apart
+
+ align:start position:0%
+apart
+ 
+
+ align:start position:0%
+apart
+and they use up the the dissolved oxygen
+
+ align:start position:0%
+and they use up the the dissolved oxygen
+ 
+
+ align:start position:0%
+and they use up the the dissolved oxygen
+so that we get lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower dissolved oxygen in the water
+
+ align:start position:0%
+lower dissolved oxygen in the water
+ 
+
+ align:start position:0%
+lower dissolved oxygen in the water
+and what that does is it leads to fish
+
+ align:start position:0%
+and what that does is it leads to fish
+ 
+
+ align:start position:0%
+and what that does is it leads to fish
+kills
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and our recreational ability is impaired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here here are some examples what i'm
+
+ align:start position:0%
+so here here are some examples what i'm
+ 
+
+ align:start position:0%
+so here here are some examples what i'm
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+this is florida 2016.
+
+ align:start position:0%
+this is florida 2016.
+ 
+
+ align:start position:0%
+this is florida 2016.
+this is lake okeechobee one of the
+
+ align:start position:0%
+this is lake okeechobee one of the
+ 
+
+ align:start position:0%
+this is lake okeechobee one of the
+largest freshwater lakes in florida
+
+ align:start position:0%
+largest freshwater lakes in florida
+ 
+
+ align:start position:0%
+largest freshwater lakes in florida
+this is a 30 mile long fish kill
+
+ align:start position:0%
+this is a 30 mile long fish kill
+ 
+
+ align:start position:0%
+this is a 30 mile long fish kill
+it involves some 50 species of fish
+
+ align:start position:0%
+it involves some 50 species of fish
+ 
+
+ align:start position:0%
+it involves some 50 species of fish
+the cause most probably an algal bloom
+
+ align:start position:0%
+the cause most probably an algal bloom
+ 
+
+ align:start position:0%
+the cause most probably an algal bloom
+the result of leaking septic systems
+
+ align:start position:0%
+the result of leaking septic systems
+ 
+
+ align:start position:0%
+the result of leaking septic systems
+uh fertilizers from lawns going into the
+
+ align:start position:0%
+uh fertilizers from lawns going into the
+ 
+
+ align:start position:0%
+uh fertilizers from lawns going into the
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+this is an economic disaster it's going
+
+ align:start position:0%
+this is an economic disaster it's going
+ 
+
+ align:start position:0%
+this is an economic disaster it's going
+to take decades to recover from this
+
+ align:start position:0%
+to take decades to recover from this
+ 
+
+ align:start position:0%
+to take decades to recover from this
+this is bradenton florida 2018.
+
+ align:start position:0%
+this is bradenton florida 2018.
+ 
+
+ align:start position:0%
+this is bradenton florida 2018.
+this is their harbor filled with dead
+
+ align:start position:0%
+this is their harbor filled with dead
+ 
+
+ align:start position:0%
+this is their harbor filled with dead
+fish
+
+ align:start position:0%
+fish
+ 
+
+ align:start position:0%
+fish
+this started from an algarve bloom that
+
+ align:start position:0%
+this started from an algarve bloom that
+ 
+
+ align:start position:0%
+this started from an algarve bloom that
+turned into a red
+
+ align:start position:0%
+turned into a red
+ 
+
+ align:start position:0%
+turned into a red
+tide and the red tide stretched about
+
+ align:start position:0%
+tide and the red tide stretched about
+ 
+
+ align:start position:0%
+tide and the red tide stretched about
+150 miles
+
+ align:start position:0%
+150 miles
+ 
+
+ align:start position:0%
+150 miles
+off the coast of florida and gradually
+
+ align:start position:0%
+off the coast of florida and gradually
+ 
+
+ align:start position:0%
+off the coast of florida and gradually
+the wind and
+
+ align:start position:0%
+the wind and
+ 
+
+ align:start position:0%
+the wind and
+the currents brought it into shore and
+
+ align:start position:0%
+the currents brought it into shore and
+ 
+
+ align:start position:0%
+the currents brought it into shore and
+when that red tide came into shore it
+
+ align:start position:0%
+when that red tide came into shore it
+ 
+
+ align:start position:0%
+when that red tide came into shore it
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+releasing toxins into the air and water
+
+ align:start position:0%
+releasing toxins into the air and water
+ 
+
+ align:start position:0%
+releasing toxins into the air and water
+and then the nutrients broke off and
+
+ align:start position:0%
+and then the nutrients broke off and
+ 
+
+ align:start position:0%
+and then the nutrients broke off and
+microbes started digesting them and used
+
+ align:start position:0%
+microbes started digesting them and used
+ 
+
+ align:start position:0%
+microbes started digesting them and used
+up the the oxygen and all these fish
+
+ align:start position:0%
+up the the oxygen and all these fish
+ 
+
+ align:start position:0%
+up the the oxygen and all these fish
+died
+
+ align:start position:0%
+died
+ 
+
+ align:start position:0%
+died
+this is australia 2019.
+
+ align:start position:0%
+this is australia 2019.
+ 
+
+ align:start position:0%
+this is australia 2019.
+this is the darling river but it also
+
+ align:start position:0%
+this is the darling river but it also
+ 
+
+ align:start position:0%
+this is the darling river but it also
+happened in the mendeleev river
+
+ align:start position:0%
+happened in the mendeleev river
+ 
+
+ align:start position:0%
+happened in the mendeleev river
+and they had a successive run of these
+
+ align:start position:0%
+and they had a successive run of these
+ 
+
+ align:start position:0%
+and they had a successive run of these
+fish kills one right after the other
+
+ align:start position:0%
+fish kills one right after the other
+ 
+
+ align:start position:0%
+fish kills one right after the other
+again it's global hot temperatures
+
+ align:start position:0%
+again it's global hot temperatures
+ 
+
+ align:start position:0%
+again it's global hot temperatures
+and agricultural runoff
+
+ align:start position:0%
+and agricultural runoff
+ 
+
+ align:start position:0%
+and agricultural runoff
+this is the charles river august 2019
+
+ align:start position:0%
+this is the charles river august 2019
+ 
+
+ align:start position:0%
+this is the charles river august 2019
+this is the largest algal bloom i think
+
+ align:start position:0%
+this is the largest algal bloom i think
+ 
+
+ align:start position:0%
+this is the largest algal bloom i think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+we've had out there it actually
+
+ align:start position:0%
+we've had out there it actually
+ 
+
+ align:start position:0%
+we've had out there it actually
+stretched from the bu
+
+ align:start position:0%
+stretched from the bu
+ 
+
+ align:start position:0%
+stretched from the bu
+bridge to the museum of science
+
+ align:start position:0%
+bridge to the museum of science
+ 
+
+ align:start position:0%
+bridge to the museum of science
+and cyanobacteria was detected
+
+ align:start position:0%
+and cyanobacteria was detected
+ 
+
+ align:start position:0%
+and cyanobacteria was detected
+this is a a health problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to be measuring
+
+ align:start position:0%
+so we're going to be measuring
+ 
+
+ align:start position:0%
+so we're going to be measuring
+phosphorus in the waters out here that's
+
+ align:start position:0%
+phosphorus in the waters out here that's
+ 
+
+ align:start position:0%
+phosphorus in the waters out here that's
+one of the things we're going to do
+
+ align:start position:0%
+one of the things we're going to do
+ 
+
+ align:start position:0%
+one of the things we're going to do
+and there are two types of phosphorus
+
+ align:start position:0%
+and there are two types of phosphorus
+ 
+
+ align:start position:0%
+and there are two types of phosphorus
+there's the
+
+ align:start position:0%
+there's the
+ 
+
+ align:start position:0%
+there's the
+inorganic which is simply
+
+ align:start position:0%
+inorganic which is simply
+ 
+
+ align:start position:0%
+inorganic which is simply
+salts of phosphoric acid and then if you
+
+ align:start position:0%
+salts of phosphoric acid and then if you
+ 
+
+ align:start position:0%
+salts of phosphoric acid and then if you
+create esters of the inorganic form you
+
+ align:start position:0%
+create esters of the inorganic form you
+ 
+
+ align:start position:0%
+create esters of the inorganic form you
+have the organic
+
+ align:start position:0%
+have the organic
+ 
+
+ align:start position:0%
+have the organic
+form of phosphate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so let's take a look for a moment at the
+
+ align:start position:0%
+so let's take a look for a moment at the
+ 
+
+ align:start position:0%
+so let's take a look for a moment at the
+inorganic
+
+ align:start position:0%
+inorganic
+ 
+
+ align:start position:0%
+inorganic
+phosphate i mean phosphorus is
+
+ align:start position:0%
+phosphate i mean phosphorus is
+ 
+
+ align:start position:0%
+phosphate i mean phosphorus is
+like the 11th most abundant element on
+
+ align:start position:0%
+like the 11th most abundant element on
+ 
+
+ align:start position:0%
+like the 11th most abundant element on
+the planet
+
+ align:start position:0%
+the planet
+ 
+
+ align:start position:0%
+the planet
+and it's not found in elemental form
+
+ align:start position:0%
+and it's not found in elemental form
+ 
+
+ align:start position:0%
+and it's not found in elemental form
+you won't find any
+
+ align:start position:0%
+you won't find any
+ 
+
+ align:start position:0%
+you won't find any
+pure phosphorus anywhere in the on the
+
+ align:start position:0%
+pure phosphorus anywhere in the on the
+ 
+
+ align:start position:0%
+pure phosphorus anywhere in the on the
+earth it's found
+
+ align:start position:0%
+earth it's found
+ 
+
+ align:start position:0%
+earth it's found
+in these types of phosphates in rocks
+
+ align:start position:0%
+in these types of phosphates in rocks
+ 
+
+ align:start position:0%
+in these types of phosphates in rocks
+and soils
+
+ align:start position:0%
+and soils
+ 
+
+ align:start position:0%
+and soils
+and that's how that's how it exists so
+
+ align:start position:0%
+and that's how that's how it exists so
+ 
+
+ align:start position:0%
+and that's how that's how it exists so
+the the main
+
+ align:start position:0%
+the the main
+ 
+
+ align:start position:0%
+the the main
+inorganic player here is the
+
+ align:start position:0%
+inorganic player here is the
+ 
+
+ align:start position:0%
+inorganic player here is the
+orthophosphate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the po4 to the three minus
+
+ align:start position:0%
+and that's the po4 to the three minus
+ 
+
+ align:start position:0%
+and that's the po4 to the three minus
+this is the most stable form of
+
+ align:start position:0%
+this is the most stable form of
+ 
+
+ align:start position:0%
+this is the most stable form of
+phosphorus
+
+ align:start position:0%
+phosphorus
+ 
+
+ align:start position:0%
+phosphorus
+and this is the form that's readily
+
+ align:start position:0%
+and this is the form that's readily
+ 
+
+ align:start position:0%
+and this is the form that's readily
+available
+
+ align:start position:0%
+available
+ 
+
+ align:start position:0%
+available
+to plants for uptake by the plants
+
+ align:start position:0%
+to plants for uptake by the plants
+ 
+
+ align:start position:0%
+to plants for uptake by the plants
+i mean all all plants and animals need
+
+ align:start position:0%
+i mean all all plants and animals need
+ 
+
+ align:start position:0%
+i mean all all plants and animals need
+phosphorus
+
+ align:start position:0%
+phosphorus
+ 
+
+ align:start position:0%
+phosphorus
+for growth it's it's the backbone of our
+
+ align:start position:0%
+for growth it's it's the backbone of our
+ 
+
+ align:start position:0%
+for growth it's it's the backbone of our
+of our dna and the krebs cycle
+
+ align:start position:0%
+of our dna and the krebs cycle
+ 
+
+ align:start position:0%
+of our dna and the krebs cycle
+plants needed in photosynthesis they
+
+ align:start position:0%
+plants needed in photosynthesis they
+ 
+
+ align:start position:0%
+plants needed in photosynthesis they
+have to extract it from their
+
+ align:start position:0%
+have to extract it from their
+ 
+
+ align:start position:0%
+have to extract it from their
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+because they're not going to make sugar
+
+ align:start position:0%
+because they're not going to make sugar
+ 
+
+ align:start position:0%
+because they're not going to make sugar
+unless they first make atp
+
+ align:start position:0%
+unless they first make atp
+ 
+
+ align:start position:0%
+unless they first make atp
+to actually connect those bonds in the
+
+ align:start position:0%
+to actually connect those bonds in the
+ 
+
+ align:start position:0%
+to actually connect those bonds in the
+sugars that that are that are that
+
+ align:start position:0%
+sugars that that are that are that
+ 
+
+ align:start position:0%
+sugars that that are that are that
+they're making
+
+ align:start position:0%
+they're making
+ 
+
+ align:start position:0%
+they're making
+so we've got this orthophosphate the
+
+ align:start position:0%
+so we've got this orthophosphate the
+ 
+
+ align:start position:0%
+so we've got this orthophosphate the
+main player here
+
+ align:start position:0%
+main player here
+ 
+
+ align:start position:0%
+main player here
+but in the inorganic category you can
+
+ align:start position:0%
+but in the inorganic category you can
+ 
+
+ align:start position:0%
+but in the inorganic category you can
+actually connect
+
+ align:start position:0%
+actually connect
+ 
+
+ align:start position:0%
+actually connect
+several of these together and form a
+
+ align:start position:0%
+several of these together and form a
+ 
+
+ align:start position:0%
+several of these together and form a
+polyphosphate
+
+ align:start position:0%
+polyphosphate
+ 
+
+ align:start position:0%
+polyphosphate
+such as our detergents a lot of
+
+ align:start position:0%
+such as our detergents a lot of
+ 
+
+ align:start position:0%
+such as our detergents a lot of
+detergents of polyphosphates
+
+ align:start position:0%
+detergents of polyphosphates
+ 
+
+ align:start position:0%
+detergents of polyphosphates
+p3 to the 5 minus would be a
+
+ align:start position:0%
+p3 to the 5 minus would be a
+ 
+
+ align:start position:0%
+p3 to the 5 minus would be a
+polyphosphate
+
+ align:start position:0%
+polyphosphate
+ 
+
+ align:start position:0%
+polyphosphate
+the interesting thing about the
+
+ align:start position:0%
+the interesting thing about the
+ 
+
+ align:start position:0%
+the interesting thing about the
+polyphosphates is as soon as they hit
+
+ align:start position:0%
+polyphosphates is as soon as they hit
+ 
+
+ align:start position:0%
+polyphosphates is as soon as they hit
+the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they hydrolyze into the orthophosphate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we've got the organic
+
+ align:start position:0%
+and then we've got the organic
+ 
+
+ align:start position:0%
+and then we've got the organic
+phosphates
+
+ align:start position:0%
+phosphates
+ 
+
+ align:start position:0%
+phosphates
+which uh which are esters of the
+
+ align:start position:0%
+which uh which are esters of the
+ 
+
+ align:start position:0%
+which uh which are esters of the
+inorganic form
+
+ align:start position:0%
+inorganic form
+ 
+
+ align:start position:0%
+inorganic form
+and organic phosphates are found in all
+
+ align:start position:0%
+and organic phosphates are found in all
+ 
+
+ align:start position:0%
+and organic phosphates are found in all
+living tissues
+
+ align:start position:0%
+living tissues
+ 
+
+ align:start position:0%
+living tissues
+so all living tissues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both plants and animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have organic phosphates and
+
+ align:start position:0%
+have organic phosphates and
+ 
+
+ align:start position:0%
+have organic phosphates and
+waste is also another form of the
+
+ align:start position:0%
+waste is also another form of the
+ 
+
+ align:start position:0%
+waste is also another form of the
+organic
+
+ align:start position:0%
+organic
+ 
+
+ align:start position:0%
+organic
+phosphates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when something living dies it starts
+
+ align:start position:0%
+so when something living dies it starts
+ 
+
+ align:start position:0%
+so when something living dies it starts
+to decay
+
+ align:start position:0%
+to decay
+ 
+
+ align:start position:0%
+to decay
+what happens is these the phosphates
+
+ align:start position:0%
+what happens is these the phosphates
+ 
+
+ align:start position:0%
+what happens is these the phosphates
+actually convert to the orthophosphate
+
+ align:start position:0%
+actually convert to the orthophosphate
+ 
+
+ align:start position:0%
+actually convert to the orthophosphate
+that's what that's what happens to them
+
+ align:start position:0%
+that's what that's what happens to them
+ 
+
+ align:start position:0%
+that's what that's what happens to them
+so this is what we're going to be
+
+ align:start position:0%
+so this is what we're going to be
+ 
+
+ align:start position:0%
+so this is what we're going to be
+measuring and
+
+ align:start position:0%
+measuring and
+ 
+
+ align:start position:0%
+measuring and
+now i'd like to talk for a few minutes
+
+ align:start position:0%
+now i'd like to talk for a few minutes
+ 
+
+ align:start position:0%
+now i'd like to talk for a few minutes
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how it gets into the water where all
+
+ align:start position:0%
+how it gets into the water where all
+ 
+
+ align:start position:0%
+how it gets into the water where all
+this stuff is coming from
+
+ align:start position:0%
+this stuff is coming from
+ 
+
+ align:start position:0%
+this stuff is coming from
+so we're going to look at some of the
+
+ align:start position:0%
+so we're going to look at some of the
+ 
+
+ align:start position:0%
+so we're going to look at some of the
+primary sources of the
+
+ align:start position:0%
+primary sources of the
+ 
+
+ align:start position:0%
+primary sources of the
+of the phosphorus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one is storm water runoff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can anyone give me an example
+
+ align:start position:0%
+can anyone give me an example
+ 
+
+ align:start position:0%
+can anyone give me an example
+of some phos phosphoruses
+
+ align:start position:0%
+of some phos phosphoruses
+ 
+
+ align:start position:0%
+of some phos phosphoruses
+phosphates that can get into the water
+
+ align:start position:0%
+phosphates that can get into the water
+ 
+
+ align:start position:0%
+phosphates that can get into the water
+from storm water runoff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes i'm not sure if there's a phosphate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely there's phosphate in in the
+
+ align:start position:0%
+absolutely there's phosphate in in the
+ 
+
+ align:start position:0%
+absolutely there's phosphate in in the
+dirt and that
+
+ align:start position:0%
+dirt and that
+ 
+
+ align:start position:0%
+dirt and that
+that would get washed in what what else
+
+ align:start position:0%
+that would get washed in what what else
+ 
+
+ align:start position:0%
+that would get washed in what what else
+yes jimmy actually plus so
+
+ align:start position:0%
+yes jimmy actually plus so
+ 
+
+ align:start position:0%
+yes jimmy actually plus so
+here but an agricultural reader's
+
+ align:start position:0%
+here but an agricultural reader's
+ 
+
+ align:start position:0%
+here but an agricultural reader's
+fertilizer oh gosh yes
+
+ align:start position:0%
+fertilizer oh gosh yes
+ 
+
+ align:start position:0%
+fertilizer oh gosh yes
+fertilizers are a big thing because of
+
+ align:start position:0%
+fertilizers are a big thing because of
+ 
+
+ align:start position:0%
+fertilizers are a big thing because of
+of lawns
+
+ align:start position:0%
+of lawns
+ 
+
+ align:start position:0%
+of lawns
+so we've got we've got soil here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and fertilizers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jimmy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely animal waste i mean think
+
+ align:start position:0%
+absolutely animal waste i mean think
+ 
+
+ align:start position:0%
+absolutely animal waste i mean think
+think about where did they put pig farms
+
+ align:start position:0%
+think about where did they put pig farms
+ 
+
+ align:start position:0%
+think about where did they put pig farms
+they put them
+
+ align:start position:0%
+they put them
+ 
+
+ align:start position:0%
+they put them
+all by a river right and
+
+ align:start position:0%
+all by a river right and
+ 
+
+ align:start position:0%
+all by a river right and
+all those geese you know the guano and
+
+ align:start position:0%
+all those geese you know the guano and
+ 
+
+ align:start position:0%
+all those geese you know the guano and
+droppings everything
+
+ align:start position:0%
+droppings everything
+ 
+
+ align:start position:0%
+droppings everything
+it's they're all out there by the river
+
+ align:start position:0%
+it's they're all out there by the river
+ 
+
+ align:start position:0%
+it's they're all out there by the river
+and all that stuff is being washed in
+
+ align:start position:0%
+and all that stuff is being washed in
+ 
+
+ align:start position:0%
+and all that stuff is being washed in
+so so uh animal waste is a big big
+
+ align:start position:0%
+so so uh animal waste is a big big
+ 
+
+ align:start position:0%
+so so uh animal waste is a big big
+source here
+
+ align:start position:0%
+source here
+ 
+
+ align:start position:0%
+source here
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you ever got your car washed in a car
+
+ align:start position:0%
+you ever got your car washed in a car
+ 
+
+ align:start position:0%
+you ever got your car washed in a car
+wash
+
+ align:start position:0%
+wash
+ 
+
+ align:start position:0%
+wash
+did you ever sit in it while you're
+
+ align:start position:0%
+did you ever sit in it while you're
+ 
+
+ align:start position:0%
+did you ever sit in it while you're
+going through see all that soap coming
+
+ align:start position:0%
+going through see all that soap coming
+ 
+
+ align:start position:0%
+going through see all that soap coming
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+tons of soap and all that soaps going
+
+ align:start position:0%
+tons of soap and all that soaps going
+ 
+
+ align:start position:0%
+tons of soap and all that soaps going
+into the sewer systems and
+
+ align:start position:0%
+into the sewer systems and
+ 
+
+ align:start position:0%
+into the sewer systems and
+you know when it when it starts to rain
+
+ align:start position:0%
+you know when it when it starts to rain
+ 
+
+ align:start position:0%
+you know when it when it starts to rain
+heavy rains it bubbles over
+
+ align:start position:0%
+heavy rains it bubbles over
+ 
+
+ align:start position:0%
+heavy rains it bubbles over
+so car washes would be a big source and
+
+ align:start position:0%
+so car washes would be a big source and
+ 
+
+ align:start position:0%
+so car washes would be a big source and
+that there
+
+ align:start position:0%
+that there
+ 
+
+ align:start position:0%
+that there
+there's your polyphosphates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another one that you might not be as
+
+ align:start position:0%
+another one that you might not be as
+ 
+
+ align:start position:0%
+another one that you might not be as
+familiar with is car exhausts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+car exhausts have a catalyst tube in
+
+ align:start position:0%
+car exhausts have a catalyst tube in
+ 
+
+ align:start position:0%
+car exhausts have a catalyst tube in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+when that tube gets hot like 500 600 700
+
+ align:start position:0%
+when that tube gets hot like 500 600 700
+ 
+
+ align:start position:0%
+when that tube gets hot like 500 600 700
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+it can form cerium phosphate which is
+
+ align:start position:0%
+it can form cerium phosphate which is
+ 
+
+ align:start position:0%
+it can form cerium phosphate which is
+released
+
+ align:start position:0%
+released
+ 
+
+ align:start position:0%
+released
+in the in the exhaust effluent so serum
+
+ align:start position:0%
+in the in the exhaust effluent so serum
+ 
+
+ align:start position:0%
+in the in the exhaust effluent so serum
+phosphate would be
+
+ align:start position:0%
+phosphate would be
+ 
+
+ align:start position:0%
+phosphate would be
+a culprit here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then probably the biggest source
+
+ align:start position:0%
+and then probably the biggest source
+ 
+
+ align:start position:0%
+and then probably the biggest source
+is discharge from waste water treatment
+
+ align:start position:0%
+is discharge from waste water treatment
+ 
+
+ align:start position:0%
+is discharge from waste water treatment
+plants
+
+ align:start position:0%
+plants
+ 
+
+ align:start position:0%
+plants
+did any of you ever go to tour a
+
+ align:start position:0%
+did any of you ever go to tour a
+ 
+
+ align:start position:0%
+did any of you ever go to tour a
+wastewater treatment plant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone oh you did
+
+ align:start position:0%
+anyone oh you did
+ 
+
+ align:start position:0%
+anyone oh you did
+kelly right yeah could you tell us tell
+
+ align:start position:0%
+kelly right yeah could you tell us tell
+ 
+
+ align:start position:0%
+kelly right yeah could you tell us tell
+us about it what your experience was
+
+ align:start position:0%
+us about it what your experience was
+ 
+
+ align:start position:0%
+us about it what your experience was
+um it's like a school finish up like a
+
+ align:start position:0%
+um it's like a school finish up like a
+ 
+
+ align:start position:0%
+um it's like a school finish up like a
+long time ago i think
+
+ align:start position:0%
+long time ago i think
+ 
+
+ align:start position:0%
+long time ago i think
+uh it was interesting so they like
+
+ align:start position:0%
+uh it was interesting so they like
+ 
+
+ align:start position:0%
+uh it was interesting so they like
+purify it or they took the water in like
+
+ align:start position:0%
+purify it or they took the water in like
+ 
+
+ align:start position:0%
+purify it or they took the water in like
+several different methods
+
+ align:start position:0%
+several different methods
+ 
+
+ align:start position:0%
+several different methods
+one which is like bacterial i think they
+
+ align:start position:0%
+one which is like bacterial i think they
+ 
+
+ align:start position:0%
+one which is like bacterial i think they
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+yeah they they aerate it with bacteria i
+
+ align:start position:0%
+yeah they they aerate it with bacteria i
+ 
+
+ align:start position:0%
+yeah they they aerate it with bacteria i
+think in the
+
+ align:start position:0%
+think in the
+ 
+
+ align:start position:0%
+think in the
+in in the secondary treatment and they
+
+ align:start position:0%
+in in the secondary treatment and they
+ 
+
+ align:start position:0%
+in in the secondary treatment and they
+do that to
+
+ align:start position:0%
+do that to
+ 
+
+ align:start position:0%
+do that to
+to get rid of organic matter and they
+
+ align:start position:0%
+to get rid of organic matter and they
+ 
+
+ align:start position:0%
+to get rid of organic matter and they
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+were to digest it down to sludge yeah
+
+ align:start position:0%
+were to digest it down to sludge yeah
+ 
+
+ align:start position:0%
+were to digest it down to sludge yeah
+and then there's like a uv very good i
+
+ align:start position:0%
+and then there's like a uv very good i
+ 
+
+ align:start position:0%
+and then there's like a uv very good i
+mean the most modern plants have this
+
+ align:start position:0%
+mean the most modern plants have this
+ 
+
+ align:start position:0%
+mean the most modern plants have this
+ultraviolet rays at the very end you can
+
+ align:start position:0%
+ultraviolet rays at the very end you can
+ 
+
+ align:start position:0%
+ultraviolet rays at the very end you can
+walk along and you can see a glass
+
+ align:start position:0%
+walk along and you can see a glass
+ 
+
+ align:start position:0%
+walk along and you can see a glass
+uh floor you can see the water going
+
+ align:start position:0%
+uh floor you can see the water going
+ 
+
+ align:start position:0%
+uh floor you can see the water going
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+with the ultraviolet rays hitting it and
+
+ align:start position:0%
+with the ultraviolet rays hitting it and
+ 
+
+ align:start position:0%
+with the ultraviolet rays hitting it and
+then at the end
+
+ align:start position:0%
+then at the end
+ 
+
+ align:start position:0%
+then at the end
+they have a faucet and they offer you a
+
+ align:start position:0%
+they have a faucet and they offer you a
+ 
+
+ align:start position:0%
+they have a faucet and they offer you a
+drink
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean there was no no one in my group
+
+ align:start position:0%
+i mean there was no no one in my group
+ 
+
+ align:start position:0%
+i mean there was no no one in my group
+that that availed themselves to
+
+ align:start position:0%
+that that availed themselves to
+ 
+
+ align:start position:0%
+that that availed themselves to
+take a sip of that water after you know
+
+ align:start position:0%
+take a sip of that water after you know
+ 
+
+ align:start position:0%
+take a sip of that water after you know
+going through that
+
+ align:start position:0%
+going through that
+ 
+
+ align:start position:0%
+going through that
+but let's let's put this in perspective
+
+ align:start position:0%
+but let's let's put this in perspective
+ 
+
+ align:start position:0%
+but let's let's put this in perspective
+so uh wastewater treatment plants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're all built along rivers or oceans
+
+ align:start position:0%
+they're all built along rivers or oceans
+ 
+
+ align:start position:0%
+they're all built along rivers or oceans
+and um you know when it had heavy rain
+
+ align:start position:0%
+and um you know when it had heavy rain
+ 
+
+ align:start position:0%
+and um you know when it had heavy rain
+they start to discharge they have to
+
+ align:start position:0%
+they start to discharge they have to
+ 
+
+ align:start position:0%
+they start to discharge they have to
+discharge they can't take the flow
+
+ align:start position:0%
+discharge they can't take the flow
+ 
+
+ align:start position:0%
+discharge they can't take the flow
+first thing they may discharge some of
+
+ align:start position:0%
+first thing they may discharge some of
+ 
+
+ align:start position:0%
+first thing they may discharge some of
+the secondary treated water
+
+ align:start position:0%
+the secondary treated water
+ 
+
+ align:start position:0%
+the secondary treated water
+sometimes they have to discharge the raw
+
+ align:start position:0%
+sometimes they have to discharge the raw
+ 
+
+ align:start position:0%
+sometimes they have to discharge the raw
+sewage
+
+ align:start position:0%
+sewage
+ 
+
+ align:start position:0%
+sewage
+but to put it in perspective all of us
+
+ align:start position:0%
+but to put it in perspective all of us
+ 
+
+ align:start position:0%
+but to put it in perspective all of us
+produce about 2.2 grams
+
+ align:start position:0%
+produce about 2.2 grams
+ 
+
+ align:start position:0%
+produce about 2.2 grams
+of pea per day
+
+ align:start position:0%
+of pea per day
+ 
+
+ align:start position:0%
+of pea per day
+i'm talking about phosphorus here
+
+ align:start position:0%
+i'm talking about phosphorus here
+ 
+
+ align:start position:0%
+i'm talking about phosphorus here
+that's about 1.8 pounds
+
+ align:start position:0%
+that's about 1.8 pounds
+ 
+
+ align:start position:0%
+that's about 1.8 pounds
+per year
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when that phosphorus hits the sewage
+
+ align:start position:0%
+now when that phosphorus hits the sewage
+ 
+
+ align:start position:0%
+now when that phosphorus hits the sewage
+treatment plant it's in the effluent
+
+ align:start position:0%
+treatment plant it's in the effluent
+ 
+
+ align:start position:0%
+treatment plant it's in the effluent
+it gets diluted down you're talking
+
+ align:start position:0%
+it gets diluted down you're talking
+ 
+
+ align:start position:0%
+it gets diluted down you're talking
+somewhere between
+
+ align:start position:0%
+somewhere between
+ 
+
+ align:start position:0%
+somewhere between
+two and probably
+
+ align:start position:0%
+two and probably
+ 
+
+ align:start position:0%
+two and probably
+20 milligrams per liter
+
+ align:start position:0%
+20 milligrams per liter
+ 
+
+ align:start position:0%
+20 milligrams per liter
+ppm of phosphorus in the water
+
+ align:start position:0%
+ppm of phosphorus in the water
+ 
+
+ align:start position:0%
+ppm of phosphorus in the water
+after the secondary treatment they only
+
+ align:start position:0%
+after the secondary treatment they only
+ 
+
+ align:start position:0%
+after the secondary treatment they only
+take out
+
+ align:start position:0%
+take out
+ 
+
+ align:start position:0%
+take out
+between one and two milligrams per liter
+
+ align:start position:0%
+between one and two milligrams per liter
+ 
+
+ align:start position:0%
+between one and two milligrams per liter
+so you've got you end up with a large
+
+ align:start position:0%
+so you've got you end up with a large
+ 
+
+ align:start position:0%
+so you've got you end up with a large
+excess
+
+ align:start position:0%
+excess
+ 
+
+ align:start position:0%
+excess
+of phosphorus in the treated water
+
+ align:start position:0%
+of phosphorus in the treated water
+ 
+
+ align:start position:0%
+of phosphorus in the treated water
+so when they release it's a ton of
+
+ align:start position:0%
+so when they release it's a ton of
+ 
+
+ align:start position:0%
+so when they release it's a ton of
+phosphorus
+
+ align:start position:0%
+phosphorus
+ 
+
+ align:start position:0%
+phosphorus
+hitting hitting the water but
+
+ align:start position:0%
+hitting hitting the water but
+ 
+
+ align:start position:0%
+hitting hitting the water but
+you know the good news is i'm going to
+
+ align:start position:0%
+you know the good news is i'm going to
+ 
+
+ align:start position:0%
+you know the good news is i'm going to
+draw
+
+ align:start position:0%
+draw
+ 
+
+ align:start position:0%
+draw
+a smiley face here because
+
+ align:start position:0%
+a smiley face here because
+ 
+
+ align:start position:0%
+a smiley face here because
+the epa just filed a regulation
+
+ align:start position:0%
+the epa just filed a regulation
+ 
+
+ align:start position:0%
+the epa just filed a regulation
+forcing they're going to force all these
+
+ align:start position:0%
+forcing they're going to force all these
+ 
+
+ align:start position:0%
+forcing they're going to force all these
+wastewater treatment plants
+
+ align:start position:0%
+wastewater treatment plants
+ 
+
+ align:start position:0%
+wastewater treatment plants
+to cut back on the get rid of the
+
+ align:start position:0%
+to cut back on the get rid of the
+ 
+
+ align:start position:0%
+to cut back on the get rid of the
+phosphorus in the water
+
+ align:start position:0%
+phosphorus in the water
+ 
+
+ align:start position:0%
+phosphorus in the water
+and they're going to have to they're
+
+ align:start position:0%
+and they're going to have to they're
+ 
+
+ align:start position:0%
+and they're going to have to they're
+going to have to take it down to
+
+ align:start position:0%
+going to have to take it down to
+ 
+
+ align:start position:0%
+going to have to take it down to
+less than 1.0
+
+ align:start position:0%
+less than 1.0
+ 
+
+ align:start position:0%
+less than 1.0
+milligrams per liter so all these plants
+
+ align:start position:0%
+milligrams per liter so all these plants
+ 
+
+ align:start position:0%
+milligrams per liter so all these plants
+are running around now
+
+ align:start position:0%
+are running around now
+ 
+
+ align:start position:0%
+are running around now
+trying to figure out how they're going
+
+ align:start position:0%
+trying to figure out how they're going
+ 
+
+ align:start position:0%
+trying to figure out how they're going
+to do that this this i believe just went
+
+ align:start position:0%
+to do that this this i believe just went
+ 
+
+ align:start position:0%
+to do that this this i believe just went
+into effect
+
+ align:start position:0%
+into effect
+ 
+
+ align:start position:0%
+into effect
+this year and it may may go may be
+
+ align:start position:0%
+this year and it may may go may be
+ 
+
+ align:start position:0%
+this year and it may may go may be
+starting
+
+ align:start position:0%
+starting
+ 
+
+ align:start position:0%
+starting
+in january 2020 but there are epa
+
+ align:start position:0%
+in january 2020 but there are epa
+ 
+
+ align:start position:0%
+in january 2020 but there are epa
+regulations that that are just coming
+
+ align:start position:0%
+regulations that that are just coming
+ 
+
+ align:start position:0%
+regulations that that are just coming
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+the other major source is sewer
+
+ align:start position:0%
+the other major source is sewer
+ 
+
+ align:start position:0%
+the other major source is sewer
+overflows
+
+ align:start position:0%
+overflows
+ 
+
+ align:start position:0%
+overflows
+and in new england everyone
+
+ align:start position:0%
+and in new england everyone
+ 
+
+ align:start position:0%
+and in new england everyone
+it's notorious that you have a sump pump
+
+ align:start position:0%
+it's notorious that you have a sump pump
+ 
+
+ align:start position:0%
+it's notorious that you have a sump pump
+in your basement
+
+ align:start position:0%
+in your basement
+ 
+
+ align:start position:0%
+in your basement
+so when your basement floods the pump
+
+ align:start position:0%
+so when your basement floods the pump
+ 
+
+ align:start position:0%
+so when your basement floods the pump
+starts up
+
+ align:start position:0%
+starts up
+ 
+
+ align:start position:0%
+starts up
+and it pumps everything they're
+
+ align:start position:0%
+and it pumps everything they're
+ 
+
+ align:start position:0%
+and it pumps everything they're
+connected to the sewer systems
+
+ align:start position:0%
+connected to the sewer systems
+ 
+
+ align:start position:0%
+connected to the sewer systems
+so everything in the kitchen sink is
+
+ align:start position:0%
+so everything in the kitchen sink is
+ 
+
+ align:start position:0%
+so everything in the kitchen sink is
+going into the sewer system
+
+ align:start position:0%
+going into the sewer system
+ 
+
+ align:start position:0%
+going into the sewer system
+and it's bubbling over so those are the
+
+ align:start position:0%
+and it's bubbling over so those are the
+ 
+
+ align:start position:0%
+and it's bubbling over so those are the
+those are the primary sources
+
+ align:start position:0%
+those are the primary sources
+ 
+
+ align:start position:0%
+those are the primary sources
+now let's look at the ecological effect
+
+ align:start position:0%
+now let's look at the ecological effect
+ 
+
+ align:start position:0%
+now let's look at the ecological effect
+of all this phosphorus
+
+ align:start position:0%
+of all this phosphorus
+ 
+
+ align:start position:0%
+of all this phosphorus
+this is the charles river the famous
+
+ align:start position:0%
+this is the charles river the famous
+ 
+
+ align:start position:0%
+this is the charles river the famous
+charles river this is up by newton mass
+
+ align:start position:0%
+charles river this is up by newton mass
+ 
+
+ align:start position:0%
+charles river this is up by newton mass
+i mean there's a guy in a canoe trying
+
+ align:start position:0%
+i mean there's a guy in a canoe trying
+ 
+
+ align:start position:0%
+i mean there's a guy in a canoe trying
+to pull out the vegetation
+
+ align:start position:0%
+to pull out the vegetation
+ 
+
+ align:start position:0%
+to pull out the vegetation
+out of the out of the water what this
+
+ align:start position:0%
+out of the out of the water what this
+ 
+
+ align:start position:0%
+out of the out of the water what this
+vegetation does is
+
+ align:start position:0%
+vegetation does is
+ 
+
+ align:start position:0%
+vegetation does is
+two things first it's blocking the
+
+ align:start position:0%
+two things first it's blocking the
+ 
+
+ align:start position:0%
+two things first it's blocking the
+sunlight
+
+ align:start position:0%
+sunlight
+ 
+
+ align:start position:0%
+sunlight
+to organisms and other plants down below
+
+ align:start position:0%
+to organisms and other plants down below
+ 
+
+ align:start position:0%
+to organisms and other plants down below
+the surface that need that sun
+
+ align:start position:0%
+the surface that need that sun
+ 
+
+ align:start position:0%
+the surface that need that sun
+and the second thing is it's it's going
+
+ align:start position:0%
+and the second thing is it's it's going
+ 
+
+ align:start position:0%
+and the second thing is it's it's going
+to die and produce these
+
+ align:start position:0%
+to die and produce these
+ 
+
+ align:start position:0%
+to die and produce these
+swamp-like odors and then
+
+ align:start position:0%
+swamp-like odors and then
+ 
+
+ align:start position:0%
+swamp-like odors and then
+it's going to get decomposed by
+
+ align:start position:0%
+it's going to get decomposed by
+ 
+
+ align:start position:0%
+it's going to get decomposed by
+microorganisms that are going to use up
+
+ align:start position:0%
+microorganisms that are going to use up
+ 
+
+ align:start position:0%
+microorganisms that are going to use up
+the oxygen
+
+ align:start position:0%
+the oxygen
+ 
+
+ align:start position:0%
+the oxygen
+this is the result this is blue green
+
+ align:start position:0%
+this is the result this is blue green
+ 
+
+ align:start position:0%
+this is the result this is blue green
+algae
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is really another name for this is
+
+ align:start position:0%
+this is really another name for this is
+ 
+
+ align:start position:0%
+this is really another name for this is
+cyanobacteria
+
+ align:start position:0%
+cyanobacteria
+ 
+
+ align:start position:0%
+cyanobacteria
+it's the cyanobacteria that give it that
+
+ align:start position:0%
+it's the cyanobacteria that give it that
+ 
+
+ align:start position:0%
+it's the cyanobacteria that give it that
+that green color
+
+ align:start position:0%
+that green color
+ 
+
+ align:start position:0%
+that green color
+on the surface of the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are here are some other forms of it
+
+ align:start position:0%
+here are here are some other forms of it
+ 
+
+ align:start position:0%
+here are here are some other forms of it
+you can get this pea soup kind of look
+
+ align:start position:0%
+you can get this pea soup kind of look
+ 
+
+ align:start position:0%
+you can get this pea soup kind of look
+or you can get this mossy look or you
+
+ align:start position:0%
+or you can get this mossy look or you
+ 
+
+ align:start position:0%
+or you can get this mossy look or you
+might get a painted look
+
+ align:start position:0%
+might get a painted look
+ 
+
+ align:start position:0%
+might get a painted look
+the bottom line is it's all bacteria
+
+ align:start position:0%
+the bottom line is it's all bacteria
+ 
+
+ align:start position:0%
+the bottom line is it's all bacteria
+it's unicellular bacteria these are
+
+ align:start position:0%
+it's unicellular bacteria these are
+ 
+
+ align:start position:0%
+it's unicellular bacteria these are
+prokaryotic bacteria
+
+ align:start position:0%
+prokaryotic bacteria
+ 
+
+ align:start position:0%
+prokaryotic bacteria
+they have no nucleus but they make their
+
+ align:start position:0%
+they have no nucleus but they make their
+ 
+
+ align:start position:0%
+they have no nucleus but they make their
+own food
+
+ align:start position:0%
+own food
+ 
+
+ align:start position:0%
+own food
+and they secrete chemicals
+
+ align:start position:0%
+and they secrete chemicals
+ 
+
+ align:start position:0%
+and they secrete chemicals
+these are the same bacteria believe it
+
+ align:start position:0%
+these are the same bacteria believe it
+ 
+
+ align:start position:0%
+these are the same bacteria believe it
+or not
+
+ align:start position:0%
+or not
+ 
+
+ align:start position:0%
+or not
+that gave us life 3.5 billion years ago
+
+ align:start position:0%
+that gave us life 3.5 billion years ago
+ 
+
+ align:start position:0%
+that gave us life 3.5 billion years ago
+and now they're out to get us isn't that
+
+ align:start position:0%
+and now they're out to get us isn't that
+ 
+
+ align:start position:0%
+and now they're out to get us isn't that
+amazing
+
+ align:start position:0%
+amazing
+ 
+
+ align:start position:0%
+amazing
+no i every time i look at this i can't
+
+ align:start position:0%
+no i every time i look at this i can't
+ 
+
+ align:start position:0%
+no i every time i look at this i can't
+believe it
+
+ align:start position:0%
+believe it
+ 
+
+ align:start position:0%
+believe it
+i mean when we had no oxygen these were
+
+ align:start position:0%
+i mean when we had no oxygen these were
+ 
+
+ align:start position:0%
+i mean when we had no oxygen these were
+the guys that were giving our
+
+ align:start position:0%
+the guys that were giving our
+ 
+
+ align:start position:0%
+the guys that were giving our
+oxygen atmosphere and now look what
+
+ align:start position:0%
+oxygen atmosphere and now look what
+ 
+
+ align:start position:0%
+oxygen atmosphere and now look what
+they're doing
+
+ align:start position:0%
+they're doing
+ 
+
+ align:start position:0%
+they're doing
+now if these are out there in in the
+
+ align:start position:0%
+now if these are out there in in the
+ 
+
+ align:start position:0%
+now if these are out there in in the
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+you don't want to go in the water if you
+
+ align:start position:0%
+you don't want to go in the water if you
+ 
+
+ align:start position:0%
+you don't want to go in the water if you
+do you are dead meat
+
+ align:start position:0%
+do you are dead meat
+ 
+
+ align:start position:0%
+do you are dead meat
+and i'll tell you why you can have all
+
+ align:start position:0%
+and i'll tell you why you can have all
+ 
+
+ align:start position:0%
+and i'll tell you why you can have all
+kinds of symptoms
+
+ align:start position:0%
+kinds of symptoms
+ 
+
+ align:start position:0%
+kinds of symptoms
+you can get covered with a rash you can
+
+ align:start position:0%
+you can get covered with a rash you can
+ 
+
+ align:start position:0%
+you can get covered with a rash you can
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+diarrhea flu-like symptoms eye and ear
+
+ align:start position:0%
+diarrhea flu-like symptoms eye and ear
+ 
+
+ align:start position:0%
+diarrhea flu-like symptoms eye and ear
+problems respiratory problems
+
+ align:start position:0%
+problems respiratory problems
+ 
+
+ align:start position:0%
+problems respiratory problems
+i gave you an article of um in the new
+
+ align:start position:0%
+i gave you an article of um in the new
+ 
+
+ align:start position:0%
+i gave you an article of um in the new
+this is the new york times central park
+
+ align:start position:0%
+this is the new york times central park
+ 
+
+ align:start position:0%
+this is the new york times central park
+in new york all of their all of their
+
+ align:start position:0%
+in new york all of their all of their
+ 
+
+ align:start position:0%
+in new york all of their all of their
+ponds
+
+ align:start position:0%
+ponds
+ 
+
+ align:start position:0%
+ponds
+infected with with blue-green algae
+
+ align:start position:0%
+infected with with blue-green algae
+ 
+
+ align:start position:0%
+infected with with blue-green algae
+um here's a good
+
+ align:start position:0%
+um here's a good
+ 
+
+ align:start position:0%
+um here's a good
+example this is today ohio strikes a
+
+ align:start position:0%
+example this is today ohio strikes a
+ 
+
+ align:start position:0%
+example this is today ohio strikes a
+blow in algae fight
+
+ align:start position:0%
+blow in algae fight
+ 
+
+ align:start position:0%
+blow in algae fight
+this is the wall street journal this
+
+ align:start position:0%
+this is the wall street journal this
+ 
+
+ align:start position:0%
+this is the wall street journal this
+morning this
+
+ align:start position:0%
+morning this
+ 
+
+ align:start position:0%
+morning this
+article just came out interestingly
+
+ align:start position:0%
+article just came out interestingly
+ 
+
+ align:start position:0%
+article just came out interestingly
+ohio had this algae problem 10 years ago
+
+ align:start position:0%
+ohio had this algae problem 10 years ago
+ 
+
+ align:start position:0%
+ohio had this algae problem 10 years ago
+and they took around one of their lakes
+
+ align:start position:0%
+and they took around one of their lakes
+ 
+
+ align:start position:0%
+and they took around one of their lakes
+and they built built up this
+
+ align:start position:0%
+and they built built up this
+ 
+
+ align:start position:0%
+and they built built up this
+uh these these wetland areas
+
+ align:start position:0%
+uh these these wetland areas
+ 
+
+ align:start position:0%
+uh these these wetland areas
+to prevent the runoff from reaching the
+
+ align:start position:0%
+to prevent the runoff from reaching the
+ 
+
+ align:start position:0%
+to prevent the runoff from reaching the
+agricultural runoff
+
+ align:start position:0%
+agricultural runoff
+ 
+
+ align:start position:0%
+agricultural runoff
+from reaching the lake and it's actually
+
+ align:start position:0%
+from reaching the lake and it's actually
+ 
+
+ align:start position:0%
+from reaching the lake and it's actually
+working so there
+
+ align:start position:0%
+working so there
+ 
+
+ align:start position:0%
+working so there
+you know there are ideas out there that
+
+ align:start position:0%
+you know there are ideas out there that
+ 
+
+ align:start position:0%
+you know there are ideas out there that
+you can come up with an idea and solve a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so some of these cyanobacteria some of
+
+ align:start position:0%
+so some of these cyanobacteria some of
+ 
+
+ align:start position:0%
+so some of these cyanobacteria some of
+the freshwater bacteria
+
+ align:start position:0%
+the freshwater bacteria
+ 
+
+ align:start position:0%
+the freshwater bacteria
+produce very toxic chemicals one form of
+
+ align:start position:0%
+produce very toxic chemicals one form of
+ 
+
+ align:start position:0%
+produce very toxic chemicals one form of
+these is
+
+ align:start position:0%
+these is
+ 
+
+ align:start position:0%
+these is
+are the microcystins there's something
+
+ align:start position:0%
+are the microcystins there's something
+ 
+
+ align:start position:0%
+are the microcystins there's something
+like 50
+
+ align:start position:0%
+like 50
+ 
+
+ align:start position:0%
+like 50
+different microcystins that have been
+
+ align:start position:0%
+different microcystins that have been
+ 
+
+ align:start position:0%
+different microcystins that have been
+identified
+
+ align:start position:0%
+identified
+ 
+
+ align:start position:0%
+identified
+to date it's a cyclic uh peptide here
+
+ align:start position:0%
+to date it's a cyclic uh peptide here
+ 
+
+ align:start position:0%
+to date it's a cyclic uh peptide here
+and this is a hepatotoxin so once this
+
+ align:start position:0%
+and this is a hepatotoxin so once this
+ 
+
+ align:start position:0%
+and this is a hepatotoxin so once this
+gets into your through your skin into
+
+ align:start position:0%
+gets into your through your skin into
+ 
+
+ align:start position:0%
+gets into your through your skin into
+your body
+
+ align:start position:0%
+your body
+ 
+
+ align:start position:0%
+your body
+your your liver is going to get attacked
+
+ align:start position:0%
+your your liver is going to get attacked
+ 
+
+ align:start position:0%
+your your liver is going to get attacked
+and you're pretty much gone there's not
+
+ align:start position:0%
+and you're pretty much gone there's not
+ 
+
+ align:start position:0%
+and you're pretty much gone there's not
+much you can do about it
+
+ align:start position:0%
+much you can do about it
+ 
+
+ align:start position:0%
+much you can do about it
+the article mentions the dogs one woman
+
+ align:start position:0%
+the article mentions the dogs one woman
+ 
+
+ align:start position:0%
+the article mentions the dogs one woman
+had three dogs
+
+ align:start position:0%
+had three dogs
+ 
+
+ align:start position:0%
+had three dogs
+in north carolina she let them go for a
+
+ align:start position:0%
+in north carolina she let them go for a
+ 
+
+ align:start position:0%
+in north carolina she let them go for a
+swim in a pond
+
+ align:start position:0%
+swim in a pond
+ 
+
+ align:start position:0%
+swim in a pond
+all three dogs died within a few hours
+
+ align:start position:0%
+all three dogs died within a few hours
+ 
+
+ align:start position:0%
+all three dogs died within a few hours
+so this is really nasty stuff and
+
+ align:start position:0%
+so this is really nasty stuff and
+ 
+
+ align:start position:0%
+so this is really nasty stuff and
+if you know i challenge you to think
+
+ align:start position:0%
+if you know i challenge you to think
+ 
+
+ align:start position:0%
+if you know i challenge you to think
+about coming up with an antidote for
+
+ align:start position:0%
+about coming up with an antidote for
+ 
+
+ align:start position:0%
+about coming up with an antidote for
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there there's your startup company right
+
+ align:start position:0%
+there there's your startup company right
+ 
+
+ align:start position:0%
+there there's your startup company right
+here i'm giving it to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you when this stuff is active you
+
+ align:start position:0%
+when you when this stuff is active you
+ 
+
+ align:start position:0%
+when you when this stuff is active you
+go out to the charles river you'll see
+
+ align:start position:0%
+go out to the charles river you'll see
+ 
+
+ align:start position:0%
+go out to the charles river you'll see
+these signs posted
+
+ align:start position:0%
+these signs posted
+ 
+
+ align:start position:0%
+these signs posted
+warning people and pets to to stay out
+
+ align:start position:0%
+warning people and pets to to stay out
+ 
+
+ align:start position:0%
+warning people and pets to to stay out
+of the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's another example this is the
+
+ align:start position:0%
+here's another example this is the
+ 
+
+ align:start position:0%
+here's another example this is the
+summer of 2014.
+
+ align:start position:0%
+summer of 2014.
+ 
+
+ align:start position:0%
+summer of 2014.
+this is a satellite picture of of lake
+
+ align:start position:0%
+this is a satellite picture of of lake
+ 
+
+ align:start position:0%
+this is a satellite picture of of lake
+erie
+
+ align:start position:0%
+erie
+ 
+
+ align:start position:0%
+erie
+one of the five great lakes in in this
+
+ align:start position:0%
+one of the five great lakes in in this
+ 
+
+ align:start position:0%
+one of the five great lakes in in this
+country
+
+ align:start position:0%
+country
+ 
+
+ align:start position:0%
+country
+and the the lake actually borders canada
+
+ align:start position:0%
+and the the lake actually borders canada
+ 
+
+ align:start position:0%
+and the the lake actually borders canada
+on one side separates canada from the us
+
+ align:start position:0%
+on one side separates canada from the us
+ 
+
+ align:start position:0%
+on one side separates canada from the us
+near ontario and then there are several
+
+ align:start position:0%
+near ontario and then there are several
+ 
+
+ align:start position:0%
+near ontario and then there are several
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+that border border the border of the
+
+ align:start position:0%
+that border border the border of the
+ 
+
+ align:start position:0%
+that border border the border of the
+lake out here to the west
+
+ align:start position:0%
+lake out here to the west
+ 
+
+ align:start position:0%
+lake out here to the west
+is toledo ohio and toledo his
+
+ align:start position:0%
+is toledo ohio and toledo his
+ 
+
+ align:start position:0%
+is toledo ohio and toledo his
+fourth largest city in ohio has a
+
+ align:start position:0%
+fourth largest city in ohio has a
+ 
+
+ align:start position:0%
+fourth largest city in ohio has a
+population of about a half million
+
+ align:start position:0%
+population of about a half million
+ 
+
+ align:start position:0%
+population of about a half million
+this is this was their tap water in 2014
+
+ align:start position:0%
+this is this was their tap water in 2014
+ 
+
+ align:start position:0%
+this is this was their tap water in 2014
+and i had a 5 3 10 student in class
+
+ align:start position:0%
+and i had a 5 3 10 student in class
+ 
+
+ align:start position:0%
+and i had a 5 3 10 student in class
+four years ago who remembers this
+
+ align:start position:0%
+four years ago who remembers this
+ 
+
+ align:start position:0%
+four years ago who remembers this
+i mean this this is serious business
+
+ align:start position:0%
+i mean this this is serious business
+ 
+
+ align:start position:0%
+i mean this this is serious business
+and it's happening all over all over the
+
+ align:start position:0%
+and it's happening all over all over the
+ 
+
+ align:start position:0%
+and it's happening all over all over the
+world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's here's another picture this is uh
+
+ align:start position:0%
+here's here's another picture this is uh
+ 
+
+ align:start position:0%
+here's here's another picture this is uh
+the largest
+
+ align:start position:0%
+the largest
+ 
+
+ align:start position:0%
+the largest
+landlocked body of water on the earth
+
+ align:start position:0%
+landlocked body of water on the earth
+ 
+
+ align:start position:0%
+landlocked body of water on the earth
+anybody from europe here recognize this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who said that yes sean exactly correct
+
+ align:start position:0%
+who said that yes sean exactly correct
+ 
+
+ align:start position:0%
+who said that yes sean exactly correct
+that's the caspian sea
+
+ align:start position:0%
+that's the caspian sea
+ 
+
+ align:start position:0%
+that's the caspian sea
+it's bordered by five countries but look
+
+ align:start position:0%
+it's bordered by five countries but look
+ 
+
+ align:start position:0%
+it's bordered by five countries but look
+at the massive
+
+ align:start position:0%
+at the massive
+ 
+
+ align:start position:0%
+at the massive
+massive algal growth from this satellite
+
+ align:start position:0%
+massive algal growth from this satellite
+ 
+
+ align:start position:0%
+massive algal growth from this satellite
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+here's the volga river europe's longest
+
+ align:start position:0%
+here's the volga river europe's longest
+ 
+
+ align:start position:0%
+here's the volga river europe's longest
+river pouring into it it's a 2 000 mile
+
+ align:start position:0%
+river pouring into it it's a 2 000 mile
+ 
+
+ align:start position:0%
+river pouring into it it's a 2 000 mile
+long river
+
+ align:start position:0%
+long river
+ 
+
+ align:start position:0%
+long river
+here's a new word for you eutrophication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's from the greek meaning well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nourished
+
+ align:start position:0%
+nourished
+ 
+
+ align:start position:0%
+nourished
+so how much phosphorus is acceptable
+
+ align:start position:0%
+so how much phosphorus is acceptable
+ 
+
+ align:start position:0%
+so how much phosphorus is acceptable
+the epa came out in 2000
+
+ align:start position:0%
+the epa came out in 2000
+ 
+
+ align:start position:0%
+the epa came out in 2000
+that was almost 20 years ago and said
+
+ align:start position:0%
+that was almost 20 years ago and said
+ 
+
+ align:start position:0%
+that was almost 20 years ago and said
+0.0238 milligrams per liter
+
+ align:start position:0%
+0.0238 milligrams per liter
+ 
+
+ align:start position:0%
+0.0238 milligrams per liter
+well we know today that
+
+ align:start position:0%
+well we know today that
+ 
+
+ align:start position:0%
+well we know today that
+if you have anything greater than
+
+ align:start position:0%
+if you have anything greater than
+ 
+
+ align:start position:0%
+if you have anything greater than
+or equal to 0.016
+
+ align:start position:0%
+or equal to 0.016
+ 
+
+ align:start position:0%
+or equal to 0.016
+milligrams per liter you're going to
+
+ align:start position:0%
+milligrams per liter you're going to
+ 
+
+ align:start position:0%
+milligrams per liter you're going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+uh really a large algal growth
+
+ align:start position:0%
+uh really a large algal growth
+ 
+
+ align:start position:0%
+uh really a large algal growth
+proliferating in in your water
+
+ align:start position:0%
+proliferating in in your water
+ 
+
+ align:start position:0%
+proliferating in in your water
+now these concentrations of phosphorus
+
+ align:start position:0%
+now these concentrations of phosphorus
+ 
+
+ align:start position:0%
+now these concentrations of phosphorus
+they're low
+
+ align:start position:0%
+they're low
+ 
+
+ align:start position:0%
+they're low
+and it's going to be challenging to
+
+ align:start position:0%
+and it's going to be challenging to
+ 
+
+ align:start position:0%
+and it's going to be challenging to
+measure those
+
+ align:start position:0%
+measure those
+ 
+
+ align:start position:0%
+measure those
+this is what we're going to do the other
+
+ align:start position:0%
+this is what we're going to do the other
+ 
+
+ align:start position:0%
+this is what we're going to do the other
+thing that that makes it challenging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+phosphates are colorless so how are we
+
+ align:start position:0%
+phosphates are colorless so how are we
+ 
+
+ align:start position:0%
+phosphates are colorless so how are we
+going to use
+
+ align:start position:0%
+going to use
+ 
+
+ align:start position:0%
+going to use
+uv vis to measure these concentrations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody have an idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe we can react them with something
+
+ align:start position:0%
+maybe we can react them with something
+ 
+
+ align:start position:0%
+maybe we can react them with something
+that can make them colorful
+
+ align:start position:0%
+that can make them colorful
+ 
+
+ align:start position:0%
+that can make them colorful
+very good very good yeah i like that
+
+ align:start position:0%
+very good very good yeah i like that
+ 
+
+ align:start position:0%
+very good very good yeah i like that
+keisha right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+giselle i'm sorry giselle okay where's
+
+ align:start position:0%
+giselle i'm sorry giselle okay where's
+ 
+
+ align:start position:0%
+giselle i'm sorry giselle okay where's
+keisha here
+
+ align:start position:0%
+keisha here
+ 
+
+ align:start position:0%
+keisha here
+there she is okay all right so
+
+ align:start position:0%
+there she is okay all right so
+ 
+
+ align:start position:0%
+there she is okay all right so
+react them with something that makes it
+
+ align:start position:0%
+react them with something that makes it
+ 
+
+ align:start position:0%
+react them with something that makes it
+colorful
+
+ align:start position:0%
+colorful
+ 
+
+ align:start position:0%
+colorful
+so here comes chemistry to the rescue
+
+ align:start position:0%
+so here comes chemistry to the rescue
+ 
+
+ align:start position:0%
+so here comes chemistry to the rescue
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so phosphates are very reactive
+
+ align:start position:0%
+so phosphates are very reactive
+ 
+
+ align:start position:0%
+so phosphates are very reactive
+so we can actually uh take um river
+
+ align:start position:0%
+so we can actually uh take um river
+ 
+
+ align:start position:0%
+so we can actually uh take um river
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+and this method here this is the
+
+ align:start position:0%
+and this method here this is the
+ 
+
+ align:start position:0%
+and this method here this is the
+ammonium metavanadate method
+
+ align:start position:0%
+ammonium metavanadate method
+ 
+
+ align:start position:0%
+ammonium metavanadate method
+when i when i tried to develop this this
+
+ align:start position:0%
+when i when i tried to develop this this
+ 
+
+ align:start position:0%
+when i when i tried to develop this this
+charles river water
+
+ align:start position:0%
+charles river water
+ 
+
+ align:start position:0%
+charles river water
+testing i started with this method
+
+ align:start position:0%
+testing i started with this method
+ 
+
+ align:start position:0%
+testing i started with this method
+because it was written up as the method
+
+ align:start position:0%
+because it was written up as the method
+ 
+
+ align:start position:0%
+because it was written up as the method
+to detect phosphorus in river water
+
+ align:start position:0%
+to detect phosphorus in river water
+ 
+
+ align:start position:0%
+to detect phosphorus in river water
+so you would take the river water mix it
+
+ align:start position:0%
+so you would take the river water mix it
+ 
+
+ align:start position:0%
+so you would take the river water mix it
+with molybdate
+
+ align:start position:0%
+with molybdate
+ 
+
+ align:start position:0%
+with molybdate
+ammonium metavanadate and you create
+
+ align:start position:0%
+ammonium metavanadate and you create
+ 
+
+ align:start position:0%
+ammonium metavanadate and you create
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+color heteropoly molybdic acid
+
+ align:start position:0%
+color heteropoly molybdic acid
+ 
+
+ align:start position:0%
+color heteropoly molybdic acid
+that has a yellow color and it absorbs
+
+ align:start position:0%
+that has a yellow color and it absorbs
+ 
+
+ align:start position:0%
+that has a yellow color and it absorbs
+light at 400 nanometers
+
+ align:start position:0%
+light at 400 nanometers
+ 
+
+ align:start position:0%
+light at 400 nanometers
+what i found is that this method was not
+
+ align:start position:0%
+what i found is that this method was not
+ 
+
+ align:start position:0%
+what i found is that this method was not
+sensitive enough to actually measure
+
+ align:start position:0%
+sensitive enough to actually measure
+ 
+
+ align:start position:0%
+sensitive enough to actually measure
+the phosphorus levels in the charles
+
+ align:start position:0%
+the phosphorus levels in the charles
+ 
+
+ align:start position:0%
+the phosphorus levels in the charles
+river
+
+ align:start position:0%
+river
+ 
+
+ align:start position:0%
+river
+it's a great method for measuring
+
+ align:start position:0%
+it's a great method for measuring
+ 
+
+ align:start position:0%
+it's a great method for measuring
+phosphorus in sewage
+
+ align:start position:0%
+phosphorus in sewage
+ 
+
+ align:start position:0%
+phosphorus in sewage
+but not the rivers so i looked around
+
+ align:start position:0%
+but not the rivers so i looked around
+ 
+
+ align:start position:0%
+but not the rivers so i looked around
+and i found
+
+ align:start position:0%
+and i found
+ 
+
+ align:start position:0%
+and i found
+what's called the ascorbic acid method
+
+ align:start position:0%
+what's called the ascorbic acid method
+ 
+
+ align:start position:0%
+what's called the ascorbic acid method
+an epa approved method where you you
+
+ align:start position:0%
+an epa approved method where you you
+ 
+
+ align:start position:0%
+an epa approved method where you you
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+took river water
+
+ align:start position:0%
+took river water
+ 
+
+ align:start position:0%
+took river water
+mixed it with molybdate sulfuric acid
+
+ align:start position:0%
+mixed it with molybdate sulfuric acid
+ 
+
+ align:start position:0%
+mixed it with molybdate sulfuric acid
+and you create this heteropoly molybdic
+
+ align:start position:0%
+and you create this heteropoly molybdic
+ 
+
+ align:start position:0%
+and you create this heteropoly molybdic
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+which is colorless but the good thing
+
+ align:start position:0%
+which is colorless but the good thing
+ 
+
+ align:start position:0%
+which is colorless but the good thing
+is this heteropoly molybdate anion
+
+ align:start position:0%
+is this heteropoly molybdate anion
+ 
+
+ align:start position:0%
+is this heteropoly molybdate anion
+can accept electrons and be reduced down
+
+ align:start position:0%
+can accept electrons and be reduced down
+ 
+
+ align:start position:0%
+can accept electrons and be reduced down
+and ascorbic acid can cause that
+
+ align:start position:0%
+and ascorbic acid can cause that
+ 
+
+ align:start position:0%
+and ascorbic acid can cause that
+reduction
+
+ align:start position:0%
+reduction
+ 
+
+ align:start position:0%
+reduction
+and you end up getting this molybdenum
+
+ align:start position:0%
+and you end up getting this molybdenum
+ 
+
+ align:start position:0%
+and you end up getting this molybdenum
+blue complex
+
+ align:start position:0%
+blue complex
+ 
+
+ align:start position:0%
+blue complex
+a mixed valence complex that absorbs
+
+ align:start position:0%
+a mixed valence complex that absorbs
+ 
+
+ align:start position:0%
+a mixed valence complex that absorbs
+light at 880 nanometers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is great because the
+
+ align:start position:0%
+so this is great because the
+ 
+
+ align:start position:0%
+so this is great because the
+concentration of the
+
+ align:start position:0%
+concentration of the
+ 
+
+ align:start position:0%
+concentration of the
+phosphorus in the complexes is
+
+ align:start position:0%
+phosphorus in the complexes is
+ 
+
+ align:start position:0%
+phosphorus in the complexes is
+proportional to the absorbance of the
+
+ align:start position:0%
+proportional to the absorbance of the
+ 
+
+ align:start position:0%
+proportional to the absorbance of the
+of the light in these things so this is
+
+ align:start position:0%
+of the light in these things so this is
+ 
+
+ align:start position:0%
+of the light in these things so this is
+what you're you're actually making it's
+
+ align:start position:0%
+what you're you're actually making it's
+ 
+
+ align:start position:0%
+what you're you're actually making it's
+beautiful
+
+ align:start position:0%
+beautiful
+ 
+
+ align:start position:0%
+beautiful
+this is a kegen structure it captures
+
+ align:start position:0%
+this is a kegen structure it captures
+ 
+
+ align:start position:0%
+this is a kegen structure it captures
+the phosphorus in the center
+
+ align:start position:0%
+the phosphorus in the center
+ 
+
+ align:start position:0%
+the phosphorus in the center
+surrounded by 12 molybdenums and 40
+
+ align:start position:0%
+surrounded by 12 molybdenums and 40
+ 
+
+ align:start position:0%
+surrounded by 12 molybdenums and 40
+oxygens
+
+ align:start position:0%
+oxygens
+ 
+
+ align:start position:0%
+oxygens
+i want you to take a moment and and look
+
+ align:start position:0%
+i want you to take a moment and and look
+ 
+
+ align:start position:0%
+i want you to take a moment and and look
+at this
+
+ align:start position:0%
+at this
+ 
+
+ align:start position:0%
+at this
+and i'd like you all to close your eyes
+
+ align:start position:0%
+and i'd like you all to close your eyes
+ 
+
+ align:start position:0%
+and i'd like you all to close your eyes
+for a moment and think about this image
+
+ align:start position:0%
+for a moment and think about this image
+ 
+
+ align:start position:0%
+for a moment and think about this image
+close your eyes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay open your eyes please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want you to carry this image with you
+
+ align:start position:0%
+i want you to carry this image with you
+ 
+
+ align:start position:0%
+i want you to carry this image with you
+into the lab when you do this experiment
+
+ align:start position:0%
+into the lab when you do this experiment
+ 
+
+ align:start position:0%
+into the lab when you do this experiment
+you're actually going to be making this
+
+ align:start position:0%
+you're actually going to be making this
+ 
+
+ align:start position:0%
+you're actually going to be making this
+in your beakers
+
+ align:start position:0%
+in your beakers
+ 
+
+ align:start position:0%
+in your beakers
+when you add the color developer to your
+
+ align:start position:0%
+when you add the color developer to your
+ 
+
+ align:start position:0%
+when you add the color developer to your
+to your water samples
+
+ align:start position:0%
+to your water samples
+ 
+
+ align:start position:0%
+to your water samples
+you're creating this in about 15 minutes
+
+ align:start position:0%
+you're creating this in about 15 minutes
+ 
+
+ align:start position:0%
+you're creating this in about 15 minutes
+in your in your beaker this is inorganic
+
+ align:start position:0%
+in your in your beaker this is inorganic
+ 
+
+ align:start position:0%
+in your in your beaker this is inorganic
+chemistry at its best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i want to spend the next
+
+ align:start position:0%
+now i want to spend the next
+ 
+
+ align:start position:0%
+now i want to spend the next
+several slides showing you how we're
+
+ align:start position:0%
+several slides showing you how we're
+ 
+
+ align:start position:0%
+several slides showing you how we're
+going to actually measure
+
+ align:start position:0%
+going to actually measure
+ 
+
+ align:start position:0%
+going to actually measure
+the concentrations of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to be shining
+
+ align:start position:0%
+so we're going to be shining
+ 
+
+ align:start position:0%
+so we're going to be shining
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+energy on on our sample
+
+ align:start position:0%
+energy on on our sample
+ 
+
+ align:start position:0%
+energy on on our sample
+and if you look at the visible light
+
+ align:start position:0%
+and if you look at the visible light
+ 
+
+ align:start position:0%
+and if you look at the visible light
+here that i broke out of this
+
+ align:start position:0%
+here that i broke out of this
+ 
+
+ align:start position:0%
+here that i broke out of this
+electromagnetic spectrum
+
+ align:start position:0%
+electromagnetic spectrum
+ 
+
+ align:start position:0%
+electromagnetic spectrum
+on the red end of this
+
+ align:start position:0%
+on the red end of this
+ 
+
+ align:start position:0%
+on the red end of this
+we're going to be looking at our samples
+
+ align:start position:0%
+we're going to be looking at our samples
+ 
+
+ align:start position:0%
+we're going to be looking at our samples
+on that far
+
+ align:start position:0%
+on that far
+ 
+
+ align:start position:0%
+on that far
+red end in the near ir
+
+ align:start position:0%
+red end in the near ir
+ 
+
+ align:start position:0%
+red end in the near ir
+so that's where you're going to be where
+
+ align:start position:0%
+so that's where you're going to be where
+ 
+
+ align:start position:0%
+so that's where you're going to be where
+you're going to be taking your readings
+
+ align:start position:0%
+you're going to be taking your readings
+ 
+
+ align:start position:0%
+you're going to be taking your readings
+now what can happen when you shine
+
+ align:start position:0%
+now what can happen when you shine
+ 
+
+ align:start position:0%
+now what can happen when you shine
+radiation on your sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of your sample could get photo
+
+ align:start position:0%
+some of your sample could get photo
+ 
+
+ align:start position:0%
+some of your sample could get photo
+bleached yeah that's that's a
+
+ align:start position:0%
+bleached yeah that's that's a
+ 
+
+ align:start position:0%
+bleached yeah that's that's a
+possibility
+
+ align:start position:0%
+possibility
+ 
+
+ align:start position:0%
+possibility
+what else yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly i mean electrons could get shoot
+
+ align:start position:0%
+exactly i mean electrons could get shoot
+ 
+
+ align:start position:0%
+exactly i mean electrons could get shoot
+up to a higher energy levels
+
+ align:start position:0%
+up to a higher energy levels
+ 
+
+ align:start position:0%
+up to a higher energy levels
+little nuclei could see that happen and
+
+ align:start position:0%
+little nuclei could see that happen and
+ 
+
+ align:start position:0%
+little nuclei could see that happen and
+get nervous and start to rearrange
+
+ align:start position:0%
+get nervous and start to rearrange
+ 
+
+ align:start position:0%
+get nervous and start to rearrange
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+and the molecule as kelly said could
+
+ align:start position:0%
+and the molecule as kelly said could
+ 
+
+ align:start position:0%
+and the molecule as kelly said could
+burst into vibration
+
+ align:start position:0%
+burst into vibration
+ 
+
+ align:start position:0%
+burst into vibration
+and your uv
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is actually monitoring all of those
+
+ align:start position:0%
+is actually monitoring all of those
+ 
+
+ align:start position:0%
+is actually monitoring all of those
+electronic transitions that we can't see
+
+ align:start position:0%
+electronic transitions that we can't see
+ 
+
+ align:start position:0%
+electronic transitions that we can't see
+with our eye
+
+ align:start position:0%
+with our eye
+ 
+
+ align:start position:0%
+with our eye
+and what the uv does is it draws you a
+
+ align:start position:0%
+and what the uv does is it draws you a
+ 
+
+ align:start position:0%
+and what the uv does is it draws you a
+smooth curve
+
+ align:start position:0%
+smooth curve
+ 
+
+ align:start position:0%
+smooth curve
+through all of those electronic
+
+ align:start position:0%
+through all of those electronic
+ 
+
+ align:start position:0%
+through all of those electronic
+transitions and you you end up
+
+ align:start position:0%
+transitions and you you end up
+ 
+
+ align:start position:0%
+transitions and you you end up
+somewhere with your lambda max
+
+ align:start position:0%
+somewhere with your lambda max
+ 
+
+ align:start position:0%
+somewhere with your lambda max
+what uv vis is a good definition
+
+ align:start position:0%
+what uv vis is a good definition
+ 
+
+ align:start position:0%
+what uv vis is a good definition
+is it's just the interaction of light
+
+ align:start position:0%
+is it's just the interaction of light
+ 
+
+ align:start position:0%
+is it's just the interaction of light
+with matter
+
+ align:start position:0%
+with matter
+ 
+
+ align:start position:0%
+with matter
+as a function of wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's your uv cuvette here's the
+
+ align:start position:0%
+so here's your uv cuvette here's the
+ 
+
+ align:start position:0%
+so here's your uv cuvette here's the
+radiation hitting that cuvette
+
+ align:start position:0%
+radiation hitting that cuvette
+ 
+
+ align:start position:0%
+radiation hitting that cuvette
+what what happens what do you see up
+
+ align:start position:0%
+what what happens what do you see up
+ 
+
+ align:start position:0%
+what what happens what do you see up
+there happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes ryan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the light's focused and what's
+
+ align:start position:0%
+yeah the light's focused and what's
+ 
+
+ align:start position:0%
+yeah the light's focused and what's
+happening to the sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm sure it's heating up yeah yes autumn
+
+ align:start position:0%
+i'm sure it's heating up yeah yes autumn
+ 
+
+ align:start position:0%
+i'm sure it's heating up yeah yes autumn
+it absorbs some light and transmits
+
+ align:start position:0%
+it absorbs some light and transmits
+ 
+
+ align:start position:0%
+it absorbs some light and transmits
+sunlight okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good so some of the lights going
+
+ align:start position:0%
+yeah good so some of the lights going
+ 
+
+ align:start position:0%
+yeah good so some of the lights going
+through and some is getting absorbed
+
+ align:start position:0%
+through and some is getting absorbed
+ 
+
+ align:start position:0%
+through and some is getting absorbed
+so um let's look at that for a minute so
+
+ align:start position:0%
+so um let's look at that for a minute so
+ 
+
+ align:start position:0%
+so um let's look at that for a minute so
+we've got absorbance
+
+ align:start position:0%
+we've got absorbance
+ 
+
+ align:start position:0%
+we've got absorbance
+it's minus the log of the transmitted
+
+ align:start position:0%
+it's minus the log of the transmitted
+ 
+
+ align:start position:0%
+it's minus the log of the transmitted
+light which is i
+
+ align:start position:0%
+light which is i
+ 
+
+ align:start position:0%
+light which is i
+over i zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now absorbance is
+
+ align:start position:0%
+now absorbance is
+ 
+
+ align:start position:0%
+now absorbance is
+is we're actually monitoring the
+
+ align:start position:0%
+is we're actually monitoring the
+ 
+
+ align:start position:0%
+is we're actually monitoring the
+absorbance we're not monitoring the
+
+ align:start position:0%
+absorbance we're not monitoring the
+ 
+
+ align:start position:0%
+absorbance we're not monitoring the
+transmittance
+
+ align:start position:0%
+transmittance
+ 
+
+ align:start position:0%
+transmittance
+because absorbance is actually directly
+
+ align:start position:0%
+because absorbance is actually directly
+ 
+
+ align:start position:0%
+because absorbance is actually directly
+proportional
+
+ align:start position:0%
+proportional
+ 
+
+ align:start position:0%
+proportional
+to concentration by beer's law
+
+ align:start position:0%
+to concentration by beer's law
+ 
+
+ align:start position:0%
+to concentration by beer's law
+so we have this relationship
+
+ align:start position:0%
+so we have this relationship
+ 
+
+ align:start position:0%
+so we have this relationship
+and e the extinction coefficient
+
+ align:start position:0%
+and e the extinction coefficient
+ 
+
+ align:start position:0%
+and e the extinction coefficient
+is the molar absorptivity constant
+
+ align:start position:0%
+is the molar absorptivity constant
+ 
+
+ align:start position:0%
+is the molar absorptivity constant
+is simply the amount of light absorbed
+
+ align:start position:0%
+is simply the amount of light absorbed
+ 
+
+ align:start position:0%
+is simply the amount of light absorbed
+per unit concentration of your of your
+
+ align:start position:0%
+per unit concentration of your of your
+ 
+
+ align:start position:0%
+per unit concentration of your of your
+sample
+
+ align:start position:0%
+sample
+ 
+
+ align:start position:0%
+sample
+let me just rewrite this let me get rid
+
+ align:start position:0%
+let me just rewrite this let me get rid
+ 
+
+ align:start position:0%
+let me just rewrite this let me get rid
+of the logarithm
+
+ align:start position:0%
+of the logarithm
+ 
+
+ align:start position:0%
+of the logarithm
+i want to show you something here so
+
+ align:start position:0%
+i want to show you something here so
+ 
+
+ align:start position:0%
+i want to show you something here so
+i'm going to rewrite this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's let's actually graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the intensity of the incoming the
+
+ align:start position:0%
+the intensity of the incoming the
+ 
+
+ align:start position:0%
+the intensity of the incoming the
+intensity of the incoming radiation here
+
+ align:start position:0%
+intensity of the incoming radiation here
+ 
+
+ align:start position:0%
+intensity of the incoming radiation here
+i'm going to graph that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a function of concentration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you if you do that you're going to
+
+ align:start position:0%
+if you if you do that you're going to
+ 
+
+ align:start position:0%
+if you if you do that you're going to
+see from that equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the transmitted light decreases
+
+ align:start position:0%
+that the transmitted light decreases
+ 
+
+ align:start position:0%
+that the transmitted light decreases
+exponentially
+
+ align:start position:0%
+exponentially
+ 
+
+ align:start position:0%
+exponentially
+as the concentration increases i want
+
+ align:start position:0%
+as the concentration increases i want
+ 
+
+ align:start position:0%
+as the concentration increases i want
+you to keep that
+
+ align:start position:0%
+you to keep that
+ 
+
+ align:start position:0%
+you to keep that
+in the back of your mind this
+
+ align:start position:0%
+in the back of your mind this
+ 
+
+ align:start position:0%
+in the back of your mind this
+equation fascinated me i you know i like
+
+ align:start position:0%
+equation fascinated me i you know i like
+ 
+
+ align:start position:0%
+equation fascinated me i you know i like
+beer's law
+
+ align:start position:0%
+beer's law
+ 
+
+ align:start position:0%
+beer's law
+what this tells you this extinction
+
+ align:start position:0%
+what this tells you this extinction
+ 
+
+ align:start position:0%
+what this tells you this extinction
+coefficient tells you that if you
+
+ align:start position:0%
+coefficient tells you that if you
+ 
+
+ align:start position:0%
+coefficient tells you that if you
+it has to be a constant so if you cut
+
+ align:start position:0%
+it has to be a constant so if you cut
+ 
+
+ align:start position:0%
+it has to be a constant so if you cut
+your concentration in half absorption
+
+ align:start position:0%
+your concentration in half absorption
+ 
+
+ align:start position:0%
+your concentration in half absorption
+should be cut in half
+
+ align:start position:0%
+should be cut in half
+ 
+
+ align:start position:0%
+should be cut in half
+so i wanted to prove this so i went out
+
+ align:start position:0%
+so i wanted to prove this so i went out
+ 
+
+ align:start position:0%
+so i wanted to prove this so i went out
+and i made this compound
+
+ align:start position:0%
+and i made this compound
+ 
+
+ align:start position:0%
+and i made this compound
+hexa cyano ferrate 3 and i made up like
+
+ align:start position:0%
+hexa cyano ferrate 3 and i made up like
+ 
+
+ align:start position:0%
+hexa cyano ferrate 3 and i made up like
+five solutions of this and then i
+
+ align:start position:0%
+five solutions of this and then i
+ 
+
+ align:start position:0%
+five solutions of this and then i
+measured the absorbance of each solution
+
+ align:start position:0%
+measured the absorbance of each solution
+ 
+
+ align:start position:0%
+measured the absorbance of each solution
+it absorbed light at 420 nanometers
+
+ align:start position:0%
+it absorbed light at 420 nanometers
+ 
+
+ align:start position:0%
+it absorbed light at 420 nanometers
+and if you look here 10 times e to the
+
+ align:start position:0%
+and if you look here 10 times e to the
+ 
+
+ align:start position:0%
+and if you look here 10 times e to the
+minus 4
+
+ align:start position:0%
+minus 4
+ 
+
+ align:start position:0%
+minus 4
+i cut that in half to five times e to
+
+ align:start position:0%
+i cut that in half to five times e to
+ 
+
+ align:start position:0%
+i cut that in half to five times e to
+the minus four
+
+ align:start position:0%
+the minus four
+ 
+
+ align:start position:0%
+the minus four
+indeed the absorption gets cut in half
+
+ align:start position:0%
+indeed the absorption gets cut in half
+ 
+
+ align:start position:0%
+indeed the absorption gets cut in half
+as it should so i graphed this
+
+ align:start position:0%
+as it should so i graphed this
+ 
+
+ align:start position:0%
+as it should so i graphed this
+got a nice straight line the change in
+
+ align:start position:0%
+got a nice straight line the change in
+ 
+
+ align:start position:0%
+got a nice straight line the change in
+absorption
+
+ align:start position:0%
+absorption
+ 
+
+ align:start position:0%
+absorption
+over the change in concentration is my
+
+ align:start position:0%
+over the change in concentration is my
+ 
+
+ align:start position:0%
+over the change in concentration is my
+slope and
+
+ align:start position:0%
+slope and
+ 
+
+ align:start position:0%
+slope and
+it's 1056.7 so that's my extinction
+
+ align:start position:0%
+it's 1056.7 so that's my extinction
+ 
+
+ align:start position:0%
+it's 1056.7 so that's my extinction
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+and this worked really well
+
+ align:start position:0%
+and this worked really well
+ 
+
+ align:start position:0%
+and this worked really well
+but i want to i want to caution you
+
+ align:start position:0%
+but i want to i want to caution you
+ 
+
+ align:start position:0%
+but i want to i want to caution you
+if you try this and you're graphing
+
+ align:start position:0%
+if you try this and you're graphing
+ 
+
+ align:start position:0%
+if you try this and you're graphing
+absorption versus concentration and
+
+ align:start position:0%
+absorption versus concentration and
+ 
+
+ align:start position:0%
+absorption versus concentration and
+you're doing beer's law
+
+ align:start position:0%
+you're doing beer's law
+ 
+
+ align:start position:0%
+you're doing beer's law
+you've got this nice straight line you
+
+ align:start position:0%
+you've got this nice straight line you
+ 
+
+ align:start position:0%
+you've got this nice straight line you
+might end up with something
+
+ align:start position:0%
+might end up with something
+ 
+
+ align:start position:0%
+might end up with something
+like this where beer's law falls apart
+
+ align:start position:0%
+like this where beer's law falls apart
+ 
+
+ align:start position:0%
+like this where beer's law falls apart
+and it all comes back to this here
+
+ align:start position:0%
+and it all comes back to this here
+ 
+
+ align:start position:0%
+and it all comes back to this here
+the intensity of the transmitted light
+
+ align:start position:0%
+the intensity of the transmitted light
+ 
+
+ align:start position:0%
+the intensity of the transmitted light
+decreases exponentially with
+
+ align:start position:0%
+decreases exponentially with
+ 
+
+ align:start position:0%
+decreases exponentially with
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+so eventually if the concentration is
+
+ align:start position:0%
+so eventually if the concentration is
+ 
+
+ align:start position:0%
+so eventually if the concentration is
+too high
+
+ align:start position:0%
+too high
+ 
+
+ align:start position:0%
+too high
+your sample becomes saturated and
+
+ align:start position:0%
+your sample becomes saturated and
+ 
+
+ align:start position:0%
+your sample becomes saturated and
+and you're you're not going to be this
+
+ align:start position:0%
+and you're you're not going to be this
+ 
+
+ align:start position:0%
+and you're you're not going to be this
+beer's law falls apart
+
+ align:start position:0%
+beer's law falls apart
+ 
+
+ align:start position:0%
+beer's law falls apart
+i just want you to be aware of that what
+
+ align:start position:0%
+i just want you to be aware of that what
+ 
+
+ align:start position:0%
+i just want you to be aware of that what
+i did is i made up
+
+ align:start position:0%
+i did is i made up
+ 
+
+ align:start position:0%
+i did is i made up
+all of my concentrations are very low
+
+ align:start position:0%
+all of my concentrations are very low
+ 
+
+ align:start position:0%
+all of my concentrations are very low
+beer's law worked fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we're going to
+
+ align:start position:0%
+so now we're going to
+ 
+
+ align:start position:0%
+so now we're going to
+get to some serious business
+
+ align:start position:0%
+get to some serious business
+ 
+
+ align:start position:0%
+get to some serious business
+this is what you have to do for this lab
+
+ align:start position:0%
+this is what you have to do for this lab
+ 
+
+ align:start position:0%
+this is what you have to do for this lab
+for it to work
+
+ align:start position:0%
+for it to work
+ 
+
+ align:start position:0%
+for it to work
+otherwise you will be a goner gonzo
+
+ align:start position:0%
+otherwise you will be a goner gonzo
+ 
+
+ align:start position:0%
+otherwise you will be a goner gonzo
+you've gotta clean this this glassware
+
+ align:start position:0%
+you've gotta clean this this glassware
+ 
+
+ align:start position:0%
+you've gotta clean this this glassware
+this is a list of the glassware that
+
+ align:start position:0%
+this is a list of the glassware that
+ 
+
+ align:start position:0%
+this is a list of the glassware that
+you'll need to clean
+
+ align:start position:0%
+you'll need to clean
+ 
+
+ align:start position:0%
+you'll need to clean
+and you've got to do it with 10 percent
+
+ align:start position:0%
+and you've got to do it with 10 percent
+ 
+
+ align:start position:0%
+and you've got to do it with 10 percent
+hydrochloric acid
+
+ align:start position:0%
+hydrochloric acid
+ 
+
+ align:start position:0%
+hydrochloric acid
+triple rinsed with millicue water
+
+ align:start position:0%
+triple rinsed with millicue water
+ 
+
+ align:start position:0%
+triple rinsed with millicue water
+why do you think you need to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes any contamination might change
+
+ align:start position:0%
+yes any contamination might change
+ 
+
+ align:start position:0%
+yes any contamination might change
+like bias the amount of concentration
+
+ align:start position:0%
+like bias the amount of concentration
+ 
+
+ align:start position:0%
+like bias the amount of concentration
+any contamination is going to just
+
+ align:start position:0%
+any contamination is going to just
+ 
+
+ align:start position:0%
+any contamination is going to just
+destroy the experiment
+
+ align:start position:0%
+destroy the experiment
+ 
+
+ align:start position:0%
+destroy the experiment
+it's kind of like the nano building
+
+ align:start position:0%
+it's kind of like the nano building
+ 
+
+ align:start position:0%
+it's kind of like the nano building
+you've seen them in there with their
+
+ align:start position:0%
+you've seen them in there with their
+ 
+
+ align:start position:0%
+you've seen them in there with their
+bunny suits on
+
+ align:start position:0%
+bunny suits on
+ 
+
+ align:start position:0%
+bunny suits on
+one speck of dust even a dander from
+
+ align:start position:0%
+one speck of dust even a dander from
+ 
+
+ align:start position:0%
+one speck of dust even a dander from
+your hair
+
+ align:start position:0%
+your hair
+ 
+
+ align:start position:0%
+your hair
+well is like a wrecking ball to the
+
+ align:start position:0%
+well is like a wrecking ball to the
+ 
+
+ align:start position:0%
+well is like a wrecking ball to the
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+well one speck of phosphate
+
+ align:start position:0%
+well one speck of phosphate
+ 
+
+ align:start position:0%
+well one speck of phosphate
+from any detergent is going to wreck
+
+ align:start position:0%
+from any detergent is going to wreck
+ 
+
+ align:start position:0%
+from any detergent is going to wreck
+this experiment
+
+ align:start position:0%
+this experiment
+ 
+
+ align:start position:0%
+this experiment
+so you've got to judiciously sit down
+
+ align:start position:0%
+so you've got to judiciously sit down
+ 
+
+ align:start position:0%
+so you've got to judiciously sit down
+there'll be two of you you'll be
+
+ align:start position:0%
+there'll be two of you you'll be
+ 
+
+ align:start position:0%
+there'll be two of you you'll be
+partnered up for this
+
+ align:start position:0%
+partnered up for this
+ 
+
+ align:start position:0%
+partnered up for this
+so you'll you clean this up and you'll
+
+ align:start position:0%
+so you'll you clean this up and you'll
+ 
+
+ align:start position:0%
+so you'll you clean this up and you'll
+do this on day two
+
+ align:start position:0%
+do this on day two
+ 
+
+ align:start position:0%
+do this on day two
+after the dissolved oxygen testing this
+
+ align:start position:0%
+after the dissolved oxygen testing this
+ 
+
+ align:start position:0%
+after the dissolved oxygen testing this
+is what you're going to need for day
+
+ align:start position:0%
+is what you're going to need for day
+ 
+
+ align:start position:0%
+is what you're going to need for day
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+for the phosphate testing so you can
+
+ align:start position:0%
+for the phosphate testing so you can
+ 
+
+ align:start position:0%
+for the phosphate testing so you can
+leave this glassware in the top
+
+ align:start position:0%
+leave this glassware in the top
+ 
+
+ align:start position:0%
+leave this glassware in the top
+drawer above your locker it's not locked
+
+ align:start position:0%
+drawer above your locker it's not locked
+ 
+
+ align:start position:0%
+drawer above your locker it's not locked
+and it'll be nice and ready for you when
+
+ align:start position:0%
+and it'll be nice and ready for you when
+ 
+
+ align:start position:0%
+and it'll be nice and ready for you when
+you come in to do the testing
+
+ align:start position:0%
+you come in to do the testing
+ 
+
+ align:start position:0%
+you come in to do the testing
+so this is what you have to do in this
+
+ align:start position:0%
+so this is what you have to do in this
+ 
+
+ align:start position:0%
+so this is what you have to do in this
+in this lab
+
+ align:start position:0%
+in this lab
+ 
+
+ align:start position:0%
+in this lab
+first of all we need to make up a set of
+
+ align:start position:0%
+first of all we need to make up a set of
+ 
+
+ align:start position:0%
+first of all we need to make up a set of
+standards
+
+ align:start position:0%
+standards
+ 
+
+ align:start position:0%
+standards
+that we can interpolate our river
+
+ align:start position:0%
+that we can interpolate our river
+ 
+
+ align:start position:0%
+that we can interpolate our river
+samples against
+
+ align:start position:0%
+samples against
+ 
+
+ align:start position:0%
+samples against
+to find the concentrations of the
+
+ align:start position:0%
+to find the concentrations of the
+ 
+
+ align:start position:0%
+to find the concentrations of the
+phosphate and phosphorus
+
+ align:start position:0%
+phosphate and phosphorus
+ 
+
+ align:start position:0%
+phosphate and phosphorus
+so you're going to make seven standards
+
+ align:start position:0%
+so you're going to make seven standards
+ 
+
+ align:start position:0%
+so you're going to make seven standards
+up and
+
+ align:start position:0%
+up and
+ 
+
+ align:start position:0%
+up and
+you're going to be using a stock
+
+ align:start position:0%
+you're going to be using a stock
+ 
+
+ align:start position:0%
+you're going to be using a stock
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the formula that to use in all these
+
+ align:start position:0%
+and the formula that to use in all these
+ 
+
+ align:start position:0%
+and the formula that to use in all these
+tables
+
+ align:start position:0%
+tables
+ 
+
+ align:start position:0%
+tables
+is you're going to use this m1 v1
+
+ align:start position:0%
+is you're going to use this m1 v1
+ 
+
+ align:start position:0%
+is you're going to use this m1 v1
+equals m2 v2
+
+ align:start position:0%
+equals m2 v2
+ 
+
+ align:start position:0%
+equals m2 v2
+so if you have a 10 to the minus third
+
+ align:start position:0%
+so if you have a 10 to the minus third
+ 
+
+ align:start position:0%
+so if you have a 10 to the minus third
+molar stock solution
+
+ align:start position:0%
+molar stock solution
+ 
+
+ align:start position:0%
+molar stock solution
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you're taking one mil of it out out
+
+ align:start position:0%
+and you're taking one mil of it out out
+ 
+
+ align:start position:0%
+and you're taking one mil of it out out
+of the bottle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how much molarity do you want to make to
+
+ align:start position:0%
+how much molarity do you want to make to
+ 
+
+ align:start position:0%
+how much molarity do you want to make to
+make up
+
+ align:start position:0%
+make up
+ 
+
+ align:start position:0%
+make up
+a hundred mil solution
+
+ align:start position:0%
+a hundred mil solution
+ 
+
+ align:start position:0%
+a hundred mil solution
+you'll be diluting this 1 mil to 100 and
+
+ align:start position:0%
+you'll be diluting this 1 mil to 100 and
+ 
+
+ align:start position:0%
+you'll be diluting this 1 mil to 100 and
+you'll see that your x is 10 to the
+
+ align:start position:0%
+you'll see that your x is 10 to the
+ 
+
+ align:start position:0%
+you'll see that your x is 10 to the
+minus 5.
+
+ align:start position:0%
+minus 5.
+ 
+
+ align:start position:0%
+minus 5.
+that's your stock solution of phosphate
+
+ align:start position:0%
+that's your stock solution of phosphate
+ 
+
+ align:start position:0%
+that's your stock solution of phosphate
+that you're that you're going to create
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you just use that formula for all
+
+ align:start position:0%
+so you just use that formula for all
+ 
+
+ align:start position:0%
+so you just use that formula for all
+these you're taking this much out of
+
+ align:start position:0%
+these you're taking this much out of
+ 
+
+ align:start position:0%
+these you're taking this much out of
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+10 to the minus 5 molar stock solution
+
+ align:start position:0%
+10 to the minus 5 molar stock solution
+ 
+
+ align:start position:0%
+10 to the minus 5 molar stock solution
+and you're diluting it up to 10 mils
+
+ align:start position:0%
+and you're diluting it up to 10 mils
+ 
+
+ align:start position:0%
+and you're diluting it up to 10 mils
+what's my concentration perfect
+
+ align:start position:0%
+what's my concentration perfect
+ 
+
+ align:start position:0%
+what's my concentration perfect
+what you'll do is you'll come into the
+
+ align:start position:0%
+what you'll do is you'll come into the
+ 
+
+ align:start position:0%
+what you'll do is you'll come into the
+lab and the tas will go through this
+
+ align:start position:0%
+lab and the tas will go through this
+ 
+
+ align:start position:0%
+lab and the tas will go through this
+with you
+
+ align:start position:0%
+with you
+ 
+
+ align:start position:0%
+with you
+you'll make up your stock solutions and
+
+ align:start position:0%
+you'll make up your stock solutions and
+ 
+
+ align:start position:0%
+you'll make up your stock solutions and
+then you'll go to the river to get your
+
+ align:start position:0%
+then you'll go to the river to get your
+ 
+
+ align:start position:0%
+then you'll go to the river to get your
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+and when you bring the water back to the
+
+ align:start position:0%
+and when you bring the water back to the
+ 
+
+ align:start position:0%
+and when you bring the water back to the
+lab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there'll be two of you so one of you
+
+ align:start position:0%
+there'll be two of you so one of you
+ 
+
+ align:start position:0%
+there'll be two of you so one of you
+will go over to the hoods
+
+ align:start position:0%
+will go over to the hoods
+ 
+
+ align:start position:0%
+will go over to the hoods
+and get the color developer and these
+
+ align:start position:0%
+and get the color developer and these
+ 
+
+ align:start position:0%
+and get the color developer and these
+are the four
+
+ align:start position:0%
+are the four
+ 
+
+ align:start position:0%
+are the four
+chemicals that we talked about in the
+
+ align:start position:0%
+chemicals that we talked about in the
+ 
+
+ align:start position:0%
+chemicals that we talked about in the
+color developer
+
+ align:start position:0%
+color developer
+ 
+
+ align:start position:0%
+color developer
+the ammonium molybdate uh sulfuric acid
+
+ align:start position:0%
+the ammonium molybdate uh sulfuric acid
+ 
+
+ align:start position:0%
+the ammonium molybdate uh sulfuric acid
+ascorbic
+
+ align:start position:0%
+ascorbic
+ 
+
+ align:start position:0%
+ascorbic
+acid potassium animal tartrate
+
+ align:start position:0%
+acid potassium animal tartrate
+ 
+
+ align:start position:0%
+acid potassium animal tartrate
+potassium anamonotartrate is there to
+
+ align:start position:0%
+potassium anamonotartrate is there to
+ 
+
+ align:start position:0%
+potassium anamonotartrate is there to
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+speed up the reduction that's going on
+
+ align:start position:0%
+speed up the reduction that's going on
+ 
+
+ align:start position:0%
+speed up the reduction that's going on
+with ascorbic acid
+
+ align:start position:0%
+with ascorbic acid
+ 
+
+ align:start position:0%
+with ascorbic acid
+that's important that uh and if i didn't
+
+ align:start position:0%
+that's important that uh and if i didn't
+ 
+
+ align:start position:0%
+that's important that uh and if i didn't
+mention that before that's the purpose
+
+ align:start position:0%
+mention that before that's the purpose
+ 
+
+ align:start position:0%
+mention that before that's the purpose
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+the ammonium molybdate sulfuric acid
+
+ align:start position:0%
+the ammonium molybdate sulfuric acid
+ 
+
+ align:start position:0%
+the ammonium molybdate sulfuric acid
+you're creating that
+
+ align:start position:0%
+you're creating that
+ 
+
+ align:start position:0%
+you're creating that
+kegen structure that colorless molybdick
+
+ align:start position:0%
+kegen structure that colorless molybdick
+ 
+
+ align:start position:0%
+kegen structure that colorless molybdick
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+you also have to take this color
+
+ align:start position:0%
+you also have to take this color
+ 
+
+ align:start position:0%
+you also have to take this color
+developer in the order
+
+ align:start position:0%
+developer in the order
+ 
+
+ align:start position:0%
+developer in the order
+that it's written here it'll be set up
+
+ align:start position:0%
+that it's written here it'll be set up
+ 
+
+ align:start position:0%
+that it's written here it'll be set up
+in burettes
+
+ align:start position:0%
+in burettes
+ 
+
+ align:start position:0%
+in burettes
+in the hood if you for example take it
+
+ align:start position:0%
+in the hood if you for example take it
+ 
+
+ align:start position:0%
+in the hood if you for example take it
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+wrong order you could have a side
+
+ align:start position:0%
+wrong order you could have a side
+ 
+
+ align:start position:0%
+wrong order you could have a side
+reaction and not
+
+ align:start position:0%
+reaction and not
+ 
+
+ align:start position:0%
+reaction and not
+get the color developer that you want to
+
+ align:start position:0%
+get the color developer that you want to
+ 
+
+ align:start position:0%
+get the color developer that you want to
+put in your sample
+
+ align:start position:0%
+put in your sample
+ 
+
+ align:start position:0%
+put in your sample
+so it's important so one of you will go
+
+ align:start position:0%
+so it's important so one of you will go
+ 
+
+ align:start position:0%
+so it's important so one of you will go
+to the hood get the color developer
+
+ align:start position:0%
+to the hood get the color developer
+ 
+
+ align:start position:0%
+to the hood get the color developer
+the other one will be go to the river
+
+ align:start position:0%
+the other one will be go to the river
+ 
+
+ align:start position:0%
+the other one will be go to the river
+water you brought back
+
+ align:start position:0%
+water you brought back
+ 
+
+ align:start position:0%
+water you brought back
+use a clean pipette 10 ml pipette
+
+ align:start position:0%
+use a clean pipette 10 ml pipette
+ 
+
+ align:start position:0%
+use a clean pipette 10 ml pipette
+and pipette five beakers with river
+
+ align:start position:0%
+and pipette five beakers with river
+ 
+
+ align:start position:0%
+and pipette five beakers with river
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+five 10 ml beakers so you'll end up with
+
+ align:start position:0%
+five 10 ml beakers so you'll end up with
+ 
+
+ align:start position:0%
+five 10 ml beakers so you'll end up with
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+7 standards and five samples
+
+ align:start position:0%
+7 standards and five samples
+ 
+
+ align:start position:0%
+7 standards and five samples
+and then you add the color developer and
+
+ align:start position:0%
+and then you add the color developer and
+ 
+
+ align:start position:0%
+and then you add the color developer and
+you wait 20 minutes
+
+ align:start position:0%
+you wait 20 minutes
+ 
+
+ align:start position:0%
+you wait 20 minutes
+and you're ready to go just a couple
+
+ align:start position:0%
+and you're ready to go just a couple
+ 
+
+ align:start position:0%
+and you're ready to go just a couple
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+precautions that you should take
+
+ align:start position:0%
+precautions that you should take
+ 
+
+ align:start position:0%
+precautions that you should take
+we're going to be using four mil
+
+ align:start position:0%
+we're going to be using four mil
+ 
+
+ align:start position:0%
+we're going to be using four mil
+cuvettes these are big
+
+ align:start position:0%
+cuvettes these are big
+ 
+
+ align:start position:0%
+cuvettes these are big
+inside don't use the one and a half mil
+
+ align:start position:0%
+inside don't use the one and a half mil
+ 
+
+ align:start position:0%
+inside don't use the one and a half mil
+cuvettes
+
+ align:start position:0%
+cuvettes
+ 
+
+ align:start position:0%
+cuvettes
+the other thing is all these cuvettes
+
+ align:start position:0%
+the other thing is all these cuvettes
+ 
+
+ align:start position:0%
+the other thing is all these cuvettes
+have a fill line
+
+ align:start position:0%
+have a fill line
+ 
+
+ align:start position:0%
+have a fill line
+it becomes frosted at one point
+
+ align:start position:0%
+it becomes frosted at one point
+ 
+
+ align:start position:0%
+it becomes frosted at one point
+and you you want to stop pouring when
+
+ align:start position:0%
+and you you want to stop pouring when
+ 
+
+ align:start position:0%
+and you you want to stop pouring when
+you get to that line
+
+ align:start position:0%
+you get to that line
+ 
+
+ align:start position:0%
+you get to that line
+you're going to take your beakers and
+
+ align:start position:0%
+you're going to take your beakers and
+ 
+
+ align:start position:0%
+you're going to take your beakers and
+you're going to swirl them
+
+ align:start position:0%
+you're going to swirl them
+ 
+
+ align:start position:0%
+you're going to swirl them
+gently and you're going to pour them by
+
+ align:start position:0%
+gently and you're going to pour them by
+ 
+
+ align:start position:0%
+gently and you're going to pour them by
+hand until you reach the fill line
+
+ align:start position:0%
+hand until you reach the fill line
+ 
+
+ align:start position:0%
+hand until you reach the fill line
+don't go beyond that also all of these
+
+ align:start position:0%
+don't go beyond that also all of these
+ 
+
+ align:start position:0%
+don't go beyond that also all of these
+uv cuvettes have an
+
+ align:start position:0%
+uv cuvettes have an
+ 
+
+ align:start position:0%
+uv cuvettes have an
+arrow on one side you want to be sure
+
+ align:start position:0%
+arrow on one side you want to be sure
+ 
+
+ align:start position:0%
+arrow on one side you want to be sure
+that the arrow is in the light beam
+
+ align:start position:0%
+that the arrow is in the light beam
+ 
+
+ align:start position:0%
+that the arrow is in the light beam
+when you put these cuvettes in the uv
+
+ align:start position:0%
+when you put these cuvettes in the uv
+ 
+
+ align:start position:0%
+when you put these cuvettes in the uv
+spectrometer
+
+ align:start position:0%
+spectrometer
+ 
+
+ align:start position:0%
+spectrometer
+a lot of people have made mistakes put
+
+ align:start position:0%
+a lot of people have made mistakes put
+ 
+
+ align:start position:0%
+a lot of people have made mistakes put
+them in the wrong way and then you're
+
+ align:start position:0%
+them in the wrong way and then you're
+ 
+
+ align:start position:0%
+them in the wrong way and then you're
+not going to get
+
+ align:start position:0%
+not going to get
+ 
+
+ align:start position:0%
+not going to get
+very good readings so the arrows clear
+
+ align:start position:0%
+very good readings so the arrows clear
+ 
+
+ align:start position:0%
+very good readings so the arrows clear
+to see
+
+ align:start position:0%
+to see
+ 
+
+ align:start position:0%
+to see
+what i usually do is arrange all my
+
+ align:start position:0%
+what i usually do is arrange all my
+ 
+
+ align:start position:0%
+what i usually do is arrange all my
+cuvettes in a box ahead of time
+
+ align:start position:0%
+cuvettes in a box ahead of time
+ 
+
+ align:start position:0%
+cuvettes in a box ahead of time
+and then i pour my samples and put them
+
+ align:start position:0%
+and then i pour my samples and put them
+ 
+
+ align:start position:0%
+and then i pour my samples and put them
+in the box and i know the arrows in the
+
+ align:start position:0%
+in the box and i know the arrows in the
+ 
+
+ align:start position:0%
+in the box and i know the arrows in the
+right place
+
+ align:start position:0%
+right place
+ 
+
+ align:start position:0%
+right place
+and when i go to the uv i just lift them
+
+ align:start position:0%
+and when i go to the uv i just lift them
+ 
+
+ align:start position:0%
+and when i go to the uv i just lift them
+up and put them in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also keep in mind with
+
+ align:start position:0%
+also keep in mind with
+ 
+
+ align:start position:0%
+also keep in mind with
+dr sarah you told you the other day that
+
+ align:start position:0%
+dr sarah you told you the other day that
+ 
+
+ align:start position:0%
+dr sarah you told you the other day that
+there's two kinds of pipettes in the lab
+
+ align:start position:0%
+there's two kinds of pipettes in the lab
+ 
+
+ align:start position:0%
+there's two kinds of pipettes in the lab
+this one is a blowout pipette you've got
+
+ align:start position:0%
+this one is a blowout pipette you've got
+ 
+
+ align:start position:0%
+this one is a blowout pipette you've got
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+blow it all out to get your ten mils
+
+ align:start position:0%
+blow it all out to get your ten mils
+ 
+
+ align:start position:0%
+blow it all out to get your ten mils
+this one is a two
+
+ align:start position:0%
+this one is a two
+ 
+
+ align:start position:0%
+this one is a two
+deliver pipette you only go up to that
+
+ align:start position:0%
+deliver pipette you only go up to that
+ 
+
+ align:start position:0%
+deliver pipette you only go up to that
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+line you don't blow the tip in otherwise
+
+ align:start position:0%
+line you don't blow the tip in otherwise
+ 
+
+ align:start position:0%
+line you don't blow the tip in otherwise
+you put too much
+
+ align:start position:0%
+you put too much
+ 
+
+ align:start position:0%
+you put too much
+gonna wreck your experiment so make sure
+
+ align:start position:0%
+gonna wreck your experiment so make sure
+ 
+
+ align:start position:0%
+gonna wreck your experiment so make sure
+you look at the pipettes carefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're going to get your graph here a
+
+ align:start position:0%
+so you're going to get your graph here a
+ 
+
+ align:start position:0%
+so you're going to get your graph here a
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+graph and what you're going to do is
+
+ align:start position:0%
+graph and what you're going to do is
+ 
+
+ align:start position:0%
+graph and what you're going to do is
+you're going to interpolate
+
+ align:start position:0%
+you're going to interpolate
+ 
+
+ align:start position:0%
+you're going to interpolate
+now your river absorbances against the
+
+ align:start position:0%
+now your river absorbances against the
+ 
+
+ align:start position:0%
+now your river absorbances against the
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+so you can read off the concentrations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the concentrations in that graph
+
+ align:start position:0%
+so the concentrations in that graph
+ 
+
+ align:start position:0%
+so the concentrations in that graph
+are in micro molar
+
+ align:start position:0%
+are in micro molar
+ 
+
+ align:start position:0%
+are in micro molar
+so you're going to want to take those
+
+ align:start position:0%
+so you're going to want to take those
+ 
+
+ align:start position:0%
+so you're going to want to take those
+and convert them to milligrams per liter
+
+ align:start position:0%
+and convert them to milligrams per liter
+ 
+
+ align:start position:0%
+and convert them to milligrams per liter
+so you want to convert this first to a
+
+ align:start position:0%
+so you want to convert this first to a
+ 
+
+ align:start position:0%
+so you want to convert this first to a
+molarity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moles per liter
+
+ align:start position:0%
+moles per liter
+ 
+
+ align:start position:0%
+moles per liter
+then you you take that and you uh
+
+ align:start position:0%
+then you you take that and you uh
+ 
+
+ align:start position:0%
+then you you take that and you uh
+you you want to go down to grams per
+
+ align:start position:0%
+you you want to go down to grams per
+ 
+
+ align:start position:0%
+you you want to go down to grams per
+liter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then finally milligrams per liter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're going to be calculating two
+
+ align:start position:0%
+so you're going to be calculating two
+ 
+
+ align:start position:0%
+so you're going to be calculating two
+things you want to calculate the
+
+ align:start position:0%
+things you want to calculate the
+ 
+
+ align:start position:0%
+things you want to calculate the
+uh the phosphate concentration
+
+ align:start position:0%
+uh the phosphate concentration
+ 
+
+ align:start position:0%
+uh the phosphate concentration
+in ppm which is milligrams per liter and
+
+ align:start position:0%
+in ppm which is milligrams per liter and
+ 
+
+ align:start position:0%
+in ppm which is milligrams per liter and
+the phosphorus concentration
+
+ align:start position:0%
+the phosphorus concentration
+ 
+
+ align:start position:0%
+the phosphorus concentration
+so you'll take your mass from the from
+
+ align:start position:0%
+so you'll take your mass from the from
+ 
+
+ align:start position:0%
+so you'll take your mass from the from
+the curve
+
+ align:start position:0%
+the curve
+ 
+
+ align:start position:0%
+the curve
+in milligrams per liter and
+
+ align:start position:0%
+in milligrams per liter and
+ 
+
+ align:start position:0%
+in milligrams per liter and
+take it times the ratio for phosphate of
+
+ align:start position:0%
+take it times the ratio for phosphate of
+ 
+
+ align:start position:0%
+take it times the ratio for phosphate of
+po4
+
+ align:start position:0%
+po4
+ 
+
+ align:start position:0%
+po4
+over kh2po4 and that ratio is 0.70
+
+ align:start position:0%
+over kh2po4 and that ratio is 0.70
+ 
+
+ align:start position:0%
+over kh2po4 and that ratio is 0.70
+and then for phosphorus do the same
+
+ align:start position:0%
+and then for phosphorus do the same
+ 
+
+ align:start position:0%
+and then for phosphorus do the same
+thing the ratio there is 0.23
+
+ align:start position:0%
+thing the ratio there is 0.23
+ 
+
+ align:start position:0%
+thing the ratio there is 0.23
+and this is the most important part of
+
+ align:start position:0%
+and this is the most important part of
+ 
+
+ align:start position:0%
+and this is the most important part of
+this slab this is the whole
+
+ align:start position:0%
+this slab this is the whole
+ 
+
+ align:start position:0%
+this slab this is the whole
+thing calculating these concentrations
+
+ align:start position:0%
+thing calculating these concentrations
+ 
+
+ align:start position:0%
+thing calculating these concentrations
+in the end so it's important to
+
+ align:start position:0%
+in the end so it's important to
+ 
+
+ align:start position:0%
+in the end so it's important to
+to know how to do that so once you get
+
+ align:start position:0%
+to know how to do that so once you get
+ 
+
+ align:start position:0%
+to know how to do that so once you get
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+concentrations you've got a series of
+
+ align:start position:0%
+concentrations you've got a series of
+ 
+
+ align:start position:0%
+concentrations you've got a series of
+things to to go through here for your
+
+ align:start position:0%
+things to to go through here for your
+ 
+
+ align:start position:0%
+things to to go through here for your
+data analysis
+
+ align:start position:0%
+data analysis
+ 
+
+ align:start position:0%
+data analysis
+uh there's no error propagation on this
+
+ align:start position:0%
+uh there's no error propagation on this
+ 
+
+ align:start position:0%
+uh there's no error propagation on this
+part of the lab
+
+ align:start position:0%
+part of the lab
+ 
+
+ align:start position:0%
+part of the lab
+which is which is good for you um
+
+ align:start position:0%
+which is which is good for you um
+ 
+
+ align:start position:0%
+which is which is good for you um
+you will have to use the linus equation
+
+ align:start position:0%
+you will have to use the linus equation
+ 
+
+ align:start position:0%
+you will have to use the linus equation
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that sarah talked about which is pretty
+
+ align:start position:0%
+that sarah talked about which is pretty
+ 
+
+ align:start position:0%
+that sarah talked about which is pretty
+easy to use and
+
+ align:start position:0%
+easy to use and
+ 
+
+ align:start position:0%
+easy to use and
+that'll help you calculate the errors of
+
+ align:start position:0%
+that'll help you calculate the errors of
+ 
+
+ align:start position:0%
+that'll help you calculate the errors of
+your slope intercept and y values
+
+ align:start position:0%
+your slope intercept and y values
+ 
+
+ align:start position:0%
+your slope intercept and y values
+and then you find your average and
+
+ align:start position:0%
+and then you find your average and
+ 
+
+ align:start position:0%
+and then you find your average and
+standard deviation
+
+ align:start position:0%
+standard deviation
+ 
+
+ align:start position:0%
+standard deviation
+of the five measurements calculate the
+
+ align:start position:0%
+of the five measurements calculate the
+ 
+
+ align:start position:0%
+of the five measurements calculate the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+confidence interval most importantly
+
+ align:start position:0%
+confidence interval most importantly
+ 
+
+ align:start position:0%
+confidence interval most importantly
+report the final concentration of p
+
+ align:start position:0%
+report the final concentration of p
+ 
+
+ align:start position:0%
+report the final concentration of p
+and po4 make sure all these results
+
+ align:start position:0%
+and po4 make sure all these results
+ 
+
+ align:start position:0%
+and po4 make sure all these results
+show up in your abstract first thing i
+
+ align:start position:0%
+show up in your abstract first thing i
+ 
+
+ align:start position:0%
+show up in your abstract first thing i
+do when i get lab reports is i look at
+
+ align:start position:0%
+do when i get lab reports is i look at
+ 
+
+ align:start position:0%
+do when i get lab reports is i look at
+the abstract
+
+ align:start position:0%
+the abstract
+ 
+
+ align:start position:0%
+the abstract
+i want to see a line that that shows my
+
+ align:start position:0%
+i want to see a line that that shows my
+ 
+
+ align:start position:0%
+i want to see a line that that shows my
+my results and they also should appear
+
+ align:start position:0%
+my results and they also should appear
+ 
+
+ align:start position:0%
+my results and they also should appear
+in your conclusion
+
+ align:start position:0%
+in your conclusion
+ 
+
+ align:start position:0%
+in your conclusion
+and then you can discuss them in your
+
+ align:start position:0%
+and then you can discuss them in your
+ 
+
+ align:start position:0%
+and then you can discuss them in your
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+of your of your lab report
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so any questions about about this
+
+ align:start position:0%
+so any questions about about this
+ 
+
+ align:start position:0%
+so any questions about about this
+i know you're you're going to have a
+
+ align:start position:0%
+i know you're you're going to have a
+ 
+
+ align:start position:0%
+i know you're you're going to have a
+busy weekend because you're
+
+ align:start position:0%
+busy weekend because you're
+ 
+
+ align:start position:0%
+busy weekend because you're
+you're going to be working on your your
+
+ align:start position:0%
+you're going to be working on your your
+ 
+
+ align:start position:0%
+you're going to be working on your your
+ferrising lab your first
+
+ align:start position:0%
+ferrising lab your first
+ 
+
+ align:start position:0%
+ferrising lab your first
+lab report and i want to tell you that
+
+ align:start position:0%
+lab report and i want to tell you that
+ 
+
+ align:start position:0%
+lab report and i want to tell you that
+please
+
+ align:start position:0%
+please
+ 
+
+ align:start position:0%
+please
+feel free to reach out to me or sarah
+
+ align:start position:0%
+feel free to reach out to me or sarah
+ 
+
+ align:start position:0%
+feel free to reach out to me or sarah
+if you have any questions i'm going to
+
+ align:start position:0%
+if you have any questions i'm going to
+ 
+
+ align:start position:0%
+if you have any questions i'm going to
+be here
+
+ align:start position:0%
+be here
+ 
+
+ align:start position:0%
+be here
+tomorrow i probably will be here
+
+ align:start position:0%
+tomorrow i probably will be here
+ 
+
+ align:start position:0%
+tomorrow i probably will be here
+saturday and sunday so if there's a last
+
+ align:start position:0%
+saturday and sunday so if there's a last
+ 
+
+ align:start position:0%
+saturday and sunday so if there's a last
+minute question
+
+ align:start position:0%
+minute question
+ 
+
+ align:start position:0%
+minute question
+just send me an email and i'm happy to
+
+ align:start position:0%
+just send me an email and i'm happy to
+ 
+
+ align:start position:0%
+just send me an email and i'm happy to
+invite you in and you know we can answer
+
+ align:start position:0%
+invite you in and you know we can answer
+ 
+
+ align:start position:0%
+invite you in and you know we can answer
+your question
+
+ align:start position:0%
+your question
+ 
+
+ align:start position:0%
+your question
+i should be here in the afternoon
+
+ align:start position:0%
+i should be here in the afternoon
+ 
+
+ align:start position:0%
+i should be here in the afternoon
+probably on saturday and sunday
+
+ align:start position:0%
+probably on saturday and sunday
+ 
+
+ align:start position:0%
+probably on saturday and sunday
+okay now i'd like to
+
+ align:start position:0%
+okay now i'd like to
+ 
+
+ align:start position:0%
+okay now i'd like to
+i'd like to end this the lecture today
+
+ align:start position:0%
+i'd like to end this the lecture today
+ 
+
+ align:start position:0%
+i'd like to end this the lecture today
+by doing doing a demonstration um
+
+ align:start position:0%
+by doing doing a demonstration um
+ 
+
+ align:start position:0%
+by doing doing a demonstration um
+when i'm actually did i turn that off i
+
+ align:start position:0%
+when i'm actually did i turn that off i
+ 
+
+ align:start position:0%
+when i'm actually did i turn that off i
+can show you this
+
+ align:start position:0%
+can show you this
+ 
+
+ align:start position:0%
+can show you this
+here i'm going to do this briggs rosher
+
+ align:start position:0%
+here i'm going to do this briggs rosher
+ 
+
+ align:start position:0%
+here i'm going to do this briggs rosher
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+where we're actually going to we're
+
+ align:start position:0%
+where we're actually going to we're
+ 
+
+ align:start position:0%
+where we're actually going to we're
+going to make this iodo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+malonic acid we're going to actually
+
+ align:start position:0%
+malonic acid we're going to actually
+ 
+
+ align:start position:0%
+malonic acid we're going to actually
+attach an iodine to malonic acid we're
+
+ align:start position:0%
+attach an iodine to malonic acid we're
+ 
+
+ align:start position:0%
+attach an iodine to malonic acid we're
+going to create this in a beaker
+
+ align:start position:0%
+going to create this in a beaker
+ 
+
+ align:start position:0%
+going to create this in a beaker
+the reason i'm showing you this reaction
+
+ align:start position:0%
+the reason i'm showing you this reaction
+ 
+
+ align:start position:0%
+the reason i'm showing you this reaction
+is because
+
+ align:start position:0%
+is because
+ 
+
+ align:start position:0%
+is because
+it has everything in it including starch
+
+ align:start position:0%
+it has everything in it including starch
+ 
+
+ align:start position:0%
+it has everything in it including starch
+and it has a lot of colors and these
+
+ align:start position:0%
+and it has a lot of colors and these
+ 
+
+ align:start position:0%
+and it has a lot of colors and these
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+are things that we're going to talk
+
+ align:start position:0%
+are things that we're going to talk
+ 
+
+ align:start position:0%
+are things that we're going to talk
+about in the next lecture
+
+ align:start position:0%
+about in the next lecture
+ 
+
+ align:start position:0%
+about in the next lecture
+yeah what what starch does and how it
+
+ align:start position:0%
+yeah what what starch does and how it
+ 
+
+ align:start position:0%
+yeah what what starch does and how it
+works and
+
+ align:start position:0%
+works and
+ 
+
+ align:start position:0%
+works and
+this is kind of a preview to that this
+
+ align:start position:0%
+this is kind of a preview to that this
+ 
+
+ align:start position:0%
+this is kind of a preview to that this
+reaction that you're going to see was
+
+ align:start position:0%
+reaction that you're going to see was
+ 
+
+ align:start position:0%
+reaction that you're going to see was
+actually discovered by two high school
+
+ align:start position:0%
+actually discovered by two high school
+ 
+
+ align:start position:0%
+actually discovered by two high school
+chemistry teachers from their briggs and
+
+ align:start position:0%
+chemistry teachers from their briggs and
+ 
+
+ align:start position:0%
+chemistry teachers from their briggs and
+washer
+
+ align:start position:0%
+washer
+ 
+
+ align:start position:0%
+washer
+from galileo high school my favorite
+
+ align:start position:0%
+from galileo high school my favorite
+ 
+
+ align:start position:0%
+from galileo high school my favorite
+city san francisco
+
+ align:start position:0%
+city san francisco
+ 
+
+ align:start position:0%
+city san francisco
+so these guys came up with this back in
+
+ align:start position:0%
+so these guys came up with this back in
+ 
+
+ align:start position:0%
+so these guys came up with this back in
+i think 1973
+
+ align:start position:0%
+i think 1973
+ 
+
+ align:start position:0%
+i think 1973
+they published a paper in the journal of
+
+ align:start position:0%
+they published a paper in the journal of
+ 
+
+ align:start position:0%
+they published a paper in the journal of
+chemical education
+
+ align:start position:0%
+chemical education
+ 
+
+ align:start position:0%
+chemical education
+and they had every scientist in the
+
+ align:start position:0%
+and they had every scientist in the
+ 
+
+ align:start position:0%
+and they had every scientist in the
+country puzzled
+
+ align:start position:0%
+country puzzled
+ 
+
+ align:start position:0%
+country puzzled
+and it took about 10 years to work out
+
+ align:start position:0%
+and it took about 10 years to work out
+ 
+
+ align:start position:0%
+and it took about 10 years to work out
+all the insundry
+
+ align:start position:0%
+all the insundry
+ 
+
+ align:start position:0%
+all the insundry
+reactions that are going on in this in
+
+ align:start position:0%
+reactions that are going on in this in
+ 
+
+ align:start position:0%
+reactions that are going on in this in
+this reaction
+
+ align:start position:0%
+this reaction
+ 
+
+ align:start position:0%
+this reaction
+so i'm going to put on some safety
+
+ align:start position:0%
+so i'm going to put on some safety
+ 
+
+ align:start position:0%
+so i'm going to put on some safety
+glasses
+
+ align:start position:0%
+glasses
+ 
+
+ align:start position:0%
+glasses
+and what i'm going to be doing is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to be mixing three colorless
+
+ align:start position:0%
+i'm going to be mixing three colorless
+ 
+
+ align:start position:0%
+i'm going to be mixing three colorless
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+in here this is my first one
+
+ align:start position:0%
+in here this is my first one
+ 
+
+ align:start position:0%
+in here this is my first one
+and i'm going to use kitchen chemistry
+
+ align:start position:0%
+and i'm going to use kitchen chemistry
+ 
+
+ align:start position:0%
+and i'm going to use kitchen chemistry
+which means i'm kind of looking at that
+
+ align:start position:0%
+which means i'm kind of looking at that
+ 
+
+ align:start position:0%
+which means i'm kind of looking at that
+scale over there and i'm going to pour
+
+ align:start position:0%
+scale over there and i'm going to pour
+ 
+
+ align:start position:0%
+scale over there and i'm going to pour
+these in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's i'll put a little more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's colorless right okay
+
+ align:start position:0%
+that's colorless right okay
+ 
+
+ align:start position:0%
+that's colorless right okay
+next colorless solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's about right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the final colorless solution keep
+
+ align:start position:0%
+and the final colorless solution keep
+ 
+
+ align:start position:0%
+and the final colorless solution keep
+your eye on it
+
+ align:start position:0%
+your eye on it
+ 
+
+ align:start position:0%
+your eye on it
+oh my goodness wow
+
+ align:start position:0%
+oh my goodness wow
+ 
+
+ align:start position:0%
+oh my goodness wow
+i wasn't supposed to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are you kidding me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's going on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get your clock out this is a clock
+
+ align:start position:0%
+get your clock out this is a clock
+ 
+
+ align:start position:0%
+get your clock out this is a clock
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+can keep time with this
+
+ align:start position:0%
+can keep time with this
+ 
+
+ align:start position:0%
+can keep time with this
+so i'll give you a little hint
+
+ align:start position:0%
+so i'll give you a little hint
+ 
+
+ align:start position:0%
+so i'll give you a little hint
+there there's there's iodide in there i
+
+ align:start position:0%
+there there's there's iodide in there i
+ 
+
+ align:start position:0%
+there there's there's iodide in there i
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i minus is colorless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's iodine in there and iodine is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when they're both when they're both
+
+ align:start position:0%
+when they're both when they're both
+ 
+
+ align:start position:0%
+when they're both when they're both
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+it's blue black and we're going to see
+
+ align:start position:0%
+it's blue black and we're going to see
+ 
+
+ align:start position:0%
+it's blue black and we're going to see
+why that is
+
+ align:start position:0%
+why that is
+ 
+
+ align:start position:0%
+why that is
+in the next lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a lot of a lot of reactions
+
+ align:start position:0%
+so there's a lot of a lot of reactions
+ 
+
+ align:start position:0%
+so there's a lot of a lot of reactions
+going on in there
+
+ align:start position:0%
+going on in there
+ 
+
+ align:start position:0%
+going on in there
+when these two these reactants react
+
+ align:start position:0%
+when these two these reactants react
+ 
+
+ align:start position:0%
+when these two these reactants react
+they form hypoiodous
+
+ align:start position:0%
+they form hypoiodous
+ 
+
+ align:start position:0%
+they form hypoiodous
+acid and sometimes the hypoiodous acid
+
+ align:start position:0%
+acid and sometimes the hypoiodous acid
+ 
+
+ align:start position:0%
+acid and sometimes the hypoiodous acid
+is actually oxidizes iodide to iodine
+
+ align:start position:0%
+is actually oxidizes iodide to iodine
+ 
+
+ align:start position:0%
+is actually oxidizes iodide to iodine
+so you've got colorless going to amber
+
+ align:start position:0%
+so you've got colorless going to amber
+ 
+
+ align:start position:0%
+so you've got colorless going to amber
+but sometimes there's so much
+
+ align:start position:0%
+but sometimes there's so much
+ 
+
+ align:start position:0%
+but sometimes there's so much
+hypoiodous acid formed it can't handle
+
+ align:start position:0%
+hypoiodous acid formed it can't handle
+ 
+
+ align:start position:0%
+hypoiodous acid formed it can't handle
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+and and and and what happens you have a
+
+ align:start position:0%
+and and and and what happens you have a
+ 
+
+ align:start position:0%
+and and and and what happens you have a
+little bit of i minus and i tube present
+
+ align:start position:0%
+little bit of i minus and i tube present
+ 
+
+ align:start position:0%
+little bit of i minus and i tube present
+at the same time
+
+ align:start position:0%
+at the same time
+ 
+
+ align:start position:0%
+at the same time
+and you get blue black this is kind of
+
+ align:start position:0%
+and you get blue black this is kind of
+ 
+
+ align:start position:0%
+and you get blue black this is kind of
+the color you're going to get when you
+
+ align:start position:0%
+the color you're going to get when you
+ 
+
+ align:start position:0%
+the color you're going to get when you
+do your titrations and you add the
+
+ align:start position:0%
+do your titrations and you add the
+ 
+
+ align:start position:0%
+do your titrations and you add the
+starch
+
+ align:start position:0%
+starch
+ 
+
+ align:start position:0%
+starch
+because there is starch present in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm going to leave you with that and
+
+ align:start position:0%
+so i'm going to leave you with that and
+ 
+
+ align:start position:0%
+so i'm going to leave you with that and
+i'll see some of you up in the lab yes
+
+ align:start position:0%
+i'll see some of you up in the lab yes
+ 
+
+ align:start position:0%
+i'll see some of you up in the lab yes
+you have a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she just asked me if this will ever stop
+
+ align:start position:0%
+she just asked me if this will ever stop
+ 
+
+ align:start position:0%
+she just asked me if this will ever stop
+can someone against hannah wants to know
+
+ align:start position:0%
+can someone against hannah wants to know
+ 
+
+ align:start position:0%
+can someone against hannah wants to know
+if this is going to ever stop
+
+ align:start position:0%
+if this is going to ever stop
+ 
+
+ align:start position:0%
+if this is going to ever stop
+who who who can who can tell me
+
+ align:start position:0%
+who who who can who can tell me
+ 
+
+ align:start position:0%
+who who who can who can tell me
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says it probably won't because it's not
+
+ align:start position:0%
+says it probably won't because it's not
+ 
+
+ align:start position:0%
+says it probably won't because it's not
+releasing gas
+
+ align:start position:0%
+releasing gas
+ 
+
+ align:start position:0%
+releasing gas
+but in a minute it's going to iodine
+
+ align:start position:0%
+but in a minute it's going to iodine
+ 
+
+ align:start position:0%
+but in a minute it's going to iodine
+iodine vapor is going to start pouring
+
+ align:start position:0%
+iodine vapor is going to start pouring
+ 
+
+ align:start position:0%
+iodine vapor is going to start pouring
+out of it and tristan is going to
+
+ align:start position:0%
+out of it and tristan is going to
+ 
+
+ align:start position:0%
+out of it and tristan is going to
+carry it up to the lab in a bucket
+
+ align:start position:0%
+carry it up to the lab in a bucket
+ 
+
+ align:start position:0%
+carry it up to the lab in a bucket
+quickly
+
+ align:start position:0%
+quickly
+ 
+
+ align:start position:0%
+quickly
+but in answer to hannah's question is
+
+ align:start position:0%
+but in answer to hannah's question is
+ 
+
+ align:start position:0%
+but in answer to hannah's question is
+do you guys will this stop limiting
+
+ align:start position:0%
+do you guys will this stop limiting
+ 
+
+ align:start position:0%
+do you guys will this stop limiting
+reagent
+
+ align:start position:0%
+reagent
+ 
+
+ align:start position:0%
+reagent
+right there's always a limiting reagent
+
+ align:start position:0%
+right there's always a limiting reagent
+ 
+
+ align:start position:0%
+right there's always a limiting reagent
+okay see you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/PoaWyf6Nn6Y.txt b/PoaWyf6Nn6Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ef645f8ffb5d8275aa01ea84b5b10eee90123fc
--- /dev/null
+++ b/PoaWyf6Nn6Y.txt
@@ -0,0 +1,8763 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT opencourseware continue to
+
+ align:start position:0%
+will help MIT opencourseware continue to
+ 
+
+ align:start position:0%
+will help MIT opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I have talked yet about
+
+ align:start position:0%
+okay I have talked yet about
+ 
+
+ align:start position:0%
+okay I have talked yet about
+topography and I
+
+ align:start position:0%
+topography and I
+ 
+
+ align:start position:0%
+topography and I
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+I just want you to understand how the
+
+ align:start position:0%
+I just want you to understand how the
+ 
+
+ align:start position:0%
+I just want you to understand how the
+optic tract is laid out and
+
+ align:start position:0%
+optic tract is laid out and
+ 
+
+ align:start position:0%
+optic tract is laid out and
+but before we do that I'll show you
+
+ align:start position:0%
+but before we do that I'll show you
+ 
+
+ align:start position:0%
+but before we do that I'll show you
+midbrain of a few different species
+
+ align:start position:0%
+midbrain of a few different species
+ 
+
+ align:start position:0%
+midbrain of a few different species
+there's one that occurred earlier in the
+
+ align:start position:0%
+there's one that occurred earlier in the
+ 
+
+ align:start position:0%
+there's one that occurred earlier in the
+book I think it was chapter 11 yes
+
+ align:start position:0%
+book I think it was chapter 11 yes
+ 
+
+ align:start position:0%
+book I think it was chapter 11 yes
+where I compared Road human and tree
+
+ align:start position:0%
+where I compared Road human and tree
+ 
+
+ align:start position:0%
+where I compared Road human and tree
+shoe where the you see these chapter 11
+
+ align:start position:0%
+shoe where the you see these chapter 11
+ 
+
+ align:start position:0%
+shoe where the you see these chapter 11
+was the midbrain chapter
+
+ align:start position:0%
+was the midbrain chapter
+ 
+
+ align:start position:0%
+was the midbrain chapter
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and you can see how the size of the
+
+ align:start position:0%
+and you can see how the size of the
+ 
+
+ align:start position:0%
+and you can see how the size of the
+tectum and the size of the peduncle
+
+ align:start position:0%
+tectum and the size of the peduncle
+ 
+
+ align:start position:0%
+tectum and the size of the peduncle
+or what's so different in these three
+
+ align:start position:0%
+or what's so different in these three
+ 
+
+ align:start position:0%
+or what's so different in these three
+species the humans with a huge peduncle
+
+ align:start position:0%
+species the humans with a huge peduncle
+ 
+
+ align:start position:0%
+species the humans with a huge peduncle
+and the spirit colliculus that's not so
+
+ align:start position:0%
+and the spirit colliculus that's not so
+ 
+
+ align:start position:0%
+and the spirit colliculus that's not so
+huge even though we're very visual
+
+ align:start position:0%
+huge even though we're very visual
+ 
+
+ align:start position:0%
+huge even though we're very visual
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we depend a lot more on the genital
+
+ align:start position:0%
+we depend a lot more on the genital
+ 
+
+ align:start position:0%
+we depend a lot more on the genital
+Australia system because
+
+ align:start position:0%
+Australia system because
+ 
+
+ align:start position:0%
+Australia system because
+we depend more on learning
+
+ align:start position:0%
+we depend more on learning
+ 
+
+ align:start position:0%
+we depend more on learning
+whereas the tree shoe
+
+ align:start position:0%
+whereas the tree shoe
+ 
+
+ align:start position:0%
+whereas the tree shoe
+and squirrel would be very similar
+
+ align:start position:0%
+and squirrel would be very similar
+ 
+
+ align:start position:0%
+and squirrel would be very similar
+much more dependent on innate visual
+
+ align:start position:0%
+much more dependent on innate visual
+ 
+
+ align:start position:0%
+much more dependent on innate visual
+reactions
+
+ align:start position:0%
+reactions
+ 
+
+ align:start position:0%
+reactions
+and they have the huge Detective
+
+ align:start position:0%
+and they have the huge Detective
+ 
+
+ align:start position:0%
+and they have the huge Detective
+okay I'm asked these are some of the
+
+ align:start position:0%
+okay I'm asked these are some of the
+ 
+
+ align:start position:0%
+okay I'm asked these are some of the
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+I asked you to describe four different
+
+ align:start position:0%
+I asked you to describe four different
+ 
+
+ align:start position:0%
+I asked you to describe four different
+anatomical methods that can be used to
+
+ align:start position:0%
+anatomical methods that can be used to
+ 
+
+ align:start position:0%
+anatomical methods that can be used to
+unjust to uncover the layers of the
+
+ align:start position:0%
+unjust to uncover the layers of the
+ 
+
+ align:start position:0%
+unjust to uncover the layers of the
+objective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course I just mean
+
+ align:start position:0%
+and of course I just mean
+ 
+
+ align:start position:0%
+and of course I just mean
+just stains of normal material like
+
+ align:start position:0%
+just stains of normal material like
+ 
+
+ align:start position:0%
+just stains of normal material like
+fiber stains and cell stains
+
+ align:start position:0%
+fiber stains and cell stains
+ 
+
+ align:start position:0%
+fiber stains and cell stains
+you can name any fiber stain and of
+
+ align:start position:0%
+you can name any fiber stain and of
+ 
+
+ align:start position:0%
+you can name any fiber stain and of
+course missile stains
+
+ align:start position:0%
+course missile stains
+ 
+
+ align:start position:0%
+course missile stains
+come in a number of varieties but also
+
+ align:start position:0%
+come in a number of varieties but also
+ 
+
+ align:start position:0%
+come in a number of varieties but also
+there's histochemical stains and I
+
+ align:start position:0%
+there's histochemical stains and I
+ 
+
+ align:start position:0%
+there's histochemical stains and I
+showed you some of those in the methods
+
+ align:start position:0%
+showed you some of those in the methods
+ 
+
+ align:start position:0%
+showed you some of those in the methods
+chapter chapter 2.
+
+ align:start position:0%
+chapter chapter 2.
+ 
+
+ align:start position:0%
+chapter chapter 2.
+and then of course the Golgi so we'll
+
+ align:start position:0%
+and then of course the Golgi so we'll
+ 
+
+ align:start position:0%
+and then of course the Golgi so we'll
+look at that just briefly today
+
+ align:start position:0%
+look at that just briefly today
+ 
+
+ align:start position:0%
+look at that just briefly today
+you should also know a little bit about
+
+ align:start position:0%
+you should also know a little bit about
+ 
+
+ align:start position:0%
+you should also know a little bit about
+these species varieties what are the
+
+ align:start position:0%
+these species varieties what are the
+ 
+
+ align:start position:0%
+these species varieties what are the
+animals with the huge Detective
+
+ align:start position:0%
+animals with the huge Detective
+ 
+
+ align:start position:0%
+animals with the huge Detective
+it's not only the
+
+ align:start position:0%
+it's not only the
+ 
+
+ align:start position:0%
+it's not only the
+non-mammalians like the fish some
+
+ align:start position:0%
+non-mammalians like the fish some
+ 
+
+ align:start position:0%
+non-mammalians like the fish some
+reptile the visual reptiles
+
+ align:start position:0%
+reptile the visual reptiles
+ 
+
+ align:start position:0%
+reptile the visual reptiles
+I'm sure that the dinosaurs had a very
+
+ align:start position:0%
+I'm sure that the dinosaurs had a very
+ 
+
+ align:start position:0%
+I'm sure that the dinosaurs had a very
+large victim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and why is the term optic tectum a
+
+ align:start position:0%
+and why is the term optic tectum a
+ 
+
+ align:start position:0%
+and why is the term optic tectum a
+misleading term
+
+ align:start position:0%
+misleading term
+ 
+
+ align:start position:0%
+misleading term
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're so loud in here you have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it could still be an optic pectin
+
+ align:start position:0%
+but it could still be an optic pectin
+ 
+
+ align:start position:0%
+but it could still be an optic pectin
+it's optic that's not accurate
+
+ align:start position:0%
+it's optic that's not accurate
+ 
+
+ align:start position:0%
+it's optic that's not accurate
+it's just the superficial layers that
+
+ align:start position:0%
+it's just the superficial layers that
+ 
+
+ align:start position:0%
+it's just the superficial layers that
+get the visual input
+
+ align:start position:0%
+get the visual input
+ 
+
+ align:start position:0%
+get the visual input
+from the op this optic or visual sense
+
+ align:start position:0%
+from the op this optic or visual sense
+ 
+
+ align:start position:0%
+from the op this optic or visual sense
+it gets them at a sensory and auditory
+
+ align:start position:0%
+it gets them at a sensory and auditory
+ 
+
+ align:start position:0%
+it gets them at a sensory and auditory
+input as well and it gets cerebellar
+
+ align:start position:0%
+input as well and it gets cerebellar
+ 
+
+ align:start position:0%
+input as well and it gets cerebellar
+input okay so but especially all that
+
+ align:start position:0%
+input okay so but especially all that
+ 
+
+ align:start position:0%
+input okay so but especially all that
+auditoring some of the sensory input
+
+ align:start position:0%
+auditoring some of the sensory input
+ 
+
+ align:start position:0%
+auditoring some of the sensory input
+coming in there
+
+ align:start position:0%
+coming in there
+ 
+
+ align:start position:0%
+coming in there
+uh it's a lot more than just an optic
+
+ align:start position:0%
+uh it's a lot more than just an optic
+ 
+
+ align:start position:0%
+uh it's a lot more than just an optic
+tectum so sometimes I call it a
+
+ align:start position:0%
+tectum so sometimes I call it a
+ 
+
+ align:start position:0%
+tectum so sometimes I call it a
+correlation Center it brings in
+
+ align:start position:0%
+correlation Center it brings in
+ 
+
+ align:start position:0%
+correlation Center it brings in
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+all these different modalities that can
+
+ align:start position:0%
+all these different modalities that can
+ 
+
+ align:start position:0%
+all these different modalities that can
+all you know arise from a similar part
+
+ align:start position:0%
+all you know arise from a similar part
+ 
+
+ align:start position:0%
+all you know arise from a similar part
+of space around the head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is a ray Fin fish and I'm just
+
+ align:start position:0%
+okay this is a ray Fin fish and I'm just
+ 
+
+ align:start position:0%
+okay this is a ray Fin fish and I'm just
+showing around my projections here on
+
+ align:start position:0%
+showing around my projections here on
+ 
+
+ align:start position:0%
+showing around my projections here on
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+this animal
+
+ align:start position:0%
+this animal
+ 
+
+ align:start position:0%
+this animal
+is a fairly simple but in large tecton
+
+ align:start position:0%
+is a fairly simple but in large tecton
+ 
+
+ align:start position:0%
+is a fairly simple but in large tecton
+and you see a little bit of one of the
+
+ align:start position:0%
+and you see a little bit of one of the
+ 
+
+ align:start position:0%
+and you see a little bit of one of the
+accessory optic nuclei there
+
+ align:start position:0%
+accessory optic nuclei there
+ 
+
+ align:start position:0%
+accessory optic nuclei there
+this huge structure down here is
+
+ align:start position:0%
+this huge structure down here is
+ 
+
+ align:start position:0%
+this huge structure down here is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+a backward protrusion of the
+
+ align:start position:0%
+a backward protrusion of the
+ 
+
+ align:start position:0%
+a backward protrusion of the
+hypothalamus that's the inferior lobe of
+
+ align:start position:0%
+hypothalamus that's the inferior lobe of
+ 
+
+ align:start position:0%
+hypothalamus that's the inferior lobe of
+the hypothalamus in this fish
+
+ align:start position:0%
+the hypothalamus in this fish
+ 
+
+ align:start position:0%
+the hypothalamus in this fish
+this in animals of this group shows what
+
+ align:start position:0%
+this in animals of this group shows what
+ 
+
+ align:start position:0%
+this in animals of this group shows what
+the tectum is like and how the
+
+ align:start position:0%
+the tectum is like and how the
+ 
+
+ align:start position:0%
+the tectum is like and how the
+axons from the retina come in and
+
+ align:start position:0%
+axons from the retina come in and
+ 
+
+ align:start position:0%
+axons from the retina come in and
+terminate on The Superficial parts of
+
+ align:start position:0%
+terminate on The Superficial parts of
+ 
+
+ align:start position:0%
+terminate on The Superficial parts of
+the dendrites of the deep layer cells
+
+ align:start position:0%
+the dendrites of the deep layer cells
+ 
+
+ align:start position:0%
+the dendrites of the deep layer cells
+there are also a few cells up in that
+
+ align:start position:0%
+there are also a few cells up in that
+ 
+
+ align:start position:0%
+there are also a few cells up in that
+superficial layer and then and this is
+
+ align:start position:0%
+superficial layer and then and this is
+ 
+
+ align:start position:0%
+superficial layer and then and this is
+true of mammals too where the retinal
+
+ align:start position:0%
+true of mammals too where the retinal
+ 
+
+ align:start position:0%
+true of mammals too where the retinal
+input and input from visual cortex come
+
+ align:start position:0%
+input and input from visual cortex come
+ 
+
+ align:start position:0%
+input and input from visual cortex come
+in superficially and then in the layers
+
+ align:start position:0%
+in superficially and then in the layers
+ 
+
+ align:start position:0%
+in superficially and then in the layers
+Below in this fish it's mainly some
+
+ align:start position:0%
+Below in this fish it's mainly some
+ 
+
+ align:start position:0%
+Below in this fish it's mainly some
+medicine
+
+ align:start position:0%
+medicine
+ 
+
+ align:start position:0%
+medicine
+in mammals it's auditory below the
+
+ align:start position:0%
+in mammals it's auditory below the
+ 
+
+ align:start position:0%
+in mammals it's auditory below the
+visual and then in the deepest layers
+
+ align:start position:0%
+visual and then in the deepest layers
+ 
+
+ align:start position:0%
+visual and then in the deepest layers
+submit a century
+
+ align:start position:0%
+submit a century
+ 
+
+ align:start position:0%
+submit a century
+remember spinal the spinal tectal
+
+ align:start position:0%
+remember spinal the spinal tectal
+ 
+
+ align:start position:0%
+remember spinal the spinal tectal
+pathway coming from spinal cord this is
+
+ align:start position:0%
+pathway coming from spinal cord this is
+ 
+
+ align:start position:0%
+pathway coming from spinal cord this is
+Smith essentially input especially from
+
+ align:start position:0%
+Smith essentially input especially from
+ 
+
+ align:start position:0%
+Smith essentially input especially from
+the face
+
+ align:start position:0%
+the face
+ 
+
+ align:start position:0%
+the face
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+part of the cryogen it's a trigeminal
+
+ align:start position:0%
+part of the cryogen it's a trigeminal
+ 
+
+ align:start position:0%
+part of the cryogen it's a trigeminal
+pathway
+
+ align:start position:0%
+pathway
+ 
+
+ align:start position:0%
+pathway
+but it joins those spinal tectal inputs
+
+ align:start position:0%
+but it joins those spinal tectal inputs
+ 
+
+ align:start position:0%
+but it joins those spinal tectal inputs
+okay here's a tea Leon fish and if you
+
+ align:start position:0%
+okay here's a tea Leon fish and if you
+ 
+
+ align:start position:0%
+okay here's a tea Leon fish and if you
+just look at the low power over here you
+
+ align:start position:0%
+just look at the low power over here you
+ 
+
+ align:start position:0%
+just look at the low power over here you
+see this huge tectum the largest single
+
+ align:start position:0%
+see this huge tectum the largest single
+ 
+
+ align:start position:0%
+see this huge tectum the largest single
+structure there
+
+ align:start position:0%
+structure there
+ 
+
+ align:start position:0%
+structure there
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+here's that
+
+ align:start position:0%
+here's that
+ 
+
+ align:start position:0%
+here's that
+huge lobe of the hypothems this is
+
+ align:start position:0%
+huge lobe of the hypothems this is
+ 
+
+ align:start position:0%
+huge lobe of the hypothems this is
+cerebellum here
+
+ align:start position:0%
+cerebellum here
+ 
+
+ align:start position:0%
+cerebellum here
+you can see that tectum is larger than
+
+ align:start position:0%
+you can see that tectum is larger than
+ 
+
+ align:start position:0%
+you can see that tectum is larger than
+the whole two encephalon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and here is a chilliest hectum done
+
+ align:start position:0%
+okay and here is a chilliest hectum done
+ 
+
+ align:start position:0%
+okay and here is a chilliest hectum done
+in a series of studies by Venegas in his
+
+ align:start position:0%
+in a series of studies by Venegas in his
+ 
+
+ align:start position:0%
+in a series of studies by Venegas in his
+collaborators where they this is a
+
+ align:start position:0%
+collaborators where they this is a
+ 
+
+ align:start position:0%
+collaborators where they this is a
+composite from a number of different
+
+ align:start position:0%
+composite from a number of different
+ 
+
+ align:start position:0%
+composite from a number of different
+studies on the cell types
+
+ align:start position:0%
+studies on the cell types
+ 
+
+ align:start position:0%
+studies on the cell types
+in the tractor and you can see this
+
+ align:start position:0%
+in the tractor and you can see this
+ 
+
+ align:start position:0%
+in the tractor and you can see this
+beautiful laminar pattern that you can
+
+ align:start position:0%
+beautiful laminar pattern that you can
+ 
+
+ align:start position:0%
+beautiful laminar pattern that you can
+just see in the way axons arborize and
+
+ align:start position:0%
+just see in the way axons arborize and
+ 
+
+ align:start position:0%
+just see in the way axons arborize and
+the way dendrites are drives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it reminds me a lot of the retina effect
+
+ align:start position:0%
+it reminds me a lot of the retina effect
+ 
+
+ align:start position:0%
+it reminds me a lot of the retina effect
+okay now this is a frog uh I didn't put
+
+ align:start position:0%
+okay now this is a frog uh I didn't put
+ 
+
+ align:start position:0%
+okay now this is a frog uh I didn't put
+this I don't think I put this one in the
+
+ align:start position:0%
+this I don't think I put this one in the
+ 
+
+ align:start position:0%
+this I don't think I put this one in the
+book I put the Iguana
+
+ align:start position:0%
+book I put the Iguana
+ 
+
+ align:start position:0%
+book I put the Iguana
+next to this picture I was trying to
+
+ align:start position:0%
+next to this picture I was trying to
+ 
+
+ align:start position:0%
+next to this picture I was trying to
+there's a limit to how many figures I
+
+ align:start position:0%
+there's a limit to how many figures I
+ 
+
+ align:start position:0%
+there's a limit to how many figures I
+could use and I just decided
+
+ align:start position:0%
+could use and I just decided
+ 
+
+ align:start position:0%
+could use and I just decided
+you see a few more in the classroom but
+
+ align:start position:0%
+you see a few more in the classroom but
+ 
+
+ align:start position:0%
+you see a few more in the classroom but
+this is a fraud with initial stain and
+
+ align:start position:0%
+this is a fraud with initial stain and
+ 
+
+ align:start position:0%
+this is a fraud with initial stain and
+this is from a study of zekai who did a
+
+ align:start position:0%
+this is from a study of zekai who did a
+ 
+
+ align:start position:0%
+this is from a study of zekai who did a
+number of studies of the Frog
+
+ align:start position:0%
+number of studies of the Frog
+ 
+
+ align:start position:0%
+number of studies of the Frog
+especially a detective and what I've
+
+ align:start position:0%
+especially a detective and what I've
+ 
+
+ align:start position:0%
+especially a detective and what I've
+done is because he identified
+
+ align:start position:0%
+done is because he identified
+ 
+
+ align:start position:0%
+done is because he identified
+a number the retinal fibers coming in in
+
+ align:start position:0%
+a number the retinal fibers coming in in
+ 
+
+ align:start position:0%
+a number the retinal fibers coming in in
+these four layers
+
+ align:start position:0%
+these four layers
+ 
+
+ align:start position:0%
+these four layers
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+use tiny little labels so I blew up the
+
+ align:start position:0%
+use tiny little labels so I blew up the
+ 
+
+ align:start position:0%
+use tiny little labels so I blew up the
+figure and I colored those axons in so
+
+ align:start position:0%
+figure and I colored those axons in so
+ 
+
+ align:start position:0%
+figure and I colored those axons in so
+you can the retinal fibers can be seen
+
+ align:start position:0%
+you can the retinal fibers can be seen
+ 
+
+ align:start position:0%
+you can the retinal fibers can be seen
+terminating in these four distinct
+
+ align:start position:0%
+terminating in these four distinct
+ 
+
+ align:start position:0%
+terminating in these four distinct
+layers and that
+
+ align:start position:0%
+layers and that
+ 
+
+ align:start position:0%
+layers and that
+corresponded very well to the findings
+
+ align:start position:0%
+corresponded very well to the findings
+ 
+
+ align:start position:0%
+corresponded very well to the findings
+here at MIT of Gary leppen and his
+
+ align:start position:0%
+here at MIT of Gary leppen and his
+ 
+
+ align:start position:0%
+here at MIT of Gary leppen and his
+collaborators where they were recording
+
+ align:start position:0%
+collaborators where they were recording
+ 
+
+ align:start position:0%
+collaborators where they were recording
+from these axon Indies
+
+ align:start position:0%
+from these axon Indies
+ 
+
+ align:start position:0%
+from these axon Indies
+they were recording the activity of the
+
+ align:start position:0%
+they were recording the activity of the
+ 
+
+ align:start position:0%
+they were recording the activity of the
+four different classes of retinal gang
+
+ align:start position:0%
+four different classes of retinal gang
+ 
+
+ align:start position:0%
+four different classes of retinal gang
+on its cells but they actually recorded
+
+ align:start position:0%
+on its cells but they actually recorded
+ 
+
+ align:start position:0%
+on its cells but they actually recorded
+in the tectum
+
+ align:start position:0%
+in the tectum
+ 
+
+ align:start position:0%
+in the tectum
+and you can see that again a lot of the
+
+ align:start position:0%
+and you can see that again a lot of the
+ 
+
+ align:start position:0%
+and you can see that again a lot of the
+cells are down you see over here in the
+
+ align:start position:0%
+cells are down you see over here in the
+ 
+
+ align:start position:0%
+cells are down you see over here in the
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+results from the cell stain cell and
+
+ align:start position:0%
+results from the cell stain cell and
+ 
+
+ align:start position:0%
+results from the cell stain cell and
+fiber stings you can see fewer cells in
+
+ align:start position:0%
+fiber stings you can see fewer cells in
+ 
+
+ align:start position:0%
+fiber stings you can see fewer cells in
+The Superficial the top seven layers and
+
+ align:start position:0%
+The Superficial the top seven layers and
+ 
+
+ align:start position:0%
+The Superficial the top seven layers and
+then in these deeper six layers you have
+
+ align:start position:0%
+then in these deeper six layers you have
+ 
+
+ align:start position:0%
+then in these deeper six layers you have
+two main three major cell layers and
+
+ align:start position:0%
+two main three major cell layers and
+ 
+
+ align:start position:0%
+two main three major cell layers and
+that's where you see these cells with
+
+ align:start position:0%
+that's where you see these cells with
+ 
+
+ align:start position:0%
+that's where you see these cells with
+axons just like the pyramidal cells
+
+ align:start position:0%
+axons just like the pyramidal cells
+ 
+
+ align:start position:0%
+axons just like the pyramidal cells
+really just like in neocortex
+
+ align:start position:0%
+really just like in neocortex
+ 
+
+ align:start position:0%
+really just like in neocortex
+if the pyramidal cell dendrites and
+
+ align:start position:0%
+if the pyramidal cell dendrites and
+ 
+
+ align:start position:0%
+if the pyramidal cell dendrites and
+cortex also go up to this peel surface
+
+ align:start position:0%
+cortex also go up to this peel surface
+ 
+
+ align:start position:0%
+cortex also go up to this peel surface
+just like you see here and there the
+
+ align:start position:0%
+just like you see here and there the
+ 
+
+ align:start position:0%
+just like you see here and there the
+inputs are terminating mainly on those
+
+ align:start position:0%
+inputs are terminating mainly on those
+ 
+
+ align:start position:0%
+inputs are terminating mainly on those
+dendrites this is the
+
+ align:start position:0%
+dendrites this is the
+ 
+
+ align:start position:0%
+dendrites this is the
+iguana
+
+ align:start position:0%
+iguana
+ 
+
+ align:start position:0%
+iguana
+where the laminations particularly clear
+
+ align:start position:0%
+where the laminations particularly clear
+ 
+
+ align:start position:0%
+where the laminations particularly clear
+this is from Bill Hall down at Duke
+
+ align:start position:0%
+this is from Bill Hall down at Duke
+ 
+
+ align:start position:0%
+this is from Bill Hall down at Duke
+University
+
+ align:start position:0%
+University
+ 
+
+ align:start position:0%
+University
+this is a hamster in the nissl stand
+
+ align:start position:0%
+this is a hamster in the nissl stand
+ 
+
+ align:start position:0%
+this is a hamster in the nissl stand
+where I've not removed the cortex but
+
+ align:start position:0%
+where I've not removed the cortex but
+ 
+
+ align:start position:0%
+where I've not removed the cortex but
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+the evidence of lamination and remember
+
+ align:start position:0%
+the evidence of lamination and remember
+ 
+
+ align:start position:0%
+the evidence of lamination and remember
+this structure
+
+ align:start position:0%
+this structure
+ 
+
+ align:start position:0%
+this structure
+the central gray area and that's the
+
+ align:start position:0%
+the central gray area and that's the
+ 
+
+ align:start position:0%
+the central gray area and that's the
+aqueduct of service there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is also the hamster but
+
+ align:start position:0%
+okay and this is also the hamster but
+ 
+
+ align:start position:0%
+okay and this is also the hamster but
+now we're looking at a myelin stain and
+
+ align:start position:0%
+now we're looking at a myelin stain and
+ 
+
+ align:start position:0%
+now we're looking at a myelin stain and
+you see compared to the cell stain the
+
+ align:start position:0%
+you see compared to the cell stain the
+ 
+
+ align:start position:0%
+you see compared to the cell stain the
+myelin is even clearer about these
+
+ align:start position:0%
+myelin is even clearer about these
+ 
+
+ align:start position:0%
+myelin is even clearer about these
+layers you see not so many myelinated
+
+ align:start position:0%
+layers you see not so many myelinated
+ 
+
+ align:start position:0%
+layers you see not so many myelinated
+axons in The Superficial layer where the
+
+ align:start position:0%
+axons in The Superficial layer where the
+ 
+
+ align:start position:0%
+axons in The Superficial layer where the
+retinal axons are terminating and also
+
+ align:start position:0%
+retinal axons are terminating and also
+ 
+
+ align:start position:0%
+retinal axons are terminating and also
+accidents from visual cortex
+
+ align:start position:0%
+accidents from visual cortex
+ 
+
+ align:start position:0%
+accidents from visual cortex
+and then these are it's right below it
+
+ align:start position:0%
+and then these are it's right below it
+ 
+
+ align:start position:0%
+and then these are it's right below it
+is the layer of longitudinal fibers so
+
+ align:start position:0%
+is the layer of longitudinal fibers so
+ 
+
+ align:start position:0%
+is the layer of longitudinal fibers so
+we've cut across them okay these are
+
+ align:start position:0%
+we've cut across them okay these are
+ 
+
+ align:start position:0%
+we've cut across them okay these are
+including all the retinal fibers and
+
+ align:start position:0%
+including all the retinal fibers and
+ 
+
+ align:start position:0%
+including all the retinal fibers and
+fibers from visual quotas they come in
+
+ align:start position:0%
+fibers from visual quotas they come in
+ 
+
+ align:start position:0%
+fibers from visual quotas they come in
+to that layer
+
+ align:start position:0%
+to that layer
+ 
+
+ align:start position:0%
+to that layer
+before they get to detect them they're
+
+ align:start position:0%
+before they get to detect them they're
+ 
+
+ align:start position:0%
+before they get to detect them they're
+traveling mostly on the surface of the
+
+ align:start position:0%
+traveling mostly on the surface of the
+ 
+
+ align:start position:0%
+traveling mostly on the surface of the
+brain but not in detect them
+
+ align:start position:0%
+brain but not in detect them
+ 
+
+ align:start position:0%
+brain but not in detect them
+and then there's another layer of fibers
+
+ align:start position:0%
+and then there's another layer of fibers
+ 
+
+ align:start position:0%
+and then there's another layer of fibers
+like that they come from cortex and from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+auditorians and at a sensory input
+
+ align:start position:0%
+auditorians and at a sensory input
+ 
+
+ align:start position:0%
+auditorians and at a sensory input
+there are these fibers
+
+ align:start position:0%
+there are these fibers
+ 
+
+ align:start position:0%
+there are these fibers
+and then you have the layer it's called
+
+ align:start position:0%
+and then you have the layer it's called
+ 
+
+ align:start position:0%
+and then you have the layer it's called
+the layer transverse fibers and for how
+
+ align:start position:0%
+the layer transverse fibers and for how
+ 
+
+ align:start position:0%
+the layer transverse fibers and for how
+because they're traveling the transverse
+
+ align:start position:0%
+because they're traveling the transverse
+ 
+
+ align:start position:0%
+because they're traveling the transverse
+plane it's the two kinds of fibers that
+
+ align:start position:0%
+plane it's the two kinds of fibers that
+ 
+
+ align:start position:0%
+plane it's the two kinds of fibers that
+are fibers of the commissure or the
+
+ align:start position:0%
+are fibers of the commissure or the
+ 
+
+ align:start position:0%
+are fibers of the commissure or the
+superior colliculus but fibers from Big
+
+ align:start position:0%
+superior colliculus but fibers from Big
+ 
+
+ align:start position:0%
+superior colliculus but fibers from Big
+cells in these deeper layers I don't
+
+ align:start position:0%
+cells in these deeper layers I don't
+ 
+
+ align:start position:0%
+cells in these deeper layers I don't
+know if we can
+
+ align:start position:0%
+know if we can
+ 
+
+ align:start position:0%
+know if we can
+yes you see some of the big cells here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the axons of those cells join these
+
+ align:start position:0%
+the axons of those cells join these
+ 
+
+ align:start position:0%
+the axons of those cells join these
+transverse fibers and then
+
+ align:start position:0%
+transverse fibers and then
+ 
+
+ align:start position:0%
+transverse fibers and then
+go down across the midline become the
+
+ align:start position:0%
+go down across the midline become the
+ 
+
+ align:start position:0%
+go down across the midline become the
+tectospinal tract
+
+ align:start position:0%
+tectospinal tract
+ 
+
+ align:start position:0%
+tectospinal tract
+that's it you see some of those big
+
+ align:start position:0%
+that's it you see some of those big
+ 
+
+ align:start position:0%
+that's it you see some of those big
+cells here in the rat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's rat and spirit glucose
+
+ align:start position:0%
+that's rat and spirit glucose
+ 
+
+ align:start position:0%
+that's rat and spirit glucose
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+topography let's just talk again about
+
+ align:start position:0%
+topography let's just talk again about
+ 
+
+ align:start position:0%
+topography let's just talk again about
+the major methods for doing topography
+
+ align:start position:0%
+the major methods for doing topography
+ 
+
+ align:start position:0%
+the major methods for doing topography
+this illustrates the
+
+ align:start position:0%
+this illustrates the
+ 
+
+ align:start position:0%
+this illustrates the
+electrophysiological methods where
+
+ align:start position:0%
+electrophysiological methods where
+ 
+
+ align:start position:0%
+electrophysiological methods where
+they're recording
+
+ align:start position:0%
+they're recording
+ 
+
+ align:start position:0%
+they're recording
+in a systematic way here's the dorsal
+
+ align:start position:0%
+in a systematic way here's the dorsal
+ 
+
+ align:start position:0%
+in a systematic way here's the dorsal
+view of the the goldfish tectum
+
+ align:start position:0%
+view of the the goldfish tectum
+ 
+
+ align:start position:0%
+view of the the goldfish tectum
+and you see how they insert the
+
+ align:start position:0%
+and you see how they insert the
+ 
+
+ align:start position:0%
+and you see how they insert the
+electrodes in a grid
+
+ align:start position:0%
+electrodes in a grid
+ 
+
+ align:start position:0%
+electrodes in a grid
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+sometimes to avoid avoid blood vessels
+
+ align:start position:0%
+sometimes to avoid avoid blood vessels
+ 
+
+ align:start position:0%
+sometimes to avoid avoid blood vessels
+they don't get the entire tattoo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but they could get it if they nudge
+
+ align:start position:0%
+but they could get it if they nudge
+ 
+
+ align:start position:0%
+but they could get it if they nudge
+those vessels aside that it's dangerous
+
+ align:start position:0%
+those vessels aside that it's dangerous
+ 
+
+ align:start position:0%
+those vessels aside that it's dangerous
+and they lose a lot of animals that way
+
+ align:start position:0%
+and they lose a lot of animals that way
+ 
+
+ align:start position:0%
+and they lose a lot of animals that way
+but anyway you can see as they move the
+
+ align:start position:0%
+but anyway you can see as they move the
+ 
+
+ align:start position:0%
+but anyway you can see as they move the
+electrode from one position to the other
+
+ align:start position:0%
+electrode from one position to the other
+ 
+
+ align:start position:0%
+electrode from one position to the other
+the center of the receptive Fields move
+
+ align:start position:0%
+the center of the receptive Fields move
+ 
+
+ align:start position:0%
+the center of the receptive Fields move
+and so this is the map of the visual
+
+ align:start position:0%
+and so this is the map of the visual
+ 
+
+ align:start position:0%
+and so this is the map of the visual
+field of the fish
+
+ align:start position:0%
+field of the fish
+ 
+
+ align:start position:0%
+field of the fish
+and you can see the results of the
+
+ align:start position:0%
+and you can see the results of the
+ 
+
+ align:start position:0%
+and you can see the results of the
+connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+they connected the roster's throttle
+
+ align:start position:0%
+they connected the roster's throttle
+ 
+
+ align:start position:0%
+they connected the roster's throttle
+rows of penetration sites
+
+ align:start position:0%
+rows of penetration sites
+ 
+
+ align:start position:0%
+rows of penetration sites
+showing how it the orderly Topography of
+
+ align:start position:0%
+showing how it the orderly Topography of
+ 
+
+ align:start position:0%
+showing how it the orderly Topography of
+the projection and then this one we
+
+ align:start position:0%
+the projection and then this one we
+ 
+
+ align:start position:0%
+the projection and then this one we
+talked about before this is one from uh
+
+ align:start position:0%
+talked about before this is one from uh
+ 
+
+ align:start position:0%
+talked about before this is one from uh
+work of me and my students in the
+
+ align:start position:0%
+work of me and my students in the
+ 
+
+ align:start position:0%
+work of me and my students in the
+hamster where the initial method was
+
+ align:start position:0%
+hamster where the initial method was
+ 
+
+ align:start position:0%
+hamster where the initial method was
+anatomical making lesions
+
+ align:start position:0%
+anatomical making lesions
+ 
+
+ align:start position:0%
+anatomical making lesions
+in the retina and tracing degeneration
+
+ align:start position:0%
+in the retina and tracing degeneration
+ 
+
+ align:start position:0%
+in the retina and tracing degeneration
+to detect them
+
+ align:start position:0%
+to detect them
+ 
+
+ align:start position:0%
+to detect them
+now it would be more likely done with
+
+ align:start position:0%
+now it would be more likely done with
+ 
+
+ align:start position:0%
+now it would be more likely done with
+injection methods I've done that also
+
+ align:start position:0%
+injection methods I've done that also
+ 
+
+ align:start position:0%
+injection methods I've done that also
+where you can get a more limited number
+
+ align:start position:0%
+where you can get a more limited number
+ 
+
+ align:start position:0%
+where you can get a more limited number
+of retinal gang initials when you make
+
+ align:start position:0%
+of retinal gang initials when you make
+ 
+
+ align:start position:0%
+of retinal gang initials when you make
+lesions of course you get all the
+
+ align:start position:0%
+lesions of course you get all the
+ 
+
+ align:start position:0%
+lesions of course you get all the
+accidents traveling towards the optic
+
+ align:start position:0%
+accidents traveling towards the optic
+ 
+
+ align:start position:0%
+accidents traveling towards the optic
+disc from the most more peripheral Parts
+
+ align:start position:0%
+disc from the most more peripheral Parts
+ 
+
+ align:start position:0%
+disc from the most more peripheral Parts
+but anyway you can get a nice map
+
+ align:start position:0%
+but anyway you can get a nice map
+ 
+
+ align:start position:0%
+but anyway you can get a nice map
+the letters there are stand for the
+
+ align:start position:0%
+the letters there are stand for the
+ 
+
+ align:start position:0%
+the letters there are stand for the
+center of the eye muscles at the
+
+ align:start position:0%
+center of the eye muscles at the
+ 
+
+ align:start position:0%
+center of the eye muscles at the
+temporal pole the nasal pole of the
+
+ align:start position:0%
+temporal pole the nasal pole of the
+ 
+
+ align:start position:0%
+temporal pole the nasal pole of the
+retina Superior and inferior
+
+ align:start position:0%
+retina Superior and inferior
+ 
+
+ align:start position:0%
+retina Superior and inferior
+you call them the rectus muscles
+
+ align:start position:0%
+you call them the rectus muscles
+ 
+
+ align:start position:0%
+you call them the rectus muscles
+superior rectus
+
+ align:start position:0%
+superior rectus
+ 
+
+ align:start position:0%
+superior rectus
+temporal rectus
+
+ align:start position:0%
+temporal rectus
+ 
+
+ align:start position:0%
+temporal rectus
+actually for temporal Reckless we call
+
+ align:start position:0%
+actually for temporal Reckless we call
+ 
+
+ align:start position:0%
+actually for temporal Reckless we call
+it the lateral Rexes
+
+ align:start position:0%
+it the lateral Rexes
+ 
+
+ align:start position:0%
+it the lateral Rexes
+similarly for the nasal one we call the
+
+ align:start position:0%
+similarly for the nasal one we call the
+ 
+
+ align:start position:0%
+similarly for the nasal one we call the
+medial rectus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but they're
+
+ align:start position:0%
+but they're
+ 
+
+ align:start position:0%
+but they're
+easily repeated landmarks from one
+
+ align:start position:0%
+easily repeated landmarks from one
+ 
+
+ align:start position:0%
+easily repeated landmarks from one
+animal to the other so we get consistent
+
+ align:start position:0%
+animal to the other so we get consistent
+ 
+
+ align:start position:0%
+animal to the other so we get consistent
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+and then we take this is the view of the
+
+ align:start position:0%
+and then we take this is the view of the
+ 
+
+ align:start position:0%
+and then we take this is the view of the
+embryonic hamster
+
+ align:start position:0%
+embryonic hamster
+ 
+
+ align:start position:0%
+embryonic hamster
+up here and this is that flattened View
+
+ align:start position:0%
+up here and this is that flattened View
+ 
+
+ align:start position:0%
+up here and this is that flattened View
+and if we take the flattened view here
+
+ align:start position:0%
+and if we take the flattened view here
+ 
+
+ align:start position:0%
+and if we take the flattened view here
+we can show the topography
+
+ align:start position:0%
+we can show the topography
+ 
+
+ align:start position:0%
+we can show the topography
+I show the superior inferior retinal
+
+ align:start position:0%
+I show the superior inferior retinal
+ 
+
+ align:start position:0%
+I show the superior inferior retinal
+axis just once out of here because the
+
+ align:start position:0%
+axis just once out of here because the
+ 
+
+ align:start position:0%
+axis just once out of here because the
+axons assume that topography very early
+
+ align:start position:0%
+axons assume that topography very early
+ 
+
+ align:start position:0%
+axons assume that topography very early
+when you get not very far beyond the
+
+ align:start position:0%
+when you get not very far beyond the
+ 
+
+ align:start position:0%
+when you get not very far beyond the
+Kaizen by the time they get to the
+
+ align:start position:0%
+Kaizen by the time they get to the
+ 
+
+ align:start position:0%
+Kaizen by the time they get to the
+genicular bodies
+
+ align:start position:0%
+genicular bodies
+ 
+
+ align:start position:0%
+genicular bodies
+you have the inferior
+
+ align:start position:0%
+you have the inferior
+ 
+
+ align:start position:0%
+you have the inferior
+retina fibers all at one Edge and the
+
+ align:start position:0%
+retina fibers all at one Edge and the
+ 
+
+ align:start position:0%
+retina fibers all at one Edge and the
+superior retinal fibers are at the other
+
+ align:start position:0%
+superior retinal fibers are at the other
+ 
+
+ align:start position:0%
+superior retinal fibers are at the other
+Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+of course you have to know which is this
+
+ align:start position:0%
+of course you have to know which is this
+ 
+
+ align:start position:0%
+of course you have to know which is this
+would be the The rostral Edge and then
+
+ align:start position:0%
+would be the The rostral Edge and then
+ 
+
+ align:start position:0%
+would be the The rostral Edge and then
+it becomes the medial edge of the optic
+
+ align:start position:0%
+it becomes the medial edge of the optic
+ 
+
+ align:start position:0%
+it becomes the medial edge of the optic
+tract here
+
+ align:start position:0%
+tract here
+ 
+
+ align:start position:0%
+tract here
+and this would be the
+
+ align:start position:0%
+and this would be the
+ 
+
+ align:start position:0%
+and this would be the
+coddle
+
+ align:start position:0%
+coddle
+ 
+
+ align:start position:0%
+coddle
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+Edge which becomes the lateral edge of
+
+ align:start position:0%
+Edge which becomes the lateral edge of
+ 
+
+ align:start position:0%
+Edge which becomes the lateral edge of
+the object here and then I'm showing how
+
+ align:start position:0%
+the object here and then I'm showing how
+ 
+
+ align:start position:0%
+the object here and then I'm showing how
+the nasal Temple
+
+ align:start position:0%
+the nasal Temple
+ 
+
+ align:start position:0%
+the nasal Temple
+now actually those actions are all mixed
+
+ align:start position:0%
+now actually those actions are all mixed
+ 
+
+ align:start position:0%
+now actually those actions are all mixed
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+when they're in the track here and they
+
+ align:start position:0%
+when they're in the track here and they
+ 
+
+ align:start position:0%
+when they're in the track here and they
+stay mixed together even when they're
+
+ align:start position:0%
+stay mixed together even when they're
+ 
+
+ align:start position:0%
+stay mixed together even when they're
+reaching the genital advice
+
+ align:start position:0%
+reaching the genital advice
+ 
+
+ align:start position:0%
+reaching the genital advice
+but then they're forming the following
+
+ align:start position:0%
+but then they're forming the following
+ 
+
+ align:start position:0%
+but then they're forming the following
+the chemical cues
+
+ align:start position:0%
+the chemical cues
+ 
+
+ align:start position:0%
+the chemical cues
+that determines where they branch and
+
+ align:start position:0%
+that determines where they branch and
+ 
+
+ align:start position:0%
+that determines where they branch and
+enter the nucleus
+
+ align:start position:0%
+enter the nucleus
+ 
+
+ align:start position:0%
+enter the nucleus
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+which you see here
+
+ align:start position:0%
+which you see here
+ 
+
+ align:start position:0%
+which you see here
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+here I've added the topography soap
+
+ align:start position:0%
+here I've added the topography soap
+ 
+
+ align:start position:0%
+here I've added the topography soap
+and notice here that
+
+ align:start position:0%
+and notice here that
+ 
+
+ align:start position:0%
+and notice here that
+in the geniculate bodies and the protect
+
+ align:start position:0%
+in the geniculate bodies and the protect
+ 
+
+ align:start position:0%
+in the geniculate bodies and the protect
+them you get the same kind topography
+
+ align:start position:0%
+them you get the same kind topography
+ 
+
+ align:start position:0%
+them you get the same kind topography
+nasal first then temporal retina
+
+ align:start position:0%
+nasal first then temporal retina
+ 
+
+ align:start position:0%
+nasal first then temporal retina
+and then it switches there's hole again
+
+ align:start position:0%
+and then it switches there's hole again
+ 
+
+ align:start position:0%
+and then it switches there's hole again
+Temple
+
+ align:start position:0%
+Temple
+ 
+
+ align:start position:0%
+Temple
+pre-tectin doesn't have very precise
+
+ align:start position:0%
+pre-tectin doesn't have very precise
+ 
+
+ align:start position:0%
+pre-tectin doesn't have very precise
+topography but there still is a clear
+
+ align:start position:0%
+topography but there still is a clear
+ 
+
+ align:start position:0%
+topography but there still is a clear
+tendency for the nasal retina to
+
+ align:start position:0%
+tendency for the nasal retina to
+ 
+
+ align:start position:0%
+tendency for the nasal retina to
+terminate first here and then the
+
+ align:start position:0%
+terminate first here and then the
+ 
+
+ align:start position:0%
+terminate first here and then the
+temporal retinal then in the tectum it
+
+ align:start position:0%
+temporal retinal then in the tectum it
+ 
+
+ align:start position:0%
+temporal retinal then in the tectum it
+switches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these
+
+ align:start position:0%
+so these
+ 
+
+ align:start position:0%
+so these
+terminal areas are strung out along the
+
+ align:start position:0%
+terminal areas are strung out along the
+ 
+
+ align:start position:0%
+terminal areas are strung out along the
+optic track that's a string of beads
+
+ align:start position:0%
+optic track that's a string of beads
+ 
+
+ align:start position:0%
+optic track that's a string of beads
+very orderly arrangement of axons and
+
+ align:start position:0%
+very orderly arrangement of axons and
+ 
+
+ align:start position:0%
+very orderly arrangement of axons and
+orderly terminations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the dorsal geniculate as you would
+
+ align:start position:0%
+so in the dorsal geniculate as you would
+ 
+
+ align:start position:0%
+so in the dorsal geniculate as you would
+expect here in the temporal part
+
+ align:start position:0%
+expect here in the temporal part
+ 
+
+ align:start position:0%
+expect here in the temporal part
+temporal retina or representing the
+
+ align:start position:0%
+temporal retina or representing the
+ 
+
+ align:start position:0%
+temporal retina or representing the
+field right in front of the the nasal
+
+ align:start position:0%
+field right in front of the the nasal
+ 
+
+ align:start position:0%
+field right in front of the the nasal
+field that's where you get the bilateral
+
+ align:start position:0%
+field that's where you get the bilateral
+ 
+
+ align:start position:0%
+field that's where you get the bilateral
+projections
+
+ align:start position:0%
+projections
+ 
+
+ align:start position:0%
+projections
+with projections from
+
+ align:start position:0%
+with projections from
+ 
+
+ align:start position:0%
+with projections from
+the two eyes in separate layers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this the beginning here today this today
+
+ align:start position:0%
+this the beginning here today this today
+ 
+
+ align:start position:0%
+this the beginning here today this today
+I really want to talk mainly about the
+
+ align:start position:0%
+I really want to talk mainly about the
+ 
+
+ align:start position:0%
+I really want to talk mainly about the
+multiple roots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+major transcortical fibers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make sure you can relate these kinds of
+
+ align:start position:0%
+make sure you can relate these kinds of
+ 
+
+ align:start position:0%
+make sure you can relate these kinds of
+pictures so you're looking at a real
+
+ align:start position:0%
+pictures so you're looking at a real
+ 
+
+ align:start position:0%
+pictures so you're looking at a real
+brain from the side
+
+ align:start position:0%
+brain from the side
+ 
+
+ align:start position:0%
+brain from the side
+looking at the stretched out View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all let's see what the
+
+ align:start position:0%
+first of all let's see what the
+ 
+
+ align:start position:0%
+first of all let's see what the
+accessory optic tract is
+
+ align:start position:0%
+accessory optic tract is
+ 
+
+ align:start position:0%
+accessory optic tract is
+in this kind of picture it's these
+
+ align:start position:0%
+in this kind of picture it's these
+ 
+
+ align:start position:0%
+in this kind of picture it's these
+accents that leave the main track
+
+ align:start position:0%
+accents that leave the main track
+ 
+
+ align:start position:0%
+accents that leave the main track
+and in many small animals they leave in
+
+ align:start position:0%
+and in many small animals they leave in
+ 
+
+ align:start position:0%
+and in many small animals they leave in
+three different places
+
+ align:start position:0%
+three different places
+ 
+
+ align:start position:0%
+three different places
+and if you look at a reconstruction
+
+ align:start position:0%
+and if you look at a reconstruction
+ 
+
+ align:start position:0%
+and if you look at a reconstruction
+they're leaving up here they're leaving
+
+ align:start position:0%
+they're leaving up here they're leaving
+ 
+
+ align:start position:0%
+they're leaving up here they're leaving
+here and they're leaving here so I can
+
+ align:start position:0%
+here and they're leaving here so I can
+ 
+
+ align:start position:0%
+here and they're leaving here so I can
+show you where they're terminating the
+
+ align:start position:0%
+show you where they're terminating the
+ 
+
+ align:start position:0%
+show you where they're terminating the
+accessory optic tract nuclei there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here this nucleus is mostly behind
+
+ align:start position:0%
+and here this nucleus is mostly behind
+ 
+
+ align:start position:0%
+and here this nucleus is mostly behind
+the peduncle and the Nigro okay
+
+ align:start position:0%
+the peduncle and the Nigro okay
+ 
+
+ align:start position:0%
+the peduncle and the Nigro okay
+but I'm drawing this as if the brain
+
+ align:start position:0%
+but I'm drawing this as if the brain
+ 
+
+ align:start position:0%
+but I'm drawing this as if the brain
+were transparent
+
+ align:start position:0%
+were transparent
+ 
+
+ align:start position:0%
+were transparent
+so this is the medial thermonucleus the
+
+ align:start position:0%
+so this is the medial thermonucleus the
+ 
+
+ align:start position:0%
+so this is the medial thermonucleus the
+lateral term nucleus and the dorsal
+
+ align:start position:0%
+lateral term nucleus and the dorsal
+ 
+
+ align:start position:0%
+lateral term nucleus and the dorsal
+terminal piece and the axons that get to
+
+ align:start position:0%
+terminal piece and the axons that get to
+ 
+
+ align:start position:0%
+terminal piece and the axons that get to
+the lateral are going like that and like
+
+ align:start position:0%
+the lateral are going like that and like
+ 
+
+ align:start position:0%
+the lateral are going like that and like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+here we have this in what we call the
+
+ align:start position:0%
+here we have this in what we call the
+ 
+
+ align:start position:0%
+here we have this in what we call the
+inferior fasciculus which is traveling
+
+ align:start position:0%
+inferior fasciculus which is traveling
+ 
+
+ align:start position:0%
+inferior fasciculus which is traveling
+along the lateral edge of the
+
+ align:start position:0%
+along the lateral edge of the
+ 
+
+ align:start position:0%
+along the lateral edge of the
+hypothalamus
+
+ align:start position:0%
+hypothalamus
+ 
+
+ align:start position:0%
+hypothalamus
+and then here
+
+ align:start position:0%
+and then here
+ 
+
+ align:start position:0%
+and then here
+you have axons going in both directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two-terminal nuclei
+
+ align:start position:0%
+two-terminal nuclei
+ 
+
+ align:start position:0%
+two-terminal nuclei
+the dorsal one is really
+
+ align:start position:0%
+the dorsal one is really
+ 
+
+ align:start position:0%
+the dorsal one is really
+it's just like a little addition to the
+
+ align:start position:0%
+it's just like a little addition to the
+ 
+
+ align:start position:0%
+it's just like a little addition to the
+nucleus the optic tract which is
+
+ align:start position:0%
+nucleus the optic tract which is
+ 
+
+ align:start position:0%
+nucleus the optic tract which is
+could be considered part of the
+
+ align:start position:0%
+could be considered part of the
+ 
+
+ align:start position:0%
+could be considered part of the
+the accessory optic system and the way
+
+ align:start position:0%
+the accessory optic system and the way
+ 
+
+ align:start position:0%
+the accessory optic system and the way
+it cells respond
+
+ align:start position:0%
+it cells respond
+ 
+
+ align:start position:0%
+it cells respond
+so what is the function do you remember
+
+ align:start position:0%
+so what is the function do you remember
+ 
+
+ align:start position:0%
+so what is the function do you remember
+I've mentioned it a few times
+
+ align:start position:0%
+I've mentioned it a few times
+ 
+
+ align:start position:0%
+I've mentioned it a few times
+discovered by one of my former students
+
+ align:start position:0%
+discovered by one of my former students
+ 
+
+ align:start position:0%
+discovered by one of my former students
+who heard me talk about it decided he
+
+ align:start position:0%
+who heard me talk about it decided he
+ 
+
+ align:start position:0%
+who heard me talk about it decided he
+was going to solve the problem his name
+
+ align:start position:0%
+was going to solve the problem his name
+ 
+
+ align:start position:0%
+was going to solve the problem his name
+was Simpson he thought recorded from
+
+ align:start position:0%
+was Simpson he thought recorded from
+ 
+
+ align:start position:0%
+was Simpson he thought recorded from
+these groups
+
+ align:start position:0%
+these groups
+ 
+
+ align:start position:0%
+these groups
+of neurons and found that they always
+
+ align:start position:0%
+of neurons and found that they always
+ 
+
+ align:start position:0%
+of neurons and found that they always
+responded
+
+ align:start position:0%
+responded
+ 
+
+ align:start position:0%
+responded
+to movement of the whole visual field
+
+ align:start position:0%
+to movement of the whole visual field
+ 
+
+ align:start position:0%
+to movement of the whole visual field
+across the retina
+
+ align:start position:0%
+across the retina
+ 
+
+ align:start position:0%
+across the retina
+so not small objects when everything
+
+ align:start position:0%
+so not small objects when everything
+ 
+
+ align:start position:0%
+so not small objects when everything
+moved on the retina the kind of thing
+
+ align:start position:0%
+moved on the retina the kind of thing
+ 
+
+ align:start position:0%
+moved on the retina the kind of thing
+that happens when
+
+ align:start position:0%
+that happens when
+ 
+
+ align:start position:0%
+that happens when
+you turn your head and your locomotive
+
+ align:start position:0%
+you turn your head and your locomotive
+ 
+
+ align:start position:0%
+you turn your head and your locomotive
+or when you're tipping over
+
+ align:start position:0%
+or when you're tipping over
+ 
+
+ align:start position:0%
+or when you're tipping over
+so it's a vestibular like function that
+
+ align:start position:0%
+so it's a vestibular like function that
+ 
+
+ align:start position:0%
+so it's a vestibular like function that
+they're serving signaling head movement
+
+ align:start position:0%
+they're serving signaling head movement
+ 
+
+ align:start position:0%
+they're serving signaling head movement
+and head position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now the multiple roots from the
+
+ align:start position:0%
+okay now the multiple roots from the
+ 
+
+ align:start position:0%
+okay now the multiple roots from the
+retina to the in brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll discuss the optic radiations
+
+ align:start position:0%
+and we'll discuss the optic radiations
+ 
+
+ align:start position:0%
+and we'll discuss the optic radiations
+which refers
+
+ align:start position:0%
+which refers
+ 
+
+ align:start position:0%
+which refers
+to the root from the bowel and the major
+
+ align:start position:0%
+to the root from the bowel and the major
+ 
+
+ align:start position:0%
+to the root from the bowel and the major
+roots from the thalamus to the visual
+
+ align:start position:0%
+roots from the thalamus to the visual
+ 
+
+ align:start position:0%
+roots from the thalamus to the visual
+areas of the cortex
+
+ align:start position:0%
+areas of the cortex
+ 
+
+ align:start position:0%
+areas of the cortex
+usually textbooks
+
+ align:start position:0%
+usually textbooks
+ 
+
+ align:start position:0%
+usually textbooks
+only mentioned two of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+I had to mention more for one thing I'm
+
+ align:start position:0%
+I had to mention more for one thing I'm
+ 
+
+ align:start position:0%
+I had to mention more for one thing I'm
+dealing with Evolution and I want you to
+
+ align:start position:0%
+dealing with Evolution and I want you to
+ 
+
+ align:start position:0%
+dealing with Evolution and I want you to
+understand it didn't
+
+ align:start position:0%
+understand it didn't
+ 
+
+ align:start position:0%
+understand it didn't
+there's a lot more to Evolution the
+
+ align:start position:0%
+there's a lot more to Evolution the
+ 
+
+ align:start position:0%
+there's a lot more to Evolution the
+visual system than just those two
+
+ align:start position:0%
+visual system than just those two
+ 
+
+ align:start position:0%
+visual system than just those two
+pathways
+
+ align:start position:0%
+pathways
+ 
+
+ align:start position:0%
+pathways
+and secondly because at least one more
+
+ align:start position:0%
+and secondly because at least one more
+ 
+
+ align:start position:0%
+and secondly because at least one more
+of those and maybe more than one are
+
+ align:start position:0%
+of those and maybe more than one are
+ 
+
+ align:start position:0%
+of those and maybe more than one are
+still very important
+
+ align:start position:0%
+still very important
+ 
+
+ align:start position:0%
+still very important
+just because it's neglected by
+
+ align:start position:0%
+just because it's neglected by
+ 
+
+ align:start position:0%
+just because it's neglected by
+neuroscientists doesn't mean it's not
+
+ align:start position:0%
+neuroscientists doesn't mean it's not
+ 
+
+ align:start position:0%
+neuroscientists doesn't mean it's not
+important it just means they don't study
+
+ align:start position:0%
+important it just means they don't study
+ 
+
+ align:start position:0%
+important it just means they don't study
+it so much
+
+ align:start position:0%
+it so much
+ 
+
+ align:start position:0%
+it so much
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+first of all let's bring up this rule
+
+ align:start position:0%
+first of all let's bring up this rule
+ 
+
+ align:start position:0%
+first of all let's bring up this rule
+about Evolution what is Deacon's rule we
+
+ align:start position:0%
+about Evolution what is Deacon's rule we
+ 
+
+ align:start position:0%
+about Evolution what is Deacon's rule we
+summarize it by saying it means large
+
+ align:start position:0%
+summarize it by saying it means large
+ 
+
+ align:start position:0%
+summarize it by saying it means large
+equals well connected
+
+ align:start position:0%
+equals well connected
+ 
+
+ align:start position:0%
+equals well connected
+it's an important rule of common brand
+
+ align:start position:0%
+it's an important rule of common brand
+ 
+
+ align:start position:0%
+it's an important rule of common brand
+so what does it suggest about the
+
+ align:start position:0%
+so what does it suggest about the
+ 
+
+ align:start position:0%
+so what does it suggest about the
+multiple roots to the forebrain for
+
+ align:start position:0%
+multiple roots to the forebrain for
+ 
+
+ align:start position:0%
+multiple roots to the forebrain for
+visual information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the large structure that gets
+
+ align:start position:0%
+what is the large structure that gets
+ 
+
+ align:start position:0%
+what is the large structure that gets
+retinal input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of all those structures are only off the
+
+ align:start position:0%
+of all those structures are only off the
+ 
+
+ align:start position:0%
+of all those structures are only off the
+track what's the biggest one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably Superior colliculous in most
+
+ align:start position:0%
+probably Superior colliculous in most
+ 
+
+ align:start position:0%
+probably Superior colliculous in most
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+remember we started with a fish and saw
+
+ align:start position:0%
+remember we started with a fish and saw
+ 
+
+ align:start position:0%
+remember we started with a fish and saw
+the top detectives bigger than the whole
+
+ align:start position:0%
+the top detectives bigger than the whole
+ 
+
+ align:start position:0%
+the top detectives bigger than the whole
+in brain
+
+ align:start position:0%
+in brain
+ 
+
+ align:start position:0%
+in brain
+I showed you a photograph talking about
+
+ align:start position:0%
+I showed you a photograph talking about
+ 
+
+ align:start position:0%
+I showed you a photograph talking about
+midbrain of a barracuda a predator fish
+
+ align:start position:0%
+midbrain of a barracuda a predator fish
+ 
+
+ align:start position:0%
+midbrain of a barracuda a predator fish
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+chicken was so huge it dwarfs the rest
+
+ align:start position:0%
+chicken was so huge it dwarfs the rest
+ 
+
+ align:start position:0%
+chicken was so huge it dwarfs the rest
+of the brain
+
+ align:start position:0%
+of the brain
+ 
+
+ align:start position:0%
+of the brain
+and all the predatory fish that are very
+
+ align:start position:0%
+and all the predatory fish that are very
+ 
+
+ align:start position:0%
+and all the predatory fish that are very
+visual predatory fish are like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehow some of them like sharks use
+
+ align:start position:0%
+somehow some of them like sharks use
+ 
+
+ align:start position:0%
+somehow some of them like sharks use
+olfaction quite a bit as well
+
+ align:start position:0%
+olfaction quite a bit as well
+ 
+
+ align:start position:0%
+olfaction quite a bit as well
+and they also use the other sentences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but many predatory fish depend mainly on
+
+ align:start position:0%
+but many predatory fish depend mainly on
+ 
+
+ align:start position:0%
+but many predatory fish depend mainly on
+vision
+
+ align:start position:0%
+vision
+ 
+
+ align:start position:0%
+vision
+okay so it's a guess if it's better
+
+ align:start position:0%
+okay so it's a guess if it's better
+ 
+
+ align:start position:0%
+okay so it's a guess if it's better
+connected than the others it suggests
+
+ align:start position:0%
+connected than the others it suggests
+ 
+
+ align:start position:0%
+connected than the others it suggests
+that you should look at tectum for the
+
+ align:start position:0%
+that you should look at tectum for the
+ 
+
+ align:start position:0%
+that you should look at tectum for the
+source of accents that reach the injury
+
+ align:start position:0%
+source of accents that reach the injury
+ 
+
+ align:start position:0%
+source of accents that reach the injury
+well it turns out the midbrain didn't
+
+ align:start position:0%
+well it turns out the midbrain didn't
+ 
+
+ align:start position:0%
+well it turns out the midbrain didn't
+connect directly
+
+ align:start position:0%
+connect directly
+ 
+
+ align:start position:0%
+connect directly
+to the end brain
+
+ align:start position:0%
+to the end brain
+ 
+
+ align:start position:0%
+to the end brain
+okay there might be a few exceptions but
+
+ align:start position:0%
+okay there might be a few exceptions but
+ 
+
+ align:start position:0%
+okay there might be a few exceptions but
+not many we know that those axons that
+
+ align:start position:0%
+not many we know that those axons that
+ 
+
+ align:start position:0%
+not many we know that those axons that
+determine brain State like the
+
+ align:start position:0%
+determine brain State like the
+ 
+
+ align:start position:0%
+determine brain State like the
+narpinephrine axons and the serotonin
+
+ align:start position:0%
+narpinephrine axons and the serotonin
+ 
+
+ align:start position:0%
+narpinephrine axons and the serotonin
+accents they they come from midbrain and
+
+ align:start position:0%
+accents they they come from midbrain and
+ 
+
+ align:start position:0%
+accents they they come from midbrain and
+hindbrain
+
+ align:start position:0%
+hindbrain
+ 
+
+ align:start position:0%
+hindbrain
+and they certainly project into the end
+
+ align:start position:0%
+and they certainly project into the end
+ 
+
+ align:start position:0%
+and they certainly project into the end
+brain but they're not the ones carrying
+
+ align:start position:0%
+brain but they're not the ones carrying
+ 
+
+ align:start position:0%
+brain but they're not the ones carrying
+specific information
+
+ align:start position:0%
+specific information
+ 
+
+ align:start position:0%
+specific information
+they determine the state of the whole
+
+ align:start position:0%
+they determine the state of the whole
+ 
+
+ align:start position:0%
+they determine the state of the whole
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the two roots to the end brain
+
+ align:start position:0%
+what are the two roots to the end brain
+ 
+
+ align:start position:0%
+what are the two roots to the end brain
+taken by visual information that are
+
+ align:start position:0%
+taken by visual information that are
+ 
+
+ align:start position:0%
+taken by visual information that are
+usually considered the major ones
+
+ align:start position:0%
+usually considered the major ones
+ 
+
+ align:start position:0%
+usually considered the major ones
+by now you should be getting getting
+
+ align:start position:0%
+by now you should be getting getting
+ 
+
+ align:start position:0%
+by now you should be getting getting
+that figured out
+
+ align:start position:0%
+that figured out
+ 
+
+ align:start position:0%
+that figured out
+what do we talk about all the time
+
+ align:start position:0%
+what do we talk about all the time
+ 
+
+ align:start position:0%
+what do we talk about all the time
+if someone just talks about
+
+ align:start position:0%
+if someone just talks about
+ 
+
+ align:start position:0%
+if someone just talks about
+he's giving a talk in our department and
+
+ align:start position:0%
+he's giving a talk in our department and
+ 
+
+ align:start position:0%
+he's giving a talk in our department and
+you say giving a talk about the visual
+
+ align:start position:0%
+you say giving a talk about the visual
+ 
+
+ align:start position:0%
+you say giving a talk about the visual
+system what does it usually mean
+
+ align:start position:0%
+system what does it usually mean
+ 
+
+ align:start position:0%
+system what does it usually mean
+shouldn't they close the right system
+
+ align:start position:0%
+shouldn't they close the right system
+ 
+
+ align:start position:0%
+shouldn't they close the right system
+because it's become so dominant in the
+
+ align:start position:0%
+because it's become so dominant in the
+ 
+
+ align:start position:0%
+because it's become so dominant in the
+primates
+
+ align:start position:0%
+primates
+ 
+
+ align:start position:0%
+primates
+okay but what's the other big one
+
+ align:start position:0%
+okay but what's the other big one
+ 
+
+ align:start position:0%
+okay but what's the other big one
+it became very clear from the studies of
+
+ align:start position:0%
+it became very clear from the studies of
+ 
+
+ align:start position:0%
+it became very clear from the studies of
+birds
+
+ align:start position:0%
+birds
+ 
+
+ align:start position:0%
+birds
+that birds have something like a genital
+
+ align:start position:0%
+that birds have something like a genital
+ 
+
+ align:start position:0%
+that birds have something like a genital
+straight system
+
+ align:start position:0%
+straight system
+ 
+
+ align:start position:0%
+straight system
+but in fact they have a bigger pathway
+
+ align:start position:0%
+but in fact they have a bigger pathway
+ 
+
+ align:start position:0%
+but in fact they have a bigger pathway
+coming from remember the control comes
+
+ align:start position:0%
+coming from remember the control comes
+ 
+
+ align:start position:0%
+coming from remember the control comes
+from the tecton protect him to Thalamus
+
+ align:start position:0%
+from the tecton protect him to Thalamus
+ 
+
+ align:start position:0%
+from the tecton protect him to Thalamus
+to a nucleus and the bird is called
+
+ align:start position:0%
+to a nucleus and the bird is called
+ 
+
+ align:start position:0%
+to a nucleus and the bird is called
+nucleus redundus and that projects
+
+ align:start position:0%
+nucleus redundus and that projects
+ 
+
+ align:start position:0%
+nucleus redundus and that projects
+to the end break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to part of the so-called Knight of paleo
+
+ align:start position:0%
+to part of the so-called Knight of paleo
+ 
+
+ align:start position:0%
+to part of the so-called Knight of paleo
+show you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in mammals
+
+ align:start position:0%
+in mammals
+ 
+
+ align:start position:0%
+in mammals
+in the book I list six Roots here at
+
+ align:start position:0%
+in the book I list six Roots here at
+ 
+
+ align:start position:0%
+in the book I list six Roots here at
+seven they're actually all in the
+
+ align:start position:0%
+seven they're actually all in the
+ 
+
+ align:start position:0%
+seven they're actually all in the
+booktube but
+
+ align:start position:0%
+booktube but
+ 
+
+ align:start position:0%
+booktube but
+I had discussed number six here the one
+
+ align:start position:0%
+I had discussed number six here the one
+ 
+
+ align:start position:0%
+I had discussed number six here the one
+going to the amygdala which isn't as
+
+ align:start position:0%
+going to the amygdala which isn't as
+ 
+
+ align:start position:0%
+going to the amygdala which isn't as
+well known as the auditory Pathway to
+
+ align:start position:0%
+well known as the auditory Pathway to
+ 
+
+ align:start position:0%
+well known as the auditory Pathway to
+the amygdala and I mentioned it in
+
+ align:start position:0%
+the amygdala and I mentioned it in
+ 
+
+ align:start position:0%
+the amygdala and I mentioned it in
+the first official chapter chapter 20.
+
+ align:start position:0%
+the first official chapter chapter 20.
+ 
+
+ align:start position:0%
+the first official chapter chapter 20.
+and I don't know why I didn't get it
+
+ align:start position:0%
+and I don't know why I didn't get it
+ 
+
+ align:start position:0%
+and I don't know why I didn't get it
+back into this list probably because I
+
+ align:start position:0%
+back into this list probably because I
+ 
+
+ align:start position:0%
+back into this list probably because I
+had written this chapter already when I
+
+ align:start position:0%
+had written this chapter already when I
+ 
+
+ align:start position:0%
+had written this chapter already when I
+I didn't always write these in order so
+
+ align:start position:0%
+I didn't always write these in order so
+ 
+
+ align:start position:0%
+I didn't always write these in order so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but this is the way it probably should
+
+ align:start position:0%
+but this is the way it probably should
+ 
+
+ align:start position:0%
+but this is the way it probably should
+be it was seven major Pathways the
+
+ align:start position:0%
+be it was seven major Pathways the
+ 
+
+ align:start position:0%
+be it was seven major Pathways the
+visual information to take to the end
+
+ align:start position:0%
+visual information to take to the end
+ 
+
+ align:start position:0%
+visual information to take to the end
+brain these are the two biggest and most
+
+ align:start position:0%
+brain these are the two biggest and most
+ 
+
+ align:start position:0%
+brain these are the two biggest and most
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but there's a route from the sub balance
+
+ align:start position:0%
+but there's a route from the sub balance
+ 
+
+ align:start position:0%
+but there's a route from the sub balance
+recently they've even found roots from
+
+ align:start position:0%
+recently they've even found roots from
+ 
+
+ align:start position:0%
+recently they've even found roots from
+the sub parliaments directly to Cortex
+
+ align:start position:0%
+the sub parliaments directly to Cortex
+ 
+
+ align:start position:0%
+the sub parliaments directly to Cortex
+but we don't think it's we don't know
+
+ align:start position:0%
+but we don't think it's we don't know
+ 
+
+ align:start position:0%
+but we don't think it's we don't know
+how many species it occurs in it goes to
+
+ align:start position:0%
+how many species it occurs in it goes to
+ 
+
+ align:start position:0%
+how many species it occurs in it goes to
+the Barrel Fields
+
+ align:start position:0%
+the Barrel Fields
+ 
+
+ align:start position:0%
+the Barrel Fields
+okay but the more I think more important
+
+ align:start position:0%
+okay but the more I think more important
+ 
+
+ align:start position:0%
+okay but the more I think more important
+for most animals is that that area in
+
+ align:start position:0%
+for most animals is that that area in
+ 
+
+ align:start position:0%
+for most animals is that that area in
+the zone inserted here does the initial
+
+ align:start position:0%
+the zone inserted here does the initial
+ 
+
+ align:start position:0%
+the zone inserted here does the initial
+input from an eventual adults nuclear
+
+ align:start position:0%
+input from an eventual adults nuclear
+ 
+
+ align:start position:0%
+input from an eventual adults nuclear
+body and it doesn't just project to the
+
+ align:start position:0%
+body and it doesn't just project to the
+ 
+
+ align:start position:0%
+body and it doesn't just project to the
+locomotor area of the midbrain
+
+ align:start position:0%
+locomotor area of the midbrain
+ 
+
+ align:start position:0%
+locomotor area of the midbrain
+control Escape behavior that way it also
+
+ align:start position:0%
+control Escape behavior that way it also
+ 
+
+ align:start position:0%
+control Escape behavior that way it also
+projects to the dorsal balance the
+
+ align:start position:0%
+projects to the dorsal balance the
+ 
+
+ align:start position:0%
+projects to the dorsal balance the
+midline and interlamina nuclei which
+
+ align:start position:0%
+midline and interlamina nuclei which
+ 
+
+ align:start position:0%
+midline and interlamina nuclei which
+affect the whole balance certainly
+
+ align:start position:0%
+affect the whole balance certainly
+ 
+
+ align:start position:0%
+affect the whole balance certainly
+sending visual information to the end
+
+ align:start position:0%
+sending visual information to the end
+ 
+
+ align:start position:0%
+sending visual information to the end
+brain to the cortex and the striatum
+
+ align:start position:0%
+brain to the cortex and the striatum
+ 
+
+ align:start position:0%
+brain to the cortex and the striatum
+those structures project the both
+
+ align:start position:0%
+those structures project the both
+ 
+
+ align:start position:0%
+those structures project the both
+striatomic cortex and then I'll detect
+
+ align:start position:0%
+striatomic cortex and then I'll detect
+ 
+
+ align:start position:0%
+striatomic cortex and then I'll detect
+them and protect them have deeper layers
+
+ align:start position:0%
+them and protect them have deeper layers
+ 
+
+ align:start position:0%
+them and protect them have deeper layers
+that are multimodal But it includes
+
+ align:start position:0%
+that are multimodal But it includes
+ 
+
+ align:start position:0%
+that are multimodal But it includes
+visual information they project into the
+
+ align:start position:0%
+visual information they project into the
+ 
+
+ align:start position:0%
+visual information they project into the
+lateral films and then The Superficial
+
+ align:start position:0%
+lateral films and then The Superficial
+ 
+
+ align:start position:0%
+lateral films and then The Superficial
+visual layers
+
+ align:start position:0%
+visual layers
+ 
+
+ align:start position:0%
+visual layers
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+including Arctic tectum and pretense
+
+ align:start position:0%
+including Arctic tectum and pretense
+ 
+
+ align:start position:0%
+including Arctic tectum and pretense
+they both have Pathways care in specific
+
+ align:start position:0%
+they both have Pathways care in specific
+ 
+
+ align:start position:0%
+they both have Pathways care in specific
+visual information into the thalamus
+
+ align:start position:0%
+visual information into the thalamus
+ 
+
+ align:start position:0%
+visual information into the thalamus
+some of it does go to the genital
+
+ align:start position:0%
+some of it does go to the genital
+ 
+
+ align:start position:0%
+some of it does go to the genital
+genicular part in fact most of it goes
+
+ align:start position:0%
+genicular part in fact most of it goes
+ 
+
+ align:start position:0%
+genicular part in fact most of it goes
+into the lateral Thalamus near the jeep
+
+ align:start position:0%
+into the lateral Thalamus near the jeep
+ 
+
+ align:start position:0%
+into the lateral Thalamus near the jeep
+that goes to LP
+
+ align:start position:0%
+that goes to LP
+ 
+
+ align:start position:0%
+that goes to LP
+or primates usually called pulvenar
+
+ align:start position:0%
+or primates usually called pulvenar
+ 
+
+ align:start position:0%
+or primates usually called pulvenar
+and that goes to posture in your cortex
+
+ align:start position:0%
+and that goes to posture in your cortex
+ 
+
+ align:start position:0%
+and that goes to posture in your cortex
+not primarily strike
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to encounter this one
+
+ align:start position:0%
+and we're going to encounter this one
+ 
+
+ align:start position:0%
+and we're going to encounter this one
+from protectors yeah
+
+ align:start position:0%
+from protectors yeah
+ 
+
+ align:start position:0%
+from protectors yeah
+is it signaling changes in head
+
+ align:start position:0%
+is it signaling changes in head
+ 
+
+ align:start position:0%
+is it signaling changes in head
+Direction which turn out to be really
+
+ align:start position:0%
+Direction which turn out to be really
+ 
+
+ align:start position:0%
+Direction which turn out to be really
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+where we are and where we're going
+
+ align:start position:0%
+where we are and where we're going
+ 
+
+ align:start position:0%
+where we are and where we're going
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I pointed out here that that first
+
+ align:start position:0%
+so I pointed out here that that first
+ 
+
+ align:start position:0%
+so I pointed out here that that first
+Pathways almost always usually ignored
+
+ align:start position:0%
+Pathways almost always usually ignored
+ 
+
+ align:start position:0%
+Pathways almost always usually ignored
+despite of its possible importance and
+
+ align:start position:0%
+despite of its possible importance and
+ 
+
+ align:start position:0%
+despite of its possible importance and
+evolution especially
+
+ align:start position:0%
+evolution especially
+ 
+
+ align:start position:0%
+evolution especially
+the second third and fourth have
+
+ align:start position:0%
+the second third and fourth have
+ 
+
+ align:start position:0%
+the second third and fourth have
+attracted a few researchers but they're
+
+ align:start position:0%
+attracted a few researchers but they're
+ 
+
+ align:start position:0%
+attracted a few researchers but they're
+usually not mentioned two and three and
+
+ align:start position:0%
+usually not mentioned two and three and
+ 
+
+ align:start position:0%
+usually not mentioned two and three and
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+it's this one that I think
+
+ align:start position:0%
+it's this one that I think
+ 
+
+ align:start position:0%
+it's this one that I think
+is going to attract a lot more attention
+
+ align:start position:0%
+is going to attract a lot more attention
+ 
+
+ align:start position:0%
+is going to attract a lot more attention
+in the future
+
+ align:start position:0%
+in the future
+ 
+
+ align:start position:0%
+in the future
+major
+
+ align:start position:0%
+major
+ 
+
+ align:start position:0%
+major
+Topic in the book on in the in the book
+
+ align:start position:0%
+Topic in the book on in the in the book
+ 
+
+ align:start position:0%
+Topic in the book on in the in the book
+and when we talk about hippocampus
+
+ align:start position:0%
+and when we talk about hippocampus
+ 
+
+ align:start position:0%
+and when we talk about hippocampus
+but it's and the one to the amygdala
+
+ align:start position:0%
+but it's and the one to the amygdala
+ 
+
+ align:start position:0%
+but it's and the one to the amygdala
+it's the auditory system that's
+
+ align:start position:0%
+it's the auditory system that's
+ 
+
+ align:start position:0%
+it's the auditory system that's
+dominated that study but it turns out
+
+ align:start position:0%
+dominated that study but it turns out
+ 
+
+ align:start position:0%
+dominated that study but it turns out
+it's a visual pathway going there too it
+
+ align:start position:0%
+it's a visual pathway going there too it
+ 
+
+ align:start position:0%
+it's a visual pathway going there too it
+might be very important and affecting
+
+ align:start position:0%
+might be very important and affecting
+ 
+
+ align:start position:0%
+might be very important and affecting
+emotions yeah
+
+ align:start position:0%
+emotions yeah
+ 
+
+ align:start position:0%
+emotions yeah
+but the architectum and the LGB
+
+ align:start position:0%
+but the architectum and the LGB
+ 
+
+ align:start position:0%
+but the architectum and the LGB
+are the main ones uh I just talked a
+
+ align:start position:0%
+are the main ones uh I just talked a
+ 
+
+ align:start position:0%
+are the main ones uh I just talked a
+little bit here this is some speculative
+
+ align:start position:0%
+little bit here this is some speculative
+ 
+
+ align:start position:0%
+little bit here this is some speculative
+it's about how these this organization
+
+ align:start position:0%
+it's about how these this organization
+ 
+
+ align:start position:0%
+it's about how these this organization
+between Pathways from midbrain and to
+
+ align:start position:0%
+between Pathways from midbrain and to
+ 
+
+ align:start position:0%
+between Pathways from midbrain and to
+Palomas form
+
+ align:start position:0%
+Palomas form
+ 
+
+ align:start position:0%
+Palomas form
+but this is the one I want to stress
+
+ align:start position:0%
+but this is the one I want to stress
+ 
+
+ align:start position:0%
+but this is the one I want to stress
+here in the class that shows those two
+
+ align:start position:0%
+here in the class that shows those two
+ 
+
+ align:start position:0%
+here in the class that shows those two
+major Pathways I've used the same color
+
+ align:start position:0%
+major Pathways I've used the same color
+ 
+
+ align:start position:0%
+major Pathways I've used the same color
+code for enamels reptiles and birds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it shows that the geniculate body
+
+ align:start position:0%
+and it shows that the geniculate body
+ 
+
+ align:start position:0%
+and it shows that the geniculate body
+goes to strive
+
+ align:start position:0%
+goes to strive
+ 
+
+ align:start position:0%
+goes to strive
+LP Palvin are primarily to extra strike
+
+ align:start position:0%
+LP Palvin are primarily to extra strike
+ 
+
+ align:start position:0%
+LP Palvin are primarily to extra strike
+I say primarily because it does have
+
+ align:start position:0%
+I say primarily because it does have
+ 
+
+ align:start position:0%
+I say primarily because it does have
+more widespread projections
+
+ align:start position:0%
+more widespread projections
+ 
+
+ align:start position:0%
+more widespread projections
+some of its neurons do as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in reptile they get different names
+
+ align:start position:0%
+in reptile they get different names
+ 
+
+ align:start position:0%
+in reptile they get different names
+but you still have separate projections
+
+ align:start position:0%
+but you still have separate projections
+ 
+
+ align:start position:0%
+but you still have separate projections
+in relative terms the one that gets
+
+ align:start position:0%
+in relative terms the one that gets
+ 
+
+ align:start position:0%
+in relative terms the one that gets
+direct retinal input
+
+ align:start position:0%
+direct retinal input
+ 
+
+ align:start position:0%
+direct retinal input
+threshold of optic nucleus
+
+ align:start position:0%
+threshold of optic nucleus
+ 
+
+ align:start position:0%
+threshold of optic nucleus
+and this optic nucleus in the thalamus
+
+ align:start position:0%
+and this optic nucleus in the thalamus
+ 
+
+ align:start position:0%
+and this optic nucleus in the thalamus
+the bird
+
+ align:start position:0%
+the bird
+ 
+
+ align:start position:0%
+the bird
+they project directly to
+
+ align:start position:0%
+they project directly to
+ 
+
+ align:start position:0%
+they project directly to
+wallstormatic equations
+
+ align:start position:0%
+wallstormatic equations
+ 
+
+ align:start position:0%
+wallstormatic equations
+it's part of the dorsal cortex in the
+
+ align:start position:0%
+it's part of the dorsal cortex in the
+ 
+
+ align:start position:0%
+it's part of the dorsal cortex in the
+reptile it's just given a different name
+
+ align:start position:0%
+reptile it's just given a different name
+ 
+
+ align:start position:0%
+reptile it's just given a different name
+in the bird
+
+ align:start position:0%
+in the bird
+ 
+
+ align:start position:0%
+in the bird
+wolstein's bulge and because it does in
+
+ align:start position:0%
+wolstein's bulge and because it does in
+ 
+
+ align:start position:0%
+wolstein's bulge and because it does in
+some birds where it's well developed
+
+ align:start position:0%
+some birds where it's well developed
+ 
+
+ align:start position:0%
+some birds where it's well developed
+like the owl it does form a prominent
+
+ align:start position:0%
+like the owl it does form a prominent
+ 
+
+ align:start position:0%
+like the owl it does form a prominent
+bulge in the end break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direct part of it gets directed visual
+
+ align:start position:0%
+direct part of it gets directed visual
+ 
+
+ align:start position:0%
+direct part of it gets directed visual
+input there's a some sensory wolves as
+
+ align:start position:0%
+input there's a some sensory wolves as
+ 
+
+ align:start position:0%
+input there's a some sensory wolves as
+well and a motor wolves
+
+ align:start position:0%
+well and a motor wolves
+ 
+
+ align:start position:0%
+well and a motor wolves
+and the other one
+
+ align:start position:0%
+and the other one
+ 
+
+ align:start position:0%
+and the other one
+in these reptiles and birds goes
+
+ align:start position:0%
+in these reptiles and birds goes
+ 
+
+ align:start position:0%
+in these reptiles and birds goes
+subcortically to this dorsal ventricular
+
+ align:start position:0%
+subcortically to this dorsal ventricular
+ 
+
+ align:start position:0%
+subcortically to this dorsal ventricular
+Ridge area that has been found in its
+
+ align:start position:0%
+Ridge area that has been found in its
+ 
+
+ align:start position:0%
+Ridge area that has been found in its
+connections to be like neocortex amounts
+
+ align:start position:0%
+connections to be like neocortex amounts
+ 
+
+ align:start position:0%
+connections to be like neocortex amounts
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but in terms of connections they have
+
+ align:start position:0%
+but in terms of connections they have
+ 
+
+ align:start position:0%
+but in terms of connections they have
+the same Pathways same kinds of
+
+ align:start position:0%
+the same Pathways same kinds of
+ 
+
+ align:start position:0%
+the same Pathways same kinds of
+connections
+
+ align:start position:0%
+connections
+ 
+
+ align:start position:0%
+connections
+the difference is just the arrangement
+
+ align:start position:0%
+the difference is just the arrangement
+ 
+
+ align:start position:0%
+the difference is just the arrangement
+of the cells really terminate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right uh this just is I I took a
+
+ align:start position:0%
+all right uh this just is I I took a
+ 
+
+ align:start position:0%
+all right uh this just is I I took a
+picture of a turtle where I found those
+
+ align:start position:0%
+picture of a turtle where I found those
+ 
+
+ align:start position:0%
+picture of a turtle where I found those
+nice studies of these different
+
+ align:start position:0%
+nice studies of these different
+ 
+
+ align:start position:0%
+nice studies of these different
+projections and here I've shown where
+
+ align:start position:0%
+projections and here I've shown where
+ 
+
+ align:start position:0%
+projections and here I've shown where
+the visual projections are going and
+
+ align:start position:0%
+the visual projections are going and
+ 
+
+ align:start position:0%
+the visual projections are going and
+they there's a ventricular Ridge of the
+
+ align:start position:0%
+they there's a ventricular Ridge of the
+ 
+
+ align:start position:0%
+they there's a ventricular Ridge of the
+turtle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can see the cells farming nice
+
+ align:start position:0%
+and you can see the cells farming nice
+ 
+
+ align:start position:0%
+and you can see the cells farming nice
+stint pattern there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is where the more direct projection
+
+ align:start position:0%
+this is where the more direct projection
+ 
+
+ align:start position:0%
+this is where the more direct projection
+goes and the rotundas of the turtle
+
+ align:start position:0%
+goes and the rotundas of the turtle
+ 
+
+ align:start position:0%
+goes and the rotundas of the turtle
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most of the studies are concentrated on
+
+ align:start position:0%
+most of the studies are concentrated on
+ 
+
+ align:start position:0%
+most of the studies are concentrated on
+this area but
+
+ align:start position:0%
+this area but
+ 
+
+ align:start position:0%
+this area but
+my readings are very clear that it goes
+
+ align:start position:0%
+my readings are very clear that it goes
+ 
+
+ align:start position:0%
+my readings are very clear that it goes
+also to this
+
+ align:start position:0%
+also to this
+ 
+
+ align:start position:0%
+also to this
+second area of here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so those are the two pathways
+
+ align:start position:0%
+all right so those are the two pathways
+ 
+
+ align:start position:0%
+all right so those are the two pathways
+Sean a little more detail for the turtle
+
+ align:start position:0%
+Sean a little more detail for the turtle
+ 
+
+ align:start position:0%
+Sean a little more detail for the turtle
+and here is a raccoons striae cortex I
+
+ align:start position:0%
+and here is a raccoons striae cortex I
+ 
+
+ align:start position:0%
+and here is a raccoons striae cortex I
+didn't put this one in the book I put
+
+ align:start position:0%
+didn't put this one in the book I put
+ 
+
+ align:start position:0%
+didn't put this one in the book I put
+the monkey
+
+ align:start position:0%
+the monkey
+ 
+
+ align:start position:0%
+the monkey
+but you see even in a very low power
+
+ align:start position:0%
+but you see even in a very low power
+ 
+
+ align:start position:0%
+but you see even in a very low power
+here look how the strike cortex stands
+
+ align:start position:0%
+here look how the strike cortex stands
+ 
+
+ align:start position:0%
+here look how the strike cortex stands
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+you see that very dense layer of granule
+
+ align:start position:0%
+you see that very dense layer of granule
+ 
+
+ align:start position:0%
+you see that very dense layer of granule
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next to a layer of fibers that looks
+
+ align:start position:0%
+next to a layer of fibers that looks
+ 
+
+ align:start position:0%
+next to a layer of fibers that looks
+whiter
+
+ align:start position:0%
+whiter
+ 
+
+ align:start position:0%
+whiter
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is the Caltrain Fisher in the
+
+ align:start position:0%
+this is the Caltrain Fisher in the
+ 
+
+ align:start position:0%
+this is the Caltrain Fisher in the
+in the raccoon
+
+ align:start position:0%
+in the raccoon
+ 
+
+ align:start position:0%
+in the raccoon
+but you can very clearly see the strike
+
+ align:start position:0%
+but you can very clearly see the strike
+ 
+
+ align:start position:0%
+but you can very clearly see the strike
+cortex and then you see the sudden
+
+ align:start position:0%
+cortex and then you see the sudden
+ 
+
+ align:start position:0%
+cortex and then you see the sudden
+change when you get to the border of
+
+ align:start position:0%
+change when you get to the border of
+ 
+
+ align:start position:0%
+change when you get to the border of
+strife and the extra striders
+
+ align:start position:0%
+strife and the extra striders
+ 
+
+ align:start position:0%
+strife and the extra striders
+okay this is the one I took out of the
+
+ align:start position:0%
+okay this is the one I took out of the
+ 
+
+ align:start position:0%
+okay this is the one I took out of the
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+comes from
+
+ align:start position:0%
+comes from
+ 
+
+ align:start position:0%
+comes from
+eight tables
+
+ align:start position:0%
+eight tables
+ 
+
+ align:start position:0%
+eight tables
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where again it's even clearer this
+
+ align:start position:0%
+where again it's even clearer this
+ 
+
+ align:start position:0%
+where again it's even clearer this
+magnification for the monkey you see the
+
+ align:start position:0%
+magnification for the monkey you see the
+ 
+
+ align:start position:0%
+magnification for the monkey you see the
+stride quartets
+
+ align:start position:0%
+stride quartets
+ 
+
+ align:start position:0%
+stride quartets
+very clear lamination and you see the
+
+ align:start position:0%
+very clear lamination and you see the
+ 
+
+ align:start position:0%
+very clear lamination and you see the
+sudden change he's he's labeled that
+
+ align:start position:0%
+sudden change he's he's labeled that
+ 
+
+ align:start position:0%
+sudden change he's he's labeled that
+more to D here between stride area and
+
+ align:start position:0%
+more to D here between stride area and
+ 
+
+ align:start position:0%
+more to D here between stride area and
+extra straight you see the sudden change
+
+ align:start position:0%
+extra straight you see the sudden change
+ 
+
+ align:start position:0%
+extra straight you see the sudden change
+in the cycle architecture
+
+ align:start position:0%
+in the cycle architecture
+ 
+
+ align:start position:0%
+in the cycle architecture
+very easy to pick up so if I showed you
+
+ align:start position:0%
+very easy to pick up so if I showed you
+ 
+
+ align:start position:0%
+very easy to pick up so if I showed you
+this picture and didn't label it for you
+
+ align:start position:0%
+this picture and didn't label it for you
+ 
+
+ align:start position:0%
+this picture and didn't label it for you
+you should be able to label that
+
+ align:start position:0%
+you should be able to label that
+ 
+
+ align:start position:0%
+you should be able to label that
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+at least there
+
+ align:start position:0%
+at least there
+ 
+
+ align:start position:0%
+at least there
+and here okay and here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are the visual areas of the
+
+ align:start position:0%
+so what are the visual areas of the
+ 
+
+ align:start position:0%
+so what are the visual areas of the
+neocortex that are the most primitive
+
+ align:start position:0%
+neocortex that are the most primitive
+ 
+
+ align:start position:0%
+neocortex that are the most primitive
+that we keep seeing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're talking about neocortex so we're
+
+ align:start position:0%
+we're talking about neocortex so we're
+ 
+
+ align:start position:0%
+we're talking about neocortex so we're
+only talking about mammals Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we look at all them animals that have
+
+ align:start position:0%
+if we look at all them animals that have
+ 
+
+ align:start position:0%
+if we look at all them animals that have
+been studied including some very
+
+ align:start position:0%
+been studied including some very
+ 
+
+ align:start position:0%
+been studied including some very
+primitive ones you keep seeing
+
+ align:start position:0%
+primitive ones you keep seeing
+ 
+
+ align:start position:0%
+primitive ones you keep seeing
+primary visual cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does that mean about those other
+
+ align:start position:0%
+what does that mean about those other
+ 
+
+ align:start position:0%
+what does that mean about those other
+Pathways well we see those Anonymous as
+
+ align:start position:0%
+Pathways well we see those Anonymous as
+ 
+
+ align:start position:0%
+Pathways well we see those Anonymous as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and there were no doubt there in the
+
+ align:start position:0%
+and there were no doubt there in the
+ 
+
+ align:start position:0%
+and there were no doubt there in the
+sign of Dance
+
+ align:start position:0%
+sign of Dance
+ 
+
+ align:start position:0%
+sign of Dance
+that led to mammals the evolution of
+
+ align:start position:0%
+that led to mammals the evolution of
+ 
+
+ align:start position:0%
+that led to mammals the evolution of
+mammals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for mammals we say the stride cortex
+
+ align:start position:0%
+so for mammals we say the stride cortex
+ 
+
+ align:start position:0%
+so for mammals we say the stride cortex
+and the immediately adjacent area the
+
+ align:start position:0%
+and the immediately adjacent area the
+ 
+
+ align:start position:0%
+and the immediately adjacent area the
+what we call V2 if we're physiologists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it consists actually of a number of
+
+ align:start position:0%
+it consists actually of a number of
+ 
+
+ align:start position:0%
+it consists actually of a number of
+different representations of the visual
+
+ align:start position:0%
+different representations of the visual
+ 
+
+ align:start position:0%
+different representations of the visual
+field as we will see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they've been called V2 V3 V4 and so
+
+ align:start position:0%
+they've been called V2 V3 V4 and so
+ 
+
+ align:start position:0%
+they've been called V2 V3 V4 and so
+forth by physiologists that are
+
+ align:start position:0%
+forth by physiologists that are
+ 
+
+ align:start position:0%
+forth by physiologists that are
+divided it up according to
+
+ align:start position:0%
+divided it up according to
+ 
+
+ align:start position:0%
+divided it up according to
+representations of the visual field
+
+ align:start position:0%
+representations of the visual field
+ 
+
+ align:start position:0%
+representations of the visual field
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then what do we mean by
+
+ align:start position:0%
+and then what do we mean by
+ 
+
+ align:start position:0%
+and then what do we mean by
+temporalization of the cerebral
+
+ align:start position:0%
+temporalization of the cerebral
+ 
+
+ align:start position:0%
+temporalization of the cerebral
+hemispheres
+
+ align:start position:0%
+hemispheres
+ 
+
+ align:start position:0%
+hemispheres
+in development and evolution it's
+
+ align:start position:0%
+in development and evolution it's
+ 
+
+ align:start position:0%
+in development and evolution it's
+correlated with the expansion of one
+
+ align:start position:0%
+correlated with the expansion of one
+ 
+
+ align:start position:0%
+correlated with the expansion of one
+group of Thalamus which ones am I
+
+ align:start position:0%
+group of Thalamus which ones am I
+ 
+
+ align:start position:0%
+group of Thalamus which ones am I
+talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temporalization formation
+
+ align:start position:0%
+temporalization formation
+ 
+
+ align:start position:0%
+temporalization formation
+of a prominent temporal lobe that's what
+
+ align:start position:0%
+of a prominent temporal lobe that's what
+ 
+
+ align:start position:0%
+of a prominent temporal lobe that's what
+temporalization is what's happening that
+
+ align:start position:0%
+temporalization is what's happening that
+ 
+
+ align:start position:0%
+temporalization is what's happening that
+caused that
+
+ align:start position:0%
+caused that
+ 
+
+ align:start position:0%
+caused that
+it's an expansion
+
+ align:start position:0%
+it's an expansion
+ 
+
+ align:start position:0%
+it's an expansion
+of the unimodal and multimodal
+
+ align:start position:0%
+of the unimodal and multimodal
+ 
+
+ align:start position:0%
+of the unimodal and multimodal
+association areas of posterior cortex
+
+ align:start position:0%
+association areas of posterior cortex
+ 
+
+ align:start position:0%
+association areas of posterior cortex
+primarily visual
+
+ align:start position:0%
+primarily visual
+ 
+
+ align:start position:0%
+primarily visual
+okay it expands so much
+
+ align:start position:0%
+okay it expands so much
+ 
+
+ align:start position:0%
+okay it expands so much
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh It's associated with the lateral
+
+ align:start position:0%
+oh It's associated with the lateral
+ 
+
+ align:start position:0%
+oh It's associated with the lateral
+thalamic nucleus
+
+ align:start position:0%
+thalamic nucleus
+ 
+
+ align:start position:0%
+thalamic nucleus
+in primates it's mostly pulvenar see
+
+ align:start position:0%
+in primates it's mostly pulvenar see
+ 
+
+ align:start position:0%
+in primates it's mostly pulvenar see
+here I show an animal like a rodent that
+
+ align:start position:0%
+here I show an animal like a rodent that
+ 
+
+ align:start position:0%
+here I show an animal like a rodent that
+doesn't have a temporal lobe and then
+
+ align:start position:0%
+doesn't have a temporal lobe and then
+ 
+
+ align:start position:0%
+doesn't have a temporal lobe and then
+I'm showing what happens if the
+
+ align:start position:0%
+I'm showing what happens if the
+ 
+
+ align:start position:0%
+I'm showing what happens if the
+posterior areas
+
+ align:start position:0%
+posterior areas
+ 
+
+ align:start position:0%
+posterior areas
+concerned with vision and audition it's
+
+ align:start position:0%
+concerned with vision and audition it's
+ 
+
+ align:start position:0%
+concerned with vision and audition it's
+spanned
+
+ align:start position:0%
+spanned
+ 
+
+ align:start position:0%
+spanned
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+I mean there's not room in the sculpture
+
+ align:start position:0%
+I mean there's not room in the sculpture
+ 
+
+ align:start position:0%
+I mean there's not room in the sculpture
+just to expand and expand and expand so
+
+ align:start position:0%
+just to expand and expand and expand so
+ 
+
+ align:start position:0%
+just to expand and expand and expand so
+it you know it forms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a whole lobe that folds in
+
+ align:start position:0%
+a whole lobe that folds in
+ 
+
+ align:start position:0%
+a whole lobe that folds in
+like a glove here
+
+ align:start position:0%
+like a glove here
+ 
+
+ align:start position:0%
+like a glove here
+and with it comes to hippocampus I'm
+
+ align:start position:0%
+and with it comes to hippocampus I'm
+ 
+
+ align:start position:0%
+and with it comes to hippocampus I'm
+showing how the position of the
+
+ align:start position:0%
+showing how the position of the
+ 
+
+ align:start position:0%
+showing how the position of the
+hippocampus changes in relative position
+
+ align:start position:0%
+hippocampus changes in relative position
+ 
+
+ align:start position:0%
+hippocampus changes in relative position
+but the topography the topology is the
+
+ align:start position:0%
+but the topography the topology is the
+ 
+
+ align:start position:0%
+but the topography the topology is the
+same okay
+
+ align:start position:0%
+same okay
+ 
+
+ align:start position:0%
+same okay
+this is all visual areas
+
+ align:start position:0%
+this is all visual areas
+ 
+
+ align:start position:0%
+this is all visual areas
+from about here
+
+ align:start position:0%
+from about here
+ 
+
+ align:start position:0%
+from about here
+all the way down to here
+
+ align:start position:0%
+all the way down to here
+ 
+
+ align:start position:0%
+all the way down to here
+in the climate Okay
+
+ align:start position:0%
+in the climate Okay
+ 
+
+ align:start position:0%
+in the climate Okay
+and there's hippocampus nearby
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the process
+
+ align:start position:0%
+so that's the process
+ 
+
+ align:start position:0%
+so that's the process
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+well let's look at that in the optic
+
+ align:start position:0%
+well let's look at that in the optic
+ 
+
+ align:start position:0%
+well let's look at that in the optic
+radiations which are the fibers coming
+
+ align:start position:0%
+radiations which are the fibers coming
+ 
+
+ align:start position:0%
+radiations which are the fibers coming
+from Talons you know up to that visual
+
+ align:start position:0%
+from Talons you know up to that visual
+ 
+
+ align:start position:0%
+from Talons you know up to that visual
+cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we saw it in this picture that
+
+ align:start position:0%
+we saw it in this picture that
+ 
+
+ align:start position:0%
+we saw it in this picture that
+I think I had very early on from
+
+ align:start position:0%
+I think I had very early on from
+ 
+
+ align:start position:0%
+I think I had very early on from
+plexig's work German anatomist published
+
+ align:start position:0%
+plexig's work German anatomist published
+ 
+
+ align:start position:0%
+plexig's work German anatomist published
+a developmental study of myelinization
+
+ align:start position:0%
+a developmental study of myelinization
+ 
+
+ align:start position:0%
+a developmental study of myelinization
+this is from a seven-week human
+
+ align:start position:0%
+this is from a seven-week human
+ 
+
+ align:start position:0%
+this is from a seven-week human
+where myelin is just beginning to appear
+
+ align:start position:0%
+where myelin is just beginning to appear
+ 
+
+ align:start position:0%
+where myelin is just beginning to appear
+in the hemispheres and he shows its
+
+ align:start position:0%
+in the hemispheres and he shows its
+ 
+
+ align:start position:0%
+in the hemispheres and he shows its
+appearing first
+
+ align:start position:0%
+appearing first
+ 
+
+ align:start position:0%
+appearing first
+in this Pathway to the occipital lobe
+
+ align:start position:0%
+in this Pathway to the occipital lobe
+ 
+
+ align:start position:0%
+in this Pathway to the occipital lobe
+that's the general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it also appears in the primary auditory
+
+ align:start position:0%
+it also appears in the primary auditory
+ 
+
+ align:start position:0%
+it also appears in the primary auditory
+radiations
+
+ align:start position:0%
+radiations
+ 
+
+ align:start position:0%
+radiations
+to the auditory cortex and it appears
+
+ align:start position:0%
+to the auditory cortex and it appears
+ 
+
+ align:start position:0%
+to the auditory cortex and it appears
+it's actually earliest here I'm going to
+
+ align:start position:0%
+it's actually earliest here I'm going to
+ 
+
+ align:start position:0%
+it's actually earliest here I'm going to
+submit to the small sensory cortex from
+
+ align:start position:0%
+submit to the small sensory cortex from
+ 
+
+ align:start position:0%
+submit to the small sensory cortex from
+the ventral posterior thalamus
+
+ align:start position:0%
+the ventral posterior thalamus
+ 
+
+ align:start position:0%
+the ventral posterior thalamus
+so there's a lot of myelin in the
+
+ align:start position:0%
+so there's a lot of myelin in the
+ 
+
+ align:start position:0%
+so there's a lot of myelin in the
+cerebellum is a lot of myelin and the
+
+ align:start position:0%
+cerebellum is a lot of myelin and the
+ 
+
+ align:start position:0%
+cerebellum is a lot of myelin and the
+hindbrain and other other parts of the
+
+ align:start position:0%
+hindbrain and other other parts of the
+ 
+
+ align:start position:0%
+hindbrain and other other parts of the
+brain stem
+
+ align:start position:0%
+brain stem
+ 
+
+ align:start position:0%
+brain stem
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+just starting in the hemispheres
+
+ align:start position:0%
+just starting in the hemispheres
+ 
+
+ align:start position:0%
+just starting in the hemispheres
+appears first the indigenous right
+
+ align:start position:0%
+appears first the indigenous right
+ 
+
+ align:start position:0%
+appears first the indigenous right
+pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this just shows you how what I did to
+
+ align:start position:0%
+this just shows you how what I did to
+ 
+
+ align:start position:0%
+this just shows you how what I did to
+make this picture I had the original
+
+ align:start position:0%
+make this picture I had the original
+ 
+
+ align:start position:0%
+make this picture I had the original
+plexig picture
+
+ align:start position:0%
+plexig picture
+ 
+
+ align:start position:0%
+plexig picture
+which I got from the University of
+
+ align:start position:0%
+which I got from the University of
+ 
+
+ align:start position:0%
+which I got from the University of
+Chicago and
+
+ align:start position:0%
+Chicago and
+ 
+
+ align:start position:0%
+Chicago and
+these were German labels that he had in
+
+ align:start position:0%
+these were German labels that he had in
+ 
+
+ align:start position:0%
+these were German labels that he had in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so and carefully remove them
+
+ align:start position:0%
+so and carefully remove them
+ 
+
+ align:start position:0%
+so and carefully remove them
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+the artist felt removing the lines here
+
+ align:start position:0%
+the artist felt removing the lines here
+ 
+
+ align:start position:0%
+the artist felt removing the lines here
+and everything
+
+ align:start position:0%
+and everything
+ 
+
+ align:start position:0%
+and everything
+and I put in the major labels we needed
+
+ align:start position:0%
+and I put in the major labels we needed
+ 
+
+ align:start position:0%
+and I put in the major labels we needed
+to understand that picture okay and
+
+ align:start position:0%
+to understand that picture okay and
+ 
+
+ align:start position:0%
+to understand that picture okay and
+these are some very nice pictures of the
+
+ align:start position:0%
+these are some very nice pictures of the
+ 
+
+ align:start position:0%
+these are some very nice pictures of the
+growth of the human brains you can see
+
+ align:start position:0%
+growth of the human brains you can see
+ 
+
+ align:start position:0%
+growth of the human brains you can see
+the change in relative size
+
+ align:start position:0%
+the change in relative size
+ 
+
+ align:start position:0%
+the change in relative size
+these are all to the same scale
+
+ align:start position:0%
+these are all to the same scale
+ 
+
+ align:start position:0%
+these are all to the same scale
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 weeks
+
+ align:start position:0%
+10 weeks
+ 
+
+ align:start position:0%
+10 weeks
+up to 41 weeks just
+
+ align:start position:0%
+up to 41 weeks just
+ 
+
+ align:start position:0%
+up to 41 weeks just
+so this is it for
+
+ align:start position:0%
+so this is it for
+ 
+
+ align:start position:0%
+so this is it for
+birth is 40 or 40.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so back here
+
+ align:start position:0%
+so back here
+ 
+
+ align:start position:0%
+so back here
+you have a brain that's about the stage
+
+ align:start position:0%
+you have a brain that's about the stage
+ 
+
+ align:start position:0%
+you have a brain that's about the stage
+of development of a hamster at Birth
+
+ align:start position:0%
+of development of a hamster at Birth
+ 
+
+ align:start position:0%
+of development of a hamster at Birth
+because the hamster is born
+
+ align:start position:0%
+because the hamster is born
+ 
+
+ align:start position:0%
+because the hamster is born
+at a stage that corresponds to it
+
+ align:start position:0%
+at a stage that corresponds to it
+ 
+
+ align:start position:0%
+at a stage that corresponds to it
+premature human a
+
+ align:start position:0%
+premature human a
+ 
+
+ align:start position:0%
+premature human a
+pre-prenatal human
+
+ align:start position:0%
+pre-prenatal human
+ 
+
+ align:start position:0%
+pre-prenatal human
+okay about a two and a half month human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and there you see the temple
+
+ align:start position:0%
+all right and there you see the temple
+ 
+
+ align:start position:0%
+all right and there you see the temple
+of farming see it starts really early
+
+ align:start position:0%
+of farming see it starts really early
+ 
+
+ align:start position:0%
+of farming see it starts really early
+humans have a very large gentle Loops
+
+ align:start position:0%
+humans have a very large gentle Loops
+ 
+
+ align:start position:0%
+humans have a very large gentle Loops
+already is 12 releases beginning
+
+ align:start position:0%
+already is 12 releases beginning
+ 
+
+ align:start position:0%
+already is 12 releases beginning
+and then you'll see the progressive
+
+ align:start position:0%
+and then you'll see the progressive
+ 
+
+ align:start position:0%
+and then you'll see the progressive
+expansion of it
+
+ align:start position:0%
+expansion of it
+ 
+
+ align:start position:0%
+expansion of it
+visual areas end up being just visible
+
+ align:start position:0%
+visual areas end up being just visible
+ 
+
+ align:start position:0%
+visual areas end up being just visible
+only at the pole there in humans but if
+
+ align:start position:0%
+only at the pole there in humans but if
+ 
+
+ align:start position:0%
+only at the pole there in humans but if
+you look at the medial View
+
+ align:start position:0%
+you look at the medial View
+ 
+
+ align:start position:0%
+you look at the medial View
+very early you see the Caltrain Fisher
+
+ align:start position:0%
+very early you see the Caltrain Fisher
+ 
+
+ align:start position:0%
+very early you see the Caltrain Fisher
+folding in
+
+ align:start position:0%
+folding in
+ 
+
+ align:start position:0%
+folding in
+so this is all visual cortex here
+
+ align:start position:0%
+so this is all visual cortex here
+ 
+
+ align:start position:0%
+so this is all visual cortex here
+and in the adult it's all along the Deep
+
+ align:start position:0%
+and in the adult it's all along the Deep
+ 
+
+ align:start position:0%
+and in the adult it's all along the Deep
+Fisher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this just shows you the temporal lobe of
+
+ align:start position:0%
+this just shows you the temporal lobe of
+ 
+
+ align:start position:0%
+this just shows you the temporal lobe of
+the temple area of an animal that
+
+ align:start position:0%
+the temple area of an animal that
+ 
+
+ align:start position:0%
+the temple area of an animal that
+doesn't have a temple road but he's
+
+ align:start position:0%
+doesn't have a temple road but he's
+ 
+
+ align:start position:0%
+doesn't have a temple road but he's
+still got auditory cortex here in small
+
+ align:start position:0%
+still got auditory cortex here in small
+ 
+
+ align:start position:0%
+still got auditory cortex here in small
+areas outside the stride area which is
+
+ align:start position:0%
+areas outside the stride area which is
+ 
+
+ align:start position:0%
+areas outside the stride area which is
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+that do correspond suck of those
+
+ align:start position:0%
+that do correspond suck of those
+ 
+
+ align:start position:0%
+that do correspond suck of those
+areas outside the straight cortex in
+
+ align:start position:0%
+areas outside the straight cortex in
+ 
+
+ align:start position:0%
+areas outside the straight cortex in
+human but of course in monkeys but
+
+ align:start position:0%
+human but of course in monkeys but
+ 
+
+ align:start position:0%
+human but of course in monkeys but
+a lot of them are simply not there
+
+ align:start position:0%
+a lot of them are simply not there
+ 
+
+ align:start position:0%
+a lot of them are simply not there
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+and then it's happening happening very
+
+ align:start position:0%
+and then it's happening happening very
+ 
+
+ align:start position:0%
+and then it's happening happening very
+differently in the cast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we call this the pseudoslovine
+
+ align:start position:0%
+we call this the pseudoslovine
+ 
+
+ align:start position:0%
+we call this the pseudoslovine
+Fisher because it goes up right in the
+
+ align:start position:0%
+Fisher because it goes up right in the
+ 
+
+ align:start position:0%
+Fisher because it goes up right in the
+middle of auditory areas whereas in the
+
+ align:start position:0%
+middle of auditory areas whereas in the
+ 
+
+ align:start position:0%
+middle of auditory areas whereas in the
+primate monkey and human the auditorials
+
+ align:start position:0%
+primate monkey and human the auditorials
+ 
+
+ align:start position:0%
+primate monkey and human the auditorials
+always below the
+
+ align:start position:0%
+always below the
+ 
+
+ align:start position:0%
+always below the
+that deep Fisher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's the temporalization
+
+ align:start position:0%
+okay so there's the temporalization
+ 
+
+ align:start position:0%
+okay so there's the temporalization
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+uh once you understand simpleization you
+
+ align:start position:0%
+uh once you understand simpleization you
+ 
+
+ align:start position:0%
+uh once you understand simpleization you
+can understand what Meyer's Loop is this
+
+ align:start position:0%
+can understand what Meyer's Loop is this
+ 
+
+ align:start position:0%
+can understand what Meyer's Loop is this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this is the figure that I've used for
+
+ align:start position:0%
+this is the figure that I've used for
+ 
+
+ align:start position:0%
+this is the figure that I've used for
+the cover of the book
+
+ align:start position:0%
+the cover of the book
+ 
+
+ align:start position:0%
+the cover of the book
+and the artist chose it and
+
+ align:start position:0%
+and the artist chose it and
+ 
+
+ align:start position:0%
+and the artist chose it and
+extracted what she wanted from it and uh
+
+ align:start position:0%
+extracted what she wanted from it and uh
+ 
+
+ align:start position:0%
+extracted what she wanted from it and uh
+this is the same picture from nada
+
+ align:start position:0%
+this is the same picture from nada
+ 
+
+ align:start position:0%
+this is the same picture from nada
+where he's left the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the caudate there the cardiac nucleus
+
+ align:start position:0%
+the caudate there the cardiac nucleus
+ 
+
+ align:start position:0%
+the caudate there the cardiac nucleus
+and here the hippocampus formation
+
+ align:start position:0%
+and here the hippocampus formation
+ 
+
+ align:start position:0%
+and here the hippocampus formation
+in place and there's the amygdala
+
+ align:start position:0%
+in place and there's the amygdala
+ 
+
+ align:start position:0%
+in place and there's the amygdala
+here's here's these remove books
+
+ align:start position:0%
+here's here's these remove books
+ 
+
+ align:start position:0%
+here's here's these remove books
+because what he's showing here is fibers
+
+ align:start position:0%
+because what he's showing here is fibers
+ 
+
+ align:start position:0%
+because what he's showing here is fibers
+of the internal caps
+
+ align:start position:0%
+of the internal caps
+ 
+
+ align:start position:0%
+of the internal caps
+and the caudate is always medial to the
+
+ align:start position:0%
+and the caudate is always medial to the
+ 
+
+ align:start position:0%
+and the caudate is always medial to the
+internal capsule is he's removed the few
+
+ align:start position:0%
+internal capsule is he's removed the few
+ 
+
+ align:start position:0%
+internal capsule is he's removed the few
+payment in this dissection
+
+ align:start position:0%
+payment in this dissection
+ 
+
+ align:start position:0%
+payment in this dissection
+and here with all those structures
+
+ align:start position:0%
+and here with all those structures
+ 
+
+ align:start position:0%
+and here with all those structures
+removed you see
+
+ align:start position:0%
+removed you see
+ 
+
+ align:start position:0%
+removed you see
+the uh we call it the corona radiata
+
+ align:start position:0%
+the uh we call it the corona radiata
+ 
+
+ align:start position:0%
+the uh we call it the corona radiata
+fibers
+
+ align:start position:0%
+fibers
+ 
+
+ align:start position:0%
+fibers
+and these fibers here they're Myers Loop
+
+ align:start position:0%
+and these fibers here they're Myers Loop
+ 
+
+ align:start position:0%
+and these fibers here they're Myers Loop
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+part of the optic radiation support that
+
+ align:start position:0%
+part of the optic radiation support that
+ 
+
+ align:start position:0%
+part of the optic radiation support that
+represents the upper visual field so if
+
+ align:start position:0%
+represents the upper visual field so if
+ 
+
+ align:start position:0%
+represents the upper visual field so if
+you get a temple lobe injury in humans
+
+ align:start position:0%
+you get a temple lobe injury in humans
+ 
+
+ align:start position:0%
+you get a temple lobe injury in humans
+you seem to be very far from
+
+ align:start position:0%
+you seem to be very far from
+ 
+
+ align:start position:0%
+you seem to be very far from
+the visual cortex which is here but the
+
+ align:start position:0%
+the visual cortex which is here but the
+ 
+
+ align:start position:0%
+the visual cortex which is here but the
+fibers that go to the visual cortex
+
+ align:start position:0%
+fibers that go to the visual cortex
+ 
+
+ align:start position:0%
+fibers that go to the visual cortex
+go through part of the temple a little
+
+ align:start position:0%
+go through part of the temple a little
+ 
+
+ align:start position:0%
+go through part of the temple a little
+bit at least the ones representing the
+
+ align:start position:0%
+bit at least the ones representing the
+ 
+
+ align:start position:0%
+bit at least the ones representing the
+upper visual field so you can get a
+
+ align:start position:0%
+upper visual field so you can get a
+ 
+
+ align:start position:0%
+upper visual field so you can get a
+cortical blindness in
+
+ align:start position:0%
+cortical blindness in
+ 
+
+ align:start position:0%
+cortical blindness in
+in the upper visual field from the
+
+ align:start position:0%
+in the upper visual field from the
+ 
+
+ align:start position:0%
+in the upper visual field from the
+Temple of infantry because of that
+
+ align:start position:0%
+Temple of infantry because of that
+ 
+
+ align:start position:0%
+Temple of infantry because of that
+or a tumor in the template
+
+ align:start position:0%
+or a tumor in the template
+ 
+
+ align:start position:0%
+or a tumor in the template
+can cause that
+
+ align:start position:0%
+can cause that
+ 
+
+ align:start position:0%
+can cause that
+and it's easily understood once you
+
+ align:start position:0%
+and it's easily understood once you
+ 
+
+ align:start position:0%
+and it's easily understood once you
+understand the Topography of the optic
+
+ align:start position:0%
+understand the Topography of the optic
+ 
+
+ align:start position:0%
+understand the Topography of the optic
+radiations
+
+ align:start position:0%
+radiations
+ 
+
+ align:start position:0%
+radiations
+and these pictures are just meant to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+help you understand that concept
+
+ align:start position:0%
+help you understand that concept
+ 
+
+ align:start position:0%
+help you understand that concept
+and you can see here how some of them
+
+ align:start position:0%
+and you can see here how some of them
+ 
+
+ align:start position:0%
+and you can see here how some of them
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+so repeat uncles environmental tracks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course many of those
+
+ align:start position:0%
+and of course many of those
+ 
+
+ align:start position:0%
+and of course many of those
+grammal track fibers are coming
+
+ align:start position:0%
+grammal track fibers are coming
+ 
+
+ align:start position:0%
+grammal track fibers are coming
+from Central cortex
+
+ align:start position:0%
+from Central cortex
+ 
+
+ align:start position:0%
+from Central cortex
+motor cortex here
+
+ align:start position:0%
+motor cortex here
+ 
+
+ align:start position:0%
+motor cortex here
+it's a sensory cortex here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are two methods used by
+
+ align:start position:0%
+so what are two methods used by
+ 
+
+ align:start position:0%
+so what are two methods used by
+neuroscientists to map multiple visual
+
+ align:start position:0%
+neuroscientists to map multiple visual
+ 
+
+ align:start position:0%
+neuroscientists to map multiple visual
+areas
+
+ align:start position:0%
+areas
+ 
+
+ align:start position:0%
+areas
+and why do we believe the human brain
+
+ align:start position:0%
+and why do we believe the human brain
+ 
+
+ align:start position:0%
+and why do we believe the human brain
+contains more than the 32 areas
+
+ align:start position:0%
+contains more than the 32 areas
+ 
+
+ align:start position:0%
+contains more than the 32 areas
+described to those monkeys
+
+ align:start position:0%
+described to those monkeys
+ 
+
+ align:start position:0%
+described to those monkeys
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly the relationship is a pretty
+
+ align:start position:0%
+exactly the relationship is a pretty
+ 
+
+ align:start position:0%
+exactly the relationship is a pretty
+clear one we can
+
+ align:start position:0%
+clear one we can
+ 
+
+ align:start position:0%
+clear one we can
+here's the
+
+ align:start position:0%
+here's the
+ 
+
+ align:start position:0%
+here's the
+relationships you're talking about your
+
+ align:start position:0%
+relationships you're talking about your
+ 
+
+ align:start position:0%
+relationships you're talking about your
+plot and you according to the surface
+
+ align:start position:0%
+plot and you according to the surface
+ 
+
+ align:start position:0%
+plot and you according to the surface
+area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+against the number of visual areas
+
+ align:start position:0%
+against the number of visual areas
+ 
+
+ align:start position:0%
+against the number of visual areas
+okay in either logarithmic or linear
+
+ align:start position:0%
+okay in either logarithmic or linear
+ 
+
+ align:start position:0%
+okay in either logarithmic or linear
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+see here on the log
+
+ align:start position:0%
+see here on the log
+ 
+
+ align:start position:0%
+see here on the log
+log scale you get a pretty good line
+
+ align:start position:0%
+log scale you get a pretty good line
+ 
+
+ align:start position:0%
+log scale you get a pretty good line
+it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not totally precise
+
+ align:start position:0%
+not totally precise
+ 
+
+ align:start position:0%
+not totally precise
+this is a pretty good correspondence
+
+ align:start position:0%
+this is a pretty good correspondence
+ 
+
+ align:start position:0%
+this is a pretty good correspondence
+the animals with very small cortex have
+
+ align:start position:0%
+the animals with very small cortex have
+ 
+
+ align:start position:0%
+the animals with very small cortex have
+fewer areas
+
+ align:start position:0%
+fewer areas
+ 
+
+ align:start position:0%
+fewer areas
+some people have taken that to extremes
+
+ align:start position:0%
+some people have taken that to extremes
+ 
+
+ align:start position:0%
+some people have taken that to extremes
+and and suggested that the tiny tiny
+
+ align:start position:0%
+and and suggested that the tiny tiny
+ 
+
+ align:start position:0%
+and and suggested that the tiny tiny
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+true brains of wooden brains should only
+
+ align:start position:0%
+true brains of wooden brains should only
+ 
+
+ align:start position:0%
+true brains of wooden brains should only
+have just a few it turns out they have
+
+ align:start position:0%
+have just a few it turns out they have
+ 
+
+ align:start position:0%
+have just a few it turns out they have
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than that so uh
+
+ align:start position:0%
+than that so uh
+ 
+
+ align:start position:0%
+than that so uh
+they show here
+
+ align:start position:0%
+they show here
+ 
+
+ align:start position:0%
+they show here
+for example Mass choose having
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one area
+
+ align:start position:0%
+one area
+ 
+
+ align:start position:0%
+one area
+here's they have Mouse
+
+ align:start position:0%
+here's they have Mouse
+ 
+
+ align:start position:0%
+here's they have Mouse
+showing only
+
+ align:start position:0%
+showing only
+ 
+
+ align:start position:0%
+showing only
+two two or maybe three areas turns out
+
+ align:start position:0%
+two two or maybe three areas turns out
+ 
+
+ align:start position:0%
+two two or maybe three areas turns out
+not to be true
+
+ align:start position:0%
+not to be true
+ 
+
+ align:start position:0%
+not to be true
+so these were based on early studies
+
+ align:start position:0%
+so these were based on early studies
+ 
+
+ align:start position:0%
+so these were based on early studies
+where they simply hadn't applied these
+
+ align:start position:0%
+where they simply hadn't applied these
+ 
+
+ align:start position:0%
+where they simply hadn't applied these
+all these methods that I'm talking about
+
+ align:start position:0%
+all these methods that I'm talking about
+ 
+
+ align:start position:0%
+all these methods that I'm talking about
+now here was the usual method of
+
+ align:start position:0%
+now here was the usual method of
+ 
+
+ align:start position:0%
+now here was the usual method of
+recording uh here they're penetrating
+
+ align:start position:0%
+recording uh here they're penetrating
+ 
+
+ align:start position:0%
+recording uh here they're penetrating
+with an electrodes this is a medial view
+
+ align:start position:0%
+with an electrodes this is a medial view
+ 
+
+ align:start position:0%
+with an electrodes this is a medial view
+of the all monkeys and it shows
+
+ align:start position:0%
+of the all monkeys and it shows
+ 
+
+ align:start position:0%
+of the all monkeys and it shows
+penetrations through this one area
+
+ align:start position:0%
+penetrations through this one area
+ 
+
+ align:start position:0%
+penetrations through this one area
+and mapping the visual field when they
+
+ align:start position:0%
+and mapping the visual field when they
+ 
+
+ align:start position:0%
+and mapping the visual field when they
+find that complete Maps
+
+ align:start position:0%
+find that complete Maps
+ 
+
+ align:start position:0%
+find that complete Maps
+okay so they do that all these different
+
+ align:start position:0%
+okay so they do that all these different
+ 
+
+ align:start position:0%
+okay so they do that all these different
+areas this was done by almond and often
+
+ align:start position:0%
+areas this was done by almond and often
+ 
+
+ align:start position:0%
+areas this was done by almond and often
+working with John cos
+
+ align:start position:0%
+working with John cos
+ 
+
+ align:start position:0%
+working with John cos
+they've done it together in a number of
+
+ align:start position:0%
+they've done it together in a number of
+ 
+
+ align:start position:0%
+they've done it together in a number of
+animals and separately from other with
+
+ align:start position:0%
+animals and separately from other with
+ 
+
+ align:start position:0%
+animals and separately from other with
+other animals
+
+ align:start position:0%
+other animals
+ 
+
+ align:start position:0%
+other animals
+much of the work in the owl monkeys is
+
+ align:start position:0%
+much of the work in the owl monkeys is
+ 
+
+ align:start position:0%
+much of the work in the owl monkeys is
+done by almonds and I've used his
+
+ align:start position:0%
+done by almonds and I've used his
+ 
+
+ align:start position:0%
+done by almonds and I've used his
+pictures here
+
+ align:start position:0%
+pictures here
+ 
+
+ align:start position:0%
+pictures here
+see all these areas how this is all
+
+ align:start position:0%
+see all these areas how this is all
+ 
+
+ align:start position:0%
+see all these areas how this is all
+equal cortex okay here we call this
+
+ align:start position:0%
+equal cortex okay here we call this
+ 
+
+ align:start position:0%
+equal cortex okay here we call this
+infrotempo projects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gyrus of the temple lobe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because this is occipital
+
+ align:start position:0%
+because this is occipital
+ 
+
+ align:start position:0%
+because this is occipital
+and this is posterior crime so all of
+
+ align:start position:0%
+and this is posterior crime so all of
+ 
+
+ align:start position:0%
+and this is posterior crime so all of
+these areas
+
+ align:start position:0%
+these areas
+ 
+
+ align:start position:0%
+these areas
+have complete representation particular
+
+ align:start position:0%
+have complete representation particular
+ 
+
+ align:start position:0%
+have complete representation particular
+field getting input
+
+ align:start position:0%
+field getting input
+ 
+
+ align:start position:0%
+field getting input
+from the thalms
+
+ align:start position:0%
+from the thalms
+ 
+
+ align:start position:0%
+from the thalms
+let's answer another question right now
+
+ align:start position:0%
+let's answer another question right now
+ 
+
+ align:start position:0%
+let's answer another question right now
+each of these areas gets input from two
+
+ align:start position:0%
+each of these areas gets input from two
+ 
+
+ align:start position:0%
+each of these areas gets input from two
+major sources what are they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from thalamus
+
+ align:start position:0%
+from thalamus
+ 
+
+ align:start position:0%
+from thalamus
+and most of these we know come from the
+
+ align:start position:0%
+and most of these we know come from the
+ 
+
+ align:start position:0%
+and most of these we know come from the
+body
+
+ align:start position:0%
+body
+ 
+
+ align:start position:0%
+body
+the rest of them are coming from the
+
+ align:start position:0%
+the rest of them are coming from the
+ 
+
+ align:start position:0%
+the rest of them are coming from the
+lateral balance
+
+ align:start position:0%
+lateral balance
+ 
+
+ align:start position:0%
+lateral balance
+the different sub nuclei of the pulvenar
+
+ align:start position:0%
+the different sub nuclei of the pulvenar
+ 
+
+ align:start position:0%
+the different sub nuclei of the pulvenar
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what's the other source of inputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transport
+
+ align:start position:0%
+transport
+ 
+
+ align:start position:0%
+transport
+they get inputs from the stride
+
+ align:start position:0%
+they get inputs from the stride
+ 
+
+ align:start position:0%
+they get inputs from the stride
+so one of the methods used to map then
+
+ align:start position:0%
+so one of the methods used to map then
+ 
+
+ align:start position:0%
+so one of the methods used to map then
+uh of course the two methods I'm talking
+
+ align:start position:0%
+uh of course the two methods I'm talking
+ 
+
+ align:start position:0%
+uh of course the two methods I'm talking
+about are electrophysiology which is
+
+ align:start position:0%
+about are electrophysiology which is
+ 
+
+ align:start position:0%
+about are electrophysiology which is
+shown here on the left side and anatomy
+
+ align:start position:0%
+shown here on the left side and anatomy
+ 
+
+ align:start position:0%
+shown here on the left side and anatomy
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+here is as this picture I included in
+
+ align:start position:0%
+here is as this picture I included in
+ 
+
+ align:start position:0%
+here is as this picture I included in
+the book
+
+ align:start position:0%
+the book
+ 
+
+ align:start position:0%
+the book
+beautiful study of the mouse look what
+
+ align:start position:0%
+beautiful study of the mouse look what
+ 
+
+ align:start position:0%
+beautiful study of the mouse look what
+they've done they've taken three
+
+ align:start position:0%
+they've done they've taken three
+ 
+
+ align:start position:0%
+they've done they've taken three
+fluorescent Tracer substances
+
+ align:start position:0%
+fluorescent Tracer substances
+ 
+
+ align:start position:0%
+fluorescent Tracer substances
+and put them into separate areas
+
+ align:start position:0%
+and put them into separate areas
+ 
+
+ align:start position:0%
+and put them into separate areas
+along the Carl part of the first visual
+
+ align:start position:0%
+along the Carl part of the first visual
+ 
+
+ align:start position:0%
+along the Carl part of the first visual
+area strike cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they've let the animal survive for a
+
+ align:start position:0%
+and they've let the animal survive for a
+ 
+
+ align:start position:0%
+and they've let the animal survive for a
+while so you get transported those
+
+ align:start position:0%
+while so you get transported those
+ 
+
+ align:start position:0%
+while so you get transported those
+fluorescent labels to various terminal
+
+ align:start position:0%
+fluorescent labels to various terminal
+ 
+
+ align:start position:0%
+fluorescent labels to various terminal
+areas and look what they're gay
+
+ align:start position:0%
+areas and look what they're gay
+ 
+
+ align:start position:0%
+areas and look what they're gay
+this Topography is repeated there and
+
+ align:start position:0%
+this Topography is repeated there and
+ 
+
+ align:start position:0%
+this Topography is repeated there and
+there there to see several one two three
+
+ align:start position:0%
+there there to see several one two three
+ 
+
+ align:start position:0%
+there there to see several one two three
+four five six seven
+
+ align:start position:0%
+four five six seven
+ 
+
+ align:start position:0%
+four five six seven
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+nine
+
+ align:start position:0%
+nine
+ 
+
+ align:start position:0%
+nine
+and then additional areas where the
+
+ align:start position:0%
+and then additional areas where the
+ 
+
+ align:start position:0%
+and then additional areas where the
+topography isn't as precise but it is
+
+ align:start position:0%
+topography isn't as precise but it is
+ 
+
+ align:start position:0%
+topography isn't as precise but it is
+still there you see an enlargement of a
+
+ align:start position:0%
+still there you see an enlargement of a
+ 
+
+ align:start position:0%
+still there you see an enlargement of a
+area getting sparse input here and the
+
+ align:start position:0%
+area getting sparse input here and the
+ 
+
+ align:start position:0%
+area getting sparse input here and the
+retrospinal area on the medial side
+
+ align:start position:0%
+retrospinal area on the medial side
+ 
+
+ align:start position:0%
+retrospinal area on the medial side
+but you see there still is topography so
+
+ align:start position:0%
+but you see there still is topography so
+ 
+
+ align:start position:0%
+but you see there still is topography so
+the red axons the green accents the
+
+ align:start position:0%
+the red axons the green accents the
+ 
+
+ align:start position:0%
+the red axons the green accents the
+yellow accents not as precise but it's
+
+ align:start position:0%
+yellow accents not as precise but it's
+ 
+
+ align:start position:0%
+yellow accents not as precise but it's
+still there
+
+ align:start position:0%
+still there
+ 
+
+ align:start position:0%
+still there
+so they get at least 10 different areas
+
+ align:start position:0%
+so they get at least 10 different areas
+ 
+
+ align:start position:0%
+so they get at least 10 different areas
+in this month
+
+ align:start position:0%
+in this month
+ 
+
+ align:start position:0%
+in this month
+just to show you how the data changes
+
+ align:start position:0%
+just to show you how the data changes
+ 
+
+ align:start position:0%
+just to show you how the data changes
+here it says two or three
+
+ align:start position:0%
+here it says two or three
+ 
+
+ align:start position:0%
+here it says two or three
+if we get 10.
+
+ align:start position:0%
+if we get 10.
+ 
+
+ align:start position:0%
+if we get 10.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is just a flattened view of the
+
+ align:start position:0%
+and this is just a flattened view of the
+ 
+
+ align:start position:0%
+and this is just a flattened view of the
+cortex shows where they
+
+ align:start position:0%
+cortex shows where they
+ 
+
+ align:start position:0%
+cortex shows where they
+put those injections in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is mouse yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're culture it's lab is where they did
+
+ align:start position:0%
+we're culture it's lab is where they did
+ 
+
+ align:start position:0%
+we're culture it's lab is where they did
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+but he obviously had a really good
+
+ align:start position:0%
+but he obviously had a really good
+ 
+
+ align:start position:0%
+but he obviously had a really good
+command of this method
+
+ align:start position:0%
+command of this method
+ 
+
+ align:start position:0%
+command of this method
+I was able to get some very beautiful
+
+ align:start position:0%
+I was able to get some very beautiful
+ 
+
+ align:start position:0%
+I was able to get some very beautiful
+results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is just a picture to illustrate
+
+ align:start position:0%
+and this is just a picture to illustrate
+ 
+
+ align:start position:0%
+and this is just a picture to illustrate
+that they keep seeing V1 and V2 in all
+
+ align:start position:0%
+that they keep seeing V1 and V2 in all
+ 
+
+ align:start position:0%
+that they keep seeing V1 and V2 in all
+the different mammals including the
+
+ align:start position:0%
+the different mammals including the
+ 
+
+ align:start position:0%
+the different mammals including the
+marsupials okay
+
+ align:start position:0%
+marsupials okay
+ 
+
+ align:start position:0%
+marsupials okay
+that's all that's illustrating
+
+ align:start position:0%
+that's all that's illustrating
+ 
+
+ align:start position:0%
+that's all that's illustrating
+putting them on a cladogram
+
+ align:start position:0%
+putting them on a cladogram
+ 
+
+ align:start position:0%
+putting them on a cladogram
+and this is another one where they
+
+ align:start position:0%
+and this is another one where they
+ 
+
+ align:start position:0%
+and this is another one where they
+showed it
+
+ align:start position:0%
+showed it
+ 
+
+ align:start position:0%
+showed it
+most of those groups have Gary Mt a
+
+ align:start position:0%
+most of those groups have Gary Mt a
+ 
+
+ align:start position:0%
+most of those groups have Gary Mt a
+heavily myelinated area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty direct digital path we also like
+
+ align:start position:0%
+pretty direct digital path we also like
+ 
+
+ align:start position:0%
+pretty direct digital path we also like
+as does the strike critics but you don't
+
+ align:start position:0%
+as does the strike critics but you don't
+ 
+
+ align:start position:0%
+as does the strike critics but you don't
+find it in the marscience
+
+ align:start position:0%
+find it in the marscience
+ 
+
+ align:start position:0%
+find it in the marscience
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is fish adding besides V1 and
+
+ align:start position:0%
+and this is fish adding besides V1 and
+ 
+
+ align:start position:0%
+and this is fish adding besides V1 and
+V2 as the ancient areas even in the
+
+ align:start position:0%
+V2 as the ancient areas even in the
+ 
+
+ align:start position:0%
+V2 as the ancient areas even in the
+Hedgehog you see it
+
+ align:start position:0%
+Hedgehog you see it
+ 
+
+ align:start position:0%
+Hedgehog you see it
+but you also always see an object you
+
+ align:start position:0%
+but you also always see an object you
+ 
+
+ align:start position:0%
+but you also always see an object you
+always see
+
+ align:start position:0%
+always see
+ 
+
+ align:start position:0%
+always see
+two somatosensory areas
+
+ align:start position:0%
+two somatosensory areas
+ 
+
+ align:start position:0%
+two somatosensory areas
+and you usually but not holes
+
+ align:start position:0%
+and you usually but not holes
+ 
+
+ align:start position:0%
+and you usually but not holes
+see a motor area you don't always see a
+
+ align:start position:0%
+see a motor area you don't always see a
+ 
+
+ align:start position:0%
+see a motor area you don't always see a
+motor area separate from this medicine
+
+ align:start position:0%
+motor area separate from this medicine
+ 
+
+ align:start position:0%
+motor area separate from this medicine
+tree area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the Apostle for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think we talked about that once
+
+ align:start position:0%
+and I think we talked about that once
+ 
+
+ align:start position:0%
+and I think we talked about that once
+before the amalgam of the two areas
+
+ align:start position:0%
+before the amalgam of the two areas
+ 
+
+ align:start position:0%
+before the amalgam of the two areas
+because motor cortex appears to have
+
+ align:start position:0%
+because motor cortex appears to have
+ 
+
+ align:start position:0%
+because motor cortex appears to have
+originated as a similar sensory area
+
+ align:start position:0%
+originated as a similar sensory area
+ 
+
+ align:start position:0%
+originated as a similar sensory area
+then it became specialized
+
+ align:start position:0%
+then it became specialized
+ 
+
+ align:start position:0%
+then it became specialized
+for the more direct connections to the
+
+ align:start position:0%
+for the more direct connections to the
+ 
+
+ align:start position:0%
+for the more direct connections to the
+spinal cord for motor function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we've already answered this so next
+
+ align:start position:0%
+okay we've already answered this so next
+ 
+
+ align:start position:0%
+okay we've already answered this so next
+time we'll start with a major
+
+ align:start position:0%
+time we'll start with a major
+ 
+
+ align:start position:0%
+time we'll start with a major
+transcritical connections it won't take
+
+ align:start position:0%
+transcritical connections it won't take
+ 
+
+ align:start position:0%
+transcritical connections it won't take
+very long just read it and where it's
+
+ align:start position:0%
+very long just read it and where it's
+ 
+
+ align:start position:0%
+very long just read it and where it's
+different from other treatments in the
+
+ align:start position:0%
+different from other treatments in the
+ 
+
+ align:start position:0%
+different from other treatments in the
+current literature
+
+ align:start position:0%
+current literature
+ 
+
+ align:start position:0%
+current literature
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+I'm pointing out something that was
+
+ align:start position:0%
+I'm pointing out something that was
+ 
+
+ align:start position:0%
+I'm pointing out something that was
+neglected by other people they talk
+
+ align:start position:0%
+neglected by other people they talk
+ 
+
+ align:start position:0%
+neglected by other people they talk
+about always two pathos that were
+
+ align:start position:0%
+about always two pathos that were
+ 
+
+ align:start position:0%
+about always two pathos that were
+influenced by other other early work
+
+ align:start position:0%
+influenced by other other early work
+ 
+
+ align:start position:0%
+influenced by other other early work
+that came from MIT the two visual
+
+ align:start position:0%
+that came from MIT the two visual
+ 
+
+ align:start position:0%
+that came from MIT the two visual
+systems so there's always two visual
+
+ align:start position:0%
+systems so there's always two visual
+ 
+
+ align:start position:0%
+systems so there's always two visual
+pathways object location object
+
+ align:start position:0%
+pathways object location object
+ 
+
+ align:start position:0%
+pathways object location object
+identification so they just neglected
+
+ align:start position:0%
+identification so they just neglected
+ 
+
+ align:start position:0%
+identification so they just neglected
+the third one and now what I had pointed
+
+ align:start position:0%
+the third one and now what I had pointed
+ 
+
+ align:start position:0%
+the third one and now what I had pointed
+it out but not he wasn't focused on
+
+ align:start position:0%
+it out but not he wasn't focused on
+ 
+
+ align:start position:0%
+it out but not he wasn't focused on
+visual system but there in his results
+
+ align:start position:0%
+visual system but there in his results
+ 
+
+ align:start position:0%
+visual system but there in his results
+published results after he died I found
+
+ align:start position:0%
+published results after he died I found
+ 
+
+ align:start position:0%
+published results after he died I found
+these results and I've included it in my
+
+ align:start position:0%
+these results and I've included it in my
+ 
+
+ align:start position:0%
+these results and I've included it in my
+book as a medial pathway
+
+ align:start position:0%
+book as a medial pathway
+ 
+
+ align:start position:0%
+book as a medial pathway
+going towards the gamble formation
+
+ align:start position:0%
+going towards the gamble formation
+ 
+
+ align:start position:0%
+going towards the gamble formation
+terminates in Para hippocampal areas
+
+ align:start position:0%
+terminates in Para hippocampal areas
+ 
+
+ align:start position:0%
+terminates in Para hippocampal areas
+so we'll just go over that quickly
\ No newline at end of file
diff --git a/QWHtRR1jMEQ.txt b/QWHtRR1jMEQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..213f16c6f411957969ea496ab233d85b08bca87b
--- /dev/null
+++ b/QWHtRR1jMEQ.txt
@@ -0,0 +1,3294 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+ROBERT GALLAGER: OK.
+
+Today, I want to review
+a little bit of
+
+what we did last time.
+
+I think with all the details,
+some of you sort of lost the
+
+main pattern of what
+was going on.
+
+So let me try to talk about
+the main pattern.
+
+I don't want to talk about
+the details anymore.
+
+I think, for the most part in
+this course, the best way to
+
+understand the details of proofs
+is to read the notes
+
+where you can read them at your
+own rate, unless there's
+
+something wrong in the notes.
+
+I will typically avoid
+that from now on.
+
+The main story that we want to
+go through, first is the idea
+
+of what convergence with
+probability 1 means.
+
+This is a very peculiar
+concept.
+
+And I have to keep going through
+it, have to keep
+
+talking about it with different
+notation so that you
+
+can see it coming any
+way you look at it.
+
+So what the theorem is-- and
+it's a very useful theorem--
+
+it says let Y n be a set of
+random variables, which
+
+satisfy the condition that the
+sum of the expectations of the
+
+absolute value of each
+random variable
+
+is less than infinity.
+
+First thing I want to point
+out is what that means,
+
+because it's not entirely clear
+what is the means to
+
+start with.
+
+When you talk about a limit
+from n to infinity, from n
+
+equals 1 to infinity, what it
+remains is this sum here
+
+really means the limit
+as m goes to
+
+infinity of a finite sum.
+
+Anytime you talk about a limit
+of a set of numbers, that's
+
+exactly what you mean by it.
+
+So if we're saying that this
+quantity is less than
+
+infinity, it says two things.
+
+It says that these finite
+sums are lesson
+
+infinity for all a m.
+
+And it also says that these
+finite sums go to a limit.
+
+And the fact that these finite
+sums are going to a limit as m
+
+gets big says what's a more
+intuitive thing, which is that
+
+the limit as m goes
+to infinity.
+
+And here, instead of going from
+1 thing m, I'm going from
+
+m plus 1 to infinity, and it
+doesn't make any difference
+
+whether I go from m plus 1 to
+infinity or m to infinity.
+
+And what has to happen for this
+limit to exist is the
+
+difference between this and
+this, which is this,
+
+has to go to 0.
+
+So that what we're really saying
+here is that the tail
+
+sum has to go to 0 here.
+
+Now, this is a much stronger
+requirement than just saying
+
+that the expected value of the
+magnitudes of these random
+
+variables has to go to 0.
+
+If, for example, the expected
+value of y sub n is 1/n, then
+
+1/n, the limit of that as n
+goes to infinity, is 0.
+
+So this is satisfied.
+
+But when you sum one/n here,
+you don't get 0.
+
+And in fact, you get infinity.
+
+Yes, you get infinity.
+
+So this requires
+more than this.
+
+This limit here, the requirement
+that that equals
+
+0, implies that the sequence y
+sub n actually converges to 0
+
+in probability, rather than
+with probability 1.
+
+And the first problem in the
+homework for this coming week
+
+is to actually show that.
+
+And when you show it, I hope
+you find out that it is
+
+absolutely trivial to show it.
+
+It takes two lines to show
+it, and that's really
+
+all you need here.
+
+The stronger requirement here,
+let's us say something about
+
+the entire sample path.
+
+You see, this requirement really
+is focusing on each
+
+individual value of
+n, but it's not
+
+focusing on the sequences.
+
+This stronger quantity here is
+really focusing on these
+
+entire sample paths.
+
+OK.
+
+So let's go on and review what
+the strong law of large
+
+numbers says.
+
+And another note about the
+theorem on convergence, how
+
+useful that theorem is depends
+on how you choose these random
+
+variable, Y1, Y2,
+and so forth.
+
+When we were proving the strong
+law of large numbers in
+
+class last time, and in the
+notes, we started off by
+
+assuming that the mean
+of x is equal to 0.
+
+In fact, we'll see that that's
+just for convenience.
+
+It's not something that has
+anything to do with anything.
+
+It's just to get rid of a
+lot of extra numbers.
+
+So we assume this.
+
+We also assume that the expected
+value of x to the
+
+fourth was less than infinity.
+
+In other words, we assume that
+this random variable that we
+
+were adding, these IID
+random variables,
+
+had a fourth moment.
+
+Now, an awful lot of
+random variables
+
+have a fourth moment.
+
+The real strong law of large
+numbers, all that assumes is
+
+that the expected value
+of the magnitude of x
+
+is less than infinity.
+
+So it has a much weaker
+set of conditions.
+
+Most of the problems you run
+into, doesn't make any
+
+difference whether you assume
+this or you make the stronger
+
+assumption that the mean
+is equal to 0.
+
+When you start applying this
+theorem, it doesn't make any
+
+difference at all, because
+there's no way you can tell,
+
+in a physical situation, whether
+it is reasonable to
+
+assume that the fourth moment
+is finite and the
+
+first moment isn't.
+
+Because that question has to
+do only with the very far
+
+tails of the distribution.
+
+I can take any distribution x
+and I can truncate it at 10 to
+
+the google.
+
+And if I truncate it at 10 to
+the google, it has a finite
+
+fourth moment.
+
+If I don't truncate
+it, it might not
+
+have a fourth moment.
+
+There's no way you can tell
+from looking at physical
+
+situations.
+
+So this question here is
+primarily a question of
+
+modeling and what you're going
+to do with the models.
+
+It's not something
+which is crucial.
+
+But anyway, after we did that,
+what we said was when we
+
+assume that this is less than
+infinity, we can look at s sub
+
+n, which is x1, up to x n all
+IID We then took this sum
+
+here, took to the fourth moment
+of it, and we looked at
+
+all the cross terms and
+what could happen.
+
+And we found that the only cross
+terms that worked that
+
+were non-0 was where either
+these quantities were paired
+
+together, x1 x1, x2, x2, or
+where they were all the same.
+
+And then when we looked at that,
+we very quickly realized
+
+that the expected value of s n
+to the fourth was proportional
+
+to n squared.
+
+It was upper banded the by three
+times n squared times
+
+the fourth moment of x.
+
+So when we look at s n to the
+fourth divided by n to the
+
+fourth, that quantity, summed
+over n, goes as 1 over n
+
+squared, which has a
+finite sum over n.
+
+And therefore, the probability
+of the limit as n approaches
+
+infinity of s n to the fourth
+over n fourth equals 0.
+
+The probability of the
+sample path, the
+
+sample paths converge.
+
+The probability of that is equal
+to 1, which says all
+
+sample paths converge
+with probability 1.
+
+So this is enough, not quite
+enough to prove the strong law
+
+of large numbers.
+
+Because what we're interested
+in is not s n to the fourth
+
+over n fourth.
+
+We're interested in
+s sub n over n.
+
+So we have to go one
+step further.
+
+This is why it's tricky to
+figure out what random
+
+variables you want to use when
+you're trying to go from this
+
+theorem about convergence with
+probability 1 to the strong
+
+law, or the strong law for
+renewals, or any other kind of
+
+strong law doing
+anything else.
+
+It's a fairly tricky matter to
+choose what random variables
+
+you want to talk about there.
+
+But here, it doesn't make any
+difference, as we've said.
+
+If you let s n of omega over
+n be a sub n to the 1/4.
+
+In other words, what I'm doing
+now is I'm focusing on just
+
+one sample path.
+
+If I focus on one sample path,
+omega, and then each one of
+
+these terms has some value, a
+sub n, and then s sub n of
+
+omega over n is going to be
+equal to a sub n to the 1/4
+
+power, the 1/4 power of this
+quantity over here.
+
+Now, the question is if the
+limit of these numbers--
+
+And now remember, now we're
+talking about a single sample
+
+path, but all of these sample
+paths behave the same way.
+
+So if this limit here for one
+sample path is equal to 0,
+
+then the limit of a sub n to
+the 1/4 is also equal to 0.
+
+Why is that true?
+
+That's just a result about
+the real number system.
+
+It's a result about convergence
+of real numbers.
+
+If you take a bunch of real
+numbers, which are getting
+
+very, very small, and you take
+the fourth root of those
+
+numbers, which are getting very
+small, the fourth root is
+
+a lot bigger than the
+number itself.
+
+But nonetheless, the fourth
+root is being driven to 0
+
+also, or at least the absolute
+value of the fourth root is
+
+being driven to 0 also.
+
+You can see this intuitively
+without
+
+even proving any theorems.
+
+Except, it is a standard result,
+just talking about the
+
+real number system.
+
+OK.
+
+So what that says is the
+probability that the limit of
+
+s sub n over n equals 0.
+
+This is now is talking
+about sample paths
+
+for each sample path.
+
+This limit s n over n either
+exists or it doesn't exist.
+
+If it does exist, it's either
+equal to 0 or equal to
+
+something else.
+
+It says that the probability
+that it exists and that it's
+
+equal to 0 is equal to 1.
+
+OK.
+
+Now, remember last time we
+talked about something a
+
+little bit funny.
+
+We talked about the
+Bernoulli process.
+
+And we talked about the
+Bernoulli process using one
+
+value of p for the probability
+that x is equal to 1.
+
+And what we found is that the
+probability of the sample path
+
+where s sub n over n approach to
+p, the probability of that
+
+set was equal to 1.
+
+If we change the probability
+that x is equal to 1 to some
+
+other value, that is still a
+perfectly well-defined event.
+
+The event that a sample path,
+that sub n over n for a sample
+
+path approaches p.
+
+But that sample path, that
+event, becomes 0 as soon as
+
+you change p to some
+other value.
+
+So what we're talking
+about here is really
+
+a probability measure.
+
+We're not using any kind of
+measure theory here, but you
+
+really have to be careful about
+the fact that you're not
+
+talking about the number of
+sequences for which this limit
+
+is equal to 0.
+
+You're really talking about
+the probability of it.
+
+And you can't think of it in
+terms of number of sequences.
+
+What's the most probable
+sequence for a Bernoulli
+
+process where p is,
+say, 0.317?
+
+Who knows what the
+most probable
+
+sequence of length n is?
+
+What?
+
+There is none?
+
+Yes, there is.
+
+It's all 0's, yes.
+
+The all 0's sequence is more
+likely than anything else.
+
+So why don't these sequences
+converge to 0?
+
+I'm In this case, these
+sequences actually converge to
+
+0.317, if that's
+the value of p.
+
+So what's going on?
+
+What's going on is a trade-off
+between the number of
+
+sequences and the probability
+of those sequences.
+
+You look at a particular value
+of n, there's only one
+
+sequence which is all 0's.
+
+It's much more likely than any
+of the other sequences.
+
+There's an enormous number of
+sequences where the relative
+
+frequency of them is
+close to 0.317.
+
+They're very improbable, but
+because of the very large
+
+number of them, those are the
+ones that turn out to have all
+
+the probability here.
+
+So that's what's going
+on in this strong
+
+law of large numbers.
+
+You have all of these effects
+playing off against each
+
+other, and it's kind of
+phenomenal that you wind up
+
+with an extraordinarily strong
+theorem like this.
+
+When you call this the strong
+law of large numbers, it, in
+
+fact, is an incredibly strong
+theorem, which is not at all
+
+intuitively obvious.
+
+It's very, very far from
+intuitively obvious.
+
+If you think it's intuitively
+obvious, and you haven't
+
+studied it for a very long time,
+go back and think about
+
+it again, because there's
+something wrong in the way
+
+you're thinking about it.
+
+Because this is an absolutely
+incredible theorem.
+
+OK.
+
+So I want to be a little more
+general now and talk about
+
+sequences converging to
+a constant alpha with
+
+probability 1.
+
+If the probability of the set of
+omega such as the limit as
+
+n goes to infinity
+is z n of omega.
+
+In other words, we will look
+look at a sample path for a
+
+given omega.
+
+Let's look at the probability
+that that's equal to alpha
+
+rather than equal to 0.
+
+That's the case of the
+Bernoulli process.
+
+Bernoulli process with
+probability p, if you're
+
+looking at s n of omega as s n
+of omega over n, then this
+
+converges to alpha.
+
+You're looking at s n to the
+fourth over n to the fourth,
+
+it converges to p to
+the fourth power.
+
+And all those are equal to 1.
+
+Now, note that z n converges to
+alpha if, and only if, z n
+
+minus alpha converges to 0.
+
+In other words, we're talking
+about something that's
+
+relatively trivial here.
+
+It's not very important.
+
+Any time I have a sequence
+of random variables that
+
+converges to some non-0
+quantity, p, or alpha, or
+
+whatever, I can also talk
+about z n minus alpha.
+
+And that's another sequence
+of random variables.
+
+And if this converges to alpha,
+this converges to 0.
+
+So all I was doing when I was
+talking about this convergence
+
+theorem of everything converging
+to 0, what I was
+
+doing was really taking these
+random variables and looking
+
+at their variation around the
+mean, at their fluctuation
+
+around the mean, rather
+than the actual
+
+random variable itself.
+
+You can always do that.
+
+And by doing it, you need to
+introduce a little more
+
+terminology, and you get rid of
+a lot of mess, because then
+
+the mean doesn't
+appear anymore.
+
+So when we start talking about
+renewal processes, which we're
+
+going to do here, the
+inter-renewal
+
+intervals are positive.
+
+It's important, the the fact
+that they're positive, and
+
+that they never go negative.
+
+And because of that, we don't
+really want to subtract the
+
+mean off them, because then we
+would have a sequence of
+
+random variables that weren't
+positive anymore.
+
+So instead of taking away the
+mean to avoid a couple of
+
+extra symbols, we're going to
+leave the mean in from now on,
+
+so these random variables are
+going to converge to some
+
+constant, generally, rather
+than converge to 0.
+
+And it doesn't make
+any difference.
+
+OK.
+
+So now, the next thing I want to
+do is talk about the strong
+
+law for renewal processes.
+
+In other words, I want to talk
+about what happens when you
+
+have a renewal counting process
+where n of t is the
+
+number of arrivals
+up until time t.
+
+And we'd like to see if there's
+any kind of law of
+
+large numbers about what happens
+to n of t over t as t
+
+gets very large.
+
+And there is such a law, and
+that's the kind of thing that
+
+we want to focus on here.
+
+And that's what we're now
+starting to talk about.
+
+What was it that made us want
+to talk about the strong law
+
+of large numbers instead of the
+weak law of large numbers?
+
+It was really the fact that
+these sample paths converge.
+
+All these other kinds of
+convergence, it's the
+
+distribution function that
+converges, it's some
+
+probability of something
+that converges.
+
+It's always something gross that
+you can look at at every
+
+value of n, and then you can
+find the limit of the
+
+distribution function, or find
+the limit of the mean, or find
+
+the limit of the relative
+frequency, or find the limit
+
+of something else.
+
+When we talk about the strong
+law of large numbers, we are
+
+really talking about
+these sample paths.
+
+And the fact that we could go
+from a convergence theorem
+
+saying that s n to the fourth
+over n to the fourth
+
+approached the limit, this was
+the convergence theorem.
+
+And from that, we could show
+the s sub n over n also
+
+approached the limit, that
+really is the key to why the
+
+strong law of large numbers
+gets used so much, and
+
+particularly gets used
+when we were talking
+
+about renewal processes.
+
+What you will find when we
+study we study renewal
+
+processes is that there's
+a small part of renewal
+
+processes--
+
+there's a small part of the
+theory which really says 80%
+
+of what's important.
+
+And it's almost trivially
+simple, and it's built on the
+
+strong law for renewal
+processes.
+
+Then there's a bunch of other
+things which are not built on
+
+the strong law, they're built
+on the weak law or something
+
+else, which are quite
+tedious, and quite
+
+difficult, and quite messy.
+
+We go through them because
+they get used in a lot of
+
+other places, and they let us
+learn about a lot of things
+
+that are very important.
+
+But they still are
+more difficult.
+
+And they're more difficult
+because we're not talking
+
+about sample paths anymore.
+
+And you're going to see
+that at the end
+
+of the lecture today.
+
+You'll see, I think, what is
+probably the best illustration
+
+of why the strong law
+of large numbers
+
+makes your life simple.
+
+OK.
+
+So we had this fact here.
+
+This theorem is what's going
+to generalize this.
+
+Assume that z sub n and greater
+than or equal to 1,
+
+this is a sequence of
+random variables.
+
+And assume that this sequence of
+random variables converges
+
+to some number, alpha,
+with probability 1.
+
+In other words, you take sample
+paths of this sequence
+
+of a random variables.
+
+And those sample paths, there
+two sets of sample paths.
+
+One set of sample paths
+converged to alpha, and that
+
+has probability 1.
+
+There's another set of sample
+paths, some of them converge
+
+to something else, some of them
+converge to nothing, some
+
+of them don't converge at all.
+
+Well, they converge
+to nothing.
+
+They don't converge at all.
+
+But that set has probability 0,
+so we don't worry about it.
+
+All we're worrying about is this
+good set, which is the
+
+set which converges.
+
+And then what the theorem says
+is if we have a function f of
+
+x, if it's a real-valued
+function of a real variable,
+
+what does that mean?
+
+As an engineer, it means
+it's a function.
+
+When you're an engineer and you
+talk about functions, you
+
+don't talk about things that
+aren't continuous.
+
+You talk about things
+that are continuous.
+
+So all that's saying is it gives
+us a nice, respectable
+
+function of a variable.
+
+It belongs to the national
+academy of real variables that
+
+people like to use.
+
+Then what the theorem says is
+that the sequence of random
+
+variables f of z sub n--
+
+OK, we have a real-valued
+function of a real variable.
+
+It maps, then, sample values
+of z sub n into f of those
+
+sample values.
+
+And because of that, just as
+we've done a dozen times
+
+already when you take a
+real-valued function of a
+
+random variable, you have
+a two-step mapping.
+
+You map from omega into
+z n of omega.
+
+And then you map from z n of
+omega into f of z n of omega.
+
+That's a simple-minded idea.
+
+OK.
+
+Example one of this, suppose
+that f of x is x plus beta.
+
+All this is just a translation,
+simple-minded
+
+function, president
+of the academy.
+
+And supposes that the sequence
+of random variables
+
+converges to alpha.
+
+Then this new set of random
+variable u sub n equals z sub
+
+n plus beta.
+
+The translated version converges
+to alpha plus beta.
+
+Well, you don't even need
+a theorem to see that.
+
+I mean, you can just look at
+it and say, of course.
+
+Example two is the one
+we've already used.
+
+This one you do have to sweat
+over a little bit, but we've
+
+already sweated over it, and
+then we're not going to worry
+
+about it anymore.
+
+If f of x is equal to x to the
+1/4 for x greater than or
+
+equal to 0, and z n, random
+variable, the sequence of
+
+random variables, converges to 0
+with probability 1 and these
+
+random variables are
+non-negative, then f of z n
+
+converges to f of 0.
+
+That's the one that's a little
+less obvious, because if you
+
+look at this function, when x is
+very close to 0, but when x
+
+is equal to 0, it's 0,
+it goes like this.
+
+When x is 1, you're
+up to 1, I guess.
+
+But it really goes up with
+an infinite slope here.
+
+It's still continuous at 0 if
+you're looking only at the
+
+non-negative values.
+
+That's what we use to
+prove the strong
+
+law of large numbers.
+
+None of you complained about
+it last time, so you can't
+
+complain about it now.
+
+It's just part of what this
+theorem is saying.
+
+This is what the theorem says.
+
+I'm just rewriting it
+much more briefly.
+
+Here I'm going to give a "Pf."
+For each omega such that limit
+
+of z n of omega equals alpha,
+we use the result for a
+
+sequence of numbers that says
+the limit of f of z n of
+
+omega, this limit of a set of
+sequence of numbers, is equal
+
+to the function at
+the limit value.
+
+Let me give you a little diagram
+which shows you why
+
+that has to be true.
+
+Suppose you look at
+this function f.
+
+This is f of x.
+
+And what we're doing now is
+we're looking at a1 here.
+
+a1 is going to be f
+of z1 of omega.
+
+a2, I'm just drawing random
+numbers here.
+
+a3, a4, a5, a6, a7.
+
+And then I draw f of a1.
+
+So what I'm saying here, in
+terms of real numbers, is this
+
+quite trivial thing.
+
+If this function is continuous
+at this point, as n gets
+
+large, these numbers get
+compressed into that limiting
+
+value there.
+
+And as these numbers get
+compressed into that limiting
+
+value, these values up here
+get compressed into that
+
+limiting value also.
+
+This is not a proof, but the way
+I construct proofs is not
+
+to look for them someplace in
+a book, but it's to draw a
+
+picture which shows me what the
+idea of the proof is, then
+
+I prove it.
+
+This has an advantage in
+research, because if you ever
+
+want to get a result in
+research which you can
+
+publish, it has to be
+something that you
+
+can't find in a book.
+
+If you do find it in a book
+later, then in fact your
+
+result was not new And you're
+not supposed to publish
+
+results that aren't new.
+
+So the idea of drawing a picture
+and then proving it
+
+from the picture is really
+a very valuable
+
+aid in doing research.
+
+And if you draw this picture,
+then you can easily construct
+
+a proof of the picture.
+
+But I'm not going
+to do it here.
+
+Now, let's go onto renewal
+processes.
+
+Each and inter-renewal
+
+interval, x sub i, is positive.
+
+That was what we said
+in starting to talk
+
+about renewal processes.
+
+Assuming that the expected
+value of x exists, the
+
+expected value of x is then
+strictly greater than 0.
+
+You're going to prove that in
+the homework this time, too.
+
+When I was trying to get this
+lecture ready, I didn't want
+
+to prove anything in detail,
+so I had to follow the
+
+strategy of assigning problems,
+and the problem set
+
+where you would, in fact, prove
+these things, which are
+
+not difficult but
+which require a
+
+little bit of thought.
+
+And since the expected value of
+x is greater than or equal
+
+to 0, the expected value of s1,
+which is expected value of
+
+x, the expected value of x1 plus
+x2, which is s2, and so
+
+forth, all of these quantities
+are greater than 0 also.
+
+And for each finite n, the
+expected value of s sub n over
+
+n is greater than 0 also. so
+we're talking about a whole
+
+bunch of positive quantities.
+
+So this strong law of large
+numbers is then
+
+going to apply here.
+
+The probability of the sample
+paths, s n of omega it over n,
+
+the probability that that sample
+path converges to the
+
+mean of x, that's just 1.
+
+Then I use the theorem on
+the last page about--
+
+It's this theorem.
+
+When I use f of x equals 1/x
+that's continuous at this
+
+positive value.
+
+That's why it's important to
+have a positive value for the
+
+expected value of x.
+
+The expected value of x is
+equal to 0, 1/x is not
+
+continuous at x equals 0, and
+you're in deep trouble.
+
+That's one of the reasons why
+you really want to assume
+
+renewal theory and not allow
+any inter-renewal intervals
+
+that are equal to 0.
+
+It just louses up the whole
+theory, makes things much more
+
+difficult, and you gain
+nothing by it.
+
+So we get this statement then,
+the probability of sample
+
+points such that the limit of
+n over s n of omega is equal
+
+to 1 over x bar.
+
+That limit is equal to 1.
+
+What does that mean?
+
+I look at that and it doesn't
+mean anything to me.
+
+I can't see what it means
+until I draw a picture.
+
+I'm really into pictures
+today.
+
+This was the statement that we
+said the probability of this
+
+set of omega such that the limit
+of n over s n of omega
+
+is equal to 1 over x
+bar is equal to 1.
+
+This is valid whenever you have
+a renewal process for
+
+which x bar exists, namely,
+the expected value of the
+
+magnitude of x exists.
+
+That was one of the assumptions
+we had in here.
+
+And now, this is going
+to imply the
+
+strong law renewal processes.
+
+Here's the picture, which lets
+us interpret what this means
+
+and let's just go
+further with it.
+
+The picture now is you have this
+counting process, which
+
+also amounts to a picture of
+any set of inter-arrival
+
+instance, x1, x2, x3, x4, and
+so forth, and any set of
+
+arrival epochs, s1,
+s2, and so forth.
+
+We look at a particular
+value of t.
+
+And what I'm interested
+in is n of t over t.
+
+I have a theorem about
+n over s n of omega.
+
+That's not what I'm
+interested in.
+
+I'm interested in
+n of t over t.
+
+And this picture shows me what
+the relationship is.
+
+So I start out with a
+given value of t.
+
+For a given value of t, there's
+a well-defined random
+
+variable, which is the number
+of arrivals up to and
+
+including time t.
+
+From n of t, I get a
+well-defined random variable,
+
+which is the arrival epoch of
+the latest arrival less than
+
+or equal to time t.
+
+Now, this is a very funny
+kind of random variable.
+
+I mean, we've talked about
+random variables which are
+
+functions of other
+random variables.
+
+And in a sense, that's
+what this.
+
+But it's a little more
+awful than that.
+
+Because here we have this
+well-defined set of arrival
+
+epochs, and now we're taking a
+particular arrival, which is
+
+determined by this t
+we're looking at.
+
+So t defines n of t, and n of t
+defines s sub n of t, if we
+
+have this entire sample
+function.
+
+So this is well-defined.
+
+We will find as we proceed with
+this that this random
+
+variable, the time of the
+arrival most recently before
+
+t, it's in fact a very, very
+strange random variable.
+
+There are strange things
+associated with it.
+
+When I look at t minus s sub n
+of t, or when I look at the
+
+arrival after t, s sub n of t
+plus 1 minus t, those random
+
+variables are peculiar.
+
+And we're going to explain why
+they are peculiar and use the
+
+strong law for renewal processes
+to look at them in a
+
+kind of a simple way.
+
+But now, the thing we have
+here is if we look at the
+
+slope of b of t, the slope of
+this line here at each value
+
+of t, this slope is n
+of t divided by t.
+
+That's this slope.
+
+This slope here is n of
+t over s sub n of t.
+
+Namely, this is the slope up
+to the point of the arrival
+
+right before t.
+
+This slope is then going
+to decrease as
+
+we move across here.
+
+And at this value here, it's
+going to pop up again.
+
+So we have a family of slopes,
+which is going to look like--
+
+What's it going to do?
+
+I don't know where it's going to
+start out, so I won't even
+
+worry about that.
+
+I'll just start someplace
+here.
+
+It's going to be decreasing.
+
+Then there's going
+to be an arrival.
+
+At that point, it's going to
+increase a little bit.
+
+It's going to be decreasing.
+
+There's another arrival.
+
+So this is s sub n, s sub
+n plus 1, and so forth.
+
+So the slope is slowly
+decreasing.
+
+And then it changes
+discontinuously every time you
+
+have an arrival.
+
+That's the way this behaves.
+
+You start out here, it decreases
+slowly, it jumps up,
+
+then it decreases slowly
+until the next
+
+arrival, and so forth.
+
+So that's the kind of thing
+we're looking at.
+
+But one thing we know is that
+n of t over t, that's the
+
+slope in the middle here, is
+less than or equal to n of t
+
+over s sub n of t.
+
+Why is that?
+
+Well, n of t is equal to n of
+t, but t is greater than or
+
+equal to the time of the
+most recent arrival.
+
+So we have n of t over t is less
+than or equal to n of t
+
+over s sub n of t.
+
+The other thing that's important
+to observe is that
+
+now we want to look at
+what happens as t
+
+gets larger and larger.
+
+And what happens to this
+ratio, n of t over t?
+
+Well, this ratio n of t over t
+is this thing we were looking
+
+at here, which is
+kind of a mess.
+
+It jumps up, it goes down a
+little bit, jumps up, goes
+
+down a little bit, jumps up.
+
+But the set of values that
+it goes through--
+
+the set of values that this goes
+through, namely, the set
+
+right before each
+of these jumps--
+
+is the same set of values
+as n over s sub n.
+
+As I look through this sequence,
+I look at this n of
+
+t over s sub n of t.
+
+That's this point here, and then
+it's this point there.
+
+Anyway, n of t over s sub n of t
+is going to stay constant as
+
+t goes from here
+over to there.
+
+That's the way I've
+drawn the picture.
+
+I start out with any t in
+this interval here.
+
+This slope keeps changing as
+t goes from there to there.
+
+This slope does not change.
+
+This is determined just by which
+particular integer value
+
+of n we're talking about.
+
+So n of t over s sub n of t
+jumps at each value of n.
+
+So this now becomes just the
+sequence of numbers.
+
+And that sequence of numbers
+is the sequence n
+
+divided by s sub b.
+
+Why is that important?
+
+That's the thing we have
+some control over.
+
+That's what appears up here.
+
+So we know how to
+deal with that.
+
+That's what this result about
+convergence added to this
+
+result about functions of
+converging functions tells us.
+
+So redrawing the same figure,
+we've observed that n of t
+
+over t is less than or equal to
+n of t over s sub n of t.
+
+It goes through the same set of
+values as n over s sub n,
+
+and therefore the limit as t
+goes to infinity of n over t
+
+over s sub n of t is the same
+as the limit as n goes to
+
+infinity of n over s sub n.
+
+And that limit, with
+probability
+
+1, is 1 over x bar.
+
+That's the thing that this
+theorem, we just
+
+"pfed" said to us.
+
+There's a bit of a pf in here
+too, because you really ought
+
+to show that as t goes
+to infinity, n
+
+of t goes to infinity.
+
+And that's not hard to do.
+
+It's done in the notes.
+
+You need to do it.
+
+You can almost see intuitively
+that it has to happen.
+
+And in fact, it does
+have to happen.
+
+OK.
+
+So this, in fact, is a limit.
+
+It does exist.
+
+Now, we go on the other y, and
+we look at n of t over t,
+
+which is now greater than or
+equal to n of t over s sub n
+
+of t plus 1.
+
+s sub b of t plus 1 is the
+arrival epoch which is just
+
+larger than t.
+
+Now, n of t over s sub n of t
+plus 1 goes through the same
+
+set of values as n over
+s sub n plus 1.
+
+Namely, each time n increases,
+this goes up by 1.
+
+So the limit as t goes to
+infinity of n of t over s sub
+
+n of t plus 1 is the same as
+the limit as n goes to
+
+infinity of n over the epoch
+right after n of t.
+
+This you can rewrite as n plus
+1 over s sub n plus 1 times n
+
+over n plus 1.
+
+Why do I want to rewrite
+it this way?
+
+Because this quantity
+I have a handle on.
+
+This is the same as the limit
+of n over s sub n.
+
+I know what that limit is.
+
+This quantity, I have an even
+better handle on, because this
+
+n over n plus 1 just moves--
+
+it's something that
+starts out low.
+
+And as n gets bigger, it just
+moves up towards 1.
+
+And therefore, when you look at
+this limit, this has to be
+
+1 over x bar also.
+
+Since n of t over t is between
+these two quantities, they
+
+both have the same limit.
+
+The limit of n of t over t is
+equal to 1 over the expected
+
+value of x.
+
+STUDENT: Professor Gallager?
+
+ROBERT GALLAGER: Yeah?
+
+STUDENT: Excuse me if this is
+a dumb question, but in the
+
+previous slide it said the limit
+as t goes to infinity of
+
+the accounting process n of
+t, would equal infinity.
+
+We've also been talking a lot
+over the last week about the
+
+defectiveness and
+non-defectiveness of these
+
+counting processes.
+
+So we can still find an n that's
+sufficiently high, such
+
+that the probability of n of t
+being greater than that n is
+
+0, so it's not defective.
+
+But I don't know.
+
+How do you--
+
+ROBERT GALLAGER: n of t is
+either a random variable or a
+
+defective random variable
+of each value of t.
+
+And what I'm claiming
+here, which is not--
+
+This is something you
+have to prove.
+
+But what I would like to show is
+that for each value of t, n
+
+of t is not defective.
+
+In other words, these
+arrivals have to
+
+come sometime or other.
+
+OK.
+
+Well, let's backtrack from
+that a little bit.
+
+For n of t to be defective, I
+would have to have an infinite
+
+number of arrivals come in
+in some finite time.
+
+You did a problem in the
+homework where that could
+
+happen, because the x sub i's
+you were looking at were not
+
+identically distributed, so
+that as t increased, the
+
+number of arrivals you had were
+
+increasing very, very rapidly.
+
+Here, that can't happen.
+
+And the reason it can't happen
+is because we've started out
+
+with a renewal process where
+by definition the
+
+inter-arrival intervals all have
+the same distribution.
+
+So the rate of arrivals,
+in a sense, is
+
+staying constant forever.
+
+Now, that's not a proof.
+
+If you look at the notes, the
+notes have a proof of this.
+
+After you go through the proof,
+you say, that's a
+
+little bit tedious.
+
+But you either have to go
+through the tedious proof to
+
+see what is after you go through
+it is obvious, or you
+
+have to say it's obvious,
+which is a
+
+subject to some question.
+
+So yes, it was not a
+stupid question.
+
+It was a very good question.
+
+And in fact, you do have
+to trace that out.
+
+And that's involved here in
+this in what we've done.
+
+I want to talk a little bit
+about the central limit
+
+theorem for renewals.
+
+The notes don't prove
+the central
+
+limit theorem for renewals.
+
+I'm not going to
+prove it here.
+
+All I'm going to do is give you
+an argument why you can
+
+see that it sort of has to be
+true, if you don't look at any
+
+of the weird special cases you
+might want to look at.
+
+So there is a reference given
+in the text for where
+
+you can find it.
+
+I mean, I like to give proofs
+of very important things.
+
+I didn't give a proof of this
+because the amount of work to
+
+prove it was far greater than
+the importance of the result,
+
+which means it's a very, very
+tricky and very difficult
+
+thing to prove, even when you're
+only talking about
+
+things like Bernoulli.
+
+OK.
+
+But here's the picture.
+
+And the picture, I think, will
+make it sort of clear
+
+what's going on.
+
+We're talking now about an
+underlying random variable x.
+
+We assume it has a second
+moment, which we need to make
+
+the central limit
+theorem true.
+
+The probability that s sub n is
+less than or equal to t for
+
+n very large and for the
+difference between t--
+
+Let's look at the
+whole statement.
+
+What it's saying is if you look
+at values of t which are
+
+equal to the mean for s sub n,
+which is n x bar, plus some
+
+quantity alpha times sigma times
+the square root of n,
+
+then as n gets large and t gets
+correspondingly large,
+
+this probability is
+approximately equal to the
+
+normal distribution function.
+
+In other words, what that's
+saying is as I'm looking at
+
+the random variable, s sub n,
+and taking n very, very large.
+
+The expected value of s sub n is
+equal to n times x bar, so
+
+I'm moving way out where this
+number is very, very large.
+
+As n gets larger and larger, n
+increases and x bar increases,
+
+and they increase on a
+slope 1 over x bar.
+
+So this is n, this
+is n over x bar.
+
+The slope is n over n over x
+bar, which is this slope here.
+
+Now, when you look at this
+picture, what it sort of
+
+involves is you can choose
+any n you want.
+
+We will assume the
+x bar is fixed.
+
+You can choose any t
+that you want to.
+
+Let's first hold b fixed and
+look at a third dimension now,
+
+where for this particular
+value of n, I
+
+want to look at the--
+
+And instead of looking at the
+distribution function, let me
+
+look at a probability density,
+which makes the argument
+
+easier to see.
+
+As I look at this for a
+particular value of n, what
+
+I'm going to get is b x bar.
+
+This will be the probability
+density of s sub n of x.
+
+And that's going to look like,
+when n is large enough, it's
+
+going to look like a Gaussian
+probability density.
+
+And the mean of that Gaussian
+probability density will be
+
+mean n x bar.
+
+And the variance of this
+probability density, now, is
+
+going to be the square root
+of n times sigma.
+
+What else do I need?
+
+I guess that's it.
+
+This is the standard
+deviation.
+
+OK.
+
+So you can visualize
+what happens, now.
+
+As you start letting n get
+bigger and bigger, you have
+
+this Gaussian density
+for each value of n.
+
+Think of drawing this again for
+some larger value of n.
+
+The mean will shift out
+corresponding to a linear
+
+increase in n.
+
+The standard deviation will
+shift out, but only according
+
+to the square root of n.
+
+So what's happening is the same
+thing that always happens
+
+in the central limit theorem, is
+that as n gets large, this
+
+density here is moving out with
+n, and it's getting wider
+
+with the square root of n.
+
+So it's getting wider much
+more slowly than
+
+it's getting bigger.
+
+Than It's getting wider
+much more slowly
+
+than it's moving out.
+
+So if I try to look at what
+happens, what's the
+
+probability that n of t is
+greater than or equal to n?
+
+I now want to look at the same
+curve here, but instead of
+
+looking at it here for a fixed
+value of n, I want to look at
+
+the probability density out here
+at some fixed value of t.
+
+So what's going to happen?
+
+The probability density here is
+going to be the probability
+
+density that we we're talking
+about here, but for
+
+this value up here.
+
+The probability density here is
+going to correspond to the
+
+probability density here, and
+so forth as we move down.
+
+So what's happening to this
+probability density is that as
+
+we move up, the standard
+deviation is getting
+
+a little bit wider.
+
+As we move down, standard
+deviation is getting a little
+
+bit smaller.
+
+And as n gets bigger and bigger,
+this shouldn't make
+
+any difference.
+
+So therefore, if you buy for the
+moment the fact that this
+
+doesn't make any difference,
+you have a Gaussian density
+
+going this way, you
+have a Gaussian
+
+density centered here.
+
+Up here you have a Gaussian
+density centered
+
+here at this point.
+
+And all those Gaussian densities
+are the same, which
+
+means you have a Gaussian
+density going this way, which
+
+is centered here.
+
+Here's the upper tail of
+that Gaussian density.
+
+Here's the lower tail of
+that Gaussian density.
+
+Now, to put that analytically,
+it's saying that the
+
+probability that n of t is
+greater than or equal to n,
+
+that's the same as the
+probability that s sub n is
+
+less than or equal to t.
+
+So that is the distribution
+function of s sub n less than
+
+or equal to t.
+
+When we go from n to t, what we
+find is that n is equal to
+
+t over x bar--
+
+that's the mean we have here--
+
+minus alpha times sigma
+times the square
+
+root of n over x bar.
+
+In other words, what
+is happening is
+
+the following thing.
+
+We have a density going this
+way, which has variance, which
+
+has standard deviation
+proportional to the
+
+square root of n.
+
+When we look at that same
+density going this way,
+
+ignoring the fact that this
+distance here that we're
+
+looking at is very small, this
+density here is going to be
+
+compressed by this slope here.
+
+In other words, what we have is
+the probability that n of t
+
+greater than or equal to
+n is approximately
+
+equal to phi of alpha.
+
+n is equal to t over x bar minus
+this alpha here times
+
+sigma times the square
+root of n over x bar.
+
+Nasty equation, because
+we have an n on both
+
+sides of the equation.
+
+So we will try to solve
+this equation.
+
+And this is approximately equal
+to t over x bar minus
+
+alpha times sigma times the
+square root of n over x bar
+
+times the square root of x.
+
+Why is that true?
+
+Because it's approximately equal
+to the square root--
+
+Well, it is equal to the square
+root of t over x bar,
+
+which is this quantity here.
+
+And since this quantity here
+is small relative to this
+
+quantity here, when you solve
+this equation for t, you're
+
+going to ignore this term
+and just get this small
+
+correction term here.
+
+That's exactly the same thing
+that I said when I was looking
+
+at this graphically, when I was
+saying that if you look at
+
+the density at larger values
+than n, you get a standard
+
+deviation which is larger.
+
+When you look at a smaller
+value of n, you get is a
+
+standard deviation
+which is smaller.
+
+Which means that when you look
+at it along here, you're going
+
+to get what looks like a
+Gaussian density, except the
+
+standard deviation is a little
+expanded up there and little
+
+shrunk down here.
+
+But that doesn't make any
+difference as n gets very
+
+large, because that shrinking
+factor is proportional to the
+
+square root of n
+rather than n.
+
+Now beyond that, you just
+have to look at this
+
+and live with it.
+
+Or else you have to look up a
+proof of it, which I don't
+
+particularly recommend.
+
+So this is the central limit
+theorem for renewal processes.
+
+n of t tends to Gaussian with
+a mean t over x bar and a
+
+standard deviation sigma times
+square root of t over x bar
+
+times 1 over square root of x.
+
+And now you sort of understand
+why that is, I hope.
+
+OK.
+
+Next thing I want to
+go to is the time
+
+average residual life.
+
+You were probably somewhat
+bothered when you saw with
+
+Poisson processes that if you
+arrived to wait for a bus, the
+
+expected time between buses
+turned out to be twice the
+
+expected time from one
+bus to the next.
+
+Namely, whenever you arrive to
+look for a bus, the time until
+
+the next bus was an exponential
+random variable.
+
+The time back to the last bus,
+if you're far enough in, was
+
+an exponential random
+variable.
+
+The sum of two, the expected
+value from the time before
+
+until the time later, was
+twice what it should be.
+
+And we went through some kind
+of song and dance saying
+
+that's because you come in at a
+given point and you're more
+
+likely to come in during one of
+these longer inter-arrival
+
+periods than you are to
+come in during a short
+
+inter-arrival.
+
+And it has to be a song and a
+dance, and it didn't really
+
+explain anything very well,
+because we were locked into
+
+the exponential density.
+
+Now we have an advantage.
+
+We can explain things like that,
+because we can look at
+
+any old distribution we want to
+look at, and that will let
+
+us see what this thing which
+is called the paradox of
+
+residual life really
+amounts to.
+
+It's what tells us why we
+sometimes have to wait a very
+
+much longer time than we think
+we should if we understand
+
+some particular kind
+of process.
+
+So here's where we're
+going to start.
+
+What happened?
+
+I lost a slide.
+
+Ah.
+
+There we are.
+
+Residual life, y of t, of a
+renewal process at times t, is
+
+the remaining time until
+the next renewal.
+
+Namely, we have this counting
+process for any
+
+given renewal process.
+
+We have this random variable,
+which is the time of the first
+
+arrival after t, which is
+s sub n of t plus 1.
+
+And that difference
+is the duration
+
+until the next arrival.
+
+Starting at time t, there's a
+random variable, which is the
+
+time from t until the next
+arrival after t.
+
+That is specifically the arrival
+epoch of the arrival
+
+after time t, which is s sub n
+of t plus 1 minus the number
+
+of arrivals that have occurred
+up until time t.
+
+You take any sample path of this
+renewal process, and y of
+
+t will have some value
+in that sample path.
+
+As I say here, this is how long
+you have to wait for a
+
+bus if the bus arrivals were
+renewal processes.
+
+STUDENT: Should it also be
+s n t, where there is
+
+minus sign on that?
+
+ROBERT GALLAGER: No, because
+just by definition, a residual
+
+life, the residual life starting
+at time t is the time
+
+for the next arrival.
+
+There's also something called
+age that we'll talk about
+
+later, which is how long is it
+back to the last arrival.
+
+In other words, that age is
+the age of the particular
+
+inter-arrival interval that
+you happen to be in.
+
+Yes?
+
+STUDENT: It should be s sub n of
+t plus 1 minus t instead of
+
+minus N, because it's
+the time from t to--
+
+ROBERT GALLAGER: Yes,
+I agree with you.
+
+There's something wrong there.
+
+I'm sorry.
+
+That I should be s sub n
+of t plus 1 minus t.
+
+Good.
+
+That's what happens
+when you make up
+
+slides too late at night.
+
+And as I said, we'll talk about
+something called age,
+
+which is a of t is equal to
+t minus s sub n of t.
+
+So this is a random variable
+defined at every value of t.
+
+What we'd like to look at now is
+what does that look like as
+
+a sample function as
+a sample path.
+
+The residual life is
+a function of t--
+
+Nicest way to view residual
+life is that it's a reward
+
+function on a renewal process.
+
+A renewal process just
+consists of these--
+
+Well, you can look
+at in three ways.
+
+It's a sequence of inter-arrival
+times, all
+
+identically distributed.
+
+It's the sequence of
+arrival epochs.
+
+Or it's this unaccountably
+infinite number of random
+
+variables, n of t.
+
+Given that process, you can
+define whatever kind of reward
+
+you want to, which is the same
+kind of reward we were talking
+
+about with Markov chains, where
+you just define some
+
+kind of reward that you achieve
+at each value of t.
+
+But that reward--
+
+we'll talk about reward
+on renewal processes--
+
+is restricted to be a reward
+which is a function only of
+
+the particular inter-arrival
+interval that you
+
+happen to be in.
+
+Now, I don't want to talk about
+that too much right now,
+
+because it is easier to
+understand residual life than
+
+it is to understand the general
+idea of these renewal
+
+reward functions.
+
+So we'll just talk about
+residual life to start with,
+
+and then get back to the
+more general thing.
+
+We would like, sometimes, to
+look at the time-average value
+
+of residual life, which is you
+take the residual life at time
+
+tau, you integrate it at the
+time t, and then you
+
+divide by time t.
+
+This is the time average
+residual life from
+
+0 up to time t.
+
+We will now ask the question,
+does this have a limit as t
+
+goes to infinity?
+
+And we will see that,
+in fact, it does.
+
+So let's draw a picture.
+
+Here is a picture of some
+arbitrary renewal process.
+
+I've given the inter-arrival
+times, x1, x2, so forth, the
+
+arrival epochs, s1, s2,
+so forth, and n of t.
+
+Now, let's ask, for this
+particular sample function
+
+what is the residual life?
+
+Namely, at each value of t,
+what's the time until the next
+
+arrival occurs?
+
+Well, this is a perfectly
+specific function of this
+
+individual sample
+function here.
+
+This is a sample function, now
+in the interval from 0 to s1,
+
+the time until the
+next arrival.
+
+It starts out as x1,
+drops down to 0.
+
+Now, don't ask the question,
+what is my residual life if I
+
+don't know what the rest of
+the sample function is?
+
+That's not the question
+we're asking here.
+
+The question we're asking is
+somebody gives you a picture
+
+of this entire sample path, and
+you want to find out, for
+
+that particular picture, what is
+the residual life at every
+
+value of t.
+
+And for a value of t very close
+to 0, the residual life
+
+is the time up to s1.
+
+So it's decaying linearly
+down to 0 at s1.
+
+At s1, it jumps up immediately
+to x2, which is the time from
+
+any time after s1 to s2.
+
+I have a little circle
+down there.
+
+And from x2, it decays
+down to 0.
+
+So we have a whole bunch
+here of triangles.
+
+So for any sample function, we
+have this sample function of
+
+residual life, which is, in
+fact, just decaying triangles.
+
+It's nothing more than that.
+
+For every t in here, the amount
+of time until the next
+
+arrival is simply s2 minus t,
+which is that value there.
+
+This decay is with slope minus
+1, so there's nothing to
+
+finding out what this
+is if you know this.
+
+This is a very simple
+function of that.
+
+So a residual-life sample
+function is a sequence of
+
+isosceles triangles,
+one starting at
+
+each arrival epoch.
+
+The time average for a given
+sample function is, how do I
+
+find the time average starting
+from 0 going up to
+
+some large value t?
+
+Well, I simply integrate these
+isosceles triangles.
+
+And I can integrate these, and
+you can integrate these, and
+
+anybody who's had a high school
+education can integrate
+
+these, because it's just the
+sum of the areas of all of
+
+these triangles.
+
+So this area here is 1 over 2
+times x sub i squared, then we
+
+divide by t.
+
+So it's 1 over t times
+this integral.
+
+This integral here is the area
+of the first triangle plus the
+
+area of the second triangle plus
+1/3 plus 1/4, plus this
+
+little runt thing at the end,
+which is, if I pick t in here,
+
+this little runt thing is
+going to be that little
+
+trapezoid, which we could figure
+out if we wanted to,
+
+but we don't want to.
+
+The main thing is we get this
+sum of squares here, there
+
+that's easy enough
+to deal with.
+
+So this is what we found here.
+
+It is easier to bound this
+quantity, instead of having
+
+that little runt at the end, to
+drop the runt to this side
+
+and to extend the runt
+on this side to the
+
+entire isosceles triangles.
+
+So this time average residual
+life at the time t is between
+
+this and this.
+
+The limit of this as t goes
+to infinity is what?
+
+Well, it's just a limit
+of a sequence
+
+of IID random variables.
+
+No, excuse me.
+
+We are dealing here with
+sample function.
+
+So what we have is a limit
+as t goes to infinity.
+
+And I want to rewrite this
+here as x sub n squared
+
+divided by n of t times
+n has to t over 2t.
+
+I want to separate it, and
+just divide it and
+
+multiply by n of t.
+
+I want to look at this term.
+
+What happens to this term
+as t gets large?
+
+Well, as t gets large,
+n of t gets large.
+
+This quantity here just goes
+through the same set of values
+
+as the sum up to some finite
+limit divided by that limit
+
+goes through.
+
+So the limit of this quantity
+here is just the expected
+
+value of x squared.
+
+What is this quantity here?
+
+Well, this is what the renewal
+theorem deals with.
+
+This limit here is 1 over 2
+times the expected value of x.
+
+That's what we showed before.
+
+This goes to a limit, this goes
+to a limit, the whole
+
+thing goes to a limit.
+
+And it goes to limit
+with probability 1
+
+for all sample functions.
+
+So this time average residual
+life has the expected value of
+
+x squared divided by 2 times
+the expected value of x.
+
+Now if you look at this, you'll
+see that what we've
+
+done is something which is very
+simple, because of the
+
+fact we have renewal theory
+at this point.
+
+If we had to look at the
+probabilities of where all of
+
+these arrival epochs occur,
+and then deal with all of
+
+those random variables, and
+go through some enormously
+
+complex calculation to find
+the expected value of this
+
+residual life at the time
+t, it would be an
+
+incredibly hard problem.
+
+But looking at it in terms of
+sample paths for random
+
+variables, it's an incredibly
+simple problem.
+
+Want to look at one example
+here, because when we look at
+
+this, well, first thing
+is just a couple of
+
+examples to work out.
+
+The time average residual life
+has expected value of x
+
+squared over 2 times the
+expected value of x.
+
+If x is almost deterministic,
+then the expected value of x
+
+squared is just a square of
+the expected value of x.
+
+So we wind up with the expected
+value of x over 2,
+
+which is sort of what you would
+expect if you look from
+
+time 0 to time infinity, and
+these arrivals come along
+
+regularly, then the expected
+time you have to wait for the
+
+next arrival varies
+from 0 up to x.
+
+And the average of it is x/2.
+
+So no problem there.
+
+If x is exponential, we've
+already found out that the
+
+expected time we have to wait
+until the next arrival is the
+
+expected value of x, because
+these arrivals are memoryless.
+
+So I start looking at this
+Poisson process at a given
+
+value of t, and the time until
+the next arrival is
+
+exponential, and it's the same
+as the expected time from one
+
+arrival to the next arrival.
+
+So we have that quantity
+there, which
+
+looks a little strange.
+
+This one, this is a very
+peculiar random variable.
+
+But this really explains what's
+going on with this kind
+
+of paradoxical thing, which we
+found with a Poisson process,
+
+where if you arrive to wait for
+a bus, you're waiting time
+
+is not any less because of the
+fact that you've just arrived
+
+between two arrivals, and it
+ought to be the same distance
+
+back to the last one at a
+distance of first one.
+
+That was always a little
+surprising.
+
+This, I think, explains
+what's going on
+
+better than most things.
+
+Look at a binary random
+variable, x, where the
+
+probability that x is equal to
+epsilon is 1 minus epsilon,
+
+and the probability that
+x is equal to 1
+
+over epsilon is epsilon.
+
+And think of epsilon as
+being very large.
+
+So what happens?
+
+You got a whole bunch of little,
+tiny inter-renewal
+
+intervals, which are
+epsilon apart.
+
+And then with very small
+probability, you get an
+
+enormous one.
+
+And you wait for 1
+over epsilon for
+
+that one to be finished.
+
+Then you've got a bunch of
+little ones which are all
+
+epsilon apart.
+
+Then you get an enormous one,
+which is 1 over epsilon long.
+
+And now you can see perfectly
+well that if you arrive to
+
+wait for a bus and the buses are
+distributed this way, this
+
+is sort of what happens when you
+have a bus system which is
+
+perfectly regular but
+subject to failures.
+
+Whenever you have a failure,
+you have an
+
+incredibly long wait.
+
+Otherwise, you have
+very small waits.
+
+So what happens here?
+
+The duration of this whole
+interval here of these little,
+
+tiny inter-arrival times, the
+distance between failure in a
+
+sense, is 1 minus epsilon,
+as it turns out.
+
+It's very close to 1.
+
+This distance here is
+1 over epsilon.
+
+And this quantity here,
+if you work it out--
+
+Let's see.
+
+What is it?
+
+We take this distribution here,
+we look for the expected
+
+value of x squared.
+
+Let's see.
+
+1 over epsilon squared times
+epsilon, which is 1 over
+
+epsilon plus 1 minus epsilon
+times something.
+
+So the expected time that you
+have to wait if you arrive
+
+somewhere along here is
+1 over 2 epsilon.
+
+If epsilon is very small, you
+have a very, very long waiting
+
+time because of these very long
+distributions in here.
+
+You normally don't tend to
+arrive in any of these periods
+
+or any of these periods.
+
+But however you want to
+interpret it, this theorem
+
+about renewals tells you
+precisely that the time
+
+average residual life
+is, in fact, this
+
+quantity 1 over 2 epsilon.
+
+That's this paradox
+of residual life.
+
+Your residual life is much
+larger than it looks like it
+
+ought to be, because it's not
+by any means the same as the
+
+expected interval between
+successive arrivals, which in
+
+this case is very small.
+
+OK I think I'll stop there.
+
+And we will talk more about
+this next time.
\ No newline at end of file
diff --git a/Qs4G9ynralk.txt b/Qs4G9ynralk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8b1c5dd27b3f2f405b65f10937dc3dfc81ac765a
--- /dev/null
+++ b/Qs4G9ynralk.txt
@@ -0,0 +1,1459 @@
+align:start position:0%
+ 
+hello open course Weare Learners this is
+
+ align:start position:0%
+hello open course Weare Learners this is
+ 
+
+ align:start position:0%
+hello open course Weare Learners this is
+Professor cber talking to you and I just
+
+ align:start position:0%
+Professor cber talking to you and I just
+ 
+
+ align:start position:0%
+Professor cber talking to you and I just
+wanted to say a little bit about why the
+
+ align:start position:0%
+wanted to say a little bit about why the
+ 
+
+ align:start position:0%
+wanted to say a little bit about why the
+next two classes are not to be found um
+
+ align:start position:0%
+next two classes are not to be found um
+ 
+
+ align:start position:0%
+next two classes are not to be found um
+on this site MIT and the music
+
+ align:start position:0%
+on this site MIT and the music
+ 
+
+ align:start position:0%
+on this site MIT and the music
+department was very fortunate to be able
+
+ align:start position:0%
+department was very fortunate to be able
+ 
+
+ align:start position:0%
+department was very fortunate to be able
+to hire a new professor in computation
+
+ align:start position:0%
+to hire a new professor in computation
+ 
+
+ align:start position:0%
+to hire a new professor in computation
+music that semester and one of the
+
+ align:start position:0%
+music that semester and one of the
+ 
+
+ align:start position:0%
+music that semester and one of the
+things that we value as a department is
+
+ align:start position:0%
+things that we value as a department is
+ 
+
+ align:start position:0%
+things that we value as a department is
+people's ability to be good teachers so
+
+ align:start position:0%
+people's ability to be good teachers so
+ 
+
+ align:start position:0%
+people's ability to be good teachers so
+as part of their interview U the
+
+ align:start position:0%
+as part of their interview U the
+ 
+
+ align:start position:0%
+as part of their interview U the
+candidates came and took over one of the
+
+ align:start position:0%
+candidates came and took over one of the
+ 
+
+ align:start position:0%
+candidates came and took over one of the
+classes to uh teach the content of the
+
+ align:start position:0%
+classes to uh teach the content of the
+ 
+
+ align:start position:0%
+classes to uh teach the content of the
+class and a little bit of their
+
+ align:start position:0%
+class and a little bit of their
+ 
+
+ align:start position:0%
+class and a little bit of their
+Specialties too and two of those classes
+
+ align:start position:0%
+Specialties too and two of those classes
+ 
+
+ align:start position:0%
+Specialties too and two of those classes
+were um that were used were this class
+
+ align:start position:0%
+were um that were used were this class
+ 
+
+ align:start position:0%
+were um that were used were this class
+21 M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+383 both of the Cates I can say did
+
+ align:start position:0%
+383 both of the Cates I can say did
+ 
+
+ align:start position:0%
+383 both of the Cates I can say did
+amazing work and I wish I could share
+
+ align:start position:0%
+amazing work and I wish I could share
+ 
+
+ align:start position:0%
+amazing work and I wish I could share
+them their videos with you but we have a
+
+ align:start position:0%
+them their videos with you but we have a
+ 
+
+ align:start position:0%
+them their videos with you but we have a
+feeling that it's already stressful
+
+ align:start position:0%
+feeling that it's already stressful
+ 
+
+ align:start position:0%
+feeling that it's already stressful
+enough to be doing a job interview and
+
+ align:start position:0%
+enough to be doing a job interview and
+ 
+
+ align:start position:0%
+enough to be doing a job interview and
+to have your teaching being evaluated by
+
+ align:start position:0%
+to have your teaching being evaluated by
+ 
+
+ align:start position:0%
+to have your teaching being evaluated by
+people in the room uh and then to know
+
+ align:start position:0%
+people in the room uh and then to know
+ 
+
+ align:start position:0%
+people in the room uh and then to know
+that whatever things you did in an
+
+ align:start position:0%
+that whatever things you did in an
+ 
+
+ align:start position:0%
+that whatever things you did in an
+unfamiliar classroom with unfamiliar
+
+ align:start position:0%
+unfamiliar classroom with unfamiliar
+ 
+
+ align:start position:0%
+unfamiliar classroom with unfamiliar
+students would also be put out online uh
+
+ align:start position:0%
+students would also be put out online uh
+ 
+
+ align:start position:0%
+students would also be put out online uh
+it's just a little bit too much so these
+
+ align:start position:0%
+it's just a little bit too much so these
+ 
+
+ align:start position:0%
+it's just a little bit too much so these
+too ask too much to ask so these videos
+
+ align:start position:0%
+too ask too much to ask so these videos
+ 
+
+ align:start position:0%
+too ask too much to ask so these videos
+are not available I want to say a little
+
+ align:start position:0%
+are not available I want to say a little
+ 
+
+ align:start position:0%
+are not available I want to say a little
+bit though what was in each of
+
+ align:start position:0%
+bit though what was in each of
+ 
+
+ align:start position:0%
+bit though what was in each of
+them the first class was the
+
+ align:start position:0%
+them the first class was the
+ 
+
+ align:start position:0%
+them the first class was the
+continuation of our series on music
+
+ align:start position:0%
+continuation of our series on music
+ 
+
+ align:start position:0%
+continuation of our series on music
+cognition and computation and how
+
+ align:start position:0%
+cognition and computation and how
+ 
+
+ align:start position:0%
+cognition and computation and how
+computers can Aid the process of
+
+ align:start position:0%
+computers can Aid the process of
+ 
+
+ align:start position:0%
+computers can Aid the process of
+understanding how the brain processes
+
+ align:start position:0%
+understanding how the brain processes
+ 
+
+ align:start position:0%
+understanding how the brain processes
+music and also how historically and I
+
+ align:start position:0%
+music and also how historically and I
+ 
+
+ align:start position:0%
+music and also how historically and I
+think in the
+
+ align:start position:0%
+think in the
+ 
+
+ align:start position:0%
+think in the
+future uh insights from music cognition
+
+ align:start position:0%
+future uh insights from music cognition
+ 
+
+ align:start position:0%
+future uh insights from music cognition
+have improved the things that we do on
+
+ align:start position:0%
+have improved the things that we do on
+ 
+
+ align:start position:0%
+have improved the things that we do on
+the computer uh the most important uh
+
+ align:start position:0%
+the computer uh the most important uh
+ 
+
+ align:start position:0%
+the computer uh the most important uh
+example of this is Carol Crum hansel's
+
+ align:start position:0%
+example of this is Carol Crum hansel's
+ 
+
+ align:start position:0%
+example of this is Carol Crum hansel's
+um probe
+
+ align:start position:0%
+um probe
+ 
+
+ align:start position:0%
+um probe
+tone uh experiments uh in understanding
+
+ align:start position:0%
+tone uh experiments uh in understanding
+ 
+
+ align:start position:0%
+tone uh experiments uh in understanding
+musical expectation in scales and keys
+
+ align:start position:0%
+musical expectation in scales and keys
+ 
+
+ align:start position:0%
+musical expectation in scales and keys
+and these experiments which helped you
+
+ align:start position:0%
+and these experiments which helped you
+ 
+
+ align:start position:0%
+and these experiments which helped you
+understand how each note plays in our
+
+ align:start position:0%
+understand how each note plays in our
+ 
+
+ align:start position:0%
+understand how each note plays in our
+ability to understand what key we're in
+
+ align:start position:0%
+ability to understand what key we're in
+ 
+
+ align:start position:0%
+ability to understand what key we're in
+at this point underlies a quite a number
+
+ align:start position:0%
+at this point underlies a quite a number
+ 
+
+ align:start position:0%
+at this point underlies a quite a number
+of algorithms being used today by
+
+ align:start position:0%
+of algorithms being used today by
+ 
+
+ align:start position:0%
+of algorithms being used today by
+computers to automatically detect the
+
+ align:start position:0%
+computers to automatically detect the
+ 
+
+ align:start position:0%
+computers to automatically detect the
+keys of compositions and this includes
+
+ align:start position:0%
+keys of compositions and this includes
+ 
+
+ align:start position:0%
+keys of compositions and this includes
+music 21's default analyze key method
+
+ align:start position:0%
+music 21's default analyze key method
+ 
+
+ align:start position:0%
+music 21's default analyze key method
+and this is why the assignments on
+
+ align:start position:0%
+and this is why the assignments on
+ 
+
+ align:start position:0%
+and this is why the assignments on
+understanding uh key
+
+ align:start position:0%
+understanding uh key
+ 
+
+ align:start position:0%
+understanding uh key
+analysis went hand inand with the
+
+ align:start position:0%
+analysis went hand inand with the
+ 
+
+ align:start position:0%
+analysis went hand inand with the
+section on cognition
+
+ align:start position:0%
+section on cognition
+ 
+
+ align:start position:0%
+section on cognition
+the lecture also covered and gave the
+
+ align:start position:0%
+the lecture also covered and gave the
+ 
+
+ align:start position:0%
+the lecture also covered and gave the
+opportunity to discuss some of the
+
+ align:start position:0%
+opportunity to discuss some of the
+ 
+
+ align:start position:0%
+opportunity to discuss some of the
+experiments reported by David hon in his
+
+ align:start position:0%
+experiments reported by David hon in his
+ 
+
+ align:start position:0%
+experiments reported by David hon in his
+book sweet anticipation of which the
+
+ align:start position:0%
+book sweet anticipation of which the
+ 
+
+ align:start position:0%
+book sweet anticipation of which the
+students were assigned to do
+
+ align:start position:0%
+students were assigned to do
+ 
+
+ align:start position:0%
+students were assigned to do
+readings I would encourage as a
+
+ align:start position:0%
+readings I would encourage as a
+ 
+
+ align:start position:0%
+readings I would encourage as a
+substitute for the content of this
+
+ align:start position:0%
+substitute for the content of this
+ 
+
+ align:start position:0%
+substitute for the content of this
+lecture for you to look deeply at this
+
+ align:start position:0%
+lecture for you to look deeply at this
+ 
+
+ align:start position:0%
+lecture for you to look deeply at this
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+by a prominent U music cognition and
+
+ align:start position:0%
+by a prominent U music cognition and
+ 
+
+ align:start position:0%
+by a prominent U music cognition and
+expert and also one of the Breakthrough
+
+ align:start position:0%
+expert and also one of the Breakthrough
+ 
+
+ align:start position:0%
+expert and also one of the Breakthrough
+founders of our field of computational
+
+ align:start position:0%
+founders of our field of computational
+ 
+
+ align:start position:0%
+founders of our field of computational
+Music Theory musicology David
+
+ align:start position:0%
+Music Theory musicology David
+ 
+
+ align:start position:0%
+Music Theory musicology David
+hiron doing so I think would give a good
+
+ align:start position:0%
+hiron doing so I think would give a good
+ 
+
+ align:start position:0%
+hiron doing so I think would give a good
+sense of the majority of what was
+
+ align:start position:0%
+sense of the majority of what was
+ 
+
+ align:start position:0%
+sense of the majority of what was
+contained in the
+
+ align:start position:0%
+contained in the
+ 
+
+ align:start position:0%
+contained in the
+lecture beyond what uh the candidate
+
+ align:start position:0%
+lecture beyond what uh the candidate
+ 
+
+ align:start position:0%
+lecture beyond what uh the candidate
+spoke about her own particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expertise the second guest lecturer
+
+ align:start position:0%
+expertise the second guest lecturer
+ 
+
+ align:start position:0%
+expertise the second guest lecturer
+covered the topic of the history of
+
+ align:start position:0%
+covered the topic of the history of
+ 
+
+ align:start position:0%
+covered the topic of the history of
+algorithmic composition from its
+
+ align:start position:0%
+algorithmic composition from its
+ 
+
+ align:start position:0%
+algorithmic composition from its
+Beginnings even before the computer
+
+ align:start position:0%
+Beginnings even before the computer
+ 
+
+ align:start position:0%
+Beginnings even before the computer
+until today and this lecture
+
+ align:start position:0%
+until today and this lecture
+ 
+
+ align:start position:0%
+until today and this lecture
+covered the main reading for this week
+
+ align:start position:0%
+covered the main reading for this week
+ 
+
+ align:start position:0%
+covered the main reading for this week
+which is on the iliac
+
+ align:start position:0%
+which is on the iliac
+ 
+
+ align:start position:0%
+which is on the iliac
+Suite uh the one of the first pieces to
+
+ align:start position:0%
+Suite uh the one of the first pieces to
+ 
+
+ align:start position:0%
+Suite uh the one of the first pieces to
+be composed by computers using
+
+ align:start position:0%
+be composed by computers using
+ 
+
+ align:start position:0%
+be composed by computers using
+algorithms and to generate notes and
+
+ align:start position:0%
+algorithms and to generate notes and
+ 
+
+ align:start position:0%
+algorithms and to generate notes and
+continuing up till to today with
+
+ align:start position:0%
+continuing up till to today with
+ 
+
+ align:start position:0%
+continuing up till to today with
+advances in AI such as the music
+
+ align:start position:0%
+advances in AI such as the music
+ 
+
+ align:start position:0%
+advances in AI such as the music
+Transformer by Anna Hong at Google and
+
+ align:start position:0%
+Transformer by Anna Hong at Google and
+ 
+
+ align:start position:0%
+Transformer by Anna Hong at Google and
+other uh other new developments one of
+
+ align:start position:0%
+other uh other new developments one of
+ 
+
+ align:start position:0%
+other uh other new developments one of
+the reasons why it's so important to
+
+ align:start position:0%
+the reasons why it's so important to
+ 
+
+ align:start position:0%
+the reasons why it's so important to
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+at music algorithmic music composition
+
+ align:start position:0%
+at music algorithmic music composition
+ 
+
+ align:start position:0%
+at music algorithmic music composition
+in sort of a broader historical scope is
+
+ align:start position:0%
+in sort of a broader historical scope is
+ 
+
+ align:start position:0%
+in sort of a broader historical scope is
+it's too easy to get hung up on the
+
+ align:start position:0%
+it's too easy to get hung up on the
+ 
+
+ align:start position:0%
+it's too easy to get hung up on the
+particular problem that we have today
+
+ align:start position:0%
+particular problem that we have today
+ 
+
+ align:start position:0%
+particular problem that we have today
+where we're getting closer and closer to
+
+ align:start position:0%
+where we're getting closer and closer to
+ 
+
+ align:start position:0%
+where we're getting closer and closer to
+having the computer produce musical
+
+ align:start position:0%
+having the computer produce musical
+ 
+
+ align:start position:0%
+having the computer produce musical
+scores that sound like other
+
+ align:start position:0%
+scores that sound like other
+ 
+
+ align:start position:0%
+scores that sound like other
+compositions like by particular
+
+ align:start position:0%
+compositions like by particular
+ 
+
+ align:start position:0%
+compositions like by particular
+composers and to work on that problem
+
+ align:start position:0%
+composers and to work on that problem
+ 
+
+ align:start position:0%
+composers and to work on that problem
+without asking well why why should we
+
+ align:start position:0%
+without asking well why why should we
+ 
+
+ align:start position:0%
+without asking well why why should we
+care why do we want the computer to
+
+ align:start position:0%
+care why do we want the computer to
+ 
+
+ align:start position:0%
+care why do we want the computer to
+compose a new piece in the style of
+
+ align:start position:0%
+compose a new piece in the style of
+ 
+
+ align:start position:0%
+compose a new piece in the style of
+Johan Sebastian Bach unless by chance
+
+ align:start position:0%
+Johan Sebastian Bach unless by chance
+ 
+
+ align:start position:0%
+Johan Sebastian Bach unless by chance
+you've already heard every piece by Bach
+
+ align:start position:0%
+you've already heard every piece by Bach
+ 
+
+ align:start position:0%
+you've already heard every piece by Bach
+and you're just bored and you need more
+
+ align:start position:0%
+and you're just bored and you need more
+ 
+
+ align:start position:0%
+and you're just bored and you need more
+which most of us haven't explored what's
+
+ align:start position:0%
+which most of us haven't explored what's
+ 
+
+ align:start position:0%
+which most of us haven't explored what's
+actually out
+
+ align:start position:0%
+actually out
+ 
+
+ align:start position:0%
+actually out
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+instead by looking back at the earliest
+
+ align:start position:0%
+instead by looking back at the earliest
+ 
+
+ align:start position:0%
+instead by looking back at the earliest
+history when having a computer actually
+
+ align:start position:0%
+history when having a computer actually
+ 
+
+ align:start position:0%
+history when having a computer actually
+write music at that level of
+
+ align:start position:0%
+write music at that level of
+ 
+
+ align:start position:0%
+write music at that level of
+sophistication was so far from being
+
+ align:start position:0%
+sophistication was so far from being
+ 
+
+ align:start position:0%
+sophistication was so far from being
+possible and looking at what people
+
+ align:start position:0%
+possible and looking at what people
+ 
+
+ align:start position:0%
+possible and looking at what people
+wanted to do with the computer it helps
+
+ align:start position:0%
+wanted to do with the computer it helps
+ 
+
+ align:start position:0%
+wanted to do with the computer it helps
+to answer questions how can the computer
+
+ align:start position:0%
+to answer questions how can the computer
+ 
+
+ align:start position:0%
+to answer questions how can the computer
+be used to to come up with ideas or take
+
+ align:start position:0%
+be used to to come up with ideas or take
+ 
+
+ align:start position:0%
+be used to to come up with ideas or take
+ideas that I have that will take too
+
+ align:start position:0%
+ideas that I have that will take too
+ 
+
+ align:start position:0%
+ideas that I have that will take too
+long for me to generate on my own and
+
+ align:start position:0%
+long for me to generate on my own and
+ 
+
+ align:start position:0%
+long for me to generate on my own and
+make that part more efficient how can it
+
+ align:start position:0%
+make that part more efficient how can it
+ 
+
+ align:start position:0%
+make that part more efficient how can it
+be a tool to help me be a better human
+
+ align:start position:0%
+be a tool to help me be a better human
+ 
+
+ align:start position:0%
+be a tool to help me be a better human
+composer or just better
+
+ align:start position:0%
+composer or just better
+ 
+
+ align:start position:0%
+composer or just better
+human so the class went through some of
+
+ align:start position:0%
+human so the class went through some of
+ 
+
+ align:start position:0%
+human so the class went through some of
+the earliest algorithmic compositions
+
+ align:start position:0%
+the earliest algorithmic compositions
+ 
+
+ align:start position:0%
+the earliest algorithmic compositions
+from Guido of areto a monk living in the
+
+ align:start position:0%
+from Guido of areto a monk living in the
+ 
+
+ align:start position:0%
+from Guido of areto a monk living in the
+11th century through Mozart's musical
+
+ align:start position:0%
+11th century through Mozart's musical
+ 
+
+ align:start position:0%
+11th century through Mozart's musical
+dice games up until the ilak suite and
+
+ align:start position:0%
+dice games up until the ilak suite and
+ 
+
+ align:start position:0%
+dice games up until the ilak suite and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+beyond some of what's covered in this
+
+ align:start position:0%
+beyond some of what's covered in this
+ 
+
+ align:start position:0%
+beyond some of what's covered in this
+class also appears in the various videos
+
+ align:start position:0%
+class also appears in the various videos
+ 
+
+ align:start position:0%
+class also appears in the various videos
+that accompany this class that weren't
+
+ align:start position:0%
+that accompany this class that weren't
+ 
+
+ align:start position:0%
+that accompany this class that weren't
+shown to students this year but uh are
+
+ align:start position:0%
+shown to students this year but uh are
+ 
+
+ align:start position:0%
+shown to students this year but uh are
+available for
+
+ align:start position:0%
+available for
+ 
+
+ align:start position:0%
+available for
+you and other aspects touched on the
+
+ align:start position:0%
+you and other aspects touched on the
+ 
+
+ align:start position:0%
+you and other aspects touched on the
+guest speaker particular expertise which
+
+ align:start position:0%
+guest speaker particular expertise which
+ 
+
+ align:start position:0%
+guest speaker particular expertise which
+was very valuable to be brought in
+
+ align:start position:0%
+was very valuable to be brought in
+ 
+
+ align:start position:0%
+was very valuable to be brought in
+anybody else teaching this class would
+
+ align:start position:0%
+anybody else teaching this class would
+ 
+
+ align:start position:0%
+anybody else teaching this class would
+bring in her his own Specialties that
+
+ align:start position:0%
+bring in her his own Specialties that
+ 
+
+ align:start position:0%
+bring in her his own Specialties that
+would be make that class different from
+
+ align:start position:0%
+would be make that class different from
+ 
+
+ align:start position:0%
+would be make that class different from
+mine and nobody should teach this class
+
+ align:start position:0%
+mine and nobody should teach this class
+ 
+
+ align:start position:0%
+mine and nobody should teach this class
+exactly the same way I would teach it or
+
+ align:start position:0%
+exactly the same way I would teach it or
+ 
+
+ align:start position:0%
+exactly the same way I would teach it or
+have taught it so that gives a little
+
+ align:start position:0%
+have taught it so that gives a little
+ 
+
+ align:start position:0%
+have taught it so that gives a little
+bit of a nutshell of what's happening
+
+ align:start position:0%
+bit of a nutshell of what's happening
+ 
+
+ align:start position:0%
+bit of a nutshell of what's happening
+the students then went on to write their
+
+ align:start position:0%
+the students then went on to write their
+ 
+
+ align:start position:0%
+the students then went on to write their
+own algorithms to to generate
+
+ align:start position:0%
+own algorithms to to generate
+ 
+
+ align:start position:0%
+own algorithms to to generate
+compositions algorithmically and they
+
+ align:start position:0%
+compositions algorithmically and they
+ 
+
+ align:start position:0%
+compositions algorithmically and they
+did a very good job of avoiding the
+
+ align:start position:0%
+did a very good job of avoiding the
+ 
+
+ align:start position:0%
+did a very good job of avoiding the
+problem of trying to get the computer to
+
+ align:start position:0%
+problem of trying to get the computer to
+ 
+
+ align:start position:0%
+problem of trying to get the computer to
+do something that we already do better
+
+ align:start position:0%
+do something that we already do better
+ 
+
+ align:start position:0%
+do something that we already do better
+that we are not interested really in the
+
+ align:start position:0%
+that we are not interested really in the
+ 
+
+ align:start position:0%
+that we are not interested really in the
+computer's
+
+ align:start position:0%
+computer's
+ 
+
+ align:start position:0%
+computer's
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+and that we just would only want to
+
+ align:start position:0%
+and that we just would only want to
+ 
+
+ align:start position:0%
+and that we just would only want to
+listen to if we knew a human created and
+
+ align:start position:0%
+listen to if we knew a human created and
+ 
+
+ align:start position:0%
+listen to if we knew a human created and
+instead they went beyond that and
+
+ align:start position:0%
+instead they went beyond that and
+ 
+
+ align:start position:0%
+instead they went beyond that and
+created piece of music that were
+
+ align:start position:0%
+created piece of music that were
+ 
+
+ align:start position:0%
+created piece of music that were
+interesting in themselves and that no
+
+ align:start position:0%
+interesting in themselves and that no
+ 
+
+ align:start position:0%
+interesting in themselves and that no
+human would ever choose to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write in addition to the two classes
+
+ align:start position:0%
+write in addition to the two classes
+ 
+
+ align:start position:0%
+write in addition to the two classes
+that job candidates uh covered two other
+
+ align:start position:0%
+that job candidates uh covered two other
+ 
+
+ align:start position:0%
+that job candidates uh covered two other
+classes at around this time needed to
+
+ align:start position:0%
+classes at around this time needed to
+ 
+
+ align:start position:0%
+classes at around this time needed to
+be uh removed and the contents pushed
+
+ align:start position:0%
+be uh removed and the contents pushed
+ 
+
+ align:start position:0%
+be uh removed and the contents pushed
+into other classes because MIT was in
+
+ align:start position:0%
+into other classes because MIT was in
+ 
+
+ align:start position:0%
+into other classes because MIT was in
+the process of
+
+ align:start position:0%
+the process of
+ 
+
+ align:start position:0%
+the process of
+proposing to the full faculty a new
+
+ align:start position:0%
+proposing to the full faculty a new
+ 
+
+ align:start position:0%
+proposing to the full faculty a new
+master's program two new Master's
+
+ align:start position:0%
+master's program two new Master's
+ 
+
+ align:start position:0%
+master's program two new Master's
+programs in in music technology and
+
+ align:start position:0%
+programs in in music technology and
+ 
+
+ align:start position:0%
+programs in in music technology and
+computation and it happened that these
+
+ align:start position:0%
+computation and it happened that these
+ 
+
+ align:start position:0%
+computation and it happened that these
+uh proposals had to happen at the same
+
+ align:start position:0%
+uh proposals had to happen at the same
+ 
+
+ align:start position:0%
+uh proposals had to happen at the same
+time as this class and so a little bit
+
+ align:start position:0%
+time as this class and so a little bit
+ 
+
+ align:start position:0%
+time as this class and so a little bit
+of time was lost on that I'm hoping that
+
+ align:start position:0%
+of time was lost on that I'm hoping that
+ 
+
+ align:start position:0%
+of time was lost on that I'm hoping that
+if you've been interested in this class
+
+ align:start position:0%
+if you've been interested in this class
+ 
+
+ align:start position:0%
+if you've been interested in this class
+and want to go forward you might look
+
+ align:start position:0%
+and want to go forward you might look
+ 
+
+ align:start position:0%
+and want to go forward you might look
+into these programs which I assume will
+
+ align:start position:0%
+into these programs which I assume will
+ 
+
+ align:start position:0%
+into these programs which I assume will
+be live at the time that these videos
+
+ align:start position:0%
+be live at the time that these videos
+ 
+
+ align:start position:0%
+be live at the time that these videos
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+released I think that this is all that
+
+ align:start position:0%
+released I think that this is all that
+ 
+
+ align:start position:0%
+released I think that this is all that
+I'm going to be able to provide
+
+ align:start position:0%
+I'm going to be able to provide
+ 
+
+ align:start position:0%
+I'm going to be able to provide
+especially for the open courseware
+
+ align:start position:0%
+especially for the open courseware
+ 
+
+ align:start position:0%
+especially for the open courseware
+audience in this class except at the
+
+ align:start position:0%
+audience in this class except at the
+ 
+
+ align:start position:0%
+audience in this class except at the
+very end where I have a little message
+
+ align:start position:0%
+very end where I have a little message
+ 
+
+ align:start position:0%
+very end where I have a little message
+for you that I recorded at the time
+
+ align:start position:0%
+for you that I recorded at the time
+ 
+
+ align:start position:0%
+for you that I recorded at the time
+thank you
\ No newline at end of file
diff --git a/QsKtEuUyIdw.txt b/QsKtEuUyIdw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cfcab4af96d7cbc2eed4f23253ce87594129f966
--- /dev/null
+++ b/QsKtEuUyIdw.txt
@@ -0,0 +1,1371 @@
+align:start position:0%
+ 
+now we come to a more serious
+
+ align:start position:0%
+now we come to a more serious
+ 
+
+ align:start position:0%
+now we come to a more serious
+application of the fact that the gcd is
+
+ align:start position:0%
+application of the fact that the gcd is
+ 
+
+ align:start position:0%
+application of the fact that the gcd is
+a linear combination we're going to use
+
+ align:start position:0%
+a linear combination we're going to use
+ 
+
+ align:start position:0%
+a linear combination we're going to use
+it to prove the prime factorization
+
+ align:start position:0%
+it to prove the prime factorization
+ 
+
+ align:start position:0%
+it to prove the prime factorization
+theorem which we've talked about earlier
+
+ align:start position:0%
+theorem which we've talked about earlier
+ 
+
+ align:start position:0%
+theorem which we've talked about earlier
+this is the unique prime factorization
+
+ align:start position:0%
+this is the unique prime factorization
+ 
+
+ align:start position:0%
+this is the unique prime factorization
+theorem so let's begin by uh looking at
+
+ align:start position:0%
+theorem so let's begin by uh looking at
+ 
+
+ align:start position:0%
+theorem so let's begin by uh looking at
+a technical property of uh primes which
+
+ align:start position:0%
+a technical property of uh primes which
+ 
+
+ align:start position:0%
+a technical property of uh primes which
+is familiar but uh we're going to need
+
+ align:start position:0%
+is familiar but uh we're going to need
+ 
+
+ align:start position:0%
+is familiar but uh we're going to need
+to prove it if you believe in prime
+
+ align:start position:0%
+to prove it if you believe in prime
+ 
+
+ align:start position:0%
+to prove it if you believe in prime
+factorization then this which says that
+
+ align:start position:0%
+factorization then this which says that
+ 
+
+ align:start position:0%
+factorization then this which says that
+if P divides a product it divides one or
+
+ align:start position:0%
+if P divides a product it divides one or
+ 
+
+ align:start position:0%
+if P divides a product it divides one or
+the other of the components of the
+
+ align:start position:0%
+the other of the components of the
+ 
+
+ align:start position:0%
+the other of the components of the
+product that's an immediate consequence
+
+ align:start position:0%
+product that's an immediate consequence
+ 
+
+ align:start position:0%
+product that's an immediate consequence
+of the prime factorization theorem but
+
+ align:start position:0%
+of the prime factorization theorem but
+ 
+
+ align:start position:0%
+of the prime factorization theorem but
+we mustn't prove it that way because
+
+ align:start position:0%
+we mustn't prove it that way because
+ 
+
+ align:start position:0%
+we mustn't prove it that way because
+we're trying to use this to prove prime
+
+ align:start position:0%
+we're trying to use this to prove prime
+ 
+
+ align:start position:0%
+we're trying to use this to prove prime
+factorization so how can I prove based
+
+ align:start position:0%
+factorization so how can I prove based
+ 
+
+ align:start position:0%
+factorization so how can I prove based
+on the facts of the what we know about
+
+ align:start position:0%
+on the facts of the what we know about
+ 
+
+ align:start position:0%
+on the facts of the what we know about
+gcds uh without appealing to prime
+
+ align:start position:0%
+gcds uh without appealing to prime
+ 
+
+ align:start position:0%
+gcds uh without appealing to prime
+factorization that if p is a prime and P
+
+ align:start position:0%
+factorization that if p is a prime and P
+ 
+
+ align:start position:0%
+factorization that if p is a prime and P
+divides a product then it defi def uh
+
+ align:start position:0%
+divides a product then it defi def uh
+ 
+
+ align:start position:0%
+divides a product then it defi def uh
+then it divides one of the uh
+
+ align:start position:0%
+then it divides one of the uh
+ 
+
+ align:start position:0%
+then it divides one of the uh
+components of the product either the
+
+ align:start position:0%
+components of the product either the
+ 
+
+ align:start position:0%
+components of the product either the
+multiplier or the
+
+ align:start position:0%
+multiplier or the
+ 
+
+ align:start position:0%
+multiplier or the
+multiplicand okay well here's how to
+
+ align:start position:0%
+multiplicand okay well here's how to
+ 
+
+ align:start position:0%
+multiplicand okay well here's how to
+prove that suppose that P divides AB but
+
+ align:start position:0%
+prove that suppose that P divides AB but
+ 
+
+ align:start position:0%
+prove that suppose that P divides AB but
+it doesn't divide a of course if it does
+
+ align:start position:0%
+it doesn't divide a of course if it does
+ 
+
+ align:start position:0%
+it doesn't divide a of course if it does
+divide a I'm done so we may as well
+
+ align:start position:0%
+divide a I'm done so we may as well
+ 
+
+ align:start position:0%
+divide a I'm done so we may as well
+assume that it doesn't divide a now that
+
+ align:start position:0%
+assume that it doesn't divide a now that
+ 
+
+ align:start position:0%
+assume that it doesn't divide a now that
+means that since the only divisors of
+
+ align:start position:0%
+means that since the only divisors of
+ 
+
+ align:start position:0%
+means that since the only divisors of
+the only divisors of P are p and one the
+
+ align:start position:0%
+the only divisors of P are p and one the
+ 
+
+ align:start position:0%
+the only divisors of P are p and one the
+only positive divisors of P are p and
+
+ align:start position:0%
+only positive divisors of P are p and
+ 
+
+ align:start position:0%
+only positive divisors of P are p and
+one that if P doesn't divide a the gcd
+
+ align:start position:0%
+one that if P doesn't divide a the gcd
+ 
+
+ align:start position:0%
+one that if P doesn't divide a the gcd
+of A and P is one all right now comes
+
+ align:start position:0%
+of A and P is one all right now comes
+ 
+
+ align:start position:0%
+of A and P is one all right now comes
+the linear combination trick given that
+
+ align:start position:0%
+the linear combination trick given that
+ 
+
+ align:start position:0%
+the linear combination trick given that
+the gcd of p and a is one that means
+
+ align:start position:0%
+the gcd of p and a is one that means
+ 
+
+ align:start position:0%
+the gcd of p and a is one that means
+that I have a linear combination of A
+
+ align:start position:0%
+that I have a linear combination of A
+ 
+
+ align:start position:0%
+that I have a linear combination of A
+and P that's equal to one sa plus TP is
+
+ align:start position:0%
+and P that's equal to one sa plus TP is
+ 
+
+ align:start position:0%
+and P that's equal to one sa plus TP is
+equal to one for some coefficients s and
+
+ align:start position:0%
+equal to one for some coefficients s and
+ 
+
+ align:start position:0%
+equal to one for some coefficients s and
+t cool multiply everything by B on the
+
+ align:start position:0%
+t cool multiply everything by B on the
+ 
+
+ align:start position:0%
+t cool multiply everything by B on the
+right so that means that Sab plus TPB is
+
+ align:start position:0%
+right so that means that Sab plus TPB is
+ 
+
+ align:start position:0%
+right so that means that Sab plus TPB is
+equal to 1 * B but look at what we have
+
+ align:start position:0%
+equal to 1 * B but look at what we have
+ 
+
+ align:start position:0%
+equal to 1 * B but look at what we have
+now the first term on the left is
+
+ align:start position:0%
+now the first term on the left is
+ 
+
+ align:start position:0%
+now the first term on the left is
+something times ab and P divides AB so
+
+ align:start position:0%
+something times ab and P divides AB so
+ 
+
+ align:start position:0%
+something times ab and P divides AB so
+that first term is divisible by P the
+
+ align:start position:0%
+that first term is divisible by P the
+ 
+
+ align:start position:0%
+that first term is divisible by P the
+second term explicitly has a p in it so
+
+ align:start position:0%
+second term explicitly has a p in it so
+ 
+
+ align:start position:0%
+second term explicitly has a p in it so
+it's certainly divisible by P so the
+
+ align:start position:0%
+it's certainly divisible by P so the
+ 
+
+ align:start position:0%
+it's certainly divisible by P so the
+left hand side is a linear combination
+
+ align:start position:0%
+left hand side is a linear combination
+ 
+
+ align:start position:0%
+left hand side is a linear combination
+of multiples of p and therefore uh
+
+ align:start position:0%
+of multiples of p and therefore uh
+ 
+
+ align:start position:0%
+of multiples of p and therefore uh
+itself is a multiple of P which means
+
+ align:start position:0%
+itself is a multiple of P which means
+ 
+
+ align:start position:0%
+itself is a multiple of P which means
+the right hand side is a multiple of p
+
+ align:start position:0%
+the right hand side is a multiple of p
+ 
+
+ align:start position:0%
+the right hand side is a multiple of p
+and the right hand side is B so sure
+
+ align:start position:0%
+and the right hand side is B so sure
+ 
+
+ align:start position:0%
+and the right hand side is B so sure
+enough P divides B we're done um the
+
+ align:start position:0%
+enough P divides B we're done um the
+ 
+
+ align:start position:0%
+enough P divides B we're done um the
+very elegant little proof that follows
+
+ align:start position:0%
+very elegant little proof that follows
+ 
+
+ align:start position:0%
+very elegant little proof that follows
+immediately from the fact that you can
+
+ align:start position:0%
+immediately from the fact that you can
+ 
+
+ align:start position:0%
+immediately from the fact that you can
+express the gcd of two numbers as a
+
+ align:start position:0%
+express the gcd of two numbers as a
+ 
+
+ align:start position:0%
+express the gcd of two numbers as a
+linear combination of those numbers now
+
+ align:start position:0%
+linear combination of those numbers now
+ 
+
+ align:start position:0%
+linear combination of those numbers now
+this is the key technical Lema that we
+
+ align:start position:0%
+this is the key technical Lema that we
+ 
+
+ align:start position:0%
+this is the key technical Lema that we
+need to prove unique uh
+
+ align:start position:0%
+need to prove unique uh
+ 
+
+ align:start position:0%
+need to prove unique uh
+factorization um a corollary of this
+
+ align:start position:0%
+factorization um a corollary of this
+ 
+
+ align:start position:0%
+factorization um a corollary of this
+that I'm actually going to need is that
+
+ align:start position:0%
+that I'm actually going to need is that
+ 
+
+ align:start position:0%
+that I'm actually going to need is that
+if P divides a product of more than two
+
+ align:start position:0%
+if P divides a product of more than two
+ 
+
+ align:start position:0%
+if P divides a product of more than two
+things if P divides a product of a lot
+
+ align:start position:0%
+things if P divides a product of a lot
+ 
+
+ align:start position:0%
+things if P divides a product of a lot
+of things it has to divide at least one
+
+ align:start position:0%
+of things it has to divide at least one
+ 
+
+ align:start position:0%
+of things it has to divide at least one
+of them um and this you could prove by
+
+ align:start position:0%
+of them um and this you could prove by
+ 
+
+ align:start position:0%
+of them um and this you could prove by
+induction with the base case being that
+
+ align:start position:0%
+induction with the base case being that
+ 
+
+ align:start position:0%
+induction with the base case being that
+it works for m equals 2 uh but it's not
+
+ align:start position:0%
+it works for m equals 2 uh but it's not
+ 
+
+ align:start position:0%
+it works for m equals 2 uh but it's not
+very interesting and we're going to take
+
+ align:start position:0%
+very interesting and we're going to take
+ 
+
+ align:start position:0%
+very interesting and we're going to take
+that for granted if P divides a product
+
+ align:start position:0%
+that for granted if P divides a product
+ 
+
+ align:start position:0%
+that for granted if P divides a product
+of any size it divides one of the
+
+ align:start position:0%
+of any size it divides one of the
+ 
+
+ align:start position:0%
+of any size it divides one of the
+components of the product all right now
+
+ align:start position:0%
+components of the product all right now
+ 
+
+ align:start position:0%
+components of the product all right now
+we're ready to prove What's called the
+
+ align:start position:0%
+we're ready to prove What's called the
+ 
+
+ align:start position:0%
+we're ready to prove What's called the
+fundamental theorem of arithmetic which
+
+ align:start position:0%
+fundamental theorem of arithmetic which
+ 
+
+ align:start position:0%
+fundamental theorem of arithmetic which
+says that every integer greater than one
+
+ align:start position:0%
+says that every integer greater than one
+ 
+
+ align:start position:0%
+says that every integer greater than one
+factors uniquely into a weekly
+
+ align:start position:0%
+factors uniquely into a weekly
+ 
+
+ align:start position:0%
+factors uniquely into a weekly
+decreasing sequence of primes now the
+
+ align:start position:0%
+decreasing sequence of primes now the
+ 
+
+ align:start position:0%
+decreasing sequence of primes now the
+statement of weekly decreasing is a
+
+ align:start position:0%
+statement of weekly decreasing is a
+ 
+
+ align:start position:0%
+statement of weekly decreasing is a
+little bit Technical and unexpected what
+
+ align:start position:0%
+little bit Technical and unexpected what
+ 
+
+ align:start position:0%
+little bit Technical and unexpected what
+we want to say is that that it that a
+
+ align:start position:0%
+we want to say is that that it that a
+ 
+
+ align:start position:0%
+we want to say is that that it that a
+number factors into the same set of
+
+ align:start position:0%
+number factors into the same set of
+ 
+
+ align:start position:0%
+number factors into the same set of
+primes that's not quite right because
+
+ align:start position:0%
+primes that's not quite right because
+ 
+
+ align:start position:0%
+primes that's not quite right because
+the set of primes doesn't take into
+
+ align:start position:0%
+the set of primes doesn't take into
+ 
+
+ align:start position:0%
+the set of primes doesn't take into
+account how many times each prime occurs
+
+ align:start position:0%
+account how many times each prime occurs
+ 
+
+ align:start position:0%
+account how many times each prime occurs
+um you could try to make a statement
+
+ align:start position:0%
+um you could try to make a statement
+ 
+
+ align:start position:0%
+um you could try to make a statement
+about every number uniquely is a
+
+ align:start position:0%
+about every number uniquely is a
+ 
+
+ align:start position:0%
+about every number uniquely is a
+multiple of of a certain number of each
+
+ align:start position:0%
+multiple of of a certain number of each
+ 
+
+ align:start position:0%
+multiple of of a certain number of each
+kind of prime but a slick way to do that
+
+ align:start position:0%
+kind of prime but a slick way to do that
+ 
+
+ align:start position:0%
+kind of prime but a slick way to do that
+is simply to say take all the prime
+
+ align:start position:0%
+is simply to say take all the prime
+ 
+
+ align:start position:0%
+is simply to say take all the prime
+factors including multiple occurrences
+
+ align:start position:0%
+factors including multiple occurrences
+ 
+
+ align:start position:0%
+factors including multiple occurrences
+of a prime and line them up in weekly
+
+ align:start position:0%
+of a prime and line them up in weekly
+ 
+
+ align:start position:0%
+of a prime and line them up in weekly
+decreasing order and when you do that
+
+ align:start position:0%
+decreasing order and when you do that
+ 
+
+ align:start position:0%
+decreasing order and when you do that
+that sequence is unique okay um this
+
+ align:start position:0%
+that sequence is unique okay um this
+ 
+
+ align:start position:0%
+that sequence is unique okay um this
+fundamental theorem arithmetic is also
+
+ align:start position:0%
+fundamental theorem arithmetic is also
+ 
+
+ align:start position:0%
+fundamental theorem arithmetic is also
+called the prime factorization theorem
+
+ align:start position:0%
+called the prime factorization theorem
+ 
+
+ align:start position:0%
+called the prime factorization theorem
+and uh here's what it says when we spell
+
+ align:start position:0%
+and uh here's what it says when we spell
+ 
+
+ align:start position:0%
+and uh here's what it says when we spell
+it out uh without using the words weekly
+
+ align:start position:0%
+it out uh without using the words weekly
+ 
+
+ align:start position:0%
+it out uh without using the words weekly
+de uh weekly increasing or weekly
+
+ align:start position:0%
+de uh weekly increasing or weekly
+ 
+
+ align:start position:0%
+de uh weekly increasing or weekly
+decreasing um it says that every integer
+
+ align:start position:0%
+decreasing um it says that every integer
+ 
+
+ align:start position:0%
+decreasing um it says that every integer
+n greater than one has a unique
+
+ align:start position:0%
+n greater than one has a unique
+ 
+
+ align:start position:0%
+n greater than one has a unique
+factorization into Primes Main it can be
+
+ align:start position:0%
+factorization into Primes Main it can be
+ 
+
+ align:start position:0%
+factorization into Primes Main it can be
+namely it can be expressed as a product
+
+ align:start position:0%
+namely it can be expressed as a product
+ 
+
+ align:start position:0%
+namely it can be expressed as a product
+of P1 through PK um is equal to n um
+
+ align:start position:0%
+of P1 through PK um is equal to n um
+ 
+
+ align:start position:0%
+of P1 through PK um is equal to n um
+with P1 greater than equal to P2 greater
+
+ align:start position:0%
+with P1 greater than equal to P2 greater
+ 
+
+ align:start position:0%
+with P1 greater than equal to P2 greater
+than equal to each successive Prime in
+
+ align:start position:0%
+than equal to each successive Prime in
+ 
+
+ align:start position:0%
+than equal to each successive Prime in
+the sequence with the smallest one
+
+ align:start position:0%
+the sequence with the smallest one
+ 
+
+ align:start position:0%
+the sequence with the smallest one
+last okay um Let's do an example so uh
+
+ align:start position:0%
+last okay um Let's do an example so uh
+ 
+
+ align:start position:0%
+last okay um Let's do an example so uh
+there's a number that was not chosen by
+
+ align:start position:0%
+there's a number that was not chosen by
+ 
+
+ align:start position:0%
+there's a number that was not chosen by
+accident because I worked out what the
+
+ align:start position:0%
+accident because I worked out what the
+ 
+
+ align:start position:0%
+accident because I worked out what the
+factorization was and it factors into
+
+ align:start position:0%
+factorization was and it factors into
+ 
+
+ align:start position:0%
+factorization was and it factors into
+the following weekly decreasing sequence
+
+ align:start position:0%
+the following weekly decreasing sequence
+ 
+
+ align:start position:0%
+the following weekly decreasing sequence
+you start with the prime 53 You Follow
+
+ align:start position:0%
+you start with the prime 53 You Follow
+ 
+
+ align:start position:0%
+you start with the prime 53 You Follow
+by three occurrences of 37 2 11s a seven
+
+ align:start position:0%
+by three occurrences of 37 2 11s a seven
+ 
+
+ align:start position:0%
+by three occurrences of 37 2 11s a seven
+and 33s and the point is that if you try
+
+ align:start position:0%
+and 33s and the point is that if you try
+ 
+
+ align:start position:0%
+and 33s and the point is that if you try
+to express this ugly number as a weekly
+
+ align:start position:0%
+to express this ugly number as a weekly
+ 
+
+ align:start position:0%
+to express this ugly number as a weekly
+decreasing sequence of primes you're
+
+ align:start position:0%
+decreasing sequence of primes you're
+ 
+
+ align:start position:0%
+decreasing sequence of primes you're
+always going to get exactly this
+
+ align:start position:0%
+always going to get exactly this
+ 
+
+ align:start position:0%
+always going to get exactly this
+sequence it's the only way to do
+
+ align:start position:0%
+sequence it's the only way to do
+ 
+
+ align:start position:0%
+sequence it's the only way to do
+it all right how are we going to prove
+
+ align:start position:0%
+it all right how are we going to prove
+ 
+
+ align:start position:0%
+it all right how are we going to prove
+that well um let's suppose that it
+
+ align:start position:0%
+that well um let's suppose that it
+ 
+
+ align:start position:0%
+that well um let's suppose that it
+wasn't true suppose that there was some
+
+ align:start position:0%
+wasn't true suppose that there was some
+ 
+
+ align:start position:0%
+wasn't true suppose that there was some
+number that could be factored in two
+
+ align:start position:0%
+number that could be factored in two
+ 
+
+ align:start position:0%
+number that could be factored in two
+different ways
+
+ align:start position:0%
+different ways
+ 
+
+ align:start position:0%
+different ways
+well by the well ordering principle
+
+ align:start position:0%
+well by the well ordering principle
+ 
+
+ align:start position:0%
+well by the well ordering principle
+there's a least one so we're talking
+
+ align:start position:0%
+there's a least one so we're talking
+ 
+
+ align:start position:0%
+there's a least one so we're talking
+about numbers that are greater than one
+
+ align:start position:0%
+about numbers that are greater than one
+ 
+
+ align:start position:0%
+about numbers that are greater than one
+so there's a least number greater than
+
+ align:start position:0%
+so there's a least number greater than
+ 
+
+ align:start position:0%
+so there's a least number greater than
+one that can be factored in two
+
+ align:start position:0%
+one that can be factored in two
+ 
+
+ align:start position:0%
+one that can be factored in two
+different ways suppose that it's n so
+
+ align:start position:0%
+different ways suppose that it's n so
+ 
+
+ align:start position:0%
+different ways suppose that it's n so
+what I have is that N is a product P1
+
+ align:start position:0%
+what I have is that N is a product P1
+ 
+
+ align:start position:0%
+what I have is that N is a product P1
+through PK and it's equal to another
+
+ align:start position:0%
+through PK and it's equal to another
+ 
+
+ align:start position:0%
+through PK and it's equal to another
+product q1 through qm where the PS and
+
+ align:start position:0%
+product q1 through qm where the PS and
+ 
+
+ align:start position:0%
+product q1 through qm where the PS and
+the q's are all prime and these two
+
+ align:start position:0%
+the q's are all prime and these two
+ 
+
+ align:start position:0%
+the q's are all prime and these two
+weekly decreasing sequences are not the
+
+ align:start position:0%
+weekly decreasing sequences are not the
+ 
+
+ align:start position:0%
+weekly decreasing sequences are not the
+same they differ somehow okay
+
+ align:start position:0%
+same they differ somehow okay
+ 
+
+ align:start position:0%
+same they differ somehow okay
+uh so the we can assume that the P's are
+
+ align:start position:0%
+uh so the we can assume that the P's are
+ 
+
+ align:start position:0%
+uh so the we can assume that the P's are
+listed in a weekly decreasing order and
+
+ align:start position:0%
+listed in a weekly decreasing order and
+ 
+
+ align:start position:0%
+listed in a weekly decreasing order and
+the q's are likewise in listed in weekly
+
+ align:start position:0%
+the q's are likewise in listed in weekly
+ 
+
+ align:start position:0%
+the q's are likewise in listed in weekly
+decreasing order now the first
+
+ align:start position:0%
+decreasing order now the first
+ 
+
+ align:start position:0%
+decreasing order now the first
+observation is suppose that q1 is equal
+
+ align:start position:0%
+observation is suppose that q1 is equal
+ 
+
+ align:start position:0%
+observation is suppose that q1 is equal
+to P1 well that's not really possible
+
+ align:start position:0%
+to P1 well that's not really possible
+ 
+
+ align:start position:0%
+to P1 well that's not really possible
+because if q1 is equal to P1 then I
+
+ align:start position:0%
+because if q1 is equal to P1 then I
+ 
+
+ align:start position:0%
+because if q1 is equal to P1 then I
+could cancel the P1 from both sides and
+
+ align:start position:0%
+could cancel the P1 from both sides and
+ 
+
+ align:start position:0%
+could cancel the P1 from both sides and
+I would get that P2 through PK uh is
+
+ align:start position:0%
+I would get that P2 through PK uh is
+ 
+
+ align:start position:0%
+I would get that P2 through PK uh is
+equal to Q2 through qm and these would
+
+ align:start position:0%
+equal to Q2 through qm and these would
+ 
+
+ align:start position:0%
+equal to Q2 through qm and these would
+still be different since I they were
+
+ align:start position:0%
+still be different since I they were
+ 
+
+ align:start position:0%
+still be different since I they were
+different and I took the same thing from
+
+ align:start position:0%
+different and I took the same thing from
+ 
+
+ align:start position:0%
+different and I took the same thing from
+their beginning I'm left with a smaller
+
+ align:start position:0%
+their beginning I'm left with a smaller
+ 
+
+ align:start position:0%
+their beginning I'm left with a smaller
+number that does not have a unique
+
+ align:start position:0%
+number that does not have a unique
+ 
+
+ align:start position:0%
+number that does not have a unique
+factorization contradicting the
+
+ align:start position:0%
+factorization contradicting the
+ 
+
+ align:start position:0%
+factorization contradicting the
+minimality of n so in short um uh it's
+
+ align:start position:0%
+minimality of n so in short um uh it's
+ 
+
+ align:start position:0%
+minimality of n so in short um uh it's
+not possible for uh q1 to equal P1 so
+
+ align:start position:0%
+not possible for uh q1 to equal P1 so
+ 
+
+ align:start position:0%
+not possible for uh q1 to equal P1 so
+one of them has to be greater we may as
+
+ align:start position:0%
+one of them has to be greater we may as
+ 
+
+ align:start position:0%
+one of them has to be greater we may as
+well assume that q1 is bigger than P1
+
+ align:start position:0%
+well assume that q1 is bigger than P1
+ 
+
+ align:start position:0%
+well assume that q1 is bigger than P1
+okay so q1 is bigger than P1 and P1 is
+
+ align:start position:0%
+okay so q1 is bigger than P1 and P1 is
+ 
+
+ align:start position:0%
+okay so q1 is bigger than P1 and P1 is
+greater than equal to all the other PS
+
+ align:start position:0%
+greater than equal to all the other PS
+ 
+
+ align:start position:0%
+greater than equal to all the other PS
+so in fact q1 is bigger than every one
+
+ align:start position:0%
+so in fact q1 is bigger than every one
+ 
+
+ align:start position:0%
+so in fact q1 is bigger than every one
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+P's well that's going to reach a
+
+ align:start position:0%
+P's well that's going to reach a
+ 
+
+ align:start position:0%
+P's well that's going to reach a
+contradiction because of the co of the
+
+ align:start position:0%
+contradiction because of the co of the
+ 
+
+ align:start position:0%
+contradiction because of the co of the
+corollary what I know is that q1 divides
+
+ align:start position:0%
+corollary what I know is that q1 divides
+ 
+
+ align:start position:0%
+corollary what I know is that q1 divides
+n and n is the product of the
+
+ align:start position:0%
+n and n is the product of the
+ 
+
+ align:start position:0%
+n and n is the product of the
+P's
+
+ align:start position:0%
+P's
+ 
+
+ align:start position:0%
+P's
+and since Q divides the product of the
+
+ align:start position:0%
+and since Q divides the product of the
+ 
+
+ align:start position:0%
+and since Q divides the product of the
+PS by the corollary it's got to divide
+
+ align:start position:0%
+PS by the corollary it's got to divide
+ 
+
+ align:start position:0%
+PS by the corollary it's got to divide
+one of them q1 must divide pi for some I
+
+ align:start position:0%
+one of them q1 must divide pi for some I
+ 
+
+ align:start position:0%
+one of them q1 must divide pi for some I
+but that contradicts the fact that Qi q1
+
+ align:start position:0%
+but that contradicts the fact that Qi q1
+ 
+
+ align:start position:0%
+but that contradicts the fact that Qi q1
+is bigger than Pi that's not possible
+
+ align:start position:0%
+is bigger than Pi that's not possible
+ 
+
+ align:start position:0%
+is bigger than Pi that's not possible
+for the smaller number to divide the
+
+ align:start position:0%
+for the smaller number to divide the
+ 
+
+ align:start position:0%
+for the smaller number to divide the
+larger number to divide the smaller
+
+ align:start position:0%
+larger number to divide the smaller
+ 
+
+ align:start position:0%
+larger number to divide the smaller
+number and uh we're done and we have
+
+ align:start position:0%
+number and uh we're done and we have
+ 
+
+ align:start position:0%
+number and uh we're done and we have
+proved the unique factorization theorem
\ No newline at end of file
diff --git a/R-qlPwP9hDE.txt b/R-qlPwP9hDE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f98a9c2349ad7edbb10cdb319941bf7bb957839
--- /dev/null
+++ b/R-qlPwP9hDE.txt
@@ -0,0 +1,2779 @@
+align:start position:0%
+ 
+Now we'll hear from Chair Van Astrand
+
+ align:start position:0%
+Now we'll hear from Chair Van Astrand
+ 
+
+ align:start position:0%
+Now we'll hear from Chair Van Astrand
+who has since I believe May 2023 chaired
+
+ align:start position:0%
+who has since I believe May 2023 chaired
+ 
+
+ align:start position:0%
+who has since I believe May 2023 chaired
+the Massachusetts Department of Public
+
+ align:start position:0%
+the Massachusetts Department of Public
+ 
+
+ align:start position:0%
+the Massachusetts Department of Public
+Utilities.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Thank you.
+
+ align:start position:0%
+>> Thank you.
+ 
+
+ align:start position:0%
+>> Thank you.
+>> Thank you.
+
+ align:start position:0%
+>> Thank you.
+ 
+
+ align:start position:0%
+>> Thank you.
+Thanks everybody.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I really appreciate the opportunity
+
+ align:start position:0%
+So, I really appreciate the opportunity
+ 
+
+ align:start position:0%
+So, I really appreciate the opportunity
+to be here. Um, as Andrew mentioned,
+
+ align:start position:0%
+to be here. Um, as Andrew mentioned,
+ 
+
+ align:start position:0%
+to be here. Um, as Andrew mentioned,
+I've been chair of the commission coming
+
+ align:start position:0%
+I've been chair of the commission coming
+ 
+
+ align:start position:0%
+I've been chair of the commission coming
+up on almost two years, May of 2023. Um,
+
+ align:start position:0%
+up on almost two years, May of 2023. Um,
+ 
+
+ align:start position:0%
+up on almost two years, May of 2023. Um,
+and one of the things I inherited was
+
+ align:start position:0%
+and one of the things I inherited was
+ 
+
+ align:start position:0%
+and one of the things I inherited was
+what was a pending proceeding in
+
+ align:start position:0%
+what was a pending proceeding in
+ 
+
+ align:start position:0%
+what was a pending proceeding in
+Massachusetts called the future of gas
+
+ align:start position:0%
+Massachusetts called the future of gas
+ 
+
+ align:start position:0%
+Massachusetts called the future of gas
+proceeding where we issued an order
+
+ align:start position:0%
+proceeding where we issued an order
+ 
+
+ align:start position:0%
+proceeding where we issued an order
+that's very relevant to what we've been
+
+ align:start position:0%
+that's very relevant to what we've been
+ 
+
+ align:start position:0%
+that's very relevant to what we've been
+talking about today. I wanted to provide
+
+ align:start position:0%
+talking about today. I wanted to provide
+ 
+
+ align:start position:0%
+talking about today. I wanted to provide
+a little bit of know I had to learn when
+
+ align:start position:0%
+a little bit of know I had to learn when
+ 
+
+ align:start position:0%
+a little bit of know I had to learn when
+I got here and I I I was a law professor
+
+ align:start position:0%
+I got here and I I I was a law professor
+ 
+
+ align:start position:0%
+I got here and I I I was a law professor
+in West West Virginia University. You
+
+ align:start position:0%
+in West West Virginia University. You
+ 
+
+ align:start position:0%
+in West West Virginia University. You
+can imagine the kind of the culture
+
+ align:start position:0%
+can imagine the kind of the culture
+ 
+
+ align:start position:0%
+can imagine the kind of the culture
+shock of going from a coal state to a
+
+ align:start position:0%
+shock of going from a coal state to a
+ 
+
+ align:start position:0%
+shock of going from a coal state to a
+wonderful blue state pursuing a really
+
+ align:start position:0%
+wonderful blue state pursuing a really
+ 
+
+ align:start position:0%
+wonderful blue state pursuing a really
+aggressive clean energy targets. But
+
+ align:start position:0%
+aggressive clean energy targets. But
+ 
+
+ align:start position:0%
+aggressive clean energy targets. But
+that provides the framework for what
+
+ align:start position:0%
+that provides the framework for what
+ 
+
+ align:start position:0%
+that provides the framework for what
+we're trying to do at the at the
+
+ align:start position:0%
+we're trying to do at the at the
+ 
+
+ align:start position:0%
+we're trying to do at the at the
+Department of Public Utilities and how
+
+ align:start position:0%
+Department of Public Utilities and how
+ 
+
+ align:start position:0%
+Department of Public Utilities and how
+network geothermal potentially fits into
+
+ align:start position:0%
+network geothermal potentially fits into
+ 
+
+ align:start position:0%
+network geothermal potentially fits into
+that whole message um whole initiative.
+
+ align:start position:0%
+that whole message um whole initiative.
+ 
+
+ align:start position:0%
+that whole message um whole initiative.
+So what's what's the statutory
+
+ align:start position:0%
+So what's what's the statutory
+ 
+
+ align:start position:0%
+So what's what's the statutory
+framework? What are we doing? And then a
+
+ align:start position:0%
+framework? What are we doing? And then a
+ 
+
+ align:start position:0%
+framework? What are we doing? And then a
+little bit about the current
+
+ align:start position:0%
+little bit about the current
+ 
+
+ align:start position:0%
+little bit about the current
+demonstration projects, but I think you
+
+ align:start position:0%
+demonstration projects, but I think you
+ 
+
+ align:start position:0%
+demonstration projects, but I think you
+probably heard a lot about those
+
+ align:start position:0%
+probably heard a lot about those
+ 
+
+ align:start position:0%
+probably heard a lot about those
+already. So one of the things is the
+
+ align:start position:0%
+already. So one of the things is the
+ 
+
+ align:start position:0%
+already. So one of the things is the
+global warming solutions act of 2008. So
+
+ align:start position:0%
+global warming solutions act of 2008. So
+ 
+
+ align:start position:0%
+global warming solutions act of 2008. So
+we're going to be net zero by 2050 and
+
+ align:start position:0%
+we're going to be net zero by 2050 and
+ 
+
+ align:start position:0%
+we're going to be net zero by 2050 and
+then later on the another subsequent
+
+ align:start position:0%
+then later on the another subsequent
+ 
+
+ align:start position:0%
+then later on the another subsequent
+climate bill says we're going to
+
+ align:start position:0%
+climate bill says we're going to
+ 
+
+ align:start position:0%
+climate bill says we're going to
+establish sector specific emissions
+
+ align:start position:0%
+establish sector specific emissions
+ 
+
+ align:start position:0%
+establish sector specific emissions
+reduction targets for 2025 and 2030. So
+
+ align:start position:0%
+reduction targets for 2025 and 2030. So
+ 
+
+ align:start position:0%
+reduction targets for 2025 and 2030. So
+that was the clean energy and climate
+
+ align:start position:0%
+that was the clean energy and climate
+ 
+
+ align:start position:0%
+that was the clean energy and climate
+plan of June of 2022. And this is just
+
+ align:start position:0%
+plan of June of 2022. And this is just
+ 
+
+ align:start position:0%
+plan of June of 2022. And this is just
+an excerpt from that plan. You can see
+
+ align:start position:0%
+an excerpt from that plan. You can see
+ 
+
+ align:start position:0%
+an excerpt from that plan. You can see
+um sort of starting off in 1990 and then
+
+ align:start position:0%
+um sort of starting off in 1990 and then
+ 
+
+ align:start position:0%
+um sort of starting off in 1990 and then
+to the far right is 2030. The four
+
+ align:start position:0%
+to the far right is 2030. The four
+ 
+
+ align:start position:0%
+to the far right is 2030. The four
+various sectors and you can see the
+
+ align:start position:0%
+various sectors and you can see the
+ 
+
+ align:start position:0%
+various sectors and you can see the
+building sector. You can see that
+
+ align:start position:0%
+building sector. You can see that
+ 
+
+ align:start position:0%
+building sector. You can see that
+reduction that we need to achieve by
+
+ align:start position:0%
+reduction that we need to achieve by
+ 
+
+ align:start position:0%
+reduction that we need to achieve by
+2030. And this is that the the down
+
+ align:start position:0%
+2030. And this is that the the down
+ 
+
+ align:start position:0%
+2030. And this is that the the down
+below just excerpts that building
+
+ align:start position:0%
+below just excerpts that building
+ 
+
+ align:start position:0%
+below just excerpts that building
+sector. So that's kind of that's what
+
+ align:start position:0%
+sector. So that's kind of that's what
+ 
+
+ align:start position:0%
+sector. So that's kind of that's what
+we're striving for in terms of how does
+
+ align:start position:0%
+we're striving for in terms of how does
+ 
+
+ align:start position:0%
+we're striving for in terms of how does
+this network geothermal fit into how
+
+ align:start position:0%
+this network geothermal fit into how
+ 
+
+ align:start position:0%
+this network geothermal fit into how
+does this um the transition the natural
+
+ align:start position:0%
+does this um the transition the natural
+ 
+
+ align:start position:0%
+does this um the transition the natural
+gas industry? What are we trying to
+
+ align:start position:0%
+gas industry? What are we trying to
+ 
+
+ align:start position:0%
+gas industry? What are we trying to
+accomplish? It's really trying to
+
+ align:start position:0%
+accomplish? It's really trying to
+ 
+
+ align:start position:0%
+accomplish? It's really trying to
+achieve those goals. They're now statuto
+
+ align:start position:0%
+achieve those goals. They're now statuto
+ 
+
+ align:start position:0%
+achieve those goals. They're now statuto
+the global warming solution act and the
+
+ align:start position:0%
+the global warming solution act and the
+ 
+
+ align:start position:0%
+the global warming solution act and the
+fact that the CECP the clean energy and
+
+ align:start position:0%
+fact that the CECP the clean energy and
+ 
+
+ align:start position:0%
+fact that the CECP the clean energy and
+climate plan established these sub
+
+ align:start position:0%
+climate plan established these sub
+ 
+
+ align:start position:0%
+climate plan established these sub
+sector targets. So pretty much says
+
+ align:start position:0%
+sector targets. So pretty much says
+ 
+
+ align:start position:0%
+sector targets. So pretty much says
+residential got to get from 15.3 down to
+
+ align:start position:0%
+residential got to get from 15.3 down to
+ 
+
+ align:start position:0%
+residential got to get from 15.3 down to
+7.8 and for commercial and the total
+
+ align:start position:0%
+7.8 and for commercial and the total
+ 
+
+ align:start position:0%
+7.8 and for commercial and the total
+percent reduction 47% reduction. And so
+
+ align:start position:0%
+percent reduction 47% reduction. And so
+ 
+
+ align:start position:0%
+percent reduction 47% reduction. And so
+that's what we're trying to achieve.
+
+ align:start position:0%
+that's what we're trying to achieve.
+ 
+
+ align:start position:0%
+that's what we're trying to achieve.
+That's that's basically I see my job as
+
+ align:start position:0%
+That's that's basically I see my job as
+ 
+
+ align:start position:0%
+That's that's basically I see my job as
+a as a regulator is these policy
+
+ align:start position:0%
+a as a regulator is these policy
+ 
+
+ align:start position:0%
+a as a regulator is these policy
+decisions have been made by the
+
+ align:start position:0%
+decisions have been made by the
+ 
+
+ align:start position:0%
+decisions have been made by the
+legislature. my job is to imple
+
+ align:start position:0%
+legislature. my job is to imple
+ 
+
+ align:start position:0%
+legislature. my job is to imple
+implement them and try to make that make
+
+ align:start position:0%
+implement them and try to make that make
+ 
+
+ align:start position:0%
+implement them and try to make that make
+that happen. Um so the statutory
+
+ align:start position:0%
+that happen. Um so the statutory
+ 
+
+ align:start position:0%
+that happen. Um so the statutory
+framework I think is Ania talked about
+
+ align:start position:0%
+framework I think is Ania talked about
+ 
+
+ align:start position:0%
+framework I think is Ania talked about
+this somewhat already but sort of where
+
+ align:start position:0%
+this somewhat already but sort of where
+ 
+
+ align:start position:0%
+this somewhat already but sort of where
+where network geothermal comes in. So
+
+ align:start position:0%
+where network geothermal comes in. So
+ 
+
+ align:start position:0%
+where network geothermal comes in. So
+the 2021 climate bill expressly allowed
+
+ align:start position:0%
+the 2021 climate bill expressly allowed
+ 
+
+ align:start position:0%
+the 2021 climate bill expressly allowed
+um the gas utilities to propose these
+
+ align:start position:0%
+um the gas utilities to propose these
+ 
+
+ align:start position:0%
+um the gas utilities to propose these
+these pilot scale projects. Another
+
+ align:start position:0%
+these pilot scale projects. Another
+ 
+
+ align:start position:0%
+these pilot scale projects. Another
+piece that came in the following year
+
+ align:start position:0%
+piece that came in the following year
+ 
+
+ align:start position:0%
+piece that came in the following year
+and you may hear be hearing a lot about
+
+ align:start position:0%
+and you may hear be hearing a lot about
+ 
+
+ align:start position:0%
+and you may hear be hearing a lot about
+um GSAP or gas system enhancement plans
+
+ align:start position:0%
+um GSAP or gas system enhancement plans
+ 
+
+ align:start position:0%
+um GSAP or gas system enhancement plans
+um the gas utilities in Massachusetts
+
+ align:start position:0%
+um the gas utilities in Massachusetts
+ 
+
+ align:start position:0%
+um the gas utilities in Massachusetts
+are spending a lot of money every year
+
+ align:start position:0%
+are spending a lot of money every year
+ 
+
+ align:start position:0%
+are spending a lot of money every year
+to address what is referred to in the
+
+ align:start position:0%
+to address what is referred to in the
+ 
+
+ align:start position:0%
+to address what is referred to in the
+statute as leakprone pipes. So back in
+
+ align:start position:0%
+statute as leakprone pipes. So back in
+ 
+
+ align:start position:0%
+statute as leakprone pipes. So back in
+2014, the gas leaks act was passed that
+
+ align:start position:0%
+2014, the gas leaks act was passed that
+ 
+
+ align:start position:0%
+2014, the gas leaks act was passed that
+basically provided preferential rate
+
+ align:start position:0%
+basically provided preferential rate
+ 
+
+ align:start position:0%
+basically provided preferential rate
+recovery for costs incurred by the gas
+
+ align:start position:0%
+recovery for costs incurred by the gas
+ 
+
+ align:start position:0%
+recovery for costs incurred by the gas
+utilities to to repair or address
+
+ align:start position:0%
+utilities to to repair or address
+ 
+
+ align:start position:0%
+utilities to to repair or address
+leakprone pipe. The notion is these are
+
+ align:start position:0%
+leakprone pipe. The notion is these are
+ 
+
+ align:start position:0%
+leakprone pipe. The notion is these are
+safety issues. They're risk issues.
+
+ align:start position:0%
+safety issues. They're risk issues.
+ 
+
+ align:start position:0%
+safety issues. They're risk issues.
+Obviously, we have a lot of old
+
+ align:start position:0%
+Obviously, we have a lot of old
+ 
+
+ align:start position:0%
+Obviously, we have a lot of old
+infrastructure in Massachusetts. So that
+
+ align:start position:0%
+infrastructure in Massachusetts. So that
+ 
+
+ align:start position:0%
+infrastructure in Massachusetts. So that
+expedited rate recovery um sort of
+
+ align:start position:0%
+expedited rate recovery um sort of
+ 
+
+ align:start position:0%
+expedited rate recovery um sort of
+removes one of the tools that we have as
+
+ align:start position:0%
+removes one of the tools that we have as
+ 
+
+ align:start position:0%
+removes one of the tools that we have as
+regulators which is called regulatory
+
+ align:start position:0%
+regulators which is called regulatory
+ 
+
+ align:start position:0%
+regulators which is called regulatory
+lag that typically a utility will spend
+
+ align:start position:0%
+lag that typically a utility will spend
+ 
+
+ align:start position:0%
+lag that typically a utility will spend
+the money and then it won't recover in
+
+ align:start position:0%
+the money and then it won't recover in
+ 
+
+ align:start position:0%
+the money and then it won't recover in
+rates for a while could be a year or two
+
+ align:start position:0%
+rates for a while could be a year or two
+ 
+
+ align:start position:0%
+rates for a while could be a year or two
+years but that gap provides an incentive
+
+ align:start position:0%
+years but that gap provides an incentive
+ 
+
+ align:start position:0%
+years but that gap provides an incentive
+for cost containment. Well, what the gas
+
+ align:start position:0%
+for cost containment. Well, what the gas
+ 
+
+ align:start position:0%
+for cost containment. Well, what the gas
+leaks act did in 2014 was pretty much
+
+ align:start position:0%
+leaks act did in 2014 was pretty much
+ 
+
+ align:start position:0%
+leaks act did in 2014 was pretty much
+say you file your gas system enhancement
+
+ align:start position:0%
+say you file your gas system enhancement
+ 
+
+ align:start position:0%
+say you file your gas system enhancement
+plan with the DPU in October of 31st. we
+
+ align:start position:0%
+plan with the DPU in October of 31st. we
+ 
+
+ align:start position:0%
+plan with the DPU in October of 31st. we
+have six months to go over it and then
+
+ align:start position:0%
+have six months to go over it and then
+ 
+
+ align:start position:0%
+have six months to go over it and then
+May one you begin recovering those costs
+
+ align:start position:0%
+May one you begin recovering those costs
+ 
+
+ align:start position:0%
+May one you begin recovering those costs
+in rates. So it provides this expedited
+
+ align:start position:0%
+in rates. So it provides this expedited
+ 
+
+ align:start position:0%
+in rates. So it provides this expedited
+rate treatment to to um address the
+
+ align:start position:0%
+rate treatment to to um address the
+ 
+
+ align:start position:0%
+rate treatment to to um address the
+leakprone pipe and then so it's very
+
+ align:start position:0%
+leakprone pipe and then so it's very
+ 
+
+ align:start position:0%
+leakprone pipe and then so it's very
+controversial. We had a GEP working
+
+ align:start position:0%
+controversial. We had a GEP working
+ 
+
+ align:start position:0%
+controversial. We had a GEP working
+group that met through a lot of 2023 to
+
+ align:start position:0%
+group that met through a lot of 2023 to
+ 
+
+ align:start position:0%
+group that met through a lot of 2023 to
+figure out that gas leaks act having
+
+ align:start position:0%
+figure out that gas leaks act having
+ 
+
+ align:start position:0%
+figure out that gas leaks act having
+been passed in 2014 focusing primarily
+
+ align:start position:0%
+been passed in 2014 focusing primarily
+ 
+
+ align:start position:0%
+been passed in 2014 focusing primarily
+on the safety issue and the risk issue.
+
+ align:start position:0%
+on the safety issue and the risk issue.
+ 
+
+ align:start position:0%
+on the safety issue and the risk issue.
+Then we have the climate bill that says,
+
+ align:start position:0%
+Then we have the climate bill that says,
+ 
+
+ align:start position:0%
+Then we have the climate bill that says,
+well, we need to achieve these
+
+ align:start position:0%
+well, we need to achieve these
+ 
+
+ align:start position:0%
+well, we need to achieve these
+greenhouse gas reductions. Do we need to
+
+ align:start position:0%
+greenhouse gas reductions. Do we need to
+ 
+
+ align:start position:0%
+greenhouse gas reductions. Do we need to
+revisit the gas leaks act in light of
+
+ align:start position:0%
+revisit the gas leaks act in light of
+ 
+
+ align:start position:0%
+revisit the gas leaks act in light of
+the the new focus on reducing greenhouse
+
+ align:start position:0%
+the the new focus on reducing greenhouse
+ 
+
+ align:start position:0%
+the the new focus on reducing greenhouse
+gas emissions? And so there's a lot a
+
+ align:start position:0%
+gas emissions? And so there's a lot a
+ 
+
+ align:start position:0%
+gas emissions? And so there's a lot a
+lot of work is revisiting that. We
+
+ align:start position:0%
+lot of work is revisiting that. We
+ 
+
+ align:start position:0%
+lot of work is revisiting that. We
+currently have those filings in front of
+
+ align:start position:0%
+currently have those filings in front of
+ 
+
+ align:start position:0%
+currently have those filings in front of
+us. We'll be issuing orders in April,
+
+ align:start position:0%
+us. We'll be issuing orders in April,
+ 
+
+ align:start position:0%
+us. We'll be issuing orders in April,
+April 30th with respect to gas system
+
+ align:start position:0%
+April 30th with respect to gas system
+ 
+
+ align:start position:0%
+April 30th with respect to gas system
+enhancement plans beginning on May 1.
+
+ align:start position:0%
+enhancement plans beginning on May 1.
+ 
+
+ align:start position:0%
+enhancement plans beginning on May 1.
+But a big thing and how network
+
+ align:start position:0%
+But a big thing and how network
+ 
+
+ align:start position:0%
+But a big thing and how network
+geothermal fits into this is the 2022
+
+ align:start position:0%
+geothermal fits into this is the 2022
+ 
+
+ align:start position:0%
+geothermal fits into this is the 2022
+climate bill. I think Ania might have
+
+ align:start position:0%
+climate bill. I think Ania might have
+ 
+
+ align:start position:0%
+climate bill. I think Ania might have
+mentioned this but we can basically one
+
+ align:start position:0%
+mentioned this but we can basically one
+ 
+
+ align:start position:0%
+mentioned this but we can basically one
+means of addressing the leakprone pipe
+
+ align:start position:0%
+means of addressing the leakprone pipe
+ 
+
+ align:start position:0%
+means of addressing the leakprone pipe
+rather than just replacing it with more
+
+ align:start position:0%
+rather than just replacing it with more
+ 
+
+ align:start position:0%
+rather than just replacing it with more
+gas pipe is to replace it with a utility
+
+ align:start position:0%
+gas pipe is to replace it with a utility
+ 
+
+ align:start position:0%
+gas pipe is to replace it with a utility
+scale non-emitting renewable thermal
+
+ align:start position:0%
+scale non-emitting renewable thermal
+ 
+
+ align:start position:0%
+scale non-emitting renewable thermal
+energy infrastructure aka geothermal
+
+ align:start position:0%
+energy infrastructure aka geothermal
+ 
+
+ align:start position:0%
+energy infrastructure aka geothermal
+network. So that is a that is a big
+
+ align:start position:0%
+network. So that is a that is a big
+ 
+
+ align:start position:0%
+network. So that is a that is a big
+benefit in terms of um we're trying to
+
+ align:start position:0%
+benefit in terms of um we're trying to
+ 
+
+ align:start position:0%
+benefit in terms of um we're trying to
+avoid potentially stranded investment by
+
+ align:start position:0%
+avoid potentially stranded investment by
+ 
+
+ align:start position:0%
+avoid potentially stranded investment by
+continuing to replace gas pipes with gas
+
+ align:start position:0%
+continuing to replace gas pipes with gas
+ 
+
+ align:start position:0%
+continuing to replace gas pipes with gas
+pipes that going to last 50 or 60 years.
+
+ align:start position:0%
+pipes that going to last 50 or 60 years.
+ 
+
+ align:start position:0%
+pipes that going to last 50 or 60 years.
+This says well when you're spending that
+
+ align:start position:0%
+This says well when you're spending that
+ 
+
+ align:start position:0%
+This says well when you're spending that
+money on your GEP plan you can actually
+
+ align:start position:0%
+money on your GEP plan you can actually
+ 
+
+ align:start position:0%
+money on your GEP plan you can actually
+use a thermal energy network would be
+
+ align:start position:0%
+use a thermal energy network would be
+ 
+
+ align:start position:0%
+use a thermal energy network would be
+one way of addressing the leakprone pipe
+
+ align:start position:0%
+one way of addressing the leakprone pipe
+ 
+
+ align:start position:0%
+one way of addressing the leakprone pipe
+and avoiding that stranded cost by just
+
+ align:start position:0%
+and avoiding that stranded cost by just
+ 
+
+ align:start position:0%
+and avoiding that stranded cost by just
+putting more natural gas infrastructure
+
+ align:start position:0%
+putting more natural gas infrastructure
+ 
+
+ align:start position:0%
+putting more natural gas infrastructure
+into the ground. As Ania mentioned, the
+
+ align:start position:0%
+into the ground. As Ania mentioned, the
+ 
+
+ align:start position:0%
+into the ground. As Ania mentioned, the
+2024 climate bill um actually makes it
+
+ align:start position:0%
+2024 climate bill um actually makes it
+ 
+
+ align:start position:0%
+2024 climate bill um actually makes it
+specific that a gas company is allowed
+
+ align:start position:0%
+specific that a gas company is allowed
+ 
+
+ align:start position:0%
+specific that a gas company is allowed
+to get in the business of of creating
+
+ align:start position:0%
+to get in the business of of creating
+ 
+
+ align:start position:0%
+to get in the business of of creating
+these thermal energy networks. Um and I
+
+ align:start position:0%
+these thermal energy networks. Um and I
+ 
+
+ align:start position:0%
+these thermal energy networks. Um and I
+also mentioned um we're trying to
+
+ align:start position:0%
+also mentioned um we're trying to
+ 
+
+ align:start position:0%
+also mentioned um we're trying to
+address this obligation to serve very
+
+ align:start position:0%
+address this obligation to serve very
+ 
+
+ align:start position:0%
+address this obligation to serve very
+controversial in the states but it's
+
+ align:start position:0%
+controversial in the states but it's
+ 
+
+ align:start position:0%
+controversial in the states but it's
+basically as as you can see from Ania's
+
+ align:start position:0%
+basically as as you can see from Ania's
+ 
+
+ align:start position:0%
+basically as as you can see from Ania's
+chart if if you have a a comp a customer
+
+ align:start position:0%
+chart if if you have a a comp a customer
+ 
+
+ align:start position:0%
+chart if if you have a a comp a customer
+who does not want to give up their gas
+
+ align:start position:0%
+who does not want to give up their gas
+ 
+
+ align:start position:0%
+who does not want to give up their gas
+how can you make the case we're going to
+
+ align:start position:0%
+how can you make the case we're going to
+ 
+
+ align:start position:0%
+how can you make the case we're going to
+substitute this network geothermal for
+
+ align:start position:0%
+substitute this network geothermal for
+ 
+
+ align:start position:0%
+substitute this network geothermal for
+their for your gas very controversial.
+
+ align:start position:0%
+their for your gas very controversial.
+ 
+
+ align:start position:0%
+their for your gas very controversial.
+So, they took a shot at addressing the
+
+ align:start position:0%
+So, they took a shot at addressing the
+ 
+
+ align:start position:0%
+So, they took a shot at addressing the
+obligation to serve um at least with
+
+ align:start position:0%
+obligation to serve um at least with
+ 
+
+ align:start position:0%
+obligation to serve um at least with
+respect to new hookups by allowing the
+
+ align:start position:0%
+respect to new hookups by allowing the
+ 
+
+ align:start position:0%
+respect to new hookups by allowing the
+consideration of adequate substitutes.
+
+ align:start position:0%
+consideration of adequate substitutes.
+ 
+
+ align:start position:0%
+consideration of adequate substitutes.
+In other words, you might not have a
+
+ align:start position:0%
+In other words, you might not have a
+ 
+
+ align:start position:0%
+In other words, you might not have a
+right to gas service if they're adequate
+
+ align:start position:0%
+right to gas service if they're adequate
+ 
+
+ align:start position:0%
+right to gas service if they're adequate
+substitutes. They're non- gas
+
+ align:start position:0%
+substitutes. They're non- gas
+ 
+
+ align:start position:0%
+substitutes. They're non- gas
+substitutes. Um but we're still working
+
+ align:start position:0%
+substitutes. Um but we're still working
+ 
+
+ align:start position:0%
+substitutes. Um but we're still working
+our way through this. Um and then that
+
+ align:start position:0%
+our way through this. Um and then that
+ 
+
+ align:start position:0%
+our way through this. Um and then that
+eligible infrastructure investment in
+
+ align:start position:0%
+eligible infrastructure investment in
+ 
+
+ align:start position:0%
+eligible infrastructure investment in
+these G GE programs is not just
+
+ align:start position:0%
+these G GE programs is not just
+ 
+
+ align:start position:0%
+these G GE programs is not just
+replacement and also includes
+
+ align:start position:0%
+replacement and also includes
+ 
+
+ align:start position:0%
+replacement and also includes
+retirement, which means we can actually
+
+ align:start position:0%
+retirement, which means we can actually
+ 
+
+ align:start position:0%
+retirement, which means we can actually
+take out the pipe. One way of addressing
+
+ align:start position:0%
+take out the pipe. One way of addressing
+ 
+
+ align:start position:0%
+take out the pipe. One way of addressing
+the leak prone pipe is just remove the
+
+ align:start position:0%
+the leak prone pipe is just remove the
+ 
+
+ align:start position:0%
+the leak prone pipe is just remove the
+leak prone pipe because you're going to
+
+ align:start position:0%
+leak prone pipe because you're going to
+ 
+
+ align:start position:0%
+leak prone pipe because you're going to
+convert you're going to put customers to
+
+ align:start position:0%
+convert you're going to put customers to
+ 
+
+ align:start position:0%
+convert you're going to put customers to
+elect electrification electrified
+
+ align:start position:0%
+elect electrification electrified
+ 
+
+ align:start position:0%
+elect electrification electrified
+solutions whether it's ground source
+
+ align:start position:0%
+solutions whether it's ground source
+ 
+
+ align:start position:0%
+solutions whether it's ground source
+heat pumps or air source heat pumps.
+
+ align:start position:0%
+heat pumps or air source heat pumps.
+ 
+
+ align:start position:0%
+heat pumps or air source heat pumps.
+So when I got here in May of 2023 I
+
+ align:start position:0%
+So when I got here in May of 2023 I
+ 
+
+ align:start position:0%
+So when I got here in May of 2023 I
+inherited this docket. It had been
+
+ align:start position:0%
+inherited this docket. It had been
+ 
+
+ align:start position:0%
+inherited this docket. It had been
+started in October of 2020 and I think
+
+ align:start position:0%
+started in October of 2020 and I think
+ 
+
+ align:start position:0%
+started in October of 2020 and I think
+the record had closed in October of
+
+ align:start position:0%
+the record had closed in October of
+ 
+
+ align:start position:0%
+the record had closed in October of
+2022.
+
+ align:start position:0%
+2022.
+ 
+
+ align:start position:0%
+2022.
+I thought I think we need to probably
+
+ align:start position:0%
+I thought I think we need to probably
+ 
+
+ align:start position:0%
+I thought I think we need to probably
+issue an order in this in this docket.
+
+ align:start position:0%
+issue an order in this in this docket.
+ 
+
+ align:start position:0%
+issue an order in this in this docket.
+But it was um basically um what is going
+
+ align:start position:0%
+But it was um basically um what is going
+ 
+
+ align:start position:0%
+But it was um basically um what is going
+to be the pathway for the natural gas
+
+ align:start position:0%
+to be the pathway for the natural gas
+ 
+
+ align:start position:0%
+to be the pathway for the natural gas
+utilities? How do we achieve these
+
+ align:start position:0%
+utilities? How do we achieve these
+ 
+
+ align:start position:0%
+utilities? How do we achieve these
+greenhouse gas reduction targets which
+
+ align:start position:0%
+greenhouse gas reduction targets which
+ 
+
+ align:start position:0%
+greenhouse gas reduction targets which
+the global warming solutions act and the
+
+ align:start position:0%
+the global warming solutions act and the
+ 
+
+ align:start position:0%
+the global warming solutions act and the
+2021 climate bill require us to achieve?
+
+ align:start position:0%
+2021 climate bill require us to achieve?
+ 
+
+ align:start position:0%
+2021 climate bill require us to achieve?
+And so we issued this order uh basically
+
+ align:start position:0%
+And so we issued this order uh basically
+ 
+
+ align:start position:0%
+And so we issued this order uh basically
+ident setting forth this regulatory
+
+ align:start position:0%
+ident setting forth this regulatory
+ 
+
+ align:start position:0%
+ident setting forth this regulatory
+framework and what we basically landed
+
+ align:start position:0%
+framework and what we basically landed
+ 
+
+ align:start position:0%
+framework and what we basically landed
+on was electrification is going to be
+
+ align:start position:0%
+on was electrification is going to be
+ 
+
+ align:start position:0%
+on was electrification is going to be
+the primary pathway and that's airsource
+
+ align:start position:0%
+the primary pathway and that's airsource
+ 
+
+ align:start position:0%
+the primary pathway and that's airsource
+heat pumps ground source heat pumps
+
+ align:start position:0%
+heat pumps ground source heat pumps
+ 
+
+ align:start position:0%
+heat pumps ground source heat pumps
+which includes the geothermal energy
+
+ align:start position:0%
+which includes the geothermal energy
+ 
+
+ align:start position:0%
+which includes the geothermal energy
+networks and the way I described what we
+
+ align:start position:0%
+networks and the way I described what we
+ 
+
+ align:start position:0%
+networks and the way I described what we
+did in that order was basically point
+
+ align:start position:0%
+did in that order was basically point
+ 
+
+ align:start position:0%
+did in that order was basically point
+out to this clean energy back the clean
+
+ align:start position:0%
+out to this clean energy back the clean
+ 
+
+ align:start position:0%
+out to this clean energy back the clean
+energy framework that I had in the first
+
+ align:start position:0%
+energy framework that I had in the first
+ 
+
+ align:start position:0%
+energy framework that I had in the first
+couple of slides. We just want to put
+
+ align:start position:0%
+couple of slides. We just want to put
+ 
+
+ align:start position:0%
+couple of slides. We just want to put
+the LDC's, the local gas distribution
+
+ align:start position:0%
+the LDC's, the local gas distribution
+ 
+
+ align:start position:0%
+the LDC's, the local gas distribution
+utilities on a pathway to achieve net
+
+ align:start position:0%
+utilities on a pathway to achieve net
+ 
+
+ align:start position:0%
+utilities on a pathway to achieve net
+zero by 2050. And so part of that is is
+
+ align:start position:0%
+zero by 2050. And so part of that is is
+ 
+
+ align:start position:0%
+zero by 2050. And so part of that is is
+in a couple months, April 1, each LDC
+
+ align:start position:0%
+in a couple months, April 1, each LDC
+ 
+
+ align:start position:0%
+in a couple months, April 1, each LDC
+has to file a climate compliance plan.
+
+ align:start position:0%
+has to file a climate compliance plan.
+ 
+
+ align:start position:0%
+has to file a climate compliance plan.
+In other words, show that you are on a
+
+ align:start position:0%
+In other words, show that you are on a
+ 
+
+ align:start position:0%
+In other words, show that you are on a
+pathway that's going to get you to net
+
+ align:start position:0%
+pathway that's going to get you to net
+ 
+
+ align:start position:0%
+pathway that's going to get you to net
+zero by 2050. You're going to achieve
+
+ align:start position:0%
+zero by 2050. You're going to achieve
+ 
+
+ align:start position:0%
+zero by 2050. You're going to achieve
+those those sub limits that I had that
+
+ align:start position:0%
+those those sub limits that I had that
+ 
+
+ align:start position:0%
+those those sub limits that I had that
+on that other slide. The other big thing
+
+ align:start position:0%
+on that other slide. The other big thing
+ 
+
+ align:start position:0%
+on that other slide. The other big thing
+we did in 2080 was um put the burden on
+
+ align:start position:0%
+we did in 2080 was um put the burden on
+ 
+
+ align:start position:0%
+we did in 2080 was um put the burden on
+the LDC, the local gas distribution
+
+ align:start position:0%
+the LDC, the local gas distribution
+ 
+
+ align:start position:0%
+the LDC, the local gas distribution
+companies. Before you make any
+
+ align:start position:0%
+companies. Before you make any
+ 
+
+ align:start position:0%
+companies. Before you make any
+additional investment in natural gas
+
+ align:start position:0%
+additional investment in natural gas
+ 
+
+ align:start position:0%
+additional investment in natural gas
+distribution infrastructure, show that
+
+ align:start position:0%
+distribution infrastructure, show that
+ 
+
+ align:start position:0%
+distribution infrastructure, show that
+you considered a non- gas pipeline
+
+ align:start position:0%
+you considered a non- gas pipeline
+ 
+
+ align:start position:0%
+you considered a non- gas pipeline
+alternative. And that could be it could
+
+ align:start position:0%
+alternative. And that could be it could
+ 
+
+ align:start position:0%
+alternative. And that could be it could
+be energy efficiency, it could be
+
+ align:start position:0%
+be energy efficiency, it could be
+ 
+
+ align:start position:0%
+be energy efficiency, it could be
+electric air source heat pump, ground
+
+ align:start position:0%
+electric air source heat pump, ground
+ 
+
+ align:start position:0%
+electric air source heat pump, ground
+source heat pump, network geothermal,
+
+ align:start position:0%
+source heat pump, network geothermal,
+ 
+
+ align:start position:0%
+source heat pump, network geothermal,
+but basically we want to avoid stranded
+
+ align:start position:0%
+but basically we want to avoid stranded
+ 
+
+ align:start position:0%
+but basically we want to avoid stranded
+costs. We want to avoid putting
+
+ align:start position:0%
+costs. We want to avoid putting
+ 
+
+ align:start position:0%
+costs. We want to avoid putting
+additional pipe in the ground. So that
+
+ align:start position:0%
+additional pipe in the ground. So that
+ 
+
+ align:start position:0%
+additional pipe in the ground. So that
+was a big element and right now the the
+
+ align:start position:0%
+was a big element and right now the the
+ 
+
+ align:start position:0%
+was a big element and right now the the
+the natural gas distribution companies,
+
+ align:start position:0%
+the natural gas distribution companies,
+ 
+
+ align:start position:0%
+the natural gas distribution companies,
+they're all working together. They're
+
+ align:start position:0%
+they're all working together. They're
+ 
+
+ align:start position:0%
+they're all working together. They're
+going to be filing with us an agreed
+
+ align:start position:0%
+going to be filing with us an agreed
+ 
+
+ align:start position:0%
+going to be filing with us an agreed
+upon natural um non- gas pipeline and
+
+ align:start position:0%
+upon natural um non- gas pipeline and
+ 
+
+ align:start position:0%
+upon natural um non- gas pipeline and
+NPA framework and because we need to
+
+ align:start position:0%
+NPA framework and because we need to
+ 
+
+ align:start position:0%
+NPA framework and because we need to
+start applying that as as they're coming
+
+ align:start position:0%
+start applying that as as they're coming
+ 
+
+ align:start position:0%
+start applying that as as they're coming
+in and asking for new additional
+
+ align:start position:0%
+in and asking for new additional
+ 
+
+ align:start position:0%
+in and asking for new additional
+investment. Did have you consider the an
+
+ align:start position:0%
+investment. Did have you consider the an
+ 
+
+ align:start position:0%
+investment. Did have you consider the an
+NPA that non- gas pipeline alternative?
+
+ align:start position:0%
+NPA that non- gas pipeline alternative?
+ 
+
+ align:start position:0%
+NPA that non- gas pipeline alternative?
+And then the other thing I think they
+
+ align:start position:0%
+And then the other thing I think they
+ 
+
+ align:start position:0%
+And then the other thing I think they
+can Ian mentioned um so March one
+
+ align:start position:0%
+can Ian mentioned um so March one
+ 
+
+ align:start position:0%
+can Ian mentioned um so March one
+roughly a year from now then we're
+
+ align:start position:0%
+roughly a year from now then we're
+ 
+
+ align:start position:0%
+roughly a year from now then we're
+requiring each LDC to file a target
+
+ align:start position:0%
+requiring each LDC to file a target
+ 
+
+ align:start position:0%
+requiring each LDC to file a target
+electrification project. In other words
+
+ align:start position:0%
+electrification project. In other words
+ 
+
+ align:start position:0%
+electrification project. In other words
+try to take out a decommission a portion
+
+ align:start position:0%
+try to take out a decommission a portion
+ 
+
+ align:start position:0%
+try to take out a decommission a portion
+of a gas service territory in favor of
+
+ align:start position:0%
+of a gas service territory in favor of
+ 
+
+ align:start position:0%
+of a gas service territory in favor of
+of air source heat pump ground source
+
+ align:start position:0%
+of air source heat pump ground source
+ 
+
+ align:start position:0%
+of air source heat pump ground source
+heat pump electric or network
+
+ align:start position:0%
+heat pump electric or network
+ 
+
+ align:start position:0%
+heat pump electric or network
+geothermal. Um you have to work with
+
+ align:start position:0%
+geothermal. Um you have to work with
+ 
+
+ align:start position:0%
+geothermal. Um you have to work with
+your applicable electric distribution
+
+ align:start position:0%
+your applicable electric distribution
+ 
+
+ align:start position:0%
+your applicable electric distribution
+company because in Massachusetts we have
+
+ align:start position:0%
+company because in Massachusetts we have
+ 
+
+ align:start position:0%
+company because in Massachusetts we have
+some utilities that are both gas and
+
+ align:start position:0%
+some utilities that are both gas and
+ 
+
+ align:start position:0%
+some utilities that are both gas and
+electric. Sometimes Eversource provides
+
+ align:start position:0%
+electric. Sometimes Eversource provides
+ 
+
+ align:start position:0%
+electric. Sometimes Eversource provides
+the electric and National Grid provides
+
+ align:start position:0%
+the electric and National Grid provides
+ 
+
+ align:start position:0%
+the electric and National Grid provides
+the gas. You got to come in together.
+
+ align:start position:0%
+the gas. You got to come in together.
+ 
+
+ align:start position:0%
+the gas. You got to come in together.
+Um, National Grid actually filed a
+
+ align:start position:0%
+Um, National Grid actually filed a
+ 
+
+ align:start position:0%
+Um, National Grid actually filed a
+target electrification demonstration
+
+ align:start position:0%
+target electrification demonstration
+ 
+
+ align:start position:0%
+target electrification demonstration
+proposal in December of 2024 for the
+
+ align:start position:0%
+proposal in December of 2024 for the
+ 
+
+ align:start position:0%
+proposal in December of 2024 for the
+towns of Lminster and Winthrop where
+
+ align:start position:0%
+towns of Lminster and Winthrop where
+ 
+
+ align:start position:0%
+towns of Lminster and Winthrop where
+they're going to try to decommission
+
+ align:start position:0%
+they're going to try to decommission
+ 
+
+ align:start position:0%
+they're going to try to decommission
+part of the gas service territory in
+
+ align:start position:0%
+part of the gas service territory in
+ 
+
+ align:start position:0%
+part of the gas service territory in
+favor of electrification. But that's
+
+ align:start position:0%
+favor of electrification. But that's
+ 
+
+ align:start position:0%
+favor of electrification. But that's
+going to be a big part of um sort of how
+
+ align:start position:0%
+going to be a big part of um sort of how
+ 
+
+ align:start position:0%
+going to be a big part of um sort of how
+we manage this this this gas transition
+
+ align:start position:0%
+we manage this this this gas transition
+ 
+
+ align:start position:0%
+we manage this this this gas transition
+is the climate compliance plans and the
+
+ align:start position:0%
+is the climate compliance plans and the
+ 
+
+ align:start position:0%
+is the climate compliance plans and the
+role that these that these um
+
+ align:start position:0%
+role that these that these um
+ 
+
+ align:start position:0%
+role that these that these um
+demonstration projects are going to play
+
+ align:start position:0%
+demonstration projects are going to play
+ 
+
+ align:start position:0%
+demonstration projects are going to play
+and that's where the obligation to serve
+
+ align:start position:0%
+and that's where the obligation to serve
+ 
+
+ align:start position:0%
+and that's where the obligation to serve
+piece is so challenging because when you
+
+ align:start position:0%
+piece is so challenging because when you
+ 
+
+ align:start position:0%
+piece is so challenging because when you
+look at the chart that Ania had you know
+
+ align:start position:0%
+look at the chart that Ania had you know
+ 
+
+ align:start position:0%
+look at the chart that Ania had you know
+all it takes is one one customer who
+
+ align:start position:0%
+all it takes is one one customer who
+ 
+
+ align:start position:0%
+all it takes is one one customer who
+says I don't want to give up my gas and
+
+ align:start position:0%
+says I don't want to give up my gas and
+ 
+
+ align:start position:0%
+says I don't want to give up my gas and
+you're not able to take out that you're
+
+ align:start position:0%
+you're not able to take out that you're
+ 
+
+ align:start position:0%
+you're not able to take out that you're
+not able to decommission the pipe and
+
+ align:start position:0%
+not able to decommission the pipe and
+ 
+
+ align:start position:0%
+not able to decommission the pipe and
+the number and the numbers just don't
+
+ align:start position:0%
+the number and the numbers just don't
+ 
+
+ align:start position:0%
+the number and the numbers just don't
+work all that well if you can't
+
+ align:start position:0%
+work all that well if you can't
+ 
+
+ align:start position:0%
+work all that well if you can't
+decommission the pipe. type. So that's
+
+ align:start position:0%
+decommission the pipe. type. So that's
+ 
+
+ align:start position:0%
+decommission the pipe. type. So that's
+why states are struggling with how can
+
+ align:start position:0%
+why states are struggling with how can
+ 
+
+ align:start position:0%
+why states are struggling with how can
+we how can we substitute um the
+
+ align:start position:0%
+we how can we substitute um the
+ 
+
+ align:start position:0%
+we how can we substitute um the
+basically a another means of providing
+
+ align:start position:0%
+basically a another means of providing
+ 
+
+ align:start position:0%
+basically a another means of providing
+the essential service of heat instead of
+
+ align:start position:0%
+the essential service of heat instead of
+ 
+
+ align:start position:0%
+the essential service of heat instead of
+instead of natural gas.
+
+ align:start position:0%
+instead of natural gas.
+ 
+
+ align:start position:0%
+instead of natural gas.
+So, one of the things that um it's it's
+
+ align:start position:0%
+So, one of the things that um it's it's
+ 
+
+ align:start position:0%
+So, one of the things that um it's it's
+helpful along the lines of of of NEO's
+
+ align:start position:0%
+helpful along the lines of of of NEO's
+ 
+
+ align:start position:0%
+helpful along the lines of of of NEO's
+discussion of the demonstration projects
+
+ align:start position:0%
+discussion of the demonstration projects
+ 
+
+ align:start position:0%
+discussion of the demonstration projects
+because the 2021 climate bill
+
+ align:start position:0%
+because the 2021 climate bill
+ 
+
+ align:start position:0%
+because the 2021 climate bill
+specifically authorizes the gas
+
+ align:start position:0%
+specifically authorizes the gas
+ 
+
+ align:start position:0%
+specifically authorizes the gas
+companies to file with us demonstration
+
+ align:start position:0%
+companies to file with us demonstration
+ 
+
+ align:start position:0%
+companies to file with us demonstration
+projects proposals and and it it lays
+
+ align:start position:0%
+projects proposals and and it it lays
+ 
+
+ align:start position:0%
+projects proposals and and it it lays
+out some criteria. So when we look at
+
+ align:start position:0%
+out some criteria. So when we look at
+ 
+
+ align:start position:0%
+out some criteria. So when we look at
+these demonstration projects when
+
+ align:start position:0%
+these demonstration projects when
+ 
+
+ align:start position:0%
+these demonstration projects when
+Framingham comes in, whenever source
+
+ align:start position:0%
+Framingham comes in, whenever source
+ 
+
+ align:start position:0%
+Framingham comes in, whenever source
+comes in with the Framingham project and
+
+ align:start position:0%
+comes in with the Framingham project and
+ 
+
+ align:start position:0%
+comes in with the Framingham project and
+National Grid comes in for the Lel and
+
+ align:start position:0%
+National Grid comes in for the Lel and
+ 
+
+ align:start position:0%
+National Grid comes in for the Lel and
+and Franklin Fields projects, these are
+
+ align:start position:0%
+and Franklin Fields projects, these are
+ 
+
+ align:start position:0%
+and Franklin Fields projects, these are
+the criteria that we are going to apply
+
+ align:start position:0%
+the criteria that we are going to apply
+ 
+
+ align:start position:0%
+the criteria that we are going to apply
+and in determining the rate treatment,
+
+ align:start position:0%
+and in determining the rate treatment,
+ 
+
+ align:start position:0%
+and in determining the rate treatment,
+the rate recovery of those of those
+
+ align:start position:0%
+the rate recovery of those of those
+ 
+
+ align:start position:0%
+the rate recovery of those of those
+costs. Um pretty straightforward. Must
+
+ align:start position:0%
+costs. Um pretty straightforward. Must
+ 
+
+ align:start position:0%
+costs. Um pretty straightforward. Must
+have reasonable likelihood of
+
+ align:start position:0%
+have reasonable likelihood of
+ 
+
+ align:start position:0%
+have reasonable likelihood of
+facilitating substantial reductions.
+
+ align:start position:0%
+facilitating substantial reductions.
+ 
+
+ align:start position:0%
+facilitating substantial reductions.
+That goes back to achieving those
+
+ align:start position:0%
+That goes back to achieving those
+ 
+
+ align:start position:0%
+That goes back to achieving those
+greenhouse gas limits. We don't want you
+
+ align:start position:0%
+greenhouse gas limits. We don't want you
+ 
+
+ align:start position:0%
+greenhouse gas limits. We don't want you
+don't want you to blend in hydrogen and
+
+ align:start position:0%
+don't want you to blend in hydrogen and
+ 
+
+ align:start position:0%
+don't want you to blend in hydrogen and
+RNG and we need to use a third party
+
+ align:start position:0%
+RNG and we need to use a third party
+ 
+
+ align:start position:0%
+RNG and we need to use a third party
+evaluation. And then we consider the
+
+ align:start position:0%
+evaluation. And then we consider the
+ 
+
+ align:start position:0%
+evaluation. And then we consider the
+reasonleness of the size, scope and
+
+ align:start position:0%
+reasonleness of the size, scope and
+ 
+
+ align:start position:0%
+reasonleness of the size, scope and
+scale. In other words, do the benefits
+
+ align:start position:0%
+scale. In other words, do the benefits
+ 
+
+ align:start position:0%
+scale. In other words, do the benefits
+justify the proposed cost. And another
+
+ align:start position:0%
+justify the proposed cost. And another
+ 
+
+ align:start position:0%
+justify the proposed cost. And another
+key element is the calculation of
+
+ align:start position:0%
+key element is the calculation of
+ 
+
+ align:start position:0%
+key element is the calculation of
+benefits must include the calculations
+
+ align:start position:0%
+benefits must include the calculations
+ 
+
+ align:start position:0%
+benefits must include the calculations
+of the social value of greenhouse gas
+
+ align:start position:0%
+of the social value of greenhouse gas
+ 
+
+ align:start position:0%
+of the social value of greenhouse gas
+emissions reduction. That's going to be
+
+ align:start position:0%
+emissions reduction. That's going to be
+ 
+
+ align:start position:0%
+emissions reduction. That's going to be
+a good way of when you're looking at
+
+ align:start position:0%
+a good way of when you're looking at
+ 
+
+ align:start position:0%
+a good way of when you're looking at
+those costs and benefits that you're
+
+ align:start position:0%
+those costs and benefits that you're
+ 
+
+ align:start position:0%
+those costs and benefits that you're
+going to put a price on carbon,
+
+ align:start position:0%
+going to put a price on carbon,
+ 
+
+ align:start position:0%
+going to put a price on carbon,
+basically the carbon that you're
+
+ align:start position:0%
+basically the carbon that you're
+ 
+
+ align:start position:0%
+basically the carbon that you're
+avoiding by taking out that natural gas
+
+ align:start position:0%
+avoiding by taking out that natural gas
+ 
+
+ align:start position:0%
+avoiding by taking out that natural gas
+infrastructure and replacing it with
+
+ align:start position:0%
+infrastructure and replacing it with
+ 
+
+ align:start position:0%
+infrastructure and replacing it with
+with something else. So, real briefly, I
+
+ align:start position:0%
+with something else. So, real briefly, I
+ 
+
+ align:start position:0%
+with something else. So, real briefly, I
+think you're going to hear a lot about
+
+ align:start position:0%
+think you're going to hear a lot about
+ 
+
+ align:start position:0%
+think you're going to hear a lot about
+the Framingham project that Eversource
+
+ align:start position:0%
+the Framingham project that Eversource
+ 
+
+ align:start position:0%
+the Framingham project that Eversource
+has done. There's a phase two that was
+
+ align:start position:0%
+has done. There's a phase two that was
+ 
+
+ align:start position:0%
+has done. There's a phase two that was
+awarded a preliminary grant, I think, by
+
+ align:start position:0%
+awarded a preliminary grant, I think, by
+ 
+
+ align:start position:0%
+awarded a preliminary grant, I think, by
+the Department of Energy, which is
+
+ align:start position:0%
+the Department of Energy, which is
+ 
+
+ align:start position:0%
+the Department of Energy, which is
+caught up in all this stuff that's going
+
+ align:start position:0%
+caught up in all this stuff that's going
+ 
+
+ align:start position:0%
+caught up in all this stuff that's going
+on in Washington DC right now. Um, n so
+
+ align:start position:0%
+on in Washington DC right now. Um, n so
+ 
+
+ align:start position:0%
+on in Washington DC right now. Um, n so
+that was approved in the in the
+
+ align:start position:0%
+that was approved in the in the
+ 
+
+ align:start position:0%
+that was approved in the in the
+Eversource rate case from from 2020,
+
+ align:start position:0%
+Eversource rate case from from 2020,
+ 
+
+ align:start position:0%
+Eversource rate case from from 2020,
+DPU19120.
+
+ align:start position:0%
+DPU19120.
+ 
+
+ align:start position:0%
+DPU19120.
+And then National Grid had a separate
+
+ align:start position:0%
+And then National Grid had a separate
+ 
+
+ align:start position:0%
+And then National Grid had a separate
+proceeding where this is before I got
+
+ align:start position:0%
+proceeding where this is before I got
+ 
+
+ align:start position:0%
+proceeding where this is before I got
+here, of course, but authorizing up to
+
+ align:start position:0%
+here, of course, but authorizing up to
+ 
+
+ align:start position:0%
+here, of course, but authorizing up to
+15.6 million for four network geothermal
+
+ align:start position:0%
+15.6 million for four network geothermal
+ 
+
+ align:start position:0%
+15.6 million for four network geothermal
+projects. the first of which was in l
+
+ align:start position:0%
+projects. the first of which was in l
+ 
+
+ align:start position:0%
+projects. the first of which was in l
+and I think national good has announced
+
+ align:start position:0%
+and I think national good has announced
+ 
+
+ align:start position:0%
+and I think national good has announced
+that they are they are terminating that
+
+ align:start position:0%
+that they are they are terminating that
+ 
+
+ align:start position:0%
+that they are they are terminating that
+project um I think just the level of
+
+ align:start position:0%
+project um I think just the level of
+ 
+
+ align:start position:0%
+project um I think just the level of
+participation wasn't as wasn't as great
+
+ align:start position:0%
+participation wasn't as wasn't as great
+ 
+
+ align:start position:0%
+participation wasn't as wasn't as great
+the numbers didn't didn't work very well
+
+ align:start position:0%
+the numbers didn't didn't work very well
+ 
+
+ align:start position:0%
+the numbers didn't didn't work very well
+but they've also filed for the Franklin
+
+ align:start position:0%
+but they've also filed for the Franklin
+ 
+
+ align:start position:0%
+but they've also filed for the Franklin
+field apartments with the Boston Housing
+
+ align:start position:0%
+field apartments with the Boston Housing
+ 
+
+ align:start position:0%
+field apartments with the Boston Housing
+Authority and so that's that project is
+
+ align:start position:0%
+Authority and so that's that project is
+ 
+
+ align:start position:0%
+Authority and so that's that project is
+is moving forward and then we'll be
+
+ align:start position:0%
+is moving forward and then we'll be
+ 
+
+ align:start position:0%
+is moving forward and then we'll be
+looking like I say we'll be applying
+
+ align:start position:0%
+looking like I say we'll be applying
+ 
+
+ align:start position:0%
+looking like I say we'll be applying
+those criteria then we consider the rate
+
+ align:start position:0%
+those criteria then we consider the rate
+ 
+
+ align:start position:0%
+those criteria then we consider the rate
+recovery treatment of these of these
+
+ align:start position:0%
+recovery treatment of these of these
+ 
+
+ align:start position:0%
+recovery treatment of these of these
+demonstration projects so with that I'm
+
+ align:start position:0%
+demonstration projects so with that I'm
+ 
+
+ align:start position:0%
+demonstration projects so with that I'm
+happy to answer questions Sir,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever.
\ No newline at end of file
diff --git a/R0tFDXBZvKI.txt b/R0tFDXBZvKI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..680544069f6475c74047367360aac47d7c09794f
--- /dev/null
+++ b/R0tFDXBZvKI.txt
@@ -0,0 +1,435 @@
+align:start position:0%
+ 
+in order to build circuits that
+
+ align:start position:0%
+in order to build circuits that
+ 
+
+ align:start position:0%
+in order to build circuits that
+manipulate transmitter store information
+
+ align:start position:0%
+manipulate transmitter store information
+ 
+
+ align:start position:0%
+manipulate transmitter store information
+we are going to need some engineering
+
+ align:start position:0%
+we are going to need some engineering
+ 
+
+ align:start position:0%
+we are going to need some engineering
+tools to help us determine if we're
+
+ align:start position:0%
+tools to help us determine if we're
+ 
+
+ align:start position:0%
+tools to help us determine if we're
+choosing a good representation for the
+
+ align:start position:0%
+choosing a good representation for the
+ 
+
+ align:start position:0%
+choosing a good representation for the
+information that's the subject of this
+
+ align:start position:0%
+information that's the subject of this
+ 
+
+ align:start position:0%
+information that's the subject of this
+chapter we'll study different ways of
+
+ align:start position:0%
+chapter we'll study different ways of
+ 
+
+ align:start position:0%
+chapter we'll study different ways of
+encoding information as bits and learn
+
+ align:start position:0%
+encoding information as bits and learn
+ 
+
+ align:start position:0%
+encoding information as bits and learn
+the mathematics that help us determine
+
+ align:start position:0%
+the mathematics that help us determine
+ 
+
+ align:start position:0%
+the mathematics that help us determine
+if our encoding is a good one
+
+ align:start position:0%
+if our encoding is a good one
+ 
+
+ align:start position:0%
+if our encoding is a good one
+we'll also look into what we can do if
+
+ align:start position:0%
+we'll also look into what we can do if
+ 
+
+ align:start position:0%
+we'll also look into what we can do if
+our representation gets corrupted by
+
+ align:start position:0%
+our representation gets corrupted by
+ 
+
+ align:start position:0%
+our representation gets corrupted by
+errors it would be nice to detect that
+
+ align:start position:0%
+errors it would be nice to detect that
+ 
+
+ align:start position:0%
+errors it would be nice to detect that
+something bad has happened and possibly
+
+ align:start position:0%
+something bad has happened and possibly
+ 
+
+ align:start position:0%
+something bad has happened and possibly
+even correct the problem let's start by
+
+ align:start position:0%
+even correct the problem let's start by
+ 
+
+ align:start position:0%
+even correct the problem let's start by
+asking what is information from our
+
+ align:start position:0%
+asking what is information from our
+ 
+
+ align:start position:0%
+asking what is information from our
+engineering perspective we'll define
+
+ align:start position:0%
+engineering perspective we'll define
+ 
+
+ align:start position:0%
+engineering perspective we'll define
+information as data communicated or
+
+ align:start position:0%
+information as data communicated or
+ 
+
+ align:start position:0%
+information as data communicated or
+received that resolves uncertainty about
+
+ align:start position:0%
+received that resolves uncertainty about
+ 
+
+ align:start position:0%
+received that resolves uncertainty about
+a particular fact or circumstance in
+
+ align:start position:0%
+a particular fact or circumstance in
+ 
+
+ align:start position:0%
+a particular fact or circumstance in
+other words after receiving the data
+
+ align:start position:0%
+other words after receiving the data
+ 
+
+ align:start position:0%
+other words after receiving the data
+we'll know more about that particular
+
+ align:start position:0%
+we'll know more about that particular
+ 
+
+ align:start position:0%
+we'll know more about that particular
+factor circumstance the greater the
+
+ align:start position:0%
+factor circumstance the greater the
+ 
+
+ align:start position:0%
+factor circumstance the greater the
+uncertainty resolved by the data the
+
+ align:start position:0%
+uncertainty resolved by the data the
+ 
+
+ align:start position:0%
+uncertainty resolved by the data the
+more information that data has conveyed
+
+ align:start position:0%
+more information that data has conveyed
+ 
+
+ align:start position:0%
+more information that data has conveyed
+let's look at an example a card has been
+
+ align:start position:0%
+let's look at an example a card has been
+ 
+
+ align:start position:0%
+let's look at an example a card has been
+chosen at random from a normal deck of
+
+ align:start position:0%
+chosen at random from a normal deck of
+ 
+
+ align:start position:0%
+chosen at random from a normal deck of
+52 playing cards without any data about
+
+ align:start position:0%
+52 playing cards without any data about
+ 
+
+ align:start position:0%
+52 playing cards without any data about
+the chosen card there are 52
+
+ align:start position:0%
+the chosen card there are 52
+ 
+
+ align:start position:0%
+the chosen card there are 52
+possibilities for the type of the card
+
+ align:start position:0%
+possibilities for the type of the card
+ 
+
+ align:start position:0%
+possibilities for the type of the card
+now suppose you receive one of the
+
+ align:start position:0%
+now suppose you receive one of the
+ 
+
+ align:start position:0%
+now suppose you receive one of the
+following pieces of data about the
+
+ align:start position:0%
+following pieces of data about the
+ 
+
+ align:start position:0%
+following pieces of data about the
+choice hey you learned that the suit of
+
+ align:start position:0%
+choice hey you learned that the suit of
+ 
+
+ align:start position:0%
+choice hey you learned that the suit of
+the card is heart this narrows the
+
+ align:start position:0%
+the card is heart this narrows the
+ 
+
+ align:start position:0%
+the card is heart this narrows the
+choice down to one of 13 cards B you
+
+ align:start position:0%
+choice down to one of 13 cards B you
+ 
+
+ align:start position:0%
+choice down to one of 13 cards B you
+learn instead the card is not the ace of
+
+ align:start position:0%
+learn instead the card is not the ace of
+ 
+
+ align:start position:0%
+learn instead the card is not the ace of
+spades this still leaves 51 cards that
+
+ align:start position:0%
+spades this still leaves 51 cards that
+ 
+
+ align:start position:0%
+spades this still leaves 51 cards that
+it might be C you learn instead that the
+
+ align:start position:0%
+it might be C you learn instead that the
+ 
+
+ align:start position:0%
+it might be C you learn instead that the
+card is a face card that is a Jack queen
+
+ align:start position:0%
+card is a face card that is a Jack queen
+ 
+
+ align:start position:0%
+card is a face card that is a Jack queen
+or king so the choice is one of 12 cards
+
+ align:start position:0%
+or king so the choice is one of 12 cards
+ 
+
+ align:start position:0%
+or king so the choice is one of 12 cards
+d you learn instead that the card is the
+
+ align:start position:0%
+d you learn instead that the card is the
+ 
+
+ align:start position:0%
+d you learn instead that the card is the
+suicide King her little blue friend is
+
+ align:start position:0%
+suicide King her little blue friend is
+ 
+
+ align:start position:0%
+suicide King her little blue friend is
+showing us that this is actually a
+
+ align:start position:0%
+showing us that this is actually a
+ 
+
+ align:start position:0%
+showing us that this is actually a
+particular card the King of Hearts where
+
+ align:start position:0%
+particular card the King of Hearts where
+ 
+
+ align:start position:0%
+particular card the King of Hearts where
+the King is sticking the sword through
+
+ align:start position:0%
+the King is sticking the sword through
+ 
+
+ align:start position:0%
+the King is sticking the sword through
+his head no uncertainty here we know
+
+ align:start position:0%
+his head no uncertainty here we know
+ 
+
+ align:start position:0%
+his head no uncertainty here we know
+exactly what the choice was which of the
+
+ align:start position:0%
+exactly what the choice was which of the
+ 
+
+ align:start position:0%
+exactly what the choice was which of the
+possible pieces of data conveys the most
+
+ align:start position:0%
+possible pieces of data conveys the most
+ 
+
+ align:start position:0%
+possible pieces of data conveys the most
+information in other words which data
+
+ align:start position:0%
+information in other words which data
+ 
+
+ align:start position:0%
+information in other words which data
+resolves the most uncertainty about the
+
+ align:start position:0%
+resolves the most uncertainty about the
+ 
+
+ align:start position:0%
+resolves the most uncertainty about the
+chosen card similarly which data conveys
+
+ align:start position:0%
+chosen card similarly which data conveys
+ 
+
+ align:start position:0%
+chosen card similarly which data conveys
+the least amount of information before
+
+ align:start position:0%
+the least amount of information before
+ 
+
+ align:start position:0%
+the least amount of information before
+we talk about the mathematics behind the
+
+ align:start position:0%
+we talk about the mathematics behind the
+ 
+
+ align:start position:0%
+we talk about the mathematics behind the
+correct answers to these questions
+
+ align:start position:0%
+correct answers to these questions
+ 
+
+ align:start position:0%
+correct answers to these questions
+for your answers in the following poll
\ No newline at end of file
diff --git a/RKjvoLeojfk.txt b/RKjvoLeojfk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4b05108d5d4c5c9f082f58825fc70d8202ac6a34
--- /dev/null
+++ b/RKjvoLeojfk.txt
@@ -0,0 +1,2019 @@
+align:start position:0%
+ 
+in this video we're going to take a look
+
+ align:start position:0%
+in this video we're going to take a look
+ 
+
+ align:start position:0%
+in this video we're going to take a look
+at how the social contract issues have
+
+ align:start position:0%
+at how the social contract issues have
+ 
+
+ align:start position:0%
+at how the social contract issues have
+been addressed around the world it turns
+
+ align:start position:0%
+been addressed around the world it turns
+ 
+
+ align:start position:0%
+been addressed around the world it turns
+out there's quite a bit of experience
+
+ align:start position:0%
+out there's quite a bit of experience
+ 
+
+ align:start position:0%
+out there's quite a bit of experience
+with this sometimes with success for a
+
+ align:start position:0%
+with this sometimes with success for a
+ 
+
+ align:start position:0%
+with this sometimes with success for a
+limited period of time and sometimes
+
+ align:start position:0%
+limited period of time and sometimes
+ 
+
+ align:start position:0%
+limited period of time and sometimes
+without as much success so let's see how
+
+ align:start position:0%
+without as much success so let's see how
+ 
+
+ align:start position:0%
+without as much success so let's see how
+other countries address these issues
+
+ align:start position:0%
+other countries address these issues
+ 
+
+ align:start position:0%
+other countries address these issues
+let's start with Australia Australia has
+
+ align:start position:0%
+let's start with Australia Australia has
+ 
+
+ align:start position:0%
+let's start with Australia Australia has
+a long history in the 1980s a new prime
+
+ align:start position:0%
+a long history in the 1980s a new prime
+ 
+
+ align:start position:0%
+a long history in the 1980s a new prime
+minister came along by the name of Bob
+
+ align:start position:0%
+minister came along by the name of Bob
+ 
+
+ align:start position:0%
+minister came along by the name of Bob
+Hawk and he came into office negotiating
+
+ align:start position:0%
+Hawk and he came into office negotiating
+ 
+
+ align:start position:0%
+Hawk and he came into office negotiating
+a new labor agreement called the Accord
+
+ align:start position:0%
+a new labor agreement called the Accord
+ 
+
+ align:start position:0%
+a new labor agreement called the Accord
+with the labor movement where he was
+
+ align:start position:0%
+with the labor movement where he was
+ 
+
+ align:start position:0%
+with the labor movement where he was
+saying to labor if you limit your wage
+
+ align:start position:0%
+saying to labor if you limit your wage
+ 
+
+ align:start position:0%
+saying to labor if you limit your wage
+increases to the price increases that
+
+ align:start position:0%
+increases to the price increases that
+ 
+
+ align:start position:0%
+increases to the price increases that
+are happening in the country we will
+
+ align:start position:0%
+are happening in the country we will
+ 
+
+ align:start position:0%
+are happening in the country we will
+then find some offsetting things that we
+
+ align:start position:0%
+then find some offsetting things that we
+ 
+
+ align:start position:0%
+then find some offsetting things that we
+can do in social welfare so so they
+
+ align:start position:0%
+can do in social welfare so so they
+ 
+
+ align:start position:0%
+can do in social welfare so so they
+negotiated a national health insurance
+
+ align:start position:0%
+negotiated a national health insurance
+ 
+
+ align:start position:0%
+negotiated a national health insurance
+they negotiated a national pension
+
+ align:start position:0%
+they negotiated a national pension
+ 
+
+ align:start position:0%
+they negotiated a national pension
+program they put in place a variety of
+
+ align:start position:0%
+program they put in place a variety of
+ 
+
+ align:start position:0%
+program they put in place a variety of
+other worker adjustment programs and for
+
+ align:start position:0%
+other worker adjustment programs and for
+ 
+
+ align:start position:0%
+other worker adjustment programs and for
+business they allowed over time much
+
+ align:start position:0%
+business they allowed over time much
+ 
+
+ align:start position:0%
+business they allowed over time much
+more flexibility in promoting collective
+
+ align:start position:0%
+more flexibility in promoting collective
+ 
+
+ align:start position:0%
+more flexibility in promoting collective
+bargaining at the level of the firm that
+
+ align:start position:0%
+bargaining at the level of the firm that
+ 
+
+ align:start position:0%
+bargaining at the level of the firm that
+worked for quite a while new prime
+
+ align:start position:0%
+worked for quite a while new prime
+ 
+
+ align:start position:0%
+worked for quite a while new prime
+minister comes in from a different party
+
+ align:start position:0%
+minister comes in from a different party
+ 
+
+ align:start position:0%
+minister comes in from a different party
+says no more of this and so it hasn't
+
+ align:start position:0%
+says no more of this and so it hasn't
+ 
+
+ align:start position:0%
+says no more of this and so it hasn't
+really continued up until today but now
+
+ align:start position:0%
+really continued up until today but now
+ 
+
+ align:start position:0%
+really continued up until today but now
+in recent years Australia has taken a
+
+ align:start position:0%
+in recent years Australia has taken a
+ 
+
+ align:start position:0%
+in recent years Australia has taken a
+more modern approach it says today's
+
+ align:start position:0%
+more modern approach it says today's
+ 
+
+ align:start position:0%
+more modern approach it says today's
+Workforce needs flexibility for more
+
+ align:start position:0%
+Workforce needs flexibility for more
+ 
+
+ align:start position:0%
+Workforce needs flexibility for more
+parental leave so that women and men can
+
+ align:start position:0%
+parental leave so that women and men can
+ 
+
+ align:start position:0%
+parental leave so that women and men can
+take care of their family and work
+
+ align:start position:0%
+take care of their family and work
+ 
+
+ align:start position:0%
+take care of their family and work
+responsibilities so in 2011 their first
+
+ align:start position:0%
+responsibilities so in 2011 their first
+ 
+
+ align:start position:0%
+responsibilities so in 2011 their first
+parental leave program was put in place
+
+ align:start position:0%
+parental leave program was put in place
+ 
+
+ align:start position:0%
+parental leave program was put in place
+at a national level now they're
+
+ align:start position:0%
+at a national level now they're
+ 
+
+ align:start position:0%
+at a national level now they're
+struggling to make that work and to
+
+ align:start position:0%
+struggling to make that work and to
+ 
+
+ align:start position:0%
+struggling to make that work and to
+fight those who want to repeal it but it
+
+ align:start position:0%
+fight those who want to repeal it but it
+ 
+
+ align:start position:0%
+fight those who want to repeal it but it
+is continuing to play an important role
+
+ align:start position:0%
+is continuing to play an important role
+ 
+
+ align:start position:0%
+is continuing to play an important role
+like Australia Britain has a long
+
+ align:start position:0%
+like Australia Britain has a long
+ 
+
+ align:start position:0%
+like Australia Britain has a long
+history in the 1960s and 70s like
+
+ align:start position:0%
+history in the 1960s and 70s like
+ 
+
+ align:start position:0%
+history in the 1960s and 70s like
+Australia they were trying to limit wage
+
+ align:start position:0%
+Australia they were trying to limit wage
+ 
+
+ align:start position:0%
+Australia they were trying to limit wage
+increases to deal with inflation and
+
+ align:start position:0%
+increases to deal with inflation and
+ 
+
+ align:start position:0%
+increases to deal with inflation and
+then in the 1980s Along Comes Margaret
+
+ align:start position:0%
+then in the 1980s Along Comes Margaret
+ 
+
+ align:start position:0%
+then in the 1980s Along Comes Margaret
+Thatcher as a new prime minister called
+
+ align:start position:0%
+Thatcher as a new prime minister called
+ 
+
+ align:start position:0%
+Thatcher as a new prime minister called
+The Iron Lady and she says no more of
+
+ align:start position:0%
+The Iron Lady and she says no more of
+ 
+
+ align:start position:0%
+The Iron Lady and she says no more of
+that I'm going to take a hard line she
+
+ align:start position:0%
+that I'm going to take a hard line she
+ 
+
+ align:start position:0%
+that I'm going to take a hard line she
+took on the most powerful Union in the
+
+ align:start position:0%
+took on the most powerful Union in the
+ 
+
+ align:start position:0%
+took on the most powerful Union in the
+country the miners Union in 1984
+
+ align:start position:0%
+country the miners Union in 1984
+ 
+
+ align:start position:0%
+country the miners Union in 1984
+1985 and she basically broke a strike of
+
+ align:start position:0%
+1985 and she basically broke a strike of
+ 
+
+ align:start position:0%
+1985 and she basically broke a strike of
+that Union and started to bring down the
+
+ align:start position:0%
+that Union and started to bring down the
+ 
+
+ align:start position:0%
+that Union and started to bring down the
+rate of wage increase and help companies
+
+ align:start position:0%
+rate of wage increase and help companies
+ 
+
+ align:start position:0%
+rate of wage increase and help companies
+get more flexibility and limited Labor's
+
+ align:start position:0%
+get more flexibility and limited Labor's
+ 
+
+ align:start position:0%
+get more flexibility and limited Labor's
+power that carried forward up until the
+
+ align:start position:0%
+power that carried forward up until the
+ 
+
+ align:start position:0%
+power that carried forward up until the
+election of another new Prime Minister
+
+ align:start position:0%
+election of another new Prime Minister
+ 
+
+ align:start position:0%
+election of another new Prime Minister
+Tony Blair in the 1990s and Tony Blair
+
+ align:start position:0%
+Tony Blair in the 1990s and Tony Blair
+ 
+
+ align:start position:0%
+Tony Blair in the 1990s and Tony Blair
+basically said I'm not going to go back
+
+ align:start position:0%
+basically said I'm not going to go back
+ 
+
+ align:start position:0%
+basically said I'm not going to go back
+to the old labor policies but I'm also
+
+ align:start position:0%
+to the old labor policies but I'm also
+ 
+
+ align:start position:0%
+to the old labor policies but I'm also
+not going to continue the Thatcher
+
+ align:start position:0%
+not going to continue the Thatcher
+ 
+
+ align:start position:0%
+not going to continue the Thatcher
+approach we're going to try a third way
+
+ align:start position:0%
+approach we're going to try a third way
+ 
+
+ align:start position:0%
+approach we're going to try a third way
+and he looked at the workplace issues
+
+ align:start position:0%
+and he looked at the workplace issues
+ 
+
+ align:start position:0%
+and he looked at the workplace issues
+that were relevant for his point in time
+
+ align:start position:0%
+that were relevant for his point in time
+ 
+
+ align:start position:0%
+that were relevant for his point in time
+and he said let's negotiate let's put in
+
+ align:start position:0%
+and he said let's negotiate let's put in
+ 
+
+ align:start position:0%
+and he said let's negotiate let's put in
+place a a commission a labor business
+
+ align:start position:0%
+place a a commission a labor business
+ 
+
+ align:start position:0%
+place a a commission a labor business
+government academic commission to set up
+
+ align:start position:0%
+government academic commission to set up
+ 
+
+ align:start position:0%
+government academic commission to set up
+a minimum wage so that we can help those
+
+ align:start position:0%
+a minimum wage so that we can help those
+ 
+
+ align:start position:0%
+a minimum wage so that we can help those
+at the bottom of our income distribution
+
+ align:start position:0%
+at the bottom of our income distribution
+ 
+
+ align:start position:0%
+at the bottom of our income distribution
+and that's the most successful part of
+
+ align:start position:0%
+and that's the most successful part of
+ 
+
+ align:start position:0%
+and that's the most successful part of
+his legacy well if you really want to
+
+ align:start position:0%
+his legacy well if you really want to
+ 
+
+ align:start position:0%
+his legacy well if you really want to
+look at the longest history of Labor
+
+ align:start position:0%
+look at the longest history of Labor
+ 
+
+ align:start position:0%
+look at the longest history of Labor
+Management consultation and and
+
+ align:start position:0%
+Management consultation and and
+ 
+
+ align:start position:0%
+Management consultation and and
+cooperation you have to go to
+
+ align:start position:0%
+cooperation you have to go to
+ 
+
+ align:start position:0%
+cooperation you have to go to
+Continental Europe countries like Sweden
+
+ align:start position:0%
+Continental Europe countries like Sweden
+ 
+
+ align:start position:0%
+Continental Europe countries like Sweden
+Denmark France Germany sometimes Italy
+
+ align:start position:0%
+Denmark France Germany sometimes Italy
+ 
+
+ align:start position:0%
+Denmark France Germany sometimes Italy
+and others in Sweden for example there's
+
+ align:start position:0%
+and others in Sweden for example there's
+ 
+
+ align:start position:0%
+and others in Sweden for example there's
+a long history of business labor and
+
+ align:start position:0%
+a long history of business labor and
+ 
+
+ align:start position:0%
+a long history of business labor and
+government negotiating in a Cooperative
+
+ align:start position:0%
+government negotiating in a Cooperative
+ 
+
+ align:start position:0%
+government negotiating in a Cooperative
+way both at the national levels and more
+
+ align:start position:0%
+way both at the national levels and more
+ 
+
+ align:start position:0%
+way both at the national levels and more
+recently at the local and Regional
+
+ align:start position:0%
+recently at the local and Regional
+ 
+
+ align:start position:0%
+recently at the local and Regional
+levels and Company levels basically it's
+
+ align:start position:0%
+levels and Company levels basically it's
+ 
+
+ align:start position:0%
+levels and Company levels basically it's
+all part of the Social
+
+ align:start position:0%
+all part of the Social
+ 
+
+ align:start position:0%
+all part of the Social
+Democratic Values of the Swedish and the
+
+ align:start position:0%
+Democratic Values of the Swedish and the
+ 
+
+ align:start position:0%
+Democratic Values of the Swedish and the
+Nordic societies saying we need to work
+
+ align:start position:0%
+Nordic societies saying we need to work
+ 
+
+ align:start position:0%
+Nordic societies saying we need to work
+together to promote democracy and equity
+
+ align:start position:0%
+together to promote democracy and equity
+ 
+
+ align:start position:0%
+together to promote democracy and equity
+in our economic policies and so that
+
+ align:start position:0%
+in our economic policies and so that
+ 
+
+ align:start position:0%
+in our economic policies and so that
+policy continues today even in in times
+
+ align:start position:0%
+policy continues today even in in times
+ 
+
+ align:start position:0%
+policy continues today even in in times
+of difficult ulty or take another uh
+
+ align:start position:0%
+of difficult ulty or take another uh
+ 
+
+ align:start position:0%
+of difficult ulty or take another uh
+look at another country Denmark Denmark
+
+ align:start position:0%
+look at another country Denmark Denmark
+ 
+
+ align:start position:0%
+look at another country Denmark Denmark
+in recent years has recognize the real
+
+ align:start position:0%
+in recent years has recognize the real
+ 
+
+ align:start position:0%
+in recent years has recognize the real
+issue is how do we adjust from an
+
+ align:start position:0%
+issue is how do we adjust from an
+ 
+
+ align:start position:0%
+issue is how do we adjust from an
+industrial to a more Dynamic Innovation
+
+ align:start position:0%
+industrial to a more Dynamic Innovation
+ 
+
+ align:start position:0%
+industrial to a more Dynamic Innovation
+based economy that means firms need more
+
+ align:start position:0%
+based economy that means firms need more
+ 
+
+ align:start position:0%
+based economy that means firms need more
+flexibility to hire and fire and lay off
+
+ align:start position:0%
+flexibility to hire and fire and lay off
+ 
+
+ align:start position:0%
+flexibility to hire and fire and lay off
+people as the economy changes and so
+
+ align:start position:0%
+people as the economy changes and so
+ 
+
+ align:start position:0%
+people as the economy changes and so
+Denmark has traded off what they call
+
+ align:start position:0%
+Denmark has traded off what they call
+ 
+
+ align:start position:0%
+Denmark has traded off what they call
+flexibility for security that is firms
+
+ align:start position:0%
+flexibility for security that is firms
+ 
+
+ align:start position:0%
+flexibility for security that is firms
+are more open and and free to lay people
+
+ align:start position:0%
+are more open and and free to lay people
+ 
+
+ align:start position:0%
+are more open and and free to lay people
+off but there's an active labor market
+
+ align:start position:0%
+off but there's an active labor market
+ 
+
+ align:start position:0%
+off but there's an active labor market
+policy that then supports workers as
+
+ align:start position:0%
+policy that then supports workers as
+ 
+
+ align:start position:0%
+policy that then supports workers as
+they make the transition to new jobs
+
+ align:start position:0%
+they make the transition to new jobs
+ 
+
+ align:start position:0%
+they make the transition to new jobs
+with a stronger safety net with training
+
+ align:start position:0%
+with a stronger safety net with training
+ 
+
+ align:start position:0%
+with a stronger safety net with training
+and with adjustment and assistance so
+
+ align:start position:0%
+and with adjustment and assistance so
+ 
+
+ align:start position:0%
+and with adjustment and assistance so
+that then helps firms to maintain their
+
+ align:start position:0%
+that then helps firms to maintain their
+ 
+
+ align:start position:0%
+that then helps firms to maintain their
+flexibility and to adapt to Changing
+
+ align:start position:0%
+flexibility and to adapt to Changing
+ 
+
+ align:start position:0%
+flexibility and to adapt to Changing
+Times so around the world we see a
+
+ align:start position:0%
+Times so around the world we see a
+ 
+
+ align:start position:0%
+Times so around the world we see a
+variety of different approaches to these
+
+ align:start position:0%
+variety of different approaches to these
+ 
+
+ align:start position:0%
+variety of different approaches to these
+issues Japan is another country with a
+
+ align:start position:0%
+issues Japan is another country with a
+ 
+
+ align:start position:0%
+issues Japan is another country with a
+long history of Labor Management
+
+ align:start position:0%
+long history of Labor Management
+ 
+
+ align:start position:0%
+long history of Labor Management
+consultation for years its Ministry of
+
+ align:start position:0%
+consultation for years its Ministry of
+ 
+
+ align:start position:0%
+consultation for years its Ministry of
+international trade and
+
+ align:start position:0%
+international trade and
+ 
+
+ align:start position:0%
+international trade and
+Industry worked with business and labor
+
+ align:start position:0%
+Industry worked with business and labor
+ 
+
+ align:start position:0%
+Industry worked with business and labor
+at the national level in lots of
+
+ align:start position:0%
+at the national level in lots of
+ 
+
+ align:start position:0%
+at the national level in lots of
+consultation to say here's basically the
+
+ align:start position:0%
+consultation to say here's basically the
+ 
+
+ align:start position:0%
+consultation to say here's basically the
+wage Target for increasing wages this
+
+ align:start position:0%
+wage Target for increasing wages this
+ 
+
+ align:start position:0%
+wage Target for increasing wages this
+year and then individual companies and
+
+ align:start position:0%
+year and then individual companies and
+ 
+
+ align:start position:0%
+year and then individual companies and
+Enterprise Unions would use that Target
+
+ align:start position:0%
+Enterprise Unions would use that Target
+ 
+
+ align:start position:0%
+Enterprise Unions would use that Target
+to negotiate their specific conditions
+
+ align:start position:0%
+to negotiate their specific conditions
+ 
+
+ align:start position:0%
+to negotiate their specific conditions
+and that worked quite well for Japan and
+
+ align:start position:0%
+and that worked quite well for Japan and
+ 
+
+ align:start position:0%
+and that worked quite well for Japan and
+for business in labor in ch in that
+
+ align:start position:0%
+for business in labor in ch in that
+ 
+
+ align:start position:0%
+for business in labor in ch in that
+country for many years but then as the
+
+ align:start position:0%
+country for many years but then as the
+ 
+
+ align:start position:0%
+country for many years but then as the
+economy changed and Japan began to get
+
+ align:start position:0%
+economy changed and Japan began to get
+ 
+
+ align:start position:0%
+economy changed and Japan began to get
+competition from China and other places
+
+ align:start position:0%
+competition from China and other places
+ 
+
+ align:start position:0%
+competition from China and other places
+uh it broke down and now China is trying
+
+ align:start position:0%
+uh it broke down and now China is trying
+ 
+
+ align:start position:0%
+uh it broke down and now China is trying
+to figure out how to get wages moving
+
+ align:start position:0%
+to figure out how to get wages moving
+ 
+
+ align:start position:0%
+to figure out how to get wages moving
+more aggressively and prices increasing
+
+ align:start position:0%
+more aggressively and prices increasing
+ 
+
+ align:start position:0%
+more aggressively and prices increasing
+because it's having trouble adapting to
+
+ align:start position:0%
+because it's having trouble adapting to
+ 
+
+ align:start position:0%
+because it's having trouble adapting to
+a more Dynamic economy another example a
+
+ align:start position:0%
+a more Dynamic economy another example a
+ 
+
+ align:start position:0%
+a more Dynamic economy another example a
+very different example would be in Korea
+
+ align:start position:0%
+very different example would be in Korea
+ 
+
+ align:start position:0%
+very different example would be in Korea
+Korea has had a very tumultuous Labor
+
+ align:start position:0%
+Korea has had a very tumultuous Labor
+ 
+
+ align:start position:0%
+Korea has had a very tumultuous Labor
+Management history up until the mid
+
+ align:start position:0%
+Management history up until the mid
+ 
+
+ align:start position:0%
+Management history up until the mid
+1980s unions were suppressed in Korea
+
+ align:start position:0%
+1980s unions were suppressed in Korea
+ 
+
+ align:start position:0%
+1980s unions were suppressed in Korea
+and there were often violent strikes
+
+ align:start position:0%
+and there were often violent strikes
+ 
+
+ align:start position:0%
+and there were often violent strikes
+that would come and then get suppressed
+
+ align:start position:0%
+that would come and then get suppressed
+ 
+
+ align:start position:0%
+that would come and then get suppressed
+and the police would come in and it
+
+ align:start position:0%
+and the police would come in and it
+ 
+
+ align:start position:0%
+and the police would come in and it
+would be died it would all die down for
+
+ align:start position:0%
+would be died it would all die down for
+ 
+
+ align:start position:0%
+would be died it would all die down for
+a while and it would be quiet but then
+
+ align:start position:0%
+a while and it would be quiet but then
+ 
+
+ align:start position:0%
+a while and it would be quiet but then
+in 1987 the government began to open up
+
+ align:start position:0%
+in 1987 the government began to open up
+ 
+
+ align:start position:0%
+in 1987 the government began to open up
+the labor market to Stronger worker
+
+ align:start position:0%
+the labor market to Stronger worker
+ 
+
+ align:start position:0%
+the labor market to Stronger worker
+rights and it said let's try to work
+
+ align:start position:0%
+rights and it said let's try to work
+ 
+
+ align:start position:0%
+rights and it said let's try to work
+together but that long history of
+
+ align:start position:0%
+together but that long history of
+ 
+
+ align:start position:0%
+together but that long history of
+conflict made it very very difficult for
+
+ align:start position:0%
+conflict made it very very difficult for
+ 
+
+ align:start position:0%
+conflict made it very very difficult for
+labor and management to work together
+
+ align:start position:0%
+labor and management to work together
+ 
+
+ align:start position:0%
+labor and management to work together
+and so even today we now see big
+
+ align:start position:0%
+and so even today we now see big
+ 
+
+ align:start position:0%
+and so even today we now see big
+protests happening in Korean workplaces
+
+ align:start position:0%
+protests happening in Korean workplaces
+ 
+
+ align:start position:0%
+protests happening in Korean workplaces
+as the government tries to get Korean
+
+ align:start position:0%
+as the government tries to get Korean
+ 
+
+ align:start position:0%
+as the government tries to get Korean
+employers to be more flexible and Korean
+
+ align:start position:0%
+employers to be more flexible and Korean
+ 
+
+ align:start position:0%
+employers to be more flexible and Korean
+workers are saying we are not sharing in
+
+ align:start position:0%
+workers are saying we are not sharing in
+ 
+
+ align:start position:0%
+workers are saying we are not sharing in
+all of the prosperity of this country
+
+ align:start position:0%
+all of the prosperity of this country
+ 
+
+ align:start position:0%
+all of the prosperity of this country
+another example would be in China
+
+ align:start position:0%
+another example would be in China
+ 
+
+ align:start position:0%
+another example would be in China
+perhaps there's no country that better
+
+ align:start position:0%
+perhaps there's no country that better
+ 
+
+ align:start position:0%
+perhaps there's no country that better
+more needs a new social contract than
+
+ align:start position:0%
+more needs a new social contract than
+ 
+
+ align:start position:0%
+more needs a new social contract than
+China as we all know as the Chinese
+
+ align:start position:0%
+China as we all know as the Chinese
+ 
+
+ align:start position:0%
+China as we all know as the Chinese
+economy began to open up to more private
+
+ align:start position:0%
+economy began to open up to more private
+ 
+
+ align:start position:0%
+economy began to open up to more private
+Enterprise and foreign investment we saw
+
+ align:start position:0%
+Enterprise and foreign investment we saw
+ 
+
+ align:start position:0%
+Enterprise and foreign investment we saw
+a wave of strikes in China first at
+
+ align:start position:0%
+a wave of strikes in China first at
+ 
+
+ align:start position:0%
+a wave of strikes in China first at
+Honda in 2010 a big strike that resulted
+
+ align:start position:0%
+Honda in 2010 a big strike that resulted
+ 
+
+ align:start position:0%
+Honda in 2010 a big strike that resulted
+in a wage increase and we've seen that
+
+ align:start position:0%
+in a wage increase and we've seen that
+ 
+
+ align:start position:0%
+in a wage increase and we've seen that
+carry over in strikes at one of Apple's
+
+ align:start position:0%
+carry over in strikes at one of Apple's
+ 
+
+ align:start position:0%
+carry over in strikes at one of Apple's
+big suppliers of parts for computers
+
+ align:start position:0%
+big suppliers of parts for computers
+ 
+
+ align:start position:0%
+big suppliers of parts for computers
+called foxcon where not only Workers are
+
+ align:start position:0%
+called foxcon where not only Workers are
+ 
+
+ align:start position:0%
+called foxcon where not only Workers are
+striking but sometimes they commit
+
+ align:start position:0%
+striking but sometimes they commit
+ 
+
+ align:start position:0%
+striking but sometimes they commit
+suicide in protest of the conditions
+
+ align:start position:0%
+suicide in protest of the conditions
+ 
+
+ align:start position:0%
+suicide in protest of the conditions
+that they face so China doesn't really
+
+ align:start position:0%
+that they face so China doesn't really
+ 
+
+ align:start position:0%
+that they face so China doesn't really
+have institutions and policies to govern
+
+ align:start position:0%
+have institutions and policies to govern
+ 
+
+ align:start position:0%
+have institutions and policies to govern
+workplace negotiations it badly needs to
+
+ align:start position:0%
+workplace negotiations it badly needs to
+ 
+
+ align:start position:0%
+workplace negotiations it badly needs to
+find a way to allow workers to express
+
+ align:start position:0%
+find a way to allow workers to express
+ 
+
+ align:start position:0%
+find a way to allow workers to express
+their needs their interests their voice
+
+ align:start position:0%
+their needs their interests their voice
+ 
+
+ align:start position:0%
+their needs their interests their voice
+at the workplace and at the same time
+
+ align:start position:0%
+at the workplace and at the same time
+ 
+
+ align:start position:0%
+at the workplace and at the same time
+maintain what they call Tranquility in
+
+ align:start position:0%
+maintain what they call Tranquility in
+ 
+
+ align:start position:0%
+maintain what they call Tranquility in
+their relationships but it's very
+
+ align:start position:0%
+their relationships but it's very
+ 
+
+ align:start position:0%
+their relationships but it's very
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+today perhaps too often we find that not
+
+ align:start position:0%
+today perhaps too often we find that not
+ 
+
+ align:start position:0%
+today perhaps too often we find that not
+only are these spontaneous worker
+
+ align:start position:0%
+only are these spontaneous worker
+ 
+
+ align:start position:0%
+only are these spontaneous worker
+protests occurring but they often take
+
+ align:start position:0%
+protests occurring but they often take
+ 
+
+ align:start position:0%
+protests occurring but they often take
+the plant manager hostage so here's a
+
+ align:start position:0%
+the plant manager hostage so here's a
+ 
+
+ align:start position:0%
+the plant manager hostage so here's a
+picture of an American who has a plant
+
+ align:start position:0%
+picture of an American who has a plant
+ 
+
+ align:start position:0%
+picture of an American who has a plant
+in China who's actually waving from
+
+ align:start position:0%
+in China who's actually waving from
+ 
+
+ align:start position:0%
+in China who's actually waving from
+inside his office to people on the
+
+ align:start position:0%
+inside his office to people on the
+ 
+
+ align:start position:0%
+inside his office to people on the
+outside because the workers are saying
+
+ align:start position:0%
+outside because the workers are saying
+ 
+
+ align:start position:0%
+outside because the workers are saying
+to him you're not paying Fair wages we
+
+ align:start position:0%
+to him you're not paying Fair wages we
+ 
+
+ align:start position:0%
+to him you're not paying Fair wages we
+need to negotiate a better Arrangement
+
+ align:start position:0%
+need to negotiate a better Arrangement
+ 
+
+ align:start position:0%
+need to negotiate a better Arrangement
+so around the world we see these
+
+ align:start position:0%
+so around the world we see these
+ 
+
+ align:start position:0%
+so around the world we see these
+differences we see in Singapore for
+
+ align:start position:0%
+differences we see in Singapore for
+ 
+
+ align:start position:0%
+differences we see in Singapore for
+example a much better uh Labor
+
+ align:start position:0%
+example a much better uh Labor
+ 
+
+ align:start position:0%
+example a much better uh Labor
+Management relationship because there
+
+ align:start position:0%
+Management relationship because there
+ 
+
+ align:start position:0%
+Management relationship because there
+the government takes a strong hand
+
+ align:start position:0%
+the government takes a strong hand
+ 
+
+ align:start position:0%
+the government takes a strong hand
+controls a lot of Economic Policy but it
+
+ align:start position:0%
+controls a lot of Economic Policy but it
+ 
+
+ align:start position:0%
+controls a lot of Economic Policy but it
+does so with what we would call a high
+
+ align:start position:0%
+does so with what we would call a high
+ 
+
+ align:start position:0%
+does so with what we would call a high
+road strategy it invests in training it
+
+ align:start position:0%
+road strategy it invests in training it
+ 
+
+ align:start position:0%
+road strategy it invests in training it
+encourages firms to have good Labor
+
+ align:start position:0%
+encourages firms to have good Labor
+ 
+
+ align:start position:0%
+encourages firms to have good Labor
+Management relations it's controlled the
+
+ align:start position:0%
+Management relations it's controlled the
+ 
+
+ align:start position:0%
+Management relations it's controlled the
+the the labor movement so that there
+
+ align:start position:0%
+the the labor movement so that there
+ 
+
+ align:start position:0%
+the the labor movement so that there
+aren't as many strikes this is
+
+ align:start position:0%
+aren't as many strikes this is
+ 
+
+ align:start position:0%
+aren't as many strikes this is
+controversial because it's not quite the
+
+ align:start position:0%
+controversial because it's not quite the
+ 
+
+ align:start position:0%
+controversial because it's not quite the
+Democratic Society that we would want
+
+ align:start position:0%
+Democratic Society that we would want
+ 
+
+ align:start position:0%
+Democratic Society that we would want
+but it's the way in which they do it in
+
+ align:start position:0%
+but it's the way in which they do it in
+ 
+
+ align:start position:0%
+but it's the way in which they do it in
+Singapore if we turn to South America
+
+ align:start position:0%
+Singapore if we turn to South America
+ 
+
+ align:start position:0%
+Singapore if we turn to South America
+countries have had a more difficult time
+
+ align:start position:0%
+countries have had a more difficult time
+ 
+
+ align:start position:0%
+countries have had a more difficult time
+uh there they've had on and off
+
+ align:start position:0%
+uh there they've had on and off
+ 
+
+ align:start position:0%
+uh there they've had on and off
+approaches again often with dictatorial
+
+ align:start position:0%
+approaches again often with dictatorial
+ 
+
+ align:start position:0%
+approaches again often with dictatorial
+governments controlling labor and
+
+ align:start position:0%
+governments controlling labor and
+ 
+
+ align:start position:0%
+governments controlling labor and
+management activities but now opening up
+
+ align:start position:0%
+management activities but now opening up
+ 
+
+ align:start position:0%
+management activities but now opening up
+to more democracy but having tremendous
+
+ align:start position:0%
+to more democracy but having tremendous
+ 
+
+ align:start position:0%
+to more democracy but having tremendous
+problems with price increases and labor
+
+ align:start position:0%
+problems with price increases and labor
+ 
+
+ align:start position:0%
+problems with price increases and labor
+protests and then finally uh I think we
+
+ align:start position:0%
+protests and then finally uh I think we
+ 
+
+ align:start position:0%
+protests and then finally uh I think we
+can see some countries where uh
+
+ align:start position:0%
+can see some countries where uh
+ 
+
+ align:start position:0%
+can see some countries where uh
+organizations act on their own so in
+
+ align:start position:0%
+organizations act on their own so in
+ 
+
+ align:start position:0%
+organizations act on their own so in
+Brazil for example some companies are
+
+ align:start position:0%
+Brazil for example some companies are
+ 
+
+ align:start position:0%
+Brazil for example some companies are
+taking their own approach to uh
+
+ align:start position:0%
+taking their own approach to uh
+ 
+
+ align:start position:0%
+taking their own approach to uh
+developing a social contract and not we
+
+ align:start position:0%
+developing a social contract and not we
+ 
+
+ align:start position:0%
+developing a social contract and not we
+waiting for the government to take
+
+ align:start position:0%
+waiting for the government to take
+ 
+
+ align:start position:0%
+waiting for the government to take
+action well what lessons can we learn
+
+ align:start position:0%
+action well what lessons can we learn
+ 
+
+ align:start position:0%
+action well what lessons can we learn
+from all of this I think there are two
+
+ align:start position:0%
+from all of this I think there are two
+ 
+
+ align:start position:0%
+from all of this I think there are two
+first it often takes a crisis a crisis
+
+ align:start position:0%
+first it often takes a crisis a crisis
+ 
+
+ align:start position:0%
+first it often takes a crisis a crisis
+will lead the parties to pull together
+
+ align:start position:0%
+will lead the parties to pull together
+ 
+
+ align:start position:0%
+will lead the parties to pull together
+whether it's the end of World War II or
+
+ align:start position:0%
+whether it's the end of World War II or
+ 
+
+ align:start position:0%
+whether it's the end of World War II or
+whether it's a deep financial crisis in
+
+ align:start position:0%
+whether it's a deep financial crisis in
+ 
+
+ align:start position:0%
+whether it's a deep financial crisis in
+Asia or some kind of other uh uh natural
+
+ align:start position:0%
+Asia or some kind of other uh uh natural
+ 
+
+ align:start position:0%
+Asia or some kind of other uh uh natural
+crisis uh that might occur perhaps from
+
+ align:start position:0%
+crisis uh that might occur perhaps from
+ 
+
+ align:start position:0%
+crisis uh that might occur perhaps from
+climate change or whatever so crisis
+
+ align:start position:0%
+climate change or whatever so crisis
+ 
+
+ align:start position:0%
+climate change or whatever so crisis
+often helps parties to to set aside
+
+ align:start position:0%
+often helps parties to to set aside
+ 
+
+ align:start position:0%
+often helps parties to to set aside
+their differences and for a while they
+
+ align:start position:0%
+their differences and for a while they
+ 
+
+ align:start position:0%
+their differences and for a while they
+can work together and Forge a new uh set
+
+ align:start position:0%
+can work together and Forge a new uh set
+ 
+
+ align:start position:0%
+can work together and Forge a new uh set
+of agreements the second thing is that a
+
+ align:start position:0%
+of agreements the second thing is that a
+ 
+
+ align:start position:0%
+of agreements the second thing is that a
+it is to remember that it timing is
+
+ align:start position:0%
+it is to remember that it timing is
+ 
+
+ align:start position:0%
+it is to remember that it timing is
+everything that one has to take
+
+ align:start position:0%
+everything that one has to take
+ 
+
+ align:start position:0%
+everything that one has to take
+advantage of specific events and when
+
+ align:start position:0%
+advantage of specific events and when
+ 
+
+ align:start position:0%
+advantage of specific events and when
+they occur like a financial crisis maybe
+
+ align:start position:0%
+they occur like a financial crisis maybe
+ 
+
+ align:start position:0%
+they occur like a financial crisis maybe
+you can renegotiate pensions in an
+
+ align:start position:0%
+you can renegotiate pensions in an
+ 
+
+ align:start position:0%
+you can renegotiate pensions in an
+appropriate way or you can deal with
+
+ align:start position:0%
+appropriate way or you can deal with
+ 
+
+ align:start position:0%
+appropriate way or you can deal with
+problems of recalcitrant unions or
+
+ align:start position:0%
+problems of recalcitrant unions or
+ 
+
+ align:start position:0%
+problems of recalcitrant unions or
+recalcitrant employers and find ways to
+
+ align:start position:0%
+recalcitrant employers and find ways to
+ 
+
+ align:start position:0%
+recalcitrant employers and find ways to
+get them to work together because
+
+ align:start position:0%
+get them to work together because
+ 
+
+ align:start position:0%
+get them to work together because
+there's a specific issue that they both
+
+ align:start position:0%
+there's a specific issue that they both
+ 
+
+ align:start position:0%
+there's a specific issue that they both
+confront so timing is everything using
+
+ align:start position:0%
+confront so timing is everything using
+ 
+
+ align:start position:0%
+confront so timing is everything using
+crisis as an opportunity for change so
+
+ align:start position:0%
+crisis as an opportunity for change so
+ 
+
+ align:start position:0%
+crisis as an opportunity for change so
+all around the world workers employers
+
+ align:start position:0%
+all around the world workers employers
+ 
+
+ align:start position:0%
+all around the world workers employers
+governments Educators need to figure out
+
+ align:start position:0%
+governments Educators need to figure out
+ 
+
+ align:start position:0%
+governments Educators need to figure out
+when it's possible to negotiate a new
+
+ align:start position:0%
+when it's possible to negotiate a new
+ 
+
+ align:start position:0%
+when it's possible to negotiate a new
+social contract and what are the issues
+
+ align:start position:0%
+social contract and what are the issues
+ 
+
+ align:start position:0%
+social contract and what are the issues
+that are current and relevant to our
+
+ align:start position:0%
+that are current and relevant to our
+ 
+
+ align:start position:0%
+that are current and relevant to our
+times every country in the world needs
+
+ align:start position:0%
+times every country in the world needs
+ 
+
+ align:start position:0%
+times every country in the world needs
+to address these issues
+
+ align:start position:0%
+to address these issues
+ 
+
+ align:start position:0%
+to address these issues
+because we have serious problems in our
+
+ align:start position:0%
+because we have serious problems in our
+ 
+
+ align:start position:0%
+because we have serious problems in our
+workplaces that need to be addressed and
+
+ align:start position:0%
+workplaces that need to be addressed and
+ 
+
+ align:start position:0%
+workplaces that need to be addressed and
+so we're very interested what are your
+
+ align:start position:0%
+so we're very interested what are your
+ 
+
+ align:start position:0%
+so we're very interested what are your
+thoughts what's most important in your
+
+ align:start position:0%
+thoughts what's most important in your
+ 
+
+ align:start position:0%
+thoughts what's most important in your
+country what issues should the parties
+
+ align:start position:0%
+country what issues should the parties
+ 
+
+ align:start position:0%
+country what issues should the parties
+with your help be addressing we look
+
+ align:start position:0%
+with your help be addressing we look
+ 
+
+ align:start position:0%
+with your help be addressing we look
+forward to getting your thoughts on this
+
+ align:start position:0%
+forward to getting your thoughts on this
+ 
+
+ align:start position:0%
+forward to getting your thoughts on this
+in our discussions
\ No newline at end of file
diff --git a/RMBGQtwkoyU.txt b/RMBGQtwkoyU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1feb8d04d286dee0faf73b805e03bc8f018d08aa
--- /dev/null
+++ b/RMBGQtwkoyU.txt
@@ -0,0 +1,2073 @@
+The following content is
+provided under a Creative
+
+Commons license.
+Your support will help MIT
+
+OpenCourseWare continue to offer
+high quality educational
+
+resources for free.
+To make a donation or to view
+
+additional materials from
+hundreds of MIT courses,
+
+visit MIT OpenCourseWare at
+ocw.mit.edu.
+
+So, last week we learned how to
+do triple integrals in
+
+rectangular and cylindrical
+coordinates.
+
+And, now we have to learn about
+spherical coordinates,
+
+which you will see are a lot of
+fun.
+
+So, what's the idea of
+spherical coordinates?
+
+Well, you're going to represent
+a point in space using the
+
+distance to the origin and two
+angles.
+
+So, in a way, 
+you can think of these as a
+
+space analog of polar
+coordinates because you just use
+
+distance to the origin,
+and then you have to use angles
+
+to determine in which direction
+you're going.
+
+So, somehow they are more polar
+than cylindrical coordinates.
+
+So, how do we do that?
+So, let's say that you have a
+
+point in space at coordinates x,
+y, z.
+
+Then, instead of using x,
+y, z, you will use,
+
+well, one thing you'll use is
+the distance from the origin.
+
+OK, and that is denoted by the
+Greek letter which looks like a
+
+curly p, but actually it's the
+Greek R.
+
+So -- That's the distance from
+the origin.
+
+And so, that can take values
+anywhere between zero and
+
+infinity.
+Then, we have to use two other
+
+angles.
+And, so for that,
+
+let me actually draw the
+vertical half plane that
+
+contains our point starting from
+the z axis.
+
+OK, so then we have two new
+angles.
+
+Well, one of them is not really
+new.
+
+One is new.
+That's phi is the angle
+
+downwards from the z axis.
+And the other one,
+
+theta, is the angle
+counterclockwise from the x
+
+axis.
+OK, so phi, let me do it better.
+
+So, there's two ways to draw
+the letter phi,
+
+by the way.
+And, I recommend this one
+
+because it doesn't look like a
+rho.
+
+So, that's easier.
+That's the angle that you have
+
+to go down from the positive z
+axis.
+
+And, 
+so that angle varies from zero
+
+when you're on the z axis,
+increase to pi over two when
+
+you are on the xy plane all the
+way to pi or 180� when you are
+
+on the negative z axis.
+It doesn't go beyond that.
+
+OK, so -- Phi is always between
+zero and pi.
+
+And, finally,
+the last one,
+
+theta, is just going to be the
+same as before.
+
+So, it's the angle after you
+project to the xy plane.
+
+That's the angle
+counterclockwise from the x
+
+axis.
+OK, so that's a little bit
+
+overwhelming not just because of
+the new letters,
+
+but also because there is a lot
+of angles in there.
+
+So, let me just try to,
+you know, suggest two things
+
+that might help you a little
+bit.
+
+So, one is, these are called
+spherical coordinates because if
+
+you fix the value of rho,
+then you are moving on a sphere
+
+centered at the origin.
+OK, so let's look at what
+
+happens on a sphere centered at
+the origin, so,
+
+with equation rho equals a.
+Well, then phi measures how far
+
+south you are going,
+measures the distance from the
+
+North Pole.
+So, 
+
+if you've learned about
+latitude and longitude in
+
+geography,
+well, phi and theta you can
+
+think of as latitude and
+longitude except with slightly
+
+different conventions.
+OK, so, phi is more or less the
+
+same thing as latitude in the
+sense that it measures how far
+
+north or south you are.
+The only difference is in
+
+geography,
+latitude is zero on the equator
+
+and becomes something north,
+something south, 
+
+depending on how far you go
+from the equator.
+
+Here, you measure a latitude
+starting from the North Pole
+
+which is zero,
+increasing all the way to the
+
+South Pole, which is at pi.
+And, theta or you can think of
+
+as longitude,
+which measures how far you are
+
+east or west.
+So, the Greenwich Meridian
+
+would be here,
+now, the one on the x axis.
+
+That's the one you use as the
+origin for longitude,
+
+OK?
+Now, if you don't like
+
+geography, here's another way to
+think about it.
+
+So -- Let's start again from
+cylindrical coordinates,
+
+which hopefully you're kind of
+comfortable with now.
+
+OK, so you know about
+cylindrical coordinates where we
+
+have the z coordinates stay z,
+and the xy plane we do R and
+
+theta polar coordinates.
+And now, let's think about what
+
+happens when you look at just
+one of these vertical planes
+
+containing the z axis.
+So, you have the z axis,
+
+and then you have the direction
+away from the z axis,
+
+which I will call r,
+just because that's what r
+
+measures.
+Of course, r goes all around
+
+the z axis, but I'm just doing a
+slice through one of these
+
+vertical half planes,
+fixing the value of theta.
+
+Then, r of course is a polar
+coordinate seen from the point
+
+of view of the xy plane.
+But here, it looks more like
+
+you have rectangular coordinates
+again.
+
+So the idea of spherical
+coordinate is you're going to
+
+polar coordinates again in the
+rz plane.
+
+OK, so if I have a point here,
+then rho will be the distance
+
+from the origin.
+And phi will be the angle,
+
+except it's measured from the
+positive z axis,
+
+not from the horizontal axis.
+But, the idea in here, 
+
+see, 
+let me put that between quotes
+
+because I'm not sure how correct
+that is,
+
+but in a way, 
+you can think of this as polar
+
+coordinates in the rz plane.
+So, in particular, 
+
+that's the key to understanding
+how to switch between spherical
+
+coordinates and cylindrical
+coordinates,
+
+and then all the way to x,
+y, z if you want,
+
+right, 
+because this picture here tells
+
+us how to express z and r in
+terms of rho and phi.
+
+So, let's see how that works.
+If I project here or here,
+
+so, this line is z.
+But, it's also rho times cosine
+
+phi.
+So, I get z equals rho cos phi.
+
+And, if I look at r,
+it's the same thing,
+
+but on the other side.
+So, r will be rho sine phi.
+
+OK, so you can use this to
+switch back and forth between
+
+spherical and cylindrical.
+And of course,
+
+if you remember what x and y
+were in terms of r and theta,
+
+you can also keep doing this to
+figure out, oops.
+
+So, x is r cos theta.
+That becomes rho sine phi cos
+
+theta.
+Y is r sine theta.
+
+So, that becomes rho sine phi
+sine theta.
+
+And z is rho cos phi.
+But, basically you don't really
+
+need to remember these formulas
+as long as you remember how to
+
+express r in terms of rho sine
+phi,
+
+and x equals r cos theta.
+So, now, of course, 
+
+we're going to use spherical
+coordinates in situations where
+
+we have a lot of symmetry,
+and in particular, 
+
+where the z axis plays a
+special role.
+
+Actually, that's the same with
+cylindrical coordinates.
+
+Cylindrical and secure
+coordinates are set up so that
+
+the z axis plays a special role.
+So, that means whenever you
+
+have a geometric problem,
+and you are not told how to
+
+choose your coordinates,
+it's probably wiser to try to
+
+center things on the z axis.
+That's where these coordinates
+
+are the best adapted.
+And, 
+
+in case you ever need to switch
+backwards,
+
+I just want to point out, 
+so, rho is the square root of r
+
+squared plus z squared,
+which means it's the square
+
+root of x squared plus y squared
+plus z squared.
+
+OK, so that's basically all the
+formulas about spherical
+
+coordinates.
+OK, any questions about that?
+
+OK, let's see,
+who had seen spherical
+
+coordinates before just to see?
+OK, that's not very many.
+
+So, I'm sure for,
+one of you saw it twice.
+
+That's great.
+Sorry, oops,
+
+OK, so let's just look quickly
+at equations of some of the
+
+things.
+So, as I've said,
+
+if I set rho equals a,
+that will be just a sphere of
+
+radius a centered at the origin.
+More interesting things:
+
+let's say I give you phi equals
+pi over four.
+
+What do you think that looks
+like?
+
+Actually, let's take a quick
+poll on things.
+
+OK, yeah, everyone seems to be
+saying it's a cone,
+
+and that's indeed the correct
+answer.
+
+So, how do we see that?
+Well, remember,
+
+phi is the angle downward from
+the z axis.
+
+So, let's say that I'm going to
+look first at what happens if
+
+I'm in the right half of a plane
+of a blackboard,
+
+so, in the yz plane.
+Then, phi is the angle downward
+
+from here.
+So, if I want to get pi over
+
+four, that's 45�.
+That means I'm going to go
+
+diagonally like this.
+Of course, if I'm in the left
+
+half of a plane of a blackboard,
+it's going to be the same.
+
+I also take pi over four.
+And, I get the other half.
+
+And, because the equation does
+not involve theta,
+
+it's all the same if I rotate
+my vertical plane around the z
+
+axis.
+So, I get the same picture in
+
+any of these vertical half
+planes, actually.
+
+OK, now, so this is phi equals
+pi over four.
+
+And, just in case,
+to point out to you what's
+
+going on, when phi equals pi
+over four, cosine and sine are
+
+equal to each other.
+They are both one over root two.
+
+So, you can find,
+again, the equation of this
+
+thing in cylindrical
+coordinates, which I'll remind
+
+you was z equals r.
+OK, in general,
+
+phi equals some given number,
+or z equals some number times
+
+r.
+That will be a cone centered on
+
+the z axis.
+OK, a special case:
+
+what if I say phi equals pi
+over two?
+
+Yeah, it's just going to be the
+xy plane.
+
+OK, that's the flattest of all
+cones.
+
+OK, so phi equals pi over two
+is going to be just the xy
+
+plane.
+And, in general,
+
+if phi is less than pi over
+two, then you are in the upper
+
+half space.
+If phi is more than pi over
+
+two, you'll be in the lower half
+space.
+
+OK, so that's pretty much all
+we need to know at this point.
+
+So, what's next?
+Well, remember we were trying
+
+to do triple integrals.
+So now we're going to triple
+
+integrals in spherical
+coordinates.
+
+And, for that,
+we first need to understand
+
+what the volume element is.
+What will be dV?
+
+OK, so dV will be something,
+d rho, d phi,
+
+d theta, or in any order that
+you want.
+
+But, this one is usually the
+most convenient.
+
+So, to find out what it is,
+well, we should look at how we
+
+are going to be slicing things
+now.
+
+OK, so if you integrate d rho,
+d phi, d theta,
+
+it means that you are actually
+slicing your solid into little
+
+pieces that live,
+somehow, 
+
+if you set an interval of rows, 
+OK, 
+
+sorry, maybe I should, 
+so, if you first integrate over
+
+rho,
+it means that you will actually
+
+choose first the direction from
+the origin even by phi and
+
+theta.
+And, in that direction,
+
+you will try to figure out,
+how far does your region
+
+extend?
+And, of course,
+
+how far that goes might depend
+on phi and theta.
+
+Then, you will vary phi.
+So, you have to know,
+
+for a given value of theta,
+how far down does your solid
+
+extend?
+And, finally,
+
+the value of theta will
+correspond to,
+
+in which directions around the
+z axis do we go?
+
+So, we're going to see that in
+examples.
+
+But before we can do that,
+we need to get the volume
+
+element.
+So, what I would like to
+
+suggest is that we need to
+figure out,
+
+what is the volume of a small
+piece of solid which corresponds
+
+to a certain change,
+delta rho, 
+
+delta phi, 
+and delta theta?
+
+So, delta rho means that you
+have two concentric spheres,
+
+and you are looking at a very
+thin shell in between them.
+
+And then, you would be looking
+at a piece of that spherical
+
+shell corresponding to small
+values of phi and theta.
+
+So, because I am stretching the
+limits of my ability to draw on
+
+the board, here's a picture.
+I'm going to try to reproduce
+
+on the board,
+but so let's start by looking
+
+just at what happens on the
+sphere of radius a,
+
+and let's try to figure out the
+surface area elements on the
+
+sphere in terms of phi and
+theta.
+
+And then, we'll add the rho
+direction.
+
+OK, so -- So,
+let me say, let's start by
+
+understanding surface area on a
+sphere of radius a.
+
+So, that means we'll be looking
+at a little piece of the sphere
+
+corresponding to angles delta
+phi and in that direction here
+
+delta theta.
+OK, so when you draw a map of
+
+the world on a globe,
+that's exactly what the grid
+
+lines form for you.
+So, what's the area of this guy?
+
+Well, of course,
+all the sides are curvy.
+
+They are all on the sphere.
+None of them are straight.
+
+But still, if it's small enough
+and it looks like a rectangle,
+
+so let's just try to figure
+out, what are the sides of your
+
+rectangle?
+OK, so, let's see,
+
+well, I think I need to draw a
+bigger picture of this guy.
+
+OK, so this guy,
+so that's a piece of what's
+
+called a parallel in geography.
+That's a circle that goes
+
+east-west.
+So now, 
+
+this parallel as a circle of
+radius,
+
+well, the radius is less than a
+because if your vertical is to
+
+the North Pole,
+it will be actually much
+
+smaller.
+So, that's why when you say
+
+you're going around the world it
+depends on whether you do it at
+
+the equator or the North Pole.
+It's much easier at the North
+
+Pole.
+So, anyway, this is a piece of
+
+a circle of radius,
+well, the radius is what I
+
+would call r because that's the
+distance from the z axis.
+
+OK, that's actually pretty hard
+to see now.
+
+So if you can see it better on
+this one, then so this guy here,
+
+this length is r.
+And, r is just rho,
+
+well, what was a times sine
+phi.
+
+Remember, we have this angle
+phi in here.
+
+I should use some color.
+It's getting very cluttered.
+
+So, we have this phi,
+and so r is going to be rho
+
+sine phi.
+That rho is a.
+
+So, let me just put a sine phi.
+OK, and the corresponding angle
+
+is going to be measured by
+theta.
+
+So, the length of this is going
+to be a sine phi delta theta.
+
+That's for this side.
+Now, what about that side,
+
+the north-south side?
+Well, if you're moving
+
+north-south, it's not like
+east-west.
+
+You always have to go all the
+way from the North Pole to the
+
+South Pole.
+So, that's actually a great
+
+circle meridian of length,
+well, I mean,
+
+well, the radius is the radius
+of the sphere.
+
+Total length is 2pi a.
+So, this is a piece of a circle
+
+of radius a.
+And so, now,
+
+the length of this one is going
+to be a delta phi.
+
+OK, so, just to recap,
+this is a sine phi delta theta.
+
+And, this guy here is a delta
+phi.
+
+So, you can't read it because
+it's -- And so,
+
+that tells us if I take a small
+piece of the sphere,
+
+then its surface area, 
+delta s, 
+
+is going to be approximately a
+sine phi delta theta times a
+
+delta phi,
+which I'm going to rewrite as a
+
+squared sine phi delta phi delta
+theta.
+
+So, what that means is,
+say that I want to integrate
+
+something just on the surface of
+a sphere.
+
+Well, I would use phi and theta
+as my coordinates.
+
+And then, to know how big a
+piece of a sphere is,
+
+I would just take a squared
+sine phi d phi d theta.
+
+OK, so that's the surface
+element in a sphere.
+
+And now, what about going back
+into the third dimension,
+
+so, adding some depth to these
+things?
+
+Well, I'm not going to try to
+draw a picture because you've
+
+seen that's slightly tricky.
+Well, let me try anyway just
+
+you can have fun with my
+completely unreadable diagrams.
+
+So anyway, if you look at,
+now, something that's a bit
+
+like that piece of sphere,
+but with some thickness to it.
+
+The thickness will be delta
+rho, and so the volume will be
+
+roughly the area of the thing on
+the sphere times the thickness.
+
+So, I claim that we will get
+basically the volume element
+
+just by multiplying things by d
+rho.
+
+So, let's see that.
+So now, if I have a sphere of
+
+radius rho, and another one
+that's slightly bigger of radius
+
+rho plus delta rho,
+and then I have a little box in
+
+here.
+Then, 
+
+I know that the volume of this
+thing will be essentially,
+
+well, its thickness, 
+the thickness is going to be
+
+delta rho times the area of its
+base,
+
+although it doesn't really
+matter,
+
+which is what we've called
+delta s.
+
+OK, so we will get,
+sorry, a becomes rho now.
+
+Square sine phi, 
+delta rho, 
+
+delta phi, 
+delta theta, 
+
+and so out of that we get the
+volume element and spherical
+
+coordinates,
+which is rho squared sine phi d
+
+rho,
+d phi, 
+
+d theta.
+And, that's a formula that you
+
+should remember.
+OK, so whenever we integrate a
+
+function,
+and we decide to switch to
+
+spherical coordinates,
+then dx dy dz or r dr d theta
+
+dz will become rho squared sine
+phi d rho d phi d theta.
+
+OK, any questions on that?
+No?
+
+OK, so let's -- Let's see how
+that works.
+
+So, as an example,
+remember at the end of the last
+
+lecture, I tried to set up an
+example where we were looking at
+
+a sphere sliced by a slanted
+plane.
+
+And now, we're going to try to
+find the volume of that
+
+spherical cap again,
+but using spherical coordinates
+
+instead.
+So, I'm going to just be
+
+smarter than last time.
+So, last time,
+
+we had set up these things with
+a slanted plane that was cutting
+
+things diagonally.
+And, 
+
+if I just want to find the
+volume of this cap,
+
+then maybe it makes more sense
+to rotate things so that my
+
+plane is actually horizontal,
+and things are going to be
+
+centered on the z axis.
+So, in case you see that it's
+
+the same, then that's great.
+If not, then it doesn't really
+
+matter.
+You can just think of this as a
+
+new example.
+So, I'm going to try to find
+
+the volume of a portion of the
+unit sphere -- -- that lies
+
+above the horizontal plane,
+z equals one over root two.
+
+OK, one over root two was the
+distance from the origin to our
+
+slanted plane.
+So, after you rotate,
+
+that say you get this value.
+Anyway, it's not very important.
+
+You can just treat that as a
+good example if you want.
+
+OK, so we can compute this in
+actually pretty much any
+
+coordinate system.
+And also, of course,
+
+we can set up not only the
+volume, but we can try to find
+
+the moment of inertia about the
+central axis,
+
+or all sorts of things.
+But, we are just doing the
+
+volume for simplicity.
+So, actually,
+
+this would go pretty well in
+cylindrical coordinates.
+
+But let's do it in spherical
+coordinates because that's the
+
+topic of today.
+A good exercise:
+
+do it in cylindrical and see if
+you get the same thing.
+
+So, how do we do that?
+Well, we have to figure out how
+
+to set up our triple integral in
+spherical coordinates.
+
+So, remember we'll be
+integrating one dV.
+
+So, dV will become rho squared
+sign phi d rho d phi d theta.
+
+And, now as we start,
+we're already facing some
+
+serious problem.
+We want to set up the bounds
+
+for rho for a given,
+phi and theta.
+
+So, that means we choose
+latitude/longitude.
+
+We choose which direction we
+want to aim for,
+
+you know, which point of the
+sphere we want to aim at.
+
+And, we are going to shoot a
+ray from the origin towards this
+
+point, and we want to know what
+portion of the ray is in our
+
+solid.
+So -- We are going to choose a
+
+value of phi and theta.
+And, we are going to try to
+
+figure out what part of our ray
+is inside this side.
+
+So, what should be clear is at
+which point we leave the solid,
+
+right?
+What's the value of rho here?
+
+It's just one.
+The sphere is rho equals one.
+
+That's pretty good.
+The question is,
+
+where do we enter the region?
+So, we enter the region when we
+
+go through this plane.
+And, the plane is z equals one
+
+over root two.
+So, what does that tell us
+
+about rho?
+Well, it tells us,
+
+so remember,
+z is rho cosine phi.
+
+So, the plane is z equals one
+over root two.
+
+That means rho cosine phi is
+one over root two.
+
+That means rho equals one over
+root two cosine phi or,
+
+as some of you know it,
+one over root two times second
+
+phi.
+OK, so if we want to set up the
+
+bounds, then we'll start with
+one over root two second phi all
+
+the way to one.
+Now, what's next?
+
+Well, so we've done,
+I think that's basically the
+
+hardest part of the job.
+Next, we have to figure out,
+
+what's the range for phi?
+So, the range for phi,
+
+well, we have to figure out how
+far to the north and to the
+
+south our region goes.
+Well, the lower bound for phi
+
+is pretty easy,
+right, because we go all the
+
+way to the North Pole direction.
+So, phi starts at zero.
+
+The question is,
+where does it stop?
+
+To find out where it stops,
+we have to figure out,
+
+what is the value of phi when
+we hit the edge of the region?
+
+OK, so maybe you see it.
+Maybe you don't.
+
+One way to do it geometrically
+is to just, it's always great to
+
+draw a slice of your region.
+So, if you slice these things
+
+by a vertical plane,
+or actually even better,
+
+a vertical half plane,
+something to delete one half of
+
+the picture.
+So, I'm going to draw these r
+
+and z directions as before.
+So, my sphere is here.
+
+My plane is here at one over
+root two.
+
+And, my solid is here.
+So now, the question is what is
+
+the value of phi when I'm going
+to stop hitting the region?
+
+And, if you try to figure out
+first what is this direction
+
+here, that's also one over root
+two.
+
+And so, this is actually 45�,
+also known as pi over four.
+
+The other way to think about it
+is at this point,
+
+well, rho is equal to one
+because you are on the sphere.
+
+But, you are also on the plane.
+So, rho cos phi is one over
+
+root two.
+So, if you plug rho equals one
+
+into here, you get cos phi
+equals one over root two which
+
+gives you phi equals pi over
+four.
+
+That's the other way to do it.
+You can do it either by
+
+calculation or by looking at the
+picture.
+
+OK, so either way,
+we've decided that phi goes
+
+from zero to pi over four.
+So, this is pi over four.
+
+Finally, what about theta?
+Well, because we go all around
+
+the z axis we are going to go
+just zero to 2pi.
+
+OK, any questions about these
+bounds?
+
+OK, so note how the equation of
+this horizontal plane in
+
+spherical coordinates has become
+a little bit weird.
+
+But, 
+if you remember how we do
+
+things,
+say that you have a line in
+
+polar coordinates,
+and that line does not pass
+
+through the origin,
+then you also end up with
+
+something like that.
+You get something like r equals
+
+a second theta or a cos second
+theta for horizontal or vertical
+
+lines.
+And so, it's not surprising you
+
+should get this.
+That's in line with the idea
+
+that we are just doing again,
+polar coordinates in the rz
+
+directions.
+So of course,
+
+in general, things can be very
+messy.
+
+But, generally speaking, 
+the kinds of regions that we
+
+will be setting up things for
+are no more complicated or no
+
+less complicated than what we
+would do in the plane in polar
+
+coordinates.
+OK, so there's,
+
+you know, a small list of
+things that you should know how
+
+to set up.
+But, you won't have some
+
+really, really strange thing.
+Yes?
+
+D rho?
+Oh, you mean the bounds for rho?
+
+Yes.
+So, in the inner integral,
+
+we are going to fix values of
+phi and theta.
+
+So, that means we fix in
+advance the direction in which
+
+we are going to shoot a ray from
+the origin.
+
+So now, as we shoot this ray,
+we are going to hit our region
+
+somewhere.
+And, we are going to exit,
+
+again, somewhere else.
+OK, so first of all we have to
+
+figure out where we enter,
+where we leave.
+
+Well, we enter when the ray
+hits the flat face,
+
+when we hit the plane.
+And, we would leave when we hit
+
+the sphere.
+So, the lower bound will be
+
+given by the plane.
+The upper bound will be given
+
+by the sphere.
+So now, you have to get
+
+spherical coordinate equations
+for both the plane and the
+
+sphere.
+For the sphere, that's easy.
+
+That's rho equals one.
+For the plane,
+
+you start with z equals one
+over root two.
+
+And, you switch it into
+spherical coordinates.
+
+And then, you solve for rho.
+And, that's how you get these
+
+bounds.
+Is that OK?
+
+All right, so that's the setup
+part.
+
+And, of course,
+the evaluation part goes as
+
+usual.
+
+ 
+
+And, since I'm running short of
+time, I'm not going to actually
+
+do the evaluation.
+I'm going to let you figure out
+
+how it goes.
+Let me just say in case you
+
+want to check your answers,
+so, at the end you get 2pi over
+
+three minus 5pi over six root
+two.
+
+Yes, it looks quite complicated.
+That's basically because you
+
+get one over,
+well, you get a second square
+
+when you integrate C.
+When you integrate rho squared,
+
+you will get rho cubed over
+three.
+
+But that rho cubed will give
+you a second cube for the lower
+
+bound.
+And, when you integrate sine
+
+phi second cubed phi,
+you do a substitution.
+
+You see that integrates to one
+over second squared with a
+
+factor in front.
+So, in the second square,
+
+when you plug in,
+no, that's not quite all of it.
+
+Yeah, well, the second square
+is one thing,
+
+and also the other bound you
+get sine phi which integrates to
+
+cosine phi.
+So, anyways,
+
+you get lots of things.
+OK, enough about it.
+
+So, next, I have to tell you
+about applications.
+
+And, of course, 
+well, there's the same
+
+applications that we've seen
+that last time,
+
+finding volumes, 
+finding masses, 
+
+finding average values of
+functions.
+
+In particular,
+now, we could say to find the
+
+average distance of a point in
+this solid to the origin.
+
+Well, 
+spherical coordinates become
+
+appealing because the function
+you are averaging is just rho
+
+while in other coordinate
+systems it's a more complicated
+
+function.
+So, if you are asked to find
+
+the average distance from the
+origin, spherical coordinates
+
+can be interesting.
+Also, 
+
+well, there's moments of
+inertia,
+
+preferably the one about the z
+axis because if you have to
+
+integrate something that
+involves x or y,
+
+then your integrand will
+contain that awful rho sine phi
+
+sine theta or rho sine phi
+cosine theta,
+
+and then it won't be much fun
+to evaluate.
+
+So, that anyway,
+there's the usual ones.
+
+And then there's a new one.
+So, in physics,
+
+you've probably seen things
+about gravitational attraction.
+
+If not, well,
+it's what causes apples to fall
+
+and other things like that as
+well.
+
+So, anyway, physics tells you
+that if you have two masses,
+
+then they attract each other
+with a force that's directed
+
+towards each other.
+And in intensity,
+
+it's proportional to the two
+masses, and inversely
+
+proportional to the square of
+the distance between them.
+
+So, 
+if you have a given solid with
+
+a certain mass distribution,
+and you want to know how it
+
+attracts something else that you
+will put nearby,
+
+then you actually have to, 
+the first approximation will be
+
+to say,
+well, let's just put a point
+
+mass at its center of mass.
+But, if you're solid is
+
+actually not homogenous,
+or has a weird shape,
+
+then that's not actually the
+exact answer.
+
+So, in general,
+you would have to just take
+
+every single piece of your
+object and figure out how it
+
+attracts you,
+and then compute the sum of
+
+these.
+So, for example, 
+
+if you want to understand why
+anything that you drop in this
+
+room will fall down,
+you have to understand that
+
+Boston is actually attracting it
+towards Boston.
+
+And, Somerville's attracting it
+towards Somerville,
+
+and lots of things like that.
+And, China, which is much
+
+further on the other side is
+going to attract towards China.
+
+But, there's a lot of stuff on
+the other side of the Earth.
+
+And so, overall,
+it's supposed to end up just
+
+going down.
+OK, so now, how to find this
+
+out, well, you have to just
+integrate over the entire Earth.
+
+OK, so let's try to see how
+that goes.
+
+So, the setup that's going to
+be easiest for us to do
+
+computations is going to be that
+we are going to be the test mass
+
+that's going to be falling.
+And, we are going to put
+
+ourselves at the origin.
+And, the solid that's going to
+
+attract us is going to be
+wherever we want in space.
+
+You'll see, putting yourself at
+the origin is going to be
+
+better.
+Well, you have to put something
+
+at the origin.
+And, the one that will stay a
+
+point mass, I mean,
+in my case not really a point,
+
+but anyway, let's say that I'm
+a point.
+
+And then, I have a solid
+attracting me.
+
+Well, 
+so then if I take a small piece
+
+of it with the mass delta M,
+then that portion of the solid
+
+exerts a force on me,
+which is going to be directed
+
+towards it,
+and we'll have intensity.
+
+So, the gravitational force --
+-- exerted by the mass delta M
+
+at the point of x,
+y, z in space on a mass at the
+
+origin.
+Well, we know how to express
+
+that.
+Physics tells us that the
+
+magnitude of this force is going
+to be, well, G is just a
+
+constant.
+It's the gravitational
+
+constant, and its value depends
+on which unit system you use.
+
+Usually it's pretty small,
+times the mass delta M,
+
+times the test mass little m,
+divided by the square of the
+
+distance.
+And, the distance from U to
+
+that thing is conveniently
+called rho since we've been
+
+introducing spherical
+coordinates.
+
+So, that's the size,
+that's the magnitude of the
+
+force.
+We also need to know the
+
+direction of the force.
+And, the direction is going to
+
+be towards that point.
+So, the direction of the force
+
+is going to be that of x,
+y, z.
+
+But if I want a unit vector,
+then I should scale this down
+
+to length one.
+So, let me divide this by rho
+
+to get a unit vector.
+So, that means that the force
+
+I'm getting from this guy is
+actually going to be G delta M m
+
+over rho cubed times x,
+y, z.
+
+I'm just multiplying the
+magnitude by the unit vector in
+
+the correct direction.
+OK, so now if I have not just
+
+that little p is delta M,
+but an entire solid,
+
+then I have to sum all these
+guys together.
+
+And, I will get the vector that
+gives me the total force
+
+exerted, OK?
+So, of course,
+
+there's actually three
+different calculations in one
+
+because you have to sum the x
+components to get the x
+
+components of a total force.
+Same with the y,
+
+and same with the z.
+So, let me first write down the
+
+actual formula.
+So, if you integrate over the
+
+entire solid,
+oh, and I have to remind you,
+
+well, what's the mass,
+delta M of a small piece of
+
+volume delta V?
+Well, it's the density times
+
+the volume.
+So, the mass is going to be,
+
+sorry, density is delta.
+There is a lot of Greek letters
+
+there, times the volume element.
+So, you will get that the force
+
+is the triple integral over your
+solid of G m x,
+
+y, z over rho cubed,
+delta dV.
+
+Now, two observations about
+that.
+
+So, the first one,
+well, of course,
+
+these are just constants.
+So, they can go out.
+
+The second observation,
+so here, we are integrating a
+
+vector quantity.
+So, what does that mean?
+
+I just mean the x component of
+a force is given by integrating
+
+G m x over rho cubed delta dV.
+The y components,
+
+same thing with y.
+The z components,
+
+same thing with z.
+OK, there's no,
+
+like, you know,
+just integrate component by
+
+component to get each component
+of the force.
+
+So, now we could very well to
+this in rectangular coordinates
+
+if we want.
+But the annoying thing is this
+
+rho cubed.
+Rho cubed is going to be x
+
+squared plus y squared plus z
+squared to the three halves.
+
+That's not going to be a very
+pleasant thing to integrate.
+
+So, it's much better to set up
+these integrals in spherical
+
+coordinates.
+And, if we're going to do it in
+
+spherical coordinates,
+then probably we don't want to
+
+bother too much with x and y
+components because those would
+
+be unpleasant.
+It would give us rho sine phi
+
+cos theta or sine theta.
+So, the actual way we will set
+
+up things, set things up,
+is to place the solid so that
+
+the z axis is an axis of
+symmetry.
+
+And, of course,
+that only works if the solid
+
+has some axis of symmetry.
+Like, if you're trying to find
+
+the gravitational attraction of
+the Pyramid of Giza,
+
+then you won't be able to set
+up so that it has rotation
+
+symmetry.
+Well, that's a tough fact of
+
+life, and you have to actually
+do it in x, y,
+
+z coordinates.
+But, if at all possible,
+
+then you're going to place
+things.
+
+Well, I guess even then,
+you could center it on the z
+
+axis.
+But anyway, so you're going to
+
+mostly place things so that your
+solid is actually centered on
+
+the z-axis.
+And, what you gain by that is
+
+that by symmetry,
+the gravitational force will be
+
+directed along the z axis.
+So, you will just have to
+
+figure out the z component.
+So, then the force will be
+
+actually, you know in advance
+that it will be given by zero,
+
+zero, and some z component.
+And then, you just need to
+
+compute that component.
+And, that component will be
+
+just G times m times triple
+integral of z over rho cubed
+
+delta dV.
+OK, so that's the first
+
+simplification we can try to do.
+The second thing is,
+
+well, we have to choose our
+favorite coordinate system to do
+
+this.
+But, I claim that actually
+
+spherical coordinates are the
+best -- -- because let's see
+
+what happens.
+So, G times mass times triple
+
+integral, well,
+a z in spherical coordinates
+
+becomes rho cosine phi over rho
+cubed.
+
+Density, well,
+we can't do anything about
+
+density.
+And then, dV becomes rho
+
+squared sine phi d rho d phi d
+theta.
+
+Well, so, what happens with
+that?
+
+Well, you see that you have a
+rho, a rho squared,
+
+and a rho cubed that cancel
+each other.
+
+So, in fact,
+it simplifies quite a bit if
+
+you do it in spherical
+coordinates.
+
+ 
+ 
+
+OK, so the z component of the
+force, sorry,
+
+I'm putting a z here to remind
+you it's the z component.
+
+That is not a partial
+derivative, OK?
+
+Don't get things mixed up,
+just the z component of the
+
+force becomes Gm triple integral
+of delta cos phi sine phi d rho
+
+d phi d theta.
+And, so this thing is not dV,
+
+of course.
+dV is much bigger,
+
+but we've somehow canceled out
+most of dV with stuff that was
+
+in the integrand.
+And see, that's actually
+
+suddenly much less scary.
+OK, so just to give you an
+
+example of what you can prove it
+this way, you can prove Newton's
+
+theorem, which says the
+following thing.
+
+It says the gravitational
+attraction -- -- of a spherical
+
+planet,
+I should say with uniform
+
+density,
+or actually it's enough for the
+
+density to depend just on
+distance to the center.
+
+But we just simplify the
+statement is equal to that of a
+
+point mass -- -- with the same
+total mass at its center.
+
+OK, so what that means is that,
+so the way we would set it up
+
+is u would be sitting here and
+your planet would be over here.
+
+Or, if you're at the surface of
+it, then of course you just put
+
+it tangent to the xy plane here.
+And, you would compute that
+
+quantity.
+Computation is a little bit
+
+annoying if a sphere is sitting
+up there because,
+
+of course, you have to find
+bounds,
+
+and that's not going to be very
+pleasant.
+
+The case that we actually know
+how to do fairly well is if you
+
+are just at the surface of the
+planet.
+
+But then, 
+what the theorem says is that
+
+the force that you're going to
+feel is exactly the same as if
+
+you removed all of the planet
+and you just put an equivalent
+
+point mass here.
+So, if the earth collapsed to a
+
+black hole at the center of the
+earth with the same mass,
+
+well, you wouldn't notice the
+difference immediately,
+
+or, rather, you would, 
+but at least not in terms of
+
+your weight.
+OK, that's the end for today.
\ No newline at end of file
diff --git a/RWSypiENYfc.txt b/RWSypiENYfc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0f6afa13aaf0dc31a9077a15e7c6fb6da795e2b
--- /dev/null
+++ b/RWSypiENYfc.txt
@@ -0,0 +1,6595 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
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+your support will help MIT
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+OpenCourseWare continue to offer high
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+OpenCourseWare continue to offer high
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+quality educational resources for free
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+quality educational resources for free
+to make a donation or view additional
+
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+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+so today's reading this is kind of -
+
+ align:start position:0%
+so today's reading this is kind of -
+ 
+
+ align:start position:0%
+so today's reading this is kind of -
+there for two reasons one the David
+
+ align:start position:0%
+there for two reasons one the David
+ 
+
+ align:start position:0%
+there for two reasons one the David
+Hartless reading is to introduce to you
+
+ align:start position:0%
+Hartless reading is to introduce to you
+ 
+
+ align:start position:0%
+Hartless reading is to introduce to you
+this book which is called the history of
+
+ align:start position:0%
+this book which is called the history of
+ 
+
+ align:start position:0%
+this book which is called the history of
+board games how many of you read the
+
+ align:start position:0%
+board games how many of you read the
+ 
+
+ align:start position:0%
+board games how many of you read the
+version from stellar ok anyone get a
+
+ align:start position:0%
+version from stellar ok anyone get a
+ 
+
+ align:start position:0%
+version from stellar ok anyone get a
+book from the library because I think
+
+ align:start position:0%
+book from the library because I think
+ 
+
+ align:start position:0%
+book from the library because I think
+it's not reserved if you really want to
+
+ align:start position:0%
+it's not reserved if you really want to
+ 
+
+ align:start position:0%
+it's not reserved if you really want to
+print read read like a you know hardback
+
+ align:start position:0%
+print read read like a you know hardback
+ 
+
+ align:start position:0%
+print read read like a you know hardback
+paper you could just go to libraries and
+
+ align:start position:0%
+paper you could just go to libraries and
+ 
+
+ align:start position:0%
+paper you could just go to libraries and
+you should be able to check it out
+
+ align:start position:0%
+you should be able to check it out
+ 
+
+ align:start position:0%
+you should be able to check it out
+probably from the humanities language so
+
+ align:start position:0%
+probably from the humanities language so
+ 
+
+ align:start position:0%
+probably from the humanities language so
+just letting you know that there are
+
+ align:start position:0%
+just letting you know that there are
+ 
+
+ align:start position:0%
+just letting you know that there are
+options out there so the one of the
+
+ align:start position:0%
+options out there so the one of the
+ 
+
+ align:start position:0%
+options out there so the one of the
+reasons this one just wait would use to
+
+ align:start position:0%
+reasons this one just wait would use to
+ 
+
+ align:start position:0%
+reasons this one just wait would use to
+you a bit of what historical research
+
+ align:start position:0%
+you a bit of what historical research
+ 
+
+ align:start position:0%
+you a bit of what historical research
+looks like in game studies if there are
+
+ align:start position:0%
+looks like in game studies if there are
+ 
+
+ align:start position:0%
+looks like in game studies if there are
+people who have careers like a
+
+ align:start position:0%
+people who have careers like a
+ 
+
+ align:start position:0%
+people who have careers like a
+department who basically go deep into
+
+ align:start position:0%
+department who basically go deep into
+ 
+
+ align:start position:0%
+department who basically go deep into
+the history of how some kind of game
+
+ align:start position:0%
+the history of how some kind of game
+ 
+
+ align:start position:0%
+the history of how some kind of game
+evolved one of our own alums Jason Beghe
+
+ align:start position:0%
+evolved one of our own alums Jason Beghe
+ 
+
+ align:start position:0%
+evolved one of our own alums Jason Beghe
+he looks at Railroad games I'm pretty
+
+ align:start position:0%
+he looks at Railroad games I'm pretty
+ 
+
+ align:start position:0%
+he looks at Railroad games I'm pretty
+sure this hasn't just isa stuff again ok
+
+ align:start position:0%
+sure this hasn't just isa stuff again ok
+ 
+
+ align:start position:0%
+sure this hasn't just isa stuff again ok
+and he's he's been looking at that for
+
+ align:start position:0%
+and he's he's been looking at that for
+ 
+
+ align:start position:0%
+and he's he's been looking at that for
+like three years before yeah yeah and so
+
+ align:start position:0%
+like three years before yeah yeah and so
+ 
+
+ align:start position:0%
+like three years before yeah yeah and so
+so with the go to museum still talk to
+
+ align:start position:0%
+so with the go to museum still talk to
+ 
+
+ align:start position:0%
+so with the go to museum still talk to
+archeologists well in the case of
+
+ align:start position:0%
+archeologists well in the case of
+ 
+
+ align:start position:0%
+archeologists well in the case of
+railroad games obviously that no
+
+ align:start position:0%
+railroad games obviously that no
+ 
+
+ align:start position:0%
+railroad games obviously that no
+archaeologist involves but they talk to
+
+ align:start position:0%
+archaeologist involves but they talk to
+ 
+
+ align:start position:0%
+archaeologist involves but they talk to
+people who worked on you know classic
+
+ align:start position:0%
+people who worked on you know classic
+ 
+
+ align:start position:0%
+people who worked on you know classic
+game designs the stuff you talk to
+
+ align:start position:0%
+game designs the stuff you talk to
+ 
+
+ align:start position:0%
+game designs the stuff you talk to
+retailers these other people were
+
+ align:start position:0%
+retailers these other people were
+ 
+
+ align:start position:0%
+retailers these other people were
+actually all inoculate some of these
+
+ align:start position:0%
+actually all inoculate some of these
+ 
+
+ align:start position:0%
+actually all inoculate some of these
+games and and I'm wondering if some of
+
+ align:start position:0%
+games and and I'm wondering if some of
+ 
+
+ align:start position:0%
+games and and I'm wondering if some of
+the games you know a lot of the games
+
+ align:start position:0%
+the games you know a lot of the games
+ 
+
+ align:start position:0%
+the games you know a lot of the games
+that are written in today's reading what
+
+ align:start position:0%
+that are written in today's reading what
+ 
+
+ align:start position:0%
+that are written in today's reading what
+kind of you know ancient really really
+
+ align:start position:0%
+kind of you know ancient really really
+ 
+
+ align:start position:0%
+kind of you know ancient really really
+asian games but how many of you feel
+
+ align:start position:0%
+asian games but how many of you feel
+ 
+
+ align:start position:0%
+asian games but how many of you feel
+like you finally played a game that
+
+ align:start position:0%
+like you finally played a game that
+ 
+
+ align:start position:0%
+like you finally played a game that
+sounded like one of those that were
+
+ align:start position:0%
+sounded like one of those that were
+ 
+
+ align:start position:0%
+sounded like one of those that were
+written up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they had the dreidel in there and
+
+ align:start position:0%
+yeah they had the dreidel in there and
+ 
+
+ align:start position:0%
+yeah they had the dreidel in there and
+that's what Parinda and Chanukah is that
+
+ align:start position:0%
+that's what Parinda and Chanukah is that
+ 
+
+ align:start position:0%
+that's what Parinda and Chanukah is that
+is that that's not just attitude and
+
+ align:start position:0%
+is that that's not just attitude and
+ 
+
+ align:start position:0%
+is that that's not just attitude and
+that was pretty much just hot okay
+
+ align:start position:0%
+that was pretty much just hot okay
+ 
+
+ align:start position:0%
+that was pretty much just hot okay
+it's funny because when I was reading
+
+ align:start position:0%
+it's funny because when I was reading
+ 
+
+ align:start position:0%
+it's funny because when I was reading
+about the dreidel I was actually like
+
+ align:start position:0%
+about the dreidel I was actually like
+ 
+
+ align:start position:0%
+about the dreidel I was actually like
+the initials a great miracle happened
+
+ align:start position:0%
+the initials a great miracle happened
+ 
+
+ align:start position:0%
+the initials a great miracle happened
+there I didn't realize that that was a
+
+ align:start position:0%
+there I didn't realize that that was a
+ 
+
+ align:start position:0%
+there I didn't realize that that was a
+different version for if you play
+
+ align:start position:0%
+different version for if you play
+ 
+
+ align:start position:0%
+different version for if you play
+dreidel in Jerusalem weight is the great
+
+ align:start position:0%
+dreidel in Jerusalem weight is the great
+ 
+
+ align:start position:0%
+dreidel in Jerusalem weight is the great
+great thing happened here which makes
+
+ align:start position:0%
+great thing happened here which makes
+ 
+
+ align:start position:0%
+great thing happened here which makes
+sense for Hanukkah but I don't think
+
+ align:start position:0%
+sense for Hanukkah but I don't think
+ 
+
+ align:start position:0%
+sense for Hanukkah but I don't think
+that doesn't quite make sense for food
+
+ align:start position:0%
+that doesn't quite make sense for food
+ 
+
+ align:start position:0%
+that doesn't quite make sense for food
+because that you do Jerusalem yeah all
+
+ align:start position:0%
+because that you do Jerusalem yeah all
+ 
+
+ align:start position:0%
+because that you do Jerusalem yeah all
+right what else the other games the
+
+ align:start position:0%
+right what else the other games the
+ 
+
+ align:start position:0%
+right what else the other games the
+stake board games or the a lot of these
+
+ align:start position:0%
+stake board games or the a lot of these
+ 
+
+ align:start position:0%
+stake board games or the a lot of these
+games a border on light occur you know
+
+ align:start position:0%
+games a border on light occur you know
+ 
+
+ align:start position:0%
+games a border on light occur you know
+someone setting up shop with us and on
+
+ align:start position:0%
+someone setting up shop with us and on
+ 
+
+ align:start position:0%
+someone setting up shop with us and on
+the street and dancing with the cops
+
+ align:start position:0%
+the street and dancing with the cops
+ 
+
+ align:start position:0%
+the street and dancing with the cops
+come you know they run away that one of
+
+ align:start position:0%
+come you know they run away that one of
+ 
+
+ align:start position:0%
+come you know they run away that one of
+those kinds of cakes right let's see
+
+ align:start position:0%
+those kinds of cakes right let's see
+ 
+
+ align:start position:0%
+those kinds of cakes right let's see
+what was some of the other things they
+
+ align:start position:0%
+what was some of the other things they
+ 
+
+ align:start position:0%
+what was some of the other things they
+had a lot of lots and one of the one of
+
+ align:start position:0%
+had a lot of lots and one of the one of
+ 
+
+ align:start position:0%
+had a lot of lots and one of the one of
+the traditional Roman implements was the
+
+ align:start position:0%
+the traditional Roman implements was the
+ 
+
+ align:start position:0%
+the traditional Roman implements was the
+knuckle burn right oh I'm not quite sure
+
+ align:start position:0%
+knuckle burn right oh I'm not quite sure
+ 
+
+ align:start position:0%
+knuckle burn right oh I'm not quite sure
+if they mention what animal that was I
+
+ align:start position:0%
+if they mention what animal that was I
+ 
+
+ align:start position:0%
+if they mention what animal that was I
+think it was she she yeah but that's
+
+ align:start position:0%
+think it was she she yeah but that's
+ 
+
+ align:start position:0%
+think it was she she yeah but that's
+where the word alia comes from and alia
+
+ align:start position:0%
+where the word alia comes from and alia
+ 
+
+ align:start position:0%
+where the word alia comes from and alia
+comes up quite a bit in game studies at
+
+ align:start position:0%
+comes up quite a bit in game studies at
+ 
+
+ align:start position:0%
+comes up quite a bit in game studies at
+least since poison girls time since I
+
+ align:start position:0%
+least since poison girls time since I
+ 
+
+ align:start position:0%
+least since poison girls time since I
+think the 60s where it's introduced as a
+
+ align:start position:0%
+think the 60s where it's introduced as a
+ 
+
+ align:start position:0%
+think the 60s where it's introduced as a
+generic term to describe games of chance
+
+ align:start position:0%
+generic term to describe games of chance
+ 
+
+ align:start position:0%
+generic term to describe games of chance
+I think it might also have the word Lea
+
+ align:start position:0%
+I think it might also have the word Lea
+ 
+
+ align:start position:0%
+I think it might also have the word Lea
+might also have been used like in
+
+ align:start position:0%
+might also have been used like in
+ 
+
+ align:start position:0%
+might also have been used like in
+traditional Latin scholarship to
+
+ align:start position:0%
+traditional Latin scholarship to
+ 
+
+ align:start position:0%
+traditional Latin scholarship to
+describe games of chance but that's
+
+ align:start position:0%
+describe games of chance but that's
+ 
+
+ align:start position:0%
+describe games of chance but that's
+where you get phrases like alia actor
+
+ align:start position:0%
+where you get phrases like alia actor
+ 
+
+ align:start position:0%
+where you get phrases like alia actor
+asked which is does anyone know what
+
+ align:start position:0%
+asked which is does anyone know what
+ 
+
+ align:start position:0%
+asked which is does anyone know what
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+the die is cast it's it's it's what
+
+ align:start position:0%
+the die is cast it's it's it's what
+ 
+
+ align:start position:0%
+the die is cast it's it's it's what
+Julius Caesar
+
+ align:start position:0%
+Julius Caesar
+ 
+
+ align:start position:0%
+Julius Caesar
+Judas Kaiser says what he about cross
+
+ align:start position:0%
+Judas Kaiser says what he about cross
+ 
+
+ align:start position:0%
+Judas Kaiser says what he about cross
+the Rubicon famously and yes originally
+
+ align:start position:0%
+the Rubicon famously and yes originally
+ 
+
+ align:start position:0%
+the Rubicon famously and yes originally
+you know there was some there was some
+
+ align:start position:0%
+you know there was some there was some
+ 
+
+ align:start position:0%
+you know there was some there was some
+confusion about whether that meant that
+
+ align:start position:0%
+confusion about whether that meant that
+ 
+
+ align:start position:0%
+confusion about whether that meant that
+died like dice
+
+ align:start position:0%
+died like dice
+ 
+
+ align:start position:0%
+died like dice
+has thrown but there are whether that
+
+ align:start position:0%
+has thrown but there are whether that
+ 
+
+ align:start position:0%
+has thrown but there are whether that
+means that the dye as in as in the mold
+
+ align:start position:0%
+means that the dye as in as in the mold
+ 
+
+ align:start position:0%
+means that the dye as in as in the mold
+for something that you put liquid iron
+
+ align:start position:0%
+for something that you put liquid iron
+ 
+
+ align:start position:0%
+for something that you put liquid iron
+in and then if you and then you cast it
+
+ align:start position:0%
+in and then if you and then you cast it
+ 
+
+ align:start position:0%
+in and then if you and then you cast it
+but that's only like that bath still has
+
+ align:start position:0%
+but that's only like that bath still has
+ 
+
+ align:start position:0%
+but that's only like that bath still has
+the same sort of sense like all right
+
+ align:start position:0%
+the same sort of sense like all right
+ 
+
+ align:start position:0%
+the same sort of sense like all right
+it's out of our hands right it's already
+
+ align:start position:0%
+it's out of our hands right it's already
+ 
+
+ align:start position:0%
+it's out of our hands right it's already
+been done so I'll get the same point
+
+ align:start position:0%
+been done so I'll get the same point
+ 
+
+ align:start position:0%
+been done so I'll get the same point
+across but I've actually look at you lie
+
+ align:start position:0%
+across but I've actually look at you lie
+ 
+
+ align:start position:0%
+across but I've actually look at you lie
+to me it's specifically talking about
+
+ align:start position:0%
+to me it's specifically talking about
+ 
+
+ align:start position:0%
+to me it's specifically talking about
+these knucklebones these that that
+
+ align:start position:0%
+these knucklebones these that that
+ 
+
+ align:start position:0%
+these knucklebones these that that
+oppose that you're throwing that which
+
+ align:start position:0%
+oppose that you're throwing that which
+ 
+
+ align:start position:0%
+oppose that you're throwing that which
+are called earlier so so it's really now
+
+ align:start position:0%
+are called earlier so so it's really now
+ 
+
+ align:start position:0%
+are called earlier so so it's really now
+it's up to fate at the book makes a part
+
+ align:start position:0%
+it's up to fate at the book makes a part
+ 
+
+ align:start position:0%
+it's up to fate at the book makes a part
+that makes an interesting point that
+
+ align:start position:0%
+that makes an interesting point that
+ 
+
+ align:start position:0%
+that makes an interesting point that
+it's it in in a way it's a yeah I tried
+
+ align:start position:0%
+it's it in in a way it's a yeah I tried
+ 
+
+ align:start position:0%
+it's it in in a way it's a yeah I tried
+to simulate something that seems
+
+ align:start position:0%
+to simulate something that seems
+ 
+
+ align:start position:0%
+to simulate something that seems
+realistic that even with your best
+
+ align:start position:0%
+realistic that even with your best
+ 
+
+ align:start position:0%
+realistic that even with your best
+efforts or with the worst ever sometimes
+
+ align:start position:0%
+efforts or with the worst ever sometimes
+ 
+
+ align:start position:0%
+efforts or with the worst ever sometimes
+certain things are out of your control
+
+ align:start position:0%
+certain things are out of your control
+ 
+
+ align:start position:0%
+certain things are out of your control
+and tops
+
+ align:start position:0%
+and tops
+ 
+
+ align:start position:0%
+and tops
+simply just just just describing them
+
+ align:start position:0%
+simply just just just describing them
+ 
+
+ align:start position:0%
+simply just just just describing them
+and games of chance might be doing them
+
+ align:start position:0%
+and games of chance might be doing them
+ 
+
+ align:start position:0%
+and games of chance might be doing them
+as a disservice because you see the same
+
+ align:start position:0%
+as a disservice because you see the same
+ 
+
+ align:start position:0%
+as a disservice because you see the same
+sort of randomization elements come up
+
+ align:start position:0%
+sort of randomization elements come up
+ 
+
+ align:start position:0%
+sort of randomization elements come up
+in computer games and things like combat
+
+ align:start position:0%
+in computer games and things like combat
+ 
+
+ align:start position:0%
+in computer games and things like combat
+right you know especially strategy games
+
+ align:start position:0%
+right you know especially strategy games
+ 
+
+ align:start position:0%
+right you know especially strategy games
+well that's like a chance that something
+
+ align:start position:0%
+well that's like a chance that something
+ 
+
+ align:start position:0%
+well that's like a chance that something
+may fail a chance that something may
+
+ align:start position:0%
+may fail a chance that something may
+ 
+
+ align:start position:0%
+may fail a chance that something may
+succeed and when you think about games
+
+ align:start position:0%
+succeed and when you think about games
+ 
+
+ align:start position:0%
+succeed and when you think about games
+like more game simulations they
+
+ align:start position:0%
+like more game simulations they
+ 
+
+ align:start position:0%
+like more game simulations they
+obviously not trying to create fantastic
+
+ align:start position:0%
+obviously not trying to create fantastic
+ 
+
+ align:start position:0%
+obviously not trying to create fantastic
+you know some sort of fantasy element
+
+ align:start position:0%
+you know some sort of fantasy element
+ 
+
+ align:start position:0%
+you know some sort of fantasy element
+unless you're talking about the fight
+
+ align:start position:0%
+unless you're talking about the fight
+ 
+
+ align:start position:0%
+unless you're talking about the fight
+fire emblem or RPG fire games but we're
+
+ align:start position:0%
+fire emblem or RPG fire games but we're
+ 
+
+ align:start position:0%
+fire emblem or RPG fire games but we're
+talking like like white light like well
+
+ align:start position:0%
+talking like like white light like well
+ 
+
+ align:start position:0%
+talking like like white light like well
+well two games I think of that you try
+
+ align:start position:0%
+well two games I think of that you try
+ 
+
+ align:start position:0%
+well two games I think of that you try
+it very very hard to be to simulate
+
+ align:start position:0%
+it very very hard to be to simulate
+ 
+
+ align:start position:0%
+it very very hard to be to simulate
+something that's real and one of the
+
+ align:start position:0%
+something that's real and one of the
+ 
+
+ align:start position:0%
+something that's real and one of the
+things that are trying to simulate is
+
+ align:start position:0%
+things that are trying to simulate is
+ 
+
+ align:start position:0%
+things that are trying to simulate is
+that sometime teachers don't have
+
+ align:start position:0%
+that sometime teachers don't have
+ 
+
+ align:start position:0%
+that sometime teachers don't have
+control over everything and that's where
+
+ align:start position:0%
+control over everything and that's where
+ 
+
+ align:start position:0%
+control over everything and that's where
+randomization elements this particular
+
+ align:start position:0%
+randomization elements this particular
+ 
+
+ align:start position:0%
+randomization elements this particular
+chapter was about dice and the physical
+
+ align:start position:0%
+chapter was about dice and the physical
+ 
+
+ align:start position:0%
+chapter was about dice and the physical
+things that you use and we included
+
+ align:start position:0%
+things that you use and we included
+ 
+
+ align:start position:0%
+things that you use and we included
+spinners we included things that you
+
+ align:start position:0%
+spinners we included things that you
+ 
+
+ align:start position:0%
+spinners we included things that you
+know they were basically binary it does
+
+ align:start position:0%
+know they were basically binary it does
+ 
+
+ align:start position:0%
+know they were basically binary it does
+actually a cute idea if anybody wants to
+
+ align:start position:0%
+actually a cute idea if anybody wants to
+ 
+
+ align:start position:0%
+actually a cute idea if anybody wants to
+think about trying to introduce a bell
+
+ align:start position:0%
+think about trying to introduce a bell
+ 
+
+ align:start position:0%
+think about trying to introduce a bell
+curve to any of your results without
+
+ align:start position:0%
+curve to any of your results without
+ 
+
+ align:start position:0%
+curve to any of your results without
+having to having people enroll a whole
+
+ align:start position:0%
+having to having people enroll a whole
+ 
+
+ align:start position:0%
+having to having people enroll a whole
+bunch of dice or if you know rolling two
+
+ align:start position:0%
+bunch of dice or if you know rolling two
+ 
+
+ align:start position:0%
+bunch of dice or if you know rolling two
+dice gives you numbers into two sixteen
+
+ align:start position:0%
+dice gives you numbers into two sixteen
+ 
+
+ align:start position:0%
+dice gives you numbers into two sixteen
+after to two to twelve but you wanted a
+
+ align:start position:0%
+after to two to twelve but you wanted a
+ 
+
+ align:start position:0%
+after to two to twelve but you wanted a
+different range you could just have them
+
+ align:start position:0%
+different range you could just have them
+ 
+
+ align:start position:0%
+different range you could just have them
+draw a whole bunch of flat sticks
+
+ align:start position:0%
+draw a whole bunch of flat sticks
+ 
+
+ align:start position:0%
+draw a whole bunch of flat sticks
+and then it lands one zero one zero and
+
+ align:start position:0%
+and then it lands one zero one zero and
+ 
+
+ align:start position:0%
+and then it lands one zero one zero and
+you still get a nice bell curve so that
+
+ align:start position:0%
+you still get a nice bell curve so that
+ 
+
+ align:start position:0%
+you still get a nice bell curve so that
+that that's an idea that you can use in
+
+ align:start position:0%
+that that's an idea that you can use in
+ 
+
+ align:start position:0%
+that that's an idea that you can use in
+your games as well or you can use things
+
+ align:start position:0%
+your games as well or you can use things
+ 
+
+ align:start position:0%
+your games as well or you can use things
+like spinners which pretty much just
+
+ align:start position:0%
+like spinners which pretty much just
+ 
+
+ align:start position:0%
+like spinners which pretty much just
+give you the equal chance no matter
+
+ align:start position:0%
+give you the equal chance no matter
+ 
+
+ align:start position:0%
+give you the equal chance no matter
+which side you land and you can make our
+
+ align:start position:0%
+which side you land and you can make our
+ 
+
+ align:start position:0%
+which side you land and you can make our
+spinner of arbitrary complexity here
+
+ align:start position:0%
+spinner of arbitrary complexity here
+ 
+
+ align:start position:0%
+spinner of arbitrary complexity here
+right you could make a 20-sided spinner
+
+ align:start position:0%
+right you could make a 20-sided spinner
+ 
+
+ align:start position:0%
+right you could make a 20-sided spinner
+you look pretty sickly like a circle but
+
+ align:start position:0%
+you look pretty sickly like a circle but
+ 
+
+ align:start position:0%
+you look pretty sickly like a circle but
+you cook so but one thing that that part
+
+ align:start position:0%
+you cook so but one thing that that part
+ 
+
+ align:start position:0%
+you cook so but one thing that that part
+that also introduces is this idea that
+
+ align:start position:0%
+that also introduces is this idea that
+ 
+
+ align:start position:0%
+that also introduces is this idea that
+there is that the games of chance are
+
+ align:start position:0%
+there is that the games of chance are
+ 
+
+ align:start position:0%
+there is that the games of chance are
+also kinds of kind of like games of
+
+ align:start position:0%
+also kinds of kind of like games of
+ 
+
+ align:start position:0%
+also kinds of kind of like games of
+imperfect information and you know game
+
+ align:start position:0%
+imperfect information and you know game
+ 
+
+ align:start position:0%
+imperfect information and you know game
+something perfect and perfect
+
+ align:start position:0%
+something perfect and perfect
+ 
+
+ align:start position:0%
+something perfect and perfect
+information was the difference between
+
+ align:start position:0%
+information was the difference between
+ 
+
+ align:start position:0%
+information was the difference between
+the two of them there's the first time
+
+ align:start position:0%
+the two of them there's the first time
+ 
+
+ align:start position:0%
+the two of them there's the first time
+we're incorporating these turns in this
+
+ align:start position:0%
+we're incorporating these turns in this
+ 
+
+ align:start position:0%
+we're incorporating these turns in this
+class but I want to hazard a guess but
+
+ align:start position:0%
+class but I want to hazard a guess but
+ 
+
+ align:start position:0%
+class but I want to hazard a guess but
+what what what's an example of a game of
+
+ align:start position:0%
+what what what's an example of a game of
+ 
+
+ align:start position:0%
+what what what's an example of a game of
+perfect information Ches Ches and it's a
+
+ align:start position:0%
+perfect information Ches Ches and it's a
+ 
+
+ align:start position:0%
+perfect information Ches Ches and it's a
+game of perfect information because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right players see all the game state
+
+ align:start position:0%
+right players see all the game state
+ 
+
+ align:start position:0%
+right players see all the game state
+although parlor then go says but and
+
+ align:start position:0%
+although parlor then go says but and
+ 
+
+ align:start position:0%
+although parlor then go says but and
+they don't know and one of them got out
+
+ align:start position:0%
+they don't know and one of them got out
+ 
+
+ align:start position:0%
+they don't know and one of them got out
+of the wrong side of bed that morning
+
+ align:start position:0%
+of the wrong side of bed that morning
+ 
+
+ align:start position:0%
+of the wrong side of bed that morning
+right you know they don't necessarily
+
+ align:start position:0%
+right you know they don't necessarily
+ 
+
+ align:start position:0%
+right you know they don't necessarily
+know how experienced each other is and
+
+ align:start position:0%
+know how experienced each other is and
+ 
+
+ align:start position:0%
+know how experienced each other is and
+that's that's kind of weird is that it's
+
+ align:start position:0%
+that's that's kind of weird is that it's
+ 
+
+ align:start position:0%
+that's that's kind of weird is that it's
+that part of the game on that outside of
+
+ align:start position:0%
+that part of the game on that outside of
+ 
+
+ align:start position:0%
+that part of the game on that outside of
+the game right and other examples of
+
+ align:start position:0%
+the game right and other examples of
+ 
+
+ align:start position:0%
+the game right and other examples of
+games are perfect for imperfect
+
+ align:start position:0%
+games are perfect for imperfect
+ 
+
+ align:start position:0%
+games are perfect for imperfect
+information will get perfect poker will
+
+ align:start position:0%
+information will get perfect poker will
+ 
+
+ align:start position:0%
+information will get perfect poker will
+be imperfect because you as poker always
+
+ align:start position:0%
+be imperfect because you as poker always
+ 
+
+ align:start position:0%
+be imperfect because you as poker always
+have to be played with a single deck of
+
+ align:start position:0%
+have to be played with a single deck of
+ 
+
+ align:start position:0%
+have to be played with a single deck of
+52 cards okay you may not know so that
+
+ align:start position:0%
+52 cards okay you may not know so that
+ 
+
+ align:start position:0%
+52 cards okay you may not know so that
+that's a question to I mean typically
+
+ align:start position:0%
+that's a question to I mean typically
+ 
+
+ align:start position:0%
+that's a question to I mean typically
+replayed at home is just one deck of
+
+ align:start position:0%
+replayed at home is just one deck of
+ 
+
+ align:start position:0%
+replayed at home is just one deck of
+cards in 52 I did you know that you're
+
+ align:start position:0%
+cards in 52 I did you know that you're
+ 
+
+ align:start position:0%
+cards in 52 I did you know that you're
+holding a king of spades there's no
+
+ align:start position:0%
+holding a king of spades there's no
+ 
+
+ align:start position:0%
+holding a king of spades there's no
+other King of Spades sitting some out
+
+ align:start position:0%
+other King of Spades sitting some out
+ 
+
+ align:start position:0%
+other King of Spades sitting some out
+there but you'll play in certain casinos
+
+ align:start position:0%
+there but you'll play in certain casinos
+ 
+
+ align:start position:0%
+there but you'll play in certain casinos
+you know and they've got a five deck mix
+
+ align:start position:0%
+you know and they've got a five deck mix
+ 
+
+ align:start position:0%
+you know and they've got a five deck mix
+that could be two kings of space okay
+
+ align:start position:0%
+that could be two kings of space okay
+ 
+
+ align:start position:0%
+that could be two kings of space okay
+yeah I put poker is all about trying to
+
+ align:start position:0%
+yeah I put poker is all about trying to
+ 
+
+ align:start position:0%
+yeah I put poker is all about trying to
+figure out what other people have and
+
+ align:start position:0%
+figure out what other people have and
+ 
+
+ align:start position:0%
+figure out what other people have and
+and and what's the chances actually
+
+ align:start position:0%
+and and what's the chances actually
+ 
+
+ align:start position:0%
+and and what's the chances actually
+you'd never really know what other
+
+ align:start position:0%
+you'd never really know what other
+ 
+
+ align:start position:0%
+you'd never really know what other
+people have but you're sort of trying to
+
+ align:start position:0%
+people have but you're sort of trying to
+ 
+
+ align:start position:0%
+people have but you're sort of trying to
+read what the chances that they've got
+
+ align:start position:0%
+read what the chances that they've got
+ 
+
+ align:start position:0%
+read what the chances that they've got
+something plus what's the chances of
+
+ align:start position:0%
+something plus what's the chances of
+ 
+
+ align:start position:0%
+something plus what's the chances of
+yoga of your hand beating that and of
+
+ align:start position:0%
+yoga of your hand beating that and of
+ 
+
+ align:start position:0%
+yoga of your hand beating that and of
+course there's all the variants on poker
+
+ align:start position:0%
+course there's all the variants on poker
+ 
+
+ align:start position:0%
+course there's all the variants on poker
+like Texas Hold Em and everything which
+
+ align:start position:0%
+like Texas Hold Em and everything which
+ 
+
+ align:start position:0%
+like Texas Hold Em and everything which
+have other kinds of cars that nobody
+
+ align:start position:0%
+have other kinds of cars that nobody
+ 
+
+ align:start position:0%
+have other kinds of cars that nobody
+gets to see that everyone gets to see so
+
+ align:start position:0%
+gets to see that everyone gets to see so
+ 
+
+ align:start position:0%
+gets to see that everyone gets to see so
+perfect and imperfect information is
+
+ align:start position:0%
+perfect and imperfect information is
+ 
+
+ align:start position:0%
+perfect and imperfect information is
+kind of like a sledgehammer to deal with
+
+ align:start position:0%
+kind of like a sledgehammer to deal with
+ 
+
+ align:start position:0%
+kind of like a sledgehammer to deal with
+this because you're not quite sure
+
+ align:start position:0%
+this because you're not quite sure
+ 
+
+ align:start position:0%
+this because you're not quite sure
+they're like random numbers or random
+
+ align:start position:0%
+they're like random numbers or random
+ 
+
+ align:start position:0%
+they're like random numbers or random
+currents that you're drawing from a
+
+ align:start position:0%
+currents that you're drawing from a
+ 
+
+ align:start position:0%
+currents that you're drawing from a
+five-card spec for random numbers that
+
+ align:start position:0%
+five-card spec for random numbers that
+ 
+
+ align:start position:0%
+five-card spec for random numbers that
+you're rolling out of a die there's a
+
+ align:start position:0%
+you're rolling out of a die there's a
+ 
+
+ align:start position:0%
+you're rolling out of a die there's a
+very very different quality to that
+
+ align:start position:0%
+very very different quality to that
+ 
+
+ align:start position:0%
+very very different quality to that
+piece of information than a card that
+
+ align:start position:0%
+piece of information than a card that
+ 
+
+ align:start position:0%
+piece of information than a card that
+y'all that somebody is holding and not
+
+ align:start position:0%
+y'all that somebody is holding and not
+ 
+
+ align:start position:0%
+y'all that somebody is holding and not
+revealing to everybody else because they
+
+ align:start position:0%
+revealing to everybody else because they
+ 
+
+ align:start position:0%
+revealing to everybody else because they
+won't because that that's a fixed
+
+ align:start position:0%
+won't because that that's a fixed
+ 
+
+ align:start position:0%
+won't because that that's a fixed
+quantity it's something that was dealt
+
+ align:start position:0%
+quantity it's something that was dealt
+ 
+
+ align:start position:0%
+quantity it's something that was dealt
+in the past and partner it describes it
+
+ align:start position:0%
+in the past and partner it describes it
+ 
+
+ align:start position:0%
+in the past and partner it describes it
+as sort of past imperfect information
+
+ align:start position:0%
+as sort of past imperfect information
+ 
+
+ align:start position:0%
+as sort of past imperfect information
+and that a future imperfect information
+
+ align:start position:0%
+and that a future imperfect information
+ 
+
+ align:start position:0%
+and that a future imperfect information
+it is you're gonna roll it and then only
+
+ align:start position:0%
+it is you're gonna roll it and then only
+ 
+
+ align:start position:0%
+it is you're gonna roll it and then only
+then is that information generated even
+
+ align:start position:0%
+then is that information generated even
+ 
+
+ align:start position:0%
+then is that information generated even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+I knew it no one knows that over so
+
+ align:start position:0%
+I knew it no one knows that over so
+ 
+
+ align:start position:0%
+I knew it no one knows that over so
+there's a scholar called Celia Pierce
+
+ align:start position:0%
+there's a scholar called Celia Pierce
+ 
+
+ align:start position:0%
+there's a scholar called Celia Pierce
+over in Georgia Tech and she came up
+
+ align:start position:0%
+over in Georgia Tech and she came up
+ 
+
+ align:start position:0%
+over in Georgia Tech and she came up
+with a taxonomy just to help her discuss
+
+ align:start position:0%
+with a taxonomy just to help her discuss
+ 
+
+ align:start position:0%
+with a taxonomy just to help her discuss
+this with her design teams and I thought
+
+ align:start position:0%
+this with her design teams and I thought
+ 
+
+ align:start position:0%
+this with her design teams and I thought
+it was really really useful so instead
+
+ align:start position:0%
+it was really really useful so instead
+ 
+
+ align:start position:0%
+it was really really useful so instead
+of saying imperfect and perfect
+
+ align:start position:0%
+of saying imperfect and perfect
+ 
+
+ align:start position:0%
+of saying imperfect and perfect
+information we start off with you know
+
+ align:start position:0%
+information we start off with you know
+ 
+
+ align:start position:0%
+information we start off with you know
+the obvious one which is public
+
+ align:start position:0%
+the obvious one which is public
+ 
+
+ align:start position:0%
+the obvious one which is public
+information games of perfect information
+
+ align:start position:0%
+information games of perfect information
+ 
+
+ align:start position:0%
+information games of perfect information
+and games off every all information is
+
+ align:start position:0%
+and games off every all information is
+ 
+
+ align:start position:0%
+and games off every all information is
+public everything is public information
+
+ align:start position:0%
+public everything is public information
+ 
+
+ align:start position:0%
+public everything is public information
+the state of a board in chess or in
+
+ align:start position:0%
+the state of a board in chess or in
+ 
+
+ align:start position:0%
+the state of a board in chess or in
+checkers are probably some computer
+
+ align:start position:0%
+checkers are probably some computer
+ 
+
+ align:start position:0%
+checkers are probably some computer
+games where this is the case as well
+
+ align:start position:0%
+games where this is the case as well
+ 
+
+ align:start position:0%
+games where this is the case as well
+although they multiplayer come on video
+
+ align:start position:0%
+although they multiplayer come on video
+ 
+
+ align:start position:0%
+although they multiplayer come on video
+games but nothing's coming to mind a lot
+
+ align:start position:0%
+games but nothing's coming to mind a lot
+ 
+
+ align:start position:0%
+games but nothing's coming to mind a lot
+of a lot of computer games take
+
+ align:start position:0%
+of a lot of computer games take
+ 
+
+ align:start position:0%
+of a lot of computer games take
+advantage of the fact that everyone has
+
+ align:start position:0%
+advantage of the fact that everyone has
+ 
+
+ align:start position:0%
+advantage of the fact that everyone has
+their own screen to do imperfect
+
+ align:start position:0%
+their own screen to do imperfect
+ 
+
+ align:start position:0%
+their own screen to do imperfect
+information so when you start jumping
+
+ align:start position:0%
+information so when you start jumping
+ 
+
+ align:start position:0%
+information so when you start jumping
+into the realm of imperfect information
+
+ align:start position:0%
+into the realm of imperfect information
+ 
+
+ align:start position:0%
+into the realm of imperfect information
+that's private
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the stuff that one person at
+
+ align:start position:0%
+which is the stuff that one person at
+ 
+
+ align:start position:0%
+which is the stuff that one person at
+least one person knows for sure possibly
+
+ align:start position:0%
+least one person knows for sure possibly
+ 
+
+ align:start position:0%
+least one person knows for sure possibly
+if you're playing on a team game that's
+
+ align:start position:0%
+if you're playing on a team game that's
+ 
+
+ align:start position:0%
+if you're playing on a team game that's
+more than one person who knows this
+
+ align:start position:0%
+more than one person who knows this
+ 
+
+ align:start position:0%
+more than one person who knows this
+information for sure if you're playing a
+
+ align:start position:0%
+information for sure if you're playing a
+ 
+
+ align:start position:0%
+information for sure if you're playing a
+game like bridge where you yeah sort of
+
+ align:start position:0%
+game like bridge where you yeah sort of
+ 
+
+ align:start position:0%
+game like bridge where you yeah sort of
+communicating but in codes you know you
+
+ align:start position:0%
+communicating but in codes you know you
+ 
+
+ align:start position:0%
+communicating but in codes you know you
+you if you are if you've been playing
+
+ align:start position:0%
+you if you are if you've been playing
+ 
+
+ align:start position:0%
+you if you are if you've been playing
+with someone for a long time you can't
+
+ align:start position:0%
+with someone for a long time you can't
+ 
+
+ align:start position:0%
+with someone for a long time you can't
+get to the situation where even though I
+
+ align:start position:0%
+get to the situation where even though I
+ 
+
+ align:start position:0%
+get to the situation where even though I
+can't see your cards I pretty much know
+
+ align:start position:0%
+can't see your cards I pretty much know
+ 
+
+ align:start position:0%
+can't see your cards I pretty much know
+what cards you have because you have my
+
+ align:start position:0%
+what cards you have because you have my
+ 
+
+ align:start position:0%
+what cards you have because you have my
+teammate and you're trying to
+
+ align:start position:0%
+teammate and you're trying to
+ 
+
+ align:start position:0%
+teammate and you're trying to
+communicate with me in a way that I
+
+ align:start position:0%
+communicate with me in a way that I
+ 
+
+ align:start position:0%
+communicate with me in a way that I
+understand that's random information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuff that that that you get from say
+
+ align:start position:0%
+stuff that that that you get from say
+ 
+
+ align:start position:0%
+stuff that that that you get from say
+drawing from the top of a five step deck
+
+ align:start position:0%
+drawing from the top of a five step deck
+ 
+
+ align:start position:0%
+drawing from the top of a five step deck
+of poker cards or something that you get
+
+ align:start position:0%
+of poker cards or something that you get
+ 
+
+ align:start position:0%
+of poker cards or something that you get
+from rolling and I know stuff that you
+
+ align:start position:0%
+from rolling and I know stuff that you
+ 
+
+ align:start position:0%
+from rolling and I know stuff that you
+can't really into it what partner calls
+
+ align:start position:0%
+can't really into it what partner calls
+ 
+
+ align:start position:0%
+can't really into it what partner calls
+calls future imperfect things that will
+
+ align:start position:0%
+calls future imperfect things that will
+ 
+
+ align:start position:0%
+calls future imperfect things that will
+be sort of for all intents and purposes
+
+ align:start position:0%
+be sort of for all intents and purposes
+ 
+
+ align:start position:0%
+be sort of for all intents and purposes
+that information it's introduced the
+
+ align:start position:0%
+that information it's introduced the
+ 
+
+ align:start position:0%
+that information it's introduced the
+moment the moment you trigger that
+
+ align:start position:0%
+moment the moment you trigger that
+ 
+
+ align:start position:0%
+moment the moment you trigger that
+rendering that randomizing method the
+
+ align:start position:0%
+rendering that randomizing method the
+ 
+
+ align:start position:0%
+rendering that randomizing method the
+moment you throw the dreidel this spin
+
+ align:start position:0%
+moment you throw the dreidel this spin
+ 
+
+ align:start position:0%
+moment you throw the dreidel this spin
+the dreidel throw the rule and spin okay
+
+ align:start position:0%
+the dreidel throw the rule and spin okay
+ 
+
+ align:start position:0%
+the dreidel throw the rule and spin okay
+the moment you throw the knucklebones
+
+ align:start position:0%
+the moment you throw the knucklebones
+ 
+
+ align:start position:0%
+the moment you throw the knucklebones
+whatever it is that's the moment where
+
+ align:start position:0%
+whatever it is that's the moment where
+ 
+
+ align:start position:0%
+whatever it is that's the moment where
+the information gets generated as
+
+ align:start position:0%
+the information gets generated as
+ 
+
+ align:start position:0%
+the information gets generated as
+you know there may be some probability
+
+ align:start position:0%
+you know there may be some probability
+ 
+
+ align:start position:0%
+you know there may be some probability
+some probability on how you expect this
+
+ align:start position:0%
+some probability on how you expect this
+ 
+
+ align:start position:0%
+some probability on how you expect this
+to work out like if you're rolling two
+
+ align:start position:0%
+to work out like if you're rolling two
+ 
+
+ align:start position:0%
+to work out like if you're rolling two
+dice do you expect number seven to be
+
+ align:start position:0%
+dice do you expect number seven to be
+ 
+
+ align:start position:0%
+dice do you expect number seven to be
+the most likely outcome at number two
+
+ align:start position:0%
+the most likely outcome at number two
+ 
+
+ align:start position:0%
+the most likely outcome at number two
+and number 12 to be the least idea uh uh
+
+ align:start position:0%
+and number 12 to be the least idea uh uh
+ 
+
+ align:start position:0%
+and number 12 to be the least idea uh uh
+outcomes but that information doesn't
+
+ align:start position:0%
+outcomes but that information doesn't
+ 
+
+ align:start position:0%
+outcomes but that information doesn't
+really exist until the moment is
+
+ align:start position:0%
+really exist until the moment is
+ 
+
+ align:start position:0%
+really exist until the moment is
+generated so what's missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because listen
+
+ align:start position:0%
+because listen
+ 
+
+ align:start position:0%
+because listen
+there's information that's like
+
+ align:start position:0%
+there's information that's like
+ 
+
+ align:start position:0%
+there's information that's like
+computable move them
+
+ align:start position:0%
+computable move them
+ 
+
+ align:start position:0%
+computable move them
+that's about there so for instance if
+
+ align:start position:0%
+that's about there so for instance if
+ 
+
+ align:start position:0%
+that's about there so for instance if
+you're playing like when you're playing
+
+ align:start position:0%
+you're playing like when you're playing
+ 
+
+ align:start position:0%
+you're playing like when you're playing
+cards or something like that yeah it's
+
+ align:start position:0%
+cards or something like that yeah it's
+ 
+
+ align:start position:0%
+cards or something like that yeah it's
+enough technically that like the rules
+
+ align:start position:0%
+enough technically that like the rules
+ 
+
+ align:start position:0%
+enough technically that like the rules
+are like you can't see the rounds up in
+
+ align:start position:0%
+are like you can't see the rounds up in
+ 
+
+ align:start position:0%
+are like you can't see the rounds up in
+play right but like there's information
+
+ align:start position:0%
+play right but like there's information
+ 
+
+ align:start position:0%
+play right but like there's information
+with the stuff that's hard to remember
+
+ align:start position:0%
+with the stuff that's hard to remember
+ 
+
+ align:start position:0%
+with the stuff that's hard to remember
+that the stuff that I like let me see if
+
+ align:start position:0%
+that the stuff that I like let me see if
+ 
+
+ align:start position:0%
+that the stuff that I like let me see if
+I'm hearing you right you me so for
+
+ align:start position:0%
+I'm hearing you right you me so for
+ 
+
+ align:start position:0%
+I'm hearing you right you me so for
+instance the game of blackjack to a card
+
+ align:start position:0%
+instance the game of blackjack to a card
+ 
+
+ align:start position:0%
+instance the game of blackjack to a card
+counter is a very different for a game
+
+ align:start position:0%
+counter is a very different for a game
+ 
+
+ align:start position:0%
+counter is a very different for a game
+of blackjack for someone who sits down
+
+ align:start position:0%
+of blackjack for someone who sits down
+ 
+
+ align:start position:0%
+of blackjack for someone who sits down
+in place for one rod right because the
+
+ align:start position:0%
+in place for one rod right because the
+ 
+
+ align:start position:0%
+in place for one rod right because the
+game of like check for a card counter is
+
+ align:start position:0%
+game of like check for a card counter is
+ 
+
+ align:start position:0%
+game of like check for a card counter is
+aware that this fights that deck of
+
+ align:start position:0%
+aware that this fights that deck of
+ 
+
+ align:start position:0%
+aware that this fights that deck of
+cards has had a certain number of cards
+
+ align:start position:0%
+cards has had a certain number of cards
+ 
+
+ align:start position:0%
+cards has had a certain number of cards
+played out of it and knowing being being
+
+ align:start position:0%
+played out of it and knowing being being
+ 
+
+ align:start position:0%
+played out of it and knowing being being
+able to remember how much has been
+
+ align:start position:0%
+able to remember how much has been
+ 
+
+ align:start position:0%
+able to remember how much has been
+played out of it has changed the actual
+
+ align:start position:0%
+played out of it has changed the actual
+ 
+
+ align:start position:0%
+played out of it has changed the actual
+percentage of what's what could come out
+
+ align:start position:0%
+percentage of what's what could come out
+ 
+
+ align:start position:0%
+percentage of what's what could come out
+so what's been played before it's
+
+ align:start position:0%
+so what's been played before it's
+ 
+
+ align:start position:0%
+so what's been played before it's
+technically public information there are
+
+ align:start position:0%
+technically public information there are
+ 
+
+ align:start position:0%
+technically public information there are
+previous rounds that will play out in
+
+ align:start position:0%
+previous rounds that will play out in
+ 
+
+ align:start position:0%
+previous rounds that will play out in
+the open if you were really really
+
+ align:start position:0%
+the open if you were really really
+ 
+
+ align:start position:0%
+the open if you were really really
+paying attention you could have seen
+
+ align:start position:0%
+paying attention you could have seen
+ 
+
+ align:start position:0%
+paying attention you could have seen
+that information it's hard to remember
+
+ align:start position:0%
+that information it's hard to remember
+ 
+
+ align:start position:0%
+that information it's hard to remember
+but you could have if you are a computer
+
+ align:start position:0%
+but you could have if you are a computer
+ 
+
+ align:start position:0%
+but you could have if you are a computer
+if you're a video tape recorder you want
+
+ align:start position:0%
+if you're a video tape recorder you want
+ 
+
+ align:start position:0%
+if you're a video tape recorder you want
+to be able to see that information but
+
+ align:start position:0%
+to be able to see that information but
+ 
+
+ align:start position:0%
+to be able to see that information but
+then there's all the other cards left in
+
+ align:start position:0%
+then there's all the other cards left in
+ 
+
+ align:start position:0%
+then there's all the other cards left in
+this stack that's already been shuffled
+
+ align:start position:0%
+this stack that's already been shuffled
+ 
+
+ align:start position:0%
+this stack that's already been shuffled
+and it's kind of in a fixed order so
+
+ align:start position:0%
+and it's kind of in a fixed order so
+ 
+
+ align:start position:0%
+and it's kind of in a fixed order so
+what it was random I - before they
+
+ align:start position:0%
+what it was random I - before they
+ 
+
+ align:start position:0%
+what it was random I - before they
+shuffled it oh then now it's been
+
+ align:start position:0%
+shuffled it oh then now it's been
+ 
+
+ align:start position:0%
+shuffled it oh then now it's been
+shuffled and it's just sitting on a
+
+ align:start position:0%
+shuffled and it's just sitting on a
+ 
+
+ align:start position:0%
+shuffled and it's just sitting on a
+snack
+
+ align:start position:0%
+snack
+ 
+
+ align:start position:0%
+snack
+that's what it doesn't even have to be
+
+ align:start position:0%
+that's what it doesn't even have to be
+ 
+
+ align:start position:0%
+that's what it doesn't even have to be
+like a 5 stacked deck it could be just
+
+ align:start position:0%
+like a 5 stacked deck it could be just
+ 
+
+ align:start position:0%
+like a 5 stacked deck it could be just
+the three cards that were dealt face
+
+ align:start position:0%
+the three cards that were dealt face
+ 
+
+ align:start position:0%
+the three cards that were dealt face
+down at the beginning is it three cards
+
+ align:start position:0%
+down at the beginning is it three cards
+ 
+
+ align:start position:0%
+down at the beginning is it three cards
+for Texas poll for Texas Hold'em - okay
+
+ align:start position:0%
+for Texas poll for Texas Hold'em - okay
+ 
+
+ align:start position:0%
+for Texas poll for Texas Hold'em - okay
+the two cards that are dealt face down
+
+ align:start position:0%
+the two cards that are dealt face down
+ 
+
+ align:start position:0%
+the two cards that are dealt face down
+in the center nobody gets to see that
+
+ align:start position:0%
+in the center nobody gets to see that
+ 
+
+ align:start position:0%
+in the center nobody gets to see that
+until right the end I I but down at the
+
+ align:start position:0%
+until right the end I I but down at the
+ 
+
+ align:start position:0%
+until right the end I I but down at the
+beginning of the game or like in the
+
+ align:start position:0%
+beginning of the game or like in the
+ 
+
+ align:start position:0%
+beginning of the game or like in the
+second hand yes yes three right and at
+
+ align:start position:0%
+second hand yes yes three right and at
+ 
+
+ align:start position:0%
+second hand yes yes three right and at
+out data all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after the first reading a fifth date
+
+ align:start position:0%
+after the first reading a fifth date
+ 
+
+ align:start position:0%
+after the first reading a fifth date
+yeah all right that's right but that's
+
+ align:start position:0%
+yeah all right that's right but that's
+ 
+
+ align:start position:0%
+yeah all right that's right but that's
+been long time since I played hold it so
+
+ align:start position:0%
+been long time since I played hold it so
+ 
+
+ align:start position:0%
+been long time since I played hold it so
+okay it's all three cards the face down
+
+ align:start position:0%
+okay it's all three cards the face down
+ 
+
+ align:start position:0%
+okay it's all three cards the face down
+but they've been dealt
+
+ align:start position:0%
+but they've been dealt
+ 
+
+ align:start position:0%
+but they've been dealt
+so the randomizing thing has been
+
+ align:start position:0%
+so the randomizing thing has been
+ 
+
+ align:start position:0%
+so the randomizing thing has been
+triggered the information is there about
+
+ align:start position:0%
+triggered the information is there about
+ 
+
+ align:start position:0%
+triggered the information is there about
+no one knows it yet quite there is a
+
+ align:start position:0%
+no one knows it yet quite there is a
+ 
+
+ align:start position:0%
+no one knows it yet quite there is a
+different quality with it because that
+
+ align:start position:0%
+different quality with it because that
+ 
+
+ align:start position:0%
+different quality with it because that
+that variable can no longer change in
+
+ align:start position:0%
+that variable can no longer change in
+ 
+
+ align:start position:0%
+that variable can no longer change in
+the rest of the game
+
+ align:start position:0%
+the rest of the game
+ 
+
+ align:start position:0%
+the rest of the game
+maybe the Texas Hold'em one starts to
+
+ align:start position:0%
+maybe the Texas Hold'em one starts to
+ 
+
+ align:start position:0%
+maybe the Texas Hold'em one starts to
+get a little blurry and it's like if for
+
+ align:start position:0%
+get a little blurry and it's like if for
+ 
+
+ align:start position:0%
+get a little blurry and it's like if for
+some reason like we've decided that we
+
+ align:start position:0%
+some reason like we've decided that we
+ 
+
+ align:start position:0%
+some reason like we've decided that we
+were like what today I did I wrote like
+
+ align:start position:0%
+were like what today I did I wrote like
+ 
+
+ align:start position:0%
+were like what today I did I wrote like
+say and like the random ski and like you
+
+ align:start position:0%
+say and like the random ski and like you
+ 
+
+ align:start position:0%
+say and like the random ski and like you
+ready fuse don't look up what the next
+
+ align:start position:0%
+ready fuse don't look up what the next
+ 
+
+ align:start position:0%
+ready fuse don't look up what the next
+random seat wasn't so what the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information because yeah if you need to
+
+ align:start position:0%
+information because yeah if you need to
+ 
+
+ align:start position:0%
+information because yeah if you need to
+see that you do the randomization
+
+ align:start position:0%
+see that you do the randomization
+ 
+
+ align:start position:0%
+see that you do the randomization
+algorithm then I will argue that before
+
+ align:start position:0%
+algorithm then I will argue that before
+ 
+
+ align:start position:0%
+algorithm then I will argue that before
+me it's no longer random that's why they
+
+ align:start position:0%
+me it's no longer random that's why they
+ 
+
+ align:start position:0%
+me it's no longer random that's why they
+call it pseudo random but it's not
+
+ align:start position:0%
+call it pseudo random but it's not
+ 
+
+ align:start position:0%
+call it pseudo random but it's not
+actually random anymore you can treat it
+
+ align:start position:0%
+actually random anymore you can treat it
+ 
+
+ align:start position:0%
+actually random anymore you can treat it
+as random inflammation the first one is
+
+ align:start position:0%
+as random inflammation the first one is
+ 
+
+ align:start position:0%
+as random inflammation the first one is
+a part that's already in play and so
+
+ align:start position:0%
+a part that's already in play and so
+ 
+
+ align:start position:0%
+a part that's already in play and so
+when you take the second one that card
+
+ align:start position:0%
+when you take the second one that card
+ 
+
+ align:start position:0%
+when you take the second one that card
+has a smaller leg space of possibilities
+
+ align:start position:0%
+has a smaller leg space of possibilities
+ 
+
+ align:start position:0%
+has a smaller leg space of possibilities
+there is a specific part that that
+
+ align:start position:0%
+there is a specific part that that
+ 
+
+ align:start position:0%
+there is a specific part that that
+second one can't be the recent is the
+
+ align:start position:0%
+second one can't be the recent is the
+ 
+
+ align:start position:0%
+second one can't be the recent is the
+first what I'm saying is that if you
+
+ align:start position:0%
+first what I'm saying is that if you
+ 
+
+ align:start position:0%
+first what I'm saying is that if you
+want to if you do it on card and you
+
+ align:start position:0%
+want to if you do it on card and you
+ 
+
+ align:start position:0%
+want to if you do it on card and you
+want to reproduce the exact same
+
+ align:start position:0%
+want to reproduce the exact same
+ 
+
+ align:start position:0%
+want to reproduce the exact same
+situation elsewhere and then continue
+
+ align:start position:0%
+situation elsewhere and then continue
+ 
+
+ align:start position:0%
+situation elsewhere and then continue
+dealing for the day then you gather the
+
+ align:start position:0%
+dealing for the day then you gather the
+ 
+
+ align:start position:0%
+dealing for the day then you gather the
+deck might be maybe you're gonna shuffle
+
+ align:start position:0%
+deck might be maybe you're gonna shuffle
+ 
+
+ align:start position:0%
+deck might be maybe you're gonna shuffle
+the deck before you do a second card and
+
+ align:start position:0%
+the deck before you do a second card and
+ 
+
+ align:start position:0%
+the deck before you do a second card and
+then that green card is random the
+
+ align:start position:0%
+then that green card is random the
+ 
+
+ align:start position:0%
+then that green card is random the
+second card except it's random out of a
+
+ align:start position:0%
+second card except it's random out of a
+ 
+
+ align:start position:0%
+second card except it's random out of a
+smaller possibility and not just random
+
+ align:start position:0%
+smaller possibility and not just random
+ 
+
+ align:start position:0%
+smaller possibility and not just random
+because there's hidden information yes
+
+ align:start position:0%
+because there's hidden information yes
+ 
+
+ align:start position:0%
+because there's hidden information yes
+that's one other thing that cannot keep
+
+ align:start position:0%
+that's one other thing that cannot keep
+ 
+
+ align:start position:0%
+that's one other thing that cannot keep
+it there you're not taking into
+
+ align:start position:0%
+it there you're not taking into
+ 
+
+ align:start position:0%
+it there you're not taking into
+consideration and that's the fact that
+
+ align:start position:0%
+consideration and that's the fact that
+ 
+
+ align:start position:0%
+consideration and that's the fact that
+before the after this these three cards
+
+ align:start position:0%
+before the after this these three cards
+ 
+
+ align:start position:0%
+before the after this these three cards
+in Texas Hold'em are dealt out facedown
+
+ align:start position:0%
+in Texas Hold'em are dealt out facedown
+ 
+
+ align:start position:0%
+in Texas Hold'em are dealt out facedown
+and that one's got a chance to look at
+
+ align:start position:0%
+and that one's got a chance to look at
+ 
+
+ align:start position:0%
+and that one's got a chance to look at
+it but everyone's gotten a chance to see
+
+ align:start position:0%
+it but everyone's gotten a chance to see
+ 
+
+ align:start position:0%
+it but everyone's gotten a chance to see
+some of the cards that you have been
+
+ align:start position:0%
+some of the cards that you have been
+ 
+
+ align:start position:0%
+some of the cards that you have been
+down yeah and that has already changed
+
+ align:start position:0%
+down yeah and that has already changed
+ 
+
+ align:start position:0%
+down yeah and that has already changed
+the likelihood of what that card could
+
+ align:start position:0%
+the likelihood of what that card could
+ 
+
+ align:start position:0%
+the likelihood of what that card could
+be down because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perfectly brand uniformly random chosen
+
+ align:start position:0%
+perfectly brand uniformly random chosen
+ 
+
+ align:start position:0%
+perfectly brand uniformly random chosen
+from like the distribution of everything
+
+ align:start position:0%
+from like the distribution of everything
+ 
+
+ align:start position:0%
+from like the distribution of everything
+doesn't mean it's not so random so like
+
+ align:start position:0%
+doesn't mean it's not so random so like
+ 
+
+ align:start position:0%
+doesn't mean it's not so random so like
+what I'm saying is just because like so
+
+ align:start position:0%
+what I'm saying is just because like so
+ 
+
+ align:start position:0%
+what I'm saying is just because like so
+my so my like you learn a sound card
+
+ align:start position:0%
+my so my like you learn a sound card
+ 
+
+ align:start position:0%
+my so my like you learn a sound card
+room and then I throw a facedown card
+
+ align:start position:0%
+room and then I throw a facedown card
+ 
+
+ align:start position:0%
+room and then I throw a facedown card
+into the 5 of diamonds mmm it's even
+
+ align:start position:0%
+into the 5 of diamonds mmm it's even
+ 
+
+ align:start position:0%
+into the 5 of diamonds mmm it's even
+though I know that the facedown part is
+
+ align:start position:0%
+though I know that the facedown part is
+ 
+
+ align:start position:0%
+though I know that the facedown part is
+not the 5 of diamonds it's still random
+
+ align:start position:0%
+not the 5 of diamonds it's still random
+ 
+
+ align:start position:0%
+not the 5 of diamonds it's still random
+because it's now drawn from ohrid
+
+ align:start position:0%
+because it's now drawn from ohrid
+ 
+
+ align:start position:0%
+because it's now drawn from ohrid
+genetic studies okay no it's not because
+
+ align:start position:0%
+genetic studies okay no it's not because
+ 
+
+ align:start position:0%
+genetic studies okay no it's not because
+what happens is that you keep getting
+
+ align:start position:0%
+what happens is that you keep getting
+ 
+
+ align:start position:0%
+what happens is that you keep getting
+new cards throughout the entire game
+
+ align:start position:0%
+new cards throughout the entire game
+ 
+
+ align:start position:0%
+new cards throughout the entire game
+right and you know and and these cards
+
+ align:start position:0%
+right and you know and and these cards
+ 
+
+ align:start position:0%
+right and you know and and these cards
+slowly get revealed so let's say that if
+
+ align:start position:0%
+slowly get revealed so let's say that if
+ 
+
+ align:start position:0%
+slowly get revealed so let's say that if
+there's a distinction made between
+
+ align:start position:0%
+there's a distinction made between
+ 
+
+ align:start position:0%
+there's a distinction made between
+random and hidden for the purposes of
+
+ align:start position:0%
+random and hidden for the purposes of
+ 
+
+ align:start position:0%
+random and hidden for the purposes of
+this class of classification of games
+
+ align:start position:0%
+this class of classification of games
+ 
+
+ align:start position:0%
+this class of classification of games
+there's probably a useful reason for it
+
+ align:start position:0%
+there's probably a useful reason for it
+ 
+
+ align:start position:0%
+there's probably a useful reason for it
+and I mean sure you can think of it as
+
+ align:start position:0%
+and I mean sure you can think of it as
+ 
+
+ align:start position:0%
+and I mean sure you can think of it as
+like now there's dependence between
+
+ align:start position:0%
+like now there's dependence between
+ 
+
+ align:start position:0%
+like now there's dependence between
+different carbons things like that but
+
+ align:start position:0%
+different carbons things like that but
+ 
+
+ align:start position:0%
+different carbons things like that but
+it's probably just there for a useful
+
+ align:start position:0%
+it's probably just there for a useful
+ 
+
+ align:start position:0%
+it's probably just there for a useful
+way of thinking about games
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not talking about statistical
+
+ align:start position:0%
+I'm not talking about statistical
+ 
+
+ align:start position:0%
+I'm not talking about statistical
+difference I'm talking and talking about
+
+ align:start position:0%
+difference I'm talking and talking about
+ 
+
+ align:start position:0%
+difference I'm talking and talking about
+what the players think about these three
+
+ align:start position:0%
+what the players think about these three
+ 
+
+ align:start position:0%
+what the players think about these three
+cards they know these three cards are
+
+ align:start position:0%
+cards they know these three cards are
+ 
+
+ align:start position:0%
+cards they know these three cards are
+not being dealt read out every single
+
+ align:start position:0%
+not being dealt read out every single
+ 
+
+ align:start position:0%
+not being dealt read out every single
+hand they know that no one can say for
+
+ align:start position:0%
+hand they know that no one can say for
+ 
+
+ align:start position:0%
+hand they know that no one can say for
+instance like like someone can take the
+
+ align:start position:0%
+instance like like someone can take the
+ 
+
+ align:start position:0%
+instance like like someone can take the
+deck and shuffle it in the middle of a
+
+ align:start position:0%
+deck and shuffle it in the middle of a
+ 
+
+ align:start position:0%
+deck and shuffle it in the middle of a
+poker game no one no one complains about
+
+ align:start position:0%
+poker game no one no one complains about
+ 
+
+ align:start position:0%
+poker game no one no one complains about
+that you're allowed to do that you can't
+
+ align:start position:0%
+that you're allowed to do that you can't
+ 
+
+ align:start position:0%
+that you're allowed to do that you can't
+read eel and other three cards let yeah
+
+ align:start position:0%
+read eel and other three cards let yeah
+ 
+
+ align:start position:0%
+read eel and other three cards let yeah
+it doesn't change the probability
+
+ align:start position:0%
+it doesn't change the probability
+ 
+
+ align:start position:0%
+it doesn't change the probability
+distribution but you're not allowed to
+
+ align:start position:0%
+distribution but you're not allowed to
+ 
+
+ align:start position:0%
+distribution but you're not allowed to
+the rules do not allow you to read eel
+
+ align:start position:0%
+the rules do not allow you to read eel
+ 
+
+ align:start position:0%
+the rules do not allow you to read eel
+those three cards there is there is a
+
+ align:start position:0%
+those three cards there is there is a
+ 
+
+ align:start position:0%
+those three cards there is there is a
+different weight that the rules have
+
+ align:start position:0%
+different weight that the rules have
+ 
+
+ align:start position:0%
+different weight that the rules have
+placed on those three cards that have
+
+ align:start position:0%
+placed on those three cards that have
+ 
+
+ align:start position:0%
+placed on those three cards that have
+been down saying those things are now
+
+ align:start position:0%
+been down saying those things are now
+ 
+
+ align:start position:0%
+been down saying those things are now
+fixed whereas everything in that deck
+
+ align:start position:0%
+fixed whereas everything in that deck
+ 
+
+ align:start position:0%
+fixed whereas everything in that deck
+can can be reordered your your your hand
+
+ align:start position:0%
+can can be reordered your your your hand
+ 
+
+ align:start position:0%
+can can be reordered your your your hand
+on your head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the one person in the white room right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is actually also a
+
+ align:start position:0%
+and that is actually also a
+ 
+
+ align:start position:0%
+and that is actually also a
+statistically different example but but
+
+ align:start position:0%
+statistically different example but but
+ 
+
+ align:start position:0%
+statistically different example but but
+a much curing example of hidden
+
+ align:start position:0%
+a much curing example of hidden
+ 
+
+ align:start position:0%
+a much curing example of hidden
+information because that one as you
+
+ align:start position:0%
+information because that one as you
+ 
+
+ align:start position:0%
+information because that one as you
+played a game you are getting more and
+
+ align:start position:0%
+played a game you are getting more and
+ 
+
+ align:start position:0%
+played a game you are getting more and
+more and more information about what
+
+ align:start position:0%
+more and more information about what
+ 
+
+ align:start position:0%
+more and more information about what
+those cars could be in fact that's the
+
+ align:start position:0%
+those cars could be in fact that's the
+ 
+
+ align:start position:0%
+those cars could be in fact that's the
+whole point of the game right it was
+
+ align:start position:0%
+whole point of the game right it was
+ 
+
+ align:start position:0%
+whole point of the game right it was
+trying to figure out what what's in
+
+ align:start position:0%
+trying to figure out what what's in
+ 
+
+ align:start position:0%
+trying to figure out what what's in
+there and so in that particular case
+
+ align:start position:0%
+there and so in that particular case
+ 
+
+ align:start position:0%
+there and so in that particular case
+that's hidden information that's you
+
+ align:start position:0%
+that's hidden information that's you
+ 
+
+ align:start position:0%
+that's hidden information that's you
+know random and a plane when it was
+
+ align:start position:0%
+know random and a plane when it was
+ 
+
+ align:start position:0%
+know random and a plane when it was
+generated but after that is null is but
+
+ align:start position:0%
+generated but after that is null is but
+ 
+
+ align:start position:0%
+generated but after that is null is but
+as soon as people start playing stop
+
+ align:start position:0%
+as soon as people start playing stop
+ 
+
+ align:start position:0%
+as soon as people start playing stop
+making accusations is no longer random
+
+ align:start position:0%
+making accusations is no longer random
+ 
+
+ align:start position:0%
+making accusations is no longer random
+it's just hidden information so yeah
+
+ align:start position:0%
+it's just hidden information so yeah
+ 
+
+ align:start position:0%
+it's just hidden information so yeah
+clue is a much better example of that
+
+ align:start position:0%
+clue is a much better example of that
+ 
+
+ align:start position:0%
+clue is a much better example of that
+maybe the three huts and the Texas Hold
+
+ align:start position:0%
+maybe the three huts and the Texas Hold
+ 
+
+ align:start position:0%
+maybe the three huts and the Texas Hold
+Em are different I still maintain that
+
+ align:start position:0%
+Em are different I still maintain that
+ 
+
+ align:start position:0%
+Em are different I still maintain that
+they are positively they may not be
+
+ align:start position:0%
+they are positively they may not be
+ 
+
+ align:start position:0%
+they are positively they may not be
+statistically different but they are
+
+ align:start position:0%
+statistically different but they are
+ 
+
+ align:start position:0%
+statistically different but they are
+qualitatively different because you can
+
+ align:start position:0%
+qualitatively different because you can
+ 
+
+ align:start position:0%
+qualitatively different because you can
+never really know Mize those so the
+
+ align:start position:0%
+never really know Mize those so the
+ 
+
+ align:start position:0%
+never really know Mize those so the
+Scots according to the rules referees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first so let me go to him first and then
+
+ align:start position:0%
+first so let me go to him first and then
+ 
+
+ align:start position:0%
+first so let me go to him first and then
+we'll get back you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot right let's say that we take one
+
+ align:start position:0%
+a lot right let's say that we take one
+ 
+
+ align:start position:0%
+a lot right let's say that we take one
+card from the deck and put it facedown
+
+ align:start position:0%
+card from the deck and put it facedown
+ 
+
+ align:start position:0%
+card from the deck and put it facedown
+and then we flip a second card so that
+
+ align:start position:0%
+and then we flip a second card so that
+ 
+
+ align:start position:0%
+and then we flip a second card so that
+everyone sees sees it right and then
+
+ align:start position:0%
+everyone sees sees it right and then
+ 
+
+ align:start position:0%
+everyone sees sees it right and then
+let's say someone gets it into their
+
+ align:start position:0%
+let's say someone gets it into their
+ 
+
+ align:start position:0%
+let's say someone gets it into their
+head to take that one card though it's
+
+ align:start position:0%
+head to take that one card though it's
+ 
+
+ align:start position:0%
+head to take that one card though it's
+hidden right and shuffle it back in and
+
+ align:start position:0%
+hidden right and shuffle it back in and
+ 
+
+ align:start position:0%
+hidden right and shuffle it back in and
+dealing you one right that actually does
+
+ align:start position:0%
+dealing you one right that actually does
+ 
+
+ align:start position:0%
+dealing you one right that actually does
+the two situations where you do that
+
+ align:start position:0%
+the two situations where you do that
+ 
+
+ align:start position:0%
+the two situations where you do that
+where you don't are different because
+
+ align:start position:0%
+where you don't are different because
+ 
+
+ align:start position:0%
+where you don't are different because
+indeed in the first situation the heart
+
+ align:start position:0%
+indeed in the first situation the heart
+ 
+
+ align:start position:0%
+indeed in the first situation the heart
+that was hidden had a equal probability
+
+ align:start position:0%
+that was hidden had a equal probability
+ 
+
+ align:start position:0%
+that was hidden had a equal probability
+over all 52 cards and followed and when
+
+ align:start position:0%
+over all 52 cards and followed and when
+ 
+
+ align:start position:0%
+over all 52 cards and followed and when
+you get one piece of the extra piece of
+
+ align:start position:0%
+you get one piece of the extra piece of
+ 
+
+ align:start position:0%
+you get one piece of the extra piece of
+information after that your adjusted
+
+ align:start position:0%
+information after that your adjusted
+ 
+
+ align:start position:0%
+information after that your adjusted
+probability distribution is over equal
+
+ align:start position:0%
+probability distribution is over equal
+ 
+
+ align:start position:0%
+probability distribution is over equal
+over the 51 cards however if you reveal
+
+ align:start position:0%
+over the 51 cards however if you reveal
+ 
+
+ align:start position:0%
+over the 51 cards however if you reveal
+that one card and then take it back then
+
+ align:start position:0%
+that one card and then take it back then
+ 
+
+ align:start position:0%
+that one card and then take it back then
+if someone like you don't necessarily
+
+ align:start position:0%
+if someone like you don't necessarily
+ 
+
+ align:start position:0%
+if someone like you don't necessarily
+have that card visible to everyone very
+
+ align:start position:0%
+have that card visible to everyone very
+ 
+
+ align:start position:0%
+have that card visible to everyone very
+temple but it's true that the example to
+
+ align:start position:0%
+temple but it's true that the example to
+ 
+
+ align:start position:0%
+temple but it's true that the example to
+do it yeah you you are describing a
+
+ align:start position:0%
+do it yeah you you are describing a
+ 
+
+ align:start position:0%
+do it yeah you you are describing a
+situation where someone's actually had a
+
+ align:start position:0%
+situation where someone's actually had a
+ 
+
+ align:start position:0%
+situation where someone's actually had a
+chance to actually look at that card
+
+ align:start position:0%
+chance to actually look at that card
+ 
+
+ align:start position:0%
+chance to actually look at that card
+which I've been pasted on yeah and and
+
+ align:start position:0%
+which I've been pasted on yeah and and
+ 
+
+ align:start position:0%
+which I've been pasted on yeah and and
+and and and that and that does change
+
+ align:start position:0%
+and and and that and that does change
+ 
+
+ align:start position:0%
+and and and that and that does change
+things because that becomes private
+
+ align:start position:0%
+things because that becomes private
+ 
+
+ align:start position:0%
+things because that becomes private
+information is someone else so that
+
+ align:start position:0%
+information is someone else so that
+ 
+
+ align:start position:0%
+information is someone else so that
+makes it kind of outside of the realm of
+
+ align:start position:0%
+makes it kind of outside of the realm of
+ 
+
+ align:start position:0%
+makes it kind of outside of the realm of
+example but yeah I do agree that
+
+ align:start position:0%
+example but yeah I do agree that
+ 
+
+ align:start position:0%
+example but yeah I do agree that
+statistically there's not actually a
+
+ align:start position:0%
+statistically there's not actually a
+ 
+
+ align:start position:0%
+statistically there's not actually a
+huge amount of difference between the
+
+ align:start position:0%
+huge amount of difference between the
+ 
+
+ align:start position:0%
+huge amount of difference between the
+cards that's facedown and the cards that
+
+ align:start position:0%
+cards that's facedown and the cards that
+ 
+
+ align:start position:0%
+cards that's facedown and the cards that
+you're drawing off the top of the top
+
+ align:start position:0%
+you're drawing off the top of the top
+ 
+
+ align:start position:0%
+you're drawing off the top of the top
+100 of the deck and you'll get your hand
+
+ align:start position:0%
+100 of the deck and you'll get your hand
+ 
+
+ align:start position:0%
+100 of the deck and you'll get your hand
+in the net
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's no difference and so like as a
+
+ align:start position:0%
+there's no difference and so like as a
+ 
+
+ align:start position:0%
+there's no difference and so like as a
+player Mundi sort of like think about
+
+ align:start position:0%
+player Mundi sort of like think about
+ 
+
+ align:start position:0%
+player Mundi sort of like think about
+cards that are fixed a little bit
+
+ align:start position:0%
+cards that are fixed a little bit
+ 
+
+ align:start position:0%
+cards that are fixed a little bit
+differently than their back like if I'm
+
+ align:start position:0%
+differently than their back like if I'm
+ 
+
+ align:start position:0%
+differently than their back like if I'm
+playing to win optimally I have to
+
+ align:start position:0%
+playing to win optimally I have to
+ 
+
+ align:start position:0%
+playing to win optimally I have to
+lecture strategically you could is
+
+ align:start position:0%
+lecture strategically you could is
+ 
+
+ align:start position:0%
+lecture strategically you could is
+probably advantageous for you to think
+
+ align:start position:0%
+probably advantageous for you to think
+ 
+
+ align:start position:0%
+probably advantageous for you to think
+that I've seen that same statistical
+
+ align:start position:0%
+that I've seen that same statistical
+ 
+
+ align:start position:0%
+that I've seen that same statistical
+difference because they are and I'm not
+
+ align:start position:0%
+difference because they are and I'm not
+ 
+
+ align:start position:0%
+difference because they are and I'm not
+disagreeing that statistically they have
+
+ align:start position:0%
+disagreeing that statistically they have
+ 
+
+ align:start position:0%
+disagreeing that statistically they have
+the same likelihood I'm saying and in
+
+ align:start position:0%
+the same likelihood I'm saying and in
+ 
+
+ align:start position:0%
+the same likelihood I'm saying and in
+terms of how the rules are worded
+
+ align:start position:0%
+terms of how the rules are worded
+ 
+
+ align:start position:0%
+terms of how the rules are worded
+they're very different there's no way
+
+ align:start position:0%
+they're very different there's no way
+ 
+
+ align:start position:0%
+they're very different there's no way
+you're ever going to gain information
+
+ align:start position:0%
+you're ever going to gain information
+ 
+
+ align:start position:0%
+you're ever going to gain information
+about what the next role that is going
+
+ align:start position:0%
+about what the next role that is going
+ 
+
+ align:start position:0%
+about what the next role that is going
+to be unless you're doing some kind of
+
+ align:start position:0%
+to be unless you're doing some kind of
+ 
+
+ align:start position:0%
+to be unless you're doing some kind of
+like for a roll of a dice yeah I mean
+
+ align:start position:0%
+like for a roll of a dice yeah I mean
+ 
+
+ align:start position:0%
+like for a roll of a dice yeah I mean
+it's no it's still random there's no
+
+ align:start position:0%
+it's no it's still random there's no
+ 
+
+ align:start position:0%
+it's no it's still random there's no
+probability distribution over what it is
+
+ align:start position:0%
+probability distribution over what it is
+ 
+
+ align:start position:0%
+probability distribution over what it is
+know if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll be ok alright there's one very
+
+ align:start position:0%
+I'll be ok alright there's one very
+ 
+
+ align:start position:0%
+I'll be ok alright there's one very
+clear example when you can compute it
+
+ align:start position:0%
+clear example when you can compute it
+ 
+
+ align:start position:0%
+clear example when you can compute it
+right because you know those guys are
+
+ align:start position:0%
+right because you know those guys are
+ 
+
+ align:start position:0%
+right because you know those guys are
+loaded you know it's like yeah you know
+
+ align:start position:0%
+loaded you know it's like yeah you know
+ 
+
+ align:start position:0%
+loaded you know it's like yeah you know
+those guys are loaded six and and it's
+
+ align:start position:0%
+those guys are loaded six and and it's
+ 
+
+ align:start position:0%
+those guys are loaded six and and it's
+there and and you know and in that
+
+ align:start position:0%
+there and and you know and in that
+ 
+
+ align:start position:0%
+there and and you know and in that
+particular case you've got private it it
+
+ align:start position:0%
+particular case you've got private it it
+ 
+
+ align:start position:0%
+particular case you've got private it it
+information just in the same way that if
+
+ align:start position:0%
+information just in the same way that if
+ 
+
+ align:start position:0%
+information just in the same way that if
+you're using say a pseudo no it's it's
+
+ align:start position:0%
+you're using say a pseudo no it's it's
+ 
+
+ align:start position:0%
+you're using say a pseudo no it's it's
+important to remember that to know that
+
+ align:start position:0%
+important to remember that to know that
+ 
+
+ align:start position:0%
+important to remember that to know that
+is information cuz no player actually
+
+ align:start position:0%
+is information cuz no player actually
+ 
+
+ align:start position:0%
+is information cuz no player actually
+gets to see what that card is you wear
+
+ align:start position:0%
+gets to see what that card is you wear
+ 
+
+ align:start position:0%
+gets to see what that card is you wear
+is inserted into the envelope for so
+
+ align:start position:0%
+is inserted into the envelope for so
+ 
+
+ align:start position:0%
+is inserted into the envelope for so
+those for those people who haven't
+
+ align:start position:0%
+those for those people who haven't
+ 
+
+ align:start position:0%
+those for those people who haven't
+played clue what happens is that you've
+
+ align:start position:0%
+played clue what happens is that you've
+ 
+
+ align:start position:0%
+played clue what happens is that you've
+got a whole stack your three different
+
+ align:start position:0%
+got a whole stack your three different
+ 
+
+ align:start position:0%
+got a whole stack your three different
+stacks of people places and things that
+
+ align:start position:0%
+stacks of people places and things that
+ 
+
+ align:start position:0%
+stacks of people places and things that
+you can kill people with from by the
+
+ align:start position:0%
+you can kill people with from by the
+ 
+
+ align:start position:0%
+you can kill people with from by the
+1950s or something and then you get one
+
+ align:start position:0%
+1950s or something and then you get one
+ 
+
+ align:start position:0%
+1950s or something and then you get one
+the most three tanks are shuffled you
+
+ align:start position:0%
+the most three tanks are shuffled you
+ 
+
+ align:start position:0%
+the most three tanks are shuffled you
+pick up one card from each and those
+
+ align:start position:0%
+pick up one card from each and those
+ 
+
+ align:start position:0%
+pick up one card from each and those
+three three cards go into an envelope
+
+ align:start position:0%
+three three cards go into an envelope
+ 
+
+ align:start position:0%
+three three cards go into an envelope
+that nobody gets to see until pretty
+
+ align:start position:0%
+that nobody gets to see until pretty
+ 
+
+ align:start position:0%
+that nobody gets to see until pretty
+late in the game and that and those cars
+
+ align:start position:0%
+late in the game and that and those cars
+ 
+
+ align:start position:0%
+late in the game and that and those cars
+won't ever change that's a that's that's
+
+ align:start position:0%
+won't ever change that's a that's that's
+ 
+
+ align:start position:0%
+won't ever change that's a that's that's
+a very clear example of hidden
+
+ align:start position:0%
+a very clear example of hidden
+ 
+
+ align:start position:0%
+a very clear example of hidden
+information because at the point of
+
+ align:start position:0%
+information because at the point of
+ 
+
+ align:start position:0%
+information because at the point of
+ending was generated you're right that
+
+ align:start position:0%
+ending was generated you're right that
+ 
+
+ align:start position:0%
+ending was generated you're right that
+was random but then it gets turned to
+
+ align:start position:0%
+was random but then it gets turned to
+ 
+
+ align:start position:0%
+was random but then it gets turned to
+this piece of hidden information that
+
+ align:start position:0%
+this piece of hidden information that
+ 
+
+ align:start position:0%
+this piece of hidden information that
+everyone's trying to find out during the
+
+ align:start position:0%
+everyone's trying to find out during the
+ 
+
+ align:start position:0%
+everyone's trying to find out during the
+game the whole point of clue is that
+
+ align:start position:0%
+game the whole point of clue is that
+ 
+
+ align:start position:0%
+game the whole point of clue is that
+you're trying to do to figure it this
+
+ align:start position:0%
+you're trying to do to figure it this
+ 
+
+ align:start position:0%
+you're trying to do to figure it this
+out there are rules governing who gets
+
+ align:start position:0%
+out there are rules governing who gets
+ 
+
+ align:start position:0%
+out there are rules governing who gets
+to see that unity that hidden
+
+ align:start position:0%
+to see that unity that hidden
+ 
+
+ align:start position:0%
+to see that unity that hidden
+information when I know this rules to
+
+ align:start position:0%
+information when I know this rules to
+ 
+
+ align:start position:0%
+information when I know this rules to
+governing how you generate the
+
+ align:start position:0%
+governing how you generate the
+ 
+
+ align:start position:0%
+governing how you generate the
+information and there are mechanics for
+
+ align:start position:0%
+information and there are mechanics for
+ 
+
+ align:start position:0%
+information and there are mechanics for
+you to be able to figure out what inside
+
+ align:start position:0%
+you to be able to figure out what inside
+ 
+
+ align:start position:0%
+you to be able to figure out what inside
+there um let me see there was another
+
+ align:start position:0%
+there um let me see there was another
+ 
+
+ align:start position:0%
+there um let me see there was another
+point that I was going to make about
+
+ align:start position:0%
+point that I was going to make about
+ 
+
+ align:start position:0%
+point that I was going to make about
+that and it's true that if you say we
+
+ align:start position:0%
+that and it's true that if you say we
+ 
+
+ align:start position:0%
+that and it's true that if you say we
+implemented that on a computer or any
+
+ align:start position:0%
+implemented that on a computer or any
+ 
+
+ align:start position:0%
+implemented that on a computer or any
+game that has some sort of randomizing
+
+ align:start position:0%
+game that has some sort of randomizing
+ 
+
+ align:start position:0%
+game that has some sort of randomizing
+thing in a computer and you could figure
+
+ align:start position:0%
+thing in a computer and you could figure
+ 
+
+ align:start position:0%
+thing in a computer and you could figure
+out how the randomizing was being done
+
+ align:start position:0%
+out how the randomizing was being done
+ 
+
+ align:start position:0%
+out how the randomizing was being done
+because very few things in a computer
+
+ align:start position:0%
+because very few things in a computer
+ 
+
+ align:start position:0%
+because very few things in a computer
+are like truly right
+
+ align:start position:0%
+are like truly right
+ 
+
+ align:start position:0%
+are like truly right
+then that you will be able to say figure
+
+ align:start position:0%
+then that you will be able to say figure
+ 
+
+ align:start position:0%
+then that you will be able to say figure
+out okay the next I role should be a
+
+ align:start position:0%
+out okay the next I role should be a
+ 
+
+ align:start position:0%
+out okay the next I role should be a
+certain number the other day I talked
+
+ align:start position:0%
+certain number the other day I talked
+ 
+
+ align:start position:0%
+certain number the other day I talked
+about how when you played certain
+
+ align:start position:0%
+about how when you played certain
+ 
+
+ align:start position:0%
+about how when you played certain
+strategy games and you had like a fifty
+
+ align:start position:0%
+strategy games and you had like a fifty
+ 
+
+ align:start position:0%
+strategy games and you had like a fifty
+percent chance of succeeding at
+
+ align:start position:0%
+percent chance of succeeding at
+ 
+
+ align:start position:0%
+percent chance of succeeding at
+something then check technically if you
+
+ align:start position:0%
+something then check technically if you
+ 
+
+ align:start position:0%
+something then check technically if you
+save the game right behind right before
+
+ align:start position:0%
+save the game right behind right before
+ 
+
+ align:start position:0%
+save the game right behind right before
+you did that and you did it and you kept
+
+ align:start position:0%
+you did that and you did it and you kept
+ 
+
+ align:start position:0%
+you did that and you did it and you kept
+doing it then you will eventually have a
+
+ align:start position:0%
+doing it then you will eventually have a
+ 
+
+ align:start position:0%
+doing it then you will eventually have a
+hundred percent chance like I'm sitting
+
+ align:start position:0%
+hundred percent chance like I'm sitting
+ 
+
+ align:start position:0%
+hundred percent chance like I'm sitting
+right because you just keep playing and
+
+ align:start position:0%
+right because you just keep playing and
+ 
+
+ align:start position:0%
+right because you just keep playing and
+until you win unless it's all cause it's
+
+ align:start position:0%
+until you win unless it's all cause it's
+ 
+
+ align:start position:0%
+until you win unless it's all cause it's
+a pseudo-random number generator that is
+
+ align:start position:0%
+a pseudo-random number generator that is
+ 
+
+ align:start position:0%
+a pseudo-random number generator that is
+saving the seed and so the outcome
+
+ align:start position:0%
+saving the seed and so the outcome
+ 
+
+ align:start position:0%
+saving the seed and so the outcome
+always turns out to be the same each
+
+ align:start position:0%
+always turns out to be the same each
+ 
+
+ align:start position:0%
+always turns out to be the same each
+time and if you had that information
+
+ align:start position:0%
+time and if you had that information
+ 
+
+ align:start position:0%
+time and if you had that information
+that's actually private information the
+
+ align:start position:0%
+that's actually private information the
+ 
+
+ align:start position:0%
+that's actually private information the
+question is that is that actually going
+
+ align:start position:0%
+question is that is that actually going
+ 
+
+ align:start position:0%
+question is that is that actually going
+to be something that you are designing
+
+ align:start position:0%
+to be something that you are designing
+ 
+
+ align:start position:0%
+to be something that you are designing
+into your game or something that you
+
+ align:start position:0%
+into your game or something that you
+ 
+
+ align:start position:0%
+into your game or something that you
+just choose to live with and as a
+
+ align:start position:0%
+just choose to live with and as a
+ 
+
+ align:start position:0%
+just choose to live with and as a
+designer you get to make that decision
+
+ align:start position:0%
+designer you get to make that decision
+ 
+
+ align:start position:0%
+designer you get to make that decision
+you get to decide things like I'm going
+
+ align:start position:0%
+you get to decide things like I'm going
+ 
+
+ align:start position:0%
+you get to decide things like I'm going
+to save the random number seed when I
+
+ align:start position:0%
+to save the random number seed when I
+ 
+
+ align:start position:0%
+to save the random number seed when I
+save the save game we can decide to
+
+ align:start position:0%
+save the save game we can decide to
+ 
+
+ align:start position:0%
+save the save game we can decide to
+reveal what you're randomizing scheme is
+
+ align:start position:0%
+reveal what you're randomizing scheme is
+ 
+
+ align:start position:0%
+reveal what you're randomizing scheme is
+to the rest of the world and to a
+
+ align:start position:0%
+to the rest of the world and to a
+ 
+
+ align:start position:0%
+to the rest of the world and to a
+hardcore pro a computer hacker wouldn't
+
+ align:start position:0%
+hardcore pro a computer hacker wouldn't
+ 
+
+ align:start position:0%
+hardcore pro a computer hacker wouldn't
+be that hard to figure out what kind of
+
+ align:start position:0%
+be that hard to figure out what kind of
+ 
+
+ align:start position:0%
+be that hard to figure out what kind of
+method you're using you can you you can
+
+ align:start position:0%
+method you're using you can you you can
+ 
+
+ align:start position:0%
+method you're using you can you you can
+choose to say no this is a very closely
+
+ align:start position:0%
+choose to say no this is a very closely
+ 
+
+ align:start position:0%
+choose to say no this is a very closely
+guarded secret you know I'm actually
+
+ align:start position:0%
+guarded secret you know I'm actually
+ 
+
+ align:start position:0%
+guarded secret you know I'm actually
+generating it by you know analyzing this
+
+ align:start position:0%
+generating it by you know analyzing this
+ 
+
+ align:start position:0%
+generating it by you know analyzing this
+Geiger counter you know and seeing how
+
+ align:start position:0%
+Geiger counter you know and seeing how
+ 
+
+ align:start position:0%
+Geiger counter you know and seeing how
+and when when certain ticks government
+
+ align:start position:0%
+and when when certain ticks government
+ 
+
+ align:start position:0%
+and when when certain ticks government
+ads like as close to random as as we can
+
+ align:start position:0%
+ads like as close to random as as we can
+ 
+
+ align:start position:0%
+ads like as close to random as as we can
+get you can choose to do all of that as
+
+ align:start position:0%
+get you can choose to do all of that as
+ 
+
+ align:start position:0%
+get you can choose to do all of that as
+a designer and the question is where do
+
+ align:start position:0%
+a designer and the question is where do
+ 
+
+ align:start position:0%
+a designer and the question is where do
+you want to where do you want to set
+
+ align:start position:0%
+you want to where do you want to set
+ 
+
+ align:start position:0%
+you want to where do you want to set
+those limits for your own game
+
+ align:start position:0%
+those limits for your own game
+ 
+
+ align:start position:0%
+those limits for your own game
+things like for instance yeah
+
+ align:start position:0%
+things like for instance yeah
+ 
+
+ align:start position:0%
+things like for instance yeah
+theoretically a pair of dice can
+
+ align:start position:0%
+theoretically a pair of dice can
+ 
+
+ align:start position:0%
+theoretically a pair of dice can
+generate any number between 2 and 12 but
+
+ align:start position:0%
+generate any number between 2 and 12 but
+ 
+
+ align:start position:0%
+generate any number between 2 and 12 but
+anyone who's played games for certain
+
+ align:start position:0%
+anyone who's played games for certain
+ 
+
+ align:start position:0%
+anyone who's played games for certain
+amount of time realizes that 2 and 12
+
+ align:start position:0%
+amount of time realizes that 2 and 12
+ 
+
+ align:start position:0%
+amount of time realizes that 2 and 12
+are really rare compared to the sudden
+
+ align:start position:0%
+are really rare compared to the sudden
+ 
+
+ align:start position:0%
+are really rare compared to the sudden
+and there are games that take advantage
+
+ align:start position:0%
+and there are games that take advantage
+ 
+
+ align:start position:0%
+and there are games that take advantage
+of that and there are games who don't
+
+ align:start position:0%
+of that and there are games who don't
+ 
+
+ align:start position:0%
+of that and there are games who don't
+take advantage of that there are some
+
+ align:start position:0%
+take advantage of that there are some
+ 
+
+ align:start position:0%
+take advantage of that there are some
+games that basically treat a roll of 12
+
+ align:start position:0%
+games that basically treat a roll of 12
+ 
+
+ align:start position:0%
+games that basically treat a roll of 12
+and a roll of two exactly the same as a
+
+ align:start position:0%
+and a roll of two exactly the same as a
+ 
+
+ align:start position:0%
+and a roll of two exactly the same as a
+roll of seven is like especially like
+
+ align:start position:0%
+roll of seven is like especially like
+ 
+
+ align:start position:0%
+roll of seven is like especially like
+with a lot of race games you know that
+
+ align:start position:0%
+with a lot of race games you know that
+ 
+
+ align:start position:0%
+with a lot of race games you know that
+you move that number of steps but
+
+ align:start position:0%
+you move that number of steps but
+ 
+
+ align:start position:0%
+you move that number of steps but
+they're not like it's not like balanced
+
+ align:start position:0%
+they're not like it's not like balanced
+ 
+
+ align:start position:0%
+they're not like it's not like balanced
+so that two and
+
+ align:start position:0%
+so that two and
+ 
+
+ align:start position:0%
+so that two and
+our air you know are expected to come up
+
+ align:start position:0%
+our air you know are expected to come up
+ 
+
+ align:start position:0%
+our air you know are expected to come up
+less often or more often that's why you
+
+ align:start position:0%
+less often or more often that's why you
+ 
+
+ align:start position:0%
+less often or more often that's why you
+I've seen versions of things like
+
+ align:start position:0%
+I've seen versions of things like
+ 
+
+ align:start position:0%
+I've seen versions of things like
+Candyland where do you replace the
+
+ align:start position:0%
+Candyland where do you replace the
+ 
+
+ align:start position:0%
+Candyland where do you replace the
+spinner with dice it's like wait a
+
+ align:start position:0%
+spinner with dice it's like wait a
+ 
+
+ align:start position:0%
+spinner with dice it's like wait a
+minute that completely throws off the my
+
+ align:start position:0%
+minute that completely throws off the my
+ 
+
+ align:start position:0%
+minute that completely throws off the my
+clear the way how the pace of the game
+
+ align:start position:0%
+clear the way how the pace of the game
+ 
+
+ align:start position:0%
+clear the way how the pace of the game
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+but for Kenny Lin doesn't matter kind of
+
+ align:start position:0%
+but for Kenny Lin doesn't matter kind of
+ 
+
+ align:start position:0%
+but for Kenny Lin doesn't matter kind of
+equally likely do it so for that game
+
+ align:start position:0%
+equally likely do it so for that game
+ 
+
+ align:start position:0%
+equally likely do it so for that game
+you know that's something where you can
+
+ align:start position:0%
+you know that's something where you can
+ 
+
+ align:start position:0%
+you know that's something where you can
+do those kinds of substitutions I think
+
+ align:start position:0%
+do those kinds of substitutions I think
+ 
+
+ align:start position:0%
+do those kinds of substitutions I think
+it is actually very very useful to be
+
+ align:start position:0%
+it is actually very very useful to be
+ 
+
+ align:start position:0%
+it is actually very very useful to be
+able to talk about this when it comes to
+
+ align:start position:0%
+able to talk about this when it comes to
+ 
+
+ align:start position:0%
+able to talk about this when it comes to
+the design of your own rules it's useful
+
+ align:start position:0%
+the design of your own rules it's useful
+ 
+
+ align:start position:0%
+the design of your own rules it's useful
+to be able to talk about it with other
+
+ align:start position:0%
+to be able to talk about it with other
+ 
+
+ align:start position:0%
+to be able to talk about it with other
+designers say like here's this piece of
+
+ align:start position:0%
+designers say like here's this piece of
+ 
+
+ align:start position:0%
+designers say like here's this piece of
+information that we're storing early on
+
+ align:start position:0%
+information that we're storing early on
+ 
+
+ align:start position:0%
+information that we're storing early on
+you know maybe because maybe we got rice
+
+ align:start position:0%
+you know maybe because maybe we got rice
+ 
+
+ align:start position:0%
+you know maybe because maybe we got rice
+they're a flip-down
+
+ align:start position:0%
+they're a flip-down
+ 
+
+ align:start position:0%
+they're a flip-down
+maybe got cast for putting an envelope
+
+ align:start position:0%
+maybe got cast for putting an envelope
+ 
+
+ align:start position:0%
+maybe got cast for putting an envelope
+maybe does a quantity of things in the
+
+ align:start position:0%
+maybe does a quantity of things in the
+ 
+
+ align:start position:0%
+maybe does a quantity of things in the
+bag or something and then you have to
+
+ align:start position:0%
+bag or something and then you have to
+ 
+
+ align:start position:0%
+bag or something and then you have to
+reach each other and pull things out
+
+ align:start position:0%
+reach each other and pull things out
+ 
+
+ align:start position:0%
+reach each other and pull things out
+like like at Scrabble things that you
+
+ align:start position:0%
+like like at Scrabble things that you
+ 
+
+ align:start position:0%
+like like at Scrabble things that you
+know that you're you know that sort of
+
+ align:start position:0%
+know that you're you know that sort of
+ 
+
+ align:start position:0%
+know that you're you know that sort of
+randomize in the bag the the the actual
+
+ align:start position:0%
+randomize in the bag the the the actual
+ 
+
+ align:start position:0%
+randomize in the bag the the the actual
+which one you're going to draw mix from
+
+ align:start position:0%
+which one you're going to draw mix from
+ 
+
+ align:start position:0%
+which one you're going to draw mix from
+it is somewhat random based on some sort
+
+ align:start position:0%
+it is somewhat random based on some sort
+ 
+
+ align:start position:0%
+it is somewhat random based on some sort
+of probability but then the probability
+
+ align:start position:0%
+of probability but then the probability
+ 
+
+ align:start position:0%
+of probability but then the probability
+of that could be public information it
+
+ align:start position:0%
+of that could be public information it
+ 
+
+ align:start position:0%
+of that could be public information it
+could be hidden information you might
+
+ align:start position:0%
+could be hidden information you might
+ 
+
+ align:start position:0%
+could be hidden information you might
+not know what you know what what was the
+
+ align:start position:0%
+not know what you know what what was the
+ 
+
+ align:start position:0%
+not know what you know what what was the
+distribution of stuff inside that bag to
+
+ align:start position:0%
+distribution of stuff inside that bag to
+ 
+
+ align:start position:0%
+distribution of stuff inside that bag to
+begin with and that's why I want you to
+
+ align:start position:0%
+begin with and that's why I want you to
+ 
+
+ align:start position:0%
+begin with and that's why I want you to
+be able to use these these words in
+
+ align:start position:0%
+be able to use these these words in
+ 
+
+ align:start position:0%
+be able to use these these words in
+describing how things are working in
+
+ align:start position:0%
+describing how things are working in
+ 
+
+ align:start position:0%
+describing how things are working in
+your own game to your own teammates and
+
+ align:start position:0%
+your own game to your own teammates and
+ 
+
+ align:start position:0%
+your own game to your own teammates and
+especially to us because we want to
+
+ align:start position:0%
+especially to us because we want to
+ 
+
+ align:start position:0%
+especially to us because we want to
+understand what it is that you're trying
+
+ align:start position:0%
+understand what it is that you're trying
+ 
+
+ align:start position:0%
+understand what it is that you're trying
+to achieve with this bit of information
+
+ align:start position:0%
+to achieve with this bit of information
+ 
+
+ align:start position:0%
+to achieve with this bit of information
+you know hidden information typically is
+
+ align:start position:0%
+you know hidden information typically is
+ 
+
+ align:start position:0%
+you know hidden information typically is
+something that you are going to try to
+
+ align:start position:0%
+something that you are going to try to
+ 
+
+ align:start position:0%
+something that you are going to try to
+allow people to figure out over time and
+
+ align:start position:0%
+allow people to figure out over time and
+ 
+
+ align:start position:0%
+allow people to figure out over time and
+that's a lot of that's a lot of stake
+
+ align:start position:0%
+that's a lot of that's a lot of stake
+ 
+
+ align:start position:0%
+that's a lot of that's a lot of stake
+over what that hidden piece of
+
+ align:start position:0%
+over what that hidden piece of
+ 
+
+ align:start position:0%
+over what that hidden piece of
+information is whereas that's not a
+
+ align:start position:0%
+information is whereas that's not a
+ 
+
+ align:start position:0%
+information is whereas that's not a
+whole lot F you know that and it's kind
+
+ align:start position:0%
+whole lot F you know that and it's kind
+ 
+
+ align:start position:0%
+whole lot F you know that and it's kind
+of like shared among everybody who's
+
+ align:start position:0%
+of like shared among everybody who's
+ 
+
+ align:start position:0%
+of like shared among everybody who's
+looking at a piece of information where
+
+ align:start position:0%
+looking at a piece of information where
+ 
+
+ align:start position:0%
+looking at a piece of information where
+is something that's random it's usually
+
+ align:start position:0%
+is something that's random it's usually
+ 
+
+ align:start position:0%
+is something that's random it's usually
+kind of at that moment it's really
+
+ align:start position:0%
+kind of at that moment it's really
+ 
+
+ align:start position:0%
+kind of at that moment it's really
+important you know after that it's not
+
+ align:start position:0%
+important you know after that it's not
+ 
+
+ align:start position:0%
+important you know after that it's not
+so important it and while it has some
+
+ align:start position:0%
+so important it and while it has some
+ 
+
+ align:start position:0%
+so important it and while it has some
+sort of consequence that might be
+
+ align:start position:0%
+sort of consequence that might be
+ 
+
+ align:start position:0%
+sort of consequence that might be
+recorded in the score but it's not like
+
+ align:start position:0%
+recorded in the score but it's not like
+ 
+
+ align:start position:0%
+recorded in the score but it's not like
+from turn to turn to turn
+
+ align:start position:0%
+from turn to turn to turn
+ 
+
+ align:start position:0%
+from turn to turn to turn
+to turn that particular role or that
+
+ align:start position:0%
+to turn that particular role or that
+ 
+
+ align:start position:0%
+to turn that particular role or that
+particular spin was all that important
+
+ align:start position:0%
+particular spin was all that important
+ 
+
+ align:start position:0%
+particular spin was all that important
+private information and public
+
+ align:start position:0%
+private information and public
+ 
+
+ align:start position:0%
+private information and public
+information tend to be pretty easy to
+
+ align:start position:0%
+information tend to be pretty easy to
+ 
+
+ align:start position:0%
+information tend to be pretty easy to
+talk about so their dismissal terms due
+
+ align:start position:0%
+talk about so their dismissal terms due
+ 
+
+ align:start position:0%
+talk about so their dismissal terms due
+to people to talk about to be able to
+
+ align:start position:0%
+to people to talk about to be able to
+ 
+
+ align:start position:0%
+to people to talk about to be able to
+discuss with each other and yeah so I
+
+ align:start position:0%
+discuss with each other and yeah so I
+ 
+
+ align:start position:0%
+discuss with each other and yeah so I
+just want to introduce these terms this
+
+ align:start position:0%
+just want to introduce these terms this
+ 
+
+ align:start position:0%
+just want to introduce these terms this
+is the taxonomy that was that was
+
+ align:start position:0%
+is the taxonomy that was that was
+ 
+
+ align:start position:0%
+is the taxonomy that was that was
+provided by your peers it sort of
+
+ align:start position:0%
+provided by your peers it sort of
+ 
+
+ align:start position:0%
+provided by your peers it sort of
+expands on the perfect and imperfect
+
+ align:start position:0%
+expands on the perfect and imperfect
+ 
+
+ align:start position:0%
+expands on the perfect and imperfect
+information because if imperfect
+
+ align:start position:0%
+information because if imperfect
+ 
+
+ align:start position:0%
+information because if imperfect
+information gets kind of fuzzy because
+
+ align:start position:0%
+information gets kind of fuzzy because
+ 
+
+ align:start position:0%
+information gets kind of fuzzy because
+it has all these different versions and
+
+ align:start position:0%
+it has all these different versions and
+ 
+
+ align:start position:0%
+it has all these different versions and
+now that I think everybody who's
+
+ align:start position:0%
+now that I think everybody who's
+ 
+
+ align:start position:0%
+now that I think everybody who's
+planning on showing up today has shown
+
+ align:start position:0%
+planning on showing up today has shown
+ 
+
+ align:start position:0%
+planning on showing up today has shown
+up we should probably start setting up
+
+ align:start position:0%
+up we should probably start setting up
+ 
+
+ align:start position:0%
+up we should probably start setting up
+for playtests so it's everyone sitting
+
+ align:start position:0%
+for playtests so it's everyone sitting
+ 
+
+ align:start position:0%
+for playtests so it's everyone sitting
+here teams I think everyone's more
+
+ align:start position:0%
+here teams I think everyone's more
+ 
+
+ align:start position:0%
+here teams I think everyone's more
+listening where you were right any
+
+ align:start position:0%
+listening where you were right any
+ 
+
+ align:start position:0%
+listening where you were right any
+questions so far on other questions
+
+ align:start position:0%
+questions so far on other questions
+ 
+
+ align:start position:0%
+questions so far on other questions
+based on what are we talking about my
+
+ align:start position:0%
+based on what are we talking about my
+ 
+
+ align:start position:0%
+based on what are we talking about my
+Clair clarified why I think this should
+
+ align:start position:0%
+Clair clarified why I think this should
+ 
+
+ align:start position:0%
+Clair clarified why I think this should
+be used differently how did you have
+
+ align:start position:0%
+be used differently how did you have
+ 
+
+ align:start position:0%
+be used differently how did you have
+changed your game mechanic by the way
+
+ align:start position:0%
+changed your game mechanic by the way
+ 
+
+ align:start position:0%
+changed your game mechanic by the way
+yeah what what would you describe it as
+
+ align:start position:0%
+yeah what what would you describe it as
+ 
+
+ align:start position:0%
+yeah what what would you describe it as
+wrong it's deception it's not okay it's
+
+ align:start position:0%
+wrong it's deception it's not okay it's
+ 
+
+ align:start position:0%
+wrong it's deception it's not okay it's
+something like bluffing something like
+
+ align:start position:0%
+something like bluffing something like
+ 
+
+ align:start position:0%
+something like bluffing something like
+like you'd like by faking on your your
+
+ align:start position:0%
+like you'd like by faking on your your
+ 
+
+ align:start position:0%
+like you'd like by faking on your your
+opponent okay
+
+ align:start position:0%
+opponent okay
+ 
+
+ align:start position:0%
+opponent okay
+everyone else still pretty much sticking
+
+ align:start position:0%
+everyone else still pretty much sticking
+ 
+
+ align:start position:0%
+everyone else still pretty much sticking
+with what you bought it's just not
+
+ align:start position:0%
+with what you bought it's just not
+ 
+
+ align:start position:0%
+with what you bought it's just not
+building
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're building a board I haven't seen
+
+ align:start position:0%
+they're building a board I haven't seen
+ 
+
+ align:start position:0%
+they're building a board I haven't seen
+that part not on your building on the
+
+ align:start position:0%
+that part not on your building on the
+ 
+
+ align:start position:0%
+that part not on your building on the
+board I think I need to just play your
+
+ align:start position:0%
+board I think I need to just play your
+ 
+
+ align:start position:0%
+board I think I need to just play your
+game plus they look like the SEC
+
+ align:start position:0%
+game plus they look like the SEC
+ 
+
+ align:start position:0%
+game plus they look like the SEC
+collection alright so again can I see
+
+ align:start position:0%
+collection alright so again can I see
+ 
+
+ align:start position:0%
+collection alright so again can I see
+who has which group has two player games
+
+ align:start position:0%
+who has which group has two player games
+ 
+
+ align:start position:0%
+who has which group has two player games
+one two three
+
+ align:start position:0%
+one two three
+ 
+
+ align:start position:0%
+one two three
+okay and the rest who has four player
+
+ align:start position:0%
+okay and the rest who has four player
+ 
+
+ align:start position:0%
+okay and the rest who has four player
+games and us has to be three play games
+
+ align:start position:0%
+games and us has to be three play games
+ 
+
+ align:start position:0%
+games and us has to be three play games
+okay alright so we hold both of you are
+
+ align:start position:0%
+okay alright so we hold both of you are
+ 
+
+ align:start position:0%
+okay alright so we hold both of you are
+two player games and did you play the
+
+ align:start position:0%
+two player games and did you play the
+ 
+
+ align:start position:0%
+two player games and did you play the
+chance games nothing
+
+ align:start position:0%
+chance games nothing
+ 
+
+ align:start position:0%
+chance games nothing
+oh you did okay
+
+ align:start position:0%
+oh you did okay
+ 
+
+ align:start position:0%
+oh you did okay
+alright then then then then that's easy
+
+ align:start position:0%
+alright then then then then that's easy
+ 
+
+ align:start position:0%
+alright then then then then that's easy
+the two of you should be playing each
+
+ align:start position:0%
+the two of you should be playing each
+ 
+
+ align:start position:0%
+the two of you should be playing each
+other's teams again there should be
+
+ align:start position:0%
+other's teams again there should be
+ 
+
+ align:start position:0%
+other's teams again there should be
+observers who have recording material to
+
+ align:start position:0%
+observers who have recording material to
+ 
+
+ align:start position:0%
+observers who have recording material to
+be able to rivets you know like you Tom
+
+ align:start position:0%
+be able to rivets you know like you Tom
+ 
+
+ align:start position:0%
+be able to rivets you know like you Tom
+please I'm moving it okay yeah so that
+
+ align:start position:0%
+please I'm moving it okay yeah so that
+ 
+
+ align:start position:0%
+please I'm moving it okay yeah so that
+team comes over here plays this game
+
+ align:start position:0%
+team comes over here plays this game
+ 
+
+ align:start position:0%
+team comes over here plays this game
+then well then everybody here goes over
+
+ align:start position:0%
+then well then everybody here goes over
+ 
+
+ align:start position:0%
+then well then everybody here goes over
+their place I came that's probably not
+
+ align:start position:0%
+their place I came that's probably not
+ 
+
+ align:start position:0%
+their place I came that's probably not
+time for that I think you've helped it
+
+ align:start position:0%
+time for that I think you've helped it
+ 
+
+ align:start position:0%
+time for that I think you've helped it
+just the two of you just came up here
+
+ align:start position:0%
+just the two of you just came up here
+ 
+
+ align:start position:0%
+just the two of you just came up here
+brought your game with you and then you
+
+ align:start position:0%
+brought your game with you and then you
+ 
+
+ align:start position:0%
+brought your game with you and then you
+can just like hang out here because well
+
+ align:start position:0%
+can just like hang out here because well
+ 
+
+ align:start position:0%
+can just like hang out here because well
+anyone who act gonna end up playing one
+
+ align:start position:0%
+anyone who act gonna end up playing one
+ 
+
+ align:start position:0%
+anyone who act gonna end up playing one
+of you no idea he came on a team at one
+
+ align:start position:0%
+of you no idea he came on a team at one
+ 
+
+ align:start position:0%
+of you no idea he came on a team at one
+time you're not gonna play no game
+
+ align:start position:0%
+time you're not gonna play no game
+ 
+
+ align:start position:0%
+time you're not gonna play no game
+simultaneously the rest of you let's see
+
+ align:start position:0%
+simultaneously the rest of you let's see
+ 
+
+ align:start position:0%
+simultaneously the rest of you let's see
+how many you have your game ready to go
+
+ align:start position:0%
+how many you have your game ready to go
+ 
+
+ align:start position:0%
+how many you have your game ready to go
+how many you have a game ready to do
+
+ align:start position:0%
+how many you have a game ready to do
+ 
+
+ align:start position:0%
+how many you have a game ready to do
+ready to go okay
+
+ align:start position:0%
+ready to go okay
+ 
+
+ align:start position:0%
+ready to go okay
+oh right I played your game recently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I played one on the corner yesterday
+
+ align:start position:0%
+and I played one on the corner yesterday
+ 
+
+ align:start position:0%
+and I played one on the corner yesterday
+I have played those two okay after have
+
+ align:start position:0%
+I have played those two okay after have
+ 
+
+ align:start position:0%
+I have played those two okay after have
+these two groups played ito Skipton okay
+
+ align:start position:0%
+these two groups played ito Skipton okay
+ 
+
+ align:start position:0%
+these two groups played ito Skipton okay
+then what I'm going to suggest is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three people from this group come over
+
+ align:start position:0%
+three people from this group come over
+ 
+
+ align:start position:0%
+three people from this group come over
+here and play this game first all right
+
+ align:start position:0%
+here and play this game first all right
+ 
+
+ align:start position:0%
+here and play this game first all right
+and then Rick and I will join these two
+
+ align:start position:0%
+and then Rick and I will join these two
+ 
+
+ align:start position:0%
+and then Rick and I will join these two
+to play to play the middle game and then
+
+ align:start position:0%
+to play to play the middle game and then
+ 
+
+ align:start position:0%
+to play to play the middle game and then
+the four of you will play their game oh
+
+ align:start position:0%
+the four of you will play their game oh
+ 
+
+ align:start position:0%
+the four of you will play their game oh
+you have I think we can all four of you
+
+ align:start position:0%
+you have I think we can all four of you
+ 
+
+ align:start position:0%
+you have I think we can all four of you
+have played the same game yeah has it
+
+ align:start position:0%
+have played the same game yeah has it
+ 
+
+ align:start position:0%
+have played the same game yeah has it
+changed dramatically since I'm pretty
+
+ align:start position:0%
+changed dramatically since I'm pretty
+ 
+
+ align:start position:0%
+changed dramatically since I'm pretty
+sure after one there will be things to
+
+ align:start position:0%
+sure after one there will be things to
+ 
+
+ align:start position:0%
+sure after one there will be things to
+change yes and if we have time maybe
+
+ align:start position:0%
+change yes and if we have time maybe
+ 
+
+ align:start position:0%
+change yes and if we have time maybe
+read it let me do a quick scan see what
+
+ align:start position:0%
+read it let me do a quick scan see what
+ 
+
+ align:start position:0%
+read it let me do a quick scan see what
+others are available okay let's see
+
+ align:start position:0%
+others are available okay let's see
+ 
+
+ align:start position:0%
+others are available okay let's see
+whatever good know if you want people to
+
+ align:start position:0%
+whatever good know if you want people to
+ 
+
+ align:start position:0%
+whatever good know if you want people to
+play that game over there all right so
+
+ align:start position:0%
+play that game over there all right so
+ 
+
+ align:start position:0%
+play that game over there all right so
+let me just teach you something three of
+
+ align:start position:0%
+let me just teach you something three of
+ 
+
+ align:start position:0%
+let me just teach you something three of
+you come over here right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the presentation at the end of the
+
+ align:start position:0%
+for the presentation at the end of the
+ 
+
+ align:start position:0%
+for the presentation at the end of the
+assignment one I do want you to talk a
+
+ align:start position:0%
+assignment one I do want you to talk a
+ 
+
+ align:start position:0%
+assignment one I do want you to talk a
+little bit about your game but don't
+
+ align:start position:0%
+little bit about your game but don't
+ 
+
+ align:start position:0%
+little bit about your game but don't
+explain the rules of your game before
+
+ align:start position:0%
+explain the rules of your game before
+ 
+
+ align:start position:0%
+explain the rules of your game before
+during your presentation now use up all
+
+ align:start position:0%
+during your presentation now use up all
+ 
+
+ align:start position:0%
+during your presentation now use up all
+the time that you've got talk about the
+
+ align:start position:0%
+the time that you've got talk about the
+ 
+
+ align:start position:0%
+the time that you've got talk about the
+process talk about what you started with
+
+ align:start position:0%
+process talk about what you started with
+ 
+
+ align:start position:0%
+process talk about what you started with
+what you try what didn't work and what
+
+ align:start position:0%
+what you try what didn't work and what
+ 
+
+ align:start position:0%
+what you try what didn't work and what
+kind of changes that make you make you
+
+ align:start position:0%
+kind of changes that make you make you
+ 
+
+ align:start position:0%
+kind of changes that make you make you
+know what worked I know how and how you
+
+ align:start position:0%
+know what worked I know how and how you
+ 
+
+ align:start position:0%
+know what worked I know how and how you
+roll with it I want to hear more about
+
+ align:start position:0%
+roll with it I want to hear more about
+ 
+
+ align:start position:0%
+roll with it I want to hear more about
+the story of how you got to where you
+
+ align:start position:0%
+the story of how you got to where you
+ 
+
+ align:start position:0%
+the story of how you got to where you
+are because right after you do that the
+
+ align:start position:0%
+are because right after you do that the
+ 
+
+ align:start position:0%
+are because right after you do that the
+presentation will actually sit down and
+
+ align:start position:0%
+presentation will actually sit down and
+ 
+
+ align:start position:0%
+presentation will actually sit down and
+play each other's games just like today
+
+ align:start position:0%
+play each other's games just like today
+ 
+
+ align:start position:0%
+play each other's games just like today
+only it's not a play test so you don't
+
+ align:start position:0%
+only it's not a play test so you don't
+ 
+
+ align:start position:0%
+only it's not a play test so you don't
+do like recording or anything everyone
+
+ align:start position:0%
+do like recording or anything everyone
+ 
+
+ align:start position:0%
+do like recording or anything everyone
+just plays games it's only five minutes
+
+ align:start position:0%
+just plays games it's only five minutes
+ 
+
+ align:start position:0%
+just plays games it's only five minutes
+I should be in the syllabus I think I
+
+ align:start position:0%
+I should be in the syllabus I think I
+ 
+
+ align:start position:0%
+I should be in the syllabus I think I
+thought I wrote five minutes pretty bad
+
+ align:start position:0%
+thought I wrote five minutes pretty bad
+ 
+
+ align:start position:0%
+thought I wrote five minutes pretty bad
+yes it doesn't have to be one of those
+
+ align:start position:0%
+yes it doesn't have to be one of those
+ 
+
+ align:start position:0%
+yes it doesn't have to be one of those
+like every single person in the team has
+
+ align:start position:0%
+like every single person in the team has
+ 
+
+ align:start position:0%
+like every single person in the team has
+had to say something kind of thing but
+
+ align:start position:0%
+had to say something kind of thing but
+ 
+
+ align:start position:0%
+had to say something kind of thing but
+if you know if you want to organize it
+
+ align:start position:0%
+if you know if you want to organize it
+ 
+
+ align:start position:0%
+if you know if you want to organize it
+that that way you do totally can I just
+
+ align:start position:0%
+that that way you do totally can I just
+ 
+
+ align:start position:0%
+that that way you do totally can I just
+want to hear about what was the story of
+
+ align:start position:0%
+want to hear about what was the story of
+ 
+
+ align:start position:0%
+want to hear about what was the story of
+the game the other thing is that I
+
+ align:start position:0%
+the game the other thing is that I
+ 
+
+ align:start position:0%
+the game the other thing is that I
+actually did look up the the situation
+
+ align:start position:0%
+actually did look up the the situation
+ 
+
+ align:start position:0%
+actually did look up the the situation
+with with Texas Hold'em that I am going
+
+ align:start position:0%
+with with Texas Hold'em that I am going
+ 
+
+ align:start position:0%
+with with Texas Hold'em that I am going
+to reverse my position that is actually
+
+ align:start position:0%
+to reverse my position that is actually
+ 
+
+ align:start position:0%
+to reverse my position that is actually
+not hidden information and two things
+
+ align:start position:0%
+not hidden information and two things
+ 
+
+ align:start position:0%
+not hidden information and two things
+made me one is I started discussing it
+
+ align:start position:0%
+made me one is I started discussing it
+ 
+
+ align:start position:0%
+made me one is I started discussing it
+with a bunch of other game designers
+
+ align:start position:0%
+with a bunch of other game designers
+ 
+
+ align:start position:0%
+with a bunch of other game designers
+online and I discovered that there are a
+
+ align:start position:0%
+online and I discovered that there are a
+ 
+
+ align:start position:0%
+online and I discovered that there are a
+couple of variants of Texas Hold'em
+
+ align:start position:0%
+couple of variants of Texas Hold'em
+ 
+
+ align:start position:0%
+couple of variants of Texas Hold'em
+where you never deal the what they call
+
+ align:start position:0%
+where you never deal the what they call
+ 
+
+ align:start position:0%
+where you never deal the what they call
+the flop facedown you just play it face
+
+ align:start position:0%
+the flop facedown you just play it face
+ 
+
+ align:start position:0%
+the flop facedown you just play it face
+up one at a time yeah yeah at which
+
+ align:start position:0%
+up one at a time yeah yeah at which
+ 
+
+ align:start position:0%
+up one at a time yeah yeah at which
+point is just a random view from the top
+
+ align:start position:0%
+point is just a random view from the top
+ 
+
+ align:start position:0%
+point is just a random view from the top
+of the deck and that makes it that it
+
+ align:start position:0%
+of the deck and that makes it that it
+ 
+
+ align:start position:0%
+of the deck and that makes it that it
+was astonished to me to say me either
+
+ align:start position:0%
+was astonished to me to say me either
+ 
+
+ align:start position:0%
+was astonished to me to say me either
+way only there are this picture very
+
+ align:start position:0%
+way only there are this picture very
+ 
+
+ align:start position:0%
+way only there are this picture very
+explicit right that is basically a
+
+ align:start position:0%
+explicit right that is basically a
+ 
+
+ align:start position:0%
+explicit right that is basically a
+landing gear so yes that is in fact
+
+ align:start position:0%
+landing gear so yes that is in fact
+ 
+
+ align:start position:0%
+landing gear so yes that is in fact
+random that's a very bad example to use
+
+ align:start position:0%
+random that's a very bad example to use
+ 
+
+ align:start position:0%
+random that's a very bad example to use
+for hidden information where's the clue
+
+ align:start position:0%
+for hidden information where's the clue
+ 
+
+ align:start position:0%
+for hidden information where's the clue
+thing is because the whole point of that
+
+ align:start position:0%
+thing is because the whole point of that
+ 
+
+ align:start position:0%
+thing is because the whole point of that
+game is that it gives you all these
+
+ align:start position:0%
+game is that it gives you all these
+ 
+
+ align:start position:0%
+game is that it gives you all these
+tools to be able to reveal this
+
+ align:start position:0%
+tools to be able to reveal this
+ 
+
+ align:start position:0%
+tools to be able to reveal this
+information at that point of time when
+
+ align:start position:0%
+information at that point of time when
+ 
+
+ align:start position:0%
+information at that point of time when
+you put the cards inside in this random
+
+ align:start position:0%
+you put the cards inside in this random
+ 
+
+ align:start position:0%
+you put the cards inside in this random
+but then once it's inside there the
+
+ align:start position:0%
+but then once it's inside there the
+ 
+
+ align:start position:0%
+but then once it's inside there the
+first turn starts has now hidden
+
+ align:start position:0%
+first turn starts has now hidden
+ 
+
+ align:start position:0%
+first turn starts has now hidden
+information okay thank you very much to
+
+ align:start position:0%
+information okay thank you very much to
+ 
+
+ align:start position:0%
+information okay thank you very much to
+you all Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/RwikpgvkN_o.txt b/RwikpgvkN_o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1d3e8878c02d38b9ff99b9fa462e003dd219eda9
--- /dev/null
+++ b/RwikpgvkN_o.txt
@@ -0,0 +1,8619 @@
+align:start position:0%
+ 
+the goal for the next few lectures is to
+
+ align:start position:0%
+the goal for the next few lectures is to
+ 
+
+ align:start position:0%
+the goal for the next few lectures is to
+prove Freeman's theorem which we
+
+ align:start position:0%
+prove Freeman's theorem which we
+ 
+
+ align:start position:0%
+prove Freeman's theorem which we
+discussed last time so we started with
+
+ align:start position:0%
+discussed last time so we started with
+ 
+
+ align:start position:0%
+discussed last time so we started with
+this tool that we proved called the
+
+ align:start position:0%
+this tool that we proved called the
+ 
+
+ align:start position:0%
+this tool that we proved called the
+political Russia inequality which tells
+
+ align:start position:0%
+political Russia inequality which tells
+ 
+
+ align:start position:0%
+political Russia inequality which tells
+us that if you have a set a now in an
+
+ align:start position:0%
+us that if you have a set a now in an
+ 
+
+ align:start position:0%
+us that if you have a set a now in an
+arbitrary abelian group and if a has
+
+ align:start position:0%
+arbitrary abelian group and if a has
+ 
+
+ align:start position:0%
+arbitrary abelian group and if a has
+controlled doubling it has bounded
+
+ align:start position:0%
+controlled doubling it has bounded
+ 
+
+ align:start position:0%
+controlled doubling it has bounded
+doubling then all the further iterated
+
+ align:start position:0%
+doubling then all the further iterated
+ 
+
+ align:start position:0%
+doubling then all the further iterated
+some sets have banded growth as well so
+
+ align:start position:0%
+some sets have banded growth as well so
+ 
+
+ align:start position:0%
+some sets have banded growth as well so
+this is what we proved last time okay so
+
+ align:start position:0%
+this is what we proved last time okay so
+ 
+
+ align:start position:0%
+this is what we proved last time okay so
+we're going to be using the plant
+
+ align:start position:0%
+we're going to be using the plant
+ 
+
+ align:start position:0%
+we're going to be using the plant
+kirusha inequality many times but
+
+ align:start position:0%
+kirusha inequality many times but
+ 
+
+ align:start position:0%
+kirusha inequality many times but
+there's some other tools I need to tell
+
+ align:start position:0%
+there's some other tools I need to tell
+ 
+
+ align:start position:0%
+there's some other tools I need to tell
+you about so the next tool is no mess
+
+ align:start position:0%
+you about so the next tool is no mess
+ 
+
+ align:start position:0%
+you about so the next tool is no mess
+rules are covering lemma so let me first
+
+ align:start position:0%
+rules are covering lemma so let me first
+ 
+
+ align:start position:0%
+rules are covering lemma so let me first
+give you the statement and then I'll
+
+ align:start position:0%
+give you the statement and then I'll
+ 
+
+ align:start position:0%
+give you the statement and then I'll
+explain some intuition
+
+ align:start position:0%
+explain some intuition
+ 
+
+ align:start position:0%
+explain some intuition
+I think the technique is more important
+
+ align:start position:0%
+I think the technique is more important
+ 
+
+ align:start position:0%
+I think the technique is more important
+than the statement but in any case
+
+ align:start position:0%
+than the statement but in any case
+ 
+
+ align:start position:0%
+than the statement but in any case
+here's what it says if you have X and B
+
+ align:start position:0%
+here's what it says if you have X and B
+ 
+
+ align:start position:0%
+here's what it says if you have X and B
+there are subsets of some arbitrary
+
+ align:start position:0%
+there are subsets of some arbitrary
+ 
+
+ align:start position:0%
+there are subsets of some arbitrary
+abelian group if you have the inequality
+
+ align:start position:0%
+abelian group if you have the inequality
+ 
+
+ align:start position:0%
+abelian group if you have the inequality
+that X plus B is at most K times the
+
+ align:start position:0%
+that X plus B is at most K times the
+ 
+
+ align:start position:0%
+that X plus B is at most K times the
+size of P so the size of X plus P is at
+
+ align:start position:0%
+size of P so the size of X plus P is at
+ 
+
+ align:start position:0%
+size of P so the size of X plus P is at
+most K times the size of B then there
+
+ align:start position:0%
+most K times the size of B then there
+ 
+
+ align:start position:0%
+most K times the size of B then there
+exists some subset T of X with the size
+
+ align:start position:0%
+exists some subset T of X with the size
+ 
+
+ align:start position:0%
+exists some subset T of X with the size
+of T being at most K such that X is
+
+ align:start position:0%
+of T being at most K such that X is
+ 
+
+ align:start position:0%
+of T being at most K such that X is
+contained in T plus B minus B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the statement of Lucia
+
+ align:start position:0%
+okay so that's the statement of Lucia
+ 
+
+ align:start position:0%
+okay so that's the statement of Lucia
+covering them up so let me try to
+
+ align:start position:0%
+covering them up so let me try to
+ 
+
+ align:start position:0%
+covering them up so let me try to
+explain what it is about so the idea
+
+ align:start position:0%
+explain what it is about so the idea
+ 
+
+ align:start position:0%
+explain what it is about so the idea
+here is that if you're in a situation
+
+ align:start position:0%
+here is that if you're in a situation
+ 
+
+ align:start position:0%
+here is that if you're in a situation
+where if it looks like so you should
+
+ align:start position:0%
+where if it looks like so you should
+ 
+
+ align:start position:0%
+where if it looks like so you should
+think of B as a ball right so if it
+
+ align:start position:0%
+think of B as a ball right so if it
+ 
+
+ align:start position:0%
+think of B as a ball right so if it
+looks like X plus B might be coverable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by K translates of B so here supposed to
+
+ align:start position:0%
+by K translates of B so here supposed to
+ 
+
+ align:start position:0%
+by K translates of B so here supposed to
+think of be like a ball in in a metric
+
+ align:start position:0%
+think of be like a ball in in a metric
+ 
+
+ align:start position:0%
+think of be like a ball in in a metric
+space then X is actually coverable so if
+
+ align:start position:0%
+space then X is actually coverable so if
+ 
+
+ align:start position:0%
+space then X is actually coverable so if
+it looks like meaning just by size alone
+
+ align:start position:0%
+it looks like meaning just by size alone
+ 
+
+ align:start position:0%
+it looks like meaning just by size alone
+a size info alone so just based on the
+
+ align:start position:0%
+a size info alone so just based on the
+ 
+
+ align:start position:0%
+a size info alone so just based on the
+size if it looks like X plus B might be
+
+ align:start position:0%
+size if it looks like X plus B might be
+ 
+
+ align:start position:0%
+size if it looks like X plus B might be
+coverable by K different translator P
+
+ align:start position:0%
+coverable by K different translator P
+ 
+
+ align:start position:0%
+coverable by K different translator P
+then actually acts as coverable but you
+
+ align:start position:0%
+then actually acts as coverable but you
+ 
+
+ align:start position:0%
+then actually acts as coverable but you
+have to use slightly larger balls by K
+
+ align:start position:0%
+have to use slightly larger balls by K
+ 
+
+ align:start position:0%
+have to use slightly larger balls by K
+copies of B minus B so you should think
+
+ align:start position:0%
+copies of B minus B so you should think
+ 
+
+ align:start position:0%
+copies of B minus B so you should think
+of B minus B as slightly larger balls
+
+ align:start position:0%
+of B minus B as slightly larger balls
+ 
+
+ align:start position:0%
+of B minus B as slightly larger balls
+than be yourself right so if B were an
+
+ align:start position:0%
+than be yourself right so if B were an
+ 
+
+ align:start position:0%
+than be yourself right so if B were an
+actual ball in Euclidean space and B
+
+ align:start position:0%
+actual ball in Euclidean space and B
+ 
+
+ align:start position:0%
+actual ball in Euclidean space and B
+minus B is the same ball with twice the
+
+ align:start position:0%
+minus B is the same ball with twice the
+ 
+
+ align:start position:0%
+minus B is the same ball with twice the
+radius
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+looser covering mama is a really
+
+ align:start position:0%
+looser covering mama is a really
+ 
+
+ align:start position:0%
+looser covering mama is a really
+important tool the proof is not very
+
+ align:start position:0%
+important tool the proof is not very
+ 
+
+ align:start position:0%
+important tool the proof is not very
+long and it's important to understand
+
+ align:start position:0%
+long and it's important to understand
+ 
+
+ align:start position:0%
+long and it's important to understand
+the idea of this proof right so this is
+
+ align:start position:0%
+the idea of this proof right so this is
+ 
+
+ align:start position:0%
+the idea of this proof right so this is
+a proof not just the additive
+
+ align:start position:0%
+a proof not just the additive
+ 
+
+ align:start position:0%
+a proof not just the additive
+combinatorics but something that happens
+
+ align:start position:0%
+combinatorics but something that happens
+ 
+
+ align:start position:0%
+combinatorics but something that happens
+it's a standard idea in analysis this is
+
+ align:start position:0%
+it's a standard idea in analysis this is
+ 
+
+ align:start position:0%
+it's a standard idea in analysis this is
+very important to understand this idea
+
+ align:start position:0%
+very important to understand this idea
+ 
+
+ align:start position:0%
+very important to understand this idea
+and the key idea here I think the proof
+
+ align:start position:0%
+and the key idea here I think the proof
+ 
+
+ align:start position:0%
+and the key idea here I think the proof
+is more important than a statement up
+
+ align:start position:0%
+is more important than a statement up
+ 
+
+ align:start position:0%
+is more important than a statement up
+there the key idea here is that if you
+
+ align:start position:0%
+there the key idea here is that if you
+ 
+
+ align:start position:0%
+there the key idea here is that if you
+want to produce a covering one way to
+
+ align:start position:0%
+want to produce a covering one way to
+ 
+
+ align:start position:0%
+want to produce a covering one way to
+produce a covering is to take a maximal
+
+ align:start position:0%
+produce a covering is to take a maximal
+ 
+
+ align:start position:0%
+produce a covering is to take a maximal
+packing a maximal packing using with
+
+ align:start position:0%
+packing a maximal packing using with
+ 
+
+ align:start position:0%
+packing a maximal packing using with
+balls
+
+ align:start position:0%
+balls
+ 
+
+ align:start position:0%
+balls
+for instance implies a covering with
+
+ align:start position:0%
+for instance implies a covering with
+ 
+
+ align:start position:0%
+for instance implies a covering with
+balls twice as large ok so let me
+
+ align:start position:0%
+balls twice as large ok so let me
+ 
+
+ align:start position:0%
+balls twice as large ok so let me
+illustrate out with the picture suppose
+
+ align:start position:0%
+illustrate out with the picture suppose
+ 
+
+ align:start position:0%
+illustrate out with the picture suppose
+you have some space that I want to cover
+
+ align:start position:0%
+you have some space that I want to cover
+ 
+
+ align:start position:0%
+you have some space that I want to cover
+but you get to use let's say you need
+
+ align:start position:0%
+but you get to use let's say you need
+ 
+
+ align:start position:0%
+but you get to use let's say you need
+balls so how can I make sure I can cover
+
+ align:start position:0%
+balls so how can I make sure I can cover
+ 
+
+ align:start position:0%
+balls so how can I make sure I can cover
+the space you see unit balls and I don't
+
+ align:start position:0%
+the space you see unit balls and I don't
+ 
+
+ align:start position:0%
+the space you see unit balls and I don't
+want to use too many unit balls so what
+
+ align:start position:0%
+want to use too many unit balls so what
+ 
+
+ align:start position:0%
+want to use too many unit balls so what
+you can do is let me start by a maximal
+
+ align:start position:0%
+you can do is let me start by a maximal
+ 
+
+ align:start position:0%
+you can do is let me start by a maximal
+cut a maximal set of unit balls so with
+
+ align:start position:0%
+cut a maximal set of unit balls so with
+ 
+
+ align:start position:0%
+cut a maximal set of unit balls so with
+centers so it's not half unit balls so
+
+ align:start position:0%
+centers so it's not half unit balls so
+ 
+
+ align:start position:0%
+centers so it's not half unit balls so
+the radius is one half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I put in as many as I can so
+
+ align:start position:0%
+okay so I put in as many as I can so
+ 
+
+ align:start position:0%
+okay so I put in as many as I can so
+that I cannot pudding anymore so that's
+
+ align:start position:0%
+that I cannot pudding anymore so that's
+ 
+
+ align:start position:0%
+that I cannot pudding anymore so that's
+what Maximo means mou here
+
+ align:start position:0%
+what Maximo means mou here
+ 
+
+ align:start position:0%
+what Maximo means mou here
+doesn't mean the maximum number although
+
+ align:start position:0%
+doesn't mean the maximum number although
+ 
+
+ align:start position:0%
+doesn't mean the maximum number although
+if you put in the maximum number that's
+
+ align:start position:0%
+if you put in the maximum number that's
+ 
+
+ align:start position:0%
+if you put in the maximum number that's
+also okay but Maximo means that I just
+
+ align:start position:0%
+also okay but Maximo means that I just
+ 
+
+ align:start position:0%
+also okay but Maximo means that I just
+cannot putting any more balls that are
+
+ align:start position:0%
+cannot putting any more balls that are
+ 
+
+ align:start position:0%
+cannot putting any more balls that are
+not overlapping then if I have this
+
+ align:start position:0%
+not overlapping then if I have this
+ 
+
+ align:start position:0%
+not overlapping then if I have this
+configuration now what I do is I double
+
+ align:start position:0%
+configuration now what I do is I double
+ 
+
+ align:start position:0%
+configuration now what I do is I double
+the radii of all the balls okay so
+
+ align:start position:0%
+the radii of all the balls okay so
+ 
+
+ align:start position:0%
+the radii of all the balls okay so
+whoever takes today's knows will have a
+
+ align:start position:0%
+whoever takes today's knows will have a
+ 
+
+ align:start position:0%
+whoever takes today's knows will have a
+fun time drawing this picture so this
+
+ align:start position:0%
+fun time drawing this picture so this
+ 
+
+ align:start position:0%
+fun time drawing this picture so this
+has to be a covering of the original
+
+ align:start position:0%
+has to be a covering of the original
+ 
+
+ align:start position:0%
+has to be a covering of the original
+space because if you had missed some
+
+ align:start position:0%
+space because if you had missed some
+ 
+
+ align:start position:0%
+space because if you had missed some
+point I could have put it blue ball in
+
+ align:start position:0%
+point I could have put it blue ball in
+ 
+
+ align:start position:0%
+point I could have put it blue ball in
+yes because one of the space has some
+
+ align:start position:0%
+yes because one of the space has some
+ 
+
+ align:start position:0%
+yes because one of the space has some
+narrow portion it doesn't matter if you
+
+ align:start position:0%
+narrow portion it doesn't matter if you
+ 
+
+ align:start position:0%
+narrow portion it doesn't matter if you
+formulate this correctly so if you miss
+
+ align:start position:0%
+formulate this correctly so if you miss
+ 
+
+ align:start position:0%
+formulate this correctly so if you miss
+if you miss some point so here so it
+
+ align:start position:0%
+if you miss some point so here so it
+ 
+
+ align:start position:0%
+if you miss some point so here so it
+depends on how you formulate this
+
+ align:start position:0%
+depends on how you formulate this
+ 
+
+ align:start position:0%
+depends on how you formulate this
+discovering so the point is that if you
+
+ align:start position:0%
+discovering so the point is that if you
+ 
+
+ align:start position:0%
+discovering so the point is that if you
+take a maximal set of points when you
+
+ align:start position:0%
+take a maximal set of points when you
+ 
+
+ align:start position:0%
+take a maximal set of points when you
+expand you have to cover the whole space
+
+ align:start position:0%
+expand you have to cover the whole space
+ 
+
+ align:start position:0%
+expand you have to cover the whole space
+because if you missed some point right
+
+ align:start position:0%
+because if you missed some point right
+ 
+
+ align:start position:0%
+because if you missed some point right
+so imagine if you had for example if
+
+ align:start position:0%
+so imagine if you had for example if
+ 
+
+ align:start position:0%
+so imagine if you had for example if
+suppose you miss okay okay suppose you
+
+ align:start position:0%
+suppose you miss okay okay suppose you
+ 
+
+ align:start position:0%
+suppose you miss okay okay suppose you
+had missed some point over here then I
+
+ align:start position:0%
+had missed some point over here then I
+ 
+
+ align:start position:0%
+had missed some point over here then I
+could have put an extra ball him so if
+
+ align:start position:0%
+could have put an extra ball him so if
+ 
+
+ align:start position:0%
+could have put an extra ball him so if
+you had missed some point over here that
+
+ align:start position:0%
+you had missed some point over here that
+ 
+
+ align:start position:0%
+you had missed some point over here that
+means that I should have being able to
+
+ align:start position:0%
+means that I should have being able to
+ 
+
+ align:start position:0%
+means that I should have being able to
+put into putting that ball there
+
+ align:start position:0%
+put into putting that ball there
+ 
+
+ align:start position:0%
+put into putting that ball there
+initially so this is it's a very simple
+
+ align:start position:0%
+initially so this is it's a very simple
+ 
+
+ align:start position:0%
+initially so this is it's a very simple
+idea by the very powerful idea and it
+
+ align:start position:0%
+idea by the very powerful idea and it
+ 
+
+ align:start position:0%
+idea by the very powerful idea and it
+comes up all the time in analysis and
+
+ align:start position:0%
+comes up all the time in analysis and
+ 
+
+ align:start position:0%
+comes up all the time in analysis and
+geometry and it also comes up here so
+
+ align:start position:0%
+geometry and it also comes up here so
+ 
+
+ align:start position:0%
+geometry and it also comes up here so
+let's do the actual proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let okay so let me let P be a subset
+
+ align:start position:0%
+so let okay so let me let P be a subset
+ 
+
+ align:start position:0%
+so let okay so let me let P be a subset
+of X be a maximal subset of X such that
+
+ align:start position:0%
+of X be a maximal subset of X such that
+ 
+
+ align:start position:0%
+of X be a maximal subset of X such that
+the sets little T plus B are disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all elements little T of a set big t
+
+ align:start position:0%
+for all elements little T of a set big t
+ 
+
+ align:start position:0%
+for all elements little T of a set big t
+okay so it's it's like this picture I
+
+ align:start position:0%
+okay so it's it's like this picture I
+ 
+
+ align:start position:0%
+okay so it's it's like this picture I
+pick a subset of X so that if I send her
+
+ align:start position:0%
+pick a subset of X so that if I send her
+ 
+
+ align:start position:0%
+pick a subset of X so that if I send her
+boss around these T's then these
+
+ align:start position:0%
+boss around these T's then these
+ 
+
+ align:start position:0%
+boss around these T's then these
+translates a piece are disjoint then
+
+ align:start position:0%
+translates a piece are disjoint then
+ 
+
+ align:start position:0%
+translates a piece are disjoint then
+you're putting a maximal such set so due
+
+ align:start position:0%
+you're putting a maximal such set so due
+ 
+
+ align:start position:0%
+you're putting a maximal such set so due
+to the destroying this we find that the
+
+ align:start position:0%
+to the destroying this we find that the
+ 
+
+ align:start position:0%
+to the destroying this we find that the
+product of the sizes of T and B equals
+
+ align:start position:0%
+product of the sizes of T and B equals
+ 
+
+ align:start position:0%
+product of the sizes of T and B equals
+to the size of the sum because there's
+
+ align:start position:0%
+to the size of the sum because there's
+ 
+
+ align:start position:0%
+to the size of the sum because there's
+no overlaps but T plus B past size at
+
+ align:start position:0%
+no overlaps but T plus B past size at
+ 
+
+ align:start position:0%
+no overlaps but T plus B past size at
+most X plus B because T is a subset of X
+
+ align:start position:0%
+most X plus B because T is a subset of X
+ 
+
+ align:start position:0%
+most X plus B because T is a subset of X
+but I also from the assumption we knew
+
+ align:start position:0%
+but I also from the assumption we knew
+ 
+
+ align:start position:0%
+but I also from the assumption we knew
+that X is size of X plus B is upper
+
+ align:start position:0%
+that X is size of X plus B is upper
+ 
+
+ align:start position:0%
+that X is size of X plus B is upper
+bounded by the size of B times K so in
+
+ align:start position:0%
+bounded by the size of B times K so in
+ 
+
+ align:start position:0%
+bounded by the size of B times K so in
+particular we get that the size of T is
+
+ align:start position:0%
+particular we get that the size of T is
+ 
+
+ align:start position:0%
+particular we get that the size of T is
+at most
+
+ align:start position:0%
+at most
+ 
+
+ align:start position:0%
+at most
+okay so in other words over here the
+
+ align:start position:0%
+okay so in other words over here the
+ 
+
+ align:start position:0%
+okay so in other words over here the
+number of blue balls you can control by
+
+ align:start position:0%
+number of blue balls you can control by
+ 
+
+ align:start position:0%
+number of blue balls you can control by
+simply the volume now since T is since T
+
+ align:start position:0%
+simply the volume now since T is since T
+ 
+
+ align:start position:0%
+simply the volume now since T is since T
+is maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have that for every little X there
+
+ align:start position:0%
+we have that for every little X there
+ 
+
+ align:start position:0%
+we have that for every little X there
+exists some little key such that the
+
+ align:start position:0%
+exists some little key such that the
+ 
+
+ align:start position:0%
+exists some little key such that the
+translator be given by X intersects one
+
+ align:start position:0%
+translator be given by X intersects one
+ 
+
+ align:start position:0%
+translator be given by X intersects one
+of my children translates yes if this
+
+ align:start position:0%
+of my children translates yes if this
+ 
+
+ align:start position:0%
+of my children translates yes if this
+were not true then I could have put in
+
+ align:start position:0%
+were not true then I could have put in
+ 
+
+ align:start position:0%
+were not true then I could have put in
+an extra translate of P so in other
+
+ align:start position:0%
+an extra translate of P so in other
+ 
+
+ align:start position:0%
+an extra translate of P so in other
+words there exists two elements B and B
+
+ align:start position:0%
+words there exists two elements B and B
+ 
+
+ align:start position:0%
+words there exists two elements B and B
+prime such that T plus B equals to X
+
+ align:start position:0%
+prime such that T plus B equals to X
+ 
+
+ align:start position:0%
+prime such that T plus B equals to X
+plus B Prime and hence X licen little T
+
+ align:start position:0%
+plus B Prime and hence X licen little T
+ 
+
+ align:start position:0%
+plus B Prime and hence X licen little T
+plus B minus plus B minus B which
+
+ align:start position:0%
+plus B minus plus B minus B which
+ 
+
+ align:start position:0%
+plus B minus plus B minus B which
+implies that the set X lies in T plus B
+
+ align:start position:0%
+implies that the set X lies in T plus B
+ 
+
+ align:start position:0%
+implies that the set X lies in T plus B
+minus B okay so that's the Ruza covering
+
+ align:start position:0%
+minus B okay so that's the Ruza covering
+ 
+
+ align:start position:0%
+minus B okay so that's the Ruza covering
+lemma so it's an execution of this idea
+
+ align:start position:0%
+lemma so it's an execution of this idea
+ 
+
+ align:start position:0%
+lemma so it's an execution of this idea
+I mentioned earlier that a maximal
+
+ align:start position:0%
+I mentioned earlier that a maximal
+ 
+
+ align:start position:0%
+I mentioned earlier that a maximal
+packing implies a good covering any
+
+ align:start position:0%
+packing implies a good covering any
+ 
+
+ align:start position:0%
+packing implies a good covering any
+questions all right so now we have this
+
+ align:start position:0%
+questions all right so now we have this
+ 
+
+ align:start position:0%
+questions all right so now we have this
+tool we can prove an easier version of
+
+ align:start position:0%
+tool we can prove an easier version of
+ 
+
+ align:start position:0%
+tool we can prove an easier version of
+fragments theorem where instead of
+
+ align:start position:0%
+fragments theorem where instead of
+ 
+
+ align:start position:0%
+fragments theorem where instead of
+working the integers we're gonna work in
+
+ align:start position:0%
+working the integers we're gonna work in
+ 
+
+ align:start position:0%
+working the integers we're gonna work in
+a finite field model so usually it's
+
+ align:start position:0%
+a finite field model so usually it's
+ 
+
+ align:start position:0%
+a finite field model so usually it's
+good to start with finite field models
+
+ align:start position:0%
+good to start with finite field models
+ 
+
+ align:start position:0%
+good to start with finite field models
+things a bit cleaner and in this case
+
+ align:start position:0%
+things a bit cleaner and in this case
+ 
+
+ align:start position:0%
+things a bit cleaner and in this case
+actually only requires a subset of the
+
+ align:start position:0%
+actually only requires a subset of the
+ 
+
+ align:start position:0%
+actually only requires a subset of the
+tools that we'll need for the full
+
+ align:start position:0%
+tools that we'll need for the full
+ 
+
+ align:start position:0%
+tools that we'll need for the full
+theorem so instead of working finite
+
+ align:start position:0%
+theorem so instead of working finite
+ 
+
+ align:start position:0%
+theorem so instead of working finite
+field model we're gonna work in
+
+ align:start position:0%
+field model we're gonna work in
+ 
+
+ align:start position:0%
+field model we're gonna work in
+something just slightly more general but
+
+ align:start position:0%
+something just slightly more general but
+ 
+
+ align:start position:0%
+something just slightly more general but
+it's the same proof so we're going to be
+
+ align:start position:0%
+it's the same proof so we're going to be
+ 
+
+ align:start position:0%
+it's the same proof so we're going to be
+working in a group of bounded exponent
+
+ align:start position:0%
+working in a group of bounded exponent
+ 
+
+ align:start position:0%
+working in a group of bounded exponent
+hi mr. in groups of 10 the exponent and
+
+ align:start position:0%
+hi mr. in groups of 10 the exponent and
+ 
+
+ align:start position:0%
+hi mr. in groups of 10 the exponent and
+the word exponent in group theory means
+
+ align:start position:0%
+the word exponent in group theory means
+ 
+
+ align:start position:0%
+the word exponent in group theory means
+the following so the exponent of an
+
+ align:start position:0%
+the following so the exponent of an
+ 
+
+ align:start position:0%
+the following so the exponent of an
+abelian group is the smallest positive
+
+ align:start position:0%
+abelian group is the smallest positive
+ 
+
+ align:start position:0%
+abelian group is the smallest positive
+integer if it exists okay so the
+
+ align:start position:0%
+integer if it exists okay so the
+ 
+
+ align:start position:0%
+integer if it exists okay so the
+smallest positive integer are so that
+
+ align:start position:0%
+smallest positive integer are so that
+ 
+
+ align:start position:0%
+smallest positive integer are so that
+our x equals to 0 for all X in the group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example if you are working in FP
+
+ align:start position:0%
+so for example if you are working in FP
+ 
+
+ align:start position:0%
+so for example if you are working in FP
+to the end then the exponent is P which
+
+ align:start position:0%
+to the end then the exponent is P which
+ 
+
+ align:start position:0%
+to the end then the exponent is P which
+every element has if you add to yourself
+
+ align:start position:0%
+every element has if you add to yourself
+ 
+
+ align:start position:0%
+every element has if you add to yourself
+our x then destroys the van is just the
+
+ align:start position:0%
+our x then destroys the van is just the
+ 
+
+ align:start position:0%
+our x then destroys the van is just the
+element the name of the exponent the
+
+ align:start position:0%
+element the name of the exponent the
+ 
+
+ align:start position:0%
+element the name of the exponent the
+word exponent comes from I mean you can
+
+ align:start position:0%
+word exponent comes from I mean you can
+ 
+
+ align:start position:0%
+word exponent comes from I mean you can
+define the same thing for non abelian
+
+ align:start position:0%
+define the same thing for non abelian
+ 
+
+ align:start position:0%
+define the same thing for non abelian
+groups in which case you should write
+
+ align:start position:0%
+groups in which case you should write
+ 
+
+ align:start position:0%
+groups in which case you should write
+this expression using the exponent
+
+ align:start position:0%
+this expression using the exponent
+ 
+
+ align:start position:0%
+this expression using the exponent
+instead of addition multiplication so
+
+ align:start position:0%
+instead of addition multiplication so
+ 
+
+ align:start position:0%
+instead of addition multiplication so
+that's why it's called exponents so the
+
+ align:start position:0%
+that's why it's called exponents so the
+ 
+
+ align:start position:0%
+that's why it's called exponents so the
+names stuck even though we're still
+
+ align:start position:0%
+names stuck even though we're still
+ 
+
+ align:start position:0%
+names stuck even though we're still
+working the additive setting we're going
+
+ align:start position:0%
+working the additive setting we're going
+ 
+
+ align:start position:0%
+working the additive setting we're going
+to write this okay so the angle brackets
+
+ align:start position:0%
+to write this okay so the angle brackets
+ 
+
+ align:start position:0%
+to write this okay so the angle brackets
+to mean the subgroup generated by the
+
+ align:start position:0%
+to mean the subgroup generated by the
+ 
+
+ align:start position:0%
+to mean the subgroup generated by the
+subset a a is a subset of the group
+
+ align:start position:0%
+subset a a is a subset of the group
+ 
+
+ align:start position:0%
+subset a a is a subset of the group
+elements and so the exponent a group
+
+ align:start position:0%
+elements and so the exponent a group
+ 
+
+ align:start position:0%
+elements and so the exponent a group
+then is equal to the maximum number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you pick a good element look at
+
+ align:start position:0%
+so if you pick a good element look at
+ 
+
+ align:start position:0%
+so if you pick a good element look at
+how many group elements does it generate
+
+ align:start position:0%
+how many group elements does it generate
+ 
+
+ align:start position:0%
+how many group elements does it generate
+okay so it's equal to the max all right
+
+ align:start position:0%
+okay so it's equal to the max all right
+ 
+
+ align:start position:0%
+okay so it's equal to the max all right
+so I mean the example you can have in
+
+ align:start position:0%
+so I mean the example you can have in
+ 
+
+ align:start position:0%
+so I mean the example you can have in
+mind is f2 to the M which has exponent
+
+ align:start position:0%
+mind is f2 to the M which has exponent
+ 
+
+ align:start position:0%
+mind is f2 to the M which has exponent
+two so in general we're going to be
+
+ align:start position:0%
+two so in general we're going to be
+ 
+
+ align:start position:0%
+two so in general we're going to be
+looking at a special case in a group
+
+ align:start position:0%
+looking at a special case in a group
+ 
+
+ align:start position:0%
+looking at a special case in a group
+with bounded exponent and freeman's
+
+ align:start position:0%
+with bounded exponent and freeman's
+ 
+
+ align:start position:0%
+with bounded exponent and freeman's
+theorem in this case is due to Gousha
+
+ align:start position:0%
+theorem in this case is due to Gousha
+ 
+
+ align:start position:0%
+theorem in this case is due to Gousha
+who showed that if you have a finite
+
+ align:start position:0%
+who showed that if you have a finite
+ 
+
+ align:start position:0%
+who showed that if you have a finite
+subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a billion group with exponent are so
+
+ align:start position:0%
+in a billion group with exponent are so
+ 
+
+ align:start position:0%
+in a billion group with exponent are so
+finite exponent if a has doubling
+
+ align:start position:0%
+finite exponent if a has doubling
+ 
+
+ align:start position:0%
+finite exponent if a has doubling
+constant at most K then okay so what do
+
+ align:start position:0%
+constant at most K then okay so what do
+ 
+
+ align:start position:0%
+constant at most K then okay so what do
+we want to say we want to say just like
+
+ align:start position:0%
+we want to say we want to say just like
+ 
+
+ align:start position:0%
+we want to say we want to say just like
+in Freeman's term that if a has found a
+
+ align:start position:0%
+in Freeman's term that if a has found a
+ 
+
+ align:start position:0%
+in Freeman's term that if a has found a
+doubling then it is a large portion of
+
+ align:start position:0%
+doubling then it is a large portion of
+ 
+
+ align:start position:0%
+doubling then it is a large portion of
+some structured set and your structure
+
+ align:start position:0%
+some structured set and your structure
+ 
+
+ align:start position:0%
+some structured set and your structure
+set means subgroup well if you're going
+
+ align:start position:0%
+set means subgroup well if you're going
+ 
+
+ align:start position:0%
+set means subgroup well if you're going
+to be looking at subgroups that contain
+
+ align:start position:0%
+to be looking at subgroups that contain
+ 
+
+ align:start position:0%
+to be looking at subgroups that contain
+a you might as well look at the subgroup
+
+ align:start position:0%
+a you might as well look at the subgroup
+ 
+
+ align:start position:0%
+a you might as well look at the subgroup
+generated by a so the claim then this
+
+ align:start position:0%
+generated by a so the claim then this
+ 
+
+ align:start position:0%
+generated by a so the claim then this
+that the subgroup generated by a is only
+
+ align:start position:0%
+that the subgroup generated by a is only
+ 
+
+ align:start position:0%
+that the subgroup generated by a is only
+a constant factor bigger than a itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me say it again if you have
+
+ align:start position:0%
+okay so let me say it again if you have
+ 
+
+ align:start position:0%
+okay so let me say it again if you have
+a set a in a group of bounded exponent
+
+ align:start position:0%
+a set a in a group of bounded exponent
+ 
+
+ align:start position:0%
+a set a in a group of bounded exponent
+and a has bounded doubling then
+
+ align:start position:0%
+and a has bounded doubling then
+ 
+
+ align:start position:0%
+and a has bounded doubling then
+conclusion is that a is a large
+
+ align:start position:0%
+conclusion is that a is a large
+ 
+
+ align:start position:0%
+conclusion is that a is a large
+proportion of some subgroup conversely
+
+ align:start position:0%
+proportion of some subgroup conversely
+ 
+
+ align:start position:0%
+proportion of some subgroup conversely
+you know we saw last time if you take a
+
+ align:start position:0%
+you know we saw last time if you take a
+ 
+
+ align:start position:0%
+you know we saw last time if you take a
+subgroup it has doubling constant one so
+
+ align:start position:0%
+subgroup it has doubling constant one so
+ 
+
+ align:start position:0%
+subgroup it has doubling constant one so
+if you take a positive proportional
+
+ align:start position:0%
+if you take a positive proportional
+ 
+
+ align:start position:0%
+if you take a positive proportional
+constant proportion of the subgroup it
+
+ align:start position:0%
+constant proportion of the subgroup it
+ 
+
+ align:start position:0%
+constant proportion of the subgroup it
+also has bounded doubling and this
+
+ align:start position:0%
+also has bounded doubling and this
+ 
+
+ align:start position:0%
+also has bounded doubling and this
+statement is some sense certain some
+
+ align:start position:0%
+statement is some sense certain some
+ 
+
+ align:start position:0%
+statement is some sense certain some
+sense a converse of that observation
+
+ align:start position:0%
+sense a converse of that observation
+ 
+
+ align:start position:0%
+sense a converse of that observation
+this bound here is not optimal I'll make
+
+ align:start position:0%
+this bound here is not optimal I'll make
+ 
+
+ align:start position:0%
+this bound here is not optimal I'll make
+some comments about what we know about
+
+ align:start position:0%
+some comments about what we know about
+ 
+
+ align:start position:0%
+some comments about what we know about
+these bounds but for now just view this
+
+ align:start position:0%
+these bounds but for now just view this
+ 
+
+ align:start position:0%
+these bounds but for now just view this
+number as a constant any questions about
+
+ align:start position:0%
+number as a constant any questions about
+ 
+
+ align:start position:0%
+number as a constant any questions about
+the statement all right so let's prove
+
+ align:start position:0%
+the statement all right so let's prove
+ 
+
+ align:start position:0%
+the statement all right so let's prove
+this rucious theorem giving you
+
+ align:start position:0%
+this rucious theorem giving you
+ 
+
+ align:start position:0%
+this rucious theorem giving you
+fragments theorem in groups with bounded
+
+ align:start position:0%
+fragments theorem in groups with bounded
+ 
+
+ align:start position:0%
+fragments theorem in groups with bounded
+exponent so we can be applying the tools
+
+ align:start position:0%
+exponent so we can be applying the tools
+ 
+
+ align:start position:0%
+exponent so we can be applying the tools
+we've seen so far
+
+ align:start position:0%
+we've seen so far
+ 
+
+ align:start position:0%
+we've seen so far
+starting with plain Ikaruga
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so by applying the kirusha
+
+ align:start position:0%
+okay so by applying the kirusha
+ 
+
+ align:start position:0%
+okay so by applying the kirusha
+inequality we find that okay so and you
+
+ align:start position:0%
+inequality we find that okay so and you
+ 
+
+ align:start position:0%
+inequality we find that okay so and you
+know I'm gonna write down some
+
+ align:start position:0%
+know I'm gonna write down some
+ 
+
+ align:start position:0%
+know I'm gonna write down some
+expression you might wonder why this
+
+ align:start position:0%
+expression you might wonder why this
+ 
+
+ align:start position:0%
+expression you might wonder why this
+expression because we're going to apply
+
+ align:start position:0%
+expression because we're going to apply
+ 
+
+ align:start position:0%
+expression because we're going to apply
+covering lemma in a second so this set
+
+ align:start position:0%
+covering lemma in a second so this set
+ 
+
+ align:start position:0%
+covering lemma in a second so this set
+by plane the kirusha it's size is
+
+ align:start position:0%
+by plane the kirusha it's size is
+ 
+
+ align:start position:0%
+by plane the kirusha it's size is
+bounded because ii also be written as 3a
+
+ align:start position:0%
+bounded because ii also be written as 3a
+ 
+
+ align:start position:0%
+bounded because ii also be written as 3a
+minus a so it's size is bounded by K to
+
+ align:start position:0%
+minus a so it's size is bounded by K to
+ 
+
+ align:start position:0%
+minus a so it's size is bounded by K to
+the fourth times size of a so pretty
+
+ align:start position:0%
+the fourth times size of a so pretty
+ 
+
+ align:start position:0%
+the fourth times size of a so pretty
+huge oh it's a very nice tool to have it
+
+ align:start position:0%
+huge oh it's a very nice tool to have it
+ 
+
+ align:start position:0%
+huge oh it's a very nice tool to have it
+basically tells you if you have found
+
+ align:start position:0%
+basically tells you if you have found
+ 
+
+ align:start position:0%
+basically tells you if you have found
+the doubling then oh the other iterated
+
+ align:start position:0%
+the doubling then oh the other iterated
+ 
+
+ align:start position:0%
+the doubling then oh the other iterated
+sums are essentially controlling size
+
+ align:start position:0%
+sums are essentially controlling size
+ 
+
+ align:start position:0%
+sums are essentially controlling size
+and that were using that here okay so
+
+ align:start position:0%
+and that were using that here okay so
+ 
+
+ align:start position:0%
+and that were using that here okay so
+now we're in the setting where we can
+
+ align:start position:0%
+now we're in the setting where we can
+ 
+
+ align:start position:0%
+now we're in the setting where we can
+apply the Rouge are covering lemma so by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+covering lemma we're going to apply the
+
+ align:start position:0%
+covering lemma we're going to apply the
+ 
+
+ align:start position:0%
+covering lemma we're going to apply the
+covering lemma so using the notation
+
+ align:start position:0%
+covering lemma so using the notation
+ 
+
+ align:start position:0%
+covering lemma so using the notation
+earlier with X equal to 2a minus a and B
+
+ align:start position:0%
+earlier with X equal to 2a minus a and B
+ 
+
+ align:start position:0%
+earlier with X equal to 2a minus a and B
+equal to a by covering them up there
+
+ align:start position:0%
+equal to a by covering them up there
+ 
+
+ align:start position:0%
+equal to a by covering them up there
+exists some key being a subset of to a
+
+ align:start position:0%
+exists some key being a subset of to a
+ 
+
+ align:start position:0%
+exists some key being a subset of to a
+minus a with P not too large because of
+
+ align:start position:0%
+minus a with P not too large because of
+ 
+
+ align:start position:0%
+minus a with P not too large because of
+our earlier estimate and such that 2a
+
+ align:start position:0%
+our earlier estimate and such that 2a
+ 
+
+ align:start position:0%
+our earlier estimate and such that 2a
+minus a is contained in P plus a minus a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so it's easy to get lost in the
+
+ align:start position:0%
+right so it's easy to get lost in the
+ 
+
+ align:start position:0%
+right so it's easy to get lost in the
+details but what's happening here is
+
+ align:start position:0%
+details but what's happening here is
+ 
+
+ align:start position:0%
+details but what's happening here is
+that I start with a and I'm looking at
+
+ align:start position:0%
+that I start with a and I'm looking at
+ 
+
+ align:start position:0%
+that I start with a and I'm looking at
+how big these iterated growing some sets
+
+ align:start position:0%
+how big these iterated growing some sets
+ 
+
+ align:start position:0%
+how big these iterated growing some sets
+can be and if I keep on doing this
+
+ align:start position:0%
+can be and if I keep on doing this
+ 
+
+ align:start position:0%
+can be and if I keep on doing this
+operation like if I just apply plan the
+
+ align:start position:0%
+operation like if I just apply plan the
+ 
+
+ align:start position:0%
+operation like if I just apply plan the
+kirusha
+
+ align:start position:0%
+kirusha
+ 
+
+ align:start position:0%
+kirusha
+I can't really control the iterated sums
+
+ align:start position:0%
+I can't really control the iterated sums
+ 
+
+ align:start position:0%
+I can't really control the iterated sums
+by an absolute down this bound will keep
+
+ align:start position:0%
+by an absolute down this bound will keep
+ 
+
+ align:start position:0%
+by an absolute down this bound will keep
+growing if I take bigger iterations but
+
+ align:start position:0%
+growing if I take bigger iterations but
+ 
+
+ align:start position:0%
+growing if I take bigger iterations but
+rules are covering lemma gives me
+
+ align:start position:0%
+rules are covering lemma gives me
+ 
+
+ align:start position:0%
+rules are covering lemma gives me
+another way
+
+ align:start position:0%
+another way
+ 
+
+ align:start position:0%
+another way
+to control the bounded iterations access
+
+ align:start position:0%
+to control the bounded iterations access
+ 
+
+ align:start position:0%
+to control the bounded iterations access
+their some bounded set T such that this
+
+ align:start position:0%
+their some bounded set T such that this
+ 
+
+ align:start position:0%
+their some bounded set T such that this
+iterator some is nicely controlled so
+
+ align:start position:0%
+iterator some is nicely controlled so
+ 
+
+ align:start position:0%
+iterator some is nicely controlled so
+let me iterate this bound even further
+
+ align:start position:0%
+let me iterate this bound even further
+ 
+
+ align:start position:0%
+let me iterate this bound even further
+we're going to iterate the containment
+
+ align:start position:0%
+we're going to iterate the containment
+ 
+
+ align:start position:0%
+we're going to iterate the containment
+by adding a to both sides a to both
+
+ align:start position:0%
+by adding a to both sides a to both
+ 
+
+ align:start position:0%
+by adding a to both sides a to both
+sides and we obtained that 3a minus a is
+
+ align:start position:0%
+sides and we obtained that 3a minus a is
+ 
+
+ align:start position:0%
+sides and we obtained that 3a minus a is
+contained in T plus to a minus a but now
+
+ align:start position:0%
+contained in T plus to a minus a but now
+ 
+
+ align:start position:0%
+contained in T plus to a minus a but now
+to a - a was containing T plus a minus a
+
+ align:start position:0%
+to a - a was containing T plus a minus a
+ 
+
+ align:start position:0%
+to a - a was containing T plus a minus a
+so you got two T plus a minus a okay so
+
+ align:start position:0%
+so you got two T plus a minus a okay so
+ 
+
+ align:start position:0%
+so you got two T plus a minus a okay so
+now we've we've gained quite a bit
+
+ align:start position:0%
+now we've we've gained quite a bit
+ 
+
+ align:start position:0%
+now we've we've gained quite a bit
+because we can make this iteration go up
+
+ align:start position:0%
+because we can make this iteration go up
+ 
+
+ align:start position:0%
+because we can make this iteration go up
+but not at the cost of iterating a but
+
+ align:start position:0%
+but not at the cost of iterating a but
+ 
+
+ align:start position:0%
+but not at the cost of iterating a but
+at the cost of iterating T but T is a
+
+ align:start position:0%
+at the cost of iterating T but T is a
+ 
+
+ align:start position:0%
+at the cost of iterating T but T is a
+bounded side bounded size T is bounded
+
+ align:start position:0%
+bounded side bounded size T is bounded
+ 
+
+ align:start position:0%
+bounded side bounded size T is bounded
+size so T will have very nice control
+
+ align:start position:0%
+size so T will have very nice control
+ 
+
+ align:start position:0%
+size so T will have very nice control
+will be able to very nicely control the
+
+ align:start position:0%
+will be able to very nicely control the
+ 
+
+ align:start position:0%
+will be able to very nicely control the
+iterations of T if we keep going so we
+
+ align:start position:0%
+iterations of T if we keep going so we
+ 
+
+ align:start position:0%
+iterations of T if we keep going so we
+find that for all integer and positive
+
+ align:start position:0%
+find that for all integer and positive
+ 
+
+ align:start position:0%
+find that for all integer and positive
+integer n n plus 1 a minus a is
+
+ align:start position:0%
+integer n n plus 1 a minus a is
+ 
+
+ align:start position:0%
+integer n n plus 1 a minus a is
+contained in NT plus a minus a but for
+
+ align:start position:0%
+contained in NT plus a minus a but for
+ 
+
+ align:start position:0%
+contained in NT plus a minus a but for
+every integer n the iterated sums of T
+
+ align:start position:0%
+every integer n the iterated sums of T
+ 
+
+ align:start position:0%
+every integer n the iterated sums of T
+are contained in the subgroup generated
+
+ align:start position:0%
+are contained in the subgroup generated
+ 
+
+ align:start position:0%
+are contained in the subgroup generated
+by T so therefore if we take n to be as
+
+ align:start position:0%
+by T so therefore if we take n to be as
+ 
+
+ align:start position:0%
+by T so therefore if we take n to be as
+largest you won't see that the left-hand
+
+ align:start position:0%
+largest you won't see that the left-hand
+ 
+
+ align:start position:0%
+largest you won't see that the left-hand
+side eventually becomes the subgroup
+
+ align:start position:0%
+side eventually becomes the subgroup
+ 
+
+ align:start position:0%
+side eventually becomes the subgroup
+generated by a and the right-hand side
+
+ align:start position:0%
+generated by a and the right-hand side
+ 
+
+ align:start position:0%
+generated by a and the right-hand side
+does not depend on and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have this containment over here
+
+ align:start position:0%
+so you have this containment over here
+ 
+
+ align:start position:0%
+so you have this containment over here
+we would like to estimate how large the
+
+ align:start position:0%
+we would like to estimate how large the
+ 
+
+ align:start position:0%
+we would like to estimate how large the
+subgroup generated by a s so you look at
+
+ align:start position:0%
+subgroup generated by a s so you look at
+ 
+
+ align:start position:0%
+subgroup generated by a s so you look at
+that formula and we see that the size of
+
+ align:start position:0%
+that formula and we see that the size of
+ 
+
+ align:start position:0%
+that formula and we see that the size of
+the subgroup generated by T and here's
+
+ align:start position:0%
+the subgroup generated by T and here's
+ 
+
+ align:start position:0%
+the subgroup generated by T and here's
+where we're going to use the fact that
+
+ align:start position:0%
+where we're going to use the fact that
+ 
+
+ align:start position:0%
+where we're going to use the fact that
+the assumption that the group has
+
+ align:start position:0%
+the assumption that the group has
+ 
+
+ align:start position:0%
+the assumption that the group has
+bounded exponent or so think F 2 to the
+
+ align:start position:0%
+bounded exponent or so think F 2 to the
+ 
+
+ align:start position:0%
+bounded exponent or so think F 2 to the
+N if you will I mean F 2 to the N if I
+
+ align:start position:0%
+N if you will I mean F 2 to the N if I
+ 
+
+ align:start position:0%
+N if you will I mean F 2 to the N if I
+give you a set T what's the space
+
+ align:start position:0%
+give you a set T what's the space
+ 
+
+ align:start position:0%
+give you a set T what's the space
+subspace spanned by T what's the maximum
+
+ align:start position:0%
+subspace spanned by T what's the maximum
+ 
+
+ align:start position:0%
+subspace spanned by T what's the maximum
+possible size it's a most 2 raised to
+
+ align:start position:0%
+possible size it's a most 2 raised to
+ 
+
+ align:start position:0%
+possible size it's a most 2 raised to
+the number so in general you also have
+
+ align:start position:0%
+the number so in general you also have
+ 
+
+ align:start position:0%
+the number so in general you also have
+that the subgroup generated by T has
+
+ align:start position:0%
+that the subgroup generated by T has
+ 
+
+ align:start position:0%
+that the subgroup generated by T has
+size at most R raised to the size of T
+
+ align:start position:0%
+size at most R raised to the size of T
+ 
+
+ align:start position:0%
+size at most R raised to the size of T
+in a group of exponent or which we can
+
+ align:start position:0%
+in a group of exponent or which we can
+ 
+
+ align:start position:0%
+in a group of exponent or which we can
+control because T has bounded size and
+
+ align:start position:0%
+control because T has bounded size and
+ 
+
+ align:start position:0%
+control because T has bounded size and
+the second term a minus a we also know
+
+ align:start position:0%
+the second term a minus a we also know
+ 
+
+ align:start position:0%
+the second term a minus a we also know
+how to control that by plan Ikaruga
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore okay so putting these two
+
+ align:start position:0%
+therefore okay so putting these two
+ 
+
+ align:start position:0%
+therefore okay so putting these two
+together we see that the size up here is
+
+ align:start position:0%
+together we see that the size up here is
+ 
+
+ align:start position:0%
+together we see that the size up here is
+at most R to the K to the four times K
+
+ align:start position:0%
+at most R to the K to the four times K
+ 
+
+ align:start position:0%
+at most R to the K to the four times K
+squared size of a which is the bound
+
+ align:start position:0%
+squared size of a which is the bound
+ 
+
+ align:start position:0%
+squared size of a which is the bound
+that we kind any questions so the trick
+
+ align:start position:0%
+that we kind any questions so the trick
+ 
+
+ align:start position:0%
+that we kind any questions so the trick
+here is to only use clinical Russa
+
+ align:start position:0%
+here is to only use clinical Russa
+ 
+
+ align:start position:0%
+here is to only use clinical Russa
+somehow a bounded number of times if you
+
+ align:start position:0%
+somehow a bounded number of times if you
+ 
+
+ align:start position:0%
+somehow a bounded number of times if you
+use it too many times you can't I mean
+
+ align:start position:0%
+use it too many times you can't I mean
+ 
+
+ align:start position:0%
+use it too many times you can't I mean
+this bound blows up but you use it only
+
+ align:start position:0%
+this bound blows up but you use it only
+ 
+
+ align:start position:0%
+this bound blows up but you use it only
+a small number of times and then you use
+
+ align:start position:0%
+a small number of times and then you use
+ 
+
+ align:start position:0%
+a small number of times and then you use
+the ruler covering them up so that you
+
+ align:start position:0%
+the ruler covering them up so that you
+ 
+
+ align:start position:0%
+the ruler covering them up so that you
+get this bounded set T that I can
+
+ align:start position:0%
+get this bounded set T that I can
+ 
+
+ align:start position:0%
+get this bounded set T that I can
+iterate let me make some comments about
+
+ align:start position:0%
+iterate let me make some comments about
+ 
+
+ align:start position:0%
+iterate let me make some comments about
+the bounds that come out of this proof
+
+ align:start position:0%
+the bounds that come out of this proof
+ 
+
+ align:start position:0%
+the bounds that come out of this proof
+so you get this very clean bound just
+
+ align:start position:0%
+so you get this very clean bound just
+ 
+
+ align:start position:0%
+so you get this very clean bound just
+following this proof but what about
+
+ align:start position:0%
+following this proof but what about
+ 
+
+ align:start position:0%
+following this proof but what about
+examples so what kinds of examples can
+
+ align:start position:0%
+examples so what kinds of examples can
+ 
+
+ align:start position:0%
+examples so what kinds of examples can
+you think of where you have a set of
+
+ align:start position:0%
+you think of where you have a set of
+ 
+
+ align:start position:0%
+you think of where you have a set of
+bounded doubling but the said generated
+
+ align:start position:0%
+bounded doubling but the said generated
+ 
+
+ align:start position:0%
+bounded doubling but the said generated
+a group generated by that set is
+
+ align:start position:0%
+a group generated by that set is
+ 
+
+ align:start position:0%
+a group generated by that set is
+potentially large so even in f2 f2 to
+
+ align:start position:0%
+potentially large so even in f2 f2 to
+ 
+
+ align:start position:0%
+potentially large so even in f2 f2 to
+the M so if a is an independent set so
+
+ align:start position:0%
+the M so if a is an independent set so
+ 
+
+ align:start position:0%
+the M so if a is an independent set so
+basis or subset of a basis for instance
+
+ align:start position:0%
+basis or subset of a basis for instance
+ 
+
+ align:start position:0%
+basis or subset of a basis for instance
+then okay so independence that so all
+
+ align:start position:0%
+then okay so independence that so all
+ 
+
+ align:start position:0%
+then okay so independence that so all
+the pairwise sums are distinct so K is
+
+ align:start position:0%
+the pairwise sums are distinct so K is
+ 
+
+ align:start position:0%
+the pairwise sums are distinct so K is
+about size of eight over two that's the
+
+ align:start position:0%
+about size of eight over two that's the
+ 
+
+ align:start position:0%
+about size of eight over two that's the
+doubling constant whereas the group
+
+ align:start position:0%
+doubling constant whereas the group
+ 
+
+ align:start position:0%
+doubling constant whereas the group
+generated by a has size two to the size
+
+ align:start position:0%
+generated by a has size two to the size
+ 
+
+ align:start position:0%
+generated by a has size two to the size
+of a which is around two to the 2k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the size of a okay so you see that
+
+ align:start position:0%
+times the size of a okay so you see that
+ 
+
+ align:start position:0%
+times the size of a okay so you see that
+you do need some exponential blow-up
+
+ align:start position:0%
+you do need some exponential blow-up
+ 
+
+ align:start position:0%
+you do need some exponential blow-up
+from k2 this constant over here and
+
+ align:start position:0%
+from k2 this constant over here and
+ 
+
+ align:start position:0%
+from k2 this constant over here and
+turns out that's more or less correct so
+
+ align:start position:0%
+turns out that's more or less correct so
+ 
+
+ align:start position:0%
+turns out that's more or less correct so
+so the optimal constant for F 2 to the N
+
+ align:start position:0%
+so the optimal constant for F 2 to the N
+ 
+
+ align:start position:0%
+so the optimal constant for F 2 to the N
+is now known very precisely I said if
+
+ align:start position:0%
+is now known very precisely I said if
+ 
+
+ align:start position:0%
+is now known very precisely I said if
+you give me a real value of K then I can
+
+ align:start position:0%
+you give me a real value of K then I can
+ 
+
+ align:start position:0%
+you give me a real value of K then I can
+tell you you know there are some recent
+
+ align:start position:0%
+tell you you know there are some recent
+ 
+
+ align:start position:0%
+tell you you know there are some recent
+results that tells you exactly what is
+
+ align:start position:0%
+results that tells you exactly what is
+ 
+
+ align:start position:0%
+results that tells you exactly what is
+the optimal constant you can put in
+
+ align:start position:0%
+the optimal constant you can put in
+ 
+
+ align:start position:0%
+the optimal constant you can put in
+front of the age so very precisely
+
+ align:start position:0%
+front of the age so very precisely
+ 
+
+ align:start position:0%
+front of the age so very precisely
+asymptotically it looks like 2 to the 2
+
+ align:start position:0%
+asymptotically it looks like 2 to the 2
+ 
+
+ align:start position:0%
+asymptotically it looks like 2 to the 2
+K divided by K so that's that's what it
+
+ align:start position:0%
+K divided by K so that's that's what it
+ 
+
+ align:start position:0%
+K divided by K so that's that's what it
+looks like so this example is basically
+
+ align:start position:0%
+looks like so this example is basically
+ 
+
+ align:start position:0%
+looks like so this example is basically
+correct for general are we expect a
+
+ align:start position:0%
+correct for general are we expect a
+ 
+
+ align:start position:0%
+correct for general are we expect a
+similar phenomenon so roots are
+
+ align:start position:0%
+similar phenomenon so roots are
+ 
+
+ align:start position:0%
+similar phenomenon so roots are
+conjectured that in the hypothesis of
+
+ align:start position:0%
+conjectured that in the hypothesis of
+ 
+
+ align:start position:0%
+conjectured that in the hypothesis of
+the theorem the constant you can take is
+
+ align:start position:0%
+the theorem the constant you can take is
+ 
+
+ align:start position:0%
+the theorem the constant you can take is
+only exponential in K so R to the some
+
+ align:start position:0%
+only exponential in K so R to the some
+ 
+
+ align:start position:0%
+only exponential in K so R to the some
+constant C times K and it has been
+
+ align:start position:0%
+constant C times K and it has been
+ 
+
+ align:start position:0%
+constant C times K and it has been
+verified for some values of our but not
+
+ align:start position:0%
+verified for some values of our but not
+ 
+
+ align:start position:0%
+verified for some values of our but not
+in general so know for some are for
+
+ align:start position:0%
+in general so know for some are for
+ 
+
+ align:start position:0%
+in general so know for some are for
+example primes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions all right so this is
+
+ align:start position:0%
+okay any questions all right so this is
+ 
+
+ align:start position:0%
+okay any questions all right so this is
+a good milestone so we've developed some
+
+ align:start position:0%
+a good milestone so we've developed some
+ 
+
+ align:start position:0%
+a good milestone so we've developed some
+tools and we were able to prove a easier
+
+ align:start position:0%
+tools and we were able to prove a easier
+ 
+
+ align:start position:0%
+tools and we were able to prove a easier
+version of Fryman serum in a group of
+
+ align:start position:0%
+version of Fryman serum in a group of
+ 
+
+ align:start position:0%
+version of Fryman serum in a group of
+bounded exponent and you can ask
+
+ align:start position:0%
+bounded exponent and you can ask
+ 
+
+ align:start position:0%
+bounded exponent and you can ask
+yourself you know does this proof work
+
+ align:start position:0%
+yourself you know does this proof work
+ 
+
+ align:start position:0%
+yourself you know does this proof work
+in two integers and well literally not
+
+ align:start position:0%
+in two integers and well literally not
+ 
+
+ align:start position:0%
+in two integers and well literally not
+because if you look at this proof you
+
+ align:start position:0%
+because if you look at this proof you
+ 
+
+ align:start position:0%
+because if you look at this proof you
+know this set here is infinite unlike
+
+ align:start position:0%
+know this set here is infinite unlike
+ 
+
+ align:start position:0%
+know this set here is infinite unlike
+you know finite field setting in the
+
+ align:start position:0%
+you know finite field setting in the
+ 
+
+ align:start position:0%
+you know finite field setting in the
+integers well that's not very good
+
+ align:start position:0%
+integers well that's not very good
+ 
+
+ align:start position:0%
+integers well that's not very good
+so the strategy of Freeman's theorem the
+
+ align:start position:0%
+so the strategy of Freeman's theorem the
+ 
+
+ align:start position:0%
+so the strategy of Freeman's theorem the
+proof of prime minster is to start with
+
+ align:start position:0%
+proof of prime minster is to start with
+ 
+
+ align:start position:0%
+proof of prime minster is to start with
+the integers and then try to not work in
+
+ align:start position:0%
+the integers and then try to not work in
+ 
+
+ align:start position:0%
+the integers and then try to not work in
+the integers but try to work in a
+
+ align:start position:0%
+the integers but try to work in a
+ 
+
+ align:start position:0%
+the integers but try to work in a
+smaller group even though you start you
+
+ align:start position:0%
+smaller group even though you start you
+ 
+
+ align:start position:0%
+smaller group even though you start you
+know may be very spread out set of
+
+ align:start position:0%
+know may be very spread out set of
+ 
+
+ align:start position:0%
+know may be very spread out set of
+integers I want to work in a much
+
+ align:start position:0%
+integers I want to work in a much
+ 
+
+ align:start position:0%
+integers I want to work in a much
+smaller group so that I can control
+
+ align:start position:0%
+smaller group so that I can control
+ 
+
+ align:start position:0%
+smaller group so that I can control
+things within that group and this is an
+
+ align:start position:0%
+things within that group and this is an
+ 
+
+ align:start position:0%
+things within that group and this is an
+idea called modeling a big set and want
+
+ align:start position:0%
+idea called modeling a big set and want
+ 
+
+ align:start position:0%
+idea called modeling a big set and want
+to model it by something in a small
+
+ align:start position:0%
+to model it by something in a small
+ 
+
+ align:start position:0%
+to model it by something in a small
+group okay we're gonna see this idea but
+
+ align:start position:0%
+group okay we're gonna see this idea but
+ 
+
+ align:start position:0%
+group okay we're gonna see this idea but
+to understand what does it mean to have
+
+ align:start position:0%
+to understand what does it mean to have
+ 
+
+ align:start position:0%
+to understand what does it mean to have
+a good model for set in a sense of
+
+ align:start position:0%
+a good model for set in a sense of
+ 
+
+ align:start position:0%
+a good model for set in a sense of
+additive combinatorics I need to
+
+ align:start position:0%
+additive combinatorics I need to
+ 
+
+ align:start position:0%
+additive combinatorics I need to
+introduce the notion of Fryman
+
+ align:start position:0%
+introduce the notion of Fryman
+ 
+
+ align:start position:0%
+introduce the notion of Fryman
+homomorphisms
+
+ align:start position:0%
+homomorphisms
+ 
+
+ align:start position:0%
+homomorphisms
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of the central philosophies
+
+ align:start position:0%
+so one of the central philosophies
+ 
+
+ align:start position:0%
+so one of the central philosophies
+across mathematics is that if you want
+
+ align:start position:0%
+across mathematics is that if you want
+ 
+
+ align:start position:0%
+across mathematics is that if you want
+to study objects you should try to
+
+ align:start position:0%
+to study objects you should try to
+ 
+
+ align:start position:0%
+to study objects you should try to
+understand maps between objects and
+
+ align:start position:0%
+understand maps between objects and
+ 
+
+ align:start position:0%
+understand maps between objects and
+understand properties that preserves map
+
+ align:start position:0%
+understand properties that preserves map
+ 
+
+ align:start position:0%
+understand properties that preserves map
+never preserved under those maps so if
+
+ align:start position:0%
+never preserved under those maps so if
+ 
+
+ align:start position:0%
+never preserved under those maps so if
+you want to study groups I don't really
+
+ align:start position:0%
+you want to study groups I don't really
+ 
+
+ align:start position:0%
+you want to study groups I don't really
+care how you label your group elements
+
+ align:start position:0%
+care how you label your group elements
+ 
+
+ align:start position:0%
+care how you label your group elements
+by one two three or ABC what I care
+
+ align:start position:0%
+by one two three or ABC what I care
+ 
+
+ align:start position:0%
+by one two three or ABC what I care
+about is the relationships and those are
+
+ align:start position:0%
+about is the relationships and those are
+ 
+
+ align:start position:0%
+about is the relationships and those are
+the data that I care about and then of
+
+ align:start position:0%
+the data that I care about and then of
+ 
+
+ align:start position:0%
+the data that I care about and then of
+course then you have concepts like group
+
+ align:start position:0%
+course then you have concepts like group
+ 
+
+ align:start position:0%
+course then you have concepts like group
+homomorphisms group isomorphisms that
+
+ align:start position:0%
+homomorphisms group isomorphisms that
+ 
+
+ align:start position:0%
+homomorphisms group isomorphisms that
+preserve all the relevant data similarly
+
+ align:start position:0%
+preserve all the relevant data similarly
+ 
+
+ align:start position:0%
+preserve all the relevant data similarly
+any other area you know in geometry you
+
+ align:start position:0%
+any other area you know in geometry you
+ 
+
+ align:start position:0%
+any other area you know in geometry you
+have manifolds you understand not
+
+ align:start position:0%
+have manifolds you understand not
+ 
+
+ align:start position:0%
+have manifolds you understand not
+specifically how they embed into space
+
+ align:start position:0%
+specifically how they embed into space
+ 
+
+ align:start position:0%
+specifically how they embed into space
+but what are the intrinsic properties so
+
+ align:start position:0%
+but what are the intrinsic properties so
+ 
+
+ align:start position:0%
+but what are the intrinsic properties so
+we would like to understand what are the
+
+ align:start position:0%
+we would like to understand what are the
+ 
+
+ align:start position:0%
+we would like to understand what are the
+intrinsic properties of a subset of an
+
+ align:start position:0%
+intrinsic properties of a subset of an
+ 
+
+ align:start position:0%
+intrinsic properties of a subset of an
+abelian group that we care about for the
+
+ align:start position:0%
+abelian group that we care about for the
+ 
+
+ align:start position:0%
+abelian group that we care about for the
+purpose of additive combinatorics and
+
+ align:start position:0%
+purpose of additive combinatorics and
+ 
+
+ align:start position:0%
+purpose of additive combinatorics and
+specifically for fragments theorem and
+
+ align:start position:0%
+specifically for fragments theorem and
+ 
+
+ align:start position:0%
+specifically for fragments theorem and
+what we care about is what kinds of
+
+ align:start position:0%
+what we care about is what kinds of
+ 
+
+ align:start position:0%
+what we care about is what kinds of
+additive relationships are preserved and
+
+ align:start position:0%
+additive relationships are preserved and
+ 
+
+ align:start position:0%
+additive relationships are preserved and
+Fryman homomorphisms capture that notion
+
+ align:start position:0%
+Fryman homomorphisms capture that notion
+ 
+
+ align:start position:0%
+Fryman homomorphisms capture that notion
+so roughly speaking we would like to
+
+ align:start position:0%
+so roughly speaking we would like to
+ 
+
+ align:start position:0%
+so roughly speaking we would like to
+understand maps between sets impossibly
+
+ align:start position:0%
+understand maps between sets impossibly
+ 
+
+ align:start position:0%
+understand maps between sets impossibly
+different groups in possibly different
+
+ align:start position:0%
+different groups in possibly different
+ 
+
+ align:start position:0%
+different groups in possibly different
+abelian groups that preserve only
+
+ align:start position:0%
+abelian groups that preserve only
+ 
+
+ align:start position:0%
+abelian groups that preserve only
+partially preserved additive structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a definition suppose we
+
+ align:start position:0%
+okay so here's a definition suppose we
+ 
+
+ align:start position:0%
+okay so here's a definition suppose we
+have a and B and there are subsets
+
+ align:start position:0%
+have a and B and there are subsets
+ 
+
+ align:start position:0%
+have a and B and there are subsets
+between subsets in possibly different
+
+ align:start position:0%
+between subsets in possibly different
+ 
+
+ align:start position:0%
+between subsets in possibly different
+abelian groups could be the same but
+
+ align:start position:0%
+abelian groups could be the same but
+ 
+
+ align:start position:0%
+abelian groups could be the same but
+possibly different and everything's
+
+ align:start position:0%
+possibly different and everything's
+ 
+
+ align:start position:0%
+possibly different and everything's
+written under addition as usual so we
+
+ align:start position:0%
+written under addition as usual so we
+ 
+
+ align:start position:0%
+written under addition as usual so we
+say that a map fee from A to B is a
+
+ align:start position:0%
+say that a map fee from A to B is a
+ 
+
+ align:start position:0%
+say that a map fee from A to B is a
+Fryman as homomorphism so that's the
+
+ align:start position:0%
+Fryman as homomorphism so that's the
+ 
+
+ align:start position:0%
+Fryman as homomorphism so that's the
+term Fryman s homomorphism sometimes
+
+ align:start position:0%
+term Fryman s homomorphism sometimes
+ 
+
+ align:start position:0%
+term Fryman s homomorphism sometimes
+also the whole frame and homomorphism of
+
+ align:start position:0%
+also the whole frame and homomorphism of
+ 
+
+ align:start position:0%
+also the whole frame and homomorphism of
+order s so that's equivalently I can
+
+ align:start position:0%
+order s so that's equivalently I can
+ 
+
+ align:start position:0%
+order s so that's equivalently I can
+call it that as well if the following
+
+ align:start position:0%
+call it that as well if the following
+ 
+
+ align:start position:0%
+call it that as well if the following
+holds if we have the equation P of a
+
+ align:start position:0%
+holds if we have the equation P of a
+ 
+
+ align:start position:0%
+holds if we have the equation P of a
+plus da da da plus fee of a sub s equal
+
+ align:start position:0%
+plus da da da plus fee of a sub s equal
+ 
+
+ align:start position:0%
+plus da da da plus fee of a sub s equal
+to fee of a prime 1 plus da da da plus
+
+ align:start position:0%
+to fee of a prime 1 plus da da da plus
+ 
+
+ align:start position:0%
+to fee of a prime 1 plus da da da plus
+fee of a prime s
+
+ align:start position:0%
+fee of a prime s
+ 
+
+ align:start position:0%
+fee of a prime s
+whenever a to AAS a prime to a s prime
+
+ align:start position:0%
+whenever a to AAS a prime to a s prime
+ 
+
+ align:start position:0%
+whenever a to AAS a prime to a s prime
+to a1 prime to s prime satisfy the
+
+ align:start position:0%
+to a1 prime to s prime satisfy the
+ 
+
+ align:start position:0%
+to a1 prime to s prime satisfy the
+equation a 1 plus peridot plus is equal
+
+ align:start position:0%
+equation a 1 plus peridot plus is equal
+ 
+
+ align:start position:0%
+equation a 1 plus peridot plus is equal
+to a 1 prime plus da da
+
+ align:start position:0%
+to a 1 prime plus da da
+ 
+
+ align:start position:0%
+to a 1 prime plus da da
+plus a s Prime ok so that's the
+
+ align:start position:0%
+plus a s Prime ok so that's the
+ 
+
+ align:start position:0%
+plus a s Prime ok so that's the
+definition of a Fryman s homomorphism it
+
+ align:start position:0%
+definition of a Fryman s homomorphism it
+ 
+
+ align:start position:0%
+definition of a Fryman s homomorphism it
+should remind you of the definition of a
+
+ align:start position:0%
+should remind you of the definition of a
+ 
+
+ align:start position:0%
+should remind you of the definition of a
+group homomorphism which completely
+
+ align:start position:0%
+group homomorphism which completely
+ 
+
+ align:start position:0%
+group homomorphism which completely
+preserves additive structure let's say
+
+ align:start position:0%
+preserves additive structure let's say
+ 
+
+ align:start position:0%
+preserves additive structure let's say
+between abelian groups and for Fryman
+
+ align:start position:0%
+between abelian groups and for Fryman
+ 
+
+ align:start position:0%
+between abelian groups and for Fryman
+homomorphisms and only asking to
+
+ align:start position:0%
+homomorphisms and only asking to
+ 
+
+ align:start position:0%
+homomorphisms and only asking to
+partially preserve additive structure so
+
+ align:start position:0%
+partially preserve additive structure so
+ 
+
+ align:start position:0%
+partially preserve additive structure so
+if so the point here is that if I only
+
+ align:start position:0%
+if so the point here is that if I only
+ 
+
+ align:start position:0%
+if so the point here is that if I only
+care about let's say pairwise sums if
+
+ align:start position:0%
+care about let's say pairwise sums if
+ 
+
+ align:start position:0%
+care about let's say pairwise sums if
+that's the only data I care about then
+
+ align:start position:0%
+that's the only data I care about then
+ 
+
+ align:start position:0%
+that's the only data I care about then
+Fryman s homomorphisms preserve that
+
+ align:start position:0%
+Fryman s homomorphisms preserve that
+ 
+
+ align:start position:0%
+Fryman s homomorphisms preserve that
+data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to give you some okay one more thing if
+
+ align:start position:0%
+to give you some okay one more thing if
+ 
+
+ align:start position:0%
+to give you some okay one more thing if
+a so if be from 8p yes furthermore
+
+ align:start position:0%
+a so if be from 8p yes furthermore
+ 
+
+ align:start position:0%
+a so if be from 8p yes furthermore
+rejection and both fee and fee inverse
+
+ align:start position:0%
+rejection and both fee and fee inverse
+ 
+
+ align:start position:0%
+rejection and both fee and fee inverse
+are Fryman ask homomorphisms then we say
+
+ align:start position:0%
+are Fryman ask homomorphisms then we say
+ 
+
+ align:start position:0%
+are Fryman ask homomorphisms then we say
+that p is a Fryman s isomorphism okay so
+
+ align:start position:0%
+that p is a Fryman s isomorphism okay so
+ 
+
+ align:start position:0%
+that p is a Fryman s isomorphism okay so
+it's not enough just to be a by ejection
+
+ align:start position:0%
+it's not enough just to be a by ejection
+ 
+
+ align:start position:0%
+it's not enough just to be a by ejection
+but it's a projection and both the
+
+ align:start position:0%
+but it's a projection and both the
+ 
+
+ align:start position:0%
+but it's a projection and both the
+forward and the inverse maps are Fryman
+
+ align:start position:0%
+forward and the inverse maps are Fryman
+ 
+
+ align:start position:0%
+forward and the inverse maps are Fryman
+s I so fine Fryman homomorphisms so
+
+ align:start position:0%
+s I so fine Fryman homomorphisms so
+ 
+
+ align:start position:0%
+s I so fine Fryman homomorphisms so
+these are the definitions we're gonna
+
+ align:start position:0%
+these are the definitions we're gonna
+ 
+
+ align:start position:0%
+these are the definitions we're gonna
+use let me give you some examples so
+
+ align:start position:0%
+use let me give you some examples so
+ 
+
+ align:start position:0%
+use let me give you some examples so
+every group homomorphism is a Fryman
+
+ align:start position:0%
+every group homomorphism is a Fryman
+ 
+
+ align:start position:0%
+every group homomorphism is a Fryman
+homomorphism of every water so group
+
+ align:start position:0%
+homomorphism of every water so group
+ 
+
+ align:start position:0%
+homomorphism of every water so group
+homomorphism is preserve all additive
+
+ align:start position:0%
+homomorphism is preserve all additive
+ 
+
+ align:start position:0%
+homomorphism is preserve all additive
+structure and Fryman homomorphisms only
+
+ align:start position:0%
+structure and Fryman homomorphisms only
+ 
+
+ align:start position:0%
+structure and Fryman homomorphisms only
+partially preserve additive structure a
+
+ align:start position:0%
+partially preserve additive structure a
+ 
+
+ align:start position:0%
+partially preserve additive structure a
+composition so if p1 and p2 are Fryman s
+
+ align:start position:0%
+composition so if p1 and p2 are Fryman s
+ 
+
+ align:start position:0%
+composition so if p1 and p2 are Fryman s
+homomorphisms then c1 composed with v2
+
+ align:start position:0%
+homomorphisms then c1 composed with v2
+ 
+
+ align:start position:0%
+homomorphisms then c1 composed with v2
+is a Fryman as homomorphism okay so
+
+ align:start position:0%
+is a Fryman as homomorphism okay so
+ 
+
+ align:start position:0%
+is a Fryman as homomorphism okay so
+compositions preserve this property and
+
+ align:start position:0%
+compositions preserve this property and
+ 
+
+ align:start position:0%
+compositions preserve this property and
+likewise if you have instead of
+
+ align:start position:0%
+likewise if you have instead of
+ 
+
+ align:start position:0%
+likewise if you have instead of
+homomorphisms if you have isomorphisms
+
+ align:start position:0%
+homomorphisms if you have isomorphisms
+ 
+
+ align:start position:0%
+homomorphisms if you have isomorphisms
+then that's also true as well that's
+
+ align:start position:0%
+then that's also true as well that's
+ 
+
+ align:start position:0%
+then that's also true as well that's
+what these are straightforward things to
+
+ align:start position:0%
+what these are straightforward things to
+ 
+
+ align:start position:0%
+what these are straightforward things to
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+so a concrete example that shows you a
+
+ align:start position:0%
+so a concrete example that shows you a
+ 
+
+ align:start position:0%
+so a concrete example that shows you a
+difference between
+
+ align:start position:0%
+difference between
+ 
+
+ align:start position:0%
+difference between
+group no more isms and from isomorphic
+
+ align:start position:0%
+group no more isms and from isomorphic
+ 
+
+ align:start position:0%
+group no more isms and from isomorphic
+priming homomorphisms is supposed to
+
+ align:start position:0%
+priming homomorphisms is supposed to
+ 
+
+ align:start position:0%
+priming homomorphisms is supposed to
+take an arbitrary map fee from a set
+
+ align:start position:0%
+take an arbitrary map fee from a set
+ 
+
+ align:start position:0%
+take an arbitrary map fee from a set
+that has no additive structure okay so
+
+ align:start position:0%
+that has no additive structure okay so
+ 
+
+ align:start position:0%
+that has no additive structure okay so
+it's a four element set has no additive
+
+ align:start position:0%
+it's a four element set has no additive
+ 
+
+ align:start position:0%
+it's a four element set has no additive
+structure and I map it to the integers
+
+ align:start position:0%
+structure and I map it to the integers
+ 
+
+ align:start position:0%
+structure and I map it to the integers
+claim that this is a Fryman to
+
+ align:start position:0%
+claim that this is a Fryman to
+ 
+
+ align:start position:0%
+claim that this is a Fryman to
+homomorphism so you can check so you can
+
+ align:start position:0%
+homomorphism so you can check so you can
+ 
+
+ align:start position:0%
+homomorphism so you can check so you can
+you know whenever this is satisfied but
+
+ align:start position:0%
+you know whenever this is satisfied but
+ 
+
+ align:start position:0%
+you know whenever this is satisfied but
+that's never non trivially satisfied so
+
+ align:start position:0%
+that's never non trivially satisfied so
+ 
+
+ align:start position:0%
+that's never non trivially satisfied so
+an arbitrary map here is a fragment you
+
+ align:start position:0%
+an arbitrary map here is a fragment you
+ 
+
+ align:start position:0%
+an arbitrary map here is a fragment you
+homomorphism and if furthermore so if
+
+ align:start position:0%
+homomorphism and if furthermore so if
+ 
+
+ align:start position:0%
+homomorphism and if furthermore so if
+you have let's say I buy action between
+
+ align:start position:0%
+you have let's say I buy action between
+ 
+
+ align:start position:0%
+you have let's say I buy action between
+two sets both having no additive
+
+ align:start position:0%
+two sets both having no additive
+ 
+
+ align:start position:0%
+two sets both having no additive
+structure if it's a projection then it's
+
+ align:start position:0%
+structure if it's a projection then it's
+ 
+
+ align:start position:0%
+structure if it's a projection then it's
+a Fryman isomorphism of here order -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me give you a few more examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in you know when you look at
+
+ align:start position:0%
+so in you know when you look at
+ 
+
+ align:start position:0%
+so in you know when you look at
+homomorphisms between finite groups so
+
+ align:start position:0%
+homomorphisms between finite groups so
+ 
+
+ align:start position:0%
+homomorphisms between finite groups so
+you know that if you have a homomorphism
+
+ align:start position:0%
+you know that if you have a homomorphism
+ 
+
+ align:start position:0%
+you know that if you have a homomorphism
+and it's also a bisection then it's an
+
+ align:start position:0%
+and it's also a bisection then it's an
+ 
+
+ align:start position:0%
+and it's also a bisection then it's an
+isomorphism but that's not true for this
+
+ align:start position:0%
+isomorphism but that's not true for this
+ 
+
+ align:start position:0%
+isomorphism but that's not true for this
+notion of homomorphisms right so the
+
+ align:start position:0%
+notion of homomorphisms right so the
+ 
+
+ align:start position:0%
+notion of homomorphisms right so the
+natural embedding okay so the natural
+
+ align:start position:0%
+natural embedding okay so the natural
+ 
+
+ align:start position:0%
+natural embedding okay so the natural
+embedding that sends the boolean cube to
+
+ align:start position:0%
+embedding that sends the boolean cube to
+ 
+
+ align:start position:0%
+embedding that sends the boolean cube to
+the boolean cuba mute as Zima
+
+ align:start position:0%
+the boolean cuba mute as Zima
+ 
+
+ align:start position:0%
+the boolean cuba mute as Zima
+2 to the N so yes ok so what's happening
+
+ align:start position:0%
+2 to the N so yes ok so what's happening
+ 
+
+ align:start position:0%
+2 to the N so yes ok so what's happening
+here this is a part of a group
+
+ align:start position:0%
+here this is a part of a group
+ 
+
+ align:start position:0%
+here this is a part of a group
+homomorphism right so if you look at Z
+
+ align:start position:0%
+homomorphism right so if you look at Z
+ 
+
+ align:start position:0%
+homomorphism right so if you look at Z
+to the N and I do mod 2 when I restrict
+
+ align:start position:0%
+to the N and I do mod 2 when I restrict
+ 
+
+ align:start position:0%
+to the N and I do mod 2 when I restrict
+this boolean cube that's the group
+
+ align:start position:0%
+this boolean cube that's the group
+ 
+
+ align:start position:0%
+this boolean cube that's the group
+homomorphism if I view this as a subset
+
+ align:start position:0%
+homomorphism if I view this as a subset
+ 
+
+ align:start position:0%
+homomorphism if I view this as a subset
+of a bigger group so it is a Fryman
+
+ align:start position:0%
+of a bigger group so it is a Fryman
+ 
+
+ align:start position:0%
+of a bigger group so it is a Fryman
+homomorphism of a be water and it's by
+
+ align:start position:0%
+homomorphism of a be water and it's by
+ 
+
+ align:start position:0%
+homomorphism of a be water and it's by
+active but it is not at Fryman to
+
+ align:start position:0%
+active but it is not at Fryman to
+ 
+
+ align:start position:0%
+active but it is not at Fryman to
+isomorphism because you have additive
+
+ align:start position:0%
+isomorphism because you have additive
+ 
+
+ align:start position:0%
+isomorphism because you have additive
+relations here that are not present over
+
+ align:start position:0%
+relations here that are not present over
+ 
+
+ align:start position:0%
+relations here that are not present over
+here so if you read the definition the
+
+ align:start position:0%
+here so if you read the definition the
+ 
+
+ align:start position:0%
+here so if you read the definition the
+inverse map there are some additive
+
+ align:start position:0%
+inverse map there are some additive
+ 
+
+ align:start position:0%
+inverse map there are some additive
+relations here that are not preserved if
+
+ align:start position:0%
+relations here that are not preserved if
+ 
+
+ align:start position:0%
+relations here that are not preserved if
+you pull back so here's another example
+
+ align:start position:0%
+you pull back so here's another example
+ 
+
+ align:start position:0%
+you pull back so here's another example
+that will be more relevant to our
+
+ align:start position:0%
+that will be more relevant to our
+ 
+
+ align:start position:0%
+that will be more relevant to our
+subsequent discussion the mod n map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the mod nmap which sends Z to Z mod n
+
+ align:start position:0%
+so the mod nmap which sends Z to Z mod n
+ 
+
+ align:start position:0%
+so the mod nmap which sends Z to Z mod n
+so this is a group homomorphism so hence
+
+ align:start position:0%
+so this is a group homomorphism so hence
+ 
+
+ align:start position:0%
+so this is a group homomorphism so hence
+it's a Fryman homomorphism four of every
+
+ align:start position:0%
+it's a Fryman homomorphism four of every
+ 
+
+ align:start position:0%
+it's a Fryman homomorphism four of every
+order but it's not okay so if you look
+
+ align:start position:0%
+order but it's not okay so if you look
+ 
+
+ align:start position:0%
+order but it's not okay so if you look
+at this map and even if I restrict to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so it's not an ISIL Fryman
+
+ align:start position:0%
+here okay so it's not an ISIL Fryman
+ 
+
+ align:start position:0%
+here okay so it's not an ISIL Fryman
+isomorphism just like earlier however so
+
+ align:start position:0%
+isomorphism just like earlier however so
+ 
+
+ align:start position:0%
+isomorphism just like earlier however so
+if okay so let me go back to Z so if a
+
+ align:start position:0%
+if okay so let me go back to Z so if a
+ 
+
+ align:start position:0%
+if okay so let me go back to Z so if a
+is a subset of integers with diameter
+
+ align:start position:0%
+is a subset of integers with diameter
+ 
+
+ align:start position:0%
+is a subset of integers with diameter
+less than n over s then this map more
+
+ align:start position:0%
+less than n over s then this map more
+ 
+
+ align:start position:0%
+less than n over s then this map more
+than maps a Fryman s isomorphic T onto
+
+ align:start position:0%
+than maps a Fryman s isomorphic T onto
+ 
+
+ align:start position:0%
+than maps a Fryman s isomorphic T onto
+its image so even though mod n
+
+ align:start position:0%
+its image so even though mod n
+ 
+
+ align:start position:0%
+its image so even though mod n
+restricted to 1 to n is not a Fryman
+
+ align:start position:0%
+restricted to 1 to n is not a Fryman
+ 
+
+ align:start position:0%
+restricted to 1 to n is not a Fryman
+isomorphism of order 2 if I restrict to
+
+ align:start position:0%
+isomorphism of order 2 if I restrict to
+ 
+
+ align:start position:0%
+isomorphism of order 2 if I restrict to
+a subset that's let say contained in
+
+ align:start position:0%
+a subset that's let say contained in
+ 
+
+ align:start position:0%
+a subset that's let say contained in
+some small interval then all the
+
+ align:start position:0%
+some small interval then all the
+ 
+
+ align:start position:0%
+some small interval then all the
+additive structures are preserved ok so
+
+ align:start position:0%
+additive structures are preserved ok so
+ 
+
+ align:start position:0%
+additive structures are preserved ok so
+let me show you why so this is this is
+
+ align:start position:0%
+let me show you why so this is this is
+ 
+
+ align:start position:0%
+let me show you why so this is this is
+not too hard once you get your head
+
+ align:start position:0%
+not too hard once you get your head
+ 
+
+ align:start position:0%
+not too hard once you get your head
+around the definition so indeed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have group elements a 1/2 a s a
+
+ align:start position:0%
+if you have group elements a 1/2 a s a
+ 
+
+ align:start position:0%
+if you have group elements a 1/2 a s a
+prime 1/2 a prime s and if they satisfy
+
+ align:start position:0%
+prime 1/2 a prime s and if they satisfy
+ 
+
+ align:start position:0%
+prime 1/2 a prime s and if they satisfy
+the equation they satisfy this equation
+
+ align:start position:0%
+the equation they satisfy this equation
+ 
+
+ align:start position:0%
+the equation they satisfy this equation
+so we're trying to verify that it is a
+
+ align:start position:0%
+so we're trying to verify that it is a
+ 
+
+ align:start position:0%
+so we're trying to verify that it is a
+Fryman s isomorphism namely the inverse
+
+ align:start position:0%
+Fryman s isomorphism namely the inverse
+ 
+
+ align:start position:0%
+Fryman s isomorphism namely the inverse
+of this map is a Fryman s homomorphism
+
+ align:start position:0%
+of this map is a Fryman s homomorphism
+ 
+
+ align:start position:0%
+of this map is a Fryman s homomorphism
+so if they satisfy this equation so this
+
+ align:start position:0%
+so if they satisfy this equation so this
+ 
+
+ align:start position:0%
+so if they satisfy this equation so this
+is satisfying this interpretation in the
+
+ align:start position:0%
+is satisfying this interpretation in the
+ 
+
+ align:start position:0%
+is satisfying this interpretation in the
+image in Z mod n then note that the
+
+ align:start position:0%
+image in Z mod n then note that the
+ 
+
+ align:start position:0%
+image in Z mod n then note that the
+left-hand side so all of these aids are
+
+ align:start position:0%
+left-hand side so all of these aids are
+ 
+
+ align:start position:0%
+left-hand side so all of these aids are
+contained in a small interval because
+
+ align:start position:0%
+contained in a small interval because
+ 
+
+ align:start position:0%
+contained in a small interval because
+the diameter the set is less than n over
+
+ align:start position:0%
+the diameter the set is less than n over
+ 
+
+ align:start position:0%
+the diameter the set is less than n over
+s so if you look at how big a 1 minus a
+
+ align:start position:0%
+s so if you look at how big a 1 minus a
+ 
+
+ align:start position:0%
+s so if you look at how big a 1 minus a
+1 prime can be which most what's less
+
+ align:start position:0%
+1 prime can be which most what's less
+ 
+
+ align:start position:0%
+1 prime can be which most what's less
+than and whereas in size so the
+
+ align:start position:0%
+than and whereas in size so the
+ 
+
+ align:start position:0%
+than and whereas in size so the
+left-hand side in absolute now viewed as
+
+ align:start position:0%
+left-hand side in absolute now viewed as
+ 
+
+ align:start position:0%
+left-hand side in absolute now viewed as
+an integer so the left-hand side is less
+
+ align:start position:0%
+an integer so the left-hand side is less
+ 
+
+ align:start position:0%
+an integer so the left-hand side is less
+than and in absolute value since the
+
+ align:start position:0%
+than and in absolute value since the
+ 
+
+ align:start position:0%
+than and in absolute value since the
+diameter of a is less than n over s so
+
+ align:start position:0%
+diameter of a is less than n over s so
+ 
+
+ align:start position:0%
+diameter of a is less than n over s so
+you have some number here which is
+
+ align:start position:0%
+you have some number here which is
+ 
+
+ align:start position:0%
+you have some number here which is
+strictly less than any absolute value
+
+ align:start position:0%
+strictly less than any absolute value
+ 
+
+ align:start position:0%
+strictly less than any absolute value
+and this 0 mod n so it must be actually
+
+ align:start position:0%
+and this 0 mod n so it must be actually
+ 
+
+ align:start position:0%
+and this 0 mod n so it must be actually
+equal to 0 as a number as an integer so
+
+ align:start position:0%
+equal to 0 as a number as an integer so
+ 
+
+ align:start position:0%
+equal to 0 as a number as an integer so
+this verifies that the additive
+
+ align:start position:0%
+this verifies that the additive
+ 
+
+ align:start position:0%
+this verifies that the additive
+relations up to sy sums are preserved
+
+ align:start position:0%
+relations up to sy sums are preserved
+ 
+
+ align:start position:0%
+relations up to sy sums are preserved
+under the mod n map if you restrict to a
+
+ align:start position:0%
+under the mod n map if you restrict to a
+ 
+
+ align:start position:0%
+under the mod n map if you restrict to a
+small interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in additive combinatorics we are
+
+ align:start position:0%
+so in additive combinatorics we are
+ 
+
+ align:start position:0%
+so in additive combinatorics we are
+trying to understand you know properties
+
+ align:start position:0%
+trying to understand you know properties
+ 
+
+ align:start position:0%
+trying to understand you know properties
+specific additive properties and the
+
+ align:start position:0%
+specific additive properties and the
+ 
+
+ align:start position:0%
+specific additive properties and the
+notion of Fryman homomorphisms and
+
+ align:start position:0%
+notion of Fryman homomorphisms and
+ 
+
+ align:start position:0%
+notion of Fryman homomorphisms and
+Fryman isomorphism capture in what
+
+ align:start position:0%
+Fryman isomorphism capture in what
+ 
+
+ align:start position:0%
+Fryman isomorphism capture in what
+specific properties we need to study and
+
+ align:start position:0%
+specific properties we need to study and
+ 
+
+ align:start position:0%
+specific properties we need to study and
+what are the maps that preserve those
+
+ align:start position:0%
+what are the maps that preserve those
+ 
+
+ align:start position:0%
+what are the maps that preserve those
+properties and the next thing we will do
+
+ align:start position:0%
+properties and the next thing we will do
+ 
+
+ align:start position:0%
+properties and the next thing we will do
+is to understand this model lemma the
+
+ align:start position:0%
+is to understand this model lemma the
+ 
+
+ align:start position:0%
+is to understand this model lemma the
+modelling lemma that helps us if you
+
+ align:start position:0%
+modelling lemma that helps us if you
+ 
+
+ align:start position:0%
+modelling lemma that helps us if you
+start with a set a with small doubling
+
+ align:start position:0%
+start with a set a with small doubling
+ 
+
+ align:start position:0%
+start with a set a with small doubling
+initially a may be very much spread out
+
+ align:start position:0%
+initially a may be very much spread out
+ 
+
+ align:start position:0%
+initially a may be very much spread out
+in the integers I may have very large
+
+ align:start position:0%
+in the integers I may have very large
+ 
+
+ align:start position:0%
+in the integers I may have very large
+elements very small elements per spread
+
+ align:start position:0%
+elements very small elements per spread
+ 
+
+ align:start position:0%
+elements very small elements per spread
+out but if a has small doubling
+
+ align:start position:0%
+out but if a has small doubling
+ 
+
+ align:start position:0%
+out but if a has small doubling
+properties then I can model a by a small
+
+ align:start position:0%
+properties then I can model a by a small
+ 
+
+ align:start position:0%
+properties then I can model a by a small
+inside a small group such that all the
+
+ align:start position:0%
+inside a small group such that all the
+ 
+
+ align:start position:0%
+inside a small group such that all the
+relevant data namely relative to this
+
+ align:start position:0%
+relevant data namely relative to this
+ 
+
+ align:start position:0%
+relevant data namely relative to this
+Fryman homomorphisms are preserved under
+
+ align:start position:0%
+Fryman homomorphisms are preserved under
+ 
+
+ align:start position:0%
+Fryman homomorphisms are preserved under
+this model okay so let's move on to the
+
+ align:start position:0%
+this model okay so let's move on to the
+ 
+
+ align:start position:0%
+this model okay so let's move on to the
+modeling lemma the main message of the
+
+ align:start position:0%
+modeling lemma the main message of the
+ 
+
+ align:start position:0%
+modeling lemma the main message of the
+modeling lemma is that if a has small
+
+ align:start position:0%
+modeling lemma is that if a has small
+ 
+
+ align:start position:0%
+modeling lemma is that if a has small
+doubling then a can be modeled and here
+
+ align:start position:0%
+doubling then a can be modeled and here
+ 
+
+ align:start position:0%
+doubling then a can be modeled and here
+I mean it's being Fryman isomorphic to a
+
+ align:start position:0%
+I mean it's being Fryman isomorphic to a
+ 
+
+ align:start position:0%
+I mean it's being Fryman isomorphic to a
+subset a small coupe so first as a
+
+ align:start position:0%
+subset a small coupe so first as a
+ 
+
+ align:start position:0%
+subset a small coupe so first as a
+warm-up let's work in the finite field
+
+ align:start position:0%
+warm-up let's work in the finite field
+ 
+
+ align:start position:0%
+warm-up let's work in the finite field
+model just to see what such a result
+
+ align:start position:0%
+model just to see what such a result
+ 
+
+ align:start position:0%
+model just to see what such a result
+looks like and it contains most of the
+
+ align:start position:0%
+looks like and it contains most of the
+ 
+
+ align:start position:0%
+looks like and it contains most of the
+ideas but it's much more clear it's much
+
+ align:start position:0%
+ideas but it's much more clear it's much
+ 
+
+ align:start position:0%
+ideas but it's much more clear it's much
+cleaner than in the integers in the
+
+ align:start position:0%
+cleaner than in the integers in the
+ 
+
+ align:start position:0%
+cleaner than in the integers in the
+finite field model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifically f2 to the end okay so what
+
+ align:start position:0%
+specifically f2 to the end okay so what
+ 
+
+ align:start position:0%
+specifically f2 to the end okay so what
+do we want to say suppose you have a a
+
+ align:start position:0%
+do we want to say suppose you have a a
+ 
+
+ align:start position:0%
+do we want to say suppose you have a a
+subset of f2 to the M and suppose that M
+
+ align:start position:0%
+subset of f2 to the M and suppose that M
+ 
+
+ align:start position:0%
+subset of f2 to the M and suppose that M
+is some number such that 2 to the M yes
+
+ align:start position:0%
+is some number such that 2 to the M yes
+ 
+
+ align:start position:0%
+is some number such that 2 to the M yes
+least as large as si - si okay so
+
+ align:start position:0%
+least as large as si - si okay so
+ 
+
+ align:start position:0%
+least as large as si - si okay so
+remember from clinical Russa you know
+
+ align:start position:0%
+remember from clinical Russa you know
+ 
+
+ align:start position:0%
+remember from clinical Russa you know
+that if a plus a is small then this
+
+ align:start position:0%
+that if a plus a is small then this
+ 
+
+ align:start position:0%
+that if a plus a is small then this
+iterated sum is small so suppose we have
+
+ align:start position:0%
+iterated sum is small so suppose we have
+ 
+
+ align:start position:0%
+iterated sum is small so suppose we have
+these parameters and sets the conclusion
+
+ align:start position:0%
+these parameters and sets the conclusion
+ 
+
+ align:start position:0%
+these parameters and sets the conclusion
+is that a is Fryman s isomorphic to some
+
+ align:start position:0%
+is that a is Fryman s isomorphic to some
+ 
+
+ align:start position:0%
+is that a is Fryman s isomorphic to some
+subset of F 2 raise to M so initially a
+
+ align:start position:0%
+subset of F 2 raise to M so initially a
+ 
+
+ align:start position:0%
+subset of F 2 raise to M so initially a
+is in a potentially very large vector
+
+ align:start position:0%
+is in a potentially very large vector
+ 
+
+ align:start position:0%
+is in a potentially very large vector
+space or it could be all over the place
+
+ align:start position:0%
+space or it could be all over the place
+ 
+
+ align:start position:0%
+space or it could be all over the place
+and what we are trying to say here is
+
+ align:start position:0%
+and what we are trying to say here is
+ 
+
+ align:start position:0%
+and what we are trying to say here is
+that if a has small W so if a small
+
+ align:start position:0%
+that if a has small W so if a small
+ 
+
+ align:start position:0%
+that if a has small W so if a small
+toppling then I plan Ikaruga si - si has
+
+ align:start position:0%
+toppling then I plan Ikaruga si - si has
+ 
+
+ align:start position:0%
+toppling then I plan Ikaruga si - si has
+size not too much bigger than a yourself
+
+ align:start position:0%
+size not too much bigger than a yourself
+ 
+
+ align:start position:0%
+size not too much bigger than a yourself
+only a pound at times size of a itself
+
+ align:start position:0%
+only a pound at times size of a itself
+ 
+
+ align:start position:0%
+only a pound at times size of a itself
+so I can take an M so that the size of
+
+ align:start position:0%
+so I can take an M so that the size of
+ 
+
+ align:start position:0%
+so I can take an M so that the size of
+the scoop there's only a constant factor
+
+ align:start position:0%
+the scoop there's only a constant factor
+ 
+
+ align:start position:0%
+the scoop there's only a constant factor
+large larger than the size of a itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're in a pretty small group so we
+
+ align:start position:0%
+so we're in a pretty small group so we
+ 
+
+ align:start position:0%
+so we're in a pretty small group so we
+are able to model a even though
+
+ align:start position:0%
+are able to model a even though
+ 
+
+ align:start position:0%
+are able to model a even though
+initially it sits inside a pretty large
+
+ align:start position:0%
+initially it sits inside a pretty large
+ 
+
+ align:start position:0%
+initially it sits inside a pretty large
+and being group by some subset in a
+
+ align:start position:0%
+and being group by some subset in a
+ 
+
+ align:start position:0%
+and being group by some subset in a
+pretty small group all right so let's
+
+ align:start position:0%
+pretty small group all right so let's
+ 
+
+ align:start position:0%
+pretty small group all right so let's
+see how to prove this modeling lemma so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the final few setting is much easier to
+
+ align:start position:0%
+the final few setting is much easier to
+ 
+
+ align:start position:0%
+the final few setting is much easier to
+image and start to hard to deal with
+
+ align:start position:0%
+image and start to hard to deal with
+ 
+
+ align:start position:0%
+image and start to hard to deal with
+because we can look at linear maps so
+
+ align:start position:0%
+because we can look at linear maps so
+ 
+
+ align:start position:0%
+because we can look at linear maps so
+the following are equivalent for linear
+
+ align:start position:0%
+the following are equivalent for linear
+ 
+
+ align:start position:0%
+the following are equivalent for linear
+maps of ism's sophie is a Fryman s
+
+ align:start position:0%
+maps of ism's sophie is a Fryman s
+ 
+
+ align:start position:0%
+maps of ism's sophie is a Fryman s
+isomorphism when restricted to a so here
+
+ align:start position:0%
+isomorphism when restricted to a so here
+ 
+
+ align:start position:0%
+isomorphism when restricted to a so here
+fee I'm going to let it be a linear map
+
+ align:start position:0%
+fee I'm going to let it be a linear map
+ 
+
+ align:start position:0%
+fee I'm going to let it be a linear map
+from f2 to the N to f2 to the M the
+
+ align:start position:0%
+from f2 to the N to f2 to the M the
+ 
+
+ align:start position:0%
+from f2 to the N to f2 to the M the
+following following are equivalent so we
+
+ align:start position:0%
+following following are equivalent so we
+ 
+
+ align:start position:0%
+following following are equivalent so we
+were like fee to be a Fryman s
+
+ align:start position:0%
+were like fee to be a Fryman s
+ 
+
+ align:start position:0%
+were like fee to be a Fryman s
+isomorphism when restricted to a so
+
+ align:start position:0%
+isomorphism when restricted to a so
+ 
+
+ align:start position:0%
+isomorphism when restricted to a so
+frightened because this means that or a
+
+ align:start position:0%
+frightened because this means that or a
+ 
+
+ align:start position:0%
+frightened because this means that or a
+restricted a and I restrict to its image
+
+ align:start position:0%
+restricted a and I restrict to its image
+ 
+
+ align:start position:0%
+restricted a and I restrict to its image
+Fryman isomorphic li maps onto the image
+
+ align:start position:0%
+Fryman isomorphic li maps onto the image
+ 
+
+ align:start position:0%
+Fryman isomorphic li maps onto the image
+okay so what does that mean so well if
+
+ align:start position:0%
+okay so what does that mean so well if
+ 
+
+ align:start position:0%
+okay so what does that mean so well if
+as it sophie is already a homomorphism
+
+ align:start position:0%
+as it sophie is already a homomorphism
+ 
+
+ align:start position:0%
+as it sophie is already a homomorphism
+so it's automatically a Fryman s
+
+ align:start position:0%
+so it's automatically a Fryman s
+ 
+
+ align:start position:0%
+so it's automatically a Fryman s
+homomorphism for it to be an S
+
+ align:start position:0%
+homomorphism for it to be an S
+ 
+
+ align:start position:0%
+homomorphism for it to be an S
+isomorphism it just means that there are
+
+ align:start position:0%
+isomorphism it just means that there are
+ 
+
+ align:start position:0%
+isomorphism it just means that there are
+no additional linear relations in the
+
+ align:start position:0%
+no additional linear relations in the
+ 
+
+ align:start position:0%
+no additional linear relations in the
+image that were not present earlier
+
+ align:start position:0%
+image that were not present earlier
+ 
+
+ align:start position:0%
+image that were not present earlier
+which means that P is injective si so
+
+ align:start position:0%
+which means that P is injective si so
+ 
+
+ align:start position:0%
+which means that P is injective si so
+let's just think about the definition
+
+ align:start position:0%
+let's just think about the definition
+ 
+
+ align:start position:0%
+let's just think about the definition
+and in the definition use if you know
+
+ align:start position:0%
+and in the definition use if you know
+ 
+
+ align:start position:0%
+and in the definition use if you know
+additionally that fee is homomorphism
+
+ align:start position:0%
+additionally that fee is homomorphism
+ 
+
+ align:start position:0%
+additionally that fee is homomorphism
+everything is much cleaner it is also
+
+ align:start position:0%
+everything is much cleaner it is also
+ 
+
+ align:start position:0%
+everything is much cleaner it is also
+equivalent to the fee of X
+
+ align:start position:0%
+equivalent to the fee of X
+ 
+
+ align:start position:0%
+equivalent to the fee of X
+is nonzero for every nonzero element
+
+ align:start position:0%
+is nonzero for every nonzero element
+ 
+
+ align:start position:0%
+is nonzero for every nonzero element
+acts of si - si so so this is a very
+
+ align:start position:0%
+acts of si - si so so this is a very
+ 
+
+ align:start position:0%
+acts of si - si so so this is a very
+clean characterization of what it means
+
+ align:start position:0%
+clean characterization of what it means
+ 
+
+ align:start position:0%
+clean characterization of what it means
+to be in Fryman s isomorphism when you
+
+ align:start position:0%
+to be in Fryman s isomorphism when you
+ 
+
+ align:start position:0%
+to be in Fryman s isomorphism when you
+are in an abelian group and you have
+
+ align:start position:0%
+are in an abelian group and you have
+ 
+
+ align:start position:0%
+are in an abelian group and you have
+linear maps homomorphisms so if we start
+
+ align:start position:0%
+linear maps homomorphisms so if we start
+ 
+
+ align:start position:0%
+linear maps homomorphisms so if we start
+by taking si to be a uniformly random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear map so particular so for example
+
+ align:start position:0%
+linear map so particular so for example
+ 
+
+ align:start position:0%
+linear map so particular so for example
+you find you pick a basis and you send
+
+ align:start position:0%
+you find you pick a basis and you send
+ 
+
+ align:start position:0%
+you find you pick a basis and you send
+each basis element to a uniformly random
+
+ align:start position:0%
+each basis element to a uniformly random
+ 
+
+ align:start position:0%
+each basis element to a uniformly random
+element then we find that if QM is at
+
+ align:start position:0%
+element then we find that if QM is at
+ 
+
+ align:start position:0%
+element then we find that if QM is at
+least as a - si then let me call these
+
+ align:start position:0%
+least as a - si then let me call these
+ 
+
+ align:start position:0%
+least as a - si then let me call these
+properties one two three so then the
+
+ align:start position:0%
+properties one two three so then the
+ 
+
+ align:start position:0%
+properties one two three so then the
+probability that three is satisfied is
+
+ align:start position:0%
+probability that three is satisfied is
+ 
+
+ align:start position:0%
+probability that three is satisfied is
+positive because each element of si - si
+
+ align:start position:0%
+positive because each element of si - si
+ 
+
+ align:start position:0%
+positive because each element of si - si
+well I can also ignore zero so each
+
+ align:start position:0%
+well I can also ignore zero so each
+ 
+
+ align:start position:0%
+well I can also ignore zero so each
+nonzero element of si - si is violates
+
+ align:start position:0%
+nonzero element of si - si is violates
+ 
+
+ align:start position:0%
+nonzero element of si - si is violates
+this property with probability exactly 2
+
+ align:start position:0%
+this property with probability exactly 2
+ 
+
+ align:start position:0%
+this property with probability exactly 2
+to the minus n everything's uniform
+
+ align:start position:0%
+to the minus n everything's uniform
+ 
+
+ align:start position:0%
+to the minus n everything's uniform
+so if there are 4 few elements and space
+
+ align:start position:0%
+so if there are 4 few elements and space
+ 
+
+ align:start position:0%
+so if there are 4 few elements and space
+is large enough then the third bullet is
+
+ align:start position:0%
+is large enough then the third bullet is
+ 
+
+ align:start position:0%
+is large enough then the third bullet is
+satisfied with positive probability so
+
+ align:start position:0%
+satisfied with positive probability so
+ 
+
+ align:start position:0%
+satisfied with positive probability so
+you get Fryman s isomorphism any
+
+ align:start position:0%
+you get Fryman s isomorphism any
+ 
+
+ align:start position:0%
+you get Fryman s isomorphism any
+questions listed to get this model in
+
+ align:start position:0%
+questions listed to get this model in
+ 
+
+ align:start position:0%
+questions listed to get this model in
+this case in the finite field setting
+
+ align:start position:0%
+this case in the finite field setting
+ 
+
+ align:start position:0%
+this case in the finite field setting
+it's not so hard so you kind of project
+
+ align:start position:0%
+it's not so hard so you kind of project
+ 
+
+ align:start position:0%
+it's not so hard so you kind of project
+the whole set even though initially you
+
+ align:start position:0%
+the whole set even though initially you
+ 
+
+ align:start position:0%
+the whole set even though initially you
+might have very be very spread out into
+
+ align:start position:0%
+might have very be very spread out into
+ 
+
+ align:start position:0%
+might have very be very spread out into
+a lot of dimensions you projected down
+
+ align:start position:0%
+a lot of dimensions you projected down
+ 
+
+ align:start position:0%
+a lot of dimensions you projected down
+to a small dimensional subspace randomly
+
+ align:start position:0%
+to a small dimensional subspace randomly
+ 
+
+ align:start position:0%
+to a small dimensional subspace randomly
+and that works so that with high
+
+ align:start position:0%
+and that works so that with high
+ 
+
+ align:start position:0%
+and that works so that with high
+probability preserves all the additive
+
+ align:start position:0%
+probability preserves all the additive
+ 
+
+ align:start position:0%
+probability preserves all the additive
+structures that you want provided that
+
+ align:start position:0%
+structures that you want provided that
+ 
+
+ align:start position:0%
+structures that you want provided that
+you have small table now let's look at
+
+ align:start position:0%
+you have small table now let's look at
+ 
+
+ align:start position:0%
+you have small table now let's look at
+what happens in Z so in Z things are a
+
+ align:start position:0%
+what happens in Z so in Z things are a
+ 
+
+ align:start position:0%
+what happens in Z so in Z things are a
+bit more involved but the ideas actually
+
+ align:start position:0%
+bit more involved but the ideas actually
+ 
+
+ align:start position:0%
+bit more involved but the ideas actually
+a lot of the ideas come from this proof
+
+ align:start position:0%
+a lot of the ideas come from this proof
+ 
+
+ align:start position:0%
+a lot of the ideas come from this proof
+as well so rucious multi-link memo tells
+
+ align:start position:0%
+as well so rucious multi-link memo tells
+ 
+
+ align:start position:0%
+as well so rucious multi-link memo tells
+us that if you have a set of integers
+
+ align:start position:0%
+us that if you have a set of integers
+ 
+
+ align:start position:0%
+us that if you have a set of integers
+always a finite set and integers s and n
+
+ align:start position:0%
+always a finite set and integers s and n
+ 
+
+ align:start position:0%
+always a finite set and integers s and n
+are such that n is at least si - si then
+
+ align:start position:0%
+are such that n is at least si - si then
+ 
+
+ align:start position:0%
+are such that n is at least si - si then
+ok so it turns out you might not be able
+
+ align:start position:0%
+ok so it turns out you might not be able
+ 
+
+ align:start position:0%
+ok so it turns out you might not be able
+to model the whole set a but it will be
+
+ align:start position:0%
+to model the whole set a but it will be
+ 
+
+ align:start position:0%
+to model the whole set a but it will be
+good enough for us to model a large
+
+ align:start position:0%
+good enough for us to model a large
+ 
+
+ align:start position:0%
+good enough for us to model a large
+fraction but then there exists a a prime
+
+ align:start position:0%
+fraction but then there exists a a prime
+ 
+
+ align:start position:0%
+fraction but then there exists a a prime
+a prime subset of a with a prime being
+
+ align:start position:0%
+a prime subset of a with a prime being
+ 
+
+ align:start position:0%
+a prime subset of a with a prime being
+at least a mass fraction of the original
+
+ align:start position:0%
+at least a mass fraction of the original
+ 
+
+ align:start position:0%
+at least a mass fraction of the original
+set and a prime is Fryman s isomorphic
+
+ align:start position:0%
+set and a prime is Fryman s isomorphic
+ 
+
+ align:start position:0%
+set and a prime is Fryman s isomorphic
+to a subset of Zemo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so same message as before with extra you
+
+ align:start position:0%
+so same message as before with extra you
+ 
+
+ align:start position:0%
+so same message as before with extra you
+know so with an extra ingredient that we
+
+ align:start position:0%
+know so with an extra ingredient that we
+ 
+
+ align:start position:0%
+know so with an extra ingredient that we
+did not see before but the point is that
+
+ align:start position:0%
+did not see before but the point is that
+ 
+
+ align:start position:0%
+did not see before but the point is that
+if you have a set a with controlled
+
+ align:start position:0%
+if you have a set a with controlled
+ 
+
+ align:start position:0%
+if you have a set a with controlled
+doubling then well now you can take a
+
+ align:start position:0%
+doubling then well now you can take a
+ 
+
+ align:start position:0%
+doubling then well now you can take a
+large fraction of a that is Fryman
+
+ align:start position:0%
+large fraction of a that is Fryman
+ 
+
+ align:start position:0%
+large fraction of a that is Fryman
+isomorphic to a subset of a small group
+
+ align:start position:0%
+isomorphic to a subset of a small group
+ 
+
+ align:start position:0%
+isomorphic to a subset of a small group
+this is small because we only need n to
+
+ align:start position:0%
+this is small because we only need n to
+ 
+
+ align:start position:0%
+this is small because we only need n to
+exceed si - si which only constant
+
+ align:start position:0%
+exceed si - si which only constant
+ 
+
+ align:start position:0%
+exceed si - si which only constant
+factor more than a size of a sir x
+
+ align:start position:0%
+factor more than a size of a sir x
+ 
+
+ align:start position:0%
+factor more than a size of a sir x
+squared around - separating some integer
+
+ align:start position:0%
+squared around - separating some integer
+ 
+
+ align:start position:0%
+squared around - separating some integer
+thank you so in our application s will
+
+ align:start position:0%
+thank you so in our application s will
+ 
+
+ align:start position:0%
+thank you so in our application s will
+be a constant s will be 8 so think of SS
+
+ align:start position:0%
+be a constant s will be 8 so think of SS
+ 
+
+ align:start position:0%
+be a constant s will be 8 so think of SS
+or some specific constant any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's prove this this modelling memo
+
+ align:start position:0%
+so let's prove this this modelling memo
+ 
+
+ align:start position:0%
+so let's prove this this modelling memo
+we want to try to do some kind of random
+
+ align:start position:0%
+we want to try to do some kind of random
+ 
+
+ align:start position:0%
+we want to try to do some kind of random
+map but it's not clear how to start
+
+ align:start position:0%
+map but it's not clear how to start
+ 
+
+ align:start position:0%
+map but it's not clear how to start
+doing a random map if you just start in
+
+ align:start position:0%
+doing a random map if you just start in
+ 
+
+ align:start position:0%
+doing a random map if you just start in
+the integers so what we want to do is
+
+ align:start position:0%
+the integers so what we want to do is
+ 
+
+ align:start position:0%
+the integers so what we want to do is
+first place ourself in some group where
+
+ align:start position:0%
+first place ourself in some group where
+ 
+
+ align:start position:0%
+first place ourself in some group where
+we can consider random autumn or physics
+
+ align:start position:0%
+we can consider random autumn or physics
+ 
+
+ align:start position:0%
+we can consider random autumn or physics
+so we start by perhaps we're very
+
+ align:start position:0%
+so we start by perhaps we're very
+ 
+
+ align:start position:0%
+so we start by perhaps we're very
+wasteful choosing a prime Q bigger than
+
+ align:start position:0%
+wasteful choosing a prime Q bigger than
+ 
+
+ align:start position:0%
+wasteful choosing a prime Q bigger than
+the maximum possible si - si ok so just
+
+ align:start position:0%
+the maximum possible si - si ok so just
+ 
+
+ align:start position:0%
+the maximum possible si - si ok so just
+choose a large enough prime I don't care
+
+ align:start position:0%
+choose a large enough prime I don't care
+ 
+
+ align:start position:0%
+choose a large enough prime I don't care
+how large you pick you can be very very
+
+ align:start position:0%
+how large you pick you can be very very
+ 
+
+ align:start position:0%
+how large you pick you can be very very
+large to pick a prime and now I work
+
+ align:start position:0%
+large to pick a prime and now I work
+ 
+
+ align:start position:0%
+large to pick a prime and now I work
+inside Z mod Q I notice that if make you
+
+ align:start position:0%
+inside Z mod Q I notice that if make you
+ 
+
+ align:start position:0%
+inside Z mod Q I notice that if make you
+large enough then a sits inside Z mod Q
+
+ align:start position:0%
+large enough then a sits inside Z mod Q
+ 
+
+ align:start position:0%
+large enough then a sits inside Z mod Q
+Fryman isomorphic Li s isomorphic Li so
+
+ align:start position:0%
+Fryman isomorphic Li s isomorphic Li so
+ 
+
+ align:start position:0%
+Fryman isomorphic Li s isomorphic Li so
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+take you large enough so that you don't
+
+ align:start position:0%
+take you large enough so that you don't
+ 
+
+ align:start position:0%
+take you large enough so that you don't
+have to worry about any issues so yeah
+
+ align:start position:0%
+have to worry about any issues so yeah
+ 
+
+ align:start position:0%
+have to worry about any issues so yeah
+so the mark you map from A to Z mod Q
+
+ align:start position:0%
+so the mark you map from A to Z mod Q
+ 
+
+ align:start position:0%
+so the mark you map from A to Z mod Q
+right so it's Fryman isomorphic friendly
+
+ align:start position:0%
+right so it's Fryman isomorphic friendly
+ 
+
+ align:start position:0%
+right so it's Fryman isomorphic friendly
+s isomorphic on to its image so let's
+
+ align:start position:0%
+s isomorphic on to its image so let's
+ 
+
+ align:start position:0%
+s isomorphic on to its image so let's
+now consider a sequence of maps and
+
+ align:start position:0%
+now consider a sequence of maps and
+ 
+
+ align:start position:0%
+now consider a sequence of maps and
+we're going to notice sequence so we
+
+ align:start position:0%
+we're going to notice sequence so we
+ 
+
+ align:start position:0%
+we're going to notice sequence so we
+start with Z that's where a originally
+
+ align:start position:0%
+start with Z that's where a originally
+ 
+
+ align:start position:0%
+start with Z that's where a originally
+sets and maps to Z mod Q so that was the
+
+ align:start position:0%
+sets and maps to Z mod Q so that was the
+ 
+
+ align:start position:0%
+sets and maps to Z mod Q so that was the
+first map that we saw and now we want to
+
+ align:start position:0%
+first map that we saw and now we want to
+ 
+
+ align:start position:0%
+first map that we saw and now we want to
+do a random automorphism kind of like
+
+ align:start position:0%
+do a random automorphism kind of like
+ 
+
+ align:start position:0%
+do a random automorphism kind of like
+the random map earlier but in Z mod Q
+
+ align:start position:0%
+the random map earlier but in Z mod Q
+ 
+
+ align:start position:0%
+the random map earlier but in Z mod Q
+there are lots of nice random of
+
+ align:start position:0%
+there are lots of nice random of
+ 
+
+ align:start position:0%
+there are lots of nice random of
+morphisms namely multiplication by some
+
+ align:start position:0%
+morphisms namely multiplication by some
+ 
+
+ align:start position:0%
+morphisms namely multiplication by some
+nonzero element and finally we can
+
+ align:start position:0%
+nonzero element and finally we can
+ 
+
+ align:start position:0%
+nonzero element and finally we can
+consider the representative map where
+
+ align:start position:0%
+consider the representative map where
+ 
+
+ align:start position:0%
+consider the representative map where
+every element of Z mod Q I can associate
+
+ align:start position:0%
+every element of Z mod Q I can associate
+ 
+
+ align:start position:0%
+every element of Z mod Q I can associate
+to it a positive integer from 1 to Q
+
+ align:start position:0%
+to it a positive integer from 1 to Q
+ 
+
+ align:start position:0%
+to it a positive integer from 1 to Q
+which is greased with it so the final
+
+ align:start position:0%
+which is greased with it so the final
+ 
+
+ align:start position:0%
+which is greased with it so the final
+step is not a group homomorphism so so
+
+ align:start position:0%
+step is not a group homomorphism so so
+ 
+
+ align:start position:0%
+step is not a group homomorphism so so
+we need be more careful so let me denote
+
+ align:start position:0%
+we need be more careful so let me denote
+ 
+
+ align:start position:0%
+we need be more careful so let me denote
+by P this entire map right so from the
+
+ align:start position:0%
+by P this entire map right so from the
+ 
+
+ align:start position:0%
+by P this entire map right so from the
+beginning to the end this composition
+
+ align:start position:0%
+beginning to the end this composition
+ 
+
+ align:start position:0%
+beginning to the end this composition
+out to node by C and lambda here some
+
+ align:start position:0%
+out to node by C and lambda here some
+ 
+
+ align:start position:0%
+out to node by C and lambda here some
+element between 1 and Q minus 1 now
+
+ align:start position:0%
+element between 1 and Q minus 1 now
+ 
+
+ align:start position:0%
+element between 1 and Q minus 1 now
+remember what we said earlier that this
+
+ align:start position:0%
+remember what we said earlier that this
+ 
+
+ align:start position:0%
+remember what we said earlier that this
+map this final map here might not be a
+
+ align:start position:0%
+map this final map here might not be a
+ 
+
+ align:start position:0%
+map this final map here might not be a
+Fryman homomorphism because there are
+
+ align:start position:0%
+Fryman homomorphism because there are
+ 
+
+ align:start position:0%
+Fryman homomorphism because there are
+some additive relations here that are
+
+ align:start position:0%
+some additive relations here that are
+ 
+
+ align:start position:0%
+some additive relations here that are
+not preserved over here but if I
+
+ align:start position:0%
+not preserved over here but if I
+ 
+
+ align:start position:0%
+not preserved over here but if I
+restrict myself to a small interval then
+
+ align:start position:0%
+restrict myself to a small interval then
+ 
+
+ align:start position:0%
+restrict myself to a small interval then
+it is a Fryman home or ism if you
+
+ align:start position:0%
+it is a Fryman home or ism if you
+ 
+
+ align:start position:0%
+it is a Fryman home or ism if you
+restrict to that interval if you
+
+ align:start position:0%
+restrict to that interval if you
+ 
+
+ align:start position:0%
+restrict to that interval if you
+restrict yourself to an interval you
+
+ align:start position:0%
+restrict yourself to an interval you
+ 
+
+ align:start position:0%
+restrict yourself to an interval you
+cannot have extra relations over here
+
+ align:start position:0%
+cannot have extra relations over here
+ 
+
+ align:start position:0%
+cannot have extra relations over here
+because they cannot
+
+ align:start position:0%
+because they cannot
+ 
+
+ align:start position:0%
+because they cannot
+of all small enough you can't wrap
+
+ align:start position:0%
+of all small enough you can't wrap
+ 
+
+ align:start position:0%
+of all small enough you can't wrap
+around so let's consider restrictions to
+
+ align:start position:0%
+around so let's consider restrictions to
+ 
+
+ align:start position:0%
+around so let's consider restrictions to
+small intervals but I start with a over
+
+ align:start position:0%
+small intervals but I start with a over
+ 
+
+ align:start position:0%
+small intervals but I start with a over
+here so I want to restrict myself to
+
+ align:start position:0%
+here so I want to restrict myself to
+ 
+
+ align:start position:0%
+here so I want to restrict myself to
+some interval so that I still have lots
+
+ align:start position:0%
+some interval so that I still have lots
+ 
+
+ align:start position:0%
+some interval so that I still have lots
+of a in that restriction and you can do
+
+ align:start position:0%
+of a in that restriction and you can do
+ 
+
+ align:start position:0%
+of a in that restriction and you can do
+this by pigeonhole
+
+ align:start position:0%
+this by pigeonhole
+ 
+
+ align:start position:0%
+this by pigeonhole
+so by pigeonhole for every lambda there
+
+ align:start position:0%
+so by pigeonhole for every lambda there
+ 
+
+ align:start position:0%
+so by pigeonhole for every lambda there
+exists some interval go to Noba and i
+
+ align:start position:0%
+exists some interval go to Noba and i
+ 
+
+ align:start position:0%
+exists some interval go to Noba and i
+sub lambda inside queue okay so the
+
+ align:start position:0%
+sub lambda inside queue okay so the
+ 
+
+ align:start position:0%
+sub lambda inside queue okay so the
+length of this interval will be at most
+
+ align:start position:0%
+length of this interval will be at most
+ 
+
+ align:start position:0%
+length of this interval will be at most
+Q over s such that if I look at the
+
+ align:start position:0%
+Q over s such that if I look at the
+ 
+
+ align:start position:0%
+Q over s such that if I look at the
+restriction of this interval I pull it
+
+ align:start position:0%
+restriction of this interval I pull it
+ 
+
+ align:start position:0%
+restriction of this interval I pull it
+all the way back to the beginning then I
+
+ align:start position:0%
+all the way back to the beginning then I
+ 
+
+ align:start position:0%
+all the way back to the beginning then I
+still get lots of elements of a so a sub
+
+ align:start position:0%
+still get lots of elements of a so a sub
+ 
+
+ align:start position:0%
+still get lots of elements of a so a sub
+lambda in the elements of a whose map
+
+ align:start position:0%
+lambda in the elements of a whose map
+ 
+
+ align:start position:0%
+lambda in the elements of a whose map
+gets sent to this interval has at least
+
+ align:start position:0%
+gets sent to this interval has at least
+ 
+
+ align:start position:0%
+gets sent to this interval has at least
+a over s elements so for instance you
+
+ align:start position:0%
+a over s elements so for instance you
+ 
+
+ align:start position:0%
+a over s elements so for instance you
+can chop up Q into s0 intervals so one
+
+ align:start position:0%
+can chop up Q into s0 intervals so one
+ 
+
+ align:start position:0%
+can chop up Q into s0 intervals so one
+of them will have lots of elements that
+
+ align:start position:0%
+of them will have lots of elements that
+ 
+
+ align:start position:0%
+of them will have lots of elements that
+came from a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is why in the end we only get
+
+ align:start position:0%
+okay this is why in the end we only get
+ 
+
+ align:start position:0%
+okay this is why in the end we only get
+a large subset of da
+
+ align:start position:0%
+a large subset of da
+ 
+
+ align:start position:0%
+a large subset of da
+we're going to forget about everything
+
+ align:start position:0%
+we're going to forget about everything
+ 
+
+ align:start position:0%
+we're going to forget about everything
+else and focus our attention on the set
+
+ align:start position:0%
+else and focus our attention on the set
+ 
+
+ align:start position:0%
+else and focus our attention on the set
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus by our earlier discussion having to
+
+ align:start position:0%
+thus by our earlier discussion having to
+ 
+
+ align:start position:0%
+thus by our earlier discussion having to
+deal with the final map being the Fryman
+
+ align:start position:0%
+deal with the final map being the Fryman
+ 
+
+ align:start position:0%
+deal with the final map being the Fryman
+s homomorphism when you're working
+
+ align:start position:0%
+s homomorphism when you're working
+ 
+
+ align:start position:0%
+s homomorphism when you're working
+inside a short interval we see that fee
+
+ align:start position:0%
+inside a short interval we see that fee
+ 
+
+ align:start position:0%
+inside a short interval we see that fee
+if you restrict to this a sub lambda is
+
+ align:start position:0%
+if you restrict to this a sub lambda is
+ 
+
+ align:start position:0%
+if you restrict to this a sub lambda is
+a Fryman as homomorphism each step is a
+
+ align:start position:0%
+a Fryman as homomorphism each step is a
+ 
+
+ align:start position:0%
+a Fryman as homomorphism each step is a
+Fryman homomorphism because it's a group
+
+ align:start position:0%
+Fryman homomorphism because it's a group
+ 
+
+ align:start position:0%
+Fryman homomorphism because it's a group
+homomorphism and the final step in this
+
+ align:start position:0%
+homomorphism and the final step in this
+ 
+
+ align:start position:0%
+homomorphism and the final step in this
+direction in the restriction is also a
+
+ align:start position:0%
+direction in the restriction is also a
+ 
+
+ align:start position:0%
+direction in the restriction is also a
+Fryman homomorphism from an s
+
+ align:start position:0%
+Fryman homomorphism from an s
+ 
+
+ align:start position:0%
+Fryman homomorphism from an s
+homomorphism because what we said about
+
+ align:start position:0%
+homomorphism because what we said about
+ 
+
+ align:start position:0%
+homomorphism because what we said about
+working inside short intervals okay so
+
+ align:start position:0%
+working inside short intervals okay so
+ 
+
+ align:start position:0%
+working inside short intervals okay so
+so this part is it's very good all right
+
+ align:start position:0%
+so this part is it's very good all right
+ 
+
+ align:start position:0%
+so this part is it's very good all right
+so now let me consider one more
+
+ align:start position:0%
+so now let me consider one more
+ 
+
+ align:start position:0%
+so now let me consider one more
+competition so at the end of the day we
+
+ align:start position:0%
+competition so at the end of the day we
+ 
+
+ align:start position:0%
+competition so at the end of the day we
+would like to model this 8 lambda inside
+
+ align:start position:0%
+would like to model this 8 lambda inside
+ 
+
+ align:start position:0%
+would like to model this 8 lambda inside
+some small circular group so far we
+
+ align:start position:0%
+some small circular group so far we
+ 
+
+ align:start position:0%
+some small circular group so far we
+don't have small circular groups yet but
+
+ align:start position:0%
+don't have small circular groups yet but
+ 
+
+ align:start position:0%
+don't have small circular groups yet but
+I'm going to manufacture a small
+
+ align:start position:0%
+I'm going to manufacture a small
+ 
+
+ align:start position:0%
+I'm going to manufacture a small
+circular group so we're going to
+
+ align:start position:0%
+circular group so we're going to
+ 
+
+ align:start position:0%
+circular group so we're going to
+consider an app where first you take
+
+ align:start position:0%
+consider an app where first you take
+ 
+
+ align:start position:0%
+consider an app where first you take
+that feet all the way until the end and
+
+ align:start position:0%
+that feet all the way until the end and
+ 
+
+ align:start position:0%
+that feet all the way until the end and
+now you take a mod M map so if I don't
+
+ align:start position:0%
+now you take a mod M map so if I don't
+ 
+
+ align:start position:0%
+now you take a mod M map so if I don't
+write anything if it goes to Z mod and
+
+ align:start position:0%
+write anything if it goes to Z mod and
+ 
+
+ align:start position:0%
+write anything if it goes to Z mod and
+it means the mod n map so so let me
+
+ align:start position:0%
+it means the mod n map so so let me
+ 
+
+ align:start position:0%
+it means the mod n map so so let me
+consider feet Asylum can assign which is
+
+ align:start position:0%
+consider feet Asylum can assign which is
+ 
+
+ align:start position:0%
+consider feet Asylum can assign which is
+the composition of these two maps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all right so we would like to say that
+
+ align:start position:0%
+all right so we would like to say that
+ 
+
+ align:start position:0%
+all right so we would like to say that
+you can choose this lambda so that this
+
+ align:start position:0%
+you can choose this lambda so that this
+ 
+
+ align:start position:0%
+you can choose this lambda so that this
+a sub lambda gets mapped Fryman s
+
+ align:start position:0%
+a sub lambda gets mapped Fryman s
+ 
+
+ align:start position:0%
+a sub lambda gets mapped Fryman s
+isomorphic li until to the end so far
+
+ align:start position:0%
+isomorphic li until to the end so far
+ 
+
+ align:start position:0%
+isomorphic li until to the end so far
+everything looks pretty good so you have
+
+ align:start position:0%
+everything looks pretty good so you have
+ 
+
+ align:start position:0%
+everything looks pretty good so you have
+Fryman s homomorphism and you have a
+
+ align:start position:0%
+Fryman s homomorphism and you have a
+ 
+
+ align:start position:0%
+Fryman s homomorphism and you have a
+group homomorphism so you have a so the
+
+ align:start position:0%
+group homomorphism so you have a so the
+ 
+
+ align:start position:0%
+group homomorphism so you have a so the
+whole thing is a Fryman s homomorphism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so see the sign is restricted to a sub
+
+ align:start position:0%
+so see the sign is restricted to a sub
+ 
+
+ align:start position:0%
+so see the sign is restricted to a sub
+lambda is a Fryman s morphism but now
+
+ align:start position:0%
+lambda is a Fryman s morphism but now
+ 
+
+ align:start position:0%
+lambda is a Fryman s morphism but now
+the thing that we really want to check
+
+ align:start position:0%
+the thing that we really want to check
+ 
+
+ align:start position:0%
+the thing that we really want to check
+is if there are some relationships that
+
+ align:start position:0%
+is if there are some relationships that
+ 
+
+ align:start position:0%
+is if there are some relationships that
+are present at the end in Z mod M that
+
+ align:start position:0%
+are present at the end in Z mod M that
+ 
+
+ align:start position:0%
+are present at the end in Z mod M that
+were not present earlier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to check that claim that if
+
+ align:start position:0%
+so we need to check that claim that if
+ 
+
+ align:start position:0%
+so we need to check that claim that if
+sigh there's no map a sub lambda Fryman
+
+ align:start position:0%
+sigh there's no map a sub lambda Fryman
+ 
+
+ align:start position:0%
+sigh there's no map a sub lambda Fryman
+isomorphic Li then something has to have
+
+ align:start position:0%
+isomorphic Li then something has to have
+ 
+
+ align:start position:0%
+isomorphic Li then something has to have
+gone wrong right so if it does not map a
+
+ align:start position:0%
+gone wrong right so if it does not map a
+ 
+
+ align:start position:0%
+gone wrong right so if it does not map a
+lambda
+
+ align:start position:0%
+lambda
+ 
+
+ align:start position:0%
+lambda
+Fryman isomorphic Yeong to its image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so what could have gone wrong claim
+
+ align:start position:0%
+then so what could have gone wrong claim
+ 
+
+ align:start position:0%
+then so what could have gone wrong claim
+that there must be some D which depends
+
+ align:start position:0%
+that there must be some D which depends
+ 
+
+ align:start position:0%
+that there must be some D which depends
+on lambda in si - si and D is not zero
+
+ align:start position:0%
+on lambda in si - si and D is not zero
+ 
+
+ align:start position:0%
+on lambda in si - si and D is not zero
+such that V of T is 0 mod M okay so what
+
+ align:start position:0%
+such that V of T is 0 mod M okay so what
+ 
+
+ align:start position:0%
+such that V of T is 0 mod M okay so what
+prove this you know like before it's
+
+ align:start position:0%
+prove this you know like before it's
+ 
+
+ align:start position:0%
+prove this you know like before it's
+very similar idea to what's happening
+
+ align:start position:0%
+very similar idea to what's happening
+ 
+
+ align:start position:0%
+very similar idea to what's happening
+earlier the idea is that if you have we
+
+ align:start position:0%
+earlier the idea is that if you have we
+ 
+
+ align:start position:0%
+earlier the idea is that if you have we
+want to show that there are no
+
+ align:start position:0%
+want to show that there are no
+ 
+
+ align:start position:0%
+want to show that there are no
+additional additive relations in the
+
+ align:start position:0%
+additional additive relations in the
+ 
+
+ align:start position:0%
+additional additive relations in the
+image so we would like to so if it's
+
+ align:start position:0%
+image so we would like to so if it's
+ 
+
+ align:start position:0%
+image so we would like to so if it's
+none from isomorphism then there has to
+
+ align:start position:0%
+none from isomorphism then there has to
+ 
+
+ align:start position:0%
+none from isomorphism then there has to
+be some accidental collisions and that
+
+ align:start position:0%
+be some accidental collisions and that
+ 
+
+ align:start position:0%
+be some accidental collisions and that
+accident no collision has to be
+
+ align:start position:0%
+accident no collision has to be
+ 
+
+ align:start position:0%
+accident no collision has to be
+witnessed by some D okay so this
+
+ align:start position:0%
+witnessed by some D okay so this
+ 
+
+ align:start position:0%
+witnessed by some D okay so this
+requires some checking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose
+
+ align:start position:0%
+so suppose
+ 
+
+ align:start position:0%
+so suppose
+indeed suppose the hypothesis suppose
+
+ align:start position:0%
+indeed suppose the hypothesis suppose
+ 
+
+ align:start position:0%
+indeed suppose the hypothesis suppose
+that we suppose that the site does not
+
+ align:start position:0%
+that we suppose that the site does not
+ 
+
+ align:start position:0%
+that we suppose that the site does not
+map aesop lambda Prime and s isomorphic
+
+ align:start position:0%
+map aesop lambda Prime and s isomorphic
+ 
+
+ align:start position:0%
+map aesop lambda Prime and s isomorphic
+Li on to its image then there exists a 1
+
+ align:start position:0%
+Li on to its image then there exists a 1
+ 
+
+ align:start position:0%
+Li on to its image then there exists a 1
+to a s a 1 prime to a s Prime in a
+
+ align:start position:0%
+to a s a 1 prime to a s Prime in a
+ 
+
+ align:start position:0%
+to a s a 1 prime to a s Prime in a
+lambda such that they do not have added
+
+ align:start position:0%
+lambda such that they do not have added
+ 
+
+ align:start position:0%
+lambda such that they do not have added
+a relation but their images do have this
+
+ align:start position:0%
+a relation but their images do have this
+ 
+
+ align:start position:0%
+a relation but their images do have this
+additive relation now their images all
+
+ align:start position:0%
+additive relation now their images all
+ 
+
+ align:start position:0%
+additive relation now their images all
+the way in Kotian having the abject
+
+ align:start position:0%
+the way in Kotian having the abject
+ 
+
+ align:start position:0%
+the way in Kotian having the abject
+relation means that fee has this
+
+ align:start position:0%
+relation means that fee has this
+ 
+
+ align:start position:0%
+relation means that fee has this
+additive relation mod M ok so how can
+
+ align:start position:0%
+additive relation mod M ok so how can
+ 
+
+ align:start position:0%
+additive relation mod M ok so how can
+this be recall that since the image so
+
+ align:start position:0%
+this be recall that since the image so
+ 
+
+ align:start position:0%
+this be recall that since the image so
+all of these elements lie inside some
+
+ align:start position:0%
+all of these elements lie inside some
+ 
+
+ align:start position:0%
+all of these elements lie inside some
+short interval the interval has length
+
+ align:start position:0%
+short interval the interval has length
+ 
+
+ align:start position:0%
+short interval the interval has length
+less than 2 minus s ok so we saw this
+
+ align:start position:0%
+less than 2 minus s ok so we saw this
+ 
+
+ align:start position:0%
+less than 2 minus s ok so we saw this
+argument very similar argument earlier
+
+ align:start position:0%
+argument very similar argument earlier
+ 
+
+ align:start position:0%
+argument very similar argument earlier
+in before the break because everything
+
+ align:start position:0%
+in before the break because everything
+ 
+
+ align:start position:0%
+in before the break because everything
+lies in the short interval we see that
+
+ align:start position:0%
+lies in the short interval we see that
+ 
+
+ align:start position:0%
+lies in the short interval we see that
+this difference between the left and
+
+ align:start position:0%
+this difference between the left and
+ 
+
+ align:start position:0%
+this difference between the left and
+right hand sides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this difference is strictly less than Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now by switching the ace and a primes if
+
+ align:start position:0%
+now by switching the ace and a primes if
+ 
+
+ align:start position:0%
+now by switching the ace and a primes if
+necessary we may assume that this
+
+ align:start position:0%
+necessary we may assume that this
+ 
+
+ align:start position:0%
+necessary we may assume that this
+difference is non negative
+
+ align:start position:0%
+difference is non negative
+ 
+
+ align:start position:0%
+difference is non negative
+okay so otherwise it's just a labeling
+
+ align:start position:0%
+okay so otherwise it's just a labeling
+ 
+
+ align:start position:0%
+okay so otherwise it's just a labeling
+issue otherwise I relabeled them so then
+
+ align:start position:0%
+issue otherwise I relabeled them so then
+ 
+
+ align:start position:0%
+issue otherwise I relabeled them so then
+this here so what's inside to this
+
+ align:start position:0%
+this here so what's inside to this
+ 
+
+ align:start position:0%
+this here so what's inside to this
+expression okay so let me hold this
+
+ align:start position:0%
+expression okay so let me hold this
+ 
+
+ align:start position:0%
+expression okay so let me hold this
+expression inside the absolute value
+
+ align:start position:0%
+expression inside the absolute value
+ 
+
+ align:start position:0%
+expression inside the absolute value
+call it start so so then so star some
+
+ align:start position:0%
+call it start so so then so star some
+ 
+
+ align:start position:0%
+call it start so so then so star some
+number between 0 and strictly so at
+
+ align:start position:0%
+number between 0 and strictly so at
+ 
+
+ align:start position:0%
+number between 0 and strictly so at
+least 0 and strictly less than Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we set D to be the okay so DT this
+
+ align:start position:0%
+so if we set D to be the okay so DT this
+ 
+
+ align:start position:0%
+so if we set D to be the okay so DT this
+expressions are sum up so the difference
+
+ align:start position:0%
+expressions are sum up so the difference
+ 
+
+ align:start position:0%
+expressions are sum up so the difference
+between these two sums on one hand the
+
+ align:start position:0%
+between these two sums on one hand the
+ 
+
+ align:start position:0%
+between these two sums on one hand the
+sting here sorry
+
+ align:start position:0%
+sting here sorry
+ 
+
+ align:start position:0%
+sting here sorry
+that's what I want to say suppose you
+
+ align:start position:0%
+that's what I want to say suppose you
+ 
+
+ align:start position:0%
+that's what I want to say suppose you
+don't have an alkie so if you if you are
+
+ align:start position:0%
+don't have an alkie so if you if you are
+ 
+
+ align:start position:0%
+don't have an alkie so if you if you are
+not mapping from an isomorphic leon to
+
+ align:start position:0%
+not mapping from an isomorphic leon to
+ 
+
+ align:start position:0%
+not mapping from an isomorphic leon to
+the image then i can exhibit some
+
+ align:start position:0%
+the image then i can exhibit some
+ 
+
+ align:start position:0%
+the image then i can exhibit some
+witness for that now isomorphism meaning
+
+ align:start position:0%
+witness for that now isomorphism meaning
+ 
+
+ align:start position:0%
+witness for that now isomorphism meaning
+a bunch of elements that do not have
+
+ align:start position:0%
+a bunch of elements that do not have
+ 
+
+ align:start position:0%
+a bunch of elements that do not have
+additive relations in the domain but i
+
+ align:start position:0%
+additive relations in the domain but i
+ 
+
+ align:start position:0%
+additive relations in the domain but i
+do have a little relation in the image
+
+ align:start position:0%
+do have a little relation in the image
+ 
+
+ align:start position:0%
+do have a little relation in the image
+so if we set this D then it's some
+
+ align:start position:0%
+so if we set this D then it's some
+ 
+
+ align:start position:0%
+so if we set this D then it's some
+element of si - si and it's nonzero
+
+ align:start position:0%
+element of si - si and it's nonzero
+ 
+
+ align:start position:0%
+element of si - si and it's nonzero
+because we assume that D is non zero and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then what can we say about fee
+
+ align:start position:0%
+okay so then what can we say about fee
+ 
+
+ align:start position:0%
+okay so then what can we say about fee
+of D so fee FD I claim must be this
+
+ align:start position:0%
+of D so fee FD I claim must be this
+ 
+
+ align:start position:0%
+of D so fee FD I claim must be this
+expression over here the difference of
+
+ align:start position:0%
+expression over here the difference of
+ 
+
+ align:start position:0%
+expression over here the difference of
+the corresponding sums and the image
+
+ align:start position:0%
+the corresponding sums and the image
+ 
+
+ align:start position:0%
+the corresponding sums and the image
+because the two sides are congruent mod
+
+ align:start position:0%
+because the two sides are congruent mod
+ 
+
+ align:start position:0%
+because the two sides are congruent mod
+Q two sides are congruent mod Q and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furthermore they are in the interval
+
+ align:start position:0%
+furthermore they are in the interval
+ 
+
+ align:start position:0%
+furthermore they are in the interval
+from 0 to strictly less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is it's a slightly subtle
+
+ align:start position:0%
+so this is it's a slightly subtle
+ 
+
+ align:start position:0%
+so this is it's a slightly subtle
+argument but the ideas are over simple
+
+ align:start position:0%
+argument but the ideas are over simple
+ 
+
+ align:start position:0%
+argument but the ideas are over simple
+just have to keep track of the
+
+ align:start position:0%
+just have to keep track of the
+ 
+
+ align:start position:0%
+just have to keep track of the
+relationships between what's happening
+
+ align:start position:0%
+relationships between what's happening
+ 
+
+ align:start position:0%
+relationships between what's happening
+in domain what's happening in the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehow I think they find a few cases
+
+ align:start position:0%
+somehow I think they find a few cases
+ 
+
+ align:start position:0%
+somehow I think they find a few cases
+quite illustrative of it there you know
+
+ align:start position:0%
+quite illustrative of it there you know
+ 
+
+ align:start position:0%
+quite illustrative of it there you know
+what goes wrong is similar to what goes
+
+ align:start position:0%
+what goes wrong is similar to what goes
+ 
+
+ align:start position:0%
+what goes wrong is similar to what goes
+wrong here except here you have to keep
+
+ align:start position:0%
+wrong here except here you have to keep
+ 
+
+ align:start position:0%
+wrong here except here you have to keep
+track up in more things okay so
+
+ align:start position:0%
+track up in more things okay so
+ 
+
+ align:start position:0%
+track up in more things okay so
+consequently thus fee of T is congruent
+
+ align:start position:0%
+consequently thus fee of T is congruent
+ 
+
+ align:start position:0%
+consequently thus fee of T is congruent
+to 0 mod M which is what we're looking
+
+ align:start position:0%
+to 0 mod M which is what we're looking
+ 
+
+ align:start position:0%
+to 0 mod M which is what we're looking
+for so that proves the claim any
+
+ align:start position:0%
+for so that proves the claim any
+ 
+
+ align:start position:0%
+for so that proves the claim any
+questions yep okay so so this part so we
+
+ align:start position:0%
+questions yep okay so so this part so we
+ 
+
+ align:start position:0%
+questions yep okay so so this part so we
+said T to be this expression I claim
+
+ align:start position:0%
+said T to be this expression I claim
+ 
+
+ align:start position:0%
+said T to be this expression I claim
+this equality okay so why is the true
+
+ align:start position:0%
+this equality okay so why is the true
+ 
+
+ align:start position:0%
+this equality okay so why is the true
+first the left-hand side and the
+
+ align:start position:0%
+first the left-hand side and the
+ 
+
+ align:start position:0%
+first the left-hand side and the
+right-hand side they they are congruent
+
+ align:start position:0%
+right-hand side they they are congruent
+ 
+
+ align:start position:0%
+right-hand side they they are congruent
+to each other
+
+ align:start position:0%
+to each other
+ 
+
+ align:start position:0%
+to each other
+mount Q okay so why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly if you look at feet where was it
+
+ align:start position:0%
+exactly if you look at feet where was it
+ 
+
+ align:start position:0%
+exactly if you look at feet where was it
+there you see that everything preserves
+
+ align:start position:0%
+there you see that everything preserves
+ 
+
+ align:start position:0%
+there you see that everything preserves
+even though the very last step is not a
+
+ align:start position:0%
+even though the very last step is not a
+ 
+
+ align:start position:0%
+even though the very last step is not a
+group homomorphism mark you is preserved
+
+ align:start position:0%
+group homomorphism mark you is preserved
+ 
+
+ align:start position:0%
+group homomorphism mark you is preserved
+right so even though the last step is
+
+ align:start position:0%
+right so even though the last step is
+ 
+
+ align:start position:0%
+right so even though the last step is
+not cool homo vision it's it is so
+
+ align:start position:0%
+not cool homo vision it's it is so
+ 
+
+ align:start position:0%
+not cool homo vision it's it is so
+marquee so if you're looking at mark you
+
+ align:start position:0%
+marquee so if you're looking at mark you
+ 
+
+ align:start position:0%
+marquee so if you're looking at mark you
+everything is cool homomorphism so so
+
+ align:start position:0%
+everything is cool homomorphism so so
+ 
+
+ align:start position:0%
+everything is cool homomorphism so so
+here we're good both are in this
+
+ align:start position:0%
+here we're good both are in this
+ 
+
+ align:start position:0%
+here we're good both are in this
+interval the right hand side is in the
+
+ align:start position:0%
+interval the right hand side is in the
+ 
+
+ align:start position:0%
+interval the right hand side is in the
+interval because of our sumption about
+
+ align:start position:0%
+interval because of our sumption about
+ 
+
+ align:start position:0%
+interval because of our sumption about
+short everything living inside a short
+
+ align:start position:0%
+short everything living inside a short
+ 
+
+ align:start position:0%
+short everything living inside a short
+interval and the left hand side is by
+
+ align:start position:0%
+interval and the left hand side is by
+ 
+
+ align:start position:0%
+interval and the left hand side is by
+definition because the image of feet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's in that interval so especially
+
+ align:start position:0%
+okay it's in that interval so especially
+ 
+
+ align:start position:0%
+okay it's in that interval so especially
+if given that B is not equal to zero
+
+ align:start position:0%
+if given that B is not equal to zero
+ 
+
+ align:start position:0%
+if given that B is not equal to zero
+okay okay yeah so it's it's not hard but
+
+ align:start position:0%
+okay okay yeah so it's it's not hard but
+ 
+
+ align:start position:0%
+okay okay yeah so it's it's not hard but
+it's a bit confusing so think about it
+
+ align:start position:0%
+it's a bit confusing so think about it
+ 
+
+ align:start position:0%
+it's a bit confusing so think about it
+alright
+
+ align:start position:0%
+alright
+ 
+
+ align:start position:0%
+alright
+so we're almost done so we're almost on
+
+ align:start position:0%
+so we're almost done so we're almost on
+ 
+
+ align:start position:0%
+so we're almost done so we're almost on
+improving the Fryman so the Arusha
+
+ align:start position:0%
+improving the Fryman so the Arusha
+ 
+
+ align:start position:0%
+improving the Fryman so the Arusha
+modeling lemma in in Z mod n so let me
+
+ align:start position:0%
+modeling lemma in in Z mod n so let me
+ 
+
+ align:start position:0%
+modeling lemma in in Z mod n so let me
+finish off the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for each so for each nonzero D in
+
+ align:start position:0%
+so for each so for each nonzero D in
+ 
+
+ align:start position:0%
+so for each so for each nonzero D in
+this iterated some set we basically we
+
+ align:start position:0%
+this iterated some set we basically we
+ 
+
+ align:start position:0%
+this iterated some set we basically we
+would like to pick a lambda so that that
+
+ align:start position:0%
+would like to pick a lambda so that that
+ 
+
+ align:start position:0%
+would like to pick a lambda so that that
+map up there does what we want to do if
+
+ align:start position:0%
+map up there does what we want to do if
+ 
+
+ align:start position:0%
+map up there does what we want to do if
+it doesn't do what we want to do then
+
+ align:start position:0%
+it doesn't do what we want to do then
+ 
+
+ align:start position:0%
+it doesn't do what we want to do then
+it's witnessed by some D like this those
+
+ align:start position:0%
+it's witnessed by some D like this those
+ 
+
+ align:start position:0%
+it's witnessed by some D like this those
+are in the path lambda so that if there
+
+ align:start position:0%
+are in the path lambda so that if there
+ 
+
+ align:start position:0%
+are in the path lambda so that if there
+exists a D then this lambda is bad
+
+ align:start position:0%
+exists a D then this lambda is bad
+ 
+
+ align:start position:0%
+exists a D then this lambda is bad
+so for each D that potentially witnessed
+
+ align:start position:0%
+so for each D that potentially witnessed
+ 
+
+ align:start position:0%
+so for each D that potentially witnessed
+some bad lambda B number path lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I such that P Q V of P is
+
+ align:start position:0%
+okay so I such that P Q V of P is
+ 
+
+ align:start position:0%
+okay so I such that P Q V of P is
+congruent to 0 so here we're no longer
+
+ align:start position:0%
+congruent to 0 so here we're no longer
+ 
+
+ align:start position:0%
+congruent to 0 so here we're no longer
+even thinking about the group for
+
+ align:start position:0%
+even thinking about the group for
+ 
+
+ align:start position:0%
+even thinking about the group for
+morphisms anymore order or the Fryman
+
+ align:start position:0%
+morphisms anymore order or the Fryman
+ 
+
+ align:start position:0%
+morphisms anymore order or the Fryman
+homomorphisms just the question if I
+
+ align:start position:0%
+homomorphisms just the question if I
+ 
+
+ align:start position:0%
+homomorphisms just the question if I
+give you a nonzero integer
+
+ align:start position:0%
+give you a nonzero integer
+ 
+
+ align:start position:0%
+give you a nonzero integer
+how many lambdas are there so that P of
+
+ align:start position:0%
+how many lambdas are there so that P of
+ 
+
+ align:start position:0%
+how many lambdas are there so that P of
+P is divisible by M remember that we
+
+ align:start position:0%
+P is divisible by M remember that we
+ 
+
+ align:start position:0%
+P is divisible by M remember that we
+picked Q large enough so that initially
+
+ align:start position:0%
+picked Q large enough so that initially
+ 
+
+ align:start position:0%
+picked Q large enough so that initially
+you know you are sitting very much
+
+ align:start position:0%
+you know you are sitting very much
+ 
+
+ align:start position:0%
+you know you are sitting very much
+inside this everything's everything's
+
+ align:start position:0%
+inside this everything's everything's
+ 
+
+ align:start position:0%
+inside this everything's everything's
+really between 0 and Q so this dot
+
+ align:start position:0%
+really between 0 and Q so this dot
+ 
+
+ align:start position:0%
+really between 0 and Q so this dot
+lambda up there acts uniformly so the
+
+ align:start position:0%
+lambda up there acts uniformly so the
+ 
+
+ align:start position:0%
+lambda up there acts uniformly so the
+number of such paths lambdas is exactly
+
+ align:start position:0%
+number of such paths lambdas is exactly
+ 
+
+ align:start position:0%
+number of such paths lambdas is exactly
+the number of elements in this interval
+
+ align:start position:0%
+the number of elements in this interval
+ 
+
+ align:start position:0%
+the number of elements in this interval
+that are divisible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by EM so everything's more or less a by
+
+ align:start position:0%
+by EM so everything's more or less a by
+ 
+
+ align:start position:0%
+by EM so everything's more or less a by
+gesture if you restrict to the right
+
+ align:start position:0%
+gesture if you restrict to the right
+ 
+
+ align:start position:0%
+gesture if you restrict to the right
+places and the number of such elements
+
+ align:start position:0%
+places and the number of such elements
+ 
+
+ align:start position:0%
+places and the number of such elements
+it's at most Q minus 1 over m so
+
+ align:start position:0%
+it's at most Q minus 1 over m so
+ 
+
+ align:start position:0%
+it's at most Q minus 1 over m so
+therefore the total number of paths
+
+ align:start position:0%
+therefore the total number of paths
+ 
+
+ align:start position:0%
+therefore the total number of paths
+lambdas is at most for each element D of
+
+ align:start position:0%
+lambdas is at most for each element D of
+ 
+
+ align:start position:0%
+lambdas is at most for each element D of
+si - si a nonzero element we have a most
+
+ align:start position:0%
+si - si a nonzero element we have a most
+ 
+
+ align:start position:0%
+si - si a nonzero element we have a most
+Q minus 1 over m bad lambdas so the
+
+ align:start position:0%
+Q minus 1 over m bad lambdas so the
+ 
+
+ align:start position:0%
+Q minus 1 over m bad lambdas so the
+total number of paths lambdas is
+
+ align:start position:0%
+total number of paths lambdas is
+ 
+
+ align:start position:0%
+total number of paths lambdas is
+strictly less than Q minus 1 so there
+
+ align:start position:0%
+strictly less than Q minus 1 so there
+ 
+
+ align:start position:0%
+strictly less than Q minus 1 so there
+exists some lambda such that sy when
+
+ align:start position:0%
+exists some lambda such that sy when
+ 
+
+ align:start position:0%
+exists some lambda such that sy when
+restricted to a sub lambda maps homo
+
+ align:start position:0%
+restricted to a sub lambda maps homo
+ 
+
+ align:start position:0%
+restricted to a sub lambda maps homo
+Fryman s isomorphic tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+somehow I think it's really the same
+
+ align:start position:0%
+somehow I think it's really the same
+ 
+
+ align:start position:0%
+somehow I think it's really the same
+kind of professor why in the finite fuel
+
+ align:start position:0%
+kind of professor why in the finite fuel
+ 
+
+ align:start position:0%
+kind of professor why in the finite fuel
+case except you have this extra wrinkle
+
+ align:start position:0%
+case except you have this extra wrinkle
+ 
+
+ align:start position:0%
+case except you have this extra wrinkle
+about restricting to short diameter
+
+ align:start position:0%
+about restricting to short diameter
+ 
+
+ align:start position:0%
+about restricting to short diameter
+intervals to short intervals but the
+
+ align:start position:0%
+intervals to short intervals but the
+ 
+
+ align:start position:0%
+intervals to short intervals but the
+idea is very similar okay so that's the
+
+ align:start position:0%
+idea is very similar okay so that's the
+ 
+
+ align:start position:0%
+idea is very similar okay so that's the
+Fryman model lemma in the integers and
+
+ align:start position:0%
+Fryman model lemma in the integers and
+ 
+
+ align:start position:0%
+Fryman model lemma in the integers and
+let me summarize what we know so far
+
+ align:start position:0%
+let me summarize what we know so far
+ 
+
+ align:start position:0%
+let me summarize what we know so far
+and so that they give you a sense of
+
+ align:start position:0%
+and so that they give you a sense of
+ 
+
+ align:start position:0%
+and so that they give you a sense of
+where we're going in the proof of
+
+ align:start position:0%
+where we're going in the proof of
+ 
+
+ align:start position:0%
+where we're going in the proof of
+Freeman's theorem so what we know so far
+
+ align:start position:0%
+Freeman's theorem so what we know so far
+ 
+
+ align:start position:0%
+Freeman's theorem so what we know so far
+is that if you have a subset of integers
+
+ align:start position:0%
+is that if you have a subset of integers
+ 
+
+ align:start position:0%
+is that if you have a subset of integers
+a finite subset such that a plus a this
+
+ align:start position:0%
+a finite subset such that a plus a this
+ 
+
+ align:start position:0%
+a finite subset such that a plus a this
+size eight times okay and most doubling
+
+ align:start position:0%
+size eight times okay and most doubling
+ 
+
+ align:start position:0%
+size eight times okay and most doubling
+constant at most K then there exists
+
+ align:start position:0%
+constant at most K then there exists
+ 
+
+ align:start position:0%
+constant at most K then there exists
+some prime and at most 2k to the 16th
+
+ align:start position:0%
+some prime and at most 2k to the 16th
+ 
+
+ align:start position:0%
+some prime and at most 2k to the 16th
+times the size of a and some subset a
+
+ align:start position:0%
+times the size of a and some subset a
+ 
+
+ align:start position:0%
+times the size of a and some subset a
+prime of a such that a prime is prime
+
+ align:start position:0%
+prime of a such that a prime is prime
+ 
+
+ align:start position:0%
+prime of a such that a prime is prime
+and a isomorphic to a subset of Z mod n
+
+ align:start position:0%
+and a isomorphic to a subset of Z mod n
+ 
+
+ align:start position:0%
+and a isomorphic to a subset of Z mod n
+Z follows from two things we've seen so
+
+ align:start position:0%
+Z follows from two things we've seen so
+ 
+
+ align:start position:0%
+Z follows from two things we've seen so
+far because by the political lúcia
+
+ align:start position:0%
+far because by the political lúcia
+ 
+
+ align:start position:0%
+far because by the political lúcia
+inequality an a minus a a is and most K
+
+ align:start position:0%
+inequality an a minus a a is and most K
+ 
+
+ align:start position:0%
+inequality an a minus a a is and most K
+to the 16 times a and now we can choose
+
+ align:start position:0%
+to the 16 times a and now we can choose
+ 
+
+ align:start position:0%
+to the 16 times a and now we can choose
+a prime and between K to the 16 and 2
+
+ align:start position:0%
+a prime and between K to the 16 and 2
+ 
+
+ align:start position:0%
+a prime and between K to the 16 and 2
+times K turn 16 and apply the modeling
+
+ align:start position:0%
+times K turn 16 and apply the modeling
+ 
+
+ align:start position:0%
+times K turn 16 and apply the modeling
+lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's where we are at so you
+
+ align:start position:0%
+okay so that's where we are at so you
+ 
+
+ align:start position:0%
+okay so that's where we are at so you
+start with a set of integers with small
+
+ align:start position:0%
+start with a set of integers with small
+ 
+
+ align:start position:0%
+start with a set of integers with small
+doubling then we can conclude that by
+
+ align:start position:0%
+doubling then we can conclude that by
+ 
+
+ align:start position:0%
+doubling then we can conclude that by
+keeping a large fraction of a keeping I
+
+ align:start position:0%
+keeping a large fraction of a keeping I
+ 
+
+ align:start position:0%
+keeping a large fraction of a keeping I
+forgot to okay so very important so
+
+ align:start position:0%
+forgot to okay so very important so
+ 
+
+ align:start position:0%
+forgot to okay so very important so
+there exists some eight which is a large
+
+ align:start position:0%
+there exists some eight which is a large
+ 
+
+ align:start position:0%
+there exists some eight which is a large
+fraction so keeping a large fraction of
+
+ align:start position:0%
+fraction so keeping a large fraction of
+ 
+
+ align:start position:0%
+fraction so keeping a large fraction of
+a I can model this large subset of a by
+
+ align:start position:0%
+a I can model this large subset of a by
+ 
+
+ align:start position:0%
+a I can model this large subset of a by
+some subset of a cyclic group where the
+
+ align:start position:0%
+some subset of a cyclic group where the
+ 
+
+ align:start position:0%
+some subset of a cyclic group where the
+size of the cyclic group is only a
+
+ align:start position:0%
+size of the cyclic group is only a
+ 
+
+ align:start position:0%
+size of the cyclic group is only a
+constant times more than a size of a so
+
+ align:start position:0%
+constant times more than a size of a so
+ 
+
+ align:start position:0%
+constant times more than a size of a so
+now we are going to work inside a cyclic
+
+ align:start position:0%
+now we are going to work inside a cyclic
+ 
+
+ align:start position:0%
+now we are going to work inside a cyclic
+group and working with a set inside a
+
+ align:start position:0%
+group and working with a set inside a
+ 
+
+ align:start position:0%
+group and working with a set inside a
+cyclic group that's a constant size a
+
+ align:start position:0%
+cyclic group that's a constant size a
+ 
+
+ align:start position:0%
+cyclic group that's a constant size a
+constant fraction of the cyclic group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question is why eight okay so that will
+
+ align:start position:0%
+question is why eight okay so that will
+ 
+
+ align:start position:0%
+question is why eight okay so that will
+come up later okay so basically you need
+
+ align:start position:0%
+come up later okay so basically you need
+ 
+
+ align:start position:0%
+come up later okay so basically you need
+to choose some number so that you want
+
+ align:start position:0%
+to choose some number so that you want
+ 
+
+ align:start position:0%
+to choose some number so that you want
+to preserve the structure of G a piece
+
+ align:start position:0%
+to preserve the structure of G a piece
+ 
+
+ align:start position:0%
+to preserve the structure of G a piece
+so that will come up later and now we're
+
+ align:start position:0%
+so that will come up later and now we're
+ 
+
+ align:start position:0%
+so that will come up later and now we're
+inside a cyclic group and you have a
+
+ align:start position:0%
+inside a cyclic group and you have a
+ 
+
+ align:start position:0%
+inside a cyclic group and you have a
+constant fraction of a cyclic group
+
+ align:start position:0%
+constant fraction of a cyclic group
+ 
+
+ align:start position:0%
+constant fraction of a cyclic group
+where have we seen this before okay so
+
+ align:start position:0%
+where have we seen this before okay so
+ 
+
+ align:start position:0%
+where have we seen this before okay so
+when we proved Roth's theorem I so that
+
+ align:start position:0%
+when we proved Roth's theorem I so that
+ 
+
+ align:start position:0%
+when we proved Roth's theorem I so that
+was the setting so you're in a sick loop
+
+ align:start position:0%
+was the setting so you're in a sick loop
+ 
+
+ align:start position:0%
+was the setting so you're in a sick loop
+you have a constant fraction the
+
+ align:start position:0%
+you have a constant fraction the
+ 
+
+ align:start position:0%
+you have a constant fraction the
+circular group and you can do Fourier
+
+ align:start position:0%
+circular group and you can do Fourier
+ 
+
+ align:start position:0%
+circular group and you can do Fourier
+analysis so initially you cannot do
+
+ align:start position:0%
+analysis so initially you cannot do
+ 
+
+ align:start position:0%
+analysis so initially you cannot do
+Fourier analysis in just starting with
+
+ align:start position:0%
+Fourier analysis in just starting with
+ 
+
+ align:start position:0%
+Fourier analysis in just starting with
+Fryman Sturm because the set may be very
+
+ align:start position:0%
+Fryman Sturm because the set may be very
+ 
+
+ align:start position:0%
+Fryman Sturm because the set may be very
+very spread out but now you are a large
+
+ align:start position:0%
+very spread out but now you are a large
+ 
+
+ align:start position:0%
+very spread out but now you are a large
+fraction of a cyclic group so we're
+
+ align:start position:0%
+fraction of a cyclic group so we're
+ 
+
+ align:start position:0%
+fraction of a cyclic group so we're
+going to do Fourier analysis next time
+
+ align:start position:0%
+going to do Fourier analysis next time
+ 
+
+ align:start position:0%
+going to do Fourier analysis next time
+to show that such a set must contain
+
+ align:start position:0%
+to show that such a set must contain
+ 
+
+ align:start position:0%
+to show that such a set must contain
+lots of structure just from the fact
+
+ align:start position:0%
+lots of structure just from the fact
+ 
+
+ align:start position:0%
+lots of structure just from the fact
+that it is large so that will be the
+
+ align:start position:0%
+that it is large so that will be the
+ 
+
+ align:start position:0%
+that it is large so that will be the
+next set good happy Thanksgiving
\ No newline at end of file
diff --git a/ThP6wQkf5ec.txt b/ThP6wQkf5ec.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9da72d3a50ce15876337e046fada881269e52c38
--- /dev/null
+++ b/ThP6wQkf5ec.txt
@@ -0,0 +1,2355 @@
+align:start position:0%
+ 
+a pivoted rod held horizontal parallel
+
+ align:start position:0%
+a pivoted rod held horizontal parallel
+ 
+
+ align:start position:0%
+a pivoted rod held horizontal parallel
+to the ground and released from rest
+
+ align:start position:0%
+to the ground and released from rest
+ 
+
+ align:start position:0%
+to the ground and released from rest
+will simply fall rotating about the
+
+ align:start position:0%
+will simply fall rotating about the
+ 
+
+ align:start position:0%
+will simply fall rotating about the
+pivot point in particular suppose we
+
+ align:start position:0%
+pivot point in particular suppose we
+ 
+
+ align:start position:0%
+pivot point in particular suppose we
+have a mass attached to one end of a
+
+ align:start position:0%
+have a mass attached to one end of a
+ 
+
+ align:start position:0%
+have a mass attached to one end of a
+pivoted rod so here's my pivot here's my
+
+ align:start position:0%
+pivoted rod so here's my pivot here's my
+ 
+
+ align:start position:0%
+pivoted rod so here's my pivot here's my
+pivoted rod which we'll assume is
+
+ align:start position:0%
+pivoted rod which we'll assume is
+ 
+
+ align:start position:0%
+pivoted rod which we'll assume is
+massless and I have and it has a length
+
+ align:start position:0%
+massless and I have and it has a length
+ 
+
+ align:start position:0%
+massless and I have and it has a length
+D and I attached a mass M to one end if
+
+ align:start position:0%
+D and I attached a mass M to one end if
+ 
+
+ align:start position:0%
+D and I attached a mass M to one end if
+I let this go from rest it will simply
+
+ align:start position:0%
+I let this go from rest it will simply
+ 
+
+ align:start position:0%
+I let this go from rest it will simply
+fall rotating about the pivot point
+
+ align:start position:0%
+fall rotating about the pivot point
+ 
+
+ align:start position:0%
+fall rotating about the pivot point
+which I'll call s and it's easy to
+
+ align:start position:0%
+which I'll call s and it's easy to
+ 
+
+ align:start position:0%
+which I'll call s and it's easy to
+understand that in terms of the action
+
+ align:start position:0%
+understand that in terms of the action
+ 
+
+ align:start position:0%
+understand that in terms of the action
+of gravity which is acting downwards and
+
+ align:start position:0%
+of gravity which is acting downwards and
+ 
+
+ align:start position:0%
+of gravity which is acting downwards and
+the resulting torque about point s if I
+
+ align:start position:0%
+the resulting torque about point s if I
+ 
+
+ align:start position:0%
+the resulting torque about point s if I
+replace this point mass with a wheel of
+
+ align:start position:0%
+replace this point mass with a wheel of
+ 
+
+ align:start position:0%
+replace this point mass with a wheel of
+the same mass so in this disk is a wheel
+
+ align:start position:0%
+the same mass so in this disk is a wheel
+ 
+
+ align:start position:0%
+the same mass so in this disk is a wheel
+with let's say a radius R and the same
+
+ align:start position:0%
+with let's say a radius R and the same
+ 
+
+ align:start position:0%
+with let's say a radius R and the same
+mass M attached to a pivoted rod the rod
+
+ align:start position:0%
+mass M attached to a pivoted rod the rod
+ 
+
+ align:start position:0%
+mass M attached to a pivoted rod the rod
+is massless and has length D if I hold
+
+ align:start position:0%
+is massless and has length D if I hold
+ 
+
+ align:start position:0%
+is massless and has length D if I hold
+this horizontal parallel to the ground
+
+ align:start position:0%
+this horizontal parallel to the ground
+ 
+
+ align:start position:0%
+this horizontal parallel to the ground
+and release it from rest it will still
+
+ align:start position:0%
+and release it from rest it will still
+ 
+
+ align:start position:0%
+and release it from rest it will still
+just fall to the ground not a surprising
+
+ align:start position:0%
+just fall to the ground not a surprising
+ 
+
+ align:start position:0%
+just fall to the ground not a surprising
+result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is surprising is if I then spin up
+
+ align:start position:0%
+what is surprising is if I then spin up
+ 
+
+ align:start position:0%
+what is surprising is if I then spin up
+the wheel so if I have the wheel on
+
+ align:start position:0%
+the wheel so if I have the wheel on
+ 
+
+ align:start position:0%
+the wheel so if I have the wheel on
+rotating about its axle with some large
+
+ align:start position:0%
+rotating about its axle with some large
+ 
+
+ align:start position:0%
+rotating about its axle with some large
+angular velocity little Omega and then I
+
+ align:start position:0%
+angular velocity little Omega and then I
+ 
+
+ align:start position:0%
+angular velocity little Omega and then I
+hold it horizontal parallel to the
+
+ align:start position:0%
+hold it horizontal parallel to the
+ 
+
+ align:start position:0%
+hold it horizontal parallel to the
+ground and release it from rest then
+
+ align:start position:0%
+ground and release it from rest then
+ 
+
+ align:start position:0%
+ground and release it from rest then
+remarkably this wheel Plus axle will not
+
+ align:start position:0%
+remarkably this wheel Plus axle will not
+ 
+
+ align:start position:0%
+remarkably this wheel Plus axle will not
+fall it will remain horizontal parallel
+
+ align:start position:0%
+fall it will remain horizontal parallel
+ 
+
+ align:start position:0%
+fall it will remain horizontal parallel
+to the ground but the center of mass of
+
+ align:start position:0%
+to the ground but the center of mass of
+ 
+
+ align:start position:0%
+to the ground but the center of mass of
+the wheel will execute a small circular
+
+ align:start position:0%
+the wheel will execute a small circular
+ 
+
+ align:start position:0%
+the wheel will execute a small circular
+orbit about the vertical axis through
+
+ align:start position:0%
+orbit about the vertical axis through
+ 
+
+ align:start position:0%
+orbit about the vertical axis through
+the pivot point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this remarkable and very non-intuitive
+
+ align:start position:0%
+this remarkable and very non-intuitive
+ 
+
+ align:start position:0%
+this remarkable and very non-intuitive
+motion is called precession and the
+
+ align:start position:0%
+motion is called precession and the
+ 
+
+ align:start position:0%
+motion is called precession and the
+system that's undergoing precession is
+
+ align:start position:0%
+system that's undergoing precession is
+ 
+
+ align:start position:0%
+system that's undergoing precession is
+called a gyroscope let's see if we can
+
+ align:start position:0%
+called a gyroscope let's see if we can
+ 
+
+ align:start position:0%
+called a gyroscope let's see if we can
+understand this behavior in terms of the
+
+ align:start position:0%
+understand this behavior in terms of the
+ 
+
+ align:start position:0%
+understand this behavior in terms of the
+angular momentum of the system so what
+
+ align:start position:0%
+angular momentum of the system so what
+ 
+
+ align:start position:0%
+angular momentum of the system so what
+I've drawn here is a side view of the
+
+ align:start position:0%
+I've drawn here is a side view of the
+ 
+
+ align:start position:0%
+I've drawn here is a side view of the
+system so let's define some coordinates
+
+ align:start position:0%
+system so let's define some coordinates
+ 
+
+ align:start position:0%
+system so let's define some coordinates
+so we have our hat in the radial outward
+
+ align:start position:0%
+so we have our hat in the radial outward
+ 
+
+ align:start position:0%
+so we have our hat in the radial outward
+Direction K hat in the direction of the
+
+ align:start position:0%
+Direction K hat in the direction of the
+ 
+
+ align:start position:0%
+Direction K hat in the direction of the
+z axis the vertical axis and then we'll
+
+ align:start position:0%
+z axis the vertical axis and then we'll
+ 
+
+ align:start position:0%
+z axis the vertical axis and then we'll
+define theta hat pointing into the
+
+ align:start position:0%
+define theta hat pointing into the
+ 
+
+ align:start position:0%
+define theta hat pointing into the
+screen okay so that's a side view I'd
+
+ align:start position:0%
+screen okay so that's a side view I'd
+ 
+
+ align:start position:0%
+screen okay so that's a side view I'd
+like to now draw a top view so let's say
+
+ align:start position:0%
+like to now draw a top view so let's say
+ 
+
+ align:start position:0%
+like to now draw a top view so let's say
+we're looking down along the z axis from
+
+ align:start position:0%
+we're looking down along the z axis from
+ 
+
+ align:start position:0%
+we're looking down along the z axis from
+the top on the system so now here's my
+
+ align:start position:0%
+the top on the system so now here's my
+ 
+
+ align:start position:0%
+the top on the system so now here's my
+pivot point and here is a top view of my
+
+ align:start position:0%
+pivot point and here is a top view of my
+ 
+
+ align:start position:0%
+pivot point and here is a top view of my
+wheel okay again this is a distance D
+
+ align:start position:0%
+wheel okay again this is a distance D
+ 
+
+ align:start position:0%
+wheel okay again this is a distance D
+now this is still the R hat direction
+
+ align:start position:0%
+now this is still the R hat direction
+ 
+
+ align:start position:0%
+now this is still the R hat direction
+this is the theta hat direction and the
+
+ align:start position:0%
+this is the theta hat direction and the
+ 
+
+ align:start position:0%
+this is the theta hat direction and the
+K hat direction is pointing out of the
+
+ align:start position:0%
+K hat direction is pointing out of the
+ 
+
+ align:start position:0%
+K hat direction is pointing out of the
+screen let's draw the forces acting on
+
+ align:start position:0%
+screen let's draw the forces acting on
+ 
+
+ align:start position:0%
+screen let's draw the forces acting on
+our diagram here so the weight is acting
+
+ align:start position:0%
+our diagram here so the weight is acting
+ 
+
+ align:start position:0%
+our diagram here so the weight is acting
+at the center of mass of the wheel
+
+ align:start position:0%
+at the center of mass of the wheel
+ 
+
+ align:start position:0%
+at the center of mass of the wheel
+that's mg downward and there's a normal
+
+ align:start position:0%
+that's mg downward and there's a normal
+ 
+
+ align:start position:0%
+that's mg downward and there's a normal
+force acting upwards at the pivot point
+
+ align:start position:0%
+force acting upwards at the pivot point
+ 
+
+ align:start position:0%
+force acting upwards at the pivot point
+the torque is just given by R cross F
+
+ align:start position:0%
+the torque is just given by R cross F
+ 
+
+ align:start position:0%
+the torque is just given by R cross F
+and so relative to point s at the
+
+ align:start position:0%
+and so relative to point s at the
+ 
+
+ align:start position:0%
+and so relative to point s at the
+distance D times the weight mg so the
+
+ align:start position:0%
+distance D times the weight mg so the
+ 
+
+ align:start position:0%
+distance D times the weight mg so the
+torque is mg D and by doing R cross F
+
+ align:start position:0%
+torque is mg D and by doing R cross F
+ 
+
+ align:start position:0%
+torque is mg D and by doing R cross F
+with the right hand rule we see that
+
+ align:start position:0%
+with the right hand rule we see that
+ 
+
+ align:start position:0%
+with the right hand rule we see that
+it's directed in the plus theta hat
+
+ align:start position:0%
+it's directed in the plus theta hat
+ 
+
+ align:start position:0%
+it's directed in the plus theta hat
+direction now again let's suppose that
+
+ align:start position:0%
+direction now again let's suppose that
+ 
+
+ align:start position:0%
+direction now again let's suppose that
+I'm holding the wheel horizontal and
+
+ align:start position:0%
+I'm holding the wheel horizontal and
+ 
+
+ align:start position:0%
+I'm holding the wheel horizontal and
+release it from rest if the wheel is not
+
+ align:start position:0%
+release it from rest if the wheel is not
+ 
+
+ align:start position:0%
+release it from rest if the wheel is not
+spinning okay so this is not rotating
+
+ align:start position:0%
+spinning okay so this is not rotating
+ 
+
+ align:start position:0%
+spinning okay so this is not rotating
+this is a stationary wheel that I'm
+
+ align:start position:0%
+this is a stationary wheel that I'm
+ 
+
+ align:start position:0%
+this is a stationary wheel that I'm
+holding horizontal and I release it from
+
+ align:start position:0%
+holding horizontal and I release it from
+ 
+
+ align:start position:0%
+holding horizontal and I release it from
+rest
+
+ align:start position:0%
+rest
+ 
+
+ align:start position:0%
+rest
+then its initial angular momentum with
+
+ align:start position:0%
+then its initial angular momentum with
+ 
+
+ align:start position:0%
+then its initial angular momentum with
+respect to point s is zero over a short
+
+ align:start position:0%
+respect to point s is zero over a short
+ 
+
+ align:start position:0%
+respect to point s is zero over a short
+time interval delta T the torque which
+
+ align:start position:0%
+time interval delta T the torque which
+ 
+
+ align:start position:0%
+time interval delta T the torque which
+is acting in the theta hat direction
+
+ align:start position:0%
+is acting in the theta hat direction
+ 
+
+ align:start position:0%
+is acting in the theta hat direction
+will cause an angular impulse or change
+
+ align:start position:0%
+will cause an angular impulse or change
+ 
+
+ align:start position:0%
+will cause an angular impulse or change
+in the angular momentum that change in
+
+ align:start position:0%
+in the angular momentum that change in
+ 
+
+ align:start position:0%
+in the angular momentum that change in
+angular momentum Delta L vector is equal
+
+ align:start position:0%
+angular momentum Delta L vector is equal
+ 
+
+ align:start position:0%
+angular momentum Delta L vector is equal
+to the torque times that short time
+
+ align:start position:0%
+to the torque times that short time
+ 
+
+ align:start position:0%
+to the torque times that short time
+interval delta T and it will act in the
+
+ align:start position:0%
+interval delta T and it will act in the
+ 
+
+ align:start position:0%
+interval delta T and it will act in the
+theta hat direction the change in
+
+ align:start position:0%
+theta hat direction the change in
+ 
+
+ align:start position:0%
+theta hat direction the change in
+angular momentum will be in the theta
+
+ align:start position:0%
+angular momentum will be in the theta
+ 
+
+ align:start position:0%
+angular momentum will be in the theta
+hat direction because that's the
+
+ align:start position:0%
+hat direction because that's the
+ 
+
+ align:start position:0%
+hat direction because that's the
+direction of the torque is in so for
+
+ align:start position:0%
+direction of the torque is in so for
+ 
+
+ align:start position:0%
+direction of the torque is in so for
+this case and and by the way this view
+
+ align:start position:0%
+this case and and by the way this view
+ 
+
+ align:start position:0%
+this case and and by the way this view
+here I should have labeled is this is a
+
+ align:start position:0%
+here I should have labeled is this is a
+ 
+
+ align:start position:0%
+here I should have labeled is this is a
+top view so this is the side view this
+
+ align:start position:0%
+top view so this is the side view this
+ 
+
+ align:start position:0%
+top view so this is the side view this
+is the top view of the same system so
+
+ align:start position:0%
+is the top view of the same system so
+ 
+
+ align:start position:0%
+is the top view of the same system so
+the torque is mg D in the theta hat
+
+ align:start position:0%
+the torque is mg D in the theta hat
+ 
+
+ align:start position:0%
+the torque is mg D in the theta hat
+direction so in the side view that's
+
+ align:start position:0%
+direction so in the side view that's
+ 
+
+ align:start position:0%
+direction so in the side view that's
+going into the screen and in the in the
+
+ align:start position:0%
+going into the screen and in the in the
+ 
+
+ align:start position:0%
+going into the screen and in the in the
+top view that's going pointing upward of
+
+ align:start position:0%
+top view that's going pointing upward of
+ 
+
+ align:start position:0%
+top view that's going pointing upward of
+the theta hat direction so in the case
+
+ align:start position:0%
+the theta hat direction so in the case
+ 
+
+ align:start position:0%
+the theta hat direction so in the case
+where the wheel is not spinning if we
+
+ align:start position:0%
+where the wheel is not spinning if we
+ 
+
+ align:start position:0%
+where the wheel is not spinning if we
+think about the top view the initial
+
+ align:start position:0%
+think about the top view the initial
+ 
+
+ align:start position:0%
+think about the top view the initial
+angular momentum is zero right so I'll
+
+ align:start position:0%
+angular momentum is zero right so I'll
+ 
+
+ align:start position:0%
+angular momentum is zero right so I'll
+just draw that as a dot so that's L
+
+ align:start position:0%
+just draw that as a dot so that's L
+ 
+
+ align:start position:0%
+just draw that as a dot so that's L
+initial equals zero and then I add a
+
+ align:start position:0%
+initial equals zero and then I add a
+ 
+
+ align:start position:0%
+initial equals zero and then I add a
+small torque or small angular impulse
+
+ align:start position:0%
+small torque or small angular impulse
+ 
+
+ align:start position:0%
+small torque or small angular impulse
+due to the torque Delta L which is in
+
+ align:start position:0%
+due to the torque Delta L which is in
+ 
+
+ align:start position:0%
+due to the torque Delta L which is in
+the theta hat direction
+
+ align:start position:0%
+the theta hat direction
+ 
+
+ align:start position:0%
+the theta hat direction
+so that's pointing in the theta hat
+
+ align:start position:0%
+so that's pointing in the theta hat
+ 
+
+ align:start position:0%
+so that's pointing in the theta hat
+direction okay so that's my Delta L and
+
+ align:start position:0%
+direction okay so that's my Delta L and
+ 
+
+ align:start position:0%
+direction okay so that's my Delta L and
+when I sum those together I start out
+
+ align:start position:0%
+when I sum those together I start out
+ 
+
+ align:start position:0%
+when I sum those together I start out
+with 0 I add a small Delta L so my final
+
+ align:start position:0%
+with 0 I add a small Delta L so my final
+ 
+
+ align:start position:0%
+with 0 I add a small Delta L so my final
+and going to momentum a time delta T
+
+ align:start position:0%
+and going to momentum a time delta T
+ 
+
+ align:start position:0%
+and going to momentum a time delta T
+later is just equal to my Delta L so
+
+ align:start position:0%
+later is just equal to my Delta L so
+ 
+
+ align:start position:0%
+later is just equal to my Delta L so
+this is L final and that's pointing in
+
+ align:start position:0%
+this is L final and that's pointing in
+ 
+
+ align:start position:0%
+this is L final and that's pointing in
+the theta hat direction so a torque in
+
+ align:start position:0%
+the theta hat direction so a torque in
+ 
+
+ align:start position:0%
+the theta hat direction so a torque in
+the theta hat direction into the screen
+
+ align:start position:0%
+the theta hat direction into the screen
+ 
+
+ align:start position:0%
+the theta hat direction into the screen
+for the side view is consistent with the
+
+ align:start position:0%
+for the side view is consistent with the
+ 
+
+ align:start position:0%
+for the side view is consistent with the
+wheel falling down so with theta hat
+
+ align:start position:0%
+wheel falling down so with theta hat
+ 
+
+ align:start position:0%
+wheel falling down so with theta hat
+pointing into the screen the wheel will
+
+ align:start position:0%
+pointing into the screen the wheel will
+ 
+
+ align:start position:0%
+pointing into the screen the wheel will
+basically fall
+
+ align:start position:0%
+basically fall
+ 
+
+ align:start position:0%
+basically fall
+this way it's rotating about point s and
+
+ align:start position:0%
+this way it's rotating about point s and
+ 
+
+ align:start position:0%
+this way it's rotating about point s and
+that's consistent with the torque
+
+ align:start position:0%
+that's consistent with the torque
+ 
+
+ align:start position:0%
+that's consistent with the torque
+pointing in the theta hat direction
+
+ align:start position:0%
+pointing in the theta hat direction
+ 
+
+ align:start position:0%
+pointing in the theta hat direction
+now as the wheel Falls the torque
+
+ align:start position:0%
+now as the wheel Falls the torque
+ 
+
+ align:start position:0%
+now as the wheel Falls the torque
+continues to point in the theta hat
+
+ align:start position:0%
+continues to point in the theta hat
+ 
+
+ align:start position:0%
+continues to point in the theta hat
+direction and so the angular
+
+ align:start position:0%
+direction and so the angular
+ 
+
+ align:start position:0%
+direction and so the angular
+acceleration will increase now what
+
+ align:start position:0%
+acceleration will increase now what
+ 
+
+ align:start position:0%
+acceleration will increase now what
+happens if this wheel is not stationary
+
+ align:start position:0%
+happens if this wheel is not stationary
+ 
+
+ align:start position:0%
+happens if this wheel is not stationary
+but instead is spinning rapidly in that
+
+ align:start position:0%
+but instead is spinning rapidly in that
+ 
+
+ align:start position:0%
+but instead is spinning rapidly in that
+case the torque remains the same it's
+
+ align:start position:0%
+case the torque remains the same it's
+ 
+
+ align:start position:0%
+case the torque remains the same it's
+still mg d in the theta hat direction
+
+ align:start position:0%
+still mg d in the theta hat direction
+ 
+
+ align:start position:0%
+still mg d in the theta hat direction
+but now the initial angular momentum is
+
+ align:start position:0%
+but now the initial angular momentum is
+ 
+
+ align:start position:0%
+but now the initial angular momentum is
+not zero rather it is a very large
+
+ align:start position:0%
+not zero rather it is a very large
+ 
+
+ align:start position:0%
+not zero rather it is a very large
+vector pointing along the spin axis
+
+ align:start position:0%
+vector pointing along the spin axis
+ 
+
+ align:start position:0%
+vector pointing along the spin axis
+let's choose the sense of rotation such
+
+ align:start position:0%
+let's choose the sense of rotation such
+ 
+
+ align:start position:0%
+let's choose the sense of rotation such
+that L points in the plus R hat
+
+ align:start position:0%
+that L points in the plus R hat
+ 
+
+ align:start position:0%
+that L points in the plus R hat
+direction that's actually the way I've
+
+ align:start position:0%
+direction that's actually the way I've
+ 
+
+ align:start position:0%
+direction that's actually the way I've
+drawn it here so in that case the
+
+ align:start position:0%
+drawn it here so in that case the
+ 
+
+ align:start position:0%
+drawn it here so in that case the
+angular momentum vector initially points
+
+ align:start position:0%
+angular momentum vector initially points
+ 
+
+ align:start position:0%
+angular momentum vector initially points
+in the plus R hat direction
+
+ align:start position:0%
+in the plus R hat direction
+ 
+
+ align:start position:0%
+in the plus R hat direction
+so then what happens over a short time
+
+ align:start position:0%
+so then what happens over a short time
+ 
+
+ align:start position:0%
+so then what happens over a short time
+delta T so now let's consider the case
+
+ align:start position:0%
+delta T so now let's consider the case
+ 
+
+ align:start position:0%
+delta T so now let's consider the case
+where the wheel is spinning so now my
+
+ align:start position:0%
+where the wheel is spinning so now my
+ 
+
+ align:start position:0%
+where the wheel is spinning so now my
+initial angular momentum is a large
+
+ align:start position:0%
+initial angular momentum is a large
+ 
+
+ align:start position:0%
+initial angular momentum is a large
+vector pointing in the r hat direction
+
+ align:start position:0%
+vector pointing in the r hat direction
+ 
+
+ align:start position:0%
+vector pointing in the r hat direction
+that's l initial i'm adding a small
+
+ align:start position:0%
+that's l initial i'm adding a small
+ 
+
+ align:start position:0%
+that's l initial i'm adding a small
+perpendicular vector Delta L in the
+
+ align:start position:0%
+perpendicular vector Delta L in the
+ 
+
+ align:start position:0%
+perpendicular vector Delta L in the
+theta hat direction and so the sum of
+
+ align:start position:0%
+theta hat direction and so the sum of
+ 
+
+ align:start position:0%
+theta hat direction and so the sum of
+those two things if this is the original
+
+ align:start position:0%
+those two things if this is the original
+ 
+
+ align:start position:0%
+those two things if this is the original
+r hat direction what's happened is that
+
+ align:start position:0%
+r hat direction what's happened is that
+ 
+
+ align:start position:0%
+r hat direction what's happened is that
+my new vector is at a small angle with
+
+ align:start position:0%
+my new vector is at a small angle with
+ 
+
+ align:start position:0%
+my new vector is at a small angle with
+respect to the original ER hat direction
+
+ align:start position:0%
+respect to the original ER hat direction
+ 
+
+ align:start position:0%
+respect to the original ER hat direction
+I'll call that angle Delta Theta so what
+
+ align:start position:0%
+I'll call that angle Delta Theta so what
+ 
+
+ align:start position:0%
+I'll call that angle Delta Theta so what
+I've done is I've rotated my initial
+
+ align:start position:0%
+I've done is I've rotated my initial
+ 
+
+ align:start position:0%
+I've done is I've rotated my initial
+angular momentum vector by a small angle
+
+ align:start position:0%
+angular momentum vector by a small angle
+ 
+
+ align:start position:0%
+angular momentum vector by a small angle
+without changing its length okay notice
+
+ align:start position:0%
+without changing its length okay notice
+ 
+
+ align:start position:0%
+without changing its length okay notice
+the two very different situations in one
+
+ align:start position:0%
+the two very different situations in one
+ 
+
+ align:start position:0%
+the two very different situations in one
+case I start out with zero angular
+
+ align:start position:0%
+case I start out with zero angular
+ 
+
+ align:start position:0%
+case I start out with zero angular
+momentum and all the angular momentum I
+
+ align:start position:0%
+momentum and all the angular momentum I
+ 
+
+ align:start position:0%
+momentum and all the angular momentum I
+end up with comes from the angular
+
+ align:start position:0%
+end up with comes from the angular
+ 
+
+ align:start position:0%
+end up with comes from the angular
+impulse due to the torque in the second
+
+ align:start position:0%
+impulse due to the torque in the second
+ 
+
+ align:start position:0%
+impulse due to the torque in the second
+case where the wheel is spinning I start
+
+ align:start position:0%
+case where the wheel is spinning I start
+ 
+
+ align:start position:0%
+case where the wheel is spinning I start
+out with a very large initial angular
+
+ align:start position:0%
+out with a very large initial angular
+ 
+
+ align:start position:0%
+out with a very large initial angular
+momentum I then add in
+
+ align:start position:0%
+momentum I then add in
+ 
+
+ align:start position:0%
+momentum I then add in
+the small angular impulse small compared
+
+ align:start position:0%
+the small angular impulse small compared
+ 
+
+ align:start position:0%
+the small angular impulse small compared
+to my initial angular momentum in the
+
+ align:start position:0%
+to my initial angular momentum in the
+ 
+
+ align:start position:0%
+to my initial angular momentum in the
+perpendicular direction and that causes
+
+ align:start position:0%
+perpendicular direction and that causes
+ 
+
+ align:start position:0%
+perpendicular direction and that causes
+not a change in the length of the vector
+
+ align:start position:0%
+not a change in the length of the vector
+ 
+
+ align:start position:0%
+not a change in the length of the vector
+but a change in its direction which
+
+ align:start position:0%
+but a change in its direction which
+ 
+
+ align:start position:0%
+but a change in its direction which
+means that the angular momentum vector
+
+ align:start position:0%
+means that the angular momentum vector
+ 
+
+ align:start position:0%
+means that the angular momentum vector
+rotates that's why the system processes
+
+ align:start position:0%
+rotates that's why the system processes
+ 
+
+ align:start position:0%
+rotates that's why the system processes
+when the wheel is rotating rapidly
+
+ align:start position:0%
+when the wheel is rotating rapidly
+ 
+
+ align:start position:0%
+when the wheel is rotating rapidly
+before we can understand precession more
+
+ align:start position:0%
+before we can understand precession more
+ 
+
+ align:start position:0%
+before we can understand precession more
+carefully it will be useful to review
+
+ align:start position:0%
+carefully it will be useful to review
+ 
+
+ align:start position:0%
+carefully it will be useful to review
+the mathematics of rotating vectors so
+
+ align:start position:0%
+the mathematics of rotating vectors so
+ 
+
+ align:start position:0%
+the mathematics of rotating vectors so
+first suppose we have a vector that I'll
+
+ align:start position:0%
+first suppose we have a vector that I'll
+ 
+
+ align:start position:0%
+first suppose we have a vector that I'll
+call r1 and I'm going to add a vector
+
+ align:start position:0%
+call r1 and I'm going to add a vector
+ 
+
+ align:start position:0%
+call r1 and I'm going to add a vector
+Delta R to this and I'm going to have
+
+ align:start position:0%
+Delta R to this and I'm going to have
+ 
+
+ align:start position:0%
+Delta R to this and I'm going to have
+the condition that the length of Delta R
+
+ align:start position:0%
+the condition that the length of Delta R
+ 
+
+ align:start position:0%
+the condition that the length of Delta R
+is much much smaller than the length of
+
+ align:start position:0%
+is much much smaller than the length of
+ 
+
+ align:start position:0%
+is much much smaller than the length of
+my original vector r1 and that Delta R
+
+ align:start position:0%
+my original vector r1 and that Delta R
+ 
+
+ align:start position:0%
+my original vector r1 and that Delta R
+is perpendicular is perpendicular to R 1
+
+ align:start position:0%
+is perpendicular is perpendicular to R 1
+ 
+
+ align:start position:0%
+is perpendicular is perpendicular to R 1
+so here's my Delta R and so if I add
+
+ align:start position:0%
+so here's my Delta R and so if I add
+ 
+
+ align:start position:0%
+so here's my Delta R and so if I add
+these two vectors let's say r2 is the
+
+ align:start position:0%
+these two vectors let's say r2 is the
+ 
+
+ align:start position:0%
+these two vectors let's say r2 is the
+sum of r1 plus Delta R so that's my
+
+ align:start position:0%
+sum of r1 plus Delta R so that's my
+ 
+
+ align:start position:0%
+sum of r1 plus Delta R so that's my
+vector r2 and I'm going to call this
+
+ align:start position:0%
+vector r2 and I'm going to call this
+ 
+
+ align:start position:0%
+vector r2 and I'm going to call this
+angle Delta Theta and now a few things
+
+ align:start position:0%
+angle Delta Theta and now a few things
+ 
+
+ align:start position:0%
+angle Delta Theta and now a few things
+to note first of all this is a right
+
+ align:start position:0%
+to note first of all this is a right
+ 
+
+ align:start position:0%
+to note first of all this is a right
+triangle notice that the length r2 is
+
+ align:start position:0%
+triangle notice that the length r2 is
+ 
+
+ align:start position:0%
+triangle notice that the length r2 is
+equal to r1 divided by the cosine of
+
+ align:start position:0%
+equal to r1 divided by the cosine of
+ 
+
+ align:start position:0%
+equal to r1 divided by the cosine of
+Delta Theta but if that angle is small
+
+ align:start position:0%
+Delta Theta but if that angle is small
+ 
+
+ align:start position:0%
+Delta Theta but if that angle is small
+if Delta Theta is a small angle then
+
+ align:start position:0%
+if Delta Theta is a small angle then
+ 
+
+ align:start position:0%
+if Delta Theta is a small angle then
+cosine theta is well approximated by one
+
+ align:start position:0%
+cosine theta is well approximated by one
+ 
+
+ align:start position:0%
+cosine theta is well approximated by one
+and so this is just my original length R
+
+ align:start position:0%
+and so this is just my original length R
+ 
+
+ align:start position:0%
+and so this is just my original length R
+1 and since r1 is equal to r2 I'm just
+
+ align:start position:0%
+1 and since r1 is equal to r2 I'm just
+ 
+
+ align:start position:0%
+1 and since r1 is equal to r2 I'm just
+going to call that call them both R and
+
+ align:start position:0%
+going to call that call them both R and
+ 
+
+ align:start position:0%
+going to call that call them both R and
+this is for small
+
+ align:start position:0%
+this is for small
+ 
+
+ align:start position:0%
+this is for small
+delta theta okay so that tells us that
+
+ align:start position:0%
+delta theta okay so that tells us that
+ 
+
+ align:start position:0%
+delta theta okay so that tells us that
+the vector just rotates when I have a
+
+ align:start position:0%
+the vector just rotates when I have a
+ 
+
+ align:start position:0%
+the vector just rotates when I have a
+large vector and I add a small
+
+ align:start position:0%
+large vector and I add a small
+ 
+
+ align:start position:0%
+large vector and I add a small
+perpendicular vector the result is to
+
+ align:start position:0%
+perpendicular vector the result is to
+ 
+
+ align:start position:0%
+perpendicular vector the result is to
+rotate the original vector without
+
+ align:start position:0%
+rotate the original vector without
+ 
+
+ align:start position:0%
+rotate the original vector without
+changing its length as long as the angle
+
+ align:start position:0%
+changing its length as long as the angle
+ 
+
+ align:start position:0%
+changing its length as long as the angle
+is small or equivalently as long as
+
+ align:start position:0%
+is small or equivalently as long as
+ 
+
+ align:start position:0%
+is small or equivalently as long as
+Delta R is very small compared to my
+
+ align:start position:0%
+Delta R is very small compared to my
+ 
+
+ align:start position:0%
+Delta R is very small compared to my
+original vector length I'll get a pure
+
+ align:start position:0%
+original vector length I'll get a pure
+ 
+
+ align:start position:0%
+original vector length I'll get a pure
+rotation in addition again looking at
+
+ align:start position:0%
+rotation in addition again looking at
+ 
+
+ align:start position:0%
+rotation in addition again looking at
+this triangle notice that Delta R is
+
+ align:start position:0%
+this triangle notice that Delta R is
+ 
+
+ align:start position:0%
+this triangle notice that Delta R is
+equal to which I can just write as R
+
+ align:start position:0%
+equal to which I can just write as R
+ 
+
+ align:start position:0%
+equal to which I can just write as R
+times the sine of Delta Theta and again
+
+ align:start position:0%
+times the sine of Delta Theta and again
+ 
+
+ align:start position:0%
+times the sine of Delta Theta and again
+if the angle is small of data if Delta
+
+ align:start position:0%
+if the angle is small of data if Delta
+ 
+
+ align:start position:0%
+if the angle is small of data if Delta
+Theta is a small angle then this is well
+
+ align:start position:0%
+Theta is a small angle then this is well
+ 
+
+ align:start position:0%
+Theta is a small angle then this is well
+approximated by R times the angle Delta
+
+ align:start position:0%
+approximated by R times the angle Delta
+ 
+
+ align:start position:0%
+approximated by R times the angle Delta
+Theta in radians and again this is for
+
+ align:start position:0%
+Theta in radians and again this is for
+ 
+
+ align:start position:0%
+Theta in radians and again this is for
+small Delta Theta so now if I divide
+
+ align:start position:0%
+small Delta Theta so now if I divide
+ 
+
+ align:start position:0%
+small Delta Theta so now if I divide
+this last equation by delta T a small
+
+ align:start position:0%
+this last equation by delta T a small
+ 
+
+ align:start position:0%
+this last equation by delta T a small
+time interval in which this rotation is
+
+ align:start position:0%
+time interval in which this rotation is
+ 
+
+ align:start position:0%
+time interval in which this rotation is
+happening then I write this is Delta R
+
+ align:start position:0%
+happening then I write this is Delta R
+ 
+
+ align:start position:0%
+happening then I write this is Delta R
+vector divided by delta T and I take the
+
+ align:start position:0%
+vector divided by delta T and I take the
+ 
+
+ align:start position:0%
+vector divided by delta T and I take the
+magnitude of that that is equal to R
+
+ align:start position:0%
+magnitude of that that is equal to R
+ 
+
+ align:start position:0%
+magnitude of that that is equal to R
+Delta Theta divided by delta T and if I
+
+ align:start position:0%
+Delta Theta divided by delta T and if I
+ 
+
+ align:start position:0%
+Delta Theta divided by delta T and if I
+go to the limit as delta T gets small as
+
+ align:start position:0%
+go to the limit as delta T gets small as
+ 
+
+ align:start position:0%
+go to the limit as delta T gets small as
+delta T approaches zero then I can write
+
+ align:start position:0%
+delta T approaches zero then I can write
+ 
+
+ align:start position:0%
+delta T approaches zero then I can write
+this as the derivative of the vector R
+
+ align:start position:0%
+this as the derivative of the vector R
+ 
+
+ align:start position:0%
+this as the derivative of the vector R
+the time derivative I should say the
+
+ align:start position:0%
+the time derivative I should say the
+ 
+
+ align:start position:0%
+the time derivative I should say the
+magnitude of the time derivative of
+
+ align:start position:0%
+magnitude of the time derivative of
+ 
+
+ align:start position:0%
+magnitude of the time derivative of
+vector R and that's equal to the length
+
+ align:start position:0%
+vector R and that's equal to the length
+ 
+
+ align:start position:0%
+vector R and that's equal to the length
+R times the time derivative of the angle
+
+ align:start position:0%
+R times the time derivative of the angle
+ 
+
+ align:start position:0%
+R times the time derivative of the angle
+D theta DT but D theta DT is just the
+
+ align:start position:0%
+D theta DT but D theta DT is just the
+ 
+
+ align:start position:0%
+D theta DT but D theta DT is just the
+angular velocity so I could write that
+
+ align:start position:0%
+angular velocity so I could write that
+ 
+
+ align:start position:0%
+angular velocity so I could write that
+as R times capital Omega for the angular
+
+ align:start position:0%
+as R times capital Omega for the angular
+ 
+
+ align:start position:0%
+as R times capital Omega for the angular
+velocity and this is just our familiar
+
+ align:start position:0%
+velocity and this is just our familiar
+ 
+
+ align:start position:0%
+velocity and this is just our familiar
+result that for
+
+ align:start position:0%
+result that for
+ 
+
+ align:start position:0%
+result that for
+circular motion for the rotation of a
+
+ align:start position:0%
+circular motion for the rotation of a
+ 
+
+ align:start position:0%
+circular motion for the rotation of a
+position vector the velocity is equal to
+
+ align:start position:0%
+position vector the velocity is equal to
+ 
+
+ align:start position:0%
+position vector the velocity is equal to
+the radius of the circle times the
+
+ align:start position:0%
+the radius of the circle times the
+ 
+
+ align:start position:0%
+the radius of the circle times the
+angular velocity of the rotation another
+
+ align:start position:0%
+angular velocity of the rotation another
+ 
+
+ align:start position:0%
+angular velocity of the rotation another
+way of thinking of that is that the
+
+ align:start position:0%
+way of thinking of that is that the
+ 
+
+ align:start position:0%
+way of thinking of that is that the
+magnitude of the rate of change of the
+
+ align:start position:0%
+magnitude of the rate of change of the
+ 
+
+ align:start position:0%
+magnitude of the rate of change of the
+position vector which we call the
+
+ align:start position:0%
+position vector which we call the
+ 
+
+ align:start position:0%
+position vector which we call the
+velocity is equal to the length of the
+
+ align:start position:0%
+velocity is equal to the length of the
+ 
+
+ align:start position:0%
+velocity is equal to the length of the
+rotating vector R times the angular
+
+ align:start position:0%
+rotating vector R times the angular
+ 
+
+ align:start position:0%
+rotating vector R times the angular
+velocity of the rotation but there's
+
+ align:start position:0%
+velocity of the rotation but there's
+ 
+
+ align:start position:0%
+velocity of the rotation but there's
+nothing special about the position
+
+ align:start position:0%
+nothing special about the position
+ 
+
+ align:start position:0%
+nothing special about the position
+vector that I used in order to do this
+
+ align:start position:0%
+vector that I used in order to do this
+ 
+
+ align:start position:0%
+vector that I used in order to do this
+analysis so if instead of a position
+
+ align:start position:0%
+analysis so if instead of a position
+ 
+
+ align:start position:0%
+analysis so if instead of a position
+vector I considered any vector so let's
+
+ align:start position:0%
+vector I considered any vector so let's
+ 
+
+ align:start position:0%
+vector I considered any vector so let's
+say this is my rotational motion of a
+
+ align:start position:0%
+say this is my rotational motion of a
+ 
+
+ align:start position:0%
+say this is my rotational motion of a
+vector that I'll call a so that's a at
+
+ align:start position:0%
+vector that I'll call a so that's a at
+ 
+
+ align:start position:0%
+vector that I'll call a so that's a at
+time T and then at some later time
+
+ align:start position:0%
+time T and then at some later time
+ 
+
+ align:start position:0%
+time T and then at some later time
+that's a of T plus delta-t this vector
+
+ align:start position:0%
+that's a of T plus delta-t this vector
+ 
+
+ align:start position:0%
+that's a of T plus delta-t this vector
+is my Delta a I'll call this angle Delta
+
+ align:start position:0%
+is my Delta a I'll call this angle Delta
+ 
+
+ align:start position:0%
+is my Delta a I'll call this angle Delta
+Theta and so the vector a is rotating in
+
+ align:start position:0%
+Theta and so the vector a is rotating in
+ 
+
+ align:start position:0%
+Theta and so the vector a is rotating in
+that direction with an angular velocity
+
+ align:start position:0%
+that direction with an angular velocity
+ 
+
+ align:start position:0%
+that direction with an angular velocity
+capital Omega now in the example I just
+
+ align:start position:0%
+capital Omega now in the example I just
+ 
+
+ align:start position:0%
+capital Omega now in the example I just
+did my vector a is actually R of T ok
+
+ align:start position:0%
+did my vector a is actually R of T ok
+ 
+
+ align:start position:0%
+did my vector a is actually R of T ok
+but so everywhere where I have an R here
+
+ align:start position:0%
+but so everywhere where I have an R here
+ 
+
+ align:start position:0%
+but so everywhere where I have an R here
+I can just write an a this is now just
+
+ align:start position:0%
+I can just write an a this is now just
+ 
+
+ align:start position:0%
+I can just write an a this is now just
+an arbitrary vector in space that is
+
+ align:start position:0%
+an arbitrary vector in space that is
+ 
+
+ align:start position:0%
+an arbitrary vector in space that is
+rotating at an angular velocity capital
+
+ align:start position:0%
+rotating at an angular velocity capital
+ 
+
+ align:start position:0%
+rotating at an angular velocity capital
+Omega and what we see using the same
+
+ align:start position:0%
+Omega and what we see using the same
+ 
+
+ align:start position:0%
+Omega and what we see using the same
+analysis we would find that the
+
+ align:start position:0%
+analysis we would find that the
+ 
+
+ align:start position:0%
+analysis we would find that the
+magnitude of the time rate of change of
+
+ align:start position:0%
+magnitude of the time rate of change of
+ 
+
+ align:start position:0%
+magnitude of the time rate of change of
+the vector that's the rotating vector is
+
+ align:start position:0%
+the vector that's the rotating vector is
+ 
+
+ align:start position:0%
+the vector that's the rotating vector is
+equal to the length of the rotating
+
+ align:start position:0%
+equal to the length of the rotating
+ 
+
+ align:start position:0%
+equal to the length of the rotating
+vector which is a times D theta DT or in
+
+ align:start position:0%
+vector which is a times D theta DT or in
+ 
+
+ align:start position:0%
+vector which is a times D theta DT or in
+other words the length of the rotating
+
+ align:start position:0%
+other words the length of the rotating
+ 
+
+ align:start position:0%
+other words the length of the rotating
+vector time is the angular velocity of
+
+ align:start position:0%
+vector time is the angular velocity of
+ 
+
+ align:start position:0%
+vector time is the angular velocity of
+the rotation that's true for any vector
+
+ align:start position:0%
+the rotation that's true for any vector
+ 
+
+ align:start position:0%
+the rotation that's true for any vector
+okay this is a general result
+
+ align:start position:0%
+okay this is a general result
+ 
+
+ align:start position:0%
+okay this is a general result
+equals our Omega is just a special case
+
+ align:start position:0%
+equals our Omega is just a special case
+ 
+
+ align:start position:0%
+equals our Omega is just a special case
+of this general rule where in that case
+
+ align:start position:0%
+of this general rule where in that case
+ 
+
+ align:start position:0%
+of this general rule where in that case
+by rotating vector is a position vector
+
+ align:start position:0%
+by rotating vector is a position vector
+ 
+
+ align:start position:0%
+by rotating vector is a position vector
+but this is true for any vector that's
+
+ align:start position:0%
+but this is true for any vector that's
+ 
+
+ align:start position:0%
+but this is true for any vector that's
+rotating in space in particular for a
+
+ align:start position:0%
+rotating in space in particular for a
+ 
+
+ align:start position:0%
+rotating in space in particular for a
+rotating angular momentum for a rotating
+
+ align:start position:0%
+rotating angular momentum for a rotating
+ 
+
+ align:start position:0%
+rotating angular momentum for a rotating
+angular momentum vector I have that the
+
+ align:start position:0%
+angular momentum vector I have that the
+ 
+
+ align:start position:0%
+angular momentum vector I have that the
+magnitude of the time derivative of the
+
+ align:start position:0%
+magnitude of the time derivative of the
+ 
+
+ align:start position:0%
+magnitude of the time derivative of the
+rotating angular momentum vector is just
+
+ align:start position:0%
+rotating angular momentum vector is just
+ 
+
+ align:start position:0%
+rotating angular momentum vector is just
+equal to the length of the angular
+
+ align:start position:0%
+equal to the length of the angular
+ 
+
+ align:start position:0%
+equal to the length of the angular
+momentum vector the magnitude of the
+
+ align:start position:0%
+momentum vector the magnitude of the
+ 
+
+ align:start position:0%
+momentum vector the magnitude of the
+angle mentum times the angular velocity
+
+ align:start position:0%
+angle mentum times the angular velocity
+ 
+
+ align:start position:0%
+angle mentum times the angular velocity
+of rotation now in addition in the
+
+ align:start position:0%
+of rotation now in addition in the
+ 
+
+ align:start position:0%
+of rotation now in addition in the
+particular case of a rotating angular
+
+ align:start position:0%
+particular case of a rotating angular
+ 
+
+ align:start position:0%
+particular case of a rotating angular
+momentum vector or any angular momentum
+
+ align:start position:0%
+momentum vector or any angular momentum
+ 
+
+ align:start position:0%
+momentum vector or any angular momentum
+vector rather we know that the time
+
+ align:start position:0%
+vector rather we know that the time
+ 
+
+ align:start position:0%
+vector rather we know that the time
+derivative of the angular momentum
+
+ align:start position:0%
+derivative of the angular momentum
+ 
+
+ align:start position:0%
+derivative of the angular momentum
+vector is also equal to the torque
+
+ align:start position:0%
+vector is also equal to the torque
+ 
+
+ align:start position:0%
+vector is also equal to the torque
+vector so I can set these two things
+
+ align:start position:0%
+vector so I can set these two things
+ 
+
+ align:start position:0%
+vector so I can set these two things
+equal in the case of a rotating angular
+
+ align:start position:0%
+equal in the case of a rotating angular
+ 
+
+ align:start position:0%
+equal in the case of a rotating angular
+momentum vector the magnitude of the
+
+ align:start position:0%
+momentum vector the magnitude of the
+ 
+
+ align:start position:0%
+momentum vector the magnitude of the
+torque is given by the magnitude of the
+
+ align:start position:0%
+torque is given by the magnitude of the
+ 
+
+ align:start position:0%
+torque is given by the magnitude of the
+rotating angular momentum vector times
+
+ align:start position:0%
+rotating angular momentum vector times
+ 
+
+ align:start position:0%
+rotating angular momentum vector times
+the angular speed of rotation and that's
+
+ align:start position:0%
+the angular speed of rotation and that's
+ 
+
+ align:start position:0%
+the angular speed of rotation and that's
+just using the general behavior of a
+
+ align:start position:0%
+just using the general behavior of a
+ 
+
+ align:start position:0%
+just using the general behavior of a
+rotating vector in space
\ No newline at end of file
diff --git a/Tx7zzD4aeiA.txt b/Tx7zzD4aeiA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e126a38834e004545f89955f1dc731986a1580b7
--- /dev/null
+++ b/Tx7zzD4aeiA.txt
@@ -0,0 +1,2278 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: We're going to finish
+today our discussion of
+
+limit theorems.
+
+I'm going to remind you what the
+central limit theorem is,
+
+which we introduced
+briefly last time.
+
+We're going to discuss what
+exactly it says and its
+
+implications.
+
+And then we're going to apply
+to a couple of examples,
+
+mostly on the binomial
+distribution.
+
+OK, so the situation is that
+we are dealing with a large
+
+number of independent,
+identically
+
+distributed random variables.
+
+And we want to look at the sum
+of them and say something
+
+about the distribution
+of the sum.
+
+We might want to say that
+the sum is distributed
+
+approximately as a normal random
+variable, although,
+
+formally, this is
+not quite right.
+
+As n goes to infinity, the
+distribution of the sum
+
+becomes very spread out, and
+it doesn't converge to a
+
+limiting distribution.
+
+In order to get an interesting
+limit, we need first to take
+
+the sum and standardize it.
+
+By standardizing it, what we
+mean is to subtract the mean
+
+and then divide by the
+standard deviation.
+
+Now, the mean is, of course, n
+times the expected value of
+
+each one of the X's.
+
+And the standard deviation
+is the
+
+square root of the variance.
+
+The variance is n times sigma
+squared, where sigma is the
+
+variance of the X's --
+
+so that's the standard
+deviation.
+
+And after we do this, we obtain
+a random variable that
+
+has 0 mean -- its centered
+-- and the
+
+variance is equal to 1.
+
+And so the variance stays the
+same, no matter how large n is
+
+going to be.
+
+So the distribution of Zn keeps
+changing with n, but it
+
+cannot change too much.
+
+It stays in place.
+
+The mean is 0, and the width
+remains also roughly the same
+
+because the variance is 1.
+
+The surprising thing is that, as
+n grows, that distribution
+
+of Zn kind of settles in a
+certain asymptotic shape.
+
+And that's the shape
+of a standard
+
+normal random variable.
+
+So standard normal means
+that it has 0
+
+mean and unit variance.
+
+More precisely, what the central
+limit theorem tells us
+
+is a relation between the
+cumulative distribution
+
+function of Zn and its relation
+to the cumulative
+
+distribution function of
+the standard normal.
+
+So for any given number, c,
+the probability that Zn is
+
+less than or equal to c, in the
+limit, becomes the same as
+
+the probability that the
+standard normal becomes less
+
+than or equal to c.
+
+And of course, this is useful
+because these probabilities
+
+are available from the normal
+tables, whereas the
+
+distribution of Zn might be a
+very complicated expression if
+
+you were to calculate
+it exactly.
+
+So some comments about the
+central limit theorem.
+
+First thing is that it's quite
+amazing that it's universal.
+
+It doesn't matter what the
+distribution of the X's is.
+
+It can be any distribution
+whatsoever, as long as it has
+
+finite mean and finite
+variance.
+
+And when you go and do your
+approximations using the
+
+central limit theorem, the only
+thing that you need to
+
+know about the distribution
+of the X's are the
+
+mean and the variance.
+
+You need those in order
+to standardize Sn.
+
+I mean -- to subtract the mean
+and divide by the standard
+
+deviation --
+
+you need to know the mean
+and the variance.
+
+But these are the only things
+that you need to know in order
+
+to apply it.
+
+In addition, it's
+a very accurate
+
+computational shortcut.
+
+So the distribution of this
+Zn's, in principle, you can
+
+calculate it by convolution of
+the distribution of the X's
+
+with itself many, many times.
+
+But this is tedious, and if you
+try to do it analytically,
+
+it might be a very complicated
+expression.
+
+Whereas by just appealing to the
+standard normal table for
+
+the standard normal random
+variable, things are done in a
+
+very quick way.
+
+So it's a nice computational
+shortcut if you don't want to
+
+get an exact answer to a
+probability problem.
+
+Now, at a more philosophical
+level, it justifies why we are
+
+really interested in normal
+random variables.
+
+Whenever you have a phenomenon
+which is noisy, and the noise
+
+that you observe is created by
+adding the lots of little
+
+pieces of randomness that are
+independent of each other, the
+
+overall effect that you're
+going to observe can be
+
+described by a normal
+random variable.
+
+So in a classic example that
+goes 100 years back or so,
+
+suppose that you have a fluid,
+and inside that fluid, there's
+
+a little particle of dust
+or whatever that's
+
+suspended in there.
+
+That little particle gets
+hit by molecules
+
+completely at random --
+
+and so what you're going to see
+is that particle kind of
+
+moving randomly inside
+that liquid.
+
+Now that random motion, if you
+ask, after one second, how
+
+much is my particle displaced,
+let's say, in the x-axis along
+
+the x direction.
+
+That displacement is very, very
+well modeled by a normal
+
+random variable.
+
+And the reason is that the
+position of that particle is
+
+decided by the cumulative effect
+of lots of random hits
+
+by molecules that hit
+that particle.
+
+So that's a sort of celebrated
+physical model that goes under
+
+the name of Brownian motion.
+
+And it's the same model that
+some people use to describe
+
+the movement in the
+financial markets.
+
+The argument might go that the
+movement of prices has to do
+
+with lots of little decisions
+and lots of little events by
+
+many, many different
+actors that are
+
+involved in the market.
+
+So the distribution of stock
+prices might be well described
+
+by normal random variables.
+
+At least that's what people
+wanted to believe until
+
+somewhat recently.
+
+Now, the evidence is that,
+actually, these distributions
+
+are a little more heavy-tailed
+in the sense that extreme
+
+events are a little more likely
+to occur that what
+
+normal random variables would
+seem to indicate.
+
+But as a first model, again,
+it could be a plausible
+
+argument to have, at least as
+a starting model, one that
+
+involves normal random
+variables.
+
+So this is the philosophical
+side of things.
+
+On the more accurate,
+mathematical side, it's
+
+important to appreciate
+exactly quite kind of
+
+statement the central
+limit theorem is.
+
+It's a statement about the
+convergence of the CDF of
+
+these standardized random
+variables to
+
+the CDF of a normal.
+
+So it's a statement about
+convergence of CDFs.
+
+It's not a statement about
+convergence of PMFs, or
+
+convergence of PDFs.
+
+Now, if one makes additional
+mathematical assumptions,
+
+there are variations of the
+central limit theorem that
+
+talk about PDFs and PMFs.
+
+But in general, that's not
+necessarily the case.
+
+And I'm going to illustrate
+this with--
+
+I have a plot here which
+is not in your slides.
+
+But just to make the point,
+consider two different
+
+discrete distributions.
+
+This discrete distribution
+takes values 1, 4, 7.
+
+This discrete distribution can
+take values 1, 2, 4, 6, and 7.
+
+So this one has sort of a
+periodicity of 3, this one,
+
+the range of values is a little
+more interesting.
+
+The numbers in these two
+distributions are cooked up so
+
+that they have the same mean
+and the same variance.
+
+Now, what I'm going to do is
+to take eight independent
+
+copies of the random variable
+and plot the PMF of the sum of
+
+eight random variables.
+
+Now, if I plot the PMF of the
+sum of 8 of these, I get the
+
+plot, which corresponds to these
+bullets in this diagram.
+
+If I take 8 random variables,
+according to this
+
+distribution, and add them up
+and compute their PMF, the PMF
+
+I get is the one denoted
+here by the X's.
+
+The two PMFs look really
+different, at least, when you
+
+eyeball them.
+
+On the other hand, if you were
+to plot the CDFs of them, then
+
+the CDFs, if you compare them
+with the normal CDF, which is
+
+this continuous curve, the CDF,
+of course, it goes up in
+
+steps because we're looking at
+discrete random variables.
+
+But it's very close
+to the normal CDF.
+
+And if we, instead of n equal to
+8, we were to take 16, then
+
+the coincidence would
+be even better.
+
+So in terms of CDFs, when we add
+8 or 16 of these, we get
+
+very close to the normal CDF.
+
+We would get essentially the
+same picture if I were to take
+
+8 or 16 of these.
+
+So the CDFs sit, essentially, on
+top of each other, although
+
+the two PMFs look
+quite different.
+
+So this is to appreciate that,
+formally speaking, we only
+
+have a statement about
+CDFs, not about PMFs.
+
+Now in practice, how do you use
+the central limit theorem?
+
+Well, it tells us that we can
+calculate probabilities by
+
+treating Zn as if it
+were a standard
+
+normal random variable.
+
+Now Zn is a linear
+function of Sn.
+
+Conversely, Sn is a linear
+function of Zn.
+
+Linear functions of normals
+are normal.
+
+So if I pretend that Zn is
+normal, it's essentially the
+
+same as if we pretend
+that Sn is normal.
+
+And so we can calculate
+probabilities that have to do
+
+with Sn as if Sn were normal.
+
+Now, the central limit theorem
+does not tell us that Sn is
+
+approximately normal.
+
+The formal statement is about
+Zn, but, practically speaking,
+
+when you use the result,
+you can just
+
+pretend that Sn is normal.
+
+Finally, it's a limit theorem,
+so it tells us about what
+
+happens when n goes
+to infinity.
+
+If we are to use it in practice,
+of course, n is not
+
+going to be infinity.
+
+Maybe n is equal to 15.
+
+Can we use a limit theorem when
+n is a small number, as
+
+small as 15?
+
+Well, it turns out that it's
+a very good approximation.
+
+Even for quite small values
+of n, it gives us
+
+very accurate answers.
+
+So n over the order of 15, or
+20, or so give us very good
+
+results in practice.
+
+There are no good theorems
+that will give us hard
+
+guarantees because the quality
+of the approximation does
+
+depend on the details of the
+distribution of the X's.
+
+If the X's have a distribution
+that, from the outset, looks a
+
+little bit like the normal, then
+for small values of n,
+
+you are going to see,
+essentially, a normal
+
+distribution for the sum.
+
+If the distribution of the X's
+is very different from the
+
+normal, it's going to take a
+larger value of n for the
+
+central limit theorem
+to take effect.
+
+So let's illustrates this with
+a few representative plots.
+
+So here, we're starting with a
+discrete uniform distribution
+
+that goes from 1 to 8.
+
+Let's add 2 of these random
+variables, 2 random variables
+
+with this PMF, and find
+the PMF of the sum.
+
+This is a convolution of 2
+discrete uniforms, and I
+
+believe you have seen this
+exercise before.
+
+When you convolve this with
+itself, you get a triangle.
+
+So this is the PMF for the sum
+of two discrete uniforms.
+
+Now let's continue.
+
+Let's convolve this
+with itself.
+
+These was going to give
+us the PMF of a sum
+
+of 4 discrete uniforms.
+
+And we get this, which starts
+looking like a normal.
+
+If we go to n equal to 32, then
+it looks, essentially,
+
+exactly like a normal.
+
+And it's an excellent
+approximation.
+
+So this is the PMF of the sum
+of 32 discrete random
+
+variables with this uniform
+distribution.
+
+If we start with a PMF which
+is not symmetric--
+
+this one is symmetric
+around the mean.
+
+But if we start with a PMF which
+is non-symmetric, so
+
+this is, here, is a truncated
+geometric PMF, then things do
+
+not work out as nicely when
+I add 8 of these.
+
+That is, if I convolve this
+with itself 8 times, I get
+
+this PMF, which maybe resembles
+a little bit to the
+
+normal one.
+
+But you can really tell that
+it's different from the normal
+
+if you focus at the details
+here and there.
+
+Here it sort of rises sharply.
+
+Here it tails off
+a bit slower.
+
+So there's an asymmetry here
+that's present, and which is a
+
+consequence of the
+asymmetry of the
+
+distribution we started with.
+
+If we go to 16, it looks a
+little better, but still you
+
+can see the asymmetry between
+this tail and that tail.
+
+If you get to 32 there's still a
+little bit of asymmetry, but
+
+at least now it starts looking
+like a normal distribution.
+
+So the moral from these plots
+is that it might vary, a
+
+little bit, what kind of values
+of n you need before
+
+you get the really good
+approximation.
+
+But for values of n in the range
+20 to 30 or so, usually
+
+you expect to get a pretty
+good approximation.
+
+At least that's what the visual
+inspection of these
+
+graphs tells us.
+
+So now that we know that we have
+a good approximation in
+
+our hands, let's use it.
+
+Let's use it by revisiting an
+example from last time.
+
+This is the polling problem.
+
+We're interested in the fraction
+of population that
+
+has a certain habit been.
+
+And we try to find what f is.
+
+And the way we do it is by
+polling people at random and
+
+recording the answers that they
+give, whether they have
+
+the habit or not.
+
+So for each person, we get the
+Bernoulli random variable.
+
+With probability f, a person is
+going to respond 1, or yes,
+
+so this is with probability f.
+
+And with the remaining
+probability 1-f, the person
+
+responds no.
+
+We record this number, which
+is how many people answered
+
+yes, divided by the total
+number of people.
+
+That's the fraction of the
+population that we asked.
+
+This is the fraction inside our
+sample that answered yes.
+
+And as we discussed last time,
+you might start with some
+
+specs for the poll.
+
+And the specs have
+two parameters--
+
+the accuracy that you want and
+the confidence that you want
+
+to have that you did really
+obtain the desired accuracy.
+
+So the specs here is that we
+want, probability 95% that our
+
+estimate is within 1 % point
+from the true answer.
+
+So the event of interest
+is this.
+
+That's the result of the poll
+minus distance from the true
+
+answer is less or bigger
+than 1 % point.
+
+And we're interested in
+calculating or approximating
+
+this particular probability.
+
+So we want to do it using the
+central limit theorem.
+
+And one way of arranging the
+mechanics of this calculation
+
+is to take the event of interest
+and massage it by
+
+subtracting and dividing things
+from both sides of this
+
+inequality so that you bring
+him to the picture the
+
+standardized random variable,
+the Zn, and then apply the
+
+central limit theorem.
+
+So the event of interest, let
+me write it in full, Mn is
+
+this quantity, so I'm putting it
+here, minus f, which is the
+
+same as nf divided by n.
+
+So this is the same
+as that event.
+
+We're going to calculate the
+probability of this.
+
+This is not exactly in the form
+in which we apply the
+
+central limit theorem.
+
+To apply the central limit
+theorem, we need, down here,
+
+to have sigma square root n.
+
+So how can I put sigma
+square root n here?
+
+I can divide both sides of
+this inequality by sigma.
+
+And then I can take a factor of
+square root n from here and
+
+send it to the other side.
+
+So this event is the
+same as that event.
+
+This will happen if and only
+if that will happen.
+
+So calculating the probability
+of this event here is the same
+
+as calculating the probability
+that this events happens.
+
+And now we are in business
+because the random variable
+
+that we got in here is Zn, or
+the absolute value of Zn, and
+
+we're talking about the
+probability that Zn, absolute
+
+value of Zn, is bigger than
+a certain number.
+
+Since Zn is to be approximated
+by a standard normal random
+
+variable, our approximation is
+going to be, instead of asking
+
+for Zn being bigger than this
+number, we will ask for Z,
+
+absolute value of Z, being
+bigger than this number.
+
+So this is the probability that
+we want to calculate.
+
+And now Z is a standard normal
+random variable.
+
+There's a small difficulty,
+the one that we also
+
+encountered last time.
+
+And the difficulty is that the
+standard deviation, sigma, of
+
+the Xi's is not known.
+
+Sigma is equal to f times--
+
+sigma, in this example, is f
+times (1-f), and the only
+
+thing that we know about sigma
+is that it's going to be a
+
+number less than 1/2.
+
+OK, so we're going to have to
+use an inequality here.
+
+We're going to use a
+conservative value of sigma,
+
+the value of sigma equal to 1/2
+and use that instead of
+
+the exact value of sigma.
+
+And this gives us an inequality
+going this way.
+
+Let's just make sure why the
+inequality goes this way.
+
+We got, on our axis,
+two numbers.
+
+One number is 0.01 square
+root n divided by sigma.
+
+And the other number is
+0.02 square root of n.
+
+And my claim is that the numbers
+are related to each
+
+other in this particular way.
+
+Why is this?
+
+Sigma is less than 2.
+
+So 1/sigma is bigger than 2.
+
+So since 1/sigma is bigger than
+2 this means that this
+
+numbers sits to the right
+of that number.
+
+So here we have the probability
+that Z is bigger
+
+than this number.
+
+The probability of falling out
+there is less than the
+
+probability of falling
+in this interval.
+
+So that's what that last
+inequality is saying--
+
+this probability is smaller
+than that probability.
+
+This is the probability that
+we're interested in, but since
+
+we don't know sigma, we take the
+conservative value, and we
+
+use an upper bound in terms
+of the probability of this
+
+interval here.
+
+And now we are in business.
+
+We can start using our normal
+tables to calculate
+
+probabilities of interest.
+
+So for example, let's say that's
+we take n to be 10,000.
+
+How is the calculation
+going to go?
+
+We want to calculate the
+probability that the absolute
+
+value of Z is bigger than 0.2
+times 1000, which is the
+
+probability that the absolute
+value of Z is larger than or
+
+equal to 2.
+
+And here let's do
+some mechanics,
+
+just to stay in shape.
+
+The probability that you're
+larger than or equal to 2 in
+
+absolute value, since the normal
+is symmetric around the
+
+mean, this is going to be twice
+the probability that Z
+
+is larger than or equal to 2.
+
+Can we use the cumulative
+distribution function of Z to
+
+calculate this?
+
+Well, almost the cumulative
+gives us probabilities of
+
+being less than something, not
+bigger than something.
+
+So we need one more step and
+write this as 1 minus the
+
+probability that Z is less
+than or equal to 2.
+
+And this probability, now,
+you can read off
+
+from the normal tables.
+
+And the normal tables will
+tell you that this
+
+probability is 0.9772.
+
+And you do get an answer.
+
+And the answer is 0.0456.
+
+OK, so we tried 10,000.
+
+And we find that our probably
+of error is 4.5%, so we're
+
+doing better than the
+spec that we had.
+
+So this tells us that maybe
+we have some leeway.
+
+Maybe we can use a smaller
+sample size and still stay
+
+without our specs.
+
+Let's try to find how much
+we can push the envelope.
+
+How much smaller
+can we take n?
+
+To answer that question, we
+need to do this kind of
+
+calculation, essentially,
+going backwards.
+
+We're going to fix this number
+to be 0.05 and work backwards
+
+here to find--
+
+did I do a mistake here?
+
+10,000.
+
+So I'm missing a 0 here.
+
+Ah, but I'm taking the square
+root, so it's 100.
+
+Where did the 0.02
+come in from?
+
+Ah, from here.
+
+OK, all right.
+
+0.02 times 100, that
+gives us 2.
+
+OK, all right.
+
+Very good, OK.
+
+So we'll have to do this
+calculation now backwards,
+
+figure out if this is 0.05,
+what kind of number we're
+
+going to need here and then
+here, and from this we will be
+
+able to tell what value
+of n do we need.
+
+OK, so we want to find n such
+that the probability that Z is
+
+bigger than 0.02 square
+root n is 0.05.
+
+OK, so Z is a standard normal
+random variable.
+
+And we want the probability
+that we are
+
+outside this range.
+
+We want the probability of
+those two tails together.
+
+Those two tails together
+should have
+
+probability of 0.05.
+
+This means that this tail,
+by itself, should have
+
+probability 0.025.
+
+And this means that this
+probability should be 0.975.
+
+Now, if this probability
+is to be 0.975, what
+
+should that number be?
+
+You go to the normal tables,
+and you find which is the
+
+entry that corresponds
+to that number.
+
+I actually brought a normal
+table with me.
+
+And 0.975 is down here.
+
+And it tells you that
+to the number that
+
+corresponds to it is 1.96.
+
+So this tells us that
+this number
+
+should be equal to 1.96.
+
+And now, from here, you
+do the calculations.
+
+And you find that n is 9604.
+
+So with a sample of 10,000, we
+got probability of error 4.5%.
+
+With a slightly smaller sample
+size of 9,600, we can get the
+
+probability of a mistake
+to be 0.05, which
+
+was exactly our spec.
+
+So these are essentially the two
+ways that you're going to
+
+be using the central
+limit theorem.
+
+Either you're given n and
+you try to calculate
+
+probabilities.
+
+Or you're given the
+probabilities, and you want to
+
+work backwards to
+find n itself.
+
+So in this example, the random
+variable that we dealt with
+
+was, of course, a binomial
+random variable.
+
+The Xi's were Bernoulli,
+so the sum of
+
+the Xi's were binomial.
+
+So the central limit theorem
+certainly applies to the
+
+binomial distribution.
+
+To be more precise, of course,
+it applies to the standardized
+
+version of the binomial
+random variable.
+
+So here's what we did,
+essentially, in
+
+the previous example.
+
+We fixed the number p, which is
+the probability of success
+
+in our experiments.
+
+p corresponds to f in the
+previous example.
+
+Let every Xi a Bernoulli
+random variable and are
+
+standing assumption is that
+these random variables are
+
+independent.
+
+When we add them, we get a
+random variable that has a
+
+binomial distribution.
+
+We know the mean and the
+variance of the binomial, so
+
+we take Sn, we subtract the
+mean, which is this, divide by
+
+the standard deviation.
+
+The central limit theorem tells
+us that the cumulative
+
+distribution function of this
+random variable is a standard
+
+normal random variable
+in the limit.
+
+So let's do one more example
+of a calculation.
+
+Let's take n to be--
+
+let's choose some specific
+numbers to work with.
+
+So in this example, first thing
+to do is to find the
+
+expected value of Sn,
+which is n times p.
+
+It's 18.
+
+Then we need to write down
+the standard deviation.
+
+The variance of Sn is the
+sum of the variances.
+
+It's np times (1-p).
+
+And in this particular example,
+p times (1-p) is 1/4,
+
+n is 36, so this is 9.
+
+And that tells us that the
+standard deviation of this n
+
+is equal to 3.
+
+So what we're going to do is to
+take the event of interest,
+
+which is Sn less than 21, and
+rewrite it in a way that
+
+involves the standardized
+random variable.
+
+So to do that, we need
+to subtract the mean.
+
+So we write this as Sn-3
+should be less
+
+than or equal to 21-3.
+
+This is the same event.
+
+And then divide by the standard
+deviation, which is
+
+3, and we end up with this.
+
+So the event itself of--
+
+AUDIENCE: [INAUDIBLE].
+
+Should subtract, 18, yes, which
+gives me a much nicer
+
+number out here, which is 1.
+
+So the event of interest, that
+Sn is less than 21, is the
+
+same as the event that a
+standard normal random
+
+variable is less than
+or equal to 1.
+
+And once more, you can look this
+up at the normal tables.
+
+And you find that the answer
+that you get is 0.43.
+
+Now it's interesting to compare
+this answer that we
+
+got through the central limit
+theorem with the exact answer.
+
+The exact answer involves the
+exact binomial distribution.
+
+What we have here is the
+binomial probability that, Sn
+
+is equal to k.
+
+Sn being equal to k is given
+by this formula.
+
+And we add, over all values for
+k going from 0 up to 21,
+
+we write a two lines code to
+calculate this sum, and we get
+
+the exact answer,
+which is 0.8785.
+
+So there's a pretty good
+agreements between the two,
+
+although you wouldn't
+call that's
+
+necessarily excellent agreement.
+
+Can we do a little
+better than that?
+
+OK.
+
+It turns out that we can.
+
+And here's the idea.
+
+So our random variable
+Sn has a mean of 18.
+
+It has a binomial
+distribution.
+
+It's described by a PMF that has
+a shape roughly like this
+
+and which keeps going on.
+
+Using the central limit
+theorem is basically
+
+pretending that Sn is
+normal with the
+
+right mean and variance.
+
+So pretending that Zn has
+0 mean unit variance, we
+
+approximate it with Z, that
+has 0 mean unit variance.
+
+If you were to pretend that
+Sn is normal, you would
+
+approximate it with a normal
+that has the correct mean and
+
+correct variance.
+
+So it would still be
+centered at 18.
+
+And it would have the same
+variance as the binomial PMF.
+
+So using the central limit
+theorem essentially means that
+
+we keep the mean and the
+variance what they are but we
+
+pretend that our distribution
+is normal.
+
+We want to calculate the
+probability that Sn is less
+
+than or equal to 21.
+
+I pretend that my random
+variable is normal, so I draw
+
+a line here and I calculate
+the area under the normal
+
+curve going up to 21.
+
+That's essentially
+what we did.
+
+Now, a smart person comes
+around and says, Sn is a
+
+discrete random variable.
+
+So the event that Sn is less
+than or equal to 21 is the
+
+same as Sn being strictly less
+than 22 because nothing in
+
+between can happen.
+
+So I'm going to use the
+central limit theorem
+
+approximation by pretending
+again that Sn is normal and
+
+finding the probability of this
+event while pretending
+
+that Sn is normal.
+
+So what this person would do
+would be to draw a line here,
+
+at 22, and calculate the area
+under the normal curve
+
+all the way to 22.
+
+Who is right?
+
+Which one is better?
+
+Well neither, but we can do
+better than both if we sort of
+
+split the difference.
+
+So another way of writing the
+same event for Sn is to write
+
+it as Sn being less than 21.5.
+
+In terms of the discrete random
+variable Sn, all three
+
+of these are exactly
+the same event.
+
+But when you do the continuous
+approximation, they give you
+
+different probabilities.
+
+It's a matter of whether you
+integrate the area under the
+
+normal curve up to here, up to
+the midway point, or up to 22.
+
+It turns out that integrating
+up to the midpoint is what
+
+gives us the better
+numerical results.
+
+So we take here 21 and 1/2,
+and we integrate the area
+
+under the normal curve
+up to here.
+
+So let's do this calculation
+and see what we get.
+
+What would we change here?
+
+Instead of 21, we would
+now write 21 and 1/2.
+
+This 18 becomes, no, that
+18 stays what it is.
+
+But this 21 becomes
+21 and 1/2.
+
+And so this one becomes
+1 + 0.5 by 3.
+
+This is 117.
+
+So we now look up into the
+normal tables and ask for the
+
+probability that Z is
+less than 1.17.
+
+So this here gets approximated
+by the probability that the
+
+standard normal is
+less than 1.17.
+
+And the normal tables will
+tell us this is 0.879.
+
+Going back to the previous
+slide, what we got this time
+
+with this improved approximation
+is 0.879.
+
+This is a really good
+approximation
+
+of the correct number.
+
+This is what we got
+using the 21.
+
+This is what we get using
+the 21 and 1/2.
+
+And it's an approximation that's
+sort of right on-- a
+
+very good one.
+
+The moral from this numerical
+example is that doing this 1
+
+and 1/2 correction does give
+us better approximations.
+
+In fact, we can use this 1/2
+idea to even calculate
+
+individual probabilities.
+
+So suppose you want to
+approximate the probability
+
+that Sn equal to 19.
+
+If you were to pretend that Sn
+is normal and calculate this
+
+probability, the probability
+that the normal random
+
+variable is equal to 19 is 0.
+
+So you don't get an interesting
+answer.
+
+You get a more interesting
+answer by writing this event,
+
+19 as being the same as the
+event of falling between 18
+
+and 1/2 and 19 and 1/2 and using
+the normal approximation
+
+to calculate this probability.
+
+In terms of our previous
+picture, this corresponds to
+
+the following.
+
+We are interested in the
+probability that
+
+Sn is equal to 19.
+
+So we're interested in the
+height of this bar.
+
+We're going to consider the area
+under the normal curve
+
+going from here to here,
+and use this area as an
+
+approximation for the height
+of that particular bar.
+
+So what we're basically doing
+is, we take the probability
+
+under the normal curve that's
+assigned over a continuum of
+
+values and attributed it to
+different discrete values.
+
+Whatever is above the midpoint
+gets attributed to 19.
+
+Whatever is below that
+midpoint gets
+
+attributed to 18.
+
+So this is green area is our
+approximation of the value of
+
+the PMF at 19.
+
+So similarly, if you wanted to
+approximate the value of the
+
+PMF at this point, you would
+take this interval and
+
+integrate the area
+under the normal
+
+curve over that interval.
+
+It turns out that this gives a
+very good approximation of the
+
+PMF of the binomial.
+
+And actually, this was the
+context in which the central
+
+limit theorem was proved in
+the first place, when this
+
+business started.
+
+So this business goes back
+a few hundred years.
+
+And the central limit theorem
+was first approved by
+
+considering the PMF of a
+binomial random variable when
+
+p is equal to 1/2.
+
+People did the algebra, and they
+found out that the exact
+
+expression for the PMF is quite
+well approximated by
+
+that expression hat you would
+get from a normal
+
+distribution.
+
+Then the proof was extended to
+binomials for more general
+
+values of p.
+
+So here we talk about this as
+a refinement of the general
+
+central limit theorem, but,
+historically, that refinement
+
+was where the whole business
+got started
+
+in the first place.
+
+All right, so let's go through
+the mechanics of approximating
+
+the probability that
+Sn is equal to 19--
+
+exactly 19.
+
+As we said, we're going to write
+this event as an event
+
+that covers an interval of unit
+length from 18 and 1/2 to
+
+19 and 1/2.
+
+This is the event of interest.
+
+First step is to massage the
+event of interest so that it
+
+involves our Zn random
+variable.
+
+So subtract 18 from all sides.
+
+Divide by the standard deviation
+of 3 from all sides.
+
+That's the equivalent
+representation of the event.
+
+This is our standardized
+random variable Zn.
+
+These are just these numbers.
+
+And to do an approximation, we
+want to find the probability
+
+of this event, but Zn is
+approximately normal, so we
+
+plug in here the Z, which
+is the standard normal.
+
+So we want to find the
+probability that the standard
+
+normal falls inside
+this interval.
+
+You find these using CDFs
+because this is the
+
+probability that you're
+less than this but
+
+not less than that.
+
+So it's a difference between two
+cumulative probabilities.
+
+Then, you look up your
+normal tables.
+
+You find two numbers for these
+quantities, and, finally, you
+
+get a numerical answer for an
+individual entry of the PMF of
+
+the binomial.
+
+This is a pretty good
+approximation, it turns out.
+
+If you were to do the
+calculations using the exact
+
+formula, you would
+get something
+
+which is pretty close--
+
+an error in the third digit--
+
+this is pretty good.
+
+So I guess what we did here
+with our discussion of the
+
+binomial slightly contradicts
+what I said before--
+
+that the central limit theorem
+is a statement about
+
+cumulative distribution
+functions.
+
+In general, it doesn't tell you
+what to do to approximate
+
+PMFs themselves.
+
+And that's indeed the
+case in general.
+
+One the other hand, for the
+special case of a binomial
+
+distribution, the central limit
+theorem approximation,
+
+with this 1/2 correction, is a
+very good approximation even
+
+for the individual PMF.
+
+All right, so we spent quite
+a bit of time on mechanics.
+
+So let's spend the last few
+minutes today thinking a bit
+
+and look at a small puzzle.
+
+So the puzzle is
+the following.
+
+Consider Poisson process that
+runs over a unit interval.
+
+And where the arrival
+rate is equal to 1.
+
+So this is the unit interval.
+
+And let X be the number
+of arrivals.
+
+And this is Poisson,
+with mean 1.
+
+Now, let me take this interval
+and divide it
+
+into n little pieces.
+
+So each piece has length 1/n.
+
+And let Xi be the number
+of arrivals during
+
+the Ith little interval.
+
+OK, what do we know about
+the random variables Xi?
+
+Is they are themselves
+Poisson.
+
+It's a number of arrivals
+during a small interval.
+
+We also know that when n is
+big, so the length of the
+
+interval is small, these Xi's
+are approximately Bernoulli,
+
+with mean 1/n.
+
+Guess it doesn't matter whether
+we model them as
+
+Bernoulli or not.
+
+What matters is that the
+Xi's are independent.
+
+Why are they independent?
+
+Because, in a Poisson process,
+these joint intervals are
+
+independent of each other.
+
+So the Xi's are independent.
+
+And they also have the
+same distribution.
+
+And we have that X, the total
+number of arrivals, is the sum
+
+over the Xn's.
+
+So the central limit theorem
+tells us that, approximately,
+
+the sum of independent,
+identically distributed random
+
+variables, when we have lots
+of these random variables,
+
+behaves like a normal
+random variable.
+
+So by using this decomposition
+of X into a sum of i.i.d
+
+random variables, and by using
+values of n that are bigger
+
+and bigger, by taking the limit,
+it should follow that X
+
+has a normal distribution.
+
+On the other hand, we know
+that X has a Poisson
+
+distribution.
+
+So something must be wrong
+in this argument here.
+
+Can we really use the
+central limit
+
+theorem in this situation?
+
+So what do we need for the
+central limit theorem?
+
+We need to have independent,
+identically
+
+distributed random variables.
+
+We have it here.
+
+We want them to have a finite
+mean and finite variance.
+
+We also have it here, means
+variances are finite.
+
+What is another assumption that
+was never made explicit,
+
+but essentially was there?
+
+Or in other words, what is the
+flaw in this argument that
+
+uses the central limit
+theorem here?
+
+Any thoughts?
+
+So in the central limit theorem,
+we said, consider--
+
+fix a probability distribution,
+and let the Xi's
+
+be distributed according to that
+probability distribution,
+
+and add a larger and larger
+number or Xi's.
+
+But the underlying, unstated
+assumption is that we fix the
+
+distribution of the Xi's.
+
+As we let n increase,
+the statistics of
+
+each Xi do not change.
+
+Whereas here, I'm playing
+a trick on you.
+
+As I'm taking more and more
+random variables, I'm actually
+
+changing what those random
+variables are.
+
+When I take a larger n, the Xi's
+are random variables with
+
+a different mean and
+different variance.
+
+So I'm adding more of these, but
+at the same time, in this
+
+example, I'm changing
+their distributions.
+
+That's something that doesn't
+fit the setting of the central
+
+limit theorem.
+
+In the central limit theorem,
+you first fix the distribution
+
+of the X's.
+
+You keep it fixed, and then you
+consider adding more and
+
+more according to that
+particular fixed distribution.
+
+So that's the catch.
+
+That's why the central limit
+theorem does not
+
+apply to this situation.
+
+And we're lucky that it
+doesn't apply because,
+
+otherwise, we would have a huge
+contradiction destroying
+
+probability theory.
+
+OK, but now that's still
+leaves us with a
+
+little bit of a dilemma.
+
+Suppose that, here, essentially
+we're adding
+
+independent Bernoulli
+random variables.
+
+So the issue is that the central
+limit theorem has to
+
+do with asymptotics as
+n goes to infinity.
+
+And if we consider a binomial,
+and somebody gives us specific
+
+numbers about the parameters of
+that binomial, it might not
+
+necessarily be obvious
+what kind of
+
+approximation do we use.
+
+In particular, we do have two
+different approximations for
+
+the binomial.
+
+If we fix p, then the binomial
+is the sum of Bernoulli's that
+
+come from a fixed distribution,
+we consider more
+
+and more of these.
+
+When we add them, the central
+limit theorem tells us that we
+
+get the normal distribution.
+
+There's another sort of limit,
+which has the flavor of this
+
+example, in which we still deal
+with a binomial, sum of n
+
+Bernoulli's.
+
+We let that sum, the
+number of the
+
+Bernoulli's go to infinity.
+
+But each Bernoulli has a
+probability of success that
+
+goes to 0, and we do this in a
+way so that np, the expected
+
+number of successes,
+stays finite.
+
+This is the situation that we
+dealt with when we first
+
+defined our Poisson process.
+
+We have a very, very large
+number so lots, of time slots,
+
+but during each time slot,
+there's a tiny probability of
+
+obtaining an arrival.
+
+Under that setting, in discrete
+time, we have a
+
+binomial distribution, or
+Bernoulli process, but when we
+
+take the limit, we obtain the
+Poisson process and the
+
+Poisson approximation.
+
+So these are two equally valid
+
+approximations of the binomial.
+
+But they're valid in different
+asymptotic regimes.
+
+In one regime, we fixed p,
+let n go to infinity.
+
+In the other regime, we let
+both n and p change
+
+simultaneously.
+
+Now, in real life, you're
+never dealing with the
+
+limiting situations.
+
+You're dealing with
+actual numbers.
+
+So if somebody tells you that
+the numbers are like this,
+
+then you should probably say
+that this is the situation
+
+that fits the Poisson
+description--
+
+large number of slots with
+each slot having a tiny
+
+probability of success.
+
+On the other hand, if p is
+something like this, and n is
+
+500, then you expect to get
+the distribution for the
+
+number of successes.
+
+It's going to have a mean of 50
+and to have a fair amount
+
+of spread around there.
+
+It turns out that the normal
+approximation would be better
+
+in this context.
+
+As a rule of thumb, if n times p
+is bigger than 10 or 20, you
+
+can start using the normal
+approximation.
+
+If n times p is a small number,
+then you prefer to use
+
+the Poisson approximation.
+
+But there's no hard theorems
+or rules about
+
+how to go about this.
+
+OK, so from next time we're
+going to switch base again.
+
+And we're going to put together
+everything we learned
+
+in this class to start solving
+inference problems.
\ No newline at end of file
diff --git a/UbQcqFH33G0.txt b/UbQcqFH33G0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..706fc2029043819f1b6530e9a51990ec0f773f9f
--- /dev/null
+++ b/UbQcqFH33G0.txt
@@ -0,0 +1,867 @@
+align:start position:0%
+ 
+suppose I have a fair coin which I toss
+
+ align:start position:0%
+suppose I have a fair coin which I toss
+ 
+
+ align:start position:0%
+suppose I have a fair coin which I toss
+multiple times I want to model a
+
+ align:start position:0%
+multiple times I want to model a
+ 
+
+ align:start position:0%
+multiple times I want to model a
+situation where the results of previous
+
+ align:start position:0%
+situation where the results of previous
+ 
+
+ align:start position:0%
+situation where the results of previous
+flips do not affect my beliefs about the
+
+ align:start position:0%
+flips do not affect my beliefs about the
+ 
+
+ align:start position:0%
+flips do not affect my beliefs about the
+likelihood of heads in the next flip and
+
+ align:start position:0%
+likelihood of heads in the next flip and
+ 
+
+ align:start position:0%
+likelihood of heads in the next flip and
+I would like to describe the situation
+
+ align:start position:0%
+I would like to describe the situation
+ 
+
+ align:start position:0%
+I would like to describe the situation
+by saying that the coin tosses are
+
+ align:start position:0%
+by saying that the coin tosses are
+ 
+
+ align:start position:0%
+by saying that the coin tosses are
+independent you may say we already
+
+ align:start position:0%
+independent you may say we already
+ 
+
+ align:start position:0%
+independent you may say we already
+defined the notion of independent events
+
+ align:start position:0%
+defined the notion of independent events
+ 
+
+ align:start position:0%
+defined the notion of independent events
+doesn't this notion apply well not quite
+
+ align:start position:0%
+doesn't this notion apply well not quite
+ 
+
+ align:start position:0%
+doesn't this notion apply well not quite
+we defined independence of two events
+
+ align:start position:0%
+we defined independence of two events
+ 
+
+ align:start position:0%
+we defined independence of two events
+but here we want to talk about
+
+ align:start position:0%
+but here we want to talk about
+ 
+
+ align:start position:0%
+but here we want to talk about
+independence of a collection of events
+
+ align:start position:0%
+independence of a collection of events
+ 
+
+ align:start position:0%
+independence of a collection of events
+for example we would like to say that
+
+ align:start position:0%
+for example we would like to say that
+ 
+
+ align:start position:0%
+for example we would like to say that
+the events hands in the first toss heads
+
+ align:start position:0%
+the events hands in the first toss heads
+ 
+
+ align:start position:0%
+the events hands in the first toss heads
+in the second toss hands in the third
+
+ align:start position:0%
+in the second toss hands in the third
+ 
+
+ align:start position:0%
+in the second toss hands in the third
+toss and so on are all independent what
+
+ align:start position:0%
+toss and so on are all independent what
+ 
+
+ align:start position:0%
+toss and so on are all independent what
+is the right definition let us start
+
+ align:start position:0%
+is the right definition let us start
+ 
+
+ align:start position:0%
+is the right definition let us start
+with intuition we will say that a family
+
+ align:start position:0%
+with intuition we will say that a family
+ 
+
+ align:start position:0%
+with intuition we will say that a family
+of events are independent if knowledge
+
+ align:start position:0%
+of events are independent if knowledge
+ 
+
+ align:start position:0%
+of events are independent if knowledge
+about some of the events does not change
+
+ align:start position:0%
+about some of the events does not change
+ 
+
+ align:start position:0%
+about some of the events does not change
+my beliefs my probability model for the
+
+ align:start position:0%
+my beliefs my probability model for the
+ 
+
+ align:start position:0%
+my beliefs my probability model for the
+remaining events for example if I want
+
+ align:start position:0%
+remaining events for example if I want
+ 
+
+ align:start position:0%
+remaining events for example if I want
+to say that events a1 a2 and so on are
+
+ align:start position:0%
+to say that events a1 a2 and so on are
+ 
+
+ align:start position:0%
+to say that events a1 a2 and so on are
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+I would like relations such as the
+
+ align:start position:0%
+I would like relations such as the
+ 
+
+ align:start position:0%
+I would like relations such as the
+following to be true the probability
+
+ align:start position:0%
+following to be true the probability
+ 
+
+ align:start position:0%
+following to be true the probability
+that event a3 happened and
+
+ align:start position:0%
+that event a3 happened and
+ 
+
+ align:start position:0%
+that event a3 happened and
+event a4 does not happen remains the
+
+ align:start position:0%
+event a4 does not happen remains the
+ 
+
+ align:start position:0%
+event a4 does not happen remains the
+same even if I condition on some
+
+ align:start position:0%
+same even if I condition on some
+ 
+
+ align:start position:0%
+same even if I condition on some
+information about some other events
+
+ align:start position:0%
+information about some other events
+ 
+
+ align:start position:0%
+information about some other events
+let's say if I tell you that a 1
+
+ align:start position:0%
+let's say if I tell you that a 1
+ 
+
+ align:start position:0%
+let's say if I tell you that a 1
+happened or that both a to happen and a5
+
+ align:start position:0%
+happened or that both a to happen and a5
+ 
+
+ align:start position:0%
+happened or that both a to happen and a5
+did not happen the important thing to
+
+ align:start position:0%
+did not happen the important thing to
+ 
+
+ align:start position:0%
+did not happen the important thing to
+notice here is that the indices involved
+
+ align:start position:0%
+notice here is that the indices involved
+ 
+
+ align:start position:0%
+notice here is that the indices involved
+in the event of interest are distinct
+
+ align:start position:0%
+in the event of interest are distinct
+ 
+
+ align:start position:0%
+in the event of interest are distinct
+from the indices associated with the
+
+ align:start position:0%
+from the indices associated with the
+ 
+
+ align:start position:0%
+from the indices associated with the
+events on which I am given some
+
+ align:start position:0%
+events on which I am given some
+ 
+
+ align:start position:0%
+events on which I am given some
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+I'm given some information about events
+
+ align:start position:0%
+I'm given some information about events
+ 
+
+ align:start position:0%
+I'm given some information about events
+a 1 a 2 and a 5 what happens to them
+
+ align:start position:0%
+a 1 a 2 and a 5 what happens to them
+ 
+
+ align:start position:0%
+a 1 a 2 and a 5 what happens to them
+and this information does not affect my
+
+ align:start position:0%
+and this information does not affect my
+ 
+
+ align:start position:0%
+and this information does not affect my
+beliefs about something that has to do
+
+ align:start position:0%
+beliefs about something that has to do
+ 
+
+ align:start position:0%
+beliefs about something that has to do
+with events a 3 and a 4 I would like all
+
+ align:start position:0%
+with events a 3 and a 4 I would like all
+ 
+
+ align:start position:0%
+with events a 3 and a 4 I would like all
+relations of this kind to be true this
+
+ align:start position:0%
+relations of this kind to be true this
+ 
+
+ align:start position:0%
+relations of this kind to be true this
+could be one possible definition just
+
+ align:start position:0%
+could be one possible definition just
+ 
+
+ align:start position:0%
+could be one possible definition just
+saying that the family of events are
+
+ align:start position:0%
+saying that the family of events are
+ 
+
+ align:start position:0%
+saying that the family of events are
+independent if and only if any relation
+
+ align:start position:0%
+independent if and only if any relation
+ 
+
+ align:start position:0%
+independent if and only if any relation
+of this type is true but such a
+
+ align:start position:0%
+of this type is true but such a
+ 
+
+ align:start position:0%
+of this type is true but such a
+definition would not be aesthetically
+
+ align:start position:0%
+definition would not be aesthetically
+ 
+
+ align:start position:0%
+definition would not be aesthetically
+pleasing instead we introduce the
+
+ align:start position:0%
+pleasing instead we introduce the
+ 
+
+ align:start position:0%
+pleasing instead we introduce the
+following definition which mimics or
+
+ align:start position:0%
+following definition which mimics or
+ 
+
+ align:start position:0%
+following definition which mimics or
+parallels our earlier definition of
+
+ align:start position:0%
+parallels our earlier definition of
+ 
+
+ align:start position:0%
+parallels our earlier definition of
+independence of two events we will say
+
+ align:start position:0%
+independence of two events we will say
+ 
+
+ align:start position:0%
+independence of two events we will say
+that a collection of events are
+
+ align:start position:0%
+that a collection of events are
+ 
+
+ align:start position:0%
+that a collection of events are
+independent if you can calculate
+
+ align:start position:0%
+independent if you can calculate
+ 
+
+ align:start position:0%
+independent if you can calculate
+probabilities of intersections of these
+
+ align:start position:0%
+probabilities of intersections of these
+ 
+
+ align:start position:0%
+probabilities of intersections of these
+events by multiplying individual
+
+ align:start position:0%
+events by multiplying individual
+ 
+
+ align:start position:0%
+events by multiplying individual
+probabilities and this should be
+
+ align:start position:0%
+probabilities and this should be
+ 
+
+ align:start position:0%
+probabilities and this should be
+possible for all choices of indices
+
+ align:start position:0%
+possible for all choices of indices
+ 
+
+ align:start position:0%
+possible for all choices of indices
+involved and for any number of events
+
+ align:start position:0%
+involved and for any number of events
+ 
+
+ align:start position:0%
+involved and for any number of events
+ever involved let us translate this into
+
+ align:start position:0%
+ever involved let us translate this into
+ 
+
+ align:start position:0%
+ever involved let us translate this into
+something concrete consider the case of
+
+ align:start position:0%
+something concrete consider the case of
+ 
+
+ align:start position:0%
+something concrete consider the case of
+three events a1 a2 and a3 our definition
+
+ align:start position:0%
+three events a1 a2 and a3 our definition
+ 
+
+ align:start position:0%
+three events a1 a2 and a3 our definition
+requires that we can calculate
+
+ align:start position:0%
+requires that we can calculate
+ 
+
+ align:start position:0%
+requires that we can calculate
+probability the probability of the
+
+ align:start position:0%
+probability the probability of the
+ 
+
+ align:start position:0%
+probability the probability of the
+intersection of two events by
+
+ align:start position:0%
+intersection of two events by
+ 
+
+ align:start position:0%
+intersection of two events by
+multiplying individual probabilities and
+
+ align:start position:0%
+multiplying individual probabilities and
+ 
+
+ align:start position:0%
+multiplying individual probabilities and
+we would like all these three relations
+
+ align:start position:0%
+we would like all these three relations
+ 
+
+ align:start position:0%
+we would like all these three relations
+to be true because this property should
+
+ align:start position:0%
+to be true because this property should
+ 
+
+ align:start position:0%
+to be true because this property should
+be true for any choice of the indices
+
+ align:start position:0%
+be true for any choice of the indices
+ 
+
+ align:start position:0%
+be true for any choice of the indices
+what do we have here this relation tells
+
+ align:start position:0%
+what do we have here this relation tells
+ 
+
+ align:start position:0%
+what do we have here this relation tells
+us that a1 and a2 are independent this
+
+ align:start position:0%
+us that a1 and a2 are independent this
+ 
+
+ align:start position:0%
+us that a1 and a2 are independent this
+relation tells us that a1 and a3 are
+
+ align:start position:0%
+relation tells us that a1 and a3 are
+ 
+
+ align:start position:0%
+relation tells us that a1 and a3 are
+independent this relation tells us that
+
+ align:start position:0%
+independent this relation tells us that
+ 
+
+ align:start position:0%
+independent this relation tells us that
+a2 and a3 are independent we call this
+
+ align:start position:0%
+a2 and a3 are independent we call this
+ 
+
+ align:start position:0%
+a2 and a3 are independent we call this
+situation pairwise independence but the
+
+ align:start position:0%
+situation pairwise independence but the
+ 
+
+ align:start position:0%
+situation pairwise independence but the
+definition requires something more it
+
+ align:start position:0%
+definition requires something more it
+ 
+
+ align:start position:0%
+definition requires something more it
+requires that the probability of 3-way
+
+ align:start position:0%
+requires that the probability of 3-way
+ 
+
+ align:start position:0%
+requires that the probability of 3-way
+intersections can also be calculated the
+
+ align:start position:0%
+intersections can also be calculated the
+ 
+
+ align:start position:0%
+intersections can also be calculated the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+way by multiplying individual
+
+ align:start position:0%
+way by multiplying individual
+ 
+
+ align:start position:0%
+way by multiplying individual
+probabilities and this additional
+
+ align:start position:0%
+probabilities and this additional
+ 
+
+ align:start position:0%
+probabilities and this additional
+condition does make a difference as
+
+ align:start position:0%
+condition does make a difference as
+ 
+
+ align:start position:0%
+condition does make a difference as
+we're going to see in a later example is
+
+ align:start position:0%
+we're going to see in a later example is
+ 
+
+ align:start position:0%
+we're going to see in a later example is
+this the right definition yes one can
+
+ align:start position:0%
+this the right definition yes one can
+ 
+
+ align:start position:0%
+this the right definition yes one can
+prove formally that if the conditions in
+
+ align:start position:0%
+prove formally that if the conditions in
+ 
+
+ align:start position:0%
+prove formally that if the conditions in
+this definition are satisfied then any
+
+ align:start position:0%
+this definition are satisfied then any
+ 
+
+ align:start position:0%
+this definition are satisfied then any
+formula of this kind is true in
+
+ align:start position:0%
+formula of this kind is true in
+ 
+
+ align:start position:0%
+formula of this kind is true in
+particular we also have relations such
+
+ align:start position:0%
+particular we also have relations such
+ 
+
+ align:start position:0%
+particular we also have relations such
+as the following the probability of
+
+ align:start position:0%
+as the following the probability of
+ 
+
+ align:start position:0%
+as the following the probability of
+event a 3 is the same as the probability
+
+ align:start position:0%
+event a 3 is the same as the probability
+ 
+
+ align:start position:0%
+event a 3 is the same as the probability
+of event a 3 given that a1 and a2
+
+ align:start position:0%
+of event a 3 given that a1 and a2
+ 
+
+ align:start position:0%
+of event a 3 given that a1 and a2
+occurred or the probability of a 3
+
+ align:start position:0%
+occurred or the probability of a 3
+ 
+
+ align:start position:0%
+occurred or the probability of a 3
+given that a1 occurred but a2 didn't or
+
+ align:start position:0%
+given that a1 occurred but a2 didn't or
+ 
+
+ align:start position:0%
+given that a1 occurred but a2 didn't or
+we can continually similarly the
+
+ align:start position:0%
+we can continually similarly the
+ 
+
+ align:start position:0%
+we can continually similarly the
+probability of a 3 given that a1 did not
+
+ align:start position:0%
+probability of a 3 given that a1 did not
+ 
+
+ align:start position:0%
+probability of a 3 given that a1 did not
+occur and a2 occurred and so on so any
+
+ align:start position:0%
+occur and a2 occurred and so on so any
+ 
+
+ align:start position:0%
+occur and a2 occurred and so on so any
+kind of information that I might give
+
+ align:start position:0%
+kind of information that I might give
+ 
+
+ align:start position:0%
+kind of information that I might give
+you about events a1 and a2 which one of
+
+ align:start position:0%
+you about events a1 and a2 which one of
+ 
+
+ align:start position:0%
+you about events a1 and a2 which one of
+them occurred and which one didn't is
+
+ align:start position:0%
+them occurred and which one didn't is
+ 
+
+ align:start position:0%
+them occurred and which one didn't is
+not going to affect my beliefs about
+
+ align:start position:0%
+not going to affect my beliefs about
+ 
+
+ align:start position:0%
+not going to affect my beliefs about
+event a3 the conditional probabilities
+
+ align:start position:0%
+event a3 the conditional probabilities
+ 
+
+ align:start position:0%
+event a3 the conditional probabilities
+are going to be the same as the
+
+ align:start position:0%
+are going to be the same as the
+ 
+
+ align:start position:0%
+are going to be the same as the
+unconditional probabilities I told you
+
+ align:start position:0%
+unconditional probabilities I told you
+ 
+
+ align:start position:0%
+unconditional probabilities I told you
+that this definition implies that all
+
+ align:start position:0%
+that this definition implies that all
+ 
+
+ align:start position:0%
+that this definition implies that all
+relations of this kind is true this can
+
+ align:start position:0%
+relations of this kind is true this can
+ 
+
+ align:start position:0%
+relations of this kind is true this can
+be proved the proof is a bit tedious and
+
+ align:start position:0%
+be proved the proof is a bit tedious and
+ 
+
+ align:start position:0%
+be proved the proof is a bit tedious and
+we will not go through it
\ No newline at end of file
diff --git a/VvQhR9o1RPw.txt b/VvQhR9o1RPw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3b35bade2bf4d1c65578210370450cc36bff7754
--- /dev/null
+++ b/VvQhR9o1RPw.txt
@@ -0,0 +1,26835 @@
+align:start position:0%
+ 
+what I want to do today is to start with
+
+ align:start position:0%
+what I want to do today is to start with
+ 
+
+ align:start position:0%
+what I want to do today is to start with
+the um chapter I gave you on marriage
+
+ align:start position:0%
+the um chapter I gave you on marriage
+ 
+
+ align:start position:0%
+the um chapter I gave you on marriage
+same seex and opposite
+
+ align:start position:0%
+same seex and opposite
+ 
+
+ align:start position:0%
+same seex and opposite
+sex and Veronica I think was going to
+
+ align:start position:0%
+sex and Veronica I think was going to
+ 
+
+ align:start position:0%
+sex and Veronica I think was going to
+give a
+
+ align:start position:0%
+give a
+ 
+
+ align:start position:0%
+give a
+presentation which could I don't know
+
+ align:start position:0%
+presentation which could I don't know
+ 
+
+ align:start position:0%
+presentation which could I don't know
+whether I asked for that uh cover that
+
+ align:start position:0%
+whether I asked for that uh cover that
+ 
+
+ align:start position:0%
+whether I asked for that uh cover that
+as well as the reading in the pursuit of
+
+ align:start position:0%
+as well as the reading in the pursuit of
+ 
+
+ align:start position:0%
+as well as the reading in the pursuit of
+love I mainly focused on the pursuit of
+
+ align:start position:0%
+love I mainly focused on the pursuit of
+ 
+
+ align:start position:0%
+love I mainly focused on the pursuit of
+love that
+
+ align:start position:0%
+love that
+ 
+
+ align:start position:0%
+love that
+could talk a little bit about the
+
+ align:start position:0%
+could talk a little bit about the
+ 
+
+ align:start position:0%
+could talk a little bit about the
+marriage one I've read it
+
+ align:start position:0%
+marriage one I've read it
+ 
+
+ align:start position:0%
+marriage one I've read it
+but well then should we wait for your uh
+
+ align:start position:0%
+but well then should we wait for your uh
+ 
+
+ align:start position:0%
+but well then should we wait for your uh
+presentation until people have had a
+
+ align:start position:0%
+presentation until people have had a
+ 
+
+ align:start position:0%
+presentation until people have had a
+chance to air their opinions about the
+
+ align:start position:0%
+chance to air their opinions about the
+ 
+
+ align:start position:0%
+chance to air their opinions about the
+uh about the marriage chapter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure I'm waiting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many um um Veronica could you take a
+
+ align:start position:0%
+how many um um Veronica could you take a
+ 
+
+ align:start position:0%
+how many um um Veronica could you take a
+head count not counting St
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us yeah I got that right stas uh who's
+
+ align:start position:0%
+us yeah I got that right stas uh who's
+ 
+
+ align:start position:0%
+us yeah I got that right stas uh who's
+just arrived uh but on the people who
+
+ align:start position:0%
+just arrived uh but on the people who
+ 
+
+ align:start position:0%
+just arrived uh but on the people who
+the other people how many have read that
+
+ align:start position:0%
+the other people how many have read that
+ 
+
+ align:start position:0%
+the other people how many have read that
+and how many how many have read it okay
+
+ align:start position:0%
+and how many how many have read it okay
+ 
+
+ align:start position:0%
+and how many how many have read it okay
+how many have read it 100% % well yes
+
+ align:start position:0%
+how many have read it 100% % well yes
+ 
+
+ align:start position:0%
+how many have read it 100% % well yes
+everyone everyone then I'm sure you must
+
+ align:start position:0%
+everyone everyone then I'm sure you must
+ 
+
+ align:start position:0%
+everyone everyone then I'm sure you must
+have some ideas about him should I give
+
+ align:start position:0%
+have some ideas about him should I give
+ 
+
+ align:start position:0%
+have some ideas about him should I give
+you a little introduction to get you
+
+ align:start position:0%
+you a little introduction to get you
+ 
+
+ align:start position:0%
+you a little introduction to get you
+started it's a subject that um has been
+
+ align:start position:0%
+started it's a subject that um has been
+ 
+
+ align:start position:0%
+started it's a subject that um has been
+Taboo in various respects first even to
+
+ align:start position:0%
+Taboo in various respects first even to
+ 
+
+ align:start position:0%
+Taboo in various respects first even to
+talk about homosexuality when I was your
+
+ align:start position:0%
+talk about homosexuality when I was your
+ 
+
+ align:start position:0%
+talk about homosexuality when I was your
+age was something nobody ever did uh and
+
+ align:start position:0%
+age was something nobody ever did uh and
+ 
+
+ align:start position:0%
+age was something nobody ever did uh and
+when I was your age I had I'm pretty
+
+ align:start position:0%
+when I was your age I had I'm pretty
+ 
+
+ align:start position:0%
+when I was your age I had I'm pretty
+sure no ideas what that could be or who
+
+ align:start position:0%
+sure no ideas what that could be or who
+ 
+
+ align:start position:0%
+sure no ideas what that could be or who
+who might indulge in such
+
+ align:start position:0%
+who might indulge in such
+ 
+
+ align:start position:0%
+who might indulge in such
+behavior um people didn't talk about it
+
+ align:start position:0%
+behavior um people didn't talk about it
+ 
+
+ align:start position:0%
+behavior um people didn't talk about it
+and the Assumption was if you were a
+
+ align:start position:0%
+and the Assumption was if you were a
+ 
+
+ align:start position:0%
+and the Assumption was if you were a
+normal person which we all think we are
+
+ align:start position:0%
+normal person which we all think we are
+ 
+
+ align:start position:0%
+normal person which we all think we are
+um that um we would grow up in a very
+
+ align:start position:0%
+um that um we would grow up in a very
+ 
+
+ align:start position:0%
+um that um we would grow up in a very
+different way the boys one way
+
+ align:start position:0%
+different way the boys one way
+ 
+
+ align:start position:0%
+different way the boys one way
+aggressive manly and viral um chasing
+
+ align:start position:0%
+aggressive manly and viral um chasing
+ 
+
+ align:start position:0%
+aggressive manly and viral um chasing
+the girls and the girls in their own way
+
+ align:start position:0%
+the girls and the girls in their own way
+ 
+
+ align:start position:0%
+the girls and the girls in their own way
+delicate gentle not terribly um uh
+
+ align:start position:0%
+delicate gentle not terribly um uh
+ 
+
+ align:start position:0%
+delicate gentle not terribly um uh
+academic or intellectual and delighted
+
+ align:start position:0%
+academic or intellectual and delighted
+ 
+
+ align:start position:0%
+academic or intellectual and delighted
+to have the boys chasing them um all
+
+ align:start position:0%
+to have the boys chasing them um all
+ 
+
+ align:start position:0%
+to have the boys chasing them um all
+sorts of variations on that like in the
+
+ align:start position:0%
+sorts of variations on that like in the
+ 
+
+ align:start position:0%
+sorts of variations on that like in the
+um saying that
+
+ align:start position:0%
+um saying that
+ 
+
+ align:start position:0%
+um saying that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um a woman a man chases a woman until
+
+ align:start position:0%
+um a woman a man chases a woman until
+ 
+
+ align:start position:0%
+um a woman a man chases a woman until
+she catches
+
+ align:start position:0%
+she catches
+ 
+
+ align:start position:0%
+she catches
+him so that there was a kind of
+
+ align:start position:0%
+him so that there was a kind of
+ 
+
+ align:start position:0%
+him so that there was a kind of
+compliance in this stereotypical kind of
+
+ align:start position:0%
+compliance in this stereotypical kind of
+ 
+
+ align:start position:0%
+compliance in this stereotypical kind of
+relation ship in which the males were
+
+ align:start position:0%
+relation ship in which the males were
+ 
+
+ align:start position:0%
+relation ship in which the males were
+out to capture the women the women out
+
+ align:start position:0%
+out to capture the women the women out
+ 
+
+ align:start position:0%
+out to capture the women the women out
+to escape to run off uh but the women
+
+ align:start position:0%
+to escape to run off uh but the women
+ 
+
+ align:start position:0%
+to escape to run off uh but the women
+also wanting to be caught so that there
+
+ align:start position:0%
+also wanting to be caught so that there
+ 
+
+ align:start position:0%
+also wanting to be caught so that there
+could be some harmonious
+
+ align:start position:0%
+could be some harmonious
+ 
+
+ align:start position:0%
+could be some harmonious
+relationship that was that was sex as we
+
+ align:start position:0%
+relationship that was that was sex as we
+ 
+
+ align:start position:0%
+relationship that was that was sex as we
+knew it in my day uh which is a long
+
+ align:start position:0%
+knew it in my day uh which is a long
+ 
+
+ align:start position:0%
+knew it in my day uh which is a long
+time ago but nevertheless was
+
+ align:start position:0%
+time ago but nevertheless was
+ 
+
+ align:start position:0%
+time ago but nevertheless was
+characteristic of the much of the
+
+ align:start position:0%
+characteristic of the much of the
+ 
+
+ align:start position:0%
+characteristic of the much of the
+western world uh except that there was
+
+ align:start position:0%
+western world uh except that there was
+ 
+
+ align:start position:0%
+western world uh except that there was
+this subculture that nobody knew very
+
+ align:start position:0%
+this subculture that nobody knew very
+ 
+
+ align:start position:0%
+this subculture that nobody knew very
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+about about a hundred years ago people
+
+ align:start position:0%
+about about a hundred years ago people
+ 
+
+ align:start position:0%
+about about a hundred years ago people
+began
+
+ align:start position:0%
+began
+ 
+
+ align:start position:0%
+began
+um discussing and writing about that but
+
+ align:start position:0%
+um discussing and writing about that but
+ 
+
+ align:start position:0%
+um discussing and writing about that but
+it was always as a kind of subculture on
+
+ align:start position:0%
+it was always as a kind of subculture on
+ 
+
+ align:start position:0%
+it was always as a kind of subculture on
+on the fringes one good example of this
+
+ align:start position:0%
+on the fringes one good example of this
+ 
+
+ align:start position:0%
+on the fringes one good example of this
+situation is the writings of um marel
+
+ align:start position:0%
+situation is the writings of um marel
+ 
+
+ align:start position:0%
+situation is the writings of um marel
+po have any of you read his work but you
+
+ align:start position:0%
+po have any of you read his work but you
+ 
+
+ align:start position:0%
+po have any of you read his work but you
+by now you've all heard the name at
+
+ align:start position:0%
+by now you've all heard the name at
+ 
+
+ align:start position:0%
+by now you've all heard the name at
+least p r s hands down please um Marcel
+
+ align:start position:0%
+least p r s hands down please um Marcel
+ 
+
+ align:start position:0%
+least p r s hands down please um Marcel
+PR uh a a French author who died in
+
+ align:start position:0%
+PR uh a a French author who died in
+ 
+
+ align:start position:0%
+PR uh a a French author who died in
+1923 um and uh in my opinion and in the
+
+ align:start position:0%
+1923 um and uh in my opinion and in the
+ 
+
+ align:start position:0%
+1923 um and uh in my opinion and in the
+opinion of many people he was the
+
+ align:start position:0%
+opinion of many people he was the
+ 
+
+ align:start position:0%
+opinion of many people he was the
+greatest
+
+ align:start position:0%
+greatest
+ 
+
+ align:start position:0%
+greatest
+philosophical literary
+
+ align:start position:0%
+philosophical literary
+ 
+
+ align:start position:0%
+philosophical literary
+figure that ever
+
+ align:start position:0%
+figure that ever
+ 
+
+ align:start position:0%
+figure that ever
+existed um he was a novelist and also a
+
+ align:start position:0%
+existed um he was a novelist and also a
+ 
+
+ align:start position:0%
+existed um he was a novelist and also a
+Critic and short story writer but
+
+ align:start position:0%
+Critic and short story writer but
+ 
+
+ align:start position:0%
+Critic and short story writer but
+primarily well famous for u a work of
+
+ align:start position:0%
+primarily well famous for u a work of
+ 
+
+ align:start position:0%
+primarily well famous for u a work of
+his that came out in 13 volumes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called uh which is differently
+
+ align:start position:0%
+called uh which is differently
+ 
+
+ align:start position:0%
+called uh which is differently
+translated literally it means in
+
+ align:start position:0%
+translated literally it means in
+ 
+
+ align:start position:0%
+translated literally it means in
+research for lost
+
+ align:start position:0%
+research for lost
+ 
+
+ align:start position:0%
+research for lost
+time um and uh but it became famous in
+
+ align:start position:0%
+time um and uh but it became famous in
+ 
+
+ align:start position:0%
+time um and uh but it became famous in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+translation of uh Scott
+
+ align:start position:0%
+translation of uh Scott
+ 
+
+ align:start position:0%
+translation of uh Scott
+monrie uh of which is very different and
+
+ align:start position:0%
+monrie uh of which is very different and
+ 
+
+ align:start position:0%
+monrie uh of which is very different and
+we don't have to go into that but the um
+
+ align:start position:0%
+we don't have to go into that but the um
+ 
+
+ align:start position:0%
+we don't have to go into that but the um
+the point is that PR was homosexual
+
+ align:start position:0%
+the point is that PR was homosexual
+ 
+
+ align:start position:0%
+the point is that PR was homosexual
+never married
+
+ align:start position:0%
+never married
+ 
+
+ align:start position:0%
+never married
+uh he um condemns homosexuality in the
+
+ align:start position:0%
+uh he um condemns homosexuality in the
+ 
+
+ align:start position:0%
+uh he um condemns homosexuality in the
+novel he is one of the great figures in
+
+ align:start position:0%
+novel he is one of the great figures in
+ 
+
+ align:start position:0%
+novel he is one of the great figures in
+homosexual literature he talks about it
+
+ align:start position:0%
+homosexual literature he talks about it
+ 
+
+ align:start position:0%
+homosexual literature he talks about it
+and talks about different kinds of
+
+ align:start position:0%
+and talks about different kinds of
+ 
+
+ align:start position:0%
+and talks about different kinds of
+relationships but always in a way that
+
+ align:start position:0%
+relationships but always in a way that
+ 
+
+ align:start position:0%
+relationships but always in a way that
+is pajara of and uh in one one volume in
+
+ align:start position:0%
+is pajara of and uh in one one volume in
+ 
+
+ align:start position:0%
+is pajara of and uh in one one volume in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ales uh called um uh the cities cities
+
+ align:start position:0%
+ales uh called um uh the cities cities
+ 
+
+ align:start position:0%
+ales uh called um uh the cities cities
+of the plain or Sodom and gomorah um he
+
+ align:start position:0%
+of the plain or Sodom and gomorah um he
+ 
+
+ align:start position:0%
+of the plain or Sodom and gomorah um he
+has an essay about the evil of
+
+ align:start position:0%
+has an essay about the evil of
+ 
+
+ align:start position:0%
+has an essay about the evil of
+homosexuality and so one wonders what's
+
+ align:start position:0%
+homosexuality and so one wonders what's
+ 
+
+ align:start position:0%
+homosexuality and so one wonders what's
+going on with him but it was not
+
+ align:start position:0%
+going on with him but it was not
+ 
+
+ align:start position:0%
+going on with him but it was not
+uncharacteristic that um people were
+
+ align:start position:0%
+uncharacteristic that um people were
+ 
+
+ align:start position:0%
+uncharacteristic that um people were
+homosexual felt guilty felt that they
+
+ align:start position:0%
+homosexual felt guilty felt that they
+ 
+
+ align:start position:0%
+homosexual felt guilty felt that they
+were doing something wrong felt that
+
+ align:start position:0%
+were doing something wrong felt that
+ 
+
+ align:start position:0%
+were doing something wrong felt that
+they were evil and then they coped with
+
+ align:start position:0%
+they were evil and then they coped with
+ 
+
+ align:start position:0%
+they were evil and then they coped with
+it in all sorts of different ways two
+
+ align:start position:0%
+it in all sorts of different ways two
+ 
+
+ align:start position:0%
+it in all sorts of different ways two
+examples of homosexuals that who the
+
+ align:start position:0%
+examples of homosexuals that who the
+ 
+
+ align:start position:0%
+examples of homosexuals that who the
+names of whom you I'm sure know one is
+
+ align:start position:0%
+names of whom you I'm sure know one is
+ 
+
+ align:start position:0%
+names of whom you I'm sure know one is
+Leonardo
+
+ align:start position:0%
+Leonardo
+ 
+
+ align:start position:0%
+Leonardo
+DaVinci famous at MIT because he was a
+
+ align:start position:0%
+DaVinci famous at MIT because he was a
+ 
+
+ align:start position:0%
+DaVinci famous at MIT because he was a
+great inventor as well as a great artist
+
+ align:start position:0%
+great inventor as well as a great artist
+ 
+
+ align:start position:0%
+great inventor as well as a great artist
+and sculptor and the other was
+
+ align:start position:0%
+and sculptor and the other was
+ 
+
+ align:start position:0%
+and sculptor and the other was
+Michelangelo Da Vinci uh was uh a person
+
+ align:start position:0%
+Michelangelo Da Vinci uh was uh a person
+ 
+
+ align:start position:0%
+Michelangelo Da Vinci uh was uh a person
+who was very even
+
+ align:start position:0%
+who was very even
+ 
+
+ align:start position:0%
+who was very even
+tempered and he never showed signs of
+
+ align:start position:0%
+tempered and he never showed signs of
+ 
+
+ align:start position:0%
+tempered and he never showed signs of
+feeling guilty or miserable because of
+
+ align:start position:0%
+feeling guilty or miserable because of
+ 
+
+ align:start position:0%
+feeling guilty or miserable because of
+his sexual
+
+ align:start position:0%
+his sexual
+ 
+
+ align:start position:0%
+his sexual
+inclinations which which were not
+
+ align:start position:0%
+inclinations which which were not
+ 
+
+ align:start position:0%
+inclinations which which were not
+uncommon in the Renaissance
+
+ align:start position:0%
+uncommon in the Renaissance
+ 
+
+ align:start position:0%
+uncommon in the Renaissance
+uh Michelangelo who was devoutly
+
+ align:start position:0%
+uh Michelangelo who was devoutly
+ 
+
+ align:start position:0%
+uh Michelangelo who was devoutly
+Christian grew up lived into his 9s as a
+
+ align:start position:0%
+Christian grew up lived into his 9s as a
+ 
+
+ align:start position:0%
+Christian grew up lived into his 9s as a
+guilt rck person who was very forceful
+
+ align:start position:0%
+guilt rck person who was very forceful
+ 
+
+ align:start position:0%
+guilt rck person who was very forceful
+angry the you know the famous cliche
+
+ align:start position:0%
+angry the you know the famous cliche
+ 
+
+ align:start position:0%
+angry the you know the famous cliche
+about Michelangelo who was so aggressive
+
+ align:start position:0%
+about Michelangelo who was so aggressive
+ 
+
+ align:start position:0%
+about Michelangelo who was so aggressive
+well part of it was this fervor of guilt
+
+ align:start position:0%
+well part of it was this fervor of guilt
+ 
+
+ align:start position:0%
+well part of it was this fervor of guilt
+feeling that was operating in him they
+
+ align:start position:0%
+feeling that was operating in him they
+ 
+
+ align:start position:0%
+feeling that was operating in him they
+were both homosexuals both at the same
+
+ align:start position:0%
+were both homosexuals both at the same
+ 
+
+ align:start position:0%
+were both homosexuals both at the same
+time very different kinds of
+
+ align:start position:0%
+time very different kinds of
+ 
+
+ align:start position:0%
+time very different kinds of
+temperaments and very different
+
+ align:start position:0%
+temperaments and very different
+ 
+
+ align:start position:0%
+temperaments and very different
+attitudes toward their own sexual
+
+ align:start position:0%
+attitudes toward their own sexual
+ 
+
+ align:start position:0%
+attitudes toward their own sexual
+behavior uh in the case of Leonardo D
+
+ align:start position:0%
+behavior uh in the case of Leonardo D
+ 
+
+ align:start position:0%
+behavior uh in the case of Leonardo D
+Vino D Vinci he drew magnificent
+
+ align:start position:0%
+Vino D Vinci he drew magnificent
+ 
+
+ align:start position:0%
+Vino D Vinci he drew magnificent
+paintings of women the monaa is the most
+
+ align:start position:0%
+paintings of women the monaa is the most
+ 
+
+ align:start position:0%
+paintings of women the monaa is the most
+famous uh he seemed to understand the
+
+ align:start position:0%
+famous uh he seemed to understand the
+ 
+
+ align:start position:0%
+famous uh he seemed to understand the
+soul of women and could capture their
+
+ align:start position:0%
+soul of women and could capture their
+ 
+
+ align:start position:0%
+soul of women and could capture their
+beauty in various ways particularly uh
+
+ align:start position:0%
+beauty in various ways particularly uh
+ 
+
+ align:start position:0%
+beauty in various ways particularly uh
+the Virgin Mary uh in various religious
+
+ align:start position:0%
+the Virgin Mary uh in various religious
+ 
+
+ align:start position:0%
+the Virgin Mary uh in various religious
+paintings in the case of
+
+ align:start position:0%
+paintings in the case of
+ 
+
+ align:start position:0%
+paintings in the case of
+Michelangelo um he also um
+
+ align:start position:0%
+Michelangelo um he also um
+ 
+
+ align:start position:0%
+Michelangelo um he also um
+understood women and wrote poetry
+
+ align:start position:0%
+understood women and wrote poetry
+ 
+
+ align:start position:0%
+understood women and wrote poetry
+particularly toward the end of his life
+
+ align:start position:0%
+particularly toward the end of his life
+ 
+
+ align:start position:0%
+particularly toward the end of his life
+and um it's um love poetry of the sorts
+
+ align:start position:0%
+and um it's um love poetry of the sorts
+ 
+
+ align:start position:0%
+and um it's um love poetry of the sorts
+that people were writing men about
+
+ align:start position:0%
+that people were writing men about
+ 
+
+ align:start position:0%
+that people were writing men about
+women he had a very close
+
+ align:start position:0%
+women he had a very close
+ 
+
+ align:start position:0%
+women he had a very close
+relationship uh with a famous woman and
+
+ align:start position:0%
+relationship uh with a famous woman and
+ 
+
+ align:start position:0%
+relationship uh with a famous woman and
+um it's not clear whether how well well
+
+ align:start position:0%
+um it's not clear whether how well well
+ 
+
+ align:start position:0%
+um it's not clear whether how well well
+he knew her but people speak of his
+
+ align:start position:0%
+he knew her but people speak of his
+ 
+
+ align:start position:0%
+he knew her but people speak of his
+affair with her undoubtedly it was not a
+
+ align:start position:0%
+affair with her undoubtedly it was not a
+ 
+
+ align:start position:0%
+affair with her undoubtedly it was not a
+physical affair it was a very intimate
+
+ align:start position:0%
+physical affair it was a very intimate
+ 
+
+ align:start position:0%
+physical affair it was a very intimate
+kind of relationship that doesn't
+
+ align:start position:0%
+kind of relationship that doesn't
+ 
+
+ align:start position:0%
+kind of relationship that doesn't
+necessarily have to involve sex and they
+
+ align:start position:0%
+necessarily have to involve sex and they
+ 
+
+ align:start position:0%
+necessarily have to involve sex and they
+were both getting on in years uh so that
+
+ align:start position:0%
+were both getting on in years uh so that
+ 
+
+ align:start position:0%
+were both getting on in years uh so that
+through all of these complications and
+
+ align:start position:0%
+through all of these complications and
+ 
+
+ align:start position:0%
+through all of these complications and
+the case of PR what's interesting is
+
+ align:start position:0%
+the case of PR what's interesting is
+ 
+
+ align:start position:0%
+the case of PR what's interesting is
+that he should be explicitly attacking
+
+ align:start position:0%
+that he should be explicitly attacking
+ 
+
+ align:start position:0%
+that he should be explicitly attacking
+homosexuality while also being
+
+ align:start position:0%
+homosexuality while also being
+ 
+
+ align:start position:0%
+homosexuality while also being
+homosexual himself well this is a
+
+ align:start position:0%
+homosexual himself well this is a
+ 
+
+ align:start position:0%
+homosexual himself well this is a
+pattern to be studied but overtly or in
+
+ align:start position:0%
+pattern to be studied but overtly or in
+ 
+
+ align:start position:0%
+pattern to be studied but overtly or in
+ordinary Society at least the kind of
+
+ align:start position:0%
+ordinary Society at least the kind of
+ 
+
+ align:start position:0%
+ordinary Society at least the kind of
+lower class society that I grew up in no
+
+ align:start position:0%
+lower class society that I grew up in no
+ 
+
+ align:start position:0%
+lower class society that I grew up in no
+one knew anything about that when I was
+
+ align:start position:0%
+one knew anything about that when I was
+ 
+
+ align:start position:0%
+one knew anything about that when I was
+in the Army um I at one point I was um
+
+ align:start position:0%
+in the Army um I at one point I was um
+ 
+
+ align:start position:0%
+in the Army um I at one point I was um
+uh assigned a room in a hotel in which
+
+ align:start position:0%
+uh assigned a room in a hotel in which
+ 
+
+ align:start position:0%
+uh assigned a room in a hotel in which
+my unit was being bued uh in France and
+
+ align:start position:0%
+my unit was being bued uh in France and
+ 
+
+ align:start position:0%
+my unit was being bued uh in France and
+um there was there was a um it was a
+
+ align:start position:0%
+um there was there was a um it was a
+ 
+
+ align:start position:0%
+um there was there was a um it was a
+deluxe hotel it had only one bed in it
+
+ align:start position:0%
+deluxe hotel it had only one bed in it
+ 
+
+ align:start position:0%
+deluxe hotel it had only one bed in it
+but two soldiers so we slept in the same
+
+ align:start position:0%
+but two soldiers so we slept in the same
+ 
+
+ align:start position:0%
+but two soldiers so we slept in the same
+bed the idea that this might somehow be
+
+ align:start position:0%
+bed the idea that this might somehow be
+ 
+
+ align:start position:0%
+bed the idea that this might somehow be
+uh a danger to me who was not who didn't
+
+ align:start position:0%
+uh a danger to me who was not who didn't
+ 
+
+ align:start position:0%
+uh a danger to me who was not who didn't
+know know what homosexuality was
+
+ align:start position:0%
+know know what homosexuality was
+ 
+
+ align:start position:0%
+know know what homosexuality was
+probably or at least had no such
+
+ align:start position:0%
+probably or at least had no such
+ 
+
+ align:start position:0%
+probably or at least had no such
+inclinations and wasn't even experienced
+
+ align:start position:0%
+inclinations and wasn't even experienced
+ 
+
+ align:start position:0%
+inclinations and wasn't even experienced
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+heterosexuality that the idea of
+
+ align:start position:0%
+heterosexuality that the idea of
+ 
+
+ align:start position:0%
+heterosexuality that the idea of
+sleeping with another man didn't mean
+
+ align:start position:0%
+sleeping with another man didn't mean
+ 
+
+ align:start position:0%
+sleeping with another man didn't mean
+anything it was something people did uh
+
+ align:start position:0%
+anything it was something people did uh
+ 
+
+ align:start position:0%
+anything it was something people did uh
+especially poor people throughout the
+
+ align:start position:0%
+especially poor people throughout the
+ 
+
+ align:start position:0%
+especially poor people throughout the
+world have slept together in beds with
+
+ align:start position:0%
+world have slept together in beds with
+ 
+
+ align:start position:0%
+world have slept together in beds with
+people of the same sex without anything
+
+ align:start position:0%
+people of the same sex without anything
+ 
+
+ align:start position:0%
+people of the same sex without anything
+sexual occurring between them so that
+
+ align:start position:0%
+sexual occurring between them so that
+ 
+
+ align:start position:0%
+sexual occurring between them so that
+what's especially interesting and that's
+
+ align:start position:0%
+what's especially interesting and that's
+ 
+
+ align:start position:0%
+what's especially interesting and that's
+how I begin is how um revolutionary the
+
+ align:start position:0%
+how I begin is how um revolutionary the
+ 
+
+ align:start position:0%
+how I begin is how um revolutionary the
+present generation is the generation
+
+ align:start position:0%
+present generation is the generation
+ 
+
+ align:start position:0%
+present generation is the generation
+that you've grown into who talk about
+
+ align:start position:0%
+that you've grown into who talk about
+ 
+
+ align:start position:0%
+that you've grown into who talk about
+these things on television and in
+
+ align:start position:0%
+these things on television and in
+ 
+
+ align:start position:0%
+these things on television and in
+various other ways and in which U there
+
+ align:start position:0%
+various other ways and in which U there
+ 
+
+ align:start position:0%
+various other ways and in which U there
+has been a sexual revolution in the 60s
+
+ align:start position:0%
+has been a sexual revolution in the 60s
+ 
+
+ align:start position:0%
+has been a sexual revolution in the 60s
+and70s which liberated people to express
+
+ align:start position:0%
+and70s which liberated people to express
+ 
+
+ align:start position:0%
+and70s which liberated people to express
+their attitudes more fre than they ever
+
+ align:start position:0%
+their attitudes more fre than they ever
+ 
+
+ align:start position:0%
+their attitudes more fre than they ever
+could have previously and one of these
+
+ align:start position:0%
+could have previously and one of these
+ 
+
+ align:start position:0%
+could have previously and one of these
+forms of Liberation occurred in a
+
+ align:start position:0%
+forms of Liberation occurred in a
+ 
+
+ align:start position:0%
+forms of Liberation occurred in a
+greater awareness about
+
+ align:start position:0%
+greater awareness about
+ 
+
+ align:start position:0%
+greater awareness about
+homosexuality it's more complicated in
+
+ align:start position:0%
+homosexuality it's more complicated in
+ 
+
+ align:start position:0%
+homosexuality it's more complicated in
+one important respect that I didn't want
+
+ align:start position:0%
+one important respect that I didn't want
+ 
+
+ align:start position:0%
+one important respect that I didn't want
+to go into and that is um the U work of
+
+ align:start position:0%
+to go into and that is um the U work of
+ 
+
+ align:start position:0%
+to go into and that is um the U work of
+Sigman
+
+ align:start position:0%
+Sigman
+ 
+
+ align:start position:0%
+Sigman
+Freud Freud's idea was that everybody is
+
+ align:start position:0%
+Freud Freud's idea was that everybody is
+ 
+
+ align:start position:0%
+Freud Freud's idea was that everybody is
+bisexual and if that's true which and so
+
+ align:start position:0%
+bisexual and if that's true which and so
+ 
+
+ align:start position:0%
+bisexual and if that's true which and so
+much of Freud has entered into the
+
+ align:start position:0%
+much of Freud has entered into the
+ 
+
+ align:start position:0%
+much of Freud has entered into the
+present day culture because things that
+
+ align:start position:0%
+present day culture because things that
+ 
+
+ align:start position:0%
+present day culture because things that
+he said people
+
+ align:start position:0%
+he said people
+ 
+
+ align:start position:0%
+he said people
+seem to believe in um well then why
+
+ align:start position:0%
+seem to believe in um well then why
+ 
+
+ align:start position:0%
+seem to believe in um well then why
+wouldn't it be normal for everybody to
+
+ align:start position:0%
+wouldn't it be normal for everybody to
+ 
+
+ align:start position:0%
+wouldn't it be normal for everybody to
+have the possibility of or the the
+
+ align:start position:0%
+have the possibility of or the the
+ 
+
+ align:start position:0%
+have the possibility of or the the
+potential of being
+
+ align:start position:0%
+potential of being
+ 
+
+ align:start position:0%
+potential of being
+homosexual um in a book of mine that I
+
+ align:start position:0%
+homosexual um in a book of mine that I
+ 
+
+ align:start position:0%
+homosexual um in a book of mine that I
+published three years ago uh called
+
+ align:start position:0%
+published three years ago uh called
+ 
+
+ align:start position:0%
+published three years ago uh called
+feeling and Imagination I think it's
+
+ align:start position:0%
+feeling and Imagination I think it's
+ 
+
+ align:start position:0%
+feeling and Imagination I think it's
+there one of my books no I think it is
+
+ align:start position:0%
+there one of my books no I think it is
+ 
+
+ align:start position:0%
+there one of my books no I think it is
+feeling imagination I attack the concept
+
+ align:start position:0%
+feeling imagination I attack the concept
+ 
+
+ align:start position:0%
+feeling imagination I attack the concept
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+bisexuality or latent uality
+
+ align:start position:0%
+bisexuality or latent uality
+ 
+
+ align:start position:0%
+bisexuality or latent uality
+which is related to it these two
+
+ align:start position:0%
+which is related to it these two
+ 
+
+ align:start position:0%
+which is related to it these two
+concepts coming out of Freud it seems to
+
+ align:start position:0%
+concepts coming out of Freud it seems to
+ 
+
+ align:start position:0%
+concepts coming out of Freud it seems to
+me to be a cliche nowadays that everyone
+
+ align:start position:0%
+me to be a cliche nowadays that everyone
+ 
+
+ align:start position:0%
+me to be a cliche nowadays that everyone
+is bisexual even if uh one doesn't act
+
+ align:start position:0%
+is bisexual even if uh one doesn't act
+ 
+
+ align:start position:0%
+is bisexual even if uh one doesn't act
+on that um and um it's a um a dogma of
+
+ align:start position:0%
+on that um and um it's a um a dogma of
+ 
+
+ align:start position:0%
+on that um and um it's a um a dogma of
+freuds that I contest that there's no
+
+ align:start position:0%
+freuds that I contest that there's no
+ 
+
+ align:start position:0%
+freuds that I contest that there's no
+reason to think that everyone is and if
+
+ align:start position:0%
+reason to think that everyone is and if
+ 
+
+ align:start position:0%
+reason to think that everyone is and if
+um a great novelist not crued so much CU
+
+ align:start position:0%
+um a great novelist not crued so much CU
+ 
+
+ align:start position:0%
+um a great novelist not crued so much CU
+he was no be homosexual but Thomas M for
+
+ align:start position:0%
+he was no be homosexual but Thomas M for
+ 
+
+ align:start position:0%
+he was no be homosexual but Thomas M for
+instance who wrote about
+
+ align:start position:0%
+instance who wrote about
+ 
+
+ align:start position:0%
+instance who wrote about
+um Fascination between men and in Death
+
+ align:start position:0%
+um Fascination between men and in Death
+ 
+
+ align:start position:0%
+um Fascination between men and in Death
+in Venice uh about uh a kind of
+
+ align:start position:0%
+in Venice uh about uh a kind of
+ 
+
+ align:start position:0%
+in Venice uh about uh a kind of
+obsession that an older man has for a
+
+ align:start position:0%
+obsession that an older man has for a
+ 
+
+ align:start position:0%
+obsession that an older man has for a
+younger one it he is interpreted as
+
+ align:start position:0%
+younger one it he is interpreted as
+ 
+
+ align:start position:0%
+younger one it he is interpreted as
+having spoken as a homosexual and uh I
+
+ align:start position:0%
+having spoken as a homosexual and uh I
+ 
+
+ align:start position:0%
+having spoken as a homosexual and uh I
+contest that that charge so the whole
+
+ align:start position:0%
+contest that that charge so the whole
+ 
+
+ align:start position:0%
+contest that that charge so the whole
+question of what homosexuality is how it
+
+ align:start position:0%
+question of what homosexuality is how it
+ 
+
+ align:start position:0%
+question of what homosexuality is how it
+enters into literature um and how it has
+
+ align:start position:0%
+enters into literature um and how it has
+ 
+
+ align:start position:0%
+enters into literature um and how it has
+to be thought about in various context
+
+ align:start position:0%
+to be thought about in various context
+ 
+
+ align:start position:0%
+to be thought about in various context
+is suddenly very much alive and
+
+ align:start position:0%
+is suddenly very much alive and
+ 
+
+ align:start position:0%
+is suddenly very much alive and
+especially so in the legal area that I
+
+ align:start position:0%
+especially so in the legal area that I
+ 
+
+ align:start position:0%
+especially so in the legal area that I
+address in the essay about same-sex
+
+ align:start position:0%
+address in the essay about same-sex
+ 
+
+ align:start position:0%
+address in the essay about same-sex
+marriage uh I gather there seems to be
+
+ align:start position:0%
+marriage uh I gather there seems to be
+ 
+
+ align:start position:0%
+marriage uh I gather there seems to be
+no lessening of the intensity of
+
+ align:start position:0%
+no lessening of the intensity of
+ 
+
+ align:start position:0%
+no lessening of the intensity of
+argumentation in this country uh uh
+
+ align:start position:0%
+argumentation in this country uh uh
+ 
+
+ align:start position:0%
+argumentation in this country uh uh
+since the book is coming out next month
+
+ align:start position:0%
+since the book is coming out next month
+ 
+
+ align:start position:0%
+since the book is coming out next month
+you can be sure it was written the
+
+ align:start position:0%
+you can be sure it was written the
+ 
+
+ align:start position:0%
+you can be sure it was written the
+chapter was written a few months ago I
+
+ align:start position:0%
+chapter was written a few months ago I
+ 
+
+ align:start position:0%
+chapter was written a few months ago I
+hadn't foreseen how long the agitation
+
+ align:start position:0%
+hadn't foreseen how long the agitation
+ 
+
+ align:start position:0%
+hadn't foreseen how long the agitation
+would go on and it seems to be going on
+
+ align:start position:0%
+would go on and it seems to be going on
+ 
+
+ align:start position:0%
+would go on and it seems to be going on
+and will go on for quite a
+
+ align:start position:0%
+and will go on for quite a
+ 
+
+ align:start position:0%
+and will go on for quite a
+while now you've read about this and
+
+ align:start position:0%
+while now you've read about this and
+ 
+
+ align:start position:0%
+while now you've read about this and
+therefore I would like to know what you
+
+ align:start position:0%
+therefore I would like to know what you
+ 
+
+ align:start position:0%
+therefore I would like to know what you
+think about it about this question about
+
+ align:start position:0%
+think about it about this question about
+ 
+
+ align:start position:0%
+think about it about this question about
+love love between a man and a man in
+
+ align:start position:0%
+love love between a man and a man in
+ 
+
+ align:start position:0%
+love love between a man and a man in
+relation to marital love or marital
+
+ align:start position:0%
+relation to marital love or marital
+ 
+
+ align:start position:0%
+relation to marital love or marital
+attachment and love between a woman and
+
+ align:start position:0%
+attachment and love between a woman and
+ 
+
+ align:start position:0%
+attachment and love between a woman and
+a woman in relation to marital
+
+ align:start position:0%
+a woman in relation to marital
+ 
+
+ align:start position:0%
+a woman in relation to marital
+attachments in other words the whole
+
+ align:start position:0%
+attachments in other words the whole
+ 
+
+ align:start position:0%
+attachments in other words the whole
+question question about same-sex
+
+ align:start position:0%
+question question about same-sex
+ 
+
+ align:start position:0%
+question question about same-sex
+marriage which I put at the beginning of
+
+ align:start position:0%
+marriage which I put at the beginning of
+ 
+
+ align:start position:0%
+marriage which I put at the beginning of
+the course because it's it's um uh what
+
+ align:start position:0%
+the course because it's it's um uh what
+ 
+
+ align:start position:0%
+the course because it's it's um uh what
+at MIT people used to like to call The
+
+ align:start position:0%
+at MIT people used to like to call The
+ 
+
+ align:start position:0%
+at MIT people used to like to call The
+Cutting Edge it's The Cutting Edge of
+
+ align:start position:0%
+Cutting Edge it's The Cutting Edge of
+ 
+
+ align:start position:0%
+Cutting Edge it's The Cutting Edge of
+philosophy of love it's the most recent
+
+ align:start position:0%
+philosophy of love it's the most recent
+ 
+
+ align:start position:0%
+philosophy of love it's the most recent
+Uh current uh thing that people are
+
+ align:start position:0%
+Uh current uh thing that people are
+ 
+
+ align:start position:0%
+Uh current uh thing that people are
+talking about and thinking about and
+
+ align:start position:0%
+talking about and thinking about and
+ 
+
+ align:start position:0%
+talking about and thinking about and
+that philosophers ought to engage in but
+
+ align:start position:0%
+that philosophers ought to engage in but
+ 
+
+ align:start position:0%
+that philosophers ought to engage in but
+very few philosophers as I was telling
+
+ align:start position:0%
+very few philosophers as I was telling
+ 
+
+ align:start position:0%
+very few philosophers as I was telling
+you last time nowadays do engage in this
+
+ align:start position:0%
+you last time nowadays do engage in this
+ 
+
+ align:start position:0%
+you last time nowadays do engage in this
+kind of question and that's why I felt
+
+ align:start position:0%
+kind of question and that's why I felt
+ 
+
+ align:start position:0%
+kind of question and that's why I felt
+that I
+
+ align:start position:0%
+that I
+ 
+
+ align:start position:0%
+that I
+shouldn't all right now does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+help remember my image of St Sebastian
+
+ align:start position:0%
+help remember my image of St Sebastian
+ 
+
+ align:start position:0%
+help remember my image of St Sebastian
+standing at the pillar shoot your arrows
+
+ align:start position:0%
+standing at the pillar shoot your arrows
+ 
+
+ align:start position:0%
+standing at the pillar shoot your arrows
+at me I've given you a good opportunity
+
+ align:start position:0%
+at me I've given you a good opportunity
+ 
+
+ align:start position:0%
+at me I've given you a good opportunity
+because it's such a
+
+ align:start position:0%
+because it's such a
+ 
+
+ align:start position:0%
+because it's such a
+controversial
+
+ align:start position:0%
+controversial
+ 
+
+ align:start position:0%
+controversial
+question and um the majority of people
+
+ align:start position:0%
+question and um the majority of people
+ 
+
+ align:start position:0%
+question and um the majority of people
+in the United States would certainly not
+
+ align:start position:0%
+in the United States would certainly not
+ 
+
+ align:start position:0%
+in the United States would certainly not
+agree with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me so what do you think what do you I
+
+ align:start position:0%
+me so what do you think what do you I
+ 
+
+ align:start position:0%
+me so what do you think what do you I
+what do you think about the issue and
+
+ align:start position:0%
+what do you think about the issue and
+ 
+
+ align:start position:0%
+what do you think about the issue and
+what do you think about what I've asked
+
+ align:start position:0%
+what do you think about what I've asked
+ 
+
+ align:start position:0%
+what do you think about what I've asked
+you to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+read well I think that one of
+
+ align:start position:0%
+read well I think that one of
+ 
+
+ align:start position:0%
+read well I think that one of
+the most important points that I think
+
+ align:start position:0%
+the most important points that I think
+ 
+
+ align:start position:0%
+the most important points that I think
+you bring up is the fact that this
+
+ align:start position:0%
+you bring up is the fact that this
+ 
+
+ align:start position:0%
+you bring up is the fact that this
+is more of an issue because of the
+
+ align:start position:0%
+is more of an issue because of the
+ 
+
+ align:start position:0%
+is more of an issue because of the
+social aspects of what comes with
+
+ align:start position:0%
+social aspects of what comes with
+ 
+
+ align:start position:0%
+social aspects of what comes with
+marriage and I think that that is one of
+
+ align:start position:0%
+marriage and I think that that is one of
+ 
+
+ align:start position:0%
+marriage and I think that that is one of
+the main fights for the same-sex
+
+ align:start position:0%
+the main fights for the same-sex
+ 
+
+ align:start position:0%
+the main fights for the same-sex
+marriage between social aspects of which
+
+ align:start position:0%
+marriage between social aspects of which
+ 
+
+ align:start position:0%
+marriage between social aspects of which
+song um I think you mentioned things
+
+ align:start position:0%
+song um I think you mentioned things
+ 
+
+ align:start position:0%
+song um I think you mentioned things
+like uh being socially accepted as a
+
+ align:start position:0%
+like uh being socially accepted as a
+ 
+
+ align:start position:0%
+like uh being socially accepted as a
+couple and getting the uh benefits of
+
+ align:start position:0%
+couple and getting the uh benefits of
+ 
+
+ align:start position:0%
+couple and getting the uh benefits of
+being a couple because I think it's very
+
+ align:start position:0%
+being a couple because I think it's very
+ 
+
+ align:start position:0%
+being a couple because I think it's very
+hard for someone to argue and say that
+
+ align:start position:0%
+hard for someone to argue and say that
+ 
+
+ align:start position:0%
+hard for someone to argue and say that
+these two people don't love each other
+
+ align:start position:0%
+these two people don't love each other
+ 
+
+ align:start position:0%
+these two people don't love each other
+you can't argue against someone's love
+
+ align:start position:0%
+you can't argue against someone's love
+ 
+
+ align:start position:0%
+you can't argue against someone's love
+so um I think it's more of a whether or
+
+ align:start position:0%
+so um I think it's more of a whether or
+ 
+
+ align:start position:0%
+so um I think it's more of a whether or
+not they have the right to exist as a
+
+ align:start position:0%
+not they have the right to exist as a
+ 
+
+ align:start position:0%
+not they have the right to exist as a
+couple in marriage
+
+ align:start position:0%
+couple in marriage
+ 
+
+ align:start position:0%
+couple in marriage
+and I find it hard to say that you can
+
+ align:start position:0%
+and I find it hard to say that you can
+ 
+
+ align:start position:0%
+and I find it hard to say that you can
+deny people most of the benefits that
+
+ align:start position:0%
+deny people most of the benefits that
+ 
+
+ align:start position:0%
+deny people most of the benefits that
+come with marriage such as um being able
+
+ align:start position:0%
+come with marriage such as um being able
+ 
+
+ align:start position:0%
+come with marriage such as um being able
+to adopt or do things like that because
+
+ align:start position:0%
+to adopt or do things like that because
+ 
+
+ align:start position:0%
+to adopt or do things like that because
+I think especially in the society we
+
+ align:start position:0%
+I think especially in the society we
+ 
+
+ align:start position:0%
+I think especially in the society we
+live in right now there's already the
+
+ align:start position:0%
+live in right now there's already the
+ 
+
+ align:start position:0%
+live in right now there's already the
+idea of marriage is already so broken
+
+ align:start position:0%
+idea of marriage is already so broken
+ 
+
+ align:start position:0%
+idea of marriage is already so broken
+and faltering
+
+ align:start position:0%
+and faltering
+ 
+
+ align:start position:0%
+and faltering
+that if there are two people that have
+
+ align:start position:0%
+that if there are two people that have
+ 
+
+ align:start position:0%
+that if there are two people that have
+love between each other then how could
+
+ align:start position:0%
+love between each other then how could
+ 
+
+ align:start position:0%
+love between each other then how could
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+deny them that type of experience let me
+
+ align:start position:0%
+deny them that type of experience let me
+ 
+
+ align:start position:0%
+deny them that type of experience let me
+sum up two principles one legitimization
+
+ align:start position:0%
+sum up two principles one legitimization
+ 
+
+ align:start position:0%
+sum up two principles one legitimization
+and the other um benefits that come with
+
+ align:start position:0%
+and the other um benefits that come with
+ 
+
+ align:start position:0%
+and the other um benefits that come with
+being legitimized as legally Maring you
+
+ align:start position:0%
+being legitimized as legally Maring you
+ 
+
+ align:start position:0%
+being legitimized as legally Maring you
+mentioned benefits of
+
+ align:start position:0%
+mentioned benefits of
+ 
+
+ align:start position:0%
+mentioned benefits of
+um um sort of personal one adop the
+
+ align:start position:0%
+um um sort of personal one adop the
+ 
+
+ align:start position:0%
+um um sort of personal one adop the
+ability to adopt children but then
+
+ align:start position:0%
+ability to adopt children but then
+ 
+
+ align:start position:0%
+ability to adopt children but then
+they're also material benefits money
+
+ align:start position:0%
+they're also material benefits money
+ 
+
+ align:start position:0%
+they're also material benefits money
+right okay so that's that's the of the
+
+ align:start position:0%
+right okay so that's that's the of the
+ 
+
+ align:start position:0%
+right okay so that's that's the of the
+problem right um and the um children
+
+ align:start position:0%
+problem right um and the um children
+ 
+
+ align:start position:0%
+problem right um and the um children
+come into it in interesting ways there's
+
+ align:start position:0%
+come into it in interesting ways there's
+ 
+
+ align:start position:0%
+come into it in interesting ways there's
+one um woman I know who um is um has
+
+ align:start position:0%
+one um woman I know who um is um has
+ 
+
+ align:start position:0%
+one um woman I know who um is um has
+been living in a lesbian relationship
+
+ align:start position:0%
+been living in a lesbian relationship
+ 
+
+ align:start position:0%
+been living in a lesbian relationship
+with another woman and uh she has two
+
+ align:start position:0%
+with another woman and uh she has two
+ 
+
+ align:start position:0%
+with another woman and uh she has two
+children I don't know where she got the
+
+ align:start position:0%
+children I don't know where she got the
+ 
+
+ align:start position:0%
+children I don't know where she got the
+children whether she adopted them or was
+
+ align:start position:0%
+children whether she adopted them or was
+ 
+
+ align:start position:0%
+children whether she adopted them or was
+previously married and divorced but she
+
+ align:start position:0%
+previously married and divorced but she
+ 
+
+ align:start position:0%
+previously married and divorced but she
+has two children when she was asked in
+
+ align:start position:0%
+has two children when she was asked in
+ 
+
+ align:start position:0%
+has two children when she was asked in
+my presence I didn't ask cuz I try not
+
+ align:start position:0%
+my presence I didn't ask cuz I try not
+ 
+
+ align:start position:0%
+my presence I didn't ask cuz I try not
+to pry but someone else did why is it
+
+ align:start position:0%
+to pry but someone else did why is it
+ 
+
+ align:start position:0%
+to pry but someone else did why is it
+that you care
+
+ align:start position:0%
+that you care
+ 
+
+ align:start position:0%
+that you care
+about marriage getting married to your
+
+ align:start position:0%
+about marriage getting married to your
+ 
+
+ align:start position:0%
+about marriage getting married to your
+friend um and she said because of the
+
+ align:start position:0%
+friend um and she said because of the
+ 
+
+ align:start position:0%
+friend um and she said because of the
+boys who were small uh I don't know
+
+ align:start position:0%
+boys who were small uh I don't know
+ 
+
+ align:start position:0%
+boys who were small uh I don't know
+exact ages but they're fairly small um
+
+ align:start position:0%
+exact ages but they're fairly small um
+ 
+
+ align:start position:0%
+exact ages but they're fairly small um
+because of the boys um my son so and so
+
+ align:start position:0%
+because of the boys um my son so and so
+ 
+
+ align:start position:0%
+because of the boys um my son so and so
+says that the kids uh kid him about it
+
+ align:start position:0%
+says that the kids uh kid him about it
+ 
+
+ align:start position:0%
+says that the kids uh kid him about it
+that his mother is not even married
+
+ align:start position:0%
+that his mother is not even married
+ 
+
+ align:start position:0%
+that his mother is not even married
+uh and he's afraid that they're going to
+
+ align:start position:0%
+uh and he's afraid that they're going to
+ 
+
+ align:start position:0%
+uh and he's afraid that they're going to
+beat him up kids you know can be very
+
+ align:start position:0%
+beat him up kids you know can be very
+ 
+
+ align:start position:0%
+beat him up kids you know can be very
+vicious they can be they're on the look
+
+ align:start position:0%
+vicious they can be they're on the look
+ 
+
+ align:start position:0%
+vicious they can be they're on the look
+for some vulnerable comrade of theirs
+
+ align:start position:0%
+for some vulnerable comrade of theirs
+ 
+
+ align:start position:0%
+for some vulnerable comrade of theirs
+that they can all gang up on right you
+
+ align:start position:0%
+that they can all gang up on right you
+ 
+
+ align:start position:0%
+that they can all gang up on right you
+you all know how how
+
+ align:start position:0%
+you all know how how
+ 
+
+ align:start position:0%
+you all know how how
+dangerous little children can be with
+
+ align:start position:0%
+dangerous little children can be with
+ 
+
+ align:start position:0%
+dangerous little children can be with
+each other and so he's afraid that
+
+ align:start position:0%
+each other and so he's afraid that
+ 
+
+ align:start position:0%
+each other and so he's afraid that
+um uh if if she remains
+
+ align:start position:0%
+um uh if if she remains
+ 
+
+ align:start position:0%
+um uh if if she remains
+unmarried maybe in this cont text of
+
+ align:start position:0%
+unmarried maybe in this cont text of
+ 
+
+ align:start position:0%
+unmarried maybe in this cont text of
+living with another woman uh that he
+
+ align:start position:0%
+living with another woman uh that he
+ 
+
+ align:start position:0%
+living with another woman uh that he
+will be um
+
+ align:start position:0%
+will be um
+ 
+
+ align:start position:0%
+will be um
+hurt now the reasoning on his part would
+
+ align:start position:0%
+hurt now the reasoning on his part would
+ 
+
+ align:start position:0%
+hurt now the reasoning on his part would
+be if she gets legally married then
+
+ align:start position:0%
+be if she gets legally married then
+ 
+
+ align:start position:0%
+be if she gets legally married then
+somehow they're going to leave him alone
+
+ align:start position:0%
+somehow they're going to leave him alone
+ 
+
+ align:start position:0%
+somehow they're going to leave him alone
+because their parents are legally
+
+ align:start position:0%
+because their parents are legally
+ 
+
+ align:start position:0%
+because their parents are legally
+married I'm not convinced that that
+
+ align:start position:0%
+married I'm not convinced that that
+ 
+
+ align:start position:0%
+married I'm not convinced that that
+reasoning
+
+ align:start position:0%
+reasoning
+ 
+
+ align:start position:0%
+reasoning
+works but but the question of adoption
+
+ align:start position:0%
+works but but the question of adoption
+ 
+
+ align:start position:0%
+works but but the question of adoption
+and of um legitimacy and relationship to
+
+ align:start position:0%
+and of um legitimacy and relationship to
+ 
+
+ align:start position:0%
+and of um legitimacy and relationship to
+the whole family the children
+
+ align:start position:0%
+the whole family the children
+ 
+
+ align:start position:0%
+the whole family the children
+uh is certainly a part of it and now
+
+ align:start position:0%
+uh is certainly a part of it and now
+ 
+
+ align:start position:0%
+uh is certainly a part of it and now
+that was the reason that the um the
+
+ align:start position:0%
+that was the reason that the um the
+ 
+
+ align:start position:0%
+that was the reason that the um the
+mother of the two children said she
+
+ align:start position:0%
+mother of the two children said she
+ 
+
+ align:start position:0%
+mother of the two children said she
+wanted to be legally married and then
+
+ align:start position:0%
+wanted to be legally married and then
+ 
+
+ align:start position:0%
+wanted to be legally married and then
+she did get me legally
+
+ align:start position:0%
+she did get me legally
+ 
+
+ align:start position:0%
+she did get me legally
+married um she said that she herself
+
+ align:start position:0%
+married um she said that she herself
+ 
+
+ align:start position:0%
+married um she said that she herself
+doesn't care very much one way or the
+
+ align:start position:0%
+doesn't care very much one way or the
+ 
+
+ align:start position:0%
+doesn't care very much one way or the
+other that U she and her friend have
+
+ align:start position:0%
+other that U she and her friend have
+ 
+
+ align:start position:0%
+other that U she and her friend have
+made out Wills
+
+ align:start position:0%
+made out Wills
+ 
+
+ align:start position:0%
+made out Wills
+that protect each other against
+
+ align:start position:0%
+that protect each other against
+ 
+
+ align:start position:0%
+that protect each other against
+Financial hazards um so that apparently
+
+ align:start position:0%
+Financial hazards um so that apparently
+ 
+
+ align:start position:0%
+Financial hazards um so that apparently
+they're sufficiently dead dedicated to
+
+ align:start position:0%
+they're sufficiently dead dedicated to
+ 
+
+ align:start position:0%
+they're sufficiently dead dedicated to
+each other that she didn't feel any need
+
+ align:start position:0%
+each other that she didn't feel any need
+ 
+
+ align:start position:0%
+each other that she didn't feel any need
+to have the um uh certificate of
+
+ align:start position:0%
+to have the um uh certificate of
+ 
+
+ align:start position:0%
+to have the um uh certificate of
+marriage and did wanted it only for the
+
+ align:start position:0%
+marriage and did wanted it only for the
+ 
+
+ align:start position:0%
+marriage and did wanted it only for the
+sake of the
+
+ align:start position:0%
+sake of the
+ 
+
+ align:start position:0%
+sake of the
+kids well for whatever
+
+ align:start position:0%
+kids well for whatever
+ 
+
+ align:start position:0%
+kids well for whatever
+reason um the question is whether uh
+
+ align:start position:0%
+reason um the question is whether uh
+ 
+
+ align:start position:0%
+reason um the question is whether uh
+women in her situation or men in in a
+
+ align:start position:0%
+women in her situation or men in in a
+ 
+
+ align:start position:0%
+women in her situation or men in in a
+comparable one should or should not be
+
+ align:start position:0%
+comparable one should or should not be
+ 
+
+ align:start position:0%
+comparable one should or should not be
+denied the opportunity to get married
+
+ align:start position:0%
+denied the opportunity to get married
+ 
+
+ align:start position:0%
+denied the opportunity to get married
+legally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did I say anything in that that you
+
+ align:start position:0%
+did I say anything in that that you
+ 
+
+ align:start position:0%
+did I say anything in that that you
+didn't already know and
+
+ align:start position:0%
+didn't already know and
+ 
+
+ align:start position:0%
+didn't already know and
+feel
+
+ align:start position:0%
+feel
+ 
+
+ align:start position:0%
+feel
+this U this is that yes not really you
+
+ align:start position:0%
+this U this is that yes not really you
+ 
+
+ align:start position:0%
+this U this is that yes not really you
+just kind of brought to the surface I
+
+ align:start position:0%
+just kind of brought to the surface I
+ 
+
+ align:start position:0%
+just kind of brought to the surface I
+guess what most people are that but not
+
+ align:start position:0%
+guess what most people are that but not
+ 
+
+ align:start position:0%
+guess what most people are that but not
+the problem Li mostly in what people
+
+ align:start position:0%
+the problem Li mostly in what people
+ 
+
+ align:start position:0%
+the problem Li mostly in what people
+believe marriage is like you said like
+
+ align:start position:0%
+believe marriage is like you said like
+ 
+
+ align:start position:0%
+believe marriage is like you said like
+whether or not marriage is something
+
+ align:start position:0%
+whether or not marriage is something
+ 
+
+ align:start position:0%
+whether or not marriage is something
+that's a more of a religious context
+
+ align:start position:0%
+that's a more of a religious context
+ 
+
+ align:start position:0%
+that's a more of a religious context
+where it's a man and a woman getting
+
+ align:start position:0%
+where it's a man and a woman getting
+ 
+
+ align:start position:0%
+where it's a man and a woman getting
+together to make a like the starting of
+
+ align:start position:0%
+together to make a like the starting of
+ 
+
+ align:start position:0%
+together to make a like the starting of
+a family or if it's more of a legal
+
+ align:start position:0%
+a family or if it's more of a legal
+ 
+
+ align:start position:0%
+a family or if it's more of a legal
+aspect that you know has the monetary
+
+ align:start position:0%
+aspect that you know has the monetary
+ 
+
+ align:start position:0%
+aspect that you know has the monetary
+and other legal issues with it and I
+
+ align:start position:0%
+and other legal issues with it and I
+ 
+
+ align:start position:0%
+and other legal issues with it and I
+guess where people differ there probably
+
+ align:start position:0%
+guess where people differ there probably
+ 
+
+ align:start position:0%
+guess where people differ there probably
+you know has a lot to do with their
+
+ align:start position:0%
+you know has a lot to do with their
+ 
+
+ align:start position:0%
+you know has a lot to do with their
+religion since they're religious they'll
+
+ align:start position:0%
+religion since they're religious they'll
+ 
+
+ align:start position:0%
+religion since they're religious they'll
+probably fall more in religious side and
+
+ align:start position:0%
+probably fall more in religious side and
+ 
+
+ align:start position:0%
+probably fall more in religious side and
+if they're more liberal then they'll
+
+ align:start position:0%
+if they're more liberal then they'll
+ 
+
+ align:start position:0%
+if they're more liberal then they'll
+probably fall the legal side if they
+
+ align:start position:0%
+probably fall the legal side if they
+ 
+
+ align:start position:0%
+probably fall the legal side if they
+oppose it or if they're for it either
+
+ align:start position:0%
+oppose it or if they're for it either
+ 
+
+ align:start position:0%
+oppose it or if they're for it either
+way can you talk to each other in this
+
+ align:start position:0%
+way can you talk to each other in this
+ 
+
+ align:start position:0%
+way can you talk to each other in this
+if there's anything you don't agree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah I I think that the the main
+
+ align:start position:0%
+um yeah I I think that the the main
+ 
+
+ align:start position:0%
+um yeah I I think that the the main
+problem is um how society looks at this
+
+ align:start position:0%
+problem is um how society looks at this
+ 
+
+ align:start position:0%
+problem is um how society looks at this
+at this new issue of same-sex marriage
+
+ align:start position:0%
+at this new issue of same-sex marriage
+ 
+
+ align:start position:0%
+at this new issue of same-sex marriage
+because in other societies I know that
+
+ align:start position:0%
+because in other societies I know that
+ 
+
+ align:start position:0%
+because in other societies I know that
+it in some Nordic countries It's
+
+ align:start position:0%
+it in some Nordic countries It's
+ 
+
+ align:start position:0%
+it in some Nordic countries It's
+Perfectly Normal but not legal except in
+
+ align:start position:0%
+Perfectly Normal but not legal except in
+ 
+
+ align:start position:0%
+Perfectly Normal but not legal except in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Netherlands in the ne the Netherlands is
+
+ align:start position:0%
+Netherlands in the ne the Netherlands is
+ 
+
+ align:start position:0%
+Netherlands in the ne the Netherlands is
+the only
+
+ align:start position:0%
+the only
+ 
+
+ align:start position:0%
+the only
+country that has exactly
+
+ align:start position:0%
+country that has exactly
+ 
+
+ align:start position:0%
+country that has exactly
+identical legal
+
+ align:start position:0%
+identical legal
+ 
+
+ align:start position:0%
+identical legal
+status for marriage between men and
+
+ align:start position:0%
+status for marriage between men and
+ 
+
+ align:start position:0%
+status for marriage between men and
+marriage between or women and marriage
+
+ align:start position:0%
+marriage between or women and marriage
+ 
+
+ align:start position:0%
+marriage between or women and marriage
+between a man and a
+
+ align:start position:0%
+between a man and a
+ 
+
+ align:start position:0%
+between a man and a
+woman um the others are more complicated
+
+ align:start position:0%
+woman um the others are more complicated
+ 
+
+ align:start position:0%
+woman um the others are more complicated
+France and Belgium approximate that uh I
+
+ align:start position:0%
+France and Belgium approximate that uh I
+ 
+
+ align:start position:0%
+France and Belgium approximate that uh I
+don't know about Sweden you would have
+
+ align:start position:0%
+don't know about Sweden you would have
+ 
+
+ align:start position:0%
+don't know about Sweden you would have
+Sweden and Norway that well maybe Norway
+
+ align:start position:0%
+Sweden and Norway that well maybe Norway
+ 
+
+ align:start position:0%
+Sweden and Norway that well maybe Norway
+may be different but Sweden is generally
+
+ align:start position:0%
+may be different but Sweden is generally
+ 
+
+ align:start position:0%
+may be different but Sweden is generally
+a leader in terms of sex reform but I
+
+ align:start position:0%
+a leader in terms of sex reform but I
+ 
+
+ align:start position:0%
+a leader in terms of sex reform but I
+don't think they're even politicians
+
+ align:start position:0%
+don't think they're even politicians
+ 
+
+ align:start position:0%
+don't think they're even politicians
+equivalent a politician was married to
+
+ align:start position:0%
+equivalent a politician was married to
+ 
+
+ align:start position:0%
+equivalent a politician was married to
+another one I think in Sweden was it
+
+ align:start position:0%
+another one I think in Sweden was it
+ 
+
+ align:start position:0%
+another one I think in Sweden was it
+last year I don't know but in Sweden two
+
+ align:start position:0%
+last year I don't know but in Sweden two
+ 
+
+ align:start position:0%
+last year I don't know but in Sweden two
+women you mean oh there was I'm pretty
+
+ align:start position:0%
+women you mean oh there was I'm pretty
+ 
+
+ align:start position:0%
+women you mean oh there was I'm pretty
+sure it was it was in Sweden or Norway
+
+ align:start position:0%
+sure it was it was in Sweden or Norway
+ 
+
+ align:start position:0%
+sure it was it was in Sweden or Norway
+I'm not I don't remember um yeah were
+
+ align:start position:0%
+I'm not I don't remember um yeah were
+ 
+
+ align:start position:0%
+I'm not I don't remember um yeah were
+they married or they just lived together
+
+ align:start position:0%
+they married or they just lived together
+ 
+
+ align:start position:0%
+they married or they just lived together
+or had a civil union they were married I
+
+ align:start position:0%
+or had a civil union they were married I
+ 
+
+ align:start position:0%
+or had a civil union they were married I
+remember was headline news in Greece
+
+ align:start position:0%
+remember was headline news in Greece
+ 
+
+ align:start position:0%
+remember was headline news in Greece
+that was some years ago yeah two years
+
+ align:start position:0%
+that was some years ago yeah two years
+ 
+
+ align:start position:0%
+that was some years ago yeah two years
+then why is it in all the things I read
+
+ align:start position:0%
+then why is it in all the things I read
+ 
+
+ align:start position:0%
+then why is it in all the things I read
+it's only the the Netherlands that is
+
+ align:start position:0%
+it's only the the Netherlands that is
+ 
+
+ align:start position:0%
+it's only the the Netherlands that is
+cited as being um uh
+
+ align:start position:0%
+cited as being um uh
+ 
+
+ align:start position:0%
+cited as being um uh
+completely egalitarian in this respect
+
+ align:start position:0%
+completely egalitarian in this respect
+ 
+
+ align:start position:0%
+completely egalitarian in this respect
+well they probably got married they
+
+ align:start position:0%
+well they probably got married they
+ 
+
+ align:start position:0%
+well they probably got married they
+still have the same right they may not
+
+ align:start position:0%
+still have the same right they may not
+ 
+
+ align:start position:0%
+still have the same right they may not
+have the same right same rights oh oh
+
+ align:start position:0%
+have the same right same rights oh oh
+ 
+
+ align:start position:0%
+have the same right same rights oh oh
+that's crucial then they're not fully
+
+ align:start position:0%
+that's crucial then they're not fully
+ 
+
+ align:start position:0%
+that's crucial then they're not fully
+married no maybe that's what I should
+
+ align:start position:0%
+married no maybe that's what I should
+ 
+
+ align:start position:0%
+married no maybe that's what I should
+have said it's only in Netherlands at
+
+ align:start position:0%
+have said it's only in Netherlands at
+ 
+
+ align:start position:0%
+have said it's only in Netherlands at
+the moment that um people of the same
+
+ align:start position:0%
+the moment that um people of the same
+ 
+
+ align:start position:0%
+the moment that um people of the same
+sex can be married in the same sense of
+
+ align:start position:0%
+sex can be married in the same sense of
+ 
+
+ align:start position:0%
+sex can be married in the same sense of
+Rights the fullness of rights as the
+
+ align:start position:0%
+Rights the fullness of rights as the
+ 
+
+ align:start position:0%
+Rights the fullness of rights as the
+heterosexuals that might be is BR um in
+
+ align:start position:0%
+heterosexuals that might be is BR um in
+ 
+
+ align:start position:0%
+heterosexuals that might be is BR um in
+my opinion the way Society accepts this
+
+ align:start position:0%
+my opinion the way Society accepts this
+ 
+
+ align:start position:0%
+my opinion the way Society accepts this
+is very important for facilitating the
+
+ align:start position:0%
+is very important for facilitating the
+ 
+
+ align:start position:0%
+is very important for facilitating the
+legalization of same-sex marriage for
+
+ align:start position:0%
+legalization of same-sex marriage for
+ 
+
+ align:start position:0%
+legalization of same-sex marriage for
+example if here there wasn't so much
+
+ align:start position:0%
+example if here there wasn't so much
+ 
+
+ align:start position:0%
+example if here there wasn't so much
+opposition probably
+
+ align:start position:0%
+opposition probably
+ 
+
+ align:start position:0%
+opposition probably
+it would be easier to legalize it and
+
+ align:start position:0%
+it would be easier to legalize it and
+ 
+
+ align:start position:0%
+it would be easier to legalize it and
+the in the example you just gave that
+
+ align:start position:0%
+the in the example you just gave that
+ 
+
+ align:start position:0%
+the in the example you just gave that
+the kid is scared because they are going
+
+ align:start position:0%
+the kid is scared because they are going
+ 
+
+ align:start position:0%
+the kid is scared because they are going
+to beat him up um in those countries it
+
+ align:start position:0%
+to beat him up um in those countries it
+ 
+
+ align:start position:0%
+to beat him up um in those countries it
+it's totally normal and well let me I I
+
+ align:start position:0%
+it's totally normal and well let me I I
+ 
+
+ align:start position:0%
+it's totally normal and well let me I I
+don't know you can tell me better about
+
+ align:start position:0%
+don't know you can tell me better about
+ 
+
+ align:start position:0%
+don't know you can tell me better about
+a country like Mexico for instance but
+
+ align:start position:0%
+a country like Mexico for instance but
+ 
+
+ align:start position:0%
+a country like Mexico for instance but
+when I lived in
+
+ align:start position:0%
+when I lived in
+ 
+
+ align:start position:0%
+when I lived in
+Italy um the church was still Fa l
+
+ align:start position:0%
+Italy um the church was still Fa l
+ 
+
+ align:start position:0%
+Italy um the church was still Fa l
+strong more so than
+
+ align:start position:0%
+strong more so than
+ 
+
+ align:start position:0%
+strong more so than
+now and that meant that the people
+
+ align:start position:0%
+now and that meant that the people
+ 
+
+ align:start position:0%
+now and that meant that the people
+didn't get
+
+ align:start position:0%
+didn't get
+ 
+
+ align:start position:0%
+didn't get
+divorced but uh they separated and uh
+
+ align:start position:0%
+divorced but uh they separated and uh
+ 
+
+ align:start position:0%
+divorced but uh they separated and uh
+the men and the women um hooked up other
+
+ align:start position:0%
+the men and the women um hooked up other
+ 
+
+ align:start position:0%
+the men and the women um hooked up other
+people of the opposite sex so it was
+
+ align:start position:0%
+people of the opposite sex so it was
+ 
+
+ align:start position:0%
+people of the opposite sex so it was
+sort of routine everybody knew that
+
+ align:start position:0%
+sort of routine everybody knew that
+ 
+
+ align:start position:0%
+sort of routine everybody knew that
+you'd be married to the man and would be
+
+ align:start position:0%
+you'd be married to the man and would be
+ 
+
+ align:start position:0%
+you'd be married to the man and would be
+married to one woman but live in a
+
+ align:start position:0%
+married to one woman but live in a
+ 
+
+ align:start position:0%
+married to one woman but live in a
+marital relationship with another woman
+
+ align:start position:0%
+marital relationship with another woman
+ 
+
+ align:start position:0%
+marital relationship with another woman
+and it was that was the way things
+
+ align:start position:0%
+and it was that was the way things
+ 
+
+ align:start position:0%
+and it was that was the way things
+were um I don't know about homosexuality
+
+ align:start position:0%
+were um I don't know about homosexuality
+ 
+
+ align:start position:0%
+were um I don't know about homosexuality
+whether how openly that was
+
+ align:start position:0%
+whether how openly that was
+ 
+
+ align:start position:0%
+whether how openly that was
+understood but it isn't just a question
+
+ align:start position:0%
+understood but it isn't just a question
+ 
+
+ align:start position:0%
+understood but it isn't just a question
+of how people
+
+ align:start position:0%
+of how people
+ 
+
+ align:start position:0%
+of how people
+behave it's what you call the Social
+
+ align:start position:0%
+behave it's what you call the Social
+ 
+
+ align:start position:0%
+behave it's what you call the Social
+acceptance that's important because
+
+ align:start position:0%
+acceptance that's important because
+ 
+
+ align:start position:0%
+acceptance that's important because
+that's how the um the material goods are
+
+ align:start position:0%
+that's how the um the material goods are
+ 
+
+ align:start position:0%
+that's how the um the material goods are
+distributed that gives a kind of
+
+ align:start position:0%
+distributed that gives a kind of
+ 
+
+ align:start position:0%
+distributed that gives a kind of
+structure to the morality to and to
+
+ align:start position:0%
+structure to the morality to and to
+ 
+
+ align:start position:0%
+structure to the morality to and to
+the society
+
+ align:start position:0%
+the society
+ 
+
+ align:start position:0%
+the society
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+different from the alternative which
+
+ align:start position:0%
+different from the alternative which
+ 
+
+ align:start position:0%
+different from the alternative which
+would be to fully
+
+ align:start position:0%
+would be to fully
+ 
+
+ align:start position:0%
+would be to fully
+legalize relationships regardless of
+
+ align:start position:0%
+legalize relationships regardless of
+ 
+
+ align:start position:0%
+legalize relationships regardless of
+gender incident tell me what the
+
+ align:start position:0%
+gender incident tell me what the
+ 
+
+ align:start position:0%
+gender incident tell me what the
+situation is in Mexico well in Mexico I
+
+ align:start position:0%
+situation is in Mexico well in Mexico I
+ 
+
+ align:start position:0%
+situation is in Mexico well in Mexico I
+don't think that uh it's even close to
+
+ align:start position:0%
+don't think that uh it's even close to
+ 
+
+ align:start position:0%
+don't think that uh it's even close to
+being legalized because it's a very
+
+ align:start position:0%
+being legalized because it's a very
+ 
+
+ align:start position:0%
+being legalized because it's a very
+matal
+
+ align:start position:0%
+matal
+ 
+
+ align:start position:0%
+matal
+Society
+
+ align:start position:0%
+Society
+ 
+
+ align:start position:0%
+Society
+so uh homosexual people aren't as open
+
+ align:start position:0%
+so uh homosexual people aren't as open
+ 
+
+ align:start position:0%
+so uh homosexual people aren't as open
+about their sexual inclination as they
+
+ align:start position:0%
+about their sexual inclination as they
+ 
+
+ align:start position:0%
+about their sexual inclination as they
+are in America for example a lot of
+
+ align:start position:0%
+are in America for example a lot of
+ 
+
+ align:start position:0%
+are in America for example a lot of
+homosexuals are very
+
+ align:start position:0%
+homosexuals are very
+ 
+
+ align:start position:0%
+homosexuals are very
+matcho they they're Macho with women who
+
+ align:start position:0%
+matcho they they're Macho with women who
+ 
+
+ align:start position:0%
+matcho they they're Macho with women who
+like that kind of thing even though the
+
+ align:start position:0%
+like that kind of thing even though the
+ 
+
+ align:start position:0%
+like that kind of thing even though the
+man might be really not heterosexual but
+
+ align:start position:0%
+man might be really not heterosexual but
+ 
+
+ align:start position:0%
+man might be really not heterosexual but
+he can he can perform and he can
+
+ align:start position:0%
+he can he can perform and he can
+ 
+
+ align:start position:0%
+he can he can perform and he can
+dominate a woman The Pimps of
+
+ align:start position:0%
+dominate a woman The Pimps of
+ 
+
+ align:start position:0%
+dominate a woman The Pimps of
+prostitutes uh generally uh have other
+
+ align:start position:0%
+prostitutes uh generally uh have other
+ 
+
+ align:start position:0%
+prostitutes uh generally uh have other
+interests but they know they know how to
+
+ align:start position:0%
+interests but they know they know how to
+ 
+
+ align:start position:0%
+interests but they know they know how to
+get the love and uh dependence of the
+
+ align:start position:0%
+get the love and uh dependence of the
+ 
+
+ align:start position:0%
+get the love and uh dependence of the
+women who support them uh and they can
+
+ align:start position:0%
+women who support them uh and they can
+ 
+
+ align:start position:0%
+women who support them uh and they can
+be macho in relationship to each other
+
+ align:start position:0%
+be macho in relationship to each other
+ 
+
+ align:start position:0%
+be macho in relationship to each other
+so it's more than just Macho unless by
+
+ align:start position:0%
+so it's more than just Macho unless by
+ 
+
+ align:start position:0%
+so it's more than just Macho unless by
+Macho you mean a way a man treats a
+
+ align:start position:0%
+Macho you mean a way a man treats a
+ 
+
+ align:start position:0%
+Macho you mean a way a man treats a
+woman that he's in love with you know
+
+ align:start position:0%
+woman that he's in love with you know
+ 
+
+ align:start position:0%
+woman that he's in love with you know
+like in the
+
+ align:start position:0%
+like in the
+ 
+
+ align:start position:0%
+like in the
+Tango I I also mean the fact that um
+
+ align:start position:0%
+Tango I I also mean the fact that um
+ 
+
+ align:start position:0%
+Tango I I also mean the fact that um
+it's not considered very manly if a man
+
+ align:start position:0%
+it's not considered very manly if a man
+ 
+
+ align:start position:0%
+it's not considered very manly if a man
+feels attracted to another man
+
+ align:start position:0%
+feels attracted to another man
+ 
+
+ align:start position:0%
+feels attracted to another man
+um you mean if he's a
+
+ align:start position:0%
+um you mean if he's a
+ 
+
+ align:start position:0%
+um you mean if he's a
+feminine e either that or or a
+
+ align:start position:0%
+feminine e either that or or a
+ 
+
+ align:start position:0%
+feminine e either that or or a
+homosexual but all of these Concepts
+
+ align:start position:0%
+homosexual but all of these Concepts
+ 
+
+ align:start position:0%
+homosexual but all of these Concepts
+have to be analyzed more minutely I
+
+ align:start position:0%
+have to be analyzed more minutely I
+ 
+
+ align:start position:0%
+have to be analyzed more minutely I
+don't even go into it here uh being
+
+ align:start position:0%
+don't even go into it here uh being
+ 
+
+ align:start position:0%
+don't even go into it here uh being
+homosexual means that there is a sex
+
+ align:start position:0%
+homosexual means that there is a sex
+ 
+
+ align:start position:0%
+homosexual means that there is a sex
+sexual attachment or urge or interest in
+
+ align:start position:0%
+sexual attachment or urge or interest in
+ 
+
+ align:start position:0%
+sexual attachment or urge or interest in
+a person another person of the same sex
+
+ align:start position:0%
+a person another person of the same sex
+ 
+
+ align:start position:0%
+a person another person of the same sex
+but the nature of that attachment can be
+
+ align:start position:0%
+but the nature of that attachment can be
+ 
+
+ align:start position:0%
+but the nature of that attachment can be
+almost as variable as in heterosexual
+
+ align:start position:0%
+almost as variable as in heterosexual
+ 
+
+ align:start position:0%
+almost as variable as in heterosexual
+Arrangements uh the uh some of the men
+
+ align:start position:0%
+Arrangements uh the uh some of the men
+ 
+
+ align:start position:0%
+Arrangements uh the uh some of the men
+might be
+
+ align:start position:0%
+might be
+ 
+
+ align:start position:0%
+might be
+effeminate some might be very viral very
+
+ align:start position:0%
+effeminate some might be very viral very
+ 
+
+ align:start position:0%
+effeminate some might be very viral very
+Macho among the effeminate ones there
+
+ align:start position:0%
+Macho among the effeminate ones there
+ 
+
+ align:start position:0%
+Macho among the effeminate ones there
+are those who feel submissive in ways
+
+ align:start position:0%
+are those who feel submissive in ways
+ 
+
+ align:start position:0%
+are those who feel submissive in ways
+that women used to be and maybe often
+
+ align:start position:0%
+that women used to be and maybe often
+ 
+
+ align:start position:0%
+that women used to be and maybe often
+still are towards men who are going to
+
+ align:start position:0%
+still are towards men who are going to
+ 
+
+ align:start position:0%
+still are towards men who are going to
+protect them and some of them uh sort of
+
+ align:start position:0%
+protect them and some of them uh sort of
+ 
+
+ align:start position:0%
+protect them and some of them uh sort of
+mimic traits that we associate with
+
+ align:start position:0%
+mimic traits that we associate with
+ 
+
+ align:start position:0%
+mimic traits that we associate with
+women though nowadays we realize how not
+
+ align:start position:0%
+women though nowadays we realize how not
+ 
+
+ align:start position:0%
+women though nowadays we realize how not
+all women have those traits other words
+
+ align:start position:0%
+all women have those traits other words
+ 
+
+ align:start position:0%
+all women have those traits other words
+shaking their hips and lisping and you
+
+ align:start position:0%
+shaking their hips and lisping and you
+ 
+
+ align:start position:0%
+shaking their hips and lisping and you
+know the word eminate the way it's
+
+ align:start position:0%
+know the word eminate the way it's
+ 
+
+ align:start position:0%
+know the word eminate the way it's
+ordinarily used refers to only this one
+
+ align:start position:0%
+ordinarily used refers to only this one
+ 
+
+ align:start position:0%
+ordinarily used refers to only this one
+subclass of men right and a feminite man
+
+ align:start position:0%
+subclass of men right and a feminite man
+ 
+
+ align:start position:0%
+subclass of men right and a feminite man
+doesn't yet tell you whether he's
+
+ align:start position:0%
+doesn't yet tell you whether he's
+ 
+
+ align:start position:0%
+doesn't yet tell you whether he's
+homosexual or heterosexual something
+
+ align:start position:0%
+homosexual or heterosexual something
+ 
+
+ align:start position:0%
+homosexual or heterosexual something
+about his uh his attitude um his way of
+
+ align:start position:0%
+about his uh his attitude um his way of
+ 
+
+ align:start position:0%
+about his uh his attitude um his way of
+presenting himself to the world
+
+ align:start position:0%
+presenting himself to the world
+ 
+
+ align:start position:0%
+presenting himself to the world
+world one further complication is that
+
+ align:start position:0%
+world one further complication is that
+ 
+
+ align:start position:0%
+world one further complication is that
+um in many art
+
+ align:start position:0%
+um in many art
+ 
+
+ align:start position:0%
+um in many art
+forms having the kind of Grace and
+
+ align:start position:0%
+forms having the kind of Grace and
+ 
+
+ align:start position:0%
+forms having the kind of Grace and
+suavity and intuitive power that women
+
+ align:start position:0%
+suavity and intuitive power that women
+ 
+
+ align:start position:0%
+suavity and intuitive power that women
+have is part of the male role so that if
+
+ align:start position:0%
+have is part of the male role so that if
+ 
+
+ align:start position:0%
+have is part of the male role so that if
+you see if you go to the ballet and you
+
+ align:start position:0%
+you see if you go to the ballet and you
+ 
+
+ align:start position:0%
+you see if you go to the ballet and you
+see a very graceful
+
+ align:start position:0%
+see a very graceful
+ 
+
+ align:start position:0%
+see a very graceful
+man you might say oh it's because he's
+
+ align:start position:0%
+man you might say oh it's because he's
+ 
+
+ align:start position:0%
+man you might say oh it's because he's
+homosexual but he might it might not be
+
+ align:start position:0%
+homosexual but he might it might not be
+ 
+
+ align:start position:0%
+homosexual but he might it might not be
+because he's homosexual it might be
+
+ align:start position:0%
+because he's homosexual it might be
+ 
+
+ align:start position:0%
+because he's homosexual it might be
+because he's
+
+ align:start position:0%
+because he's
+ 
+
+ align:start position:0%
+because he's
+graceful he may have interpreted that
+
+ align:start position:0%
+graceful he may have interpreted that
+ 
+
+ align:start position:0%
+graceful he may have interpreted that
+himself it's meaning he must be
+
+ align:start position:0%
+himself it's meaning he must be
+ 
+
+ align:start position:0%
+himself it's meaning he must be
+homosexual and it might be in our
+
+ align:start position:0%
+homosexual and it might be in our
+ 
+
+ align:start position:0%
+homosexual and it might be in our
+society that it's only once you find
+
+ align:start position:0%
+society that it's only once you find
+ 
+
+ align:start position:0%
+society that it's only once you find
+some uh some Haven among people who are
+
+ align:start position:0%
+some uh some Haven among people who are
+ 
+
+ align:start position:0%
+some uh some Haven among people who are
+homosexual that you can't get away with
+
+ align:start position:0%
+homosexual that you can't get away with
+ 
+
+ align:start position:0%
+homosexual that you can't get away with
+being graceful in the dominant
+
+ align:start position:0%
+being graceful in the dominant
+ 
+
+ align:start position:0%
+being graceful in the dominant
+heterosexual Society we live in I've
+
+ align:start position:0%
+heterosexual Society we live in I've
+ 
+
+ align:start position:0%
+heterosexual Society we live in I've
+always long before this became
+
+ align:start position:0%
+always long before this became
+ 
+
+ align:start position:0%
+always long before this became
+controversial felt the um unfairness of
+
+ align:start position:0%
+controversial felt the um unfairness of
+ 
+
+ align:start position:0%
+controversial felt the um unfairness of
+this because I try and do I think see
+
+ align:start position:0%
+this because I try and do I think see
+ 
+
+ align:start position:0%
+this because I try and do I think see
+the world aesthetically and if somebody
+
+ align:start position:0%
+the world aesthetically and if somebody
+ 
+
+ align:start position:0%
+the world aesthetically and if somebody
+is extremely
+
+ align:start position:0%
+is extremely
+ 
+
+ align:start position:0%
+is extremely
+graceful in a work of art a
+
+ align:start position:0%
+graceful in a work of art a
+ 
+
+ align:start position:0%
+graceful in a work of art a
+ballet I don't care what he is and I
+
+ align:start position:0%
+ballet I don't care what he is and I
+ 
+
+ align:start position:0%
+ballet I don't care what he is and I
+don't want to make any inferences about
+
+ align:start position:0%
+don't want to make any inferences about
+ 
+
+ align:start position:0%
+don't want to make any inferences about
+what he is anymore than I would about a
+
+ align:start position:0%
+what he is anymore than I would about a
+ 
+
+ align:start position:0%
+what he is anymore than I would about a
+woman who's very graceful you know I
+
+ align:start position:0%
+woman who's very graceful you know I
+ 
+
+ align:start position:0%
+woman who's very graceful you know I
+don't want to say you know she's not
+
+ align:start position:0%
+don't want to say you know she's not
+ 
+
+ align:start position:0%
+don't want to say you know she's not
+representative of all the other women
+
+ align:start position:0%
+representative of all the other women
+ 
+
+ align:start position:0%
+representative of all the other women
+who are tough who are who are determined
+
+ align:start position:0%
+who are tough who are who are determined
+ 
+
+ align:start position:0%
+who are tough who are who are determined
+who you know who are going out to beat
+
+ align:start position:0%
+who you know who are going out to beat
+ 
+
+ align:start position:0%
+who you know who are going out to beat
+the males um they great variety and
+
+ align:start position:0%
+the males um they great variety and
+ 
+
+ align:start position:0%
+the males um they great variety and
+self-presentations among women and among
+
+ align:start position:0%
+self-presentations among women and among
+ 
+
+ align:start position:0%
+self-presentations among women and among
+men and a man who is very graceful if
+
+ align:start position:0%
+men and a man who is very graceful if
+ 
+
+ align:start position:0%
+men and a man who is very graceful if
+he's a good
+
+ align:start position:0%
+he's a good
+ 
+
+ align:start position:0%
+he's a good
+artist he's wonderful the sex doesn't
+
+ align:start position:0%
+artist he's wonderful the sex doesn't
+ 
+
+ align:start position:0%
+artist he's wonderful the sex doesn't
+matter it has nothing to do with it and
+
+ align:start position:0%
+matter it has nothing to do with it and
+ 
+
+ align:start position:0%
+matter it has nothing to do with it and
+yet unfairly has always come into it now
+
+ align:start position:0%
+yet unfairly has always come into it now
+ 
+
+ align:start position:0%
+yet unfairly has always come into it now
+part of the excitement of this
+
+ align:start position:0%
+part of the excitement of this
+ 
+
+ align:start position:0%
+part of the excitement of this
+intellectual issue that we're talking
+
+ align:start position:0%
+intellectual issue that we're talking
+ 
+
+ align:start position:0%
+intellectual issue that we're talking
+about is that all of this has
+
+ align:start position:0%
+about is that all of this has
+ 
+
+ align:start position:0%
+about is that all of this has
+erupted so that if people can say I am
+
+ align:start position:0%
+erupted so that if people can say I am
+ 
+
+ align:start position:0%
+erupted so that if people can say I am
+ex or I am let the person says I am
+
+ align:start position:0%
+ex or I am let the person says I am
+ 
+
+ align:start position:0%
+ex or I am let the person says I am
+homosexual and I want to get married to
+
+ align:start position:0%
+homosexual and I want to get married to
+ 
+
+ align:start position:0%
+homosexual and I want to get married to
+another homosexual sexual well that's
+
+ align:start position:0%
+another homosexual sexual well that's
+ 
+
+ align:start position:0%
+another homosexual sexual well that's
+taking it this complication as far as it
+
+ align:start position:0%
+taking it this complication as far as it
+ 
+
+ align:start position:0%
+taking it this complication as far as it
+can go because without that somebody
+
+ align:start position:0%
+can go because without that somebody
+ 
+
+ align:start position:0%
+can go because without that somebody
+might say um I'm not interested in
+
+ align:start position:0%
+might say um I'm not interested in
+ 
+
+ align:start position:0%
+might say um I'm not interested in
+married being married
+
+ align:start position:0%
+married being married
+ 
+
+ align:start position:0%
+married being married
+but I want to be graceful and doesn't
+
+ align:start position:0%
+but I want to be graceful and doesn't
+ 
+
+ align:start position:0%
+but I want to be graceful and doesn't
+follow I'm homosexual or I'm homosexual
+
+ align:start position:0%
+follow I'm homosexual or I'm homosexual
+ 
+
+ align:start position:0%
+follow I'm homosexual or I'm homosexual
+and I'm graceful all of this is now more
+
+ align:start position:0%
+and I'm graceful all of this is now more
+ 
+
+ align:start position:0%
+and I'm graceful all of this is now more
+overt than it ever has before there were
+
+ align:start position:0%
+overt than it ever has before there were
+ 
+
+ align:start position:0%
+overt than it ever has before there were
+movies like Victoria Victor Victoria you
+
+ align:start position:0%
+movies like Victoria Victor Victoria you
+ 
+
+ align:start position:0%
+movies like Victoria Victor Victoria you
+probably know and uh um uh what's the
+
+ align:start position:0%
+probably know and uh um uh what's the
+ 
+
+ align:start position:0%
+probably know and uh um uh what's the
+one the musical comedy well was also
+
+ align:start position:0%
+one the musical comedy well was also
+ 
+
+ align:start position:0%
+one the musical comedy well was also
+before became musical company was a
+
+ align:start position:0%
+before became musical company was a
+ 
+
+ align:start position:0%
+before became musical company was a
+mover uh the bird cage or there were and
+
+ align:start position:0%
+mover uh the bird cage or there were and
+ 
+
+ align:start position:0%
+mover uh the bird cage or there were and
+then there was a sequel whatever it's
+
+ align:start position:0%
+then there was a sequel whatever it's
+ 
+
+ align:start position:0%
+then there was a sequel whatever it's
+called birds of paral I'm not sure uh in
+
+ align:start position:0%
+called birds of paral I'm not sure uh in
+ 
+
+ align:start position:0%
+called birds of paral I'm not sure uh in
+which the whole question the lifestyle
+
+ align:start position:0%
+which the whole question the lifestyle
+ 
+
+ align:start position:0%
+which the whole question the lifestyle
+of uh of overate
+
+ align:start position:0%
+of uh of overate
+ 
+
+ align:start position:0%
+of uh of overate
+homosexuals uh is treated very clearly
+
+ align:start position:0%
+homosexuals uh is treated very clearly
+ 
+
+ align:start position:0%
+homosexuals uh is treated very clearly
+and it's comically times because people
+
+ align:start position:0%
+and it's comically times because people
+ 
+
+ align:start position:0%
+and it's comically times because people
+can be comical but um that's that's what
+
+ align:start position:0%
+can be comical but um that's that's what
+ 
+
+ align:start position:0%
+can be comical but um that's that's what
+they are and there's even that song in
+
+ align:start position:0%
+they are and there's even that song in
+ 
+
+ align:start position:0%
+they are and there's even that song in
+the musical I am what I am which is uh a
+
+ align:start position:0%
+the musical I am what I am which is uh a
+ 
+
+ align:start position:0%
+the musical I am what I am which is uh a
+kind of manif Veo uh of acceptance of
+
+ align:start position:0%
+kind of manif Veo uh of acceptance of
+ 
+
+ align:start position:0%
+kind of manif Veo uh of acceptance of
+oneself now one one of the
+
+ align:start position:0%
+oneself now one one of the
+ 
+
+ align:start position:0%
+oneself now one one of the
+U variation or derivations or
+
+ align:start position:0%
+U variation or derivations or
+ 
+
+ align:start position:0%
+U variation or derivations or
+complications in my philosophy of Love
+
+ align:start position:0%
+complications in my philosophy of Love
+ 
+
+ align:start position:0%
+complications in my philosophy of Love
+Is that uh love consists in acceptance
+
+ align:start position:0%
+Is that uh love consists in acceptance
+ 
+
+ align:start position:0%
+Is that uh love consists in acceptance
+of the other person as that person is um
+
+ align:start position:0%
+of the other person as that person is um
+ 
+
+ align:start position:0%
+of the other person as that person is um
+I'll talk about that later uh because it
+
+ align:start position:0%
+I'll talk about that later uh because it
+ 
+
+ align:start position:0%
+I'll talk about that later uh because it
+it it is one of the consequences of some
+
+ align:start position:0%
+it it is one of the consequences of some
+ 
+
+ align:start position:0%
+it it is one of the consequences of some
+of my earlier ideas that I may have
+
+ align:start position:0%
+of my earlier ideas that I may have
+ 
+
+ align:start position:0%
+of my earlier ideas that I may have
+talked about Bolen appraisal did I talk
+
+ align:start position:0%
+talked about Bolen appraisal did I talk
+ 
+
+ align:start position:0%
+talked about Bolen appraisal did I talk
+about last time well I'll be talking
+
+ align:start position:0%
+about last time well I'll be talking
+ 
+
+ align:start position:0%
+about last time well I'll be talking
+about all of them um now if that's true
+
+ align:start position:0%
+about all of them um now if that's true
+ 
+
+ align:start position:0%
+about all of them um now if that's true
+then somebody who accepts himself has
+
+ align:start position:0%
+then somebody who accepts himself has
+ 
+
+ align:start position:0%
+then somebody who accepts himself has
+self-love and why isn't that a good
+
+ align:start position:0%
+self-love and why isn't that a good
+ 
+
+ align:start position:0%
+self-love and why isn't that a good
+thing if that's what you are and you can
+
+ align:start position:0%
+thing if that's what you are and you can
+ 
+
+ align:start position:0%
+thing if that's what you are and you can
+accept yourself for what you are what's
+
+ align:start position:0%
+accept yourself for what you are what's
+ 
+
+ align:start position:0%
+accept yourself for what you are what's
+wrong with that it's a kind of self love
+
+ align:start position:0%
+wrong with that it's a kind of self love
+ 
+
+ align:start position:0%
+wrong with that it's a kind of self love
+that is very admirable and very few
+
+ align:start position:0%
+that is very admirable and very few
+ 
+
+ align:start position:0%
+that is very admirable and very few
+people can get away with it's not being
+
+ align:start position:0%
+people can get away with it's not being
+ 
+
+ align:start position:0%
+people can get away with it's not being
+selfish it's simply accepting yourself
+
+ align:start position:0%
+selfish it's simply accepting yourself
+ 
+
+ align:start position:0%
+selfish it's simply accepting yourself
+as you are and we all have a great deal
+
+ align:start position:0%
+as you are and we all have a great deal
+ 
+
+ align:start position:0%
+as you are and we all have a great deal
+of trouble about that because when we're
+
+ align:start position:0%
+of trouble about that because when we're
+ 
+
+ align:start position:0%
+of trouble about that because when we're
+young we don't identify with our Origins
+
+ align:start position:0%
+young we don't identify with our Origins
+ 
+
+ align:start position:0%
+young we don't identify with our Origins
+and sometimes it's unwise but eventually
+
+ align:start position:0%
+and sometimes it's unwise but eventually
+ 
+
+ align:start position:0%
+and sometimes it's unwise but eventually
+we work it out I'm sorry go on um I have
+
+ align:start position:0%
+we work it out I'm sorry go on um I have
+ 
+
+ align:start position:0%
+we work it out I'm sorry go on um I have
+a question because in the beginning like
+
+ align:start position:0%
+a question because in the beginning like
+ 
+
+ align:start position:0%
+a question because in the beginning like
+in the middle I guess you were talking
+
+ align:start position:0%
+in the middle I guess you were talking
+ 
+
+ align:start position:0%
+in the middle I guess you were talking
+about like how it's been like pretty
+
+ align:start position:0%
+about like how it's been like pretty
+ 
+
+ align:start position:0%
+about like how it's been like pretty
+much proven our society right now how
+
+ align:start position:0%
+much proven our society right now how
+ 
+
+ align:start position:0%
+much proven our society right now how
+separate but equal doesn't really work
+
+ align:start position:0%
+separate but equal doesn't really work
+ 
+
+ align:start position:0%
+separate but equal doesn't really work
+like like through the Civil that's
+
+ align:start position:0%
+like like through the Civil that's
+ 
+
+ align:start position:0%
+like like through the Civil that's
+separate but equal the separate but
+
+ align:start position:0%
+separate but equal the separate but
+ 
+
+ align:start position:0%
+separate but equal the separate but
+equal like marriage versus the does or
+
+ align:start position:0%
+equal like marriage versus the does or
+ 
+
+ align:start position:0%
+equal like marriage versus the does or
+does not does not that was the the
+
+ align:start position:0%
+does not does not that was the the
+ 
+
+ align:start position:0%
+does not does not that was the the
+ruling of um the Massachusetts Supreme
+
+ align:start position:0%
+ruling of um the Massachusetts Supreme
+ 
+
+ align:start position:0%
+ruling of um the Massachusetts Supreme
+Court right it wasn't my view because on
+
+ align:start position:0%
+Court right it wasn't my view because on
+ 
+
+ align:start position:0%
+Court right it wasn't my view because on
+the contrary what I was saying was right
+
+ align:start position:0%
+the contrary what I was saying was right
+ 
+
+ align:start position:0%
+the contrary what I was saying was right
+then you went on to say that marriage is
+
+ align:start position:0%
+then you went on to say that marriage is
+ 
+
+ align:start position:0%
+then you went on to say that marriage is
+just like the societal like view no in
+
+ align:start position:0%
+just like the societal like view no in
+ 
+
+ align:start position:0%
+just like the societal like view no in
+in context does anybody want to clarify
+
+ align:start position:0%
+in context does anybody want to clarify
+ 
+
+ align:start position:0%
+in context does anybody want to clarify
+this maybe I didn't do it well enough
+
+ align:start position:0%
+this maybe I didn't do it well enough
+ 
+
+ align:start position:0%
+this maybe I didn't do it well enough
+but I was trying to say was let's say
+
+ align:start position:0%
+but I was trying to say was let's say
+ 
+
+ align:start position:0%
+but I was trying to say was let's say
+that um The Situation's finally resolved
+
+ align:start position:0%
+that um The Situation's finally resolved
+ 
+
+ align:start position:0%
+that um The Situation's finally resolved
+and there are being two kinds of
+
+ align:start position:0%
+and there are being two kinds of
+ 
+
+ align:start position:0%
+and there are being two kinds of
+marriage or two orders of Quasi marital
+
+ align:start position:0%
+marriage or two orders of Quasi marital
+ 
+
+ align:start position:0%
+marriage or two orders of Quasi marital
+relationship and the civil union that's
+
+ align:start position:0%
+relationship and the civil union that's
+ 
+
+ align:start position:0%
+relationship and the civil union that's
+right that was the context civil union
+
+ align:start position:0%
+right that was the context civil union
+ 
+
+ align:start position:0%
+right that was the context civil union
+and marriage um and then uh some gay
+
+ align:start position:0%
+and marriage um and then uh some gay
+ 
+
+ align:start position:0%
+and marriage um and then uh some gay
+liberationists might say oh but that's
+
+ align:start position:0%
+liberationists might say oh but that's
+ 
+
+ align:start position:0%
+liberationists might say oh but that's
+separate but equal and we know that
+
+ align:start position:0%
+separate but equal and we know that
+ 
+
+ align:start position:0%
+separate but equal and we know that
+doesn't work in in terms of ethnic
+
+ align:start position:0%
+doesn't work in in terms of ethnic
+ 
+
+ align:start position:0%
+doesn't work in in terms of ethnic
+origin in terms of religion in terms of
+
+ align:start position:0%
+origin in terms of religion in terms of
+ 
+
+ align:start position:0%
+origin in terms of religion in terms of
+the color of people's skin and
+
+ align:start position:0%
+the color of people's skin and
+ 
+
+ align:start position:0%
+the color of people's skin and
+fortunately though this too took a long
+
+ align:start position:0%
+fortunately though this too took a long
+ 
+
+ align:start position:0%
+fortunately though this too took a long
+period of development but fortunately
+
+ align:start position:0%
+period of development but fortunately
+ 
+
+ align:start position:0%
+period of development but fortunately
+that is widely recognized by the laws
+
+ align:start position:0%
+that is widely recognized by the laws
+ 
+
+ align:start position:0%
+that is widely recognized by the laws
+though maybe not in every situation uh
+
+ align:start position:0%
+though maybe not in every situation uh
+ 
+
+ align:start position:0%
+though maybe not in every situation uh
+so there's still a lot of discrimination
+
+ align:start position:0%
+so there's still a lot of discrimination
+ 
+
+ align:start position:0%
+so there's still a lot of discrimination
+but you know there's been a a very
+
+ align:start position:0%
+but you know there's been a a very
+ 
+
+ align:start position:0%
+but you know there's been a a very
+radical change about that all right so
+
+ align:start position:0%
+radical change about that all right so
+ 
+
+ align:start position:0%
+radical change about that all right so
+separate but equal doesn't work in
+
+ align:start position:0%
+separate but equal doesn't work in
+ 
+
+ align:start position:0%
+separate but equal doesn't work in
+education for instance uh the gab
+
+ align:start position:0%
+education for instance uh the gab
+ 
+
+ align:start position:0%
+education for instance uh the gab
+liberations would say neither would it
+
+ align:start position:0%
+liberations would say neither would it
+ 
+
+ align:start position:0%
+liberations would say neither would it
+work in terms of marriage and my idea
+
+ align:start position:0%
+work in terms of marriage and my idea
+ 
+
+ align:start position:0%
+work in terms of marriage and my idea
+was um why wouldn't it work let's let's
+
+ align:start position:0%
+was um why wouldn't it work let's let's
+ 
+
+ align:start position:0%
+was um why wouldn't it work let's let's
+say that people who are heterosexual can
+
+ align:start position:0%
+say that people who are heterosexual can
+ 
+
+ align:start position:0%
+say that people who are heterosexual can
+get married because that's what the
+
+ align:start position:0%
+get married because that's what the
+ 
+
+ align:start position:0%
+get married because that's what the
+majority want and that those who are not
+
+ align:start position:0%
+majority want and that those who are not
+ 
+
+ align:start position:0%
+majority want and that those who are not
+heterosexual have a civil union which is
+
+ align:start position:0%
+heterosexual have a civil union which is
+ 
+
+ align:start position:0%
+heterosexual have a civil union which is
+identical in terms of Rights and
+
+ align:start position:0%
+identical in terms of Rights and
+ 
+
+ align:start position:0%
+identical in terms of Rights and
+Privileges and responsibilities with
+
+ align:start position:0%
+Privileges and responsibilities with
+ 
+
+ align:start position:0%
+Privileges and responsibilities with
+marriage it simply gets to be a verbal
+
+ align:start position:0%
+marriage it simply gets to be a verbal
+ 
+
+ align:start position:0%
+marriage it simply gets to be a verbal
+issue well I don't consider verbal
+
+ align:start position:0%
+issue well I don't consider verbal
+ 
+
+ align:start position:0%
+issue well I don't consider verbal
+issues worth fighting up fighting over
+
+ align:start position:0%
+issues worth fighting up fighting over
+ 
+
+ align:start position:0%
+issues worth fighting up fighting over
+if it that's all it
+
+ align:start position:0%
+if it that's all it
+ 
+
+ align:start position:0%
+if it that's all it
+is it would be a way of enabling the
+
+ align:start position:0%
+is it would be a way of enabling the
+ 
+
+ align:start position:0%
+is it would be a way of enabling the
+bigoted heterosexuals to save
+
+ align:start position:0%
+bigoted heterosexuals to save
+ 
+
+ align:start position:0%
+bigoted heterosexuals to save
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+course or particularly those who are
+
+ align:start position:0%
+course or particularly those who are
+ 
+
+ align:start position:0%
+course or particularly those who are
+religious like in the the state one of
+
+ align:start position:0%
+religious like in the the state one of
+ 
+
+ align:start position:0%
+religious like in the the state one of
+the was it a Southern state or a middle
+
+ align:start position:0%
+the was it a Southern state or a middle
+ 
+
+ align:start position:0%
+the was it a Southern state or a middle
+was it Missouri I can't remember just
+
+ align:start position:0%
+was it Missouri I can't remember just
+ 
+
+ align:start position:0%
+was it Missouri I can't remember just
+just recently which which state was that
+
+ align:start position:0%
+just recently which which state was that
+ 
+
+ align:start position:0%
+just recently which which state was that
+I it was which Louisiana I thought it
+
+ align:start position:0%
+I it was which Louisiana I thought it
+ 
+
+ align:start position:0%
+I it was which Louisiana I thought it
+was Missouri she what I thought it was
+
+ align:start position:0%
+was Missouri she what I thought it was
+ 
+
+ align:start position:0%
+was Missouri she what I thought it was
+Louisiana she thinks it's Missour so no
+
+ align:start position:0%
+Louisiana she thinks it's Missour so no
+ 
+
+ align:start position:0%
+Louisiana she thinks it's Missour so no
+I no I think it is Louisiana um that's
+
+ align:start position:0%
+I no I think it is Louisiana um that's
+ 
+
+ align:start position:0%
+I no I think it is Louisiana um that's
+part of the Bible Belt uh people are U
+
+ align:start position:0%
+part of the Bible Belt uh people are U
+ 
+
+ align:start position:0%
+part of the Bible Belt uh people are U
+very conservative Baptists U of A Sort
+
+ align:start position:0%
+very conservative Baptists U of A Sort
+ 
+
+ align:start position:0%
+very conservative Baptists U of A Sort
+who um try to adhere to the fundamental
+
+ align:start position:0%
+who um try to adhere to the fundamental
+ 
+
+ align:start position:0%
+who um try to adhere to the fundamental
+teachings of their religion now they all
+
+ align:start position:0%
+teachings of their religion now they all
+ 
+
+ align:start position:0%
+teachings of their religion now they all
+want to keep the word marriage for
+
+ align:start position:0%
+want to keep the word marriage for
+ 
+
+ align:start position:0%
+want to keep the word marriage for
+people who are
+
+ align:start position:0%
+people who are
+ 
+
+ align:start position:0%
+people who are
+heterosexual because of their own
+
+ align:start position:0%
+heterosexual because of their own
+ 
+
+ align:start position:0%
+heterosexual because of their own
+religious
+
+ align:start position:0%
+religious
+ 
+
+ align:start position:0%
+religious
+views I don't feel it's worth having a
+
+ align:start position:0%
+views I don't feel it's worth having a
+ 
+
+ align:start position:0%
+views I don't feel it's worth having a
+civil war over um provided that those
+
+ align:start position:0%
+civil war over um provided that those
+ 
+
+ align:start position:0%
+civil war over um provided that those
+who are not said to be married have
+
+ align:start position:0%
+who are not said to be married have
+ 
+
+ align:start position:0%
+who are not said to be married have
+civil or allowed civil unions that are
+
+ align:start position:0%
+civil or allowed civil unions that are
+ 
+
+ align:start position:0%
+civil or allowed civil unions that are
+equal in every respect that it's just a
+
+ align:start position:0%
+equal in every respect that it's just a
+ 
+
+ align:start position:0%
+equal in every respect that it's just a
+verbal issue unfortunately in the case
+
+ align:start position:0%
+verbal issue unfortunately in the case
+ 
+
+ align:start position:0%
+verbal issue unfortunately in the case
+of the the
+
+ align:start position:0%
+of the the
+ 
+
+ align:start position:0%
+of the the
+Louisiana decision they banned both
+
+ align:start position:0%
+Louisiana decision they banned both
+ 
+
+ align:start position:0%
+Louisiana decision they banned both
+civil unions and uh homosexual marriage
+
+ align:start position:0%
+civil unions and uh homosexual marriage
+ 
+
+ align:start position:0%
+civil unions and uh homosexual marriage
+so that's a complication but I wasn't
+
+ align:start position:0%
+so that's a complication but I wasn't
+ 
+
+ align:start position:0%
+so that's a complication but I wasn't
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+that what did you go no I just think
+
+ align:start position:0%
+that what did you go no I just think
+ 
+
+ align:start position:0%
+that what did you go no I just think
+that it might be like in theory it might
+
+ align:start position:0%
+that it might be like in theory it might
+ 
+
+ align:start position:0%
+that it might be like in theory it might
+sound like reasonable oh you know if
+
+ align:start position:0%
+sound like reasonable oh you know if
+ 
+
+ align:start position:0%
+sound like reasonable oh you know if
+they don't want use marriage then um
+
+ align:start position:0%
+they don't want use marriage then um
+ 
+
+ align:start position:0%
+they don't want use marriage then um
+then let's just give them the same
+
+ align:start position:0%
+then let's just give them the same
+ 
+
+ align:start position:0%
+then let's just give them the same
+rights and just call it something else
+
+ align:start position:0%
+rights and just call it something else
+ 
+
+ align:start position:0%
+rights and just call it something else
+but I think that's just like avoiding
+
+ align:start position:0%
+but I think that's just like avoiding
+ 
+
+ align:start position:0%
+but I think that's just like avoiding
+the conflict and like it is it is trying
+
+ align:start position:0%
+the conflict and like it is it is trying
+ 
+
+ align:start position:0%
+the conflict and like it is it is trying
+to save face I agree it's it is trying
+
+ align:start position:0%
+to save face I agree it's it is trying
+ 
+
+ align:start position:0%
+to save face I agree it's it is trying
+to avoid the conflict not all not all
+
+ align:start position:0%
+to avoid the conflict not all not all
+ 
+
+ align:start position:0%
+to avoid the conflict not all not all
+issues have to lead to as much agitation
+
+ align:start position:0%
+issues have to lead to as much agitation
+ 
+
+ align:start position:0%
+issues have to lead to as much agitation
+and misery as this one seems to be on
+
+ align:start position:0%
+and misery as this one seems to be on
+ 
+
+ align:start position:0%
+and misery as this one seems to be on
+the way to do I I always felt that if
+
+ align:start position:0%
+the way to do I I always felt that if
+ 
+
+ align:start position:0%
+the way to do I I always felt that if
+President
+
+ align:start position:0%
+President
+ 
+
+ align:start position:0%
+President
+Kennedy had been the president at the
+
+ align:start position:0%
+Kennedy had been the president at the
+ 
+
+ align:start position:0%
+Kennedy had been the president at the
+time that Lincoln was
+
+ align:start position:0%
+time that Lincoln was
+ 
+
+ align:start position:0%
+time that Lincoln was
+elected we might not have had a civil
+
+ align:start position:0%
+elected we might not have had a civil
+ 
+
+ align:start position:0%
+elected we might not have had a civil
+war he might because his practice was to
+
+ align:start position:0%
+war he might because his practice was to
+ 
+
+ align:start position:0%
+war he might because his practice was to
+get everybody to talk to bring them in
+
+ align:start position:0%
+get everybody to talk to bring them in
+ 
+
+ align:start position:0%
+get everybody to talk to bring them in
+and try to try to work things out um and
+
+ align:start position:0%
+and try to try to work things out um and
+ 
+
+ align:start position:0%
+and try to try to work things out um and
+if necessary to bring in um uh the
+
+ align:start position:0%
+if necessary to bring in um uh the
+ 
+
+ align:start position:0%
+if necessary to bring in um uh the
+National Guard as he did in the question
+
+ align:start position:0%
+National Guard as he did in the question
+ 
+
+ align:start position:0%
+National Guard as he did in the question
+of um black children being admitted to
+
+ align:start position:0%
+of um black children being admitted to
+ 
+
+ align:start position:0%
+of um black children being admitted to
+the University of uh Mississippi ne's
+
+ align:start position:0%
+the University of uh Mississippi ne's
+ 
+
+ align:start position:0%
+the University of uh Mississippi ne's
+education he he brought in that was
+
+ align:start position:0%
+education he he brought in that was
+ 
+
+ align:start position:0%
+education he he brought in that was
+taking strong military action but prior
+
+ align:start position:0%
+taking strong military action but prior
+ 
+
+ align:start position:0%
+taking strong military action but prior
+to that um he was very very prone to
+
+ align:start position:0%
+to that um he was very very prone to
+ 
+
+ align:start position:0%
+to that um he was very very prone to
+negotiation and I don't think Lincoln
+
+ align:start position:0%
+negotiation and I don't think Lincoln
+ 
+
+ align:start position:0%
+negotiation and I don't think Lincoln
+was I don't think Lincoln was a good
+
+ align:start position:0%
+was I don't think Lincoln was a good
+ 
+
+ align:start position:0%
+was I don't think Lincoln was a good
+president in that respect no he was
+
+ align:start position:0%
+president in that respect no he was
+ 
+
+ align:start position:0%
+president in that respect no he was
+admirable in other ways but um I don't
+
+ align:start position:0%
+admirable in other ways but um I don't
+ 
+
+ align:start position:0%
+admirable in other ways but um I don't
+think he knew how to handle the
+
+ align:start position:0%
+think he knew how to handle the
+ 
+
+ align:start position:0%
+think he knew how to handle the
+situation uh and in general these deep
+
+ align:start position:0%
+situation uh and in general these deep
+ 
+
+ align:start position:0%
+situation uh and in general these deep
+deep uh problems like
+
+ align:start position:0%
+deep uh problems like
+ 
+
+ align:start position:0%
+deep uh problems like
+abortion um uh uh slavery um uh same-sex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+marriage are are very difficult to
+
+ align:start position:0%
+marriage are are very difficult to
+ 
+
+ align:start position:0%
+marriage are are very difficult to
+resolve and not worth
+
+ align:start position:0%
+resolve and not worth
+ 
+
+ align:start position:0%
+resolve and not worth
+resolving the way that the slavery issue
+
+ align:start position:0%
+resolving the way that the slavery issue
+ 
+
+ align:start position:0%
+resolving the way that the slavery issue
+was where
+
+ align:start position:0%
+was where
+ 
+
+ align:start position:0%
+was where
+600,000 men were killed and whole parts
+
+ align:start position:0%
+600,000 men were killed and whole parts
+ 
+
+ align:start position:0%
+600,000 men were killed and whole parts
+of the country devastated and the
+
+ align:start position:0%
+of the country devastated and the
+ 
+
+ align:start position:0%
+of the country devastated and the
+country in turmoil for four even more
+
+ align:start position:0%
+country in turmoil for four even more
+ 
+
+ align:start position:0%
+country in turmoil for four even more
+years not that I think that they should
+
+ align:start position:0%
+years not that I think that they should
+ 
+
+ align:start position:0%
+years not that I think that they should
+have uh tolerated slavery but it didn't
+
+ align:start position:0%
+have uh tolerated slavery but it didn't
+ 
+
+ align:start position:0%
+have uh tolerated slavery but it didn't
+have to lead to a civil war
+
+ align:start position:0%
+have to lead to a civil war
+ 
+
+ align:start position:0%
+have to lead to a civil war
+but or I hope or I would hope it
+
+ align:start position:0%
+but or I hope or I would hope it
+ 
+
+ align:start position:0%
+but or I hope or I would hope it
+wouldn't have in my opinion I think the
+
+ align:start position:0%
+wouldn't have in my opinion I think the
+ 
+
+ align:start position:0%
+wouldn't have in my opinion I think the
+whole civil union thing that you propos
+
+ align:start position:0%
+whole civil union thing that you propos
+ 
+
+ align:start position:0%
+whole civil union thing that you propos
+might be a good way to like just
+
+ align:start position:0%
+might be a good way to like just
+ 
+
+ align:start position:0%
+might be a good way to like just
+Institute that for the time being and
+
+ align:start position:0%
+Institute that for the time being and
+ 
+
+ align:start position:0%
+Institute that for the time being and
+then keep the lines of communication I
+
+ align:start position:0%
+then keep the lines of communication I
+ 
+
+ align:start position:0%
+then keep the lines of communication I
+guess open and keep talking to like
+
+ align:start position:0%
+guess open and keep talking to like
+ 
+
+ align:start position:0%
+guess open and keep talking to like
+build up to the point where on the model
+
+ align:start position:0%
+build up to the point where on the model
+ 
+
+ align:start position:0%
+build up to the point where on the model
+of the Netherlands I mentioned that in
+
+ align:start position:0%
+of the Netherlands I mentioned that in
+ 
+
+ align:start position:0%
+of the Netherlands I mentioned that in
+the Netherlands first there was civil
+
+ align:start position:0%
+the Netherlands first there was civil
+ 
+
+ align:start position:0%
+the Netherlands first there was civil
+unions and then there was marriage but
+
+ align:start position:0%
+unions and then there was marriage but
+ 
+
+ align:start position:0%
+unions and then there was marriage but
+if there is going to be a large public
+
+ align:start position:0%
+if there is going to be a large public
+ 
+
+ align:start position:0%
+if there is going to be a large public
+sentiment against even civil union then
+
+ align:start position:0%
+sentiment against even civil union then
+ 
+
+ align:start position:0%
+sentiment against even civil union then
+you should take then that's a
+
+ align:start position:0%
+you should take then that's a
+ 
+
+ align:start position:0%
+you should take then that's a
+complication and then I'm not sure I
+
+ align:start position:0%
+complication and then I'm not sure I
+ 
+
+ align:start position:0%
+complication and then I'm not sure I
+know what to say I I think there is I
+
+ align:start position:0%
+know what to say I I think there is I
+ 
+
+ align:start position:0%
+know what to say I I think there is I
+mean I think like unfortunately a lot of
+
+ align:start position:0%
+mean I think like unfortunately a lot of
+ 
+
+ align:start position:0%
+mean I think like unfortunately a lot of
+these people are are against
+
+ align:start position:0%
+these people are are against
+ 
+
+ align:start position:0%
+these people are are against
+homosexuality itself right and and think
+
+ align:start position:0%
+homosexuality itself right and and think
+ 
+
+ align:start position:0%
+homosexuality itself right and and think
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+that in what way well I I think in
+
+ align:start position:0%
+that in what way well I I think in
+ 
+
+ align:start position:0%
+that in what way well I I think in
+largely religious sense no but no I mean
+
+ align:start position:0%
+largely religious sense no but no I mean
+ 
+
+ align:start position:0%
+largely religious sense no but no I mean
+is it that they don't want their
+
+ align:start position:0%
+is it that they don't want their
+ 
+
+ align:start position:0%
+is it that they don't want their
+children to be one they don't want their
+
+ align:start position:0%
+children to be one they don't want their
+ 
+
+ align:start position:0%
+children to be one they don't want their
+children to marry one they they think I
+
+ align:start position:0%
+children to marry one they they think I
+ 
+
+ align:start position:0%
+children to marry one they they think I
+I think that they feel it it would be uh
+
+ align:start position:0%
+I think that they feel it it would be uh
+ 
+
+ align:start position:0%
+I think that they feel it it would be uh
+it would be no it would be it it's it
+
+ align:start position:0%
+it would be no it would be it it's it
+ 
+
+ align:start position:0%
+it would be no it would be it it's it
+would be bad for soci would also not be
+
+ align:start position:0%
+would be bad for soci would also not be
+ 
+
+ align:start position:0%
+would be bad for soci would also not be
+right for them to even tolerate it but
+
+ align:start position:0%
+right for them to even tolerate it but
+ 
+
+ align:start position:0%
+right for them to even tolerate it but
+they have the same way but it's already
+
+ align:start position:0%
+they have the same way but it's already
+ 
+
+ align:start position:0%
+they have the same way but it's already
+tolerated because all of the anti gave
+
+ align:start position:0%
+tolerated because all of the anti gave
+ 
+
+ align:start position:0%
+tolerated because all of the anti gave
+laws have been taken off the books in
+
+ align:start position:0%
+laws have been taken off the books in
+ 
+
+ align:start position:0%
+laws have been taken off the books in
+terms of uh behavior and lifestyle until
+
+ align:start position:0%
+terms of uh behavior and lifestyle until
+ 
+
+ align:start position:0%
+terms of uh behavior and lifestyle until
+recently being homosexual was a criminal
+
+ align:start position:0%
+recently being homosexual was a criminal
+ 
+
+ align:start position:0%
+recently being homosexual was a criminal
+act and so is so is abortion right but I
+
+ align:start position:0%
+act and so is so is abortion right but I
+ 
+
+ align:start position:0%
+act and so is so is abortion right but I
+wouldn't really call either of these
+
+ align:start position:0%
+wouldn't really call either of these
+ 
+
+ align:start position:0%
+wouldn't really call either of these
+things tolerated I mean they're
+
+ align:start position:0%
+things tolerated I mean they're
+ 
+
+ align:start position:0%
+things tolerated I mean they're
+tolerated by the law sure but that's
+
+ align:start position:0%
+tolerated by the law sure but that's
+ 
+
+ align:start position:0%
+tolerated by the law sure but that's
+we're talking a societal issue I well no
+
+ align:start position:0%
+we're talking a societal issue I well no
+ 
+
+ align:start position:0%
+we're talking a societal issue I well no
+there there's a complication here it's
+
+ align:start position:0%
+there there's a complication here it's
+ 
+
+ align:start position:0%
+there there's a complication here it's
+not a question of whom you like because
+
+ align:start position:0%
+not a question of whom you like because
+ 
+
+ align:start position:0%
+not a question of whom you like because
+that people in a sense may not tolerate
+
+ align:start position:0%
+that people in a sense may not tolerate
+ 
+
+ align:start position:0%
+that people in a sense may not tolerate
+homosexuality that they will be free to
+
+ align:start position:0%
+homosexuality that they will be free to
+ 
+
+ align:start position:0%
+homosexuality that they will be free to
+show their dislike of those who engage
+
+ align:start position:0%
+show their dislike of those who engage
+ 
+
+ align:start position:0%
+show their dislike of those who engage
+in it and to teach their children say
+
+ align:start position:0%
+in it and to teach their children say
+ 
+
+ align:start position:0%
+in it and to teach their children say
+the children know you must never do this
+
+ align:start position:0%
+the children know you must never do this
+ 
+
+ align:start position:0%
+the children know you must never do this
+sort of thing that that's a First
+
+ align:start position:0%
+sort of thing that that's a First
+ 
+
+ align:start position:0%
+sort of thing that that's a First
+Amendment freedom people have a right to
+
+ align:start position:0%
+Amendment freedom people have a right to
+ 
+
+ align:start position:0%
+Amendment freedom people have a right to
+that and the same sense and the same is
+
+ align:start position:0%
+that and the same sense and the same is
+ 
+
+ align:start position:0%
+that and the same sense and the same is
+true about their you know their feelings
+
+ align:start position:0%
+true about their you know their feelings
+ 
+
+ align:start position:0%
+true about their you know their feelings
+of any sort I mean they may not like
+
+ align:start position:0%
+of any sort I mean they may not like
+ 
+
+ align:start position:0%
+of any sort I mean they may not like
+Jews so um they may not like
+
+ align:start position:0%
+Jews so um they may not like
+ 
+
+ align:start position:0%
+Jews so um they may not like
+Catholics I don't like my colleagues
+
+ align:start position:0%
+Catholics I don't like my colleagues
+ 
+
+ align:start position:0%
+Catholics I don't like my colleagues
+that doesn't mean that doesn't mean that
+
+ align:start position:0%
+that doesn't mean that doesn't mean that
+ 
+
+ align:start position:0%
+that doesn't mean that doesn't mean that
+doesn't mean that um they should be
+
+ align:start position:0%
+doesn't mean that um they should be
+ 
+
+ align:start position:0%
+doesn't mean that um they should be
+prevented from going on and living their
+
+ align:start position:0%
+prevented from going on and living their
+ 
+
+ align:start position:0%
+prevented from going on and living their
+own life we're free to have any feelings
+
+ align:start position:0%
+own life we're free to have any feelings
+ 
+
+ align:start position:0%
+own life we're free to have any feelings
+we want when it comes to
+
+ align:start position:0%
+we want when it comes to
+ 
+
+ align:start position:0%
+we want when it comes to
+actions then uh that's decided by the
+
+ align:start position:0%
+actions then uh that's decided by the
+ 
+
+ align:start position:0%
+actions then uh that's decided by the
+Constitution and the laws and the
+
+ align:start position:0%
+Constitution and the laws and the
+ 
+
+ align:start position:0%
+Constitution and the laws and the
+structure of
+
+ align:start position:0%
+structure of
+ 
+
+ align:start position:0%
+structure of
+society the way the um um attitude
+
+ align:start position:0%
+society the way the um um attitude
+ 
+
+ align:start position:0%
+society the way the um um attitude
+toward homosexuality is now handled is
+
+ align:start position:0%
+toward homosexuality is now handled is
+ 
+
+ align:start position:0%
+toward homosexuality is now handled is
+that it is tolerated in so far as it's
+
+ align:start position:0%
+that it is tolerated in so far as it's
+ 
+
+ align:start position:0%
+that it is tolerated in so far as it's
+no longer illegal it wasn't tolerated
+
+ align:start position:0%
+no longer illegal it wasn't tolerated
+ 
+
+ align:start position:0%
+no longer illegal it wasn't tolerated
+until fairly recently because it was
+
+ align:start position:0%
+until fairly recently because it was
+ 
+
+ align:start position:0%
+until fairly recently because it was
+criminal decriminalizing
+
+ align:start position:0%
+criminal decriminalizing
+ 
+
+ align:start position:0%
+criminal decriminalizing
+it see is a kind of Toler Toleration the
+
+ align:start position:0%
+it see is a kind of Toler Toleration the
+ 
+
+ align:start position:0%
+it see is a kind of Toler Toleration the
+question of
+
+ align:start position:0%
+question of
+ 
+
+ align:start position:0%
+question of
+marriage is a form of Toleration that
+
+ align:start position:0%
+marriage is a form of Toleration that
+ 
+
+ align:start position:0%
+marriage is a form of Toleration that
+we're talking about so could you clarify
+
+ align:start position:0%
+we're talking about so could you clarify
+ 
+
+ align:start position:0%
+we're talking about so could you clarify
+what you want to say in terms of that
+
+ align:start position:0%
+what you want to say in terms of that
+ 
+
+ align:start position:0%
+what you want to say in terms of that
+distinction well well I guess we're
+
+ align:start position:0%
+distinction well well I guess we're
+ 
+
+ align:start position:0%
+distinction well well I guess we're
+talking about a case in
+
+ align:start position:0%
+talking about a case in
+ 
+
+ align:start position:0%
+talking about a case in
+which there like all forms of like
+
+ align:start position:0%
+which there like all forms of like
+ 
+
+ align:start position:0%
+which there like all forms of like
+homosexual civil union were declared
+
+ align:start position:0%
+homosexual civil union were declared
+ 
+
+ align:start position:0%
+homosexual civil union were declared
+illegal right in Mississippi or
+
+ align:start position:0%
+illegal right in Mississippi or
+ 
+
+ align:start position:0%
+illegal right in Mississippi or
+Louisiana or Louisiana Massachusetts
+
+ align:start position:0%
+Louisiana or Louisiana Massachusetts
+ 
+
+ align:start position:0%
+Louisiana or Louisiana Massachusetts
+ined red in
+
+ align:start position:0%
+ined red in
+ 
+
+ align:start position:0%
+ined red in
+Massachusetts I don't know when it
+
+ align:start position:0%
+Massachusetts I don't know when it
+ 
+
+ align:start position:0%
+Massachusetts I don't know when it
+stopped but I remember when I got
+
+ align:start position:0%
+stopped but I remember when I got
+ 
+
+ align:start position:0%
+stopped but I remember when I got
+married um it was something of interest
+
+ align:start position:0%
+married um it was something of interest
+ 
+
+ align:start position:0%
+married um it was something of interest
+uh any kind of um anal intercourse
+
+ align:start position:0%
+uh any kind of um anal intercourse
+ 
+
+ align:start position:0%
+uh any kind of um anal intercourse
+between a husband and a wife for
+
+ align:start position:0%
+between a husband and a wife for
+ 
+
+ align:start position:0%
+between a husband and a wife for
+instance was
+
+ align:start position:0%
+instance was
+ 
+
+ align:start position:0%
+instance was
+illegal adultery was
+
+ align:start position:0%
+illegal adultery was
+ 
+
+ align:start position:0%
+illegal adultery was
+illegal there were all sorts of uh laws
+
+ align:start position:0%
+illegal there were all sorts of uh laws
+ 
+
+ align:start position:0%
+illegal there were all sorts of uh laws
+against intimate behavior that um went
+
+ align:start position:0%
+against intimate behavior that um went
+ 
+
+ align:start position:0%
+against intimate behavior that um went
+back to the Puritans who thought that
+
+ align:start position:0%
+back to the Puritans who thought that
+ 
+
+ align:start position:0%
+back to the Puritans who thought that
+God had prescribed these things as evil
+
+ align:start position:0%
+God had prescribed these things as evil
+ 
+
+ align:start position:0%
+God had prescribed these things as evil
+Now by now they're all off the and
+
+ align:start position:0%
+Now by now they're all off the and
+ 
+
+ align:start position:0%
+Now by now they're all off the and
+they've been taken out of law books and
+
+ align:start position:0%
+they've been taken out of law books and
+ 
+
+ align:start position:0%
+they've been taken out of law books and
+the same thing about
+
+ align:start position:0%
+the same thing about
+ 
+
+ align:start position:0%
+the same thing about
+homosexuality no I'm sorry go
+
+ align:start position:0%
+homosexuality no I'm sorry go
+ 
+
+ align:start position:0%
+homosexuality no I'm sorry go
+on well I I I guess I was I was just
+
+ align:start position:0%
+on well I I I guess I was I was just
+ 
+
+ align:start position:0%
+on well I I I guess I was I was just
+saying I think you know I mean I think
+
+ align:start position:0%
+saying I think you know I mean I think
+ 
+
+ align:start position:0%
+saying I think you know I mean I think
+uh Massachusetts is kind of the
+
+ align:start position:0%
+uh Massachusetts is kind of the
+ 
+
+ align:start position:0%
+uh Massachusetts is kind of the
+exception to the rule in a lot of these
+
+ align:start position:0%
+exception to the rule in a lot of these
+ 
+
+ align:start position:0%
+exception to the rule in a lot of these
+cases right I mean it's I I mean it
+
+ align:start position:0%
+cases right I mean it's I I mean it
+ 
+
+ align:start position:0%
+cases right I mean it's I I mean it
+tends to it tends to be pretty liberal
+
+ align:start position:0%
+tends to it tends to be pretty liberal
+ 
+
+ align:start position:0%
+tends to it tends to be pretty liberal
+right but I mean I think a lot of these
+
+ align:start position:0%
+right but I mean I think a lot of these
+ 
+
+ align:start position:0%
+right but I mean I think a lot of these
+Bible Bel States and so forth um you
+
+ align:start position:0%
+Bible Bel States and so forth um you
+ 
+
+ align:start position:0%
+Bible Bel States and so forth um you
+know the people who make the laws I
+
+ align:start position:0%
+know the people who make the laws I
+ 
+
+ align:start position:0%
+know the people who make the laws I
+think are often of of this opinion that
+
+ align:start position:0%
+think are often of of this opinion that
+ 
+
+ align:start position:0%
+think are often of of this opinion that
+that homosexuality itself is inherently
+
+ align:start position:0%
+that homosexuality itself is inherently
+ 
+
+ align:start position:0%
+that homosexuality itself is inherently
+like wrong it would be wrong for them to
+
+ align:start position:0%
+like wrong it would be wrong for them to
+ 
+
+ align:start position:0%
+like wrong it would be wrong for them to
+even tolerate it right the law is
+
+ align:start position:0%
+even tolerate it right the law is
+ 
+
+ align:start position:0%
+even tolerate it right the law is
+tolerated in that sense um in
+
+ align:start position:0%
+tolerated in that sense um in
+ 
+
+ align:start position:0%
+tolerated in that sense um in
+Massachusetts I don't know what the laws
+
+ align:start position:0%
+Massachusetts I don't know what the laws
+ 
+
+ align:start position:0%
+Massachusetts I don't know what the laws
+in the southern states are but the
+
+ align:start position:0%
+in the southern states are but the
+ 
+
+ align:start position:0%
+in the southern states are but the
+federal law um has
+
+ align:start position:0%
+federal law um has
+ 
+
+ align:start position:0%
+federal law um has
+decriminalized that kind of relationship
+
+ align:start position:0%
+decriminalized that kind of relationship
+ 
+
+ align:start position:0%
+decriminalized that kind of relationship
+that's the crucial thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+um what was your M main point that it's
+
+ align:start position:0%
+um what was your M main point that it's
+ 
+
+ align:start position:0%
+um what was your M main point that it's
+it's the fact of homosexuality that the
+
+ align:start position:0%
+it's the fact of homosexuality that the
+ 
+
+ align:start position:0%
+it's the fact of homosexuality that the
+present agitation is really about so I
+
+ align:start position:0%
+present agitation is really about so I
+ 
+
+ align:start position:0%
+present agitation is really about so I
+mean I think I I think uh so like my
+
+ align:start position:0%
+mean I think I I think uh so like my
+ 
+
+ align:start position:0%
+mean I think I I think uh so like my
+personal opinion right is is is like I I
+
+ align:start position:0%
+personal opinion right is is is like I I
+ 
+
+ align:start position:0%
+personal opinion right is is is like I I
+have no problems about you know about
+
+ align:start position:0%
+have no problems about you know about
+ 
+
+ align:start position:0%
+have no problems about you know about
+like people being homosexual and and
+
+ align:start position:0%
+like people being homosexual and and
+ 
+
+ align:start position:0%
+like people being homosexual and and
+like um getting married and stuff right
+
+ align:start position:0%
+like um getting married and stuff right
+ 
+
+ align:start position:0%
+like um getting married and stuff right
+I that I I I don't feel that hurts me in
+
+ align:start position:0%
+I that I I I don't feel that hurts me in
+ 
+
+ align:start position:0%
+I that I I I don't feel that hurts me in
+any way right so um so like I I would be
+
+ align:start position:0%
+any way right so um so like I I would be
+ 
+
+ align:start position:0%
+any way right so um so like I I would be
+in full support of civil unions and and
+
+ align:start position:0%
+in full support of civil unions and and
+ 
+
+ align:start position:0%
+in full support of civil unions and and
+even full marriage to some extent right
+
+ align:start position:0%
+even full marriage to some extent right
+ 
+
+ align:start position:0%
+even full marriage to some extent right
+but um I I mean I guess I'm I'm just
+
+ align:start position:0%
+but um I I mean I guess I'm I'm just
+ 
+
+ align:start position:0%
+but um I I mean I guess I'm I'm just
+trying to get in the mind with someone
+
+ align:start position:0%
+trying to get in the mind with someone
+ 
+
+ align:start position:0%
+trying to get in the mind with someone
+who is against even civil unions right
+
+ align:start position:0%
+who is against even civil unions right
+ 
+
+ align:start position:0%
+who is against even civil unions right
+and and try to understand why would they
+
+ align:start position:0%
+and and try to understand why would they
+ 
+
+ align:start position:0%
+and and try to understand why would they
+be against even this thing where they're
+
+ align:start position:0%
+be against even this thing where they're
+ 
+
+ align:start position:0%
+be against even this thing where they're
+trying to sort of sterilize marriage and
+
+ align:start position:0%
+trying to sort of sterilize marriage and
+ 
+
+ align:start position:0%
+trying to sort of sterilize marriage and
+take all the religious things out of and
+
+ align:start position:0%
+take all the religious things out of and
+ 
+
+ align:start position:0%
+take all the religious things out of and
+make it just the legal and um sort of
+
+ align:start position:0%
+make it just the legal and um sort of
+ 
+
+ align:start position:0%
+make it just the legal and um sort of
+you know practical benefits to being
+
+ align:start position:0%
+you know practical benefits to being
+ 
+
+ align:start position:0%
+you know practical benefits to being
+married um and and I guess the only way
+
+ align:start position:0%
+married um and and I guess the only way
+ 
+
+ align:start position:0%
+married um and and I guess the only way
+the only I can only understand that in
+
+ align:start position:0%
+the only I can only understand that in
+ 
+
+ align:start position:0%
+the only I can only understand that in
+the context of thinking that
+
+ align:start position:0%
+the context of thinking that
+ 
+
+ align:start position:0%
+the context of thinking that
+homosexuality itself is actually
+
+ align:start position:0%
+homosexuality itself is actually
+ 
+
+ align:start position:0%
+homosexuality itself is actually
+evil I no I think you're probably right
+
+ align:start position:0%
+evil I no I think you're probably right
+ 
+
+ align:start position:0%
+evil I no I think you're probably right
+that that's what their view is and
+
+ align:start position:0%
+that that's what their view is and
+ 
+
+ align:start position:0%
+that that's what their view is and
+that's why it's such a difficult thing
+
+ align:start position:0%
+that's why it's such a difficult thing
+ 
+
+ align:start position:0%
+that's why it's such a difficult thing
+to resolve because how can you commit
+
+ align:start position:0%
+to resolve because how can you commit
+ 
+
+ align:start position:0%
+to resolve because how can you commit
+convince somebody that he should allow
+
+ align:start position:0%
+convince somebody that he should allow
+ 
+
+ align:start position:0%
+convince somebody that he should allow
+the laws to tolerate something that's
+
+ align:start position:0%
+the laws to tolerate something that's
+ 
+
+ align:start position:0%
+the laws to tolerate something that's
+evil but um
+
+ align:start position:0%
+evil but um
+ 
+
+ align:start position:0%
+evil but um
+when that makes the issue comparable to
+
+ align:start position:0%
+when that makes the issue comparable to
+ 
+
+ align:start position:0%
+when that makes the issue comparable to
+abortion because people but then the
+
+ align:start position:0%
+abortion because people but then the
+ 
+
+ align:start position:0%
+abortion because people but then the
+laws do tolerate they can they can try
+
+ align:start position:0%
+laws do tolerate they can they can try
+ 
+
+ align:start position:0%
+laws do tolerate they can they can try
+to get the a change in the Supreme Court
+
+ align:start position:0%
+to get the a change in the Supreme Court
+ 
+
+ align:start position:0%
+to get the a change in the Supreme Court
+decision but as of now they haven't yet
+
+ align:start position:0%
+decision but as of now they haven't yet
+ 
+
+ align:start position:0%
+decision but as of now they haven't yet
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+it I think it might be possible that um
+
+ align:start position:0%
+it I think it might be possible that um
+ 
+
+ align:start position:0%
+it I think it might be possible that um
+um same-sex marriages and same-sex civil
+
+ align:start position:0%
+um same-sex marriages and same-sex civil
+ 
+
+ align:start position:0%
+um same-sex marriages and same-sex civil
+unions will not be tolerated in that
+
+ align:start position:0%
+unions will not be tolerated in that
+ 
+
+ align:start position:0%
+unions will not be tolerated in that
+sense for many many years simply because
+
+ align:start position:0%
+sense for many many years simply because
+ 
+
+ align:start position:0%
+sense for many many years simply because
+because there seems to be such a backlog
+
+ align:start position:0%
+because there seems to be such a backlog
+ 
+
+ align:start position:0%
+because there seems to be such a backlog
+of uh resistance to it particularly in a
+
+ align:start position:0%
+of uh resistance to it particularly in a
+ 
+
+ align:start position:0%
+of uh resistance to it particularly in a
+large part of the
+
+ align:start position:0%
+large part of the
+ 
+
+ align:start position:0%
+large part of the
+country um which is your
+
+ align:start position:0%
+country um which is your
+ 
+
+ align:start position:0%
+country um which is your
+state uh I'm from New Jersey oh New
+
+ align:start position:0%
+state uh I'm from New Jersey oh New
+ 
+
+ align:start position:0%
+state uh I'm from New Jersey oh New
+Jersey is um probably more liberal um
+
+ align:start position:0%
+Jersey is um probably more liberal um
+ 
+
+ align:start position:0%
+Jersey is um probably more liberal um
+but people from California would be more
+
+ align:start position:0%
+but people from California would be more
+ 
+
+ align:start position:0%
+but people from California would be more
+tolerant I would think people from
+
+ align:start position:0%
+tolerant I would think people from
+ 
+
+ align:start position:0%
+tolerant I would think people from
+Hawaii very much so because Hawaii gets
+
+ align:start position:0%
+Hawaii very much so because Hawaii gets
+ 
+
+ align:start position:0%
+Hawaii very much so because Hawaii gets
+close to allowing same-sex marriage um
+
+ align:start position:0%
+close to allowing same-sex marriage um
+ 
+
+ align:start position:0%
+close to allowing same-sex marriage um
+and and but for in the Florida or or
+
+ align:start position:0%
+and and but for in the Florida or or
+ 
+
+ align:start position:0%
+and and but for in the Florida or or
+Louisiana Mississippi Alabama Georgia
+
+ align:start position:0%
+Louisiana Mississippi Alabama Georgia
+ 
+
+ align:start position:0%
+Louisiana Mississippi Alabama Georgia
+those those States um maybe they'll
+
+ align:start position:0%
+those those States um maybe they'll
+ 
+
+ align:start position:0%
+those those States um maybe they'll
+never come around to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that do you think they'll they'll never
+
+ align:start position:0%
+that do you think they'll they'll never
+ 
+
+ align:start position:0%
+that do you think they'll they'll never
+come around I mean I the like the issue
+
+ align:start position:0%
+come around I mean I the like the issue
+ 
+
+ align:start position:0%
+come around I mean I the like the issue
+has always seemed to me is kind of one
+
+ align:start position:0%
+has always seemed to me is kind of one
+ 
+
+ align:start position:0%
+has always seemed to me is kind of one
+of inevitability I don't know I I just
+
+ align:start position:0%
+of inevitability I don't know I I just
+ 
+
+ align:start position:0%
+of inevitability I don't know I I just
+think if you go back in history and and
+
+ align:start position:0%
+think if you go back in history and and
+ 
+
+ align:start position:0%
+think if you go back in history and and
+look at all these big societal issues
+
+ align:start position:0%
+look at all these big societal issues
+ 
+
+ align:start position:0%
+look at all these big societal issues
+and changes like the the people who try
+
+ align:start position:0%
+and changes like the the people who try
+ 
+
+ align:start position:0%
+and changes like the the people who try
+to resist it lose every time it seems to
+
+ align:start position:0%
+to resist it lose every time it seems to
+ 
+
+ align:start position:0%
+to resist it lose every time it seems to
+me I don't know well not all of those
+
+ align:start position:0%
+me I don't know well not all of those
+ 
+
+ align:start position:0%
+me I don't know well not all of those
+issues um actually can anyone think of
+
+ align:start position:0%
+issues um actually can anyone think of
+ 
+
+ align:start position:0%
+issues um actually can anyone think of
+one that in which
+
+ align:start position:0%
+one that in which
+ 
+
+ align:start position:0%
+one that in which
+people yeah I'd be interested to know of
+
+ align:start position:0%
+people yeah I'd be interested to know of
+ 
+
+ align:start position:0%
+people yeah I'd be interested to know of
+an example
+
+ align:start position:0%
+an example
+ 
+
+ align:start position:0%
+an example
+also right would look like I don't know
+
+ align:start position:0%
+also right would look like I don't know
+ 
+
+ align:start position:0%
+also right would look like I don't know
+was there like a cannibal movement at
+
+ align:start position:0%
+was there like a cannibal movement at
+ 
+
+ align:start position:0%
+was there like a cannibal movement at
+some point I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know this this however I you think I
+
+ align:start position:0%
+know this this however I you think I
+ 
+
+ align:start position:0%
+know this this however I you think I
+think you go back and look at slavery
+
+ align:start position:0%
+think you go back and look at slavery
+ 
+
+ align:start position:0%
+think you go back and look at slavery
+abortion or civil rights or you know
+
+ align:start position:0%
+abortion or civil rights or you know
+ 
+
+ align:start position:0%
+abortion or civil rights or you know
+look at where stem cell research and all
+
+ align:start position:0%
+look at where stem cell research and all
+ 
+
+ align:start position:0%
+look at where stem cell research and all
+those it seems to me like the side that
+
+ align:start position:0%
+those it seems to me like the side that
+ 
+
+ align:start position:0%
+those it seems to me like the side that
+tries to resist these types of things
+
+ align:start position:0%
+tries to resist these types of things
+ 
+
+ align:start position:0%
+tries to resist these types of things
+like loses always I don't
+
+ align:start position:0%
+like loses always I don't
+ 
+
+ align:start position:0%
+like loses always I don't
+know um maybe maybe that's true um but
+
+ align:start position:0%
+know um maybe maybe that's true um but
+ 
+
+ align:start position:0%
+know um maybe maybe that's true um but
+this is a very one that is very deeply
+
+ align:start position:0%
+this is a very one that is very deeply
+ 
+
+ align:start position:0%
+this is a very one that is very deeply
+rooted because by defining yourself as
+
+ align:start position:0%
+rooted because by defining yourself as
+ 
+
+ align:start position:0%
+rooted because by defining yourself as
+homosexual or heterosexual you're really
+
+ align:start position:0%
+homosexual or heterosexual you're really
+ 
+
+ align:start position:0%
+homosexual or heterosexual you're really
+getting to the roots of your feelings
+
+ align:start position:0%
+getting to the roots of your feelings
+ 
+
+ align:start position:0%
+getting to the roots of your feelings
+the roots of your
+
+ align:start position:0%
+the roots of your
+ 
+
+ align:start position:0%
+the roots of your
+being that's why this whole area of
+
+ align:start position:0%
+being that's why this whole area of
+ 
+
+ align:start position:0%
+being that's why this whole area of
+philosophy is for me so important
+
+ align:start position:0%
+philosophy is for me so important
+ 
+
+ align:start position:0%
+philosophy is for me so important
+because that seems to me the kind of
+
+ align:start position:0%
+because that seems to me the kind of
+ 
+
+ align:start position:0%
+because that seems to me the kind of
+question that philosophers should be
+
+ align:start position:0%
+question that philosophers should be
+ 
+
+ align:start position:0%
+question that philosophers should be
+trying to resolve who are we what are we
+
+ align:start position:0%
+trying to resolve who are we what are we
+ 
+
+ align:start position:0%
+trying to resolve who are we what are we
+how do we determine what our feelings
+
+ align:start position:0%
+how do we determine what our feelings
+ 
+
+ align:start position:0%
+how do we determine what our feelings
+are and how we should adjust to those
+
+ align:start position:0%
+are and how we should adjust to those
+ 
+
+ align:start position:0%
+are and how we should adjust to those
+feelings or make the feelings adjust to
+
+ align:start position:0%
+feelings or make the feelings adjust to
+ 
+
+ align:start position:0%
+feelings or make the feelings adjust to
+something else uh but it's so it's so
+
+ align:start position:0%
+something else uh but it's so it's so
+ 
+
+ align:start position:0%
+something else uh but it's so it's so
+difficult and so complicated that or so
+
+ align:start position:0%
+difficult and so complicated that or so
+ 
+
+ align:start position:0%
+difficult and so complicated that or so
+maybe embarrassing I don't know uh
+
+ align:start position:0%
+maybe embarrassing I don't know uh
+ 
+
+ align:start position:0%
+maybe embarrassing I don't know uh
+philosophers have ignored it but that
+
+ align:start position:0%
+philosophers have ignored it but that
+ 
+
+ align:start position:0%
+philosophers have ignored it but that
+for me was the Big Challenge and I hope
+
+ align:start position:0%
+for me was the Big Challenge and I hope
+ 
+
+ align:start position:0%
+for me was the Big Challenge and I hope
+you feel that way too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s yeah I just wanted to point out that I
+
+ align:start position:0%
+s yeah I just wanted to point out that I
+ 
+
+ align:start position:0%
+s yeah I just wanted to point out that I
+even if they make it a a civil union I
+
+ align:start position:0%
+even if they make it a a civil union I
+ 
+
+ align:start position:0%
+even if they make it a a civil union I
+still don't think that's good
+
+ align:start position:0%
+still don't think that's good
+ 
+
+ align:start position:0%
+still don't think that's good
+because for instance okay they will have
+
+ align:start position:0%
+because for instance okay they will have
+ 
+
+ align:start position:0%
+because for instance okay they will have
+equal rights according to the law but
+
+ align:start position:0%
+equal rights according to the law but
+ 
+
+ align:start position:0%
+equal rights according to the law but
+they will be socially stigmatized like
+
+ align:start position:0%
+they will be socially stigmatized like
+ 
+
+ align:start position:0%
+they will be socially stigmatized like
+if they want to apply for something and
+
+ align:start position:0%
+if they want to apply for something and
+ 
+
+ align:start position:0%
+if they want to apply for something and
+they'll say are you married yes no or
+
+ align:start position:0%
+they'll say are you married yes no or
+ 
+
+ align:start position:0%
+they'll say are you married yes no or
+civil United and if you just inevitably
+
+ align:start position:0%
+civil United and if you just inevitably
+ 
+
+ align:start position:0%
+civil United and if you just inevitably
+the there will still be social racism
+
+ align:start position:0%
+the there will still be social racism
+ 
+
+ align:start position:0%
+the there will still be social racism
+against them until you can just make
+
+ align:start position:0%
+against them until you can just make
+ 
+
+ align:start position:0%
+against them until you can just make
+sure that they're equalized it's hard to
+
+ align:start position:0%
+sure that they're equalized it's hard to
+ 
+
+ align:start position:0%
+sure that they're equalized it's hard to
+know when I was depends on who's going
+
+ align:start position:0%
+know when I was depends on who's going
+ 
+
+ align:start position:0%
+know when I was depends on who's going
+to get that application or whatever but
+
+ align:start position:0%
+to get that application or whatever but
+ 
+
+ align:start position:0%
+to get that application or whatever but
+it seems like I feel like that would
+
+ align:start position:0%
+it seems like I feel like that would
+ 
+
+ align:start position:0%
+it seems like I feel like that would
+also fall under like the equal
+
+ align:start position:0%
+also fall under like the equal
+ 
+
+ align:start position:0%
+also fall under like the equal
+opportunities you know can't
+
+ align:start position:0%
+opportunities you know can't
+ 
+
+ align:start position:0%
+opportunities you know can't
+discriminate against someone based on
+
+ align:start position:0%
+discriminate against someone based on
+ 
+
+ align:start position:0%
+discriminate against someone based on
+like their race
+
+ align:start position:0%
+like their race
+ 
+
+ align:start position:0%
+like their race
+ethnicity uh physical abilities or if
+
+ align:start position:0%
+ethnicity uh physical abilities or if
+ 
+
+ align:start position:0%
+ethnicity uh physical abilities or if
+they marriage or civil union you know
+
+ align:start position:0%
+they marriage or civil union you know
+ 
+
+ align:start position:0%
+they marriage or civil union you know
+like no but you know in all of these
+
+ align:start position:0%
+like no but you know in all of these
+ 
+
+ align:start position:0%
+like no but you know in all of these
+movements there are two there are two
+
+ align:start position:0%
+movements there are two there are two
+ 
+
+ align:start position:0%
+movements there are two there are two
+attitudes um among groups who are
+
+ align:start position:0%
+attitudes um among groups who are
+ 
+
+ align:start position:0%
+attitudes um among groups who are
+liberating themselves whether they're
+
+ align:start position:0%
+liberating themselves whether they're
+ 
+
+ align:start position:0%
+liberating themselves whether they're
+Jews or blacks or Latin uh Latinos or
+
+ align:start position:0%
+Jews or blacks or Latin uh Latinos or
+ 
+
+ align:start position:0%
+Jews or blacks or Latin uh Latinos or
+Asians
+
+ align:start position:0%
+Asians
+ 
+
+ align:start position:0%
+Asians
+um one is to want to assimilate with
+
+ align:start position:0%
+um one is to want to assimilate with
+ 
+
+ align:start position:0%
+um one is to want to assimilate with
+everybody else to be treated just like
+
+ align:start position:0%
+everybody else to be treated just like
+ 
+
+ align:start position:0%
+everybody else to be treated just like
+everybody else right so that there's
+
+ align:start position:0%
+everybody else right so that there's
+ 
+
+ align:start position:0%
+everybody else right so that there's
+great sensitivity if somebody calls it
+
+ align:start position:0%
+great sensitivity if somebody calls it
+ 
+
+ align:start position:0%
+great sensitivity if somebody calls it
+if an authority for instance even
+
+ align:start position:0%
+if an authority for instance even
+ 
+
+ align:start position:0%
+if an authority for instance even
+Professor calls attention to the color
+
+ align:start position:0%
+Professor calls attention to the color
+ 
+
+ align:start position:0%
+Professor calls attention to the color
+of somebody else's skin because then W
+
+ align:start position:0%
+of somebody else's skin because then W
+ 
+
+ align:start position:0%
+of somebody else's skin because then W
+he's not he's categorizing he's treating
+
+ align:start position:0%
+he's not he's categorizing he's treating
+ 
+
+ align:start position:0%
+he's not he's categorizing he's treating
+me as whatever it is uh and I want to be
+
+ align:start position:0%
+me as whatever it is uh and I want to be
+ 
+
+ align:start position:0%
+me as whatever it is uh and I want to be
+treated like everybody else on the other
+
+ align:start position:0%
+treated like everybody else on the other
+ 
+
+ align:start position:0%
+treated like everybody else on the other
+hand uh once that has been established
+
+ align:start position:0%
+hand uh once that has been established
+ 
+
+ align:start position:0%
+hand uh once that has been established
+what happens in the Dynamics of this
+
+ align:start position:0%
+what happens in the Dynamics of this
+ 
+
+ align:start position:0%
+what happens in the Dynamics of this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+of self-discovery Liberation and
+
+ align:start position:0%
+of self-discovery Liberation and
+ 
+
+ align:start position:0%
+of self-discovery Liberation and
+ultimate
+
+ align:start position:0%
+ultimate
+ 
+
+ align:start position:0%
+ultimate
+Equalization is a realization that it
+
+ align:start position:0%
+Equalization is a realization that it
+ 
+
+ align:start position:0%
+Equalization is a realization that it
+Unity brings about strength and so you
+
+ align:start position:0%
+Unity brings about strength and so you
+ 
+
+ align:start position:0%
+Unity brings about strength and so you
+if you're black you join the
+
+ align:start position:0%
+if you're black you join the
+ 
+
+ align:start position:0%
+if you're black you join the
+NAACP or you vote for uh black
+
+ align:start position:0%
+NAACP or you vote for uh black
+ 
+
+ align:start position:0%
+NAACP or you vote for uh black
+representatives for your District that
+
+ align:start position:0%
+representatives for your District that
+ 
+
+ align:start position:0%
+representatives for your District that
+there is the black vote in Congress
+
+ align:start position:0%
+there is the black vote in Congress
+ 
+
+ align:start position:0%
+there is the black vote in Congress
+because otherwise there won't be any
+
+ align:start position:0%
+because otherwise there won't be any
+ 
+
+ align:start position:0%
+because otherwise there won't be any
+political power and the interests of
+
+ align:start position:0%
+political power and the interests of
+ 
+
+ align:start position:0%
+political power and the interests of
+people who happen to be black whatever
+
+ align:start position:0%
+people who happen to be black whatever
+ 
+
+ align:start position:0%
+people who happen to be black whatever
+that means by black because uh in this
+
+ align:start position:0%
+that means by black because uh in this
+ 
+
+ align:start position:0%
+that means by black because uh in this
+country anybody who is brown or tan or
+
+ align:start position:0%
+country anybody who is brown or tan or
+ 
+
+ align:start position:0%
+country anybody who is brown or tan or
+anything tend it used to be tend to be
+
+ align:start position:0%
+anything tend it used to be tend to be
+ 
+
+ align:start position:0%
+anything tend it used to be tend to be
+called black but not really black but
+
+ align:start position:0%
+called black but not really black but
+ 
+
+ align:start position:0%
+called black but not really black but
+all of that lump together and the only
+
+ align:start position:0%
+all of that lump together and the only
+ 
+
+ align:start position:0%
+all of that lump together and the only
+way to um to um get Equalization is by
+
+ align:start position:0%
+way to um to um get Equalization is by
+ 
+
+ align:start position:0%
+way to um to um get Equalization is by
+identifying yourself as the minority
+
+ align:start position:0%
+identifying yourself as the minority
+ 
+
+ align:start position:0%
+identifying yourself as the minority
+that you don't want to be stigmatized by
+
+ align:start position:0%
+that you don't want to be stigmatized by
+ 
+
+ align:start position:0%
+that you don't want to be stigmatized by
+and it's it's a very delicate and
+
+ align:start position:0%
+and it's it's a very delicate and
+ 
+
+ align:start position:0%
+and it's it's a very delicate and
+difficult process for a young person to
+
+ align:start position:0%
+difficult process for a young person to
+ 
+
+ align:start position:0%
+difficult process for a young person to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+through um I know because I was born
+
+ align:start position:0%
+through um I know because I was born
+ 
+
+ align:start position:0%
+through um I know because I was born
+Jewish and part of me wanted to go out
+
+ align:start position:0%
+Jewish and part of me wanted to go out
+ 
+
+ align:start position:0%
+Jewish and part of me wanted to go out
+in the world and be like all the
+
+ align:start position:0%
+in the world and be like all the
+ 
+
+ align:start position:0%
+in the world and be like all the
+Anglo-Saxons my parents were immigrants
+
+ align:start position:0%
+Anglo-Saxons my parents were immigrants
+ 
+
+ align:start position:0%
+Anglo-Saxons my parents were immigrants
+and their Hope was for me at any cost to
+
+ align:start position:0%
+and their Hope was for me at any cost to
+ 
+
+ align:start position:0%
+and their Hope was for me at any cost to
+go out and succeed in the outside world
+
+ align:start position:0%
+go out and succeed in the outside world
+ 
+
+ align:start position:0%
+go out and succeed in the outside world
+of America the process of
+
+ align:start position:0%
+of America the process of
+ 
+
+ align:start position:0%
+of America the process of
+Americanization all of the immigrants
+
+ align:start position:0%
+Americanization all of the immigrants
+ 
+
+ align:start position:0%
+Americanization all of the immigrants
+went through that at the same time uh
+
+ align:start position:0%
+went through that at the same time uh
+ 
+
+ align:start position:0%
+went through that at the same time uh
+you always feel well you're denying your
+
+ align:start position:0%
+you always feel well you're denying your
+ 
+
+ align:start position:0%
+you always feel well you're denying your
+Origins and then as you older you
+
+ align:start position:0%
+Origins and then as you older you
+ 
+
+ align:start position:0%
+Origins and then as you older you
+realize how much of you is is a function
+
+ align:start position:0%
+realize how much of you is is a function
+ 
+
+ align:start position:0%
+realize how much of you is is a function
+of your Origins and it's a question of
+
+ align:start position:0%
+of your Origins and it's a question of
+ 
+
+ align:start position:0%
+of your Origins and it's a question of
+how how to adjudicate and if you don't
+
+ align:start position:0%
+how how to adjudicate and if you don't
+ 
+
+ align:start position:0%
+how how to adjudicate and if you don't
+agree with religion and I never did
+
+ align:start position:0%
+agree with religion and I never did
+ 
+
+ align:start position:0%
+agree with religion and I never did
+think or thought of myself as Jewish in
+
+ align:start position:0%
+think or thought of myself as Jewish in
+ 
+
+ align:start position:0%
+think or thought of myself as Jewish in
+terms of religion and you are out in the
+
+ align:start position:0%
+terms of religion and you are out in the
+ 
+
+ align:start position:0%
+terms of religion and you are out in the
+world and don't live with the Jews and
+
+ align:start position:0%
+world and don't live with the Jews and
+ 
+
+ align:start position:0%
+world and don't live with the Jews and
+their habits don't mean that much to you
+
+ align:start position:0%
+their habits don't mean that much to you
+ 
+
+ align:start position:0%
+their habits don't mean that much to you
+what are you supposed to do it's a great
+
+ align:start position:0%
+what are you supposed to do it's a great
+ 
+
+ align:start position:0%
+what are you supposed to do it's a great
+problem particularly when you're young
+
+ align:start position:0%
+problem particularly when you're young
+ 
+
+ align:start position:0%
+problem particularly when you're young
+because Youth and Adolescence is a time
+
+ align:start position:0%
+because Youth and Adolescence is a time
+ 
+
+ align:start position:0%
+because Youth and Adolescence is a time
+of discovering yourself and what are you
+
+ align:start position:0%
+of discovering yourself and what are you
+ 
+
+ align:start position:0%
+of discovering yourself and what are you
+right okay now the same thing is even
+
+ align:start position:0%
+right okay now the same thing is even
+ 
+
+ align:start position:0%
+right okay now the same thing is even
+more so I think um in the question of um
+
+ align:start position:0%
+more so I think um in the question of um
+ 
+
+ align:start position:0%
+more so I think um in the question of um
+sexuality so
+
+ align:start position:0%
+sexuality so
+ 
+
+ align:start position:0%
+sexuality so
+that how can a young person know whether
+
+ align:start position:0%
+that how can a young person know whether
+ 
+
+ align:start position:0%
+that how can a young person know whether
+he or she really is homosexual or
+
+ align:start position:0%
+he or she really is homosexual or
+ 
+
+ align:start position:0%
+he or she really is homosexual or
+heterosexual or anything and
+
+ align:start position:0%
+heterosexual or anything and
+ 
+
+ align:start position:0%
+heterosexual or anything and
+yet now I'm beginning to forget what
+
+ align:start position:0%
+yet now I'm beginning to forget what
+ 
+
+ align:start position:0%
+yet now I'm beginning to forget what
+your original point was why do we go
+
+ align:start position:0%
+your original point was why do we go
+ 
+
+ align:start position:0%
+your original point was why do we go
+back to that my point was that I don't
+
+ align:start position:0%
+back to that my point was that I don't
+ 
+
+ align:start position:0%
+back to that my point was that I don't
+think a civil union would be a
+
+ align:start position:0%
+think a civil union would be a
+ 
+
+ align:start position:0%
+think a civil union would be a
+satisfactory solution oh no no I see now
+
+ align:start position:0%
+satisfactory solution oh no no I see now
+ 
+
+ align:start position:0%
+satisfactory solution oh no no I see now
+what it
+
+ align:start position:0%
+what it
+ 
+
+ align:start position:0%
+what it
+was I I remember now what touched this
+
+ align:start position:0%
+was I I remember now what touched this
+ 
+
+ align:start position:0%
+was I I remember now what touched this
+off when I was in the Army I they issued
+
+ align:start position:0%
+off when I was in the Army I they issued
+ 
+
+ align:start position:0%
+off when I was in the Army I they issued
+me um dog tags I don't know if they
+
+ align:start position:0%
+me um dog tags I don't know if they
+ 
+
+ align:start position:0%
+me um dog tags I don't know if they
+still use they they literally are dog
+
+ align:start position:0%
+still use they they literally are dog
+ 
+
+ align:start position:0%
+still use they they literally are dog
+tags metal tags like that are those are
+
+ align:start position:0%
+tags metal tags like that are those are
+ 
+
+ align:start position:0%
+tags metal tags like that are those are
+you in the ROTC yes huh yes is there a
+
+ align:start position:0%
+you in the ROTC yes huh yes is there a
+ 
+
+ align:start position:0%
+you in the ROTC yes huh yes is there a
+letter for your religious affiliation
+
+ align:start position:0%
+letter for your religious affiliation
+ 
+
+ align:start position:0%
+letter for your religious affiliation
+yes okay
+
+ align:start position:0%
+yes okay
+ 
+
+ align:start position:0%
+yes okay
+uh it's p or C no they spell it out oh
+
+ align:start position:0%
+uh it's p or C no they spell it out oh
+ 
+
+ align:start position:0%
+uh it's p or C no they spell it out oh
+in my case it was just lettering if if
+
+ align:start position:0%
+in my case it was just lettering if if
+ 
+
+ align:start position:0%
+in my case it was just lettering if if
+you were Protestant there was a p and if
+
+ align:start position:0%
+you were Protestant there was a p and if
+ 
+
+ align:start position:0%
+you were Protestant there was a p and if
+if Catholic it was a c and that made
+
+ align:start position:0%
+if Catholic it was a c and that made
+ 
+
+ align:start position:0%
+if Catholic it was a c and that made
+sense because if somebody got killed in
+
+ align:start position:0%
+sense because if somebody got killed in
+ 
+
+ align:start position:0%
+sense because if somebody got killed in
+battle um one had to know where to bury
+
+ align:start position:0%
+battle um one had to know where to bury
+ 
+
+ align:start position:0%
+battle um one had to know where to bury
+him or you use a cross or a star or or
+
+ align:start position:0%
+him or you use a cross or a star or or
+ 
+
+ align:start position:0%
+him or you use a cross or a star or or
+what kind of preacher to or or priest to
+
+ align:start position:0%
+what kind of preacher to or or priest to
+ 
+
+ align:start position:0%
+what kind of preacher to or or priest to
+um say the final rights right my case
+
+ align:start position:0%
+um say the final rights right my case
+ 
+
+ align:start position:0%
+um say the final rights right my case
+casee my metal tag said H which meant
+
+ align:start position:0%
+casee my metal tag said H which meant
+ 
+
+ align:start position:0%
+casee my metal tag said H which meant
+Hebrew and and I never thought of myself
+
+ align:start position:0%
+Hebrew and and I never thought of myself
+ 
+
+ align:start position:0%
+Hebrew and and I never thought of myself
+as a Hebrew it was even something I
+
+ align:start position:0%
+as a Hebrew it was even something I
+ 
+
+ align:start position:0%
+as a Hebrew it was even something I
+remember one time being in the south in
+
+ align:start position:0%
+remember one time being in the south in
+ 
+
+ align:start position:0%
+remember one time being in the south in
+America and somebody on the bus that I
+
+ align:start position:0%
+America and somebody on the bus that I
+ 
+
+ align:start position:0%
+America and somebody on the bus that I
+was on was furious at a uh uh ticket
+
+ align:start position:0%
+was on was furious at a uh uh ticket
+ 
+
+ align:start position:0%
+was on was furious at a uh uh ticket
+agent or something and he was shouting
+
+ align:start position:0%
+agent or something and he was shouting
+ 
+
+ align:start position:0%
+agent or something and he was shouting
+uh you know that that Hebrew and it
+
+ align:start position:0%
+uh you know that that Hebrew and it
+ 
+
+ align:start position:0%
+uh you know that that Hebrew and it
+wasn't the man was Jewish or anything
+
+ align:start position:0%
+wasn't the man was Jewish or anything
+ 
+
+ align:start position:0%
+wasn't the man was Jewish or anything
+just that it was a curse word he's a
+
+ align:start position:0%
+just that it was a curse word he's a
+ 
+
+ align:start position:0%
+just that it was a curse word he's a
+Hebrew he probably never met a Jew and I
+
+ align:start position:0%
+Hebrew he probably never met a Jew and I
+ 
+
+ align:start position:0%
+Hebrew he probably never met a Jew and I
+knew that but I was 17 or 18 and I felt
+
+ align:start position:0%
+knew that but I was 17 or 18 and I felt
+ 
+
+ align:start position:0%
+knew that but I was 17 or 18 and I felt
+hurt by it so that H was you know not
+
+ align:start position:0%
+hurt by it so that H was you know not
+ 
+
+ align:start position:0%
+hurt by it so that H was you know not
+something I would have identified myself
+
+ align:start position:0%
+something I would have identified myself
+ 
+
+ align:start position:0%
+something I would have identified myself
+with but of course now looking back of
+
+ align:start position:0%
+with but of course now looking back of
+ 
+
+ align:start position:0%
+with but of course now looking back of
+course I'm Jewish that's the way I grew
+
+ align:start position:0%
+course I'm Jewish that's the way I grew
+ 
+
+ align:start position:0%
+course I'm Jewish that's the way I grew
+up my so much of my life is a function
+
+ align:start position:0%
+up my so much of my life is a function
+ 
+
+ align:start position:0%
+up my so much of my life is a function
+of that early origin I can live with
+
+ align:start position:0%
+of that early origin I can live with
+ 
+
+ align:start position:0%
+of that early origin I can live with
+that that's my point being told that I
+
+ align:start position:0%
+that that's my point being told that I
+ 
+
+ align:start position:0%
+that that's my point being told that I
+can't get
+
+ align:start position:0%
+can't get
+ 
+
+ align:start position:0%
+can't get
+married or not doesn't apply to me but
+
+ align:start position:0%
+married or not doesn't apply to me but
+ 
+
+ align:start position:0%
+married or not doesn't apply to me but
+if somebody is told that he can't get
+
+ align:start position:0%
+if somebody is told that he can't get
+ 
+
+ align:start position:0%
+if somebody is told that he can't get
+married legally but he can have a civil
+
+ align:start position:0%
+married legally but he can have a civil
+ 
+
+ align:start position:0%
+married legally but he can have a civil
+union would I think be as insignificant
+
+ align:start position:0%
+union would I think be as insignificant
+ 
+
+ align:start position:0%
+union would I think be as insignificant
+as having the letter H on his talk
+
+ align:start position:0%
+as having the letter H on his talk
+ 
+
+ align:start position:0%
+as having the letter H on his talk
+tag um and anyhow in your case it says
+
+ align:start position:0%
+tag um and anyhow in your case it says
+ 
+
+ align:start position:0%
+tag um and anyhow in your case it says
+are you Protestant or Catholic atheist
+
+ align:start position:0%
+are you Protestant or Catholic atheist
+ 
+
+ align:start position:0%
+are you Protestant or Catholic atheist
+which atheist atheist
+
+ align:start position:0%
+which atheist atheist
+ 
+
+ align:start position:0%
+which atheist atheist
+why do they there's no a no atheist that
+
+ align:start position:0%
+why do they there's no a no atheist that
+ 
+
+ align:start position:0%
+why do they there's no a no atheist that
+you can claim to be no they read on oh
+
+ align:start position:0%
+you can claim to be no they read on oh
+ 
+
+ align:start position:0%
+you can claim to be no they read on oh
+they are oh on yours it says atheist
+
+ align:start position:0%
+they are oh on yours it says atheist
+ 
+
+ align:start position:0%
+they are oh on yours it says atheist
+they spell it all oh that's interesting
+
+ align:start position:0%
+they spell it all oh that's interesting
+ 
+
+ align:start position:0%
+they spell it all oh that's interesting
+because I thought um if it was
+
+ align:start position:0%
+because I thought um if it was
+ 
+
+ align:start position:0%
+because I thought um if it was
+Protestant you might say well I'm not a
+
+ align:start position:0%
+Protestant you might say well I'm not a
+ 
+
+ align:start position:0%
+Protestant you might say well I'm not a
+Protestant I'm a Wesleyan or
+
+ align:start position:0%
+Protestant I'm a Wesleyan or
+ 
+
+ align:start position:0%
+Protestant I'm a Wesleyan or
+Episcopalian or Presbyterian or
+
+ align:start position:0%
+Episcopalian or Presbyterian or
+ 
+
+ align:start position:0%
+Episcopalian or Presbyterian or
+Methodist or Baptist what's this
+
+ align:start position:0%
+Methodist or Baptist what's this
+ 
+
+ align:start position:0%
+Methodist or Baptist what's this
+Protestant stuff or if a Catholic well
+
+ align:start position:0%
+Protestant stuff or if a Catholic well
+ 
+
+ align:start position:0%
+Protestant stuff or if a Catholic well
+they're different kinds of Catholics
+
+ align:start position:0%
+they're different kinds of Catholics
+ 
+
+ align:start position:0%
+they're different kinds of Catholics
+they've expanded but atheist seems very
+
+ align:start position:0%
+they've expanded but atheist seems very
+ 
+
+ align:start position:0%
+they've expanded but atheist seems very
+explicit they've expanded the religious
+
+ align:start position:0%
+explicit they've expanded the religious
+ 
+
+ align:start position:0%
+explicit they've expanded the religious
+core like in the Navy from
+
+ align:start position:0%
+core like in the Navy from
+ 
+
+ align:start position:0%
+core like in the Navy from
+um they used to have like five now
+
+ align:start position:0%
+um they used to have like five now
+ 
+
+ align:start position:0%
+um they used to have like five now
+they're up to like 30 plus they even
+
+ align:start position:0%
+they're up to like 30 plus they even
+ 
+
+ align:start position:0%
+they're up to like 30 plus they even
+have like
+
+ align:start position:0%
+have like
+ 
+
+ align:start position:0%
+have like
+Wiccan well well then my point isn't
+
+ align:start position:0%
+Wiccan well well then my point isn't
+ 
+
+ align:start position:0%
+Wiccan well well then my point isn't
+quite as relevant I was thinking that
+
+ align:start position:0%
+quite as relevant I was thinking that
+ 
+
+ align:start position:0%
+quite as relevant I was thinking that
+you one could live with this artificial
+
+ align:start position:0%
+you one could live with this artificial
+ 
+
+ align:start position:0%
+you one could live with this artificial
+denomination because they've given you H
+
+ align:start position:0%
+denomination because they've given you H
+ 
+
+ align:start position:0%
+denomination because they've given you H
+or t or whatever uh but a is something
+
+ align:start position:0%
+or t or whatever uh but a is something
+ 
+
+ align:start position:0%
+or t or whatever uh but a is something
+more explicit so on philosophical
+
+ align:start position:0%
+more explicit so on philosophical
+ 
+
+ align:start position:0%
+more explicit so on philosophical
+grounds we could argue about what it is
+
+ align:start position:0%
+grounds we could argue about what it is
+ 
+
+ align:start position:0%
+grounds we could argue about what it is
+to be an atheist but um you can even you
+
+ align:start position:0%
+to be an atheist but um you can even you
+ 
+
+ align:start position:0%
+to be an atheist but um you can even you
+could live with the
+
+ align:start position:0%
+could live with the
+ 
+
+ align:start position:0%
+could live with the
+ambiguity um and way a could oh it says
+
+ align:start position:0%
+ambiguity um and way a could oh it says
+ 
+
+ align:start position:0%
+ambiguity um and way a could oh it says
+atheist not agnostic it's not an a
+
+ align:start position:0%
+atheist not agnostic it's not an a
+ 
+
+ align:start position:0%
+atheist not agnostic it's not an a
+atheist okay um whatever it is you could
+
+ align:start position:0%
+atheist okay um whatever it is you could
+ 
+
+ align:start position:0%
+atheist okay um whatever it is you could
+live with that artificial
+
+ align:start position:0%
+live with that artificial
+ 
+
+ align:start position:0%
+live with that artificial
+categorization who cares and the same
+
+ align:start position:0%
+categorization who cares and the same
+ 
+
+ align:start position:0%
+categorization who cares and the same
+thing with being called uh having a
+
+ align:start position:0%
+thing with being called uh having a
+ 
+
+ align:start position:0%
+thing with being called uh having a
+relationship that's called a civil Union
+
+ align:start position:0%
+relationship that's called a civil Union
+ 
+
+ align:start position:0%
+relationship that's called a civil Union
+it would be a sort of joke you provided
+
+ align:start position:0%
+it would be a sort of joke you provided
+ 
+
+ align:start position:0%
+it would be a sort of joke you provided
+you get the same rights and Privileges
+
+ align:start position:0%
+you get the same rights and Privileges
+ 
+
+ align:start position:0%
+you get the same rights and Privileges
+and are understood to have the same same
+
+ align:start position:0%
+and are understood to have the same same
+ 
+
+ align:start position:0%
+and are understood to have the same same
+responsibilities but you you're not an M
+
+ align:start position:0%
+responsibilities but you you're not an M
+ 
+
+ align:start position:0%
+responsibilities but you you're not an M
+you're a c or well I mean a CU see you
+
+ align:start position:0%
+you're a c or well I mean a CU see you
+ 
+
+ align:start position:0%
+you're a c or well I mean a CU see you
+instead of them no but that's not that
+
+ align:start position:0%
+instead of them no but that's not that
+ 
+
+ align:start position:0%
+instead of them no but that's not that
+my point is that okay so let's say you
+
+ align:start position:0%
+my point is that okay so let's say you
+ 
+
+ align:start position:0%
+my point is that okay so let's say you
+had a card and they asked you what would
+
+ align:start position:0%
+had a card and they asked you what would
+ 
+
+ align:start position:0%
+had a card and they asked you what would
+you be when you filled out an
+
+ align:start position:0%
+you be when you filled out an
+ 
+
+ align:start position:0%
+you be when you filled out an
+application for I'm just bringing this
+
+ align:start position:0%
+application for I'm just bringing this
+ 
+
+ align:start position:0%
+application for I'm just bringing this
+as an example would you do you think
+
+ align:start position:0%
+as an example would you do you think
+ 
+
+ align:start position:0%
+as an example would you do you think
+it's um it's correct for them to have a
+
+ align:start position:0%
+it's um it's correct for them to have a
+ 
+
+ align:start position:0%
+it's um it's correct for them to have a
+question what is your religion if it's
+
+ align:start position:0%
+question what is your religion if it's
+ 
+
+ align:start position:0%
+question what is your religion if it's
+to apply for a job to apply for a
+
+ align:start position:0%
+to apply for a job to apply for a
+ 
+
+ align:start position:0%
+to apply for a job to apply for a
+position for something do you think that
+
+ align:start position:0%
+position for something do you think that
+ 
+
+ align:start position:0%
+position for something do you think that
+they should have um like a question says
+
+ align:start position:0%
+they should have um like a question says
+ 
+
+ align:start position:0%
+they should have um like a question says
+what is your religion I think that is no
+
+ align:start position:0%
+what is your religion I think that is no
+ 
+
+ align:start position:0%
+what is your religion I think that is no
+longer legal it used to be yeah so it is
+
+ align:start position:0%
+longer legal it used to be yeah so it is
+ 
+
+ align:start position:0%
+longer legal it used to be yeah so it is
+legal you can't ask you can't ask that's
+
+ align:start position:0%
+legal you can't ask you can't ask that's
+ 
+
+ align:start position:0%
+legal you can't ask you can't ask that's
+what I meant it's no longer to ask for
+
+ align:start position:0%
+what I meant it's no longer to ask for
+ 
+
+ align:start position:0%
+what I meant it's no longer to ask for
+religion and the reason was that uh
+
+ align:start position:0%
+religion and the reason was that uh
+ 
+
+ align:start position:0%
+religion and the reason was that uh
+there has been religious discrimination
+
+ align:start position:0%
+there has been religious discrimination
+ 
+
+ align:start position:0%
+there has been religious discrimination
+in all countries but in this country
+
+ align:start position:0%
+in all countries but in this country
+ 
+
+ align:start position:0%
+in all countries but in this country
+until very recently and still in this
+
+ align:start position:0%
+until very recently and still in this
+ 
+
+ align:start position:0%
+until very recently and still in this
+country but it's something the
+
+ align:start position:0%
+country but it's something the
+ 
+
+ align:start position:0%
+country but it's something the
+government recognizes is illegal
+
+ align:start position:0%
+government recognizes is illegal
+ 
+
+ align:start position:0%
+government recognizes is illegal
+undesireable exctly right in the case of
+
+ align:start position:0%
+undesireable exctly right in the case of
+ 
+
+ align:start position:0%
+undesireable exctly right in the case of
+um marriage um one if you had equal
+
+ align:start position:0%
+um marriage um one if you had equal
+ 
+
+ align:start position:0%
+um marriage um one if you had equal
+rights for the M's and for the
+
+ align:start position:0%
+rights for the M's and for the
+ 
+
+ align:start position:0%
+rights for the M's and for the
+cus that too could be something you
+
+ align:start position:0%
+cus that too could be something you
+ 
+
+ align:start position:0%
+cus that too could be something you
+can't you can't um uh require on an
+
+ align:start position:0%
+can't you can't um uh require on an
+ 
+
+ align:start position:0%
+can't you can't um uh require on an
+application form it was little like the
+
+ align:start position:0%
+application form it was little like the
+ 
+
+ align:start position:0%
+application form it was little like the
+policy of don't ask and don't tell
+
+ align:start position:0%
+policy of don't ask and don't tell
+ 
+
+ align:start position:0%
+policy of don't ask and don't tell
+for homosexuals in the armed forces they
+
+ align:start position:0%
+for homosexuals in the armed forces they
+ 
+
+ align:start position:0%
+for homosexuals in the armed forces they
+can't ask whether somebody is homosexual
+
+ align:start position:0%
+can't ask whether somebody is homosexual
+ 
+
+ align:start position:0%
+can't ask whether somebody is homosexual
+because he might be discriminated
+
+ align:start position:0%
+because he might be discriminated
+ 
+
+ align:start position:0%
+because he might be discriminated
+against or she uh and they
+
+ align:start position:0%
+against or she uh and they
+ 
+
+ align:start position:0%
+against or she uh and they
+don't they're advis or maybe they're not
+
+ align:start position:0%
+don't they're advis or maybe they're not
+ 
+
+ align:start position:0%
+don't they're advis or maybe they're not
+supposed to tell it's nobody's business
+
+ align:start position:0%
+supposed to tell it's nobody's business
+ 
+
+ align:start position:0%
+supposed to tell it's nobody's business
+yeah I mean okay so my point is well
+
+ align:start position:0%
+yeah I mean okay so my point is well
+ 
+
+ align:start position:0%
+yeah I mean okay so my point is well
+they still ask if you're married or not
+
+ align:start position:0%
+they still ask if you're married or not
+ 
+
+ align:start position:0%
+they still ask if you're married or not
+when but do but you but as veron's point
+
+ align:start position:0%
+when but do but you but as veron's point
+ 
+
+ align:start position:0%
+when but do but you but as veron's point
+I anything Financial is very relevant
+
+ align:start position:0%
+I anything Financial is very relevant
+ 
+
+ align:start position:0%
+I anything Financial is very relevant
+whether you're married or not for lots
+
+ align:start position:0%
+whether you're married or not for lots
+ 
+
+ align:start position:0%
+whether you're married or not for lots
+of things that have to
+
+ align:start position:0%
+of things that have to
+ 
+
+ align:start position:0%
+of things that have to
+yeah that's I don't think but I I feel
+
+ align:start position:0%
+yeah that's I don't think but I I feel
+ 
+
+ align:start position:0%
+yeah that's I don't think but I I feel
+like civil union that would work just as
+
+ align:start position:0%
+like civil union that would work just as
+ 
+
+ align:start position:0%
+like civil union that would work just as
+much as a marriage because the only
+
+ align:start position:0%
+much as a marriage because the only
+ 
+
+ align:start position:0%
+much as a marriage because the only
+reason they're asking if you're married
+
+ align:start position:0%
+reason they're asking if you're married
+ 
+
+ align:start position:0%
+reason they're asking if you're married
+is because they want to know do you have
+
+ align:start position:0%
+is because they want to know do you have
+ 
+
+ align:start position:0%
+is because they want to know do you have
+another income working with yours so if
+
+ align:start position:0%
+another income working with yours so if
+ 
+
+ align:start position:0%
+another income working with yours so if
+you have a civil union that's the same
+
+ align:start position:0%
+you have a civil union that's the same
+ 
+
+ align:start position:0%
+you have a civil union that's the same
+thing you would still have the other
+
+ align:start position:0%
+thing you would still have the other
+ 
+
+ align:start position:0%
+thing you would still have the other
+income so I don't see how they would be
+
+ align:start position:0%
+income so I don't see how they would be
+ 
+
+ align:start position:0%
+income so I don't see how they would be
+able to discriminate based on that
+
+ align:start position:0%
+able to discriminate based on that
+ 
+
+ align:start position:0%
+able to discriminate based on that
+because it's simply like a financial
+
+ align:start position:0%
+because it's simply like a financial
+ 
+
+ align:start position:0%
+because it's simply like a financial
+matter not like okay the financial
+
+ align:start position:0%
+matter not like okay the financial
+ 
+
+ align:start position:0%
+matter not like okay the financial
+didn't they ask you for the MIT
+
+ align:start position:0%
+didn't they ask you for the MIT
+ 
+
+ align:start position:0%
+didn't they ask you for the MIT
+application if you were uh married or
+
+ align:start position:0%
+application if you were uh married or
+ 
+
+ align:start position:0%
+application if you were uh married or
+not I think that's because of
+
+ align:start position:0%
+not I think that's because of
+ 
+
+ align:start position:0%
+not I think that's because of
+housing well and I feel like you didn't
+
+ align:start position:0%
+housing well and I feel like you didn't
+ 
+
+ align:start position:0%
+housing well and I feel like you didn't
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+that would they like not let you if you
+
+ align:start position:0%
+that would they like not let you if you
+ 
+
+ align:start position:0%
+that would they like not let you if you
+that's for the units that accommodate
+
+ align:start position:0%
+that's for the units that accommodate
+ 
+
+ align:start position:0%
+that's for the units that accommodate
+married couples but couldn't you also
+
+ align:start position:0%
+married couples but couldn't you also
+ 
+
+ align:start position:0%
+married couples but couldn't you also
+have access to them because you want to
+
+ align:start position:0%
+have access to them because you want to
+ 
+
+ align:start position:0%
+have access to them because you want to
+live with somebody you're not married to
+
+ align:start position:0%
+live with somebody you're not married to
+ 
+
+ align:start position:0%
+live with somebody you're not married to
+no I don't think so you don't if if uh I
+
+ align:start position:0%
+no I don't think so you don't if if uh I
+ 
+
+ align:start position:0%
+no I don't think so you don't if if uh I
+think you have to I mean there are there
+
+ align:start position:0%
+think you have to I mean there are there
+ 
+
+ align:start position:0%
+think you have to I mean there are there
+are double Apartments so to speak or
+
+ align:start position:0%
+are double Apartments so to speak or
+ 
+
+ align:start position:0%
+are double Apartments so to speak or
+one-bedroom apartments for married
+
+ align:start position:0%
+one-bedroom apartments for married
+ 
+
+ align:start position:0%
+one-bedroom apartments for married
+people right and there's not for a
+
+ align:start position:0%
+people right and there's not for a
+ 
+
+ align:start position:0%
+people right and there's not for a
+couple who are unmarried they they're
+
+ align:start position:0%
+couple who are unmarried they they're
+ 
+
+ align:start position:0%
+couple who are unmarried they they're
+excluded I would have think that would
+
+ align:start position:0%
+excluded I would have think that would
+ 
+
+ align:start position:0%
+excluded I would have think that would
+be IL legalish MIT would be in Pro in
+
+ align:start position:0%
+be IL legalish MIT would be in Pro in
+ 
+
+ align:start position:0%
+be IL legalish MIT would be in Pro in
+trouble discrimin that would be
+
+ align:start position:0%
+trouble discrimin that would be
+ 
+
+ align:start position:0%
+trouble discrimin that would be
+discrimination on the bis I think they
+
+ align:start position:0%
+discrimination on the bis I think they
+ 
+
+ align:start position:0%
+discrimination on the bis I think they
+have limited amounts of that housing and
+
+ align:start position:0%
+have limited amounts of that housing and
+ 
+
+ align:start position:0%
+have limited amounts of that housing and
+they give it preferentially to people
+
+ align:start position:0%
+they give it preferentially to people
+ 
+
+ align:start position:0%
+they give it preferentially to people
+who are married and who have children
+
+ align:start position:0%
+who are married and who have children
+ 
+
+ align:start position:0%
+who are married and who have children
+and usually I think that if you oh
+
+ align:start position:0%
+and usually I think that if you oh
+ 
+
+ align:start position:0%
+and usually I think that if you oh
+children complicates things because
+
+ align:start position:0%
+children complicates things because
+ 
+
+ align:start position:0%
+children complicates things because
+that's another head yeah exactly and so
+
+ align:start position:0%
+that's another head yeah exactly and so
+ 
+
+ align:start position:0%
+that's another head yeah exactly and so
+um I think if you just want to live with
+
+ align:start position:0%
+um I think if you just want to live with
+ 
+
+ align:start position:0%
+um I think if you just want to live with
+someone they would probably like they
+
+ align:start position:0%
+someone they would probably like they
+ 
+
+ align:start position:0%
+someone they would probably like they
+wouldn't have enough
+
+ align:start position:0%
+wouldn't have enough
+ 
+
+ align:start position:0%
+wouldn't have enough
+spaces for those types of things I'm
+
+ align:start position:0%
+spaces for those types of things I'm
+ 
+
+ align:start position:0%
+spaces for those types of things I'm
+pretty sure the housing laws in Boston
+
+ align:start position:0%
+pretty sure the housing laws in Boston
+ 
+
+ align:start position:0%
+pretty sure the housing laws in Boston
+are such that you can't ask whether the
+
+ align:start position:0%
+are such that you can't ask whether the
+ 
+
+ align:start position:0%
+are such that you can't ask whether the
+occupants are married
+
+ align:start position:0%
+occupants are married
+ 
+
+ align:start position:0%
+occupants are married
+or living
+
+ align:start position:0%
+or living
+ 
+
+ align:start position:0%
+or living
+together in some
+
+ align:start position:0%
+together in some
+ 
+
+ align:start position:0%
+together in some
+relationship um that that's
+
+ align:start position:0%
+relationship um that that's
+ 
+
+ align:start position:0%
+relationship um that that's
+discrimination you can ask for the
+
+ align:start position:0%
+discrimination you can ask for the
+ 
+
+ align:start position:0%
+discrimination you can ask for the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+occupants but uh you'd be discriminating
+
+ align:start position:0%
+occupants but uh you'd be discriminating
+ 
+
+ align:start position:0%
+occupants but uh you'd be discriminating
+if you said well I don't I don't um rent
+
+ align:start position:0%
+if you said well I don't I don't um rent
+ 
+
+ align:start position:0%
+if you said well I don't I don't um rent
+to homosexuals or I don't rent to people
+
+ align:start position:0%
+to homosexuals or I don't rent to people
+ 
+
+ align:start position:0%
+to homosexuals or I don't rent to people
+who might be uh engaged in sex without
+
+ align:start position:0%
+who might be uh engaged in sex without
+ 
+
+ align:start position:0%
+who might be uh engaged in sex without
+being married or something that would be
+
+ align:start position:0%
+being married or something that would be
+ 
+
+ align:start position:0%
+being married or something that would be
+discrimination in fact that would you
+
+ align:start position:0%
+discrimination in fact that would you
+ 
+
+ align:start position:0%
+discrimination in fact that would you
+know I'm sure this is what the the gay
+
+ align:start position:0%
+know I'm sure this is what the the gay
+ 
+
+ align:start position:0%
+know I'm sure this is what the the gay
+liberationist movement would say that
+
+ align:start position:0%
+liberationist movement would say that
+ 
+
+ align:start position:0%
+liberationist movement would say that
+what I'm going to say now that uh the
+
+ align:start position:0%
+what I'm going to say now that uh the
+ 
+
+ align:start position:0%
+what I'm going to say now that uh the
+reason against Banning same-sex marriage
+
+ align:start position:0%
+reason against Banning same-sex marriage
+ 
+
+ align:start position:0%
+reason against Banning same-sex marriage
+is its discrimination on the basis of
+
+ align:start position:0%
+is its discrimination on the basis of
+ 
+
+ align:start position:0%
+is its discrimination on the basis of
+U what is it U
+
+ align:start position:0%
+U what is it U
+ 
+
+ align:start position:0%
+U what is it U
+lifestyle and that isn't that one of the
+
+ align:start position:0%
+lifestyle and that isn't that one of the
+ 
+
+ align:start position:0%
+lifestyle and that isn't that one of the
+things that the uh Supreme Court ruled
+
+ align:start position:0%
+things that the uh Supreme Court ruled
+ 
+
+ align:start position:0%
+things that the uh Supreme Court ruled
+out that they cannot the federal Supreme
+
+ align:start position:0%
+out that they cannot the federal Supreme
+ 
+
+ align:start position:0%
+out that they cannot the federal Supreme
+Court that they cannot be discrimination
+
+ align:start position:0%
+Court that they cannot be discrimination
+ 
+
+ align:start position:0%
+Court that they cannot be discrimination
+on the basis of Lifestyle just as there
+
+ align:start position:0%
+on the basis of Lifestyle just as there
+ 
+
+ align:start position:0%
+on the basis of Lifestyle just as there
+can't be discrimination on basis of
+
+ align:start position:0%
+can't be discrimination on basis of
+ 
+
+ align:start position:0%
+can't be discrimination on basis of
+religion or ethnic origin well why not
+
+ align:start position:0%
+religion or ethnic origin well why not
+ 
+
+ align:start position:0%
+religion or ethnic origin well why not
+the lifestyle since the lifestyle see
+
+ align:start position:0%
+the lifestyle since the lifestyle see
+ 
+
+ align:start position:0%
+the lifestyle since the lifestyle see
+that's the uh that's the paradox in this
+
+ align:start position:0%
+that's the uh that's the paradox in this
+ 
+
+ align:start position:0%
+that's the uh that's the paradox in this
+the lifestyle is now tolerated legally
+
+ align:start position:0%
+the lifestyle is now tolerated legally
+ 
+
+ align:start position:0%
+the lifestyle is now tolerated legally
+because in the federal laws and some of
+
+ align:start position:0%
+because in the federal laws and some of
+ 
+
+ align:start position:0%
+because in the federal laws and some of
+the states maybe most of the states now
+
+ align:start position:0%
+the states maybe most of the states now
+ 
+
+ align:start position:0%
+the states maybe most of the states now
+uh your behavior in your at home is
+
+ align:start position:0%
+uh your behavior in your at home is
+ 
+
+ align:start position:0%
+uh your behavior in your at home is
+nobody's business what you do in bed is
+
+ align:start position:0%
+nobody's business what you do in bed is
+ 
+
+ align:start position:0%
+nobody's business what you do in bed is
+nobody else's business uh so it's
+
+ align:start position:0%
+nobody else's business uh so it's
+ 
+
+ align:start position:0%
+nobody else's business uh so it's
+tolerated but then if that's true why
+
+ align:start position:0%
+tolerated but then if that's true why
+ 
+
+ align:start position:0%
+tolerated but then if that's true why
+wouldn't you have a responsibility to
+
+ align:start position:0%
+wouldn't you have a responsibility to
+ 
+
+ align:start position:0%
+wouldn't you have a responsibility to
+tolerate the lifestyle of people who
+
+ align:start position:0%
+tolerate the lifestyle of people who
+ 
+
+ align:start position:0%
+tolerate the lifestyle of people who
+engage in such Behavior so is the term
+
+ align:start position:0%
+engage in such Behavior so is the term
+ 
+
+ align:start position:0%
+engage in such Behavior so is the term
+marriage actually
+
+ align:start position:0%
+marriage actually
+ 
+
+ align:start position:0%
+marriage actually
+religious the origin I suppose is
+
+ align:start position:0%
+religious the origin I suppose is
+ 
+
+ align:start position:0%
+religious the origin I suppose is
+religious and it could still be you know
+
+ align:start position:0%
+religious and it could still be you know
+ 
+
+ align:start position:0%
+religious and it could still be you know
+you might that that's one solution to um
+
+ align:start position:0%
+you might that that's one solution to um
+ 
+
+ align:start position:0%
+you might that that's one solution to um
+Del legalize all marriages that marriage
+
+ align:start position:0%
+Del legalize all marriages that marriage
+ 
+
+ align:start position:0%
+Del legalize all marriages that marriage
+is a private activity you can go and get
+
+ align:start position:0%
+is a private activity you can go and get
+ 
+
+ align:start position:0%
+is a private activity you can go and get
+married at in a church if you want um
+
+ align:start position:0%
+married at in a church if you want um
+ 
+
+ align:start position:0%
+married at in a church if you want um
+and it's for the church to decide whom
+
+ align:start position:0%
+and it's for the church to decide whom
+ 
+
+ align:start position:0%
+and it's for the church to decide whom
+they will give the marriage to but it
+
+ align:start position:0%
+they will give the marriage to but it
+ 
+
+ align:start position:0%
+they will give the marriage to but it
+doesn't affect the legal rights and
+
+ align:start position:0%
+doesn't affect the legal rights and
+ 
+
+ align:start position:0%
+doesn't affect the legal rights and
+responsibilities is it a specific Rel
+
+ align:start position:0%
+responsibilities is it a specific Rel
+ 
+
+ align:start position:0%
+responsibilities is it a specific Rel
+religion that it would have to be in the
+
+ align:start position:0%
+religion that it would have to be in the
+ 
+
+ align:start position:0%
+religion that it would have to be in the
+you know if you go to one
+
+ align:start position:0%
+you know if you go to one
+ 
+
+ align:start position:0%
+you know if you go to one
+religion they might tolerate marriage uh
+
+ align:start position:0%
+religion they might tolerate marriage uh
+ 
+
+ align:start position:0%
+religion they might tolerate marriage uh
+if you go to another they might not so
+
+ align:start position:0%
+if you go to another they might not so
+ 
+
+ align:start position:0%
+if you go to another they might not so
+the Catholic uh clergy might refuse to
+
+ align:start position:0%
+the Catholic uh clergy might refuse to
+ 
+
+ align:start position:0%
+the Catholic uh clergy might refuse to
+marry people who are homosexual or
+
+ align:start position:0%
+marry people who are homosexual or
+ 
+
+ align:start position:0%
+marry people who are homosexual or
+overtly and homosexual that's my point
+
+ align:start position:0%
+overtly and homosexual that's my point
+ 
+
+ align:start position:0%
+overtly and homosexual that's my point
+though is but the Episcopalian probably
+
+ align:start position:0%
+though is but the Episcopalian probably
+ 
+
+ align:start position:0%
+though is but the Episcopalian probably
+would because they now have a bishop
+
+ align:start position:0%
+would because they now have a bishop
+ 
+
+ align:start position:0%
+would because they now have a bishop
+who's overtly homosexual and living in a
+
+ align:start position:0%
+who's overtly homosexual and living in a
+ 
+
+ align:start position:0%
+who's overtly homosexual and living in a
+permanent relationship with another man
+
+ align:start position:0%
+permanent relationship with another man
+ 
+
+ align:start position:0%
+permanent relationship with another man
+but if you have a um if you have a
+
+ align:start position:0%
+but if you have a um if you have a
+ 
+
+ align:start position:0%
+but if you have a um if you have a
+freedom of religion in the United States
+
+ align:start position:0%
+freedom of religion in the United States
+ 
+
+ align:start position:0%
+freedom of religion in the United States
+you know you can have whatever religion
+
+ align:start position:0%
+you know you can have whatever religion
+ 
+
+ align:start position:0%
+you know you can have whatever religion
+you desire so you can get married by
+
+ align:start position:0%
+you desire so you can get married by
+ 
+
+ align:start position:0%
+you desire so you can get married by
+under whatever religion whatever
+
+ align:start position:0%
+under whatever religion whatever
+ 
+
+ align:start position:0%
+under whatever religion whatever
+religious beliefs you have is that you
+
+ align:start position:0%
+religious beliefs you have is that you
+ 
+
+ align:start position:0%
+religious beliefs you have is that you
+can even have a homosexual religion
+
+ align:start position:0%
+can even have a homosexual religion
+ 
+
+ align:start position:0%
+can even have a homosexual religion
+which uh to participate you have to be
+
+ align:start position:0%
+which uh to participate you have to be
+ 
+
+ align:start position:0%
+which uh to participate you have to be
+homosexual and that in that religion you
+
+ align:start position:0%
+homosexual and that in that religion you
+ 
+
+ align:start position:0%
+homosexual and that in that religion you
+could be made as married as anybody else
+
+ align:start position:0%
+could be made as married as anybody else
+ 
+
+ align:start position:0%
+could be made as married as anybody else
+the question is whether any of these
+
+ align:start position:0%
+the question is whether any of these
+ 
+
+ align:start position:0%
+the question is whether any of these
+opportunities or
+
+ align:start position:0%
+opportunities or
+ 
+
+ align:start position:0%
+opportunities or
+Alternatives should have a special legal
+
+ align:start position:0%
+Alternatives should have a special legal
+ 
+
+ align:start position:0%
+Alternatives should have a special legal
+status which is the present
+
+ align:start position:0%
+status which is the present
+ 
+
+ align:start position:0%
+status which is the present
+situation presently the only marriages
+
+ align:start position:0%
+situation presently the only marriages
+ 
+
+ align:start position:0%
+situation presently the only marriages
+that are legally accepted in the United
+
+ align:start position:0%
+that are legally accepted in the United
+ 
+
+ align:start position:0%
+that are legally accepted in the United
+States are the ones that take
+
+ align:start position:0%
+States are the ones that take
+ 
+
+ align:start position:0%
+States are the ones that take
+place not in church necessarily but
+
+ align:start position:0%
+place not in church necessarily but
+ 
+
+ align:start position:0%
+place not in church necessarily but
+between people who of different Sexes I
+
+ align:start position:0%
+between people who of different Sexes I
+ 
+
+ align:start position:0%
+between people who of different Sexes I
+have a question so um because priests
+
+ align:start position:0%
+have a question so um because priests
+ 
+
+ align:start position:0%
+have a question so um because priests
+and people within different religions um
+
+ align:start position:0%
+and people within different religions um
+ 
+
+ align:start position:0%
+and people within different religions um
+are I guess recognized by the law to
+
+ align:start position:0%
+are I guess recognized by the law to
+ 
+
+ align:start position:0%
+are I guess recognized by the law to
+perform a marriage so when they perform
+
+ align:start position:0%
+perform a marriage so when they perform
+ 
+
+ align:start position:0%
+perform a marriage so when they perform
+the marriage it's also recognized that
+
+ align:start position:0%
+the marriage it's also recognized that
+ 
+
+ align:start position:0%
+the marriage it's also recognized that
+they can sign a form or something like
+
+ align:start position:0%
+they can sign a form or something like
+ 
+
+ align:start position:0%
+they can sign a form or something like
+that is that how it works that a form
+
+ align:start position:0%
+that is that how it works that a form
+ 
+
+ align:start position:0%
+that is that how it works that a form
+doing what that will also legalize the
+
+ align:start position:0%
+doing what that will also legalize the
+ 
+
+ align:start position:0%
+doing what that will also legalize the
+marriage to the
+
+ align:start position:0%
+marriage to the
+ 
+
+ align:start position:0%
+marriage to the
+state is
+
+ align:start position:0%
+state is
+ 
+
+ align:start position:0%
+state is
+this Li but does the priest have any
+
+ align:start position:0%
+this Li but does the priest have any
+ 
+
+ align:start position:0%
+this Li but does the priest have any
+certifi no priest the Catholic priest or
+
+ align:start position:0%
+certifi no priest the Catholic priest or
+ 
+
+ align:start position:0%
+certifi no priest the Catholic priest or
+any sort of minister or whatever did do
+
+ align:start position:0%
+any sort of minister or whatever did do
+ 
+
+ align:start position:0%
+any sort of minister or whatever did do
+they actually signed the like legal form
+
+ align:start position:0%
+they actually signed the like legal form
+ 
+
+ align:start position:0%
+they actually signed the like legal form
+that makes that makes according to the
+
+ align:start position:0%
+that makes that makes according to the
+ 
+
+ align:start position:0%
+that makes that makes according to the
+state they say the PRI says they got
+
+ align:start position:0%
+state they say the PRI says they got
+ 
+
+ align:start position:0%
+state they say the PRI says they got
+married yeah that mean they get divorced
+
+ align:start position:0%
+married yeah that mean they get divorced
+ 
+
+ align:start position:0%
+married yeah that mean they get divorced
+thei has to be certified to be okay
+
+ align:start position:0%
+thei has to be certified to be okay
+ 
+
+ align:start position:0%
+thei has to be certified to be okay
+exactly so my question is if we were
+
+ align:start position:0%
+exactly so my question is if we were
+ 
+
+ align:start position:0%
+exactly so my question is if we were
+to legalize marriage for homosexuals
+
+ align:start position:0%
+to legalize marriage for homosexuals
+ 
+
+ align:start position:0%
+to legalize marriage for homosexuals
+would it be discrimination for these
+
+ align:start position:0%
+would it be discrimination for these
+ 
+
+ align:start position:0%
+would it be discrimination for these
+priests to say that I will not marry
+
+ align:start position:0%
+priests to say that I will not marry
+ 
+
+ align:start position:0%
+priests to say that I will not marry
+you because technically like to the
+
+ align:start position:0%
+you because technically like to the
+ 
+
+ align:start position:0%
+you because technically like to the
+state they are
+
+ align:start position:0%
+state they are
+ 
+
+ align:start position:0%
+state they are
+like uh I guess Advocates of the state
+
+ align:start position:0%
+like uh I guess Advocates of the state
+ 
+
+ align:start position:0%
+like uh I guess Advocates of the state
+to perform like some sort of uh service
+
+ align:start position:0%
+to perform like some sort of uh service
+ 
+
+ align:start position:0%
+to perform like some sort of uh service
+all right your point is if a
+
+ align:start position:0%
+all right your point is if a
+ 
+
+ align:start position:0%
+all right your point is if a
+Catholic wants priest wants to marry a
+
+ align:start position:0%
+Catholic wants priest wants to marry a
+ 
+
+ align:start position:0%
+Catholic wants priest wants to marry a
+man his church will not allow that and
+
+ align:start position:0%
+man his church will not allow that and
+ 
+
+ align:start position:0%
+man his church will not allow that and
+might even defro
+
+ align:start position:0%
+might even defro
+ 
+
+ align:start position:0%
+might even defro
+him but there would be nothing to stop
+
+ align:start position:0%
+him but there would be nothing to stop
+ 
+
+ align:start position:0%
+him but there would be nothing to stop
+him from getting married in court and
+
+ align:start position:0%
+him from getting married in court and
+ 
+
+ align:start position:0%
+him from getting married in court and
+that would be legal but that's that's
+
+ align:start position:0%
+that would be legal but that's that's
+ 
+
+ align:start position:0%
+that would be legal but that's that's
+presently the case uh mean priest do get
+
+ align:start position:0%
+presently the case uh mean priest do get
+ 
+
+ align:start position:0%
+presently the case uh mean priest do get
+defro actually what I was trying to say
+
+ align:start position:0%
+defro actually what I was trying to say
+ 
+
+ align:start position:0%
+defro actually what I was trying to say
+was would a priest be required to marry
+
+ align:start position:0%
+was would a priest be required to marry
+ 
+
+ align:start position:0%
+was would a priest be required to marry
+a homosexual couple require require Mar
+
+ align:start position:0%
+a homosexual couple require require Mar
+ 
+
+ align:start position:0%
+a homosexual couple require require Mar
+I thought it for himself you would say
+
+ align:start position:0%
+I thought it for himself you would say
+ 
+
+ align:start position:0%
+I thought it for himself you would say
+would officiate with the marriage yes
+
+ align:start position:0%
+would officiate with the marriage yes
+ 
+
+ align:start position:0%
+would officiate with the marriage yes
+officiate with the marriage even if he
+
+ align:start position:0%
+officiate with the marriage even if he
+ 
+
+ align:start position:0%
+officiate with the marriage even if he
+didn't want to
+
+ align:start position:0%
+didn't want to
+ 
+
+ align:start position:0%
+didn't want to
+Simply Mar they don't even marry people
+
+ align:start position:0%
+Simply Mar they don't even marry people
+ 
+
+ align:start position:0%
+Simply Mar they don't even marry people
+have been like you have to have your
+
+ align:start position:0%
+have been like you have to have your
+ 
+
+ align:start position:0%
+have been like you have to have your
+marriage adult in order for the Catholic
+
+ align:start position:0%
+marriage adult in order for the Catholic
+ 
+
+ align:start position:0%
+marriage adult in order for the Catholic
+Church to marry you like even if you're
+
+ align:start position:0%
+Church to marry you like even if you're
+ 
+
+ align:start position:0%
+Church to marry you like even if you're
+divorced but the marriage isn't analed
+
+ align:start position:0%
+divorced but the marriage isn't analed
+ 
+
+ align:start position:0%
+divorced but the marriage isn't analed
+they won't marry you so I have no doubt
+
+ align:start position:0%
+they won't marry you so I have no doubt
+ 
+
+ align:start position:0%
+they won't marry you so I have no doubt
+in my mind that they won't marry
+
+ align:start position:0%
+in my mind that they won't marry
+ 
+
+ align:start position:0%
+in my mind that they won't marry
+homosexuals no no but the point is that
+
+ align:start position:0%
+homosexuals no no but the point is that
+ 
+
+ align:start position:0%
+homosexuals no no but the point is that
+um it doesn't matter what the church
+
+ align:start position:0%
+um it doesn't matter what the church
+ 
+
+ align:start position:0%
+um it doesn't matter what the church
+does the question is what is legal so
+
+ align:start position:0%
+does the question is what is legal so
+ 
+
+ align:start position:0%
+does the question is what is legal so
+the church might say that um we won't
+
+ align:start position:0%
+the church might say that um we won't
+ 
+
+ align:start position:0%
+the church might say that um we won't
+marry a homosexual couple but the couple
+
+ align:start position:0%
+marry a homosexual couple but the couple
+ 
+
+ align:start position:0%
+marry a homosexual couple but the couple
+can go and be legally married like
+
+ align:start position:0%
+can go and be legally married like
+ 
+
+ align:start position:0%
+can go and be legally married like
+anybody else right well I I I I think
+
+ align:start position:0%
+anybody else right well I I I I think
+ 
+
+ align:start position:0%
+anybody else right well I I I I think
+the question is since the the the priest
+
+ align:start position:0%
+the question is since the the the priest
+ 
+
+ align:start position:0%
+the question is since the the the priest
+in this case is licensed by the state is
+
+ align:start position:0%
+in this case is licensed by the state is
+ 
+
+ align:start position:0%
+in this case is licensed by the state is
+he therefore kind of an agent of the
+
+ align:start position:0%
+he therefore kind of an agent of the
+ 
+
+ align:start position:0%
+he therefore kind of an agent of the
+state and therefore practicing
+
+ align:start position:0%
+state and therefore practicing
+ 
+
+ align:start position:0%
+state and therefore practicing
+discrimination as an agent of the
+
+ align:start position:0%
+discrimination as an agent of the
+ 
+
+ align:start position:0%
+discrimination as an agent of the
+state in in not marrying homosexual
+
+ align:start position:0%
+state in in not marrying homosexual
+ 
+
+ align:start position:0%
+state in in not marrying homosexual
+couples or or whatever other is wrong is
+
+ align:start position:0%
+couples or or whatever other is wrong is
+ 
+
+ align:start position:0%
+couples or or whatever other is wrong is
+is are priests an agent of the state
+
+ align:start position:0%
+is are priests an agent of the state
+ 
+
+ align:start position:0%
+is are priests an agent of the state
+well I think I think that's the question
+
+ align:start position:0%
+well I think I think that's the question
+ 
+
+ align:start position:0%
+well I think I think that's the question
+no I don't think they are I think
+
+ align:start position:0%
+no I don't think they are I think
+ 
+
+ align:start position:0%
+no I don't think they are I think
+U marriage and church is one thing and
+
+ align:start position:0%
+U marriage and church is one thing and
+ 
+
+ align:start position:0%
+U marriage and church is one thing and
+marriage question is what is entailed by
+
+ align:start position:0%
+marriage question is what is entailed by
+ 
+
+ align:start position:0%
+marriage question is what is entailed by
+this becoming certified by the state to
+
+ align:start position:0%
+this becoming certified by the state to
+ 
+
+ align:start position:0%
+this becoming certified by the state to
+marry people um you can go on the
+
+ align:start position:0%
+marry people um you can go on the
+ 
+
+ align:start position:0%
+marry people um you can go on the
+internet and get certified to do it for
+
+ align:start position:0%
+internet and get certified to do it for
+ 
+
+ align:start position:0%
+internet and get certified to do it for
+15 bucks or something so yeah I mean I
+
+ align:start position:0%
+15 bucks or something so yeah I mean I
+ 
+
+ align:start position:0%
+15 bucks or something so yeah I mean I
+think it's becoming like less of an
+
+ align:start position:0%
+think it's becoming like less of an
+ 
+
+ align:start position:0%
+think it's becoming like less of an
+issue but I mean I think before that was
+
+ align:start position:0%
+issue but I mean I think before that was
+ 
+
+ align:start position:0%
+issue but I mean I think before that was
+the case then I think this was a Val
+
+ align:start position:0%
+the case then I think this was a Val
+ 
+
+ align:start position:0%
+the case then I think this was a Val
+this I think this is a very valid
+
+ align:start position:0%
+this I think this is a very valid
+ 
+
+ align:start position:0%
+this I think this is a very valid
+question like the internet thing aside
+
+ align:start position:0%
+question like the internet thing aside
+ 
+
+ align:start position:0%
+question like the internet thing aside
+right if if it were hard to get the
+
+ align:start position:0%
+right if if it were hard to get the
+ 
+
+ align:start position:0%
+right if if it were hard to get the
+certification right if you had to be a
+
+ align:start position:0%
+certification right if you had to be a
+ 
+
+ align:start position:0%
+certification right if you had to be a
+priest in you know a church or the
+
+ align:start position:0%
+priest in you know a church or the
+ 
+
+ align:start position:0%
+priest in you know a church or the
+steeple and stuff but you can get
+
+ align:start position:0%
+steeple and stuff but you can get
+ 
+
+ align:start position:0%
+steeple and stuff but you can get
+married by a
+
+ align:start position:0%
+married by a
+ 
+
+ align:start position:0%
+married by a
+judge and I guess that's what like
+
+ align:start position:0%
+judge and I guess that's what like
+ 
+
+ align:start position:0%
+judge and I guess that's what like
+homosexuals would like if even if
+
+ align:start position:0%
+homosexuals would like if even if
+ 
+
+ align:start position:0%
+homosexuals would like if even if
+marriage was
+
+ align:start position:0%
+marriage was
+ 
+
+ align:start position:0%
+marriage was
+legalized and they were like I mean if
+
+ align:start position:0%
+legalized and they were like I mean if
+ 
+
+ align:start position:0%
+legalized and they were like I mean if
+they were catholic and they wanted to
+
+ align:start position:0%
+they were catholic and they wanted to
+ 
+
+ align:start position:0%
+they were catholic and they wanted to
+get married they probably wouldn't be
+
+ align:start position:0%
+get married they probably wouldn't be
+ 
+
+ align:start position:0%
+get married they probably wouldn't be
+getting married in the church they would
+
+ align:start position:0%
+getting married in the church they would
+ 
+
+ align:start position:0%
+getting married in the church they would
+get married by the judge I mean my
+
+ align:start position:0%
+get married by the judge I mean my
+ 
+
+ align:start position:0%
+get married by the judge I mean my
+parent my dad was divorced before he got
+
+ align:start position:0%
+parent my dad was divorced before he got
+ 
+
+ align:start position:0%
+parent my dad was divorced before he got
+married and my mom and my dad got
+
+ align:start position:0%
+married and my mom and my dad got
+ 
+
+ align:start position:0%
+married and my mom and my dad got
+married and they weren't married by the
+
+ align:start position:0%
+married and they weren't married by the
+ 
+
+ align:start position:0%
+married and they weren't married by the
+Catholic church that was like 10 but
+
+ align:start position:0%
+Catholic church that was like 10 but
+ 
+
+ align:start position:0%
+Catholic church that was like 10 but
+that didn't mean that they W
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+married so I I I mean I guess I guess
+
+ align:start position:0%
+married so I I I mean I guess I guess
+ 
+
+ align:start position:0%
+married so I I I mean I guess I guess
+the the issue is
+
+ align:start position:0%
+the the issue is
+ 
+
+ align:start position:0%
+the the issue is
+um you know MIT isn't allowed to
+
+ align:start position:0%
+um you know MIT isn't allowed to
+ 
+
+ align:start position:0%
+um you know MIT isn't allowed to
+discriminate
+
+ align:start position:0%
+discriminate
+ 
+
+ align:start position:0%
+discriminate
+against homosexual couples right why is
+
+ align:start position:0%
+against homosexual couples right why is
+ 
+
+ align:start position:0%
+against homosexual couples right why is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+church oh because the church is a
+
+ align:start position:0%
+church oh because the church is a
+ 
+
+ align:start position:0%
+church oh because the church is a
+private institution it's like a club you
+
+ align:start position:0%
+private institution it's like a club you
+ 
+
+ align:start position:0%
+private institution it's like a club you
+can have a club that excludes people you
+
+ align:start position:0%
+can have a club that excludes people you
+ 
+
+ align:start position:0%
+can have a club that excludes people you
+don't like well MIT excludes people
+
+ align:start position:0%
+don't like well MIT excludes people
+ 
+
+ align:start position:0%
+don't like well MIT excludes people
+without high enough SAT scores right no
+
+ align:start position:0%
+without high enough SAT scores right no
+ 
+
+ align:start position:0%
+without high enough SAT scores right no
+no no MIT uh is a nonprofit institution
+
+ align:start position:0%
+no no MIT uh is a nonprofit institution
+ 
+
+ align:start position:0%
+no no MIT uh is a nonprofit institution
+that receives a great deal of money from
+
+ align:start position:0%
+that receives a great deal of money from
+ 
+
+ align:start position:0%
+that receives a great deal of money from
+the government okay if it were just a
+
+ align:start position:0%
+the government okay if it were just a
+ 
+
+ align:start position:0%
+the government okay if it were just a
+private club okay that would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so even there I think I don't
+
+ align:start position:0%
+different so even there I think I don't
+ 
+
+ align:start position:0%
+different so even there I think I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+nowadays whether uh people could I don't
+
+ align:start position:0%
+nowadays whether uh people could I don't
+ 
+
+ align:start position:0%
+nowadays whether uh people could I don't
+see how they could claim discrimination
+
+ align:start position:0%
+see how they could claim discrimination
+ 
+
+ align:start position:0%
+see how they could claim discrimination
+if they're not admitted to some Club in
+
+ align:start position:0%
+if they're not admitted to some Club in
+ 
+
+ align:start position:0%
+if they're not admitted to some Club in
+view of their
+
+ align:start position:0%
+view of their
+ 
+
+ align:start position:0%
+view of their
+religion
+
+ align:start position:0%
+religion
+ 
+
+ align:start position:0%
+religion
+um no if it's a purely private club I
+
+ align:start position:0%
+um no if it's a purely private club I
+ 
+
+ align:start position:0%
+um no if it's a purely private club I
+think you can it's like a friendship you
+
+ align:start position:0%
+think you can it's like a friendship you
+ 
+
+ align:start position:0%
+think you can it's like a friendship you
+can have any friends you want government
+
+ align:start position:0%
+can have any friends you want government
+ 
+
+ align:start position:0%
+can have any friends you want government
+can't tell you who your friends must be
+
+ align:start position:0%
+can't tell you who your friends must be
+ 
+
+ align:start position:0%
+can't tell you who your friends must be
+um if however there is Government
+
+ align:start position:0%
+um if however there is Government
+ 
+
+ align:start position:0%
+um if however there is Government
+funding and if it is has a semi it
+
+ align:start position:0%
+funding and if it is has a semi it
+ 
+
+ align:start position:0%
+funding and if it is has a semi it
+that's a tax-free
+
+ align:start position:0%
+that's a tax-free
+ 
+
+ align:start position:0%
+that's a tax-free
+status that's very
+
+ align:start position:0%
+status that's very
+ 
+
+ align:start position:0%
+status that's very
+different so the church I think could
+
+ align:start position:0%
+different so the church I think could
+ 
+
+ align:start position:0%
+different so the church I think could
+argue well we are priv purely
+
+ align:start position:0%
+argue well we are priv purely
+ 
+
+ align:start position:0%
+argue well we are priv purely
+private uh except that of course they
+
+ align:start position:0%
+private uh except that of course they
+ 
+
+ align:start position:0%
+private uh except that of course they
+may find ways of getting money from the
+
+ align:start position:0%
+may find ways of getting money from the
+ 
+
+ align:start position:0%
+may find ways of getting money from the
+government but that's that's to be
+
+ align:start position:0%
+government but that's that's to be
+ 
+
+ align:start position:0%
+government but that's that's to be
+debated um and so they can decide whom
+
+ align:start position:0%
+debated um and so they can decide whom
+ 
+
+ align:start position:0%
+debated um and so they can decide whom
+they will marry and who they want and
+
+ align:start position:0%
+they will marry and who they want and
+ 
+
+ align:start position:0%
+they will marry and who they want and
+one of one of the solutions to the
+
+ align:start position:0%
+one of one of the solutions to the
+ 
+
+ align:start position:0%
+one of one of the solutions to the
+problem would be to uh
+
+ align:start position:0%
+problem would be to uh
+ 
+
+ align:start position:0%
+problem would be to uh
+Del legalize marriage as a whole and
+
+ align:start position:0%
+Del legalize marriage as a whole and
+ 
+
+ align:start position:0%
+Del legalize marriage as a whole and
+anybody who wants to get married can do
+
+ align:start position:0%
+anybody who wants to get married can do
+ 
+
+ align:start position:0%
+anybody who wants to get married can do
+so in his his or her religion or by
+
+ align:start position:0%
+so in his his or her religion or by
+ 
+
+ align:start position:0%
+so in his his or her religion or by
+sending in the $15 on the internet and
+
+ align:start position:0%
+sending in the $15 on the internet and
+ 
+
+ align:start position:0%
+sending in the $15 on the internet and
+there are no preferential benefits to be
+
+ align:start position:0%
+there are no preferential benefits to be
+ 
+
+ align:start position:0%
+there are no preferential benefits to be
+got from the government there is no uh
+
+ align:start position:0%
+got from the government there is no uh
+ 
+
+ align:start position:0%
+got from the government there is no uh
+no official legal status it's simply one
+
+ align:start position:0%
+no official legal status it's simply one
+ 
+
+ align:start position:0%
+no official legal status it's simply one
+of the things people do you know you can
+
+ align:start position:0%
+of the things people do you know you can
+ 
+
+ align:start position:0%
+of the things people do you know you can
+you can uh a belong you could belong to
+
+ align:start position:0%
+you can uh a belong you could belong to
+ 
+
+ align:start position:0%
+you can uh a belong you could belong to
+an atheist
+
+ align:start position:0%
+an atheist
+ 
+
+ align:start position:0%
+an atheist
+Society it's just you know few with
+
+ align:start position:0%
+Society it's just you know few with
+ 
+
+ align:start position:0%
+Society it's just you know few with
+people of similar thinking that's not a
+
+ align:start position:0%
+people of similar thinking that's not a
+ 
+
+ align:start position:0%
+people of similar thinking that's not a
+legal matter that would be one solution
+
+ align:start position:0%
+legal matter that would be one solution
+ 
+
+ align:start position:0%
+legal matter that would be one solution
+it's very complicated first because of
+
+ align:start position:0%
+it's very complicated first because of
+ 
+
+ align:start position:0%
+it's very complicated first because of
+the I think because of the primordial
+
+ align:start position:0%
+the I think because of the primordial
+ 
+
+ align:start position:0%
+the I think because of the primordial
+condition of sexuality that's why I
+
+ align:start position:0%
+condition of sexuality that's why I
+ 
+
+ align:start position:0%
+condition of sexuality that's why I
+wanted to start with this instead of
+
+ align:start position:0%
+wanted to start with this instead of
+ 
+
+ align:start position:0%
+wanted to start with this instead of
+ending with it at the end of the course
+
+ align:start position:0%
+ending with it at the end of the course
+ 
+
+ align:start position:0%
+ending with it at the end of the course
+that sex is so deeply embedded in our
+
+ align:start position:0%
+that sex is so deeply embedded in our
+ 
+
+ align:start position:0%
+that sex is so deeply embedded in our
+being and our conception of ourselves
+
+ align:start position:0%
+being and our conception of ourselves
+ 
+
+ align:start position:0%
+being and our conception of ourselves
+and one reason I I am such a severe
+
+ align:start position:0%
+and one reason I I am such a severe
+ 
+
+ align:start position:0%
+and one reason I I am such a severe
+critic of Freud about whom I've written
+
+ align:start position:0%
+critic of Freud about whom I've written
+ 
+
+ align:start position:0%
+critic of Freud about whom I've written
+I don't know well over 100 Pages I'm a
+
+ align:start position:0%
+I don't know well over 100 Pages I'm a
+ 
+
+ align:start position:0%
+I don't know well over 100 Pages I'm a
+Critic of freuds uh because he was a
+
+ align:start position:0%
+Critic of freuds uh because he was a
+ 
+
+ align:start position:0%
+Critic of freuds uh because he was a
+genius who dared first to handle this
+
+ align:start position:0%
+genius who dared first to handle this
+ 
+
+ align:start position:0%
+genius who dared first to handle this
+kind of question and was very inventive
+
+ align:start position:0%
+kind of question and was very inventive
+ 
+
+ align:start position:0%
+kind of question and was very inventive
+and wrong in many respects and but he he
+
+ align:start position:0%
+and wrong in many respects and but he he
+ 
+
+ align:start position:0%
+and wrong in many respects and but he he
+it was such a startling achievement that
+
+ align:start position:0%
+it was such a startling achievement that
+ 
+
+ align:start position:0%
+it was such a startling achievement that
+we have inherited all of this the all of
+
+ align:start position:0%
+we have inherited all of this the all of
+ 
+
+ align:start position:0%
+we have inherited all of this the all of
+the mythology and the loose thinking of
+
+ align:start position:0%
+the mythology and the loose thinking of
+ 
+
+ align:start position:0%
+the mythology and the loose thinking of
+Freud and uh I I could see through that
+
+ align:start position:0%
+Freud and uh I I could see through that
+ 
+
+ align:start position:0%
+Freud and uh I I could see through that
+and treating him as a philosopher I
+
+ align:start position:0%
+and treating him as a philosopher I
+ 
+
+ align:start position:0%
+and treating him as a philosopher I
+found him very wanting right um but he
+
+ align:start position:0%
+found him very wanting right um but he
+ 
+
+ align:start position:0%
+found him very wanting right um but he
+certainly is responsible for our
+
+ align:start position:0%
+certainly is responsible for our
+ 
+
+ align:start position:0%
+certainly is responsible for our
+realizing how deep sexuality is in us
+
+ align:start position:0%
+realizing how deep sexuality is in us
+ 
+
+ align:start position:0%
+realizing how deep sexuality is in us
+you know whether or not his account of
+
+ align:start position:0%
+you know whether or not his account of
+ 
+
+ align:start position:0%
+you know whether or not his account of
+it is correct um and I think
+
+ align:start position:0%
+it is correct um and I think
+ 
+
+ align:start position:0%
+it is correct um and I think
+that's one what makes the homosexual
+
+ align:start position:0%
+that's one what makes the homosexual
+ 
+
+ align:start position:0%
+that's one what makes the homosexual
+question so particularly the homosexual
+
+ align:start position:0%
+question so particularly the homosexual
+ 
+
+ align:start position:0%
+question so particularly the homosexual
+marriage section so important because
+
+ align:start position:0%
+marriage section so important because
+ 
+
+ align:start position:0%
+marriage section so important because
+marriage is a longstanding institution
+
+ align:start position:0%
+marriage is a longstanding institution
+ 
+
+ align:start position:0%
+marriage is a longstanding institution
+that embodies a whole system of
+
+ align:start position:0%
+that embodies a whole system of
+ 
+
+ align:start position:0%
+that embodies a whole system of
+values and it's going to take the world
+
+ align:start position:0%
+values and it's going to take the world
+ 
+
+ align:start position:0%
+values and it's going to take the world
+quite a while to straighten out its uh
+
+ align:start position:0%
+quite a while to straighten out its uh
+ 
+
+ align:start position:0%
+quite a while to straighten out its uh
+its philosophy of value in order to get
+
+ align:start position:0%
+its philosophy of value in order to get
+ 
+
+ align:start position:0%
+its philosophy of value in order to get
+this problem in order and second because
+
+ align:start position:0%
+this problem in order and second because
+ 
+
+ align:start position:0%
+this problem in order and second because
+of the question of the
+
+ align:start position:0%
+of the question of the
+ 
+
+ align:start position:0%
+of the question of the
+family um I I don't remember I don't do
+
+ align:start position:0%
+family um I I don't remember I don't do
+ 
+
+ align:start position:0%
+family um I I don't remember I don't do
+a great deal of research for the writing
+
+ align:start position:0%
+a great deal of research for the writing
+ 
+
+ align:start position:0%
+a great deal of research for the writing
+I do particularly nowadays uh I rely on
+
+ align:start position:0%
+I do particularly nowadays uh I rely on
+ 
+
+ align:start position:0%
+I do particularly nowadays uh I rely on
+my own intuition my
+
+ align:start position:0%
+my own intuition my
+ 
+
+ align:start position:0%
+my own intuition my
+own logic to be make ideas clear and in
+
+ align:start position:0%
+own logic to be make ideas clear and in
+ 
+
+ align:start position:0%
+own logic to be make ideas clear and in
+terms of my own feelings of what's
+
+ align:start position:0%
+terms of my own feelings of what's
+ 
+
+ align:start position:0%
+terms of my own feelings of what's
+import important I don't usually write
+
+ align:start position:0%
+import important I don't usually write
+ 
+
+ align:start position:0%
+import important I don't usually write
+uh paper articles in public policy the
+
+ align:start position:0%
+uh paper articles in public policy the
+ 
+
+ align:start position:0%
+uh paper articles in public policy the
+way this one is but if I feel it
+
+ align:start position:0%
+way this one is but if I feel it
+ 
+
+ align:start position:0%
+way this one is but if I feel it
+strongly enough enough and in this case
+
+ align:start position:0%
+strongly enough enough and in this case
+ 
+
+ align:start position:0%
+strongly enough enough and in this case
+as I mentioned last time I felt after
+
+ align:start position:0%
+as I mentioned last time I felt after
+ 
+
+ align:start position:0%
+as I mentioned last time I felt after
+all these years I can speak with some
+
+ align:start position:0%
+all these years I can speak with some
+ 
+
+ align:start position:0%
+all these years I can speak with some
+kind of authority and why aren't I
+
+ align:start position:0%
+kind of authority and why aren't I
+ 
+
+ align:start position:0%
+kind of authority and why aren't I
+speaking up right so I will speak up the
+
+ align:start position:0%
+speaking up right so I will speak up the
+ 
+
+ align:start position:0%
+speaking up right so I will speak up the
+way John Dewey my hero would have done
+
+ align:start position:0%
+way John Dewey my hero would have done
+ 
+
+ align:start position:0%
+way John Dewey my hero would have done
+as I told you um
+
+ align:start position:0%
+as I told you um
+ 
+
+ align:start position:0%
+as I told you um
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+nevertheless despite my ignorance of
+
+ align:start position:0%
+nevertheless despite my ignorance of
+ 
+
+ align:start position:0%
+nevertheless despite my ignorance of
+what other people have been writing I
+
+ align:start position:0%
+what other people have been writing I
+ 
+
+ align:start position:0%
+what other people have been writing I
+don't think there's been much done about
+
+ align:start position:0%
+don't think there's been much done about
+ 
+
+ align:start position:0%
+don't think there's been much done about
+the concept of the family as such what
+
+ align:start position:0%
+the concept of the family as such what
+ 
+
+ align:start position:0%
+the concept of the family as such what
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+is to be a family what is is the
+
+ align:start position:0%
+is to be a family what is is the
+ 
+
+ align:start position:0%
+is to be a family what is is the
+significance of families in human nature
+
+ align:start position:0%
+significance of families in human nature
+ 
+
+ align:start position:0%
+significance of families in human nature
+and the relationship to families of
+
+ align:start position:0%
+and the relationship to families of
+ 
+
+ align:start position:0%
+and the relationship to families of
+other creatures know all uh animals
+
+ align:start position:0%
+other creatures know all uh animals
+ 
+
+ align:start position:0%
+other creatures know all uh animals
+certainly all mammals live in families I
+
+ align:start position:0%
+certainly all mammals live in families I
+ 
+
+ align:start position:0%
+certainly all mammals live in families I
+feel like there has been some writing on
+
+ align:start position:0%
+feel like there has been some writing on
+ 
+
+ align:start position:0%
+feel like there has been some writing on
+it simply because I know there's a class
+
+ align:start position:0%
+it simply because I know there's a class
+ 
+
+ align:start position:0%
+it simply because I know there's a class
+here in MIT called the Contemporary
+
+ align:start position:0%
+here in MIT called the Contemporary
+ 
+
+ align:start position:0%
+here in MIT called the Contemporary
+American Family oh in sociology and
+
+ align:start position:0%
+American Family oh in sociology and
+ 
+
+ align:start position:0%
+American Family oh in sociology and
+anthropology there is now some and so I
+
+ align:start position:0%
+anthropology there is now some and so I
+ 
+
+ align:start position:0%
+anthropology there is now some and so I
+feel like they're probably reading but
+
+ align:start position:0%
+feel like they're probably reading but
+ 
+
+ align:start position:0%
+feel like they're probably reading but
+the philosophers the philosophy of
+
+ align:start position:0%
+the philosophers the philosophy of
+ 
+
+ align:start position:0%
+the philosophers the philosophy of
+family is something that has been
+
+ align:start position:0%
+family is something that has been
+ 
+
+ align:start position:0%
+family is something that has been
+neglected and my point here is that the
+
+ align:start position:0%
+neglected and my point here is that the
+ 
+
+ align:start position:0%
+neglected and my point here is that the
+part of the difficulty in
+
+ align:start position:0%
+part of the difficulty in
+ 
+
+ align:start position:0%
+part of the difficulty in
+this issue of uh gay marriage is that
+
+ align:start position:0%
+this issue of uh gay marriage is that
+ 
+
+ align:start position:0%
+this issue of uh gay marriage is that
+it's linked to our thinking about the
+
+ align:start position:0%
+it's linked to our thinking about the
+ 
+
+ align:start position:0%
+it's linked to our thinking about the
+nature of a family and that's why I
+
+ align:start position:0%
+nature of a family and that's why I
+ 
+
+ align:start position:0%
+nature of a family and that's why I
+referred to George W Bush's speech uh
+
+ align:start position:0%
+referred to George W Bush's speech uh
+ 
+
+ align:start position:0%
+referred to George W Bush's speech uh
+was it about about a year ago or so a
+
+ align:start position:0%
+was it about about a year ago or so a
+ 
+
+ align:start position:0%
+was it about about a year ago or so a
+year and a half in which um he said that
+
+ align:start position:0%
+year and a half in which um he said that
+ 
+
+ align:start position:0%
+year and a half in which um he said that
+marriage exists between one man and one
+
+ align:start position:0%
+marriage exists between one man and one
+ 
+
+ align:start position:0%
+marriage exists between one man and one
+woman all right and then he slipped into
+
+ align:start position:0%
+woman all right and then he slipped into
+ 
+
+ align:start position:0%
+woman all right and then he slipped into
+talking about the family that this is
+
+ align:start position:0%
+talking about the family that this is
+ 
+
+ align:start position:0%
+talking about the family that this is
+the nature of a family uh this is what
+
+ align:start position:0%
+the nature of a family uh this is what
+ 
+
+ align:start position:0%
+the nature of a family uh this is what
+government should be uh defining itself
+
+ align:start position:0%
+government should be uh defining itself
+ 
+
+ align:start position:0%
+government should be uh defining itself
+into into and that in that part of my
+
+ align:start position:0%
+into into and that in that part of my
+ 
+
+ align:start position:0%
+into into and that in that part of my
+essay you remember that section I want
+
+ align:start position:0%
+essay you remember that section I want
+ 
+
+ align:start position:0%
+essay you remember that section I want
+to separate the concepts because it
+
+ align:start position:0%
+to separate the concepts because it
+ 
+
+ align:start position:0%
+to separate the concepts because it
+doesn't follow that families and
+
+ align:start position:0%
+doesn't follow that families and
+ 
+
+ align:start position:0%
+doesn't follow that families and
+marriages depend on each other you can
+
+ align:start position:0%
+marriages depend on each other you can
+ 
+
+ align:start position:0%
+marriages depend on each other you can
+have a family without having a legal
+
+ align:start position:0%
+have a family without having a legal
+ 
+
+ align:start position:0%
+have a family without having a legal
+marriage you can have a legal marriage
+
+ align:start position:0%
+marriage you can have a legal marriage
+ 
+
+ align:start position:0%
+marriage you can have a legal marriage
+and not have a family if you don't have
+
+ align:start position:0%
+and not have a family if you don't have
+ 
+
+ align:start position:0%
+and not have a family if you don't have
+any children or or but the word is loose
+
+ align:start position:0%
+any children or or but the word is loose
+ 
+
+ align:start position:0%
+any children or or but the word is loose
+because uh a man and a woman who never
+
+ align:start position:0%
+because uh a man and a woman who never
+ 
+
+ align:start position:0%
+because uh a man and a woman who never
+have children but are married they might
+
+ align:start position:0%
+have children but are married they might
+ 
+
+ align:start position:0%
+have children but are married they might
+refer to their family in uh uh in terms
+
+ align:start position:0%
+refer to their family in uh uh in terms
+ 
+
+ align:start position:0%
+refer to their family in uh uh in terms
+of themselves alone you know that they
+
+ align:start position:0%
+of themselves alone you know that they
+ 
+
+ align:start position:0%
+of themselves alone you know that they
+they are they are the family the husband
+
+ align:start position:0%
+they are they are the family the husband
+ 
+
+ align:start position:0%
+they are they are the family the husband
+and wife without children but usually
+
+ align:start position:0%
+and wife without children but usually
+ 
+
+ align:start position:0%
+and wife without children but usually
+the word family includes um children
+
+ align:start position:0%
+the word family includes um children
+ 
+
+ align:start position:0%
+the word family includes um children
+relatives
+
+ align:start position:0%
+relatives
+ 
+
+ align:start position:0%
+relatives
+cousins uh people who are interwoven in
+
+ align:start position:0%
+cousins uh people who are interwoven in
+ 
+
+ align:start position:0%
+cousins uh people who are interwoven in
+some kind of social unit and it could
+
+ align:start position:0%
+some kind of social unit and it could
+ 
+
+ align:start position:0%
+some kind of social unit and it could
+even be Hangers On you know uh um
+
+ align:start position:0%
+even be Hangers On you know uh um
+ 
+
+ align:start position:0%
+even be Hangers On you know uh um
+servants who in the old days at least
+
+ align:start position:0%
+servants who in the old days at least
+ 
+
+ align:start position:0%
+servants who in the old days at least
+servants who uh were too old to work but
+
+ align:start position:0%
+servants who uh were too old to work but
+ 
+
+ align:start position:0%
+servants who uh were too old to work but
+they were still a part of the family so
+
+ align:start position:0%
+they were still a part of the family so
+ 
+
+ align:start position:0%
+they were still a part of the family so
+they kept living with the others even
+
+ align:start position:0%
+they kept living with the others even
+ 
+
+ align:start position:0%
+they kept living with the others even
+though there was no blood relationship
+
+ align:start position:0%
+though there was no blood relationship
+ 
+
+ align:start position:0%
+though there was no blood relationship
+so it's it the limits are are vague
+
+ align:start position:0%
+so it's it the limits are are vague
+ 
+
+ align:start position:0%
+so it's it the limits are are vague
+but that seems to me to be the proper
+
+ align:start position:0%
+but that seems to me to be the proper
+ 
+
+ align:start position:0%
+but that seems to me to be the proper
+use of the concept of family and it the
+
+ align:start position:0%
+use of the concept of family and it the
+ 
+
+ align:start position:0%
+use of the concept of family and it the
+relationship to marriage had isn't
+
+ align:start position:0%
+relationship to marriage had isn't
+ 
+
+ align:start position:0%
+relationship to marriage had isn't
+analyzed and I wanted to separate them
+
+ align:start position:0%
+analyzed and I wanted to separate them
+ 
+
+ align:start position:0%
+analyzed and I wanted to separate them
+two as against uh Bush who was uniting
+
+ align:start position:0%
+two as against uh Bush who was uniting
+ 
+
+ align:start position:0%
+two as against uh Bush who was uniting
+them well that fact that the concept of
+
+ align:start position:0%
+them well that fact that the concept of
+ 
+
+ align:start position:0%
+them well that fact that the concept of
+family is so vaguely inter over with the
+
+ align:start position:0%
+family is so vaguely inter over with the
+ 
+
+ align:start position:0%
+family is so vaguely inter over with the
+concept of marriage makes it harder yet
+
+ align:start position:0%
+concept of marriage makes it harder yet
+ 
+
+ align:start position:0%
+concept of marriage makes it harder yet
+to resolve resolve this
+
+ align:start position:0%
+to resolve resolve this
+ 
+
+ align:start position:0%
+to resolve resolve this
+and I'm sure lots of people in America
+
+ align:start position:0%
+and I'm sure lots of people in America
+ 
+
+ align:start position:0%
+and I'm sure lots of people in America
+until very very recently couldn't
+
+ align:start position:0%
+until very very recently couldn't
+ 
+
+ align:start position:0%
+until very very recently couldn't
+imagine there being uh homosexual
+
+ align:start position:0%
+imagine there being uh homosexual
+ 
+
+ align:start position:0%
+imagine there being uh homosexual
+families you mean two men two women not
+
+ align:start position:0%
+families you mean two men two women not
+ 
+
+ align:start position:0%
+families you mean two men two women not
+one in one and
+
+ align:start position:0%
+one in one and
+ 
+
+ align:start position:0%
+one in one and
+not even even um uh not the parents
+
+ align:start position:0%
+not even even um uh not the parents
+ 
+
+ align:start position:0%
+not even even um uh not the parents
+maybe adopted is that a family it's not
+
+ align:start position:0%
+maybe adopted is that a family it's not
+ 
+
+ align:start position:0%
+maybe adopted is that a family it's not
+a real you know it's very unclear so
+
+ align:start position:0%
+a real you know it's very unclear so
+ 
+
+ align:start position:0%
+a real you know it's very unclear so
+that this is a need of a lot of analysis
+
+ align:start position:0%
+that this is a need of a lot of analysis
+ 
+
+ align:start position:0%
+that this is a need of a lot of analysis
+and digestion uh in the values that will
+
+ align:start position:0%
+and digestion uh in the values that will
+ 
+
+ align:start position:0%
+and digestion uh in the values that will
+finally bring about some kind of uh
+
+ align:start position:0%
+finally bring about some kind of uh
+ 
+
+ align:start position:0%
+finally bring about some kind of uh
+resolution I don't know if any of you
+
+ align:start position:0%
+resolution I don't know if any of you
+ 
+
+ align:start position:0%
+resolution I don't know if any of you
+know a poem by um Frost Robert
+
+ align:start position:0%
+know a poem by um Frost Robert
+ 
+
+ align:start position:0%
+know a poem by um Frost Robert
+Frost um in which the line
+
+ align:start position:0%
+Frost um in which the line
+ 
+
+ align:start position:0%
+Frost um in which the line
+appears home is where when you come back
+
+ align:start position:0%
+appears home is where when you come back
+ 
+
+ align:start position:0%
+appears home is where when you come back
+to it they've got to take you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in now I think that's part of the idea
+
+ align:start position:0%
+in now I think that's part of the idea
+ 
+
+ align:start position:0%
+in now I think that's part of the idea
+of family if you're a part of the family
+
+ align:start position:0%
+of family if you're a part of the family
+ 
+
+ align:start position:0%
+of family if you're a part of the family
+even if you sinned if you've been in
+
+ align:start position:0%
+even if you sinned if you've been in
+ 
+
+ align:start position:0%
+even if you sinned if you've been in
+prison if you were a derel if you uh um
+
+ align:start position:0%
+prison if you were a derel if you uh um
+ 
+
+ align:start position:0%
+prison if you were a derel if you uh um
+Wayward
+
+ align:start position:0%
+Wayward
+ 
+
+ align:start position:0%
+Wayward
+um The Prodigal Son if you come back
+
+ align:start position:0%
+um The Prodigal Son if you come back
+ 
+
+ align:start position:0%
+um The Prodigal Son if you come back
+home they accept you as belonging there
+
+ align:start position:0%
+home they accept you as belonging there
+ 
+
+ align:start position:0%
+home they accept you as belonging there
+because you're part of the
+
+ align:start position:0%
+because you're part of the
+ 
+
+ align:start position:0%
+because you're part of the
+family and then this gets to be very
+
+ align:start position:0%
+family and then this gets to be very
+ 
+
+ align:start position:0%
+family and then this gets to be very
+important of course in in other respects
+
+ align:start position:0%
+important of course in in other respects
+ 
+
+ align:start position:0%
+important of course in in other respects
+in the mafia always talks about itself
+
+ align:start position:0%
+in the mafia always talks about itself
+ 
+
+ align:start position:0%
+in the mafia always talks about itself
+is the family there are people like us
+
+ align:start position:0%
+is the family there are people like us
+ 
+
+ align:start position:0%
+is the family there are people like us
+who we can communicate with so the
+
+ align:start position:0%
+who we can communicate with so the
+ 
+
+ align:start position:0%
+who we can communicate with so the
+concept of family is in need of a great
+
+ align:start position:0%
+concept of family is in need of a great
+ 
+
+ align:start position:0%
+concept of family is in need of a great
+deal of
+
+ align:start position:0%
+deal of
+ 
+
+ align:start position:0%
+deal of
+analysis maybe you'll be able to do that
+
+ align:start position:0%
+analysis maybe you'll be able to do that
+ 
+
+ align:start position:0%
+analysis maybe you'll be able to do that
+I don't know anybody who has done it
+
+ align:start position:0%
+I don't know anybody who has done it
+ 
+
+ align:start position:0%
+I don't know anybody who has done it
+right I feel like in general though the
+
+ align:start position:0%
+right I feel like in general though the
+ 
+
+ align:start position:0%
+right I feel like in general though the
+United States has already started to
+
+ align:start position:0%
+United States has already started to
+ 
+
+ align:start position:0%
+United States has already started to
+accept a different concept of the family
+
+ align:start position:0%
+accept a different concept of the family
+ 
+
+ align:start position:0%
+accept a different concept of the family
+I mean you kind of touch on it in your
+
+ align:start position:0%
+I mean you kind of touch on it in your
+ 
+
+ align:start position:0%
+I mean you kind of touch on it in your
+in this introduction but I mean already
+
+ align:start position:0%
+in this introduction but I mean already
+ 
+
+ align:start position:0%
+in this introduction but I mean already
+the idea of you know know
+
+ align:start position:0%
+the idea of you know know
+ 
+
+ align:start position:0%
+the idea of you know know
+um two parents uh getting a child
+
+ align:start position:0%
+um two parents uh getting a child
+ 
+
+ align:start position:0%
+um two parents uh getting a child
+through like artificial insemination or
+
+ align:start position:0%
+through like artificial insemination or
+ 
+
+ align:start position:0%
+through like artificial insemination or
+things like that I mean no one questions
+
+ align:start position:0%
+things like that I mean no one questions
+ 
+
+ align:start position:0%
+things like that I mean no one questions
+the fact when that child grows up that
+
+ align:start position:0%
+the fact when that child grows up that
+ 
+
+ align:start position:0%
+the fact when that child grows up that
+those are her parents and that that is
+
+ align:start position:0%
+those are her parents and that that is
+ 
+
+ align:start position:0%
+those are her parents and that that is
+the family and that is the home where
+
+ align:start position:0%
+the family and that is the home where
+ 
+
+ align:start position:0%
+the family and that is the home where
+the child will be accepted back into and
+
+ align:start position:0%
+the child will be accepted back into and
+ 
+
+ align:start position:0%
+the child will be accepted back into and
+I mean even the same with you know
+
+ align:start position:0%
+I mean even the same with you know
+ 
+
+ align:start position:0%
+I mean even the same with you know
+divorced parents and single families and
+
+ align:start position:0%
+divorced parents and single families and
+ 
+
+ align:start position:0%
+divorced parents and single families and
+things like that those are pretty much
+
+ align:start position:0%
+things like that those are pretty much
+ 
+
+ align:start position:0%
+things like that those are pretty much
+completely accepted everywhere in
+
+ align:start position:0%
+completely accepted everywhere in
+ 
+
+ align:start position:0%
+completely accepted everywhere in
+America everywhere in America but
+
+ align:start position:0%
+America everywhere in America but
+ 
+
+ align:start position:0%
+America everywhere in America but
+America is not represent reprentative
+
+ align:start position:0%
+America is not represent reprentative
+ 
+
+ align:start position:0%
+America is not represent reprentative
+even of the western world and if you
+
+ align:start position:0%
+even of the western world and if you
+ 
+
+ align:start position:0%
+even of the western world and if you
+bring in the Eastern world or you know
+
+ align:start position:0%
+bring in the Eastern world or you know
+ 
+
+ align:start position:0%
+bring in the Eastern world or you know
+Middle Eastern world uh the Third World
+
+ align:start position:0%
+Middle Eastern world uh the Third World
+ 
+
+ align:start position:0%
+Middle Eastern world uh the Third World
+um their idea of a family is very
+
+ align:start position:0%
+um their idea of a family is very
+ 
+
+ align:start position:0%
+um their idea of a family is very
+different such that um if u a young lady
+
+ align:start position:0%
+different such that um if u a young lady
+ 
+
+ align:start position:0%
+different such that um if u a young lady
+a daughter wants to marry somebody that
+
+ align:start position:0%
+a daughter wants to marry somebody that
+ 
+
+ align:start position:0%
+a daughter wants to marry somebody that
+the family don't approve of she won't
+
+ align:start position:0%
+the family don't approve of she won't
+ 
+
+ align:start position:0%
+the family don't approve of she won't
+marry him that she has to marry for
+
+ align:start position:0%
+marry him that she has to marry for
+ 
+
+ align:start position:0%
+marry him that she has to marry for
+reasons that are acceptable to the
+
+ align:start position:0%
+reasons that are acceptable to the
+ 
+
+ align:start position:0%
+reasons that are acceptable to the
+family and in the Middle Ages um Mar
+
+ align:start position:0%
+family and in the Middle Ages um Mar
+ 
+
+ align:start position:0%
+family and in the Middle Ages um Mar
+marage was strictly con
+
+ align:start position:0%
+marage was strictly con
+ 
+
+ align:start position:0%
+marage was strictly con
+controlled by the family and that meant
+
+ align:start position:0%
+controlled by the family and that meant
+ 
+
+ align:start position:0%
+controlled by the family and that meant
+for political and economic benefit to
+
+ align:start position:0%
+for political and economic benefit to
+ 
+
+ align:start position:0%
+for political and economic benefit to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+family and you know in ruling classes
+
+ align:start position:0%
+family and you know in ruling classes
+ 
+
+ align:start position:0%
+family and you know in ruling classes
+and royalty uh even now among the few
+
+ align:start position:0%
+and royalty uh even now among the few
+ 
+
+ align:start position:0%
+and royalty uh even now among the few
+remaining countries that have Royals uh
+
+ align:start position:0%
+remaining countries that have Royals uh
+ 
+
+ align:start position:0%
+remaining countries that have Royals uh
+they marry not purely out of love and
+
+ align:start position:0%
+they marry not purely out of love and
+ 
+
+ align:start position:0%
+they marry not purely out of love and
+sometimes not out of love at all but
+
+ align:start position:0%
+sometimes not out of love at all but
+ 
+
+ align:start position:0%
+sometimes not out of love at all but
+because it makes sense in terms of the
+
+ align:start position:0%
+because it makes sense in terms of the
+ 
+
+ align:start position:0%
+because it makes sense in terms of the
+family so there's a very different
+
+ align:start position:0%
+family so there's a very different
+ 
+
+ align:start position:0%
+family so there's a very different
+conception from what exists in the
+
+ align:start position:0%
+conception from what exists in the
+ 
+
+ align:start position:0%
+conception from what exists in the
+United
+
+ align:start position:0%
+United
+ 
+
+ align:start position:0%
+United
+States but I guess I was just trying to
+
+ align:start position:0%
+States but I guess I was just trying to
+ 
+
+ align:start position:0%
+States but I guess I was just trying to
+say that the conception of family in the
+
+ align:start position:0%
+say that the conception of family in the
+ 
+
+ align:start position:0%
+say that the conception of family in the
+United States is what's going to control
+
+ align:start position:0%
+United States is what's going to control
+ 
+
+ align:start position:0%
+United States is what's going to control
+the acceptance of homosexual families
+
+ align:start position:0%
+the acceptance of homosexual families
+ 
+
+ align:start position:0%
+the acceptance of homosexual families
+here and I think we're already leaning
+
+ align:start position:0%
+here and I think we're already leaning
+ 
+
+ align:start position:0%
+here and I think we're already leaning
+more towards that acceptance based on
+
+ align:start position:0%
+more towards that acceptance based on
+ 
+
+ align:start position:0%
+more towards that acceptance based on
+the radical changes in what we've seen
+
+ align:start position:0%
+the radical changes in what we've seen
+ 
+
+ align:start position:0%
+the radical changes in what we've seen
+in families just since I mean the 1950s
+
+ align:start position:0%
+in families just since I mean the 1950s
+ 
+
+ align:start position:0%
+in families just since I mean the 1950s
+I disagree I don't think it's going to
+
+ align:start position:0%
+I disagree I don't think it's going to
+ 
+
+ align:start position:0%
+I disagree I don't think it's going to
+be the family I think it's more just
+
+ align:start position:0%
+be the family I think it's more just
+ 
+
+ align:start position:0%
+be the family I think it's more just
+going to be acceptance of the homosexual
+
+ align:start position:0%
+going to be acceptance of the homosexual
+ 
+
+ align:start position:0%
+going to be acceptance of the homosexual
+in a religious context no but I mean as
+
+ align:start position:0%
+in a religious context no but I mean as
+ 
+
+ align:start position:0%
+in a religious context no but I mean as
+far as taking in accept
+
+ align:start position:0%
+far as taking in accept
+ 
+
+ align:start position:0%
+far as taking in accept
+family sheans yeah I mean as far as
+
+ align:start position:0%
+family sheans yeah I mean as far as
+ 
+
+ align:start position:0%
+family sheans yeah I mean as far as
+taking in like the idea that they can
+
+ align:start position:0%
+taking in like the idea that they can
+ 
+
+ align:start position:0%
+taking in like the idea that they can
+get the other rights that a family would
+
+ align:start position:0%
+get the other rights that a family would
+ 
+
+ align:start position:0%
+get the other rights that a family would
+have once we've I mean obviously gotten
+
+ align:start position:0%
+have once we've I mean obviously gotten
+ 
+
+ align:start position:0%
+have once we've I mean obviously gotten
+past that so what do you think is going
+
+ align:start position:0%
+past that so what do you think is going
+ 
+
+ align:start position:0%
+past that so what do you think is going
+to be the key because I mean we already
+
+ align:start position:0%
+to be the key because I mean we already
+ 
+
+ align:start position:0%
+to be the key because I mean we already
+have had to say basically that to an
+
+ align:start position:0%
+have had to say basically that to an
+ 
+
+ align:start position:0%
+have had to say basically that to an
+extent we legally accept homosexuality
+
+ align:start position:0%
+extent we legally accept homosexuality
+ 
+
+ align:start position:0%
+extent we legally accept homosexuality
+so now it's whether or not that uh
+
+ align:start position:0%
+so now it's whether or not that uh
+ 
+
+ align:start position:0%
+so now it's whether or not that uh
+acceptance that we've taken is really
+
+ align:start position:0%
+acceptance that we've taken is really
+ 
+
+ align:start position:0%
+acceptance that we've taken is really
+going to be allowed to go a step further
+
+ align:start position:0%
+going to be allowed to go a step further
+ 
+
+ align:start position:0%
+going to be allowed to go a step further
+to create the family through marriage so
+
+ align:start position:0%
+to create the family through marriage so
+ 
+
+ align:start position:0%
+to create the family through marriage so
+that's a legal acceptance though it
+
+ align:start position:0%
+that's a legal acceptance though it
+ 
+
+ align:start position:0%
+that's a legal acceptance though it
+wasn't a religious well I think it's
+
+ align:start position:0%
+wasn't a religious well I think it's
+ 
+
+ align:start position:0%
+wasn't a religious well I think it's
+it's mostly opposition comes from
+
+ align:start position:0%
+it's mostly opposition comes from
+ 
+
+ align:start position:0%
+it's mostly opposition comes from
+religion when people voice their
+
+ align:start position:0%
+religion when people voice their
+ 
+
+ align:start position:0%
+religion when people voice their
+opinions it's more religious groups that
+
+ align:start position:0%
+opinions it's more religious groups that
+ 
+
+ align:start position:0%
+opinions it's more religious groups that
+uh oppose it in such a grand way thus
+
+ align:start position:0%
+uh oppose it in such a grand way thus
+ 
+
+ align:start position:0%
+uh oppose it in such a grand way thus
+that the voters will you know later
+
+ align:start position:0%
+that the voters will you know later
+ 
+
+ align:start position:0%
+that the voters will you know later
+control what uh Congressman go way the
+
+ align:start position:0%
+control what uh Congressman go way the
+ 
+
+ align:start position:0%
+control what uh Congressman go way the
+congressman go because they want to be
+
+ align:start position:0%
+congressman go because they want to be
+ 
+
+ align:start position:0%
+congressman go because they want to be
+reelected so a strong religious group
+
+ align:start position:0%
+reelected so a strong religious group
+ 
+
+ align:start position:0%
+reelected so a strong religious group
+that has numbers is going to more
+
+ align:start position:0%
+that has numbers is going to more
+ 
+
+ align:start position:0%
+that has numbers is going to more
+control where that goes I think
+
+ align:start position:0%
+control where that goes I think
+ 
+
+ align:start position:0%
+control where that goes I think
+politically like George W bush can't say
+
+ align:start position:0%
+politically like George W bush can't say
+ 
+
+ align:start position:0%
+politically like George W bush can't say
+you know I I I don't want homosexual
+
+ align:start position:0%
+you know I I I don't want homosexual
+ 
+
+ align:start position:0%
+you know I I I don't want homosexual
+marriage because like I don't think like
+
+ align:start position:0%
+marriage because like I don't think like
+ 
+
+ align:start position:0%
+marriage because like I don't think like
+homosexuals should be able to marry
+
+ align:start position:0%
+homosexuals should be able to marry
+ 
+
+ align:start position:0%
+homosexuals should be able to marry
+because like I don't like homosexuals he
+
+ align:start position:0%
+because like I don't like homosexuals he
+ 
+
+ align:start position:0%
+because like I don't like homosexuals he
+can't say that so like what he has to
+
+ align:start position:0%
+can't say that so like what he has to
+ 
+
+ align:start position:0%
+can't say that so like what he has to
+say is that you know it's bad for
+
+ align:start position:0%
+say is that you know it's bad for
+ 
+
+ align:start position:0%
+say is that you know it's bad for
+society as a whole and the way he says
+
+ align:start position:0%
+society as a whole and the way he says
+ 
+
+ align:start position:0%
+society as a whole and the way he says
+that is because it's bad for the family
+
+ align:start position:0%
+that is because it's bad for the family
+ 
+
+ align:start position:0%
+that is because it's bad for the family
+um so I mean I I think it's I think like
+
+ align:start position:0%
+um so I mean I I think it's I think like
+ 
+
+ align:start position:0%
+um so I mean I I think it's I think like
+you you have a point about the the
+
+ align:start position:0%
+you you have a point about the the
+ 
+
+ align:start position:0%
+you you have a point about the the
+source of the problem is religious
+
+ align:start position:0%
+source of the problem is religious
+ 
+
+ align:start position:0%
+source of the problem is religious
+acceptance but I think from a practical
+
+ align:start position:0%
+acceptance but I think from a practical
+ 
+
+ align:start position:0%
+acceptance but I think from a practical
+and political standpoint like very much
+
+ align:start position:0%
+and political standpoint like very much
+ 
+
+ align:start position:0%
+and political standpoint like very much
+the family is very deeply inclined with
+
+ align:start position:0%
+the family is very deeply inclined with
+ 
+
+ align:start position:0%
+the family is very deeply inclined with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+issue um incident speaking of bush
+
+ align:start position:0%
+issue um incident speaking of bush
+ 
+
+ align:start position:0%
+issue um incident speaking of bush
+Carrie attitude is a kind of
+
+ align:start position:0%
+Carrie attitude is a kind of
+ 
+
+ align:start position:0%
+Carrie attitude is a kind of
+compromise um he doesn't want to
+
+ align:start position:0%
+compromise um he doesn't want to
+ 
+
+ align:start position:0%
+compromise um he doesn't want to
+alienate religious people and maybe not
+
+ align:start position:0%
+alienate religious people and maybe not
+ 
+
+ align:start position:0%
+alienate religious people and maybe not
+even the Catholic following that uh he
+
+ align:start position:0%
+even the Catholic following that uh he
+ 
+
+ align:start position:0%
+even the Catholic following that uh he
+inherits because he's Catholic um so
+
+ align:start position:0%
+inherits because he's Catholic um so
+ 
+
+ align:start position:0%
+inherits because he's Catholic um so
+when he was asked he said no he doesn't
+
+ align:start position:0%
+when he was asked he said no he doesn't
+ 
+
+ align:start position:0%
+when he was asked he said no he doesn't
+believe in uh in um homosexual gay
+
+ align:start position:0%
+believe in uh in um homosexual gay
+ 
+
+ align:start position:0%
+believe in uh in um homosexual gay
+marriage because the church is against
+
+ align:start position:0%
+marriage because the church is against
+ 
+
+ align:start position:0%
+marriage because the church is against
+it um but he does believe in civil
+
+ align:start position:0%
+it um but he does believe in civil
+ 
+
+ align:start position:0%
+it um but he does believe in civil
+unions right so that's a way of not
+
+ align:start position:0%
+unions right so that's a way of not
+ 
+
+ align:start position:0%
+unions right so that's a way of not
+entirely alienating the gay
+
+ align:start position:0%
+entirely alienating the gay
+ 
+
+ align:start position:0%
+entirely alienating the gay
+voters in while he's also trying to hold
+
+ align:start position:0%
+voters in while he's also trying to hold
+ 
+
+ align:start position:0%
+voters in while he's also trying to hold
+on to the religious one well that's a
+
+ align:start position:0%
+on to the religious one well that's a
+ 
+
+ align:start position:0%
+on to the religious one well that's a
+kind of compromise um bush is more
+
+ align:start position:0%
+kind of compromise um bush is more
+ 
+
+ align:start position:0%
+kind of compromise um bush is more
+extreme he doesn't want
+
+ align:start position:0%
+extreme he doesn't want
+ 
+
+ align:start position:0%
+extreme he doesn't want
+uh gay marriage and I'm sure he doesn't
+
+ align:start position:0%
+uh gay marriage and I'm sure he doesn't
+ 
+
+ align:start position:0%
+uh gay marriage and I'm sure he doesn't
+want civil union or if he does he's not
+
+ align:start position:0%
+want civil union or if he does he's not
+ 
+
+ align:start position:0%
+want civil union or if he does he's not
+going to say it um and he brings in the
+
+ align:start position:0%
+going to say it um and he brings in the
+ 
+
+ align:start position:0%
+going to say it um and he brings in the
+idea of the family and that's just a
+
+ align:start position:0%
+idea of the family and that's just a
+ 
+
+ align:start position:0%
+idea of the family and that's just a
+sheer
+
+ align:start position:0%
+sheer
+ 
+
+ align:start position:0%
+sheer
+confusion didn't Cheney said that he
+
+ align:start position:0%
+confusion didn't Cheney said that he
+ 
+
+ align:start position:0%
+confusion didn't Cheney said that he
+would be Pro marriage anyway he came has
+
+ align:start position:0%
+would be Pro marriage anyway he came has
+ 
+
+ align:start position:0%
+would be Pro marriage anyway he came has
+a gay daughter yeah and he came out in
+
+ align:start position:0%
+a gay daughter yeah and he came out in
+ 
+
+ align:start position:0%
+a gay daughter yeah and he came out in
+opposition to the President right so
+
+ align:start position:0%
+opposition to the President right so
+ 
+
+ align:start position:0%
+opposition to the President right so
+wouldn't that I mean but previously he
+
+ align:start position:0%
+wouldn't that I mean but previously he
+ 
+
+ align:start position:0%
+wouldn't that I mean but previously he
+hadn't hadn't said anything like that
+
+ align:start position:0%
+hadn't hadn't said anything like that
+ 
+
+ align:start position:0%
+hadn't hadn't said anything like that
+right so like wouldn't that just I guess
+
+ align:start position:0%
+right so like wouldn't that just I guess
+ 
+
+ align:start position:0%
+right so like wouldn't that just I guess
+the political machine like I guess if
+
+ align:start position:0%
+the political machine like I guess if
+ 
+
+ align:start position:0%
+the political machine like I guess if
+they know that Cheney is like totally
+
+ align:start position:0%
+they know that Cheney is like totally
+ 
+
+ align:start position:0%
+they know that Cheney is like totally
+Pro the whole marriage thing like the
+
+ align:start position:0%
+Pro the whole marriage thing like the
+ 
+
+ align:start position:0%
+Pro the whole marriage thing like the
+whole I think K might have to change his
+
+ align:start position:0%
+whole I think K might have to change his
+ 
+
+ align:start position:0%
+whole I think K might have to change his
+St just oh you think this might hurt
+
+ align:start position:0%
+St just oh you think this might hurt
+ 
+
+ align:start position:0%
+St just oh you think this might hurt
+Bush's chances because I think it might
+
+ align:start position:0%
+Bush's chances because I think it might
+ 
+
+ align:start position:0%
+Bush's chances because I think it might
+help Bush's chances just no but what if
+
+ align:start position:0%
+help Bush's chances just no but what if
+ 
+
+ align:start position:0%
+help Bush's chances just no but what if
+Bush dies and then Cheney comes
+
+ align:start position:0%
+Bush dies and then Cheney comes
+ 
+
+ align:start position:0%
+Bush dies and then Cheney comes
+in and permits gay marriages no I just
+
+ align:start position:0%
+in and permits gay marriages no I just
+ 
+
+ align:start position:0%
+in and permits gay marriages no I just
+think that um no I'm just this he his
+
+ align:start position:0%
+think that um no I'm just this he his
+ 
+
+ align:start position:0%
+think that um no I'm just this he his
+wife his wife and daughter uh who are
+
+ align:start position:0%
+wife his wife and daughter uh who are
+ 
+
+ align:start position:0%
+wife his wife and daughter uh who are
+par both are of course in favor of gay
+
+ align:start position:0%
+par both are of course in favor of gay
+ 
+
+ align:start position:0%
+par both are of course in favor of gay
+marriages um I mean the daughter would
+
+ align:start position:0%
+marriages um I mean the daughter would
+ 
+
+ align:start position:0%
+marriages um I mean the daughter would
+be but apparently his wife was before he
+
+ align:start position:0%
+be but apparently his wife was before he
+ 
+
+ align:start position:0%
+be but apparently his wife was before he
+made his view public they gang up on him
+
+ align:start position:0%
+made his view public they gang up on him
+ 
+
+ align:start position:0%
+made his view public they gang up on him
+and he ends up supporting gay marriage
+
+ align:start position:0%
+and he ends up supporting gay marriage
+ 
+
+ align:start position:0%
+and he ends up supporting gay marriage
+so you would think people with a little
+
+ align:start position:0%
+so you would think people with a little
+ 
+
+ align:start position:0%
+so you would think people with a little
+foresight might worry about that I think
+
+ align:start position:0%
+foresight might worry about that I think
+ 
+
+ align:start position:0%
+foresight might worry about that I think
+like anybody who's like very like
+
+ align:start position:0%
+like anybody who's like very like
+ 
+
+ align:start position:0%
+like anybody who's like very like
+religiously inclined might worry about
+
+ align:start position:0%
+religiously inclined might worry about
+ 
+
+ align:start position:0%
+religiously inclined might worry about
+the whole like cheny thing but people
+
+ align:start position:0%
+the whole like cheny thing but people
+ 
+
+ align:start position:0%
+the whole like cheny thing but people
+that are trying to look for a happy
+
+ align:start position:0%
+that are trying to look for a happy
+ 
+
+ align:start position:0%
+that are trying to look for a happy
+medium might just go for the bush chainy
+
+ align:start position:0%
+medium might just go for the bush chainy
+ 
+
+ align:start position:0%
+medium might just go for the bush chainy
+combination because if they need to
+
+ align:start position:0%
+combination because if they need to
+ 
+
+ align:start position:0%
+combination because if they need to
+agree like if they both come into power
+
+ align:start position:0%
+agree like if they both come into power
+ 
+
+ align:start position:0%
+agree like if they both come into power
+they're going to have to like talk it
+
+ align:start position:0%
+they're going to have to like talk it
+ 
+
+ align:start position:0%
+they're going to have to like talk it
+out and they're going to be the ones
+
+ align:start position:0%
+out and they're going to be the ones
+ 
+
+ align:start position:0%
+out and they're going to be the ones
+that are going to be putting the
+
+ align:start position:0%
+that are going to be putting the
+ 
+
+ align:start position:0%
+that are going to be putting the
+foundation of like what's going to
+
+ align:start position:0%
+foundation of like what's going to
+ 
+
+ align:start position:0%
+foundation of like what's going to
+actually happen I don't know technically
+
+ align:start position:0%
+actually happen I don't know technically
+ 
+
+ align:start position:0%
+actually happen I don't know technically
+technically well yeah it's another kind
+
+ align:start position:0%
+technically well yeah it's another kind
+ 
+
+ align:start position:0%
+technically well yeah it's another kind
+of compromise a different kind from
+
+ align:start position:0%
+of compromise a different kind from
+ 
+
+ align:start position:0%
+of compromise a different kind from
+Terri's that's true jie has power over
+
+ align:start position:0%
+Terri's that's true jie has power over
+ 
+
+ align:start position:0%
+Terri's that's true jie has power over
+other things but over game marriage
+
+ align:start position:0%
+other things but over game marriage
+ 
+
+ align:start position:0%
+other things but over game marriage
+probably you know I mean I think it's
+
+ align:start position:0%
+probably you know I mean I think it's
+ 
+
+ align:start position:0%
+probably you know I mean I think it's
+really interesting right that dick CH is
+
+ align:start position:0%
+really interesting right that dick CH is
+ 
+
+ align:start position:0%
+really interesting right that dick CH is
+one of the most like Infamous Darth
+
+ align:start position:0%
+one of the most like Infamous Darth
+ 
+
+ align:start position:0%
+one of the most like Infamous Darth
+Vader rightwing Hawks there is right and
+
+ align:start position:0%
+Vader rightwing Hawks there is right and
+ 
+
+ align:start position:0%
+Vader rightwing Hawks there is right and
+yet when it comes to this issue when it
+
+ align:start position:0%
+yet when it comes to this issue when it
+ 
+
+ align:start position:0%
+yet when it comes to this issue when it
+really personally affects him right he's
+
+ align:start position:0%
+really personally affects him right he's
+ 
+
+ align:start position:0%
+really personally affects him right he's
+he's way on the other side of the issue
+
+ align:start position:0%
+he's way on the other side of the issue
+ 
+
+ align:start position:0%
+he's way on the other side of the issue
+right I mean I I I just think that
+
+ align:start position:0%
+right I mean I I I just think that
+ 
+
+ align:start position:0%
+right I mean I I I just think that
+that's really interesting and you know
+
+ align:start position:0%
+that's really interesting and you know
+ 
+
+ align:start position:0%
+that's really interesting and you know
+an interesting way to think about a lot
+
+ align:start position:0%
+an interesting way to think about a lot
+ 
+
+ align:start position:0%
+an interesting way to think about a lot
+of issues like when people try to you
+
+ align:start position:0%
+of issues like when people try to you
+ 
+
+ align:start position:0%
+of issues like when people try to you
+know have have these really really
+
+ align:start position:0%
+know have have these really really
+ 
+
+ align:start position:0%
+know have have these really really
+conservative views on them you know how
+
+ align:start position:0%
+conservative views on them you know how
+ 
+
+ align:start position:0%
+conservative views on them you know how
+many of them are are really personally
+
+ align:start position:0%
+many of them are are really personally
+ 
+
+ align:start position:0%
+many of them are are really personally
+affected by but n's view is that this
+
+ align:start position:0%
+affected by but n's view is that this
+ 
+
+ align:start position:0%
+affected by but n's view is that this
+might be a shrewd political compromise
+
+ align:start position:0%
+might be a shrewd political compromise
+ 
+
+ align:start position:0%
+might be a shrewd political compromise
+so that people who want to be rep
+
+ align:start position:0%
+so that people who want to be rep
+ 
+
+ align:start position:0%
+so that people who want to be rep
+Republican can always point to Bush if
+
+ align:start position:0%
+Republican can always point to Bush if
+ 
+
+ align:start position:0%
+Republican can always point to Bush if
+they're against day marriage and if they
+
+ align:start position:0%
+they're against day marriage and if they
+ 
+
+ align:start position:0%
+they're against day marriage and if they
+want to be Republican but are for gay
+
+ align:start position:0%
+want to be Republican but are for gay
+ 
+
+ align:start position:0%
+want to be Republican but are for gay
+marriage they can always point to Cheney
+
+ align:start position:0%
+marriage they can always point to Cheney
+ 
+
+ align:start position:0%
+marriage they can always point to Cheney
+I think that that might be right it's
+
+ align:start position:0%
+I think that that might be right it's
+ 
+
+ align:start position:0%
+I think that that might be right it's
+like talking out of both sides of your
+
+ align:start position:0%
+like talking out of both sides of your
+ 
+
+ align:start position:0%
+like talking out of both sides of your
+mouth right I I I think which
+
+ align:start position:0%
+mouth right I I I think which
+ 
+
+ align:start position:0%
+mouth right I I I think which
+politicians do very of politicians do
+
+ align:start position:0%
+politicians do very of politicians do
+ 
+
+ align:start position:0%
+politicians do very of politicians do
+very regularly that should be the reason
+
+ align:start position:0%
+very regularly that should be the reason
+ 
+
+ align:start position:0%
+very regularly that should be the reason
+well in a normal if people if follow PE
+
+ align:start position:0%
+well in a normal if people if follow PE
+ 
+
+ align:start position:0%
+well in a normal if people if follow PE
+voters logic was normal I think they
+
+ align:start position:0%
+voters logic was normal I think they
+ 
+
+ align:start position:0%
+voters logic was normal I think they
+would that should be a bad thing cuz it
+
+ align:start position:0%
+would that should be a bad thing cuz it
+ 
+
+ align:start position:0%
+would that should be a bad thing cuz it
+shows that they have a double standard
+
+ align:start position:0%
+shows that they have a double standard
+ 
+
+ align:start position:0%
+shows that they have a double standard
+and that they disagree with something
+
+ align:start position:0%
+and that they disagree with something
+ 
+
+ align:start position:0%
+and that they disagree with something
+unless it affects them obviously if
+
+ align:start position:0%
+unless it affects them obviously if
+ 
+
+ align:start position:0%
+unless it affects them obviously if
+busha suddenly was left paralyzed he
+
+ align:start position:0%
+busha suddenly was left paralyzed he
+ 
+
+ align:start position:0%
+busha suddenly was left paralyzed he
+would be all for stemell research you
+
+ align:start position:0%
+would be all for stemell research you
+ 
+
+ align:start position:0%
+would be all for stemell research you
+know but I think we diverted from our
+
+ align:start position:0%
+know but I think we diverted from our
+ 
+
+ align:start position:0%
+know but I think we diverted from our
+topic
+
+ align:start position:0%
+topic
+ 
+
+ align:start position:0%
+topic
+yeah why don't we take a break and
+
+ align:start position:0%
+yeah why don't we take a break and
+ 
+
+ align:start position:0%
+yeah why don't we take a break and
+afterwards um Veronica will give a
+
+ align:start position:0%
+afterwards um Veronica will give a
+ 
+
+ align:start position:0%
+afterwards um Veronica will give a
+presentation on the pursuit of
+
+ align:start position:0%
+presentation on the pursuit of
+ 
+
+ align:start position:0%
+presentation on the pursuit of
+love right don't stay away long five
+
+ align:start position:0%
+love right don't stay away long five
+ 
+
+ align:start position:0%
+love right don't stay away long five
+minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I kind of wanted to start with
+
+ align:start position:0%
+what I kind of wanted to start with
+ 
+
+ align:start position:0%
+what I kind of wanted to start with
+oh you did indeed um what I kind of
+
+ align:start position:0%
+oh you did indeed um what I kind of
+ 
+
+ align:start position:0%
+oh you did indeed um what I kind of
+wanted to start with was what uh the
+
+ align:start position:0%
+wanted to start with was what uh the
+ 
+
+ align:start position:0%
+wanted to start with was what uh the
+chapter that interested me most which
+
+ align:start position:0%
+chapter that interested me most which
+ 
+
+ align:start position:0%
+chapter that interested me most which
+was uh the chapter the two myths about
+
+ align:start position:0%
+was uh the chapter the two myths about
+ 
+
+ align:start position:0%
+was uh the chapter the two myths about
+love MH uh which basically dealt with uh
+
+ align:start position:0%
+love MH uh which basically dealt with uh
+ 
+
+ align:start position:0%
+love MH uh which basically dealt with uh
+the first myth with uh had to do about
+
+ align:start position:0%
+the first myth with uh had to do about
+ 
+
+ align:start position:0%
+the first myth with uh had to do about
+love basically being a universal thing
+
+ align:start position:0%
+love basically being a universal thing
+ 
+
+ align:start position:0%
+love basically being a universal thing
+that you feel uh just because we're
+
+ align:start position:0%
+that you feel uh just because we're
+ 
+
+ align:start position:0%
+that you feel uh just because we're
+humans and that it's
+
+ align:start position:0%
+humans and that it's
+ 
+
+ align:start position:0%
+humans and that it's
+explains the reason for our existence
+
+ align:start position:0%
+explains the reason for our existence
+ 
+
+ align:start position:0%
+explains the reason for our existence
+and the way that we always are and then
+
+ align:start position:0%
+and the way that we always are and then
+ 
+
+ align:start position:0%
+and the way that we always are and then
+the second myth with the idea that
+
+ align:start position:0%
+the second myth with the idea that
+ 
+
+ align:start position:0%
+the second myth with the idea that
+um love brings about a merging of two
+
+ align:start position:0%
+um love brings about a merging of two
+ 
+
+ align:start position:0%
+um love brings about a merging of two
+identities and that two people become
+
+ align:start position:0%
+identities and that two people become
+ 
+
+ align:start position:0%
+identities and that two people become
+like one and form a union and um I guess
+
+ align:start position:0%
+like one and form a union and um I guess
+ 
+
+ align:start position:0%
+like one and form a union and um I guess
+that kind of summarizes the two main
+
+ align:start position:0%
+that kind of summarizes the two main
+ 
+
+ align:start position:0%
+that kind of summarizes the two main
+ideas that are being opposed I guess
+
+ align:start position:0%
+ideas that are being opposed I guess
+ 
+
+ align:start position:0%
+ideas that are being opposed I guess
+generally Throughout the chapter what do
+
+ align:start position:0%
+generally Throughout the chapter what do
+ 
+
+ align:start position:0%
+generally Throughout the chapter what do
+you think about
+
+ align:start position:0%
+you think about
+ 
+
+ align:start position:0%
+you think about
+those with the second I'll start with
+
+ align:start position:0%
+those with the second I'll start with
+ 
+
+ align:start position:0%
+those with the second I'll start with
+the second one because I have kind of
+
+ align:start position:0%
+the second one because I have kind of
+ 
+
+ align:start position:0%
+the second one because I have kind of
+more cont like ideas against the first
+
+ align:start position:0%
+more cont like ideas against the first
+ 
+
+ align:start position:0%
+more cont like ideas against the first
+but with the second one I think I
+
+ align:start position:0%
+but with the second one I think I
+ 
+
+ align:start position:0%
+but with the second one I think I
+generally agree with the idea that two
+
+ align:start position:0%
+generally agree with the idea that two
+ 
+
+ align:start position:0%
+generally agree with the idea that two
+people still remain independent after
+
+ align:start position:0%
+people still remain independent after
+ 
+
+ align:start position:0%
+people still remain independent after
+they feel after they fall in love or
+
+ align:start position:0%
+they feel after they fall in love or
+ 
+
+ align:start position:0%
+they feel after they fall in love or
+whatever happens and that there's not
+
+ align:start position:0%
+whatever happens and that there's not
+ 
+
+ align:start position:0%
+whatever happens and that there's not
+exactly any type of merging because you
+
+ align:start position:0%
+exactly any type of merging because you
+ 
+
+ align:start position:0%
+exactly any type of merging because you
+still are your own person with your own
+
+ align:start position:0%
+still are your own person with your own
+ 
+
+ align:start position:0%
+still are your own person with your own
+ideas and I think
+
+ align:start position:0%
+ideas and I think
+ 
+
+ align:start position:0%
+ideas and I think
+the the term interdependence does more
+
+ align:start position:0%
+the the term interdependence does more
+ 
+
+ align:start position:0%
+the the term interdependence does more
+greatly qualify The
+
+ align:start position:0%
+greatly qualify The
+ 
+
+ align:start position:0%
+greatly qualify The
+Experience however you do say
+
+ align:start position:0%
+Experience however you do say
+ 
+
+ align:start position:0%
+Experience however you do say
+that you still that there is no creation
+
+ align:start position:0%
+that you still that there is no creation
+ 
+
+ align:start position:0%
+that you still that there is no creation
+of a new self or of a new
+
+ align:start position:0%
+of a new self or of a new
+ 
+
+ align:start position:0%
+of a new self or of a new
+person and maybe I'm just not
+
+ align:start position:0%
+person and maybe I'm just not
+ 
+
+ align:start position:0%
+person and maybe I'm just not
+understanding exactly in what way you
+
+ align:start position:0%
+understanding exactly in what way you
+ 
+
+ align:start position:0%
+understanding exactly in what way you
+mean that but I feel like most people
+
+ align:start position:0%
+mean that but I feel like most people
+ 
+
+ align:start position:0%
+mean that but I feel like most people
+who have been in any sort of long-term
+
+ align:start position:0%
+who have been in any sort of long-term
+ 
+
+ align:start position:0%
+who have been in any sort of long-term
+relationship or married or anything like
+
+ align:start position:0%
+relationship or married or anything like
+ 
+
+ align:start position:0%
+relationship or married or anything like
+that would say that they have changed as
+
+ align:start position:0%
+that would say that they have changed as
+ 
+
+ align:start position:0%
+that would say that they have changed as
+a result of their experiences and that
+
+ align:start position:0%
+a result of their experiences and that
+ 
+
+ align:start position:0%
+a result of their experiences and that
+you do act in way way that you wouldn't
+
+ align:start position:0%
+you do act in way way that you wouldn't
+ 
+
+ align:start position:0%
+you do act in way way that you wouldn't
+if you hadn't been in that relationship
+
+ align:start position:0%
+if you hadn't been in that relationship
+ 
+
+ align:start position:0%
+if you hadn't been in that relationship
+and you although you do make your own
+
+ align:start position:0%
+and you although you do make your own
+ 
+
+ align:start position:0%
+and you although you do make your own
+decisions and form your own opinions you
+
+ align:start position:0%
+decisions and form your own opinions you
+ 
+
+ align:start position:0%
+decisions and form your own opinions you
+do so so greatly based on the situation
+
+ align:start position:0%
+do so so greatly based on the situation
+ 
+
+ align:start position:0%
+do so so greatly based on the situation
+that you're in that you are different
+
+ align:start position:0%
+that you're in that you are different
+ 
+
+ align:start position:0%
+that you're in that you are different
+cuz if at that moment in time you were
+
+ align:start position:0%
+cuz if at that moment in time you were
+ 
+
+ align:start position:0%
+cuz if at that moment in time you were
+single or you know something else you
+
+ align:start position:0%
+single or you know something else you
+ 
+
+ align:start position:0%
+single or you know something else you
+would not be acting in that way notice
+
+ align:start position:0%
+would not be acting in that way notice
+ 
+
+ align:start position:0%
+would not be acting in that way notice
+that you you're now are talking about a
+
+ align:start position:0%
+that you you're now are talking about a
+ 
+
+ align:start position:0%
+that you you're now are talking about a
+change having happened and I don't deny
+
+ align:start position:0%
+change having happened and I don't deny
+ 
+
+ align:start position:0%
+change having happened and I don't deny
+that and you're saying that you're you
+
+ align:start position:0%
+that and you're saying that you're you
+ 
+
+ align:start position:0%
+that and you're saying that you're you
+are a different person what I was
+
+ align:start position:0%
+are a different person what I was
+ 
+
+ align:start position:0%
+are a different person what I was
+denying was that there would be a change
+
+ align:start position:0%
+denying was that there would be a change
+ 
+
+ align:start position:0%
+denying was that there would be a change
+of the sort that is built into the
+
+ align:start position:0%
+of the sort that is built into the
+ 
+
+ align:start position:0%
+of the sort that is built into the
+concept of
+
+ align:start position:0%
+concept of
+ 
+
+ align:start position:0%
+concept of
+merging and second that there is a third
+
+ align:start position:0%
+merging and second that there is a third
+ 
+
+ align:start position:0%
+merging and second that there is a third
+person different from the two people who
+
+ align:start position:0%
+person different from the two people who
+ 
+
+ align:start position:0%
+person different from the two people who
+are merging resulting from the
+
+ align:start position:0%
+are merging resulting from the
+ 
+
+ align:start position:0%
+are merging resulting from the
+relationship so that there is a another
+
+ align:start position:0%
+relationship so that there is a another
+ 
+
+ align:start position:0%
+relationship so that there is a another
+self but it isn't as if so that's what
+
+ align:start position:0%
+self but it isn't as if so that's what
+ 
+
+ align:start position:0%
+self but it isn't as if so that's what
+I'm questioning both of that um but but
+
+ align:start position:0%
+I'm questioning both of that um but but
+ 
+
+ align:start position:0%
+I'm questioning both of that um but but
+I don't deny that people change because
+
+ align:start position:0%
+I don't deny that people change because
+ 
+
+ align:start position:0%
+I don't deny that people change because
+of their relationships and that
+
+ align:start position:0%
+of their relationships and that
+ 
+
+ align:start position:0%
+of their relationships and that
+um um they become different cells just
+
+ align:start position:0%
+um um they become different cells just
+ 
+
+ align:start position:0%
+um um they become different cells just
+that they're not part of this new
+
+ align:start position:0%
+that they're not part of this new
+ 
+
+ align:start position:0%
+that they're not part of this new
+supercell so to speak which um is true
+
+ align:start position:0%
+supercell so to speak which um is true
+ 
+
+ align:start position:0%
+supercell so to speak which um is true
+in nature I think I give the example of
+
+ align:start position:0%
+in nature I think I give the example of
+ 
+
+ align:start position:0%
+in nature I think I give the example of
+um sodium chloride making salt or two
+
+ align:start position:0%
+um sodium chloride making salt or two
+ 
+
+ align:start position:0%
+um sodium chloride making salt or two
+rivulets merging in a stream or
+
+ align:start position:0%
+rivulets merging in a stream or
+ 
+
+ align:start position:0%
+rivulets merging in a stream or
+uh a scrambled egg that's a good example
+
+ align:start position:0%
+uh a scrambled egg that's a good example
+ 
+
+ align:start position:0%
+uh a scrambled egg that's a good example
+uh you can't separate the albumen from
+
+ align:start position:0%
+uh you can't separate the albumen from
+ 
+
+ align:start position:0%
+uh you can't separate the albumen from
+the Yoke once it's been scrambled right
+
+ align:start position:0%
+the Yoke once it's been scrambled right
+ 
+
+ align:start position:0%
+the Yoke once it's been scrambled right
+is that what it's like to be in love and
+
+ align:start position:0%
+is that what it's like to be in love and
+ 
+
+ align:start position:0%
+is that what it's like to be in love and
+the answer is yes according to the
+
+ align:start position:0%
+the answer is yes according to the
+ 
+
+ align:start position:0%
+the answer is yes according to the
+Romantic
+
+ align:start position:0%
+Romantic
+ 
+
+ align:start position:0%
+Romantic
+Theory which thinks of love as this
+
+ align:start position:0%
+Theory which thinks of love as this
+ 
+
+ align:start position:0%
+Theory which thinks of love as this
+overwhelming experience in which you are
+
+ align:start position:0%
+overwhelming experience in which you are
+ 
+
+ align:start position:0%
+overwhelming experience in which you are
+taken out of yourself and that I think
+
+ align:start position:0%
+taken out of yourself and that I think
+ 
+
+ align:start position:0%
+taken out of yourself and that I think
+is a very common idea I think it's the
+
+ align:start position:0%
+is a very common idea I think it's the
+ 
+
+ align:start position:0%
+is a very common idea I think it's the
+most common idea and people who somehow
+
+ align:start position:0%
+most common idea and people who somehow
+ 
+
+ align:start position:0%
+most common idea and people who somehow
+don't feel they've merged adequately
+
+ align:start position:0%
+don't feel they've merged adequately
+ 
+
+ align:start position:0%
+don't feel they've merged adequately
+feel they're maybe not really in
+
+ align:start position:0%
+feel they're maybe not really in
+ 
+
+ align:start position:0%
+feel they're maybe not really in
+love uh it's the basis of a great deal
+
+ align:start position:0%
+love uh it's the basis of a great deal
+ 
+
+ align:start position:0%
+love uh it's the basis of a great deal
+of uh philosophy and great art some of
+
+ align:start position:0%
+of uh philosophy and great art some of
+ 
+
+ align:start position:0%
+of uh philosophy and great art some of
+which you are going to be watching in
+
+ align:start position:0%
+which you are going to be watching in
+ 
+
+ align:start position:0%
+which you are going to be watching in
+this class because when we get to 19th
+
+ align:start position:0%
+this class because when we get to 19th
+ 
+
+ align:start position:0%
+this class because when we get to 19th
+century um philosophy of n for instance
+
+ align:start position:0%
+century um philosophy of n for instance
+ 
+
+ align:start position:0%
+century um philosophy of n for instance
+and of Vagner Richard Vagner the opera
+
+ align:start position:0%
+and of Vagner Richard Vagner the opera
+ 
+
+ align:start position:0%
+and of Vagner Richard Vagner the opera
+composer we're going to be we'll watch
+
+ align:start position:0%
+composer we're going to be we'll watch
+ 
+
+ align:start position:0%
+composer we're going to be we'll watch
+um a
+
+ align:start position:0%
+um a
+ 
+
+ align:start position:0%
+um a
+um a documentary about Tristan un's
+
+ align:start position:0%
+um a documentary about Tristan un's
+ 
+
+ align:start position:0%
+um a documentary about Tristan un's
+older vogner's Opera which is all about
+
+ align:start position:0%
+older vogner's Opera which is all about
+ 
+
+ align:start position:0%
+older vogner's Opera which is all about
+merging and the words that they lovers
+
+ align:start position:0%
+merging and the words that they lovers
+ 
+
+ align:start position:0%
+merging and the words that they lovers
+use in their love duet is no more
+
+ align:start position:0%
+use in their love duet is no more
+ 
+
+ align:start position:0%
+use in their love duet is no more
+Tristan no more is isolda uh that th
+
+ align:start position:0%
+Tristan no more is isolda uh that th
+ 
+
+ align:start position:0%
+Tristan no more is isolda uh that th
+those old persons don't exist there is
+
+ align:start position:0%
+those old persons don't exist there is
+ 
+
+ align:start position:0%
+those old persons don't exist there is
+just this new merged Unity that they
+
+ align:start position:0%
+just this new merged Unity that they
+ 
+
+ align:start position:0%
+just this new merged Unity that they
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+become um and that is what I deny that's
+
+ align:start position:0%
+become um and that is what I deny that's
+ 
+
+ align:start position:0%
+become um and that is what I deny that's
+what I claim is not capable in human
+
+ align:start position:0%
+what I claim is not capable in human
+ 
+
+ align:start position:0%
+what I claim is not capable in human
+beings it's capable in rivers and in
+
+ align:start position:0%
+beings it's capable in rivers and in
+ 
+
+ align:start position:0%
+beings it's capable in rivers and in
+chemicals um but not in human beings as
+
+ align:start position:0%
+chemicals um but not in human beings as
+ 
+
+ align:start position:0%
+chemicals um but not in human beings as
+far as the changing is concerned you
+
+ align:start position:0%
+far as the changing is concerned you
+ 
+
+ align:start position:0%
+far as the changing is concerned you
+reminded me of something that a
+
+ align:start position:0%
+reminded me of something that a
+ 
+
+ align:start position:0%
+reminded me of something that a
+professor I had at Harvard used to say
+
+ align:start position:0%
+professor I had at Harvard used to say
+ 
+
+ align:start position:0%
+professor I had at Harvard used to say
+about a man and his dog
+
+ align:start position:0%
+about a man and his dog
+ 
+
+ align:start position:0%
+about a man and his dog
+the man walks the dog every night and um
+
+ align:start position:0%
+the man walks the dog every night and um
+ 
+
+ align:start position:0%
+the man walks the dog every night and um
+they get so bound up together the man
+
+ align:start position:0%
+they get so bound up together the man
+ 
+
+ align:start position:0%
+they get so bound up together the man
+ends up walking like the dog and you
+
+ align:start position:0%
+ends up walking like the dog and you
+ 
+
+ align:start position:0%
+ends up walking like the dog and you
+find this often with married couples who
+
+ align:start position:0%
+find this often with married couples who
+ 
+
+ align:start position:0%
+find this often with married couples who
+have been together a long time and they
+
+ align:start position:0%
+have been together a long time and they
+ 
+
+ align:start position:0%
+have been together a long time and they
+somehow walk the same way and they
+
+ align:start position:0%
+somehow walk the same way and they
+ 
+
+ align:start position:0%
+somehow walk the same way and they
+finish each other's
+
+ align:start position:0%
+finish each other's
+ 
+
+ align:start position:0%
+finish each other's
+sentences um uh they
+
+ align:start position:0%
+sentences um uh they
+ 
+
+ align:start position:0%
+sentences um uh they
+are sharing their being with each other
+
+ align:start position:0%
+are sharing their being with each other
+ 
+
+ align:start position:0%
+are sharing their being with each other
+but it isn't quite emerging because if
+
+ align:start position:0%
+but it isn't quite emerging because if
+ 
+
+ align:start position:0%
+but it isn't quite emerging because if
+that were true uh they would no longer
+
+ align:start position:0%
+that were true uh they would no longer
+ 
+
+ align:start position:0%
+that were true uh they would no longer
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+persons and the with other animals even
+
+ align:start position:0%
+persons and the with other animals even
+ 
+
+ align:start position:0%
+persons and the with other animals even
+though we get very close to them they're
+
+ align:start position:0%
+though we get very close to them they're
+ 
+
+ align:start position:0%
+though we get very close to them they're
+still very different from
+
+ align:start position:0%
+still very different from
+ 
+
+ align:start position:0%
+still very different from
+us but you know you can love your dog
+
+ align:start position:0%
+us but you know you can love your dog
+ 
+
+ align:start position:0%
+us but you know you can love your dog
+you love your cat uh but that your
+
+ align:start position:0%
+you love your cat uh but that your
+ 
+
+ align:start position:0%
+you love your cat uh but that your
+marage is not and I'm continually
+
+ align:start position:0%
+marage is not and I'm continually
+ 
+
+ align:start position:0%
+marage is not and I'm continually
+reminded of that with my
+
+ align:start position:0%
+reminded of that with my
+ 
+
+ align:start position:0%
+reminded of that with my
+cat um one of the issues that I don't
+
+ align:start position:0%
+cat um one of the issues that I don't
+ 
+
+ align:start position:0%
+cat um one of the issues that I don't
+know if I discuss in this book but it's
+
+ align:start position:0%
+know if I discuss in this book but it's
+ 
+
+ align:start position:0%
+know if I discuss in this book but it's
+an issue I discussed in other books and
+
+ align:start position:0%
+an issue I discussed in other books and
+ 
+
+ align:start position:0%
+an issue I discussed in other books and
+some recent philosophers have discussed
+
+ align:start position:0%
+some recent philosophers have discussed
+ 
+
+ align:start position:0%
+some recent philosophers have discussed
+Robert Solomon for instance who claims
+
+ align:start position:0%
+Robert Solomon for instance who claims
+ 
+
+ align:start position:0%
+Robert Solomon for instance who claims
+that animals don't love and we don't
+
+ align:start position:0%
+that animals don't love and we don't
+ 
+
+ align:start position:0%
+that animals don't love and we don't
+really love
+
+ align:start position:0%
+really love
+ 
+
+ align:start position:0%
+really love
+animals uh but I love my cat my cat
+
+ align:start position:0%
+animals uh but I love my cat my cat
+ 
+
+ align:start position:0%
+animals uh but I love my cat my cat
+loves me and I can tell when his
+
+ align:start position:0%
+loves me and I can tell when his
+ 
+
+ align:start position:0%
+loves me and I can tell when his
+gestures are loving and when they're not
+
+ align:start position:0%
+gestures are loving and when they're not
+ 
+
+ align:start position:0%
+gestures are loving and when they're not
+when they're loving uh he gives me
+
+ align:start position:0%
+when they're loving uh he gives me
+ 
+
+ align:start position:0%
+when they're loving uh he gives me
+velvet Paws he retracts his his claws
+
+ align:start position:0%
+velvet Paws he retracts his his claws
+ 
+
+ align:start position:0%
+velvet Paws he retracts his his claws
+and sometimes times Strokes my Strokes
+
+ align:start position:0%
+and sometimes times Strokes my Strokes
+ 
+
+ align:start position:0%
+and sometimes times Strokes my Strokes
+my face and even kisses me all over um
+
+ align:start position:0%
+my face and even kisses me all over um
+ 
+
+ align:start position:0%
+my face and even kisses me all over um
+occasionally when he's lying on the bed
+
+ align:start position:0%
+occasionally when he's lying on the bed
+ 
+
+ align:start position:0%
+occasionally when he's lying on the bed
+and I walk by he'll put out his arm just
+
+ align:start position:0%
+and I walk by he'll put out his arm just
+ 
+
+ align:start position:0%
+and I walk by he'll put out his arm just
+to touch me that's love I don't know I
+
+ align:start position:0%
+to touch me that's love I don't know I
+ 
+
+ align:start position:0%
+to touch me that's love I don't know I
+don't know what more to say about it and
+
+ align:start position:0%
+don't know what more to say about it and
+ 
+
+ align:start position:0%
+don't know what more to say about it and
+or even want more to expect of another
+
+ align:start position:0%
+or even want more to expect of another
+ 
+
+ align:start position:0%
+or even want more to expect of another
+human human being but at other times if
+
+ align:start position:0%
+human human being but at other times if
+ 
+
+ align:start position:0%
+human human being but at other times if
+I reciprocate with him and he's not I
+
+ align:start position:0%
+I reciprocate with him and he's not I
+ 
+
+ align:start position:0%
+I reciprocate with him and he's not I
+don't do it quite right I suppose or
+
+ align:start position:0%
+don't do it quite right I suppose or
+ 
+
+ align:start position:0%
+don't do it quite right I suppose or
+he's not in the mood uh he'll his claws
+
+ align:start position:0%
+he's not in the mood uh he'll his claws
+ 
+
+ align:start position:0%
+he's not in the mood uh he'll his claws
+will come out and he won't attack me but
+
+ align:start position:0%
+will come out and he won't attack me but
+ 
+
+ align:start position:0%
+will come out and he won't attack me but
+I will feel the claws as an indication
+
+ align:start position:0%
+I will feel the claws as an indication
+ 
+
+ align:start position:0%
+I will feel the claws as an indication
+don't forget I may be smaller than you
+
+ align:start position:0%
+don't forget I may be smaller than you
+ 
+
+ align:start position:0%
+don't forget I may be smaller than you
+and you can do me harm but uh don't try
+
+ align:start position:0%
+and you can do me harm but uh don't try
+ 
+
+ align:start position:0%
+and you can do me harm but uh don't try
+it um I'm not I'm not
+
+ align:start position:0%
+it um I'm not I'm not
+ 
+
+ align:start position:0%
+it um I'm not I'm not
+your subservient
+
+ align:start position:0%
+your subservient
+ 
+
+ align:start position:0%
+your subservient
+creature uh we don't merge with animals
+
+ align:start position:0%
+creature uh we don't merge with animals
+ 
+
+ align:start position:0%
+creature uh we don't merge with animals
+that the way the theory goes and we
+
+ align:start position:0%
+that the way the theory goes and we
+ 
+
+ align:start position:0%
+that the way the theory goes and we
+don't merge with other human beings CU
+
+ align:start position:0%
+don't merge with other human beings CU
+ 
+
+ align:start position:0%
+don't merge with other human beings CU
+they also can have laws that you might
+
+ align:start position:0%
+they also can have laws that you might
+ 
+
+ align:start position:0%
+they also can have laws that you might
+not have recognized and if they didn't
+
+ align:start position:0%
+not have recognized and if they didn't
+ 
+
+ align:start position:0%
+not have recognized and if they didn't
+we wouldn't love them they would just be
+
+ align:start position:0%
+we wouldn't love them they would just be
+ 
+
+ align:start position:0%
+we wouldn't love them they would just be
+sort of puppets or um terribly supine uh
+
+ align:start position:0%
+sort of puppets or um terribly supine uh
+ 
+
+ align:start position:0%
+sort of puppets or um terribly supine uh
+creatures so that there is the dual
+
+ align:start position:0%
+creatures so that there is the dual
+ 
+
+ align:start position:0%
+creatures so that there is the dual
+capacity
+
+ align:start position:0%
+capacity
+ 
+
+ align:start position:0%
+capacity
+to share their lives and to withhold
+
+ align:start position:0%
+to share their lives and to withhold
+ 
+
+ align:start position:0%
+to share their lives and to withhold
+themselves and that's very different
+
+ align:start position:0%
+themselves and that's very different
+ 
+
+ align:start position:0%
+themselves and that's very different
+from the concept of
+
+ align:start position:0%
+from the concept of
+ 
+
+ align:start position:0%
+from the concept of
+merging which I think is the prevalent
+
+ align:start position:0%
+merging which I think is the prevalent
+ 
+
+ align:start position:0%
+merging which I think is the prevalent
+concept among people who believe
+
+ align:start position:0%
+concept among people who believe
+ 
+
+ align:start position:0%
+concept among people who believe
+romantic love with a capital R coming
+
+ align:start position:0%
+romantic love with a capital R coming
+ 
+
+ align:start position:0%
+romantic love with a capital R coming
+out of the 19th century flourishing
+
+ align:start position:0%
+out of the 19th century flourishing
+ 
+
+ align:start position:0%
+out of the 19th century flourishing
+throughout the 19th century uh and into
+
+ align:start position:0%
+throughout the 19th century uh and into
+ 
+
+ align:start position:0%
+throughout the 19th century uh and into
+the 20th and nowadays back and forth as
+
+ align:start position:0%
+the 20th and nowadays back and forth as
+ 
+
+ align:start position:0%
+the 20th and nowadays back and forth as
+I point out in the first chapter uh
+
+ align:start position:0%
+I point out in the first chapter uh
+ 
+
+ align:start position:0%
+I point out in the first chapter uh
+being something where suspicious of but
+
+ align:start position:0%
+being something where suspicious of but
+ 
+
+ align:start position:0%
+being something where suspicious of but
+also something we give ourselves
+
+ align:start position:0%
+also something we give ourselves
+ 
+
+ align:start position:0%
+also something we give ourselves
+to I I haven't done any sociological
+
+ align:start position:0%
+to I I haven't done any sociological
+ 
+
+ align:start position:0%
+to I I haven't done any sociological
+work with
+
+ align:start position:0%
+work with
+ 
+
+ align:start position:0%
+work with
+popular um Arts low culture as it's
+
+ align:start position:0%
+popular um Arts low culture as it's
+ 
+
+ align:start position:0%
+popular um Arts low culture as it's
+called but I would think that if you
+
+ align:start position:0%
+called but I would think that if you
+ 
+
+ align:start position:0%
+called but I would think that if you
+tabulated the songs or the elements of
+
+ align:start position:0%
+tabulated the songs or the elements of
+ 
+
+ align:start position:0%
+tabulated the songs or the elements of
+songs or whatever units you as a
+
+ align:start position:0%
+songs or whatever units you as a
+ 
+
+ align:start position:0%
+songs or whatever units you as a
+scientists sociological scientists focus
+
+ align:start position:0%
+scientists sociological scientists focus
+ 
+
+ align:start position:0%
+scientists sociological scientists focus
+on in order to make a generalization you
+
+ align:start position:0%
+on in order to make a generalization you
+ 
+
+ align:start position:0%
+on in order to make a generalization you
+would find that there's a mixture
+
+ align:start position:0%
+would find that there's a mixture
+ 
+
+ align:start position:0%
+would find that there's a mixture
+sometimes it's this
+
+ align:start position:0%
+sometimes it's this
+ 
+
+ align:start position:0%
+sometimes it's this
+desire to give yourself or even to to
+
+ align:start position:0%
+desire to give yourself or even to to
+ 
+
+ align:start position:0%
+desire to give yourself or even to to
+merge and then at other times it's
+
+ align:start position:0%
+merge and then at other times it's
+ 
+
+ align:start position:0%
+merge and then at other times it's
+disappointment and
+
+ align:start position:0%
+disappointment and
+ 
+
+ align:start position:0%
+disappointment and
+withholding uh and that we fluctuate
+
+ align:start position:0%
+withholding uh and that we fluctuate
+ 
+
+ align:start position:0%
+withholding uh and that we fluctuate
+back and forth
+
+ align:start position:0%
+back and forth
+ 
+
+ align:start position:0%
+back and forth
+um so that on the one hand there you can
+
+ align:start position:0%
+um so that on the one hand there you can
+ 
+
+ align:start position:0%
+um so that on the one hand there you can
+imagine any number
+
+ align:start position:0%
+imagine any number
+ 
+
+ align:start position:0%
+imagine any number
+of romantic popular songs
+
+ align:start position:0%
+of romantic popular songs
+ 
+
+ align:start position:0%
+of romantic popular songs
+uh uh I don't know that merging can
+
+ align:start position:0%
+uh uh I don't know that merging can
+ 
+
+ align:start position:0%
+uh uh I don't know that merging can
+anyone think of one right off hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I I I can think of one that I'm fond
+
+ align:start position:0%
+um I I I can think of one that I'm fond
+ 
+
+ align:start position:0%
+um I I I can think of one that I'm fond
+of which is Bob Dylan's song that you
+
+ align:start position:0%
+of which is Bob Dylan's song that you
+ 
+
+ align:start position:0%
+of which is Bob Dylan's song that you
+your generation still know who Bob Dylan
+
+ align:start position:0%
+your generation still know who Bob Dylan
+ 
+
+ align:start position:0%
+your generation still know who Bob Dylan
+is um and sung by Joan
+
+ align:start position:0%
+is um and sung by Joan
+ 
+
+ align:start position:0%
+is um and sung by Joan
+bz who you you know her she's not you
+
+ align:start position:0%
+bz who you you know her she's not you
+ 
+
+ align:start position:0%
+bz who you you know her she's not you
+don't remember her she was a great and
+
+ align:start position:0%
+don't remember her she was a great and
+ 
+
+ align:start position:0%
+don't remember her she was a great and
+still is a wonderful folk singer when I
+
+ align:start position:0%
+still is a wonderful folk singer when I
+ 
+
+ align:start position:0%
+still is a wonderful folk singer when I
+when I was young she started out and it
+
+ align:start position:0%
+when I was young she started out and it
+ 
+
+ align:start position:0%
+when I was young she started out and it
+was a real Revelation what a genius she
+
+ align:start position:0%
+was a real Revelation what a genius she
+ 
+
+ align:start position:0%
+was a real Revelation what a genius she
+was uh in folk music and there's a bob
+
+ align:start position:0%
+was uh in folk music and there's a bob
+ 
+
+ align:start position:0%
+was uh in folk music and there's a bob
+Dyan song that Bob Dyan song that she
+
+ align:start position:0%
+Dyan song that Bob Dyan song that she
+ 
+
+ align:start position:0%
+Dyan song that Bob Dyan song that she
+sings Called It Ain't Me Babe you know
+
+ align:start position:0%
+sings Called It Ain't Me Babe you know
+ 
+
+ align:start position:0%
+sings Called It Ain't Me Babe you know
+that uh you want somebody who will
+
+ align:start position:0%
+that uh you want somebody who will
+ 
+
+ align:start position:0%
+that uh you want somebody who will
+always be there for you It Ain't Me Babe
+
+ align:start position:0%
+always be there for you It Ain't Me Babe
+ 
+
+ align:start position:0%
+always be there for you It Ain't Me Babe
+you want somebody you can trust
+
+ align:start position:0%
+you want somebody you can trust
+ 
+
+ align:start position:0%
+you want somebody you can trust
+completely somebody who will stand by
+
+ align:start position:0%
+completely somebody who will stand by
+ 
+
+ align:start position:0%
+completely somebody who will stand by
+you somebody who will you know support
+
+ align:start position:0%
+you somebody who will you know support
+ 
+
+ align:start position:0%
+you somebody who will you know support
+you in everything uh something who will
+
+ align:start position:0%
+you in everything uh something who will
+ 
+
+ align:start position:0%
+you in everything uh something who will
+pour out our love I'm I'm fabricating
+
+ align:start position:0%
+pour out our love I'm I'm fabricating
+ 
+
+ align:start position:0%
+pour out our love I'm I'm fabricating
+because I don't remember the U the exact
+
+ align:start position:0%
+because I don't remember the U the exact
+ 
+
+ align:start position:0%
+because I don't remember the U the exact
+words uh but the refrain is it ain't me
+
+ align:start position:0%
+words uh but the refrain is it ain't me
+ 
+
+ align:start position:0%
+words uh but the refrain is it ain't me
+babe and then her voice gets lower it
+
+ align:start position:0%
+babe and then her voice gets lower it
+ 
+
+ align:start position:0%
+babe and then her voice gets lower it
+ain't Ain me babe and that seems to me
+
+ align:start position:0%
+ain't Ain me babe and that seems to me
+ 
+
+ align:start position:0%
+ain't Ain me babe and that seems to me
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+love always poses as a potentiality that
+
+ align:start position:0%
+love always poses as a potentiality that
+ 
+
+ align:start position:0%
+love always poses as a potentiality that
+the claws of the cat can always come out
+
+ align:start position:0%
+the claws of the cat can always come out
+ 
+
+ align:start position:0%
+the claws of the cat can always come out
+as a way of
+
+ align:start position:0%
+as a way of
+ 
+
+ align:start position:0%
+as a way of
+asserting his separateness for
+
+ align:start position:0%
+asserting his separateness for
+ 
+
+ align:start position:0%
+asserting his separateness for
+me um and that's why I attack the
+
+ align:start position:0%
+me um and that's why I attack the
+ 
+
+ align:start position:0%
+me um and that's why I attack the
+concept of merging in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Romanticism I think I tend to agree
+
+ align:start position:0%
+Romanticism I think I tend to agree
+ 
+
+ align:start position:0%
+Romanticism I think I tend to agree
+though with the rest of I tend to agree
+
+ align:start position:0%
+though with the rest of I tend to agree
+ 
+
+ align:start position:0%
+though with the rest of I tend to agree
+with also with the rest of what you have
+
+ align:start position:0%
+with also with the rest of what you have
+ 
+
+ align:start position:0%
+with also with the rest of what you have
+to say about the merging I guess I just
+
+ align:start position:0%
+to say about the merging I guess I just
+ 
+
+ align:start position:0%
+to say about the merging I guess I just
+wasn't very clear on that one point that
+
+ align:start position:0%
+wasn't very clear on that one point that
+ 
+
+ align:start position:0%
+wasn't very clear on that one point that
+you were making
+
+ align:start position:0%
+you were making
+ 
+
+ align:start position:0%
+you were making
+because I think the idea that was stated
+
+ align:start position:0%
+because I think the idea that was stated
+ 
+
+ align:start position:0%
+because I think the idea that was stated
+somewhere about trying to find the
+
+ align:start position:0%
+somewhere about trying to find the
+ 
+
+ align:start position:0%
+somewhere about trying to find the
+person that is just like you and your
+
+ align:start position:0%
+person that is just like you and your
+ 
+
+ align:start position:0%
+person that is just like you and your
+alter egoo who you will mes with that's
+
+ align:start position:0%
+alter egoo who you will mes with that's
+ 
+
+ align:start position:0%
+alter egoo who you will mes with that's
+I think obviously not the case
+
+ align:start position:0%
+I think obviously not the case
+ 
+
+ align:start position:0%
+I think obviously not the case
+because many of times it's the
+
+ align:start position:0%
+because many of times it's the
+ 
+
+ align:start position:0%
+because many of times it's the
+differences between people that make
+
+ align:start position:0%
+differences between people that make
+ 
+
+ align:start position:0%
+differences between people that make
+them right you know so compatible is
+
+ align:start position:0%
+them right you know so compatible is
+ 
+
+ align:start position:0%
+them right you know so compatible is
+that you don't want want to be with
+
+ align:start position:0%
+that you don't want want to be with
+ 
+
+ align:start position:0%
+that you don't want want to be with
+someone who's just like you in every
+
+ align:start position:0%
+someone who's just like you in every
+ 
+
+ align:start position:0%
+someone who's just like you in every
+single aspect because that's boring you
+
+ align:start position:0%
+single aspect because that's boring you
+ 
+
+ align:start position:0%
+single aspect because that's boring you
+know now that fit that idea that you
+
+ align:start position:0%
+know now that fit that idea that you
+ 
+
+ align:start position:0%
+know now that fit that idea that you
+love someone different from yourself is
+
+ align:start position:0%
+love someone different from yourself is
+ 
+
+ align:start position:0%
+love someone different from yourself is
+a common one and it fits in with my idea
+
+ align:start position:0%
+a common one and it fits in with my idea
+ 
+
+ align:start position:0%
+a common one and it fits in with my idea
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+sharing that um the rough man and uh
+
+ align:start position:0%
+sharing that um the rough man and uh
+ 
+
+ align:start position:0%
+sharing that um the rough man and uh
+truck driver Macho type he falls in love
+
+ align:start position:0%
+truck driver Macho type he falls in love
+ 
+
+ align:start position:0%
+truck driver Macho type he falls in love
+with a gentle woman because he knows
+
+ align:start position:0%
+with a gentle woman because he knows
+ 
+
+ align:start position:0%
+with a gentle woman because he knows
+he's not gentle and feels an inadequacy
+
+ align:start position:0%
+he's not gentle and feels an inadequacy
+ 
+
+ align:start position:0%
+he's not gentle and feels an inadequacy
+she supplements him and she falls in
+
+ align:start position:0%
+she supplements him and she falls in
+ 
+
+ align:start position:0%
+she supplements him and she falls in
+love with him because he's big and
+
+ align:start position:0%
+love with him because he's big and
+ 
+
+ align:start position:0%
+love with him because he's big and
+strong will take care of her that
+
+ align:start position:0%
+strong will take care of her that
+ 
+
+ align:start position:0%
+strong will take care of her that
+there's a kind of compensation that you
+
+ align:start position:0%
+there's a kind of compensation that you
+ 
+
+ align:start position:0%
+there's a kind of compensation that you
+get from the other person that you
+
+ align:start position:0%
+get from the other person that you
+ 
+
+ align:start position:0%
+get from the other person that you
+couldn't have got except in a Unity now
+
+ align:start position:0%
+couldn't have got except in a Unity now
+ 
+
+ align:start position:0%
+couldn't have got except in a Unity now
+the unity can take place in a
+
+ align:start position:0%
+the unity can take place in a
+ 
+
+ align:start position:0%
+the unity can take place in a
+marriage and uh
+
+ align:start position:0%
+marriage and uh
+ 
+
+ align:start position:0%
+marriage and uh
+often the contribution of different
+
+ align:start position:0%
+often the contribution of different
+ 
+
+ align:start position:0%
+often the contribution of different
+assets makes it a stable marriage for
+
+ align:start position:0%
+assets makes it a stable marriage for
+ 
+
+ align:start position:0%
+assets makes it a stable marriage for
+there to be
+
+ align:start position:0%
+there to be
+ 
+
+ align:start position:0%
+there to be
+love um the unity has to be more deeply
+
+ align:start position:0%
+love um the unity has to be more deeply
+ 
+
+ align:start position:0%
+love um the unity has to be more deeply
+embedded
+
+ align:start position:0%
+embedded
+ 
+
+ align:start position:0%
+embedded
+in some kind of uh Union it it's not
+
+ align:start position:0%
+in some kind of uh Union it it's not
+ 
+
+ align:start position:0%
+in some kind of uh Union it it's not
+just she relying on him for protection
+
+ align:start position:0%
+just she relying on him for protection
+ 
+
+ align:start position:0%
+just she relying on him for protection
+him relying on
+
+ align:start position:0%
+him relying on
+ 
+
+ align:start position:0%
+him relying on
+her for for children he wants or his
+
+ align:start position:0%
+her for for children he wants or his
+ 
+
+ align:start position:0%
+her for for children he wants or his
+being uh rugged and her being beautiful
+
+ align:start position:0%
+being uh rugged and her being beautiful
+ 
+
+ align:start position:0%
+being uh rugged and her being beautiful
+it's got to be a a richer exchange and
+
+ align:start position:0%
+it's got to be a a richer exchange and
+ 
+
+ align:start position:0%
+it's got to be a a richer exchange and
+to explain that richer exchange I
+
+ align:start position:0%
+to explain that richer exchange I
+ 
+
+ align:start position:0%
+to explain that richer exchange I
+introduced the concepts of bestow and
+
+ align:start position:0%
+introduced the concepts of bestow and
+ 
+
+ align:start position:0%
+introduced the concepts of bestow and
+Appraisal which I touch on here
+
+ align:start position:0%
+Appraisal which I touch on here
+ 
+
+ align:start position:0%
+Appraisal which I touch on here
+and I won't launch into until you've had
+
+ align:start position:0%
+and I won't launch into until you've had
+ 
+
+ align:start position:0%
+and I won't launch into until you've had
+more chance but to finish my sentence
+
+ align:start position:0%
+more chance but to finish my sentence
+ 
+
+ align:start position:0%
+more chance but to finish my sentence
+the trilogy the nature of
+
+ align:start position:0%
+the trilogy the nature of
+ 
+
+ align:start position:0%
+the trilogy the nature of
+Love 1,400 Pages which I don't assign to
+
+ align:start position:0%
+Love 1,400 Pages which I don't assign to
+ 
+
+ align:start position:0%
+Love 1,400 Pages which I don't assign to
+you because that would be too much
+
+ align:start position:0%
+you because that would be too much
+ 
+
+ align:start position:0%
+you because that would be too much
+though I have in previous courses um and
+
+ align:start position:0%
+though I have in previous courses um and
+ 
+
+ align:start position:0%
+though I have in previous courses um and
+people seem to get get something out of
+
+ align:start position:0%
+people seem to get get something out of
+ 
+
+ align:start position:0%
+people seem to get get something out of
+them but that's a different kind of
+
+ align:start position:0%
+them but that's a different kind of
+ 
+
+ align:start position:0%
+them but that's a different kind of
+course uh the trilogy starts out with a
+
+ align:start position:0%
+course uh the trilogy starts out with a
+ 
+
+ align:start position:0%
+course uh the trilogy starts out with a
+chapter on the distinction between the
+
+ align:start position:0%
+chapter on the distinction between the
+ 
+
+ align:start position:0%
+chapter on the distinction between the
+praisal and best
+
+ align:start position:0%
+praisal and best
+ 
+
+ align:start position:0%
+praisal and best
+and then the whole rest of it that's the
+
+ align:start position:0%
+and then the whole rest of it that's the
+ 
+
+ align:start position:0%
+and then the whole rest of it that's the
+guiding theme that's the dominant to
+
+ align:start position:0%
+guiding theme that's the dominant to
+ 
+
+ align:start position:0%
+guiding theme that's the dominant to
+which the rest of the chapters
+
+ align:start position:0%
+which the rest of the chapters
+ 
+
+ align:start position:0%
+which the rest of the chapters
+return uh about appraisal and besto as
+
+ align:start position:0%
+return uh about appraisal and besto as
+ 
+
+ align:start position:0%
+return uh about appraisal and besto as
+constructive of the philosophy as well
+
+ align:start position:0%
+constructive of the philosophy as well
+ 
+
+ align:start position:0%
+constructive of the philosophy as well
+as being a view about love that the
+
+ align:start position:0%
+as being a view about love that the
+ 
+
+ align:start position:0%
+as being a view about love that the
+philosophies the different philosophies
+
+ align:start position:0%
+philosophies the different philosophies
+ 
+
+ align:start position:0%
+philosophies the different philosophies
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+about well that for me is a way of
+
+ align:start position:0%
+about well that for me is a way of
+ 
+
+ align:start position:0%
+about well that for me is a way of
+showing how this uh sharing takes place
+
+ align:start position:0%
+showing how this uh sharing takes place
+ 
+
+ align:start position:0%
+showing how this uh sharing takes place
+and we'll we'll come back to it but why
+
+ align:start position:0%
+and we'll we'll come back to it but why
+ 
+
+ align:start position:0%
+and we'll we'll come back to it but why
+don't we go to to what you were saying
+
+ align:start position:0%
+don't we go to to what you were saying
+ 
+
+ align:start position:0%
+don't we go to to what you were saying
+about the first merging I mean the first
+
+ align:start position:0%
+about the first merging I mean the first
+ 
+
+ align:start position:0%
+about the first merging I mean the first
+uh of the two myths so unless somebody
+
+ align:start position:0%
+uh of the two myths so unless somebody
+ 
+
+ align:start position:0%
+uh of the two myths so unless somebody
+wants to
+
+ align:start position:0%
+wants to
+ 
+
+ align:start position:0%
+wants to
+interrupt
+
+ align:start position:0%
+interrupt
+ 
+
+ align:start position:0%
+interrupt
+com if I can say something I almost
+
+ align:start position:0%
+com if I can say something I almost
+ 
+
+ align:start position:0%
+com if I can say something I almost
+think that or it's confusing to me how
+
+ align:start position:0%
+think that or it's confusing to me how
+ 
+
+ align:start position:0%
+think that or it's confusing to me how
+uh you say that two people cannot really
+
+ align:start position:0%
+uh you say that two people cannot really
+ 
+
+ align:start position:0%
+uh you say that two people cannot really
+merge yet I feel as if complimentary
+
+ align:start position:0%
+merge yet I feel as if complimentary
+ 
+
+ align:start position:0%
+merge yet I feel as if complimentary
+personalities being a basis for love
+
+ align:start position:0%
+personalities being a basis for love
+ 
+
+ align:start position:0%
+personalities being a basis for love
+almost prompts
+
+ align:start position:0%
+almost prompts
+ 
+
+ align:start position:0%
+almost prompts
+emerging you can't work unless there is
+
+ align:start position:0%
+emerging you can't work unless there is
+ 
+
+ align:start position:0%
+emerging you can't work unless there is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+merger there there could be an intimacy
+
+ align:start position:0%
+merger there there could be an intimacy
+ 
+
+ align:start position:0%
+merger there there could be an intimacy
+because of these these these uh combined
+
+ align:start position:0%
+because of these these these uh combined
+ 
+
+ align:start position:0%
+because of these these these uh combined
+efforts the way in which they complement
+
+ align:start position:0%
+efforts the way in which they complement
+ 
+
+ align:start position:0%
+efforts the way in which they complement
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+other but wouldn't if they were merged
+
+ align:start position:0%
+other but wouldn't if they were merged
+ 
+
+ align:start position:0%
+other but wouldn't if they were merged
+they wouldn't really be people persons
+
+ align:start position:0%
+they wouldn't really be people persons
+ 
+
+ align:start position:0%
+they wouldn't really be people persons
+anymore they would be part of this new
+
+ align:start position:0%
+anymore they would be part of this new
+ 
+
+ align:start position:0%
+anymore they would be part of this new
+entity and I feel like also if they
+
+ align:start position:0%
+entity and I feel like also if they
+ 
+
+ align:start position:0%
+entity and I feel like also if they
+merged then they would didn't have those
+
+ align:start position:0%
+merged then they would didn't have those
+ 
+
+ align:start position:0%
+merged then they would didn't have those
+different things that would be able to
+
+ align:start position:0%
+different things that would be able to
+ 
+
+ align:start position:0%
+different things that would be able to
+complement anymore that the idea that
+
+ align:start position:0%
+complement anymore that the idea that
+ 
+
+ align:start position:0%
+complement anymore that the idea that
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+different automatically suggests that
+
+ align:start position:0%
+different automatically suggests that
+ 
+
+ align:start position:0%
+different automatically suggests that
+they can't become one thing which is the
+
+ align:start position:0%
+they can't become one thing which is the
+ 
+
+ align:start position:0%
+they can't become one thing which is the
+same do you do you know the uh novel and
+
+ align:start position:0%
+same do you do you know the uh novel and
+ 
+
+ align:start position:0%
+same do you do you know the uh novel and
+the movie called weather and Heights no
+
+ align:start position:0%
+the movie called weather and Heights no
+ 
+
+ align:start position:0%
+the movie called weather and Heights no
+none of you saided
+
+ align:start position:0%
+none of you saided
+ 
+
+ align:start position:0%
+none of you saided
+that you do Alana do you remember the
+
+ align:start position:0%
+that you do Alana do you remember the
+ 
+
+ align:start position:0%
+that you do Alana do you remember the
+place in the novel which also comes out
+
+ align:start position:0%
+place in the novel which also comes out
+ 
+
+ align:start position:0%
+place in the novel which also comes out
+in at least no I think both of the uh I
+
+ align:start position:0%
+in at least no I think both of the uh I
+ 
+
+ align:start position:0%
+in at least no I think both of the uh I
+I know two or maybe three versions comes
+
+ align:start position:0%
+I know two or maybe three versions comes
+ 
+
+ align:start position:0%
+I know two or maybe three versions comes
+out in the movies too uh the most famous
+
+ align:start position:0%
+out in the movies too uh the most famous
+ 
+
+ align:start position:0%
+out in the movies too uh the most famous
+of these movies is the one with Lawrence
+
+ align:start position:0%
+of these movies is the one with Lawrence
+ 
+
+ align:start position:0%
+of these movies is the one with Lawrence
+olier and Merl lubron made about
+
+ align:start position:0%
+olier and Merl lubron made about
+ 
+
+ align:start position:0%
+olier and Merl lubron made about
+1941 um in which
+
+ align:start position:0%
+1941 um in which
+ 
+
+ align:start position:0%
+1941 um in which
+Kathy who was fallen in love with this
+
+ align:start position:0%
+Kathy who was fallen in love with this
+ 
+
+ align:start position:0%
+Kathy who was fallen in love with this
+slave boy not slave boy servant boy
+
+ align:start position:0%
+slave boy not slave boy servant boy
+ 
+
+ align:start position:0%
+slave boy not slave boy servant boy
+who's very rough um who his name is
+
+ align:start position:0%
+who's very rough um who his name is
+ 
+
+ align:start position:0%
+who's very rough um who his name is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+heathcliffe um she says after he's left
+
+ align:start position:0%
+heathcliffe um she says after he's left
+ 
+
+ align:start position:0%
+heathcliffe um she says after he's left
+and after she's married somebody else
+
+ align:start position:0%
+and after she's married somebody else
+ 
+
+ align:start position:0%
+and after she's married somebody else
+whom she doesn't love that way though
+
+ align:start position:0%
+whom she doesn't love that way though
+ 
+
+ align:start position:0%
+whom she doesn't love that way though
+they have a good marriage she says I am
+
+ align:start position:0%
+they have a good marriage she says I am
+ 
+
+ align:start position:0%
+they have a good marriage she says I am
+heathcliffe I am
+
+ align:start position:0%
+heathcliffe I am
+ 
+
+ align:start position:0%
+heathcliffe I am
+heathcliffe now I think that's the idea
+
+ align:start position:0%
+heathcliffe now I think that's the idea
+ 
+
+ align:start position:0%
+heathcliffe now I think that's the idea
+of merging and for me that's very poetic
+
+ align:start position:0%
+of merging and for me that's very poetic
+ 
+
+ align:start position:0%
+of merging and for me that's very poetic
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+metaphoric uh if she's saying
+
+ align:start position:0%
+metaphoric uh if she's saying
+ 
+
+ align:start position:0%
+metaphoric uh if she's saying
+heathcliffe is all I think about
+
+ align:start position:0%
+heathcliffe is all I think about
+ 
+
+ align:start position:0%
+heathcliffe is all I think about
+heathcliffe is the person I should have
+
+ align:start position:0%
+heathcliffe is the person I should have
+ 
+
+ align:start position:0%
+heathcliffe is the person I should have
+married heathcliffe is the one for whom
+
+ align:start position:0%
+married heathcliffe is the one for whom
+ 
+
+ align:start position:0%
+married heathcliffe is the one for whom
+I feel strong sexual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+passion but not for my husband you see
+
+ align:start position:0%
+passion but not for my husband you see
+ 
+
+ align:start position:0%
+passion but not for my husband you see
+um I can understand that but that's her
+
+ align:start position:0%
+um I can understand that but that's her
+ 
+
+ align:start position:0%
+um I can understand that but that's her
+expressing her feelings how does that
+
+ align:start position:0%
+expressing her feelings how does that
+ 
+
+ align:start position:0%
+expressing her feelings how does that
+make her
+
+ align:start position:0%
+make her
+ 
+
+ align:start position:0%
+make her
+Heathcliff she is going to respond to
+
+ align:start position:0%
+Heathcliff she is going to respond to
+ 
+
+ align:start position:0%
+Heathcliff she is going to respond to
+him in a way that is distinctive of her
+
+ align:start position:0%
+him in a way that is distinctive of her
+ 
+
+ align:start position:0%
+him in a way that is distinctive of her
+and he will respond to her ideally um
+
+ align:start position:0%
+and he will respond to her ideally um
+ 
+
+ align:start position:0%
+and he will respond to her ideally um
+though it's a tragic tragedy and it
+
+ align:start position:0%
+though it's a tragic tragedy and it
+ 
+
+ align:start position:0%
+though it's a tragic tragedy and it
+doesn't ever really work work out um in
+
+ align:start position:0%
+doesn't ever really work work out um in
+ 
+
+ align:start position:0%
+doesn't ever really work work out um in
+a in a related way but it won't be
+
+ align:start position:0%
+a in a related way but it won't be
+ 
+
+ align:start position:0%
+a in a related way but it won't be
+either them being the other and that
+
+ align:start position:0%
+either them being the other and that
+ 
+
+ align:start position:0%
+either them being the other and that
+built into the idea of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+merging maybe I'm just unlearned but the
+
+ align:start position:0%
+merging maybe I'm just unlearned but the
+ 
+
+ align:start position:0%
+merging maybe I'm just unlearned but the
+whole concept of of the merging just
+
+ align:start position:0%
+whole concept of of the merging just
+ 
+
+ align:start position:0%
+whole concept of of the merging just
+seemed completely foreign to me like
+
+ align:start position:0%
+seemed completely foreign to me like
+ 
+
+ align:start position:0%
+seemed completely foreign to me like
+like when when I read about I I don't
+
+ align:start position:0%
+like when when I read about I I don't
+ 
+
+ align:start position:0%
+like when when I read about I I don't
+think it was something that at any point
+
+ align:start position:0%
+think it was something that at any point
+ 
+
+ align:start position:0%
+think it was something that at any point
+I've ever believed in like the to me
+
+ align:start position:0%
+I've ever believed in like the to me
+ 
+
+ align:start position:0%
+I've ever believed in like the to me
+again maybe I'm just young and naive but
+
+ align:start position:0%
+again maybe I'm just young and naive but
+ 
+
+ align:start position:0%
+again maybe I'm just young and naive but
+the like the whole concept that that
+
+ align:start position:0%
+the like the whole concept that that
+ 
+
+ align:start position:0%
+the like the whole concept that that
+you're saying with interdependence and
+
+ align:start position:0%
+you're saying with interdependence and
+ 
+
+ align:start position:0%
+you're saying with interdependence and
+and stuff like that was was much more
+
+ align:start position:0%
+and stuff like that was was much more
+ 
+
+ align:start position:0%
+and stuff like that was was much more
+the more natural and obvious description
+
+ align:start position:0%
+the more natural and obvious description
+ 
+
+ align:start position:0%
+the more natural and obvious description
+for me I
+
+ align:start position:0%
+for me I
+ 
+
+ align:start position:0%
+for me I
+don't does anybody want to comment on
+
+ align:start position:0%
+don't does anybody want to comment on
+ 
+
+ align:start position:0%
+don't does anybody want to comment on
+that I can comment on it do you think
+
+ align:start position:0%
+that I can comment on it do you think
+ 
+
+ align:start position:0%
+that I can comment on it do you think
+that I've never really felt that about
+
+ align:start position:0%
+that I've never really felt that about
+ 
+
+ align:start position:0%
+that I've never really felt that about
+anybody and I'm much older than you it
+
+ align:start position:0%
+anybody and I'm much older than you it
+ 
+
+ align:start position:0%
+anybody and I'm much older than you it
+isn't a question of you're being young I
+
+ align:start position:0%
+isn't a question of you're being young I
+ 
+
+ align:start position:0%
+isn't a question of you're being young I
+think it's temperamental some people do
+
+ align:start position:0%
+think it's temperamental some people do
+ 
+
+ align:start position:0%
+think it's temperamental some people do
+have that feeling I don't want to CL
+
+ align:start position:0%
+have that feeling I don't want to CL
+ 
+
+ align:start position:0%
+have that feeling I don't want to CL
+that it's all a confusion on the part of
+
+ align:start position:0%
+that it's all a confusion on the part of
+ 
+
+ align:start position:0%
+that it's all a confusion on the part of
+these poets and philosophers who were
+
+ align:start position:0%
+these poets and philosophers who were
+ 
+
+ align:start position:0%
+these poets and philosophers who were
+Carried Away by language I think some
+
+ align:start position:0%
+Carried Away by language I think some
+ 
+
+ align:start position:0%
+Carried Away by language I think some
+people really feel that and want that
+
+ align:start position:0%
+people really feel that and want that
+ 
+
+ align:start position:0%
+people really feel that and want that
+desperately sometimes pathologically
+
+ align:start position:0%
+desperately sometimes pathologically
+ 
+
+ align:start position:0%
+desperately sometimes pathologically
+even I just want to say that uh the
+
+ align:start position:0%
+even I just want to say that uh the
+ 
+
+ align:start position:0%
+even I just want to say that uh the
+feeling is just a feeling and not a
+
+ align:start position:0%
+feeling is just a feeling and not a
+ 
+
+ align:start position:0%
+feeling is just a feeling and not a
+representation of what is really
+
+ align:start position:0%
+representation of what is really
+ 
+
+ align:start position:0%
+representation of what is really
+possible it can be a beautiful feeling
+
+ align:start position:0%
+possible it can be a beautiful feeling
+ 
+
+ align:start position:0%
+possible it can be a beautiful feeling
+which I've always felt was is denied to
+
+ align:start position:0%
+which I've always felt was is denied to
+ 
+
+ align:start position:0%
+which I've always felt was is denied to
+me because I'm such a cold fish I'm not
+
+ align:start position:0%
+me because I'm such a cold fish I'm not
+ 
+
+ align:start position:0%
+me because I'm such a cold fish I'm not
+a cold fish in the sense of having
+
+ align:start position:0%
+a cold fish in the sense of having
+ 
+
+ align:start position:0%
+a cold fish in the sense of having
+feelings and emotions and crying on all
+
+ align:start position:0%
+feelings and emotions and crying on all
+ 
+
+ align:start position:0%
+feelings and emotions and crying on all
+sorts of occasions it's just that I
+
+ align:start position:0%
+sorts of occasions it's just that I
+ 
+
+ align:start position:0%
+sorts of occasions it's just that I
+don't have this
+
+ align:start position:0%
+don't have this
+ 
+
+ align:start position:0%
+don't have this
+feeling which is so many other
+
+ align:start position:0%
+feeling which is so many other
+ 
+
+ align:start position:0%
+feeling which is so many other
+people think of as what they are what
+
+ align:start position:0%
+people think of as what they are what
+ 
+
+ align:start position:0%
+people think of as what they are what
+they feel and what they want and and I
+
+ align:start position:0%
+they feel and what they want and and I
+ 
+
+ align:start position:0%
+they feel and what they want and and I
+guess cuz you said the claws come out
+
+ align:start position:0%
+guess cuz you said the claws come out
+ 
+
+ align:start position:0%
+guess cuz you said the claws come out
+any time do you think it's it's kind of
+
+ align:start position:0%
+any time do you think it's it's kind of
+ 
+
+ align:start position:0%
+any time do you think it's it's kind of
+like feeling that way is kind of bad
+
+ align:start position:0%
+like feeling that way is kind of bad
+ 
+
+ align:start position:0%
+like feeling that way is kind of bad
+kind of like setting yourself up like to
+
+ align:start position:0%
+kind of like setting yourself up like to
+ 
+
+ align:start position:0%
+kind of like setting yourself up like to
+be harmed um
+
+ align:start position:0%
+be harmed um
+ 
+
+ align:start position:0%
+be harmed um
+I don't know I think it's a bad concept
+
+ align:start position:0%
+I don't know I think it's a bad concept
+ 
+
+ align:start position:0%
+I don't know I think it's a bad concept
+because I'm a philosopher I think it
+
+ align:start position:0%
+because I'm a philosopher I think it
+ 
+
+ align:start position:0%
+because I'm a philosopher I think it
+doesn't sustain analysis but Arthur May
+
+ align:start position:0%
+doesn't sustain analysis but Arthur May
+ 
+
+ align:start position:0%
+doesn't sustain analysis but Arthur May
+disagree in terms of it's a bad thing
+
+ align:start position:0%
+disagree in terms of it's a bad thing
+ 
+
+ align:start position:0%
+disagree in terms of it's a bad thing
+for people to have I think probably on
+
+ align:start position:0%
+for people to have I think probably on
+ 
+
+ align:start position:0%
+for people to have I think probably on
+balance they more often get hurt than
+
+ align:start position:0%
+balance they more often get hurt than
+ 
+
+ align:start position:0%
+balance they more often get hurt than
+benefit from it but then it it must give
+
+ align:start position:0%
+benefit from it but then it it must give
+ 
+
+ align:start position:0%
+benefit from it but then it it must give
+a wonderfully ecstatic feeling as long
+
+ align:start position:0%
+a wonderfully ecstatic feeling as long
+ 
+
+ align:start position:0%
+a wonderfully ecstatic feeling as long
+as it lasts it's just that uh I can't
+
+ align:start position:0%
+as it lasts it's just that uh I can't
+ 
+
+ align:start position:0%
+as it lasts it's just that uh I can't
+believe it lasts very long uh
+
+ align:start position:0%
+believe it lasts very long uh
+ 
+
+ align:start position:0%
+believe it lasts very long uh
+Freud writes a great deal about uh his
+
+ align:start position:0%
+Freud writes a great deal about uh his
+ 
+
+ align:start position:0%
+Freud writes a great deal about uh his
+patience you know he his case histories
+
+ align:start position:0%
+patience you know he his case histories
+ 
+
+ align:start position:0%
+patience you know he his case histories
+and the early development of theories
+
+ align:start position:0%
+and the early development of theories
+ 
+
+ align:start position:0%
+and the early development of theories
+and one thing he discovered was a lot of
+
+ align:start position:0%
+and one thing he discovered was a lot of
+ 
+
+ align:start position:0%
+and one thing he discovered was a lot of
+the people who come to him with their
+
+ align:start position:0%
+the people who come to him with their
+ 
+
+ align:start position:0%
+the people who come to him with their
+problems and whom he classifies as
+
+ align:start position:0%
+problems and whom he classifies as
+ 
+
+ align:start position:0%
+problems and whom he classifies as
+neurotics or sick in some sense that
+
+ align:start position:0%
+neurotics or sick in some sense that
+ 
+
+ align:start position:0%
+neurotics or sick in some sense that
+they're somehow living under a romantic
+
+ align:start position:0%
+they're somehow living under a romantic
+ 
+
+ align:start position:0%
+they're somehow living under a romantic
+dream a romantic illusion and that they
+
+ align:start position:0%
+dream a romantic illusion and that they
+ 
+
+ align:start position:0%
+dream a romantic illusion and that they
+fall in love with somebody in a way that
+
+ align:start position:0%
+fall in love with somebody in a way that
+ 
+
+ align:start position:0%
+fall in love with somebody in a way that
+so powerful they can't be satisfied and
+
+ align:start position:0%
+so powerful they can't be satisfied and
+ 
+
+ align:start position:0%
+so powerful they can't be satisfied and
+the other person ditches them and they
+
+ align:start position:0%
+the other person ditches them and they
+ 
+
+ align:start position:0%
+the other person ditches them and they
+can't get over that now that's a
+
+ align:start position:0%
+can't get over that now that's a
+ 
+
+ align:start position:0%
+can't get over that now that's a
+reality but one of the profound things
+
+ align:start position:0%
+reality but one of the profound things
+ 
+
+ align:start position:0%
+reality but one of the profound things
+flud said about every well he said many
+
+ align:start position:0%
+flud said about every well he said many
+ 
+
+ align:start position:0%
+flud said about every well he said many
+profound things but this one is about um
+
+ align:start position:0%
+profound things but this one is about um
+ 
+
+ align:start position:0%
+profound things but this one is about um
+Neurosis in general he
+
+ align:start position:0%
+Neurosis in general he
+ 
+
+ align:start position:0%
+Neurosis in general he
+says neurosis must be very
+
+ align:start position:0%
+says neurosis must be very
+ 
+
+ align:start position:0%
+says neurosis must be very
+satisfying it seems like a you know
+
+ align:start position:0%
+satisfying it seems like a you know
+ 
+
+ align:start position:0%
+satisfying it seems like a you know
+Paradox uh course it means being sick
+
+ align:start position:0%
+Paradox uh course it means being sick
+ 
+
+ align:start position:0%
+Paradox uh course it means being sick
+Neurosis must be very satisfying in view
+
+ align:start position:0%
+Neurosis must be very satisfying in view
+ 
+
+ align:start position:0%
+Neurosis must be very satisfying in view
+of all the trouble that people go to in
+
+ align:start position:0%
+of all the trouble that people go to in
+ 
+
+ align:start position:0%
+of all the trouble that people go to in
+order to carry it out well I think this
+
+ align:start position:0%
+order to carry it out well I think this
+ 
+
+ align:start position:0%
+order to carry it out well I think this
+is a good example uh this falling in
+
+ align:start position:0%
+is a good example uh this falling in
+ 
+
+ align:start position:0%
+is a good example uh this falling in
+love and being
+
+ align:start position:0%
+love and being
+ 
+
+ align:start position:0%
+love and being
+hurt falling in love with love that song
+
+ align:start position:0%
+hurt falling in love with love that song
+ 
+
+ align:start position:0%
+hurt falling in love with love that song
+that marlina dri sings must be ecsta
+
+ align:start position:0%
+that marlina dri sings must be ecsta
+ 
+
+ align:start position:0%
+that marlina dri sings must be ecsta
+is ecstatic I don't deny it you know I
+
+ align:start position:0%
+is ecstatic I don't deny it you know I
+ 
+
+ align:start position:0%
+is ecstatic I don't deny it you know I
+observe it with awe um as long as it
+
+ align:start position:0%
+observe it with awe um as long as it
+ 
+
+ align:start position:0%
+observe it with awe um as long as it
+lasts but it doesn't usually last very
+
+ align:start position:0%
+lasts but it doesn't usually last very
+ 
+
+ align:start position:0%
+lasts but it doesn't usually last very
+long uh some sociologists have done a
+
+ align:start position:0%
+long uh some sociologists have done a
+ 
+
+ align:start position:0%
+long uh some sociologists have done a
+statistical study and they say that
+
+ align:start position:0%
+statistical study and they say that
+ 
+
+ align:start position:0%
+statistical study and they say that
+most people who fall in love literally
+
+ align:start position:0%
+most people who fall in love literally
+ 
+
+ align:start position:0%
+most people who fall in love literally
+fall in love because that's another
+
+ align:start position:0%
+fall in love because that's another
+ 
+
+ align:start position:0%
+fall in love because that's another
+distinction I make between falling in
+
+ align:start position:0%
+distinction I make between falling in
+ 
+
+ align:start position:0%
+distinction I make between falling in
+love being in love and staying in love
+
+ align:start position:0%
+love being in love and staying in love
+ 
+
+ align:start position:0%
+love being in love and staying in love
+we'll come back to that but you know
+
+ align:start position:0%
+we'll come back to that but you know
+ 
+
+ align:start position:0%
+we'll come back to that but you know
+falling in love in the strong romantic
+
+ align:start position:0%
+falling in love in the strong romantic
+ 
+
+ align:start position:0%
+falling in love in the strong romantic
+sense that you all understand and that
+
+ align:start position:0%
+sense that you all understand and that
+ 
+
+ align:start position:0%
+sense that you all understand and that
+some of you have gone through and some
+
+ align:start position:0%
+some of you have gone through and some
+ 
+
+ align:start position:0%
+some of you have gone through and some
+of you may be in right now uh that it
+
+ align:start position:0%
+of you may be in right now uh that it
+ 
+
+ align:start position:0%
+of you may be in right now uh that it
+doesn't usually last more I mean the on
+
+ align:start position:0%
+doesn't usually last more I mean the on
+ 
+
+ align:start position:0%
+doesn't usually last more I mean the on
+the average it doesn't last more than
+
+ align:start position:0%
+the average it doesn't last more than
+ 
+
+ align:start position:0%
+the average it doesn't last more than
+two months that's the statistical Norm
+
+ align:start position:0%
+two months that's the statistical Norm
+ 
+
+ align:start position:0%
+two months that's the statistical Norm
+that they found in their
+
+ align:start position:0%
+that they found in their
+ 
+
+ align:start position:0%
+that they found in their
+sociological uh research maybe but uh
+
+ align:start position:0%
+sociological uh research maybe but uh
+ 
+
+ align:start position:0%
+sociological uh research maybe but uh
+what a jol that gives you know it's like
+
+ align:start position:0%
+what a jol that gives you know it's like
+ 
+
+ align:start position:0%
+what a jol that gives you know it's like
+getting drunk and I can't say it's bad
+
+ align:start position:0%
+getting drunk and I can't say it's bad
+ 
+
+ align:start position:0%
+getting drunk and I can't say it's bad
+to get drunk I can't say it's bad to
+
+ align:start position:0%
+to get drunk I can't say it's bad to
+ 
+
+ align:start position:0%
+to get drunk I can't say it's bad to
+have ecstatic feelings for those who are
+
+ align:start position:0%
+have ecstatic feelings for those who are
+ 
+
+ align:start position:0%
+have ecstatic feelings for those who are
+willing to run the risk of being hurt
+
+ align:start position:0%
+willing to run the risk of being hurt
+ 
+
+ align:start position:0%
+willing to run the risk of being hurt
+for those who have somehow managed to
+
+ align:start position:0%
+for those who have somehow managed to
+ 
+
+ align:start position:0%
+for those who have somehow managed to
+learn the secret of falling out of love
+
+ align:start position:0%
+learn the secret of falling out of love
+ 
+
+ align:start position:0%
+learn the secret of falling out of love
+and then some people keep doing this
+
+ align:start position:0%
+and then some people keep doing this
+ 
+
+ align:start position:0%
+and then some people keep doing this
+over and over again they fall in love
+
+ align:start position:0%
+over and over again they fall in love
+ 
+
+ align:start position:0%
+over and over again they fall in love
+they fall out of love they fall in love
+
+ align:start position:0%
+they fall out of love they fall in love
+ 
+
+ align:start position:0%
+they fall out of love they fall in love
+fall out of love um maybe it's a way of
+
+ align:start position:0%
+fall out of love um maybe it's a way of
+ 
+
+ align:start position:0%
+fall out of love um maybe it's a way of
+life that I am simply incapable of
+
+ align:start position:0%
+life that I am simply incapable of
+ 
+
+ align:start position:0%
+life that I am simply incapable of
+having and uh you also being a uh a
+
+ align:start position:0%
+having and uh you also being a uh a
+ 
+
+ align:start position:0%
+having and uh you also being a uh a
+person of intellect you may suffer from
+
+ align:start position:0%
+person of intellect you may suffer from
+ 
+
+ align:start position:0%
+person of intellect you may suffer from
+the same disability than I am so can't
+
+ align:start position:0%
+the same disability than I am so can't
+ 
+
+ align:start position:0%
+the same disability than I am so can't
+say it's good or bad but Freud would
+
+ align:start position:0%
+say it's good or bad but Freud would
+ 
+
+ align:start position:0%
+say it's good or bad but Freud would
+have said it was bad he was an enemy of
+
+ align:start position:0%
+have said it was bad he was an enemy of
+ 
+
+ align:start position:0%
+have said it was bad he was an enemy of
+romantic love because he says it brings
+
+ align:start position:0%
+romantic love because he says it brings
+ 
+
+ align:start position:0%
+romantic love because he says it brings
+about so much suffering all these
+
+ align:start position:0%
+about so much suffering all these
+ 
+
+ align:start position:0%
+about so much suffering all these
+patients come to me now he doesn't rub
+
+ align:start position:0%
+patients come to me now he doesn't rub
+ 
+
+ align:start position:0%
+patients come to me now he doesn't rub
+his hands with Glee and say all this all
+
+ align:start position:0%
+his hands with Glee and say all this all
+ 
+
+ align:start position:0%
+his hands with Glee and say all this all
+the money I'm getting from from my
+
+ align:start position:0%
+the money I'm getting from from my
+ 
+
+ align:start position:0%
+the money I'm getting from from my
+clients he Grieves that there are so
+
+ align:start position:0%
+clients he Grieves that there are so
+ 
+
+ align:start position:0%
+clients he Grieves that there are so
+many sick people who need his help well
+
+ align:start position:0%
+many sick people who need his help well
+ 
+
+ align:start position:0%
+many sick people who need his help well
+that's the reason they need
+
+ align:start position:0%
+that's the reason they need
+ 
+
+ align:start position:0%
+that's the reason they need
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so well that all all I can recognize are
+
+ align:start position:0%
+so well that all all I can recognize are
+ 
+
+ align:start position:0%
+so well that all all I can recognize are
+what the facts are and I can't start
+
+ align:start position:0%
+what the facts are and I can't start
+ 
+
+ align:start position:0%
+what the facts are and I can't start
+using the evaluative terms of good and
+
+ align:start position:0%
+using the evaluative terms of good and
+ 
+
+ align:start position:0%
+using the evaluative terms of good and
+bad unless you give me a particular
+
+ align:start position:0%
+bad unless you give me a particular
+ 
+
+ align:start position:0%
+bad unless you give me a particular
+situation you know here's so and so who
+
+ align:start position:0%
+situation you know here's so and so who
+ 
+
+ align:start position:0%
+situation you know here's so and so who
+had such a brilliant career in front of
+
+ align:start position:0%
+had such a brilliant career in front of
+ 
+
+ align:start position:0%
+had such a brilliant career in front of
+him who was a genius and um who was
+
+ align:start position:0%
+him who was a genius and um who was
+ 
+
+ align:start position:0%
+him who was a genius and um who was
+capable of doing marvelous things and
+
+ align:start position:0%
+capable of doing marvelous things and
+ 
+
+ align:start position:0%
+capable of doing marvelous things and
+did marvelous things he had it in him uh
+
+ align:start position:0%
+did marvelous things he had it in him uh
+ 
+
+ align:start position:0%
+did marvelous things he had it in him uh
+he was so creative the world would have
+
+ align:start position:0%
+he was so creative the world would have
+ 
+
+ align:start position:0%
+he was so creative the world would have
+benefited and then he he fell in love
+
+ align:start position:0%
+benefited and then he he fell in love
+ 
+
+ align:start position:0%
+benefited and then he he fell in love
+with a woman who who ditched him and it
+
+ align:start position:0%
+with a woman who who ditched him and it
+ 
+
+ align:start position:0%
+with a woman who who ditched him and it
+was so painful that he committed suicide
+
+ align:start position:0%
+was so painful that he committed suicide
+ 
+
+ align:start position:0%
+was so painful that he committed suicide
+no then that was bad certainly right
+
+ align:start position:0%
+no then that was bad certainly right
+ 
+
+ align:start position:0%
+no then that was bad certainly right
+other people grow out of it and then and
+
+ align:start position:0%
+other people grow out of it and then and
+ 
+
+ align:start position:0%
+other people grow out of it and then and
+they learn from it and they
+
+ align:start position:0%
+they learn from it and they
+ 
+
+ align:start position:0%
+they learn from it and they
+develop and maybe then it's
+
+ align:start position:0%
+develop and maybe then it's
+ 
+
+ align:start position:0%
+develop and maybe then it's
+good verical you were saying something
+
+ align:start position:0%
+good verical you were saying something
+ 
+
+ align:start position:0%
+good verical you were saying something
+you just quickly explain your
+
+ align:start position:0%
+you just quickly explain your
+ 
+
+ align:start position:0%
+you just quickly explain your
+distinction between I think you just
+
+ align:start position:0%
+distinction between I think you just
+ 
+
+ align:start position:0%
+distinction between I think you just
+said falling in love being in love and
+
+ align:start position:0%
+said falling in love being in love and
+ 
+
+ align:start position:0%
+said falling in love being in love and
+staying in love okay I don't know that I
+
+ align:start position:0%
+staying in love okay I don't know that I
+ 
+
+ align:start position:0%
+staying in love okay I don't know that I
+go into it it's not in in there in the
+
+ align:start position:0%
+go into it it's not in in there in the
+ 
+
+ align:start position:0%
+go into it it's not in in there in the
+beginning it comes out in the third
+
+ align:start position:0%
+beginning it comes out in the third
+ 
+
+ align:start position:0%
+beginning it comes out in the third
+volume of the trilogy so if you look
+
+ align:start position:0%
+volume of the trilogy so if you look
+ 
+
+ align:start position:0%
+volume of the trilogy so if you look
+that up in the library under those words
+
+ align:start position:0%
+that up in the library under those words
+ 
+
+ align:start position:0%
+that up in the library under those words
+you might get more of treatment but I
+
+ align:start position:0%
+you might get more of treatment but I
+ 
+
+ align:start position:0%
+you might get more of treatment but I
+have to say before I get to there if you
+
+ align:start position:0%
+have to say before I get to there if you
+ 
+
+ align:start position:0%
+have to say before I get to there if you
+allow me um
+
+ align:start position:0%
+allow me um
+ 
+
+ align:start position:0%
+allow me um
+my philosophical life as I think I
+
+ align:start position:0%
+my philosophical life as I think I
+ 
+
+ align:start position:0%
+my philosophical life as I think I
+mentioned last time is in the making of
+
+ align:start position:0%
+mentioned last time is in the making of
+ 
+
+ align:start position:0%
+mentioned last time is in the making of
+distinctions and so I start out with one
+
+ align:start position:0%
+distinctions and so I start out with one
+ 
+
+ align:start position:0%
+distinctions and so I start out with one
+distinction see that philosophers have
+
+ align:start position:0%
+distinction see that philosophers have
+ 
+
+ align:start position:0%
+distinction see that philosophers have
+made have reified the alternatives and
+
+ align:start position:0%
+made have reified the alternatives and
+ 
+
+ align:start position:0%
+made have reified the alternatives and
+they've made them into a kind of dualism
+
+ align:start position:0%
+they've made them into a kind of dualism
+ 
+
+ align:start position:0%
+they've made them into a kind of dualism
+that can't be resolved and that's the
+
+ align:start position:0%
+that can't be resolved and that's the
+ 
+
+ align:start position:0%
+that can't be resolved and that's the
+big problem and for me the the solution
+
+ align:start position:0%
+big problem and for me the the solution
+ 
+
+ align:start position:0%
+big problem and for me the the solution
+is to show that um they they interweave
+
+ align:start position:0%
+is to show that um they they interweave
+ 
+
+ align:start position:0%
+is to show that um they they interweave
+in a way in Practical life and are
+
+ align:start position:0%
+in a way in Practical life and are
+ 
+
+ align:start position:0%
+in a way in Practical life and are
+presented artificially by philosophers
+
+ align:start position:0%
+presented artificially by philosophers
+ 
+
+ align:start position:0%
+presented artificially by philosophers
+because that's what the brain works well
+
+ align:start position:0%
+because that's what the brain works well
+ 
+
+ align:start position:0%
+because that's what the brain works well
+at making these Alternatives but in life
+
+ align:start position:0%
+at making these Alternatives but in life
+ 
+
+ align:start position:0%
+at making these Alternatives but in life
+somehow life harmonizes them so my
+
+ align:start position:0%
+somehow life harmonizes them so my
+ 
+
+ align:start position:0%
+somehow life harmonizes them so my
+methological procedure which I haven't
+
+ align:start position:0%
+methological procedure which I haven't
+ 
+
+ align:start position:0%
+methological procedure which I haven't
+which I don't do as a matter of
+
+ align:start position:0%
+which I don't do as a matter of
+ 
+
+ align:start position:0%
+which I don't do as a matter of
+calculation but this is seems to be the
+
+ align:start position:0%
+calculation but this is seems to be the
+ 
+
+ align:start position:0%
+calculation but this is seems to be the
+way I work this is the way my mind works
+
+ align:start position:0%
+way I work this is the way my mind works
+ 
+
+ align:start position:0%
+way I work this is the way my mind works
+is to make a distinction and then to
+
+ align:start position:0%
+is to make a distinction and then to
+ 
+
+ align:start position:0%
+is to make a distinction and then to
+attack people who carry out a similar
+
+ align:start position:0%
+attack people who carry out a similar
+ 
+
+ align:start position:0%
+attack people who carry out a similar
+distinction to extremes and then feel
+
+ align:start position:0%
+distinction to extremes and then feel
+ 
+
+ align:start position:0%
+distinction to extremes and then feel
+the need to harmonize the
+
+ align:start position:0%
+the need to harmonize the
+ 
+
+ align:start position:0%
+the need to harmonize the
+two having done that I then go on to
+
+ align:start position:0%
+two having done that I then go on to
+ 
+
+ align:start position:0%
+two having done that I then go on to
+another distinction and so particularly
+
+ align:start position:0%
+another distinction and so particularly
+ 
+
+ align:start position:0%
+another distinction and so particularly
+in the case of love work is a series of
+
+ align:start position:0%
+in the case of love work is a series of
+ 
+
+ align:start position:0%
+in the case of love work is a series of
+distinctions the first of which was
+
+ align:start position:0%
+distinctions the first of which was
+ 
+
+ align:start position:0%
+distinctions the first of which was
+bestow and Appraisal then there's
+
+ align:start position:0%
+bestow and Appraisal then there's
+ 
+
+ align:start position:0%
+bestow and Appraisal then there's
+dependence and interdependence then
+
+ align:start position:0%
+dependence and interdependence then
+ 
+
+ align:start position:0%
+dependence and interdependence then
+there's acceptance and rejection um U
+
+ align:start position:0%
+there's acceptance and rejection um U
+ 
+
+ align:start position:0%
+there's acceptance and rejection um U
+then then there is the U the sensuous
+
+ align:start position:0%
+then then there is the U the sensuous
+ 
+
+ align:start position:0%
+then then there is the U the sensuous
+and the passionate then there is falling
+
+ align:start position:0%
+and the passionate then there is falling
+ 
+
+ align:start position:0%
+and the passionate then there is falling
+in love with ideals being different from
+
+ align:start position:0%
+in love with ideals being different from
+ 
+
+ align:start position:0%
+in love with ideals being different from
+falling in love with things or falling
+
+ align:start position:0%
+falling in love with things or falling
+ 
+
+ align:start position:0%
+falling in love with things or falling
+in love with persons and that I do go
+
+ align:start position:0%
+in love with persons and that I do go
+ 
+
+ align:start position:0%
+in love with persons and that I do go
+into here and how the
+
+ align:start position:0%
+into here and how the
+ 
+
+ align:start position:0%
+into here and how the
+into weave in some way um I all of that
+
+ align:start position:0%
+into weave in some way um I all of that
+ 
+
+ align:start position:0%
+into weave in some way um I all of that
+comes out of the trilogy too but
+
+ align:start position:0%
+comes out of the trilogy too but
+ 
+
+ align:start position:0%
+comes out of the trilogy too but
+presented in a later at a later period
+
+ align:start position:0%
+presented in a later at a later period
+ 
+
+ align:start position:0%
+presented in a later at a later period
+in in the book and staying in love
+
+ align:start position:0%
+in in the book and staying in love
+ 
+
+ align:start position:0%
+in in the book and staying in love
+falling in love and being in love are
+
+ align:start position:0%
+falling in love and being in love are
+ 
+
+ align:start position:0%
+falling in love and being in love are
+are distinctions that I make and yet
+
+ align:start position:0%
+are distinctions that I make and yet
+ 
+
+ align:start position:0%
+are distinctions that I make and yet
+they can all occur
+
+ align:start position:0%
+they can all occur
+ 
+
+ align:start position:0%
+they can all occur
+simultaneously by Falling in
+
+ align:start position:0%
+simultaneously by Falling in
+ 
+
+ align:start position:0%
+simultaneously by Falling in
+Love I mean a very powerful ardent
+
+ align:start position:0%
+Love I mean a very powerful ardent
+ 
+
+ align:start position:0%
+Love I mean a very powerful ardent
+feeling that usually happens very
+
+ align:start position:0%
+feeling that usually happens very
+ 
+
+ align:start position:0%
+feeling that usually happens very
+suddenly that changes one's whole whole
+
+ align:start position:0%
+suddenly that changes one's whole whole
+ 
+
+ align:start position:0%
+suddenly that changes one's whole whole
+life and that sometimes can be so strong
+
+ align:start position:0%
+life and that sometimes can be so strong
+ 
+
+ align:start position:0%
+life and that sometimes can be so strong
+as a feeling that it undermines
+
+ align:start position:0%
+as a feeling that it undermines
+ 
+
+ align:start position:0%
+as a feeling that it undermines
+one's cognitive
+
+ align:start position:0%
+one's cognitive
+ 
+
+ align:start position:0%
+one's cognitive
+capacity it's what people of usually
+
+ align:start position:0%
+capacity it's what people of usually
+ 
+
+ align:start position:0%
+capacity it's what people of usually
+mean when they talk about love except
+
+ align:start position:0%
+mean when they talk about love except
+ 
+
+ align:start position:0%
+mean when they talk about love except
+they mean falling in love and then that
+
+ align:start position:0%
+they mean falling in love and then that
+ 
+
+ align:start position:0%
+they mean falling in love and then that
+gets to be interpreted in relation to
+
+ align:start position:0%
+gets to be interpreted in relation to
+ 
+
+ align:start position:0%
+gets to be interpreted in relation to
+19th century
+
+ align:start position:0%
+19th century
+ 
+
+ align:start position:0%
+19th century
+uh romantic philosophy which um uh I
+
+ align:start position:0%
+uh romantic philosophy which um uh I
+ 
+
+ align:start position:0%
+uh romantic philosophy which um uh I
+spent about 200 pages on in in the
+
+ align:start position:0%
+spent about 200 pages on in in the
+ 
+
+ align:start position:0%
+spent about 200 pages on in in the
+second volume uh and which is based on
+
+ align:start position:0%
+second volume uh and which is based on
+ 
+
+ align:start position:0%
+second volume uh and which is based on
+the idea of merging and and other other
+
+ align:start position:0%
+the idea of merging and and other other
+ 
+
+ align:start position:0%
+the idea of merging and and other other
+Concepts um that's falling
+
+ align:start position:0%
+Concepts um that's falling
+ 
+
+ align:start position:0%
+Concepts um that's falling
+love um do you know you might you
+
+ align:start position:0%
+love um do you know you might you
+ 
+
+ align:start position:0%
+love um do you know you might you
+probably do know a movie called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's with share and um
+
+ align:start position:0%
+um it's with share and um
+ 
+
+ align:start position:0%
+um it's with share and um
+and a uh a afo what is his name uh
+
+ align:start position:0%
+and a uh a afo what is his name uh
+ 
+
+ align:start position:0%
+and a uh a afo what is his name uh
+Affleck Affleck yeah um Ben Affleck
+
+ align:start position:0%
+Affleck Affleck yeah um Ben Affleck
+ 
+
+ align:start position:0%
+Affleck Affleck yeah um Ben Affleck
+um in which he uh falls in love with
+
+ align:start position:0%
+um in which he uh falls in love with
+ 
+
+ align:start position:0%
+um in which he uh falls in love with
+her and she uh doesn't feel that way
+
+ align:start position:0%
+her and she uh doesn't feel that way
+ 
+
+ align:start position:0%
+her and she uh doesn't feel that way
+towards him and or anybody and is ready
+
+ align:start position:0%
+towards him and or anybody and is ready
+ 
+
+ align:start position:0%
+towards him and or anybody and is ready
+to marry an older man who will take care
+
+ align:start position:0%
+to marry an older man who will take care
+ 
+
+ align:start position:0%
+to marry an older man who will take care
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+her but he he suddenly falls in love
+
+ align:start position:0%
+her but he he suddenly falls in love
+ 
+
+ align:start position:0%
+her but he he suddenly falls in love
+with her and at one point declares
+
+ align:start position:0%
+with her and at one point declares
+ 
+
+ align:start position:0%
+with her and at one point declares
+himself and she slaps him in the face
+
+ align:start position:0%
+himself and she slaps him in the face
+ 
+
+ align:start position:0%
+himself and she slaps him in the face
+you know share the kind of character
+
+ align:start position:0%
+you know share the kind of character
+ 
+
+ align:start position:0%
+you know share the kind of character
+that she usually portrays she slaps in
+
+ align:start position:0%
+that she usually portrays she slaps in
+ 
+
+ align:start position:0%
+that she usually portrays she slaps in
+her face and she says snap out of it in
+
+ align:start position:0%
+her face and she says snap out of it in
+ 
+
+ align:start position:0%
+her face and she says snap out of it in
+other words it's something that happens
+
+ align:start position:0%
+other words it's something that happens
+ 
+
+ align:start position:0%
+other words it's something that happens
+to you and then you're Gaga and can't
+
+ align:start position:0%
+to you and then you're Gaga and can't
+ 
+
+ align:start position:0%
+to you and then you're Gaga and can't
+see things right but it's very strong
+
+ align:start position:0%
+see things right but it's very strong
+ 
+
+ align:start position:0%
+see things right but it's very strong
+very powerful uh could be joyful if the
+
+ align:start position:0%
+very powerful uh could be joyful if the
+ 
+
+ align:start position:0%
+very powerful uh could be joyful if the
+other person resp wants it could be hell
+
+ align:start position:0%
+other person resp wants it could be hell
+ 
+
+ align:start position:0%
+other person resp wants it could be hell
+on Earth if you feel rejected but you
+
+ align:start position:0%
+on Earth if you feel rejected but you
+ 
+
+ align:start position:0%
+on Earth if you feel rejected but you
+can't turn your back on it you're
+
+ align:start position:0%
+can't turn your back on it you're
+ 
+
+ align:start position:0%
+can't turn your back on it you're
+dependent on that feeling That's Falling
+
+ align:start position:0%
+dependent on that feeling That's Falling
+ 
+
+ align:start position:0%
+dependent on that feeling That's Falling
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Love um and all and it usually is uh
+
+ align:start position:0%
+Love um and all and it usually is uh
+ 
+
+ align:start position:0%
+Love um and all and it usually is uh
+directly related to some sexual
+
+ align:start position:0%
+directly related to some sexual
+ 
+
+ align:start position:0%
+directly related to some sexual
+excitement and sexual excitement of the
+
+ align:start position:0%
+excitement and sexual excitement of the
+ 
+
+ align:start position:0%
+excitement and sexual excitement of the
+sort that I call the
+
+ align:start position:0%
+sort that I call the
+ 
+
+ align:start position:0%
+sort that I call the
+passionate in my analysis very briefly
+
+ align:start position:0%
+passionate in my analysis very briefly
+ 
+
+ align:start position:0%
+passionate in my analysis very briefly
+well I maybe I go into it there I don't
+
+ align:start position:0%
+well I maybe I go into it there I don't
+ 
+
+ align:start position:0%
+well I maybe I go into it there I don't
+remember um
+
+ align:start position:0%
+remember um
+ 
+
+ align:start position:0%
+remember um
+that comes out in other books of the
+
+ align:start position:0%
+that comes out in other books of the
+ 
+
+ align:start position:0%
+that comes out in other books of the
+sensuous and the passionate the
+
+ align:start position:0%
+sensuous and the passionate the
+ 
+
+ align:start position:0%
+sensuous and the passionate the
+passionate is having a sexual feeling
+
+ align:start position:0%
+passionate is having a sexual feeling
+ 
+
+ align:start position:0%
+passionate is having a sexual feeling
+that is very strong usually libidinal
+
+ align:start position:0%
+that is very strong usually libidinal
+ 
+
+ align:start position:0%
+that is very strong usually libidinal
+that is related to the genitals um a
+
+ align:start position:0%
+that is related to the genitals um a
+ 
+
+ align:start position:0%
+that is related to the genitals um a
+very strong inclination of
+
+ align:start position:0%
+very strong inclination of
+ 
+
+ align:start position:0%
+very strong inclination of
+feeling uh for Oneness with another
+
+ align:start position:0%
+feeling uh for Oneness with another
+ 
+
+ align:start position:0%
+feeling uh for Oneness with another
+person it's not cool it's hot right cool
+
+ align:start position:0%
+person it's not cool it's hot right cool
+ 
+
+ align:start position:0%
+person it's not cool it's hot right cool
+cool sex is what I call the sensuous and
+
+ align:start position:0%
+cool sex is what I call the sensuous and
+ 
+
+ align:start position:0%
+cool sex is what I call the sensuous and
+that's uh result from some kind of
+
+ align:start position:0%
+that's uh result from some kind of
+ 
+
+ align:start position:0%
+that's uh result from some kind of
+arousal or stimulation of uh one of the
+
+ align:start position:0%
+arousal or stimulation of uh one of the
+ 
+
+ align:start position:0%
+arousal or stimulation of uh one of the
+erotic zones in one's
+
+ align:start position:0%
+erotic zones in one's
+ 
+
+ align:start position:0%
+erotic zones in one's
+body and the way in which I like to
+
+ align:start position:0%
+body and the way in which I like to
+ 
+
+ align:start position:0%
+body and the way in which I like to
+illustrate that is
+
+ align:start position:0%
+illustrate that is
+ 
+
+ align:start position:0%
+illustrate that is
+um with the short little hairs on your
+
+ align:start position:0%
+um with the short little hairs on your
+ 
+
+ align:start position:0%
+um with the short little hairs on your
+wrist if you you can this is forgive me
+
+ align:start position:0%
+wrist if you you can this is forgive me
+ 
+
+ align:start position:0%
+wrist if you you can this is forgive me
+for engaging in a eroticism in
+
+ align:start position:0%
+for engaging in a eroticism in
+ 
+
+ align:start position:0%
+for engaging in a eroticism in
+public it's something you can do by
+
+ align:start position:0%
+public it's something you can do by
+ 
+
+ align:start position:0%
+public it's something you can do by
+yourself if you just stroke your the
+
+ align:start position:0%
+yourself if you just stroke your the
+ 
+
+ align:start position:0%
+yourself if you just stroke your the
+little hairs it's cool it's Pleasant
+
+ align:start position:0%
+little hairs it's cool it's Pleasant
+ 
+
+ align:start position:0%
+little hairs it's cool it's Pleasant
+it's a sensuous enjoyment there's
+
+ align:start position:0%
+it's a sensuous enjoyment there's
+ 
+
+ align:start position:0%
+it's a sensuous enjoyment there's
+something in the sense organs that is
+
+ align:start position:0%
+something in the sense organs that is
+ 
+
+ align:start position:0%
+something in the sense organs that is
+enjoyable well that is a very important
+
+ align:start position:0%
+enjoyable well that is a very important
+ 
+
+ align:start position:0%
+enjoyable well that is a very important
+part of sex and for some people that's
+
+ align:start position:0%
+part of sex and for some people that's
+ 
+
+ align:start position:0%
+part of sex and for some people that's
+the main part of sex they just like
+
+ align:start position:0%
+the main part of sex they just like
+ 
+
+ align:start position:0%
+the main part of sex they just like
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+stimulated um they don't their emotions
+
+ align:start position:0%
+stimulated um they don't their emotions
+ 
+
+ align:start position:0%
+stimulated um they don't their emotions
+don't get involved it's a sensory
+
+ align:start position:0%
+don't get involved it's a sensory
+ 
+
+ align:start position:0%
+don't get involved it's a sensory
+experience rather than an
+
+ align:start position:0%
+experience rather than an
+ 
+
+ align:start position:0%
+experience rather than an
+emotional experience it's cool the way
+
+ align:start position:0%
+emotional experience it's cool the way
+ 
+
+ align:start position:0%
+emotional experience it's cool the way
+this is cooling it's very cooling um and
+
+ align:start position:0%
+this is cooling it's very cooling um and
+ 
+
+ align:start position:0%
+this is cooling it's very cooling um and
+uh not hot right in the case of falling
+
+ align:start position:0%
+uh not hot right in the case of falling
+ 
+
+ align:start position:0%
+uh not hot right in the case of falling
+in love I don't think one could really
+
+ align:start position:0%
+in love I don't think one could really
+ 
+
+ align:start position:0%
+in love I don't think one could really
+understand it if one thought of it as
+
+ align:start position:0%
+understand it if one thought of it as
+ 
+
+ align:start position:0%
+understand it if one thought of it as
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+sensuous it's TD it's hot it's strongly
+
+ align:start position:0%
+sensuous it's TD it's hot it's strongly
+ 
+
+ align:start position:0%
+sensuous it's TD it's hot it's strongly
+emotional a sex drive usually directed
+
+ align:start position:0%
+emotional a sex drive usually directed
+ 
+
+ align:start position:0%
+emotional a sex drive usually directed
+toward some person that you fall in love
+
+ align:start position:0%
+toward some person that you fall in love
+ 
+
+ align:start position:0%
+toward some person that you fall in love
+with or some image of a person or
+
+ align:start position:0%
+with or some image of a person or
+ 
+
+ align:start position:0%
+with or some image of a person or
+whatever the the sex object may happen
+
+ align:start position:0%
+whatever the the sex object may happen
+ 
+
+ align:start position:0%
+whatever the the sex object may happen
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be That's Falling in Love right being in
+
+ align:start position:0%
+be That's Falling in Love right being in
+ 
+
+ align:start position:0%
+be That's Falling in Love right being in
+love is uh a different state though one
+
+ align:start position:0%
+love is uh a different state though one
+ 
+
+ align:start position:0%
+love is uh a different state though one
+that can happen after falling in love
+
+ align:start position:0%
+that can happen after falling in love
+ 
+
+ align:start position:0%
+that can happen after falling in love
+very often people fall in love and then
+
+ align:start position:0%
+very often people fall in love and then
+ 
+
+ align:start position:0%
+very often people fall in love and then
+they fall out of love and that's usually
+
+ align:start position:0%
+they fall out of love and that's usually
+ 
+
+ align:start position:0%
+they fall out of love and that's usually
+that may be what the sociologists are
+
+ align:start position:0%
+that may be what the sociologists are
+ 
+
+ align:start position:0%
+that may be what the sociologists are
+usually studying when they say that it
+
+ align:start position:0%
+usually studying when they say that it
+ 
+
+ align:start position:0%
+usually studying when they say that it
+lasts love lasts only a coule romantic
+
+ align:start position:0%
+lasts love lasts only a coule romantic
+ 
+
+ align:start position:0%
+lasts love lasts only a coule romantic
+lovees lasts only a couple of months but
+
+ align:start position:0%
+lovees lasts only a couple of months but
+ 
+
+ align:start position:0%
+lovees lasts only a couple of months but
+there are many people who uh start out
+
+ align:start position:0%
+there are many people who uh start out
+ 
+
+ align:start position:0%
+there are many people who uh start out
+with that strong powerful
+
+ align:start position:0%
+with that strong powerful
+ 
+
+ align:start position:0%
+with that strong powerful
+feeling and then they sort of settle
+
+ align:start position:0%
+feeling and then they sort of settle
+ 
+
+ align:start position:0%
+feeling and then they sort of settle
+down um either Society forces or their
+
+ align:start position:0%
+down um either Society forces or their
+ 
+
+ align:start position:0%
+down um either Society forces or their
+feelings about Society or forces them to
+
+ align:start position:0%
+feelings about Society or forces them to
+ 
+
+ align:start position:0%
+feelings about Society or forces them to
+get married maybe the woman becomes
+
+ align:start position:0%
+get married maybe the woman becomes
+ 
+
+ align:start position:0%
+get married maybe the woman becomes
+pregnant and is embarrassed to admit her
+
+ align:start position:0%
+pregnant and is embarrassed to admit her
+ 
+
+ align:start position:0%
+pregnant and is embarrassed to admit her
+condition or they just sort of work
+
+ align:start position:0%
+condition or they just sort of work
+ 
+
+ align:start position:0%
+condition or they just sort of work
+things out in a way that they make sense
+
+ align:start position:0%
+things out in a way that they make sense
+ 
+
+ align:start position:0%
+things out in a way that they make sense
+out of their inter inter interdependence
+
+ align:start position:0%
+out of their inter inter interdependence
+ 
+
+ align:start position:0%
+out of their inter inter interdependence
+of living together and uh they would be
+
+ align:start position:0%
+of living together and uh they would be
+ 
+
+ align:start position:0%
+of living together and uh they would be
+in love because they get to be attached
+
+ align:start position:0%
+in love because they get to be attached
+ 
+
+ align:start position:0%
+in love because they get to be attached
+to each other and they develop as as a
+
+ align:start position:0%
+to each other and they develop as as a
+ 
+
+ align:start position:0%
+to each other and they develop as as a
+unit and they start thinking in
+
+ align:start position:0%
+unit and they start thinking in
+ 
+
+ align:start position:0%
+unit and they start thinking in
+comparable ways instead of his thinking
+
+ align:start position:0%
+comparable ways instead of his thinking
+ 
+
+ align:start position:0%
+comparable ways instead of his thinking
+about how to succeed in the world he
+
+ align:start position:0%
+about how to succeed in the world he
+ 
+
+ align:start position:0%
+about how to succeed in the world he
+thinks about how to make a living for
+
+ align:start position:0%
+thinks about how to make a living for
+ 
+
+ align:start position:0%
+thinks about how to make a living for
+his family for his wife and maybe and
+
+ align:start position:0%
+his family for his wife and maybe and
+ 
+
+ align:start position:0%
+his family for his wife and maybe and
+possibly future children U uh instead of
+
+ align:start position:0%
+possibly future children U uh instead of
+ 
+
+ align:start position:0%
+possibly future children U uh instead of
+worrying about his own self-preservation
+
+ align:start position:0%
+worrying about his own self-preservation
+ 
+
+ align:start position:0%
+worrying about his own self-preservation
+he also worries about hers that's being
+
+ align:start position:0%
+he also worries about hers that's being
+ 
+
+ align:start position:0%
+he also worries about hers that's being
+in love but you see it doesn't have to
+
+ align:start position:0%
+in love but you see it doesn't have to
+ 
+
+ align:start position:0%
+in love but you see it doesn't have to
+be tared it can be a phase after
+
+ align:start position:0%
+be tared it can be a phase after
+ 
+
+ align:start position:0%
+be tared it can be a phase after
+that it or it can be independent of that
+
+ align:start position:0%
+that it or it can be independent of that
+ 
+
+ align:start position:0%
+that it or it can be independent of that
+people can be in love without ever
+
+ align:start position:0%
+people can be in love without ever
+ 
+
+ align:start position:0%
+people can be in love without ever
+having fallen in love the great
+
+ align:start position:0%
+having fallen in love the great
+ 
+
+ align:start position:0%
+having fallen in love the great
+tradition of marriage even in the
+
+ align:start position:0%
+tradition of marriage even in the
+ 
+
+ align:start position:0%
+tradition of marriage even in the
+western world but above all in the
+
+ align:start position:0%
+western world but above all in the
+ 
+
+ align:start position:0%
+western world but above all in the
+Eastern world where um the spouses were
+
+ align:start position:0%
+Eastern world where um the spouses were
+ 
+
+ align:start position:0%
+Eastern world where um the spouses were
+determined by the Elders of the group or
+
+ align:start position:0%
+determined by the Elders of the group or
+ 
+
+ align:start position:0%
+determined by the Elders of the group or
+by some political or economic necessity
+
+ align:start position:0%
+by some political or economic necessity
+ 
+
+ align:start position:0%
+by some political or economic necessity
+right sometimes without even knowing
+
+ align:start position:0%
+right sometimes without even knowing
+ 
+
+ align:start position:0%
+right sometimes without even knowing
+each other right or just getting a GL a
+
+ align:start position:0%
+each other right or just getting a GL a
+ 
+
+ align:start position:0%
+each other right or just getting a GL a
+glance at each other but that's
+
+ align:start position:0%
+glance at each other but that's
+ 
+
+ align:start position:0%
+glance at each other but that's
+all uh an arranged marriage through some
+
+ align:start position:0%
+all uh an arranged marriage through some
+ 
+
+ align:start position:0%
+all uh an arranged marriage through some
+kind of uh uh intermediary or the elders
+
+ align:start position:0%
+kind of uh uh intermediary or the elders
+ 
+
+ align:start position:0%
+kind of uh uh intermediary or the elders
+right that's by that's the great
+
+ align:start position:0%
+right that's by that's the great
+ 
+
+ align:start position:0%
+right that's by that's the great
+majority of human marriages it's not
+
+ align:start position:0%
+majority of human marriages it's not
+ 
+
+ align:start position:0%
+majority of human marriages it's not
+because of the western romantic ideas of
+
+ align:start position:0%
+because of the western romantic ideas of
+ 
+
+ align:start position:0%
+because of the western romantic ideas of
+falling in love with somebody and being
+
+ align:start position:0%
+falling in love with somebody and being
+ 
+
+ align:start position:0%
+falling in love with somebody and being
+on your own to decide whom you're going
+
+ align:start position:0%
+on your own to decide whom you're going
+ 
+
+ align:start position:0%
+on your own to decide whom you're going
+to live with there's a great tradition
+
+ align:start position:0%
+to live with there's a great tradition
+ 
+
+ align:start position:0%
+to live with there's a great tradition
+uh and Shakespeare is right in the
+
+ align:start position:0%
+uh and Shakespeare is right in the
+ 
+
+ align:start position:0%
+uh and Shakespeare is right in the
+middle in the Western World of the
+
+ align:start position:0%
+middle in the Western World of the
+ 
+
+ align:start position:0%
+middle in the Western World of the
+struggle to attain the modern democratic
+
+ align:start position:0%
+struggle to attain the modern democratic
+ 
+
+ align:start position:0%
+struggle to attain the modern democratic
+individualistic personal attachment and
+
+ align:start position:0%
+individualistic personal attachment and
+ 
+
+ align:start position:0%
+individualistic personal attachment and
+of a romantic sort but that's by and
+
+ align:start position:0%
+of a romantic sort but that's by and
+ 
+
+ align:start position:0%
+of a romantic sort but that's by and
+large has not been characteristic of the
+
+ align:start position:0%
+large has not been characteristic of the
+ 
+
+ align:start position:0%
+large has not been characteristic of the
+human race right so that people who get
+
+ align:start position:0%
+human race right so that people who get
+ 
+
+ align:start position:0%
+human race right so that people who get
+married under those
+
+ align:start position:0%
+married under those
+ 
+
+ align:start position:0%
+married under those
+conditions May sometimes be miserable
+
+ align:start position:0%
+conditions May sometimes be miserable
+ 
+
+ align:start position:0%
+conditions May sometimes be miserable
+because it's a bad marriage or they hate
+
+ align:start position:0%
+because it's a bad marriage or they hate
+ 
+
+ align:start position:0%
+because it's a bad marriage or they hate
+their husband or wife very shortly uh
+
+ align:start position:0%
+their husband or wife very shortly uh
+ 
+
+ align:start position:0%
+their husband or wife very shortly uh
+you know I didn't want her how did I get
+
+ align:start position:0%
+you know I didn't want her how did I get
+ 
+
+ align:start position:0%
+you know I didn't want her how did I get
+how you know it was good for the family
+
+ align:start position:0%
+how you know it was good for the family
+ 
+
+ align:start position:0%
+how you know it was good for the family
+but it's not good for me but if it's a
+
+ align:start position:0%
+but it's not good for me but if it's a
+ 
+
+ align:start position:0%
+but it's not good for me but if it's a
+wise family and if it comes out of a
+
+ align:start position:0%
+wise family and if it comes out of a
+ 
+
+ align:start position:0%
+wise family and if it comes out of a
+uh a healthy family and the parents are
+
+ align:start position:0%
+uh a healthy family and the parents are
+ 
+
+ align:start position:0%
+uh a healthy family and the parents are
+wise or whoever makes the decision they
+
+ align:start position:0%
+wise or whoever makes the decision they
+ 
+
+ align:start position:0%
+wise or whoever makes the decision they
+might or if they have good luck they end
+
+ align:start position:0%
+might or if they have good luck they end
+ 
+
+ align:start position:0%
+might or if they have good luck they end
+up with just a good person somebody they
+
+ align:start position:0%
+up with just a good person somebody they
+ 
+
+ align:start position:0%
+up with just a good person somebody they
+can live with very
+
+ align:start position:0%
+can live with very
+ 
+
+ align:start position:0%
+can live with very
+well if they don't have any emotions
+
+ align:start position:0%
+well if they don't have any emotions
+ 
+
+ align:start position:0%
+well if they don't have any emotions
+then it's what's called The Marriage of
+
+ align:start position:0%
+then it's what's called The Marriage of
+ 
+
+ align:start position:0%
+then it's what's called The Marriage of
+convenience so that it's convenient to
+
+ align:start position:0%
+convenience so that it's convenient to
+ 
+
+ align:start position:0%
+convenience so that it's convenient to
+the wife to have a support and to get
+
+ align:start position:0%
+the wife to have a support and to get
+ 
+
+ align:start position:0%
+the wife to have a support and to get
+money and um to have a husband who will
+
+ align:start position:0%
+money and um to have a husband who will
+ 
+
+ align:start position:0%
+money and um to have a husband who will
+not beat her but uh will give her
+
+ align:start position:0%
+not beat her but uh will give her
+ 
+
+ align:start position:0%
+not beat her but uh will give her
+children
+
+ align:start position:0%
+children
+ 
+
+ align:start position:0%
+children
+and it's socially
+
+ align:start position:0%
+and it's socially
+ 
+
+ align:start position:0%
+and it's socially
+advantageous or in in France where uh
+
+ align:start position:0%
+advantageous or in in France where uh
+ 
+
+ align:start position:0%
+advantageous or in in France where uh
+dualism has been a philosophy for
+
+ align:start position:0%
+dualism has been a philosophy for
+ 
+
+ align:start position:0%
+dualism has been a philosophy for
+centuries at the various points women
+
+ align:start position:0%
+centuries at the various points women
+ 
+
+ align:start position:0%
+centuries at the various points women
+married a man in order to be married and
+
+ align:start position:0%
+married a man in order to be married and
+ 
+
+ align:start position:0%
+married a man in order to be married and
+after they were married they would take
+
+ align:start position:0%
+after they were married they would take
+ 
+
+ align:start position:0%
+after they were married they would take
+any lovers they wanted because they
+
+ align:start position:0%
+any lovers they wanted because they
+ 
+
+ align:start position:0%
+any lovers they wanted because they
+would be a married woman with money and
+
+ align:start position:0%
+would be a married woman with money and
+ 
+
+ align:start position:0%
+would be a married woman with money and
+so on and the husband probably had uh
+
+ align:start position:0%
+so on and the husband probably had uh
+ 
+
+ align:start position:0%
+so on and the husband probably had uh
+Mistresses so either he wouldn't care uh
+
+ align:start position:0%
+Mistresses so either he wouldn't care uh
+ 
+
+ align:start position:0%
+Mistresses so either he wouldn't care uh
+or if he was afraid of being called or
+
+ align:start position:0%
+or if he was afraid of being called or
+ 
+
+ align:start position:0%
+or if he was afraid of being called or
+cockled U the woman would contrive that
+
+ align:start position:0%
+cockled U the woman would contrive that
+ 
+
+ align:start position:0%
+cockled U the woman would contrive that
+he didn't know you see provided the
+
+ align:start position:0%
+he didn't know you see provided the
+ 
+
+ align:start position:0%
+he didn't know you see provided the
+woman being married provided her a
+
+ align:start position:0%
+woman being married provided her a
+ 
+
+ align:start position:0%
+woman being married provided her a
+degree of strength and Independence such
+
+ align:start position:0%
+degree of strength and Independence such
+ 
+
+ align:start position:0%
+degree of strength and Independence such
+that she could exercise her freedom to
+
+ align:start position:0%
+that she could exercise her freedom to
+ 
+
+ align:start position:0%
+that she could exercise her freedom to
+fall in love with somebody she does one
+
+ align:start position:0%
+fall in love with somebody she does one
+ 
+
+ align:start position:0%
+fall in love with somebody she does one
+that would be more like a marriage of
+
+ align:start position:0%
+that would be more like a marriage of
+ 
+
+ align:start position:0%
+that would be more like a marriage of
+convenience but uh being in love would
+
+ align:start position:0%
+convenience but uh being in love would
+ 
+
+ align:start position:0%
+convenience but uh being in love would
+be a situation which is more like the
+
+ align:start position:0%
+be a situation which is more like the
+ 
+
+ align:start position:0%
+be a situation which is more like the
+present contemporary scene because in
+
+ align:start position:0%
+present contemporary scene because in
+ 
+
+ align:start position:0%
+present contemporary scene because in
+America we haven't gone into these
+
+ align:start position:0%
+America we haven't gone into these
+ 
+
+ align:start position:0%
+America we haven't gone into these
+marriages of
+
+ align:start position:0%
+marriages of
+ 
+
+ align:start position:0%
+marriages of
+conveniences very much people are
+
+ align:start position:0%
+conveniences very much people are
+ 
+
+ align:start position:0%
+conveniences very much people are
+expected to marry somebody they will
+
+ align:start position:0%
+expected to marry somebody they will
+ 
+
+ align:start position:0%
+expected to marry somebody they will
+love and try very hard and fail very
+
+ align:start position:0%
+love and try very hard and fail very
+ 
+
+ align:start position:0%
+love and try very hard and fail very
+often and so we have an enormous
+
+ align:start position:0%
+often and so we have an enormous
+ 
+
+ align:start position:0%
+often and so we have an enormous
+marriage uh rate of marri uh I mean rate
+
+ align:start position:0%
+marriage uh rate of marri uh I mean rate
+ 
+
+ align:start position:0%
+marriage uh rate of marri uh I mean rate
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+divorce um enormous rate of divorce lead
+
+ align:start position:0%
+divorce um enormous rate of divorce lead
+ 
+
+ align:start position:0%
+divorce um enormous rate of divorce lead
+uh and therefore a large number of
+
+ align:start position:0%
+uh and therefore a large number of
+ 
+
+ align:start position:0%
+uh and therefore a large number of
+remarriages or you know all the people
+
+ align:start position:0%
+remarriages or you know all the people
+ 
+
+ align:start position:0%
+remarriages or you know all the people
+get divorced in this country generally
+
+ align:start position:0%
+get divorced in this country generally
+ 
+
+ align:start position:0%
+get divorced in this country generally
+remarry so it isn't as if divorce is
+
+ align:start position:0%
+remarry so it isn't as if divorce is
+ 
+
+ align:start position:0%
+remarry so it isn't as if divorce is
+destroying marriage in this country it's
+
+ align:start position:0%
+destroying marriage in this country it's
+ 
+
+ align:start position:0%
+destroying marriage in this country it's
+uh part of the perpetuation of it it's
+
+ align:start position:0%
+uh part of the perpetuation of it it's
+ 
+
+ align:start position:0%
+uh part of the perpetuation of it it's
+in succession Mar success of marriages
+
+ align:start position:0%
+in succession Mar success of marriages
+ 
+
+ align:start position:0%
+in succession Mar success of marriages
+and then with your generation there are
+
+ align:start position:0%
+and then with your generation there are
+ 
+
+ align:start position:0%
+and then with your generation there are
+complications because they all of the
+
+ align:start position:0%
+complications because they all of the
+ 
+
+ align:start position:0%
+complications because they all of the
+informal marriages um trial marriages in
+
+ align:start position:0%
+informal marriages um trial marriages in
+ 
+
+ align:start position:0%
+informal marriages um trial marriages in
+which people live as if they were
+
+ align:start position:0%
+which people live as if they were
+ 
+
+ align:start position:0%
+which people live as if they were
+married and then separate or don't but
+
+ align:start position:0%
+married and then separate or don't but
+ 
+
+ align:start position:0%
+married and then separate or don't but
+uh the point about the American dream
+
+ align:start position:0%
+uh the point about the American dream
+ 
+
+ align:start position:0%
+uh the point about the American dream
+until recent L was people would uh marry
+
+ align:start position:0%
+until recent L was people would uh marry
+ 
+
+ align:start position:0%
+until recent L was people would uh marry
+somebody they can be in love with
+
+ align:start position:0%
+somebody they can be in love with
+ 
+
+ align:start position:0%
+somebody they can be in love with
+whether or not they actually fall in in
+
+ align:start position:0%
+whether or not they actually fall in in
+ 
+
+ align:start position:0%
+whether or not they actually fall in in
+love they need may need a little proding
+
+ align:start position:0%
+love they need may need a little proding
+ 
+
+ align:start position:0%
+love they need may need a little proding
+from the family they may have a need it
+
+ align:start position:0%
+from the family they may have a need it
+ 
+
+ align:start position:0%
+from the family they may have a need it
+would help for them to fall in love but
+
+ align:start position:0%
+would help for them to fall in love but
+ 
+
+ align:start position:0%
+would help for them to fall in love but
+not completely because then they'll end
+
+ align:start position:0%
+not completely because then they'll end
+ 
+
+ align:start position:0%
+not completely because then they'll end
+up being carried away uh and losing
+
+ align:start position:0%
+up being carried away uh and losing
+ 
+
+ align:start position:0%
+up being carried away uh and losing
+their reason but to be sufficiently
+
+ align:start position:0%
+their reason but to be sufficiently
+ 
+
+ align:start position:0%
+their reason but to be sufficiently
+engaged so that when they do marry they
+
+ align:start position:0%
+engaged so that when they do marry they
+ 
+
+ align:start position:0%
+engaged so that when they do marry they
+real feel they feel authentic love for
+
+ align:start position:0%
+real feel they feel authentic love for
+ 
+
+ align:start position:0%
+real feel they feel authentic love for
+the other person that's being in love
+
+ align:start position:0%
+the other person that's being in love
+ 
+
+ align:start position:0%
+the other person that's being in love
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right staying in
+
+ align:start position:0%
+right staying in
+ 
+
+ align:start position:0%
+right staying in
+love um and being in love is usually
+
+ align:start position:0%
+love um and being in love is usually
+ 
+
+ align:start position:0%
+love um and being in love is usually
+sexual because that's what marriage is
+
+ align:start position:0%
+sexual because that's what marriage is
+ 
+
+ align:start position:0%
+sexual because that's what marriage is
+all about marriage is a way of
+
+ align:start position:0%
+all about marriage is a way of
+ 
+
+ align:start position:0%
+all about marriage is a way of
+approving the unlimited access to the
+
+ align:start position:0%
+approving the unlimited access to the
+ 
+
+ align:start position:0%
+approving the unlimited access to the
+per the other person the person of the
+
+ align:start position:0%
+per the other person the person of the
+ 
+
+ align:start position:0%
+per the other person the person of the
+opposite sex for sexual P purposes so
+
+ align:start position:0%
+opposite sex for sexual P purposes so
+ 
+
+ align:start position:0%
+opposite sex for sexual P purposes so
+that uh if your promiscuous at least the
+
+ align:start position:0%
+that uh if your promiscuous at least the
+ 
+
+ align:start position:0%
+that uh if your promiscuous at least the
+way it was in my you know until recently
+
+ align:start position:0%
+way it was in my you know until recently
+ 
+
+ align:start position:0%
+way it was in my you know until recently
+if you were a promiscuous woman um every
+
+ align:start position:0%
+if you were a promiscuous woman um every
+ 
+
+ align:start position:0%
+if you were a promiscuous woman um every
+the society frowned on you if you were a
+
+ align:start position:0%
+the society frowned on you if you were a
+ 
+
+ align:start position:0%
+the society frowned on you if you were a
+prostitute meaning a professional
+
+ align:start position:0%
+prostitute meaning a professional
+ 
+
+ align:start position:0%
+prostitute meaning a professional
+Society considered you sinful evil and
+
+ align:start position:0%
+Society considered you sinful evil and
+ 
+
+ align:start position:0%
+Society considered you sinful evil and
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+criminal but still the men kept the kept
+
+ align:start position:0%
+criminal but still the men kept the kept
+ 
+
+ align:start position:0%
+criminal but still the men kept the kept
+encouraging the perpetuation of that
+
+ align:start position:0%
+encouraging the perpetuation of that
+ 
+
+ align:start position:0%
+encouraging the perpetuation of that
+institution uh if however you're a woman
+
+ align:start position:0%
+institution uh if however you're a woman
+ 
+
+ align:start position:0%
+institution uh if however you're a woman
+who with her husband is is very lustful
+
+ align:start position:0%
+who with her husband is is very lustful
+ 
+
+ align:start position:0%
+who with her husband is is very lustful
+and has as much sex with him as some
+
+ align:start position:0%
+and has as much sex with him as some
+ 
+
+ align:start position:0%
+and has as much sex with him as some
+prostitutes have with their clients and
+
+ align:start position:0%
+prostitutes have with their clients and
+ 
+
+ align:start position:0%
+prostitutes have with their clients and
+the Kinsey Report I don't know I was
+
+ align:start position:0%
+the Kinsey Report I don't know I was
+ 
+
+ align:start position:0%
+the Kinsey Report I don't know I was
+surprised in one of my classes nobody
+
+ align:start position:0%
+surprised in one of my classes nobody
+ 
+
+ align:start position:0%
+surprised in one of my classes nobody
+knew what the Kinsey reports were it he
+
+ align:start position:0%
+knew what the Kinsey reports were it he
+ 
+
+ align:start position:0%
+knew what the Kinsey reports were it he
+was the first one to take uh polls and
+
+ align:start position:0%
+was the first one to take uh polls and
+ 
+
+ align:start position:0%
+was the first one to take uh polls and
+find out how many times people had what
+
+ align:start position:0%
+find out how many times people had what
+ 
+
+ align:start position:0%
+find out how many times people had what
+he called sexual outlets and in marriage
+
+ align:start position:0%
+he called sexual outlets and in marriage
+ 
+
+ align:start position:0%
+he called sexual outlets and in marriage
+and out of marriage and um in some cases
+
+ align:start position:0%
+and out of marriage and um in some cases
+ 
+
+ align:start position:0%
+and out of marriage and um in some cases
+there were I remember seven a day per
+
+ align:start position:0%
+there were I remember seven a day per
+ 
+
+ align:start position:0%
+there were I remember seven a day per
+every day of the week for married
+
+ align:start position:0%
+every day of the week for married
+ 
+
+ align:start position:0%
+every day of the week for married
+people that may not equal what some
+
+ align:start position:0%
+people that may not equal what some
+ 
+
+ align:start position:0%
+people that may not equal what some
+prostitutes do but probably maybe it's
+
+ align:start position:0%
+prostitutes do but probably maybe it's
+ 
+
+ align:start position:0%
+prostitutes do but probably maybe it's
+more than some but the point is that if
+
+ align:start position:0%
+more than some but the point is that if
+ 
+
+ align:start position:0%
+more than some but the point is that if
+you're married that's toally respectful
+
+ align:start position:0%
+you're married that's toally respectful
+ 
+
+ align:start position:0%
+you're married that's toally respectful
+who's nobody cares you're married you
+
+ align:start position:0%
+who's nobody cares you're married you
+ 
+
+ align:start position:0%
+who's nobody cares you're married you
+can do what you want in your bedroom
+
+ align:start position:0%
+can do what you want in your bedroom
+ 
+
+ align:start position:0%
+can do what you want in your bedroom
+with your husband as long as it's
+
+ align:start position:0%
+with your husband as long as it's
+ 
+
+ align:start position:0%
+with your husband as long as it's
+consensual and he doesn't rape the wife
+
+ align:start position:0%
+consensual and he doesn't rape the wife
+ 
+
+ align:start position:0%
+consensual and he doesn't rape the wife
+or she doesn't beat him into submission
+
+ align:start position:0%
+or she doesn't beat him into submission
+ 
+
+ align:start position:0%
+or she doesn't beat him into submission
+or or uh hurt him when they she uh gets
+
+ align:start position:0%
+or or uh hurt him when they she uh gets
+ 
+
+ align:start position:0%
+or or uh hurt him when they she uh gets
+him into satom masochistic situations uh
+
+ align:start position:0%
+him into satom masochistic situations uh
+ 
+
+ align:start position:0%
+him into satom masochistic situations uh
+nobody cares uh so that marriage
+
+ align:start position:0%
+nobody cares uh so that marriage
+ 
+
+ align:start position:0%
+nobody cares uh so that marriage
+perpetuates
+
+ align:start position:0%
+perpetuates
+ 
+
+ align:start position:0%
+perpetuates
+love and it is part of being in love or
+
+ align:start position:0%
+love and it is part of being in love or
+ 
+
+ align:start position:0%
+love and it is part of being in love or
+can be depending on the individuals you
+
+ align:start position:0%
+can be depending on the individuals you
+ 
+
+ align:start position:0%
+can be depending on the individuals you
+can be in love with somebody and have a
+
+ align:start position:0%
+can be in love with somebody and have a
+ 
+
+ align:start position:0%
+can be in love with somebody and have a
+sexless marriage which
+
+ align:start position:0%
+sexless marriage which
+ 
+
+ align:start position:0%
+sexless marriage which
+exists but in most cases sex is a very
+
+ align:start position:0%
+exists but in most cases sex is a very
+ 
+
+ align:start position:0%
+exists but in most cases sex is a very
+important part of being in love in that
+
+ align:start position:0%
+important part of being in love in that
+ 
+
+ align:start position:0%
+important part of being in love in that
+inter intermediary stage I say
+
+ align:start position:0%
+inter intermediary stage I say
+ 
+
+ align:start position:0%
+inter intermediary stage I say
+intermediary because uh people live very
+
+ align:start position:0%
+intermediary because uh people live very
+ 
+
+ align:start position:0%
+intermediary because uh people live very
+long particularly
+
+ align:start position:0%
+long particularly
+ 
+
+ align:start position:0%
+long particularly
+nowadays and they don't they're not the
+
+ align:start position:0%
+nowadays and they don't they're not the
+ 
+
+ align:start position:0%
+nowadays and they don't they're not the
+sexual creatures very long uh the
+
+ align:start position:0%
+sexual creatures very long uh the
+ 
+
+ align:start position:0%
+sexual creatures very long uh the
+passionate sex uh is directly related to
+
+ align:start position:0%
+passionate sex uh is directly related to
+ 
+
+ align:start position:0%
+passionate sex uh is directly related to
+hormones uh above all testosterone in
+
+ align:start position:0%
+hormones uh above all testosterone in
+ 
+
+ align:start position:0%
+hormones uh above all testosterone in
+the men and progestin and and and EST
+
+ align:start position:0%
+the men and progestin and and and EST
+ 
+
+ align:start position:0%
+the men and progestin and and and EST
+estrogen in the woman and that which and
+
+ align:start position:0%
+estrogen in the woman and that which and
+ 
+
+ align:start position:0%
+estrogen in the woman and that which and
+those are all geared to reproductive
+
+ align:start position:0%
+those are all geared to reproductive
+ 
+
+ align:start position:0%
+those are all geared to reproductive
+Necessities so
+
+ align:start position:0%
+Necessities so
+ 
+
+ align:start position:0%
+Necessities so
+estrogen um is at a peak in women just
+
+ align:start position:0%
+estrogen um is at a peak in women just
+ 
+
+ align:start position:0%
+estrogen um is at a peak in women just
+before the period of ovulation so that
+
+ align:start position:0%
+before the period of ovulation so that
+ 
+
+ align:start position:0%
+before the period of ovulation so that
+she'll get excited and available and
+
+ align:start position:0%
+she'll get excited and available and
+ 
+
+ align:start position:0%
+she'll get excited and available and
+then it uh in her ludal phase which is
+
+ align:start position:0%
+then it uh in her ludal phase which is
+ 
+
+ align:start position:0%
+then it uh in her ludal phase which is
+the menopause not the menopause the
+
+ align:start position:0%
+the menopause not the menopause the
+ 
+
+ align:start position:0%
+the menopause not the menopause the
+menstrual per part of the uh period uh
+
+ align:start position:0%
+menstrual per part of the uh period uh
+ 
+
+ align:start position:0%
+menstrual per part of the uh period uh
+it won't be Estrin it'll be other
+
+ align:start position:0%
+it won't be Estrin it'll be other
+ 
+
+ align:start position:0%
+it won't be Estrin it'll be other
+chemicals
+
+ align:start position:0%
+chemicals
+ 
+
+ align:start position:0%
+chemicals
+so that she isn't excited because that's
+
+ align:start position:0%
+so that she isn't excited because that's
+ 
+
+ align:start position:0%
+so that she isn't excited because that's
+not a good time uh to become a
+
+ align:start position:0%
+not a good time uh to become a
+ 
+
+ align:start position:0%
+not a good time uh to become a
+fertilized right uh so that passionate
+
+ align:start position:0%
+fertilized right uh so that passionate
+ 
+
+ align:start position:0%
+fertilized right uh so that passionate
+sex is surely geared to the requisite
+
+ align:start position:0%
+sex is surely geared to the requisite
+ 
+
+ align:start position:0%
+sex is surely geared to the requisite
+hormones in men and in women they're
+
+ align:start position:0%
+hormones in men and in women they're
+ 
+
+ align:start position:0%
+hormones in men and in women they're
+different than men and from women but
+
+ align:start position:0%
+different than men and from women but
+ 
+
+ align:start position:0%
+different than men and from women but
+still the hormones are important for
+
+ align:start position:0%
+still the hormones are important for
+ 
+
+ align:start position:0%
+still the hormones are important for
+passionate
+
+ align:start position:0%
+passionate
+ 
+
+ align:start position:0%
+passionate
+sex uh sensuous sex you can have forever
+
+ align:start position:0%
+sex uh sensuous sex you can have forever
+ 
+
+ align:start position:0%
+sex uh sensuous sex you can have forever
+because it means somebody's stroking you
+
+ align:start position:0%
+because it means somebody's stroking you
+ 
+
+ align:start position:0%
+because it means somebody's stroking you
+or you're feeling sensuous pleasures
+
+ align:start position:0%
+or you're feeling sensuous pleasures
+ 
+
+ align:start position:0%
+or you're feeling sensuous pleasures
+espe especially if they're related to
+
+ align:start position:0%
+espe especially if they're related to
+ 
+
+ align:start position:0%
+espe especially if they're related to
+your genitals but it may not there may
+
+ align:start position:0%
+your genitals but it may not there may
+ 
+
+ align:start position:0%
+your genitals but it may not there may
+not be much that's happening to your
+
+ align:start position:0%
+not be much that's happening to your
+ 
+
+ align:start position:0%
+not be much that's happening to your
+feelings and eventually they may not be
+
+ align:start position:0%
+feelings and eventually they may not be
+ 
+
+ align:start position:0%
+feelings and eventually they may not be
+much that's going to be happening in the
+
+ align:start position:0%
+much that's going to be happening in the
+ 
+
+ align:start position:0%
+much that's going to be happening in the
+genitals because of the diminution of
+
+ align:start position:0%
+genitals because of the diminution of
+ 
+
+ align:start position:0%
+genitals because of the diminution of
+the um of the
+
+ align:start position:0%
+the um of the
+ 
+
+ align:start position:0%
+the um of the
+hormones if you live long enough and if
+
+ align:start position:0%
+hormones if you live long enough and if
+ 
+
+ align:start position:0%
+hormones if you live long enough and if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+become intimate enough not not talking
+
+ align:start position:0%
+become intimate enough not not talking
+ 
+
+ align:start position:0%
+become intimate enough not not talking
+sexually but if you become close enough
+
+ align:start position:0%
+sexually but if you become close enough
+ 
+
+ align:start position:0%
+sexually but if you become close enough
+and interpenetrate in enough and share
+
+ align:start position:0%
+and interpenetrate in enough and share
+ 
+
+ align:start position:0%
+and interpenetrate in enough and share
+your life enough with another person if
+
+ align:start position:0%
+your life enough with another person if
+ 
+
+ align:start position:0%
+your life enough with another person if
+you depend on each other in this
+
+ align:start position:0%
+you depend on each other in this
+ 
+
+ align:start position:0%
+you depend on each other in this
+interdependent way that I talk about you
+
+ align:start position:0%
+interdependent way that I talk about you
+ 
+
+ align:start position:0%
+interdependent way that I talk about you
+may very well Outlast the period of
+
+ align:start position:0%
+may very well Outlast the period of
+ 
+
+ align:start position:0%
+may very well Outlast the period of
+sexual excitement but you won't care
+
+ align:start position:0%
+sexual excitement but you won't care
+ 
+
+ align:start position:0%
+sexual excitement but you won't care
+anymore you know if you had a choice at
+
+ align:start position:0%
+anymore you know if you had a choice at
+ 
+
+ align:start position:0%
+anymore you know if you had a choice at
+that age between going back to the days
+
+ align:start position:0%
+that age between going back to the days
+ 
+
+ align:start position:0%
+that age between going back to the days
+when uh the man for instance gets
+
+ align:start position:0%
+when uh the man for instance gets
+ 
+
+ align:start position:0%
+when uh the man for instance gets
+excited by a beautiful young girl
+
+ align:start position:0%
+excited by a beautiful young girl
+ 
+
+ align:start position:0%
+excited by a beautiful young girl
+walking by or not having that excitement
+
+ align:start position:0%
+walking by or not having that excitement
+ 
+
+ align:start position:0%
+walking by or not having that excitement
+but having your beloved wife with you
+
+ align:start position:0%
+but having your beloved wife with you
+ 
+
+ align:start position:0%
+but having your beloved wife with you
+the wife that you've had for the last 60
+
+ align:start position:0%
+the wife that you've had for the last 60
+ 
+
+ align:start position:0%
+the wife that you've had for the last 60
+years let's say their in their 80s uh
+
+ align:start position:0%
+years let's say their in their 80s uh
+ 
+
+ align:start position:0%
+years let's say their in their 80s uh
+and whom you can't bear to think of
+
+ align:start position:0%
+and whom you can't bear to think of
+ 
+
+ align:start position:0%
+and whom you can't bear to think of
+Living
+
+ align:start position:0%
+Living
+ 
+
+ align:start position:0%
+Living
+Without You Might Pro prefer the
+
+ align:start position:0%
+Without You Might Pro prefer the
+ 
+
+ align:start position:0%
+Without You Might Pro prefer the
+latter now that's staying in love that's
+
+ align:start position:0%
+latter now that's staying in love that's
+ 
+
+ align:start position:0%
+latter now that's staying in love that's
+a different that's a prolongation of the
+
+ align:start position:0%
+a different that's a prolongation of the
+ 
+
+ align:start position:0%
+a different that's a prolongation of the
+being in love which involves alterations
+
+ align:start position:0%
+being in love which involves alterations
+ 
+
+ align:start position:0%
+being in love which involves alterations
+that happen in human being given our
+
+ align:start position:0%
+that happen in human being given our
+ 
+
+ align:start position:0%
+that happen in human being given our
+nature given our physiology over the
+
+ align:start position:0%
+nature given our physiology over the
+ 
+
+ align:start position:0%
+nature given our physiology over the
+course of many
+
+ align:start position:0%
+course of many
+ 
+
+ align:start position:0%
+course of many
+years can you have all at
+
+ align:start position:0%
+years can you have all at
+ 
+
+ align:start position:0%
+years can you have all at
+once maybe uh can you have all three I
+
+ align:start position:0%
+once maybe uh can you have all three I
+ 
+
+ align:start position:0%
+once maybe uh can you have all three I
+think that does happen that some people
+
+ align:start position:0%
+think that does happen that some people
+ 
+
+ align:start position:0%
+think that does happen that some people
+fall in love and then they are are in
+
+ align:start position:0%
+fall in love and then they are are in
+ 
+
+ align:start position:0%
+fall in love and then they are are in
+love and they stay together that would
+
+ align:start position:0%
+love and they stay together that would
+ 
+
+ align:start position:0%
+love and they stay together that would
+be a happy really happy marriage there
+
+ align:start position:0%
+be a happy really happy marriage there
+ 
+
+ align:start position:0%
+be a happy really happy marriage there
+are lots of divorces but there all there
+
+ align:start position:0%
+are lots of divorces but there all there
+ 
+
+ align:start position:0%
+are lots of divorces but there all there
+are surely people who succeed in their
+
+ align:start position:0%
+are surely people who succeed in their
+ 
+
+ align:start position:0%
+are surely people who succeed in their
+marriages in the sense of having all
+
+ align:start position:0%
+marriages in the sense of having all
+ 
+
+ align:start position:0%
+marriages in the sense of having all
+three of these maybe at different phases
+
+ align:start position:0%
+three of these maybe at different phases
+ 
+
+ align:start position:0%
+three of these maybe at different phases
+and then the question is could they have
+
+ align:start position:0%
+and then the question is could they have
+ 
+
+ align:start position:0%
+and then the question is could they have
+them all at the same time in middleaged
+
+ align:start position:0%
+them all at the same time in middleaged
+ 
+
+ align:start position:0%
+them all at the same time in middleaged
+let's say I don't know I mean it's so
+
+ align:start position:0%
+let's say I don't know I mean it's so
+ 
+
+ align:start position:0%
+let's say I don't know I mean it's so
+remote from my own experience I don't
+
+ align:start position:0%
+remote from my own experience I don't
+ 
+
+ align:start position:0%
+remote from my own experience I don't
+know what to say and nobody has done
+
+ align:start position:0%
+know what to say and nobody has done
+ 
+
+ align:start position:0%
+know what to say and nobody has done
+much with these concepts of mind um
+
+ align:start position:0%
+much with these concepts of mind um
+ 
+
+ align:start position:0%
+much with these concepts of mind um
+there haven't been people attacking and
+
+ align:start position:0%
+there haven't been people attacking and
+ 
+
+ align:start position:0%
+there haven't been people attacking and
+defending Me Maybe was just a bright
+
+ align:start position:0%
+defending Me Maybe was just a bright
+ 
+
+ align:start position:0%
+defending Me Maybe was just a bright
+idea of mind there wasn't any good but
+
+ align:start position:0%
+idea of mind there wasn't any good but
+ 
+
+ align:start position:0%
+idea of mind there wasn't any good but
+um maybe I don't know what to say I mean
+
+ align:start position:0%
+um maybe I don't know what to say I mean
+ 
+
+ align:start position:0%
+um maybe I don't know what to say I mean
+you've got to work that out for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yourself what do you think um a lot of
+
+ align:start position:0%
+yourself what do you think um a lot of
+ 
+
+ align:start position:0%
+yourself what do you think um a lot of
+people when they have their a lot of
+
+ align:start position:0%
+people when they have their a lot of
+ 
+
+ align:start position:0%
+people when they have their a lot of
+people when they have their first sexual
+
+ align:start position:0%
+people when they have their first sexual
+ 
+
+ align:start position:0%
+people when they have their first sexual
+experience kind of end up falling in
+
+ align:start position:0%
+experience kind of end up falling in
+ 
+
+ align:start position:0%
+experience kind of end up falling in
+love with that person yeah because the
+
+ align:start position:0%
+love with that person yeah because the
+ 
+
+ align:start position:0%
+love with that person yeah because the
+first experience can be so powerful for
+
+ align:start position:0%
+first experience can be so powerful for
+ 
+
+ align:start position:0%
+first experience can be so powerful for
+well particularly since the time when
+
+ align:start position:0%
+well particularly since the time when
+ 
+
+ align:start position:0%
+well particularly since the time when
+when you usually have your first
+
+ align:start position:0%
+when you usually have your first
+ 
+
+ align:start position:0%
+when you usually have your first
+experience is not when you're a
+
+ align:start position:0%
+experience is not when you're a
+ 
+
+ align:start position:0%
+experience is not when you're a
+middle-aged man or woman but rather when
+
+ align:start position:0%
+middle-aged man or woman but rather when
+ 
+
+ align:start position:0%
+middle-aged man or woman but rather when
+you're at the point where your hormones
+
+ align:start position:0%
+you're at the point where your hormones
+ 
+
+ align:start position:0%
+you're at the point where your hormones
+are at their peak in the case of men the
+
+ align:start position:0%
+are at their peak in the case of men the
+ 
+
+ align:start position:0%
+are at their peak in the case of men the
+testosterone which is the crucial male
+
+ align:start position:0%
+testosterone which is the crucial male
+ 
+
+ align:start position:0%
+testosterone which is the crucial male
+hormone is at a Peak at the age of about
+
+ align:start position:0%
+hormone is at a Peak at the age of about
+ 
+
+ align:start position:0%
+hormone is at a Peak at the age of about
+16 and then it declines a little and
+
+ align:start position:0%
+16 and then it declines a little and
+ 
+
+ align:start position:0%
+16 and then it declines a little and
+sort of levels off at around 20
+
+ align:start position:0%
+sort of levels off at around 20
+ 
+
+ align:start position:0%
+sort of levels off at around 20
+23 and then uh it continues on a plateau
+
+ align:start position:0%
+23 and then uh it continues on a plateau
+ 
+
+ align:start position:0%
+23 and then uh it continues on a plateau
+but then it sort of goes down right so
+
+ align:start position:0%
+but then it sort of goes down right so
+ 
+
+ align:start position:0%
+but then it sort of goes down right so
+it a if you have your first experience
+
+ align:start position:0%
+it a if you have your first experience
+ 
+
+ align:start position:0%
+it a if you have your first experience
+when you're a teenager which is probably
+
+ align:start position:0%
+when you're a teenager which is probably
+ 
+
+ align:start position:0%
+when you're a teenager which is probably
+not uncommon in in America at least it
+
+ align:start position:0%
+not uncommon in in America at least it
+ 
+
+ align:start position:0%
+not uncommon in in America at least it
+could be tremendous unless you're so
+
+ align:start position:0%
+could be tremendous unless you're so
+ 
+
+ align:start position:0%
+could be tremendous unless you're so
+blade because of everybody every what
+
+ align:start position:0%
+blade because of everybody every what
+ 
+
+ align:start position:0%
+blade because of everybody every what
+everybody is saying I actually brought
+
+ align:start position:0%
+everybody is saying I actually brought
+ 
+
+ align:start position:0%
+everybody is saying I actually brought
+in an example
+
+ align:start position:0%
+in an example
+ 
+
+ align:start position:0%
+in an example
+of like I guess um issue of science
+
+ align:start position:0%
+of like I guess um issue of science
+ 
+
+ align:start position:0%
+of like I guess um issue of science
+which kind of backs up this idea of that
+
+ align:start position:0%
+which kind of backs up this idea of that
+ 
+
+ align:start position:0%
+which kind of backs up this idea of that
+it is innate in us to want to be with
+
+ align:start position:0%
+it is innate in us to want to be with
+ 
+
+ align:start position:0%
+it is innate in us to want to be with
+another person based on I guess our
+
+ align:start position:0%
+another person based on I guess our
+ 
+
+ align:start position:0%
+another person based on I guess our
+hormones and our uh bodily the way we've
+
+ align:start position:0%
+hormones and our uh bodily the way we've
+ 
+
+ align:start position:0%
+hormones and our uh bodily the way we've
+been made as humans uh actually promotes
+
+ align:start position:0%
+been made as humans uh actually promotes
+ 
+
+ align:start position:0%
+been made as humans uh actually promotes
+the wanting to be with just one other
+
+ align:start position:0%
+the wanting to be with just one other
+ 
+
+ align:start position:0%
+the wanting to be with just one other
+person at least one well one at a time
+
+ align:start position:0%
+person at least one well one at a time
+ 
+
+ align:start position:0%
+person at least one well one at a time
+maybe I mean no no I think no the reason
+
+ align:start position:0%
+maybe I mean no no I think no the reason
+ 
+
+ align:start position:0%
+maybe I mean no no I think no the reason
+I'm saying that is because in love or
+
+ align:start position:0%
+I'm saying that is because in love or
+ 
+
+ align:start position:0%
+I'm saying that is because in love or
+sex it may be that you really want to be
+
+ align:start position:0%
+sex it may be that you really want to be
+ 
+
+ align:start position:0%
+sex it may be that you really want to be
+at one person person with one person but
+
+ align:start position:0%
+at one person person with one person but
+ 
+
+ align:start position:0%
+at one person person with one person but
+you wouldn't want to be in a society
+
+ align:start position:0%
+you wouldn't want to be in a society
+ 
+
+ align:start position:0%
+you wouldn't want to be in a society
+where there's nobody else you finally
+
+ align:start position:0%
+where there's nobody else you finally
+ 
+
+ align:start position:0%
+where there's nobody else you finally
+get bored with each other well I think
+
+ align:start position:0%
+get bored with each other well I think
+ 
+
+ align:start position:0%
+get bored with each other well I think
+it more has to do with the idea that you
+
+ align:start position:0%
+it more has to do with the idea that you
+ 
+
+ align:start position:0%
+it more has to do with the idea that you
+would like
+
+ align:start position:0%
+would like
+ 
+
+ align:start position:0%
+would like
+to be able to be with one person and be
+
+ align:start position:0%
+to be able to be with one person and be
+ 
+
+ align:start position:0%
+to be able to be with one person and be
+able to have a role
+
+ align:start position:0%
+able to have a role
+ 
+
+ align:start position:0%
+able to have a role
+as taking care of the family and doing
+
+ align:start position:0%
+as taking care of the family and doing
+ 
+
+ align:start position:0%
+as taking care of the family and doing
+those types of things that that's
+
+ align:start position:0%
+those types of things that that's
+ 
+
+ align:start position:0%
+those types of things that that's
+actually the falling in love is actually
+
+ align:start position:0%
+actually the falling in love is actually
+ 
+
+ align:start position:0%
+actually the falling in love is actually
+a part of who we are as humans that's
+
+ align:start position:0%
+a part of who we are as humans that's
+ 
+
+ align:start position:0%
+a part of who we are as humans that's
+something different about that I read
+
+ align:start position:0%
+something different about that I read
+ 
+
+ align:start position:0%
+something different about that I read
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um I forget where it was but it was kind
+
+ align:start position:0%
+um I forget where it was but it was kind
+ 
+
+ align:start position:0%
+um I forget where it was but it was kind
+of trying to characterize and in like a
+
+ align:start position:0%
+of trying to characterize and in like a
+ 
+
+ align:start position:0%
+of trying to characterize and in like a
+biological way why men are so
+
+ align:start position:0%
+biological way why men are so
+ 
+
+ align:start position:0%
+biological way why men are so
+promiscuous and women aren't and it was
+
+ align:start position:0%
+promiscuous and women aren't and it was
+ 
+
+ align:start position:0%
+promiscuous and women aren't and it was
+kind of like you know the whole like
+
+ align:start position:0%
+kind of like you know the whole like
+ 
+
+ align:start position:0%
+kind of like you know the whole like
+animalistic thing where the women would
+
+ align:start position:0%
+animalistic thing where the women would
+ 
+
+ align:start position:0%
+animalistic thing where the women would
+be raising the children at home so
+
+ align:start position:0%
+be raising the children at home so
+ 
+
+ align:start position:0%
+be raising the children at home so
+they'd be more inclined to just stick
+
+ align:start position:0%
+they'd be more inclined to just stick
+ 
+
+ align:start position:0%
+they'd be more inclined to just stick
+with one person oras the man was trying
+
+ align:start position:0%
+with one person oras the man was trying
+ 
+
+ align:start position:0%
+with one person oras the man was trying
+to spread his seeds so we'd want many
+
+ align:start position:0%
+to spread his seeds so we'd want many
+ 
+
+ align:start position:0%
+to spread his seeds so we'd want many
+different uh the the invention of the
+
+ align:start position:0%
+different uh the the invention of the
+ 
+
+ align:start position:0%
+different uh the the invention of the
+pill altered that a great deal because
+
+ align:start position:0%
+pill altered that a great deal because
+ 
+
+ align:start position:0%
+pill altered that a great deal because
+before the pill um there were hardly any
+
+ align:start position:0%
+before the pill um there were hardly any
+ 
+
+ align:start position:0%
+before the pill um there were hardly any
+contraceptions that really worked um
+
+ align:start position:0%
+contraceptions that really worked um
+ 
+
+ align:start position:0%
+contraceptions that really worked um
+Casanova the famous writer who had lots
+
+ align:start position:0%
+Casanova the famous writer who had lots
+ 
+
+ align:start position:0%
+Casanova the famous writer who had lots
+of love affairs so he his name has
+
+ align:start position:0%
+of love affairs so he his name has
+ 
+
+ align:start position:0%
+of love affairs so he his name has
+become synonymous with a Don Juan kind
+
+ align:start position:0%
+become synonymous with a Don Juan kind
+ 
+
+ align:start position:0%
+become synonymous with a Don Juan kind
+of character right a Casanova he wrote
+
+ align:start position:0%
+of character right a Casanova he wrote
+ 
+
+ align:start position:0%
+of character right a Casanova he wrote
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+Memoirs and in one volume of these
+
+ align:start position:0%
+Memoirs and in one volume of these
+ 
+
+ align:start position:0%
+Memoirs and in one volume of these
+Memoirs this is the end of the 18th
+
+ align:start position:0%
+Memoirs this is the end of the 18th
+ 
+
+ align:start position:0%
+Memoirs this is the end of the 18th
+century he talks about this terrific um
+
+ align:start position:0%
+century he talks about this terrific um
+ 
+
+ align:start position:0%
+century he talks about this terrific um
+technological Discovery the
+
+ align:start position:0%
+technological Discovery the
+ 
+
+ align:start position:0%
+technological Discovery the
+technological
+
+ align:start position:0%
+technological
+ 
+
+ align:start position:0%
+technological
+invention um I think he calls it the the
+
+ align:start position:0%
+invention um I think he calls it the the
+ 
+
+ align:start position:0%
+invention um I think he calls it the the
+Dutch slip well it's a condom that the
+
+ align:start position:0%
+Dutch slip well it's a condom that the
+ 
+
+ align:start position:0%
+Dutch slip well it's a condom that the
+point is Until then people didn't have
+
+ align:start position:0%
+point is Until then people didn't have
+ 
+
+ align:start position:0%
+point is Until then people didn't have
+condoms after then U the condoms weren't
+
+ align:start position:0%
+condoms after then U the condoms weren't
+ 
+
+ align:start position:0%
+condoms after then U the condoms weren't
+well enough constructed so they weren't
+
+ align:start position:0%
+well enough constructed so they weren't
+ 
+
+ align:start position:0%
+well enough constructed so they weren't
+very reliable um and the men often
+
+ align:start position:0%
+very reliable um and the men often
+ 
+
+ align:start position:0%
+very reliable um and the men often
+wouldn't use and because of sensuous
+
+ align:start position:0%
+wouldn't use and because of sensuous
+ 
+
+ align:start position:0%
+wouldn't use and because of sensuous
+reasons they wanted to feel the body of
+
+ align:start position:0%
+reasons they wanted to feel the body of
+ 
+
+ align:start position:0%
+reasons they wanted to feel the body of
+the woman instead of having put putting
+
+ align:start position:0%
+the woman instead of having put putting
+ 
+
+ align:start position:0%
+the woman instead of having put putting
+on a a glove so to speak um so that the
+
+ align:start position:0%
+on a a glove so to speak um so that the
+ 
+
+ align:start position:0%
+on a a glove so to speak um so that the
+woman was at the mercy of um her uh
+
+ align:start position:0%
+woman was at the mercy of um her uh
+ 
+
+ align:start position:0%
+woman was at the mercy of um her uh
+physiology that if she had sex she would
+
+ align:start position:0%
+physiology that if she had sex she would
+ 
+
+ align:start position:0%
+physiology that if she had sex she would
+probably have a baby sooner or later the
+
+ align:start position:0%
+probably have a baby sooner or later the
+ 
+
+ align:start position:0%
+probably have a baby sooner or later the
+what was used to be called
+
+ align:start position:0%
+what was used to be called
+ 
+
+ align:start position:0%
+what was used to be called
+in a generation before mine uh
+
+ align:start position:0%
+in a generation before mine uh
+ 
+
+ align:start position:0%
+in a generation before mine uh
+the inevitable happens the inevitable
+
+ align:start position:0%
+the inevitable happens the inevitable
+ 
+
+ align:start position:0%
+the inevitable happens the inevitable
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+happen uh and so she'd pay the price and
+
+ align:start position:0%
+happen uh and so she'd pay the price and
+ 
+
+ align:start position:0%
+happen uh and so she'd pay the price and
+if the man uh didn't have a marry her
+
+ align:start position:0%
+if the man uh didn't have a marry her
+ 
+
+ align:start position:0%
+if the man uh didn't have a marry her
+and have a to think of her as a
+
+ align:start position:0%
+and have a to think of her as a
+ 
+
+ align:start position:0%
+and have a to think of her as a
+legitimate spouse she would be
+
+ align:start position:0%
+legitimate spouse she would be
+ 
+
+ align:start position:0%
+legitimate spouse she would be
+ostracized she would have either kill
+
+ align:start position:0%
+ostracized she would have either kill
+ 
+
+ align:start position:0%
+ostracized she would have either kill
+the baby or and the abortion was very
+
+ align:start position:0%
+the baby or and the abortion was very
+ 
+
+ align:start position:0%
+the baby or and the abortion was very
+very dangerous until recently um uh or
+
+ align:start position:0%
+very dangerous until recently um uh or
+ 
+
+ align:start position:0%
+very dangerous until recently um uh or
+she would have to support it on her own
+
+ align:start position:0%
+she would have to support it on her own
+ 
+
+ align:start position:0%
+she would have to support it on her own
+in a miserable condition so for that
+
+ align:start position:0%
+in a miserable condition so for that
+ 
+
+ align:start position:0%
+in a miserable condition so for that
+reason the male attitude would be very
+
+ align:start position:0%
+reason the male attitude would be very
+ 
+
+ align:start position:0%
+reason the male attitude would be very
+different to the woman from the woman's
+
+ align:start position:0%
+different to the woman from the woman's
+ 
+
+ align:start position:0%
+different to the woman from the woman's
+but the pill changes all that because
+
+ align:start position:0%
+but the pill changes all that because
+ 
+
+ align:start position:0%
+but the pill changes all that because
+with the pill there's greater Security
+
+ align:start position:0%
+with the pill there's greater Security
+ 
+
+ align:start position:0%
+with the pill there's greater Security
+even more than a diaphragm had been um
+
+ align:start position:0%
+even more than a diaphragm had been um
+ 
+
+ align:start position:0%
+even more than a diaphragm had been um
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+women might expect to be able to emulate
+
+ align:start position:0%
+women might expect to be able to emulate
+ 
+
+ align:start position:0%
+women might expect to be able to emulate
+the male desire for trial to trial
+
+ align:start position:0%
+the male desire for trial to trial
+ 
+
+ align:start position:0%
+the male desire for trial to trial
+experimentation with a sex
+
+ align:start position:0%
+experimentation with a sex
+ 
+
+ align:start position:0%
+experimentation with a sex
+sex uh partner without being becoming
+
+ align:start position:0%
+sex uh partner without being becoming
+ 
+
+ align:start position:0%
+sex uh partner without being becoming
+prostitutes who are are a different
+
+ align:start position:0%
+prostitutes who are are a different
+ 
+
+ align:start position:0%
+prostitutes who are are a different
+order have a different kind of problem
+
+ align:start position:0%
+order have a different kind of problem
+ 
+
+ align:start position:0%
+order have a different kind of problem
+entirely so that generalization about
+
+ align:start position:0%
+entirely so that generalization about
+ 
+
+ align:start position:0%
+entirely so that generalization about
+the biology of male and females May to
+
+ align:start position:0%
+the biology of male and females May to
+ 
+
+ align:start position:0%
+the biology of male and females May to
+some extent be a function of the society
+
+ align:start position:0%
+some extent be a function of the society
+ 
+
+ align:start position:0%
+some extent be a function of the society
+whether or not it's before the pill or
+
+ align:start position:0%
+whether or not it's before the pill or
+ 
+
+ align:start position:0%
+whether or not it's before the pill or
+after the pill and what the attitude
+
+ align:start position:0%
+after the pill and what the attitude
+ 
+
+ align:start position:0%
+after the pill and what the attitude
+toward techn technological devices like
+
+ align:start position:0%
+toward techn technological devices like
+ 
+
+ align:start position:0%
+toward techn technological devices like
+that is in different societies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um men are
+
+ align:start position:0%
+um men are
+ 
+
+ align:start position:0%
+um men are
+rendered very aggressive by the
+
+ align:start position:0%
+rendered very aggressive by the
+ 
+
+ align:start position:0%
+rendered very aggressive by the
+testosterone that also makes them
+
+ align:start position:0%
+testosterone that also makes them
+ 
+
+ align:start position:0%
+testosterone that also makes them
+sexual that's a f biological fact about
+
+ align:start position:0%
+sexual that's a f biological fact about
+ 
+
+ align:start position:0%
+sexual that's a f biological fact about
+men that the testosterone makes them
+
+ align:start position:0%
+men that the testosterone makes them
+ 
+
+ align:start position:0%
+men that the testosterone makes them
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+lidly
+
+ align:start position:0%
+lidly
+ 
+
+ align:start position:0%
+lidly
+eager and very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aggressive women depending more on
+
+ align:start position:0%
+aggressive women depending more on
+ 
+
+ align:start position:0%
+aggressive women depending more on
+estrogen and proes are not like that and
+
+ align:start position:0%
+estrogen and proes are not like that and
+ 
+
+ align:start position:0%
+estrogen and proes are not like that and
+so that would be one reason another
+
+ align:start position:0%
+so that would be one reason another
+ 
+
+ align:start position:0%
+so that would be one reason another
+additional reason why the men would be
+
+ align:start position:0%
+additional reason why the men would be
+ 
+
+ align:start position:0%
+additional reason why the men would be
+eager for sex and the woman uh would be
+
+ align:start position:0%
+eager for sex and the woman uh would be
+ 
+
+ align:start position:0%
+eager for sex and the woman uh would be
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+reluctant COI and not ready simply to be
+
+ align:start position:0%
+reluctant COI and not ready simply to be
+ 
+
+ align:start position:0%
+reluctant COI and not ready simply to be
+available um and worried about the
+
+ align:start position:0%
+available um and worried about the
+ 
+
+ align:start position:0%
+available um and worried about the
+future because they would be the ones
+
+ align:start position:0%
+future because they would be the ones
+ 
+
+ align:start position:0%
+future because they would be the ones
+who would have the
+
+ align:start position:0%
+who would have the
+ 
+
+ align:start position:0%
+who would have the
+babies and they're more nurturing
+
+ align:start position:0%
+babies and they're more nurturing
+ 
+
+ align:start position:0%
+babies and they're more nurturing
+because they're less aggressive they for
+
+ align:start position:0%
+because they're less aggressive they for
+ 
+
+ align:start position:0%
+because they're less aggressive they for
+they're more suitable for bringing up
+
+ align:start position:0%
+they're more suitable for bringing up
+ 
+
+ align:start position:0%
+they're more suitable for bringing up
+babies but men can learn how to do that
+
+ align:start position:0%
+babies but men can learn how to do that
+ 
+
+ align:start position:0%
+babies but men can learn how to do that
+too it's just that in the state of
+
+ align:start position:0%
+too it's just that in the state of
+ 
+
+ align:start position:0%
+too it's just that in the state of
+nature that's how the biology would seem
+
+ align:start position:0%
+nature that's how the biology would seem
+ 
+
+ align:start position:0%
+nature that's how the biology would seem
+to fall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out you want to go Ahad yes um I wanted
+
+ align:start position:0%
+out you want to go Ahad yes um I wanted
+ 
+
+ align:start position:0%
+out you want to go Ahad yes um I wanted
+to talk about and that's the sensuous
+
+ align:start position:0%
+to talk about and that's the sensuous
+ 
+
+ align:start position:0%
+to talk about and that's the sensuous
+and the passionate and staying in love
+
+ align:start position:0%
+and the passionate and staying in love
+ 
+
+ align:start position:0%
+and the passionate and staying in love
+being in love and uh falling in love so
+
+ align:start position:0%
+being in love and uh falling in love so
+ 
+
+ align:start position:0%
+being in love and uh falling in love so
+are we going beyond that now uh yeah I
+
+ align:start position:0%
+are we going beyond that now uh yeah I
+ 
+
+ align:start position:0%
+are we going beyond that now uh yeah I
+wanted to talk about the first myth we
+
+ align:start position:0%
+wanted to talk about the first myth we
+ 
+
+ align:start position:0%
+wanted to talk about the first myth we
+haven't gotten today go ahead
+
+ align:start position:0%
+haven't gotten today go ahead
+ 
+
+ align:start position:0%
+haven't gotten today go ahead
+um on page 20 I don't know if everybody
+
+ align:start position:0%
+um on page 20 I don't know if everybody
+ 
+
+ align:start position:0%
+um on page 20 I don't know if everybody
+has the same book but
+
+ align:start position:0%
+has the same book but
+ 
+
+ align:start position:0%
+has the same book but
+um you bring up a point about I'm not
+
+ align:start position:0%
+um you bring up a point about I'm not
+ 
+
+ align:start position:0%
+um you bring up a point about I'm not
+sure how to say this person's name La
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ruk um
+
+ align:start position:0%
+ruk um
+ 
+
+ align:start position:0%
+ruk um
+den no wa L rash Fuko yes oh I know
+
+ align:start position:0%
+den no wa L rash Fuko yes oh I know
+ 
+
+ align:start position:0%
+den no wa L rash Fuko yes oh I know
+there's D roual who wrote a book called
+
+ align:start position:0%
+there's D roual who wrote a book called
+ 
+
+ align:start position:0%
+there's D roual who wrote a book called
+love in the western world no uh this
+
+ align:start position:0%
+love in the western world no uh this
+ 
+
+ align:start position:0%
+love in the western world no uh this
+uh is the Duke
+
+ align:start position:0%
+uh is the Duke
+ 
+
+ align:start position:0%
+uh is the Duke
+de L FCO who wrote in the 17th century
+
+ align:start position:0%
+de L FCO who wrote in the 17th century
+ 
+
+ align:start position:0%
+de L FCO who wrote in the 17th century
+uh about um life and sex and love and
+
+ align:start position:0%
+uh about um life and sex and love and
+ 
+
+ align:start position:0%
+uh about um life and sex and love and
+was very witty and one of the things I
+
+ align:start position:0%
+was very witty and one of the things I
+ 
+
+ align:start position:0%
+was very witty and one of the things I
+quote there uh yes what he says is that
+
+ align:start position:0%
+quote there uh yes what he says is that
+ 
+
+ align:start position:0%
+quote there uh yes what he says is that
+some people would never have fallen in
+
+ align:start position:0%
+some people would never have fallen in
+ 
+
+ align:start position:0%
+some people would never have fallen in
+love if they had not heard about it yeah
+
+ align:start position:0%
+love if they had not heard about it yeah
+ 
+
+ align:start position:0%
+love if they had not heard about it yeah
+and you say that in a sense you think
+
+ align:start position:0%
+and you say that in a sense you think
+ 
+
+ align:start position:0%
+and you say that in a sense you think
+this is true of everyone yeah love is a
+
+ align:start position:0%
+this is true of everyone yeah love is a
+ 
+
+ align:start position:0%
+this is true of everyone yeah love is a
+concept that we conru and then try
+
+ align:start position:0%
+concept that we conru and then try
+ 
+
+ align:start position:0%
+concept that we conru and then try
+to fix fix it to experience and if you
+
+ align:start position:0%
+to fix fix it to experience and if you
+ 
+
+ align:start position:0%
+to fix fix it to experience and if you
+didn't have the concept that might be
+
+ align:start position:0%
+didn't have the concept that might be
+ 
+
+ align:start position:0%
+didn't have the concept that might be
+you might never have that kind of
+
+ align:start position:0%
+you might never have that kind of
+ 
+
+ align:start position:0%
+you might never have that kind of
+experience I kind
+
+ align:start position:0%
+experience I kind
+ 
+
+ align:start position:0%
+experience I kind
+of I feel like that it also plays in a
+
+ align:start position:0%
+of I feel like that it also plays in a
+ 
+
+ align:start position:0%
+of I feel like that it also plays in a
+different way and because of you do talk
+
+ align:start position:0%
+different way and because of you do talk
+ 
+
+ align:start position:0%
+different way and because of you do talk
+about how we are systematically
+
+ align:start position:0%
+about how we are systematically
+ 
+
+ align:start position:0%
+about how we are systematically
+mislabeled by the fables that present
+
+ align:start position:0%
+mislabeled by the fables that present
+ 
+
+ align:start position:0%
+mislabeled by the fables that present
+love is Magic and I think almost by
+
+ align:start position:0%
+love is Magic and I think almost by
+ 
+
+ align:start position:0%
+love is Magic and I think almost by
+being fed all of this magic and all of
+
+ align:start position:0%
+being fed all of this magic and all of
+ 
+
+ align:start position:0%
+being fed all of this magic and all of
+this oh love is such a grand explosion
+
+ align:start position:0%
+this oh love is such a grand explosion
+ 
+
+ align:start position:0%
+this oh love is such a grand explosion
+that you're going to feel all these
+
+ align:start position:0%
+that you're going to feel all these
+ 
+
+ align:start position:0%
+that you're going to feel all these
+amazing things and you're just going to
+
+ align:start position:0%
+amazing things and you're just going to
+ 
+
+ align:start position:0%
+amazing things and you're just going to
+automatically be you know attracted to
+
+ align:start position:0%
+automatically be you know attracted to
+ 
+
+ align:start position:0%
+automatically be you know attracted to
+this person and all of this stuff that
+
+ align:start position:0%
+this person and all of this stuff that
+ 
+
+ align:start position:0%
+this person and all of this stuff that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+actually could prevent some people from
+
+ align:start position:0%
+actually could prevent some people from
+ 
+
+ align:start position:0%
+actually could prevent some people from
+falling in love because everyone's
+
+ align:start position:0%
+falling in love because everyone's
+ 
+
+ align:start position:0%
+falling in love because everyone's
+always waiting for this stuff to happen
+
+ align:start position:0%
+always waiting for this stuff to happen
+ 
+
+ align:start position:0%
+always waiting for this stuff to happen
+that never actually does and so in a way
+
+ align:start position:0%
+that never actually does and so in a way
+ 
+
+ align:start position:0%
+that never actually does and so in a way
+maybe we don't experience love
+
+ align:start position:0%
+maybe we don't experience love
+ 
+
+ align:start position:0%
+maybe we don't experience love
+because of that as
+
+ align:start position:0%
+because of that as
+ 
+
+ align:start position:0%
+because of that as
+well the point point in the history of
+
+ align:start position:0%
+well the point point in the history of
+ 
+
+ align:start position:0%
+well the point point in the history of
+ideas and for this you really would have
+
+ align:start position:0%
+ideas and for this you really would have
+ 
+
+ align:start position:0%
+ideas and for this you really would have
+to slog your way through the 14400 pages
+
+ align:start position:0%
+to slog your way through the 14400 pages
+ 
+
+ align:start position:0%
+to slog your way through the 14400 pages
+um there is a
+
+ align:start position:0%
+um there is a
+ 
+
+ align:start position:0%
+um there is a
+literary
+
+ align:start position:0%
+literary
+ 
+
+ align:start position:0%
+literary
+poetic also um novelistic in novels
+
+ align:start position:0%
+poetic also um novelistic in novels
+ 
+
+ align:start position:0%
+poetic also um novelistic in novels
+tradition in which they talk about
+
+ align:start position:0%
+tradition in which they talk about
+ 
+
+ align:start position:0%
+tradition in which they talk about
+falling in love falling in love falling
+
+ align:start position:0%
+falling in love falling in love falling
+ 
+
+ align:start position:0%
+falling in love falling in love falling
+in love and um people sometimes say I'm
+
+ align:start position:0%
+in love and um people sometimes say I'm
+ 
+
+ align:start position:0%
+in love and um people sometimes say I'm
+thinking now a 12th
+
+ align:start position:0%
+thinking now a 12th
+ 
+
+ align:start position:0%
+thinking now a 12th
+century
+
+ align:start position:0%
+century
+ 
+
+ align:start position:0%
+century
+um sort of novel in verse um called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um a aaas it's a story of Da and
+
+ align:start position:0%
+um a aaas it's a story of Da and
+ 
+
+ align:start position:0%
+um a aaas it's a story of Da and
+anas and the young
+
+ align:start position:0%
+anas and the young
+ 
+
+ align:start position:0%
+anas and the young
+girl saying um
+
+ align:start position:0%
+girl saying um
+ 
+
+ align:start position:0%
+girl saying um
+um what is this thing called love
+
+ align:start position:0%
+um what is this thing called love
+ 
+
+ align:start position:0%
+um what is this thing called love
+everybody talks about it and I've never
+
+ align:start position:0%
+everybody talks about it and I've never
+ 
+
+ align:start position:0%
+everybody talks about it and I've never
+experiencing anything like that and it's
+
+ align:start position:0%
+experiencing anything like that and it's
+ 
+
+ align:start position:0%
+experiencing anything like that and it's
+true in the Poo stage young kids for
+
+ align:start position:0%
+true in the Poo stage young kids for
+ 
+
+ align:start position:0%
+true in the Poo stage young kids for
+instance call you know mush you have no
+
+ align:start position:0%
+instance call you know mush you have no
+ 
+
+ align:start position:0%
+instance call you know mush you have no
+tolerance with the idea of people
+
+ align:start position:0%
+tolerance with the idea of people
+ 
+
+ align:start position:0%
+tolerance with the idea of people
+falling in love right because they
+
+ align:start position:0%
+falling in love right because they
+ 
+
+ align:start position:0%
+falling in love right because they
+haven't experienced it their hormones
+
+ align:start position:0%
+haven't experienced it their hormones
+ 
+
+ align:start position:0%
+haven't experienced it their hormones
+haven't brought them to that stage of
+
+ align:start position:0%
+haven't brought them to that stage of
+ 
+
+ align:start position:0%
+haven't brought them to that stage of
+development but um the girl says that
+
+ align:start position:0%
+development but um the girl says that
+ 
+
+ align:start position:0%
+development but um the girl says that
+and the mother says well um you won't
+
+ align:start position:0%
+and the mother says well um you won't
+ 
+
+ align:start position:0%
+and the mother says well um you won't
+know what it is until it hits you when
+
+ align:start position:0%
+know what it is until it hits you when
+ 
+
+ align:start position:0%
+know what it is until it hits you when
+it hits you you will be surprised and
+
+ align:start position:0%
+it hits you you will be surprised and
+ 
+
+ align:start position:0%
+it hits you you will be surprised and
+then she describes all of the changes
+
+ align:start position:0%
+then she describes all of the changes
+ 
+
+ align:start position:0%
+then she describes all of the changes
+that take take place when you do fall in
+
+ align:start position:0%
+that take take place when you do fall in
+ 
+
+ align:start position:0%
+that take take place when you do fall in
+love now first of all notice that this
+
+ align:start position:0%
+love now first of all notice that this
+ 
+
+ align:start position:0%
+love now first of all notice that this
+already presupposes a biological
+
+ align:start position:0%
+already presupposes a biological
+ 
+
+ align:start position:0%
+already presupposes a biological
+firmament foundation for it but it
+
+ align:start position:0%
+firmament foundation for it but it
+ 
+
+ align:start position:0%
+firmament foundation for it but it
+becomes the basis of literature and
+
+ align:start position:0%
+becomes the basis of literature and
+ 
+
+ align:start position:0%
+becomes the basis of literature and
+people in an intermediary stage young
+
+ align:start position:0%
+people in an intermediary stage young
+ 
+
+ align:start position:0%
+people in an intermediary stage young
+girls for instance who may be slow to
+
+ align:start position:0%
+girls for instance who may be slow to
+ 
+
+ align:start position:0%
+girls for instance who may be slow to
+develop or young boys like me who I was
+
+ align:start position:0%
+develop or young boys like me who I was
+ 
+
+ align:start position:0%
+develop or young boys like me who I was
+very slow to develop uh sexually um you
+
+ align:start position:0%
+very slow to develop uh sexually um you
+ 
+
+ align:start position:0%
+very slow to develop uh sexually um you
+read about this and you think you know
+
+ align:start position:0%
+read about this and you think you know
+ 
+
+ align:start position:0%
+read about this and you think you know
+what what is it this I'm missing I
+
+ align:start position:0%
+what what is it this I'm missing I
+ 
+
+ align:start position:0%
+what what is it this I'm missing I
+wonder you know but I feel like what you
+
+ align:start position:0%
+wonder you know but I feel like what you
+ 
+
+ align:start position:0%
+wonder you know but I feel like what you
+know what it is why am I somehow
+
+ align:start position:0%
+know what it is why am I somehow
+ 
+
+ align:start position:0%
+know what it is why am I somehow
+or or or something wrong with me
+
+ align:start position:0%
+or or or something wrong with me
+ 
+
+ align:start position:0%
+or or or something wrong with me
+and this they they talk about love so
+
+ align:start position:0%
+and this they they talk about love so
+ 
+
+ align:start position:0%
+and this they they talk about love so
+much what is it and then
+
+ align:start position:0%
+much what is it and then
+ 
+
+ align:start position:0%
+much what is it and then
+finally you you carry out the myth in
+
+ align:start position:0%
+finally you you carry out the myth in
+ 
+
+ align:start position:0%
+finally you you carry out the myth in
+yourself but I feel like that idea of
+
+ align:start position:0%
+yourself but I feel like that idea of
+ 
+
+ align:start position:0%
+yourself but I feel like that idea of
+Love is such a cultural thing and kind
+
+ align:start position:0%
+Love is such a cultural thing and kind
+ 
+
+ align:start position:0%
+Love is such a cultural thing and kind
+of just a result of our society that
+
+ align:start position:0%
+of just a result of our society that
+ 
+
+ align:start position:0%
+of just a result of our society that
+idea that love is this General thing but
+
+ align:start position:0%
+idea that love is this General thing but
+ 
+
+ align:start position:0%
+idea that love is this General thing but
+I think think without if that didn't
+
+ align:start position:0%
+I think think without if that didn't
+ 
+
+ align:start position:0%
+I think think without if that didn't
+exist we would still all feel some sense
+
+ align:start position:0%
+exist we would still all feel some sense
+ 
+
+ align:start position:0%
+exist we would still all feel some sense
+of love we all have we all have some
+
+ align:start position:0%
+of love we all have we all have some
+ 
+
+ align:start position:0%
+of love we all have we all have some
+sort
+
+ align:start position:0%
+sort
+ 
+
+ align:start position:0%
+sort
+of innateness to love and to be loved
+
+ align:start position:0%
+of innateness to love and to be loved
+ 
+
+ align:start position:0%
+of innateness to love and to be loved
+but that doesn't necessarily mean that
+
+ align:start position:0%
+but that doesn't necessarily mean that
+ 
+
+ align:start position:0%
+but that doesn't necessarily mean that
+we would feel it in the way that society
+
+ align:start position:0%
+we would feel it in the way that society
+ 
+
+ align:start position:0%
+we would feel it in the way that society
+says oh well you hold hands with the
+
+ align:start position:0%
+says oh well you hold hands with the
+ 
+
+ align:start position:0%
+says oh well you hold hands with the
+person and you you know those are like
+
+ align:start position:0%
+person and you you know those are like
+ 
+
+ align:start position:0%
+person and you you know those are like
+those things are result of what we know
+
+ align:start position:0%
+those things are result of what we know
+ 
+
+ align:start position:0%
+those things are result of what we know
+that love is supposed to be do any you
+
+ align:start position:0%
+that love is supposed to be do any you
+ 
+
+ align:start position:0%
+that love is supposed to be do any you
+know who darthy parker
+
+ align:start position:0%
+know who darthy parker
+ 
+
+ align:start position:0%
+know who darthy parker
+was she uh wrote in the 1920s and
+
+ align:start position:0%
+was she uh wrote in the 1920s and
+ 
+
+ align:start position:0%
+was she uh wrote in the 1920s and
+30s and was one of the wittiest people
+
+ align:start position:0%
+30s and was one of the wittiest people
+ 
+
+ align:start position:0%
+30s and was one of the wittiest people
+who ever lived she had her own column in
+
+ align:start position:0%
+who ever lived she had her own column in
+ 
+
+ align:start position:0%
+who ever lived she had her own column in
+the New Yorker and all sorts of places
+
+ align:start position:0%
+the New Yorker and all sorts of places
+ 
+
+ align:start position:0%
+the New Yorker and all sorts of places
+she's was a very very witty very very
+
+ align:start position:0%
+she's was a very very witty very very
+ 
+
+ align:start position:0%
+she's was a very very witty very very
+witty writer um and and daring and this
+
+ align:start position:0%
+witty writer um and and daring and this
+ 
+
+ align:start position:0%
+witty writer um and and daring and this
+is one of one example that comes to mind
+
+ align:start position:0%
+is one of one example that comes to mind
+ 
+
+ align:start position:0%
+is one of one example that comes to mind
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+can you can take a you can take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you can take a hortic culture but you
+
+ align:start position:0%
+um you can take a hortic culture but you
+ 
+
+ align:start position:0%
+um you can take a hortic culture but you
+can't make her
+
+ align:start position:0%
+can't make her
+ 
+
+ align:start position:0%
+can't make her
+drink you know you can take a w you can
+
+ align:start position:0%
+drink you know you can take a w you can
+ 
+
+ align:start position:0%
+drink you know you can take a w you can
+take a horse to culture but you can't
+
+ align:start position:0%
+take a horse to culture but you can't
+ 
+
+ align:start position:0%
+take a horse to culture but you can't
+take a horse to water but you can't make
+
+ align:start position:0%
+take a horse to water but you can't make
+ 
+
+ align:start position:0%
+take a horse to water but you can't make
+a drink this way of fooling you because
+
+ align:start position:0%
+a drink this way of fooling you because
+ 
+
+ align:start position:0%
+a drink this way of fooling you because
+you think she's talking about
+
+ align:start position:0%
+you think she's talking about
+ 
+
+ align:start position:0%
+you think she's talking about
+horiculture but she's talking about a
+
+ align:start position:0%
+horiculture but she's talking about a
+ 
+
+ align:start position:0%
+horiculture but she's talking about a
+word with that was a little taboo then
+
+ align:start position:0%
+word with that was a little taboo then
+ 
+
+ align:start position:0%
+word with that was a little taboo then
+right uh that's typical I there's a poem
+
+ align:start position:0%
+right uh that's typical I there's a poem
+ 
+
+ align:start position:0%
+right uh that's typical I there's a poem
+of hers there's a poem of hers uh many I
+
+ align:start position:0%
+of hers there's a poem of hers uh many I
+ 
+
+ align:start position:0%
+of hers there's a poem of hers uh many I
+wish I could think of some other witty
+
+ align:start position:0%
+wish I could think of some other witty
+ 
+
+ align:start position:0%
+wish I could think of some other witty
+things Wittier even than that
+
+ align:start position:0%
+things Wittier even than that
+ 
+
+ align:start position:0%
+things Wittier even than that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um that I wish I could remember but it's
+
+ align:start position:0%
+um that I wish I could remember but it's
+ 
+
+ align:start position:0%
+um that I wish I could remember but it's
+about love is Love Is a thing that is
+
+ align:start position:0%
+about love is Love Is a thing that is
+ 
+
+ align:start position:0%
+about love is Love Is a thing that is
+always wonderful love is a beautiful
+
+ align:start position:0%
+always wonderful love is a beautiful
+ 
+
+ align:start position:0%
+always wonderful love is a beautiful
+experience I'm just inventing the the
+
+ align:start position:0%
+experience I'm just inventing the the
+ 
+
+ align:start position:0%
+experience I'm just inventing the the
+lines she writes it as a short poem uh
+
+ align:start position:0%
+lines she writes it as a short poem uh
+ 
+
+ align:start position:0%
+lines she writes it as a short poem uh
+love is uh a constant
+
+ align:start position:0%
+love is uh a constant
+ 
+
+ align:start position:0%
+love is uh a constant
+Joy uh and finally love is a a joyous
+
+ align:start position:0%
+Joy uh and finally love is a a joyous
+ 
+
+ align:start position:0%
+Joy uh and finally love is a a joyous
+form of
+
+ align:start position:0%
+form of
+ 
+
+ align:start position:0%
+form of
+mania and I am Maria of Romania
+
+ align:start position:0%
+mania and I am Maria of Romania
+ 
+
+ align:start position:0%
+mania and I am Maria of Romania
+R Marie do you ever heard Maria of
+
+ align:start position:0%
+R Marie do you ever heard Maria of
+ 
+
+ align:start position:0%
+R Marie do you ever heard Maria of
+Romania was the queen of Romania at that
+
+ align:start position:0%
+Romania was the queen of Romania at that
+ 
+
+ align:start position:0%
+Romania was the queen of Romania at that
+time right in other words only a crazy
+
+ align:start position:0%
+time right in other words only a crazy
+ 
+
+ align:start position:0%
+time right in other words only a crazy
+person would talk this way about love
+
+ align:start position:0%
+person would talk this way about love
+ 
+
+ align:start position:0%
+person would talk this way about love
+right the idea that everyone experiences
+
+ align:start position:0%
+right the idea that everyone experiences
+ 
+
+ align:start position:0%
+right the idea that everyone experiences
+it is what she's ridiculing and I think
+
+ align:start position:0%
+it is what she's ridiculing and I think
+ 
+
+ align:start position:0%
+it is what she's ridiculing and I think
+it probably is not true that just
+
+ align:start position:0%
+it probably is not true that just
+ 
+
+ align:start position:0%
+it probably is not true that just
+without having read anything or heard
+
+ align:start position:0%
+without having read anything or heard
+ 
+
+ align:start position:0%
+without having read anything or heard
+anything about it that everyone is going
+
+ align:start position:0%
+anything about it that everyone is going
+ 
+
+ align:start position:0%
+anything about it that everyone is going
+to have this loving experience of Love
+
+ align:start position:0%
+to have this loving experience of Love
+ 
+
+ align:start position:0%
+to have this loving experience of Love
+or falling in love I'm think there must
+
+ align:start position:0%
+or falling in love I'm think there must
+ 
+
+ align:start position:0%
+or falling in love I'm think there must
+be millions of peasants in the world who
+
+ align:start position:0%
+be millions of peasants in the world who
+ 
+
+ align:start position:0%
+be millions of peasants in the world who
+illiterate people who never fell in love
+
+ align:start position:0%
+illiterate people who never fell in love
+ 
+
+ align:start position:0%
+illiterate people who never fell in love
+with anybody
+
+ align:start position:0%
+with anybody
+ 
+
+ align:start position:0%
+with anybody
+um they married they had families they
+
+ align:start position:0%
+um they married they had families they
+ 
+
+ align:start position:0%
+um they married they had families they
+had sex but they wouldn't wouldn't have
+
+ align:start position:0%
+had sex but they wouldn't wouldn't have
+ 
+
+ align:start position:0%
+had sex but they wouldn't wouldn't have
+fallen in love I think that's my point
+
+ align:start position:0%
+fallen in love I think that's my point
+ 
+
+ align:start position:0%
+fallen in love I think that's my point
+exactly is that they don't fall in love
+
+ align:start position:0%
+exactly is that they don't fall in love
+ 
+
+ align:start position:0%
+exactly is that they don't fall in love
+in the sense of love as we know it just
+
+ align:start position:0%
+in the sense of love as we know it just
+ 
+
+ align:start position:0%
+in the sense of love as we know it just
+because that doesn't mean that the love
+
+ align:start position:0%
+because that doesn't mean that the love
+ 
+
+ align:start position:0%
+because that doesn't mean that the love
+of oh I love you so much because you
+
+ align:start position:0%
+of oh I love you so much because you
+ 
+
+ align:start position:0%
+of oh I love you so much because you
+know you do all sorts of great things to
+
+ align:start position:0%
+know you do all sorts of great things to
+ 
+
+ align:start position:0%
+know you do all sorts of great things to
+me that doesn't mean that that's the
+
+ align:start position:0%
+me that doesn't mean that that's the
+ 
+
+ align:start position:0%
+me that doesn't mean that that's the
+only thing that love is all right so
+
+ align:start position:0%
+only thing that love is all right so
+ 
+
+ align:start position:0%
+only thing that love is all right so
+falling in love is not
+
+ align:start position:0%
+falling in love is not
+ 
+
+ align:start position:0%
+falling in love is not
+Universal right but there may be other
+
+ align:start position:0%
+Universal right but there may be other
+ 
+
+ align:start position:0%
+Universal right but there may be other
+kinds
+
+ align:start position:0%
+kinds
+ 
+
+ align:start position:0%
+kinds
+I don't know that there do you think
+
+ align:start position:0%
+I don't know that there do you think
+ 
+
+ align:start position:0%
+I don't know that there do you think
+everyone has a finds love lots of people
+
+ align:start position:0%
+everyone has a finds love lots of people
+ 
+
+ align:start position:0%
+everyone has a finds love lots of people
+don't you might say that's sad um I see
+
+ align:start position:0%
+don't you might say that's sad um I see
+ 
+
+ align:start position:0%
+don't you might say that's sad um I see
+people in the street all the time and
+
+ align:start position:0%
+people in the street all the time and
+ 
+
+ align:start position:0%
+people in the street all the time and
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+uh this one or that one looks as if it's
+
+ align:start position:0%
+uh this one or that one looks as if it's
+ 
+
+ align:start position:0%
+uh this one or that one looks as if it's
+never been a moment of love in his or
+
+ align:start position:0%
+never been a moment of love in his or
+ 
+
+ align:start position:0%
+never been a moment of love in his or
+her life we may all be capable of it but
+
+ align:start position:0%
+her life we may all be capable of it but
+ 
+
+ align:start position:0%
+her life we may all be capable of it but
+it doesn't mean that in every society
+
+ align:start position:0%
+it doesn't mean that in every society
+ 
+
+ align:start position:0%
+it doesn't mean that in every society
+everyone is going to realize that life
+
+ align:start position:0%
+everyone is going to realize that life
+ 
+
+ align:start position:0%
+everyone is going to realize that life
+has no meaning without love would be a
+
+ align:start position:0%
+has no meaning without love would be a
+ 
+
+ align:start position:0%
+has no meaning without love would be a
+very sad thing to say because but there
+
+ align:start position:0%
+very sad thing to say because but there
+ 
+
+ align:start position:0%
+very sad thing to say because but there
+are many sad people in the world exactly
+
+ align:start position:0%
+are many sad people in the world exactly
+ 
+
+ align:start position:0%
+are many sad people in the world exactly
+because you can exist without loving you
+
+ align:start position:0%
+because you can exist without loving you
+ 
+
+ align:start position:0%
+because you can exist without loving you
+can still have your life and many things
+
+ align:start position:0%
+can still have your life and many things
+ 
+
+ align:start position:0%
+can still have your life and many things
+that you do that are important and could
+
+ align:start position:0%
+that you do that are important and could
+ 
+
+ align:start position:0%
+that you do that are important and could
+affect others but that doesn't mean you
+
+ align:start position:0%
+affect others but that doesn't mean you
+ 
+
+ align:start position:0%
+affect others but that doesn't mean you
+have to love psychiatrists regularly get
+
+ align:start position:0%
+have to love psychiatrists regularly get
+ 
+
+ align:start position:0%
+have to love psychiatrists regularly get
+patients who have been so abused and
+
+ align:start position:0%
+patients who have been so abused and
+ 
+
+ align:start position:0%
+patients who have been so abused and
+maltreated when they were young and
+
+ align:start position:0%
+maltreated when they were young and
+ 
+
+ align:start position:0%
+maltreated when they were young and
+maybe afterwards
+
+ align:start position:0%
+maybe afterwards
+ 
+
+ align:start position:0%
+maybe afterwards
+or different patients who were abused
+
+ align:start position:0%
+or different patients who were abused
+ 
+
+ align:start position:0%
+or different patients who were abused
+and Mal treated by their
+
+ align:start position:0%
+and Mal treated by their
+ 
+
+ align:start position:0%
+and Mal treated by their
+society by the world and maybe people
+
+ align:start position:0%
+society by the world and maybe people
+ 
+
+ align:start position:0%
+society by the world and maybe people
+who have been abused Mal Tre by both and
+
+ align:start position:0%
+who have been abused Mal Tre by both and
+ 
+
+ align:start position:0%
+who have been abused Mal Tre by both and
+who don't have any fire of inspiration
+
+ align:start position:0%
+who don't have any fire of inspiration
+ 
+
+ align:start position:0%
+who don't have any fire of inspiration
+who are just ordinary people
+
+ align:start position:0%
+who are just ordinary people
+ 
+
+ align:start position:0%
+who are just ordinary people
+without terrible terribly exceptional
+
+ align:start position:0%
+without terrible terribly exceptional
+ 
+
+ align:start position:0%
+without terrible terribly exceptional
+cortical ability who have never
+
+ align:start position:0%
+cortical ability who have never
+ 
+
+ align:start position:0%
+cortical ability who have never
+experienced love they don't agree with
+
+ align:start position:0%
+experienced love they don't agree with
+ 
+
+ align:start position:0%
+experienced love they don't agree with
+your example there though cuz you find
+
+ align:start position:0%
+your example there though cuz you find
+ 
+
+ align:start position:0%
+your example there though cuz you find
+like I don't agree with the example
+
+ align:start position:0%
+like I don't agree with the example
+ 
+
+ align:start position:0%
+like I don't agree with the example
+there you can always find some like
+
+ align:start position:0%
+there you can always find some like
+ 
+
+ align:start position:0%
+there you can always find some like
+abnormal psychology person you know
+
+ align:start position:0%
+abnormal psychology person you know
+ 
+
+ align:start position:0%
+abnormal psychology person you know
+doesn't experience something because of
+
+ align:start position:0%
+doesn't experience something because of
+ 
+
+ align:start position:0%
+doesn't experience something because of
+their past but I mean I think people on
+
+ align:start position:0%
+their past but I mean I think people on
+ 
+
+ align:start position:0%
+their past but I mean I think people on
+a whole
+
+ align:start position:0%
+a whole
+ 
+
+ align:start position:0%
+a whole
+are I don't think you need to introduce
+
+ align:start position:0%
+are I don't think you need to introduce
+ 
+
+ align:start position:0%
+are I don't think you need to introduce
+the concept of love in order for when
+
+ align:start position:0%
+the concept of love in order for when
+ 
+
+ align:start position:0%
+the concept of love in order for when
+you say abnormal psychology mean you
+
+ align:start position:0%
+you say abnormal psychology mean you
+ 
+
+ align:start position:0%
+you say abnormal psychology mean you
+mean it's a tiny minority making such an
+
+ align:start position:0%
+mean it's a tiny minority making such an
+ 
+
+ align:start position:0%
+mean it's a tiny minority making such an
+exception I think he's trying to say
+
+ align:start position:0%
+exception I think he's trying to say
+ 
+
+ align:start position:0%
+exception I think he's trying to say
+that you're just making such an
+
+ align:start position:0%
+that you're just making such an
+ 
+
+ align:start position:0%
+that you're just making such an
+exception right now it's not true of
+
+ align:start position:0%
+exception right now it's not true of
+ 
+
+ align:start position:0%
+exception right now it's not true of
+almost everybody yes I think well we
+
+ align:start position:0%
+almost everybody yes I think well we
+ 
+
+ align:start position:0%
+almost everybody yes I think well we
+don't I don't know I mean that would
+
+ align:start position:0%
+don't I don't know I mean that would
+ 
+
+ align:start position:0%
+don't I don't know I mean that would
+take some research which you can do
+
+ align:start position:0%
+take some research which you can do
+ 
+
+ align:start position:0%
+take some research which you can do
+because what I think what I'm trying to
+
+ align:start position:0%
+because what I think what I'm trying to
+ 
+
+ align:start position:0%
+because what I think what I'm trying to
+say overall is that in most people
+
+ align:start position:0%
+say overall is that in most people
+ 
+
+ align:start position:0%
+say overall is that in most people
+should are capable of of feeling love in
+
+ align:start position:0%
+should are capable of of feeling love in
+ 
+
+ align:start position:0%
+should are capable of of feeling love in
+any in some sort of sense regardless if
+
+ align:start position:0%
+any in some sort of sense regardless if
+ 
+
+ align:start position:0%
+any in some sort of sense regardless if
+they had known about it or if they had
+
+ align:start position:0%
+they had known about it or if they had
+ 
+
+ align:start position:0%
+they had known about it or if they had
+you know been shown with it they don't
+
+ align:start position:0%
+you know been shown with it they don't
+ 
+
+ align:start position:0%
+you know been shown with it they don't
+want nobody wants the capacity who want
+
+ align:start position:0%
+want nobody wants the capacity who want
+ 
+
+ align:start position:0%
+want nobody wants the capacity who want
+the realization but even if maybe your
+
+ align:start position:0%
+the realization but even if maybe your
+ 
+
+ align:start position:0%
+the realization but even if maybe your
+circumstances don't allow you to be in
+
+ align:start position:0%
+circumstances don't allow you to be in
+ 
+
+ align:start position:0%
+circumstances don't allow you to be in
+the position to where you can fall in
+
+ align:start position:0%
+the position to where you can fall in
+ 
+
+ align:start position:0%
+the position to where you can fall in
+love or when you love a thing or love
+
+ align:start position:0%
+love or when you love a thing or love
+ 
+
+ align:start position:0%
+love or when you love a thing or love
+you know anything but I think that as
+
+ align:start position:0%
+you know anything but I think that as
+ 
+
+ align:start position:0%
+you know anything but I think that as
+humans that is one of the things that
+
+ align:start position:0%
+humans that is one of the things that
+ 
+
+ align:start position:0%
+humans that is one of the things that
+distinguishes us oh I'm not denying that
+
+ align:start position:0%
+distinguishes us oh I'm not denying that
+ 
+
+ align:start position:0%
+distinguishes us oh I'm not denying that
+it exists among human beings and that we
+
+ align:start position:0%
+it exists among human beings and that we
+ 
+
+ align:start position:0%
+it exists among human beings and that we
+have the capability of loving oh I
+
+ align:start position:0%
+have the capability of loving oh I
+ 
+
+ align:start position:0%
+have the capability of loving oh I
+believe no but who can deny that that's
+
+ align:start position:0%
+believe no but who can deny that that's
+ 
+
+ align:start position:0%
+believe no but who can deny that that's
+it seems to me to be a trism but it
+
+ align:start position:0%
+it seems to me to be a trism but it
+ 
+
+ align:start position:0%
+it seems to me to be a trism but it
+seems to me that just because you know
+
+ align:start position:0%
+seems to me that just because you know
+ 
+
+ align:start position:0%
+seems to me that just because you know
+that and if you include one kind or
+
+ align:start position:0%
+that and if you include one kind or
+ 
+
+ align:start position:0%
+that and if you include one kind or
+another yes this is a common
+
+ align:start position:0%
+another yes this is a common
+ 
+
+ align:start position:0%
+another yes this is a common
+phenomenon and it'll be different with
+
+ align:start position:0%
+phenomenon and it'll be different with
+ 
+
+ align:start position:0%
+phenomenon and it'll be different with
+us from it is from what it is with
+
+ align:start position:0%
+us from it is from what it is with
+ 
+
+ align:start position:0%
+us from it is from what it is with
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+um animals I'm sure
+
+ align:start position:0%
+um animals I'm sure
+ 
+
+ align:start position:0%
+um animals I'm sure
+love as much as we do but they do it in
+
+ align:start position:0%
+love as much as we do but they do it in
+ 
+
+ align:start position:0%
+love as much as we do but they do it in
+such a different way that we don't
+
+ align:start position:0%
+such a different way that we don't
+ 
+
+ align:start position:0%
+such a different way that we don't
+recognize it um there is um that term
+
+ align:start position:0%
+recognize it um there is um that term
+ 
+
+ align:start position:0%
+recognize it um there is um that term
+that I mentioned last time instead of
+
+ align:start position:0%
+that I mentioned last time instead of
+ 
+
+ align:start position:0%
+that I mentioned last time instead of
+sympathy I ought to get I picked it up
+
+ align:start position:0%
+sympathy I ought to get I picked it up
+ 
+
+ align:start position:0%
+sympathy I ought to get I picked it up
+in an article by somebody and I liked it
+
+ align:start position:0%
+in an article by somebody and I liked it
+ 
+
+ align:start position:0%
+in an article by somebody and I liked it
+and so I developed it made a big thing
+
+ align:start position:0%
+and so I developed it made a big thing
+ 
+
+ align:start position:0%
+and so I developed it made a big thing
+out of it in one of my books uh instead
+
+ align:start position:0%
+out of it in one of my books uh instead
+ 
+
+ align:start position:0%
+out of it in one of my books uh instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a a mother cat doesn't feel sympathy for
+
+ align:start position:0%
+a a mother cat doesn't feel sympathy for
+ 
+
+ align:start position:0%
+a a mother cat doesn't feel sympathy for
+her
+
+ align:start position:0%
+her
+ 
+
+ align:start position:0%
+her
+kitten but doesn't mean that she doesn't
+
+ align:start position:0%
+kitten but doesn't mean that she doesn't
+ 
+
+ align:start position:0%
+kitten but doesn't mean that she doesn't
+love it she shows her feeling through
+
+ align:start position:0%
+love it she shows her feeling through
+ 
+
+ align:start position:0%
+love it she shows her feeling through
+bodily contact she doesn't sympathy
+
+ align:start position:0%
+bodily contact she doesn't sympathy
+ 
+
+ align:start position:0%
+bodily contact she doesn't sympathy
+means having feelings you know oh poor
+
+ align:start position:0%
+means having feelings you know oh poor
+ 
+
+ align:start position:0%
+means having feelings you know oh poor
+thing or that you got a boo boo or your
+
+ align:start position:0%
+thing or that you got a boo boo or your
+ 
+
+ align:start position:0%
+thing or that you got a boo boo or your
+the mother shows love to the human child
+
+ align:start position:0%
+the mother shows love to the human child
+ 
+
+ align:start position:0%
+the mother shows love to the human child
+through language and through Concepts
+
+ align:start position:0%
+through language and through Concepts
+ 
+
+ align:start position:0%
+through language and through Concepts
+and through these uh very complicated
+
+ align:start position:0%
+and through these uh very complicated
+ 
+
+ align:start position:0%
+and through these uh very complicated
+system of feelings like what we call
+
+ align:start position:0%
+system of feelings like what we call
+ 
+
+ align:start position:0%
+system of feelings like what we call
+sympathy which are also need of analysis
+
+ align:start position:0%
+sympathy which are also need of analysis
+ 
+
+ align:start position:0%
+sympathy which are also need of analysis
+and which I give analysis to in my most
+
+ align:start position:0%
+and which I give analysis to in my most
+ 
+
+ align:start position:0%
+and which I give analysis to in my most
+recent books so I don't think I or maybe
+
+ align:start position:0%
+recent books so I don't think I or maybe
+ 
+
+ align:start position:0%
+recent books so I don't think I or maybe
+I get into sympathy here I'm not sure uh
+
+ align:start position:0%
+I get into sympathy here I'm not sure uh
+ 
+
+ align:start position:0%
+I get into sympathy here I'm not sure uh
+in any event it continued over a period
+
+ align:start position:0%
+in any event it continued over a period
+ 
+
+ align:start position:0%
+in any event it continued over a period
+of many years with me uh that's
+
+ align:start position:0%
+of many years with me uh that's
+ 
+
+ align:start position:0%
+of many years with me uh that's
+something human uh cats don't go around
+
+ align:start position:0%
+something human uh cats don't go around
+ 
+
+ align:start position:0%
+something human uh cats don't go around
+moaning and they don't have language
+
+ align:start position:0%
+moaning and they don't have language
+ 
+
+ align:start position:0%
+moaning and they don't have language
+they don't have Concepts but uh they
+
+ align:start position:0%
+they don't have Concepts but uh they
+ 
+
+ align:start position:0%
+they don't have Concepts but uh they
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+contact and show their love for the for
+
+ align:start position:0%
+contact and show their love for the for
+ 
+
+ align:start position:0%
+contact and show their love for the for
+their baby
+
+ align:start position:0%
+their baby
+ 
+
+ align:start position:0%
+their baby
+by making it accessible to them uh
+
+ align:start position:0%
+by making it accessible to them uh
+ 
+
+ align:start position:0%
+by making it accessible to them uh
+looking at them touching them feeling
+
+ align:start position:0%
+looking at them touching them feeling
+ 
+
+ align:start position:0%
+looking at them touching them feeling
+them um uh the word let's see instead of
+
+ align:start position:0%
+them um uh the word let's see instead of
+ 
+
+ align:start position:0%
+them um uh the word let's see instead of
+sympathy this person whose term I picked
+
+ align:start position:0%
+sympathy this person whose term I picked
+ 
+
+ align:start position:0%
+sympathy this person whose term I picked
+up uh was uh syphy
+
+ align:start position:0%
+up uh was uh syphy
+ 
+
+ align:start position:0%
+up uh was uh syphy
+Sy
+
+ align:start position:0%
+Sy
+ 
+
+ align:start position:0%
+Sy
+Sy I I'll try to remember look it up for
+
+ align:start position:0%
+Sy I I'll try to remember look it up for
+ 
+
+ align:start position:0%
+Sy I I'll try to remember look it up for
+you next time it's um it's a bodily
+
+ align:start position:0%
+you next time it's um it's a bodily
+ 
+
+ align:start position:0%
+you next time it's um it's a bodily
+equipment making contact through the
+
+ align:start position:0%
+equipment making contact through the
+ 
+
+ align:start position:0%
+equipment making contact through the
+body rather than through words or
+
+ align:start position:0%
+body rather than through words or
+ 
+
+ align:start position:0%
+body rather than through words or
+feelings so it's not just human beings
+
+ align:start position:0%
+feelings so it's not just human beings
+ 
+
+ align:start position:0%
+feelings so it's not just human beings
+who love but the other animals do in
+
+ align:start position:0%
+who love but the other animals do in
+ 
+
+ align:start position:0%
+who love but the other animals do in
+different ways that we hardly understand
+
+ align:start position:0%
+different ways that we hardly understand
+ 
+
+ align:start position:0%
+different ways that we hardly understand
+and we do it in a great panoramic way
+
+ align:start position:0%
+and we do it in a great panoramic way
+ 
+
+ align:start position:0%
+and we do it in a great panoramic way
+remember I'm a pluralist so there isn't
+
+ align:start position:0%
+remember I'm a pluralist so there isn't
+ 
+
+ align:start position:0%
+remember I'm a pluralist so there isn't
+any one definition for the word love I
+
+ align:start position:0%
+any one definition for the word love I
+ 
+
+ align:start position:0%
+any one definition for the word love I
+never give a definition for love is not
+
+ align:start position:0%
+never give a definition for love is not
+ 
+
+ align:start position:0%
+never give a definition for love is not
+it isn't just one thing it's a gamut
+
+ align:start position:0%
+it isn't just one thing it's a gamut
+ 
+
+ align:start position:0%
+it isn't just one thing it's a gamut
+that's very important in life as we know
+
+ align:start position:0%
+that's very important in life as we know
+ 
+
+ align:start position:0%
+that's very important in life as we know
+it and so my job as a humanist
+
+ align:start position:0%
+it and so my job as a humanist
+ 
+
+ align:start position:0%
+it and so my job as a humanist
+pluralist um non-reductive philosopher
+
+ align:start position:0%
+pluralist um non-reductive philosopher
+ 
+
+ align:start position:0%
+pluralist um non-reductive philosopher
+is to see the different aspects the
+
+ align:start position:0%
+is to see the different aspects the
+ 
+
+ align:start position:0%
+is to see the different aspects the
+different ways in which something could
+
+ align:start position:0%
+different ways in which something could
+ 
+
+ align:start position:0%
+different ways in which something could
+be called a phenomenon of love and then
+
+ align:start position:0%
+be called a phenomenon of love and then
+ 
+
+ align:start position:0%
+be called a phenomenon of love and then
+to make sense out of that I'll give you
+
+ align:start position:0%
+to make sense out of that I'll give you
+ 
+
+ align:start position:0%
+to make sense out of that I'll give you
+an example people in fact This was um it
+
+ align:start position:0%
+an example people in fact This was um it
+ 
+
+ align:start position:0%
+an example people in fact This was um it
+came out in that Symposium there was a
+
+ align:start position:0%
+came out in that Symposium there was a
+ 
+
+ align:start position:0%
+came out in that Symposium there was a
+very nice Jesuit priest who wrote a
+
+ align:start position:0%
+very nice Jesuit priest who wrote a
+ 
+
+ align:start position:0%
+very nice Jesuit priest who wrote a
+paper about about me oh no well there
+
+ align:start position:0%
+paper about about me oh no well there
+ 
+
+ align:start position:0%
+paper about about me oh no well there
+were there were nice Jesuit P priests
+
+ align:start position:0%
+were there were nice Jesuit P priests
+ 
+
+ align:start position:0%
+were there were nice Jesuit P priests
+but I think this woman is not a Jesuit
+
+ align:start position:0%
+but I think this woman is not a Jesuit
+ 
+
+ align:start position:0%
+but I think this woman is not a Jesuit
+actually I forget what his order was
+
+ align:start position:0%
+actually I forget what his order was
+ 
+
+ align:start position:0%
+actually I forget what his order was
+maybe he was a polist in any event he
+
+ align:start position:0%
+maybe he was a polist in any event he
+ 
+
+ align:start position:0%
+maybe he was a polist in any event he
+criticized me because he said um I talk
+
+ align:start position:0%
+criticized me because he said um I talk
+ 
+
+ align:start position:0%
+criticized me because he said um I talk
+very fervently and with great
+
+ align:start position:0%
+very fervently and with great
+ 
+
+ align:start position:0%
+very fervently and with great
+appreciation of what I call the love of
+
+ align:start position:0%
+appreciation of what I call the love of
+ 
+
+ align:start position:0%
+appreciation of what I call the love of
+things that will come into your reading
+
+ align:start position:0%
+things that will come into your reading
+ 
+
+ align:start position:0%
+things that will come into your reading
+if it hasn't already um and he said that
+
+ align:start position:0%
+if it hasn't already um and he said that
+ 
+
+ align:start position:0%
+if it hasn't already um and he said that
+isn't love
+
+ align:start position:0%
+isn't love
+ 
+
+ align:start position:0%
+isn't love
+um only God can be loved and we love God
+
+ align:start position:0%
+um only God can be loved and we love God
+ 
+
+ align:start position:0%
+um only God can be loved and we love God
+because uh God is a person and we love
+
+ align:start position:0%
+because uh God is a person and we love
+ 
+
+ align:start position:0%
+because uh God is a person and we love
+other persons because they are created
+
+ align:start position:0%
+other persons because they are created
+ 
+
+ align:start position:0%
+other persons because they are created
+in the image of God so the only true
+
+ align:start position:0%
+in the image of God so the only true
+ 
+
+ align:start position:0%
+in the image of God so the only true
+love has to
+
+ align:start position:0%
+love has to
+ 
+
+ align:start position:0%
+love has to
+be a love of persons you can't have a
+
+ align:start position:0%
+be a love of persons you can't have a
+ 
+
+ align:start position:0%
+be a love of persons you can't have a
+love of
+
+ align:start position:0%
+love of
+ 
+
+ align:start position:0%
+love of
+things and I and we argued and it comes
+
+ align:start position:0%
+things and I and we argued and it comes
+ 
+
+ align:start position:0%
+things and I and we argued and it comes
+out in what you'll be reading based on
+
+ align:start position:0%
+out in what you'll be reading based on
+ 
+
+ align:start position:0%
+out in what you'll be reading based on
+my commentary my the uh
+
+ align:start position:0%
+my commentary my the uh
+ 
+
+ align:start position:0%
+my commentary my the uh
+um uh my reply to
+
+ align:start position:0%
+um uh my reply to
+ 
+
+ align:start position:0%
+um uh my reply to
+my um friendly commentators and my reply
+
+ align:start position:0%
+my um friendly commentators and my reply
+ 
+
+ align:start position:0%
+my um friendly commentators and my reply
+to my critics and friendly commentators
+
+ align:start position:0%
+to my critics and friendly commentators
+ 
+
+ align:start position:0%
+to my critics and friendly commentators
+remember I told you that'll come up in
+
+ align:start position:0%
+remember I told you that'll come up in
+ 
+
+ align:start position:0%
+remember I told you that'll come up in
+the reading later on so I defend my idea
+
+ align:start position:0%
+the reading later on so I defend my idea
+ 
+
+ align:start position:0%
+the reading later on so I defend my idea
+of the love of things but um to me that
+
+ align:start position:0%
+of the love of things but um to me that
+ 
+
+ align:start position:0%
+of the love of things but um to me that
+is that is an authentic love and has to
+
+ align:start position:0%
+is that is an authentic love and has to
+ 
+
+ align:start position:0%
+is that is an authentic love and has to
+be cultivated if you're a
+
+ align:start position:0%
+be cultivated if you're a
+ 
+
+ align:start position:0%
+be cultivated if you're a
+carpenter you love those tools you
+
+ align:start position:0%
+carpenter you love those tools you
+ 
+
+ align:start position:0%
+carpenter you love those tools you
+depend on them you get to understand
+
+ align:start position:0%
+depend on them you get to understand
+ 
+
+ align:start position:0%
+depend on them you get to understand
+them there's the kind of love I have for
+
+ align:start position:0%
+them there's the kind of love I have for
+ 
+
+ align:start position:0%
+them there's the kind of love I have for
+my computer
+
+ align:start position:0%
+my computer
+ 
+
+ align:start position:0%
+my computer
+like all love it's based on my
+
+ align:start position:0%
+like all love it's based on my
+ 
+
+ align:start position:0%
+like all love it's based on my
+self-interest because I I'm dependent on
+
+ align:start position:0%
+self-interest because I I'm dependent on
+ 
+
+ align:start position:0%
+self-interest because I I'm dependent on
+it I need it but also it it's become a
+
+ align:start position:0%
+it I need it but also it it's become a
+ 
+
+ align:start position:0%
+it I need it but also it it's become a
+kind of collaborator of mine it gives me
+
+ align:start position:0%
+kind of collaborator of mine it gives me
+ 
+
+ align:start position:0%
+kind of collaborator of mine it gives me
+ideas sitting in the way my teaching
+
+ align:start position:0%
+ideas sitting in the way my teaching
+ 
+
+ align:start position:0%
+ideas sitting in the way my teaching
+with you which one reason I love
+
+ align:start position:0%
+with you which one reason I love
+ 
+
+ align:start position:0%
+with you which one reason I love
+teaching at MIT because I can have
+
+ align:start position:0%
+teaching at MIT because I can have
+ 
+
+ align:start position:0%
+teaching at MIT because I can have
+students like you is that it elicits
+
+ align:start position:0%
+students like you is that it elicits
+ 
+
+ align:start position:0%
+students like you is that it elicits
+ideas for me it gives me a sense of life
+
+ align:start position:0%
+ideas for me it gives me a sense of life
+ 
+
+ align:start position:0%
+ideas for me it gives me a sense of life
+and I then I'm able to be sometimes be
+
+ align:start position:0%
+and I then I'm able to be sometimes be
+ 
+
+ align:start position:0%
+and I then I'm able to be sometimes be
+creative that way well computer is like
+
+ align:start position:0%
+creative that way well computer is like
+ 
+
+ align:start position:0%
+creative that way well computer is like
+that you're not things only you're also
+
+ align:start position:0%
+that you're not things only you're also
+ 
+
+ align:start position:0%
+that you're not things only you're also
+persons the computer is just a thing I'm
+
+ align:start position:0%
+persons the computer is just a thing I'm
+ 
+
+ align:start position:0%
+persons the computer is just a thing I'm
+not going to say the computer is a
+
+ align:start position:0%
+not going to say the computer is a
+ 
+
+ align:start position:0%
+not going to say the computer is a
+person but when I think about human
+
+ align:start position:0%
+person but when I think about human
+ 
+
+ align:start position:0%
+person but when I think about human
+beings they are both persons and things
+
+ align:start position:0%
+beings they are both persons and things
+ 
+
+ align:start position:0%
+beings they are both persons and things
+and that was the basis of my reply to
+
+ align:start position:0%
+and that was the basis of my reply to
+ 
+
+ align:start position:0%
+and that was the basis of my reply to
+the priest uh very lovable man I like
+
+ align:start position:0%
+the priest uh very lovable man I like
+ 
+
+ align:start position:0%
+the priest uh very lovable man I like
+lik them very much um my reply
+
+ align:start position:0%
+lik them very much um my reply
+ 
+
+ align:start position:0%
+lik them very much um my reply
+was if you're a human being you are a
+
+ align:start position:0%
+was if you're a human being you are a
+ 
+
+ align:start position:0%
+was if you're a human being you are a
+person but there are no persons who are
+
+ align:start position:0%
+person but there are no persons who are
+ 
+
+ align:start position:0%
+person but there are no persons who are
+human beings who aren't also things
+
+ align:start position:0%
+human beings who aren't also things
+ 
+
+ align:start position:0%
+human beings who aren't also things
+that's what is so special about us we
+
+ align:start position:0%
+that's what is so special about us we
+ 
+
+ align:start position:0%
+that's what is so special about us we
+are both things and persons our
+
+ align:start position:0%
+are both things and persons our
+ 
+
+ align:start position:0%
+are both things and persons our
+thingness comes to us through our body
+
+ align:start position:0%
+thingness comes to us through our body
+ 
+
+ align:start position:0%
+thingness comes to us through our body
+and if you don't love your body you
+
+ align:start position:0%
+and if you don't love your body you
+ 
+
+ align:start position:0%
+and if you don't love your body you
+can't love yourself and if you don't
+
+ align:start position:0%
+can't love yourself and if you don't
+ 
+
+ align:start position:0%
+can't love yourself and if you don't
+love yourself you can't love in the way
+
+ align:start position:0%
+love yourself you can't love in the way
+ 
+
+ align:start position:0%
+love yourself you can't love in the way
+that a person loves so that for us there
+
+ align:start position:0%
+that a person loves so that for us there
+ 
+
+ align:start position:0%
+that a person loves so that for us there
+is an Inseparable love of body and love
+
+ align:start position:0%
+is an Inseparable love of body and love
+ 
+
+ align:start position:0%
+is an Inseparable love of body and love
+love of things and and love of persons
+
+ align:start position:0%
+love of things and and love of persons
+ 
+
+ align:start position:0%
+love of things and and love of persons
+and that's definitive of human nature
+
+ align:start position:0%
+and that's definitive of human nature
+ 
+
+ align:start position:0%
+and that's definitive of human nature
+and I don't know with other species one
+
+ align:start position:0%
+and I don't know with other species one
+ 
+
+ align:start position:0%
+and I don't know with other species one
+might have to say something different
+
+ align:start position:0%
+might have to say something different
+ 
+
+ align:start position:0%
+might have to say something different
+but for me the love of persons is a
+
+ align:start position:0%
+but for me the love of persons is a
+ 
+
+ align:start position:0%
+but for me the love of persons is a
+crucial but that can't be separated from
+
+ align:start position:0%
+crucial but that can't be separated from
+ 
+
+ align:start position:0%
+crucial but that can't be separated from
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+love of
+
+ align:start position:0%
+love of
+ 
+
+ align:start position:0%
+love of
+bodies and that's why
+
+ align:start position:0%
+bodies and that's why
+ 
+
+ align:start position:0%
+bodies and that's why
+um that's another thing that comes into
+
+ align:start position:0%
+um that's another thing that comes into
+ 
+
+ align:start position:0%
+um that's another thing that comes into
+the analysis at some point the caring
+
+ align:start position:0%
+the analysis at some point the caring
+ 
+
+ align:start position:0%
+the analysis at some point the caring
+love is caring caring for for and caring
+
+ align:start position:0%
+love is caring caring for for and caring
+ 
+
+ align:start position:0%
+love is caring caring for for and caring
+about and caring for do you know the
+
+ align:start position:0%
+about and caring for do you know the
+ 
+
+ align:start position:0%
+about and caring for do you know the
+movie
+
+ align:start position:0%
+movie
+ 
+
+ align:start position:0%
+movie
+um The Elephant Man or clay it was a
+
+ align:start position:0%
+um The Elephant Man or clay it was a
+ 
+
+ align:start position:0%
+um The Elephant Man or clay it was a
+terribly def
+
+ align:start position:0%
+terribly def
+ 
+
+ align:start position:0%
+terribly def
+figured person that Anthony Hopkins is a
+
+ align:start position:0%
+figured person that Anthony Hopkins is a
+ 
+
+ align:start position:0%
+figured person that Anthony Hopkins is a
+doctor in 19th century England tries to
+
+ align:start position:0%
+doctor in 19th century England tries to
+ 
+
+ align:start position:0%
+doctor in 19th century England tries to
+help and he's so hideous that he would
+
+ align:start position:0%
+help and he's so hideous that he would
+ 
+
+ align:start position:0%
+help and he's so hideous that he would
+never appear in public or covered and at
+
+ align:start position:0%
+never appear in public or covered and at
+ 
+
+ align:start position:0%
+never appear in public or covered and at
+the same time he had a very sensitive
+
+ align:start position:0%
+the same time he had a very sensitive
+ 
+
+ align:start position:0%
+the same time he had a very sensitive
+refined Soul so was a terrible tragedy
+
+ align:start position:0%
+refined Soul so was a terrible tragedy
+ 
+
+ align:start position:0%
+refined Soul so was a terrible tragedy
+that his appearance was so
+
+ align:start position:0%
+that his appearance was so
+ 
+
+ align:start position:0%
+that his appearance was so
+grotesque um in the sense of the
+
+ align:start position:0%
+grotesque um in the sense of the
+ 
+
+ align:start position:0%
+grotesque um in the sense of the
+variation on Beauty and the Beast he was
+
+ align:start position:0%
+variation on Beauty and the Beast he was
+ 
+
+ align:start position:0%
+variation on Beauty and the Beast he was
+both simultaneously had a beautiful soul
+
+ align:start position:0%
+both simultaneously had a beautiful soul
+ 
+
+ align:start position:0%
+both simultaneously had a beautiful soul
+and and a beastly grotesque appearance
+
+ align:start position:0%
+and and a beastly grotesque appearance
+ 
+
+ align:start position:0%
+and and a beastly grotesque appearance
+because of some anatomical
+
+ align:start position:0%
+because of some anatomical
+ 
+
+ align:start position:0%
+because of some anatomical
+abnormality uh in one place in one part
+
+ align:start position:0%
+abnormality uh in one place in one part
+ 
+
+ align:start position:0%
+abnormality uh in one place in one part
+of the movie at least he is profected by
+
+ align:start position:0%
+of the movie at least he is profected by
+ 
+
+ align:start position:0%
+of the movie at least he is profected by
+a couple of U
+
+ align:start position:0%
+a couple of U
+ 
+
+ align:start position:0%
+a couple of U
+actresses and and who are very much
+
+ align:start position:0%
+actresses and and who are very much
+ 
+
+ align:start position:0%
+actresses and and who are very much
+struck by his sensitivity uh and they
+
+ align:start position:0%
+struck by his sensitivity uh and they
+ 
+
+ align:start position:0%
+struck by his sensitivity uh and they
+are Shakespearean actors so he reads
+
+ align:start position:0%
+are Shakespearean actors so he reads
+ 
+
+ align:start position:0%
+are Shakespearean actors so he reads
+Shakespeare and he discusses it with him
+
+ align:start position:0%
+Shakespeare and he discusses it with him
+ 
+
+ align:start position:0%
+Shakespeare and he discusses it with him
+and at one point he discusses Romeo and
+
+ align:start position:0%
+and at one point he discusses Romeo and
+ 
+
+ align:start position:0%
+and at one point he discusses Romeo and
+Juliet and he says to them in his
+
+ align:start position:0%
+Juliet and he says to them in his
+ 
+
+ align:start position:0%
+Juliet and he says to them in his
+halting way because of his
+
+ align:start position:0%
+halting way because of his
+ 
+
+ align:start position:0%
+halting way because of his
+def defigurates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Juliet and they said oh no he was
+
+ align:start position:0%
+Juliet and they said oh no he was
+ 
+
+ align:start position:0%
+Juliet and they said oh no he was
+tremendously in love with her he why do
+
+ align:start position:0%
+tremendously in love with her he why do
+ 
+
+ align:start position:0%
+tremendously in love with her he why do
+you say that and that's the whole point
+
+ align:start position:0%
+you say that and that's the whole point
+ 
+
+ align:start position:0%
+you say that and that's the whole point
+of the play and he said
+
+ align:start position:0%
+of the play and he said
+ 
+
+ align:start position:0%
+of the play and he said
+well I know he cared for her but he
+
+ align:start position:0%
+well I know he cared for her but he
+ 
+
+ align:start position:0%
+well I know he cared for her but he
+didn't take care of her he didn't care
+
+ align:start position:0%
+didn't take care of her he didn't care
+ 
+
+ align:start position:0%
+didn't take care of her he didn't care
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+her and that and the the actresses are
+
+ align:start position:0%
+her and that and the the actresses are
+ 
+
+ align:start position:0%
+her and that and the the actresses are
+stunned by the wisdom of that comment
+
+ align:start position:0%
+stunned by the wisdom of that comment
+ 
+
+ align:start position:0%
+stunned by the wisdom of that comment
+and it's very profound distinction if
+
+ align:start position:0%
+and it's very profound distinction if
+ 
+
+ align:start position:0%
+and it's very profound distinction if
+you love somebody it isn't merely this
+
+ align:start position:0%
+you love somebody it isn't merely this
+ 
+
+ align:start position:0%
+you love somebody it isn't merely this
+personal relation but you take care of
+
+ align:start position:0%
+personal relation but you take care of
+ 
+
+ align:start position:0%
+personal relation but you take care of
+that person which means the body you
+
+ align:start position:0%
+that person which means the body you
+ 
+
+ align:start position:0%
+that person which means the body you
+worry about her condition you worry
+
+ align:start position:0%
+worry about her condition you worry
+ 
+
+ align:start position:0%
+worry about her condition you worry
+about her needs about her her bodily as
+
+ align:start position:0%
+about her needs about her her bodily as
+ 
+
+ align:start position:0%
+about her needs about her her bodily as
+a body not just as sex object or the
+
+ align:start position:0%
+a body not just as sex object or the
+ 
+
+ align:start position:0%
+a body not just as sex object or the
+body the uh that's beautiful so that you
+
+ align:start position:0%
+body the uh that's beautiful so that you
+ 
+
+ align:start position:0%
+body the uh that's beautiful so that you
+love her as a beautiful person you love
+
+ align:start position:0%
+love her as a beautiful person you love
+ 
+
+ align:start position:0%
+love her as a beautiful person you love
+her as a thing the way the carpenter
+
+ align:start position:0%
+her as a thing the way the carpenter
+ 
+
+ align:start position:0%
+her as a thing the way the carpenter
+loves his tools and the way that one can
+
+ align:start position:0%
+loves his tools and the way that one can
+ 
+
+ align:start position:0%
+loves his tools and the way that one can
+love one's computer because there's such
+
+ align:start position:0%
+love one's computer because there's such
+ 
+
+ align:start position:0%
+love one's computer because there's such
+wonderful they are things that live in
+
+ align:start position:0%
+wonderful they are things that live in
+ 
+
+ align:start position:0%
+wonderful they are things that live in
+their own domain and have to be taken
+
+ align:start position:0%
+their own domain and have to be taken
+ 
+
+ align:start position:0%
+their own domain and have to be taken
+care of as such you can't love your
+
+ align:start position:0%
+care of as such you can't love your
+ 
+
+ align:start position:0%
+care of as such you can't love your
+tools you just throw them around and let
+
+ align:start position:0%
+tools you just throw them around and let
+ 
+
+ align:start position:0%
+tools you just throw them around and let
+them get out in the rain and and Rusty
+
+ align:start position:0%
+them get out in the rain and and Rusty
+ 
+
+ align:start position:0%
+them get out in the rain and and Rusty
+you show your love for your tools by
+
+ align:start position:0%
+you show your love for your tools by
+ 
+
+ align:start position:0%
+you show your love for your tools by
+taking care of them and caring about
+
+ align:start position:0%
+taking care of them and caring about
+ 
+
+ align:start position:0%
+taking care of them and caring about
+them and you love your body uh not by
+
+ align:start position:0%
+them and you love your body uh not by
+ 
+
+ align:start position:0%
+them and you love your body uh not by
+eating what comes to mind but taking
+
+ align:start position:0%
+eating what comes to mind but taking
+ 
+
+ align:start position:0%
+eating what comes to mind but taking
+care of your body right and that's love
+
+ align:start position:0%
+care of your body right and that's love
+ 
+
+ align:start position:0%
+care of your body right and that's love
+that kind of love is for me very
+
+ align:start position:0%
+that kind of love is for me very
+ 
+
+ align:start position:0%
+that kind of love is for me very
+important in understanding love and
+
+ align:start position:0%
+important in understanding love and
+ 
+
+ align:start position:0%
+important in understanding love and
+General and that was my argument against
+
+ align:start position:0%
+General and that was my argument against
+ 
+
+ align:start position:0%
+General and that was my argument against
+the priest that somehow you you believe
+
+ align:start position:0%
+the priest that somehow you you believe
+ 
+
+ align:start position:0%
+the priest that somehow you you believe
+in a spiritual love which is pure spirit
+
+ align:start position:0%
+in a spiritual love which is pure spirit
+ 
+
+ align:start position:0%
+in a spiritual love which is pure spirit
+and I don't think of spirit that way I
+
+ align:start position:0%
+and I don't think of spirit that way I
+ 
+
+ align:start position:0%
+and I don't think of spirit that way I
+think of spirit as incorporating all
+
+ align:start position:0%
+think of spirit as incorporating all
+ 
+
+ align:start position:0%
+think of spirit as incorporating all
+human values including the ones that
+
+ align:start position:0%
+human values including the ones that
+ 
+
+ align:start position:0%
+human values including the ones that
+involve the love of of the body it's not
+
+ align:start position:0%
+involve the love of of the body it's not
+ 
+
+ align:start position:0%
+involve the love of of the body it's not
+a deep you know de
+
+ align:start position:0%
+a deep you know de
+ 
+
+ align:start position:0%
+a deep you know de
+deared one the way God is pure spirit
+
+ align:start position:0%
+deared one the way God is pure spirit
+ 
+
+ align:start position:0%
+deared one the way God is pure spirit
+and you experience love only if you have
+
+ align:start position:0%
+and you experience love only if you have
+ 
+
+ align:start position:0%
+and you experience love only if you have
+love of God as a pure Spirit otherwise
+
+ align:start position:0%
+love of God as a pure Spirit otherwise
+ 
+
+ align:start position:0%
+love of God as a pure Spirit otherwise
+it's a pagan idolatry if you make a
+
+ align:start position:0%
+it's a pagan idolatry if you make a
+ 
+
+ align:start position:0%
+it's a pagan idolatry if you make a
+Graven image and fall in love with that
+
+ align:start position:0%
+Graven image and fall in love with that
+ 
+
+ align:start position:0%
+Graven image and fall in love with that
+well if you think of God as that Graven
+
+ align:start position:0%
+well if you think of God as that Graven
+ 
+
+ align:start position:0%
+well if you think of God as that Graven
+image that I think is is not very
+
+ align:start position:0%
+image that I think is is not very
+ 
+
+ align:start position:0%
+image that I think is is not very
+commendable but if the reason for not
+
+ align:start position:0%
+commendable but if the reason for not
+ 
+
+ align:start position:0%
+commendable but if the reason for not
+loving Craven images you know Idols is
+
+ align:start position:0%
+loving Craven images you know Idols is
+ 
+
+ align:start position:0%
+loving Craven images you know Idols is
+because they are things but God is pure
+
+ align:start position:0%
+because they are things but God is pure
+ 
+
+ align:start position:0%
+because they are things but God is pure
+Spirit then we part compy I don't know
+
+ align:start position:0%
+Spirit then we part compy I don't know
+ 
+
+ align:start position:0%
+Spirit then we part compy I don't know
+I've never experienced pure spirit I
+
+ align:start position:0%
+I've never experienced pure spirit I
+ 
+
+ align:start position:0%
+I've never experienced pure spirit I
+don't know what I would be like to have
+
+ align:start position:0%
+don't know what I would be like to have
+ 
+
+ align:start position:0%
+don't know what I would be like to have
+pure spirit I know what it's like to be
+
+ align:start position:0%
+pure spirit I know what it's like to be
+ 
+
+ align:start position:0%
+pure spirit I know what it's like to be
+spiritual because people in their body
+
+ align:start position:0%
+spiritual because people in their body
+ 
+
+ align:start position:0%
+spiritual because people in their body
+are able to transcend their bodies and
+
+ align:start position:0%
+are able to transcend their bodies and
+ 
+
+ align:start position:0%
+are able to transcend their bodies and
+even sacrifice them s out of love for
+
+ align:start position:0%
+even sacrifice them s out of love for
+ 
+
+ align:start position:0%
+even sacrifice them s out of love for
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+person which means that person has a
+
+ align:start position:0%
+person which means that person has a
+ 
+
+ align:start position:0%
+person which means that person has a
+body who wants to live that's a
+
+ align:start position:0%
+body who wants to live that's a
+ 
+
+ align:start position:0%
+body who wants to live that's a
+spiritual wonderment and the value I can
+
+ align:start position:0%
+spiritual wonderment and the value I can
+ 
+
+ align:start position:0%
+spiritual wonderment and the value I can
+understand but pure spirit I can't
+
+ align:start position:0%
+understand but pure spirit I can't
+ 
+
+ align:start position:0%
+understand but pure spirit I can't
+understand because it makes this
+
+ align:start position:0%
+understand because it makes this
+ 
+
+ align:start position:0%
+understand because it makes this
+separation between the love of persons
+
+ align:start position:0%
+separation between the love of persons
+ 
+
+ align:start position:0%
+separation between the love of persons
+and the love of things and I want to
+
+ align:start position:0%
+and the love of things and I want to
+ 
+
+ align:start position:0%
+and the love of things and I want to
+analyze those and so a good deal of my
+
+ align:start position:0%
+analyze those and so a good deal of my
+ 
+
+ align:start position:0%
+analyze those and so a good deal of my
+life goes into that kind of approach
+
+ align:start position:0%
+life goes into that kind of approach
+ 
+
+ align:start position:0%
+life goes into that kind of approach
+rather than
+
+ align:start position:0%
+rather than
+ 
+
+ align:start position:0%
+rather than
+any cut and dry defici of definition of
+
+ align:start position:0%
+any cut and dry defici of definition of
+ 
+
+ align:start position:0%
+any cut and dry defici of definition of
+what love is uh is this relevant isn't
+
+ align:start position:0%
+what love is uh is this relevant isn't
+ 
+
+ align:start position:0%
+what love is uh is this relevant isn't
+it or have I been carried away I think
+
+ align:start position:0%
+it or have I been carried away I think
+ 
+
+ align:start position:0%
+it or have I been carried away I think
+slightly carried away okay well then you
+
+ align:start position:0%
+slightly carried away okay well then you
+ 
+
+ align:start position:0%
+slightly carried away okay well then you
+can always stop me okay no it's
+
+ align:start position:0%
+can always stop me okay no it's
+ 
+
+ align:start position:0%
+can always stop me okay no it's
+okay have we had enough for today it's
+
+ align:start position:0%
+okay have we had enough for today it's
+ 
+
+ align:start position:0%
+okay have we had enough for today it's
+after 5: why don't we stop
\ No newline at end of file
diff --git a/WDUPvNCbLhs.txt b/WDUPvNCbLhs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f297d35432d9683f158cd072dd45f14b92fbd996
--- /dev/null
+++ b/WDUPvNCbLhs.txt
@@ -0,0 +1,12981 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well welcome
+
+ align:start position:0%
+okay well welcome
+ 
+
+ align:start position:0%
+okay well welcome
+to uh the third lecture
+
+ align:start position:0%
+to uh the third lecture
+ 
+
+ align:start position:0%
+to uh the third lecture
+a quick review of what we did last time
+
+ align:start position:0%
+a quick review of what we did last time
+ 
+
+ align:start position:0%
+a quick review of what we did last time
+in the first slide
+
+ align:start position:0%
+in the first slide
+ 
+
+ align:start position:0%
+in the first slide
+we talked
+
+ align:start position:0%
+we talked
+ 
+
+ align:start position:0%
+we talked
+about purification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of basically at every level
+
+ align:start position:0%
+of basically at every level
+ 
+
+ align:start position:0%
+of basically at every level
+of the hierarchy in complexity from the
+
+ align:start position:0%
+of the hierarchy in complexity from the
+ 
+
+ align:start position:0%
+of the hierarchy in complexity from the
+elements all the way up to
+
+ align:start position:0%
+elements all the way up to
+ 
+
+ align:start position:0%
+elements all the way up to
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+and in particular the awesome
+
+ align:start position:0%
+and in particular the awesome
+ 
+
+ align:start position:0%
+and in particular the awesome
+purification we can contain get by
+
+ align:start position:0%
+purification we can contain get by
+ 
+
+ align:start position:0%
+purification we can contain get by
+serial dilution down to single molecules
+
+ align:start position:0%
+serial dilution down to single molecules
+ 
+
+ align:start position:0%
+serial dilution down to single molecules
+recombinant dna molecules in this case
+
+ align:start position:0%
+recombinant dna molecules in this case
+ 
+
+ align:start position:0%
+recombinant dna molecules in this case
+embedded in uh e coli cells and how this
+
+ align:start position:0%
+embedded in uh e coli cells and how this
+ 
+
+ align:start position:0%
+embedded in uh e coli cells and how this
+purification led to a revolution
+
+ align:start position:0%
+purification led to a revolution
+ 
+
+ align:start position:0%
+purification led to a revolution
+um first pure pure first in biochemistry
+
+ align:start position:0%
+um first pure pure first in biochemistry
+ 
+
+ align:start position:0%
+um first pure pure first in biochemistry
+then recombinant dna molecular biology
+
+ align:start position:0%
+then recombinant dna molecular biology
+ 
+
+ align:start position:0%
+then recombinant dna molecular biology
+then led to genome project and systems
+
+ align:start position:0%
+then led to genome project and systems
+ 
+
+ align:start position:0%
+then led to genome project and systems
+biology which brings us to
+
+ align:start position:0%
+biology which brings us to
+ 
+
+ align:start position:0%
+biology which brings us to
+models of
+
+ align:start position:0%
+models of
+ 
+
+ align:start position:0%
+models of
+interconnections
+
+ align:start position:0%
+interconnections
+ 
+
+ align:start position:0%
+interconnections
+and one of the
+
+ align:start position:0%
+and one of the
+ 
+
+ align:start position:0%
+and one of the
+uh to start in with algorithms that are
+
+ align:start position:0%
+uh to start in with algorithms that are
+ 
+
+ align:start position:0%
+uh to start in with algorithms that are
+useful in systems biology we start with
+
+ align:start position:0%
+useful in systems biology we start with
+ 
+
+ align:start position:0%
+useful in systems biology we start with
+one of the simplest and most robust ones
+
+ align:start position:0%
+one of the simplest and most robust ones
+ 
+
+ align:start position:0%
+one of the simplest and most robust ones
+which is the genetic code shown here in
+
+ align:start position:0%
+which is the genetic code shown here in
+ 
+
+ align:start position:0%
+which is the genetic code shown here in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+lower right hand corner
+
+ align:start position:0%
+lower right hand corner
+ 
+
+ align:start position:0%
+lower right hand corner
+but as what looks at the
+
+ align:start position:0%
+but as what looks at the
+ 
+
+ align:start position:0%
+but as what looks at the
+huge diversity in the tree of life you
+
+ align:start position:0%
+huge diversity in the tree of life you
+ 
+
+ align:start position:0%
+huge diversity in the tree of life you
+find examples
+
+ align:start position:0%
+find examples
+ 
+
+ align:start position:0%
+find examples
+of exceptions to almost everything you
+
+ align:start position:0%
+of exceptions to almost everything you
+ 
+
+ align:start position:0%
+of exceptions to almost everything you
+can come up with including the genetic
+
+ align:start position:0%
+can come up with including the genetic
+ 
+
+ align:start position:0%
+can come up with including the genetic
+code and we and we talked about how to
+
+ align:start position:0%
+code and we and we talked about how to
+ 
+
+ align:start position:0%
+code and we and we talked about how to
+cherish the exceptions as usual here
+
+ align:start position:0%
+cherish the exceptions as usual here
+ 
+
+ align:start position:0%
+cherish the exceptions as usual here
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+getting back to systems biology in terms
+
+ align:start position:0%
+getting back to systems biology in terms
+ 
+
+ align:start position:0%
+getting back to systems biology in terms
+of how one creates qualitative and
+
+ align:start position:0%
+of how one creates qualitative and
+ 
+
+ align:start position:0%
+of how one creates qualitative and
+quantitative models for functional
+
+ align:start position:0%
+quantitative models for functional
+ 
+
+ align:start position:0%
+quantitative models for functional
+genomics data and establishes evidence
+
+ align:start position:0%
+genomics data and establishes evidence
+ 
+
+ align:start position:0%
+genomics data and establishes evidence
+finally we ended on mutations as
+
+ align:start position:0%
+finally we ended on mutations as
+ 
+
+ align:start position:0%
+finally we ended on mutations as
+selection as we have been
+
+ align:start position:0%
+selection as we have been
+ 
+
+ align:start position:0%
+selection as we have been
+we will do in all three lectures here
+
+ align:start position:0%
+we will do in all three lectures here
+ 
+
+ align:start position:0%
+we will do in all three lectures here
+this this lecture in particular will
+
+ align:start position:0%
+this this lecture in particular will
+ 
+
+ align:start position:0%
+this this lecture in particular will
+focus on mutations and selection
+
+ align:start position:0%
+focus on mutations and selection
+ 
+
+ align:start position:0%
+focus on mutations and selection
+so what is today's uh
+
+ align:start position:0%
+so what is today's uh
+ 
+
+ align:start position:0%
+so what is today's uh
+menu
+
+ align:start position:0%
+menu
+ 
+
+ align:start position:0%
+menu
+we'll start with types of mutants
+
+ align:start position:0%
+we'll start with types of mutants
+ 
+
+ align:start position:0%
+we'll start with types of mutants
+and how they're represented for
+
+ align:start position:0%
+and how they're represented for
+ 
+
+ align:start position:0%
+and how they're represented for
+bioinformatics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+purposes
+
+ align:start position:0%
+purposes
+ 
+
+ align:start position:0%
+purposes
+we'll talk about uh what the three main
+
+ align:start position:0%
+we'll talk about uh what the three main
+ 
+
+ align:start position:0%
+we'll talk about uh what the three main
+methods by which mutations
+
+ align:start position:0%
+methods by which mutations
+ 
+
+ align:start position:0%
+methods by which mutations
+occur drift and select so that you can
+
+ align:start position:0%
+occur drift and select so that you can
+ 
+
+ align:start position:0%
+occur drift and select so that you can
+determine these things determine the
+
+ align:start position:0%
+determine these things determine the
+ 
+
+ align:start position:0%
+determine these things determine the
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+of different alleles in populations
+
+ align:start position:0%
+of different alleles in populations
+ 
+
+ align:start position:0%
+of different alleles in populations
+in doing that we'll uh
+
+ align:start position:0%
+in doing that we'll uh
+ 
+
+ align:start position:0%
+in doing that we'll uh
+rely on our friend from the first
+
+ align:start position:0%
+rely on our friend from the first
+ 
+
+ align:start position:0%
+rely on our friend from the first
+lecture the binomial distribution in the
+
+ align:start position:0%
+lecture the binomial distribution in the
+ 
+
+ align:start position:0%
+lecture the binomial distribution in the
+context of
+
+ align:start position:0%
+context of
+ 
+
+ align:start position:0%
+context of
+an exponentially
+
+ align:start position:0%
+an exponentially
+ 
+
+ align:start position:0%
+an exponentially
+growing population
+
+ align:start position:0%
+growing population
+ 
+
+ align:start position:0%
+growing population
+we have uh
+
+ align:start position:0%
+we have uh
+ 
+
+ align:start position:0%
+we have uh
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+give you some very practical uh
+
+ align:start position:0%
+give you some very practical uh
+ 
+
+ align:start position:0%
+give you some very practical uh
+training here on association studies
+
+ align:start position:0%
+training here on association studies
+ 
+
+ align:start position:0%
+training here on association studies
+where we illustrate it with a very
+
+ align:start position:0%
+where we illustrate it with a very
+ 
+
+ align:start position:0%
+where we illustrate it with a very
+important uh example of hiv resistance
+
+ align:start position:0%
+important uh example of hiv resistance
+ 
+
+ align:start position:0%
+important uh example of hiv resistance
+and and a very useful statistic easily
+
+ align:start position:0%
+and and a very useful statistic easily
+ 
+
+ align:start position:0%
+and and a very useful statistic easily
+as useful as the binomial and the
+
+ align:start position:0%
+as useful as the binomial and the
+ 
+
+ align:start position:0%
+as useful as the binomial and the
+gaussian the chi-square statistic
+
+ align:start position:0%
+gaussian the chi-square statistic
+ 
+
+ align:start position:0%
+gaussian the chi-square statistic
+and then we'll continue to talk about
+
+ align:start position:0%
+and then we'll continue to talk about
+ 
+
+ align:start position:0%
+and then we'll continue to talk about
+association in the context of
+
+ align:start position:0%
+association in the context of
+ 
+
+ align:start position:0%
+association in the context of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+causative alleles and
+
+ align:start position:0%
+causative alleles and
+ 
+
+ align:start position:0%
+causative alleles and
+importance of getting haplotypes and
+
+ align:start position:0%
+importance of getting haplotypes and
+ 
+
+ align:start position:0%
+importance of getting haplotypes and
+then technologies that are required
+
+ align:start position:0%
+then technologies that are required
+ 
+
+ align:start position:0%
+then technologies that are required
+that have been used to get the the
+
+ align:start position:0%
+that have been used to get the the
+ 
+
+ align:start position:0%
+that have been used to get the the
+framework first genome and how one might
+
+ align:start position:0%
+framework first genome and how one might
+ 
+
+ align:start position:0%
+framework first genome and how one might
+change strategy in getting subsequent
+
+ align:start position:0%
+change strategy in getting subsequent
+ 
+
+ align:start position:0%
+change strategy in getting subsequent
+genomes
+
+ align:start position:0%
+genomes
+ 
+
+ align:start position:0%
+genomes
+in order to make
+
+ align:start position:0%
+in order to make
+ 
+
+ align:start position:0%
+in order to make
+cost-effective these very large
+
+ align:start position:0%
+cost-effective these very large
+ 
+
+ align:start position:0%
+cost-effective these very large
+association studies
+
+ align:start position:0%
+association studies
+ 
+
+ align:start position:0%
+association studies
+and finally in the context of that we'll
+
+ align:start position:0%
+and finally in the context of that we'll
+ 
+
+ align:start position:0%
+and finally in the context of that we'll
+talk about uh random and systematic
+
+ align:start position:0%
+talk about uh random and systematic
+ 
+
+ align:start position:0%
+talk about uh random and systematic
+errors in more detail so you get lots of
+
+ align:start position:0%
+errors in more detail so you get lots of
+ 
+
+ align:start position:0%
+errors in more detail so you get lots of
+examples and ways of dealing with it
+
+ align:start position:0%
+examples and ways of dealing with it
+ 
+
+ align:start position:0%
+examples and ways of dealing with it
+computationally
+
+ align:start position:0%
+computationally
+ 
+
+ align:start position:0%
+computationally
+so just to go from our brief discussion
+
+ align:start position:0%
+so just to go from our brief discussion
+ 
+
+ align:start position:0%
+so just to go from our brief discussion
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+our friends
+
+ align:start position:0%
+our friends
+ 
+
+ align:start position:0%
+our friends
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+100 percent
+
+ align:start position:0%
+100 percent
+ 
+
+ align:start position:0%
+100 percent
+dna sequence identity or amino acid
+
+ align:start position:0%
+dna sequence identity or amino acid
+ 
+
+ align:start position:0%
+dna sequence identity or amino acid
+sequence identity that you might find
+
+ align:start position:0%
+sequence identity that you might find
+ 
+
+ align:start position:0%
+sequence identity that you might find
+in the lens protein and elase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enzyme
+
+ align:start position:0%
+enzyme
+ 
+
+ align:start position:0%
+enzyme
+we we can see that even at 100 you can
+
+ align:start position:0%
+we we can see that even at 100 you can
+ 
+
+ align:start position:0%
+we we can see that even at 100 you can
+find differences in function and so
+
+ align:start position:0%
+find differences in function and so
+ 
+
+ align:start position:0%
+find differences in function and so
+functional measures are are a good uh
+
+ align:start position:0%
+functional measures are are a good uh
+ 
+
+ align:start position:0%
+functional measures are are a good uh
+adjunct to
+
+ align:start position:0%
+adjunct to
+ 
+
+ align:start position:0%
+adjunct to
+dna or amino acids identity
+
+ align:start position:0%
+dna or amino acids identity
+ 
+
+ align:start position:0%
+dna or amino acids identity
+at 99.9 percent
+
+ align:start position:0%
+at 99.9 percent
+ 
+
+ align:start position:0%
+at 99.9 percent
+identity we're talking about the level
+
+ align:start position:0%
+identity we're talking about the level
+ 
+
+ align:start position:0%
+identity we're talking about the level
+of single nucleotide polymorphisms that
+
+ align:start position:0%
+of single nucleotide polymorphisms that
+ 
+
+ align:start position:0%
+of single nucleotide polymorphisms that
+might exist between any
+
+ align:start position:0%
+might exist between any
+ 
+
+ align:start position:0%
+might exist between any
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+positions in your mother and your
+
+ align:start position:0%
+positions in your mother and your
+ 
+
+ align:start position:0%
+positions in your mother and your
+father's chromosomes in your body
+
+ align:start position:0%
+father's chromosomes in your body
+ 
+
+ align:start position:0%
+father's chromosomes in your body
+or the differences between one of your
+
+ align:start position:0%
+or the differences between one of your
+ 
+
+ align:start position:0%
+or the differences between one of your
+genomes and one of my genomes about once
+
+ align:start position:0%
+genomes and one of my genomes about once
+ 
+
+ align:start position:0%
+genomes and one of my genomes about once
+every kilobase there will be
+
+ align:start position:0%
+every kilobase there will be
+ 
+
+ align:start position:0%
+every kilobase there will be
+a a polymorphism a difference
+
+ align:start position:0%
+a a polymorphism a difference
+ 
+
+ align:start position:0%
+a a polymorphism a difference
+as often a single nucleotide in a for a
+
+ align:start position:0%
+as often a single nucleotide in a for a
+ 
+
+ align:start position:0%
+as often a single nucleotide in a for a
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+then as we go to 98 differences then
+
+ align:start position:0%
+then as we go to 98 differences then
+ 
+
+ align:start position:0%
+then as we go to 98 differences then
+we're talking about the differences
+
+ align:start position:0%
+we're talking about the differences
+ 
+
+ align:start position:0%
+we're talking about the differences
+between one of our genomes and a
+
+ align:start position:0%
+between one of our genomes and a
+ 
+
+ align:start position:0%
+between one of our genomes and a
+chimpanzee genome in other words a
+
+ align:start position:0%
+chimpanzee genome in other words a
+ 
+
+ align:start position:0%
+chimpanzee genome in other words a
+completely different genus and species
+
+ align:start position:0%
+completely different genus and species
+ 
+
+ align:start position:0%
+completely different genus and species
+however by the criterion we mentioned in
+
+ align:start position:0%
+however by the criterion we mentioned in
+ 
+
+ align:start position:0%
+however by the criterion we mentioned in
+a previous lecture about
+
+ align:start position:0%
+a previous lecture about
+ 
+
+ align:start position:0%
+a previous lecture about
+bacterial definitions of species those
+
+ align:start position:0%
+bacterial definitions of species those
+ 
+
+ align:start position:0%
+bacterial definitions of species those
+would be almost identical and you'd have
+
+ align:start position:0%
+would be almost identical and you'd have
+ 
+
+ align:start position:0%
+would be almost identical and you'd have
+to go to differences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identities less than 70 percent in order
+
+ align:start position:0%
+identities less than 70 percent in order
+ 
+
+ align:start position:0%
+identities less than 70 percent in order
+to call it a new bacterial species so
+
+ align:start position:0%
+to call it a new bacterial species so
+ 
+
+ align:start position:0%
+to call it a new bacterial species so
+you can see this is a very soft number
+
+ align:start position:0%
+you can see this is a very soft number
+ 
+
+ align:start position:0%
+you can see this is a very soft number
+very dependent upon
+
+ align:start position:0%
+very dependent upon
+ 
+
+ align:start position:0%
+very dependent upon
+the context and the and the
+
+ align:start position:0%
+the context and the and the
+ 
+
+ align:start position:0%
+the context and the and the
+branch of the trio life that you're
+
+ align:start position:0%
+branch of the trio life that you're
+ 
+
+ align:start position:0%
+branch of the trio life that you're
+working with
+
+ align:start position:0%
+working with
+ 
+
+ align:start position:0%
+working with
+then uh
+
+ align:start position:0%
+then uh
+ 
+
+ align:start position:0%
+then uh
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence homology and very distant
+
+ align:start position:0%
+sequence homology and very distant
+ 
+
+ align:start position:0%
+sequence homology and very distant
+homologues which are only detectable as
+
+ align:start position:0%
+homologues which are only detectable as
+ 
+
+ align:start position:0%
+homologues which are only detectable as
+we'll see when we get to the proteomics
+
+ align:start position:0%
+we'll see when we get to the proteomics
+ 
+
+ align:start position:0%
+we'll see when we get to the proteomics
+section of this course are only
+
+ align:start position:0%
+section of this course are only
+ 
+
+ align:start position:0%
+section of this course are only
+detectable um
+
+ align:start position:0%
+detectable um
+ 
+
+ align:start position:0%
+detectable um
+by three-dimensional structures not by
+
+ align:start position:0%
+by three-dimensional structures not by
+ 
+
+ align:start position:0%
+by three-dimensional structures not by
+sequence and that that switch over
+
+ align:start position:0%
+sequence and that that switch over
+ 
+
+ align:start position:0%
+sequence and that that switch over
+between secret homology will be that's
+
+ align:start position:0%
+between secret homology will be that's
+ 
+
+ align:start position:0%
+between secret homology will be that's
+the topic of uh next lecture um and the
+
+ align:start position:0%
+the topic of uh next lecture um and the
+ 
+
+ align:start position:0%
+the topic of uh next lecture um and the
+very distant one uh in 3d structures
+
+ align:start position:0%
+very distant one uh in 3d structures
+ 
+
+ align:start position:0%
+very distant one uh in 3d structures
+will be later in proteomics but that
+
+ align:start position:0%
+will be later in proteomics but that
+ 
+
+ align:start position:0%
+will be later in proteomics but that
+occurs at about
+
+ align:start position:0%
+occurs at about
+ 
+
+ align:start position:0%
+occurs at about
+25 to 30 percent
+
+ align:start position:0%
+25 to 30 percent
+ 
+
+ align:start position:0%
+25 to 30 percent
+uh this is just a
+
+ align:start position:0%
+uh this is just a
+ 
+
+ align:start position:0%
+uh this is just a
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+in a reminder and an introductory slide
+
+ align:start position:0%
+in a reminder and an introductory slide
+ 
+
+ align:start position:0%
+in a reminder and an introductory slide
+to the next slide
+
+ align:start position:0%
+to the next slide
+ 
+
+ align:start position:0%
+to the next slide
+we have the different types of
+
+ align:start position:0%
+we have the different types of
+ 
+
+ align:start position:0%
+we have the different types of
+phenotypic
+
+ align:start position:0%
+phenotypic
+ 
+
+ align:start position:0%
+phenotypic
+different phenotypic effects due to
+
+ align:start position:0%
+different phenotypic effects due to
+ 
+
+ align:start position:0%
+different phenotypic effects due to
+different types of mutations
+
+ align:start position:0%
+different types of mutations
+ 
+
+ align:start position:0%
+different types of mutations
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+ignoring the phenotypes that we talked
+
+ align:start position:0%
+ignoring the phenotypes that we talked
+ 
+
+ align:start position:0%
+ignoring the phenotypes that we talked
+about before you have the types of
+
+ align:start position:0%
+about before you have the types of
+ 
+
+ align:start position:0%
+about before you have the types of
+mutations classes are null mutations
+
+ align:start position:0%
+mutations classes are null mutations
+ 
+
+ align:start position:0%
+mutations classes are null mutations
+uh dosage conditional mutations gain of
+
+ align:start position:0%
+uh dosage conditional mutations gain of
+ 
+
+ align:start position:0%
+uh dosage conditional mutations gain of
+function altered ligand specificity
+
+ align:start position:0%
+function altered ligand specificity
+ 
+
+ align:start position:0%
+function altered ligand specificity
+now now that's in broad terms colloquial
+
+ align:start position:0%
+now now that's in broad terms colloquial
+ 
+
+ align:start position:0%
+now now that's in broad terms colloquial
+but how is this achieved on a more
+
+ align:start position:0%
+but how is this achieved on a more
+ 
+
+ align:start position:0%
+but how is this achieved on a more
+molecular level and how do we represent
+
+ align:start position:0%
+molecular level and how do we represent
+ 
+
+ align:start position:0%
+molecular level and how do we represent
+it compactly for bioinformatic
+
+ align:start position:0%
+it compactly for bioinformatic
+ 
+
+ align:start position:0%
+it compactly for bioinformatic
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+so we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+single substitutions these can be
+
+ align:start position:0%
+single substitutions these can be
+ 
+
+ align:start position:0%
+single substitutions these can be
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a single base pair an at base pair to a
+
+ align:start position:0%
+a single base pair an at base pair to a
+ 
+
+ align:start position:0%
+a single base pair an at base pair to a
+cg base pair or a gc base pair to ta
+
+ align:start position:0%
+cg base pair or a gc base pair to ta
+ 
+
+ align:start position:0%
+cg base pair or a gc base pair to ta
+base pair and so on um
+
+ align:start position:0%
+base pair and so on um
+ 
+
+ align:start position:0%
+base pair and so on um
+there can be deletions and duplications
+
+ align:start position:0%
+there can be deletions and duplications
+ 
+
+ align:start position:0%
+there can be deletions and duplications
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+these can range the deletion or
+
+ align:start position:0%
+these can range the deletion or
+ 
+
+ align:start position:0%
+these can range the deletion or
+duplication can be as large as a
+
+ align:start position:0%
+duplication can be as large as a
+ 
+
+ align:start position:0%
+duplication can be as large as a
+chromosome or as small as a single base
+
+ align:start position:0%
+chromosome or as small as a single base
+ 
+
+ align:start position:0%
+chromosome or as small as a single base
+pair you can delete that a rather than
+
+ align:start position:0%
+pair you can delete that a rather than
+ 
+
+ align:start position:0%
+pair you can delete that a rather than
+change it into a c
+
+ align:start position:0%
+change it into a c
+ 
+
+ align:start position:0%
+change it into a c
+and that would be one base up here
+
+ align:start position:0%
+and that would be one base up here
+ 
+
+ align:start position:0%
+and that would be one base up here
+a very so when you're doing an entire
+
+ align:start position:0%
+a very so when you're doing an entire
+ 
+
+ align:start position:0%
+a very so when you're doing an entire
+chromosome that's called aneuploidy the
+
+ align:start position:0%
+chromosome that's called aneuploidy the
+ 
+
+ align:start position:0%
+chromosome that's called aneuploidy the
+expl the example in the previous slide
+
+ align:start position:0%
+expl the example in the previous slide
+ 
+
+ align:start position:0%
+expl the example in the previous slide
+was trisomy 21.
+
+ align:start position:0%
+was trisomy 21.
+ 
+
+ align:start position:0%
+was trisomy 21.
+um if you remove that chromosome 21
+
+ align:start position:0%
+um if you remove that chromosome 21
+ 
+
+ align:start position:0%
+um if you remove that chromosome 21
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+having three copies of it it would be
+
+ align:start position:0%
+having three copies of it it would be
+ 
+
+ align:start position:0%
+having three copies of it it would be
+monosomi
+
+ align:start position:0%
+monosomi
+ 
+
+ align:start position:0%
+monosomi
+and these have huge uh consequences
+
+ align:start position:0%
+and these have huge uh consequences
+ 
+
+ align:start position:0%
+and these have huge uh consequences
+even though they're fairly subtle
+
+ align:start position:0%
+even though they're fairly subtle
+ 
+
+ align:start position:0%
+even though they're fairly subtle
+changes in dosage
+
+ align:start position:0%
+changes in dosage
+ 
+
+ align:start position:0%
+changes in dosage
+now a special class of deletion and
+
+ align:start position:0%
+now a special class of deletion and
+ 
+
+ align:start position:0%
+now a special class of deletion and
+duplication occurs when you have a a
+
+ align:start position:0%
+duplication occurs when you have a a
+ 
+
+ align:start position:0%
+duplication occurs when you have a a
+tandem repeat of a sequence when you
+
+ align:start position:0%
+tandem repeat of a sequence when you
+ 
+
+ align:start position:0%
+tandem repeat of a sequence when you
+have uh anywhere from a single base
+
+ align:start position:0%
+have uh anywhere from a single base
+ 
+
+ align:start position:0%
+have uh anywhere from a single base
+repeat aaaa
+
+ align:start position:0%
+repeat aaaa
+ 
+
+ align:start position:0%
+repeat aaaa
+or dinucleotide trinucleotide all the
+
+ align:start position:0%
+or dinucleotide trinucleotide all the
+ 
+
+ align:start position:0%
+or dinucleotide trinucleotide all the
+way up
+
+ align:start position:0%
+way up
+ 
+
+ align:start position:0%
+way up
+those have a tendency
+
+ align:start position:0%
+those have a tendency
+ 
+
+ align:start position:0%
+those have a tendency
+a very high tendency for both forward
+
+ align:start position:0%
+a very high tendency for both forward
+ 
+
+ align:start position:0%
+a very high tendency for both forward
+and reverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mutation both deletions and duplications
+
+ align:start position:0%
+mutation both deletions and duplications
+ 
+
+ align:start position:0%
+mutation both deletions and duplications
+because at the very small level you have
+
+ align:start position:0%
+because at the very small level you have
+ 
+
+ align:start position:0%
+because at the very small level you have
+polymerase slippage and other uh
+
+ align:start position:0%
+polymerase slippage and other uh
+ 
+
+ align:start position:0%
+polymerase slippage and other uh
+sort of microscopic events
+
+ align:start position:0%
+sort of microscopic events
+ 
+
+ align:start position:0%
+sort of microscopic events
+and then uh at the larger level you have
+
+ align:start position:0%
+and then uh at the larger level you have
+ 
+
+ align:start position:0%
+and then uh at the larger level you have
+some kind of
+
+ align:start position:0%
+some kind of
+ 
+
+ align:start position:0%
+some kind of
+some kind of recombination often
+
+ align:start position:0%
+some kind of recombination often
+ 
+
+ align:start position:0%
+some kind of recombination often
+homologous recombination that occurs to
+
+ align:start position:0%
+homologous recombination that occurs to
+ 
+
+ align:start position:0%
+homologous recombination that occurs to
+cause deletions and duplications of
+
+ align:start position:0%
+cause deletions and duplications of
+ 
+
+ align:start position:0%
+cause deletions and duplications of
+tandem repeats
+
+ align:start position:0%
+tandem repeats
+ 
+
+ align:start position:0%
+tandem repeats
+now an inversion here
+
+ align:start position:0%
+now an inversion here
+ 
+
+ align:start position:0%
+now an inversion here
+this is we're representing a complicated
+
+ align:start position:0%
+this is we're representing a complicated
+ 
+
+ align:start position:0%
+this is we're representing a complicated
+chemical event which involves double
+
+ align:start position:0%
+chemical event which involves double
+ 
+
+ align:start position:0%
+chemical event which involves double
+stranded dna going five prime to three
+
+ align:start position:0%
+stranded dna going five prime to three
+ 
+
+ align:start position:0%
+stranded dna going five prime to three
+prime on the top strand from left to
+
+ align:start position:0%
+prime on the top strand from left to
+ 
+
+ align:start position:0%
+prime on the top strand from left to
+right and five from the three from the
+
+ align:start position:0%
+right and five from the three from the
+ 
+
+ align:start position:0%
+right and five from the three from the
+bottom strand going from right to left
+
+ align:start position:0%
+bottom strand going from right to left
+ 
+
+ align:start position:0%
+bottom strand going from right to left
+and you're taking a little chunk of that
+
+ align:start position:0%
+and you're taking a little chunk of that
+ 
+
+ align:start position:0%
+and you're taking a little chunk of that
+and flipping it so that you break some
+
+ align:start position:0%
+and flipping it so that you break some
+ 
+
+ align:start position:0%
+and flipping it so that you break some
+bonds and remake them uh
+
+ align:start position:0%
+bonds and remake them uh
+ 
+
+ align:start position:0%
+bonds and remake them uh
+all the five prime to the three prime is
+
+ align:start position:0%
+all the five prime to the three prime is
+ 
+
+ align:start position:0%
+all the five prime to the three prime is
+is conserved but you've
+
+ align:start position:0%
+is conserved but you've
+ 
+
+ align:start position:0%
+is conserved but you've
+uh done it a reverse complement of the
+
+ align:start position:0%
+uh done it a reverse complement of the
+ 
+
+ align:start position:0%
+uh done it a reverse complement of the
+top strand and the bottom strand
+
+ align:start position:0%
+top strand and the bottom strand
+ 
+
+ align:start position:0%
+top strand and the bottom strand
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+reverse complement you basically turn
+
+ align:start position:0%
+reverse complement you basically turn
+ 
+
+ align:start position:0%
+reverse complement you basically turn
+c's into g's and change the order this
+
+ align:start position:0%
+c's into g's and change the order this
+ 
+
+ align:start position:0%
+c's into g's and change the order this
+is sometimes abbreviated
+
+ align:start position:0%
+is sometimes abbreviated
+ 
+
+ align:start position:0%
+is sometimes abbreviated
+you know for for simple genetic
+
+ align:start position:0%
+you know for for simple genetic
+ 
+
+ align:start position:0%
+you know for for simple genetic
+description where let's say we inverted
+
+ align:start position:0%
+description where let's say we inverted
+ 
+
+ align:start position:0%
+description where let's say we inverted
+cde
+
+ align:start position:0%
+cde
+ 
+
+ align:start position:0%
+cde
+you might change the case or add primes
+
+ align:start position:0%
+you might change the case or add primes
+ 
+
+ align:start position:0%
+you might change the case or add primes
+to it um color it in some way or you
+
+ align:start position:0%
+to it um color it in some way or you
+ 
+
+ align:start position:0%
+to it um color it in some way or you
+indicate that it's now a reverse
+
+ align:start position:0%
+indicate that it's now a reverse
+ 
+
+ align:start position:0%
+indicate that it's now a reverse
+complement and of course the gene order
+
+ align:start position:0%
+complement and of course the gene order
+ 
+
+ align:start position:0%
+complement and of course the gene order
+or the dna segment order is in is uh is
+
+ align:start position:0%
+or the dna segment order is in is uh is
+ 
+
+ align:start position:0%
+or the dna segment order is in is uh is
+reversed to indicate that inversion
+
+ align:start position:0%
+reversed to indicate that inversion
+ 
+
+ align:start position:0%
+reversed to indicate that inversion
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+translocations insertions in
+
+ align:start position:0%
+translocations insertions in
+ 
+
+ align:start position:0%
+translocations insertions in
+recombination have in common that you
+
+ align:start position:0%
+recombination have in common that you
+ 
+
+ align:start position:0%
+recombination have in common that you
+will make a break
+
+ align:start position:0%
+will make a break
+ 
+
+ align:start position:0%
+will make a break
+betw somewhere and then you will
+
+ align:start position:0%
+betw somewhere and then you will
+ 
+
+ align:start position:0%
+betw somewhere and then you will
+bring in a new piece of dna just like
+
+ align:start position:0%
+bring in a new piece of dna just like
+ 
+
+ align:start position:0%
+bring in a new piece of dna just like
+the inversion where you where you
+
+ align:start position:0%
+the inversion where you where you
+ 
+
+ align:start position:0%
+the inversion where you where you
+inverted in place here involves
+
+ align:start position:0%
+inverted in place here involves
+ 
+
+ align:start position:0%
+inverted in place here involves
+something acting at more of a distance
+
+ align:start position:0%
+something acting at more of a distance
+ 
+
+ align:start position:0%
+something acting at more of a distance
+you'll break between b and c and x and y
+
+ align:start position:0%
+you'll break between b and c and x and y
+ 
+
+ align:start position:0%
+you'll break between b and c and x and y
+and you'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case do a reciprocal
+
+ align:start position:0%
+in this case do a reciprocal
+ 
+
+ align:start position:0%
+in this case do a reciprocal
+translocation where you conserve all the
+
+ align:start position:0%
+translocation where you conserve all the
+ 
+
+ align:start position:0%
+translocation where you conserve all the
+dna and
+
+ align:start position:0%
+dna and
+ 
+
+ align:start position:0%
+dna and
+a and b is now next to y and z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and insertion is is like that but now
+
+ align:start position:0%
+and insertion is is like that but now
+ 
+
+ align:start position:0%
+and insertion is is like that but now
+the dna
+
+ align:start position:0%
+the dna
+ 
+
+ align:start position:0%
+the dna
+need not be reciprocal in any sense it
+
+ align:start position:0%
+need not be reciprocal in any sense it
+ 
+
+ align:start position:0%
+need not be reciprocal in any sense it
+can come in more or less from outer
+
+ align:start position:0%
+can come in more or less from outer
+ 
+
+ align:start position:0%
+can come in more or less from outer
+space uh here it came from greece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can it uh
+
+ align:start position:0%
+you can it uh
+ 
+
+ align:start position:0%
+you can it uh
+it can it can be a transposable element
+
+ align:start position:0%
+it can it can be a transposable element
+ 
+
+ align:start position:0%
+it can it can be a transposable element
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+that came in from who knows where and
+
+ align:start position:0%
+that came in from who knows where and
+ 
+
+ align:start position:0%
+that came in from who knows where and
+inserted in between the a and b
+
+ align:start position:0%
+inserted in between the a and b
+ 
+
+ align:start position:0%
+inserted in between the a and b
+recombination here i illustrated is
+
+ align:start position:0%
+recombination here i illustrated is
+ 
+
+ align:start position:0%
+recombination here i illustrated is
+homologous recombination and uh you can
+
+ align:start position:0%
+homologous recombination and uh you can
+ 
+
+ align:start position:0%
+homologous recombination and uh you can
+have non-homologous recombinants but
+
+ align:start position:0%
+have non-homologous recombinants but
+ 
+
+ align:start position:0%
+have non-homologous recombinants but
+this is by far the most uh common and
+
+ align:start position:0%
+this is by far the most uh common and
+ 
+
+ align:start position:0%
+this is by far the most uh common and
+interesting even some non-homologous
+
+ align:start position:0%
+interesting even some non-homologous
+ 
+
+ align:start position:0%
+interesting even some non-homologous
+combination involves short reasons of
+
+ align:start position:0%
+combination involves short reasons of
+ 
+
+ align:start position:0%
+combination involves short reasons of
+homology where you basically have two
+
+ align:start position:0%
+homology where you basically have two
+ 
+
+ align:start position:0%
+homology where you basically have two
+either two
+
+ align:start position:0%
+either two
+ 
+
+ align:start position:0%
+either two
+sister chromosomes uh or you know
+
+ align:start position:0%
+sister chromosomes uh or you know
+ 
+
+ align:start position:0%
+sister chromosomes uh or you know
+homologs from mother and father or uh
+
+ align:start position:0%
+homologs from mother and father or uh
+ 
+
+ align:start position:0%
+homologs from mother and father or uh
+paralogs within the genome where you've
+
+ align:start position:0%
+paralogs within the genome where you've
+ 
+
+ align:start position:0%
+paralogs within the genome where you've
+got a duplicated gene
+
+ align:start position:0%
+got a duplicated gene
+ 
+
+ align:start position:0%
+got a duplicated gene
+that might even be on the same
+
+ align:start position:0%
+that might even be on the same
+ 
+
+ align:start position:0%
+that might even be on the same
+chromosome arm and now just as with the
+
+ align:start position:0%
+chromosome arm and now just as with the
+ 
+
+ align:start position:0%
+chromosome arm and now just as with the
+deletions of duplication where you have
+
+ align:start position:0%
+deletions of duplication where you have
+ 
+
+ align:start position:0%
+deletions of duplication where you have
+tandem repeats you can if you have
+
+ align:start position:0%
+tandem repeats you can if you have
+ 
+
+ align:start position:0%
+tandem repeats you can if you have
+repeats anywhere in the genome you can
+
+ align:start position:0%
+repeats anywhere in the genome you can
+ 
+
+ align:start position:0%
+repeats anywhere in the genome you can
+um take a small difference we're
+
+ align:start position:0%
+um take a small difference we're
+ 
+
+ align:start position:0%
+um take a small difference we're
+emphasizing the similarities here but
+
+ align:start position:0%
+emphasizing the similarities here but
+ 
+
+ align:start position:0%
+emphasizing the similarities here but
+they have a few small differences allow
+
+ align:start position:0%
+they have a few small differences allow
+ 
+
+ align:start position:0%
+they have a few small differences allow
+you to track them
+
+ align:start position:0%
+you to track them
+ 
+
+ align:start position:0%
+you to track them
+those can be exchanged by single strand
+
+ align:start position:0%
+those can be exchanged by single strand
+ 
+
+ align:start position:0%
+those can be exchanged by single strand
+or double-stranded
+
+ align:start position:0%
+or double-stranded
+ 
+
+ align:start position:0%
+or double-stranded
+dna
+
+ align:start position:0%
+dna
+ 
+
+ align:start position:0%
+dna
+various chemistries
+
+ align:start position:0%
+various chemistries
+ 
+
+ align:start position:0%
+various chemistries
+and you could you can either uh do a
+
+ align:start position:0%
+and you could you can either uh do a
+ 
+
+ align:start position:0%
+and you could you can either uh do a
+nice reciprocal exchange here where you
+
+ align:start position:0%
+nice reciprocal exchange here where you
+ 
+
+ align:start position:0%
+nice reciprocal exchange here where you
+preserve all the dna and the little c
+
+ align:start position:0%
+preserve all the dna and the little c
+ 
+
+ align:start position:0%
+preserve all the dna and the little c
+gets just
+
+ align:start position:0%
+gets just
+ 
+
+ align:start position:0%
+gets just
+replacing the big c by some kind of
+
+ align:start position:0%
+replacing the big c by some kind of
+ 
+
+ align:start position:0%
+replacing the big c by some kind of
+crossover between d and e somewhere
+
+ align:start position:0%
+crossover between d and e somewhere
+ 
+
+ align:start position:0%
+crossover between d and e somewhere
+between c and f
+
+ align:start position:0%
+between c and f
+ 
+
+ align:start position:0%
+between c and f
+or you could have a non-reciprocal
+
+ align:start position:0%
+or you could have a non-reciprocal
+ 
+
+ align:start position:0%
+or you could have a non-reciprocal
+exchange where you pick up a little bit
+
+ align:start position:0%
+exchange where you pick up a little bit
+ 
+
+ align:start position:0%
+exchange where you pick up a little bit
+of c
+
+ align:start position:0%
+of c
+ 
+
+ align:start position:0%
+of c
+and duplicate it and now there's no big
+
+ align:start position:0%
+and duplicate it and now there's no big
+ 
+
+ align:start position:0%
+and duplicate it and now there's no big
+c left over and only little c
+
+ align:start position:0%
+c left over and only little c
+ 
+
+ align:start position:0%
+c left over and only little c
+called gene conversion
+
+ align:start position:0%
+called gene conversion
+ 
+
+ align:start position:0%
+called gene conversion
+but you get the ideas that the these are
+
+ align:start position:0%
+but you get the ideas that the these are
+ 
+
+ align:start position:0%
+but you get the ideas that the these are
+fairly exhaustive lists of the kinds of
+
+ align:start position:0%
+fairly exhaustive lists of the kinds of
+ 
+
+ align:start position:0%
+fairly exhaustive lists of the kinds of
+mutations the kinds of simple elementary
+
+ align:start position:0%
+mutations the kinds of simple elementary
+ 
+
+ align:start position:0%
+mutations the kinds of simple elementary
+mutations you can have now you can pile
+
+ align:start position:0%
+mutations you can have now you can pile
+ 
+
+ align:start position:0%
+mutations you can have now you can pile
+these in various combinations with each
+
+ align:start position:0%
+these in various combinations with each
+ 
+
+ align:start position:0%
+these in various combinations with each
+other and over long periods of time you
+
+ align:start position:0%
+other and over long periods of time you
+ 
+
+ align:start position:0%
+other and over long periods of time you
+can get completely new sequences uh
+
+ align:start position:0%
+can get completely new sequences uh
+ 
+
+ align:start position:0%
+can get completely new sequences uh
+there's even ways that you can get de
+
+ align:start position:0%
+there's even ways that you can get de
+ 
+
+ align:start position:0%
+there's even ways that you can get de
+novo synthesis of of dna such as uh
+
+ align:start position:0%
+novo synthesis of of dna such as uh
+ 
+
+ align:start position:0%
+novo synthesis of of dna such as uh
+mechanisms of terminal transferase which
+
+ align:start position:0%
+mechanisms of terminal transferase which
+ 
+
+ align:start position:0%
+mechanisms of terminal transferase which
+is used yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to get to that a little bit
+
+ align:start position:0%
+we're going to get to that a little bit
+ 
+
+ align:start position:0%
+we're going to get to that a little bit
+later on but i can give you a preview
+
+ align:start position:0%
+later on but i can give you a preview
+ 
+
+ align:start position:0%
+later on but i can give you a preview
+it's uh
+
+ align:start position:0%
+it's uh
+ 
+
+ align:start position:0%
+it's uh
+this uh and say in human genome uh these
+
+ align:start position:0%
+this uh and say in human genome uh these
+ 
+
+ align:start position:0%
+this uh and say in human genome uh these
+point mutations occurred about uh 10 to
+
+ align:start position:0%
+point mutations occurred about uh 10 to
+ 
+
+ align:start position:0%
+point mutations occurred about uh 10 to
+the minus eight
+
+ align:start position:0%
+the minus eight
+ 
+
+ align:start position:0%
+the minus eight
+um per base pair per generation
+
+ align:start position:0%
+um per base pair per generation
+ 
+
+ align:start position:0%
+um per base pair per generation
+and um there are deletions and
+
+ align:start position:0%
+and um there are deletions and
+ 
+
+ align:start position:0%
+and um there are deletions and
+duplications especially in tandem
+
+ align:start position:0%
+duplications especially in tandem
+ 
+
+ align:start position:0%
+duplications especially in tandem
+regions can be as much as six orders of
+
+ align:start position:0%
+regions can be as much as six orders of
+ 
+
+ align:start position:0%
+regions can be as much as six orders of
+magnitude higher frequency than that
+
+ align:start position:0%
+magnitude higher frequency than that
+ 
+
+ align:start position:0%
+magnitude higher frequency than that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so so there's a huge variation from
+
+ align:start position:0%
+so so there's a huge variation from
+ 
+
+ align:start position:0%
+so so there's a huge variation from
+position to position and types of
+
+ align:start position:0%
+position to position and types of
+ 
+
+ align:start position:0%
+position to position and types of
+alleles that will determine the mutation
+
+ align:start position:0%
+alleles that will determine the mutation
+ 
+
+ align:start position:0%
+alleles that will determine the mutation
+rate and you should be quite
+
+ align:start position:0%
+rate and you should be quite
+ 
+
+ align:start position:0%
+rate and you should be quite
+aware of that as you go through
+
+ align:start position:0%
+aware of that as you go through
+ 
+
+ align:start position:0%
+aware of that as you go through
+various computational exercises
+
+ align:start position:0%
+various computational exercises
+ 
+
+ align:start position:0%
+various computational exercises
+okay this is just a a bit of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+commonly accepted nomenclature is that
+
+ align:start position:0%
+commonly accepted nomenclature is that
+ 
+
+ align:start position:0%
+commonly accepted nomenclature is that
+mutations and polymorphisms are
+
+ align:start position:0%
+mutations and polymorphisms are
+ 
+
+ align:start position:0%
+mutations and polymorphisms are
+basically the same thing they're
+
+ align:start position:0%
+basically the same thing they're
+ 
+
+ align:start position:0%
+basically the same thing they're
+differences between
+
+ align:start position:0%
+differences between
+ 
+
+ align:start position:0%
+differences between
+you and me
+
+ align:start position:0%
+you and me
+ 
+
+ align:start position:0%
+you and me
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+they become polymorphisms meaning you
+
+ align:start position:0%
+they become polymorphisms meaning you
+ 
+
+ align:start position:0%
+they become polymorphisms meaning you
+know when they're when they are common
+
+ align:start position:0%
+know when they're when they are common
+ 
+
+ align:start position:0%
+know when they're when they are common
+alleles when their frequency is greater
+
+ align:start position:0%
+alleles when their frequency is greater
+ 
+
+ align:start position:0%
+alleles when their frequency is greater
+than one percent in a population this is
+
+ align:start position:0%
+than one percent in a population this is
+ 
+
+ align:start position:0%
+than one percent in a population this is
+common in the human
+
+ align:start position:0%
+common in the human
+ 
+
+ align:start position:0%
+common in the human
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+genome community it it may differ for
+
+ align:start position:0%
+genome community it it may differ for
+ 
+
+ align:start position:0%
+genome community it it may differ for
+other ones but this this is roughly
+
+ align:start position:0%
+other ones but this this is roughly
+ 
+
+ align:start position:0%
+other ones but this this is roughly
+where you a mutation which is rare less
+
+ align:start position:0%
+where you a mutation which is rare less
+ 
+
+ align:start position:0%
+where you a mutation which is rare less
+than one percent becomes a polymorphism
+
+ align:start position:0%
+than one percent becomes a polymorphism
+ 
+
+ align:start position:0%
+than one percent becomes a polymorphism
+which is frequent more than one percent
+
+ align:start position:0%
+which is frequent more than one percent
+ 
+
+ align:start position:0%
+which is frequent more than one percent
+as a counterpoint to that i would i
+
+ align:start position:0%
+as a counterpoint to that i would i
+ 
+
+ align:start position:0%
+as a counterpoint to that i would i
+would say that uh there is a good chance
+
+ align:start position:0%
+would say that uh there is a good chance
+ 
+
+ align:start position:0%
+would say that uh there is a good chance
+that every possible single nucleotide
+
+ align:start position:0%
+that every possible single nucleotide
+ 
+
+ align:start position:0%
+that every possible single nucleotide
+polymorphism that could exist does exist
+
+ align:start position:0%
+polymorphism that could exist does exist
+ 
+
+ align:start position:0%
+polymorphism that could exist does exist
+in a population as large as ours
+
+ align:start position:0%
+in a population as large as ours
+ 
+
+ align:start position:0%
+in a population as large as ours
+and mutation rates which are
+
+ align:start position:0%
+and mutation rates which are
+ 
+
+ align:start position:0%
+and mutation rates which are
+modest but still over long periods of
+
+ align:start position:0%
+modest but still over long periods of
+ 
+
+ align:start position:0%
+modest but still over long periods of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+allow the accumulation of mutations such
+
+ align:start position:0%
+allow the accumulation of mutations such
+ 
+
+ align:start position:0%
+allow the accumulation of mutations such
+that rather than having maybe three
+
+ align:start position:0%
+that rather than having maybe three
+ 
+
+ align:start position:0%
+that rather than having maybe three
+million commons single nucleotide
+
+ align:start position:0%
+million commons single nucleotide
+ 
+
+ align:start position:0%
+million commons single nucleotide
+polymorphisms or snips
+
+ align:start position:0%
+polymorphisms or snips
+ 
+
+ align:start position:0%
+polymorphisms or snips
+um we might have 12 billion one at every
+
+ align:start position:0%
+um we might have 12 billion one at every
+ 
+
+ align:start position:0%
+um we might have 12 billion one at every
+position and in a lighter slide we'll
+
+ align:start position:0%
+position and in a lighter slide we'll
+ 
+
+ align:start position:0%
+position and in a lighter slide we'll
+actually go through and calculate
+
+ align:start position:0%
+actually go through and calculate
+ 
+
+ align:start position:0%
+actually go through and calculate
+crudely
+
+ align:start position:0%
+crudely
+ 
+
+ align:start position:0%
+crudely
+just how many just what those frequent
+
+ align:start position:0%
+just how many just what those frequent
+ 
+
+ align:start position:0%
+just how many just what those frequent
+why the frequency should be around 10 to
+
+ align:start position:0%
+why the frequency should be around 10 to
+ 
+
+ align:start position:0%
+why the frequency should be around 10 to
+the minus five and why there should be
+
+ align:start position:0%
+the minus five and why there should be
+ 
+
+ align:start position:0%
+the minus five and why there should be
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh 10 000 of us representing each of
+
+ align:start position:0%
+uh 10 000 of us representing each of
+ 
+
+ align:start position:0%
+uh 10 000 of us representing each of
+these uh
+
+ align:start position:0%
+these uh
+ 
+
+ align:start position:0%
+these uh
+so-called rare alleles they're rare
+
+ align:start position:0%
+so-called rare alleles they're rare
+ 
+
+ align:start position:0%
+so-called rare alleles they're rare
+individually but they're common as a as
+
+ align:start position:0%
+individually but they're common as a as
+ 
+
+ align:start position:0%
+individually but they're common as a as
+a group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it will make a difference whether
+
+ align:start position:0%
+uh it will make a difference whether
+ 
+
+ align:start position:0%
+uh it will make a difference whether
+we're talking about whether these
+
+ align:start position:0%
+we're talking about whether these
+ 
+
+ align:start position:0%
+we're talking about whether these
+polymorphisms are linked to your
+
+ align:start position:0%
+polymorphisms are linked to your
+ 
+
+ align:start position:0%
+polymorphisms are linked to your
+favorite
+
+ align:start position:0%
+favorite
+ 
+
+ align:start position:0%
+favorite
+trait or whether they actually cause it
+
+ align:start position:0%
+trait or whether they actually cause it
+ 
+
+ align:start position:0%
+trait or whether they actually cause it
+whether they're part of the cause no
+
+ align:start position:0%
+whether they're part of the cause no
+ 
+
+ align:start position:0%
+whether they're part of the cause no
+you know no particular one
+
+ align:start position:0%
+you know no particular one
+ 
+
+ align:start position:0%
+you know no particular one
+can be said to be one-to-one with a
+
+ align:start position:0%
+can be said to be one-to-one with a
+ 
+
+ align:start position:0%
+can be said to be one-to-one with a
+cause it's all a collection of mutations
+
+ align:start position:0%
+cause it's all a collection of mutations
+ 
+
+ align:start position:0%
+cause it's all a collection of mutations
+and environment
+
+ align:start position:0%
+and environment
+ 
+
+ align:start position:0%
+and environment
+now haplotypes what do we mean by
+
+ align:start position:0%
+now haplotypes what do we mean by
+ 
+
+ align:start position:0%
+now haplotypes what do we mean by
+haplotypes we've introduced snips single
+
+ align:start position:0%
+haplotypes we've introduced snips single
+ 
+
+ align:start position:0%
+haplotypes we've introduced snips single
+nucleotide polymorphisms if you have
+
+ align:start position:0%
+nucleotide polymorphisms if you have
+ 
+
+ align:start position:0%
+nucleotide polymorphisms if you have
+uh a snip that causes
+
+ align:start position:0%
+uh a snip that causes
+ 
+
+ align:start position:0%
+uh a snip that causes
+let's say is involved in in causing a um
+
+ align:start position:0%
+let's say is involved in in causing a um
+ 
+
+ align:start position:0%
+let's say is involved in in causing a um
+apoe4 we'll introduce in just a moment a
+
+ align:start position:0%
+apoe4 we'll introduce in just a moment a
+ 
+
+ align:start position:0%
+apoe4 we'll introduce in just a moment a
+an allele that is associated with uh
+
+ align:start position:0%
+an allele that is associated with uh
+ 
+
+ align:start position:0%
+an allele that is associated with uh
+increased risk of alzheimer's disease
+
+ align:start position:0%
+increased risk of alzheimer's disease
+ 
+
+ align:start position:0%
+increased risk of alzheimer's disease
+and let's say that protein has it it has
+
+ align:start position:0%
+and let's say that protein has it it has
+ 
+
+ align:start position:0%
+and let's say that protein has it it has
+a known change in the protein
+
+ align:start position:0%
+a known change in the protein
+ 
+
+ align:start position:0%
+a known change in the protein
+three-dimensional
+
+ align:start position:0%
+three-dimensional
+ 
+
+ align:start position:0%
+three-dimensional
+structure and
+
+ align:start position:0%
+structure and
+ 
+
+ align:start position:0%
+structure and
+you can call that the bad allele okay or
+
+ align:start position:0%
+you can call that the bad allele okay or
+ 
+
+ align:start position:0%
+you can call that the bad allele okay or
+the associated allele
+
+ align:start position:0%
+the associated allele
+ 
+
+ align:start position:0%
+the associated allele
+now if that were allele word uh that
+
+ align:start position:0%
+now if that were allele word uh that
+ 
+
+ align:start position:0%
+now if that were allele word uh that
+protein will express at a low level for
+
+ align:start position:0%
+protein will express at a low level for
+ 
+
+ align:start position:0%
+protein will express at a low level for
+example if you had a promoter mutation
+
+ align:start position:0%
+example if you had a promoter mutation
+ 
+
+ align:start position:0%
+example if you had a promoter mutation
+or enhancer mutation then that haplotype
+
+ align:start position:0%
+or enhancer mutation then that haplotype
+ 
+
+ align:start position:0%
+or enhancer mutation then that haplotype
+that combination promoter mutation and
+
+ align:start position:0%
+that combination promoter mutation and
+ 
+
+ align:start position:0%
+that combination promoter mutation and
+protein mutation is is is a significant
+
+ align:start position:0%
+protein mutation is is is a significant
+ 
+
+ align:start position:0%
+protein mutation is is is a significant
+more significant predictor than either
+
+ align:start position:0%
+more significant predictor than either
+ 
+
+ align:start position:0%
+more significant predictor than either
+one of them separately and the fact that
+
+ align:start position:0%
+one of them separately and the fact that
+ 
+
+ align:start position:0%
+one of them separately and the fact that
+they're on the same chromosome is
+
+ align:start position:0%
+they're on the same chromosome is
+ 
+
+ align:start position:0%
+they're on the same chromosome is
+important because if
+
+ align:start position:0%
+important because if
+ 
+
+ align:start position:0%
+important because if
+the the promoter enhancer that
+
+ align:start position:0%
+the the promoter enhancer that
+ 
+
+ align:start position:0%
+the the promoter enhancer that
+determines the
+
+ align:start position:0%
+determines the
+ 
+
+ align:start position:0%
+determines the
+the level of the protein is in cis
+
+ align:start position:0%
+the level of the protein is in cis
+ 
+
+ align:start position:0%
+the level of the protein is in cis
+meaning on the same dna or in trans
+
+ align:start position:0%
+meaning on the same dna or in trans
+ 
+
+ align:start position:0%
+meaning on the same dna or in trans
+makes a huge difference so that's what
+
+ align:start position:0%
+makes a huge difference so that's what
+ 
+
+ align:start position:0%
+makes a huge difference so that's what
+haplotyping is all about it's
+
+ align:start position:0%
+haplotyping is all about it's
+ 
+
+ align:start position:0%
+haplotyping is all about it's
+determining what mutations are in cis on
+
+ align:start position:0%
+determining what mutations are in cis on
+ 
+
+ align:start position:0%
+determining what mutations are in cis on
+the same dna
+
+ align:start position:0%
+the same dna
+ 
+
+ align:start position:0%
+the same dna
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+make associations biologically
+
+ align:start position:0%
+make associations biologically
+ 
+
+ align:start position:0%
+make associations biologically
+meaningful and in terms of systems
+
+ align:start position:0%
+meaningful and in terms of systems
+ 
+
+ align:start position:0%
+meaningful and in terms of systems
+biology interpreting them in terms of
+
+ align:start position:0%
+biology interpreting them in terms of
+ 
+
+ align:start position:0%
+biology interpreting them in terms of
+what you know about regulatory elements
+
+ align:start position:0%
+what you know about regulatory elements
+ 
+
+ align:start position:0%
+what you know about regulatory elements
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+these haplotypes can be inferred
+
+ align:start position:0%
+these haplotypes can be inferred
+ 
+
+ align:start position:0%
+these haplotypes can be inferred
+indirectly from uh
+
+ align:start position:0%
+indirectly from uh
+ 
+
+ align:start position:0%
+indirectly from uh
+diploid data from how alleles segregate
+
+ align:start position:0%
+diploid data from how alleles segregate
+ 
+
+ align:start position:0%
+diploid data from how alleles segregate
+um in
+
+ align:start position:0%
+um in
+ 
+
+ align:start position:0%
+um in
+in uh small families or or in siblings
+
+ align:start position:0%
+in uh small families or or in siblings
+ 
+
+ align:start position:0%
+in uh small families or or in siblings
+and so forth
+
+ align:start position:0%
+and so forth
+ 
+
+ align:start position:0%
+and so forth
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+easier to think about and and probably
+
+ align:start position:0%
+easier to think about and and probably
+ 
+
+ align:start position:0%
+easier to think about and and probably
+more accurate in general especially
+
+ align:start position:0%
+more accurate in general especially
+ 
+
+ align:start position:0%
+more accurate in general especially
+limited data sets is direct observation
+
+ align:start position:0%
+limited data sets is direct observation
+ 
+
+ align:start position:0%
+limited data sets is direct observation
+the most extreme direct observation is
+
+ align:start position:0%
+the most extreme direct observation is
+ 
+
+ align:start position:0%
+the most extreme direct observation is
+is you pull out a dna molecule that has
+
+ align:start position:0%
+is you pull out a dna molecule that has
+ 
+
+ align:start position:0%
+is you pull out a dna molecule that has
+say your promoter mutation in your
+
+ align:start position:0%
+say your promoter mutation in your
+ 
+
+ align:start position:0%
+say your promoter mutation in your
+putative uh protein mutation or just a
+
+ align:start position:0%
+putative uh protein mutation or just a
+ 
+
+ align:start position:0%
+putative uh protein mutation or just a
+series of linked uh polymorphisms
+
+ align:start position:0%
+series of linked uh polymorphisms
+ 
+
+ align:start position:0%
+series of linked uh polymorphisms
+by cl by cloning out or otherwise
+
+ align:start position:0%
+by cl by cloning out or otherwise
+ 
+
+ align:start position:0%
+by cl by cloning out or otherwise
+physically isolating that dna molecule
+
+ align:start position:0%
+physically isolating that dna molecule
+ 
+
+ align:start position:0%
+physically isolating that dna molecule
+you can uh sequence it and you can
+
+ align:start position:0%
+you can uh sequence it and you can
+ 
+
+ align:start position:0%
+you can uh sequence it and you can
+determine what by definition if this if
+
+ align:start position:0%
+determine what by definition if this if
+ 
+
+ align:start position:0%
+determine what by definition if this if
+they're all in the same sequence uh one
+
+ align:start position:0%
+they're all in the same sequence uh one
+ 
+
+ align:start position:0%
+they're all in the same sequence uh one
+then they're on the same molecule but
+
+ align:start position:0%
+then they're on the same molecule but
+ 
+
+ align:start position:0%
+then they're on the same molecule but
+you have to be careful about the
+
+ align:start position:0%
+you have to be careful about the
+ 
+
+ align:start position:0%
+you have to be careful about the
+sequencing method that you're using
+
+ align:start position:0%
+sequencing method that you're using
+ 
+
+ align:start position:0%
+sequencing method that you're using
+there and the specific cloning and or
+
+ align:start position:0%
+there and the specific cloning and or
+ 
+
+ align:start position:0%
+there and the specific cloning and or
+physical separation method because you
+
+ align:start position:0%
+physical separation method because you
+ 
+
+ align:start position:0%
+physical separation method because you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+there are certain methods where you can
+
+ align:start position:0%
+there are certain methods where you can
+ 
+
+ align:start position:0%
+there are certain methods where you can
+get a chimeric sequence either due to
+
+ align:start position:0%
+get a chimeric sequence either due to
+ 
+
+ align:start position:0%
+get a chimeric sequence either due to
+kind of cloning of two species together
+
+ align:start position:0%
+kind of cloning of two species together
+ 
+
+ align:start position:0%
+kind of cloning of two species together
+or somehow misassembling them
+
+ align:start position:0%
+or somehow misassembling them
+ 
+
+ align:start position:0%
+or somehow misassembling them
+through bioinformatics
+
+ align:start position:0%
+through bioinformatics
+ 
+
+ align:start position:0%
+through bioinformatics
+you can also directly observe it when
+
+ align:start position:0%
+you can also directly observe it when
+ 
+
+ align:start position:0%
+you can also directly observe it when
+you go through uh
+
+ align:start position:0%
+you go through uh
+ 
+
+ align:start position:0%
+you go through uh
+the genetic processes of of mitosis
+
+ align:start position:0%
+the genetic processes of of mitosis
+ 
+
+ align:start position:0%
+the genetic processes of of mitosis
+which we've talked about before which is
+
+ align:start position:0%
+which we've talked about before which is
+ 
+
+ align:start position:0%
+which we've talked about before which is
+the as the cells divide they split up
+
+ align:start position:0%
+the as the cells divide they split up
+ 
+
+ align:start position:0%
+the as the cells divide they split up
+the chromosomes or meiosis which is the
+
+ align:start position:0%
+the chromosomes or meiosis which is the
+ 
+
+ align:start position:0%
+the chromosomes or meiosis which is the
+process by which they get prepared for a
+
+ align:start position:0%
+process by which they get prepared for a
+ 
+
+ align:start position:0%
+process by which they get prepared for a
+combination which we'll come back to in
+
+ align:start position:0%
+combination which we'll come back to in
+ 
+
+ align:start position:0%
+combination which we'll come back to in
+a little while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so when you do want to do it by linkage
+
+ align:start position:0%
+so when you do want to do it by linkage
+ 
+
+ align:start position:0%
+so when you do want to do it by linkage
+you want to do a direct observation and
+
+ align:start position:0%
+you want to do a direct observation and
+ 
+
+ align:start position:0%
+you want to do a direct observation and
+you want you need to you need to have
+
+ align:start position:0%
+you want you need to you need to have
+ 
+
+ align:start position:0%
+you want you need to you need to have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the best way to to follow the haplotype
+
+ align:start position:0%
+the best way to to follow the haplotype
+ 
+
+ align:start position:0%
+the best way to to follow the haplotype
+is if there is a difference at every
+
+ align:start position:0%
+is if there is a difference at every
+ 
+
+ align:start position:0%
+is if there is a difference at every
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in in both the parents and the child and
+
+ align:start position:0%
+in in both the parents and the child and
+ 
+
+ align:start position:0%
+in in both the parents and the child and
+the child inherits um those differences
+
+ align:start position:0%
+the child inherits um those differences
+ 
+
+ align:start position:0%
+the child inherits um those differences
+then it's called informative if if the
+
+ align:start position:0%
+then it's called informative if if the
+ 
+
+ align:start position:0%
+then it's called informative if if the
+parents happen to share a single
+
+ align:start position:0%
+parents happen to share a single
+ 
+
+ align:start position:0%
+parents happen to share a single
+nucleotide polymorphism um even though
+
+ align:start position:0%
+nucleotide polymorphism um even though
+ 
+
+ align:start position:0%
+nucleotide polymorphism um even though
+the child is a heterozygote for one of
+
+ align:start position:0%
+the child is a heterozygote for one of
+ 
+
+ align:start position:0%
+the child is a heterozygote for one of
+them it could be that the the parents
+
+ align:start position:0%
+them it could be that the the parents
+ 
+
+ align:start position:0%
+them it could be that the the parents
+have additional alleles that can confuse
+
+ align:start position:0%
+have additional alleles that can confuse
+ 
+
+ align:start position:0%
+have additional alleles that can confuse
+things and it's not informative but the
+
+ align:start position:0%
+things and it's not informative but the
+ 
+
+ align:start position:0%
+things and it's not informative but the
+point is if you have
+
+ align:start position:0%
+point is if you have
+ 
+
+ align:start position:0%
+point is if you have
+enough single lucified polymorphisms you
+
+ align:start position:0%
+enough single lucified polymorphisms you
+ 
+
+ align:start position:0%
+enough single lucified polymorphisms you
+can do a case control study where you
+
+ align:start position:0%
+can do a case control study where you
+ 
+
+ align:start position:0%
+can do a case control study where you
+have lots of children that are affected
+
+ align:start position:0%
+have lots of children that are affected
+ 
+
+ align:start position:0%
+have lots of children that are affected
+for whatever trait you're interested in
+
+ align:start position:0%
+for whatever trait you're interested in
+ 
+
+ align:start position:0%
+for whatever trait you're interested in
+and hopefully a close to equal number
+
+ align:start position:0%
+and hopefully a close to equal number
+ 
+
+ align:start position:0%
+and hopefully a close to equal number
+which are in the control group which do
+
+ align:start position:0%
+which are in the control group which do
+ 
+
+ align:start position:0%
+which are in the control group which do
+not have it an example of that and i'm
+
+ align:start position:0%
+not have it an example of that and i'm
+ 
+
+ align:start position:0%
+not have it an example of that and i'm
+just trying to give you a flavor for
+
+ align:start position:0%
+just trying to give you a flavor for
+ 
+
+ align:start position:0%
+just trying to give you a flavor for
+this and where to look rather than to
+
+ align:start position:0%
+this and where to look rather than to
+ 
+
+ align:start position:0%
+this and where to look rather than to
+completely empower you on this because
+
+ align:start position:0%
+completely empower you on this because
+ 
+
+ align:start position:0%
+completely empower you on this because
+that would be an entire separate course
+
+ align:start position:0%
+that would be an entire separate course
+ 
+
+ align:start position:0%
+that would be an entire separate course
+but you can look for association
+
+ align:start position:0%
+but you can look for association
+ 
+
+ align:start position:0%
+but you can look for association
+and you have to worry about things like
+
+ align:start position:0%
+and you have to worry about things like
+ 
+
+ align:start position:0%
+and you have to worry about things like
+structure and admixture where you've had
+
+ align:start position:0%
+structure and admixture where you've had
+ 
+
+ align:start position:0%
+structure and admixture where you've had
+populations that have developed
+
+ align:start position:0%
+populations that have developed
+ 
+
+ align:start position:0%
+populations that have developed
+independently in different parts of the
+
+ align:start position:0%
+independently in different parts of the
+ 
+
+ align:start position:0%
+independently in different parts of the
+world and developed you know have been
+
+ align:start position:0%
+world and developed you know have been
+ 
+
+ align:start position:0%
+world and developed you know have been
+randomly mixing
+
+ align:start position:0%
+randomly mixing
+ 
+
+ align:start position:0%
+randomly mixing
+which is part of the model in these
+
+ align:start position:0%
+which is part of the model in these
+ 
+
+ align:start position:0%
+which is part of the model in these
+separate populations but then you bring
+
+ align:start position:0%
+separate populations but then you bring
+ 
+
+ align:start position:0%
+separate populations but then you bring
+them together very
+
+ align:start position:0%
+them together very
+ 
+
+ align:start position:0%
+them together very
+recently and now it looks like uh
+
+ align:start position:0%
+recently and now it looks like uh
+ 
+
+ align:start position:0%
+recently and now it looks like uh
+now it's no longer fair to model it as
+
+ align:start position:0%
+now it's no longer fair to model it as
+ 
+
+ align:start position:0%
+now it's no longer fair to model it as
+if it were a uniformly mixing population
+
+ align:start position:0%
+if it were a uniformly mixing population
+ 
+
+ align:start position:0%
+if it were a uniformly mixing population
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+the null hypothesis will refer
+
+ align:start position:0%
+the null hypothesis will refer
+ 
+
+ align:start position:0%
+the null hypothesis will refer
+throughout the course to the null
+
+ align:start position:0%
+throughout the course to the null
+ 
+
+ align:start position:0%
+throughout the course to the null
+hypothesis which is the the
+
+ align:start position:0%
+hypothesis which is the the
+ 
+
+ align:start position:0%
+hypothesis which is the the
+uh thing that you're trying that you're
+
+ align:start position:0%
+uh thing that you're trying that you're
+ 
+
+ align:start position:0%
+uh thing that you're trying that you're
+trying to rule out and the probability
+
+ align:start position:0%
+trying to rule out and the probability
+ 
+
+ align:start position:0%
+trying to rule out and the probability
+refers to the the probability that you
+
+ align:start position:0%
+refers to the the probability that you
+ 
+
+ align:start position:0%
+refers to the the probability that you
+can reject this null hypothesis and in
+
+ align:start position:0%
+can reject this null hypothesis and in
+ 
+
+ align:start position:0%
+can reject this null hypothesis and in
+this case you're trying to reject that
+
+ align:start position:0%
+this case you're trying to reject that
+ 
+
+ align:start position:0%
+this case you're trying to reject that
+the allele frequencies in the candidate
+
+ align:start position:0%
+the allele frequencies in the candidate
+ 
+
+ align:start position:0%
+the allele frequencies in the candidate
+locus whatever you picked um do not
+
+ align:start position:0%
+locus whatever you picked um do not
+ 
+
+ align:start position:0%
+locus whatever you picked um do not
+depend on the phenotype within the
+
+ align:start position:0%
+depend on the phenotype within the
+ 
+
+ align:start position:0%
+depend on the phenotype within the
+subpopulations and that's the way that
+
+ align:start position:0%
+subpopulations and that's the way that
+ 
+
+ align:start position:0%
+subpopulations and that's the way that
+they deal with these case studies
+
+ align:start position:0%
+they deal with these case studies
+ 
+
+ align:start position:0%
+they deal with these case studies
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+what are some of the motivations for
+
+ align:start position:0%
+what are some of the motivations for
+ 
+
+ align:start position:0%
+what are some of the motivations for
+studying
+
+ align:start position:0%
+studying
+ 
+
+ align:start position:0%
+studying
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+either individual polymorphisms or
+
+ align:start position:0%
+either individual polymorphisms or
+ 
+
+ align:start position:0%
+either individual polymorphisms or
+haplotypes combinations of polymorphisms
+
+ align:start position:0%
+haplotypes combinations of polymorphisms
+ 
+
+ align:start position:0%
+haplotypes combinations of polymorphisms
+can affect the activity of a protein now
+
+ align:start position:0%
+can affect the activity of a protein now
+ 
+
+ align:start position:0%
+can affect the activity of a protein now
+i could use
+
+ align:start position:0%
+i could use
+ 
+
+ align:start position:0%
+i could use
+hundreds of different examples of
+
+ align:start position:0%
+hundreds of different examples of
+ 
+
+ align:start position:0%
+hundreds of different examples of
+well-established and useful um examples
+
+ align:start position:0%
+well-established and useful um examples
+ 
+
+ align:start position:0%
+well-established and useful um examples
+but here's one that that hopefully will
+
+ align:start position:0%
+but here's one that that hopefully will
+ 
+
+ align:start position:0%
+but here's one that that hopefully will
+hit a resonant
+
+ align:start position:0%
+hit a resonant
+ 
+
+ align:start position:0%
+hit a resonant
+resonating court in the sense that these
+
+ align:start position:0%
+resonating court in the sense that these
+ 
+
+ align:start position:0%
+resonating court in the sense that these
+are actually used now in certain
+
+ align:start position:0%
+are actually used now in certain
+ 
+
+ align:start position:0%
+are actually used now in certain
+clinical settings
+
+ align:start position:0%
+clinical settings
+ 
+
+ align:start position:0%
+clinical settings
+and certainly in clinical research
+
+ align:start position:0%
+and certainly in clinical research
+ 
+
+ align:start position:0%
+and certainly in clinical research
+to ask whether a patient population
+
+ align:start position:0%
+to ask whether a patient population
+ 
+
+ align:start position:0%
+to ask whether a patient population
+either in the process of developing a
+
+ align:start position:0%
+either in the process of developing a
+ 
+
+ align:start position:0%
+either in the process of developing a
+new drug
+
+ align:start position:0%
+new drug
+ 
+
+ align:start position:0%
+new drug
+or using an established drug to keep the
+
+ align:start position:0%
+or using an established drug to keep the
+ 
+
+ align:start position:0%
+or using an established drug to keep the
+patient
+
+ align:start position:0%
+patient
+ 
+
+ align:start position:0%
+patient
+toxicity
+
+ align:start position:0%
+toxicity
+ 
+
+ align:start position:0%
+toxicity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+down and the effectiveness up
+
+ align:start position:0%
+down and the effectiveness up
+ 
+
+ align:start position:0%
+down and the effectiveness up
+and so in the far
+
+ align:start position:0%
+and so in the far
+ 
+
+ align:start position:0%
+and so in the far
+left hand column is the gene or enzyme
+
+ align:start position:0%
+left hand column is the gene or enzyme
+ 
+
+ align:start position:0%
+left hand column is the gene or enzyme
+affected
+
+ align:start position:0%
+affected
+ 
+
+ align:start position:0%
+affected
+and in the middle is are examples of
+
+ align:start position:0%
+and in the middle is are examples of
+ 
+
+ align:start position:0%
+and in the middle is are examples of
+drugs which interact with this enzyme
+
+ align:start position:0%
+drugs which interact with this enzyme
+ 
+
+ align:start position:0%
+drugs which interact with this enzyme
+and then the quantitative effect is in
+
+ align:start position:0%
+and then the quantitative effect is in
+ 
+
+ align:start position:0%
+and then the quantitative effect is in
+the far right hand side
+
+ align:start position:0%
+the far right hand side
+ 
+
+ align:start position:0%
+the far right hand side
+and these
+
+ align:start position:0%
+and these
+ 
+
+ align:start position:0%
+and these
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+thiopurine methyltransferase
+
+ align:start position:0%
+thiopurine methyltransferase
+ 
+
+ align:start position:0%
+thiopurine methyltransferase
+is something which if you have a large
+
+ align:start position:0%
+is something which if you have a large
+ 
+
+ align:start position:0%
+is something which if you have a large
+amount of the activity whether you have
+
+ align:start position:0%
+amount of the activity whether you have
+ 
+
+ align:start position:0%
+amount of the activity whether you have
+you say that
+
+ align:start position:0%
+you say that
+ 
+
+ align:start position:0%
+you say that
+a very active enzyme and or a very
+
+ align:start position:0%
+a very active enzyme and or a very
+ 
+
+ align:start position:0%
+a very active enzyme and or a very
+active promoter element that causes high
+
+ align:start position:0%
+active promoter element that causes high
+ 
+
+ align:start position:0%
+active promoter element that causes high
+levels of it
+
+ align:start position:0%
+levels of it
+ 
+
+ align:start position:0%
+levels of it
+then these various chemotherapeutics
+
+ align:start position:0%
+then these various chemotherapeutics
+ 
+
+ align:start position:0%
+then these various chemotherapeutics
+that are used for fighting cancers
+
+ align:start position:0%
+that are used for fighting cancers
+ 
+
+ align:start position:0%
+that are used for fighting cancers
+need to be the amount of them need to be
+
+ align:start position:0%
+need to be the amount of them need to be
+ 
+
+ align:start position:0%
+need to be the amount of them need to be
+adjusted so you have lots of the methyl
+
+ align:start position:0%
+adjusted so you have lots of the methyl
+ 
+
+ align:start position:0%
+adjusted so you have lots of the methyl
+transfer rates that means you have to
+
+ align:start position:0%
+transfer rates that means you have to
+ 
+
+ align:start position:0%
+transfer rates that means you have to
+give lots of the drug or else you will
+
+ align:start position:0%
+give lots of the drug or else you will
+ 
+
+ align:start position:0%
+give lots of the drug or else you will
+your drug study will fail or your or
+
+ align:start position:0%
+your drug study will fail or your or
+ 
+
+ align:start position:0%
+your drug study will fail or your or
+your patient will succumb to cancer
+
+ align:start position:0%
+your patient will succumb to cancer
+ 
+
+ align:start position:0%
+your patient will succumb to cancer
+because it's ineffective you haven't
+
+ align:start position:0%
+because it's ineffective you haven't
+ 
+
+ align:start position:0%
+because it's ineffective you haven't
+added enough
+
+ align:start position:0%
+added enough
+ 
+
+ align:start position:0%
+added enough
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+thiopurine methyltransferase
+
+ align:start position:0%
+thiopurine methyltransferase
+ 
+
+ align:start position:0%
+thiopurine methyltransferase
+is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is overcoming the drug
+
+ align:start position:0%
+is overcoming the drug
+ 
+
+ align:start position:0%
+is overcoming the drug
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when you on the other hand if you have
+
+ align:start position:0%
+when you on the other hand if you have
+ 
+
+ align:start position:0%
+when you on the other hand if you have
+very low levels of it then you want to
+
+ align:start position:0%
+very low levels of it then you want to
+ 
+
+ align:start position:0%
+very low levels of it then you want to
+give extra dose of it
+
+ align:start position:0%
+give extra dose of it
+ 
+
+ align:start position:0%
+give extra dose of it
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+if you have very low levels of the
+
+ align:start position:0%
+if you have very low levels of the
+ 
+
+ align:start position:0%
+if you have very low levels of the
+modifying enzyme you want to lower the
+
+ align:start position:0%
+modifying enzyme you want to lower the
+ 
+
+ align:start position:0%
+modifying enzyme you want to lower the
+dose or else you'll have a
+
+ align:start position:0%
+dose or else you'll have a
+ 
+
+ align:start position:0%
+dose or else you'll have a
+toxicity okay so that's an example
+
+ align:start position:0%
+toxicity okay so that's an example
+ 
+
+ align:start position:0%
+toxicity okay so that's an example
+that's actually being used in clinical
+
+ align:start position:0%
+that's actually being used in clinical
+ 
+
+ align:start position:0%
+that's actually being used in clinical
+situations where you can
+
+ align:start position:0%
+situations where you can
+ 
+
+ align:start position:0%
+situations where you can
+use the information
+
+ align:start position:0%
+use the information
+ 
+
+ align:start position:0%
+use the information
+to adjust
+
+ align:start position:0%
+to adjust
+ 
+
+ align:start position:0%
+to adjust
+drug levels or to stratify your patient
+
+ align:start position:0%
+drug levels or to stratify your patient
+ 
+
+ align:start position:0%
+drug levels or to stratify your patient
+population so that you put patients into
+
+ align:start position:0%
+population so that you put patients into
+ 
+
+ align:start position:0%
+population so that you put patients into
+different classes
+
+ align:start position:0%
+different classes
+ 
+
+ align:start position:0%
+different classes
+or exclude them from the study
+
+ align:start position:0%
+or exclude them from the study
+ 
+
+ align:start position:0%
+or exclude them from the study
+altogether because you know that the
+
+ align:start position:0%
+altogether because you know that the
+ 
+
+ align:start position:0%
+altogether because you know that the
+drug will have some bad effect this
+
+ align:start position:0%
+drug will have some bad effect this
+ 
+
+ align:start position:0%
+drug will have some bad effect this
+increases hopefully decreases the cost
+
+ align:start position:0%
+increases hopefully decreases the cost
+ 
+
+ align:start position:0%
+increases hopefully decreases the cost
+on the downside to pharmaceutical
+
+ align:start position:0%
+on the downside to pharmaceutical
+ 
+
+ align:start position:0%
+on the downside to pharmaceutical
+development if you do stratify your
+
+ align:start position:0%
+development if you do stratify your
+ 
+
+ align:start position:0%
+development if you do stratify your
+patient population and you make it
+
+ align:start position:0%
+patient population and you make it
+ 
+
+ align:start position:0%
+patient population and you make it
+through the drug study with that caveat
+
+ align:start position:0%
+through the drug study with that caveat
+ 
+
+ align:start position:0%
+through the drug study with that caveat
+then the fda will require that that you
+
+ align:start position:0%
+then the fda will require that that you
+ 
+
+ align:start position:0%
+then the fda will require that that you
+put that proviso in and that makes the
+
+ align:start position:0%
+put that proviso in and that makes the
+ 
+
+ align:start position:0%
+put that proviso in and that makes the
+the size of the population that will be
+
+ align:start position:0%
+the size of the population that will be
+ 
+
+ align:start position:0%
+the size of the population that will be
+buying the drug smaller which makes the
+
+ align:start position:0%
+buying the drug smaller which makes the
+ 
+
+ align:start position:0%
+buying the drug smaller which makes the
+since the costs of developing the drug
+
+ align:start position:0%
+since the costs of developing the drug
+ 
+
+ align:start position:0%
+since the costs of developing the drug
+are fairly fixed
+
+ align:start position:0%
+are fairly fixed
+ 
+
+ align:start position:0%
+are fairly fixed
+it decreases the profit
+
+ align:start position:0%
+it decreases the profit
+ 
+
+ align:start position:0%
+it decreases the profit
+now uh
+
+ align:start position:0%
+now uh
+ 
+
+ align:start position:0%
+now uh
+i pointed out that there may be a very
+
+ align:start position:0%
+i pointed out that there may be a very
+ 
+
+ align:start position:0%
+i pointed out that there may be a very
+large number of rare single nucleotide
+
+ align:start position:0%
+large number of rare single nucleotide
+ 
+
+ align:start position:0%
+large number of rare single nucleotide
+polymorphisms but in terms of common
+
+ align:start position:0%
+polymorphisms but in terms of common
+ 
+
+ align:start position:0%
+polymorphisms but in terms of common
+ones there's you know we're getting
+
+ align:start position:0%
+ones there's you know we're getting
+ 
+
+ align:start position:0%
+ones there's you know we're getting
+pretty close to saturating the common
+
+ align:start position:0%
+pretty close to saturating the common
+ 
+
+ align:start position:0%
+pretty close to saturating the common
+ones now these
+
+ align:start position:0%
+ones now these
+ 
+
+ align:start position:0%
+ones now these
+and their databases of these just like
+
+ align:start position:0%
+and their databases of these just like
+ 
+
+ align:start position:0%
+and their databases of these just like
+their databases almost everything you
+
+ align:start position:0%
+their databases almost everything you
+ 
+
+ align:start position:0%
+their databases almost everything you
+can imagine some of them better than
+
+ align:start position:0%
+can imagine some of them better than
+ 
+
+ align:start position:0%
+can imagine some of them better than
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+the common ones will of course be the
+
+ align:start position:0%
+the common ones will of course be the
+ 
+
+ align:start position:0%
+the common ones will of course be the
+ones that tend either are neutral with
+
+ align:start position:0%
+ones that tend either are neutral with
+ 
+
+ align:start position:0%
+ones that tend either are neutral with
+respect to their phenotypic effect that
+
+ align:start position:0%
+respect to their phenotypic effect that
+ 
+
+ align:start position:0%
+respect to their phenotypic effect that
+is to say they it doesn't really matter
+
+ align:start position:0%
+is to say they it doesn't really matter
+ 
+
+ align:start position:0%
+is to say they it doesn't really matter
+whether they're uh
+
+ align:start position:0%
+whether they're uh
+ 
+
+ align:start position:0%
+whether they're uh
+one common allele or the other one you
+
+ align:start position:0%
+one common allele or the other one you
+ 
+
+ align:start position:0%
+one common allele or the other one you
+know the one allele might be at 30
+
+ align:start position:0%
+know the one allele might be at 30
+ 
+
+ align:start position:0%
+know the one allele might be at 30
+percent the other one is 70 percent but
+
+ align:start position:0%
+percent the other one is 70 percent but
+ 
+
+ align:start position:0%
+percent the other one is 70 percent but
+they're both fairly neutral with respect
+
+ align:start position:0%
+they're both fairly neutral with respect
+ 
+
+ align:start position:0%
+they're both fairly neutral with respect
+to function
+
+ align:start position:0%
+to function
+ 
+
+ align:start position:0%
+to function
+or it could be that they both
+
+ align:start position:0%
+or it could be that they both
+ 
+
+ align:start position:0%
+or it could be that they both
+provide
+
+ align:start position:0%
+provide
+ 
+
+ align:start position:0%
+provide
+different advantages in different
+
+ align:start position:0%
+different advantages in different
+ 
+
+ align:start position:0%
+different advantages in different
+scenarios or the heterozygote where you
+
+ align:start position:0%
+scenarios or the heterozygote where you
+ 
+
+ align:start position:0%
+scenarios or the heterozygote where you
+have one over the other provide some
+
+ align:start position:0%
+have one over the other provide some
+ 
+
+ align:start position:0%
+have one over the other provide some
+advantage and that's kept it in the
+
+ align:start position:0%
+advantage and that's kept it in the
+ 
+
+ align:start position:0%
+advantage and that's kept it in the
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+but it's unlikely that they're highly
+
+ align:start position:0%
+but it's unlikely that they're highly
+ 
+
+ align:start position:0%
+but it's unlikely that they're highly
+deleterious because the highly
+
+ align:start position:0%
+deleterious because the highly
+ 
+
+ align:start position:0%
+deleterious because the highly
+deleterious alleles are going to be rare
+
+ align:start position:0%
+deleterious alleles are going to be rare
+ 
+
+ align:start position:0%
+deleterious alleles are going to be rare
+they're going to be selected against and
+
+ align:start position:0%
+they're going to be selected against and
+ 
+
+ align:start position:0%
+they're going to be selected against and
+we're going to fully model that in just
+
+ align:start position:0%
+we're going to fully model that in just
+ 
+
+ align:start position:0%
+we're going to fully model that in just
+a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now say that we could uh somehow anybody
+
+ align:start position:0%
+now say that we could uh somehow anybody
+ 
+
+ align:start position:0%
+now say that we could uh somehow anybody
+who wanted their genome could have their
+
+ align:start position:0%
+who wanted their genome could have their
+ 
+
+ align:start position:0%
+who wanted their genome could have their
+genome
+
+ align:start position:0%
+genome
+ 
+
+ align:start position:0%
+genome
+tomorrow you could have your complete
+
+ align:start position:0%
+tomorrow you could have your complete
+ 
+
+ align:start position:0%
+tomorrow you could have your complete
+genome sequence how would you then as
+
+ align:start position:0%
+genome sequence how would you then as
+ 
+
+ align:start position:0%
+genome sequence how would you then as
+computational biologists
+
+ align:start position:0%
+computational biologists
+ 
+
+ align:start position:0%
+computational biologists
+prioritize
+
+ align:start position:0%
+prioritize
+ 
+
+ align:start position:0%
+prioritize
+those single nucleotide polymorphisms
+
+ align:start position:0%
+those single nucleotide polymorphisms
+ 
+
+ align:start position:0%
+those single nucleotide polymorphisms
+you find in there relative to the whole
+
+ align:start position:0%
+you find in there relative to the whole
+ 
+
+ align:start position:0%
+you find in there relative to the whole
+genome sequence which is in gen pang now
+
+ align:start position:0%
+genome sequence which is in gen pang now
+ 
+
+ align:start position:0%
+genome sequence which is in gen pang now
+this would be an excellent project for
+
+ align:start position:0%
+this would be an excellent project for
+ 
+
+ align:start position:0%
+this would be an excellent project for
+you to do for the term project
+
+ align:start position:0%
+you to do for the term project
+ 
+
+ align:start position:0%
+you to do for the term project
+but what you might say first of all
+
+ align:start position:0%
+but what you might say first of all
+ 
+
+ align:start position:0%
+but what you might say first of all
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+well actually anybody what what what
+
+ align:start position:0%
+well actually anybody what what what
+ 
+
+ align:start position:0%
+well actually anybody what what what
+single nuclear type only misses would
+
+ align:start position:0%
+single nuclear type only misses would
+ 
+
+ align:start position:0%
+single nuclear type only misses would
+you throw out
+
+ align:start position:0%
+you throw out
+ 
+
+ align:start position:0%
+you throw out
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+or deep put low on your priority list or
+
+ align:start position:0%
+or deep put low on your priority list or
+ 
+
+ align:start position:0%
+or deep put low on your priority list or
+which one should you put high on your
+
+ align:start position:0%
+which one should you put high on your
+ 
+
+ align:start position:0%
+which one should you put high on your
+priority list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+that's that's fine i mean you could you
+
+ align:start position:0%
+that's that's fine i mean you could you
+ 
+
+ align:start position:0%
+that's that's fine i mean you could you
+everybody has their own pet part of the
+
+ align:start position:0%
+everybody has their own pet part of the
+ 
+
+ align:start position:0%
+everybody has their own pet part of the
+genome they don't like introns almost
+
+ align:start position:0%
+genome they don't like introns almost
+ 
+
+ align:start position:0%
+genome they don't like introns almost
+sunk the genome project they said why
+
+ align:start position:0%
+sunk the genome project they said why
+ 
+
+ align:start position:0%
+sunk the genome project they said why
+are we going to speak with the 98 of the
+
+ align:start position:0%
+are we going to speak with the 98 of the
+ 
+
+ align:start position:0%
+are we going to speak with the 98 of the
+genome that doesn't code for proteins
+
+ align:start position:0%
+genome that doesn't code for proteins
+ 
+
+ align:start position:0%
+genome that doesn't code for proteins
+fortunately we went ahead and sequenced
+
+ align:start position:0%
+fortunately we went ahead and sequenced
+ 
+
+ align:start position:0%
+fortunately we went ahead and sequenced
+it anyway another
+
+ align:start position:0%
+it anyway another
+ 
+
+ align:start position:0%
+it anyway another
+favorite thing that people mentioned
+
+ align:start position:0%
+favorite thing that people mentioned
+ 
+
+ align:start position:0%
+favorite thing that people mentioned
+that is is repetitive dna that was
+
+ align:start position:0%
+that is is repetitive dna that was
+ 
+
+ align:start position:0%
+that is is repetitive dna that was
+another part of the genome they didn't
+
+ align:start position:0%
+another part of the genome they didn't
+ 
+
+ align:start position:0%
+another part of the genome they didn't
+actually sequence it from drosophila
+
+ align:start position:0%
+actually sequence it from drosophila
+ 
+
+ align:start position:0%
+actually sequence it from drosophila
+the repetitive dna
+
+ align:start position:0%
+the repetitive dna
+ 
+
+ align:start position:0%
+the repetitive dna
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and it's considered
+
+ align:start position:0%
+and it's considered
+ 
+
+ align:start position:0%
+and it's considered
+also not protein coding and uh
+
+ align:start position:0%
+also not protein coding and uh
+ 
+
+ align:start position:0%
+also not protein coding and uh
+and i'm gonna give you a couple examples
+
+ align:start position:0%
+and i'm gonna give you a couple examples
+ 
+
+ align:start position:0%
+and i'm gonna give you a couple examples
+as we go through here to illustrate
+
+ align:start position:0%
+as we go through here to illustrate
+ 
+
+ align:start position:0%
+as we go through here to illustrate
+other points but also to illustrate that
+
+ align:start position:0%
+other points but also to illustrate that
+ 
+
+ align:start position:0%
+other points but also to illustrate that
+repetitive regions that are not in
+
+ align:start position:0%
+repetitive regions that are not in
+ 
+
+ align:start position:0%
+repetitive regions that are not in
+protein coding regions whether introns
+
+ align:start position:0%
+protein coding regions whether introns
+ 
+
+ align:start position:0%
+protein coding regions whether introns
+or other non-coding regions can be
+
+ align:start position:0%
+or other non-coding regions can be
+ 
+
+ align:start position:0%
+or other non-coding regions can be
+important and here's an example this is
+
+ align:start position:0%
+important and here's an example this is
+ 
+
+ align:start position:0%
+important and here's an example this is
+one of the most repetitive elements in
+
+ align:start position:0%
+one of the most repetitive elements in
+ 
+
+ align:start position:0%
+one of the most repetitive elements in
+the human genome it's called an alloy
+
+ align:start position:0%
+the human genome it's called an alloy
+ 
+
+ align:start position:0%
+the human genome it's called an alloy
+repeat
+
+ align:start position:0%
+repeat
+ 
+
+ align:start position:0%
+repeat
+as you as those of you who have done
+
+ align:start position:0%
+as you as those of you who have done
+ 
+
+ align:start position:0%
+as you as those of you who have done
+bioinformatics before realize that it's
+
+ align:start position:0%
+bioinformatics before realize that it's
+ 
+
+ align:start position:0%
+bioinformatics before realize that it's
+the bane of our existence uh in terms of
+
+ align:start position:0%
+the bane of our existence uh in terms of
+ 
+
+ align:start position:0%
+the bane of our existence uh in terms of
+assembling and searching and so forth
+
+ align:start position:0%
+assembling and searching and so forth
+ 
+
+ align:start position:0%
+assembling and searching and so forth
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it here's an example of a single base
+
+ align:start position:0%
+it here's an example of a single base
+ 
+
+ align:start position:0%
+it here's an example of a single base
+mutation in this repeat there's about
+
+ align:start position:0%
+mutation in this repeat there's about
+ 
+
+ align:start position:0%
+mutation in this repeat there's about
+500 000 copies of the human genome
+
+ align:start position:0%
+500 000 copies of the human genome
+ 
+
+ align:start position:0%
+500 000 copies of the human genome
+scattered about it's called an
+
+ align:start position:0%
+scattered about it's called an
+ 
+
+ align:start position:0%
+scattered about it's called an
+intersperse repeat as a consequence
+
+ align:start position:0%
+intersperse repeat as a consequence
+ 
+
+ align:start position:0%
+intersperse repeat as a consequence
+and this a to g transition is found
+
+ align:start position:0%
+and this a to g transition is found
+ 
+
+ align:start position:0%
+and this a to g transition is found
+upstream from the myeloperoxidase enzyme
+
+ align:start position:0%
+upstream from the myeloperoxidase enzyme
+ 
+
+ align:start position:0%
+upstream from the myeloperoxidase enzyme
+encoding gene
+
+ align:start position:0%
+encoding gene
+ 
+
+ align:start position:0%
+encoding gene
+it is uh
+
+ align:start position:0%
+it is uh
+ 
+
+ align:start position:0%
+it is uh
+so how do we find out whether this is
+
+ align:start position:0%
+so how do we find out whether this is
+ 
+
+ align:start position:0%
+so how do we find out whether this is
+important in any sense first of all the
+
+ align:start position:0%
+important in any sense first of all the
+ 
+
+ align:start position:0%
+important in any sense first of all the
+observation is it it is associated with
+
+ align:start position:0%
+observation is it it is associated with
+ 
+
+ align:start position:0%
+observation is it it is associated with
+a several-fold less transcriptional
+
+ align:start position:0%
+a several-fold less transcriptional
+ 
+
+ align:start position:0%
+a several-fold less transcriptional
+activity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it it
+
+ align:start position:0%
+it it
+ 
+
+ align:start position:0%
+it it
+that particular position creates binding
+
+ align:start position:0%
+that particular position creates binding
+ 
+
+ align:start position:0%
+that particular position creates binding
+sites or creates or destroys binding
+
+ align:start position:0%
+sites or creates or destroys binding
+ 
+
+ align:start position:0%
+sites or creates or destroys binding
+sites for these um
+
+ align:start position:0%
+sites for these um
+ 
+
+ align:start position:0%
+sites for these um
+transcription elements and that might be
+
+ align:start position:0%
+transcription elements and that might be
+ 
+
+ align:start position:0%
+transcription elements and that might be
+the reason that it has lower
+
+ align:start position:0%
+the reason that it has lower
+ 
+
+ align:start position:0%
+the reason that it has lower
+transcriptional activity and finally it
+
+ align:start position:0%
+transcriptional activity and finally it
+ 
+
+ align:start position:0%
+transcriptional activity and finally it
+is over represented in a particular type
+
+ align:start position:0%
+is over represented in a particular type
+ 
+
+ align:start position:0%
+is over represented in a particular type
+of cancer
+
+ align:start position:0%
+of cancer
+ 
+
+ align:start position:0%
+of cancer
+and we're going to go through the the
+
+ align:start position:0%
+and we're going to go through the the
+ 
+
+ align:start position:0%
+and we're going to go through the the
+ways that we that we
+
+ align:start position:0%
+ways that we that we
+ 
+
+ align:start position:0%
+ways that we that we
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+an observation
+
+ align:start position:0%
+an observation
+ 
+
+ align:start position:0%
+an observation
+like a polymorphism move to an
+
+ align:start position:0%
+like a polymorphism move to an
+ 
+
+ align:start position:0%
+like a polymorphism move to an
+association like here with cancer
+
+ align:start position:0%
+association like here with cancer
+ 
+
+ align:start position:0%
+association like here with cancer
+then take it to a mechanism such as here
+
+ align:start position:0%
+then take it to a mechanism such as here
+ 
+
+ align:start position:0%
+then take it to a mechanism such as here
+with the transcriptional uh regulators
+
+ align:start position:0%
+with the transcriptional uh regulators
+ 
+
+ align:start position:0%
+with the transcriptional uh regulators
+i think that's that's what this is about
+
+ align:start position:0%
+i think that's that's what this is about
+ 
+
+ align:start position:0%
+i think that's that's what this is about
+it's not sufficient to observe the
+
+ align:start position:0%
+it's not sufficient to observe the
+ 
+
+ align:start position:0%
+it's not sufficient to observe the
+polymorphism you can't say a priori
+
+ align:start position:0%
+polymorphism you can't say a priori
+ 
+
+ align:start position:0%
+polymorphism you can't say a priori
+whether it's important or not whether
+
+ align:start position:0%
+whether it's important or not whether
+ 
+
+ align:start position:0%
+whether it's important or not whether
+it's it's alley repeats are not
+
+ align:start position:0%
+it's it's alley repeats are not
+ 
+
+ align:start position:0%
+it's it's alley repeats are not
+conserved that's another thing that
+
+ align:start position:0%
+conserved that's another thing that
+ 
+
+ align:start position:0%
+conserved that's another thing that
+people say throw out all the
+
+ align:start position:0%
+people say throw out all the
+ 
+
+ align:start position:0%
+people say throw out all the
+non-conserved uh single nucleotide
+
+ align:start position:0%
+non-conserved uh single nucleotide
+ 
+
+ align:start position:0%
+non-conserved uh single nucleotide
+polymorphisms it's not conserved it's
+
+ align:start position:0%
+polymorphisms it's not conserved it's
+ 
+
+ align:start position:0%
+polymorphisms it's not conserved it's
+not present in mouse
+
+ align:start position:0%
+not present in mouse
+ 
+
+ align:start position:0%
+not present in mouse
+for example uh it's non-coding and it's
+
+ align:start position:0%
+for example uh it's non-coding and it's
+ 
+
+ align:start position:0%
+for example uh it's non-coding and it's
+repetitive
+
+ align:start position:0%
+repetitive
+ 
+
+ align:start position:0%
+repetitive
+now in addition to the types of
+
+ align:start position:0%
+now in addition to the types of
+ 
+
+ align:start position:0%
+now in addition to the types of
+mutations we have the modes of
+
+ align:start position:0%
+mutations we have the modes of
+ 
+
+ align:start position:0%
+mutations we have the modes of
+inheritance that is to say
+
+ align:start position:0%
+inheritance that is to say
+ 
+
+ align:start position:0%
+inheritance that is to say
+the different ways in which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a change a polymorphism can be
+
+ align:start position:0%
+a change a polymorphism can be
+ 
+
+ align:start position:0%
+a change a polymorphism can be
+transmitted and i include this kind of
+
+ align:start position:0%
+transmitted and i include this kind of
+ 
+
+ align:start position:0%
+transmitted and i include this kind of
+broaden your perspective rather than
+
+ align:start position:0%
+broaden your perspective rather than
+ 
+
+ align:start position:0%
+broaden your perspective rather than
+getting in entirely fixated on the three
+
+ align:start position:0%
+getting in entirely fixated on the three
+ 
+
+ align:start position:0%
+getting in entirely fixated on the three
+million dna snips let's broaden the
+
+ align:start position:0%
+million dna snips let's broaden the
+ 
+
+ align:start position:0%
+million dna snips let's broaden the
+discussion here a little bit you can
+
+ align:start position:0%
+discussion here a little bit you can
+ 
+
+ align:start position:0%
+discussion here a little bit you can
+have not only dna polymorphisms but you
+
+ align:start position:0%
+have not only dna polymorphisms but you
+ 
+
+ align:start position:0%
+have not only dna polymorphisms but you
+can have rna polymorphisms which are
+
+ align:start position:0%
+can have rna polymorphisms which are
+ 
+
+ align:start position:0%
+can have rna polymorphisms which are
+heritable
+
+ align:start position:0%
+heritable
+ 
+
+ align:start position:0%
+heritable
+for example and i use this as a extreme
+
+ align:start position:0%
+for example and i use this as a extreme
+ 
+
+ align:start position:0%
+for example and i use this as a extreme
+case rnai 22 nucleotide or so probably a
+
+ align:start position:0%
+case rnai 22 nucleotide or so probably a
+ 
+
+ align:start position:0%
+case rnai 22 nucleotide or so probably a
+variety of mechanisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bits of rna can uh
+
+ align:start position:0%
+bits of rna can uh
+ 
+
+ align:start position:0%
+bits of rna can uh
+be induced in various ways and once
+
+ align:start position:0%
+be induced in various ways and once
+ 
+
+ align:start position:0%
+be induced in various ways and once
+induced they can
+
+ align:start position:0%
+induced they can
+ 
+
+ align:start position:0%
+induced they can
+they can uh replicate essentially within
+
+ align:start position:0%
+they can uh replicate essentially within
+ 
+
+ align:start position:0%
+they can uh replicate essentially within
+a cell and between cells they can spread
+
+ align:start position:0%
+a cell and between cells they can spread
+ 
+
+ align:start position:0%
+a cell and between cells they can spread
+throughout an organism and probably be
+
+ align:start position:0%
+throughout an organism and probably be
+ 
+
+ align:start position:0%
+throughout an organism and probably be
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+propagated over generations between
+
+ align:start position:0%
+propagated over generations between
+ 
+
+ align:start position:0%
+propagated over generations between
+different generations organisms so this
+
+ align:start position:0%
+different generations organisms so this
+ 
+
+ align:start position:0%
+different generations organisms so this
+is heritable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can consider it epigenetic or
+
+ align:start position:0%
+and you can consider it epigenetic or
+ 
+
+ align:start position:0%
+and you can consider it epigenetic or
+genetic polymorphism depending on the
+
+ align:start position:0%
+genetic polymorphism depending on the
+ 
+
+ align:start position:0%
+genetic polymorphism depending on the
+nomenclature that you adopt
+
+ align:start position:0%
+nomenclature that you adopt
+ 
+
+ align:start position:0%
+nomenclature that you adopt
+even a protein confirmation can be
+
+ align:start position:0%
+even a protein confirmation can be
+ 
+
+ align:start position:0%
+even a protein confirmation can be
+considered a polymorphism that is
+
+ align:start position:0%
+considered a polymorphism that is
+ 
+
+ align:start position:0%
+considered a polymorphism that is
+heritable
+
+ align:start position:0%
+heritable
+ 
+
+ align:start position:0%
+heritable
+the central dogma tells us this protein
+
+ align:start position:0%
+the central dogma tells us this protein
+ 
+
+ align:start position:0%
+the central dogma tells us this protein
+is encoded by a nucleic acid and that
+
+ align:start position:0%
+is encoded by a nucleic acid and that
+ 
+
+ align:start position:0%
+is encoded by a nucleic acid and that
+certainly is still the case even the
+
+ align:start position:0%
+certainly is still the case even the
+ 
+
+ align:start position:0%
+certainly is still the case even the
+these heritable uh
+
+ align:start position:0%
+these heritable uh
+ 
+
+ align:start position:0%
+these heritable uh
+polymorphisms and proteins but it has a
+
+ align:start position:0%
+polymorphisms and proteins but it has a
+ 
+
+ align:start position:0%
+polymorphisms and proteins but it has a
+different conformation and that
+
+ align:start position:0%
+different conformation and that
+ 
+
+ align:start position:0%
+different conformation and that
+conformation recruits other
+
+ align:start position:0%
+conformation recruits other
+ 
+
+ align:start position:0%
+conformation recruits other
+conformations
+
+ align:start position:0%
+conformations
+ 
+
+ align:start position:0%
+conformations
+and so and so is inherited not only
+
+ align:start position:0%
+and so and so is inherited not only
+ 
+
+ align:start position:0%
+and so and so is inherited not only
+within a cell but between cells and
+
+ align:start position:0%
+within a cell but between cells and
+ 
+
+ align:start position:0%
+within a cell but between cells and
+between organisms and as the causation
+
+ align:start position:0%
+between organisms and as the causation
+ 
+
+ align:start position:0%
+between organisms and as the causation
+of things like mad cow disease so on
+
+ align:start position:0%
+of things like mad cow disease so on
+ 
+
+ align:start position:0%
+of things like mad cow disease so on
+and finally modifications of
+
+ align:start position:0%
+and finally modifications of
+ 
+
+ align:start position:0%
+and finally modifications of
+biopolymers such as methylation can
+
+ align:start position:0%
+biopolymers such as methylation can
+ 
+
+ align:start position:0%
+biopolymers such as methylation can
+occur and this is not formally a dna
+
+ align:start position:0%
+occur and this is not formally a dna
+ 
+
+ align:start position:0%
+occur and this is not formally a dna
+sequence change but it is uh either
+
+ align:start position:0%
+sequence change but it is uh either
+ 
+
+ align:start position:0%
+sequence change but it is uh either
+it's a it's a heritable change
+
+ align:start position:0%
+it's a it's a heritable change
+ 
+
+ align:start position:0%
+it's a it's a heritable change
+that can have
+
+ align:start position:0%
+that can have
+ 
+
+ align:start position:0%
+that can have
+very significant effects on things like
+
+ align:start position:0%
+very significant effects on things like
+ 
+
+ align:start position:0%
+very significant effects on things like
+cancer
+
+ align:start position:0%
+cancer
+ 
+
+ align:start position:0%
+cancer
+and other and gene expression in general
+
+ align:start position:0%
+and other and gene expression in general
+ 
+
+ align:start position:0%
+and other and gene expression in general
+okay now that's these are not
+
+ align:start position:0%
+okay now that's these are not
+ 
+
+ align:start position:0%
+okay now that's these are not
+these is the broadening of the
+
+ align:start position:0%
+these is the broadening of the
+ 
+
+ align:start position:0%
+these is the broadening of the
+definition of polymorphisms
+
+ align:start position:0%
+definition of polymorphisms
+ 
+
+ align:start position:0%
+definition of polymorphisms
+and now let's talk in uh
+
+ align:start position:0%
+and now let's talk in uh
+ 
+
+ align:start position:0%
+and now let's talk in uh
+thoroughly about the different of the
+
+ align:start position:0%
+thoroughly about the different of the
+ 
+
+ align:start position:0%
+thoroughly about the different of the
+ways it can be inher inherited as
+
+ align:start position:0%
+ways it can be inher inherited as
+ 
+
+ align:start position:0%
+ways it can be inher inherited as
+horizontal or vertical okay horizontal
+
+ align:start position:0%
+horizontal or vertical okay horizontal
+ 
+
+ align:start position:0%
+horizontal or vertical okay horizontal
+typically means between species
+
+ align:start position:0%
+typically means between species
+ 
+
+ align:start position:0%
+typically means between species
+but in a certain sense it could be it
+
+ align:start position:0%
+but in a certain sense it could be it
+ 
+
+ align:start position:0%
+but in a certain sense it could be it
+could reflect some of the things that
+
+ align:start position:0%
+could reflect some of the things that
+ 
+
+ align:start position:0%
+could reflect some of the things that
+are going on here with rna and protein
+
+ align:start position:0%
+are going on here with rna and protein
+ 
+
+ align:start position:0%
+are going on here with rna and protein
+inheritance in the sense that is being
+
+ align:start position:0%
+inheritance in the sense that is being
+ 
+
+ align:start position:0%
+inheritance in the sense that is being
+horizontally transmitted between
+
+ align:start position:0%
+horizontally transmitted between
+ 
+
+ align:start position:0%
+horizontally transmitted between
+different cells within the same organism
+
+ align:start position:0%
+different cells within the same organism
+ 
+
+ align:start position:0%
+different cells within the same organism
+but generally it's it's uh it's a
+
+ align:start position:0%
+but generally it's it's uh it's a
+ 
+
+ align:start position:0%
+but generally it's it's uh it's a
+mechanism that does not involve mitosis
+
+ align:start position:0%
+mechanism that does not involve mitosis
+ 
+
+ align:start position:0%
+mechanism that does not involve mitosis
+or meiosis
+
+ align:start position:0%
+or meiosis
+ 
+
+ align:start position:0%
+or meiosis
+of of the
+
+ align:start position:0%
+of of the
+ 
+
+ align:start position:0%
+of of the
+nuclear or or
+
+ align:start position:0%
+nuclear or or
+ 
+
+ align:start position:0%
+nuclear or or
+organeller genomes
+
+ align:start position:0%
+organeller genomes
+ 
+
+ align:start position:0%
+organeller genomes
+and this the natural processes are
+
+ align:start position:0%
+and this the natural processes are
+ 
+
+ align:start position:0%
+and this the natural processes are
+transduction and transformation
+
+ align:start position:0%
+transduction and transformation
+ 
+
+ align:start position:0%
+transduction and transformation
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+being distinguished but transduction
+
+ align:start position:0%
+being distinguished but transduction
+ 
+
+ align:start position:0%
+being distinguished but transduction
+typically involves a viral or protein
+
+ align:start position:0%
+typically involves a viral or protein
+ 
+
+ align:start position:0%
+typically involves a viral or protein
+coat for the nucleic acid and
+
+ align:start position:0%
+coat for the nucleic acid and
+ 
+
+ align:start position:0%
+coat for the nucleic acid and
+transformation involves something closer
+
+ align:start position:0%
+transformation involves something closer
+ 
+
+ align:start position:0%
+transformation involves something closer
+to naked nucleic acids transgenic is a
+
+ align:start position:0%
+to naked nucleic acids transgenic is a
+ 
+
+ align:start position:0%
+to naked nucleic acids transgenic is a
+completely laboratory based version of
+
+ align:start position:0%
+completely laboratory based version of
+ 
+
+ align:start position:0%
+completely laboratory based version of
+these two more natural
+
+ align:start position:0%
+these two more natural
+ 
+
+ align:start position:0%
+these two more natural
+methods i think vertical we've already
+
+ align:start position:0%
+methods i think vertical we've already
+ 
+
+ align:start position:0%
+methods i think vertical we've already
+talked about this is what we normally
+
+ align:start position:0%
+talked about this is what we normally
+ 
+
+ align:start position:0%
+talked about this is what we normally
+think of inheritance rather for a
+
+ align:start position:0%
+think of inheritance rather for a
+ 
+
+ align:start position:0%
+think of inheritance rather for a
+horizontal we saw in the in the tree of
+
+ align:start position:0%
+horizontal we saw in the in the tree of
+ 
+
+ align:start position:0%
+horizontal we saw in the in the tree of
+life is very common even in the late
+
+ align:start position:0%
+life is very common even in the late
+ 
+
+ align:start position:0%
+life is very common even in the late
+branches in the early branches vertical
+
+ align:start position:0%
+branches in the early branches vertical
+ 
+
+ align:start position:0%
+branches in the early branches vertical
+though is what we normally think about
+
+ align:start position:0%
+though is what we normally think about
+ 
+
+ align:start position:0%
+though is what we normally think about
+when we're doing crosses
+
+ align:start position:0%
+when we're doing crosses
+ 
+
+ align:start position:0%
+when we're doing crosses
+in laboratory some of these are
+
+ align:start position:0%
+in laboratory some of these are
+ 
+
+ align:start position:0%
+in laboratory some of these are
+maternally inherited like mitochondria
+
+ align:start position:0%
+maternally inherited like mitochondria
+ 
+
+ align:start position:0%
+maternally inherited like mitochondria
+and chloroplasts
+
+ align:start position:0%
+and chloroplasts
+ 
+
+ align:start position:0%
+and chloroplasts
+but it's still the same kind of process
+
+ align:start position:0%
+but it's still the same kind of process
+ 
+
+ align:start position:0%
+but it's still the same kind of process
+mitosis
+
+ align:start position:0%
+mitosis
+ 
+
+ align:start position:0%
+mitosis
+segregation of dna okay so now we've got
+
+ align:start position:0%
+segregation of dna okay so now we've got
+ 
+
+ align:start position:0%
+segregation of dna okay so now we've got
+types of mutations we want to talk about
+
+ align:start position:0%
+types of mutations we want to talk about
+ 
+
+ align:start position:0%
+types of mutations we want to talk about
+mutation drift and selection as the main
+
+ align:start position:0%
+mutation drift and selection as the main
+ 
+
+ align:start position:0%
+mutation drift and selection as the main
+source of uh the frequencies
+
+ align:start position:0%
+source of uh the frequencies
+ 
+
+ align:start position:0%
+source of uh the frequencies
+that we that we find in populations we
+
+ align:start position:0%
+that we that we find in populations we
+ 
+
+ align:start position:0%
+that we that we find in populations we
+want to know where do allele frequencies
+
+ align:start position:0%
+want to know where do allele frequencies
+ 
+
+ align:start position:0%
+want to know where do allele frequencies
+come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i will maintain that that
+
+ align:start position:0%
+and i will maintain that that
+ 
+
+ align:start position:0%
+and i will maintain that that
+generally speaking in almost all living
+
+ align:start position:0%
+generally speaking in almost all living
+ 
+
+ align:start position:0%
+generally speaking in almost all living
+systems whether they're cells from
+
+ align:start position:0%
+systems whether they're cells from
+ 
+
+ align:start position:0%
+systems whether they're cells from
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+that are mutating or whole organisms
+
+ align:start position:0%
+that are mutating or whole organisms
+ 
+
+ align:start position:0%
+that are mutating or whole organisms
+whether they do recombination or not
+
+ align:start position:0%
+whether they do recombination or not
+ 
+
+ align:start position:0%
+whether they do recombination or not
+they will do mutation selection and
+
+ align:start position:0%
+they will do mutation selection and
+ 
+
+ align:start position:0%
+they will do mutation selection and
+drift
+
+ align:start position:0%
+drift
+ 
+
+ align:start position:0%
+drift
+now to develop a fairly rigorous model
+
+ align:start position:0%
+now to develop a fairly rigorous model
+ 
+
+ align:start position:0%
+now to develop a fairly rigorous model
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+yet simple we have some assumptions
+
+ align:start position:0%
+yet simple we have some assumptions
+ 
+
+ align:start position:0%
+yet simple we have some assumptions
+we always have assumptions and models if
+
+ align:start position:0%
+we always have assumptions and models if
+ 
+
+ align:start position:0%
+we always have assumptions and models if
+people tell you that there's no
+
+ align:start position:0%
+people tell you that there's no
+ 
+
+ align:start position:0%
+people tell you that there's no
+assumptions then you need to you need to
+
+ align:start position:0%
+assumptions then you need to you need to
+ 
+
+ align:start position:0%
+assumptions then you need to you need to
+dig a little further
+
+ align:start position:0%
+dig a little further
+ 
+
+ align:start position:0%
+dig a little further
+the con that the functions that we'll
+
+ align:start position:0%
+the con that the functions that we'll
+ 
+
+ align:start position:0%
+the con that the functions that we'll
+make here for a little while and and
+
+ align:start position:0%
+make here for a little while and and
+ 
+
+ align:start position:0%
+make here for a little while and and
+then i'll give you a nice example that
+
+ align:start position:0%
+then i'll give you a nice example that
+ 
+
+ align:start position:0%
+then i'll give you a nice example that
+undermined them all but it's constant
+
+ align:start position:0%
+undermined them all but it's constant
+ 
+
+ align:start position:0%
+undermined them all but it's constant
+population size n
+
+ align:start position:0%
+population size n
+ 
+
+ align:start position:0%
+population size n
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that you have random mating remember we
+
+ align:start position:0%
+that you have random mating remember we
+ 
+
+ align:start position:0%
+that you have random mating remember we
+were talking about admixture before we
+
+ align:start position:0%
+were talking about admixture before we
+ 
+
+ align:start position:0%
+were talking about admixture before we
+have everything every every
+
+ align:start position:0%
+have everything every every
+ 
+
+ align:start position:0%
+have everything every every
+member of the population randomly made
+
+ align:start position:0%
+member of the population randomly made
+ 
+
+ align:start position:0%
+member of the population randomly made
+they're non-overlapping generations this
+
+ align:start position:0%
+they're non-overlapping generations this
+ 
+
+ align:start position:0%
+they're non-overlapping generations this
+is a convenience
+
+ align:start position:0%
+is a convenience
+ 
+
+ align:start position:0%
+is a convenience
+we are not making any assumptions about
+
+ align:start position:0%
+we are not making any assumptions about
+ 
+
+ align:start position:0%
+we are not making any assumptions about
+the population
+
+ align:start position:0%
+the population
+ 
+
+ align:start position:0%
+the population
+allele frequencies being at equilibrium
+
+ align:start position:0%
+allele frequencies being at equilibrium
+ 
+
+ align:start position:0%
+allele frequencies being at equilibrium
+this is something those of you have
+
+ align:start position:0%
+this is something those of you have
+ 
+
+ align:start position:0%
+this is something those of you have
+taken biology courses with hardy
+
+ align:start position:0%
+taken biology courses with hardy
+ 
+
+ align:start position:0%
+taken biology courses with hardy
+weinberg makes that assumption here this
+
+ align:start position:0%
+weinberg makes that assumption here this
+ 
+
+ align:start position:0%
+weinberg makes that assumption here this
+is a much more general model it includes
+
+ align:start position:0%
+is a much more general model it includes
+ 
+
+ align:start position:0%
+is a much more general model it includes
+non-equilibrium and equilibrium can be a
+
+ align:start position:0%
+non-equilibrium and equilibrium can be a
+ 
+
+ align:start position:0%
+non-equilibrium and equilibrium can be a
+special case so this is
+
+ align:start position:0%
+special case so this is
+ 
+
+ align:start position:0%
+special case so this is
+relatively minor
+
+ align:start position:0%
+relatively minor
+ 
+
+ align:start position:0%
+relatively minor
+non-assumption
+
+ align:start position:0%
+non-assumption
+ 
+
+ align:start position:0%
+non-assumption
+but but we are assuming that we do not
+
+ align:start position:0%
+but but we are assuming that we do not
+ 
+
+ align:start position:0%
+but but we are assuming that we do not
+have an infinite number of alleles nor
+
+ align:start position:0%
+have an infinite number of alleles nor
+ 
+
+ align:start position:0%
+have an infinite number of alleles nor
+an infinite number
+
+ align:start position:0%
+an infinite number
+ 
+
+ align:start position:0%
+an infinite number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+population size
+
+ align:start position:0%
+population size
+ 
+
+ align:start position:0%
+population size
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ignore everything on this slide but the
+
+ align:start position:0%
+ignore everything on this slide but the
+ 
+
+ align:start position:0%
+ignore everything on this slide but the
+upper left-hand corner of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide 15 here is this should look
+
+ align:start position:0%
+slide 15 here is this should look
+ 
+
+ align:start position:0%
+slide 15 here is this should look
+familiar this should look somewhat like
+
+ align:start position:0%
+familiar this should look somewhat like
+ 
+
+ align:start position:0%
+familiar this should look somewhat like
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+logistic map where we had
+
+ align:start position:0%
+logistic map where we had
+ 
+
+ align:start position:0%
+logistic map where we had
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+incremental exponent slow exponential
+
+ align:start position:0%
+incremental exponent slow exponential
+ 
+
+ align:start position:0%
+incremental exponent slow exponential
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+allele in a population over another
+
+ align:start position:0%
+allele in a population over another
+ 
+
+ align:start position:0%
+allele in a population over another
+or one organism over another based on
+
+ align:start position:0%
+or one organism over another based on
+ 
+
+ align:start position:0%
+or one organism over another based on
+the different selection coefficients of
+
+ align:start position:0%
+the different selection coefficients of
+ 
+
+ align:start position:0%
+the different selection coefficients of
+those organisms
+
+ align:start position:0%
+those organisms
+ 
+
+ align:start position:0%
+those organisms
+and you know this could be a very small
+
+ align:start position:0%
+and you know this could be a very small
+ 
+
+ align:start position:0%
+and you know this could be a very small
+difference say a one percent increase
+
+ align:start position:0%
+difference say a one percent increase
+ 
+
+ align:start position:0%
+difference say a one percent increase
+per generation will uh will dominate
+
+ align:start position:0%
+per generation will uh will dominate
+ 
+
+ align:start position:0%
+per generation will uh will dominate
+after a thousand generations or so um
+
+ align:start position:0%
+after a thousand generations or so um
+ 
+
+ align:start position:0%
+after a thousand generations or so um
+quite definitely and so that's what
+
+ align:start position:0%
+quite definitely and so that's what
+ 
+
+ align:start position:0%
+quite definitely and so that's what
+you're seeing the exponential curve and
+
+ align:start position:0%
+you're seeing the exponential curve and
+ 
+
+ align:start position:0%
+you're seeing the exponential curve and
+the plateaus um
+
+ align:start position:0%
+the plateaus um
+ 
+
+ align:start position:0%
+the plateaus um
+as it gets uh to 100 percent allele
+
+ align:start position:0%
+as it gets uh to 100 percent allele
+ 
+
+ align:start position:0%
+as it gets uh to 100 percent allele
+frequency that that's the full range on
+
+ align:start position:0%
+frequency that that's the full range on
+ 
+
+ align:start position:0%
+frequency that that's the full range on
+the vertical axis of zero to 100 percent
+
+ align:start position:0%
+the vertical axis of zero to 100 percent
+ 
+
+ align:start position:0%
+the vertical axis of zero to 100 percent
+wheel frequency and generation goes from
+
+ align:start position:0%
+wheel frequency and generation goes from
+ 
+
+ align:start position:0%
+wheel frequency and generation goes from
+zero to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fourteen hundred
+
+ align:start position:0%
+fourteen hundred
+ 
+
+ align:start position:0%
+fourteen hundred
+now what it actually represents in this
+
+ align:start position:0%
+now what it actually represents in this
+ 
+
+ align:start position:0%
+now what it actually represents in this
+particular case is closely related a
+
+ align:start position:0%
+particular case is closely related a
+ 
+
+ align:start position:0%
+particular case is closely related a
+little more complicated than just one
+
+ align:start position:0%
+little more complicated than just one
+ 
+
+ align:start position:0%
+little more complicated than just one
+allele replacing another because here we
+
+ align:start position:0%
+allele replacing another because here we
+ 
+
+ align:start position:0%
+allele replacing another because here we
+have um
+
+ align:start position:0%
+have um
+ 
+
+ align:start position:0%
+have um
+diploids that is to say not a halfway
+
+ align:start position:0%
+diploids that is to say not a halfway
+ 
+
+ align:start position:0%
+diploids that is to say not a halfway
+that just has one allele like in
+
+ align:start position:0%
+that just has one allele like in
+ 
+
+ align:start position:0%
+that just has one allele like in
+in the bacterial species that we've kind
+
+ align:start position:0%
+in the bacterial species that we've kind
+ 
+
+ align:start position:0%
+in the bacterial species that we've kind
+of implicitly been talking about
+
+ align:start position:0%
+of implicitly been talking about
+ 
+
+ align:start position:0%
+of implicitly been talking about
+but you can have here now three
+
+ align:start position:0%
+but you can have here now three
+ 
+
+ align:start position:0%
+but you can have here now three
+combinations of alleles you can have say
+
+ align:start position:0%
+combinations of alleles you can have say
+ 
+
+ align:start position:0%
+combinations of alleles you can have say
+the the reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genotype of of capillae
+
+ align:start position:0%
+genotype of of capillae
+ 
+
+ align:start position:0%
+genotype of of capillae
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+which we just call
+
+ align:start position:0%
+which we just call
+ 
+
+ align:start position:0%
+which we just call
+uh 100
+
+ align:start position:0%
+uh 100
+ 
+
+ align:start position:0%
+uh 100
+percent of fitness so we have fitness
+
+ align:start position:0%
+percent of fitness so we have fitness
+ 
+
+ align:start position:0%
+percent of fitness so we have fitness
+and selection coefficient which are
+
+ align:start position:0%
+and selection coefficient which are
+ 
+
+ align:start position:0%
+and selection coefficient which are
+interchangeable terms that are very
+
+ align:start position:0%
+interchangeable terms that are very
+ 
+
+ align:start position:0%
+interchangeable terms that are very
+trivial mathematical relationship
+
+ align:start position:0%
+trivial mathematical relationship
+ 
+
+ align:start position:0%
+trivial mathematical relationship
+between them so we'll use w and s
+
+ align:start position:0%
+between them so we'll use w and s
+ 
+
+ align:start position:0%
+between them so we'll use w and s
+in different contexts here it just does
+
+ align:start position:0%
+in different contexts here it just does
+ 
+
+ align:start position:0%
+in different contexts here it just does
+population geneticists do then you can
+
+ align:start position:0%
+population geneticists do then you can
+ 
+
+ align:start position:0%
+population geneticists do then you can
+have big a big a little a little a and
+
+ align:start position:0%
+have big a big a little a little a and
+ 
+
+ align:start position:0%
+have big a big a little a little a and
+big a little a as the heterozygote and
+
+ align:start position:0%
+big a little a as the heterozygote and
+ 
+
+ align:start position:0%
+big a little a as the heterozygote and
+we're assuming an additive model here
+
+ align:start position:0%
+we're assuming an additive model here
+ 
+
+ align:start position:0%
+we're assuming an additive model here
+where you get a little more selection
+
+ align:start position:0%
+where you get a little more selection
+ 
+
+ align:start position:0%
+where you get a little more selection
+with one allele of little a and then two
+
+ align:start position:0%
+with one allele of little a and then two
+ 
+
+ align:start position:0%
+with one allele of little a and then two
+alleles of little a results in 2s one
+
+ align:start position:0%
+alleles of little a results in 2s one
+ 
+
+ align:start position:0%
+alleles of little a results in 2s one
+plus 2s
+
+ align:start position:0%
+plus 2s
+ 
+
+ align:start position:0%
+plus 2s
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and this has a very similar curve to uh
+
+ align:start position:0%
+and this has a very similar curve to uh
+ 
+
+ align:start position:0%
+and this has a very similar curve to uh
+the logistic map if you had a simple
+
+ align:start position:0%
+the logistic map if you had a simple
+ 
+
+ align:start position:0%
+the logistic map if you had a simple
+allele replacement
+
+ align:start position:0%
+allele replacement
+ 
+
+ align:start position:0%
+allele replacement
+on the other hand and and what you tend
+
+ align:start position:0%
+on the other hand and and what you tend
+ 
+
+ align:start position:0%
+on the other hand and and what you tend
+to have in this population since a
+
+ align:start position:0%
+to have in this population since a
+ 
+
+ align:start position:0%
+to have in this population since a
+thousand generations in the big scheme
+
+ align:start position:0%
+thousand generations in the big scheme
+ 
+
+ align:start position:0%
+thousand generations in the big scheme
+of things it may seem like a lot to you
+
+ align:start position:0%
+of things it may seem like a lot to you
+ 
+
+ align:start position:0%
+of things it may seem like a lot to you
+but the big scheme is it's a very short
+
+ align:start position:0%
+but the big scheme is it's a very short
+ 
+
+ align:start position:0%
+but the big scheme is it's a very short
+period of time and so you tend to have
+
+ align:start position:0%
+period of time and so you tend to have
+ 
+
+ align:start position:0%
+period of time and so you tend to have
+alleles at frequency of zero
+
+ align:start position:0%
+alleles at frequency of zero
+ 
+
+ align:start position:0%
+alleles at frequency of zero
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+on the other hand if you have over
+
+ align:start position:0%
+on the other hand if you have over
+ 
+
+ align:start position:0%
+on the other hand if you have over
+dominant mode where the heterozygote has
+
+ align:start position:0%
+dominant mode where the heterozygote has
+ 
+
+ align:start position:0%
+dominant mode where the heterozygote has
+the highest fitness of the three
+
+ align:start position:0%
+the highest fitness of the three
+ 
+
+ align:start position:0%
+the highest fitness of the three
+possibilities where one plus s is larger
+
+ align:start position:0%
+possibilities where one plus s is larger
+ 
+
+ align:start position:0%
+possibilities where one plus s is larger
+than one or one plus t
+
+ align:start position:0%
+than one or one plus t
+ 
+
+ align:start position:0%
+than one or one plus t
+then you aim for equilibrium whether
+
+ align:start position:0%
+then you aim for equilibrium whether
+ 
+
+ align:start position:0%
+then you aim for equilibrium whether
+you're in starting at close to zero
+
+ align:start position:0%
+you're in starting at close to zero
+ 
+
+ align:start position:0%
+you're in starting at close to zero
+percent or close to 100 percent the
+
+ align:start position:0%
+percent or close to 100 percent the
+ 
+
+ align:start position:0%
+percent or close to 100 percent the
+allele frequency will converge on some
+
+ align:start position:0%
+allele frequency will converge on some
+ 
+
+ align:start position:0%
+allele frequency will converge on some
+equilibrium point um
+
+ align:start position:0%
+equilibrium point um
+ 
+
+ align:start position:0%
+equilibrium point um
+in this case somewhere around 0.6 to 0.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.6 for 1 allele 1.4 for the other and
+
+ align:start position:0%
+0.6 for 1 allele 1.4 for the other and
+ 
+
+ align:start position:0%
+0.6 for 1 allele 1.4 for the other and
+it could be anywhere it depends on the
+
+ align:start position:0%
+it could be anywhere it depends on the
+ 
+
+ align:start position:0%
+it could be anywhere it depends on the
+relative fitnesses s and t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is just a reminder slide combining
+
+ align:start position:0%
+this is just a reminder slide combining
+ 
+
+ align:start position:0%
+this is just a reminder slide combining
+two slides from before
+
+ align:start position:0%
+two slides from before
+ 
+
+ align:start position:0%
+two slides from before
+just to connect that slide connects the
+
+ align:start position:0%
+just to connect that slide connects the
+ 
+
+ align:start position:0%
+just to connect that slide connects the
+logistic map from lecture one
+
+ align:start position:0%
+logistic map from lecture one
+ 
+
+ align:start position:0%
+logistic map from lecture one
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+the selection coefficients we've been
+
+ align:start position:0%
+the selection coefficients we've been
+ 
+
+ align:start position:0%
+the selection coefficients we've been
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+in lecture two to the the diploids that
+
+ align:start position:0%
+in lecture two to the the diploids that
+ 
+
+ align:start position:0%
+in lecture two to the the diploids that
+we're mainly talking about in this
+
+ align:start position:0%
+we're mainly talking about in this
+ 
+
+ align:start position:0%
+we're mainly talking about in this
+lecture because humans are diploids and
+
+ align:start position:0%
+lecture because humans are diploids and
+ 
+
+ align:start position:0%
+lecture because humans are diploids and
+here's just to just connect this um to
+
+ align:start position:0%
+here's just to just connect this um to
+ 
+
+ align:start position:0%
+here's just to just connect this um to
+the fact that the selection coefficients
+
+ align:start position:0%
+the fact that the selection coefficients
+ 
+
+ align:start position:0%
+the fact that the selection coefficients
+s or the fitness w
+
+ align:start position:0%
+s or the fitness w
+ 
+
+ align:start position:0%
+s or the fitness w
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+relevant to different environments and
+
+ align:start position:0%
+relevant to different environments and
+ 
+
+ align:start position:0%
+relevant to different environments and
+the different times that organisms spend
+
+ align:start position:0%
+the different times that organisms spend
+ 
+
+ align:start position:0%
+the different times that organisms spend
+in those different environments and all
+
+ align:start position:0%
+in those different environments and all
+ 
+
+ align:start position:0%
+in those different environments and all
+mutants are tagged by their dna and
+
+ align:start position:0%
+mutants are tagged by their dna and
+ 
+
+ align:start position:0%
+mutants are tagged by their dna and
+they're pooled and they're selected and
+
+ align:start position:0%
+they're pooled and they're selected and
+ 
+
+ align:start position:0%
+they're pooled and they're selected and
+you can read them out in a variety of
+
+ align:start position:0%
+you can read them out in a variety of
+ 
+
+ align:start position:0%
+you can read them out in a variety of
+methods
+
+ align:start position:0%
+methods
+ 
+
+ align:start position:0%
+methods
+so now let's dig down into where the
+
+ align:start position:0%
+so now let's dig down into where the
+ 
+
+ align:start position:0%
+so now let's dig down into where the
+allele frequencies come from based on
+
+ align:start position:0%
+allele frequencies come from based on
+ 
+
+ align:start position:0%
+allele frequencies come from based on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+mutation migration and selection
+
+ align:start position:0%
+mutation migration and selection
+ 
+
+ align:start position:0%
+mutation migration and selection
+i'm sorry mutation or migration which
+
+ align:start position:0%
+i'm sorry mutation or migration which
+ 
+
+ align:start position:0%
+i'm sorry mutation or migration which
+we'll lump together here as m
+
+ align:start position:0%
+we'll lump together here as m
+ 
+
+ align:start position:0%
+we'll lump together here as m
+selection and drift now the
+
+ align:start position:0%
+selection and drift now the
+ 
+
+ align:start position:0%
+selection and drift now the
+mutation will have a forward rate
+
+ align:start position:0%
+mutation will have a forward rate
+ 
+
+ align:start position:0%
+mutation will have a forward rate
+constant and a reverse this is this
+
+ align:start position:0%
+constant and a reverse this is this
+ 
+
+ align:start position:0%
+constant and a reverse this is this
+should remind you the conversation we
+
+ align:start position:0%
+should remind you the conversation we
+ 
+
+ align:start position:0%
+should remind you the conversation we
+just had about of
+
+ align:start position:0%
+just had about of
+ 
+
+ align:start position:0%
+just had about of
+the different kinds of alleles the
+
+ align:start position:0%
+the different kinds of alleles the
+ 
+
+ align:start position:0%
+the different kinds of alleles the
+duplications and deletions how they can
+
+ align:start position:0%
+duplications and deletions how they can
+ 
+
+ align:start position:0%
+duplications and deletions how they can
+have different
+
+ align:start position:0%
+have different
+ 
+
+ align:start position:0%
+have different
+rates
+
+ align:start position:0%
+rates
+ 
+
+ align:start position:0%
+rates
+if they're tandem duplication then that
+
+ align:start position:0%
+if they're tandem duplication then that
+ 
+
+ align:start position:0%
+if they're tandem duplication then that
+has a great tendency to delete
+
+ align:start position:0%
+has a great tendency to delete
+ 
+
+ align:start position:0%
+has a great tendency to delete
+if it deletes down to a single
+
+ align:start position:0%
+if it deletes down to a single
+ 
+
+ align:start position:0%
+if it deletes down to a single
+repeat there's now no longer any repeat
+
+ align:start position:0%
+repeat there's now no longer any repeat
+ 
+
+ align:start position:0%
+repeat there's now no longer any repeat
+and so the chance of generating the
+
+ align:start position:0%
+and so the chance of generating the
+ 
+
+ align:start position:0%
+and so the chance of generating the
+exact duplicate is low so that the
+
+ align:start position:0%
+exact duplicate is low so that the
+ 
+
+ align:start position:0%
+exact duplicate is low so that the
+forward in reverse here the frequency of
+
+ align:start position:0%
+forward in reverse here the frequency of
+ 
+
+ align:start position:0%
+forward in reverse here the frequency of
+forward and reverse mutation is
+
+ align:start position:0%
+forward and reverse mutation is
+ 
+
+ align:start position:0%
+forward and reverse mutation is
+represented by f and r respectively
+
+ align:start position:0%
+represented by f and r respectively
+ 
+
+ align:start position:0%
+represented by f and r respectively
+now what you'll see
+
+ align:start position:0%
+now what you'll see
+ 
+
+ align:start position:0%
+now what you'll see
+we're going to walk through this
+
+ align:start position:0%
+we're going to walk through this
+ 
+
+ align:start position:0%
+we're going to walk through this
+starting with a a frequency t sub i
+
+ align:start position:0%
+starting with a a frequency t sub i
+ 
+
+ align:start position:0%
+starting with a a frequency t sub i
+for where
+
+ align:start position:0%
+for where
+ 
+
+ align:start position:0%
+for where
+i is the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of mutants in a population size n
+
+ align:start position:0%
+number of mutants in a population size n
+ 
+
+ align:start position:0%
+number of mutants in a population size n
+so here and
+
+ align:start position:0%
+so here and
+ 
+
+ align:start position:0%
+so here and
+down at the bottom is i mutants have
+
+ align:start position:0%
+down at the bottom is i mutants have
+ 
+
+ align:start position:0%
+down at the bottom is i mutants have
+population size then and we'll see that
+
+ align:start position:0%
+population size then and we'll see that
+ 
+
+ align:start position:0%
+population size then and we'll see that
+applying the mutation
+
+ align:start position:0%
+applying the mutation
+ 
+
+ align:start position:0%
+applying the mutation
+applying the selection and applying the
+
+ align:start position:0%
+applying the selection and applying the
+ 
+
+ align:start position:0%
+applying the selection and applying the
+drift are all applications of binomial
+
+ align:start position:0%
+drift are all applications of binomial
+ 
+
+ align:start position:0%
+drift are all applications of binomial
+distributions when we're talking about
+
+ align:start position:0%
+distributions when we're talking about
+ 
+
+ align:start position:0%
+distributions when we're talking about
+this discrete population of individuals
+
+ align:start position:0%
+this discrete population of individuals
+ 
+
+ align:start position:0%
+this discrete population of individuals
+it makes remember that the three
+
+ align:start position:0%
+it makes remember that the three
+ 
+
+ align:start position:0%
+it makes remember that the three
+bell-shaped curves are
+
+ align:start position:0%
+bell-shaped curves are
+ 
+
+ align:start position:0%
+bell-shaped curves are
+curves that can be bell-shaped
+
+ align:start position:0%
+curves that can be bell-shaped
+ 
+
+ align:start position:0%
+curves that can be bell-shaped
+here it's clearly a discrete uh
+
+ align:start position:0%
+here it's clearly a discrete uh
+ 
+
+ align:start position:0%
+here it's clearly a discrete uh
+population because we have in
+
+ align:start position:0%
+population because we have in
+ 
+
+ align:start position:0%
+population because we have in
+individuals taking i mutants at a time
+
+ align:start position:0%
+individuals taking i mutants at a time
+ 
+
+ align:start position:0%
+individuals taking i mutants at a time
+so we have so the binomials that we'll
+
+ align:start position:0%
+so we have so the binomials that we'll
+ 
+
+ align:start position:0%
+so we have so the binomials that we'll
+be using all all three processes have
+
+ align:start position:0%
+be using all all three processes have
+ 
+
+ align:start position:0%
+be using all all three processes have
+the same form where you have a
+
+ align:start position:0%
+the same form where you have a
+ 
+
+ align:start position:0%
+the same form where you have a
+combination of of some population n and
+
+ align:start position:0%
+combination of of some population n and
+ 
+
+ align:start position:0%
+combination of of some population n and
+a sub population i and of course the
+
+ align:start position:0%
+a sub population i and of course the
+ 
+
+ align:start position:0%
+a sub population i and of course the
+recipe the remainder is n minus i
+
+ align:start position:0%
+recipe the remainder is n minus i
+ 
+
+ align:start position:0%
+recipe the remainder is n minus i
+and that comp the different combinations
+
+ align:start position:0%
+and that comp the different combinations
+ 
+
+ align:start position:0%
+and that comp the different combinations
+are times some probability this
+
+ align:start position:0%
+are times some probability this
+ 
+
+ align:start position:0%
+are times some probability this
+probability is the
+
+ align:start position:0%
+probability is the
+ 
+
+ align:start position:0%
+probability is the
+is the last
+
+ align:start position:0%
+is the last
+ 
+
+ align:start position:0%
+is the last
+parameter in the binomial here which a
+
+ align:start position:0%
+parameter in the binomial here which a
+ 
+
+ align:start position:0%
+parameter in the binomial here which a
+binomial is a function of the n i and p
+
+ align:start position:0%
+binomial is a function of the n i and p
+ 
+
+ align:start position:0%
+binomial is a function of the n i and p
+the population size sub population size
+
+ align:start position:0%
+the population size sub population size
+ 
+
+ align:start position:0%
+the population size sub population size
+and some frequency it can be either a
+
+ align:start position:0%
+and some frequency it can be either a
+ 
+
+ align:start position:0%
+and some frequency it can be either a
+forward or reverse mutation frequency it
+
+ align:start position:0%
+forward or reverse mutation frequency it
+ 
+
+ align:start position:0%
+forward or reverse mutation frequency it
+can be a selection
+
+ align:start position:0%
+can be a selection
+ 
+
+ align:start position:0%
+can be a selection
+probability or it can be a drift
+
+ align:start position:0%
+probability or it can be a drift
+ 
+
+ align:start position:0%
+probability or it can be a drift
+probability and we'll see how each of
+
+ align:start position:0%
+probability and we'll see how each of
+ 
+
+ align:start position:0%
+probability and we'll see how each of
+these work out
+
+ align:start position:0%
+these work out
+ 
+
+ align:start position:0%
+these work out
+so let's we start with a a frequency
+
+ align:start position:0%
+so let's we start with a a frequency
+ 
+
+ align:start position:0%
+so let's we start with a a frequency
+of i you can have i ranges from 0 to n
+
+ align:start position:0%
+of i you can have i ranges from 0 to n
+ 
+
+ align:start position:0%
+of i you can have i ranges from 0 to n
+you could have
+
+ align:start position:0%
+you could have
+ 
+
+ align:start position:0%
+you could have
+if i is
+
+ align:start position:0%
+if i is
+ 
+
+ align:start position:0%
+if i is
+0 then the frequency is zero over n or
+
+ align:start position:0%
+0 then the frequency is zero over n or
+ 
+
+ align:start position:0%
+0 then the frequency is zero over n or
+zero if i is n it's n over n or
+
+ align:start position:0%
+zero if i is n it's n over n or
+ 
+
+ align:start position:0%
+zero if i is n it's n over n or
+frequency is a hundred percent just that
+
+ align:start position:0%
+frequency is a hundred percent just that
+ 
+
+ align:start position:0%
+frequency is a hundred percent just that
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+vertical axis we had in all previous
+
+ align:start position:0%
+vertical axis we had in all previous
+ 
+
+ align:start position:0%
+vertical axis we had in all previous
+slides
+
+ align:start position:0%
+slides
+ 
+
+ align:start position:0%
+slides
+the starting frequencies have some
+
+ align:start position:0%
+the starting frequencies have some
+ 
+
+ align:start position:0%
+the starting frequencies have some
+distribution t t sub i for i going from
+
+ align:start position:0%
+distribution t t sub i for i going from
+ 
+
+ align:start position:0%
+distribution t t sub i for i going from
+one zero to n
+
+ align:start position:0%
+one zero to n
+ 
+
+ align:start position:0%
+one zero to n
+and we want now i want to derive a new
+
+ align:start position:0%
+and we want now i want to derive a new
+ 
+
+ align:start position:0%
+and we want now i want to derive a new
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+vector of
+
+ align:start position:0%
+vector of
+ 
+
+ align:start position:0%
+vector of
+frequencies which would be m
+
+ align:start position:0%
+frequencies which would be m
+ 
+
+ align:start position:0%
+frequencies which would be m
+and all we do is we apply the binomial
+
+ align:start position:0%
+and all we do is we apply the binomial
+ 
+
+ align:start position:0%
+and all we do is we apply the binomial
+distribution for the forward process of
+
+ align:start position:0%
+distribution for the forward process of
+ 
+
+ align:start position:0%
+distribution for the forward process of
+forward mutation and then
+
+ align:start position:0%
+forward mutation and then
+ 
+
+ align:start position:0%
+forward mutation and then
+once we're done with that we apply
+
+ align:start position:0%
+once we're done with that we apply
+ 
+
+ align:start position:0%
+once we're done with that we apply
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we now use the new the m's and adjust it
+
+ align:start position:0%
+we now use the new the m's and adjust it
+ 
+
+ align:start position:0%
+we now use the new the m's and adjust it
+so that's now give a chance to do the
+
+ align:start position:0%
+so that's now give a chance to do the
+ 
+
+ align:start position:0%
+so that's now give a chance to do the
+reverse mutation because you'll generate
+
+ align:start position:0%
+reverse mutation because you'll generate
+ 
+
+ align:start position:0%
+reverse mutation because you'll generate
+this binomial distribution forwards and
+
+ align:start position:0%
+this binomial distribution forwards and
+ 
+
+ align:start position:0%
+this binomial distribution forwards and
+then you'll give them a chance to to
+
+ align:start position:0%
+then you'll give them a chance to to
+ 
+
+ align:start position:0%
+then you'll give them a chance to to
+revert
+
+ align:start position:0%
+revert
+ 
+
+ align:start position:0%
+revert
+then you apply selection a new binomial
+
+ align:start position:0%
+then you apply selection a new binomial
+ 
+
+ align:start position:0%
+then you apply selection a new binomial
+now here the probability of a transition
+
+ align:start position:0%
+now here the probability of a transition
+ 
+
+ align:start position:0%
+now here the probability of a transition
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+your mutants
+
+ align:start position:0%
+your mutants
+ 
+
+ align:start position:0%
+your mutants
+starting with t then you go to m now to
+
+ align:start position:0%
+starting with t then you go to m now to
+ 
+
+ align:start position:0%
+starting with t then you go to m now to
+get to s the transition probability is a
+
+ align:start position:0%
+get to s the transition probability is a
+ 
+
+ align:start position:0%
+get to s the transition probability is a
+function of this
+
+ align:start position:0%
+function of this
+ 
+
+ align:start position:0%
+function of this
+fitness remember w and s fitness and
+
+ align:start position:0%
+fitness remember w and s fitness and
+ 
+
+ align:start position:0%
+fitness remember w and s fitness and
+selection
+
+ align:start position:0%
+selection
+ 
+
+ align:start position:0%
+selection
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the fitness determines a probability
+
+ align:start position:0%
+the the fitness determines a probability
+ 
+
+ align:start position:0%
+the the fitness determines a probability
+of a transition
+
+ align:start position:0%
+of a transition
+ 
+
+ align:start position:0%
+of a transition
+in a in a binomial distribution and
+
+ align:start position:0%
+in a in a binomial distribution and
+ 
+
+ align:start position:0%
+in a in a binomial distribution and
+there's there's two slightly different
+
+ align:start position:0%
+there's there's two slightly different
+ 
+
+ align:start position:0%
+there's there's two slightly different
+uh equations that you use depending on
+
+ align:start position:0%
+uh equations that you use depending on
+ 
+
+ align:start position:0%
+uh equations that you use depending on
+whether the fitness is
+
+ align:start position:0%
+whether the fitness is
+ 
+
+ align:start position:0%
+whether the fitness is
+uh greater than one or less than one in
+
+ align:start position:0%
+uh greater than one or less than one in
+ 
+
+ align:start position:0%
+uh greater than one or less than one in
+other words whether it has a tendency to
+
+ align:start position:0%
+other words whether it has a tendency to
+ 
+
+ align:start position:0%
+other words whether it has a tendency to
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+um with time
+
+ align:start position:0%
+um with time
+ 
+
+ align:start position:0%
+um with time
+due to selection or to decrease that
+
+ align:start position:0%
+due to selection or to decrease that
+ 
+
+ align:start position:0%
+due to selection or to decrease that
+allele with time as a function of
+
+ align:start position:0%
+allele with time as a function of
+ 
+
+ align:start position:0%
+allele with time as a function of
+selection and then that's what these two
+
+ align:start position:0%
+selection and then that's what these two
+ 
+
+ align:start position:0%
+selection and then that's what these two
+cases are here
+
+ align:start position:0%
+cases are here
+ 
+
+ align:start position:0%
+cases are here
+and then finally you have after you've
+
+ align:start position:0%
+and then finally you have after you've
+ 
+
+ align:start position:0%
+and then finally you have after you've
+applied forward inverse mutation and
+
+ align:start position:0%
+applied forward inverse mutation and
+ 
+
+ align:start position:0%
+applied forward inverse mutation and
+selection whether it's more fit or less
+
+ align:start position:0%
+selection whether it's more fit or less
+ 
+
+ align:start position:0%
+selection whether it's more fit or less
+fit than
+
+ align:start position:0%
+fit than
+ 
+
+ align:start position:0%
+fit than
+then you apply drift now drift just
+
+ align:start position:0%
+then you apply drift now drift just
+ 
+
+ align:start position:0%
+then you apply drift now drift just
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if you have a small popular think of if
+
+ align:start position:0%
+if you have a small popular think of if
+ 
+
+ align:start position:0%
+if you have a small popular think of if
+you have a small population of uh
+
+ align:start position:0%
+you have a small population of uh
+ 
+
+ align:start position:0%
+you have a small population of uh
+individuals let's say they're
+
+ align:start position:0%
+individuals let's say they're
+ 
+
+ align:start position:0%
+individuals let's say they're
+you know a set of colored balls in a jar
+
+ align:start position:0%
+you know a set of colored balls in a jar
+ 
+
+ align:start position:0%
+you know a set of colored balls in a jar
+in front of us here it's a small number
+
+ align:start position:0%
+in front of us here it's a small number
+ 
+
+ align:start position:0%
+in front of us here it's a small number
+and i pull a handful out
+
+ align:start position:0%
+and i pull a handful out
+ 
+
+ align:start position:0%
+and i pull a handful out
+because in each generation you're gonna
+
+ align:start position:0%
+because in each generation you're gonna
+ 
+
+ align:start position:0%
+because in each generation you're gonna
+you're gonna duplicate the population
+
+ align:start position:0%
+you're gonna duplicate the population
+ 
+
+ align:start position:0%
+you're gonna duplicate the population
+but remember the assumption of constant
+
+ align:start position:0%
+but remember the assumption of constant
+ 
+
+ align:start position:0%
+but remember the assumption of constant
+population size if i pull out
+
+ align:start position:0%
+population size if i pull out
+ 
+
+ align:start position:0%
+population size if i pull out
+the new generation and forget about the
+
+ align:start position:0%
+the new generation and forget about the
+ 
+
+ align:start position:0%
+the new generation and forget about the
+the rest of the duplicated they could
+
+ align:start position:0%
+the rest of the duplicated they could
+ 
+
+ align:start position:0%
+the rest of the duplicated they could
+all be the same color and that's the
+
+ align:start position:0%
+all be the same color and that's the
+ 
+
+ align:start position:0%
+all be the same color and that's the
+chance you could drift to fixation where
+
+ align:start position:0%
+chance you could drift to fixation where
+ 
+
+ align:start position:0%
+chance you could drift to fixation where
+one of them
+
+ align:start position:0%
+one of them
+ 
+
+ align:start position:0%
+one of them
+now dominates not because it's superior
+
+ align:start position:0%
+now dominates not because it's superior
+ 
+
+ align:start position:0%
+now dominates not because it's superior
+from a selection standpoint not because
+
+ align:start position:0%
+from a selection standpoint not because
+ 
+
+ align:start position:0%
+from a selection standpoint not because
+it's been uh you know mutated in a
+
+ align:start position:0%
+it's been uh you know mutated in a
+ 
+
+ align:start position:0%
+it's been uh you know mutated in a
+directed way to that point but just
+
+ align:start position:0%
+directed way to that point but just
+ 
+
+ align:start position:0%
+directed way to that point but just
+because of random drift that you have a
+
+ align:start position:0%
+because of random drift that you have a
+ 
+
+ align:start position:0%
+because of random drift that you have a
+constant population
+
+ align:start position:0%
+constant population
+ 
+
+ align:start position:0%
+constant population
+and uh and you and so you can see how
+
+ align:start position:0%
+and uh and you and so you can see how
+ 
+
+ align:start position:0%
+and uh and you and so you can see how
+that would depend on how many are in the
+
+ align:start position:0%
+that would depend on how many are in the
+ 
+
+ align:start position:0%
+that would depend on how many are in the
+in the jar if i take half of them out of
+
+ align:start position:0%
+in the jar if i take half of them out of
+ 
+
+ align:start position:0%
+in the jar if i take half of them out of
+the jar and and the jar only has five in
+
+ align:start position:0%
+the jar and and the jar only has five in
+ 
+
+ align:start position:0%
+the jar and and the jar only has five in
+it then it's a hot much higher chance it
+
+ align:start position:0%
+it then it's a hot much higher chance it
+ 
+
+ align:start position:0%
+it then it's a hot much higher chance it
+will go to fixation quickly than if the
+
+ align:start position:0%
+will go to fixation quickly than if the
+ 
+
+ align:start position:0%
+will go to fixation quickly than if the
+jar has millions in it if i take half of
+
+ align:start position:0%
+jar has millions in it if i take half of
+ 
+
+ align:start position:0%
+jar has millions in it if i take half of
+half a million out it's very likely that
+
+ align:start position:0%
+half a million out it's very likely that
+ 
+
+ align:start position:0%
+half a million out it's very likely that
+it will still be the more or less the
+
+ align:start position:0%
+it will still be the more or less the
+ 
+
+ align:start position:0%
+it will still be the more or less the
+same ratios and this is exactly how it
+
+ align:start position:0%
+same ratios and this is exactly how it
+ 
+
+ align:start position:0%
+same ratios and this is exactly how it
+plays out when you look at
+
+ align:start position:0%
+plays out when you look at
+ 
+
+ align:start position:0%
+plays out when you look at
+random genetic drift it's very dependent
+
+ align:start position:0%
+random genetic drift it's very dependent
+ 
+
+ align:start position:0%
+random genetic drift it's very dependent
+on population size so here here are
+
+ align:start position:0%
+on population size so here here are
+ 
+
+ align:start position:0%
+on population size so here here are
+simulations going out to say 150
+
+ align:start position:0%
+simulations going out to say 150
+ 
+
+ align:start position:0%
+simulations going out to say 150
+generations on the horizontal axis and
+
+ align:start position:0%
+generations on the horizontal axis and
+ 
+
+ align:start position:0%
+generations on the horizontal axis and
+the allele frequency as usual going from
+
+ align:start position:0%
+the allele frequency as usual going from
+ 
+
+ align:start position:0%
+the allele frequency as usual going from
+zero to 100 percent
+
+ align:start position:0%
+zero to 100 percent
+ 
+
+ align:start position:0%
+zero to 100 percent
+and they we start with a population with
+
+ align:start position:0%
+and they we start with a population with
+ 
+
+ align:start position:0%
+and they we start with a population with
+50 50 ratio of two alleles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you see is if the population
+
+ align:start position:0%
+and what you see is if the population
+ 
+
+ align:start position:0%
+and what you see is if the population
+the number of individuals is only 25
+
+ align:start position:0%
+the number of individuals is only 25
+ 
+
+ align:start position:0%
+the number of individuals is only 25
+then you quickly fix maybe in a few
+
+ align:start position:0%
+then you quickly fix maybe in a few
+ 
+
+ align:start position:0%
+then you quickly fix maybe in a few
+generate maybe
+
+ align:start position:0%
+generate maybe
+ 
+
+ align:start position:0%
+generate maybe
+uh 30 generations you can and this this
+
+ align:start position:0%
+uh 30 generations you can and this this
+ 
+
+ align:start position:0%
+uh 30 generations you can and this this
+is anecdotal of get fixation
+
+ align:start position:0%
+is anecdotal of get fixation
+ 
+
+ align:start position:0%
+is anecdotal of get fixation
+as it goes up to a population size of
+
+ align:start position:0%
+as it goes up to a population size of
+ 
+
+ align:start position:0%
+as it goes up to a population size of
+2500 you can see it for all intensive
+
+ align:start position:0%
+2500 you can see it for all intensive
+ 
+
+ align:start position:0%
+2500 you can see it for all intensive
+purposes it's flat it will eventually
+
+ align:start position:0%
+purposes it's flat it will eventually
+ 
+
+ align:start position:0%
+purposes it's flat it will eventually
+fix i assure you this simulation if you
+
+ align:start position:0%
+fix i assure you this simulation if you
+ 
+
+ align:start position:0%
+fix i assure you this simulation if you
+run it long enough it
+
+ align:start position:0%
+run it long enough it
+ 
+
+ align:start position:0%
+run it long enough it
+one of the two alleles will go to zero
+
+ align:start position:0%
+one of the two alleles will go to zero
+ 
+
+ align:start position:0%
+one of the two alleles will go to zero
+and the other one will go to 100 percent
+
+ align:start position:0%
+and the other one will go to 100 percent
+ 
+
+ align:start position:0%
+and the other one will go to 100 percent
+and you do another simulation and it may
+
+ align:start position:0%
+and you do another simulation and it may
+ 
+
+ align:start position:0%
+and you do another simulation and it may
+be the other one because this is random
+
+ align:start position:0%
+be the other one because this is random
+ 
+
+ align:start position:0%
+be the other one because this is random
+drift not selection
+
+ align:start position:0%
+drift not selection
+ 
+
+ align:start position:0%
+drift not selection
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so you can see the final frequencies are
+
+ align:start position:0%
+so you can see the final frequencies are
+ 
+
+ align:start position:0%
+so you can see the final frequencies are
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+some complicated function of mutation
+
+ align:start position:0%
+some complicated function of mutation
+ 
+
+ align:start position:0%
+some complicated function of mutation
+rates and selection rates and drift
+
+ align:start position:0%
+rates and selection rates and drift
+ 
+
+ align:start position:0%
+rates and selection rates and drift
+rates and pop which and that last one is
+
+ align:start position:0%
+rates and pop which and that last one is
+ 
+
+ align:start position:0%
+rates and pop which and that last one is
+a function of population size
+
+ align:start position:0%
+a function of population size
+ 
+
+ align:start position:0%
+a function of population size
+when the drift when the population size
+
+ align:start position:0%
+when the drift when the population size
+ 
+
+ align:start position:0%
+when the drift when the population size
+is very very large you can see that's
+
+ align:start position:0%
+is very very large you can see that's
+ 
+
+ align:start position:0%
+is very very large you can see that's
+going to be constant enough that's why
+
+ align:start position:0%
+going to be constant enough that's why
+ 
+
+ align:start position:0%
+going to be constant enough that's why
+you can see very subtle differences in
+
+ align:start position:0%
+you can see very subtle differences in
+ 
+
+ align:start position:0%
+you can see very subtle differences in
+selection coefficient
+
+ align:start position:0%
+selection coefficient
+ 
+
+ align:start position:0%
+selection coefficient
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we're going to come back to the
+
+ align:start position:0%
+now we're going to come back to the
+ 
+
+ align:start position:0%
+now we're going to come back to the
+mutation selection and drift in the
+
+ align:start position:0%
+mutation selection and drift in the
+ 
+
+ align:start position:0%
+mutation selection and drift in the
+context of human genetics in just a
+
+ align:start position:0%
+context of human genetics in just a
+ 
+
+ align:start position:0%
+context of human genetics in just a
+moment but first i want to tell you the
+
+ align:start position:0%
+moment but first i want to tell you the
+ 
+
+ align:start position:0%
+moment but first i want to tell you the
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+uh component of population genetics
+
+ align:start position:0%
+uh component of population genetics
+ 
+
+ align:start position:0%
+uh component of population genetics
+that we'll be talking about which is
+
+ align:start position:0%
+that we'll be talking about which is
+ 
+
+ align:start position:0%
+that we'll be talking about which is
+recombination now this doesn't occur in
+
+ align:start position:0%
+recombination now this doesn't occur in
+ 
+
+ align:start position:0%
+recombination now this doesn't occur in
+every biological system i made the
+
+ align:start position:0%
+every biological system i made the
+ 
+
+ align:start position:0%
+every biological system i made the
+argument before that mutation
+
+ align:start position:0%
+argument before that mutation
+ 
+
+ align:start position:0%
+argument before that mutation
+selection and drift occurs in every
+
+ align:start position:0%
+selection and drift occurs in every
+ 
+
+ align:start position:0%
+selection and drift occurs in every
+biological system from cells to
+
+ align:start position:0%
+biological system from cells to
+ 
+
+ align:start position:0%
+biological system from cells to
+organisms of all types
+
+ align:start position:0%
+organisms of all types
+ 
+
+ align:start position:0%
+organisms of all types
+those that in those biological systems
+
+ align:start position:0%
+those that in those biological systems
+ 
+
+ align:start position:0%
+those that in those biological systems
+where dna can be exchanged by
+
+ align:start position:0%
+where dna can be exchanged by
+ 
+
+ align:start position:0%
+where dna can be exchanged by
+transduction transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meiotic fusion and so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you can get recombination and these
+
+ align:start position:0%
+then you can get recombination and these
+ 
+
+ align:start position:0%
+then you can get recombination and these
+two figures illustrate that on the
+
+ align:start position:0%
+two figures illustrate that on the
+ 
+
+ align:start position:0%
+two figures illustrate that on the
+left-hand side
+
+ align:start position:0%
+left-hand side
+ 
+
+ align:start position:0%
+left-hand side
+of slide 19 is the
+
+ align:start position:0%
+of slide 19 is the
+ 
+
+ align:start position:0%
+of slide 19 is the
+non-recombination scenario and on the
+
+ align:start position:0%
+non-recombination scenario and on the
+ 
+
+ align:start position:0%
+non-recombination scenario and on the
+right hand side
+
+ align:start position:0%
+right hand side
+ 
+
+ align:start position:0%
+right hand side
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+sexual or recombination mediated
+
+ align:start position:0%
+sexual or recombination mediated
+ 
+
+ align:start position:0%
+sexual or recombination mediated
+gene
+
+ align:start position:0%
+gene
+ 
+
+ align:start position:0%
+gene
+change in gene combinations so let's
+
+ align:start position:0%
+change in gene combinations so let's
+ 
+
+ align:start position:0%
+change in gene combinations so let's
+look at this time is going horizontally
+
+ align:start position:0%
+look at this time is going horizontally
+ 
+
+ align:start position:0%
+look at this time is going horizontally
+and you can see at the very begi at the
+
+ align:start position:0%
+and you can see at the very begi at the
+ 
+
+ align:start position:0%
+and you can see at the very begi at the
+very left-hand side the beginning of
+
+ align:start position:0%
+very left-hand side the beginning of
+ 
+
+ align:start position:0%
+very left-hand side the beginning of
+each of these scenarios you get
+
+ align:start position:0%
+each of these scenarios you get
+ 
+
+ align:start position:0%
+each of these scenarios you get
+a certain rate of occurrence of
+
+ align:start position:0%
+a certain rate of occurrence of
+ 
+
+ align:start position:0%
+a certain rate of occurrence of
+mutations this is based on the forward
+
+ align:start position:0%
+mutations this is based on the forward
+ 
+
+ align:start position:0%
+mutations this is based on the forward
+mutation rate in our previous um
+
+ align:start position:0%
+mutation rate in our previous um
+ 
+
+ align:start position:0%
+mutation rate in our previous um
+equations and they occur very early on a
+
+ align:start position:0%
+equations and they occur very early on a
+ 
+
+ align:start position:0%
+equations and they occur very early on a
+b and c all occur
+
+ align:start position:0%
+b and c all occur
+ 
+
+ align:start position:0%
+b and c all occur
+but they tend to die out because of
+
+ align:start position:0%
+but they tend to die out because of
+ 
+
+ align:start position:0%
+but they tend to die out because of
+because of drift
+
+ align:start position:0%
+because of drift
+ 
+
+ align:start position:0%
+because of drift
+okay and the population size is small
+
+ align:start position:0%
+okay and the population size is small
+ 
+
+ align:start position:0%
+okay and the population size is small
+enough that this is about that that half
+
+ align:start position:0%
+enough that this is about that that half
+ 
+
+ align:start position:0%
+enough that this is about that that half
+of them die out and one of them fixes
+
+ align:start position:0%
+of them die out and one of them fixes
+ 
+
+ align:start position:0%
+of them die out and one of them fixes
+okay and a is destined to fix it but it
+
+ align:start position:0%
+okay and a is destined to fix it but it
+ 
+
+ align:start position:0%
+okay and a is destined to fix it but it
+takes some time for it to fix and until
+
+ align:start position:0%
+takes some time for it to fix and until
+ 
+
+ align:start position:0%
+takes some time for it to fix and until
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+a huge front it starts at a frequency
+
+ align:start position:0%
+a huge front it starts at a frequency
+ 
+
+ align:start position:0%
+a huge front it starts at a frequency
+close to zero and by the time it's fifty
+
+ align:start position:0%
+close to zero and by the time it's fifty
+ 
+
+ align:start position:0%
+close to zero and by the time it's fifty
+percent to a hundred percent it's ready
+
+ align:start position:0%
+percent to a hundred percent it's ready
+ 
+
+ align:start position:0%
+percent to a hundred percent it's ready
+to start picking up a second mutation at
+
+ align:start position:0%
+to start picking up a second mutation at
+ 
+
+ align:start position:0%
+to start picking up a second mutation at
+the same frequency they were occurring
+
+ align:start position:0%
+the same frequency they were occurring
+ 
+
+ align:start position:0%
+the same frequency they were occurring
+before now you can pick up the b
+
+ align:start position:0%
+before now you can pick up the b
+ 
+
+ align:start position:0%
+before now you can pick up the b
+mutations while the c dies off you know
+
+ align:start position:0%
+mutations while the c dies off you know
+ 
+
+ align:start position:0%
+mutations while the c dies off you know
+it comes and goes due to drift
+
+ align:start position:0%
+it comes and goes due to drift
+ 
+
+ align:start position:0%
+it comes and goes due to drift
+and finally
+
+ align:start position:0%
+and finally
+ 
+
+ align:start position:0%
+and finally
+once a b fixes then you can pick up the
+
+ align:start position:0%
+once a b fixes then you can pick up the
+ 
+
+ align:start position:0%
+once a b fixes then you can pick up the
+c and you get abc that was a long slow
+
+ align:start position:0%
+c and you get abc that was a long slow
+ 
+
+ align:start position:0%
+c and you get abc that was a long slow
+serial process
+
+ align:start position:0%
+serial process
+ 
+
+ align:start position:0%
+serial process
+on the right hand side we see the what
+
+ align:start position:0%
+on the right hand side we see the what
+ 
+
+ align:start position:0%
+on the right hand side we see the what
+can happen in the in the case of of
+
+ align:start position:0%
+can happen in the in the case of of
+ 
+
+ align:start position:0%
+can happen in the in the case of of
+exchange of genetic material in a freely
+
+ align:start position:0%
+exchange of genetic material in a freely
+ 
+
+ align:start position:0%
+exchange of genetic material in a freely
+mixing population is now that a b and c
+
+ align:start position:0%
+mixing population is now that a b and c
+ 
+
+ align:start position:0%
+mixing population is now that a b and c
+all occur
+
+ align:start position:0%
+all occur
+ 
+
+ align:start position:0%
+all occur
+at the same frequency as on the left but
+
+ align:start position:0%
+at the same frequency as on the left but
+ 
+
+ align:start position:0%
+at the same frequency as on the left but
+now because they're exchanging
+
+ align:start position:0%
+now because they're exchanging
+ 
+
+ align:start position:0%
+now because they're exchanging
+information very early on before b has a
+
+ align:start position:0%
+information very early on before b has a
+ 
+
+ align:start position:0%
+information very early on before b has a
+chance
+
+ align:start position:0%
+chance
+ 
+
+ align:start position:0%
+chance
+to die off due to drift it combines its
+
+ align:start position:0%
+to die off due to drift it combines its
+ 
+
+ align:start position:0%
+to die off due to drift it combines its
+dna with a and you get a b
+
+ align:start position:0%
+dna with a and you get a b
+ 
+
+ align:start position:0%
+dna with a and you get a b
+and some of the small a population is
+
+ align:start position:0%
+and some of the small a population is
+ 
+
+ align:start position:0%
+and some of the small a population is
+destined to be fixed anyway but happens
+
+ align:start position:0%
+destined to be fixed anyway but happens
+ 
+
+ align:start position:0%
+destined to be fixed anyway but happens
+to combine with
+
+ align:start position:0%
+to combine with
+ 
+
+ align:start position:0%
+to combine with
+c and again before before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drift can wipe them out
+
+ align:start position:0%
+drift can wipe them out
+ 
+
+ align:start position:0%
+drift can wipe them out
+selection
+
+ align:start position:0%
+selection
+ 
+
+ align:start position:0%
+selection
+the very small selection that you have
+
+ align:start position:0%
+the very small selection that you have
+ 
+
+ align:start position:0%
+the very small selection that you have
+that couldn't overcome drift in the in
+
+ align:start position:0%
+that couldn't overcome drift in the in
+ 
+
+ align:start position:0%
+that couldn't overcome drift in the in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+left-hand panel now fixes them all the
+
+ align:start position:0%
+left-hand panel now fixes them all the
+ 
+
+ align:start position:0%
+left-hand panel now fixes them all the
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+favorable combination of a b and c very
+
+ align:start position:0%
+favorable combination of a b and c very
+ 
+
+ align:start position:0%
+favorable combination of a b and c very
+early on and so
+
+ align:start position:0%
+early on and so
+ 
+
+ align:start position:0%
+early on and so
+there is there's a whole series of
+
+ align:start position:0%
+there is there's a whole series of
+ 
+
+ align:start position:0%
+there is there's a whole series of
+arguments and counter arguments in the
+
+ align:start position:0%
+arguments and counter arguments in the
+ 
+
+ align:start position:0%
+arguments and counter arguments in the
+population genetics literature about why
+
+ align:start position:0%
+population genetics literature about why
+ 
+
+ align:start position:0%
+population genetics literature about why
+is there sex of course you know we all
+
+ align:start position:0%
+is there sex of course you know we all
+ 
+
+ align:start position:0%
+is there sex of course you know we all
+know uh we have our own reasons but but
+
+ align:start position:0%
+know uh we have our own reasons but but
+ 
+
+ align:start position:0%
+know uh we have our own reasons but but
+in here they say there's a huge cost the
+
+ align:start position:0%
+in here they say there's a huge cost the
+ 
+
+ align:start position:0%
+in here they say there's a huge cost the
+count the counter argument is there's a
+
+ align:start position:0%
+count the counter argument is there's a
+ 
+
+ align:start position:0%
+count the counter argument is there's a
+there's a huge cost of having two
+
+ align:start position:0%
+there's a huge cost of having two
+ 
+
+ align:start position:0%
+there's a huge cost of having two
+genders uh maybe as much as fifty
+
+ align:start position:0%
+genders uh maybe as much as fifty
+ 
+
+ align:start position:0%
+genders uh maybe as much as fifty
+percent possibly higher
+
+ align:start position:0%
+percent possibly higher
+ 
+
+ align:start position:0%
+percent possibly higher
+uh because they don't they have uh they
+
+ align:start position:0%
+uh because they don't they have uh they
+ 
+
+ align:start position:0%
+uh because they don't they have uh they
+have different morphologies and
+
+ align:start position:0%
+have different morphologies and
+ 
+
+ align:start position:0%
+have different morphologies and
+different capabilities and so on
+
+ align:start position:0%
+different capabilities and so on
+ 
+
+ align:start position:0%
+different capabilities and so on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but then there's this benefit this is
+
+ align:start position:0%
+but then there's this benefit this is
+ 
+
+ align:start position:0%
+but then there's this benefit this is
+the risk and the benefit is the earlier
+
+ align:start position:0%
+the risk and the benefit is the earlier
+ 
+
+ align:start position:0%
+the risk and the benefit is the earlier
+recombination but then there's counter
+
+ align:start position:0%
+recombination but then there's counter
+ 
+
+ align:start position:0%
+recombination but then there's counter
+arguments and so forth that we won't go
+
+ align:start position:0%
+arguments and so forth that we won't go
+ 
+
+ align:start position:0%
+arguments and so forth that we won't go
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+oh yeah
+
+ align:start position:0%
+oh yeah
+ 
+
+ align:start position:0%
+oh yeah
+what if actually random what is it that
+
+ align:start position:0%
+what if actually random what is it that
+ 
+
+ align:start position:0%
+what if actually random what is it that
+causes either a real fix
+
+ align:start position:0%
+causes either a real fix
+ 
+
+ align:start position:0%
+causes either a real fix
+if you have two different elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why wouldn't it just eventually
+
+ align:start position:0%
+why wouldn't it just eventually
+ 
+
+ align:start position:0%
+why wouldn't it just eventually
+come back well it can you can see here
+
+ align:start position:0%
+come back well it can you can see here
+ 
+
+ align:start position:0%
+come back well it can you can see here
+uh that it's it's starting to head so
+
+ align:start position:0%
+uh that it's it's starting to head so
+ 
+
+ align:start position:0%
+uh that it's it's starting to head so
+that it's fixing uh on on one allele and
+
+ align:start position:0%
+that it's fixing uh on on one allele and
+ 
+
+ align:start position:0%
+that it's fixing uh on on one allele and
+it changes direction and it fixes the
+
+ align:start position:0%
+it changes direction and it fixes the
+ 
+
+ align:start position:0%
+it changes direction and it fixes the
+other one so it can it can go all the
+
+ align:start position:0%
+other one so it can it can go all the
+ 
+
+ align:start position:0%
+other one so it can it can go all the
+way down to to
+
+ align:start position:0%
+way down to to
+ 
+
+ align:start position:0%
+way down to to
+to close to zero and then bounce back up
+
+ align:start position:0%
+to close to zero and then bounce back up
+ 
+
+ align:start position:0%
+to close to zero and then bounce back up
+and it's all this is just some typical
+
+ align:start position:0%
+and it's all this is just some typical
+ 
+
+ align:start position:0%
+and it's all this is just some typical
+simulations here uh if you do enough of
+
+ align:start position:0%
+simulations here uh if you do enough of
+ 
+
+ align:start position:0%
+simulations here uh if you do enough of
+these you'll find every possible
+
+ align:start position:0%
+these you'll find every possible
+ 
+
+ align:start position:0%
+these you'll find every possible
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+um it's cool basically eventually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will fix you can't necessarily
+
+ align:start position:0%
+it will fix you can't necessarily
+ 
+
+ align:start position:0%
+it will fix you can't necessarily
+predict which one will fix on
+
+ align:start position:0%
+predict which one will fix on
+ 
+
+ align:start position:0%
+predict which one will fix on
+half you know if there's no selection
+
+ align:start position:0%
+half you know if there's no selection
+ 
+
+ align:start position:0%
+half you know if there's no selection
+half the time it will fix on one half on
+
+ align:start position:0%
+half the time it will fix on one half on
+ 
+
+ align:start position:0%
+half the time it will fix on one half on
+the other if they start out at a
+
+ align:start position:0%
+the other if they start out at a
+ 
+
+ align:start position:0%
+the other if they start out at a
+frequency of 50 50.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but you have to think of it in the
+
+ align:start position:0%
+but you have to think of it in the
+ 
+
+ align:start position:0%
+but you have to think of it in the
+context of mutation and selection too
+
+ align:start position:0%
+context of mutation and selection too
+ 
+
+ align:start position:0%
+context of mutation and selection too
+because they're all acting there and
+
+ align:start position:0%
+because they're all acting there and
+ 
+
+ align:start position:0%
+because they're all acting there and
+when you say that something is
+
+ align:start position:0%
+when you say that something is
+ 
+
+ align:start position:0%
+when you say that something is
+selectively neutral what you really mean
+
+ align:start position:0%
+selectively neutral what you really mean
+ 
+
+ align:start position:0%
+selectively neutral what you really mean
+i mean everything has some very very
+
+ align:start position:0%
+i mean everything has some very very
+ 
+
+ align:start position:0%
+i mean everything has some very very
+tiny selective coefficient but if that
+
+ align:start position:0%
+tiny selective coefficient but if that
+ 
+
+ align:start position:0%
+tiny selective coefficient but if that
+is if it's tiny enough then drift and
+
+ align:start position:0%
+is if it's tiny enough then drift and
+ 
+
+ align:start position:0%
+is if it's tiny enough then drift and
+the population size is small enough then
+
+ align:start position:0%
+the population size is small enough then
+ 
+
+ align:start position:0%
+the population size is small enough then
+drift will blind you and you can't see
+
+ align:start position:0%
+drift will blind you and you can't see
+ 
+
+ align:start position:0%
+drift will blind you and you can't see
+it but if you get really big populations
+
+ align:start position:0%
+it but if you get really big populations
+ 
+
+ align:start position:0%
+it but if you get really big populations
+then you'll get small drift and then
+
+ align:start position:0%
+then you'll get small drift and then
+ 
+
+ align:start position:0%
+then you'll get small drift and then
+you'll see
+
+ align:start position:0%
+you'll see
+ 
+
+ align:start position:0%
+you'll see
+subtle more subtle selection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the human population is very
+
+ align:start position:0%
+you know the human population is very
+ 
+
+ align:start position:0%
+you know the human population is very
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+some of the oceanic species are truly
+
+ align:start position:0%
+some of the oceanic species are truly
+ 
+
+ align:start position:0%
+some of the oceanic species are truly
+enormous so you need to think about that
+
+ align:start position:0%
+enormous so you need to think about that
+ 
+
+ align:start position:0%
+enormous so you need to think about that
+as a possibility so now let's talk about
+
+ align:start position:0%
+as a possibility so now let's talk about
+ 
+
+ align:start position:0%
+as a possibility so now let's talk about
+common diseases
+
+ align:start position:0%
+common diseases
+ 
+
+ align:start position:0%
+common diseases
+we have the question is
+
+ align:start position:0%
+we have the question is
+ 
+
+ align:start position:0%
+we have the question is
+uh our common diseases really to what
+
+ align:start position:0%
+uh our common diseases really to what
+ 
+
+ align:start position:0%
+uh our common diseases really to what
+extent are they caused by common
+
+ align:start position:0%
+extent are they caused by common
+ 
+
+ align:start position:0%
+extent are they caused by common
+variants clearly some of them are caused
+
+ align:start position:0%
+variants clearly some of them are caused
+ 
+
+ align:start position:0%
+variants clearly some of them are caused
+by common variants and we've said that
+
+ align:start position:0%
+by common variants and we've said that
+ 
+
+ align:start position:0%
+by common variants and we've said that
+well common variants really shouldn't be
+
+ align:start position:0%
+well common variants really shouldn't be
+ 
+
+ align:start position:0%
+well common variants really shouldn't be
+deleterious
+
+ align:start position:0%
+deleterious
+ 
+
+ align:start position:0%
+deleterious
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because they would be wiped out by
+
+ align:start position:0%
+because they would be wiped out by
+ 
+
+ align:start position:0%
+because they would be wiped out by
+selection
+
+ align:start position:0%
+selection
+ 
+
+ align:start position:0%
+selection
+they they could be very very mildly
+
+ align:start position:0%
+they they could be very very mildly
+ 
+
+ align:start position:0%
+they they could be very very mildly
+deleterious such that drift will
+
+ align:start position:0%
+deleterious such that drift will
+ 
+
+ align:start position:0%
+deleterious such that drift will
+cause them to get fixated or persist but
+
+ align:start position:0%
+cause them to get fixated or persist but
+ 
+
+ align:start position:0%
+cause them to get fixated or persist but
+they really they can't be
+
+ align:start position:0%
+they really they can't be
+ 
+
+ align:start position:0%
+they really they can't be
+really noticeably they get they you know
+
+ align:start position:0%
+really noticeably they get they you know
+ 
+
+ align:start position:0%
+really noticeably they get they you know
+selection coefficients of 10 to the
+
+ align:start position:0%
+selection coefficients of 10 to the
+ 
+
+ align:start position:0%
+selection coefficients of 10 to the
+minus 4 very very tiny effects can be uh
+
+ align:start position:0%
+minus 4 very very tiny effects can be uh
+ 
+
+ align:start position:0%
+minus 4 very very tiny effects can be uh
+wiped out in in populations
+
+ align:start position:0%
+wiped out in in populations
+ 
+
+ align:start position:0%
+wiped out in in populations
+sort of normal size populations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here are three examples of common
+
+ align:start position:0%
+here are three examples of common
+ 
+
+ align:start position:0%
+here are three examples of common
+variants that almost certainly are
+
+ align:start position:0%
+variants that almost certainly are
+ 
+
+ align:start position:0%
+variants that almost certainly are
+associated with common diseases so why
+
+ align:start position:0%
+associated with common diseases so why
+ 
+
+ align:start position:0%
+associated with common diseases so why
+are these special cases rather than in
+
+ align:start position:0%
+are these special cases rather than in
+ 
+
+ align:start position:0%
+are these special cases rather than in
+my opinion rather than the general case
+
+ align:start position:0%
+my opinion rather than the general case
+ 
+
+ align:start position:0%
+my opinion rather than the general case
+apoe4 i only alluded to is associated
+
+ align:start position:0%
+apoe4 i only alluded to is associated
+ 
+
+ align:start position:0%
+apoe4 i only alluded to is associated
+with alzheimer's dementia it's involved
+
+ align:start position:0%
+with alzheimer's dementia it's involved
+ 
+
+ align:start position:0%
+with alzheimer's dementia it's involved
+in lipid transport and metabolism
+
+ align:start position:0%
+in lipid transport and metabolism
+ 
+
+ align:start position:0%
+in lipid transport and metabolism
+and this particular allele the the uh
+
+ align:start position:0%
+and this particular allele the the uh
+ 
+
+ align:start position:0%
+and this particular allele the the uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+e4 allele
+
+ align:start position:0%
+e4 allele
+ 
+
+ align:start position:0%
+e4 allele
+is uh present 20 percent in humans about
+
+ align:start position:0%
+is uh present 20 percent in humans about
+ 
+
+ align:start position:0%
+is uh present 20 percent in humans about
+80 percent is the other allele the most
+
+ align:start position:0%
+80 percent is the other allele the most
+ 
+
+ align:start position:0%
+80 percent is the other allele the most
+second most common allele is the three
+
+ align:start position:0%
+second most common allele is the three
+ 
+
+ align:start position:0%
+second most common allele is the three
+allele
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you might say well this this
+
+ align:start position:0%
+and so you might say well this this
+ 
+
+ align:start position:0%
+and so you might say well this this
+battle theolous e4
+
+ align:start position:0%
+battle theolous e4
+ 
+
+ align:start position:0%
+battle theolous e4
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+you know it's the one that should be
+
+ align:start position:0%
+you know it's the one that should be
+ 
+
+ align:start position:0%
+you know it's the one that should be
+present in the common ancestors of
+
+ align:start position:0%
+present in the common ancestors of
+ 
+
+ align:start position:0%
+present in the common ancestors of
+humans uh it should be if sorry the e3
+
+ align:start position:0%
+humans uh it should be if sorry the e3
+ 
+
+ align:start position:0%
+humans uh it should be if sorry the e3
+the good one should be present the
+
+ align:start position:0%
+the good one should be present the
+ 
+
+ align:start position:0%
+the good one should be present the
+common ancestors and this ae4 is a
+
+ align:start position:0%
+common ancestors and this ae4 is a
+ 
+
+ align:start position:0%
+common ancestors and this ae4 is a
+recent aberration um it's it's somehow
+
+ align:start position:0%
+recent aberration um it's it's somehow
+ 
+
+ align:start position:0%
+recent aberration um it's it's somehow
+getting into human population but
+
+ align:start position:0%
+getting into human population but
+ 
+
+ align:start position:0%
+getting into human population but
+actually the e4 is the ancestral one
+
+ align:start position:0%
+actually the e4 is the ancestral one
+ 
+
+ align:start position:0%
+actually the e4 is the ancestral one
+presumably due to some difference in
+
+ align:start position:0%
+presumably due to some difference in
+ 
+
+ align:start position:0%
+presumably due to some difference in
+diet or some other
+
+ align:start position:0%
+diet or some other
+ 
+
+ align:start position:0%
+diet or some other
+selective effects
+
+ align:start position:0%
+selective effects
+ 
+
+ align:start position:0%
+selective effects
+the e4 which is currently bad for us we
+
+ align:start position:0%
+the e4 which is currently bad for us we
+ 
+
+ align:start position:0%
+the e4 which is currently bad for us we
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+is really good for some of our
+
+ align:start position:0%
+is really good for some of our
+ 
+
+ align:start position:0%
+is really good for some of our
+related species and so we need to think
+
+ align:start position:0%
+related species and so we need to think
+ 
+
+ align:start position:0%
+related species and so we need to think
+very carefully before we
+
+ align:start position:0%
+very carefully before we
+ 
+
+ align:start position:0%
+very carefully before we
+do anything drastic about eliminating
+
+ align:start position:0%
+do anything drastic about eliminating
+ 
+
+ align:start position:0%
+do anything drastic about eliminating
+this allele from say the human
+
+ align:start position:0%
+this allele from say the human
+ 
+
+ align:start position:0%
+this allele from say the human
+population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hemoglobin sickle cell
+
+ align:start position:0%
+hemoglobin sickle cell
+ 
+
+ align:start position:0%
+hemoglobin sickle cell
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sickle cell allele
+
+ align:start position:0%
+sickle cell allele
+ 
+
+ align:start position:0%
+sickle cell allele
+is probably the oldest and most famous
+
+ align:start position:0%
+is probably the oldest and most famous
+ 
+
+ align:start position:0%
+is probably the oldest and most famous
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+molecularly characterized alleles
+
+ align:start position:0%
+molecularly characterized alleles
+ 
+
+ align:start position:0%
+molecularly characterized alleles
+such a london polling made this famous
+
+ align:start position:0%
+such a london polling made this famous
+ 
+
+ align:start position:0%
+such a london polling made this famous
+many decades ago
+
+ align:start position:0%
+many decades ago
+ 
+
+ align:start position:0%
+many decades ago
+and it exists in 17 of the human
+
+ align:start position:0%
+and it exists in 17 of the human
+ 
+
+ align:start position:0%
+and it exists in 17 of the human
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+and this is uh responsible
+
+ align:start position:0%
+and this is uh responsible
+ 
+
+ align:start position:0%
+and this is uh responsible
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+oxygen transport in red blood cells and
+
+ align:start position:0%
+oxygen transport in red blood cells and
+ 
+
+ align:start position:0%
+oxygen transport in red blood cells and
+we saw you saw in one of the earlier
+
+ align:start position:0%
+we saw you saw in one of the earlier
+ 
+
+ align:start position:0%
+we saw you saw in one of the earlier
+slides today those sickled shaped cells
+
+ align:start position:0%
+slides today those sickled shaped cells
+ 
+
+ align:start position:0%
+slides today those sickled shaped cells
+which have a huge effect on the
+
+ align:start position:0%
+which have a huge effect on the
+ 
+
+ align:start position:0%
+which have a huge effect on the
+hemodynamics of the red blood cell
+
+ align:start position:0%
+hemodynamics of the red blood cell
+ 
+
+ align:start position:0%
+hemodynamics of the red blood cell
+well another red blood cell component an
+
+ align:start position:0%
+well another red blood cell component an
+ 
+
+ align:start position:0%
+well another red blood cell component an
+enzyme g6pd which is involved in
+
+ align:start position:0%
+enzyme g6pd which is involved in
+ 
+
+ align:start position:0%
+enzyme g6pd which is involved in
+maintaining the redox function in the
+
+ align:start position:0%
+maintaining the redox function in the
+ 
+
+ align:start position:0%
+maintaining the redox function in the
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+is as high as 40 percent the the mutant
+
+ align:start position:0%
+is as high as 40 percent the the mutant
+ 
+
+ align:start position:0%
+is as high as 40 percent the the mutant
+whichever one you want they're so close
+
+ align:start position:0%
+whichever one you want they're so close
+ 
+
+ align:start position:0%
+whichever one you want they're so close
+to 50
+
+ align:start position:0%
+to 50
+ 
+
+ align:start position:0%
+to 50
+they're just they're just two alleles um
+
+ align:start position:0%
+they're just they're just two alleles um
+ 
+
+ align:start position:0%
+they're just they're just two alleles um
+and one of them
+
+ align:start position:0%
+and one of them
+ 
+
+ align:start position:0%
+and one of them
+is a deleterious in a certain sense
+
+ align:start position:0%
+is a deleterious in a certain sense
+ 
+
+ align:start position:0%
+is a deleterious in a certain sense
+a biochemical sense
+
+ align:start position:0%
+a biochemical sense
+ 
+
+ align:start position:0%
+a biochemical sense
+but both of these have a
+
+ align:start position:0%
+but both of these have a
+ 
+
+ align:start position:0%
+but both of these have a
+heterozygote advantage in being malarial
+
+ align:start position:0%
+heterozygote advantage in being malarial
+ 
+
+ align:start position:0%
+heterozygote advantage in being malarial
+resistant and so probably that's the
+
+ align:start position:0%
+resistant and so probably that's the
+ 
+
+ align:start position:0%
+resistant and so probably that's the
+reason it is common in the population
+
+ align:start position:0%
+reason it is common in the population
+ 
+
+ align:start position:0%
+reason it is common in the population
+and this uh is
+
+ align:start position:0%
+and this uh is
+ 
+
+ align:start position:0%
+and this uh is
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+probably proving to be the rule that
+
+ align:start position:0%
+probably proving to be the rule that
+ 
+
+ align:start position:0%
+probably proving to be the rule that
+that these are examples of that
+
+ align:start position:0%
+that these are examples of that
+ 
+
+ align:start position:0%
+that these are examples of that
+convergence that we saw in the case of
+
+ align:start position:0%
+convergence that we saw in the case of
+ 
+
+ align:start position:0%
+convergence that we saw in the case of
+balanced polymorphisms where the
+
+ align:start position:0%
+balanced polymorphisms where the
+ 
+
+ align:start position:0%
+balanced polymorphisms where the
+heterozygote has some advantage and so
+
+ align:start position:0%
+heterozygote has some advantage and so
+ 
+
+ align:start position:0%
+heterozygote has some advantage and so
+you get a balanced point rather than one
+
+ align:start position:0%
+you get a balanced point rather than one
+ 
+
+ align:start position:0%
+you get a balanced point rather than one
+or the other dominating through the
+
+ align:start position:0%
+or the other dominating through the
+ 
+
+ align:start position:0%
+or the other dominating through the
+drift or selection
+
+ align:start position:0%
+drift or selection
+ 
+
+ align:start position:0%
+drift or selection
+and the third example is which we will
+
+ align:start position:0%
+and the third example is which we will
+ 
+
+ align:start position:0%
+and the third example is which we will
+develop in much more detail
+
+ align:start position:0%
+develop in much more detail
+ 
+
+ align:start position:0%
+develop in much more detail
+a ccr5 there's a deletion of 32 base
+
+ align:start position:0%
+a ccr5 there's a deletion of 32 base
+ 
+
+ align:start position:0%
+a ccr5 there's a deletion of 32 base
+pairs which confers resistance to one of
+
+ align:start position:0%
+pairs which confers resistance to one of
+ 
+
+ align:start position:0%
+pairs which confers resistance to one of
+the greatest plagues in the history of
+
+ align:start position:0%
+the greatest plagues in the history of
+ 
+
+ align:start position:0%
+the greatest plagues in the history of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+human race which is uh to the aids virus
+
+ align:start position:0%
+human race which is uh to the aids virus
+ 
+
+ align:start position:0%
+human race which is uh to the aids virus
+and its frequency is nine percent
+
+ align:start position:0%
+and its frequency is nine percent
+ 
+
+ align:start position:0%
+and its frequency is nine percent
+caucasians i think we wish that it were
+
+ align:start position:0%
+caucasians i think we wish that it were
+ 
+
+ align:start position:0%
+caucasians i think we wish that it were
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+when we worry about hiv but we need to
+
+ align:start position:0%
+when we worry about hiv but we need to
+ 
+
+ align:start position:0%
+when we worry about hiv but we need to
+wonder why it's not 100 there may be
+
+ align:start position:0%
+wonder why it's not 100 there may be
+ 
+
+ align:start position:0%
+wonder why it's not 100 there may be
+some other
+
+ align:start position:0%
+some other
+ 
+
+ align:start position:0%
+some other
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+for it
+
+ align:start position:0%
+for it
+ 
+
+ align:start position:0%
+for it
+being a non-deleted version
+
+ align:start position:0%
+being a non-deleted version
+ 
+
+ align:start position:0%
+being a non-deleted version
+in so many humans and we need to
+
+ align:start position:0%
+in so many humans and we need to
+ 
+
+ align:start position:0%
+in so many humans and we need to
+understand that and as far as i know we
+
+ align:start position:0%
+understand that and as far as i know we
+ 
+
+ align:start position:0%
+understand that and as far as i know we
+don't understand that
+
+ align:start position:0%
+don't understand that
+ 
+
+ align:start position:0%
+don't understand that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh this is the last slide before the
+
+ align:start position:0%
+uh this is the last slide before the
+ 
+
+ align:start position:0%
+uh this is the last slide before the
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+i want
+
+ align:start position:0%
+i want
+ 
+
+ align:start position:0%
+i want
+to now that i promised you that we would
+
+ align:start position:0%
+to now that i promised you that we would
+ 
+
+ align:start position:0%
+to now that i promised you that we would
+take that
+
+ align:start position:0%
+take that
+ 
+
+ align:start position:0%
+take that
+simple mathematical treatment of
+
+ align:start position:0%
+simple mathematical treatment of
+ 
+
+ align:start position:0%
+simple mathematical treatment of
+mutation selection and drift and show
+
+ align:start position:0%
+mutation selection and drift and show
+ 
+
+ align:start position:0%
+mutation selection and drift and show
+that it actually has some impact
+
+ align:start position:0%
+that it actually has some impact
+ 
+
+ align:start position:0%
+that it actually has some impact
+that is actually used in uh in human
+
+ align:start position:0%
+that is actually used in uh in human
+ 
+
+ align:start position:0%
+that is actually used in uh in human
+genetics now i must
+
+ align:start position:0%
+genetics now i must
+ 
+
+ align:start position:0%
+genetics now i must
+warn you that that this is not a
+
+ align:start position:0%
+warn you that that this is not a
+ 
+
+ align:start position:0%
+warn you that that this is not a
+consensus view this is a view that i
+
+ align:start position:0%
+consensus view this is a view that i
+ 
+
+ align:start position:0%
+consensus view this is a view that i
+find appealing in slide 21 that uh john
+
+ align:start position:0%
+find appealing in slide 21 that uh john
+ 
+
+ align:start position:0%
+find appealing in slide 21 that uh john
+pritchard
+
+ align:start position:0%
+pritchard
+ 
+
+ align:start position:0%
+pritchard
+has has authored
+
+ align:start position:0%
+has has authored
+ 
+
+ align:start position:0%
+has has authored
+and he titled it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a uh provocative way are rare
+
+ align:start position:0%
+in a uh provocative way are rare
+ 
+
+ align:start position:0%
+in a uh provocative way are rare
+variants responsible for susceptibility
+
+ align:start position:0%
+variants responsible for susceptibility
+ 
+
+ align:start position:0%
+variants responsible for susceptibility
+to complex diseases
+
+ align:start position:0%
+to complex diseases
+ 
+
+ align:start position:0%
+to complex diseases
+and uh this is a quote that cust it's
+
+ align:start position:0%
+and uh this is a quote that cust it's
+ 
+
+ align:start position:0%
+and uh this is a quote that cust it's
+customary and theoretical work relating
+
+ align:start position:0%
+customary and theoretical work relating
+ 
+
+ align:start position:0%
+customary and theoretical work relating
+to complex diseases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the allele frequencies are treated
+
+ align:start position:0%
+that the allele frequencies are treated
+ 
+
+ align:start position:0%
+that the allele frequencies are treated
+as parameters of the model and then
+
+ align:start position:0%
+as parameters of the model and then
+ 
+
+ align:start position:0%
+as parameters of the model and then
+typically in models you'll have
+
+ align:start position:0%
+typically in models you'll have
+ 
+
+ align:start position:0%
+typically in models you'll have
+derived
+
+ align:start position:0%
+derived
+ 
+
+ align:start position:0%
+derived
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+values and parameters which are input
+
+ align:start position:0%
+values and parameters which are input
+ 
+
+ align:start position:0%
+values and parameters which are input
+the things that you that the user is
+
+ align:start position:0%
+the things that you that the user is
+ 
+
+ align:start position:0%
+the things that you that the user is
+expected to provide and
+
+ align:start position:0%
+expected to provide and
+ 
+
+ align:start position:0%
+expected to provide and
+and you don't want to have to be
+
+ align:start position:0%
+and you don't want to have to be
+ 
+
+ align:start position:0%
+and you don't want to have to be
+guessing at all frequencies
+
+ align:start position:0%
+guessing at all frequencies
+ 
+
+ align:start position:0%
+guessing at all frequencies
+and having those parameters so what's
+
+ align:start position:0%
+and having those parameters so what's
+ 
+
+ align:start position:0%
+and having those parameters so what's
+new here is that
+
+ align:start position:0%
+new here is that
+ 
+
+ align:start position:0%
+new here is that
+that using an evolutionary process which
+
+ align:start position:0%
+that using an evolutionary process which
+ 
+
+ align:start position:0%
+that using an evolutionary process which
+includes you guessed it selection
+
+ align:start position:0%
+includes you guessed it selection
+ 
+
+ align:start position:0%
+includes you guessed it selection
+mutation and genetic drift they can we
+
+ align:start position:0%
+mutation and genetic drift they can we
+ 
+
+ align:start position:0%
+mutation and genetic drift they can we
+can learn or as they model the
+
+ align:start position:0%
+can learn or as they model the
+ 
+
+ align:start position:0%
+can learn or as they model the
+underlying allele frequencies they can
+
+ align:start position:0%
+underlying allele frequencies they can
+ 
+
+ align:start position:0%
+underlying allele frequencies they can
+be derived rather than being required as
+
+ align:start position:0%
+be derived rather than being required as
+ 
+
+ align:start position:0%
+be derived rather than being required as
+an input
+
+ align:start position:0%
+an input
+ 
+
+ align:start position:0%
+an input
+and so i think this this um
+
+ align:start position:0%
+and so i think this this um
+ 
+
+ align:start position:0%
+and so i think this this um
+and this is illustrated here
+
+ align:start position:0%
+and this is illustrated here
+ 
+
+ align:start position:0%
+and this is illustrated here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+with uh a model which which you know
+
+ align:start position:0%
+with uh a model which which you know
+ 
+
+ align:start position:0%
+with uh a model which which you know
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+entirely theoretical but it is based the
+
+ align:start position:0%
+entirely theoretical but it is based the
+ 
+
+ align:start position:0%
+entirely theoretical but it is based the
+parameters that are used are based on
+
+ align:start position:0%
+parameters that are used are based on
+ 
+
+ align:start position:0%
+parameters that are used are based on
+some genetic studies that have been done
+
+ align:start position:0%
+some genetic studies that have been done
+ 
+
+ align:start position:0%
+some genetic studies that have been done
+for example on autism and so let me just
+
+ align:start position:0%
+for example on autism and so let me just
+ 
+
+ align:start position:0%
+for example on autism and so let me just
+define some of the terms here we have
+
+ align:start position:0%
+define some of the terms here we have
+ 
+
+ align:start position:0%
+define some of the terms here we have
+this risk ratio is related in a certain
+
+ align:start position:0%
+this risk ratio is related in a certain
+ 
+
+ align:start position:0%
+this risk ratio is related in a certain
+sense to the selection and fitness
+
+ align:start position:0%
+sense to the selection and fitness
+ 
+
+ align:start position:0%
+sense to the selection and fitness
+coefficient we were talking about before
+
+ align:start position:0%
+coefficient we were talking about before
+ 
+
+ align:start position:0%
+coefficient we were talking about before
+now selection and fitness coefficients
+
+ align:start position:0%
+now selection and fitness coefficients
+ 
+
+ align:start position:0%
+now selection and fitness coefficients
+refer to reproductive fitness
+
+ align:start position:0%
+refer to reproductive fitness
+ 
+
+ align:start position:0%
+refer to reproductive fitness
+and in human genetics we're much more
+
+ align:start position:0%
+and in human genetics we're much more
+ 
+
+ align:start position:0%
+and in human genetics we're much more
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+we have broader interests and all sorts
+
+ align:start position:0%
+we have broader interests and all sorts
+ 
+
+ align:start position:0%
+we have broader interests and all sorts
+of things that that either don't affect
+
+ align:start position:0%
+of things that that either don't affect
+ 
+
+ align:start position:0%
+of things that that either don't affect
+reproductive fitness or or we don't know
+
+ align:start position:0%
+reproductive fitness or or we don't know
+ 
+
+ align:start position:0%
+reproductive fitness or or we don't know
+how it affects people but it affects
+
+ align:start position:0%
+how it affects people but it affects
+ 
+
+ align:start position:0%
+how it affects people but it affects
+some kind of medical
+
+ align:start position:0%
+some kind of medical
+ 
+
+ align:start position:0%
+some kind of medical
+or just uh just some trait of interest
+
+ align:start position:0%
+or just uh just some trait of interest
+ 
+
+ align:start position:0%
+or just uh just some trait of interest
+in this case um
+
+ align:start position:0%
+in this case um
+ 
+
+ align:start position:0%
+in this case um
+the the risk ratio replaces the
+
+ align:start position:0%
+the the risk ratio replaces the
+ 
+
+ align:start position:0%
+the the risk ratio replaces the
+selection coefficient and this is
+
+ align:start position:0%
+selection coefficient and this is
+ 
+
+ align:start position:0%
+selection coefficient and this is
+basically saying
+
+ align:start position:0%
+basically saying
+ 
+
+ align:start position:0%
+basically saying
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+brother or sister has also if if they
+
+ align:start position:0%
+brother or sister has also if if they
+ 
+
+ align:start position:0%
+brother or sister has also if if they
+did then i would have a 75 fold higher
+
+ align:start position:0%
+did then i would have a 75 fold higher
+ 
+
+ align:start position:0%
+did then i would have a 75 fold higher
+chance of having it
+
+ align:start position:0%
+chance of having it
+ 
+
+ align:start position:0%
+chance of having it
+than someone selected randomly from the
+
+ align:start position:0%
+than someone selected randomly from the
+ 
+
+ align:start position:0%
+than someone selected randomly from the
+same population as i come from so this
+
+ align:start position:0%
+same population as i come from so this
+ 
+
+ align:start position:0%
+same population as i come from so this
+70 fold increase is a very high
+
+ align:start position:0%
+70 fold increase is a very high
+ 
+
+ align:start position:0%
+70 fold increase is a very high
+heritability
+
+ align:start position:0%
+heritability
+ 
+
+ align:start position:0%
+heritability
+for this particular
+
+ align:start position:0%
+for this particular
+ 
+
+ align:start position:0%
+for this particular
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+also in this example
+
+ align:start position:0%
+also in this example
+ 
+
+ align:start position:0%
+also in this example
+through some genetics we won't discuss
+
+ align:start position:0%
+through some genetics we won't discuss
+ 
+
+ align:start position:0%
+through some genetics we won't discuss
+it it seemed reasonable that the number
+
+ align:start position:0%
+it it seemed reasonable that the number
+ 
+
+ align:start position:0%
+it it seemed reasonable that the number
+of loci involved might be much great you
+
+ align:start position:0%
+of loci involved might be much great you
+ 
+
+ align:start position:0%
+of loci involved might be much great you
+know might be a large number on the
+
+ align:start position:0%
+know might be a large number on the
+ 
+
+ align:start position:0%
+know might be a large number on the
+order of 100 or so and you can think
+
+ align:start position:0%
+order of 100 or so and you can think
+ 
+
+ align:start position:0%
+order of 100 or so and you can think
+that a lot of common diseases when you
+
+ align:start position:0%
+that a lot of common diseases when you
+ 
+
+ align:start position:0%
+that a lot of common diseases when you
+start listing the
+
+ align:start position:0%
+start listing the
+ 
+
+ align:start position:0%
+start listing the
+the the well characterized ones we start
+
+ align:start position:0%
+the the well characterized ones we start
+ 
+
+ align:start position:0%
+the the well characterized ones we start
+losing the number of genes that are
+
+ align:start position:0%
+losing the number of genes that are
+ 
+
+ align:start position:0%
+losing the number of genes that are
+either known or plausible like cancer or
+
+ align:start position:0%
+either known or plausible like cancer or
+ 
+
+ align:start position:0%
+either known or plausible like cancer or
+uh you know walking down the street or
+
+ align:start position:0%
+uh you know walking down the street or
+ 
+
+ align:start position:0%
+uh you know walking down the street or
+whatever these really complicated traits
+
+ align:start position:0%
+whatever these really complicated traits
+ 
+
+ align:start position:0%
+whatever these really complicated traits
+involve a very large number of
+
+ align:start position:0%
+involve a very large number of
+ 
+
+ align:start position:0%
+involve a very large number of
+uh cell types a large number of cell
+
+ align:start position:0%
+uh cell types a large number of cell
+ 
+
+ align:start position:0%
+uh cell types a large number of cell
+components and hence a large number of
+
+ align:start position:0%
+components and hence a large number of
+ 
+
+ align:start position:0%
+components and hence a large number of
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+so here they've assumed a model with 100
+
+ align:start position:0%
+so here they've assumed a model with 100
+ 
+
+ align:start position:0%
+so here they've assumed a model with 100
+loci 100 different genes
+
+ align:start position:0%
+loci 100 different genes
+ 
+
+ align:start position:0%
+loci 100 different genes
+and they have multiplicative effects
+
+ align:start position:0%
+and they have multiplicative effects
+ 
+
+ align:start position:0%
+and they have multiplicative effects
+of the of the polymorphisms in those
+
+ align:start position:0%
+of the of the polymorphisms in those
+ 
+
+ align:start position:0%
+of the of the polymorphisms in those
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+between loci that is to say you need to
+
+ align:start position:0%
+between loci that is to say you need to
+ 
+
+ align:start position:0%
+between loci that is to say you need to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+gene one working and gene two and gene
+
+ align:start position:0%
+gene one working and gene two and gene
+ 
+
+ align:start position:0%
+gene one working and gene two and gene
+three so that's multiplicative but then
+
+ align:start position:0%
+three so that's multiplicative but then
+ 
+
+ align:start position:0%
+three so that's multiplicative but then
+the polymorphisms you introduce into a
+
+ align:start position:0%
+the polymorphisms you introduce into a
+ 
+
+ align:start position:0%
+the polymorphisms you introduce into a
+gene you could think there are a lot of
+
+ align:start position:0%
+gene you could think there are a lot of
+ 
+
+ align:start position:0%
+gene you could think there are a lot of
+genes involved and there are a lot of
+
+ align:start position:0%
+genes involved and there are a lot of
+ 
+
+ align:start position:0%
+genes involved and there are a lot of
+different positions within the gene that
+
+ align:start position:0%
+different positions within the gene that
+ 
+
+ align:start position:0%
+different positions within the gene that
+can be involved and each of those is
+
+ align:start position:0%
+can be involved and each of those is
+ 
+
+ align:start position:0%
+can be involved and each of those is
+additive you have a little uh
+
+ align:start position:0%
+additive you have a little uh
+ 
+
+ align:start position:0%
+additive you have a little uh
+reduction in activity
+
+ align:start position:0%
+reduction in activity
+ 
+
+ align:start position:0%
+reduction in activity
+due to first mutation and then a second
+
+ align:start position:0%
+due to first mutation and then a second
+ 
+
+ align:start position:0%
+due to first mutation and then a second
+mutation the third each of those is a
+
+ align:start position:0%
+mutation the third each of those is a
+ 
+
+ align:start position:0%
+mutation the third each of those is a
+this or this or this or this and so
+
+ align:start position:0%
+this or this or this or this and so
+ 
+
+ align:start position:0%
+this or this or this or this and so
+that's an additive effect and so they
+
+ align:start position:0%
+that's an additive effect and so they
+ 
+
+ align:start position:0%
+that's an additive effect and so they
+they have various you know historical
+
+ align:start position:0%
+they have various you know historical
+ 
+
+ align:start position:0%
+they have various you know historical
+justifications for having additive
+
+ align:start position:0%
+justifications for having additive
+ 
+
+ align:start position:0%
+justifications for having additive
+penetrance within the gene and
+
+ align:start position:0%
+penetrance within the gene and
+ 
+
+ align:start position:0%
+penetrance within the gene and
+multiplicative um across different loci
+
+ align:start position:0%
+multiplicative um across different loci
+ 
+
+ align:start position:0%
+multiplicative um across different loci
+different genes in the genome
+
+ align:start position:0%
+different genes in the genome
+ 
+
+ align:start position:0%
+different genes in the genome
+now for these hundred loci there will be
+
+ align:start position:0%
+now for these hundred loci there will be
+ 
+
+ align:start position:0%
+now for these hundred loci there will be
+a top
+
+ align:start position:0%
+a top
+ 
+
+ align:start position:0%
+a top
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+five that affect the relative risk the
+
+ align:start position:0%
+five that affect the relative risk the
+ 
+
+ align:start position:0%
+five that affect the relative risk the
+most and that's what's been plotted here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the zero curve you see is in the in the
+
+ align:start position:0%
+the zero curve you see is in the in the
+ 
+
+ align:start position:0%
+the zero curve you see is in the in the
+absence of any of these
+
+ align:start position:0%
+absence of any of these
+ 
+
+ align:start position:0%
+absence of any of these
+multiplicative effects this is if you
+
+ align:start position:0%
+multiplicative effects this is if you
+ 
+
+ align:start position:0%
+multiplicative effects this is if you
+had no loci that were affecting the
+
+ align:start position:0%
+had no loci that were affecting the
+ 
+
+ align:start position:0%
+had no loci that were affecting the
+frequency of susceptibility alleles and
+
+ align:start position:0%
+frequency of susceptibility alleles and
+ 
+
+ align:start position:0%
+frequency of susceptibility alleles and
+so as in most
+
+ align:start position:0%
+so as in most
+ 
+
+ align:start position:0%
+so as in most
+unselective
+
+ align:start position:0%
+unselective
+ 
+
+ align:start position:0%
+unselective
+populations you'll have
+
+ align:start position:0%
+populations you'll have
+ 
+
+ align:start position:0%
+populations you'll have
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+you'll have mostly alleles being either
+
+ align:start position:0%
+you'll have mostly alleles being either
+ 
+
+ align:start position:0%
+you'll have mostly alleles being either
+zero frequency or 100 percent basically
+
+ align:start position:0%
+zero frequency or 100 percent basically
+ 
+
+ align:start position:0%
+zero frequency or 100 percent basically
+the zero representing you know the
+
+ align:start position:0%
+the zero representing you know the
+ 
+
+ align:start position:0%
+the zero representing you know the
+absence of the the the other the
+
+ align:start position:0%
+absence of the the the other the
+ 
+
+ align:start position:0%
+absence of the the the other the
+alternatives the 100 that's there but if
+
+ align:start position:0%
+alternatives the 100 that's there but if
+ 
+
+ align:start position:0%
+alternatives the 100 that's there but if
+you have this this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these uh the top five loci out of 100
+
+ align:start position:0%
+these uh the top five loci out of 100
+ 
+
+ align:start position:0%
+these uh the top five loci out of 100
+that contribute to the risk ratio then
+
+ align:start position:0%
+that contribute to the risk ratio then
+ 
+
+ align:start position:0%
+that contribute to the risk ratio then
+those are represented by these four
+
+ align:start position:0%
+those are represented by these four
+ 
+
+ align:start position:0%
+those are represented by these four
+curves which which say this frequency of
+
+ align:start position:0%
+curves which which say this frequency of
+ 
+
+ align:start position:0%
+curves which which say this frequency of
+susceptibility alleles which range along
+
+ align:start position:0%
+susceptibility alleles which range along
+ 
+
+ align:start position:0%
+susceptibility alleles which range along
+the horizontal axis now from zero to 100
+
+ align:start position:0%
+the horizontal axis now from zero to 100
+ 
+
+ align:start position:0%
+the horizontal axis now from zero to 100
+percent have what he calls a probability
+
+ align:start position:0%
+percent have what he calls a probability
+ 
+
+ align:start position:0%
+percent have what he calls a probability
+density i mean it's it's clearly not a
+
+ align:start position:0%
+density i mean it's it's clearly not a
+ 
+
+ align:start position:0%
+density i mean it's it's clearly not a
+probability density because it's not
+
+ align:start position:0%
+probability density because it's not
+ 
+
+ align:start position:0%
+probability density because it's not
+going to integrate to one but
+
+ align:start position:0%
+going to integrate to one but
+ 
+
+ align:start position:0%
+going to integrate to one but
+here it's the the probability
+
+ align:start position:0%
+here it's the the probability
+ 
+
+ align:start position:0%
+here it's the the probability
+uh the sort of the histogram of risk
+
+ align:start position:0%
+uh the sort of the histogram of risk
+ 
+
+ align:start position:0%
+uh the sort of the histogram of risk
+ratios
+
+ align:start position:0%
+ratios
+ 
+
+ align:start position:0%
+ratios
+okay so let's take a break and uh
+
+ align:start position:0%
+okay so let's take a break and uh
+ 
+
+ align:start position:0%
+okay so let's take a break and uh
+we'll pick up uh
+
+ align:start position:0%
+we'll pick up uh
+ 
+
+ align:start position:0%
+we'll pick up uh
+on our on an exact i will go drill down
+
+ align:start position:0%
+on our on an exact i will go drill down
+ 
+
+ align:start position:0%
+on our on an exact i will go drill down
+on the association study in a very
+
+ align:start position:0%
+on the association study in a very
+ 
+
+ align:start position:0%
+on the association study in a very
+interesting case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody who any problem sets
+
+ align:start position:0%
+anybody who any problem sets
+ 
+
+ align:start position:0%
+anybody who any problem sets
+to hand in can put them
+
+ align:start position:0%
+to hand in can put them
+ 
+
+ align:start position:0%
+to hand in can put them
+here during the break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i understand about modeling
+
+ align:start position:0%
+so i understand about modeling
+ 
+
+ align:start position:0%
+so i understand about modeling
+mutations
\ No newline at end of file
diff --git a/WHWyW5DIVSU.txt b/WHWyW5DIVSU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8b695a6eac27f899a5eaf857688ba30b5201ca83
--- /dev/null
+++ b/WHWyW5DIVSU.txt
@@ -0,0 +1,1491 @@
+align:start position:0%
+ 
+welcome back to recitation today we're
+
+ align:start position:0%
+welcome back to recitation today we're
+ 
+
+ align:start position:0%
+welcome back to recitation today we're
+going to work on a problem involving
+
+ align:start position:0%
+going to work on a problem involving
+ 
+
+ align:start position:0%
+going to work on a problem involving
+differential equations I'm going to read
+
+ align:start position:0%
+differential equations I'm going to read
+ 
+
+ align:start position:0%
+differential equations I'm going to read
+it to you give you a little hint give
+
+ align:start position:0%
+it to you give you a little hint give
+ 
+
+ align:start position:0%
+it to you give you a little hint give
+you some time to work on it and then
+
+ align:start position:0%
+you some time to work on it and then
+ 
+
+ align:start position:0%
+you some time to work on it and then
+I'll be back and work it out for you so
+
+ align:start position:0%
+I'll be back and work it out for you so
+ 
+
+ align:start position:0%
+I'll be back and work it out for you so
+the problem is to find a function yals f
+
+ align:start position:0%
+the problem is to find a function yals f
+ 
+
+ align:start position:0%
+the problem is to find a function yals f
+ofx that has the following two
+
+ align:start position:0%
+ofx that has the following two
+ 
+
+ align:start position:0%
+ofx that has the following two
+properties uh d^2 Y dx^ 2 is equal to 6X
+
+ align:start position:0%
+properties uh d^2 Y dx^ 2 is equal to 6X
+ 
+
+ align:start position:0%
+properties uh d^2 Y dx^ 2 is equal to 6X
+and just to remind you what this means
+
+ align:start position:0%
+and just to remind you what this means
+ 
+
+ align:start position:0%
+and just to remind you what this means
+this is really this is the second
+
+ align:start position:0%
+this is really this is the second
+ 
+
+ align:start position:0%
+this is really this is the second
+derivative of y with respect to X okay
+
+ align:start position:0%
+derivative of y with respect to X okay
+ 
+
+ align:start position:0%
+derivative of y with respect to X okay
+so its second derivative with respect to
+
+ align:start position:0%
+so its second derivative with respect to
+ 
+
+ align:start position:0%
+so its second derivative with respect to
+X should be 6X and the second condition
+
+ align:start position:0%
+X should be 6X and the second condition
+ 
+
+ align:start position:0%
+X should be 6X and the second condition
+is kind of long but it says the graph of
+
+ align:start position:0%
+is kind of long but it says the graph of
+ 
+
+ align:start position:0%
+is kind of long but it says the graph of
+the function in the XY plane passes
+
+ align:start position:0%
+the function in the XY plane passes
+ 
+
+ align:start position:0%
+the function in the XY plane passes
+through the0 one one with a horizontal
+
+ align:start position:0%
+through the0 one one with a horizontal
+ 
+
+ align:start position:0%
+through the0 one one with a horizontal
+tangent there so let me give you one
+
+ align:start position:0%
+tangent there so let me give you one
+ 
+
+ align:start position:0%
+tangent there so let me give you one
+hint and that hint is that there are
+
+ align:start position:0%
+hint and that hint is that there are
+ 
+
+ align:start position:0%
+hint and that hint is that there are
+some initial conditions buried in here
+
+ align:start position:0%
+some initial conditions buried in here
+ 
+
+ align:start position:0%
+some initial conditions buried in here
+that's why we have this condition so I'm
+
+ align:start position:0%
+that's why we have this condition so I'm
+ 
+
+ align:start position:0%
+that's why we have this condition so I'm
+going to give you a little bit to of
+
+ align:start position:0%
+going to give you a little bit to of
+ 
+
+ align:start position:0%
+going to give you a little bit to of
+time to work on it and I'll be back and
+
+ align:start position:0%
+time to work on it and I'll be back and
+ 
+
+ align:start position:0%
+time to work on it and I'll be back and
+I'll work it out with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you welcome back hopefully you were able
+
+ align:start position:0%
+you welcome back hopefully you were able
+ 
+
+ align:start position:0%
+you welcome back hopefully you were able
+to start at least solving the problem uh
+
+ align:start position:0%
+to start at least solving the problem uh
+ 
+
+ align:start position:0%
+to start at least solving the problem uh
+initially give give yourself a little
+
+ align:start position:0%
+initially give give yourself a little
+ 
+
+ align:start position:0%
+initially give give yourself a little
+Direction so let's see how you
+
+ align:start position:0%
+Direction so let's see how you
+ 
+
+ align:start position:0%
+Direction so let's see how you
+did okay so the first thing I would like
+
+ align:start position:0%
+did okay so the first thing I would like
+ 
+
+ align:start position:0%
+did okay so the first thing I would like
+to do is is try and figure out maybe
+
+ align:start position:0%
+to do is is try and figure out maybe
+ 
+
+ align:start position:0%
+to do is is try and figure out maybe
+what the first derivative of the
+
+ align:start position:0%
+what the first derivative of the
+ 
+
+ align:start position:0%
+what the first derivative of the
+function yal f ofx is I have it second
+
+ align:start position:0%
+function yal f ofx is I have it second
+ 
+
+ align:start position:0%
+function yal f ofx is I have it second
+derivative so in order to find the first
+
+ align:start position:0%
+derivative so in order to find the first
+ 
+
+ align:start position:0%
+derivative so in order to find the first
+derivative I I want to find ultimately a
+
+ align:start position:0%
+derivative I I want to find ultimately a
+ 
+
+ align:start position:0%
+derivative I I want to find ultimately a
+function that when I take its derivative
+
+ align:start position:0%
+function that when I take its derivative
+ 
+
+ align:start position:0%
+function that when I take its derivative
+I get 6X right so we can think about
+
+ align:start position:0%
+I get 6X right so we can think about
+ 
+
+ align:start position:0%
+I get 6X right so we can think about
+this maybe the easiest thing for us to
+
+ align:start position:0%
+this maybe the easiest thing for us to
+ 
+
+ align:start position:0%
+this maybe the easiest thing for us to
+do would actually be to consider another
+
+ align:start position:0%
+do would actually be to consider another
+ 
+
+ align:start position:0%
+do would actually be to consider another
+function whose derivative is 6X and
+
+ align:start position:0%
+function whose derivative is 6X and
+ 
+
+ align:start position:0%
+function whose derivative is 6X and
+we'll we'll know that's dydx so I'm
+
+ align:start position:0%
+we'll we'll know that's dydx so I'm
+ 
+
+ align:start position:0%
+we'll we'll know that's dydx so I'm
+going to say this Dy sorry d^2 y DX s
+
+ align:start position:0%
+going to say this Dy sorry d^2 y DX s
+ 
+
+ align:start position:0%
+going to say this Dy sorry d^2 y DX s
+I'm going to say is the first derivative
+
+ align:start position:0%
+I'm going to say is the first derivative
+ 
+
+ align:start position:0%
+I'm going to say is the first derivative
+of another function we'll say DWD
+
+ align:start position:0%
+of another function we'll say DWD
+ 
+
+ align:start position:0%
+of another function we'll say DWD
+X and the reason I'm going to do that is
+
+ align:start position:0%
+X and the reason I'm going to do that is
+ 
+
+ align:start position:0%
+X and the reason I'm going to do that is
+so we're not too nervous about about how
+
+ align:start position:0%
+so we're not too nervous about about how
+ 
+
+ align:start position:0%
+so we're not too nervous about about how
+we solve this problem so let's just
+
+ align:start position:0%
+we solve this problem so let's just
+ 
+
+ align:start position:0%
+we solve this problem so let's just
+let's just assume that so I'm
+
+ align:start position:0%
+let's just assume that so I'm
+ 
+
+ align:start position:0%
+let's just assume that so I'm
+introducing another function W which is
+
+ align:start position:0%
+introducing another function W which is
+ 
+
+ align:start position:0%
+introducing another function W which is
+the first derivative of of Y with
+
+ align:start position:0%
+the first derivative of of Y with
+ 
+
+ align:start position:0%
+the first derivative of of Y with
+respect to X ultimately because its
+
+ align:start position:0%
+respect to X ultimately because its
+ 
+
+ align:start position:0%
+respect to X ultimately because its
+derivative is the second derivative of y
+
+ align:start position:0%
+derivative is the second derivative of y
+ 
+
+ align:start position:0%
+derivative is the second derivative of y
+with respect to X so let's see how to
+
+ align:start position:0%
+with respect to X so let's see how to
+ 
+
+ align:start position:0%
+with respect to X so let's see how to
+solve the differential equation
+
+ align:start position:0%
+solve the differential equation
+ 
+
+ align:start position:0%
+solve the differential equation
+dwdx equal 6x now you may be able to do
+
+ align:start position:0%
+dwdx equal 6x now you may be able to do
+ 
+
+ align:start position:0%
+dwdx equal 6x now you may be able to do
+that right away you may see what this is
+
+ align:start position:0%
+that right away you may see what this is
+ 
+
+ align:start position:0%
+that right away you may see what this is
+right away if you're a little nervous we
+
+ align:start position:0%
+right away if you're a little nervous we
+ 
+
+ align:start position:0%
+right away if you're a little nervous we
+can do a separation of variables so
+
+ align:start position:0%
+can do a separation of variables so
+ 
+
+ align:start position:0%
+can do a separation of variables so
+right away maybe some of you can see
+
+ align:start position:0%
+right away maybe some of you can see
+ 
+
+ align:start position:0%
+right away maybe some of you can see
+that this will be 2x sorry
+
+ align:start position:0%
+that this will be 2x sorry
+ 
+
+ align:start position:0%
+that this will be 2x sorry
+3x^2 but let's just double check so
+
+ align:start position:0%
+3x^2 but let's just double check so
+ 
+
+ align:start position:0%
+3x^2 but let's just double check so
+separation of variables on this side we
+
+ align:start position:0%
+separation of variables on this side we
+ 
+
+ align:start position:0%
+separation of variables on this side we
+get the integral of DW on this side we
+
+ align:start position:0%
+get the integral of DW on this side we
+ 
+
+ align:start position:0%
+get the integral of DW on this side we
+get the integral of 6X
+
+ align:start position:0%
+get the integral of 6X
+ 
+
+ align:start position:0%
+get the integral of 6X
+DX here we get a
+
+ align:start position:0%
+DX here we get a
+ 
+
+ align:start position:0%
+DX here we get a
+w and here again we get we should really
+
+ align:start position:0%
+w and here again we get we should really
+ 
+
+ align:start position:0%
+w and here again we get we should really
+do 6
+
+ align:start position:0%
+do 6
+ 
+
+ align:start position:0%
+do 6
+x^2 over 2
+
+ align:start position:0%
+x^2 over 2
+ 
+
+ align:start position:0%
+x^2 over 2
+plus a constant so that's
+
+ align:start position:0%
+plus a constant so that's
+ 
+
+ align:start position:0%
+plus a constant so that's
+3x^2 plus a constant I'm going to write
+
+ align:start position:0%
+3x^2 plus a constant I'm going to write
+ 
+
+ align:start position:0%
+3x^2 plus a constant I'm going to write
+C1 here because we're going to need um
+
+ align:start position:0%
+C1 here because we're going to need um
+ 
+
+ align:start position:0%
+C1 here because we're going to need um
+we're going to need a little bit of
+
+ align:start position:0%
+we're going to need a little bit of
+ 
+
+ align:start position:0%
+we're going to need a little bit of
+information we're going to need another
+
+ align:start position:0%
+information we're going to need another
+ 
+
+ align:start position:0%
+information we're going to need another
+constant later so we actually now know
+
+ align:start position:0%
+constant later so we actually now know
+ 
+
+ align:start position:0%
+constant later so we actually now know
+the derivative of y with respect to x
+
+ align:start position:0%
+the derivative of y with respect to x
+ 
+
+ align:start position:0%
+the derivative of y with respect to x
+what we found
+
+ align:start position:0%
+what we found
+ 
+
+ align:start position:0%
+what we found
+here I'll just write that
+
+ align:start position:0%
+here I'll just write that
+ 
+
+ align:start position:0%
+here I'll just write that
+in is dydx again let me remind you why
+
+ align:start position:0%
+in is dydx again let me remind you why
+ 
+
+ align:start position:0%
+in is dydx again let me remind you why
+we we had we were saying the second
+
+ align:start position:0%
+we we had we were saying the second
+ 
+
+ align:start position:0%
+we we had we were saying the second
+derivative of y with respect to X we're
+
+ align:start position:0%
+derivative of y with respect to X we're
+ 
+
+ align:start position:0%
+derivative of y with respect to X we're
+going to call
+
+ align:start position:0%
+going to call
+ 
+
+ align:start position:0%
+going to call
+dwdx so when I when I took an integral
+
+ align:start position:0%
+dwdx so when I when I took an integral
+ 
+
+ align:start position:0%
+dwdx so when I when I took an integral
+of of dwdx I got W so that means I've
+
+ align:start position:0%
+of of dwdx I got W so that means I've
+ 
+
+ align:start position:0%
+of of dwdx I got W so that means I've
+taken one anti-derivative here and so
+
+ align:start position:0%
+taken one anti-derivative here and so
+ 
+
+ align:start position:0%
+taken one anti-derivative here and so
+now I have dydx so this is
+
+ align:start position:0%
+now I have dydx so this is
+ 
+
+ align:start position:0%
+now I have dydx so this is
+dydx going to draw a line and now we
+
+ align:start position:0%
+dydx going to draw a line and now we
+ 
+
+ align:start position:0%
+dydx going to draw a line and now we
+want to find Y and again we can use
+
+ align:start position:0%
+want to find Y and again we can use
+ 
+
+ align:start position:0%
+want to find Y and again we can use
+separation of variables or this time I'm
+
+ align:start position:0%
+separation of variables or this time I'm
+ 
+
+ align:start position:0%
+separation of variables or this time I'm
+just going to to do the problem without
+
+ align:start position:0%
+just going to to do the problem without
+ 
+
+ align:start position:0%
+just going to to do the problem without
+separating variables because I actually
+
+ align:start position:0%
+separating variables because I actually
+ 
+
+ align:start position:0%
+separating variables because I actually
+know uh what an anti-derivative is of
+
+ align:start position:0%
+know uh what an anti-derivative is of
+ 
+
+ align:start position:0%
+know uh what an anti-derivative is of
+this what an anti-derivative is of this
+
+ align:start position:0%
+this what an anti-derivative is of this
+ 
+
+ align:start position:0%
+this what an anti-derivative is of this
+and then I need to add one more constant
+
+ align:start position:0%
+and then I need to add one more constant
+ 
+
+ align:start position:0%
+and then I need to add one more constant
+so I can say that Y is definitely equal
+
+ align:start position:0%
+so I can say that Y is definitely equal
+ 
+
+ align:start position:0%
+so I can say that Y is definitely equal
+to X cubed +
+
+ align:start position:0%
+to X cubed +
+ 
+
+ align:start position:0%
+to X cubed +
+c1x + C2 and let me just again let's see
+
+ align:start position:0%
+c1x + C2 and let me just again let's see
+ 
+
+ align:start position:0%
+c1x + C2 and let me just again let's see
+why that is right this anti-der
+
+ align:start position:0%
+why that is right this anti-der
+ 
+
+ align:start position:0%
+why that is right this anti-der
+anti-derivative of this is X cubed
+
+ align:start position:0%
+anti-derivative of this is X cubed
+ 
+
+ align:start position:0%
+anti-derivative of this is X cubed
+anti-derivative of this is it's a
+
+ align:start position:0%
+anti-derivative of this is it's a
+ 
+
+ align:start position:0%
+anti-derivative of this is it's a
+constant so it's anti-derivative is is
+
+ align:start position:0%
+constant so it's anti-derivative is is
+ 
+
+ align:start position:0%
+constant so it's anti-derivative is is
+C1 * X and then I have to add on another
+
+ align:start position:0%
+C1 * X and then I have to add on another
+ 
+
+ align:start position:0%
+C1 * X and then I have to add on another
+constant because I have a whole family
+
+ align:start position:0%
+constant because I have a whole family
+ 
+
+ align:start position:0%
+constant because I have a whole family
+of possible solutions so here I have y
+
+ align:start position:0%
+of possible solutions so here I have y
+ 
+
+ align:start position:0%
+of possible solutions so here I have y
+and now I need to figure out how to use
+
+ align:start position:0%
+and now I need to figure out how to use
+ 
+
+ align:start position:0%
+and now I need to figure out how to use
+uh number two maybe before you even go
+
+ align:start position:0%
+uh number two maybe before you even go
+ 
+
+ align:start position:0%
+uh number two maybe before you even go
+on you want to check does this really
+
+ align:start position:0%
+on you want to check does this really
+ 
+
+ align:start position:0%
+on you want to check does this really
+satisfy number one so if we wanted to
+
+ align:start position:0%
+satisfy number one so if we wanted to
+ 
+
+ align:start position:0%
+satisfy number one so if we wanted to
+check that we just take two derivatives
+
+ align:start position:0%
+check that we just take two derivatives
+ 
+
+ align:start position:0%
+check that we just take two derivatives
+of this expression on the right hand
+
+ align:start position:0%
+of this expression on the right hand
+ 
+
+ align:start position:0%
+of this expression on the right hand
+side two derivatives of this is zero two
+
+ align:start position:0%
+side two derivatives of this is zero two
+ 
+
+ align:start position:0%
+side two derivatives of this is zero two
+derivatives of this is zero and two
+
+ align:start position:0%
+derivatives of this is zero and two
+ 
+
+ align:start position:0%
+derivatives of this is zero and two
+derivatives of this is 6X so I do indeed
+
+ align:start position:0%
+derivatives of this is 6X so I do indeed
+ 
+
+ align:start position:0%
+derivatives of this is 6X so I do indeed
+get what I want so now we definitely can
+
+ align:start position:0%
+get what I want so now we definitely can
+ 
+
+ align:start position:0%
+get what I want so now we definitely can
+go on to number two
+
+ align:start position:0%
+go on to number two
+ 
+
+ align:start position:0%
+go on to number two
+okay so what do we have number two it
+
+ align:start position:0%
+okay so what do we have number two it
+ 
+
+ align:start position:0%
+okay so what do we have number two it
+says we have some initial conditions
+
+ align:start position:0%
+says we have some initial conditions
+ 
+
+ align:start position:0%
+says we have some initial conditions
+here the graph in the XY plane passes
+
+ align:start position:0%
+here the graph in the XY plane passes
+ 
+
+ align:start position:0%
+here the graph in the XY plane passes
+through the point 11 one and it has a
+
+ align:start position:0%
+through the point 11 one and it has a
+ 
+
+ align:start position:0%
+through the point 11 one and it has a
+horizontal tangent there now what does
+
+ align:start position:0%
+horizontal tangent there now what does
+ 
+
+ align:start position:0%
+horizontal tangent there now what does
+that actually mean let's think about
+
+ align:start position:0%
+that actually mean let's think about
+ 
+
+ align:start position:0%
+that actually mean let's think about
+that that actually means
+
+ align:start position:0%
+that that actually means
+ 
+
+ align:start position:0%
+that that actually means
+that 2
+
+ align:start position:0%
+that 2
+ 
+
+ align:start position:0%
+that 2
+says F of one equals
+
+ align:start position:0%
+says F of one equals
+ 
+
+ align:start position:0%
+says F of one equals
+1 right Y is equal to F ofx so we can
+
+ align:start position:0%
+1 right Y is equal to F ofx so we can
+ 
+
+ align:start position:0%
+1 right Y is equal to F ofx so we can
+write this also as F ofx so to the first
+
+ align:start position:0%
+write this also as F ofx so to the first
+ 
+
+ align:start position:0%
+write this also as F ofx so to the first
+part says F of one is one
+
+ align:start position:0%
+part says F of one is one
+ 
+
+ align:start position:0%
+part says F of one is one
+and what does this second condition
+
+ align:start position:0%
+and what does this second condition
+ 
+
+ align:start position:0%
+and what does this second condition
+let's check the second condition it says
+
+ align:start position:0%
+let's check the second condition it says
+ 
+
+ align:start position:0%
+let's check the second condition it says
+it has a horizontal tangent there
+
+ align:start position:0%
+it has a horizontal tangent there
+ 
+
+ align:start position:0%
+it has a horizontal tangent there
+horizontal tangent means that it's
+
+ align:start position:0%
+horizontal tangent means that it's
+ 
+
+ align:start position:0%
+horizontal tangent means that it's
+derivative at that x value is zero so
+
+ align:start position:0%
+derivative at that x value is zero so
+ 
+
+ align:start position:0%
+derivative at that x value is zero so
+let me write down that in a nice form
+
+ align:start position:0%
+let me write down that in a nice form
+ 
+
+ align:start position:0%
+let me write down that in a nice form
+the derivative at that x value is equal
+
+ align:start position:0%
+the derivative at that x value is equal
+ 
+
+ align:start position:0%
+the derivative at that x value is equal
+to zero this is a little different maybe
+
+ align:start position:0%
+to zero this is a little different maybe
+ 
+
+ align:start position:0%
+to zero this is a little different maybe
+from what we've seen previously in the
+
+ align:start position:0%
+from what we've seen previously in the
+ 
+
+ align:start position:0%
+from what we've seen previously in the
+lecture you saw examples at least
+
+ align:start position:0%
+lecture you saw examples at least
+ 
+
+ align:start position:0%
+lecture you saw examples at least
+certainly where you had one initial
+
+ align:start position:0%
+certainly where you had one initial
+ 
+
+ align:start position:0%
+certainly where you had one initial
+condition here we need two initial
+
+ align:start position:0%
+condition here we need two initial
+ 
+
+ align:start position:0%
+condition here we need two initial
+conditions and you see why is because we
+
+ align:start position:0%
+conditions and you see why is because we
+ 
+
+ align:start position:0%
+conditions and you see why is because we
+actually have two constants where did
+
+ align:start position:0%
+actually have two constants where did
+ 
+
+ align:start position:0%
+actually have two constants where did
+that come from it's because we started
+
+ align:start position:0%
+that come from it's because we started
+ 
+
+ align:start position:0%
+that come from it's because we started
+with a second derivative instead of just
+
+ align:start position:0%
+with a second derivative instead of just
+ 
+
+ align:start position:0%
+with a second derivative instead of just
+a first derivative so that's kind of
+
+ align:start position:0%
+a first derivative so that's kind of
+ 
+
+ align:start position:0%
+a first derivative so that's kind of
+that's why you see more initial
+
+ align:start position:0%
+that's why you see more initial
+ 
+
+ align:start position:0%
+that's why you see more initial
+conditions than maybe you've seen
+
+ align:start position:0%
+conditions than maybe you've seen
+ 
+
+ align:start position:0%
+conditions than maybe you've seen
+previously so let's plug these in and
+
+ align:start position:0%
+previously so let's plug these in and
+ 
+
+ align:start position:0%
+previously so let's plug these in and
+let's see what we get if F of 1 equals 1
+
+ align:start position:0%
+let's see what we get if F of 1 equals 1
+ 
+
+ align:start position:0%
+let's see what we get if F of 1 equals 1
+then let's let's evaluate that F of one
+
+ align:start position:0%
+then let's let's evaluate that F of one
+ 
+
+ align:start position:0%
+then let's let's evaluate that F of one
+is equal to 1 cubed + 1 *
+
+ align:start position:0%
+is equal to 1 cubed + 1 *
+ 
+
+ align:start position:0%
+is equal to 1 cubed + 1 *
+C1 plus one time or just one there or C2
+
+ align:start position:0%
+C1 plus one time or just one there or C2
+ 
+
+ align:start position:0%
+C1 plus one time or just one there or C2
+there sorry there's no X there there so
+
+ align:start position:0%
+there sorry there's no X there there so
+ 
+
+ align:start position:0%
+there sorry there's no X there there so
+just C2 and that all has to equal
+
+ align:start position:0%
+just C2 and that all has to equal
+ 
+
+ align:start position:0%
+just C2 and that all has to equal
+one right and then let's look at what
+
+ align:start position:0%
+one right and then let's look at what
+ 
+
+ align:start position:0%
+one right and then let's look at what
+the derivative is the derivative is
+
+ align:start position:0%
+the derivative is the derivative is
+ 
+
+ align:start position:0%
+the derivative is the derivative is
+still over
+
+ align:start position:0%
+still over
+ 
+
+ align:start position:0%
+still over
+here so frime at 1 is equal to 3 * 1^ 2
+
+ align:start position:0%
+here so frime at 1 is equal to 3 * 1^ 2
+ 
+
+ align:start position:0%
+here so frime at 1 is equal to 3 * 1^ 2
+so 3 * 1 plus
+
+ align:start position:0%
+so 3 * 1 plus
+ 
+
+ align:start position:0%
+so 3 * 1 plus
+C1 and the condition says that equals
+
+ align:start position:0%
+C1 and the condition says that equals
+ 
+
+ align:start position:0%
+C1 and the condition says that equals
+zero equals zero so we can read off the
+
+ align:start position:0%
+zero equals zero so we can read off the
+ 
+
+ align:start position:0%
+zero equals zero so we can read off the
+nice thing is this is a system of
+
+ align:start position:0%
+nice thing is this is a system of
+ 
+
+ align:start position:0%
+nice thing is this is a system of
+equations but one of them is very easy
+
+ align:start position:0%
+equations but one of them is very easy
+ 
+
+ align:start position:0%
+equations but one of them is very easy
+to solve initially then we can
+
+ align:start position:0%
+to solve initially then we can
+ 
+
+ align:start position:0%
+to solve initially then we can
+substitute so what does this say well 3
+
+ align:start position:0%
+substitute so what does this say well 3
+ 
+
+ align:start position:0%
+substitute so what does this say well 3
++ C1 equal 0 so C1 is equal to Min -3 -3
+
+ align:start position:0%
++ C1 equal 0 so C1 is equal to Min -3 -3
+ 
+
+ align:start position:0%
++ C1 equal 0 so C1 is equal to Min -3 -3
+if I plug in3 for C1 in this expression
+
+ align:start position:0%
+if I plug in3 for C1 in this expression
+ 
+
+ align:start position:0%
+if I plug in3 for C1 in this expression
+in this equation up here I get -3 + 1
+
+ align:start position:0%
+in this equation up here I get -3 + 1
+ 
+
+ align:start position:0%
+in this equation up here I get -3 + 1
+plus C2 has to equal one if I subtract
+
+ align:start position:0%
+plus C2 has to equal one if I subtract
+ 
+
+ align:start position:0%
+plus C2 has to equal one if I subtract
+the ones from both sides I get -3 plus
+
+ align:start position:0%
+the ones from both sides I get -3 plus
+ 
+
+ align:start position:0%
+the ones from both sides I get -3 plus
+C2 has to equal zero so C2 has to
+
+ align:start position:0%
+C2 has to equal zero so C2 has to
+ 
+
+ align:start position:0%
+C2 has to equal zero so C2 has to
+actually equal
+
+ align:start position:0%
+actually equal
+ 
+
+ align:start position:0%
+actually equal
+three so the final final answer is is
+
+ align:start position:0%
+three so the final final answer is is
+ 
+
+ align:start position:0%
+three so the final final answer is is
+evaluating or plugging in the C1 and the
+
+ align:start position:0%
+evaluating or plugging in the C1 and the
+ 
+
+ align:start position:0%
+evaluating or plugging in the C1 and the
+C2 in for the constants there the final
+
+ align:start position:0%
+C2 in for the constants there the final
+ 
+
+ align:start position:0%
+C2 in for the constants there the final
+final answer is X
+
+ align:start position:0%
+final answer is X
+ 
+
+ align:start position:0%
+final answer is X
+cubed -
+
+ align:start position:0%
+cubed -
+ 
+
+ align:start position:0%
+cubed -
+3x +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 so we started with a differential
+
+ align:start position:0%
+3 so we started with a differential
+ 
+
+ align:start position:0%
+3 so we started with a differential
+equation and two sets of initial
+
+ align:start position:0%
+equation and two sets of initial
+ 
+
+ align:start position:0%
+equation and two sets of initial
+conditions and we came up with one
+
+ align:start position:0%
+conditions and we came up with one
+ 
+
+ align:start position:0%
+conditions and we came up with one
+solution that satisfies that now you can
+
+ align:start position:0%
+solution that satisfies that now you can
+ 
+
+ align:start position:0%
+solution that satisfies that now you can
+look at this you could graph this on a
+
+ align:start position:0%
+look at this you could graph this on a
+ 
+
+ align:start position:0%
+look at this you could graph this on a
+calculator or a computer and look can
+
+ align:start position:0%
+calculator or a computer and look can
+ 
+
+ align:start position:0%
+calculator or a computer and look can
+see if it satisfies that it's that it's
+
+ align:start position:0%
+see if it satisfies that it's that it's
+ 
+
+ align:start position:0%
+see if it satisfies that it's that it's
+actually passes through the 0.11 and has
+
+ align:start position:0%
+actually passes through the 0.11 and has
+ 
+
+ align:start position:0%
+actually passes through the 0.11 and has
+a horizontal tangent there but we know
+
+ align:start position:0%
+a horizontal tangent there but we know
+ 
+
+ align:start position:0%
+a horizontal tangent there but we know
+based on our work that that actually
+
+ align:start position:0%
+based on our work that that actually
+ 
+
+ align:start position:0%
+based on our work that that actually
+should happen so I think that's where
+
+ align:start position:0%
+should happen so I think that's where
+ 
+
+ align:start position:0%
+should happen so I think that's where
+I'll stop
\ No newline at end of file
diff --git a/WJUHzSQPRVM.txt b/WJUHzSQPRVM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..020740ca9d9196fe27b81e2ecab3241f94d5c5c0
--- /dev/null
+++ b/WJUHzSQPRVM.txt
@@ -0,0 +1,1531 @@
+align:start position:0%
+ 
+we all know that we are in a global
+
+ align:start position:0%
+we all know that we are in a global
+ 
+
+ align:start position:0%
+we all know that we are in a global
+World Companies have operations all over
+
+ align:start position:0%
+World Companies have operations all over
+ 
+
+ align:start position:0%
+World Companies have operations all over
+the planet and a big question we have to
+
+ align:start position:0%
+the planet and a big question we have to
+ 
+
+ align:start position:0%
+the planet and a big question we have to
+face is how do we keep these Global
+
+ align:start position:0%
+face is how do we keep these Global
+ 
+
+ align:start position:0%
+face is how do we keep these Global
+corporations accountable for providing
+
+ align:start position:0%
+corporations accountable for providing
+ 
+
+ align:start position:0%
+corporations accountable for providing
+good jobs and decent work in far-flung
+
+ align:start position:0%
+good jobs and decent work in far-flung
+ 
+
+ align:start position:0%
+good jobs and decent work in far-flung
+places and let's do it through a company
+
+ align:start position:0%
+places and let's do it through a company
+ 
+
+ align:start position:0%
+places and let's do it through a company
+we all know and love Nike Nike was a
+
+ align:start position:0%
+we all know and love Nike Nike was a
+ 
+
+ align:start position:0%
+we all know and love Nike Nike was a
+Pioneer in this area in the 1960s Nike
+
+ align:start position:0%
+Pioneer in this area in the 1960s Nike
+ 
+
+ align:start position:0%
+Pioneer in this area in the 1960s Nike
+was one of the first companies that said
+
+ align:start position:0%
+was one of the first companies that said
+ 
+
+ align:start position:0%
+was one of the first companies that said
+we will Design our work here we will
+
+ align:start position:0%
+we will Design our work here we will
+ 
+
+ align:start position:0%
+we will Design our work here we will
+market and sell our products around the
+
+ align:start position:0%
+market and sell our products around the
+ 
+
+ align:start position:0%
+market and sell our products around the
+world particularly in the United States
+
+ align:start position:0%
+world particularly in the United States
+ 
+
+ align:start position:0%
+world particularly in the United States
+but we can find cheaper places to
+
+ align:start position:0%
+but we can find cheaper places to
+ 
+
+ align:start position:0%
+but we can find cheaper places to
+manufacture them first they started in
+
+ align:start position:0%
+manufacture them first they started in
+ 
+
+ align:start position:0%
+manufacture them first they started in
+Japan and then Korea and then Indonesia
+
+ align:start position:0%
+Japan and then Korea and then Indonesia
+ 
+
+ align:start position:0%
+Japan and then Korea and then Indonesia
+and Vietnam and China and
+
+ align:start position:0%
+and Vietnam and China and
+ 
+
+ align:start position:0%
+and Vietnam and China and
+Bangladesh and as they did so a number
+
+ align:start position:0%
+Bangladesh and as they did so a number
+ 
+
+ align:start position:0%
+Bangladesh and as they did so a number
+of problems became known the Nike
+
+ align:start position:0%
+of problems became known the Nike
+ 
+
+ align:start position:0%
+of problems became known the Nike
+products were marketed well with Michael
+
+ align:start position:0%
+products were marketed well with Michael
+ 
+
+ align:start position:0%
+products were marketed well with Michael
+Jordan and so on but labor standards
+
+ align:start position:0%
+Jordan and so on but labor standards
+ 
+
+ align:start position:0%
+Jordan and so on but labor standards
+became a problem they were famously
+
+ align:start position:0%
+became a problem they were famously
+ 
+
+ align:start position:0%
+became a problem they were famously
+found having child labor to having
+
+ align:start position:0%
+found having child labor to having
+ 
+
+ align:start position:0%
+found having child labor to having
+unsafe working conditions to having long
+
+ align:start position:0%
+unsafe working conditions to having long
+ 
+
+ align:start position:0%
+unsafe working conditions to having long
+hours of unpaid overtime in their
+
+ align:start position:0%
+hours of unpaid overtime in their
+ 
+
+ align:start position:0%
+hours of unpaid overtime in their
+factories abroad and what was Nike's
+
+ align:start position:0%
+factories abroad and what was Nike's
+ 
+
+ align:start position:0%
+factories abroad and what was Nike's
+response well wait a minute these aren't
+
+ align:start position:0%
+response well wait a minute these aren't
+ 
+
+ align:start position:0%
+response well wait a minute these aren't
+our problems these are our contractors
+
+ align:start position:0%
+our problems these are our contractors
+ 
+
+ align:start position:0%
+our problems these are our contractors
+these are not our employees we don't
+
+ align:start position:0%
+these are not our employees we don't
+ 
+
+ align:start position:0%
+these are not our employees we don't
+treat our employees that way somebody
+
+ align:start position:0%
+treat our employees that way somebody
+ 
+
+ align:start position:0%
+treat our employees that way somebody
+else's problem that lasted for a while
+
+ align:start position:0%
+else's problem that lasted for a while
+ 
+
+ align:start position:0%
+else's problem that lasted for a while
+but it by the middle of the the
+
+ align:start position:0%
+but it by the middle of the the
+ 
+
+ align:start position:0%
+but it by the middle of the the
+1990s Nike watched its stock price Begin
+
+ align:start position:0%
+1990s Nike watched its stock price Begin
+ 
+
+ align:start position:0%
+1990s Nike watched its stock price Begin
+to Fall it saw the publicity begin to to
+
+ align:start position:0%
+to Fall it saw the publicity begin to to
+ 
+
+ align:start position:0%
+to Fall it saw the publicity begin to to
+grow and grow and finally Phil Knight
+
+ align:start position:0%
+grow and grow and finally Phil Knight
+ 
+
+ align:start position:0%
+grow and grow and finally Phil Knight
+the CEO of Nike made this famous
+
+ align:start position:0%
+the CEO of Nike made this famous
+ 
+
+ align:start position:0%
+the CEO of Nike made this famous
+statement he said Nike's products have
+
+ align:start position:0%
+statement he said Nike's products have
+ 
+
+ align:start position:0%
+statement he said Nike's products have
+become synonymous with slave wages
+
+ align:start position:0%
+become synonymous with slave wages
+ 
+
+ align:start position:0%
+become synonymous with slave wages
+forced overtime and arbitrary abuse and
+
+ align:start position:0%
+forced overtime and arbitrary abuse and
+ 
+
+ align:start position:0%
+forced overtime and arbitrary abuse and
+we need to do something about it to
+
+ align:start position:0%
+we need to do something about it to
+ 
+
+ align:start position:0%
+we need to do something about it to
+change that image or we're going to
+
+ align:start position:0%
+change that image or we're going to
+ 
+
+ align:start position:0%
+change that image or we're going to
+suffer as a company so what did Nike do
+
+ align:start position:0%
+suffer as a company so what did Nike do
+ 
+
+ align:start position:0%
+suffer as a company so what did Nike do
+well to its credit it took a whole set
+
+ align:start position:0%
+well to its credit it took a whole set
+ 
+
+ align:start position:0%
+well to its credit it took a whole set
+of actions first it created a social
+
+ align:start position:0%
+of actions first it created a social
+ 
+
+ align:start position:0%
+of actions first it created a social
+responsibility unit within its
+
+ align:start position:0%
+responsibility unit within its
+ 
+
+ align:start position:0%
+responsibility unit within its
+organization and assigned people the
+
+ align:start position:0%
+organization and assigned people the
+ 
+
+ align:start position:0%
+organization and assigned people the
+responsibility to say fix this problem
+
+ align:start position:0%
+responsibility to say fix this problem
+ 
+
+ align:start position:0%
+responsibility to say fix this problem
+that was a good start but not enough
+
+ align:start position:0%
+that was a good start but not enough
+ 
+
+ align:start position:0%
+that was a good start but not enough
+second they created what are called
+
+ align:start position:0%
+second they created what are called
+ 
+
+ align:start position:0%
+second they created what are called
+codes of conduct they established
+
+ align:start position:0%
+codes of conduct they established
+ 
+
+ align:start position:0%
+codes of conduct they established
+minimum wages and uh rules against
+
+ align:start position:0%
+minimum wages and uh rules against
+ 
+
+ align:start position:0%
+minimum wages and uh rules against
+sexual harassment and rules for
+
+ align:start position:0%
+sexual harassment and rules for
+ 
+
+ align:start position:0%
+sexual harassment and rules for
+maximum hours and overtime and freedom
+
+ align:start position:0%
+maximum hours and overtime and freedom
+ 
+
+ align:start position:0%
+maximum hours and overtime and freedom
+of Association and they started to apply
+
+ align:start position:0%
+of Association and they started to apply
+ 
+
+ align:start position:0%
+of Association and they started to apply
+that code of conduct to all factories
+
+ align:start position:0%
+that code of conduct to all factories
+ 
+
+ align:start position:0%
+that code of conduct to all factories
+that they contracted with throughout
+
+ align:start position:0%
+that they contracted with throughout
+ 
+
+ align:start position:0%
+that they contracted with throughout
+their Global Supply Chain they sent
+
+ align:start position:0%
+their Global Supply Chain they sent
+ 
+
+ align:start position:0%
+their Global Supply Chain they sent
+Auditors out there to measure compliance
+
+ align:start position:0%
+Auditors out there to measure compliance
+ 
+
+ align:start position:0%
+Auditors out there to measure compliance
+with its code of conduct they took some
+
+ align:start position:0%
+with its code of conduct they took some
+ 
+
+ align:start position:0%
+with its code of conduct they took some
+of their expert operations managers and
+
+ align:start position:0%
+of their expert operations managers and
+ 
+
+ align:start position:0%
+of their expert operations managers and
+Manufacturing experts sent them to some
+
+ align:start position:0%
+Manufacturing experts sent them to some
+ 
+
+ align:start position:0%
+Manufacturing experts sent them to some
+of these plants to help consult to help
+
+ align:start position:0%
+of these plants to help consult to help
+ 
+
+ align:start position:0%
+of these plants to help consult to help
+people both build safe working
+
+ align:start position:0%
+people both build safe working
+ 
+
+ align:start position:0%
+people both build safe working
+conditions but also aici efficient uh
+
+ align:start position:0%
+conditions but also aici efficient uh
+ 
+
+ align:start position:0%
+conditions but also aici efficient uh
+ways of manufacturing products to
+
+ align:start position:0%
+ways of manufacturing products to
+ 
+
+ align:start position:0%
+ways of manufacturing products to
+improve safety improve quality improve
+
+ align:start position:0%
+improve safety improve quality improve
+ 
+
+ align:start position:0%
+improve safety improve quality improve
+productivity they went on and worked
+
+ align:start position:0%
+productivity they went on and worked
+ 
+
+ align:start position:0%
+productivity they went on and worked
+with a variety of non-governmental
+
+ align:start position:0%
+with a variety of non-governmental
+ 
+
+ align:start position:0%
+with a variety of non-governmental
+organizations or NOS in these countries
+
+ align:start position:0%
+organizations or NOS in these countries
+ 
+
+ align:start position:0%
+organizations or NOS in these countries
+who are advocating for improved
+
+ align:start position:0%
+who are advocating for improved
+ 
+
+ align:start position:0%
+who are advocating for improved
+employment conditions safety standards
+
+ align:start position:0%
+employment conditions safety standards
+ 
+
+ align:start position:0%
+employment conditions safety standards
+and in some cases environmental
+
+ align:start position:0%
+and in some cases environmental
+ 
+
+ align:start position:0%
+and in some cases environmental
+standards in these factories they shared
+
+ align:start position:0%
+standards in these factories they shared
+ 
+
+ align:start position:0%
+standards in these factories they shared
+this Auto data with academic researchers
+
+ align:start position:0%
+this Auto data with academic researchers
+ 
+
+ align:start position:0%
+this Auto data with academic researchers
+including a team of researchers here at
+
+ align:start position:0%
+including a team of researchers here at
+ 
+
+ align:start position:0%
+including a team of researchers here at
+MIT where they start started to analyze
+
+ align:start position:0%
+MIT where they start started to analyze
+ 
+
+ align:start position:0%
+MIT where they start started to analyze
+the data and learn what works and what
+
+ align:start position:0%
+the data and learn what works and what
+ 
+
+ align:start position:0%
+the data and learn what works and what
+didn't they also created a website and
+
+ align:start position:0%
+didn't they also created a website and
+ 
+
+ align:start position:0%
+didn't they also created a website and
+to their credit you can go on this
+
+ align:start position:0%
+to their credit you can go on this
+ 
+
+ align:start position:0%
+to their credit you can go on this
+website and you can find all of their
+
+ align:start position:0%
+website and you can find all of their
+ 
+
+ align:start position:0%
+website and you can find all of their
+factories listed you can find the audit
+
+ align:start position:0%
+factories listed you can find the audit
+ 
+
+ align:start position:0%
+factories listed you can find the audit
+scores and you can find an analysis of
+
+ align:start position:0%
+scores and you can find an analysis of
+ 
+
+ align:start position:0%
+scores and you can find an analysis of
+what is working and a very Frank
+
+ align:start position:0%
+what is working and a very Frank
+ 
+
+ align:start position:0%
+what is working and a very Frank
+analysis of what isn't working they met
+
+ align:start position:0%
+analysis of what isn't working they met
+ 
+
+ align:start position:0%
+analysis of what isn't working they met
+here at MIT and later at at at Stanford
+
+ align:start position:0%
+here at MIT and later at at at Stanford
+ 
+
+ align:start position:0%
+here at MIT and later at at at Stanford
+with multiple stakeholders NOS academics
+
+ align:start position:0%
+with multiple stakeholders NOS academics
+ 
+
+ align:start position:0%
+with multiple stakeholders NOS academics
+competitors suppliers in forming what
+
+ align:start position:0%
+competitors suppliers in forming what
+ 
+
+ align:start position:0%
+competitors suppliers in forming what
+they call a just supply chain uh project
+
+ align:start position:0%
+they call a just supply chain uh project
+ 
+
+ align:start position:0%
+they call a just supply chain uh project
+and set of practices the research
+
+ align:start position:0%
+and set of practices the research
+ 
+
+ align:start position:0%
+and set of practices the research
+findings from our MIT project led by my
+
+ align:start position:0%
+findings from our MIT project led by my
+ 
+
+ align:start position:0%
+findings from our MIT project led by my
+colleague Richard lock reached a number
+
+ align:start position:0%
+colleague Richard lock reached a number
+ 
+
+ align:start position:0%
+colleague Richard lock reached a number
+of conclusions first they found that NGO
+
+ align:start position:0%
+of conclusions first they found that NGO
+ 
+
+ align:start position:0%
+of conclusions first they found that NGO
+pressure was really important to get
+
+ align:start position:0%
+pressure was really important to get
+ 
+
+ align:start position:0%
+pressure was really important to get
+this thing going Nike and other
+
+ align:start position:0%
+this thing going Nike and other
+ 
+
+ align:start position:0%
+this thing going Nike and other
+companies like hulet Packard and other
+
+ align:start position:0%
+companies like hulet Packard and other
+ 
+
+ align:start position:0%
+companies like hulet Packard and other
+electronics firms and other consumer uh
+
+ align:start position:0%
+electronics firms and other consumer uh
+ 
+
+ align:start position:0%
+electronics firms and other consumer uh
+uh companies that followed in Nike's
+
+ align:start position:0%
+uh companies that followed in Nike's
+ 
+
+ align:start position:0%
+uh companies that followed in Nike's
+footsteps did it because there was
+
+ align:start position:0%
+footsteps did it because there was
+ 
+
+ align:start position:0%
+footsteps did it because there was
+transparency and pressure that was being
+
+ align:start position:0%
+transparency and pressure that was being
+ 
+
+ align:start position:0%
+transparency and pressure that was being
+brought to bear to get them to do so the
+
+ align:start position:0%
+brought to bear to get them to do so the
+ 
+
+ align:start position:0%
+brought to bear to get them to do so the
+codes of conduct were successful and the
+
+ align:start position:0%
+codes of conduct were successful and the
+ 
+
+ align:start position:0%
+codes of conduct were successful and the
+audits were successful but only
+
+ align:start position:0%
+audits were successful but only
+ 
+
+ align:start position:0%
+audits were successful but only
+partially they seem to bring the
+
+ align:start position:0%
+partially they seem to bring the
+ 
+
+ align:start position:0%
+partially they seem to bring the
+practices up to about 50 to 60% of the
+
+ align:start position:0%
+practices up to about 50 to 60% of the
+ 
+
+ align:start position:0%
+practices up to about 50 to 60% of the
+overall goals that were established and
+
+ align:start position:0%
+overall goals that were established and
+ 
+
+ align:start position:0%
+overall goals that were established and
+the standards that were set so there's
+
+ align:start position:0%
+the standards that were set so there's
+ 
+
+ align:start position:0%
+the standards that were set so there's
+lots of room for improvement the
+
+ align:start position:0%
+lots of room for improvement the
+ 
+
+ align:start position:0%
+lots of room for improvement the
+standard that was most frequently
+
+ align:start position:0%
+standard that was most frequently
+ 
+
+ align:start position:0%
+standard that was most frequently
+violated was around working hours and
+
+ align:start position:0%
+violated was around working hours and
+ 
+
+ align:start position:0%
+violated was around working hours and
+overtime hours why is that it's
+
+ align:start position:0%
+overtime hours why is that it's
+ 
+
+ align:start position:0%
+overtime hours why is that it's
+important for us to know because we are
+
+ align:start position:0%
+important for us to know because we are
+ 
+
+ align:start position:0%
+important for us to know because we are
+part of the problem as we are fickle
+
+ align:start position:0%
+part of the problem as we are fickle
+ 
+
+ align:start position:0%
+part of the problem as we are fickle
+consumers and all of a sudden we want uh
+
+ align:start position:0%
+consumers and all of a sudden we want uh
+ 
+
+ align:start position:0%
+consumers and all of a sudden we want uh
+the latest uh logo or the latest scarf
+
+ align:start position:0%
+the latest uh logo or the latest scarf
+ 
+
+ align:start position:0%
+the latest uh logo or the latest scarf
+or the latest shirt and so the the
+
+ align:start position:0%
+or the latest shirt and so the the
+ 
+
+ align:start position:0%
+or the latest shirt and so the the
+company puts pressure on the supply
+
+ align:start position:0%
+company puts pressure on the supply
+ 
+
+ align:start position:0%
+company puts pressure on the supply
+chain to get those products in a hurry
+
+ align:start position:0%
+chain to get those products in a hurry
+ 
+
+ align:start position:0%
+chain to get those products in a hurry
+and the contractor there out in Asia or
+
+ align:start position:0%
+and the contractor there out in Asia or
+ 
+
+ align:start position:0%
+and the contractor there out in Asia or
+somewhere else says to employees I need
+
+ align:start position:0%
+somewhere else says to employees I need
+ 
+
+ align:start position:0%
+somewhere else says to employees I need
+those I need them today and get them
+
+ align:start position:0%
+those I need them today and get them
+ 
+
+ align:start position:0%
+those I need them today and get them
+done no matter what or we're going to
+
+ align:start position:0%
+done no matter what or we're going to
+ 
+
+ align:start position:0%
+done no matter what or we're going to
+lose this contract and so they work long
+
+ align:start position:0%
+lose this contract and so they work long
+ 
+
+ align:start position:0%
+lose this contract and so they work long
+hours and they're forced to work
+
+ align:start position:0%
+hours and they're forced to work
+ 
+
+ align:start position:0%
+hours and they're forced to work
+overtime and all kinds of bad things
+
+ align:start position:0%
+overtime and all kinds of bad things
+ 
+
+ align:start position:0%
+overtime and all kinds of bad things
+happen after that
+
+ align:start position:0%
+happen after that
+ 
+
+ align:start position:0%
+happen after that
+but the scores of suppliers that got
+
+ align:start position:0%
+but the scores of suppliers that got
+ 
+
+ align:start position:0%
+but the scores of suppliers that got
+better had three key ingredients first
+
+ align:start position:0%
+better had three key ingredients first
+ 
+
+ align:start position:0%
+better had three key ingredients first
+they got management help from Nike and
+
+ align:start position:0%
+they got management help from Nike and
+ 
+
+ align:start position:0%
+they got management help from Nike and
+other companies secondly they were in
+
+ align:start position:0%
+other companies secondly they were in
+ 
+
+ align:start position:0%
+other companies secondly they were in
+countries that had stronger rules of law
+
+ align:start position:0%
+countries that had stronger rules of law
+ 
+
+ align:start position:0%
+countries that had stronger rules of law
+less corrupt governments and they had
+
+ align:start position:0%
+less corrupt governments and they had
+ 
+
+ align:start position:0%
+less corrupt governments and they had
+stronger rules governing human rights
+
+ align:start position:0%
+stronger rules governing human rights
+ 
+
+ align:start position:0%
+stronger rules governing human rights
+and Commercial practices and so the
+
+ align:start position:0%
+and Commercial practices and so the
+ 
+
+ align:start position:0%
+and Commercial practices and so the
+environment of the country matters so
+
+ align:start position:0%
+environment of the country matters so
+ 
+
+ align:start position:0%
+environment of the country matters so
+this is all great progress companies
+
+ align:start position:0%
+this is all great progress companies
+ 
+
+ align:start position:0%
+this is all great progress companies
+have learned how to do this but what
+
+ align:start position:0%
+have learned how to do this but what
+ 
+
+ align:start position:0%
+have learned how to do this but what
+about us us if we're part of the problem
+
+ align:start position:0%
+about us us if we're part of the problem
+ 
+
+ align:start position:0%
+about us us if we're part of the problem
+we ought to be part of the solution
+
+ align:start position:0%
+we ought to be part of the solution
+ 
+
+ align:start position:0%
+we ought to be part of the solution
+there are a number of things that have
+
+ align:start position:0%
+there are a number of things that have
+ 
+
+ align:start position:0%
+there are a number of things that have
+been very positive there's an
+
+ align:start position:0%
+been very positive there's an
+ 
+
+ align:start position:0%
+been very positive there's an
+organization on college campuses around
+
+ align:start position:0%
+organization on college campuses around
+ 
+
+ align:start position:0%
+organization on college campuses around
+the country called United students
+
+ align:start position:0%
+the country called United students
+ 
+
+ align:start position:0%
+the country called United students
+against sweat shops and they have put
+
+ align:start position:0%
+against sweat shops and they have put
+ 
+
+ align:start position:0%
+against sweat shops and they have put
+pressure on their universities
+
+ align:start position:0%
+pressure on their universities
+ 
+
+ align:start position:0%
+pressure on their universities
+universities like Cornell and brown and
+
+ align:start position:0%
+universities like Cornell and brown and
+ 
+
+ align:start position:0%
+universities like Cornell and brown and
+Wisconsin and others to make sure that
+
+ align:start position:0%
+Wisconsin and others to make sure that
+ 
+
+ align:start position:0%
+Wisconsin and others to make sure that
+they're only buying their University
+
+ align:start position:0%
+they're only buying their University
+ 
+
+ align:start position:0%
+they're only buying their University
+logo apparel and athletic wear from
+
+ align:start position:0%
+logo apparel and athletic wear from
+ 
+
+ align:start position:0%
+logo apparel and athletic wear from
+companies that have these kinds of uh
+
+ align:start position:0%
+companies that have these kinds of uh
+ 
+
+ align:start position:0%
+companies that have these kinds of uh
+just supply chain practic in place so we
+
+ align:start position:0%
+just supply chain practic in place so we
+ 
+
+ align:start position:0%
+just supply chain practic in place so we
+can do this but it takes a lot of energy
+
+ align:start position:0%
+can do this but it takes a lot of energy
+ 
+
+ align:start position:0%
+can do this but it takes a lot of energy
+and a lot of collective effort and it
+
+ align:start position:0%
+and a lot of collective effort and it
+ 
+
+ align:start position:0%
+and a lot of collective effort and it
+has to be done by all the parties
+
+ align:start position:0%
+has to be done by all the parties
+ 
+
+ align:start position:0%
+has to be done by all the parties
+working together companies can't do it
+
+ align:start position:0%
+working together companies can't do it
+ 
+
+ align:start position:0%
+working together companies can't do it
+alone NOS can't do it alone local
+
+ align:start position:0%
+alone NOS can't do it alone local
+ 
+
+ align:start position:0%
+alone NOS can't do it alone local
+governments can't do it alone but if
+
+ align:start position:0%
+governments can't do it alone but if
+ 
+
+ align:start position:0%
+governments can't do it alone but if
+they all work together and build a
+
+ align:start position:0%
+they all work together and build a
+ 
+
+ align:start position:0%
+they all work together and build a
+sustained effort to improve the
+
+ align:start position:0%
+sustained effort to improve the
+ 
+
+ align:start position:0%
+sustained effort to improve the
+conditions and then produce the data
+
+ align:start position:0%
+conditions and then produce the data
+ 
+
+ align:start position:0%
+conditions and then produce the data
+that makes it all transparent for us as
+
+ align:start position:0%
+that makes it all transparent for us as
+ 
+
+ align:start position:0%
+that makes it all transparent for us as
+consumers we can make a difference in
+
+ align:start position:0%
+consumers we can make a difference in
+ 
+
+ align:start position:0%
+consumers we can make a difference in
+improving the conditions of very low
+
+ align:start position:0%
+improving the conditions of very low
+ 
+
+ align:start position:0%
+improving the conditions of very low
+wage workers in many developing
+
+ align:start position:0%
+wage workers in many developing
+ 
+
+ align:start position:0%
+wage workers in many developing
+countries so I'd like to ask you two
+
+ align:start position:0%
+countries so I'd like to ask you two
+ 
+
+ align:start position:0%
+countries so I'd like to ask you two
+questions Apple our computer friends and
+
+ align:start position:0%
+questions Apple our computer friends and
+ 
+
+ align:start position:0%
+questions Apple our computer friends and
+iPhone friends and iPod friends are
+
+ align:start position:0%
+iPhone friends and iPod friends are
+ 
+
+ align:start position:0%
+iPhone friends and iPod friends are
+about two decades behind Nike they have
+
+ align:start position:0%
+about two decades behind Nike they have
+ 
+
+ align:start position:0%
+about two decades behind Nike they have
+experienced terrible problems with their
+
+ align:start position:0%
+experienced terrible problems with their
+ 
+
+ align:start position:0%
+experienced terrible problems with their
+contractors in China and elsewhere you
+
+ align:start position:0%
+contractors in China and elsewhere you
+ 
+
+ align:start position:0%
+contractors in China and elsewhere you
+may have heard about foxcon with
+
+ align:start position:0%
+may have heard about foxcon with
+ 
+
+ align:start position:0%
+may have heard about foxcon with
+suicides of workers frustrated with
+
+ align:start position:0%
+suicides of workers frustrated with
+ 
+
+ align:start position:0%
+suicides of workers frustrated with
+terrible working conditions if you were
+
+ align:start position:0%
+terrible working conditions if you were
+ 
+
+ align:start position:0%
+terrible working conditions if you were
+to write to the CEO of Apple what should
+
+ align:start position:0%
+to write to the CEO of Apple what should
+ 
+
+ align:start position:0%
+to write to the CEO of Apple what should
+Apple learn from Nike's experiences and
+
+ align:start position:0%
+Apple learn from Nike's experiences and
+ 
+
+ align:start position:0%
+Apple learn from Nike's experiences and
+then more broadly what can you do to
+
+ align:start position:0%
+then more broadly what can you do to
+ 
+
+ align:start position:0%
+then more broadly what can you do to
+hold companies accountable for their
+
+ align:start position:0%
+hold companies accountable for their
+ 
+
+ align:start position:0%
+hold companies accountable for their
+Global operations how can we take
+
+ align:start position:0%
+Global operations how can we take
+ 
+
+ align:start position:0%
+Global operations how can we take
+responsibility for making sure that
+
+ align:start position:0%
+responsibility for making sure that
+ 
+
+ align:start position:0%
+responsibility for making sure that
+every shirt every tie every sweatshirt
+
+ align:start position:0%
+every shirt every tie every sweatshirt
+ 
+
+ align:start position:0%
+every shirt every tie every sweatshirt
+that we buy is made in ajust supply
+
+ align:start position:0%
+that we buy is made in ajust supply
+ 
+
+ align:start position:0%
+that we buy is made in ajust supply
+chain and keep asking and be willing to
+
+ align:start position:0%
+chain and keep asking and be willing to
+ 
+
+ align:start position:0%
+chain and keep asking and be willing to
+pay for products that are made under
+
+ align:start position:0%
+pay for products that are made under
+ 
+
+ align:start position:0%
+pay for products that are made under
+Fair working conditions we can do that
+
+ align:start position:0%
+Fair working conditions we can do that
+ 
+
+ align:start position:0%
+Fair working conditions we can do that
+individually as consumers and we can
+
+ align:start position:0%
+individually as consumers and we can
+ 
+
+ align:start position:0%
+individually as consumers and we can
+collectively set the Norms that is that
+
+ align:start position:0%
+collectively set the Norms that is that
+ 
+
+ align:start position:0%
+collectively set the Norms that is that
+essentially say to any company if you
+
+ align:start position:0%
+essentially say to any company if you
+ 
+
+ align:start position:0%
+essentially say to any company if you
+want our business then you've got to
+
+ align:start position:0%
+want our business then you've got to
+ 
+
+ align:start position:0%
+want our business then you've got to
+demonstrate that you are providing safe
+
+ align:start position:0%
+demonstrate that you are providing safe
+ 
+
+ align:start position:0%
+demonstrate that you are providing safe
+and healthy working conditions Fair
+
+ align:start position:0%
+and healthy working conditions Fair
+ 
+
+ align:start position:0%
+and healthy working conditions Fair
+wages for people wherever they make
+
+ align:start position:0%
+wages for people wherever they make
+ 
+
+ align:start position:0%
+wages for people wherever they make
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products e
\ No newline at end of file
diff --git a/XeTsZhYHY_E.txt b/XeTsZhYHY_E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f438de4e0415df626ba9800905c5d8bef61cdad
--- /dev/null
+++ b/XeTsZhYHY_E.txt
@@ -0,0 +1,1443 @@
+align:start position:0%
+ 
+let's consider what we call the window
+
+ align:start position:0%
+let's consider what we call the window
+ 
+
+ align:start position:0%
+let's consider what we call the window
+washer problem what we have is suspended
+
+ align:start position:0%
+washer problem what we have is suspended
+ 
+
+ align:start position:0%
+washer problem what we have is suspended
+from some ceiling we have a pulley and
+
+ align:start position:0%
+from some ceiling we have a pulley and
+ 
+
+ align:start position:0%
+from some ceiling we have a pulley and
+the pulley is suspended by a rope which
+
+ align:start position:0%
+the pulley is suspended by a rope which
+ 
+
+ align:start position:0%
+the pulley is suspended by a rope which
+we're going to call this string 3 and we
+
+ align:start position:0%
+we're going to call this string 3 and we
+ 
+
+ align:start position:0%
+we're going to call this string 3 and we
+have a rope that is wrapping around this
+
+ align:start position:0%
+have a rope that is wrapping around this
+ 
+
+ align:start position:0%
+have a rope that is wrapping around this
+pulley and then it wraps around another
+
+ align:start position:0%
+pulley and then it wraps around another
+ 
+
+ align:start position:0%
+pulley and then it wraps around another
+pulley so this rope is going around
+
+ align:start position:0%
+pulley so this rope is going around
+ 
+
+ align:start position:0%
+pulley so this rope is going around
+another pulley and it's fixed to the
+
+ align:start position:0%
+another pulley and it's fixed to the
+ 
+
+ align:start position:0%
+another pulley and it's fixed to the
+ceiling and this is what we're gonna
+
+ align:start position:0%
+ceiling and this is what we're gonna
+ 
+
+ align:start position:0%
+ceiling and this is what we're gonna
+call string 1 and then this string
+
+ align:start position:0%
+call string 1 and then this string
+ 
+
+ align:start position:0%
+call string 1 and then this string
+there's another string that comes down
+
+ align:start position:0%
+there's another string that comes down
+ 
+
+ align:start position:0%
+there's another string that comes down
+to a platform and this one we're gonna
+
+ align:start position:0%
+to a platform and this one we're gonna
+ 
+
+ align:start position:0%
+to a platform and this one we're gonna
+call string 2 and sitting on the
+
+ align:start position:0%
+call string 2 and sitting on the
+ 
+
+ align:start position:0%
+call string 2 and sitting on the
+platform is a person so we have a person
+
+ align:start position:0%
+platform is a person so we have a person
+ 
+
+ align:start position:0%
+platform is a person so we have a person
+sitting on the platform and that person
+
+ align:start position:0%
+sitting on the platform and that person
+ 
+
+ align:start position:0%
+sitting on the platform and that person
+is pulling the rope down now this is a
+
+ align:start position:0%
+is pulling the rope down now this is a
+ 
+
+ align:start position:0%
+is pulling the rope down now this is a
+very complicated problem and it's a
+
+ align:start position:0%
+very complicated problem and it's a
+ 
+
+ align:start position:0%
+very complicated problem and it's a
+classic example of how do we choose
+
+ align:start position:0%
+classic example of how do we choose
+ 
+
+ align:start position:0%
+classic example of how do we choose
+systems so that we can apply Newton's
+
+ align:start position:0%
+systems so that we can apply Newton's
+ 
+
+ align:start position:0%
+systems so that we can apply Newton's
+second law now one of the important
+
+ align:start position:0%
+second law now one of the important
+ 
+
+ align:start position:0%
+second law now one of the important
+things we're going to do is learn to see
+
+ align:start position:0%
+things we're going to do is learn to see
+ 
+
+ align:start position:0%
+things we're going to do is learn to see
+what when we choose a system what forces
+
+ align:start position:0%
+what when we choose a system what forces
+ 
+
+ align:start position:0%
+what when we choose a system what forces
+are internal and external and that will
+
+ align:start position:0%
+are internal and external and that will
+ 
+
+ align:start position:0%
+are internal and external and that will
+enable us to pick a very nice system
+
+ align:start position:0%
+enable us to pick a very nice system
+ 
+
+ align:start position:0%
+enable us to pick a very nice system
+which will make the analysis easy the
+
+ align:start position:0%
+which will make the analysis easy the
+ 
+
+ align:start position:0%
+which will make the analysis easy the
+way we'll do this is we'll approach it
+
+ align:start position:0%
+way we'll do this is we'll approach it
+ 
+
+ align:start position:0%
+way we'll do this is we'll approach it
+in stages
+
+ align:start position:0%
+in stages
+ 
+
+ align:start position:0%
+in stages
+well first focus on the person the
+
+ align:start position:0%
+well first focus on the person the
+ 
+
+ align:start position:0%
+well first focus on the person the
+platform and this pulley by the way this
+
+ align:start position:0%
+platform and this pulley by the way this
+ 
+
+ align:start position:0%
+platform and this pulley by the way this
+is pulley a and this one is pulley B and
+
+ align:start position:0%
+is pulley a and this one is pulley B and
+ 
+
+ align:start position:0%
+is pulley a and this one is pulley B and
+let's use the symbol P for the platform
+
+ align:start position:0%
+let's use the symbol P for the platform
+ 
+
+ align:start position:0%
+let's use the symbol P for the platform
+and we'll call this a washer person and
+
+ align:start position:0%
+and we'll call this a washer person and
+ 
+
+ align:start position:0%
+and we'll call this a washer person and
+we're going to use the symbol W for the
+
+ align:start position:0%
+we're going to use the symbol W for the
+ 
+
+ align:start position:0%
+we're going to use the symbol W for the
+person so what makes this problem
+
+ align:start position:0%
+person so what makes this problem
+ 
+
+ align:start position:0%
+person so what makes this problem
+complicated is all these different
+
+ align:start position:0%
+complicated is all these different
+ 
+
+ align:start position:0%
+complicated is all these different
+elements now the first stage is that
+
+ align:start position:0%
+elements now the first stage is that
+ 
+
+ align:start position:0%
+elements now the first stage is that
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+separately look at the purse
+
+ align:start position:0%
+separately look at the purse
+ 
+
+ align:start position:0%
+separately look at the purse
+the platform and then combine them into
+
+ align:start position:0%
+the platform and then combine them into
+ 
+
+ align:start position:0%
+the platform and then combine them into
+a system of person and platform but
+
+ align:start position:0%
+a system of person and platform but
+ 
+
+ align:start position:0%
+a system of person and platform but
+notice the rope is connected to the
+
+ align:start position:0%
+notice the rope is connected to the
+ 
+
+ align:start position:0%
+notice the rope is connected to the
+platform so the next stages will also
+
+ align:start position:0%
+platform so the next stages will also
+ 
+
+ align:start position:0%
+platform so the next stages will also
+consider a system consisting of pulley a
+
+ align:start position:0%
+consider a system consisting of pulley a
+ 
+
+ align:start position:0%
+consider a system consisting of pulley a
+person and the platform and the washer
+
+ align:start position:0%
+person and the platform and the washer
+ 
+
+ align:start position:0%
+person and the platform and the washer
+now let's draw the Freebody diagrams
+
+ align:start position:0%
+now let's draw the Freebody diagrams
+ 
+
+ align:start position:0%
+now let's draw the Freebody diagrams
+let's begin by drawing the free body
+
+ align:start position:0%
+let's begin by drawing the free body
+ 
+
+ align:start position:0%
+let's begin by drawing the free body
+diagram on the washer so washer what do
+
+ align:start position:0%
+diagram on the washer so washer what do
+ 
+
+ align:start position:0%
+diagram on the washer so washer what do
+we have on the washer the first thing to
+
+ align:start position:0%
+we have on the washer the first thing to
+ 
+
+ align:start position:0%
+we have on the washer the first thing to
+think about is the string the washer is
+
+ align:start position:0%
+think about is the string the washer is
+ 
+
+ align:start position:0%
+think about is the string the washer is
+pulling the string down so the string is
+
+ align:start position:0%
+pulling the string down so the string is
+ 
+
+ align:start position:0%
+pulling the string down so the string is
+pulling the washer up so that's a force
+
+ align:start position:0%
+pulling the washer up so that's a force
+ 
+
+ align:start position:0%
+pulling the washer up so that's a force
+of string 1 on the washer now there's
+
+ align:start position:0%
+of string 1 on the washer now there's
+ 
+
+ align:start position:0%
+of string 1 on the washer now there's
+also the gravitational force and washer
+
+ align:start position:0%
+also the gravitational force and washer
+ 
+
+ align:start position:0%
+also the gravitational force and washer
+G and what we also have to consider the
+
+ align:start position:0%
+G and what we also have to consider the
+ 
+
+ align:start position:0%
+G and what we also have to consider the
+fact is is that the person is sitting on
+
+ align:start position:0%
+fact is is that the person is sitting on
+ 
+
+ align:start position:0%
+fact is is that the person is sitting on
+the platform so the platform is pushing
+
+ align:start position:0%
+the platform so the platform is pushing
+ 
+
+ align:start position:0%
+the platform so the platform is pushing
+the person up and we'll call that a
+
+ align:start position:0%
+the person up and we'll call that a
+ 
+
+ align:start position:0%
+the person up and we'll call that a
+normal force on the washer due to the
+
+ align:start position:0%
+normal force on the washer due to the
+ 
+
+ align:start position:0%
+normal force on the washer due to the
+platform and those are the free body
+
+ align:start position:0%
+platform and those are the free body
+ 
+
+ align:start position:0%
+platform and those are the free body
+diagram for the free body diagram on the
+
+ align:start position:0%
+diagram for the free body diagram on the
+ 
+
+ align:start position:0%
+diagram for the free body diagram on the
+washer now let's focus on the platform
+
+ align:start position:0%
+washer now let's focus on the platform
+ 
+
+ align:start position:0%
+washer now let's focus on the platform
+so here we'll draw the platform and now
+
+ align:start position:0%
+so here we'll draw the platform and now
+ 
+
+ align:start position:0%
+so here we'll draw the platform and now
+let's look at the forces on the platform
+
+ align:start position:0%
+let's look at the forces on the platform
+ 
+
+ align:start position:0%
+let's look at the forces on the platform
+let's begin by looking for the internal
+
+ align:start position:0%
+let's begin by looking for the internal
+ 
+
+ align:start position:0%
+let's begin by looking for the internal
+forces the the Newton's third law pairs
+
+ align:start position:0%
+forces the the Newton's third law pairs
+ 
+
+ align:start position:0%
+forces the the Newton's third law pairs
+the platform is pushing the person up
+
+ align:start position:0%
+the platform is pushing the person up
+ 
+
+ align:start position:0%
+the platform is pushing the person up
+the person is pushing the platform down
+
+ align:start position:0%
+the person is pushing the platform down
+ 
+
+ align:start position:0%
+the person is pushing the platform down
+so we'll write that for says n on the
+
+ align:start position:0%
+so we'll write that for says n on the
+ 
+
+ align:start position:0%
+so we'll write that for says n on the
+platform due to the washer and
+
+ align:start position:0%
+platform due to the washer and
+ 
+
+ align:start position:0%
+platform due to the washer and
+immediately let's just circle this third
+
+ align:start position:0%
+immediately let's just circle this third
+ 
+
+ align:start position:0%
+immediately let's just circle this third
+law pair now string two is pulling the
+
+ align:start position:0%
+law pair now string two is pulling the
+ 
+
+ align:start position:0%
+law pair now string two is pulling the
+platform up so let's draw that force we
+
+ align:start position:0%
+platform up so let's draw that force we
+ 
+
+ align:start position:0%
+platform up so let's draw that force we
+have we'll call that a tension force in
+
+ align:start position:0%
+have we'll call that a tension force in
+ 
+
+ align:start position:0%
+have we'll call that a tension force in
+the string it's on the platform due to
+
+ align:start position:0%
+the string it's on the platform due to
+ 
+
+ align:start position:0%
+the string it's on the platform due to
+string two and finally we have the
+
+ align:start position:0%
+string two and finally we have the
+ 
+
+ align:start position:0%
+string two and finally we have the
+gravitational force on the platform and
+
+ align:start position:0%
+gravitational force on the platform and
+ 
+
+ align:start position:0%
+gravitational force on the platform and
+that's our free body diagram on the
+
+ align:start position:0%
+that's our free body diagram on the
+ 
+
+ align:start position:0%
+that's our free body diagram on the
+platform now you may have said well why
+
+ align:start position:0%
+platform now you may have said well why
+ 
+
+ align:start position:0%
+platform now you may have said well why
+should I separate these out why didn't I
+
+ align:start position:0%
+should I separate these out why didn't I
+ 
+
+ align:start position:0%
+should I separate these out why didn't I
+just use the person and the platform so
+
+ align:start position:0%
+just use the person and the platform so
+ 
+
+ align:start position:0%
+just use the person and the platform so
+let's draw that picture so now imagine
+
+ align:start position:0%
+let's draw that picture so now imagine
+ 
+
+ align:start position:0%
+let's draw that picture so now imagine
+underneath this you
+
+ align:start position:0%
+underneath this you
+ 
+
+ align:start position:0%
+underneath this you
+a system consisting of the person and
+
+ align:start position:0%
+a system consisting of the person and
+ 
+
+ align:start position:0%
+a system consisting of the person and
+the platform and I'll just draw that
+
+ align:start position:0%
+the platform and I'll just draw that
+ 
+
+ align:start position:0%
+the platform and I'll just draw that
+system like that so what we're doing is
+
+ align:start position:0%
+system like that so what we're doing is
+ 
+
+ align:start position:0%
+system like that so what we're doing is
+we're taking these two separate Freebody
+
+ align:start position:0%
+we're taking these two separate Freebody
+ 
+
+ align:start position:0%
+we're taking these two separate Freebody
+diagrams and we're going to combine them
+
+ align:start position:0%
+diagrams and we're going to combine them
+ 
+
+ align:start position:0%
+diagrams and we're going to combine them
+here and by Newton's third law all
+
+ align:start position:0%
+here and by Newton's third law all
+ 
+
+ align:start position:0%
+here and by Newton's third law all
+internal forces should cancel in pairs
+
+ align:start position:0%
+internal forces should cancel in pairs
+ 
+
+ align:start position:0%
+internal forces should cancel in pairs
+so now let's separately think about the
+
+ align:start position:0%
+so now let's separately think about the
+ 
+
+ align:start position:0%
+so now let's separately think about the
+forces and see that that's the case well
+
+ align:start position:0%
+forces and see that that's the case well
+ 
+
+ align:start position:0%
+forces and see that that's the case well
+we have the gravitational force on the
+
+ align:start position:0%
+we have the gravitational force on the
+ 
+
+ align:start position:0%
+we have the gravitational force on the
+system which is the mass of the platform
+
+ align:start position:0%
+system which is the mass of the platform
+ 
+
+ align:start position:0%
+system which is the mass of the platform
+plus the mass of the washer times G we
+
+ align:start position:0%
+plus the mass of the washer times G we
+ 
+
+ align:start position:0%
+plus the mass of the washer times G we
+still have the string pulling the person
+
+ align:start position:0%
+still have the string pulling the person
+ 
+
+ align:start position:0%
+still have the string pulling the person
+up because the person is pulling the
+
+ align:start position:0%
+up because the person is pulling the
+ 
+
+ align:start position:0%
+up because the person is pulling the
+string down so we still have the force
+
+ align:start position:0%
+string down so we still have the force
+ 
+
+ align:start position:0%
+string down so we still have the force
+f1 on the washer that's string 1 on the
+
+ align:start position:0%
+f1 on the washer that's string 1 on the
+ 
+
+ align:start position:0%
+f1 on the washer that's string 1 on the
+washer and we still have the pulley the
+
+ align:start position:0%
+washer and we still have the pulley the
+ 
+
+ align:start position:0%
+washer and we still have the pulley the
+tension in string 2 pulling it up so we
+
+ align:start position:0%
+tension in string 2 pulling it up so we
+ 
+
+ align:start position:0%
+tension in string 2 pulling it up so we
+still have the force t2 on the platform
+
+ align:start position:0%
+still have the force t2 on the platform
+ 
+
+ align:start position:0%
+still have the force t2 on the platform
+now when you look at this what we're
+
+ align:start position:0%
+now when you look at this what we're
+ 
+
+ align:start position:0%
+now when you look at this what we're
+doing is we're adding these two Freebody
+
+ align:start position:0%
+doing is we're adding these two Freebody
+ 
+
+ align:start position:0%
+doing is we're adding these two Freebody
+diagrams together the internal forces
+
+ align:start position:0%
+diagrams together the internal forces
+ 
+
+ align:start position:0%
+diagrams together the internal forces
+now are the normal force they're equal
+
+ align:start position:0%
+now are the normal force they're equal
+ 
+
+ align:start position:0%
+now are the normal force they're equal
+in magnitude opposite and direction so
+
+ align:start position:0%
+in magnitude opposite and direction so
+ 
+
+ align:start position:0%
+in magnitude opposite and direction so
+when you add them together they cancel
+
+ align:start position:0%
+when you add them together they cancel
+ 
+
+ align:start position:0%
+when you add them together they cancel
+and we're just left with that with that
+
+ align:start position:0%
+and we're just left with that with that
+ 
+
+ align:start position:0%
+and we're just left with that with that
+with that and with that and so this is
+
+ align:start position:0%
+with that and with that and so this is
+ 
+
+ align:start position:0%
+with that and with that and so this is
+now the combined system now you might
+
+ align:start position:0%
+now the combined system now you might
+ 
+
+ align:start position:0%
+now the combined system now you might
+ask why did we not include the pulley
+
+ align:start position:0%
+ask why did we not include the pulley
+ 
+
+ align:start position:0%
+ask why did we not include the pulley
+well let's take a look at that so I'm
+
+ align:start position:0%
+well let's take a look at that so I'm
+ 
+
+ align:start position:0%
+well let's take a look at that so I'm
+gonna draw the Freebody diagram just on
+
+ align:start position:0%
+gonna draw the Freebody diagram just on
+ 
+
+ align:start position:0%
+gonna draw the Freebody diagram just on
+pulley 8 so let's draw a pulley a now
+
+ align:start position:0%
+pulley 8 so let's draw a pulley a now
+ 
+
+ align:start position:0%
+pulley 8 so let's draw a pulley a now
+what we have here is the string on both
+
+ align:start position:0%
+what we have here is the string on both
+ 
+
+ align:start position:0%
+what we have here is the string on both
+sides is pulling pulley a up and that's
+
+ align:start position:0%
+sides is pulling pulley a up and that's
+ 
+
+ align:start position:0%
+sides is pulling pulley a up and that's
+the tension in string 1 so what we have
+
+ align:start position:0%
+the tension in string 1 so what we have
+ 
+
+ align:start position:0%
+the tension in string 1 so what we have
+is I'm going to call that tension in
+
+ align:start position:0%
+is I'm going to call that tension in
+ 
+
+ align:start position:0%
+is I'm going to call that tension in
+string 1 tension in string 1 and just to
+
+ align:start position:0%
+string 1 tension in string 1 and just to
+ 
+
+ align:start position:0%
+string 1 tension in string 1 and just to
+alert you that keep in mind that this
+
+ align:start position:0%
+alert you that keep in mind that this
+ 
+
+ align:start position:0%
+alert you that keep in mind that this
+force here is the force of the string on
+
+ align:start position:0%
+force here is the force of the string on
+ 
+
+ align:start position:0%
+force here is the force of the string on
+the person and
+
+ align:start position:0%
+the person and
+ 
+
+ align:start position:0%
+the person and
+- is also tension in the string because
+
+ align:start position:0%
+- is also tension in the string because
+ 
+
+ align:start position:0%
+- is also tension in the string because
+this is our sumption of a massless
+
+ align:start position:0%
+this is our sumption of a massless
+ 
+
+ align:start position:0%
+this is our sumption of a massless
+string so notice that everywhere in a
+
+ align:start position:0%
+string so notice that everywhere in a
+ 
+
+ align:start position:0%
+string so notice that everywhere in a
+string the tension is uniform so I'm
+
+ align:start position:0%
+string the tension is uniform so I'm
+ 
+
+ align:start position:0%
+string the tension is uniform so I'm
+just going to simplify that by calling a
+
+ align:start position:0%
+just going to simplify that by calling a
+ 
+
+ align:start position:0%
+just going to simplify that by calling a
+t1 what are the other forces on the
+
+ align:start position:0%
+t1 what are the other forces on the
+ 
+
+ align:start position:0%
+t1 what are the other forces on the
+pulley well we're assuming that these
+
+ align:start position:0%
+pulley well we're assuming that these
+ 
+
+ align:start position:0%
+pulley well we're assuming that these
+pulleys are massless and so there's no
+
+ align:start position:0%
+pulleys are massless and so there's no
+ 
+
+ align:start position:0%
+pulleys are massless and so there's no
+gravitational force on the pulley and
+
+ align:start position:0%
+gravitational force on the pulley and
+ 
+
+ align:start position:0%
+gravitational force on the pulley and
+the only thing we have is the string
+
+ align:start position:0%
+the only thing we have is the string
+ 
+
+ align:start position:0%
+the only thing we have is the string
+pulling there's the tension in the
+
+ align:start position:0%
+pulling there's the tension in the
+ 
+
+ align:start position:0%
+pulling there's the tension in the
+string so now this is a little bit
+
+ align:start position:0%
+string so now this is a little bit
+ 
+
+ align:start position:0%
+string so now this is a little bit
+different this is a force on the pulley
+
+ align:start position:0%
+different this is a force on the pulley
+ 
+
+ align:start position:0%
+different this is a force on the pulley
+- so at the moment let's do something a
+
+ align:start position:0%
+- so at the moment let's do something a
+ 
+
+ align:start position:0%
+- so at the moment let's do something a
+little bit different let's consider our
+
+ align:start position:0%
+little bit different let's consider our
+ 
+
+ align:start position:0%
+little bit different let's consider our
+system to be the string so it's pulley a
+
+ align:start position:0%
+system to be the string so it's pulley a
+ 
+
+ align:start position:0%
+system to be the string so it's pulley a
+we call that string - that's our system
+
+ align:start position:0%
+we call that string - that's our system
+ 
+
+ align:start position:0%
+we call that string - that's our system
+so I modified that a little bit I just
+
+ align:start position:0%
+so I modified that a little bit I just
+ 
+
+ align:start position:0%
+so I modified that a little bit I just
+didn't consider the pulley separately I
+
+ align:start position:0%
+didn't consider the pulley separately I
+ 
+
+ align:start position:0%
+didn't consider the pulley separately I
+consider the pulley and the string as
+
+ align:start position:0%
+consider the pulley and the string as
+ 
+
+ align:start position:0%
+consider the pulley and the string as
+the system then here the string is
+
+ align:start position:0%
+the system then here the string is
+ 
+
+ align:start position:0%
+the system then here the string is
+pulling the platform up the platform
+
+ align:start position:0%
+pulling the platform up the platform
+ 
+
+ align:start position:0%
+pulling the platform up the platform
+there for is pulling the string down and
+
+ align:start position:0%
+there for is pulling the string down and
+ 
+
+ align:start position:0%
+there for is pulling the string down and
+once again we have a third law pair and
+
+ align:start position:0%
+once again we have a third law pair and
+ 
+
+ align:start position:0%
+once again we have a third law pair and
+so if I added these two together then
+
+ align:start position:0%
+so if I added these two together then
+ 
+
+ align:start position:0%
+so if I added these two together then
+what I'll now have and this is why this
+
+ align:start position:0%
+what I'll now have and this is why this
+ 
+
+ align:start position:0%
+what I'll now have and this is why this
+problem is kind of complex we have
+
+ align:start position:0%
+problem is kind of complex we have
+ 
+
+ align:start position:0%
+problem is kind of complex we have
+pulley a string - platform P and washer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+person and if we know and these two
+
+ align:start position:0%
+person and if we know and these two
+ 
+
+ align:start position:0%
+person and if we know and these two
+systems together we have this
+
+ align:start position:0%
+systems together we have this
+ 
+
+ align:start position:0%
+systems together we have this
+complicated system but what are the
+
+ align:start position:0%
+complicated system but what are the
+ 
+
+ align:start position:0%
+complicated system but what are the
+forces on this system
+
+ align:start position:0%
+forces on this system
+ 
+
+ align:start position:0%
+forces on this system
+well the Rope is pulling it up the
+
+ align:start position:0%
+well the Rope is pulling it up the
+ 
+
+ align:start position:0%
+well the Rope is pulling it up the
+person was remember we had this force W
+
+ align:start position:0%
+person was remember we had this force W
+ 
+
+ align:start position:0%
+person was remember we had this force W
+one was the force of string one on the
+
+ align:start position:0%
+one was the force of string one on the
+ 
+
+ align:start position:0%
+one was the force of string one on the
+washer that also was the tension
+
+ align:start position:0%
+washer that also was the tension
+ 
+
+ align:start position:0%
+washer that also was the tension
+everywhere in the string so we have
+
+ align:start position:0%
+everywhere in the string so we have
+ 
+
+ align:start position:0%
+everywhere in the string so we have
+another T one up these two forces no
+
+ align:start position:0%
+another T one up these two forces no
+ 
+
+ align:start position:0%
+another T one up these two forces no
+cancel in pairs the internal forces
+
+ align:start position:0%
+cancel in pairs the internal forces
+ 
+
+ align:start position:0%
+cancel in pairs the internal forces
+there and so down we just have mass
+
+ align:start position:0%
+there and so down we just have mass
+ 
+
+ align:start position:0%
+there and so down we just have mass
+platform plus mass of a washer times G
+
+ align:start position:0%
+platform plus mass of a washer times G
+ 
+
+ align:start position:0%
+platform plus mass of a washer times G
+and so you see in this problem if we try
+
+ align:start position:0%
+and so you see in this problem if we try
+ 
+
+ align:start position:0%
+and so you see in this problem if we try
+to treat everything separate and I could
+
+ align:start position:0%
+to treat everything separate and I could
+ 
+
+ align:start position:0%
+to treat everything separate and I could
+have even had the string separate I have
+
+ align:start position:0%
+have even had the string separate I have
+ 
+
+ align:start position:0%
+have even had the string separate I have
+a lot of free body diagrams but when I
+
+ align:start position:0%
+a lot of free body diagrams but when I
+ 
+
+ align:start position:0%
+a lot of free body diagrams but when I
+think about what's internal and what's
+
+ align:start position:0%
+think about what's internal and what's
+ 
+
+ align:start position:0%
+think about what's internal and what's
+external I can take these two pieces
+
+ align:start position:0%
+external I can take these two pieces
+ 
+
+ align:start position:0%
+external I can take these two pieces
+combine them here internal forces cancel
+
+ align:start position:0%
+combine them here internal forces cancel
+ 
+
+ align:start position:0%
+combine them here internal forces cancel
+in pairs
+
+ align:start position:0%
+in pairs
+ 
+
+ align:start position:0%
+in pairs
+I can draw these two separate systems
+
+ align:start position:0%
+I can draw these two separate systems
+ 
+
+ align:start position:0%
+I can draw these two separate systems
+again combine them internal forces
+
+ align:start position:0%
+again combine them internal forces
+ 
+
+ align:start position:0%
+again combine them internal forces
+cancelling pair and now I have this
+
+ align:start position:0%
+cancelling pair and now I have this
+ 
+
+ align:start position:0%
+cancelling pair and now I have this
+pulley a now I can write down Newton's
+
+ align:start position:0%
+pulley a now I can write down Newton's
+ 
+
+ align:start position:0%
+pulley a now I can write down Newton's
+second law so what I'll do next is I'll
+
+ align:start position:0%
+second law so what I'll do next is I'll
+ 
+
+ align:start position:0%
+second law so what I'll do next is I'll
+introduce I still have to consider
+
+ align:start position:0%
+introduce I still have to consider
+ 
+
+ align:start position:0%
+introduce I still have to consider
+pulley B I'll use this is my system and
+
+ align:start position:0%
+pulley B I'll use this is my system and
+ 
+
+ align:start position:0%
+pulley B I'll use this is my system and
+I'll write down Newton's second law and
+
+ align:start position:0%
+I'll write down Newton's second law and
+ 
+
+ align:start position:0%
+I'll write down Newton's second law and
+we'll be able to solve this problem
\ No newline at end of file
diff --git a/XrdcGZppwI4.txt b/XrdcGZppwI4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bdba72b63171c8c0f7918b340699025ced6198b1
--- /dev/null
+++ b/XrdcGZppwI4.txt
@@ -0,0 +1,11736 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay and they T home
+
+ align:start position:0%
+ocw.mit.edu okay and they T home
+ 
+
+ align:start position:0%
+ocw.mit.edu okay and they T home
+exam um you did very well uh the I think
+
+ align:start position:0%
+exam um you did very well uh the I think
+ 
+
+ align:start position:0%
+exam um you did very well uh the I think
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh the average was 88 it's very
+
+ align:start position:0%
+uh the average was 88 it's very
+ 
+
+ align:start position:0%
+uh the average was 88 it's very
+comfortable uh means everybody has
+
+ align:start position:0%
+comfortable uh means everybody has
+ 
+
+ align:start position:0%
+comfortable uh means everybody has
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+something so uh um I think
+
+ align:start position:0%
+something so uh um I think
+ 
+
+ align:start position:0%
+something so uh um I think
+uh uh you you'll say that I took a quick
+
+ align:start position:0%
+uh uh you you'll say that I took a quick
+ 
+
+ align:start position:0%
+uh uh you you'll say that I took a quick
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+johnon read very carefully and uh
+
+ align:start position:0%
+johnon read very carefully and uh
+ 
+
+ align:start position:0%
+johnon read very carefully and uh
+overall very
+
+ align:start position:0%
+overall very
+ 
+
+ align:start position:0%
+overall very
+pleased I was impressed that there a lot
+
+ align:start position:0%
+pleased I was impressed that there a lot
+ 
+
+ align:start position:0%
+pleased I was impressed that there a lot
+of math everybody reading down a lot of
+
+ align:start position:0%
+of math everybody reading down a lot of
+ 
+
+ align:start position:0%
+of math everybody reading down a lot of
+formulas
+
+ align:start position:0%
+formulas
+ 
+
+ align:start position:0%
+formulas
+okay uh so the last is the best and
+
+ align:start position:0%
+okay uh so the last is the best and
+ 
+
+ align:start position:0%
+okay uh so the last is the best and
+after today you can go out uh celebrate
+
+ align:start position:0%
+after today you can go out uh celebrate
+ 
+
+ align:start position:0%
+after today you can go out uh celebrate
+uh hopefully and we have a new
+
+ align:start position:0%
+uh hopefully and we have a new
+ 
+
+ align:start position:0%
+uh hopefully and we have a new
+president you hear it okay uh so what uh
+
+ align:start position:0%
+president you hear it okay uh so what uh
+ 
+
+ align:start position:0%
+president you hear it okay uh so what uh
+I was planning to talk about is on the
+
+ align:start position:0%
+I was planning to talk about is on the
+ 
+
+ align:start position:0%
+I was planning to talk about is on the
+molecular dyamic
+
+ align:start position:0%
+molecular dyamic
+ 
+
+ align:start position:0%
+molecular dyamic
+simulation and uh really uh how the
+
+ align:start position:0%
+simulation and uh really uh how the
+ 
+
+ align:start position:0%
+simulation and uh really uh how the
+emphasizing the analysis
+
+ align:start position:0%
+emphasizing the analysis
+ 
+
+ align:start position:0%
+emphasizing the analysis
+of molecular dyamic
+
+ align:start position:0%
+of molecular dyamic
+ 
+
+ align:start position:0%
+of molecular dyamic
+simulation so uh molecular dyamic
+
+ align:start position:0%
+simulation so uh molecular dyamic
+ 
+
+ align:start position:0%
+simulation so uh molecular dyamic
+simulation comput say
+
+ align:start position:0%
+simulation comput say
+ 
+
+ align:start position:0%
+simulation comput say
+conceptually is very easy right uh what
+
+ align:start position:0%
+conceptually is very easy right uh what
+ 
+
+ align:start position:0%
+conceptually is very easy right uh what
+we want uh is actually most of the
+
+ align:start position:0%
+we want uh is actually most of the
+ 
+
+ align:start position:0%
+we want uh is actually most of the
+molecular Dynamic simulation
+
+ align:start position:0%
+molecular Dynamic simulation
+ 
+
+ align:start position:0%
+molecular Dynamic simulation
+nowadays uh is based on classical
+
+ align:start position:0%
+nowadays uh is based on classical
+ 
+
+ align:start position:0%
+nowadays uh is based on classical
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+Dynamics and uh in fact the people think
+
+ align:start position:0%
+Dynamics and uh in fact the people think
+ 
+
+ align:start position:0%
+Dynamics and uh in fact the people think
+it's done so the choke I like this thick
+
+ align:start position:0%
+it's done so the choke I like this thick
+ 
+
+ align:start position:0%
+it's done so the choke I like this thick
+choke CH
+
+ align:start position:0%
+choke CH
+ 
+
+ align:start position:0%
+choke CH
+noral we have to use a different
+
+ align:start position:0%
+noral we have to use a different
+ 
+
+ align:start position:0%
+noral we have to use a different
+one okay so the
+
+ align:start position:0%
+one okay so the
+ 
+
+ align:start position:0%
+one okay so the
+uh classical molecular Dynamics is FAL
+
+ align:start position:0%
+uh classical molecular Dynamics is FAL
+ 
+
+ align:start position:0%
+uh classical molecular Dynamics is FAL
+ma right and uh uh so Force equals Ma so
+
+ align:start position:0%
+ma right and uh uh so Force equals Ma so
+ 
+
+ align:start position:0%
+ma right and uh uh so Force equals Ma so
+if I have for example a simulation
+
+ align:start position:0%
+if I have for example a simulation
+ 
+
+ align:start position:0%
+if I have for example a simulation
+box uh I have a crystal I want to
+
+ align:start position:0%
+box uh I have a crystal I want to
+ 
+
+ align:start position:0%
+box uh I have a crystal I want to
+simulate its
+
+ align:start position:0%
+simulate its
+ 
+
+ align:start position:0%
+simulate its
+properties and
+
+ align:start position:0%
+properties and
+ 
+
+ align:start position:0%
+properties and
+what I have Newton Second Law will tell
+
+ align:start position:0%
+what I have Newton Second Law will tell
+ 
+
+ align:start position:0%
+what I have Newton Second Law will tell
+you tell me the mass of the is atom uh
+
+ align:start position:0%
+you tell me the mass of the is atom uh
+ 
+
+ align:start position:0%
+you tell me the mass of the is atom uh
+ma so the
+
+ align:start position:0%
+ma so the
+ 
+
+ align:start position:0%
+ma so the
+acceleration of
+
+ align:start position:0%
+acceleration of
+ 
+
+ align:start position:0%
+acceleration of
+the is
+
+ align:start position:0%
+the is
+ 
+
+ align:start position:0%
+the is
+atom right equals the force acting on
+
+ align:start position:0%
+atom right equals the force acting on
+ 
+
+ align:start position:0%
+atom right equals the force acting on
+the atom so we have the
+
+ align:start position:0%
+the atom so we have the
+ 
+
+ align:start position:0%
+the atom so we have the
+force of all the other atoms J equal 1
+
+ align:start position:0%
+force of all the other atoms J equal 1
+ 
+
+ align:start position:0%
+force of all the other atoms J equal 1
+to n that's the N is the number of atoms
+
+ align:start position:0%
+to n that's the N is the number of atoms
+ 
+
+ align:start position:0%
+to n that's the N is the number of atoms
+simulating in the domain and uh fig J so
+
+ align:start position:0%
+simulating in the domain and uh fig J so
+ 
+
+ align:start position:0%
+simulating in the domain and uh fig J so
+that's the force acting on the specific
+
+ align:start position:0%
+that's the force acting on the specific
+ 
+
+ align:start position:0%
+that's the force acting on the specific
+atom and of course J doesn't equal to I
+
+ align:start position:0%
+atom and of course J doesn't equal to I
+ 
+
+ align:start position:0%
+atom and of course J doesn't equal to I
+so that's the concept right it's very
+
+ align:start position:0%
+so that's the concept right it's very
+ 
+
+ align:start position:0%
+so that's the concept right it's very
+easy and in fact uh uh you have
+
+ align:start position:0%
+easy and in fact uh uh you have
+ 
+
+ align:start position:0%
+easy and in fact uh uh you have
+a anytime you give say when you student
+
+ align:start position:0%
+a anytime you give say when you student
+ 
+
+ align:start position:0%
+a anytime you give say when you student
+come in and say okay this is easiest to
+
+ align:start position:0%
+come in and say okay this is easiest to
+ 
+
+ align:start position:0%
+come in and say okay this is easiest to
+you startop from
+
+ align:start position:0%
+you startop from
+ 
+
+ align:start position:0%
+you startop from
+here uh of course you can think about
+
+ align:start position:0%
+here uh of course you can think about
+ 
+
+ align:start position:0%
+here uh of course you can think about
+the your your task then is doing
+
+ align:start position:0%
+the your your task then is doing
+ 
+
+ align:start position:0%
+the your your task then is doing
+integration of FAL Ma and you you make
+
+ align:start position:0%
+integration of FAL Ma and you you make
+ 
+
+ align:start position:0%
+integration of FAL Ma and you you make
+sure that you have the proper potential
+
+ align:start position:0%
+sure that you have the proper potential
+ 
+
+ align:start position:0%
+sure that you have the proper potential
+the force right Remember the force
+
+ align:start position:0%
+the force right Remember the force
+ 
+
+ align:start position:0%
+the force right Remember the force
+equals the
+
+ align:start position:0%
+equals the
+ 
+
+ align:start position:0%
+equals the
+gradient of the
+
+ align:start position:0%
+gradient of the
+ 
+
+ align:start position:0%
+gradient of the
+potential right so we need a proper
+
+ align:start position:0%
+potential right so we need a proper
+ 
+
+ align:start position:0%
+potential right so we need a proper
+potential and uh uh at least
+
+ align:start position:0%
+potential and uh uh at least
+ 
+
+ align:start position:0%
+potential and uh uh at least
+conceptually you have we have discussed
+
+ align:start position:0%
+conceptually you have we have discussed
+ 
+
+ align:start position:0%
+conceptually you have we have discussed
+uh in this course different potentials
+
+ align:start position:0%
+uh in this course different potentials
+ 
+
+ align:start position:0%
+uh in this course different potentials
+wers potential uh ionic potentials
+
+ align:start position:0%
+wers potential uh ionic potentials
+ 
+
+ align:start position:0%
+wers potential uh ionic potentials
+calent potential so all those potential
+
+ align:start position:0%
+calent potential so all those potential
+ 
+
+ align:start position:0%
+calent potential so all those potential
+interactions and uh the reality is for
+
+ align:start position:0%
+interactions and uh the reality is for
+ 
+
+ align:start position:0%
+interactions and uh the reality is for
+each different material when you do
+
+ align:start position:0%
+each different material when you do
+ 
+
+ align:start position:0%
+each different material when you do
+classical molecular Dynamic
+
+ align:start position:0%
+classical molecular Dynamic
+ 
+
+ align:start position:0%
+classical molecular Dynamic
+simulation uh the different material
+
+ align:start position:0%
+simulation uh the different material
+ 
+
+ align:start position:0%
+simulation uh the different material
+people have spent notot of time to put
+
+ align:start position:0%
+people have spent notot of time to put
+ 
+
+ align:start position:0%
+people have spent notot of time to put
+the proper potential so that they can
+
+ align:start position:0%
+the proper potential so that they can
+ 
+
+ align:start position:0%
+the proper potential so that they can
+reproduce some of the materials basic
+
+ align:start position:0%
+reproduce some of the materials basic
+ 
+
+ align:start position:0%
+reproduce some of the materials basic
+properties like a melting point when you
+
+ align:start position:0%
+properties like a melting point when you
+ 
+
+ align:start position:0%
+properties like a melting point when you
+heat it up uh it melts and uh uh so or
+
+ align:start position:0%
+heat it up uh it melts and uh uh so or
+ 
+
+ align:start position:0%
+heat it up uh it melts and uh uh so or
+the mechanical
+
+ align:start position:0%
+the mechanical
+ 
+
+ align:start position:0%
+the mechanical
+properties and uh uh because those are
+
+ align:start position:0%
+properties and uh uh because those are
+ 
+
+ align:start position:0%
+properties and uh uh because those are
+not Potential from first principle when
+
+ align:start position:0%
+not Potential from first principle when
+ 
+
+ align:start position:0%
+not Potential from first principle when
+I say first principle is a quantum
+
+ align:start position:0%
+I say first principle is a quantum
+ 
+
+ align:start position:0%
+I say first principle is a quantum
+mechanics right this are the classical
+
+ align:start position:0%
+mechanics right this are the classical
+ 
+
+ align:start position:0%
+mechanics right this are the classical
+potential and typically you start with
+
+ align:start position:0%
+potential and typically you start with
+ 
+
+ align:start position:0%
+potential and typically you start with
+some concept and uh you put in the
+
+ align:start position:0%
+some concept and uh you put in the
+ 
+
+ align:start position:0%
+some concept and uh you put in the
+feeding parameters uh adjustable
+
+ align:start position:0%
+feeding parameters uh adjustable
+ 
+
+ align:start position:0%
+feeding parameters uh adjustable
+parameter to rep uh to say this are the
+
+ align:start position:0%
+parameter to rep uh to say this are the
+ 
+
+ align:start position:0%
+parameter to rep uh to say this are the
+best the parameters uh for those
+
+ align:start position:0%
+best the parameters uh for those
+ 
+
+ align:start position:0%
+best the parameters uh for those
+materials but uh we're not going into uh
+
+ align:start position:0%
+materials but uh we're not going into uh
+ 
+
+ align:start position:0%
+materials but uh we're not going into uh
+into discussion how to construct this
+
+ align:start position:0%
+into discussion how to construct this
+ 
+
+ align:start position:0%
+into discussion how to construct this
+potential people typically if you are
+
+ align:start position:0%
+potential people typically if you are
+ 
+
+ align:start position:0%
+potential people typically if you are
+able to construct the potential that's
+
+ align:start position:0%
+able to construct the potential that's
+ 
+
+ align:start position:0%
+able to construct the potential that's
+more General many people use you have
+
+ align:start position:0%
+more General many people use you have
+ 
+
+ align:start position:0%
+more General many people use you have
+already achieved a good success in this
+
+ align:start position:0%
+already achieved a good success in this
+ 
+
+ align:start position:0%
+already achieved a good success in this
+field it's not easy to construct those
+
+ align:start position:0%
+field it's not easy to construct those
+ 
+
+ align:start position:0%
+field it's not easy to construct those
+potentials and uh once you have the
+
+ align:start position:0%
+potentials and uh once you have the
+ 
+
+ align:start position:0%
+potentials and uh once you have the
+potential oh this second order
+
+ align:start position:0%
+potential oh this second order
+ 
+
+ align:start position:0%
+potential oh this second order
+derivative you have you have the
+
+ align:start position:0%
+derivative you have you have the
+ 
+
+ align:start position:0%
+derivative you have you have the
+potential you do a integration right and
+
+ align:start position:0%
+potential you do a integration right and
+ 
+
+ align:start position:0%
+potential you do a integration right and
+you want to find the uh
+
+ align:start position:0%
+you want to find the uh
+ 
+
+ align:start position:0%
+you want to find the uh
+position of the atoms
+
+ align:start position:0%
+position of the atoms
+ 
+
+ align:start position:0%
+position of the atoms
+molecules as a function of time in your
+
+ align:start position:0%
+molecules as a function of time in your
+ 
+
+ align:start position:0%
+molecules as a function of time in your
+simulation domain so um we can do the um
+
+ align:start position:0%
+simulation domain so um we can do the um
+ 
+
+ align:start position:0%
+simulation domain so um we can do the um
+integration so for example the second
+
+ align:start position:0%
+integration so for example the second
+ 
+
+ align:start position:0%
+integration so for example the second
+order derivative we now uh let's uh drop
+
+ align:start position:0%
+order derivative we now uh let's uh drop
+ 
+
+ align:start position:0%
+order derivative we now uh let's uh drop
+the vector rotation so the the uh second
+
+ align:start position:0%
+the vector rotation so the the uh second
+ 
+
+ align:start position:0%
+the vector rotation so the the uh second
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+derivative uh drop the
+
+ align:start position:0%
+derivative uh drop the
+ 
+
+ align:start position:0%
+derivative uh drop the
+vector I and DT s equals r i and t+
+
+ align:start position:0%
+vector I and DT s equals r i and t+
+ 
+
+ align:start position:0%
+vector I and DT s equals r i and t+
+delta T I use Central difference method
+
+ align:start position:0%
+delta T I use Central difference method
+ 
+
+ align:start position:0%
+delta T I use Central difference method
+for example and plus r t i t minus delta
+
+ align:start position:0%
+for example and plus r t i t minus delta
+ 
+
+ align:start position:0%
+for example and plus r t i t minus delta
+T Min 2 r i t this is a time integration
+
+ align:start position:0%
+T Min 2 r i t this is a time integration
+ 
+
+ align:start position:0%
+T Min 2 r i t this is a time integration
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+and two delta T
+
+ align:start position:0%
+and two delta T
+ 
+
+ align:start position:0%
+and two delta T
+square right so if you go to check the
+
+ align:start position:0%
+square right so if you go to check the
+ 
+
+ align:start position:0%
+square right so if you go to check the
+accuracy of this uh this is actually of
+
+ align:start position:0%
+accuracy of this uh this is actually of
+ 
+
+ align:start position:0%
+accuracy of this uh this is actually of
+the order of delta T um uh this is the
+
+ align:start position:0%
+the order of delta T um uh this is the
+ 
+
+ align:start position:0%
+the order of delta T um uh this is the
+the fourth order so fourth power so
+
+ align:start position:0%
+the fourth order so fourth power so
+ 
+
+ align:start position:0%
+the fourth order so fourth power so
+that's the you actually have relatively
+
+ align:start position:0%
+that's the you actually have relatively
+ 
+
+ align:start position:0%
+that's the you actually have relatively
+high accuracy uh when you use uh the
+
+ align:start position:0%
+high accuracy uh when you use uh the
+ 
+
+ align:start position:0%
+high accuracy uh when you use uh the
+central difference method
+
+ align:start position:0%
+central difference method
+ 
+
+ align:start position:0%
+central difference method
+and then I can uh if I write this I I
+
+ align:start position:0%
+and then I can uh if I write this I I
+ 
+
+ align:start position:0%
+and then I can uh if I write this I I
+can do your you take you choose a Time
+
+ align:start position:0%
+can do your you take you choose a Time
+ 
+
+ align:start position:0%
+can do your you take you choose a Time
+step so this is a uh explicit method you
+
+ align:start position:0%
+step so this is a uh explicit method you
+ 
+
+ align:start position:0%
+step so this is a uh explicit method you
+choose a Time step you advancing in time
+
+ align:start position:0%
+choose a Time step you advancing in time
+ 
+
+ align:start position:0%
+choose a Time step you advancing in time
+to find the position of the atoms at the
+
+ align:start position:0%
+to find the position of the atoms at the
+ 
+
+ align:start position:0%
+to find the position of the atoms at the
+next time so you use the uh say the next
+
+ align:start position:0%
+next time so you use the uh say the next
+ 
+
+ align:start position:0%
+next time so you use the uh say the next
+times t plus Del T you use the
+
+ align:start position:0%
+times t plus Del T you use the
+ 
+
+ align:start position:0%
+times t plus Del T you use the
+information previous time step the
+
+ align:start position:0%
+information previous time step the
+ 
+
+ align:start position:0%
+information previous time step the
+current time step and previous time step
+
+ align:start position:0%
+current time step and previous time step
+ 
+
+ align:start position:0%
+current time step and previous time step
+so I can integrate I say I can March in
+
+ align:start position:0%
+so I can integrate I say I can March in
+ 
+
+ align:start position:0%
+so I can integrate I say I can March in
+time t+ delta
+
+ align:start position:0%
+time t+ delta
+ 
+
+ align:start position:0%
+time t+ delta
+T and uh what I have here is then um
+
+ align:start position:0%
+T and uh what I have here is then um
+ 
+
+ align:start position:0%
+T and uh what I have here is then um
+this one is if you look at the new
+
+ align:start position:0%
+this one is if you look at the new
+ 
+
+ align:start position:0%
+this one is if you look at the new
+second law is really just the F divide
+
+ align:start position:0%
+second law is really just the F divide
+ 
+
+ align:start position:0%
+second law is really just the F divide
+by m so what I have here is 2 r i t
+
+ align:start position:0%
+by m so what I have here is 2 r i t
+ 
+
+ align:start position:0%
+by m so what I have here is 2 r i t
+minus r i t Min T right and then I have
+
+ align:start position:0%
+minus r i t Min T right and then I have
+ 
+
+ align:start position:0%
+minus r i t Min T right and then I have
+the derivative of the acceleration which
+
+ align:start position:0%
+the derivative of the acceleration which
+ 
+
+ align:start position:0%
+the derivative of the acceleration which
+is 2 Delta t² times the force acting on
+
+ align:start position:0%
+is 2 Delta t² times the force acting on
+ 
+
+ align:start position:0%
+is 2 Delta t² times the force acting on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+atom in that specific Direction divid
+
+ align:start position:0%
+atom in that specific Direction divid
+ 
+
+ align:start position:0%
+atom in that specific Direction divid
+the mass that's my
+
+ align:start position:0%
+the mass that's my
+ 
+
+ align:start position:0%
+the mass that's my
+acceleration and I know if I do this
+
+ align:start position:0%
+acceleration and I know if I do this
+ 
+
+ align:start position:0%
+acceleration and I know if I do this
+what I accurate is to Del T4 power
+
+ align:start position:0%
+what I accurate is to Del T4 power
+ 
+
+ align:start position:0%
+what I accurate is to Del T4 power
+that's the I the terms that I
+
+ align:start position:0%
+that's the I the terms that I
+ 
+
+ align:start position:0%
+that's the I the terms that I
+dropped right so um this is a uh uh to
+
+ align:start position:0%
+dropped right so um this is a uh uh to
+ 
+
+ align:start position:0%
+dropped right so um this is a uh uh to
+the fource power is qu High numerical
+
+ align:start position:0%
+the fource power is qu High numerical
+ 
+
+ align:start position:0%
+the fource power is qu High numerical
+accuracy and uh uh the what's important
+
+ align:start position:0%
+accuracy and uh uh the what's important
+ 
+
+ align:start position:0%
+accuracy and uh uh the what's important
+is your time step right you say okay I'm
+
+ align:start position:0%
+is your time step right you say okay I'm
+ 
+
+ align:start position:0%
+is your time step right you say okay I'm
+going to exate my integration I choose a
+
+ align:start position:0%
+going to exate my integration I choose a
+ 
+
+ align:start position:0%
+going to exate my integration I choose a
+very large time
+
+ align:start position:0%
+very large time
+ 
+
+ align:start position:0%
+very large time
+step but uh uh remember your time step
+
+ align:start position:0%
+step but uh uh remember your time step
+ 
+
+ align:start position:0%
+step but uh uh remember your time step
+has to be smaller than the physical
+
+ align:start position:0%
+has to be smaller than the physical
+ 
+
+ align:start position:0%
+has to be smaller than the physical
+process that goes on right if I have
+
+ align:start position:0%
+process that goes on right if I have
+ 
+
+ align:start position:0%
+process that goes on right if I have
+atoms oscillate 10 to the 14 her
+
+ align:start position:0%
+atoms oscillate 10 to the 14 her
+ 
+
+ align:start position:0%
+atoms oscillate 10 to the 14 her
+that means 10 to the Min 14 second or
+
+ align:start position:0%
+that means 10 to the Min 14 second or
+ 
+
+ align:start position:0%
+that means 10 to the Min 14 second or
+period then my delta T has to be if I
+
+ align:start position:0%
+period then my delta T has to be if I
+ 
+
+ align:start position:0%
+period then my delta T has to be if I
+want to capture one period of the atom
+
+ align:start position:0%
+want to capture one period of the atom
+ 
+
+ align:start position:0%
+want to capture one period of the atom
+oscillation you see that the sign
+
+ align:start position:0%
+oscillation you see that the sign
+ 
+
+ align:start position:0%
+oscillation you see that the sign
+function I have to at least how accurate
+
+ align:start position:0%
+function I have to at least how accurate
+ 
+
+ align:start position:0%
+function I have to at least how accurate
+I say okay maybe I'll take one1 that's
+
+ align:start position:0%
+I say okay maybe I'll take one1 that's
+ 
+
+ align:start position:0%
+I say okay maybe I'll take one1 that's
+not very fine points for a sign function
+
+ align:start position:0%
+not very fine points for a sign function
+ 
+
+ align:start position:0%
+not very fine points for a sign function
+you know right so you can see then
+
+ align:start position:0%
+you know right so you can see then
+ 
+
+ align:start position:0%
+you know right so you can see then
+easily you get to F second and very
+
+ align:start position:0%
+easily you get to F second and very
+ 
+
+ align:start position:0%
+easily you get to F second and very
+small time steps and and uh because of
+
+ align:start position:0%
+small time steps and and uh because of
+ 
+
+ align:start position:0%
+small time steps and and uh because of
+that your integration time uh you you
+
+ align:start position:0%
+that your integration time uh you you
+ 
+
+ align:start position:0%
+that your integration time uh you you
+want to simulate the event that last
+
+ align:start position:0%
+want to simulate the event that last
+ 
+
+ align:start position:0%
+want to simulate the event that last
+lanc right and nanc 10 to- 9 if you
+
+ align:start position:0%
+lanc right and nanc 10 to- 9 if you
+ 
+
+ align:start position:0%
+lanc right and nanc 10 to- 9 if you
+start from 10 to uh- 15 time step you
+
+ align:start position:0%
+start from 10 to uh- 15 time step you
+ 
+
+ align:start position:0%
+start from 10 to uh- 15 time step you
+can imagine that's a lot of um uh margin
+
+ align:start position:0%
+can imagine that's a lot of um uh margin
+ 
+
+ align:start position:0%
+can imagine that's a lot of um uh margin
+and lot of computation and each time
+
+ align:start position:0%
+and lot of computation and each time
+ 
+
+ align:start position:0%
+and lot of computation and each time
+step you have to re calculate uh the
+
+ align:start position:0%
+step you have to re calculate uh the
+ 
+
+ align:start position:0%
+step you have to re calculate uh the
+force uh because theic position change
+
+ align:start position:0%
+force uh because theic position change
+ 
+
+ align:start position:0%
+force uh because theic position change
+and that will change the force
+
+ align:start position:0%
+and that will change the force
+ 
+
+ align:start position:0%
+and that will change the force
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+so this is the uh uh time and uh uh with
+
+ align:start position:0%
+so this is the uh uh time and uh uh with
+ 
+
+ align:start position:0%
+so this is the uh uh time and uh uh with
+this you can also calcul the velocity
+
+ align:start position:0%
+this you can also calcul the velocity
+ 
+
+ align:start position:0%
+this you can also calcul the velocity
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+velocity uh of the uh at time uh T is
+
+ align:start position:0%
+velocity uh of the uh at time uh T is
+ 
+
+ align:start position:0%
+velocity uh of the uh at time uh T is
+just the uh GED derivative right so we
+
+ align:start position:0%
+just the uh GED derivative right so we
+ 
+
+ align:start position:0%
+just the uh GED derivative right so we
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+derivative of di DT then I have r i t+
+
+ align:start position:0%
+derivative of di DT then I have r i t+
+ 
+
+ align:start position:0%
+derivative of di DT then I have r i t+
+delta T which I calculate in this time
+
+ align:start position:0%
+delta T which I calculate in this time
+ 
+
+ align:start position:0%
+delta T which I calculate in this time
+step and I have r i t and divide by
+
+ align:start position:0%
+step and I have r i t and divide by
+ 
+
+ align:start position:0%
+step and I have r i t and divide by
+delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and uh uh the uh disadvantage of this
+
+ align:start position:0%
+T and uh uh the uh disadvantage of this
+ 
+
+ align:start position:0%
+T and uh uh the uh disadvantage of this
+compared to Central difference this
+
+ align:start position:0%
+compared to Central difference this
+ 
+
+ align:start position:0%
+compared to Central difference this
+accuracy is lower it's only
+
+ align:start position:0%
+accuracy is lower it's only
+ 
+
+ align:start position:0%
+accuracy is lower it's only
+t² and uh but the um uh uh it's lucky
+
+ align:start position:0%
+t² and uh but the um uh uh it's lucky
+ 
+
+ align:start position:0%
+t² and uh but the um uh uh it's lucky
+that this is doesn't quite affect this
+
+ align:start position:0%
+that this is doesn't quite affect this
+ 
+
+ align:start position:0%
+that this is doesn't quite affect this
+does not in fact does not affect my
+
+ align:start position:0%
+does not in fact does not affect my
+ 
+
+ align:start position:0%
+does not in fact does not affect my
+calculation of r I because my RI
+
+ align:start position:0%
+calculation of r I because my RI
+ 
+
+ align:start position:0%
+calculation of r I because my RI
+calculation is independent of the
+
+ align:start position:0%
+calculation is independent of the
+ 
+
+ align:start position:0%
+calculation is independent of the
+Velocity so my velocity is not that
+
+ align:start position:0%
+Velocity so my velocity is not that
+ 
+
+ align:start position:0%
+Velocity so my velocity is not that
+accurate my position is much more
+
+ align:start position:0%
+accurate my position is much more
+ 
+
+ align:start position:0%
+accurate my position is much more
+accurate depends on the time step uh you
+
+ align:start position:0%
+accurate depends on the time step uh you
+ 
+
+ align:start position:0%
+accurate depends on the time step uh you
+take so that's easy right so in
+
+ align:start position:0%
+take so that's easy right so in
+ 
+
+ align:start position:0%
+take so that's easy right so in
+principle you can write uh a code and do
+
+ align:start position:0%
+principle you can write uh a code and do
+ 
+
+ align:start position:0%
+principle you can write uh a code and do
+this calculation
+
+ align:start position:0%
+this calculation
+ 
+
+ align:start position:0%
+this calculation
+quickly and uh the key question is how
+
+ align:start position:0%
+quickly and uh the key question is how
+ 
+
+ align:start position:0%
+quickly and uh the key question is how
+do you do your analysis how you
+
+ align:start position:0%
+do you do your analysis how you
+ 
+
+ align:start position:0%
+do you do your analysis how you
+understand your analysis doing a
+
+ align:start position:0%
+understand your analysis doing a
+ 
+
+ align:start position:0%
+understand your analysis doing a
+numerical simulation uh many times
+
+ align:start position:0%
+numerical simulation uh many times
+ 
+
+ align:start position:0%
+numerical simulation uh many times
+people like to say I'm doing a numerical
+
+ align:start position:0%
+people like to say I'm doing a numerical
+ 
+
+ align:start position:0%
+people like to say I'm doing a numerical
+experiment I don't like that terminology
+
+ align:start position:0%
+experiment I don't like that terminology
+ 
+
+ align:start position:0%
+experiment I don't like that terminology
+but if you are doing computation you
+
+ align:start position:0%
+but if you are doing computation you
+ 
+
+ align:start position:0%
+but if you are doing computation you
+like to say you're doing numerical
+
+ align:start position:0%
+like to say you're doing numerical
+ 
+
+ align:start position:0%
+like to say you're doing numerical
+experiment uh the question is how you
+
+ align:start position:0%
+experiment uh the question is how you
+ 
+
+ align:start position:0%
+experiment uh the question is how you
+analyze your
+
+ align:start position:0%
+analyze your
+ 
+
+ align:start position:0%
+analyze your
+experiment right so uh what we're going
+
+ align:start position:0%
+experiment right so uh what we're going
+ 
+
+ align:start position:0%
+experiment right so uh what we're going
+to uh discuss uh focus is really this
+
+ align:start position:0%
+to uh discuss uh focus is really this
+ 
+
+ align:start position:0%
+to uh discuss uh focus is really this
+statistic
+
+ align:start position:0%
+statistic
+ 
+
+ align:start position:0%
+statistic
+Foundation of uh numerical
+
+ align:start position:0%
+Foundation of uh numerical
+ 
+
+ align:start position:0%
+Foundation of uh numerical
+analysis one more common is um before we
+
+ align:start position:0%
+analysis one more common is um before we
+ 
+
+ align:start position:0%
+analysis one more common is um before we
+go there is that when you do U molecular
+
+ align:start position:0%
+go there is that when you do U molecular
+ 
+
+ align:start position:0%
+go there is that when you do U molecular
+Dynamic simulation already said uh your
+
+ align:start position:0%
+Dynamic simulation already said uh your
+ 
+
+ align:start position:0%
+Dynamic simulation already said uh your
+time step has to be very short let's say
+
+ align:start position:0%
+time step has to be very short let's say
+ 
+
+ align:start position:0%
+time step has to be very short let's say
+if you do solid uh you have to go to F
+
+ align:start position:0%
+if you do solid uh you have to go to F
+ 
+
+ align:start position:0%
+if you do solid uh you have to go to F
+second or even sub to second right
+
+ align:start position:0%
+second or even sub to second right
+ 
+
+ align:start position:0%
+second or even sub to second right
+depends on the oscillation frequency of
+
+ align:start position:0%
+depends on the oscillation frequency of
+ 
+
+ align:start position:0%
+depends on the oscillation frequency of
+the atoms
+
+ align:start position:0%
+the atoms
+ 
+
+ align:start position:0%
+the atoms
+and the other is the L of atoms you can
+
+ align:start position:0%
+and the other is the L of atoms you can
+ 
+
+ align:start position:0%
+and the other is the L of atoms you can
+simulate right and if I think about I
+
+ align:start position:0%
+simulate right and if I think about I
+ 
+
+ align:start position:0%
+simulate right and if I think about I
+want to simulate one micron Q right and
+
+ align:start position:0%
+want to simulate one micron Q right and
+ 
+
+ align:start position:0%
+want to simulate one micron Q right and
+uh uh if you see the typical let's say
+
+ align:start position:0%
+uh uh if you see the typical let's say
+ 
+
+ align:start position:0%
+uh uh if you see the typical let's say
+silicon silicon crystal right a silicon
+
+ align:start position:0%
+silicon silicon crystal right a silicon
+ 
+
+ align:start position:0%
+silicon silicon crystal right a silicon
+crystal lce constant is about five unst
+
+ align:start position:0%
+crystal lce constant is about five unst
+ 
+
+ align:start position:0%
+crystal lce constant is about five unst
+strong so in a five unstr strong Cube
+
+ align:start position:0%
+strong so in a five unstr strong Cube
+ 
+
+ align:start position:0%
+strong so in a five unstr strong Cube
+there are eight
+
+ align:start position:0%
+there are eight
+ 
+
+ align:start position:0%
+there are eight
+atoms and uh one nom
+
+ align:start position:0%
+atoms and uh one nom
+ 
+
+ align:start position:0%
+atoms and uh one nom
+Cube that's say uh 8 * 8
+
+ align:start position:0%
+Cube that's say uh 8 * 8
+ 
+
+ align:start position:0%
+Cube that's say uh 8 * 8
+64 and the one micron is 10 to the
+
+ align:start position:0%
+64 and the one micron is 10 to the
+ 
+
+ align:start position:0%
+64 and the one micron is 10 to the
+L power right because there three order
+
+ align:start position:0%
+L power right because there three order
+ 
+
+ align:start position:0%
+L power right because there three order
+magnitude higher in each
+
+ align:start position:0%
+magnitude higher in each
+ 
+
+ align:start position:0%
+magnitude higher in each
+Direction and that's 10 to lines times
+
+ align:start position:0%
+Direction and that's 10 to lines times
+ 
+
+ align:start position:0%
+Direction and that's 10 to lines times
+64 that's the number of
+
+ align:start position:0%
+64 that's the number of
+ 
+
+ align:start position:0%
+64 that's the number of
+atoms you got in one micron Cube and
+
+ align:start position:0%
+atoms you got in one micron Cube and
+ 
+
+ align:start position:0%
+atoms you got in one micron Cube and
+with that many time steps and that needs
+
+ align:start position:0%
+with that many time steps and that needs
+ 
+
+ align:start position:0%
+with that many time steps and that needs
+very high powerful computer to even
+
+ align:start position:0%
+very high powerful computer to even
+ 
+
+ align:start position:0%
+very high powerful computer to even
+simulate one
+
+ align:start position:0%
+simulate one
+ 
+
+ align:start position:0%
+simulate one
+micron so that's very hard and typically
+
+ align:start position:0%
+micron so that's very hard and typically
+ 
+
+ align:start position:0%
+micron so that's very hard and typically
+people do uh periodic boundary condition
+
+ align:start position:0%
+people do uh periodic boundary condition
+ 
+
+ align:start position:0%
+people do uh periodic boundary condition
+so they try to simul use a much smaller
+
+ align:start position:0%
+so they try to simul use a much smaller
+ 
+
+ align:start position:0%
+so they try to simul use a much smaller
+simulation box right and you have
+
+ align:start position:0%
+simulation box right and you have
+ 
+
+ align:start position:0%
+simulation box right and you have
+molecules or atoms in the box and the
+
+ align:start position:0%
+molecules or atoms in the box and the
+ 
+
+ align:start position:0%
+molecules or atoms in the box and the
+next moment this atom can move out of
+
+ align:start position:0%
+next moment this atom can move out of
+ 
+
+ align:start position:0%
+next moment this atom can move out of
+the simulation
+
+ align:start position:0%
+the simulation
+ 
+
+ align:start position:0%
+the simulation
+box and the way that Clarity taken into
+
+ align:start position:0%
+box and the way that Clarity taken into
+ 
+
+ align:start position:0%
+box and the way that Clarity taken into
+this uh moving out is in the opposite
+
+ align:start position:0%
+this uh moving out is in the opposite
+ 
+
+ align:start position:0%
+this uh moving out is in the opposite
+direction opposite boundary so here it
+
+ align:start position:0%
+direction opposite boundary so here it
+ 
+
+ align:start position:0%
+direction opposite boundary so here it
+goes out of boundary and it comes
+
+ align:start position:0%
+goes out of boundary and it comes
+ 
+
+ align:start position:0%
+goes out of boundary and it comes
+in this atom comes in at the position at
+
+ align:start position:0%
+in this atom comes in at the position at
+ 
+
+ align:start position:0%
+in this atom comes in at the position at
+the velocity the corresponding position
+
+ align:start position:0%
+the velocity the corresponding position
+ 
+
+ align:start position:0%
+the velocity the corresponding position
+on the opposite boundary and the
+
+ align:start position:0%
+on the opposite boundary and the
+ 
+
+ align:start position:0%
+on the opposite boundary and the
+velocity that the exit so this is the
+
+ align:start position:0%
+velocity that the exit so this is the
+ 
+
+ align:start position:0%
+velocity that the exit so this is the
+trick that people use periodic boundary
+
+ align:start position:0%
+trick that people use periodic boundary
+ 
+
+ align:start position:0%
+trick that people use periodic boundary
+condition and with that you hope to
+
+ align:start position:0%
+condition and with that you hope to
+ 
+
+ align:start position:0%
+condition and with that you hope to
+recapture uh the effects of infinite
+
+ align:start position:0%
+recapture uh the effects of infinite
+ 
+
+ align:start position:0%
+recapture uh the effects of infinite
+simulation right anytime you use a
+
+ align:start position:0%
+simulation right anytime you use a
+ 
+
+ align:start position:0%
+simulation right anytime you use a
+periodic boundary condition you'll
+
+ align:start position:0%
+periodic boundary condition you'll
+ 
+
+ align:start position:0%
+periodic boundary condition you'll
+actually say in the specific Direction
+
+ align:start position:0%
+actually say in the specific Direction
+ 
+
+ align:start position:0%
+actually say in the specific Direction
+where it's periodic it's
+
+ align:start position:0%
+where it's periodic it's
+ 
+
+ align:start position:0%
+where it's periodic it's
+infinite and uh uh there are also
+
+ align:start position:0%
+infinite and uh uh there are also
+ 
+
+ align:start position:0%
+infinite and uh uh there are also
+artifacts that's caused by this periodic
+
+ align:start position:0%
+artifacts that's caused by this periodic
+ 
+
+ align:start position:0%
+artifacts that's caused by this periodic
+boundary condition as you will say uh
+
+ align:start position:0%
+boundary condition as you will say uh
+ 
+
+ align:start position:0%
+boundary condition as you will say uh
+very uh say much easier once we get into
+
+ align:start position:0%
+very uh say much easier once we get into
+ 
+
+ align:start position:0%
+very uh say much easier once we get into
+this statistical
+
+ align:start position:0%
+this statistical
+ 
+
+ align:start position:0%
+this statistical
+aspects and
+
+ align:start position:0%
+aspects and
+ 
+
+ align:start position:0%
+aspects and
+uh let's look into the statistical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foundation and uh um first uh in chapter
+
+ align:start position:0%
+foundation and uh um first uh in chapter
+ 
+
+ align:start position:0%
+foundation and uh um first uh in chapter
+four we when we do the statistics
+
+ align:start position:0%
+four we when we do the statistics
+ 
+
+ align:start position:0%
+four we when we do the statistics
+we introduce the concept of emble
+
+ align:start position:0%
+we introduce the concept of emble
+ 
+
+ align:start position:0%
+we introduce the concept of emble
+average right in the old days uh you do
+
+ align:start position:0%
+average right in the old days uh you do
+ 
+
+ align:start position:0%
+average right in the old days uh you do
+not actually trace the trajectory the
+
+ align:start position:0%
+not actually trace the trajectory the
+ 
+
+ align:start position:0%
+not actually trace the trajectory the
+time trajectory of atoms remember
+
+ align:start position:0%
+time trajectory of atoms remember
+ 
+
+ align:start position:0%
+time trajectory of atoms remember
+molecular Dynamics is a uh looking the
+
+ align:start position:0%
+molecular Dynamics is a uh looking the
+ 
+
+ align:start position:0%
+molecular Dynamics is a uh looking the
+way we describe is looking to the time
+
+ align:start position:0%
+way we describe is looking to the time
+ 
+
+ align:start position:0%
+way we describe is looking to the time
+trajectory of the atoms and when we
+
+ align:start position:0%
+trajectory of the atoms and when we
+ 
+
+ align:start position:0%
+trajectory of the atoms and when we
+discuss the statistic we said that's too
+
+ align:start position:0%
+discuss the statistic we said that's too
+ 
+
+ align:start position:0%
+discuss the statistic we said that's too
+complicated that we're actually going to
+
+ align:start position:0%
+complicated that we're actually going to
+ 
+
+ align:start position:0%
+complicated that we're actually going to
+do emble average rather than time
+
+ align:start position:0%
+do emble average rather than time
+ 
+
+ align:start position:0%
+do emble average rather than time
+average right and then we introduce the
+
+ align:start position:0%
+average right and then we introduce the
+ 
+
+ align:start position:0%
+average right and then we introduce the
+concept of or odicity or system for AIC
+
+ align:start position:0%
+concept of or odicity or system for AIC
+ 
+
+ align:start position:0%
+concept of or odicity or system for AIC
+system the emble average equals the time
+
+ align:start position:0%
+system the emble average equals the time
+ 
+
+ align:start position:0%
+system the emble average equals the time
+average right so the uh time uh of
+
+ align:start position:0%
+average right so the uh time uh of
+ 
+
+ align:start position:0%
+average right so the uh time uh of
+course the time average if I have a
+
+ align:start position:0%
+course the time average if I have a
+ 
+
+ align:start position:0%
+course the time average if I have a
+quantity uh this quantity is a quantity
+
+ align:start position:0%
+quantity uh this quantity is a quantity
+ 
+
+ align:start position:0%
+quantity uh this quantity is a quantity
+in face space for example is a position
+
+ align:start position:0%
+in face space for example is a position
+ 
+
+ align:start position:0%
+in face space for example is a position
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+momentum of many particles I'm just
+
+ align:start position:0%
+momentum of many particles I'm just
+ 
+
+ align:start position:0%
+momentum of many particles I'm just
+using our represent the maybe uh
+
+ align:start position:0%
+using our represent the maybe uh
+ 
+
+ align:start position:0%
+using our represent the maybe uh
+millions or bons of atoms position and M
+
+ align:start position:0%
+millions or bons of atoms position and M
+ 
+
+ align:start position:0%
+millions or bons of atoms position and M
+corresponding momentum and when I do the
+
+ align:start position:0%
+corresponding momentum and when I do the
+ 
+
+ align:start position:0%
+corresponding momentum and when I do the
+time average of this quantity I say this
+
+ align:start position:0%
+time average of this quantity I say this
+ 
+
+ align:start position:0%
+time average of this quantity I say this
+is I observe this quantity over a
+
+ align:start position:0%
+is I observe this quantity over a
+ 
+
+ align:start position:0%
+is I observe this quantity over a
+certain period of time starting any time
+
+ align:start position:0%
+certain period of time starting any time
+ 
+
+ align:start position:0%
+certain period of time starting any time
+t plus delta T So this
+
+ align:start position:0%
+t plus delta T So this
+ 
+
+ align:start position:0%
+t plus delta T So this
+origin if I do my average correctly and
+
+ align:start position:0%
+origin if I do my average correctly and
+ 
+
+ align:start position:0%
+origin if I do my average correctly and
+this origin doesn't matter so here I
+
+ align:start position:0%
+this origin doesn't matter so here I
+ 
+
+ align:start position:0%
+this origin doesn't matter so here I
+have this is r a that face space VAR for
+
+ align:start position:0%
+have this is r a that face space VAR for
+ 
+
+ align:start position:0%
+have this is r a that face space VAR for
+example I can write the potential energy
+
+ align:start position:0%
+example I can write the potential energy
+ 
+
+ align:start position:0%
+example I can write the potential energy
+or kinetic energy or total energy in
+
+ align:start position:0%
+or kinetic energy or total energy in
+ 
+
+ align:start position:0%
+or kinetic energy or total energy in
+terms of the energy of every particles
+
+ align:start position:0%
+terms of the energy of every particles
+ 
+
+ align:start position:0%
+terms of the energy of every particles
+and uh I uh uh in uh this is the total
+
+ align:start position:0%
+and uh I uh uh in uh this is the total
+ 
+
+ align:start position:0%
+and uh I uh uh in uh this is the total
+energy I average over a certain amount
+
+ align:start position:0%
+energy I average over a certain amount
+ 
+
+ align:start position:0%
+energy I average over a certain amount
+of time right so here this R remember is
+
+ align:start position:0%
+of time right so here this R remember is
+ 
+
+ align:start position:0%
+of time right so here this R remember is
+a function of time momentum is a
+
+ align:start position:0%
+a function of time momentum is a
+ 
+
+ align:start position:0%
+a function of time momentum is a
+function of time and I
+
+ align:start position:0%
+function of time and I
+ 
+
+ align:start position:0%
+function of time and I
+integrate and that's a
+
+ align:start position:0%
+integrate and that's a
+ 
+
+ align:start position:0%
+integrate and that's a
+definition I if I look long enough I get
+
+ align:start position:0%
+definition I if I look long enough I get
+ 
+
+ align:start position:0%
+definition I if I look long enough I get
+my average
+
+ align:start position:0%
+my average
+ 
+
+ align:start position:0%
+my average
+quantity energy or
+
+ align:start position:0%
+quantity energy or
+ 
+
+ align:start position:0%
+quantity energy or
+momentum or pressure right they share
+
+ align:start position:0%
+momentum or pressure right they share
+ 
+
+ align:start position:0%
+momentum or pressure right they share
+stress all those uh quantities of the uh
+
+ align:start position:0%
+stress all those uh quantities of the uh
+ 
+
+ align:start position:0%
+stress all those uh quantities of the uh
+system so this is the uh time
+
+ align:start position:0%
+system so this is the uh time
+ 
+
+ align:start position:0%
+system so this is the uh time
+averaging and then when I do uh the
+
+ align:start position:0%
+averaging and then when I do uh the
+ 
+
+ align:start position:0%
+averaging and then when I do uh the
+emble
+
+ align:start position:0%
+emble
+ 
+
+ align:start position:0%
+emble
+average right in Sample average of this
+
+ align:start position:0%
+average right in Sample average of this
+ 
+
+ align:start position:0%
+average right in Sample average of this
+quantity I use a
+
+ align:start position:0%
+quantity I use a
+ 
+
+ align:start position:0%
+quantity I use a
+bracket and uh remember in Sample
+
+ align:start position:0%
+bracket and uh remember in Sample
+ 
+
+ align:start position:0%
+bracket and uh remember in Sample
+average is I look at the probability
+
+ align:start position:0%
+average is I look at the probability
+ 
+
+ align:start position:0%
+average is I look at the probability
+function right we see microcon colonic
+
+ align:start position:0%
+function right we see microcon colonic
+ 
+
+ align:start position:0%
+function right we see microcon colonic
+emble each each of the system in the
+
+ align:start position:0%
+emble each each of the system in the
+ 
+
+ align:start position:0%
+emble each each of the system in the
+emble is equal probability colonic emble
+
+ align:start position:0%
+emble is equal probability colonic emble
+ 
+
+ align:start position:0%
+emble is equal probability colonic emble
+is bman distribution or we also
+
+ align:start position:0%
+is bman distribution or we also
+ 
+
+ align:start position:0%
+is bman distribution or we also
+introduced where the GES uh uh uh emble
+
+ align:start position:0%
+introduced where the GES uh uh uh emble
+ 
+
+ align:start position:0%
+introduced where the GES uh uh uh emble
+there where uh there is not only
+
+ align:start position:0%
+there where uh there is not only
+ 
+
+ align:start position:0%
+there where uh there is not only
+constant temperature but also mass flow
+
+ align:start position:0%
+constant temperature but also mass flow
+ 
+
+ align:start position:0%
+constant temperature but also mass flow
+flux within ENT right so at the end when
+
+ align:start position:0%
+flux within ENT right so at the end when
+ 
+
+ align:start position:0%
+flux within ENT right so at the end when
+I do the emble average I average over
+
+ align:start position:0%
+I do the emble average I average over
+ 
+
+ align:start position:0%
+I do the emble average I average over
+the probability right so the uh the
+
+ align:start position:0%
+the probability right so the uh the
+ 
+
+ align:start position:0%
+the probability right so the uh the
+emble average is I will have this face
+
+ align:start position:0%
+emble average is I will have this face
+ 
+
+ align:start position:0%
+emble average is I will have this face
+space variable R and
+
+ align:start position:0%
+space variable R and
+ 
+
+ align:start position:0%
+space variable R and
+P and then I
+
+ align:start position:0%
+P and then I
+ 
+
+ align:start position:0%
+P and then I
+integrate our the face space
+
+ align:start position:0%
+integrate our the face space
+ 
+
+ align:start position:0%
+integrate our the face space
+variables and then I have my probability
+
+ align:start position:0%
+variables and then I have my probability
+ 
+
+ align:start position:0%
+variables and then I have my probability
+distribution right for n particle in the
+
+ align:start position:0%
+distribution right for n particle in the
+ 
+
+ align:start position:0%
+distribution right for n particle in the
+system and R and P and I will this is my
+
+ align:start position:0%
+system and R and P and I will this is my
+ 
+
+ align:start position:0%
+system and R and P and I will this is my
+integration in when I do double I really
+
+ align:start position:0%
+integration in when I do double I really
+ 
+
+ align:start position:0%
+integration in when I do double I really
+mean many because R and P is all the
+
+ align:start position:0%
+mean many because R and P is all the
+ 
+
+ align:start position:0%
+mean many because R and P is all the
+particles momentum and position so a
+
+ align:start position:0%
+particles momentum and position so a
+ 
+
+ align:start position:0%
+particles momentum and position so a
+goic system means my time average equals
+
+ align:start position:0%
+goic system means my time average equals
+ 
+
+ align:start position:0%
+goic system means my time average equals
+emble average
+
+ align:start position:0%
+emble average
+ 
+
+ align:start position:0%
+emble average
+right and in the past we had really
+
+ align:start position:0%
+right and in the past we had really
+ 
+
+ align:start position:0%
+right and in the past we had really
+follow this trajectory we were when Sol
+
+ align:start position:0%
+follow this trajectory we were when Sol
+ 
+
+ align:start position:0%
+follow this trajectory we were when Sol
+bman equation I simplify this n particle
+
+ align:start position:0%
+bman equation I simplify this n particle
+ 
+
+ align:start position:0%
+bman equation I simplify this n particle
+distribution function into one particle
+
+ align:start position:0%
+distribution function into one particle
+ 
+
+ align:start position:0%
+distribution function into one particle
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+function and uh uh I do uh the average
+
+ align:start position:0%
+function and uh uh I do uh the average
+ 
+
+ align:start position:0%
+function and uh uh I do uh the average
+velocity or uh heat flux as we have been
+
+ align:start position:0%
+velocity or uh heat flux as we have been
+ 
+
+ align:start position:0%
+velocity or uh heat flux as we have been
+doing and uh when you do molecular
+
+ align:start position:0%
+doing and uh when you do molecular
+ 
+
+ align:start position:0%
+doing and uh when you do molecular
+Dynamics you're simulating time
+
+ align:start position:0%
+Dynamics you're simulating time
+ 
+
+ align:start position:0%
+Dynamics you're simulating time
+trajectory so you're really interested
+
+ align:start position:0%
+trajectory so you're really interested
+ 
+
+ align:start position:0%
+trajectory so you're really interested
+how I'm going to do the time average to
+
+ align:start position:0%
+how I'm going to do the time average to
+ 
+
+ align:start position:0%
+how I'm going to do the time average to
+get the
+
+ align:start position:0%
+get the
+ 
+
+ align:start position:0%
+get the
+quantities that I'm interested for
+
+ align:start position:0%
+quantities that I'm interested for
+ 
+
+ align:start position:0%
+quantities that I'm interested for
+example if I want to compute the thermal
+
+ align:start position:0%
+example if I want to compute the thermal
+ 
+
+ align:start position:0%
+example if I want to compute the thermal
+connectivity
+
+ align:start position:0%
+connectivity
+ 
+
+ align:start position:0%
+connectivity
+viscosity of the system right I will
+
+ align:start position:0%
+viscosity of the system right I will
+ 
+
+ align:start position:0%
+viscosity of the system right I will
+look at the atomic positions as a
+
+ align:start position:0%
+look at the atomic positions as a
+ 
+
+ align:start position:0%
+look at the atomic positions as a
+function of time and how I can extract
+
+ align:start position:0%
+function of time and how I can extract
+ 
+
+ align:start position:0%
+function of time and how I can extract
+this information that I'm interested in
+
+ align:start position:0%
+this information that I'm interested in
+ 
+
+ align:start position:0%
+this information that I'm interested in
+so those are the uh
+
+ align:start position:0%
+so those are the uh
+ 
+
+ align:start position:0%
+so those are the uh
+questions and uh let's look at I I'm
+
+ align:start position:0%
+questions and uh let's look at I I'm
+ 
+
+ align:start position:0%
+questions and uh let's look at I I'm
+interested in the property right thermal
+
+ align:start position:0%
+interested in the property right thermal
+ 
+
+ align:start position:0%
+interested in the property right thermal
+conductivity electric
+
+ align:start position:0%
+conductivity electric
+ 
+
+ align:start position:0%
+conductivity electric
+conductivity and uh so in
+
+ align:start position:0%
+conductivity and uh so in
+ 
+
+ align:start position:0%
+conductivity and uh so in
+general those are the uh response if I
+
+ align:start position:0%
+general those are the uh response if I
+ 
+
+ align:start position:0%
+general those are the uh response if I
+so let's discuss the response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and uh let me look into a
+
+ align:start position:0%
+function and uh let me look into a
+ 
+
+ align:start position:0%
+function and uh let me look into a
+system that that is initially uh at
+
+ align:start position:0%
+system that that is initially uh at
+ 
+
+ align:start position:0%
+system that that is initially uh at
+equilibrium so system equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and the system
+
+ align:start position:0%
+system and the system
+ 
+
+ align:start position:0%
+system and the system
+Honan right the Honan typically you can
+
+ align:start position:0%
+Honan right the Honan typically you can
+ 
+
+ align:start position:0%
+Honan right the Honan typically you can
+understand the Honan as the kinetic
+
+ align:start position:0%
+understand the Honan as the kinetic
+ 
+
+ align:start position:0%
+understand the Honan as the kinetic
+energy plus the potential energy so the
+
+ align:start position:0%
+energy plus the potential energy so the
+ 
+
+ align:start position:0%
+energy plus the potential energy so the
+system Honan is
+
+ align:start position:0%
+system Honan is
+ 
+
+ align:start position:0%
+system Honan is
+h0
+
+ align:start position:0%
+h0
+ 
+
+ align:start position:0%
+h0
+equinum let's say the volume is a
+
+ align:start position:0%
+equinum let's say the volume is a
+ 
+
+ align:start position:0%
+equinum let's say the volume is a
+V and then I'm going to give a
+
+ align:start position:0%
+V and then I'm going to give a
+ 
+
+ align:start position:0%
+V and then I'm going to give a
+disturbance to the system right I push
+
+ align:start position:0%
+disturbance to the system right I push
+ 
+
+ align:start position:0%
+disturbance to the system right I push
+the system I push every atom or I I
+
+ align:start position:0%
+the system I push every atom or I I
+ 
+
+ align:start position:0%
+the system I push every atom or I I
+somehow inject some heat so right now my
+
+ align:start position:0%
+somehow inject some heat so right now my
+ 
+
+ align:start position:0%
+somehow inject some heat so right now my
+disturbance I'm going to say I'm going
+
+ align:start position:0%
+disturbance I'm going to say I'm going
+ 
+
+ align:start position:0%
+disturbance I'm going to say I'm going
+to give a small disturbance and uniform
+
+ align:start position:0%
+to give a small disturbance and uniform
+ 
+
+ align:start position:0%
+to give a small disturbance and uniform
+through this
+
+ align:start position:0%
+through this
+ 
+
+ align:start position:0%
+through this
+space and this doesn't really matter you
+
+ align:start position:0%
+space and this doesn't really matter you
+ 
+
+ align:start position:0%
+space and this doesn't really matter you
+can extend to Long uniform but uh
+
+ align:start position:0%
+can extend to Long uniform but uh
+ 
+
+ align:start position:0%
+can extend to Long uniform but uh
+because uh I have a perturbation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+due to a force so I use a force to perur
+
+ align:start position:0%
+due to a force so I use a force to perur
+ 
+
+ align:start position:0%
+due to a force so I use a force to perur
+it and because I'm applying Force the
+
+ align:start position:0%
+it and because I'm applying Force the
+ 
+
+ align:start position:0%
+it and because I'm applying Force the
+system hon the energy of the system will
+
+ align:start position:0%
+system hon the energy of the system will
+ 
+
+ align:start position:0%
+system hon the energy of the system will
+change and that's change is H Prim right
+
+ align:start position:0%
+change and that's change is H Prim right
+ 
+
+ align:start position:0%
+change and that's change is H Prim right
+small change so I will say this is the
+
+ align:start position:0%
+small change so I will say this is the
+ 
+
+ align:start position:0%
+small change so I will say this is the
+perturbation to the Honan of the uh
+
+ align:start position:0%
+perturbation to the Honan of the uh
+ 
+
+ align:start position:0%
+perturbation to the Honan of the uh
+system and I can write this peration
+
+ align:start position:0%
+system and I can write this peration
+ 
+
+ align:start position:0%
+system and I can write this peration
+because this is the for Force apply so
+
+ align:start position:0%
+because this is the for Force apply so
+ 
+
+ align:start position:0%
+because this is the for Force apply so
+this will be uh related to the position
+
+ align:start position:0%
+this will be uh related to the position
+ 
+
+ align:start position:0%
+this will be uh related to the position
+and kinetic energy or of the each atom
+
+ align:start position:0%
+and kinetic energy or of the each atom
+ 
+
+ align:start position:0%
+and kinetic energy or of the each atom
+in the system right so this relation
+
+ align:start position:0%
+in the system right so this relation
+ 
+
+ align:start position:0%
+in the system right so this relation
+Honan is
+
+ align:start position:0%
+Honan is
+ 
+
+ align:start position:0%
+Honan is
+expressed in this
+
+ align:start position:0%
+expressed in this
+ 
+
+ align:start position:0%
+expressed in this
+perturbation and this is the
+
+ align:start position:0%
+perturbation and this is the
+ 
+
+ align:start position:0%
+perturbation and this is the
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+apply and I do a normalization to the
+
+ align:start position:0%
+apply and I do a normalization to the
+ 
+
+ align:start position:0%
+apply and I do a normalization to the
+volume so have my volume there and I put
+
+ align:start position:0%
+volume so have my volume there and I put
+ 
+
+ align:start position:0%
+volume so have my volume there and I put
+a negative sign that doesn't matter
+
+ align:start position:0%
+a negative sign that doesn't matter
+ 
+
+ align:start position:0%
+a negative sign that doesn't matter
+because that could be absorbed into
+
+ align:start position:0%
+because that could be absorbed into
+ 
+
+ align:start position:0%
+because that could be absorbed into
+me right so this is my uh perturbed
+
+ align:start position:0%
+me right so this is my uh perturbed
+ 
+
+ align:start position:0%
+me right so this is my uh perturbed
+honia and uh now so this this is really
+
+ align:start position:0%
+honia and uh now so this this is really
+ 
+
+ align:start position:0%
+honia and uh now so this this is really
+the water is perturbing due to this
+
+ align:start position:0%
+the water is perturbing due to this
+ 
+
+ align:start position:0%
+the water is perturbing due to this
+Force to individual atoms or molecules
+
+ align:start position:0%
+Force to individual atoms or molecules
+ 
+
+ align:start position:0%
+Force to individual atoms or molecules
+right and uh sometime later I want to
+
+ align:start position:0%
+right and uh sometime later I want to
+ 
+
+ align:start position:0%
+right and uh sometime later I want to
+look at the response
+
+ align:start position:0%
+look at the response
+ 
+
+ align:start position:0%
+look at the response
+I want to look at the how the heat flux
+
+ align:start position:0%
+I want to look at the how the heat flux
+ 
+
+ align:start position:0%
+I want to look at the how the heat flux
+change how the Shar stress
+
+ align:start position:0%
+change how the Shar stress
+ 
+
+ align:start position:0%
+change how the Shar stress
+change right and the uh the Shar stress
+
+ align:start position:0%
+change right and the uh the Shar stress
+ 
+
+ align:start position:0%
+change right and the uh the Shar stress
+again is reflected by another quantity
+
+ align:start position:0%
+again is reflected by another quantity
+ 
+
+ align:start position:0%
+again is reflected by another quantity
+let's say this is a b again is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+individual face bace variable right and
+
+ align:start position:0%
+individual face bace variable right and
+ 
+
+ align:start position:0%
+individual face bace variable right and
+uh uh this one this is the
+
+ align:start position:0%
+uh uh this one this is the
+ 
+
+ align:start position:0%
+uh uh this one this is the
+response this this is the
+
+ align:start position:0%
+response this this is the
+ 
+
+ align:start position:0%
+response this this is the
+disturbance right so in the case where
+
+ align:start position:0%
+disturbance right so in the case where
+ 
+
+ align:start position:0%
+disturbance right so in the case where
+the system is
+
+ align:start position:0%
+the system is
+ 
+
+ align:start position:0%
+the system is
+linear my force is not very
+
+ align:start position:0%
+linear my force is not very
+ 
+
+ align:start position:0%
+linear my force is not very
+large then this response I know will be
+
+ align:start position:0%
+large then this response I know will be
+ 
+
+ align:start position:0%
+large then this response I know will be
+proportional to the
+
+ align:start position:0%
+proportional to the
+ 
+
+ align:start position:0%
+proportional to the
+force right so this is a linear
+
+ align:start position:0%
+force right so this is a linear
+ 
+
+ align:start position:0%
+force right so this is a linear
+disturbance linear response
+
+ align:start position:0%
+disturbance linear response
+ 
+
+ align:start position:0%
+disturbance linear response
+regime and uh my uh so what I have is
+
+ align:start position:0%
+regime and uh my uh so what I have is
+ 
+
+ align:start position:0%
+regime and uh my uh so what I have is
+this is my Force I apply a certain time
+
+ align:start position:0%
+this is my Force I apply a certain time
+ 
+
+ align:start position:0%
+this is my Force I apply a certain time
+T Prime and this Force could be
+
+ align:start position:0%
+T Prime and this Force could be
+ 
+
+ align:start position:0%
+T Prime and this Force could be
+continuously vary in time varing and
+
+ align:start position:0%
+continuously vary in time varing and
+ 
+
+ align:start position:0%
+continuously vary in time varing and
+then uh from uh the start of time to the
+
+ align:start position:0%
+then uh from uh the start of time to the
+ 
+
+ align:start position:0%
+then uh from uh the start of time to the
+current time because this R and P of the
+
+ align:start position:0%
+current time because this R and P of the
+ 
+
+ align:start position:0%
+current time because this R and P of the
+atoms in the system could be a function
+
+ align:start position:0%
+atoms in the system could be a function
+ 
+
+ align:start position:0%
+atoms in the system could be a function
+of time is changing because apply
+
+ align:start position:0%
+of time is changing because apply
+ 
+
+ align:start position:0%
+of time is changing because apply
+external Force
+
+ align:start position:0%
+external Force
+ 
+
+ align:start position:0%
+external Force
+right and this is just related to a resp
+
+ align:start position:0%
+right and this is just related to a resp
+ 
+
+ align:start position:0%
+right and this is just related to a resp
+FSE function
+
+ align:start position:0%
+FSE function
+ 
+
+ align:start position:0%
+FSE function
+here and that's a function that I'm
+
+ align:start position:0%
+here and that's a function that I'm
+ 
+
+ align:start position:0%
+here and that's a function that I'm
+interested so B A and this is T Prime
+
+ align:start position:0%
+interested so B A and this is T Prime
+ 
+
+ align:start position:0%
+interested so B A and this is T Prime
+this I'm looking at a t time T So T
+
+ align:start position:0%
+this I'm looking at a t time T So T
+ 
+
+ align:start position:0%
+this I'm looking at a t time T So T
+minus t Prime so this is the uh the
+
+ align:start position:0%
+minus t Prime so this is the uh the
+ 
+
+ align:start position:0%
+minus t Prime so this is the uh the
+instant is aced and after some time
+
+ align:start position:0%
+instant is aced and after some time
+ 
+
+ align:start position:0%
+instant is aced and after some time
+what's my system
+
+ align:start position:0%
+what's my system
+ 
+
+ align:start position:0%
+what's my system
+response what's this response this
+
+ align:start position:0%
+response what's this response this
+ 
+
+ align:start position:0%
+response what's this response this
+quantity is
+
+ align:start position:0%
+quantity is
+ 
+
+ align:start position:0%
+quantity is
+responding right it's just a the only
+
+ align:start position:0%
+responding right it's just a the only
+ 
+
+ align:start position:0%
+responding right it's just a the only
+assumption I have here is a linear small
+
+ align:start position:0%
+assumption I have here is a linear small
+ 
+
+ align:start position:0%
+assumption I have here is a linear small
+disturbance so that this response is
+
+ align:start position:0%
+disturbance so that this response is
+ 
+
+ align:start position:0%
+disturbance so that this response is
+proportional to the first Power of my
+
+ align:start position:0%
+proportional to the first Power of my
+ 
+
+ align:start position:0%
+proportional to the first Power of my
+Force so here uh this
+
+ align:start position:0%
+Force so here uh this
+ 
+
+ align:start position:0%
+Force so here uh this
+ba uh say five is after effect function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is a general describe what happens
+
+ align:start position:0%
+is is a general describe what happens
+ 
+
+ align:start position:0%
+is is a general describe what happens
+after apply a disturbance to the system
+
+ align:start position:0%
+after apply a disturbance to the system
+ 
+
+ align:start position:0%
+after apply a disturbance to the system
+right so it should be a real observ real
+
+ align:start position:0%
+right so it should be a real observ real
+ 
+
+ align:start position:0%
+right so it should be a real observ real
+quantity and this is in fact is also
+
+ align:start position:0%
+quantity and this is in fact is also
+ 
+
+ align:start position:0%
+quantity and this is in fact is also
+sometimes you probably uh some of you
+
+ align:start position:0%
+sometimes you probably uh some of you
+ 
+
+ align:start position:0%
+sometimes you probably uh some of you
+heard the
+
+ align:start position:0%
+heard the
+ 
+
+ align:start position:0%
+heard the
+causality right f is the
+
+ align:start position:0%
+causality right f is the
+ 
+
+ align:start position:0%
+causality right f is the
+cause and uh later on it has a response
+
+ align:start position:0%
+cause and uh later on it has a response
+ 
+
+ align:start position:0%
+cause and uh later on it has a response
+so you should not this result are
+
+ align:start position:0%
+so you should not this result are
+ 
+
+ align:start position:0%
+so you should not this result are
+General you cannot VI violate and this
+
+ align:start position:0%
+General you cannot VI violate and this
+ 
+
+ align:start position:0%
+General you cannot VI violate and this
+are the causality
+
+ align:start position:0%
+are the causality
+ 
+
+ align:start position:0%
+are the causality
+uh uh uh uh
+
+ align:start position:0%
+uh uh uh uh
+ 
+
+ align:start position:0%
+uh uh uh uh
+requirement okay so what we have
+
+ align:start position:0%
+requirement okay so what we have
+ 
+
+ align:start position:0%
+requirement okay so what we have
+written is uh in real
+
+ align:start position:0%
+written is uh in real
+ 
+
+ align:start position:0%
+written is uh in real
+time and of course you can always
+
+ align:start position:0%
+time and of course you can always
+ 
+
+ align:start position:0%
+time and of course you can always
+express uh those properties in the
+
+ align:start position:0%
+express uh those properties in the
+ 
+
+ align:start position:0%
+express uh those properties in the
+frequency domain you can do the fer
+
+ align:start position:0%
+frequency domain you can do the fer
+ 
+
+ align:start position:0%
+frequency domain you can do the fer
+transform of
+
+ align:start position:0%
+transform of
+ 
+
+ align:start position:0%
+transform of
+force and if you do your fer transform
+
+ align:start position:0%
+force and if you do your fer transform
+ 
+
+ align:start position:0%
+force and if you do your fer transform
+and uh um we have here I'm I should do
+
+ align:start position:0%
+and uh um we have here I'm I should do
+ 
+
+ align:start position:0%
+and uh um we have here I'm I should do
+do the emble average I want to look at
+
+ align:start position:0%
+do the emble average I want to look at
+ 
+
+ align:start position:0%
+do the emble average I want to look at
+the the uh FAL
+
+ align:start position:0%
+the the uh FAL
+ 
+
+ align:start position:0%
+the the uh FAL
+transform uh and then I can use
+
+ align:start position:0%
+transform uh and then I can use
+ 
+
+ align:start position:0%
+transform uh and then I can use
+the for
+
+ align:start position:0%
+the for
+ 
+
+ align:start position:0%
+the for
+space response and I'm not going to
+
+ align:start position:0%
+space response and I'm not going to
+ 
+
+ align:start position:0%
+space response and I'm not going to
+derive it but this can be proven and uh
+
+ align:start position:0%
+derive it but this can be proven and uh
+ 
+
+ align:start position:0%
+derive it but this can be proven and uh
+ba a so this is a the disturbance start
+
+ align:start position:0%
+ba a so this is a the disturbance start
+ 
+
+ align:start position:0%
+ba a so this is a the disturbance start
+with a and uh dist disturb quantity due
+
+ align:start position:0%
+with a and uh dist disturb quantity due
+ 
+
+ align:start position:0%
+with a and uh dist disturb quantity due
+to that force and response is a specific
+
+ align:start position:0%
+to that force and response is a specific
+ 
+
+ align:start position:0%
+to that force and response is a specific
+response for example like I said
+
+ align:start position:0%
+response for example like I said
+ 
+
+ align:start position:0%
+response for example like I said
+viscosity so here is a
+
+ align:start position:0%
+viscosity so here is a
+ 
+
+ align:start position:0%
+viscosity so here is a
+frequency and the force is also foral
+
+ align:start position:0%
+frequency and the force is also foral
+ 
+
+ align:start position:0%
+frequency and the force is also foral
+transform and exponential I Omega
+
+ align:start position:0%
+transform and exponential I Omega
+ 
+
+ align:start position:0%
+transform and exponential I Omega
+T and D Omega so you can say that this
+
+ align:start position:0%
+T and D Omega so you can say that this
+ 
+
+ align:start position:0%
+T and D Omega so you can say that this
+uh susceptibility that we usually call
+
+ align:start position:0%
+uh susceptibility that we usually call
+ 
+
+ align:start position:0%
+uh susceptibility that we usually call
+dyamic sessility of the system must be
+
+ align:start position:0%
+dyamic sessility of the system must be
+ 
+
+ align:start position:0%
+dyamic sessility of the system must be
+related to the after effect function
+
+ align:start position:0%
+related to the after effect function
+ 
+
+ align:start position:0%
+related to the after effect function
+here right in fact this
+
+ align:start position:0%
+here right in fact this
+ 
+
+ align:start position:0%
+here right in fact this
+susceptibility uh so here we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dyamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scept
+
+ align:start position:0%
+scept
+ 
+
+ align:start position:0%
+scept
+ability of the system uh
+
+ align:start position:0%
+ability of the system uh
+ 
+
+ align:start position:0%
+ability of the system uh
+xba Omega is actually the fal
+
+ align:start position:0%
+xba Omega is actually the fal
+ 
+
+ align:start position:0%
+xba Omega is actually the fal
+transform uh of so it's Z to
+
+ align:start position:0%
+transform uh of so it's Z to
+ 
+
+ align:start position:0%
+transform uh of so it's Z to
+infinite 5 ba T
+
+ align:start position:0%
+infinite 5 ba T
+ 
+
+ align:start position:0%
+infinite 5 ba T
+exponential um Mass I
+
+ align:start position:0%
+exponential um Mass I
+ 
+
+ align:start position:0%
+exponential um Mass I
+om D
+
+ align:start position:0%
+om D
+ 
+
+ align:start position:0%
+om D
+to so if I know this I know the after
+
+ align:start position:0%
+to so if I know this I know the after
+ 
+
+ align:start position:0%
+to so if I know this I know the after
+effect function or if I know after
+
+ align:start position:0%
+effect function or if I know after
+ 
+
+ align:start position:0%
+effect function or if I know after
+effect function I know the
+
+ align:start position:0%
+effect function I know the
+ 
+
+ align:start position:0%
+effect function I know the
+susceptibility okay and uh uh in fact uh
+
+ align:start position:0%
+susceptibility okay and uh uh in fact uh
+ 
+
+ align:start position:0%
+susceptibility okay and uh uh in fact uh
+there is a really interesting relation
+
+ align:start position:0%
+there is a really interesting relation
+ 
+
+ align:start position:0%
+there is a really interesting relation
+between this one could be real part and
+
+ align:start position:0%
+between this one could be real part and
+ 
+
+ align:start position:0%
+between this one could be real part and
+imaginary part because I'm here I have
+
+ align:start position:0%
+imaginary part because I'm here I have
+ 
+
+ align:start position:0%
+imaginary part because I'm here I have
+uh in the F transform I have I there
+
+ align:start position:0%
+uh in the F transform I have I there
+ 
+
+ align:start position:0%
+uh in the F transform I have I there
+right so I have a real part I have
+
+ align:start position:0%
+right so I have a real part I have
+ 
+
+ align:start position:0%
+right so I have a real part I have
+imaginary part uh I can write okay I
+
+ align:start position:0%
+imaginary part uh I can write okay I
+ 
+
+ align:start position:0%
+imaginary part uh I can write okay I
+have real part plus I imagining part and
+
+ align:start position:0%
+have real part plus I imagining part and
+ 
+
+ align:start position:0%
+have real part plus I imagining part and
+both are frequency dependent and you can
+
+ align:start position:0%
+both are frequency dependent and you can
+ 
+
+ align:start position:0%
+both are frequency dependent and you can
+say because this is really just a cosine
+
+ align:start position:0%
+say because this is really just a cosine
+ 
+
+ align:start position:0%
+say because this is really just a cosine
+or sign part of the for transform if I
+
+ align:start position:0%
+or sign part of the for transform if I
+ 
+
+ align:start position:0%
+or sign part of the for transform if I
+do a cosine so if I not real part of
+
+ align:start position:0%
+do a cosine so if I not real part of
+ 
+
+ align:start position:0%
+do a cosine so if I not real part of
+this frequency dependence I can go
+
+ align:start position:0%
+this frequency dependence I can go
+ 
+
+ align:start position:0%
+this frequency dependence I can go
+inverse cosine transform and get this
+
+ align:start position:0%
+inverse cosine transform and get this
+ 
+
+ align:start position:0%
+inverse cosine transform and get this
+function here from this function I can
+
+ align:start position:0%
+function here from this function I can
+ 
+
+ align:start position:0%
+function here from this function I can
+do a sign transform I can get the
+
+ align:start position:0%
+do a sign transform I can get the
+ 
+
+ align:start position:0%
+do a sign transform I can get the
+imaginary part right so which means the
+
+ align:start position:0%
+imaginary part right so which means the
+ 
+
+ align:start position:0%
+imaginary part right so which means the
+real and imagin part always
+
+ align:start position:0%
+real and imagin part always
+ 
+
+ align:start position:0%
+real and imagin part always
+related and this relation is the cramar
+
+ align:start position:0%
+related and this relation is the cramar
+ 
+
+ align:start position:0%
+related and this relation is the cramar
+chronical relation it's very general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do theral radi
+
+ align:start position:0%
+if you do theral radi
+ 
+
+ align:start position:0%
+if you do theral radi
+radiation uh you probably heard for
+
+ align:start position:0%
+radiation uh you probably heard for
+ 
+
+ align:start position:0%
+radiation uh you probably heard for
+example the dialectric constant or Optic
+
+ align:start position:0%
+example the dialectric constant or Optic
+ 
+
+ align:start position:0%
+example the dialectric constant or Optic
+constant you can calculate if you
+
+ align:start position:0%
+constant you can calculate if you
+ 
+
+ align:start position:0%
+constant you can calculate if you
+measure real part you can calculate
+
+ align:start position:0%
+measure real part you can calculate
+ 
+
+ align:start position:0%
+measure real part you can calculate
+imagin part if you measure imagin part
+
+ align:start position:0%
+imagin part if you measure imagin part
+ 
+
+ align:start position:0%
+imagin part if you measure imagin part
+you can calculate real part it's example
+
+ align:start position:0%
+you can calculate real part it's example
+ 
+
+ align:start position:0%
+you can calculate real part it's example
+of the Chron chal chronic
+
+ align:start position:0%
+of the Chron chal chronic
+ 
+
+ align:start position:0%
+of the Chron chal chronic
+relation and uh uh so uh the real part
+
+ align:start position:0%
+relation and uh uh so uh the real part
+ 
+
+ align:start position:0%
+relation and uh uh so uh the real part
+for example can be calculated from
+
+ align:start position:0%
+for example can be calculated from
+ 
+
+ align:start position:0%
+for example can be calculated from
+imaginary
+
+ align:start position:0%
+imaginary
+ 
+
+ align:start position:0%
+imaginary
+part and Min infinite to plus infinite
+
+ align:start position:0%
+part and Min infinite to plus infinite
+ 
+
+ align:start position:0%
+part and Min infinite to plus infinite
+imaginary
+
+ align:start position:0%
+imaginary
+ 
+
+ align:start position:0%
+imaginary
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+Prime and Omega primeus Omega D Omega
+
+ align:start position:0%
+Prime and Omega primeus Omega D Omega
+ 
+
+ align:start position:0%
+Prime and Omega primeus Omega D Omega
+Prime so you can say uh the problem of
+
+ align:start position:0%
+Prime so you can say uh the problem of
+ 
+
+ align:start position:0%
+Prime so you can say uh the problem of
+this integration is when Omega Prime
+
+ align:start position:0%
+this integration is when Omega Prime
+ 
+
+ align:start position:0%
+this integration is when Omega Prime
+equals Omega because I'm integrating
+
+ align:start position:0%
+equals Omega because I'm integrating
+ 
+
+ align:start position:0%
+equals Omega because I'm integrating
+from minus infinite to plus infinite
+
+ align:start position:0%
+from minus infinite to plus infinite
+ 
+
+ align:start position:0%
+from minus infinite to plus infinite
+this blow up so this has to be uh uh
+
+ align:start position:0%
+this blow up so this has to be uh uh
+ 
+
+ align:start position:0%
+this blow up so this has to be uh uh
+this is a in the in the front you put a
+
+ align:start position:0%
+this is a in the in the front you put a
+ 
+
+ align:start position:0%
+this is a in the in the front you put a
+Koshi uh principle value so actually
+
+ align:start position:0%
+Koshi uh principle value so actually
+ 
+
+ align:start position:0%
+Koshi uh principle value so actually
+there's a negative sign for this
+
+ align:start position:0%
+there's a negative sign for this
+ 
+
+ align:start position:0%
+there's a negative sign for this
+part and uh let's just say when they uh
+
+ align:start position:0%
+part and uh let's just say when they uh
+ 
+
+ align:start position:0%
+part and uh let's just say when they uh
+going from left approaching to Omega or
+
+ align:start position:0%
+going from left approaching to Omega or
+ 
+
+ align:start position:0%
+going from left approaching to Omega or
+from right approaching to Omega is
+
+ align:start position:0%
+from right approaching to Omega is
+ 
+
+ align:start position:0%
+from right approaching to Omega is
+separated through the limit uh at this
+
+ align:start position:0%
+separated through the limit uh at this
+ 
+
+ align:start position:0%
+separated through the limit uh at this
+Singularity point and similarly there is
+
+ align:start position:0%
+Singularity point and similarly there is
+ 
+
+ align:start position:0%
+Singularity point and similarly there is
+relation uh is switch the there's no
+
+ align:start position:0%
+relation uh is switch the there's no
+ 
+
+ align:start position:0%
+relation uh is switch the there's no
+more sign it's a positive sign you
+
+ align:start position:0%
+more sign it's a positive sign you
+ 
+
+ align:start position:0%
+more sign it's a positive sign you
+switch this with this you get another
+
+ align:start position:0%
+switch this with this you get another
+ 
+
+ align:start position:0%
+switch this with this you get another
+relation so either way if you know the
+
+ align:start position:0%
+relation so either way if you know the
+ 
+
+ align:start position:0%
+relation so either way if you know the
+real and no imaginary part but you need
+
+ align:start position:0%
+real and no imaginary part but you need
+ 
+
+ align:start position:0%
+real and no imaginary part but you need
+to say if you look at this function here
+
+ align:start position:0%
+to say if you look at this function here
+ 
+
+ align:start position:0%
+to say if you look at this function here
+you need to know the whole function as a
+
+ align:start position:0%
+you need to know the whole function as a
+ 
+
+ align:start position:0%
+you need to know the whole function as a
+function of frequency right if you just
+
+ align:start position:0%
+function of frequency right if you just
+ 
+
+ align:start position:0%
+function of frequency right if you just
+have if you do op measurement and you
+
+ align:start position:0%
+have if you do op measurement and you
+ 
+
+ align:start position:0%
+have if you do op measurement and you
+know only a section of that you may not
+
+ align:start position:0%
+know only a section of that you may not
+ 
+
+ align:start position:0%
+know only a section of that you may not
+be accurate enough to do this inverse
+
+ align:start position:0%
+be accurate enough to do this inverse
+ 
+
+ align:start position:0%
+be accurate enough to do this inverse
+using The cramar Chronic relation
+
+ align:start position:0%
+using The cramar Chronic relation
+ 
+
+ align:start position:0%
+using The cramar Chronic relation
+and there's uh this is a causality what
+
+ align:start position:0%
+and there's uh this is a causality what
+ 
+
+ align:start position:0%
+and there's uh this is a causality what
+sometimes people say this is a causality
+
+ align:start position:0%
+sometimes people say this is a causality
+ 
+
+ align:start position:0%
+sometimes people say this is a causality
+requirement right you can say that we
+
+ align:start position:0%
+requirement right you can say that we
+ 
+
+ align:start position:0%
+requirement right you can say that we
+don't have uh um uh assumptions
+
+ align:start position:0%
+don't have uh um uh assumptions
+ 
+
+ align:start position:0%
+don't have uh um uh assumptions
+there and uh what's also
+
+ align:start position:0%
+there and uh what's also
+ 
+
+ align:start position:0%
+there and uh what's also
+interesting right if you say this is a
+
+ align:start position:0%
+interesting right if you say this is a
+ 
+
+ align:start position:0%
+interesting right if you say this is a
+response on different uh face space
+
+ align:start position:0%
+response on different uh face space
+ 
+
+ align:start position:0%
+response on different uh face space
+variable but if B is the same as a right
+
+ align:start position:0%
+variable but if B is the same as a right
+ 
+
+ align:start position:0%
+variable but if B is the same as a right
+and a is related to the because the a is
+
+ align:start position:0%
+and a is related to the because the a is
+ 
+
+ align:start position:0%
+and a is related to the because the a is
+here is a disturbance to the
+
+ align:start position:0%
+here is a disturbance to the
+ 
+
+ align:start position:0%
+here is a disturbance to the
+honia right the energy of the
+
+ align:start position:0%
+honia right the energy of the
+ 
+
+ align:start position:0%
+honia right the energy of the
+system so in fact when b equal a there's
+
+ align:start position:0%
+system so in fact when b equal a there's
+ 
+
+ align:start position:0%
+system so in fact when b equal a there's
+a useful relation that's uh b equals a
+
+ align:start position:0%
+a useful relation that's uh b equals a
+ 
+
+ align:start position:0%
+a useful relation that's uh b equals a
+what we have is the energy
+
+ align:start position:0%
+what we have is the energy
+ 
+
+ align:start position:0%
+what we have is the energy
+dissipated in the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+due to this external
+
+ align:start position:0%
+due to this external
+ 
+
+ align:start position:0%
+due to this external
+disturbance right and the uh eal is
+
+ align:start position:0%
+disturbance right and the uh eal is
+ 
+
+ align:start position:0%
+disturbance right and the uh eal is
+relate to the imaginary part of the
+
+ align:start position:0%
+relate to the imaginary part of the
+ 
+
+ align:start position:0%
+relate to the imaginary part of the
+dynamic susceptibility so Omega over 2 v
+
+ align:start position:0%
+dynamic susceptibility so Omega over 2 v
+ 
+
+ align:start position:0%
+dynamic susceptibility so Omega over 2 v
+x a a so b equal a now the imagin part
+
+ align:start position:0%
+x a a so b equal a now the imagin part
+ 
+
+ align:start position:0%
+x a a so b equal a now the imagin part
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+Omega F
+
+ align:start position:0%
+Omega F
+ 
+
+ align:start position:0%
+Omega F
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+Square so this is a uh just a
+
+ align:start position:0%
+Square so this is a uh just a
+ 
+
+ align:start position:0%
+Square so this is a uh just a
+uh result out of again the uh
+
+ align:start position:0%
+uh result out of again the uh
+ 
+
+ align:start position:0%
+uh result out of again the uh
+causality and it's gen it's
+
+ align:start position:0%
+causality and it's gen it's
+ 
+
+ align:start position:0%
+causality and it's gen it's
+General okay and uh here we're
+
+ align:start position:0%
+General okay and uh here we're
+ 
+
+ align:start position:0%
+General okay and uh here we're
+discussing the uh response
+
+ align:start position:0%
+discussing the uh response
+ 
+
+ align:start position:0%
+discussing the uh response
+function and next let's move on so I
+
+ align:start position:0%
+function and next let's move on so I
+ 
+
+ align:start position:0%
+function and next let's move on so I
+have now the system has a small
+
+ align:start position:0%
+have now the system has a small
+ 
+
+ align:start position:0%
+have now the system has a small
+peration H Prime and initially it was at
+
+ align:start position:0%
+peration H Prime and initially it was at
+ 
+
+ align:start position:0%
+peration H Prime and initially it was at
+a equilibrium situation right we have
+
+ align:start position:0%
+a equilibrium situation right we have
+ 
+
+ align:start position:0%
+a equilibrium situation right we have
+have F say the uh
+
+ align:start position:0%
+have F say the uh
+ 
+
+ align:start position:0%
+have F say the uh
+h0 and now after this probation the
+
+ align:start position:0%
+h0 and now after this probation the
+ 
+
+ align:start position:0%
+h0 and now after this probation the
+distribution function will change right
+
+ align:start position:0%
+distribution function will change right
+ 
+
+ align:start position:0%
+distribution function will change right
+because the Honan of the system change
+
+ align:start position:0%
+because the Honan of the system change
+ 
+
+ align:start position:0%
+because the Honan of the system change
+and distribution function change so now
+
+ align:start position:0%
+and distribution function change so now
+ 
+
+ align:start position:0%
+and distribution function change so now
+I'm you see the approach I mentioned
+
+ align:start position:0%
+I'm you see the approach I mentioned
+ 
+
+ align:start position:0%
+I'm you see the approach I mentioned
+before one of this approach is going to
+
+ align:start position:0%
+before one of this approach is going to
+ 
+
+ align:start position:0%
+before one of this approach is going to
+BMA equation the FN the N particle
+
+ align:start position:0%
+BMA equation the FN the N particle
+ 
+
+ align:start position:0%
+BMA equation the FN the N particle
+distribution function is reduced to one
+
+ align:start position:0%
+distribution function is reduced to one
+ 
+
+ align:start position:0%
+distribution function is reduced to one
+particle distribution function function
+
+ align:start position:0%
+particle distribution function function
+ 
+
+ align:start position:0%
+particle distribution function function
+and that's the BS M equation
+
+ align:start position:0%
+and that's the BS M equation
+ 
+
+ align:start position:0%
+and that's the BS M equation
+approach and uh what we go in in this
+
+ align:start position:0%
+approach and uh what we go in in this
+ 
+
+ align:start position:0%
+approach and uh what we go in in this
+approach is a linearize is actually
+
+ align:start position:0%
+approach is a linearize is actually
+ 
+
+ align:start position:0%
+approach is a linearize is actually
+taking the N particle distribution
+
+ align:start position:0%
+taking the N particle distribution
+ 
+
+ align:start position:0%
+taking the N particle distribution
+function so the linear response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory start from the Lal
+
+ align:start position:0%
+Theory start from the Lal
+ 
+
+ align:start position:0%
+Theory start from the Lal
+equation and uh but it's a nariz Lal
+
+ align:start position:0%
+equation and uh but it's a nariz Lal
+ 
+
+ align:start position:0%
+equation and uh but it's a nariz Lal
+equation but still keep the N particle
+
+ align:start position:0%
+equation but still keep the N particle
+ 
+
+ align:start position:0%
+equation but still keep the N particle
+distribution so if we go back to the Lal
+
+ align:start position:0%
+distribution so if we go back to the Lal
+ 
+
+ align:start position:0%
+distribution so if we go back to the Lal
+equation and this is a Lal equation
+
+ align:start position:0%
+equation and this is a Lal equation
+ 
+
+ align:start position:0%
+equation and this is a Lal equation
+written in operator form so the Lal
+
+ align:start position:0%
+written in operator form so the Lal
+ 
+
+ align:start position:0%
+written in operator form so the Lal
+equation is a equation for the N par
+
+ align:start position:0%
+equation is a equation for the N par
+ 
+
+ align:start position:0%
+equation is a equation for the N par
+distribution function as a function of
+
+ align:start position:0%
+distribution function as a function of
+ 
+
+ align:start position:0%
+distribution function as a function of
+time and uh we could write this in
+
+ align:start position:0%
+time and uh we could write this in
+ 
+
+ align:start position:0%
+time and uh we could write this in
+operator so it's the H the honia of the
+
+ align:start position:0%
+operator so it's the H the honia of the
+ 
+
+ align:start position:0%
+operator so it's the H the honia of the
+system and
+
+ align:start position:0%
+system and
+ 
+
+ align:start position:0%
+system and
+FN this bracket is called a posum
+
+ align:start position:0%
+FN this bracket is called a posum
+ 
+
+ align:start position:0%
+FN this bracket is called a posum
+bracket I'll explain what it mean uh ma
+
+ align:start position:0%
+bracket I'll explain what it mean uh ma
+ 
+
+ align:start position:0%
+bracket I'll explain what it mean uh ma
+see and then see there's also another
+
+ align:start position:0%
+see and then see there's also another
+ 
+
+ align:start position:0%
+see and then see there's also another
+rotation and this is using I gamma
+
+ align:start position:0%
+rotation and this is using I gamma
+ 
+
+ align:start position:0%
+rotation and this is using I gamma
+operator and the
+
+ align:start position:0%
+operator and the
+ 
+
+ align:start position:0%
+operator and the
+FN okay here the point is I'm writing a
+
+ align:start position:0%
+FN okay here the point is I'm writing a
+ 
+
+ align:start position:0%
+FN okay here the point is I'm writing a
+l equation with and this is original L
+
+ align:start position:0%
+l equation with and this is original L
+ 
+
+ align:start position:0%
+l equation with and this is original L
+equation with the Imp paral distribution
+
+ align:start position:0%
+equation with the Imp paral distribution
+ 
+
+ align:start position:0%
+equation with the Imp paral distribution
+function and
+
+ align:start position:0%
+function and
+ 
+
+ align:start position:0%
+function and
+uh and notation wise what we have on the
+
+ align:start position:0%
+uh and notation wise what we have on the
+ 
+
+ align:start position:0%
+uh and notation wise what we have on the
+right hand side first that's the
+
+ align:start position:0%
+right hand side first that's the
+ 
+
+ align:start position:0%
+right hand side first that's the
+curve curly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bracket is
+
+ align:start position:0%
+bracket is
+ 
+
+ align:start position:0%
+bracket is
+person bracket
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's just a rotation if you have a
+
+ align:start position:0%
+and that's just a rotation if you have a
+ 
+
+ align:start position:0%
+and that's just a rotation if you have a
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+b and uh what it means is
+
+ align:start position:0%
+b and uh what it means is
+ 
+
+ align:start position:0%
+b and uh what it means is
+uh because I have I particle so I equal
+
+ align:start position:0%
+uh because I have I particle so I equal
+ 
+
+ align:start position:0%
+uh because I have I particle so I equal
+one to uh in fact say this are the total
+
+ align:start position:0%
+one to uh in fact say this are the total
+ 
+
+ align:start position:0%
+one to uh in fact say this are the total
+number of degree Freedom if I have
+
+ align:start position:0%
+number of degree Freedom if I have
+ 
+
+ align:start position:0%
+number of degree Freedom if I have
+capital N particle and each n particle
+
+ align:start position:0%
+capital N particle and each n particle
+ 
+
+ align:start position:0%
+capital N particle and each n particle
+each particle has three degree that's a
+
+ align:start position:0%
+each particle has three degree that's a
+ 
+
+ align:start position:0%
+each particle has three degree that's a
+three n it's a six degree it's a six
+
+ align:start position:0%
+three n it's a six degree it's a six
+ 
+
+ align:start position:0%
+three n it's a six degree it's a six
+right so this is a um and then I have da
+
+ align:start position:0%
+right so this is a um and then I have da
+ 
+
+ align:start position:0%
+right so this is a um and then I have da
+a and uh d r i DB
+
+ align:start position:0%
+a and uh d r i DB
+ 
+
+ align:start position:0%
+a and uh d r i DB
+DP I minus uh da
+
+ align:start position:0%
+DP I minus uh da
+ 
+
+ align:start position:0%
+DP I minus uh da
+a DP I DB d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r and with this rotation you put in back
+
+ align:start position:0%
+r and with this rotation you put in back
+ 
+
+ align:start position:0%
+r and with this rotation you put in back
+into the right hand side you get back to
+
+ align:start position:0%
+into the right hand side you get back to
+ 
+
+ align:start position:0%
+into the right hand side you get back to
+the original Lal equation that we have
+
+ align:start position:0%
+the original Lal equation that we have
+ 
+
+ align:start position:0%
+the original Lal equation that we have
+written down before
+
+ align:start position:0%
+written down before
+ 
+
+ align:start position:0%
+written down before
+okay and uh this one gamma here is a
+
+ align:start position:0%
+okay and uh this one gamma here is a
+ 
+
+ align:start position:0%
+okay and uh this one gamma here is a
+operator so gamma is is def definition
+
+ align:start position:0%
+operator so gamma is is def definition
+ 
+
+ align:start position:0%
+operator so gamma is is def definition
+is operator is m i and H and whatever
+
+ align:start position:0%
+is operator is m i and H and whatever
+ 
+
+ align:start position:0%
+is operator is m i and H and whatever
+behind this function is putting here
+
+ align:start position:0%
+behind this function is putting here
+ 
+
+ align:start position:0%
+behind this function is putting here
+this is the operator
+
+ align:start position:0%
+this is the operator
+ 
+
+ align:start position:0%
+this is the operator
+loation okay and the uh uh use of the
+
+ align:start position:0%
+loation okay and the uh uh use of the
+ 
+
+ align:start position:0%
+loation okay and the uh uh use of the
+this is the Lal operator the use of this
+
+ align:start position:0%
+this is the Lal operator the use of this
+ 
+
+ align:start position:0%
+this is the Lal operator the use of this
+Lal operator is now with this written as
+
+ align:start position:0%
+Lal operator is now with this written as
+ 
+
+ align:start position:0%
+Lal operator is now with this written as
+this form you can just think this is
+
+ align:start position:0%
+this form you can just think this is
+ 
+
+ align:start position:0%
+this form you can just think this is
+like ordinary differential
+
+ align:start position:0%
+like ordinary differential
+ 
+
+ align:start position:0%
+like ordinary differential
+equation okay and you have to go in back
+
+ align:start position:0%
+equation okay and you have to go in back
+ 
+
+ align:start position:0%
+equation okay and you have to go in back
+into all this detail math but think this
+
+ align:start position:0%
+into all this detail math but think this
+ 
+
+ align:start position:0%
+into all this detail math but think this
+as ordinary differential equation you
+
+ align:start position:0%
+as ordinary differential equation you
+ 
+
+ align:start position:0%
+as ordinary differential equation you
+solve it as exponential function that's
+
+ align:start position:0%
+solve it as exponential function that's
+ 
+
+ align:start position:0%
+solve it as exponential function that's
+the use of this Noble and of course the
+
+ align:start position:0%
+the use of this Noble and of course the
+ 
+
+ align:start position:0%
+the use of this Noble and of course the
+gamma you keep it as a operator
+
+ align:start position:0%
+gamma you keep it as a operator
+ 
+
+ align:start position:0%
+gamma you keep it as a operator
+form and and now so what we have the
+
+ align:start position:0%
+form and and now so what we have the
+ 
+
+ align:start position:0%
+form and and now so what we have the
+system Honan is h0 plus h
+
+ align:start position:0%
+system Honan is h0 plus h
+ 
+
+ align:start position:0%
+system Honan is h0 plus h
+Prime right I have a peration to the
+
+ align:start position:0%
+Prime right I have a peration to the
+ 
+
+ align:start position:0%
+Prime right I have a peration to the
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+energy and then correspondingly the N
+
+ align:start position:0%
+energy and then correspondingly the N
+ 
+
+ align:start position:0%
+energy and then correspondingly the N
+particle distribution function is
+
+ align:start position:0%
+particle distribution function is
+ 
+
+ align:start position:0%
+particle distribution function is
+f0n that's corresponding to
+
+ align:start position:0%
+f0n that's corresponding to
+ 
+
+ align:start position:0%
+f0n that's corresponding to
+equilibrium and
+
+ align:start position:0%
+equilibrium and
+ 
+
+ align:start position:0%
+equilibrium and
+then a small peration
+
+ align:start position:0%
+then a small peration
+ 
+
+ align:start position:0%
+then a small peration
+F1 uh and that due to the
+
+ align:start position:0%
+F1 uh and that due to the
+ 
+
+ align:start position:0%
+F1 uh and that due to the
+peration H Prime
+
+ align:start position:0%
+peration H Prime
+ 
+
+ align:start position:0%
+peration H Prime
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f0n is related to because it's at the
+
+ align:start position:0%
+f0n is related to because it's at the
+ 
+
+ align:start position:0%
+f0n is related to because it's at the
+equilibrium so it's a you can write it
+
+ align:start position:0%
+equilibrium so it's a you can write it
+ 
+
+ align:start position:0%
+equilibrium so it's a you can write it
+as H KBT that's a board M uh
+
+ align:start position:0%
+as H KBT that's a board M uh
+ 
+
+ align:start position:0%
+as H KBT that's a board M uh
+distribution there right at uh for
+
+ align:start position:0%
+distribution there right at uh for
+ 
+
+ align:start position:0%
+distribution there right at uh for
+system at uh so the way that I'm wring
+
+ align:start position:0%
+system at uh so the way that I'm wring
+ 
+
+ align:start position:0%
+system at uh so the way that I'm wring
+here F0 here is a
+
+ align:start position:0%
+here F0 here is a
+ 
+
+ align:start position:0%
+here F0 here is a
+canonical distribution canonical system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and uh so once I have those I put
+
+ align:start position:0%
+right and uh so once I have those I put
+ 
+
+ align:start position:0%
+right and uh so once I have those I put
+in here into this equation I use the
+
+ align:start position:0%
+in here into this equation I use the
+ 
+
+ align:start position:0%
+in here into this equation I use the
+operator and I neglect the the term I
+
+ align:start position:0%
+operator and I neglect the the term I
+ 
+
+ align:start position:0%
+operator and I neglect the the term I
+neglect is H prime time fub1 because
+
+ align:start position:0%
+neglect is H prime time fub1 because
+ 
+
+ align:start position:0%
+neglect is H prime time fub1 because
+that's H Prime is lower order small
+
+ align:start position:0%
+that's H Prime is lower order small
+ 
+
+ align:start position:0%
+that's H Prime is lower order small
+disturbance F1 is small disturbance so I
+
+ align:start position:0%
+disturbance F1 is small disturbance so I
+ 
+
+ align:start position:0%
+disturbance F1 is small disturbance so I
+drop that cross term that's a higher
+
+ align:start position:0%
+drop that cross term that's a higher
+ 
+
+ align:start position:0%
+drop that cross term that's a higher
+order and with that I can solve for F1
+
+ align:start position:0%
+order and with that I can solve for F1
+ 
+
+ align:start position:0%
+order and with that I can solve for F1
+in the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation so I will have
+
+ align:start position:0%
+rotation so I will have
+ 
+
+ align:start position:0%
+rotation so I will have
+fub1 n and T
+
+ align:start position:0%
+fub1 n and T
+ 
+
+ align:start position:0%
+fub1 n and T
+RP right that's the face space variable
+
+ align:start position:0%
+RP right that's the face space variable
+ 
+
+ align:start position:0%
+RP right that's the face space variable
+or the is a V
+
+ align:start position:0%
+or the is a V
+ 
+
+ align:start position:0%
+or the is a V
+KBT that comes V KBT comes from
+
+ align:start position:0%
+KBT that comes V KBT comes from
+ 
+
+ align:start position:0%
+KBT that comes V KBT comes from
+f0n and uh Mass infinite to T and
+
+ align:start position:0%
+f0n and uh Mass infinite to T and
+ 
+
+ align:start position:0%
+f0n and uh Mass infinite to T and
+exponential Mass
+
+ align:start position:0%
+exponential Mass
+ 
+
+ align:start position:0%
+exponential Mass
+i t t
+
+ align:start position:0%
+i t t
+ 
+
+ align:start position:0%
+i t t
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+GMA right if you look at this
+
+ align:start position:0%
+GMA right if you look at this
+ 
+
+ align:start position:0%
+GMA right if you look at this
+exponential that come from I treated
+
+ align:start position:0%
+exponential that come from I treated
+ 
+
+ align:start position:0%
+exponential that come from I treated
+that gamma just like a constant I do
+
+ align:start position:0%
+that gamma just like a constant I do
+ 
+
+ align:start position:0%
+that gamma just like a constant I do
+integration that's the operator math
+
+ align:start position:0%
+integration that's the operator math
+ 
+
+ align:start position:0%
+integration that's the operator math
+there and uh
+
+ align:start position:0%
+there and uh
+ 
+
+ align:start position:0%
+there and uh
+gamma Z this gamma Z is corresponding to
+
+ align:start position:0%
+gamma Z this gamma Z is corresponding to
+ 
+
+ align:start position:0%
+gamma Z this gamma Z is corresponding to
+when H is
+
+ align:start position:0%
+when H is
+ 
+
+ align:start position:0%
+when H is
+h0 and uh then I have
+
+ align:start position:0%
+h0 and uh then I have
+ 
+
+ align:start position:0%
+h0 and uh then I have
+uh the uh time derivative this because H
+
+ align:start position:0%
+uh the uh time derivative this because H
+ 
+
+ align:start position:0%
+uh the uh time derivative this because H
+Prime has a so I have time derivative in
+
+ align:start position:0%
+Prime has a so I have time derivative in
+ 
+
+ align:start position:0%
+Prime has a so I have time derivative in
+a I have R is function of time and P is
+
+ align:start position:0%
+a I have R is function of time and P is
+ 
+
+ align:start position:0%
+a I have R is function of time and P is
+a function of time that's why I can do
+
+ align:start position:0%
+a function of time that's why I can do
+ 
+
+ align:start position:0%
+a function of time that's why I can do
+the time derivative
+
+ align:start position:0%
+the time derivative
+ 
+
+ align:start position:0%
+the time derivative
+and uh I have f t Prime and this is a
+
+ align:start position:0%
+and uh I have f t Prime and this is a
+ 
+
+ align:start position:0%
+and uh I have f t Prime and this is a
+all T Prime and then I have
+
+ align:start position:0%
+all T Prime and then I have
+ 
+
+ align:start position:0%
+all T Prime and then I have
+F0 to n and the d t Prime so this is the
+
+ align:start position:0%
+F0 to n and the d t Prime so this is the
+ 
+
+ align:start position:0%
+F0 to n and the d t Prime so this is the
+solution to the perturbed distribution
+
+ align:start position:0%
+solution to the perturbed distribution
+ 
+
+ align:start position:0%
+solution to the perturbed distribution
+function and particle distribution
+
+ align:start position:0%
+function and particle distribution
+ 
+
+ align:start position:0%
+function and particle distribution
+function remember GMA is a operator it
+
+ align:start position:0%
+function remember GMA is a operator it
+ 
+
+ align:start position:0%
+function remember GMA is a operator it
+looks simple but is its
+
+ align:start position:0%
+looks simple but is its
+ 
+
+ align:start position:0%
+looks simple but is its
+operator and for this operator in fact
+
+ align:start position:0%
+operator and for this operator in fact
+ 
+
+ align:start position:0%
+operator and for this operator in fact
+if you want to operate with the function
+
+ align:start position:0%
+if you want to operate with the function
+ 
+
+ align:start position:0%
+if you want to operate with the function
+behind you have to expand this into back
+
+ align:start position:0%
+behind you have to expand this into back
+ 
+
+ align:start position:0%
+behind you have to expand this into back
+into using the tailor expansion so that
+
+ align:start position:0%
+into using the tailor expansion so that
+ 
+
+ align:start position:0%
+into using the tailor expansion so that
+you can you can't just put this stuff
+
+ align:start position:0%
+you can you can't just put this stuff
+ 
+
+ align:start position:0%
+you can you can't just put this stuff
+inside the
+
+ align:start position:0%
+inside the
+ 
+
+ align:start position:0%
+inside the
+exponent okay so the uh uh what's the
+
+ align:start position:0%
+exponent okay so the uh uh what's the
+ 
+
+ align:start position:0%
+exponent okay so the uh uh what's the
+use of this is once I have this former
+
+ align:start position:0%
+use of this is once I have this former
+ 
+
+ align:start position:0%
+use of this is once I have this former
+solution I can go back to
+
+ align:start position:0%
+solution I can go back to
+ 
+
+ align:start position:0%
+solution I can go back to
+calculate the uh
+
+ align:start position:0%
+calculate the uh
+ 
+
+ align:start position:0%
+calculate the uh
+emble average right because my emble
+
+ align:start position:0%
+emble average right because my emble
+ 
+
+ align:start position:0%
+emble average right because my emble
+average is any
+
+ align:start position:0%
+average is any
+ 
+
+ align:start position:0%
+average is any
+quantity in terms of the uh momentum and
+
+ align:start position:0%
+quantity in terms of the uh momentum and
+ 
+
+ align:start position:0%
+quantity in terms of the uh momentum and
+the location of the system times
+
+ align:start position:0%
+the location of the system times
+ 
+
+ align:start position:0%
+the location of the system times
+distribution function now distribution
+
+ align:start position:0%
+distribution function now distribution
+ 
+
+ align:start position:0%
+distribution function now distribution
+function consists of for equilibrium
+
+ align:start position:0%
+function consists of for equilibrium
+ 
+
+ align:start position:0%
+function consists of for equilibrium
+part and the peration part right in in
+
+ align:start position:0%
+part and the peration part right in in
+ 
+
+ align:start position:0%
+part and the peration part right in in
+most transport if I deal with transport
+
+ align:start position:0%
+most transport if I deal with transport
+ 
+
+ align:start position:0%
+most transport if I deal with transport
+I know that equ part will drop out and
+
+ align:start position:0%
+I know that equ part will drop out and
+ 
+
+ align:start position:0%
+I know that equ part will drop out and
+this is the deviation part that gives me
+
+ align:start position:0%
+this is the deviation part that gives me
+ 
+
+ align:start position:0%
+this is the deviation part that gives me
+the response right so I do this I I go
+
+ align:start position:0%
+the response right so I do this I I go
+ 
+
+ align:start position:0%
+the response right so I do this I I go
+to calculate and U uh for example we
+
+ align:start position:0%
+to calculate and U uh for example we
+ 
+
+ align:start position:0%
+to calculate and U uh for example we
+were writing this before the uh response
+
+ align:start position:0%
+were writing this before the uh response
+ 
+
+ align:start position:0%
+were writing this before the uh response
+will be uh you can uh say this is once
+
+ align:start position:0%
+will be uh you can uh say this is once
+ 
+
+ align:start position:0%
+will be uh you can uh say this is once
+you uh do the uh uh substitute into the
+
+ align:start position:0%
+you uh do the uh uh substitute into the
+ 
+
+ align:start position:0%
+you uh do the uh uh substitute into the
+um in par averaging expression at the
+
+ align:start position:0%
+um in par averaging expression at the
+ 
+
+ align:start position:0%
+um in par averaging expression at the
+end what you get is DT Prime f t Prime
+
+ align:start position:0%
+end what you get is DT Prime f t Prime
+ 
+
+ align:start position:0%
+end what you get is DT Prime f t Prime
+that's the uh and then here we have uh
+
+ align:start position:0%
+that's the uh and then here we have uh
+ 
+
+ align:start position:0%
+that's the uh and then here we have uh
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+KBT uh way
+
+ align:start position:0%
+KBT uh way
+ 
+
+ align:start position:0%
+KBT uh way
+KBT and uh uh
+
+ align:start position:0%
+KBT and uh uh
+ 
+
+ align:start position:0%
+KBT and uh uh
+integration of F0
+
+ align:start position:0%
+integration of F0
+ 
+
+ align:start position:0%
+integration of F0
+n um and then we have
+
+ align:start position:0%
+n um and then we have
+ 
+
+ align:start position:0%
+n um and then we have
+b r
+
+ align:start position:0%
+b r
+ 
+
+ align:start position:0%
+b r
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+t and exponential Mass
+
+ align:start position:0%
+t and exponential Mass
+ 
+
+ align:start position:0%
+t and exponential Mass
+i t t
+
+ align:start position:0%
+i t t
+ 
+
+ align:start position:0%
+i t t
+Prime GMA
+
+ align:start position:0%
+Prime GMA
+ 
+
+ align:start position:0%
+Prime GMA
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+DOT and uh uh here I have r t
+
+ align:start position:0%
+DOT and uh uh here I have r t
+ 
+
+ align:start position:0%
+DOT and uh uh here I have r t
+Prime p t
+
+ align:start position:0%
+Prime p t
+ 
+
+ align:start position:0%
+Prime p t
+Prime and Dr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DP okay and here the
+
+ align:start position:0%
+DP okay and here the
+ 
+
+ align:start position:0%
+DP okay and here the
+bracket and the reason I'm writing into
+
+ align:start position:0%
+bracket and the reason I'm writing into
+ 
+
+ align:start position:0%
+bracket and the reason I'm writing into
+this form is because inside the
+
+ align:start position:0%
+this form is because inside the
+ 
+
+ align:start position:0%
+this form is because inside the
+bracket is my after effect function
+
+ align:start position:0%
+bracket is my after effect function
+ 
+
+ align:start position:0%
+bracket is my after effect function
+right this is the uh
+
+ align:start position:0%
+right this is the uh
+ 
+
+ align:start position:0%
+right this is the uh
+disturbance this is the response I'm
+
+ align:start position:0%
+disturbance this is the response I'm
+ 
+
+ align:start position:0%
+disturbance this is the response I'm
+interesting the quantity of response and
+
+ align:start position:0%
+interesting the quantity of response and
+ 
+
+ align:start position:0%
+interesting the quantity of response and
+then this one is my after effect
+
+ align:start position:0%
+then this one is my after effect
+ 
+
+ align:start position:0%
+then this one is my after effect
+function due to that disturbance that
+
+ align:start position:0%
+function due to that disturbance that
+ 
+
+ align:start position:0%
+function due to that disturbance that
+created uh the uh a which is the face
+
+ align:start position:0%
+created uh the uh a which is the face
+ 
+
+ align:start position:0%
+created uh the uh a which is the face
+function uh in the uh homon so this one
+
+ align:start position:0%
+function uh in the uh homon so this one
+ 
+
+ align:start position:0%
+function uh in the uh homon so this one
+is my after effect of function ba t t
+
+ align:start position:0%
+is my after effect of function ba t t
+ 
+
+ align:start position:0%
+is my after effect of function ba t t
+Prime as I defined before right here I
+
+ align:start position:0%
+Prime as I defined before right here I
+ 
+
+ align:start position:0%
+Prime as I defined before right here I
+have a t Min T Prime and if you uh use
+
+ align:start position:0%
+have a t Min T Prime and if you uh use
+ 
+
+ align:start position:0%
+have a t Min T Prime and if you uh use
+further the operator uh rotation uh this
+
+ align:start position:0%
+further the operator uh rotation uh this
+ 
+
+ align:start position:0%
+further the operator uh rotation uh this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh the operator properties you can get
+
+ align:start position:0%
+uh the operator properties you can get
+ 
+
+ align:start position:0%
+uh the operator properties you can get
+the following so here we're not going to
+
+ align:start position:0%
+the following so here we're not going to
+ 
+
+ align:start position:0%
+the following so here we're not going to
+write all the derivation now this is a
+
+ align:start position:0%
+write all the derivation now this is a
+ 
+
+ align:start position:0%
+write all the derivation now this is a
+pretty lot of writing I want to
+
+ align:start position:0%
+pretty lot of writing I want to
+ 
+
+ align:start position:0%
+pretty lot of writing I want to
+appreciate right because I said before
+
+ align:start position:0%
+appreciate right because I said before
+ 
+
+ align:start position:0%
+appreciate right because I said before
+you have bman approach you have linear
+
+ align:start position:0%
+you have bman approach you have linear
+ 
+
+ align:start position:0%
+you have bman approach you have linear
+response Theory approach and linear
+
+ align:start position:0%
+response Theory approach and linear
+ 
+
+ align:start position:0%
+response Theory approach and linear
+response theory is really developed
+
+ align:start position:0%
+response theory is really developed
+ 
+
+ align:start position:0%
+response theory is really developed
+after the computational power uh say in
+
+ align:start position:0%
+after the computational power uh say in
+ 
+
+ align:start position:0%
+after the computational power uh say in
+combination with the computational
+
+ align:start position:0%
+combination with the computational
+ 
+
+ align:start position:0%
+combination with the computational
+techniques so T Min t
+
+ align:start position:0%
+techniques so T Min t
+ 
+
+ align:start position:0%
+techniques so T Min t
+Prime now the uh if you uh look at this
+
+ align:start position:0%
+Prime now the uh if you uh look at this
+ 
+
+ align:start position:0%
+Prime now the uh if you uh look at this
+it could be V
+
+ align:start position:0%
+it could be V
+ 
+
+ align:start position:0%
+it could be V
+KBT after you uh actually do this
+
+ align:start position:0%
+KBT after you uh actually do this
+ 
+
+ align:start position:0%
+KBT after you uh actually do this
+operation uh use that say operator
+
+ align:start position:0%
+operation uh use that say operator
+ 
+
+ align:start position:0%
+operation uh use that say operator
+properties and we can say here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f0n and uh uh
+
+ align:start position:0%
+f0n and uh uh
+ 
+
+ align:start position:0%
+f0n and uh uh
+a DOT that's a Time derivative RT Prime
+
+ align:start position:0%
+a DOT that's a Time derivative RT Prime
+ 
+
+ align:start position:0%
+a DOT that's a Time derivative RT Prime
+Prime p t Prime and look at the time
+
+ align:start position:0%
+Prime p t Prime and look at the time
+ 
+
+ align:start position:0%
+Prime p t Prime and look at the time
+origin
+
+ align:start position:0%
+origin
+ 
+
+ align:start position:0%
+origin
+is uh important B here is r t minus t
+
+ align:start position:0%
+is uh important B here is r t minus t
+ 
+
+ align:start position:0%
+is uh important B here is r t minus t
+Prime because of this
+
+ align:start position:0%
+Prime because of this
+ 
+
+ align:start position:0%
+Prime because of this
+operator and the P T minus t Prime so
+
+ align:start position:0%
+operator and the P T minus t Prime so
+ 
+
+ align:start position:0%
+operator and the P T minus t Prime so
+now this is the quantity in the time uh
+
+ align:start position:0%
+now this is the quantity in the time uh
+ 
+
+ align:start position:0%
+now this is the quantity in the time uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+before uh Dr
+
+ align:start position:0%
+before uh Dr
+ 
+
+ align:start position:0%
+before uh Dr
+DP right here you can see this is
+
+ align:start position:0%
+DP right here you can see this is
+ 
+
+ align:start position:0%
+DP right here you can see this is
+this face space average because here is
+
+ align:start position:0%
+this face space average because here is
+ 
+
+ align:start position:0%
+this face space average because here is
+distribution function equin distribution
+
+ align:start position:0%
+distribution function equin distribution
+ 
+
+ align:start position:0%
+distribution function equin distribution
+function and uh this disturbance is out
+
+ align:start position:0%
+function and uh this disturbance is out
+ 
+
+ align:start position:0%
+function and uh this disturbance is out
+it actually does not get into my a does
+
+ align:start position:0%
+it actually does not get into my a does
+ 
+
+ align:start position:0%
+it actually does not get into my a does
+not get into my B it's independent of
+
+ align:start position:0%
+not get into my B it's independent of
+ 
+
+ align:start position:0%
+not get into my B it's independent of
+that dis disturbance this is one I do
+
+ align:start position:0%
+that dis disturbance this is one I do
+ 
+
+ align:start position:0%
+that dis disturbance this is one I do
+theral connectivity viscosity is a
+
+ align:start position:0%
+theral connectivity viscosity is a
+ 
+
+ align:start position:0%
+theral connectivity viscosity is a
+physical property of the system right
+
+ align:start position:0%
+physical property of the system right
+ 
+
+ align:start position:0%
+physical property of the system right
+and uh this is a statistical The
+
+ align:start position:0%
+and uh this is a statistical The
+ 
+
+ align:start position:0%
+and uh this is a statistical The
+Ensemble average because here that's
+
+ align:start position:0%
+Ensemble average because here that's
+ 
+
+ align:start position:0%
+Ensemble average because here that's
+what we Define and this is the quantity
+
+ align:start position:0%
+what we Define and this is the quantity
+ 
+
+ align:start position:0%
+what we Define and this is the quantity
+at two different time so this is a
+
+ align:start position:0%
+at two different time so this is a
+ 
+
+ align:start position:0%
+at two different time so this is a
+crosscorrelation
+
+ align:start position:0%
+crosscorrelation
+ 
+
+ align:start position:0%
+crosscorrelation
+function and uh with this you can
+
+ align:start position:0%
+function and uh with this you can
+ 
+
+ align:start position:0%
+function and uh with this you can
+convert also back into the time because
+
+ align:start position:0%
+convert also back into the time because
+ 
+
+ align:start position:0%
+convert also back into the time because
+we say it's oric system right here is in
+
+ align:start position:0%
+we say it's oric system right here is in
+ 
+
+ align:start position:0%
+we say it's oric system right here is in
+emble average now you can convert back
+
+ align:start position:0%
+emble average now you can convert back
+ 
+
+ align:start position:0%
+emble average now you can convert back
+into the time
+
+ align:start position:0%
+into the time
+ 
+
+ align:start position:0%
+into the time
+average so uh we could write
+
+ align:start position:0%
+average so uh we could write
+ 
+
+ align:start position:0%
+average so uh we could write
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+KBT that's the uh emble average of
+
+ align:start position:0%
+KBT that's the uh emble average of
+ 
+
+ align:start position:0%
+KBT that's the uh emble average of
+quantity uh tus T Prime and the quantity
+
+ align:start position:0%
+quantity uh tus T Prime and the quantity
+ 
+
+ align:start position:0%
+quantity uh tus T Prime and the quantity
+at the T Prime
+
+ align:start position:0%
+at the T Prime
+ 
+
+ align:start position:0%
+at the T Prime
+derivative and this uh is a uh this time
+
+ align:start position:0%
+derivative and this uh is a uh this time
+ 
+
+ align:start position:0%
+derivative and this uh is a uh this time
+origin is not important so you can write
+
+ align:start position:0%
+origin is not important so you can write
+ 
+
+ align:start position:0%
+origin is not important so you can write
+T and A at this origin you choose
+
+ align:start position:0%
+T and A at this origin you choose
+ 
+
+ align:start position:0%
+T and A at this origin you choose
+whatever time is
+
+ align:start position:0%
+whatever time is
+ 
+
+ align:start position:0%
+whatever time is
+zero and um uh and this one there are
+
+ align:start position:0%
+zero and um uh and this one there are
+ 
+
+ align:start position:0%
+zero and um uh and this one there are
+different ways to write it you can write
+
+ align:start position:0%
+different ways to write it you can write
+ 
+
+ align:start position:0%
+different ways to write it you can write
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+KBT and uh rather than uh the derivative
+
+ align:start position:0%
+KBT and uh rather than uh the derivative
+ 
+
+ align:start position:0%
+KBT and uh rather than uh the derivative
+of a you can write in derivative of
+
+ align:start position:0%
+of a you can write in derivative of
+ 
+
+ align:start position:0%
+of a you can write in derivative of
+B and time T and this all can be proven
+
+ align:start position:0%
+B and time T and this all can be proven
+ 
+
+ align:start position:0%
+B and time T and this all can be proven
+I'm just giving you the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expression and what it means here is all
+
+ align:start position:0%
+expression and what it means here is all
+ 
+
+ align:start position:0%
+expression and what it means here is all
+time averaging uh the inle averaging but
+
+ align:start position:0%
+time averaging uh the inle averaging but
+ 
+
+ align:start position:0%
+time averaging uh the inle averaging but
+when I do uh molecular Dynamics I do the
+
+ align:start position:0%
+when I do uh molecular Dynamics I do the
+ 
+
+ align:start position:0%
+when I do uh molecular Dynamics I do the
+time averaging because so what it means
+
+ align:start position:0%
+time averaging because so what it means
+ 
+
+ align:start position:0%
+time averaging because so what it means
+is I have this emble averaging is equal
+
+ align:start position:0%
+is I have this emble averaging is equal
+ 
+
+ align:start position:0%
+is I have this emble averaging is equal
+to time averaging so T prime plus T and
+
+ align:start position:0%
+to time averaging so T prime plus T and
+ 
+
+ align:start position:0%
+to time averaging so T prime plus T and
+A T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the bar in the up is the time
+
+ align:start position:0%
+right so the bar in the up is the time
+ 
+
+ align:start position:0%
+right so the bar in the up is the time
+averaging as we introduced so now we
+
+ align:start position:0%
+averaging as we introduced so now we
+ 
+
+ align:start position:0%
+averaging as we introduced so now we
+have so you can simulate a equilibrium
+
+ align:start position:0%
+have so you can simulate a equilibrium
+ 
+
+ align:start position:0%
+have so you can simulate a equilibrium
+system and get the properties R response
+
+ align:start position:0%
+system and get the properties R response
+ 
+
+ align:start position:0%
+system and get the properties R response
+because the force is taken
+
+ align:start position:0%
+because the force is taken
+ 
+
+ align:start position:0%
+because the force is taken
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay and uh uh with this of course you
+
+ align:start position:0%
+okay and uh uh with this of course you
+ 
+
+ align:start position:0%
+okay and uh uh with this of course you
+know the after effect function you can
+
+ align:start position:0%
+know the after effect function you can
+ 
+
+ align:start position:0%
+know the after effect function you can
+get the frequency
+
+ align:start position:0%
+get the frequency
+ 
+
+ align:start position:0%
+get the frequency
+component right uh as we have written
+
+ align:start position:0%
+component right uh as we have written
+ 
+
+ align:start position:0%
+component right uh as we have written
+down the uh susceptibility as function
+
+ align:start position:0%
+down the uh susceptibility as function
+ 
+
+ align:start position:0%
+down the uh susceptibility as function
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+frequency and uh in fact if you write
+
+ align:start position:0%
+frequency and uh in fact if you write
+ 
+
+ align:start position:0%
+frequency and uh in fact if you write
+further because uh the susceptibility
+
+ align:start position:0%
+further because uh the susceptibility
+ 
+
+ align:start position:0%
+further because uh the susceptibility
+now can be calculated as here if I look
+
+ align:start position:0%
+now can be calculated as here if I look
+ 
+
+ align:start position:0%
+now can be calculated as here if I look
+at this one the autocorrelation when a
+
+ align:start position:0%
+at this one the autocorrelation when a
+ 
+
+ align:start position:0%
+at this one the autocorrelation when a
+goes to itself that's Auto correlation
+
+ align:start position:0%
+goes to itself that's Auto correlation
+ 
+
+ align:start position:0%
+goes to itself that's Auto correlation
+when go to different quantity is a cross
+
+ align:start position:0%
+when go to different quantity is a cross
+ 
+
+ align:start position:0%
+when go to different quantity is a cross
+correlation right so now the imagin part
+
+ align:start position:0%
+correlation right so now the imagin part
+ 
+
+ align:start position:0%
+correlation right so now the imagin part
+can be related to the uh Auto
+
+ align:start position:0%
+can be related to the uh Auto
+ 
+
+ align:start position:0%
+can be related to the uh Auto
+correlation function when b equals a and
+
+ align:start position:0%
+correlation function when b equals a and
+ 
+
+ align:start position:0%
+correlation function when b equals a and
+what you have here that from that
+
+ align:start position:0%
+what you have here that from that
+ 
+
+ align:start position:0%
+what you have here that from that
+expression I can write
+
+ align:start position:0%
+expression I can write
+ 
+
+ align:start position:0%
+expression I can write
+the imaginary part of this
+
+ align:start position:0%
+the imaginary part of this
+ 
+
+ align:start position:0%
+the imaginary part of this
+suitability as a function of
+
+ align:start position:0%
+suitability as a function of
+ 
+
+ align:start position:0%
+suitability as a function of
+frequency is V Omega and 2
+
+ align:start position:0%
+frequency is V Omega and 2
+ 
+
+ align:start position:0%
+frequency is V Omega and 2
+KBT and mass infinite to plus infinite
+
+ align:start position:0%
+KBT and mass infinite to plus infinite
+ 
+
+ align:start position:0%
+KBT and mass infinite to plus infinite
+exponential Mass I Omega
+
+ align:start position:0%
+exponential Mass I Omega
+ 
+
+ align:start position:0%
+exponential Mass I Omega
+t and
+
+ align:start position:0%
+t and
+ 
+
+ align:start position:0%
+t and
+a um e t a as
+
+ align:start position:0%
+a um e t a as
+ 
+
+ align:start position:0%
+a um e t a as
+Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT so from the cross correlation uh the
+
+ align:start position:0%
+DT so from the cross correlation uh the
+ 
+
+ align:start position:0%
+DT so from the cross correlation uh the
+auto correlation I can calculate
+
+ align:start position:0%
+auto correlation I can calculate
+ 
+
+ align:start position:0%
+auto correlation I can calculate
+imagining
+
+ align:start position:0%
+imagining
+ 
+
+ align:start position:0%
+imagining
+part and this is I mentioned it many
+
+ align:start position:0%
+part and this is I mentioned it many
+ 
+
+ align:start position:0%
+part and this is I mentioned it many
+times this is actually the
+
+ align:start position:0%
+times this is actually the
+ 
+
+ align:start position:0%
+times this is actually the
+fluctuation dissipation theorem
+
+ align:start position:0%
+fluctuation dissipation theorem
+ 
+
+ align:start position:0%
+fluctuation dissipation theorem
+this is the fluctuation all the
+
+ align:start position:0%
+this is the fluctuation all the
+ 
+
+ align:start position:0%
+this is the fluctuation all the
+correlation the imagin
+
+ align:start position:0%
+correlation the imagin
+ 
+
+ align:start position:0%
+correlation the imagin
+part is the
+
+ align:start position:0%
+part is the
+ 
+
+ align:start position:0%
+part is the
+dissipation because that imagin part is
+
+ align:start position:0%
+dissipation because that imagin part is
+ 
+
+ align:start position:0%
+dissipation because that imagin part is
+relate to the energy dissipated in the
+
+ align:start position:0%
+relate to the energy dissipated in the
+ 
+
+ align:start position:0%
+relate to the energy dissipated in the
+system right so this is a fluctuation
+
+ align:start position:0%
+system right so this is a fluctuation
+ 
+
+ align:start position:0%
+system right so this is a fluctuation
+distribtion
+
+ align:start position:0%
+distribtion
+ 
+
+ align:start position:0%
+distribtion
+theorem general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form and when I do for example nearfield
+
+ align:start position:0%
+form and when I do for example nearfield
+ 
+
+ align:start position:0%
+form and when I do for example nearfield
+radiation simulation I with we use a lot
+
+ align:start position:0%
+radiation simulation I with we use a lot
+ 
+
+ align:start position:0%
+radiation simulation I with we use a lot
+of this fluctuation dissipation theorem
+
+ align:start position:0%
+of this fluctuation dissipation theorem
+ 
+
+ align:start position:0%
+of this fluctuation dissipation theorem
+and what I do is the current fluctuation
+
+ align:start position:0%
+and what I do is the current fluctuation
+ 
+
+ align:start position:0%
+and what I do is the current fluctuation
+is related to imag part of the
+
+ align:start position:0%
+is related to imag part of the
+ 
+
+ align:start position:0%
+is related to imag part of the
+dialectric constant that's one example
+
+ align:start position:0%
+dialectric constant that's one example
+ 
+
+ align:start position:0%
+dialectric constant that's one example
+of the fluctuation disspation
+
+ align:start position:0%
+of the fluctuation disspation
+ 
+
+ align:start position:0%
+of the fluctuation disspation
+theorem and uh if you do the quantum you
+
+ align:start position:0%
+theorem and uh if you do the quantum you
+ 
+
+ align:start position:0%
+theorem and uh if you do the quantum you
+can generalize in the quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit and what you have here the imagur
+
+ align:start position:0%
+limit and what you have here the imagur
+ 
+
+ align:start position:0%
+limit and what you have here the imagur
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+uh you will have
+
+ align:start position:0%
+uh you will have
+ 
+
+ align:start position:0%
+uh you will have
+to uh write this as H bar and the
+
+ align:start position:0%
+to uh write this as H bar and the
+ 
+
+ align:start position:0%
+to uh write this as H bar and the
+cotangent uh so this is a uh
+
+ align:start position:0%
+cotangent uh so this is a uh
+ 
+
+ align:start position:0%
+cotangent uh so this is a uh
+hyperbolic cotangent function H bar
+
+ align:start position:0%
+hyperbolic cotangent function H bar
+ 
+
+ align:start position:0%
+hyperbolic cotangent function H bar
+Omega 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KBT and Min infinite to plus infinite
+
+ align:start position:0%
+KBT and Min infinite to plus infinite
+ 
+
+ align:start position:0%
+KBT and Min infinite to plus infinite
+expon
+
+ align:start position:0%
+expon
+ 
+
+ align:start position:0%
+expon
+t and a t a
+
+ align:start position:0%
+t and a t a
+ 
+
+ align:start position:0%
+t and a t a
+z so that that's uh the the quantum
+
+ align:start position:0%
+z so that that's uh the the quantum
+ 
+
+ align:start position:0%
+z so that that's uh the the quantum
+form of modification the fluctuation
+
+ align:start position:0%
+form of modification the fluctuation
+ 
+
+ align:start position:0%
+form of modification the fluctuation
+disspation
+
+ align:start position:0%
+disspation
+ 
+
+ align:start position:0%
+disspation
+theorem okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now this is the uh uh the essence of
+
+ align:start position:0%
+so now this is the uh uh the essence of
+ 
+
+ align:start position:0%
+so now this is the uh uh the essence of
+the linear response and what I need Le
+
+ align:start position:0%
+the linear response and what I need Le
+ 
+
+ align:start position:0%
+the linear response and what I need Le
+is to give you few examples for example
+
+ align:start position:0%
+is to give you few examples for example
+ 
+
+ align:start position:0%
+is to give you few examples for example
+how I can relate the electric
+
+ align:start position:0%
+how I can relate the electric
+ 
+
+ align:start position:0%
+how I can relate the electric
+conductivity and calculate the based on
+
+ align:start position:0%
+conductivity and calculate the based on
+ 
+
+ align:start position:0%
+conductivity and calculate the based on
+the if I have irons in the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so writing down
+
+ align:start position:0%
+right so writing down
+ 
+
+ align:start position:0%
+right so writing down
+the corresponding form so if I have
+
+ align:start position:0%
+the corresponding form so if I have
+ 
+
+ align:start position:0%
+the corresponding form so if I have
+ions in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and and uh uh I apply a electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field to the
+
+ align:start position:0%
+field to the
+ 
+
+ align:start position:0%
+field to the
+system and each so now the each
+
+ align:start position:0%
+system and each so now the each
+ 
+
+ align:start position:0%
+system and each so now the each
+ions will be uh say do so the field will
+
+ align:start position:0%
+ions will be uh say do so the field will
+ 
+
+ align:start position:0%
+ions will be uh say do so the field will
+give a force force will move the iron
+
+ align:start position:0%
+give a force force will move the iron
+ 
+
+ align:start position:0%
+give a force force will move the iron
+and force times
+
+ align:start position:0%
+and force times
+ 
+
+ align:start position:0%
+and force times
+distance it gives me the work right
+
+ align:start position:0%
+distance it gives me the work right
+ 
+
+ align:start position:0%
+distance it gives me the work right
+that's the uh additional energy that the
+
+ align:start position:0%
+that's the uh additional energy that the
+ 
+
+ align:start position:0%
+that's the uh additional energy that the
+Sy system is subject to peration right
+
+ align:start position:0%
+Sy system is subject to peration right
+ 
+
+ align:start position:0%
+Sy system is subject to peration right
+so we have then uh look at the uh
+
+ align:start position:0%
+so we have then uh look at the uh
+ 
+
+ align:start position:0%
+so we have then uh look at the uh
+peration in
+
+ align:start position:0%
+peration in
+ 
+
+ align:start position:0%
+peration in
+homon can be written as I = 1 to n n
+
+ align:start position:0%
+homon can be written as I = 1 to n n
+ 
+
+ align:start position:0%
+homon can be written as I = 1 to n n
+particles and the uh displacement r i
+
+ align:start position:0%
+particles and the uh displacement r i
+ 
+
+ align:start position:0%
+particles and the uh displacement r i
+you can do r i minus r0 but let say then
+
+ align:start position:0%
+you can do r i minus r0 but let say then
+ 
+
+ align:start position:0%
+you can do r i minus r0 but let say then
+r0 is the original honia right so it's
+
+ align:start position:0%
+r0 is the original honia right so it's
+ 
+
+ align:start position:0%
+r0 is the original honia right so it's
+RI and uh uh then the
+
+ align:start position:0%
+RI and uh uh then the
+ 
+
+ align:start position:0%
+RI and uh uh then the
+force is uh the charge so I have the is
+
+ align:start position:0%
+force is uh the charge so I have the is
+ 
+
+ align:start position:0%
+force is uh the charge so I have the is
+atom has see the uh ions Z charge and I
+
+ align:start position:0%
+atom has see the uh ions Z charge and I
+ 
+
+ align:start position:0%
+atom has see the uh ions Z charge and I
+have then e which is a function of
+
+ align:start position:0%
+have then e which is a function of
+ 
+
+ align:start position:0%
+have then e which is a function of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+right this is the
+
+ align:start position:0%
+right this is the
+ 
+
+ align:start position:0%
+right this is the
+probation and from here going back to
+
+ align:start position:0%
+probation and from here going back to
+ 
+
+ align:start position:0%
+probation and from here going back to
+definition I know my a because I want to
+
+ align:start position:0%
+definition I know my a because I want to
+ 
+
+ align:start position:0%
+definition I know my a because I want to
+express the a in terms of the face
+
+ align:start position:0%
+express the a in terms of the face
+ 
+
+ align:start position:0%
+express the a in terms of the face
+variable right this should equal to
+
+ align:start position:0%
+variable right this should equal to
+ 
+
+ align:start position:0%
+variable right this should equal to
+according to my definition mass a v uh e
+
+ align:start position:0%
+according to my definition mass a v uh e
+ 
+
+ align:start position:0%
+according to my definition mass a v uh e
+which is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disturbance and uh so my a here then
+
+ align:start position:0%
+disturbance and uh so my a here then
+ 
+
+ align:start position:0%
+disturbance and uh so my a here then
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+minus uh V Sigma I = 1 to n uh z i e r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i okay
+
+ align:start position:0%
+i okay
+ 
+
+ align:start position:0%
+i okay
+and uh uh I can look at for example
+
+ align:start position:0%
+and uh uh I can look at for example
+ 
+
+ align:start position:0%
+and uh uh I can look at for example
+current what's my
+
+ align:start position:0%
+current what's my
+ 
+
+ align:start position:0%
+current what's my
+response right giving a electric field I
+
+ align:start position:0%
+response right giving a electric field I
+ 
+
+ align:start position:0%
+response right giving a electric field I
+want to look at what's the current in
+
+ align:start position:0%
+want to look at what's the current in
+ 
+
+ align:start position:0%
+want to look at what's the current in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+system so my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current of the system is the charge
+
+ align:start position:0%
+current of the system is the charge
+ 
+
+ align:start position:0%
+current of the system is the charge
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+velocity right so the current in the
+
+ align:start position:0%
+velocity right so the current in the
+ 
+
+ align:start position:0%
+velocity right so the current in the
+system is charge times velocity so a i e
+
+ align:start position:0%
+system is charge times velocity so a i e
+ 
+
+ align:start position:0%
+system is charge times velocity so a i e
+and d r i
+
+ align:start position:0%
+and d r i
+ 
+
+ align:start position:0%
+and d r i
+DT I = 1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n right and uh uh so uh I do in terms of
+
+ align:start position:0%
+n right and uh uh so uh I do in terms of
+ 
+
+ align:start position:0%
+n right and uh uh so uh I do in terms of
+the per unit volume
+
+ align:start position:0%
+the per unit volume
+ 
+
+ align:start position:0%
+the per unit volume
+again and you can say here uh I was
+
+ align:start position:0%
+again and you can say here uh I was
+ 
+
+ align:start position:0%
+again and you can say here uh I was
+little bit I'm trying to reconcile my
+
+ align:start position:0%
+little bit I'm trying to reconcile my
+ 
+
+ align:start position:0%
+little bit I'm trying to reconcile my
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+I haven't been able to reconcile my sign
+
+ align:start position:0%
+I haven't been able to reconcile my sign
+ 
+
+ align:start position:0%
+I haven't been able to reconcile my sign
+so I write this as the gradient because
+
+ align:start position:0%
+so I write this as the gradient because
+ 
+
+ align:start position:0%
+so I write this as the gradient because
+here is drdt here is
+
+ align:start position:0%
+here is drdt here is
+ 
+
+ align:start position:0%
+here is drdt here is
+drdt
+
+ align:start position:0%
+drdt
+ 
+
+ align:start position:0%
+drdt
+right okay so with that I can then now
+
+ align:start position:0%
+right okay so with that I can then now
+ 
+
+ align:start position:0%
+right okay so with that I can then now
+look at that this is essentially this is
+
+ align:start position:0%
+look at that this is essentially this is
+ 
+
+ align:start position:0%
+look at that this is essentially this is
+the response I want to look at and
+
+ align:start position:0%
+the response I want to look at and
+ 
+
+ align:start position:0%
+the response I want to look at and
+that's my
+
+ align:start position:0%
+that's my
+ 
+
+ align:start position:0%
+that's my
+B right so I have a I have B and now uh
+
+ align:start position:0%
+B right so I have a I have B and now uh
+ 
+
+ align:start position:0%
+B right so I have a I have B and now uh
+I can write the use the uh uh the
+
+ align:start position:0%
+I can write the use the uh uh the
+ 
+
+ align:start position:0%
+I can write the use the uh uh the
+expression we have the after effect
+
+ align:start position:0%
+expression we have the after effect
+ 
+
+ align:start position:0%
+expression we have the after effect
+function and effect what we have here is
+
+ align:start position:0%
+function and effect what we have here is
+ 
+
+ align:start position:0%
+function and effect what we have here is
+uh if I write into the frequency form J
+
+ align:start position:0%
+uh if I write into the frequency form J
+ 
+
+ align:start position:0%
+uh if I write into the frequency form J
+Omega equals the electric conductivity
+
+ align:start position:0%
+Omega equals the electric conductivity
+ 
+
+ align:start position:0%
+Omega equals the electric conductivity
+which is usually
+
+ align:start position:0%
+which is usually
+ 
+
+ align:start position:0%
+which is usually
+tenso okay thermal conductivity is tenso
+
+ align:start position:0%
+tenso okay thermal conductivity is tenso
+ 
+
+ align:start position:0%
+tenso okay thermal conductivity is tenso
+electric conductivity is
+
+ align:start position:0%
+electric conductivity is
+ 
+
+ align:start position:0%
+electric conductivity is
+tenso and uh uh six component and is
+
+ align:start position:0%
+tenso and uh uh six component and is
+ 
+
+ align:start position:0%
+tenso and uh uh six component and is
+related to the potential product to the
+
+ align:start position:0%
+related to the potential product to the
+ 
+
+ align:start position:0%
+related to the potential product to the
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+field right that's the
+
+ align:start position:0%
+field right that's the
+ 
+
+ align:start position:0%
+field right that's the
+response and this is the after effect
+
+ align:start position:0%
+response and this is the after effect
+ 
+
+ align:start position:0%
+response and this is the after effect
+that's the frequency component here is a
+
+ align:start position:0%
+that's the frequency component here is a
+ 
+
+ align:start position:0%
+that's the frequency component here is a
+real time component and that's a
+
+ align:start position:0%
+real time component and that's a
+ 
+
+ align:start position:0%
+real time component and that's a
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+expression and I can use the real time
+
+ align:start position:0%
+expression and I can use the real time
+ 
+
+ align:start position:0%
+expression and I can use the real time
+real component and uh so what I have
+
+ align:start position:0%
+real component and uh so what I have
+ 
+
+ align:start position:0%
+real component and uh so what I have
+here then the electric conductivity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the uh electric conductivity if you
+
+ align:start position:0%
+so the uh electric conductivity if you
+ 
+
+ align:start position:0%
+so the uh electric conductivity if you
+use uh what we have here is can be
+
+ align:start position:0%
+use uh what we have here is can be
+ 
+
+ align:start position:0%
+use uh what we have here is can be
+written particularly if I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isotopic I can write each Direction but
+
+ align:start position:0%
+isotopic I can write each Direction but
+ 
+
+ align:start position:0%
+isotopic I can write each Direction but
+now I do isotropic so then I don't have
+
+ align:start position:0%
+now I do isotropic so then I don't have
+ 
+
+ align:start position:0%
+now I do isotropic so then I don't have
+uh the uh all the tensor component only
+
+ align:start position:0%
+uh the uh all the tensor component only
+ 
+
+ align:start position:0%
+uh the uh all the tensor component only
+diagonal and in that case I can average
+
+ align:start position:0%
+diagonal and in that case I can average
+ 
+
+ align:start position:0%
+diagonal and in that case I can average
+so is 3
+
+ align:start position:0%
+so is 3
+ 
+
+ align:start position:0%
+so is 3
+KBT and zero infinite J XT j z uh JX at
+
+ align:start position:0%
+KBT and zero infinite J XT j z uh JX at
+ 
+
+ align:start position:0%
+KBT and zero infinite J XT j z uh JX at
+zero and uh plus JY t j y at time Z j z
+
+ align:start position:0%
+zero and uh plus JY t j y at time Z j z
+ 
+
+ align:start position:0%
+zero and uh plus JY t j y at time Z j z
+t j z time Z time Z is the origin you
+
+ align:start position:0%
+t j z time Z time Z is the origin you
+ 
+
+ align:start position:0%
+t j z time Z time Z is the origin you
+choose and and then I have exponential
+
+ align:start position:0%
+choose and and then I have exponential
+ 
+
+ align:start position:0%
+choose and and then I have exponential
+Mass I Omega T DT so this is my
+
+ align:start position:0%
+Mass I Omega T DT so this is my
+ 
+
+ align:start position:0%
+Mass I Omega T DT so this is my
+frequency component of the electric
+
+ align:start position:0%
+frequency component of the electric
+ 
+
+ align:start position:0%
+frequency component of the electric
+conductivity of this system I
+
+ align:start position:0%
+conductivity of this system I
+ 
+
+ align:start position:0%
+conductivity of this system I
+simulated so in uh real
+
+ align:start position:0%
+simulated so in uh real
+ 
+
+ align:start position:0%
+simulated so in uh real
+simulation you solve FAL ma if you know
+
+ align:start position:0%
+simulation you solve FAL ma if you know
+ 
+
+ align:start position:0%
+simulation you solve FAL ma if you know
+the force interaction between these
+
+ align:start position:0%
+the force interaction between these
+ 
+
+ align:start position:0%
+the force interaction between these
+atoms and once you have that you
+
+ align:start position:0%
+atoms and once you have that you
+ 
+
+ align:start position:0%
+atoms and once you have that you
+write the time
+
+ align:start position:0%
+write the time
+ 
+
+ align:start position:0%
+write the time
+derivative that's your current
+
+ align:start position:0%
+derivative that's your current
+ 
+
+ align:start position:0%
+derivative that's your current
+flux and then you calculate this time
+
+ align:start position:0%
+flux and then you calculate this time
+ 
+
+ align:start position:0%
+flux and then you calculate this time
+autocorrelation
+
+ align:start position:0%
+autocorrelation
+ 
+
+ align:start position:0%
+autocorrelation
+function and then see one3 because I say
+
+ align:start position:0%
+function and then see one3 because I say
+ 
+
+ align:start position:0%
+function and then see one3 because I say
+isotopic so I'm averaging over three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions right so this is in fact what
+
+ align:start position:0%
+directions right so this is in fact what
+ 
+
+ align:start position:0%
+directions right so this is in fact what
+we have here is the green
+
+ align:start position:0%
+we have here is the green
+ 
+
+ align:start position:0%
+we have here is the green
+cobal formulation this is the green
+
+ align:start position:0%
+cobal formulation this is the green
+ 
+
+ align:start position:0%
+cobal formulation this is the green
+cobal formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+green kual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula and we can write from the say uh
+
+ align:start position:0%
+formula and we can write from the say uh
+ 
+
+ align:start position:0%
+formula and we can write from the say uh
+we can calculate the time response uh uh
+
+ align:start position:0%
+we can calculate the time response uh uh
+ 
+
+ align:start position:0%
+we can calculate the time response uh uh
+and uh from there we can calculate also
+
+ align:start position:0%
+and uh from there we can calculate also
+ 
+
+ align:start position:0%
+and uh from there we can calculate also
+the frequency it's a simple frequency uh
+
+ align:start position:0%
+the frequency it's a simple frequency uh
+ 
+
+ align:start position:0%
+the frequency it's a simple frequency uh
+the fal
+
+ align:start position:0%
+the fal
+ 
+
+ align:start position:0%
+the fal
+transform okay and uh green kobal is
+
+ align:start position:0%
+transform okay and uh green kobal is
+ 
+
+ align:start position:0%
+transform okay and uh green kobal is
+they didn't write one paper they
+
+ align:start position:0%
+they didn't write one paper they
+ 
+
+ align:start position:0%
+they didn't write one paper they
+developed
+
+ align:start position:0%
+developed
+ 
+
+ align:start position:0%
+developed
+this independent of each other so this
+
+ align:start position:0%
+this independent of each other so this
+ 
+
+ align:start position:0%
+this independent of each other so this
+is the uh case for the electrical the
+
+ align:start position:0%
+is the uh case for the electrical the
+ 
+
+ align:start position:0%
+is the uh case for the electrical the
+expression final expression for the
+
+ align:start position:0%
+expression final expression for the
+ 
+
+ align:start position:0%
+expression final expression for the
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+conductivity and in fact say to derive a
+
+ align:start position:0%
+conductivity and in fact say to derive a
+ 
+
+ align:start position:0%
+conductivity and in fact say to derive a
+green cable formula for thermal
+
+ align:start position:0%
+green cable formula for thermal
+ 
+
+ align:start position:0%
+green cable formula for thermal
+conductivity was not
+
+ align:start position:0%
+conductivity was not
+ 
+
+ align:start position:0%
+conductivity was not
+easy and the reason for that is uh in
+
+ align:start position:0%
+easy and the reason for that is uh in
+ 
+
+ align:start position:0%
+easy and the reason for that is uh in
+this case the derivation process we were
+
+ align:start position:0%
+this case the derivation process we were
+ 
+
+ align:start position:0%
+this case the derivation process we were
+using the system have an external
+
+ align:start position:0%
+using the system have an external
+ 
+
+ align:start position:0%
+using the system have an external
+disturbance F right and Thal is a
+
+ align:start position:0%
+disturbance F right and Thal is a
+ 
+
+ align:start position:0%
+disturbance F right and Thal is a
+internal disturbance the Thal
+
+ align:start position:0%
+internal disturbance the Thal
+ 
+
+ align:start position:0%
+internal disturbance the Thal
+fluctuation of the
+
+ align:start position:0%
+fluctuation of the
+ 
+
+ align:start position:0%
+fluctuation of the
+system and uh uh there are many
+
+ align:start position:0%
+system and uh uh there are many
+ 
+
+ align:start position:0%
+system and uh uh there are many
+derivations the the clean derivation
+
+ align:start position:0%
+derivations the the clean derivation
+ 
+
+ align:start position:0%
+derivations the the clean derivation
+which doesn't have any simple uh any
+
+ align:start position:0%
+which doesn't have any simple uh any
+ 
+
+ align:start position:0%
+which doesn't have any simple uh any
+physical uh uh uh say um meaning was
+
+ align:start position:0%
+physical uh uh uh say um meaning was
+ 
+
+ align:start position:0%
+physical uh uh uh say um meaning was
+actually using gravitational field to
+
+ align:start position:0%
+actually using gravitational field to
+ 
+
+ align:start position:0%
+actually using gravitational field to
+drive the molecule as a as a as as a
+
+ align:start position:0%
+drive the molecule as a as a as as a
+ 
+
+ align:start position:0%
+drive the molecule as a as a as as a
+disturbance and deriv the heat flux
+
+ align:start position:0%
+disturbance and deriv the heat flux
+ 
+
+ align:start position:0%
+disturbance and deriv the heat flux
+correlation but say what we need is uh
+
+ align:start position:0%
+correlation but say what we need is uh
+ 
+
+ align:start position:0%
+correlation but say what we need is uh
+so uh the uh the book I I I present this
+
+ align:start position:0%
+so uh the uh the book I I I present this
+ 
+
+ align:start position:0%
+so uh the uh the book I I I present this
+in fact I'm still not very comfortable
+
+ align:start position:0%
+in fact I'm still not very comfortable
+ 
+
+ align:start position:0%
+in fact I'm still not very comfortable
+about that section so what we have the
+
+ align:start position:0%
+about that section so what we have the
+ 
+
+ align:start position:0%
+about that section so what we have the
+for thermal
+
+ align:start position:0%
+for thermal
+ 
+
+ align:start position:0%
+for thermal
+disturbance and uh the distribution
+
+ align:start position:0%
+disturbance and uh the distribution
+ 
+
+ align:start position:0%
+disturbance and uh the distribution
+function is
+
+ align:start position:0%
+function is
+ 
+
+ align:start position:0%
+function is
+exponential Min I say uh we can write
+
+ align:start position:0%
+exponential Min I say uh we can write
+ 
+
+ align:start position:0%
+exponential Min I say uh we can write
+exponential uh the Honan H the energy
+
+ align:start position:0%
+exponential uh the Honan H the energy
+ 
+
+ align:start position:0%
+exponential uh the Honan H the energy
+a small volume and KB t+ delta T let's
+
+ align:start position:0%
+a small volume and KB t+ delta T let's
+ 
+
+ align:start position:0%
+a small volume and KB t+ delta T let's
+suppose so what I'm looking at is the
+
+ align:start position:0%
+suppose so what I'm looking at is the
+ 
+
+ align:start position:0%
+suppose so what I'm looking at is the
+temperature fluctuation inside the
+
+ align:start position:0%
+temperature fluctuation inside the
+ 
+
+ align:start position:0%
+temperature fluctuation inside the
+system because of temperature
+
+ align:start position:0%
+system because of temperature
+ 
+
+ align:start position:0%
+system because of temperature
+fluctuation the local energy has a
+
+ align:start position:0%
+fluctuation the local energy has a
+ 
+
+ align:start position:0%
+fluctuation the local energy has a
+fluctuation and I want to write what's H
+
+ align:start position:0%
+fluctuation and I want to write what's H
+ 
+
+ align:start position:0%
+fluctuation and I want to write what's H
+Prime the case I want to write what H
+
+ align:start position:0%
+Prime the case I want to write what H
+ 
+
+ align:start position:0%
+Prime the case I want to write what H
+Prime right and with this distribution I
+
+ align:start position:0%
+Prime right and with this distribution I
+ 
+
+ align:start position:0%
+Prime right and with this distribution I
+uh and I can write from here I can write
+
+ align:start position:0%
+uh and I can write from here I can write
+ 
+
+ align:start position:0%
+uh and I can write from here I can write
+the H Prime
+
+ align:start position:0%
+the H Prime
+ 
+
+ align:start position:0%
+the H Prime
+equals if I nalize it is the H itself
+
+ align:start position:0%
+equals if I nalize it is the H itself
+ 
+
+ align:start position:0%
+equals if I nalize it is the H itself
+which is the the energy honia which is a
+
+ align:start position:0%
+which is the the energy honia which is a
+ 
+
+ align:start position:0%
+which is the the energy honia which is a
+function of position and velocity for
+
+ align:start position:0%
+function of position and velocity for
+ 
+
+ align:start position:0%
+function of position and velocity for
+example is T delta T which could be
+
+ align:start position:0%
+example is T delta T which could be
+ 
+
+ align:start position:0%
+example is T delta T which could be
+function of R and
+
+ align:start position:0%
+function of R and
+ 
+
+ align:start position:0%
+function of R and
+T and d uh integration over the volume
+
+ align:start position:0%
+T and d uh integration over the volume
+ 
+
+ align:start position:0%
+T and d uh integration over the volume
+so this is my H
+
+ align:start position:0%
+so this is my H
+ 
+
+ align:start position:0%
+so this is my H
+Prime right and then you have to plug in
+
+ align:start position:0%
+Prime right and then you have to plug in
+ 
+
+ align:start position:0%
+Prime right and then you have to plug in
+this H Prime and go back to the
+
+ align:start position:0%
+this H Prime and go back to the
+ 
+
+ align:start position:0%
+this H Prime and go back to the
+derivation and find that uh what's the f
+
+ align:start position:0%
+derivation and find that uh what's the f
+ 
+
+ align:start position:0%
+derivation and find that uh what's the f
+one okay and in the process I have to
+
+ align:start position:0%
+one okay and in the process I have to
+ 
+
+ align:start position:0%
+one okay and in the process I have to
+use energy conservation and then I was
+
+ align:start position:0%
+use energy conservation and then I was
+ 
+
+ align:start position:0%
+use energy conservation and then I was
+say then you have to integrate over the
+
+ align:start position:0%
+say then you have to integrate over the
+ 
+
+ align:start position:0%
+say then you have to integrate over the
+volume your considering and what's the
+
+ align:start position:0%
+volume your considering and what's the
+ 
+
+ align:start position:0%
+volume your considering and what's the
+boundary condition you check and uh I
+
+ align:start position:0%
+boundary condition you check and uh I
+ 
+
+ align:start position:0%
+boundary condition you check and uh I
+looked into many books I was never
+
+ align:start position:0%
+looked into many books I was never
+ 
+
+ align:start position:0%
+looked into many books I was never
+satisfied and I put a what I finally say
+
+ align:start position:0%
+satisfied and I put a what I finally say
+ 
+
+ align:start position:0%
+satisfied and I put a what I finally say
+I have to complete this so you can check
+
+ align:start position:0%
+I have to complete this so you can check
+ 
+
+ align:start position:0%
+I have to complete this so you can check
+my book
+
+ align:start position:0%
+my book
+ 
+
+ align:start position:0%
+my book
+and uh so at if you do this what you
+
+ align:start position:0%
+and uh so at if you do this what you
+ 
+
+ align:start position:0%
+and uh so at if you do this what you
+have is you will derive a thermal
+
+ align:start position:0%
+have is you will derive a thermal
+ 
+
+ align:start position:0%
+have is you will derive a thermal
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+tensor and this is because I have now a
+
+ align:start position:0%
+tensor and this is because I have now a
+ 
+
+ align:start position:0%
+tensor and this is because I have now a
+delta T in the system right temperature
+
+ align:start position:0%
+delta T in the system right temperature
+ 
+
+ align:start position:0%
+delta T in the system right temperature
+fluctuation and from temperature this
+
+ align:start position:0%
+fluctuation and from temperature this
+ 
+
+ align:start position:0%
+fluctuation and from temperature this
+delta T I can eventually derive a
+
+ align:start position:0%
+delta T I can eventually derive a
+ 
+
+ align:start position:0%
+delta T I can eventually derive a
+thermal connectivity tensor that is way
+
+ align:start position:0%
+thermal connectivity tensor that is way
+ 
+
+ align:start position:0%
+thermal connectivity tensor that is way
+KB
+
+ align:start position:0%
+KB
+ 
+
+ align:start position:0%
+KB
+t² and uh 0 to infinite and the heat
+
+ align:start position:0%
+t² and uh 0 to infinite and the heat
+ 
+
+ align:start position:0%
+t² and uh 0 to infinite and the heat
+flux uh expression uh at uh T and the
+
+ align:start position:0%
+flux uh expression uh at uh T and the
+ 
+
+ align:start position:0%
+flux uh expression uh at uh T and the
+auto correlation of heat flux between
+
+ align:start position:0%
+auto correlation of heat flux between
+ 
+
+ align:start position:0%
+auto correlation of heat flux between
+zero and T exponential Mass I Omega t b
+
+ align:start position:0%
+zero and T exponential Mass I Omega t b
+ 
+
+ align:start position:0%
+zero and T exponential Mass I Omega t b
+so this is the green cobal expression
+
+ align:start position:0%
+so this is the green cobal expression
+ 
+
+ align:start position:0%
+so this is the green cobal expression
+for thermal
+
+ align:start position:0%
+for thermal
+ 
+
+ align:start position:0%
+for thermal
+conductivity and uh thermal connectivity
+
+ align:start position:0%
+conductivity and uh thermal connectivity
+ 
+
+ align:start position:0%
+conductivity and uh thermal connectivity
+itself again could be a function
+
+ align:start position:0%
+itself again could be a function
+ 
+
+ align:start position:0%
+itself again could be a function
+frequency is normally when we do heat
+
+ align:start position:0%
+frequency is normally when we do heat
+ 
+
+ align:start position:0%
+frequency is normally when we do heat
+we don't do very high temperature a high
+
+ align:start position:0%
+we don't do very high temperature a high
+ 
+
+ align:start position:0%
+we don't do very high temperature a high
+frequency so uh this is a in fact this
+
+ align:start position:0%
+frequency so uh this is a in fact this
+ 
+
+ align:start position:0%
+frequency so uh this is a in fact this
+is relate to the conton equation but
+
+ align:start position:0%
+is relate to the conton equation but
+ 
+
+ align:start position:0%
+is relate to the conton equation but
+Canon equation is level correct I made a
+
+ align:start position:0%
+Canon equation is level correct I made a
+ 
+
+ align:start position:0%
+Canon equation is level correct I made a
+comment before oh it's very hard to be
+
+ align:start position:0%
+comment before oh it's very hard to be
+ 
+
+ align:start position:0%
+comment before oh it's very hard to be
+correct because when you have a very
+
+ align:start position:0%
+correct because when you have a very
+ 
+
+ align:start position:0%
+correct because when you have a very
+fast temperature distrib temperature
+
+ align:start position:0%
+fast temperature distrib temperature
+ 
+
+ align:start position:0%
+fast temperature distrib temperature
+disturbance you typically have a special
+
+ align:start position:0%
+disturbance you typically have a special
+ 
+
+ align:start position:0%
+disturbance you typically have a special
+temperature gradient and if that
+
+ align:start position:0%
+temperature gradient and if that
+ 
+
+ align:start position:0%
+temperature gradient and if that
+gradient is longer uh shorter than mean
+
+ align:start position:0%
+gradient is longer uh shorter than mean
+ 
+
+ align:start position:0%
+gradient is longer uh shorter than mean
+free path you can just use Canon
+
+ align:start position:0%
+free path you can just use Canon
+ 
+
+ align:start position:0%
+free path you can just use Canon
+equation so what you should do is
+
+ align:start position:0%
+equation so what you should do is
+ 
+
+ align:start position:0%
+equation so what you should do is
+actually write both of frequency and
+
+ align:start position:0%
+actually write both of frequency and
+ 
+
+ align:start position:0%
+actually write both of frequency and
+space dependent so time and space
+
+ align:start position:0%
+space dependent so time and space
+ 
+
+ align:start position:0%
+space dependent so time and space
+dependent thermal connectivity and that
+
+ align:start position:0%
+dependent thermal connectivity and that
+ 
+
+ align:start position:0%
+dependent thermal connectivity and that
+gives you long noore thermal
+
+ align:start position:0%
+gives you long noore thermal
+ 
+
+ align:start position:0%
+gives you long noore thermal
+conductivity which will be not only a
+
+ align:start position:0%
+conductivity which will be not only a
+ 
+
+ align:start position:0%
+conductivity which will be not only a
+function of frequency but also be a
+
+ align:start position:0%
+function of frequency but also be a
+ 
+
+ align:start position:0%
+function of frequency but also be a
+function of v
+
+ align:start position:0%
+function of v
+ 
+
+ align:start position:0%
+function of v
+Vector nobody has done that okay I'm
+
+ align:start position:0%
+Vector nobody has done that okay I'm
+ 
+
+ align:start position:0%
+Vector nobody has done that okay I'm
+just telling I think that should be the
+
+ align:start position:0%
+just telling I think that should be the
+ 
+
+ align:start position:0%
+just telling I think that should be the
+case and in fact I say you see the
+
+ align:start position:0%
+case and in fact I say you see the
+ 
+
+ align:start position:0%
+case and in fact I say you see the
+derivation I had before the f I said the
+
+ align:start position:0%
+derivation I had before the f I said the
+ 
+
+ align:start position:0%
+derivation I had before the f I said the
+system is a uniform form force and here
+
+ align:start position:0%
+system is a uniform form force and here
+ 
+
+ align:start position:0%
+system is a uniform form force and here
+that disturbance
+
+ align:start position:0%
+that disturbance
+ 
+
+ align:start position:0%
+that disturbance
+temperature could be special dependent
+
+ align:start position:0%
+temperature could be special dependent
+ 
+
+ align:start position:0%
+temperature could be special dependent
+if that's special dependence you can
+
+ align:start position:0%
+if that's special dependence you can
+ 
+
+ align:start position:0%
+if that's special dependence you can
+write actually uh a corresponding space
+
+ align:start position:0%
+write actually uh a corresponding space
+ 
+
+ align:start position:0%
+write actually uh a corresponding space
+dependent uh wave vector and frequency
+
+ align:start position:0%
+dependent uh wave vector and frequency
+ 
+
+ align:start position:0%
+dependent uh wave vector and frequency
+dependent expression Theron
+
+ align:start position:0%
+dependent expression Theron
+ 
+
+ align:start position:0%
+dependent expression Theron
+con okay so now you have GRE
+
+ align:start position:0%
+con okay so now you have GRE
+ 
+
+ align:start position:0%
+con okay so now you have GRE
+Cal and the beauty you should say here
+
+ align:start position:0%
+Cal and the beauty you should say here
+ 
+
+ align:start position:0%
+Cal and the beauty you should say here
+the beauty is it's a equilibrium
+
+ align:start position:0%
+the beauty is it's a equilibrium
+ 
+
+ align:start position:0%
+the beauty is it's a equilibrium
+simulation you simulate a system box up
+
+ align:start position:0%
+simulation you simulate a system box up
+ 
+
+ align:start position:0%
+simulation you simulate a system box up
+there even though we say the derivation
+
+ align:start position:0%
+there even though we say the derivation
+ 
+
+ align:start position:0%
+there even though we say the derivation
+process I have external Force but I and
+
+ align:start position:0%
+process I have external Force but I and
+ 
+
+ align:start position:0%
+process I have external Force but I and
+all this transer
+
+ align:start position:0%
+all this transer
+ 
+
+ align:start position:0%
+all this transer
+property is I don't have disturbance
+
+ align:start position:0%
+property is I don't have disturbance
+ 
+
+ align:start position:0%
+property is I don't have disturbance
+anymore or say external Force anymore I
+
+ align:start position:0%
+anymore or say external Force anymore I
+ 
+
+ align:start position:0%
+anymore or say external Force anymore I
+just can simulate the equilibrium system
+
+ align:start position:0%
+just can simulate the equilibrium system
+ 
+
+ align:start position:0%
+just can simulate the equilibrium system
+and do my autocorrelation function and
+
+ align:start position:0%
+and do my autocorrelation function and
+ 
+
+ align:start position:0%
+and do my autocorrelation function and
+calculate transport properties viscosity
+
+ align:start position:0%
+calculate transport properties viscosity
+ 
+
+ align:start position:0%
+calculate transport properties viscosity
+all those but you have to have the
+
+ align:start position:0%
+all those but you have to have the
+ 
+
+ align:start position:0%
+all those but you have to have the
+expression for what's the
+
+ align:start position:0%
+expression for what's the
+ 
+
+ align:start position:0%
+expression for what's the
+microscopic JQ in the case of current I
+
+ align:start position:0%
+microscopic JQ in the case of current I
+ 
+
+ align:start position:0%
+microscopic JQ in the case of current I
+have expression here
+
+ align:start position:0%
+have expression here
+ 
+
+ align:start position:0%
+have expression here
+right so deriving this microscopic
+
+ align:start position:0%
+right so deriving this microscopic
+ 
+
+ align:start position:0%
+right so deriving this microscopic
+expression for the quantity of your
+
+ align:start position:0%
+expression for the quantity of your
+ 
+
+ align:start position:0%
+expression for the quantity of your
+interest uh is the next step so what are
+
+ align:start position:0%
+interest uh is the next step so what are
+ 
+
+ align:start position:0%
+interest uh is the next step so what are
+those microscopic quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so for example kinetic energy I
+
+ align:start position:0%
+right so for example kinetic energy I
+ 
+
+ align:start position:0%
+right so for example kinetic energy I
+want to calculate that's very easy uh
+
+ align:start position:0%
+want to calculate that's very easy uh
+ 
+
+ align:start position:0%
+want to calculate that's very easy uh
+say I = 1 to n and p i 2 to
+
+ align:start position:0%
+say I = 1 to n and p i 2 to
+ 
+
+ align:start position:0%
+say I = 1 to n and p i 2 to
+m i right and you can write the kinetic
+
+ align:start position:0%
+m i right and you can write the kinetic
+ 
+
+ align:start position:0%
+m i right and you can write the kinetic
+potential honia at our kinetic and
+
+ align:start position:0%
+potential honia at our kinetic and
+ 
+
+ align:start position:0%
+potential honia at our kinetic and
+potential so simple ones easy and uh uh
+
+ align:start position:0%
+potential so simple ones easy and uh uh
+ 
+
+ align:start position:0%
+potential so simple ones easy and uh uh
+for heat flux and they're also they uh
+
+ align:start position:0%
+for heat flux and they're also they uh
+ 
+
+ align:start position:0%
+for heat flux and they're also they uh
+heat and mass flux in fact is very easy
+
+ align:start position:0%
+heat and mass flux in fact is very easy
+ 
+
+ align:start position:0%
+heat and mass flux in fact is very easy
+right the mass
+
+ align:start position:0%
+right the mass
+ 
+
+ align:start position:0%
+right the mass
+flux is just the quantity is
+
+ align:start position:0%
+flux is just the quantity is
+ 
+
+ align:start position:0%
+flux is just the quantity is
+MV of say Mi I VI and I equals one to n
+
+ align:start position:0%
+MV of say Mi I VI and I equals one to n
+ 
+
+ align:start position:0%
+MV of say Mi I VI and I equals one to n
+and now if you do your heat
+
+ align:start position:0%
+and now if you do your heat
+ 
+
+ align:start position:0%
+and now if you do your heat
+flux and the heat
+
+ align:start position:0%
+flux and the heat
+ 
+
+ align:start position:0%
+flux and the heat
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+is I = 1 to
+
+ align:start position:0%
+is I = 1 to
+ 
+
+ align:start position:0%
+is I = 1 to
+n and V I hi is the
+
+ align:start position:0%
+n and V I hi is the
+ 
+
+ align:start position:0%
+n and V I hi is the
+enthalpy of per molecule or atom you're
+
+ align:start position:0%
+enthalpy of per molecule or atom you're
+ 
+
+ align:start position:0%
+enthalpy of per molecule or atom you're
+dealing with and plus 12 of the um
+
+ align:start position:0%
+dealing with and plus 12 of the um
+ 
+
+ align:start position:0%
+dealing with and plus 12 of the um
+interraction i j = 1 J does not equal to
+
+ align:start position:0%
+interraction i j = 1 J does not equal to
+ 
+
+ align:start position:0%
+interraction i j = 1 J does not equal to
+I and and r i j that's the distance
+
+ align:start position:0%
+I and and r i j that's the distance
+ 
+
+ align:start position:0%
+I and and r i j that's the distance
+between the two atoms and fig
+
+ align:start position:0%
+between the two atoms and fig
+ 
+
+ align:start position:0%
+between the two atoms and fig
+J dot V I
+
+ align:start position:0%
+J dot V I
+ 
+
+ align:start position:0%
+J dot V I
+so this one is uh this expression is
+
+ align:start position:0%
+so this one is uh this expression is
+ 
+
+ align:start position:0%
+so this one is uh this expression is
+actually derived from uh the uh really
+
+ align:start position:0%
+actually derived from uh the uh really
+ 
+
+ align:start position:0%
+actually derived from uh the uh really
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+write the energy conservation for uh
+
+ align:start position:0%
+write the energy conservation for uh
+ 
+
+ align:start position:0%
+write the energy conservation for uh
+each atom and in the process you can
+
+ align:start position:0%
+each atom and in the process you can
+ 
+
+ align:start position:0%
+each atom and in the process you can
+derive uh the expression microscop
+
+ align:start position:0%
+derive uh the expression microscop
+ 
+
+ align:start position:0%
+derive uh the expression microscop
+expression for the thermal uh the heat
+
+ align:start position:0%
+expression for the thermal uh the heat
+ 
+
+ align:start position:0%
+expression for the thermal uh the heat
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+okay and uh the uh there so there are
+
+ align:start position:0%
+okay and uh the uh there so there are
+ 
+
+ align:start position:0%
+okay and uh the uh there so there are
+many different uh uh microscopic
+
+ align:start position:0%
+many different uh uh microscopic
+ 
+
+ align:start position:0%
+many different uh uh microscopic
+expression for different
+
+ align:start position:0%
+expression for different
+ 
+
+ align:start position:0%
+expression for different
+quantities the final comment uh I want
+
+ align:start position:0%
+quantities the final comment uh I want
+ 
+
+ align:start position:0%
+quantities the final comment uh I want
+to make is uh when you simulate so here
+
+ align:start position:0%
+to make is uh when you simulate so here
+ 
+
+ align:start position:0%
+to make is uh when you simulate so here
+in the derivation linear response Theory
+
+ align:start position:0%
+in the derivation linear response Theory
+ 
+
+ align:start position:0%
+in the derivation linear response Theory
+I am doing actually a canonic system
+
+ align:start position:0%
+I am doing actually a canonic system
+ 
+
+ align:start position:0%
+I am doing actually a canonic system
+right constant
+
+ align:start position:0%
+right constant
+ 
+
+ align:start position:0%
+right constant
+temperature now when you do a molecular
+
+ align:start position:0%
+temperature now when you do a molecular
+ 
+
+ align:start position:0%
+temperature now when you do a molecular
+Dynamic simulation you typically fix
+
+ align:start position:0%
+Dynamic simulation you typically fix
+ 
+
+ align:start position:0%
+Dynamic simulation you typically fix
+number of atoms you try maintain the
+
+ align:start position:0%
+number of atoms you try maintain the
+ 
+
+ align:start position:0%
+number of atoms you try maintain the
+energy is
+
+ align:start position:0%
+energy is
+ 
+
+ align:start position:0%
+energy is
+constant right and when you have a
+
+ align:start position:0%
+constant right and when you have a
+ 
+
+ align:start position:0%
+constant right and when you have a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+energy constant volume constant number
+
+ align:start position:0%
+energy constant volume constant number
+ 
+
+ align:start position:0%
+energy constant volume constant number
+of molecules what do you
+
+ align:start position:0%
+of molecules what do you
+ 
+
+ align:start position:0%
+of molecules what do you
+have you have a microcononical
+
+ align:start position:0%
+have you have a microcononical
+ 
+
+ align:start position:0%
+have you have a microcononical
+emble right so how you can do a microc
+
+ align:start position:0%
+emble right so how you can do a microc
+ 
+
+ align:start position:0%
+emble right so how you can do a microc
+canonic
+
+ align:start position:0%
+canonic
+ 
+
+ align:start position:0%
+canonic
+simulation and yet to represent I'm
+
+ align:start position:0%
+simulation and yet to represent I'm
+ 
+
+ align:start position:0%
+simulation and yet to represent I'm
+simulating system as constant
+
+ align:start position:0%
+simulating system as constant
+ 
+
+ align:start position:0%
+simulating system as constant
+temperature or I'm simula system
+
+ align:start position:0%
+temperature or I'm simula system
+ 
+
+ align:start position:0%
+temperature or I'm simula system
+constant pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a uh people have spent a lot
+
+ align:start position:0%
+and this is a uh people have spent a lot
+ 
+
+ align:start position:0%
+and this is a uh people have spent a lot
+of time trying to deal with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question and here is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so how you stat Sumer stat uh the
+
+ align:start position:0%
+uh so how you stat Sumer stat uh the
+ 
+
+ align:start position:0%
+uh so how you stat Sumer stat uh the
+emble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+serat in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+samples
+
+ align:start position:0%
+samples
+ 
+
+ align:start position:0%
+samples
+okay so uh to do this you actually also
+
+ align:start position:0%
+okay so uh to do this you actually also
+ 
+
+ align:start position:0%
+okay so uh to do this you actually also
+uh have to get uh used to the fact that
+
+ align:start position:0%
+uh have to get uh used to the fact that
+ 
+
+ align:start position:0%
+uh have to get uh used to the fact that
+normally you do f equals ma right that's
+
+ align:start position:0%
+normally you do f equals ma right that's
+ 
+
+ align:start position:0%
+normally you do f equals ma right that's
+equation of motion but there are many
+
+ align:start position:0%
+equation of motion but there are many
+ 
+
+ align:start position:0%
+equation of motion but there are many
+different ways that to write the fal
+
+ align:start position:0%
+different ways that to write the fal
+ 
+
+ align:start position:0%
+different ways that to write the fal
+Ma and uh uh there are Lan equation of
+
+ align:start position:0%
+Ma and uh uh there are Lan equation of
+ 
+
+ align:start position:0%
+Ma and uh uh there are Lan equation of
+motion Honan equation of motion they are
+
+ align:start position:0%
+motion Honan equation of motion they are
+ 
+
+ align:start position:0%
+motion Honan equation of motion they are
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+equivalent uh not like equation of
+
+ align:start position:0%
+equivalent uh not like equation of
+ 
+
+ align:start position:0%
+equivalent uh not like equation of
+motion and homona so uh for example when
+
+ align:start position:0%
+motion and homona so uh for example when
+ 
+
+ align:start position:0%
+motion and homona so uh for example when
+you do a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lin equation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion right and what you use is uh
+
+ align:start position:0%
+motion right and what you use is uh
+ 
+
+ align:start position:0%
+motion right and what you use is uh
+r r
+
+ align:start position:0%
+r r
+ 
+
+ align:start position:0%
+r r
+dot okay that's you you use this uh uh
+
+ align:start position:0%
+dot okay that's you you use this uh uh
+ 
+
+ align:start position:0%
+dot okay that's you you use this uh uh
+the velocity and
+
+ align:start position:0%
+the velocity and
+ 
+
+ align:start position:0%
+the velocity and
+space as your uh say as your
+
+ align:start position:0%
+space as your uh say as your
+ 
+
+ align:start position:0%
+space as your uh say as your
+variable and uh you construct the Ling
+
+ align:start position:0%
+variable and uh you construct the Ling
+ 
+
+ align:start position:0%
+variable and uh you construct the Ling
+of the system which is a function of
+
+ align:start position:0%
+of the system which is a function of
+ 
+
+ align:start position:0%
+of the system which is a function of
+time function of r function of velocity
+
+ align:start position:0%
+time function of r function of velocity
+ 
+
+ align:start position:0%
+time function of r function of velocity
+and L of the system is r r dot Min the
+
+ align:start position:0%
+and L of the system is r r dot Min the
+ 
+
+ align:start position:0%
+and L of the system is r r dot Min the
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+energy so it's kinetic energy Mass
+
+ align:start position:0%
+energy so it's kinetic energy Mass
+ 
+
+ align:start position:0%
+energy so it's kinetic energy Mass
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+energy maybe you learned this in
+
+ align:start position:0%
+energy maybe you learned this in
+ 
+
+ align:start position:0%
+energy maybe you learned this in
+dyamics and uh uh so the uh Honan
+
+ align:start position:0%
+dyamics and uh uh so the uh Honan
+ 
+
+ align:start position:0%
+dyamics and uh uh so the uh Honan
+principle so what's like equation of
+
+ align:start position:0%
+principle so what's like equation of
+ 
+
+ align:start position:0%
+principle so what's like equation of
+motion is the there's this Honan
+
+ align:start position:0%
+motion is the there's this Honan
+ 
+
+ align:start position:0%
+motion is the there's this Honan
+principle say when your system go from
+
+ align:start position:0%
+principle say when your system go from
+ 
+
+ align:start position:0%
+principle say when your system go from
+uh 0.1 to0 2
+
+ align:start position:0%
+uh 0.1 to0 2
+ 
+
+ align:start position:0%
+uh 0.1 to0 2
+uh the Len uh so the uh integral
+
+ align:start position:0%
+uh the Len uh so the uh integral
+ 
+
+ align:start position:0%
+uh the Len uh so the uh integral
+here integral this is the action
+
+ align:start position:0%
+here integral this is the action
+ 
+
+ align:start position:0%
+here integral this is the action
+integral from 1 to two of the
+
+ align:start position:0%
+integral from 1 to two of the
+ 
+
+ align:start position:0%
+integral from 1 to two of the
+logen and t
+
+ align:start position:0%
+logen and t
+ 
+
+ align:start position:0%
+logen and t
+r r dot and integrate over time and this
+
+ align:start position:0%
+r r dot and integrate over time and this
+ 
+
+ align:start position:0%
+r r dot and integrate over time and this
+should be extreme it's maximum or
+
+ align:start position:0%
+should be extreme it's maximum or
+ 
+
+ align:start position:0%
+should be extreme it's maximum or
+minimum and in fact I don't know whether
+
+ align:start position:0%
+minimum and in fact I don't know whether
+ 
+
+ align:start position:0%
+minimum and in fact I don't know whether
+it should be maximum minimum but say
+
+ align:start position:0%
+it should be maximum minimum but say
+ 
+
+ align:start position:0%
+it should be maximum minimum but say
+it's a derivative is zero
+
+ align:start position:0%
+it's a derivative is zero
+ 
+
+ align:start position:0%
+it's a derivative is zero
+okay derivative Zero from there you do
+
+ align:start position:0%
+okay derivative Zero from there you do
+ 
+
+ align:start position:0%
+okay derivative Zero from there you do
+variation you actually get the equation
+
+ align:start position:0%
+variation you actually get the equation
+ 
+
+ align:start position:0%
+variation you actually get the equation
+of motion for the L
+
+ align:start position:0%
+of motion for the L
+ 
+
+ align:start position:0%
+of motion for the L
+ranging so uh you do your uh um here you
+
+ align:start position:0%
+ranging so uh you do your uh um here you
+ 
+
+ align:start position:0%
+ranging so uh you do your uh um here you
+do the equation of motion then you will
+
+ align:start position:0%
+do the equation of motion then you will
+ 
+
+ align:start position:0%
+do the equation of motion then you will
+get this is xtrem you'll get
+
+ align:start position:0%
+get this is xtrem you'll get
+ 
+
+ align:start position:0%
+get this is xtrem you'll get
+DL uh d
+
+ align:start position:0%
+DL uh d
+ 
+
+ align:start position:0%
+DL uh d
+r um here I have I'm writing in each
+
+ align:start position:0%
+r um here I have I'm writing in each
+ 
+
+ align:start position:0%
+r um here I have I'm writing in each
+component
+
+ align:start position:0%
+component
+ 
+
+ align:start position:0%
+component
+uh the velocity and D L Dr R itself
+
+ align:start position:0%
+uh the velocity and D L Dr R itself
+ 
+
+ align:start position:0%
+uh the velocity and D L Dr R itself
+equal zero so this is actually FAL ma
+
+ align:start position:0%
+equal zero so this is actually FAL ma
+ 
+
+ align:start position:0%
+equal zero so this is actually FAL ma
+under the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lin okay the L
+
+ align:start position:0%
+Lin okay the L
+ 
+
+ align:start position:0%
+Lin okay the L
+rangin is uh useful but uh it has one
+
+ align:start position:0%
+rangin is uh useful but uh it has one
+ 
+
+ align:start position:0%
+rangin is uh useful but uh it has one
+defect it's not
+
+ align:start position:0%
+defect it's not
+ 
+
+ align:start position:0%
+defect it's not
+symmetric okay it LS a symmetry
+
+ align:start position:0%
+symmetric okay it LS a symmetry
+ 
+
+ align:start position:0%
+symmetric okay it LS a symmetry
+and uh so if you rather than use r and r
+
+ align:start position:0%
+and uh so if you rather than use r and r
+ 
+
+ align:start position:0%
+and uh so if you rather than use r and r
+dot if you use R and the P this will
+
+ align:start position:0%
+dot if you use R and the P this will
+ 
+
+ align:start position:0%
+dot if you use R and the P this will
+come back to the face space right if you
+
+ align:start position:0%
+come back to the face space right if you
+ 
+
+ align:start position:0%
+come back to the face space right if you
+use position and
+
+ align:start position:0%
+use position and
+ 
+
+ align:start position:0%
+use position and
+momentum and you actually can do a
+
+ align:start position:0%
+momentum and you actually can do a
+ 
+
+ align:start position:0%
+momentum and you actually can do a
+transformation into the ponal equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion so you can write rather than use
+
+ align:start position:0%
+motion so you can write rather than use
+ 
+
+ align:start position:0%
+motion so you can write rather than use
+and uh R if you do your new variable P
+
+ align:start position:0%
+and uh R if you do your new variable P
+ 
+
+ align:start position:0%
+and uh R if you do your new variable P
+momentum if you define
+
+ align:start position:0%
+momentum if you define
+ 
+
+ align:start position:0%
+momentum if you define
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Lin derivative that's a momentum and you
+
+ align:start position:0%
+Lin derivative that's a momentum and you
+ 
+
+ align:start position:0%
+Lin derivative that's a momentum and you
+can go right the ction coordin you'll
+
+ align:start position:0%
+can go right the ction coordin you'll
+ 
+
+ align:start position:0%
+can go right the ction coordin you'll
+find this all come back to FAL ma
+
+ align:start position:0%
+find this all come back to FAL ma
+ 
+
+ align:start position:0%
+find this all come back to FAL ma
+everything makes sense and then you can
+
+ align:start position:0%
+everything makes sense and then you can
+ 
+
+ align:start position:0%
+everything makes sense and then you can
+constract your
+
+ align:start position:0%
+constract your
+ 
+
+ align:start position:0%
+constract your
+Honan
+
+ align:start position:0%
+Honan
+ 
+
+ align:start position:0%
+Honan
+TR P so now my variable in Lan is r and
+
+ align:start position:0%
+TR P so now my variable in Lan is r and
+ 
+
+ align:start position:0%
+TR P so now my variable in Lan is r and
+r dot in katonia is R and P right so in
+
+ align:start position:0%
+r dot in katonia is R and P right so in
+ 
+
+ align:start position:0%
+r dot in katonia is R and P right so in
+the uh so this uh is Sigma d l d r i r
+
+ align:start position:0%
+the uh so this uh is Sigma d l d r i r
+ 
+
+ align:start position:0%
+the uh so this uh is Sigma d l d r i r
+i uh Mass L and you can say in this
+
+ align:start position:0%
+i uh Mass L and you can say in this
+ 
+
+ align:start position:0%
+i uh Mass L and you can say in this
+simple uh uh say case uh of for
+
+ align:start position:0%
+simple uh uh say case uh of for
+ 
+
+ align:start position:0%
+simple uh uh say case uh of for
+kinetic plus potential is essentially if
+
+ align:start position:0%
+kinetic plus potential is essentially if
+ 
+
+ align:start position:0%
+kinetic plus potential is essentially if
+you in ction coordinate you really say
+
+ align:start position:0%
+you in ction coordinate you really say
+ 
+
+ align:start position:0%
+you in ction coordinate you really say
+kinetic energy plus potential energy
+
+ align:start position:0%
+kinetic energy plus potential energy
+ 
+
+ align:start position:0%
+kinetic energy plus potential energy
+this is what we typically think about
+
+ align:start position:0%
+this is what we typically think about
+ 
+
+ align:start position:0%
+this is what we typically think about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+homon okay and uh once you have the
+
+ align:start position:0%
+homon okay and uh once you have the
+ 
+
+ align:start position:0%
+homon okay and uh once you have the
+Honan you write the uh the uh equation
+
+ align:start position:0%
+Honan you write the uh the uh equation
+ 
+
+ align:start position:0%
+Honan you write the uh the uh equation
+of motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Honan is r i and uh r the so the
+
+ align:start position:0%
+for Honan is r i and uh r the so the
+ 
+
+ align:start position:0%
+for Honan is r i and uh r the so the
+momentum derivative and space derivative
+
+ align:start position:0%
+momentum derivative and space derivative
+ 
+
+ align:start position:0%
+momentum derivative and space derivative
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+DH
+
+ align:start position:0%
+DH
+ 
+
+ align:start position:0%
+DH
+DPI so this one you can say compared to
+
+ align:start position:0%
+DPI so this one you can say compared to
+ 
+
+ align:start position:0%
+DPI so this one you can say compared to
+Lan equation of motion this is homoni
+
+ align:start position:0%
+Lan equation of motion this is homoni
+ 
+
+ align:start position:0%
+Lan equation of motion this is homoni
+equation of motion the momentum and
+
+ align:start position:0%
+equation of motion the momentum and
+ 
+
+ align:start position:0%
+equation of motion the momentum and
+space derivative and they are symmetric
+
+ align:start position:0%
+space derivative and they are symmetric
+ 
+
+ align:start position:0%
+space derivative and they are symmetric
+so that's a the homon is often
+
+ align:start position:0%
+so that's a the homon is often
+ 
+
+ align:start position:0%
+so that's a the homon is often
+used why I'm saying this why I don't uh
+
+ align:start position:0%
+used why I'm saying this why I don't uh
+ 
+
+ align:start position:0%
+used why I'm saying this why I don't uh
+uh I say I'm going into rather than FAL
+
+ align:start position:0%
+uh I say I'm going into rather than FAL
+ 
+
+ align:start position:0%
+uh I say I'm going into rather than FAL
+ma
+
+ align:start position:0%
+ma
+ 
+
+ align:start position:0%
+ma
+Len and
+
+ align:start position:0%
+Len and
+ 
+
+ align:start position:0%
+Len and
+honia that's because well sometimes for
+
+ align:start position:0%
+honia that's because well sometimes for
+ 
+
+ align:start position:0%
+honia that's because well sometimes for
+example if you write uh if you do a
+
+ align:start position:0%
+example if you write uh if you do a
+ 
+
+ align:start position:0%
+example if you write uh if you do a
+simulation of molecules right the
+
+ align:start position:0%
+simulation of molecules right the
+ 
+
+ align:start position:0%
+simulation of molecules right the
+molecule of a diatomic molecule has a uh
+
+ align:start position:0%
+molecule of a diatomic molecule has a uh
+ 
+
+ align:start position:0%
+molecule of a diatomic molecule has a uh
+of course each each molecule has two
+
+ align:start position:0%
+of course each each molecule has two
+ 
+
+ align:start position:0%
+of course each each molecule has two
+atoms if you say I'm going to simulate
+
+ align:start position:0%
+atoms if you say I'm going to simulate
+ 
+
+ align:start position:0%
+atoms if you say I'm going to simulate
+just a r position and velocity I have to
+
+ align:start position:0%
+just a r position and velocity I have to
+ 
+
+ align:start position:0%
+just a r position and velocity I have to
+I split I have to split this molecule
+
+ align:start position:0%
+I split I have to split this molecule
+ 
+
+ align:start position:0%
+I split I have to split this molecule
+into two atoms right but say I can use
+
+ align:start position:0%
+into two atoms right but say I can use
+ 
+
+ align:start position:0%
+into two atoms right but say I can use
+Theta uh say the angle rotation and the
+
+ align:start position:0%
+Theta uh say the angle rotation and the
+ 
+
+ align:start position:0%
+Theta uh say the angle rotation and the
+relative vibration so in that case I
+
+ align:start position:0%
+relative vibration so in that case I
+ 
+
+ align:start position:0%
+relative vibration so in that case I
+have different variable different
+
+ align:start position:0%
+have different variable different
+ 
+
+ align:start position:0%
+have different variable different
+momentum different coordinate so the
+
+ align:start position:0%
+momentum different coordinate so the
+ 
+
+ align:start position:0%
+momentum different coordinate so the
+beauty of the honia is you can write
+
+ align:start position:0%
+beauty of the honia is you can write
+ 
+
+ align:start position:0%
+beauty of the honia is you can write
+that much
+
+ align:start position:0%
+that much
+ 
+
+ align:start position:0%
+that much
+easier now what's the relation to this
+
+ align:start position:0%
+easier now what's the relation to this
+ 
+
+ align:start position:0%
+easier now what's the relation to this
+my original question I want to my I do
+
+ align:start position:0%
+my original question I want to my I do
+ 
+
+ align:start position:0%
+my original question I want to my I do
+aim simulation that's a micronic
+
+ align:start position:0%
+aim simulation that's a micronic
+ 
+
+ align:start position:0%
+aim simulation that's a micronic
+ample right and how I can simulate a
+
+ align:start position:0%
+ample right and how I can simulate a
+ 
+
+ align:start position:0%
+ample right and how I can simulate a
+canonic using a can say to actually do a
+
+ align:start position:0%
+canonic using a can say to actually do a
+ 
+
+ align:start position:0%
+canonic using a can say to actually do a
+canonical system with constant
+
+ align:start position:0%
+canonical system with constant
+ 
+
+ align:start position:0%
+canonical system with constant
+temperature and uh the uh trick here is
+
+ align:start position:0%
+temperature and uh the uh trick here is
+ 
+
+ align:start position:0%
+temperature and uh the uh trick here is
+this was a a creating uh
+
+ align:start position:0%
+this was a a creating uh
+ 
+
+ align:start position:0%
+this was a a creating uh
+artificial honia okay so for example
+
+ align:start position:0%
+artificial honia okay so for example
+ 
+
+ align:start position:0%
+artificial honia okay so for example
+nose
+
+ align:start position:0%
+nose
+ 
+
+ align:start position:0%
+nose
+introduce a
+
+ align:start position:0%
+introduce a
+ 
+
+ align:start position:0%
+introduce a
+Honan and uh the Honan uh he wrote this
+
+ align:start position:0%
+Honan and uh the Honan uh he wrote this
+ 
+
+ align:start position:0%
+Honan and uh the Honan uh he wrote this
+is a uh he wrote the r not only R but
+
+ align:start position:0%
+is a uh he wrote the r not only R but
+ 
+
+ align:start position:0%
+is a uh he wrote the r not only R but
+also additional variable and the P Prime
+
+ align:start position:0%
+also additional variable and the P Prime
+ 
+
+ align:start position:0%
+also additional variable and the P Prime
+momentum and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PS okay and in his konium the time is a
+
+ align:start position:0%
+PS okay and in his konium the time is a
+ 
+
+ align:start position:0%
+PS okay and in his konium the time is a
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+Prime and uh then they say it's not even
+
+ align:start position:0%
+Prime and uh then they say it's not even
+ 
+
+ align:start position:0%
+Prime and uh then they say it's not even
+the real
+
+ align:start position:0%
+the real
+ 
+
+ align:start position:0%
+the real
+time the time is say related to so say
+
+ align:start position:0%
+time the time is say related to so say
+ 
+
+ align:start position:0%
+time the time is say related to so say
+DT equals
+
+ align:start position:0%
+DT equals
+ 
+
+ align:start position:0%
+DT equals
+sdt so you have this
+
+ align:start position:0%
+sdt so you have this
+ 
+
+ align:start position:0%
+sdt so you have this
+additional uh s is your equivalent one
+
+ align:start position:0%
+additional uh s is your equivalent one
+ 
+
+ align:start position:0%
+additional uh s is your equivalent one
+of the r and then you have a p
+
+ align:start position:0%
+of the r and then you have a p
+ 
+
+ align:start position:0%
+of the r and then you have a p
+additional momentum that was
+
+ align:start position:0%
+additional momentum that was
+ 
+
+ align:start position:0%
+additional momentum that was
+introduced and he say this one
+
+ align:start position:0%
+introduced and he say this one
+ 
+
+ align:start position:0%
+introduced and he say this one
+equals Sigma I to n p i Prime p i Prime
+
+ align:start position:0%
+equals Sigma I to n p i Prime p i Prime
+ 
+
+ align:start position:0%
+equals Sigma I to n p i Prime p i Prime
+and 2
+
+ align:start position:0%
+and 2
+ 
+
+ align:start position:0%
+and 2
+m s² + uh potential energy is still the
+
+ align:start position:0%
+m s² + uh potential energy is still the
+ 
+
+ align:start position:0%
+m s² + uh potential energy is still the
+real space but he has additional add
+
+ align:start position:0%
+real space but he has additional add
+ 
+
+ align:start position:0%
+real space but he has additional add
+another term this momentum so is this 2
+
+ align:start position:0%
+another term this momentum so is this 2
+ 
+
+ align:start position:0%
+another term this momentum so is this 2
+MN so and plus uh here is NF +
+
+ align:start position:0%
+MN so and plus uh here is NF +
+ 
+
+ align:start position:0%
+MN so and plus uh here is NF +
+1 and
+
+ align:start position:0%
+1 and
+ 
+
+ align:start position:0%
+1 and
+KBT log s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he cook this
+
+ align:start position:0%
+he cook this
+ 
+
+ align:start position:0%
+he cook this
+up okay and the reason he cook this up
+
+ align:start position:0%
+up okay and the reason he cook this up
+ 
+
+ align:start position:0%
+up okay and the reason he cook this up
+is you write the honia you can write the
+
+ align:start position:0%
+is you write the honia you can write the
+ 
+
+ align:start position:0%
+is you write the honia you can write the
+equation of
+
+ align:start position:0%
+equation of
+ 
+
+ align:start position:0%
+equation of
+motion okay and it say if I simulate
+
+ align:start position:0%
+motion okay and it say if I simulate
+ 
+
+ align:start position:0%
+motion okay and it say if I simulate
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+system even though I simulated that it's
+
+ align:start position:0%
+system even though I simulated that it's
+ 
+
+ align:start position:0%
+system even though I simulated that it's
+a micro colon insample at the end I get
+
+ align:start position:0%
+a micro colon insample at the end I get
+ 
+
+ align:start position:0%
+a micro colon insample at the end I get
+a colon ample result for the original
+
+ align:start position:0%
+a colon ample result for the original
+ 
+
+ align:start position:0%
+a colon ample result for the original
+system so he actually proved it so the
+
+ align:start position:0%
+system so he actually proved it so the
+ 
+
+ align:start position:0%
+system so he actually proved it so the
+way you prove it in a micronic example
+
+ align:start position:0%
+way you prove it in a micronic example
+ 
+
+ align:start position:0%
+way you prove it in a micronic example
+you remember the entropy is a k log
+
+ align:start position:0%
+you remember the entropy is a k log
+ 
+
+ align:start position:0%
+you remember the entropy is a k log
+Omega right Omega is L of states right
+
+ align:start position:0%
+Omega right Omega is L of states right
+ 
+
+ align:start position:0%
+Omega right Omega is L of states right
+so L of states is really uh just uh
+
+ align:start position:0%
+so L of states is really uh just uh
+ 
+
+ align:start position:0%
+so L of states is really uh just uh
+Dr
+
+ align:start position:0%
+Dr
+ 
+
+ align:start position:0%
+Dr
+DP
+
+ align:start position:0%
+DP
+ 
+
+ align:start position:0%
+DP
+Prime and now I have extra DS
+
+ align:start position:0%
+Prime and now I have extra DS
+ 
+
+ align:start position:0%
+Prime and now I have extra DS
+DPS right and then they
+
+ align:start position:0%
+DPS right and then they
+ 
+
+ align:start position:0%
+DPS right and then they
+this is a counting number of states so
+
+ align:start position:0%
+this is a counting number of states so
+ 
+
+ align:start position:0%
+this is a counting number of states so
+is when the energy of the system is
+
+ align:start position:0%
+is when the energy of the system is
+ 
+
+ align:start position:0%
+is when the energy of the system is
+equal to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Honan that Delta I have one state right
+
+ align:start position:0%
+Honan that Delta I have one state right
+ 
+
+ align:start position:0%
+Honan that Delta I have one state right
+so this integration is just a summation
+
+ align:start position:0%
+so this integration is just a summation
+ 
+
+ align:start position:0%
+so this integration is just a summation
+what it says so starting from
+
+ align:start position:0%
+what it says so starting from
+ 
+
+ align:start position:0%
+what it says so starting from
+here using this
+
+ align:start position:0%
+here using this
+ 
+
+ align:start position:0%
+here using this
+Honan integrate the S and the P Prime uh
+
+ align:start position:0%
+Honan integrate the S and the P Prime uh
+ 
+
+ align:start position:0%
+Honan integrate the S and the P Prime uh
+PS right this are the two extra he
+
+ align:start position:0%
+PS right this are the two extra he
+ 
+
+ align:start position:0%
+PS right this are the two extra he
+roduced he actually show that after your
+
+ align:start position:0%
+roduced he actually show that after your
+ 
+
+ align:start position:0%
+roduced he actually show that after your
+integration what you have here is say uh
+
+ align:start position:0%
+integration what you have here is say uh
+ 
+
+ align:start position:0%
+integration what you have here is say uh
+NF + 1 this is the last equation I'm
+
+ align:start position:0%
+NF + 1 this is the last equation I'm
+ 
+
+ align:start position:0%
+NF + 1 this is the last equation I'm
+going to write 2
+
+ align:start position:0%
+going to write 2
+ 
+
+ align:start position:0%
+going to write 2
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+MN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KBT 12
+
+ align:start position:0%
+KBT 12
+ 
+
+ align:start position:0%
+KBT 12
+exponential e
+
+ align:start position:0%
+exponential e
+ 
+
+ align:start position:0%
+exponential e
+KBT I saw this is a for the people
+
+ align:start position:0%
+KBT I saw this is a for the people
+ 
+
+ align:start position:0%
+KBT I saw this is a for the people
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+conour those ways of doing things that's
+
+ align:start position:0%
+conour those ways of doing things that's
+ 
+
+ align:start position:0%
+conour those ways of doing things that's
+why I want to write to you and this is h
+
+ align:start position:0%
+why I want to write to you and this is h
+ 
+
+ align:start position:0%
+why I want to write to you and this is h
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+p and
+
+ align:start position:0%
+p and
+ 
+
+ align:start position:0%
+p and
+KBT so you see the trick is he actually
+
+ align:start position:0%
+KBT so you see the trick is he actually
+ 
+
+ align:start position:0%
+KBT so you see the trick is he actually
+come going from this Delta he was able
+
+ align:start position:0%
+come going from this Delta he was able
+ 
+
+ align:start position:0%
+come going from this Delta he was able
+to integrate that
+
+ align:start position:0%
+to integrate that
+ 
+
+ align:start position:0%
+to integrate that
+dsdp and because he add this log here
+
+ align:start position:0%
+dsdp and because he add this log here
+ 
+
+ align:start position:0%
+dsdp and because he add this log here
+here right in the equation of motion he
+
+ align:start position:0%
+here right in the equation of motion he
+ 
+
+ align:start position:0%
+here right in the equation of motion he
+add this log he got the exponent and
+
+ align:start position:0%
+add this log he got the exponent and
+ 
+
+ align:start position:0%
+add this log he got the exponent and
+convert back into here is
+
+ align:start position:0%
+convert back into here is
+ 
+
+ align:start position:0%
+convert back into here is
+your bman
+
+ align:start position:0%
+your bman
+ 
+
+ align:start position:0%
+your bman
+statistics right and you can also prove
+
+ align:start position:0%
+statistics right and you can also prove
+ 
+
+ align:start position:0%
+statistics right and you can also prove
+if you do a quantity of A and R say
+
+ align:start position:0%
+if you do a quantity of A and R say
+ 
+
+ align:start position:0%
+if you do a quantity of A and R say
+that's the time average uh is same as
+
+ align:start position:0%
+that's the time average uh is same as
+ 
+
+ align:start position:0%
+that's the time average uh is same as
+inem average except the nose had a one
+
+ align:start position:0%
+inem average except the nose had a one
+ 
+
+ align:start position:0%
+inem average except the nose had a one
+problem Cu uh uh so it was later Hoover
+
+ align:start position:0%
+problem Cu uh uh so it was later Hoover
+ 
+
+ align:start position:0%
+problem Cu uh uh so it was later Hoover
+said this was not
+
+ align:start position:0%
+said this was not
+ 
+
+ align:start position:0%
+said this was not
+necessary and going back to actually go
+
+ align:start position:0%
+necessary and going back to actually go
+ 
+
+ align:start position:0%
+necessary and going back to actually go
+to real space and that actually solve
+
+ align:start position:0%
+to real space and that actually solve
+ 
+
+ align:start position:0%
+to real space and that actually solve
+his problem so it's called This is
+
+ align:start position:0%
+his problem so it's called This is
+ 
+
+ align:start position:0%
+his problem so it's called This is
+called the lose van hope
+
+ align:start position:0%
+called the lose van hope
+ 
+
+ align:start position:0%
+called the lose van hope
+thermostat right and there are people
+
+ align:start position:0%
+thermostat right and there are people
+ 
+
+ align:start position:0%
+thermostat right and there are people
+develop say for example Anderson he
+
+ align:start position:0%
+develop say for example Anderson he
+ 
+
+ align:start position:0%
+develop say for example Anderson he
+develop a therat where you can trate the
+
+ align:start position:0%
+develop a therat where you can trate the
+ 
+
+ align:start position:0%
+develop a therat where you can trate the
+constant pressure system so you have
+
+ align:start position:0%
+constant pressure system so you have
+ 
+
+ align:start position:0%
+constant pressure system so you have
+different equ so with that you can write
+
+ align:start position:0%
+different equ so with that you can write
+ 
+
+ align:start position:0%
+different equ so with that you can write
+different equation of motion so the you
+
+ align:start position:0%
+different equation of motion so the you
+ 
+
+ align:start position:0%
+different equation of motion so the you
+add essentially one equation into a
+
+ align:start position:0%
+add essentially one equation into a
+ 
+
+ align:start position:0%
+add essentially one equation into a
+system of n particles you can solve the
+
+ align:start position:0%
+system of n particles you can solve the
+ 
+
+ align:start position:0%
+system of n particles you can solve the
+uh uh using that you can deal with
+
+ align:start position:0%
+uh uh using that you can deal with
+ 
+
+ align:start position:0%
+uh uh using that you can deal with
+constant temperature constant pressure
+
+ align:start position:0%
+constant temperature constant pressure
+ 
+
+ align:start position:0%
+constant temperature constant pressure
+different constructions and
+
+ align:start position:0%
+different constructions and
+ 
+
+ align:start position:0%
+different constructions and
+samples
+
+ align:start position:0%
+samples
+ 
+
+ align:start position:0%
+samples
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1230 I thought I was going to
+
+ align:start position:0%
+1230 I thought I was going to
+ 
+
+ align:start position:0%
+1230 I thought I was going to
+show some slides but
+
+ align:start position:0%
+show some slides but
+ 
+
+ align:start position:0%
+show some slides but
+remember if you haven't done your uh um
+
+ align:start position:0%
+remember if you haven't done your uh um
+ 
+
+ align:start position:0%
+remember if you haven't done your uh um
+uh evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I at least I use time
+
+ align:start position:0%
+see I at least I use time
+ 
+
+ align:start position:0%
+see I at least I use time
+up thank you
\ No newline at end of file
diff --git a/Y1lsWOtvVgY.txt b/Y1lsWOtvVgY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..854df8ccbf7c04302dcee7bcffa051a184ea34b7
--- /dev/null
+++ b/Y1lsWOtvVgY.txt
@@ -0,0 +1,11155 @@
+align:start position:0%
+ 
+and let's get started because uh today
+
+ align:start position:0%
+and let's get started because uh today
+ 
+
+ align:start position:0%
+and let's get started because uh today
+we have a lot to talk about and we also
+
+ align:start position:0%
+we have a lot to talk about and we also
+ 
+
+ align:start position:0%
+we have a lot to talk about and we also
+have a guest speaker Professor get
+
+ align:start position:0%
+have a guest speaker Professor get
+ 
+
+ align:start position:0%
+have a guest speaker Professor get
+Golding is here so he will need 30
+
+ align:start position:0%
+Golding is here so he will need 30
+ 
+
+ align:start position:0%
+Golding is here so he will need 30
+minutes 20 minutes okay okay and uh so
+
+ align:start position:0%
+minutes 20 minutes okay okay and uh so
+ 
+
+ align:start position:0%
+minutes 20 minutes okay okay and uh so
+since since ad is already here I'm going
+
+ align:start position:0%
+since since ad is already here I'm going
+ 
+
+ align:start position:0%
+since since ad is already here I'm going
+to first introduce ad and later you can
+
+ align:start position:0%
+to first introduce ad and later you can
+ 
+
+ align:start position:0%
+to first introduce ad and later you can
+just we can just switch so Professor ad
+
+ align:start position:0%
+just we can just switch so Professor ad
+ 
+
+ align:start position:0%
+just we can just switch so Professor ad
+Golding is the uh senior lecturer at
+
+ align:start position:0%
+Golding is the uh senior lecturer at
+ 
+
+ align:start position:0%
+Golding is the uh senior lecturer at
+slong school and also the executive
+
+ align:start position:0%
+slong school and also the executive
+ 
+
+ align:start position:0%
+slong school and also the executive
+director of the m center for finance and
+
+ align:start position:0%
+director of the m center for finance and
+ 
+
+ align:start position:0%
+director of the m center for finance and
+policy go goab go goab Center for
+
+ align:start position:0%
+policy go goab go goab Center for
+ 
+
+ align:start position:0%
+policy go goab go goab Center for
+finance and policy but most importantly
+
+ align:start position:0%
+finance and policy but most importantly
+ 
+
+ align:start position:0%
+finance and policy but most importantly
+before coming to MIT ad was a head of
+
+ align:start position:0%
+before coming to MIT ad was a head of
+ 
+
+ align:start position:0%
+before coming to MIT ad was a head of
+the federal housing
+
+ align:start position:0%
+the federal housing
+ 
+
+ align:start position:0%
+the federal housing
+Administration uh uh between 2015 to
+
+ align:start position:0%
+Administration uh uh between 2015 to
+ 
+
+ align:start position:0%
+Administration uh uh between 2015 to
+2017 uh yes and also was senior adviser
+
+ align:start position:0%
+2017 uh yes and also was senior adviser
+ 
+
+ align:start position:0%
+2017 uh yes and also was senior adviser
+in the US Department of Housing and
+
+ align:start position:0%
+in the US Department of Housing and
+ 
+
+ align:start position:0%
+in the US Department of Housing and
+Urban Development hot and also and also
+
+ align:start position:0%
+Urban Development hot and also and also
+ 
+
+ align:start position:0%
+Urban Development hot and also and also
+in the senior senior executive at the
+
+ align:start position:0%
+in the senior senior executive at the
+ 
+
+ align:start position:0%
+in the senior senior executive at the
+federal Home Loan mortgage corporation
+
+ align:start position:0%
+federal Home Loan mortgage corporation
+ 
+
+ align:start position:0%
+federal Home Loan mortgage corporation
+fedy uh Freddy Mack from 1989 to 2012 so
+
+ align:start position:0%
+fedy uh Freddy Mack from 1989 to 2012 so
+ 
+
+ align:start position:0%
+fedy uh Freddy Mack from 1989 to 2012 so
+basically ad is a big expert on and a
+
+ align:start position:0%
+basically ad is a big expert on and a
+ 
+
+ align:start position:0%
+basically ad is a big expert on and a
+huge National reputation for the
+
+ align:start position:0%
+huge National reputation for the
+ 
+
+ align:start position:0%
+huge National reputation for the
+Visionary leadership in Housing Finance
+
+ align:start position:0%
+Visionary leadership in Housing Finance
+ 
+
+ align:start position:0%
+Visionary leadership in Housing Finance
+policy so today that's why I got add
+
+ align:start position:0%
+policy so today that's why I got add
+ 
+
+ align:start position:0%
+policy so today that's why I got add
+here and to talk about the Housing
+
+ align:start position:0%
+here and to talk about the Housing
+ 
+
+ align:start position:0%
+here and to talk about the Housing
+Finance and climate risk how to consider
+
+ align:start position:0%
+Finance and climate risk how to consider
+ 
+
+ align:start position:0%
+Finance and climate risk how to consider
+climate risk in Housing Finance at first
+
+ align:start position:0%
+climate risk in Housing Finance at first
+ 
+
+ align:start position:0%
+climate risk in Housing Finance at first
+it was not considered at all now it's be
+
+ align:start position:0%
+it was not considered at all now it's be
+ 
+
+ align:start position:0%
+it was not considered at all now it's be
+lot of problems now they started to wake
+
+ align:start position:0%
+lot of problems now they started to wake
+ 
+
+ align:start position:0%
+lot of problems now they started to wake
+up and consider uh clim the risk in in
+
+ align:start position:0%
+up and consider uh clim the risk in in
+ 
+
+ align:start position:0%
+up and consider uh clim the risk in in
+in all the mortgage risk financing uh
+
+ align:start position:0%
+in all the mortgage risk financing uh
+ 
+
+ align:start position:0%
+in all the mortgage risk financing uh
+mortgage
+
+ align:start position:0%
+mortgage
+ 
+
+ align:start position:0%
+mortgage
+risk pricing so that's what we'll be add
+
+ align:start position:0%
+risk pricing so that's what we'll be add
+ 
+
+ align:start position:0%
+risk pricing so that's what we'll be add
+last 20 minutes but but before that I
+
+ align:start position:0%
+last 20 minutes but but before that I
+ 
+
+ align:start position:0%
+last 20 minutes but but before that I
+still have 1 hour to talk about this uh
+
+ align:start position:0%
+still have 1 hour to talk about this uh
+ 
+
+ align:start position:0%
+still have 1 hour to talk about this uh
+third lecture of the climate and real
+
+ align:start position:0%
+third lecture of the climate and real
+ 
+
+ align:start position:0%
+third lecture of the climate and real
+estate okay today so basically for the
+
+ align:start position:0%
+estate okay today so basically for the
+ 
+
+ align:start position:0%
+estate okay today so basically for the
+first climate real estate uh session
+
+ align:start position:0%
+first climate real estate uh session
+ 
+
+ align:start position:0%
+first climate real estate uh session
+taught by Juan and that's a Basics like
+
+ align:start position:0%
+taught by Juan and that's a Basics like
+ 
+
+ align:start position:0%
+taught by Juan and that's a Basics like
+a climate science and how to consider
+
+ align:start position:0%
+a climate science and how to consider
+ 
+
+ align:start position:0%
+a climate science and how to consider
+that in the real estate uh sector and
+
+ align:start position:0%
+that in the real estate uh sector and
+ 
+
+ align:start position:0%
+that in the real estate uh sector and
+the second one taught by me also some
+
+ align:start position:0%
+the second one taught by me also some
+ 
+
+ align:start position:0%
+the second one taught by me also some
+Basics and techniques like the Apple to
+
+ align:start position:0%
+Basics and techniques like the Apple to
+ 
+
+ align:start position:0%
+Basics and techniques like the Apple to
+Apple comparison in the D setting how to
+
+ align:start position:0%
+Apple comparison in the D setting how to
+ 
+
+ align:start position:0%
+Apple comparison in the D setting how to
+quantify the impact of climate risk on
+
+ align:start position:0%
+quantify the impact of climate risk on
+ 
+
+ align:start position:0%
+quantify the impact of climate risk on
+uh on real say values but that for that
+
+ align:start position:0%
+uh on real say values but that for that
+ 
+
+ align:start position:0%
+uh on real say values but that for that
+one basically I I just stopped at the
+
+ align:start position:0%
+one basically I I just stopped at the
+ 
+
+ align:start position:0%
+one basically I I just stopped at the
+residential because I run out of time
+
+ align:start position:0%
+residential because I run out of time
+ 
+
+ align:start position:0%
+residential because I run out of time
+but today's lecture will be not like
+
+ align:start position:0%
+but today's lecture will be not like
+ 
+
+ align:start position:0%
+but today's lecture will be not like
+very like Basics it will be a lot of
+
+ align:start position:0%
+very like Basics it will be a lot of
+ 
+
+ align:start position:0%
+very like Basics it will be a lot of
+topical topical uh discussions because
+
+ align:start position:0%
+topical topical uh discussions because
+ 
+
+ align:start position:0%
+topical topical uh discussions because
+now this is such a new area it's such an
+
+ align:start position:0%
+now this is such a new area it's such an
+ 
+
+ align:start position:0%
+now this is such a new area it's such an
+emerging area no matter is in the
+
+ align:start position:0%
+emerging area no matter is in the
+ 
+
+ align:start position:0%
+emerging area no matter is in the
+industry like the mortgage like the
+
+ align:start position:0%
+industry like the mortgage like the
+ 
+
+ align:start position:0%
+industry like the mortgage like the
+banks all in Academia it's very new so
+
+ align:start position:0%
+banks all in Academia it's very new so
+ 
+
+ align:start position:0%
+banks all in Academia it's very new so
+it's not like very very established the
+
+ align:start position:0%
+it's not like very very established the
+ 
+
+ align:start position:0%
+it's not like very very established the
+theory of framework and
+
+ align:start position:0%
+theory of framework and
+ 
+
+ align:start position:0%
+theory of framework and
+methodologies to study this so today I
+
+ align:start position:0%
+methodologies to study this so today I
+ 
+
+ align:start position:0%
+methodologies to study this so today I
+will just touch on a few very Frontier
+
+ align:start position:0%
+will just touch on a few very Frontier
+ 
+
+ align:start position:0%
+will just touch on a few very Frontier
+topics now it's a lot of debate and
+
+ align:start position:0%
+topics now it's a lot of debate and
+ 
+
+ align:start position:0%
+topics now it's a lot of debate and
+parles and people don't know how to do
+
+ align:start position:0%
+parles and people don't know how to do
+ 
+
+ align:start position:0%
+parles and people don't know how to do
+and like that and I want to get your
+
+ align:start position:0%
+and like that and I want to get your
+ 
+
+ align:start position:0%
+and like that and I want to get your
+thoughts on this so for today's topics
+
+ align:start position:0%
+thoughts on this so for today's topics
+ 
+
+ align:start position:0%
+thoughts on this so for today's topics
+always we don't have a answer we don't
+
+ align:start position:0%
+always we don't have a answer we don't
+ 
+
+ align:start position:0%
+always we don't have a answer we don't
+have an answer it's not like the or the
+
+ align:start position:0%
+have an answer it's not like the or the
+ 
+
+ align:start position:0%
+have an answer it's not like the or the
+model and data things no answer but just
+
+ align:start position:0%
+model and data things no answer but just
+ 
+
+ align:start position:0%
+model and data things no answer but just
+put this things on the table for your
+
+ align:start position:0%
+put this things on the table for your
+ 
+
+ align:start position:0%
+put this things on the table for your
+consideration but also which means if
+
+ align:start position:0%
+consideration but also which means if
+ 
+
+ align:start position:0%
+consideration but also which means if
+you want to look into this maybe there
+
+ align:start position:0%
+you want to look into this maybe there
+ 
+
+ align:start position:0%
+you want to look into this maybe there
+will be very good opportunities for you
+
+ align:start position:0%
+will be very good opportunities for you
+ 
+
+ align:start position:0%
+will be very good opportunities for you
+no matter for your future jobs or your
+
+ align:start position:0%
+no matter for your future jobs or your
+ 
+
+ align:start position:0%
+no matter for your future jobs or your
+future research so that's for
+
+ align:start position:0%
+future research so that's for
+ 
+
+ align:start position:0%
+future research so that's for
+today so yes last time I spent a lot of
+
+ align:start position:0%
+today so yes last time I spent a lot of
+ 
+
+ align:start position:0%
+today so yes last time I spent a lot of
+time for you to understand the
+
+ align:start position:0%
+time for you to understand the
+ 
+
+ align:start position:0%
+time for you to understand the
+did so that we use the before and after
+
+ align:start position:0%
+did so that we use the before and after
+ 
+
+ align:start position:0%
+did so that we use the before and after
+Hurricane data to quantify before and
+
+ align:start position:0%
+Hurricane data to quantify before and
+ 
+
+ align:start position:0%
+Hurricane data to quantify before and
+after and also treatment group and
+
+ align:start position:0%
+after and also treatment group and
+ 
+
+ align:start position:0%
+after and also treatment group and
+control group to quantify the climate
+
+ align:start position:0%
+control group to quantify the climate
+ 
+
+ align:start position:0%
+control group to quantify the climate
+risk impact on uh residential real
+
+ align:start position:0%
+risk impact on uh residential real
+ 
+
+ align:start position:0%
+risk impact on uh residential real
+estate in the paper I mentioned the most
+
+ align:start position:0%
+estate in the paper I mentioned the most
+ 
+
+ align:start position:0%
+estate in the paper I mentioned the most
+and also in the reading list is a
+
+ align:start position:0%
+and also in the reading list is a
+ 
+
+ align:start position:0%
+and also in the reading list is a
+hurricane Sandy paper and New York City
+
+ align:start position:0%
+hurricane Sandy paper and New York City
+ 
+
+ align:start position:0%
+hurricane Sandy paper and New York City
+remember that and then for that paper
+
+ align:start position:0%
+remember that and then for that paper
+ 
+
+ align:start position:0%
+remember that and then for that paper
+that's they look at uh residential
+
+ align:start position:0%
+that's they look at uh residential
+ 
+
+ align:start position:0%
+that's they look at uh residential
+housing and then they quantify a
+
+ align:start position:0%
+housing and then they quantify a
+ 
+
+ align:start position:0%
+housing and then they quantify a
+long-term permanent price discount of 8%
+
+ align:start position:0%
+long-term permanent price discount of 8%
+ 
+
+ align:start position:0%
+long-term permanent price discount of 8%
+remember that's a hurricane candy and
+
+ align:start position:0%
+remember that's a hurricane candy and
+ 
+
+ align:start position:0%
+remember that's a hurricane candy and
+New York City and the 8% as permanent uh
+
+ align:start position:0%
+New York City and the 8% as permanent uh
+ 
+
+ align:start position:0%
+New York City and the 8% as permanent uh
+price discount after that and then there
+
+ align:start position:0%
+price discount after that and then there
+ 
+
+ align:start position:0%
+price discount after that and then there
+so many other papers also found similar
+
+ align:start position:0%
+so many other papers also found similar
+ 
+
+ align:start position:0%
+so many other papers also found similar
+results Miami and uh and also Texas all
+
+ align:start position:0%
+results Miami and uh and also Texas all
+ 
+
+ align:start position:0%
+results Miami and uh and also Texas all
+the things then we talk about okay now
+
+ align:start position:0%
+the things then we talk about okay now
+ 
+
+ align:start position:0%
+the things then we talk about okay now
+let's think about switch to commercial
+
+ align:start position:0%
+let's think about switch to commercial
+ 
+
+ align:start position:0%
+let's think about switch to commercial
+real estate not just the houses but
+
+ align:start position:0%
+real estate not just the houses but
+ 
+
+ align:start position:0%
+real estate not just the houses but
+commercial real estate office buildings
+
+ align:start position:0%
+commercial real estate office buildings
+ 
+
+ align:start position:0%
+commercial real estate office buildings
+shopping malls hotels and also
+
+ align:start position:0%
+shopping malls hotels and also
+ 
+
+ align:start position:0%
+shopping malls hotels and also
+Apartments so that's basically I want to
+
+ align:start position:0%
+Apartments so that's basically I want to
+ 
+
+ align:start position:0%
+Apartments so that's basically I want to
+use a few minutes to cover this but
+
+ align:start position:0%
+use a few minutes to cover this but
+ 
+
+ align:start position:0%
+use a few minutes to cover this but
+first of all I want you to think about
+
+ align:start position:0%
+first of all I want you to think about
+ 
+
+ align:start position:0%
+first of all I want you to think about
+tell me some your your thoughts about
+
+ align:start position:0%
+tell me some your your thoughts about
+ 
+
+ align:start position:0%
+tell me some your your thoughts about
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+difference why I have two separate
+
+ align:start position:0%
+difference why I have two separate
+ 
+
+ align:start position:0%
+difference why I have two separate
+separate uh subsections one is on
+
+ align:start position:0%
+separate uh subsections one is on
+ 
+
+ align:start position:0%
+separate uh subsections one is on
+Commercial uh one is on residential last
+
+ align:start position:0%
+Commercial uh one is on residential last
+ 
+
+ align:start position:0%
+Commercial uh one is on residential last
+time and the other you one commercial so
+
+ align:start position:0%
+time and the other you one commercial so
+ 
+
+ align:start position:0%
+time and the other you one commercial so
+because they share a lot of things when
+
+ align:start position:0%
+because they share a lot of things when
+ 
+
+ align:start position:0%
+because they share a lot of things when
+you think about hurricane and the
+
+ align:start position:0%
+you think about hurricane and the
+ 
+
+ align:start position:0%
+you think about hurricane and the
+flooding right and
+
+ align:start position:0%
+flooding right and
+ 
+
+ align:start position:0%
+flooding right and
+Wildfire all those uh climate events
+
+ align:start position:0%
+Wildfire all those uh climate events
+ 
+
+ align:start position:0%
+Wildfire all those uh climate events
+they will cause damage physical damage
+
+ align:start position:0%
+they will cause damage physical damage
+ 
+
+ align:start position:0%
+they will cause damage physical damage
+to the no matter which which kind of
+
+ align:start position:0%
+to the no matter which which kind of
+ 
+
+ align:start position:0%
+to the no matter which which kind of
+properties this buildings and then they
+
+ align:start position:0%
+properties this buildings and then they
+ 
+
+ align:start position:0%
+properties this buildings and then they
+may increase insurance cost and then if
+
+ align:start position:0%
+may increase insurance cost and then if
+ 
+
+ align:start position:0%
+may increase insurance cost and then if
+this place become so vulnerable people
+
+ align:start position:0%
+this place become so vulnerable people
+ 
+
+ align:start position:0%
+this place become so vulnerable people
+leave and auto decline so what these are
+
+ align:start position:0%
+leave and auto decline so what these are
+ 
+
+ align:start position:0%
+leave and auto decline so what these are
+common ground of commercial real estate
+
+ align:start position:0%
+common ground of commercial real estate
+ 
+
+ align:start position:0%
+common ground of commercial real estate
+and residential and what are the
+
+ align:start position:0%
+and residential and what are the
+ 
+
+ align:start position:0%
+and residential and what are the
+differences when you think
+
+ align:start position:0%
+differences when you think
+ 
+
+ align:start position:0%
+differences when you think
+about this um real uh climate climate
+
+ align:start position:0%
+about this um real uh climate climate
+ 
+
+ align:start position:0%
+about this um real uh climate climate
+impact do you have some ideas why we
+
+ align:start position:0%
+impact do you have some ideas why we
+ 
+
+ align:start position:0%
+impact do you have some ideas why we
+have this we we we we want to make this
+
+ align:start position:0%
+have this we we we we want to make this
+ 
+
+ align:start position:0%
+have this we we we we want to make this
+special for commercial real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State any songs all the things are the
+
+ align:start position:0%
+State any songs all the things are the
+ 
+
+ align:start position:0%
+State any songs all the things are the
+same if we use commercial we also get
+
+ align:start position:0%
+same if we use commercial we also get
+ 
+
+ align:start position:0%
+same if we use commercial we also get
+that result like 8% or something uh as a
+
+ align:start position:0%
+that result like 8% or something uh as a
+ 
+
+ align:start position:0%
+that result like 8% or something uh as a
+impact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+more language different language what
+
+ align:start position:0%
+more language different language what
+ 
+
+ align:start position:0%
+more language different language what
+kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+cont okay contract will be different yes
+
+ align:start position:0%
+cont okay contract will be different yes
+ 
+
+ align:start position:0%
+cont okay contract will be different yes
+but okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay that's also good but think
+
+ align:start position:0%
+well okay that's also good but think
+ 
+
+ align:start position:0%
+well okay that's also good but think
+about yes that's a that's a fundamental
+
+ align:start position:0%
+about yes that's a that's a fundamental
+ 
+
+ align:start position:0%
+about yes that's a that's a fundamental
+difference between commercial and the
+
+ align:start position:0%
+difference between commercial and the
+ 
+
+ align:start position:0%
+difference between commercial and the
+residential real estate but let's link
+
+ align:start position:0%
+residential real estate but let's link
+ 
+
+ align:start position:0%
+residential real estate but let's link
+to climate risks think about climate
+
+ align:start position:0%
+to climate risks think about climate
+ 
+
+ align:start position:0%
+to climate risks think about climate
+risks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+night when people are sleeping okay good
+
+ align:start position:0%
+night when people are sleeping okay good
+ 
+
+ align:start position:0%
+night when people are sleeping okay good
+and what else yes please so commercial
+
+ align:start position:0%
+and what else yes please so commercial
+ 
+
+ align:start position:0%
+and what else yes please so commercial
+they tend to be on the ground floor so
+
+ align:start position:0%
+they tend to be on the ground floor so
+ 
+
+ align:start position:0%
+they tend to be on the ground floor so
+they might be more impacted if there's
+
+ align:start position:0%
+they might be more impacted if there's
+ 
+
+ align:start position:0%
+they might be more impacted if there's
+happening where resal there that can be
+
+ align:start position:0%
+happening where resal there that can be
+ 
+
+ align:start position:0%
+happening where resal there that can be
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+impacted okay good so all those are I
+
+ align:start position:0%
+impacted okay good so all those are I
+ 
+
+ align:start position:0%
+impacted okay good so all those are I
+are very good what uh valid factors of
+
+ align:start position:0%
+are very good what uh valid factors of
+ 
+
+ align:start position:0%
+are very good what uh valid factors of
+the commercial real estate versus
+
+ align:start position:0%
+the commercial real estate versus
+ 
+
+ align:start position:0%
+the commercial real estate versus
+residential and let's think about how
+
+ align:start position:0%
+residential and let's think about how
+ 
+
+ align:start position:0%
+residential and let's think about how
+people will feel because last lecture
+
+ align:start position:0%
+people will feel because last lecture
+ 
+
+ align:start position:0%
+people will feel because last lecture
+remember I talk about belief I talk
+
+ align:start position:0%
+remember I talk about belief I talk
+ 
+
+ align:start position:0%
+remember I talk about belief I talk
+about whether people really believe in
+
+ align:start position:0%
+about whether people really believe in
+ 
+
+ align:start position:0%
+about whether people really believe in
+climate risk or not and then what do you
+
+ align:start position:0%
+climate risk or not and then what do you
+ 
+
+ align:start position:0%
+climate risk or not and then what do you
+think if we compare this common
+
+ align:start position:0%
+think if we compare this common
+ 
+
+ align:start position:0%
+think if we compare this common
+households like us Common People of
+
+ align:start position:0%
+households like us Common People of
+ 
+
+ align:start position:0%
+households like us Common People of
+course in this classroom we have a we
+
+ align:start position:0%
+course in this classroom we have a we
+ 
+
+ align:start position:0%
+course in this classroom we have a we
+have a stronger belief and we are more
+
+ align:start position:0%
+have a stronger belief and we are more
+ 
+
+ align:start position:0%
+have a stronger belief and we are more
+sophisticated in term of the climate
+
+ align:start position:0%
+sophisticated in term of the climate
+ 
+
+ align:start position:0%
+sophisticated in term of the climate
+knowledge because we are educated by MIT
+
+ align:start position:0%
+knowledge because we are educated by MIT
+ 
+
+ align:start position:0%
+knowledge because we are educated by MIT
+but think about common people residents
+
+ align:start position:0%
+but think about common people residents
+ 
+
+ align:start position:0%
+but think about common people residents
+versus commercial real EST estate owners
+
+ align:start position:0%
+versus commercial real EST estate owners
+ 
+
+ align:start position:0%
+versus commercial real EST estate owners
+what do you think on average who will
+
+ align:start position:0%
+what do you think on average who will
+ 
+
+ align:start position:0%
+what do you think on average who will
+believe more about climate
+
+ align:start position:0%
+believe more about climate
+ 
+
+ align:start position:0%
+believe more about climate
+risk and understand more I guess is the
+
+ align:start position:0%
+risk and understand more I guess is the
+ 
+
+ align:start position:0%
+risk and understand more I guess is the
+residential um only because commercial
+
+ align:start position:0%
+residential um only because commercial
+ 
+
+ align:start position:0%
+residential um only because commercial
+real estate owners are more worried
+
+ align:start position:0%
+real estate owners are more worried
+ 
+
+ align:start position:0%
+real estate owners are more worried
+about the bottom line and worried about
+
+ align:start position:0%
+about the bottom line and worried about
+ 
+
+ align:start position:0%
+about the bottom line and worried about
+the financials which
+
+ align:start position:0%
+the financials which
+ 
+
+ align:start position:0%
+the financials which
+RK yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay they they care more about the
+
+ align:start position:0%
+okay they they care more about the
+ 
+
+ align:start position:0%
+okay they they care more about the
+financial value and that matters a lot
+
+ align:start position:0%
+financial value and that matters a lot
+ 
+
+ align:start position:0%
+financial value and that matters a lot
+and the bottom line right for resal
+
+ align:start position:0%
+and the bottom line right for resal
+ 
+
+ align:start position:0%
+and the bottom line right for resal
+anyway you have your own house you need
+
+ align:start position:0%
+anyway you have your own house you need
+ 
+
+ align:start position:0%
+anyway you have your own house you need
+to live there and you get flooded then
+
+ align:start position:0%
+to live there and you get flooded then
+ 
+
+ align:start position:0%
+to live there and you get flooded then
+you need to find our way okay so so we
+
+ align:start position:0%
+you need to find our way okay so so we
+ 
+
+ align:start position:0%
+you need to find our way okay so so we
+have three major differences here I want
+
+ align:start position:0%
+have three major differences here I want
+ 
+
+ align:start position:0%
+have three major differences here I want
+to highlight of course also all the
+
+ align:start position:0%
+to highlight of course also all the
+ 
+
+ align:start position:0%
+to highlight of course also all the
+factors you mentioned just not also
+
+ align:start position:0%
+factors you mentioned just not also
+ 
+
+ align:start position:0%
+factors you mentioned just not also
+valid but most most important thing from
+
+ align:start position:0%
+valid but most most important thing from
+ 
+
+ align:start position:0%
+valid but most most important thing from
+the literature or from all the all the
+
+ align:start position:0%
+the literature or from all the all the
+ 
+
+ align:start position:0%
+the literature or from all the all the
+industry is that first commercial real
+
+ align:start position:0%
+industry is that first commercial real
+ 
+
+ align:start position:0%
+industry is that first commercial real
+estate C it's not our own C it's a
+
+ align:start position:0%
+estate C it's not our own C it's a
+ 
+
+ align:start position:0%
+estate C it's not our own C it's a
+commercial real estate also C first more
+
+ align:start position:0%
+commercial real estate also C first more
+ 
+
+ align:start position:0%
+commercial real estate also C first more
+sophisticated investors there's a big
+
+ align:start position:0%
+sophisticated investors there's a big
+ 
+
+ align:start position:0%
+sophisticated investors there's a big
+survey 2020 to start a how this for the
+
+ align:start position:0%
+survey 2020 to start a how this for the
+ 
+
+ align:start position:0%
+survey 2020 to start a how this for the
+institutional investors because the
+
+ align:start position:0%
+institutional investors because the
+ 
+
+ align:start position:0%
+institutional investors because the
+commercial real estate always owned by
+
+ align:start position:0%
+commercial real estate always owned by
+ 
+
+ align:start position:0%
+commercial real estate always owned by
+big guys like black rock and all these
+
+ align:start position:0%
+big guys like black rock and all these
+ 
+
+ align:start position:0%
+big guys like black rock and all these
+uh uh Boston properties race and the big
+
+ align:start position:0%
+uh uh Boston properties race and the big
+ 
+
+ align:start position:0%
+uh uh Boston properties race and the big
+big asset management companies
+
+ align:start position:0%
+big asset management companies
+ 
+
+ align:start position:0%
+big asset management companies
+those institutional investors the senior
+
+ align:start position:0%
+those institutional investors the senior
+ 
+
+ align:start position:0%
+those institutional investors the senior
+managers they this survey and found that
+
+ align:start position:0%
+managers they this survey and found that
+ 
+
+ align:start position:0%
+managers they this survey and found that
+this 439 Executives they understand more
+
+ align:start position:0%
+this 439 Executives they understand more
+ 
+
+ align:start position:0%
+this 439 Executives they understand more
+because this is more relevant to their
+
+ align:start position:0%
+because this is more relevant to their
+ 
+
+ align:start position:0%
+because this is more relevant to their
+daily business their bottom line so they
+
+ align:start position:0%
+daily business their bottom line so they
+ 
+
+ align:start position:0%
+daily business their bottom line so they
+they understand more about climate risk
+
+ align:start position:0%
+they understand more about climate risk
+ 
+
+ align:start position:0%
+they understand more about climate risk
+and also they have a team they have the
+
+ align:start position:0%
+and also they have a team they have the
+ 
+
+ align:start position:0%
+and also they have a team they have the
+research department they have a team of
+
+ align:start position:0%
+research department they have a team of
+ 
+
+ align:start position:0%
+research department they have a team of
+MIT graduates and doing the modeling and
+
+ align:start position:0%
+MIT graduates and doing the modeling and
+ 
+
+ align:start position:0%
+MIT graduates and doing the modeling and
+all the work so they are more
+
+ align:start position:0%
+all the work so they are more
+ 
+
+ align:start position:0%
+all the work so they are more
+sophisticated they understand more so
+
+ align:start position:0%
+sophisticated they understand more so
+ 
+
+ align:start position:0%
+sophisticated they understand more so
+that's why you'll see all the all the
+
+ align:start position:0%
+that's why you'll see all the all the
+ 
+
+ align:start position:0%
+that's why you'll see all the all the
+highlights on the media not they they
+
+ align:start position:0%
+highlights on the media not they they
+ 
+
+ align:start position:0%
+highlights on the media not they they
+want to understand how they can respond
+
+ align:start position:0%
+want to understand how they can respond
+ 
+
+ align:start position:0%
+want to understand how they can respond
+to the climate risk to cities to to your
+
+ align:start position:0%
+to the climate risk to cities to to your
+ 
+
+ align:start position:0%
+to the climate risk to cities to to your
+portfolio and to your
+
+ align:start position:0%
+portfolio and to your
+ 
+
+ align:start position:0%
+portfolio and to your
+assets secondly the more important thing
+
+ align:start position:0%
+assets secondly the more important thing
+ 
+
+ align:start position:0%
+assets secondly the more important thing
+is they are big they always because they
+
+ align:start position:0%
+is they are big they always because they
+ 
+
+ align:start position:0%
+is they are big they always because they
+are big because they are big so they
+
+ align:start position:0%
+are big because they are big so they
+ 
+
+ align:start position:0%
+are big because they are big so they
+have the capacity to hire people to St
+
+ align:start position:0%
+have the capacity to hire people to St
+ 
+
+ align:start position:0%
+have the capacity to hire people to St
+hire researchers to study this they are
+
+ align:start position:0%
+hire researchers to study this they are
+ 
+
+ align:start position:0%
+hire researchers to study this they are
+big so they worry about their coroporate
+
+ align:start position:0%
+big so they worry about their coroporate
+ 
+
+ align:start position:0%
+big so they worry about their coroporate
+image and uh and and also also many of
+
+ align:start position:0%
+image and uh and and also also many of
+ 
+
+ align:start position:0%
+image and uh and and also also many of
+them then Black Rock they are
+
+ align:start position:0%
+them then Black Rock they are
+ 
+
+ align:start position:0%
+them then Black Rock they are
+fiduciaries so they have the huge
+
+ align:start position:0%
+fiduciaries so they have the huge
+ 
+
+ align:start position:0%
+fiduciaries so they have the huge
+responsibility for the small investors
+
+ align:start position:0%
+responsibility for the small investors
+ 
+
+ align:start position:0%
+responsibility for the small investors
+behind them give money to them to invest
+
+ align:start position:0%
+behind them give money to them to invest
+ 
+
+ align:start position:0%
+behind them give money to them to invest
+so then no matter is a social
+
+ align:start position:0%
+so then no matter is a social
+ 
+
+ align:start position:0%
+so then no matter is a social
+responsibility or their own interest
+
+ align:start position:0%
+responsibility or their own interest
+ 
+
+ align:start position:0%
+responsibility or their own interest
+they need to stand up and say we are
+
+ align:start position:0%
+they need to stand up and say we are
+ 
+
+ align:start position:0%
+they need to stand up and say we are
+responsible we we need to address this
+
+ align:start position:0%
+responsible we we need to address this
+ 
+
+ align:start position:0%
+responsible we we need to address this
+we need to put high standard on
+
+ align:start position:0%
+we need to put high standard on
+ 
+
+ align:start position:0%
+we need to put high standard on
+ourselves so that's the that's the
+
+ align:start position:0%
+ourselves so that's the that's the
+ 
+
+ align:start position:0%
+ourselves so that's the that's the
+second reason that you will find
+
+ align:start position:0%
+second reason that you will find
+ 
+
+ align:start position:0%
+second reason that you will find
+actually the commercial real sector will
+
+ align:start position:0%
+actually the commercial real sector will
+ 
+
+ align:start position:0%
+actually the commercial real sector will
+respond faster and earlier to climbing
+
+ align:start position:0%
+respond faster and earlier to climbing
+ 
+
+ align:start position:0%
+respond faster and earlier to climbing
+risk because they are big they have a
+
+ align:start position:0%
+risk because they are big they have a
+ 
+
+ align:start position:0%
+risk because they are big they have a
+capacity and they care about their face
+
+ align:start position:0%
+capacity and they care about their face
+ 
+
+ align:start position:0%
+capacity and they care about their face
+that's a put a simple word care about
+
+ align:start position:0%
+that's a put a simple word care about
+ 
+
+ align:start position:0%
+that's a put a simple word care about
+their face and uh and that's so
+
+ align:start position:0%
+their face and uh and that's so
+ 
+
+ align:start position:0%
+their face and uh and that's so
+important for them if they say I don't
+
+ align:start position:0%
+important for them if they say I don't
+ 
+
+ align:start position:0%
+important for them if they say I don't
+care then underlying all the small
+
+ align:start position:0%
+care then underlying all the small
+ 
+
+ align:start position:0%
+care then underlying all the small
+investors behind them they will they
+
+ align:start position:0%
+investors behind them they will they
+ 
+
+ align:start position:0%
+investors behind them they will they
+will not give money to them the third
+
+ align:start position:0%
+will not give money to them the third
+ 
+
+ align:start position:0%
+will not give money to them the third
+Factor also very important is also
+
+ align:start position:0%
+Factor also very important is also
+ 
+
+ align:start position:0%
+Factor also very important is also
+because they are big I always get to
+
+ align:start position:0%
+because they are big I always get to
+ 
+
+ align:start position:0%
+because they are big I always get to
+this they are big see they are big so
+
+ align:start position:0%
+this they are big see they are big so
+ 
+
+ align:start position:0%
+this they are big see they are big so
+they are always easily targeted by The
+
+ align:start position:0%
+they are always easily targeted by The
+ 
+
+ align:start position:0%
+they are always easily targeted by The
+Regulators like at
+
+ align:start position:0%
+Regulators like at
+ 
+
+ align:start position:0%
+Regulators like at
+Goldie before you came to MIT right
+
+ align:start position:0%
+Goldie before you came to MIT right
+ 
+
+ align:start position:0%
+Goldie before you came to MIT right
+regulators and also the Mayors the City
+
+ align:start position:0%
+regulators and also the Mayors the City
+ 
+
+ align:start position:0%
+regulators and also the Mayors the City
+Mayors as I mentioned all the City
+
+ align:start position:0%
+Mayors as I mentioned all the City
+ 
+
+ align:start position:0%
+Mayors as I mentioned all the City
+Mayors all the all the state Governors
+
+ align:start position:0%
+Mayors all the all the state Governors
+ 
+
+ align:start position:0%
+Mayors all the all the state Governors
+they all pledge 20 30 20 40 2050 not
+
+ align:start position:0%
+they all pledge 20 30 20 40 2050 not
+ 
+
+ align:start position:0%
+they all pledge 20 30 20 40 2050 not
+zero and then after they pledge after
+
+ align:start position:0%
+zero and then after they pledge after
+ 
+
+ align:start position:0%
+zero and then after they pledge after
+they talk to the media and then they
+
+ align:start position:0%
+they talk to the media and then they
+ 
+
+ align:start position:0%
+they talk to the media and then they
+come back to office they say how can I
+
+ align:start position:0%
+come back to office they say how can I
+ 
+
+ align:start position:0%
+come back to office they say how can I
+achieve that and then they start to
+
+ align:start position:0%
+achieve that and then they start to
+ 
+
+ align:start position:0%
+achieve that and then they start to
+Target at this big guys because they for
+
+ align:start position:0%
+Target at this big guys because they for
+ 
+
+ align:start position:0%
+Target at this big guys because they for
+example New York City for example Boston
+
+ align:start position:0%
+example New York City for example Boston
+ 
+
+ align:start position:0%
+example New York City for example Boston
+for those big cities the commercial real
+
+ align:start position:0%
+for those big cities the commercial real
+ 
+
+ align:start position:0%
+for those big cities the commercial real
+estate actually is is majority of the
+
+ align:start position:0%
+estate actually is is majority of the
+ 
+
+ align:start position:0%
+estate actually is is majority of the
+total energy use for the building centor
+
+ align:start position:0%
+total energy use for the building centor
+ 
+
+ align:start position:0%
+total energy use for the building centor
+because they highrise buildings downtown
+
+ align:start position:0%
+because they highrise buildings downtown
+ 
+
+ align:start position:0%
+because they highrise buildings downtown
+all the area so they say you must do
+
+ align:start position:0%
+all the area so they say you must do
+ 
+
+ align:start position:0%
+all the area so they say you must do
+this and that you must meet my cap of
+
+ align:start position:0%
+this and that you must meet my cap of
+ 
+
+ align:start position:0%
+this and that you must meet my cap of
+the carbon if you don't meet you pay the
+
+ align:start position:0%
+the carbon if you don't meet you pay the
+ 
+
+ align:start position:0%
+the carbon if you don't meet you pay the
+penalty you must renovate your buildings
+
+ align:start position:0%
+penalty you must renovate your buildings
+ 
+
+ align:start position:0%
+penalty you must renovate your buildings
+and also easier for them to control
+
+ align:start position:0%
+and also easier for them to control
+ 
+
+ align:start position:0%
+and also easier for them to control
+because they are big they are so so so
+
+ align:start position:0%
+because they are big they are so so so
+ 
+
+ align:start position:0%
+because they are big they are so so so
+visible so and they are rich so they
+
+ align:start position:0%
+visible so and they are rich so they
+ 
+
+ align:start position:0%
+visible so and they are rich so they
+target this they won't Target as a small
+
+ align:start position:0%
+target this they won't Target as a small
+ 
+
+ align:start position:0%
+target this they won't Target as a small
+household and they're poor and then
+
+ align:start position:0%
+household and they're poor and then
+ 
+
+ align:start position:0%
+household and they're poor and then
+become like a a housing affordability
+
+ align:start position:0%
+become like a a housing affordability
+ 
+
+ align:start position:0%
+become like a a housing affordability
+problem all the problem so Target as a
+
+ align:start position:0%
+problem all the problem so Target as a
+ 
+
+ align:start position:0%
+problem all the problem so Target as a
+rich guys speak so that's why commercial
+
+ align:start position:0%
+rich guys speak so that's why commercial
+ 
+
+ align:start position:0%
+rich guys speak so that's why commercial
+real estate really really is responding
+
+ align:start position:0%
+real estate really really is responding
+ 
+
+ align:start position:0%
+real estate really really is responding
+relatively fast faster than the
+
+ align:start position:0%
+relatively fast faster than the
+ 
+
+ align:start position:0%
+relatively fast faster than the
+residential households
+
+ align:start position:0%
+residential households
+ 
+
+ align:start position:0%
+residential households
+and this is a reading I highly recommend
+
+ align:start position:0%
+and this is a reading I highly recommend
+ 
+
+ align:start position:0%
+and this is a reading I highly recommend
+you to read that's in our reading list
+
+ align:start position:0%
+you to read that's in our reading list
+ 
+
+ align:start position:0%
+you to read that's in our reading list
+this report this actually a survey uh a
+
+ align:start position:0%
+this report this actually a survey uh a
+ 
+
+ align:start position:0%
+this report this actually a survey uh a
+literat review and Analysis of the
+
+ align:start position:0%
+literat review and Analysis of the
+ 
+
+ align:start position:0%
+literat review and Analysis of the
+literature uh and there um James Clayton
+
+ align:start position:0%
+literature uh and there um James Clayton
+ 
+
+ align:start position:0%
+literature uh and there um James Clayton
+a very good professor and they started
+
+ align:start position:0%
+a very good professor and they started
+ 
+
+ align:start position:0%
+a very good professor and they started
+this they started they review so many
+
+ align:start position:0%
+this they started they review so many
+ 
+
+ align:start position:0%
+this they started they review so many
+papers then they gave us a very good
+
+ align:start position:0%
+papers then they gave us a very good
+ 
+
+ align:start position:0%
+papers then they gave us a very good
+framework to understand the commercial
+
+ align:start position:0%
+framework to understand the commercial
+ 
+
+ align:start position:0%
+framework to understand the commercial
+rules the owners the impact of that uh
+
+ align:start position:0%
+rules the owners the impact of that uh
+ 
+
+ align:start position:0%
+rules the owners the impact of that uh
+climate on that so I I put us a person
+
+ align:start position:0%
+climate on that so I I put us a person
+ 
+
+ align:start position:0%
+climate on that so I I put us a person
+here this is the owner of the commercial
+
+ align:start position:0%
+here this is the owner of the commercial
+ 
+
+ align:start position:0%
+here this is the owner of the commercial
+real estate and then you can see they
+
+ align:start position:0%
+real estate and then you can see they
+ 
+
+ align:start position:0%
+real estate and then you can see they
+summarize into three major channels
+
+ align:start position:0%
+summarize into three major channels
+ 
+
+ align:start position:0%
+summarize into three major channels
+three major channels and then you have
+
+ align:start position:0%
+three major channels and then you have
+ 
+
+ align:start position:0%
+three major channels and then you have
+many many small channels right so the
+
+ align:start position:0%
+many many small channels right so the
+ 
+
+ align:start position:0%
+many many small channels right so the
+first channel is effect on cash flow so
+
+ align:start position:0%
+first channel is effect on cash flow so
+ 
+
+ align:start position:0%
+first channel is effect on cash flow so
+that's a commercial real estate this is
+
+ align:start position:0%
+that's a commercial real estate this is
+ 
+
+ align:start position:0%
+that's a commercial real estate this is
+owner right the owner own this
+
+ align:start position:0%
+owner right the owner own this
+ 
+
+ align:start position:0%
+owner right the owner own this
+commercial real estate then you have the
+
+ align:start position:0%
+commercial real estate then you have the
+ 
+
+ align:start position:0%
+commercial real estate then you have the
+rental income like that that's Office
+
+ align:start position:0%
+rental income like that that's Office
+ 
+
+ align:start position:0%
+rental income like that that's Office
+Buildings and then you know that if
+
+ align:start position:0%
+Buildings and then you know that if
+ 
+
+ align:start position:0%
+Buildings and then you know that if
+later will become flooded and and a
+
+ align:start position:0%
+later will become flooded and and a
+ 
+
+ align:start position:0%
+later will become flooded and and a
+wifire and you you cannot get uh you
+
+ align:start position:0%
+wifire and you you cannot get uh you
+ 
+
+ align:start position:0%
+wifire and you you cannot get uh you
+cannot get talant then you lose either
+
+ align:start position:0%
+cannot get talant then you lose either
+ 
+
+ align:start position:0%
+cannot get talant then you lose either
+this physical damage to your building or
+
+ align:start position:0%
+this physical damage to your building or
+ 
+
+ align:start position:0%
+this physical damage to your building or
+you just lose talant because you are in
+
+ align:start position:0%
+you just lose talant because you are in
+ 
+
+ align:start position:0%
+you just lose talant because you are in
+such a bad location and reduce income so
+
+ align:start position:0%
+such a bad location and reduce income so
+ 
+
+ align:start position:0%
+such a bad location and reduce income so
+that's a cash flow effect then you say
+
+ align:start position:0%
+that's a cash flow effect then you say
+ 
+
+ align:start position:0%
+that's a cash flow effect then you say
+income and all things so that's one one
+
+ align:start position:0%
+income and all things so that's one one
+ 
+
+ align:start position:0%
+income and all things so that's one one
+channel and another channel is increased
+
+ align:start position:0%
+channel and another channel is increased
+ 
+
+ align:start position:0%
+channel and another channel is increased
+uh increased cost cost right that's
+
+ align:start position:0%
+uh increased cost cost right that's
+ 
+
+ align:start position:0%
+uh increased cost cost right that's
+that's this one oh these two are
+
+ align:start position:0%
+that's this one oh these two are
+ 
+
+ align:start position:0%
+that's this one oh these two are
+together with the cash flow so income
+
+ align:start position:0%
+together with the cash flow so income
+ 
+
+ align:start position:0%
+together with the cash flow so income
+reduce and the cost increase because you
+
+ align:start position:0%
+reduce and the cost increase because you
+ 
+
+ align:start position:0%
+reduce and the cost increase because you
+need to do renovation you need to do all
+
+ align:start position:0%
+need to do renovation you need to do all
+ 
+
+ align:start position:0%
+need to do renovation you need to do all
+the residency investment all the things
+
+ align:start position:0%
+the residency investment all the things
+ 
+
+ align:start position:0%
+the residency investment all the things
+to to elevate your flow and all change
+
+ align:start position:0%
+to to elevate your flow and all change
+ 
+
+ align:start position:0%
+to to elevate your flow and all change
+all the systems so that's a lot of cost
+
+ align:start position:0%
+all the systems so that's a lot of cost
+ 
+
+ align:start position:0%
+all the systems so that's a lot of cost
+so that's this effect on cash flow
+
+ align:start position:0%
+so that's this effect on cash flow
+ 
+
+ align:start position:0%
+so that's this effect on cash flow
+anyway it's so negative it's become uh
+
+ align:start position:0%
+anyway it's so negative it's become uh
+ 
+
+ align:start position:0%
+anyway it's so negative it's become uh
+smaller and
+
+ align:start position:0%
+smaller and
+ 
+
+ align:start position:0%
+smaller and
+smaller and the higher discount rate
+
+ align:start position:0%
+smaller and the higher discount rate
+ 
+
+ align:start position:0%
+smaller and the higher discount rate
+right that's that's because is such a
+
+ align:start position:0%
+right that's that's because is such a
+ 
+
+ align:start position:0%
+right that's that's because is such a
+high risk think about future this cash
+
+ align:start position:0%
+high risk think about future this cash
+ 
+
+ align:start position:0%
+high risk think about future this cash
+flow is now for now if you are in a
+
+ align:start position:0%
+flow is now for now if you are in a
+ 
+
+ align:start position:0%
+flow is now for now if you are in a
+flooding flood zone and unfortunately
+
+ align:start position:0%
+flooding flood zone and unfortunately
+ 
+
+ align:start position:0%
+flooding flood zone and unfortunately
+got flooded right so that's for now but
+
+ align:start position:0%
+got flooded right so that's for now but
+ 
+
+ align:start position:0%
+got flooded right so that's for now but
+think about the future next 20 years 50
+
+ align:start position:0%
+think about the future next 20 years 50
+ 
+
+ align:start position:0%
+think about the future next 20 years 50
+years so then because the risk is so
+
+ align:start position:0%
+years so then because the risk is so
+ 
+
+ align:start position:0%
+years so then because the risk is so
+clear and the climate sent public report
+
+ align:start position:0%
+clear and the climate sent public report
+ 
+
+ align:start position:0%
+clear and the climate sent public report
+and and all the things then the expected
+
+ align:start position:0%
+and and all the things then the expected
+ 
+
+ align:start position:0%
+and and all the things then the expected
+growth is so low and risk premium so
+
+ align:start position:0%
+growth is so low and risk premium so
+ 
+
+ align:start position:0%
+growth is so low and risk premium so
+high anyway then you will have a higher
+
+ align:start position:0%
+high anyway then you will have a higher
+ 
+
+ align:start position:0%
+high anyway then you will have a higher
+discount rate so that's another say will
+
+ align:start position:0%
+discount rate so that's another say will
+ 
+
+ align:start position:0%
+discount rate so that's another say will
+damage the
+
+ align:start position:0%
+damage the
+ 
+
+ align:start position:0%
+damage the
+value finally very hard for you to get
+
+ align:start position:0%
+value finally very hard for you to get
+ 
+
+ align:start position:0%
+value finally very hard for you to get
+financing that's financing yeah you go
+
+ align:start position:0%
+financing that's financing yeah you go
+ 
+
+ align:start position:0%
+financing that's financing yeah you go
+to the banks you go you go to the equity
+
+ align:start position:0%
+to the banks you go you go to the equity
+ 
+
+ align:start position:0%
+to the banks you go you go to the equity
+Market sorry your building in such a
+
+ align:start position:0%
+Market sorry your building in such a
+ 
+
+ align:start position:0%
+Market sorry your building in such a
+vulnerable location the future RIS is so
+
+ align:start position:0%
+vulnerable location the future RIS is so
+ 
+
+ align:start position:0%
+vulnerable location the future RIS is so
+high and so many hurricanes H this area
+
+ align:start position:0%
+high and so many hurricanes H this area
+ 
+
+ align:start position:0%
+high and so many hurricanes H this area
+we cannot lend money to you or we will
+
+ align:start position:0%
+we cannot lend money to you or we will
+ 
+
+ align:start position:0%
+we cannot lend money to you or we will
+charge you a very high cost of capital
+
+ align:start position:0%
+charge you a very high cost of capital
+ 
+
+ align:start position:0%
+charge you a very high cost of capital
+so then this a higher C cost uh cost of
+
+ align:start position:0%
+so then this a higher C cost uh cost of
+ 
+
+ align:start position:0%
+so then this a higher C cost uh cost of
+capital and for this I say after midterm
+
+ align:start position:0%
+capital and for this I say after midterm
+ 
+
+ align:start position:0%
+capital and for this I say after midterm
+I will discuss more about this but
+
+ align:start position:0%
+I will discuss more about this but
+ 
+
+ align:start position:0%
+I will discuss more about this but
+anyway you know these three big channels
+
+ align:start position:0%
+anyway you know these three big channels
+ 
+
+ align:start position:0%
+anyway you know these three big channels
+cash flow decrease for now future risk
+
+ align:start position:0%
+cash flow decrease for now future risk
+ 
+
+ align:start position:0%
+cash flow decrease for now future risk
+higher discount rate and hard to get
+
+ align:start position:0%
+higher discount rate and hard to get
+ 
+
+ align:start position:0%
+higher discount rate and hard to get
+financing so that's all bad news and the
+
+ align:start position:0%
+financing so that's all bad news and the
+ 
+
+ align:start position:0%
+financing so that's all bad news and the
+commercial real estate price must go
+
+ align:start position:0%
+commercial real estate price must go
+ 
+
+ align:start position:0%
+commercial real estate price must go
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+so so that's that's the that's a basic
+
+ align:start position:0%
+so so that's that's the that's a basic
+ 
+
+ align:start position:0%
+so so that's that's the that's a basic
+idea any questions
+
+ align:start position:0%
+idea any questions
+ 
+
+ align:start position:0%
+idea any questions
+here any I think it's not like
+
+ align:start position:0%
+here any I think it's not like
+ 
+
+ align:start position:0%
+here any I think it's not like
+definitely I need to say all the topic I
+
+ align:start position:0%
+definitely I need to say all the topic I
+ 
+
+ align:start position:0%
+definitely I need to say all the topic I
+talk today it's just some some
+
+ align:start position:0%
+talk today it's just some some
+ 
+
+ align:start position:0%
+talk today it's just some some
+discussions now the very Frontier
+
+ align:start position:0%
+discussions now the very Frontier
+ 
+
+ align:start position:0%
+discussions now the very Frontier
+discussions in this industry and in in
+
+ align:start position:0%
+discussions in this industry and in in
+ 
+
+ align:start position:0%
+discussions in this industry and in in
+the Academia so although we have this
+
+ align:start position:0%
+the Academia so although we have this
+ 
+
+ align:start position:0%
+the Academia so although we have this
+kind of preliminary framework to
+
+ align:start position:0%
+kind of preliminary framework to
+ 
+
+ align:start position:0%
+kind of preliminary framework to
+understand but you don't take this for
+
+ align:start position:0%
+understand but you don't take this for
+ 
+
+ align:start position:0%
+understand but you don't take this for
+granted say oh of of course they will be
+
+ align:start position:0%
+granted say oh of of course they will be
+ 
+
+ align:start position:0%
+granted say oh of of course they will be
+all happened together no for example our
+
+ align:start position:0%
+all happened together no for example our
+ 
+
+ align:start position:0%
+all happened together no for example our
+own bill weon Professor Bill weon and
+
+ align:start position:0%
+own bill weon Professor Bill weon and
+ 
+
+ align:start position:0%
+own bill weon Professor Bill weon and
+he's doing a research he's doing a
+
+ align:start position:0%
+he's doing a research he's doing a
+ 
+
+ align:start position:0%
+he's doing a research he's doing a
+research I think in Florida or Miami
+
+ align:start position:0%
+research I think in Florida or Miami
+ 
+
+ align:start position:0%
+research I think in Florida or Miami
+anyway so he he is using the data from
+
+ align:start position:0%
+anyway so he he is using the data from
+ 
+
+ align:start position:0%
+anyway so he he is using the data from
+the apartment to do that research and
+
+ align:start position:0%
+the apartment to do that research and
+ 
+
+ align:start position:0%
+the apartment to do that research and
+then he found out
+
+ align:start position:0%
+then he found out
+ 
+
+ align:start position:0%
+then he found out
+preliminarily this cash flow didn't
+
+ align:start position:0%
+preliminarily this cash flow didn't
+ 
+
+ align:start position:0%
+preliminarily this cash flow didn't
+change that much he compared Apple to
+
+ align:start position:0%
+change that much he compared Apple to
+ 
+
+ align:start position:0%
+change that much he compared Apple to
+Apple some apartments in the flat zone
+
+ align:start position:0%
+Apple some apartments in the flat zone
+ 
+
+ align:start position:0%
+Apple some apartments in the flat zone
+some apartment outside of flone then he
+
+ align:start position:0%
+some apartment outside of flone then he
+ 
+
+ align:start position:0%
+some apartment outside of flone then he
+compared cash flow not significant
+
+ align:start position:0%
+compared cash flow not significant
+ 
+
+ align:start position:0%
+compared cash flow not significant
+different people still want to live
+
+ align:start position:0%
+different people still want to live
+ 
+
+ align:start position:0%
+different people still want to live
+there people still want to tendon still
+
+ align:start position:0%
+there people still want to tendon still
+ 
+
+ align:start position:0%
+there people still want to tendon still
+want to leave in those places however
+
+ align:start position:0%
+want to leave in those places however
+ 
+
+ align:start position:0%
+want to leave in those places however
+they found a big discount rate increase
+
+ align:start position:0%
+they found a big discount rate increase
+ 
+
+ align:start position:0%
+they found a big discount rate increase
+for those areas because investors they
+
+ align:start position:0%
+for those areas because investors they
+ 
+
+ align:start position:0%
+for those areas because investors they
+understand the investor they understand
+
+ align:start position:0%
+understand the investor they understand
+ 
+
+ align:start position:0%
+understand the investor they understand
+for the long run there may be a risk so
+
+ align:start position:0%
+for the long run there may be a risk so
+ 
+
+ align:start position:0%
+for the long run there may be a risk so
+the cap rate increase but the onlyi
+
+ align:start position:0%
+the cap rate increase but the onlyi
+ 
+
+ align:start position:0%
+the cap rate increase but the onlyi
+doesn't change so that's noi and cap
+
+ align:start position:0%
+doesn't change so that's noi and cap
+ 
+
+ align:start position:0%
+doesn't change so that's noi and cap
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+remember from your R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Finance so this is the value right so
+
+ align:start position:0%
+Finance so this is the value right so
+ 
+
+ align:start position:0%
+Finance so this is the value right so
+for uh be this is empirical study this
+
+ align:start position:0%
+for uh be this is empirical study this
+ 
+
+ align:start position:0%
+for uh be this is empirical study this
+one same this one going up because the
+
+ align:start position:0%
+one same this one going up because the
+ 
+
+ align:start position:0%
+one same this one going up because the
+risk premium and he argued that for the
+
+ align:start position:0%
+risk premium and he argued that for the
+ 
+
+ align:start position:0%
+risk premium and he argued that for the
+tenants they only consider short run
+
+ align:start position:0%
+tenants they only consider short run
+ 
+
+ align:start position:0%
+tenants they only consider short run
+they are now considering like next 10
+
+ align:start position:0%
+they are now considering like next 10
+ 
+
+ align:start position:0%
+they are now considering like next 10
+years 20 years no problem we're going to
+
+ align:start position:0%
+years 20 years no problem we're going to
+ 
+
+ align:start position:0%
+years 20 years no problem we're going to
+still uh run these apartments so that's
+
+ align:start position:0%
+still uh run these apartments so that's
+ 
+
+ align:start position:0%
+still uh run these apartments so that's
+fun and investors worried they are
+
+ align:start position:0%
+fun and investors worried they are
+ 
+
+ align:start position:0%
+fun and investors worried they are
+thinking about they holding period of 20
+
+ align:start position:0%
+thinking about they holding period of 20
+ 
+
+ align:start position:0%
+thinking about they holding period of 20
+5050 years so they worried so I just
+
+ align:start position:0%
+5050 years so they worried so I just
+ 
+
+ align:start position:0%
+5050 years so they worried so I just
+give you one example to say not all the
+
+ align:start position:0%
+give you one example to say not all the
+ 
+
+ align:start position:0%
+give you one example to say not all the
+three channels immed happen and for all
+
+ align:start position:0%
+three channels immed happen and for all
+ 
+
+ align:start position:0%
+three channels immed happen and for all
+the places for all the commercial real
+
+ align:start position:0%
+the places for all the commercial real
+ 
+
+ align:start position:0%
+the places for all the commercial real
+estate some happen here some happen
+
+ align:start position:0%
+estate some happen here some happen
+ 
+
+ align:start position:0%
+estate some happen here some happen
+there some happens in other places which
+
+ align:start position:0%
+there some happens in other places which
+ 
+
+ align:start position:0%
+there some happens in other places which
+means we need more research and now I'm
+
+ align:start position:0%
+means we need more research and now I'm
+ 
+
+ align:start position:0%
+means we need more research and now I'm
+going to introduce our research so
+
+ align:start position:0%
+going to introduce our research so
+ 
+
+ align:start position:0%
+going to introduce our research so
+today's lecture you will see I I I
+
+ align:start position:0%
+today's lecture you will see I I I
+ 
+
+ align:start position:0%
+today's lecture you will see I I I
+impose many many questions and if you're
+
+ align:start position:0%
+impose many many questions and if you're
+ 
+
+ align:start position:0%
+impose many many questions and if you're
+interested say we just had our uh C CIS
+
+ align:start position:0%
+interested say we just had our uh C CIS
+ 
+
+ align:start position:0%
+interested say we just had our uh C CIS
+prep right to discuss topics if you are
+
+ align:start position:0%
+prep right to discuss topics if you are
+ 
+
+ align:start position:0%
+prep right to discuss topics if you are
+interest in some of the topics come to
+
+ align:start position:0%
+interest in some of the topics come to
+ 
+
+ align:start position:0%
+interest in some of the topics come to
+me we can discuss how to do thesis
+
+ align:start position:0%
+me we can discuss how to do thesis
+ 
+
+ align:start position:0%
+me we can discuss how to do thesis
+together to look into these
+
+ align:start position:0%
+together to look into these
+ 
+
+ align:start position:0%
+together to look into these
+topics and one thing I want to say is
+
+ align:start position:0%
+topics and one thing I want to say is
+ 
+
+ align:start position:0%
+topics and one thing I want to say is
+this very interesting thing maybe we can
+
+ align:start position:0%
+this very interesting thing maybe we can
+ 
+
+ align:start position:0%
+this very interesting thing maybe we can
+do thises together last last session
+
+ align:start position:0%
+do thises together last last session
+ 
+
+ align:start position:0%
+do thises together last last session
+Moody came right moodies analytics uh uh
+
+ align:start position:0%
+Moody came right moodies analytics uh uh
+ 
+
+ align:start position:0%
+Moody came right moodies analytics uh uh
+Kevin Kevin fungan came and he gave us a
+
+ align:start position:0%
+Kevin Kevin fungan came and he gave us a
+ 
+
+ align:start position:0%
+Kevin Kevin fungan came and he gave us a
+very good lecture on how moodies
+
+ align:start position:0%
+very good lecture on how moodies
+ 
+
+ align:start position:0%
+very good lecture on how moodies
+analytics their their research
+
+ align:start position:0%
+analytics their their research
+ 
+
+ align:start position:0%
+analytics their their research
+Department are doing this climate risk
+
+ align:start position:0%
+Department are doing this climate risk
+ 
+
+ align:start position:0%
+Department are doing this climate risk
+modeling and I just uh still I I I I
+
+ align:start position:0%
+modeling and I just uh still I I I I
+ 
+
+ align:start position:0%
+modeling and I just uh still I I I I
+stole this two two slide decks from from
+
+ align:start position:0%
+stole this two two slide decks from from
+ 
+
+ align:start position:0%
+stole this two two slide decks from from
+his two slides with from his uh lecture
+
+ align:start position:0%
+his two slides with from his uh lecture
+ 
+
+ align:start position:0%
+his two slides with from his uh lecture
+remember he said then I asked him
+
+ align:start position:0%
+remember he said then I asked him
+ 
+
+ align:start position:0%
+remember he said then I asked him
+actually so moodies you are doing this
+
+ align:start position:0%
+actually so moodies you are doing this
+ 
+
+ align:start position:0%
+actually so moodies you are doing this
+and how we can contribute because we are
+
+ align:start position:0%
+and how we can contribute because we are
+ 
+
+ align:start position:0%
+and how we can contribute because we are
+not talking about research collaboration
+
+ align:start position:0%
+not talking about research collaboration
+ 
+
+ align:start position:0%
+not talking about research collaboration
+and he gave us all the data of the
+
+ align:start position:0%
+and he gave us all the data of the
+ 
+
+ align:start position:0%
+and he gave us all the data of the
+climate risk indexes for all the
+
+ align:start position:0%
+climate risk indexes for all the
+ 
+
+ align:start position:0%
+climate risk indexes for all the
+locations in the United States and also
+
+ align:start position:0%
+locations in the United States and also
+ 
+
+ align:start position:0%
+locations in the United States and also
+commercial real estate transaction data
+
+ align:start position:0%
+commercial real estate transaction data
+ 
+
+ align:start position:0%
+commercial real estate transaction data
+that's their expertise they they become
+
+ align:start position:0%
+that's their expertise they they become
+ 
+
+ align:start position:0%
+that's their expertise they they become
+a member of my my climate uh research
+
+ align:start position:0%
+a member of my my climate uh research
+ 
+
+ align:start position:0%
+a member of my my climate uh research
+team and then they say okay and and from
+
+ align:start position:0%
+team and then they say okay and and from
+ 
+
+ align:start position:0%
+team and then they say okay and and from
+K you know their idea is
+
+ align:start position:0%
+K you know their idea is
+ 
+
+ align:start position:0%
+K you know their idea is
+following they will first get some
+
+ align:start position:0%
+following they will first get some
+ 
+
+ align:start position:0%
+following they will first get some
+literature they also do literary review
+
+ align:start position:0%
+literature they also do literary review
+ 
+
+ align:start position:0%
+literature they also do literary review
+then they they got this uh disaster
+
+ align:start position:0%
+then they they got this uh disaster
+ 
+
+ align:start position:0%
+then they they got this uh disaster
+impact derived from empirical analysis
+
+ align:start position:0%
+impact derived from empirical analysis
+ 
+
+ align:start position:0%
+impact derived from empirical analysis
+see here so they they are not doing this
+
+ align:start position:0%
+see here so they they are not doing this
+ 
+
+ align:start position:0%
+see here so they they are not doing this
+empirical did work by themselves instead
+
+ align:start position:0%
+empirical did work by themselves instead
+ 
+
+ align:start position:0%
+empirical did work by themselves instead
+they are they are looking at papers and
+
+ align:start position:0%
+they are they are looking at papers and
+ 
+
+ align:start position:0%
+they are they are looking at papers and
+they try to get papers to justify to
+
+ align:start position:0%
+they try to get papers to justify to
+ 
+
+ align:start position:0%
+they try to get papers to justify to
+find this parameter as given so that's
+
+ align:start position:0%
+find this parameter as given so that's
+ 
+
+ align:start position:0%
+find this parameter as given so that's
+moodies I think they are now using like
+
+ align:start position:0%
+moodies I think they are now using like
+ 
+
+ align:start position:0%
+moodies I think they are now using like
+7% for commercial real estate or
+
+ align:start position:0%
+7% for commercial real estate or
+ 
+
+ align:start position:0%
+7% for commercial real estate or
+something I remember but anyway they
+
+ align:start position:0%
+something I remember but anyway they
+ 
+
+ align:start position:0%
+something I remember but anyway they
+reveal some many many papers they got
+
+ align:start position:0%
+reveal some many many papers they got
+ 
+
+ align:start position:0%
+reveal some many many papers they got
+this coefficient they're not doing this
+
+ align:start position:0%
+this coefficient they're not doing this
+ 
+
+ align:start position:0%
+this coefficient they're not doing this
+work and then they have their
+
+ align:start position:0%
+work and then they have their
+ 
+
+ align:start position:0%
+work and then they have their
+engineering model of the event
+
+ align:start position:0%
+engineering model of the event
+ 
+
+ align:start position:0%
+engineering model of the event
+likelihood or next five years next 10
+
+ align:start position:0%
+likelihood or next five years next 10
+ 
+
+ align:start position:0%
+likelihood or next five years next 10
+years what's the likelihood of a
+
+ align:start position:0%
+years what's the likelihood of a
+ 
+
+ align:start position:0%
+years what's the likelihood of a
+flooding in this area Wi-Fi is
+
+ align:start position:0%
+flooding in this area Wi-Fi is
+ 
+
+ align:start position:0%
+flooding in this area Wi-Fi is
+flooding and and then they combine them
+
+ align:start position:0%
+flooding and and then they combine them
+ 
+
+ align:start position:0%
+flooding and and then they combine them
+together so this likelihood times the
+
+ align:start position:0%
+together so this likelihood times the
+ 
+
+ align:start position:0%
+together so this likelihood times the
+damage that will be the damage to the
+
+ align:start position:0%
+damage that will be the damage to the
+ 
+
+ align:start position:0%
+damage that will be the damage to the
+cash flow to the cap rate and then they
+
+ align:start position:0%
+cash flow to the cap rate and then they
+ 
+
+ align:start position:0%
+cash flow to the cap rate and then they
+they they derive to model noi they they
+
+ align:start position:0%
+they they derive to model noi they they
+ 
+
+ align:start position:0%
+they they derive to model noi they they
+model this so basically they have this
+
+ align:start position:0%
+model this so basically they have this
+ 
+
+ align:start position:0%
+model this so basically they have this
+um from a literature literature if
+
+ align:start position:0%
+um from a literature literature if
+ 
+
+ align:start position:0%
+um from a literature literature if
+there's event and the and and the impact
+
+ align:start position:0%
+there's event and the and and the impact
+ 
+
+ align:start position:0%
+there's event and the and and the impact
+is x% of the discount times
+
+ align:start position:0%
+is x% of the discount times
+ 
+
+ align:start position:0%
+is x% of the discount times
+the likelihood likelihood I think they
+
+ align:start position:0%
+the likelihood likelihood I think they
+ 
+
+ align:start position:0%
+the likelihood likelihood I think they
+have a inhouse team to do this
+
+ align:start position:0%
+have a inhouse team to do this
+ 
+
+ align:start position:0%
+have a inhouse team to do this
+engineering model and then impact Oni
+
+ align:start position:0%
+engineering model and then impact Oni
+ 
+
+ align:start position:0%
+engineering model and then impact Oni
+they have scenario
+
+ align:start position:0%
+they have scenario
+ 
+
+ align:start position:0%
+they have scenario
+analysis then they have all for the
+
+ align:start position:0%
+analysis then they have all for the
+ 
+
+ align:start position:0%
+analysis then they have all for the
+future of thei then they estimate the uh
+
+ align:start position:0%
+future of thei then they estimate the uh
+ 
+
+ align:start position:0%
+future of thei then they estimate the uh
+as lost impact on their properties and
+
+ align:start position:0%
+as lost impact on their properties and
+ 
+
+ align:start position:0%
+as lost impact on their properties and
+all the loans of the banks so that's
+
+ align:start position:0%
+all the loans of the banks so that's
+ 
+
+ align:start position:0%
+all the loans of the banks so that's
+their model so then we discuss how we
+
+ align:start position:0%
+their model so then we discuss how we
+ 
+
+ align:start position:0%
+their model so then we discuss how we
+work together how we work together here
+
+ align:start position:0%
+work together how we work together here
+ 
+
+ align:start position:0%
+work together how we work together here
+we say
+
+ align:start position:0%
+we say
+ 
+
+ align:start position:0%
+we say
+next one is our C expertise because we
+
+ align:start position:0%
+next one is our C expertise because we
+ 
+
+ align:start position:0%
+next one is our C expertise because we
+are not going to just grab a number from
+
+ align:start position:0%
+are not going to just grab a number from
+ 
+
+ align:start position:0%
+are not going to just grab a number from
+other papers because those papers are so
+
+ align:start position:0%
+other papers because those papers are so
+ 
+
+ align:start position:0%
+other papers because those papers are so
+they have different data sample they
+
+ align:start position:0%
+they have different data sample they
+ 
+
+ align:start position:0%
+they have different data sample they
+have different contact they have
+
+ align:start position:0%
+have different contact they have
+ 
+
+ align:start position:0%
+have different contact they have
+different uh this uh this uh research
+
+ align:start position:0%
+different uh this uh this uh research
+ 
+
+ align:start position:0%
+different uh this uh this uh research
+research methodology we cannot just grab
+
+ align:start position:0%
+research methodology we cannot just grab
+ 
+
+ align:start position:0%
+research methodology we cannot just grab
+a 7% or 8% to the literature then we
+
+ align:start position:0%
+a 7% or 8% to the literature then we
+ 
+
+ align:start position:0%
+a 7% or 8% to the literature then we
+just multiply with the engineering model
+
+ align:start position:0%
+just multiply with the engineering model
+ 
+
+ align:start position:0%
+just multiply with the engineering model
+instead we will do a very good sorrow
+
+ align:start position:0%
+instead we will do a very good sorrow
+ 
+
+ align:start position:0%
+instead we will do a very good sorrow
+analysis of the real empirical that's
+
+ align:start position:0%
+analysis of the real empirical that's
+ 
+
+ align:start position:0%
+analysis of the real empirical that's
+our expertise
+
+ align:start position:0%
+our expertise
+ 
+
+ align:start position:0%
+our expertise
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then MIT has climate scientists we have
+
+ align:start position:0%
+then MIT has climate scientists we have
+ 
+
+ align:start position:0%
+then MIT has climate scientists we have
+the global climate Research Center or
+
+ align:start position:0%
+the global climate Research Center or
+ 
+
+ align:start position:0%
+the global climate Research Center or
+something and uh also another climate
+
+ align:start position:0%
+something and uh also another climate
+ 
+
+ align:start position:0%
+something and uh also another climate
+and cl uh uh sustainability consumption
+
+ align:start position:0%
+and cl uh uh sustainability consumption
+ 
+
+ align:start position:0%
+and cl uh uh sustainability consumption
+so that's from engineering school from
+
+ align:start position:0%
+so that's from engineering school from
+ 
+
+ align:start position:0%
+so that's from engineering school from
+all the all the engineering school then
+
+ align:start position:0%
+all the all the engineering school then
+ 
+
+ align:start position:0%
+all the all the engineering school then
+we have a better model many many people
+
+ align:start position:0%
+we have a better model many many people
+ 
+
+ align:start position:0%
+we have a better model many many people
+are now doing the modeling we have the
+
+ align:start position:0%
+are now doing the modeling we have the
+ 
+
+ align:start position:0%
+are now doing the modeling we have the
+likelihood combine these two then we
+
+ align:start position:0%
+likelihood combine these two then we
+ 
+
+ align:start position:0%
+likelihood combine these two then we
+should have a better model to
+
+ align:start position:0%
+should have a better model to
+ 
+
+ align:start position:0%
+should have a better model to
+predict forecast the impact of the noi
+
+ align:start position:0%
+predict forecast the impact of the noi
+ 
+
+ align:start position:0%
+predict forecast the impact of the noi
+better than this and the C said yes
+
+ align:start position:0%
+better than this and the C said yes
+ 
+
+ align:start position:0%
+better than this and the C said yes
+that's exactly what we need from MIT so
+
+ align:start position:0%
+that's exactly what we need from MIT so
+ 
+
+ align:start position:0%
+that's exactly what we need from MIT so
+that's basically how you can see MIT and
+
+ align:start position:0%
+that's basically how you can see MIT and
+ 
+
+ align:start position:0%
+that's basically how you can see MIT and
+this uh this kind of consultancy work
+
+ align:start position:0%
+this uh this kind of consultancy work
+ 
+
+ align:start position:0%
+this uh this kind of consultancy work
+together to improve the methodology of
+
+ align:start position:0%
+together to improve the methodology of
+ 
+
+ align:start position:0%
+together to improve the methodology of
+the how to quantify the uh climate risk
+
+ align:start position:0%
+the how to quantify the uh climate risk
+ 
+
+ align:start position:0%
+the how to quantify the uh climate risk
+on real estate if you are interested in
+
+ align:start position:0%
+on real estate if you are interested in
+ 
+
+ align:start position:0%
+on real estate if you are interested in
+this part or how you translate this into
+
+ align:start position:0%
+this part or how you translate this into
+ 
+
+ align:start position:0%
+this part or how you translate this into
+this part I think that will'll be very
+
+ align:start position:0%
+this part I think that will'll be very
+ 
+
+ align:start position:0%
+this part I think that will'll be very
+good thesis topic so then you can you
+
+ align:start position:0%
+good thesis topic so then you can you
+ 
+
+ align:start position:0%
+good thesis topic so then you can you
+can talk to me and we can help even we
+
+ align:start position:0%
+can talk to me and we can help even we
+ 
+
+ align:start position:0%
+can talk to me and we can help even we
+can as I mentioned we can do a
+
+ align:start position:0%
+can as I mentioned we can do a
+ 
+
+ align:start position:0%
+can as I mentioned we can do a
+collaboration and you can be the CIS and
+
+ align:start position:0%
+collaboration and you can be the CIS and
+ 
+
+ align:start position:0%
+collaboration and you can be the CIS and
+the gly with smothies you can jly with
+
+ align:start position:0%
+the gly with smothies you can jly with
+ 
+
+ align:start position:0%
+the gly with smothies you can jly with
+smothies and uh and us so that you get
+
+ align:start position:0%
+smothies and uh and us so that you get
+ 
+
+ align:start position:0%
+smothies and uh and us so that you get
+some exposure to that maybe later this
+
+ align:start position:0%
+some exposure to that maybe later this
+ 
+
+ align:start position:0%
+some exposure to that maybe later this
+will help your your your your
+
+ align:start position:0%
+will help your your your your
+ 
+
+ align:start position:0%
+will help your your your your
+job okay give you a very very a little
+
+ align:start position:0%
+job okay give you a very very a little
+ 
+
+ align:start position:0%
+job okay give you a very very a little
+bit flavor of what we are doing this
+
+ align:start position:0%
+bit flavor of what we are doing this
+ 
+
+ align:start position:0%
+bit flavor of what we are doing this
+this because this I have my colleagues
+
+ align:start position:0%
+this because this I have my colleagues
+ 
+
+ align:start position:0%
+this because this I have my colleagues
+from engine in school they are doing
+
+ align:start position:0%
+from engine in school they are doing
+ 
+
+ align:start position:0%
+from engine in school they are doing
+this for this we are doing okay so this
+
+ align:start position:0%
+this for this we are doing okay so this
+ 
+
+ align:start position:0%
+this for this we are doing okay so this
+is a a small flavor of this that's my
+
+ align:start position:0%
+is a a small flavor of this that's my
+ 
+
+ align:start position:0%
+is a a small flavor of this that's my
+research we are not doing very soon will
+
+ align:start position:0%
+research we are not doing very soon will
+ 
+
+ align:start position:0%
+research we are not doing very soon will
+come out as a paper so hurricane is
+
+ align:start position:0%
+come out as a paper so hurricane is
+ 
+
+ align:start position:0%
+come out as a paper so hurricane is
+commercial real estate so you we
+
+ align:start position:0%
+commercial real estate so you we
+ 
+
+ align:start position:0%
+commercial real estate so you we
+understand so our point is to estimate
+
+ align:start position:0%
+understand so our point is to estimate
+ 
+
+ align:start position:0%
+understand so our point is to estimate
+X this is our purpose of this paper so
+
+ align:start position:0%
+X this is our purpose of this paper so
+ 
+
+ align:start position:0%
+X this is our purpose of this paper so
+we look at this uh we look at this uh
+
+ align:start position:0%
+we look at this uh we look at this uh
+ 
+
+ align:start position:0%
+we look at this uh we look at this uh
+hurricanes as the then we got data and
+
+ align:start position:0%
+hurricanes as the then we got data and
+ 
+
+ align:start position:0%
+hurricanes as the then we got data and
+we got this uh commercial R transaction
+
+ align:start position:0%
+we got this uh commercial R transaction
+ 
+
+ align:start position:0%
+we got this uh commercial R transaction
+from RCA RCA is our also collaborator
+
+ align:start position:0%
+from RCA RCA is our also collaborator
+ 
+
+ align:start position:0%
+from RCA RCA is our also collaborator
+they give us all data then we look at
+
+ align:start position:0%
+they give us all data then we look at
+ 
+
+ align:start position:0%
+they give us all data then we look at
+Hurricane Sandy from New York and
+
+ align:start position:0%
+Hurricane Sandy from New York and
+ 
+
+ align:start position:0%
+Hurricane Sandy from New York and
+hurricane Harve from Texas so these two
+
+ align:start position:0%
+hurricane Harve from Texas so these two
+ 
+
+ align:start position:0%
+hurricane Harve from Texas so these two
+before and after five years because I'm
+
+ align:start position:0%
+before and after five years because I'm
+ 
+
+ align:start position:0%
+before and after five years because I'm
+going to use D difference in differences
+
+ align:start position:0%
+going to use D difference in differences
+ 
+
+ align:start position:0%
+going to use D difference in differences
+so we got data from them and then we
+
+ align:start position:0%
+so we got data from them and then we
+ 
+
+ align:start position:0%
+so we got data from them and then we
+have all this hyic hyic regression
+
+ align:start position:0%
+have all this hyic hyic regression
+ 
+
+ align:start position:0%
+have all this hyic hyic regression
+variables all of things and most
+
+ align:start position:0%
+variables all of things and most
+ 
+
+ align:start position:0%
+variables all of things and most
+importantly the RC data this is
+
+ align:start position:0%
+importantly the RC data this is
+ 
+
+ align:start position:0%
+importantly the RC data this is
+commercial real different from the
+
+ align:start position:0%
+commercial real different from the
+ 
+
+ align:start position:0%
+commercial real different from the
+residential I'm not going to do a
+
+ align:start position:0%
+residential I'm not going to do a
+ 
+
+ align:start position:0%
+residential I'm not going to do a
+residential because there so many papers
+
+ align:start position:0%
+residential because there so many papers
+ 
+
+ align:start position:0%
+residential because there so many papers
+already on residential so that's why I
+
+ align:start position:0%
+already on residential so that's why I
+ 
+
+ align:start position:0%
+already on residential so that's why I
+chose to do commercial for the
+
+ align:start position:0%
+chose to do commercial for the
+ 
+
+ align:start position:0%
+chose to do commercial for the
+commercial and uh and the good thing is
+
+ align:start position:0%
+commercial and uh and the good thing is
+ 
+
+ align:start position:0%
+commercial and uh and the good thing is
+for that data set we even know who are
+
+ align:start position:0%
+for that data set we even know who are
+ 
+
+ align:start position:0%
+for that data set we even know who are
+the buyers and who are sellers of this
+
+ align:start position:0%
+the buyers and who are sellers of this
+ 
+
+ align:start position:0%
+the buyers and who are sellers of this
+big uh commercial buildings then we can
+
+ align:start position:0%
+big uh commercial buildings then we can
+ 
+
+ align:start position:0%
+big uh commercial buildings then we can
+de out the buyer and seller uh
+
+ align:start position:0%
+de out the buyer and seller uh
+ 
+
+ align:start position:0%
+de out the buyer and seller uh
+attributes whether they are they are uh
+
+ align:start position:0%
+attributes whether they are they are uh
+ 
+
+ align:start position:0%
+attributes whether they are they are uh
+National institutional or they local or
+
+ align:start position:0%
+National institutional or they local or
+ 
+
+ align:start position:0%
+National institutional or they local or
+whether small that and even their
+
+ align:start position:0%
+whether small that and even their
+ 
+
+ align:start position:0%
+whether small that and even their
+beliefs whether they believe in climate
+
+ align:start position:0%
+beliefs whether they believe in climate
+ 
+
+ align:start position:0%
+beliefs whether they believe in climate
+change so then we have 10,000
+
+ align:start position:0%
+change so then we have 10,000
+ 
+
+ align:start position:0%
+change so then we have 10,000
+transactions in New York City and 15,000
+
+ align:start position:0%
+transactions in New York City and 15,000
+ 
+
+ align:start position:0%
+transactions in New York City and 15,000
+in Texas uh not in New York City New
+
+ align:start position:0%
+in Texas uh not in New York City New
+ 
+
+ align:start position:0%
+in Texas uh not in New York City New
+York
+
+ align:start position:0%
+York
+ 
+
+ align:start position:0%
+York
+State then I'm not going to do this but
+
+ align:start position:0%
+State then I'm not going to do this but
+ 
+
+ align:start position:0%
+State then I'm not going to do this but
+you can see this is very for familiar if
+
+ align:start position:0%
+you can see this is very for familiar if
+ 
+
+ align:start position:0%
+you can see this is very for familiar if
+you still remember what I taugh last
+
+ align:start position:0%
+you still remember what I taugh last
+ 
+
+ align:start position:0%
+you still remember what I taugh last
+session of the did right this is the
+
+ align:start position:0%
+session of the did right this is the
+ 
+
+ align:start position:0%
+session of the did right this is the
+price transaction price and this is uh
+
+ align:start position:0%
+price transaction price and this is uh
+ 
+
+ align:start position:0%
+price transaction price and this is uh
+did this is the interaction term of the
+
+ align:start position:0%
+did this is the interaction term of the
+ 
+
+ align:start position:0%
+did this is the interaction term of the
+Serge is a damage is a search damy or
+
+ align:start position:0%
+Serge is a damage is a search damy or
+ 
+
+ align:start position:0%
+Serge is a damage is a search damy or
+it's a lower damage medium high damage
+
+ align:start position:0%
+it's a lower damage medium high damage
+ 
+
+ align:start position:0%
+it's a lower damage medium high damage
+like that and this be up after post and
+
+ align:start position:0%
+like that and this be up after post and
+ 
+
+ align:start position:0%
+like that and this be up after post and
+then we we do all the things then we
+
+ align:start position:0%
+then we we do all the things then we
+ 
+
+ align:start position:0%
+then we we do all the things then we
+quantify this is our Baseline model what
+
+ align:start position:0%
+quantify this is our Baseline model what
+ 
+
+ align:start position:0%
+quantify this is our Baseline model what
+quantif find the impact of this
+
+ align:start position:0%
+quantif find the impact of this
+ 
+
+ align:start position:0%
+quantif find the impact of this
+hurricane on the commercial realate and
+
+ align:start position:0%
+hurricane on the commercial realate and
+ 
+
+ align:start position:0%
+hurricane on the commercial realate and
+you will see in Texas it's like because
+
+ align:start position:0%
+you will see in Texas it's like because
+ 
+
+ align:start position:0%
+you will see in Texas it's like because
+it's in lock
+
+ align:start position:0%
+it's in lock
+ 
+
+ align:start position:0%
+it's in lock
+3.5% decrease after after H har and for
+
+ align:start position:0%
+3.5% decrease after after H har and for
+ 
+
+ align:start position:0%
+3.5% decrease after after H har and for
+New York City is 1.5 decrease after har
+
+ align:start position:0%
+New York City is 1.5 decrease after har
+ 
+
+ align:start position:0%
+New York City is 1.5 decrease after har
+in Sandy so I'm not sure this is
+
+ align:start position:0%
+in Sandy so I'm not sure this is
+ 
+
+ align:start position:0%
+in Sandy so I'm not sure this is
+universally uh applicable to others but
+
+ align:start position:0%
+universally uh applicable to others but
+ 
+
+ align:start position:0%
+universally uh applicable to others but
+that's our data set of the commercial
+
+ align:start position:0%
+that's our data set of the commercial
+ 
+
+ align:start position:0%
+that's our data set of the commercial
+real estate then we quantify the impact
+
+ align:start position:0%
+real estate then we quantify the impact
+ 
+
+ align:start position:0%
+real estate then we quantify the impact
+based on mood's model if they want to
+
+ align:start position:0%
+based on mood's model if they want to
+ 
+
+ align:start position:0%
+based on mood's model if they want to
+use us our result they will grab this
+
+ align:start position:0%
+use us our result they will grab this
+ 
+
+ align:start position:0%
+use us our result they will grab this
+coefficient this
+
+ align:start position:0%
+coefficient this
+ 
+
+ align:start position:0%
+coefficient this
+coefficient to their model and multiply
+
+ align:start position:0%
+coefficient to their model and multiply
+ 
+
+ align:start position:0%
+coefficient to their model and multiply
+this with their likelihood and
+
+ align:start position:0%
+this with their likelihood and
+ 
+
+ align:start position:0%
+this with their likelihood and
+engineering model so that's our
+
+ align:start position:0%
+engineering model so that's our
+ 
+
+ align:start position:0%
+engineering model so that's our
+contribution to to the
+
+ align:start position:0%
+contribution to to the
+ 
+
+ align:start position:0%
+contribution to to the
+moodies okay and then you will see why
+
+ align:start position:0%
+moodies okay and then you will see why
+ 
+
+ align:start position:0%
+moodies okay and then you will see why
+is this small why if New York state is
+
+ align:start position:0%
+is this small why if New York state is
+ 
+
+ align:start position:0%
+is this small why if New York state is
+even smaller any sound on
+
+ align:start position:0%
+even smaller any sound on
+ 
+
+ align:start position:0%
+even smaller any sound on
+this why it's not like 10% or 15% where
+
+ align:start position:0%
+this why it's not like 10% or 15% where
+ 
+
+ align:start position:0%
+this why it's not like 10% or 15% where
+it's like 3.5 of course it's can we it's
+
+ align:start position:0%
+it's like 3.5 of course it's can we it's
+ 
+
+ align:start position:0%
+it's like 3.5 of course it's can we it's
+a very random number but do you have any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea to just Define this number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+songs no so you will just accept any
+
+ align:start position:0%
+songs no so you will just accept any
+ 
+
+ align:start position:0%
+songs no so you will just accept any
+number I gave
+
+ align:start position:0%
+number I gave
+ 
+
+ align:start position:0%
+number I gave
+you is all right later if you go to
+
+ align:start position:0%
+you is all right later if you go to
+ 
+
+ align:start position:0%
+you is all right later if you go to
+moodies to do work and we collaborate
+
+ align:start position:0%
+moodies to do work and we collaborate
+ 
+
+ align:start position:0%
+moodies to do work and we collaborate
+then I will give you a number and you
+
+ align:start position:0%
+then I will give you a number and you
+ 
+
+ align:start position:0%
+then I will give you a number and you
+will believe with
+
+ align:start position:0%
+will believe with
+ 
+
+ align:start position:0%
+will believe with
+me I have two ideas first one is we know
+
+ align:start position:0%
+me I have two ideas first one is we know
+ 
+
+ align:start position:0%
+me I have two ideas first one is we know
+that New York City is doing a lot of
+
+ align:start position:0%
+that New York City is doing a lot of
+ 
+
+ align:start position:0%
+that New York City is doing a lot of
+actions on building a wall to protect
+
+ align:start position:0%
+actions on building a wall to protect
+ 
+
+ align:start position:0%
+actions on building a wall to protect
+the city from climber risk and the
+
+ align:start position:0%
+the city from climber risk and the
+ 
+
+ align:start position:0%
+the city from climber risk and the
+second fact
+
+ align:start position:0%
+second fact
+ 
+
+ align:start position:0%
+second fact
+that City housing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more hous Market the price tend to stay
+
+ align:start position:0%
+more hous Market the price tend to stay
+ 
+
+ align:start position:0%
+more hous Market the price tend to stay
+higher okay very good I think that's two
+
+ align:start position:0%
+higher okay very good I think that's two
+ 
+
+ align:start position:0%
+higher okay very good I think that's two
+factors very valid and very good so but
+
+ align:start position:0%
+factors very valid and very good so but
+ 
+
+ align:start position:0%
+factors very valid and very good so but
+I also want to add another thing is a is
+
+ align:start position:0%
+I also want to add another thing is a is
+ 
+
+ align:start position:0%
+I also want to add another thing is a is
+is the information so information the
+
+ align:start position:0%
+is the information so information the
+ 
+
+ align:start position:0%
+is the information so information the
+new news this hurricane is a is a bad
+
+ align:start position:0%
+new news this hurricane is a is a bad
+ 
+
+ align:start position:0%
+new news this hurricane is a is a bad
+news right it's a piece of bad news
+
+ align:start position:0%
+news right it's a piece of bad news
+ 
+
+ align:start position:0%
+news right it's a piece of bad news
+shock and whether it's shock is old news
+
+ align:start position:0%
+shock and whether it's shock is old news
+ 
+
+ align:start position:0%
+shock and whether it's shock is old news
+or new news right so the thing
+
+ align:start position:0%
+or new news right so the thing
+ 
+
+ align:start position:0%
+or new news right so the thing
+is we we look at actually you know this
+
+ align:start position:0%
+is we we look at actually you know this
+ 
+
+ align:start position:0%
+is we we look at actually you know this
+uh FEMA they did a very bad job of the
+
+ align:start position:0%
+uh FEMA they did a very bad job of the
+ 
+
+ align:start position:0%
+uh FEMA they did a very bad job of the
+flly Zone they they give the flly Zone
+
+ align:start position:0%
+flly Zone they they give the flly Zone
+ 
+
+ align:start position:0%
+flly Zone they they give the flly Zone
+say this is the flood zone uh flone
+
+ align:start position:0%
+say this is the flood zone uh flone
+ 
+
+ align:start position:0%
+say this is the flood zone uh flone
+means 100 Year this 1% every year
+
+ align:start position:0%
+means 100 Year this 1% every year
+ 
+
+ align:start position:0%
+means 100 Year this 1% every year
+likelihood of get flooded 1% FL Zone
+
+ align:start position:0%
+likelihood of get flooded 1% FL Zone
+ 
+
+ align:start position:0%
+likelihood of get flooded 1% FL Zone
+that's a FL F said this is FL and then
+
+ align:start position:0%
+that's a FL F said this is FL and then
+ 
+
+ align:start position:0%
+that's a FL F said this is FL and then
+all the people especially for the is
+
+ align:start position:0%
+all the people especially for the is
+ 
+
+ align:start position:0%
+all the people especially for the is
+sophisticated investors they understand
+
+ align:start position:0%
+sophisticated investors they understand
+ 
+
+ align:start position:0%
+sophisticated investors they understand
+a lot about flooding and climate risk
+
+ align:start position:0%
+a lot about flooding and climate risk
+ 
+
+ align:start position:0%
+a lot about flooding and climate risk
+they understand if this building is in
+
+ align:start position:0%
+they understand if this building is in
+ 
+
+ align:start position:0%
+they understand if this building is in
+flly Z then very dangerous very risky if
+
+ align:start position:0%
+flly Z then very dangerous very risky if
+ 
+
+ align:start position:0%
+flly Z then very dangerous very risky if
+the building is outside flly Z better so
+
+ align:start position:0%
+the building is outside flly Z better so
+ 
+
+ align:start position:0%
+the building is outside flly Z better so
+they just use the femous old version not
+
+ align:start position:0%
+they just use the femous old version not
+ 
+
+ align:start position:0%
+they just use the femous old version not
+always out ofd flat they they they they
+
+ align:start position:0%
+always out ofd flat they they they they
+ 
+
+ align:start position:0%
+always out ofd flat they they they they
+don't have money to update their FL
+
+ align:start position:0%
+don't have money to update their FL
+ 
+
+ align:start position:0%
+don't have money to update their FL
+don't map frequently so out of dat
+
+ align:start position:0%
+don't map frequently so out of dat
+ 
+
+ align:start position:0%
+don't map frequently so out of dat
+however the market participate they use
+
+ align:start position:0%
+however the market participate they use
+ 
+
+ align:start position:0%
+however the market participate they use
+this to update their information and the
+
+ align:start position:0%
+this to update their information and the
+ 
+
+ align:start position:0%
+this to update their information and the
+belief they say oh dangerous okay area
+
+ align:start position:0%
+belief they say oh dangerous okay area
+ 
+
+ align:start position:0%
+belief they say oh dangerous okay area
+for those
+
+ align:start position:0%
+for those
+ 
+
+ align:start position:0%
+for those
+places they already understood as risky
+
+ align:start position:0%
+places they already understood as risky
+ 
+
+ align:start position:0%
+places they already understood as risky
+so this new hricane is not a new news
+
+ align:start position:0%
+so this new hricane is not a new news
+ 
+
+ align:start position:0%
+so this new hricane is not a new news
+right because they understood the H
+
+ align:start position:0%
+right because they understood the H
+ 
+
+ align:start position:0%
+right because they understood the H
+already this area the taxes got hit by
+
+ align:start position:0%
+already this area the taxes got hit by
+ 
+
+ align:start position:0%
+already this area the taxes got hit by
+so many hurricanes in in the past and
+
+ align:start position:0%
+so many hurricanes in in the past and
+ 
+
+ align:start position:0%
+so many hurricanes in in the past and
+then they also know this is a flone so
+
+ align:start position:0%
+then they also know this is a flone so
+ 
+
+ align:start position:0%
+then they also know this is a flone so
+this old news
+
+ align:start position:0%
+this old news
+ 
+
+ align:start position:0%
+this old news
+if this old news
+
+ align:start position:0%
+if this old news
+ 
+
+ align:start position:0%
+if this old news
+then the already capitalized into the
+
+ align:start position:0%
+then the already capitalized into the
+ 
+
+ align:start position:0%
+then the already capitalized into the
+price it's not like oh I I don't know
+
+ align:start position:0%
+price it's not like oh I I don't know
+ 
+
+ align:start position:0%
+price it's not like oh I I don't know
+anything suddenly tomorrow is Hurricane
+
+ align:start position:0%
+anything suddenly tomorrow is Hurricane
+ 
+
+ align:start position:0%
+anything suddenly tomorrow is Hurricane
+then I immediately adjust my price down
+
+ align:start position:0%
+then I immediately adjust my price down
+ 
+
+ align:start position:0%
+then I immediately adjust my price down
+by 10% no they already understood so
+
+ align:start position:0%
+by 10% no they already understood so
+ 
+
+ align:start position:0%
+by 10% no they already understood so
+they already capitalized the in the new
+
+ align:start position:0%
+they already capitalized the in the new
+ 
+
+ align:start position:0%
+they already capitalized the in the new
+the bad thing into their price so an
+
+ align:start position:0%
+the bad thing into their price so an
+ 
+
+ align:start position:0%
+the bad thing into their price so an
+additional hurricane hit and won't cause
+
+ align:start position:0%
+additional hurricane hit and won't cause
+ 
+
+ align:start position:0%
+additional hurricane hit and won't cause
+a huge discount because already cap
+
+ align:start position:0%
+a huge discount because already cap
+ 
+
+ align:start position:0%
+a huge discount because already cap
+capitalized if this is a new news
+
+ align:start position:0%
+capitalized if this is a new news
+ 
+
+ align:start position:0%
+capitalized if this is a new news
+at first you you don't know for example
+
+ align:start position:0%
+at first you you don't know for example
+ 
+
+ align:start position:0%
+at first you you don't know for example
+this one at first this one is is is
+
+ align:start position:0%
+this one at first this one is is is
+ 
+
+ align:start position:0%
+this one at first this one is is is
+rightly safe because all have the Zone
+
+ align:start position:0%
+rightly safe because all have the Zone
+ 
+
+ align:start position:0%
+rightly safe because all have the Zone
+but this hurricane just hit and this get
+
+ align:start position:0%
+but this hurricane just hit and this get
+ 
+
+ align:start position:0%
+but this hurricane just hit and this get
+inundated that's very very possible
+
+ align:start position:0%
+inundated that's very very possible
+ 
+
+ align:start position:0%
+inundated that's very very possible
+because the Fone is out of date and
+
+ align:start position:0%
+because the Fone is out of date and
+ 
+
+ align:start position:0%
+because the Fone is out of date and
+every hurricane is different so this got
+
+ align:start position:0%
+every hurricane is different so this got
+ 
+
+ align:start position:0%
+every hurricane is different so this got
+inundated then this one is new news so
+
+ align:start position:0%
+inundated then this one is new news so
+ 
+
+ align:start position:0%
+inundated then this one is new news so
+this one you will see a big discount so
+
+ align:start position:0%
+this one you will see a big discount so
+ 
+
+ align:start position:0%
+this one you will see a big discount so
+we tested this we tested outside of the
+
+ align:start position:0%
+we tested this we tested outside of the
+ 
+
+ align:start position:0%
+we tested this we tested outside of the
+FMA Zone compared to the inside of the
+
+ align:start position:0%
+FMA Zone compared to the inside of the
+ 
+
+ align:start position:0%
+FMA Zone compared to the inside of the
+FMA Zone you will see outside Zone but
+
+ align:start position:0%
+FMA Zone you will see outside Zone but
+ 
+
+ align:start position:0%
+FMA Zone you will see outside Zone but
+get really get flooded have a much
+
+ align:start position:0%
+get really get flooded have a much
+ 
+
+ align:start position:0%
+get really get flooded have a much
+larger discount because this is a
+
+ align:start position:0%
+larger discount because this is a
+ 
+
+ align:start position:0%
+larger discount because this is a
+negative new news so this one this one
+
+ align:start position:0%
+negative new news so this one this one
+ 
+
+ align:start position:0%
+negative new news so this one this one
+already capitalized already negative
+
+ align:start position:0%
+already capitalized already negative
+ 
+
+ align:start position:0%
+already capitalized already negative
+already price is right below so that's
+
+ align:start position:0%
+already price is right below so that's
+ 
+
+ align:start position:0%
+already price is right below so that's
+that's the one factor I want to add but
+
+ align:start position:0%
+that's the one factor I want to add but
+ 
+
+ align:start position:0%
+that's the one factor I want to add but
+just now the this other factors also
+
+ align:start position:0%
+just now the this other factors also
+ 
+
+ align:start position:0%
+just now the this other factors also
+hold true New York City is a huge demand
+
+ align:start position:0%
+hold true New York City is a huge demand
+ 
+
+ align:start position:0%
+hold true New York City is a huge demand
+no matter what people still want to have
+
+ align:start position:0%
+no matter what people still want to have
+ 
+
+ align:start position:0%
+no matter what people still want to have
+their office headquarters there so it's
+
+ align:start position:0%
+their office headquarters there so it's
+ 
+
+ align:start position:0%
+their office headquarters there so it's
+strong strong demand and New York City
+
+ align:start position:0%
+strong strong demand and New York City
+ 
+
+ align:start position:0%
+strong strong demand and New York City
+may be very rich this is um invest all
+
+ align:start position:0%
+may be very rich this is um invest all
+ 
+
+ align:start position:0%
+may be very rich this is um invest all
+the resiliency so the investor won't go
+
+ align:start position:0%
+the resiliency so the investor won't go
+ 
+
+ align:start position:0%
+the resiliency so the investor won't go
+panic so but for some small places they
+
+ align:start position:0%
+panic so but for some small places they
+ 
+
+ align:start position:0%
+panic so but for some small places they
+have no money to invest in
+
+ align:start position:0%
+have no money to invest in
+ 
+
+ align:start position:0%
+have no money to invest in
+resiliency and then the companies flee
+
+ align:start position:0%
+resiliency and then the companies flee
+ 
+
+ align:start position:0%
+resiliency and then the companies flee
+companies oh I don't want to stay here
+
+ align:start position:0%
+companies oh I don't want to stay here
+ 
+
+ align:start position:0%
+companies oh I don't want to stay here
+then they have a
+
+ align:start position:0%
+then they have a
+ 
+
+ align:start position:0%
+then they have a
+discount okay so that's the another
+
+ align:start position:0%
+discount okay so that's the another
+ 
+
+ align:start position:0%
+discount okay so that's the another
+paper so this is my paper this is my
+
+ align:start position:0%
+paper so this is my paper this is my
+ 
+
+ align:start position:0%
+paper so this is my paper this is my
+paper working paper but we will soon
+
+ align:start position:0%
+paper working paper but we will soon
+ 
+
+ align:start position:0%
+paper working paper but we will soon
+publish this is another
+
+ align:start position:0%
+publish this is another
+ 
+
+ align:start position:0%
+publish this is another
+paper uh this another paper already
+
+ align:start position:0%
+paper uh this another paper already
+ 
+
+ align:start position:0%
+paper uh this another paper already
+published still working paper but anyway
+
+ align:start position:0%
+published still working paper but anyway
+ 
+
+ align:start position:0%
+published still working paper but anyway
+you will see this that actually they are
+
+ align:start position:0%
+you will see this that actually they are
+ 
+
+ align:start position:0%
+you will see this that actually they are
+saying for those who are get hit and as
+
+ align:start position:0%
+saying for those who are get hit and as
+ 
+
+ align:start position:0%
+saying for those who are get hit and as
+a big discount and they they only uh not
+
+ align:start position:0%
+a big discount and they they only uh not
+ 
+
+ align:start position:0%
+a big discount and they they only uh not
+get h a smaller discount but it's a
+
+ align:start position:0%
+get h a smaller discount but it's a
+ 
+
+ align:start position:0%
+get h a smaller discount but it's a
+information it's a information channel
+
+ align:start position:0%
+information it's a information channel
+ 
+
+ align:start position:0%
+information it's a information channel
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so the sand still Sandy directly hit New
+
+ align:start position:0%
+so the sand still Sandy directly hit New
+ 
+
+ align:start position:0%
+so the sand still Sandy directly hit New
+York big discount and Boston uh nearby
+
+ align:start position:0%
+York big discount and Boston uh nearby
+ 
+
+ align:start position:0%
+York big discount and Boston uh nearby
+but they also feel oh it's risky now I
+
+ align:start position:0%
+but they also feel oh it's risky now I
+ 
+
+ align:start position:0%
+but they also feel oh it's risky now I
+understand even we in the the Northeast
+
+ align:start position:0%
+understand even we in the the Northeast
+ 
+
+ align:start position:0%
+understand even we in the the Northeast
+we may still uh get hit by that some
+
+ align:start position:0%
+we may still uh get hit by that some
+ 
+
+ align:start position:0%
+we may still uh get hit by that some
+discount but Chicago not discount after
+
+ align:start position:0%
+discount but Chicago not discount after
+ 
+
+ align:start position:0%
+discount but Chicago not discount after
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+events so that's that's about all about
+
+ align:start position:0%
+events so that's that's about all about
+ 
+
+ align:start position:0%
+events so that's that's about all about
+this I I think I thr uh some new
+
+ align:start position:0%
+this I I think I thr uh some new
+ 
+
+ align:start position:0%
+this I I think I thr uh some new
+questions on the table without clear
+
+ align:start position:0%
+questions on the table without clear
+ 
+
+ align:start position:0%
+questions on the table without clear
+answer but I hope you understand my
+
+ align:start position:0%
+answer but I hope you understand my
+ 
+
+ align:start position:0%
+answer but I hope you understand my
+point here is what what we can do to
+
+ align:start position:0%
+point here is what what we can do to
+ 
+
+ align:start position:0%
+point here is what what we can do to
+contribute maybe later will become your
+
+ align:start position:0%
+contribute maybe later will become your
+ 
+
+ align:start position:0%
+contribute maybe later will become your
+expertise when you take on your job is
+
+ align:start position:0%
+expertise when you take on your job is
+ 
+
+ align:start position:0%
+expertise when you take on your job is
+to understand the how to quantify this
+
+ align:start position:0%
+to understand the how to quantify this
+ 
+
+ align:start position:0%
+to understand the how to quantify this
+to go to the real estate valuation we
+
+ align:start position:0%
+to go to the real estate valuation we
+ 
+
+ align:start position:0%
+to go to the real estate valuation we
+are now real State valuation noi and cap
+
+ align:start position:0%
+are now real State valuation noi and cap
+ 
+
+ align:start position:0%
+are now real State valuation noi and cap
+rate noi is a current caate is Future
+
+ align:start position:0%
+rate noi is a current caate is Future
+ 
+
+ align:start position:0%
+rate noi is a current caate is Future
+uncertainly and they work together to
+
+ align:start position:0%
+uncertainly and they work together to
+ 
+
+ align:start position:0%
+uncertainly and they work together to
+influence the wi and then we quantify
+
+ align:start position:0%
+influence the wi and then we quantify
+ 
+
+ align:start position:0%
+influence the wi and then we quantify
+this now I'm going to use another uh
+
+ align:start position:0%
+this now I'm going to use another uh
+ 
+
+ align:start position:0%
+this now I'm going to use another uh
+like 20 minutes to discuss in Insurance
+
+ align:start position:0%
+like 20 minutes to discuss in Insurance
+ 
+
+ align:start position:0%
+like 20 minutes to discuss in Insurance
+Market crisis I think that be natural
+
+ align:start position:0%
+Market crisis I think that be natural
+ 
+
+ align:start position:0%
+Market crisis I think that be natural
+link to what I want to talk about uh in
+
+ align:start position:0%
+link to what I want to talk about uh in
+ 
+
+ align:start position:0%
+link to what I want to talk about uh in
+the mortgage Market how to how to price
+
+ align:start position:0%
+the mortgage Market how to how to price
+ 
+
+ align:start position:0%
+the mortgage Market how to how to price
+the the climate
+
+ align:start position:0%
+the the climate
+ 
+
+ align:start position:0%
+the the climate
+risks but first I think we both of us me
+
+ align:start position:0%
+risks but first I think we both of us me
+ 
+
+ align:start position:0%
+risks but first I think we both of us me
+and all of you we need have some basic
+
+ align:start position:0%
+and all of you we need have some basic
+ 
+
+ align:start position:0%
+and all of you we need have some basic
+knowledge of the of the uh we use flood
+
+ align:start position:0%
+knowledge of the of the uh we use flood
+ 
+
+ align:start position:0%
+knowledge of the of the uh we use flood
+as example the flood insurance in this
+
+ align:start position:0%
+as example the flood insurance in this
+ 
+
+ align:start position:0%
+as example the flood insurance in this
+country at first I didn't know even I
+
+ align:start position:0%
+country at first I didn't know even I
+ 
+
+ align:start position:0%
+country at first I didn't know even I
+don't know whether I'm I'm paying lot
+
+ align:start position:0%
+don't know whether I'm I'm paying lot
+ 
+
+ align:start position:0%
+don't know whether I'm I'm paying lot
+for my house here in in LX I don't know
+
+ align:start position:0%
+for my house here in in LX I don't know
+ 
+
+ align:start position:0%
+for my house here in in LX I don't know
+so I dig into this but this flat
+
+ align:start position:0%
+so I dig into this but this flat
+ 
+
+ align:start position:0%
+so I dig into this but this flat
+insurance now is a lot of debates that's
+
+ align:start position:0%
+insurance now is a lot of debates that's
+ 
+
+ align:start position:0%
+insurance now is a lot of debates that's
+why I call it crisis Insurance Market
+
+ align:start position:0%
+why I call it crisis Insurance Market
+ 
+
+ align:start position:0%
+why I call it crisis Insurance Market
+crisis now it's in a crisis situation
+
+ align:start position:0%
+crisis now it's in a crisis situation
+ 
+
+ align:start position:0%
+crisis now it's in a crisis situation
+but now first we understand basics of
+
+ align:start position:0%
+but now first we understand basics of
+ 
+
+ align:start position:0%
+but now first we understand basics of
+the flood insurance program this called
+
+ align:start position:0%
+the flood insurance program this called
+ 
+
+ align:start position:0%
+the flood insurance program this called
+National flood insurance program
+
+ align:start position:0%
+National flood insurance program
+ 
+
+ align:start position:0%
+National flood insurance program
+nfip so this terminology we need to
+
+ align:start position:0%
+nfip so this terminology we need to
+ 
+
+ align:start position:0%
+nfip so this terminology we need to
+understand now we understand this
+
+ align:start position:0%
+understand now we understand this
+ 
+
+ align:start position:0%
+understand now we understand this
+insurance
+
+ align:start position:0%
+insurance
+ 
+
+ align:start position:0%
+insurance
+rate is determined by the location of
+
+ align:start position:0%
+rate is determined by the location of
+ 
+
+ align:start position:0%
+rate is determined by the location of
+your property with respect to the flat
+
+ align:start position:0%
+your property with respect to the flat
+ 
+
+ align:start position:0%
+your property with respect to the flat
+zans okay now go back to FL Z I just
+
+ align:start position:0%
+zans okay now go back to FL Z I just
+ 
+
+ align:start position:0%
+zans okay now go back to FL Z I just
+said FEMA is a is a in is institution
+
+ align:start position:0%
+said FEMA is a is a in is institution
+ 
+
+ align:start position:0%
+said FEMA is a is a in is institution
+that to publish flat
+
+ align:start position:0%
+that to publish flat
+ 
+
+ align:start position:0%
+that to publish flat
+zones this is the C Port area you are
+
+ align:start position:0%
+zones this is the C Port area you are
+ 
+
+ align:start position:0%
+zones this is the C Port area you are
+now doing Studio project here the FL
+
+ align:start position:0%
+now doing Studio project here the FL
+ 
+
+ align:start position:0%
+now doing Studio project here the FL
+zones you must make sure you understand
+
+ align:start position:0%
+zones you must make sure you understand
+ 
+
+ align:start position:0%
+zones you must make sure you understand
+your land whether it is in the flat zone
+
+ align:start position:0%
+your land whether it is in the flat zone
+ 
+
+ align:start position:0%
+your land whether it is in the flat zone
+or not is it in flat zone I'm not sure
+
+ align:start position:0%
+or not is it in flat zone I'm not sure
+ 
+
+ align:start position:0%
+or not is it in flat zone I'm not sure
+who are doing studio right
+
+ align:start position:0%
+who are doing studio right
+ 
+
+ align:start position:0%
+who are doing studio right
+now yes whether that area is in flat
+
+ align:start position:0%
+now yes whether that area is in flat
+ 
+
+ align:start position:0%
+now yes whether that area is in flat
+zone you mean some parts I think was
+
+ align:start position:0%
+zone you mean some parts I think was
+ 
+
+ align:start position:0%
+zone you mean some parts I think was
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay some some lots are in some are
+
+ align:start position:0%
+and okay some some lots are in some are
+ 
+
+ align:start position:0%
+and okay some some lots are in some are
+not right okay so that's your so because
+
+ align:start position:0%
+not right okay so that's your so because
+ 
+
+ align:start position:0%
+not right okay so that's your so because
+this is linked to our final project so
+
+ align:start position:0%
+this is linked to our final project so
+ 
+
+ align:start position:0%
+this is linked to our final project so
+in your studio maybe your your parel is
+
+ align:start position:0%
+in your studio maybe your your parel is
+ 
+
+ align:start position:0%
+in your studio maybe your your parel is
+here there lck some losss are here some
+
+ align:start position:0%
+here there lck some losss are here some
+ 
+
+ align:start position:0%
+here there lck some losss are here some
+losss are not in the flood room so from
+
+ align:start position:0%
+losss are not in the flood room so from
+ 
+
+ align:start position:0%
+losss are not in the flood room so from
+the legal perspective no matter whether
+
+ align:start position:0%
+the legal perspective no matter whether
+ 
+
+ align:start position:0%
+the legal perspective no matter whether
+this will real be get flooded but when
+
+ align:start position:0%
+this will real be get flooded but when
+ 
+
+ align:start position:0%
+this will real be get flooded but when
+you are located in the flat zone
+
+ align:start position:0%
+you are located in the flat zone
+ 
+
+ align:start position:0%
+you are located in the flat zone
+unfortunately you need to buy insurance
+
+ align:start position:0%
+unfortunately you need to buy insurance
+ 
+
+ align:start position:0%
+unfortunately you need to buy insurance
+by the flood insurance if you want to
+
+ align:start position:0%
+by the flood insurance if you want to
+ 
+
+ align:start position:0%
+by the flood insurance if you want to
+borrow mortgage from the bank if you say
+
+ align:start position:0%
+borrow mortgage from the bank if you say
+ 
+
+ align:start position:0%
+borrow mortgage from the bank if you say
+I'm so rich I just put cash on the table
+
+ align:start position:0%
+I'm so rich I just put cash on the table
+ 
+
+ align:start position:0%
+I'm so rich I just put cash on the table
+and buy the house 2 million then you are
+
+ align:start position:0%
+and buy the house 2 million then you are
+ 
+
+ align:start position:0%
+and buy the house 2 million then you are
+not obligated to buy the insurance but
+
+ align:start position:0%
+not obligated to buy the insurance but
+ 
+
+ align:start position:0%
+not obligated to buy the insurance but
+you say I can only pay the down payment
+
+ align:start position:0%
+you say I can only pay the down payment
+ 
+
+ align:start position:0%
+you say I can only pay the down payment
+I need to borrow money from the bank and
+
+ align:start position:0%
+I need to borrow money from the bank and
+ 
+
+ align:start position:0%
+I need to borrow money from the bank and
+your house is in the flat zone you must
+
+ align:start position:0%
+your house is in the flat zone you must
+ 
+
+ align:start position:0%
+your house is in the flat zone you must
+buy
+
+ align:start position:0%
+buy
+ 
+
+ align:start position:0%
+buy
+insurance so that's a logic okay that's
+
+ align:start position:0%
+insurance so that's a logic okay that's
+ 
+
+ align:start position:0%
+insurance so that's a logic okay that's
+a logic first and then the flat pre flat
+
+ align:start position:0%
+a logic first and then the flat pre flat
+ 
+
+ align:start position:0%
+a logic first and then the flat pre flat
+uh insurance premium is based on some
+
+ align:start position:0%
+uh insurance premium is based on some
+ 
+
+ align:start position:0%
+uh insurance premium is based on some
+parameters and if you can reduce you you
+
+ align:start position:0%
+parameters and if you can reduce you you
+ 
+
+ align:start position:0%
+parameters and if you can reduce you you
+can IND reduce the insurance premium by
+
+ align:start position:0%
+can IND reduce the insurance premium by
+ 
+
+ align:start position:0%
+can IND reduce the insurance premium by
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+strategies although unfortunately your
+
+ align:start position:0%
+strategies although unfortunately your
+ 
+
+ align:start position:0%
+strategies although unfortunately your
+building your house
+
+ align:start position:0%
+building your house
+ 
+
+ align:start position:0%
+building your house
+is in the flood
+
+ align:start position:0%
+is in the flood
+ 
+
+ align:start position:0%
+is in the flood
+zone but you can still help yourself
+
+ align:start position:0%
+zone but you can still help yourself
+ 
+
+ align:start position:0%
+zone but you can still help yourself
+protect
+
+ align:start position:0%
+protect
+ 
+
+ align:start position:0%
+protect
+yourself for example if like
+
+ align:start position:0%
+yourself for example if like
+ 
+
+ align:start position:0%
+yourself for example if like
+premium uh for this this base they have
+
+ align:start position:0%
+premium uh for this this base they have
+ 
+
+ align:start position:0%
+premium uh for this this base they have
+a base flood elevation another
+
+ align:start position:0%
+a base flood elevation another
+ 
+
+ align:start position:0%
+a base flood elevation another
+terminology BF base flood elevation you
+
+ align:start position:0%
+terminology BF base flood elevation you
+ 
+
+ align:start position:0%
+terminology BF base flood elevation you
+just think of the water level it's a
+
+ align:start position:0%
+just think of the water level it's a
+ 
+
+ align:start position:0%
+just think of the water level it's a
+base water level if you get flooded and
+
+ align:start position:0%
+base water level if you get flooded and
+ 
+
+ align:start position:0%
+base water level if you get flooded and
+if you are so low and you get flooded
+
+ align:start position:0%
+if you are so low and you get flooded
+ 
+
+ align:start position:0%
+if you are so low and you get flooded
+9,500
+
+ align:start position:0%
+9,500
+ 
+
+ align:start position:0%
+9,500
+Year
+
+ align:start position:0%
+Year
+ 
+
+ align:start position:0%
+Year
+big now you say okay I will use some
+
+ align:start position:0%
+big now you say okay I will use some
+ 
+
+ align:start position:0%
+big now you say okay I will use some
+pillars to to elevate my ground
+
+ align:start position:0%
+pillars to to elevate my ground
+ 
+
+ align:start position:0%
+pillars to to elevate my ground
+floor and then you become taller your
+
+ align:start position:0%
+floor and then you become taller your
+ 
+
+ align:start position:0%
+floor and then you become taller your
+building and you have less exposure to
+
+ align:start position:0%
+building and you have less exposure to
+ 
+
+ align:start position:0%
+building and you have less exposure to
+the FL risk then you can reduce your
+
+ align:start position:0%
+the FL risk then you can reduce your
+ 
+
+ align:start position:0%
+the FL risk then you can reduce your
+premium to 1,400 per year that's big
+
+ align:start position:0%
+premium to 1,400 per year that's big
+ 
+
+ align:start position:0%
+premium to 1,400 per year that's big
+right at first the 9 9,000 now is
+
+ align:start position:0%
+right at first the 9 9,000 now is
+ 
+
+ align:start position:0%
+right at first the 9 9,000 now is
+1,400 it's a huge decrease then if you
+
+ align:start position:0%
+1,400 it's a huge decrease then if you
+ 
+
+ align:start position:0%
+1,400 it's a huge decrease then if you
+forther Elevate $400 a year $400 a year
+
+ align:start position:0%
+forther Elevate $400 a year $400 a year
+ 
+
+ align:start position:0%
+forther Elevate $400 a year $400 a year
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+decrease this means you think about this
+
+ align:start position:0%
+decrease this means you think about this
+ 
+
+ align:start position:0%
+decrease this means you think about this
+if you are household you say oh how can
+
+ align:start position:0%
+if you are household you say oh how can
+ 
+
+ align:start position:0%
+if you are household you say oh how can
+I invest to elevate my house now of
+
+ align:start position:0%
+I invest to elevate my house now of
+ 
+
+ align:start position:0%
+I invest to elevate my house now of
+course you need money you get this this
+
+ align:start position:0%
+course you need money you get this this
+ 
+
+ align:start position:0%
+course you need money you get this this
+is expensive then you say whether do I
+
+ align:start position:0%
+is expensive then you say whether do I
+ 
+
+ align:start position:0%
+is expensive then you say whether do I
+Elevate if I Elevate I pay less
+
+ align:start position:0%
+Elevate if I Elevate I pay less
+ 
+
+ align:start position:0%
+Elevate if I Elevate I pay less
+insurance if I don't Elevate I pay high
+
+ align:start position:0%
+insurance if I don't Elevate I pay high
+ 
+
+ align:start position:0%
+insurance if I don't Elevate I pay high
+insurance premium this is this is your
+
+ align:start position:0%
+insurance premium this is this is your
+ 
+
+ align:start position:0%
+insurance premium this is this is your
+US money
+
+ align:start position:0%
+US money
+ 
+
+ align:start position:0%
+US money
+so this is very interesting because I'm
+
+ align:start position:0%
+so this is very interesting because I'm
+ 
+
+ align:start position:0%
+so this is very interesting because I'm
+not sure whether later you will have a
+
+ align:start position:0%
+not sure whether later you will have a
+ 
+
+ align:start position:0%
+not sure whether later you will have a
+visit to Cort so you go ahead a quick
+
+ align:start position:0%
+visit to Cort so you go ahead a quick
+ 
+
+ align:start position:0%
+visit to Cort so you go ahead a quick
+question looking at the bottom note that
+
+ align:start position:0%
+question looking at the bottom note that
+ 
+
+ align:start position:0%
+question looking at the bottom note that
+this numbers are calculated for single
+
+ align:start position:0%
+this numbers are calculated for single
+ 
+
+ align:start position:0%
+this numbers are calculated for single
+family one story structure and talking
+
+ align:start position:0%
+family one story structure and talking
+ 
+
+ align:start position:0%
+family one story structure and talking
+specifically about the seport which I
+
+ align:start position:0%
+specifically about the seport which I
+ 
+
+ align:start position:0%
+specifically about the seport which I
+don't think people are going to build
+
+ align:start position:0%
+don't think people are going to build
+ 
+
+ align:start position:0%
+don't think people are going to build
+single family hous yes family what's the
+
+ align:start position:0%
+single family hous yes family what's the
+ 
+
+ align:start position:0%
+single family hous yes family what's the
+relation or what's the implicit cost for
+
+ align:start position:0%
+relation or what's the implicit cost for
+ 
+
+ align:start position:0%
+relation or what's the implicit cost for
+like multi family buildings knowing that
+
+ align:start position:0%
+like multi family buildings knowing that
+ 
+
+ align:start position:0%
+like multi family buildings knowing that
+they are already like elevated from SE
+
+ align:start position:0%
+they are already like elevated from SE
+ 
+
+ align:start position:0%
+they are already like elevated from SE
+level yes and uh it's not like one
+
+ align:start position:0%
+level yes and uh it's not like one
+ 
+
+ align:start position:0%
+level yes and uh it's not like one
+household decision right if you're are
+
+ align:start position:0%
+household decision right if you're are
+ 
+
+ align:start position:0%
+household decision right if you're are
+multif family you cannot say I'm going
+
+ align:start position:0%
+multif family you cannot say I'm going
+ 
+
+ align:start position:0%
+multif family you cannot say I'm going
+to elevate then you need to have a
+
+ align:start position:0%
+to elevate then you need to have a
+ 
+
+ align:start position:0%
+to elevate then you need to have a
+committee to discuss the entire building
+
+ align:start position:0%
+committee to discuss the entire building
+ 
+
+ align:start position:0%
+committee to discuss the entire building
+or the developer to do this up front
+
+ align:start position:0%
+or the developer to do this up front
+ 
+
+ align:start position:0%
+or the developer to do this up front
+this a very good question caros and you
+
+ align:start position:0%
+this a very good question caros and you
+ 
+
+ align:start position:0%
+this a very good question caros and you
+see this one is from single family
+
+ align:start position:0%
+see this one is from single family
+ 
+
+ align:start position:0%
+see this one is from single family
+perspective is try try to let let you
+
+ align:start position:0%
+perspective is try try to let let you
+ 
+
+ align:start position:0%
+perspective is try try to let let you
+understand easily so this is a very
+
+ align:start position:0%
+understand easily so this is a very
+ 
+
+ align:start position:0%
+understand easily so this is a very
+simple example this one is more
+
+ align:start position:0%
+simple example this one is more
+ 
+
+ align:start position:0%
+simple example this one is more
+complicated ated but the logic will be
+
+ align:start position:0%
+complicated ated but the logic will be
+ 
+
+ align:start position:0%
+complicated ated but the logic will be
+the same this commercial buildings and
+
+ align:start position:0%
+the same this commercial buildings and
+ 
+
+ align:start position:0%
+the same this commercial buildings and
+multif family houses and all the
+
+ align:start position:0%
+multif family houses and all the
+ 
+
+ align:start position:0%
+multif family houses and all the
+commercial buildings you are going to do
+
+ align:start position:0%
+commercial buildings you are going to do
+ 
+
+ align:start position:0%
+commercial buildings you are going to do
+design your studio area Lear area more
+
+ align:start position:0%
+design your studio area Lear area more
+ 
+
+ align:start position:0%
+design your studio area Lear area more
+complicated but logic is still you
+
+ align:start position:0%
+complicated but logic is still you
+ 
+
+ align:start position:0%
+complicated but logic is still you
+elevate your insurance premium will go
+
+ align:start position:0%
+elevate your insurance premium will go
+ 
+
+ align:start position:0%
+elevate your insurance premium will go
+down and if you have a chance to visit
+
+ align:start position:0%
+down and if you have a chance to visit
+ 
+
+ align:start position:0%
+down and if you have a chance to visit
+there so I remember I I had a
+
+ align:start position:0%
+there so I remember I I had a
+ 
+
+ align:start position:0%
+there so I remember I I had a
+conversation with yanis Janis is one of
+
+ align:start position:0%
+conversation with yanis Janis is one of
+ 
+
+ align:start position:0%
+conversation with yanis Janis is one of
+your instructors right from the building
+
+ align:start position:0%
+your instructors right from the building
+ 
+
+ align:start position:0%
+your instructors right from the building
+system class I talk to him because he's
+
+ align:start position:0%
+system class I talk to him because he's
+ 
+
+ align:start position:0%
+system class I talk to him because he's
+now a big developer WS in this area
+
+ align:start position:0%
+now a big developer WS in this area
+ 
+
+ align:start position:0%
+now a big developer WS in this area
+build many many buildings here and his
+
+ align:start position:0%
+build many many buildings here and his
+ 
+
+ align:start position:0%
+build many many buildings here and his
+area his
+
+ align:start position:0%
+area his
+ 
+
+ align:start position:0%
+area his
+buildings many of his buildings are in
+
+ align:start position:0%
+buildings many of his buildings are in
+ 
+
+ align:start position:0%
+buildings many of his buildings are in
+the flat zone many of his building are
+
+ align:start position:0%
+the flat zone many of his building are
+ 
+
+ align:start position:0%
+the flat zone many of his building are
+in flat Z so which means later no matter
+
+ align:start position:0%
+in flat Z so which means later no matter
+ 
+
+ align:start position:0%
+in flat Z so which means later no matter
+whether they hold those buildings or
+
+ align:start position:0%
+whether they hold those buildings or
+ 
+
+ align:start position:0%
+whether they hold those buildings or
+they sell the buildings to other
+
+ align:start position:0%
+they sell the buildings to other
+ 
+
+ align:start position:0%
+they sell the buildings to other
+investors the owners will pay very
+
+ align:start position:0%
+investors the owners will pay very
+ 
+
+ align:start position:0%
+investors the owners will pay very
+high uh insurance
+
+ align:start position:0%
+high uh insurance
+ 
+
+ align:start position:0%
+high uh insurance
+premium and then Yan told us now we are
+
+ align:start position:0%
+premium and then Yan told us now we are
+ 
+
+ align:start position:0%
+premium and then Yan told us now we are
+investing a lot to do this they are
+
+ align:start position:0%
+investing a lot to do this they are
+ 
+
+ align:start position:0%
+investing a lot to do this they are
+investing a lot in this uh climate
+
+ align:start position:0%
+investing a lot in this uh climate
+ 
+
+ align:start position:0%
+investing a lot in this uh climate
+resiliency investment and Elevate this
+
+ align:start position:0%
+resiliency investment and Elevate this
+ 
+
+ align:start position:0%
+resiliency investment and Elevate this
+is very simple but they are doing many
+
+ align:start position:0%
+is very simple but they are doing many
+ 
+
+ align:start position:0%
+is very simple but they are doing many
+many other things and they are doing
+
+ align:start position:0%
+many other things and they are doing
+ 
+
+ align:start position:0%
+many other things and they are doing
+many other things they elevate so much
+
+ align:start position:0%
+many other things they elevate so much
+ 
+
+ align:start position:0%
+many other things they elevate so much
+and to the extent the city agreed that
+
+ align:start position:0%
+and to the extent the city agreed that
+ 
+
+ align:start position:0%
+and to the extent the city agreed that
+they out of the
+
+ align:start position:0%
+they out of the
+ 
+
+ align:start position:0%
+they out of the
+FL which means Al physically if you look
+
+ align:start position:0%
+FL which means Al physically if you look
+ 
+
+ align:start position:0%
+FL which means Al physically if you look
+from from Google Map their buildings are
+
+ align:start position:0%
+from from Google Map their buildings are
+ 
+
+ align:start position:0%
+from from Google Map their buildings are
+in flone but they elevate so much and
+
+ align:start position:0%
+in flone but they elevate so much and
+ 
+
+ align:start position:0%
+in flone but they elevate so much and
+they have done so much they are also
+
+ align:start position:0%
+they have done so much they are also
+ 
+
+ align:start position:0%
+they have done so much they are also
+side in the flat Z because flat Z cannot
+
+ align:start position:0%
+side in the flat Z because flat Z cannot
+ 
+
+ align:start position:0%
+side in the flat Z because flat Z cannot
+just like uh horizontal they also
+
+ align:start position:0%
+just like uh horizontal they also
+ 
+
+ align:start position:0%
+just like uh horizontal they also
+understand the vertical side then Yani
+
+ align:start position:0%
+understand the vertical side then Yani
+ 
+
+ align:start position:0%
+understand the vertical side then Yani
+use that as a selling point of their WS
+
+ align:start position:0%
+use that as a selling point of their WS
+ 
+
+ align:start position:0%
+use that as a selling point of their WS
+project in Cort say okay if you buy our
+
+ align:start position:0%
+project in Cort say okay if you buy our
+ 
+
+ align:start position:0%
+project in Cort say okay if you buy our
+properties you don't need to pay such a
+
+ align:start position:0%
+properties you don't need to pay such a
+ 
+
+ align:start position:0%
+properties you don't need to pay such a
+flat Insurance because we have done so
+
+ align:start position:0%
+flat Insurance because we have done so
+ 
+
+ align:start position:0%
+flat Insurance because we have done so
+much and got out of the flat loan and
+
+ align:start position:0%
+much and got out of the flat loan and
+ 
+
+ align:start position:0%
+much and got out of the flat loan and
+approved by the city like that then you
+
+ align:start position:0%
+approved by the city like that then you
+ 
+
+ align:start position:0%
+approved by the city like that then you
+will see money that is logic I don't
+
+ align:start position:0%
+will see money that is logic I don't
+ 
+
+ align:start position:0%
+will see money that is logic I don't
+know whether the market will believe in
+
+ align:start position:0%
+know whether the market will believe in
+ 
+
+ align:start position:0%
+know whether the market will believe in
+that not we can observe but this as you
+
+ align:start position:0%
+that not we can observe but this as you
+ 
+
+ align:start position:0%
+that not we can observe but this as you
+know this also the example that you can
+
+ align:start position:0%
+know this also the example that you can
+ 
+
+ align:start position:0%
+know this also the example that you can
+do something by yourself to reduce
+
+ align:start position:0%
+do something by yourself to reduce
+ 
+
+ align:start position:0%
+do something by yourself to reduce
+future insurance premium and also
+
+ align:start position:0%
+future insurance premium and also
+ 
+
+ align:start position:0%
+future insurance premium and also
+because of the risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduction okay this is another example
+
+ align:start position:0%
+reduction okay this is another example
+ 
+
+ align:start position:0%
+reduction okay this is another example
+for you to understand this is a New York
+
+ align:start position:0%
+for you to understand this is a New York
+ 
+
+ align:start position:0%
+for you to understand this is a New York
+building just know this that one is
+
+ align:start position:0%
+building just know this that one is
+ 
+
+ align:start position:0%
+building just know this that one is
+Massachusetts this is New York building
+
+ align:start position:0%
+Massachusetts this is New York building
+ 
+
+ align:start position:0%
+Massachusetts this is New York building
+and if you you will do this and that
+
+ align:start position:0%
+and if you you will do this and that
+ 
+
+ align:start position:0%
+and if you you will do this and that
+mitigate the properties against flooding
+
+ align:start position:0%
+mitigate the properties against flooding
+ 
+
+ align:start position:0%
+mitigate the properties against flooding
+can signific reduce the far risk and
+
+ align:start position:0%
+can signific reduce the far risk and
+ 
+
+ align:start position:0%
+can signific reduce the far risk and
+insurance premiums for example Elevate
+
+ align:start position:0%
+insurance premiums for example Elevate
+ 
+
+ align:start position:0%
+insurance premiums for example Elevate
+elevation move up and uh and put a
+
+ align:start position:0%
+elevation move up and uh and put a
+ 
+
+ align:start position:0%
+elevation move up and uh and put a
+basement infi just infi your basement
+
+ align:start position:0%
+basement infi just infi your basement
+ 
+
+ align:start position:0%
+basement infi just infi your basement
+otherwise your basement get flooded the
+
+ align:start position:0%
+otherwise your basement get flooded the
+ 
+
+ align:start position:0%
+otherwise your basement get flooded the
+problem damage right infi the basement
+
+ align:start position:0%
+problem damage right infi the basement
+ 
+
+ align:start position:0%
+problem damage right infi the basement
+you have no basement now and just uh
+
+ align:start position:0%
+you have no basement now and just uh
+ 
+
+ align:start position:0%
+you have no basement now and just uh
+then we'll
+
+ align:start position:0%
+then we'll
+ 
+
+ align:start position:0%
+then we'll
+reduce and uh and uh also move your
+
+ align:start position:0%
+reduce and uh and uh also move your
+ 
+
+ align:start position:0%
+reduce and uh and uh also move your
+machines and equipment from the bottom
+
+ align:start position:0%
+machines and equipment from the bottom
+ 
+
+ align:start position:0%
+machines and equipment from the bottom
+from the bottom to the Top If You you
+
+ align:start position:0%
+from the bottom to the Top If You you
+ 
+
+ align:start position:0%
+from the bottom to the Top If You you
+have several several flaws right because
+
+ align:start position:0%
+have several several flaws right because
+ 
+
+ align:start position:0%
+have several several flaws right because
+then your your mechanical system will
+
+ align:start position:0%
+then your your mechanical system will
+ 
+
+ align:start position:0%
+then your your mechanical system will
+avoid to be flooded so then reduce and
+
+ align:start position:0%
+avoid to be flooded so then reduce and
+ 
+
+ align:start position:0%
+avoid to be flooded so then reduce and
+put a rent or something so this all this
+
+ align:start position:0%
+put a rent or something so this all this
+ 
+
+ align:start position:0%
+put a rent or something so this all this
+uh all this small and big investment
+
+ align:start position:0%
+uh all this small and big investment
+ 
+
+ align:start position:0%
+uh all this small and big investment
+then you change the real your real risk
+
+ align:start position:0%
+then you change the real your real risk
+ 
+
+ align:start position:0%
+then you change the real your real risk
+is pooser so your insurance premium will
+
+ align:start position:0%
+is pooser so your insurance premium will
+ 
+
+ align:start position:0%
+is pooser so your insurance premium will
+change just want to you understand this
+
+ align:start position:0%
+change just want to you understand this
+ 
+
+ align:start position:0%
+change just want to you understand this
+is not fixed I'll say okay in Google map
+
+ align:start position:0%
+is not fixed I'll say okay in Google map
+ 
+
+ align:start position:0%
+is not fixed I'll say okay in Google map
+you are here then you have the same
+
+ align:start position:0%
+you are here then you have the same
+ 
+
+ align:start position:0%
+you are here then you have the same
+premium no this will be determined all
+
+ align:start position:0%
+premium no this will be determined all
+ 
+
+ align:start position:0%
+premium no this will be determined all
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+factors okay it seems that it's very
+
+ align:start position:0%
+factors okay it seems that it's very
+ 
+
+ align:start position:0%
+factors okay it seems that it's very
+complicated it's very sophisticated very
+
+ align:start position:0%
+complicated it's very sophisticated very
+ 
+
+ align:start position:0%
+complicated it's very sophisticated very
+good very scientific in this way and I
+
+ align:start position:0%
+good very scientific in this way and I
+ 
+
+ align:start position:0%
+good very scientific in this way and I
+don't know how they derive those
+
+ align:start position:0%
+don't know how they derive those
+ 
+
+ align:start position:0%
+don't know how they derive those
+numbers but it seems that they consider
+
+ align:start position:0%
+numbers but it seems that they consider
+ 
+
+ align:start position:0%
+numbers but it seems that they consider
+many many factors however there is a big
+
+ align:start position:0%
+many many factors however there is a big
+ 
+
+ align:start position:0%
+many many factors however there is a big
+question high level Big Challenge that
+
+ align:start position:0%
+question high level Big Challenge that
+ 
+
+ align:start position:0%
+question high level Big Challenge that
+related to the crisis the insurance
+
+ align:start position:0%
+related to the crisis the insurance
+ 
+
+ align:start position:0%
+related to the crisis the insurance
+Market crisis is can we really Ensure
+
+ align:start position:0%
+Market crisis is can we really Ensure
+ 
+
+ align:start position:0%
+Market crisis is can we really Ensure
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+climate risk always can we always ensure
+
+ align:start position:0%
+climate risk always can we always ensure
+ 
+
+ align:start position:0%
+climate risk always can we always ensure
+climate risk if we can always ensure if
+
+ align:start position:0%
+climate risk if we can always ensure if
+ 
+
+ align:start position:0%
+climate risk if we can always ensure if
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+insurance system is perfect and we
+
+ align:start position:0%
+insurance system is perfect and we
+ 
+
+ align:start position:0%
+insurance system is perfect and we
+always insure we don't need to worry we
+
+ align:start position:0%
+always insure we don't need to worry we
+ 
+
+ align:start position:0%
+always insure we don't need to worry we
+just pay insurance premium uh up front
+
+ align:start position:0%
+just pay insurance premium uh up front
+ 
+
+ align:start position:0%
+just pay insurance premium uh up front
+later you get the damage you go to the
+
+ align:start position:0%
+later you get the damage you go to the
+ 
+
+ align:start position:0%
+later you get the damage you go to the
+insurance company they pay you back down
+
+ align:start position:0%
+insurance company they pay you back down
+ 
+
+ align:start position:0%
+insurance company they pay you back down
+then we don't need to worry too much and
+
+ align:start position:0%
+then we don't need to worry too much and
+ 
+
+ align:start position:0%
+then we don't need to worry too much and
+what do you think whether it's is a
+
+ align:start position:0%
+what do you think whether it's is a
+ 
+
+ align:start position:0%
+what do you think whether it's is a
+always can solve all the all the
+
+ align:start position:0%
+always can solve all the all the
+ 
+
+ align:start position:0%
+always can solve all the all the
+troubles
+
+ align:start position:0%
+troubles
+ 
+
+ align:start position:0%
+troubles
+please go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why are unpredictable unpredictable but
+
+ align:start position:0%
+why are unpredictable unpredictable but
+ 
+
+ align:start position:0%
+why are unpredictable unpredictable but
+if we have a likelihood like uh uh
+
+ align:start position:0%
+if we have a likelihood like uh uh
+ 
+
+ align:start position:0%
+if we have a likelihood like uh uh
+Kevin's Moody theme they say they
+
+ align:start position:0%
+Kevin's Moody theme they say they
+ 
+
+ align:start position:0%
+Kevin's Moody theme they say they
+calculate the distribution like that do
+
+ align:start position:0%
+calculate the distribution like that do
+ 
+
+ align:start position:0%
+calculate the distribution like that do
+you think that's that's that's can help
+
+ align:start position:0%
+you think that's that's that's can help
+ 
+
+ align:start position:0%
+you think that's that's that's can help
+it can help yes but there still still
+
+ align:start position:0%
+it can help yes but there still still
+ 
+
+ align:start position:0%
+it can help yes but there still still
+cannot any other
+
+ align:start position:0%
+cannot any other
+ 
+
+ align:start position:0%
+cannot any other
+sounds can we fully ensure climate risks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any sounds please the the so it doesn't
+
+ align:start position:0%
+any sounds please the the so it doesn't
+ 
+
+ align:start position:0%
+any sounds please the the so it doesn't
+ensure against
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the okay so the fundamental is the
+
+ align:start position:0%
+the okay so the fundamental is the
+ 
+
+ align:start position:0%
+the okay so the fundamental is the
+insurance system the rational of a
+
+ align:start position:0%
+insurance system the rational of a
+ 
+
+ align:start position:0%
+insurance system the rational of a
+insurance system is the
+
+ align:start position:0%
+insurance system is the
+ 
+
+ align:start position:0%
+insurance system is the
+following is to stabilize income right
+
+ align:start position:0%
+following is to stabilize income right
+ 
+
+ align:start position:0%
+following is to stabilize income right
+so basically insurance company helps all
+
+ align:start position:0%
+so basically insurance company helps all
+ 
+
+ align:start position:0%
+so basically insurance company helps all
+of us to stab ize stabilize the income
+
+ align:start position:0%
+of us to stab ize stabilize the income
+ 
+
+ align:start position:0%
+of us to stab ize stabilize the income
+to move money from the good times to bad
+
+ align:start position:0%
+to move money from the good times to bad
+ 
+
+ align:start position:0%
+to move money from the good times to bad
+times think about our house insurance
+
+ align:start position:0%
+times think about our house insurance
+ 
+
+ align:start position:0%
+times think about our house insurance
+right and house insurance we pay house
+
+ align:start position:0%
+right and house insurance we pay house
+ 
+
+ align:start position:0%
+right and house insurance we pay house
+insurance money now we are we are we are
+
+ align:start position:0%
+insurance money now we are we are we are
+ 
+
+ align:start position:0%
+insurance money now we are we are we are
+we are all young relatively young we are
+
+ align:start position:0%
+we are all young relatively young we are
+ 
+
+ align:start position:0%
+we are all young relatively young we are
+not like outlay so our likelihood to get
+
+ align:start position:0%
+not like outlay so our likelihood to get
+ 
+
+ align:start position:0%
+not like outlay so our likelihood to get
+very sick or go go to the hospital or
+
+ align:start position:0%
+very sick or go go to the hospital or
+ 
+
+ align:start position:0%
+very sick or go go to the hospital or
+even die is not very very small so but
+
+ align:start position:0%
+even die is not very very small so but
+ 
+
+ align:start position:0%
+even die is not very very small so but
+we are still paying health insurance and
+
+ align:start position:0%
+we are still paying health insurance and
+ 
+
+ align:start position:0%
+we are still paying health insurance and
+when you are old and you have higher
+
+ align:start position:0%
+when you are old and you have higher
+ 
+
+ align:start position:0%
+when you are old and you have higher
+likelihood to to to to to get sick and
+
+ align:start position:0%
+likelihood to to to to to get sick and
+ 
+
+ align:start position:0%
+likelihood to to to to to get sick and
+get hospitalized then you withdraw so
+
+ align:start position:0%
+get hospitalized then you withdraw so
+ 
+
+ align:start position:0%
+get hospitalized then you withdraw so
+that's the basic logic of the insurance
+
+ align:start position:0%
+that's the basic logic of the insurance
+ 
+
+ align:start position:0%
+that's the basic logic of the insurance
+to move money from good time you you
+
+ align:start position:0%
+to move money from good time you you
+ 
+
+ align:start position:0%
+to move money from good time you you
+feel good you you have more income you
+
+ align:start position:0%
+feel good you you have more income you
+ 
+
+ align:start position:0%
+feel good you you have more income you
+pay and later suddenly you are so
+
+ align:start position:0%
+pay and later suddenly you are so
+ 
+
+ align:start position:0%
+pay and later suddenly you are so
+unfortunate you're so unlucky you get a
+
+ align:start position:0%
+unfortunate you're so unlucky you get a
+ 
+
+ align:start position:0%
+unfortunate you're so unlucky you get a
+a bad thing then you get insurance back
+
+ align:start position:0%
+a bad thing then you get insurance back
+ 
+
+ align:start position:0%
+a bad thing then you get insurance back
+so that's a
+
+ align:start position:0%
+so that's a
+ 
+
+ align:start position:0%
+so that's a
+model however the thing is a systematic
+
+ align:start position:0%
+model however the thing is a systematic
+ 
+
+ align:start position:0%
+model however the thing is a systematic
+thing happen is now happening for the
+
+ align:start position:0%
+thing happen is now happening for the
+ 
+
+ align:start position:0%
+thing happen is now happening for the
+climate which impose a big question mark
+
+ align:start position:0%
+climate which impose a big question mark
+ 
+
+ align:start position:0%
+climate which impose a big question mark
+on this system
+
+ align:start position:0%
+on this system
+ 
+
+ align:start position:0%
+on this system
+is the rising numbers of disasters right
+
+ align:start position:0%
+is the rising numbers of disasters right
+ 
+
+ align:start position:0%
+is the rising numbers of disasters right
+so if if the climate change is still
+
+ align:start position:0%
+so if if the climate change is still
+ 
+
+ align:start position:0%
+so if if the climate change is still
+always con always static like we can PR
+
+ align:start position:0%
+always con always static like we can PR
+ 
+
+ align:start position:0%
+always con always static like we can PR
+we can always we can always predict the
+
+ align:start position:0%
+we can always we can always predict the
+ 
+
+ align:start position:0%
+we can always we can always predict the
+next next 50 years next 100 years the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likelihood the likelihood of the
+
+ align:start position:0%
+likelihood the likelihood of the
+ 
+
+ align:start position:0%
+likelihood the likelihood of the
+flooding then we use this distribution
+
+ align:start position:0%
+flooding then we use this distribution
+ 
+
+ align:start position:0%
+flooding then we use this distribution
+to design the premium so that we collect
+
+ align:start position:0%
+to design the premium so that we collect
+ 
+
+ align:start position:0%
+to design the premium so that we collect
+the insurance money is the insurance
+
+ align:start position:0%
+the insurance money is the insurance
+ 
+
+ align:start position:0%
+the insurance money is the insurance
+company can collect enough money in Good
+
+ align:start position:0%
+company can collect enough money in Good
+ 
+
+ align:start position:0%
+company can collect enough money in Good
+Times so because this is 100% likelihood
+
+ align:start position:0%
+Times so because this is 100% likelihood
+ 
+
+ align:start position:0%
+Times so because this is 100% likelihood
+99 years you are good one year got hit
+
+ align:start position:0%
+99 years you are good one year got hit
+ 
+
+ align:start position:0%
+99 years you are good one year got hit
+so that's a that's a 1% likelihood story
+
+ align:start position:0%
+so that's a that's a 1% likelihood story
+ 
+
+ align:start position:0%
+so that's a that's a 1% likelihood story
+then you use 99 years of the insurance
+
+ align:start position:0%
+then you use 99 years of the insurance
+ 
+
+ align:start position:0%
+then you use 99 years of the insurance
+premium you paid to cover your one year
+
+ align:start position:0%
+premium you paid to cover your one year
+ 
+
+ align:start position:0%
+premium you paid to cover your one year
+loss that's that's idea now
+
+ align:start position:0%
+loss that's that's idea now
+ 
+
+ align:start position:0%
+loss that's that's idea now
+unfortunately because you are we are
+
+ align:start position:0%
+unfortunately because you are we are
+ 
+
+ align:start position:0%
+unfortunately because you are we are
+still emitting so so much of the carbon
+
+ align:start position:0%
+still emitting so so much of the carbon
+ 
+
+ align:start position:0%
+still emitting so so much of the carbon
+and the rising number of disasters I
+
+ align:start position:0%
+and the rising number of disasters I
+ 
+
+ align:start position:0%
+and the rising number of disasters I
+think you heard from the media all the
+
+ align:start position:0%
+think you heard from the media all the
+ 
+
+ align:start position:0%
+think you heard from the media all the
+time oh this year so bad and so many
+
+ align:start position:0%
+time oh this year so bad and so many
+ 
+
+ align:start position:0%
+time oh this year so bad and so many
+hurricanes and one fire this and that
+
+ align:start position:0%
+hurricanes and one fire this and that
+ 
+
+ align:start position:0%
+hurricanes and one fire this and that
+Rising so then the distribution become
+
+ align:start position:0%
+Rising so then the distribution become
+ 
+
+ align:start position:0%
+Rising so then the distribution become
+like not 100 two two two of 100 years
+
+ align:start position:0%
+like not 100 two two two of 100 years
+ 
+
+ align:start position:0%
+like not 100 two two two of 100 years
+three of 100 years four of 100
+
+ align:start position:0%
+three of 100 years four of 100
+ 
+
+ align:start position:0%
+three of 100 years four of 100
+years so that impose a
+
+ align:start position:0%
+years so that impose a
+ 
+
+ align:start position:0%
+years so that impose a
+big challenge to these insurance
+
+ align:start position:0%
+big challenge to these insurance
+ 
+
+ align:start position:0%
+big challenge to these insurance
+companies because more more disasters
+
+ align:start position:0%
+companies because more more disasters
+ 
+
+ align:start position:0%
+companies because more more disasters
+they couldn't clct enough money from
+
+ align:start position:0%
+they couldn't clct enough money from
+ 
+
+ align:start position:0%
+they couldn't clct enough money from
+Good Times because Back Time more and
+
+ align:start position:0%
+Good Times because Back Time more and
+ 
+
+ align:start position:0%
+Good Times because Back Time more and
+more then they they go bankrupt bcrafty
+
+ align:start position:0%
+more then they they go bankrupt bcrafty
+ 
+
+ align:start position:0%
+more then they they go bankrupt bcrafty
+almost because they couldn't collect but
+
+ align:start position:0%
+almost because they couldn't collect but
+ 
+
+ align:start position:0%
+almost because they couldn't collect but
+you can you can argue say why not if we
+
+ align:start position:0%
+you can you can argue say why not if we
+ 
+
+ align:start position:0%
+you can you can argue say why not if we
+later so oh because we are emitting CO2
+
+ align:start position:0%
+later so oh because we are emitting CO2
+ 
+
+ align:start position:0%
+later so oh because we are emitting CO2
+so much now it's not one out of 100
+
+ align:start position:0%
+so much now it's not one out of 100
+ 
+
+ align:start position:0%
+so much now it's not one out of 100
+years it's four four out of 100 years
+
+ align:start position:0%
+years it's four four out of 100 years
+ 
+
+ align:start position:0%
+years it's four four out of 100 years
+then you just increase the insurance
+
+ align:start position:0%
+then you just increase the insurance
+ 
+
+ align:start position:0%
+then you just increase the insurance
+premium right then charge more the
+
+ align:start position:0%
+premium right then charge more the
+ 
+
+ align:start position:0%
+premium right then charge more the
+insurance charge more not not 10 10,000
+
+ align:start position:0%
+insurance charge more not not 10 10,000
+ 
+
+ align:start position:0%
+insurance charge more not not 10 10,000
+but 100,000 money in the good time and
+
+ align:start position:0%
+but 100,000 money in the good time and
+ 
+
+ align:start position:0%
+but 100,000 money in the good time and
+move to the bad time still can work do
+
+ align:start position:0%
+move to the bad time still can work do
+ 
+
+ align:start position:0%
+move to the bad time still can work do
+you think this works you say okay the
+
+ align:start position:0%
+you think this works you say okay the
+ 
+
+ align:start position:0%
+you think this works you say okay the
+climate disasters are are happening more
+
+ align:start position:0%
+climate disasters are are happening more
+ 
+
+ align:start position:0%
+climate disasters are are happening more
+and more frequently
+
+ align:start position:0%
+and more frequently
+ 
+
+ align:start position:0%
+and more frequently
+so more bad times less good times so to
+
+ align:start position:0%
+so more bad times less good times so to
+ 
+
+ align:start position:0%
+so more bad times less good times so to
+make sure the insurance company can
+
+ align:start position:0%
+make sure the insurance company can
+ 
+
+ align:start position:0%
+make sure the insurance company can
+still collect enough money then we
+
+ align:start position:0%
+still collect enough money then we
+ 
+
+ align:start position:0%
+still collect enough money then we
+increase the insurance premium so that
+
+ align:start position:0%
+increase the insurance premium so that
+ 
+
+ align:start position:0%
+increase the insurance premium so that
+they can collect
+
+ align:start position:0%
+they can collect
+ 
+
+ align:start position:0%
+they can collect
+more so that we are all safe do you
+
+ align:start position:0%
+more so that we are all safe do you
+ 
+
+ align:start position:0%
+more so that we are all safe do you
+think this logic can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work doesn't make any sense to Ure
+
+ align:start position:0%
+work doesn't make any sense to Ure
+ 
+
+ align:start position:0%
+work doesn't make any sense to Ure
+proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anymore like se4 going to rise 20 ft
+
+ align:start position:0%
+anymore like se4 going to rise 20 ft
+ 
+
+ align:start position:0%
+anymore like se4 going to rise 20 ft
+over the next 15 years build ground
+
+ align:start position:0%
+over the next 15 years build ground
+ 
+
+ align:start position:0%
+over the next 15 years build ground
+floor going to be in water there's no
+
+ align:start position:0%
+floor going to be in water there's no
+ 
+
+ align:start position:0%
+floor going to be in water there's no
+insurance comp insure that okay it's too
+
+ align:start position:0%
+insurance comp insure that okay it's too
+ 
+
+ align:start position:0%
+insurance comp insure that okay it's too
+much damage you cannot save that that
+
+ align:start position:0%
+much damage you cannot save that that
+ 
+
+ align:start position:0%
+much damage you cannot save that that
+area even right okay that's very good
+
+ align:start position:0%
+area even right okay that's very good
+ 
+
+ align:start position:0%
+area even right okay that's very good
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+other other other sounds whether we can
+
+ align:start position:0%
+other other other sounds whether we can
+ 
+
+ align:start position:0%
+other other other sounds whether we can
+continue to increase the insurance
+
+ align:start position:0%
+continue to increase the insurance
+ 
+
+ align:start position:0%
+continue to increase the insurance
+premium to move money from bad times to
+
+ align:start position:0%
+premium to move money from bad times to
+ 
+
+ align:start position:0%
+premium to move money from bad times to
+from Good Times to B times to double
+
+ align:start position:0%
+from Good Times to B times to double
+ 
+
+ align:start position:0%
+from Good Times to B times to double
+triple the insurance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so it's very hard for the
+
+ align:start position:0%
+okay good so it's very hard for the
+ 
+
+ align:start position:0%
+okay good so it's very hard for the
+insurance companies because it's
+
+ align:start position:0%
+insurance companies because it's
+ 
+
+ align:start position:0%
+insurance companies because it's
+permanent damage to your house right
+
+ align:start position:0%
+permanent damage to your house right
+ 
+
+ align:start position:0%
+permanent damage to your house right
+okay then I'm talking about insurance
+
+ align:start position:0%
+okay then I'm talking about insurance
+ 
+
+ align:start position:0%
+okay then I'm talking about insurance
+companies I'm talking about these
+
+ align:start position:0%
+companies I'm talking about these
+ 
+
+ align:start position:0%
+companies I'm talking about these
+mortgage Market Banks so that I want to
+
+ align:start position:0%
+mortgage Market Banks so that I want to
+ 
+
+ align:start position:0%
+mortgage Market Banks so that I want to
+let you know this is a huge it's so bad
+
+ align:start position:0%
+let you know this is a huge it's so bad
+ 
+
+ align:start position:0%
+let you know this is a huge it's so bad
+situation now crisis but also it's a
+
+ align:start position:0%
+situation now crisis but also it's a
+ 
+
+ align:start position:0%
+situation now crisis but also it's a
+huge demand for all of us to do rigorous
+
+ align:start position:0%
+huge demand for all of us to do rigorous
+ 
+
+ align:start position:0%
+huge demand for all of us to do rigorous
+research and later for your jobs to
+
+ align:start position:0%
+research and later for your jobs to
+ 
+
+ align:start position:0%
+research and later for your jobs to
+contribute to this and try to at least
+
+ align:start position:0%
+contribute to this and try to at least
+ 
+
+ align:start position:0%
+contribute to this and try to at least
+improve us some situation and have this
+
+ align:start position:0%
+improve us some situation and have this
+ 
+
+ align:start position:0%
+improve us some situation and have this
+system to work function more like a sta
+
+ align:start position:0%
+system to work function more like a sta
+ 
+
+ align:start position:0%
+system to work function more like a sta
+so then just now I talk about insurance
+
+ align:start position:0%
+so then just now I talk about insurance
+ 
+
+ align:start position:0%
+so then just now I talk about insurance
+company in crisis and they cannot insure
+
+ align:start position:0%
+company in crisis and they cannot insure
+ 
+
+ align:start position:0%
+company in crisis and they cannot insure
+so much and and also they claim risk in
+
+ align:start position:0%
+so much and and also they claim risk in
+ 
+
+ align:start position:0%
+so much and and also they claim risk in
+mortgage Market I think I will leave
+
+ align:start position:0%
+mortgage Market I think I will leave
+ 
+
+ align:start position:0%
+mortgage Market I think I will leave
+that to ad because ad is a boss of The
+
+ align:start position:0%
+that to ad because ad is a boss of The
+ 
+
+ align:start position:0%
+that to ad because ad is a boss of The
+Fanny May Freddy Mac you understand much
+
+ align:start position:0%
+Fanny May Freddy Mac you understand much
+ 
+
+ align:start position:0%
+Fanny May Freddy Mac you understand much
+more better than me but I think I only
+
+ align:start position:0%
+more better than me but I think I only
+ 
+
+ align:start position:0%
+more better than me but I think I only
+want to see one thing and I want to ask
+
+ align:start position:0%
+want to see one thing and I want to ask
+ 
+
+ align:start position:0%
+want to see one thing and I want to ask
+a question is the following of course
+
+ align:start position:0%
+a question is the following of course
+ 
+
+ align:start position:0%
+a question is the following of course
+this fny man and Fred Mack they have all
+
+ align:start position:0%
+this fny man and Fred Mack they have all
+ 
+
+ align:start position:0%
+this fny man and Fred Mack they have all
+kind of economists they hire a lot of
+
+ align:start position:0%
+kind of economists they hire a lot of
+ 
+
+ align:start position:0%
+kind of economists they hire a lot of
+economists to do this kind of research
+
+ align:start position:0%
+economists to do this kind of research
+ 
+
+ align:start position:0%
+economists to do this kind of research
+they are so smart they understand the
+
+ align:start position:0%
+they are so smart they understand the
+ 
+
+ align:start position:0%
+they are so smart they understand the
+impact of climate risk on property
+
+ align:start position:0%
+impact of climate risk on property
+ 
+
+ align:start position:0%
+impact of climate risk on property
+values they understand the loans they
+
+ align:start position:0%
+values they understand the loans they
+ 
+
+ align:start position:0%
+values they understand the loans they
+borrow the the loans they lend to this
+
+ align:start position:0%
+borrow the the loans they lend to this
+ 
+
+ align:start position:0%
+borrow the the loans they lend to this
+this household and then later securitize
+
+ align:start position:0%
+this household and then later securitize
+ 
+
+ align:start position:0%
+this household and then later securitize
+and sold to the investors are subject to
+
+ align:start position:0%
+and sold to the investors are subject to
+ 
+
+ align:start position:0%
+and sold to the investors are subject to
+these risks they understand that very
+
+ align:start position:0%
+these risks they understand that very
+ 
+
+ align:start position:0%
+these risks they understand that very
+well and they even have this imp crical
+
+ align:start position:0%
+well and they even have this imp crical
+ 
+
+ align:start position:0%
+well and they even have this imp crical
+analysis right and then these two big
+
+ align:start position:0%
+analysis right and then these two big
+ 
+
+ align:start position:0%
+analysis right and then these two big
+government sponsored
+
+ align:start position:0%
+government sponsored
+ 
+
+ align:start position:0%
+government sponsored
+Enterprises they they are back they are
+
+ align:start position:0%
+Enterprises they they are back they are
+ 
+
+ align:start position:0%
+Enterprises they they are back they are
+backing all this uh all those
+
+ align:start position:0%
+backing all this uh all those
+ 
+
+ align:start position:0%
+backing all this uh all those
+Residential Mortgage in the country
+
+ align:start position:0%
+Residential Mortgage in the country
+ 
+
+ align:start position:0%
+Residential Mortgage in the country
+especially median low-income households
+
+ align:start position:0%
+especially median low-income households
+ 
+
+ align:start position:0%
+especially median low-income households
+right this household can get their loan
+
+ align:start position:0%
+right this household can get their loan
+ 
+
+ align:start position:0%
+right this household can get their loan
+security high and and by fedy m and fedy
+
+ align:start position:0%
+security high and and by fedy m and fedy
+ 
+
+ align:start position:0%
+security high and and by fedy m and fedy
+Mac that's a implicit subsidy from the
+
+ align:start position:0%
+Mac that's a implicit subsidy from the
+ 
+
+ align:start position:0%
+Mac that's a implicit subsidy from the
+government to the mortgage Market
+
+ align:start position:0%
+government to the mortgage Market
+ 
+
+ align:start position:0%
+government to the mortgage Market
+however these two big guys FY and fedy
+
+ align:start position:0%
+however these two big guys FY and fedy
+ 
+
+ align:start position:0%
+however these two big guys FY and fedy
+Ma they said we don't want to price
+
+ align:start position:0%
+Ma they said we don't want to price
+ 
+
+ align:start position:0%
+Ma they said we don't want to price
+differently loans which and without
+
+ align:start position:0%
+differently loans which and without
+ 
+
+ align:start position:0%
+differently loans which and without
+climate risks when we decide the rate
+
+ align:start position:0%
+climate risks when we decide the rate
+ 
+
+ align:start position:0%
+climate risks when we decide the rate
+the mortgage rate to the household when
+
+ align:start position:0%
+the mortgage rate to the household when
+ 
+
+ align:start position:0%
+the mortgage rate to the household when
+we decide whether we we we we lend the
+
+ align:start position:0%
+we decide whether we we we we lend the
+ 
+
+ align:start position:0%
+we decide whether we we we we lend the
+loans to to to to the households why
+
+ align:start position:0%
+loans to to to to the households why
+ 
+
+ align:start position:0%
+loans to to to to the households why
+they understand the real
+
+ align:start position:0%
+they understand the real
+ 
+
+ align:start position:0%
+they understand the real
+impact of the climate risks
+
+ align:start position:0%
+impact of the climate risks
+ 
+
+ align:start position:0%
+impact of the climate risks
+flooding um hurricane and and all those
+
+ align:start position:0%
+flooding um hurricane and and all those
+ 
+
+ align:start position:0%
+flooding um hurricane and and all those
+things on property values and and if
+
+ align:start position:0%
+things on property values and and if
+ 
+
+ align:start position:0%
+things on property values and and if
+this houses in these places get hit
+
+ align:start position:0%
+this houses in these places get hit
+ 
+
+ align:start position:0%
+this houses in these places get hit
+maybe will default default means loss to
+
+ align:start position:0%
+maybe will default default means loss to
+ 
+
+ align:start position:0%
+maybe will default default means loss to
+the bank
+
+ align:start position:0%
+the bank
+ 
+
+ align:start position:0%
+the bank
+and loss for the fatty made fatty Mac
+
+ align:start position:0%
+and loss for the fatty made fatty Mac
+ 
+
+ align:start position:0%
+and loss for the fatty made fatty Mac
+they they understand all the imperal
+
+ align:start position:0%
+they they understand all the imperal
+ 
+
+ align:start position:0%
+they they understand all the imperal
+studies such is work and this work not
+
+ align:start position:0%
+studies such is work and this work not
+ 
+
+ align:start position:0%
+studies such is work and this work not
+work then they said okay I understand
+
+ align:start position:0%
+work then they said okay I understand
+ 
+
+ align:start position:0%
+work then they said okay I understand
+but I don't want to
+
+ align:start position:0%
+but I don't want to
+ 
+
+ align:start position:0%
+but I don't want to
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+guess what do you
+
+ align:start position:0%
+guess what do you
+ 
+
+ align:start position:0%
+guess what do you
+think um
+
+ align:start position:0%
+think um
+ 
+
+ align:start position:0%
+think um
+well it just it just uh with
+
+ align:start position:0%
+well it just it just uh with
+ 
+
+ align:start position:0%
+well it just it just uh with
+disadvantage people obviously want to
+
+ align:start position:0%
+disadvantage people obviously want to
+ 
+
+ align:start position:0%
+disadvantage people obviously want to
+live in climate risky areas which of
+
+ align:start position:0%
+live in climate risky areas which of
+ 
+
+ align:start position:0%
+live in climate risky areas which of
+course you could say you don't need to
+
+ align:start position:0%
+course you could say you don't need to
+ 
+
+ align:start position:0%
+course you could say you don't need to
+live there live somewhere else but
+
+ align:start position:0%
+live there live somewhere else but
+ 
+
+ align:start position:0%
+live there live somewhere else but
+there's you know histories of why people
+
+ align:start position:0%
+there's you know histories of why people
+ 
+
+ align:start position:0%
+there's you know histories of why people
+want to live there in their communities
+
+ align:start position:0%
+want to live there in their communities
+ 
+
+ align:start position:0%
+want to live there in their communities
+that are attached to that place so um so
+
+ align:start position:0%
+that are attached to that place so um so
+ 
+
+ align:start position:0%
+that are attached to that place so um so
+it's it's very unfair good that's a very
+
+ align:start position:0%
+it's it's very unfair good that's a very
+ 
+
+ align:start position:0%
+it's it's very unfair good that's a very
+very good answer what do you think
+
+ align:start position:0%
+very good answer what do you think
+ 
+
+ align:start position:0%
+very good answer what do you think
+you're also from d right okay talk about
+
+ align:start position:0%
+you're also from d right okay talk about
+ 
+
+ align:start position:0%
+you're also from d right okay talk about
+from this uh Equity perspective yeah I
+
+ align:start position:0%
+from this uh Equity perspective yeah I
+ 
+
+ align:start position:0%
+from this uh Equity perspective yeah I
+was thinking about the equity
+
+ align:start position:0%
+was thinking about the equity
+ 
+
+ align:start position:0%
+was thinking about the equity
+perspective like almost all public
+
+ align:start position:0%
+perspective like almost all public
+ 
+
+ align:start position:0%
+perspective like almost all public
+housing is in a flood zone as well so
+
+ align:start position:0%
+housing is in a flood zone as well so
+ 
+
+ align:start position:0%
+housing is in a flood zone as well so
+most of the people that are already in
+
+ align:start position:0%
+most of the people that are already in
+ 
+
+ align:start position:0%
+most of the people that are already in
+climate risky areas that aren't able to
+
+ align:start position:0%
+climate risky areas that aren't able to
+ 
+
+ align:start position:0%
+climate risky areas that aren't able to
+adapt as easily yes and would get priced
+
+ align:start position:0%
+adapt as easily yes and would get priced
+ 
+
+ align:start position:0%
+adapt as easily yes and would get priced
+out of the market okay yes so yes that's
+
+ align:start position:0%
+out of the market okay yes so yes that's
+ 
+
+ align:start position:0%
+out of the market okay yes so yes that's
+exactly the social justice perspective
+
+ align:start position:0%
+exactly the social justice perspective
+ 
+
+ align:start position:0%
+exactly the social justice perspective
+yes because if you really accurately
+
+ align:start position:0%
+yes because if you really accurately
+ 
+
+ align:start position:0%
+yes because if you really accurately
+price the climate risk in those um areas
+
+ align:start position:0%
+price the climate risk in those um areas
+ 
+
+ align:start position:0%
+price the climate risk in those um areas
+Coastal and especially those places that
+
+ align:start position:0%
+Coastal and especially those places that
+ 
+
+ align:start position:0%
+Coastal and especially those places that
+may introduce discrimination in the
+
+ align:start position:0%
+may introduce discrimination in the
+ 
+
+ align:start position:0%
+may introduce discrimination in the
+housing market because
+
+ align:start position:0%
+housing market because
+ 
+
+ align:start position:0%
+housing market because
+disproportionately those low and
+
+ align:start position:0%
+disproportionately those low and
+ 
+
+ align:start position:0%
+disproportionately those low and
+marginalized communities they are in the
+
+ align:start position:0%
+marginalized communities they are in the
+ 
+
+ align:start position:0%
+marginalized communities they are in the
+placees they cannot move the mobility
+
+ align:start position:0%
+placees they cannot move the mobility
+ 
+
+ align:start position:0%
+placees they cannot move the mobility
+relatively low they cannot move out oh
+
+ align:start position:0%
+relatively low they cannot move out oh
+ 
+
+ align:start position:0%
+relatively low they cannot move out oh
+yes you can also move move to the to the
+
+ align:start position:0%
+yes you can also move move to the to the
+ 
+
+ align:start position:0%
+yes you can also move move to the to the
+to The High Ground but it's very hard
+
+ align:start position:0%
+to The High Ground but it's very hard
+ 
+
+ align:start position:0%
+to The High Ground but it's very hard
+for them to move to leave the community
+
+ align:start position:0%
+for them to move to leave the community
+ 
+
+ align:start position:0%
+for them to move to leave the community
+they they lose jobs like that that and
+
+ align:start position:0%
+they they lose jobs like that that and
+ 
+
+ align:start position:0%
+they they lose jobs like that that and
+if you price this and then you will
+
+ align:start position:0%
+if you price this and then you will
+ 
+
+ align:start position:0%
+if you price this and then you will
+compromise social justice because of
+
+ align:start position:0%
+compromise social justice because of
+ 
+
+ align:start position:0%
+compromise social justice because of
+this problem so that's they have to
+
+ align:start position:0%
+this problem so that's they have to
+ 
+
+ align:start position:0%
+this problem so that's they have to
+balance not just the efficiency but also
+
+ align:start position:0%
+balance not just the efficiency but also
+ 
+
+ align:start position:0%
+balance not just the efficiency but also
+the equity of the morgage market and how
+
+ align:start position:0%
+the equity of the morgage market and how
+ 
+
+ align:start position:0%
+the equity of the morgage market and how
+if you price what's a what's a
+
+ align:start position:0%
+if you price what's a what's a
+ 
+
+ align:start position:0%
+if you price what's a what's a
+consequences unless you have another
+
+ align:start position:0%
+consequences unless you have another
+ 
+
+ align:start position:0%
+consequences unless you have another
+program to subsidize that
+
+ align:start position:0%
+program to subsidize that
+ 
+
+ align:start position:0%
+program to subsidize that
+so that I will leave to add so that's
+
+ align:start position:0%
+so that I will leave to add so that's
+ 
+
+ align:start position:0%
+so that I will leave to add so that's
+but that's clearly that in indu a
+
+ align:start position:0%
+but that's clearly that in indu a
+ 
+
+ align:start position:0%
+but that's clearly that in indu a
+problem right yes you you you you are
+
+ align:start position:0%
+problem right yes you you you you are
+ 
+
+ align:start position:0%
+problem right yes you you you you are
+worried about uh Equity you are worried
+
+ align:start position:0%
+worried about uh Equity you are worried
+ 
+
+ align:start position:0%
+worried about uh Equity you are worried
+about discrimination if you price the
+
+ align:start position:0%
+about discrimination if you price the
+ 
+
+ align:start position:0%
+about discrimination if you price the
+climate risks but if you don't price
+
+ align:start position:0%
+climate risks but if you don't price
+ 
+
+ align:start position:0%
+climate risks but if you don't price
+that will be big problem to the entire
+
+ align:start position:0%
+that will be big problem to the entire
+ 
+
+ align:start position:0%
+that will be big problem to the entire
+society which is already show here so
+
+ align:start position:0%
+society which is already show here so
+ 
+
+ align:start position:0%
+society which is already show here so
+then from the from uh from 2006 to
+
+ align:start position:0%
+then from the from uh from 2006 to
+ 
+
+ align:start position:0%
+then from the from uh from 2006 to
+Upward there's so many new houses built
+
+ align:start position:0%
+Upward there's so many new houses built
+ 
+
+ align:start position:0%
+Upward there's so many new houses built
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+flone so many because there's no
+
+ align:start position:0%
+flone so many because there's no
+ 
+
+ align:start position:0%
+flone so many because there's no
+additional cost you just build and then
+
+ align:start position:0%
+additional cost you just build and then
+ 
+
+ align:start position:0%
+additional cost you just build and then
+you can still get mortgage from the bank
+
+ align:start position:0%
+you can still get mortgage from the bank
+ 
+
+ align:start position:0%
+you can still get mortgage from the bank
+they are not going to consider flly risk
+
+ align:start position:0%
+they are not going to consider flly risk
+ 
+
+ align:start position:0%
+they are not going to consider flly risk
+build build build and the house go there
+
+ align:start position:0%
+build build build and the house go there
+ 
+
+ align:start position:0%
+build build build and the house go there
+to buy there so many new houses built
+
+ align:start position:0%
+to buy there so many new houses built
+ 
+
+ align:start position:0%
+to buy there so many new houses built
+and they borrow all the mortgage from
+
+ align:start position:0%
+and they borrow all the mortgage from
+ 
+
+ align:start position:0%
+and they borrow all the mortgage from
+Banks because they they don't consider
+
+ align:start position:0%
+Banks because they they don't consider
+ 
+
+ align:start position:0%
+Banks because they they don't consider
+risk then they borrow Mortgage in FL
+
+ align:start position:0%
+risk then they borrow Mortgage in FL
+ 
+
+ align:start position:0%
+risk then they borrow Mortgage in FL
+zones increase so much
+
+ align:start position:0%
+zones increase so much
+ 
+
+ align:start position:0%
+zones increase so much
+but for the for the for the for the
+
+ align:start position:0%
+but for the for the for the for the
+ 
+
+ align:start position:0%
+but for the for the for the for the
+houses really insured by this National
+
+ align:start position:0%
+houses really insured by this National
+ 
+
+ align:start position:0%
+houses really insured by this National
+flood insurance program just now
+
+ align:start position:0%
+flood insurance program just now
+ 
+
+ align:start position:0%
+flood insurance program just now
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+nfip declined they declined why because
+
+ align:start position:0%
+nfip declined they declined why because
+ 
+
+ align:start position:0%
+nfip declined they declined why because
+more so many new houses built and they
+
+ align:start position:0%
+more so many new houses built and they
+ 
+
+ align:start position:0%
+more so many new houses built and they
+are going to borrow money from the bank
+
+ align:start position:0%
+are going to borrow money from the bank
+ 
+
+ align:start position:0%
+are going to borrow money from the bank
+and Bank just lend money to them and
+
+ align:start position:0%
+and Bank just lend money to them and
+ 
+
+ align:start position:0%
+and Bank just lend money to them and
+then they all go to this mfip to ask for
+
+ align:start position:0%
+then they all go to this mfip to ask for
+ 
+
+ align:start position:0%
+then they all go to this mfip to ask for
+insurance when nfip run out of money
+
+ align:start position:0%
+insurance when nfip run out of money
+ 
+
+ align:start position:0%
+insurance when nfip run out of money
+nfip is a federal government not federal
+
+ align:start position:0%
+nfip is a federal government not federal
+ 
+
+ align:start position:0%
+nfip is a federal government not federal
+a federal agency they also need money to
+
+ align:start position:0%
+a federal agency they also need money to
+ 
+
+ align:start position:0%
+a federal agency they also need money to
+provide Insurance just now I already
+
+ align:start position:0%
+provide Insurance just now I already
+ 
+
+ align:start position:0%
+provide Insurance just now I already
+said the insurance is in a crisis
+
+ align:start position:0%
+said the insurance is in a crisis
+ 
+
+ align:start position:0%
+said the insurance is in a crisis
+because the increasing number of these
+
+ align:start position:0%
+because the increasing number of these
+ 
+
+ align:start position:0%
+because the increasing number of these
+disasters and uh and also they are
+
+ align:start position:0%
+disasters and uh and also they are
+ 
+
+ align:start position:0%
+disasters and uh and also they are
+federal agency they cannot increase the
+
+ align:start position:0%
+federal agency they cannot increase the
+ 
+
+ align:start position:0%
+federal agency they cannot increase the
+premium too much then nobody can pay Out
+
+ align:start position:0%
+premium too much then nobody can pay Out
+ 
+
+ align:start position:0%
+premium too much then nobody can pay Out
+Of Reach of the of those household so
+
+ align:start position:0%
+Of Reach of the of those household so
+ 
+
+ align:start position:0%
+Of Reach of the of those household so
+they have a subsidized the insurance
+
+ align:start position:0%
+they have a subsidized the insurance
+ 
+
+ align:start position:0%
+they have a subsidized the insurance
+premium and they have to cover more and
+
+ align:start position:0%
+premium and they have to cover more and
+ 
+
+ align:start position:0%
+premium and they have to cover more and
+more disasters they run out of money
+
+ align:start position:0%
+more disasters they run out of money
+ 
+
+ align:start position:0%
+more disasters they run out of money
+they went to Congress said okay I run
+
+ align:start position:0%
+they went to Congress said okay I run
+ 
+
+ align:start position:0%
+they went to Congress said okay I run
+out of money how should I do either the
+
+ align:start position:0%
+out of money how should I do either the
+ 
+
+ align:start position:0%
+out of money how should I do either the
+Congress give me more money or we cannot
+
+ align:start position:0%
+Congress give me more money or we cannot
+ 
+
+ align:start position:0%
+Congress give me more money or we cannot
+offer this subsidize insurance for those
+
+ align:start position:0%
+offer this subsidize insurance for those
+ 
+
+ align:start position:0%
+offer this subsidize insurance for those
+households in this areas so insurance
+
+ align:start position:0%
+households in this areas so insurance
+ 
+
+ align:start position:0%
+households in this areas so insurance
+rate declined so that's a big problem
+
+ align:start position:0%
+rate declined so that's a big problem
+ 
+
+ align:start position:0%
+rate declined so that's a big problem
+right okay we we cannot uh price the
+
+ align:start position:0%
+right okay we we cannot uh price the
+ 
+
+ align:start position:0%
+right okay we we cannot uh price the
+risk then more how they build
+
+ align:start position:0%
+risk then more how they build
+ 
+
+ align:start position:0%
+risk then more how they build
+and they got mortgage and and FIP when
+
+ align:start position:0%
+and they got mortgage and and FIP when
+ 
+
+ align:start position:0%
+and they got mortgage and and FIP when
+got bankr and run out of money go to
+
+ align:start position:0%
+got bankr and run out of money go to
+ 
+
+ align:start position:0%
+got bankr and run out of money go to
+Congress Congress I think they give them
+
+ align:start position:0%
+Congress Congress I think they give them
+ 
+
+ align:start position:0%
+Congress Congress I think they give them
+some money but they cannot continuous
+
+ align:start position:0%
+some money but they cannot continuous
+ 
+
+ align:start position:0%
+some money but they cannot continuous
+endlessly give them money so I think
+
+ align:start position:0%
+endlessly give them money so I think
+ 
+
+ align:start position:0%
+endlessly give them money so I think
+that's the current situation I'm not
+
+ align:start position:0%
+that's the current situation I'm not
+ 
+
+ align:start position:0%
+that's the current situation I'm not
+sure how we can help we will listen to
+
+ align:start position:0%
+sure how we can help we will listen to
+ 
+
+ align:start position:0%
+sure how we can help we will listen to
+that okay now we have a new research
+
+ align:start position:0%
+that okay now we have a new research
+ 
+
+ align:start position:0%
+that okay now we have a new research
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+fanime if you are interested in doing
+
+ align:start position:0%
+fanime if you are interested in doing
+ 
+
+ align:start position:0%
+fanime if you are interested in doing
+sis on this talk to me again so it's say
+
+ align:start position:0%
+sis on this talk to me again so it's say
+ 
+
+ align:start position:0%
+sis on this talk to me again so it's say
+so many good research right okay this
+
+ align:start position:0%
+so many good research right okay this
+ 
+
+ align:start position:0%
+so many good research right okay this
+just got approved by fime we're going to
+
+ align:start position:0%
+just got approved by fime we're going to
+ 
+
+ align:start position:0%
+just got approved by fime we're going to
+do this we really want to
+
+ align:start position:0%
+do this we really want to
+ 
+
+ align:start position:0%
+do this we really want to
+see if we want to change this situation
+
+ align:start position:0%
+see if we want to change this situation
+ 
+
+ align:start position:0%
+see if we want to change this situation
+baby steps the first baby step is to
+
+ align:start position:0%
+baby steps the first baby step is to
+ 
+
+ align:start position:0%
+baby steps the first baby step is to
+train appraisers in fin May and Freddy
+
+ align:start position:0%
+train appraisers in fin May and Freddy
+ 
+
+ align:start position:0%
+train appraisers in fin May and Freddy
+ma when you appr when you appra the
+
+ align:start position:0%
+ma when you appr when you appra the
+ 
+
+ align:start position:0%
+ma when you appr when you appra the
+houses you know appraisal right you can
+
+ align:start position:0%
+houses you know appraisal right you can
+ 
+
+ align:start position:0%
+houses you know appraisal right you can
+say location a this now if there's a CL
+
+ align:start position:0%
+say location a this now if there's a CL
+ 
+
+ align:start position:0%
+say location a this now if there's a CL
+risk no matter whether we will really
+
+ align:start position:0%
+risk no matter whether we will really
+ 
+
+ align:start position:0%
+risk no matter whether we will really
+take action to do that but you need to
+
+ align:start position:0%
+take action to do that but you need to
+ 
+
+ align:start position:0%
+take action to do that but you need to
+do the sense you first understand how
+
+ align:start position:0%
+do the sense you first understand how
+ 
+
+ align:start position:0%
+do the sense you first understand how
+the appraisers you can
+
+ align:start position:0%
+the appraisers you can
+ 
+
+ align:start position:0%
+the appraisers you can
+really really price the climate risk
+
+ align:start position:0%
+really really price the climate risk
+ 
+
+ align:start position:0%
+really really price the climate risk
+into these uh loans so that's our
+
+ align:start position:0%
+into these uh loans so that's our
+ 
+
+ align:start position:0%
+into these uh loans so that's our
+project to understand whether there is
+
+ align:start position:0%
+project to understand whether there is
+ 
+
+ align:start position:0%
+project to understand whether there is
+the appraisal buyers when you don't
+
+ align:start position:0%
+the appraisal buyers when you don't
+ 
+
+ align:start position:0%
+the appraisal buyers when you don't
+consider climate risk and what see
+
+ align:start position:0%
+consider climate risk and what see
+ 
+
+ align:start position:0%
+consider climate risk and what see
+heterogenity with a variation different
+
+ align:start position:0%
+heterogenity with a variation different
+ 
+
+ align:start position:0%
+heterogenity with a variation different
+locations different household like that
+
+ align:start position:0%
+locations different household like that
+ 
+
+ align:start position:0%
+locations different household like that
+is and that so that's our real project
+
+ align:start position:0%
+is and that so that's our real project
+ 
+
+ align:start position:0%
+is and that so that's our real project
+we're going to do in this coming year
+
+ align:start position:0%
+we're going to do in this coming year
+ 
+
+ align:start position:0%
+we're going to do in this coming year
+from now a year and uh to quantify the
+
+ align:start position:0%
+from now a year and uh to quantify the
+ 
+
+ align:start position:0%
+from now a year and uh to quantify the
+appraisal buyers of because of the
+
+ align:start position:0%
+appraisal buyers of because of the
+ 
+
+ align:start position:0%
+appraisal buyers of because of the
+climate risk and then go there to to to
+
+ align:start position:0%
+climate risk and then go there to to to
+ 
+
+ align:start position:0%
+climate risk and then go there to to to
+train those appraisers if you want to do
+
+ align:start position:0%
+train those appraisers if you want to do
+ 
+
+ align:start position:0%
+train those appraisers if you want to do
+this in right way you should do this and
+
+ align:start position:0%
+this in right way you should do this and
+ 
+
+ align:start position:0%
+this in right way you should do this and
+this that's that's our project and uh so
+
+ align:start position:0%
+this that's that's our project and uh so
+ 
+
+ align:start position:0%
+this that's that's our project and uh so
+that's a Fanny May project so now I have
+
+ align:start position:0%
+that's a Fanny May project so now I have
+ 
+
+ align:start position:0%
+that's a Fanny May project so now I have
+two projects Fanny May project and that
+
+ align:start position:0%
+two projects Fanny May project and that
+ 
+
+ align:start position:0%
+two projects Fanny May project and that
+Moody
+
+ align:start position:0%
+Moody
+ 
+
+ align:start position:0%
+Moody
+project okay so we already talked about
+
+ align:start position:0%
+project okay so we already talked about
+ 
+
+ align:start position:0%
+project okay so we already talked about
+the uh this this this this uh f Federal
+
+ align:start position:0%
+the uh this this this this uh f Federal
+ 
+
+ align:start position:0%
+the uh this this this this uh f Federal
+agency nfip run out of money because the
+
+ align:start position:0%
+agency nfip run out of money because the
+ 
+
+ align:start position:0%
+agency nfip run out of money because the
+subsidized flood insurance and so many
+
+ align:start position:0%
+subsidized flood insurance and so many
+ 
+
+ align:start position:0%
+subsidized flood insurance and so many
+new houses and so many new mortgages you
+
+ align:start position:0%
+new houses and so many new mortgages you
+ 
+
+ align:start position:0%
+new houses and so many new mortgages you
+run out of money and from the other side
+
+ align:start position:0%
+run out of money and from the other side
+ 
+
+ align:start position:0%
+run out of money and from the other side
+it's a low take off low take up of the
+
+ align:start position:0%
+it's a low take off low take up of the
+ 
+
+ align:start position:0%
+it's a low take off low take up of the
+flat Insurance even if you are in flat
+
+ align:start position:0%
+flat Insurance even if you are in flat
+ 
+
+ align:start position:0%
+flat Insurance even if you are in flat
+zones now because FP R money and the
+
+ align:start position:0%
+zones now because FP R money and the
+ 
+
+ align:start position:0%
+zones now because FP R money and the
+other way is this very low awareness of
+
+ align:start position:0%
+other way is this very low awareness of
+ 
+
+ align:start position:0%
+other way is this very low awareness of
+the things the households they also they
+
+ align:start position:0%
+the things the households they also they
+ 
+
+ align:start position:0%
+the things the households they also they
+they don't understand and then they say
+
+ align:start position:0%
+they don't understand and then they say
+ 
+
+ align:start position:0%
+they don't understand and then they say
+why I need to pay act extra money I
+
+ align:start position:0%
+why I need to pay act extra money I
+ 
+
+ align:start position:0%
+why I need to pay act extra money I
+don't want to pay so that's a low take
+
+ align:start position:0%
+don't want to pay so that's a low take
+ 
+
+ align:start position:0%
+don't want to pay so that's a low take
+up of the insurance both from the supply
+
+ align:start position:0%
+up of the insurance both from the supply
+ 
+
+ align:start position:0%
+up of the insurance both from the supply
+side of the insurance no money and the
+
+ align:start position:0%
+side of the insurance no money and the
+ 
+
+ align:start position:0%
+side of the insurance no money and the
+demand side they don't want to pay extra
+
+ align:start position:0%
+demand side they don't want to pay extra
+ 
+
+ align:start position:0%
+demand side they don't want to pay extra
+money and they are they they have very
+
+ align:start position:0%
+money and they are they they have very
+ 
+
+ align:start position:0%
+money and they are they they have very
+low awareness of the thing so and then
+
+ align:start position:0%
+low awareness of the thing so and then
+ 
+
+ align:start position:0%
+low awareness of the thing so and then
+you then at first I couldn't understand
+
+ align:start position:0%
+you then at first I couldn't understand
+ 
+
+ align:start position:0%
+you then at first I couldn't understand
+this I thought it's mandatory right it's
+
+ align:start position:0%
+this I thought it's mandatory right it's
+ 
+
+ align:start position:0%
+this I thought it's mandatory right it's
+mandatory if you buy a house if you want
+
+ align:start position:0%
+mandatory if you buy a house if you want
+ 
+
+ align:start position:0%
+mandatory if you buy a house if you want
+to borrow money from the bank if you are
+
+ align:start position:0%
+to borrow money from the bank if you are
+ 
+
+ align:start position:0%
+to borrow money from the bank if you are
+in the flat zone then you must buy
+
+ align:start position:0%
+in the flat zone then you must buy
+ 
+
+ align:start position:0%
+in the flat zone then you must buy
+the insurance that's
+
+ align:start position:0%
+the insurance that's
+ 
+
+ align:start position:0%
+the insurance that's
+required then later I I got to know that
+
+ align:start position:0%
+required then later I I got to know that
+ 
+
+ align:start position:0%
+required then later I I got to know that
+yes when you buy the house borrow money
+
+ align:start position:0%
+yes when you buy the house borrow money
+ 
+
+ align:start position:0%
+yes when you buy the house borrow money
+you need to buy that's Mand mandatory
+
+ align:start position:0%
+you need to buy that's Mand mandatory
+ 
+
+ align:start position:0%
+you need to buy that's Mand mandatory
+but just one year after a year you need
+
+ align:start position:0%
+but just one year after a year you need
+ 
+
+ align:start position:0%
+but just one year after a year you need
+to renew and many household forget about
+
+ align:start position:0%
+to renew and many household forget about
+ 
+
+ align:start position:0%
+to renew and many household forget about
+this they don't renew so you only when
+
+ align:start position:0%
+this they don't renew so you only when
+ 
+
+ align:start position:0%
+this they don't renew so you only when
+you are borrowing money that's that's
+
+ align:start position:0%
+you are borrowing money that's that's
+ 
+
+ align:start position:0%
+you are borrowing money that's that's
+year you buy then later I don't want to
+
+ align:start position:0%
+year you buy then later I don't want to
+ 
+
+ align:start position:0%
+year you buy then later I don't want to
+renew then they they just they just out
+
+ align:start position:0%
+renew then they they just they just out
+ 
+
+ align:start position:0%
+renew then they they just they just out
+of this thing so only 20%
+
+ align:start position:0%
+of this thing so only 20%
+ 
+
+ align:start position:0%
+of this thing so only 20%
+% only 20% among hous of flooded in New
+
+ align:start position:0%
+% only 20% among hous of flooded in New
+ 
+
+ align:start position:0%
+% only 20% among hous of flooded in New
+York City uh Hurricane Sandy and uh
+
+ align:start position:0%
+York City uh Hurricane Sandy and uh
+ 
+
+ align:start position:0%
+York City uh Hurricane Sandy and uh
+Haring ho all the all the hous got
+
+ align:start position:0%
+Haring ho all the all the hous got
+ 
+
+ align:start position:0%
+Haring ho all the all the hous got
+flooded only 20% they have insurance
+
+ align:start position:0%
+flooded only 20% they have insurance
+ 
+
+ align:start position:0%
+flooded only 20% they have insurance
+that's a big problem and of course
+
+ align:start position:0%
+that's a big problem and of course
+ 
+
+ align:start position:0%
+that's a big problem and of course
+Highly Educated they have higher take up
+
+ align:start position:0%
+Highly Educated they have higher take up
+ 
+
+ align:start position:0%
+Highly Educated they have higher take up
+rate like that because they understand
+
+ align:start position:0%
+rate like that because they understand
+ 
+
+ align:start position:0%
+rate like that because they understand
+for those who they don't understand
+
+ align:start position:0%
+for those who they don't understand
+ 
+
+ align:start position:0%
+for those who they don't understand
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+problem now the insurance Market start
+
+ align:start position:0%
+problem now the insurance Market start
+ 
+
+ align:start position:0%
+problem now the insurance Market start
+to wake up they start to wake up oh this
+
+ align:start position:0%
+to wake up they start to wake up oh this
+ 
+
+ align:start position:0%
+to wake up they start to wake up oh this
+a big problem we cannot stay in this
+
+ align:start position:0%
+a big problem we cannot stay in this
+ 
+
+ align:start position:0%
+a big problem we cannot stay in this
+forever then they have the risk reading
+
+ align:start position:0%
+forever then they have the risk reading
+ 
+
+ align:start position:0%
+forever then they have the risk reading
+2.0 error they say okay we must make
+
+ align:start position:0%
+2.0 error they say okay we must make
+ 
+
+ align:start position:0%
+2.0 error they say okay we must make
+sure the insurance premium really
+
+ align:start position:0%
+sure the insurance premium really
+ 
+
+ align:start position:0%
+sure the insurance premium really
+reflect the risk that we move money from
+
+ align:start position:0%
+reflect the risk that we move money from
+ 
+
+ align:start position:0%
+reflect the risk that we move money from
+the good time to B time in the right way
+
+ align:start position:0%
+the good time to B time in the right way
+ 
+
+ align:start position:0%
+the good time to B time in the right way
+that's kind of Reform right now for the
+
+ align:start position:0%
+that's kind of Reform right now for the
+ 
+
+ align:start position:0%
+that's kind of Reform right now for the
+insurance Market of
+
+ align:start position:0%
+insurance Market of
+ 
+
+ align:start position:0%
+insurance Market of
+2.0 so I will be very brief but anyway
+
+ align:start position:0%
+2.0 so I will be very brief but anyway
+ 
+
+ align:start position:0%
+2.0 so I will be very brief but anyway
+you understand so this will introduce
+
+ align:start position:0%
+you understand so this will introduce
+ 
+
+ align:start position:0%
+you understand so this will introduce
+more and more
+
+ align:start position:0%
+more and more
+ 
+
+ align:start position:0%
+more and more
+differences variations in the insurance
+
+ align:start position:0%
+differences variations in the insurance
+ 
+
+ align:start position:0%
+differences variations in the insurance
+premium based on the kind of the risk
+
+ align:start position:0%
+premium based on the kind of the risk
+ 
+
+ align:start position:0%
+premium based on the kind of the risk
+increase and also because this National
+
+ align:start position:0%
+increase and also because this National
+ 
+
+ align:start position:0%
+increase and also because this National
+agency run out of money Federal agency
+
+ align:start position:0%
+agency run out of money Federal agency
+ 
+
+ align:start position:0%
+agency run out of money Federal agency
+run out money and then overall all the
+
+ align:start position:0%
+run out money and then overall all the
+ 
+
+ align:start position:0%
+run out money and then overall all the
+household will see a
+
+ align:start position:0%
+household will see a
+ 
+
+ align:start position:0%
+household will see a
+increase we'll see a increase only about
+
+ align:start position:0%
+increase we'll see a increase only about
+ 
+
+ align:start position:0%
+increase we'll see a increase only about
+23% will see a decrease and all those
+
+ align:start position:0%
+23% will see a decrease and all those
+ 
+
+ align:start position:0%
+23% will see a decrease and all those
+will see the increase and more and more
+
+ align:start position:0%
+will see the increase and more and more
+ 
+
+ align:start position:0%
+will see the increase and more and more
+increase of your insurance premium if
+
+ align:start position:0%
+increase of your insurance premium if
+ 
+
+ align:start position:0%
+increase of your insurance premium if
+you are in the FL zone of course a lot
+
+ align:start position:0%
+you are in the FL zone of course a lot
+ 
+
+ align:start position:0%
+you are in the FL zone of course a lot
+of push back from communities and the
+
+ align:start position:0%
+of push back from communities and the
+ 
+
+ align:start position:0%
+of push back from communities and the
+household the home buyers why we say the
+
+ align:start position:0%
+household the home buyers why we say the
+ 
+
+ align:start position:0%
+household the home buyers why we say the
+insurance the government need to
+
+ align:start position:0%
+insurance the government need to
+ 
+
+ align:start position:0%
+insurance the government need to
+subsidize like that but anyway the thing
+
+ align:start position:0%
+subsidize like that but anyway the thing
+ 
+
+ align:start position:0%
+subsidize like that but anyway the thing
+is an f r of money they go to Congress
+
+ align:start position:0%
+is an f r of money they go to Congress
+ 
+
+ align:start position:0%
+is an f r of money they go to Congress
+they give some money but still run out
+
+ align:start position:0%
+they give some money but still run out
+ 
+
+ align:start position:0%
+they give some money but still run out
+of money still will continue to lose
+
+ align:start position:0%
+of money still will continue to lose
+ 
+
+ align:start position:0%
+of money still will continue to lose
+money so increase and
+
+ align:start position:0%
+money so increase and
+ 
+
+ align:start position:0%
+money so increase and
+reflect and then they also understand
+
+ align:start position:0%
+reflect and then they also understand
+ 
+
+ align:start position:0%
+reflect and then they also understand
+now now the nfip insurance premium so in
+
+ align:start position:0%
+now now the nfip insurance premium so in
+ 
+
+ align:start position:0%
+now now the nfip insurance premium so in
+accurate although they have these
+
+ align:start position:0%
+accurate although they have these
+ 
+
+ align:start position:0%
+accurate although they have these
+numbers all if you elevate your premium
+
+ align:start position:0%
+numbers all if you elevate your premium
+ 
+
+ align:start position:0%
+numbers all if you elevate your premium
+reduce like that but look at the country
+
+ align:start position:0%
+reduce like that but look at the country
+ 
+
+ align:start position:0%
+reduce like that but look at the country
+look at the country average expected
+
+ align:start position:0%
+look at the country average expected
+ 
+
+ align:start position:0%
+look at the country average expected
+annual loss for damage CL damage higher
+
+ align:start position:0%
+annual loss for damage CL damage higher
+ 
+
+ align:start position:0%
+annual loss for damage CL damage higher
+than the average premium all these dark
+
+ align:start position:0%
+than the average premium all these dark
+ 
+
+ align:start position:0%
+than the average premium all these dark
+areas the real damage much higher than
+
+ align:start position:0%
+areas the real damage much higher than
+ 
+
+ align:start position:0%
+areas the real damage much higher than
+the premium only those places because I
+
+ align:start position:0%
+the premium only those places because I
+ 
+
+ align:start position:0%
+the premium only those places because I
+think this risk may be lower and the
+
+ align:start position:0%
+think this risk may be lower and the
+ 
+
+ align:start position:0%
+think this risk may be lower and the
+coastal areas this W wif fire area all
+
+ align:start position:0%
+coastal areas this W wif fire area all
+ 
+
+ align:start position:0%
+coastal areas this W wif fire area all
+those places hurricane places insurance
+
+ align:start position:0%
+those places hurricane places insurance
+ 
+
+ align:start position:0%
+those places hurricane places insurance
+premium low damage high so cannot
+
+ align:start position:0%
+premium low damage high so cannot
+ 
+
+ align:start position:0%
+premium low damage high so cannot
+sustain however low income communities
+
+ align:start position:0%
+sustain however low income communities
+ 
+
+ align:start position:0%
+sustain however low income communities
+very difficult for them right so
+
+ align:start position:0%
+very difficult for them right so
+ 
+
+ align:start position:0%
+very difficult for them right so
+difficult for them and uh for example
+
+ align:start position:0%
+difficult for them and uh for example
+ 
+
+ align:start position:0%
+difficult for them and uh for example
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+area is uh West Virginia more than a
+
+ align:start position:0%
+area is uh West Virginia more than a
+ 
+
+ align:start position:0%
+area is uh West Virginia more than a
+fifth of the household for below the
+
+ align:start position:0%
+fifth of the household for below the
+ 
+
+ align:start position:0%
+fifth of the household for below the
+federal poverty level and they have to
+
+ align:start position:0%
+federal poverty level and they have to
+ 
+
+ align:start position:0%
+federal poverty level and they have to
+pay the premium higher like five 500
+
+ align:start position:0%
+pay the premium higher like five 500
+ 
+
+ align:start position:0%
+pay the premium higher like five 500
+higher than nowadays the rate the
+
+ align:start position:0%
+higher than nowadays the rate the
+ 
+
+ align:start position:0%
+higher than nowadays the rate the
+premium how can they pay they are below
+
+ align:start position:0%
+premium how can they pay they are below
+ 
+
+ align:start position:0%
+premium how can they pay they are below
+the poverty line and they are they are
+
+ align:start position:0%
+the poverty line and they are they are
+ 
+
+ align:start position:0%
+the poverty line and they are they are
+living in this vulnerable locations and
+
+ align:start position:0%
+living in this vulnerable locations and
+ 
+
+ align:start position:0%
+living in this vulnerable locations and
+then they say Okay risk rating 2.0
+
+ align:start position:0%
+then they say Okay risk rating 2.0
+ 
+
+ align:start position:0%
+then they say Okay risk rating 2.0
+increase the pre premium to reflect the
+
+ align:start position:0%
+increase the pre premium to reflect the
+ 
+
+ align:start position:0%
+increase the pre premium to reflect the
+real risk then how can they
+
+ align:start position:0%
+real risk then how can they
+ 
+
+ align:start position:0%
+real risk then how can they
+pay and then okay another final point I
+
+ align:start position:0%
+pay and then okay another final point I
+ 
+
+ align:start position:0%
+pay and then okay another final point I
+want to make is another crisis is the
+
+ align:start position:0%
+want to make is another crisis is the
+ 
+
+ align:start position:0%
+want to make is another crisis is the
+following now I talk about nfip is a in
+
+ align:start position:0%
+following now I talk about nfip is a in
+ 
+
+ align:start position:0%
+following now I talk about nfip is a in
+is a agency Federal agency run Auto
+
+ align:start position:0%
+is a agency Federal agency run Auto
+ 
+
+ align:start position:0%
+is a agency Federal agency run Auto
+money because it's Federal so they
+
+ align:start position:0%
+money because it's Federal so they
+ 
+
+ align:start position:0%
+money because it's Federal so they
+subsidize subsidize that can justify and
+
+ align:start position:0%
+subsidize subsidize that can justify and
+ 
+
+ align:start position:0%
+subsidize subsidize that can justify and
+they subsidize okay if the Congress
+
+ align:start position:0%
+they subsidize okay if the Congress
+ 
+
+ align:start position:0%
+they subsidize okay if the Congress
+continue to give money to them and there
+
+ align:start position:0%
+continue to give money to them and there
+ 
+
+ align:start position:0%
+continue to give money to them and there
+are private insurance companies
+
+ align:start position:0%
+are private insurance companies
+ 
+
+ align:start position:0%
+are private insurance companies
+also right the private insurance
+
+ align:start position:0%
+also right the private insurance
+ 
+
+ align:start position:0%
+also right the private insurance
+companies is the following the problem I
+
+ align:start position:0%
+companies is the following the problem I
+ 
+
+ align:start position:0%
+companies is the following the problem I
+think this last five is the states
+
+ align:start position:0%
+think this last five is the states
+ 
+
+ align:start position:0%
+think this last five is the states
+depending which state you are in if the
+
+ align:start position:0%
+depending which state you are in if the
+ 
+
+ align:start position:0%
+depending which state you are in if the
+states say okay we want to regulate the
+
+ align:start position:0%
+states say okay we want to regulate the
+ 
+
+ align:start position:0%
+states say okay we want to regulate the
+insurance companies you cannot charge
+
+ align:start position:0%
+insurance companies you cannot charge
+ 
+
+ align:start position:0%
+insurance companies you cannot charge
+very high insurance premium because
+
+ align:start position:0%
+very high insurance premium because
+ 
+
+ align:start position:0%
+very high insurance premium because
+that's will hurt all all my people then
+
+ align:start position:0%
+that's will hurt all all my people then
+ 
+
+ align:start position:0%
+that's will hurt all all my people then
+they say okay the The
+
+ align:start position:0%
+they say okay the The
+ 
+
+ align:start position:0%
+they say okay the The
+Regulators they require home insurance
+
+ align:start position:0%
+Regulators they require home insurance
+ 
+
+ align:start position:0%
+Regulators they require home insurance
+those companies no matter you are you
+
+ align:start position:0%
+those companies no matter you are you
+ 
+
+ align:start position:0%
+those companies no matter you are you
+are you are you are public companies or
+
+ align:start position:0%
+are you are you are public companies or
+ 
+
+ align:start position:0%
+are you are you are public companies or
+you are private companies based on the
+
+ align:start position:0%
+you are private companies based on the
+ 
+
+ align:start position:0%
+you are private companies based on the
+historical loss not the future
+
+ align:start position:0%
+historical loss not the future
+ 
+
+ align:start position:0%
+historical loss not the future
+loss and then they say you cannot charge
+
+ align:start position:0%
+loss and then they say you cannot charge
+ 
+
+ align:start position:0%
+loss and then they say you cannot charge
+too high if you charge too high that
+
+ align:start position:0%
+too high if you charge too high that
+ 
+
+ align:start position:0%
+too high if you charge too high that
+will become a problem and will hurt the
+
+ align:start position:0%
+will become a problem and will hurt the
+ 
+
+ align:start position:0%
+will become a problem and will hurt the
+communities then we call it a high
+
+ align:start position:0%
+communities then we call it a high
+ 
+
+ align:start position:0%
+communities then we call it a high
+frequency not high friction States and
+
+ align:start position:0%
+frequency not high friction States and
+ 
+
+ align:start position:0%
+frequency not high friction States and
+then and the insurance the private
+
+ align:start position:0%
+then and the insurance the private
+ 
+
+ align:start position:0%
+then and the insurance the private
+insurance companies they they they are
+
+ align:start position:0%
+insurance companies they they they are
+ 
+
+ align:start position:0%
+insurance companies they they they are
+leaving those States because the private
+
+ align:start position:0%
+leaving those States because the private
+ 
+
+ align:start position:0%
+leaving those States because the private
+insurance companies they don't have the
+
+ align:start position:0%
+insurance companies they don't have the
+ 
+
+ align:start position:0%
+insurance companies they don't have the
+obligation to subsidize right they will
+
+ align:start position:0%
+obligation to subsidize right they will
+ 
+
+ align:start position:0%
+obligation to subsidize right they will
+price in a market way when they Price
+
+ align:start position:0%
+price in a market way when they Price
+ 
+
+ align:start position:0%
+price in a market way when they Price
+Market they want to increase the
+
+ align:start position:0%
+Market they want to increase the
+ 
+
+ align:start position:0%
+Market they want to increase the
+insurance premium because they
+
+ align:start position:0%
+insurance premium because they
+ 
+
+ align:start position:0%
+insurance premium because they
+understand we need to look at the future
+
+ align:start position:0%
+understand we need to look at the future
+ 
+
+ align:start position:0%
+understand we need to look at the future
+not the past because all the disasters
+
+ align:start position:0%
+not the past because all the disasters
+ 
+
+ align:start position:0%
+not the past because all the disasters
+are rising and they say we want to
+
+ align:start position:0%
+are rising and they say we want to
+ 
+
+ align:start position:0%
+are rising and they say we want to
+increase the state Governor said you
+
+ align:start position:0%
+increase the state Governor said you
+ 
+
+ align:start position:0%
+increase the state Governor said you
+cannot increase we have the regulation
+
+ align:start position:0%
+cannot increase we have the regulation
+ 
+
+ align:start position:0%
+cannot increase we have the regulation
+you must do you must look at the hisory
+
+ align:start position:0%
+you must do you must look at the hisory
+ 
+
+ align:start position:0%
+you must do you must look at the hisory
+not the future and we we don't want to
+
+ align:start position:0%
+not the future and we we don't want to
+ 
+
+ align:start position:0%
+not the future and we we don't want to
+increase the premium too high then they
+
+ align:start position:0%
+increase the premium too high then they
+ 
+
+ align:start position:0%
+increase the premium too high then they
+okay byebye I don't want to run business
+
+ align:start position:0%
+okay byebye I don't want to run business
+ 
+
+ align:start position:0%
+okay byebye I don't want to run business
+in States it's hard I'm losing money
+
+ align:start position:0%
+in States it's hard I'm losing money
+ 
+
+ align:start position:0%
+in States it's hard I'm losing money
+so they are leaving those those States
+
+ align:start position:0%
+so they are leaving those those States
+ 
+
+ align:start position:0%
+so they are leaving those those States
+those States because for those High
+
+ align:start position:0%
+those States because for those High
+ 
+
+ align:start position:0%
+those States because for those High
+frequen States the loss and the rate are
+
+ align:start position:0%
+frequen States the loss and the rate are
+ 
+
+ align:start position:0%
+frequen States the loss and the rate are
+almost flat no matter how big loss you
+
+ align:start position:0%
+almost flat no matter how big loss you
+ 
+
+ align:start position:0%
+almost flat no matter how big loss you
+are you cannot increase your rate but
+
+ align:start position:0%
+are you cannot increase your rate but
+ 
+
+ align:start position:0%
+are you cannot increase your rate but
+they they are leaving then the
+
+ align:start position:0%
+they they are leaving then the
+ 
+
+ align:start position:0%
+they they are leaving then the
+households in that state cannot find
+
+ align:start position:0%
+households in that state cannot find
+ 
+
+ align:start position:0%
+households in that state cannot find
+enough insurance company to buy
+
+ align:start position:0%
+enough insurance company to buy
+ 
+
+ align:start position:0%
+enough insurance company to buy
+Insurance even if they want to buy
+
+ align:start position:0%
+Insurance even if they want to buy
+ 
+
+ align:start position:0%
+Insurance even if they want to buy
+because that Federal agency cannot
+
+ align:start position:0%
+because that Federal agency cannot
+ 
+
+ align:start position:0%
+because that Federal agency cannot
+Supply so much Insurance although it's
+
+ align:start position:0%
+Supply so much Insurance although it's
+ 
+
+ align:start position:0%
+Supply so much Insurance although it's
+very low rate so those all the parles
+
+ align:start position:0%
+very low rate so those all the parles
+ 
+
+ align:start position:0%
+very low rate so those all the parles
+and we don't know how to resolve
\ No newline at end of file
diff --git a/Y9QVFYjiOIA.txt b/Y9QVFYjiOIA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3540307d23a433258e1360ada4a6a7653f042cfb
--- /dev/null
+++ b/Y9QVFYjiOIA.txt
@@ -0,0 +1,2933 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, let's
+get started here.
+
+Go ahead and take 10 more
+seconds on the clicker
+
+question, which probably looks
+all too familiar at this
+
+point, if you went to recitation
+yesterday.
+
+All right, and let's
+see how we do here.
+
+OK.
+
+So, let's talk about this
+for one second.
+
+So what we're asking here, if we
+can settle down and listen
+
+up, is which equations can be
+used if we're talking about
+
+converting wavelength to
+energy for an electron.
+
+Remember, the key word
+here is electron.
+
+This might look familiar to the
+first part of problem one
+
+on the exam, and problem one on
+the exam is what tended to
+
+be the huge problem
+on the exam.
+
+I think over 2/3 of you decided
+on the exam to use
+
+this first equation, e equals
+h c over wavelength.
+
+So I just want to reiterate one
+more time, why can we not
+
+use this equation if we're
+talking about an electron?
+
+C. OK, good, good,
+I'm hearing it.
+
+So the answer is c.
+
+What you need to do is you need
+to ask yourself if you're
+
+trying to convert from
+wavelength to energy for an
+
+electron, and you are tempted,
+because we are all tempted to
+
+use this equation, and if you
+were tempted, say, does an
+
+electron travel at the
+speed of light?
+
+And if the answer is no, an
+electron does not travel at
+
+the speed of light, light
+travels at the speed of light,
+
+then you want to stay away
+from using this equation.
+
+And I know how tempting it is to
+do that, but we have other
+
+equations we can use -- the
+DeBroglie wavelength, and this
+
+is just a combination of energy
+equals 1/2 m v squared,
+
+and the definition of momentum,
+so we can combine
+
+those things to get it.
+
+You might be wondering why I'm
+telling you this now, you've
+
+already -- if you've lost
+points on that, lost the
+
+points on it, and what I'm
+saying to you is if there are
+
+parts of exam 1 that you did not
+do well on, you will have
+
+a chance to show us again that
+you now understand that
+
+material on the final.
+
+One quarter of the final is
+going to be exam 1 material,
+
+and what that means is when we
+look at your grade at the end
+
+of the semester, and we take a
+look at what you got on exam
+
+1, and you're right at that
+borderline, and we say well,
+
+what happened, did they
+understand more at the end of
+
+the semester, did the
+concepts kind of
+
+solidify over the semester?
+
+And if they did and if you
+showed us that they did, then
+
+you're going to get bumped up
+into that next grade category.
+
+So keep that in mind as you're
+reviewing the exam, sometimes
+
+if things don't go as well
+as you want them to, the
+
+temptation is just to put that
+exam away forever and ever.
+
+But the reality is that new
+material builds on that
+
+material, and specifically exam
+1 a, question 1 a that
+
+deals with converting
+wavelength to
+
+energy for an electron.
+
+I really want you guys know this
+and to understand it, so
+
+I can guarantee you that you
+will see this on the final.
+
+Specifically, question
+1, part a.
+
+You will see something
+very, very similar
+
+to this on the final.
+
+If you are thinking about 1
+thing to go back and study on
+
+exam 1, 1 a is a really
+good choice for that.
+
+This is important to me,
+so you're going to
+
+see it on the final.
+
+So if you have friends that
+aren't here, you might want to
+
+mention it to them, or maybe
+not, maybe this is your reward
+
+for coming to class, which
+is fine with me as well.
+
+All right.
+
+So I want to talk a little
+bit about exam 1.
+
+I know most you picked up your
+examine in recitation.
+
+If you didn't, any extra exams
+can be picked up in the
+
+Chemistry Education office,
+that's room 2204.
+
+So, the class average for the
+exam was a 68%, which is
+
+actually a strong, solid average
+for an exam 1 grade in
+
+the fall semester of 511-1.
+
+What we typically see is
+something right in this range,
+
+either ranging from the 50's
+for an exam 1 average to
+
+occasionally getting into the
+70's, but most commonly what
+
+we've seen for exam 1 averages
+is 60, 61 -- those low 60's.
+
+So in many ways, seeing this 68
+here, this is a great sign
+
+that we are off to a good
+start for this semester.
+
+And I do want to address,
+because I know many of you,
+
+this is only your second exam
+at MIT, and perhaps you've
+
+never gotten an exam back that
+didn't start with a 90 or
+
+start with an 80 in terms
+of the grades.
+
+So one thing you need to keep in
+mind is don't just look at
+
+the number grade.
+
+The reason that we give you
+these letters grade categories
+
+is that you can understand what
+it actually means, what
+
+your exam score actually says
+in terms of how we perceive
+
+you as understanding
+the material.
+
+So, for example, and this is the
+same categories that were
+
+shared in recitation, so I
+apologize for repeating, but I
+
+know sometimes when you get an
+exam back, no more information
+
+comes into your head except
+obsessing over the exam, so
+
+I'm just going to say it one
+more time, and that is between
+
+88 and 100, so that's 20% of
+you got an A. This is just
+
+absolutely fantastic, you really
+nailed this very hard
+
+material and these hard
+questions on the exam where
+
+you had to both use equations
+and solve problems, but also
+
+understand the concept in order
+to get yourself started
+
+on solving the problem.
+
+The same with the B, the B range
+was between 69 and 87 --
+
+anywhere in between those
+ranges, you've got a B, some
+
+sort of B on the exam.
+
+So again, if you're in the A or
+the B category here, this
+
+is really something to be proud
+of, you really earned
+
+these grades.
+
+You know these exams, our 511-1
+exams, we're not giving
+
+you points here, there are no
+give me, easy points, you
+
+earned every single one
+of these points.
+
+So, A and B here, these are
+refrigerator-worthy grades,
+
+hang those up in your dorm.
+
+This is something to
+feel good about.
+
+All right.
+
+So, for those of you that got
+between a 51 and a 68, this is
+
+somewhere in the C range.
+
+For some people, they feel
+comfortable being in the C
+
+range, other people really do
+not like being in this range.
+
+We understand that, there is
+plenty of room up there with
+
+the A's and the B's.
+
+You are welcome to come up to
+these higher ranges starting
+
+with the next exam.
+
+And what I want to tell you if
+you are in the C range, and
+
+this is not a place that you
+want to be in, anyone that's
+
+got below the class average,
+so below a 68 -- or a 68 or
+
+below, is eligible for free
+tutoring, and I put the
+
+website on the front
+page of your notes.
+
+This means you get a one-on-one
+tutor paid for by
+
+the Chemistry Department to
+help you if it's concepts
+
+you're not quite up on, if it's
+exam strategy that you
+
+need to work on more.
+
+Whatever it is that you need
+to work on, we want to help
+
+you get there.
+
+So, if you have a grade that
+you're not happy with, that
+
+you're feeling upset or
+discouraged about, please, I'm
+
+happy to talk to all of
+you about your grades
+
+individually.
+
+You can come talk to me, bring
+your exam, and we'll go over
+
+what the strategy should
+be in terms of you
+
+succeeding on the next exam.
+
+You can do the same thing with
+all of your TAs are more than
+
+happy to meet with each
+and every one of you.
+
+And then in addition to that, we
+can set you up with a tutor
+
+if you are in the C range
+or below, in terms
+
+of this first exam.
+
+All right.
+
+So 44 to 50, this is going
+to be in the D range.
+
+And then anything below
+a 44 is going to be
+
+failing on this exam.
+
+And also keep in mind, for
+those of you that are
+
+freshman, you need at least
+a C to pass the class.
+
+So, if you did get a D or an F
+on the first exam, you are
+
+going to need to really evaluate
+why that happened and
+
+make some changes, and
+we're absolutely here
+
+to help you do that.
+
+So the real key is identifying
+where the problem is -- is it
+
+with understanding the concepts,
+are you in a study
+
+group that's dragging you
+along but you're not
+
+understanding?
+
+Do you kind of panic when
+you get in the exam?
+
+There are all sorts of scenarios
+we can talk about
+
+and we want to talk about
+them with you.
+
+Seriously, even if we had a huge
+range in this exam from
+
+17 to 100, if you're sitting
+there and you're the 17, and
+
+actually there's more than 1 so
+don't feel alone, if you're
+
+a 17 or you're a 20, it's not
+time to give up, it's not time
+
+to drop the class and
+say I'm no good at
+
+chemistry, I can't do this.
+
+You still can, this is your
+first couple of exams,
+
+certainly your first in this
+class, potentially one of your
+
+first at MIT, so there's
+tons of room to improve
+
+from here on out.
+
+This is only 100 points
+out of 750.
+
+So, the same thing goes if you
+did really well, you still
+
+have 650 other points that
+you need to deal with.
+
+So, make sure you don't just
+rest on your high score from
+
+this first exam.
+
+So, OK, so that's pretty much
+what I wanted to say about the
+
+exam, and in terms of there's
+tons of resources if things
+
+didn't work out quite
+as you wanted.
+
+If you feel upset in any way,
+please come and talk to me.
+
+We want you to love chemistry
+and feel good about your
+
+ability to do it.
+
+Nobody get into MIT by mistake,
+so you all deserve to
+
+be sitting here, and you all
+can pass this class and do
+
+well in it, so we can help you
+get there no matter what.
+
+You all absolutely
+can do this.
+
+And then one more time, to
+reiterate, in case anyone
+
+missed it, 1 a, make sure you
+understand that, I feel like
+
+that's important.
+
+And actually all of 1 --
+
+I really feel like the
+photoelectric effect is
+
+important for understanding all
+of these energy concepts.
+
+So, as you go on in this class,
+make sure you don't go
+
+on before you go back
+and make sure you
+
+understand that problem.
+
+All right, so let's move on to
+material for exam 2 now, and
+
+we're already three lectures
+into exam 2 material.
+
+And I do want to say that in
+terms of 511-1, what tends to
+
+happen is the exam scores go up
+and up and up, in terms of
+
+as we go from exam 1, to
+exam 2, to exam 3.
+
+One of these reasons is we are
+building on material, the
+
+other reason is you'll be
+shocked at how much better you
+
+are at taking an exam just
+a few weeks from now.
+
+So this will be on, starting
+with the Lewis structures, so
+
+go back in your notes -- if this
+doesn't sound familiar,
+
+if you spent too much time -- or
+not too much time, spent a
+
+lot of time studying exam 1
+and didn't move on here.
+
+Today we're going to talk about
+the breakdown of the
+
+octet rule.
+
+Cases where we don't have eight
+electrons around our
+
+Lewis structures, then
+we'll move on to
+
+talking about ionic bonds.
+
+We had already talked about
+covalent bonds, and then we
+
+talked about Lewis structures,
+which describe the electron
+
+configuration in
+covalent bonds.
+
+So now let's think about the
+other extreme of ionic bonds,
+
+and then we'll talk about polar
+covalent bonds to end,
+
+if we get there or will start
+with that in class on Monday.
+
+Also, public service
+announcement for all of you,
+
+voter registration in
+Massachusetts, which is where
+
+we are, is on Monday, the
+deadline if you want to
+
+register to vote.
+
+There's some websites up there
+that can guide you through
+
+registering and also can guide
+you through, if you need an
+
+absentee ballot for
+your home state.
+
+And I actually saw, and I saw
+a 5.111 student manning,
+
+there's some booths around MIT
+that will register you or get
+
+you an absentee ballot.
+
+So, the deadline's coming soon,
+so patriotic duty, I
+
+need to remind you of that as
+your chemistry teacher --
+
+chemistry issues are important
+in politics as well.
+
+So make sure you get
+registered to vote.
+
+I just remembered one more
+announcement, too, that I did
+
+want to mention, some of you may
+have friends in 511-2 and
+
+have heard their class
+average for exam 1.
+
+And I want to tell you, this
+happens every year, their
+
+average was 15 points higher
+than our average.
+
+Last year, their average
+was 15 points
+
+higher than our average.
+
+This is for exam 1.
+
+This is what tends to happen
+to 511-2 grades as
+
+the exam goes on.
+
+This is what happens to 511-1.
+
+You guys are in a good spot.
+
+Also, I want to point out that
+what's not important is just
+
+that number grade, but also the
+letter that goes with it.
+
+So, for example, if you got a 69
+in this class on this exam,
+
+that's a B minus.
+
+If you got a 69 on your exam
+in 511-2, that's a D, you
+
+didn't pass the exam.
+
+So keep that in mind when your
+friend might have gotten a
+
+higher number grade than you
+and you know you understand
+
+the similar material
+just as well.
+
+Similarly, an 80 in this class
+on the exam was a B plus, a
+
+very high B. An 80 in that class
+is going to be a C. So,
+
+just don't worry so much about
+exactly where that average
+
+lies, you really want to
+think about what the
+
+letter grade means.
+
+OK, I've said enough.
+
+I just --
+
+I hate to see people
+discouraged, and I know that a
+
+few people have been feeling
+discouraged, so that's my
+
+long-winded explanation
+of exam 1 grades.
+
+All right.
+
+So, let's move on with life
+though, so talking about the
+
+breakdown of the octet rule.
+
+The first example where we're
+going to see a breakdown is
+
+any time we have an odd number
+of valence electrons.
+
+This is probably the easiest to
+explain and to think about,
+
+because if we have an odd number
+that means that we
+
+can't have our octet rule,
+because our octet rule works
+
+by pairing electrons.
+
+And if we have an odd number,
+we automatically have an odd
+
+electron out.
+
+So, if we look at an example,
+the methyl radical, we can
+
+first think about how we draw
+the Lewis structure -- we draw
+
+the skeletal structure here.
+
+And then what we're going to
+do is add up our valence
+
+electrons -- we have 3 times 1
+for the hydrogen atoms, carbon
+
+has 4 valence electrons, so
+we have a total of 7.
+
+If we want to fill all of our
+valence shells in each of
+
+these atoms, we're going to need
+a total of 14 electrons.
+
+So, what we see we're
+left with is that we
+
+have 7 bonding electrons.
+
+So we can fill in 6 of those
+straightforward here, because
+
+we know that we need to make
+3 different bonds.
+
+And now we're left over
+with 1 electron, we
+
+can't make a bond.
+
+So, what we'll do is carbon does
+not have an octet yet.
+
+We can't get it one, but we
+can do the best we can and
+
+help it out with adding that
+extra electron onto the carbon
+
+atom, so that at least we're
+getting as close as possible
+
+to filling our octets.
+
+This is what we call a radical
+species or a free radical.
+
+Free radical or radical species
+is essentially any
+
+type of a molecule that has this
+unpaired electron on one
+
+of the atoms. This might look
+really strange, we're used to
+
+seeing octets.
+
+But you'll realize, if you
+calculate the formal charge on
+
+this molecule, that
+it's not the worst
+
+situation ever for carbon.
+
+At least it's formal charge is
+zero, even if it doesn't have
+
+-- it would rather have
+an extra bond
+
+and have a full octet.
+
+But it's not the worst scenario
+that we can imagine.
+
+But still, radicals tend to be
+incredibly reactive because
+
+they do want to fill
+that octet.
+
+So, what happens when you have a
+radical is it tends to react
+
+with the first thing that it
+runs into, especially highly
+
+reactive radicals that are not
+stabilized in some other way,
+
+which you'll tend to talk about
+it organic chemistry --
+
+how you can stabilize
+radicals.
+
+So the term free radical should
+sound familiar to you,
+
+whether you've heard it in
+chemistry before, or you
+
+haven't heard it in chemistry,
+but maybe have heard it, I
+
+don't know, commercials
+for facial
+
+products or other things.
+
+People like to talk about free
+radicals, and they're sort of
+
+the hero that gets rid of
+free radicals, which are
+
+antioxidants.
+
+So you hear in a lot of
+different creams or products
+
+or vitamins that they have
+antioxidants in them, which
+
+get rid of free radicals.
+
+The reason you would want to
+get rid of free radicals is
+
+that free radicals can
+damage DNA, so
+
+they're incredibly reactive.
+
+It makes sense that if they hit
+a strand of DNA, they're
+
+going to react with the DNA,
+you end up breaking the
+
+strands of DNA and causing
+DNA damage.
+
+So, this is actually what
+happens in aging because we
+
+have a lot of free radicals
+in our body.
+
+We can introduce them
+artificially, for example,
+
+cigarette smoke has a lot of
+really dangerous free radicals
+
+that get into the cells in your
+lungs, which damage your
+
+lung DNA, which can
+cause lung cancer.
+
+But also, all of us are living
+and breathing, which means
+
+we're having metabolism go on in
+our body, which means that
+
+as we use oxygen and as we
+metabolize our food, we are
+
+actually producing free
+radicals as well.
+
+So it's kind of a paradox
+because we need them because
+
+they are a natural by-product of
+these important processes,
+
+but then they can go on and
+damage cells, which is what
+
+kind of is causing aging
+and can lead to cancer.
+
+We have enzymes in our body
+that repair damage that is
+
+done by free radicals, that will
+put the strands of DNA
+
+back together.
+
+And we also have antioxidants
+in our body.
+
+So, you might know that, for
+example, very brightly colored
+
+fruit is full of antioxidants,
+they're full of chemicals that
+
+will neutralize free radicals.
+
+Lots of vitamins are also
+antioxidants, so we have
+
+vitamin A on the top there
+and vitamin E.
+
+So, the most common thing we
+think of when we think of free
+
+radicals is very reactive,
+bad for your
+
+body, causes DNA damage.
+
+But the reality is that
+free radicals are also
+
+essential for life.
+
+So this is kind of interesting
+to think about.
+
+And, for example, certain
+enzymes or proteins actually
+
+use free radicals in order to
+carry out the reactions that
+
+they carry out in your body.
+
+So, for example, this is a
+picture or a snapshot of a
+
+protein, this is a crystal
+structure of ribonucleotide
+
+reductase is what it's called.
+
+It's an enzyme that catalyzes
+the reaction of an essential
+
+step in both DNA synthesis and
+also DNA repair, and it
+
+requires having radicals within
+its active site in
+
+order to carry out
+the chemistry.
+
+So, this is kind of a neat
+paradox, because radicals
+
+damage DNA, but in order to
+repair your DNA, you need
+
+certain enzymes, and those
+enzymes require different
+
+types of free radicals.
+
+So, free radicals are definitely
+very interesting,
+
+and once we get -- or hopefully
+you will get into
+
+organic chemistry at some point
+and get to really think
+
+about what they do in terms
+of a radical mechanism.
+
+We can think about radicals that
+are also more stable, so
+
+let's do another example with
+the molecule nitric acid.
+
+So we can again, draw the
+skeleton here, and just by
+
+looking at it we might not know
+it's a radical, but as we
+
+start to count valence
+electrons, we should be able
+
+to figure it out very quickly,
+because what we have is 11
+
+valence electrons.
+
+We need 16 electrons to
+have full octets.
+
+So, we're left with 5
+bonding electrons.
+
+We put a double bond in between
+our nitrogen and our
+
+oxygen, so what we're left
+over with is this single
+
+bonding electron, and we'll put
+that on the nitrogen here.
+
+And I'll explain why we put it
+on the nitrogen and not the
+
+oxygen in just a minute.
+
+But what we find is then once
+we fill in the rest of the
+
+valence electrons in terms of
+lone pairs, this is the
+
+structure that we get.
+
+And if you add up all of the
+formal charges on the nitrogen
+
+and on the oxygen, what you'll
+see is they're both 0.
+
+So if you happen to try drawing
+this structure and you
+
+put the lone pair on oxygen and
+then you figured out the
+
+formal charge and saw that you
+had a split charge, a plus 1
+
+and a minus 1, the first thing
+you might want to try is
+
+putting it on the other atom,
+and once you did that you'd
+
+see that you had a
+better structure
+
+with no formal charge.
+
+I have to mention what nitric
+oxide does, because it's a
+
+very interesting molecule.
+
+Don't get it confused with
+nitrous oxide, which is happy
+
+gas, that's n o 2.
+
+This is nitric oxide, and it's
+actually much more interesting
+
+than nitrous oxide.
+
+It's a signaling molecule in
+your body, it's one of the
+
+very few signaling molecules
+that is a gas, and obviously,
+
+it's also a radical.
+
+What happens with n o is that
+it's produced in the
+
+endothelium of your blood
+vessels, so the inner lining
+
+of your blood vessels, and it
+signals for smooth muscle that
+
+line your blood vessels
+to relax, which causes
+
+vasodilation , and by
+vasodilation, I just mean a
+
+widening of the blood vessels.
+
+So, n o signals for your blood
+vessels to get wider and allow
+
+more blood to flow through.
+
+And if you think about what
+consequences this could have,
+
+in terms of places where they
+have high altitude, so they
+
+have lower oxygen levels, do
+you think that they produce
+
+more or less and
+n o their body?
+
+More?
+
+Yeah, it turns out they
+do produce more.
+
+The reason they produce more is
+that they want to have more
+
+blood flowing through their
+veins so that they can get
+
+more oxygenated blood into
+different parts of their body.
+
+N o is also a target in the
+pharmaceutical industry.
+
+A very famous one that became
+famous I guess over 10 years
+
+ago now, and this is from a drug
+that actually targets one
+
+of n o's receptors, and this
+drug has the net effect of
+
+vasodilation or widening of
+blood vessels in a certain
+
+area in the body.
+
+So this is viagra, some of you
+may be familiar, I think
+
+everyone's heard of viagra.
+
+Now you know how viagra works.
+
+Viagra breaks down, or it
+inhibits the breakdown of n
+
+o's binding partner in just
+certain areas, not everywhere
+
+in your body.
+
+So, in those areas, what happens
+is you get more n o
+
+signaling, you get more
+vasodilation, you get
+
+increased blood flow.
+
+So that's a little bit
+of pharmacology
+
+for you here today.
+
+All right, so let's talk about
+one more example in terms of
+
+the breakdown of the octet
+rule with radicals.
+
+Let's think about molecular
+oxygen.
+
+So let's go ahead and quickly
+draw this Lewis structure.
+
+We have o 2.
+
+The second thing we
+need to do is
+
+figure out valence electrons.
+
+6 plus 6, so we would
+expect to see 12.
+
+For a complete octet we would
+need 8 electrons each, so 16.
+
+So in terms of bonding
+electrons, what we have is 4
+
+bonding electrons.
+
+So, we can go ahead and fill
+those in as a double bond
+
+between the two oxygens.
+
+So, what we end up having left,
+and this would be step
+
+six then because five was just
+filling in that, is 12 minus
+
+4, so we have 8 lone pair
+electrons left.
+
+So we can just fill it in to
+our oxygens like this.
+
+All right, so using everything
+we've learned about Lewis
+
+structures, we here have the
+structure of molecular oxygen.
+
+And I just want to point out for
+anyone that gets confused,
+
+when we talk about oxygen as
+an atom, that's o, but
+
+molecular oxygen is actually
+o 2, the same for molecular
+
+hydrogen, for example.
+
+All right, so let's look at
+what the actual Lewis
+
+structure is for molecular
+oxygen, and it turns out that
+
+actually we don't have a double
+bond, we have a single
+
+bond, and we have
+two radicals.
+
+And any time we have two
+radicals, we talk about what's
+
+called a biradical.
+
+And while using this exception
+to the Lewis structure rule,
+
+to the octet rule for odd
+numbers of valence electrons
+
+can clue us into the fact that
+we have a radical, there's
+
+really no way for us to use
+Lewis structures to predict
+
+when we have a biradical, right,
+because we would just
+
+predict that we would get this
+Lewis structure here.
+
+So, when I first introduced
+Lewis structures, I said these
+
+are great, they're really easy
+to use and they work about 90%
+
+of the time.
+
+This falls into that 10%
+that Lewis structures
+
+don't work for us.
+
+It turns out, in order to
+understand that this is the
+
+electron configuration for o
+2, we need to use something
+
+called molecular orbital theory,
+and just wait till
+
+next Wednesday and we will tell
+you what that is, and we
+
+will, in fact, use
+it for oxygen.
+
+But until that point, I'll just
+tell you that molecular
+
+orbital theory takes into
+account quantum mechanics,
+
+which Lewis theory does not.
+
+So that's why, in fact, there
+are those 10% of cases that
+
+Lewis structures
+don't work for.
+
+All right, the second case of
+exceptions to the octet rule
+
+are when we have octet
+deficient molecules.
+
+So basically, this means we're
+going to have a molecule
+
+that's stable, even though it
+doesn't have a complete octet.
+
+And these tend to happen in
+group 13 molecules, and
+
+actually happen almost
+exclusively in group 13
+
+molecules, specifically with
+boron and aluminum.
+
+So, any time you see a Lewis
+structure with boron or
+
+aluminum, you want to just
+remember that I should look
+
+out to make sure that these
+might have an incomplete
+
+octet, so look out for that
+when you see those atoms.
+
+So, let's look at b f 3
+as our example here.
+
+And what we see for b f 3
+is the number of valence
+
+electrons that we have are 24,
+because the valence number of
+
+electrons for boron
+is 3, and then 3
+
+times 7 for each fluorine.
+
+For total filled octets we need
+32, so that means we need
+
+8 bonding electrons.
+
+So, let's assign two to each
+bond here, and then we're
+
+going to have two extra bonding
+electrons, so let's
+
+just arbitrarily pick
+a fluorine to give
+
+a double bond to.
+
+And then we can fill in the lone
+pair electrons, we have
+
+16 left over.
+
+So thinking about what the
+formal charge is, if we want
+
+to figure out the formal charge
+for the boron here,
+
+what we're talking about is the
+valence number for boron,
+
+which is 3, minus 0 because
+there are no lone pairs, minus
+
+1/2 of 8 because there are
+eight shared electrons.
+
+We get a formal charge
+of minus 1.
+
+What is our formal charge
+since we learned this on
+
+Monday for thinking
+about the double
+
+bonded fluorine in boron?
+
+So, look at your notes and look
+at the fluorine that has
+
+a double bond with it, and I
+want you to go ahead and tell
+
+me what that formal
+charge should be.
+
+All right, let's take 10
+more seconds on that.
+
+OK, so 49%.
+
+So, let's go look back at the
+notes, we'll talk about why
+
+about 50% of you are right, and
+50% need to review, which
+
+I totally understand you haven't
+had time to do yet,
+
+your formal charge rules from
+Monday's class, there were
+
+other things going on.
+
+But let's talk about how we
+figure out formal charge.
+
+Formal charge is just the number
+of valence electrons
+
+you have. So fluorine has 7.
+
+You should be able to look at a
+periodic table and see that
+
+fluorine has seven.
+
+What we subtract from that is
+the number of lone pair
+
+electrons, and there are four
+lone pair electrons on this
+
+double bonded fluorine,
+so it's minus 4.
+
+Then we subtract 1/2 of
+the shared electrons.
+
+Well we have a double bond with
+boron here, so we have a
+
+total of 4 shared electrons.
+
+And when we do the subtraction
+here, what we end up with is a
+
+formal charge plus 1 on the
+double bonded fluorine.
+
+Without even doing a
+calculation, what do you think
+
+that the formal charge
+should be on you
+
+single bonded fluorines?
+
+Good.
+
+OK, it should be
+0 and it is 0.
+
+The reason it's zero in terms of
+calculating it is 7 minus 6
+
+lone pair electrons minus
+1/2 half of 2 shared
+
+electrons is 0.
+
+The reason that you all told
+me, I think, and I hope, is
+
+that you know that the formal
+charge on individual atoms has
+
+to equal the total charge
+on the molecule.
+
+So if we already have a minus 1
+and a plus 1, and we know we
+
+have no charge in the molecule,
+and we only have one
+
+type of atom left to talk about,
+that formal charge had
+
+better be 0.
+
+OK.
+
+So this looks pretty good in
+terms of a Lewis structure, we
+
+figured out our formal
+charges.
+
+These also look pretty good,
+too, we don't have too much
+
+charge separation.
+
+But what actually it turns out
+is that if you experimentally
+
+look at what type of bonds you
+have, it turns out that all
+
+three of the b f bonds are equal
+in length, and they all
+
+have a length that would
+correspond to a single bond.
+
+So, experimentally, we know we
+have to throw out this Lewis
+
+structure here, we have some
+more information, let's think
+
+about how this could happen.
+
+So this could happen, for
+example, is if we take this
+
+two of the electrons that are in
+the b f double bond and we
+
+put it right on to the fluorine
+here, so now we have
+
+all single bonds.
+
+And let's think about what the
+formal charge situation would
+
+be in this case here.
+
+What happens here is now we
+would have a formal charge of
+
+0 on the boron, we'd have a
+formal charge of 0 on all of
+
+the fluorine molecules
+as well.
+
+So, it turns out that actually
+looking at formal charge, even
+
+though the first case didn't
+look too bad, this case
+
+actually looks a lot better.
+
+We have absolutely no formal
+charge separation whatsoever.
+
+It turns out again, boron and
+aluminum, those are the two
+
+that you want to look out for.
+
+They can be perfectly happy
+without a full octet, they're
+
+perfectly happy with 6 instead
+of 8 in terms of electrons in
+
+their valence shell.
+
+So that is our exception
+the number two.
+
+We have one more exception and
+this is a valence shell
+
+expansion, and this can be the
+hardest to look out for,
+
+students tend to forget to look
+for this one, but it's
+
+very important as well, because
+there are a lot of
+
+structures that are affected
+for this .
+
+And this is only applicable if
+we're talking about a central
+
+atom that has an n value or
+a principle quantum number
+
+that's equal to or greater
+than three.
+
+What happens when we have n
+that's equal to or greater to
+
+three, is that now, in addition
+to s orbitals and p
+
+orbitals, what else do we
+have available to us?
+
+D orbitals, great.
+
+So what we see is we have some
+empty d orbitals, which means
+
+that we can have more than
+eight electrons that fit
+
+around that central atom.
+
+If you're looking to see if this
+is going to happen, do
+
+you think this would happen
+with a large or
+
+small central atom?
+
+So think of it in terms
+of just fitting.
+
+We've got to fit more than
+8 electrons around here.
+
+Yeah, so it's going to be, we
+need to have a large central
+
+atom in order for this
+to take place.
+
+Literally, we just need to fit
+everything around is probably
+
+the easiest way to
+think about it.
+
+And what happens is it also
+tends to have small atoms that
+
+it's bonded to.
+
+Again, just think of it in terms
+of all fitting in there.
+
+So, let's take an
+example p c l 5.
+
+The first example is the more
+straightforward example,
+
+because let's start to draw the
+Lewis structure, and what
+
+we see is that phosphorous has
+five chlorines around it.
+
+So we already know if we want
+to form five bonds we've
+
+broken our octet rule.
+
+But let's go through and figure
+this out and see how
+
+that happens.
+
+What we know is we need
+40 valence electrons,
+
+we have those --
+
+5 from the phosphorous, and
+we have 7 from each of the
+
+chlorine atoms. If we were to
+fill out all of those octets,
+
+that would be 48 electrons.
+
+So what we end up with when
+we do our Lewis structure
+
+calculation is that we only
+have 8 bonding electrons
+
+available to us.
+
+So we can fill those in between
+the phosphorous and
+
+the chlorine, those 8
+bonding electrons.
+
+So, this is obviously
+a problem.
+
+To make 5 p c l bonds we need
+10 shared electrons, and we
+
+know that that's the situation
+because it's called p c l 5
+
+and not p c l 4, so we can go
+right ahead and add in that
+
+extra electron pair.
+
+So we've used up 10 for bonding,
+so that means what we
+
+have left is 30 lone pair
+electrons, and I would not
+
+recommend filling all of these
+in your notes right now, you
+
+can go back and do that, but
+just know the rest end up
+
+filling up the octets for
+all of the chlorines.
+
+So, in this first case where you
+actually need to make more
+
+than for bonds, you will
+immediately know you need to
+
+use this exception to the Lewis
+structure octet rule,
+
+but sometimes it won't
+be as obvious.
+
+So, let's look at c r o 4, the
+2 minus version here, so a
+
+chromate ion, and if we draw
+the skeletal structure, we
+
+have four things that the
+chromate needs to bond to.
+
+So, let's do the Lewis
+structure again.
+
+When we figure out the valence
+electrons, we have total, we
+
+have 6 from the chromium, we
+have 6 from each of the
+
+different oxygens, and where
+did this 2 come from?
+
+Yup, the negative charge.
+
+So, remember, we have 2 extra
+electrons hanging out in our
+
+molecule, so we need
+to include those.
+
+We have a total of 32.
+
+40 are needed to
+fill up octets.
+
+So again, we have 8 bonding
+electrons available, so we can
+
+go ahead and fill these in
+between each of the bonds.
+
+What happens is that we then
+have 24 lone pair electrons
+
+left, and we can fill
+those in like this.
+
+And the problem comes
+now when we figure
+
+out the formal charge.
+
+So, when we do that what we find
+is that the chromium has
+
+a formal charge of plus 1, and
+that each of the oxygens has a
+
+total charge of minus 1.
+
+So we actually have a bit of
+charge separation here.
+
+Without even doing a
+calculation, what is the total
+
+charge of these that
+are added up?
+
+OK, it's minus 2,
+that's right.
+
+We know that the total charge of
+each of the formal charges
+
+has to add up to minus 2,
+because that's the charge in
+
+our molecule.
+
+We can also just calculate it
+-- the chromate gives us a
+
+plus 2, then we have 4 times
+minus 1 for each of the
+
+oxygens, so we have a minus 2.
+
+So, we have some charge
+separation here, and in some
+
+cases, if we're not at n equals
+3 or higher, there's
+
+really nothing we can do about
+it, this would be the best
+
+structure we can do.
+
+But since we have these d
+orbitals available, we can use
+
+them, and it turns out that
+experimentally this is what's
+
+found, that the length and the
+strength are not single bonds,
+
+but they're actually something
+between a single bond and a
+
+double bond.
+
+So how do we get a 1 and 1/2
+bond, for example, what's the
+
+term that let's us do that?
+
+Resonance.
+
+That's right.
+
+So that's exactly what's
+happening here.
+
+So, if we went ahead and drew
+this structure here where we
+
+have now two double bonds and
+two single bonds, that would
+
+be in resonance with another
+structure where we have two
+
+double bonds instead to these
+two oxygens, and now, single
+
+bonds to these two oxygens.
+
+We can actually also have
+several other resonance
+
+structures as well.
+
+Remember, the definition of a
+resonance structure is where
+
+all the atoms stay the same,
+but what we can do is move
+
+around the electrons -- we're
+moving around those extra two
+
+electrons that can be
+in double bonds.
+
+So, why don't you tell me
+how many other resonance
+
+structures you would expect to
+see for this chromate ion?
+
+All right, let's take 10
+more seconds on this.
+
+All right.
+
+This is good.
+
+I know this is a real split
+response, but the right answer
+
+is the one that is indicated
+in the graph
+
+here that it's four.
+
+This takes a little bit of time
+to get used to thinking
+
+about all the different Lewis
+structures you can have. So,
+
+you guys should all go back
+home if you can't see it
+
+immediately right now and try
+drawing out those four other
+
+Lewis structures, for chromate,
+
+there are four others.
+
+You'll probably get a chance to
+literally do this example
+
+in recitation where you draw
+out all four, but it's even
+
+better to make sure you
+understand it before you get
+
+to that point.
+
+So, we can go back to
+the class notes.
+
+So it turns out there's four
+other Lewis structures, so
+
+basically just think about
+all the other different
+
+combinations where you can have
+single and double bonds,
+
+and when you draw those out,
+you end up with four.
+
+So, for every single one of
+these Lewis structures, we
+
+could figure out what the formal
+charges are, and what
+
+we would find is that it's 0
+on the chromium, it's 0 for
+
+the double bonded oxygens, and
+it's going to be negative 1
+
+for the single bonded oxygens.
+
+So, what you can see is that in
+this situation, we end up
+
+having less formal charge
+separation, and that's what
+
+we're looking for, that's the
+more stable structure.
+
+So any time you can have an
+expanded octet -- an expanded
+
+valence shell, where you have n
+is equal to or greater than
+
+3, and by expanding and adding
+more electrons into that
+
+valence shell, you lower
+the charge separation,
+
+you want to do that.
+
+I also want to point out, I
+basically said there's 6
+
+different ways we can draw this
+in terms of drawing all
+
+the resonance structures.
+
+You might be wondering if you
+have to figure out the formal
+
+charge for each structure
+individually, and the answer
+
+is no, you can pick any single
+structure and the formal
+
+charges will work
+out the same.
+
+So, for example, if you pick
+this structure and your friend
+
+picks this structure, you'll
+both get the right answer that
+
+there's just the negative 1 on
+the oxygens and no other
+
+formal charges in the molecule.
+
+All right.
+
+So those are the end of our
+exceptions to the octet rule
+
+for Lewis structures, that's
+everything we're going to say
+
+about Lewis structures.
+
+And remember, that when we talk
+about Lewis structures,
+
+what they tell us is the
+electron configuration in
+
+covalent bonds, so that
+valence shell electron
+
+configuration.
+
+So we talked a lot about
+covalent bonds before we got
+
+into Lewis structures, and then
+how to represent covalent
+
+bonds by Lewis structures.
+
+So now I'll say a little bit
+about ionic bonds, which are
+
+the other extreme, and when you
+have an ionic bond, what
+
+you have now is a complete
+transfer of either one or many
+
+electrons between two atoms. So
+the key word for covalent
+
+bond was electron sharing, the
+key word for ionic bonds is
+
+electron transfer.
+
+And the bonding between the two
+atoms ends up resulting
+
+from an attraction that we're
+very familiar with, which is
+
+the Coulomb or the electrostatic
+attraction
+
+between the negatively
+charged and the
+
+positively charged ions.
+
+So let's take an example.
+
+The easiest one to think about
+is where we have a negative 1
+
+and a positive 1 ion.
+
+So this is salt, n a c l --
+actually lots of things are
+
+call salt, but this is what
+we think of a table salt.
+
+So, let's think about what we
+have to do if we want the form
+
+sodium chloride from the neutral
+sodium and chlorine
+
+atoms. So, the first thing that
+we're going to need to do
+
+is we need to convert sodium
+into sodium plus.
+
+What does this process
+look like to you?
+
+Is this one of those periodic
+trends, perhaps?
+
+Can anyone name what we're
+looking at here?
+
+Exactly, ionization energy.
+
+So, if we're going to talk about
+the energy difference
+
+here, what we're going to
+be talking about is the
+
+ionization energy, or the energy
+it takes to rip off an
+
+electron from sodium in order
+to form the sodium plus ion.
+
+So, we can just put right
+here, that's 494
+
+kilojoules per mole.
+
+The next thing that we want to
+look at is chlorine, so in
+
+terms of chlorine we need to
+go to chlorine minus, so we
+
+actually need to add
+an electron.
+
+This is actually the reverse of
+one of the periodic trends
+
+we talked about.
+
+Which trend is that this
+is the reverse of?
+
+Electron affinity, right.
+
+Because if we go backwards we're
+saying how badly does
+
+chlorine want to grab
+an electron?
+
+Chlorine wants to do this very
+badly, and it turns out the
+
+electron affinity for chlorine
+is huge, it's 349 kilojoules
+
+per mole, but remember, we're
+going in reverse, so we need
+
+to talk about it as negative
+349 kilojoules per mole.
+
+So if we talk about the sum of
+what's happening here, what we
+
+need to do is think about going
+from the neutrals to the
+
+ions, so we can just add those
+two energies together, and
+
+what we end up with is plus 145
+kilojoules per mole, in
+
+order to go from neutral
+sodium in
+
+chlorine to the ions.
+
+So, the problem here is that we
+have to actually put energy
+
+into our system, so this doesn't
+seem favorable, right.
+
+What's favorable is when we
+actually get energy out and
+
+our energy gets lower, but what
+we're saying here is that
+
+we actually need to
+put in energy.
+
+So another way to say
+this is this process
+
+actually requires energy.
+
+It does not emit energy, it
+does not give off excess
+
+energy, it requires energy.
+
+So, we need to think about how
+can we solve this problem in
+
+terms of thinking about ionic
+bonds, and the answer is
+
+Coulomb attraction.
+
+So there's one more force that
+we need to talk about, and
+
+that is when we talk about the
+attraction between the
+
+negatively and the positively
+charged ions, such that we
+
+form sodium chloride.
+
+So this process here has a
+delta energy, a change in
+
+energy of negative 589
+kilojoules per mole.
+
+So that's huge, we're giving
+off a lot of energy by this
+
+attraction.
+
+So if we add up the net energy
+for all of this process, all
+
+we need to do is add negative
+589 to plus 145.
+
+So what we end up getting is the
+net energy change is going
+
+to be negative 444 kilojoules
+per mole, so you can see that,
+
+in fact, it is very favorable
+for neutral sodium and neutral
+
+chloride to form sodium chloride
+in an ionic bond.
+
+And the net increase then,
+is a decrease in energy.
+
+So, I just gave you the number
+in terms of what that Coulomb
+
+potential would be in
+attraction, but we can I
+
+easily calculate it as well
+using this equation here where
+
+the energy is equal to the
+charge on each of the ions,
+
+and this is just multiplied by
+the value of charge for an
+
+electron divided by 4 pi epsilon
+nought times r, are r
+
+is just the distance in terms
+of the bond length we could
+
+talk about.
+
+So, let's calculate and make
+sure that I didn't tell you a
+
+false number here.
+
+Let's say we do the calculation
+with the bond
+
+length that we've looked
+up, which is 2 .
+
+3 6 angstroms for
+the bond length
+
+between sodium and chloride.
+
+So we should be able to figure
+out the Coulombic
+
+attraction for this.
+
+So, if we talk about the energy
+of attraction, we need
+
+to multiply plus 1, that's the
+charge on the sodium, times
+
+minus 1, the charge on the
+chlorine, times the charge in
+
+an electron, 1 .
+
+6 0 2 times 10 the negative 19
+Coulombs, and that's all
+
+divided by 4 pi, and then I've
+written out epsilon nought in
+
+your notes, so I won't write
+it on the board.
+
+And then r, so r is
+going to be 2 .
+
+3 6 and times -- what is
+angstrom, everyone?
+
+Yup, 10 to the negative 10.
+
+So 10 to the negative
+10 meters.
+
+So, if we do this calculation
+here, what we end up with is
+
+negative 9.774 times 10 to
+the negative 19 joules.
+
+So that's what we have in
+terms of our energy.
+
+That does not look the same as
+what we saw -- yup, do you
+
+have a question?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+Luckily, although, I did not
+write it in my own notes, I
+
+did it when I put in my
+calculator, thank you.
+
+So you need to square this value
+here and then you should
+
+get this value right here,
+negative 9.77.
+
+All right, so what we need to
+do though is convert from
+
+joules into kilojoules per mole,
+because that's what we
+
+were using.
+
+So if we multiply that number
+there by kilojoules per mole
+
+-- or excuse me, first
+kilojoules per joule, so we
+
+have 1,000 joules in
+every kilojoule.
+
+And then we multiply that by
+Avagadro's number, 6.022 times
+
+10 to the 23 per mole.
+
+What we end up with
+is negative 589
+
+kilojoules per mole.
+
+So this is that same Coulombic
+attraction that we saw in the
+
+first place.
+
+So, notice that you will
+naturally get out a negative
+
+charge here, remember negative
+means an attractive force in
+
+this case, because you
+have the plus and
+
+the minus 1 in here.
+
+So we should be able to easily
+do that calculation, and what
+
+we end up getting matches up
+with what I just told you,
+
+luckily, and thank you for
+catching the square, that's an
+
+important part in getting
+the right answer.
+
+So, experimentally then, what we
+find is that the change in
+
+energy for this reaction
+is negative 444
+
+kilojoules per mole.
+
+If we look experimentally what
+we see, it's actually a little
+
+bit different, it's negative
+411 kilojoules per mole.
+
+So, in terms of this class, this
+is the method that we're
+
+going to use, and we're going
+to say this gets us close
+
+enough such that we can make
+comparisons and have a
+
+meaningful conversations about
+different types of ionic bonds
+
+and the attraction
+between them.
+
+But let's think about where this
+discrepancy comes from,
+
+and before I do that I want to
+point out, one term we use a
+
+lot is change in energy for a
+reaction where, for example,
+
+you break a bond.
+
+Remember that the negative of
+the change in energy is what's
+
+called delta e sub d.
+
+We first saw this when we first
+introduced the idea of
+
+covalent bonds.
+
+Do you remember what this term
+here means, delta e sub d?
+
+A little bit and some no's,
+which this was pre-exam, I
+
+understand, you still need to
+review those notes, it's
+
+dissociation energy.
+
+So you get a negative energy
+out by breaking the bond.
+
+The dissociation energy means
+how much energy that bond is
+
+worth in terms of strength, so
+it's the opposite of the
+
+energy you get out of breaking
+the bond -- or excuse me, the
+
+energy that you get out
+of forming the bond.
+
+It's the amount of energy you
+need to put in to break the
+
+bond is dissociation energy.
+
+It takes this much energy
+to dissociate your
+
+bond, excuse me.
+
+All right.
+
+So, let's take a look here at
+our predictions, so I just put
+
+them both ways so we
+don't get confused.
+
+The dissociation
+energy is 444.
+
+The change in energy
+for forming the
+
+bond is negative 444.
+
+We made the following
+approximations, which explain
+
+why, in fact, we got a different
+experimental energy,
+
+if we look at that.
+
+The first thing is that we
+ignored any repulsive
+
+interactions.
+
+If you think about salt, it's
+not just two single atoms that
+
+you are talking about.
+
+It's actually in a whole network
+or whole lattice of
+
+other molecules, so you actually
+have some other
+
+chlorines around that are going
+to be having repulsive
+
+interactions with our chlorine
+that we're talking about.
+
+We're going to ignore those,
+make the approximation that
+
+those don't matter, at this
+point, in these calculations.
+
+And the result for that is that
+we end up with a larger
+
+dissociation energy than
+the experimental value.
+
+That's because the bond is going
+to be a little bit more
+
+broken than it was in our
+calculation, because we do
+
+have these repulsive
+interactions.
+
+The other thing that we did is
+that we treated both sodium
+
+and the chlorine as
+point charges.
+
+And this is what actually
+allowed us to make this
+
+calculation and calculate the
+Coulomb potential so easily,
+
+we just treated them as if
+they're point charges.
+
+We're ignoring quantum mechanics
+in this -- this is
+
+sort of the class where we
+ignore quantum mechanics, we
+
+ignored it for Lewis
+structures,
+
+we're ignoring it here.
+
+We will be back to paying a lot
+of attention to quantum
+
+mechanics in lecture 14 when we
+talk about MO theory, but
+
+for now, these are
+approximations, these are
+
+models where we don't take
+it into consideration.
+
+And I think you'll agree that we
+come reasonably close such
+
+that we'll be able to make
+comparisons between different
+
+kinds of ionic bonds.
+
+All right.
+
+So, the last thing I want to
+introduce today is talking
+
+about polar covalent bonds.
+
+We've now covered the
+two extremes.
+
+One extreme is complete total
+electron sharing -- if we have
+
+a perfectly covalent bond,
+we have perfect sharing.
+
+The other is electron transfer
+in terms of ionic bonds.
+
+So when we talk about a polar
+covalent bond, what we're now
+
+talking about is an unequal
+sharing of electrons between
+
+two atoms.
+
+So, this is essentially
+something we've seen before,
+
+we just never formally talked
+about what we would call it.
+
+This is any time you have a
+bond forming between two
+
+non-metals that have different
+electronegativities, so, for
+
+example, hydrogen
+choride, h c l.
+
+The electronegativity for
+hydrogen is 2.2, for
+
+chlorine it's 3.2.
+
+And in general, what we say is
+we consider a difference in
+
+terms of a first approximation
+if the difference in
+
+electronegativity
+is more than 0.
+
+5, so this is on the Pauling
+electronegativity scale.
+
+So what we end up having is we
+sort of have a kind of, and
+
+what we call it is a partial
+negative charge on the
+
+chlorine, and a partial
+positive
+
+charge in the hydrogen.
+
+The reason we have that is
+because the chlorine's more
+
+electronegative, it wants to
+pull more of that shared
+
+electron density to itself.
+
+If it has more electron density,
+it's going to have a
+
+little bit of a negative charge
+and the hydrogen's
+
+going to be left with a little
+bit of a positive charge.
+
+So, we can compare this, for
+example to, molecular hydrogen
+
+where they're going to have
+that complete sharing, so
+
+there's not going to be a delta
+plus or a delta minus,
+
+delta is going to be equal to
+zero on each of the atoms.
+
+They are completely sharing
+their electrons.
+
+And we can also explain this
+in another way by talking
+
+about a dipole moment where we
+have a charged distribution
+
+that results in this dipole,
+this electric dipole.
+
+And we talk about this using
+the term mu, which is a
+
+measurement of what
+the dipole is.
+
+A dipole is always written in
+terms of writing an arrow from
+
+the positive charge to
+the negative charge.
+
+In chemistry, we are always
+incredibly interested in what
+
+the electrons are doing, so we
+tend to pay attention to them
+
+in terms of arrows.
+
+Oh, the electrons are going over
+to the chlorine, so we're
+
+going to draw our arrow toward
+the chlorine atom.
+
+So, we measure this here, so mu
+is equal to q times r, the
+
+distance between the two.
+
+And q, that charge is just equal
+to the partial negative
+
+or the partial positive times
+the charge on the electron.
+
+So this is measured in Coulomb
+meters, you won't ever see a
+
+measurement of electronegativity
+in Coulomb
+
+meters -- we tend to talk about
+it in terms of debye or
+
+1 d, or sometimes there's no
+units at all, so the d is just
+
+assumed, and it's because 1
+debye is just equal to this
+
+very tiny number of Coulomb
+meters and it's a lot easier
+
+to work with debye's here.
+
+So, when we talk about polar
+molecules, we can actually
+
+extend our idea of talking about
+polar bonds to talking
+
+about polar molecules.
+
+So, actually let's start
+with that on Monday.
+
+So everyone have a
+great weekend.
\ No newline at end of file
diff --git a/_ax4eNMI9Dw.txt b/_ax4eNMI9Dw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86b6a1378e3920ddb8efd48e0bb543f0e96f971e
--- /dev/null
+++ b/_ax4eNMI9Dw.txt
@@ -0,0 +1,323 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu this is my definition
+
+ align:start position:0%
+ocw.mit.edu this is my definition
+ 
+
+ align:start position:0%
+ocw.mit.edu this is my definition
+including the method to paint the car so
+
+ align:start position:0%
+including the method to paint the car so
+ 
+
+ align:start position:0%
+including the method to paint the car so
+to change it
+
+ align:start position:0%
+to change it
+ 
+
+ align:start position:0%
+to change it
+color and the question says you create a
+
+ align:start position:0%
+color and the question says you create a
+ 
+
+ align:start position:0%
+color and the question says you create a
+car with this line here so you're
+
+ align:start position:0%
+car with this line here so you're
+ 
+
+ align:start position:0%
+car with this line here so you're
+initializing it with four comma 2 what's
+
+ align:start position:0%
+initializing it with four comma 2 what's
+ 
+
+ align:start position:0%
+initializing it with four comma 2 what's
+a line of code that changes the color
+
+ align:start position:0%
+a line of code that changes the color
+ 
+
+ align:start position:0%
+a line of code that changes the color
+from uh whatever initially is to
+
+ align:start position:0%
+from uh whatever initially is to
+ 
+
+ align:start position:0%
+from uh whatever initially is to
+Red the first one car. paint red is sort
+
+ align:start position:0%
+Red the first one car. paint red is sort
+ 
+
+ align:start position:0%
+Red the first one car. paint red is sort
+of attempting to do the the way that we
+
+ align:start position:0%
+of attempting to do the the way that we
+ 
+
+ align:start position:0%
+of attempting to do the the way that we
+saw on the right in the slides where
+
+ align:start position:0%
+saw on the right in the slides where
+ 
+
+ align:start position:0%
+saw on the right in the slides where
+you're calling the class name dot but
+
+ align:start position:0%
+you're calling the class name dot but
+ 
+
+ align:start position:0%
+you're calling the class name dot but
+it's missing the self so we don't know
+
+ align:start position:0%
+it's missing the self so we don't know
+ 
+
+ align:start position:0%
+it's missing the self so we don't know
+what object to call it on so that one's
+
+ align:start position:0%
+what object to call it on so that one's
+ 
+
+ align:start position:0%
+what object to call it on so that one's
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+running the second second one is closer
+
+ align:start position:0%
+running the second second one is closer
+ 
+
+ align:start position:0%
+running the second second one is closer
+but we have red here as a variable as
+
+ align:start position:0%
+but we have red here as a variable as
+ 
+
+ align:start position:0%
+but we have red here as a variable as
+opposed to a
+
+ align:start position:0%
+opposed to a
+ 
+
+ align:start position:0%
+opposed to a
+string so that one's not not going to
+
+ align:start position:0%
+string so that one's not not going to
+ 
+
+ align:start position:0%
+string so that one's not not going to
+work the third one looks good and the
+
+ align:start position:0%
+work the third one looks good and the
+ 
+
+ align:start position:0%
+work the third one looks good and the
+fourth one is just weird I don't think
+
+ align:start position:0%
+fourth one is just weird I don't think
+ 
+
+ align:start position:0%
+fourth one is just weird I don't think
+that one will work it's attempting to
+
+ align:start position:0%
+that one will work it's attempting to
+ 
+
+ align:start position:0%
+that one will work it's attempting to
+put a value for self but you've already
+
+ align:start position:0%
+put a value for self but you've already
+ 
+
+ align:start position:0%
+put a value for self but you've already
+called my car dot instead of the um
+
+ align:start position:0%
+called my car dot instead of the um
+ 
+
+ align:start position:0%
+called my car dot instead of the um
+instead of the uh class class name dot
+
+ align:start position:0%
+instead of the uh class class name dot
+ 
+
+ align:start position:0%
+instead of the uh class class name dot
+so here um this isn't going to work
+
+ align:start position:0%
+so here um this isn't going to work
+ 
+
+ align:start position:0%
+so here um this isn't going to work
+so since you already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called um the object name dot method
+
+ align:start position:0%
+called um the object name dot method
+ 
+
+ align:start position:0%
+called um the object name dot method
+name you just have to give it the other
+
+ align:start position:0%
+name you just have to give it the other
+ 
+
+ align:start position:0%
+name you just have to give it the other
+parameter that it needs which is the
+
+ align:start position:0%
+parameter that it needs which is the
+ 
+
+ align:start position:0%
+parameter that it needs which is the
+color okay and I think the majority have
+
+ align:start position:0%
+color okay and I think the majority have
+ 
+
+ align:start position:0%
+color okay and I think the majority have
+gotten it
+
+ align:start position:0%
+gotten it
+ 
+
+ align:start position:0%
+gotten it
+right
\ No newline at end of file
diff --git a/_hDfZF64wic.txt b/_hDfZF64wic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..391b94df79ad9984f246244ea257aa7ac70df498
--- /dev/null
+++ b/_hDfZF64wic.txt
@@ -0,0 +1,979 @@
+align:start position:0%
+ 
+in this lecture sequence we introduced
+
+ align:start position:0%
+in this lecture sequence we introduced
+ 
+
+ align:start position:0%
+in this lecture sequence we introduced
+quite a few new concepts and went
+
+ align:start position:0%
+quite a few new concepts and went
+ 
+
+ align:start position:0%
+quite a few new concepts and went
+through a fair number of examples so for
+
+ align:start position:0%
+through a fair number of examples so for
+ 
+
+ align:start position:0%
+through a fair number of examples so for
+this reason it is useful now to just
+
+ align:start position:0%
+this reason it is useful now to just
+ 
+
+ align:start position:0%
+this reason it is useful now to just
+take stock and summarize the key ideas
+
+ align:start position:0%
+take stock and summarize the key ideas
+ 
+
+ align:start position:0%
+take stock and summarize the key ideas
+and concepts the starting point in a
+
+ align:start position:0%
+and concepts the starting point in a
+ 
+
+ align:start position:0%
+and concepts the starting point in a
+Bayesian inference problem is the
+
+ align:start position:0%
+Bayesian inference problem is the
+ 
+
+ align:start position:0%
+Bayesian inference problem is the
+following there is an unknown parameter
+
+ align:start position:0%
+following there is an unknown parameter
+ 
+
+ align:start position:0%
+following there is an unknown parameter
+theta and were given a prior
+
+ align:start position:0%
+theta and were given a prior
+ 
+
+ align:start position:0%
+theta and were given a prior
+distribution for that parameter we're
+
+ align:start position:0%
+distribution for that parameter we're
+ 
+
+ align:start position:0%
+distribution for that parameter we're
+also given a model for the observations
+
+ align:start position:0%
+also given a model for the observations
+ 
+
+ align:start position:0%
+also given a model for the observations
+X in terms of a distribution that
+
+ align:start position:0%
+X in terms of a distribution that
+ 
+
+ align:start position:0%
+X in terms of a distribution that
+depends on the unknown parameter theta
+
+ align:start position:0%
+depends on the unknown parameter theta
+ 
+
+ align:start position:0%
+depends on the unknown parameter theta
+the inference problem is as follows we
+
+ align:start position:0%
+the inference problem is as follows we
+ 
+
+ align:start position:0%
+the inference problem is as follows we
+will be given the value of the random
+
+ align:start position:0%
+will be given the value of the random
+ 
+
+ align:start position:0%
+will be given the value of the random
+variable X and then we want to find the
+
+ align:start position:0%
+variable X and then we want to find the
+ 
+
+ align:start position:0%
+variable X and then we want to find the
+posterior distribution of theta that is
+
+ align:start position:0%
+posterior distribution of theta that is
+ 
+
+ align:start position:0%
+posterior distribution of theta that is
+given this particular value of x what is
+
+ align:start position:0%
+given this particular value of x what is
+ 
+
+ align:start position:0%
+given this particular value of x what is
+the conditional distribution of theta in
+
+ align:start position:0%
+the conditional distribution of theta in
+ 
+
+ align:start position:0%
+the conditional distribution of theta in
+the case where theta is discrete this
+
+ align:start position:0%
+the case where theta is discrete this
+ 
+
+ align:start position:0%
+the case where theta is discrete this
+will be in terms of a PMF if theta is
+
+ align:start position:0%
+will be in terms of a PMF if theta is
+ 
+
+ align:start position:0%
+will be in terms of a PMF if theta is
+continuous this would be a PDF we find
+
+ align:start position:0%
+continuous this would be a PDF we find
+ 
+
+ align:start position:0%
+continuous this would be a PDF we find
+the posterior distribution by using an
+
+ align:start position:0%
+the posterior distribution by using an
+ 
+
+ align:start position:0%
+the posterior distribution by using an
+appropriate version of the Bayes rule
+
+ align:start position:0%
+appropriate version of the Bayes rule
+ 
+
+ align:start position:0%
+appropriate version of the Bayes rule
+and here we have four different
+
+ align:start position:0%
+and here we have four different
+ 
+
+ align:start position:0%
+and here we have four different
+combinations or four choices depending
+
+ align:start position:0%
+combinations or four choices depending
+ 
+
+ align:start position:0%
+combinations or four choices depending
+on which variables are discrete or
+
+ align:start position:0%
+on which variables are discrete or
+ 
+
+ align:start position:0%
+on which variables are discrete or
+continuous this is a complete solution
+
+ align:start position:0%
+continuous this is a complete solution
+ 
+
+ align:start position:0%
+continuous this is a complete solution
+to a Bayesian inference problem a
+
+ align:start position:0%
+to a Bayesian inference problem a
+ 
+
+ align:start position:0%
+to a Bayesian inference problem a
+posterior distribution but if we want to
+
+ align:start position:0%
+posterior distribution but if we want to
+ 
+
+ align:start position:0%
+posterior distribution but if we want to
+come up with a single guess of what
+
+ align:start position:0%
+come up with a single guess of what
+ 
+
+ align:start position:0%
+come up with a single guess of what
+theta is then we use a so-called
+
+ align:start position:0%
+theta is then we use a so-called
+ 
+
+ align:start position:0%
+theta is then we use a so-called
+estimator what an estimator does is that
+
+ align:start position:0%
+estimator what an estimator does is that
+ 
+
+ align:start position:0%
+estimator what an estimator does is that
+it calculates a certain value as a
+
+ align:start position:0%
+it calculates a certain value as a
+ 
+
+ align:start position:0%
+it calculates a certain value as a
+function of the observed data so G
+
+ align:start position:0%
+function of the observed data so G
+ 
+
+ align:start position:0%
+function of the observed data so G
+describes the way that the data are
+
+ align:start position:0%
+describes the way that the data are
+ 
+
+ align:start position:0%
+describes the way that the data are
+processed because X is random the
+
+ align:start position:0%
+processed because X is random the
+ 
+
+ align:start position:0%
+processed because X is random the
+estimator itself will be a random
+
+ align:start position:0%
+estimator itself will be a random
+ 
+
+ align:start position:0%
+estimator itself will be a random
+variable but once we obtain a specific
+
+ align:start position:0%
+variable but once we obtain a specific
+ 
+
+ align:start position:0%
+variable but once we obtain a specific
+value of our random variable and we
+
+ align:start position:0%
+value of our random variable and we
+ 
+
+ align:start position:0%
+value of our random variable and we
+apply this particular estimator then we
+
+ align:start position:0%
+apply this particular estimator then we
+ 
+
+ align:start position:0%
+apply this particular estimator then we
+get the realized value of the estimator
+
+ align:start position:0%
+get the realized value of the estimator
+ 
+
+ align:start position:0%
+get the realized value of the estimator
+so we apply G now to the lower case X
+
+ align:start position:0%
+so we apply G now to the lower case X
+ 
+
+ align:start position:0%
+so we apply G now to the lower case X
+and this gives us an estimate which is
+
+ align:start position:0%
+and this gives us an estimate which is
+ 
+
+ align:start position:0%
+and this gives us an estimate which is
+actually a number we have seen two
+
+ align:start position:0%
+actually a number we have seen two
+ 
+
+ align:start position:0%
+actually a number we have seen two
+particular ways of constructing
+
+ align:start position:0%
+particular ways of constructing
+ 
+
+ align:start position:0%
+particular ways of constructing
+estimates or estimators one of them is
+
+ align:start position:0%
+estimates or estimators one of them is
+ 
+
+ align:start position:0%
+estimates or estimators one of them is
+the maximum a posteriori probability
+
+ align:start position:0%
+the maximum a posteriori probability
+ 
+
+ align:start position:0%
+the maximum a posteriori probability
+rule in which we choose
+
+ align:start position:0%
+rule in which we choose
+ 
+
+ align:start position:0%
+rule in which we choose
+estimate that maximizes the posterior
+
+ align:start position:0%
+estimate that maximizes the posterior
+ 
+
+ align:start position:0%
+estimate that maximizes the posterior
+distribution so in the case where theta
+
+ align:start position:0%
+distribution so in the case where theta
+ 
+
+ align:start position:0%
+distribution so in the case where theta
+is discrete this finds the value of
+
+ align:start position:0%
+is discrete this finds the value of
+ 
+
+ align:start position:0%
+is discrete this finds the value of
+theta which is the most likely one given
+
+ align:start position:0%
+theta which is the most likely one given
+ 
+
+ align:start position:0%
+theta which is the most likely one given
+our observation and similarly in the
+
+ align:start position:0%
+our observation and similarly in the
+ 
+
+ align:start position:0%
+our observation and similarly in the
+continuous case it finds the value of
+
+ align:start position:0%
+continuous case it finds the value of
+ 
+
+ align:start position:0%
+continuous case it finds the value of
+theta at which the conditional PDF of
+
+ align:start position:0%
+theta at which the conditional PDF of
+ 
+
+ align:start position:0%
+theta at which the conditional PDF of
+theta would be largest another estimator
+
+ align:start position:0%
+theta would be largest another estimator
+ 
+
+ align:start position:0%
+theta would be largest another estimator
+is the one that we call the LMS or least
+
+ align:start position:0%
+is the one that we call the LMS or least
+ 
+
+ align:start position:0%
+is the one that we call the LMS or least
+mean squares estimator which calculates
+
+ align:start position:0%
+mean squares estimator which calculates
+ 
+
+ align:start position:0%
+mean squares estimator which calculates
+the conditional expectation of the
+
+ align:start position:0%
+the conditional expectation of the
+ 
+
+ align:start position:0%
+the conditional expectation of the
+unknown parameter given the observations
+
+ align:start position:0%
+unknown parameter given the observations
+ 
+
+ align:start position:0%
+unknown parameter given the observations
+that we have obtained finally we may be
+
+ align:start position:0%
+that we have obtained finally we may be
+ 
+
+ align:start position:0%
+that we have obtained finally we may be
+interested in evaluating the performance
+
+ align:start position:0%
+interested in evaluating the performance
+ 
+
+ align:start position:0%
+interested in evaluating the performance
+of a given estimator for hypothesis
+
+ align:start position:0%
+of a given estimator for hypothesis
+ 
+
+ align:start position:0%
+of a given estimator for hypothesis
+testing problems were interested in the
+
+ align:start position:0%
+testing problems were interested in the
+ 
+
+ align:start position:0%
+testing problems were interested in the
+probability of error and we have the
+
+ align:start position:0%
+probability of error and we have the
+ 
+
+ align:start position:0%
+probability of error and we have the
+conditional probability of error given
+
+ align:start position:0%
+conditional probability of error given
+ 
+
+ align:start position:0%
+conditional probability of error given
+the data that I have just observed and
+
+ align:start position:0%
+the data that I have just observed and
+ 
+
+ align:start position:0%
+the data that I have just observed and
+given that I'm using a specific
+
+ align:start position:0%
+given that I'm using a specific
+ 
+
+ align:start position:0%
+given that I'm using a specific
+estimator what is the probability that I
+
+ align:start position:0%
+estimator what is the probability that I
+ 
+
+ align:start position:0%
+estimator what is the probability that I
+make a mistake and then there's the
+
+ align:start position:0%
+make a mistake and then there's the
+ 
+
+ align:start position:0%
+make a mistake and then there's the
+overall evaluation of the estimator how
+
+ align:start position:0%
+overall evaluation of the estimator how
+ 
+
+ align:start position:0%
+overall evaluation of the estimator how
+well does it do on the average before I
+
+ align:start position:0%
+well does it do on the average before I
+ 
+
+ align:start position:0%
+well does it do on the average before I
+know what X is going to be and this is
+
+ align:start position:0%
+know what X is going to be and this is
+ 
+
+ align:start position:0%
+know what X is going to be and this is
+just the probability that I will be
+
+ align:start position:0%
+just the probability that I will be
+ 
+
+ align:start position:0%
+just the probability that I will be
+making an incorrect decision for
+
+ align:start position:0%
+making an incorrect decision for
+ 
+
+ align:start position:0%
+making an incorrect decision for
+estimation problems on the other hand
+
+ align:start position:0%
+estimation problems on the other hand
+ 
+
+ align:start position:0%
+estimation problems on the other hand
+were interested in the distance between
+
+ align:start position:0%
+were interested in the distance between
+ 
+
+ align:start position:0%
+were interested in the distance between
+our estimates from the true value of
+
+ align:start position:0%
+our estimates from the true value of
+ 
+
+ align:start position:0%
+our estimates from the true value of
+theta and this leads us to the following
+
+ align:start position:0%
+theta and this leads us to the following
+ 
+
+ align:start position:0%
+theta and this leads us to the following
+conditional mean squared error given
+
+ align:start position:0%
+conditional mean squared error given
+ 
+
+ align:start position:0%
+conditional mean squared error given
+that we have already obtained an
+
+ align:start position:0%
+that we have already obtained an
+ 
+
+ align:start position:0%
+that we have already obtained an
+observation and we come up with an
+
+ align:start position:0%
+observation and we come up with an
+ 
+
+ align:start position:0%
+observation and we come up with an
+estimator in particular the value of the
+
+ align:start position:0%
+estimator in particular the value of the
+ 
+
+ align:start position:0%
+estimator in particular the value of the
+estimator at this time will be
+
+ align:start position:0%
+estimator at this time will be
+ 
+
+ align:start position:0%
+estimator at this time will be
+completely determined by the data that
+
+ align:start position:0%
+completely determined by the data that
+ 
+
+ align:start position:0%
+completely determined by the data that
+we obtained but theta the unknown
+
+ align:start position:0%
+we obtained but theta the unknown
+ 
+
+ align:start position:0%
+we obtained but theta the unknown
+parameter remains random and there's
+
+ align:start position:0%
+parameter remains random and there's
+ 
+
+ align:start position:0%
+parameter remains random and there's
+going to be a certain squared error we
+
+ align:start position:0%
+going to be a certain squared error we
+ 
+
+ align:start position:0%
+going to be a certain squared error we
+find the conditional expectation of this
+
+ align:start position:0%
+find the conditional expectation of this
+ 
+
+ align:start position:0%
+find the conditional expectation of this
+squared error in this particular
+
+ align:start position:0%
+squared error in this particular
+ 
+
+ align:start position:0%
+squared error in this particular
+situation where we have obtained a
+
+ align:start position:0%
+situation where we have obtained a
+ 
+
+ align:start position:0%
+situation where we have obtained a
+specific value of the random variable
+
+ align:start position:0%
+specific value of the random variable
+ 
+
+ align:start position:0%
+specific value of the random variable
+capital X on the other hand if we're
+
+ align:start position:0%
+capital X on the other hand if we're
+ 
+
+ align:start position:0%
+capital X on the other hand if we're
+looking at the estimator more generally
+
+ align:start position:0%
+looking at the estimator more generally
+ 
+
+ align:start position:0%
+looking at the estimator more generally
+how well it does on the average then we
+
+ align:start position:0%
+how well it does on the average then we
+ 
+
+ align:start position:0%
+how well it does on the average then we
+look at the unconditional means
+
+ align:start position:0%
+look at the unconditional means
+ 
+
+ align:start position:0%
+look at the unconditional means
+squared error then this gives us an
+
+ align:start position:0%
+squared error then this gives us an
+ 
+
+ align:start position:0%
+squared error then this gives us an
+overall performance evaluation how do we
+
+ align:start position:0%
+overall performance evaluation how do we
+ 
+
+ align:start position:0%
+overall performance evaluation how do we
+calculate these performance measures
+
+ align:start position:0%
+calculate these performance measures
+ 
+
+ align:start position:0%
+calculate these performance measures
+here we live in a conditional universe
+
+ align:start position:0%
+here we live in a conditional universe
+ 
+
+ align:start position:0%
+here we live in a conditional universe
+and in a Bayesian estimation problem at
+
+ align:start position:0%
+and in a Bayesian estimation problem at
+ 
+
+ align:start position:0%
+and in a Bayesian estimation problem at
+some point we do calculate the posterior
+
+ align:start position:0%
+some point we do calculate the posterior
+ 
+
+ align:start position:0%
+some point we do calculate the posterior
+distribution of theta given the
+
+ align:start position:0%
+distribution of theta given the
+ 
+
+ align:start position:0%
+distribution of theta given the
+measurements so these calculations
+
+ align:start position:0%
+measurements so these calculations
+ 
+
+ align:start position:0%
+measurements so these calculations
+involved here consists of just an
+
+ align:start position:0%
+involved here consists of just an
+ 
+
+ align:start position:0%
+involved here consists of just an
+integration or summation using the
+
+ align:start position:0%
+integration or summation using the
+ 
+
+ align:start position:0%
+integration or summation using the
+conditional distribution for example
+
+ align:start position:0%
+conditional distribution for example
+ 
+
+ align:start position:0%
+conditional distribution for example
+here we would integrate this quantity
+
+ align:start position:0%
+here we would integrate this quantity
+ 
+
+ align:start position:0%
+here we would integrate this quantity
+using the conditional density of theta
+
+ align:start position:0%
+using the conditional density of theta
+ 
+
+ align:start position:0%
+using the conditional density of theta
+given the particular value that we have
+
+ align:start position:0%
+given the particular value that we have
+ 
+
+ align:start position:0%
+given the particular value that we have
+obtained if we want to now calculate the
+
+ align:start position:0%
+obtained if we want to now calculate the
+ 
+
+ align:start position:0%
+obtained if we want to now calculate the
+unconditional performance then we will
+
+ align:start position:0%
+unconditional performance then we will
+ 
+
+ align:start position:0%
+unconditional performance then we will
+have to use the total probability or
+
+ align:start position:0%
+have to use the total probability or
+ 
+
+ align:start position:0%
+have to use the total probability or
+expectation theorem and in that case we
+
+ align:start position:0%
+expectation theorem and in that case we
+ 
+
+ align:start position:0%
+expectation theorem and in that case we
+can average over all the possible values
+
+ align:start position:0%
+can average over all the possible values
+ 
+
+ align:start position:0%
+can average over all the possible values
+of X to find the overall error so all of
+
+ align:start position:0%
+of X to find the overall error so all of
+ 
+
+ align:start position:0%
+of X to find the overall error so all of
+the calculations involve tools and
+
+ align:start position:0%
+the calculations involve tools and
+ 
+
+ align:start position:0%
+the calculations involve tools and
+equations that we have seen and that we
+
+ align:start position:0%
+equations that we have seen and that we
+ 
+
+ align:start position:0%
+equations that we have seen and that we
+have used in the past so it is just a
+
+ align:start position:0%
+have used in the past so it is just a
+ 
+
+ align:start position:0%
+have used in the past so it is just a
+matter of connecting those tools with
+
+ align:start position:0%
+matter of connecting those tools with
+ 
+
+ align:start position:0%
+matter of connecting those tools with
+the specific new concepts that we have
+
+ align:start position:0%
+the specific new concepts that we have
+ 
+
+ align:start position:0%
+the specific new concepts that we have
+introduced here
\ No newline at end of file
diff --git a/apP5SWitnyw.txt b/apP5SWitnyw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2b8cf6437a5095b309a638770d6a7c8297d74e49
--- /dev/null
+++ b/apP5SWitnyw.txt
@@ -0,0 +1,7667 @@
+align:start position:0%
+ 
+okay we'll get started I've got
+
+ align:start position:0%
+okay we'll get started I've got
+ 
+
+ align:start position:0%
+okay we'll get started I've got
+everything turned on here so a couple of
+
+ align:start position:0%
+everything turned on here so a couple of
+ 
+
+ align:start position:0%
+everything turned on here so a couple of
+things I've been mentioning that it's
+
+ align:start position:0%
+things I've been mentioning that it's
+ 
+
+ align:start position:0%
+things I've been mentioning that it's
+really kind of cool I think at this
+
+ align:start position:0%
+really kind of cool I think at this
+ 
+
+ align:start position:0%
+really kind of cool I think at this
+stage where you've gathered enough steam
+
+ align:start position:0%
+stage where you've gathered enough steam
+ 
+
+ align:start position:0%
+stage where you've gathered enough steam
+in some of the topics that many things
+
+ align:start position:0%
+in some of the topics that many things
+ 
+
+ align:start position:0%
+in some of the topics that many things
+that come out in the news mate start
+
+ align:start position:0%
+that come out in the news mate start
+ 
+
+ align:start position:0%
+that come out in the news mate start
+looking of interest or relevant to you
+
+ align:start position:0%
+looking of interest or relevant to you
+ 
+
+ align:start position:0%
+looking of interest or relevant to you
+and I found this it was ad it had a news
+
+ align:start position:0%
+and I found this it was ad it had a news
+ 
+
+ align:start position:0%
+and I found this it was ad it had a news
+brief in the scientist and then I went
+
+ align:start position:0%
+brief in the scientist and then I went
+ 
+
+ align:start position:0%
+brief in the scientist and then I went
+to the original paper which is in Nature
+
+ align:start position:0%
+to the original paper which is in Nature
+ 
+
+ align:start position:0%
+to the original paper which is in Nature
+Biotechnology and if you recall towards
+
+ align:start position:0%
+Biotechnology and if you recall towards
+ 
+
+ align:start position:0%
+Biotechnology and if you recall towards
+the end of the work on proteins we were
+
+ align:start position:0%
+the end of the work on proteins we were
+ 
+
+ align:start position:0%
+the end of the work on proteins we were
+talking about phenylketonuria which is a
+
+ align:start position:0%
+talking about phenylketonuria which is a
+ 
+
+ align:start position:0%
+talking about phenylketonuria which is a
+genetic li linked disorder where people
+
+ align:start position:0%
+genetic li linked disorder where people
+ 
+
+ align:start position:0%
+genetic li linked disorder where people
+cannot metabolize phenylalanine to keep
+
+ align:start position:0%
+cannot metabolize phenylalanine to keep
+ 
+
+ align:start position:0%
+cannot metabolize phenylalanine to keep
+the levels of phenylalanine in check so
+
+ align:start position:0%
+the levels of phenylalanine in check so
+ 
+
+ align:start position:0%
+the levels of phenylalanine in check so
+what happens is the phenylalanine gets
+
+ align:start position:0%
+what happens is the phenylalanine gets
+ 
+
+ align:start position:0%
+what happens is the phenylalanine gets
+converted to a toxic material and it
+
+ align:start position:0%
+converted to a toxic material and it
+ 
+
+ align:start position:0%
+converted to a toxic material and it
+causes a lot of fundamental physiologic
+
+ align:start position:0%
+causes a lot of fundamental physiologic
+ 
+
+ align:start position:0%
+causes a lot of fundamental physiologic
+disorders that moves a lot of neurologic
+
+ align:start position:0%
+disorders that moves a lot of neurologic
+ 
+
+ align:start position:0%
+disorders that moves a lot of neurologic
+disorders so what a small company in the
+
+ align:start position:0%
+disorders so what a small company in the
+ 
+
+ align:start position:0%
+disorders so what a small company in the
+area called what's the name of the
+
+ align:start position:0%
+area called what's the name of the
+ 
+
+ align:start position:0%
+area called what's the name of the
+company I can see it here anyway
+
+ align:start position:0%
+company I can see it here anyway
+ 
+
+ align:start position:0%
+company I can see it here anyway
+sin logic is a synthetic biology company
+
+ align:start position:0%
+sin logic is a synthetic biology company
+ 
+
+ align:start position:0%
+sin logic is a synthetic biology company
+which basically engineers bacterial
+
+ align:start position:0%
+which basically engineers bacterial
+ 
+
+ align:start position:0%
+which basically engineers bacterial
+strains as probiotics that can be used
+
+ align:start position:0%
+strains as probiotics that can be used
+ 
+
+ align:start position:0%
+strains as probiotics that can be used
+to mitigate some genetic disorders and
+
+ align:start position:0%
+to mitigate some genetic disorders and
+ 
+
+ align:start position:0%
+to mitigate some genetic disorders and
+so they've created a bacterial strain
+
+ align:start position:0%
+so they've created a bacterial strain
+ 
+
+ align:start position:0%
+so they've created a bacterial strain
+that can metabolize phenylalanine so do
+
+ align:start position:0%
+that can metabolize phenylalanine so do
+ 
+
+ align:start position:0%
+that can metabolize phenylalanine so do
+a good job of sort of not letting your
+
+ align:start position:0%
+a good job of sort of not letting your
+ 
+
+ align:start position:0%
+a good job of sort of not letting your
+phenylalanine levels get too high so in
+
+ align:start position:0%
+phenylalanine levels get too high so in
+ 
+
+ align:start position:0%
+phenylalanine levels get too high so in
+the in the GI system this bacterium
+
+ align:start position:0%
+the in the GI system this bacterium
+ 
+
+ align:start position:0%
+the in the GI system this bacterium
+basically works on phenylalanine to
+
+ align:start position:0%
+basically works on phenylalanine to
+ 
+
+ align:start position:0%
+basically works on phenylalanine to
+metabolize it so that then people don't
+
+ align:start position:0%
+metabolize it so that then people don't
+ 
+
+ align:start position:0%
+metabolize it so that then people don't
+have to lead such a strict dietary
+
+ align:start position:0%
+have to lead such a strict dietary
+ 
+
+ align:start position:0%
+have to lead such a strict dietary
+regime don't and have way less risk so I
+
+ align:start position:0%
+regime don't and have way less risk so I
+ 
+
+ align:start position:0%
+regime don't and have way less risk so I
+think it's a really cool thing this
+
+ align:start position:0%
+think it's a really cool thing this
+ 
+
+ align:start position:0%
+think it's a really cool thing this
+probiotic is in one to clinical trials
+
+ align:start position:0%
+probiotic is in one to clinical trials
+ 
+
+ align:start position:0%
+probiotic is in one to clinical trials
+it's being fast-tracked and the company
+
+ align:start position:0%
+it's being fast-tracked and the company
+ 
+
+ align:start position:0%
+it's being fast-tracked and the company
+in general is a synthetic biology
+
+ align:start position:0%
+in general is a synthetic biology
+ 
+
+ align:start position:0%
+in general is a synthetic biology
+company working on solutions to certain
+
+ align:start position:0%
+company working on solutions to certain
+ 
+
+ align:start position:0%
+company working on solutions to certain
+types of diseases that could either save
+
+ align:start position:0%
+types of diseases that could either save
+ 
+
+ align:start position:0%
+types of diseases that could either save
+you from having a lot of restrictions on
+
+ align:start position:0%
+you from having a lot of restrictions on
+ 
+
+ align:start position:0%
+you from having a lot of restrictions on
+the way on your lifestyle or
+
+ align:start position:0%
+the way on your lifestyle or
+ 
+
+ align:start position:0%
+the way on your lifestyle or
+alternatively save you from taking
+
+ align:start position:0%
+alternatively save you from taking
+ 
+
+ align:start position:0%
+alternatively save you from taking
+medications and stuff so that's
+
+ align:start position:0%
+medications and stuff so that's
+ 
+
+ align:start position:0%
+medications and stuff so that's
+something that that caught my eye I want
+
+ align:start position:0%
+something that that caught my eye I want
+ 
+
+ align:start position:0%
+something that that caught my eye I want
+to remind you that I have now put the
+
+ align:start position:0%
+to remind you that I have now put the
+ 
+
+ align:start position:0%
+to remind you that I have now put the
+link to the scientist in the sidebar of
+
+ align:start position:0%
+link to the scientist in the sidebar of
+ 
+
+ align:start position:0%
+link to the scientist in the sidebar of
+the website so it's much easier for you
+
+ align:start position:0%
+the website so it's much easier for you
+ 
+
+ align:start position:0%
+the website so it's much easier for you
+to grab it and take a look what's in the
+
+ align:start position:0%
+to grab it and take a look what's in the
+ 
+
+ align:start position:0%
+to grab it and take a look what's in the
+news there's stuff in the news every two
+
+ align:start position:0%
+news there's stuff in the news every two
+ 
+
+ align:start position:0%
+news there's stuff in the news every two
+or three days and there are things that
+
+ align:start position:0%
+or three days and there are things that
+ 
+
+ align:start position:0%
+or three days and there are things that
+I think you'll find interesting that
+
+ align:start position:0%
+I think you'll find interesting that
+ 
+
+ align:start position:0%
+I think you'll find interesting that
+really relate to technology engineering
+
+ align:start position:0%
+really relate to technology engineering
+ 
+
+ align:start position:0%
+really relate to technology engineering
+and fundamental science that are related
+
+ align:start position:0%
+and fundamental science that are related
+ 
+
+ align:start position:0%
+and fundamental science that are related
+to biology the other thing I want to do
+
+ align:start position:0%
+to biology the other thing I want to do
+ 
+
+ align:start position:0%
+to biology the other thing I want to do
+is remind you that towards the last the
+
+ align:start position:0%
+is remind you that towards the last the
+ 
+
+ align:start position:0%
+is remind you that towards the last the
+end of the class but you know time like
+
+ align:start position:0%
+end of the class but you know time like
+ 
+
+ align:start position:0%
+end of the class but you know time like
+the present because it is a sort of the
+
+ align:start position:0%
+the present because it is a sort of the
+ 
+
+ align:start position:0%
+the present because it is a sort of the
+equivalent of one of the problem sets
+
+ align:start position:0%
+equivalent of one of the problem sets
+ 
+
+ align:start position:0%
+equivalent of one of the problem sets
+but in fact worth a little bit more than
+
+ align:start position:0%
+but in fact worth a little bit more than
+ 
+
+ align:start position:0%
+but in fact worth a little bit more than
+the problem set is I want to encourage
+
+ align:start position:0%
+the problem set is I want to encourage
+ 
+
+ align:start position:0%
+the problem set is I want to encourage
+you to keep an eye on the scientist link
+
+ align:start position:0%
+you to keep an eye on the scientist link
+ 
+
+ align:start position:0%
+you to keep an eye on the scientist link
+and maybe pick out a topic that two or
+
+ align:start position:0%
+and maybe pick out a topic that two or
+ 
+
+ align:start position:0%
+and maybe pick out a topic that two or
+three of you would like to write a news
+
+ align:start position:0%
+three of you would like to write a news
+ 
+
+ align:start position:0%
+three of you would like to write a news
+brief on with a paragraph of writing on
+
+ align:start position:0%
+brief on with a paragraph of writing on
+ 
+
+ align:start position:0%
+brief on with a paragraph of writing on
+introduction and what the technology is
+
+ align:start position:0%
+introduction and what the technology is
+ 
+
+ align:start position:0%
+introduction and what the technology is
+how technology has addressed a
+
+ align:start position:0%
+how technology has addressed a
+ 
+
+ align:start position:0%
+how technology has addressed a
+particular scientific or biological
+
+ align:start position:0%
+particular scientific or biological
+ 
+
+ align:start position:0%
+particular scientific or biological
+problem and then there should also be a
+
+ align:start position:0%
+problem and then there should also be a
+ 
+
+ align:start position:0%
+problem and then there should also be a
+graphic but describes it not stuff
+
+ align:start position:0%
+graphic but describes it not stuff
+ 
+
+ align:start position:0%
+graphic but describes it not stuff
+snipped out of whatever you're reading
+
+ align:start position:0%
+snipped out of whatever you're reading
+ 
+
+ align:start position:0%
+snipped out of whatever you're reading
+something that you create as a team to
+
+ align:start position:0%
+something that you create as a team to
+ 
+
+ align:start position:0%
+something that you create as a team to
+scribe a concept to people there's
+
+ align:start position:0%
+scribe a concept to people there's
+ 
+
+ align:start position:0%
+scribe a concept to people there's
+alternatives with that assignment you
+
+ align:start position:0%
+alternatives with that assignment you
+ 
+
+ align:start position:0%
+alternatives with that assignment you
+can also pick an interesting protein
+
+ align:start position:0%
+can also pick an interesting protein
+ 
+
+ align:start position:0%
+can also pick an interesting protein
+from the PDB make a 3d print a bit learn
+
+ align:start position:0%
+from the PDB make a 3d print a bit learn
+ 
+
+ align:start position:0%
+from the PDB make a 3d print a bit learn
+how to print it and go to the 3d
+
+ align:start position:0%
+how to print it and go to the 3d
+ 
+
+ align:start position:0%
+how to print it and go to the 3d
+printers in the maker labs and print the
+
+ align:start position:0%
+printers in the maker labs and print the
+ 
+
+ align:start position:0%
+printers in the maker labs and print the
+protein and then write a brief summary
+
+ align:start position:0%
+protein and then write a brief summary
+ 
+
+ align:start position:0%
+protein and then write a brief summary
+of what it is and one other idea I had
+
+ align:start position:0%
+of what it is and one other idea I had
+ 
+
+ align:start position:0%
+of what it is and one other idea I had
+for the engineers of U is I would love a
+
+ align:start position:0%
+for the engineers of U is I would love a
+ 
+
+ align:start position:0%
+for the engineers of U is I would love a
+better less clunky to topoisomerase
+
+ align:start position:0%
+better less clunky to topoisomerase
+ 
+
+ align:start position:0%
+better less clunky to topoisomerase
+demonstration in particular I'd really
+
+ align:start position:0%
+demonstration in particular I'd really
+ 
+
+ align:start position:0%
+demonstration in particular I'd really
+like one where you can snip the pieces
+
+ align:start position:0%
+like one where you can snip the pieces
+ 
+
+ align:start position:0%
+like one where you can snip the pieces
+apart let the untangling happen and put
+
+ align:start position:0%
+apart let the untangling happen and put
+ 
+
+ align:start position:0%
+apart let the untangling happen and put
+them back together so some of you could
+
+ align:start position:0%
+them back together so some of you could
+ 
+
+ align:start position:0%
+them back together so some of you could
+work with a couple of colleagues and you
+
+ align:start position:0%
+work with a couple of colleagues and you
+ 
+
+ align:start position:0%
+work with a couple of colleagues and you
+make something which I know a lot of you
+
+ align:start position:0%
+make something which I know a lot of you
+ 
+
+ align:start position:0%
+make something which I know a lot of you
+are really keen on which is why your
+
+ align:start position:0%
+are really keen on which is why your
+ 
+
+ align:start position:0%
+are really keen on which is why your
+engineers alright okay any questions
+
+ align:start position:0%
+engineers alright okay any questions
+ 
+
+ align:start position:0%
+engineers alright okay any questions
+about any of this I'm trying to make
+
+ align:start position:0%
+about any of this I'm trying to make
+ 
+
+ align:start position:0%
+about any of this I'm trying to make
+sure that this doesn't creep up on you
+
+ align:start position:0%
+sure that this doesn't creep up on you
+ 
+
+ align:start position:0%
+sure that this doesn't creep up on you
+it's just something you do it's great to
+
+ align:start position:0%
+it's just something you do it's great to
+ 
+
+ align:start position:0%
+it's just something you do it's great to
+get awareness
+
+ align:start position:0%
+get awareness
+ 
+
+ align:start position:0%
+get awareness
+of Technology in the but in the life
+
+ align:start position:0%
+of Technology in the but in the life
+ 
+
+ align:start position:0%
+of Technology in the but in the life
+sciences because of how much
+
+ align:start position:0%
+sciences because of how much
+ 
+
+ align:start position:0%
+sciences because of how much
+contribution it makes so if you keep an
+
+ align:start position:0%
+contribution it makes so if you keep an
+ 
+
+ align:start position:0%
+contribution it makes so if you keep an
+eye on things you won't be forced to
+
+ align:start position:0%
+eye on things you won't be forced to
+ 
+
+ align:start position:0%
+eye on things you won't be forced to
+suddenly find something good at the last
+
+ align:start position:0%
+suddenly find something good at the last
+ 
+
+ align:start position:0%
+suddenly find something good at the last
+minute you'll just have found something
+
+ align:start position:0%
+minute you'll just have found something
+ 
+
+ align:start position:0%
+minute you'll just have found something
+and go that's the perfect thing to
+
+ align:start position:0%
+and go that's the perfect thing to
+ 
+
+ align:start position:0%
+and go that's the perfect thing to
+describe alright questions and the other
+
+ align:start position:0%
+describe alright questions and the other
+ 
+
+ align:start position:0%
+describe alright questions and the other
+thing is if you if you're not unsure you
+
+ align:start position:0%
+thing is if you if you're not unsure you
+ 
+
+ align:start position:0%
+thing is if you if you're not unsure you
+can always let us know what you've
+
+ align:start position:0%
+can always let us know what you've
+ 
+
+ align:start position:0%
+can always let us know what you've
+chosen or what you think you're gonna
+
+ align:start position:0%
+chosen or what you think you're gonna
+ 
+
+ align:start position:0%
+chosen or what you think you're gonna
+choose and the chat with us and we'll
+
+ align:start position:0%
+choose and the chat with us and we'll
+ 
+
+ align:start position:0%
+choose and the chat with us and we'll
+say yeah it looks like looks like a good
+
+ align:start position:0%
+say yeah it looks like looks like a good
+ 
+
+ align:start position:0%
+say yeah it looks like looks like a good
+idea okay so let's move forward now all
+
+ align:start position:0%
+idea okay so let's move forward now all
+ 
+
+ align:start position:0%
+idea okay so let's move forward now all
+right so what I want to do first of all
+
+ align:start position:0%
+right so what I want to do first of all
+ 
+
+ align:start position:0%
+right so what I want to do first of all
+is just remind you it kind of flew by a
+
+ align:start position:0%
+is just remind you it kind of flew by a
+ 
+
+ align:start position:0%
+is just remind you it kind of flew by a
+little bit that DNA replication is
+
+ align:start position:0%
+little bit that DNA replication is
+ 
+
+ align:start position:0%
+little bit that DNA replication is
+bi-directional okay so what that means
+
+ align:start position:0%
+bi-directional okay so what that means
+ 
+
+ align:start position:0%
+bi-directional okay so what that means
+is wherever you have an origin of
+
+ align:start position:0%
+is wherever you have an origin of
+ 
+
+ align:start position:0%
+is wherever you have an origin of
+replication you can replicate in two
+
+ align:start position:0%
+replication you can replicate in two
+ 
+
+ align:start position:0%
+replication you can replicate in two
+directions and I was sort of falling
+
+ align:start position:0%
+directions and I was sort of falling
+ 
+
+ align:start position:0%
+directions and I was sort of falling
+asleep thinking about this I sure wonder
+
+ align:start position:0%
+asleep thinking about this I sure wonder
+ 
+
+ align:start position:0%
+asleep thinking about this I sure wonder
+what happens at the other side of the
+
+ align:start position:0%
+what happens at the other side of the
+ 
+
+ align:start position:0%
+what happens at the other side of the
+circular plasmid when the machineries
+
+ align:start position:0%
+circular plasmid when the machineries
+ 
+
+ align:start position:0%
+circular plasmid when the machineries
+kind of collide and you spit out a brand
+
+ align:start position:0%
+kind of collide and you spit out a brand
+ 
+
+ align:start position:0%
+kind of collide and you spit out a brand
+new copy of a circular chunk of DNA but
+
+ align:start position:0%
+new copy of a circular chunk of DNA but
+ 
+
+ align:start position:0%
+new copy of a circular chunk of DNA but
+don't think about that too much would
+
+ align:start position:0%
+don't think about that too much would
+ 
+
+ align:start position:0%
+don't think about that too much would
+probably keep you awake too much so this
+
+ align:start position:0%
+probably keep you awake too much so this
+ 
+
+ align:start position:0%
+probably keep you awake too much so this
+is circular DNA so what organisms have
+
+ align:start position:0%
+is circular DNA so what organisms have
+ 
+
+ align:start position:0%
+is circular DNA so what organisms have
+circular DNA prokaryotes that remember
+
+ align:start position:0%
+circular DNA prokaryotes that remember
+ 
+
+ align:start position:0%
+circular DNA prokaryotes that remember
+the eukaryotic DNA is linear and
+
+ align:start position:0%
+the eukaryotic DNA is linear and
+ 
+
+ align:start position:0%
+the eukaryotic DNA is linear and
+actually we're going to talk about a
+
+ align:start position:0%
+actually we're going to talk about a
+ 
+
+ align:start position:0%
+actually we're going to talk about a
+conundrum with the eukaryotic DNA
+
+ align:start position:0%
+conundrum with the eukaryotic DNA
+ 
+
+ align:start position:0%
+conundrum with the eukaryotic DNA
+because of the ends of the DNA the ends
+
+ align:start position:0%
+because of the ends of the DNA the ends
+ 
+
+ align:start position:0%
+because of the ends of the DNA the ends
+of the chromosomes and they're copying
+
+ align:start position:0%
+of the chromosomes and they're copying
+ 
+
+ align:start position:0%
+of the chromosomes and they're copying
+when we talk about telomerase but this
+
+ align:start position:0%
+when we talk about telomerase but this
+ 
+
+ align:start position:0%
+when we talk about telomerase but this
+is typical of a bacterial circular DNA
+
+ align:start position:0%
+is typical of a bacterial circular DNA
+ 
+
+ align:start position:0%
+is typical of a bacterial circular DNA
+it's usually super coiled and becomes
+
+ align:start position:0%
+it's usually super coiled and becomes
+ 
+
+ align:start position:0%
+it's usually super coiled and becomes
+uncoiled in order to be replicated so
+
+ align:start position:0%
+uncoiled in order to be replicated so
+ 
+
+ align:start position:0%
+uncoiled in order to be replicated so
+obviously going by directionally gives
+
+ align:start position:0%
+obviously going by directionally gives
+ 
+
+ align:start position:0%
+obviously going by directionally gives
+you twice the speed because you're
+
+ align:start position:0%
+you twice the speed because you're
+ 
+
+ align:start position:0%
+you twice the speed because you're
+roaring around the same time the
+
+ align:start position:0%
+roaring around the same time the
+ 
+
+ align:start position:0%
+roaring around the same time the
+helicase opens up the DNA DNA polymerase
+
+ align:start position:0%
+helicase opens up the DNA DNA polymerase
+ 
+
+ align:start position:0%
+helicase opens up the DNA DNA polymerase
+does its job the pink strand here would
+
+ align:start position:0%
+does its job the pink strand here would
+ 
+
+ align:start position:0%
+does its job the pink strand here would
+be the leading strand and there's gob
+
+ align:start position:0%
+be the leading strand and there's gob
+ 
+
+ align:start position:0%
+be the leading strand and there's gob
+viously going to be one on both strands
+
+ align:start position:0%
+viously going to be one on both strands
+ 
+
+ align:start position:0%
+viously going to be one on both strands
+of DNA which will replicate very well
+
+ align:start position:0%
+of DNA which will replicate very well
+ 
+
+ align:start position:0%
+of DNA which will replicate very well
+but don't
+
+ align:start position:0%
+but don't
+ 
+
+ align:start position:0%
+but don't
+forget you're going to have to deal with
+
+ align:start position:0%
+forget you're going to have to deal with
+ 
+
+ align:start position:0%
+forget you're going to have to deal with
+the lagging strands in both cases so in
+
+ align:start position:0%
+the lagging strands in both cases so in
+ 
+
+ align:start position:0%
+the lagging strands in both cases so in
+both cases what you would do ooop
+
+ align:start position:0%
+both cases what you would do ooop
+ 
+
+ align:start position:0%
+both cases what you would do ooop
+station
+
+ align:start position:0%
+station
+ 
+
+ align:start position:0%
+station
+you stick down a primer in order to be
+
+ align:start position:0%
+you stick down a primer in order to be
+ 
+
+ align:start position:0%
+you stick down a primer in order to be
+able to build those lagging strands
+
+ align:start position:0%
+able to build those lagging strands
+ 
+
+ align:start position:0%
+able to build those lagging strands
+otherwise DNA polymerase can't get a
+
+ align:start position:0%
+otherwise DNA polymerase can't get a
+ 
+
+ align:start position:0%
+otherwise DNA polymerase can't get a
+grip on the double-stranded DNA in order
+
+ align:start position:0%
+grip on the double-stranded DNA in order
+ 
+
+ align:start position:0%
+grip on the double-stranded DNA in order
+to carry out the synthesis so in those
+
+ align:start position:0%
+to carry out the synthesis so in those
+ 
+
+ align:start position:0%
+to carry out the synthesis so in those
+cases there would be a primer to set up
+
+ align:start position:0%
+cases there would be a primer to set up
+ 
+
+ align:start position:0%
+cases there would be a primer to set up
+the lagging strand and then DNA
+
+ align:start position:0%
+the lagging strand and then DNA
+ 
+
+ align:start position:0%
+the lagging strand and then DNA
+synthesis can occur so let's put that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once there's a primer here DNA synthesis
+
+ align:start position:0%
+once there's a primer here DNA synthesis
+ 
+
+ align:start position:0%
+once there's a primer here DNA synthesis
+can occur and then what happens with
+
+ align:start position:0%
+can occur and then what happens with
+ 
+
+ align:start position:0%
+can occur and then what happens with
+respect to the pieces that we're dealing
+
+ align:start position:0%
+respect to the pieces that we're dealing
+ 
+
+ align:start position:0%
+respect to the pieces that we're dealing
+with what do you what happens with the
+
+ align:start position:0%
+with what do you what happens with the
+ 
+
+ align:start position:0%
+with what do you what happens with the
+primer what do we have to do to get to a
+
+ align:start position:0%
+primer what do we have to do to get to a
+ 
+
+ align:start position:0%
+primer what do we have to do to get to a
+nice complete intact strand of DNA which
+
+ align:start position:0%
+nice complete intact strand of DNA which
+ 
+
+ align:start position:0%
+nice complete intact strand of DNA which
+enzymes are involved yeah here there
+
+ align:start position:0%
+enzymes are involved yeah here there
+ 
+
+ align:start position:0%
+enzymes are involved yeah here there
+would be like A's activity we need that
+
+ align:start position:0%
+would be like A's activity we need that
+ 
+
+ align:start position:0%
+would be like A's activity we need that
+what about at the other end what do we
+
+ align:start position:0%
+what about at the other end what do we
+ 
+
+ align:start position:0%
+what about at the other end what do we
+do with the primer and then how can we
+
+ align:start position:0%
+do with the primer and then how can we
+ 
+
+ align:start position:0%
+do with the primer and then how can we
+move forward someone else what happens
+
+ align:start position:0%
+move forward someone else what happens
+ 
+
+ align:start position:0%
+move forward someone else what happens
+with the primer if it's it's oftentimes
+
+ align:start position:0%
+with the primer if it's it's oftentimes
+ 
+
+ align:start position:0%
+with the primer if it's it's oftentimes
+an RNA primer you'll see in a moment
+
+ align:start position:0%
+an RNA primer you'll see in a moment
+ 
+
+ align:start position:0%
+an RNA primer you'll see in a moment
+that RNA doesn't need a prime a so it's
+
+ align:start position:0%
+that RNA doesn't need a prime a so it's
+ 
+
+ align:start position:0%
+that RNA doesn't need a prime a so it's
+very easy for RNA polymerase to stitch
+
+ align:start position:0%
+very easy for RNA polymerase to stitch
+ 
+
+ align:start position:0%
+very easy for RNA polymerase to stitch
+in little pieces what do we have to do
+
+ align:start position:0%
+in little pieces what do we have to do
+ 
+
+ align:start position:0%
+in little pieces what do we have to do
+though to get an intact strand of DNA
+
+ align:start position:0%
+though to get an intact strand of DNA
+ 
+
+ align:start position:0%
+though to get an intact strand of DNA
+okay yep so you're gonna remove the RNA
+
+ align:start position:0%
+okay yep so you're gonna remove the RNA
+ 
+
+ align:start position:0%
+okay yep so you're gonna remove the RNA
+then the polymerase later on when we
+
+ align:start position:0%
+then the polymerase later on when we
+ 
+
+ align:start position:0%
+then the polymerase later on when we
+keep going can sort of build this piece
+
+ align:start position:0%
+keep going can sort of build this piece
+ 
+
+ align:start position:0%
+keep going can sort of build this piece
+and then we'll have to ligate that as
+
+ align:start position:0%
+and then we'll have to ligate that as
+ 
+
+ align:start position:0%
+and then we'll have to ligate that as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+so you want to remember all the
+
+ align:start position:0%
+so you want to remember all the
+ 
+
+ align:start position:0%
+so you want to remember all the
+functions of those enzymes that are
+
+ align:start position:0%
+functions of those enzymes that are
+ 
+
+ align:start position:0%
+functions of those enzymes that are
+involved in replication it's a little
+
+ align:start position:0%
+involved in replication it's a little
+ 
+
+ align:start position:0%
+involved in replication it's a little
+worrisome that people I know you don't
+
+ align:start position:0%
+worrisome that people I know you don't
+ 
+
+ align:start position:0%
+worrisome that people I know you don't
+want to talk or you think that's an
+
+ align:start position:0%
+want to talk or you think that's an
+ 
+
+ align:start position:0%
+want to talk or you think that's an
+obvious answer but it's really important
+
+ align:start position:0%
+obvious answer but it's really important
+ 
+
+ align:start position:0%
+obvious answer but it's really important
+that you have them at your fingertips
+
+ align:start position:0%
+that you have them at your fingertips
+ 
+
+ align:start position:0%
+that you have them at your fingertips
+some of these enzymes that are involved
+
+ align:start position:0%
+some of these enzymes that are involved
+ 
+
+ align:start position:0%
+some of these enzymes that are involved
+in this process because they should
+
+ align:start position:0%
+in this process because they should
+ 
+
+ align:start position:0%
+in this process because they should
+start to become second
+
+ align:start position:0%
+start to become second
+ 
+
+ align:start position:0%
+start to become second
+nature when you have to make a full DNA
+
+ align:start position:0%
+nature when you have to make a full DNA
+ 
+
+ align:start position:0%
+nature when you have to make a full DNA
+copy of an entire genome there's a lot
+
+ align:start position:0%
+copy of an entire genome there's a lot
+ 
+
+ align:start position:0%
+copy of an entire genome there's a lot
+of moving parts but if you start walking
+
+ align:start position:0%
+of moving parts but if you start walking
+ 
+
+ align:start position:0%
+of moving parts but if you start walking
+through the logic of them they make
+
+ align:start position:0%
+through the logic of them they make
+ 
+
+ align:start position:0%
+through the logic of them they make
+sense if I'm gonna unpeel DNA I need a
+
+ align:start position:0%
+sense if I'm gonna unpeel DNA I need a
+ 
+
+ align:start position:0%
+sense if I'm gonna unpeel DNA I need a
+helicase if I'm gonna keep it
+
+ align:start position:0%
+helicase if I'm gonna keep it
+ 
+
+ align:start position:0%
+helicase if I'm gonna keep it
+single-stranded I need single strand
+
+ align:start position:0%
+single-stranded I need single strand
+ 
+
+ align:start position:0%
+single-stranded I need single strand
+binding proteins if I'm gonna move
+
+ align:start position:0%
+binding proteins if I'm gonna move
+ 
+
+ align:start position:0%
+binding proteins if I'm gonna move
+forward sure I need the polymerase but
+
+ align:start position:0%
+forward sure I need the polymerase but
+ 
+
+ align:start position:0%
+forward sure I need the polymerase but
+what does the polymerase need it
+
+ align:start position:0%
+what does the polymerase need it
+ 
+
+ align:start position:0%
+what does the polymerase need it
+sometimes needs a needs a primer in
+
+ align:start position:0%
+sometimes needs a needs a primer in
+ 
+
+ align:start position:0%
+sometimes needs a needs a primer in
+order to have double strand because DNA
+
+ align:start position:0%
+order to have double strand because DNA
+ 
+
+ align:start position:0%
+order to have double strand because DNA
+polymerase only wants to lock on to a
+
+ align:start position:0%
+polymerase only wants to lock on to a
+ 
+
+ align:start position:0%
+polymerase only wants to lock on to a
+double strand to go start doing its job
+
+ align:start position:0%
+double strand to go start doing its job
+ 
+
+ align:start position:0%
+double strand to go start doing its job
+these complications with the lagging
+
+ align:start position:0%
+these complications with the lagging
+ 
+
+ align:start position:0%
+these complications with the lagging
+strands that are really annoying but
+
+ align:start position:0%
+strands that are really annoying but
+ 
+
+ align:start position:0%
+strands that are really annoying but
+it's pretty remarkable Nature has
+
+ align:start position:0%
+it's pretty remarkable Nature has
+ 
+
+ align:start position:0%
+it's pretty remarkable Nature has
+addressed this and is able remember to
+
+ align:start position:0%
+addressed this and is able remember to
+ 
+
+ align:start position:0%
+addressed this and is able remember to
+replicate DNA in bacteria at a speed of
+
+ align:start position:0%
+replicate DNA in bacteria at a speed of
+ 
+
+ align:start position:0%
+replicate DNA in bacteria at a speed of
+100 base pairs per second so that's
+
+ align:start position:0%
+100 base pairs per second so that's
+ 
+
+ align:start position:0%
+100 base pairs per second so that's
+what's going on this entire processor
+
+ align:start position:0%
+what's going on this entire processor
+ 
+
+ align:start position:0%
+what's going on this entire processor
+excuse me a thousand base pairs a second
+
+ align:start position:0%
+excuse me a thousand base pairs a second
+ 
+
+ align:start position:0%
+excuse me a thousand base pairs a second
+I just want you to remember this process
+
+ align:start position:0%
+I just want you to remember this process
+ 
+
+ align:start position:0%
+I just want you to remember this process
+is slower in eukaryotes it's about 30 to
+
+ align:start position:0%
+is slower in eukaryotes it's about 30 to
+ 
+
+ align:start position:0%
+is slower in eukaryotes it's about 30 to
+50 base pairs per second obviously when
+
+ align:start position:0%
+50 base pairs per second obviously when
+ 
+
+ align:start position:0%
+50 base pairs per second obviously when
+you're speeding you make more mistakes
+
+ align:start position:0%
+you're speeding you make more mistakes
+ 
+
+ align:start position:0%
+you're speeding you make more mistakes
+so there are more mistakes in bacterial
+
+ align:start position:0%
+so there are more mistakes in bacterial
+ 
+
+ align:start position:0%
+so there are more mistakes in bacterial
+genome replication what what is why does
+
+ align:start position:0%
+genome replication what what is why does
+ 
+
+ align:start position:0%
+genome replication what what is why does
+it not matter so much if there's a
+
+ align:start position:0%
+it not matter so much if there's a
+ 
+
+ align:start position:0%
+it not matter so much if there's a
+mistake in a bacterial genome right what
+
+ align:start position:0%
+mistake in a bacterial genome right what
+ 
+
+ align:start position:0%
+mistake in a bacterial genome right what
+do you know about bacteria and their
+
+ align:start position:0%
+do you know about bacteria and their
+ 
+
+ align:start position:0%
+do you know about bacteria and their
+lifestyles do they stick around a long
+
+ align:start position:0%
+lifestyles do they stick around a long
+ 
+
+ align:start position:0%
+lifestyles do they stick around a long
+time no so they divide quickly they live
+
+ align:start position:0%
+time no so they divide quickly they live
+ 
+
+ align:start position:0%
+time no so they divide quickly they live
+and die quickly so you're not having to
+
+ align:start position:0%
+and die quickly so you're not having to
+ 
+
+ align:start position:0%
+and die quickly so you're not having to
+keep an intact genome without mistakes
+
+ align:start position:0%
+keep an intact genome without mistakes
+ 
+
+ align:start position:0%
+keep an intact genome without mistakes
+in it for a long time because you're
+
+ align:start position:0%
+in it for a long time because you're
+ 
+
+ align:start position:0%
+in it for a long time because you're
+just turning over back to if there's a
+
+ align:start position:0%
+just turning over back to if there's a
+ 
+
+ align:start position:0%
+just turning over back to if there's a
+mistake it probably dies out or heaven
+
+ align:start position:0%
+mistake it probably dies out or heaven
+ 
+
+ align:start position:0%
+mistake it probably dies out or heaven
+forbid there's resistance to drugs
+
+ align:start position:0%
+forbid there's resistance to drugs
+ 
+
+ align:start position:0%
+forbid there's resistance to drugs
+developed and we'll talk about those
+
+ align:start position:0%
+developed and we'll talk about those
+ 
+
+ align:start position:0%
+developed and we'll talk about those
+later because those occur due to
+
+ align:start position:0%
+later because those occur due to
+ 
+
+ align:start position:0%
+later because those occur due to
+mistakes in in bacterial replication but
+
+ align:start position:0%
+mistakes in in bacterial replication but
+ 
+
+ align:start position:0%
+mistakes in in bacterial replication but
+in a eukaryotic genome we have to
+
+ align:start position:0%
+in a eukaryotic genome we have to
+ 
+
+ align:start position:0%
+in a eukaryotic genome we have to
+preserve the integrity of the genome so
+
+ align:start position:0%
+preserve the integrity of the genome so
+ 
+
+ align:start position:0%
+preserve the integrity of the genome so
+I'm going to talk about two things that
+
+ align:start position:0%
+I'm going to talk about two things that
+ 
+
+ align:start position:0%
+I'm going to talk about two things that
+are related to the accuracy of
+
+ align:start position:0%
+are related to the accuracy of
+ 
+
+ align:start position:0%
+are related to the accuracy of
+replication now because that's a really
+
+ align:start position:0%
+replication now because that's a really
+ 
+
+ align:start position:0%
+replication now because that's a really
+important component
+
+ align:start position:0%
+important component
+ 
+
+ align:start position:0%
+important component
+right so the first thing is to think
+
+ align:start position:0%
+right so the first thing is to think
+ 
+
+ align:start position:0%
+right so the first thing is to think
+about what's the basal rate of making
+
+ align:start position:0%
+about what's the basal rate of making
+ 
+
+ align:start position:0%
+about what's the basal rate of making
+mistakes of DNA polymerase so for that
+
+ align:start position:0%
+mistakes of DNA polymerase so for that
+ 
+
+ align:start position:0%
+mistakes of DNA polymerase so for that
+purpose I'm just gonna put down a piece
+
+ align:start position:0%
+purpose I'm just gonna put down a piece
+ 
+
+ align:start position:0%
+purpose I'm just gonna put down a piece
+of DNA with its partner that's being
+
+ align:start position:0%
+of DNA with its partner that's being
+ 
+
+ align:start position:0%
+of DNA with its partner that's being
+synthesized 5 prime to 3 Prime and I'll
+
+ align:start position:0%
+synthesized 5 prime to 3 Prime and I'll
+ 
+
+ align:start position:0%
+synthesized 5 prime to 3 Prime and I'll
+put in some bases so a so that would
+
+ align:start position:0%
+put in some bases so a so that would
+ 
+
+ align:start position:0%
+put in some bases so a so that would
+have had a T put in opposite G that
+
+ align:start position:0%
+have had a T put in opposite G that
+ 
+
+ align:start position:0%
+have had a T put in opposite G that
+would have had a c p-- so these have two
+
+ align:start position:0%
+would have had a c p-- so these have two
+ 
+
+ align:start position:0%
+would have had a c p-- so these have two
+hydrogen bonds these have 3 hydrogen
+
+ align:start position:0%
+hydrogen bonds these have 3 hydrogen
+ 
+
+ align:start position:0%
+hydrogen bonds these have 3 hydrogen
+bonds and let's say we now have a C here
+
+ align:start position:0%
+bonds and let's say we now have a C here
+ 
+
+ align:start position:0%
+bonds and let's say we now have a C here
+so we want to put in a G at the position
+
+ align:start position:0%
+so we want to put in a G at the position
+ 
+
+ align:start position:0%
+so we want to put in a G at the position
+opposite DNA polymerase wants to add the
+
+ align:start position:0%
+opposite DNA polymerase wants to add the
+ 
+
+ align:start position:0%
+opposite DNA polymerase wants to add the
+next the next base pair it should be a G
+
+ align:start position:0%
+next the next base pair it should be a G
+ 
+
+ align:start position:0%
+next the next base pair it should be a G
+because it's going in opposite a C it's
+
+ align:start position:0%
+because it's going in opposite a C it's
+ 
+
+ align:start position:0%
+because it's going in opposite a C it's
+being grown in the right direction 5
+
+ align:start position:0%
+being grown in the right direction 5
+ 
+
+ align:start position:0%
+being grown in the right direction 5
+prime to 3 prime so the basal error rate
+
+ align:start position:0%
+prime to 3 prime so the basal error rate
+ 
+
+ align:start position:0%
+prime to 3 prime so the basal error rate
+is about a thousand to one so a thousand
+
+ align:start position:0%
+is about a thousand to one so a thousand
+ 
+
+ align:start position:0%
+is about a thousand to one so a thousand
+999 times out of a thousand the right
+
+ align:start position:0%
+999 times out of a thousand the right
+ 
+
+ align:start position:0%
+999 times out of a thousand the right
+base gets put in one time out of a
+
+ align:start position:0%
+base gets put in one time out of a
+ 
+
+ align:start position:0%
+base gets put in one time out of a
+thousand you might put in the wrong rate
+
+ align:start position:0%
+thousand you might put in the wrong rate
+ 
+
+ align:start position:0%
+thousand you might put in the wrong rate
+so the error rate is about one in ten to
+
+ align:start position:0%
+so the error rate is about one in ten to
+ 
+
+ align:start position:0%
+so the error rate is about one in ten to
+three that's really all that's all
+
+ align:start position:0%
+three that's really all that's all
+ 
+
+ align:start position:0%
+three that's really all that's all
+that's at play here is energetics just
+
+ align:start position:0%
+that's at play here is energetics just
+ 
+
+ align:start position:0%
+that's at play here is energetics just
+how favorable putting in the right base
+
+ align:start position:0%
+how favorable putting in the right base
+ 
+
+ align:start position:0%
+how favorable putting in the right base
+is but there's a slight chance that the
+
+ align:start position:0%
+is but there's a slight chance that the
+ 
+
+ align:start position:0%
+is but there's a slight chance that the
+wrong base will just go in because yeah
+
+ align:start position:0%
+wrong base will just go in because yeah
+ 
+
+ align:start position:0%
+wrong base will just go in because yeah
+that's the the energetics are
+
+ align:start position:0%
+that's the the energetics are
+ 
+
+ align:start position:0%
+that's the the energetics are
+sufficiently different but you're gonna
+
+ align:start position:0%
+sufficiently different but you're gonna
+ 
+
+ align:start position:0%
+sufficiently different but you're gonna
+make mistakes just because of thermo the
+
+ align:start position:0%
+make mistakes just because of thermo the
+ 
+
+ align:start position:0%
+make mistakes just because of thermo the
+thermodynamic balance if you're putting
+
+ align:start position:0%
+thermodynamic balance if you're putting
+ 
+
+ align:start position:0%
+thermodynamic balance if you're putting
+in 999 you're gonna get it wrong some of
+
+ align:start position:0%
+in 999 you're gonna get it wrong some of
+ 
+
+ align:start position:0%
+in 999 you're gonna get it wrong some of
+the time just statistically because
+
+ align:start position:0%
+the time just statistically because
+ 
+
+ align:start position:0%
+the time just statistically because
+they're the difference in energy between
+
+ align:start position:0%
+they're the difference in energy between
+ 
+
+ align:start position:0%
+they're the difference in energy between
+putting in the right base or putting in
+
+ align:start position:0%
+putting in the right base or putting in
+ 
+
+ align:start position:0%
+putting in the right base or putting in
+a wrong base so that error rate is too
+
+ align:start position:0%
+a wrong base so that error rate is too
+ 
+
+ align:start position:0%
+a wrong base so that error rate is too
+high if we replicated our genome 32
+
+ align:start position:0%
+high if we replicated our genome 32
+ 
+
+ align:start position:0%
+high if we replicated our genome 32
+billion base pairs we had an one in ten
+
+ align:start position:0%
+billion base pairs we had an one in ten
+ 
+
+ align:start position:0%
+billion base pairs we had an one in ten
+to the three error rate we have a lot of
+
+ align:start position:0%
+to the three error rate we have a lot of
+ 
+
+ align:start position:0%
+to the three error rate we have a lot of
+mistakes in the genome right
+
+ align:start position:0%
+mistakes in the genome right
+ 
+
+ align:start position:0%
+mistakes in the genome right
+and we cannot tolerate that because all
+
+ align:start position:0%
+and we cannot tolerate that because all
+ 
+
+ align:start position:0%
+and we cannot tolerate that because all
+those mistakes in our genome will then
+
+ align:start position:0%
+those mistakes in our genome will then
+ 
+
+ align:start position:0%
+those mistakes in our genome will then
+propagate to mistakes in our proteome if
+
+ align:start position:0%
+propagate to mistakes in our proteome if
+ 
+
+ align:start position:0%
+propagate to mistakes in our proteome if
+we're in the right segments of the
+
+ align:start position:0%
+we're in the right segments of the
+ 
+
+ align:start position:0%
+we're in the right segments of the
+genome so this is pretty unacceptable
+
+ align:start position:0%
+genome so this is pretty unacceptable
+ 
+
+ align:start position:0%
+genome so this is pretty unacceptable
+with respect to an error rate so one way
+
+ align:start position:0%
+with respect to an error rate so one way
+ 
+
+ align:start position:0%
+with respect to an error rate so one way
+that nature deals with this is the DNA
+
+ align:start position:0%
+that nature deals with this is the DNA
+ 
+
+ align:start position:0%
+that nature deals with this is the DNA
+polymerase actually does some
+
+ align:start position:0%
+polymerase actually does some
+ 
+
+ align:start position:0%
+polymerase actually does some
+proofreading all right so it has a
+
+ align:start position:0%
+proofreading all right so it has a
+ 
+
+ align:start position:0%
+proofreading all right so it has a
+proofreading function so what do you do
+
+ align:start position:0%
+proofreading function so what do you do
+ 
+
+ align:start position:0%
+proofreading function so what do you do
+when you're proofreading you take a
+
+ align:start position:0%
+when you're proofreading you take a
+ 
+
+ align:start position:0%
+when you're proofreading you take a
+quick look at what you've just written
+
+ align:start position:0%
+quick look at what you've just written
+ 
+
+ align:start position:0%
+quick look at what you've just written
+and say oh yeah that looks good that
+
+ align:start position:0%
+and say oh yeah that looks good that
+ 
+
+ align:start position:0%
+and say oh yeah that looks good that
+looks good
+
+ align:start position:0%
+looks good
+ 
+
+ align:start position:0%
+looks good
+so what DNA polymerase is it more or
+
+ align:start position:0%
+so what DNA polymerase is it more or
+ 
+
+ align:start position:0%
+so what DNA polymerase is it more or
+less reaches back to the base it puts in
+
+ align:start position:0%
+less reaches back to the base it puts in
+ 
+
+ align:start position:0%
+less reaches back to the base it puts in
+and check the checks that it's okay it
+
+ align:start position:0%
+and check the checks that it's okay it
+ 
+
+ align:start position:0%
+and check the checks that it's okay it
+can only proofread one base back it
+
+ align:start position:0%
+can only proofread one base back it
+ 
+
+ align:start position:0%
+can only proofread one base back it
+can't proofread from work that's been
+
+ align:start position:0%
+can't proofread from work that's been
+ 
+
+ align:start position:0%
+can't proofread from work that's been
+done a long time ago it can just
+
+ align:start position:0%
+done a long time ago it can just
+ 
+
+ align:start position:0%
+done a long time ago it can just
+proofread very recent work and if it
+
+ align:start position:0%
+proofread very recent work and if it
+ 
+
+ align:start position:0%
+proofread very recent work and if it
+looks like it's the wrong base DNA
+
+ align:start position:0%
+looks like it's the wrong base DNA
+ 
+
+ align:start position:0%
+looks like it's the wrong base DNA
+polymerase has an opposite function it
+
+ align:start position:0%
+polymerase has an opposite function it
+ 
+
+ align:start position:0%
+polymerase has an opposite function it
+has what's known as a three prime
+
+ align:start position:0%
+has what's known as a three prime
+ 
+
+ align:start position:0%
+has what's known as a three prime
+exonuclease activity so I'll write that
+
+ align:start position:0%
+exonuclease activity so I'll write that
+ 
+
+ align:start position:0%
+exonuclease activity so I'll write that
+down and then we'll talk about what that
+
+ align:start position:0%
+down and then we'll talk about what that
+ 
+
+ align:start position:0%
+down and then we'll talk about what that
+means three prime and so nucleates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say we put in instead of G we
+
+ align:start position:0%
+so let's say we put in instead of G we
+ 
+
+ align:start position:0%
+so let's say we put in instead of G we
+put in a T that's bad news so what they
+
+ align:start position:0%
+put in a T that's bad news so what they
+ 
+
+ align:start position:0%
+put in a T that's bad news so what they
+can do is it can reach back and cut off
+
+ align:start position:0%
+can do is it can reach back and cut off
+ 
+
+ align:start position:0%
+can do is it can reach back and cut off
+from the three prime end a single
+
+ align:start position:0%
+from the three prime end a single
+ 
+
+ align:start position:0%
+from the three prime end a single
+nucleotide just the one that just got
+
+ align:start position:0%
+nucleotide just the one that just got
+ 
+
+ align:start position:0%
+nucleotide just the one that just got
+put in alright and then allow the
+
+ align:start position:0%
+put in alright and then allow the
+ 
+
+ align:start position:0%
+put in alright and then allow the
+process to reoccur to get the right base
+
+ align:start position:0%
+process to reoccur to get the right base
+ 
+
+ align:start position:0%
+process to reoccur to get the right base
+pairing so a lot of enzymes will
+
+ align:start position:0%
+pairing so a lot of enzymes will
+ 
+
+ align:start position:0%
+pairing so a lot of enzymes will
+catalyze both forwards and backwards
+
+ align:start position:0%
+catalyze both forwards and backwards
+ 
+
+ align:start position:0%
+catalyze both forwards and backwards
+reactions DNA polymerase the energetics
+
+ align:start position:0%
+reactions DNA polymerase the energetics
+ 
+
+ align:start position:0%
+reactions DNA polymerase the energetics
+of such are that it will is able to
+
+ align:start position:0%
+of such are that it will is able to
+ 
+
+ align:start position:0%
+of such are that it will is able to
+catalyze both the addition of a
+
+ align:start position:0%
+catalyze both the addition of a
+ 
+
+ align:start position:0%
+catalyze both the addition of a
+nucleotide and the removal of a single
+
+ align:start position:0%
+nucleotide and the removal of a single
+ 
+
+ align:start position:0%
+nucleotide and the removal of a single
+nucleotide only if it's at the three
+
+ align:start position:0%
+nucleotide only if it's at the three
+ 
+
+ align:start position:0%
+nucleotide only if it's at the three
+prime end only if it's at an open end
+
+ align:start position:0%
+prime end only if it's at an open end
+ 
+
+ align:start position:0%
+prime end only if it's at an open end
+it's just been put in so that remember
+
+ align:start position:0%
+it's just been put in so that remember
+ 
+
+ align:start position:0%
+it's just been put in so that remember
+the DNA polymerase is still here because
+
+ align:start position:0%
+the DNA polymerase is still here because
+ 
+
+ align:start position:0%
+the DNA polymerase is still here because
+its plan is to move forward and keep on
+
+ align:start position:0%
+its plan is to move forward and keep on
+ 
+
+ align:start position:0%
+its plan is to move forward and keep on
+putting in nucleotides but he actually
+
+ align:start position:0%
+putting in nucleotides but he actually
+ 
+
+ align:start position:0%
+putting in nucleotides but he actually
+checks back you could picture DNA
+
+ align:start position:0%
+checks back you could picture DNA
+ 
+
+ align:start position:0%
+checks back you could picture DNA
+polishes sort of quickly looking over
+
+ align:start position:0%
+polishes sort of quickly looking over
+ 
+
+ align:start position:0%
+polishes sort of quickly looking over
+its shoulder at the work it's just done
+
+ align:start position:0%
+its shoulder at the work it's just done
+ 
+
+ align:start position:0%
+its shoulder at the work it's just done
+and realizing that's the wrong one so
+
+ align:start position:0%
+and realizing that's the wrong one so
+ 
+
+ align:start position:0%
+and realizing that's the wrong one so
+what this does is brings the Riera rates
+
+ align:start position:0%
+what this does is brings the Riera rates
+ 
+
+ align:start position:0%
+what this does is brings the Riera rates
+down considerably goes in one in ten for
+
+ align:start position:0%
+down considerably goes in one in ten for
+ 
+
+ align:start position:0%
+down considerably goes in one in ten for
+the five so that's way better one in a
+
+ align:start position:0%
+the five so that's way better one in a
+ 
+
+ align:start position:0%
+the five so that's way better one in a
+hundred thousand is much better and
+
+ align:start position:0%
+hundred thousand is much better and
+ 
+
+ align:start position:0%
+hundred thousand is much better and
+that's pretty acceptable so it means
+
+ align:start position:0%
+that's pretty acceptable so it means
+ 
+
+ align:start position:0%
+that's pretty acceptable so it means
+you're really making very minimal
+
+ align:start position:0%
+you're really making very minimal
+ 
+
+ align:start position:0%
+you're really making very minimal
+mistakes in the replication okay so this
+
+ align:start position:0%
+mistakes in the replication okay so this
+ 
+
+ align:start position:0%
+mistakes in the replication okay so this
+apart the proofreading brings the error
+
+ align:start position:0%
+apart the proofreading brings the error
+ 
+
+ align:start position:0%
+apart the proofreading brings the error
+rate from one in 10 to the 3 10 to the 3
+
+ align:start position:0%
+rate from one in 10 to the 3 10 to the 3
+ 
+
+ align:start position:0%
+rate from one in 10 to the 3 10 to the 3
+to 1 in 10 to the 5 but it can only work
+
+ align:start position:0%
+to 1 in 10 to the 5 but it can only work
+ 
+
+ align:start position:0%
+to 1 in 10 to the 5 but it can only work
+during trans doing DNA polymerase
+
+ align:start position:0%
+during trans doing DNA polymerase
+ 
+
+ align:start position:0%
+during trans doing DNA polymerase
+activity and it can only work on the
+
+ align:start position:0%
+activity and it can only work on the
+ 
+
+ align:start position:0%
+activity and it can only work on the
+most recent nucleotide that has been put
+
+ align:start position:0%
+most recent nucleotide that has been put
+ 
+
+ align:start position:0%
+most recent nucleotide that has been put
+in so this is basically a summary of yes
+
+ align:start position:0%
+in so this is basically a summary of yes
+ 
+
+ align:start position:0%
+in so this is basically a summary of yes
+question they are and they are similar
+
+ align:start position:0%
+question they are and they are similar
+ 
+
+ align:start position:0%
+question they are and they are similar
+they're similar actually there's
+
+ align:start position:0%
+they're similar actually there's
+ 
+
+ align:start position:0%
+they're similar actually there's
+slightly less error rates in eukaryotes
+
+ align:start position:0%
+slightly less error rates in eukaryotes
+ 
+
+ align:start position:0%
+slightly less error rates in eukaryotes
+because the speed is slower so the
+
+ align:start position:0%
+because the speed is slower so the
+ 
+
+ align:start position:0%
+because the speed is slower so the
+opportunity to fix things is going to be
+
+ align:start position:0%
+opportunity to fix things is going to be
+ 
+
+ align:start position:0%
+opportunity to fix things is going to be
+a little bit better so in the end you
+
+ align:start position:0%
+a little bit better so in the end you
+ 
+
+ align:start position:0%
+a little bit better so in the end you
+your goal really is to bring your error
+
+ align:start position:0%
+your goal really is to bring your error
+ 
+
+ align:start position:0%
+your goal really is to bring your error
+rate between 10 to the 5 and 10 to the 6
+
+ align:start position:0%
+rate between 10 to the 5 and 10 to the 6
+ 
+
+ align:start position:0%
+rate between 10 to the 5 and 10 to the 6
+but for bacteria because this speed is
+
+ align:start position:0%
+but for bacteria because this speed is
+ 
+
+ align:start position:0%
+but for bacteria because this speed is
+so much larger this is sort of the down
+
+ align:start position:0%
+so much larger this is sort of the down
+ 
+
+ align:start position:0%
+so much larger this is sort of the down
+with the limit of it but in Eukarya it
+
+ align:start position:0%
+with the limit of it but in Eukarya it
+ 
+
+ align:start position:0%
+with the limit of it but in Eukarya it
+can be a little bit better because the
+
+ align:start position:0%
+can be a little bit better because the
+ 
+
+ align:start position:0%
+can be a little bit better because the
+speed is slower so you could imagine if
+
+ align:start position:0%
+speed is slower so you could imagine if
+ 
+
+ align:start position:0%
+speed is slower so you could imagine if
+you're quickly proofreading you're doing
+
+ align:start position:0%
+you're quickly proofreading you're doing
+ 
+
+ align:start position:0%
+you're quickly proofreading you're doing
+a less good job than if you're slowly
+
+ align:start position:0%
+a less good job than if you're slowly
+ 
+
+ align:start position:0%
+a less good job than if you're slowly
+proofreading but the enzymes that I'll
+
+ align:start position:0%
+proofreading but the enzymes that I'll
+ 
+
+ align:start position:0%
+proofreading but the enzymes that I'll
+talk to you about in a second in Eukarya
+
+ align:start position:0%
+talk to you about in a second in Eukarya
+ 
+
+ align:start position:0%
+talk to you about in a second in Eukarya
+are to fix entire work that's already
+
+ align:start position:0%
+are to fix entire work that's already
+ 
+
+ align:start position:0%
+are to fix entire work that's already
+been done we'll see that in a moment and
+
+ align:start position:0%
+been done we'll see that in a moment and
+ 
+
+ align:start position:0%
+been done we'll see that in a moment and
+that's what really cleans up these
+
+ align:start position:0%
+that's what really cleans up these
+ 
+
+ align:start position:0%
+that's what really cleans up these
+enzymes are called the guardians of the
+
+ align:start position:0%
+enzymes are called the guardians of the
+ 
+
+ align:start position:0%
+enzymes are called the guardians of the
+genome so it's and they're much more
+
+ align:start position:0%
+genome so it's and they're much more
+ 
+
+ align:start position:0%
+genome so it's and they're much more
+sophisticated in Eukarya ok so it's very
+
+ align:start position:0%
+sophisticated in Eukarya ok so it's very
+ 
+
+ align:start position:0%
+sophisticated in Eukarya ok so it's very
+good point all right so here's the the
+
+ align:start position:0%
+good point all right so here's the the
+ 
+
+ align:start position:0%
+good point all right so here's the the
+general plot of the general scheme
+
+ align:start position:0%
+general plot of the general scheme
+ 
+
+ align:start position:0%
+general plot of the general scheme
+there is an extension there's a mistake
+
+ align:start position:0%
+there is an extension there's a mistake
+ 
+
+ align:start position:0%
+there is an extension there's a mistake
+so there's proofreading the mistake gets
+
+ align:start position:0%
+so there's proofreading the mistake gets
+ 
+
+ align:start position:0%
+so there's proofreading the mistake gets
+taken out and then you keep on extending
+
+ align:start position:0%
+taken out and then you keep on extending
+ 
+
+ align:start position:0%
+taken out and then you keep on extending
+again all right
+
+ align:start position:0%
+again all right
+ 
+
+ align:start position:0%
+again all right
+so this now becomes pretty pretty good
+
+ align:start position:0%
+so this now becomes pretty pretty good
+ 
+
+ align:start position:0%
+so this now becomes pretty pretty good
+but what we need to talk about now is
+
+ align:start position:0%
+but what we need to talk about now is
+ 
+
+ align:start position:0%
+but what we need to talk about now is
+what are the enzymes that go to work and
+
+ align:start position:0%
+what are the enzymes that go to work and
+ 
+
+ align:start position:0%
+what are the enzymes that go to work and
+I'm leaving what's on that border there
+
+ align:start position:0%
+I'm leaving what's on that border there
+ 
+
+ align:start position:0%
+I'm leaving what's on that border there
+because I'm going to come back to it to
+
+ align:start position:0%
+because I'm going to come back to it to
+ 
+
+ align:start position:0%
+because I'm going to come back to it to
+actually correct mistakes in DNA so
+
+ align:start position:0%
+actually correct mistakes in DNA so
+ 
+
+ align:start position:0%
+actually correct mistakes in DNA so
+let's talk about the guardians of the
+
+ align:start position:0%
+let's talk about the guardians of the
+ 
+
+ align:start position:0%
+let's talk about the guardians of the
+genome because remember that your DNA is
+
+ align:start position:0%
+genome because remember that your DNA is
+ 
+
+ align:start position:0%
+genome because remember that your DNA is
+your permanent record of what needs to
+
+ align:start position:0%
+your permanent record of what needs to
+ 
+
+ align:start position:0%
+your permanent record of what needs to
+be made all right so the types of
+
+ align:start position:0%
+be made all right so the types of
+ 
+
+ align:start position:0%
+be made all right so the types of
+mistakes that can be fixed with roof
+
+ align:start position:0%
+mistakes that can be fixed with roof
+ 
+
+ align:start position:0%
+mistakes that can be fixed with roof
+reading are only recent mistakes the
+
+ align:start position:0%
+reading are only recent mistakes the
+ 
+
+ align:start position:0%
+reading are only recent mistakes the
+types of enzymes are going to talk to
+
+ align:start position:0%
+types of enzymes are going to talk to
+ 
+
+ align:start position:0%
+types of enzymes are going to talk to
+you about a mistakes that are found
+
+ align:start position:0%
+you about a mistakes that are found
+ 
+
+ align:start position:0%
+you about a mistakes that are found
+globally within double-stranded DNA and
+
+ align:start position:0%
+globally within double-stranded DNA and
+ 
+
+ align:start position:0%
+globally within double-stranded DNA and
+these are mistakes wherever they may be
+
+ align:start position:0%
+these are mistakes wherever they may be
+ 
+
+ align:start position:0%
+these are mistakes wherever they may be
+mistakes that didn't get corrected by
+
+ align:start position:0%
+mistakes that didn't get corrected by
+ 
+
+ align:start position:0%
+mistakes that didn't get corrected by
+proofreading but more importantly
+
+ align:start position:0%
+proofreading but more importantly
+ 
+
+ align:start position:0%
+proofreading but more importantly
+they're mistakes that occur due to some
+
+ align:start position:0%
+they're mistakes that occur due to some
+ 
+
+ align:start position:0%
+they're mistakes that occur due to some
+kind of damage on the D on the DNA so
+
+ align:start position:0%
+kind of damage on the D on the DNA so
+ 
+
+ align:start position:0%
+kind of damage on the D on the DNA so
+what kind of things might impact the
+
+ align:start position:0%
+what kind of things might impact the
+ 
+
+ align:start position:0%
+what kind of things might impact the
+integrity of our DNA on a day to day
+
+ align:start position:0%
+integrity of our DNA on a day to day
+ 
+
+ align:start position:0%
+integrity of our DNA on a day to day
+basis yeah
+
+ align:start position:0%
+basis yeah
+ 
+
+ align:start position:0%
+basis yeah
+sunlights so terrible stuff UV light
+
+ align:start position:0%
+sunlights so terrible stuff UV light
+ 
+
+ align:start position:0%
+sunlights so terrible stuff UV light
+will actually cause some cross links
+
+ align:start position:0%
+will actually cause some cross links
+ 
+
+ align:start position:0%
+will actually cause some cross links
+that and I'll show you one of those that
+
+ align:start position:0%
+that and I'll show you one of those that
+ 
+
+ align:start position:0%
+that and I'll show you one of those that
+are very serious in DNA what else might
+
+ align:start position:0%
+are very serious in DNA what else might
+ 
+
+ align:start position:0%
+are very serious in DNA what else might
+hurt the Dean of the genome so sunlight
+
+ align:start position:0%
+hurt the Dean of the genome so sunlight
+ 
+
+ align:start position:0%
+hurt the Dean of the genome so sunlight
+people say don't go in the Sun like that
+
+ align:start position:0%
+people say don't go in the Sun like that
+ 
+
+ align:start position:0%
+people say don't go in the Sun like that
+right about that what else yeah the
+
+ align:start position:0%
+right about that what else yeah the
+ 
+
+ align:start position:0%
+right about that what else yeah the
+radiation is another form so that's some
+
+ align:start position:0%
+radiation is another form so that's some
+ 
+
+ align:start position:0%
+radiation is another form so that's some
+like radioactivity radiation is
+
+ align:start position:0%
+like radioactivity radiation is
+ 
+
+ align:start position:0%
+like radioactivity radiation is
+important right so if our ozone layer
+
+ align:start position:0%
+important right so if our ozone layer
+ 
+
+ align:start position:0%
+important right so if our ozone layer
+gets thin there's more risk there as
+
+ align:start position:0%
+gets thin there's more risk there as
+ 
+
+ align:start position:0%
+gets thin there's more risk there as
+well what about barbeque yeah yeah awful
+
+ align:start position:0%
+well what about barbeque yeah yeah awful
+ 
+
+ align:start position:0%
+well what about barbeque yeah yeah awful
+chemicals right so chemicals
+
+ align:start position:0%
+chemicals right so chemicals
+ 
+
+ align:start position:0%
+chemicals right so chemicals
+so these are things like poly poly
+
+ align:start position:0%
+so these are things like poly poly
+ 
+
+ align:start position:0%
+so these are things like poly poly
+aromatic structures that actually slip
+
+ align:start position:0%
+aromatic structures that actually slip
+ 
+
+ align:start position:0%
+aromatic structures that actually slip
+into your genome and cause mistakes in
+
+ align:start position:0%
+into your genome and cause mistakes in
+ 
+
+ align:start position:0%
+into your genome and cause mistakes in
+the reading or they actually physically
+
+ align:start position:0%
+the reading or they actually physically
+ 
+
+ align:start position:0%
+the reading or they actually physically
+modify the basis to make it a base that
+
+ align:start position:0%
+modify the basis to make it a base that
+ 
+
+ align:start position:0%
+modify the basis to make it a base that
+doesn't look like a base anymore so
+
+ align:start position:0%
+doesn't look like a base anymore so
+ 
+
+ align:start position:0%
+doesn't look like a base anymore so
+these are commonly very reactive
+
+ align:start position:0%
+these are commonly very reactive
+ 
+
+ align:start position:0%
+these are commonly very reactive
+chemicals these are all very serious
+
+ align:start position:0%
+chemicals these are all very serious
+ 
+
+ align:start position:0%
+chemicals these are all very serious
+things to the genome and so the the
+
+ align:start position:0%
+things to the genome and so the the
+ 
+
+ align:start position:0%
+things to the genome and so the the
+enzymes that mitigate the damage to the
+
+ align:start position:0%
+enzymes that mitigate the damage to the
+ 
+
+ align:start position:0%
+enzymes that mitigate the damage to the
+DNA basically screen along the
+
+ align:start position:0%
+DNA basically screen along the
+ 
+
+ align:start position:0%
+DNA basically screen along the
+double-stranded DNA to look for defects
+
+ align:start position:0%
+double-stranded DNA to look for defects
+ 
+
+ align:start position:0%
+double-stranded DNA to look for defects
+because if you have perfectly paired DNA
+
+ align:start position:0%
+because if you have perfectly paired DNA
+ 
+
+ align:start position:0%
+because if you have perfectly paired DNA
+then you're not you're gonna have a very
+
+ align:start position:0%
+then you're not you're gonna have a very
+ 
+
+ align:start position:0%
+then you're not you're gonna have a very
+regular structure whereas if something
+
+ align:start position:0%
+regular structure whereas if something
+ 
+
+ align:start position:0%
+regular structure whereas if something
+has happened to the DNA there's
+
+ align:start position:0%
+has happened to the DNA there's
+ 
+
+ align:start position:0%
+has happened to the DNA there's
+something wrong with the base it's not
+
+ align:start position:0%
+something wrong with the base it's not
+ 
+
+ align:start position:0%
+something wrong with the base it's not
+base pairing well or something has
+
+ align:start position:0%
+base pairing well or something has
+ 
+
+ align:start position:0%
+base pairing well or something has
+actually happened between bases where
+
+ align:start position:0%
+actually happened between bases where
+ 
+
+ align:start position:0%
+actually happened between bases where
+they're causing a bulge in the genome
+
+ align:start position:0%
+they're causing a bulge in the genome
+ 
+
+ align:start position:0%
+they're causing a bulge in the genome
+then these enzymes will come into play
+
+ align:start position:0%
+then these enzymes will come into play
+ 
+
+ align:start position:0%
+then these enzymes will come into play
+and about a few years ago actually it
+
+ align:start position:0%
+and about a few years ago actually it
+ 
+
+ align:start position:0%
+and about a few years ago actually it
+was one on a class day so I always enjoy
+
+ align:start position:0%
+was one on a class day so I always enjoy
+ 
+
+ align:start position:0%
+was one on a class day so I always enjoy
+these there was a the Nobel Prize was
+
+ align:start position:0%
+these there was a the Nobel Prize was
+ 
+
+ align:start position:0%
+these there was a the Nobel Prize was
+awarded in 12 2015 for the researchers
+
+ align:start position:0%
+awarded in 12 2015 for the researchers
+ 
+
+ align:start position:0%
+awarded in 12 2015 for the researchers
+who deciphered the mechanisms for
+
+ align:start position:0%
+who deciphered the mechanisms for
+ 
+
+ align:start position:0%
+who deciphered the mechanisms for
+correcting the genome through DNA repair
+
+ align:start position:0%
+correcting the genome through DNA repair
+ 
+
+ align:start position:0%
+correcting the genome through DNA repair
+mechanisms so there are two basic
+
+ align:start position:0%
+mechanisms so there are two basic
+ 
+
+ align:start position:0%
+mechanisms so there are two basic
+mechanisms that I'll talk to you about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is base excision repair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other one has to be is a lot
+
+ align:start position:0%
+and the other one has to be is a lot
+ 
+
+ align:start position:0%
+and the other one has to be is a lot
+more serious it's actually the entire
+
+ align:start position:0%
+more serious it's actually the entire
+ 
+
+ align:start position:0%
+more serious it's actually the entire
+nucleotide excision repair so one fixes
+
+ align:start position:0%
+nucleotide excision repair so one fixes
+ 
+
+ align:start position:0%
+nucleotide excision repair so one fixes
+just the base that's gone wrong but the
+
+ align:start position:0%
+just the base that's gone wrong but the
+ 
+
+ align:start position:0%
+just the base that's gone wrong but the
+other one takes much more of the
+
+ align:start position:0%
+other one takes much more of the
+ 
+
+ align:start position:0%
+other one takes much more of the
+structure out to fix it so it's
+
+ align:start position:0%
+structure out to fix it so it's
+ 
+
+ align:start position:0%
+structure out to fix it so it's
+nucleotide excision repair so BER and
+
+ align:start position:0%
+nucleotide excision repair so BER and
+ 
+
+ align:start position:0%
+nucleotide excision repair so BER and
+we're gonna talk about both of those
+
+ align:start position:0%
+we're gonna talk about both of those
+ 
+
+ align:start position:0%
+we're gonna talk about both of those
+mechanisms because they're very
+
+ align:start position:0%
+mechanisms because they're very
+ 
+
+ align:start position:0%
+mechanisms because they're very
+fascinating and they kind of lean on
+
+ align:start position:0%
+fascinating and they kind of lean on
+ 
+
+ align:start position:0%
+fascinating and they kind of lean on
+some of what you've learnt already so
+
+ align:start position:0%
+some of what you've learnt already so
+ 
+
+ align:start position:0%
+some of what you've learnt already so
+base excision repair occurs when there's
+
+ align:start position:0%
+base excision repair occurs when there's
+ 
+
+ align:start position:0%
+base excision repair occurs when there's
+a defect in the base maybe it's the
+
+ align:start position:0%
+a defect in the base maybe it's the
+ 
+
+ align:start position:0%
+a defect in the base maybe it's the
+wrong base maybe it's just been modified
+
+ align:start position:0%
+wrong base maybe it's just been modified
+ 
+
+ align:start position:0%
+wrong base maybe it's just been modified
+a little bit so what happens in base
+
+ align:start position:0%
+a little bit so what happens in base
+ 
+
+ align:start position:0%
+a little bit so what happens in base
+excision repair is that the base gets
+
+ align:start position:0%
+excision repair is that the base gets
+ 
+
+ align:start position:0%
+excision repair is that the base gets
+alright I'm going to just use the
+
+ align:start position:0%
+alright I'm going to just use the
+ 
+
+ align:start position:0%
+alright I'm going to just use the
+pointer because my little spotlight
+
+ align:start position:0%
+pointer because my little spotlight
+ 
+
+ align:start position:0%
+pointer because my little spotlight
+it'll pop back it's a bit magical so in
+
+ align:start position:0%
+it'll pop back it's a bit magical so in
+ 
+
+ align:start position:0%
+it'll pop back it's a bit magical so in
+base excision repair only the base a
+
+ align:start position:0%
+base excision repair only the base a
+ 
+
+ align:start position:0%
+base excision repair only the base a
+single localized base is damaged there
+
+ align:start position:0%
+single localized base is damaged there
+ 
+
+ align:start position:0%
+single localized base is damaged there
+is some chemistry for example that will
+
+ align:start position:0%
+is some chemistry for example that will
+ 
+
+ align:start position:0%
+is some chemistry for example that will
+convert cytosine to uracil called a
+
+ align:start position:0%
+convert cytosine to uracil called a
+ 
+
+ align:start position:0%
+convert cytosine to uracil called a
+deamination mechanism and in fact once
+
+ align:start position:0%
+deamination mechanism and in fact once
+ 
+
+ align:start position:0%
+deamination mechanism and in fact once
+if you replace a cytosine with a uracil
+
+ align:start position:0%
+if you replace a cytosine with a uracil
+ 
+
+ align:start position:0%
+if you replace a cytosine with a uracil
+then you get in trouble with respect to
+
+ align:start position:0%
+then you get in trouble with respect to
+ 
+
+ align:start position:0%
+then you get in trouble with respect to
+its base pairing with its appropriate
+
+ align:start position:0%
+its base pairing with its appropriate
+ 
+
+ align:start position:0%
+its base pairing with its appropriate
+purine partner so in base excision
+
+ align:start position:0%
+purine partner so in base excision
+ 
+
+ align:start position:0%
+purine partner so in base excision
+repair what will happen is that base
+
+ align:start position:0%
+repair what will happen is that base
+ 
+
+ align:start position:0%
+repair what will happen is that base
+will be detected it will be flicked out
+
+ align:start position:0%
+will be detected it will be flicked out
+ 
+
+ align:start position:0%
+will be detected it will be flicked out
+from the context of double-stranded DNA
+
+ align:start position:0%
+from the context of double-stranded DNA
+ 
+
+ align:start position:0%
+from the context of double-stranded DNA
+if it's tucked in the double stranded
+
+ align:start position:0%
+if it's tucked in the double stranded
+ 
+
+ align:start position:0%
+if it's tucked in the double stranded
+DNA
+
+ align:start position:0%
+DNA
+ 
+
+ align:start position:0%
+DNA
+you can't quite cut the bond that's
+
+ align:start position:0%
+you can't quite cut the bond that's
+ 
+
+ align:start position:0%
+you can't quite cut the bond that's
+attached from the ribose sugar to the
+
+ align:start position:0%
+attached from the ribose sugar to the
+ 
+
+ align:start position:0%
+attached from the ribose sugar to the
+base so the base gets flipped out of the
+
+ align:start position:0%
+base so the base gets flipped out of the
+ 
+
+ align:start position:0%
+base so the base gets flipped out of the
+DNA structure and there's an enzyme
+
+ align:start position:0%
+DNA structure and there's an enzyme
+ 
+
+ align:start position:0%
+DNA structure and there's an enzyme
+known as a glycosylase that cuts the
+
+ align:start position:0%
+known as a glycosylase that cuts the
+ 
+
+ align:start position:0%
+known as a glycosylase that cuts the
+bond between the ribose and the base and
+
+ align:start position:0%
+bond between the ribose and the base and
+ 
+
+ align:start position:0%
+bond between the ribose and the base and
+gets rid of it and then what happens is
+
+ align:start position:0%
+gets rid of it and then what happens is
+ 
+
+ align:start position:0%
+gets rid of it and then what happens is
+the rest of the nucleotide just that one
+
+ align:start position:0%
+the rest of the nucleotide just that one
+ 
+
+ align:start position:0%
+the rest of the nucleotide just that one
+nucleotide gets removed and then DNA
+
+ align:start position:0%
+nucleotide gets removed and then DNA
+ 
+
+ align:start position:0%
+nucleotide gets removed and then DNA
+polymerase fills the gap and the strand
+
+ align:start position:0%
+polymerase fills the gap and the strand
+ 
+
+ align:start position:0%
+polymerase fills the gap and the strand
+is sealed by a ligase so glycosylase
+
+ align:start position:0%
+is sealed by a ligase so glycosylase
+ 
+
+ align:start position:0%
+is sealed by a ligase so glycosylase
+cuts the base out there's a couple
+
+ align:start position:0%
+cuts the base out there's a couple
+ 
+
+ align:start position:0%
+cuts the base out there's a couple
+there's a couple of enzymes that
+
+ align:start position:0%
+there's a couple of enzymes that
+ 
+
+ align:start position:0%
+there's a couple of enzymes that
+actually cut the ribose the
+
+ align:start position:0%
+actually cut the ribose the
+ 
+
+ align:start position:0%
+actually cut the ribose the
+phosphodiester linkages out
+
+ align:start position:0%
+phosphodiester linkages out
+ 
+
+ align:start position:0%
+phosphodiester linkages out
+and then the two enzymes remember that
+
+ align:start position:0%
+and then the two enzymes remember that
+ 
+
+ align:start position:0%
+and then the two enzymes remember that
+are important when we're making DNA the
+
+ align:start position:0%
+are important when we're making DNA the
+ 
+
+ align:start position:0%
+are important when we're making DNA the
+the polymerase and the ligase cut work
+
+ align:start position:0%
+the polymerase and the ligase cut work
+ 
+
+ align:start position:0%
+the polymerase and the ligase cut work
+together to put a base in to this
+
+ align:start position:0%
+together to put a base in to this
+ 
+
+ align:start position:0%
+together to put a base in to this
+position and then they put they put the
+
+ align:start position:0%
+position and then they put they put the
+ 
+
+ align:start position:0%
+position and then they put they put the
+base back in and then the ligase joins
+
+ align:start position:0%
+base back in and then the ligase joins
+ 
+
+ align:start position:0%
+base back in and then the ligase joins
+the gaps so DNA polymerase will make one
+
+ align:start position:0%
+the gaps so DNA polymerase will make one
+ 
+
+ align:start position:0%
+the gaps so DNA polymerase will make one
+of the bonds the ligase will make the
+
+ align:start position:0%
+of the bonds the ligase will make the
+ 
+
+ align:start position:0%
+of the bonds the ligase will make the
+other bond all right so that's nuclear
+
+ align:start position:0%
+other bond all right so that's nuclear
+ 
+
+ align:start position:0%
+other bond all right so that's nuclear
+that's base excision repair and it's
+
+ align:start position:0%
+that's base excision repair and it's
+ 
+
+ align:start position:0%
+that's base excision repair and it's
+monitored by finding that there is a
+
+ align:start position:0%
+monitored by finding that there is a
+ 
+
+ align:start position:0%
+monitored by finding that there is a
+lack of integrity in the double-stranded
+
+ align:start position:0%
+lack of integrity in the double-stranded
+ 
+
+ align:start position:0%
+lack of integrity in the double-stranded
+DNA it's only a base that's affected so
+
+ align:start position:0%
+DNA it's only a base that's affected so
+ 
+
+ align:start position:0%
+DNA it's only a base that's affected so
+that base gets removed the rest of the
+
+ align:start position:0%
+that base gets removed the rest of the
+ 
+
+ align:start position:0%
+that base gets removed the rest of the
+nucleotide is removed but only one of
+
+ align:start position:0%
+nucleotide is removed but only one of
+ 
+
+ align:start position:0%
+nucleotide is removed but only one of
+them and then they're replaced through
+
+ align:start position:0%
+them and then they're replaced through
+ 
+
+ align:start position:0%
+them and then they're replaced through
+the concerted action of polymerase and
+
+ align:start position:0%
+the concerted action of polymerase and
+ 
+
+ align:start position:0%
+the concerted action of polymerase and
+ligase now there is another mechanism
+
+ align:start position:0%
+ligase now there is another mechanism
+ 
+
+ align:start position:0%
+ligase now there is another mechanism
+that's much more serious and this is
+
+ align:start position:0%
+that's much more serious and this is
+ 
+
+ align:start position:0%
+that's much more serious and this is
+very typical of the types of damage that
+
+ align:start position:0%
+very typical of the types of damage that
+ 
+
+ align:start position:0%
+very typical of the types of damage that
+get formed from sunlight and UV
+
+ align:start position:0%
+get formed from sunlight and UV
+ 
+
+ align:start position:0%
+get formed from sunlight and UV
+radiation is when two Thema Dean's and
+
+ align:start position:0%
+radiation is when two Thema Dean's and
+ 
+
+ align:start position:0%
+radiation is when two Thema Dean's and
+adjacent to each other they will undergo
+
+ align:start position:0%
+adjacent to each other they will undergo
+ 
+
+ align:start position:0%
+adjacent to each other they will undergo
+quite commonly a chemical reaction where
+
+ align:start position:0%
+quite commonly a chemical reaction where
+ 
+
+ align:start position:0%
+quite commonly a chemical reaction where
+they form a dimeric structure so there's
+
+ align:start position:0%
+they form a dimeric structure so there's
+ 
+
+ align:start position:0%
+they form a dimeric structure so there's
+much more wrong with the the nuclei of
+
+ align:start position:0%
+much more wrong with the the nuclei of
+ 
+
+ align:start position:0%
+much more wrong with the the nuclei of
+the DNA strand in that situation so
+
+ align:start position:0%
+the DNA strand in that situation so
+ 
+
+ align:start position:0%
+the DNA strand in that situation so
+those get noticed as things driving me
+
+ align:start position:0%
+those get noticed as things driving me
+ 
+
+ align:start position:0%
+those get noticed as things driving me
+nuts
+
+ align:start position:0%
+nuts
+ 
+
+ align:start position:0%
+nuts
+those get noticed as a real defect in
+
+ align:start position:0%
+those get noticed as a real defect in
+ 
+
+ align:start position:0%
+those get noticed as a real defect in
+the DNA base excision repair won't work
+
+ align:start position:0%
+the DNA base excision repair won't work
+ 
+
+ align:start position:0%
+the DNA base excision repair won't work
+why wouldn't it work yeah yeah they're
+
+ align:start position:0%
+why wouldn't it work yeah yeah they're
+ 
+
+ align:start position:0%
+why wouldn't it work yeah yeah they're
+bound together you can't peel them back
+
+ align:start position:0%
+bound together you can't peel them back
+ 
+
+ align:start position:0%
+bound together you can't peel them back
+out you can't break enough structure so
+
+ align:start position:0%
+out you can't break enough structure so
+ 
+
+ align:start position:0%
+out you can't break enough structure so
+you've got to move to a much more sort
+
+ align:start position:0%
+you've got to move to a much more sort
+ 
+
+ align:start position:0%
+you've got to move to a much more sort
+of major fixing of the the of the DNA
+
+ align:start position:0%
+of major fixing of the the of the DNA
+ 
+
+ align:start position:0%
+of major fixing of the the of the DNA
+strand so there is a genetically linked
+
+ align:start position:0%
+strand so there is a genetically linked
+ 
+
+ align:start position:0%
+strand so there is a genetically linked
+disorder where the enzymes involved in
+
+ align:start position:0%
+disorder where the enzymes involved in
+ 
+
+ align:start position:0%
+disorder where the enzymes involved in
+nucleotide excision repair do not work
+
+ align:start position:0%
+nucleotide excision repair do not work
+ 
+
+ align:start position:0%
+nucleotide excision repair do not work
+and when people when a child has a copy
+
+ align:start position:0%
+and when people when a child has a copy
+ 
+
+ align:start position:0%
+and when people when a child has a copy
+of both the affected genes from the
+
+ align:start position:0%
+of both the affected genes from the
+ 
+
+ align:start position:0%
+of both the affected genes from the
+parents both one from the mother and the
+
+ align:start position:0%
+parents both one from the mother and the
+ 
+
+ align:start position:0%
+parents both one from the mother and the
+father it's impossible for them to fix
+
+ align:start position:0%
+father it's impossible for them to fix
+ 
+
+ align:start position:0%
+father it's impossible for them to fix
+these defects in the da
+
+ align:start position:0%
+these defects in the da
+ 
+
+ align:start position:0%
+these defects in the da
+and they get a lot of physiologic
+
+ align:start position:0%
+and they get a lot of physiologic
+ 
+
+ align:start position:0%
+and they get a lot of physiologic
+problems like sort of scarring and some
+
+ align:start position:0%
+problems like sort of scarring and some
+ 
+
+ align:start position:0%
+problems like sort of scarring and some
+burns nothing barely anything at all and
+
+ align:start position:0%
+burns nothing barely anything at all and
+ 
+
+ align:start position:0%
+burns nothing barely anything at all and
+so this is this is a group of children
+
+ align:start position:0%
+so this is this is a group of children
+ 
+
+ align:start position:0%
+so this is this is a group of children
+that are so afflicted with this new this
+
+ align:start position:0%
+that are so afflicted with this new this
+ 
+
+ align:start position:0%
+that are so afflicted with this new this
+genetic disorders that they cannot go
+
+ align:start position:0%
+genetic disorders that they cannot go
+ 
+
+ align:start position:0%
+genetic disorders that they cannot go
+out in the daytime at all
+
+ align:start position:0%
+out in the daytime at all
+ 
+
+ align:start position:0%
+out in the daytime at all
+so you're sometimes see they're called
+
+ align:start position:0%
+so you're sometimes see they're called
+ 
+
+ align:start position:0%
+so you're sometimes see they're called
+children of the night because basically
+
+ align:start position:0%
+children of the night because basically
+ 
+
+ align:start position:0%
+children of the night because basically
+they have to flip their schedules they
+
+ align:start position:0%
+they have to flip their schedules they
+ 
+
+ align:start position:0%
+they have to flip their schedules they
+just can't go near sunlight and if they
+
+ align:start position:0%
+just can't go near sunlight and if they
+ 
+
+ align:start position:0%
+just can't go near sunlight and if they
+go out they basically have to be covered
+
+ align:start position:0%
+go out they basically have to be covered
+ 
+
+ align:start position:0%
+go out they basically have to be covered
+from head to toe and that's including
+
+ align:start position:0%
+from head to toe and that's including
+ 
+
+ align:start position:0%
+from head to toe and that's including
+their eyes because you can get sunburned
+
+ align:start position:0%
+their eyes because you can get sunburned
+ 
+
+ align:start position:0%
+their eyes because you can get sunburned
+of the eyes you can sort of see in some
+
+ align:start position:0%
+of the eyes you can sort of see in some
+ 
+
+ align:start position:0%
+of the eyes you can sort of see in some
+of these pictures that looks really
+
+ align:start position:0%
+of these pictures that looks really
+ 
+
+ align:start position:0%
+of these pictures that looks really
+serious defects and this is just the
+
+ align:start position:0%
+serious defects and this is just the
+ 
+
+ align:start position:0%
+serious defects and this is just the
+external manifestation the entire
+
+ align:start position:0%
+external manifestation the entire
+ 
+
+ align:start position:0%
+external manifestation the entire
+manifestation would be cases of skin
+
+ align:start position:0%
+manifestation would be cases of skin
+ 
+
+ align:start position:0%
+manifestation would be cases of skin
+cancer very very readily so if you don't
+
+ align:start position:0%
+cancer very very readily so if you don't
+ 
+
+ align:start position:0%
+cancer very very readily so if you don't
+have at least one good copy of the
+
+ align:start position:0%
+have at least one good copy of the
+ 
+
+ align:start position:0%
+have at least one good copy of the
+enzyme that does nucleotide excision
+
+ align:start position:0%
+enzyme that does nucleotide excision
+ 
+
+ align:start position:0%
+enzyme that does nucleotide excision
+repair then you're in trouble and the
+
+ align:start position:0%
+repair then you're in trouble and the
+ 
+
+ align:start position:0%
+repair then you're in trouble and the
+defects are called
+
+ align:start position:0%
+defects are called
+ 
+
+ align:start position:0%
+defects are called
+is called xeroderma pigmentosum and
+
+ align:start position:0%
+is called xeroderma pigmentosum and
+ 
+
+ align:start position:0%
+is called xeroderma pigmentosum and
+there's actually a lot of family groups
+
+ align:start position:0%
+there's actually a lot of family groups
+ 
+
+ align:start position:0%
+there's actually a lot of family groups
+that get together because the best way
+
+ align:start position:0%
+that get together because the best way
+ 
+
+ align:start position:0%
+that get together because the best way
+is just to form a sort of social network
+
+ align:start position:0%
+is just to form a sort of social network
+ 
+
+ align:start position:0%
+is just to form a sort of social network
+so the children understand what each
+
+ align:start position:0%
+so the children understand what each
+ 
+
+ align:start position:0%
+so the children understand what each
+other the limitations that they all have
+
+ align:start position:0%
+other the limitations that they all have
+ 
+
+ align:start position:0%
+other the limitations that they all have
+and they can play together and beyond
+
+ align:start position:0%
+and they can play together and beyond
+ 
+
+ align:start position:0%
+and they can play together and beyond
+these sort of flip schedules in order to
+
+ align:start position:0%
+these sort of flip schedules in order to
+ 
+
+ align:start position:0%
+these sort of flip schedules in order to
+avoid any sunlight so in this case it's
+
+ align:start position:0%
+avoid any sunlight so in this case it's
+ 
+
+ align:start position:0%
+avoid any sunlight so in this case it's
+essential to basically clip out a large
+
+ align:start position:0%
+essential to basically clip out a large
+ 
+
+ align:start position:0%
+essential to basically clip out a large
+chunk of the DNA so what happens in this
+
+ align:start position:0%
+chunk of the DNA so what happens in this
+ 
+
+ align:start position:0%
+chunk of the DNA so what happens in this
+case is that the DNA is recognized and
+
+ align:start position:0%
+case is that the DNA is recognized and
+ 
+
+ align:start position:0%
+case is that the DNA is recognized and
+then a large portion of it about a dozen
+
+ align:start position:0%
+then a large portion of it about a dozen
+ 
+
+ align:start position:0%
+then a large portion of it about a dozen
+nucleotides are cleaved out and then
+
+ align:start position:0%
+nucleotides are cleaved out and then
+ 
+
+ align:start position:0%
+nucleotides are cleaved out and then
+once again DNA polymerase fills the gap
+
+ align:start position:0%
+once again DNA polymerase fills the gap
+ 
+
+ align:start position:0%
+once again DNA polymerase fills the gap
+and DNA ligase seals the last gaps so
+
+ align:start position:0%
+and DNA ligase seals the last gaps so
+ 
+
+ align:start position:0%
+and DNA ligase seals the last gaps so
+DNA polymerase will be able to fill
+
+ align:start position:0%
+DNA polymerase will be able to fill
+ 
+
+ align:start position:0%
+DNA polymerase will be able to fill
+going from the 5 prime to 3 prime
+
+ align:start position:0%
+going from the 5 prime to 3 prime
+ 
+
+ align:start position:0%
+going from the 5 prime to 3 prime
+they'll still be one gap and then the
+
+ align:start position:0%
+they'll still be one gap and then the
+ 
+
+ align:start position:0%
+they'll still be one gap and then the
+ligase fixes it so I think these kinds
+
+ align:start position:0%
+ligase fixes it so I think these kinds
+ 
+
+ align:start position:0%
+ligase fixes it so I think these kinds
+of things that are done to mitigate
+
+ align:start position:0%
+of things that are done to mitigate
+ 
+
+ align:start position:0%
+of things that are done to mitigate
+damage on the genome are very important
+
+ align:start position:0%
+damage on the genome are very important
+ 
+
+ align:start position:0%
+damage on the genome are very important
+to understand because this is happening
+
+ align:start position:0%
+to understand because this is happening
+ 
+
+ align:start position:0%
+to understand because this is happening
+all the time any minor things that get
+
+ align:start position:0%
+all the time any minor things that get
+ 
+
+ align:start position:0%
+all the time any minor things that get
+fixed the need fixing due to sunlight
+
+ align:start position:0%
+fixed the need fixing due to sunlight
+ 
+
+ align:start position:0%
+fixed the need fixing due to sunlight
+radiation chemicals will will be fixed
+
+ align:start position:0%
+radiation chemicals will will be fixed
+ 
+
+ align:start position:0%
+radiation chemicals will will be fixed
+through these methods to keep that rate
+
+ align:start position:0%
+through these methods to keep that rate
+ 
+
+ align:start position:0%
+through these methods to keep that rate
+that error rate in your genome down to
+
+ align:start position:0%
+that error rate in your genome down to
+ 
+
+ align:start position:0%
+that error rate in your genome down to
+like one in a billion or something like
+
+ align:start position:0%
+like one in a billion or something like
+ 
+
+ align:start position:0%
+like one in a billion or something like
+that alright so I'm just gonna flash
+
+ align:start position:0%
+that alright so I'm just gonna flash
+ 
+
+ align:start position:0%
+that alright so I'm just gonna flash
+this up I'm gonna very quickly I'm gonna
+
+ align:start position:0%
+this up I'm gonna very quickly I'm gonna
+ 
+
+ align:start position:0%
+this up I'm gonna very quickly I'm gonna
+give you guys what a copy of this but
+
+ align:start position:0%
+give you guys what a copy of this but
+ 
+
+ align:start position:0%
+give you guys what a copy of this but
+these are the components that you want
+
+ align:start position:0%
+these are the components that you want
+ 
+
+ align:start position:0%
+these are the components that you want
+to be able to understand the function of
+
+ align:start position:0%
+to be able to understand the function of
+ 
+
+ align:start position:0%
+to be able to understand the function of
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+when thinking about DNA replication so
+
+ align:start position:0%
+when thinking about DNA replication so
+ 
+
+ align:start position:0%
+when thinking about DNA replication so
+you don't have that on your slides but
+
+ align:start position:0%
+you don't have that on your slides but
+ 
+
+ align:start position:0%
+you don't have that on your slides but
+we're going to give you a copy so that
+
+ align:start position:0%
+we're going to give you a copy so that
+ 
+
+ align:start position:0%
+we're going to give you a copy so that
+you can really make sure that you
+
+ align:start position:0%
+you can really make sure that you
+ 
+
+ align:start position:0%
+you can really make sure that you
+understand all the moving parts and how
+
+ align:start position:0%
+understand all the moving parts and how
+ 
+
+ align:start position:0%
+understand all the moving parts and how
+to they come together for replication
+
+ align:start position:0%
+to they come together for replication
+ 
+
+ align:start position:0%
+to they come together for replication
+now I want to talk about one last
+
+ align:start position:0%
+now I want to talk about one last
+ 
+
+ align:start position:0%
+now I want to talk about one last
+conundrum with DNA and that is the issue
+
+ align:start position:0%
+conundrum with DNA and that is the issue
+ 
+
+ align:start position:0%
+conundrum with DNA and that is the issue
+of telomerase and this is particularly
+
+ align:start position:0%
+of telomerase and this is particularly
+ 
+
+ align:start position:0%
+of telomerase and this is particularly
+critical in eukaryotes that have linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chromosomes now if you think about DNA
+
+ align:start position:0%
+chromosomes now if you think about DNA
+ 
+
+ align:start position:0%
+chromosomes now if you think about DNA
+being replicated what when you look at
+
+ align:start position:0%
+being replicated what when you look at
+ 
+
+ align:start position:0%
+being replicated what when you look at
+the two strands of DNA as you approach
+
+ align:start position:0%
+the two strands of DNA as you approach
+ 
+
+ align:start position:0%
+the two strands of DNA as you approach
+the as you approach the very end of the
+
+ align:start position:0%
+the as you approach the very end of the
+ 
+
+ align:start position:0%
+the as you approach the very end of the
+chromosome you'll do just fine
+
+ align:start position:0%
+chromosome you'll do just fine
+ 
+
+ align:start position:0%
+chromosome you'll do just fine
+making the copy that's built five primes
+
+ align:start position:0%
+making the copy that's built five primes
+ 
+
+ align:start position:0%
+making the copy that's built five primes
+that's built worried about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll do just fine making the copy that
+
+ align:start position:0%
+you'll do just fine making the copy that
+ 
+
+ align:start position:0%
+you'll do just fine making the copy that
+is built in this direction because it's
+
+ align:start position:0%
+is built in this direction because it's
+ 
+
+ align:start position:0%
+is built in this direction because it's
+the leading strand and it's built by
+
+ align:start position:0%
+the leading strand and it's built by
+ 
+
+ align:start position:0%
+the leading strand and it's built by
+prime am I going wrong here it's built
+
+ align:start position:0%
+prime am I going wrong here it's built
+ 
+
+ align:start position:0%
+prime am I going wrong here it's built
+five prime to three prime can someone
+
+ align:start position:0%
+five prime to three prime can someone
+ 
+
+ align:start position:0%
+five prime to three prime can someone
+help me out here I'm losing my mind okay
+
+ align:start position:0%
+help me out here I'm losing my mind okay
+ 
+
+ align:start position:0%
+help me out here I'm losing my mind okay
+this is so this piece is built five
+
+ align:start position:0%
+this is so this piece is built five
+ 
+
+ align:start position:0%
+this is so this piece is built five
+prime to three prime so therefore this
+
+ align:start position:0%
+prime to three prime so therefore this
+ 
+
+ align:start position:0%
+prime to three prime so therefore this
+was five-prime and three-prime but then
+
+ align:start position:0%
+was five-prime and three-prime but then
+ 
+
+ align:start position:0%
+was five-prime and three-prime but then
+on the other strand you have a problem
+
+ align:start position:0%
+on the other strand you have a problem
+ 
+
+ align:start position:0%
+on the other strand you have a problem
+because you need to put in a primer here
+
+ align:start position:0%
+because you need to put in a primer here
+ 
+
+ align:start position:0%
+because you need to put in a primer here
+in order to build the other strand does
+
+ align:start position:0%
+in order to build the other strand does
+ 
+
+ align:start position:0%
+in order to build the other strand does
+that make sense so we've got to have put
+
+ align:start position:0%
+that make sense so we've got to have put
+ 
+
+ align:start position:0%
+that make sense so we've got to have put
+in that short primer because DNA polymer
+
+ align:start position:0%
+in that short primer because DNA polymer
+ 
+
+ align:start position:0%
+in that short primer because DNA polymer
+is will not work otherwise and then we
+
+ align:start position:0%
+is will not work otherwise and then we
+ 
+
+ align:start position:0%
+is will not work otherwise and then we
+need to build this strand of DNA all
+
+ align:start position:0%
+need to build this strand of DNA all
+ 
+
+ align:start position:0%
+need to build this strand of DNA all
+right so what's the problem here with
+
+ align:start position:0%
+right so what's the problem here with
+ 
+
+ align:start position:0%
+right so what's the problem here with
+respect to these ends what's gonna
+
+ align:start position:0%
+respect to these ends what's gonna
+ 
+
+ align:start position:0%
+respect to these ends what's gonna
+happen next it's an RNA primer what
+
+ align:start position:0%
+happen next it's an RNA primer what
+ 
+
+ align:start position:0%
+happen next it's an RNA primer what
+happens next
+
+ align:start position:0%
+happens next
+ 
+
+ align:start position:0%
+happens next
+we nibble it up right with the full
+
+ align:start position:0%
+we nibble it up right with the full
+ 
+
+ align:start position:0%
+we nibble it up right with the full
+intention of replacing that bit of day
+
+ align:start position:0%
+intention of replacing that bit of day
+ 
+
+ align:start position:0%
+intention of replacing that bit of day
+in the DNA but then what can DNA
+
+ align:start position:0%
+in the DNA but then what can DNA
+ 
+
+ align:start position:0%
+in the DNA but then what can DNA
+polymerase do it can't do anything right
+
+ align:start position:0%
+polymerase do it can't do anything right
+ 
+
+ align:start position:0%
+polymerase do it can't do anything right
+DNA polymerase needs double-stranded DNA
+
+ align:start position:0%
+DNA polymerase needs double-stranded DNA
+ 
+
+ align:start position:0%
+DNA polymerase needs double-stranded DNA
+to hold on to so it could fill this gap
+
+ align:start position:0%
+to hold on to so it could fill this gap
+ 
+
+ align:start position:0%
+to hold on to so it could fill this gap
+so what happens is every time you
+
+ align:start position:0%
+so what happens is every time you
+ 
+
+ align:start position:0%
+so what happens is every time you
+replicate DNA you end up with a gap with
+
+ align:start position:0%
+replicate DNA you end up with a gap with
+ 
+
+ align:start position:0%
+replicate DNA you end up with a gap with
+a small amount you don't quite copy is
+
+ align:start position:0%
+a small amount you don't quite copy is
+ 
+
+ align:start position:0%
+a small amount you don't quite copy is
+everyone following me and that's a
+
+ align:start position:0%
+everyone following me and that's a
+ 
+
+ align:start position:0%
+everyone following me and that's a
+problem right because doesn't it mean
+
+ align:start position:0%
+problem right because doesn't it mean
+ 
+
+ align:start position:0%
+problem right because doesn't it mean
+every time my cells divide my genes get
+
+ align:start position:0%
+every time my cells divide my genes get
+ 
+
+ align:start position:0%
+every time my cells divide my genes get
+a little bit shorter and a little bit
+
+ align:start position:0%
+a little bit shorter and a little bit
+ 
+
+ align:start position:0%
+a little bit shorter and a little bit
+shorter and a little bit shorter so
+
+ align:start position:0%
+shorter and a little bit shorter so
+ 
+
+ align:start position:0%
+shorter and a little bit shorter so
+there are things in place that help one
+
+ align:start position:0%
+there are things in place that help one
+ 
+
+ align:start position:0%
+there are things in place that help one
+important feature is that usually you
+
+ align:start position:0%
+important feature is that usually you
+ 
+
+ align:start position:0%
+important feature is that usually you
+don't have important genetic material at
+
+ align:start position:0%
+don't have important genetic material at
+ 
+
+ align:start position:0%
+don't have important genetic material at
+the ends of your genes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the ends of chromosomes rather
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's sort of extra DNA that doesn't
+
+ align:start position:0%
+there's sort of extra DNA that doesn't
+ 
+
+ align:start position:0%
+there's sort of extra DNA that doesn't
+need to be copied but the basic theory
+
+ align:start position:0%
+need to be copied but the basic theory
+ 
+
+ align:start position:0%
+need to be copied but the basic theory
+the whole theory about telomerase is
+
+ align:start position:0%
+the whole theory about telomerase is
+ 
+
+ align:start position:0%
+the whole theory about telomerase is
+that for certain types of cells these
+
+ align:start position:0%
+that for certain types of cells these
+ 
+
+ align:start position:0%
+that for certain types of cells these
+are sent stem cells and germ cells there
+
+ align:start position:0%
+are sent stem cells and germ cells there
+ 
+
+ align:start position:0%
+are sent stem cells and germ cells there
+is an enzyme that can fill this gap
+
+ align:start position:0%
+is an enzyme that can fill this gap
+ 
+
+ align:start position:0%
+is an enzyme that can fill this gap
+it's called telomerase so in those cells
+
+ align:start position:0%
+it's called telomerase so in those cells
+ 
+
+ align:start position:0%
+it's called telomerase so in those cells
+what's special about these types of
+
+ align:start position:0%
+what's special about these types of
+ 
+
+ align:start position:0%
+what's special about these types of
+cells we need to keep them good there
+
+ align:start position:0%
+cells we need to keep them good there
+ 
+
+ align:start position:0%
+cells we need to keep them good there
+what defines your starting DNA the stem
+
+ align:start position:0%
+what defines your starting DNA the stem
+ 
+
+ align:start position:0%
+what defines your starting DNA the stem
+cells and the and the germ cells like in
+
+ align:start position:0%
+cells and the and the germ cells like in
+ 
+
+ align:start position:0%
+cells and the and the germ cells like in
+this sperm and egg have to have in have
+
+ align:start position:0%
+this sperm and egg have to have in have
+ 
+
+ align:start position:0%
+this sperm and egg have to have in have
+to have a good copy of DNA they can't be
+
+ align:start position:0%
+to have a good copy of DNA they can't be
+ 
+
+ align:start position:0%
+to have a good copy of DNA they can't be
+getting shorter and shorter every time a
+
+ align:start position:0%
+getting shorter and shorter every time a
+ 
+
+ align:start position:0%
+getting shorter and shorter every time a
+new generation is born but once your
+
+ align:start position:0%
+new generation is born but once your
+ 
+
+ align:start position:0%
+new generation is born but once your
+cells are the somatic cells the DNA gets
+
+ align:start position:0%
+cells are the somatic cells the DNA gets
+ 
+
+ align:start position:0%
+cells are the somatic cells the DNA gets
+shorter and shorter because the those
+
+ align:start position:0%
+shorter and shorter because the those
+ 
+
+ align:start position:0%
+shorter and shorter because the those
+cells don't have telomerase and this is
+
+ align:start position:0%
+cells don't have telomerase and this is
+ 
+
+ align:start position:0%
+cells don't have telomerase and this is
+associated with theories of aging so the
+
+ align:start position:0%
+associated with theories of aging so the
+ 
+
+ align:start position:0%
+associated with theories of aging so the
+cells you get the ones that are finally
+
+ align:start position:0%
+cells you get the ones that are finally
+ 
+
+ align:start position:0%
+cells you get the ones that are finally
+the ones in your body every time they
+
+ align:start position:0%
+the ones in your body every time they
+ 
+
+ align:start position:0%
+the ones in your body every time they
+divide the ends of the chromosomes will
+
+ align:start position:0%
+divide the ends of the chromosomes will
+ 
+
+ align:start position:0%
+divide the ends of the chromosomes will
+get a little shorter but there's no
+
+ align:start position:0%
+get a little shorter but there's no
+ 
+
+ align:start position:0%
+get a little shorter but there's no
+mechanism to replace those and so it's
+
+ align:start position:0%
+mechanism to replace those and so it's
+ 
+
+ align:start position:0%
+mechanism to replace those and so it's
+associated with the belief that at a
+
+ align:start position:0%
+associated with the belief that at a
+ 
+
+ align:start position:0%
+associated with the belief that at a
+certain stage you've divided the cells
+
+ align:start position:0%
+certain stage you've divided the cells
+ 
+
+ align:start position:0%
+certain stage you've divided the cells
+enough times and then you can't they
+
+ align:start position:0%
+enough times and then you can't they
+ 
+
+ align:start position:0%
+enough times and then you can't they
+you're actually starting to nibble in
+
+ align:start position:0%
+you're actually starting to nibble in
+ 
+
+ align:start position:0%
+you're actually starting to nibble in
+two important coding DNA does everybody
+
+ align:start position:0%
+two important coding DNA does everybody
+ 
+
+ align:start position:0%
+two important coding DNA does everybody
+understand that what would be the
+
+ align:start position:0%
+understand that what would be the
+ 
+
+ align:start position:0%
+understand that what would be the
+significance of that does that make
+
+ align:start position:0%
+significance of that does that make
+ 
+
+ align:start position:0%
+significance of that does that make
+sense yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No so the telomerase keeps the the the
+
+ align:start position:0%
+No so the telomerase keeps the the the
+ 
+
+ align:start position:0%
+No so the telomerase keeps the the the
+DNA in those types of cells in good
+
+ align:start position:0%
+DNA in those types of cells in good
+ 
+
+ align:start position:0%
+DNA in those types of cells in good
+condition in the cells that divide daily
+
+ align:start position:0%
+condition in the cells that divide daily
+ 
+
+ align:start position:0%
+condition in the cells that divide daily
+in your body once these are the somatic
+
+ align:start position:0%
+in your body once these are the somatic
+ 
+
+ align:start position:0%
+in your body once these are the somatic
+cells you will keep on shortening but
+
+ align:start position:0%
+cells you will keep on shortening but
+ 
+
+ align:start position:0%
+cells you will keep on shortening but
+they'll just be more mistakes basically
+
+ align:start position:0%
+they'll just be more mistakes basically
+ 
+
+ align:start position:0%
+they'll just be more mistakes basically
+and those are the sorts of things that
+
+ align:start position:0%
+and those are the sorts of things that
+ 
+
+ align:start position:0%
+and those are the sorts of things that
+would be associated with an organism
+
+ align:start position:0%
+would be associated with an organism
+ 
+
+ align:start position:0%
+would be associated with an organism
+that's growing to a certain age because
+
+ align:start position:0%
+that's growing to a certain age because
+ 
+
+ align:start position:0%
+that's growing to a certain age because
+there's just a certain number of cells
+
+ align:start position:0%
+there's just a certain number of cells
+ 
+
+ align:start position:0%
+there's just a certain number of cells
+so the cells may not divide or there may
+
+ align:start position:0%
+so the cells may not divide or there may
+ 
+
+ align:start position:0%
+so the cells may not divide or there may
+be mistakes in certain parts of the
+
+ align:start position:0%
+be mistakes in certain parts of the
+ 
+
+ align:start position:0%
+be mistakes in certain parts of the
+coding genome anything any other
+
+ align:start position:0%
+coding genome anything any other
+ 
+
+ align:start position:0%
+coding genome anything any other
+questions okay so
+
+ align:start position:0%
+questions okay so
+ 
+
+ align:start position:0%
+questions okay so
+Kalama raised was also another important
+
+ align:start position:0%
+Kalama raised was also another important
+ 
+
+ align:start position:0%
+Kalama raised was also another important
+discovery that was awarded a nobel prize
+
+ align:start position:0%
+discovery that was awarded a nobel prize
+ 
+
+ align:start position:0%
+discovery that was awarded a nobel prize
+and this gives you details so the
+
+ align:start position:0%
+and this gives you details so the
+ 
+
+ align:start position:0%
+and this gives you details so the
+telomerase is protects the genetic
+
+ align:start position:0%
+telomerase is protects the genetic
+ 
+
+ align:start position:0%
+telomerase is protects the genetic
+information on every cell division
+
+ align:start position:0%
+information on every cell division
+ 
+
+ align:start position:0%
+information on every cell division
+though you will you will lose a little
+
+ align:start position:0%
+though you will you will lose a little
+ 
+
+ align:start position:0%
+though you will you will lose a little
+bit of genetic information so it limits
+
+ align:start position:0%
+bit of genetic information so it limits
+ 
+
+ align:start position:0%
+bit of genetic information so it limits
+the number of divisions a cell can make
+
+ align:start position:0%
+the number of divisions a cell can make
+ 
+
+ align:start position:0%
+the number of divisions a cell can make
+in a lifetime alright so we're gonna
+
+ align:start position:0%
+in a lifetime alright so we're gonna
+ 
+
+ align:start position:0%
+in a lifetime alright so we're gonna
+move on now and I've spent quite a bit
+
+ align:start position:0%
+move on now and I've spent quite a bit
+ 
+
+ align:start position:0%
+move on now and I've spent quite a bit
+of time on this but I want to guarantee
+
+ align:start position:0%
+of time on this but I want to guarantee
+ 
+
+ align:start position:0%
+of time on this but I want to guarantee
+you that we're now as we move forward to
+
+ align:start position:0%
+you that we're now as we move forward to
+ 
+
+ align:start position:0%
+you that we're now as we move forward to
+transcription there's a few
+
+ align:start position:0%
+transcription there's a few
+ 
+
+ align:start position:0%
+transcription there's a few
+simplifications that we can make in the
+
+ align:start position:0%
+simplifications that we can make in the
+ 
+
+ align:start position:0%
+simplifications that we can make in the
+in the story of transcription so moving
+
+ align:start position:0%
+in the story of transcription so moving
+ 
+
+ align:start position:0%
+in the story of transcription so moving
+on alright so what have we done so far
+
+ align:start position:0%
+on alright so what have we done so far
+ 
+
+ align:start position:0%
+on alright so what have we done so far
+we've seen replication now we're moving
+
+ align:start position:0%
+we've seen replication now we're moving
+ 
+
+ align:start position:0%
+we've seen replication now we're moving
+to the process of transcription
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you transcribe something you're
+
+ align:start position:0%
+so when you transcribe something you're
+ 
+
+ align:start position:0%
+so when you transcribe something you're
+basically making a copy of something but
+
+ align:start position:0%
+basically making a copy of something but
+ 
+
+ align:start position:0%
+basically making a copy of something but
+in a slightly different format so for
+
+ align:start position:0%
+in a slightly different format so for
+ 
+
+ align:start position:0%
+in a slightly different format so for
+example if you're transcribing from
+
+ align:start position:0%
+example if you're transcribing from
+ 
+
+ align:start position:0%
+example if you're transcribing from
+handwritten to a typed version you go
+
+ align:start position:0%
+handwritten to a typed version you go
+ 
+
+ align:start position:0%
+handwritten to a typed version you go
+from something that's in the script to
+
+ align:start position:0%
+from something that's in the script to
+ 
+
+ align:start position:0%
+from something that's in the script to
+something that's typed it has the same
+
+ align:start position:0%
+something that's typed it has the same
+ 
+
+ align:start position:0%
+something that's typed it has the same
+content but it's in a different format
+
+ align:start position:0%
+content but it's in a different format
+ 
+
+ align:start position:0%
+content but it's in a different format
+so this is that what the process is
+
+ align:start position:0%
+so this is that what the process is
+ 
+
+ align:start position:0%
+so this is that what the process is
+called when you convert DNA into RNA and
+
+ align:start position:0%
+called when you convert DNA into RNA and
+ 
+
+ align:start position:0%
+called when you convert DNA into RNA and
+very specifically this is part of the
+
+ align:start position:0%
+very specifically this is part of the
+ 
+
+ align:start position:0%
+very specifically this is part of the
+process to make what's known as the
+
+ align:start position:0%
+process to make what's known as the
+ 
+
+ align:start position:0%
+process to make what's known as the
+messenger RNA the first phase of
+
+ align:start position:0%
+messenger RNA the first phase of
+ 
+
+ align:start position:0%
+messenger RNA the first phase of
+transcription in eukaryotic cells gets
+
+ align:start position:0%
+transcription in eukaryotic cells gets
+ 
+
+ align:start position:0%
+transcription in eukaryotic cells gets
+us to a pre messenger RNA so there's a
+
+ align:start position:0%
+us to a pre messenger RNA so there's a
+ 
+
+ align:start position:0%
+us to a pre messenger RNA so there's a
+little bit needs more needs to be done
+
+ align:start position:0%
+little bit needs more needs to be done
+ 
+
+ align:start position:0%
+little bit needs more needs to be done
+to it before it can leave the nucleus to
+
+ align:start position:0%
+to it before it can leave the nucleus to
+ 
+
+ align:start position:0%
+to it before it can leave the nucleus to
+encode protein translation but in
+
+ align:start position:0%
+encode protein translation but in
+ 
+
+ align:start position:0%
+encode protein translation but in
+bacteria you're basically just going
+
+ align:start position:0%
+bacteria you're basically just going
+ 
+
+ align:start position:0%
+bacteria you're basically just going
+straight from the DNA to the messenger
+
+ align:start position:0%
+straight from the DNA to the messenger
+ 
+
+ align:start position:0%
+straight from the DNA to the messenger
+RNA at the beginning of the next class
+
+ align:start position:0%
+RNA at the beginning of the next class
+ 
+
+ align:start position:0%
+RNA at the beginning of the next class
+we will also talk about going from the
+
+ align:start position:0%
+we will also talk about going from the
+ 
+
+ align:start position:0%
+we will also talk about going from the
+pre messenger RNA to the messenger RNA
+
+ align:start position:0%
+pre messenger RNA to the messenger RNA
+ 
+
+ align:start position:0%
+pre messenger RNA to the messenger RNA
+and let's take a look at the cell up
+
+ align:start position:0%
+and let's take a look at the cell up
+ 
+
+ align:start position:0%
+and let's take a look at the cell up
+here where what we're focusing in on
+
+ align:start position:0%
+here where what we're focusing in on
+ 
+
+ align:start position:0%
+here where what we're focusing in on
+here is the process whereby we're
+
+ align:start position:0%
+here is the process whereby we're
+ 
+
+ align:start position:0%
+here is the process whereby we're
+copying that DNA I have no idea why this
+
+ align:start position:0%
+copying that DNA I have no idea why this
+ 
+
+ align:start position:0%
+copying that DNA I have no idea why this
+is really being monstrously behaved like
+
+ align:start position:0%
+is really being monstrously behaved like
+ 
+
+ align:start position:0%
+is really being monstrously behaved like
+I'm done done with these gizmos the
+
+ align:start position:0%
+I'm done done with these gizmos the
+ 
+
+ align:start position:0%
+I'm done done with these gizmos the
+process whereby the double-stranded DNA
+
+ align:start position:0%
+process whereby the double-stranded DNA
+ 
+
+ align:start position:0%
+process whereby the double-stranded DNA
+opens up a little bit and we make that
+
+ align:start position:0%
+opens up a little bit and we make that
+ 
+
+ align:start position:0%
+opens up a little bit and we make that
+pre messenger RNA copy alright so I want
+
+ align:start position:0%
+pre messenger RNA copy alright so I want
+ 
+
+ align:start position:0%
+pre messenger RNA copy alright so I want
+you to think back to the processes that
+
+ align:start position:0%
+you to think back to the processes that
+ 
+
+ align:start position:0%
+you to think back to the processes that
+we learnt about for translation and now
+
+ align:start position:0%
+we learnt about for translation and now
+ 
+
+ align:start position:0%
+we learnt about for translation and now
+we're going to move forward to take a
+
+ align:start position:0%
+we're going to move forward to take a
+ 
+
+ align:start position:0%
+we're going to move forward to take a
+look at transcription and frankly it's a
+
+ align:start position:0%
+look at transcription and frankly it's a
+ 
+
+ align:start position:0%
+look at transcription and frankly it's a
+lot simpler so let's just look at the
+
+ align:start position:0%
+lot simpler so let's just look at the
+ 
+
+ align:start position:0%
+lot simpler so let's just look at the
+players in transcription and you've got
+
+ align:start position:0%
+players in transcription and you've got
+ 
+
+ align:start position:0%
+players in transcription and you've got
+a copy of this in your notes so I don't
+
+ align:start position:0%
+a copy of this in your notes so I don't
+ 
+
+ align:start position:0%
+a copy of this in your notes so I don't
+need to necessarily put it all on the
+
+ align:start position:0%
+need to necessarily put it all on the
+ 
+
+ align:start position:0%
+need to necessarily put it all on the
+board so in DNA remember we had a GC T
+
+ align:start position:0%
+board so in DNA remember we had a GC T
+ 
+
+ align:start position:0%
+board so in DNA remember we had a GC T
+we have a deoxyribose and it's mostly
+
+ align:start position:0%
+we have a deoxyribose and it's mostly
+ 
+
+ align:start position:0%
+we have a deoxyribose and it's mostly
+used as
+
+ align:start position:0%
+used as
+ 
+
+ align:start position:0%
+used as
+ready Terry genetic information but in
+
+ align:start position:0%
+ready Terry genetic information but in
+ 
+
+ align:start position:0%
+ready Terry genetic information but in
+RNA we're making a new copy of the DNA
+
+ align:start position:0%
+RNA we're making a new copy of the DNA
+ 
+
+ align:start position:0%
+RNA we're making a new copy of the DNA
+where we use slightly different building
+
+ align:start position:0%
+where we use slightly different building
+ 
+
+ align:start position:0%
+where we use slightly different building
+blocks a GC u u instead of T plus there
+
+ align:start position:0%
+blocks a GC u u instead of T plus there
+ 
+
+ align:start position:0%
+blocks a GC u u instead of T plus there
+are some modified bases that occur in
+
+ align:start position:0%
+are some modified bases that occur in
+ 
+
+ align:start position:0%
+are some modified bases that occur in
+some of the types of RNA and the sugar
+
+ align:start position:0%
+some of the types of RNA and the sugar
+ 
+
+ align:start position:0%
+some of the types of RNA and the sugar
+is a ribose so the first main thing
+
+ align:start position:0%
+is a ribose so the first main thing
+ 
+
+ align:start position:0%
+is a ribose so the first main thing
+about the RNA copy relative to the DNA
+
+ align:start position:0%
+about the RNA copy relative to the DNA
+ 
+
+ align:start position:0%
+about the RNA copy relative to the DNA
+copy is that ribose deoxyribose
+
+ align:start position:0%
+copy is that ribose deoxyribose
+ 
+
+ align:start position:0%
+copy is that ribose deoxyribose
+difference what's quite remarkable is
+
+ align:start position:0%
+difference what's quite remarkable is
+ 
+
+ align:start position:0%
+difference what's quite remarkable is
+that when you have two deoxyribose in
+
+ align:start position:0%
+that when you have two deoxyribose in
+ 
+
+ align:start position:0%
+that when you have two deoxyribose in
+your DNA it's nice and stable we need it
+
+ align:start position:0%
+your DNA it's nice and stable we need it
+ 
+
+ align:start position:0%
+your DNA it's nice and stable we need it
+to be nice and stable
+
+ align:start position:0%
+to be nice and stable
+ 
+
+ align:start position:0%
+to be nice and stable
+it's our genome we can't let our genome
+
+ align:start position:0%
+it's our genome we can't let our genome
+ 
+
+ align:start position:0%
+it's our genome we can't let our genome
+be falling apart as we're sort of
+
+ align:start position:0%
+be falling apart as we're sort of
+ 
+
+ align:start position:0%
+be falling apart as we're sort of
+walking down the street in contrast when
+
+ align:start position:0%
+walking down the street in contrast when
+ 
+
+ align:start position:0%
+walking down the street in contrast when
+RNA is used it's much more transient we
+
+ align:start position:0%
+RNA is used it's much more transient we
+ 
+
+ align:start position:0%
+RNA is used it's much more transient we
+make a messenger RNA copy of part of DNA
+
+ align:start position:0%
+make a messenger RNA copy of part of DNA
+ 
+
+ align:start position:0%
+make a messenger RNA copy of part of DNA
+to move forward to make proteins but we
+
+ align:start position:0%
+to move forward to make proteins but we
+ 
+
+ align:start position:0%
+to move forward to make proteins but we
+don't need that to stick around forever
+
+ align:start position:0%
+don't need that to stick around forever
+ 
+
+ align:start position:0%
+don't need that to stick around forever
+and when you have the ribose with the 2
+
+ align:start position:0%
+and when you have the ribose with the 2
+ 
+
+ align:start position:0%
+and when you have the ribose with the 2
+hydroxyl zat 2 & 3 it's a much more
+
+ align:start position:0%
+hydroxyl zat 2 & 3 it's a much more
+ 
+
+ align:start position:0%
+hydroxyl zat 2 & 3 it's a much more
+fragile material it is a transient
+
+ align:start position:0%
+fragile material it is a transient
+ 
+
+ align:start position:0%
+fragile material it is a transient
+message and it's got it gets degraded
+
+ align:start position:0%
+message and it's got it gets degraded
+ 
+
+ align:start position:0%
+message and it's got it gets degraded
+quite quickly so that difference in the
+
+ align:start position:0%
+quite quickly so that difference in the
+ 
+
+ align:start position:0%
+quite quickly so that difference in the
+sugar really dictates the stability that
+
+ align:start position:0%
+sugar really dictates the stability that
+ 
+
+ align:start position:0%
+sugar really dictates the stability that
+RNA is found in a lot of polymers
+
+ align:start position:0%
+RNA is found in a lot of polymers
+ 
+
+ align:start position:0%
+RNA is found in a lot of polymers
+biopolymers will talk will focus mostly
+
+ align:start position:0%
+biopolymers will talk will focus mostly
+ 
+
+ align:start position:0%
+biopolymers will talk will focus mostly
+on the messenger RNA and RNA today it's
+
+ align:start position:0%
+on the messenger RNA and RNA today it's
+ 
+
+ align:start position:0%
+on the messenger RNA and RNA today it's
+about 1 less than 1% of the DNA and then
+
+ align:start position:0%
+about 1 less than 1% of the DNA and then
+ 
+
+ align:start position:0%
+about 1 less than 1% of the DNA and then
+on Friday we'll be talking about the
+
+ align:start position:0%
+on Friday we'll be talking about the
+ 
+
+ align:start position:0%
+on Friday we'll be talking about the
+transfer RNA and the ribosomal RNA so
+
+ align:start position:0%
+transfer RNA and the ribosomal RNA so
+ 
+
+ align:start position:0%
+transfer RNA and the ribosomal RNA so
+we're really gonna focus in right now on
+
+ align:start position:0%
+we're really gonna focus in right now on
+ 
+
+ align:start position:0%
+we're really gonna focus in right now on
+the messenger RNA and the one thing
+
+ align:start position:0%
+the messenger RNA and the one thing
+ 
+
+ align:start position:0%
+the messenger RNA and the one thing
+about RNA structures I'm will elaborate
+
+ align:start position:0%
+about RNA structures I'm will elaborate
+ 
+
+ align:start position:0%
+about RNA structures I'm will elaborate
+later is they have very different
+
+ align:start position:0%
+later is they have very different
+ 
+
+ align:start position:0%
+later is they have very different
+structures two canonical DNA which are
+
+ align:start position:0%
+structures two canonical DNA which are
+ 
+
+ align:start position:0%
+structures two canonical DNA which are
+drops the double-stranded anti parallel
+
+ align:start position:0%
+drops the double-stranded anti parallel
+ 
+
+ align:start position:0%
+drops the double-stranded anti parallel
+structure RNA structures are much more
+
+ align:start position:0%
+structure RNA structures are much more
+ 
+
+ align:start position:0%
+structure RNA structures are much more
+like folded protein structures where
+
+ align:start position:0%
+like folded protein structures where
+ 
+
+ align:start position:0%
+like folded protein structures where
+there may be sections of base pairing
+
+ align:start position:0%
+there may be sections of base pairing
+ 
+
+ align:start position:0%
+there may be sections of base pairing
+but there'll also be lots of loops and
+
+ align:start position:0%
+but there'll also be lots of loops and
+ 
+
+ align:start position:0%
+but there'll also be lots of loops and
+different characteristics so even the
+
+ align:start position:0%
+different characteristics so even the
+ 
+
+ align:start position:0%
+different characteristics so even the
+ribose structure makes a difference in
+
+ align:start position:0%
+ribose structure makes a difference in
+ 
+
+ align:start position:0%
+ribose structure makes a difference in
+the stability of the double-stranded
+
+ align:start position:0%
+the stability of the double-stranded
+ 
+
+ align:start position:0%
+the stability of the double-stranded
+structure and encourages a lot more of
+
+ align:start position:0%
+structure and encourages a lot more of
+ 
+
+ align:start position:0%
+structure and encourages a lot more of
+these unusual structures which
+
+ align:start position:0%
+these unusual structures which
+ 
+
+ align:start position:0%
+these unusual structures which
+really why people have a lot of faith in
+
+ align:start position:0%
+really why people have a lot of faith in
+ 
+
+ align:start position:0%
+really why people have a lot of faith in
+the in the theories about the RNA world
+
+ align:start position:0%
+the in the theories about the RNA world
+ 
+
+ align:start position:0%
+the in the theories about the RNA world
+okay so let's look at DNA polymerase RNA
+
+ align:start position:0%
+okay so let's look at DNA polymerase RNA
+ 
+
+ align:start position:0%
+okay so let's look at DNA polymerase RNA
+polymerase so here's the here's all the
+
+ align:start position:0%
+polymerase so here's the here's all the
+ 
+
+ align:start position:0%
+polymerase so here's the here's all the
+good news that we'll be able to describe
+
+ align:start position:0%
+good news that we'll be able to describe
+ 
+
+ align:start position:0%
+good news that we'll be able to describe
+to you okay so when you copy DNA you
+
+ align:start position:0%
+to you okay so when you copy DNA you
+ 
+
+ align:start position:0%
+to you okay so when you copy DNA you
+copy all of it when you copy RNA you
+
+ align:start position:0%
+copy all of it when you copy RNA you
+ 
+
+ align:start position:0%
+copy all of it when you copy RNA you
+only copy when you make the copy of
+
+ align:start position:0%
+only copy when you make the copy of
+ 
+
+ align:start position:0%
+only copy when you make the copy of
+messenger RNA you only copy about 1.5
+
+ align:start position:0%
+messenger RNA you only copy about 1.5
+ 
+
+ align:start position:0%
+messenger RNA you only copy about 1.5
+percent of the genome so you do not copy
+
+ align:start position:0%
+percent of the genome so you do not copy
+ 
+
+ align:start position:0%
+percent of the genome so you do not copy
+the entire thing so the process is much
+
+ align:start position:0%
+the entire thing so the process is much
+ 
+
+ align:start position:0%
+the entire thing so the process is much
+more restricted to sections of DNA that
+
+ align:start position:0%
+more restricted to sections of DNA that
+ 
+
+ align:start position:0%
+more restricted to sections of DNA that
+needs to be copied and we'll talk about
+
+ align:start position:0%
+needs to be copied and we'll talk about
+ 
+
+ align:start position:0%
+needs to be copied and we'll talk about
+the the features of the DNA that tell
+
+ align:start position:0%
+the the features of the DNA that tell
+ 
+
+ align:start position:0%
+the the features of the DNA that tell
+you about that later okay here's the
+
+ align:start position:0%
+you about that later okay here's the
+ 
+
+ align:start position:0%
+you about that later okay here's the
+important details so in eukaryotes
+
+ align:start position:0%
+important details so in eukaryotes
+ 
+
+ align:start position:0%
+important details so in eukaryotes
+transcription happens in the nucleus and
+
+ align:start position:0%
+transcription happens in the nucleus and
+ 
+
+ align:start position:0%
+transcription happens in the nucleus and
+the key enzyme involved is RNA
+
+ align:start position:0%
+the key enzyme involved is RNA
+ 
+
+ align:start position:0%
+the key enzyme involved is RNA
+polymerase RNA pol and there it has very
+
+ align:start position:0%
+polymerase RNA pol and there it has very
+ 
+
+ align:start position:0%
+polymerase RNA pol and there it has very
+different features to DNA polymerase but
+
+ align:start position:0%
+different features to DNA polymerase but
+ 
+
+ align:start position:0%
+different features to DNA polymerase but
+there are two big things that are
+
+ align:start position:0%
+there are two big things that are
+ 
+
+ align:start position:0%
+there are two big things that are
+different it includes its own helicase
+
+ align:start position:0%
+different it includes its own helicase
+ 
+
+ align:start position:0%
+different it includes its own helicase
+so you remember with replication we
+
+ align:start position:0%
+so you remember with replication we
+ 
+
+ align:start position:0%
+so you remember with replication we
+needed a DNA polymerase and the helicase
+
+ align:start position:0%
+needed a DNA polymerase and the helicase
+ 
+
+ align:start position:0%
+needed a DNA polymerase and the helicase
+RNA polymerase is much smarter than that
+
+ align:start position:0%
+RNA polymerase is much smarter than that
+ 
+
+ align:start position:0%
+RNA polymerase is much smarter than that
+it actually includes both functions
+
+ align:start position:0%
+it actually includes both functions
+ 
+
+ align:start position:0%
+it actually includes both functions
+within its structure so it's an RNA
+
+ align:start position:0%
+within its structure so it's an RNA
+ 
+
+ align:start position:0%
+within its structure so it's an RNA
+polymerase the grows the new nucleotide
+
+ align:start position:0%
+polymerase the grows the new nucleotide
+ 
+
+ align:start position:0%
+polymerase the grows the new nucleotide
+5 prime to 3 prime but it also has a
+
+ align:start position:0%
+5 prime to 3 prime but it also has a
+ 
+
+ align:start position:0%
+5 prime to 3 prime but it also has a
+built-in helicase so that's an advantage
+
+ align:start position:0%
+built-in helicase so that's an advantage
+ 
+
+ align:start position:0%
+built-in helicase so that's an advantage
+it still grows the messenger RNA 5 prime
+
+ align:start position:0%
+it still grows the messenger RNA 5 prime
+ 
+
+ align:start position:0%
+it still grows the messenger RNA 5 prime
+to 3 prime but it uses the different
+
+ align:start position:0%
+to 3 prime but it uses the different
+ 
+
+ align:start position:0%
+to 3 prime but it uses the different
+nucleotide triphosphate building blocks
+
+ align:start position:0%
+nucleotide triphosphate building blocks
+ 
+
+ align:start position:0%
+nucleotide triphosphate building blocks
+or one of them is different so UTP ATP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember that you replaces the T in
+
+ align:start position:0%
+so remember that you replaces the T in
+ 
+
+ align:start position:0%
+so remember that you replaces the T in
+RNA so that's one key difference it
+
+ align:start position:0%
+RNA so that's one key difference it
+ 
+
+ align:start position:0%
+RNA so that's one key difference it
+includes a helicase activity and the
+
+ align:start position:0%
+includes a helicase activity and the
+ 
+
+ align:start position:0%
+includes a helicase activity and the
+other really neat things because it's
+
+ align:start position:0%
+other really neat things because it's
+ 
+
+ align:start position:0%
+other really neat things because it's
+such a complication in replication is it
+
+ align:start position:0%
+such a complication in replication is it
+ 
+
+ align:start position:0%
+such a complication in replication is it
+doesn't require a primer that is why
+
+ align:start position:0%
+doesn't require a primer that is why
+ 
+
+ align:start position:0%
+doesn't require a primer that is why
+even when we were replicating the DNA we
+
+ align:start position:0%
+even when we were replicating the DNA we
+ 
+
+ align:start position:0%
+even when we were replicating the DNA we
+were using RNA polymerase to make those
+
+ align:start position:0%
+were using RNA polymerase to make those
+ 
+
+ align:start position:0%
+were using RNA polymerase to make those
+little pieces of primers because it
+
+ align:start position:0%
+little pieces of primers because it
+ 
+
+ align:start position:0%
+little pieces of primers because it
+didn't need prior priming sequence so
+
+ align:start position:0%
+didn't need prior priming sequence so
+ 
+
+ align:start position:0%
+didn't need prior priming sequence so
+there's a really fundamental difference
+
+ align:start position:0%
+there's a really fundamental difference
+ 
+
+ align:start position:0%
+there's a really fundamental difference
+is about the RNA polymerase and then the
+
+ align:start position:0%
+is about the RNA polymerase and then the
+ 
+
+ align:start position:0%
+is about the RNA polymerase and then the
+other thing is that only one of the two
+
+ align:start position:0%
+other thing is that only one of the two
+ 
+
+ align:start position:0%
+other thing is that only one of the two
+strands of DNA is transcribed and in a
+
+ align:start position:0%
+strands of DNA is transcribed and in a
+ 
+
+ align:start position:0%
+strands of DNA is transcribed and in a
+moment or maybe the beginning of next
+
+ align:start position:0%
+moment or maybe the beginning of next
+ 
+
+ align:start position:0%
+moment or maybe the beginning of next
+husk will judge how we can understand
+
+ align:start position:0%
+husk will judge how we can understand
+ 
+
+ align:start position:0%
+husk will judge how we can understand
+which sequence is transcribed and then
+
+ align:start position:0%
+which sequence is transcribed and then
+ 
+
+ align:start position:0%
+which sequence is transcribed and then
+obviously the messenger RNA is a
+
+ align:start position:0%
+obviously the messenger RNA is a
+ 
+
+ align:start position:0%
+obviously the messenger RNA is a
+complementary sequence to the sequence
+
+ align:start position:0%
+complementary sequence to the sequence
+ 
+
+ align:start position:0%
+complementary sequence to the sequence
+of DNA that is being copied
+
+ align:start position:0%
+of DNA that is being copied
+ 
+
+ align:start position:0%
+of DNA that is being copied
+finally only part of the DNA is
+
+ align:start position:0%
+finally only part of the DNA is
+ 
+
+ align:start position:0%
+finally only part of the DNA is
+transcribed under unlike the process of
+
+ align:start position:0%
+transcribed under unlike the process of
+ 
+
+ align:start position:0%
+transcribed under unlike the process of
+replication all right so you can see
+
+ align:start position:0%
+replication all right so you can see
+ 
+
+ align:start position:0%
+replication all right so you can see
+already that there are a lot of
+
+ align:start position:0%
+already that there are a lot of
+ 
+
+ align:start position:0%
+already that there are a lot of
+simplifications in transcription that we
+
+ align:start position:0%
+simplifications in transcription that we
+ 
+
+ align:start position:0%
+simplifications in transcription that we
+did not have the advantage of in
+
+ align:start position:0%
+did not have the advantage of in
+ 
+
+ align:start position:0%
+did not have the advantage of in
+replication so the helicase activity and
+
+ align:start position:0%
+replication so the helicase activity and
+ 
+
+ align:start position:0%
+replication so the helicase activity and
+the primer issue are two key features
+
+ align:start position:0%
+the primer issue are two key features
+ 
+
+ align:start position:0%
+the primer issue are two key features
+the mate life a lot simpler I just
+
+ align:start position:0%
+the mate life a lot simpler I just
+ 
+
+ align:start position:0%
+the mate life a lot simpler I just
+wanted to show you this small detail
+
+ align:start position:0%
+wanted to show you this small detail
+ 
+
+ align:start position:0%
+wanted to show you this small detail
+about RNA polymerase there are a lot of
+
+ align:start position:0%
+about RNA polymerase there are a lot of
+ 
+
+ align:start position:0%
+about RNA polymerase there are a lot of
+natural products out there that are
+
+ align:start position:0%
+natural products out there that are
+ 
+
+ align:start position:0%
+natural products out there that are
+known to be inhibitors of vital
+
+ align:start position:0%
+known to be inhibitors of vital
+ 
+
+ align:start position:0%
+known to be inhibitors of vital
+processes and one that caught my eye is
+
+ align:start position:0%
+processes and one that caught my eye is
+ 
+
+ align:start position:0%
+processes and one that caught my eye is
+the the ends I of the small molecules
+
+ align:start position:0%
+the the ends I of the small molecules
+ 
+
+ align:start position:0%
+the the ends I of the small molecules
+that are found in mushrooms the really
+
+ align:start position:0%
+that are found in mushrooms the really
+ 
+
+ align:start position:0%
+that are found in mushrooms the really
+toxic mushrooms when you see some of
+
+ align:start position:0%
+toxic mushrooms when you see some of
+ 
+
+ align:start position:0%
+toxic mushrooms when you see some of
+these in fact never eat a mushroom that
+
+ align:start position:0%
+these in fact never eat a mushroom that
+ 
+
+ align:start position:0%
+these in fact never eat a mushroom that
+that you don't know and you know where
+
+ align:start position:0%
+that you don't know and you know where
+ 
+
+ align:start position:0%
+that you don't know and you know where
+it came from because there's problems
+
+ align:start position:0%
+it came from because there's problems
+ 
+
+ align:start position:0%
+it came from because there's problems
+with them because a lot of these
+
+ align:start position:0%
+with them because a lot of these
+ 
+
+ align:start position:0%
+with them because a lot of these
+mushrooms include potent natural
+
+ align:start position:0%
+mushrooms include potent natural
+ 
+
+ align:start position:0%
+mushrooms include potent natural
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+and in fact there's a compound known as
+
+ align:start position:0%
+and in fact there's a compound known as
+ 
+
+ align:start position:0%
+and in fact there's a compound known as
+a Manton alpha a mountain and it's found
+
+ align:start position:0%
+a Manton alpha a mountain and it's found
+ 
+
+ align:start position:0%
+a Manton alpha a mountain and it's found
+in a in certain mushrooms known as
+
+ align:start position:0%
+in a in certain mushrooms known as
+ 
+
+ align:start position:0%
+in a in certain mushrooms known as
+either the death cap or destroying angel
+
+ align:start position:0%
+either the death cap or destroying angel
+ 
+
+ align:start position:0%
+either the death cap or destroying angel
+mushrooms so you could tell from their
+
+ align:start position:0%
+mushrooms so you could tell from their
+ 
+
+ align:start position:0%
+mushrooms so you could tell from their
+names that they are a real problem and
+
+ align:start position:0%
+names that they are a real problem and
+ 
+
+ align:start position:0%
+names that they are a real problem and
+what the mountain does is it actually
+
+ align:start position:0%
+what the mountain does is it actually
+ 
+
+ align:start position:0%
+what the mountain does is it actually
+interferes directly with RNA polymerase
+
+ align:start position:0%
+interferes directly with RNA polymerase
+ 
+
+ align:start position:0%
+interferes directly with RNA polymerase
+by acting as an allosteric inhibitor of
+
+ align:start position:0%
+by acting as an allosteric inhibitor of
+ 
+
+ align:start position:0%
+by acting as an allosteric inhibitor of
+RNA polymerase and locking it into a
+
+ align:start position:0%
+RNA polymerase and locking it into a
+ 
+
+ align:start position:0%
+RNA polymerase and locking it into a
+closed state so it can't keep on
+
+ align:start position:0%
+closed state so it can't keep on
+ 
+
+ align:start position:0%
+closed state so it can't keep on
+transcribing so I thought this was very
+
+ align:start position:0%
+transcribing so I thought this was very
+ 
+
+ align:start position:0%
+transcribing so I thought this was very
+interesting incredibly like one you know
+
+ align:start position:0%
+interesting incredibly like one you know
+ 
+
+ align:start position:0%
+interesting incredibly like one you know
+tiny tiny tiny doses will hold a rest
+
+ align:start position:0%
+tiny tiny tiny doses will hold a rest
+ 
+
+ align:start position:0%
+tiny tiny tiny doses will hold a rest
+transcription and cause your and cause
+
+ align:start position:0%
+transcription and cause your and cause
+ 
+
+ align:start position:0%
+transcription and cause your and cause
+dire consequences so I think what's very
+
+ align:start position:0%
+dire consequences so I think what's very
+ 
+
+ align:start position:0%
+dire consequences so I think what's very
+interesting is that it's it's an
+
+ align:start position:0%
+interesting is that it's it's an
+ 
+
+ align:start position:0%
+interesting is that it's it's an
+allosteric inhibitor it's very potent
+
+ align:start position:0%
+allosteric inhibitor it's very potent
+ 
+
+ align:start position:0%
+allosteric inhibitor it's very potent
+and what it does is it seals the
+
+ align:start position:0%
+and what it does is it seals the
+ 
+
+ align:start position:0%
+and what it does is it seals the
+polymerase in a locked closed state that
+
+ align:start position:0%
+polymerase in a locked closed state that
+ 
+
+ align:start position:0%
+polymerase in a locked closed state that
+it can't move forward for transcriptions
+
+ align:start position:0%
+it can't move forward for transcriptions
+ 
+
+ align:start position:0%
+it can't move forward for transcriptions
+okay now finally the couple of points
+
+ align:start position:0%
+okay now finally the couple of points
+ 
+
+ align:start position:0%
+okay now finally the couple of points
+when we decide that a portion of gene is
+
+ align:start position:0%
+when we decide that a portion of gene is
+ 
+
+ align:start position:0%
+when we decide that a portion of gene is
+going to be transcribed there are a lot
+
+ align:start position:0%
+going to be transcribed there are a lot
+ 
+
+ align:start position:0%
+going to be transcribed there are a lot
+of mechanisms in place to identify the
+
+ align:start position:0%
+of mechanisms in place to identify the
+ 
+
+ align:start position:0%
+of mechanisms in place to identify the
+portion of that gene and one of the key
+
+ align:start position:0%
+portion of that gene and one of the key
+ 
+
+ align:start position:0%
+portion of that gene and one of the key
+things that is known is that there are
+
+ align:start position:0%
+things that is known is that there are
+ 
+
+ align:start position:0%
+things that is known is that there are
+what are called promoter sites which are
+
+ align:start position:0%
+what are called promoter sites which are
+ 
+
+ align:start position:0%
+what are called promoter sites which are
+actually upstream of the portion of gene
+
+ align:start position:0%
+actually upstream of the portion of gene
+ 
+
+ align:start position:0%
+actually upstream of the portion of gene
+that's to be transcribed where you
+
+ align:start position:0%
+that's to be transcribed where you
+ 
+
+ align:start position:0%
+that's to be transcribed where you
+recruit a bunch of proteins that
+
+ align:start position:0%
+recruit a bunch of proteins that
+ 
+
+ align:start position:0%
+recruit a bunch of proteins that
+actually Park down on the
+
+ align:start position:0%
+actually Park down on the
+ 
+
+ align:start position:0%
+actually Park down on the
+double-stranded DNA and then at the end
+
+ align:start position:0%
+double-stranded DNA and then at the end
+ 
+
+ align:start position:0%
+double-stranded DNA and then at the end
+of the day recruits the RNA polymerase
+
+ align:start position:0%
+of the day recruits the RNA polymerase
+ 
+
+ align:start position:0%
+of the day recruits the RNA polymerase
+so all that extra genome some of it is
+
+ align:start position:0%
+so all that extra genome some of it is
+ 
+
+ align:start position:0%
+so all that extra genome some of it is
+not transcribed into messenger RNA for
+
+ align:start position:0%
+not transcribed into messenger RNA for
+ 
+
+ align:start position:0%
+not transcribed into messenger RNA for
+making proteins but it's part of an area
+
+ align:start position:0%
+making proteins but it's part of an area
+ 
+
+ align:start position:0%
+making proteins but it's part of an area
+of the gene that gets recognized by all
+
+ align:start position:0%
+of the gene that gets recognized by all
+ 
+
+ align:start position:0%
+of the gene that gets recognized by all
+of the proteins that collaborate to
+
+ align:start position:0%
+of the proteins that collaborate to
+ 
+
+ align:start position:0%
+of the proteins that collaborate to
+bring in the RNA polymerase in order for
+
+ align:start position:0%
+bring in the RNA polymerase in order for
+ 
+
+ align:start position:0%
+bring in the RNA polymerase in order for
+your RNA to be transcribed so what I'm
+
+ align:start position:0%
+your RNA to be transcribed so what I'm
+ 
+
+ align:start position:0%
+your RNA to be transcribed so what I'm
+showing you here is a stranded
+
+ align:start position:0%
+showing you here is a stranded
+ 
+
+ align:start position:0%
+showing you here is a stranded
+double-stranded DNA with one of the very
+
+ align:start position:0%
+double-stranded DNA with one of the very
+ 
+
+ align:start position:0%
+double-stranded DNA with one of the very
+common promoters that's just upstream of
+
+ align:start position:0%
+common promoters that's just upstream of
+ 
+
+ align:start position:0%
+common promoters that's just upstream of
+the part of the DNA that gets
+
+ align:start position:0%
+the part of the DNA that gets
+ 
+
+ align:start position:0%
+the part of the DNA that gets
+transcribed and it's called the tata box
+
+ align:start position:0%
+transcribed and it's called the tata box
+ 
+
+ align:start position:0%
+transcribed and it's called the tata box
+because it's ta ta sequence it's
+
+ align:start position:0%
+because it's ta ta sequence it's
+ 
+
+ align:start position:0%
+because it's ta ta sequence it's
+appalling it's got a complement that
+
+ align:start position:0%
+appalling it's got a complement that
+ 
+
+ align:start position:0%
+appalling it's got a complement that
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+and it's shown in pink here and then the
+
+ align:start position:0%
+and it's shown in pink here and then the
+ 
+
+ align:start position:0%
+and it's shown in pink here and then the
+ends I are the proteins that bind to the
+
+ align:start position:0%
+ends I are the proteins that bind to the
+ 
+
+ align:start position:0%
+ends I are the proteins that bind to the
+DNA at the tata box actually drape over
+
+ align:start position:0%
+DNA at the tata box actually drape over
+ 
+
+ align:start position:0%
+DNA at the tata box actually drape over
+that segment of double-stranded DNA and
+
+ align:start position:0%
+that segment of double-stranded DNA and
+ 
+
+ align:start position:0%
+that segment of double-stranded DNA and
+then serve as recruitment entities to
+
+ align:start position:0%
+then serve as recruitment entities to
+ 
+
+ align:start position:0%
+then serve as recruitment entities to
+bring in all the machinery that's needed
+
+ align:start position:0%
+bring in all the machinery that's needed
+ 
+
+ align:start position:0%
+bring in all the machinery that's needed
+for transcription of the gene beyond it
+
+ align:start position:0%
+for transcription of the gene beyond it
+ 
+
+ align:start position:0%
+for transcription of the gene beyond it
+so some of the identity of all that
+
+ align:start position:0%
+so some of the identity of all that
+ 
+
+ align:start position:0%
+so some of the identity of all that
+extra double-stranded DNA is actually as
+
+ align:start position:0%
+extra double-stranded DNA is actually as
+ 
+
+ align:start position:0%
+extra double-stranded DNA is actually as
+guide places to guide where the
+
+ align:start position:0%
+guide places to guide where the
+ 
+
+ align:start position:0%
+guide places to guide where the
+machinery for transcription has to Park
+
+ align:start position:0%
+machinery for transcription has to Park
+ 
+
+ align:start position:0%
+machinery for transcription has to Park
+in order for a messenger RNA to be
+
+ align:start position:0%
+in order for a messenger RNA to be
+ 
+
+ align:start position:0%
+in order for a messenger RNA to be
+formed so immediately you can see we're
+
+ align:start position:0%
+formed so immediately you can see we're
+ 
+
+ align:start position:0%
+formed so immediately you can see we're
+only going to transcribe part of this
+
+ align:start position:0%
+only going to transcribe part of this
+ 
+
+ align:start position:0%
+only going to transcribe part of this
+genetic material beyond here but we need
+
+ align:start position:0%
+genetic material beyond here but we need
+ 
+
+ align:start position:0%
+genetic material beyond here but we need
+a whole bunch of genetic material that's
+
+ align:start position:0%
+a whole bunch of genetic material that's
+ 
+
+ align:start position:0%
+a whole bunch of genetic material that's
+actually just serving as sort of the
+
+ align:start position:0%
+actually just serving as sort of the
+ 
+
+ align:start position:0%
+actually just serving as sort of the
+runway for the plane landing in the
+
+ align:start position:0%
+runway for the plane landing in the
+ 
+
+ align:start position:0%
+runway for the plane landing in the
+right position all right so I'm going to
+
+ align:start position:0%
+right position all right so I'm going to
+ 
+
+ align:start position:0%
+right position all right so I'm going to
+put up the puzzle that you can think
+
+ align:start position:0%
+put up the puzzle that you can think
+ 
+
+ align:start position:0%
+put up the puzzle that you can think
+about and then we'll start with these at
+
+ align:start position:0%
+about and then we'll start with these at
+ 
+
+ align:start position:0%
+about and then we'll start with these at
+the beginning of the next class because
+
+ align:start position:0%
+the beginning of the next class because
+ 
+
+ align:start position:0%
+the beginning of the next class because
+I don't want to rush them when you
+
+ align:start position:0%
+I don't want to rush them when you
+ 
+
+ align:start position:0%
+I don't want to rush them when you
+decide to transcribe a gene let's say
+
+ align:start position:0%
+decide to transcribe a gene let's say
+ 
+
+ align:start position:0%
+decide to transcribe a gene let's say
+you've got a promoter site here the
+
+ align:start position:0%
+you've got a promoter site here the
+ 
+
+ align:start position:0%
+you've got a promoter site here the
+thing that I want you to think about is
+
+ align:start position:0%
+thing that I want you to think about is
+ 
+
+ align:start position:0%
+thing that I want you to think about is
+which strand would you transcribe and
+
+ align:start position:0%
+which strand would you transcribe and
+ 
+
+ align:start position:0%
+which strand would you transcribe and
+what's the logic behind this and then
+
+ align:start position:0%
+what's the logic behind this and then
+ 
+
+ align:start position:0%
+what's the logic behind this and then
+we'll just do a recap on this at the
+
+ align:start position:0%
+we'll just do a recap on this at the
+ 
+
+ align:start position:0%
+we'll just do a recap on this at the
+beginning of the next class because I
+
+ align:start position:0%
+beginning of the next class because I
+ 
+
+ align:start position:0%
+beginning of the next class because I
+just want you to think about it because
+
+ align:start position:0%
+just want you to think about it because
+ 
+
+ align:start position:0%
+just want you to think about it because
+the information a lot of the information
+
+ align:start position:0%
+the information a lot of the information
+ 
+
+ align:start position:0%
+the information a lot of the information
+you need is directly here hi there we're
+
+ align:start position:0%
+you need is directly here hi there we're
+ 
+
+ align:start position:0%
+you need is directly here hi there we're
+just wrapping up okay so that's it for
+
+ align:start position:0%
+just wrapping up okay so that's it for
+ 
+
+ align:start position:0%
+just wrapping up okay so that's it for
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/azzrfdysfI0.txt b/azzrfdysfI0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d07a5a81c5e2a838d506955750d16e7bce7dd68e
--- /dev/null
+++ b/azzrfdysfI0.txt
@@ -0,0 +1,2019 @@
+align:start position:0%
+ 
+okay here's the well the title slide I
+
+ align:start position:0%
+okay here's the well the title slide I
+ 
+
+ align:start position:0%
+okay here's the well the title slide I
+sense this year happen to be 2020 and
+
+ align:start position:0%
+sense this year happen to be 2020 and
+ 
+
+ align:start position:0%
+sense this year happen to be 2020 and
+that means clear vision I thought I'd
+
+ align:start position:0%
+that means clear vision I thought I'd
+ 
+
+ align:start position:0%
+that means clear vision I thought I'd
+get that into the title of this these
+
+ align:start position:0%
+get that into the title of this these
+ 
+
+ align:start position:0%
+get that into the title of this these
+slides and then you've seen in these six
+
+ align:start position:0%
+slides and then you've seen in these six
+ 
+
+ align:start position:0%
+slides and then you've seen in these six
+pieces as a sort of look ahead and I'm
+
+ align:start position:0%
+pieces as a sort of look ahead and I'm
+ 
+
+ align:start position:0%
+pieces as a sort of look ahead and I'm
+gonna start on that first piece a equals
+
+ align:start position:0%
+gonna start on that first piece a equals
+ 
+
+ align:start position:0%
+gonna start on that first piece a equals
+CR that's the new way I like to start
+
+ align:start position:0%
+CR that's the new way I like to start
+ 
+
+ align:start position:0%
+CR that's the new way I like to start
+teaching linear algebra and I'll tell
+
+ align:start position:0%
+teaching linear algebra and I'll tell
+ 
+
+ align:start position:0%
+teaching linear algebra and I'll tell
+you why okay oh here we have a few
+
+ align:start position:0%
+you why okay oh here we have a few
+ 
+
+ align:start position:0%
+you why okay oh here we have a few
+examples well that will lead to our
+
+ align:start position:0%
+examples well that will lead to our
+ 
+
+ align:start position:0%
+examples well that will lead to our
+ideas you see that matrix a zero a
+
+ align:start position:0%
+ideas you see that matrix a zero a
+ 
+
+ align:start position:0%
+ideas you see that matrix a zero a
+matrix is just a square or rectangle of
+
+ align:start position:0%
+matrix is just a square or rectangle of
+ 
+
+ align:start position:0%
+matrix is just a square or rectangle of
+numbers and but those are those numbers
+
+ align:start position:0%
+numbers and but those are those numbers
+ 
+
+ align:start position:0%
+numbers and but those are those numbers
+have special features if you look
+
+ align:start position:0%
+have special features if you look
+ 
+
+ align:start position:0%
+have special features if you look
+closely well you see 1 3 2 as row 1 and
+
+ align:start position:0%
+closely well you see 1 3 2 as row 1 and
+ 
+
+ align:start position:0%
+closely well you see 1 3 2 as row 1 and
+then what do you see for Row 3 2 6 4 and
+
+ align:start position:0%
+then what do you see for Row 3 2 6 4 and
+ 
+
+ align:start position:0%
+then what do you see for Row 3 2 6 4 and
+there's like those are - those are two
+
+ align:start position:0%
+there's like those are - those are two
+ 
+
+ align:start position:0%
+there's like those are - those are two
+vectors in the same direction why is
+
+ align:start position:0%
+vectors in the same direction why is
+ 
+
+ align:start position:0%
+vectors in the same direction why is
+that because 2 6 4 is exactly 2 times 1
+
+ align:start position:0%
+that because 2 6 4 is exactly 2 times 1
+ 
+
+ align:start position:0%
+that because 2 6 4 is exactly 2 times 1
+3 2 and in the middle there is 4 times 1
+
+ align:start position:0%
+3 2 and in the middle there is 4 times 1
+ 
+
+ align:start position:0%
+3 2 and in the middle there is 4 times 1
+3 2 so I have 3 rows in the same
+
+ align:start position:0%
+3 2 so I have 3 rows in the same
+ 
+
+ align:start position:0%
+3 2 so I have 3 rows in the same
+direction and actually also this is the
+
+ align:start position:0%
+direction and actually also this is the
+ 
+
+ align:start position:0%
+direction and actually also this is the
+MAGIX can I tell you this right at the
+
+ align:start position:0%
+MAGIX can I tell you this right at the
+ 
+
+ align:start position:0%
+MAGIX can I tell you this right at the
+start their columns look at the columns
+
+ align:start position:0%
+start their columns look at the columns
+ 
+
+ align:start position:0%
+start their columns look at the columns
+1 for 2 if I multiply that by 3 I get 3
+
+ align:start position:0%
+1 for 2 if I multiply that by 3 I get 3
+ 
+
+ align:start position:0%
+1 for 2 if I multiply that by 3 I get 3
+12 6 if I multiply it by 2 I get 2 8 4
+
+ align:start position:0%
+12 6 if I multiply it by 2 I get 2 8 4
+ 
+
+ align:start position:0%
+12 6 if I multiply it by 2 I get 2 8 4
+so sometimes somehow magically the
+
+ align:start position:0%
+so sometimes somehow magically the
+ 
+
+ align:start position:0%
+so sometimes somehow magically the
+columns are in the same direction
+
+ align:start position:0%
+columns are in the same direction
+ 
+
+ align:start position:0%
+columns are in the same direction
+exactly when the rows are in the same
+
+ align:start position:0%
+exactly when the rows are in the same
+ 
+
+ align:start position:0%
+exactly when the rows are in the same
+direction they're different
+
+ align:start position:0%
+direction they're different
+ 
+
+ align:start position:0%
+direction they're different
+that's what linear algebra is about the
+
+ align:start position:0%
+that's what linear algebra is about the
+ 
+
+ align:start position:0%
+that's what linear algebra is about the
+relations between columns and rows okay
+
+ align:start position:0%
+relations between columns and rows okay
+ 
+
+ align:start position:0%
+relations between columns and rows okay
+and here well here's another one I'll
+
+ align:start position:0%
+and here well here's another one I'll
+ 
+
+ align:start position:0%
+and here well here's another one I'll
+look at there again you see rho1 plus
+
+ align:start position:0%
+look at there again you see rho1 plus
+ 
+
+ align:start position:0%
+look at there again you see rho1 plus
+rho2 equal Row 3 so it's not quite like
+
+ align:start position:0%
+rho2 equal Row 3 so it's not quite like
+ 
+
+ align:start position:0%
+rho2 equal Row 3 so it's not quite like
+this where every row was a was in the
+
+ align:start position:0%
+this where every row was a was in the
+ 
+
+ align:start position:0%
+this where every row was a was in the
+same direction but here's if I add rows
+
+ align:start position:0%
+same direction but here's if I add rows
+ 
+
+ align:start position:0%
+same direction but here's if I add rows
+1 & 2 I get Row 3 so that's a matrix of
+
+ align:start position:0%
+1 & 2 I get Row 3 so that's a matrix of
+ 
+
+ align:start position:0%
+1 & 2 I get Row 3 so that's a matrix of
+- we'll say you'll see it okay then here
+
+ align:start position:0%
+- we'll say you'll see it okay then here
+ 
+
+ align:start position:0%
+- we'll say you'll see it okay then here
+s is for symmetric matrices though those
+
+ align:start position:0%
+s is for symmetric matrices though those
+ 
+
+ align:start position:0%
+s is for symmetric matrices though those
+are the kings of linear algebra and here
+
+ align:start position:0%
+are the kings of linear algebra and here
+ 
+
+ align:start position:0%
+are the kings of linear algebra and here
+are a few small samples and the queens
+
+ align:start position:0%
+are a few small samples and the queens
+ 
+
+ align:start position:0%
+are a few small samples and the queens
+of linear algebra are these matrices I
+
+ align:start position:0%
+of linear algebra are these matrices I
+ 
+
+ align:start position:0%
+of linear algebra are these matrices I
+call Q those are called orthogonal
+
+ align:start position:0%
+call Q those are called orthogonal
+ 
+
+ align:start position:0%
+call Q those are called orthogonal
+matrices orthogonal meaning
+
+ align:start position:0%
+matrices orthogonal meaning
+ 
+
+ align:start position:0%
+matrices orthogonal meaning
+perpendicular so there's and they tend
+
+ align:start position:0%
+perpendicular so there's and they tend
+ 
+
+ align:start position:0%
+perpendicular so there's and they tend
+to express a rotation so that's a
+
+ align:start position:0%
+to express a rotation so that's a
+ 
+
+ align:start position:0%
+to express a rotation so that's a
+rotation matrix and orthogonal matrix
+
+ align:start position:0%
+rotation matrix and orthogonal matrix
+ 
+
+ align:start position:0%
+rotation matrix and orthogonal matrix
+that rotates the plane and there's a
+
+ align:start position:0%
+that rotates the plane and there's a
+ 
+
+ align:start position:0%
+that rotates the plane and there's a
+pretty general matrix that we'll see at
+
+ align:start position:0%
+pretty general matrix that we'll see at
+ 
+
+ align:start position:0%
+pretty general matrix that we'll see at
+the very end okay so I'm into the start
+
+ align:start position:0%
+the very end okay so I'm into the start
+ 
+
+ align:start position:0%
+the very end okay so I'm into the start
+of the column space so that's a word I
+
+ align:start position:0%
+of the column space so that's a word I
+ 
+
+ align:start position:0%
+of the column space so that's a word I
+don't use in the videos for quite a
+
+ align:start position:0%
+don't use in the videos for quite a
+ 
+
+ align:start position:0%
+don't use in the videos for quite a
+while but here you see I'm using it in
+
+ align:start position:0%
+while but here you see I'm using it in
+ 
+
+ align:start position:0%
+while but here you see I'm using it in
+the first minutes so I look at a matrix
+
+ align:start position:0%
+the first minutes so I look at a matrix
+ 
+
+ align:start position:0%
+the first minutes so I look at a matrix
+well first let's just remember how to
+
+ align:start position:0%
+well first let's just remember how to
+ 
+
+ align:start position:0%
+well first let's just remember how to
+multiply a matrix by a vector okay there
+
+ align:start position:0%
+multiply a matrix by a vector okay there
+ 
+
+ align:start position:0%
+multiply a matrix by a vector okay there
+is a matrix a there's a vector X with
+
+ align:start position:0%
+is a matrix a there's a vector X with
+ 
+
+ align:start position:0%
+is a matrix a there's a vector X with
+three components and the way I like to
+
+ align:start position:0%
+three components and the way I like to
+ 
+
+ align:start position:0%
+three components and the way I like to
+multiply them is to take the columns of
+
+ align:start position:0%
+multiply them is to take the columns of
+ 
+
+ align:start position:0%
+multiply them is to take the columns of
+a that's what I'm focusing on columns of
+
+ align:start position:0%
+a that's what I'm focusing on columns of
+ 
+
+ align:start position:0%
+a that's what I'm focusing on columns of
+a there they are 1 2 & 3 I multiply them
+
+ align:start position:0%
+a there they are 1 2 & 3 I multiply them
+ 
+
+ align:start position:0%
+a there they are 1 2 & 3 I multiply them
+by those three numbers X 1 X 2 X 3 and I
+
+ align:start position:0%
+by those three numbers X 1 X 2 X 3 and I
+ 
+
+ align:start position:0%
+by those three numbers X 1 X 2 X 3 and I
+add and that's called a linear
+
+ align:start position:0%
+add and that's called a linear
+ 
+
+ align:start position:0%
+add and that's called a linear
+combination linear because nothing is
+
+ align:start position:0%
+combination linear because nothing is
+ 
+
+ align:start position:0%
+combination linear because nothing is
+squared or cubed or anything and
+
+ align:start position:0%
+squared or cubed or anything and
+ 
+
+ align:start position:0%
+squared or cubed or anything and
+combination because I'm putting them
+
+ align:start position:0%
+combination because I'm putting them
+ 
+
+ align:start position:0%
+combination because I'm putting them
+together adding them together okay so
+
+ align:start position:0%
+together adding them together okay so
+ 
+
+ align:start position:0%
+together adding them together okay so
+that's the idea and now the big idea is
+
+ align:start position:0%
+that's the idea and now the big idea is
+ 
+
+ align:start position:0%
+that's the idea and now the big idea is
+in that top line I want to think of all
+
+ align:start position:0%
+in that top line I want to think of all
+ 
+
+ align:start position:0%
+in that top line I want to think of all
+combinations so this is one particular
+
+ align:start position:0%
+combinations so this is one particular
+ 
+
+ align:start position:0%
+combinations so this is one particular
+combination with a particular X 1 and X
+
+ align:start position:0%
+combination with a particular X 1 and X
+ 
+
+ align:start position:0%
+combination with a particular X 1 and X
+2 and X 3 but now I let every I think of
+
+ align:start position:0%
+2 and X 3 but now I let every I think of
+ 
+
+ align:start position:0%
+2 and X 3 but now I let every I think of
+every X 1 and X 2 and X 3 all the
+
+ align:start position:0%
+every X 1 and X 2 and X 3 all the
+ 
+
+ align:start position:0%
+every X 1 and X 2 and X 3 all the
+vectors that I could get well of course
+
+ align:start position:0%
+vectors that I could get well of course
+ 
+
+ align:start position:0%
+vectors that I could get well of course
+I could get the first column by taking 1
+
+ align:start position:0%
+I could get the first column by taking 1
+ 
+
+ align:start position:0%
+I could get the first column by taking 1
++ 0 + 0 that would give me the first
+
+ align:start position:0%
++ 0 + 0 that would give me the first
+ 
+
+ align:start position:0%
++ 0 + 0 that would give me the first
+column but it's really mixtures of the
+
+ align:start position:0%
+column but it's really mixtures of the
+ 
+
+ align:start position:0%
+column but it's really mixtures of the
+columns that this produces and it fills
+
+ align:start position:0%
+columns that this produces and it fills
+ 
+
+ align:start position:0%
+columns that this produces and it fills
+out it fills out in this case a whole
+
+ align:start position:0%
+out it fills out in this case a whole
+ 
+
+ align:start position:0%
+out it fills out in this case a whole
+plane in three dimensions
+
+ align:start position:0%
+plane in three dimensions
+ 
+
+ align:start position:0%
+plane in three dimensions
+these vectors have three components were
+
+ align:start position:0%
+these vectors have three components were
+ 
+
+ align:start position:0%
+these vectors have three components were
+in three dimensions and can you just
+
+ align:start position:0%
+in three dimensions and can you just
+ 
+
+ align:start position:0%
+in three dimensions and can you just
+imagine in your head two lines meeting
+
+ align:start position:0%
+imagine in your head two lines meeting
+ 
+
+ align:start position:0%
+imagine in your head two lines meeting
+at zero zero zero so they they cross but
+
+ align:start position:0%
+at zero zero zero so they they cross but
+ 
+
+ align:start position:0%
+at zero zero zero so they they cross but
+I just have two lines and now I take I
+
+ align:start position:0%
+I just have two lines and now I take I
+ 
+
+ align:start position:0%
+I just have two lines and now I take I
+fill in between those lines so it's
+
+ align:start position:0%
+fill in between those lines so it's
+ 
+
+ align:start position:0%
+fill in between those lines so it's
+filling in between those two lines is
+
+ align:start position:0%
+filling in between those two lines is
+ 
+
+ align:start position:0%
+filling in between those two lines is
+taking the linear combinations that's
+
+ align:start position:0%
+taking the linear combinations that's
+ 
+
+ align:start position:0%
+taking the linear combinations that's
+where they are and the result is I get a
+
+ align:start position:0%
+where they are and the result is I get a
+ 
+
+ align:start position:0%
+where they are and the result is I get a
+plane I do not get the whole space
+
+ align:start position:0%
+plane I do not get the whole space
+ 
+
+ align:start position:0%
+plane I do not get the whole space
+because nothing is going in a third
+
+ align:start position:0%
+because nothing is going in a third
+ 
+
+ align:start position:0%
+because nothing is going in a third
+direction for this matrix all right so
+
+ align:start position:0%
+direction for this matrix all right so
+ 
+
+ align:start position:0%
+direction for this matrix all right so
+let's see more about this so that's that
+
+ align:start position:0%
+let's see more about this so that's that
+ 
+
+ align:start position:0%
+let's see more about this so that's that
+word column space and I use the capital
+
+ align:start position:0%
+word column space and I use the capital
+ 
+
+ align:start position:0%
+word column space and I use the capital
+C for that and it's all the vectors I
+
+ align:start position:0%
+C for that and it's all the vectors I
+ 
+
+ align:start position:0%
+C for that and it's all the vectors I
+can get that way all the combinations of
+
+ align:start position:0%
+can get that way all the combinations of
+ 
+
+ align:start position:0%
+can get that way all the combinations of
+the columns and now I ask oh oh and me I
+
+ align:start position:0%
+the columns and now I ask oh oh and me I
+ 
+
+ align:start position:0%
+the columns and now I ask oh oh and me I
+just answered this question sorry I
+
+ align:start position:0%
+just answered this question sorry I
+ 
+
+ align:start position:0%
+just answered this question sorry I
+asked is the column space all the
+
+ align:start position:0%
+asked is the column space all the
+ 
+
+ align:start position:0%
+asked is the column space all the
+combinations is that the whole 3d space
+
+ align:start position:0%
+combinations is that the whole 3d space
+ 
+
+ align:start position:0%
+combinations is that the whole 3d space
+which everybody calls r3 for real three
+
+ align:start position:0%
+which everybody calls r3 for real three
+ 
+
+ align:start position:0%
+which everybody calls r3 for real three
+or is it a plane or is it just a line
+
+ align:start position:0%
+or is it a plane or is it just a line
+ 
+
+ align:start position:0%
+or is it a plane or is it just a line
+well the answer is plane it probably
+
+ align:start position:0%
+well the answer is plane it probably
+ 
+
+ align:start position:0%
+well the answer is plane it probably
+even gives us the answer that's a good
+
+ align:start position:0%
+even gives us the answer that's a good
+ 
+
+ align:start position:0%
+even gives us the answer that's a good
+thing about this subject the answer is a
+
+ align:start position:0%
+thing about this subject the answer is a
+ 
+
+ align:start position:0%
+thing about this subject the answer is a
+plane because I have two different lines
+
+ align:start position:0%
+plane because I have two different lines
+ 
+
+ align:start position:0%
+plane because I have two different lines
+that meet at the zero and when I fill in
+
+ align:start position:0%
+that meet at the zero and when I fill in
+ 
+
+ align:start position:0%
+that meet at the zero and when I fill in
+between them I have a flat plane I don't
+
+ align:start position:0%
+between them I have a flat plane I don't
+ 
+
+ align:start position:0%
+between them I have a flat plane I don't
+go in the third Direction good so that's
+
+ align:start position:0%
+go in the third Direction good so that's
+ 
+
+ align:start position:0%
+go in the third Direction good so that's
+the column space for this matrix and I
+
+ align:start position:0%
+the column space for this matrix and I
+ 
+
+ align:start position:0%
+the column space for this matrix and I
+and and and and here's a little more
+
+ align:start position:0%
+and and and and here's a little more
+ 
+
+ align:start position:0%
+and and and and here's a little more
+saying about that we kept column 1 and
+
+ align:start position:0%
+saying about that we kept column 1 and
+ 
+
+ align:start position:0%
+saying about that we kept column 1 and
+we kept column 2 because you remember
+
+ align:start position:0%
+we kept column 2 because you remember
+ 
+
+ align:start position:0%
+we kept column 2 because you remember
+those two columns the first two were
+
+ align:start position:0%
+those two columns the first two were
+ 
+
+ align:start position:0%
+those two columns the first two were
+different they went in different
+
+ align:start position:0%
+different they went in different
+ 
+
+ align:start position:0%
+different they went in different
+directions they go in different
+
+ align:start position:0%
+directions they go in different
+ 
+
+ align:start position:0%
+directions they go in different
+direction we did not keep the third
+
+ align:start position:0%
+direction we did not keep the third
+ 
+
+ align:start position:0%
+direction we did not keep the third
+column because it was just a sum of the
+
+ align:start position:0%
+column because it was just a sum of the
+ 
+
+ align:start position:0%
+column because it was just a sum of the
+first two it's on the plane nothing new
+
+ align:start position:0%
+first two it's on the plane nothing new
+ 
+
+ align:start position:0%
+first two it's on the plane nothing new
+so if so the real meat of the matrix a
+
+ align:start position:0%
+so if so the real meat of the matrix a
+ 
+
+ align:start position:0%
+so if so the real meat of the matrix a
+is in the column matrix see that has
+
+ align:start position:0%
+is in the column matrix see that has
+ 
+
+ align:start position:0%
+is in the column matrix see that has
+just the two columns and what about our
+
+ align:start position:0%
+just the two columns and what about our
+ 
+
+ align:start position:0%
+just the two columns and what about our
+because this is my plan for the
+
+ align:start position:0%
+because this is my plan for the
+ 
+
+ align:start position:0%
+because this is my plan for the
+first few weeks first two to three weeks
+
+ align:start position:0%
+first few weeks first two to three weeks
+ 
+
+ align:start position:0%
+first few weeks first two to three weeks
+of linear algebra is is to understand so
+
+ align:start position:0%
+of linear algebra is is to understand so
+ 
+
+ align:start position:0%
+of linear algebra is is to understand so
+that five five three would be called a
+
+ align:start position:0%
+that five five three would be called a
+ 
+
+ align:start position:0%
+that five five three would be called a
+dependent vector because it depends on
+
+ align:start position:0%
+dependent vector because it depends on
+ 
+
+ align:start position:0%
+dependent vector because it depends on
+the first two those were independent so
+
+ align:start position:0%
+the first two those were independent so
+ 
+
+ align:start position:0%
+the first two those were independent so
+those are the two that I keep in the
+
+ align:start position:0%
+those are the two that I keep in the
+ 
+
+ align:start position:0%
+those are the two that I keep in the
+matrix C and then that matrix R oh well
+
+ align:start position:0%
+matrix C and then that matrix R oh well
+ 
+
+ align:start position:0%
+matrix C and then that matrix R oh well
+I know I'm multiplying two matrices and
+
+ align:start position:0%
+I know I'm multiplying two matrices and
+ 
+
+ align:start position:0%
+I know I'm multiplying two matrices and
+you know how to do that but I always
+
+ align:start position:0%
+you know how to do that but I always
+ 
+
+ align:start position:0%
+you know how to do that but I always
+have another way to look at it so the
+
+ align:start position:0%
+have another way to look at it so the
+ 
+
+ align:start position:0%
+have another way to look at it so the
+way I look at it is my linear
+
+ align:start position:0%
+way I look at it is my linear
+ 
+
+ align:start position:0%
+way I look at it is my linear
+combinations you remember those so
+
+ align:start position:0%
+combinations you remember those so
+ 
+
+ align:start position:0%
+combinations you remember those so
+multiplying is a combination of these
+
+ align:start position:0%
+multiplying is a combination of these
+ 
+
+ align:start position:0%
+multiplying is a combination of these
+guys first I have one of the first
+
+ align:start position:0%
+guys first I have one of the first
+ 
+
+ align:start position:0%
+guys first I have one of the first
+column that's my first column the next
+
+ align:start position:0%
+column that's my first column the next
+ 
+
+ align:start position:0%
+column that's my first column the next
+time I have one of the second column
+
+ align:start position:0%
+time I have one of the second column
+ 
+
+ align:start position:0%
+time I have one of the second column
+that's my second vector and the third
+
+ align:start position:0%
+that's my second vector and the third
+ 
+
+ align:start position:0%
+that's my second vector and the third
+one is this guy one of that and one of
+
+ align:start position:0%
+one is this guy one of that and one of
+ 
+
+ align:start position:0%
+one is this guy one of that and one of
+that so these two are the independent
+
+ align:start position:0%
+that so these two are the independent
+ 
+
+ align:start position:0%
+that so these two are the independent
+ones and that's dependent and then a
+
+ align:start position:0%
+ones and that's dependent and then a
+ 
+
+ align:start position:0%
+ones and that's dependent and then a
+full set of independent ones that's
+
+ align:start position:0%
+full set of independent ones that's
+ 
+
+ align:start position:0%
+full set of independent ones that's
+called a basis really fundamental so I
+
+ align:start position:0%
+called a basis really fundamental so I
+ 
+
+ align:start position:0%
+called a basis really fundamental so I
+guess I think that the linear algebra
+
+ align:start position:0%
+guess I think that the linear algebra
+ 
+
+ align:start position:0%
+guess I think that the linear algebra
+should just start with these key ideas
+
+ align:start position:0%
+should just start with these key ideas
+ 
+
+ align:start position:0%
+should just start with these key ideas
+just go with them and we learned
+
+ align:start position:0%
+just go with them and we learned
+ 
+
+ align:start position:0%
+just go with them and we learned
+something it almost falls in our laps
+
+ align:start position:0%
+something it almost falls in our laps
+ 
+
+ align:start position:0%
+something it almost falls in our laps
+it's a great first great and not obvious
+
+ align:start position:0%
+it's a great first great and not obvious
+ 
+
+ align:start position:0%
+it's a great first great and not obvious
+fact about linear algebra I'm just
+
+ align:start position:0%
+fact about linear algebra I'm just
+ 
+
+ align:start position:0%
+fact about linear algebra I'm just
+amazed to have it here the number of
+
+ align:start position:0%
+amazed to have it here the number of
+ 
+
+ align:start position:0%
+amazed to have it here the number of
+independent columns in a which it was
+
+ align:start position:0%
+independent columns in a which it was
+ 
+
+ align:start position:0%
+independent columns in a which it was
+two is equal to the number of
+
+ align:start position:0%
+two is equal to the number of
+ 
+
+ align:start position:0%
+two is equal to the number of
+independent rows in are also two you
+
+ align:start position:0%
+independent rows in are also two you
+ 
+
+ align:start position:0%
+independent rows in are also two you
+remember that we had two rows and two
+
+ align:start position:0%
+remember that we had two rows and two
+ 
+
+ align:start position:0%
+remember that we had two rows and two
+columns so two two two columns first in
+
+ align:start position:0%
+columns so two two two columns first in
+ 
+
+ align:start position:0%
+columns so two two two columns first in
+C two rows and our and the point is that
+
+ align:start position:0%
+C two rows and our and the point is that
+ 
+
+ align:start position:0%
+C two rows and our and the point is that
+that's telling us and we just checked
+
+ align:start position:0%
+that's telling us and we just checked
+ 
+
+ align:start position:0%
+that's telling us and we just checked
+that those two rows were into two
+
+ align:start position:0%
+that those two rows were into two
+ 
+
+ align:start position:0%
+that those two rows were into two
+columns were independent the two rows
+
+ align:start position:0%
+columns were independent the two rows
+ 
+
+ align:start position:0%
+columns were independent the two rows
+are independent they're the basis and
+
+ align:start position:0%
+are independent they're the basis and
+ 
+
+ align:start position:0%
+are independent they're the basis and
+then we learned that the column space
+
+ align:start position:0%
+then we learned that the column space
+ 
+
+ align:start position:0%
+then we learned that the column space
+has dimension to R equals two for this
+
+ align:start position:0%
+has dimension to R equals two for this
+ 
+
+ align:start position:0%
+has dimension to R equals two for this
+example and the row space
+
+ align:start position:0%
+example and the row space
+ 
+
+ align:start position:0%
+example and the row space
+has the same dimension so the rank is a
+
+ align:start position:0%
+has the same dimension so the rank is a
+ 
+
+ align:start position:0%
+has the same dimension so the rank is a
+column rank R equals the row rank R it's
+
+ align:start position:0%
+column rank R equals the row rank R it's
+ 
+
+ align:start position:0%
+column rank R equals the row rank R it's
+like you know if you had a 50 by 80
+
+ align:start position:0%
+like you know if you had a 50 by 80
+ 
+
+ align:start position:0%
+like you know if you had a 50 by 80
+matrix okay that's 4,000 numbers you
+
+ align:start position:0%
+matrix okay that's 4,000 numbers you
+ 
+
+ align:start position:0%
+matrix okay that's 4,000 numbers you
+couldn't see what those these dimensions
+
+ align:start position:0%
+couldn't see what those these dimensions
+ 
+
+ align:start position:0%
+couldn't see what those these dimensions
+are but linear algebra is telling you
+
+ align:start position:0%
+are but linear algebra is telling you
+ 
+
+ align:start position:0%
+are but linear algebra is telling you
+the dimension of the row space and the
+
+ align:start position:0%
+the dimension of the row space and the
+ 
+
+ align:start position:0%
+the dimension of the row space and the
+column space 50 of 1 and 80 and another
+
+ align:start position:0%
+column space 50 of 1 and 80 and another
+ 
+
+ align:start position:0%
+column space 50 of 1 and 80 and another
+are equal okay so this is again coming
+
+ align:start position:0%
+are equal okay so this is again coming
+ 
+
+ align:start position:0%
+are equal okay so this is again coming
+early and we'll see it again but but
+
+ align:start position:0%
+early and we'll see it again but but
+ 
+
+ align:start position:0%
+early and we'll see it again but but
+it's good to start linear algebra from
+
+ align:start position:0%
+it's good to start linear algebra from
+ 
+
+ align:start position:0%
+it's good to start linear algebra from
+day one and then here's another great
+
+ align:start position:0%
+day one and then here's another great
+ 
+
+ align:start position:0%
+day one and then here's another great
+fact about equations because matrices
+
+ align:start position:0%
+fact about equations because matrices
+ 
+
+ align:start position:0%
+fact about equations because matrices
+lead to a lead to equations where X is
+
+ align:start position:0%
+lead to a lead to equations where X is
+ 
+
+ align:start position:0%
+lead to a lead to equations where X is
+the unknown and this equation has zero
+
+ align:start position:0%
+the unknown and this equation has zero
+ 
+
+ align:start position:0%
+the unknown and this equation has zero
+on the right-hand sides so you how could
+
+ align:start position:0%
+on the right-hand sides so you how could
+ 
+
+ align:start position:0%
+on the right-hand sides so you how could
+we get 0 on the right-hand side we could
+
+ align:start position:0%
+we get 0 on the right-hand side we could
+ 
+
+ align:start position:0%
+we get 0 on the right-hand side we could
+take one of that and let me change that
+
+ align:start position:0%
+take one of that and let me change that
+ 
+
+ align:start position:0%
+take one of that and let me change that
+to a minus sign and that to a minus sign
+
+ align:start position:0%
+to a minus sign and that to a minus sign
+ 
+
+ align:start position:0%
+to a minus sign and that to a minus sign
+one of those minus one of those minus
+
+ align:start position:0%
+one of those minus one of those minus
+ 
+
+ align:start position:0%
+one of those minus one of those minus
+one of those would be zero zero zero so
+
+ align:start position:0%
+one of those would be zero zero zero so
+ 
+
+ align:start position:0%
+one of those would be zero zero zero so
+that one and minus one and minus one
+
+ align:start position:0%
+that one and minus one and minus one
+ 
+
+ align:start position:0%
+that one and minus one and minus one
+would tell us an X and that's the
+
+ align:start position:0%
+would tell us an X and that's the
+ 
+
+ align:start position:0%
+would tell us an X and that's the
+solution we're in applying linear
+
+ align:start position:0%
+solution we're in applying linear
+ 
+
+ align:start position:0%
+solution we're in applying linear
+algebra and engineering in physics in in
+
+ align:start position:0%
+algebra and engineering in physics in in
+ 
+
+ align:start position:0%
+algebra and engineering in physics in in
+economics in business you end up with
+
+ align:start position:0%
+economics in business you end up with
+ 
+
+ align:start position:0%
+economics in business you end up with
+equations things balance and you want to
+
+ align:start position:0%
+equations things balance and you want to
+ 
+
+ align:start position:0%
+equations things balance and you want to
+know how many solutions there are and
+
+ align:start position:0%
+know how many solutions there are and
+ 
+
+ align:start position:0%
+know how many solutions there are and
+linear algebra is created to answer that
+
+ align:start position:0%
+linear algebra is created to answer that
+ 
+
+ align:start position:0%
+linear algebra is created to answer that
+question okay so now I'm just going to
+
+ align:start position:0%
+question okay so now I'm just going to
+ 
+
+ align:start position:0%
+question okay so now I'm just going to
+say a little more about this starting
+
+ align:start position:0%
+say a little more about this starting
+ 
+
+ align:start position:0%
+say a little more about this starting
+method of the course oh I want to focus
+
+ align:start position:0%
+method of the course oh I want to focus
+ 
+
+ align:start position:0%
+method of the course oh I want to focus
+here on these interesting method
+
+ align:start position:0%
+here on these interesting method
+ 
+
+ align:start position:0%
+here on these interesting method
+interesting matrices where every column
+
+ align:start position:0%
+interesting matrices where every column
+ 
+
+ align:start position:0%
+interesting matrices where every column
+is a multiple of the first column every
+
+ align:start position:0%
+is a multiple of the first column every
+ 
+
+ align:start position:0%
+is a multiple of the first column every
+Row is a multiple of the first row the
+
+ align:start position:0%
+Row is a multiple of the first row the
+ 
+
+ align:start position:0%
+Row is a multiple of the first row the
+instead of having two independent
+
+ align:start position:0%
+instead of having two independent
+ 
+
+ align:start position:0%
+instead of having two independent
+columns and rows these matrices have
+
+ align:start position:0%
+columns and rows these matrices have
+ 
+
+ align:start position:0%
+columns and rows these matrices have
+only one so then C has one column and R
+
+ align:start position:0%
+only one so then C has one column and R
+ 
+
+ align:start position:0%
+only one so then C has one column and R
+has one row and the rank is one these
+
+ align:start position:0%
+has one row and the rank is one these
+ 
+
+ align:start position:0%
+has one row and the rank is one these
+are the building blocks of linear
+
+ align:start position:0%
+are the building blocks of linear
+ 
+
+ align:start position:0%
+are the building blocks of linear
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+these rank one matrices column times row
+
+ align:start position:0%
+these rank one matrices column times row
+ 
+
+ align:start position:0%
+these rank one matrices column times row
+the previous matrix would would have one
+
+ align:start position:0%
+the previous matrix would would have one
+ 
+
+ align:start position:0%
+the previous matrix would would have one
+of those blocks and a second block a big
+
+ align:start position:0%
+of those blocks and a second block a big
+ 
+
+ align:start position:0%
+of those blocks and a second block a big
+matrix from data science would have
+
+ align:start position:0%
+matrix from data science would have
+ 
+
+ align:start position:0%
+matrix from data science would have
+hundreds of blocks but great theorem in
+
+ align:start position:0%
+hundreds of blocks but great theorem in
+ 
+
+ align:start position:0%
+hundreds of blocks but great theorem in
+linear in linear algebra is to break
+
+ align:start position:0%
+linear in linear algebra is to break
+ 
+
+ align:start position:0%
+linear in linear algebra is to break
+that big matrix into these simple pieces
+
+ align:start position:0%
+that big matrix into these simple pieces
+ 
+
+ align:start position:0%
+that big matrix into these simple pieces
+so that's the goal for the end of the
+
+ align:start position:0%
+so that's the goal for the end of the
+ 
+
+ align:start position:0%
+so that's the goal for the end of the
+course okay and finally a last thought
+
+ align:start position:0%
+course okay and finally a last thought
+ 
+
+ align:start position:0%
+course okay and finally a last thought
+about these so this is C times R I'm
+
+ align:start position:0%
+about these so this is C times R I'm
+ 
+
+ align:start position:0%
+about these so this is C times R I'm
+urging teachers to present that part at
+
+ align:start position:0%
+urging teachers to present that part at
+ 
+
+ align:start position:0%
+urging teachers to present that part at
+the early so what are the good things
+
+ align:start position:0%
+the early so what are the good things
+ 
+
+ align:start position:0%
+the early so what are the good things
+I've marked with a plus first of all the
+
+ align:start position:0%
+I've marked with a plus first of all the
+ 
+
+ align:start position:0%
+I've marked with a plus first of all the
+the columns we're looking at them in C
+
+ align:start position:0%
+the columns we're looking at them in C
+ 
+
+ align:start position:0%
+the columns we're looking at them in C
+in and we see them from a we take them
+
+ align:start position:0%
+in and we see them from a we take them
+ 
+
+ align:start position:0%
+in and we see them from a we take them
+directly from a our turns out to be a
+
+ align:start position:0%
+directly from a our turns out to be a
+ 
+
+ align:start position:0%
+directly from a our turns out to be a
+famous matrix row reduced echelon form
+
+ align:start position:0%
+famous matrix row reduced echelon form
+ 
+
+ align:start position:0%
+famous matrix row reduced echelon form
+it's called so to see that pop up here
+
+ align:start position:0%
+it's called so to see that pop up here
+ 
+
+ align:start position:0%
+it's called so to see that pop up here
+is terrific and then this wonderful fact
+
+ align:start position:0%
+is terrific and then this wonderful fact
+ 
+
+ align:start position:0%
+is terrific and then this wonderful fact
+that row rank equal column rank is clear
+
+ align:start position:0%
+that row rank equal column rank is clear
+ 
+
+ align:start position:0%
+that row rank equal column rank is clear
+from this C times R so those are all
+
+ align:start position:0%
+from this C times R so those are all
+ 
+
+ align:start position:0%
+from this C times R so those are all
+terrifically good things the other thing
+
+ align:start position:0%
+terrifically good things the other thing
+ 
+
+ align:start position:0%
+terrifically good things the other thing
+I have to say is that c and r are not
+
+ align:start position:0%
+I have to say is that c and r are not
+ 
+
+ align:start position:0%
+I have to say is that c and r are not
+great for avoiding roundoff for being
+
+ align:start position:0%
+great for avoiding roundoff for being
+ 
+
+ align:start position:0%
+great for avoiding roundoff for being
+good in large computations this is a
+
+ align:start position:0%
+good in large computations this is a
+ 
+
+ align:start position:0%
+good in large computations this is a
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+factorization but not the best one for
+
+ align:start position:0%
+factorization but not the best one for
+ 
+
+ align:start position:0%
+factorization but not the best one for
+computing for big computing right so
+
+ align:start position:0%
+computing for big computing right so
+ 
+
+ align:start position:0%
+computing for big computing right so
+that's ill-conditioned means could
+
+ align:start position:0%
+that's ill-conditioned means could
+ 
+
+ align:start position:0%
+that's ill-conditioned means could
+they're difficult to deal with and also
+
+ align:start position:0%
+they're difficult to deal with and also
+ 
+
+ align:start position:0%
+they're difficult to deal with and also
+we often have a matrix with all the
+
+ align:start position:0%
+we often have a matrix with all the
+ 
+
+ align:start position:0%
+we often have a matrix with all the
+columns are independent and it's a
+
+ align:start position:0%
+columns are independent and it's a
+ 
+
+ align:start position:0%
+columns are independent and it's a
+square matrix all the columns are
+
+ align:start position:0%
+square matrix all the columns are
+ 
+
+ align:start position:0%
+square matrix all the columns are
+independent we can solve ax equal B all
+
+ align:start position:0%
+independent we can solve ax equal B all
+ 
+
+ align:start position:0%
+independent we can solve ax equal B all
+the time but then then if all the
+
+ align:start position:0%
+the time but then then if all the
+ 
+
+ align:start position:0%
+the time but then then if all the
+columns are independent then our matrix
+
+ align:start position:0%
+columns are independent then our matrix
+ 
+
+ align:start position:0%
+columns are independent then our matrix
+C is just the same as a we didn't get
+
+ align:start position:0%
+C is just the same as a we didn't get
+ 
+
+ align:start position:0%
+C is just the same as a we didn't get
+anywhere an R would be the identity
+
+ align:start position:0%
+anywhere an R would be the identity
+ 
+
+ align:start position:0%
+anywhere an R would be the identity
+matrix like a 1 because a equals C so
+
+ align:start position:0%
+matrix like a 1 because a equals C so
+ 
+
+ align:start position:0%
+matrix like a 1 because a equals C so
+so this is the starting point picking
+
+ align:start position:0%
+so this is the starting point picking
+ 
+
+ align:start position:0%
+so this is the starting point picking
+out the independent columns but not the
+
+ align:start position:0%
+out the independent columns but not the
+ 
+
+ align:start position:0%
+out the independent columns but not the
+end of course and I'll stop here and
+
+ align:start position:0%
+end of course and I'll stop here and
+ 
+
+ align:start position:0%
+end of course and I'll stop here and
+pick up on the next factorization right
+
+ align:start position:0%
+pick up on the next factorization right
+ 
+
+ align:start position:0%
+pick up on the next factorization right
+away Thanks
\ No newline at end of file
diff --git a/bXSSQgtF9zA.txt b/bXSSQgtF9zA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..595334cb44a7baf69e129bab2fe2bf7045354a90
--- /dev/null
+++ b/bXSSQgtF9zA.txt
@@ -0,0 +1,9987 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> All right. So, uh this is our first lab
+
+ align:start position:0%
+>> All right. So, uh this is our first lab
+ 
+
+ align:start position:0%
+>> All right. So, uh this is our first lab
+session for CMS 608. And uh for folks
+
+ align:start position:0%
+session for CMS 608. And uh for folks
+ 
+
+ align:start position:0%
+session for CMS 608. And uh for folks
+who who wasn't here last Wednesday uh
+
+ align:start position:0%
+who who wasn't here last Wednesday uh
+ 
+
+ align:start position:0%
+who who wasn't here last Wednesday uh
+this past Wednesday.
+
+ align:start position:0%
+this past Wednesday.
+ 
+
+ align:start position:0%
+this past Wednesday.
+>> So one two
+
+ align:start position:0%
+>> So one two
+ 
+
+ align:start position:0%
+>> So one two
+>> who wasn't
+
+ align:start position:0%
+>> who wasn't
+ 
+
+ align:start position:0%
+>> who wasn't
+>> who was not here on Wednesday.
+
+ align:start position:0%
+>> who was not here on Wednesday.
+ 
+
+ align:start position:0%
+>> who was not here on Wednesday.
+>> Yeah. And then you guys So you weren't
+
+ align:start position:0%
+>> Yeah. And then you guys So you weren't
+ 
+
+ align:start position:0%
+>> Yeah. And then you guys So you weren't
+here. Um let's see. We have some blank
+
+ align:start position:0%
+here. Um let's see. We have some blank
+ 
+
+ align:start position:0%
+here. Um let's see. We have some blank
+index cards underneath the uh the
+
+ align:start position:0%
+index cards underneath the uh the
+ 
+
+ align:start position:0%
+index cards underneath the uh the
+plastic Tupperware.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So if you can just fill in your name,
+
+ align:start position:0%
+>> So if you can just fill in your name,
+ 
+
+ align:start position:0%
+>> So if you can just fill in your name,
+your email address or favorite board
+
+ align:start position:0%
+your email address or favorite board
+ 
+
+ align:start position:0%
+your email address or favorite board
+game or card game. Uh the email address
+
+ align:start position:0%
+game or card game. Uh the email address
+ 
+
+ align:start position:0%
+game or card game. Uh the email address
+basically just gets added to the email
+
+ align:start position:0%
+basically just gets added to the email
+ 
+
+ align:start position:0%
+basically just gets added to the email
+list. Um did anyone not get an email
+
+ align:start position:0%
+list. Um did anyone not get an email
+ 
+
+ align:start position:0%
+list. Um did anyone not get an email
+from Jason this like yesterday?
+
+ align:start position:0%
+from Jason this like yesterday?
+ 
+
+ align:start position:0%
+from Jason this like yesterday?
+>> Yeah, last night
+
+ align:start position:0%
+>> Yeah, last night
+ 
+
+ align:start position:0%
+>> Yeah, last night
+>> you didn't get an email. I don't think
+
+ align:start position:0%
+>> you didn't get an email. I don't think
+ 
+
+ align:start position:0%
+>> you didn't get an email. I don't think
+so.
+
+ align:start position:0%
+so.
+ 
+
+ align:start position:0%
+so.
+>> Okay. So
+
+ align:start position:0%
+>> Okay. So
+ 
+
+ align:start position:0%
+>> Okay. So
+>> uh the email basically said that there
+
+ align:start position:0%
+>> uh the email basically said that there
+ 
+
+ align:start position:0%
+>> uh the email basically said that there
+was a swap
+
+ align:start position:0%
+was a swap
+ 
+
+ align:start position:0%
+was a swap
+>> uh of um Friday the 17th
+
+ align:start position:0%
+>> uh of um Friday the 17th
+ 
+
+ align:start position:0%
+>> uh of um Friday the 17th
+>> and the 20th. So we're basically
+
+ align:start position:0%
+>> and the 20th. So we're basically
+ 
+
+ align:start position:0%
+>> and the 20th. So we're basically
+swapping the readings around. Uh and uh
+
+ align:start position:0%
+swapping the readings around. Uh and uh
+ 
+
+ align:start position:0%
+swapping the readings around. Uh and uh
+that's that's that's really the only
+
+ align:start position:0%
+that's that's that's really the only
+ 
+
+ align:start position:0%
+that's that's that's really the only
+thing, right? Oh, and I fixed the link
+
+ align:start position:0%
+thing, right? Oh, and I fixed the link
+ 
+
+ align:start position:0%
+thing, right? Oh, and I fixed the link
+for Zimmerman's article.
+
+ align:start position:0%
+for Zimmerman's article.
+ 
+
+ align:start position:0%
+for Zimmerman's article.
+>> Yeah. And unfortunately, Eric Zimmerman
+
+ align:start position:0%
+>> Yeah. And unfortunately, Eric Zimmerman
+ 
+
+ align:start position:0%
+>> Yeah. And unfortunately, Eric Zimmerman
+didn't migrate his website terribly
+
+ align:start position:0%
+didn't migrate his website terribly
+ 
+
+ align:start position:0%
+didn't migrate his website terribly
+well, so all his pictures are broken.
+
+ align:start position:0%
+well, so all his pictures are broken.
+ 
+
+ align:start position:0%
+well, so all his pictures are broken.
+This is
+
+ align:start position:0%
+This is
+ 
+
+ align:start position:0%
+This is
+>> a pity. But I actually have one of his
+
+ align:start position:0%
+>> a pity. But I actually have one of his
+ 
+
+ align:start position:0%
+>> a pity. But I actually have one of his
+games, uh, Cifi 3000. Um, in fact,
+
+ align:start position:0%
+games, uh, Cifi 3000. Um, in fact,
+ 
+
+ align:start position:0%
+games, uh, Cifi 3000. Um, in fact,
+this is like before CI5 3000. So, the
+
+ align:start position:0%
+this is like before CI5 3000. So, the
+ 
+
+ align:start position:0%
+this is like before CI5 3000. So, the
+CIFI 2,999, which is going to be the
+
+ align:start position:0%
+CIFI 2,999, which is going to be the
+ 
+
+ align:start position:0%
+CIFI 2,999, which is going to be the
+non-digital version, uh, which is the
+
+ align:start position:0%
+non-digital version, uh, which is the
+ 
+
+ align:start position:0%
+non-digital version, uh, which is the
+whole point. Um, it is actually a
+
+ align:start position:0%
+whole point. Um, it is actually a
+ 
+
+ align:start position:0%
+whole point. Um, it is actually a
+computer game. It's actually a pretty
+
+ align:start position:0%
+computer game. It's actually a pretty
+ 
+
+ align:start position:0%
+computer game. It's actually a pretty
+decent flash multiplayer game. uh back
+
+ align:start position:0%
+decent flash multiplayer game. uh back
+ 
+
+ align:start position:0%
+decent flash multiplayer game. uh back
+in the day when flash multiplayer games
+
+ align:start position:0%
+in the day when flash multiplayer games
+ 
+
+ align:start position:0%
+in the day when flash multiplayer games
+were not that common. And uh if you
+
+ align:start position:0%
+were not that common. And uh if you
+ 
+
+ align:start position:0%
+were not that common. And uh if you
+haven't played it before online, uh
+
+ align:start position:0%
+haven't played it before online, uh
+ 
+
+ align:start position:0%
+haven't played it before online, uh
+after today, if you especially if you
+
+ align:start position:0%
+after today, if you especially if you
+ 
+
+ align:start position:0%
+after today, if you especially if you
+had a chance to play with the the
+
+ align:start position:0%
+had a chance to play with the the
+ 
+
+ align:start position:0%
+had a chance to play with the the
+cardboard the the card deck, uh try out
+
+ align:start position:0%
+cardboard the the card deck, uh try out
+ 
+
+ align:start position:0%
+cardboard the the card deck, uh try out
+the online version, do a Google search
+
+ align:start position:0%
+the online version, do a Google search
+ 
+
+ align:start position:0%
+the online version, do a Google search
+for 65 3000 and try it online.
+
+ align:start position:0%
+for 65 3000 and try it online.
+ 
+
+ align:start position:0%
+for 65 3000 and try it online.
+Hopefully, you'll be able there are
+
+ align:start position:0%
+Hopefully, you'll be able there are
+ 
+
+ align:start position:0%
+Hopefully, you'll be able there are
+still people playing it because you need
+
+ align:start position:0%
+still people playing it because you need
+ 
+
+ align:start position:0%
+still people playing it because you need
+kind of like a minimum of five people to
+
+ align:start position:0%
+kind of like a minimum of five people to
+ 
+
+ align:start position:0%
+kind of like a minimum of five people to
+be able to get a good good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Oh, suck. It was such a pretty game.
+
+ align:start position:0%
+>> Oh, suck. It was such a pretty game.
+ 
+
+ align:start position:0%
+>> Oh, suck. It was such a pretty game.
+Okay, never mind. You know, um it's uh
+
+ align:start position:0%
+Okay, never mind. You know, um it's uh
+ 
+
+ align:start position:0%
+Okay, never mind. You know, um it's uh
+basically what you had were you got
+
+ align:start position:0%
+basically what you had were you got
+ 
+
+ align:start position:0%
+basically what you had were you got
+avatar customization in the games. You
+
+ align:start position:0%
+avatar customization in the games. You
+ 
+
+ align:start position:0%
+avatar customization in the games. You
+could create your character and you
+
+ align:start position:0%
+could create your character and you
+ 
+
+ align:start position:0%
+could create your character and you
+could um you had this really cool retro
+
+ align:start position:0%
+could um you had this really cool retro
+ 
+
+ align:start position:0%
+could um you had this really cool retro
+pixelated uh look back in the time uh
+
+ align:start position:0%
+pixelated uh look back in the time uh
+ 
+
+ align:start position:0%
+pixelated uh look back in the time uh
+back in the day when retro pixelated
+
+ align:start position:0%
+back in the day when retro pixelated
+ 
+
+ align:start position:0%
+back in the day when retro pixelated
+stuff was not that popular yet. Uh but
+
+ align:start position:0%
+stuff was not that popular yet. Uh but
+ 
+
+ align:start position:0%
+stuff was not that popular yet. Uh but
+uh the gameplay was is pretty much
+
+ align:start position:0%
+uh the gameplay was is pretty much
+ 
+
+ align:start position:0%
+uh the gameplay was is pretty much
+exactly the same as what a card game
+
+ align:start position:0%
+exactly the same as what a card game
+ 
+
+ align:start position:0%
+exactly the same as what a card game
+has.
+
+ align:start position:0%
+has.
+ 
+
+ align:start position:0%
+has.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+the readings today basically uh covered
+
+ align:start position:0%
+the readings today basically uh covered
+ 
+
+ align:start position:0%
+the readings today basically uh covered
+a lot of uh jargon uh that we're going
+
+ align:start position:0%
+a lot of uh jargon uh that we're going
+ 
+
+ align:start position:0%
+a lot of uh jargon uh that we're going
+to be going through. We're going to be
+
+ align:start position:0%
+to be going through. We're going to be
+ 
+
+ align:start position:0%
+to be going through. We're going to be
+using a lot of that for the rest of the
+
+ align:start position:0%
+using a lot of that for the rest of the
+ 
+
+ align:start position:0%
+using a lot of that for the rest of the
+class. Uh for the most part, I'm not
+
+ align:start position:0%
+class. Uh for the most part, I'm not
+ 
+
+ align:start position:0%
+class. Uh for the most part, I'm not
+going to go through every single one of
+
+ align:start position:0%
+going to go through every single one of
+ 
+
+ align:start position:0%
+going to go through every single one of
+them because for the because you folks
+
+ align:start position:0%
+them because for the because you folks
+ 
+
+ align:start position:0%
+them because for the because you folks
+can read and if you if we mention
+
+ align:start position:0%
+can read and if you if we mention
+ 
+
+ align:start position:0%
+can read and if you if we mention
+something and you don't get it, you can
+
+ align:start position:0%
+something and you don't get it, you can
+ 
+
+ align:start position:0%
+something and you don't get it, you can
+always check back there. So just
+
+ align:start position:0%
+always check back there. So just
+ 
+
+ align:start position:0%
+always check back there. So just
+remember that that the that first
+
+ align:start position:0%
+remember that that the that first
+ 
+
+ align:start position:0%
+remember that that the that first
+chapter in breath has is a pretty good
+
+ align:start position:0%
+chapter in breath has is a pretty good
+ 
+
+ align:start position:0%
+chapter in breath has is a pretty good
+glossery of terminology that we're going
+
+ align:start position:0%
+glossery of terminology that we're going
+ 
+
+ align:start position:0%
+glossery of terminology that we're going
+to keep using. Um, but uh, one of the
+
+ align:start position:0%
+to keep using. Um, but uh, one of the
+ 
+
+ align:start position:0%
+to keep using. Um, but uh, one of the
+big things that they ask is what is a
+
+ align:start position:0%
+big things that they ask is what is a
+ 
+
+ align:start position:0%
+big things that they ask is what is a
+game? And, uh, it's one of those,
+
+ align:start position:0%
+game? And, uh, it's one of those,
+ 
+
+ align:start position:0%
+game? And, uh, it's one of those,
+does anyone actually want to offer their
+
+ align:start position:0%
+does anyone actually want to offer their
+ 
+
+ align:start position:0%
+does anyone actually want to offer their
+pet definition of what a game is?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Go for it. A game is something that
+
+ align:start position:0%
+>> Go for it. A game is something that
+ 
+
+ align:start position:0%
+>> Go for it. A game is something that
+involves uh, players in a set of defined
+
+ align:start position:0%
+involves uh, players in a set of defined
+ 
+
+ align:start position:0%
+involves uh, players in a set of defined
+rules beforehand. rules that you have to
+
+ align:start position:0%
+rules beforehand. rules that you have to
+ 
+
+ align:start position:0%
+rules beforehand. rules that you have to
+abide by whether they be you can't uh go
+
+ align:start position:0%
+abide by whether they be you can't uh go
+ 
+
+ align:start position:0%
+abide by whether they be you can't uh go
+outside it limits you have to abide by
+
+ align:start position:0%
+outside it limits you have to abide by
+ 
+
+ align:start position:0%
+outside it limits you have to abide by
+certain uh you have to do certain
+
+ align:start position:0%
+certain uh you have to do certain
+ 
+
+ align:start position:0%
+certain uh you have to do certain
+questions certain orders something that
+
+ align:start position:0%
+questions certain orders something that
+ 
+
+ align:start position:0%
+questions certain orders something that
+has structure that is meant for one
+
+ align:start position:0%
+has structure that is meant for one
+ 
+
+ align:start position:0%
+has structure that is meant for one
+person to go from point A to point B
+
+ align:start position:0%
+person to go from point A to point B
+ 
+
+ align:start position:0%
+person to go from point A to point B
+>> okay structure rules limits players
+
+ align:start position:0%
+>> okay structure rules limits players
+ 
+
+ align:start position:0%
+>> okay structure rules limits players
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+>> it's fun.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> It accomplishes some goal.
+
+ align:start position:0%
+>> It accomplishes some goal.
+ 
+
+ align:start position:0%
+>> It accomplishes some goal.
+>> He always has some kind of goal.
+
+ align:start position:0%
+>> He always has some kind of goal.
+ 
+
+ align:start position:0%
+>> He always has some kind of goal.
+>> Are you working towards something?
+
+ align:start position:0%
+>> Are you working towards something?
+ 
+
+ align:start position:0%
+>> Are you working towards something?
+>> Anything else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Always an abstract system. Often an
+
+ align:start position:0%
+>> Always an abstract system. Often an
+ 
+
+ align:start position:0%
+>> Always an abstract system. Often an
+abstraction of some system.
+
+ align:start position:0%
+abstraction of some system.
+ 
+
+ align:start position:0%
+abstraction of some system.
+>> An abstract system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um
+
+ align:start position:0%
+>> Um
+ 
+
+ align:start position:0%
+>> Um
+so so these these are actually pretty
+
+ align:start position:0%
+so so these these are actually pretty
+ 
+
+ align:start position:0%
+so so these these are actually pretty
+good uh uh pretty good benchmarks. Now
+
+ align:start position:0%
+good uh uh pretty good benchmarks. Now
+ 
+
+ align:start position:0%
+good uh uh pretty good benchmarks. Now
+there there are again as Brenda
+
+ align:start position:0%
+there there are again as Brenda
+ 
+
+ align:start position:0%
+there there are again as Brenda
+describes there isn't one that's just
+
+ align:start position:0%
+describes there isn't one that's just
+ 
+
+ align:start position:0%
+describes there isn't one that's just
+the canonical answer for everything. It
+
+ align:start position:0%
+the canonical answer for everything. It
+ 
+
+ align:start position:0%
+the canonical answer for everything. It
+really depends on which theorist you're
+
+ align:start position:0%
+really depends on which theorist you're
+ 
+
+ align:start position:0%
+really depends on which theorist you're
+reading at any given time. Uh but
+
+ align:start position:0%
+reading at any given time. Uh but
+ 
+
+ align:start position:0%
+reading at any given time. Uh but
+usually they will involve a significant
+
+ align:start position:0%
+usually they will involve a significant
+ 
+
+ align:start position:0%
+usually they will involve a significant
+subset of all of these uh in the
+
+ align:start position:0%
+subset of all of these uh in the
+ 
+
+ align:start position:0%
+subset of all of these uh in the
+definition. Um, and I kind of like to
+
+ align:start position:0%
+definition. Um, and I kind of like to
+ 
+
+ align:start position:0%
+definition. Um, and I kind of like to
+keep things broad and vague because for
+
+ align:start position:0%
+keep things broad and vague because for
+ 
+
+ align:start position:0%
+keep things broad and vague because for
+the most part, um,
+
+ align:start position:0%
+the most part, um,
+ 
+
+ align:start position:0%
+the most part, um,
+by if you if you define yourselves too
+
+ align:start position:0%
+by if you if you define yourselves too
+ 
+
+ align:start position:0%
+by if you if you define yourselves too
+strictly, it might be useful if you're
+
+ align:start position:0%
+strictly, it might be useful if you're
+ 
+
+ align:start position:0%
+strictly, it might be useful if you're
+an academic and you need to write papers
+
+ align:start position:0%
+an academic and you need to write papers
+ 
+
+ align:start position:0%
+an academic and you need to write papers
+about it. But if you're a designer and
+
+ align:start position:0%
+about it. But if you're a designer and
+ 
+
+ align:start position:0%
+about it. But if you're a designer and
+you're just trying to create something
+
+ align:start position:0%
+you're just trying to create something
+ 
+
+ align:start position:0%
+you're just trying to create something
+fun, uh, or the word I would prefer to
+
+ align:start position:0%
+fun, uh, or the word I would prefer to
+ 
+
+ align:start position:0%
+fun, uh, or the word I would prefer to
+use is engaging because, you know, fun
+
+ align:start position:0%
+use is engaging because, you know, fun
+ 
+
+ align:start position:0%
+use is engaging because, you know, fun
+means a lot of different things to a lot
+
+ align:start position:0%
+means a lot of different things to a lot
+ 
+
+ align:start position:0%
+means a lot of different things to a lot
+of different people. Engaging, you know,
+
+ align:start position:0%
+of different people. Engaging, you know,
+ 
+
+ align:start position:0%
+of different people. Engaging, you know,
+basically means that this is going to be
+
+ align:start position:0%
+basically means that this is going to be
+ 
+
+ align:start position:0%
+basically means that this is going to be
+something that you're going to want to
+
+ align:start position:0%
+something that you're going to want to
+ 
+
+ align:start position:0%
+something that you're going to want to
+do for a while. uh that that is
+
+ align:start position:0%
+do for a while. uh that that is
+ 
+
+ align:start position:0%
+do for a while. uh that that is
+motivating. It might be terrifying you
+
+ align:start position:0%
+motivating. It might be terrifying you
+ 
+
+ align:start position:0%
+motivating. It might be terrifying you
+out of your wits, you know, but some
+
+ align:start position:0%
+out of your wits, you know, but some
+ 
+
+ align:start position:0%
+out of your wits, you know, but some
+people enjoy that uh you know or will
+
+ align:start position:0%
+people enjoy that uh you know or will
+ 
+
+ align:start position:0%
+people enjoy that uh you know or will
+find that experience compelling, but
+
+ align:start position:0%
+find that experience compelling, but
+ 
+
+ align:start position:0%
+find that experience compelling, but
+they may not call it fun. Um so so I I
+
+ align:start position:0%
+they may not call it fun. Um so so I I
+ 
+
+ align:start position:0%
+they may not call it fun. Um so so I I
+call that engagement. Um the problem
+
+ align:start position:0%
+call that engagement. Um the problem
+ 
+
+ align:start position:0%
+call that engagement. Um the problem
+with using fun and engaging as a metric
+
+ align:start position:0%
+with using fun and engaging as a metric
+ 
+
+ align:start position:0%
+with using fun and engaging as a metric
+for defining what a game is is that that
+
+ align:start position:0%
+for defining what a game is is that that
+ 
+
+ align:start position:0%
+for defining what a game is is that that
+means that a bad game is not a game. uh
+
+ align:start position:0%
+means that a bad game is not a game. uh
+ 
+
+ align:start position:0%
+means that a bad game is not a game. uh
+a game that fails to achieve fun, that
+
+ align:start position:0%
+a game that fails to achieve fun, that
+ 
+
+ align:start position:0%
+a game that fails to achieve fun, that
+fails to be engaging, you know, is not a
+
+ align:start position:0%
+fails to be engaging, you know, is not a
+ 
+
+ align:start position:0%
+fails to be engaging, you know, is not a
+game. But I will I wouldn't go that far.
+
+ align:start position:0%
+game. But I will I wouldn't go that far.
+ 
+
+ align:start position:0%
+game. But I will I wouldn't go that far.
+Uh largely because that means a lot of
+
+ align:start position:0%
+Uh largely because that means a lot of
+ 
+
+ align:start position:0%
+Uh largely because that means a lot of
+stuff that I've created is not a game.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um but but you know, it should give you
+
+ align:start position:0%
+Um but but you know, it should give you
+ 
+
+ align:start position:0%
+Um but but you know, it should give you
+the the the the you know there is no
+
+ align:start position:0%
+the the the the you know there is no
+ 
+
+ align:start position:0%
+the the the the you know there is no
+magic point where your game becomes
+
+ align:start position:0%
+magic point where your game becomes
+ 
+
+ align:start position:0%
+magic point where your game becomes
+where the thing that you're building
+
+ align:start position:0%
+where the thing that you're building
+ 
+
+ align:start position:0%
+where the thing that you're building
+becomes fun and then suddenly becomes a
+
+ align:start position:0%
+becomes fun and then suddenly becomes a
+ 
+
+ align:start position:0%
+becomes fun and then suddenly becomes a
+game you know. Uh I can imagine someone
+
+ align:start position:0%
+game you know. Uh I can imagine someone
+ 
+
+ align:start position:0%
+game you know. Uh I can imagine someone
+making that argument. is like it's not
+
+ align:start position:0%
+making that argument. is like it's not
+ 
+
+ align:start position:0%
+making that argument. is like it's not
+the game until it's fun. But uh I much
+
+ align:start position:0%
+the game until it's fun. But uh I much
+ 
+
+ align:start position:0%
+the game until it's fun. But uh I much
+rather sort of say fun engagement is
+
+ align:start position:0%
+rather sort of say fun engagement is
+ 
+
+ align:start position:0%
+rather sort of say fun engagement is
+kind of more of a metric of how
+
+ align:start position:0%
+kind of more of a metric of how
+ 
+
+ align:start position:0%
+kind of more of a metric of how
+well-designed your game is, not
+
+ align:start position:0%
+well-designed your game is, not
+ 
+
+ align:start position:0%
+well-designed your game is, not
+necessarily
+
+ align:start position:0%
+necessarily
+ 
+
+ align:start position:0%
+necessarily
+whether your game is a game. Um but you
+
+ align:start position:0%
+whether your game is a game. Um but you
+ 
+
+ align:start position:0%
+whether your game is a game. Um but you
+know what but but but that is a goal of
+
+ align:start position:0%
+know what but but but that is a goal of
+ 
+
+ align:start position:0%
+know what but but but that is a goal of
+a game designer to try to create a a a
+
+ align:start position:0%
+a game designer to try to create a a a
+ 
+
+ align:start position:0%
+a game designer to try to create a a a
+engaging experience. Uh something that
+
+ align:start position:0%
+engaging experience. Uh something that
+ 
+
+ align:start position:0%
+engaging experience. Uh something that
+people are going to want to do. Um there
+
+ align:start position:0%
+people are going to want to do. Um there
+ 
+
+ align:start position:0%
+people are going to want to do. Um there
+are I know some game designers who think
+
+ align:start position:0%
+are I know some game designers who think
+ 
+
+ align:start position:0%
+are I know some game designers who think
+that is not in fact their job. um their
+
+ align:start position:0%
+that is not in fact their job. um their
+ 
+
+ align:start position:0%
+that is not in fact their job. um their
+job is to maximize revenue for instance
+
+ align:start position:0%
+job is to maximize revenue for instance
+ 
+
+ align:start position:0%
+job is to maximize revenue for instance
+especially if you work in social games
+
+ align:start position:0%
+especially if you work in social games
+ 
+
+ align:start position:0%
+especially if you work in social games
+uh that there's a lot of discussion now
+
+ align:start position:0%
+uh that there's a lot of discussion now
+ 
+
+ align:start position:0%
+uh that there's a lot of discussion now
+in how business and game design is
+
+ align:start position:0%
+in how business and game design is
+ 
+
+ align:start position:0%
+in how business and game design is
+basically just one thing now you know
+
+ align:start position:0%
+basically just one thing now you know
+ 
+
+ align:start position:0%
+basically just one thing now you know
+the whole point of game design is how do
+
+ align:start position:0%
+the whole point of game design is how do
+ 
+
+ align:start position:0%
+the whole point of game design is how do
+we get people to pay a little bit more
+
+ align:start position:0%
+we get people to pay a little bit more
+ 
+
+ align:start position:0%
+we get people to pay a little bit more
+um Zinga is going to be on town by the
+
+ align:start position:0%
+um Zinga is going to be on town by the
+ 
+
+ align:start position:0%
+um Zinga is going to be on town by the
+way on September 30th and giving a talk
+
+ align:start position:0%
+way on September 30th and giving a talk
+ 
+
+ align:start position:0%
+way on September 30th and giving a talk
+uh so that has those two points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> so Um, so I I will sort of coordinate
+
+ align:start position:0%
+>> so Um, so I I will sort of coordinate
+ 
+
+ align:start position:0%
+>> so Um, so I I will sort of coordinate
+this out there as something that you
+
+ align:start position:0%
+this out there as something that you
+ 
+
+ align:start position:0%
+this out there as something that you
+that you're working towards, but all
+
+ align:start position:0%
+that you're working towards, but all
+ 
+
+ align:start position:0%
+that you're working towards, but all
+these other things, you know, um, a game
+
+ align:start position:0%
+these other things, you know, um, a game
+ 
+
+ align:start position:0%
+these other things, you know, um, a game
+should have players. Uh, again, I don't
+
+ align:start position:0%
+should have players. Uh, again, I don't
+ 
+
+ align:start position:0%
+should have players. Uh, again, I don't
+want to be too strict on that because
+
+ align:start position:0%
+want to be too strict on that because
+ 
+
+ align:start position:0%
+want to be too strict on that because
+I've certainly seen games that play
+
+ align:start position:0%
+I've certainly seen games that play
+ 
+
+ align:start position:0%
+I've certainly seen games that play
+themselves and um, anyone here involved
+
+ align:start position:0%
+themselves and um, anyone here involved
+ 
+
+ align:start position:0%
+themselves and um, anyone here involved
+in battle code that that game pretty
+
+ align:start position:0%
+in battle code that that game pretty
+ 
+
+ align:start position:0%
+in battle code that that game pretty
+much plays itself, right? I mean you set
+
+ align:start position:0%
+much plays itself, right? I mean you set
+ 
+
+ align:start position:0%
+much plays itself, right? I mean you set
+it going and then someone one side wins
+
+ align:start position:0%
+it going and then someone one side wins
+ 
+
+ align:start position:0%
+it going and then someone one side wins
+but no there's no human person at least
+
+ align:start position:0%
+but no there's no human person at least
+ 
+
+ align:start position:0%
+but no there's no human person at least
+during the time when the game is
+
+ align:start position:0%
+during the time when the game is
+ 
+
+ align:start position:0%
+during the time when the game is
+actually being played or you could argue
+
+ align:start position:0%
+actually being played or you could argue
+ 
+
+ align:start position:0%
+actually being played or you could argue
+that a whole course of uh of battle code
+
+ align:start position:0%
+that a whole course of uh of battle code
+ 
+
+ align:start position:0%
+that a whole course of uh of battle code
+for those people who don't know it's
+
+ align:start position:0%
+for those people who don't know it's
+ 
+
+ align:start position:0%
+for those people who don't know it's
+this IP course I believe where uh core 6
+
+ align:start position:0%
+this IP course I believe where uh core 6
+ 
+
+ align:start position:0%
+this IP course I believe where uh core 6
+students basically write bits of AI to
+
+ align:start position:0%
+students basically write bits of AI to
+ 
+
+ align:start position:0%
+students basically write bits of AI to
+play a realtime strategy game against
+
+ align:start position:0%
+play a realtime strategy game against
+ 
+
+ align:start position:0%
+play a realtime strategy game against
+some other team's AI and uh the basic
+
+ align:start position:0%
+some other team's AI and uh the basic
+ 
+
+ align:start position:0%
+some other team's AI and uh the basic
+idea is that you know if you win a real
+
+ align:start position:0%
+idea is that you know if you win a real
+ 
+
+ align:start position:0%
+idea is that you know if you win a real
+time strategy game your AI wins but
+
+ align:start position:0%
+time strategy game your AI wins but
+ 
+
+ align:start position:0%
+time strategy game your AI wins but
+there's no human actually playing it at
+
+ align:start position:0%
+there's no human actually playing it at
+ 
+
+ align:start position:0%
+there's no human actually playing it at
+a given time. But of course there are
+
+ align:start position:0%
+a given time. But of course there are
+ 
+
+ align:start position:0%
+a given time. But of course there are
+humans writing the AI. So if if you
+
+ align:start position:0%
+humans writing the AI. So if if you
+ 
+
+ align:start position:0%
+humans writing the AI. So if if you
+think of the entire class as a game uh
+
+ align:start position:0%
+think of the entire class as a game uh
+ 
+
+ align:start position:0%
+think of the entire class as a game uh
+then there are players there are people
+
+ align:start position:0%
+then there are players there are people
+ 
+
+ align:start position:0%
+then there are players there are people
+um there are I have certainly seen
+
+ align:start position:0%
+um there are I have certainly seen
+ 
+
+ align:start position:0%
+um there are I have certainly seen
+people make a case that there are games
+
+ align:start position:0%
+people make a case that there are games
+ 
+
+ align:start position:0%
+people make a case that there are games
+that are zero player and uh and I've
+
+ align:start position:0%
+that are zero player and uh and I've
+ 
+
+ align:start position:0%
+that are zero player and uh and I've
+heard um for example there's a game out
+
+ align:start position:0%
+heard um for example there's a game out
+ 
+
+ align:start position:0%
+heard um for example there's a game out
+there called Nomic which is largely a
+
+ align:start position:0%
+there called Nomic which is largely a
+ 
+
+ align:start position:0%
+there called Nomic which is largely a
+game about coming up with rules and um
+
+ align:start position:0%
+game about coming up with rules and um
+ 
+
+ align:start position:0%
+game about coming up with rules and um
+and there are there is a system which
+
+ align:start position:0%
+and there are there is a system which
+ 
+
+ align:start position:0%
+and there are there is a system which
+are actually in the rules themselves
+
+ align:start position:0%
+are actually in the rules themselves
+ 
+
+ align:start position:0%
+are actually in the rules themselves
+about how you change rules and you And
+
+ align:start position:0%
+about how you change rules and you And
+ 
+
+ align:start position:0%
+about how you change rules and you And
+um of course those rules themselves can
+
+ align:start position:0%
+um of course those rules themselves can
+ 
+
+ align:start position:0%
+um of course those rules themselves can
+be changed. Uh and and that changes the
+
+ align:start position:0%
+be changed. Uh and and that changes the
+ 
+
+ align:start position:0%
+be changed. Uh and and that changes the
+way how you change rules. And by the
+
+ align:start position:0%
+way how you change rules. And by the
+ 
+
+ align:start position:0%
+way how you change rules. And by the
+time you actually play the game,
+
+ align:start position:0%
+time you actually play the game,
+ 
+
+ align:start position:0%
+time you actually play the game,
+someone's already won because somebody
+
+ align:start position:0%
+someone's already won because somebody
+ 
+
+ align:start position:0%
+someone's already won because somebody
+in the game has no legal moves. Uh
+
+ align:start position:0%
+in the game has no legal moves. Uh
+ 
+
+ align:start position:0%
+in the game has no legal moves. Uh
+that's that's the whole game. It's
+
+ align:start position:0%
+that's that's the whole game. It's
+ 
+
+ align:start position:0%
+that's that's the whole game. It's
+basically making it impossible for
+
+ align:start position:0%
+basically making it impossible for
+ 
+
+ align:start position:0%
+basically making it impossible for
+someone else for someone else except for
+
+ align:start position:0%
+someone else for someone else except for
+ 
+
+ align:start position:0%
+someone else for someone else except for
+you to win. Um so does that game
+
+ align:start position:0%
+you to win. Um so does that game
+ 
+
+ align:start position:0%
+you to win. Um so does that game
+actually have players? Well, yes it does
+
+ align:start position:0%
+actually have players? Well, yes it does
+ 
+
+ align:start position:0%
+actually have players? Well, yes it does
+because you guys are arguing over who uh
+
+ align:start position:0%
+because you guys are arguing over who uh
+ 
+
+ align:start position:0%
+because you guys are arguing over who uh
+all the rule changes, you know, and
+
+ align:start position:0%
+all the rule changes, you know, and
+ 
+
+ align:start position:0%
+all the rule changes, you know, and
+through uh through the rules of the
+
+ align:start position:0%
+through uh through the rules of the
+ 
+
+ align:start position:0%
+through uh through the rules of the
+game. But in a sense, it had no players
+
+ align:start position:0%
+game. But in a sense, it had no players
+ 
+
+ align:start position:0%
+game. But in a sense, it had no players
+because the game never actually got
+
+ align:start position:0%
+because the game never actually got
+ 
+
+ align:start position:0%
+because the game never actually got
+played. The the the rules are basically
+
+ align:start position:0%
+played. The the the rules are basically
+ 
+
+ align:start position:0%
+played. The the the rules are basically
+stating, you know, this is an unplayable
+
+ align:start position:0%
+stating, you know, this is an unplayable
+ 
+
+ align:start position:0%
+stating, you know, this is an unplayable
+game for everybody but except for one
+
+ align:start position:0%
+game for everybody but except for one
+ 
+
+ align:start position:0%
+game for everybody but except for one
+person uh in the in in who's playing the
+
+ align:start position:0%
+person uh in the in in who's playing the
+ 
+
+ align:start position:0%
+person uh in the in in who's playing the
+game. Um
+
+ align:start position:0%
+game. Um
+ 
+
+ align:start position:0%
+game. Um
+goals. Goals are one of those things
+
+ align:start position:0%
+goals. Goals are one of those things
+ 
+
+ align:start position:0%
+goals. Goals are one of those things
+that I used to be very very adamant
+
+ align:start position:0%
+that I used to be very very adamant
+ 
+
+ align:start position:0%
+that I used to be very very adamant
+about like like a game had to have a
+
+ align:start position:0%
+about like like a game had to have a
+ 
+
+ align:start position:0%
+about like like a game had to have a
+goal. You you have to know what you're
+
+ align:start position:0%
+goal. You you have to know what you're
+ 
+
+ align:start position:0%
+goal. You you have to know what you're
+going towards and and if you don't have
+
+ align:start position:0%
+going towards and and if you don't have
+ 
+
+ align:start position:0%
+going towards and and if you don't have
+that then it's a toy or something you
+
+ align:start position:0%
+that then it's a toy or something you
+ 
+
+ align:start position:0%
+that then it's a toy or something you
+know it's a dollhouse. It's an
+
+ align:start position:0%
+know it's a dollhouse. It's an
+ 
+
+ align:start position:0%
+know it's a dollhouse. It's an
+experiment. The Sims was the one that I
+
+ align:start position:0%
+experiment. The Sims was the one that I
+ 
+
+ align:start position:0%
+experiment. The Sims was the one that I
+was like railing about when I was in an
+
+ align:start position:0%
+was like railing about when I was in an
+ 
+
+ align:start position:0%
+was like railing about when I was in an
+undergraduate. Um you know that's not a
+
+ align:start position:0%
+undergraduate. Um you know that's not a
+ 
+
+ align:start position:0%
+undergraduate. Um you know that's not a
+game. Um and of course my uh uh um I was
+
+ align:start position:0%
+game. Um and of course my uh uh um I was
+ 
+
+ align:start position:0%
+game. Um and of course my uh uh um I was
+working with many colleagues and
+
+ align:start position:0%
+working with many colleagues and
+ 
+
+ align:start position:0%
+working with many colleagues and
+eventually came across uh came over to
+
+ align:start position:0%
+eventually came across uh came over to
+ 
+
+ align:start position:0%
+eventually came across uh came over to
+the site that it doesn't matter whether
+
+ align:start position:0%
+the site that it doesn't matter whether
+ 
+
+ align:start position:0%
+the site that it doesn't matter whether
+I think it's a game or not. If it's in
+
+ align:start position:0%
+I think it's a game or not. If it's in
+ 
+
+ align:start position:0%
+I think it's a game or not. If it's in
+the game shelf of Best Buy, it's a game.
+
+ align:start position:0%
+the game shelf of Best Buy, it's a game.
+ 
+
+ align:start position:0%
+the game shelf of Best Buy, it's a game.
+So, you know, because people think it's
+
+ align:start position:0%
+So, you know, because people think it's
+ 
+
+ align:start position:0%
+So, you know, because people think it's
+a game. And if enough people think it's
+
+ align:start position:0%
+a game. And if enough people think it's
+ 
+
+ align:start position:0%
+a game. And if enough people think it's
+a game, then it might as well be a game,
+
+ align:start position:0%
+a game, then it might as well be a game,
+ 
+
+ align:start position:0%
+a game, then it might as well be a game,
+you know, because otherwise what what uh
+
+ align:start position:0%
+you know, because otherwise what what uh
+ 
+
+ align:start position:0%
+you know, because otherwise what what uh
+uh uh because that's what people think
+
+ align:start position:0%
+uh uh because that's what people think
+ 
+
+ align:start position:0%
+uh uh because that's what people think
+it's going to be. So when when when you
+
+ align:start position:0%
+it's going to be. So when when when you
+ 
+
+ align:start position:0%
+it's going to be. So when when when you
+come up with your game,
+
+ align:start position:0%
+come up with your game,
+ 
+
+ align:start position:0%
+come up with your game,
+I would say that goals are one of those
+
+ align:start position:0%
+I would say that goals are one of those
+ 
+
+ align:start position:0%
+I would say that goals are one of those
+things that helps steer player behavior.
+
+ align:start position:0%
+things that helps steer player behavior.
+ 
+
+ align:start position:0%
+things that helps steer player behavior.
+So and it gives it's one of those tools
+
+ align:start position:0%
+So and it gives it's one of those tools
+ 
+
+ align:start position:0%
+So and it gives it's one of those tools
+that you have as a designer to basically
+
+ align:start position:0%
+that you have as a designer to basically
+ 
+
+ align:start position:0%
+that you have as a designer to basically
+say this is important, this is not.
+
+ align:start position:0%
+say this is important, this is not.
+ 
+
+ align:start position:0%
+say this is important, this is not.
+Reaching the end of 100 meters is
+
+ align:start position:0%
+Reaching the end of 100 meters is
+ 
+
+ align:start position:0%
+Reaching the end of 100 meters is
+important for a sprinter. Um that that
+
+ align:start position:0%
+important for a sprinter. Um that that
+ 
+
+ align:start position:0%
+important for a sprinter. Um that that
+end is really not interesting for you
+
+ align:start position:0%
+end is really not interesting for you
+ 
+
+ align:start position:0%
+end is really not interesting for you
+know somebody who's running 400 400
+
+ align:start position:0%
+know somebody who's running 400 400
+ 
+
+ align:start position:0%
+know somebody who's running 400 400
+meters or 50 meter dash. Um but uh that
+
+ align:start position:0%
+meters or 50 meter dash. Um but uh that
+ 
+
+ align:start position:0%
+meters or 50 meter dash. Um but uh that
+gives someone a direction for them to go
+
+ align:start position:0%
+gives someone a direction for them to go
+ 
+
+ align:start position:0%
+gives someone a direction for them to go
+towards. But there are plenty of games
+
+ align:start position:0%
+towards. But there are plenty of games
+ 
+
+ align:start position:0%
+towards. But there are plenty of games
+where you have to invent your own goals.
+
+ align:start position:0%
+where you have to invent your own goals.
+ 
+
+ align:start position:0%
+where you have to invent your own goals.
+Can other than Sims, anyone can think of
+
+ align:start position:0%
+Can other than Sims, anyone can think of
+ 
+
+ align:start position:0%
+Can other than Sims, anyone can think of
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+where inventing your own goals is kind
+
+ align:start position:0%
+where inventing your own goals is kind
+ 
+
+ align:start position:0%
+where inventing your own goals is kind
+of the fun
+
+ align:start position:0%
+of the fun
+ 
+
+ align:start position:0%
+of the fun
+>> RPGs.
+
+ align:start position:0%
+>> RPGs.
+ 
+
+ align:start position:0%
+>> RPGs.
+>> A lot of MMO RPGs have have that they
+
+ align:start position:0%
+>> A lot of MMO RPGs have have that they
+ 
+
+ align:start position:0%
+>> A lot of MMO RPGs have have that they
+have goals. They have quests, but you
+
+ align:start position:0%
+have goals. They have quests, but you
+ 
+
+ align:start position:0%
+have goals. They have quests, but you
+know that's not where a lot of the fun
+
+ align:start position:0%
+know that's not where a lot of the fun
+ 
+
+ align:start position:0%
+know that's not where a lot of the fun
+is.
+
+ align:start position:0%
+is.
+ 
+
+ align:start position:0%
+is.
+>> Second life.
+
+ align:start position:0%
+>> Second life.
+ 
+
+ align:start position:0%
+>> Second life.
+>> Second Life. A lot of virtual worlds.
+
+ align:start position:0%
+>> Second Life. A lot of virtual worlds.
+ 
+
+ align:start position:0%
+>> Second Life. A lot of virtual worlds.
+>> Game like Eve.
+
+ align:start position:0%
+>> Game like Eve.
+ 
+
+ align:start position:0%
+>> Game like Eve.
+>> Uh Eve. Yeah. I mean Eve. if if you you
+
+ align:start position:0%
+>> Uh Eve. Yeah. I mean Eve. if if you you
+ 
+
+ align:start position:0%
+>> Uh Eve. Yeah. I mean Eve. if if you you
+you kind of want to you like you have to
+
+ align:start position:0%
+you kind of want to you like you have to
+ 
+
+ align:start position:0%
+you kind of want to you like you have to
+set your own goals, right? Because
+
+ align:start position:0%
+set your own goals, right? Because
+ 
+
+ align:start position:0%
+set your own goals, right? Because
+whatever's in the game is only good
+
+ align:start position:0%
+whatever's in the game is only good
+ 
+
+ align:start position:0%
+whatever's in the game is only good
+enough for like a single player to uh to
+
+ align:start position:0%
+enough for like a single player to uh to
+ 
+
+ align:start position:0%
+enough for like a single player to uh to
+to tell whether a single player whether
+
+ align:start position:0%
+to tell whether a single player whether
+ 
+
+ align:start position:0%
+to tell whether a single player whether
+they're doing well or not.
+
+ align:start position:0%
+they're doing well or not.
+ 
+
+ align:start position:0%
+they're doing well or not.
+>> But the Eve is not about a single
+
+ align:start position:0%
+>> But the Eve is not about a single
+ 
+
+ align:start position:0%
+>> But the Eve is not about a single
+player. Eve is about what thousands and
+
+ align:start position:0%
+player. Eve is about what thousands and
+ 
+
+ align:start position:0%
+player. Eve is about what thousands and
+thousands of people playing
+
+ align:start position:0%
+thousands of people playing
+ 
+
+ align:start position:0%
+thousands of people playing
+simultaneously.
+
+ align:start position:0%
+simultaneously.
+ 
+
+ align:start position:0%
+simultaneously.
+>> Um
+
+ align:start position:0%
+>> Um
+ 
+
+ align:start position:0%
+>> Um
+um actually have people heard of Eve?
+
+ align:start position:0%
+um actually have people heard of Eve?
+ 
+
+ align:start position:0%
+um actually have people heard of Eve?
+>> Okay. Right. So yeah. Cool. Cool.
+
+ align:start position:0%
+>> Okay. Right. So yeah. Cool. Cool.
+ 
+
+ align:start position:0%
+>> Okay. Right. So yeah. Cool. Cool.
+>> I stopped the development.
+
+ align:start position:0%
+>> I stopped the development.
+ 
+
+ align:start position:0%
+>> I stopped the development.
+>> Oh, cool. In Iceland. Yeah.
+
+ align:start position:0%
+>> Oh, cool. In Iceland. Yeah.
+ 
+
+ align:start position:0%
+>> Oh, cool. In Iceland. Yeah.
+>> Was it like really cheap when you went
+
+ align:start position:0%
+>> Was it like really cheap when you went
+ 
+
+ align:start position:0%
+>> Was it like really cheap when you went
+over there? Could could you have bought
+
+ align:start position:0%
+over there? Could could you have bought
+ 
+
+ align:start position:0%
+over there? Could could you have bought
+the entire studio?
+
+ align:start position:0%
+the entire studio?
+ 
+
+ align:start position:0%
+the entire studio?
+>> No.
+
+ align:start position:0%
+>> No.
+ 
+
+ align:start position:0%
+>> No.
+>> Unfortunately.
+
+ align:start position:0%
+>> Unfortunately.
+ 
+
+ align:start position:0%
+>> Unfortunately.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> It was really cheap.
+
+ align:start position:0%
+>> It was really cheap.
+ 
+
+ align:start position:0%
+>> It was really cheap.
+>> Yeah. Like months ago.
+
+ align:start position:0%
+>> Yeah. Like months ago.
+ 
+
+ align:start position:0%
+>> Yeah. Like months ago.
+>> So they must have been making tons of
+
+ align:start position:0%
+>> So they must have been making tons of
+ 
+
+ align:start position:0%
+>> So they must have been making tons of
+money because Yeah. They're making money
+
+ align:start position:0%
+money because Yeah. They're making money
+ 
+
+ align:start position:0%
+money because Yeah. They're making money
+in US dollars and
+
+ align:start position:0%
+in US dollars and
+ 
+
+ align:start position:0%
+in US dollars and
+>> euros.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. They probably hire most of Yeah.
+
+ align:start position:0%
+Yeah. They probably hire most of Yeah.
+ 
+
+ align:start position:0%
+Yeah. They probably hire most of Yeah.
+support most of the economy.
+
+ align:start position:0%
+support most of the economy.
+ 
+
+ align:start position:0%
+support most of the economy.
+>> Icelandic economy.
+
+ align:start position:0%
+>> Icelandic economy.
+ 
+
+ align:start position:0%
+>> Icelandic economy.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> The capital is 20,000 people.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yep.
+
+ align:start position:0%
+Yep.
+ 
+
+ align:start position:0%
+Yep.
+>> Um
+
+ align:start position:0%
+>> Um
+ 
+
+ align:start position:0%
+>> Um
+so um so I would say goals are very
+
+ align:start position:0%
+so um so I would say goals are very
+ 
+
+ align:start position:0%
+so um so I would say goals are very
+important tools and as a result of that
+
+ align:start position:0%
+important tools and as a result of that
+ 
+
+ align:start position:0%
+important tools and as a result of that
+you see them in a lot of the games and
+
+ align:start position:0%
+you see them in a lot of the games and
+ 
+
+ align:start position:0%
+you see them in a lot of the games and
+you know uh for most of the games that
+
+ align:start position:0%
+you know uh for most of the games that
+ 
+
+ align:start position:0%
+you know uh for most of the games that
+you guys are going to be building. Yeah.
+
+ align:start position:0%
+you guys are going to be building. Yeah.
+ 
+
+ align:start position:0%
+you guys are going to be building. Yeah.
+Uh you're going to give a very clear
+
+ align:start position:0%
+Uh you're going to give a very clear
+ 
+
+ align:start position:0%
+Uh you're going to give a very clear
+goal of this is what you want to do.
+
+ align:start position:0%
+goal of this is what you want to do.
+ 
+
+ align:start position:0%
+goal of this is what you want to do.
+Earn a certain amount of money. Uh
+
+ align:start position:0%
+Earn a certain amount of money. Uh
+ 
+
+ align:start position:0%
+Earn a certain amount of money. Uh
+prevent your opponent from doing
+
+ align:start position:0%
+prevent your opponent from doing
+ 
+
+ align:start position:0%
+prevent your opponent from doing
+anything else. you know, uh, take over
+
+ align:start position:0%
+anything else. you know, uh, take over
+ 
+
+ align:start position:0%
+anything else. you know, uh, take over
+all of the land, that sort of thing. Um,
+
+ align:start position:0%
+all of the land, that sort of thing. Um,
+ 
+
+ align:start position:0%
+all of the land, that sort of thing. Um,
+let's see.
+
+ align:start position:0%
+let's see.
+ 
+
+ align:start position:0%
+let's see.
+Well, I'll get to rules last. Um, but,
+
+ align:start position:0%
+Well, I'll get to rules last. Um, but,
+ 
+
+ align:start position:0%
+Well, I'll get to rules last. Um, but,
+um, systems are, um, I might already
+
+ align:start position:0%
+um, systems are, um, I might already
+ 
+
+ align:start position:0%
+um, systems are, um, I might already
+have mentioned this in the last class,
+
+ align:start position:0%
+have mentioned this in the last class,
+ 
+
+ align:start position:0%
+have mentioned this in the last class,
+but, uh, games are systems in a way that
+
+ align:start position:0%
+but, uh, games are systems in a way that
+ 
+
+ align:start position:0%
+but, uh, games are systems in a way that
+most MIT engineers would think of
+
+ align:start position:0%
+most MIT engineers would think of
+ 
+
+ align:start position:0%
+most MIT engineers would think of
+systems. you know, they're a bunch of
+
+ align:start position:0%
+systems. you know, they're a bunch of
+ 
+
+ align:start position:0%
+systems. you know, they're a bunch of
+interconnected little modules, all of
+
+ align:start position:0%
+interconnected little modules, all of
+ 
+
+ align:start position:0%
+interconnected little modules, all of
+them with sort of predictable behavior,
+
+ align:start position:0%
+them with sort of predictable behavior,
+ 
+
+ align:start position:0%
+them with sort of predictable behavior,
+and then you put them into a big
+
+ align:start position:0%
+and then you put them into a big
+ 
+
+ align:start position:0%
+and then you put them into a big
+interconnected system, and it is no
+
+ align:start position:0%
+interconnected system, and it is no
+ 
+
+ align:start position:0%
+interconnected system, and it is no
+longer really all that predictable
+
+ align:start position:0%
+longer really all that predictable
+ 
+
+ align:start position:0%
+longer really all that predictable
+anymore. Um, at least that's the kind of
+
+ align:start position:0%
+anymore. Um, at least that's the kind of
+ 
+
+ align:start position:0%
+anymore. Um, at least that's the kind of
+games that we're interested in this
+
+ align:start position:0%
+games that we're interested in this
+ 
+
+ align:start position:0%
+games that we're interested in this
+class. There's also the game theory
+
+ align:start position:0%
+class. There's also the game theory
+ 
+
+ align:start position:0%
+class. There's also the game theory
+games where like the whole point of it
+
+ align:start position:0%
+games where like the whole point of it
+ 
+
+ align:start position:0%
+games where like the whole point of it
+is trying to predict what could possibly
+
+ align:start position:0%
+is trying to predict what could possibly
+ 
+
+ align:start position:0%
+is trying to predict what could possibly
+happen. uh and uh those are those are
+
+ align:start position:0%
+happen. uh and uh those are those are
+ 
+
+ align:start position:0%
+happen. uh and uh those are those are
+great thought experiments and there's
+
+ align:start position:0%
+great thought experiments and there's
+ 
+
+ align:start position:0%
+great thought experiments and there's
+some really really interesting math
+
+ align:start position:0%
+some really really interesting math
+ 
+
+ align:start position:0%
+some really really interesting math
+behind all all them and some interesting
+
+ align:start position:0%
+behind all all them and some interesting
+ 
+
+ align:start position:0%
+behind all all them and some interesting
+rules of thumb that can come out but for
+
+ align:start position:0%
+rules of thumb that can come out but for
+ 
+
+ align:start position:0%
+rules of thumb that can come out but for
+the most part we aren't going to go into
+
+ align:start position:0%
+the most part we aren't going to go into
+ 
+
+ align:start position:0%
+the most part we aren't going to go into
+too much detail about that largely
+
+ align:start position:0%
+too much detail about that largely
+ 
+
+ align:start position:0%
+too much detail about that largely
+because I'm not a mathematician or
+
+ align:start position:0%
+because I'm not a mathematician or
+ 
+
+ align:start position:0%
+because I'm not a mathematician or
+economist so I don't really have a good
+
+ align:start position:0%
+economist so I don't really have a good
+ 
+
+ align:start position:0%
+economist so I don't really have a good
+a good sense of game theory uh just be
+
+ align:start position:0%
+a good sense of game theory uh just be
+ 
+
+ align:start position:0%
+a good sense of game theory uh just be
+aware that you know there is this whole
+
+ align:start position:0%
+aware that you know there is this whole
+ 
+
+ align:start position:0%
+aware that you know there is this whole
+field of game theory in economics uh if
+
+ align:start position:0%
+field of game theory in economics uh if
+ 
+
+ align:start position:0%
+field of game theory in economics uh if
+you're doing a game like an auction
+
+ align:start position:0%
+you're doing a game like an auction
+ 
+
+ align:start position:0%
+you're doing a game like an auction
+system if you're doing a game where
+
+ align:start position:0%
+system if you're doing a game where
+ 
+
+ align:start position:0%
+system if you're doing a game where
+people are doing uh either a lot of
+
+ align:start position:0%
+people are doing uh either a lot of
+ 
+
+ align:start position:0%
+people are doing uh either a lot of
+simultaneous moves or um yeah or the
+
+ align:start position:0%
+simultaneous moves or um yeah or the
+ 
+
+ align:start position:0%
+simultaneous moves or um yeah or the
+whole point of the game is trying to
+
+ align:start position:0%
+whole point of the game is trying to
+ 
+
+ align:start position:0%
+whole point of the game is trying to
+predict what your what strategy your
+
+ align:start position:0%
+predict what your what strategy your
+ 
+
+ align:start position:0%
+predict what your what strategy your
+your opponent is going to do. You might
+
+ align:start position:0%
+your opponent is going to do. You might
+ 
+
+ align:start position:0%
+your opponent is going to do. You might
+actually want to read up a little bit of
+
+ align:start position:0%
+actually want to read up a little bit of
+ 
+
+ align:start position:0%
+actually want to read up a little bit of
+game theory if nothing else just to give
+
+ align:start position:0%
+game theory if nothing else just to give
+ 
+
+ align:start position:0%
+game theory if nothing else just to give
+you some vocabulary to talk about it
+
+ align:start position:0%
+you some vocabulary to talk about it
+ 
+
+ align:start position:0%
+you some vocabulary to talk about it
+with your teammates uh and some tools to
+
+ align:start position:0%
+with your teammates uh and some tools to
+ 
+
+ align:start position:0%
+with your teammates uh and some tools to
+be able to think through some of the
+
+ align:start position:0%
+be able to think through some of the
+ 
+
+ align:start position:0%
+be able to think through some of the
+design problems that you've got. Um and
+
+ align:start position:0%
+design problems that you've got. Um and
+ 
+
+ align:start position:0%
+design problems that you've got. Um and
+then we we we do have one session where
+
+ align:start position:0%
+then we we we do have one session where
+ 
+
+ align:start position:0%
+then we we we do have one session where
+we I'll introduce some of them. Um and
+
+ align:start position:0%
+we I'll introduce some of them. Um and
+ 
+
+ align:start position:0%
+we I'll introduce some of them. Um and
+finally we're getting to rules. Um you
+
+ align:start position:0%
+finally we're getting to rules. Um you
+ 
+
+ align:start position:0%
+finally we're getting to rules. Um you
+know the the things that give that give
+
+ align:start position:0%
+know the the things that give that give
+ 
+
+ align:start position:0%
+know the the things that give that give
+your game structure and you know the
+
+ align:start position:0%
+your game structure and you know the
+ 
+
+ align:start position:0%
+your game structure and you know the
+limit the constraints of the things that
+
+ align:start position:0%
+limit the constraints of the things that
+ 
+
+ align:start position:0%
+limit the constraints of the things that
+you can't do. You you can't move from
+
+ align:start position:0%
+you can't do. You you can't move from
+ 
+
+ align:start position:0%
+you can't do. You you can't move from
+here to there without having your foot
+
+ align:start position:0%
+here to there without having your foot
+ 
+
+ align:start position:0%
+here to there without having your foot
+tied to another player. You know that
+
+ align:start position:0%
+tied to another player. You know that
+ 
+
+ align:start position:0%
+tied to another player. You know that
+that sort of constraint uh or a rule
+
+ align:start position:0%
+that sort of constraint uh or a rule
+ 
+
+ align:start position:0%
+that sort of constraint uh or a rule
+being you know you can't say anything uh
+
+ align:start position:0%
+being you know you can't say anything uh
+ 
+
+ align:start position:0%
+being you know you can't say anything uh
+during a a certain part of part of the
+
+ align:start position:0%
+during a a certain part of part of the
+ 
+
+ align:start position:0%
+during a a certain part of part of the
+game. Um there are two uh there are two
+
+ align:start position:0%
+game. Um there are two uh there are two
+ 
+
+ align:start position:0%
+game. Um there are two uh there are two
+bits of terminology introduced by Brendo
+
+ align:start position:0%
+bits of terminology introduced by Brendo
+ 
+
+ align:start position:0%
+bits of terminology introduced by Brendo
+uh and and Ian Shriber in in their book
+
+ align:start position:0%
+uh and and Ian Shriber in in their book
+ 
+
+ align:start position:0%
+uh and and Ian Shriber in in their book
+which is um core mechanic and core
+
+ align:start position:0%
+which is um core mechanic and core
+ 
+
+ align:start position:0%
+which is um core mechanic and core
+dynamic. Um so before I'm going to go
+
+ align:start position:0%
+dynamic. Um so before I'm going to go
+ 
+
+ align:start position:0%
+dynamic. Um so before I'm going to go
+into core mechanic and core dynamic and
+
+ align:start position:0%
+into core mechanic and core dynamic and
+ 
+
+ align:start position:0%
+into core mechanic and core dynamic and
+then talk about mechanic and dynamic. Um
+
+ align:start position:0%
+then talk about mechanic and dynamic. Um
+ 
+
+ align:start position:0%
+then talk about mechanic and dynamic. Um
+anyone want to throw out the definition
+
+ align:start position:0%
+anyone want to throw out the definition
+ 
+
+ align:start position:0%
+anyone want to throw out the definition
+of mechanic?
+
+ align:start position:0%
+of mechanic?
+ 
+
+ align:start position:0%
+of mechanic?
+It's sort of the uh the actions like a
+
+ align:start position:0%
+It's sort of the uh the actions like a
+ 
+
+ align:start position:0%
+It's sort of the uh the actions like a
+player takes during a game like the
+
+ align:start position:0%
+player takes during a game like the
+ 
+
+ align:start position:0%
+player takes during a game like the
+physical uh physical actions he takes.
+
+ align:start position:0%
+physical uh physical actions he takes.
+ 
+
+ align:start position:0%
+physical uh physical actions he takes.
+>> Okay. The the actions that a player
+
+ align:start position:0%
+>> Okay. The the actions that a player
+ 
+
+ align:start position:0%
+>> Okay. The the actions that a player
+decides to take
+
+ align:start position:0%
+decides to take
+ 
+
+ align:start position:0%
+decides to take
+>> decides to take action.
+
+ align:start position:0%
+>> decides to take action.
+ 
+
+ align:start position:0%
+>> decides to take action.
+>> Sorry if this is a little
+
+ align:start position:0%
+>> Sorry if this is a little
+ 
+
+ align:start position:0%
+>> Sorry if this is a little
+>> um I saw Patrick and Oh, did those hands
+
+ align:start position:0%
+>> um I saw Patrick and Oh, did those hands
+ 
+
+ align:start position:0%
+>> um I saw Patrick and Oh, did those hands
+just go there?
+
+ align:start position:0%
+just go there?
+ 
+
+ align:start position:0%
+just go there?
+>> I thought I saw a few more hands.
+
+ align:start position:0%
+>> I thought I saw a few more hands.
+ 
+
+ align:start position:0%
+>> I thought I saw a few more hands.
+>> Actions that are sort of designed by the
+
+ align:start position:0%
+>> Actions that are sort of designed by the
+ 
+
+ align:start position:0%
+>> Actions that are sort of designed by the
+game designer.
+
+ align:start position:0%
+game designer.
+ 
+
+ align:start position:0%
+game designer.
+>> Okay. So, intensive actions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um, design is definitely a good point.
+
+ align:start position:0%
+>> Um, design is definitely a good point.
+ 
+
+ align:start position:0%
+>> Um, design is definitely a good point.
+Uh, a game mechanic is definitely
+
+ align:start position:0%
+Uh, a game mechanic is definitely
+ 
+
+ align:start position:0%
+Uh, a game mechanic is definitely
+something that you're uh that you as a
+
+ align:start position:0%
+something that you're uh that you as a
+ 
+
+ align:start position:0%
+something that you're uh that you as a
+game designer control. Uh there are you
+
+ align:start position:0%
+game designer control. Uh there are you
+ 
+
+ align:start position:0%
+game designer control. Uh there are you
+know if if if a player decides to do
+
+ align:start position:0%
+know if if if a player decides to do
+ 
+
+ align:start position:0%
+know if if if a player decides to do
+something in the game that you did not
+
+ align:start position:0%
+something in the game that you did not
+ 
+
+ align:start position:0%
+something in the game that you did not
+explicitly think about and you did not
+
+ align:start position:0%
+explicitly think about and you did not
+ 
+
+ align:start position:0%
+explicitly think about and you did not
+explicitly say all right this is what
+
+ align:start position:0%
+explicitly say all right this is what
+ 
+
+ align:start position:0%
+explicitly say all right this is what
+players are going to be doing in the
+
+ align:start position:0%
+players are going to be doing in the
+ 
+
+ align:start position:0%
+players are going to be doing in the
+game then it might not not actually be a
+
+ align:start position:0%
+game then it might not not actually be a
+ 
+
+ align:start position:0%
+game then it might not not actually be a
+mechanic. It might be something that
+
+ align:start position:0%
+mechanic. It might be something that
+ 
+
+ align:start position:0%
+mechanic. It might be something that
+you're discovering in your play play
+
+ align:start position:0%
+you're discovering in your play play
+ 
+
+ align:start position:0%
+you're discovering in your play play
+testing that you will turn into a
+
+ align:start position:0%
+testing that you will turn into a
+ 
+
+ align:start position:0%
+testing that you will turn into a
+mechanic but because it's not designed
+
+ align:start position:0%
+mechanic but because it's not designed
+ 
+
+ align:start position:0%
+mechanic but because it's not designed
+uh it's kind of it becomes more like a
+
+ align:start position:0%
+uh it's kind of it becomes more like a
+ 
+
+ align:start position:0%
+uh it's kind of it becomes more like a
+strategy actually like a immersion
+
+ align:start position:0%
+strategy actually like a immersion
+ 
+
+ align:start position:0%
+strategy actually like a immersion
+strategy. Sorry, you were saying Jeremy.
+
+ align:start position:0%
+strategy. Sorry, you were saying Jeremy.
+ 
+
+ align:start position:0%
+strategy. Sorry, you were saying Jeremy.
+>> Is it more like a dynamic?
+
+ align:start position:0%
+>> Is it more like a dynamic?
+ 
+
+ align:start position:0%
+>> Is it more like a dynamic?
+>> Um, possibly. There are times where it
+
+ align:start position:0%
+>> Um, possibly. There are times where it
+ 
+
+ align:start position:0%
+>> Um, possibly. There are times where it
+is. Yeah. And yeah, um, actually let's
+
+ align:start position:0%
+is. Yeah. And yeah, um, actually let's
+ 
+
+ align:start position:0%
+is. Yeah. And yeah, um, actually let's
+throw out some definitions of dynamic.
+
+ align:start position:0%
+throw out some definitions of dynamic.
+ 
+
+ align:start position:0%
+throw out some definitions of dynamic.
+Uh, what do people
+
+ align:start position:0%
+Uh, what do people
+ 
+
+ align:start position:0%
+Uh, what do people
+uh, well, Jeremy,
+
+ align:start position:0%
+uh, well, Jeremy,
+ 
+
+ align:start position:0%
+uh, well, Jeremy,
+>> behavior that emerges from mechanics.
+
+ align:start position:0%
+>> behavior that emerges from mechanics.
+ 
+
+ align:start position:0%
+>> behavior that emerges from mechanics.
+>> Okay. So, so emerges emergent behavior.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What what else
+
+ align:start position:0%
+What what else
+ 
+
+ align:start position:0%
+What what else
+uh use of mechanics that isn't uh
+
+ align:start position:0%
+uh use of mechanics that isn't uh
+ 
+
+ align:start position:0%
+uh use of mechanics that isn't uh
+directly stated in the rules of the
+
+ align:start position:0%
+directly stated in the rules of the
+ 
+
+ align:start position:0%
+directly stated in the rules of the
+game?
+
+ align:start position:0%
+game?
+ 
+
+ align:start position:0%
+game?
+>> Okay, so so unstated.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I'm running out of space here.
+
+ align:start position:0%
+>> I'm running out of space here.
+ 
+
+ align:start position:0%
+>> I'm running out of space here.
+>> I thought I saw a hand.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No. Okay. Uh All right. So, um yeah,
+
+ align:start position:0%
+No. Okay. Uh All right. So, um yeah,
+ 
+
+ align:start position:0%
+No. Okay. Uh All right. So, um yeah,
+dynamics are basically interactions of
+
+ align:start position:0%
+dynamics are basically interactions of
+ 
+
+ align:start position:0%
+dynamics are basically interactions of
+mechanics. you know, it's like you don't
+
+ align:start position:0%
+mechanics. you know, it's like you don't
+ 
+
+ align:start position:0%
+mechanics. you know, it's like you don't
+have a uh uh you don't have anything
+
+ align:start position:0%
+have a uh uh you don't have anything
+ 
+
+ align:start position:0%
+have a uh uh you don't have anything
+that may necessarily explicitly say, you
+
+ align:start position:0%
+that may necessarily explicitly say, you
+ 
+
+ align:start position:0%
+that may necessarily explicitly say, you
+know, because of this one rule and
+
+ align:start position:0%
+know, because of this one rule and
+ 
+
+ align:start position:0%
+know, because of this one rule and
+because of one this other rule and
+
+ align:start position:0%
+because of one this other rule and
+ 
+
+ align:start position:0%
+because of one this other rule and
+because of the things that the players
+
+ align:start position:0%
+because of the things that the players
+ 
+
+ align:start position:0%
+because of the things that the players
+can do in that, you know, a a good
+
+ align:start position:0%
+can do in that, you know, a a good
+ 
+
+ align:start position:0%
+can do in that, you know, a a good
+strategy is to do something else. So,
+
+ align:start position:0%
+strategy is to do something else. So,
+ 
+
+ align:start position:0%
+strategy is to do something else. So,
+let me see whether I can think of an
+
+ align:start position:0%
+let me see whether I can think of an
+ 
+
+ align:start position:0%
+let me see whether I can think of an
+example. Right now, everything that's
+
+ align:start position:0%
+example. Right now, everything that's
+ 
+
+ align:start position:0%
+example. Right now, everything that's
+coming to my head is Starcraft. Um,
+
+ align:start position:0%
+coming to my head is Starcraft. Um,
+ 
+
+ align:start position:0%
+coming to my head is Starcraft. Um,
+>> has that been the case for the past few
+
+ align:start position:0%
+>> has that been the case for the past few
+ 
+
+ align:start position:0%
+>> has that been the case for the past few
+weeks?
+
+ align:start position:0%
+weeks?
+ 
+
+ align:start position:0%
+weeks?
+>> Unfortunately, yes. Uh, by the way, if
+
+ align:start position:0%
+>> Unfortunately, yes. Uh, by the way, if
+ 
+
+ align:start position:0%
+>> Unfortunately, yes. Uh, by the way, if
+anybody is playing Starcraft, I need
+
+ align:start position:0%
+anybody is playing Starcraft, I need
+ 
+
+ align:start position:0%
+anybody is playing Starcraft, I need
+testers. Uh, because
+
+ align:start position:0%
+testers. Uh, because
+ 
+
+ align:start position:0%
+testers. Uh, because
+>> yes,
+
+ align:start position:0%
+>> yes,
+ 
+
+ align:start position:0%
+>> yes,
+>> I I I need testers for a map that I'm
+
+ align:start position:0%
+>> I I I need testers for a map that I'm
+ 
+
+ align:start position:0%
+>> I I I need testers for a map that I'm
+resigning. Um,
+
+ align:start position:0%
+resigning. Um,
+ 
+
+ align:start position:0%
+resigning. Um,
+>> especially
+
+ align:start position:0%
+>> especially
+ 
+
+ align:start position:0%
+>> especially
+I play
+
+ align:start position:0%
+I play
+ 
+
+ align:start position:0%
+I play
+>> there's a good example in Puerto Rico.
+
+ align:start position:0%
+>> there's a good example in Puerto Rico.
+ 
+
+ align:start position:0%
+>> there's a good example in Puerto Rico.
+>> Oh, yeah.
+
+ align:start position:0%
+>> Oh, yeah.
+ 
+
+ align:start position:0%
+>> Oh, yeah.
+>> Right. So, there's this role selection
+
+ align:start position:0%
+>> Right. So, there's this role selection
+ 
+
+ align:start position:0%
+>> Right. So, there's this role selection
+mechanic where everybody picks the thing
+
+ align:start position:0%
+mechanic where everybody picks the thing
+ 
+
+ align:start position:0%
+mechanic where everybody picks the thing
+which they want to happen during the
+
+ align:start position:0%
+which they want to happen during the
+ 
+
+ align:start position:0%
+which they want to happen during the
+turn and they get a bonus for doing it.
+
+ align:start position:0%
+turn and they get a bonus for doing it.
+ 
+
+ align:start position:0%
+turn and they get a bonus for doing it.
+Um and also everybody chooses to like
+
+ align:start position:0%
+Um and also everybody chooses to like
+ 
+
+ align:start position:0%
+Um and also everybody chooses to like
+build particular crops.
+
+ align:start position:0%
+build particular crops.
+ 
+
+ align:start position:0%
+build particular crops.
+>> Um and the dynamic that emerges from the
+
+ align:start position:0%
+>> Um and the dynamic that emerges from the
+ 
+
+ align:start position:0%
+>> Um and the dynamic that emerges from the
+sequence of play which goes clockwise is
+
+ align:start position:0%
+sequence of play which goes clockwise is
+ 
+
+ align:start position:0%
+sequence of play which goes clockwise is
+that it's best to
+
+ align:start position:0%
+that it's best to
+ 
+
+ align:start position:0%
+that it's best to
+optimize your strategy so that you are
+
+ align:start position:0%
+optimize your strategy so that you are
+ 
+
+ align:start position:0%
+optimize your strategy so that you are
+doing so that you are benefiting from
+
+ align:start position:0%
+doing so that you are benefiting from
+ 
+
+ align:start position:0%
+doing so that you are benefiting from
+the role that the person to your right
+
+ align:start position:0%
+the role that the person to your right
+ 
+
+ align:start position:0%
+the role that the person to your right
+is most likely to choose.
+
+ align:start position:0%
+is most likely to choose.
+ 
+
+ align:start position:0%
+is most likely to choose.
+>> But you're making the goods that the
+
+ align:start position:0%
+>> But you're making the goods that the
+ 
+
+ align:start position:0%
+>> But you're making the goods that the
+person to your left is most likely to
+
+ align:start position:0%
+person to your left is most likely to
+ 
+
+ align:start position:0%
+person to your left is most likely to
+want to ship or sell. So the mechanic is
+
+ align:start position:0%
+want to ship or sell. So the mechanic is
+ 
+
+ align:start position:0%
+want to ship or sell. So the mechanic is
+roll selection and turn order
+
+ align:start position:0%
+roll selection and turn order
+ 
+
+ align:start position:0%
+roll selection and turn order
+>> and then the dynamic is the strategy
+
+ align:start position:0%
+>> and then the dynamic is the strategy
+ 
+
+ align:start position:0%
+>> and then the dynamic is the strategy
+written purpose out of that
+
+ align:start position:0%
+written purpose out of that
+ 
+
+ align:start position:0%
+written purpose out of that
+>> which which gives you some idea on what
+
+ align:start position:0%
+>> which which gives you some idea on what
+ 
+
+ align:start position:0%
+>> which which gives you some idea on what
+to select as oo you know the the
+
+ align:start position:0%
+to select as oo you know the the
+ 
+
+ align:start position:0%
+to select as oo you know the the
+mechanic is you can select the dynamic
+
+ align:start position:0%
+mechanic is you can select the dynamic
+ 
+
+ align:start position:0%
+mechanic is you can select the dynamic
+is here are a couple of strategies that
+
+ align:start position:0%
+is here are a couple of strategies that
+ 
+
+ align:start position:0%
+is here are a couple of strategies that
+you can use in sort of assessing what
+
+ align:start position:0%
+you can use in sort of assessing what
+ 
+
+ align:start position:0%
+you can use in sort of assessing what
+would be best to select. Um, and if all
+
+ align:start position:0%
+would be best to select. Um, and if all
+ 
+
+ align:start position:0%
+would be best to select. Um, and if all
+the players start to understand that,
+
+ align:start position:0%
+the players start to understand that,
+ 
+
+ align:start position:0%
+the players start to understand that,
+then it almost becomes like a, you know,
+
+ align:start position:0%
+then it almost becomes like a, you know,
+ 
+
+ align:start position:0%
+then it almost becomes like a, you know,
+like a second layer of rules almost. And
+
+ align:start position:0%
+like a second layer of rules almost. And
+ 
+
+ align:start position:0%
+like a second layer of rules almost. And
+if anyone's played a game like Bridge,
+
+ align:start position:0%
+if anyone's played a game like Bridge,
+ 
+
+ align:start position:0%
+if anyone's played a game like Bridge,
+for instance, there's actually a ton of
+
+ align:start position:0%
+for instance, there's actually a ton of
+ 
+
+ align:start position:0%
+for instance, there's actually a ton of
+things that are assumed in the play
+
+ align:start position:0%
+things that are assumed in the play
+ 
+
+ align:start position:0%
+things that are assumed in the play
+which are not actually in the rules of
+
+ align:start position:0%
+which are not actually in the rules of
+ 
+
+ align:start position:0%
+which are not actually in the rules of
+bridge. Uh, when it comes to bidding,
+
+ align:start position:0%
+bridge. Uh, when it comes to bidding,
+ 
+
+ align:start position:0%
+bridge. Uh, when it comes to bidding,
+like when you call out a bid, it's
+
+ align:start position:0%
+like when you call out a bid, it's
+ 
+
+ align:start position:0%
+like when you call out a bid, it's
+highly dependent on what you actually
+
+ align:start position:0%
+highly dependent on what you actually
+ 
+
+ align:start position:0%
+highly dependent on what you actually
+have in your cart uh in in in your card
+
+ align:start position:0%
+have in your cart uh in in in your card
+ 
+
+ align:start position:0%
+have in your cart uh in in in your card
+hand. And that's not actually written in
+
+ align:start position:0%
+hand. And that's not actually written in
+ 
+
+ align:start position:0%
+hand. And that's not actually written in
+the rules anywhere. Um but the
+
+ align:start position:0%
+the rules anywhere. Um but the
+ 
+
+ align:start position:0%
+the rules anywhere. Um but the
+assumption is that there is optimal way
+
+ align:start position:0%
+assumption is that there is optimal way
+ 
+
+ align:start position:0%
+assumption is that there is optimal way
+to do it and since there's optimal way
+
+ align:start position:0%
+to do it and since there's optimal way
+ 
+
+ align:start position:0%
+to do it and since there's optimal way
+to do it everyone's expected to know
+
+ align:start position:0%
+to do it everyone's expected to know
+ 
+
+ align:start position:0%
+to do it everyone's expected to know
+there's optimal ways. Um the example in
+
+ align:start position:0%
+there's optimal ways. Um the example in
+ 
+
+ align:start position:0%
+there's optimal ways. Um the example in
+the book was chess moves like you know
+
+ align:start position:0%
+the book was chess moves like you know
+ 
+
+ align:start position:0%
+the book was chess moves like you know
+every single move uh piece of chess uh
+
+ align:start position:0%
+every single move uh piece of chess uh
+ 
+
+ align:start position:0%
+every single move uh piece of chess uh
+has a set of moves that it can perform
+
+ align:start position:0%
+has a set of moves that it can perform
+ 
+
+ align:start position:0%
+has a set of moves that it can perform
+right pawns go one or two squares
+
+ align:start position:0%
+right pawns go one or two squares
+ 
+
+ align:start position:0%
+right pawns go one or two squares
+depending whether the starting uh
+
+ align:start position:0%
+depending whether the starting uh
+ 
+
+ align:start position:0%
+depending whether the starting uh
+bishops move diagonally but there are
+
+ align:start position:0%
+bishops move diagonally but there are
+ 
+
+ align:start position:0%
+bishops move diagonally but there are
+also opening gambits.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There are opening habits that that that
+
+ align:start position:0%
+There are opening habits that that that
+ 
+
+ align:start position:0%
+There are opening habits that that that
+that are uh that are also wellknown at
+
+ align:start position:0%
+that are uh that are also wellknown at
+ 
+
+ align:start position:0%
+that are uh that are also wellknown at
+least among professional uh chess
+
+ align:start position:0%
+least among professional uh chess
+ 
+
+ align:start position:0%
+least among professional uh chess
+players. And the idea being oh this
+
+ align:start position:0%
+players. And the idea being oh this
+ 
+
+ align:start position:0%
+players. And the idea being oh this
+person is using this opening therefore
+
+ align:start position:0%
+person is using this opening therefore
+ 
+
+ align:start position:0%
+person is using this opening therefore
+if I counter it with this response I
+
+ align:start position:0%
+if I counter it with this response I
+ 
+
+ align:start position:0%
+if I counter it with this response I
+actually have uh you know a reasonable
+
+ align:start position:0%
+actually have uh you know a reasonable
+ 
+
+ align:start position:0%
+actually have uh you know a reasonable
+chance of actually winning the the this
+
+ align:start position:0%
+chance of actually winning the the this
+ 
+
+ align:start position:0%
+chance of actually winning the the this
+game and professional chess players know
+
+ align:start position:0%
+game and professional chess players know
+ 
+
+ align:start position:0%
+game and professional chess players know
+this. Um the other thing that comes up
+
+ align:start position:0%
+this. Um the other thing that comes up
+ 
+
+ align:start position:0%
+this. Um the other thing that comes up
+in chess which is not in the book is uh
+
+ align:start position:0%
+in chess which is not in the book is uh
+ 
+
+ align:start position:0%
+in chess which is not in the book is uh
+there is um there is the concept of
+
+ align:start position:0%
+there is um there is the concept of
+ 
+
+ align:start position:0%
+there is um there is the concept of
+threatened squares. If you if you move u
+
+ align:start position:0%
+threatened squares. If you if you move u
+ 
+
+ align:start position:0%
+threatened squares. If you if you move u
+if there is a square where there is no
+
+ align:start position:0%
+if there is a square where there is no
+ 
+
+ align:start position:0%
+if there is a square where there is no
+piece on a chess board. Everyone here
+
+ align:start position:0%
+piece on a chess board. Everyone here
+ 
+
+ align:start position:0%
+piece on a chess board. Everyone here
+knows the rules of chess more or less.
+
+ align:start position:0%
+knows the rules of chess more or less.
+ 
+
+ align:start position:0%
+knows the rules of chess more or less.
+Yeah. Um, so say you've got a bishop and
+
+ align:start position:0%
+Yeah. Um, so say you've got a bishop and
+ 
+
+ align:start position:0%
+Yeah. Um, so say you've got a bishop and
+you know this is my very simple chess
+
+ align:start position:0%
+you know this is my very simple chess
+ 
+
+ align:start position:0%
+you know this is my very simple chess
+board and you've got a bishop
+
+ align:start position:0%
+board and you've got a bishop
+ 
+
+ align:start position:0%
+board and you've got a bishop
+um and and and it can move like that,
+
+ align:start position:0%
+um and and and it can move like that,
+ 
+
+ align:start position:0%
+um and and and it can move like that,
+right? So every single square along
+
+ align:start position:0%
+right? So every single square along
+ 
+
+ align:start position:0%
+right? So every single square along
+these lines uh is threatened. It's it's
+
+ align:start position:0%
+these lines uh is threatened. It's it's
+ 
+
+ align:start position:0%
+these lines uh is threatened. It's it's
+something which a uh which which a uh
+
+ align:start position:0%
+something which a uh which which a uh
+ 
+
+ align:start position:0%
+something which a uh which which a uh
+the bishop could move to unless of
+
+ align:start position:0%
+the bishop could move to unless of
+ 
+
+ align:start position:0%
+the bishop could move to unless of
+course it's you know blocked by by a
+
+ align:start position:0%
+course it's you know blocked by by a
+ 
+
+ align:start position:0%
+course it's you know blocked by by a
+pawn or something and these are no
+
+ align:start position:0%
+pawn or something and these are no
+ 
+
+ align:start position:0%
+pawn or something and these are no
+longer threatened. what it honest um
+
+ align:start position:0%
+longer threatened. what it honest um
+ 
+
+ align:start position:0%
+longer threatened. what it honest um
+uh if if you're a knight obviously is no
+
+ align:start position:0%
+uh if if you're a knight obviously is no
+ 
+
+ align:start position:0%
+uh if if you're a knight obviously is no
+longer straight lines. It becomes, you
+
+ align:start position:0%
+longer straight lines. It becomes, you
+ 
+
+ align:start position:0%
+longer straight lines. It becomes, you
+know, specific sort of like a weird
+
+ align:start position:0%
+know, specific sort of like a weird
+ 
+
+ align:start position:0%
+know, specific sort of like a weird
+stochastic pattern of squares that
+
+ align:start position:0%
+stochastic pattern of squares that
+ 
+
+ align:start position:0%
+stochastic pattern of squares that
+become threatened. Uh but uh but but but
+
+ align:start position:0%
+become threatened. Uh but uh but but but
+ 
+
+ align:start position:0%
+become threatened. Uh but uh but but but
+but the idea of here's this square now
+
+ align:start position:0%
+but the idea of here's this square now
+ 
+
+ align:start position:0%
+but the idea of here's this square now
+that nobody dares move into until
+
+ align:start position:0%
+that nobody dares move into until
+ 
+
+ align:start position:0%
+that nobody dares move into until
+something's done about that bishop.
+
+ align:start position:0%
+something's done about that bishop.
+ 
+
+ align:start position:0%
+something's done about that bishop.
+Either move something gets moved in its
+
+ align:start position:0%
+Either move something gets moved in its
+ 
+
+ align:start position:0%
+Either move something gets moved in its
+way or you know some something takes out
+
+ align:start position:0%
+way or you know some something takes out
+ 
+
+ align:start position:0%
+way or you know some something takes out
+that bishop or forces the bishop to move
+
+ align:start position:0%
+that bishop or forces the bishop to move
+ 
+
+ align:start position:0%
+that bishop or forces the bishop to move
+by threatening. it instead in a way that
+
+ align:start position:0%
+by threatening. it instead in a way that
+ 
+
+ align:start position:0%
+by threatening. it instead in a way that
+they cannot respond. So threats and
+
+ align:start position:0%
+they cannot respond. So threats and
+ 
+
+ align:start position:0%
+they cannot respond. So threats and
+squares is not a rule in in in in uh in
+
+ align:start position:0%
+squares is not a rule in in in in uh in
+ 
+
+ align:start position:0%
+squares is not a rule in in in in uh in
+chess but it greatly shapes your
+
+ align:start position:0%
+chess but it greatly shapes your
+ 
+
+ align:start position:0%
+chess but it greatly shapes your
+decision m your decision making and
+
+ align:start position:0%
+decision m your decision making and
+ 
+
+ align:start position:0%
+decision m your decision making and
+that's the difference between dynamic
+
+ align:start position:0%
+that's the difference between dynamic
+ 
+
+ align:start position:0%
+that's the difference between dynamic
+and mechanic. Um there's a lot of strong
+
+ align:start position:0%
+and mechanic. Um there's a lot of strong
+ 
+
+ align:start position:0%
+and mechanic. Um there's a lot of strong
+correspondence between uh mechanics and
+
+ align:start position:0%
+correspondence between uh mechanics and
+ 
+
+ align:start position:0%
+correspondence between uh mechanics and
+weights. Um but uh and and I had a long
+
+ align:start position:0%
+weights. Um but uh and and I had a long
+ 
+
+ align:start position:0%
+weights. Um but uh and and I had a long
+long uh little rant about exactly what
+
+ align:start position:0%
+long uh little rant about exactly what
+ 
+
+ align:start position:0%
+long uh little rant about exactly what
+the difference is between mechanics and
+
+ align:start position:0%
+the difference is between mechanics and
+ 
+
+ align:start position:0%
+the difference is between mechanics and
+rules and uh and what I basically I I
+
+ align:start position:0%
+rules and uh and what I basically I I
+ 
+
+ align:start position:0%
+rules and uh and what I basically I I
+I'm not going to give the rant right now
+
+ align:start position:0%
+I'm not going to give the rant right now
+ 
+
+ align:start position:0%
+I'm not going to give the rant right now
+but but it's like overlapping ven
+
+ align:start position:0%
+but but it's like overlapping ven
+ 
+
+ align:start position:0%
+but but it's like overlapping ven
+diagram you know there's a very very
+
+ align:start position:0%
+diagram you know there's a very very
+ 
+
+ align:start position:0%
+diagram you know there's a very very
+large area where it's exactly the same
+
+ align:start position:0%
+large area where it's exactly the same
+ 
+
+ align:start position:0%
+large area where it's exactly the same
+thing. Um, my general rubric for you for
+
+ align:start position:0%
+thing. Um, my general rubric for you for
+ 
+
+ align:start position:0%
+thing. Um, my general rubric for you for
+trying to figure out whether something
+
+ align:start position:0%
+trying to figure out whether something
+ 
+
+ align:start position:0%
+trying to figure out whether something
+is a mechanic or not is whether this is
+
+ align:start position:0%
+is a mechanic or not is whether this is
+ 
+
+ align:start position:0%
+is a mechanic or not is whether this is
+the thing that changes the state of the
+
+ align:start position:0%
+the thing that changes the state of the
+ 
+
+ align:start position:0%
+the thing that changes the state of the
+game. If it's an action, if it's if it's
+
+ align:start position:0%
+game. If it's an action, if it's if it's
+ 
+
+ align:start position:0%
+game. If it's an action, if it's if it's
+something that someone's going to be
+
+ align:start position:0%
+something that someone's going to be
+ 
+
+ align:start position:0%
+something that someone's going to be
+doing to change the state of what the
+
+ align:start position:0%
+doing to change the state of what the
+ 
+
+ align:start position:0%
+doing to change the state of what the
+game is, you know, in chess, that's
+
+ align:start position:0%
+game is, you know, in chess, that's
+ 
+
+ align:start position:0%
+game is, you know, in chess, that's
+largely the move the movement of of a
+
+ align:start position:0%
+largely the move the movement of of a
+ 
+
+ align:start position:0%
+largely the move the movement of of a
+piece. Um if it's um
+
+ align:start position:0%
+piece. Um if it's um
+ 
+
+ align:start position:0%
+piece. Um if it's um
+uh if it's ultimate you know it could be
+
+ align:start position:0%
+uh if it's ultimate you know it could be
+ 
+
+ align:start position:0%
+uh if it's ultimate you know it could be
+just physical movement you know you are
+
+ align:start position:0%
+just physical movement you know you are
+ 
+
+ align:start position:0%
+just physical movement you know you are
+limited on when you can physically move
+
+ align:start position:0%
+limited on when you can physically move
+ 
+
+ align:start position:0%
+limited on when you can physically move
+if you have that frisbee you're not
+
+ align:start position:0%
+if you have that frisbee you're not
+ 
+
+ align:start position:0%
+if you have that frisbee you're not
+moving uh well you're feet are not
+
+ align:start position:0%
+moving uh well you're feet are not
+ 
+
+ align:start position:0%
+moving uh well you're feet are not
+moving I believe that's a of
+
+ align:start position:0%
+moving I believe that's a of
+ 
+
+ align:start position:0%
+moving I believe that's a of
+um so so uh the the reason why I use
+
+ align:start position:0%
+um so so uh the the reason why I use
+ 
+
+ align:start position:0%
+um so so uh the the reason why I use
+that definition is because there are
+
+ align:start position:0%
+that definition is because there are
+ 
+
+ align:start position:0%
+that definition is because there are
+occasionally times where I need to talk
+
+ align:start position:0%
+occasionally times where I need to talk
+ 
+
+ align:start position:0%
+occasionally times where I need to talk
+about mechanics that players aren't
+
+ align:start position:0%
+about mechanics that players aren't
+ 
+
+ align:start position:0%
+about mechanics that players aren't
+actually doing like the game requires
+
+ align:start position:0%
+actually doing like the game requires
+ 
+
+ align:start position:0%
+actually doing like the game requires
+certain pieces to move in a certain way,
+
+ align:start position:0%
+certain pieces to move in a certain way,
+ 
+
+ align:start position:0%
+certain pieces to move in a certain way,
+certain things to happen in the game.
+
+ align:start position:0%
+certain things to happen in the game.
+ 
+
+ align:start position:0%
+certain things to happen in the game.
+You know, um in Settlers of Katan, for
+
+ align:start position:0%
+You know, um in Settlers of Katan, for
+ 
+
+ align:start position:0%
+You know, um in Settlers of Katan, for
+instance, you have these die rolls. Uh
+
+ align:start position:0%
+instance, you have these die rolls. Uh
+ 
+
+ align:start position:0%
+instance, you have these die rolls. Uh
+and um actually that's not a good
+
+ align:start position:0%
+and um actually that's not a good
+ 
+
+ align:start position:0%
+and um actually that's not a good
+example, let me think. Um well, right at
+
+ align:start position:0%
+example, let me think. Um well, right at
+ 
+
+ align:start position:0%
+example, let me think. Um well, right at
+the beginning of Setters of Katanda is
+
+ align:start position:0%
+the beginning of Setters of Katanda is
+ 
+
+ align:start position:0%
+the beginning of Setters of Katanda is
+the way how you set up the board and
+
+ align:start position:0%
+the way how you set up the board and
+ 
+
+ align:start position:0%
+the way how you set up the board and
+that establishes what a game state is
+
+ align:start position:0%
+that establishes what a game state is
+ 
+
+ align:start position:0%
+that establishes what a game state is
+going to be. You know, it it changes the
+
+ align:start position:0%
+going to be. You know, it it changes the
+ 
+
+ align:start position:0%
+going to be. You know, it it changes the
+game state by giving you a game state in
+
+ align:start position:0%
+game state by giving you a game state in
+ 
+
+ align:start position:0%
+game state by giving you a game state in
+the first place. um that I I I consider
+
+ align:start position:0%
+the first place. um that I I I consider
+ 
+
+ align:start position:0%
+the first place. um that I I I consider
+that a mechanic that that is something
+
+ align:start position:0%
+that a mechanic that that is something
+ 
+
+ align:start position:0%
+that a mechanic that that is something
+that's going uh that that it's but
+
+ align:start position:0%
+that's going uh that that it's but
+ 
+
+ align:start position:0%
+that's going uh that that it's but
+that's not one one rule. It's actually a
+
+ align:start position:0%
+that's not one one rule. It's actually a
+ 
+
+ align:start position:0%
+that's not one one rule. It's actually a
+whole collection of rules and if you're
+
+ align:start position:0%
+whole collection of rules and if you're
+ 
+
+ align:start position:0%
+whole collection of rules and if you're
+interested in finding out what those
+
+ align:start position:0%
+interested in finding out what those
+ 
+
+ align:start position:0%
+interested in finding out what those
+rules are, the box is actually in that
+
+ align:start position:0%
+rules are, the box is actually in that
+ 
+
+ align:start position:0%
+rules are, the box is actually in that
+closet over there. Um but it's like
+
+ align:start position:0%
+closet over there. Um but it's like
+ 
+
+ align:start position:0%
+closet over there. Um but it's like
+something like five or six different
+
+ align:start position:0%
+something like five or six different
+ 
+
+ align:start position:0%
+something like five or six different
+rules on this is how you set up your
+
+ align:start position:0%
+rules on this is how you set up your
+ 
+
+ align:start position:0%
+rules on this is how you set up your
+board. It's going to set up your game
+
+ align:start position:0%
+board. It's going to set up your game
+ 
+
+ align:start position:0%
+board. It's going to set up your game
+state and I consider that a mechanic. Um
+
+ align:start position:0%
+state and I consider that a mechanic. Um
+ 
+
+ align:start position:0%
+state and I consider that a mechanic. Um
+how people do bidding and buying things
+
+ align:start position:0%
+how people do bidding and buying things
+ 
+
+ align:start position:0%
+how people do bidding and buying things
+in setters of katan that's dynamic. you
+
+ align:start position:0%
+in setters of katan that's dynamic. you
+ 
+
+ align:start position:0%
+in setters of katan that's dynamic. you
+know that's that you know there are no
+
+ align:start position:0%
+know that's that you know there are no
+ 
+
+ align:start position:0%
+know that's that you know there are no
+real rules on how much something costs
+
+ align:start position:0%
+real rules on how much something costs
+ 
+
+ align:start position:0%
+real rules on how much something costs
+that's up to the players to work out on
+
+ align:start position:0%
+that's up to the players to work out on
+ 
+
+ align:start position:0%
+that's up to the players to work out on
+their own um so that's how I sort of
+
+ align:start position:0%
+their own um so that's how I sort of
+ 
+
+ align:start position:0%
+their own um so that's how I sort of
+consider the difference between core
+
+ align:start position:0%
+consider the difference between core
+ 
+
+ align:start position:0%
+consider the difference between core
+dynamic uh between dynamic and and and
+
+ align:start position:0%
+dynamic uh between dynamic and and and
+ 
+
+ align:start position:0%
+dynamic uh between dynamic and and and
+mechanic um really really useful
+
+ align:start position:0%
+mechanic um really really useful
+ 
+
+ align:start position:0%
+mechanic um really really useful
+concepts because really for the most
+
+ align:start position:0%
+concepts because really for the most
+ 
+
+ align:start position:0%
+concepts because really for the most
+part as a designer you have an idea of
+
+ align:start position:0%
+part as a designer you have an idea of
+ 
+
+ align:start position:0%
+part as a designer you have an idea of
+what kind of dynamics are interesting uh
+
+ align:start position:0%
+what kind of dynamics are interesting uh
+ 
+
+ align:start position:0%
+what kind of dynamics are interesting uh
+and the more games that you play the and
+
+ align:start position:0%
+and the more games that you play the and
+ 
+
+ align:start position:0%
+and the more games that you play the and
+you know the more inspiration that you
+
+ align:start position:0%
+you know the more inspiration that you
+ 
+
+ align:start position:0%
+you know the more inspiration that you
+get from various sources. Uh your vocab
+
+ align:start position:0%
+get from various sources. Uh your vocab
+ 
+
+ align:start position:0%
+get from various sources. Uh your vocab
+your range of different ideas of what
+
+ align:start position:0%
+your range of different ideas of what
+ 
+
+ align:start position:0%
+your range of different ideas of what
+kind of dynamics might be interesting is
+
+ align:start position:0%
+kind of dynamics might be interesting is
+ 
+
+ align:start position:0%
+kind of dynamics might be interesting is
+going to expand. Uh but all you have
+
+ align:start position:0%
+going to expand. Uh but all you have
+ 
+
+ align:start position:0%
+going to expand. Uh but all you have
+control on are mechanics are the
+
+ align:start position:0%
+control on are mechanics are the
+ 
+
+ align:start position:0%
+control on are mechanics are the
+specific rules that that you're giving
+
+ align:start position:0%
+specific rules that that you're giving
+ 
+
+ align:start position:0%
+specific rules that that you're giving
+your your
+
+ align:start position:0%
+your your
+ 
+
+ align:start position:0%
+your your
+note that game mechanics don't
+
+ align:start position:0%
+note that game mechanics don't
+ 
+
+ align:start position:0%
+note that game mechanics don't
+necessarily need to be written uh or
+
+ align:start position:0%
+necessarily need to be written uh or
+ 
+
+ align:start position:0%
+necessarily need to be written uh or
+described out. Um, this is one thing
+
+ align:start position:0%
+described out. Um, this is one thing
+ 
+
+ align:start position:0%
+described out. Um, this is one thing
+that I think you and your teammates
+
+ align:start position:0%
+that I think you and your teammates
+ 
+
+ align:start position:0%
+that I think you and your teammates
+should figure out when you're talking
+
+ align:start position:0%
+should figure out when you're talking
+ 
+
+ align:start position:0%
+should figure out when you're talking
+about mechanics for a given project. Are
+
+ align:start position:0%
+about mechanics for a given project. Are
+ 
+
+ align:start position:0%
+about mechanics for a given project. Are
+we just talking about the things that
+
+ align:start position:0%
+we just talking about the things that
+ 
+
+ align:start position:0%
+we just talking about the things that
+we're writing down? Because there are
+
+ align:start position:0%
+we're writing down? Because there are
+ 
+
+ align:start position:0%
+we're writing down? Because there are
+some assumptions that uh that are just
+
+ align:start position:0%
+some assumptions that uh that are just
+ 
+
+ align:start position:0%
+some assumptions that uh that are just
+given. Um, we are playing a game in,
+
+ align:start position:0%
+given. Um, we are playing a game in,
+ 
+
+ align:start position:0%
+given. Um, we are playing a game in,
+you know, we're playing some sort of
+
+ align:start position:0%
+you know, we're playing some sort of
+ 
+
+ align:start position:0%
+you know, we're playing some sort of
+schoolyard game or something, you know,
+
+ align:start position:0%
+schoolyard game or something, you know,
+ 
+
+ align:start position:0%
+schoolyard game or something, you know,
+uh, hitting people with large solid
+
+ align:start position:0%
+uh, hitting people with large solid
+ 
+
+ align:start position:0%
+uh, hitting people with large solid
+solid objects is disallowed or something
+
+ align:start position:0%
+solid objects is disallowed or something
+ 
+
+ align:start position:0%
+solid objects is disallowed or something
+like that, you know, not necessarily
+
+ align:start position:0%
+like that, you know, not necessarily
+ 
+
+ align:start position:0%
+like that, you know, not necessarily
+something you need to write down unless
+
+ align:start position:0%
+something you need to write down unless
+ 
+
+ align:start position:0%
+something you need to write down unless
+you're playing with certain people, but
+
+ align:start position:0%
+you're playing with certain people, but
+ 
+
+ align:start position:0%
+you're playing with certain people, but
+you have uh, you know, but you can
+
+ align:start position:0%
+you have uh, you know, but you can
+ 
+
+ align:start position:0%
+you have uh, you know, but you can
+assume that's a game a game mechanic
+
+ align:start position:0%
+assume that's a game a game mechanic
+ 
+
+ align:start position:0%
+assume that's a game a game mechanic
+there. Um, things like how fast, you
+
+ align:start position:0%
+there. Um, things like how fast, you
+ 
+
+ align:start position:0%
+there. Um, things like how fast, you
+know, people normally do things. There's
+
+ align:start position:0%
+know, people normally do things. There's
+ 
+
+ align:start position:0%
+know, people normally do things. There's
+a game over there over over here called
+
+ align:start position:0%
+a game over there over over here called
+ 
+
+ align:start position:0%
+a game over there over over here called
+Falling uh which is actually a real-time
+
+ align:start position:0%
+Falling uh which is actually a real-time
+ 
+
+ align:start position:0%
+Falling uh which is actually a real-time
+card game. It it goes as fast as you can
+
+ align:start position:0%
+card game. It it goes as fast as you can
+ 
+
+ align:start position:0%
+card game. It it goes as fast as you can
+possibly play it. And uh there is no
+
+ align:start position:0%
+possibly play it. And uh there is no
+ 
+
+ align:start position:0%
+possibly play it. And uh there is no
+there is no limit on how fast you can
+
+ align:start position:0%
+there is no limit on how fast you can
+ 
+
+ align:start position:0%
+there is no limit on how fast you can
+play these cards, but there is a real
+
+ align:start position:0%
+play these cards, but there is a real
+ 
+
+ align:start position:0%
+play these cards, but there is a real
+physical limit on how fast you can
+
+ align:start position:0%
+physical limit on how fast you can
+ 
+
+ align:start position:0%
+physical limit on how fast you can
+physically grab a card out of your hand
+
+ align:start position:0%
+physically grab a card out of your hand
+ 
+
+ align:start position:0%
+physically grab a card out of your hand
+and put it down. Uh so actually it's not
+
+ align:start position:0%
+and put it down. Uh so actually it's not
+ 
+
+ align:start position:0%
+and put it down. Uh so actually it's not
+even on your hand. You're just moving
+
+ align:start position:0%
+even on your hand. You're just moving
+ 
+
+ align:start position:0%
+even on your hand. You're just moving
+cards on the table. So uh so make sure
+
+ align:start position:0%
+cards on the table. So uh so make sure
+ 
+
+ align:start position:0%
+cards on the table. So uh so make sure
+you give that a try uh today.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh um finally uh we'll we'll we'll we'll
+
+ align:start position:0%
+Oh um finally uh we'll we'll we'll we'll
+ 
+
+ align:start position:0%
+Oh um finally uh we'll we'll we'll we'll
+be getting to aesthetics uh I think next
+
+ align:start position:0%
+be getting to aesthetics uh I think next
+ 
+
+ align:start position:0%
+be getting to aesthetics uh I think next
+class next week.
+
+ align:start position:0%
+class next week.
+ 
+
+ align:start position:0%
+class next week.
+>> Yeah. Okay. So, so which is another
+
+ align:start position:0%
+>> Yeah. Okay. So, so which is another
+ 
+
+ align:start position:0%
+>> Yeah. Okay. So, so which is another
+thing which uh a game designer uh in
+
+ align:start position:0%
+thing which uh a game designer uh in
+ 
+
+ align:start position:0%
+thing which uh a game designer uh in
+fact which is what I would like game
+
+ align:start position:0%
+fact which is what I would like game
+ 
+
+ align:start position:0%
+fact which is what I would like game
+designers to actually spend more time
+
+ align:start position:0%
+designers to actually spend more time
+ 
+
+ align:start position:0%
+designers to actually spend more time
+thinking about which is what is the
+
+ align:start position:0%
+thinking about which is what is the
+ 
+
+ align:start position:0%
+thinking about which is what is the
+feeling you want your player to have as
+
+ align:start position:0%
+feeling you want your player to have as
+ 
+
+ align:start position:0%
+feeling you want your player to have as
+opposed to this might be fun you know
+
+ align:start position:0%
+opposed to this might be fun you know
+ 
+
+ align:start position:0%
+opposed to this might be fun you know
+it's like oh this might be engaging it's
+
+ align:start position:0%
+it's like oh this might be engaging it's
+ 
+
+ align:start position:0%
+it's like oh this might be engaging it's
+like specifically how is it fun how is
+
+ align:start position:0%
+like specifically how is it fun how is
+ 
+
+ align:start position:0%
+like specifically how is it fun how is
+it engaging is it fun as in like yes
+
+ align:start position:0%
+it engaging is it fun as in like yes
+ 
+
+ align:start position:0%
+it engaging is it fun as in like yes
+victory I have crushed all my opponents
+
+ align:start position:0%
+victory I have crushed all my opponents
+ 
+
+ align:start position:0%
+victory I have crushed all my opponents
+or is it fun as in wow we had a really
+
+ align:start position:0%
+or is it fun as in wow we had a really
+ 
+
+ align:start position:0%
+or is it fun as in wow we had a really
+good time together and we got to know
+
+ align:start position:0%
+good time together and we got to know
+ 
+
+ align:start position:0%
+good time together and we got to know
+each other really well you know there
+
+ align:start position:0%
+each other really well you know there
+ 
+
+ align:start position:0%
+each other really well you know there
+are games that are designed for both of
+
+ align:start position:0%
+are games that are designed for both of
+ 
+
+ align:start position:0%
+are games that are designed for both of
+those Um and uh and what what is the
+
+ align:start position:0%
+those Um and uh and what what is the
+ 
+
+ align:start position:0%
+those Um and uh and what what is the
+aesthetic you're going for? You going
+
+ align:start position:0%
+aesthetic you're going for? You going
+ 
+
+ align:start position:0%
+aesthetic you're going for? You going
+for something poetic? Are you going for
+
+ align:start position:0%
+for something poetic? Are you going for
+ 
+
+ align:start position:0%
+for something poetic? Are you going for
+something, you know, fiercely
+
+ align:start position:0%
+something, you know, fiercely
+ 
+
+ align:start position:0%
+something, you know, fiercely
+competitive, uh tournament competitive,
+
+ align:start position:0%
+competitive, uh tournament competitive,
+ 
+
+ align:start position:0%
+competitive, uh tournament competitive,
+or you going for, you know, just a nice
+
+ align:start position:0%
+or you going for, you know, just a nice
+ 
+
+ align:start position:0%
+or you going for, you know, just a nice
+little social experiment? Um
+
+ align:start position:0%
+little social experiment? Um
+ 
+
+ align:start position:0%
+little social experiment? Um
+core mechanics and core dynamics are uh
+
+ align:start position:0%
+core mechanics and core dynamics are uh
+ 
+
+ align:start position:0%
+core mechanics and core dynamics are uh
+are a tool again for designers. uh the
+
+ align:start position:0%
+are a tool again for designers. uh the
+ 
+
+ align:start position:0%
+are a tool again for designers. uh the
+idea of there there really isn't a huge
+
+ align:start position:0%
+idea of there there really isn't a huge
+ 
+
+ align:start position:0%
+idea of there there really isn't a huge
+difference between what's a core
+
+ align:start position:0%
+difference between what's a core
+ 
+
+ align:start position:0%
+difference between what's a core
+mechanic and what's just a mechanic uh
+
+ align:start position:0%
+mechanic and what's just a mechanic uh
+ 
+
+ align:start position:0%
+mechanic and what's just a mechanic uh
+except inside a designer or a design
+
+ align:start position:0%
+except inside a designer or a design
+ 
+
+ align:start position:0%
+except inside a designer or a design
+team's uh discussion. Um the idea of
+
+ align:start position:0%
+team's uh discussion. Um the idea of
+ 
+
+ align:start position:0%
+team's uh discussion. Um the idea of
+having a core core mechanic as you
+
+ align:start position:0%
+having a core core mechanic as you
+ 
+
+ align:start position:0%
+having a core core mechanic as you
+identify this is what our game's about
+
+ align:start position:0%
+identify this is what our game's about
+ 
+
+ align:start position:0%
+identify this is what our game's about
+uh or a core dynamic mean this is what
+
+ align:start position:0%
+uh or a core dynamic mean this is what
+ 
+
+ align:start position:0%
+uh or a core dynamic mean this is what
+our game uh our game's about. And a lot
+
+ align:start position:0%
+our game uh our game's about. And a lot
+ 
+
+ align:start position:0%
+our game uh our game's about. And a lot
+of core core mechanics in first-person
+
+ align:start position:0%
+of core core mechanics in first-person
+ 
+
+ align:start position:0%
+of core core mechanics in first-person
+shooters is pointing and shooting,
+
+ align:start position:0%
+shooters is pointing and shooting,
+ 
+
+ align:start position:0%
+shooters is pointing and shooting,
+right? I'm going to point at something
+
+ align:start position:0%
+right? I'm going to point at something
+ 
+
+ align:start position:0%
+right? I'm going to point at something
+and I'm going to launch a projectile
+
+ align:start position:0%
+and I'm going to launch a projectile
+ 
+
+ align:start position:0%
+and I'm going to launch a projectile
+that way and that projectile is going to
+
+ align:start position:0%
+that way and that projectile is going to
+ 
+
+ align:start position:0%
+that way and that projectile is going to
+move in a certain some physical
+
+ align:start position:0%
+move in a certain some physical
+ 
+
+ align:start position:0%
+move in a certain some physical
+properties. You know, maybe it arcs,
+
+ align:start position:0%
+properties. You know, maybe it arcs,
+ 
+
+ align:start position:0%
+properties. You know, maybe it arcs,
+maybe it goes straight. Um, and other
+
+ align:start position:0%
+maybe it goes straight. Um, and other
+ 
+
+ align:start position:0%
+maybe it goes straight. Um, and other
+core uh I would say that the core
+
+ align:start position:0%
+core uh I would say that the core
+ 
+
+ align:start position:0%
+core uh I would say that the core
+mechanic of Halo isn't actually that
+
+ align:start position:0%
+mechanic of Halo isn't actually that
+ 
+
+ align:start position:0%
+mechanic of Halo isn't actually that
+core uh who has not played Halo or seen
+
+ align:start position:0%
+core uh who has not played Halo or seen
+ 
+
+ align:start position:0%
+core uh who has not played Halo or seen
+someone play Halo. Okay. Um, so like the
+
+ align:start position:0%
+someone play Halo. Okay. Um, so like the
+ 
+
+ align:start position:0%
+someone play Halo. Okay. Um, so like the
+I the core mechanic or I think my Budgie
+
+ align:start position:0%
+I the core mechanic or I think my Budgie
+ 
+
+ align:start position:0%
+I the core mechanic or I think my Budgie
+calls it the core gameplay loop um uh of
+
+ align:start position:0%
+calls it the core gameplay loop um uh of
+ 
+
+ align:start position:0%
+calls it the core gameplay loop um uh of
+uh of Halo is you shoot at something,
+
+ align:start position:0%
+uh of Halo is you shoot at something,
+ 
+
+ align:start position:0%
+uh of Halo is you shoot at something,
+you take cover, you throw a grenade at
+
+ align:start position:0%
+you take cover, you throw a grenade at
+ 
+
+ align:start position:0%
+you take cover, you throw a grenade at
+it, you wait for the grenade to go off,
+
+ align:start position:0%
+it, you wait for the grenade to go off,
+ 
+
+ align:start position:0%
+it, you wait for the grenade to go off,
+and then you shoot it again until it
+
+ align:start position:0%
+and then you shoot it again until it
+ 
+
+ align:start position:0%
+and then you shoot it again until it
+dies. Um, right. That's pretty much all
+
+ align:start position:0%
+dies. Um, right. That's pretty much all
+ 
+
+ align:start position:0%
+dies. Um, right. That's pretty much all
+you're doing for the entirety of Halo 1.
+
+ align:start position:0%
+you're doing for the entirety of Halo 1.
+ 
+
+ align:start position:0%
+you're doing for the entirety of Halo 1.
+Um sure Halo 2 Halo 3 gets complicated.
+
+ align:start position:0%
+Um sure Halo 2 Halo 3 gets complicated.
+ 
+
+ align:start position:0%
+Um sure Halo 2 Halo 3 gets complicated.
+Yeah. You know um but but but they
+
+ align:start position:0%
+Yeah. You know um but but but they
+ 
+
+ align:start position:0%
+Yeah. You know um but but but they
+identify that if you actually read the
+
+ align:start position:0%
+identify that if you actually read the
+ 
+
+ align:start position:0%
+identify that if you actually read the
+postmortems and and if you read at the
+
+ align:start position:0%
+postmortems and and if you read at the
+ 
+
+ align:start position:0%
+postmortems and and if you read at the
+talks that they've given they say those
+
+ align:start position:0%
+talks that they've given they say those
+ 
+
+ align:start position:0%
+talks that they've given they say those
+I can't I can't remember it's 20 seconds
+
+ align:start position:0%
+I can't I can't remember it's 20 seconds
+ 
+
+ align:start position:0%
+I can't I can't remember it's 20 seconds
+or 5 seconds of gameplay which they use
+
+ align:start position:0%
+or 5 seconds of gameplay which they use
+ 
+
+ align:start position:0%
+or 5 seconds of gameplay which they use
+to describe that. I think it's five that
+
+ align:start position:0%
+to describe that. I think it's five that
+ 
+
+ align:start position:0%
+to describe that. I think it's five that
+5second of game play is what they
+
+ align:start position:0%
+5second of game play is what they
+ 
+
+ align:start position:0%
+5second of game play is what they
+focused on. And if they could get every
+
+ align:start position:0%
+focused on. And if they could get every
+ 
+
+ align:start position:0%
+focused on. And if they could get every
+little thing in that sequence correct
+
+ align:start position:0%
+little thing in that sequence correct
+ 
+
+ align:start position:0%
+little thing in that sequence correct
+they can repeat that same thing at
+
+ align:start position:0%
+they can repeat that same thing at
+ 
+
+ align:start position:0%
+they can repeat that same thing at
+infinitum and you'll still be having
+
+ align:start position:0%
+infinitum and you'll still be having
+ 
+
+ align:start position:0%
+infinitum and you'll still be having
+fun.
+
+ align:start position:0%
+fun.
+ 
+
+ align:start position:0%
+fun.
+um Halo one everyone,
+
+ align:start position:0%
+um Halo one everyone,
+ 
+
+ align:start position:0%
+um Halo one everyone,
+you know, they're they're kind of right.
+
+ align:start position:0%
+you know, they're they're kind of right.
+ 
+
+ align:start position:0%
+you know, they're they're kind of right.
+But the idea being, you know, if you've
+
+ align:start position:0%
+But the idea being, you know, if you've
+ 
+
+ align:start position:0%
+But the idea being, you know, if you've
+got a core mechanic, if you've got one
+
+ align:start position:0%
+got a core mechanic, if you've got one
+ 
+
+ align:start position:0%
+got a core mechanic, if you've got one
+thing in your game that someone's going
+
+ align:start position:0%
+thing in your game that someone's going
+ 
+
+ align:start position:0%
+thing in your game that someone's going
+to be doing over and over and over
+
+ align:start position:0%
+to be doing over and over and over
+ 
+
+ align:start position:0%
+to be doing over and over and over
+again, all your players are going to be
+
+ align:start position:0%
+again, all your players are going to be
+ 
+
+ align:start position:0%
+again, all your players are going to be
+doing over and over again, maybe it's
+
+ align:start position:0%
+doing over and over again, maybe it's
+ 
+
+ align:start position:0%
+doing over and over again, maybe it's
+bidding because they're making some kind
+
+ align:start position:0%
+bidding because they're making some kind
+ 
+
+ align:start position:0%
+bidding because they're making some kind
+of auction game. Um, in falling, it's
+
+ align:start position:0%
+of auction game. Um, in falling, it's
+ 
+
+ align:start position:0%
+of auction game. Um, in falling, it's
+and in pit it's transferring cards to
+
+ align:start position:0%
+and in pit it's transferring cards to
+ 
+
+ align:start position:0%
+and in pit it's transferring cards to
+other people. Um,
+
+ align:start position:0%
+other people. Um,
+ 
+
+ align:start position:0%
+other people. Um,
+uh, I'm trying to think of the other
+
+ align:start position:0%
+uh, I'm trying to think of the other
+ 
+
+ align:start position:0%
+uh, I'm trying to think of the other
+games that we've got here. Um in in Siss
+
+ align:start position:0%
+games that we've got here. Um in in Siss
+ 
+
+ align:start position:0%
+games that we've got here. Um in in Siss
+fight, I would imagine is the the main
+
+ align:start position:0%
+fight, I would imagine is the the main
+ 
+
+ align:start position:0%
+fight, I would imagine is the the main
+the main core mechanic would be uh
+
+ align:start position:0%
+the main core mechanic would be uh
+ 
+
+ align:start position:0%
+the main core mechanic would be uh
+putting down the card uh and and
+
+ align:start position:0%
+putting down the card uh and and
+ 
+
+ align:start position:0%
+putting down the card uh and and
+everyone revealing the card
+
+ align:start position:0%
+everyone revealing the card
+ 
+
+ align:start position:0%
+everyone revealing the card
+simultaneously because you you you all
+
+ align:start position:0%
+simultaneously because you you you all
+ 
+
+ align:start position:0%
+simultaneously because you you you all
+take simultaneous turns. You know, make
+
+ align:start position:0%
+take simultaneous turns. You know, make
+ 
+
+ align:start position:0%
+take simultaneous turns. You know, make
+sure that's really really fun and Yazi
+
+ align:start position:0%
+sure that's really really fun and Yazi
+ 
+
+ align:start position:0%
+sure that's really really fun and Yazi
+is rolling dice. You know, that's that
+
+ align:start position:0%
+is rolling dice. You know, that's that
+ 
+
+ align:start position:0%
+is rolling dice. You know, that's that
+action, that thing that you're going to
+
+ align:start position:0%
+action, that thing that you're going to
+ 
+
+ align:start position:0%
+action, that thing that you're going to
+be doing over and over again has to be
+
+ align:start position:0%
+be doing over and over again has to be
+ 
+
+ align:start position:0%
+be doing over and over again has to be
+at least fairly engaging. Um because if
+
+ align:start position:0%
+at least fairly engaging. Um because if
+ 
+
+ align:start position:0%
+at least fairly engaging. Um because if
+you c if you can't get that right then
+
+ align:start position:0%
+you c if you can't get that right then
+ 
+
+ align:start position:0%
+you c if you can't get that right then
+what happens is that that same movement
+
+ align:start position:0%
+what happens is that that same movement
+ 
+
+ align:start position:0%
+what happens is that that same movement
+that happens 30 50 times in your game
+
+ align:start position:0%
+that happens 30 50 times in your game
+ 
+
+ align:start position:0%
+that happens 30 50 times in your game
+you know just gets m the badness just
+
+ align:start position:0%
+you know just gets m the badness just
+ 
+
+ align:start position:0%
+you know just gets m the badness just
+gets multiplied by 30 or 50 uh and and
+
+ align:start position:0%
+gets multiplied by 30 or 50 uh and and
+ 
+
+ align:start position:0%
+gets multiplied by 30 or 50 uh and and
+and you don't want that. So for core
+
+ align:start position:0%
+and you don't want that. So for core
+ 
+
+ align:start position:0%
+and you don't want that. So for core
+mechanics you know I I would say the
+
+ align:start position:0%
+mechanics you know I I would say the
+ 
+
+ align:start position:0%
+mechanics you know I I would say the
+thing that happens in your game the most
+
+ align:start position:0%
+thing that happens in your game the most
+ 
+
+ align:start position:0%
+thing that happens in your game the most
+and uh and you want to make sure that
+
+ align:start position:0%
+and uh and you want to make sure that
+ 
+
+ align:start position:0%
+and uh and you want to make sure that
+that part is is as engaging as possible.
+
+ align:start position:0%
+that part is is as engaging as possible.
+ 
+
+ align:start position:0%
+that part is is as engaging as possible.
+It also gives you a rubric to say what's
+
+ align:start position:0%
+It also gives you a rubric to say what's
+ 
+
+ align:start position:0%
+It also gives you a rubric to say what's
+not a core mechanic might be in fact
+
+ align:start position:0%
+not a core mechanic might be in fact
+ 
+
+ align:start position:0%
+not a core mechanic might be in fact
+expendable. You might not actually need
+
+ align:start position:0%
+expendable. You might not actually need
+ 
+
+ align:start position:0%
+expendable. You might not actually need
+it in your game. So if you've got a
+
+ align:start position:0%
+it in your game. So if you've got a
+ 
+
+ align:start position:0%
+it in your game. So if you've got a
+problem, this game takes too long to
+
+ align:start position:0%
+problem, this game takes too long to
+ 
+
+ align:start position:0%
+problem, this game takes too long to
+play, this game's too hard to learn, uh
+
+ align:start position:0%
+play, this game's too hard to learn, uh
+ 
+
+ align:start position:0%
+play, this game's too hard to learn, uh
+this game's over too fast, it's too
+
+ align:start position:0%
+this game's over too fast, it's too
+ 
+
+ align:start position:0%
+this game's over too fast, it's too
+random or something, take a look at all
+
+ align:start position:0%
+random or something, take a look at all
+ 
+
+ align:start position:0%
+random or something, take a look at all
+the things that are, you know, of course
+
+ align:start position:0%
+the things that are, you know, of course
+ 
+
+ align:start position:0%
+the things that are, you know, of course
+make sure that your core mechanic is not
+
+ align:start position:0%
+make sure that your core mechanic is not
+ 
+
+ align:start position:0%
+make sure that your core mechanic is not
+the cause of the problem. But if the
+
+ align:start position:0%
+the cause of the problem. But if the
+ 
+
+ align:start position:0%
+the cause of the problem. But if the
+your core mechanic doesn't seem to be
+
+ align:start position:0%
+your core mechanic doesn't seem to be
+ 
+
+ align:start position:0%
+your core mechanic doesn't seem to be
+the cause of the problem, that seems to
+
+ align:start position:0%
+the cause of the problem, that seems to
+ 
+
+ align:start position:0%
+the cause of the problem, that seems to
+be working. Something else in the game
+
+ align:start position:0%
+be working. Something else in the game
+ 
+
+ align:start position:0%
+be working. Something else in the game
+is not working. Everything else is
+
+ align:start position:0%
+is not working. Everything else is
+ 
+
+ align:start position:0%
+is not working. Everything else is
+expandable. And so you you you you can
+
+ align:start position:0%
+expandable. And so you you you you can
+ 
+
+ align:start position:0%
+expandable. And so you you you you can
+look at everything else in your game,
+
+ align:start position:0%
+look at everything else in your game,
+ 
+
+ align:start position:0%
+look at everything else in your game,
+all these other rules that you've got
+
+ align:start position:0%
+all these other rules that you've got
+ 
+
+ align:start position:0%
+all these other rules that you've got
+and say, "How does that work with the
+
+ align:start position:0%
+and say, "How does that work with the
+ 
+
+ align:start position:0%
+and say, "How does that work with the
+coral mechanic? How does that help? How
+
+ align:start position:0%
+coral mechanic? How does that help? How
+ 
+
+ align:start position:0%
+coral mechanic? How does that help? How
+does that hurt the coral mechanic?" It
+
+ align:start position:0%
+does that hurt the coral mechanic?" It
+ 
+
+ align:start position:0%
+does that hurt the coral mechanic?" It
+just helps your discussion as a team. Uh
+
+ align:start position:0%
+just helps your discussion as a team. Uh
+ 
+
+ align:start position:0%
+just helps your discussion as a team. Uh
+or as a game or as an individual game
+
+ align:start position:0%
+or as a game or as an individual game
+ 
+
+ align:start position:0%
+or as a game or as an individual game
+designer, it helps your thinking about
+
+ align:start position:0%
+designer, it helps your thinking about
+ 
+
+ align:start position:0%
+designer, it helps your thinking about
+what could we throw out, what could we
+
+ align:start position:0%
+what could we throw out, what could we
+ 
+
+ align:start position:0%
+what could we throw out, what could we
+keep.
+
+ align:start position:0%
+keep.
+ 
+
+ align:start position:0%
+keep.
+Um similarly for core dynamic it's you
+
+ align:start position:0%
+Um similarly for core dynamic it's you
+ 
+
+ align:start position:0%
+Um similarly for core dynamic it's you
+know it's like here's this particular
+
+ align:start position:0%
+know it's like here's this particular
+ 
+
+ align:start position:0%
+know it's like here's this particular
+um uh particular interaction that we
+
+ align:start position:0%
+um uh particular interaction that we
+ 
+
+ align:start position:0%
+um uh particular interaction that we
+really really want um in cisifi is
+
+ align:start position:0%
+really really want um in cisifi is
+ 
+
+ align:start position:0%
+really really want um in cisifi is
+guessing what other people are going to
+
+ align:start position:0%
+guessing what other people are going to
+ 
+
+ align:start position:0%
+guessing what other people are going to
+do um and uh I'm trying to think of
+
+ align:start position:0%
+do um and uh I'm trying to think of
+ 
+
+ align:start position:0%
+do um and uh I'm trying to think of
+other examples and like territorial
+
+ align:start position:0%
+other examples and like territorial
+ 
+
+ align:start position:0%
+other examples and like territorial
+uh space acquisition I guess go is about
+
+ align:start position:0%
+uh space acquisition I guess go is about
+ 
+
+ align:start position:0%
+uh space acquisition I guess go is about
+taking over territory in space um you
+
+ align:start position:0%
+taking over territory in space um you
+ 
+
+ align:start position:0%
+taking over territory in space um you
+know if that's your core dynamic if you
+
+ align:start position:0%
+know if that's your core dynamic if you
+ 
+
+ align:start position:0%
+know if that's your core dynamic if you
+say that's kind of fun. Just making sure
+
+ align:start position:0%
+say that's kind of fun. Just making sure
+ 
+
+ align:start position:0%
+say that's kind of fun. Just making sure
+that I'm in control of a space and
+
+ align:start position:0%
+that I'm in control of a space and
+ 
+
+ align:start position:0%
+that I'm in control of a space and
+nobody else can do anything that they
+
+ align:start position:0%
+nobody else can do anything that they
+ 
+
+ align:start position:0%
+nobody else can do anything that they
+want to do in a certain part of the
+
+ align:start position:0%
+want to do in a certain part of the
+ 
+
+ align:start position:0%
+want to do in a certain part of the
+board. That's fun. Um that's what I'm
+
+ align:start position:0%
+board. That's fun. Um that's what I'm
+ 
+
+ align:start position:0%
+board. That's fun. Um that's what I'm
+going for. That's my core dynamic.
+
+ align:start position:0%
+going for. That's my core dynamic.
+ 
+
+ align:start position:0%
+going for. That's my core dynamic.
+That's what this game is all about. Then
+
+ align:start position:0%
+That's what this game is all about. Then
+ 
+
+ align:start position:0%
+That's what this game is all about. Then
+you can look at every single mechanic,
+
+ align:start position:0%
+you can look at every single mechanic,
+ 
+
+ align:start position:0%
+you can look at every single mechanic,
+even your core mechanics, and say, is it
+
+ align:start position:0%
+even your core mechanics, and say, is it
+ 
+
+ align:start position:0%
+even your core mechanics, and say, is it
+all serving that goal? Now, there's a
+
+ align:start position:0%
+all serving that goal? Now, there's a
+ 
+
+ align:start position:0%
+all serving that goal? Now, there's a
+whole bunch of uh tips right at the end
+
+ align:start position:0%
+whole bunch of uh tips right at the end
+ 
+
+ align:start position:0%
+whole bunch of uh tips right at the end
+of chapter one of uh of uh challenges
+
+ align:start position:0%
+of chapter one of uh of uh challenges
+ 
+
+ align:start position:0%
+of chapter one of uh of uh challenges
+for game designers about how to break
+
+ align:start position:0%
+for game designers about how to break
+ 
+
+ align:start position:0%
+for game designers about how to break
+designer block. Um but I would say
+
+ align:start position:0%
+designer block. Um but I would say
+ 
+
+ align:start position:0%
+designer block. Um but I would say
+actually those things are just things
+
+ align:start position:0%
+actually those things are just things
+ 
+
+ align:start position:0%
+actually those things are just things
+that you should be doing all the time.
+
+ align:start position:0%
+that you should be doing all the time.
+ 
+
+ align:start position:0%
+that you should be doing all the time.
+Um not not just when you have a problem,
+
+ align:start position:0%
+Um not not just when you have a problem,
+ 
+
+ align:start position:0%
+Um not not just when you have a problem,
+but you should be experimenting things
+
+ align:start position:0%
+but you should be experimenting things
+ 
+
+ align:start position:0%
+but you should be experimenting things
+like, you know, okay, you've got a
+
+ align:start position:0%
+like, you know, okay, you've got a
+ 
+
+ align:start position:0%
+like, you know, okay, you've got a
+variable, you know, draw two cards every
+
+ align:start position:0%
+variable, you know, draw two cards every
+ 
+
+ align:start position:0%
+variable, you know, draw two cards every
+turn or something. Multiply it by two,
+
+ align:start position:0%
+turn or something. Multiply it by two,
+ 
+
+ align:start position:0%
+turn or something. Multiply it by two,
+see what it does to your game. Have it,
+
+ align:start position:0%
+see what it does to your game. Have it,
+ 
+
+ align:start position:0%
+see what it does to your game. Have it,
+draw one card, see what it does to your
+
+ align:start position:0%
+draw one card, see what it does to your
+ 
+
+ align:start position:0%
+draw one card, see what it does to your
+game. um you know throw a rule out you
+
+ align:start position:0%
+game. um you know throw a rule out you
+ 
+
+ align:start position:0%
+game. um you know throw a rule out you
+know um it and and that sort of gets you
+
+ align:start position:0%
+know um it and and that sort of gets you
+ 
+
+ align:start position:0%
+know um it and and that sort of gets you
+to the whole iterative design thing is
+
+ align:start position:0%
+to the whole iterative design thing is
+ 
+
+ align:start position:0%
+to the whole iterative design thing is
+that you don't actually because games
+
+ align:start position:0%
+that you don't actually because games
+ 
+
+ align:start position:0%
+that you don't actually because games
+are systems they're these complex little
+
+ align:start position:0%
+are systems they're these complex little
+ 
+
+ align:start position:0%
+are systems they're these complex little
+collections of seemingly simple things
+
+ align:start position:0%
+collections of seemingly simple things
+ 
+
+ align:start position:0%
+collections of seemingly simple things
+you don't actually know how these
+
+ align:start position:0%
+you don't actually know how these
+ 
+
+ align:start position:0%
+you don't actually know how these
+changes are really going to affect your
+
+ align:start position:0%
+changes are really going to affect your
+ 
+
+ align:start position:0%
+changes are really going to affect your
+game. You may have a hunch but until you
+
+ align:start position:0%
+game. You may have a hunch but until you
+ 
+
+ align:start position:0%
+game. You may have a hunch but until you
+actually play it out you don't actually
+
+ align:start position:0%
+actually play it out you don't actually
+ 
+
+ align:start position:0%
+actually play it out you don't actually
+know. So um so the whole point of
+
+ align:start position:0%
+know. So um so the whole point of
+ 
+
+ align:start position:0%
+know. So um so the whole point of
+iterative of iterative the design in in
+
+ align:start position:0%
+iterative of iterative the design in in
+ 
+
+ align:start position:0%
+iterative of iterative the design in in
+engineering as well as in game design is
+
+ align:start position:0%
+engineering as well as in game design is
+ 
+
+ align:start position:0%
+engineering as well as in game design is
+that you know you you make the change.
+
+ align:start position:0%
+that you know you you make the change.
+ 
+
+ align:start position:0%
+that you know you you make the change.
+There has to be a substantial change. Um
+
+ align:start position:0%
+There has to be a substantial change. Um
+ 
+
+ align:start position:0%
+There has to be a substantial change. Um
+and then you actually put it to the test
+
+ align:start position:0%
+and then you actually put it to the test
+ 
+
+ align:start position:0%
+and then you actually put it to the test
+and see what happens. Um this means of
+
+ align:start position:0%
+and see what happens. Um this means of
+ 
+
+ align:start position:0%
+and see what happens. Um this means of
+course testing and testing takes a long
+
+ align:start position:0%
+course testing and testing takes a long
+ 
+
+ align:start position:0%
+course testing and testing takes a long
+time and if you're going to be making a
+
+ align:start position:0%
+time and if you're going to be making a
+ 
+
+ align:start position:0%
+time and if you're going to be making a
+game that takes a long time then your
+
+ align:start position:0%
+game that takes a long time then your
+ 
+
+ align:start position:0%
+game that takes a long time then your
+testing gets even longer. So, uh, for
+
+ align:start position:0%
+testing gets even longer. So, uh, for
+ 
+
+ align:start position:0%
+testing gets even longer. So, uh, for
+the first project that's going to be
+
+ align:start position:0%
+the first project that's going to be
+ 
+
+ align:start position:0%
+the first project that's going to be
+coming out, the assignment, uh,
+
+ align:start position:0%
+coming out, the assignment, uh,
+ 
+
+ align:start position:0%
+coming out, the assignment, uh,
+assignment one, you want to be aiming
+
+ align:start position:0%
+assignment one, you want to be aiming
+ 
+
+ align:start position:0%
+assignment one, you want to be aiming
+for games that take really not very long
+
+ align:start position:0%
+for games that take really not very long
+ 
+
+ align:start position:0%
+for games that take really not very long
+to play. Um, these games that we've got
+
+ align:start position:0%
+to play. Um, these games that we've got
+ 
+
+ align:start position:0%
+to play. Um, these games that we've got
+today, I'm not sure about shake, but I
+
+ align:start position:0%
+today, I'm not sure about shake, but I
+ 
+
+ align:start position:0%
+today, I'm not sure about shake, but I
+know everything else that we've got on
+
+ align:start position:0%
+know everything else that we've got on
+ 
+
+ align:start position:0%
+know everything else that we've got on
+that table is pretty darn fast, which
+
+ align:start position:0%
+that table is pretty darn fast, which
+ 
+
+ align:start position:0%
+that table is pretty darn fast, which
+means, you know, if you've got an hour
+
+ align:start position:0%
+means, you know, if you've got an hour
+ 
+
+ align:start position:0%
+means, you know, if you've got an hour
+with four people, uh, who've never
+
+ align:start position:0%
+with four people, uh, who've never
+ 
+
+ align:start position:0%
+with four people, uh, who've never
+played your game before, maybe you get
+
+ align:start position:0%
+played your game before, maybe you get
+ 
+
+ align:start position:0%
+played your game before, maybe you get
+through two or three rounds, four rounds
+
+ align:start position:0%
+through two or three rounds, four rounds
+ 
+
+ align:start position:0%
+through two or three rounds, four rounds
+of them, you know, each time maybe
+
+ align:start position:0%
+of them, you know, each time maybe
+ 
+
+ align:start position:0%
+of them, you know, each time maybe
+tweaking a rule once, uh, uh, here and
+
+ align:start position:0%
+tweaking a rule once, uh, uh, here and
+ 
+
+ align:start position:0%
+tweaking a rule once, uh, uh, here and
+there and seeing how that change that
+
+ align:start position:0%
+there and seeing how that change that
+ 
+
+ align:start position:0%
+there and seeing how that change that
+that changed the game. If you've got a
+
+ align:start position:0%
+that changed the game. If you've got a
+ 
+
+ align:start position:0%
+that changed the game. If you've got a
+game that takes an hour to play, and
+
+ align:start position:0%
+game that takes an hour to play, and
+ 
+
+ align:start position:0%
+game that takes an hour to play, and
+believe me, a lot of the of the projects
+
+ align:start position:0%
+believe me, a lot of the of the projects
+ 
+
+ align:start position:0%
+believe me, a lot of the of the projects
+that we've gotten from previous
+
+ align:start position:0%
+that we've gotten from previous
+ 
+
+ align:start position:0%
+that we've gotten from previous
+semesters take at least an hour to play,
+
+ align:start position:0%
+semesters take at least an hour to play,
+ 
+
+ align:start position:0%
+semesters take at least an hour to play,
+um, then you know you've got four people
+
+ align:start position:0%
+um, then you know you've got four people
+ 
+
+ align:start position:0%
+um, then you know you've got four people
+for an hour and they're not going to
+
+ align:start position:0%
+for an hour and they're not going to
+ 
+
+ align:start position:0%
+for an hour and they're not going to
+finish the a single play of the game
+
+ align:start position:0%
+finish the a single play of the game
+ 
+
+ align:start position:0%
+finish the a single play of the game
+because by the time they finish learning
+
+ align:start position:0%
+because by the time they finish learning
+ 
+
+ align:start position:0%
+because by the time they finish learning
+your your your game, half your time is
+
+ align:start position:0%
+your your your game, half your time is
+ 
+
+ align:start position:0%
+your your your game, half your time is
+up.
+
+ align:start position:0%
+up.
+ 
+
+ align:start position:0%
+up.
+Um, so that's the process that we would
+
+ align:start position:0%
+Um, so that's the process that we would
+ 
+
+ align:start position:0%
+Um, so that's the process that we would
+like you all to be using in your teams,
+
+ align:start position:0%
+like you all to be using in your teams,
+ 
+
+ align:start position:0%
+like you all to be using in your teams,
+in your assignments. this iterative
+
+ align:start position:0%
+in your assignments. this iterative
+ 
+
+ align:start position:0%
+in your assignments. this iterative
+design pro process right from the
+
+ align:start position:0%
+design pro process right from the
+ 
+
+ align:start position:0%
+design pro process right from the
+beginning uh I wish I had more space um
+
+ align:start position:0%
+beginning uh I wish I had more space um
+ 
+
+ align:start position:0%
+beginning uh I wish I had more space um
+but uh we're going to start with
+
+ align:start position:0%
+but uh we're going to start with
+ 
+
+ align:start position:0%
+but uh we're going to start with
+brainstorming uh there that's actually
+
+ align:start position:0%
+brainstorming uh there that's actually
+ 
+
+ align:start position:0%
+brainstorming uh there that's actually
+going to be Friday the 17th where we'll
+
+ align:start position:0%
+going to be Friday the 17th where we'll
+ 
+
+ align:start position:0%
+going to be Friday the 17th where we'll
+actually sort of uh for folks who
+
+ align:start position:0%
+actually sort of uh for folks who
+ 
+
+ align:start position:0%
+actually sort of uh for folks who
+haven't necessarily formally learned uh
+
+ align:start position:0%
+haven't necessarily formally learned uh
+ 
+
+ align:start position:0%
+haven't necessarily formally learned uh
+bra bra bra bra bra bra bra bra bra bra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+bra bra bra bra bra bra bra bra bra bra
+brainstorming, we're just going to do a
+
+ align:start position:0%
+brainstorming, we're just going to do a
+ 
+
+ align:start position:0%
+brainstorming, we're just going to do a
+quick refresher uh so that everyone s
+
+ align:start position:0%
+quick refresher uh so that everyone s
+ 
+
+ align:start position:0%
+quick refresher uh so that everyone s
+sort of is on the same page. You learn
+
+ align:start position:0%
+sort of is on the same page. You learn
+ 
+
+ align:start position:0%
+sort of is on the same page. You learn
+how to do brainstorming. Um, you come up
+
+ align:start position:0%
+how to do brainstorming. Um, you come up
+ 
+
+ align:start position:0%
+how to do brainstorming. Um, you come up
+with a basic idea of your game and you
+
+ align:start position:0%
+with a basic idea of your game and you
+ 
+
+ align:start position:0%
+with a basic idea of your game and you
+start to identify things that could be
+
+ align:start position:0%
+start to identify things that could be
+ 
+
+ align:start position:0%
+start to identify things that could be
+your core dynamics. You know, you think
+
+ align:start position:0%
+your core dynamics. You know, you think
+ 
+
+ align:start position:0%
+your core dynamics. You know, you think
+of what what sort of core mechanics
+
+ align:start position:0%
+of what what sort of core mechanics
+ 
+
+ align:start position:0%
+of what what sort of core mechanics
+could address that. Knock something up
+
+ align:start position:0%
+could address that. Knock something up
+ 
+
+ align:start position:0%
+could address that. Knock something up
+really really quickly with the crappiest
+
+ align:start position:0%
+really really quickly with the crappiest
+ 
+
+ align:start position:0%
+really really quickly with the crappiest
+materials you can get your hands on and
+
+ align:start position:0%
+materials you can get your hands on and
+ 
+
+ align:start position:0%
+materials you can get your hands on and
+start playing. Um, since nobody in your
+
+ align:start position:0%
+start playing. Um, since nobody in your
+ 
+
+ align:start position:0%
+start playing. Um, since nobody in your
+team knows really what game you're
+
+ align:start position:0%
+team knows really what game you're
+ 
+
+ align:start position:0%
+team knows really what game you're
+making at that point of time, you can
+
+ align:start position:0%
+making at that point of time, you can
+ 
+
+ align:start position:0%
+making at that point of time, you can
+probably test it with your team. As soon
+
+ align:start position:0%
+probably test it with your team. As soon
+ 
+
+ align:start position:0%
+probably test it with your team. As soon
+as you do that a few times, your team
+
+ align:start position:0%
+as you do that a few times, your team
+ 
+
+ align:start position:0%
+as you do that a few times, your team
+becomes useless as play as testers
+
+ align:start position:0%
+becomes useless as play as testers
+ 
+
+ align:start position:0%
+becomes useless as play as testers
+because you already know too much about
+
+ align:start position:0%
+because you already know too much about
+ 
+
+ align:start position:0%
+because you already know too much about
+about the game and what and and what the
+
+ align:start position:0%
+about the game and what and and what the
+ 
+
+ align:start position:0%
+about the game and what and and what the
+game could have been and you start
+
+ align:start position:0%
+game could have been and you start
+ 
+
+ align:start position:0%
+game could have been and you start
+playing it in ways that a fresh person
+
+ align:start position:0%
+playing it in ways that a fresh person
+ 
+
+ align:start position:0%
+playing it in ways that a fresh person
+who's never seen your game before
+
+ align:start position:0%
+who's never seen your game before
+ 
+
+ align:start position:0%
+who's never seen your game before
+wouldn't even consider. Um, so you
+
+ align:start position:0%
+wouldn't even consider. Um, so you
+ 
+
+ align:start position:0%
+wouldn't even consider. Um, so you
+actually want to keep looking for people
+
+ align:start position:0%
+actually want to keep looking for people
+ 
+
+ align:start position:0%
+actually want to keep looking for people
+who've never played your game before. So
+
+ align:start position:0%
+who've never played your game before. So
+ 
+
+ align:start position:0%
+who've never played your game before. So
+the next step would be to broaden it to
+
+ align:start position:0%
+the next step would be to broaden it to
+ 
+
+ align:start position:0%
+the next step would be to broaden it to
+other teams in this class. Um, since
+
+ align:start position:0%
+other teams in this class. Um, since
+ 
+
+ align:start position:0%
+other teams in this class. Um, since
+everyone's going to be broken up in more
+
+ align:start position:0%
+everyone's going to be broken up in more
+ 
+
+ align:start position:0%
+everyone's going to be broken up in more
+or less teams of three or four, that's
+
+ align:start position:0%
+or less teams of three or four, that's
+ 
+
+ align:start position:0%
+or less teams of three or four, that's
+pretty much, you know, I'm going to take
+
+ align:start position:0%
+pretty much, you know, I'm going to take
+ 
+
+ align:start position:0%
+pretty much, you know, I'm going to take
+this game that we designed for a team of
+
+ align:start position:0%
+this game that we designed for a team of
+ 
+
+ align:start position:0%
+this game that we designed for a team of
+three or four and give it to that team
+
+ align:start position:0%
+three or four and give it to that team
+ 
+
+ align:start position:0%
+three or four and give it to that team
+of three or four and then you play their
+
+ align:start position:0%
+of three or four and then you play their
+ 
+
+ align:start position:0%
+of three or four and then you play their
+game and, you know, give each other
+
+ align:start position:0%
+game and, you know, give each other
+ 
+
+ align:start position:0%
+game and, you know, give each other
+feedback. And that lasts for about one
+
+ align:start position:0%
+feedback. And that lasts for about one
+ 
+
+ align:start position:0%
+feedback. And that lasts for about one
+more session and after that, everyone in
+
+ align:start position:0%
+more session and after that, everyone in
+ 
+
+ align:start position:0%
+more session and after that, everyone in
+the class has used this now. So, you
+
+ align:start position:0%
+the class has used this now. So, you
+ 
+
+ align:start position:0%
+the class has used this now. So, you
+have to go and look for doormates,
+
+ align:start position:0%
+have to go and look for doormates,
+ 
+
+ align:start position:0%
+have to go and look for doormates,
+friends, you know, um, people on the
+
+ align:start position:0%
+friends, you know, um, people on the
+ 
+
+ align:start position:0%
+friends, you know, um, people on the
+street, you know, just go right ahead
+
+ align:start position:0%
+street, you know, just go right ahead
+ 
+
+ align:start position:0%
+street, you know, just go right ahead
+and try to get as much feedback as you
+
+ align:start position:0%
+and try to get as much feedback as you
+ 
+
+ align:start position:0%
+and try to get as much feedback as you
+can.
+
+ align:start position:0%
+can.
+ 
+
+ align:start position:0%
+can.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+there is some value in replaying um
+
+ align:start position:0%
+there is some value in replaying um
+ 
+
+ align:start position:0%
+there is some value in replaying um
+especially later on once your rules are
+
+ align:start position:0%
+especially later on once your rules are
+ 
+
+ align:start position:0%
+especially later on once your rules are
+pretty set uh in that people start
+
+ align:start position:0%
+pretty set uh in that people start
+ 
+
+ align:start position:0%
+pretty set uh in that people start
+developing strategies those sort of
+
+ align:start position:0%
+developing strategies those sort of
+ 
+
+ align:start position:0%
+developing strategies those sort of
+emergent uh uh behaviors and you start
+
+ align:start position:0%
+emergent uh uh behaviors and you start
+ 
+
+ align:start position:0%
+emergent uh uh behaviors and you start
+understanding sort of higher level play
+
+ align:start position:0%
+understanding sort of higher level play
+ 
+
+ align:start position:0%
+understanding sort of higher level play
+of your game and you do want to test
+
+ align:start position:0%
+of your game and you do want to test
+ 
+
+ align:start position:0%
+of your game and you do want to test
+that um but don't let that prevent you
+
+ align:start position:0%
+that um but don't let that prevent you
+ 
+
+ align:start position:0%
+that um but don't let that prevent you
+from also testing with fresh players uh
+
+ align:start position:0%
+from also testing with fresh players uh
+ 
+
+ align:start position:0%
+from also testing with fresh players uh
+because in the end um you have to get
+
+ align:start position:0%
+because in the end um you have to get
+ 
+
+ align:start position:0%
+because in the end um you have to get
+past that initial hurdle. Anytime
+
+ align:start position:0%
+past that initial hurdle. Anytime
+ 
+
+ align:start position:0%
+past that initial hurdle. Anytime
+someone sees your game, they are going
+
+ align:start position:0%
+someone sees your game, they are going
+ 
+
+ align:start position:0%
+someone sees your game, they are going
+to have to learn to learn your game from
+
+ align:start position:0%
+to have to learn to learn your game from
+ 
+
+ align:start position:0%
+to have to learn to learn your game from
+scratch at least once. And if they don't
+
+ align:start position:0%
+scratch at least once. And if they don't
+ 
+
+ align:start position:0%
+scratch at least once. And if they don't
+even get that far, they're never playing
+
+ align:start position:0%
+even get that far, they're never playing
+ 
+
+ align:start position:0%
+even get that far, they're never playing
+it your game a second or a third time.
+
+ align:start position:0%
+it your game a second or a third time.
+ 
+
+ align:start position:0%
+it your game a second or a third time.
+So don't optimize for the people who
+
+ align:start position:0%
+So don't optimize for the people who
+ 
+
+ align:start position:0%
+So don't optimize for the people who
+played your game, you know, for for
+
+ align:start position:0%
+played your game, you know, for for
+ 
+
+ align:start position:0%
+played your game, you know, for for
+weeks because the um because you really
+
+ align:start position:0%
+weeks because the um because you really
+ 
+
+ align:start position:0%
+weeks because the um because you really
+want the people who've only played it
+
+ align:start position:0%
+want the people who've only played it
+ 
+
+ align:start position:0%
+want the people who've only played it
+once uh to have a good time as well.
+
+ align:start position:0%
+once uh to have a good time as well.
+ 
+
+ align:start position:0%
+once uh to have a good time as well.
+Um, that's not necessarily the case if
+
+ align:start position:0%
+Um, that's not necessarily the case if
+ 
+
+ align:start position:0%
+Um, that's not necessarily the case if
+you're making, you know, uh, a huge
+
+ align:start position:0%
+you're making, you know, uh, a huge
+ 
+
+ align:start position:0%
+you're making, you know, uh, a huge
+wellunded game with based on a franchise
+
+ align:start position:0%
+wellunded game with based on a franchise
+ 
+
+ align:start position:0%
+wellunded game with based on a franchise
+that, you know, that's been around
+
+ align:start position:0%
+that, you know, that's been around
+ 
+
+ align:start position:0%
+that, you know, that's been around
+forever. If you're doing Halo 3 or
+
+ align:start position:0%
+forever. If you're doing Halo 3 or
+ 
+
+ align:start position:0%
+forever. If you're doing Halo 3 or
+Modern Warfare 3 or something like that,
+
+ align:start position:0%
+Modern Warfare 3 or something like that,
+ 
+
+ align:start position:0%
+Modern Warfare 3 or something like that,
+you know, then sure, you can sort of
+
+ align:start position:0%
+you know, then sure, you can sort of
+ 
+
+ align:start position:0%
+you know, then sure, you can sort of
+cater to the fans uh, who've already
+
+ align:start position:0%
+cater to the fans uh, who've already
+ 
+
+ align:start position:0%
+cater to the fans uh, who've already
+developed these strategies and and
+
+ align:start position:0%
+developed these strategies and and
+ 
+
+ align:start position:0%
+developed these strategies and and
+skills. But in in our case, we're
+
+ align:start position:0%
+skills. But in in our case, we're
+ 
+
+ align:start position:0%
+skills. But in in our case, we're
+develop we're going after a new
+
+ align:start position:0%
+develop we're going after a new
+ 
+
+ align:start position:0%
+develop we're going after a new
+audience. We're going after someone
+
+ align:start position:0%
+audience. We're going after someone
+ 
+
+ align:start position:0%
+audience. We're going after someone
+who's never played anything like what
+
+ align:start position:0%
+who's never played anything like what
+ 
+
+ align:start position:0%
+who's never played anything like what
+what you've played before.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool. Any
+
+ align:start position:0%
+Cool. Any
+ 
+
+ align:start position:0%
+Cool. Any
+questions?
+
+ align:start position:0%
+questions?
+ 
+
+ align:start position:0%
+questions?
+I've been soap boxing here for a while
+
+ align:start position:0%
+I've been soap boxing here for a while
+ 
+
+ align:start position:0%
+I've been soap boxing here for a while
+Jason.
+
+ align:start position:0%
+Jason.
+ 
+
+ align:start position:0%
+Jason.
+>> Um,
+
+ align:start position:0%
+>> Um,
+ 
+
+ align:start position:0%
+>> Um,
+so I guess the other thing that I would
+
+ align:start position:0%
+so I guess the other thing that I would
+ 
+
+ align:start position:0%
+so I guess the other thing that I would
+that I would add from my experience,
+
+ align:start position:0%
+that I would add from my experience,
+ 
+
+ align:start position:0%
+that I would add from my experience,
+especially with iterative design, is a
+
+ align:start position:0%
+especially with iterative design, is a
+ 
+
+ align:start position:0%
+especially with iterative design, is a
+big trick of it is learning to kind of
+
+ align:start position:0%
+big trick of it is learning to kind of
+ 
+
+ align:start position:0%
+big trick of it is learning to kind of
+distance yourself emotionally from what
+
+ align:start position:0%
+distance yourself emotionally from what
+ 
+
+ align:start position:0%
+distance yourself emotionally from what
+you're working on. Um, because half the
+
+ align:start position:0%
+you're working on. Um, because half the
+ 
+
+ align:start position:0%
+you're working on. Um, because half the
+time you end up chucking things that you
+
+ align:start position:0%
+time you end up chucking things that you
+ 
+
+ align:start position:0%
+time you end up chucking things that you
+really like. you think, "Oh, this would
+
+ align:start position:0%
+really like. you think, "Oh, this would
+ 
+
+ align:start position:0%
+really like. you think, "Oh, this would
+be so great, but it's best to just
+
+ align:start position:0%
+be so great, but it's best to just
+ 
+
+ align:start position:0%
+be so great, but it's best to just
+remove it." Um, it helps to think of it
+
+ align:start position:0%
+remove it." Um, it helps to think of it
+ 
+
+ align:start position:0%
+remove it." Um, it helps to think of it
+as putting kind of putting it on the
+
+ align:start position:0%
+as putting kind of putting it on the
+ 
+
+ align:start position:0%
+as putting kind of putting it on the
+shelf for later and saying, "Okay, I'll
+
+ align:start position:0%
+shelf for later and saying, "Okay, I'll
+ 
+
+ align:start position:0%
+shelf for later and saying, "Okay, I'll
+deal with this later. I can try this in
+
+ align:start position:0%
+deal with this later. I can try this in
+ 
+
+ align:start position:0%
+deal with this later. I can try this in
+another game." Um, and on a related
+
+ align:start position:0%
+another game." Um, and on a related
+ 
+
+ align:start position:0%
+another game." Um, and on a related
+note, I don't know about you, but I
+
+ align:start position:0%
+note, I don't know about you, but I
+ 
+
+ align:start position:0%
+note, I don't know about you, but I
+found that when games I'm designing have
+
+ align:start position:0%
+found that when games I'm designing have
+ 
+
+ align:start position:0%
+found that when games I'm designing have
+a problem, it's almost always fixed by
+
+ align:start position:0%
+a problem, it's almost always fixed by
+ 
+
+ align:start position:0%
+a problem, it's almost always fixed by
+removing something as opposed to adding
+
+ align:start position:0%
+removing something as opposed to adding
+ 
+
+ align:start position:0%
+removing something as opposed to adding
+more stuff on. Um, unless you're going
+
+ align:start position:0%
+more stuff on. Um, unless you're going
+ 
+
+ align:start position:0%
+more stuff on. Um, unless you're going
+for something, I think really complex
+
+ align:start position:0%
+for something, I think really complex
+ 
+
+ align:start position:0%
+for something, I think really complex
+off the start, I always prefer to try
+
+ align:start position:0%
+off the start, I always prefer to try
+ 
+
+ align:start position:0%
+off the start, I always prefer to try
+and take something out something out and
+
+ align:start position:0%
+and take something out something out and
+ 
+
+ align:start position:0%
+and take something out something out and
+simplify it.
+
+ align:start position:0%
+simplify it.
+ 
+
+ align:start position:0%
+simplify it.
+>> Yeah, especially in short projects like
+
+ align:start position:0%
+>> Yeah, especially in short projects like
+ 
+
+ align:start position:0%
+>> Yeah, especially in short projects like
+these, it almost always works better.
+
+ align:start position:0%
+these, it almost always works better.
+ 
+
+ align:start position:0%
+these, it almost always works better.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+and then and in terms of testing too,
+
+ align:start position:0%
+and then and in terms of testing too,
+ 
+
+ align:start position:0%
+and then and in terms of testing too,
+one thing just kind of a a tip that I
+
+ align:start position:0%
+one thing just kind of a a tip that I
+ 
+
+ align:start position:0%
+one thing just kind of a a tip that I
+find works is if you're designing a game
+
+ align:start position:0%
+find works is if you're designing a game
+ 
+
+ align:start position:0%
+find works is if you're designing a game
+that has a lot of different um like
+
+ align:start position:0%
+that has a lot of different um like
+ 
+
+ align:start position:0%
+that has a lot of different um like
+paths to victory, and this is a little
+
+ align:start position:0%
+paths to victory, and this is a little
+ 
+
+ align:start position:0%
+paths to victory, and this is a little
+bit higher level, but you'll see what I
+
+ align:start position:0%
+bit higher level, but you'll see what I
+ 
+
+ align:start position:0%
+bit higher level, but you'll see what I
+mean when we get there, where if you
+
+ align:start position:0%
+mean when we get there, where if you
+ 
+
+ align:start position:0%
+mean when we get there, where if you
+want a game that has different viable
+
+ align:start position:0%
+want a game that has different viable
+ 
+
+ align:start position:0%
+want a game that has different viable
+strategies, a really good testing method
+
+ align:start position:0%
+strategies, a really good testing method
+ 
+
+ align:start position:0%
+strategies, a really good testing method
+is to have different people kind of play
+
+ align:start position:0%
+is to have different people kind of play
+ 
+
+ align:start position:0%
+is to have different people kind of play
+like a perfect version of that strategy.
+
+ align:start position:0%
+like a perfect version of that strategy.
+ 
+
+ align:start position:0%
+like a perfect version of that strategy.
+And you say, I'm going to do this
+
+ align:start position:0%
+And you say, I'm going to do this
+ 
+
+ align:start position:0%
+And you say, I'm going to do this
+strategy or I'm always going to do X.
+
+ align:start position:0%
+strategy or I'm always going to do X.
+ 
+
+ align:start position:0%
+strategy or I'm always going to do X.
+And it doesn't matter if I think it's
+
+ align:start position:0%
+And it doesn't matter if I think it's
+ 
+
+ align:start position:0%
+And it doesn't matter if I think it's
+dumb, I'm just going to do it. Um
+
+ align:start position:0%
+dumb, I'm just going to do it. Um
+ 
+
+ align:start position:0%
+dumb, I'm just going to do it. Um
+because that'll really help you find
+
+ align:start position:0%
+because that'll really help you find
+ 
+
+ align:start position:0%
+because that'll really help you find
+rules that are broken or find something
+
+ align:start position:0%
+rules that are broken or find something
+ 
+
+ align:start position:0%
+rules that are broken or find something
+that's overpowered. Um a good example
+
+ align:start position:0%
+that's overpowered. Um a good example
+ 
+
+ align:start position:0%
+that's overpowered. Um a good example
+would be Settlers, right? Like if you
+
+ align:start position:0%
+would be Settlers, right? Like if you
+ 
+
+ align:start position:0%
+would be Settlers, right? Like if you
+say, "I'm obviously this wouldn't work
+
+ align:start position:0%
+say, "I'm obviously this wouldn't work
+ 
+
+ align:start position:0%
+say, "I'm obviously this wouldn't work
+because the game is a good game, but
+
+ align:start position:0%
+because the game is a good game, but
+ 
+
+ align:start position:0%
+because the game is a good game, but
+like I'm always going to build roads."
+
+ align:start position:0%
+like I'm always going to build roads."
+ 
+
+ align:start position:0%
+like I'm always going to build roads."
+You know what I mean? Like in practice
+
+ align:start position:0%
+You know what I mean? Like in practice
+ 
+
+ align:start position:0%
+You know what I mean? Like in practice
+that would be stupid, but if you're when
+
+ align:start position:0%
+that would be stupid, but if you're when
+ 
+
+ align:start position:0%
+that would be stupid, but if you're when
+you're designing a game, you do that
+
+ align:start position:0%
+you're designing a game, you do that
+ 
+
+ align:start position:0%
+you're designing a game, you do that
+kind of strategy and you just limit
+
+ align:start position:0%
+kind of strategy and you just limit
+ 
+
+ align:start position:0%
+kind of strategy and you just limit
+yourself to one action, you can really
+
+ align:start position:0%
+yourself to one action, you can really
+ 
+
+ align:start position:0%
+yourself to one action, you can really
+find things that are broken really
+
+ align:start position:0%
+find things that are broken really
+ 
+
+ align:start position:0%
+find things that are broken really
+quickly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+thanks. Yeah.
+
+ align:start position:0%
+thanks. Yeah.
+ 
+
+ align:start position:0%
+thanks. Yeah.
+Much appreciated. Cookies, dude. We have
+
+ align:start position:0%
+Much appreciated. Cookies, dude. We have
+ 
+
+ align:start position:0%
+Much appreciated. Cookies, dude. We have
+cookies.
+
+ align:start position:0%
+cookies.
+ 
+
+ align:start position:0%
+cookies.
+Thanks, Google. Just the Google family.
+
+ align:start position:0%
+Thanks, Google. Just the Google family.
+ 
+
+ align:start position:0%
+Thanks, Google. Just the Google family.
+Uh,
+
+ align:start position:0%
+Uh,
+ 
+
+ align:start position:0%
+Uh,
+uh, let's see. So, um, so yeah, we I
+
+ align:start position:0%
+uh, let's see. So, um, so yeah, we I
+ 
+
+ align:start position:0%
+uh, let's see. So, um, so yeah, we I
+think after this we're just going to
+
+ align:start position:0%
+think after this we're just going to
+ 
+
+ align:start position:0%
+think after this we're just going to
+play games. Uh well um we do have a play
+
+ align:start position:0%
+play games. Uh well um we do have a play
+ 
+
+ align:start position:0%
+play games. Uh well um we do have a play
+testing as a topic coming up later in
+
+ align:start position:0%
+testing as a topic coming up later in
+ 
+
+ align:start position:0%
+testing as a topic coming up later in
+the semester where we'll actually sort
+
+ align:start position:0%
+the semester where we'll actually sort
+ 
+
+ align:start position:0%
+the semester where we'll actually sort
+of talk about the discipline on how you
+
+ align:start position:0%
+of talk about the discipline on how you
+ 
+
+ align:start position:0%
+of talk about the discipline on how you
+do testing. Uh uh honestly it's
+
+ align:start position:0%
+do testing. Uh uh honestly it's
+ 
+
+ align:start position:0%
+do testing. Uh uh honestly it's
+you shouldn't wait for that class to
+
+ align:start position:0%
+you shouldn't wait for that class to
+ 
+
+ align:start position:0%
+you shouldn't wait for that class to
+necessarily start practicing. Uh you
+
+ align:start position:0%
+necessarily start practicing. Uh you
+ 
+
+ align:start position:0%
+necessarily start practicing. Uh you
+know if you it could be as simple as
+
+ align:start position:0%
+know if you it could be as simple as
+ 
+
+ align:start position:0%
+know if you it could be as simple as
+just grabbing a game that you have never
+
+ align:start position:0%
+just grabbing a game that you have never
+ 
+
+ align:start position:0%
+just grabbing a game that you have never
+seen before and just trying to get a
+
+ align:start position:0%
+seen before and just trying to get a
+ 
+
+ align:start position:0%
+seen before and just trying to get a
+whole bunch of people to play it and
+
+ align:start position:0%
+whole bunch of people to play it and
+ 
+
+ align:start position:0%
+whole bunch of people to play it and
+critiquing it at the same time. you
+
+ align:start position:0%
+critiquing it at the same time. you
+ 
+
+ align:start position:0%
+critiquing it at the same time. you
+know, it's like why did I do that? Why
+
+ align:start position:0%
+know, it's like why did I do that? Why
+ 
+
+ align:start position:0%
+know, it's like why did I do that? Why
+did you do that? Why did you do that
+
+ align:start position:0%
+did you do that? Why did you do that
+ 
+
+ align:start position:0%
+did you do that? Why did you do that
+move? You know, and um there are sort of
+
+ align:start position:0%
+move? You know, and um there are sort of
+ 
+
+ align:start position:0%
+move? You know, and um there are sort of
+practices to make sure that when it's
+
+ align:start position:0%
+practices to make sure that when it's
+ 
+
+ align:start position:0%
+practices to make sure that when it's
+your game, you are not sort of telling
+
+ align:start position:0%
+your game, you are not sort of telling
+ 
+
+ align:start position:0%
+your game, you are not sort of telling
+the players what they should be doing uh
+
+ align:start position:0%
+the players what they should be doing uh
+ 
+
+ align:start position:0%
+the players what they should be doing uh
+while they are trying to play the game
+
+ align:start position:0%
+while they are trying to play the game
+ 
+
+ align:start position:0%
+while they are trying to play the game
+because that affects their player uh in
+
+ align:start position:0%
+because that affects their player uh in
+ 
+
+ align:start position:0%
+because that affects their player uh in
+the game in a way that biases it. Uh but
+
+ align:start position:0%
+the game in a way that biases it. Uh but
+ 
+
+ align:start position:0%
+the game in a way that biases it. Uh but
+uh but we'll get to that later in the
+
+ align:start position:0%
+uh but we'll get to that later in the
+ 
+
+ align:start position:0%
+uh but we'll get to that later in the
+semester. for now, you know, uh just
+
+ align:start position:0%
+semester. for now, you know, uh just
+ 
+
+ align:start position:0%
+semester. for now, you know, uh just
+just be aware the more that you're
+
+ align:start position:0%
+just be aware the more that you're
+ 
+
+ align:start position:0%
+just be aware the more that you're
+testing, the more that you're sort of
+
+ align:start position:0%
+testing, the more that you're sort of
+ 
+
+ align:start position:0%
+testing, the more that you're sort of
+tweaking your rules in between tests and
+
+ align:start position:0%
+tweaking your rules in between tests and
+ 
+
+ align:start position:0%
+tweaking your rules in between tests and
+then getting another chance to test and
+
+ align:start position:0%
+then getting another chance to test and
+ 
+
+ align:start position:0%
+then getting another chance to test and
+test and test, the closer you are to
+
+ align:start position:0%
+test and test, the closer you are to
+ 
+
+ align:start position:0%
+test and test, the closer you are to
+getting a game that's actually fun and
+
+ align:start position:0%
+getting a game that's actually fun and
+ 
+
+ align:start position:0%
+getting a game that's actually fun and
+engaging to play. Um, and that's what
+
+ align:start position:0%
+engaging to play. Um, and that's what
+ 
+
+ align:start position:0%
+engaging to play. Um, and that's what
+we're looking for. That's the process
+
+ align:start position:0%
+we're looking for. That's the process
+ 
+
+ align:start position:0%
+we're looking for. That's the process
+that we expect you folks to to stick in.
+
+ align:start position:0%
+that we expect you folks to to stick in.
+ 
+
+ align:start position:0%
+that we expect you folks to to stick in.
+Whe whether you ever get to fun and
+
+ align:start position:0%
+Whe whether you ever get to fun and
+ 
+
+ align:start position:0%
+Whe whether you ever get to fun and
+engaging, who knows? We don't know
+
+ align:start position:0%
+engaging, who knows? We don't know
+ 
+
+ align:start position:0%
+engaging, who knows? We don't know
+whether you're going to get there. So,
+
+ align:start position:0%
+whether you're going to get there. So,
+ 
+
+ align:start position:0%
+whether you're going to get there. So,
+we're not grading you based on that.
+
+ align:start position:0%
+we're not grading you based on that.
+ 
+
+ align:start position:0%
+we're not grading you based on that.
+Just remember that. We're not grading
+
+ align:start position:0%
+Just remember that. We're not grading
+ 
+
+ align:start position:0%
+Just remember that. We're not grading
+you on how engaging your games are, but
+
+ align:start position:0%
+you on how engaging your games are, but
+ 
+
+ align:start position:0%
+you on how engaging your games are, but
+how well you stick to the process. Yes,
+
+ align:start position:0%
+how well you stick to the process. Yes,
+ 
+
+ align:start position:0%
+how well you stick to the process. Yes,
+absolutely.
+
+ align:start position:0%
+absolutely.
+ 
+
+ align:start position:0%
+absolutely.
+Um, there was a question on the forums
+
+ align:start position:0%
+Um, there was a question on the forums
+ 
+
+ align:start position:0%
+Um, there was a question on the forums
+about when do you stop, right?
+
+ align:start position:0%
+about when do you stop, right?
+ 
+
+ align:start position:0%
+about when do you stop, right?
+Did you put it up? Um, I didn't get a
+
+ align:start position:0%
+Did you put it up? Um, I didn't get a
+ 
+
+ align:start position:0%
+Did you put it up? Um, I didn't get a
+chance to look too closely at it. What?
+
+ align:start position:0%
+chance to look too closely at it. What?
+ 
+
+ align:start position:0%
+chance to look too closely at it. What?
+Um, can can you repeat?
+
+ align:start position:0%
+Um, can can you repeat?
+ 
+
+ align:start position:0%
+Um, can can you repeat?
+>> So, essentially, it's the question of so
+
+ align:start position:0%
+>> So, essentially, it's the question of so
+ 
+
+ align:start position:0%
+>> So, essentially, it's the question of so
+there's this iterative design process
+
+ align:start position:0%
+there's this iterative design process
+ 
+
+ align:start position:0%
+there's this iterative design process
+and when do you know when to sort of get
+
+ align:start position:0%
+and when do you know when to sort of get
+ 
+
+ align:start position:0%
+and when do you know when to sort of get
+out of that process?
+
+ align:start position:0%
+out of that process?
+ 
+
+ align:start position:0%
+out of that process?
+>> Due date.
+
+ align:start position:0%
+>> Due date.
+ 
+
+ align:start position:0%
+>> Due date.
+>> The due date. Okay. All right. That's
+
+ align:start position:0%
+>> The due date. Okay. All right. That's
+ 
+
+ align:start position:0%
+>> The due date. Okay. All right. That's
+always a good reason. Uh,
+
+ align:start position:0%
+always a good reason. Uh,
+ 
+
+ align:start position:0%
+always a good reason. Uh,
+>> but I guess like if you didn't have a
+
+ align:start position:0%
+>> but I guess like if you didn't have a
+ 
+
+ align:start position:0%
+>> but I guess like if you didn't have a
+due date, like how would you know when
+
+ align:start position:0%
+due date, like how would you know when
+ 
+
+ align:start position:0%
+due date, like how would you know when
+to ship or let's say you have control
+
+ align:start position:0%
+to ship or let's say you have control
+ 
+
+ align:start position:0%
+to ship or let's say you have control
+over the due date?
+
+ align:start position:0%
+over the due date?
+ 
+
+ align:start position:0%
+over the due date?
+>> Um, I guess part of that is you should
+
+ align:start position:0%
+>> Um, I guess part of that is you should
+ 
+
+ align:start position:0%
+>> Um, I guess part of that is you should
+always be iterate like you should always
+
+ align:start position:0%
+always be iterate like you should always
+ 
+
+ align:start position:0%
+always be iterate like you should always
+be updating blah blah.
+
+ align:start position:0%
+be updating blah blah.
+ 
+
+ align:start position:0%
+be updating blah blah.
+>> So I guess the question is when do you
+
+ align:start position:0%
+>> So I guess the question is when do you
+ 
+
+ align:start position:0%
+>> So I guess the question is when do you
+know when you have something that you
+
+ align:start position:0%
+know when you have something that you
+ 
+
+ align:start position:0%
+know when you have something that you
+can put out into like the world?
+
+ align:start position:0%
+can put out into like the world?
+ 
+
+ align:start position:0%
+can put out into like the world?
+>> Um, so the cynical answer yeah is that
+
+ align:start position:0%
+>> Um, so the cynical answer yeah is that
+ 
+
+ align:start position:0%
+>> Um, so the cynical answer yeah is that
+is that you wait for you know you have
+
+ align:start position:0%
+is that you wait for you know you have
+ 
+
+ align:start position:0%
+is that you wait for you know you have
+to ship right or you're not getting any
+
+ align:start position:0%
+to ship right or you're not getting any
+ 
+
+ align:start position:0%
+to ship right or you're not getting any
+cash. Um, the I personally think it will
+
+ align:start position:0%
+cash. Um, the I personally think it will
+ 
+
+ align:start position:0%
+cash. Um, the I personally think it will
+be sooner soon. s sooner than you think.
+
+ align:start position:0%
+be sooner soon. s sooner than you think.
+ 
+
+ align:start position:0%
+be sooner soon. s sooner than you think.
+It's like, you know, oh, my game's
+
+ align:start position:0%
+It's like, you know, oh, my game's
+ 
+
+ align:start position:0%
+It's like, you know, oh, my game's
+almost ready, but I notice something
+
+ align:start position:0%
+almost ready, but I notice something
+ 
+
+ align:start position:0%
+almost ready, but I notice something
+wrong with it. Especially when you're a
+
+ align:start position:0%
+wrong with it. Especially when you're a
+ 
+
+ align:start position:0%
+wrong with it. Especially when you're a
+student. Um, right. Right now, I'm in
+
+ align:start position:0%
+student. Um, right. Right now, I'm in
+ 
+
+ align:start position:0%
+student. Um, right. Right now, I'm in
+this I'm in this mode with my Starcraft
+
+ align:start position:0%
+this I'm in this mode with my Starcraft
+ 
+
+ align:start position:0%
+this I'm in this mode with my Starcraft
+apps, which is this map is crap. I know
+
+ align:start position:0%
+apps, which is this map is crap. I know
+ 
+
+ align:start position:0%
+apps, which is this map is crap. I know
+there's something wrong with it. I have
+
+ align:start position:0%
+there's something wrong with it. I have
+ 
+
+ align:start position:0%
+there's something wrong with it. I have
+no idea what it is. Therefore, I'm going
+
+ align:start position:0%
+no idea what it is. Therefore, I'm going
+ 
+
+ align:start position:0%
+no idea what it is. Therefore, I'm going
+to release it. Uh, because until I do
+
+ align:start position:0%
+to release it. Uh, because until I do
+ 
+
+ align:start position:0%
+to release it. Uh, because until I do
+that, I have no idea what's wrong with
+
+ align:start position:0%
+that, I have no idea what's wrong with
+ 
+
+ align:start position:0%
+that, I have no idea what's wrong with
+it. I need to get that that that
+
+ align:start position:0%
+it. I need to get that that that
+ 
+
+ align:start position:0%
+it. I need to get that that that
+information. The nice thing about stuff
+
+ align:start position:0%
+information. The nice thing about stuff
+ 
+
+ align:start position:0%
+information. The nice thing about stuff
+like, you know, uh, computer games is
+
+ align:start position:0%
+like, you know, uh, computer games is
+ 
+
+ align:start position:0%
+like, you know, uh, computer games is
+that you can ship updates. Um, it's
+
+ align:start position:0%
+that you can ship updates. Um, it's
+ 
+
+ align:start position:0%
+that you can ship updates. Um, it's
+annoying, but you can. But even board
+
+ align:start position:0%
+annoying, but you can. But even board
+ 
+
+ align:start position:0%
+annoying, but you can. But even board
+games and card games now have re rule
+
+ align:start position:0%
+games and card games now have re rule
+ 
+
+ align:start position:0%
+games and card games now have re rule
+revisions, rule clarifications that you
+
+ align:start position:0%
+revisions, rule clarifications that you
+ 
+
+ align:start position:0%
+revisions, rule clarifications that you
+can release o um, uh, over the net. Uh,
+
+ align:start position:0%
+can release o um, uh, over the net. Uh,
+ 
+
+ align:start position:0%
+can release o um, uh, over the net. Uh,
+for the most part, if you are going to
+
+ align:start position:0%
+for the most part, if you are going to
+ 
+
+ align:start position:0%
+for the most part, if you are going to
+go professional, your publisher will
+
+ align:start position:0%
+go professional, your publisher will
+ 
+
+ align:start position:0%
+go professional, your publisher will
+tell you and then the answer really is
+
+ align:start position:0%
+tell you and then the answer really is
+ 
+
+ align:start position:0%
+tell you and then the answer really is
+due date, right? You know, it's like
+
+ align:start position:0%
+due date, right? You know, it's like
+ 
+
+ align:start position:0%
+due date, right? You know, it's like
+it's going to the presses on this date.
+
+ align:start position:0%
+it's going to the presses on this date.
+ 
+
+ align:start position:0%
+it's going to the presses on this date.
+And uh that's one maxim which is game
+
+ align:start position:0%
+And uh that's one maxim which is game
+ 
+
+ align:start position:0%
+And uh that's one maxim which is game
+projects are never finished. They're
+
+ align:start position:0%
+projects are never finished. They're
+ 
+
+ align:start position:0%
+projects are never finished. They're
+just abandoned. Um you know it's just
+
+ align:start position:0%
+just abandoned. Um you know it's just
+ 
+
+ align:start position:0%
+just abandoned. Um you know it's just
+all you know I can't do anything else
+
+ align:start position:0%
+all you know I can't do anything else
+ 
+
+ align:start position:0%
+all you know I can't do anything else
+about this because I'm out of time. Ship
+
+ align:start position:0%
+about this because I'm out of time. Ship
+ 
+
+ align:start position:0%
+about this because I'm out of time. Ship
+it. Um but one thing that you can do to
+
+ align:start position:0%
+it. Um but one thing that you can do to
+ 
+
+ align:start position:0%
+it. Um but one thing that you can do to
+prepare for that um let me see is there
+
+ align:start position:0%
+prepare for that um let me see is there
+ 
+
+ align:start position:0%
+prepare for that um let me see is there
+an er
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there there's a guy who runs a blog
+
+ align:start position:0%
+there there's a guy who runs a blog
+ 
+
+ align:start position:0%
+there there's a guy who runs a blog
+called Lost Garden. His name is Dan
+
+ align:start position:0%
+called Lost Garden. His name is Dan
+ 
+
+ align:start position:0%
+called Lost Garden. His name is Dan
+Cook. He works over in Microsoft and he
+
+ align:start position:0%
+Cook. He works over in Microsoft and he
+ 
+
+ align:start position:0%
+Cook. He works over in Microsoft and he
+talks a lot about game design um
+
+ align:start position:0%
+talks a lot about game design um
+ 
+
+ align:start position:0%
+talks a lot about game design um
+specifically about video game design,
+
+ align:start position:0%
+specifically about video game design,
+ 
+
+ align:start position:0%
+specifically about video game design,
+but actually his stuff is actually
+
+ align:start position:0%
+but actually his stuff is actually
+ 
+
+ align:start position:0%
+but actually his stuff is actually
+really really applicable and he has this
+
+ align:start position:0%
+really really applicable and he has this
+ 
+
+ align:start position:0%
+really really applicable and he has this
+concept that you know game design or
+
+ align:start position:0%
+concept that you know game design or
+ 
+
+ align:start position:0%
+concept that you know game design or
+iterative game design kind of goes in
+
+ align:start position:0%
+iterative game design kind of goes in
+ 
+
+ align:start position:0%
+iterative game design kind of goes in
+this in this kind of cycle where uh this
+
+ align:start position:0%
+this in this kind of cycle where uh this
+ 
+
+ align:start position:0%
+this in this kind of cycle where uh this
+is this width down here is the number of
+
+ align:start position:0%
+is this width down here is the number of
+ 
+
+ align:start position:0%
+is this width down here is the number of
+features that you've got in your game.
+
+ align:start position:0%
+features that you've got in your game.
+ 
+
+ align:start position:0%
+features that you've got in your game.
+Uh the trick though is that um what you
+
+ align:start position:0%
+Uh the trick though is that um what you
+ 
+
+ align:start position:0%
+Uh the trick though is that um what you
+are really doing is you are taking
+
+ align:start position:0%
+are really doing is you are taking
+ 
+
+ align:start position:0%
+are really doing is you are taking
+let me see if this is right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is all the good stuff. This is
+
+ align:start position:0%
+So this is all the good stuff. This is
+ 
+
+ align:start position:0%
+So this is all the good stuff. This is
+all the stuff that's not so good. Um,
+
+ align:start position:0%
+all the stuff that's not so good. Um,
+ 
+
+ align:start position:0%
+all the stuff that's not so good. Um,
+and the whole idea of of of
+
+ align:start position:0%
+and the whole idea of of of
+ 
+
+ align:start position:0%
+and the whole idea of of of
+sort of like using iterative design is
+
+ align:start position:0%
+sort of like using iterative design is
+ 
+
+ align:start position:0%
+sort of like using iterative design is
+to allow yourself to the space to come
+
+ align:start position:0%
+to allow yourself to the space to come
+ 
+
+ align:start position:0%
+to allow yourself to the space to come
+up with a whole bunch of ideas not
+
+ align:start position:0%
+up with a whole bunch of ideas not
+ 
+
+ align:start position:0%
+up with a whole bunch of ideas not
+knowing whether they're good or bad, but
+
+ align:start position:0%
+knowing whether they're good or bad, but
+ 
+
+ align:start position:0%
+knowing whether they're good or bad, but
+then also give you a gate to cut out all
+
+ align:start position:0%
+then also give you a gate to cut out all
+ 
+
+ align:start position:0%
+then also give you a gate to cut out all
+the bad stuff. So at any so at frequent
+
+ align:start position:0%
+the bad stuff. So at any so at frequent
+ 
+
+ align:start position:0%
+the bad stuff. So at any so at frequent
+periodic intervals you have a collection
+
+ align:start position:0%
+periodic intervals you have a collection
+ 
+
+ align:start position:0%
+periodic intervals you have a collection
+of rules of cards of designs of whatever
+
+ align:start position:0%
+of rules of cards of designs of whatever
+ 
+
+ align:start position:0%
+of rules of cards of designs of whatever
+consists your game that is pretty much
+
+ align:start position:0%
+consists your game that is pretty much
+ 
+
+ align:start position:0%
+consists your game that is pretty much
+as good as you possibly could have made
+
+ align:start position:0%
+as good as you possibly could have made
+ 
+
+ align:start position:0%
+as good as you possibly could have made
+it given the amount of time that you've
+
+ align:start position:0%
+it given the amount of time that you've
+ 
+
+ align:start position:0%
+it given the amount of time that you've
+got and that could ship. Um so you know
+
+ align:start position:0%
+got and that could ship. Um so you know
+ 
+
+ align:start position:0%
+got and that could ship. Um so you know
+so if if your ship date was here you
+
+ align:start position:0%
+so if if your ship date was here you
+ 
+
+ align:start position:0%
+so if if your ship date was here you
+would have as good a game as you
+
+ align:start position:0%
+would have as good a game as you
+ 
+
+ align:start position:0%
+would have as good a game as you
+possibly could doing it. if ship date
+
+ align:start position:0%
+possibly could doing it. if ship date
+ 
+
+ align:start position:0%
+possibly could doing it. if ship date
+turned out to be there all of a sudden.
+
+ align:start position:0%
+turned out to be there all of a sudden.
+ 
+
+ align:start position:0%
+turned out to be there all of a sudden.
+You know, you've still got you still had
+
+ align:start position:0%
+You know, you've still got you still had
+ 
+
+ align:start position:0%
+You know, you've still got you still had
+the opportunity to quiddle out all of
+
+ align:start position:0%
+the opportunity to quiddle out all of
+ 
+
+ align:start position:0%
+the opportunity to quiddle out all of
+the all the stuff that you knew was bad.
+
+ align:start position:0%
+the all the stuff that you knew was bad.
+ 
+
+ align:start position:0%
+the all the stuff that you knew was bad.
+Um so iterative design is not about
+
+ align:start position:0%
+Um so iterative design is not about
+ 
+
+ align:start position:0%
+Um so iterative design is not about
+let's just keep accreating more and more
+
+ align:start position:0%
+let's just keep accreating more and more
+ 
+
+ align:start position:0%
+let's just keep accreating more and more
+and more and more features. It's more
+
+ align:start position:0%
+and more and more features. It's more
+ 
+
+ align:start position:0%
+and more and more features. It's more
+about you know we're going to add some
+
+ align:start position:0%
+about you know we're going to add some
+ 
+
+ align:start position:0%
+about you know we're going to add some
+features and then we're going to remove
+
+ align:start position:0%
+features and then we're going to remove
+ 
+
+ align:start position:0%
+features and then we're going to remove
+the ones that don't work. Um and that's
+
+ align:start position:0%
+the ones that don't work. Um and that's
+ 
+
+ align:start position:0%
+the ones that don't work. Um and that's
+really really important. Uh so that at
+
+ align:start position:0%
+really really important. Uh so that at
+ 
+
+ align:start position:0%
+really really important. Uh so that at
+any given time you're prepared to sort
+
+ align:start position:0%
+any given time you're prepared to sort
+ 
+
+ align:start position:0%
+any given time you're prepared to sort
+of release it. Um, and as for when you
+
+ align:start position:0%
+of release it. Um, and as for when you
+ 
+
+ align:start position:0%
+of release it. Um, and as for when you
+actually decide that this is now ready
+
+ align:start position:0%
+actually decide that this is now ready
+ 
+
+ align:start position:0%
+actually decide that this is now ready
+to go out, I would again I would I would
+
+ align:start position:0%
+to go out, I would again I would I would
+ 
+
+ align:start position:0%
+to go out, I would again I would I would
+repeat sooner than than you think
+
+ align:start position:0%
+repeat sooner than than you think
+ 
+
+ align:start position:0%
+repeat sooner than than you think
+because you need that feedback. U
+
+ align:start position:0%
+because you need that feedback. U
+ 
+
+ align:start position:0%
+because you need that feedback. U
+sometimes uh you don't know how a market
+
+ align:start position:0%
+sometimes uh you don't know how a market
+ 
+
+ align:start position:0%
+sometimes uh you don't know how a market
+is going to respond until you actually
+
+ align:start position:0%
+is going to respond until you actually
+ 
+
+ align:start position:0%
+is going to respond until you actually
+do it. But you can do a soft launch. Uh
+
+ align:start position:0%
+do it. But you can do a soft launch. Uh
+ 
+
+ align:start position:0%
+do it. But you can do a soft launch. Uh
+if you're doing uh commercial product,
+
+ align:start position:0%
+if you're doing uh commercial product,
+ 
+
+ align:start position:0%
+if you're doing uh commercial product,
+you you can do things where we're going
+
+ align:start position:0%
+you you can do things where we're going
+ 
+
+ align:start position:0%
+you you can do things where we're going
+to release it to a few select stores and
+
+ align:start position:0%
+to release it to a few select stores and
+ 
+
+ align:start position:0%
+to release it to a few select stores and
+get that feedback before we go into
+
+ align:start position:0%
+get that feedback before we go into
+ 
+
+ align:start position:0%
+get that feedback before we go into
+major print run uh or you know uh burn
+
+ align:start position:0%
+major print run uh or you know uh burn
+ 
+
+ align:start position:0%
+major print run uh or you know uh burn
+burn 10,000 different copies of the same
+
+ align:start position:0%
+burn 10,000 different copies of the same
+ 
+
+ align:start position:0%
+burn 10,000 different copies of the same
+board game. Uh we're going to do 200
+
+ align:start position:0%
+board game. Uh we're going to do 200
+ 
+
+ align:start position:0%
+board game. Uh we're going to do 200
+copies and see how that does for us. It
+
+ align:start position:0%
+copies and see how that does for us. It
+ 
+
+ align:start position:0%
+copies and see how that does for us. It
+gives you the opportunity to to make a
+
+ align:start position:0%
+gives you the opportunity to to make a
+ 
+
+ align:start position:0%
+gives you the opportunity to to make a
+revision, but it's still an official
+
+ align:start position:0%
+revision, but it's still an official
+ 
+
+ align:start position:0%
+revision, but it's still an official
+release because those 200 people think
+
+ align:start position:0%
+release because those 200 people think
+ 
+
+ align:start position:0%
+release because those 200 people think
+that this is the final package product.
+
+ align:start position:0%
+that this is the final package product.
+ 
+
+ align:start position:0%
+that this is the final package product.
+Um that's pretty much how a lot of
+
+ align:start position:0%
+Um that's pretty much how a lot of
+ 
+
+ align:start position:0%
+Um that's pretty much how a lot of
+manufacturing industries actually work
+
+ align:start position:0%
+manufacturing industries actually work
+ 
+
+ align:start position:0%
+manufacturing industries actually work
+anyway. So if you think about u any kind
+
+ align:start position:0%
+anyway. So if you think about u any kind
+ 
+
+ align:start position:0%
+anyway. So if you think about u any kind
+of product design, a lot of them have a
+
+ align:start position:0%
+of product design, a lot of them have a
+ 
+
+ align:start position:0%
+of product design, a lot of them have a
+sort of like trial period.
+
+ align:start position:0%
+sort of like trial period.
+ 
+
+ align:start position:0%
+sort of like trial period.
+>> Soft drinks
+
+ align:start position:0%
+>> Soft drinks
+ 
+
+ align:start position:0%
+>> Soft drinks
+>> soft drinks you get a lot um Japanese
+
+ align:start position:0%
+>> soft drinks you get a lot um Japanese
+ 
+
+ align:start position:0%
+>> soft drinks you get a lot um Japanese
+electronics you know it's like you
+
+ align:start position:0%
+electronics you know it's like you
+ 
+
+ align:start position:0%
+electronics you know it's like you
+release it in Tokyo and then you release
+
+ align:start position:0%
+release it in Tokyo and then you release
+ 
+
+ align:start position:0%
+release it in Tokyo and then you release
+it in the rest of Japan. Uh and
+
+ align:start position:0%
+it in the rest of Japan. Uh and
+ 
+
+ align:start position:0%
+it in the rest of Japan. Uh and
+sometimes it never makes it out out of
+
+ align:start position:0%
+sometimes it never makes it out out of
+ 
+
+ align:start position:0%
+sometimes it never makes it out out of
+Japan. uh because you know that initial
+
+ align:start position:0%
+Japan. uh because you know that initial
+ 
+
+ align:start position:0%
+Japan. uh because you know that initial
+test yeah it was it was a good product
+
+ align:start position:0%
+test yeah it was it was a good product
+ 
+
+ align:start position:0%
+test yeah it was it was a good product
+but not enough people bought it because
+
+ align:start position:0%
+but not enough people bought it because
+ 
+
+ align:start position:0%
+but not enough people bought it because
+of these problems. So instead of
+
+ align:start position:0%
+of these problems. So instead of
+ 
+
+ align:start position:0%
+of these problems. So instead of
+releasing into the world we're going to
+
+ align:start position:0%
+releasing into the world we're going to
+ 
+
+ align:start position:0%
+releasing into the world we're going to
+make version two and maybe that will be
+
+ align:start position:0%
+make version two and maybe that will be
+ 
+
+ align:start position:0%
+make version two and maybe that will be
+one release too. That's that's that's
+
+ align:start position:0%
+one release too. That's that's that's
+ 
+
+ align:start position:0%
+one release too. That's that's that's
+one example.
+
+ align:start position:0%
+one example.
+ 
+
+ align:start position:0%
+one example.
+All right. So we have games
+
+ align:start position:0%
+All right. So we have games
+ 
+
+ align:start position:0%
+All right. So we have games
+um but who has not played?
+
+ align:start position:0%
+um but who has not played?
+ 
+
+ align:start position:0%
+um but who has not played?
+>> Okay. All right. We have more games than
+
+ align:start position:0%
+>> Okay. All right. We have more games than
+ 
+
+ align:start position:0%
+>> Okay. All right. We have more games than
+we have.
+
+ align:start position:0%
+we have.
+ 
+
+ align:start position:0%
+we have.
+No. Okay. So, um Jason, you're going to
+
+ align:start position:0%
+No. Okay. So, um Jason, you're going to
+ 
+
+ align:start position:0%
+No. Okay. So, um Jason, you're going to
+do a youer uh table. So, um
+
+ align:start position:0%
+do a youer uh table. So, um
+ 
+
+ align:start position:0%
+do a youer uh table. So, um
+>> like just a four player trick taking
+
+ align:start position:0%
+>> like just a four player trick taking
+ 
+
+ align:start position:0%
+>> like just a four player trick taking
+game. Kind of vehicles.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um looks like we have exactly four
+
+ align:start position:0%
+>> Um looks like we have exactly four
+ 
+
+ align:start position:0%
+>> Um looks like we have exactly four
+people. One, two, three. One, two,
+
+ align:start position:0%
+people. One, two, three. One, two,
+ 
+
+ align:start position:0%
+people. One, two, three. One, two,
+three. Oh, yeah. We have an average of
+
+ align:start position:0%
+three. Oh, yeah. We have an average of
+ 
+
+ align:start position:0%
+three. Oh, yeah. We have an average of
+three people per table. That table is
+
+ align:start position:0%
+three people per table. That table is
+ 
+
+ align:start position:0%
+three people per table. That table is
+four. Um, I think most of these games
+
+ align:start position:0%
+four. Um, I think most of these games
+ 
+
+ align:start position:0%
+four. Um, I think most of these games
+are three to five players, although I'm
+
+ align:start position:0%
+are three to five players, although I'm
+ 
+
+ align:start position:0%
+are three to five players, although I'm
+going to be absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. This is like four to eight.
+
+ align:start position:0%
+>> Yeah. This is like four to eight.
+ 
+
+ align:start position:0%
+>> Yeah. This is like four to eight.
+>> You guys play fully.
+
+ align:start position:0%
+>> You guys play fully.
+ 
+
+ align:start position:0%
+>> You guys play fully.
+>> Yeah. So, so falling might want to be
+
+ align:start position:0%
+>> Yeah. So, so falling might want to be
+ 
+
+ align:start position:0%
+>> Yeah. So, so falling might want to be
+larger table. You guys might actually
+
+ align:start position:0%
+larger table. You guys might actually
+ 
+
+ align:start position:0%
+larger table. You guys might actually
+want to try the round table in the
+
+ align:start position:0%
+want to try the round table in the
+ 
+
+ align:start position:0%
+want to try the round table in the
+corner.
+
+ align:start position:0%
+corner.
+ 
+
+ align:start position:0%
+corner.
+>> Yeah. It says table.
+
+ align:start position:0%
+>> Yeah. It says table.
+ 
+
+ align:start position:0%
+>> Yeah. It says table.
+>> Yeah. 48 people.
+
+ align:start position:0%
+>> Yeah. 48 people.
+ 
+
+ align:start position:0%
+>> Yeah. 48 people.
+>> I really want to play.
+
+ align:start position:0%
+>> I really want to play.
+ 
+
+ align:start position:0%
+>> I really want to play.
+>> All right. Let's do this play.
+
+ align:start position:0%
+>> All right. Let's do this play.
+ 
+
+ align:start position:0%
+>> All right. Let's do this play.
+Please. Um,
+
+ align:start position:0%
+Please. Um,
+ 
+
+ align:start position:0%
+Please. Um,
+>> so basically take a game um uh from the
+
+ align:start position:0%
+>> so basically take a game um uh from the
+ 
+
+ align:start position:0%
+>> so basically take a game um uh from the
+table. Uh, I'll I'll bring some out and
+
+ align:start position:0%
+table. Uh, I'll I'll bring some out and
+ 
+
+ align:start position:0%
+table. Uh, I'll I'll bring some out and
+I'll see that play uh play them. Once
+
+ align:start position:0%
+I'll see that play uh play them. Once
+ 
+
+ align:start position:0%
+I'll see that play uh play them. Once
+you've had a chance to play a few times,
+
+ align:start position:0%
+you've had a chance to play a few times,
+ 
+
+ align:start position:0%
+you've had a chance to play a few times,
+feel free to switch
+
+ align:start position:0%
+feel free to switch
+ 
+
+ align:start position:0%
+feel free to switch
+>> and try to get as many games played as
+
+ align:start position:0%
+>> and try to get as many games played as
+ 
+
+ align:start position:0%
+>> and try to get as many games played as
+possible during during the next couple
+
+ align:start position:0%
+possible during during the next couple
+ 
+
+ align:start position:0%
+possible during during the next couple
+of hours and stuff.
+
+ align:start position:0%
+of hours and stuff.
+ 
+
+ align:start position:0%
+of hours and stuff.
+>> Cool.
\ No newline at end of file
diff --git a/bhBQbi9sWFA.txt b/bhBQbi9sWFA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c5486248cd6cffd440da9bb6be14cff5cd83f29a
--- /dev/null
+++ b/bhBQbi9sWFA.txt
@@ -0,0 +1,11067 @@
+align:start position:0%
+ 
+Okay. So, so today we want to talk a
+
+ align:start position:0%
+Okay. So, so today we want to talk a
+ 
+
+ align:start position:0%
+Okay. So, so today we want to talk a
+little bit more about sequences and how
+
+ align:start position:0%
+little bit more about sequences and how
+ 
+
+ align:start position:0%
+little bit more about sequences and how
+sequence connect to
+
+ align:start position:0%
+sequence connect to
+ 
+
+ align:start position:0%
+sequence connect to
+um to um uh a function being continuous.
+
+ align:start position:0%
+um to um uh a function being continuous.
+ 
+
+ align:start position:0%
+um to um uh a function being continuous.
+And then the second thing we will talk
+
+ align:start position:0%
+And then the second thing we will talk
+ 
+
+ align:start position:0%
+And then the second thing we will talk
+about is metric spaces.
+
+ align:start position:0%
+about is metric spaces.
+ 
+
+ align:start position:0%
+about is metric spaces.
+So let me just remind you first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that if you take a subset here say of
+
+ align:start position:0%
+uh that if you take a subset here say of
+ 
+
+ align:start position:0%
+uh that if you take a subset here say of
+r and you have a function on a into r
+
+ align:start position:0%
+r and you have a function on a into r
+ 
+
+ align:start position:0%
+r and you have a function on a into r
+then uh f is set to be continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh if for all x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+uh uh um the function is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0 and and it is the function is
+
+ align:start position:0%
+at x0 and and it is the function is
+ 
+
+ align:start position:0%
+at x0 and and it is the function is
+continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh at x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If um for all
+
+ align:start position:0%
+If um for all
+ 
+
+ align:start position:0%
+If um for all
+if for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon greater than zero there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta greater than zero such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the
+
+ align:start position:0%
+if the
+ 
+
+ align:start position:0%
+if the
+two points so x0 and this other point X
+
+ align:start position:0%
+two points so x0 and this other point X
+ 
+
+ align:start position:0%
+two points so x0 and this other point X
+they deviate at most by delta
+
+ align:start position:0%
+they deviate at most by delta
+ 
+
+ align:start position:0%
+they deviate at most by delta
+then their images deviate at most by
+
+ align:start position:0%
+then their images deviate at most by
+ 
+
+ align:start position:0%
+then their images deviate at most by
+epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in general right this delta here
+
+ align:start position:0%
+and in general right this delta here
+ 
+
+ align:start position:0%
+and in general right this delta here
+depends not only on x0 but also on on
+
+ align:start position:0%
+depends not only on x0 but also on on
+ 
+
+ align:start position:0%
+depends not only on x0 but also on on
+epsilon. So delta would in general be
+
+ align:start position:0%
+epsilon. So delta would in general be
+ 
+
+ align:start position:0%
+epsilon. So delta would in general be
+expected to depend on both of these
+
+ align:start position:0%
+expected to depend on both of these
+ 
+
+ align:start position:0%
+expected to depend on both of these
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Okay, so this is what so we talked about
+
+ align:start position:0%
+Okay, so this is what so we talked about
+ 
+
+ align:start position:0%
+Okay, so this is what so we talked about
+this a number of times and we will also
+
+ align:start position:0%
+this a number of times and we will also
+ 
+
+ align:start position:0%
+this a number of times and we will also
+generalize this later in the lecture. So
+
+ align:start position:0%
+generalize this later in the lecture. So
+ 
+
+ align:start position:0%
+generalize this later in the lecture. So
+this is what it means to be continuous
+
+ align:start position:0%
+this is what it means to be continuous
+ 
+
+ align:start position:0%
+this is what it means to be continuous
+that it needs to be continuous at all
+
+ align:start position:0%
+that it needs to be continuous at all
+ 
+
+ align:start position:0%
+that it needs to be continuous at all
+points and this is what it means need
+
+ align:start position:0%
+points and this is what it means need
+ 
+
+ align:start position:0%
+points and this is what it means need
+what it means to be continuous at a
+
+ align:start position:0%
+what it means to be continuous at a
+ 
+
+ align:start position:0%
+what it means to be continuous at a
+point.
+
+ align:start position:0%
+point.
+ 
+
+ align:start position:0%
+point.
+Now, two things we talked about before
+
+ align:start position:0%
+Now, two things we talked about before
+ 
+
+ align:start position:0%
+Now, two things we talked about before
+is the extreme value theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the intermediate value.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I want to think about these two
+
+ align:start position:0%
+And I want to think about these two
+ 
+
+ align:start position:0%
+And I want to think about these two
+theorems in terms of sequences.
+
+ align:start position:0%
+theorems in terms of sequences.
+ 
+
+ align:start position:0%
+theorems in terms of sequences.
+And so this is and and and that's often
+
+ align:start position:0%
+And so this is and and and that's often
+ 
+
+ align:start position:0%
+And so this is and and and that's often
+a really useful way of thinking about
+
+ align:start position:0%
+a really useful way of thinking about
+ 
+
+ align:start position:0%
+a really useful way of thinking about
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+So the extreme value theorem is that we
+
+ align:start position:0%
+So the extreme value theorem is that we
+ 
+
+ align:start position:0%
+So the extreme value theorem is that we
+have a function. So the extreme value
+
+ align:start position:0%
+have a function. So the extreme value
+ 
+
+ align:start position:0%
+have a function. So the extreme value
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+abbreviated like this. Um that's the
+
+ align:start position:0%
+abbreviated like this. Um that's the
+ 
+
+ align:start position:0%
+abbreviated like this. Um that's the
+theorem that say that if you take a
+
+ align:start position:0%
+theorem that say that if you take a
+ 
+
+ align:start position:0%
+theorem that say that if you take a
+function on some interval from a to b a
+
+ align:start position:0%
+function on some interval from a to b a
+ 
+
+ align:start position:0%
+function on some interval from a to b a
+and b are both included
+
+ align:start position:0%
+and b are both included
+ 
+
+ align:start position:0%
+and b are both included
+into r and this function is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the claim is that then there exist
+
+ align:start position:0%
+then the claim is that then there exist
+ 
+
+ align:start position:0%
+then the claim is that then there exist
+then they exist.
+
+ align:start position:0%
+then they exist.
+ 
+
+ align:start position:0%
+then they exist.
+So one way I formulated it is that then
+
+ align:start position:0%
+So one way I formulated it is that then
+ 
+
+ align:start position:0%
+So one way I formulated it is that then
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x m capital m this is something in that
+
+ align:start position:0%
+x m capital m this is something in that
+ 
+
+ align:start position:0%
+x m capital m this is something in that
+interval. So there exist some point that
+
+ align:start position:0%
+interval. So there exist some point that
+ 
+
+ align:start position:0%
+interval. So there exist some point that
+we call x capital m and and x little m
+
+ align:start position:0%
+we call x capital m and and x little m
+ 
+
+ align:start position:0%
+we call x capital m and and x little m
+also in the interval.
+
+ align:start position:0%
+also in the interval.
+ 
+
+ align:start position:0%
+also in the interval.
+And the first one has a property that
+
+ align:start position:0%
+And the first one has a property that
+ 
+
+ align:start position:0%
+And the first one has a property that
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+x in x in the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have that f ofx
+
+ align:start position:0%
+you have that f ofx
+ 
+
+ align:start position:0%
+you have that f ofx
+is less or equal to the value
+
+ align:start position:0%
+is less or equal to the value
+ 
+
+ align:start position:0%
+is less or equal to the value
+at xm. So you have this and you also
+
+ align:start position:0%
+at xm. So you have this and you also
+ 
+
+ align:start position:0%
+at xm. So you have this and you also
+have that f ofx at this here is bigger
+
+ align:start position:0%
+have that f ofx at this here is bigger
+ 
+
+ align:start position:0%
+have that f ofx at this here is bigger
+equal to the value at this other point.
+
+ align:start position:0%
+equal to the value at this other point.
+ 
+
+ align:start position:0%
+equal to the value at this other point.
+Right? So this means in particular that
+
+ align:start position:0%
+Right? So this means in particular that
+ 
+
+ align:start position:0%
+Right? So this means in particular that
+the maximum and the minimum is achieved.
+
+ align:start position:0%
+the maximum and the minimum is achieved.
+ 
+
+ align:start position:0%
+the maximum and the minimum is achieved.
+It also means that the function is
+
+ align:start position:0%
+It also means that the function is
+ 
+
+ align:start position:0%
+It also means that the function is
+actually bounded on that interval. So
+
+ align:start position:0%
+actually bounded on that interval. So
+ 
+
+ align:start position:0%
+actually bounded on that interval. So
+that's a extreme value theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we talked about that before but I
+
+ align:start position:0%
+and we talked about that before but I
+ 
+
+ align:start position:0%
+and we talked about that before but I
+want to think about it in terms of
+
+ align:start position:0%
+want to think about it in terms of
+ 
+
+ align:start position:0%
+want to think about it in terms of
+sequences. So and the other thing I want
+
+ align:start position:0%
+sequences. So and the other thing I want
+ 
+
+ align:start position:0%
+sequences. So and the other thing I want
+to think about in terms of sequences is
+
+ align:start position:0%
+to think about in terms of sequences is
+ 
+
+ align:start position:0%
+to think about in terms of sequences is
+the inter the uh intermediate value
+
+ align:start position:0%
+the inter the uh intermediate value
+ 
+
+ align:start position:0%
+the inter the uh intermediate value
+theorem.
+
+ align:start position:0%
+theorem.
+ 
+
+ align:start position:0%
+theorem.
+So the intermediate values theorem say
+
+ align:start position:0%
+So the intermediate values theorem say
+ 
+
+ align:start position:0%
+So the intermediate values theorem say
+that um that all values let me just
+
+ align:start position:0%
+that um that all values let me just
+ 
+
+ align:start position:0%
+that um that all values let me just
+formulate it loosely
+
+ align:start position:0%
+formulate it loosely
+ 
+
+ align:start position:0%
+formulate it loosely
+all values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+so sorry uh f here is as above. So f is
+
+ align:start position:0%
+so sorry uh f here is as above. So f is
+ 
+
+ align:start position:0%
+so sorry uh f here is as above. So f is
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+so you have again a function
+
+ align:start position:0%
+so you have again a function
+ 
+
+ align:start position:0%
+so you have again a function
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+from there into r like this into r and
+
+ align:start position:0%
+from there into r like this into r and
+ 
+
+ align:start position:0%
+from there into r like this into r and
+this is is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have this continuous function
+
+ align:start position:0%
+So you have this continuous function
+ 
+
+ align:start position:0%
+So you have this continuous function
+and then the intermediate value theorem.
+
+ align:start position:0%
+and then the intermediate value theorem.
+ 
+
+ align:start position:0%
+and then the intermediate value theorem.
+So a loosely formulated is say that all
+
+ align:start position:0%
+So a loosely formulated is say that all
+ 
+
+ align:start position:0%
+So a loosely formulated is say that all
+values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of a
+
+ align:start position:0%
+f of a
+ 
+
+ align:start position:0%
+f of a
+and f of b
+
+ align:start position:0%
+and f of b
+ 
+
+ align:start position:0%
+and f of b
+are achieved.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this means that if you take a
+
+ align:start position:0%
+So this means that if you take a
+ 
+
+ align:start position:0%
+So this means that if you take a
+function so you have a function it's
+
+ align:start position:0%
+function so you have a function it's
+ 
+
+ align:start position:0%
+function so you have a function it's
+it's this here is the value at the end
+
+ align:start position:0%
+it's this here is the value at the end
+ 
+
+ align:start position:0%
+it's this here is the value at the end
+point this here is here you have the
+
+ align:start position:0%
+point this here is here you have the
+ 
+
+ align:start position:0%
+point this here is here you have the
+value in the beginning then it's say
+
+ align:start position:0%
+value in the beginning then it's say
+ 
+
+ align:start position:0%
+value in the beginning then it's say
+that everything in between these two
+
+ align:start position:0%
+that everything in between these two
+ 
+
+ align:start position:0%
+that everything in between these two
+these here is the image of something
+
+ align:start position:0%
+these here is the image of something
+ 
+
+ align:start position:0%
+these here is the image of something
+right that's what the inter uh the
+
+ align:start position:0%
+right that's what the inter uh the
+ 
+
+ align:start position:0%
+right that's what the inter uh the
+intermediate I'm
+
+ align:start position:0%
+intermediate I'm
+ 
+
+ align:start position:0%
+intermediate I'm
+Okay. And I want to prove these two
+
+ align:start position:0%
+Okay. And I want to prove these two
+ 
+
+ align:start position:0%
+Okay. And I want to prove these two
+using uh sequences.
+
+ align:start position:0%
+using uh sequences.
+ 
+
+ align:start position:0%
+using uh sequences.
+And so in order to do that and we need
+
+ align:start position:0%
+And so in order to do that and we need
+ 
+
+ align:start position:0%
+And so in order to do that and we need
+the following lema which is which is
+
+ align:start position:0%
+the following lema which is which is
+ 
+
+ align:start position:0%
+the following lema which is which is
+often
+
+ align:start position:0%
+often
+ 
+
+ align:start position:0%
+often
+so again this here is like the
+
+ align:start position:0%
+so again this here is like the
+ 
+
+ align:start position:0%
+so again this here is like the
+definition of being continuous right but
+
+ align:start position:0%
+definition of being continuous right but
+ 
+
+ align:start position:0%
+definition of being continuous right but
+often you uh often when you're proving
+
+ align:start position:0%
+often you uh often when you're proving
+ 
+
+ align:start position:0%
+often you uh often when you're proving
+that something is continuous you would
+
+ align:start position:0%
+that something is continuous you would
+ 
+
+ align:start position:0%
+that something is continuous you would
+instead use this lema here.
+
+ align:start position:0%
+instead use this lema here.
+ 
+
+ align:start position:0%
+instead use this lema here.
+So if it's really an if and only if
+
+ align:start position:0%
+So if it's really an if and only if
+ 
+
+ align:start position:0%
+So if it's really an if and only if
+statement but I will just uh prove the
+
+ align:start position:0%
+statement but I will just uh prove the
+ 
+
+ align:start position:0%
+statement but I will just uh prove the
+if statement. So if f is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the it's only the if statement I need
+
+ align:start position:0%
+So the it's only the if statement I need
+ 
+
+ align:start position:0%
+So the it's only the if statement I need
+in this case here. But in other cases
+
+ align:start position:0%
+in this case here. But in other cases
+ 
+
+ align:start position:0%
+in this case here. But in other cases
+you it would it's useful to have the if
+
+ align:start position:0%
+you it would it's useful to have the if
+ 
+
+ align:start position:0%
+you it would it's useful to have the if
+and only if statement. So if f is
+
+ align:start position:0%
+and only if statement. So if f is
+ 
+
+ align:start position:0%
+and only if statement. So if f is
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+xn so it's continuous
+
+ align:start position:0%
+xn so it's continuous
+ 
+
+ align:start position:0%
+xn so it's continuous
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's continuous let me just say where
+
+ align:start position:0%
+it's continuous let me just say where
+ 
+
+ align:start position:0%
+it's continuous let me just say where
+the function is defined so in this case
+
+ align:start position:0%
+the function is defined so in this case
+ 
+
+ align:start position:0%
+the function is defined so in this case
+it's just defined on some subset of r.
+
+ align:start position:0%
+it's just defined on some subset of r.
+ 
+
+ align:start position:0%
+it's just defined on some subset of r.
+If this is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and xn is a sequence in a and xn
+
+ align:start position:0%
+and xn is a sequence in a and xn
+ 
+
+ align:start position:0%
+and xn is a sequence in a and xn
+converge to x and x is also in a
+
+ align:start position:0%
+converge to x and x is also in a
+ 
+
+ align:start position:0%
+converge to x and x is also in a
+then then the claim is that then
+
+ align:start position:0%
+then then the claim is that then
+ 
+
+ align:start position:0%
+then then the claim is that then
+this sequence here
+
+ align:start position:0%
+this sequence here
+ 
+
+ align:start position:0%
+this sequence here
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+to to this
+
+ align:start position:0%
+to to this
+ 
+
+ align:start position:0%
+to to this
+And sometimes remember that
+
+ align:start position:0%
+And sometimes remember that
+ 
+
+ align:start position:0%
+And sometimes remember that
+if this here is the case then we write
+
+ align:start position:0%
+if this here is the case then we write
+ 
+
+ align:start position:0%
+if this here is the case then we write
+this here as x is the limit of xn as n
+
+ align:start position:0%
+this here as x is the limit of xn as n
+ 
+
+ align:start position:0%
+this here as x is the limit of xn as n
+go to infinity.
+
+ align:start position:0%
+go to infinity.
+ 
+
+ align:start position:0%
+go to infinity.
+This statement here can be written as
+
+ align:start position:0%
+This statement here can be written as
+ 
+
+ align:start position:0%
+This statement here can be written as
+that f ofx is the limit as n goes to
+
+ align:start position:0%
+that f ofx is the limit as n goes to
+ 
+
+ align:start position:0%
+that f ofx is the limit as n goes to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+of um of of this thing here.
+
+ align:start position:0%
+of um of of this thing here.
+ 
+
+ align:start position:0%
+of um of of this thing here.
+And so if you combine these two things,
+
+ align:start position:0%
+And so if you combine these two things,
+ 
+
+ align:start position:0%
+And so if you combine these two things,
+if you fill in x is equal to that, then
+
+ align:start position:0%
+if you fill in x is equal to that, then
+ 
+
+ align:start position:0%
+if you fill in x is equal to that, then
+this here can also be written as that f
+
+ align:start position:0%
+this here can also be written as that f
+ 
+
+ align:start position:0%
+this here can also be written as that f
+of the limit
+
+ align:start position:0%
+of the limit
+ 
+
+ align:start position:0%
+of the limit
+of x n as n goes to infinity.
+
+ align:start position:0%
+of x n as n goes to infinity.
+ 
+
+ align:start position:0%
+of x n as n goes to infinity.
+This is this right filling in this and
+
+ align:start position:0%
+This is this right filling in this and
+ 
+
+ align:start position:0%
+This is this right filling in this and
+then equal to the limit. So in a way
+
+ align:start position:0%
+then equal to the limit. So in a way
+ 
+
+ align:start position:0%
+then equal to the limit. So in a way
+if you want to think about it
+
+ align:start position:0%
+if you want to think about it
+ 
+
+ align:start position:0%
+if you want to think about it
+like it's something about that if it's
+
+ align:start position:0%
+like it's something about that if it's
+ 
+
+ align:start position:0%
+like it's something about that if it's
+continuous you can exchange the order of
+
+ align:start position:0%
+continuous you can exchange the order of
+ 
+
+ align:start position:0%
+continuous you can exchange the order of
+taking limits right okay so but but you
+
+ align:start position:0%
+taking limits right okay so but but you
+ 
+
+ align:start position:0%
+taking limits right okay so but but you
+yeah but that's like a more formal way
+
+ align:start position:0%
+yeah but that's like a more formal way
+ 
+
+ align:start position:0%
+yeah but that's like a more formal way
+in a way but I I always just think about
+
+ align:start position:0%
+in a way but I I always just think about
+ 
+
+ align:start position:0%
+in a way but I I always just think about
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+okay so we want to prove this lema and
+
+ align:start position:0%
+okay so we want to prove this lema and
+ 
+
+ align:start position:0%
+okay so we want to prove this lema and
+so then we want to use this lema to
+
+ align:start position:0%
+so then we want to use this lema to
+ 
+
+ align:start position:0%
+so then we want to use this lema to
+prove these two theorems
+
+ align:start position:0%
+prove these two theorems
+ 
+
+ align:start position:0%
+prove these two theorems
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay. So now
+
+ align:start position:0%
+Okay. So now
+ 
+
+ align:start position:0%
+Okay. So now
+let's prove this lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So uh so I want to show that that this
+
+ align:start position:0%
+So uh so I want to show that that this
+ 
+
+ align:start position:0%
+So uh so I want to show that that this
+so I want to show so we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that f of xn converts to f ofx.
+
+ align:start position:0%
+that f of xn converts to f ofx.
+ 
+
+ align:start position:0%
+that f of xn converts to f ofx.
+So I'm first going to use that f. So use
+
+ align:start position:0%
+So I'm first going to use that f. So use
+ 
+
+ align:start position:0%
+So I'm first going to use that f. So use
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this point x. So this is some point
+
+ align:start position:0%
+at this point x. So this is some point
+ 
+
+ align:start position:0%
+at this point x. So this is some point
+in a. So this means that given epsilon
+
+ align:start position:0%
+in a. So this means that given epsilon
+ 
+
+ align:start position:0%
+in a. So this means that given epsilon
+therefore given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given epsilon greater than zero there
+
+ align:start position:0%
+given epsilon greater than zero there
+ 
+
+ align:start position:0%
+given epsilon greater than zero there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta greater than zero
+
+ align:start position:0%
+delta greater than zero
+ 
+
+ align:start position:0%
+delta greater than zero
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+x minus
+
+ align:start position:0%
+x minus
+ 
+
+ align:start position:0%
+x minus
+uh so any other element y
+
+ align:start position:0%
+uh so any other element y
+ 
+
+ align:start position:0%
+uh so any other element y
+if this thing here is less than delta
+
+ align:start position:0%
+if this thing here is less than delta
+ 
+
+ align:start position:0%
+if this thing here is less than delta
+then their images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviate at most epsilon right this is
+
+ align:start position:0%
+deviate at most epsilon right this is
+ 
+
+ align:start position:0%
+deviate at most epsilon right this is
+just using the definition that x here x
+
+ align:start position:0%
+just using the definition that x here x
+ 
+
+ align:start position:0%
+just using the definition that x here x
+here is now thought about as being some
+
+ align:start position:0%
+here is now thought about as being some
+ 
+
+ align:start position:0%
+here is now thought about as being some
+fixed point right a fixed point and then
+
+ align:start position:0%
+fixed point right a fixed point and then
+ 
+
+ align:start position:0%
+fixed point right a fixed point and then
+y is like any other point right okay so
+
+ align:start position:0%
+y is like any other point right okay so
+ 
+
+ align:start position:0%
+y is like any other point right okay so
+we have that
+
+ align:start position:0%
+we have that
+ 
+
+ align:start position:0%
+we have that
+but then we second we use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second use
+
+ align:start position:0%
+second use
+ 
+
+ align:start position:0%
+second use
+that the sequence xn converts to x. So
+
+ align:start position:0%
+that the sequence xn converts to x. So
+ 
+
+ align:start position:0%
+that the sequence xn converts to x. So
+this means that now thinking about this
+
+ align:start position:0%
+this means that now thinking about this
+ 
+
+ align:start position:0%
+this means that now thinking about this
+delta here that this epsilon is spitting
+
+ align:start position:0%
+delta here that this epsilon is spitting
+ 
+
+ align:start position:0%
+delta here that this epsilon is spitting
+out. So this means that uh for this
+
+ align:start position:0%
+out. So this means that uh for this
+ 
+
+ align:start position:0%
+out. So this means that uh for this
+delta for delta there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital n. So that such that if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little n is bigger than the capital n
+
+ align:start position:0%
+little n is bigger than the capital n
+ 
+
+ align:start position:0%
+little n is bigger than the capital n
+then actually x n
+
+ align:start position:0%
+then actually x n
+ 
+
+ align:start position:0%
+then actually x n
+minus x
+
+ align:start position:0%
+minus x
+ 
+
+ align:start position:0%
+minus x
+is smaller than delta
+
+ align:start position:0%
+is smaller than delta
+ 
+
+ align:start position:0%
+is smaller than delta
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but you see that so now combining this
+
+ align:start position:0%
+but you see that so now combining this
+ 
+
+ align:start position:0%
+but you see that so now combining this
+so combining this
+
+ align:start position:0%
+so combining this
+ 
+
+ align:start position:0%
+so combining this
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So maybe I'll go over here. So combining
+
+ align:start position:0%
+So maybe I'll go over here. So combining
+ 
+
+ align:start position:0%
+So maybe I'll go over here. So combining
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh combining this then we get that if n
+
+ align:start position:0%
+uh combining this then we get that if n
+ 
+
+ align:start position:0%
+uh combining this then we get that if n
+here is bigger than capital n then x n
+
+ align:start position:0%
+here is bigger than capital n then x n
+ 
+
+ align:start position:0%
+here is bigger than capital n then x n
+minus x is smaller than delta.
+
+ align:start position:0%
+minus x is smaller than delta.
+ 
+
+ align:start position:0%
+minus x is smaller than delta.
+But this means that now if if they are
+
+ align:start position:0%
+But this means that now if if they are
+ 
+
+ align:start position:0%
+But this means that now if if they are
+smaller than delta then the first part
+
+ align:start position:0%
+smaller than delta then the first part
+ 
+
+ align:start position:0%
+smaller than delta then the first part
+say that their images so this means that
+
+ align:start position:0%
+say that their images so this means that
+ 
+
+ align:start position:0%
+say that their images so this means that
+f of xn minus f ofx
+
+ align:start position:0%
+f of xn minus f ofx
+ 
+
+ align:start position:0%
+f of xn minus f ofx
+is smaller than epsilon right and that's
+
+ align:start position:0%
+is smaller than epsilon right and that's
+ 
+
+ align:start position:0%
+is smaller than epsilon right and that's
+exactly what we wanted to prove to show
+
+ align:start position:0%
+exactly what we wanted to prove to show
+ 
+
+ align:start position:0%
+exactly what we wanted to prove to show
+that this that if you are sufficiently
+
+ align:start position:0%
+that this that if you are sufficiently
+ 
+
+ align:start position:0%
+that this that if you are sufficiently
+far out then these two things are very
+
+ align:start position:0%
+far out then these two things are very
+ 
+
+ align:start position:0%
+far out then these two things are very
+close together right so that was quite
+
+ align:start position:0%
+close together right so that was quite
+ 
+
+ align:start position:0%
+close together right so that was quite
+easy right
+
+ align:start position:0%
+easy right
+ 
+
+ align:start position:0%
+easy right
+Now I want to use this but this is like
+
+ align:start position:0%
+Now I want to use this but this is like
+ 
+
+ align:start position:0%
+Now I want to use this but this is like
+you know like you use this sort of thing
+
+ align:start position:0%
+you know like you use this sort of thing
+ 
+
+ align:start position:0%
+you know like you use this sort of thing
+to you know for continuity this is like
+
+ align:start position:0%
+to you know for continuity this is like
+ 
+
+ align:start position:0%
+to you know for continuity this is like
+a standard thing to use it's kind of
+
+ align:start position:0%
+a standard thing to use it's kind of
+ 
+
+ align:start position:0%
+a standard thing to use it's kind of
+used implicitly and again there's this
+
+ align:start position:0%
+used implicitly and again there's this
+ 
+
+ align:start position:0%
+used implicitly and again there's this
+one has a converse and the converse is
+
+ align:start position:0%
+one has a converse and the converse is
+ 
+
+ align:start position:0%
+one has a converse and the converse is
+also very useful.
+
+ align:start position:0%
+also very useful.
+ 
+
+ align:start position:0%
+also very useful.
+So now let's come back to the extreme
+
+ align:start position:0%
+So now let's come back to the extreme
+ 
+
+ align:start position:0%
+So now let's come back to the extreme
+value theorem and the intermediate value
+
+ align:start position:0%
+value theorem and the intermediate value
+ 
+
+ align:start position:0%
+value theorem and the intermediate value
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now let's try to prove. So using the
+
+ align:start position:0%
+So now let's try to prove. So using the
+ 
+
+ align:start position:0%
+So now let's try to prove. So using the
+lema.
+
+ align:start position:0%
+lema.
+ 
+
+ align:start position:0%
+lema.
+So, so, so using the lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we'll prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll show
+
+ align:start position:0%
+we'll show
+ 
+
+ align:start position:0%
+we'll show
+the extreme value theorem
+
+ align:start position:0%
+the extreme value theorem
+ 
+
+ align:start position:0%
+the extreme value theorem
+uh and the intermediate value theorem.
+
+ align:start position:0%
+uh and the intermediate value theorem.
+ 
+
+ align:start position:0%
+uh and the intermediate value theorem.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so now first to prove the extreme
+
+ align:start position:0%
+And so now first to prove the extreme
+ 
+
+ align:start position:0%
+And so now first to prove the extreme
+value theorem. So prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the extreme value.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm first going to prove that the image
+
+ align:start position:0%
+I'm first going to prove that the image
+ 
+
+ align:start position:0%
+I'm first going to prove that the image
+so first show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the image of this interval here
+
+ align:start position:0%
+that the image of this interval here
+ 
+
+ align:start position:0%
+that the image of this interval here
+is bounded.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this is what I first want to
+
+ align:start position:0%
+Okay. So this is what I first want to
+ 
+
+ align:start position:0%
+Okay. So this is what I first want to
+show and so I suppose not. So suppose
+
+ align:start position:0%
+show and so I suppose not. So suppose
+ 
+
+ align:start position:0%
+show and so I suppose not. So suppose
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this means that um that um if I for each
+
+ align:start position:0%
+this means that um that um if I for each
+ 
+
+ align:start position:0%
+this means that um that um if I for each
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each n which is a integer
+
+ align:start position:0%
+for each n which is a integer
+ 
+
+ align:start position:0%
+for each n which is a integer
+let's say that it's not bounded from
+
+ align:start position:0%
+let's say that it's not bounded from
+ 
+
+ align:start position:0%
+let's say that it's not bounded from
+above right to show that it's not
+
+ align:start position:0%
+above right to show that it's not
+ 
+
+ align:start position:0%
+above right to show that it's not
+bounded from below is similar. So I'm
+
+ align:start position:0%
+bounded from below is similar. So I'm
+ 
+
+ align:start position:0%
+bounded from below is similar. So I'm
+just going to prove that is is bounded
+
+ align:start position:0%
+just going to prove that is is bounded
+ 
+
+ align:start position:0%
+just going to prove that is is bounded
+from above
+
+ align:start position:0%
+from above
+ 
+
+ align:start position:0%
+from above
+but but the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it is uh bounded from below is is
+
+ align:start position:0%
+that it is uh bounded from below is is
+ 
+
+ align:start position:0%
+that it is uh bounded from below is is
+similar with obvious modifications.
+
+ align:start position:0%
+similar with obvious modifications.
+ 
+
+ align:start position:0%
+similar with obvious modifications.
+So suppose it's not bounded from below
+
+ align:start position:0%
+So suppose it's not bounded from below
+ 
+
+ align:start position:0%
+So suppose it's not bounded from below
+above then for each integer there exist
+
+ align:start position:0%
+above then for each integer there exist
+ 
+
+ align:start position:0%
+above then for each integer there exist
+there must exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+in this interval
+
+ align:start position:0%
+in this interval
+ 
+
+ align:start position:0%
+in this interval
+so that such that
+
+ align:start position:0%
+so that such that
+ 
+
+ align:start position:0%
+so that such that
+f ofx
+
+ align:start position:0%
+f ofx
+ 
+
+ align:start position:0%
+f ofx
+is bigger equal to n right because
+
+ align:start position:0%
+is bigger equal to n right because
+ 
+
+ align:start position:0%
+is bigger equal to n right because
+otherwise n would have been an upper
+
+ align:start position:0%
+otherwise n would have been an upper
+ 
+
+ align:start position:0%
+otherwise n would have been an upper
+bound right and so I can So I just pick
+
+ align:start position:0%
+bound right and so I can So I just pick
+ 
+
+ align:start position:0%
+bound right and so I can So I just pick
+such a n. So pick
+
+ align:start position:0%
+such a n. So pick
+ 
+
+ align:start position:0%
+such a n. So pick
+such n x
+
+ align:start position:0%
+such n x
+ 
+
+ align:start position:0%
+such n x
+and and let's call it xn. Right? So for
+
+ align:start position:0%
+and and let's call it xn. Right? So for
+ 
+
+ align:start position:0%
+and and let's call it xn. Right? So for
+each n you now have xn and it has a
+
+ align:start position:0%
+each n you now have xn and it has a
+ 
+
+ align:start position:0%
+each n you now have xn and it has a
+property that f of xn is bigger equal to
+
+ align:start position:0%
+property that f of xn is bigger equal to
+ 
+
+ align:start position:0%
+property that f of xn is bigger equal to
+n.
+
+ align:start position:0%
+n.
+ 
+
+ align:start position:0%
+n.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now you have that that this gives you a
+
+ align:start position:0%
+Now you have that that this gives you a
+ 
+
+ align:start position:0%
+Now you have that that this gives you a
+sequence. So you have that xn here is a
+
+ align:start position:0%
+sequence. So you have that xn here is a
+ 
+
+ align:start position:0%
+sequence. So you have that xn here is a
+sequence. It's a sequence
+
+ align:start position:0%
+sequence. It's a sequence
+ 
+
+ align:start position:0%
+sequence. It's a sequence
+in sorry it's not in this interval here.
+
+ align:start position:0%
+in sorry it's not in this interval here.
+ 
+
+ align:start position:0%
+in sorry it's not in this interval here.
+But this means that it's so it's a
+
+ align:start position:0%
+But this means that it's so it's a
+ 
+
+ align:start position:0%
+But this means that it's so it's a
+bounded sequence. It's a bounded
+
+ align:start position:0%
+bounded sequence. It's a bounded
+ 
+
+ align:start position:0%
+bounded sequence. It's a bounded
+sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that by the vias
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So by the bolano vasium
+
+ align:start position:0%
+So by the bolano vasium
+ 
+
+ align:start position:0%
+So by the bolano vasium
+um it has
+
+ align:start position:0%
+um it has
+ 
+
+ align:start position:0%
+um it has
+a convergent subsequent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and K right so you have that X and K
+
+ align:start position:0%
+X and K right so you have that X and K
+ 
+
+ align:start position:0%
+X and K right so you have that X and K
+so this is this sequence subsequence
+
+ align:start position:0%
+so this is this sequence subsequence
+ 
+
+ align:start position:0%
+so this is this sequence subsequence
+and it converts to some X right but this
+
+ align:start position:0%
+and it converts to some X right but this
+ 
+
+ align:start position:0%
+and it converts to some X right but this
+means that but now this means that there
+
+ align:start position:0%
+means that but now this means that there
+ 
+
+ align:start position:0%
+means that but now this means that there
+are by the lema over there you have that
+
+ align:start position:0%
+are by the lema over there you have that
+ 
+
+ align:start position:0%
+are by the lema over there you have that
+this sequence this sequence then because
+
+ align:start position:0%
+this sequence this sequence then because
+ 
+
+ align:start position:0%
+this sequence this sequence then because
+the function was continuous converts to
+
+ align:start position:0%
+the function was continuous converts to
+ 
+
+ align:start position:0%
+the function was continuous converts to
+this right but on the other hand this
+
+ align:start position:0%
+this right but on the other hand this
+ 
+
+ align:start position:0%
+this right but on the other hand this
+here x n k is a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of xn but this means that this number
+
+ align:start position:0%
+of xn but this means that this number
+ 
+
+ align:start position:0%
+of xn but this means that this number
+here remember that a subsequence just
+
+ align:start position:0%
+here remember that a subsequence just
+ 
+
+ align:start position:0%
+here remember that a subsequence just
+means that this here I mean it means in
+
+ align:start position:0%
+means that this here I mean it means in
+ 
+
+ align:start position:0%
+means that this here I mean it means in
+particular that this here would be
+
+ align:start position:0%
+particular that this here would be
+ 
+
+ align:start position:0%
+particular that this here would be
+further out than n. So, so you have that
+
+ align:start position:0%
+further out than n. So, so you have that
+ 
+
+ align:start position:0%
+further out than n. So, so you have that
+f of x n k is supposed to be bigger
+
+ align:start position:0%
+f of x n k is supposed to be bigger
+ 
+
+ align:start position:0%
+f of x n k is supposed to be bigger
+equal to n k but this is supposed to be
+
+ align:start position:0%
+equal to n k but this is supposed to be
+ 
+
+ align:start position:0%
+equal to n k but this is supposed to be
+bigger than n
+
+ align:start position:0%
+bigger than n
+ 
+
+ align:start position:0%
+bigger than n
+right? So, so these guys here, this here
+
+ align:start position:0%
+right? So, so these guys here, this here
+ 
+
+ align:start position:0%
+right? So, so these guys here, this here
+goes to these here goes to, you know,
+
+ align:start position:0%
+goes to these here goes to, you know,
+ 
+
+ align:start position:0%
+goes to these here goes to, you know,
+these here are are unbounded, right? But
+
+ align:start position:0%
+these here are are unbounded, right? But
+ 
+
+ align:start position:0%
+these here are are unbounded, right? But
+this on the other hand, we're saying
+
+ align:start position:0%
+this on the other hand, we're saying
+ 
+
+ align:start position:0%
+this on the other hand, we're saying
+that this sequence converts to this
+
+ align:start position:0%
+that this sequence converts to this
+ 
+
+ align:start position:0%
+that this sequence converts to this
+sequence. So any convergence sequence is
+
+ align:start position:0%
+sequence. So any convergence sequence is
+ 
+
+ align:start position:0%
+sequence. So any convergence sequence is
+bounded. So that's a contradiction,
+
+ align:start position:0%
+bounded. So that's a contradiction,
+ 
+
+ align:start position:0%
+bounded. So that's a contradiction,
+right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's that's so this is like
+
+ align:start position:0%
+Okay. So that's that's so this is like
+ 
+
+ align:start position:0%
+Okay. So that's that's so this is like
+proving first using the lema we have now
+
+ align:start position:0%
+proving first using the lema we have now
+ 
+
+ align:start position:0%
+proving first using the lema we have now
+that the image here is bounded from
+
+ align:start position:0%
+that the image here is bounded from
+ 
+
+ align:start position:0%
+that the image here is bounded from
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+the almost exact same proof with obvious
+
+ align:start position:0%
+the almost exact same proof with obvious
+ 
+
+ align:start position:0%
+the almost exact same proof with obvious
+modification give that is bounded from
+
+ align:start position:0%
+modification give that is bounded from
+ 
+
+ align:start position:0%
+modification give that is bounded from
+below. So now you have that the image of
+
+ align:start position:0%
+below. So now you have that the image of
+ 
+
+ align:start position:0%
+below. So now you have that the image of
+this is actually bounded from both above
+
+ align:start position:0%
+this is actually bounded from both above
+ 
+
+ align:start position:0%
+this is actually bounded from both above
+and below.
+
+ align:start position:0%
+and below.
+ 
+
+ align:start position:0%
+and below.
+And and now
+
+ align:start position:0%
+And and now
+ 
+
+ align:start position:0%
+And and now
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+um so now this means that if you're
+
+ align:start position:0%
+um so now this means that if you're
+ 
+
+ align:start position:0%
+um so now this means that if you're
+looking at the image here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you uh this here is a bounded subset. So
+
+ align:start position:0%
+you uh this here is a bounded subset. So
+ 
+
+ align:start position:0%
+you uh this here is a bounded subset. So
+this is is a bounded substance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you can look at the soup
+
+ align:start position:0%
+and so you can look at the soup
+ 
+
+ align:start position:0%
+and so you can look at the soup
+of this set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You can look at the soup of the set.
+
+ align:start position:0%
+You can look at the soup of the set.
+ 
+
+ align:start position:0%
+You can look at the soup of the set.
+And I'm going to take the soup. I'm
+
+ align:start position:0%
+And I'm going to take the soup. I'm
+ 
+
+ align:start position:0%
+And I'm going to take the soup. I'm
+going to call this capital M.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now for each
+
+ align:start position:0%
+And now for each
+ 
+
+ align:start position:0%
+And now for each
+for each
+
+ align:start position:0%
+for each
+ 
+
+ align:start position:0%
+for each
+little n the n is an integer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then I can look at m minus 1 / n. Right?
+
+ align:start position:0%
+Then I can look at m minus 1 / n. Right?
+ 
+
+ align:start position:0%
+Then I can look at m minus 1 / n. Right?
+So this is obviously strictly smaller
+
+ align:start position:0%
+So this is obviously strictly smaller
+ 
+
+ align:start position:0%
+So this is obviously strictly smaller
+than capital m. So it's not an upper
+
+ align:start position:0%
+than capital m. So it's not an upper
+ 
+
+ align:start position:0%
+than capital m. So it's not an upper
+bound. Right? So this means that for
+
+ align:start position:0%
+bound. Right? So this means that for
+ 
+
+ align:start position:0%
+bound. Right? So this means that for
+little n this here is not an upper bound
+
+ align:start position:0%
+little n this here is not an upper bound
+ 
+
+ align:start position:0%
+little n this here is not an upper bound
+for this set. So this means that there
+
+ align:start position:0%
+for this set. So this means that there
+ 
+
+ align:start position:0%
+for this set. So this means that there
+must exist a x. So so that you have this
+
+ align:start position:0%
+must exist a x. So so that you have this
+ 
+
+ align:start position:0%
+must exist a x. So so that you have this
+for some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x in this interval here.
+
+ align:start position:0%
+x in this interval here.
+ 
+
+ align:start position:0%
+x in this interval here.
+Right? Because this here is not an upper
+
+ align:start position:0%
+Right? Because this here is not an upper
+ 
+
+ align:start position:0%
+Right? Because this here is not an upper
+bound. This means that there must be
+
+ align:start position:0%
+bound. This means that there must be
+ 
+
+ align:start position:0%
+bound. This means that there must be
+something larger than that. Right?
+
+ align:start position:0%
+something larger than that. Right?
+ 
+
+ align:start position:0%
+something larger than that. Right?
+And now so you just pick for each little
+
+ align:start position:0%
+And now so you just pick for each little
+ 
+
+ align:start position:0%
+And now so you just pick for each little
+n you just pick such a x and we call
+
+ align:start position:0%
+n you just pick such a x and we call
+ 
+
+ align:start position:0%
+n you just pick such a x and we call
+this xn. So we have that so xn is in the
+
+ align:start position:0%
+this xn. So we have that so xn is in the
+ 
+
+ align:start position:0%
+this xn. So we have that so xn is in the
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+and we have that m -1 / little n is
+
+ align:start position:0%
+and we have that m -1 / little n is
+ 
+
+ align:start position:0%
+and we have that m -1 / little n is
+strictly less than f of xn.
+
+ align:start position:0%
+strictly less than f of xn.
+ 
+
+ align:start position:0%
+strictly less than f of xn.
+Remember that this thing here is of
+
+ align:start position:0%
+Remember that this thing here is of
+ 
+
+ align:start position:0%
+Remember that this thing here is of
+course obviously less than the soup over
+
+ align:start position:0%
+course obviously less than the soup over
+ 
+
+ align:start position:0%
+course obviously less than the soup over
+all images. So you even have that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now, but now you see that now you
+
+ align:start position:0%
+Okay. Now, but now you see that now you
+ 
+
+ align:start position:0%
+Okay. Now, but now you see that now you
+have a sequence here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now you have a sequence
+
+ align:start position:0%
+So now you have a sequence
+ 
+
+ align:start position:0%
+So now you have a sequence
+and so you have a sequence XN
+
+ align:start position:0%
+and so you have a sequence XN
+ 
+
+ align:start position:0%
+and so you have a sequence XN
+and so by the bulani. So by the bosani
+
+ align:start position:0%
+and so by the bulani. So by the bosani
+ 
+
+ align:start position:0%
+and so by the bulani. So by the bosani
+by the person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this sequence here
+
+ align:start position:0%
+um this sequence here
+ 
+
+ align:start position:0%
+um this sequence here
+has a convergent subsequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? This is because this is a
+
+ align:start position:0%
+Right? This is because this is a
+ 
+
+ align:start position:0%
+Right? This is because this is a
+sequence. The xn lie in this bounded
+
+ align:start position:0%
+sequence. The xn lie in this bounded
+ 
+
+ align:start position:0%
+sequence. The xn lie in this bounded
+interval. So it's a bounded sequence,
+
+ align:start position:0%
+interval. So it's a bounded sequence,
+ 
+
+ align:start position:0%
+interval. So it's a bounded sequence,
+right? So it has a convergent
+
+ align:start position:0%
+right? So it has a convergent
+ 
+
+ align:start position:0%
+right? So it has a convergent
+subsequence and this convergence
+
+ align:start position:0%
+subsequence and this convergence
+ 
+
+ align:start position:0%
+subsequence and this convergence
+subsequence I call xn
+
+ align:start position:0%
+subsequence I call xn
+ 
+
+ align:start position:0%
+subsequence I call xn
+k like that. So this is converging to
+
+ align:start position:0%
+k like that. So this is converging to
+ 
+
+ align:start position:0%
+k like that. So this is converging to
+some something
+
+ align:start position:0%
+some something
+ 
+
+ align:start position:0%
+some something
+and that something I'm going to call xm.
+
+ align:start position:0%
+and that something I'm going to call xm.
+ 
+
+ align:start position:0%
+and that something I'm going to call xm.
+Right? Okay. and I then will prove that
+
+ align:start position:0%
+Right? Okay. and I then will prove that
+ 
+
+ align:start position:0%
+Right? Okay. and I then will prove that
+this has the property that I wanted.
+
+ align:start position:0%
+this has the property that I wanted.
+ 
+
+ align:start position:0%
+this has the property that I wanted.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So I have that and so I have because f
+
+ align:start position:0%
+So I have that and so I have because f
+ 
+
+ align:start position:0%
+So I have that and so I have because f
+was continuous then I have that the
+
+ align:start position:0%
+was continuous then I have that the
+ 
+
+ align:start position:0%
+was continuous then I have that the
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+converge to the image of this
+
+ align:start position:0%
+converge to the image of this
+ 
+
+ align:start position:0%
+converge to the image of this
+right this is by continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f right and the and by the continuity
+
+ align:start position:0%
+of f right and the and by the continuity
+ 
+
+ align:start position:0%
+of f right and the and by the continuity
+of f and the little lema we proved
+
+ align:start position:0%
+of f and the little lema we proved
+ 
+
+ align:start position:0%
+of f and the little lema we proved
+before mine
+
+ align:start position:0%
+before mine
+ 
+
+ align:start position:0%
+before mine
+so So you have that but now we have you
+
+ align:start position:0%
+so So you have that but now we have you
+ 
+
+ align:start position:0%
+so So you have that but now we have you
+see that this here tells us this here
+
+ align:start position:0%
+see that this here tells us this here
+ 
+
+ align:start position:0%
+see that this here tells us this here
+right we have this inequality here but
+
+ align:start position:0%
+right we have this inequality here but
+ 
+
+ align:start position:0%
+right we have this inequality here but
+this is just saying that as as n go to
+
+ align:start position:0%
+this is just saying that as as n go to
+ 
+
+ align:start position:0%
+this is just saying that as as n go to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+this sequence here converge to m right
+
+ align:start position:0%
+this sequence here converge to m right
+ 
+
+ align:start position:0%
+this sequence here converge to m right
+so we also have that this sequence here
+
+ align:start position:0%
+so we also have that this sequence here
+ 
+
+ align:start position:0%
+so we also have that this sequence here
+converts to m this is just because it's
+
+ align:start position:0%
+converts to m this is just because it's
+ 
+
+ align:start position:0%
+converts to m this is just because it's
+squeezed
+
+ align:start position:0%
+squeezed
+ 
+
+ align:start position:0%
+squeezed
+It's squeezed here in this interval and
+
+ align:start position:0%
+It's squeezed here in this interval and
+ 
+
+ align:start position:0%
+It's squeezed here in this interval and
+this here is going this lower bound is
+
+ align:start position:0%
+this here is going this lower bound is
+ 
+
+ align:start position:0%
+this here is going this lower bound is
+going to the upper bound. Right?
+
+ align:start position:0%
+going to the upper bound. Right?
+ 
+
+ align:start position:0%
+going to the upper bound. Right?
+But but so if you have that this here is
+
+ align:start position:0%
+But but so if you have that this here is
+ 
+
+ align:start position:0%
+But but so if you have that this here is
+converging then any subsequence would
+
+ align:start position:0%
+converging then any subsequence would
+ 
+
+ align:start position:0%
+converging then any subsequence would
+also converge to the same thing. Right?
+
+ align:start position:0%
+also converge to the same thing. Right?
+ 
+
+ align:start position:0%
+also converge to the same thing. Right?
+So this imply that for the sub this here
+
+ align:start position:0%
+So this imply that for the sub this here
+ 
+
+ align:start position:0%
+So this imply that for the sub this here
+that is a subsequence of these but this
+
+ align:start position:0%
+that is a subsequence of these but this
+ 
+
+ align:start position:0%
+that is a subsequence of these but this
+is then converging to the same thing.
+
+ align:start position:0%
+is then converging to the same thing.
+ 
+
+ align:start position:0%
+is then converging to the same thing.
+So now you see that we have that this is
+
+ align:start position:0%
+So now you see that we have that this is
+ 
+
+ align:start position:0%
+So now you see that we have that this is
+converging to that but it's also
+
+ align:start position:0%
+converging to that but it's also
+ 
+
+ align:start position:0%
+converging to that but it's also
+converging to this by uniqueness of
+
+ align:start position:0%
+converging to this by uniqueness of
+ 
+
+ align:start position:0%
+converging to this by uniqueness of
+limits we have by uniqueness of limits.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then we have that f of x m is equal to
+
+ align:start position:0%
+Then we have that f of x m is equal to
+ 
+
+ align:start position:0%
+Then we have that f of x m is equal to
+this right and and capital m again was
+
+ align:start position:0%
+this right and and capital m again was
+ 
+
+ align:start position:0%
+this right and and capital m again was
+the soup. So this means that the soup is
+
+ align:start position:0%
+the soup. So this means that the soup is
+ 
+
+ align:start position:0%
+the soup. So this means that the soup is
+actually achieved. You found a point
+
+ align:start position:0%
+actually achieved. You found a point
+ 
+
+ align:start position:0%
+actually achieved. You found a point
+where the soup was achieved right. Okay.
+
+ align:start position:0%
+where the soup was achieved right. Okay.
+ 
+
+ align:start position:0%
+where the soup was achieved right. Okay.
+So that proves the extreme value
+
+ align:start position:0%
+So that proves the extreme value
+ 
+
+ align:start position:0%
+So that proves the extreme value
+theorem. It proves by one of the two
+
+ align:start position:0%
+theorem. It proves by one of the two
+ 
+
+ align:start position:0%
+theorem. It proves by one of the two
+parts of the extreme value theorem. It
+
+ align:start position:0%
+parts of the extreme value theorem. It
+ 
+
+ align:start position:0%
+parts of the extreme value theorem. It
+proved that the soup was achieved and
+
+ align:start position:0%
+proved that the soup was achieved and
+ 
+
+ align:start position:0%
+proved that the soup was achieved and
+the proof that the inf is achieved is is
+
+ align:start position:0%
+the proof that the inf is achieved is is
+ 
+
+ align:start position:0%
+the proof that the inf is achieved is is
+is almost identical with some obvious
+
+ align:start position:0%
+is almost identical with some obvious
+ 
+
+ align:start position:0%
+is almost identical with some obvious
+changes.
+
+ align:start position:0%
+changes.
+ 
+
+ align:start position:0%
+changes.
+Now for the intermediate value theorem,
+
+ align:start position:0%
+Now for the intermediate value theorem,
+ 
+
+ align:start position:0%
+Now for the intermediate value theorem,
+so let's try to prove that. So how do we
+
+ align:start position:0%
+so let's try to prove that. So how do we
+ 
+
+ align:start position:0%
+so let's try to prove that. So how do we
+prove the intermediate value theorem?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so proof of intermediate values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to prove but it's not
+
+ align:start position:0%
+and I'm going to prove but it's not
+ 
+
+ align:start position:0%
+and I'm going to prove but it's not
+really I mean it is it's uh the general
+
+ align:start position:0%
+really I mean it is it's uh the general
+ 
+
+ align:start position:0%
+really I mean it is it's uh the general
+case follow uh easily from this so I'm
+
+ align:start position:0%
+case follow uh easily from this so I'm
+ 
+
+ align:start position:0%
+case follow uh easily from this so I'm
+going to make an assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to assume that the value at A
+
+ align:start position:0%
+I'm going to assume that the value at A
+ 
+
+ align:start position:0%
+I'm going to assume that the value at A
+is strictly less than zero and the value
+
+ align:start position:0%
+is strictly less than zero and the value
+ 
+
+ align:start position:0%
+is strictly less than zero and the value
+of B is strictly bigger than zero.
+
+ align:start position:0%
+of B is strictly bigger than zero.
+ 
+
+ align:start position:0%
+of B is strictly bigger than zero.
+And then I want to show that zero is
+
+ align:start position:0%
+And then I want to show that zero is
+ 
+
+ align:start position:0%
+And then I want to show that zero is
+achieved as the image of something.
+
+ align:start position:0%
+achieved as the image of something.
+ 
+
+ align:start position:0%
+achieved as the image of something.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+You can say that sounds like a special
+
+ align:start position:0%
+You can say that sounds like a special
+ 
+
+ align:start position:0%
+You can say that sounds like a special
+case. It is a special case. But once you
+
+ align:start position:0%
+case. It is a special case. But once you
+ 
+
+ align:start position:0%
+case. It is a special case. But once you
+can prove this, it's easy to uh get this
+
+ align:start position:0%
+can prove this, it's easy to uh get this
+ 
+
+ align:start position:0%
+can prove this, it's easy to uh get this
+the general case. You can either get it
+
+ align:start position:0%
+the general case. You can either get it
+ 
+
+ align:start position:0%
+the general case. You can either get it
+directly from this by modifying the
+
+ align:start position:0%
+directly from this by modifying the
+ 
+
+ align:start position:0%
+directly from this by modifying the
+function by or you can once you see how
+
+ align:start position:0%
+function by or you can once you see how
+ 
+
+ align:start position:0%
+function by or you can once you see how
+the proof of this go then it's easy to
+
+ align:start position:0%
+the proof of this go then it's easy to
+ 
+
+ align:start position:0%
+the proof of this go then it's easy to
+to prove it to set up the you know what
+
+ align:start position:0%
+to prove it to set up the you know what
+ 
+
+ align:start position:0%
+to prove it to set up the you know what
+are the different possible cases right
+
+ align:start position:0%
+are the different possible cases right
+ 
+
+ align:start position:0%
+are the different possible cases right
+and then prove the them using the same
+
+ align:start position:0%
+and then prove the them using the same
+ 
+
+ align:start position:0%
+and then prove the them using the same
+sort of argument as we do here.
+
+ align:start position:0%
+sort of argument as we do here.
+ 
+
+ align:start position:0%
+sort of argument as we do here.
+Okay. So, so this is what I'm going to
+
+ align:start position:0%
+Okay. So, so this is what I'm going to
+ 
+
+ align:start position:0%
+Okay. So, so this is what I'm going to
+show want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x between a and b
+
+ align:start position:0%
+x between a and b
+ 
+
+ align:start position:0%
+x between a and b
+such that f ofx
+
+ align:start position:0%
+such that f ofx
+ 
+
+ align:start position:0%
+such that f ofx
+is equal to uh zero. So this is what we
+
+ align:start position:0%
+is equal to uh zero. So this is what we
+ 
+
+ align:start position:0%
+is equal to uh zero. So this is what we
+want to show.
+
+ align:start position:0%
+want to show.
+ 
+
+ align:start position:0%
+want to show.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+and again of of course the function f is
+
+ align:start position:0%
+and again of of course the function f is
+ 
+
+ align:start position:0%
+and again of of course the function f is
+obviously continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let me define
+
+ align:start position:0%
+okay so now let me define
+ 
+
+ align:start position:0%
+okay so now let me define
+a inter set. It's actually an interval.
+
+ align:start position:0%
+a inter set. It's actually an interval.
+ 
+
+ align:start position:0%
+a inter set. It's actually an interval.
+So I define E here
+
+ align:start position:0%
+So I define E here
+ 
+
+ align:start position:0%
+So I define E here
+to be the sets of uh of X
+
+ align:start position:0%
+to be the sets of uh of X
+ 
+
+ align:start position:0%
+to be the sets of uh of X
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+uh let's call this here. So I want to
+
+ align:start position:0%
+uh let's call this here. So I want to
+ 
+
+ align:start position:0%
+uh let's call this here. So I want to
+show that exists some
+
+ align:start position:0%
+show that exists some
+ 
+
+ align:start position:0%
+show that exists some
+um X let's call it X0 just to have
+
+ align:start position:0%
+um X let's call it X0 just to have
+ 
+
+ align:start position:0%
+um X let's call it X0 just to have
+something to refer to just it's I call
+
+ align:start position:0%
+something to refer to just it's I call
+ 
+
+ align:start position:0%
+something to refer to just it's I call
+it X0 because the value is going to be
+
+ align:start position:0%
+it X0 because the value is going to be
+ 
+
+ align:start position:0%
+it X0 because the value is going to be
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+So I define a set a a x e sorry e and
+
+ align:start position:0%
+So I define a set a a x e sorry e and
+ 
+
+ align:start position:0%
+So I define a set a a x e sorry e and
+this is the x in the interval but I'm
+
+ align:start position:0%
+this is the x in the interval but I'm
+ 
+
+ align:start position:0%
+this is the x in the interval but I'm
+now requiring that that f of y
+
+ align:start position:0%
+now requiring that that f of y
+ 
+
+ align:start position:0%
+now requiring that that f of y
+is lesser equal to zero for all
+
+ align:start position:0%
+is lesser equal to zero for all
+ 
+
+ align:start position:0%
+is lesser equal to zero for all
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all y which is between A and X.
+
+ align:start position:0%
+for all y which is between A and X.
+ 
+
+ align:start position:0%
+for all y which is between A and X.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now E here is not empty.
+
+ align:start position:0%
+Now E here is not empty.
+ 
+
+ align:start position:0%
+Now E here is not empty.
+E is not empty. E here is not the empty
+
+ align:start position:0%
+E is not empty. E here is not the empty
+ 
+
+ align:start position:0%
+E is not empty. E here is not the empty
+set. Why?
+
+ align:start position:0%
+set. Why?
+ 
+
+ align:start position:0%
+set. Why?
+Because actually a here this is since
+
+ align:start position:0%
+Because actually a here this is since
+ 
+
+ align:start position:0%
+Because actually a here this is since
+A here is in E. Why? Because if you take
+
+ align:start position:0%
+A here is in E. Why? Because if you take
+ 
+
+ align:start position:0%
+A here is in E. Why? Because if you take
+a then the value is actually strictly
+
+ align:start position:0%
+a then the value is actually strictly
+ 
+
+ align:start position:0%
+a then the value is actually strictly
+less than zero right
+
+ align:start position:0%
+less than zero right
+ 
+
+ align:start position:0%
+less than zero right
+and and and everything that lies in here
+
+ align:start position:0%
+and and and everything that lies in here
+ 
+
+ align:start position:0%
+and and and everything that lies in here
+but lies to the left of a well that's
+
+ align:start position:0%
+but lies to the left of a well that's
+ 
+
+ align:start position:0%
+but lies to the left of a well that's
+only a right so this is kind of trivial
+
+ align:start position:0%
+only a right so this is kind of trivial
+ 
+
+ align:start position:0%
+only a right so this is kind of trivial
+statement so this is not zero
+
+ align:start position:0%
+statement so this is not zero
+ 
+
+ align:start position:0%
+statement so this is not zero
+so now you can take the soup of this
+
+ align:start position:0%
+so now you can take the soup of this
+ 
+
+ align:start position:0%
+so now you can take the soup of this
+right so maybe I should make one more
+
+ align:start position:0%
+right so maybe I should make one more
+ 
+
+ align:start position:0%
+right so maybe I should make one more
+remark
+
+ align:start position:0%
+remark
+ 
+
+ align:start position:0%
+remark
+that of course not only is it not the
+
+ align:start position:0%
+that of course not only is it not the
+ 
+
+ align:start position:0%
+that of course not only is it not the
+triv the empty set but E here is bounded
+
+ align:start position:0%
+triv the empty set but E here is bounded
+ 
+
+ align:start position:0%
+triv the empty set but E here is bounded
+so the soup
+
+ align:start position:0%
+so the soup
+ 
+
+ align:start position:0%
+so the soup
+of E is less or equal to B right because
+
+ align:start position:0%
+of E is less or equal to B right because
+ 
+
+ align:start position:0%
+of E is less or equal to B right because
+E all of the elements in E are in this
+
+ align:start position:0%
+E all of the elements in E are in this
+ 
+
+ align:start position:0%
+E all of the elements in E are in this
+set so they're trivally bounded by B
+
+ align:start position:0%
+set so they're trivally bounded by B
+ 
+
+ align:start position:0%
+set so they're trivally bounded by B
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so I now can look at the soup so the
+
+ align:start position:0%
+so I now can look at the soup so the
+ 
+
+ align:start position:0%
+so I now can look at the soup so the
+soup soup here is is a nice number
+
+ align:start position:0%
+soup soup here is is a nice number
+ 
+
+ align:start position:0%
+soup soup here is is a nice number
+and I can look at the soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I claim so the claim here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh that so claim that if set
+
+ align:start position:0%
+that uh that so claim that if set
+ 
+
+ align:start position:0%
+that uh that so claim that if set
+or maybe maybe let me just first say set
+
+ align:start position:0%
+or maybe maybe let me just first say set
+ 
+
+ align:start position:0%
+or maybe maybe let me just first say set
+x0 equal to that soup
+
+ align:start position:0%
+x0 equal to that soup
+ 
+
+ align:start position:0%
+x0 equal to that soup
+V and then the claim is
+
+ align:start position:0%
+V and then the claim is
+ 
+
+ align:start position:0%
+V and then the claim is
+that f of x0
+
+ align:start position:0%
+that f of x0
+ 
+
+ align:start position:0%
+that f of x0
+is actually zero. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so
+
+ align:start position:0%
+And so
+ 
+
+ align:start position:0%
+And so
+now you see that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you take
+
+ align:start position:0%
+If you take
+ 
+
+ align:start position:0%
+If you take
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right. So now take uh look at the soup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So like so so for each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each n
+
+ align:start position:0%
+for each n
+ 
+
+ align:start position:0%
+for each n
+say integer
+
+ align:start position:0%
+say integer
+ 
+
+ align:start position:0%
+say integer
+if you're looking at x0
+
+ align:start position:0%
+if you're looking at x0
+ 
+
+ align:start position:0%
+if you're looking at x0
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+1 / n right this is not the soup of e so
+
+ align:start position:0%
+1 / n right this is not the soup of e so
+ 
+
+ align:start position:0%
+1 / n right this is not the soup of e so
+this means that there exist an element
+
+ align:start position:0%
+this means that there exist an element
+ 
+
+ align:start position:0%
+this means that there exist an element
+uh that is there exist an element For
+
+ align:start position:0%
+uh that is there exist an element For
+ 
+
+ align:start position:0%
+uh that is there exist an element For
+for each n there exist an element which
+
+ align:start position:0%
+for each n there exist an element which
+ 
+
+ align:start position:0%
+for each n there exist an element which
+are called xn
+
+ align:start position:0%
+are called xn
+ 
+
+ align:start position:0%
+are called xn
+and this xn here and it's larger than
+
+ align:start position:0%
+and this xn here and it's larger than
+ 
+
+ align:start position:0%
+and this xn here and it's larger than
+this and the xn is in in e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but you see that that's for it to be an
+
+ align:start position:0%
+but you see that that's for it to be an
+ 
+
+ align:start position:0%
+but you see that that's for it to be an
+E then in fact this element has to be
+
+ align:start position:0%
+E then in fact this element has to be
+ 
+
+ align:start position:0%
+E then in fact this element has to be
+the value has to be less or equal to
+
+ align:start position:0%
+the value has to be less or equal to
+ 
+
+ align:start position:0%
+the value has to be less or equal to
+zero. So f of xn
+
+ align:start position:0%
+zero. So f of xn
+ 
+
+ align:start position:0%
+zero. So f of xn
+has to be lesser equal to zero
+
+ align:start position:0%
+has to be lesser equal to zero
+ 
+
+ align:start position:0%
+has to be lesser equal to zero
+right because since it's an e right so
+
+ align:start position:0%
+right because since it's an e right so
+ 
+
+ align:start position:0%
+right because since it's an e right so
+since it's in e then we have that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now of course the xns
+
+ align:start position:0%
+but now of course the xns
+ 
+
+ align:start position:0%
+but now of course the xns
+the xns they converge this it's bigger
+
+ align:start position:0%
+the xns they converge this it's bigger
+ 
+
+ align:start position:0%
+the xns they converge this it's bigger
+than this but they're less than right
+
+ align:start position:0%
+than this but they're less than right
+ 
+
+ align:start position:0%
+than this but they're less than right
+the soup of all such guys. Right? So
+
+ align:start position:0%
+the soup of all such guys. Right? So
+ 
+
+ align:start position:0%
+the soup of all such guys. Right? So
+this means that the xn so the xn
+
+ align:start position:0%
+this means that the xn so the xn
+ 
+
+ align:start position:0%
+this means that the xn so the xn
+converge to x0
+
+ align:start position:0%
+converge to x0
+ 
+
+ align:start position:0%
+converge to x0
+and so this means that f of xn
+
+ align:start position:0%
+and so this means that f of xn
+ 
+
+ align:start position:0%
+and so this means that f of xn
+converge to f of x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+this means that this here is so and
+
+ align:start position:0%
+this means that this here is so and
+ 
+
+ align:start position:0%
+this means that this here is so and
+these here are all non negative numbers.
+
+ align:start position:0%
+these here are all non negative numbers.
+ 
+
+ align:start position:0%
+these here are all non negative numbers.
+This means that this number here must be
+
+ align:start position:0%
+This means that this number here must be
+ 
+
+ align:start position:0%
+This means that this number here must be
+non- negative,
+
+ align:start position:0%
+non- negative,
+ 
+
+ align:start position:0%
+non- negative,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+If it's actually zero, then that's what
+
+ align:start position:0%
+If it's actually zero, then that's what
+ 
+
+ align:start position:0%
+If it's actually zero, then that's what
+we wanted, right? So, so we're done.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If f ofx0
+
+ align:start position:0%
+If f ofx0
+ 
+
+ align:start position:0%
+If f ofx0
+is actually zero. So we will assume so
+
+ align:start position:0%
+is actually zero. So we will assume so
+ 
+
+ align:start position:0%
+is actually zero. So we will assume so
+assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that f of x0
+
+ align:start position:0%
+that f of x0
+ 
+
+ align:start position:0%
+that f of x0
+is then strictly less than zero.
+
+ align:start position:0%
+is then strictly less than zero.
+ 
+
+ align:start position:0%
+is then strictly less than zero.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+But if the value here is strictly less
+
+ align:start position:0%
+But if the value here is strictly less
+ 
+
+ align:start position:0%
+But if the value here is strictly less
+than zero.
+
+ align:start position:0%
+than zero.
+ 
+
+ align:start position:0%
+than zero.
+If the value is strictly if this is the
+
+ align:start position:0%
+If the value is strictly if this is the
+ 
+
+ align:start position:0%
+If the value is strictly if this is the
+case then there exist then if you take
+
+ align:start position:0%
+case then there exist then if you take
+ 
+
+ align:start position:0%
+case then there exist then if you take
+so if you take so here you have here you
+
+ align:start position:0%
+so if you take so here you have here you
+ 
+
+ align:start position:0%
+so if you take so here you have here you
+have um here you have zero
+
+ align:start position:0%
+have um here you have zero
+ 
+
+ align:start position:0%
+have um here you have zero
+here you have f of x0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You can then take a little interval
+
+ align:start position:0%
+You can then take a little interval
+ 
+
+ align:start position:0%
+You can then take a little interval
+around it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now so now take so take
+
+ align:start position:0%
+And now so now take so take
+ 
+
+ align:start position:0%
+And now so now take so take
+uh take epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger than zero.
+
+ align:start position:0%
+bigger than zero.
+ 
+
+ align:start position:0%
+bigger than zero.
+So that uh such that
+
+ align:start position:0%
+So that uh such that
+ 
+
+ align:start position:0%
+So that uh such that
+if um
+
+ align:start position:0%
+if um
+ 
+
+ align:start position:0%
+if um
+uh by such that um this thing here such
+
+ align:start position:0%
+uh by such that um this thing here such
+ 
+
+ align:start position:0%
+uh by such that um this thing here such
+that f of x0
+
+ align:start position:0%
+that f of x0
+ 
+
+ align:start position:0%
+that f of x0
+plus epsilon this is still negative
+
+ align:start position:0%
+plus epsilon this is still negative
+ 
+
+ align:start position:0%
+plus epsilon this is still negative
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I'm looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to look at so here I have f
+
+ align:start position:0%
+so I'm going to look at so here I have f
+ 
+
+ align:start position:0%
+so I'm going to look at so here I have f
+of x0 zero this is actually negative
+
+ align:start position:0%
+of x0 zero this is actually negative
+ 
+
+ align:start position:0%
+of x0 zero this is actually negative
+and I'm taking a interval around it so
+
+ align:start position:0%
+and I'm taking a interval around it so
+ 
+
+ align:start position:0%
+and I'm taking a interval around it so
+this is like a interval here we have f
+
+ align:start position:0%
+this is like a interval here we have f
+ 
+
+ align:start position:0%
+this is like a interval here we have f
+of x0 plus epsilon and here we have f of
+
+ align:start position:0%
+of x0 plus epsilon and here we have f of
+ 
+
+ align:start position:0%
+of x0 plus epsilon and here we have f of
+x0
+
+ align:start position:0%
+x0
+ 
+
+ align:start position:0%
+x0
+minus epsilon right so I'm looking at
+
+ align:start position:0%
+minus epsilon right so I'm looking at
+ 
+
+ align:start position:0%
+minus epsilon right so I'm looking at
+this little interval here around f of x0
+
+ align:start position:0%
+this little interval here around f of x0
+ 
+
+ align:start position:0%
+this little interval here around f of x0
+and here I have here I have x0
+
+ align:start position:0%
+and here I have here I have x0
+ 
+
+ align:start position:0%
+and here I have here I have x0
+but now I I know that there is because
+
+ align:start position:0%
+but now I I know that there is because
+ 
+
+ align:start position:0%
+but now I I know that there is because
+the function is continuous. I know that
+
+ align:start position:0%
+the function is continuous. I know that
+ 
+
+ align:start position:0%
+the function is continuous. I know that
+there exist an interval. So there exists
+
+ align:start position:0%
+there exist an interval. So there exists
+ 
+
+ align:start position:0%
+there exist an interval. So there exists
+some delta. There exist delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta bigger than zero. So that if I'm
+
+ align:start position:0%
+delta bigger than zero. So that if I'm
+ 
+
+ align:start position:0%
+delta bigger than zero. So that if I'm
+in this little interval, this is the
+
+ align:start position:0%
+in this little interval, this is the
+ 
+
+ align:start position:0%
+in this little interval, this is the
+interval from x0 minus delta x0 plus
+
+ align:start position:0%
+interval from x0 minus delta x0 plus
+ 
+
+ align:start position:0%
+interval from x0 minus delta x0 plus
+delta.
+
+ align:start position:0%
+delta.
+ 
+
+ align:start position:0%
+delta.
+If I'm looking at this little integ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I have in other words I have
+
+ align:start position:0%
+right so I have in other words I have
+ 
+
+ align:start position:0%
+right so I have in other words I have
+that if x minus x0 is less than delta
+
+ align:start position:0%
+that if x minus x0 is less than delta
+ 
+
+ align:start position:0%
+that if x minus x0 is less than delta
+then uh f of x
+
+ align:start position:0%
+then uh f of x
+ 
+
+ align:start position:0%
+then uh f of x
+minus f of x0
+
+ align:start position:0%
+minus f of x0
+ 
+
+ align:start position:0%
+minus f of x0
+is less than epsilon. But everything
+
+ align:start position:0%
+is less than epsilon. But everything
+ 
+
+ align:start position:0%
+is less than epsilon. But everything
+that is in this interim here is still
+
+ align:start position:0%
+that is in this interim here is still
+ 
+
+ align:start position:0%
+that is in this interim here is still
+strictly negative. So this means that in
+
+ align:start position:0%
+strictly negative. So this means that in
+ 
+
+ align:start position:0%
+strictly negative. So this means that in
+fact I have that f ofx
+
+ align:start position:0%
+fact I have that f ofx
+ 
+
+ align:start position:0%
+fact I have that f ofx
+uh is actually in particular this
+
+ align:start position:0%
+uh is actually in particular this
+ 
+
+ align:start position:0%
+uh is actually in particular this
+implied that such a f ofx is actually
+
+ align:start position:0%
+implied that such a f ofx is actually
+ 
+
+ align:start position:0%
+implied that such a f ofx is actually
+negative right
+
+ align:start position:0%
+negative right
+ 
+
+ align:start position:0%
+negative right
+and so now you see that that so now I
+
+ align:start position:0%
+and so now you see that that so now I
+ 
+
+ align:start position:0%
+and so now you see that that so now I
+want to get a contradiction
+
+ align:start position:0%
+want to get a contradiction
+ 
+
+ align:start position:0%
+want to get a contradiction
+because I know so I have now so now I
+
+ align:start position:0%
+because I know so I have now so now I
+ 
+
+ align:start position:0%
+because I know so I have now so now I
+have this picture Here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have my I have my X0 here. The X0 was
+
+ align:start position:0%
+I have my I have my X0 here. The X0 was
+ 
+
+ align:start position:0%
+I have my I have my X0 here. The X0 was
+supposed to be the the soup of the set
+
+ align:start position:0%
+supposed to be the the soup of the set
+ 
+
+ align:start position:0%
+supposed to be the the soup of the set
+A,
+
+ align:start position:0%
+A,
+ 
+
+ align:start position:0%
+A,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And then I know that so I know that
+
+ align:start position:0%
+And then I know that so I know that
+ 
+
+ align:start position:0%
+And then I know that so I know that
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+on a little interval around this Xure
+
+ align:start position:0%
+on a little interval around this Xure
+ 
+
+ align:start position:0%
+on a little interval around this Xure
+everything is T the if I take anything
+
+ align:start position:0%
+everything is T the if I take anything
+ 
+
+ align:start position:0%
+everything is T the if I take anything
+in a little interval around this x0 then
+
+ align:start position:0%
+in a little interval around this x0 then
+ 
+
+ align:start position:0%
+in a little interval around this x0 then
+the values of f under is are actually
+
+ align:start position:0%
+the values of f under is are actually
+ 
+
+ align:start position:0%
+the values of f under is are actually
+negative right
+
+ align:start position:0%
+negative right
+ 
+
+ align:start position:0%
+negative right
+but you see that this x0 was was limits
+
+ align:start position:0%
+but you see that this x0 was was limits
+ 
+
+ align:start position:0%
+but you see that this x0 was was limits
+of points where
+
+ align:start position:0%
+of points where
+ 
+
+ align:start position:0%
+of points where
+everything to the left was was
+
+ align:start position:0%
+everything to the left was was
+ 
+
+ align:start position:0%
+everything to the left was was
+non-positive
+
+ align:start position:0%
+non-positive
+ 
+
+ align:start position:0%
+non-positive
+but so it means that everything to the
+
+ align:start position:0%
+but so it means that everything to the
+ 
+
+ align:start position:0%
+but so it means that everything to the
+left was nonpositive
+
+ align:start position:0%
+left was nonpositive
+ 
+
+ align:start position:0%
+left was nonpositive
+but then even a little bit further was
+
+ align:start position:0%
+but then even a little bit further was
+ 
+
+ align:start position:0%
+but then even a little bit further was
+still non positive, right?
+
+ align:start position:0%
+still non positive, right?
+ 
+
+ align:start position:0%
+still non positive, right?
+But then it wasn't like the soup, right?
+
+ align:start position:0%
+But then it wasn't like the soup, right?
+ 
+
+ align:start position:0%
+But then it wasn't like the soup, right?
+Because you could actually any here
+
+ align:start position:0%
+Because you could actually any here
+ 
+
+ align:start position:0%
+Because you could actually any here
+would be larger and it still would have
+
+ align:start position:0%
+would be larger and it still would have
+ 
+
+ align:start position:0%
+would be larger and it still would have
+the property that everything to the left
+
+ align:start position:0%
+the property that everything to the left
+ 
+
+ align:start position:0%
+the property that everything to the left
+was was uh under f was non negative.
+
+ align:start position:0%
+was was uh under f was non negative.
+ 
+
+ align:start position:0%
+was was uh under f was non negative.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's like the proof of the extreme
+
+ align:start position:0%
+so that's like the proof of the extreme
+ 
+
+ align:start position:0%
+so that's like the proof of the extreme
+value theorem and intermediate value
+
+ align:start position:0%
+value theorem and intermediate value
+ 
+
+ align:start position:0%
+value theorem and intermediate value
+theorem using this using sequences and
+
+ align:start position:0%
+theorem using this using sequences and
+ 
+
+ align:start position:0%
+theorem using this using sequences and
+using that little lema from before.
+
+ align:start position:0%
+using that little lema from before.
+ 
+
+ align:start position:0%
+using that little lema from before.
+Okay. So now the next thing I want to
+
+ align:start position:0%
+Okay. So now the next thing I want to
+ 
+
+ align:start position:0%
+Okay. So now the next thing I want to
+talk about is another really important
+
+ align:start position:0%
+talk about is another really important
+ 
+
+ align:start position:0%
+talk about is another really important
+concept and that's a generalization to
+
+ align:start position:0%
+concept and that's a generalization to
+ 
+
+ align:start position:0%
+concept and that's a generalization to
+some extent it's a generalization of
+
+ align:start position:0%
+some extent it's a generalization of
+ 
+
+ align:start position:0%
+some extent it's a generalization of
+things we know from the real numbers.
+
+ align:start position:0%
+things we know from the real numbers.
+ 
+
+ align:start position:0%
+things we know from the real numbers.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+and so this is this concept of a metric
+
+ align:start position:0%
+and so this is this concept of a metric
+ 
+
+ align:start position:0%
+and so this is this concept of a metric
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so let me just give you a definition
+
+ align:start position:0%
+and so let me just give you a definition
+ 
+
+ align:start position:0%
+and so let me just give you a definition
+and then I'll give you a bunch of
+
+ align:start position:0%
+and then I'll give you a bunch of
+ 
+
+ align:start position:0%
+and then I'll give you a bunch of
+examples.
+
+ align:start position:0%
+examples.
+ 
+
+ align:start position:0%
+examples.
+So a metric space it's a set X. So this
+
+ align:start position:0%
+So a metric space it's a set X. So this
+ 
+
+ align:start position:0%
+So a metric space it's a set X. So this
+is the set
+
+ align:start position:0%
+is the set
+ 
+
+ align:start position:0%
+is the set
+and then it's a map
+
+ align:start position:0%
+and then it's a map
+ 
+
+ align:start position:0%
+and then it's a map
+for each pair of points.
+
+ align:start position:0%
+for each pair of points.
+ 
+
+ align:start position:0%
+for each pair of points.
+So let me explain what this what I mean
+
+ align:start position:0%
+So let me explain what this what I mean
+ 
+
+ align:start position:0%
+So let me explain what this what I mean
+by this. So whenever you have x in in x
+
+ align:start position:0%
+by this. So whenever you have x in in x
+ 
+
+ align:start position:0%
+by this. So whenever you have x in in x
+and and another element in this space
+
+ align:start position:0%
+and and another element in this space
+ 
+
+ align:start position:0%
+and and another element in this space
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+when you have any such pair then d x
+
+ align:start position:0%
+when you have any such pair then d x
+ 
+
+ align:start position:0%
+when you have any such pair then d x
+comma y this is should be this gives you
+
+ align:start position:0%
+comma y this is should be this gives you
+ 
+
+ align:start position:0%
+comma y this is should be this gives you
+a real number. Okay
+
+ align:start position:0%
+a real number. Okay
+ 
+
+ align:start position:0%
+a real number. Okay
+and so this here is what you usually
+
+ align:start position:0%
+and so this here is what you usually
+ 
+
+ align:start position:0%
+and so this here is what you usually
+call the distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and Y.
+
+ align:start position:0%
+X and Y.
+ 
+
+ align:start position:0%
+X and Y.
+Okay, that's the distance between X and
+
+ align:start position:0%
+Okay, that's the distance between X and
+ 
+
+ align:start position:0%
+Okay, that's the distance between X and
+Y. Now, what property should this have?
+
+ align:start position:0%
+Y. Now, what property should this have?
+ 
+
+ align:start position:0%
+Y. Now, what property should this have?
+It's just it's not just any any map from
+
+ align:start position:0%
+It's just it's not just any any map from
+ 
+
+ align:start position:0%
+It's just it's not just any any map from
+the space the space cross itself into R.
+
+ align:start position:0%
+the space the space cross itself into R.
+ 
+
+ align:start position:0%
+the space the space cross itself into R.
+It has three properties. The first is
+
+ align:start position:0%
+It has three properties. The first is
+ 
+
+ align:start position:0%
+It has three properties. The first is
+that the distance
+
+ align:start position:0%
+that the distance
+ 
+
+ align:start position:0%
+that the distance
+between parent points
+
+ align:start position:0%
+between parent points
+ 
+
+ align:start position:0%
+between parent points
+I mean and then there are generalization
+
+ align:start position:0%
+I mean and then there are generalization
+ 
+
+ align:start position:0%
+I mean and then there are generalization
+of this but but anyway so I'll talk
+
+ align:start position:0%
+of this but but anyway so I'll talk
+ 
+
+ align:start position:0%
+of this but but anyway so I'll talk
+about it that's generalization like if
+
+ align:start position:0%
+about it that's generalization like if
+ 
+
+ align:start position:0%
+about it that's generalization like if
+you're working with like general
+
+ align:start position:0%
+you're working with like general
+ 
+
+ align:start position:0%
+you're working with like general
+relativity then you would actually not
+
+ align:start position:0%
+relativity then you would actually not
+ 
+
+ align:start position:0%
+relativity then you would actually not
+quite work with this definition you work
+
+ align:start position:0%
+quite work with this definition you work
+ 
+
+ align:start position:0%
+quite work with this definition you work
+with some generalization of this but so
+
+ align:start position:0%
+with some generalization of this but so
+ 
+
+ align:start position:0%
+with some generalization of this but so
+what property should this distance have
+
+ align:start position:0%
+what property should this distance have
+ 
+
+ align:start position:0%
+what property should this distance have
+it should have three properties
+
+ align:start position:0%
+it should have three properties
+ 
+
+ align:start position:0%
+it should have three properties
+The first is that for any x and y
+
+ align:start position:0%
+The first is that for any x and y
+ 
+
+ align:start position:0%
+The first is that for any x and y
+the distance between any two points
+
+ align:start position:0%
+the distance between any two points
+ 
+
+ align:start position:0%
+the distance between any two points
+should always give you a non- negative
+
+ align:start position:0%
+should always give you a non- negative
+ 
+
+ align:start position:0%
+should always give you a non- negative
+number. Right? So this here should be
+
+ align:start position:0%
+number. Right? So this here should be
+ 
+
+ align:start position:0%
+number. Right? So this here should be
+non- negative. And
+
+ align:start position:0%
+non- negative. And
+ 
+
+ align:start position:0%
+non- negative. And
+if the distance between two points is
+
+ align:start position:0%
+if the distance between two points is
+ 
+
+ align:start position:0%
+if the distance between two points is
+zero then
+
+ align:start position:0%
+zero then
+ 
+
+ align:start position:0%
+zero then
+those two points should be the same.
+
+ align:start position:0%
+those two points should be the same.
+ 
+
+ align:start position:0%
+those two points should be the same.
+So in fact the distance here is equal to
+
+ align:start position:0%
+So in fact the distance here is equal to
+ 
+
+ align:start position:0%
+So in fact the distance here is equal to
+zero if and only if x is equal to y.
+
+ align:start position:0%
+zero if and only if x is equal to y.
+ 
+
+ align:start position:0%
+zero if and only if x is equal to y.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So that's the first property.
+
+ align:start position:0%
+So that's the first property.
+ 
+
+ align:start position:0%
+So that's the first property.
+And the second property is
+
+ align:start position:0%
+And the second property is
+ 
+
+ align:start position:0%
+And the second property is
+so just that distances are non- negative
+
+ align:start position:0%
+so just that distances are non- negative
+ 
+
+ align:start position:0%
+so just that distances are non- negative
+if you will. The second property is that
+
+ align:start position:0%
+if you will. The second property is that
+ 
+
+ align:start position:0%
+if you will. The second property is that
+if you looking at what is the distance
+
+ align:start position:0%
+if you looking at what is the distance
+ 
+
+ align:start position:0%
+if you looking at what is the distance
+from X to Y, the distance from X to Y
+
+ align:start position:0%
+from X to Y, the distance from X to Y
+ 
+
+ align:start position:0%
+from X to Y, the distance from X to Y
+should be the same as the distance from
+
+ align:start position:0%
+should be the same as the distance from
+ 
+
+ align:start position:0%
+should be the same as the distance from
+Y to X. So this is
+
+ align:start position:0%
+Y to X. So this is
+ 
+
+ align:start position:0%
+Y to X. So this is
+so this is this and this is sometimes
+
+ align:start position:0%
+so this is this and this is sometimes
+ 
+
+ align:start position:0%
+so this is this and this is sometimes
+referred to that is symmetric.
+
+ align:start position:0%
+referred to that is symmetric.
+ 
+
+ align:start position:0%
+referred to that is symmetric.
+It doesn't matter whether you first you
+
+ align:start position:0%
+It doesn't matter whether you first you
+ 
+
+ align:start position:0%
+It doesn't matter whether you first you
+begin at X and go to Y or you begin at Y
+
+ align:start position:0%
+begin at X and go to Y or you begin at Y
+ 
+
+ align:start position:0%
+begin at X and go to Y or you begin at Y
+and go to X.
+
+ align:start position:0%
+and go to X.
+ 
+
+ align:start position:0%
+and go to X.
+And then the third thing which is kind
+
+ align:start position:0%
+And then the third thing which is kind
+ 
+
+ align:start position:0%
+And then the third thing which is kind
+of like the non-trivial part of it and
+
+ align:start position:0%
+of like the non-trivial part of it and
+ 
+
+ align:start position:0%
+of like the non-trivial part of it and
+the thing that makes it really useful
+
+ align:start position:0%
+the thing that makes it really useful
+ 
+
+ align:start position:0%
+the thing that makes it really useful
+which is called the triangle inequality
+
+ align:start position:0%
+which is called the triangle inequality
+ 
+
+ align:start position:0%
+which is called the triangle inequality
+that if you have three points X Y and Z
+
+ align:start position:0%
+that if you have three points X Y and Z
+ 
+
+ align:start position:0%
+that if you have three points X Y and Z
+in this space and you're looking at the
+
+ align:start position:0%
+in this space and you're looking at the
+ 
+
+ align:start position:0%
+in this space and you're looking at the
+distance from X to C.
+
+ align:start position:0%
+distance from X to C.
+ 
+
+ align:start position:0%
+distance from X to C.
+So if you imagine that you take you have
+
+ align:start position:0%
+So if you imagine that you take you have
+ 
+
+ align:start position:0%
+So if you imagine that you take you have
+three points X Y and then you have
+
+ align:start position:0%
+three points X Y and then you have
+ 
+
+ align:start position:0%
+three points X Y and then you have
+another point C sorry no it's not so X
+
+ align:start position:0%
+another point C sorry no it's not so X
+ 
+
+ align:start position:0%
+another point C sorry no it's not so X
+you have three point X Y and Z but you
+
+ align:start position:0%
+you have three point X Y and Z but you
+ 
+
+ align:start position:0%
+you have three point X Y and Z but you
+think about that you're looking at the
+
+ align:start position:0%
+think about that you're looking at the
+ 
+
+ align:start position:0%
+think about that you're looking at the
+distance from X to C.
+
+ align:start position:0%
+distance from X to C.
+ 
+
+ align:start position:0%
+distance from X to C.
+Well instead of going kind of directly
+
+ align:start position:0%
+Well instead of going kind of directly
+ 
+
+ align:start position:0%
+Well instead of going kind of directly
+from X to C. If you went over y then
+
+ align:start position:0%
+from X to C. If you went over y then
+ 
+
+ align:start position:0%
+from X to C. If you went over y then
+this distance here should be longer than
+
+ align:start position:0%
+this distance here should be longer than
+ 
+
+ align:start position:0%
+this distance here should be longer than
+if you went directly. So this thing here
+
+ align:start position:0%
+if you went directly. So this thing here
+ 
+
+ align:start position:0%
+if you went directly. So this thing here
+should be less or equal to the distance
+
+ align:start position:0%
+should be less or equal to the distance
+ 
+
+ align:start position:0%
+should be less or equal to the distance
+from x to y plus the distance from y to
+
+ align:start position:0%
+from x to y plus the distance from y to
+ 
+
+ align:start position:0%
+from x to y plus the distance from y to
+c. And this here is like the non-trivial
+
+ align:start position:0%
+c. And this here is like the non-trivial
+ 
+
+ align:start position:0%
+c. And this here is like the non-trivial
+part of it.
+
+ align:start position:0%
+part of it.
+ 
+
+ align:start position:0%
+part of it.
+And this is called the triangular.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now what are some examples of this? And
+
+ align:start position:0%
+Now what are some examples of this? And
+ 
+
+ align:start position:0%
+Now what are some examples of this? And
+then let's look at a bunch of examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The first example is
+
+ align:start position:0%
+The first example is
+ 
+
+ align:start position:0%
+The first example is
+the first example is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just where x is r
+
+ align:start position:0%
+is just where x is r
+ 
+
+ align:start position:0%
+is just where x is r
+and so you have two points in x in r and
+
+ align:start position:0%
+and so you have two points in x in r and
+ 
+
+ align:start position:0%
+and so you have two points in x in r and
+now the distance between them is simply
+
+ align:start position:0%
+now the distance between them is simply
+ 
+
+ align:start position:0%
+now the distance between them is simply
+x minus one
+
+ align:start position:0%
+x minus one
+ 
+
+ align:start position:0%
+x minus one
+right this is obviously non- negative if
+
+ align:start position:0%
+right this is obviously non- negative if
+ 
+
+ align:start position:0%
+right this is obviously non- negative if
+It's zero that means that x is equal to
+
+ align:start position:0%
+It's zero that means that x is equal to
+ 
+
+ align:start position:0%
+It's zero that means that x is equal to
+y. It's obviously also symmetric. And
+
+ align:start position:0%
+y. It's obviously also symmetric. And
+ 
+
+ align:start position:0%
+y. It's obviously also symmetric. And
+the triangle inequality is this
+
+ align:start position:0%
+the triangle inequality is this
+ 
+
+ align:start position:0%
+the triangle inequality is this
+inequality that we're using all the
+
+ align:start position:0%
+inequality that we're using all the
+ 
+
+ align:start position:0%
+inequality that we're using all the
+time. Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Another example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is uh if you're looking at where x
+
+ align:start position:0%
+uh is uh if you're looking at where x
+ 
+
+ align:start position:0%
+uh is uh if you're looking at where x
+here is r squ say and then you're
+
+ align:start position:0%
+here is r squ say and then you're
+ 
+
+ align:start position:0%
+here is r squ say and then you're
+looking at you're thinking about x and y
+
+ align:start position:0%
+looking at you're thinking about x and y
+ 
+
+ align:start position:0%
+looking at you're thinking about x and y
+you may think about it as vector or
+
+ align:start position:0%
+you may think about it as vector or
+ 
+
+ align:start position:0%
+you may think about it as vector or
+whatever you want to think about it. So
+
+ align:start position:0%
+whatever you want to think about it. So
+ 
+
+ align:start position:0%
+whatever you want to think about it. So
+this means that X here has coordinates
+
+ align:start position:0%
+this means that X here has coordinates
+ 
+
+ align:start position:0%
+this means that X here has coordinates
+X1 and X2
+
+ align:start position:0%
+X1 and X2
+ 
+
+ align:start position:0%
+X1 and X2
+and Y has coordinates
+
+ align:start position:0%
+and Y has coordinates
+ 
+
+ align:start position:0%
+and Y has coordinates
+Y1 and Y2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now the distance between these two
+
+ align:start position:0%
+And now the distance between these two
+ 
+
+ align:start position:0%
+And now the distance between these two
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just the square root
+
+ align:start position:0%
+is just the square root
+ 
+
+ align:start position:0%
+is just the square root
+of x1 - y1
+
+ align:start position:0%
+of x1 - y1
+ 
+
+ align:start position:0%
+of x1 - y1
+squared plus x2 -
+
+ align:start position:0%
+squared plus x2 -
+ 
+
+ align:start position:0%
+squared plus x2 -
+uh y2
+
+ align:start position:0%
+uh y2
+ 
+
+ align:start position:0%
+uh y2
+squared. That's the distance. And this
+
+ align:start position:0%
+squared. That's the distance. And this
+ 
+
+ align:start position:0%
+squared. That's the distance. And this
+here is often referred to as a uking
+
+ align:start position:0%
+here is often referred to as a uking
+ 
+
+ align:start position:0%
+here is often referred to as a uking
+distance.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So this is this distance that you
+
+ align:start position:0%
+Right. So this is this distance that you
+ 
+
+ align:start position:0%
+Right. So this is this distance that you
+know this is like the distance is given
+
+ align:start position:0%
+know this is like the distance is given
+ 
+
+ align:start position:0%
+know this is like the distance is given
+by pagas here. Right. And so that is so
+
+ align:start position:0%
+by pagas here. Right. And so that is so
+ 
+
+ align:start position:0%
+by pagas here. Right. And so that is so
+it's clear the first two property but
+
+ align:start position:0%
+it's clear the first two property but
+ 
+
+ align:start position:0%
+it's clear the first two property but
+those are always clear and the triangle
+
+ align:start position:0%
+those are always clear and the triangle
+ 
+
+ align:start position:0%
+those are always clear and the triangle
+inequality that's the one that sometimes
+
+ align:start position:0%
+inequality that's the one that sometimes
+ 
+
+ align:start position:0%
+inequality that's the one that sometimes
+is tricky to prove.
+
+ align:start position:0%
+is tricky to prove.
+ 
+
+ align:start position:0%
+is tricky to prove.
+Okay. So that's another example of a
+
+ align:start position:0%
+Okay. So that's another example of a
+ 
+
+ align:start position:0%
+Okay. So that's another example of a
+distance.
+
+ align:start position:0%
+distance.
+ 
+
+ align:start position:0%
+distance.
+I want to give you a few more examples.
+
+ align:start position:0%
+I want to give you a few more examples.
+ 
+
+ align:start position:0%
+I want to give you a few more examples.
+Uh and so another example is like where
+
+ align:start position:0%
+Uh and so another example is like where
+ 
+
+ align:start position:0%
+Uh and so another example is like where
+you do this in R3 and so you have
+
+ align:start position:0%
+you do this in R3 and so you have
+ 
+
+ align:start position:0%
+you do this in R3 and so you have
+instead of points having two coordinates
+
+ align:start position:0%
+instead of points having two coordinates
+ 
+
+ align:start position:0%
+instead of points having two coordinates
+they now have three coordinates and you
+
+ align:start position:0%
+they now have three coordinates and you
+ 
+
+ align:start position:0%
+they now have three coordinates and you
+do the same sort of thing but now there
+
+ align:start position:0%
+do the same sort of thing but now there
+ 
+
+ align:start position:0%
+do the same sort of thing but now there
+would be a third term in under the
+
+ align:start position:0%
+would be a third term in under the
+ 
+
+ align:start position:0%
+would be a third term in under the
+square root sign which be the square of
+
+ align:start position:0%
+square root sign which be the square of
+ 
+
+ align:start position:0%
+square root sign which be the square of
+the difference between the third
+
+ align:start position:0%
+the difference between the third
+ 
+
+ align:start position:0%
+the difference between the third
+coordinates. Right?
+
+ align:start position:0%
+coordinates. Right?
+ 
+
+ align:start position:0%
+coordinates. Right?
+Okay. Uh then
+
+ align:start position:0%
+Okay. Uh then
+ 
+
+ align:start position:0%
+Okay. Uh then
+then let me give you a few more
+
+ align:start position:0%
+then let me give you a few more
+ 
+
+ align:start position:0%
+then let me give you a few more
+examples.
+
+ align:start position:0%
+examples.
+ 
+
+ align:start position:0%
+examples.
+Uh there's a one that is to some extent
+
+ align:start position:0%
+Uh there's a one that is to some extent
+ 
+
+ align:start position:0%
+Uh there's a one that is to some extent
+simpler than this one here
+
+ align:start position:0%
+simpler than this one here
+ 
+
+ align:start position:0%
+simpler than this one here
+and it's sometimes useful but it's not
+
+ align:start position:0%
+and it's sometimes useful but it's not
+ 
+
+ align:start position:0%
+and it's sometimes useful but it's not
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+useful as the
+
+ align:start position:0%
+useful as the
+ 
+
+ align:start position:0%
+useful as the
+as the
+
+ align:start position:0%
+as the
+ 
+
+ align:start position:0%
+as the
+ukian distances.
+
+ align:start position:0%
+ukian distances.
+ 
+
+ align:start position:0%
+ukian distances.
+And again these sort of things are
+
+ align:start position:0%
+And again these sort of things are
+ 
+
+ align:start position:0%
+And again these sort of things are
+generalized there are you know example
+
+ align:start position:0%
+generalized there are you know example
+ 
+
+ align:start position:0%
+generalized there are you know example
+of something much more general like this
+
+ align:start position:0%
+of something much more general like this
+ 
+
+ align:start position:0%
+of something much more general like this
+here is what's called a helper space
+
+ align:start position:0%
+here is what's called a helper space
+ 
+
+ align:start position:0%
+here is what's called a helper space
+example of a helper space the next is
+
+ align:start position:0%
+example of a helper space the next is
+ 
+
+ align:start position:0%
+example of a helper space the next is
+some something which is example of
+
+ align:start position:0%
+some something which is example of
+ 
+
+ align:start position:0%
+some something which is example of
+something called a bar space but so the
+
+ align:start position:0%
+something called a bar space but so the
+ 
+
+ align:start position:0%
+something called a bar space but so the
+next example I will look at is what is
+
+ align:start position:0%
+next example I will look at is what is
+ 
+
+ align:start position:0%
+next example I will look at is what is
+sometimes called the box distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if space in this case is is R2.
+
+ align:start position:0%
+and so if space in this case is is R2.
+ 
+
+ align:start position:0%
+and so if space in this case is is R2.
+I mean you could do it in R3 also if you
+
+ align:start position:0%
+I mean you could do it in R3 also if you
+ 
+
+ align:start position:0%
+I mean you could do it in R3 also if you
+wanted and you take two points here X
+
+ align:start position:0%
+wanted and you take two points here X
+ 
+
+ align:start position:0%
+wanted and you take two points here X
+and Y
+
+ align:start position:0%
+and Y
+ 
+
+ align:start position:0%
+and Y
+in R2 and so so X this here underline X
+
+ align:start position:0%
+in R2 and so so X this here underline X
+ 
+
+ align:start position:0%
+in R2 and so so X this here underline X
+has coordinates X1 and X2 and now the
+
+ align:start position:0%
+has coordinates X1 and X2 and now the
+ 
+
+ align:start position:0%
+has coordinates X1 and X2 and now the
+distance between these two points
+
+ align:start position:0%
+distance between these two points
+ 
+
+ align:start position:0%
+distance between these two points
+would be uh would be you didn't do this
+
+ align:start position:0%
+would be uh would be you didn't do this
+ 
+
+ align:start position:0%
+would be uh would be you didn't do this
+fancy thing with square root but you did
+
+ align:start position:0%
+fancy thing with square root but you did
+ 
+
+ align:start position:0%
+fancy thing with square root but you did
+the more trivial thing where you're just
+
+ align:start position:0%
+the more trivial thing where you're just
+ 
+
+ align:start position:0%
+the more trivial thing where you're just
+adding right so you're taking two points
+
+ align:start position:0%
+adding right so you're taking two points
+ 
+
+ align:start position:0%
+adding right so you're taking two points
+here in R2 this is maybe x1 comma x2
+
+ align:start position:0%
+here in R2 this is maybe x1 comma x2
+ 
+
+ align:start position:0%
+here in R2 this is maybe x1 comma x2
+this is y1
+
+ align:start position:0%
+this is y1
+ 
+
+ align:start position:0%
+this is y1
+y1 comma y2 the ukian distance is simply
+
+ align:start position:0%
+y1 comma y2 the ukian distance is simply
+ 
+
+ align:start position:0%
+y1 comma y2 the ukian distance is simply
+this distance here the box distance is
+
+ align:start position:0%
+this distance here the box distance is
+ 
+
+ align:start position:0%
+this distance here the box distance is
+where you take this distance here and
+
+ align:start position:0%
+where you take this distance here and
+ 
+
+ align:start position:0%
+where you take this distance here and
+you add in this distance here so this is
+
+ align:start position:0%
+you add in this distance here so this is
+ 
+
+ align:start position:0%
+you add in this distance here so this is
+this here plus uh x2 2 minus Y2.
+
+ align:start position:0%
+this here plus uh x2 2 minus Y2.
+ 
+
+ align:start position:0%
+this here plus uh x2 2 minus Y2.
+That's a box distance. And obviously
+
+ align:start position:0%
+That's a box distance. And obviously
+ 
+
+ align:start position:0%
+That's a box distance. And obviously
+this is a non- negative. It gives you
+
+ align:start position:0%
+this is a non- negative. It gives you
+ 
+
+ align:start position:0%
+this is a non- negative. It gives you
+for any pair. It's non- negative. It's
+
+ align:start position:0%
+for any pair. It's non- negative. It's
+ 
+
+ align:start position:0%
+for any pair. It's non- negative. It's
+obviously symmetric. It doesn't matter
+
+ align:start position:0%
+obviously symmetric. It doesn't matter
+ 
+
+ align:start position:0%
+obviously symmetric. It doesn't matter
+the ordering of these two, right? It's
+
+ align:start position:0%
+the ordering of these two, right? It's
+ 
+
+ align:start position:0%
+the ordering of these two, right? It's
+just switching the order, but you're
+
+ align:start position:0%
+just switching the order, but you're
+ 
+
+ align:start position:0%
+just switching the order, but you're
+taking absolute value sign anyway. So it
+
+ align:start position:0%
+taking absolute value sign anyway. So it
+ 
+
+ align:start position:0%
+taking absolute value sign anyway. So it
+doesn't matter. And it's also clear that
+
+ align:start position:0%
+doesn't matter. And it's also clear that
+ 
+
+ align:start position:0%
+doesn't matter. And it's also clear that
+it's zero if and only if these two
+
+ align:start position:0%
+it's zero if and only if these two
+ 
+
+ align:start position:0%
+it's zero if and only if these two
+points. It means that the coordinates
+
+ align:start position:0%
+points. It means that the coordinates
+ 
+
+ align:start position:0%
+points. It means that the coordinates
+are are the same, right?
+
+ align:start position:0%
+are are the same, right?
+ 
+
+ align:start position:0%
+are are the same, right?
+So and and then in this case the
+
+ align:start position:0%
+So and and then in this case the
+ 
+
+ align:start position:0%
+So and and then in this case the
+triangle inequality is not very hard to
+
+ align:start position:0%
+triangle inequality is not very hard to
+ 
+
+ align:start position:0%
+triangle inequality is not very hard to
+establish, right? I mean proving the
+
+ align:start position:0%
+establish, right? I mean proving the
+ 
+
+ align:start position:0%
+establish, right? I mean proving the
+trigon even just for the ukleian are
+
+ align:start position:0%
+trigon even just for the ukleian are
+ 
+
+ align:start position:0%
+trigon even just for the ukleian are
+non-trivial thing.
+
+ align:start position:0%
+non-trivial thing.
+ 
+
+ align:start position:0%
+non-trivial thing.
+Okay. Now so that's another example and
+
+ align:start position:0%
+Okay. Now so that's another example and
+ 
+
+ align:start position:0%
+Okay. Now so that's another example and
+I want to give you a few more examples.
+
+ align:start position:0%
+I want to give you a few more examples.
+ 
+
+ align:start position:0%
+I want to give you a few more examples.
+Here's a sort of interesting
+
+ align:start position:0%
+Here's a sort of interesting
+ 
+
+ align:start position:0%
+Here's a sort of interesting
+um example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you take suppose you take a
+
+ align:start position:0%
+that if you take suppose you take a
+ 
+
+ align:start position:0%
+that if you take suppose you take a
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+let's just make the interval from 0 to
+
+ align:start position:0%
+let's just make the interval from 0 to
+ 
+
+ align:start position:0%
+let's just make the interval from 0 to
+one so suppose you're looking at the
+
+ align:start position:0%
+one so suppose you're looking at the
+ 
+
+ align:start position:0%
+one so suppose you're looking at the
+interval from 0 to one and now looking
+
+ align:start position:0%
+interval from 0 to one and now looking
+ 
+
+ align:start position:0%
+interval from 0 to one and now looking
+at so this here this is now your space x
+
+ align:start position:0%
+at so this here this is now your space x
+ 
+
+ align:start position:0%
+at so this here this is now your space x
+and so this means by that I mean that
+
+ align:start position:0%
+and so this means by that I mean that
+ 
+
+ align:start position:0%
+and so this means by that I mean that
+that x
+
+ align:start position:0%
+that x
+ 
+
+ align:start position:0%
+that x
+x consist of so x there consists of.
+
+ align:start position:0%
+x consist of so x there consists of.
+ 
+
+ align:start position:0%
+x consist of so x there consists of.
+So an an element in X is an element in X
+
+ align:start position:0%
+So an an element in X is an element in X
+ 
+
+ align:start position:0%
+So an an element in X is an element in X
+an element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in X is a continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the interval from 0 to one.
+
+ align:start position:0%
+on the interval from 0 to one.
+ 
+
+ align:start position:0%
+on the interval from 0 to one.
+So this means that if you take two
+
+ align:start position:0%
+So this means that if you take two
+ 
+
+ align:start position:0%
+So this means that if you take two
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+So if you take one continuous function
+
+ align:start position:0%
+So if you take one continuous function
+ 
+
+ align:start position:0%
+So if you take one continuous function
+on the interval from 0 to one and
+
+ align:start position:0%
+on the interval from 0 to one and
+ 
+
+ align:start position:0%
+on the interval from 0 to one and
+another continuous function what should
+
+ align:start position:0%
+another continuous function what should
+ 
+
+ align:start position:0%
+another continuous function what should
+be the distance between two continuous
+
+ align:start position:0%
+be the distance between two continuous
+ 
+
+ align:start position:0%
+be the distance between two continuous
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+well the distance here so this here is
+
+ align:start position:0%
+well the distance here so this here is
+ 
+
+ align:start position:0%
+well the distance here so this here is
+defined to be the maximum
+
+ align:start position:0%
+defined to be the maximum
+ 
+
+ align:start position:0%
+defined to be the maximum
+of so if you're looking at the if you're
+
+ align:start position:0%
+of so if you're looking at the if you're
+ 
+
+ align:start position:0%
+of so if you're looking at the if you're
+looking at f minus g if f is continuous.
+
+ align:start position:0%
+looking at f minus g if f is continuous.
+ 
+
+ align:start position:0%
+looking at f minus g if f is continuous.
+G is continuous. This here is
+
+ align:start position:0%
+G is continuous. This here is
+ 
+
+ align:start position:0%
+G is continuous. This here is
+continuous.
+
+ align:start position:0%
+continuous.
+ 
+
+ align:start position:0%
+continuous.
+Right? So this means that and now this
+
+ align:start position:0%
+Right? So this means that and now this
+ 
+
+ align:start position:0%
+Right? So this means that and now this
+is a continuous function defined on this
+
+ align:start position:0%
+is a continuous function defined on this
+ 
+
+ align:start position:0%
+is a continuous function defined on this
+interval.
+
+ align:start position:0%
+interval.
+ 
+
+ align:start position:0%
+interval.
+So the extreme value theorem say that
+
+ align:start position:0%
+So the extreme value theorem say that
+ 
+
+ align:start position:0%
+So the extreme value theorem say that
+the maximum
+
+ align:start position:0%
+the maximum
+ 
+
+ align:start position:0%
+the maximum
+in so this here is continuous and in
+
+ align:start position:0%
+in so this here is continuous and in
+ 
+
+ align:start position:0%
+in so this here is continuous and in
+fact even this here is continuous. So
+
+ align:start position:0%
+fact even this here is continuous. So
+ 
+
+ align:start position:0%
+fact even this here is continuous. So
+the maximum of this here is achieved.
+
+ align:start position:0%
+the maximum of this here is achieved.
+ 
+
+ align:start position:0%
+the maximum of this here is achieved.
+So this is the maximum
+
+ align:start position:0%
+So this is the maximum
+ 
+
+ align:start position:0%
+So this is the maximum
+where x is in 0 to one. So this is
+
+ align:start position:0%
+where x is in 0 to one. So this is
+ 
+
+ align:start position:0%
+where x is in 0 to one. So this is
+achieved right and this is clearly again
+
+ align:start position:0%
+achieved right and this is clearly again
+ 
+
+ align:start position:0%
+achieved right and this is clearly again
+symmetric because of the absolute value
+
+ align:start position:0%
+symmetric because of the absolute value
+ 
+
+ align:start position:0%
+symmetric because of the absolute value
+sign is clearly symmetric
+
+ align:start position:0%
+sign is clearly symmetric
+ 
+
+ align:start position:0%
+sign is clearly symmetric
+uh in terms of f and g. It's also clear
+
+ align:start position:0%
+uh in terms of f and g. It's also clear
+ 
+
+ align:start position:0%
+uh in terms of f and g. It's also clear
+that it's non- negative and it's also
+
+ align:start position:0%
+that it's non- negative and it's also
+ 
+
+ align:start position:0%
+that it's non- negative and it's also
+clear that it's zero if and only if the
+
+ align:start position:0%
+clear that it's zero if and only if the
+ 
+
+ align:start position:0%
+clear that it's zero if and only if the
+two functions are the same. And in this
+
+ align:start position:0%
+two functions are the same. And in this
+ 
+
+ align:start position:0%
+two functions are the same. And in this
+case it's quite easy to prove that uh
+
+ align:start position:0%
+case it's quite easy to prove that uh
+ 
+
+ align:start position:0%
+case it's quite easy to prove that uh
+that this is a um a metric.
+
+ align:start position:0%
+that this is a um a metric.
+ 
+
+ align:start position:0%
+that this is a um a metric.
+Okay. So maybe I'll just leave that.
+
+ align:start position:0%
+Okay. So maybe I'll just leave that.
+ 
+
+ align:start position:0%
+Okay. So maybe I'll just leave that.
+Okay. Now I want to give you a couple of
+
+ align:start position:0%
+Okay. Now I want to give you a couple of
+ 
+
+ align:start position:0%
+Okay. Now I want to give you a couple of
+more examples and then then I'll stop
+
+ align:start position:0%
+more examples and then then I'll stop
+ 
+
+ align:start position:0%
+more examples and then then I'll stop
+with examples and talk about I want to
+
+ align:start position:0%
+with examples and talk about I want to
+ 
+
+ align:start position:0%
+with examples and talk about I want to
+give you a couple of more examples. And
+
+ align:start position:0%
+give you a couple of more examples. And
+ 
+
+ align:start position:0%
+give you a couple of more examples. And
+the the two next examples
+
+ align:start position:0%
+the the two next examples
+ 
+
+ align:start position:0%
+the the two next examples
+are one is um
+
+ align:start position:0%
+are one is um
+ 
+
+ align:start position:0%
+are one is um
+one I mean so and the reason why I want
+
+ align:start position:0%
+one I mean so and the reason why I want
+ 
+
+ align:start position:0%
+one I mean so and the reason why I want
+to give you two other examples is that
+
+ align:start position:0%
+to give you two other examples is that
+ 
+
+ align:start position:0%
+to give you two other examples is that
+it's the I mean just so you know a lot
+
+ align:start position:0%
+it's the I mean just so you know a lot
+ 
+
+ align:start position:0%
+it's the I mean just so you know a lot
+of things about distances already and
+
+ align:start position:0%
+of things about distances already and
+ 
+
+ align:start position:0%
+of things about distances already and
+this give you excellent intuition to
+
+ align:start position:0%
+this give you excellent intuition to
+ 
+
+ align:start position:0%
+this give you excellent intuition to
+proving many things
+
+ align:start position:0%
+proving many things
+ 
+
+ align:start position:0%
+proving many things
+but you should just keep in mind that a
+
+ align:start position:0%
+but you should just keep in mind that a
+ 
+
+ align:start position:0%
+but you should just keep in mind that a
+metric space could be very wild. Okay,
+
+ align:start position:0%
+metric space could be very wild. Okay,
+ 
+
+ align:start position:0%
+metric space could be very wild. Okay,
+so I give you an example of some strange
+
+ align:start position:0%
+so I give you an example of some strange
+ 
+
+ align:start position:0%
+so I give you an example of some strange
+and directly wild metric spaces. So the
+
+ align:start position:0%
+and directly wild metric spaces. So the
+ 
+
+ align:start position:0%
+and directly wild metric spaces. So the
+first one is kind of a strange and then
+
+ align:start position:0%
+first one is kind of a strange and then
+ 
+
+ align:start position:0%
+first one is kind of a strange and then
+I'll give you another example which is
+
+ align:start position:0%
+I'll give you another example which is
+ 
+
+ align:start position:0%
+I'll give you another example which is
+which is wild. to the strange one to a
+
+ align:start position:0%
+which is wild. to the strange one to a
+ 
+
+ align:start position:0%
+which is wild. to the strange one to a
+strange example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so this is like if you're looking at
+
+ align:start position:0%
+And so this is like if you're looking at
+ 
+
+ align:start position:0%
+And so this is like if you're looking at
+the integers. So the space is now the
+
+ align:start position:0%
+the integers. So the space is now the
+ 
+
+ align:start position:0%
+the integers. So the space is now the
+integers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so you want to look at what is the
+
+ align:start position:0%
+And so you want to look at what is the
+ 
+
+ align:start position:0%
+And so you want to look at what is the
+distance between two integers. Right?
+
+ align:start position:0%
+distance between two integers. Right?
+ 
+
+ align:start position:0%
+distance between two integers. Right?
+Now of course your sort of intuition
+
+ align:start position:0%
+Now of course your sort of intuition
+ 
+
+ align:start position:0%
+Now of course your sort of intuition
+would say that if one dis one integer is
+
+ align:start position:0%
+would say that if one dis one integer is
+ 
+
+ align:start position:0%
+would say that if one dis one integer is
+really large and the other one is not
+
+ align:start position:0%
+really large and the other one is not
+ 
+
+ align:start position:0%
+really large and the other one is not
+very large you would think that the
+
+ align:start position:0%
+very large you would think that the
+ 
+
+ align:start position:0%
+very large you would think that the
+distance was large right but it doesn't
+
+ align:start position:0%
+distance was large right but it doesn't
+ 
+
+ align:start position:0%
+distance was large right but it doesn't
+have to be large so I defined this
+
+ align:start position:0%
+have to be large so I defined this
+ 
+
+ align:start position:0%
+have to be large so I defined this
+distance to be 1 / n minus one / m
+
+ align:start position:0%
+distance to be 1 / n minus one / m
+ 
+
+ align:start position:0%
+distance to be 1 / n minus one / m
+this here gives you so the absolute
+
+ align:start position:0%
+this here gives you so the absolute
+ 
+
+ align:start position:0%
+this here gives you so the absolute
+value of the difference of one over each
+
+ align:start position:0%
+value of the difference of one over each
+ 
+
+ align:start position:0%
+value of the difference of one over each
+of Um this here gives you a distance
+
+ align:start position:0%
+of Um this here gives you a distance
+ 
+
+ align:start position:0%
+of Um this here gives you a distance
+and and in particular um you see that if
+
+ align:start position:0%
+and and in particular um you see that if
+ 
+
+ align:start position:0%
+and and in particular um you see that if
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+N and M are really large then they are
+
+ align:start position:0%
+N and M are really large then they are
+ 
+
+ align:start position:0%
+N and M are really large then they are
+in this metric they're very close
+
+ align:start position:0%
+in this metric they're very close
+ 
+
+ align:start position:0%
+in this metric they're very close
+together right it looks like that the
+
+ align:start position:0%
+together right it looks like that the
+ 
+
+ align:start position:0%
+together right it looks like that the
+distance is very small
+
+ align:start position:0%
+distance is very small
+ 
+
+ align:start position:0%
+distance is very small
+now instead of actually proving that
+
+ align:start position:0%
+now instead of actually proving that
+ 
+
+ align:start position:0%
+now instead of actually proving that
+this thing here is so you could try to
+
+ align:start position:0%
+this thing here is so you could try to
+ 
+
+ align:start position:0%
+this thing here is so you could try to
+prove so I mean The as usual to prove
+
+ align:start position:0%
+prove so I mean The as usual to prove
+ 
+
+ align:start position:0%
+prove so I mean The as usual to prove
+that this is a metric the first and
+
+ align:start position:0%
+that this is a metric the first and
+ 
+
+ align:start position:0%
+that this is a metric the first and
+second property the property that is
+
+ align:start position:0%
+second property the property that is
+ 
+
+ align:start position:0%
+second property the property that is
+non- negative that's obvious. It's also
+
+ align:start position:0%
+non- negative that's obvious. It's also
+ 
+
+ align:start position:0%
+non- negative that's obvious. It's also
+obvious that is zero if and only if n
+
+ align:start position:0%
+obvious that is zero if and only if n
+ 
+
+ align:start position:0%
+obvious that is zero if and only if n
+and m are the same. It's also obvious
+
+ align:start position:0%
+and m are the same. It's also obvious
+ 
+
+ align:start position:0%
+and m are the same. It's also obvious
+that it's symmetric right the triangle
+
+ align:start position:0%
+that it's symmetric right the triangle
+ 
+
+ align:start position:0%
+that it's symmetric right the triangle
+equality might be not quite as obvious.
+
+ align:start position:0%
+equality might be not quite as obvious.
+ 
+
+ align:start position:0%
+equality might be not quite as obvious.
+It's not very hard in this case, but it
+
+ align:start position:0%
+It's not very hard in this case, but it
+ 
+
+ align:start position:0%
+It's not very hard in this case, but it
+actually is a triviality
+
+ align:start position:0%
+actually is a triviality
+ 
+
+ align:start position:0%
+actually is a triviality
+because you could think about this one
+
+ align:start position:0%
+because you could think about this one
+ 
+
+ align:start position:0%
+because you could think about this one
+here as a map.
+
+ align:start position:0%
+here as a map.
+ 
+
+ align:start position:0%
+here as a map.
+Suppose you take a map from the integers
+
+ align:start position:0%
+Suppose you take a map from the integers
+ 
+
+ align:start position:0%
+Suppose you take a map from the integers
+into the real numbers
+
+ align:start position:0%
+into the real numbers
+ 
+
+ align:start position:0%
+into the real numbers
+and the map is just that you take a the
+
+ align:start position:0%
+and the map is just that you take a the
+ 
+
+ align:start position:0%
+and the map is just that you take a the
+image of a integer. It's just one over
+
+ align:start position:0%
+image of a integer. It's just one over
+ 
+
+ align:start position:0%
+image of a integer. It's just one over
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+If you think about the usual distance
+
+ align:start position:0%
+If you think about the usual distance
+ 
+
+ align:start position:0%
+If you think about the usual distance
+over here, right? And so the usual
+
+ align:start position:0%
+over here, right? And so the usual
+ 
+
+ align:start position:0%
+over here, right? And so the usual
+distance by that I mean that the
+
+ align:start position:0%
+distance by that I mean that the
+ 
+
+ align:start position:0%
+distance by that I mean that the
+distance between X and Y is just this,
+
+ align:start position:0%
+distance between X and Y is just this,
+ 
+
+ align:start position:0%
+distance between X and Y is just this,
+right? If you think about this but now
+
+ align:start position:0%
+right? If you think about this but now
+ 
+
+ align:start position:0%
+right? If you think about this but now
+thinking about that sinks here that's
+
+ align:start position:0%
+thinking about that sinks here that's
+ 
+
+ align:start position:0%
+thinking about that sinks here that's
+that's and so you think about the usual
+
+ align:start position:0%
+that's and so you think about the usual
+ 
+
+ align:start position:0%
+that's and so you think about the usual
+distance but you're now restricted to
+
+ align:start position:0%
+distance but you're now restricted to
+ 
+
+ align:start position:0%
+distance but you're now restricted to
+everything not just all real numbers but
+
+ align:start position:0%
+everything not just all real numbers but
+ 
+
+ align:start position:0%
+everything not just all real numbers but
+just things that are one over integers
+
+ align:start position:0%
+just things that are one over integers
+ 
+
+ align:start position:0%
+just things that are one over integers
+right on that space it gives you a
+
+ align:start position:0%
+right on that space it gives you a
+ 
+
+ align:start position:0%
+right on that space it gives you a
+a metric okay and but then you can just
+
+ align:start position:0%
+a metric okay and but then you can just
+ 
+
+ align:start position:0%
+a metric okay and but then you can just
+think about that this gives you another
+
+ align:start position:0%
+think about that this gives you another
+ 
+
+ align:start position:0%
+think about that this gives you another
+way of labeling things. And so it's kind
+
+ align:start position:0%
+way of labeling things. And so it's kind
+ 
+
+ align:start position:0%
+way of labeling things. And so it's kind
+of a triviality that it is a metric
+
+ align:start position:0%
+of a triviality that it is a metric
+ 
+
+ align:start position:0%
+of a triviality that it is a metric
+space. But it but distances looks a
+
+ align:start position:0%
+space. But it but distances looks a
+ 
+
+ align:start position:0%
+space. But it but distances looks a
+little counterintuitive because right if
+
+ align:start position:0%
+little counterintuitive because right if
+ 
+
+ align:start position:0%
+little counterintuitive because right if
+you have two very large numbers then
+
+ align:start position:0%
+you have two very large numbers then
+ 
+
+ align:start position:0%
+you have two very large numbers then
+actually the distance between them is
+
+ align:start position:0%
+actually the distance between them is
+ 
+
+ align:start position:0%
+actually the distance between them is
+small even though those two large number
+
+ align:start position:0%
+small even though those two large number
+ 
+
+ align:start position:0%
+small even though those two large number
+could be very far apart. Okay. So the
+
+ align:start position:0%
+could be very far apart. Okay. So the
+ 
+
+ align:start position:0%
+could be very far apart. Okay. So the
+other thing the the last example I want
+
+ align:start position:0%
+other thing the the last example I want
+ 
+
+ align:start position:0%
+other thing the the last example I want
+to give you that's a kind of example of
+
+ align:start position:0%
+to give you that's a kind of example of
+ 
+
+ align:start position:0%
+to give you that's a kind of example of
+a wild metric
+
+ align:start position:0%
+a wild metric
+ 
+
+ align:start position:0%
+a wild metric
+and so this is
+
+ align:start position:0%
+and so this is
+ 
+
+ align:start position:0%
+and so this is
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is one
+
+ align:start position:0%
+this is one
+ 
+
+ align:start position:0%
+this is one
+vitamin and so essentially all of these
+
+ align:start position:0%
+vitamin and so essentially all of these
+ 
+
+ align:start position:0%
+vitamin and so essentially all of these
+occur naturally
+
+ align:start position:0%
+occur naturally
+ 
+
+ align:start position:0%
+occur naturally
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this example is what's called the
+
+ align:start position:0%
+and so this example is what's called the
+ 
+
+ align:start position:0%
+and so this example is what's called the
+French well metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Which is maybe not a super
+
+ align:start position:0%
+right? Which is maybe not a super
+ 
+
+ align:start position:0%
+right? Which is maybe not a super
+flattering name uh but probably
+
+ align:start position:0%
+flattering name uh but probably
+ 
+
+ align:start position:0%
+flattering name uh but probably
+accurate. So the thing is that if you
+
+ align:start position:0%
+accurate. So the thing is that if you
+ 
+
+ align:start position:0%
+accurate. So the thing is that if you
+travel in France, if you travel, so if
+
+ align:start position:0%
+travel in France, if you travel, so if
+ 
+
+ align:start position:0%
+travel in France, if you travel, so if
+you imagine that this sort of as France
+
+ align:start position:0%
+you imagine that this sort of as France
+ 
+
+ align:start position:0%
+you imagine that this sort of as France
+here, here you have Paris
+
+ align:start position:0%
+here, here you have Paris
+ 
+
+ align:start position:0%
+here, here you have Paris
+and if you want to go to
+
+ align:start position:0%
+and if you want to go to
+ 
+
+ align:start position:0%
+and if you want to go to
+the French Riviera, which is maybe down
+
+ align:start position:0%
+the French Riviera, which is maybe down
+ 
+
+ align:start position:0%
+the French Riviera, which is maybe down
+here. So, two cities on the French
+
+ align:start position:0%
+here. So, two cities on the French
+ 
+
+ align:start position:0%
+here. So, two cities on the French
+Riviera that are incredibly close
+
+ align:start position:0%
+Riviera that are incredibly close
+ 
+
+ align:start position:0%
+Riviera that are incredibly close
+together is K
+
+ align:start position:0%
+together is K
+ 
+
+ align:start position:0%
+together is K
+uh and Nice. This is Can and here you
+
+ align:start position:0%
+uh and Nice. This is Can and here you
+ 
+
+ align:start position:0%
+uh and Nice. This is Can and here you
+have Nice. They're very very close
+
+ align:start position:0%
+have Nice. They're very very close
+ 
+
+ align:start position:0%
+have Nice. They're very very close
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+But if you were going to go with the
+
+ align:start position:0%
+But if you were going to go with the
+ 
+
+ align:start position:0%
+But if you were going to go with the
+French railroad, then you would have to
+
+ align:start position:0%
+French railroad, then you would have to
+ 
+
+ align:start position:0%
+French railroad, then you would have to
+go to Paris first.
+
+ align:start position:0%
+go to Paris first.
+ 
+
+ align:start position:0%
+go to Paris first.
+I mean, so this here would take you
+
+ align:start position:0%
+I mean, so this here would take you
+ 
+
+ align:start position:0%
+I mean, so this here would take you
+maybe 20 minutes uh by train if there
+
+ align:start position:0%
+maybe 20 minutes uh by train if there
+ 
+
+ align:start position:0%
+maybe 20 minutes uh by train if there
+was a train, but you have to go to Paris
+
+ align:start position:0%
+was a train, but you have to go to Paris
+ 
+
+ align:start position:0%
+was a train, but you have to go to Paris
+first. And that's really far, right? I
+
+ align:start position:0%
+first. And that's really far, right? I
+ 
+
+ align:start position:0%
+first. And that's really far, right? I
+mean, the good thing is that the French
+
+ align:start position:0%
+mean, the good thing is that the French
+ 
+
+ align:start position:0%
+mean, the good thing is that the French
+have this TGB, which is this incredible
+
+ align:start position:0%
+have this TGB, which is this incredible
+ 
+
+ align:start position:0%
+have this TGB, which is this incredible
+fast train, but it still would take him
+
+ align:start position:0%
+fast train, but it still would take him
+ 
+
+ align:start position:0%
+fast train, but it still would take him
+many hours.
+
+ align:start position:0%
+many hours.
+ 
+
+ align:start position:0%
+many hours.
+Okay. And so that's the idea of the
+
+ align:start position:0%
+Okay. And so that's the idea of the
+ 
+
+ align:start position:0%
+Okay. And so that's the idea of the
+French railway metric that the space
+
+ align:start position:0%
+French railway metric that the space
+ 
+
+ align:start position:0%
+French railway metric that the space
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+is R2.
+
+ align:start position:0%
+is R2.
+ 
+
+ align:start position:0%
+is R2.
+And if you take two points X and Y in
+
+ align:start position:0%
+And if you take two points X and Y in
+ 
+
+ align:start position:0%
+And if you take two points X and Y in
+R2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now if then what is the distance between
+
+ align:start position:0%
+Now if then what is the distance between
+ 
+
+ align:start position:0%
+Now if then what is the distance between
+this this pair?
+
+ align:start position:0%
+this this pair?
+ 
+
+ align:start position:0%
+this this pair?
+So the distance between the pair is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the distance here is
+
+ align:start position:0%
+uh the distance here is
+ 
+
+ align:start position:0%
+uh the distance here is
+distance between x and y
+
+ align:start position:0%
+distance between x and y
+ 
+
+ align:start position:0%
+distance between x and y
+is um if
+
+ align:start position:0%
+is um if
+ 
+
+ align:start position:0%
+is um if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if x and y
+
+ align:start position:0%
+if x and y
+ 
+
+ align:start position:0%
+if x and y
+lie on the same. So imagine that this
+
+ align:start position:0%
+lie on the same. So imagine that this
+ 
+
+ align:start position:0%
+lie on the same. So imagine that this
+here is Paris
+
+ align:start position:0%
+here is Paris
+ 
+
+ align:start position:0%
+here is Paris
+and so just think about Paris as being
+
+ align:start position:0%
+and so just think about Paris as being
+ 
+
+ align:start position:0%
+and so just think about Paris as being
+the origin.
+
+ align:start position:0%
+the origin.
+ 
+
+ align:start position:0%
+the origin.
+So if X and Y lie on the same line, so
+
+ align:start position:0%
+So if X and Y lie on the same line, so
+ 
+
+ align:start position:0%
+So if X and Y lie on the same line, so
+lying on the same line just means that X
+
+ align:start position:0%
+lying on the same line just means that X
+ 
+
+ align:start position:0%
+lying on the same line just means that X
+here is equal to some constant, right?
+
+ align:start position:0%
+here is equal to some constant, right?
+ 
+
+ align:start position:0%
+here is equal to some constant, right?
+If this has Y,
+
+ align:start position:0%
+If this has Y,
+ 
+
+ align:start position:0%
+If this has Y,
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+X is like a constant times Y. Or you
+
+ align:start position:0%
+X is like a constant times Y. Or you
+ 
+
+ align:start position:0%
+X is like a constant times Y. Or you
+could have I mean if one of them was
+
+ align:start position:0%
+could have I mean if one of them was
+ 
+
+ align:start position:0%
+could have I mean if one of them was
+zero then you could have that y is equal
+
+ align:start position:0%
+zero then you could have that y is equal
+ 
+
+ align:start position:0%
+zero then you could have that y is equal
+to constant times x. So this just means
+
+ align:start position:0%
+to constant times x. So this just means
+ 
+
+ align:start position:0%
+to constant times x. So this just means
+that these x and y lie on the same line.
+
+ align:start position:0%
+that these x and y lie on the same line.
+ 
+
+ align:start position:0%
+that these x and y lie on the same line.
+Okay. So if they lie on the same line.
+
+ align:start position:0%
+Okay. So if they lie on the same line.
+ 
+
+ align:start position:0%
+Okay. So if they lie on the same line.
+So if x here is equal to
+
+ align:start position:0%
+So if x here is equal to
+ 
+
+ align:start position:0%
+So if x here is equal to
+c * y or y is equal to c * x for some uh
+
+ align:start position:0%
+c * y or y is equal to c * x for some uh
+ 
+
+ align:start position:0%
+c * y or y is equal to c * x for some uh
+real number.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If that's the case then it's just the
+
+ align:start position:0%
+If that's the case then it's just the
+ 
+
+ align:start position:0%
+If that's the case then it's just the
+the distance between them. It's just
+
+ align:start position:0%
+the distance between them. It's just
+ 
+
+ align:start position:0%
+the distance between them. It's just
+like this usual distance here right
+
+ align:start position:0%
+like this usual distance here right
+ 
+
+ align:start position:0%
+like this usual distance here right
+between them.
+
+ align:start position:0%
+between them.
+ 
+
+ align:start position:0%
+between them.
+But if they don't lie on the same line,
+
+ align:start position:0%
+But if they don't lie on the same line,
+ 
+
+ align:start position:0%
+But if they don't lie on the same line,
+they may lie on two lines that are very
+
+ align:start position:0%
+they may lie on two lines that are very
+ 
+
+ align:start position:0%
+they may lie on two lines that are very
+very close together.
+
+ align:start position:0%
+very close together.
+ 
+
+ align:start position:0%
+very close together.
+Then the distance here would be the sum
+
+ align:start position:0%
+Then the distance here would be the sum
+ 
+
+ align:start position:0%
+Then the distance here would be the sum
+of these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's a French word mic
+
+ align:start position:0%
+Okay. So that's a French word mic
+ 
+
+ align:start position:0%
+Okay. So that's a French word mic
+if I didn't have some sort of strange
+
+ align:start position:0%
+if I didn't have some sort of strange
+ 
+
+ align:start position:0%
+if I didn't have some sort of strange
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+some somewhat counterintuitive
+
+ align:start position:0%
+some somewhat counterintuitive
+ 
+
+ align:start position:0%
+some somewhat counterintuitive
+properties.
+
+ align:start position:0%
+properties.
+ 
+
+ align:start position:0%
+properties.
+Um the next thing I want to talk about
+
+ align:start position:0%
+Um the next thing I want to talk about
+ 
+
+ align:start position:0%
+Um the next thing I want to talk about
+is um is convergence in a metric space.
+
+ align:start position:0%
+is um is convergence in a metric space.
+ 
+
+ align:start position:0%
+is um is convergence in a metric space.
+So a lot of the things we have done
+
+ align:start position:0%
+So a lot of the things we have done
+ 
+
+ align:start position:0%
+So a lot of the things we have done
+generalizes to uh general metric spaces.
+
+ align:start position:0%
+generalizes to uh general metric spaces.
+ 
+
+ align:start position:0%
+generalizes to uh general metric spaces.
+So first let's talk about what is a
+
+ align:start position:0%
+So first let's talk about what is a
+ 
+
+ align:start position:0%
+So first let's talk about what is a
+sequence in a metric space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now you have a metric space here. So
+
+ align:start position:0%
+So now you have a metric space here. So
+ 
+
+ align:start position:0%
+So now you have a metric space here. So
+this is a metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a sequence xn is a sequence. So if
+
+ align:start position:0%
+and a sequence xn is a sequence. So if
+ 
+
+ align:start position:0%
+and a sequence xn is a sequence. So if
+you have a maybe I should say like
+
+ align:start position:0%
+you have a maybe I should say like
+ 
+
+ align:start position:0%
+you have a maybe I should say like
+before that if you take a map from the
+
+ align:start position:0%
+before that if you take a map from the
+ 
+
+ align:start position:0%
+before that if you take a map from the
+integers into X.
+
+ align:start position:0%
+integers into X.
+ 
+
+ align:start position:0%
+integers into X.
+This is is a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as before the image
+
+ align:start position:0%
+and as before the image
+ 
+
+ align:start position:0%
+and as before the image
+of a integer you would usually denote it
+
+ align:start position:0%
+of a integer you would usually denote it
+ 
+
+ align:start position:0%
+of a integer you would usually denote it
+like this. Right? So this is the same
+
+ align:start position:0%
+like this. Right? So this is the same
+ 
+
+ align:start position:0%
+like this. Right? So this is the same
+definition that we use for the wheel.
+
+ align:start position:0%
+definition that we use for the wheel.
+ 
+
+ align:start position:0%
+definition that we use for the wheel.
+So this is a sequence a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subsequence of a given sequence. Well,
+
+ align:start position:0%
+a subsequence of a given sequence. Well,
+ 
+
+ align:start position:0%
+a subsequence of a given sequence. Well,
+then then you have another map another
+
+ align:start position:0%
+then then you have another map another
+ 
+
+ align:start position:0%
+then then you have another map another
+map G from the integers into the
+
+ align:start position:0%
+map G from the integers into the
+ 
+
+ align:start position:0%
+map G from the integers into the
+integers and it's supposed to be
+
+ align:start position:0%
+integers and it's supposed to be
+ 
+
+ align:start position:0%
+integers and it's supposed to be
+strictly increasing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you're looking at f of g of n.
+
+ align:start position:0%
+And then you're looking at f of g of n.
+ 
+
+ align:start position:0%
+And then you're looking at f of g of n.
+And you think about this, you will
+
+ align:start position:0%
+And you think about this, you will
+ 
+
+ align:start position:0%
+And you think about this, you will
+typically write it like this. f of g of
+
+ align:start position:0%
+typically write it like this. f of g of
+ 
+
+ align:start position:0%
+typically write it like this. f of g of
+k say and you would typically write this
+
+ align:start position:0%
+k say and you would typically write this
+ 
+
+ align:start position:0%
+k say and you would typically write this
+as n k right this is a subsequences
+
+ align:start position:0%
+as n k right this is a subsequences
+ 
+
+ align:start position:0%
+as n k right this is a subsequences
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so it's just exactly like the way
+
+ align:start position:0%
+right so it's just exactly like the way
+ 
+
+ align:start position:0%
+right so it's just exactly like the way
+we define it for for the real numbers
+
+ align:start position:0%
+we define it for for the real numbers
+ 
+
+ align:start position:0%
+we define it for for the real numbers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a sequence is converging in a
+
+ align:start position:0%
+that a sequence is converging in a
+ 
+
+ align:start position:0%
+that a sequence is converging in a
+metric space that makes also sense
+
+ align:start position:0%
+metric space that makes also sense
+ 
+
+ align:start position:0%
+metric space that makes also sense
+So suppose that you have suppose that
+
+ align:start position:0%
+So suppose that you have suppose that
+ 
+
+ align:start position:0%
+So suppose that you have suppose that
+you now have a general metric space
+
+ align:start position:0%
+you now have a general metric space
+ 
+
+ align:start position:0%
+you now have a general metric space
+and xn is a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in x then we say that we say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that xn converts to x. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so x here is another element in x. If
+
+ align:start position:0%
+so x here is another element in x. If
+ 
+
+ align:start position:0%
+so x here is another element in x. If
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+uh epsilon greater than zero, there
+
+ align:start position:0%
+uh epsilon greater than zero, there
+ 
+
+ align:start position:0%
+uh epsilon greater than zero, there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist a capital n. So that if
+
+ align:start position:0%
+there exist a capital n. So that if
+ 
+
+ align:start position:0%
+there exist a capital n. So that if
+little n is bigger equal to capital n
+
+ align:start position:0%
+little n is bigger equal to capital n
+ 
+
+ align:start position:0%
+little n is bigger equal to capital n
+uh then the distance
+
+ align:start position:0%
+uh then the distance
+ 
+
+ align:start position:0%
+uh then the distance
+between xn and x is smaller than
+
+ align:start position:0%
+between xn and x is smaller than
+ 
+
+ align:start position:0%
+between xn and x is smaller than
+epsilon. This is what it means to
+
+ align:start position:0%
+epsilon. This is what it means to
+ 
+
+ align:start position:0%
+epsilon. This is what it means to
+converge.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now similarly
+
+ align:start position:0%
+Now similarly
+ 
+
+ align:start position:0%
+Now similarly
+the concept of big accusence
+
+ align:start position:0%
+the concept of big accusence
+ 
+
+ align:start position:0%
+the concept of big accusence
+this also extends to metric spaces. So
+
+ align:start position:0%
+this also extends to metric spaces. So
+ 
+
+ align:start position:0%
+this also extends to metric spaces. So
+accus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the following.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's a sequence. So, so a cruise
+
+ align:start position:0%
+So it's a sequence. So, so a cruise
+ 
+
+ align:start position:0%
+So it's a sequence. So, so a cruise
+sequence let's call it xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the following that for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all epsilon greater than zero there
+
+ align:start position:0%
+for all epsilon greater than zero there
+ 
+
+ align:start position:0%
+for all epsilon greater than zero there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital n such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if uh little m and little n are bigger
+
+ align:start position:0%
+if uh little m and little n are bigger
+ 
+
+ align:start position:0%
+if uh little m and little n are bigger
+than this capital n then the distance
+
+ align:start position:0%
+than this capital n then the distance
+ 
+
+ align:start position:0%
+than this capital n then the distance
+between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is smaller than epsilon. This is what it
+
+ align:start position:0%
+is smaller than epsilon. This is what it
+ 
+
+ align:start position:0%
+is smaller than epsilon. This is what it
+means to be a sequence. Okay.
+
+ align:start position:0%
+means to be a sequence. Okay.
+ 
+
+ align:start position:0%
+means to be a sequence. Okay.
+Now we have a theorem that is like the
+
+ align:start position:0%
+Now we have a theorem that is like the
+ 
+
+ align:start position:0%
+Now we have a theorem that is like the
+same theorem. The proof is like the same
+
+ align:start position:0%
+same theorem. The proof is like the same
+ 
+
+ align:start position:0%
+same theorem. The proof is like the same
+proof but we'll just go over it.
+
+ align:start position:0%
+proof but we'll just go over it.
+ 
+
+ align:start position:0%
+proof but we'll just go over it.
+So we have a theorem let's say that if
+
+ align:start position:0%
+So we have a theorem let's say that if
+ 
+
+ align:start position:0%
+So we have a theorem let's say that if
+you have a this theorem is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so again x comma d is a metric
+
+ align:start position:0%
+that so again x comma d is a metric
+ 
+
+ align:start position:0%
+that so again x comma d is a metric
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if
+
+ align:start position:0%
+and if
+ 
+
+ align:start position:0%
+and if
+XN
+
+ align:start position:0%
+XN
+ 
+
+ align:start position:0%
+XN
+is a convergent sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in X
+
+ align:start position:0%
+in X
+ 
+
+ align:start position:0%
+in X
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+XN is a cushy sequence is also
+
+ align:start position:0%
+XN is a cushy sequence is also
+ 
+
+ align:start position:0%
+XN is a cushy sequence is also
+accus C sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now, how do we prove this? So, the
+
+ align:start position:0%
+Okay. Now, how do we prove this? So, the
+ 
+
+ align:start position:0%
+Okay. Now, how do we prove this? So, the
+proof really is kind of the same as we
+
+ align:start position:0%
+proof really is kind of the same as we
+ 
+
+ align:start position:0%
+proof really is kind of the same as we
+did before. So, prove
+
+ align:start position:0%
+did before. So, prove
+ 
+
+ align:start position:0%
+did before. So, prove
+so we have that xn converge. Let's say
+
+ align:start position:0%
+so we have that xn converge. Let's say
+ 
+
+ align:start position:0%
+so we have that xn converge. Let's say
+that the limit is x.
+
+ align:start position:0%
+that the limit is x.
+ 
+
+ align:start position:0%
+that the limit is x.
+So this means that given
+
+ align:start position:0%
+So this means that given
+ 
+
+ align:start position:0%
+So this means that given
+given epsilon greater than zero there
+
+ align:start position:0%
+given epsilon greater than zero there
+ 
+
+ align:start position:0%
+given epsilon greater than zero there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital n such that
+
+ align:start position:0%
+capital n such that
+ 
+
+ align:start position:0%
+capital n such that
+if little n is bigger equal to capital n
+
+ align:start position:0%
+if little n is bigger equal to capital n
+ 
+
+ align:start position:0%
+if little n is bigger equal to capital n
+then the distance here
+
+ align:start position:0%
+then the distance here
+ 
+
+ align:start position:0%
+then the distance here
+and I'm using now in a definition of
+
+ align:start position:0%
+and I'm using now in a definition of
+ 
+
+ align:start position:0%
+and I'm using now in a definition of
+convergence I'm using not epsilon But
+
+ align:start position:0%
+convergence I'm using not epsilon But
+ 
+
+ align:start position:0%
+convergence I'm using not epsilon But
+epsilon / two, right? So I have that,
+
+ align:start position:0%
+epsilon / two, right? So I have that,
+ 
+
+ align:start position:0%
+epsilon / two, right? So I have that,
+right? But this means that if you take
+
+ align:start position:0%
+right? But this means that if you take
+ 
+
+ align:start position:0%
+right? But this means that if you take
+therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if little M and little M if they're both
+
+ align:start position:0%
+if little M and little M if they're both
+ 
+
+ align:start position:0%
+if little M and little M if they're both
+bigger than capital N and you're now
+
+ align:start position:0%
+bigger than capital N and you're now
+ 
+
+ align:start position:0%
+bigger than capital N and you're now
+looking at the distance from X M to XN.
+
+ align:start position:0%
+looking at the distance from X M to XN.
+ 
+
+ align:start position:0%
+looking at the distance from X M to XN.
+Well, by the triangle inequality, this
+
+ align:start position:0%
+Well, by the triangle inequality, this
+ 
+
+ align:start position:0%
+Well, by the triangle inequality, this
+thing here, it's it's worse or it's
+
+ align:start position:0%
+thing here, it's it's worse or it's
+ 
+
+ align:start position:0%
+thing here, it's it's worse or it's
+certainly not better if you go over this
+
+ align:start position:0%
+certainly not better if you go over this
+ 
+
+ align:start position:0%
+certainly not better if you go over this
+other point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But you see this one here and this one
+
+ align:start position:0%
+But you see this one here and this one
+ 
+
+ align:start position:0%
+But you see this one here and this one
+each of them is smaller than epsilon
+
+ align:start position:0%
+each of them is smaller than epsilon
+ 
+
+ align:start position:0%
+each of them is smaller than epsilon
+over two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this thing here is so the difference
+
+ align:start position:0%
+So this thing here is so the difference
+ 
+
+ align:start position:0%
+So this thing here is so the difference
+here is bounded by epsilon as it should
+
+ align:start position:0%
+here is bounded by epsilon as it should
+ 
+
+ align:start position:0%
+here is bounded by epsilon as it should
+be. So this proved that if you take a
+
+ align:start position:0%
+be. So this proved that if you take a
+ 
+
+ align:start position:0%
+be. So this proved that if you take a
+convergence sequence then it is a cushy
+
+ align:start position:0%
+convergence sequence then it is a cushy
+ 
+
+ align:start position:0%
+convergence sequence then it is a cushy
+sequence. Remember that cushi
+
+ align:start position:0%
+sequence. Remember that cushi
+ 
+
+ align:start position:0%
+sequence. Remember that cushi
+convergence theorem was saying that in
+
+ align:start position:0%
+convergence theorem was saying that in
+ 
+
+ align:start position:0%
+convergence theorem was saying that in
+Rh if you have a cushi sequence
+
+ align:start position:0%
+Rh if you have a cushi sequence
+ 
+
+ align:start position:0%
+Rh if you have a cushi sequence
+then it was also convergent right but
+
+ align:start position:0%
+then it was also convergent right but
+ 
+
+ align:start position:0%
+then it was also convergent right but
+that actually fails this is not true and
+
+ align:start position:0%
+that actually fails this is not true and
+ 
+
+ align:start position:0%
+that actually fails this is not true and
+it's like some important property of a
+
+ align:start position:0%
+it's like some important property of a
+ 
+
+ align:start position:0%
+it's like some important property of a
+metric space if it has the cush
+
+ align:start position:0%
+metric space if it has the cush
+ 
+
+ align:start position:0%
+metric space if it has the cush
+convergence property so let me give you
+
+ align:start position:0%
+convergence property so let me give you
+ 
+
+ align:start position:0%
+convergence property so let me give you
+a very simple example
+
+ align:start position:0%
+a very simple example
+ 
+
+ align:start position:0%
+a very simple example
+so suppose
+
+ align:start position:0%
+so suppose
+ 
+
+ align:start position:0%
+so suppose
+that your metric space. So the space
+
+ align:start position:0%
+that your metric space. So the space
+ 
+
+ align:start position:0%
+that your metric space. So the space
+here,
+
+ align:start position:0%
+here,
+ 
+
+ align:start position:0%
+here,
+let's just take the interval
+
+ align:start position:0%
+let's just take the interval
+ 
+
+ align:start position:0%
+let's just take the interval
+from 0 to one. And what is the distance
+
+ align:start position:0%
+from 0 to one. And what is the distance
+ 
+
+ align:start position:0%
+from 0 to one. And what is the distance
+between two elements? So x and y
+
+ align:start position:0%
+between two elements? So x and y
+ 
+
+ align:start position:0%
+between two elements? So x and y
+are in this interval from 0 to one.
+
+ align:start position:0%
+are in this interval from 0 to one.
+ 
+
+ align:start position:0%
+are in this interval from 0 to one.
+What is the distance? I just take the
+
+ align:start position:0%
+What is the distance? I just take the
+ 
+
+ align:start position:0%
+What is the distance? I just take the
+usual distance,
+
+ align:start position:0%
+usual distance,
+ 
+
+ align:start position:0%
+usual distance,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+But now if I'm looking at this sequence
+
+ align:start position:0%
+But now if I'm looking at this sequence
+ 
+
+ align:start position:0%
+But now if I'm looking at this sequence
+here xn which is 1 / n right this thing
+
+ align:start position:0%
+here xn which is 1 / n right this thing
+ 
+
+ align:start position:0%
+here xn which is 1 / n right this thing
+here is a cushy sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It is a cushy sequence. Right.
+
+ align:start position:0%
+It is a cushy sequence. Right.
+ 
+
+ align:start position:0%
+It is a cushy sequence. Right.
+Right. Because when n and n are really
+
+ align:start position:0%
+Right. Because when n and n are really
+ 
+
+ align:start position:0%
+Right. Because when n and n are really
+large then both of them is close to this
+
+ align:start position:0%
+large then both of them is close to this
+ 
+
+ align:start position:0%
+large then both of them is close to this
+end point right but they don't converge
+
+ align:start position:0%
+end point right but they don't converge
+ 
+
+ align:start position:0%
+end point right but they don't converge
+because they in the larger space are
+
+ align:start position:0%
+because they in the larger space are
+ 
+
+ align:start position:0%
+because they in the larger space are
+they converge to zero but zero is not
+
+ align:start position:0%
+they converge to zero but zero is not
+ 
+
+ align:start position:0%
+they converge to zero but zero is not
+part of the space so they don't converge
+
+ align:start position:0%
+part of the space so they don't converge
+ 
+
+ align:start position:0%
+part of the space so they don't converge
+to anything in this space right so this
+
+ align:start position:0%
+to anything in this space right so this
+ 
+
+ align:start position:0%
+to anything in this space right so this
+is an example so this is an example so
+
+ align:start position:0%
+is an example so this is an example so
+ 
+
+ align:start position:0%
+is an example so this is an example so
+so it's a sequence but
+
+ align:start position:0%
+so it's a sequence but
+ 
+
+ align:start position:0%
+so it's a sequence but
+XN does not converge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in x
+
+ align:start position:0%
+in x
+ 
+
+ align:start position:0%
+in x
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+This is because zero is not part of this
+
+ align:start position:0%
+This is because zero is not part of this
+ 
+
+ align:start position:0%
+This is because zero is not part of this
+interval,
+
+ align:start position:0%
+interval,
+ 
+
+ align:start position:0%
+interval,
+right? And zero would have to be the
+
+ align:start position:0%
+right? And zero would have to be the
+ 
+
+ align:start position:0%
+right? And zero would have to be the
+limit. Yeah. Is that the only
+
+ align:start position:0%
+limit. Yeah. Is that the only
+ 
+
+ align:start position:0%
+limit. Yeah. Is that the only
+>> No, no, this but this is this does
+
+ align:start position:0%
+>> No, no, this but this is this does
+ 
+
+ align:start position:0%
+>> No, no, this but this is this does
+provide an important example of counter
+
+ align:start position:0%
+provide an important example of counter
+ 
+
+ align:start position:0%
+provide an important example of counter
+examples because then it becomes like a
+
+ align:start position:0%
+examples because then it becomes like a
+ 
+
+ align:start position:0%
+examples because then it becomes like a
+question can you make the space cushy
+
+ align:start position:0%
+question can you make the space cushy
+ 
+
+ align:start position:0%
+question can you make the space cushy
+complete okay and sometimes you can
+
+ align:start position:0%
+complete okay and sometimes you can
+ 
+
+ align:start position:0%
+complete okay and sometimes you can
+sometimes you can't so but it's that's a
+
+ align:start position:0%
+sometimes you can't so but it's that's a
+ 
+
+ align:start position:0%
+sometimes you can't so but it's that's a
+good question and and but it is I mean
+
+ align:start position:0%
+good question and and but it is I mean
+ 
+
+ align:start position:0%
+good question and and but it is I mean
+it seems utterly trivial example but
+
+ align:start position:0%
+it seems utterly trivial example but
+ 
+
+ align:start position:0%
+it seems utterly trivial example but
+it's not I mean it is kind of I mean it
+
+ align:start position:0%
+it's not I mean it is kind of I mean it
+ 
+
+ align:start position:0%
+it's not I mean it is kind of I mean it
+does show you this sort of important
+
+ align:start position:0%
+does show you this sort of important
+ 
+
+ align:start position:0%
+does show you this sort of important
+part that you uh that is useful. It's
+
+ align:start position:0%
+part that you uh that is useful. It's
+ 
+
+ align:start position:0%
+part that you uh that is useful. It's
+often useful to have the kushik
+
+ align:start position:0%
+often useful to have the kushik
+ 
+
+ align:start position:0%
+often useful to have the kushik
+convergence property and so can you
+
+ align:start position:0%
+convergence property and so can you
+ 
+
+ align:start position:0%
+convergence property and so can you
+enlarge the space to to get that
+
+ align:start position:0%
+enlarge the space to to get that
+ 
+
+ align:start position:0%
+enlarge the space to to get that
+property.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um okay
+
+ align:start position:0%
+Um okay
+ 
+
+ align:start position:0%
+Um okay
+uh let's
+
+ align:start position:0%
+uh let's
+ 
+
+ align:start position:0%
+uh let's
+talk about uh what it means for a
+
+ align:start position:0%
+talk about uh what it means for a
+ 
+
+ align:start position:0%
+talk about uh what it means for a
+function to be continuous also.
+
+ align:start position:0%
+function to be continuous also.
+ 
+
+ align:start position:0%
+function to be continuous also.
+So uh and now so now I want to
+
+ align:start position:0%
+So uh and now so now I want to
+ 
+
+ align:start position:0%
+So uh and now so now I want to
+now I want to think about so I have a
+
+ align:start position:0%
+now I want to think about so I have a
+ 
+
+ align:start position:0%
+now I want to think about so I have a
+so I want to think about continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for general metric spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one can do this even more generally
+
+ align:start position:0%
+and one can do this even more generally
+ 
+
+ align:start position:0%
+and one can do this even more generally
+but let me settle on something sort of
+
+ align:start position:0%
+but let me settle on something sort of
+ 
+
+ align:start position:0%
+but let me settle on something sort of
+in between something more general and
+
+ align:start position:0%
+in between something more general and
+ 
+
+ align:start position:0%
+in between something more general and
+and what we already have.
+
+ align:start position:0%
+and what we already have.
+ 
+
+ align:start position:0%
+and what we already have.
+So I have a metric space here
+
+ align:start position:0%
+So I have a metric space here
+ 
+
+ align:start position:0%
+So I have a metric space here
+and I'm thinking about that I have a map
+
+ align:start position:0%
+and I'm thinking about that I have a map
+ 
+
+ align:start position:0%
+and I'm thinking about that I have a map
+from this space into R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I I want to and so what does it
+
+ align:start position:0%
+and then I I want to and so what does it
+ 
+
+ align:start position:0%
+and then I I want to and so what does it
+mean for this function here to be
+
+ align:start position:0%
+mean for this function here to be
+ 
+
+ align:start position:0%
+mean for this function here to be
+continuous? So f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at some point x0
+
+ align:start position:0%
+at some point x0
+ 
+
+ align:start position:0%
+at some point x0
+in this space.
+
+ align:start position:0%
+in this space.
+ 
+
+ align:start position:0%
+in this space.
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+epsilon greater than zero they exist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They're also greater than zero. So that
+
+ align:start position:0%
+They're also greater than zero. So that
+ 
+
+ align:start position:0%
+They're also greater than zero. So that
+if the distance between X and this X0
+
+ align:start position:0%
+if the distance between X and this X0
+ 
+
+ align:start position:0%
+if the distance between X and this X0
+is smaller than delta
+
+ align:start position:0%
+is smaller than delta
+ 
+
+ align:start position:0%
+is smaller than delta
+then their images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is epsilon close together. Okay. So you
+
+ align:start position:0%
+is epsilon close together. Okay. So you
+ 
+
+ align:start position:0%
+is epsilon close together. Okay. So you
+see this is kind of like you know this
+
+ align:start position:0%
+see this is kind of like you know this
+ 
+
+ align:start position:0%
+see this is kind of like you know this
+is like a kind of obvious generalization
+
+ align:start position:0%
+is like a kind of obvious generalization
+ 
+
+ align:start position:0%
+is like a kind of obvious generalization
+of how we defined continuity at a point
+
+ align:start position:0%
+of how we defined continuity at a point
+ 
+
+ align:start position:0%
+of how we defined continuity at a point
+for when x was part of r. And so of
+
+ align:start position:0%
+for when x was part of r. And so of
+ 
+
+ align:start position:0%
+for when x was part of r. And so of
+course the function is so this is a
+
+ align:start position:0%
+course the function is so this is a
+ 
+
+ align:start position:0%
+course the function is so this is a
+continuous in a point and so f is set to
+
+ align:start position:0%
+continuous in a point and so f is set to
+ 
+
+ align:start position:0%
+continuous in a point and so f is set to
+be continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh at all points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this is what it means for a
+
+ align:start position:0%
+Okay. So this is what it means for a
+ 
+
+ align:start position:0%
+Okay. So this is what it means for a
+function to be continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um okay. Now
+
+ align:start position:0%
+Um okay. Now
+ 
+
+ align:start position:0%
+Um okay. Now
+uh let's just let me just give you an
+
+ align:start position:0%
+uh let's just let me just give you an
+ 
+
+ align:start position:0%
+uh let's just let me just give you an
+example of something like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So remember before we looked at the
+
+ align:start position:0%
+So remember before we looked at the
+ 
+
+ align:start position:0%
+So remember before we looked at the
+continuous functions. So we looked at
+
+ align:start position:0%
+continuous functions. So we looked at
+ 
+
+ align:start position:0%
+continuous functions. So we looked at
+where the space was the continuous
+
+ align:start position:0%
+where the space was the continuous
+ 
+
+ align:start position:0%
+where the space was the continuous
+function on the interval from 0 to one
+
+ align:start position:0%
+function on the interval from 0 to one
+ 
+
+ align:start position:0%
+function on the interval from 0 to one
+and we said that the distance between
+
+ align:start position:0%
+and we said that the distance between
+ 
+
+ align:start position:0%
+and we said that the distance between
+two continuous functions defined on the
+
+ align:start position:0%
+two continuous functions defined on the
+ 
+
+ align:start position:0%
+two continuous functions defined on the
+interval this thing here is um is the
+
+ align:start position:0%
+interval this thing here is um is the
+ 
+
+ align:start position:0%
+interval this thing here is um is the
+max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the differences here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+And that was that's quite easy to see,
+
+ align:start position:0%
+And that was that's quite easy to see,
+ 
+
+ align:start position:0%
+And that was that's quite easy to see,
+but it's a good exercise to do. It's
+
+ align:start position:0%
+but it's a good exercise to do. It's
+ 
+
+ align:start position:0%
+but it's a good exercise to do. It's
+quite easy to see that this is a metric.
+
+ align:start position:0%
+quite easy to see that this is a metric.
+ 
+
+ align:start position:0%
+quite easy to see that this is a metric.
+Now I can so I have so this is a metric
+
+ align:start position:0%
+Now I can so I have so this is a metric
+ 
+
+ align:start position:0%
+Now I can so I have so this is a metric
+space. So now I can think about so now
+
+ align:start position:0%
+space. So now I can think about so now
+ 
+
+ align:start position:0%
+space. So now I can think about so now
+here's an example of a function. This is
+
+ align:start position:0%
+here's an example of a function. This is
+ 
+
+ align:start position:0%
+here's an example of a function. This is
+a function that
+
+ align:start position:0%
+a function that
+ 
+
+ align:start position:0%
+a function that
+is like evaluating. So, so now you see
+
+ align:start position:0%
+is like evaluating. So, so now you see
+ 
+
+ align:start position:0%
+is like evaluating. So, so now you see
+this getting a little bit abstract
+
+ align:start position:0%
+this getting a little bit abstract
+ 
+
+ align:start position:0%
+this getting a little bit abstract
+because now I'm thinking about a
+
+ align:start position:0%
+because now I'm thinking about a
+ 
+
+ align:start position:0%
+because now I'm thinking about a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+on so I now looking at the function
+
+ align:start position:0%
+on so I now looking at the function
+ 
+
+ align:start position:0%
+on so I now looking at the function
+so from x into r
+
+ align:start position:0%
+so from x into r
+ 
+
+ align:start position:0%
+so from x into r
+but in this case x here is a space of
+
+ align:start position:0%
+but in this case x here is a space of
+ 
+
+ align:start position:0%
+but in this case x here is a space of
+continuous function on the interval.
+
+ align:start position:0%
+continuous function on the interval.
+ 
+
+ align:start position:0%
+continuous function on the interval.
+Okay. So what should be my So my
+
+ align:start position:0%
+Okay. So what should be my So my
+ 
+
+ align:start position:0%
+Okay. So what should be my So my
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is now supposed to be defined on a
+
+ align:start position:0%
+is now supposed to be defined on a
+ 
+
+ align:start position:0%
+is now supposed to be defined on a
+continuous function, right? And I just
+
+ align:start position:0%
+continuous function, right? And I just
+ 
+
+ align:start position:0%
+continuous function, right? And I just
+take it to be equal to the value of this
+
+ align:start position:0%
+take it to be equal to the value of this
+ 
+
+ align:start position:0%
+take it to be equal to the value of this
+continuous function at the initial end
+
+ align:start position:0%
+continuous function at the initial end
+ 
+
+ align:start position:0%
+continuous function at the initial end
+point initial point in the interval.
+
+ align:start position:0%
+point initial point in the interval.
+ 
+
+ align:start position:0%
+point initial point in the interval.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I claim that this function here so
+
+ align:start position:0%
+And I claim that this function here so
+ 
+
+ align:start position:0%
+And I claim that this function here so
+so the claim is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this capital f is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so again it's it's it's it's like
+
+ align:start position:0%
+So, so again it's it's it's it's like
+ 
+
+ align:start position:0%
+So, so again it's it's it's it's like
+continuous in this sense that you have
+
+ align:start position:0%
+continuous in this sense that you have
+ 
+
+ align:start position:0%
+continuous in this sense that you have
+this general metric space and this here
+
+ align:start position:0%
+this general metric space and this here
+ 
+
+ align:start position:0%
+this general metric space and this here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+sort of just so that it lines up with
+
+ align:start position:0%
+sort of just so that it lines up with
+ 
+
+ align:start position:0%
+sort of just so that it lines up with
+with u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the example.
+
+ align:start position:0%
+with the example.
+ 
+
+ align:start position:0%
+with the example.
+So we have this general metric space and
+
+ align:start position:0%
+So we have this general metric space and
+ 
+
+ align:start position:0%
+So we have this general metric space and
+we have now a map from this general
+
+ align:start position:0%
+we have now a map from this general
+ 
+
+ align:start position:0%
+we have now a map from this general
+metric space into R. This is definitely
+
+ align:start position:0%
+metric space into R. This is definitely
+ 
+
+ align:start position:0%
+metric space into R. This is definitely
+a map from this general metric space
+
+ align:start position:0%
+a map from this general metric space
+ 
+
+ align:start position:0%
+a map from this general metric space
+into R. Right?
+
+ align:start position:0%
+into R. Right?
+ 
+
+ align:start position:0%
+into R. Right?
+And I claim that this is continuous in
+
+ align:start position:0%
+And I claim that this is continuous in
+ 
+
+ align:start position:0%
+And I claim that this is continuous in
+this sense here. Okay. And uh and that's
+
+ align:start position:0%
+this sense here. Okay. And uh and that's
+ 
+
+ align:start position:0%
+this sense here. Okay. And uh and that's
+also quite easy to prove. And let me
+
+ align:start position:0%
+also quite easy to prove. And let me
+ 
+
+ align:start position:0%
+also quite easy to prove. And let me
+just give you uh so let me just make one
+
+ align:start position:0%
+just give you uh so let me just make one
+ 
+
+ align:start position:0%
+just give you uh so let me just make one
+observation.
+
+ align:start position:0%
+observation.
+ 
+
+ align:start position:0%
+observation.
+that if I'm looking at this thing here,
+
+ align:start position:0%
+that if I'm looking at this thing here,
+ 
+
+ align:start position:0%
+that if I'm looking at this thing here,
+so this is the image or under this map
+
+ align:start position:0%
+so this is the image or under this map
+ 
+
+ align:start position:0%
+so this is the image or under this map
+in one continuous function and then I
+
+ align:start position:0%
+in one continuous function and then I
+ 
+
+ align:start position:0%
+in one continuous function and then I
+subtract the image in another continuous
+
+ align:start position:0%
+subtract the image in another continuous
+ 
+
+ align:start position:0%
+subtract the image in another continuous
+function and now I'm looking at this
+
+ align:start position:0%
+function and now I'm looking at this
+ 
+
+ align:start position:0%
+function and now I'm looking at this
+difference here.
+
+ align:start position:0%
+difference here.
+ 
+
+ align:start position:0%
+difference here.
+But this thing here is nothing but f of
+
+ align:start position:0%
+But this thing here is nothing but f of
+ 
+
+ align:start position:0%
+But this thing here is nothing but f of
+zero and this is nothing but g of zero.
+
+ align:start position:0%
+zero and this is nothing but g of zero.
+ 
+
+ align:start position:0%
+zero and this is nothing but g of zero.
+Right? But you see that this is
+
+ align:start position:0%
+Right? But you see that this is
+ 
+
+ align:start position:0%
+Right? But you see that this is
+obviously less or equal to the maximum
+
+ align:start position:0%
+obviously less or equal to the maximum
+ 
+
+ align:start position:0%
+obviously less or equal to the maximum
+of all x in this interval
+
+ align:start position:0%
+of all x in this interval
+ 
+
+ align:start position:0%
+of all x in this interval
+of f ofx minus g of x.
+
+ align:start position:0%
+of f ofx minus g of x.
+ 
+
+ align:start position:0%
+of f ofx minus g of x.
+Right? Like that. But that is the
+
+ align:start position:0%
+Right? Like that. But that is the
+ 
+
+ align:start position:0%
+Right? Like that. But that is the
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+between these two elements of this
+
+ align:start position:0%
+between these two elements of this
+ 
+
+ align:start position:0%
+between these two elements of this
+general metric space. Right? And so you
+
+ align:start position:0%
+general metric space. Right? And so you
+ 
+
+ align:start position:0%
+general metric space. Right? And so you
+see that you see that this here is an
+
+ align:start position:0%
+see that you see that this here is an
+ 
+
+ align:start position:0%
+see that you see that this here is an
+example with that if you so for given
+
+ align:start position:0%
+example with that if you so for given
+ 
+
+ align:start position:0%
+example with that if you so for given
+epsilon I'm going to pick delta equal to
+
+ align:start position:0%
+epsilon I'm going to pick delta equal to
+ 
+
+ align:start position:0%
+epsilon I'm going to pick delta equal to
+that epsilon because if these guys here
+
+ align:start position:0%
+that epsilon because if these guys here
+ 
+
+ align:start position:0%
+that epsilon because if these guys here
+are now epsilon close by this inequality
+
+ align:start position:0%
+are now epsilon close by this inequality
+ 
+
+ align:start position:0%
+are now epsilon close by this inequality
+their images is also epsilon close right
+
+ align:start position:0%
+their images is also epsilon close right
+ 
+
+ align:start position:0%
+their images is also epsilon close right
+so so this map is clearly continuous
+
+ align:start position:0%
+so so this map is clearly continuous
+ 
+
+ align:start position:0%
+so so this map is clearly continuous
+okay so I'll stop here so there's a
+
+ align:start position:0%
+okay so I'll stop here so there's a
+ 
+
+ align:start position:0%
+okay so I'll stop here so there's a
+little lema in the note that we didn't
+
+ align:start position:0%
+little lema in the note that we didn't
+ 
+
+ align:start position:0%
+little lema in the note that we didn't
+go through and that lema is just the
+
+ align:start position:0%
+go through and that lema is just the
+ 
+
+ align:start position:0%
+go through and that lema is just the
+lema that I had over here that if I had
+
+ align:start position:0%
+lema that I had over here that if I had
+ 
+
+ align:start position:0%
+lema that I had over here that if I had
+a a continuous function and I have a
+
+ align:start position:0%
+a a continuous function and I have a
+ 
+
+ align:start position:0%
+a a continuous function and I have a
+sequence that converge to a limit then I
+
+ align:start position:0%
+sequence that converge to a limit then I
+ 
+
+ align:start position:0%
+sequence that converge to a limit then I
+could exchange the order of limits and
+
+ align:start position:0%
+could exchange the order of limits and
+ 
+
+ align:start position:0%
+could exchange the order of limits and
+the same proof works in a general metric
+
+ align:start position:0%
+the same proof works in a general metric
+ 
+
+ align:start position:0%
+the same proof works in a general metric
+space. Okay.
+
+ align:start position:0%
+space. Okay.
+ 
+
+ align:start position:0%
+space. Okay.
+>> Okay. Great.
+
+ align:start position:0%
+>> Okay. Great.
+ 
+
+ align:start position:0%
+>> Okay. Great.
+>> Yep.
+
+ align:start position:0%
+>> Yep.
+ 
+
+ align:start position:0%
+>> Yep.
+>> What kind of properties do you need to
+
+ align:start position:0%
+>> What kind of properties do you need to
+ 
+
+ align:start position:0%
+>> What kind of properties do you need to
+kind of like
+
+ align:start position:0%
+kind of like
+ 
+
+ align:start position:0%
+kind of like
+space like
+
+ align:start position:0%
+space like
+ 
+
+ align:start position:0%
+space like
+some kind of like closure under
+
+ align:start position:0%
+some kind of like closure under
+ 
+
+ align:start position:0%
+some kind of like closure under
+>> Yeah. Yeah. Right. That's right. I mean,
+
+ align:start position:0%
+>> Yeah. Yeah. Right. That's right. I mean,
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Right. That's right. I mean,
+so addition, right, is something about a
+
+ align:start position:0%
+so addition, right, is something about a
+ 
+
+ align:start position:0%
+so addition, right, is something about a
+field, right? And so in for these
+
+ align:start position:0%
+field, right? And so in for these
+ 
+
+ align:start position:0%
+field, right? And so in for these
+spaces, I mean, you know, most of the
+
+ align:start position:0%
+spaces, I mean, you know, most of the
+ 
+
+ align:start position:0%
+spaces, I mean, you know, most of the
+things I looked at here, I mean, some of
+
+ align:start position:0%
+things I looked at here, I mean, some of
+ 
+
+ align:start position:0%
+things I looked at here, I mean, some of
+it does. I mean, like the continuous
+
+ align:start position:0%
+it does. I mean, like the continuous
+ 
+
+ align:start position:0%
+it does. I mean, like the continuous
+function has some structure. The space
+
+ align:start position:0%
+function has some structure. The space
+ 
+
+ align:start position:0%
+function has some structure. The space
+of continuous function has some
+
+ align:start position:0%
+of continuous function has some
+ 
+
+ align:start position:0%
+of continuous function has some
+structure. It's not exactly a field, but
+
+ align:start position:0%
+structure. It's not exactly a field, but
+ 
+
+ align:start position:0%
+structure. It's not exactly a field, but
+it has some of those properties, some of
+
+ align:start position:0%
+it has some of those properties, some of
+ 
+
+ align:start position:0%
+it has some of those properties, some of
+these algebra. It's like a a important
+
+ align:start position:0%
+these algebra. It's like a a important
+ 
+
+ align:start position:0%
+these algebra. It's like a a important
+example of something called a sea star
+
+ align:start position:0%
+example of something called a sea star
+ 
+
+ align:start position:0%
+example of something called a sea star
+of algebra. So it's have this algebraic
+
+ align:start position:0%
+of algebra. So it's have this algebraic
+ 
+
+ align:start position:0%
+of algebra. So it's have this algebraic
+structure.
+
+ align:start position:0%
+structure.
+ 
+
+ align:start position:0%
+structure.
+Um but but it's not the algebraic
+
+ align:start position:0%
+Um but but it's not the algebraic
+ 
+
+ align:start position:0%
+Um but but it's not the algebraic
+structure you need in order to be
+
+ align:start position:0%
+structure you need in order to be
+ 
+
+ align:start position:0%
+structure you need in order to be
+completeness, right? It's not that.
+
+ align:start position:0%
+completeness, right? It's not that.
+ 
+
+ align:start position:0%
+completeness, right? It's not that.
+Yeah. And and it's like but it and and
+
+ align:start position:0%
+Yeah. And and it's like but it and and
+ 
+
+ align:start position:0%
+Yeah. And and it's like but it and and
+yeah um I think it's sort of taken us a
+
+ align:start position:0%
+yeah um I think it's sort of taken us a
+ 
+
+ align:start position:0%
+yeah um I think it's sort of taken us a
+little bit far field but it's the same.
+
+ align:start position:0%
+little bit far field but it's the same.
+ 
+
+ align:start position:0%
+little bit far field but it's the same.
+You see this sort of property also in uh
+
+ align:start position:0%
+You see this sort of property also in uh
+ 
+
+ align:start position:0%
+You see this sort of property also in uh
+in you see it so the these are prop you
+
+ align:start position:0%
+in you see it so the these are prop you
+ 
+
+ align:start position:0%
+in you see it so the these are prop you
+know like metric space is extremely
+
+ align:start position:0%
+know like metric space is extremely
+ 
+
+ align:start position:0%
+know like metric space is extremely
+useful you see it all over the place I
+
+ align:start position:0%
+useful you see it all over the place I
+ 
+
+ align:start position:0%
+useful you see it all over the place I
+mean like one of many places where you
+
+ align:start position:0%
+mean like one of many places where you
+ 
+
+ align:start position:0%
+mean like one of many places where you
+see it is also in general reactivity and
+
+ align:start position:0%
+see it is also in general reactivity and
+ 
+
+ align:start position:0%
+see it is also in general reactivity and
+in general reactivativity the space you
+
+ align:start position:0%
+in general reactivativity the space you
+ 
+
+ align:start position:0%
+in general reactivativity the space you
+looking at are typically not complete
+
+ align:start position:0%
+looking at are typically not complete
+ 
+
+ align:start position:0%
+looking at are typically not complete
+okay so so that you know there's
+
+ align:start position:0%
+okay so so that you know there's
+ 
+
+ align:start position:0%
+okay so so that you know there's
+something about that is you know that
+
+ align:start position:0%
+something about that is you know that
+ 
+
+ align:start position:0%
+something about that is you know that
+you reach something in finite time you
+
+ align:start position:0%
+you reach something in finite time you
+ 
+
+ align:start position:0%
+you reach something in finite time you
+reach it you you're going this is like
+
+ align:start position:0%
+reach it you you're going this is like
+ 
+
+ align:start position:0%
+reach it you you're going this is like
+the same thing that you reach like the
+
+ align:start position:0%
+the same thing that you reach like the
+ 
+
+ align:start position:0%
+the same thing that you reach like the
+end of things
+
+ align:start position:0%
+end of things
+ 
+
+ align:start position:0%
+end of things
+anyway but yeah but it's not the
+
+ align:start position:0%
+anyway but yeah but it's not the
+ 
+
+ align:start position:0%
+anyway but yeah but it's not the
+algebraic property that is is used for
\ No newline at end of file
diff --git a/dBNELFi5XiY.txt b/dBNELFi5XiY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be0971740324dd976dbffcb0520bf7f2a8ea683a
--- /dev/null
+++ b/dBNELFi5XiY.txt
@@ -0,0 +1,771 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sublimation
+
+ align:start position:0%
+sublimation
+ 
+
+ align:start position:0%
+sublimation
+the physical transformation of a solid
+
+ align:start position:0%
+the physical transformation of a solid
+ 
+
+ align:start position:0%
+the physical transformation of a solid
+into a gas without intermediate melting
+
+ align:start position:0%
+into a gas without intermediate melting
+ 
+
+ align:start position:0%
+into a gas without intermediate melting
+to the liquid is called
+
+ align:start position:0%
+to the liquid is called
+ 
+
+ align:start position:0%
+to the liquid is called
+sublimation while this particular phase
+
+ align:start position:0%
+sublimation while this particular phase
+ 
+
+ align:start position:0%
+sublimation while this particular phase
+transformation only occurs with solids
+
+ align:start position:0%
+transformation only occurs with solids
+ 
+
+ align:start position:0%
+transformation only occurs with solids
+that have appreciable vapor pressure
+
+ align:start position:0%
+that have appreciable vapor pressure
+ 
+
+ align:start position:0%
+that have appreciable vapor pressure
+below the melting point in these cases
+
+ align:start position:0%
+below the melting point in these cases
+ 
+
+ align:start position:0%
+below the melting point in these cases
+it can sometimes be used as a
+
+ align:start position:0%
+it can sometimes be used as a
+ 
+
+ align:start position:0%
+it can sometimes be used as a
+purification technique this video will
+
+ align:start position:0%
+purification technique this video will
+ 
+
+ align:start position:0%
+purification technique this video will
+illustrate the atmospheric pressure
+
+ align:start position:0%
+illustrate the atmospheric pressure
+ 
+
+ align:start position:0%
+illustrate the atmospheric pressure
+sublimation of
+
+ align:start position:0%
+sublimation of
+ 
+
+ align:start position:0%
+sublimation of
+ferine while sublimations can also be
+
+ align:start position:0%
+ferine while sublimations can also be
+ 
+
+ align:start position:0%
+ferine while sublimations can also be
+carried out under reduced pressure the
+
+ align:start position:0%
+carried out under reduced pressure the
+ 
+
+ align:start position:0%
+carried out under reduced pressure the
+basic principles and steps are the same
+
+ align:start position:0%
+basic principles and steps are the same
+ 
+
+ align:start position:0%
+basic principles and steps are the same
+so A reduced pressure sublimation will
+
+ align:start position:0%
+so A reduced pressure sublimation will
+ 
+
+ align:start position:0%
+so A reduced pressure sublimation will
+not be
+
+ align:start position:0%
+not be
+ 
+
+ align:start position:0%
+not be
+demonstrated sublimation can occur when
+
+ align:start position:0%
+demonstrated sublimation can occur when
+ 
+
+ align:start position:0%
+demonstrated sublimation can occur when
+a compound has appreciable vapor
+
+ align:start position:0%
+a compound has appreciable vapor
+ 
+
+ align:start position:0%
+a compound has appreciable vapor
+pressure below its melting point in
+
+ align:start position:0%
+pressure below its melting point in
+ 
+
+ align:start position:0%
+pressure below its melting point in
+certain cases sublimation can be used as
+
+ align:start position:0%
+certain cases sublimation can be used as
+ 
+
+ align:start position:0%
+certain cases sublimation can be used as
+a purification technique in the
+
+ align:start position:0%
+a purification technique in the
+ 
+
+ align:start position:0%
+a purification technique in the
+laboratory it only works when a compound
+
+ align:start position:0%
+laboratory it only works when a compound
+ 
+
+ align:start position:0%
+laboratory it only works when a compound
+can undergo sublimation and subsequent
+
+ align:start position:0%
+can undergo sublimation and subsequent
+ 
+
+ align:start position:0%
+can undergo sublimation and subsequent
+condensation without decomposition
+
+ align:start position:0%
+condensation without decomposition
+ 
+
+ align:start position:0%
+condensation without decomposition
+it is also essential that none of the
+
+ align:start position:0%
+it is also essential that none of the
+ 
+
+ align:start position:0%
+it is also essential that none of the
+impurities in the sample Sublime under
+
+ align:start position:0%
+impurities in the sample Sublime under
+ 
+
+ align:start position:0%
+impurities in the sample Sublime under
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions an atmospheric pressure
+
+ align:start position:0%
+conditions an atmospheric pressure
+ 
+
+ align:start position:0%
+conditions an atmospheric pressure
+sublimation setup is very
+
+ align:start position:0%
+sublimation setup is very
+ 
+
+ align:start position:0%
+sublimation setup is very
+simple it consists of a hot
+
+ align:start position:0%
+simple it consists of a hot
+ 
+
+ align:start position:0%
+simple it consists of a hot
+plate the bottom of a culture dish
+
+ align:start position:0%
+plate the bottom of a culture dish
+ 
+
+ align:start position:0%
+plate the bottom of a culture dish
+containing the impure
+
+ align:start position:0%
+containing the impure
+ 
+
+ align:start position:0%
+containing the impure
+sample the lid of the culture
+
+ align:start position:0%
+sample the lid of the culture
+ 
+
+ align:start position:0%
+sample the lid of the culture
+dish and an ice
+
+ align:start position:0%
+dish and an ice
+ 
+
+ align:start position:0%
+dish and an ice
+bath
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Simple Start by transferring your impure
+
+ align:start position:0%
+Simple Start by transferring your impure
+ 
+
+ align:start position:0%
+Simple Start by transferring your impure
+sample to the culture
+
+ align:start position:0%
+sample to the culture
+ 
+
+ align:start position:0%
+sample to the culture
+dish spread it out so that it is no more
+
+ align:start position:0%
+dish spread it out so that it is no more
+ 
+
+ align:start position:0%
+dish spread it out so that it is no more
+than 5 mm thick at any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point place the sample on the hot plate
+
+ align:start position:0%
+point place the sample on the hot plate
+ 
+
+ align:start position:0%
+point place the sample on the hot plate
+and top it with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lid the ice bath on the lid and turn the
+
+ align:start position:0%
+lid the ice bath on the lid and turn the
+ 
+
+ align:start position:0%
+lid the ice bath on the lid and turn the
+heat on very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low be patient sublimation takes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time caution overheating will destroy
+
+ align:start position:0%
+time caution overheating will destroy
+ 
+
+ align:start position:0%
+time caution overheating will destroy
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+material but it's a good way to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotar with a little patience and the
+
+ align:start position:0%
+rotar with a little patience and the
+ 
+
+ align:start position:0%
+rotar with a little patience and the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+conditions you will soon observe
+
+ align:start position:0%
+conditions you will soon observe
+ 
+
+ align:start position:0%
+conditions you will soon observe
+formation of crystals on the lid of the
+
+ align:start position:0%
+formation of crystals on the lid of the
+ 
+
+ align:start position:0%
+formation of crystals on the lid of the
+culture
+
+ align:start position:0%
+culture
+ 
+
+ align:start position:0%
+culture
+dish let a layer of crystals grow and
+
+ align:start position:0%
+dish let a layer of crystals grow and
+ 
+
+ align:start position:0%
+dish let a layer of crystals grow and
+then turn off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heat let this setup cool down a little
+
+ align:start position:0%
+heat let this setup cool down a little
+ 
+
+ align:start position:0%
+heat let this setup cool down a little
+bit before you gently slide the ice bath
+
+ align:start position:0%
+bit before you gently slide the ice bath
+ 
+
+ align:start position:0%
+bit before you gently slide the ice bath
+off of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lid caution
+
+ align:start position:0%
+lid caution
+ 
+
+ align:start position:0%
+lid caution
+if you're not
+
+ align:start position:0%
+if you're not
+ 
+
+ align:start position:0%
+if you're not
+careful you'll lose your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystals careful the lid might stick to
+
+ align:start position:0%
+crystals careful the lid might stick to
+ 
+
+ align:start position:0%
+crystals careful the lid might stick to
+the bath which can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disastrous if you were careful enough
+
+ align:start position:0%
+disastrous if you were careful enough
+ 
+
+ align:start position:0%
+disastrous if you were careful enough
+you can now lift the lid and see the
+
+ align:start position:0%
+you can now lift the lid and see the
+ 
+
+ align:start position:0%
+you can now lift the lid and see the
+layer of beautiful purified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystals scrape the crystals into a
+
+ align:start position:0%
+crystals scrape the crystals into a
+ 
+
+ align:start position:0%
+crystals scrape the crystals into a
+clean watch glass and Marvel over the
+
+ align:start position:0%
+clean watch glass and Marvel over the
+ 
+
+ align:start position:0%
+clean watch glass and Marvel over the
+dramatic improvement over your initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sample I know it doesn't look like a lot
+
+ align:start position:0%
+sample I know it doesn't look like a lot
+ 
+
+ align:start position:0%
+sample I know it doesn't look like a lot
+of crystals but remember this is just
+
+ align:start position:0%
+of crystals but remember this is just
+ 
+
+ align:start position:0%
+of crystals but remember this is just
+the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+batch replace the lid on the culture
+
+ align:start position:0%
+batch replace the lid on the culture
+ 
+
+ align:start position:0%
+batch replace the lid on the culture
+disc
+
+ align:start position:0%
+disc
+ 
+
+ align:start position:0%
+disc
+top it with the ice bath and turn the
+
+ align:start position:0%
+top it with the ice bath and turn the
+ 
+
+ align:start position:0%
+top it with the ice bath and turn the
+heat back on to harvest another batch of
+
+ align:start position:0%
+heat back on to harvest another batch of
+ 
+
+ align:start position:0%
+heat back on to harvest another batch of
+beautiful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystals repeat these steps until you
+
+ align:start position:0%
+crystals repeat these steps until you
+ 
+
+ align:start position:0%
+crystals repeat these steps until you
+have purified all of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound remember this video is intended
+
+ align:start position:0%
+compound remember this video is intended
+ 
+
+ align:start position:0%
+compound remember this video is intended
+to help you prepare for lab by providing
+
+ align:start position:0%
+to help you prepare for lab by providing
+ 
+
+ align:start position:0%
+to help you prepare for lab by providing
+a demonstration of the proper
+
+ align:start position:0%
+a demonstration of the proper
+ 
+
+ align:start position:0%
+a demonstration of the proper
+experimental technique it is not
+
+ align:start position:0%
+experimental technique it is not
+ 
+
+ align:start position:0%
+experimental technique it is not
+intended as a replacement for reading
+
+ align:start position:0%
+intended as a replacement for reading
+ 
+
+ align:start position:0%
+intended as a replacement for reading
+your lab manual or the supplementary
+
+ align:start position:0%
+your lab manual or the supplementary
+ 
+
+ align:start position:0%
+your lab manual or the supplementary
+material in order to become a great
+
+ align:start position:0%
+material in order to become a great
+ 
+
+ align:start position:0%
+material in order to become a great
+experimentalist it is important that you
+
+ align:start position:0%
+experimentalist it is important that you
+ 
+
+ align:start position:0%
+experimentalist it is important that you
+understand both Theory and technique now
+
+ align:start position:0%
+understand both Theory and technique now
+ 
+
+ align:start position:0%
+understand both Theory and technique now
+it's your turn good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+luck
+
+ align:start position:0%
+luck
+ 
+
+ align:start position:0%
+luck
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+[Music]
\ No newline at end of file
diff --git a/dZgI16nMuqE.txt b/dZgI16nMuqE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..56de561f48ef0a97b6b80b46ecdf1799c91fea9e
--- /dev/null
+++ b/dZgI16nMuqE.txt
@@ -0,0 +1,3075 @@
+align:start position:0%
+ 
+another way to talk about congruence and
+
+ align:start position:0%
+another way to talk about congruence and
+ 
+
+ align:start position:0%
+another way to talk about congruence and
+remainder arithmetic is to work strictly
+
+ align:start position:0%
+remainder arithmetic is to work strictly
+ 
+
+ align:start position:0%
+remainder arithmetic is to work strictly
+with remainders which makes things a
+
+ align:start position:0%
+with remainders which makes things a
+ 
+
+ align:start position:0%
+with remainders which makes things a
+little simpler because you don't have to
+
+ align:start position:0%
+little simpler because you don't have to
+ 
+
+ align:start position:0%
+little simpler because you don't have to
+worry about the fact that the product of
+
+ align:start position:0%
+worry about the fact that the product of
+ 
+
+ align:start position:0%
+worry about the fact that the product of
+two remainders May for example be too
+
+ align:start position:0%
+two remainders May for example be too
+ 
+
+ align:start position:0%
+two remainders May for example be too
+big to be a remainder to not it back in
+
+ align:start position:0%
+big to be a remainder to not it back in
+ 
+
+ align:start position:0%
+big to be a remainder to not it back in
+range you have to take the remainder
+
+ align:start position:0%
+range you have to take the remainder
+ 
+
+ align:start position:0%
+range you have to take the remainder
+again and that's what this abstract idea
+
+ align:start position:0%
+again and that's what this abstract idea
+ 
+
+ align:start position:0%
+again and that's what this abstract idea
+of the Ring of integers modulo n the
+
+ align:start position:0%
+of the Ring of integers modulo n the
+ 
+
+ align:start position:0%
+of the Ring of integers modulo n the
+ring Z subn captures in a quite elegant
+
+ align:start position:0%
+ring Z subn captures in a quite elegant
+ 
+
+ align:start position:0%
+ring Z subn captures in a quite elegant
+way so it's going to allow us to talk
+
+ align:start position:0%
+way so it's going to allow us to talk
+ 
+
+ align:start position:0%
+way so it's going to allow us to talk
+strictly about equality instead of
+
+ align:start position:0%
+strictly about equality instead of
+ 
+
+ align:start position:0%
+strictly about equality instead of
+congruence and let's remind ourselves
+
+ align:start position:0%
+congruence and let's remind ourselves
+ 
+
+ align:start position:0%
+congruence and let's remind ourselves
+that the the basic idea behind working
+
+ align:start position:0%
+that the the basic idea behind working
+ 
+
+ align:start position:0%
+that the the basic idea behind working
+with a remainder arithmetic was that um
+
+ align:start position:0%
+with a remainder arithmetic was that um
+ 
+
+ align:start position:0%
+with a remainder arithmetic was that um
+every time we got a number that was too
+
+ align:start position:0%
+every time we got a number that was too
+ 
+
+ align:start position:0%
+every time we got a number that was too
+big to be a remainder we just hit it
+
+ align:start position:0%
+big to be a remainder we just hit it
+ 
+
+ align:start position:0%
+big to be a remainder we just hit it
+with the remainder operation again to
+
+ align:start position:0%
+with the remainder operation again to
+ 
+
+ align:start position:0%
+with the remainder operation again to
+bring it back in range and so the
+
+ align:start position:0%
+bring it back in range and so the
+ 
+
+ align:start position:0%
+bring it back in range and so the
+operations in ZN work exactly that way
+
+ align:start position:0%
+operations in ZN work exactly that way
+ 
+
+ align:start position:0%
+operations in ZN work exactly that way
+the elements of ZN are the remainders
+
+ align:start position:0%
+the elements of ZN are the remainders
+ 
+
+ align:start position:0%
+the elements of ZN are the remainders
+that is the numbers from zero including
+
+ align:start position:0%
+that is the numbers from zero including
+ 
+
+ align:start position:0%
+that is the numbers from zero including
+zero up to n but not including n so
+
+ align:start position:0%
+zero up to n but not including n so
+ 
+
+ align:start position:0%
+zero up to n but not including n so
+there are n of them from0 0 1 up through
+
+ align:start position:0%
+there are n of them from0 0 1 up through
+ 
+
+ align:start position:0%
+there are n of them from0 0 1 up through
+n minus1 and the definitions of the
+
+ align:start position:0%
+n minus1 and the definitions of the
+ 
+
+ align:start position:0%
+n minus1 and the definitions of the
+operations in ZN are given right here
+
+ align:start position:0%
+operations in ZN are given right here
+ 
+
+ align:start position:0%
+operations in ZN are given right here
+addition is just means take the sum but
+
+ align:start position:0%
+addition is just means take the sum but
+ 
+
+ align:start position:0%
+addition is just means take the sum but
+then take the remainder immediately and
+
+ align:start position:0%
+then take the remainder immediately and
+ 
+
+ align:start position:0%
+then take the remainder immediately and
+just in case it's too big and likewise
+
+ align:start position:0%
+just in case it's too big and likewise
+ 
+
+ align:start position:0%
+just in case it's too big and likewise
+the product in ZN is simply uh multiply
+
+ align:start position:0%
+the product in ZN is simply uh multiply
+ 
+
+ align:start position:0%
+the product in ZN is simply uh multiply
+them and take the remainder so this
+
+ align:start position:0%
+them and take the remainder so this
+ 
+
+ align:start position:0%
+them and take the remainder so this
+isn't really uh a very dramatic idea but
+
+ align:start position:0%
+isn't really uh a very dramatic idea but
+ 
+
+ align:start position:0%
+isn't really uh a very dramatic idea but
+it turns out to pay off in making some
+
+ align:start position:0%
+it turns out to pay off in making some
+ 
+
+ align:start position:0%
+it turns out to pay off in making some
+things just a little bit easier to say
+
+ align:start position:0%
+things just a little bit easier to say
+ 
+
+ align:start position:0%
+things just a little bit easier to say
+because we're talking about equality
+
+ align:start position:0%
+because we're talking about equality
+ 
+
+ align:start position:0%
+because we're talking about equality
+instead of congruence um so this package
+
+ align:start position:0%
+instead of congruence um so this package
+ 
+
+ align:start position:0%
+instead of congruence um so this package
+together this mathematical structure
+
+ align:start position:0%
+together this mathematical structure
+ 
+
+ align:start position:0%
+together this mathematical structure
+consisting of the integers in this
+
+ align:start position:0%
+consisting of the integers in this
+ 
+
+ align:start position:0%
+consisting of the integers in this
+interval remember this notation square
+
+ align:start position:0%
+interval remember this notation square
+ 
+
+ align:start position:0%
+interval remember this notation square
+bracket means inclusive and round uh
+
+ align:start position:0%
+bracket means inclusive and round uh
+ 
+
+ align:start position:0%
+bracket means inclusive and round uh
+parenthesis means exclusive so this
+
+ align:start position:0%
+parenthesis means exclusive so this
+ 
+
+ align:start position:0%
+parenthesis means exclusive so this
+includes zero and doesn't include n the
+
+ align:start position:0%
+includes zero and doesn't include n the
+ 
+
+ align:start position:0%
+includes zero and doesn't include n the
+integers in that interval uh under the
+
+ align:start position:0%
+integers in that interval uh under the
+ 
+
+ align:start position:0%
+integers in that interval uh under the
+operations of plus and times modulo ZN
+
+ align:start position:0%
+operations of plus and times modulo ZN
+ 
+
+ align:start position:0%
+operations of plus and times modulo ZN
+as defined here uh is called The Ring of
+
+ align:start position:0%
+as defined here uh is called The Ring of
+ 
+
+ align:start position:0%
+as defined here uh is called The Ring of
+integers ZN so it's got two operations
+
+ align:start position:0%
+integers ZN so it's got two operations
+ 
+
+ align:start position:0%
+integers ZN so it's got two operations
+and a bunch of things that are operated
+
+ align:start position:0%
+and a bunch of things that are operated
+ 
+
+ align:start position:0%
+and a bunch of things that are operated
+on now um I guess it's worth
+
+ align:start position:0%
+on now um I guess it's worth
+ 
+
+ align:start position:0%
+on now um I guess it's worth
+highlighting that's what ZN is the ring
+
+ align:start position:0%
+highlighting that's what ZN is the ring
+ 
+
+ align:start position:0%
+highlighting that's what ZN is the ring
+of integers mod n or modulo n now
+
+ align:start position:0%
+of integers mod n or modulo n now
+ 
+
+ align:start position:0%
+of integers mod n or modulo n now
+arithmetic and ZN is really just
+
+ align:start position:0%
+arithmetic and ZN is really just
+ 
+
+ align:start position:0%
+arithmetic and ZN is really just
+arithmetic congruence arithmetic except
+
+ align:start position:0%
+arithmetic congruence arithmetic except
+ 
+
+ align:start position:0%
+arithmetic congruence arithmetic except
+that uh uh it's equality now instead
+
+ align:start position:0%
+that uh uh it's equality now instead
+ 
+
+ align:start position:0%
+that uh uh it's equality now instead
+of congruence so we can say for example
+
+ align:start position:0%
+of congruence so we can say for example
+ 
+
+ align:start position:0%
+of congruence so we can say for example
+in z7 that 3 plus 6 is literally equal
+
+ align:start position:0%
+in z7 that 3 plus 6 is literally equal
+ 
+
+ align:start position:0%
+in z7 that 3 plus 6 is literally equal
+to two because well 3 + 6 is 9 the
+
+ align:start position:0%
+to two because well 3 + 6 is 9 the
+ 
+
+ align:start position:0%
+to two because well 3 + 6 is 9 the
+remainder on division by seven is two
+
+ align:start position:0%
+remainder on division by seven is two
+ 
+
+ align:start position:0%
+remainder on division by seven is two
+and we go directly to the two in ZN
+
+ align:start position:0%
+and we go directly to the two in ZN
+ 
+
+ align:start position:0%
+and we go directly to the two in ZN
+suppressing it the mention of taking
+
+ align:start position:0%
+suppressing it the mention of taking
+ 
+
+ align:start position:0%
+suppressing it the mention of taking
+remainders and not even really having to
+
+ align:start position:0%
+remainders and not even really having to
+ 
+
+ align:start position:0%
+remainders and not even really having to
+think about it which is what's helpful
+
+ align:start position:0%
+think about it which is what's helpful
+ 
+
+ align:start position:0%
+think about it which is what's helpful
+about working with ZN likewise 9 * 8 is
+
+ align:start position:0%
+about working with ZN likewise 9 * 8 is
+ 
+
+ align:start position:0%
+about working with ZN likewise 9 * 8 is
+literally equal to six in
+
+ align:start position:0%
+literally equal to six in
+ 
+
+ align:start position:0%
+literally equal to six in
+z11 um so what's the connection between
+
+ align:start position:0%
+z11 um so what's the connection between
+ 
+
+ align:start position:0%
+z11 um so what's the connection between
+the set of all the integers and the
+
+ align:start position:0%
+the set of all the integers and the
+ 
+
+ align:start position:0%
+the set of all the integers and the
+integers mod n and we can State this
+
+ align:start position:0%
+integers mod n and we can State this
+ 
+
+ align:start position:0%
+integers mod n and we can State this
+abstractly uh in the following way let's
+
+ align:start position:0%
+abstractly uh in the following way let's
+ 
+
+ align:start position:0%
+abstractly uh in the following way let's
+just uh for convenience abbreviate the
+
+ align:start position:0%
+just uh for convenience abbreviate the
+ 
+
+ align:start position:0%
+just uh for convenience abbreviate the
+remainder of K on division by n is R of
+
+ align:start position:0%
+remainder of K on division by n is R of
+ 
+
+ align:start position:0%
+remainder of K on division by n is R of
+K so n is fixed and what's the
+
+ align:start position:0%
+K so n is fixed and what's the
+ 
+
+ align:start position:0%
+K so n is fixed and what's the
+connection between Z and ZN well it's
+
+ align:start position:0%
+connection between Z and ZN well it's
+ 
+
+ align:start position:0%
+connection between Z and ZN well it's
+fairly simple if you take the remainder
+
+ align:start position:0%
+fairly simple if you take the remainder
+ 
+
+ align:start position:0%
+fairly simple if you take the remainder
+of I + J um that's literally equal to
+
+ align:start position:0%
+of I + J um that's literally equal to
+ 
+
+ align:start position:0%
+of I + J um that's literally equal to
+taking the sum of the remainders in
+
+ align:start position:0%
+taking the sum of the remainders in
+ 
+
+ align:start position:0%
+taking the sum of the remainders in
+ZN once you've taken the remainders
+
+ align:start position:0%
+ZN once you've taken the remainders
+ 
+
+ align:start position:0%
+ZN once you've taken the remainders
+you're in the range of numbers that ZN
+
+ align:start position:0%
+you're in the range of numbers that ZN
+ 
+
+ align:start position:0%
+you're in the range of numbers that ZN
+works with um and this sum then keeps
+
+ align:start position:0%
+works with um and this sum then keeps
+ 
+
+ align:start position:0%
+works with um and this sum then keeps
+you in on the ZN side likewise uh if you
+
+ align:start position:0%
+you in on the ZN side likewise uh if you
+ 
+
+ align:start position:0%
+you in on the ZN side likewise uh if you
+take the remainder of a product of real
+
+ align:start position:0%
+take the remainder of a product of real
+ 
+
+ align:start position:0%
+take the remainder of a product of real
+integers that's literally equal to the
+
+ align:start position:0%
+integers that's literally equal to the
+ 
+
+ align:start position:0%
+integers that's literally equal to the
+product of the ERS in ZN this operation
+
+ align:start position:0%
+product of the ERS in ZN this operation
+ 
+
+ align:start position:0%
+product of the ERS in ZN this operation
+by the way this connection between
+
+ align:start position:0%
+by the way this connection between
+ 
+
+ align:start position:0%
+by the way this connection between
+mathematical structures the structure of
+
+ align:start position:0%
+mathematical structures the structure of
+ 
+
+ align:start position:0%
+mathematical structures the structure of
+the integers under plus and times and ZN
+
+ align:start position:0%
+the integers under plus and times and ZN
+ 
+
+ align:start position:0%
+the integers under plus and times and ZN
+under plus and times is called a
+
+ align:start position:0%
+under plus and times is called a
+ 
+
+ align:start position:0%
+under plus and times is called a
+homomorphism r in this case is defining
+
+ align:start position:0%
+homomorphism r in this case is defining
+ 
+
+ align:start position:0%
+homomorphism r in this case is defining
+a homomorphism from Z to ZN that's a
+
+ align:start position:0%
+a homomorphism from Z to ZN that's a
+ 
+
+ align:start position:0%
+a homomorphism from Z to ZN that's a
+basic concept in algebra that you'll
+
+ align:start position:0%
+basic concept in algebra that you'll
+ 
+
+ align:start position:0%
+basic concept in algebra that you'll
+learn more about if you take some
+
+ align:start position:0%
+learn more about if you take some
+ 
+
+ align:start position:0%
+learn more about if you take some
+courses in algebra but I'm just
+
+ align:start position:0%
+courses in algebra but I'm just
+ 
+
+ align:start position:0%
+courses in algebra but I'm just
+mentioning it for cultural reasons we're
+
+ align:start position:0%
+mentioning it for cultural reasons we're
+ 
+
+ align:start position:0%
+mentioning it for cultural reasons we're
+not going to exploit it any further or
+
+ align:start position:0%
+not going to exploit it any further or
+ 
+
+ align:start position:0%
+not going to exploit it any further or
+look further into this idea okay uh
+
+ align:start position:0%
+look further into this idea okay uh
+ 
+
+ align:start position:0%
+look further into this idea okay uh
+what's the connection between
+
+ align:start position:0%
+what's the connection between
+ 
+
+ align:start position:0%
+what's the connection between
+equivalence mod n or congruence mod n
+
+ align:start position:0%
+equivalence mod n or congruence mod n
+ 
+
+ align:start position:0%
+equivalence mod n or congruence mod n
+and ZN well it's fairly simple um uh Z
+
+ align:start position:0%
+and ZN well it's fairly simple um uh Z
+ 
+
+ align:start position:0%
+and ZN well it's fairly simple um uh Z
+in ZN we convert congruences into
+
+ align:start position:0%
+in ZN we convert congruences into
+ 
+
+ align:start position:0%
+in ZN we convert congruences into
+equalities so I is congruent to J mod n
+
+ align:start position:0%
+equalities so I is congruent to J mod n
+ 
+
+ align:start position:0%
+equalities so I is congruent to J mod n
+if and only if R of I is equal to R of J
+
+ align:start position:0%
+if and only if R of I is equal to R of J
+ 
+
+ align:start position:0%
+if and only if R of I is equal to R of J
+in ZN and this is just a rephrasing of
+
+ align:start position:0%
+in ZN and this is just a rephrasing of
+ 
+
+ align:start position:0%
+in ZN and this is just a rephrasing of
+the fact that two numbers are congruent
+
+ align:start position:0%
+the fact that two numbers are congruent
+ 
+
+ align:start position:0%
+the fact that two numbers are congruent
+if and only if they have the same
+
+ align:start position:0%
+if and only if they have the same
+ 
+
+ align:start position:0%
+if and only if they have the same
+remainder now once you've got the
+
+ align:start position:0%
+remainder now once you've got the
+ 
+
+ align:start position:0%
+remainder now once you've got the
+self-contained system ZN you can start
+
+ align:start position:0%
+self-contained system ZN you can start
+ 
+
+ align:start position:0%
+self-contained system ZN you can start
+talking about algebraic rules that it
+
+ align:start position:0%
+talking about algebraic rules that it
+ 
+
+ align:start position:0%
+talking about algebraic rules that it
+satisfies and now they hold with
+
+ align:start position:0%
+satisfies and now they hold with
+ 
+
+ align:start position:0%
+satisfies and now they hold with
+equality and they're pretty familiar so
+
+ align:start position:0%
+equality and they're pretty familiar so
+ 
+
+ align:start position:0%
+equality and they're pretty familiar so
+let's look at some of the rules for
+
+ align:start position:0%
+let's look at some of the rules for
+ 
+
+ align:start position:0%
+let's look at some of the rules for
+addition for example that hold true in
+
+ align:start position:0%
+addition for example that hold true in
+ 
+
+ align:start position:0%
+addition for example that hold true in
+ZN first of all addition is associative
+
+ align:start position:0%
+ZN first of all addition is associative
+ 
+
+ align:start position:0%
+ZN first of all addition is associative
+I plus J plus K is I plus J plus K we
+
+ align:start position:0%
+I plus J plus K is I plus J plus K we
+ 
+
+ align:start position:0%
+I plus J plus K is I plus J plus K we
+have an identity element literally zero
+
+ align:start position:0%
+have an identity element literally zero
+ 
+
+ align:start position:0%
+have an identity element literally zero
+0 plus any I is I we have a minus
+
+ align:start position:0%
+0 plus any I is I we have a minus
+ 
+
+ align:start position:0%
+0 plus any I is I we have a minus
+operation an inverse operation with
+
+ align:start position:0%
+operation an inverse operation with
+ 
+
+ align:start position:0%
+operation an inverse operation with
+respect to um addition uh which is um
+
+ align:start position:0%
+respect to um addition uh which is um
+ 
+
+ align:start position:0%
+respect to um addition uh which is um
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+what how did I get back some slides
+
+ align:start position:0%
+what how did I get back some slides
+ 
+
+ align:start position:0%
+what how did I get back some slides
+excuse me okay let's keep going I have
+
+ align:start position:0%
+excuse me okay let's keep going I have
+ 
+
+ align:start position:0%
+excuse me okay let's keep going I have
+an inverse operation uh which is that
+
+ align:start position:0%
+an inverse operation uh which is that
+ 
+
+ align:start position:0%
+an inverse operation uh which is that
+for every I there's an element called
+
+ align:start position:0%
+for every I there's an element called
+ 
+
+ align:start position:0%
+for every I there's an element called
+minus I it's additive inverse such that
+
+ align:start position:0%
+minus I it's additive inverse such that
+ 
+
+ align:start position:0%
+minus I it's additive inverse such that
+if you add I and minus I you get zero
+
+ align:start position:0%
+if you add I and minus I you get zero
+ 
+
+ align:start position:0%
+if you add I and minus I you get zero
+and finally commutativity which is that
+
+ align:start position:0%
+and finally commutativity which is that
+ 
+
+ align:start position:0%
+and finally commutativity which is that
+I plus J is the same as J plus I uh you
+
+ align:start position:0%
+I plus J is the same as J plus I uh you
+ 
+
+ align:start position:0%
+I plus J is the same as J plus I uh you
+don't really need to memorize these
+
+ align:start position:0%
+don't really need to memorize these
+ 
+
+ align:start position:0%
+don't really need to memorize these
+names but uh you will probably hear them
+
+ align:start position:0%
+names but uh you will probably hear them
+ 
+
+ align:start position:0%
+names but uh you will probably hear them
+a lot in various other contexts
+
+ align:start position:0%
+a lot in various other contexts
+ 
+
+ align:start position:0%
+a lot in various other contexts
+especially in algebra courses but even
+
+ align:start position:0%
+especially in algebra courses but even
+ 
+
+ align:start position:0%
+especially in algebra courses but even
+in terms of arithmetic these are some of
+
+ align:start position:0%
+in terms of arithmetic these are some of
+ 
+
+ align:start position:0%
+in terms of arithmetic these are some of
+the basic rules that addition satisfies
+
+ align:start position:0%
+the basic rules that addition satisfies
+ 
+
+ align:start position:0%
+the basic rules that addition satisfies
+and in fact multiplication satisfies
+
+ align:start position:0%
+and in fact multiplication satisfies
+ 
+
+ align:start position:0%
+and in fact multiplication satisfies
+pretty much the same rules
+
+ align:start position:0%
+pretty much the same rules
+ 
+
+ align:start position:0%
+pretty much the same rules
+multiplication is likewise associative
+
+ align:start position:0%
+multiplication is likewise associative
+ 
+
+ align:start position:0%
+multiplication is likewise associative
+there's an identity from multiplication
+
+ align:start position:0%
+there's an identity from multiplication
+ 
+
+ align:start position:0%
+there's an identity from multiplication
+called one 1 time I is I multiplication
+
+ align:start position:0%
+called one 1 time I is I multiplication
+ 
+
+ align:start position:0%
+called one 1 time I is I multiplication
+is also commutative the one obvious
+
+ align:start position:0%
+is also commutative the one obvious
+ 
+
+ align:start position:0%
+is also commutative the one obvious
+Omission here is inverses you can't
+
+ align:start position:0%
+Omission here is inverses you can't
+ 
+
+ align:start position:0%
+Omission here is inverses you can't
+count on there being inverses in
+
+ align:start position:0%
+count on there being inverses in
+ 
+
+ align:start position:0%
+count on there being inverses in
+ZN um and finally there's an operation
+
+ align:start position:0%
+ZN um and finally there's an operation
+ 
+
+ align:start position:0%
+ZN um and finally there's an operation
+that connects addition and
+
+ align:start position:0%
+that connects addition and
+ 
+
+ align:start position:0%
+that connects addition and
+multiplication called distributivity
+
+ align:start position:0%
+multiplication called distributivity
+ 
+
+ align:start position:0%
+multiplication called distributivity
+namely I * J + K is i j + i k as you
+
+ align:start position:0%
+namely I * J + K is i j + i k as you
+ 
+
+ align:start position:0%
+namely I * J + K is i j + i k as you
+well know from ordinary arithmetic and
+
+ align:start position:0%
+well know from ordinary arithmetic and
+ 
+
+ align:start position:0%
+well know from ordinary arithmetic and
+this rule works fine for remainders and
+
+ align:start position:0%
+this rule works fine for remainders and
+ 
+
+ align:start position:0%
+this rule works fine for remainders and
+working in
+
+ align:start position:0%
+working in
+ 
+
+ align:start position:0%
+working in
+ZN as I said the one thing we have to
+
+ align:start position:0%
+ZN as I said the one thing we have to
+ 
+
+ align:start position:0%
+ZN as I said the one thing we have to
+watch out for it shouldn't be a surprise
+
+ align:start position:0%
+watch out for it shouldn't be a surprise
+ 
+
+ align:start position:0%
+watch out for it shouldn't be a surprise
+is we know that you can't cancel with
+
+ align:start position:0%
+is we know that you can't cancel with
+ 
+
+ align:start position:0%
+is we know that you can't cancel with
+respect to congruence mod n and that's
+
+ align:start position:0%
+respect to congruence mod n and that's
+ 
+
+ align:start position:0%
+respect to congruence mod n and that's
+reflected in the fact that you can't
+
+ align:start position:0%
+reflected in the fact that you can't
+ 
+
+ align:start position:0%
+reflected in the fact that you can't
+cancel in ZN namely in z12 for example 3
+
+ align:start position:0%
+cancel in ZN namely in z12 for example 3
+ 
+
+ align:start position:0%
+cancel in ZN namely in z12 for example 3
+* 2 is equal to 2 * 8 again 3 * 2 is 6 2
+
+ align:start position:0%
+* 2 is equal to 2 * 8 again 3 * 2 is 6 2
+ 
+
+ align:start position:0%
+* 2 is equal to 2 * 8 again 3 * 2 is 6 2
+* 8 is 16 you immediately take the
+
+ align:start position:0%
+* 8 is 16 you immediately take the
+ 
+
+ align:start position:0%
+* 8 is 16 you immediately take the
+remainder to get back to six in z12
+
+ align:start position:0%
+remainder to get back to six in z12
+ 
+
+ align:start position:0%
+remainder to get back to six in z12
+these two things are equal but if you
+
+ align:start position:0%
+these two things are equal but if you
+ 
+
+ align:start position:0%
+these two things are equal but if you
+try to cancel the two you'd conclude
+
+ align:start position:0%
+try to cancel the two you'd conclude
+ 
+
+ align:start position:0%
+try to cancel the two you'd conclude
+that three was 8 and neither three three
+
+ align:start position:0%
+that three was 8 and neither three three
+ 
+
+ align:start position:0%
+that three was 8 and neither three three
+and eight are different numbers in the
+
+ align:start position:0%
+and eight are different numbers in the
+ 
+
+ align:start position:0%
+and eight are different numbers in the
+range from 0o to uh to 12 and they're
+
+ align:start position:0%
+range from 0o to uh to 12 and they're
+ 
+
+ align:start position:0%
+range from 0o to uh to 12 and they're
+different in z12 so you can't cancel to
+
+ align:start position:0%
+different in z12 so you can't cancel to
+ 
+
+ align:start position:0%
+different in z12 so you can't cancel to
+okay now the rules that we already
+
+ align:start position:0%
+okay now the rules that we already
+ 
+
+ align:start position:0%
+okay now the rules that we already
+figured out for when you can cancel in
+
+ align:start position:0%
+figured out for when you can cancel in
+ 
+
+ align:start position:0%
+figured out for when you can cancel in
+congruence translate directly over to
+
+ align:start position:0%
+congruence translate directly over to
+ 
+
+ align:start position:0%
+congruence translate directly over to
+when you can cancel in ZN and now
+
+ align:start position:0%
+when you can cancel in ZN and now
+ 
+
+ align:start position:0%
+when you can cancel in ZN and now
+there's a standard abbreviation that's
+
+ align:start position:0%
+there's a standard abbreviation that's
+ 
+
+ align:start position:0%
+there's a standard abbreviation that's
+useful to use here if I write ZN star
+
+ align:start position:0%
+useful to use here if I write ZN star
+ 
+
+ align:start position:0%
+useful to use here if I write ZN star
+what I mean is the elements in ZN that
+
+ align:start position:0%
+what I mean is the elements in ZN that
+ 
+
+ align:start position:0%
+what I mean is the elements in ZN that
+are relatively prime to n the elements
+
+ align:start position:0%
+are relatively prime to n the elements
+ 
+
+ align:start position:0%
+are relatively prime to n the elements
+whose gcd with n is one so um what we
+
+ align:start position:0%
+whose gcd with n is one so um what we
+ 
+
+ align:start position:0%
+whose gcd with n is one so um what we
+have is the following equivalent
+
+ align:start position:0%
+have is the following equivalent
+ 
+
+ align:start position:0%
+have is the following equivalent
+formulations of ZN star which correspond
+
+ align:start position:0%
+formulations of ZN star which correspond
+ 
+
+ align:start position:0%
+formulations of ZN star which correspond
+to the facts we've already figured out
+
+ align:start position:0%
+to the facts we've already figured out
+ 
+
+ align:start position:0%
+to the facts we've already figured out
+about congruence namely um an integer I
+
+ align:start position:0%
+about congruence namely um an integer I
+ 
+
+ align:start position:0%
+about congruence namely um an integer I
+in the range from0 to n is in ZN star if
+
+ align:start position:0%
+in the range from0 to n is in ZN star if
+ 
+
+ align:start position:0%
+in the range from0 to n is in ZN star if
+and only if the gcd of I Inn is one or I
+
+ align:start position:0%
+and only if the gcd of I Inn is one or I
+ 
+
+ align:start position:0%
+and only if the gcd of I Inn is one or I
+is canceled able in ZN or I has an
+
+ align:start position:0%
+is canceled able in ZN or I has an
+ 
+
+ align:start position:0%
+is canceled able in ZN or I has an
+inverse in ZN all of these three things
+
+ align:start position:0%
+inverse in ZN all of these three things
+ 
+
+ align:start position:0%
+inverse in ZN all of these three things
+are equivalent they give you the sense
+
+ align:start position:0%
+are equivalent they give you the sense
+ 
+
+ align:start position:0%
+are equivalent they give you the sense
+that ZN star is a kind of robust uh
+
+ align:start position:0%
+that ZN star is a kind of robust uh
+ 
+
+ align:start position:0%
+that ZN star is a kind of robust uh
+subset of ZN that uh uh you want to be
+
+ align:start position:0%
+subset of ZN that uh uh you want to be
+ 
+
+ align:start position:0%
+subset of ZN that uh uh you want to be
+thinking about and in fact it's very
+
+ align:start position:0%
+thinking about and in fact it's very
+ 
+
+ align:start position:0%
+thinking about and in fact it's very
+valuable to be paying attention to what
+
+ align:start position:0%
+valuable to be paying attention to what
+ 
+
+ align:start position:0%
+valuable to be paying attention to what
+else do we know about ZN star well the
+
+ align:start position:0%
+else do we know about ZN star well the
+ 
+
+ align:start position:0%
+else do we know about ZN star well the
+definition of f of n was the number of
+
+ align:start position:0%
+definition of f of n was the number of
+ 
+
+ align:start position:0%
+definition of f of n was the number of
+uh integers in the interval from 0 to n
+
+ align:start position:0%
+uh integers in the interval from 0 to n
+ 
+
+ align:start position:0%
+uh integers in the interval from 0 to n
+that are relatively prime to n of course
+
+ align:start position:0%
+that are relatively prime to n of course
+ 
+
+ align:start position:0%
+that are relatively prime to n of course
+that's exactly the size of ZN star um so
+
+ align:start position:0%
+that's exactly the size of ZN star um so
+ 
+
+ align:start position:0%
+that's exactly the size of ZN star um so
+V ofn is simply the size of that
+
+ align:start position:0%
+V ofn is simply the size of that
+ 
+
+ align:start position:0%
+V ofn is simply the size of that
+collection of elements not surprising
+
+ align:start position:0%
+collection of elements not surprising
+ 
+
+ align:start position:0%
+collection of elements not surprising
+they were defined that way so now we can
+
+ align:start position:0%
+they were defined that way so now we can
+ 
+
+ align:start position:0%
+they were defined that way so now we can
+restate Oilers theorem in a slightly
+
+ align:start position:0%
+restate Oilers theorem in a slightly
+ 
+
+ align:start position:0%
+restate Oilers theorem in a slightly
+convenient way instead of mentioning
+
+ align:start position:0%
+convenient way instead of mentioning
+ 
+
+ align:start position:0%
+convenient way instead of mentioning
+congruence we can just talk about
+
+ align:start position:0%
+congruence we can just talk about
+ 
+
+ align:start position:0%
+congruence we can just talk about
+equality Oilers theorem says that if you
+
+ align:start position:0%
+equality Oilers theorem says that if you
+ 
+
+ align:start position:0%
+equality Oilers theorem says that if you
+raise a number K to the power Fe of n
+
+ align:start position:0%
+raise a number K to the power Fe of n
+ 
+
+ align:start position:0%
+raise a number K to the power Fe of n
+it's literally equal to one in ZN at
+
+ align:start position:0%
+it's literally equal to one in ZN at
+ 
+
+ align:start position:0%
+it's literally equal to one in ZN at
+least for those KS that are relatively
+
+ align:start position:0%
+least for those KS that are relatively
+ 
+
+ align:start position:0%
+least for those KS that are relatively
+prime to n that is those KS that are in
+
+ align:start position:0%
+prime to n that is those KS that are in
+ 
+
+ align:start position:0%
+prime to n that is those KS that are in
+ZN star and it's going to turn out that
+
+ align:start position:0%
+ZN star and it's going to turn out that
+ 
+
+ align:start position:0%
+ZN star and it's going to turn out that
+the proof of Oilers theem is actually
+
+ align:start position:0%
+the proof of Oilers theem is actually
+ 
+
+ align:start position:0%
+the proof of Oilers theem is actually
+pretty easy it just follows in a couple
+
+ align:start position:0%
+pretty easy it just follows in a couple
+ 
+
+ align:start position:0%
+pretty easy it just follows in a couple
+of steps from a couple of simple
+
+ align:start position:0%
+of steps from a couple of simple
+ 
+
+ align:start position:0%
+of steps from a couple of simple
+observations so let's start on those so
+
+ align:start position:0%
+observations so let's start on those so
+ 
+
+ align:start position:0%
+observations so let's start on those so
+the first remark is that if I have any
+
+ align:start position:0%
+the first remark is that if I have any
+ 
+
+ align:start position:0%
+the first remark is that if I have any
+subset s of elements in ZN I don't care
+
+ align:start position:0%
+subset s of elements in ZN I don't care
+ 
+
+ align:start position:0%
+subset s of elements in ZN I don't care
+whether they're relatively prime to n or
+
+ align:start position:0%
+whether they're relatively prime to n or
+ 
+
+ align:start position:0%
+whether they're relatively prime to n or
+not if I multiply each of them by K this
+
+ align:start position:0%
+not if I multiply each of them by K this
+ 
+
+ align:start position:0%
+not if I multiply each of them by K this
+notation for K * s means that I'm taking
+
+ align:start position:0%
+notation for K * s means that I'm taking
+ 
+
+ align:start position:0%
+notation for K * s means that I'm taking
+the set of elements that uh are of the
+
+ align:start position:0%
+the set of elements that uh are of the
+ 
+
+ align:start position:0%
+the set of elements that uh are of the
+form K times an element of s over all
+
+ align:start position:0%
+form K times an element of s over all
+ 
+
+ align:start position:0%
+form K times an element of s over all
+the elements of s so KS which is this
+
+ align:start position:0%
+the elements of s so KS which is this
+ 
+
+ align:start position:0%
+the elements of s so KS which is this
+set of multiples of K multiples of
+
+ align:start position:0%
+set of multiples of K multiples of
+ 
+
+ align:start position:0%
+set of multiples of K multiples of
+elements of s by k um has the exactly
+
+ align:start position:0%
+elements of s by k um has the exactly
+ 
+
+ align:start position:0%
+elements of s by k um has the exactly
+the same size as s now why is that well
+
+ align:start position:0%
+the same size as s now why is that well
+ 
+
+ align:start position:0%
+the same size as s now why is that well
+this of course is only true for K that
+
+ align:start position:0%
+this of course is only true for K that
+ 
+
+ align:start position:0%
+this of course is only true for K that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+cancelable but uh the Lemma is no matter
+
+ align:start position:0%
+cancelable but uh the Lemma is no matter
+ 
+
+ align:start position:0%
+cancelable but uh the Lemma is no matter
+what subset you take of ZN if you
+
+ align:start position:0%
+what subset you take of ZN if you
+ 
+
+ align:start position:0%
+what subset you take of ZN if you
+multiply every one of them by an element
+
+ align:start position:0%
+multiply every one of them by an element
+ 
+
+ align:start position:0%
+multiply every one of them by an element
+that's cancelable in ZN star you get a
+
+ align:start position:0%
+that's cancelable in ZN star you get a
+ 
+
+ align:start position:0%
+that's cancelable in ZN star you get a
+set of the same size and that's uh clear
+
+ align:start position:0%
+set of the same size and that's uh clear
+ 
+
+ align:start position:0%
+set of the same size and that's uh clear
+because how could ks1 and ks2 be equal
+
+ align:start position:0%
+because how could ks1 and ks2 be equal
+ 
+
+ align:start position:0%
+because how could ks1 and ks2 be equal
+well only if S1 and S2 were equal or
+
+ align:start position:0%
+well only if S1 and S2 were equal or
+ 
+
+ align:start position:0%
+well only if S1 and S2 were equal or
+another way to say it is that if you had
+
+ align:start position:0%
+another way to say it is that if you had
+ 
+
+ align:start position:0%
+another way to say it is that if you had
+different elements in s S1 not equal to
+
+ align:start position:0%
+different elements in s S1 not equal to
+ 
+
+ align:start position:0%
+different elements in s S1 not equal to
+S2 when you multiply them by K you have
+
+ align:start position:0%
+S2 when you multiply them by K you have
+ 
+
+ align:start position:0%
+S2 when you multiply them by K you have
+to get different elements of KS because
+
+ align:start position:0%
+to get different elements of KS because
+ 
+
+ align:start position:0%
+to get different elements of KS because
+uh K is cancelable okay so that's an
+
+ align:start position:0%
+uh K is cancelable okay so that's an
+ 
+
+ align:start position:0%
+uh K is cancelable okay so that's an
+easy remark holds uh in general multiply
+
+ align:start position:0%
+easy remark holds uh in general multiply
+ 
+
+ align:start position:0%
+easy remark holds uh in general multiply
+by any subset by uh a cancelable element
+
+ align:start position:0%
+by any subset by uh a cancelable element
+ 
+
+ align:start position:0%
+by any subset by uh a cancelable element
+and you get a new set that's the same
+
+ align:start position:0%
+and you get a new set that's the same
+ 
+
+ align:start position:0%
+and you get a new set that's the same
+size the second remark is that if you
+
+ align:start position:0%
+size the second remark is that if you
+ 
+
+ align:start position:0%
+size the second remark is that if you
+look at numbers I and J that are in the
+
+ align:start position:0%
+look at numbers I and J that are in the
+ 
+
+ align:start position:0%
+look at numbers I and J that are in the
+interval from 0 to n in ZN then um if
+
+ align:start position:0%
+interval from 0 to n in ZN then um if
+ 
+
+ align:start position:0%
+interval from 0 to n in ZN then um if
+you multiply the two of them um then
+
+ align:start position:0%
+you multiply the two of them um then
+ 
+
+ align:start position:0%
+you multiply the two of them um then
+you're going to get uh an element in ZN
+
+ align:start position:0%
+you're going to get uh an element in ZN
+ 
+
+ align:start position:0%
+you're going to get uh an element in ZN
+star if and only if the original two
+
+ align:start position:0%
+star if and only if the original two
+ 
+
+ align:start position:0%
+star if and only if the original two
+elements were in ZN star well let's just
+
+ align:start position:0%
+elements were in ZN star well let's just
+ 
+
+ align:start position:0%
+elements were in ZN star well let's just
+look at it in the left to right
+
+ align:start position:0%
+look at it in the left to right
+ 
+
+ align:start position:0%
+look at it in the left to right
+direction which is the only one we need
+
+ align:start position:0%
+direction which is the only one we need
+ 
+
+ align:start position:0%
+direction which is the only one we need
+if I and J are relatively prime to ZN
+
+ align:start position:0%
+if I and J are relatively prime to ZN
+ 
+
+ align:start position:0%
+if I and J are relatively prime to ZN
+star then so is their product because if
+
+ align:start position:0%
+star then so is their product because if
+ 
+
+ align:start position:0%
+star then so is their product because if
+neither I nor J has a prime factor in
+
+ align:start position:0%
+neither I nor J has a prime factor in
+ 
+
+ align:start position:0%
+neither I nor J has a prime factor in
+common with n then their product
+
+ align:start position:0%
+common with n then their product
+ 
+
+ align:start position:0%
+common with n then their product
+obviously doesn't have a uh a factor in
+
+ align:start position:0%
+obviously doesn't have a uh a factor in
+ 
+
+ align:start position:0%
+obviously doesn't have a uh a factor in
+common with n and then when you take
+
+ align:start position:0%
+common with n and then when you take
+ 
+
+ align:start position:0%
+common with n and then when you take
+remainders it's still going to be a
+
+ align:start position:0%
+remainders it's still going to be a
+ 
+
+ align:start position:0%
+remainders it's still going to be a
+number whose gcd is the same um and so
+
+ align:start position:0%
+number whose gcd is the same um and so
+ 
+
+ align:start position:0%
+number whose gcd is the same um and so
+we have this remark that if you multiply
+
+ align:start position:0%
+we have this remark that if you multiply
+ 
+
+ align:start position:0%
+we have this remark that if you multiply
+two cancelable elements you get a
+
+ align:start position:0%
+two cancelable elements you get a
+ 
+
+ align:start position:0%
+two cancelable elements you get a
+cancelable element if you multiply two
+
+ align:start position:0%
+cancelable element if you multiply two
+ 
+
+ align:start position:0%
+cancelable element if you multiply two
+elements relatively prime to ZN star you
+
+ align:start position:0%
+elements relatively prime to ZN star you
+ 
+
+ align:start position:0%
+elements relatively prime to ZN star you
+get an element of ZN star there's about
+
+ align:start position:0%
+get an element of ZN star there's about
+ 
+
+ align:start position:0%
+get an element of ZN star there's about
+every one of these formulations of ZN
+
+ align:start position:0%
+every one of these formulations of ZN
+ 
+
+ align:start position:0%
+every one of these formulations of ZN
+star in terms of gcds are cancelable or
+
+ align:start position:0%
+star in terms of gcds are cancelable or
+ 
+
+ align:start position:0%
+star in terms of gcds are cancelable or
+inverse um will and each of them gives a
+
+ align:start position:0%
+inverse um will and each of them gives a
+ 
+
+ align:start position:0%
+inverse um will and each of them gives a
+separate and and straightforward proof
+
+ align:start position:0%
+separate and and straightforward proof
+ 
+
+ align:start position:0%
+separate and and straightforward proof
+of the fact that if I and J are in ZN
+
+ align:start position:0%
+of the fact that if I and J are in ZN
+ 
+
+ align:start position:0%
+of the fact that if I and J are in ZN
+star then so is their product it's worth
+
+ align:start position:0%
+star then so is their product it's worth
+ 
+
+ align:start position:0%
+star then so is their product it's worth
+mentioning by the way that in general
+
+ align:start position:0%
+mentioning by the way that in general
+ 
+
+ align:start position:0%
+mentioning by the way that in general
+their sum is not if you add two elements
+
+ align:start position:0%
+their sum is not if you add two elements
+ 
+
+ align:start position:0%
+their sum is not if you add two elements
+that are relatively prime uh to ZN star
+
+ align:start position:0%
+that are relatively prime uh to ZN star
+ 
+
+ align:start position:0%
+that are relatively prime uh to ZN star
+um uh even if their sum is non zero you
+
+ align:start position:0%
+um uh even if their sum is non zero you
+ 
+
+ align:start position:0%
+um uh even if their sum is non zero you
+will typically get an element that uh is
+
+ align:start position:0%
+will typically get an element that uh is
+ 
+
+ align:start position:0%
+will typically get an element that uh is
+uh is no longer relatively prime to n
+
+ align:start position:0%
+uh is no longer relatively prime to n
+ 
+
+ align:start position:0%
+uh is no longer relatively prime to n
+but for multiplication it works great
+
+ align:start position:0%
+but for multiplication it works great
+ 
+
+ align:start position:0%
+but for multiplication it works great
+and that's what matters to
+
+ align:start position:0%
+and that's what matters to
+ 
+
+ align:start position:0%
+and that's what matters to
+us okay so as a Cory of this is that I
+
+ align:start position:0%
+us okay so as a Cory of this is that I
+ 
+
+ align:start position:0%
+us okay so as a Cory of this is that I
+can actually include that if I choose an
+
+ align:start position:0%
+can actually include that if I choose an
+ 
+
+ align:start position:0%
+can actually include that if I choose an
+element that's cancelable an element in
+
+ align:start position:0%
+element that's cancelable an element in
+ 
+
+ align:start position:0%
+element that's cancelable an element in
+ZN star if I take the whole set ZN star
+
+ align:start position:0%
+ZN star if I take the whole set ZN star
+ 
+
+ align:start position:0%
+ZN star if I take the whole set ZN star
+all those elements that are relatively
+
+ align:start position:0%
+all those elements that are relatively
+ 
+
+ align:start position:0%
+all those elements that are relatively
+prime to n and I take multiples of K by
+
+ align:start position:0%
+prime to n and I take multiples of K by
+ 
+
+ align:start position:0%
+prime to n and I take multiples of K by
+each of them then in fact I get the same
+
+ align:start position:0%
+each of them then in fact I get the same
+ 
+
+ align:start position:0%
+each of them then in fact I get the same
+set ZN star and the proof of that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really straightforward let's think about
+
+ align:start position:0%
+really straightforward let's think about
+ 
+
+ align:start position:0%
+really straightforward let's think about
+it for a minute CU what do I know is
+
+ align:start position:0%
+it for a minute CU what do I know is
+ 
+
+ align:start position:0%
+it for a minute CU what do I know is
+that these two sets are the same size K
+
+ align:start position:0%
+that these two sets are the same size K
+ 
+
+ align:start position:0%
+that these two sets are the same size K
+ZN star and ZN star the same size as
+
+ align:start position:0%
+ZN star and ZN star the same size as
+ 
+
+ align:start position:0%
+ZN star and ZN star the same size as
+long as K is cancelable I didn't even
+
+ align:start position:0%
+long as K is cancelable I didn't even
+ 
+
+ align:start position:0%
+long as K is cancelable I didn't even
+care that this was ZN star yeah on the
+
+ align:start position:0%
+care that this was ZN star yeah on the
+ 
+
+ align:start position:0%
+care that this was ZN star yeah on the
+other hand um if K is in ZN star k * ZN
+
+ align:start position:0%
+other hand um if K is in ZN star k * ZN
+ 
+
+ align:start position:0%
+other hand um if K is in ZN star k * ZN
+star only gives you elements in ZN star
+
+ align:start position:0%
+star only gives you elements in ZN star
+ 
+
+ align:start position:0%
+star only gives you elements in ZN star
+so K ZN star is a subset of the left
+
+ align:start position:0%
+so K ZN star is a subset of the left
+ 
+
+ align:start position:0%
+so K ZN star is a subset of the left
+hand side and it's the same size by the
+
+ align:start position:0%
+hand side and it's the same size by the
+ 
+
+ align:start position:0%
+hand side and it's the same size by the
+Lemma that says that multiplying GE pres
+
+ align:start position:0%
+Lemma that says that multiplying GE pres
+ 
+
+ align:start position:0%
+Lemma that says that multiplying GE pres
+preserves sizes so they have to be equal
+
+ align:start position:0%
+preserves sizes so they have to be equal
+ 
+
+ align:start position:0%
+preserves sizes so they have to be equal
+so basically what that means is that if
+
+ align:start position:0%
+so basically what that means is that if
+ 
+
+ align:start position:0%
+so basically what that means is that if
+you take all the elements in Z star the
+
+ align:start position:0%
+you take all the elements in Z star the
+ 
+
+ align:start position:0%
+you take all the elements in Z star the
+elements relatively prime to n and you
+
+ align:start position:0%
+elements relatively prime to n and you
+ 
+
+ align:start position:0%
+elements relatively prime to n and you
+take another one of them pick one out of
+
+ align:start position:0%
+take another one of them pick one out of
+ 
+
+ align:start position:0%
+take another one of them pick one out of
+that set and multiply every element in
+
+ align:start position:0%
+that set and multiply every element in
+ 
+
+ align:start position:0%
+that set and multiply every element in
+the set by that element K if you had
+
+ align:start position:0%
+the set by that element K if you had
+ 
+
+ align:start position:0%
+the set by that element K if you had
+them lined up in one order beforehand
+
+ align:start position:0%
+them lined up in one order beforehand
+ 
+
+ align:start position:0%
+them lined up in one order beforehand
+when you multiply by K you get exactly
+
+ align:start position:0%
+when you multiply by K you get exactly
+ 
+
+ align:start position:0%
+when you multiply by K you get exactly
+the same elements but just reordered
+
+ align:start position:0%
+the same elements but just reordered
+ 
+
+ align:start position:0%
+the same elements but just reordered
+that is multiplying by K has the effect
+
+ align:start position:0%
+that is multiplying by K has the effect
+ 
+
+ align:start position:0%
+that is multiplying by K has the effect
+of permuting the elements of ZN
+
+ align:start position:0%
+of permuting the elements of ZN
+ 
+
+ align:start position:0%
+of permuting the elements of ZN
+star uh let's look at an example so um
+
+ align:start position:0%
+star uh let's look at an example so um
+ 
+
+ align:start position:0%
+star uh let's look at an example so um
+let's look at z9 and we know that F of 9
+
+ align:start position:0%
+let's look at z9 and we know that F of 9
+ 
+
+ align:start position:0%
+let's look at z9 and we know that F of 9
+by the previous formula is 3^2 - 3 or 6
+
+ align:start position:0%
+by the previous formula is 3^2 - 3 or 6
+ 
+
+ align:start position:0%
+by the previous formula is 3^2 - 3 or 6
+they're going to be six elements from 0
+
+ align:start position:0%
+they're going to be six elements from 0
+ 
+
+ align:start position:0%
+they're going to be six elements from 0
+to n that are relatively prime to nine
+
+ align:start position:0%
+to n that are relatively prime to nine
+ 
+
+ align:start position:0%
+to n that are relatively prime to nine
+and that are that comprise ZN star so
+
+ align:start position:0%
+and that are that comprise ZN star so
+ 
+
+ align:start position:0%
+and that are that comprise ZN star so
+let's look at what they are so you can
+
+ align:start position:0%
+let's look at what they are so you can
+ 
+
+ align:start position:0%
+let's look at what they are so you can
+do check the calculation but ZN star is
+
+ align:start position:0%
+do check the calculation but ZN star is
+ 
+
+ align:start position:0%
+do check the calculation but ZN star is
+exactly the elements uh 1 2 4 5 78 we
+
+ align:start position:0%
+exactly the elements uh 1 2 4 5 78 we
+ 
+
+ align:start position:0%
+exactly the elements uh 1 2 4 5 78 we
+know we got them all CU there's only
+
+ align:start position:0%
+know we got them all CU there's only
+ 
+
+ align:start position:0%
+know we got them all CU there's only
+supposed to be six of them and we can
+
+ align:start position:0%
+supposed to be six of them and we can
+ 
+
+ align:start position:0%
+supposed to be six of them and we can
+check that those are all relatively
+
+ align:start position:0%
+check that those are all relatively
+ 
+
+ align:start position:0%
+check that those are all relatively
+prime to nine none of them has three as
+
+ align:start position:0%
+prime to nine none of them has three as
+ 
+
+ align:start position:0%
+prime to nine none of them has three as
+a divisor now what happens for example
+
+ align:start position:0%
+a divisor now what happens for example
+ 
+
+ align:start position:0%
+a divisor now what happens for example
+if I multiply them all by two two is
+
+ align:start position:0%
+if I multiply them all by two two is
+ 
+
+ align:start position:0%
+if I multiply them all by two two is
+another good number it's right here
+
+ align:start position:0%
+another good number it's right here
+ 
+
+ align:start position:0%
+another good number it's right here
+that's in ZN star and multiplying them
+
+ align:start position:0%
+that's in ZN star and multiplying them
+ 
+
+ align:start position:0%
+that's in ZN star and multiplying them
+by two well let's check 2 * 1 is 2 2 * 2
+
+ align:start position:0%
+by two well let's check 2 * 1 is 2 2 * 2
+ 
+
+ align:start position:0%
+by two well let's check 2 * 1 is 2 2 * 2
+is 4 2 * 4 is 8 2 * 5 is 1 cuz it's 10
+
+ align:start position:0%
+is 4 2 * 4 is 8 2 * 5 is 1 cuz it's 10
+ 
+
+ align:start position:0%
+is 4 2 * 4 is 8 2 * 5 is 1 cuz it's 10
+with a remainder of one um uh 2 * 7 is
+
+ align:start position:0%
+with a remainder of one um uh 2 * 7 is
+ 
+
+ align:start position:0%
+with a remainder of one um uh 2 * 7 is
+14 translates into 5 2 * 8 is 16 uh mod
+
+ align:start position:0%
+14 translates into 5 2 * 8 is 16 uh mod
+ 
+
+ align:start position:0%
+14 translates into 5 2 * 8 is 16 uh mod
+9 translates into seven and as claimed
+
+ align:start position:0%
+9 translates into seven and as claimed
+ 
+
+ align:start position:0%
+9 translates into seven and as claimed
+look at this Here's 2
+
+ align:start position:0%
+look at this Here's 2
+ 
+
+ align:start position:0%
+look at this Here's 2
+48157 it's the same numbers as 1 2 4 5
+
+ align:start position:0%
+48157 it's the same numbers as 1 2 4 5
+ 
+
+ align:start position:0%
+48157 it's the same numbers as 1 2 4 5
+78 just in in a different order let's do
+
+ align:start position:0%
+78 just in in a different order let's do
+ 
+
+ align:start position:0%
+78 just in in a different order let's do
+one more example uh let's try
+
+ align:start position:0%
+one more example uh let's try
+ 
+
+ align:start position:0%
+one more example uh let's try
+multiplying by seven it's another
+
+ align:start position:0%
+multiplying by seven it's another
+ 
+
+ align:start position:0%
+multiplying by seven it's another
+respectable element over here 7 * 1 is 7
+
+ align:start position:0%
+respectable element over here 7 * 1 is 7
+ 
+
+ align:start position:0%
+respectable element over here 7 * 1 is 7
+7 * 2 is 14 which means uh it's five uh
+
+ align:start position:0%
+7 * 2 is 14 which means uh it's five uh
+ 
+
+ align:start position:0%
+7 * 2 is 14 which means uh it's five uh
+in z9 uh 4 * 7 is 28 well 3 * 7 uh is 27
+
+ align:start position:0%
+in z9 uh 4 * 7 is 28 well 3 * 7 uh is 27
+ 
+
+ align:start position:0%
+in z9 uh 4 * 7 is 28 well 3 * 7 uh is 27
+so that leaves a remainder of 1 and 4 *
+
+ align:start position:0%
+so that leaves a remainder of 1 and 4 *
+ 
+
+ align:start position:0%
+so that leaves a remainder of 1 and 4 *
+7 is 1 and z9 likewise 5 * 7 is 8 uh 7 *
+
+ align:start position:0%
+7 is 1 and z9 likewise 5 * 7 is 8 uh 7 *
+ 
+
+ align:start position:0%
+7 is 1 and z9 likewise 5 * 7 is 8 uh 7 *
+7 is 4 and 7 * 8 is 56 um which which
+
+ align:start position:0%
+7 is 4 and 7 * 8 is 56 um which which
+ 
+
+ align:start position:0%
+7 is 4 and 7 * 8 is 56 um which which
+translates to two and sure enough as
+
+ align:start position:0%
+translates to two and sure enough as
+ 
+
+ align:start position:0%
+translates to two and sure enough as
+claimed I see the same numbers 7518 42
+
+ align:start position:0%
+claimed I see the same numbers 7518 42
+ 
+
+ align:start position:0%
+claimed I see the same numbers 7518 42
+just these numbers scrambled in order
+
+ align:start position:0%
+just these numbers scrambled in order
+ 
+
+ align:start position:0%
+just these numbers scrambled in order
+they're permuted which is the outcome of
+
+ align:start position:0%
+they're permuted which is the outcome of
+ 
+
+ align:start position:0%
+they're permuted which is the outcome of
+multiplying by seven okay so let's go
+
+ align:start position:0%
+multiplying by seven okay so let's go
+ 
+
+ align:start position:0%
+multiplying by seven okay so let's go
+back what we've just Illustrated is this
+
+ align:start position:0%
+back what we've just Illustrated is this
+ 
+
+ align:start position:0%
+back what we've just Illustrated is this
+fact that we've already concluded that
+
+ align:start position:0%
+fact that we've already concluded that
+ 
+
+ align:start position:0%
+fact that we've already concluded that
+if you take ZN star and you multiply it
+
+ align:start position:0%
+if you take ZN star and you multiply it
+ 
+
+ align:start position:0%
+if you take ZN star and you multiply it
+by an element K in ZN star you get the
+
+ align:start position:0%
+by an element K in ZN star you get the
+ 
+
+ align:start position:0%
+by an element K in ZN star you get the
+same set in different order so ZN star
+
+ align:start position:0%
+same set in different order so ZN star
+ 
+
+ align:start position:0%
+same set in different order so ZN star
+is equal to K * the N star and now we're
+
+ align:start position:0%
+is equal to K * the N star and now we're
+ 
+
+ align:start position:0%
+is equal to K * the N star and now we're
+on the brink of proving Oilers theorem
+
+ align:start position:0%
+on the brink of proving Oilers theorem
+ 
+
+ align:start position:0%
+on the brink of proving Oilers theorem
+because what I want to do is say look
+
+ align:start position:0%
+because what I want to do is say look
+ 
+
+ align:start position:0%
+because what I want to do is say look
+these two sets are the same let's
+
+ align:start position:0%
+these two sets are the same let's
+ 
+
+ align:start position:0%
+these two sets are the same let's
+multiply all the elements on the left
+
+ align:start position:0%
+multiply all the elements on the left
+ 
+
+ align:start position:0%
+multiply all the elements on the left
+together and multiply all the elements
+
+ align:start position:0%
+together and multiply all the elements
+ 
+
+ align:start position:0%
+together and multiply all the elements
+on the right together let's take the
+
+ align:start position:0%
+on the right together let's take the
+ 
+
+ align:start position:0%
+on the right together let's take the
+product of those elements so let's take
+
+ align:start position:0%
+product of those elements so let's take
+ 
+
+ align:start position:0%
+product of those elements so let's take
+the product of ZN star and compare it to
+
+ align:start position:0%
+the product of ZN star and compare it to
+ 
+
+ align:start position:0%
+the product of ZN star and compare it to
+the product of kzn star so big Pi here
+
+ align:start position:0%
+the product of kzn star so big Pi here
+ 
+
+ align:start position:0%
+the product of kzn star so big Pi here
+is indicating the product of all of the
+
+ align:start position:0%
+is indicating the product of all of the
+ 
+
+ align:start position:0%
+is indicating the product of all of the
+elements in this set the product of all
+
+ align:start position:0%
+elements in this set the product of all
+ 
+
+ align:start position:0%
+elements in this set the product of all
+of the elements in this set well um
+
+ align:start position:0%
+of the elements in this set well um
+ 
+
+ align:start position:0%
+of the elements in this set well um
+let's look at the set on the right um
+
+ align:start position:0%
+let's look at the set on the right um
+ 
+
+ align:start position:0%
+let's look at the set on the right um
+this is the product of K times all the
+
+ align:start position:0%
+this is the product of K times all the
+ 
+
+ align:start position:0%
+this is the product of K times all the
+elements in Z Star well how many
+
+ align:start position:0%
+elements in Z Star well how many
+ 
+
+ align:start position:0%
+elements in Z Star well how many
+elements are there fee of n elements in
+
+ align:start position:0%
+elements are there fee of n elements in
+ 
+
+ align:start position:0%
+elements are there fee of n elements in
+Z Star by definition and let's factor
+
+ align:start position:0%
+Z Star by definition and let's factor
+ 
+
+ align:start position:0%
+Z Star by definition and let's factor
+out all the ks so this expression here
+
+ align:start position:0%
+out all the ks so this expression here
+ 
+
+ align:start position:0%
+out all the ks so this expression here
+the product of of K times each element
+
+ align:start position:0%
+the product of of K times each element
+ 
+
+ align:start position:0%
+the product of of K times each element
+in ZN star is the same as the product of
+
+ align:start position:0%
+in ZN star is the same as the product of
+ 
+
+ align:start position:0%
+in ZN star is the same as the product of
+the elements in Z and star times K to as
+
+ align:start position:0%
+the elements in Z and star times K to as
+ 
+
+ align:start position:0%
+the elements in Z and star times K to as
+many elements is there were namely K to
+
+ align:start position:0%
+many elements is there were namely K to
+ 
+
+ align:start position:0%
+many elements is there were namely K to
+the fee of n I'm just factoring k out of
+
+ align:start position:0%
+the fee of n I'm just factoring k out of
+ 
+
+ align:start position:0%
+the fee of n I'm just factoring k out of
+this product there's my K to the fee of
+
+ align:start position:0%
+this product there's my K to the fee of
+ 
+
+ align:start position:0%
+this product there's my K to the fee of
+N and now look what I got here that's Pi
+
+ align:start position:0%
+N and now look what I got here that's Pi
+ 
+
+ align:start position:0%
+N and now look what I got here that's Pi
+ZN star and that's Pi ZN star what do I
+
+ align:start position:0%
+ZN star and that's Pi ZN star what do I
+ 
+
+ align:start position:0%
+ZN star and that's Pi ZN star what do I
+know about multiplying elements in ZN
+
+ align:start position:0%
+know about multiplying elements in ZN
+ 
+
+ align:start position:0%
+know about multiplying elements in ZN
+star they're in ZN star this product
+
+ align:start position:0%
+star they're in ZN star this product
+ 
+
+ align:start position:0%
+star they're in ZN star this product
+will be some other element in ZN star so
+
+ align:start position:0%
+will be some other element in ZN star so
+ 
+
+ align:start position:0%
+will be some other element in ZN star so
+will this product but what do I know
+
+ align:start position:0%
+will this product but what do I know
+ 
+
+ align:start position:0%
+will this product but what do I know
+about ZN star they're cancelable so um
+
+ align:start position:0%
+about ZN star they're cancelable so um
+ 
+
+ align:start position:0%
+about ZN star they're cancelable so um
+just looking ignoring the middle term
+
+ align:start position:0%
+just looking ignoring the middle term
+ 
+
+ align:start position:0%
+just looking ignoring the middle term
+now what I'm concluding is that the
+
+ align:start position:0%
+now what I'm concluding is that the
+ 
+
+ align:start position:0%
+now what I'm concluding is that the
+product of ZN is K to the fee of n * the
+
+ align:start position:0%
+product of ZN is K to the fee of n * the
+ 
+
+ align:start position:0%
+product of ZN is K to the fee of n * the
+product of ZN star let's cancel those
+
+ align:start position:0%
+product of ZN star let's cancel those
+ 
+
+ align:start position:0%
+product of ZN star let's cancel those
+cancelable terms and I'm done I've just
+
+ align:start position:0%
+cancelable terms and I'm done I've just
+ 
+
+ align:start position:0%
+cancelable terms and I'm done I've just
+figured out that one which is the result
+
+ align:start position:0%
+figured out that one which is the result
+ 
+
+ align:start position:0%
+figured out that one which is the result
+of canceling the term on the left um is
+
+ align:start position:0%
+of canceling the term on the left um is
+ 
+
+ align:start position:0%
+of canceling the term on the left um is
+equal to K to the Fe of N and we have
+
+ align:start position:0%
+equal to K to the Fe of N and we have
+ 
+
+ align:start position:0%
+equal to K to the Fe of N and we have
+successfully proved Oilers theorem which
+
+ align:start position:0%
+successfully proved Oilers theorem which
+ 
+
+ align:start position:0%
+successfully proved Oilers theorem which
+is what we were aiming for in this
+
+ align:start position:0%
+is what we were aiming for in this
+ 
+
+ align:start position:0%
+is what we were aiming for in this
+segment
\ No newline at end of file
diff --git a/edLnZgF9mUg.txt b/edLnZgF9mUg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc47a5acf2df9adf2fa57737b3f105a241ddfb44
--- /dev/null
+++ b/edLnZgF9mUg.txt
@@ -0,0 +1,12403 @@
+align:start position:0%
+ 
+all right so as we discussed we're gonna
+
+ align:start position:0%
+all right so as we discussed we're gonna
+ 
+
+ align:start position:0%
+all right so as we discussed we're gonna
+start off with the most basic question
+
+ align:start position:0%
+start off with the most basic question
+ 
+
+ align:start position:0%
+start off with the most basic question
+how do airplanes fly it's a very
+
+ align:start position:0%
+how do airplanes fly it's a very
+ 
+
+ align:start position:0%
+how do airplanes fly it's a very
+critical question I think everybody
+
+ align:start position:0%
+critical question I think everybody
+ 
+
+ align:start position:0%
+critical question I think everybody
+should know the answer to this going
+
+ align:start position:0%
+should know the answer to this going
+ 
+
+ align:start position:0%
+should know the answer to this going
+back to the comic that Meenakshi had
+
+ align:start position:0%
+back to the comic that Meenakshi had
+ 
+
+ align:start position:0%
+back to the comic that Meenakshi had
+with Calvin and Hobbes and not knowing
+
+ align:start position:0%
+with Calvin and Hobbes and not knowing
+ 
+
+ align:start position:0%
+with Calvin and Hobbes and not knowing
+how airplanes fly I'm thinking that it's
+
+ align:start position:0%
+how airplanes fly I'm thinking that it's
+ 
+
+ align:start position:0%
+how airplanes fly I'm thinking that it's
+magic is not the way that any MIT
+
+ align:start position:0%
+magic is not the way that any MIT
+ 
+
+ align:start position:0%
+magic is not the way that any MIT
+students should be so we're gonna cover
+
+ align:start position:0%
+students should be so we're gonna cover
+ 
+
+ align:start position:0%
+students should be so we're gonna cover
+how airplanes fly and we're actually
+
+ align:start position:0%
+how airplanes fly and we're actually
+ 
+
+ align:start position:0%
+how airplanes fly and we're actually
+gonna go beyond what the FAA requires
+
+ align:start position:0%
+gonna go beyond what the FAA requires
+ 
+
+ align:start position:0%
+gonna go beyond what the FAA requires
+you to know because frankly you should
+
+ align:start position:0%
+you to know because frankly you should
+ 
+
+ align:start position:0%
+you to know because frankly you should
+know how airplanes fly so just so that
+
+ align:start position:0%
+know how airplanes fly so just so that
+ 
+
+ align:start position:0%
+know how airplanes fly so just so that
+we have a common vocabulary with which
+
+ align:start position:0%
+we have a common vocabulary with which
+ 
+
+ align:start position:0%
+we have a common vocabulary with which
+to discuss we're going to talk a little
+
+ align:start position:0%
+to discuss we're going to talk a little
+ 
+
+ align:start position:0%
+to discuss we're going to talk a little
+bit about airplane parts so here in my
+
+ align:start position:0%
+bit about airplane parts so here in my
+ 
+
+ align:start position:0%
+bit about airplane parts so here in my
+my little airplane it's kind of a model
+
+ align:start position:0%
+my little airplane it's kind of a model
+ 
+
+ align:start position:0%
+my little airplane it's kind of a model
+there so you can see that at the at the
+
+ align:start position:0%
+there so you can see that at the at the
+ 
+
+ align:start position:0%
+there so you can see that at the at the
+front you have your your propeller and
+
+ align:start position:0%
+front you have your your propeller and
+ 
+
+ align:start position:0%
+front you have your your propeller and
+so the engine the propeller and this
+
+ align:start position:0%
+so the engine the propeller and this
+ 
+
+ align:start position:0%
+so the engine the propeller and this
+little plane is up here at the front
+
+ align:start position:0%
+little plane is up here at the front
+ 
+
+ align:start position:0%
+little plane is up here at the front
+who knows what a fuselage is just shout
+
+ align:start position:0%
+who knows what a fuselage is just shout
+ 
+
+ align:start position:0%
+who knows what a fuselage is just shout
+it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the middle part the body that's where
+
+ align:start position:0%
+the middle part the body that's where
+ 
+
+ align:start position:0%
+the middle part the body that's where
+the passengers sit yeah so that that
+
+ align:start position:0%
+the passengers sit yeah so that that
+ 
+
+ align:start position:0%
+the passengers sit yeah so that that
+whole middle part where people sit so if
+
+ align:start position:0%
+whole middle part where people sit so if
+ 
+
+ align:start position:0%
+whole middle part where people sit so if
+you're thinking about a big jet engine
+
+ align:start position:0%
+you're thinking about a big jet engine
+ 
+
+ align:start position:0%
+you're thinking about a big jet engine
+it's where all the rows of seats are
+
+ align:start position:0%
+it's where all the rows of seats are
+ 
+
+ align:start position:0%
+it's where all the rows of seats are
+where everybody sits that tube in the
+
+ align:start position:0%
+where everybody sits that tube in the
+ 
+
+ align:start position:0%
+where everybody sits that tube in the
+middle is called the fuselage and the
+
+ align:start position:0%
+middle is called the fuselage and the
+ 
+
+ align:start position:0%
+middle is called the fuselage and the
+wings stick out the side so the middle
+
+ align:start position:0%
+wings stick out the side so the middle
+ 
+
+ align:start position:0%
+wings stick out the side so the middle
+part is a fuselage and then one thing
+
+ align:start position:0%
+part is a fuselage and then one thing
+ 
+
+ align:start position:0%
+part is a fuselage and then one thing
+that's interesting is that the tail
+
+ align:start position:0%
+that's interesting is that the tail
+ 
+
+ align:start position:0%
+that's interesting is that the tail
+actually has a lot more components
+
+ align:start position:0%
+actually has a lot more components
+ 
+
+ align:start position:0%
+actually has a lot more components
+people kind of casually refer to it as
+
+ align:start position:0%
+people kind of casually refer to it as
+ 
+
+ align:start position:0%
+people kind of casually refer to it as
+the tail but there's a vertical part
+
+ align:start position:0%
+the tail but there's a vertical part
+ 
+
+ align:start position:0%
+the tail but there's a vertical part
+that comes up in the back of the
+
+ align:start position:0%
+that comes up in the back of the
+ 
+
+ align:start position:0%
+that comes up in the back of the
+vertical part of the tail can actually
+
+ align:start position:0%
+vertical part of the tail can actually
+ 
+
+ align:start position:0%
+vertical part of the tail can actually
+tilt side to side and then you have a
+
+ align:start position:0%
+tilt side to side and then you have a
+ 
+
+ align:start position:0%
+tilt side to side and then you have a
+flat horizontal part and that actually
+
+ align:start position:0%
+flat horizontal part and that actually
+ 
+
+ align:start position:0%
+flat horizontal part and that actually
+has a back part that can go down and up
+
+ align:start position:0%
+has a back part that can go down and up
+ 
+
+ align:start position:0%
+has a back part that can go down and up
+and so we're going to talk about what
+
+ align:start position:0%
+and so we're going to talk about what
+ 
+
+ align:start position:0%
+and so we're going to talk about what
+all of these are so the the back
+
+ align:start position:0%
+all of these are so the the back
+ 
+
+ align:start position:0%
+all of these are so the the back
+vertical part when it goes side to side
+
+ align:start position:0%
+vertical part when it goes side to side
+ 
+
+ align:start position:0%
+vertical part when it goes side to side
+is your rudder the flat part is your
+
+ align:start position:0%
+is your rudder the flat part is your
+ 
+
+ align:start position:0%
+is your rudder the flat part is your
+elevator that you can move up and down
+
+ align:start position:0%
+elevator that you can move up and down
+ 
+
+ align:start position:0%
+elevator that you can move up and down
+it allows you to control the airplane we
+
+ align:start position:0%
+it allows you to control the airplane we
+ 
+
+ align:start position:0%
+it allows you to control the airplane we
+also have of course the the wings
+
+ align:start position:0%
+also have of course the the wings
+ 
+
+ align:start position:0%
+also have of course the the wings
+sometimes there are struts that support
+
+ align:start position:0%
+sometimes there are struts that support
+ 
+
+ align:start position:0%
+sometimes there are struts that support
+the wings so they go from the wing down
+
+ align:start position:0%
+the wings so they go from the wing down
+ 
+
+ align:start position:0%
+the wings so they go from the wing down
+to that fuselage and then you have a
+
+ align:start position:0%
+to that fuselage and then you have a
+ 
+
+ align:start position:0%
+to that fuselage and then you have a
+landing gear in this case you have these
+
+ align:start position:0%
+landing gear in this case you have these
+ 
+
+ align:start position:0%
+landing gear in this case you have these
+wheels down at the bottom we're also
+
+ align:start position:0%
+wheels down at the bottom we're also
+ 
+
+ align:start position:0%
+wheels down at the bottom we're also
+going to talk to you during this course
+
+ align:start position:0%
+going to talk to you during this course
+ 
+
+ align:start position:0%
+going to talk to you during this course
+about sea planes so they have slightly
+
+ align:start position:0%
+about sea planes so they have slightly
+ 
+
+ align:start position:0%
+about sea planes so they have slightly
+different landing gear but this is a
+
+ align:start position:0%
+different landing gear but this is a
+ 
+
+ align:start position:0%
+different landing gear but this is a
+good good place to start okay the other
+
+ align:start position:0%
+good good place to start okay the other
+ 
+
+ align:start position:0%
+good good place to start okay the other
+thing that we need to talk about are
+
+ align:start position:0%
+thing that we need to talk about are
+ 
+
+ align:start position:0%
+thing that we need to talk about are
+just the the main four forces that are
+
+ align:start position:0%
+just the the main four forces that are
+ 
+
+ align:start position:0%
+just the the main four forces that are
+on an airplane so they're they're pretty
+
+ align:start position:0%
+on an airplane so they're they're pretty
+ 
+
+ align:start position:0%
+on an airplane so they're they're pretty
+straightforward so the the force going
+
+ align:start position:0%
+straightforward so the the force going
+ 
+
+ align:start position:0%
+straightforward so the the force going
+up is lift and that force is opposed by
+
+ align:start position:0%
+up is lift and that force is opposed by
+ 
+
+ align:start position:0%
+up is lift and that force is opposed by
+the downward force of weight okay and
+
+ align:start position:0%
+the downward force of weight okay and
+ 
+
+ align:start position:0%
+the downward force of weight okay and
+then when you're moving the airplane
+
+ align:start position:0%
+then when you're moving the airplane
+ 
+
+ align:start position:0%
+then when you're moving the airplane
+forward that's thrust and it is opposed
+
+ align:start position:0%
+forward that's thrust and it is opposed
+ 
+
+ align:start position:0%
+forward that's thrust and it is opposed
+by drag so what we're going to talk
+
+ align:start position:0%
+by drag so what we're going to talk
+ 
+
+ align:start position:0%
+by drag so what we're going to talk
+about is that in order for an airplane
+
+ align:start position:0%
+about is that in order for an airplane
+ 
+
+ align:start position:0%
+about is that in order for an airplane
+to go up the lift has to exceed the drag
+
+ align:start position:0%
+to go up the lift has to exceed the drag
+ 
+
+ align:start position:0%
+to go up the lift has to exceed the drag
+in order for the airplane to go forward
+
+ align:start position:0%
+in order for the airplane to go forward
+ 
+
+ align:start position:0%
+in order for the airplane to go forward
+the thrust has to exceed the dress
+
+ align:start position:0%
+the thrust has to exceed the dress
+ 
+
+ align:start position:0%
+the thrust has to exceed the dress
+excuse me the lift has to exceed the
+
+ align:start position:0%
+excuse me the lift has to exceed the
+ 
+
+ align:start position:0%
+excuse me the lift has to exceed the
+weight and the thrust has to exceed the
+
+ align:start position:0%
+weight and the thrust has to exceed the
+ 
+
+ align:start position:0%
+weight and the thrust has to exceed the
+drag so those are the the main four
+
+ align:start position:0%
+drag so those are the the main four
+ 
+
+ align:start position:0%
+drag so those are the the main four
+forces we're gonna be working with today
+
+ align:start position:0%
+forces we're gonna be working with today
+ 
+
+ align:start position:0%
+forces we're gonna be working with today
+so now I'm gonna spend a little bit time
+
+ align:start position:0%
+so now I'm gonna spend a little bit time
+ 
+
+ align:start position:0%
+so now I'm gonna spend a little bit time
+over here on the blackboard
+
+ align:start position:0%
+over here on the blackboard
+ 
+
+ align:start position:0%
+over here on the blackboard
+video folks platform they said this way
+
+ align:start position:0%
+video folks platform they said this way
+ 
+
+ align:start position:0%
+video folks platform they said this way
+boy this one's better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah fancy colored truck alright
+
+ align:start position:0%
+yeah fancy colored truck alright
+ 
+
+ align:start position:0%
+yeah fancy colored truck alright
+shocks of color alright okay so I will
+
+ align:start position:0%
+shocks of color alright okay so I will
+ 
+
+ align:start position:0%
+shocks of color alright okay so I will
+preface the discussion about lift with
+
+ align:start position:0%
+preface the discussion about lift with
+ 
+
+ align:start position:0%
+preface the discussion about lift with
+the fact that there are a lot of
+
+ align:start position:0%
+the fact that there are a lot of
+ 
+
+ align:start position:0%
+the fact that there are a lot of
+theories of lift out there some of which
+
+ align:start position:0%
+theories of lift out there some of which
+ 
+
+ align:start position:0%
+theories of lift out there some of which
+are wrong so if you spend some time
+
+ align:start position:0%
+are wrong so if you spend some time
+ 
+
+ align:start position:0%
+are wrong so if you spend some time
+googling lift before coming here you
+
+ align:start position:0%
+googling lift before coming here you
+ 
+
+ align:start position:0%
+googling lift before coming here you
+might have actually found a couple
+
+ align:start position:0%
+might have actually found a couple
+ 
+
+ align:start position:0%
+might have actually found a couple
+scenarios that are completely false so
+
+ align:start position:0%
+scenarios that are completely false so
+ 
+
+ align:start position:0%
+scenarios that are completely false so
+we're gonna focus on what's true but I
+
+ align:start position:0%
+we're gonna focus on what's true but I
+ 
+
+ align:start position:0%
+we're gonna focus on what's true but I
+will cover at least one of those false
+
+ align:start position:0%
+will cover at least one of those false
+ 
+
+ align:start position:0%
+will cover at least one of those false
+theories to make sure you guys don't get
+
+ align:start position:0%
+theories to make sure you guys don't get
+ 
+
+ align:start position:0%
+theories to make sure you guys don't get
+hung up on that so in order to talk
+
+ align:start position:0%
+hung up on that so in order to talk
+ 
+
+ align:start position:0%
+hung up on that so in order to talk
+about it we're going to think about an
+
+ align:start position:0%
+about it we're going to think about an
+ 
+
+ align:start position:0%
+about it we're going to think about an
+an airplane and we're gonna do a
+
+ align:start position:0%
+an airplane and we're gonna do a
+ 
+
+ align:start position:0%
+an airplane and we're gonna do a
+cross-section of the airplane so if you
+
+ align:start position:0%
+cross-section of the airplane so if you
+ 
+
+ align:start position:0%
+cross-section of the airplane so if you
+took a saw and you cut off the wing what
+
+ align:start position:0%
+took a saw and you cut off the wing what
+ 
+
+ align:start position:0%
+took a saw and you cut off the wing what
+are what are you left with I don't do it
+
+ align:start position:0%
+are what are you left with I don't do it
+ 
+
+ align:start position:0%
+are what are you left with I don't do it
+this way so if you cut off the wing at
+
+ align:start position:0%
+this way so if you cut off the wing at
+ 
+
+ align:start position:0%
+this way so if you cut off the wing at
+the front of the wing is the leading
+
+ align:start position:0%
+the front of the wing is the leading
+ 
+
+ align:start position:0%
+the front of the wing is the leading
+edge the back of the wing is the
+
+ align:start position:0%
+edge the back of the wing is the
+ 
+
+ align:start position:0%
+edge the back of the wing is the
+trailing edge if you did it if you cut
+
+ align:start position:0%
+trailing edge if you did it if you cut
+ 
+
+ align:start position:0%
+trailing edge if you did it if you cut
+that off what does it look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it looks like this and this shape is
+
+ align:start position:0%
+so it looks like this and this shape is
+ 
+
+ align:start position:0%
+so it looks like this and this shape is
+called an airfoil and we'll get into the
+
+ align:start position:0%
+called an airfoil and we'll get into the
+ 
+
+ align:start position:0%
+called an airfoil and we'll get into the
+specifics later but first we'll just
+
+ align:start position:0%
+specifics later but first we'll just
+ 
+
+ align:start position:0%
+specifics later but first we'll just
+we'll talk about a simple way to
+
+ align:start position:0%
+we'll talk about a simple way to
+ 
+
+ align:start position:0%
+we'll talk about a simple way to
+understand how lift works so if this is
+
+ align:start position:0%
+understand how lift works so if this is
+ 
+
+ align:start position:0%
+understand how lift works so if this is
+the the wing and you have air coming in
+
+ align:start position:0%
+the the wing and you have air coming in
+ 
+
+ align:start position:0%
+the the wing and you have air coming in
+the air is pushed down by the shape of
+
+ align:start position:0%
+the air is pushed down by the shape of
+ 
+
+ align:start position:0%
+the air is pushed down by the shape of
+this wing so that means as as air flows
+
+ align:start position:0%
+this wing so that means as as air flows
+ 
+
+ align:start position:0%
+this wing so that means as as air flows
+by it gets pushed down now what is air
+
+ align:start position:0%
+by it gets pushed down now what is air
+ 
+
+ align:start position:0%
+by it gets pushed down now what is air
+air is not nothing air has molecules it
+
+ align:start position:0%
+air is not nothing air has molecules it
+ 
+
+ align:start position:0%
+air is not nothing air has molecules it
+has mass so if you think about
+
+ align:start position:0%
+has mass so if you think about
+ 
+
+ align:start position:0%
+has mass so if you think about
+conservation of momentum this is I think
+
+ align:start position:0%
+conservation of momentum this is I think
+ 
+
+ align:start position:0%
+conservation of momentum this is I think
+the easiest way to think about lips so
+
+ align:start position:0%
+the easiest way to think about lips so
+ 
+
+ align:start position:0%
+the easiest way to think about lips so
+conservation of momentum you have a
+
+ align:start position:0%
+conservation of momentum you have a
+ 
+
+ align:start position:0%
+conservation of momentum you have a
+bunch of air pal air molecules and those
+
+ align:start position:0%
+bunch of air pal air molecules and those
+ 
+
+ align:start position:0%
+bunch of air pal air molecules and those
+air molecules are pushed down so you
+
+ align:start position:0%
+air molecules are pushed down so you
+ 
+
+ align:start position:0%
+air molecules are pushed down so you
+have mass being pushed down so if mass
+
+ align:start position:0%
+have mass being pushed down so if mass
+ 
+
+ align:start position:0%
+have mass being pushed down so if mass
+is being pushed down for conservation of
+
+ align:start position:0%
+is being pushed down for conservation of
+ 
+
+ align:start position:0%
+is being pushed down for conservation of
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+something must be pushed up and that's
+
+ align:start position:0%
+something must be pushed up and that's
+ 
+
+ align:start position:0%
+something must be pushed up and that's
+the wing so that's the easiest way to
+
+ align:start position:0%
+the wing so that's the easiest way to
+ 
+
+ align:start position:0%
+the wing so that's the easiest way to
+think about it that if you're deflecting
+
+ align:start position:0%
+think about it that if you're deflecting
+ 
+
+ align:start position:0%
+think about it that if you're deflecting
+the air downward in order to have
+
+ align:start position:0%
+the air downward in order to have
+ 
+
+ align:start position:0%
+the air downward in order to have
+conservation of momentum the mass of the
+
+ align:start position:0%
+conservation of momentum the mass of the
+ 
+
+ align:start position:0%
+conservation of momentum the mass of the
+wing is lifted upwards we're gonna break
+
+ align:start position:0%
+wing is lifted upwards we're gonna break
+ 
+
+ align:start position:0%
+wing is lifted upwards we're gonna break
+that down but I think that's a good
+
+ align:start position:0%
+that down but I think that's a good
+ 
+
+ align:start position:0%
+that down but I think that's a good
+place to start I'm just gonna take one
+
+ align:start position:0%
+place to start I'm just gonna take one
+ 
+
+ align:start position:0%
+place to start I'm just gonna take one
+moment to talk about an incorrect theory
+
+ align:start position:0%
+moment to talk about an incorrect theory
+ 
+
+ align:start position:0%
+moment to talk about an incorrect theory
+of lift so let me emphasize it's wrong
+
+ align:start position:0%
+of lift so let me emphasize it's wrong
+ 
+
+ align:start position:0%
+of lift so let me emphasize it's wrong
+one of them is called equal transit
+
+ align:start position:0%
+one of them is called equal transit
+ 
+
+ align:start position:0%
+one of them is called equal transit
+theory has anyone heard about this
+
+ align:start position:0%
+theory has anyone heard about this
+ 
+
+ align:start position:0%
+theory has anyone heard about this
+getting a lot of head nods okay it's
+
+ align:start position:0%
+getting a lot of head nods okay it's
+ 
+
+ align:start position:0%
+getting a lot of head nods okay it's
+wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal transit theory which is incorrect
+
+ align:start position:0%
+equal transit theory which is incorrect
+ 
+
+ align:start position:0%
+equal transit theory which is incorrect
+says that basically a molecule of air
+
+ align:start position:0%
+says that basically a molecule of air
+ 
+
+ align:start position:0%
+says that basically a molecule of air
+that's coming over that starts over here
+
+ align:start position:0%
+that's coming over that starts over here
+ 
+
+ align:start position:0%
+that's coming over that starts over here
+at the front has to go around the bottom
+
+ align:start position:0%
+at the front has to go around the bottom
+ 
+
+ align:start position:0%
+at the front has to go around the bottom
+and meet the tail at the same time that
+
+ align:start position:0%
+and meet the tail at the same time that
+ 
+
+ align:start position:0%
+and meet the tail at the same time that
+a molecule that goes over the top has to
+
+ align:start position:0%
+a molecule that goes over the top has to
+ 
+
+ align:start position:0%
+a molecule that goes over the top has to
+meet it at the back there is no physical
+
+ align:start position:0%
+meet it at the back there is no physical
+ 
+
+ align:start position:0%
+meet it at the back there is no physical
+principle that says that it is false and
+
+ align:start position:0%
+principle that says that it is false and
+ 
+
+ align:start position:0%
+principle that says that it is false and
+in fact we have measured that they don't
+
+ align:start position:0%
+in fact we have measured that they don't
+ 
+
+ align:start position:0%
+in fact we have measured that they don't
+the molecules that go under the bottom
+
+ align:start position:0%
+the molecules that go under the bottom
+ 
+
+ align:start position:0%
+the molecules that go under the bottom
+of the wing versus the top of the wing
+
+ align:start position:0%
+of the wing versus the top of the wing
+ 
+
+ align:start position:0%
+of the wing versus the top of the wing
+don't actually reach the end at the same
+
+ align:start position:0%
+don't actually reach the end at the same
+ 
+
+ align:start position:0%
+don't actually reach the end at the same
+time but in this false theory equal
+
+ align:start position:0%
+time but in this false theory equal
+ 
+
+ align:start position:0%
+time but in this false theory equal
+transit Theory they say that you have to
+
+ align:start position:0%
+transit Theory they say that you have to
+ 
+
+ align:start position:0%
+transit Theory they say that you have to
+reach the bottom at the same time they
+
+ align:start position:0%
+reach the bottom at the same time they
+ 
+
+ align:start position:0%
+reach the bottom at the same time they
+also say that there is more distance
+
+ align:start position:0%
+also say that there is more distance
+ 
+
+ align:start position:0%
+also say that there is more distance
+basically to cover because of the shape
+
+ align:start position:0%
+basically to cover because of the shape
+ 
+
+ align:start position:0%
+basically to cover because of the shape
+of the airfoil so in order for the
+
+ align:start position:0%
+of the airfoil so in order for the
+ 
+
+ align:start position:0%
+of the airfoil so in order for the
+molecules going over the top to reach at
+
+ align:start position:0%
+molecules going over the top to reach at
+ 
+
+ align:start position:0%
+molecules going over the top to reach at
+the same time as the molecules over the
+
+ align:start position:0%
+the same time as the molecules over the
+ 
+
+ align:start position:0%
+the same time as the molecules over the
+bottom they have to go faster and so
+
+ align:start position:0%
+bottom they have to go faster and so
+ 
+
+ align:start position:0%
+bottom they have to go faster and so
+since the air is moving faster over the
+
+ align:start position:0%
+since the air is moving faster over the
+ 
+
+ align:start position:0%
+since the air is moving faster over the
+top and the bottom that's what creates
+
+ align:start position:0%
+top and the bottom that's what creates
+ 
+
+ align:start position:0%
+top and the bottom that's what creates
+lift so that's false and there are many
+
+ align:start position:0%
+lift so that's false and there are many
+ 
+
+ align:start position:0%
+lift so that's false and there are many
+reasons why it's false you know the
+
+ align:start position:0%
+reasons why it's false you know the
+ 
+
+ align:start position:0%
+reasons why it's false you know the
+biggest one being that there's there's
+
+ align:start position:0%
+biggest one being that there's there's
+ 
+
+ align:start position:0%
+biggest one being that there's there's
+no physical principle that says that two
+
+ align:start position:0%
+no physical principle that says that two
+ 
+
+ align:start position:0%
+no physical principle that says that two
+molecules starting at the same time one
+
+ align:start position:0%
+molecules starting at the same time one
+ 
+
+ align:start position:0%
+molecules starting at the same time one
+going over the top and one going over
+
+ align:start position:0%
+going over the top and one going over
+ 
+
+ align:start position:0%
+going over the top and one going over
+the bottom reaches the end at the same
+
+ align:start position:0%
+the bottom reaches the end at the same
+ 
+
+ align:start position:0%
+the bottom reaches the end at the same
+time that's just not true
+
+ align:start position:0%
+time that's just not true
+ 
+
+ align:start position:0%
+time that's just not true
+and we'll show you some more diagrams
+
+ align:start position:0%
+and we'll show you some more diagrams
+ 
+
+ align:start position:0%
+and we'll show you some more diagrams
+that show in fact it doesn't happen the
+
+ align:start position:0%
+that show in fact it doesn't happen the
+ 
+
+ align:start position:0%
+that show in fact it doesn't happen the
+molecules don't reach at the same time
+
+ align:start position:0%
+molecules don't reach at the same time
+ 
+
+ align:start position:0%
+molecules don't reach at the same time
+anyway so please despite that being very
+
+ align:start position:0%
+anyway so please despite that being very
+ 
+
+ align:start position:0%
+anyway so please despite that being very
+widely propagated that is not true
+
+ align:start position:0%
+widely propagated that is not true
+ 
+
+ align:start position:0%
+widely propagated that is not true
+and please don't spend time on that that
+
+ align:start position:0%
+and please don't spend time on that that
+ 
+
+ align:start position:0%
+and please don't spend time on that that
+theory all right so let's focus on what
+
+ align:start position:0%
+theory all right so let's focus on what
+ 
+
+ align:start position:0%
+theory all right so let's focus on what
+is true how does it really work actually
+
+ align:start position:0%
+is true how does it really work actually
+ 
+
+ align:start position:0%
+is true how does it really work actually
+let me give you one more reason why
+
+ align:start position:0%
+let me give you one more reason why
+ 
+
+ align:start position:0%
+let me give you one more reason why
+that's false the real reason that equal
+
+ align:start position:0%
+that's false the real reason that equal
+ 
+
+ align:start position:0%
+that's false the real reason that equal
+transit theory is trying to tell you
+
+ align:start position:0%
+transit theory is trying to tell you
+ 
+
+ align:start position:0%
+transit theory is trying to tell you
+that that generates lift is that because
+
+ align:start position:0%
+that that generates lift is that because
+ 
+
+ align:start position:0%
+that that generates lift is that because
+of the shape of the airfoil the shape of
+
+ align:start position:0%
+of the shape of the airfoil the shape of
+ 
+
+ align:start position:0%
+of the shape of the airfoil the shape of
+the wing that's why the distance that it
+
+ align:start position:0%
+the wing that's why the distance that it
+ 
+
+ align:start position:0%
+the wing that's why the distance that it
+has to travel is different over the top
+
+ align:start position:0%
+has to travel is different over the top
+ 
+
+ align:start position:0%
+has to travel is different over the top
+versus the bottom but one reason that's
+
+ align:start position:0%
+versus the bottom but one reason that's
+ 
+
+ align:start position:0%
+versus the bottom but one reason that's
+wrong can you pass me that paper
+
+ align:start position:0%
+wrong can you pass me that paper
+ 
+
+ align:start position:0%
+wrong can you pass me that paper
+airplane please who has built a paper
+
+ align:start position:0%
+airplane please who has built a paper
+ 
+
+ align:start position:0%
+airplane please who has built a paper
+airplane before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I see at least two people who
+
+ align:start position:0%
+okay I see at least two people who
+ 
+
+ align:start position:0%
+okay I see at least two people who
+didn't raise their hand do we need to do
+
+ align:start position:0%
+didn't raise their hand do we need to do
+ 
+
+ align:start position:0%
+didn't raise their hand do we need to do
+a class exercise if you have not filled
+
+ align:start position:0%
+a class exercise if you have not filled
+ 
+
+ align:start position:0%
+a class exercise if you have not filled
+a paper airplane it's really important
+
+ align:start position:0%
+a paper airplane it's really important
+ 
+
+ align:start position:0%
+a paper airplane it's really important
+that you do just as it as a general
+
+ align:start position:0%
+that you do just as it as a general
+ 
+
+ align:start position:0%
+that you do just as it as a general
+childhood experience here's a paper
+
+ align:start position:0%
+childhood experience here's a paper
+ 
+
+ align:start position:0%
+childhood experience here's a paper
+airplane thank you
+
+ align:start position:0%
+airplane thank you
+ 
+
+ align:start position:0%
+airplane thank you
+you know actually for building it for me
+
+ align:start position:0%
+you know actually for building it for me
+ 
+
+ align:start position:0%
+you know actually for building it for me
+if we took this paper airplane instead
+
+ align:start position:0%
+if we took this paper airplane instead
+ 
+
+ align:start position:0%
+if we took this paper airplane instead
+of this this fancy this fancy airplane
+
+ align:start position:0%
+of this this fancy this fancy airplane
+ 
+
+ align:start position:0%
+of this this fancy this fancy airplane
+and we did a cross-section of this wing
+
+ align:start position:0%
+and we did a cross-section of this wing
+ 
+
+ align:start position:0%
+and we did a cross-section of this wing
+what would it look like yes you
+
+ align:start position:0%
+what would it look like yes you
+ 
+
+ align:start position:0%
+what would it look like yes you
+demonstrated with your hands but shout
+
+ align:start position:0%
+demonstrated with your hands but shout
+ 
+
+ align:start position:0%
+demonstrated with your hands but shout
+it out yeah maybe the same at the top of
+
+ align:start position:0%
+it out yeah maybe the same at the top of
+ 
+
+ align:start position:0%
+it out yeah maybe the same at the top of
+the bottom top in the bottom it's just a
+
+ align:start position:0%
+the bottom top in the bottom it's just a
+ 
+
+ align:start position:0%
+the bottom top in the bottom it's just a
+piece of paper exactly it's just like a
+
+ align:start position:0%
+piece of paper exactly it's just like a
+ 
+
+ align:start position:0%
+piece of paper exactly it's just like a
+little flat rectangle so instead of this
+
+ align:start position:0%
+little flat rectangle so instead of this
+ 
+
+ align:start position:0%
+little flat rectangle so instead of this
+fancy shape that you have here we're
+
+ align:start position:0%
+fancy shape that you have here we're
+ 
+
+ align:start position:0%
+fancy shape that you have here we're
+knees red for wrong okay it's like a
+
+ align:start position:0%
+knees red for wrong okay it's like a
+ 
+
+ align:start position:0%
+knees red for wrong okay it's like a
+little rectangle right that's what the
+
+ align:start position:0%
+little rectangle right that's what the
+ 
+
+ align:start position:0%
+little rectangle right that's what the
+paper airplanes cross-section of its
+
+ align:start position:0%
+paper airplanes cross-section of its
+ 
+
+ align:start position:0%
+paper airplanes cross-section of its
+wing looks like well surprise surprise
+
+ align:start position:0%
+wing looks like well surprise surprise
+ 
+
+ align:start position:0%
+wing looks like well surprise surprise
+as you said it's the same at the top at
+
+ align:start position:0%
+as you said it's the same at the top at
+ 
+
+ align:start position:0%
+as you said it's the same at the top at
+the bottom so the distance that a air
+
+ align:start position:0%
+the bottom so the distance that a air
+ 
+
+ align:start position:0%
+the bottom so the distance that a air
+molecule would have to travel over the
+
+ align:start position:0%
+molecule would have to travel over the
+ 
+
+ align:start position:0%
+molecule would have to travel over the
+top and the bottom is identical so
+
+ align:start position:0%
+top and the bottom is identical so
+ 
+
+ align:start position:0%
+top and the bottom is identical so
+really the equal transit Theory
+
+ align:start position:0%
+really the equal transit Theory
+ 
+
+ align:start position:0%
+really the equal transit Theory
+completely falls apart yet a paper
+
+ align:start position:0%
+completely falls apart yet a paper
+ 
+
+ align:start position:0%
+completely falls apart yet a paper
+airplane still flies so why is that the
+
+ align:start position:0%
+airplane still flies so why is that the
+ 
+
+ align:start position:0%
+airplane still flies so why is that the
+case again remember the actual reason is
+
+ align:start position:0%
+case again remember the actual reason is
+ 
+
+ align:start position:0%
+case again remember the actual reason is
+that if this paper airplane is inclined
+
+ align:start position:0%
+that if this paper airplane is inclined
+ 
+
+ align:start position:0%
+that if this paper airplane is inclined
+it is pushing air down so air that's
+
+ align:start position:0%
+it is pushing air down so air that's
+ 
+
+ align:start position:0%
+it is pushing air down so air that's
+coming up is bumping into it and being
+
+ align:start position:0%
+coming up is bumping into it and being
+ 
+
+ align:start position:0%
+coming up is bumping into it and being
+pushed down and therefore as you deflect
+
+ align:start position:0%
+pushed down and therefore as you deflect
+ 
+
+ align:start position:0%
+pushed down and therefore as you deflect
+air molecules down conservation of
+
+ align:start position:0%
+air molecules down conservation of
+ 
+
+ align:start position:0%
+air molecules down conservation of
+momentum the wing is lifted up all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we're going to break this down in
+
+ align:start position:0%
+so now we're going to break this down in
+ 
+
+ align:start position:0%
+so now we're going to break this down in
+a little bit more detail and we gonna go
+
+ align:start position:0%
+a little bit more detail and we gonna go
+ 
+
+ align:start position:0%
+a little bit more detail and we gonna go
+back over here to the slides so one
+
+ align:start position:0%
+back over here to the slides so one
+ 
+
+ align:start position:0%
+back over here to the slides so one
+thing that's important you know as I
+
+ align:start position:0%
+thing that's important you know as I
+ 
+
+ align:start position:0%
+thing that's important you know as I
+said a really detailed mathematical
+
+ align:start position:0%
+said a really detailed mathematical
+ 
+
+ align:start position:0%
+said a really detailed mathematical
+description is not really necessary to
+
+ align:start position:0%
+description is not really necessary to
+ 
+
+ align:start position:0%
+description is not really necessary to
+fly a plane or become a pilot the FAA
+
+ align:start position:0%
+fly a plane or become a pilot the FAA
+ 
+
+ align:start position:0%
+fly a plane or become a pilot the FAA
+doesn't require some of this detail but
+
+ align:start position:0%
+doesn't require some of this detail but
+ 
+
+ align:start position:0%
+doesn't require some of this detail but
+it is important to know it to the extent
+
+ align:start position:0%
+it is important to know it to the extent
+ 
+
+ align:start position:0%
+it is important to know it to the extent
+that it helps you control the airplane
+
+ align:start position:0%
+that it helps you control the airplane
+ 
+
+ align:start position:0%
+that it helps you control the airplane
+and fly it so here's a good reference in
+
+ align:start position:0%
+and fly it so here's a good reference in
+ 
+
+ align:start position:0%
+and fly it so here's a good reference in
+terms of that but one of the biggest
+
+ align:start position:0%
+terms of that but one of the biggest
+ 
+
+ align:start position:0%
+terms of that but one of the biggest
+things is just that for a lift you have
+
+ align:start position:0%
+things is just that for a lift you have
+ 
+
+ align:start position:0%
+things is just that for a lift you have
+to increase that downward momentum of
+
+ align:start position:0%
+to increase that downward momentum of
+ 
+
+ align:start position:0%
+to increase that downward momentum of
+the air and air foils are this shape
+
+ align:start position:0%
+the air and air foils are this shape
+ 
+
+ align:start position:0%
+the air and air foils are this shape
+which is called an airfoil is it is a
+
+ align:start position:0%
+which is called an airfoil is it is a
+ 
+
+ align:start position:0%
+which is called an airfoil is it is a
+type of shape that is very efficient at
+
+ align:start position:0%
+type of shape that is very efficient at
+ 
+
+ align:start position:0%
+type of shape that is very efficient at
+increasing that downward momentum now
+
+ align:start position:0%
+increasing that downward momentum now
+ 
+
+ align:start position:0%
+increasing that downward momentum now
+who knows what Bernoulli's principle is
+
+ align:start position:0%
+who knows what Bernoulli's principle is
+ 
+
+ align:start position:0%
+who knows what Bernoulli's principle is
+who's heard of Bernoulli's good
+
+ align:start position:0%
+who's heard of Bernoulli's good
+ 
+
+ align:start position:0%
+who's heard of Bernoulli's good
+everyone's heard of Bernoulli can anyone
+
+ align:start position:0%
+everyone's heard of Bernoulli can anyone
+ 
+
+ align:start position:0%
+everyone's heard of Bernoulli can anyone
+articulate Bernoulli's principle yes
+
+ align:start position:0%
+articulate Bernoulli's principle yes
+ 
+
+ align:start position:0%
+articulate Bernoulli's principle yes
+like D plus one-half MV squared equals
+
+ align:start position:0%
+like D plus one-half MV squared equals
+ 
+
+ align:start position:0%
+like D plus one-half MV squared equals
+constant indifferent squared so when the
+
+ align:start position:0%
+constant indifferent squared so when the
+ 
+
+ align:start position:0%
+constant indifferent squared so when the
+pressure goes down somewhere
+
+ align:start position:0%
+pressure goes down somewhere
+ 
+
+ align:start position:0%
+pressure goes down somewhere
+speed of the particle has to go up yes
+
+ align:start position:0%
+speed of the particle has to go up yes
+ 
+
+ align:start position:0%
+speed of the particle has to go up yes
+absolutely absolutely so so what
+
+ align:start position:0%
+absolutely absolutely so so what
+ 
+
+ align:start position:0%
+absolutely absolutely so so what
+Bernoulli observed was the case that
+
+ align:start position:0%
+Bernoulli observed was the case that
+ 
+
+ align:start position:0%
+Bernoulli observed was the case that
+when there is a decrease in pressure
+
+ align:start position:0%
+when there is a decrease in pressure
+ 
+
+ align:start position:0%
+when there is a decrease in pressure
+there's an increase in velocity that's
+
+ align:start position:0%
+there's an increase in velocity that's
+ 
+
+ align:start position:0%
+there's an increase in velocity that's
+the the core concept that you have to
+
+ align:start position:0%
+the the core concept that you have to
+ 
+
+ align:start position:0%
+the the core concept that you have to
+understand and so when we think about an
+
+ align:start position:0%
+understand and so when we think about an
+ 
+
+ align:start position:0%
+understand and so when we think about an
+airfoil when we see that and I'll draw
+
+ align:start position:0%
+airfoil when we see that and I'll draw
+ 
+
+ align:start position:0%
+airfoil when we see that and I'll draw
+another airfoil for us to talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+when we have air that's moving very fast
+
+ align:start position:0%
+when we have air that's moving very fast
+ 
+
+ align:start position:0%
+when we have air that's moving very fast
+over the top of the wing that means you
+
+ align:start position:0%
+over the top of the wing that means you
+ 
+
+ align:start position:0%
+over the top of the wing that means you
+know an increase in velocity means
+
+ align:start position:0%
+know an increase in velocity means
+ 
+
+ align:start position:0%
+know an increase in velocity means
+there's a decrease in pressure so this
+
+ align:start position:0%
+there's a decrease in pressure so this
+ 
+
+ align:start position:0%
+there's a decrease in pressure so this
+is the extent to which you really need
+
+ align:start position:0%
+is the extent to which you really need
+ 
+
+ align:start position:0%
+is the extent to which you really need
+to know it for the FAA exam so which
+
+ align:start position:0%
+to know it for the FAA exam so which
+ 
+
+ align:start position:0%
+to know it for the FAA exam so which
+statement relates to Bernoulli's
+
+ align:start position:0%
+statement relates to Bernoulli's
+ 
+
+ align:start position:0%
+statement relates to Bernoulli's
+principle I'll let you read those
+
+ align:start position:0%
+principle I'll let you read those
+ 
+
+ align:start position:0%
+principle I'll let you read those
+answers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is it a B or C shout it out
+
+ align:start position:0%
+so is it a B or C shout it out
+ 
+
+ align:start position:0%
+so is it a B or C shout it out
+C good job well done okay we're gonna
+
+ align:start position:0%
+C good job well done okay we're gonna
+ 
+
+ align:start position:0%
+C good job well done okay we're gonna
+discuss a little bit more details though
+
+ align:start position:0%
+discuss a little bit more details though
+ 
+
+ align:start position:0%
+discuss a little bit more details though
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order for any wing to generate lift
+
+ align:start position:0%
+in order for any wing to generate lift
+ 
+
+ align:start position:0%
+in order for any wing to generate lift
+it has to be in a fluid if this airplane
+
+ align:start position:0%
+it has to be in a fluid if this airplane
+ 
+
+ align:start position:0%
+it has to be in a fluid if this airplane
+was in space or in a vacuum and there
+
+ align:start position:0%
+was in space or in a vacuum and there
+ 
+
+ align:start position:0%
+was in space or in a vacuum and there
+wasn't any fluid passing by it then
+
+ align:start position:0%
+wasn't any fluid passing by it then
+ 
+
+ align:start position:0%
+wasn't any fluid passing by it then
+there wouldn't be any molecules to
+
+ align:start position:0%
+there wouldn't be any molecules to
+ 
+
+ align:start position:0%
+there wouldn't be any molecules to
+deflect downward and therefore you
+
+ align:start position:0%
+deflect downward and therefore you
+ 
+
+ align:start position:0%
+deflect downward and therefore you
+couldn't push the the wing up but the
+
+ align:start position:0%
+couldn't push the the wing up but the
+ 
+
+ align:start position:0%
+couldn't push the the wing up but the
+fluid doesn't always have to be air you
+
+ align:start position:0%
+fluid doesn't always have to be air you
+ 
+
+ align:start position:0%
+fluid doesn't always have to be air you
+might see similar designs underwater for
+
+ align:start position:0%
+might see similar designs underwater for
+ 
+
+ align:start position:0%
+might see similar designs underwater for
+underwater drones it just has to be a
+
+ align:start position:0%
+underwater drones it just has to be a
+ 
+
+ align:start position:0%
+underwater drones it just has to be a
+fluid that's passing by the object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so when you have this airfoil in
+
+ align:start position:0%
+okay so when you have this airfoil in
+ 
+
+ align:start position:0%
+okay so when you have this airfoil in
+fluid when the fluid is not moving when
+
+ align:start position:0%
+fluid when the fluid is not moving when
+ 
+
+ align:start position:0%
+fluid when the fluid is not moving when
+it's stationary then all of the fluid is
+
+ align:start position:0%
+it's stationary then all of the fluid is
+ 
+
+ align:start position:0%
+it's stationary then all of the fluid is
+exerting pressure on the airfoil so you
+
+ align:start position:0%
+exerting pressure on the airfoil so you
+ 
+
+ align:start position:0%
+exerting pressure on the airfoil so you
+get all these little normal forces
+
+ align:start position:0%
+get all these little normal forces
+ 
+
+ align:start position:0%
+get all these little normal forces
+exerting pressure when the fluids not
+
+ align:start position:0%
+exerting pressure when the fluids not
+ 
+
+ align:start position:0%
+exerting pressure when the fluids not
+moving and the airfoil is stationary in
+
+ align:start position:0%
+moving and the airfoil is stationary in
+ 
+
+ align:start position:0%
+moving and the airfoil is stationary in
+the fluid then all of those pressure
+
+ align:start position:0%
+the fluid then all of those pressure
+ 
+
+ align:start position:0%
+the fluid then all of those pressure
+forces all those normal forces or forces
+
+ align:start position:0%
+forces all those normal forces or forces
+ 
+
+ align:start position:0%
+forces all those normal forces or forces
+perpendicular sum to zero because
+
+ align:start position:0%
+perpendicular sum to zero because
+ 
+
+ align:start position:0%
+perpendicular sum to zero because
+there's no net force it's just sitting
+
+ align:start position:0%
+there's no net force it's just sitting
+ 
+
+ align:start position:0%
+there's no net force it's just sitting
+in the fluid but when that fluid is
+
+ align:start position:0%
+in the fluid but when that fluid is
+ 
+
+ align:start position:0%
+in the fluid but when that fluid is
+moving it generates a force so that's
+
+ align:start position:0%
+moving it generates a force so that's
+ 
+
+ align:start position:0%
+moving it generates a force so that's
+the force it generates generally when
+
+ align:start position:0%
+the force it generates generally when
+ 
+
+ align:start position:0%
+the force it generates generally when
+the fluid is moving forward force is a
+
+ align:start position:0%
+the fluid is moving forward force is a
+ 
+
+ align:start position:0%
+the fluid is moving forward force is a
+is a vector so it has direction as well
+
+ align:start position:0%
+is a vector so it has direction as well
+ 
+
+ align:start position:0%
+is a vector so it has direction as well
+as magnitude so they're the vertical
+
+ align:start position:0%
+as magnitude so they're the vertical
+ 
+
+ align:start position:0%
+as magnitude so they're the vertical
+component and a horizontal component to
+
+ align:start position:0%
+component and a horizontal component to
+ 
+
+ align:start position:0%
+component and a horizontal component to
+that so we call the the vertical
+
+ align:start position:0%
+that so we call the the vertical
+ 
+
+ align:start position:0%
+that so we call the the vertical
+component the lift does anyone know what
+
+ align:start position:0%
+component the lift does anyone know what
+ 
+
+ align:start position:0%
+component the lift does anyone know what
+we call the horizontal component drag
+
+ align:start position:0%
+we call the horizontal component drag
+ 
+
+ align:start position:0%
+we call the horizontal component drag
+good job all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here's a here's a dumb question what
+
+ align:start position:0%
+now here's a here's a dumb question what
+ 
+
+ align:start position:0%
+now here's a here's a dumb question what
+part of the aircraft generates lift yes
+
+ align:start position:0%
+part of the aircraft generates lift yes
+ 
+
+ align:start position:0%
+part of the aircraft generates lift yes
+the whole aircraft a good job so a lot
+
+ align:start position:0%
+the whole aircraft a good job so a lot
+ 
+
+ align:start position:0%
+the whole aircraft a good job so a lot
+of people might be under the
+
+ align:start position:0%
+of people might be under the
+ 
+
+ align:start position:0%
+of people might be under the
+misimpression that it's only the wings
+
+ align:start position:0%
+misimpression that it's only the wings
+ 
+
+ align:start position:0%
+misimpression that it's only the wings
+that are generating the lift
+
+ align:start position:0%
+that are generating the lift
+ 
+
+ align:start position:0%
+that are generating the lift
+well actually the whole aircraft is
+
+ align:start position:0%
+well actually the whole aircraft is
+ 
+
+ align:start position:0%
+well actually the whole aircraft is
+generating lift and it's not just
+
+ align:start position:0%
+generating lift and it's not just
+ 
+
+ align:start position:0%
+generating lift and it's not just
+aircraft any objects that are moving
+
+ align:start position:0%
+aircraft any objects that are moving
+ 
+
+ align:start position:0%
+aircraft any objects that are moving
+through fluid have have this phenomenon
+
+ align:start position:0%
+through fluid have have this phenomenon
+ 
+
+ align:start position:0%
+through fluid have have this phenomenon
+and sometimes it's not a good thing so
+
+ align:start position:0%
+and sometimes it's not a good thing so
+ 
+
+ align:start position:0%
+and sometimes it's not a good thing so
+what is this a picture of a race car
+
+ align:start position:0%
+what is this a picture of a race car
+ 
+
+ align:start position:0%
+what is this a picture of a race car
+come on guys I know we're in an airplane
+
+ align:start position:0%
+come on guys I know we're in an airplane
+ 
+
+ align:start position:0%
+come on guys I know we're in an airplane
+class but okay who can tell me what is
+
+ align:start position:0%
+class but okay who can tell me what is
+ 
+
+ align:start position:0%
+class but okay who can tell me what is
+that thing sticking up at the back of
+
+ align:start position:0%
+that thing sticking up at the back of
+ 
+
+ align:start position:0%
+that thing sticking up at the back of
+the race car a spoiler what's a spoiler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it spoils the airflow so when a race car
+
+ align:start position:0%
+it spoils the airflow so when a race car
+ 
+
+ align:start position:0%
+it spoils the airflow so when a race car
+is driving on a racetrack and it's going
+
+ align:start position:0%
+is driving on a racetrack and it's going
+ 
+
+ align:start position:0%
+is driving on a racetrack and it's going
+through the air that fluid is air
+
+ align:start position:0%
+through the air that fluid is air
+ 
+
+ align:start position:0%
+through the air that fluid is air
+actually just the the the race car
+
+ align:start position:0%
+actually just the the the race car
+ 
+
+ align:start position:0%
+actually just the the the race car
+itself is generating lift and that lift
+
+ align:start position:0%
+itself is generating lift and that lift
+ 
+
+ align:start position:0%
+itself is generating lift and that lift
+can cause the racecar to kind of lift
+
+ align:start position:0%
+can cause the racecar to kind of lift
+ 
+
+ align:start position:0%
+can cause the racecar to kind of lift
+upward and not be as much in traction
+
+ align:start position:0%
+upward and not be as much in traction
+ 
+
+ align:start position:0%
+upward and not be as much in traction
+with the with the ground and when you're
+
+ align:start position:0%
+with the with the ground and when you're
+ 
+
+ align:start position:0%
+with the with the ground and when you're
+a race car you want to go really really
+
+ align:start position:0%
+a race car you want to go really really
+ 
+
+ align:start position:0%
+a race car you want to go really really
+fast you want to have very good traction
+
+ align:start position:0%
+fast you want to have very good traction
+ 
+
+ align:start position:0%
+fast you want to have very good traction
+with your wheels against the ground so
+
+ align:start position:0%
+with your wheels against the ground so
+ 
+
+ align:start position:0%
+with your wheels against the ground so
+you can go as fast as you can so the
+
+ align:start position:0%
+you can go as fast as you can so the
+ 
+
+ align:start position:0%
+you can go as fast as you can so the
+reason that you have a spoiler at the
+
+ align:start position:0%
+reason that you have a spoiler at the
+ 
+
+ align:start position:0%
+reason that you have a spoiler at the
+back is actually to counteract the lift
+
+ align:start position:0%
+back is actually to counteract the lift
+ 
+
+ align:start position:0%
+back is actually to counteract the lift
+that's being generated by the racecar so
+
+ align:start position:0%
+that's being generated by the racecar so
+ 
+
+ align:start position:0%
+that's being generated by the racecar so
+it's not just airplanes and and wings
+
+ align:start position:0%
+it's not just airplanes and and wings
+ 
+
+ align:start position:0%
+it's not just airplanes and and wings
+that generate lift but really anything
+
+ align:start position:0%
+that generate lift but really anything
+ 
+
+ align:start position:0%
+that generate lift but really anything
+moving through a fluid can generate lift
+
+ align:start position:0%
+moving through a fluid can generate lift
+ 
+
+ align:start position:0%
+moving through a fluid can generate lift
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're gonna talk a little bit about
+
+ align:start position:0%
+so we're gonna talk a little bit about
+ 
+
+ align:start position:0%
+so we're gonna talk a little bit about
+equations don't get scared here we'll
+
+ align:start position:0%
+equations don't get scared here we'll
+ 
+
+ align:start position:0%
+equations don't get scared here we'll
+just we'll just dive into it step by
+
+ align:start position:0%
+just we'll just dive into it step by
+ 
+
+ align:start position:0%
+just we'll just dive into it step by
+step so we have F equals MA
+
+ align:start position:0%
+step so we have F equals MA
+ 
+
+ align:start position:0%
+step so we have F equals MA
+hopefully this is not the first time
+
+ align:start position:0%
+hopefully this is not the first time
+ 
+
+ align:start position:0%
+hopefully this is not the first time
+you're hearing about that equation all
+
+ align:start position:0%
+you're hearing about that equation all
+ 
+
+ align:start position:0%
+you're hearing about that equation all
+right so can somebody just shout out
+
+ align:start position:0%
+right so can somebody just shout out
+ 
+
+ align:start position:0%
+right so can somebody just shout out
+what is acceleration change in velocity
+
+ align:start position:0%
+what is acceleration change in velocity
+ 
+
+ align:start position:0%
+what is acceleration change in velocity
+over time very good
+
+ align:start position:0%
+over time very good
+ 
+
+ align:start position:0%
+over time very good
+so velocity again is also a vector so
+
+ align:start position:0%
+so velocity again is also a vector so
+ 
+
+ align:start position:0%
+so velocity again is also a vector so
+velocity being a vector has both
+
+ align:start position:0%
+velocity being a vector has both
+ 
+
+ align:start position:0%
+velocity being a vector has both
+magnitude and direction so you can
+
+ align:start position:0%
+magnitude and direction so you can
+ 
+
+ align:start position:0%
+magnitude and direction so you can
+change the velocity either by changing
+
+ align:start position:0%
+change the velocity either by changing
+ 
+
+ align:start position:0%
+change the velocity either by changing
+the magnitude or the direction in the
+
+ align:start position:0%
+the magnitude or the direction in the
+ 
+
+ align:start position:0%
+the magnitude or the direction in the
+case of an airfoil we're changing the
+
+ align:start position:0%
+case of an airfoil we're changing the
+ 
+
+ align:start position:0%
+case of an airfoil we're changing the
+direction of the air so the air has
+
+ align:start position:0%
+direction of the air so the air has
+ 
+
+ align:start position:0%
+direction of the air so the air has
+velocity it's coming in we're changing
+
+ align:start position:0%
+velocity it's coming in we're changing
+ 
+
+ align:start position:0%
+velocity it's coming in we're changing
+the direction of that air and that's
+
+ align:start position:0%
+the direction of that air and that's
+ 
+
+ align:start position:0%
+the direction of that air and that's
+generating the lift so because we
+
+ align:start position:0%
+generating the lift so because we
+ 
+
+ align:start position:0%
+generating the lift so because we
+changed the direction of the velocity
+
+ align:start position:0%
+changed the direction of the velocity
+ 
+
+ align:start position:0%
+changed the direction of the velocity
+that creates a force that's our force F
+
+ align:start position:0%
+that creates a force that's our force F
+ 
+
+ align:start position:0%
+that creates a force that's our force F
+so f is actually here representing the
+
+ align:start position:0%
+so f is actually here representing the
+ 
+
+ align:start position:0%
+so f is actually here representing the
+rate of change of momentum above pushing
+
+ align:start position:0%
+rate of change of momentum above pushing
+ 
+
+ align:start position:0%
+rate of change of momentum above pushing
+those air molecules down and generating
+
+ align:start position:0%
+those air molecules down and generating
+ 
+
+ align:start position:0%
+those air molecules down and generating
+a force creating the airfoil to be
+
+ align:start position:0%
+a force creating the airfoil to be
+ 
+
+ align:start position:0%
+a force creating the airfoil to be
+lifted up so that's why we discussed
+
+ align:start position:0%
+lifted up so that's why we discussed
+ 
+
+ align:start position:0%
+lifted up so that's why we discussed
+again and that equal transit theory is
+
+ align:start position:0%
+again and that equal transit theory is
+ 
+
+ align:start position:0%
+again and that equal transit theory is
+false because even an an paper airplane
+
+ align:start position:0%
+false because even an an paper airplane
+ 
+
+ align:start position:0%
+false because even an an paper airplane
+with a with a completely flat cross
+
+ align:start position:0%
+with a with a completely flat cross
+ 
+
+ align:start position:0%
+with a with a completely flat cross
+section of its wing as long as it's
+
+ align:start position:0%
+section of its wing as long as it's
+ 
+
+ align:start position:0%
+section of its wing as long as it's
+inclined upwards such that the air is
+
+ align:start position:0%
+inclined upwards such that the air is
+ 
+
+ align:start position:0%
+inclined upwards such that the air is
+being pushed down will fly okay so
+
+ align:start position:0%
+being pushed down will fly okay so
+ 
+
+ align:start position:0%
+being pushed down will fly okay so
+here's another question which moves
+
+ align:start position:0%
+here's another question which moves
+ 
+
+ align:start position:0%
+here's another question which moves
+faster the wing through the air or the
+
+ align:start position:0%
+faster the wing through the air or the
+ 
+
+ align:start position:0%
+faster the wing through the air or the
+air past the wing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you're very quiet which moves
+
+ align:start position:0%
+well you're very quiet which moves
+ 
+
+ align:start position:0%
+well you're very quiet which moves
+faster yes the air over the wing we have
+
+ align:start position:0%
+faster yes the air over the wing we have
+ 
+
+ align:start position:0%
+faster yes the air over the wing we have
+one for the air over the wing is moving
+
+ align:start position:0%
+one for the air over the wing is moving
+ 
+
+ align:start position:0%
+one for the air over the wing is moving
+faster than the wing through the air
+
+ align:start position:0%
+faster than the wing through the air
+ 
+
+ align:start position:0%
+faster than the wing through the air
+anyone else
+
+ align:start position:0%
+anyone else
+ 
+
+ align:start position:0%
+anyone else
+yes depends on where on the wing you're
+
+ align:start position:0%
+yes depends on where on the wing you're
+ 
+
+ align:start position:0%
+yes depends on where on the wing you're
+talking about yes as you find air to be
+
+ align:start position:0%
+talking about yes as you find air to be
+ 
+
+ align:start position:0%
+talking about yes as you find air to be
+the air that's immediately thanks to the
+
+ align:start position:0%
+the air that's immediately thanks to the
+ 
+
+ align:start position:0%
+the air that's immediately thanks to the
+like that is in contact with the air yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so depends on which air you're talking
+
+ align:start position:0%
+so depends on which air you're talking
+ 
+
+ align:start position:0%
+so depends on which air you're talking
+about okay true actually what we're
+
+ align:start position:0%
+about okay true actually what we're
+ 
+
+ align:start position:0%
+about okay true actually what we're
+discussing is about frame of reference
+
+ align:start position:0%
+discussing is about frame of reference
+ 
+
+ align:start position:0%
+discussing is about frame of reference
+so depending on your frame of reference
+
+ align:start position:0%
+so depending on your frame of reference
+ 
+
+ align:start position:0%
+so depending on your frame of reference
+you if your frame of reference is the
+
+ align:start position:0%
+you if your frame of reference is the
+ 
+
+ align:start position:0%
+you if your frame of reference is the
+airfoil you can take it to be that the
+
+ align:start position:0%
+airfoil you can take it to be that the
+ 
+
+ align:start position:0%
+airfoil you can take it to be that the
+airfoil is stationary and you see the
+
+ align:start position:0%
+airfoil is stationary and you see the
+ 
+
+ align:start position:0%
+airfoil is stationary and you see the
+air this the wing to be stationary in
+
+ align:start position:0%
+air this the wing to be stationary in
+ 
+
+ align:start position:0%
+air this the wing to be stationary in
+the air to be moving past you if your
+
+ align:start position:0%
+the air to be moving past you if your
+ 
+
+ align:start position:0%
+the air to be moving past you if your
+frame of reference is out here you might
+
+ align:start position:0%
+frame of reference is out here you might
+ 
+
+ align:start position:0%
+frame of reference is out here you might
+see the air to be stationary and the
+
+ align:start position:0%
+see the air to be stationary and the
+ 
+
+ align:start position:0%
+see the air to be stationary and the
+airplane to be moving through it so
+
+ align:start position:0%
+airplane to be moving through it so
+ 
+
+ align:start position:0%
+airplane to be moving through it so
+depending on what your frame of
+
+ align:start position:0%
+depending on what your frame of
+ 
+
+ align:start position:0%
+depending on what your frame of
+reference is you can actually have the
+
+ align:start position:0%
+reference is you can actually have the
+ 
+
+ align:start position:0%
+reference is you can actually have the
+identical result so the answer is
+
+ align:start position:0%
+identical result so the answer is
+ 
+
+ align:start position:0%
+identical result so the answer is
+actually that it's the same so depending
+
+ align:start position:0%
+actually that it's the same so depending
+ 
+
+ align:start position:0%
+actually that it's the same so depending
+on your frame of reference it's exactly
+
+ align:start position:0%
+on your frame of reference it's exactly
+ 
+
+ align:start position:0%
+on your frame of reference it's exactly
+the same the speed of the air moving
+
+ align:start position:0%
+the same the speed of the air moving
+ 
+
+ align:start position:0%
+the same the speed of the air moving
+past the airfoil versus the airfoil
+
+ align:start position:0%
+past the airfoil versus the airfoil
+ 
+
+ align:start position:0%
+past the airfoil versus the airfoil
+moving through the air and and the
+
+ align:start position:0%
+moving through the air and and the
+ 
+
+ align:start position:0%
+moving through the air and and the
+reason so does anyone want to dive more
+
+ align:start position:0%
+reason so does anyone want to dive more
+ 
+
+ align:start position:0%
+reason so does anyone want to dive more
+into that who are you guys familiar with
+
+ align:start position:0%
+into that who are you guys familiar with
+ 
+
+ align:start position:0%
+into that who are you guys familiar with
+this concept of frame of reference yes a
+
+ align:start position:0%
+this concept of frame of reference yes a
+ 
+
+ align:start position:0%
+this concept of frame of reference yes a
+lot of head nodding okay great so the
+
+ align:start position:0%
+lot of head nodding okay great so the
+ 
+
+ align:start position:0%
+lot of head nodding okay great so the
+reason that's significant is that as we
+
+ align:start position:0%
+reason that's significant is that as we
+ 
+
+ align:start position:0%
+reason that's significant is that as we
+learn about lift and as we study this we
+
+ align:start position:0%
+learn about lift and as we study this we
+ 
+
+ align:start position:0%
+learn about lift and as we study this we
+actually could create a whole bunch of
+
+ align:start position:0%
+actually could create a whole bunch of
+ 
+
+ align:start position:0%
+actually could create a whole bunch of
+different air foils and then build
+
+ align:start position:0%
+different air foils and then build
+ 
+
+ align:start position:0%
+different air foils and then build
+airplanes and then fly them through the
+
+ align:start position:0%
+airplanes and then fly them through the
+ 
+
+ align:start position:0%
+airplanes and then fly them through the
+air and measure them but that's very
+
+ align:start position:0%
+air and measure them but that's very
+ 
+
+ align:start position:0%
+air and measure them but that's very
+expensive so instead what we do is we
+
+ align:start position:0%
+expensive so instead what we do is we
+ 
+
+ align:start position:0%
+expensive so instead what we do is we
+basically we basically take the take the
+
+ align:start position:0%
+basically we basically take the take the
+ 
+
+ align:start position:0%
+basically we basically take the take the
+airfoil and we put it on a stick and
+
+ align:start position:0%
+airfoil and we put it on a stick and
+ 
+
+ align:start position:0%
+airfoil and we put it on a stick and
+then we put it inside a wind tunnel has
+
+ align:start position:0%
+then we put it inside a wind tunnel has
+ 
+
+ align:start position:0%
+then we put it inside a wind tunnel has
+anyone been in a wind tunnel
+
+ align:start position:0%
+anyone been in a wind tunnel
+ 
+
+ align:start position:0%
+anyone been in a wind tunnel
+got a couple people hey we saw that like
+
+ align:start position:0%
+got a couple people hey we saw that like
+ 
+
+ align:start position:0%
+got a couple people hey we saw that like
+over 60 of you guys were aero-astro you
+
+ align:start position:0%
+over 60 of you guys were aero-astro you
+ 
+
+ align:start position:0%
+over 60 of you guys were aero-astro you
+need to go to your Wright brothers wind
+
+ align:start position:0%
+need to go to your Wright brothers wind
+ 
+
+ align:start position:0%
+need to go to your Wright brothers wind
+tunnel it's being upgraded actually
+
+ align:start position:0%
+tunnel it's being upgraded actually
+ 
+
+ align:start position:0%
+tunnel it's being upgraded actually
+right now over in your building 33 so
+
+ align:start position:0%
+right now over in your building 33 so
+ 
+
+ align:start position:0%
+right now over in your building 33 so
+because it's exactly identical the air
+
+ align:start position:0%
+because it's exactly identical the air
+ 
+
+ align:start position:0%
+because it's exactly identical the air
+moving past the airfoil or the airfoil
+
+ align:start position:0%
+moving past the airfoil or the airfoil
+ 
+
+ align:start position:0%
+moving past the airfoil or the airfoil
+moving through the air it's a lot
+
+ align:start position:0%
+moving through the air it's a lot
+ 
+
+ align:start position:0%
+moving through the air it's a lot
+cheaper to put the airfoil on a stick in
+
+ align:start position:0%
+cheaper to put the airfoil on a stick in
+ 
+
+ align:start position:0%
+cheaper to put the airfoil on a stick in
+a wind tunnel and then shoot air past it
+
+ align:start position:0%
+a wind tunnel and then shoot air past it
+ 
+
+ align:start position:0%
+a wind tunnel and then shoot air past it
+and then do your measurements rather
+
+ align:start position:0%
+and then do your measurements rather
+ 
+
+ align:start position:0%
+and then do your measurements rather
+than continuing to take off airplanes
+
+ align:start position:0%
+than continuing to take off airplanes
+ 
+
+ align:start position:0%
+than continuing to take off airplanes
+and fly them through the air so we're
+
+ align:start position:0%
+and fly them through the air so we're
+ 
+
+ align:start position:0%
+and fly them through the air so we're
+going to be talking about that a little
+
+ align:start position:0%
+going to be talking about that a little
+ 
+
+ align:start position:0%
+going to be talking about that a little
+bit so the question is what what factors
+
+ align:start position:0%
+bit so the question is what what factors
+ 
+
+ align:start position:0%
+bit so the question is what what factors
+affect lift so there are a lot of things
+
+ align:start position:0%
+affect lift so there are a lot of things
+ 
+
+ align:start position:0%
+affect lift so there are a lot of things
+that affect lift so one has to do with
+
+ align:start position:0%
+that affect lift so one has to do with
+ 
+
+ align:start position:0%
+that affect lift so one has to do with
+the object itself so I was talking about
+
+ align:start position:0%
+the object itself so I was talking about
+ 
+
+ align:start position:0%
+the object itself so I was talking about
+the shape of the of the airfoil so you
+
+ align:start position:0%
+the shape of the of the airfoil so you
+ 
+
+ align:start position:0%
+the shape of the of the airfoil so you
+know we talked about a different shape
+
+ align:start position:0%
+know we talked about a different shape
+ 
+
+ align:start position:0%
+know we talked about a different shape
+which is just a flat piece of paper or
+
+ align:start position:0%
+which is just a flat piece of paper or
+ 
+
+ align:start position:0%
+which is just a flat piece of paper or
+rectangle as a shape you can have a more
+
+ align:start position:0%
+rectangle as a shape you can have a more
+ 
+
+ align:start position:0%
+rectangle as a shape you can have a more
+slender shape and the way that you
+
+ align:start position:0%
+slender shape and the way that you
+ 
+
+ align:start position:0%
+slender shape and the way that you
+modify the shape can significantly
+
+ align:start position:0%
+modify the shape can significantly
+ 
+
+ align:start position:0%
+modify the shape can significantly
+impact your lift so for example one of
+
+ align:start position:0%
+impact your lift so for example one of
+ 
+
+ align:start position:0%
+impact your lift so for example one of
+the modifications can be back here at
+
+ align:start position:0%
+the modifications can be back here at
+ 
+
+ align:start position:0%
+the modifications can be back here at
+the end if you made your airfoil longer
+
+ align:start position:0%
+the end if you made your airfoil longer
+ 
+
+ align:start position:0%
+the end if you made your airfoil longer
+like this and point even farther down
+
+ align:start position:0%
+like this and point even farther down
+ 
+
+ align:start position:0%
+like this and point even farther down
+then it would push the air in a slightly
+
+ align:start position:0%
+then it would push the air in a slightly
+ 
+
+ align:start position:0%
+then it would push the air in a slightly
+different way so that would affect the
+
+ align:start position:0%
+different way so that would affect the
+ 
+
+ align:start position:0%
+different way so that would affect the
+lift that that airfoil could generate it
+
+ align:start position:0%
+lift that that airfoil could generate it
+ 
+
+ align:start position:0%
+lift that that airfoil could generate it
+would also affect the drag that it
+
+ align:start position:0%
+would also affect the drag that it
+ 
+
+ align:start position:0%
+would also affect the drag that it
+induces okay another aspect is just the
+
+ align:start position:0%
+induces okay another aspect is just the
+ 
+
+ align:start position:0%
+induces okay another aspect is just the
+size of the wing and the shape of the
+
+ align:start position:0%
+size of the wing and the shape of the
+ 
+
+ align:start position:0%
+size of the wing and the shape of the
+wing so we see a lot of different kinds
+
+ align:start position:0%
+wing so we see a lot of different kinds
+ 
+
+ align:start position:0%
+wing so we see a lot of different kinds
+so you know this is a big rectangular
+
+ align:start position:0%
+so you know this is a big rectangular
+ 
+
+ align:start position:0%
+so you know this is a big rectangular
+wing in a jet you might see a swept wing
+
+ align:start position:0%
+wing in a jet you might see a swept wing
+ 
+
+ align:start position:0%
+wing in a jet you might see a swept wing
+there are different types of shapes and
+
+ align:start position:0%
+there are different types of shapes and
+ 
+
+ align:start position:0%
+there are different types of shapes and
+then there's also just the area so
+
+ align:start position:0%
+then there's also just the area so
+ 
+
+ align:start position:0%
+then there's also just the area so
+regardless of whether you know if this
+
+ align:start position:0%
+regardless of whether you know if this
+ 
+
+ align:start position:0%
+regardless of whether you know if this
+is your if you're looking down at an
+
+ align:start position:0%
+is your if you're looking down at an
+ 
+
+ align:start position:0%
+is your if you're looking down at an
+airplane so this is kind of the broad
+
+ align:start position:0%
+airplane so this is kind of the broad
+ 
+
+ align:start position:0%
+airplane so this is kind of the broad
+flat wings or you could have very thin
+
+ align:start position:0%
+flat wings or you could have very thin
+ 
+
+ align:start position:0%
+flat wings or you could have very thin
+skinny wings that you might see on a
+
+ align:start position:0%
+skinny wings that you might see on a
+ 
+
+ align:start position:0%
+skinny wings that you might see on a
+glider regardless there is a surface
+
+ align:start position:0%
+glider regardless there is a surface
+ 
+
+ align:start position:0%
+glider regardless there is a surface
+area of the wing
+
+ align:start position:0%
+area of the wing
+ 
+
+ align:start position:0%
+area of the wing
+area also impacts the the lift quite a
+
+ align:start position:0%
+area also impacts the the lift quite a
+ 
+
+ align:start position:0%
+area also impacts the the lift quite a
+bit and and the aspect ratios we just
+
+ align:start position:0%
+bit and and the aspect ratios we just
+ 
+
+ align:start position:0%
+bit and and the aspect ratios we just
+discussed and the shape can affect lift
+
+ align:start position:0%
+discussed and the shape can affect lift
+ 
+
+ align:start position:0%
+discussed and the shape can affect lift
+the other thing other than the object
+
+ align:start position:0%
+the other thing other than the object
+ 
+
+ align:start position:0%
+the other thing other than the object
+itself other than the wing itself motion
+
+ align:start position:0%
+itself other than the wing itself motion
+ 
+
+ align:start position:0%
+itself other than the wing itself motion
+can affect lift so the velocity of the
+
+ align:start position:0%
+can affect lift so the velocity of the
+ 
+
+ align:start position:0%
+can affect lift so the velocity of the
+air and the very importantly is what's
+
+ align:start position:0%
+air and the very importantly is what's
+ 
+
+ align:start position:0%
+air and the very importantly is what's
+called the angle of attack so it's the
+
+ align:start position:0%
+called the angle of attack so it's the
+ 
+
+ align:start position:0%
+called the angle of attack so it's the
+angle with which this airfoil has to the
+
+ align:start position:0%
+angle with which this airfoil has to the
+ 
+
+ align:start position:0%
+angle with which this airfoil has to the
+air so if you had one airfoil that was
+
+ align:start position:0%
+air so if you had one airfoil that was
+ 
+
+ align:start position:0%
+air so if you had one airfoil that was
+pointed kind of up like this versus one
+
+ align:start position:0%
+pointed kind of up like this versus one
+ 
+
+ align:start position:0%
+pointed kind of up like this versus one
+the same one but it was not tilted up
+
+ align:start position:0%
+the same one but it was not tilted up
+ 
+
+ align:start position:0%
+the same one but it was not tilted up
+this airfoil would be having a higher
+
+ align:start position:0%
+this airfoil would be having a higher
+ 
+
+ align:start position:0%
+this airfoil would be having a higher
+angle of attack or angle to the wind
+
+ align:start position:0%
+angle of attack or angle to the wind
+ 
+
+ align:start position:0%
+angle of attack or angle to the wind
+than this one now this might seem like a
+
+ align:start position:0%
+than this one now this might seem like a
+ 
+
+ align:start position:0%
+than this one now this might seem like a
+very fancy description but who has been
+
+ align:start position:0%
+very fancy description but who has been
+ 
+
+ align:start position:0%
+very fancy description but who has been
+in a car driving down the highway and
+
+ align:start position:0%
+in a car driving down the highway and
+ 
+
+ align:start position:0%
+in a car driving down the highway and
+you've stuck your hand out outside and
+
+ align:start position:0%
+you've stuck your hand out outside and
+ 
+
+ align:start position:0%
+you've stuck your hand out outside and
+if you tilt your hand up a little bit
+
+ align:start position:0%
+if you tilt your hand up a little bit
+ 
+
+ align:start position:0%
+if you tilt your hand up a little bit
+you'll see that the the wind kind of
+
+ align:start position:0%
+you'll see that the the wind kind of
+ 
+
+ align:start position:0%
+you'll see that the the wind kind of
+pushes your hand up and if you push it
+
+ align:start position:0%
+pushes your hand up and if you push it
+ 
+
+ align:start position:0%
+pushes your hand up and if you push it
+if you tilt it down and you know your
+
+ align:start position:0%
+if you tilt it down and you know your
+ 
+
+ align:start position:0%
+if you tilt it down and you know your
+hand pushes up and you kind of glide
+
+ align:start position:0%
+hand pushes up and you kind of glide
+ 
+
+ align:start position:0%
+hand pushes up and you kind of glide
+your hand out the window so okay I'm
+
+ align:start position:0%
+your hand out the window so okay I'm
+ 
+
+ align:start position:0%
+your hand out the window so okay I'm
+getting a lot of head nods so that's
+
+ align:start position:0%
+getting a lot of head nods so that's
+ 
+
+ align:start position:0%
+getting a lot of head nods so that's
+really all that angle of attack is
+
+ align:start position:0%
+really all that angle of attack is
+ 
+
+ align:start position:0%
+really all that angle of attack is
+talking about that if you if you angle
+
+ align:start position:0%
+talking about that if you if you angle
+ 
+
+ align:start position:0%
+talking about that if you if you angle
+your hand up it gets pushed up a lot
+
+ align:start position:0%
+your hand up it gets pushed up a lot
+ 
+
+ align:start position:0%
+your hand up it gets pushed up a lot
+more if you angle it down it gets pushed
+
+ align:start position:0%
+more if you angle it down it gets pushed
+ 
+
+ align:start position:0%
+more if you angle it down it gets pushed
+down that's the angle of attack and
+
+ align:start position:0%
+down that's the angle of attack and
+ 
+
+ align:start position:0%
+down that's the angle of attack and
+we're gonna define it more specifically
+
+ align:start position:0%
+we're gonna define it more specifically
+ 
+
+ align:start position:0%
+we're gonna define it more specifically
+when we talk about the terms associated
+
+ align:start position:0%
+when we talk about the terms associated
+ 
+
+ align:start position:0%
+when we talk about the terms associated
+with an airfoil and the shape but it's
+
+ align:start position:0%
+with an airfoil and the shape but it's
+ 
+
+ align:start position:0%
+with an airfoil and the shape but it's
+good to get the general general concept
+
+ align:start position:0%
+good to get the general general concept
+ 
+
+ align:start position:0%
+good to get the general general concept
+first okay and then another factor
+
+ align:start position:0%
+first okay and then another factor
+ 
+
+ align:start position:0%
+first okay and then another factor
+affecting lift is the air the the fluid
+
+ align:start position:0%
+affecting lift is the air the the fluid
+ 
+
+ align:start position:0%
+affecting lift is the air the the fluid
+that it's in so the actual mass of the
+
+ align:start position:0%
+that it's in so the actual mass of the
+ 
+
+ align:start position:0%
+that it's in so the actual mass of the
+air flow coming around you so there are
+
+ align:start position:0%
+air flow coming around you so there are
+ 
+
+ align:start position:0%
+air flow coming around you so there are
+a lot of aspects to that you know we
+
+ align:start position:0%
+a lot of aspects to that you know we
+ 
+
+ align:start position:0%
+a lot of aspects to that you know we
+talked about whether you're in water or
+
+ align:start position:0%
+talked about whether you're in water or
+ 
+
+ align:start position:0%
+talked about whether you're in water or
+whether you're an air or the density
+
+ align:start position:0%
+whether you're an air or the density
+ 
+
+ align:start position:0%
+whether you're an air or the density
+density of the air another component of
+
+ align:start position:0%
+density of the air another component of
+ 
+
+ align:start position:0%
+density of the air another component of
+that air is the viscosity does anyone
+
+ align:start position:0%
+that air is the viscosity does anyone
+ 
+
+ align:start position:0%
+that air is the viscosity does anyone
+know what viscosity is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes resistance to flow the way I like to
+
+ align:start position:0%
+yes resistance to flow the way I like to
+ 
+
+ align:start position:0%
+yes resistance to flow the way I like to
+think about it is if you've ever baked
+
+ align:start position:0%
+think about it is if you've ever baked
+ 
+
+ align:start position:0%
+think about it is if you've ever baked
+brownies and you have your mixing bowl
+
+ align:start position:0%
+brownies and you have your mixing bowl
+ 
+
+ align:start position:0%
+brownies and you have your mixing bowl
+and your spatula in there and if you
+
+ align:start position:0%
+and your spatula in there and if you
+ 
+
+ align:start position:0%
+and your spatula in there and if you
+just have you know the the water and the
+
+ align:start position:0%
+just have you know the the water and the
+ 
+
+ align:start position:0%
+just have you know the the water and the
+oil and the eggs and you're mixing it
+
+ align:start position:0%
+oil and the eggs and you're mixing it
+ 
+
+ align:start position:0%
+oil and the eggs and you're mixing it
+around you know you can you can mix
+
+ align:start position:0%
+around you know you can you can mix
+ 
+
+ align:start position:0%
+around you know you can you can mix
+pretty quickly and it doesn't stick to
+
+ align:start position:0%
+pretty quickly and it doesn't stick to
+ 
+
+ align:start position:0%
+pretty quickly and it doesn't stick to
+the spatula that much but if you were
+
+ align:start position:0%
+the spatula that much but if you were
+ 
+
+ align:start position:0%
+the spatula that much but if you were
+mixing molasses or once you get all that
+
+ align:start position:0%
+mixing molasses or once you get all that
+ 
+
+ align:start position:0%
+mixing molasses or once you get all that
+brownie batter in there it really it's
+
+ align:start position:0%
+brownie batter in there it really it's
+ 
+
+ align:start position:0%
+brownie batter in there it really it's
+harder to do it and it sticks to the
+
+ align:start position:0%
+harder to do it and it sticks to the
+ 
+
+ align:start position:0%
+harder to do it and it sticks to the
+spatula so that's what we're talking
+
+ align:start position:0%
+spatula so that's what we're talking
+ 
+
+ align:start position:0%
+spatula so that's what we're talking
+about when we're talking about viscosity
+
+ align:start position:0%
+about when we're talking about viscosity
+ 
+
+ align:start position:0%
+about when we're talking about viscosity
+so it's the tendency for these molecules
+
+ align:start position:0%
+so it's the tendency for these molecules
+ 
+
+ align:start position:0%
+so it's the tendency for these molecules
+to stick stick to each other and just
+
+ align:start position:0%
+to stick stick to each other and just
+ 
+
+ align:start position:0%
+to stick stick to each other and just
+stick to the object that's moving
+
+ align:start position:0%
+stick to the object that's moving
+ 
+
+ align:start position:0%
+stick to the object that's moving
+through them so with the case of the
+
+ align:start position:0%
+through them so with the case of the
+ 
+
+ align:start position:0%
+through them so with the case of the
+airfoil we're talking about and we were
+
+ align:start position:0%
+airfoil we're talking about and we were
+ 
+
+ align:start position:0%
+airfoil we're talking about and we were
+discussing this just in just a moment
+
+ align:start position:0%
+discussing this just in just a moment
+ 
+
+ align:start position:0%
+discussing this just in just a moment
+ago about which which air were we
+
+ align:start position:0%
+ago about which which air were we
+ 
+
+ align:start position:0%
+ago about which which air were we
+talking about so some air that might be
+
+ align:start position:0%
+talking about so some air that might be
+ 
+
+ align:start position:0%
+talking about so some air that might be
+very close might kind of stick to that
+
+ align:start position:0%
+very close might kind of stick to that
+ 
+
+ align:start position:0%
+very close might kind of stick to that
+airfoil or stick to the wing versus just
+
+ align:start position:0%
+airfoil or stick to the wing versus just
+ 
+
+ align:start position:0%
+airfoil or stick to the wing versus just
+moving smoothly past it so viscosity and
+
+ align:start position:0%
+moving smoothly past it so viscosity and
+ 
+
+ align:start position:0%
+moving smoothly past it so viscosity and
+then compressibility also affects lift
+
+ align:start position:0%
+then compressibility also affects lift
+ 
+
+ align:start position:0%
+then compressibility also affects lift
+so the compressibility of the air did I
+
+ align:start position:0%
+so the compressibility of the air did I
+ 
+
+ align:start position:0%
+so the compressibility of the air did I
+turn off my mic all right
+
+ align:start position:0%
+turn off my mic all right
+ 
+
+ align:start position:0%
+turn off my mic all right
+so certain types of fluids are
+
+ align:start position:0%
+so certain types of fluids are
+ 
+
+ align:start position:0%
+so certain types of fluids are
+compressible so you could take a balloon
+
+ align:start position:0%
+compressible so you could take a balloon
+ 
+
+ align:start position:0%
+compressible so you could take a balloon
+of air and you can move it into a cold
+
+ align:start position:0%
+of air and you can move it into a cold
+ 
+
+ align:start position:0%
+of air and you can move it into a cold
+environment and have it shrink or in a
+
+ align:start position:0%
+environment and have it shrink or in a
+ 
+
+ align:start position:0%
+environment and have it shrink or in a
+hot environment and have it expand while
+
+ align:start position:0%
+hot environment and have it expand while
+ 
+
+ align:start position:0%
+hot environment and have it expand while
+having the same amount of mass inside
+
+ align:start position:0%
+having the same amount of mass inside
+ 
+
+ align:start position:0%
+having the same amount of mass inside
+the balloon so I'm getting a lot of head
+
+ align:start position:0%
+the balloon so I'm getting a lot of head
+ 
+
+ align:start position:0%
+the balloon so I'm getting a lot of head
+nods so that just shows the
+
+ align:start position:0%
+nods so that just shows the
+ 
+
+ align:start position:0%
+nods so that just shows the
+compressibility of the air whereas some
+
+ align:start position:0%
+compressibility of the air whereas some
+ 
+
+ align:start position:0%
+compressibility of the air whereas some
+types of fluids are not compressible
+
+ align:start position:0%
+types of fluids are not compressible
+ 
+
+ align:start position:0%
+types of fluids are not compressible
+they're incompressible and they they
+
+ align:start position:0%
+they're incompressible and they they
+ 
+
+ align:start position:0%
+they're incompressible and they they
+affect lift in a different way so
+
+ align:start position:0%
+affect lift in a different way so
+ 
+
+ align:start position:0%
+affect lift in a different way so
+although I've told you all these things
+
+ align:start position:0%
+although I've told you all these things
+ 
+
+ align:start position:0%
+although I've told you all these things
+that effect lift one thing I will admit
+
+ align:start position:0%
+that effect lift one thing I will admit
+ 
+
+ align:start position:0%
+that effect lift one thing I will admit
+to you is that calculating lift is
+
+ align:start position:0%
+to you is that calculating lift is
+ 
+
+ align:start position:0%
+to you is that calculating lift is
+difficult it's very difficult in fact we
+
+ align:start position:0%
+difficult it's very difficult in fact we
+ 
+
+ align:start position:0%
+difficult it's very difficult in fact we
+don't really know how to do it properly
+
+ align:start position:0%
+don't really know how to do it properly
+ 
+
+ align:start position:0%
+don't really know how to do it properly
+this is a snapshot from Wikipedia of all
+
+ align:start position:0%
+this is a snapshot from Wikipedia of all
+ 
+
+ align:start position:0%
+this is a snapshot from Wikipedia of all
+the different theories of lift so there
+
+ align:start position:0%
+the different theories of lift so there
+ 
+
+ align:start position:0%
+the different theories of lift so there
+are a lot of different ways that people
+
+ align:start position:0%
+are a lot of different ways that people
+ 
+
+ align:start position:0%
+are a lot of different ways that people
+go about trying to calculate lift and it
+
+ align:start position:0%
+go about trying to calculate lift and it
+ 
+
+ align:start position:0%
+go about trying to calculate lift and it
+turns out that it's very hard to do so
+
+ align:start position:0%
+turns out that it's very hard to do so
+ 
+
+ align:start position:0%
+turns out that it's very hard to do so
+one that you
+
+ align:start position:0%
+one that you
+ 
+
+ align:start position:0%
+one that you
+you see up there is is navier-stokes so
+
+ align:start position:0%
+you see up there is is navier-stokes so
+ 
+
+ align:start position:0%
+you see up there is is navier-stokes so
+navier-stokes is a set of equations that
+
+ align:start position:0%
+navier-stokes is a set of equations that
+ 
+
+ align:start position:0%
+navier-stokes is a set of equations that
+does a really good job of predicting
+
+ align:start position:0%
+does a really good job of predicting
+ 
+
+ align:start position:0%
+does a really good job of predicting
+lift and it really it really takes into
+
+ align:start position:0%
+lift and it really it really takes into
+ 
+
+ align:start position:0%
+lift and it really it really takes into
+account a lot of things it takes into
+
+ align:start position:0%
+account a lot of things it takes into
+ 
+
+ align:start position:0%
+account a lot of things it takes into
+account conservation of energy
+
+ align:start position:0%
+account conservation of energy
+ 
+
+ align:start position:0%
+account conservation of energy
+conservation of mass conservation of
+
+ align:start position:0%
+conservation of mass conservation of
+ 
+
+ align:start position:0%
+conservation of mass conservation of
+momentum viscosity even a lot of things
+
+ align:start position:0%
+momentum viscosity even a lot of things
+ 
+
+ align:start position:0%
+momentum viscosity even a lot of things
+like thermal conductivity and a whole
+
+ align:start position:0%
+like thermal conductivity and a whole
+ 
+
+ align:start position:0%
+like thermal conductivity and a whole
+bunch of considerations but the the
+
+ align:start position:0%
+bunch of considerations but the the
+ 
+
+ align:start position:0%
+bunch of considerations but the the
+problem is that solving those equations
+
+ align:start position:0%
+problem is that solving those equations
+ 
+
+ align:start position:0%
+problem is that solving those equations
+is very hard you know we try to use
+
+ align:start position:0%
+is very hard you know we try to use
+ 
+
+ align:start position:0%
+is very hard you know we try to use
+supercomputers to estimate every little
+
+ align:start position:0%
+supercomputers to estimate every little
+ 
+
+ align:start position:0%
+supercomputers to estimate every little
+aspect and it's very difficult to do and
+
+ align:start position:0%
+aspect and it's very difficult to do and
+ 
+
+ align:start position:0%
+aspect and it's very difficult to do and
+we're not really able to solve those
+
+ align:start position:0%
+we're not really able to solve those
+ 
+
+ align:start position:0%
+we're not really able to solve those
+equations to determine precisely what
+
+ align:start position:0%
+equations to determine precisely what
+ 
+
+ align:start position:0%
+equations to determine precisely what
+the lift is going to be let me talk
+
+ align:start position:0%
+the lift is going to be let me talk
+ 
+
+ align:start position:0%
+the lift is going to be let me talk
+about some of the limitations that we
+
+ align:start position:0%
+about some of the limitations that we
+ 
+
+ align:start position:0%
+about some of the limitations that we
+have in solving these equations so first
+
+ align:start position:0%
+have in solving these equations so first
+ 
+
+ align:start position:0%
+have in solving these equations so first
+of all it has to do with how the air
+
+ align:start position:0%
+of all it has to do with how the air
+ 
+
+ align:start position:0%
+of all it has to do with how the air
+flows over the wing if the air is moving
+
+ align:start position:0%
+flows over the wing if the air is moving
+ 
+
+ align:start position:0%
+flows over the wing if the air is moving
+very smoothly past past the airfoil then
+
+ align:start position:0%
+very smoothly past past the airfoil then
+ 
+
+ align:start position:0%
+very smoothly past past the airfoil then
+it's very easy to come up not easy but
+
+ align:start position:0%
+it's very easy to come up not easy but
+ 
+
+ align:start position:0%
+it's very easy to come up not easy but
+it's easier to approximate you know we
+
+ align:start position:0%
+it's easier to approximate you know we
+ 
+
+ align:start position:0%
+it's easier to approximate you know we
+can predict what a particular air
+
+ align:start position:0%
+can predict what a particular air
+ 
+
+ align:start position:0%
+can predict what a particular air
+molecule is going to do but as you see
+
+ align:start position:0%
+molecule is going to do but as you see
+ 
+
+ align:start position:0%
+molecule is going to do but as you see
+there when it starts spinning around and
+
+ align:start position:0%
+there when it starts spinning around and
+ 
+
+ align:start position:0%
+there when it starts spinning around and
+becoming turbulent so if you start
+
+ align:start position:0%
+becoming turbulent so if you start
+ 
+
+ align:start position:0%
+becoming turbulent so if you start
+seeing a particular air molecule that's
+
+ align:start position:0%
+seeing a particular air molecule that's
+ 
+
+ align:start position:0%
+seeing a particular air molecule that's
+moving around and becoming turbulence
+
+ align:start position:0%
+moving around and becoming turbulence
+ 
+
+ align:start position:0%
+moving around and becoming turbulence
+and not not doing laminar flow but but
+
+ align:start position:0%
+and not not doing laminar flow but but
+ 
+
+ align:start position:0%
+and not not doing laminar flow but but
+turbulent and moving around and bumping
+
+ align:start position:0%
+turbulent and moving around and bumping
+ 
+
+ align:start position:0%
+turbulent and moving around and bumping
+into other air molecules then predicting
+
+ align:start position:0%
+into other air molecules then predicting
+ 
+
+ align:start position:0%
+into other air molecules then predicting
+what that molecule does and what all the
+
+ align:start position:0%
+what that molecule does and what all the
+ 
+
+ align:start position:0%
+what that molecule does and what all the
+molecules do around it become very very
+
+ align:start position:0%
+molecules do around it become very very
+ 
+
+ align:start position:0%
+molecules do around it become very very
+difficult in fact we have a very hard
+
+ align:start position:0%
+difficult in fact we have a very hard
+ 
+
+ align:start position:0%
+difficult in fact we have a very hard
+time doing that and so instead we
+
+ align:start position:0%
+time doing that and so instead we
+ 
+
+ align:start position:0%
+time doing that and so instead we
+basically assume that that doesn't
+
+ align:start position:0%
+basically assume that that doesn't
+ 
+
+ align:start position:0%
+basically assume that that doesn't
+happen and and we propose limitations or
+
+ align:start position:0%
+happen and and we propose limitations or
+ 
+
+ align:start position:0%
+happen and and we propose limitations or
+conditions on the air flow which are not
+
+ align:start position:0%
+conditions on the air flow which are not
+ 
+
+ align:start position:0%
+conditions on the air flow which are not
+actually true but help help us with
+
+ align:start position:0%
+actually true but help help us with
+ 
+
+ align:start position:0%
+actually true but help help us with
+approximating lift so one of those is
+
+ align:start position:0%
+approximating lift so one of those is
+ 
+
+ align:start position:0%
+approximating lift so one of those is
+the Kutta condition that you see at the
+
+ align:start position:0%
+the Kutta condition that you see at the
+ 
+
+ align:start position:0%
+the Kutta condition that you see at the
+bottom left which is this smooth flow
+
+ align:start position:0%
+bottom left which is this smooth flow
+ 
+
+ align:start position:0%
+bottom left which is this smooth flow
+off so basically you say that
+
+ align:start position:0%
+off so basically you say that
+ 
+
+ align:start position:0%
+off so basically you say that
+none of this turbulence is happening and
+
+ align:start position:0%
+none of this turbulence is happening and
+ 
+
+ align:start position:0%
+none of this turbulence is happening and
+the air moves very cleanly off and you
+
+ align:start position:0%
+the air moves very cleanly off and you
+ 
+
+ align:start position:0%
+the air moves very cleanly off and you
+also have a couple other specific
+
+ align:start position:0%
+also have a couple other specific
+ 
+
+ align:start position:0%
+also have a couple other specific
+requirements such as that no air
+
+ align:start position:0%
+requirements such as that no air
+ 
+
+ align:start position:0%
+requirements such as that no air
+molecule from the top comes over to the
+
+ align:start position:0%
+molecule from the top comes over to the
+ 
+
+ align:start position:0%
+molecule from the top comes over to the
+bottom and no air molecule from the
+
+ align:start position:0%
+bottom and no air molecule from the
+ 
+
+ align:start position:0%
+bottom and no air molecule from the
+bottom goes around to the top and you
+
+ align:start position:0%
+bottom goes around to the top and you
+ 
+
+ align:start position:0%
+bottom goes around to the top and you
+just assume that they they moves
+
+ align:start position:0%
+just assume that they they moves
+ 
+
+ align:start position:0%
+just assume that they they moves
+smoothly off and so that Kutta condition
+
+ align:start position:0%
+smoothly off and so that Kutta condition
+ 
+
+ align:start position:0%
+smoothly off and so that Kutta condition
+is actually very helpful in in
+
+ align:start position:0%
+is actually very helpful in in
+ 
+
+ align:start position:0%
+is actually very helpful in in
+approximating lift we also make other
+
+ align:start position:0%
+approximating lift we also make other
+ 
+
+ align:start position:0%
+approximating lift we also make other
+assumptions that there's no viscosity or
+
+ align:start position:0%
+assumptions that there's no viscosity or
+ 
+
+ align:start position:0%
+assumptions that there's no viscosity or
+that the fluid is not compressible
+
+ align:start position:0%
+that the fluid is not compressible
+ 
+
+ align:start position:0%
+that the fluid is not compressible
+sometimes these assumptions are
+
+ align:start position:0%
+sometimes these assumptions are
+ 
+
+ align:start position:0%
+sometimes these assumptions are
+appropriate and sometimes they're not
+
+ align:start position:0%
+appropriate and sometimes they're not
+ 
+
+ align:start position:0%
+appropriate and sometimes they're not
+another thing that's really critical
+
+ align:start position:0%
+another thing that's really critical
+ 
+
+ align:start position:0%
+another thing that's really critical
+about our ability to estimate lift is
+
+ align:start position:0%
+about our ability to estimate lift is
+ 
+
+ align:start position:0%
+about our ability to estimate lift is
+that as I've been talking to you here on
+
+ align:start position:0%
+that as I've been talking to you here on
+ 
+
+ align:start position:0%
+that as I've been talking to you here on
+the blackboard I have talked about a
+
+ align:start position:0%
+the blackboard I have talked about a
+ 
+
+ align:start position:0%
+the blackboard I have talked about a
+cross section right that you just you
+
+ align:start position:0%
+cross section right that you just you
+ 
+
+ align:start position:0%
+cross section right that you just you
+cut off the wing and you're only looking
+
+ align:start position:0%
+cut off the wing and you're only looking
+ 
+
+ align:start position:0%
+cut off the wing and you're only looking
+at one cross section so since we're
+
+ align:start position:0%
+at one cross section so since we're
+ 
+
+ align:start position:0%
+at one cross section so since we're
+talking about a cross section we're
+
+ align:start position:0%
+talking about a cross section we're
+ 
+
+ align:start position:0%
+talking about a cross section we're
+talking in two-dimensional space well we
+
+ align:start position:0%
+talking in two-dimensional space well we
+ 
+
+ align:start position:0%
+talking in two-dimensional space well we
+can actually do a pretty good job of
+
+ align:start position:0%
+can actually do a pretty good job of
+ 
+
+ align:start position:0%
+can actually do a pretty good job of
+estimating lift in a two-dimensional
+
+ align:start position:0%
+estimating lift in a two-dimensional
+ 
+
+ align:start position:0%
+estimating lift in a two-dimensional
+environment but the fact of the matter
+
+ align:start position:0%
+environment but the fact of the matter
+ 
+
+ align:start position:0%
+environment but the fact of the matter
+is wings are not two-dimensional and the
+
+ align:start position:0%
+is wings are not two-dimensional and the
+ 
+
+ align:start position:0%
+is wings are not two-dimensional and the
+wing comes out into the classroom and
+
+ align:start position:0%
+wing comes out into the classroom and
+ 
+
+ align:start position:0%
+wing comes out into the classroom and
+back back into the blackboard and to
+
+ align:start position:0%
+back back into the blackboard and to
+ 
+
+ align:start position:0%
+back back into the blackboard and to
+estimate actually how all these air
+
+ align:start position:0%
+estimate actually how all these air
+ 
+
+ align:start position:0%
+estimate actually how all these air
+flows work at the edge of the wing is
+
+ align:start position:0%
+flows work at the edge of the wing is
+ 
+
+ align:start position:0%
+flows work at the edge of the wing is
+very difficult has anyone heard about
+
+ align:start position:0%
+very difficult has anyone heard about
+ 
+
+ align:start position:0%
+very difficult has anyone heard about
+tip vortices couple head nods okay all
+
+ align:start position:0%
+tip vortices couple head nods okay all
+ 
+
+ align:start position:0%
+tip vortices couple head nods okay all
+right so we have a picture there that
+
+ align:start position:0%
+right so we have a picture there that
+ 
+
+ align:start position:0%
+right so we have a picture there that
+shows a a jet to just show a little bit
+
+ align:start position:0%
+shows a a jet to just show a little bit
+ 
+
+ align:start position:0%
+shows a a jet to just show a little bit
+about what the air does when it comes
+
+ align:start position:0%
+about what the air does when it comes
+ 
+
+ align:start position:0%
+about what the air does when it comes
+off the edge the end of of the wing
+
+ align:start position:0%
+off the edge the end of of the wing
+ 
+
+ align:start position:0%
+off the edge the end of of the wing
+we're going to talk about tip vortices a
+
+ align:start position:0%
+we're going to talk about tip vortices a
+ 
+
+ align:start position:0%
+we're going to talk about tip vortices a
+little bit but the problem is that it no
+
+ align:start position:0%
+little bit but the problem is that it no
+ 
+
+ align:start position:0%
+little bit but the problem is that it no
+longer is adhering to all of our
+
+ align:start position:0%
+longer is adhering to all of our
+ 
+
+ align:start position:0%
+longer is adhering to all of our
+conditions now we don't have smooth flow
+
+ align:start position:0%
+conditions now we don't have smooth flow
+ 
+
+ align:start position:0%
+conditions now we don't have smooth flow
+we definitely have turbulent flow we
+
+ align:start position:0%
+we definitely have turbulent flow we
+ 
+
+ align:start position:0%
+we definitely have turbulent flow we
+have spinning flow and we have air
+
+ align:start position:0%
+have spinning flow and we have air
+ 
+
+ align:start position:0%
+have spinning flow and we have air
+molecules hitting other air molecules
+
+ align:start position:0%
+molecules hitting other air molecules
+ 
+
+ align:start position:0%
+molecules hitting other air molecules
+and it becomes extremely difficult for
+
+ align:start position:0%
+and it becomes extremely difficult for
+ 
+
+ align:start position:0%
+and it becomes extremely difficult for
+us to model all of those air molecules
+
+ align:start position:0%
+us to model all of those air molecules
+ 
+
+ align:start position:0%
+us to model all of those air molecules
+we really can't do it so so going from
+
+ align:start position:0%
+we really can't do it so so going from
+ 
+
+ align:start position:0%
+we really can't do it so so going from
+two dimensions to three dimensions is
+
+ align:start position:0%
+two dimensions to three dimensions is
+ 
+
+ align:start position:0%
+two dimensions to three dimensions is
+really a limitation of a lot of the
+
+ align:start position:0%
+really a limitation of a lot of the
+ 
+
+ align:start position:0%
+really a limitation of a lot of the
+equations that we have to approximate
+
+ align:start position:0%
+equations that we have to approximate
+ 
+
+ align:start position:0%
+equations that we have to approximate
+lift so what do we do well first of all
+
+ align:start position:0%
+lift so what do we do well first of all
+ 
+
+ align:start position:0%
+lift so what do we do well first of all
+we go
+
+ align:start position:0%
+we go
+ 
+
+ align:start position:0%
+we go
+to our two-dimensional surface and we
+
+ align:start position:0%
+to our two-dimensional surface and we
+ 
+
+ align:start position:0%
+to our two-dimensional surface and we
+talked about all of these normal forces
+
+ align:start position:0%
+talked about all of these normal forces
+ 
+
+ align:start position:0%
+talked about all of these normal forces
+so when you're you have all the fluid
+
+ align:start position:0%
+so when you're you have all the fluid
+ 
+
+ align:start position:0%
+so when you're you have all the fluid
+going past has pressure and it's
+
+ align:start position:0%
+going past has pressure and it's
+ 
+
+ align:start position:0%
+going past has pressure and it's
+supplying all these forces perpendicular
+
+ align:start position:0%
+supplying all these forces perpendicular
+ 
+
+ align:start position:0%
+supplying all these forces perpendicular
+to the airfoil all around so how do you
+
+ align:start position:0%
+to the airfoil all around so how do you
+ 
+
+ align:start position:0%
+to the airfoil all around so how do you
+approximate lift while you say oh that's
+
+ align:start position:0%
+approximate lift while you say oh that's
+ 
+
+ align:start position:0%
+approximate lift while you say oh that's
+fine you just sum all those forces
+
+ align:start position:0%
+fine you just sum all those forces
+ 
+
+ align:start position:0%
+fine you just sum all those forces
+around well that's great if you know
+
+ align:start position:0%
+around well that's great if you know
+ 
+
+ align:start position:0%
+around well that's great if you know
+what all of those forces are but it's
+
+ align:start position:0%
+what all of those forces are but it's
+ 
+
+ align:start position:0%
+what all of those forces are but it's
+not great if you don't know what all of
+
+ align:start position:0%
+not great if you don't know what all of
+ 
+
+ align:start position:0%
+not great if you don't know what all of
+them are so what is the the solution
+
+ align:start position:0%
+them are so what is the the solution
+ 
+
+ align:start position:0%
+them are so what is the the solution
+that we what we do basically we
+
+ align:start position:0%
+that we what we do basically we
+ 
+
+ align:start position:0%
+that we what we do basically we
+calculate what we can and then we
+
+ align:start position:0%
+calculate what we can and then we
+ 
+
+ align:start position:0%
+calculate what we can and then we
+measure the rest experimentally so in
+
+ align:start position:0%
+measure the rest experimentally so in
+ 
+
+ align:start position:0%
+measure the rest experimentally so in
+this equation of lift for example so we
+
+ align:start position:0%
+this equation of lift for example so we
+ 
+
+ align:start position:0%
+this equation of lift for example so we
+have Ellis for lift some of the the
+
+ align:start position:0%
+have Ellis for lift some of the the
+ 
+
+ align:start position:0%
+have Ellis for lift some of the the
+other terms that you have there Rho is
+
+ align:start position:0%
+other terms that you have there Rho is
+ 
+
+ align:start position:0%
+other terms that you have there Rho is
+the one that looks like a P so Rho is
+
+ align:start position:0%
+the one that looks like a P so Rho is
+ 
+
+ align:start position:0%
+the one that looks like a P so Rho is
+talking about the air density you have
+
+ align:start position:0%
+talking about the air density you have
+ 
+
+ align:start position:0%
+talking about the air density you have
+velocity and a is the wing area we
+
+ align:start position:0%
+velocity and a is the wing area we
+ 
+
+ align:start position:0%
+velocity and a is the wing area we
+talked about and then we have this fancy
+
+ align:start position:0%
+talked about and then we have this fancy
+ 
+
+ align:start position:0%
+talked about and then we have this fancy
+little symbol there C sub L or the
+
+ align:start position:0%
+little symbol there C sub L or the
+ 
+
+ align:start position:0%
+little symbol there C sub L or the
+coefficient of lift and basically we say
+
+ align:start position:0%
+coefficient of lift and basically we say
+ 
+
+ align:start position:0%
+coefficient of lift and basically we say
+that you know I don't know how to come
+
+ align:start position:0%
+that you know I don't know how to come
+ 
+
+ align:start position:0%
+that you know I don't know how to come
+up with characterizing all those
+
+ align:start position:0%
+up with characterizing all those
+ 
+
+ align:start position:0%
+up with characterizing all those
+complications about you know viscosity
+
+ align:start position:0%
+complications about you know viscosity
+ 
+
+ align:start position:0%
+complications about you know viscosity
+and some of the the effects like that
+
+ align:start position:0%
+and some of the the effects like that
+ 
+
+ align:start position:0%
+and some of the the effects like that
+have to do with turbulence and shock
+
+ align:start position:0%
+have to do with turbulence and shock
+ 
+
+ align:start position:0%
+have to do with turbulence and shock
+waves Mach number Reynolds number all
+
+ align:start position:0%
+waves Mach number Reynolds number all
+ 
+
+ align:start position:0%
+waves Mach number Reynolds number all
+these types of things and so we say you
+
+ align:start position:0%
+these types of things and so we say you
+ 
+
+ align:start position:0%
+these types of things and so we say you
+know well measure what we can and then
+
+ align:start position:0%
+know well measure what we can and then
+ 
+
+ align:start position:0%
+know well measure what we can and then
+we'll or will well calculate what we can
+
+ align:start position:0%
+we'll or will well calculate what we can
+ 
+
+ align:start position:0%
+we'll or will well calculate what we can
+and then we'll actually in a wind tunnel
+
+ align:start position:0%
+and then we'll actually in a wind tunnel
+ 
+
+ align:start position:0%
+and then we'll actually in a wind tunnel
+where we put this guy on a stick we'll
+
+ align:start position:0%
+where we put this guy on a stick we'll
+ 
+
+ align:start position:0%
+where we put this guy on a stick we'll
+actually measure the coefficient of lift
+
+ align:start position:0%
+actually measure the coefficient of lift
+ 
+
+ align:start position:0%
+actually measure the coefficient of lift
+and that's how we really calculate lift
+
+ align:start position:0%
+and that's how we really calculate lift
+ 
+
+ align:start position:0%
+and that's how we really calculate lift
+these days is using a lot of measurement
+
+ align:start position:0%
+these days is using a lot of measurement
+ 
+
+ align:start position:0%
+these days is using a lot of measurement
+to inform what's actually happening
+
+ align:start position:0%
+to inform what's actually happening
+ 
+
+ align:start position:0%
+to inform what's actually happening
+because it's just very complicated you
+
+ align:start position:0%
+because it's just very complicated you
+ 
+
+ align:start position:0%
+because it's just very complicated you
+know that velocity is squared right so
+
+ align:start position:0%
+know that velocity is squared right so
+ 
+
+ align:start position:0%
+know that velocity is squared right so
+if you go twice as fast you get four
+
+ align:start position:0%
+if you go twice as fast you get four
+ 
+
+ align:start position:0%
+if you go twice as fast you get four
+times as much lift that is the
+
+ align:start position:0%
+times as much lift that is the
+ 
+
+ align:start position:0%
+times as much lift that is the
+relationship absolutely and the other
+
+ align:start position:0%
+relationship absolutely and the other
+ 
+
+ align:start position:0%
+relationship absolutely and the other
+thing that's really important is that
+
+ align:start position:0%
+thing that's really important is that
+ 
+
+ align:start position:0%
+thing that's really important is that
+that coefficient of lift is measured for
+
+ align:start position:0%
+that coefficient of lift is measured for
+ 
+
+ align:start position:0%
+that coefficient of lift is measured for
+a given angle of attack so we talked a
+
+ align:start position:0%
+a given angle of attack so we talked a
+ 
+
+ align:start position:0%
+a given angle of attack so we talked a
+little bit about angle of attack with
+
+ align:start position:0%
+little bit about angle of attack with
+ 
+
+ align:start position:0%
+little bit about angle of attack with
+your hand outside the window so let's
+
+ align:start position:0%
+your hand outside the window so let's
+ 
+
+ align:start position:0%
+your hand outside the window so let's
+get into
+
+ align:start position:0%
+get into
+ 
+
+ align:start position:0%
+get into
+finding it a little bit more in detail
+
+ align:start position:0%
+finding it a little bit more in detail
+ 
+
+ align:start position:0%
+finding it a little bit more in detail
+so in order to describe it I have to
+
+ align:start position:0%
+so in order to describe it I have to
+ 
+
+ align:start position:0%
+so in order to describe it I have to
+come up with a few more terms that have
+
+ align:start position:0%
+come up with a few more terms that have
+ 
+
+ align:start position:0%
+come up with a few more terms that have
+to do with the airfoil so we talked
+
+ align:start position:0%
+to do with the airfoil so we talked
+ 
+
+ align:start position:0%
+to do with the airfoil so we talked
+about the very front of the airfoil or
+
+ align:start position:0%
+about the very front of the airfoil or
+ 
+
+ align:start position:0%
+about the very front of the airfoil or
+the front the front of the wing is
+
+ align:start position:0%
+the front the front of the wing is
+ 
+
+ align:start position:0%
+the front the front of the wing is
+called the leading edge and then the
+
+ align:start position:0%
+called the leading edge and then the
+ 
+
+ align:start position:0%
+called the leading edge and then the
+back is the trailing edge okay and we
+
+ align:start position:0%
+back is the trailing edge okay and we
+ 
+
+ align:start position:0%
+back is the trailing edge okay and we
+talked about the trailing edge a little
+
+ align:start position:0%
+talked about the trailing edge a little
+ 
+
+ align:start position:0%
+talked about the trailing edge a little
+bit when we were talking about the
+
+ align:start position:0%
+bit when we were talking about the
+ 
+
+ align:start position:0%
+bit when we were talking about the
+cutter condition that no air mall where
+
+ align:start position:0%
+cutter condition that no air mall where
+ 
+
+ align:start position:0%
+cutter condition that no air mall where
+assuming no air molecule can cross the
+
+ align:start position:0%
+assuming no air molecule can cross the
+ 
+
+ align:start position:0%
+assuming no air molecule can cross the
+trailing edge to the other side so then
+
+ align:start position:0%
+trailing edge to the other side so then
+ 
+
+ align:start position:0%
+trailing edge to the other side so then
+the camber is in there so that's just
+
+ align:start position:0%
+the camber is in there so that's just
+ 
+
+ align:start position:0%
+the camber is in there so that's just
+talking about really representing the
+
+ align:start position:0%
+talking about really representing the
+ 
+
+ align:start position:0%
+talking about really representing the
+curvature of that airfoil and then a
+
+ align:start position:0%
+curvature of that airfoil and then a
+ 
+
+ align:start position:0%
+curvature of that airfoil and then a
+cord line that goes in between so you
+
+ align:start position:0%
+cord line that goes in between so you
+ 
+
+ align:start position:0%
+cord line that goes in between so you
+can measure how that is so try and do
+
+ align:start position:0%
+can measure how that is so try and do
+ 
+
+ align:start position:0%
+can measure how that is so try and do
+your little zoom in fanciness that you
+
+ align:start position:0%
+your little zoom in fanciness that you
+ 
+
+ align:start position:0%
+your little zoom in fanciness that you
+were doing I'll just point at it so this
+
+ align:start position:0%
+were doing I'll just point at it so this
+ 
+
+ align:start position:0%
+were doing I'll just point at it so this
+is the cord line of the wing so you can
+
+ align:start position:0%
+is the cord line of the wing so you can
+ 
+
+ align:start position:0%
+is the cord line of the wing so you can
+see that this is a full airplane that
+
+ align:start position:0%
+see that this is a full airplane that
+ 
+
+ align:start position:0%
+see that this is a full airplane that
+the airfoil is right here and you see
+
+ align:start position:0%
+the airfoil is right here and you see
+ 
+
+ align:start position:0%
+the airfoil is right here and you see
+this cord line going from the back to
+
+ align:start position:0%
+this cord line going from the back to
+ 
+
+ align:start position:0%
+this cord line going from the back to
+the front
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody trying to come in the door
+
+ align:start position:0%
+somebody trying to come in the door
+ 
+
+ align:start position:0%
+somebody trying to come in the door
+there all right okay great
+
+ align:start position:0%
+there all right okay great
+ 
+
+ align:start position:0%
+there all right okay great
+and then and we'll talk about some of
+
+ align:start position:0%
+and then and we'll talk about some of
+ 
+
+ align:start position:0%
+and then and we'll talk about some of
+these terms one of the basically the
+
+ align:start position:0%
+these terms one of the basically the
+ 
+
+ align:start position:0%
+these terms one of the basically the
+most important thing to think about is
+
+ align:start position:0%
+most important thing to think about is
+ 
+
+ align:start position:0%
+most important thing to think about is
+the angle of attack thank you for for
+
+ align:start position:0%
+the angle of attack thank you for for
+ 
+
+ align:start position:0%
+the angle of attack thank you for for
+checking on the door okay so talking
+
+ align:start position:0%
+checking on the door okay so talking
+ 
+
+ align:start position:0%
+checking on the door okay so talking
+about how we can control the lift so
+
+ align:start position:0%
+about how we can control the lift so
+ 
+
+ align:start position:0%
+about how we can control the lift so
+some of the things we can do have to do
+
+ align:start position:0%
+some of the things we can do have to do
+ 
+
+ align:start position:0%
+some of the things we can do have to do
+with the aircraft design so we can build
+
+ align:start position:0%
+with the aircraft design so we can build
+ 
+
+ align:start position:0%
+with the aircraft design so we can build
+an airfoil and we can talk about you
+
+ align:start position:0%
+an airfoil and we can talk about you
+ 
+
+ align:start position:0%
+an airfoil and we can talk about you
+know how curved that airfoil is you know
+
+ align:start position:0%
+know how curved that airfoil is you know
+ 
+
+ align:start position:0%
+know how curved that airfoil is you know
+the curvature on the top how curved it
+
+ align:start position:0%
+the curvature on the top how curved it
+ 
+
+ align:start position:0%
+the curvature on the top how curved it
+is we can design the wing area when
+
+ align:start position:0%
+is we can design the wing area when
+ 
+
+ align:start position:0%
+is we can design the wing area when
+we're flying we can control the airspeed
+
+ align:start position:0%
+we're flying we can control the airspeed
+ 
+
+ align:start position:0%
+we're flying we can control the airspeed
+and then the angle of attack is
+
+ align:start position:0%
+and then the angle of attack is
+ 
+
+ align:start position:0%
+and then the angle of attack is
+something that you can control when
+
+ align:start position:0%
+something that you can control when
+ 
+
+ align:start position:0%
+something that you can control when
+you're in the airplane by kind of
+
+ align:start position:0%
+you're in the airplane by kind of
+ 
+
+ align:start position:0%
+you're in the airplane by kind of
+pitching down or pitching up and well
+
+ align:start position:0%
+pitching down or pitching up and well
+ 
+
+ align:start position:0%
+pitching down or pitching up and well
+will describe pitching and how you
+
+ align:start position:0%
+will describe pitching and how you
+ 
+
+ align:start position:0%
+will describe pitching and how you
+control an airplane in more detail
+
+ align:start position:0%
+control an airplane in more detail
+ 
+
+ align:start position:0%
+control an airplane in more detail
+another thing that's relevant is flaps
+
+ align:start position:0%
+another thing that's relevant is flaps
+ 
+
+ align:start position:0%
+another thing that's relevant is flaps
+so I talked about in this drawing right
+
+ align:start position:0%
+so I talked about in this drawing right
+ 
+
+ align:start position:0%
+so I talked about in this drawing right
+here where I added this white part of
+
+ align:start position:0%
+here where I added this white part of
+ 
+
+ align:start position:0%
+here where I added this white part of
+the trailing edge that moves down that
+
+ align:start position:0%
+the trailing edge that moves down that
+ 
+
+ align:start position:0%
+the trailing edge that moves down that
+really is kind of similar to flaps so
+
+ align:start position:0%
+really is kind of similar to flaps so
+ 
+
+ align:start position:0%
+really is kind of similar to flaps so
+when your flaps are up they're sort of
+
+ align:start position:0%
+when your flaps are up they're sort of
+ 
+
+ align:start position:0%
+when your flaps are up they're sort of
+in line with the rest of the wing but
+
+ align:start position:0%
+in line with the rest of the wing but
+ 
+
+ align:start position:0%
+in line with the rest of the wing but
+when your flaps are down it's the
+
+ align:start position:0%
+when your flaps are down it's the
+ 
+
+ align:start position:0%
+when your flaps are down it's the
+effective thing like pushing pulling a
+
+ align:start position:0%
+effective thing like pushing pulling a
+ 
+
+ align:start position:0%
+effective thing like pushing pulling a
+piece of your trailing edge downward
+
+ align:start position:0%
+piece of your trailing edge downward
+ 
+
+ align:start position:0%
+piece of your trailing edge downward
+which causes again more of that air to
+
+ align:start position:0%
+which causes again more of that air to
+ 
+
+ align:start position:0%
+which causes again more of that air to
+be deflected downward so it increases
+
+ align:start position:0%
+be deflected downward so it increases
+ 
+
+ align:start position:0%
+be deflected downward so it increases
+your drag but it but it also increases
+
+ align:start position:0%
+your drag but it but it also increases
+ 
+
+ align:start position:0%
+your drag but it but it also increases
+your lift because you're deflecting more
+
+ align:start position:0%
+your lift because you're deflecting more
+ 
+
+ align:start position:0%
+your lift because you're deflecting more
+air molecules down and then we also
+
+ align:start position:0%
+air molecules down and then we also
+ 
+
+ align:start position:0%
+air molecules down and then we also
+talked about spoilers for example it's
+
+ align:start position:0%
+talked about spoilers for example it's
+ 
+
+ align:start position:0%
+talked about spoilers for example it's
+something that can like on a car that
+
+ align:start position:0%
+something that can like on a car that
+ 
+
+ align:start position:0%
+something that can like on a car that
+can actually disrupt the lift by
+
+ align:start position:0%
+can actually disrupt the lift by
+ 
+
+ align:start position:0%
+can actually disrupt the lift by
+disrupting the airflow and when we
+
+ align:start position:0%
+disrupting the airflow and when we
+ 
+
+ align:start position:0%
+disrupting the airflow and when we
+talked about the four forces of flight
+
+ align:start position:0%
+talked about the four forces of flight
+ 
+
+ align:start position:0%
+talked about the four forces of flight
+if you're doing steady flight you're not
+
+ align:start position:0%
+if you're doing steady flight you're not
+ 
+
+ align:start position:0%
+if you're doing steady flight you're not
+climbing or you're descending but you're
+
+ align:start position:0%
+climbing or you're descending but you're
+ 
+
+ align:start position:0%
+climbing or you're descending but you're
+just flying straight that means that
+
+ align:start position:0%
+just flying straight that means that
+ 
+
+ align:start position:0%
+just flying straight that means that
+your lift and your weight basically
+
+ align:start position:0%
+your lift and your weight basically
+ 
+
+ align:start position:0%
+your lift and your weight basically
+cancel cancel each other out if your
+
+ align:start position:0%
+cancel cancel each other out if your
+ 
+
+ align:start position:0%
+cancel cancel each other out if your
+lift is greater than your weight then
+
+ align:start position:0%
+lift is greater than your weight then
+ 
+
+ align:start position:0%
+lift is greater than your weight then
+you can climb and if your weight is
+
+ align:start position:0%
+you can climb and if your weight is
+ 
+
+ align:start position:0%
+you can climb and if your weight is
+greater than your lift then you descend
+
+ align:start position:0%
+greater than your lift then you descend
+ 
+
+ align:start position:0%
+greater than your lift then you descend
+but if you're just flying straight
+
+ align:start position:0%
+but if you're just flying straight
+ 
+
+ align:start position:0%
+but if you're just flying straight
+you're in an equilibrium where those two
+
+ align:start position:0%
+you're in an equilibrium where those two
+ 
+
+ align:start position:0%
+you're in an equilibrium where those two
+forces cancel out okay so good I have a
+
+ align:start position:0%
+forces cancel out okay so good I have a
+ 
+
+ align:start position:0%
+forces cancel out okay so good I have a
+more detailed diagram of angle of attack
+
+ align:start position:0%
+more detailed diagram of angle of attack
+ 
+
+ align:start position:0%
+more detailed diagram of angle of attack
+so you can see here the cord line
+
+ align:start position:0%
+so you can see here the cord line
+ 
+
+ align:start position:0%
+so you can see here the cord line
+you can also see the relative wind and
+
+ align:start position:0%
+you can also see the relative wind and
+ 
+
+ align:start position:0%
+you can also see the relative wind and
+same things that I drew here the the
+
+ align:start position:0%
+same things that I drew here the the
+ 
+
+ align:start position:0%
+same things that I drew here the the
+lift and the drag and then that
+
+ align:start position:0%
+lift and the drag and then that
+ 
+
+ align:start position:0%
+lift and the drag and then that
+resultant force vector alright so you
+
+ align:start position:0%
+resultant force vector alright so you
+ 
+
+ align:start position:0%
+resultant force vector alright so you
+can actually control the angle of attack
+
+ align:start position:0%
+can actually control the angle of attack
+ 
+
+ align:start position:0%
+can actually control the angle of attack
+in a number of ways one of the the ways
+
+ align:start position:0%
+in a number of ways one of the the ways
+ 
+
+ align:start position:0%
+in a number of ways one of the the ways
+that we talked about is is pitching down
+
+ align:start position:0%
+that we talked about is is pitching down
+ 
+
+ align:start position:0%
+that we talked about is is pitching down
+so pushing your your yoke forward causes
+
+ align:start position:0%
+so pushing your your yoke forward causes
+ 
+
+ align:start position:0%
+so pushing your your yoke forward causes
+the airplane to pitch down and it does
+
+ align:start position:0%
+the airplane to pitch down and it does
+ 
+
+ align:start position:0%
+the airplane to pitch down and it does
+that by changing the elevator at the
+
+ align:start position:0%
+that by changing the elevator at the
+ 
+
+ align:start position:0%
+that by changing the elevator at the
+back of the airplane we'll describe that
+
+ align:start position:0%
+back of the airplane we'll describe that
+ 
+
+ align:start position:0%
+back of the airplane we'll describe that
+in more detail but the other things that
+
+ align:start position:0%
+in more detail but the other things that
+ 
+
+ align:start position:0%
+in more detail but the other things that
+can affect the angle of attack you can
+
+ align:start position:0%
+can affect the angle of attack you can
+ 
+
+ align:start position:0%
+can affect the angle of attack you can
+actually affect before you even take off
+
+ align:start position:0%
+actually affect before you even take off
+ 
+
+ align:start position:0%
+actually affect before you even take off
+so it has to do with your aircraft
+
+ align:start position:0%
+so it has to do with your aircraft
+ 
+
+ align:start position:0%
+so it has to do with your aircraft
+weight for example and the center of
+
+ align:start position:0%
+weight for example and the center of
+ 
+
+ align:start position:0%
+weight for example and the center of
+gravity as well as your airspeed when
+
+ align:start position:0%
+gravity as well as your airspeed when
+ 
+
+ align:start position:0%
+gravity as well as your airspeed when
+you're flying so here are a couple
+
+ align:start position:0%
+you're flying so here are a couple
+ 
+
+ align:start position:0%
+you're flying so here are a couple
+diagrams that show you how the lift
+
+ align:start position:0%
+diagrams that show you how the lift
+ 
+
+ align:start position:0%
+diagrams that show you how the lift
+changes with the effective angle of
+
+ align:start position:0%
+changes with the effective angle of
+ 
+
+ align:start position:0%
+changes with the effective angle of
+attack and then there is a critical
+
+ align:start position:0%
+attack and then there is a critical
+ 
+
+ align:start position:0%
+attack and then there is a critical
+angle of attack so that's when you know
+
+ align:start position:0%
+angle of attack so that's when you know
+ 
+
+ align:start position:0%
+angle of attack so that's when you know
+you can be keep keep climbing for a
+
+ align:start position:0%
+you can be keep keep climbing for a
+ 
+
+ align:start position:0%
+you can be keep keep climbing for a
+while but if you get too steep what
+
+ align:start position:0%
+while but if you get too steep what
+ 
+
+ align:start position:0%
+while but if you get too steep what
+happens who knows what happens when you
+
+ align:start position:0%
+happens who knows what happens when you
+ 
+
+ align:start position:0%
+happens who knows what happens when you
+go too steep you stall that's right so
+
+ align:start position:0%
+go too steep you stall that's right so
+ 
+
+ align:start position:0%
+go too steep you stall that's right so
+the the air can't really effectively go
+
+ align:start position:0%
+the the air can't really effectively go
+ 
+
+ align:start position:0%
+the the air can't really effectively go
+over the wing and it starts separating
+
+ align:start position:0%
+over the wing and it starts separating
+ 
+
+ align:start position:0%
+over the wing and it starts separating
+and so you you're no longer effectively
+
+ align:start position:0%
+and so you you're no longer effectively
+ 
+
+ align:start position:0%
+and so you you're no longer effectively
+pushing the air down and you lose the
+
+ align:start position:0%
+pushing the air down and you lose the
+ 
+
+ align:start position:0%
+pushing the air down and you lose the
+lift that you were generating and one
+
+ align:start position:0%
+lift that you were generating and one
+ 
+
+ align:start position:0%
+lift that you were generating and one
+thing I also want to point out here in
+
+ align:start position:0%
+thing I also want to point out here in
+ 
+
+ align:start position:0%
+thing I also want to point out here in
+this in these diagrams is you see with
+
+ align:start position:0%
+this in these diagrams is you see with
+ 
+
+ align:start position:0%
+this in these diagrams is you see with
+these little colored lines the air
+
+ align:start position:0%
+these little colored lines the air
+ 
+
+ align:start position:0%
+these little colored lines the air
+that's just coming in and it's going out
+
+ align:start position:0%
+that's just coming in and it's going out
+ 
+
+ align:start position:0%
+that's just coming in and it's going out
+and you can see that in this case the
+
+ align:start position:0%
+and you can see that in this case the
+ 
+
+ align:start position:0%
+and you can see that in this case the
+the blue lines are showing that the air
+
+ align:start position:0%
+the blue lines are showing that the air
+ 
+
+ align:start position:0%
+the blue lines are showing that the air
+that went over the top of the airfoil
+
+ align:start position:0%
+that went over the top of the airfoil
+ 
+
+ align:start position:0%
+that went over the top of the airfoil
+went faster and actually got to the back
+
+ align:start position:0%
+went faster and actually got to the back
+ 
+
+ align:start position:0%
+went faster and actually got to the back
+faster than the air that went from the
+
+ align:start position:0%
+faster than the air that went from the
+ 
+
+ align:start position:0%
+faster than the air that went from the
+bottom so again please don't fall for
+
+ align:start position:0%
+bottom so again please don't fall for
+ 
+
+ align:start position:0%
+bottom so again please don't fall for
+the equal transit theory okay so
+
+ align:start position:0%
+the equal transit theory okay so
+ 
+
+ align:start position:0%
+the equal transit theory okay so
+practice question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a B or C Hey all right good so the
+
+ align:start position:0%
+okay a B or C Hey all right good so the
+ 
+
+ align:start position:0%
+okay a B or C Hey all right good so the
+the angle of attack is defined there and
+
+ align:start position:0%
+the angle of attack is defined there and
+ 
+
+ align:start position:0%
+the angle of attack is defined there and
+one thing that I would like to point out
+
+ align:start position:0%
+one thing that I would like to point out
+ 
+
+ align:start position:0%
+one thing that I would like to point out
+is that this is also the case for a
+
+ align:start position:0%
+is that this is also the case for a
+ 
+
+ align:start position:0%
+is that this is also the case for a
+propeller so your your propeller also
+
+ align:start position:0%
+propeller so your your propeller also
+ 
+
+ align:start position:0%
+propeller so your your propeller also
+looks a lot like an airfoil or like a
+
+ align:start position:0%
+looks a lot like an airfoil or like a
+ 
+
+ align:start position:0%
+looks a lot like an airfoil or like a
+wing that's sideways and and spinning
+
+ align:start position:0%
+wing that's sideways and and spinning
+ 
+
+ align:start position:0%
+wing that's sideways and and spinning
+around and so also the angle of attack
+
+ align:start position:0%
+around and so also the angle of attack
+ 
+
+ align:start position:0%
+around and so also the angle of attack
+for a propeller is symbol is defined
+
+ align:start position:0%
+for a propeller is symbol is defined
+ 
+
+ align:start position:0%
+for a propeller is symbol is defined
+basically the same way is the angle
+
+ align:start position:0%
+basically the same way is the angle
+ 
+
+ align:start position:0%
+basically the same way is the angle
+between the propellers chord line and
+
+ align:start position:0%
+between the propellers chord line and
+ 
+
+ align:start position:0%
+between the propellers chord line and
+the relative wind
+
+ align:start position:0%
+the relative wind
+ 
+
+ align:start position:0%
+the relative wind
+okay so let's define the center of
+
+ align:start position:0%
+okay so let's define the center of
+ 
+
+ align:start position:0%
+okay so let's define the center of
+pressure so the it's basically the point
+
+ align:start position:0%
+pressure so the it's basically the point
+ 
+
+ align:start position:0%
+pressure so the it's basically the point
+the point on the wing where the lift is
+
+ align:start position:0%
+the point on the wing where the lift is
+ 
+
+ align:start position:0%
+the point on the wing where the lift is
+centered and so that can actually move
+
+ align:start position:0%
+centered and so that can actually move
+ 
+
+ align:start position:0%
+centered and so that can actually move
+as you can see in this in this figure
+
+ align:start position:0%
+as you can see in this in this figure
+ 
+
+ align:start position:0%
+as you can see in this in this figure
+based on the angle of attack the center
+
+ align:start position:0%
+based on the angle of attack the center
+ 
+
+ align:start position:0%
+based on the angle of attack the center
+of pressure can act in a different
+
+ align:start position:0%
+of pressure can act in a different
+ 
+
+ align:start position:0%
+of pressure can act in a different
+location and that's really important to
+
+ align:start position:0%
+location and that's really important to
+ 
+
+ align:start position:0%
+location and that's really important to
+understand also that you know it's not
+
+ align:start position:0%
+understand also that you know it's not
+ 
+
+ align:start position:0%
+understand also that you know it's not
+that the lift is always coming right at
+
+ align:start position:0%
+that the lift is always coming right at
+ 
+
+ align:start position:0%
+that the lift is always coming right at
+the front depending on where you are it
+
+ align:start position:0%
+the front depending on where you are it
+ 
+
+ align:start position:0%
+the front depending on where you are it
+might be pulling you in different
+
+ align:start position:0%
+might be pulling you in different
+ 
+
+ align:start position:0%
+might be pulling you in different
+directions and that can affect the
+
+ align:start position:0%
+directions and that can affect the
+ 
+
+ align:start position:0%
+directions and that can affect the
+ability of your aircraft and we'll get
+
+ align:start position:0%
+ability of your aircraft and we'll get
+ 
+
+ align:start position:0%
+ability of your aircraft and we'll get
+into that in more detail so we talked a
+
+ align:start position:0%
+into that in more detail so we talked a
+ 
+
+ align:start position:0%
+into that in more detail so we talked a
+little bit about flaps that flaps
+
+ align:start position:0%
+little bit about flaps that flaps
+ 
+
+ align:start position:0%
+little bit about flaps that flaps
+actually can increase the lift that
+
+ align:start position:0%
+actually can increase the lift that
+ 
+
+ align:start position:0%
+actually can increase the lift that
+you're able to produce but it it's a
+
+ align:start position:0%
+you're able to produce but it it's a
+ 
+
+ align:start position:0%
+you're able to produce but it it's a
+trade-off because it also increases the
+
+ align:start position:0%
+trade-off because it also increases the
+ 
+
+ align:start position:0%
+trade-off because it also increases the
+drag so when in the course of the flight
+
+ align:start position:0%
+drag so when in the course of the flight
+ 
+
+ align:start position:0%
+drag so when in the course of the flight
+take off cruise or landing when do you
+
+ align:start position:0%
+take off cruise or landing when do you
+ 
+
+ align:start position:0%
+take off cruise or landing when do you
+use flaps does anyone know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+takeoff and landing landing yeah the
+
+ align:start position:0%
+takeoff and landing landing yeah the
+ 
+
+ align:start position:0%
+takeoff and landing landing yeah the
+reason that you especially on on landing
+
+ align:start position:0%
+reason that you especially on on landing
+ 
+
+ align:start position:0%
+reason that you especially on on landing
+many times people use flaps on takeoff
+
+ align:start position:0%
+many times people use flaps on takeoff
+ 
+
+ align:start position:0%
+many times people use flaps on takeoff
+as well but the the reason it's just
+
+ align:start position:0%
+as well but the the reason it's just
+ 
+
+ align:start position:0%
+as well but the the reason it's just
+that you like to have your aircraft
+
+ align:start position:0%
+that you like to have your aircraft
+ 
+
+ align:start position:0%
+that you like to have your aircraft
+configure that in case you didn't take
+
+ align:start position:0%
+configure that in case you didn't take
+ 
+
+ align:start position:0%
+configure that in case you didn't take
+off you can you can land without making
+
+ align:start position:0%
+off you can you can land without making
+ 
+
+ align:start position:0%
+off you can you can land without making
+a lot of lot of dramatic changes the
+
+ align:start position:0%
+a lot of lot of dramatic changes the
+ 
+
+ align:start position:0%
+a lot of lot of dramatic changes the
+reason that you do that is basically
+
+ align:start position:0%
+reason that you do that is basically
+ 
+
+ align:start position:0%
+reason that you do that is basically
+that by increasing your lift but also
+
+ align:start position:0%
+that by increasing your lift but also
+ 
+
+ align:start position:0%
+that by increasing your lift but also
+increasing the drag you know drag
+
+ align:start position:0%
+increasing the drag you know drag
+ 
+
+ align:start position:0%
+increasing the drag you know drag
+affects you know how fast you're moving
+
+ align:start position:0%
+affects you know how fast you're moving
+ 
+
+ align:start position:0%
+affects you know how fast you're moving
+forward right and so you can actually
+
+ align:start position:0%
+forward right and so you can actually
+ 
+
+ align:start position:0%
+forward right and so you can actually
+have your the airspeed be be higher with
+
+ align:start position:0%
+have your the airspeed be be higher with
+ 
+
+ align:start position:0%
+have your the airspeed be be higher with
+the ground speed being lower so without
+
+ align:start position:0%
+the ground speed being lower so without
+ 
+
+ align:start position:0%
+the ground speed being lower so without
+what it does is it allows you to go very
+
+ align:start position:0%
+what it does is it allows you to go very
+ 
+
+ align:start position:0%
+what it does is it allows you to go very
+slow without stalling and so that really
+
+ align:start position:0%
+slow without stalling and so that really
+ 
+
+ align:start position:0%
+slow without stalling and so that really
+helps you land an airplane so basically
+
+ align:start position:0%
+helps you land an airplane so basically
+ 
+
+ align:start position:0%
+helps you land an airplane so basically
+it allows you to come in at a kind of
+
+ align:start position:0%
+it allows you to come in at a kind of
+ 
+
+ align:start position:0%
+it allows you to come in at a kind of
+steeper angle to land maintaining the
+
+ align:start position:0%
+steeper angle to land maintaining the
+ 
+
+ align:start position:0%
+steeper angle to land maintaining the
+the airspeed that you need in order to
+
+ align:start position:0%
+the airspeed that you need in order to
+ 
+
+ align:start position:0%
+the airspeed that you need in order to
+do that and you'll you'll notice that
+
+ align:start position:0%
+do that and you'll you'll notice that
+ 
+
+ align:start position:0%
+do that and you'll you'll notice that
+there are different flap settings so you
+
+ align:start position:0%
+there are different flap settings so you
+ 
+
+ align:start position:0%
+there are different flap settings so you
+can either have flaps it you know 10
+
+ align:start position:0%
+can either have flaps it you know 10
+ 
+
+ align:start position:0%
+can either have flaps it you know 10
+degrees 20 degrees 30 degrees we'll
+
+ align:start position:0%
+degrees 20 degrees 30 degrees we'll
+ 
+
+ align:start position:0%
+degrees 20 degrees 30 degrees we'll
+discuss that in more detail and Philip
+
+ align:start position:0%
+discuss that in more detail and Philip
+ 
+
+ align:start position:0%
+discuss that in more detail and Philip
+will talk about it in terms of
+
+ align:start position:0%
+will talk about it in terms of
+ 
+
+ align:start position:0%
+will talk about it in terms of
+performance I think as well thrust so we
+
+ align:start position:0%
+performance I think as well thrust so we
+ 
+
+ align:start position:0%
+performance I think as well thrust so we
+talked about that forward force thrust
+
+ align:start position:0%
+talked about that forward force thrust
+ 
+
+ align:start position:0%
+talked about that forward force thrust
+in this type of an aircraft a
+
+ align:start position:0%
+in this type of an aircraft a
+ 
+
+ align:start position:0%
+in this type of an aircraft a
+single-engine propeller aircraft
+
+ align:start position:0%
+single-engine propeller aircraft
+ 
+
+ align:start position:0%
+single-engine propeller aircraft
+it's the propeller that's rotating that
+
+ align:start position:0%
+it's the propeller that's rotating that
+ 
+
+ align:start position:0%
+it's the propeller that's rotating that
+is really producing the thrust and it's
+
+ align:start position:0%
+is really producing the thrust and it's
+ 
+
+ align:start position:0%
+is really producing the thrust and it's
+really as I said the propeller blades
+
+ align:start position:0%
+really as I said the propeller blades
+ 
+
+ align:start position:0%
+really as I said the propeller blades
+are kind of like an airplane wing it's a
+
+ align:start position:0%
+are kind of like an airplane wing it's a
+ 
+
+ align:start position:0%
+are kind of like an airplane wing it's a
+good way to think about it that are just
+
+ align:start position:0%
+good way to think about it that are just
+ 
+
+ align:start position:0%
+good way to think about it that are just
+spinning round and round and in
+
+ align:start position:0%
+spinning round and round and in
+ 
+
+ align:start position:0%
+spinning round and round and in
+generating lift but in this case it's
+
+ align:start position:0%
+generating lift but in this case it's
+ 
+
+ align:start position:0%
+generating lift but in this case it's
+moving air puff fuels front to behind
+
+ align:start position:0%
+moving air puff fuels front to behind
+ 
+
+ align:start position:0%
+moving air puff fuels front to behind
+your airplane and then although this is
+
+ align:start position:0%
+your airplane and then although this is
+ 
+
+ align:start position:0%
+your airplane and then although this is
+also just a force instead of talking
+
+ align:start position:0%
+also just a force instead of talking
+ 
+
+ align:start position:0%
+also just a force instead of talking
+about in pounds we usually talk about
+
+ align:start position:0%
+about in pounds we usually talk about
+ 
+
+ align:start position:0%
+about in pounds we usually talk about
+the horsepower required to drive the
+
+ align:start position:0%
+the horsepower required to drive the
+ 
+
+ align:start position:0%
+the horsepower required to drive the
+propeller so let me also talk about drag
+
+ align:start position:0%
+propeller so let me also talk about drag
+ 
+
+ align:start position:0%
+propeller so let me also talk about drag
+so there are a couple different types of
+
+ align:start position:0%
+so there are a couple different types of
+ 
+
+ align:start position:0%
+so there are a couple different types of
+drag so one drag is just what's called
+
+ align:start position:0%
+drag so one drag is just what's called
+ 
+
+ align:start position:0%
+drag so one drag is just what's called
+parasitic drag or parasite drag it's
+
+ align:start position:0%
+parasitic drag or parasite drag it's
+ 
+
+ align:start position:0%
+parasitic drag or parasite drag it's
+basically when the aircraft is moving
+
+ align:start position:0%
+basically when the aircraft is moving
+ 
+
+ align:start position:0%
+basically when the aircraft is moving
+through the air that you get some kind
+
+ align:start position:0%
+through the air that you get some kind
+ 
+
+ align:start position:0%
+through the air that you get some kind
+of resistance to that that's parasitic
+
+ align:start position:0%
+of resistance to that that's parasitic
+ 
+
+ align:start position:0%
+of resistance to that that's parasitic
+drag where as this drag is induced drag
+
+ align:start position:0%
+drag where as this drag is induced drag
+ 
+
+ align:start position:0%
+drag where as this drag is induced drag
+which is the drag that's created by
+
+ align:start position:0%
+which is the drag that's created by
+ 
+
+ align:start position:0%
+which is the drag that's created by
+a lift so this this backwards D and so
+
+ align:start position:0%
+a lift so this this backwards D and so
+ 
+
+ align:start position:0%
+a lift so this this backwards D and so
+you can see in this figure that the the
+
+ align:start position:0%
+you can see in this figure that the the
+ 
+
+ align:start position:0%
+you can see in this figure that the the
+total drag is a sum of that induced drag
+
+ align:start position:0%
+total drag is a sum of that induced drag
+ 
+
+ align:start position:0%
+total drag is a sum of that induced drag
+in the parasite drag we do we also call
+
+ align:start position:0%
+in the parasite drag we do we also call
+ 
+
+ align:start position:0%
+in the parasite drag we do we also call
+the induced drag just lift in an
+
+ align:start position:0%
+the induced drag just lift in an
+ 
+
+ align:start position:0%
+the induced drag just lift in an
+unwanted direction lift in an unwanted
+
+ align:start position:0%
+unwanted direction lift in an unwanted
+ 
+
+ align:start position:0%
+unwanted direction lift in an unwanted
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+sure whatever can whatever can have you
+
+ align:start position:0%
+sure whatever can whatever can have you
+ 
+
+ align:start position:0%
+sure whatever can whatever can have you
+associate induced drag with lift
+
+ align:start position:0%
+associate induced drag with lift
+ 
+
+ align:start position:0%
+associate induced drag with lift
+that's the drag created by lift okay
+
+ align:start position:0%
+that's the drag created by lift okay
+ 
+
+ align:start position:0%
+that's the drag created by lift okay
+ground effect does anyone know what
+
+ align:start position:0%
+ground effect does anyone know what
+ 
+
+ align:start position:0%
+ground effect does anyone know what
+ground effect is only only a couple of
+
+ align:start position:0%
+ground effect is only only a couple of
+ 
+
+ align:start position:0%
+ground effect is only only a couple of
+you all right so so let's talk about it
+
+ align:start position:0%
+you all right so so let's talk about it
+ 
+
+ align:start position:0%
+you all right so so let's talk about it
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+so basically when you're very close to
+
+ align:start position:0%
+so basically when you're very close to
+ 
+
+ align:start position:0%
+so basically when you're very close to
+the ground within one wingspan of the
+
+ align:start position:0%
+the ground within one wingspan of the
+ 
+
+ align:start position:0%
+the ground within one wingspan of the
+ground you actually have some of the the
+
+ align:start position:0%
+ground you actually have some of the the
+ 
+
+ align:start position:0%
+ground you actually have some of the the
+air flow going on with your airplane is
+
+ align:start position:0%
+air flow going on with your airplane is
+ 
+
+ align:start position:0%
+air flow going on with your airplane is
+blocked by the ground and so you're
+
+ align:start position:0%
+blocked by the ground and so you're
+ 
+
+ align:start position:0%
+blocked by the ground and so you're
+induced drag decreases now with the
+
+ align:start position:0%
+induced drag decreases now with the
+ 
+
+ align:start position:0%
+induced drag decreases now with the
+induced drag decreases it's actually the
+
+ align:start position:0%
+induced drag decreases it's actually the
+ 
+
+ align:start position:0%
+induced drag decreases it's actually the
+case that your airplane can become
+
+ align:start position:0%
+case that your airplane can become
+ 
+
+ align:start position:0%
+case that your airplane can become
+airborne at a lower speed than it's
+
+ align:start position:0%
+airborne at a lower speed than it's
+ 
+
+ align:start position:0%
+airborne at a lower speed than it's
+supposed to so what you might notice is
+
+ align:start position:0%
+supposed to so what you might notice is
+ 
+
+ align:start position:0%
+supposed to so what you might notice is
+that when you're on the runway
+
+ align:start position:0%
+that when you're on the runway
+ 
+
+ align:start position:0%
+that when you're on the runway
+taking off it's probably the first part
+
+ align:start position:0%
+taking off it's probably the first part
+ 
+
+ align:start position:0%
+taking off it's probably the first part
+of your your flights after you did your
+
+ align:start position:0%
+of your your flights after you did your
+ 
+
+ align:start position:0%
+of your your flights after you did your
+pre-flight your engine run-up your now
+
+ align:start position:0%
+pre-flight your engine run-up your now
+ 
+
+ align:start position:0%
+pre-flight your engine run-up your now
+you pulled out onto the runway and
+
+ align:start position:0%
+you pulled out onto the runway and
+ 
+
+ align:start position:0%
+you pulled out onto the runway and
+you'll have determined in advance what
+
+ align:start position:0%
+you'll have determined in advance what
+ 
+
+ align:start position:0%
+you'll have determined in advance what
+is the air speed at which you should
+
+ align:start position:0%
+is the air speed at which you should
+ 
+
+ align:start position:0%
+is the air speed at which you should
+rotate now that's really important with
+
+ align:start position:0%
+rotate now that's really important with
+ 
+
+ align:start position:0%
+rotate now that's really important with
+a Cessna 172 for example it's around 55
+
+ align:start position:0%
+a Cessna 172 for example it's around 55
+ 
+
+ align:start position:0%
+a Cessna 172 for example it's around 55
+knots and you want to look at your
+
+ align:start position:0%
+knots and you want to look at your
+ 
+
+ align:start position:0%
+knots and you want to look at your
+airspeed indicator because if you just
+
+ align:start position:0%
+airspeed indicator because if you just
+ 
+
+ align:start position:0%
+airspeed indicator because if you just
+feel yourself you might notice that much
+
+ align:start position:0%
+feel yourself you might notice that much
+ 
+
+ align:start position:0%
+feel yourself you might notice that much
+lower like 40 knots that you the plane
+
+ align:start position:0%
+lower like 40 knots that you the plane
+ 
+
+ align:start position:0%
+lower like 40 knots that you the plane
+has already taken off you're already
+
+ align:start position:0%
+has already taken off you're already
+ 
+
+ align:start position:0%
+has already taken off you're already
+floating you're you're flying and you
+
+ align:start position:0%
+floating you're you're flying and you
+ 
+
+ align:start position:0%
+floating you're you're flying and you
+might be very excited about that and you
+
+ align:start position:0%
+might be very excited about that and you
+ 
+
+ align:start position:0%
+might be very excited about that and you
+might want to just you know pull back on
+
+ align:start position:0%
+might want to just you know pull back on
+ 
+
+ align:start position:0%
+might want to just you know pull back on
+your on your yoke to take off well you
+
+ align:start position:0%
+your on your yoke to take off well you
+ 
+
+ align:start position:0%
+your on your yoke to take off well you
+won't be able to sustain flight and and
+
+ align:start position:0%
+won't be able to sustain flight and and
+ 
+
+ align:start position:0%
+won't be able to sustain flight and and
+so this is what why ground effect is
+
+ align:start position:0%
+so this is what why ground effect is
+ 
+
+ align:start position:0%
+so this is what why ground effect is
+really important is that you can kind of
+
+ align:start position:0%
+really important is that you can kind of
+ 
+
+ align:start position:0%
+really important is that you can kind of
+float over the ground because you're so
+
+ align:start position:0%
+float over the ground because you're so
+ 
+
+ align:start position:0%
+float over the ground because you're so
+close to the ground that the ground is
+
+ align:start position:0%
+close to the ground that the ground is
+ 
+
+ align:start position:0%
+close to the ground that the ground is
+blocking some of the
+
+ align:start position:0%
+blocking some of the
+ 
+
+ align:start position:0%
+blocking some of the
+Effects of the air and so what you want
+
+ align:start position:0%
+Effects of the air and so what you want
+ 
+
+ align:start position:0%
+Effects of the air and so what you want
+to do is really make sure that you
+
+ align:start position:0%
+to do is really make sure that you
+ 
+
+ align:start position:0%
+to do is really make sure that you
+continue your ground roll continue even
+
+ align:start position:0%
+continue your ground roll continue even
+ 
+
+ align:start position:0%
+continue your ground roll continue even
+if you're a little bit airborne stay
+
+ align:start position:0%
+if you're a little bit airborne stay
+ 
+
+ align:start position:0%
+if you're a little bit airborne stay
+close to the ground until your airspeed
+
+ align:start position:0%
+close to the ground until your airspeed
+ 
+
+ align:start position:0%
+close to the ground until your airspeed
+comes up to that rotate speed so in this
+
+ align:start position:0%
+comes up to that rotate speed so in this
+ 
+
+ align:start position:0%
+comes up to that rotate speed so in this
+case 55 knots and then you pull back on
+
+ align:start position:0%
+case 55 knots and then you pull back on
+ 
+
+ align:start position:0%
+case 55 knots and then you pull back on
+your yoke to takeoff
+
+ align:start position:0%
+your yoke to takeoff
+ 
+
+ align:start position:0%
+your yoke to takeoff
+so again so when does ground effect
+
+ align:start position:0%
+so again so when does ground effect
+ 
+
+ align:start position:0%
+so again so when does ground effect
+happen when you're close to the ground
+
+ align:start position:0%
+happen when you're close to the ground
+ 
+
+ align:start position:0%
+happen when you're close to the ground
+when you're within one wingspan of the
+
+ align:start position:0%
+when you're within one wingspan of the
+ 
+
+ align:start position:0%
+when you're within one wingspan of the
+ground okay so let's talk a little bit
+
+ align:start position:0%
+ground okay so let's talk a little bit
+ 
+
+ align:start position:0%
+ground okay so let's talk a little bit
+about the stability and we'll start by
+
+ align:start position:0%
+about the stability and we'll start by
+ 
+
+ align:start position:0%
+about the stability and we'll start by
+just talking about the three axes of
+
+ align:start position:0%
+just talking about the three axes of
+ 
+
+ align:start position:0%
+just talking about the three axes of
+flight so there is a longitudinal axis
+
+ align:start position:0%
+flight so there is a longitudinal axis
+ 
+
+ align:start position:0%
+flight so there is a longitudinal axis
+which is basically from the the nose to
+
+ align:start position:0%
+which is basically from the the nose to
+ 
+
+ align:start position:0%
+which is basically from the the nose to
+the tail of your airplane and then
+
+ align:start position:0%
+the tail of your airplane and then
+ 
+
+ align:start position:0%
+the tail of your airplane and then
+there's a lateral axis which is from
+
+ align:start position:0%
+there's a lateral axis which is from
+ 
+
+ align:start position:0%
+there's a lateral axis which is from
+wingtip to wingtip and then vertical
+
+ align:start position:0%
+wingtip to wingtip and then vertical
+ 
+
+ align:start position:0%
+wingtip to wingtip and then vertical
+going straight through the plane so you
+
+ align:start position:0%
+going straight through the plane so you
+ 
+
+ align:start position:0%
+going straight through the plane so you
+have the ability to control all three of
+
+ align:start position:0%
+have the ability to control all three of
+ 
+
+ align:start position:0%
+have the ability to control all three of
+those axes so the the elevator which I
+
+ align:start position:0%
+those axes so the the elevator which I
+ 
+
+ align:start position:0%
+those axes so the the elevator which I
+keep talking about is like your yoke
+
+ align:start position:0%
+keep talking about is like your yoke
+ 
+
+ align:start position:0%
+keep talking about is like your yoke
+where you push it forward or you pull it
+
+ align:start position:0%
+where you push it forward or you pull it
+ 
+
+ align:start position:0%
+where you push it forward or you pull it
+back that allows you to pitch the
+
+ align:start position:0%
+back that allows you to pitch the
+ 
+
+ align:start position:0%
+back that allows you to pitch the
+airplane so pitch nose up pitch nose
+
+ align:start position:0%
+airplane so pitch nose up pitch nose
+ 
+
+ align:start position:0%
+airplane so pitch nose up pitch nose
+down that's you effect controlling the
+
+ align:start position:0%
+down that's you effect controlling the
+ 
+
+ align:start position:0%
+down that's you effect controlling the
+back part of this tail the elevator
+
+ align:start position:0%
+back part of this tail the elevator
+ 
+
+ align:start position:0%
+back part of this tail the elevator
+which allows you to have motion in this
+
+ align:start position:0%
+which allows you to have motion in this
+ 
+
+ align:start position:0%
+which allows you to have motion in this
+direction so pitch nose down so you
+
+ align:start position:0%
+direction so pitch nose down so you
+ 
+
+ align:start position:0%
+direction so pitch nose down so you
+might hear that a lot in case you're
+
+ align:start position:0%
+might hear that a lot in case you're
+ 
+
+ align:start position:0%
+might hear that a lot in case you're
+getting close to stalling because your
+
+ align:start position:0%
+getting close to stalling because your
+ 
+
+ align:start position:0%
+getting close to stalling because your
+angle of attack is getting too high they
+
+ align:start position:0%
+angle of attack is getting too high they
+ 
+
+ align:start position:0%
+angle of attack is getting too high they
+might say nose down or pitch nose down
+
+ align:start position:0%
+might say nose down or pitch nose down
+ 
+
+ align:start position:0%
+might say nose down or pitch nose down
+you also have a l'orange
+
+ align:start position:0%
+you also have a l'orange
+ 
+
+ align:start position:0%
+you also have a l'orange
+which are out on the the side of your
+
+ align:start position:0%
+which are out on the the side of your
+ 
+
+ align:start position:0%
+which are out on the the side of your
+wings and those ailerons control the
+
+ align:start position:0%
+wings and those ailerons control the
+ 
+
+ align:start position:0%
+wings and those ailerons control the
+roll so that's rolling along the
+
+ align:start position:0%
+roll so that's rolling along the
+ 
+
+ align:start position:0%
+roll so that's rolling along the
+longitudinal axis and then your rudder
+
+ align:start position:0%
+longitudinal axis and then your rudder
+ 
+
+ align:start position:0%
+longitudinal axis and then your rudder
+which is at the back of the the tail the
+
+ align:start position:0%
+which is at the back of the the tail the
+ 
+
+ align:start position:0%
+which is at the back of the the tail the
+vertical part of the tail that controls
+
+ align:start position:0%
+vertical part of the tail that controls
+ 
+
+ align:start position:0%
+vertical part of the tail that controls
+yaw so this is called yaw this type of
+
+ align:start position:0%
+yaw so this is called yaw this type of
+ 
+
+ align:start position:0%
+yaw so this is called yaw this type of
+motion so when you're when you're
+
+ align:start position:0%
+motion so when you're when you're
+ 
+
+ align:start position:0%
+motion so when you're when you're
+turning you actually kind of do a roll
+
+ align:start position:0%
+turning you actually kind of do a roll
+ 
+
+ align:start position:0%
+turning you actually kind of do a roll
+and yaw usually to in enacted turn okay
+
+ align:start position:0%
+and yaw usually to in enacted turn okay
+ 
+
+ align:start position:0%
+and yaw usually to in enacted turn okay
+there are some cases where you actually
+
+ align:start position:0%
+there are some cases where you actually
+ 
+
+ align:start position:0%
+there are some cases where you actually
+want to have adverse yaw or you you
+
+ align:start position:0%
+want to have adverse yaw or you you
+ 
+
+ align:start position:0%
+want to have adverse yaw or you you
+actually adverse yaw means basically
+
+ align:start position:0%
+actually adverse yaw means basically
+ 
+
+ align:start position:0%
+actually adverse yaw means basically
+you're you're using the yaw direction
+
+ align:start position:0%
+you're you're using the yaw direction
+ 
+
+ align:start position:0%
+you're you're using the yaw direction
+and maybe the opposite direction at
+
+ align:start position:0%
+and maybe the opposite direction at
+ 
+
+ align:start position:0%
+and maybe the opposite direction at
+which you're trying to turn with the
+
+ align:start position:0%
+which you're trying to turn with the
+ 
+
+ align:start position:0%
+which you're trying to turn with the
+roll or other other angles of your plane
+
+ align:start position:0%
+roll or other other angles of your plane
+ 
+
+ align:start position:0%
+roll or other other angles of your plane
+and so this just talks about an adverse
+
+ align:start position:0%
+and so this just talks about an adverse
+ 
+
+ align:start position:0%
+and so this just talks about an adverse
+yaw is when you're you're not turning
+
+ align:start position:0%
+yaw is when you're you're not turning
+ 
+
+ align:start position:0%
+yaw is when you're you're not turning
+the rudder in the same direction that
+
+ align:start position:0%
+the rudder in the same direction that
+ 
+
+ align:start position:0%
+the rudder in the same direction that
+you're using your ailerons and so this
+
+ align:start position:0%
+you're using your ailerons and so this
+ 
+
+ align:start position:0%
+you're using your ailerons and so this
+is where you talk about coordinated
+
+ align:start position:0%
+is where you talk about coordinated
+ 
+
+ align:start position:0%
+is where you talk about coordinated
+flight or uncoordinated flight when
+
+ align:start position:0%
+flight or uncoordinated flight when
+ 
+
+ align:start position:0%
+flight or uncoordinated flight when
+you're actually in an airplane the
+
+ align:start position:0%
+you're actually in an airplane the
+ 
+
+ align:start position:0%
+you're actually in an airplane the
+rudder or the yaw is controlled by your
+
+ align:start position:0%
+rudder or the yaw is controlled by your
+ 
+
+ align:start position:0%
+rudder or the yaw is controlled by your
+feet so you have feet pedals that
+
+ align:start position:0%
+feet so you have feet pedals that
+ 
+
+ align:start position:0%
+feet so you have feet pedals that
+control the the rudder and your the yoke
+
+ align:start position:0%
+control the the rudder and your the yoke
+ 
+
+ align:start position:0%
+control the the rudder and your the yoke
+that you're holding onto or a joystick
+
+ align:start position:0%
+that you're holding onto or a joystick
+ 
+
+ align:start position:0%
+that you're holding onto or a joystick
+that you're holding on to front and back
+
+ align:start position:0%
+that you're holding on to front and back
+ 
+
+ align:start position:0%
+that you're holding on to front and back
+controls the pitch and then turning it
+
+ align:start position:0%
+controls the pitch and then turning it
+ 
+
+ align:start position:0%
+controls the pitch and then turning it
+like in a steering wheel of a car is
+
+ align:start position:0%
+like in a steering wheel of a car is
+ 
+
+ align:start position:0%
+like in a steering wheel of a car is
+only controlling the roll so you
+
+ align:start position:0%
+only controlling the roll so you
+ 
+
+ align:start position:0%
+only controlling the roll so you
+actually also use your feet for that
+
+ align:start position:0%
+actually also use your feet for that
+ 
+
+ align:start position:0%
+actually also use your feet for that
+third direction of the yaw so just
+
+ align:start position:0%
+third direction of the yaw so just
+ 
+
+ align:start position:0%
+third direction of the yaw so just
+talking about stability in general this
+
+ align:start position:0%
+talking about stability in general this
+ 
+
+ align:start position:0%
+talking about stability in general this
+isn't going to dive into whole Diffie Q
+
+ align:start position:0%
+isn't going to dive into whole Diffie Q
+ 
+
+ align:start position:0%
+isn't going to dive into whole Diffie Q
+discussion or anything but just in
+
+ align:start position:0%
+discussion or anything but just in
+ 
+
+ align:start position:0%
+discussion or anything but just in
+general something that's stable so it's
+
+ align:start position:0%
+general something that's stable so it's
+ 
+
+ align:start position:0%
+general something that's stable so it's
+just talking about like a little bowl if
+
+ align:start position:0%
+just talking about like a little bowl if
+ 
+
+ align:start position:0%
+just talking about like a little bowl if
+you have a ball and a bowl even if the
+
+ align:start position:0%
+you have a ball and a bowl even if the
+ 
+
+ align:start position:0%
+you have a ball and a bowl even if the
+ball gets jostled around it'll return to
+
+ align:start position:0%
+ball gets jostled around it'll return to
+ 
+
+ align:start position:0%
+ball gets jostled around it'll return to
+the center point unstable would be the
+
+ align:start position:0%
+the center point unstable would be the
+ 
+
+ align:start position:0%
+the center point unstable would be the
+opposite so if you have a convex surface
+
+ align:start position:0%
+opposite so if you have a convex surface
+ 
+
+ align:start position:0%
+opposite so if you have a convex surface
+then if the ball moves even just a
+
+ align:start position:0%
+then if the ball moves even just a
+ 
+
+ align:start position:0%
+then if the ball moves even just a
+little bit it'll really get moved out of
+
+ align:start position:0%
+little bit it'll really get moved out of
+ 
+
+ align:start position:0%
+little bit it'll really get moved out of
+control so the reason that we talk about
+
+ align:start position:0%
+control so the reason that we talk about
+ 
+
+ align:start position:0%
+control so the reason that we talk about
+this is basically when you're flying in
+
+ align:start position:0%
+this is basically when you're flying in
+ 
+
+ align:start position:0%
+this is basically when you're flying in
+an airplane and you're talking about
+
+ align:start position:0%
+an airplane and you're talking about
+ 
+
+ align:start position:0%
+an airplane and you're talking about
+stable aircraft for example the reason I
+
+ align:start position:0%
+stable aircraft for example the reason I
+ 
+
+ align:start position:0%
+stable aircraft for example the reason I
+really love flying a Cessna 172 even
+
+ align:start position:0%
+really love flying a Cessna 172 even
+ 
+
+ align:start position:0%
+really love flying a Cessna 172 even
+though it's kind of the the training
+
+ align:start position:0%
+though it's kind of the the training
+ 
+
+ align:start position:0%
+though it's kind of the the training
+airplane is that the as people call it
+
+ align:start position:0%
+airplane is that the as people call it
+ 
+
+ align:start position:0%
+airplane is that the as people call it
+it flies itself so if you notice the
+
+ align:start position:0%
+it flies itself so if you notice the
+ 
+
+ align:start position:0%
+it flies itself so if you notice the
+planes doing something weird and turning
+
+ align:start position:0%
+planes doing something weird and turning
+ 
+
+ align:start position:0%
+planes doing something weird and turning
+almost the best thing you can do is just
+
+ align:start position:0%
+almost the best thing you can do is just
+ 
+
+ align:start position:0%
+almost the best thing you can do is just
+let go and the controls will normalize
+
+ align:start position:0%
+let go and the controls will normalize
+ 
+
+ align:start position:0%
+let go and the controls will normalize
+and then the flame will fly straight and
+
+ align:start position:0%
+and then the flame will fly straight and
+ 
+
+ align:start position:0%
+and then the flame will fly straight and
+level which is really great there are
+
+ align:start position:0%
+level which is really great there are
+ 
+
+ align:start position:0%
+level which is really great there are
+other types of aircraft that are
+
+ align:start position:0%
+other types of aircraft that are
+ 
+
+ align:start position:0%
+other types of aircraft that are
+inherently unstable so we have mean
+
+ align:start position:0%
+inherently unstable so we have mean
+ 
+
+ align:start position:0%
+inherently unstable so we have mean
+she and Roxanna over here who have who
+
+ align:start position:0%
+she and Roxanna over here who have who
+ 
+
+ align:start position:0%
+she and Roxanna over here who have who
+do Arab aerobatic flight and Mark will
+
+ align:start position:0%
+do Arab aerobatic flight and Mark will
+ 
+
+ align:start position:0%
+do Arab aerobatic flight and Mark will
+be talking about that tomorrow so that's
+
+ align:start position:0%
+be talking about that tomorrow so that's
+ 
+
+ align:start position:0%
+be talking about that tomorrow so that's
+where you actually want an airplane
+
+ align:start position:0%
+where you actually want an airplane
+ 
+
+ align:start position:0%
+where you actually want an airplane
+that's not so stable so that you can
+
+ align:start position:0%
+that's not so stable so that you can
+ 
+
+ align:start position:0%
+that's not so stable so that you can
+cause it to do all kinds of crazy
+
+ align:start position:0%
+cause it to do all kinds of crazy
+ 
+
+ align:start position:0%
+cause it to do all kinds of crazy
+maneuvers and turns and twists very
+
+ align:start position:0%
+maneuvers and turns and twists very
+ 
+
+ align:start position:0%
+maneuvers and turns and twists very
+easily you pretty much can't get a
+
+ align:start position:0%
+easily you pretty much can't get a
+ 
+
+ align:start position:0%
+easily you pretty much can't get a
+Cessna to do that it really wants to fly
+
+ align:start position:0%
+Cessna to do that it really wants to fly
+ 
+
+ align:start position:0%
+Cessna to do that it really wants to fly
+straight and level ok so then there are
+
+ align:start position:0%
+straight and level ok so then there are
+ 
+
+ align:start position:0%
+straight and level ok so then there are
+also other aspects that can affect
+
+ align:start position:0%
+also other aspects that can affect
+ 
+
+ align:start position:0%
+also other aspects that can affect
+stability such as your center of gravity
+
+ align:start position:0%
+stability such as your center of gravity
+ 
+
+ align:start position:0%
+stability such as your center of gravity
+so how you how you load the airplane
+
+ align:start position:0%
+so how you how you load the airplane
+ 
+
+ align:start position:0%
+so how you how you load the airplane
+will have a specific lecture that just
+
+ align:start position:0%
+will have a specific lecture that just
+ 
+
+ align:start position:0%
+will have a specific lecture that just
+talks about weight and balance but one
+
+ align:start position:0%
+talks about weight and balance but one
+ 
+
+ align:start position:0%
+talks about weight and balance but one
+thing to keep in mind is that you know
+
+ align:start position:0%
+thing to keep in mind is that you know
+ 
+
+ align:start position:0%
+thing to keep in mind is that you know
+as people sit in your airplane or as you
+
+ align:start position:0%
+as people sit in your airplane or as you
+ 
+
+ align:start position:0%
+as people sit in your airplane or as you
+put bags in the baggage compartment
+
+ align:start position:0%
+put bags in the baggage compartment
+ 
+
+ align:start position:0%
+put bags in the baggage compartment
+you're loading the airplane and so if
+
+ align:start position:0%
+you're loading the airplane and so if
+ 
+
+ align:start position:0%
+you're loading the airplane and so if
+you have too much weight aft of the CG
+
+ align:start position:0%
+you have too much weight aft of the CG
+ 
+
+ align:start position:0%
+you have too much weight aft of the CG
+or behind the center of gravity you can
+
+ align:start position:0%
+or behind the center of gravity you can
+ 
+
+ align:start position:0%
+or behind the center of gravity you can
+cause the plane to basically go like
+
+ align:start position:0%
+cause the plane to basically go like
+ 
+
+ align:start position:0%
+cause the plane to basically go like
+this which isn't very helpful when
+
+ align:start position:0%
+this which isn't very helpful when
+ 
+
+ align:start position:0%
+this which isn't very helpful when
+you're flying if you have things a
+
+ align:start position:0%
+you're flying if you have things a
+ 
+
+ align:start position:0%
+you're flying if you have things a
+little too too forward it actually
+
+ align:start position:0%
+little too too forward it actually
+ 
+
+ align:start position:0%
+little too too forward it actually
+pushes the the nose down in general the
+
+ align:start position:0%
+pushes the the nose down in general the
+ 
+
+ align:start position:0%
+pushes the the nose down in general the
+nose down is a little bit more more
+
+ align:start position:0%
+nose down is a little bit more more
+ 
+
+ align:start position:0%
+nose down is a little bit more more
+stable from the perspective of lift and
+
+ align:start position:0%
+stable from the perspective of lift and
+ 
+
+ align:start position:0%
+stable from the perspective of lift and
+getting air to fly over you don't want
+
+ align:start position:0%
+getting air to fly over you don't want
+ 
+
+ align:start position:0%
+getting air to fly over you don't want
+something that keeps trying to stall
+
+ align:start position:0%
+something that keeps trying to stall
+ 
+
+ align:start position:0%
+something that keeps trying to stall
+whenever you let go of it and then
+
+ align:start position:0%
+whenever you let go of it and then
+ 
+
+ align:start position:0%
+whenever you let go of it and then
+similarly you can talk about the
+
+ align:start position:0%
+similarly you can talk about the
+ 
+
+ align:start position:0%
+similarly you can talk about the
+stability in the lateral direction in
+
+ align:start position:0%
+stability in the lateral direction in
+ 
+
+ align:start position:0%
+stability in the lateral direction in
+that roll in the roll direction and some
+
+ align:start position:0%
+that roll in the roll direction and some
+ 
+
+ align:start position:0%
+that roll in the roll direction and some
+of these things like swept-back wings
+
+ align:start position:0%
+of these things like swept-back wings
+ 
+
+ align:start position:0%
+of these things like swept-back wings
+like you see on a jet can affect that
+
+ align:start position:0%
+like you see on a jet can affect that
+ 
+
+ align:start position:0%
+like you see on a jet can affect that
+type of stability and then finally
+
+ align:start position:0%
+type of stability and then finally
+ 
+
+ align:start position:0%
+type of stability and then finally
+there's a stability about the the
+
+ align:start position:0%
+there's a stability about the the
+ 
+
+ align:start position:0%
+there's a stability about the the
+vertical axes generally this is going to
+
+ align:start position:0%
+vertical axes generally this is going to
+ 
+
+ align:start position:0%
+vertical axes generally this is going to
+be kind of fixed for the given aircraft
+
+ align:start position:0%
+be kind of fixed for the given aircraft
+ 
+
+ align:start position:0%
+be kind of fixed for the given aircraft
+that you're in but you can't affect it
+
+ align:start position:0%
+that you're in but you can't affect it
+ 
+
+ align:start position:0%
+that you're in but you can't affect it
+as you design an aircraft so we started
+
+ align:start position:0%
+as you design an aircraft so we started
+ 
+
+ align:start position:0%
+as you design an aircraft so we started
+talking about stall already so when when
+
+ align:start position:0%
+talking about stall already so when when
+ 
+
+ align:start position:0%
+talking about stall already so when when
+you have your angle of attack past its
+
+ align:start position:0%
+you have your angle of attack past its
+ 
+
+ align:start position:0%
+you have your angle of attack past its
+so-called critical angle of attack it
+
+ align:start position:0%
+so-called critical angle of attack it
+ 
+
+ align:start position:0%
+so-called critical angle of attack it
+can cause the air to basically no longer
+
+ align:start position:0%
+can cause the air to basically no longer
+ 
+
+ align:start position:0%
+can cause the air to basically no longer
+be able to flow over the top and no
+
+ align:start position:0%
+be able to flow over the top and no
+ 
+
+ align:start position:0%
+be able to flow over the top and no
+longer be able to effectively deflect
+
+ align:start position:0%
+longer be able to effectively deflect
+ 
+
+ align:start position:0%
+longer be able to effectively deflect
+air down and so the air air kind of
+
+ align:start position:0%
+air down and so the air air kind of
+ 
+
+ align:start position:0%
+air down and so the air air kind of
+separates and you can stall so it's
+
+ align:start position:0%
+separates and you can stall so it's
+ 
+
+ align:start position:0%
+separates and you can stall so it's
+really important to know that you can
+
+ align:start position:0%
+really important to know that you can
+ 
+
+ align:start position:0%
+really important to know that you can
+actually stall at
+
+ align:start position:0%
+actually stall at
+ 
+
+ align:start position:0%
+actually stall at
+any air speed even with full power you
+
+ align:start position:0%
+any air speed even with full power you
+ 
+
+ align:start position:0%
+any air speed even with full power you
+can stall in fact one of the maneuvers
+
+ align:start position:0%
+can stall in fact one of the maneuvers
+ 
+
+ align:start position:0%
+can stall in fact one of the maneuvers
+you'll have to do in order to get your
+
+ align:start position:0%
+you'll have to do in order to get your
+ 
+
+ align:start position:0%
+you'll have to do in order to get your
+pilot's license is a power on stall so
+
+ align:start position:0%
+pilot's license is a power on stall so
+ 
+
+ align:start position:0%
+pilot's license is a power on stall so
+you can stall both where your engine is
+
+ align:start position:0%
+you can stall both where your engine is
+ 
+
+ align:start position:0%
+you can stall both where your engine is
+idling or coming in for a landing and
+
+ align:start position:0%
+idling or coming in for a landing and
+ 
+
+ align:start position:0%
+idling or coming in for a landing and
+you you get to steep but you can also
+
+ align:start position:0%
+you you get to steep but you can also
+ 
+
+ align:start position:0%
+you you get to steep but you can also
+stall with full power and you just you
+
+ align:start position:0%
+stall with full power and you just you
+ 
+
+ align:start position:0%
+stall with full power and you just you
+just made your angle go too steep so
+
+ align:start position:0%
+just made your angle go too steep so
+ 
+
+ align:start position:0%
+just made your angle go too steep so
+it's really affecting that that critical
+
+ align:start position:0%
+it's really affecting that that critical
+ 
+
+ align:start position:0%
+it's really affecting that that critical
+angle of attack and again once you have
+
+ align:start position:0%
+angle of attack and again once you have
+ 
+
+ align:start position:0%
+angle of attack and again once you have
+that angle of attack too steep then
+
+ align:start position:0%
+that angle of attack too steep then
+ 
+
+ align:start position:0%
+that angle of attack too steep then
+there's a very significant loss of lift
+
+ align:start position:0%
+there's a very significant loss of lift
+ 
+
+ align:start position:0%
+there's a very significant loss of lift
+which is not good when you're flying an
+
+ align:start position:0%
+which is not good when you're flying an
+ 
+
+ align:start position:0%
+which is not good when you're flying an
+airplane so when can you stall at any
+
+ align:start position:0%
+airplane so when can you stall at any
+ 
+
+ align:start position:0%
+airplane so when can you stall at any
+airspeed and any any power setting and
+
+ align:start position:0%
+airspeed and any any power setting and
+ 
+
+ align:start position:0%
+airspeed and any any power setting and
+it's really based on the angle of attack
+
+ align:start position:0%
+it's really based on the angle of attack
+ 
+
+ align:start position:0%
+it's really based on the angle of attack
+so if you
+
+ align:start position:0%
+so if you
+ 
+
+ align:start position:0%
+so if you
+yes go ahead yeah basically it's not
+
+ align:start position:0%
+yes go ahead yeah basically it's not
+ 
+
+ align:start position:0%
+yes go ahead yeah basically it's not
+generating any any lift right youyou can
+
+ align:start position:0%
+generating any any lift right youyou can
+ 
+
+ align:start position:0%
+generating any any lift right youyou can
+see this like with a paper airplane
+
+ align:start position:0%
+see this like with a paper airplane
+ 
+
+ align:start position:0%
+see this like with a paper airplane
+right sometimes if you it kind of stops
+
+ align:start position:0%
+right sometimes if you it kind of stops
+ 
+
+ align:start position:0%
+right sometimes if you it kind of stops
+and kind of crashes we'll see how I mean
+
+ align:start position:0%
+and kind of crashes we'll see how I mean
+ 
+
+ align:start position:0%
+and kind of crashes we'll see how I mean
+actually his paper airplane does here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that one I definitely had a low
+
+ align:start position:0%
+well that one I definitely had a low
+ 
+
+ align:start position:0%
+well that one I definitely had a low
+angle of attack so it flew very well
+
+ align:start position:0%
+angle of attack so it flew very well
+ 
+
+ align:start position:0%
+angle of attack so it flew very well
+let's see if I can get it to stall or if
+
+ align:start position:0%
+let's see if I can get it to stall or if
+ 
+
+ align:start position:0%
+let's see if I can get it to stall or if
+it's it's too stable of an airplane that
+
+ align:start position:0%
+it's it's too stable of an airplane that
+ 
+
+ align:start position:0%
+it's it's too stable of an airplane that
+one basically after it's stalled it
+
+ align:start position:0%
+one basically after it's stalled it
+ 
+
+ align:start position:0%
+one basically after it's stalled it
+basically went nose-down which is which
+
+ align:start position:0%
+basically went nose-down which is which
+ 
+
+ align:start position:0%
+basically went nose-down which is which
+is good it has a little extra paper
+
+ align:start position:0%
+is good it has a little extra paper
+ 
+
+ align:start position:0%
+is good it has a little extra paper
+folding at the front so that the nose
+
+ align:start position:0%
+folding at the front so that the nose
+ 
+
+ align:start position:0%
+folding at the front so that the nose
+will will go down but it's really bad
+
+ align:start position:0%
+will will go down but it's really bad
+ 
+
+ align:start position:0%
+will will go down but it's really bad
+basically if you if you stall it can it
+
+ align:start position:0%
+basically if you if you stall it can it
+ 
+
+ align:start position:0%
+basically if you if you stall it can it
+can go that way the other thing that can
+
+ align:start position:0%
+can go that way the other thing that can
+ 
+
+ align:start position:0%
+can go that way the other thing that can
+happen after you stall a lot usually is
+
+ align:start position:0%
+happen after you stall a lot usually is
+ 
+
+ align:start position:0%
+happen after you stall a lot usually is
+you can enter a spin which is actually
+
+ align:start position:0%
+you can enter a spin which is actually
+ 
+
+ align:start position:0%
+you can enter a spin which is actually
+the the next case so this is when you're
+
+ align:start position:0%
+the the next case so this is when you're
+ 
+
+ align:start position:0%
+the the next case so this is when you're
+uncoordinated in your stall so what I
+
+ align:start position:0%
+uncoordinated in your stall so what I
+ 
+
+ align:start position:0%
+uncoordinated in your stall so what I
+mean by uncoordinated so that's what I
+
+ align:start position:0%
+mean by uncoordinated so that's what I
+ 
+
+ align:start position:0%
+mean by uncoordinated so that's what I
+was just talking about before where
+
+ align:start position:0%
+was just talking about before where
+ 
+
+ align:start position:0%
+was just talking about before where
+you're your role and your yaw are not
+
+ align:start position:0%
+you're your role and your yaw are not
+ 
+
+ align:start position:0%
+you're your role and your yaw are not
+going in the same direction and here you
+
+ align:start position:0%
+going in the same direction and here you
+ 
+
+ align:start position:0%
+going in the same direction and here you
+can have a situation where both of the
+
+ align:start position:0%
+can have a situation where both of the
+ 
+
+ align:start position:0%
+can have a situation where both of the
+wings have stalled so the airflow has
+
+ align:start position:0%
+wings have stalled so the airflow has
+ 
+
+ align:start position:0%
+wings have stalled so the airflow has
+separated over both of the
+
+ align:start position:0%
+separated over both of the
+ 
+
+ align:start position:0%
+separated over both of the
+but one maybe more stalled than the
+
+ align:start position:0%
+but one maybe more stalled than the
+ 
+
+ align:start position:0%
+but one maybe more stalled than the
+other and it causes the airplane to have
+
+ align:start position:0%
+other and it causes the airplane to have
+ 
+
+ align:start position:0%
+other and it causes the airplane to have
+a very very hazardous condition or an
+
+ align:start position:0%
+a very very hazardous condition or an
+ 
+
+ align:start position:0%
+a very very hazardous condition or an
+intentional condition if your ox in over
+
+ align:start position:0%
+intentional condition if your ox in over
+ 
+
+ align:start position:0%
+intentional condition if your ox in over
+there and you're trying to spin your
+
+ align:start position:0%
+there and you're trying to spin your
+ 
+
+ align:start position:0%
+there and you're trying to spin your
+airplane to do a fancy trick is very
+
+ align:start position:0%
+airplane to do a fancy trick is very
+ 
+
+ align:start position:0%
+airplane to do a fancy trick is very
+dangerous close to the ground as you'll
+
+ align:start position:0%
+dangerous close to the ground as you'll
+ 
+
+ align:start position:0%
+dangerous close to the ground as you'll
+hear you only intentionally do this and
+
+ align:start position:0%
+hear you only intentionally do this and
+ 
+
+ align:start position:0%
+hear you only intentionally do this and
+certain types of aircraft when you're
+
+ align:start position:0%
+certain types of aircraft when you're
+ 
+
+ align:start position:0%
+certain types of aircraft when you're
+wearing parachutes in certain airspace
+
+ align:start position:0%
+wearing parachutes in certain airspace
+ 
+
+ align:start position:0%
+wearing parachutes in certain airspace
+when you're very high above the ground
+
+ align:start position:0%
+when you're very high above the ground
+ 
+
+ align:start position:0%
+when you're very high above the ground
+you don't want to do this and in fact if
+
+ align:start position:0%
+you don't want to do this and in fact if
+ 
+
+ align:start position:0%
+you don't want to do this and in fact if
+you're just getting your private pilot's
+
+ align:start position:0%
+you're just getting your private pilot's
+ 
+
+ align:start position:0%
+you're just getting your private pilot's
+license or your ppl you're not going to
+
+ align:start position:0%
+license or your ppl you're not going to
+ 
+
+ align:start position:0%
+license or your ppl you're not going to
+you're not going to practice a spin
+
+ align:start position:0%
+you're not going to practice a spin
+ 
+
+ align:start position:0%
+you're not going to practice a spin
+because it's pretty dangerous thing to
+
+ align:start position:0%
+because it's pretty dangerous thing to
+ 
+
+ align:start position:0%
+because it's pretty dangerous thing to
+do in many aircraft but you do have to
+
+ align:start position:0%
+do in many aircraft but you do have to
+ 
+
+ align:start position:0%
+do in many aircraft but you do have to
+learn about it and make sure you don't
+
+ align:start position:0%
+learn about it and make sure you don't
+ 
+
+ align:start position:0%
+learn about it and make sure you don't
+get into a spin okay so let's talk a
+
+ align:start position:0%
+get into a spin okay so let's talk a
+ 
+
+ align:start position:0%
+get into a spin okay so let's talk a
+little bit about maneuvering flight so
+
+ align:start position:0%
+little bit about maneuvering flight so
+ 
+
+ align:start position:0%
+little bit about maneuvering flight so
+basically that means when you are flying
+
+ align:start position:0%
+basically that means when you are flying
+ 
+
+ align:start position:0%
+basically that means when you are flying
+straight and level that's kind of when
+
+ align:start position:0%
+straight and level that's kind of when
+ 
+
+ align:start position:0%
+straight and level that's kind of when
+you're in equilibrium where your lift
+
+ align:start position:0%
+you're in equilibrium where your lift
+ 
+
+ align:start position:0%
+you're in equilibrium where your lift
+and your weight kind of cancel out and
+
+ align:start position:0%
+and your weight kind of cancel out and
+ 
+
+ align:start position:0%
+and your weight kind of cancel out and
+the planes just going straight and level
+
+ align:start position:0%
+the planes just going straight and level
+ 
+
+ align:start position:0%
+the planes just going straight and level
+at the same altitude but climbing is
+
+ align:start position:0%
+at the same altitude but climbing is
+ 
+
+ align:start position:0%
+at the same altitude but climbing is
+when your lift temporarily exceeds the
+
+ align:start position:0%
+when your lift temporarily exceeds the
+ 
+
+ align:start position:0%
+when your lift temporarily exceeds the
+weight so you can actually climb so once
+
+ align:start position:0%
+weight so you can actually climb so once
+ 
+
+ align:start position:0%
+weight so you can actually climb so once
+you are in a steady climb then you can
+
+ align:start position:0%
+you are in a steady climb then you can
+ 
+
+ align:start position:0%
+you are in a steady climb then you can
+actually still have your forces be in
+
+ align:start position:0%
+actually still have your forces be in
+ 
+
+ align:start position:0%
+actually still have your forces be in
+equilibrium so remember F equals M a so
+
+ align:start position:0%
+equilibrium so remember F equals M a so
+ 
+
+ align:start position:0%
+equilibrium so remember F equals M a so
+a is acceleration which is a change in
+
+ align:start position:0%
+a is acceleration which is a change in
+ 
+
+ align:start position:0%
+a is acceleration which is a change in
+velocity so if you're not changing your
+
+ align:start position:0%
+velocity so if you're not changing your
+ 
+
+ align:start position:0%
+velocity so if you're not changing your
+velocity and you're just in a steady
+
+ align:start position:0%
+velocity and you're just in a steady
+ 
+
+ align:start position:0%
+velocity and you're just in a steady
+climb then you're also not accelerating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there this is a little bit
+
+ align:start position:0%
+now there this is a little bit
+ 
+
+ align:start position:0%
+now there this is a little bit
+complicated so I will say this is a
+
+ align:start position:0%
+complicated so I will say this is a
+ 
+
+ align:start position:0%
+complicated so I will say this is a
+little bit tricky there is a tendency
+
+ align:start position:0%
+little bit tricky there is a tendency
+ 
+
+ align:start position:0%
+little bit tricky there is a tendency
+for these airplanes to turn left and
+
+ align:start position:0%
+for these airplanes to turn left and
+ 
+
+ align:start position:0%
+for these airplanes to turn left and
+there are actually multiple things that
+
+ align:start position:0%
+there are actually multiple things that
+ 
+
+ align:start position:0%
+there are actually multiple things that
+contribute to this left turning tendency
+
+ align:start position:0%
+contribute to this left turning tendency
+ 
+
+ align:start position:0%
+contribute to this left turning tendency
+and when you're in an airplane flying
+
+ align:start position:0%
+and when you're in an airplane flying
+ 
+
+ align:start position:0%
+and when you're in an airplane flying
+you might hear hear your instructor say
+
+ align:start position:0%
+you might hear hear your instructor say
+ 
+
+ align:start position:0%
+you might hear hear your instructor say
+right rudder and it's really to
+
+ align:start position:0%
+right rudder and it's really to
+ 
+
+ align:start position:0%
+right rudder and it's really to
+counteract some of these left-turning
+
+ align:start position:0%
+counteract some of these left-turning
+ 
+
+ align:start position:0%
+counteract some of these left-turning
+tendencies so we're gonna break break
+
+ align:start position:0%
+tendencies so we're gonna break break
+ 
+
+ align:start position:0%
+tendencies so we're gonna break break
+them down and talk about them but this
+
+ align:start position:0%
+them down and talk about them but this
+ 
+
+ align:start position:0%
+them down and talk about them but this
+can be a very in-depth subject so I will
+
+ align:start position:0%
+can be a very in-depth subject so I will
+ 
+
+ align:start position:0%
+can be a very in-depth subject so I will
+definitely refer to the P hack which is
+
+ align:start position:0%
+definitely refer to the P hack which is
+ 
+
+ align:start position:0%
+definitely refer to the P hack which is
+the pilot handbook of aeronautical
+
+ align:start position:0%
+the pilot handbook of aeronautical
+ 
+
+ align:start position:0%
+the pilot handbook of aeronautical
+knowledge chapter five goes into all all
+
+ align:start position:0%
+knowledge chapter five goes into all all
+ 
+
+ align:start position:0%
+knowledge chapter five goes into all all
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+so the first one is torque so basically
+
+ align:start position:0%
+so the first one is torque so basically
+ 
+
+ align:start position:0%
+so the first one is torque so basically
+the thing is when you're if you're
+
+ align:start position:0%
+the thing is when you're if you're
+ 
+
+ align:start position:0%
+the thing is when you're if you're
+sitting in the in the airplane and
+
+ align:start position:0%
+sitting in the in the airplane and
+ 
+
+ align:start position:0%
+sitting in the in the airplane and
+you're looking forward at your propeller
+
+ align:start position:0%
+you're looking forward at your propeller
+ 
+
+ align:start position:0%
+you're looking forward at your propeller
+most US engines actually have the
+
+ align:start position:0%
+most US engines actually have the
+ 
+
+ align:start position:0%
+most US engines actually have the
+propeller rotating clockwise so with and
+
+ align:start position:0%
+propeller rotating clockwise so with and
+ 
+
+ align:start position:0%
+propeller rotating clockwise so with and
+you can see that arrow that says action
+
+ align:start position:0%
+you can see that arrow that says action
+ 
+
+ align:start position:0%
+you can see that arrow that says action
+so that's the propeller rotating
+
+ align:start position:0%
+so that's the propeller rotating
+ 
+
+ align:start position:0%
+so that's the propeller rotating
+clockwise and so because of the because
+
+ align:start position:0%
+clockwise and so because of the because
+ 
+
+ align:start position:0%
+clockwise and so because of the because
+of Newton we know for every action
+
+ align:start position:0%
+of Newton we know for every action
+ 
+
+ align:start position:0%
+of Newton we know for every action
+there's an equal and opposite reaction
+
+ align:start position:0%
+there's an equal and opposite reaction
+ 
+
+ align:start position:0%
+there's an equal and opposite reaction
+so because the propeller is turning to
+
+ align:start position:0%
+so because the propeller is turning to
+ 
+
+ align:start position:0%
+so because the propeller is turning to
+the right the whole airplane is trying
+
+ align:start position:0%
+the right the whole airplane is trying
+ 
+
+ align:start position:0%
+the right the whole airplane is trying
+to roll to the left so that is the first
+
+ align:start position:0%
+to roll to the left so that is the first
+ 
+
+ align:start position:0%
+to roll to the left so that is the first
+left-turning tendency
+
+ align:start position:0%
+left-turning tendency
+ 
+
+ align:start position:0%
+left-turning tendency
+before we move to the next one are there
+
+ align:start position:0%
+before we move to the next one are there
+ 
+
+ align:start position:0%
+before we move to the next one are there
+any questions on this left turning
+
+ align:start position:0%
+any questions on this left turning
+ 
+
+ align:start position:0%
+any questions on this left turning
+tendency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay great so the next one is P factor
+
+ align:start position:0%
+okay great so the next one is P factor
+ 
+
+ align:start position:0%
+okay great so the next one is P factor
+which is an asymmetrical thrust this
+
+ align:start position:0%
+which is an asymmetrical thrust this
+ 
+
+ align:start position:0%
+which is an asymmetrical thrust this
+happens when the airplane has a high
+
+ align:start position:0%
+happens when the airplane has a high
+ 
+
+ align:start position:0%
+happens when the airplane has a high
+angle of attack so either when it's
+
+ align:start position:0%
+angle of attack so either when it's
+ 
+
+ align:start position:0%
+angle of attack so either when it's
+climbing or in this condition called
+
+ align:start position:0%
+climbing or in this condition called
+ 
+
+ align:start position:0%
+climbing or in this condition called
+slow flight which is where it's kind of
+
+ align:start position:0%
+slow flight which is where it's kind of
+ 
+
+ align:start position:0%
+slow flight which is where it's kind of
+an uncomfortable thing you have to do
+
+ align:start position:0%
+an uncomfortable thing you have to do
+ 
+
+ align:start position:0%
+an uncomfortable thing you have to do
+this in your flight training so
+
+ align:start position:0%
+this in your flight training so
+ 
+
+ align:start position:0%
+this in your flight training so
+basically you have your your power
+
+ align:start position:0%
+basically you have your your power
+ 
+
+ align:start position:0%
+basically you have your your power
+setting pretty high but you've kind of
+
+ align:start position:0%
+setting pretty high but you've kind of
+ 
+
+ align:start position:0%
+setting pretty high but you've kind of
+pitched the airplane up and so you're
+
+ align:start position:0%
+pitched the airplane up and so you're
+ 
+
+ align:start position:0%
+pitched the airplane up and so you're
+not getting as much air flow over your
+
+ align:start position:0%
+not getting as much air flow over your
+ 
+
+ align:start position:0%
+not getting as much air flow over your
+control surfaces like your ailerons and
+
+ align:start position:0%
+control surfaces like your ailerons and
+ 
+
+ align:start position:0%
+control surfaces like your ailerons and
+your elevator so it's they call your
+
+ align:start position:0%
+your elevator so it's they call your
+ 
+
+ align:start position:0%
+your elevator so it's they call your
+controls mushy so it's hard to kind of
+
+ align:start position:0%
+controls mushy so it's hard to kind of
+ 
+
+ align:start position:0%
+controls mushy so it's hard to kind of
+coordinate your airplane but you kind of
+
+ align:start position:0%
+coordinate your airplane but you kind of
+ 
+
+ align:start position:0%
+coordinate your airplane but you kind of
+sit in that in that environment to
+
+ align:start position:0%
+sit in that in that environment to
+ 
+
+ align:start position:0%
+sit in that in that environment to
+basically understand how it's difficult
+
+ align:start position:0%
+basically understand how it's difficult
+ 
+
+ align:start position:0%
+basically understand how it's difficult
+to control the airplane in that
+
+ align:start position:0%
+to control the airplane in that
+ 
+
+ align:start position:0%
+to control the airplane in that
+environment so if you're pitched up and
+
+ align:start position:0%
+environment so if you're pitched up and
+ 
+
+ align:start position:0%
+environment so if you're pitched up and
+you have a so you have a high angle of
+
+ align:start position:0%
+you have a so you have a high angle of
+ 
+
+ align:start position:0%
+you have a so you have a high angle of
+attack and you're either climbing or in
+
+ align:start position:0%
+attack and you're either climbing or in
+ 
+
+ align:start position:0%
+attack and you're either climbing or in
+slow flight you have this tendency where
+
+ align:start position:0%
+slow flight you have this tendency where
+ 
+
+ align:start position:0%
+slow flight you have this tendency where
+the because you're angled to the wind
+
+ align:start position:0%
+the because you're angled to the wind
+ 
+
+ align:start position:0%
+the because you're angled to the wind
+the right propeller blade which is
+
+ align:start position:0%
+the right propeller blade which is
+ 
+
+ align:start position:0%
+the right propeller blade which is
+descending is kind of cutting into the
+
+ align:start position:0%
+descending is kind of cutting into the
+ 
+
+ align:start position:0%
+descending is kind of cutting into the
+air that's coming in so it's actually
+
+ align:start position:0%
+air that's coming in so it's actually
+ 
+
+ align:start position:0%
+air that's coming in so it's actually
+generating more thrust whereas the
+
+ align:start position:0%
+generating more thrust whereas the
+ 
+
+ align:start position:0%
+generating more thrust whereas the
+ascending left propeller blade so the
+
+ align:start position:0%
+ascending left propeller blade so the
+ 
+
+ align:start position:0%
+ascending left propeller blade so the
+propeller blade that's going up on the
+
+ align:start position:0%
+propeller blade that's going up on the
+ 
+
+ align:start position:0%
+propeller blade that's going up on the
+left side is kind of coming away from
+
+ align:start position:0%
+left side is kind of coming away from
+ 
+
+ align:start position:0%
+left side is kind of coming away from
+the wind that's coming at it and so it's
+
+ align:start position:0%
+the wind that's coming at it and so it's
+ 
+
+ align:start position:0%
+the wind that's coming at it and so it's
+not generating as much thrust as the
+
+ align:start position:0%
+not generating as much thrust as the
+ 
+
+ align:start position:0%
+not generating as much thrust as the
+right propeller blade so that causes the
+
+ align:start position:0%
+right propeller blade so that causes the
+ 
+
+ align:start position:0%
+right propeller blade so that causes the
+center of thrust to move towards the
+
+ align:start position:0%
+center of thrust to move towards the
+ 
+
+ align:start position:0%
+center of thrust to move towards the
+right and that
+
+ align:start position:0%
+right and that
+ 
+
+ align:start position:0%
+right and that
+creates a little bit of a yaw tendency
+
+ align:start position:0%
+creates a little bit of a yaw tendency
+ 
+
+ align:start position:0%
+creates a little bit of a yaw tendency
+of the airplane does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great a lot of head nods P factor was
+
+ align:start position:0%
+great a lot of head nods P factor was
+ 
+
+ align:start position:0%
+great a lot of head nods P factor was
+one that both Philip and I spent quite a
+
+ align:start position:0%
+one that both Philip and I spent quite a
+ 
+
+ align:start position:0%
+one that both Philip and I spent quite a
+bit of time getting our heads around and
+
+ align:start position:0%
+bit of time getting our heads around and
+ 
+
+ align:start position:0%
+bit of time getting our heads around and
+professor hansman helped us out there so
+
+ align:start position:0%
+professor hansman helped us out there so
+ 
+
+ align:start position:0%
+professor hansman helped us out there so
+another one is called the corkscrew
+
+ align:start position:0%
+another one is called the corkscrew
+ 
+
+ align:start position:0%
+another one is called the corkscrew
+effect sometimes it's called slip stream
+
+ align:start position:0%
+effect sometimes it's called slip stream
+ 
+
+ align:start position:0%
+effect sometimes it's called slip stream
+or spiraling slip stream it basically
+
+ align:start position:0%
+or spiraling slip stream it basically
+ 
+
+ align:start position:0%
+or spiraling slip stream it basically
+has to do with the fact that that
+
+ align:start position:0%
+has to do with the fact that that
+ 
+
+ align:start position:0%
+has to do with the fact that that
+propeller remember it's just kind of
+
+ align:start position:0%
+propeller remember it's just kind of
+ 
+
+ align:start position:0%
+propeller remember it's just kind of
+like a wing that's spinning around and
+
+ align:start position:0%
+like a wing that's spinning around and
+ 
+
+ align:start position:0%
+like a wing that's spinning around and
+so it is it's basically push you know
+
+ align:start position:0%
+so it is it's basically push you know
+ 
+
+ align:start position:0%
+so it is it's basically push you know
+pushing the the air back and since the
+
+ align:start position:0%
+pushing the the air back and since the
+ 
+
+ align:start position:0%
+pushing the the air back and since the
+propeller is spinning around that air
+
+ align:start position:0%
+propeller is spinning around that air
+ 
+
+ align:start position:0%
+propeller is spinning around that air
+that's coming back from the propeller is
+
+ align:start position:0%
+that's coming back from the propeller is
+ 
+
+ align:start position:0%
+that's coming back from the propeller is
+spinning around the airplane and as it
+
+ align:start position:0%
+spinning around the airplane and as it
+ 
+
+ align:start position:0%
+spinning around the airplane and as it
+spins around when it comes up to the
+
+ align:start position:0%
+spins around when it comes up to the
+ 
+
+ align:start position:0%
+spins around when it comes up to the
+back it pushes on the vertical
+
+ align:start position:0%
+back it pushes on the vertical
+ 
+
+ align:start position:0%
+back it pushes on the vertical
+stabilizer that tail piece and causes
+
+ align:start position:0%
+stabilizer that tail piece and causes
+ 
+
+ align:start position:0%
+stabilizer that tail piece and causes
+causes the the plane also to do a left
+
+ align:start position:0%
+causes the the plane also to do a left
+ 
+
+ align:start position:0%
+causes the the plane also to do a left
+yaw does that make sense some good head
+
+ align:start position:0%
+yaw does that make sense some good head
+ 
+
+ align:start position:0%
+yaw does that make sense some good head
+nods yes why doesn't it also cause it to
+
+ align:start position:0%
+nods yes why doesn't it also cause it to
+ 
+
+ align:start position:0%
+nods yes why doesn't it also cause it to
+you roll was the question
+
+ align:start position:0%
+you roll was the question
+ 
+
+ align:start position:0%
+you roll was the question
+and it could especially if it's hitting
+
+ align:start position:0%
+and it could especially if it's hitting
+ 
+
+ align:start position:0%
+and it could especially if it's hitting
+hitting the wing but in general what
+
+ align:start position:0%
+hitting the wing but in general what
+ 
+
+ align:start position:0%
+hitting the wing but in general what
+we've seen is that you know and it can
+
+ align:start position:0%
+we've seen is that you know and it can
+ 
+
+ align:start position:0%
+we've seen is that you know and it can
+depend on whether you're in a high wing
+
+ align:start position:0%
+depend on whether you're in a high wing
+ 
+
+ align:start position:0%
+depend on whether you're in a high wing
+or low wing but the the biggest thing
+
+ align:start position:0%
+or low wing but the the biggest thing
+ 
+
+ align:start position:0%
+or low wing but the the biggest thing
+that it sort of hits is here now in
+
+ align:start position:0%
+that it sort of hits is here now in
+ 
+
+ align:start position:0%
+that it sort of hits is here now in
+general when you get a left yaw you you
+
+ align:start position:0%
+general when you get a left yaw you you
+ 
+
+ align:start position:0%
+general when you get a left yaw you you
+sort of kind of roll these are these are
+
+ align:start position:0%
+sort of kind of roll these are these are
+ 
+
+ align:start position:0%
+sort of kind of roll these are these are
+connected angles but I think just what
+
+ align:start position:0%
+connected angles but I think just what
+ 
+
+ align:start position:0%
+connected angles but I think just what
+we've observed is primarily that the air
+
+ align:start position:0%
+we've observed is primarily that the air
+ 
+
+ align:start position:0%
+we've observed is primarily that the air
+when it hits the vertical stabilizer is
+
+ align:start position:0%
+when it hits the vertical stabilizer is
+ 
+
+ align:start position:0%
+when it hits the vertical stabilizer is
+the biggest surface that's kind of
+
+ align:start position:0%
+the biggest surface that's kind of
+ 
+
+ align:start position:0%
+the biggest surface that's kind of
+pushing it and the angle that it's at so
+
+ align:start position:0%
+pushing it and the angle that it's at so
+ 
+
+ align:start position:0%
+pushing it and the angle that it's at so
+if you sum it all together yes I'm
+
+ align:start position:0%
+if you sum it all together yes I'm
+ 
+
+ align:start position:0%
+if you sum it all together yes I'm
+actually quite confident you'll get some
+
+ align:start position:0%
+actually quite confident you'll get some
+ 
+
+ align:start position:0%
+actually quite confident you'll get some
+roll but the biggest thing that you
+
+ align:start position:0%
+roll but the biggest thing that you
+ 
+
+ align:start position:0%
+roll but the biggest thing that you
+notice is the yaw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's see if we we understood P
+
+ align:start position:0%
+okay so let's see if we we understood P
+ 
+
+ align:start position:0%
+okay so let's see if we we understood P
+factor as well as we think we did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a B or C eh all right good job I
+
+ align:start position:0%
+okay a B or C eh all right good job I
+ 
+
+ align:start position:0%
+okay a B or C eh all right good job I
+actually have my little hint there that
+
+ align:start position:0%
+actually have my little hint there that
+ 
+
+ align:start position:0%
+actually have my little hint there that
+the B is actually talking about torque
+
+ align:start position:0%
+the B is actually talking about torque
+ 
+
+ align:start position:0%
+the B is actually talking about torque
+which is a different left turning
+
+ align:start position:0%
+which is a different left turning
+ 
+
+ align:start position:0%
+which is a different left turning
+tendency and then finally we're going to
+
+ align:start position:0%
+tendency and then finally we're going to
+ 
+
+ align:start position:0%
+tendency and then finally we're going to
+talk a little bit about gyroscopic
+
+ align:start position:0%
+talk a little bit about gyroscopic
+ 
+
+ align:start position:0%
+talk a little bit about gyroscopic
+precession is a little bit complicated
+
+ align:start position:0%
+precession is a little bit complicated
+ 
+
+ align:start position:0%
+precession is a little bit complicated
+if you're not familiar with the
+
+ align:start position:0%
+if you're not familiar with the
+ 
+
+ align:start position:0%
+if you're not familiar with the
+gyroscope but when Phillip talks to you
+
+ align:start position:0%
+gyroscope but when Phillip talks to you
+ 
+
+ align:start position:0%
+gyroscope but when Phillip talks to you
+about all the different controls in your
+
+ align:start position:0%
+about all the different controls in your
+ 
+
+ align:start position:0%
+about all the different controls in your
+airplane you'll have to learn about
+
+ align:start position:0%
+airplane you'll have to learn about
+ 
+
+ align:start position:0%
+airplane you'll have to learn about
+driver scopes all over again and a
+
+ align:start position:0%
+driver scopes all over again and a
+ 
+
+ align:start position:0%
+driver scopes all over again and a
+little bit but in general what do you
+
+ align:start position:0%
+little bit but in general what do you
+ 
+
+ align:start position:0%
+little bit but in general what do you
+need to know about a gyroscope you know
+
+ align:start position:0%
+need to know about a gyroscope you know
+ 
+
+ align:start position:0%
+need to know about a gyroscope you know
+what is a gyroscope gyroscope is
+
+ align:start position:0%
+what is a gyroscope gyroscope is
+ 
+
+ align:start position:0%
+what is a gyroscope gyroscope is
+something you can hold it's spinning you
+
+ align:start position:0%
+something you can hold it's spinning you
+ 
+
+ align:start position:0%
+something you can hold it's spinning you
+can you can play with them what they
+
+ align:start position:0%
+can you can play with them what they
+ 
+
+ align:start position:0%
+can you can play with them what they
+allow you to do is have rigidity and
+
+ align:start position:0%
+allow you to do is have rigidity and
+ 
+
+ align:start position:0%
+allow you to do is have rigidity and
+space and they also have this concept of
+
+ align:start position:0%
+space and they also have this concept of
+ 
+
+ align:start position:0%
+space and they also have this concept of
+precession and precession is basically
+
+ align:start position:0%
+precession and precession is basically
+ 
+
+ align:start position:0%
+precession and precession is basically
+that the the resultant action of a
+
+ align:start position:0%
+that the the resultant action of a
+ 
+
+ align:start position:0%
+that the the resultant action of a
+spinning rotor when a deflecting force
+
+ align:start position:0%
+spinning rotor when a deflecting force
+ 
+
+ align:start position:0%
+spinning rotor when a deflecting force
+is applied happens 90 degrees ahead of
+
+ align:start position:0%
+is applied happens 90 degrees ahead of
+ 
+
+ align:start position:0%
+is applied happens 90 degrees ahead of
+that rotation and so because of that you
+
+ align:start position:0%
+that rotation and so because of that you
+ 
+
+ align:start position:0%
+that rotation and so because of that you
+can consider that the you have the the
+
+ align:start position:0%
+can consider that the you have the the
+ 
+
+ align:start position:0%
+can consider that the you have the the
+propeller spinning and that causes this
+
+ align:start position:0%
+propeller spinning and that causes this
+ 
+
+ align:start position:0%
+propeller spinning and that causes this
+driver scopic precession and that
+
+ align:start position:0%
+driver scopic precession and that
+ 
+
+ align:start position:0%
+driver scopic precession and that
+basically causes 90 degrees out of out
+
+ align:start position:0%
+basically causes 90 degrees out of out
+ 
+
+ align:start position:0%
+basically causes 90 degrees out of out
+of that sink is this force which causes
+
+ align:start position:0%
+of that sink is this force which causes
+ 
+
+ align:start position:0%
+of that sink is this force which causes
+kind of a young movement of pitching and
+
+ align:start position:0%
+kind of a young movement of pitching and
+ 
+
+ align:start position:0%
+kind of a young movement of pitching and
+a young in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once we talk more about gyroscopes and
+
+ align:start position:0%
+once we talk more about gyroscopes and
+ 
+
+ align:start position:0%
+once we talk more about gyroscopes and
+how they work you'll also learn
+
+ align:start position:0%
+how they work you'll also learn
+ 
+
+ align:start position:0%
+how they work you'll also learn
+different flight controls that you look
+
+ align:start position:0%
+different flight controls that you look
+ 
+
+ align:start position:0%
+different flight controls that you look
+at in the plane leverage leverage these
+
+ align:start position:0%
+at in the plane leverage leverage these
+ 
+
+ align:start position:0%
+at in the plane leverage leverage these
+gyroscopes and we'll come back and
+
+ align:start position:0%
+gyroscopes and we'll come back and
+ 
+
+ align:start position:0%
+gyroscopes and we'll come back and
+circle back to making sure we understand
+
+ align:start position:0%
+circle back to making sure we understand
+ 
+
+ align:start position:0%
+circle back to making sure we understand
+the key fundamentals of gyroscopes yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure so let's go back to P factor so
+
+ align:start position:0%
+sure so let's go back to P factor so
+ 
+
+ align:start position:0%
+sure so let's go back to P factor so
+what we're talking about is the
+
+ align:start position:0%
+what we're talking about is the
+ 
+
+ align:start position:0%
+what we're talking about is the
+difference in the center of thrust so
+
+ align:start position:0%
+difference in the center of thrust so
+ 
+
+ align:start position:0%
+difference in the center of thrust so
+the thrust you know when you're when
+
+ align:start position:0%
+the thrust you know when you're when
+ 
+
+ align:start position:0%
+the thrust you know when you're when
+you're straight and level the thrust is
+
+ align:start position:0%
+you're straight and level the thrust is
+ 
+
+ align:start position:0%
+you're straight and level the thrust is
+just forward but what we're seeing is
+
+ align:start position:0%
+just forward but what we're seeing is
+ 
+
+ align:start position:0%
+just forward but what we're seeing is
+that when the the right blade because
+
+ align:start position:0%
+that when the the right blade because
+ 
+
+ align:start position:0%
+that when the the right blade because
+when you're in a high angle of attack
+
+ align:start position:0%
+when you're in a high angle of attack
+ 
+
+ align:start position:0%
+when you're in a high angle of attack
+the right blade is generating more
+
+ align:start position:0%
+the right blade is generating more
+ 
+
+ align:start position:0%
+the right blade is generating more
+thrust than the left blade so the center
+
+ align:start position:0%
+thrust than the left blade so the center
+ 
+
+ align:start position:0%
+thrust than the left blade so the center
+of thrust is slightly to the right so
+
+ align:start position:0%
+of thrust is slightly to the right so
+ 
+
+ align:start position:0%
+of thrust is slightly to the right so
+that is why because it's to the right
+
+ align:start position:0%
+that is why because it's to the right
+ 
+
+ align:start position:0%
+that is why because it's to the right
+and not up or down up or down would
+
+ align:start position:0%
+and not up or down up or down would
+ 
+
+ align:start position:0%
+and not up or down up or down would
+cause a pitch up or down but since it's
+
+ align:start position:0%
+cause a pitch up or down but since it's
+ 
+
+ align:start position:0%
+cause a pitch up or down but since it's
+to the to the right that's why it's
+
+ align:start position:0%
+to the to the right that's why it's
+ 
+
+ align:start position:0%
+to the to the right that's why it's
+causing the yaw action so precession is
+
+ align:start position:0%
+causing the yaw action so precession is
+ 
+
+ align:start position:0%
+causing the yaw action so precession is
+separate it is generating its own
+
+ align:start position:0%
+separate it is generating its own
+ 
+
+ align:start position:0%
+separate it is generating its own
+factors and dynamics so both of these
+
+ align:start position:0%
+factors and dynamics so both of these
+ 
+
+ align:start position:0%
+factors and dynamics so both of these
+things are acting at the same time so
+
+ align:start position:0%
+things are acting at the same time so
+ 
+
+ align:start position:0%
+things are acting at the same time so
+precession does in fact affect pitch
+
+ align:start position:0%
+precession does in fact affect pitch
+ 
+
+ align:start position:0%
+precession does in fact affect pitch
+just like you correctly recognized but
+
+ align:start position:0%
+just like you correctly recognized but
+ 
+
+ align:start position:0%
+just like you correctly recognized but
+this is an additional factor that's
+
+ align:start position:0%
+this is an additional factor that's
+ 
+
+ align:start position:0%
+this is an additional factor that's
+happening is that since the center of
+
+ align:start position:0%
+happening is that since the center of
+ 
+
+ align:start position:0%
+happening is that since the center of
+thrust is actually moved to the right
+
+ align:start position:0%
+thrust is actually moved to the right
+ 
+
+ align:start position:0%
+thrust is actually moved to the right
+it's causing the young did that answer
+
+ align:start position:0%
+it's causing the young did that answer
+ 
+
+ align:start position:0%
+it's causing the young did that answer
+your question
+
+ align:start position:0%
+your question
+ 
+
+ align:start position:0%
+your question
+No
+
+ align:start position:0%
+No
+ 
+
+ align:start position:0%
+No
+do you want to chime in Phyllis it's an
+
+ align:start position:0%
+do you want to chime in Phyllis it's an
+ 
+
+ align:start position:0%
+do you want to chime in Phyllis it's an
+external force as opposed to generated
+
+ align:start position:0%
+external force as opposed to generated
+ 
+
+ align:start position:0%
+external force as opposed to generated
+by the propeller it's a it's a little
+
+ align:start position:0%
+by the propeller it's a it's a little
+ 
+
+ align:start position:0%
+by the propeller it's a it's a little
+bit it's a little bit tough I think yeah
+
+ align:start position:0%
+bit it's a little bit tough I think yeah
+ 
+
+ align:start position:0%
+bit it's a little bit tough I think yeah
+we should table it and and refer you to
+
+ align:start position:0%
+we should table it and and refer you to
+ 
+
+ align:start position:0%
+we should table it and and refer you to
+that physics book see how it flies which
+
+ align:start position:0%
+that physics book see how it flies which
+ 
+
+ align:start position:0%
+that physics book see how it flies which
+has some of it but the one thing I would
+
+ align:start position:0%
+has some of it but the one thing I would
+ 
+
+ align:start position:0%
+has some of it but the one thing I would
+add on P factor is another thing to keep
+
+ align:start position:0%
+add on P factor is another thing to keep
+ 
+
+ align:start position:0%
+add on P factor is another thing to keep
+in mind is whether the propeller is
+
+ align:start position:0%
+in mind is whether the propeller is
+ 
+
+ align:start position:0%
+in mind is whether the propeller is
+advancing or retreating into the wind
+
+ align:start position:0%
+advancing or retreating into the wind
+ 
+
+ align:start position:0%
+advancing or retreating into the wind
+so if you think about it when the
+
+ align:start position:0%
+so if you think about it when the
+ 
+
+ align:start position:0%
+so if you think about it when the
+airplane is level the propeller is not
+
+ align:start position:0%
+airplane is level the propeller is not
+ 
+
+ align:start position:0%
+airplane is level the propeller is not
+moving relative to the the oncoming wind
+
+ align:start position:0%
+moving relative to the the oncoming wind
+ 
+
+ align:start position:0%
+moving relative to the the oncoming wind
+but if you tilt the airplane up as the
+
+ align:start position:0%
+but if you tilt the airplane up as the
+ 
+
+ align:start position:0%
+but if you tilt the airplane up as the
+propeller goes down it's actually
+
+ align:start position:0%
+propeller goes down it's actually
+ 
+
+ align:start position:0%
+propeller goes down it's actually
+advancing into the wind and getting a
+
+ align:start position:0%
+advancing into the wind and getting a
+ 
+
+ align:start position:0%
+advancing into the wind and getting a
+little bit of an efficiency boost that
+
+ align:start position:0%
+little bit of an efficiency boost that
+ 
+
+ align:start position:0%
+little bit of an efficiency boost that
+way whereas when it's coming up it's
+
+ align:start position:0%
+way whereas when it's coming up it's
+ 
+
+ align:start position:0%
+way whereas when it's coming up it's
+going from the front of the airplane
+
+ align:start position:0%
+going from the front of the airplane
+ 
+
+ align:start position:0%
+going from the front of the airplane
+towards the back of the airplane so it's
+
+ align:start position:0%
+towards the back of the airplane so it's
+ 
+
+ align:start position:0%
+towards the back of the airplane so it's
+retreating yeah so what Philips
+
+ align:start position:0%
+retreating yeah so what Philips
+ 
+
+ align:start position:0%
+retreating yeah so what Philips
+describing is why the why the right
+
+ align:start position:0%
+describing is why the why the right
+ 
+
+ align:start position:0%
+describing is why the why the right
+propeller blade is generating more
+
+ align:start position:0%
+propeller blade is generating more
+ 
+
+ align:start position:0%
+propeller blade is generating more
+thrust in the left propeller blade which
+
+ align:start position:0%
+thrust in the left propeller blade which
+ 
+
+ align:start position:0%
+thrust in the left propeller blade which
+is what's moving the center of thrust so
+
+ align:start position:0%
+is what's moving the center of thrust so
+ 
+
+ align:start position:0%
+is what's moving the center of thrust so
+I think the think the real thing to
+
+ align:start position:0%
+I think the think the real thing to
+ 
+
+ align:start position:0%
+I think the think the real thing to
+answer your question is that there's
+
+ align:start position:0%
+answer your question is that there's
+ 
+
+ align:start position:0%
+answer your question is that there's
+more than one effect happening
+
+ align:start position:0%
+more than one effect happening
+ 
+
+ align:start position:0%
+more than one effect happening
+simultaneously yeah
+
+ align:start position:0%
+simultaneously yeah
+ 
+
+ align:start position:0%
+simultaneously yeah
+I'm not sure that you get gyroscopic
+
+ align:start position:0%
+I'm not sure that you get gyroscopic
+ 
+
+ align:start position:0%
+I'm not sure that you get gyroscopic
+precession from that action here because
+
+ align:start position:0%
+precession from that action here because
+ 
+
+ align:start position:0%
+precession from that action here because
+it's generating the lift by pushing air
+
+ align:start position:0%
+it's generating the lift by pushing air
+ 
+
+ align:start position:0%
+it's generating the lift by pushing air
+I'm not sure that all the thrust really
+
+ align:start position:0%
+I'm not sure that all the thrust really
+ 
+
+ align:start position:0%
+I'm not sure that all the thrust really
+has to go through for P factor at least
+
+ align:start position:0%
+has to go through for P factor at least
+ 
+
+ align:start position:0%
+has to go through for P factor at least
+through the center of the spinning
+
+ align:start position:0%
+through the center of the spinning
+ 
+
+ align:start position:0%
+through the center of the spinning
+propeller also I know in helicopters in
+
+ align:start position:0%
+propeller also I know in helicopters in
+ 
+
+ align:start position:0%
+propeller also I know in helicopters in
+you know the like physics 101 answer is
+
+ align:start position:0%
+you know the like physics 101 answer is
+ 
+
+ align:start position:0%
+you know the like physics 101 answer is
+90 degrees but the real answer for
+
+ align:start position:0%
+90 degrees but the real answer for
+ 
+
+ align:start position:0%
+90 degrees but the real answer for
+engineering it is 72 degrees so it does
+
+ align:start position:0%
+engineering it is 72 degrees so it does
+ 
+
+ align:start position:0%
+engineering it is 72 degrees so it does
+get complicated fortunately it's beyond
+
+ align:start position:0%
+get complicated fortunately it's beyond
+ 
+
+ align:start position:0%
+get complicated fortunately it's beyond
+the scope of what the FAA tests you on
+
+ align:start position:0%
+the scope of what the FAA tests you on
+ 
+
+ align:start position:0%
+the scope of what the FAA tests you on
+because they themselves I'm sure don't
+
+ align:start position:0%
+because they themselves I'm sure don't
+ 
+
+ align:start position:0%
+because they themselves I'm sure don't
+understand it fully yeah how about we
+
+ align:start position:0%
+understand it fully yeah how about we
+ 
+
+ align:start position:0%
+understand it fully yeah how about we
+come back after we've talked about
+
+ align:start position:0%
+come back after we've talked about
+ 
+
+ align:start position:0%
+come back after we've talked about
+gyroscopes in excruciating detail and
+
+ align:start position:0%
+gyroscopes in excruciating detail and
+ 
+
+ align:start position:0%
+gyroscopes in excruciating detail and
+then we have a set of terminology to
+
+ align:start position:0%
+then we have a set of terminology to
+ 
+
+ align:start position:0%
+then we have a set of terminology to
+talk about let's come back to discussing
+
+ align:start position:0%
+talk about let's come back to discussing
+ 
+
+ align:start position:0%
+talk about let's come back to discussing
+that more things
+
+ align:start position:0%
+that more things
+ 
+
+ align:start position:0%
+that more things
+yes just remember I hope she's happy
+
+ align:start position:0%
+yes just remember I hope she's happy
+ 
+
+ align:start position:0%
+yes just remember I hope she's happy
+power or propeller so the the P is
+
+ align:start position:0%
+power or propeller so the the P is
+ 
+
+ align:start position:0%
+power or propeller so the the P is
+referring to that propeller want right
+
+ align:start position:0%
+referring to that propeller want right
+ 
+
+ align:start position:0%
+referring to that propeller want right
+propeller more than the left it also
+
+ align:start position:0%
+propeller more than the left it also
+ 
+
+ align:start position:0%
+propeller more than the left it also
+usually happens when you're at a higher
+
+ align:start position:0%
+usually happens when you're at a higher
+ 
+
+ align:start position:0%
+usually happens when you're at a higher
+power so some some flight instructors
+
+ align:start position:0%
+power so some some flight instructors
+ 
+
+ align:start position:0%
+power so some some flight instructors
+like you to think about when you have
+
+ align:start position:0%
+like you to think about when you have
+ 
+
+ align:start position:0%
+like you to think about when you have
+higher power and the airplane you'll
+
+ align:start position:0%
+higher power and the airplane you'll
+ 
+
+ align:start position:0%
+higher power and the airplane you'll
+need to put on more right rudder to
+
+ align:start position:0%
+need to put on more right rudder to
+ 
+
+ align:start position:0%
+need to put on more right rudder to
+counteract that left-turning tendencies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I actually almost done so I think we can
+
+ align:start position:0%
+I actually almost done so I think we can
+ 
+
+ align:start position:0%
+I actually almost done so I think we can
+finish there so so one thing is to type
+
+ align:start position:0%
+finish there so so one thing is to type
+ 
+
+ align:start position:0%
+finish there so so one thing is to type
+it so we talked about with climbing
+
+ align:start position:0%
+it so we talked about with climbing
+ 
+
+ align:start position:0%
+it so we talked about with climbing
+flight you know F equals MA so once
+
+ align:start position:0%
+flight you know F equals MA so once
+ 
+
+ align:start position:0%
+flight you know F equals MA so once
+you're done changing the velocity and
+
+ align:start position:0%
+you're done changing the velocity and
+ 
+
+ align:start position:0%
+you're done changing the velocity and
+you don't have a change in velocity your
+
+ align:start position:0%
+you don't have a change in velocity your
+ 
+
+ align:start position:0%
+you don't have a change in velocity your
+forces are in equilibrium so the same
+
+ align:start position:0%
+forces are in equilibrium so the same
+ 
+
+ align:start position:0%
+forces are in equilibrium so the same
+same is the case with with a descending
+
+ align:start position:0%
+same is the case with with a descending
+ 
+
+ align:start position:0%
+same is the case with with a descending
+flight when you're actually turning your
+
+ align:start position:0%
+flight when you're actually turning your
+ 
+
+ align:start position:0%
+flight when you're actually turning your
+forces are not in equilibrium because
+
+ align:start position:0%
+forces are not in equilibrium because
+ 
+
+ align:start position:0%
+forces are not in equilibrium because
+you're having this change in velocity
+
+ align:start position:0%
+you're having this change in velocity
+ 
+
+ align:start position:0%
+you're having this change in velocity
+and so the you actually have a number of
+
+ align:start position:0%
+and so the you actually have a number of
+ 
+
+ align:start position:0%
+and so the you actually have a number of
+changes happening and it's basically
+
+ align:start position:0%
+changes happening and it's basically
+ 
+
+ align:start position:0%
+changes happening and it's basically
+considered accelerated flight which the
+
+ align:start position:0%
+considered accelerated flight which the
+ 
+
+ align:start position:0%
+considered accelerated flight which the
+same as you know when you're driving if
+
+ align:start position:0%
+same as you know when you're driving if
+ 
+
+ align:start position:0%
+same as you know when you're driving if
+you if you're turning so when you're
+
+ align:start position:0%
+you if you're turning so when you're
+ 
+
+ align:start position:0%
+you if you're turning so when you're
+flying when you're doing a turn you're
+
+ align:start position:0%
+flying when you're doing a turn you're
+ 
+
+ align:start position:0%
+flying when you're doing a turn you're
+accelerating because you're constantly
+
+ align:start position:0%
+accelerating because you're constantly
+ 
+
+ align:start position:0%
+accelerating because you're constantly
+changing the direction of your velocity
+
+ align:start position:0%
+changing the direction of your velocity
+ 
+
+ align:start position:0%
+changing the direction of your velocity
+you also have load factor which we'll
+
+ align:start position:0%
+you also have load factor which we'll
+ 
+
+ align:start position:0%
+you also have load factor which we'll
+get into in more detail when we talk
+
+ align:start position:0%
+get into in more detail when we talk
+ 
+
+ align:start position:0%
+get into in more detail when we talk
+about performance of an aircraft and how
+
+ align:start position:0%
+about performance of an aircraft and how
+ 
+
+ align:start position:0%
+about performance of an aircraft and how
+the load affects your performance but
+
+ align:start position:0%
+the load affects your performance but
+ 
+
+ align:start position:0%
+the load affects your performance but
+another thing to think about back when
+
+ align:start position:0%
+another thing to think about back when
+ 
+
+ align:start position:0%
+another thing to think about back when
+we were talking about that zero gravity
+
+ align:start position:0%
+we were talking about that zero gravity
+ 
+
+ align:start position:0%
+we were talking about that zero gravity
+flight and a plane flying in a parabolic
+
+ align:start position:0%
+flight and a plane flying in a parabolic
+ 
+
+ align:start position:0%
+flight and a plane flying in a parabolic
+trajectory or a rollercoaster when
+
+ align:start position:0%
+trajectory or a rollercoaster when
+ 
+
+ align:start position:0%
+trajectory or a rollercoaster when
+you're at the top but when you're at the
+
+ align:start position:0%
+you're at the top but when you're at the
+ 
+
+ align:start position:0%
+you're at the top but when you're at the
+bottom of the rollercoaster you really
+
+ align:start position:0%
+bottom of the rollercoaster you really
+ 
+
+ align:start position:0%
+bottom of the rollercoaster you really
+feel like you're being pressed down into
+
+ align:start position:0%
+feel like you're being pressed down into
+ 
+
+ align:start position:0%
+feel like you're being pressed down into
+your seat in fact when you're we were on
+
+ align:start position:0%
+your seat in fact when you're we were on
+ 
+
+ align:start position:0%
+your seat in fact when you're we were on
+that zero gravity flight although at the
+
+ align:start position:0%
+that zero gravity flight although at the
+ 
+
+ align:start position:0%
+that zero gravity flight although at the
+top we had thirty seconds of
+
+ align:start position:0%
+top we had thirty seconds of
+ 
+
+ align:start position:0%
+top we had thirty seconds of
+weightlessness so we could do our
+
+ align:start position:0%
+weightlessness so we could do our
+ 
+
+ align:start position:0%
+weightlessness so we could do our
+experiments when you go to the bottom of
+
+ align:start position:0%
+experiments when you go to the bottom of
+ 
+
+ align:start position:0%
+experiments when you go to the bottom of
+the parabola you basically get two G or
+
+ align:start position:0%
+the parabola you basically get two G or
+ 
+
+ align:start position:0%
+the parabola you basically get two G or
+twice what you normally feel and so you
+
+ align:start position:0%
+twice what you normally feel and so you
+ 
+
+ align:start position:0%
+twice what you normally feel and so you
+have to kind of lay down and and let
+
+ align:start position:0%
+have to kind of lay down and and let
+ 
+
+ align:start position:0%
+have to kind of lay down and and let
+that happen before you come up again and
+
+ align:start position:0%
+that happen before you come up again and
+ 
+
+ align:start position:0%
+that happen before you come up again and
+so when you think about load factor just
+
+ align:start position:0%
+so when you think about load factor just
+ 
+
+ align:start position:0%
+so when you think about load factor just
+think about you being at the bottom of
+
+ align:start position:0%
+think about you being at the bottom of
+ 
+
+ align:start position:0%
+think about you being at the bottom of
+your roller coaster and really feeling
+
+ align:start position:0%
+your roller coaster and really feeling
+ 
+
+ align:start position:0%
+your roller coaster and really feeling
+kind of twice that
+
+ align:start position:0%
+kind of twice that
+ 
+
+ align:start position:0%
+kind of twice that
+force on you and then just to kind of
+
+ align:start position:0%
+force on you and then just to kind of
+ 
+
+ align:start position:0%
+force on you and then just to kind of
+end we want to talk about you know most
+
+ align:start position:0%
+end we want to talk about you know most
+ 
+
+ align:start position:0%
+end we want to talk about you know most
+of the time we're talking about the
+
+ align:start position:0%
+of the time we're talking about the
+ 
+
+ align:start position:0%
+of the time we're talking about the
+planes that you be flying but another
+
+ align:start position:0%
+planes that you be flying but another
+ 
+
+ align:start position:0%
+planes that you be flying but another
+type of aircraft all together is a
+
+ align:start position:0%
+type of aircraft all together is a
+ 
+
+ align:start position:0%
+type of aircraft all together is a
+blended wing body aircraft so just like
+
+ align:start position:0%
+blended wing body aircraft so just like
+ 
+
+ align:start position:0%
+blended wing body aircraft so just like
+this is one example of that so it's what
+
+ align:start position:0%
+this is one example of that so it's what
+ 
+
+ align:start position:0%
+this is one example of that so it's what
+it means is that that fuselage or that
+
+ align:start position:0%
+it means is that that fuselage or that
+ 
+
+ align:start position:0%
+it means is that that fuselage or that
+kind of tube in the middle that you sit
+
+ align:start position:0%
+kind of tube in the middle that you sit
+ 
+
+ align:start position:0%
+kind of tube in the middle that you sit
+in is blended into the wings so that the
+
+ align:start position:0%
+in is blended into the wings so that the
+ 
+
+ align:start position:0%
+in is blended into the wings so that the
+whole you know whole body is generating
+
+ align:start position:0%
+whole you know whole body is generating
+ 
+
+ align:start position:0%
+whole you know whole body is generating
+more lift because the whole surface is
+
+ align:start position:0%
+more lift because the whole surface is
+ 
+
+ align:start position:0%
+more lift because the whole surface is
+kind of designed that way it's really
+
+ align:start position:0%
+kind of designed that way it's really
+ 
+
+ align:start position:0%
+kind of designed that way it's really
+kind of cool
+
+ align:start position:0%
+kind of cool
+ 
+
+ align:start position:0%
+kind of cool
+and from an aerodynamic perspective it's
+
+ align:start position:0%
+and from an aerodynamic perspective it's
+ 
+
+ align:start position:0%
+and from an aerodynamic perspective it's
+it's got a much better lift-to-drag
+
+ align:start position:0%
+it's got a much better lift-to-drag
+ 
+
+ align:start position:0%
+it's got a much better lift-to-drag
+ratio because you know the whole thing
+
+ align:start position:0%
+ratio because you know the whole thing
+ 
+
+ align:start position:0%
+ratio because you know the whole thing
+is really deflecting that the air
+
+ align:start position:0%
+is really deflecting that the air
+ 
+
+ align:start position:0%
+is really deflecting that the air
+molecules downward and generating that
+
+ align:start position:0%
+molecules downward and generating that
+ 
+
+ align:start position:0%
+molecules downward and generating that
+lift so I just ask kind of a thought
+
+ align:start position:0%
+lift so I just ask kind of a thought
+ 
+
+ align:start position:0%
+lift so I just ask kind of a thought
+question if this is so much better it's
+
+ align:start position:0%
+question if this is so much better it's
+ 
+
+ align:start position:0%
+question if this is so much better it's
+more efficient of an aircraft and
+
+ align:start position:0%
+more efficient of an aircraft and
+ 
+
+ align:start position:0%
+more efficient of an aircraft and
+aerodynamically has much better
+
+ align:start position:0%
+aerodynamically has much better
+ 
+
+ align:start position:0%
+aerodynamically has much better
+properties why do you it actually we've
+
+ align:start position:0%
+properties why do you it actually we've
+ 
+
+ align:start position:0%
+properties why do you it actually we've
+also found that it's you know better in
+
+ align:start position:0%
+also found that it's you know better in
+ 
+
+ align:start position:0%
+also found that it's you know better in
+terms of fuel efficiency because it has
+
+ align:start position:0%
+terms of fuel efficiency because it has
+ 
+
+ align:start position:0%
+terms of fuel efficiency because it has
+less drag and more lift why do you think
+
+ align:start position:0%
+less drag and more lift why do you think
+ 
+
+ align:start position:0%
+less drag and more lift why do you think
+that you know JetBlue and American
+
+ align:start position:0%
+that you know JetBlue and American
+ 
+
+ align:start position:0%
+that you know JetBlue and American
+Airlines don't fly aircraft that look
+
+ align:start position:0%
+Airlines don't fly aircraft that look
+ 
+
+ align:start position:0%
+Airlines don't fly aircraft that look
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they don't have routes with a thousand
+
+ align:start position:0%
+they don't have routes with a thousand
+ 
+
+ align:start position:0%
+they don't have routes with a thousand
+passengers well you could make it you
+
+ align:start position:0%
+passengers well you could make it you
+ 
+
+ align:start position:0%
+passengers well you could make it you
+could make a smaller a blended wing body
+
+ align:start position:0%
+could make a smaller a blended wing body
+ 
+
+ align:start position:0%
+could make a smaller a blended wing body
+aircraft yes passengers like windows
+
+ align:start position:0%
+aircraft yes passengers like windows
+ 
+
+ align:start position:0%
+aircraft yes passengers like windows
+that's actually a big it's a big reason
+
+ align:start position:0%
+that's actually a big it's a big reason
+ 
+
+ align:start position:0%
+that's actually a big it's a big reason
+truthfully yes it's very different from
+
+ align:start position:0%
+truthfully yes it's very different from
+ 
+
+ align:start position:0%
+truthfully yes it's very different from
+what's currently made and they said so
+
+ align:start position:0%
+what's currently made and they said so
+ 
+
+ align:start position:0%
+what's currently made and they said so
+the development would be very risky
+
+ align:start position:0%
+the development would be very risky
+ 
+
+ align:start position:0%
+the development would be very risky
+actually I think it's more than just the
+
+ align:start position:0%
+actually I think it's more than just the
+ 
+
+ align:start position:0%
+actually I think it's more than just the
+development because it's different from
+
+ align:start position:0%
+development because it's different from
+ 
+
+ align:start position:0%
+development because it's different from
+what's currently made the entire
+
+ align:start position:0%
+what's currently made the entire
+ 
+
+ align:start position:0%
+what's currently made the entire
+infrastructure supports the current
+
+ align:start position:0%
+infrastructure supports the current
+ 
+
+ align:start position:0%
+infrastructure supports the current
+format of an airplane with a tube and
+
+ align:start position:0%
+format of an airplane with a tube and
+ 
+
+ align:start position:0%
+format of an airplane with a tube and
+wings so we're talking about airports
+
+ align:start position:0%
+wings so we're talking about airports
+ 
+
+ align:start position:0%
+wings so we're talking about airports
+jet bridges the way that people load
+
+ align:start position:0%
+jet bridges the way that people load
+ 
+
+ align:start position:0%
+jet bridges the way that people load
+food carts onto a plane the way that
+
+ align:start position:0%
+food carts onto a plane the way that
+ 
+
+ align:start position:0%
+food carts onto a plane the way that
+passengers get on and off the fact that
+
+ align:start position:0%
+passengers get on and off the fact that
+ 
+
+ align:start position:0%
+passengers get on and off the fact that
+passengers don't have as many windows on
+
+ align:start position:0%
+passengers don't have as many windows on
+ 
+
+ align:start position:0%
+passengers don't have as many windows on
+this type of aircraft it's unfortunately
+
+ align:start position:0%
+this type of aircraft it's unfortunately
+ 
+
+ align:start position:0%
+this type of aircraft it's unfortunately
+that whole infrastructure that surrounds
+
+ align:start position:0%
+that whole infrastructure that surrounds
+ 
+
+ align:start position:0%
+that whole infrastructure that surrounds
+it that is a big contributing factor to
+
+ align:start position:0%
+it that is a big contributing factor to
+ 
+
+ align:start position:0%
+it that is a big contributing factor to
+why even though there's a better design
+
+ align:start position:0%
+why even though there's a better design
+ 
+
+ align:start position:0%
+why even though there's a better design
+why we don't move towards that so this
+
+ align:start position:0%
+why we don't move towards that so this
+ 
+
+ align:start position:0%
+why we don't move towards that so this
+was a big big thing for me when I was an
+
+ align:start position:0%
+was a big big thing for me when I was an
+ 
+
+ align:start position:0%
+was a big big thing for me when I was an
+undergrad at MIT
+
+ align:start position:0%
+undergrad at MIT
+ 
+
+ align:start position:0%
+undergrad at MIT
+you know aero-astro I'm thinking I'm
+
+ align:start position:0%
+you know aero-astro I'm thinking I'm
+ 
+
+ align:start position:0%
+you know aero-astro I'm thinking I'm
+gonna design the next best amazing
+
+ align:start position:0%
+gonna design the next best amazing
+ 
+
+ align:start position:0%
+gonna design the next best amazing
+airplane but even if you do design the
+
+ align:start position:0%
+airplane but even if you do design the
+ 
+
+ align:start position:0%
+airplane but even if you do design the
+next best amazing airplane it may not be
+
+ align:start position:0%
+next best amazing airplane it may not be
+ 
+
+ align:start position:0%
+next best amazing airplane it may not be
+widely deployed because of these other
+
+ align:start position:0%
+widely deployed because of these other
+ 
+
+ align:start position:0%
+widely deployed because of these other
+infrastructure aspects which really got
+
+ align:start position:0%
+infrastructure aspects which really got
+ 
+
+ align:start position:0%
+infrastructure aspects which really got
+me into systems engineering but enough
+
+ align:start position:0%
+me into systems engineering but enough
+ 
+
+ align:start position:0%
+me into systems engineering but enough
+with that thought exercise for time
+
+ align:start position:0%
+with that thought exercise for time
+ 
+
+ align:start position:0%
+with that thought exercise for time
+we'll just summarize you know what did
+
+ align:start position:0%
+we'll just summarize you know what did
+ 
+
+ align:start position:0%
+we'll just summarize you know what did
+we learn today so we talked about how
+
+ align:start position:0%
+we learn today so we talked about how
+ 
+
+ align:start position:0%
+we learn today so we talked about how
+does an airplane generate lift and we
+
+ align:start position:0%
+does an airplane generate lift and we
+ 
+
+ align:start position:0%
+does an airplane generate lift and we
+talked about different factors that
+
+ align:start position:0%
+talked about different factors that
+ 
+
+ align:start position:0%
+talked about different factors that
+affect lift we also discussed the lift
+
+ align:start position:0%
+affect lift we also discussed the lift
+ 
+
+ align:start position:0%
+affect lift we also discussed the lift
+is very hard to calculate and so we
+
+ align:start position:0%
+is very hard to calculate and so we
+ 
+
+ align:start position:0%
+is very hard to calculate and so we
+experimentally measure a lot of aspects
+
+ align:start position:0%
+experimentally measure a lot of aspects
+ 
+
+ align:start position:0%
+experimentally measure a lot of aspects
+of it and we discuss the different
+
+ align:start position:0%
+of it and we discuss the different
+ 
+
+ align:start position:0%
+of it and we discuss the different
+forces on an airplane stability and kind
+
+ align:start position:0%
+forces on an airplane stability and kind
+ 
+
+ align:start position:0%
+forces on an airplane stability and kind
+of this left-turning tendencies and some
+
+ align:start position:0%
+of this left-turning tendencies and some
+ 
+
+ align:start position:0%
+of this left-turning tendencies and some
+of the different aircraft configurations
+
+ align:start position:0%
+of the different aircraft configurations
+ 
+
+ align:start position:0%
+of the different aircraft configurations
+so are there any questions about that
+
+ align:start position:0%
+so are there any questions about that
+ 
+
+ align:start position:0%
+so are there any questions about that
+yeah okay what do you think about what's
+
+ align:start position:0%
+yeah okay what do you think about what's
+ 
+
+ align:start position:0%
+yeah okay what do you think about what's
+two questions let's take the bathroom
+
+ align:start position:0%
+two questions let's take the bathroom
+ 
+
+ align:start position:0%
+two questions let's take the bathroom
+break and then yes you think about I'm
+
+ align:start position:0%
+break and then yes you think about I'm
+ 
+
+ align:start position:0%
+break and then yes you think about I'm
+gonna call the pizza people and give
+
+ align:start position:0%
+gonna call the pizza people and give
+ 
+
+ align:start position:0%
+gonna call the pizza people and give
+them my credit card
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/erHp3r6PbJk.txt b/erHp3r6PbJk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d92fc633ddf343780268a8184a4b0fc95736bcd
--- /dev/null
+++ b/erHp3r6PbJk.txt
@@ -0,0 +1,2512 @@
+PROFESSOR: Well, yesterday
+was easy.
+
+You learned all of the rules
+of programming and lived.
+
+Almost all of them.
+
+And so at this point, you're
+now certified programmers--
+
+it says.
+
+However, I suppose what we did
+is we, aah, sort of got you a
+
+little bit of into
+an easy state.
+
+Here, you still believe it's
+possible that this might be
+
+programming in BASIC or Pascal
+with just a funny syntax.
+
+Today, that illusion--
+
+or you can no longer support
+that belief.
+
+What we're going to do
+today is going to
+
+completely smash that.
+
+So let's start out by writing
+a few programs on the
+
+blackboard that have a lot in
+common with each other.
+
+What we're going to do is try to
+make them abstractions that
+
+are not ones that are easy to
+make in most languages.
+
+Let's start with some very
+simple ones that you can make
+
+in most languages.
+
+Supposing I want to write the
+mathematical expression which
+
+adds up a bunch of integers.
+
+So if I wanted to write down
+and say the sum from i
+
+equal a to b on i.
+
+Now, you know that that's an
+easy thing to compute in a
+
+closed form for it, and I'm
+not interested in that.
+
+But I'm going to write
+a program that
+
+adds up those integers.
+
+Well, that's rather easy to do
+to say I want to define the
+
+sum of the integers from
+a to b to be--
+
+well, it's the following
+two possibilities.
+
+If a is greater than b, well,
+then there's nothing to be
+
+done and the answer is zero.
+
+This is how you're going to
+have to think recursively.
+
+You're going to say if I have
+an easy case that I know the
+
+answer to, just write it down.
+
+Otherwise, I'm going to try to
+reduce this problem to a
+
+simpler problem.
+
+And maybe in this case, I'm
+going to make a subproblem of
+
+the simpler problem and then
+do something to the result.
+
+So the easiest way to do this
+is say that I'm going to add
+
+the index, which in this case is
+a, to the result of adding
+
+up the integers from
+a plus 1 to b.
+
+Now, at this point, you should
+have no trouble looking at
+
+such a definition.
+
+Indeed, coming up with such a
+thing might be a little hard
+
+in synthesis, but being able
+to read it at this point
+
+should be easy.
+
+And what it says to you is,
+well, here is the subproblem
+
+I'm going to solve.
+
+I'm going to try to add up the
+integers, one fewer integer
+
+than I added up for the
+the whole problem.
+
+I'm adding up the one fewer one,
+and that subproblem, once
+
+I've solved it, I'm going to add
+a to that, and that will
+
+be the answer to this problem.
+
+And the simplest case, I don't
+have to do any work.
+
+Now, I'm also going to write
+down another simple one just
+
+like this, which is the
+mathematical expression, the
+
+sum of the square from
+i equal a to b.
+
+And again, it's a very
+simple program.
+
+And indeed, it starts
+the same way.
+
+If a is greater than b, then
+the answer is zero.
+
+And, of course, we're beginning
+to see that there's
+
+something wrong with me writing
+this down again.
+
+It's the same program.
+
+It's the sum of the square of a
+and the sum of the square of
+
+the increment and b.
+
+Now, if you look at these
+things, these programs are
+
+almost identical.
+
+There's not much to
+distinguish them.
+
+They have the same first clause
+of the conditional and
+
+the same predicate and the
+same consequence, and the
+
+alternatives are very
+similar, too.
+
+They only differ by the fact
+that where here I have a,
+
+here, I have the square of a.
+
+The only other difference, but
+this one's sort of unessential
+
+is in the name of this procedure
+is sum int, whereas
+
+the name of the procedure
+is sum square.
+
+So the things that vary
+between these
+
+two are very small.
+
+Now, wherever you see yourself
+writing the same thing down
+
+more than once, there's
+something wrong, and you
+
+shouldn't be doing it.
+
+And the reason is not because
+it's a waste of time to write
+
+something down more than once.
+
+It's because there's some idea
+here, a very simple idea,
+
+which has to do with the
+sigma notation--
+
+this much--
+
+not depending upon what
+it is I'm adding up.
+
+And I would like
+to be able to--
+
+always, whenever trying to make
+complicated systems and
+
+understand them, it's crucial
+to divide the things up into
+
+as many pieces as I can, each
+of which I understand
+
+separately.
+
+I would like to understand the
+way of adding things up
+
+independently of what it is I'm
+adding up so I can do that
+
+having debugged it once and
+understood it once and having
+
+been able to share that among
+many different uses of it.
+
+Here, we have another example.
+
+This is Leibnitz's formula
+for finding pi over 8.
+
+It's a funny, ugly mess.
+
+What is it?
+
+It's something like 1 over 1
+times 3 plus 1 over 5 times 7
+
+plus 1 over 9 times 11 plus--
+
+and for some reason, things
+like this tend to have
+
+interesting values
+like pi over 8.
+
+But what do we see here?
+
+It's the same program or almost
+the same program.
+
+It's a sum.
+
+So we're seeing the figure
+notation, although over here,
+
+we're dealing with incrementing
+by 4, so it's a
+
+slightly different problem,
+which means that over here, I
+
+have to change a by 4, as
+you see right over here.
+
+It's not by 1.
+
+The other thing, of course,
+is that the thing that's
+
+represented by square in the
+previous sum of squares, or a
+
+when adding up the integers.
+
+Well, here, I have a different
+thing I'm adding up, a
+
+different term, which is 1
+over a times a plus 2.
+
+But the rest of this program
+is identical.
+
+Well, any time we have a bunch
+of things like this that are
+
+identical, we're going to have
+to come up with some sort of
+
+abstraction to cover them.
+
+If you think about this, what
+you've learned so far is the
+
+rules of some language, some
+primitive, some means of
+
+combination, almost all
+of them, the means of
+
+abstraction, almost
+all of them.
+
+But what you haven't learned is
+common patterns of usage.
+
+Now, most of the time, you learn
+idioms when learning a
+
+language, which is a common
+pattern that mean things that
+
+are useful to know in a flash.
+
+And if you build a great number
+of them, if you're a
+
+FORTRAN programmer, of course,
+everybody knows how to--
+
+what do you do, for example, to
+get an integer which is the
+
+biggest integer in something.
+
+It's a classic thing.
+
+Every FORTRAN programmer
+knows how to do that.
+
+And if you don't know that,
+you're in real hot water
+
+because it takes a long
+time to think it out.
+
+However, one of the things you
+can do in this language that
+
+we're showing you is not only
+do you know something like
+
+that, but you give the knowledge
+of that a name.
+
+And so that's what we're going
+to be going after right now.
+
+OK, well, let's see what these
+things have in common.
+
+Right over here we have what
+appears to be a general
+
+pattern, a general pattern which
+covers all of the cases
+
+we've seen so far.
+
+There is a sum procedure,
+which is being defined.
+
+It has two arguments, which
+are a lower bound
+
+and an upper bound.
+
+The lower bound is tested to
+be greater than the upper
+
+bound, and if it is greater,
+then the result is zero.
+
+Otherwise, we're going to do
+something to the lower bound,
+
+which is the index of the
+conversation, and add that
+
+result to the result of
+following the procedure
+
+recursively on our lower bound
+incremented by some next
+
+operation with the same upper
+bound as I had before.
+
+So this is a general pattern,
+and what I'd like to do is be
+
+able to name this general
+pattern a bit.
+
+Well, that's sort of easy,
+because one of the things I'm
+
+going to do right now is--
+there's nothing very special
+
+about numbers.
+
+Numbers are just one
+kind of data.
+
+It seems to me perfectly
+reasonable to give all sorts
+
+of names to all kinds of data,
+for example, procedures.
+
+And now many languages allow you
+have procedural arguments,
+
+and right now, we're
+going to talk
+
+about procedural arguments.
+
+They're very easy
+to deal with.
+
+And shortly, we'll do some
+remarkable things that are not
+
+like procedural arguments.
+
+So here, we'll define
+our sigma notation.
+
+This is called sum and it takes
+a term, an A, a next
+
+term, and B as arguments.
+
+So it takes four arguments,
+and there was nothing
+
+particularly special about me
+writing this in lowercase.
+
+I hope that it doesn't confuse
+you, so I'll write it in
+
+uppercase right now.
+
+The machine doesn't care.
+
+But these two arguments
+are different.
+
+These are not numbers.
+
+These are going to be procedures
+for computing
+
+something given a number.
+
+Term will be a procedure which,
+when given an index,
+
+will produce the value of
+the term for that index.
+
+Next will be given an
+index, which will
+
+produce the next index.
+
+This will be for counting.
+
+And it's very simple.
+
+It's exactly what you see.
+
+If A is greater than B,
+then the result is 0.
+
+Otherwise, it's the sum of term
+applied to A and the sum
+
+of term, next index.
+
+Let me write it this way.
+
+Now, I'd like you to see
+something, first of all.
+
+I was writing here, and
+I ran out of space.
+
+What I did is I start indenting
+according to the
+
+Pretty-printing rule, which says
+that I align all of the
+
+arguments of the procedure
+so I can see
+
+which ones go together.
+
+And this is just something I do
+automatically, and I want
+
+you to learn how to do that,
+too, so your programs can be
+
+read and understood.
+
+However, what do we have here?
+
+We have four arguments: the
+procedure, the lower index--
+
+lower bound index--
+
+the way to get the next index,
+and the upper bound.
+
+What's passed along on the
+recursive call is indeed the
+
+same procedure because I'm going
+to need it again, the
+
+next index, which is using the
+next procedure to compute it,
+
+the procedure for computing
+next, which I also have to
+
+have separately, and
+that's different.
+
+The procedure for computing
+next is different from the
+
+next index, which is the result
+of using next on the
+
+last index.
+
+And I also have to pass
+along the upper bound.
+
+So this captures both of these
+and the other nice program
+
+that we are playing with.
+
+So using this, we can write down
+the original program as
+
+instances of sum very simply.
+
+A and B. Well, I'm going to
+need an identity procedure
+
+here because ,ahh, the sum of
+the integers requires me to in
+
+this case compute a term for
+every integer, but the term
+
+procedure doesn't want to do
+anything to that integer.
+
+So the identity procedure on A
+is A or X or whatever, and I
+
+want to say the sum of using
+identity of the term procedure
+
+and using A as the initial
+index and the incrementer
+
+being the way to get the next
+index and B being the high
+
+bound, the upper bound.
+
+This procedure does exactly
+the same as the sum of the
+
+integers over here, computes
+the same answer.
+
+Now, one thing you should see,
+of course, is that there's
+
+nothing very special over here
+about what I used as the
+
+formal parameter.
+
+I could have, for example,
+written this
+
+X. It doesn't matter.
+
+I just wanted you to see that
+this name does not conflict
+
+with this one at all.
+
+It's an internal name.
+
+For the second procedure here,
+the sum of the squares, it's
+
+even a little bit easier.
+
+And what do we have to do?
+
+Nothing more than add up the
+squares, this is the procedure
+
+that each index will be given,
+will be given each--
+
+yes.
+
+Each index will have this done
+to it to get the term.
+
+That's the thing that maps
+against term over here.
+
+Then I have A as the lower
+bound, the incrementer as the
+
+next term method, and B
+as the upper bound.
+
+And finally, just for the thing
+that we did about pi
+
+sums, pi sums are sort of--
+
+well, it's even easier to think
+about them this way
+
+because I don't have to think.
+
+What I'm doing is separating the
+thing I'm adding up from
+
+the method of doing
+the addition.
+
+And so we have here, for
+example, pi sum A B
+
+of the sum of things.
+
+I'm going to write the terms
+procedure here explicitly
+
+without giving it a name.
+
+This is done anonymously.
+
+I don't necessarily have to give
+a name to something if I
+
+just want to use it once.
+
+And, of course, I can write
+sort of a expression that
+
+produces a procedure.
+
+I'm going to write the Greek
+lambda letter here instead of
+
+L-A-M-B-D-A in general to avoid
+taking up a lot of space
+
+on blackboards.
+
+But unfortunately,
+we don't have
+
+lambda keys on our keyboards.
+
+Maybe we can convince our
+friends in the computer
+
+industry that this
+is an important.
+
+Lambda of i is the quotient of 1
+and the product of i and the
+
+sum of i 2, starting at a with
+the way of incrementing being
+
+that procedure of an index i,
+which adds i to 4, and b being
+
+the upper bound.
+
+So you can see that this
+notation, the invention of the
+
+procedure that takes a
+procedural argument, allows us
+
+to compress a lot of these
+procedures into one thing.
+
+This procedure, sums, covers
+a whole bunch of ideas.
+
+Now, just why is
+this important?
+
+I tried to say before that it
+helps us divide a problem into
+
+two pieces, and indeed, it does,
+for example, if someone
+
+came up with a different way of
+implementing this, which,
+
+of course, one might.
+
+Here, for example, an iterative
+
+implementation of sum.
+
+Iterative implementation for
+some reason might be better
+
+than the recursive
+implementation.
+
+But the important thing is
+that it's different.
+
+Now, supposing I had written my
+program this way that you
+
+see on the blackboard
+on the left.
+
+That's correct, the left.
+
+Well, then if I want to change
+the method of addition, then
+
+I'd have to change
+each of these.
+
+Whereas if I write them like
+this that you see here, then
+
+the method by which I did the
+addition is encapsulated in
+
+the procedure sum.
+
+That decomposition allows me
+to independently change one
+
+part of the program and prove
+it perhaps without changing
+
+the other part that was
+written for some
+
+of the other cases.
+
+Thank you.
+
+Are there any questions?
+
+Yes, sir.
+
+AUDIENCE: Would you go over
+next A and next again on--
+
+PROFESSOR: Yes.
+
+It's the same problem.
+
+I'm sure you're going to--
+
+you're going to have
+to work on this.
+
+This is hard the first
+time you've ever seen
+
+something like this.
+
+What I have here is
+a-- procedures
+
+can be named by variables.
+
+Procedures are not special.
+
+Actually, sum square is a
+variable, which has gotten a
+
+value, which is a procedure.
+
+This is define sum square to be
+
+lambda of A and B something.
+
+So the procedure can be named.
+
+Therefore, they can be passed
+from one to another, one
+
+procedure to another,
+as arguments.
+
+Well, what we're doing here is
+we're passing the procedure
+
+term as an argument to sum just
+when we get it around in
+
+the next recursive.
+
+Here, we're passing
+the procedure next
+
+as an argument also.
+
+However, here we're using
+the procedure next.
+
+That's what the parentheses
+mean.
+
+We're applying next to A to get
+the next value of A. If
+
+you look at what next is mapped
+against, remember that
+
+the way you think about this
+is that you substitute the
+
+arguments for the formal
+parameters in the body.
+
+If you're ever confused, think
+of the thing that way.
+
+Well, over here, with
+sum of the integers.
+
+I substitute identity for
+a term and 1 plus the
+
+incrementer for next
+in the body.
+
+Well, the identity procedure
+on A is what I get here.
+
+Identity is being passed
+along, and here, I have
+
+increment 1 plus being applied
+to A and 1 plus is being
+
+passed along.
+
+Does that clarify
+the situation?
+
+AUDIENCE: We could also define
+explicitly those two
+
+functions, then pass them.
+
+PROFESSOR: Sure.
+
+What we can do is we could have
+given names to them, just
+
+like I did here.
+
+In fact, I gave you various
+ways so you
+
+could see it, a variety.
+
+Here, I define the thing which
+I passed the name of.
+
+I referenced it by its name.
+
+But the thing is, in fact, that
+procedure, one argument
+
+X, which is X. And the identity
+procedure is just
+
+lambda of X X. And that's
+what you're seeing here.
+
+Here, I happened to just write
+its canonical name there for
+
+you to see.
+
+Is it OK if we take our
+five-minute break?
+
+As I said, computers to make
+people happy, not people to
+
+make computers happy.
+
+And for the most part, the
+reason why we introduce all
+
+this abstraction stuff is to
+make it so that programs can
+
+be more easily written
+and more easily read.
+
+Let's try to understand what's
+the most complicated program
+
+we've seen so far using
+a little bit of
+
+this abstraction stuff.
+
+If you look at the slide, this
+is the Heron of Alexandria's
+
+method of computing square roots
+that we saw yesterday.
+
+And let's see.
+
+Well, in any case, this
+program is a little
+
+complicated.
+
+And at the current state of your
+thinking, you just can't
+
+look at that and say, oh,
+this obviously means
+
+something very clear.
+
+It's not obvious from
+looking at the
+
+program what it's computing.
+
+There's some loop here inside
+try, and a loop does something
+
+about trying the improvement
+of y.
+
+There's something called
+improve, which does some
+
+averaging and quotienting
+and things like that.
+
+But what's the real idea?
+
+Can we make it clear
+what the idea is?
+
+Well, I think we can.
+
+I think we can use abstraction
+that we have learned about so
+
+far to clarify what's
+going on.
+
+Now, what we have mathematically
+is a procedure
+
+for improving a guess
+for square roots.
+
+And if y is a guess for a square
+root, then what we want
+
+to get we'll call
+a function f.
+
+This is the means
+of improvement.
+
+I want to get y plus x/y over
+2, so the average of y and x
+
+divided by y as the improved
+value for the square root of x
+
+such that-- one thing you can
+notice about this function f
+
+is that f of the square root
+of f is in fact the
+
+square root of x.
+
+In other words, if I take
+the square root of x and
+
+substitute it for y here, I see
+the square root of x plus
+
+x divided by the square of x,
+which is the square root of x.
+
+That's 2 times the square root
+of x divided by 2, is the
+
+square root of x.
+
+So, in fact, what we're really
+looking for is we're looking
+
+for a fixed point, a fixed
+point of the function f.
+
+A fixed point is a place which
+has the property that if you
+
+put it into the function, you
+get the same value out.
+
+Now, I suppose if I were giving
+some nice, boring
+
+lecture, and you happened to
+have in front of you an HP-35
+
+desk calculator like I
+used to have when I
+
+went to boring lectures.
+
+And if you think it was really
+boring, you put it into
+
+radians mode, and you hit
+cosine, and you hit cosine,
+
+and you hit cosine.
+
+And eventually, you end
+up with 0.734 or
+
+something like that.
+
+0.743, I don't remember what
+exactly, and it gets closer
+
+and closer to that.
+
+Some functions have the property
+that you can find
+
+their fixed point by iterating
+the function, and that's
+
+essentially what's happening in
+the square root program by
+
+Heron's method.
+
+So let's see if we can write
+that down, that idea.
+
+Now, I'm not going to say how
+I compute fixed points yet.
+
+There might be more
+than one way.
+
+But the first thing to
+do is I'm going to
+
+say what I just said.
+
+I'm going to say it
+specifically, the square root.
+
+The square root of x is the
+fixed point of that procedure
+
+which takes an argument
+y and averages of x
+
+divided by y with y.
+
+And we're going to start up with
+the initial guess for the
+
+fixed point of 1.
+
+It doesn't matter
+where it starts.
+
+A theorem having to do
+with square roots.
+
+So what you're seeing here is
+I'm just trying to write out
+
+by wishful thinking.
+
+I don't know how I'm going to
+make fixed point happen.
+
+We'll worry about that later.
+
+But if somehow I had a way of
+finding the fixed point of the
+
+function computed by this
+procedure, then I would have--
+
+that would be the square root
+that I'm looking for.
+
+OK, well, now let's see how
+we're going to write--
+
+how we're going to come
+up with fixed points.
+
+Well, it's very simple,
+actually.
+
+I'm going to write an
+abbreviated version here just
+
+so we understand it.
+
+I'm going to find the fixed
+point of a function f--
+
+actually, the fixed point of the
+function computed by the
+
+procedure whose name will
+be f in this procedure.
+
+How's that?
+
+A long sentence--
+
+starting with a particular
+starting value.
+
+Well, I'm going to have a little
+loop inside here, which
+
+is going to push the button on
+the calculator repeatedly,
+
+hoping that it will eventually
+converge.
+
+And we will say here internal
+loops are written by defining
+
+internal procedures.
+
+Well, one thing I'm going to
+have to do is I'm going to
+
+have to say whether I'm done.
+
+And the way I'm going to decide
+when I'm done is when
+
+the old value and the new value
+are close enough so I
+
+can't distinguish
+them anymore.
+
+That's the standard thing you
+do on the calculator unless
+
+you look at more precision,
+and eventually,
+
+you run out of precision.
+
+So the old value and new value,
+and I'm going to stay
+
+here if I can't distinguish them
+if they're close enough,
+
+and we'll have to worry about
+what that is soon.
+
+The old value and the new value
+are close enough to each
+
+other and let's pick the new
+value as the answer.
+
+Otherwise, I'm going to iterate
+around again with the
+
+next value of old being the
+current value of new and the
+
+next value of new being the
+result of calling f on new.
+
+And so this is my iteration loop
+that pushes the button on
+
+the calculator.
+
+I basically think of it as
+having two registers on the
+
+calculator: old and new.
+
+And in each step, new becomes
+old, and new gets F of new.
+
+So this is the thing where I'm
+getting the next value.
+
+And now, I'm going to
+start this thing up
+
+by giving two values.
+
+I wrote down on the blackboard
+to be slow
+
+so you can see this.
+
+This is the first time you've
+seen something quite this
+
+complicated, I think.
+
+However, we might want to see
+the whole thing over here in
+
+this transparency or
+slide or whatever.
+
+What we have is all of the
+details that are required to
+
+make this thing work.
+
+I have a way of getting a
+tolerance for a close enough
+
+procedure, which we see here.
+
+The close enough procedure, it
+tests whether u and v are
+
+close enough by seeing if the
+absolute value of the
+
+difference in u and v is less
+than the given tolerance, OK?
+
+And here is the iteration loop
+that I just wrote on the
+
+blackboard and the
+initialization for it, which
+
+is right there.
+
+It's very simple.
+
+But let's see.
+
+I haven't told you enough.
+
+It's actually easier
+than this.
+
+There is more structure to
+this problem than I've
+
+already told you.
+
+Like why should this work?
+
+Why should it converge?
+
+There's a hairy theorem in
+mathematics tied up in what
+
+I've written here.
+
+Why is it that I should assume
+that by iterating averaging
+
+the quotient of x and y
+and y that I should
+
+get the right answer?
+
+It isn't so obvious.
+
+Surely there are other things,
+other procedures, which
+
+compute functions whose fixed
+points would also be the
+
+square root.
+
+For example, the obvious one
+will be a new function g,
+
+which maps y to x/y.
+
+That's even simpler.
+
+The fixed point of g is surely
+the square root also, and it's
+
+a simpler procedure.
+
+Why am I not using it?
+
+Well, I suppose you know.
+
+Supposing x is 2 and I start out
+with 1, and if I divide 1
+
+into 2, I get 2.
+
+And then if I divide
+2 into 2, I get 1.
+
+If I divide 1 into 2, I get 2,
+and 2 into 2, I get 1, and I
+
+never get any closer
+to the square root.
+
+It just oscillates.
+
+So what we have is a signal
+processing system, an
+
+electrical circuit which is
+oscillating, and I want to
+
+damp out these oscillations.
+
+Well, I can do that.
+
+See, what I'm really doing
+here when I'm taking my
+
+average, the average is
+averaging the last two values
+
+of something which oscillates,
+getting something in between.
+
+The classic way is damping out
+oscillations in a signal
+
+processing system.
+
+So why don't we write down the
+strategy that I just said in a
+
+more clear way?
+
+Well, that's easy enough.
+
+I'm going to define the square
+root of x to be a fixed point
+
+of the procedure resulting
+from average damping.
+
+So I have a procedure resulting
+from average damp of
+
+the procedure, that procedure
+of y, which divides x by y
+
+starting out at 1.
+
+Ah, but average damp is a
+special procedure that's going
+
+to take a procedure as its
+argument and return a
+
+procedure as its value.
+
+It's a generalization that says
+given a procedure, it's
+
+the thing which produces a
+procedure which averages the
+
+last value and the
+value before and
+
+after running the procedure.
+
+You can use it for anything
+if you want to damp out
+
+oscillations.
+
+So let's write that down.
+
+It's very easy.
+
+And stylistically here, I'm
+going to use lambda notation
+
+because it's much easier to
+think when you're dealing with
+
+procedure, the mid-line
+procedures, to understand that
+
+the procedures are the objects
+I'm dealing with, so I'm going
+
+to use lambda notation here.
+
+Not always.
+
+I don't always use it, but
+very specifically here to
+
+expand on that idea,
+to elucidate it.
+
+Well, average damp is a
+procedure, which takes a
+
+procedure as its argument,
+which we will call f.
+
+And what does it produce?
+
+It produces as its value--
+
+the body of this procedure is
+a thing which produces a
+
+procedure, the construct of the
+procedures right here, of
+
+one argument x, which averages
+f of x with x.
+
+This is a very special thing.
+
+I think for the first time
+you're seeing a procedure
+
+which produces a procedure
+as its value.
+
+This procedure takes the
+procedure f and does something
+
+to it to produce a new procedure
+of one argument x,
+
+which averages f--
+
+this f--
+
+applied to x and x itself.
+
+Using the context here, I apply
+average damping to the
+
+procedure, which just
+divides x by y.
+
+It's a division.
+
+And I'm finding to fixed point
+of that, and that's a clearer
+
+way of writing down what
+I wrote down over
+
+here, wherever it was.
+
+Here, because it tells why
+I am writing this down.
+
+I suppose this to some extent
+really clarifies what Heron of
+
+Alexandria was up to.
+
+I suppose I'll stop now.
+
+Are there any questions?
+
+AUDIENCE: So when you define
+average damp, don't you need
+
+to have a variable on f?
+
+PROFESSOR: Ah, the question was,
+and here we're having--
+
+again, you've got to learn
+about the syntax.
+
+The question was when defining
+average damp, don't you have
+
+to have a variable
+defined with f?
+
+What you are asking about is
+the formal parameter of f?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: OK.
+
+The formal parameter
+of f is here.
+
+The formal parameter of f--
+
+AUDIENCE: The formal parameter
+of average damp.
+
+PROFESSOR: F is being
+used to apply it to
+
+an argument, right?
+
+It's indeed true that f must
+have a formal parameter.
+
+Let's find out what f's
+formal parameter is.
+
+AUDIENCE: The formal parameter
+of average damp.
+
+PROFESSOR: Oh, f is the formal
+parameter of average damp.
+
+I'm sorry.
+
+You're just confusing
+a syntactic thing.
+
+I could have written
+this the other way.
+
+Actually, I didn't understand
+your question.
+
+Of course, I could have written
+it this other way.
+
+Those are identical notations.
+
+This is a different way
+of writing this.
+
+You're going to have to get
+used to lambda notation
+
+because I'm going to use it.
+
+What it says here, I'm defining
+the name average damp
+
+to name the procedure whose
+of one argument f.
+
+That's the formal parameter of
+the procedure average damp.
+
+What define does is it says
+give this name a value.
+
+Here is the value of for it.
+
+That there happens to be a
+funny syntax to make that
+
+easier in some cases is
+purely convenience.
+
+But the reason why I wrote it
+this way here is to emphasize
+
+that I'm dealing with a
+procedure that takes a
+
+procedure as its argument
+and produces a
+
+procedure as its value.
+
+AUDIENCE: I don't understand
+why you use lambda twice.
+
+Can you just use one
+lambda and take two
+
+arguments f and x?
+
+PROFESSOR: No.
+
+AUDIENCE: You can't?
+
+PROFESSOR: No, that would
+be a different thing.
+
+If I were to write the procedure
+lambda of f and x,
+
+the average of f of x and x,
+that would not be something
+
+which would be allowed to take a
+procedure as an argument and
+
+produce a procedure
+as its value.
+
+That would be a thing that
+takes a procedure as its
+
+argument and numbers
+its argument and
+
+produces a new number.
+
+But what I'm producing here is
+a procedure to fit in the
+
+procedure slot over here,
+which is going to
+
+be used over here.
+
+So the number has to
+come from here.
+
+This is the thing that's going
+to eventually end up in the x.
+
+And if you're confused, you
+should do some substitution
+
+and see for yourself.
+
+Yes?
+
+AUDIENCE: Will you please show
+the definition for average
+
+damp without using lambda
+notation in both cases.
+
+PROFESSOR: I can't make a very
+simple one like that.
+
+Let me do it for you, though.
+
+I can get rid of this
+lambda easily.
+
+I don't want to be--
+
+actually, I'm lying to you.
+
+I don't want to do what you want
+because I think it's more
+
+confusing than you think.
+
+I'm not going to write
+what you want.
+
+So we'll have to get a name.
+
+FOO of x to be of F of x and x
+and return as a value FOO.
+
+This is equivalent, but
+I've had to make an
+
+arbitrary name up.
+
+This is equivalent to this
+without any lambdas.
+
+Lambda is very convenient for
+naming anonymous procedures.
+
+It's the anonymous name
+of something.
+
+Now, if you really want to know
+a cute way of doing this,
+
+we'll talk about it later.
+
+We're going to have to define
+the anonymous procedure.
+
+Any other questions?
+
+And so we go for our
+break again.
+
+So now we've seen how
+to use high-order
+
+procedures, they're called.
+
+That's procedures that take
+procedural arguments and
+
+produce procedural values to
+help us clarify and abstract
+
+some otherwise complicated
+processes.
+
+I suppose what I'd like to do
+now is have a bit of fun with
+
+that and sort of a little
+practice as well.
+
+So let's play with this square
+root thing even more.
+
+Let's elaborate it and
+understand what's going on and
+
+make use of this kind of
+programming style.
+
+One thing that you might know
+is that there is a general
+
+method called Newton's method
+the purpose of which is to
+
+find the roots--
+
+that's the zeroes--
+
+of functions.
+
+So, for example, to find a y
+such that f of y equals 0, we
+
+start with some guess.
+
+This is Newton's method.
+
+And the guess we start with
+we'll call y0, and then we
+
+will iterate the following
+expression.
+
+y n plus 1-- this is a
+difference equation--
+
+is yn minus f of yn over the
+derivative with respect to y
+
+of f evaluated at y equal yn.
+
+Very strange notation.
+
+I must say ugh.
+
+The derivative of f with respect
+to y is a function.
+
+I'm having a little bit of
+unhappiness with that, but
+
+that's all right.
+
+It turns out in the programming
+language world,
+
+the notation is much clearer.
+
+Now, what is this?
+
+People call it Newton's
+method.
+
+It's a method for finding the
+roots of the function f.
+
+And it, of course, sometimes
+converges, and when it does,
+
+it does so very fast. And
+sometimes, it doesn't
+
+converge, and, oh well, we have
+to do something else.
+
+But let's talk about square
+root by Newton's method.
+
+Well, that's rather
+interesting.
+
+Let's do exactly the same thing
+we did last time: a bit
+
+of wishful thinking.
+
+We will apply Newton's method,
+assuming we knew how to do it.
+
+You don't know how
+to do it yet.
+
+Well, let's go.
+
+What do I have here?
+
+The square root of x.
+
+It's Newton's method applied
+to a procedure which will
+
+represent that function
+of y, which computes
+
+that function of y.
+
+Well, that procedure is that
+procedure of y, which is the
+
+difference between x and
+the square of y.
+
+Indeed, if I had a value of y
+for which this was zero, then
+
+y would be the square
+root of x.
+
+See that?
+
+OK, I'm going to start this
+out searching at 1.
+
+Again, completely arbitrary
+property of square roots that
+
+I can do that.
+
+Now, how am I going to compute
+Newton's method?
+
+Well, this is the method.
+
+I have it right here.
+
+In fact, what I'm doing is
+looking for a fixed point of
+
+some procedure.
+
+This procedure involves some
+complicated expressions in
+
+terms of other complicated
+things.
+
+Well, I'm trying to find the
+fixed point of this.
+
+I want to find the values of y,
+which if I put y in here, I
+
+get the same value out here up
+to some degree of accuracy.
+
+Well, I already have a
+fixed point process
+
+around to do that.
+
+And so, let's just define
+Newton's method over here.
+
+A procedure which computes
+a function and a
+
+guess, initial guess.
+
+Now, I'm going to have
+to do something here.
+
+I'm going to need the derivative
+of the function.
+
+I'm going to need a procedure
+which computes the derivative
+
+of the function computed by
+the given a procedure f.
+
+I'm trying to be very careful
+about what I'm saying.
+
+I don't want to mix up the word
+procedure and function.
+
+Function is a mathematical
+word.
+
+It says I'm mapping from values
+to other values, a set
+
+of ordered pairs.
+
+But sometimes, I'll accidentally
+mix those up.
+
+Procedures compute functions.
+
+So I'm going to define the
+derivative of f to be by
+
+wishful thinking again.
+
+I don't know how I'm
+going to do it.
+
+Let's worry about that later--
+
+of F. So if F is a procedure,
+which happens to be this one
+
+over here for a square root,
+then DF will be the derivative
+
+of it, which is also the
+derivative of the function
+
+computed by that procedure.
+
+DF will be a procedure that
+computes the derivative of the
+
+function computed by the
+procedure F. And then given
+
+that, I will just go looking
+for a fixed point.
+
+What is the fixed point
+I'm looking for?
+
+It's the one for that procedure
+of one argument x,
+
+which I compute by
+subtracting x.
+
+That's the old-- that's
+the yn here.
+
+The quotient of f of x and df
+of x, starting out with the
+
+original guess.
+
+That's all very simple.
+
+Now, I have one part left that
+I haven't written, and I want
+
+you to see the process by which
+I write these things,
+
+because this is really true.
+
+I start out with some
+mathematical idea, perhaps.
+
+By wishful thinking, I assume
+that by some magic I can do
+
+something that I have
+a name for.
+
+I'm not going to worry about
+how I do it yet.
+
+Then I go walking down here and
+say, well, by some magic,
+
+I'm somehow going to figure how
+to do that, but I'm going
+
+to write my program anyway.
+
+Wishful thinking, essential
+to good engineering, and
+
+certainly essential to a
+good computer science.
+
+So anyway, how many of
+you wished that your
+
+computer ran faster?
+
+Well, the derivative isn't
+so bad either.
+
+Sort of like average damping.
+
+The derivative is a procedure
+that takes a procedure that
+
+computes a function as its
+argument, and it produces a
+
+procedure that computes a
+function, which needs one
+
+argument x.
+
+Well, you all know
+this definition.
+
+It's f of x plus delta x minus
+f of x over delta x, right?
+
+For some small delta x.
+
+So that's the quotient of the
+difference of f of the sum of
+
+x and dx minus f point
+x divided by dx.
+
+I think the thing was lining up
+correctly when I balanced
+
+the parentheses.
+
+Now, I want you to
+look at this.
+
+Just look.
+
+I suppose I haven't told
+you what dx is.
+
+Somewhere in the world I'm going
+to have to write down
+
+something like that.
+
+I'm not interested.
+
+This is a procedure which takes
+a procedure and produces
+
+an approximation, a procedure
+that computes an approximation
+
+of the derivative of the
+function computed by the
+
+procedure given by the standard
+methods that you all
+
+know and love.
+
+Now, it may not be the case that
+doing this operation is
+
+such a good way of approximating
+a derivative.
+
+Numerical analysts here
+should jump on me and
+
+say don't do that.
+
+Computing derivatives produces
+noisy answers, which is true.
+
+However, this again is for the
+sake of understanding.
+
+Look what we've got.
+
+We started out with what is
+apparently a mathematically
+
+complex thing.
+
+and.
+
+In a few blackboards full, we
+managed to decompose the
+
+problem of computing square
+roots by the way you were
+
+taught in your college
+calculus class--
+
+Newton's method--
+
+so that it can be understood.
+
+It's clear.
+
+Let's look at the structure
+of what it is we've got.
+
+Let's look at this slide.
+
+This is a diagram of the machine
+described by the
+
+program on the blackboard.
+
+There's a machine
+described here.
+
+And what have I got?
+
+Over here is the Newton's method
+function f that we have
+
+on the left-most blackboard.
+
+It's the thing that takes an
+argument called y and puts out
+
+the difference between x and
+the square of y, where x is
+
+some sort of free variable that
+comes in from the outside
+
+by some magic.
+
+So the square root routine picks
+up an x, and builds this
+
+procedure, which I have the
+x rolled up in it by
+
+substitution.
+
+Now, this procedure in the cloud
+is fed in as the f into
+
+the Newton's method which
+is here, this box.
+
+The f is fanned out.
+
+Part of it goes into something
+else, and the other part of it
+
+goes through a derivative
+process into something else to
+
+produce a procedure, which
+computes the function which is
+
+the iteration function of
+Newton's method when we use
+
+the fixed point method.
+
+So this procedure, which
+contains it by substitution--
+
+remember, Newton's method over
+here, Newton's method builds
+
+this procedure, and Newton's
+method has in it defined f and
+
+df, so those are captured
+over here: f and df.
+
+Starting with this procedure,
+I can now feed this to the
+
+fixed point process within an
+initial guess coming out from
+
+the outside from square
+root to produce the
+
+square root of x.
+
+So what we've built is a very
+powerful engine, which allows
+
+us to make nice things
+like this.
+
+Now, I want to end this with
+basically an idea of Chris
+
+Strachey, one of the
+
+grandfathers of computer science.
+
+He's a logician who
+lived in the--
+
+I suppose about 10 years ago
+or 15 years ago, he died.
+
+I don't remember exactly when.
+
+He's one of the inventors
+of something called
+
+denotational semantics.
+
+He was a great advocate of
+making procedures or functions
+
+first-class citizens in a
+programming language.
+
+So here's the rights and
+privileges of first-class
+
+citizens in a programming
+language.
+
+It allows you to make any
+abstraction you like if you
+
+have functions as first-class
+citizens.
+
+The first-class citizens
+must be able
+
+to be named by variables.
+
+And you're seeing me doing
+that all the time.
+
+Here's a nice variable which
+names a procedure which
+
+computes something.
+
+They have to be passed as
+arguments to procedures.
+
+We've certainly seen that.
+
+We have to be able to return
+them as values from
+
+procedures.
+
+And I suppose we've seen that.
+
+We haven't yet seen anything
+about data structures.
+
+We will soon, but it's also the
+case that in order to have
+
+a first-class citizen in a
+programming language, the
+
+object has to be allowed to be
+part of a data structure.
+
+We're going to see that soon.
+
+So I just want to close with
+this and say having things
+
+like procedures as first-class
+data structures, first-class
+
+data, allows one to make
+powerful abstractions, which
+
+encode general methods
+like Newton's method
+
+in very clear way.
+
+Are there any questions?
+
+Yes.
+
+AUDIENCE: Could you put
+derivative instead of df
+
+directly in the fixed point?
+
+PROFESSOR: Oh, sure.
+
+Yes, I could have put deriv of
+f right here, no question.
+
+Any time you see something
+defined, you can put the thing
+
+that the definition is
+there because you
+
+get the same result.
+
+In fact, what that would look
+like, it's interesting.
+
+AUDIENCE: Lambda.
+
+PROFESSOR: Huh?
+
+AUDIENCE: You could put the
+lambda expression in there.
+
+PROFESSOR: I could also put
+derivative of f here.
+
+It would look interesting
+because of the open paren,
+
+open paren, deriv of f,
+closed paren on an x.
+
+Now, that would have the bad
+property of computing the
+
+derivative many times, because
+every time I would run this
+
+procedure, I would compute
+the derivative again.
+
+However, the two open parens
+here both would be meaningful.
+
+I want you to understand
+syntactically that that's a
+
+sensible thing.
+
+Because if was to rewrite this
+program-- and I should do it
+
+right here just so
+you see because
+
+that's a good question--
+
+of F and guess to be fixed point
+of that procedure of one
+
+argument x, which subtracts
+from x the quotient of F
+
+applied to x and the deriv
+of F applied to x.
+
+This is guess.
+
+This is a perfectly legitimate
+program,
+
+because what I have here--
+
+remember the evaluation rule.
+
+The evaluation rule is evaluate
+all of the parts of
+
+the combination: the operator
+and the operands.
+
+This is the operator of
+this combination.
+
+Evaluating this operator will,
+of course, produce the
+
+derivative of F.
+
+AUDIENCE: To get it one step
+further, you could put the
+
+lambda expression there, too.
+
+PROFESSOR: Oh, of course.
+
+Any time I take something which
+is define, I can put the
+
+thing it's defined to be in
+the place where the thing
+
+defined is.
+
+I can't remember which is
+definiens and which is
+
+definiendum.
+
+When I'm trying to figure out
+how to do a lecture about this
+
+in a freshman class, I use such
+words and tell everybody
+
+it's fun to tell
+their friends.
+
+OK, I think that's it.
\ No newline at end of file
diff --git a/fTNBcqb_ZeE.txt b/fTNBcqb_ZeE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..de58bd4f85a46625b668ceb60f1f2015defcb44f
--- /dev/null
+++ b/fTNBcqb_ZeE.txt
@@ -0,0 +1,1579 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today we're going to discuss the many
+
+ align:start position:0%
+hi today we're going to discuss the many
+ 
+
+ align:start position:0%
+hi today we're going to discuss the many
+D's of thermodynamics so what do I mean
+
+ align:start position:0%
+D's of thermodynamics so what do I mean
+ 
+
+ align:start position:0%
+D's of thermodynamics so what do I mean
+we're going to talk about
+
+ align:start position:0%
+we're going to talk about
+ 
+
+ align:start position:0%
+we're going to talk about
+lowercase D
+
+ align:start position:0%
+lowercase D
+ 
+
+ align:start position:0%
+lowercase D
+lowercase Greek d
+
+ align:start position:0%
+lowercase Greek d
+ 
+
+ align:start position:0%
+lowercase Greek d
+and uppercase Greek d
+
+ align:start position:0%
+and uppercase Greek d
+ 
+
+ align:start position:0%
+and uppercase Greek d
+and I want to clarify why we have
+
+ align:start position:0%
+and I want to clarify why we have
+ 
+
+ align:start position:0%
+and I want to clarify why we have
+different D's that we use when we use
+
+ align:start position:0%
+different D's that we use when we use
+ 
+
+ align:start position:0%
+different D's that we use when we use
+them and give some physical intuition
+
+ align:start position:0%
+them and give some physical intuition
+ 
+
+ align:start position:0%
+them and give some physical intuition
+for what they mean so for example
+
+ align:start position:0%
+for what they mean so for example
+ 
+
+ align:start position:0%
+for what they mean so for example
+when we write the combined statement
+
+ align:start position:0%
+when we write the combined statement
+ 
+
+ align:start position:0%
+when we write the combined statement
+of the first and second law
+
+ align:start position:0%
+of the first and second law
+ 
+
+ align:start position:0%
+of the first and second law
+we have d u
+
+ align:start position:0%
+we have d u
+ 
+
+ align:start position:0%
+we have d u
+equals t d s
+
+ align:start position:0%
+equals t d s
+ 
+
+ align:start position:0%
+equals t d s
+minus p
+
+ align:start position:0%
+minus p
+ 
+
+ align:start position:0%
+minus p
+V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the D's
+
+ align:start position:0%
+the D's
+ 
+
+ align:start position:0%
+the D's
+indicate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exact differentials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is equal
+
+ align:start position:0%
+which is equal
+ 
+
+ align:start position:0%
+which is equal
+to infinitesimal changes in state
+
+ align:start position:0%
+to infinitesimal changes in state
+ 
+
+ align:start position:0%
+to infinitesimal changes in state
+variables I'll write that out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the next D we want to talk about
+
+ align:start position:0%
+okay the next D we want to talk about
+ 
+
+ align:start position:0%
+okay the next D we want to talk about
+are the lowercase Greek D's so for
+
+ align:start position:0%
+are the lowercase Greek D's so for
+ 
+
+ align:start position:0%
+are the lowercase Greek D's so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+conservation of energy gives us the
+
+ align:start position:0%
+conservation of energy gives us the
+ 
+
+ align:start position:0%
+conservation of energy gives us the
+following expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d u
+
+ align:start position:0%
+d u
+ 
+
+ align:start position:0%
+d u
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+d q plus d
+
+ align:start position:0%
+d q plus d
+ 
+
+ align:start position:0%
+d q plus d
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+which tells us that the total change of
+
+ align:start position:0%
+which tells us that the total change of
+ 
+
+ align:start position:0%
+which tells us that the total change of
+internal energy
+
+ align:start position:0%
+internal energy
+ 
+
+ align:start position:0%
+internal energy
+for a system equals the sum of heat and
+
+ align:start position:0%
+for a system equals the sum of heat and
+ 
+
+ align:start position:0%
+for a system equals the sum of heat and
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+heat and work are process variables in
+
+ align:start position:0%
+heat and work are process variables in
+ 
+
+ align:start position:0%
+heat and work are process variables in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+the lower case Greek D's
+
+ align:start position:0%
+the lower case Greek D's
+ 
+
+ align:start position:0%
+the lower case Greek D's
+indicate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in exact differentials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is infinite decimal changes in
+
+ align:start position:0%
+that is infinite decimal changes in
+ 
+
+ align:start position:0%
+that is infinite decimal changes in
+process variables these terms exact and
+
+ align:start position:0%
+process variables these terms exact and
+ 
+
+ align:start position:0%
+process variables these terms exact and
+inexact differentials they have a
+
+ align:start position:0%
+inexact differentials they have a
+ 
+
+ align:start position:0%
+inexact differentials they have a
+specific meaning in thermodynamics which
+
+ align:start position:0%
+specific meaning in thermodynamics which
+ 
+
+ align:start position:0%
+specific meaning in thermodynamics which
+is related to but not identical to
+
+ align:start position:0%
+is related to but not identical to
+ 
+
+ align:start position:0%
+is related to but not identical to
+meanings they have in mathematics so
+
+ align:start position:0%
+meanings they have in mathematics so
+ 
+
+ align:start position:0%
+meanings they have in mathematics so
+this is a statement about thermodynamics
+
+ align:start position:0%
+this is a statement about thermodynamics
+ 
+
+ align:start position:0%
+this is a statement about thermodynamics
+okay this brings us to the third D the
+
+ align:start position:0%
+okay this brings us to the third D the
+ 
+
+ align:start position:0%
+okay this brings us to the third D the
+capital Greek d
+
+ align:start position:0%
+capital Greek d
+ 
+
+ align:start position:0%
+capital Greek d
+so I'll write an example in the context
+
+ align:start position:0%
+so I'll write an example in the context
+ 
+
+ align:start position:0%
+so I'll write an example in the context
+of the classiest clipron equation
+
+ align:start position:0%
+of the classiest clipron equation
+ 
+
+ align:start position:0%
+of the classiest clipron equation
+PP
+
+ align:start position:0%
+PP
+ 
+
+ align:start position:0%
+PP
+DT equals Delta let me get this right
+
+ align:start position:0%
+DT equals Delta let me get this right
+ 
+
+ align:start position:0%
+DT equals Delta let me get this right
+s over
+
+ align:start position:0%
+s over
+ 
+
+ align:start position:0%
+s over
+Delta V
+
+ align:start position:0%
+Delta V
+ 
+
+ align:start position:0%
+Delta V
+in this case
+
+ align:start position:0%
+in this case
+ 
+
+ align:start position:0%
+in this case
+the capital D's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indicate transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in materials thermodynamics the most
+
+ align:start position:0%
+so in materials thermodynamics the most
+ 
+
+ align:start position:0%
+so in materials thermodynamics the most
+common Transformations that we talk
+
+ align:start position:0%
+common Transformations that we talk
+ 
+
+ align:start position:0%
+common Transformations that we talk
+about are transformations to take place
+
+ align:start position:0%
+about are transformations to take place
+ 
+
+ align:start position:0%
+about are transformations to take place
+at con at constant pressure
+
+ align:start position:0%
+at con at constant pressure
+ 
+
+ align:start position:0%
+at con at constant pressure
+and constant temperature that is
+
+ align:start position:0%
+and constant temperature that is
+ 
+
+ align:start position:0%
+and constant temperature that is
+isobaric and isothermal transformations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so of the three d's
+
+ align:start position:0%
+so of the three d's
+ 
+
+ align:start position:0%
+so of the three d's
+lowercase D lowercase Greek T and
+
+ align:start position:0%
+lowercase D lowercase Greek T and
+ 
+
+ align:start position:0%
+lowercase D lowercase Greek T and
+uppercase Greek D this uppercase Greek D
+
+ align:start position:0%
+uppercase Greek D this uppercase Greek D
+ 
+
+ align:start position:0%
+uppercase Greek D this uppercase Greek D
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the one that contains the most physical
+
+ align:start position:0%
+the one that contains the most physical
+ 
+
+ align:start position:0%
+the one that contains the most physical
+uh unstated assumptions it contains the
+
+ align:start position:0%
+uh unstated assumptions it contains the
+ 
+
+ align:start position:0%
+uh unstated assumptions it contains the
+the most uh information about the system
+
+ align:start position:0%
+the most uh information about the system
+ 
+
+ align:start position:0%
+the most uh information about the system
+but as a result it also is often the
+
+ align:start position:0%
+but as a result it also is often the
+ 
+
+ align:start position:0%
+but as a result it also is often the
+hardest for students to understand when
+
+ align:start position:0%
+hardest for students to understand when
+ 
+
+ align:start position:0%
+hardest for students to understand when
+you first encounter it so we're going to
+
+ align:start position:0%
+you first encounter it so we're going to
+ 
+
+ align:start position:0%
+you first encounter it so we're going to
+take some time to draw out what is meant
+
+ align:start position:0%
+take some time to draw out what is meant
+ 
+
+ align:start position:0%
+take some time to draw out what is meant
+by Transformations and transformation
+
+ align:start position:0%
+by Transformations and transformation
+ 
+
+ align:start position:0%
+by Transformations and transformation
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+so to illustrate the concept of
+
+ align:start position:0%
+so to illustrate the concept of
+ 
+
+ align:start position:0%
+so to illustrate the concept of
+transformation quantities it helps to
+
+ align:start position:0%
+transformation quantities it helps to
+ 
+
+ align:start position:0%
+transformation quantities it helps to
+draw State function surfaces so as a
+
+ align:start position:0%
+draw State function surfaces so as a
+ 
+
+ align:start position:0%
+draw State function surfaces so as a
+reminder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a given phase and composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can draw State functions
+
+ align:start position:0%
+we can draw State functions
+ 
+
+ align:start position:0%
+we can draw State functions
+of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can draw these as surfaces that is
+
+ align:start position:0%
+we can draw these as surfaces that is
+ 
+
+ align:start position:0%
+we can draw these as surfaces that is
+State functions of two independent
+
+ align:start position:0%
+State functions of two independent
+ 
+
+ align:start position:0%
+State functions of two independent
+variables so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we could have the entropy
+
+ align:start position:0%
+we could have the entropy
+ 
+
+ align:start position:0%
+we could have the entropy
+of phase Alpha
+
+ align:start position:0%
+of phase Alpha
+ 
+
+ align:start position:0%
+of phase Alpha
+drawn as a function of temperature
+
+ align:start position:0%
+drawn as a function of temperature
+ 
+
+ align:start position:0%
+drawn as a function of temperature
+and pressure
+
+ align:start position:0%
+and pressure
+ 
+
+ align:start position:0%
+and pressure
+so I'm going to draw a representative
+
+ align:start position:0%
+so I'm going to draw a representative
+ 
+
+ align:start position:0%
+so I'm going to draw a representative
+State function surface now see we'll
+
+ align:start position:0%
+State function surface now see we'll
+ 
+
+ align:start position:0%
+State function surface now see we'll
+keep the axes
+
+ align:start position:0%
+keep the axes
+ 
+
+ align:start position:0%
+keep the axes
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we go here is for some
+
+ align:start position:0%
+so here we go here is for some
+ 
+
+ align:start position:0%
+so here we go here is for some
+hypothetical phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a state function surface let's
+
+ align:start position:0%
+that's a state function surface let's
+ 
+
+ align:start position:0%
+that's a state function surface let's
+draw the axes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll make the Y at the vertical axis
+
+ align:start position:0%
+we'll make the Y at the vertical axis
+ 
+
+ align:start position:0%
+we'll make the Y at the vertical axis
+entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the axes
+
+ align:start position:0%
+one of the axes
+ 
+
+ align:start position:0%
+one of the axes
+and the plane can be pressure
+
+ align:start position:0%
+and the plane can be pressure
+ 
+
+ align:start position:0%
+and the plane can be pressure
+and the other would be temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a 3D visualization of how the
+
+ align:start position:0%
+so this is a 3D visualization of how the
+ 
+
+ align:start position:0%
+so this is a 3D visualization of how the
+entropy for a given phase might vary
+
+ align:start position:0%
+entropy for a given phase might vary
+ 
+
+ align:start position:0%
+entropy for a given phase might vary
+with pressure and temperature at a fixed
+
+ align:start position:0%
+with pressure and temperature at a fixed
+ 
+
+ align:start position:0%
+with pressure and temperature at a fixed
+composition
+
+ align:start position:0%
+composition
+ 
+
+ align:start position:0%
+composition
+and to keep track of the fact that it's
+
+ align:start position:0%
+and to keep track of the fact that it's
+ 
+
+ align:start position:0%
+and to keep track of the fact that it's
+for a given phase
+
+ align:start position:0%
+for a given phase
+ 
+
+ align:start position:0%
+for a given phase
+I'll label it Alpha so this is the state
+
+ align:start position:0%
+I'll label it Alpha so this is the state
+ 
+
+ align:start position:0%
+I'll label it Alpha so this is the state
+function service for a given particular
+
+ align:start position:0%
+function service for a given particular
+ 
+
+ align:start position:0%
+function service for a given particular
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+so to illustrate transformation
+
+ align:start position:0%
+so to illustrate transformation
+ 
+
+ align:start position:0%
+so to illustrate transformation
+quantities I want to draw the
+
+ align:start position:0%
+quantities I want to draw the
+ 
+
+ align:start position:0%
+quantities I want to draw the
+transformation entropy for an isober
+
+ align:start position:0%
+transformation entropy for an isober
+ 
+
+ align:start position:0%
+transformation entropy for an isober
+isobaric isothermal phase transformation
+
+ align:start position:0%
+isobaric isothermal phase transformation
+ 
+
+ align:start position:0%
+isobaric isothermal phase transformation
+so it's an isobaric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to consider a transformation
+
+ align:start position:0%
+we're going to consider a transformation
+ 
+
+ align:start position:0%
+we're going to consider a transformation
+between two phases Alpha and beta so
+
+ align:start position:0%
+between two phases Alpha and beta so
+ 
+
+ align:start position:0%
+between two phases Alpha and beta so
+we're going to need two different state
+
+ align:start position:0%
+we're going to need two different state
+ 
+
+ align:start position:0%
+we're going to need two different state
+function surfaces one for each phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll label this data and I'll draw
+
+ align:start position:0%
+we'll label this data and I'll draw
+ 
+
+ align:start position:0%
+we'll label this data and I'll draw
+another state function surface for phase
+
+ align:start position:0%
+another state function surface for phase
+ 
+
+ align:start position:0%
+another state function surface for phase
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as before we'll say that we're
+
+ align:start position:0%
+and as before we'll say that we're
+ 
+
+ align:start position:0%
+and as before we'll say that we're
+measuring the transformation entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the vertical axis
+
+ align:start position:0%
+so the vertical axis
+ 
+
+ align:start position:0%
+so the vertical axis
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+and the independent variables are
+
+ align:start position:0%
+and the independent variables are
+ 
+
+ align:start position:0%
+and the independent variables are
+temperature and pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so at a given pressure and
+
+ align:start position:0%
+all right so at a given pressure and
+ 
+
+ align:start position:0%
+all right so at a given pressure and
+temperature we can visualize the
+
+ align:start position:0%
+temperature we can visualize the
+ 
+
+ align:start position:0%
+temperature we can visualize the
+transformation entropy for a
+
+ align:start position:0%
+transformation entropy for a
+ 
+
+ align:start position:0%
+transformation entropy for a
+transformation between phase Alpha and
+
+ align:start position:0%
+transformation between phase Alpha and
+ 
+
+ align:start position:0%
+transformation between phase Alpha and
+phase beta so we're going to pick
+
+ align:start position:0%
+phase beta so we're going to pick
+ 
+
+ align:start position:0%
+phase beta so we're going to pick
+a given temperature and pressure
+
+ align:start position:0%
+a given temperature and pressure
+ 
+
+ align:start position:0%
+a given temperature and pressure
+that is a point down here on the PT
+
+ align:start position:0%
+that is a point down here on the PT
+ 
+
+ align:start position:0%
+that is a point down here on the PT
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and we're going to draw a vertical line
+
+ align:start position:0%
+and we're going to draw a vertical line
+ 
+
+ align:start position:0%
+and we're going to draw a vertical line
+and see where it intercepts these
+
+ align:start position:0%
+and see where it intercepts these
+ 
+
+ align:start position:0%
+and see where it intercepts these
+surfaces
+
+ align:start position:0%
+surfaces
+ 
+
+ align:start position:0%
+surfaces
+if we come up from the
+
+ align:start position:0%
+if we come up from the
+ 
+
+ align:start position:0%
+if we come up from the
+plane and at some point
+
+ align:start position:0%
+plane and at some point
+ 
+
+ align:start position:0%
+plane and at some point
+we're going to cut
+
+ align:start position:0%
+we're going to cut
+ 
+
+ align:start position:0%
+we're going to cut
+that state function surface and keep
+
+ align:start position:0%
+that state function surface and keep
+ 
+
+ align:start position:0%
+that state function surface and keep
+coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll cut that say function surface
+
+ align:start position:0%
+we'll cut that say function surface
+ 
+
+ align:start position:0%
+we'll cut that say function surface
+and keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a given point of pressure
+
+ align:start position:0%
+so a given point of pressure
+ 
+
+ align:start position:0%
+so a given point of pressure
+and temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we now have a visualization of the
+
+ align:start position:0%
+we now have a visualization of the
+ 
+
+ align:start position:0%
+we now have a visualization of the
+transformation entropy
+
+ align:start position:0%
+transformation entropy
+ 
+
+ align:start position:0%
+transformation entropy
+it's exactly the vertical distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between these two surfaces so this is
+
+ align:start position:0%
+between these two surfaces so this is
+ 
+
+ align:start position:0%
+between these two surfaces so this is
+the transformation entropy
+
+ align:start position:0%
+the transformation entropy
+ 
+
+ align:start position:0%
+the transformation entropy
+between phase Alpha
+
+ align:start position:0%
+between phase Alpha
+ 
+
+ align:start position:0%
+between phase Alpha
+and beta
+
+ align:start position:0%
+and beta
+ 
+
+ align:start position:0%
+and beta
+at a given pressure
+
+ align:start position:0%
+at a given pressure
+ 
+
+ align:start position:0%
+at a given pressure
+and temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and using this visualization at least in
+
+ align:start position:0%
+and using this visualization at least in
+ 
+
+ align:start position:0%
+and using this visualization at least in
+your mind's eye you can see that this
+
+ align:start position:0%
+your mind's eye you can see that this
+ 
+
+ align:start position:0%
+your mind's eye you can see that this
+transformation quantity is a function
+
+ align:start position:0%
+transformation quantity is a function
+ 
+
+ align:start position:0%
+transformation quantity is a function
+of pressure and temperature
+
+ align:start position:0%
+of pressure and temperature
+ 
+
+ align:start position:0%
+of pressure and temperature
+because as I move this point around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in pressure and temperature
+
+ align:start position:0%
+in pressure and temperature
+ 
+
+ align:start position:0%
+in pressure and temperature
+the vertical distance between these
+
+ align:start position:0%
+the vertical distance between these
+ 
+
+ align:start position:0%
+the vertical distance between these
+surfaces might change
+
+ align:start position:0%
+surfaces might change
+ 
+
+ align:start position:0%
+surfaces might change
+so this is illustration for an isobaric
+
+ align:start position:0%
+so this is illustration for an isobaric
+ 
+
+ align:start position:0%
+so this is illustration for an isobaric
+isothermal transformation and we're
+
+ align:start position:0%
+isothermal transformation and we're
+ 
+
+ align:start position:0%
+isothermal transformation and we're
+illustrating this for entropy
+
+ align:start position:0%
+illustrating this for entropy
+ 
+
+ align:start position:0%
+illustrating this for entropy
+but in thermodynamics we have many
+
+ align:start position:0%
+but in thermodynamics we have many
+ 
+
+ align:start position:0%
+but in thermodynamics we have many
+different transformation quantities that
+
+ align:start position:0%
+different transformation quantities that
+ 
+
+ align:start position:0%
+different transformation quantities that
+we keep track of in Material Science our
+
+ align:start position:0%
+we keep track of in Material Science our
+ 
+
+ align:start position:0%
+we keep track of in Material Science our
+most common independent variables are
+
+ align:start position:0%
+most common independent variables are
+ 
+
+ align:start position:0%
+most common independent variables are
+pressure and temperature because those
+
+ align:start position:0%
+pressure and temperature because those
+ 
+
+ align:start position:0%
+pressure and temperature because those
+are often the easiest for us to regulate
+
+ align:start position:0%
+are often the easiest for us to regulate
+ 
+
+ align:start position:0%
+are often the easiest for us to regulate
+in the laboratory
+
+ align:start position:0%
+in the laboratory
+ 
+
+ align:start position:0%
+in the laboratory
+but for any transformation quantity you
+
+ align:start position:0%
+but for any transformation quantity you
+ 
+
+ align:start position:0%
+but for any transformation quantity you
+can at least imagine if not draw out on
+
+ align:start position:0%
+can at least imagine if not draw out on
+ 
+
+ align:start position:0%
+can at least imagine if not draw out on
+a paper piece of paper State function
+
+ align:start position:0%
+a paper piece of paper State function
+ 
+
+ align:start position:0%
+a paper piece of paper State function
+Services corresponding to the quantity
+
+ align:start position:0%
+Services corresponding to the quantity
+ 
+
+ align:start position:0%
+Services corresponding to the quantity
+that you're trying to measure
+
+ align:start position:0%
+that you're trying to measure
+ 
+
+ align:start position:0%
+that you're trying to measure
+independent variables corresponding to
+
+ align:start position:0%
+independent variables corresponding to
+ 
+
+ align:start position:0%
+independent variables corresponding to
+the variables that you're regulating and
+
+ align:start position:0%
+the variables that you're regulating and
+ 
+
+ align:start position:0%
+the variables that you're regulating and
+a vertical distance which is a function
+
+ align:start position:0%
+a vertical distance which is a function
+ 
+
+ align:start position:0%
+a vertical distance which is a function
+of those independent variables that
+
+ align:start position:0%
+of those independent variables that
+ 
+
+ align:start position:0%
+of those independent variables that
+measures the transformation quantity for
+
+ align:start position:0%
+measures the transformation quantity for
+ 
+
+ align:start position:0%
+measures the transformation quantity for
+the transformation between two different
+
+ align:start position:0%
+the transformation between two different
+ 
+
+ align:start position:0%
+the transformation between two different
+phases
\ No newline at end of file
diff --git a/ftrKlCmELm4.txt b/ftrKlCmELm4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..992411fd852bbff3fd1129a55763898cbb1974b3
--- /dev/null
+++ b/ftrKlCmELm4.txt
@@ -0,0 +1,2452 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: I want to talk a
+little bit about producing
+
+and realizing your
+visions, and give
+
+an example of some of the things
+that Chris was talking about.
+
+So we shot a video on how
+engines worked, and there
+
+is a part of the video where
+the two creators were talking
+
+about how a turbine
+engine works.
+
+And I think I might have
+told this story before,
+
+about how we ended up finding
+like an actual Boeing engine.
+
+But there are a
+lot of ways that we
+
+could have filmed this scene.
+
+We could have animated it, we
+could have done a wide frame
+
+shot with animation overlay,
+like I showed you with George's
+
+[INAUDIBLE] videos.
+
+We could have done B-roll,
+so we could have just done
+
+like close up
+shots of the engine
+
+while you heard Luke
+explaining how it worked,
+
+with his voiceover.
+
+Or we could have done
+a live explanation,
+
+which is what we went with.
+
+So this is how George shot Luke.
+
+We went with the
+traditional thirds framing.
+
+Again, this isn't necessarily
+a rule that you have to go by,
+
+it just worked really
+well for this scene.
+
+And we went with
+this because it also
+
+gave us the ability to do sort
+of an interesting point of view
+
+shot.
+
+The point of view isn't
+from the narrator,
+
+it's actually from the viewer.
+
+So I'll show you the
+clip in a second.
+
+But essentially, we
+did one long take
+
+where George moved his
+camera as Luke was explaining
+
+the parts of the engine.
+
+So we wanted it to feel like
+the camera was basically
+
+where a person would be if Luke
+was explaining how a turbine
+
+engine works to a
+person standing there.
+
+LUKE: --won't work.
+
+FEMALE IN VIDEO:
+What you really need
+
+is one engine that can
+produce enough horsepower
+
+to fly the plane.
+
+A turbine engine is capable
+of much more horse power
+
+than a piston engine
+because of the way
+
+it uses giant fans
+to compress the air.
+
+LUKE: At the front
+of the turbine
+
+engine is an intake
+fan which spins
+
+and brings a huge amount of air
+into the front of the engine.
+
+As we move backwards
+through the engine,
+
+a series of compressor blades
+makes that air more and more
+
+compressed, until we get here.
+
+And here, fuel is
+introduced and burned.
+
+And that hot, high
+pressure flow gets sent
+
+out the back of the engine.
+
+And that makes the
+thrust of the engine.
+
+But at the same time,
+that flow passes
+
+through a series of four
+or five turbine blades,
+
+and those blades are
+connected directly
+
+to a shaft at the
+middle of the engine.
+
+That shaft runs all the
+way back to the front
+
+and spins the intake fan.
+
+That's what keeps
+the engine running.
+
+PROFESSOR: So that shot
+worked because Luke
+
+was very comfortable explaining
+that in one long take.
+
+He actually ad libbed
+that whole thing.
+
+And I can see that it's a
+lot of information at once,
+
+so maybe it would have been
+better to do an animation.
+
+We certainly could've done
+it a lot of different ways.
+
+But what I like
+about that shot is
+
+that if you were
+just standing there,
+
+and Luke was
+explaining it to you,
+
+the camera would basically
+be your eyes, right?
+
+Like you would walk
+along with him,
+
+and you would look down at the
+engine when he pointed to it,
+
+you would look back up at him.
+
+So that's the type of movement
+that Chris was talking about
+
+that you can introduce
+to your video.
+
+It would be really different
+if we had just set up a tripod
+
+and had Luke explain
+the whole thing, right?
+
+Like it would have been a
+very different experience.
+
+GUEST SPEAKER: And it's
+not random movement,
+
+it's obviously very
+directed, which
+
+is the key to many of
+these kinds of things.
+
+It's not [INAUDIBLE]
+
+PROFESSOR: Right.
+
+Like we wanted to really follow
+what the natural person would
+
+do if they were just standing
+there talking to Luke.
+
+I want to talk about
+the lighting real quick.
+
+So we were in an
+airplane hangar,
+
+and it was like
+one in the morning,
+
+so it was super dark outside.
+
+I mean, we mostly relied
+on the overhead lights.
+
+I don't actually know if we
+lit this with anything else.
+
+Because it's super
+bright in there.
+
+So you don't need
+super fancy equipment
+
+to achieve the videos that
+you guys are going to do.
+
+So to talk a little bit
+more about producing,
+
+when you think of
+directing I feel
+
+like that's what most people
+think of when making a video.
+
+And directing is a lot about
+thinking in the present.
+
+So you're coaching the host,
+you're coaching the talent,
+
+telling them what to do
+right there in that moment.
+
+You're thinking about
+what the framing looks
+
+like in that moment.
+
+Producing is a lot about
+thinking about the future,
+
+anticipating what's coming
+next, the mistakes that you're
+
+going to make.
+
+So on a practical level it's a
+lot of check boxes, basically.
+
+You're thinking about
+where am I going
+
+to film, what are my backups
+going to be, where am I
+
+going to record voice over?
+
+My experience filming at MIT is
+that it is incredibly difficult
+
+to find a quiet place on campus
+to record clean voiceover.
+
+And if you're having
+trouble finding a spot,
+
+come talk to me at any time.
+
+I can help you with that.
+
+AUDIENCE: What do you mean that?
+
+Why do you mean that?
+
+PROFESSOR: So take this
+classroom for example,
+
+most of the spaces on campus
+have this hum overhead.
+
+And most of you guys will be
+relying on the lavalier mic,
+
+so it's not as bad.
+
+But there's just a lot
+of background noise
+
+that is on campus.
+
+So if you're just
+recording plain voice over
+
+that you want to
+use in your video,
+
+it would be more
+ideal if you could
+
+get something that's quieter
+than this room, for example.
+
+So you're thinking
+in checklists,
+
+and some of the boxes
+are a little more inane,
+
+like did we shoot
+all of the scenes?
+
+Which sounds stupid,
+but I actually
+
+missed that on my own video.
+
+I forgot to film
+one of the scenes.
+
+And then, did we
+get clean audio?
+
+So a tip that I would
+recommend for you guys
+
+is, even after you film
+all of your scenes,
+
+I would sit down and just record
+voiceover of your entire script
+
+in a separate audio file.
+
+Because you never know,
+looking back on the footage,
+
+there may be sections where
+the audio isn't very clean.
+
+So you may have to rely
+on your clean voiceover
+
+for that section.
+
+And maybe use B-roll to fill in.
+
+If that makes sense to people.
+
+Does anyone have
+questions so far?
+
+Yes.
+
+AUDIENCE: Like you are filming,
+and then you have a voice--
+
+PROFESSOR: Yeah.
+
+AUDIENCE: --then you want to
+use a voiceover separately.
+
+Then wouldn't the pacing off?
+
+PROFESSOR: Yeah.
+
+So for example we shot a
+video, and part of it--
+
+I'll talk more about it during
+the editing lecture next week,
+
+but if you can find a
+clean place to transition
+
+between the live footage
+and your voiceover,
+
+that's like the best
+way to do that if you
+
+find that some of your footage
+just has really bad live audio.
+
+For every place
+that you shoot, I
+
+recommend that you get room
+tone, which is basically
+
+the natural sound of the room.
+
+So for example, if you were
+going to shoot in this room,
+
+you would shoot the scene, and
+then you would take your mic
+
+and just record 30 seconds
+where everyone's quiet.
+
+And it's just going to
+record the background
+
+noise of the room.
+
+And you do that because if
+there is a case where you're
+
+relying on voiceover
+that you shot later,
+
+or you're cutting bits and
+pieces from the footage
+
+that you shot in
+this room, you're
+
+going to have this
+gap or a hiccup
+
+where the hum doesn't
+exist, and it's
+
+going to sound really
+awkward in the video.
+
+So you layer the room
+tone underneath when
+
+you're editing so that you
+don't have those hiccups
+
+between the cuts that you make.
+
+GUEST SPEAKER: It's
+kind of a decision
+
+that you have to make,
+too, based on the room.
+
+So like with Jeff, we actually
+did the voiceover in the room.
+
+Because it had a hum,
+so we could have done
+
+a better job of the voiceover.
+
+But what we decided was that it
+would be more jarring if there
+
+was a major audio quality
+difference between the voice
+
+over and the on
+camera, you know,
+
+had we done it in a studio
+or in a better space later.
+
+So, you know, it was clean
+enough, we accepted it.
+
+And that's why we
+had him do everything
+
+on the spot in the same
+place, so that it wouldn't
+
+have that drop in and out.
+
+PROFESSOR: Yeah.
+
+Does that make sense to people?
+
+Like if we took the footage,
+like this footage where
+
+I'm talking here, and then
+we cut to something where
+
+I continue to talk
+about this class,
+
+but I was doing it
+over a voiceover,
+
+and we had some B-roll
+of you guys working.
+
+The first scene, you
+would hear the hum,
+
+and you'd hear me talking.
+
+But in the second
+scene, you would just
+
+hear like very clean dead
+space while I'm talking.
+
+And you would see
+you guys working.
+
+And it would sound
+and look really weird.
+
+It would feel really
+weird to watch.
+
+GUEST SPEAKER: So we
+just did another video
+
+not unlike the
+[INAUDIBLE] video,
+
+except that the person is
+in Kendall Square talking.
+
+All the on camera stuff
+was in Kendall Square.
+
+And that's really
+noisy, so we decided in
+
+that case to do the opposite.
+
+We didn't have him record
+everything in Kendall Square,
+
+because then we would be dealing
+with problems throughout.
+
+But what we did is we recorded
+the equivalent of room tone.
+
+We just got audio
+of Kendall Square,
+
+and then we were able to
+sort of slowly fade it out
+
+after the person was
+on camera, so that it
+
+was more imperceptible.
+
+And then slowly fade it
+back in before an on camera
+
+arrived-- you know, comes back.
+
+AUDIENCE: There's no way
+you can filter it out?
+
+Just kind of--
+
+GUEST SPEAKER: Well
+you can filter audio.
+
+What I always tell
+people is don't.
+
+Especially like,
+if you're not going
+
+to spend thousands
+of dollars doing it,
+
+don't think you can do a lot.
+
+There are a lot of consumer
+tools that are available.
+
+They generally really
+degrade the voice.
+
+Everyone ends up sounding
+like I'm Stephen Hawking.
+
+PROFESSOR: Because the
+frequencies in the room tone--
+
+GUEST SPEAKER:
+Very similar, yeah.
+
+PROFESSOR: --some of the
+frequencies in the voice.
+
+GUEST SPEAKER: So very,
+very high end, very time
+
+consuming tools are
+out there to do it.
+
+But they're out of reach.
+
+PROFESSOR: Music can help
+hide that a little bit,
+
+and I'm going to show you guys
+examples of that next week.
+
+But in general like it literally
+takes 30 seconds for you
+
+to record the room tone.
+
+So that's--
+
+GUEST SPEAKER: Yeah,
+it's definitely worth it.
+
+PROFESSOR: --It's worth it.
+
+So in general, as
+a producer you're
+
+doing a lot of anticipatory
+thinking, which
+
+is to help you
+ultimately realize
+
+your big vision for your video.
+
+So you're doing all
+of these checklists,
+
+you're thinking ahead of time.
+
+Even in pre-production, which
+is where we are right now,
+
+where you're scripting.
+
+As a producer you're going to be
+thinking about the big picture
+
+the entire time.
+
+So producing is really
+looking at the big picture.
+
+You're looking at how the
+microscopic decisions like,
+
+where you're going to
+shoot for instance,
+
+or where are you going
+to record the room tone,
+
+how that all fits into
+your macroscopic plan.
+
+So as Chris said, it's really
+important to scout locations.
+
+And when you go scout locations,
+the two big things to look at
+
+are what's the lighting
+like at that place,
+
+and what's the sound like?
+
+And when you're
+looking at lighting,
+
+not only look at
+the natural light
+
+that's available in the room,
+if it's indoors for example,
+
+but how the sunlight
+affects the room.
+
+So when we were pre-producing
+this OpenCourseWare class,
+
+we came and scouted
+this classroom.
+
+And we noticed that there
+are all these big windows,
+
+and it was an afternoon class.
+
+And I knew that the
+lighting in this room
+
+would be really
+different at 1 o'clock
+
+than it would be at 4 o'clock.
+
+So we decided that it actually
+wouldn't be too big of a deal,
+
+because people
+watching the video
+
+wouldn't be like, oh my gosh
+it's dark in that classroom
+
+now, that doesn't
+make any sense.
+
+Because obviously we know
+it's a three hour class.
+
+GUEST SPEAKER:
+You'll notice Billy's
+
+on that side of the room,
+not on this side of the room.
+
+PROFESSOR: Yeah.
+
+GUEST SPEAKER: That's
+because if Elizabeth
+
+was teaching in
+that corner, we'd
+
+have a problem with the windows.
+
+PROFESSOR: And we thought
+about if we should just
+
+lower the shades the entire time
+so we have uniform lighting.
+
+So those are the
+kind of questions
+
+that you'll ask yourself
+during pre-production.
+
+And sound, again,
+take room tone.
+
+The biggest sound issues
+if you're outdoors,
+
+the wind makes a big difference.
+
+Most of you guys are going to
+just rely on your lavaliers,
+
+and they have the little cap.
+
+And that does a
+generally good job,
+
+but just take note of
+it when you go scout.
+
+My personal tip is
+look for outlets.
+
+That's always been
+like the biggest thing
+
+for us is, especially if it's
+an outdoor location, scouting
+
+ahead of time and seeing
+how many outlets there are
+
+helps you anticipate
+how many extension
+
+cords you need to bring.
+
+Which sounds like a silly
+thing, but actually makes
+
+a huge difference.
+
+So for example we
+shot this video
+
+with Jamie in the Stata
+Center on computer switches.
+
+And we were with the Digi-Comp.
+
+Or the Digi-Cart?
+
+Digi-Comp.
+
+Which we couldn't move, so we
+had to shoot in this location.
+
+And it was in Stata so we
+knew it would be really noisy.
+
+So we shot at like 6:00
+in the morning on Sunday,
+
+when no one would be around.
+
+But the thing that
+we didn't anticipate,
+
+because I didn't scout that
+location, which is bad,
+
+is that there's a skylight right
+above the Digi-Comp-- I always
+
+forget what it's called.
+
+So noon hit, and we had to
+stop filming because there
+
+was sunlight directly
+overhead that
+
+completely changed the shadows
+on the prop, and on Jamie.
+
+So we basically lost two
+hours of shooting time
+
+because we were waiting for
+the sun to pass overhead.
+
+So that's why you should scout
+your locations ahead of time.
+
+A quick note on locations,
+also look at backgrounds.
+
+And with backgrounds you
+should really be deliberate.
+
+And go big or go home.
+
+So for example,
+this is a background
+
+that I think a lot
+of people default
+
+to when they don't really
+have anything else to shoot,
+
+because they just sit-in
+their office and they're like,
+
+I need to record
+something really fast,
+
+I'll just sit here.
+
+Sitting in front of a
+window that has blinds on it
+
+is maybe the worst possible
+background that you could use.
+
+And again, this is a
+matter of personal taste,
+
+but I cringe when I see
+this for two reasons.
+
+One, it's really back-lit,
+which is what Chris
+
+was talking about earlier.
+
+So you'll have so
+much outdoor light
+
+that it makes your
+subjects look really dark.
+
+And having all the
+blinds in the background,
+
+I think having all those lines
+is really distracting as well.
+
+This is what
+happened when George
+
+tried to change the exposure
+setting on the camera
+
+to light for me.
+
+So I'm lit well, but
+now the background
+
+is completely blown out.
+
+So in general, avoid filming
+right in front of a window
+
+where there is direct
+sunlight coming in.
+
+And please don't film
+in front of blinds.
+
+If anyone is
+interested in filming
+
+in front of a green
+screen, it's possible,
+
+and I'm happy to help you.
+
+I think you should be very
+deliberate with that decision.
+
+Sometimes it works really well.
+
+This is an example.
+
+FEMALE IN VIDEO: So
+in order to turn red,
+
+neurons from the squid's
+brain sends signals
+
+to these muscles, which pull
+open all of his chromatophores
+
+at the same time.
+
+PROFESSOR: So-- oh,
+this was the wrong clip.
+
+Sorry guys.
+
+But there is one
+example where she
+
+says, take note, when I
+walk next to the squid,
+
+he turns red.
+
+And so you actually see
+her walking on screen,
+
+and then the squid turns red.
+
+And so we used a green
+screen to film this
+
+because we like
+the actual visual
+
+of seeing some sort of
+object stimulating the squid
+
+to turn colors.
+
+So that's an example of a
+green screen working well,
+
+I think in my opinion.
+
+If you want to do something like
+that, I'm happy to help you.
+
+But again, you
+don't have to do it.
+
+So more production tips.
+
+Days before, make sure
+you scout your locations.
+
+A word about props.
+
+So props don't have
+to be expensive.
+
+And I'm not just talking
+about props on screen.
+
+I'm also talking about the
+tools that you can use to film.
+
+So we're giving you a
+tripod, and that's basically
+
+your only production prop.
+
+But as Chris was saying,
+like you can use desk lamps
+
+with paper over them.
+
+Let me show you this shot.
+
+FEMALE IN VIDEO:
+Let me show you how.
+
+PROFESSOR: So those are
+all dolly shots basically,
+
+of us establishing the
+location of this video, which
+
+is in D lab, which
+is where Jack works.
+
+And they're all very smooth
+pans of looking around
+
+at the locations.
+
+And we shot that with
+a cart, like a hand
+
+cart that I just sat in,
+and George pushed me around.
+
+So you could buy a
+super expensive dolly,
+
+or you can just borrow a
+cart from our department,
+
+and sit-in it, and have
+someone push you around.
+
+The dolly is always
+nicer, but we
+
+don't have the budget for that.
+
+GUEST SPEAKER: Great job with
+steady camerawork by the way.
+
+It can be an issue if
+you're sitting on a cart,
+
+if you start getting
+a lot of this,
+
+it takes away from the
+niceness of the shot.
+
+But in this case it was great.
+
+PROFESSOR: We took a
+tripod and spread the legs
+
+out all the way, so that
+it was like really, really
+
+firm in the cart.
+
+And then I held it just
+to add more stability.
+
+So it's possible
+this is another one.
+
+FEMALE IN VIDEO: To figure
+out how the entire metabolome
+
+works, we can use it
+to engineer plants
+
+to create new bio-materials,
+medicines, and clean energy.
+
+We might even discover
+that plants have
+
+the secret to living forever.
+
+We just need to unlock
+their chemical mysteries.
+
+PROFESSOR: So that's actually
+one of my favorite shots
+
+from Science Out Loud, ever.
+
+And that was all George's idea,
+so I have to give him credit.
+
+But I like it because
+it's a reveal,
+
+like Chris was talking about.
+
+It's the way we ended the video.
+
+We start off on the
+plants, focused on it,
+
+and you reveal
+Anastasia at the end.
+
+And that's actually-- to
+get that smooth movement is
+
+actually really hard.
+
+You might be able to do
+it with these tripods
+
+because the cameras
+aren't really heavy.
+
+And you could probably get
+enough friction on them
+
+to get it to work.
+
+But what we did was, George was
+using a camera like that one.
+
+So he took the tripod, flipped
+the top head of it upside down,
+
+and then he took a boom
+pole, which is basically
+
+this long pole, and put a
+weight on one end of it,
+
+and put the camera on the
+other, and just slowly let
+
+the camera come up
+from the weight.
+
+So I'm all about MacGyvering
+props if you need to.
+
+There are creative ways to
+get around things and achieve
+
+nice effects with
+cheaper equipment.
+
+The other thing
+about days before
+
+is that you should make a shot
+list, which is something that I
+
+would like you guys to submit.
+
+I think originally
+I had specified
+
+you to do that tonight.
+
+But it's not necessary to do
+it and post it until next week.
+
+So I'll update you
+with another email.
+
+But a shot list is
+basically what it says.
+
+It's a list of all the
+shots that you need.
+
+So it doesn't have to
+look a certain way.
+
+It's for your benefit only.
+
+So organize it however
+you think is best for you.
+
+But this was my shot
+list for the reshoots
+
+that we did for the snots video.
+
+This is the first page of it.
+
+So I listed out
+all the locations
+
+that we were going to, what
+time approximately we were going
+
+to use it, so that I could
+get a good sense of what
+
+the lighting would look
+like in these locations.
+
+And then I listed out exactly
+what lines I needed to say,
+
+and what shots we needed
+to get at each location.
+
+And then at the bottom I
+specified the wardrobe.
+
+So this is a super helpful
+organizational tool
+
+to use when you're
+planning things.
+
+When you are thinking
+about locations,
+
+definitely go big or go home.
+
+You can e-mail anyone
+and just tell them
+
+you're doing a project
+for a class at MIT,
+
+and you'd be surprised
+what you could get.
+
+We shot at a horse
+farm in Acton.
+
+We shot in an airplane.
+
+We shot at a skydiving zone.
+
+We shot at the butterfly exhibit
+at the Museum of Science.
+
+Most of the labs
+here, especially
+
+since you're students, are going
+to be super open to having you.
+
+And again that's
+like your opportunity
+
+to create a window into a
+world that most people don't
+
+have access to.
+
+So definitely take
+advantage of that.
+
+If you have any issues
+getting into a location,
+
+just let me know.
+
+The day before, check
+all your equipment.
+
+Check the batteries,
+that's the biggest thing.
+
+Bring spare batteries.
+
+If you need spare
+batteries let me know.
+
+Double check your locations.
+
+If you're meeting
+people, make sure
+
+that they know
+that you're coming.
+
+And check the weather.
+
+And then day of.
+
+So to help keep you organized
+I recommend that you use
+
+camera reports or log sheets.
+
+And what that looks
+like, and again you
+
+can set this up however you
+think is most useful to you
+
+to use.
+
+These are the camera
+reports that we
+
+use for Science Out Loud.
+
+But basically it's
+to help us keep track
+
+of what video file is what.
+
+And when you're shooting
+like for six days straight,
+
+this is really important.
+
+It may not be as vital to you,
+but it'll be really useful
+
+when you go into edit.
+
+But it's basically saying,
+this video file was scene two,
+
+take two.
+
+I thought it was OK.
+
+There were two good
+takes in there.
+
+The last one was the best.
+
+Make sense to everyone?
+
+Let me know if you
+have any questions.
+
+Yeah.
+
+That's pretty straightforward.
+
+And I would also recommend
+looking at the dailies.
+
+So I guess dailies
+refers to all the footage
+
+that you take during a day.
+
+Like maybe during a movie
+production or a TV production.
+
+And the dailies
+for you guys would
+
+be like, at the
+end of the day look
+
+through all the video footage
+that you have on your camera
+
+and just take note
+of what you shot.
+
+Make sure that it's good.
+
+What you don't want is to
+shoot your entire episode
+
+and realize that the camera
+settings had somehow muted you
+
+and so you didn't
+have any audio.
+
+So that's why looking at
+the dailies is important.
+
+Also back up and label
+all your files like right
+
+after you get back from a shoot.
+
+So the biggest production
+piece of advice,
+
+or like heads up that
+I would give you guys
+
+is that it takes a lot of time.
+
+Even if the
+locations are scouted
+
+and everything's sort of
+organized perfectly the day of,
+
+you're going to take-- you're
+going to do a lot of takes.
+
+Even if the person says
+the line perfectly,
+
+try a bunch of deliveries.
+
+So remember how George
+was saying like,
+
+say it really loud!
+
+Now say it like however
+you want, right?
+
+And you got a different style.
+
+Try a bunch of deliveries.
+
+Try a different bunch of point
+of views with the camera.
+
+So maybe you shoot
+someone straight on,
+
+then you try something
+from the side.
+
+You try a different movement.
+
+And then like try
+different types of framing.
+
+And Chris's piece
+of advice, which
+
+was like, most people tend
+to not get enough footage
+
+than get too much,
+is really true.
+
+Shoot like you're going
+to use everything,
+
+and then when you
+edit, you're going
+
+to edit it like you're not
+going to keep anything.
+
+But when you're
+shooting, you always
+
+want to have more to work with,
+because the worst feeling is
+
+when you're sitting,
+editing, and you're like,
+
+I wish I had shot x y z.
+
+It's the worst feeling.
+
+So it's going to
+take a lot of time,
+
+because you want to create
+as many options for you
+
+as you can.
+
+Any questions about that?
+
+No?
+
+OK.
+
+So I'll show you
+an example of this.
+
+No, one more thing.
+
+A note about clothing, because
+sometimes this comes up.
+
+So in general you don't want
+to have really fine print.
+
+So I always try
+to avoid stripes.
+
+This is probably like
+the closest or the widest
+
+difference in your stripes
+as I would recommend getting.
+
+Generally like solid colors
+work the best on screen.
+
+And then the material,
+bring a couple
+
+different sets of shirts
+with you, because sometimes
+
+like the silkier material
+brushes up against the mic
+
+a little bit more, and you hear
+that actually on the audio.
+
+I will show you some raw
+footage from the snots video.
+
+This is super
+embarrassing for me, so.
+
+But I think it's good.
+
+And maybe will just
+sort of set the tone
+
+that this is a safe
+space where you can feel
+
+like you can just be yourself.
+
+But this was for
+B-roll at the beginning
+
+of the video that
+was literally going
+
+to last-- it's going to last
+one second in the final product.
+
+I literally mean I think it's
+going to be a one second clip.
+
+And this is the amount of
+footage we shot for it.
+
+FEMALE IN VIDEO: --little
+weight is so funny.
+
+MALE IN VIDEO: OK, thank you.
+
+And go.
+
+Put it down and get
+the little weight.
+
+Both hands.
+
+Do the thing where you
+like, you're bringing it
+
+up with your right
+hand, and then
+
+you're sort of like spotting
+it with your left a little bit.
+
+OK.
+
+No, no just two fingers
+on the other hand.
+
+On your hand, on your hand,
+the back of your hand.
+
+Like
+
+FEMALE IN VIDEO: This?
+
+MALE IN VIDEO: Higher.
+
+Turn the weight more.
+
+Yeah.
+
+Just go like this.
+
+Put-- yes, and then like,
+as if you're helping it up.
+
+MALE IN VIDEO 2: [INAUDIBLE]
+just like, supporting it.
+
+MALE IN VIDEO: Yeah, like that,
+but don't take your face out
+
+of frame.
+
+Slower.
+
+Struggle a little bit more.
+
+All right, good.
+
+PROFESSOR: So the
+point of making you
+
+guys endure that is
+that the final clip is
+
+going to be just, right?
+
+Literally a second.
+
+This is at least two
+minutes worth of footage.
+
+This was like the third take.
+
+So this is what I mean by
+get as much as possible.
+
+Try as many different
+things as you can.
+
+Because we could have used the
+first one where I just like
+
+lifted the weight, but the
+last one was really the best
+
+take out of all of them.
+
+And it wasn't-- we
+didn't achieve that.
+
+Or we achieved that
+because George made
+
+me do it for like 10 minutes.
+
+But don't tell him I said that.
+
+So these are all
+the day of things.
+
+Now for the day after,
+take a step back for now.
+
+It's going to be hard to go in
+and edit your stuff like right
+
+after you finish shooting it.
+
+You want to give yourself
+a little bit of time
+
+to sort of clear
+your perspective.
+
+And I'll talk more about this
+during the editing lecture.
+
+But even when you do
+the camera reports
+
+and you're logging sort of what
+the best takes are the day of,
+
+you might watch it
+a couple days later.
+
+And I recommend re-logging
+everything and going
+
+through footage again later.
+
+And you might find that
+the thing that you liked
+
+during the day of,
+maybe you liked it
+
+because you were
+starting to get tired,
+
+and it's going to look a
+little bit different later.
+
+So that's why I just
+recommend the day after,
+
+just taking a step back.
+
+Let's see.
+
+Oh.
+
+With the whole
+multiple takes thing,
+
+I forgot to mention this
+before, but I thought of it when
+
+you were doing your lecture.
+
+I would also
+recommend doing takes
+
+from varying degrees of
+separation from your subject.
+
+So say your host says, I'm
+going to say this line,
+
+and you shoot it from
+where Chris is standing.
+
+Even if the host like
+nails the line perfectly,
+
+tell them to do it again
+and shoot it from maybe
+
+from where Yulia's standing.
+
+And tell them to do it again,
+and shoot it from like right
+
+here.
+
+It's just good to have those
+varying degrees of separation.
+
+It'll be easier to do the
+zooming and everything in post.
+
+But again, having those
+options to work with.
+
+You're not going to
+know which one you're
+
+going to use necessarily in
+the moment that you're filming.
+
+So that's why it's good
+to have a couple options.
+
+GUEST SPEAKER: The term is--
+the technical term, not that it
+
+matters, is called, coverage.
+
+So basically, you
+cover yourself.
+
+I don't really know how I'm
+going to edit this together,
+
+so I'm going to give
+myself as many choices as
+
+possible in the edit room.
+
+Because even the best directors
+don't know exactly what
+
+they want.
+
+I mean there's Alfred Hitchcock
+supposedly only filmed
+
+exactly what he wanted.
+
+And his editors went insane
+because they could only
+
+do one way.
+
+But pretty much
+everyone else who's
+
+ever worked at any level in
+film and video does coverage.
+
+PROFESSOR: Does
+anyone have questions?
+
+The rest of class, we're
+going to let you go actually
+
+film a scene from your script.
+
+And maybe this is a good
+time to take a break,
+
+but Chris and I
+will stick around
+
+if you have questions about
+producing your specific scene,
+
+or actually using
+any of the equipment,
+
+we'll be around to help
+you with that stuff.
+
+AUDIENCE: Can I make one
+other suggestion, or just
+
+reinforce one thing
+about producing.
+
+This comes up over
+and over again,
+
+and it was a very hard lesson
+for me to learn initially.
+
+And that's being realistic
+about your schedule.
+
+You know there's a tendency to
+want to pack a ton of stuff in
+
+and to be very ambitious.
+
+And what happens
+is that you have
+
+to give enough time for setting
+things up, breaking things
+
+down, moving from
+this lab to that lab,
+
+or this location
+of that location,
+
+eating something,
+figuring something out.
+
+So if you go like, well, OK.
+
+This is a 10 minute scene,
+this will take me 20 minutes
+
+to edit.
+
+And then we'll be over at Stata,
+and we'll shoot that two minute
+
+scene in five minutes.
+
+You know, very, very
+quickly get behind schedule,
+
+and then the panic sets in.
+
+It's far better to have a
+schedule that's realistic,
+
+where you really think
+about, not just what it's
+
+going to take to
+shoot, but what it's
+
+going to take to set up,
+breakdown, figure stuff
+
+out, and move.
+
+And then execute the
+schedule in a realistic way
+
+so you're not panicking,
+you're not freaking out,
+
+you're not calling
+people and saying,
+
+I know I said I would
+be at your lab at 3:00
+
+but I can't get there till
+5:00, can you stick around?
+
+You know, whatever it may be.
+
+So just be very realistic.
+
+PROFESSOR: For the
+Science Out Loud episodes,
+
+we allot at least 12 hours
+per five minute episode
+
+in terms of filming
+time with the students.
+
+Now that's a huge number,
+mostly because the thing that's
+
+most time consuming
+for us is setting up
+
+the lights, which is
+something that you're not
+
+going to have to worry about.
+
+The lighting
+actually-- I mean, it's
+
+by far the most time
+consuming thing.
+
+But it gives you
+an idea of-- that's
+
+a really great point I'm
+glad that you made it--
+
+that it's more than
+just the amount
+
+of time it takes for
+you to say a line.
+
+Hopefully you won't
+have that panic,
+
+because the way this
+class is structured,
+
+it's very front heavy.
+
+We've had a lot
+of lectures so far
+
+but after the editing
+lecture, that's
+
+actually the very last one.
+
+And the rest of the
+class period will mostly
+
+be for you to work on
+stuff during class time.
+
+So don't worry too
+much about that.
+
+We tried to anticipate
+that for you guys.
+
+But just to let you know.
+
+I forgot had a couple examples
+for you for some of the stuff
+
+that Chris was mentioning.
+
+And I'll play them real quick.
+
+MALE IN VIDEO: What is the most
+awesome place in the world?
+
+Seems like that would be
+pretty much the most subjective
+
+question ever.
+
+But this week, scientists used
+a set of objective criteria
+
+to come up with a list of
+the world's most biologically
+
+important places.
+
+There might be--
+
+PROFESSOR: So that's an example
+of having zooms, but not
+
+actually showing you zooming
+with the camera, right?
+
+And I think they do it
+for a couple reasons.
+
+He probably-- he might have
+messed up his line in between,
+
+and so that was a way to
+sort of cut in between
+
+and not make the cuts
+like super awkward,
+
+by having a zoom
+in and a zoom out.
+
+And it's sort of like a rhythmic
+visual pacing thing, too.
+
+It cuts in like after he says--
+
+GUEST SPEAKER: It's kind
+of equivalent to, oh,
+
+different angle, pay attention.
+
+It's a different
+convention than television,
+
+but it comes from a
+very similar place.
+
+You know, if he was
+just standing there,
+
+delivering without
+edits, there'd
+
+be this-- there's this terror
+that you might turn away,
+
+and might not watch it.
+
+PROFESSOR: To
+achieve that, though,
+
+if you wanted to do something
+like that, I would say,
+
+again, you could even
+film this with a tripod
+
+and film yourself.
+
+But I would shoot
+yourself-- that sounds
+
+weird-- I would take the camera
+and put it on tripod like that
+
+far away, deliver
+your whole sentence,
+
+and then move it forward and
+deliver the whole thing again.
+
+Because you don't
+know exactly where
+
+you're going to cut into that.
+
+GUEST SPEAKER:
+And that's clearly
+
+what most people--
+I mean, this is
+
+a very conventional thing you
+see on the web all the time.
+
+And that's how they film.
+
+You know, a bunch of takes
+of wide, a bunch of takes
+
+of close, medium, whatever.
+
+Editing.
+
+PROFESSOR: But the
+point is you're
+
+going to be saying the same
+line multiple times, even
+
+if you nail it.
+
+This is where a zoom might work.
+
+[VIDEO PLAYING]
+
+PROFESSOR: So I say, or is it.
+
+But we use the zoom there
+intentionally to make it funny.
+
+Which hopefully it'll read
+funny in the actual thing.
+
+So again, there aren't
+like hard and fast rules
+
+were you should never
+ever use a zoom,
+
+or you should never
+ever center the person,
+
+or you should never ever--
+
+GUEST SPEAKER:
+It's interesting, I
+
+mean, you know, I
+was thinking about
+
+that whole centering thing
+after the other day, Monday.
+
+And a lot of times
+when people break
+
+those kind of traditional
+rules, is for comedic effect.
+
+And center frame stuff
+tends to read funny.
+
+And you see that in
+movies all the time.
+
+If you start paying
+attention to this.
+
+If you go to a comedy, things
+tend to be more center frame
+
+than if it's a drama.
+
+And I think one of the
+reasons that vlogs are often
+
+center framed is that,
+even if they're not funny,
+
+that's the affect.
+
+It's like this is amusing, this
+is light, this is not scary.
+
+And that's why
+people center frame.
+
+And you know, you can, too.
+
+If you want to.
+
+PROFESSOR: All right so, at this
+point I will let you guys free.
+
+Oh, sorry I have
+another thing to say.
+
+The film that
+you've seen today--
+
+the scene that you film today
+won't be due until at least
+
+Tuesday.
+
+If you need more
+time to work on it,
+
+we can push it to
+Wednesday, too.
+
+And that's because I
+really want your focus
+
+to be on honing the script.
+
+Because Monday will
+be our table read,
+
+where everyone reads their
+script aloud to each other.
+
+And you're really going
+to get the most out
+
+of the table read when you
+come to it with as complete
+
+as a script as you can.
+
+I'm not saying that
+what you have on Monday
+
+should be as close to
+final product as possible,
+
+but it's just really hard
+to give concrete feedback
+
+to something that isn't
+fully fleshed out.
+
+So do try to come on Monday
+with as complete of a script
+
+as you can, because Monday is
+going to be the most useful
+
+to you if you do.
+
+So that being said,
+some people have already
+
+uploaded second
+drafts onto Tumblr.
+
+If you could upload stuff
+by tomorrow at noon,
+
+I can give you feedback on it
+so that you can incorporate that
+
+before Monday.
+
+And the best way to
+get feedback from me
+
+is to double post to Tumblr, and
+then also write a Google doc,
+
+and just email it to me, and
+give me commenting permissions.
+
+That's how we actually
+edit all the scripts
+
+from Science Out Loud.
+
+So I'll show you, real quick.
+
+Season two.
+
+Let's go to this one.
+
+Yeah, so this is eventually
+how we asked the students
+
+to format their scripts.
+
+You don't have to
+do that for Monday,
+
+but eventually you're
+going to want to do it.
+
+I think it makes organizing
+things a lot easier.
+
+So it's just like a
+four column format,
+
+where you specify what scene
+number it is, the location.
+
+So OS just means on screen.
+
+It means like you're
+not going to B-roll,
+
+you're just going to
+be delivering it live.
+
+Just a description of
+what the video looks like,
+
+and what the script is itself.
+
+And if you share it
+to me on Google Docs,
+
+it just makes it easier
+for me to comment for you.
+
+And George also said that we
+will give script feedbacks
+
+this weekend too.
+
+So if you can e-mail us this
+stuff by Saturday at noon,
+
+we can give you lots of
+feedback before Monday.
+
+AUDIENCE: I have another tip
+that I usually forget about
+
+because I'm not used to talking
+for long periods of time,
+
+and you guys will probably
+get tired at some point
+
+while filming.
+
+Bring a water bottle
+and probably snacks too,
+
+if you get hungry easily.
+
+Just because when your
+voice gets really dry
+
+and starts cracking, that might
+ruin a take that otherwise
+
+went really, really well.
+
+And it helps with the
+consistency of your voice.
+
+And you can edit
+together something
+
+that you did later with
+something that you did earlier
+
+if your voice sounds
+like consistently fresh
+
+throughout it.
+
+Because I've had problems
+trying to edit audio
+
+where at the end of it, my
+voice is really, really raspy.
+
+And at the beginning
+it's still good.
+
+PROFESSOR: Yeah,
+that's a great point.
+
+I'm glad you brought that up.
+
+So we try to cram
+everything in as much
+
+as we can, which is purely
+because of logistical issues,
+
+and because of our budget.
+
+But you're going
+to have the time
+
+this month to where
+you're not going
+
+to have to shoot your
+entire video in one day.
+
+So really try to spread
+it out over the course
+
+of several days.
+
+And that's built
+into the class time.
+
+But I will just say from
+personal experience,
+
+it is so incredibly difficult
+to film for more than five
+
+or six hours straight.
+
+You just get really, really
+exhausted by the end of it.
+
+OK.
\ No newline at end of file
diff --git a/gMnQ21-pjOA.txt b/gMnQ21-pjOA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2d473d4790d20f0aaee21506e057e0e30b0f105c
--- /dev/null
+++ b/gMnQ21-pjOA.txt
@@ -0,0 +1,1115 @@
+align:start position:0%
+ 
+we're solving this equation for some
+
+ align:start position:0%
+we're solving this equation for some
+ 
+
+ align:start position:0%
+we're solving this equation for some
+potential and since ages formation we
+
+ align:start position:0%
+potential and since ages formation we
+ 
+
+ align:start position:0%
+potential and since ages formation we
+have the result that we mentioned last
+
+ align:start position:0%
+have the result that we mentioned last
+ 
+
+ align:start position:0%
+have the result that we mentioned last
+time that is the eigen function of H are
+
+ align:start position:0%
+time that is the eigen function of H are
+ 
+
+ align:start position:0%
+time that is the eigen function of H are
+gonna form an orthonormal set of
+
+ align:start position:0%
+gonna form an orthonormal set of
+ 
+
+ align:start position:0%
+gonna form an orthonormal set of
+functions that span the space you can
+
+ align:start position:0%
+functions that span the space you can
+ 
+
+ align:start position:0%
+functions that span the space you can
+expand anything of them this is what we
+
+ align:start position:0%
+expand anything of them this is what we
+ 
+
+ align:start position:0%
+expand anything of them this is what we
+prove for a general practitioner
+
+ align:start position:0%
+prove for a general practitioner
+ 
+
+ align:start position:0%
+prove for a general practitioner
+operator to some degree so of the eigen
+
+ align:start position:0%
+operator to some degree so of the eigen
+ 
+
+ align:start position:0%
+operator to some degree so of the eigen
+functions form an orthonormal set that
+
+ align:start position:0%
+functions form an orthonormal set that
+ 
+
+ align:start position:0%
+functions form an orthonormal set that
+spans sponsor space so you define a
+
+ align:start position:0%
+spans sponsor space so you define a
+ 
+
+ align:start position:0%
+spans sponsor space so you define a
+solid one
+
+ align:start position:0%
+solid one
+ 
+
+ align:start position:0%
+solid one
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in this continuous and this is
+
+ align:start position:0%
+and in this continuous and this is
+ 
+
+ align:start position:0%
+and in this continuous and this is
+called the spectrum on the theory
+
+ align:start position:0%
+called the spectrum on the theory
+ 
+
+ align:start position:0%
+called the spectrum on the theory
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because every GI in the states are
+
+ align:start position:0%
+because every GI in the states are
+ 
+
+ align:start position:0%
+because every GI in the states are
+considered the don'ts under if you want
+
+ align:start position:0%
+considered the don'ts under if you want
+ 
+
+ align:start position:0%
+considered the don'ts under if you want
+to find solving a theory means finding
+
+ align:start position:0%
+to find solving a theory means finding
+ 
+
+ align:start position:0%
+to find solving a theory means finding
+energy eigenstates because if you find
+
+ align:start position:0%
+energy eigenstates because if you find
+ 
+
+ align:start position:0%
+energy eigenstates because if you find
+energy eigenstates you can solve you can
+
+ align:start position:0%
+energy eigenstates you can solve you can
+ 
+
+ align:start position:0%
+energy eigenstates you can solve you can
+write any wave function a superposition
+
+ align:start position:0%
+write any wave function a superposition
+ 
+
+ align:start position:0%
+write any wave function a superposition
+of energy eigenstates and just let them
+
+ align:start position:0%
+of energy eigenstates and just let them
+ 
+
+ align:start position:0%
+of energy eigenstates and just let them
+evolve evolve easily but they are just
+
+ align:start position:0%
+evolve evolve easily but they are just
+ 
+
+ align:start position:0%
+evolve evolve easily but they are just
+stationary states on the spectrum of the
+
+ align:start position:0%
+stationary states on the spectrum of the
+ 
+
+ align:start position:0%
+stationary states on the spectrum of the
+field is the collection of numbers that
+
+ align:start position:0%
+field is the collection of numbers that
+ 
+
+ align:start position:0%
+field is the collection of numbers that
+are the allowed energies and of course
+
+ align:start position:0%
+are the allowed energies and of course
+ 
+
+ align:start position:0%
+are the allowed energies and of course
+the associated eigen functions so the
+
+ align:start position:0%
+the associated eigen functions so the
+ 
+
+ align:start position:0%
+the associated eigen functions so the
+energies may be mainly may be discrete
+
+ align:start position:0%
+energies may be mainly may be discrete
+ 
+
+ align:start position:0%
+energies may be mainly may be discrete
+maybe there has a little bit of
+
+ align:start position:0%
+maybe there has a little bit of
+ 
+
+ align:start position:0%
+maybe there has a little bit of
+convenience particles all kinds of
+
+ align:start position:0%
+convenience particles all kinds of
+ 
+
+ align:start position:0%
+convenience particles all kinds of
+varieties but your task is to find those
+
+ align:start position:0%
+varieties but your task is to find those
+ 
+
+ align:start position:0%
+varieties but your task is to find those
+for any problem so the equation that
+
+ align:start position:0%
+for any problem so the equation that
+ 
+
+ align:start position:0%
+for any problem so the equation that
+we're trying to solve is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at it it's a second order
+
+ align:start position:0%
+let's look at it it's a second order
+ 
+
+ align:start position:0%
+let's look at it it's a second order
+differential equation with a potential
+
+ align:start position:0%
+differential equation with a potential
+ 
+
+ align:start position:0%
+differential equation with a potential
+in general so we've had it somewhere
+
+ align:start position:0%
+in general so we've had it somewhere
+ 
+
+ align:start position:0%
+in general so we've had it somewhere
+there it's there it's box so we'll write
+
+ align:start position:0%
+there it's there it's box so we'll write
+ 
+
+ align:start position:0%
+there it's there it's box so we'll write
+it slightly different we move the
+
+ align:start position:0%
+it slightly different we move the
+ 
+
+ align:start position:0%
+it slightly different we move the
+potential to the right hand side and get
+
+ align:start position:0%
+potential to the right hand side and get
+ 
+
+ align:start position:0%
+potential to the right hand side and get
+rid of the constants here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+swear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is equation would have to
+
+ align:start position:0%
+okay so this is equation would have to
+ 
+
+ align:start position:0%
+okay so this is equation would have to
+solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yes strangers you one depending on
+
+ align:start position:0%
+so yes strangers you one depending on
+ 
+
+ align:start position:0%
+so yes strangers you one depending on
+what problems you want to solve so it's
+
+ align:start position:0%
+what problems you want to solve so it's
+ 
+
+ align:start position:0%
+what problems you want to solve so it's
+your choice now we're going to accept in
+
+ align:start position:0%
+your choice now we're going to accept in
+ 
+
+ align:start position:0%
+your choice now we're going to accept in
+fact all of those potentials for our
+
+ align:start position:0%
+fact all of those potentials for our
+ 
+
+ align:start position:0%
+fact all of those potentials for our
+analysis may be nice and smooth they may
+
+ align:start position:0%
+analysis may be nice and smooth they may
+ 
+
+ align:start position:0%
+analysis may be nice and smooth they may
+have discontinuities may have infinite
+
+ align:start position:0%
+have discontinuities may have infinite
+ 
+
+ align:start position:0%
+have discontinuities may have infinite
+discontinuities and worse things like
+
+ align:start position:0%
+discontinuities and worse things like
+ 
+
+ align:start position:0%
+discontinuities and worse things like
+Delta function but worse things than
+
+ align:start position:0%
+Delta function but worse things than
+ 
+
+ align:start position:0%
+Delta function but worse things than
+that we will ignore and there are worse
+
+ align:start position:0%
+that we will ignore and there are worse
+ 
+
+ align:start position:0%
+that we will ignore and there are worse
+things like that may be a potential is
+
+ align:start position:0%
+things like that may be a potential is
+ 
+
+ align:start position:0%
+things like that may be a potential is
+discontinuous at every point or may be
+
+ align:start position:0%
+discontinuous at every point or may be
+ 
+
+ align:start position:0%
+discontinuous at every point or may be
+potential has Delta functions and
+
+ align:start position:0%
+potential has Delta functions and
+ 
+
+ align:start position:0%
+potential has Delta functions and
+derivatives of Delta functions or
+
+ align:start position:0%
+derivatives of Delta functions or
+ 
+
+ align:start position:0%
+derivatives of Delta functions or
+potential the blow-up
+
+ align:start position:0%
+potential the blow-up
+ 
+
+ align:start position:0%
+potential the blow-up
+do all kinds of things but this is and
+
+ align:start position:0%
+do all kinds of things but this is and
+ 
+
+ align:start position:0%
+do all kinds of things but this is and
+I'm not saying you should never consider
+
+ align:start position:0%
+I'm not saying you should never consider
+ 
+
+ align:start position:0%
+I'm not saying you should never consider
+them I'm saying that we don't know any
+
+ align:start position:0%
+them I'm saying that we don't know any
+ 
+
+ align:start position:0%
+them I'm saying that we don't know any
+very useful case will be there anything
+
+ align:start position:0%
+very useful case will be there anything
+ 
+
+ align:start position:0%
+very useful case will be there anything
+interesting but it conceivable a
+
+ align:start position:0%
+interesting but it conceivable a
+ 
+
+ align:start position:0%
+interesting but it conceivable a
+particular kind of singular potential
+
+ align:start position:0%
+particular kind of singular potential
+ 
+
+ align:start position:0%
+particular kind of singular potential
+one we could be so we look at these
+
+ align:start position:0%
+one we could be so we look at these
+ 
+
+ align:start position:0%
+one we could be so we look at these
+potentials and try to understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we try to understand how to set up
+
+ align:start position:0%
+we try to understand how to set up
+ 
+
+ align:start position:0%
+we try to understand how to set up
+boundary conditions and we're going to
+
+ align:start position:0%
+boundary conditions and we're going to
+ 
+
+ align:start position:0%
+boundary conditions and we're going to
+worry about basically sigh how how does
+
+ align:start position:0%
+worry about basically sigh how how does
+ 
+
+ align:start position:0%
+worry about basically sigh how how does
+it behave and my first claim is a sign
+
+ align:start position:0%
+it behave and my first claim is a sign
+ 
+
+ align:start position:0%
+it behave and my first claim is a sign
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Delta function we think of it mr. spy
+
+ align:start position:0%
+so Delta function we think of it mr. spy
+ 
+
+ align:start position:0%
+so Delta function we think of it mr. spy
+is becoming thinner higher Monday the
+
+ align:start position:0%
+is becoming thinner higher Monday the
+ 
+
+ align:start position:0%
+is becoming thinner higher Monday the
+derivative of the Delta function first
+
+ align:start position:0%
+derivative of the Delta function first
+ 
+
+ align:start position:0%
+derivative of the Delta function first
+goes to infinity and then goes to minus
+
+ align:start position:0%
+goes to infinity and then goes to minus
+ 
+
+ align:start position:0%
+goes to infinity and then goes to minus
+infinity it's much worse if you have
+
+ align:start position:0%
+infinity it's much worse if you have
+ 
+
+ align:start position:0%
+infinity it's much worse if you have
+this differential equation and besides
+
+ align:start position:0%
+this differential equation and besides
+ 
+
+ align:start position:0%
+this differential equation and besides
+not continues well the right-hand side
+
+ align:start position:0%
+not continues well the right-hand side
+ 
+
+ align:start position:0%
+not continues well the right-hand side
+is not continues function something not
+
+ align:start position:0%
+is not continues function something not
+ 
+
+ align:start position:0%
+is not continues function something not
+continues but the left-hand side we have
+
+ align:start position:0%
+continues but the left-hand side we have
+ 
+
+ align:start position:0%
+continues but the left-hand side we have
+a derivative of the Delta function that
+
+ align:start position:0%
+a derivative of the Delta function that
+ 
+
+ align:start position:0%
+a derivative of the Delta function that
+there's no part of the right-hand side
+
+ align:start position:0%
+there's no part of the right-hand side
+ 
+
+ align:start position:0%
+there's no part of the right-hand side
+on the right-hand side we were seen the
+
+ align:start position:0%
+on the right-hand side we were seen the
+ 
+
+ align:start position:0%
+on the right-hand side we were seen the
+food sis
+
+ align:start position:0%
+food sis
+ 
+
+ align:start position:0%
+food sis
+is about the function V of X but as the
+
+ align:start position:0%
+is about the function V of X but as the
+ 
+
+ align:start position:0%
+is about the function V of X but as the
+realities of the Delta function doesn't
+
+ align:start position:0%
+realities of the Delta function doesn't
+ 
+
+ align:start position:0%
+realities of the Delta function doesn't
+exist so we can't afford to have a sigh
+
+ align:start position:0%
+exist so we can't afford to have a sigh
+ 
+
+ align:start position:0%
+exist so we can't afford to have a sigh
+that is disappointing possibilities this
+
+ align:start position:0%
+that is disappointing possibilities this
+ 
+
+ align:start position:0%
+that is disappointing possibilities this
+other will argue this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I'll leave it like that
+
+ align:start position:0%
+but I'll leave it like that
+ 
+
+ align:start position:0%
+but I'll leave it like that
+now if now how about the next case I
+
+ align:start position:0%
+now if now how about the next case I
+ 
+
+ align:start position:0%
+now if now how about the next case I
+will say the following particular sorry
+
+ align:start position:0%
+will say the following particular sorry
+ 
+
+ align:start position:0%
+will say the following particular sorry
+prime of X is continuous effects these
+
+ align:start position:0%
+prime of X is continuous effects these
+ 
+
+ align:start position:0%
+prime of X is continuous effects these
+protections will tell the functions are
+
+ align:start position:0%
+protections will tell the functions are
+ 
+
+ align:start position:0%
+protections will tell the functions are
+announcer interesting we will consider
+
+ align:start position:0%
+announcer interesting we will consider
+ 
+
+ align:start position:0%
+announcer interesting we will consider
+that the function potentials can be
+
+ align:start position:0%
+that the function potentials can be
+ 
+
+ align:start position:0%
+that the function potentials can be
+attractive potential possibilities so I
+
+ align:start position:0%
+attractive potential possibilities so I
+ 
+
+ align:start position:0%
+attractive potential possibilities so I
+clean now the site prime of X has to
+
+ align:start position:0%
+clean now the site prime of X has to
+ 
+
+ align:start position:0%
+clean now the site prime of X has to
+also be convinced why are you worrying
+
+ align:start position:0%
+also be convinced why are you worrying
+ 
+
+ align:start position:0%
+also be convinced why are you worrying
+about science i prime is because in
+
+ align:start position:0%
+about science i prime is because in
+ 
+
+ align:start position:0%
+about science i prime is because in
+acute conditions whenever you berlin
+
+ align:start position:0%
+acute conditions whenever you berlin
+ 
+
+ align:start position:0%
+acute conditions whenever you berlin
+solve this differential equation at the
+
+ align:start position:0%
+solve this differential equation at the
+ 
+
+ align:start position:0%
+solve this differential equation at the
+interface you will need to know the size
+
+ align:start position:0%
+interface you will need to know the size
+ 
+
+ align:start position:0%
+interface you will need to know the size
+and second order differential equation
+
+ align:start position:0%
+and second order differential equation
+ 
+
+ align:start position:0%
+and second order differential equation
+so suppose side prime is continuous then
+
+ align:start position:0%
+so suppose side prime is continuous then
+ 
+
+ align:start position:0%
+so suppose side prime is continuous then
+oh there's no problem our site -
+
+ align:start position:0%
+oh there's no problem our site -
+ 
+
+ align:start position:0%
+oh there's no problem our site -
+campinas the worst could happen with a
+
+ align:start position:0%
+campinas the worst could happen with a
+ 
+
+ align:start position:0%
+campinas the worst could happen with a
+potential with useful features
+
+ align:start position:0%
+potential with useful features
+ 
+
+ align:start position:0%
+potential with useful features
+so no problem sigh promise from Jesus
+
+ align:start position:0%
+so no problem sigh promise from Jesus
+ 
+
+ align:start position:0%
+so no problem sigh promise from Jesus
+but site prime can fail to be continuous
+
+ align:start position:0%
+but site prime can fail to be continuous
+ 
+
+ align:start position:0%
+but site prime can fail to be continuous
+if the potential has a delta function
+
+ align:start position:0%
+if the potential has a delta function
+ 
+
+ align:start position:0%
+if the potential has a delta function
+and let's see that
+
+ align:start position:0%
+and let's see that
+ 
+
+ align:start position:0%
+and let's see that
+sorry prime if
+
+ align:start position:0%
+sorry prime if
+ 
+
+ align:start position:0%
+sorry prime if
+Sarang is discontinued
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then sigh double prime site prime is
+
+ align:start position:0%
+then sigh double prime site prime is
+ 
+
+ align:start position:0%
+then sigh double prime site prime is
+discontinuous site prime double prime is
+
+ align:start position:0%
+discontinuous site prime double prime is
+ 
+
+ align:start position:0%
+discontinuous site prime double prime is
+proportional to Delta function but here
+
+ align:start position:0%
+proportional to Delta function but here
+ 
+
+ align:start position:0%
+proportional to Delta function but here
+sigh just take some time it's nothing
+
+ align:start position:0%
+sigh just take some time it's nothing
+ 
+
+ align:start position:0%
+sigh just take some time it's nothing
+strange about it in order to doubt the
+
+ align:start position:0%
+strange about it in order to doubt the
+ 
+
+ align:start position:0%
+strange about it in order to doubt the
+function which is subside double prime
+
+ align:start position:0%
+function which is subside double prime
+ 
+
+ align:start position:0%
+function which is subside double prime
+to be equal to this right hand side V of
+
+ align:start position:0%
+to be equal to this right hand side V of
+ 
+
+ align:start position:0%
+to be equal to this right hand side V of
+X so it would be a singular potential
+
+ align:start position:0%
+X so it would be a singular potential
+ 
+
+ align:start position:0%
+X so it would be a singular potential
+that would even look at them about but
+
+ align:start position:0%
+that would even look at them about but
+ 
+
+ align:start position:0%
+that would even look at them about but
+now this will be our guidance to solve
+
+ align:start position:0%
+now this will be our guidance to solve
+ 
+
+ align:start position:0%
+now this will be our guidance to solve
+problems because the unity of the wave
+
+ align:start position:0%
+problems because the unity of the wave
+ 
+
+ align:start position:0%
+problems because the unity of the wave
+function the limit of the derivative of
+
+ align:start position:0%
+function the limit of the derivative of
+ 
+
+ align:start position:0%
+function the limit of the derivative of
+the wave function and for this slightly
+
+ align:start position:0%
+the wave function and for this slightly
+ 
+
+ align:start position:0%
+the wave function and for this slightly
+more complicated process mention the
+
+ align:start position:0%
+more complicated process mention the
+ 
+
+ align:start position:0%
+more complicated process mention the
+potential has a delta function then you
+
+ align:start position:0%
+potential has a delta function then you
+ 
+
+ align:start position:0%
+potential has a delta function then you
+will have a discontinuity inside Prime
+
+ align:start position:0%
+will have a discontinuity inside Prime
+ 
+
+ align:start position:0%
+will have a discontinuity inside Prime
+it will be calculable it's manageable
+
+ align:start position:0%
+it will be calculable it's manageable
+ 
+
+ align:start position:0%
+it will be calculable it's manageable
+it's all very nice now you do no
+
+ align:start position:0%
+it's all very nice now you do no
+ 
+
+ align:start position:0%
+it's all very nice now you do no
+complicated and everything is kind of
+
+ align:start position:0%
+complicated and everything is kind of
+ 
+
+ align:start position:0%
+complicated and everything is kind of
+mixed up but we will see the bits where
+
+ align:start position:0%
+mixed up but we will see the bits where
+ 
+
+ align:start position:0%
+mixed up but we will see the bits where
+do
\ No newline at end of file
diff --git a/iM4DRgFqPso.txt b/iM4DRgFqPso.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bcff82c1819ff7c9426dcd6f9ba3e946d4188bc1
--- /dev/null
+++ b/iM4DRgFqPso.txt
@@ -0,0 +1,1523 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+HERBERT GROSS: Hi.
+
+Well, I guess we're in the home
+stretch of the course.
+
+We're down to our last concept,
+and it will take us
+
+essentially two lectures to
+cover this new concept.
+
+Today we'll do the concept in
+general and next time we'll
+
+apply it specifically to
+the concept of series.
+
+But the concept we want to talk
+about is something called
+
+'Uniform Convergence'.
+
+Let me say at the outset that
+this is a very subtle topic.
+
+It is difficult.
+
+It seems to be beyond the scope
+of our textbook, because
+
+it's not mentioned there.
+
+Consequently, I will try to give
+the highlights as I speak
+
+with you, but the supplementary
+notes will
+
+contain a more detailed
+explanation of the things that
+
+we're going to talk about.
+
+Now, to set the stage properly
+for our discussion of uniform
+
+convergence, I think it's wise
+that we at least review the
+
+concept of convergence
+in general.
+
+Well, let's take a
+look over here.
+
+Recall that when we write that
+the limit of ''f sub n' of x'
+
+as 'n' approaches infinity
+equals 'f of x' for all 'x' in
+
+the closed interval
+from 'a' to 'b'--
+
+when this happens, another way
+of saying this is that the
+
+sequence 'f sub n', the sequence
+of functions 'f sub
+
+n', converges to the function
+'f' on the closed interval
+
+from 'a' to 'b'.
+
+Now, again, these tend to be
+words unless you look at a
+
+specific example.
+
+Let's just pick one over here.
+
+Let ''f sub n' of x' be
+''n' over '2n plus
+
+1'' times 'x squared'.
+
+Notice, of course, that the
+value of this particular
+
+number depends both
+on 'x' and 'n'.
+
+At any rate, let's pick a fixed
+'x', hold it that way,
+
+and take the limit of
+''f sub n' of x' as
+
+'n' approaches infinity.
+
+In other words, as we let 'n'
+approach infinity in this
+
+case, notice that the limit
+of 'n' over '2n
+
+plus 1' becomes 1/2.
+
+'x' has been chosen
+independently of
+
+the choice of 'n'.
+
+Consequently, the limit function
+in this case, 'f of
+
+x', is 1/2 'x squared'.
+
+And in this case, what we say
+is that the sequence of
+
+functions 'n 'x squared'' over
+'2n plus 1' converges to 1/2
+
+'x squared'.
+
+Now what does this mean
+more specifically?
+
+In other words, let's see if we
+can look at a few specific
+
+values of 'x'.
+
+For example, if I choose
+'x' to be 2--
+
+in other words, if I choose 'x'
+to be 2, if we look over
+
+here, this says that ''f
+sub n' of x' is '4n'
+
+over '2n plus 1'.
+
+If I now take the limit as 'n'
+approaches infinity, I'm going
+
+to wind up with what?
+
+'x' is replaced by 2, 2 squared
+is 4, 1/2 of 4 is 2.
+
+In other words, the limit of ''f
+sub n' of 2', as 'n' goes
+
+to infinity, is 2.
+
+In a similar way, if I replace
+'x' by 4, 1/2 'x
+
+squared' becomes 8.
+
+And so what we have is, at the
+limit, as 'n' approaches
+
+infinity, ''f sub
+n' of 4' is 8.
+
+The key thing being that once
+you choose 'x', notice that
+
+for a fixed 'x', ''f sub n' of
+x' is a constant and you're
+
+now taking the limit of
+a sequence of numbers.
+
+At any rate, here's what
+the key point is.
+
+What does this mean by
+our basic definition?
+
+By our basic definition, it
+means that we can find the
+
+number, capital 'N sub 1', such
+that when 'n' is greater
+
+than capital 'N sub 1', the
+absolute value of ''f sub n'
+
+of 2', minus 2, is less
+than epsilon.
+
+In a similar way, this means
+that we can find the number
+
+capital 'N sub 2' such that
+for any 'n' greater than
+
+capital 'N sub 2', the absolute
+value of ''f sub n'
+
+of 4' minus 8 is also
+less than epsilon.
+
+The key point is that 'N1' and
+'N2' can be different.
+
+In other words, you may have to
+go out further to make this
+
+difference less than epsilon
+than you do to make this
+
+difference less than epsilon.
+
+In other words, you see what's
+happening here-- and we're
+
+going to review this in writing
+in a few minutes, so
+
+that you'll see it
+in front you.
+
+What happens here is that you
+see that for different values
+
+of 'x', we get different
+values of 'n'.
+
+And since there are infinitely
+many values of 'x', it means
+
+that in general, we're going
+to be in a little bit of
+
+trouble trying to find one 'n'
+that works for everything.
+
+And let me show you
+what that means
+
+again, going more slowly.
+
+I simply call this two
+basic definitions.
+
+In other words, if we have a
+sequence of functions 'f sub
+
+n', each of which is defined
+on the closed interval from
+
+'a' to 'b', we say that that
+sequence of functions
+
+converges point-wise--
+
+that means number by number--
+
+to 'f' on [a, b]
+
+if this limit, ''f sub n' of x'
+as 'n' approaches infinity,
+
+equals 'f of x' for
+each 'x' in [a,b].
+
+In other words, given epsilon
+greater than 0, we can find
+
+'N1' such that 'n' greater than
+'N1' implies that the
+
+absolute value of ''f sub n' of
+x1' minus 'f of x1' is less
+
+than epsilon for a given
+'x1' in [a,b].
+
+In general, the choice of 'N1'
+depends on the choice of 'x1',
+
+and there are infinitely many
+such choices to make in [a,b].
+
+Now the key point is this,
+and this is where uniform
+
+convergence comes in.
+
+If we can find one 'N' such that
+whenever little 'n' is
+
+greater than that capital 'N',
+''f sub n' of x' minus 'f of
+
+x' in absolute value is less
+than epsilon for every 'x' in
+
+the closed interval, then
+we say that the
+
+convergence is uniform.
+
+In other words, if we can find
+one 'N' that makes that
+
+difference less than epsilon for
+the entire interval, then
+
+we call the convergence
+uniform.
+
+Now, you see, convergence in
+general is a tough topic.
+
+In particular, uniform
+convergence may seem even more
+
+remote, and therefore what I'd
+like to do now is-- saving the
+
+formal proofs for the
+supplementary notes, let me
+
+show you pictorially just what
+the concept of uniform
+
+convergence really is.
+
+So let me give you a pictorial
+representation.
+
+Let's suppose I have the curve
+'y' equals 'f of x'.
+
+Now, to be within epsilon of 'f
+of x' means I retrace this
+
+curve displaced epsilon units
+above the original position,
+
+and epsilon units below.
+
+In other words, for a given an
+epsilon, I now draw the curve
+
+'y' equals ''f of x' plus
+epsilon' and 'y' equals ''f of
+
+x' minus epsilon'.
+
+Now, what uniform convergence
+means is this, that for this
+
+given epsilon, I can find a
+capital 'N' such that whenever
+
+'n' is greater than capital 'N',
+the curve 'y' equals ''f
+
+sub n' of x' lies in
+this shaded region.
+
+In other words, it can bounce
+around all over, but it can't
+
+get outside of this region.
+
+In other words, once I'm far
+enough out of my sequence, all
+
+of the curves lie in this
+particular region.
+
+Now, of course, the question
+is what does this all mean?
+
+And the answer is--
+well, look.
+
+Let's take epsilon to be, and I
+put this in quotation marks,
+
+"very, very small." Let's take
+epsilon, for example, to be so
+
+small that it's within the
+thickness of our chalk.
+
+If I now do this--
+
+see, I draw the curve
+'y' equals 'f of x'.
+
+Notice now that the thickness of
+my curve itself is the band
+
+width 2 epsilon.
+
+All I'm saying is that for this
+very, very small epsilon,
+
+when 'n' is sufficiently large,
+the curve 'y' equals
+
+''f sub n' of x' appears to
+lie inside of this curve.
+
+You see, in other words, what
+you're saying is that for a
+
+large enough 'n' and small
+enough epsilon--
+
+loosely speaking what you saying
+is that 'y' equals ''f
+
+sub n' of x' looks like 'y'
+equals 'f of x', for a
+
+sufficiently large
+values of 'n'.
+
+In other words, it appears that
+we can't really tell the
+
+n-th curve in the sequence
+from the limit function.
+
+And I want to make a few
+key observations
+
+about what that means.
+
+I've written the whole thing out
+on the blackboard so that
+
+you can see this after I say it,
+but what I want you to see
+
+is, can you begin to get the
+feeling that with this kind of
+
+a condition, for example--
+
+if each 'f sub n' happens to be
+continuous, in other words,
+
+if each member of my sequence
+is unbroken, then the limit
+
+function itself must
+also be unbroken.
+
+Because you see I can squeeze
+this thing down to such a
+
+narrow width that there's no
+room for a break in here.
+
+Also notice that if the curve
+'y' equals ''f sub n' of x' is
+
+caught inside this curve--
+
+if I, for example, were
+computing the area of the
+
+region 'R'--
+
+for a large enough 'n', I
+couldn't tell the difference
+
+in area if I use 'y' equals 'f
+of x' for my top curve, or
+
+whether I use 'y' equals
+''f sub n' of x'.
+
+Well, keep that in mind, and all
+I'm saying is this, that
+
+from our picture, it should
+seem clear that if the
+
+sequence 'f sub n' converges
+uniformly to 'f' on [a, b],
+
+and if each 'f sub n' is
+continuous on [a,b], then--
+
+and this is a fundamental
+result.
+
+Fundamental result one, 'f' is
+also continuous on [a, b].
+
+Now you say, look.
+
+That's what you'd expect, isn't
+it, if every member of
+
+the sequence is continuous?
+
+Why shouldn't the limit function
+also be continuous?
+
+The point is, well, maybe that's
+what you expect, but
+
+note this--
+
+in one of our earlier lectures,
+we already saw that
+
+if we only had point-wise
+convergence, this did not need
+
+to be true.
+
+In particular, recall our
+example in which we defined
+
+''f sub n' of x' to be 'x to
+the n', where the domain of
+
+'f' was the closed interval
+from 0 to 1.
+
+Remember what happened
+in that case?
+
+Each of these 'f sub
+n's is continuous.
+
+But the limit function, you
+may recall, is what?
+
+It's 0 if 'x' is less than
+1, and 1 if 'x' equals 1.
+
+In other words, the limit
+function was discontinuous at
+
+'x' equals 1.
+
+By the way, you might like to
+see what this means from
+
+another point of view.
+
+And let me show you what
+it does mean from
+
+another point of view.
+
+Since 'f' continuous at 'x'
+equals 'x sub 1' means that
+
+the limit of 'f of x' as 'x'
+approaches 'x1' is 'f of x1',
+
+and since 'f of x' itself, by
+definition, is the limit of
+
+''f sub n' of x' as 'n'
+approaches infinity, we may
+
+rewrite our first condition
+in the form-- what?
+
+We may rewrite our first
+equation, this equation here,
+
+in what form?
+
+Limit as 'x' approaches 'x1'
+of limit 'n' approaches
+
+infinity, ''f sub n' of x'.
+
+And that equals the limit as 'n'
+approaches infinity, ''f
+
+sub n' of x1'.
+
+Now keep in mind that since each
+'f sub n' is given to be
+
+continuous, by definition of
+continuity ''f sub n' of x1'
+
+is the same as saying the limit
+as 'x' approaches 'x1',
+
+''f sub n' of x'.
+
+The point I'm making is, if you
+now put this together with
+
+this, it says the rather
+remarkable thing that unless
+
+you have uniform convergence
+when you interchange the order
+
+in which you take the limits
+over here, you may very well
+
+get a different answer.
+
+In other words, when you're
+dealing with non-uniform
+
+convergence, you must be very,
+very careful to perform every
+
+operation in the given order.
+
+What we're saying is what?
+
+This will give you an answer.
+
+This will give you an answer.
+
+But if the convergence is not
+uniform, the answers may be
+
+different, and consequently by
+changing the order you destroy
+
+the whole physical meaning
+of the problem.
+
+Well, again, that's reemphasized
+in the
+
+supplementary notes.
+
+Let me continue on here.
+
+Let me tell you another
+interesting property of
+
+uniform convergence.
+
+Suppose the sequence ''f sub n'
+of x' converges uniformly
+
+to 'f of x' on [a, b].
+
+The point that's rather
+interesting is that you can
+
+reverse the order of integration
+and taking the
+
+limit in this particular case.
+
+In other words, suppose you want
+to compute the integral
+
+of the limit function
+from 'a' to 'b'.
+
+What you can do instead is
+compute the integral of the
+
+n-th number of your sequence,
+and then take the limit as 'n'
+
+goes to infinity.
+
+In other words, rewriting this,
+it says that if you have
+
+uniform convergence, you can
+take the limit inside the
+
+integral sign.
+
+And again, these results
+are proven in our
+
+supplementary notes.
+
+We also say a few words about
+corresponding results for
+
+differentiation in our
+supplementary notes.
+
+And I should point out that
+differentiation is a far more
+
+subtle thing than integration.
+
+See, remember that for
+integration, all you need is
+
+continuity.
+
+For differentiation, you
+need smoothness.
+
+The point is that as you put a
+thin band around the function
+
+'y' equals 'f of x' when you
+have uniform convergence,
+
+that's enough to make sure that
+the limit function must
+
+be continuous if each of the
+members in the sequence is
+
+continuous.
+
+But without going into the
+details of this thing, it does
+
+turn out that for the degree of
+smoothness that you need,
+
+these things can jump around
+enough so that for
+
+differentiation, we do have to
+be a little bit more careful.
+
+Rather than to becloud the
+issue, I will stick with
+
+integration topics for
+our lecture today.
+
+Now, the other thing that I want
+to mention is, again, in
+
+terms of doing what comes
+naturally, I think we are
+
+tempted to look at something
+like this and say, look, all I
+
+did was bring the
+limit inside.
+
+Why can't I do that?
+
+And instead of saying, look,
+you can't, I think the best
+
+thing to show is that when
+you don't have uniform
+
+convergence, you get two
+different answers.
+
+Again, the idea being what?
+
+We are not saying that
+you can't do this.
+
+We are not saying that you
+can't compute this.
+
+All we're saying is that if
+the convergence is not
+
+uniform, these two expressions
+may very well
+
+name different numbers.
+
+Now, to show you what I have in
+mind here, let me give you
+
+an example.
+
+See, to show you that 2 need not
+be true if the convergence
+
+is not uniform, consider
+the following example.
+
+Now, in the supplementary notes,
+I repeat this example
+
+both the way I have it on the
+board and also from an
+
+algebraic point of view, without
+using the pictures.
+
+But in terms of the picture,
+here's what we do.
+
+We define a function on the
+closed interval from 0 to 2,
+
+which I'll call 'f sub
+n', as follows.
+
+For a given 'n', I will locate
+the points '1/n' and '2/n'.
+
+For example, if 'n' happened to
+be 50, this would be 1/50
+
+and this would be 2/50.
+
+Now what I do, is at the 'x'
+value '1/n', I take as the
+
+corresponding y-value,
+'n squared'.
+
+And I draw the straight line
+that goes from the origin to
+
+this point, '1/n' comma
+'n squared'.
+
+Then I draw the straight line
+that comes right back to the
+
+x-intercept, '2/n', and I finish
+off the curve by just
+
+letting it hug the x-axis till
+we get over to 'x' equals 2.
+
+I'll come back to this on the
+next board, to show you why I
+
+chose this, but let's make a few
+observations just to make
+
+sure that you understand what
+this function looks like.
+
+I'll just make a few arbitrary
+remarks about it.
+
+First of all, for each
+'n', ''f sub n' of
+
+'1/n'' is 'n squared'.
+
+That's just another way
+of indicating a
+
+label for this point.
+
+Secondly, my claim is that for
+any number 'x sub 0', if 'x
+
+sub 0' is greater than '2/n',
+''f sub n' of x0' must be 0.
+
+And the reason for that
+is quite simple.
+
+I'm just trying to show you
+how to read this picture.
+
+Namely, notice that as soon as
+'x' gets to be as great as
+
+'2/n', the 'f' value is 0,
+because the function is
+
+hugging the x-axis.
+
+And just as a final observation,
+notice that when
+
+'x sub 0' is 0, ''f sub n' of 0'
+is 0 for every 'n', meaning
+
+that every member of my family
+of functions goes through this
+
+particular point.
+
+In other words, let me
+just label this.
+
+This is 'y' equals
+''f sub n' of x'.
+
+Well, by the way if ''f sub n'
+of 0' is 0 for each 'n', in
+
+particular the limit of ''f sub
+n' of 0' as 'n' approaches
+
+infinity is 0.
+
+What happens if we pick
+a non-zero value?
+
+For example, suppose I pick 'x0'
+to be greater than 0 but
+
+less than or equal to 2?
+
+The key point is this, that
+since the limit of '2/n' as
+
+'n' approaches infinity is 0,
+given a value of 'x0' which is
+
+not 0, I can find the capital
+'N' such that when 'n' is
+
+greater than capital 'N',
+'2/n' is less than 'x0'.
+
+In other words, if 'x0' is
+greater than 0, and '2/n'
+
+approaches 0, for large enough
+values of 'n', '2/n'
+
+be less than 'x0'.
+
+In particular, when that
+happens, if we couple this
+
+with our earlier observation--
+
+what earlier observation?
+
+Well, this one.
+
+If we couple that with our
+earlier observation, we see
+
+that when 'n' is greater than
+capital 'N', ''f sub
+
+n' of x0' is 0.
+
+Correspondingly, then, the limit
+of ''f sub n' of x0' as
+
+'n' approaches infinity,
+by definition, is 0.
+
+In other words--
+
+I'm going to reinforce this
+later, but notice that the
+
+limit function here is
+the function which
+
+is identically 0.
+
+Now, since this may look very
+abstract to you, let me take a
+
+few minutes--
+
+and I hope this doesn't insult
+your intelligence, but let me
+
+just take a few minutes and
+redraw this for a couple of
+
+different values of 'n', just
+so that you can see what's
+
+starting to happen here.
+
+Keep that picture in mind, and
+now look what this means.
+
+For example, when 'n' is 1,
+'1/n' is 1, '2/n' is 2, 'n
+
+squared' is 1.
+
+In other words, the graph 'y'
+equals 'f1 of x' is just this
+
+triangular--
+
+just this.
+
+Why give it a name?
+
+Well, let's try a tougher one.
+
+Let's see what the member
+'f sub 20' looks like.
+
+Recall how you draw this, now.
+
+With the subscript 20,
+what do you do?
+
+You come in to the point
+1/20, and at that
+
+point, you do what?
+
+You locate the point 1/20
+comma 'n squared'.
+
+In this case, it's 400.
+
+And I have obviously haven't
+drawn this to scale, but you
+
+now do what?
+
+Draw the straight line
+that goes from the
+
+origin to this point.
+
+Then from this point, you draw
+the straight line that comes
+
+back to the x-axis, hitting
+it at 'x' equals 1/10.
+
+And then you come across
+the x-axis all the way
+
+to 'x' equals 2.
+
+This would be the graph of 'y'
+equals ''f sub 20' of x'.
+
+And by the way, do you sense
+what's happening over here?
+
+See, notice that as 'n' gets
+very, very large, the curve
+
+hugs the x-axis, starting
+in closer and
+
+closer to the y-axis.
+
+But what happens is someplace
+in here, no matter how close
+
+'x sub 0' is to 0, there
+comes a very high peak.
+
+In fact, what is
+that high peak?
+
+It's 'n squared'.
+
+In other words, when this number
+is very close to the
+
+y-axis, the peak is
+very, very high.
+
+In other words, no matter how
+you put the squeeze on over
+
+here, this particular
+peak jumps out.
+
+This is why this particular
+sequence of functions is not
+
+uniformly convergent.
+
+Again, this is done more
+slowly in the notes.
+
+But at any rate, let me show you
+an interesting thing that
+
+happens over here.
+
+Let me redraw this now
+for a general 'n'.
+
+In other words, let me draw 'y'
+equals ''f sub n' of x'
+
+for any old 'n'.
+
+Recall what our definition
+was, now, especially
+
+with this as review.
+
+We locate the point '1/n'
+comma 'n squared'.
+
+We then draw the line
+that goes from the
+
+origin to that point.
+
+Then we draw the line that goes
+from that point back to
+
+the x-axis at the point '2/n'.
+
+And then we come across
+to 'x' equals 2.
+
+Let's try to visualize what the
+integral from 0 to 2, ''f
+
+sub n' of x', 'dx', means.
+
+After all, in a case of a
+continuous curve, which this
+
+is, isn't the definite integral
+interpreted just as
+
+the area under the curve?
+
+Well, you see, the curve
+coincides with the x-axis from
+
+'2/n' on to 2.
+
+Consequently, this triangular
+region which I call 'R' is the
+
+area under the curve.
+
+In other words, the integral
+from 0 to 2, ''f sub n' of x',
+
+'dx', is the area of
+the region 'R'.
+
+But here's the point.
+
+We can compute the area of the
+region 'R' very easily.
+
+It's a triangle, right?
+
+What is the area
+of a triangle?
+
+Well, it's 1/2 times
+the base--
+
+but the base is just '2/n'--
+
+times the height.
+
+The height is 'n squared'.
+
+In other words, the area of the
+region 'R' simply is 'n'.
+
+And that's rather interesting.
+
+In other words, for each 'n',
+this particular integral just
+
+turns out to be 'n' itself.
+
+That's what's interesting about
+this particular diagram.
+
+In other words, this thing rises
+so high that even though
+
+the base gets very, very small
+as 'n' gets large, the height
+
+increases so rapidly that the
+area under this curve,
+
+numerically, is always
+equal to 'n'.
+
+In fact, we can check
+that if you'd like.
+
+Come back to this
+particular case.
+
+Look at this particular
+triangle.
+
+The base is 2, the
+height is 1.
+
+The area is 1 unit.
+
+Look at this particular
+triangle.
+
+The base is 1/10, the
+height is 400.
+
+400 times 1/10 is 40, and
+half of that is 20.
+
+The area of this triangle
+is 20, which exactly
+
+matches this subscript.
+
+That's what's going to happen
+here all the time.
+
+In particular, then, if we
+compute the integral from 0 to
+
+2, 'f of n', 'x dx', and then
+let the limit as 'n' goes to
+
+infinity be computed, what
+do we get for an answer?
+
+We get that this limit is the
+limit of 'n' as 'n' approaches
+
+infinity, and that of
+course is infinity.
+
+On the other hand, suppose we
+bring the limit inside?
+
+In other words, suppose
+we compute this.
+
+Well, the point is that we have
+already shown that this
+
+is identically 0 for all 'x'.
+
+Consequently, this integral is
+the integral from 0 to 2, 0
+
+'dx', which is 0.
+
+In other words, if you first
+take the limit and then
+
+integrate, you get 0.
+
+On the other hand, if you first
+integrate and then take
+
+the limit, you get infinity.
+
+And this should be a glaring
+example to show you that the
+
+answer that you get indeed does
+depend on the order in
+
+which you do the operation.
+
+Again, let me emphasize--
+
+which of these two is wrong?
+
+The answer is, neither
+is wrong.
+
+All we're saying is that if
+you were supposed to solve
+
+this problem and by mistake you
+solve this one, you are
+
+going to get a drastically
+different answer.
+
+OK.
+
+Let's not beat this to death.
+
+So far, so good.
+
+Let me make one more remark,
+namely, what does all of this
+
+have to do with the
+study of series?
+
+See, now we're just talking
+about sequences of functions.
+
+And you see, the answer to this
+question is essentially
+
+going to be our last lecture
+of the course.
+
+But for now, what I'd like
+to do is to give you
+
+a preview of that.
+
+Namely, the application of
+uniform convergence to series
+
+is the following.
+
+Recall that when we write
+summation 'n' goes from 0 to
+
+infinity, 'a sub n', 'x
+to the n', that's an
+
+abbreviation for what?
+
+A polynomial, 'k' goes from 0 to
+'n', 'a sub k', 'x sub k',
+
+as 'n' goes to infinity.
+
+In other words, recall that
+the sum of the series is a
+
+limit of a sequence of partial
+sums, and this is the n-th
+
+member of that sequence
+of partial sums.
+
+Again, if the sigma notation is
+throwing you off, all I'm
+
+saying is to observe that 'a0'
+plus 'a1 x' plus 'a2 'x
+
+squared'' plus-- et cetera, et
+cetera, et cetera, forever,
+
+just represents the limit of
+the following sequence.
+
+'a0', next member is
+'a0 plus a1 x'.
+
+Next member is 'a0' plus 'a1
+x' plus 'a2 'x squared''.
+
+The next member is 'a0' plus 'a1
+x' plus 'a2 'x squared''
+
+plus 'a3 'x cubed''.
+
+By the way, what is each
+member of the sequence?
+
+It's a polynomial.
+
+And polynomials have very
+nice properties,
+
+among which are what?
+
+Well, a polynomial is a
+continuous function.
+
+A polynomial is an integral
+function, et cetera.
+
+The idea, therefore, is that
+if this sequence of partial
+
+sums converges uniformly to the
+limit function, then, for
+
+example, the limit function,
+namely the power series, must
+
+be continuous since each partial
+sum that makes up the
+
+sequence of partial sums
+is also continuous.
+
+Namely, every polynomial
+is continuous.
+
+Also, if, for some reason or
+other, you want to integrate
+
+that power series from 'a' to
+'b', if the convergence is
+
+uniform, I can then do what?
+
+I can then take the summation
+sign outside, integrate the
+
+n-th partial sum, and
+add these all up.
+
+You see, the idea being what?
+
+That the n-th partial sum is a
+polynomial, and a polynomial
+
+is a particularly simple
+thing to integrate.
+
+That's one of the easiest
+functions to
+
+integrate, in fact.
+
+OK.
+
+Now, here's the wrap up, then.
+
+What we shall show next time is
+that within the interval of
+
+absolute convergence, the
+sequence of partial sums,
+
+which we already know converges
+absolutely to the
+
+limit function, also converges
+uniformly.
+
+In other words, within the
+radius of convergence, the
+
+power series--
+
+and I don't know how to say
+this other than to say, it
+
+enjoys the usual polynomial
+properties associated with a
+
+polynomial such as summation 'k'
+goes from 0 to 'n', 'a sub
+
+k', 'x to the k'.
+
+In other words, then, this
+about wraps up what our
+
+introductory lecture for today
+wanted to be, namely the
+
+concept of uniform
+convergence.
+
+What I would like you to do now
+is to study this material
+
+very carefully in the
+supplementary notes, go over
+
+the learning exercises so that
+you become familiar with this.
+
+Then we will wrap up our course
+in our next lecture,
+
+when we show what a very, very
+powerful tool this particular
+
+concept of absolute convergence
+is in the study of
+
+the mathematical concept
+of convergence.
+
+At any rate, until next
+time, then, goodbye.
+
+Funding for the publication of
+this video was provided by the
+
+Gabriella and Paul Rosenbaum
+Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/iRh3Kpgg0Uc.txt b/iRh3Kpgg0Uc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab598317b915b2d9cd9f2afc2320c5ff42ed8a6e
--- /dev/null
+++ b/iRh3Kpgg0Uc.txt
@@ -0,0 +1,407 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT Open
+Courseware continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT Open Courseware at
+
+ocw.mit.edu.
+
+Hi I'm Jocelyn and today we're
+going to go over fall 2009
+
+exam 1, problem 1.
+
+So to begin with, we
+always want to
+
+read the whole problem.
+
+So in this one it says uranium
+metal can be produced by the
+
+reaction of uranium
+tetrafluoride with magnesium
+
+in a sealed reactor heated
+to 700 degrees C.
+
+So we know that we're dealing
+with a chemical reaction here.
+
+The byproduct is magnesium
+fluoride.
+
+To ensure that all the magnesium
+is consumed in the
+
+reaction, the reactor is charged
+with excess uranium
+
+fluoride, specifically 10% more
+than the stoichiometric
+
+requirement of the reactor.
+
+To produce 222 kilograms of
+uranium, how much uranium
+
+tetrafluoride must be introduced
+into the reactor?
+
+So that's what the question
+is asking us.
+
+Then it says we assume complete
+conversion of
+
+magnesium, express your
+answer in kilograms.
+
+So we know that the question is
+asking us for the uranium
+
+tetrafluoride needed to make
+222 kilograms of uranium.
+
+Right?
+
+That's the last sentence.
+
+The sentence that's before that,
+however, also gives us
+
+very important information.
+
+It tells us that we need
+the stoichiometric
+
+equivalent plus 10%.
+
+And that's very important to
+keep in mind because, as
+
+you'll see later, that's where a
+lot of people got tripped up
+
+on this problem.
+
+So then let's go to the first
+two sentences in this problem
+
+and extract the information
+given there.
+
+We know that we're dealing
+with a chemical reaction.
+
+So when we are dealing with one
+of those we always want to
+
+put down the chemical
+equation.
+
+So we have uranium tetrafluoride
+reacting with
+
+magnesium to give uranium
+with a byproduct
+
+of magnesium fluoride.
+
+And it tells us that it that
+it's at 700 degrees C.
+
+That's superfluous information
+but you can always put
+
+reaction conditions above the
+arrow just to keep track.
+
+So now that we have this
+equation are we
+
+ready to move on?
+
+No.
+
+Right?
+
+We need to have a mass
+conservation.
+
+We need to balance
+this equation.
+
+So to determine if this is
+balanced or not, we want to
+
+keep track of the amount of
+uranium, fluoride and
+
+magnesium on each side
+of the equation.
+
+So we have uranium, fluoride
+and magnesium.
+
+And then we have on
+the product side--
+
+and that's not right.
+
+This is the reactant
+side, right?
+
+And over here is the
+product side.
+
+So on the reactant side we have
+1 uranium, 4 fluoride and
+
+1 magnesium.
+
+On the product side we
+have 1 uranium, 2
+
+fluoride and 1 magnesium.
+
+So we see that we have an
+imbalance in fluoride.
+
+To fix that we can put a
+stoichiometric coefficient in
+
+front of the magnesium fluoride
+on the product side
+
+in order to have 4 fluorides.
+
+We put a 2 there.
+
+And we change that to 2.
+
+But we also have to change
+the magnesium.
+
+Right?
+
+Now, although we fixed the
+problem in the fluoride, we
+
+have an imbalance in
+the magnesium.
+
+So to fix that, we put a
+stoichiometric coefficient in
+
+front of the magnesium, switch
+our accounting down here, and
+
+we see that we now have
+conservation of mass.
+
+The two sides are balanced.
+
+So with our balanced equation we
+can now move on to what the
+
+question is actually
+asking us.
+
+And we know that we have,
+we want to make 222
+
+kilograms of uranium.
+
+We then need to figure
+out how much uranium
+
+tetrafluoride is needed.
+
+This chemical reaction
+gives us mole ratios.
+
+But we are, right now, have
+kilograms. So the first thing
+
+we need to do is convert
+kilograms to moles.
+
+And we do that using
+stoichiometry or unit
+
+conversion.
+
+So the other thing we
+need to know is the
+
+molar mas of uranium.
+
+So this is something you can
+look up on your periodic
+
+table, online, whatever
+resources you have available.
+
+So the molar mass of uranium
+is 238 grams per mole.
+
+Now we just do a simple unit
+conversion to get the moles
+
+uranium that we want.
+
+So first we need to convert to
+grams. That's 1,000 grams. And
+
+then using the molar mass,
+we convert to moles.
+
+And because I have grams up
+top here I need to put the
+
+molar grams down here in order
+to cancel everything out.
+
+And that gives us 933
+moles uranium.
+
+OK so we have the number of
+moles uranium we want to make.
+
+Now we can use the chemical
+equation over here to
+
+determine how much uranium
+tetrafluoride we need.
+
+So the chemical equation tells
+us that we need a 1:1 ratio of
+
+uranium tetrafluoride.
+
+However this is where we need to
+go back to what the problem
+
+was actually asking us.
+
+And remember that we need the
+stoichiometric equivalent,
+
+which is given by this
+mole ratio, plus 10%.
+
+So the amount of uranium
+tetrafluoride we need is the
+
+stoichiometric equivalent plus
+10% times that stoichiometric
+
+equivalent.
+
+And that equals 1,026 moles
+of uranium tetrafluoride.
+
+So we found the amount of
+uranium tetrafluoride we need.
+
+Are we done?
+
+No.
+
+Right?
+
+If we go back to the question
+we see that it asks for our
+
+answer expressed in kilograms.
+So that's why it's always
+
+important to keep track of what
+the question is actually
+
+asking you and to make sure
+you've answered that.
+
+So we have uranium tetrafluoride
+in moles.
+
+Now we need to convert it to
+kilograms. Again we need the
+
+molar mass.
+
+This time of uranium
+tetrafluoride.
+
+And it equals--
+
+so we have 1 uranium per
+molecule and 4 fluoride.
+
+And again we just look up that
+molar mass of fluoride on the
+
+periodic table.
+
+And that equals 314
+grams per mole.
+
+So we do our unit conversion
+again.
+
+And this is my favorite way of
+doing stoichiometry unit
+
+conversions.
+
+You may have another way that
+you learned in high
+
+school or later on.
+
+But this way I know that I'm
+keeping track of my units and
+
+everything's canceling
+out correctly.
+
+So we have 1,026 moles uranium
+tetrafluoride.
+
+We use the molar mass
+we just determined.
+
+And remember that this is an
+industrial scale process, so
+
+we actually care about the
+amounts in kilograms. And we
+
+get 322 kilograms uranium
+tetrafluoride.
+
+Going back to what the question
+was asking us, we
+
+know that we now have
+the correct answer.
+
+And we can put a
+box around it.
+
+So that on the exam whoever's
+grading you knows that that is
+
+your answer.
\ No newline at end of file
diff --git a/ibFeUX5F_fw.txt b/ibFeUX5F_fw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..044ef19a1d6391d050aa6e9269a3bd29c64bad99
--- /dev/null
+++ b/ibFeUX5F_fw.txt
@@ -0,0 +1,574 @@
+Hi.
+
+In this problem, we're going
+to practice setting up a
+
+Markov chain by going fishing in
+this lake, which has n fish
+
+in it, some of which
+are green.
+
+And the rest of the
+fish are blue.
+
+So, what we do is, every day
+we go to this lake, and we
+
+catch exactly 1 fish.
+
+And all the fish are equally
+likely to be
+
+the 1 that's caught.
+
+Now, if we catch a green fish,
+we paint it blue, and we throw
+
+back into the lake.
+
+And if we catch a blue fish, we
+just keep it blue, and we
+
+also throw it back.
+
+Now, what we're interested in
+modeling is, how does this
+
+lake evolve over time?
+
+And specifically what we're
+interested in is the number of
+
+green fish that are
+left in the lake.
+
+So, let's let Gi be the event
+that there are i green fish
+
+left in the lake.
+
+And we want to know, how does
+Gi evolve over time?
+
+Now, one thing that we've
+learned that we can use to
+
+model this is a Markov chain.
+
+But before we can use it, we
+need to make sure that this
+
+actually satisfies the
+Markov property.
+
+Now, recall that the Markov
+property essentially says
+
+that, given the current state of
+the system, that's all you
+
+need in order to predict
+the future states.
+
+So, any past history of the
+previous states that it was
+
+in, that's all irrelevant.
+
+All you need is the
+current state.
+
+Now, in the context of this
+particular problem, what that
+
+means is that if I tell you that
+there are 10 green fish
+
+left, that's all the information
+you need in order
+
+to predict how many fish
+there will be tomorrow.
+
+So, why is that?
+
+Well, it's because what
+influences the number of green
+
+fish that are left?
+
+What influences it is which
+fish you catch because,
+
+depending on which fish you
+catch, you may paint the green
+
+fish blue, in which case the
+number of green fish decrease.
+
+But what affects which
+fish you catch?
+
+Well, that probability is
+dictated solely based on just
+
+the number of green fish in
+the lake right now, today.
+
+So, it doesn't matter that there
+were 20 fish yesterday.
+
+All that matters is how many
+green fish there are in the
+
+lake today.
+
+And so, because of that
+argument, the
+
+number of green fish--
+
+this does satisfy the Markov
+property, so we can use this
+
+and model it as a
+Markov chain.
+
+So, like we alluded to just now,
+the key dynamic that we
+
+need to look at is, how
+does the number
+
+of green fish change?
+
+And if we look at it, we notice
+that after each day,
+
+the number of green fish can
+only have two possible
+
+transitions.
+
+One possible transition is that
+it goes down by exactly
+
+1, which happens if you happen
+to catch a green fish and
+
+paint it blue.
+
+So, that green fish is no longer
+green, so the number of
+
+green fish goes down by 1.
+
+The other possible transition
+is that Gi doesn't change
+
+because you caught a
+blue fish that day.
+
+So, all the green fish
+are still green.
+
+So, now given that, let's see
+if we can come up with a
+
+Markov chain.
+
+So, the first thing we've done
+is we've written down all the
+
+different states, right?
+
+So, this represents the
+number of green
+
+fish left in the lake.
+
+So, there could be 0 green fish
+left, 1 green fish, all
+
+the way through n, which means
+that every single fish in the
+
+lake is green.
+
+Now, we have the states.
+
+What we need to do now is to
+fill in the transition
+
+probabilities, which
+are the Pij's.
+
+And remember, the Pij is the
+probability of transitioning
+
+from state i to state j in
+the next transition.
+
+So, what that means in this
+context is, what's the
+
+probability that there will be
+j green fish tomorrow given
+
+that there are i green
+fish today?
+
+ 
+
+Now, if we go back to our
+earlier argument, we see that
+
+for any given i, you can
+only transition to
+
+two possible j's.
+
+One of them is you stay at i
+because the number of green
+
+fish doesn't change because
+you caught a blue fish.
+
+And the other is that you'd
+go from i to i minus 1.
+
+ 
+
+The number of green fish
+decreases by 1.
+
+Now, what we need to do now
+is fill in what those
+
+probabilities are.
+
+So, if j equals i, meaning that
+the number of green fish
+
+doesn't change, well, what's the
+probability that you have
+
+the same number of green fish
+tomorrow as you do today?
+
+Well, if you have i green fish
+today, that happens if you
+
+catch 1 of the n minus
+i blue fish.
+
+So, what's the probability
+of catching one of the n
+
+minus i blue fish?
+
+Well, it's n minus i over n.
+
+Now, the other possible
+transition is you go from a i
+
+to j equals i minus 1,
+so i goes down by 1.
+
+And that happens when you
+catch a green fish.
+
+So, given that there are i
+green fish, what's the
+
+probability that you
+catch 1 of those?
+
+Well, it's going to be i/n.
+
+And finally, every other
+transition has 0 probability.
+
+All right.
+
+So, now we can add those
+transitions on
+
+to our Markov chain.
+
+So, for example,
+we have these.
+
+So, let's look at this
+general case i.
+
+So, if you're state i, you
+have i green fish left.
+
+You will transition to i minus
+1 green fish left if that day
+
+you caught a green fish.
+
+And we said that that
+probability is i/n.
+
+And the self transition
+probability is you caught a
+
+blue fish that day, so you still
+stay a i green fish.
+
+And that probability, we said,
+was n minus i over n.
+
+All right.
+
+Now, it's helpful to verify
+that this formula works by
+
+looking at some cases where it's
+intuitive to calculate
+
+what these probabilities
+should be.
+
+So, let's look at state n.
+
+That is the state where
+every single fish
+
+in the lake is green.
+
+So, if ever single fish in the
+lake is green, then no matter
+
+what fish you catch, it's
+going to be green.
+
+And you're going to paint it
+blue and return it, so you're
+
+guaranteed to go down to
+n minus 1 green fish.
+
+And so, this transition
+probability down to n minus 1
+
+is guaranteed to be 1.
+
+And so, the self transition
+probability has to be 0.
+
+Now, let's go back to our
+formula and verify that
+
+actually gives us
+the right value.
+
+So, if i is n, then there's
+only these transition
+
+probabilities.
+
+So, if i is n, then the
+transition probability to j,
+
+for j is also n, is n minus
+n over n, which is 0.
+
+And that's exactly
+what we said.
+
+We argued that the
+self transition
+
+probability should be 0.
+
+And also, if i is in, the
+probability of transitioning
+
+to n minus 1 should be
+n over n, which is 1.
+
+And that's exactly what
+we argued here.
+
+So, it seems like these
+transition probabilities do
+
+make sense.
+
+And if we wanted to, we could
+fill in the rest of these.
+
+So, for example, this would be
+2/n, 1/n, n minus 1 over n, n
+
+minus 2 over n.
+
+And now, let's also consider
+the case of state 0, which
+
+means that every single
+fish is blue.
+
+There are 0 green fish left.
+
+Well, if that's the case, then
+what's the probability of
+
+staying at 0?
+
+Well, that's n minus 0 over
+n is 1, all right?
+
+So, the self transition
+probability is 1.
+
+And that makes sense because
+if you have 0 green fish,
+
+there's no way to generate more
+green fish because you
+
+don't paint blue fish green.
+
+And so, you're going to stay
+at 0 green fish forever.
+
+All right.
+
+So, we've characterized the
+entire Markov chain now.
+
+And so, now let's just
+answer some simple
+
+questions about this.
+
+So, the problem asks us to
+identify, what are the
+
+recurrent and transient
+states?
+
+So, remember that recurrent
+state means that if you start
+
+out at that state, no matter
+where you go, what other
+
+states you end up at, there is
+some positive probability path
+
+that will take you back to
+your original state.
+
+And if you're not recurrent,
+then you're transient, which
+
+means that if you're transient,
+if you start out at
+
+the transient state, there is
+some other state that you can
+
+go to, from which there's no
+way to come back to the
+
+original transient state.
+
+All right.
+
+So, now let's look at this and
+see which states are recurrent
+
+and which are transient.
+
+And we can fill this in more.
+
+ 
+
+And if we look at it, let's
+look at state n.
+
+Well, we're guaranteed
+to go from state n to
+
+state n minus 1.
+
+And once we're in state n minus
+1, there's no way for us
+
+to go back to state
+n because we can't
+
+generate more green fish.
+
+And so, n is transient.
+
+And similarly, we can use the
+same argument to show that
+
+everything from 1 through n,
+all of these states, are
+
+transient for the same reason
+because there's no way to
+
+generate more green fish.
+
+And so, the chain can
+only stay at a given
+
+state or go down 1.
+
+And so, it always goes down.
+
+It can only go left, and
+it can never go right.
+
+So, once you leave a certain
+state, there's
+
+no way to come back.
+
+And so, states 1 through
+n are all transient.
+
+And 0 the only recurrent state
+because, well, the only place
+
+you go from 0 is itself.
+
+So, you always stay at 0.
+
+And in fact, 0 is not only
+recurrent, it's absorbing
+
+because every single other
+state, no matter where you
+
+start out at, you will
+always end up at 0.
+
+So, this was just an
+example of how to
+
+set up a Markov chain.
+
+You just think about the actual
+dynamics of what's
+
+going on and make sure that it
+satisfies the Markov property.
+
+Then, figure out what all the
+states are and calculate all
+
+the transition probabilities.
+
+And once you have that, you've
+specified your Markov chain.
\ No newline at end of file
diff --git a/idZoHI9dLsk.txt b/idZoHI9dLsk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..72af6a58bb52293a30ed3936e258c3d70a2af684
--- /dev/null
+++ b/idZoHI9dLsk.txt
@@ -0,0 +1,5539 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tonight I want to try to pose the basic
+
+ align:start position:0%
+tonight I want to try to pose the basic
+ 
+
+ align:start position:0%
+tonight I want to try to pose the basic
+assumption behind the idea of
+
+ align:start position:0%
+assumption behind the idea of
+ 
+
+ align:start position:0%
+assumption behind the idea of
+facilitative leadership in the public
+
+ align:start position:0%
+facilitative leadership in the public
+ 
+
+ align:start position:0%
+facilitative leadership in the public
+sector and share a few terms a few
+
+ align:start position:0%
+sector and share a few terms a few
+ 
+
+ align:start position:0%
+sector and share a few terms a few
+Concepts I want to give you a problem to
+
+ align:start position:0%
+Concepts I want to give you a problem to
+ 
+
+ align:start position:0%
+Concepts I want to give you a problem to
+think about at dinner then ask you at
+
+ align:start position:0%
+think about at dinner then ask you at
+ 
+
+ align:start position:0%
+think about at dinner then ask you at
+your table to pursue the questions and
+
+ align:start position:0%
+your table to pursue the questions and
+ 
+
+ align:start position:0%
+your table to pursue the questions and
+then save about 10 minutes at the end to
+
+ align:start position:0%
+then save about 10 minutes at the end to
+ 
+
+ align:start position:0%
+then save about 10 minutes at the end to
+see if something different was happening
+
+ align:start position:0%
+see if something different was happening
+ 
+
+ align:start position:0%
+see if something different was happening
+at the different tables but the key idea
+
+ align:start position:0%
+at the different tables but the key idea
+ 
+
+ align:start position:0%
+at the different tables but the key idea
+tonight is raise this question and offer
+
+ align:start position:0%
+tonight is raise this question and offer
+ 
+
+ align:start position:0%
+tonight is raise this question and offer
+some terms some Concepts the goal is to
+
+ align:start position:0%
+some terms some Concepts the goal is to
+ 
+
+ align:start position:0%
+some terms some Concepts the goal is to
+begin a conversation if I had these
+
+ align:start position:0%
+begin a conversation if I had these
+ 
+
+ align:start position:0%
+begin a conversation if I had these
+ideas all worked out for myself I would
+
+ align:start position:0%
+ideas all worked out for myself I would
+ 
+
+ align:start position:0%
+ideas all worked out for myself I would
+have written a book but I definitely
+
+ align:start position:0%
+have written a book but I definitely
+ 
+
+ align:start position:0%
+have written a book but I definitely
+don't have all these ideas worked out so
+
+ align:start position:0%
+don't have all these ideas worked out so
+ 
+
+ align:start position:0%
+don't have all these ideas worked out so
+my goal is to share some thoughts
+
+ align:start position:0%
+my goal is to share some thoughts
+ 
+
+ align:start position:0%
+my goal is to share some thoughts
+provoke some
+
+ align:start position:0%
+provoke some
+ 
+
+ align:start position:0%
+provoke some
+conversation ask you to continue the
+
+ align:start position:0%
+conversation ask you to continue the
+ 
+
+ align:start position:0%
+conversation ask you to continue the
+conversation in small groups and then
+
+ align:start position:0%
+conversation in small groups and then
+ 
+
+ align:start position:0%
+conversation in small groups and then
+all together and I'm hoping that I can
+
+ align:start position:0%
+all together and I'm hoping that I can
+ 
+
+ align:start position:0%
+all together and I'm hoping that I can
+get you to write a couple Pages at the
+
+ align:start position:0%
+get you to write a couple Pages at the
+ 
+
+ align:start position:0%
+get you to write a couple Pages at the
+end of the fourth week or sooner should
+
+ align:start position:0%
+end of the fourth week or sooner should
+ 
+
+ align:start position:0%
+end of the fourth week or sooner should
+you be mo motivated and that I can take
+
+ align:start position:0%
+you be mo motivated and that I can take
+ 
+
+ align:start position:0%
+you be mo motivated and that I can take
+all of those and work them into the kind
+
+ align:start position:0%
+all of those and work them into the kind
+ 
+
+ align:start position:0%
+all of those and work them into the kind
+of uh summary or synthesis I will draft
+
+ align:start position:0%
+of uh summary or synthesis I will draft
+ 
+
+ align:start position:0%
+of uh summary or synthesis I will draft
+something and then encourage anybody
+
+ align:start position:0%
+something and then encourage anybody
+ 
+
+ align:start position:0%
+something and then encourage anybody
+that contributed to continue to work to
+
+ align:start position:0%
+that contributed to continue to work to
+ 
+
+ align:start position:0%
+that contributed to continue to work to
+take that draft develop it further and
+
+ align:start position:0%
+take that draft develop it further and
+ 
+
+ align:start position:0%
+take that draft develop it further and
+have it be a departmental publication
+
+ align:start position:0%
+have it be a departmental publication
+ 
+
+ align:start position:0%
+have it be a departmental publication
+which we don't have but I don't see why
+
+ align:start position:0%
+which we don't have but I don't see why
+ 
+
+ align:start position:0%
+which we don't have but I don't see why
+we can't do that because I think the
+
+ align:start position:0%
+we can't do that because I think the
+ 
+
+ align:start position:0%
+we can't do that because I think the
+question will continue um to be of
+
+ align:start position:0%
+question will continue um to be of
+ 
+
+ align:start position:0%
+question will continue um to be of
+interest and concern so all
+
+ align:start position:0%
+interest and concern so all
+ 
+
+ align:start position:0%
+interest and concern so all
+started last spring at the end of uh the
+
+ align:start position:0%
+started last spring at the end of uh the
+ 
+
+ align:start position:0%
+started last spring at the end of uh the
+semester my course on negotiation and
+
+ align:start position:0%
+semester my course on negotiation and
+ 
+
+ align:start position:0%
+semester my course on negotiation and
+dispute resolution in the public sector
+
+ align:start position:0%
+dispute resolution in the public sector
+ 
+
+ align:start position:0%
+dispute resolution in the public sector
+uh said you know I've looked around for
+
+ align:start position:0%
+uh said you know I've looked around for
+ 
+
+ align:start position:0%
+uh said you know I've looked around for
+leadership courses they have them at the
+
+ align:start position:0%
+leadership courses they have them at the
+ 
+
+ align:start position:0%
+leadership courses they have them at the
+Kennedy School they have them at the
+
+ align:start position:0%
+Kennedy School they have them at the
+ 
+
+ align:start position:0%
+Kennedy School they have them at the
+business school at Harvard they have
+
+ align:start position:0%
+business school at Harvard they have
+ 
+
+ align:start position:0%
+business school at Harvard they have
+them at
+
+ align:start position:0%
+them at
+ 
+
+ align:start position:0%
+them at
+Sloan but they all seem to assume you're
+
+ align:start position:0%
+Sloan but they all seem to assume you're
+ 
+
+ align:start position:0%
+Sloan but they all seem to assume you're
+somebody working in a private
+
+ align:start position:0%
+somebody working in a private
+ 
+
+ align:start position:0%
+somebody working in a private
+organization it's not the same thing as
+
+ align:start position:0%
+organization it's not the same thing as
+ 
+
+ align:start position:0%
+organization it's not the same thing as
+leadership in the public context really
+
+ align:start position:0%
+leadership in the public context really
+ 
+
+ align:start position:0%
+leadership in the public context really
+the assumption is you're in an
+
+ align:start position:0%
+the assumption is you're in an
+ 
+
+ align:start position:0%
+the assumption is you're in an
+organization and it's a private
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organization how do you manage as a
+
+ align:start position:0%
+organization how do you manage as a
+ 
+
+ align:start position:0%
+organization how do you manage as a
+leader there's nothing said differently
+
+ align:start position:0%
+leader there's nothing said differently
+ 
+
+ align:start position:0%
+leader there's nothing said differently
+about being in a leadership role in the
+
+ align:start position:0%
+about being in a leadership role in the
+ 
+
+ align:start position:0%
+about being in a leadership role in the
+public sector and I think it's very
+
+ align:start position:0%
+public sector and I think it's very
+ 
+
+ align:start position:0%
+public sector and I think it's very
+different that's the what I'm trying to
+
+ align:start position:0%
+different that's the what I'm trying to
+ 
+
+ align:start position:0%
+different that's the what I'm trying to
+work out in what ways is it different
+
+ align:start position:0%
+work out in what ways is it different
+ 
+
+ align:start position:0%
+work out in what ways is it different
+should all the basic assumptions be
+
+ align:start position:0%
+should all the basic assumptions be
+ 
+
+ align:start position:0%
+should all the basic assumptions be
+questioned about leadership SL
+
+ align:start position:0%
+questioned about leadership SL
+ 
+
+ align:start position:0%
+questioned about leadership SL
+management of groups organizations
+
+ align:start position:0%
+management of groups organizations
+ 
+
+ align:start position:0%
+management of groups organizations
+networks um in the public sector I've
+
+ align:start position:0%
+networks um in the public sector I've
+ 
+
+ align:start position:0%
+networks um in the public sector I've
+spent 50 years working in dispute
+
+ align:start position:0%
+spent 50 years working in dispute
+ 
+
+ align:start position:0%
+spent 50 years working in dispute
+resolution in the public sector in 30
+
+ align:start position:0%
+resolution in the public sector in 30
+ 
+
+ align:start position:0%
+resolution in the public sector in 30
+countries um I want to think
+
+ align:start position:0%
+countries um I want to think
+ 
+
+ align:start position:0%
+countries um I want to think
+comparatively about this so please do
+
+ align:start position:0%
+comparatively about this so please do
+ 
+
+ align:start position:0%
+comparatively about this so please do
+not constrain yourself unnecessarily to
+
+ align:start position:0%
+not constrain yourself unnecessarily to
+ 
+
+ align:start position:0%
+not constrain yourself unnecessarily to
+imagine only something in a US context
+
+ align:start position:0%
+imagine only something in a US context
+ 
+
+ align:start position:0%
+imagine only something in a US context
+when we're talking um at table
+
+ align:start position:0%
+when we're talking um at table
+ 
+
+ align:start position:0%
+when we're talking um at table
+conversation if you're thinking very
+
+ align:start position:0%
+conversation if you're thinking very
+ 
+
+ align:start position:0%
+conversation if you're thinking very
+much in your culture your context your
+
+ align:start position:0%
+much in your culture your context your
+ 
+
+ align:start position:0%
+much in your culture your context your
+country just say so don't not do it but
+
+ align:start position:0%
+country just say so don't not do it but
+ 
+
+ align:start position:0%
+country just say so don't not do it but
+let everybody else know that you're
+
+ align:start position:0%
+let everybody else know that you're
+ 
+
+ align:start position:0%
+let everybody else know that you're
+starting from a different point in the
+
+ align:start position:0%
+starting from a different point in the
+ 
+
+ align:start position:0%
+starting from a different point in the
+conversation and I don't know about how
+
+ align:start position:0%
+conversation and I don't know about how
+ 
+
+ align:start position:0%
+conversation and I don't know about how
+far generalizations can go about the
+
+ align:start position:0%
+far generalizations can go about the
+ 
+
+ align:start position:0%
+far generalizations can go about the
+public sector when we switch from
+
+ align:start position:0%
+public sector when we switch from
+ 
+
+ align:start position:0%
+public sector when we switch from
+country and culture to Country culture
+
+ align:start position:0%
+country and culture to Country culture
+ 
+
+ align:start position:0%
+country and culture to Country culture
+we'll see what you think about
+
+ align:start position:0%
+we'll see what you think about
+ 
+
+ align:start position:0%
+we'll see what you think about
+that imagine a city government has
+
+ align:start position:0%
+that imagine a city government has
+ 
+
+ align:start position:0%
+that imagine a city government has
+appointed a task force to give the city
+
+ align:start position:0%
+appointed a task force to give the city
+ 
+
+ align:start position:0%
+appointed a task force to give the city
+advice regarding the decision the city
+
+ align:start position:0%
+advice regarding the decision the city
+ 
+
+ align:start position:0%
+advice regarding the decision the city
+has to make regarding the use of a
+
+ align:start position:0%
+has to make regarding the use of a
+ 
+
+ align:start position:0%
+has to make regarding the use of a
+particular piece of public land that was
+
+ align:start position:0%
+particular piece of public land that was
+ 
+
+ align:start position:0%
+particular piece of public land that was
+abandoned not used and now there are
+
+ align:start position:0%
+abandoned not used and now there are
+ 
+
+ align:start position:0%
+abandoned not used and now there are
+multiple proposals for how it should be
+
+ align:start position:0%
+multiple proposals for how it should be
+ 
+
+ align:start position:0%
+multiple proposals for how it should be
+used within that neighborhood within the
+
+ align:start position:0%
+used within that neighborhood within the
+ 
+
+ align:start position:0%
+used within that neighborhood within the
+city within the metropolitan area and
+
+ align:start position:0%
+city within the metropolitan area and
+ 
+
+ align:start position:0%
+city within the metropolitan area and
+the cities asked a task force of people
+
+ align:start position:0%
+the cities asked a task force of people
+ 
+
+ align:start position:0%
+the cities asked a task force of people
+the uh the usual the Blue Ribbon
+
+ align:start position:0%
+the uh the usual the Blue Ribbon
+ 
+
+ align:start position:0%
+the uh the usual the Blue Ribbon
+committee was announced and a lot of
+
+ align:start position:0%
+committee was announced and a lot of
+ 
+
+ align:start position:0%
+committee was announced and a lot of
+folks yelled about that and so more
+
+ align:start position:0%
+folks yelled about that and so more
+ 
+
+ align:start position:0%
+folks yelled about that and so more
+people got added that was the solution
+
+ align:start position:0%
+people got added that was the solution
+ 
+
+ align:start position:0%
+people got added that was the solution
+to representation that that mayor chose
+
+ align:start position:0%
+to representation that that mayor chose
+ 
+
+ align:start position:0%
+to representation that that mayor chose
+okay fine we'll just add more people
+
+ align:start position:0%
+okay fine we'll just add more people
+ 
+
+ align:start position:0%
+okay fine we'll just add more people
+especially the ones who've made noise
+
+ align:start position:0%
+especially the ones who've made noise
+ 
+
+ align:start position:0%
+especially the ones who've made noise
+you be on the
+
+ align:start position:0%
+you be on the
+ 
+
+ align:start position:0%
+you be on the
+committee begging the
+
+ align:start position:0%
+committee begging the
+ 
+
+ align:start position:0%
+committee begging the
+question of the representativeness and
+
+ align:start position:0%
+question of the representativeness and
+ 
+
+ align:start position:0%
+question of the representativeness and
+thus The
+
+ align:start position:0%
+thus The
+ 
+
+ align:start position:0%
+thus The
+credibility of this group and whatever
+
+ align:start position:0%
+credibility of this group and whatever
+ 
+
+ align:start position:0%
+credibility of this group and whatever
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+recommends but since the city wasn't
+
+ align:start position:0%
+recommends but since the city wasn't
+ 
+
+ align:start position:0%
+recommends but since the city wasn't
+giving away final decision-making
+
+ align:start position:0%
+giving away final decision-making
+ 
+
+ align:start position:0%
+giving away final decision-making
+Authority was just asking for advice
+
+ align:start position:0%
+Authority was just asking for advice
+ 
+
+ align:start position:0%
+Authority was just asking for advice
+from a task force didn't worry too much
+
+ align:start position:0%
+from a task force didn't worry too much
+ 
+
+ align:start position:0%
+from a task force didn't worry too much
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representativeness it didn't worry too
+
+ align:start position:0%
+representativeness it didn't worry too
+ 
+
+ align:start position:0%
+representativeness it didn't worry too
+much about
+
+ align:start position:0%
+much about
+ 
+
+ align:start position:0%
+much about
+credibility in the eyes of the groups
+
+ align:start position:0%
+credibility in the eyes of the groups
+ 
+
+ align:start position:0%
+credibility in the eyes of the groups
+that weren't at the
+
+ align:start position:0%
+that weren't at the
+ 
+
+ align:start position:0%
+that weren't at the
+table and so this task
+
+ align:start position:0%
+table and so this task
+ 
+
+ align:start position:0%
+table and so this task
+force has been
+
+ align:start position:0%
+force has been
+ 
+
+ align:start position:0%
+force has been
+meeting it didn't have much of a mandate
+
+ align:start position:0%
+meeting it didn't have much of a mandate
+ 
+
+ align:start position:0%
+meeting it didn't have much of a mandate
+just we like your advice about this
+
+ align:start position:0%
+just we like your advice about this
+ 
+
+ align:start position:0%
+just we like your advice about this
+undeveloped parcel that's been sitting
+
+ align:start position:0%
+undeveloped parcel that's been sitting
+ 
+
+ align:start position:0%
+undeveloped parcel that's been sitting
+here for a long time what do you think
+
+ align:start position:0%
+here for a long time what do you think
+ 
+
+ align:start position:0%
+here for a long time what do you think
+City should do with it and my question
+
+ align:start position:0%
+City should do with it and my question
+ 
+
+ align:start position:0%
+City should do with it and my question
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+is how would you know who's the real
+
+ align:start position:0%
+is how would you know who's the real
+ 
+
+ align:start position:0%
+is how would you know who's the real
+leader of that task force they've met
+
+ align:start position:0%
+leader of that task force they've met
+ 
+
+ align:start position:0%
+leader of that task force they've met
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+times they have whatever mandate they
+
+ align:start position:0%
+times they have whatever mandate they
+ 
+
+ align:start position:0%
+times they have whatever mandate they
+had from the mayor's office how would we
+
+ align:start position:0%
+had from the mayor's office how would we
+ 
+
+ align:start position:0%
+had from the mayor's office how would we
+know who's the real leader of this 25
+
+ align:start position:0%
+know who's the real leader of this 25
+ 
+
+ align:start position:0%
+know who's the real leader of this 25
+person group you could clearly tell that
+
+ align:start position:0%
+person group you could clearly tell that
+ 
+
+ align:start position:0%
+person group you could clearly tell that
+a couple of people had way more
+
+ align:start position:0%
+a couple of people had way more
+ 
+
+ align:start position:0%
+a couple of people had way more
+knowledge and experience with regard to
+
+ align:start position:0%
+knowledge and experience with regard to
+ 
+
+ align:start position:0%
+knowledge and experience with regard to
+the city city politics City Planning
+
+ align:start position:0%
+the city city politics City Planning
+ 
+
+ align:start position:0%
+the city city politics City Planning
+City development real estate development
+
+ align:start position:0%
+City development real estate development
+ 
+
+ align:start position:0%
+City development real estate development
+and they were showing it off in the
+
+ align:start position:0%
+and they were showing it off in the
+ 
+
+ align:start position:0%
+and they were showing it off in the
+conversation did that make them the
+
+ align:start position:0%
+conversation did that make them the
+ 
+
+ align:start position:0%
+conversation did that make them the
+leader or maybe we're listening and one
+
+ align:start position:0%
+leader or maybe we're listening and one
+ 
+
+ align:start position:0%
+leader or maybe we're listening and one
+person soft
+
+ align:start position:0%
+person soft
+ 
+
+ align:start position:0%
+person soft
+voice not pushing hard at all on the
+
+ align:start position:0%
+voice not pushing hard at all on the
+ 
+
+ align:start position:0%
+voice not pushing hard at all on the
+substantive question but says well I've
+
+ align:start position:0%
+substantive question but says well I've
+ 
+
+ align:start position:0%
+substantive question but says well I've
+been on a bunch of task forces like this
+
+ align:start position:0%
+been on a bunch of task forces like this
+ 
+
+ align:start position:0%
+been on a bunch of task forces like this
+before in the city and my sense is we
+
+ align:start position:0%
+before in the city and my sense is we
+ 
+
+ align:start position:0%
+before in the city and my sense is we
+ought to do this this and this and use
+
+ align:start position:0%
+ought to do this this and this and use
+ 
+
+ align:start position:0%
+ought to do this this and this and use
+our time this way way and get the
+
+ align:start position:0%
+our time this way way and get the
+ 
+
+ align:start position:0%
+our time this way way and get the
+involvement of other people like so and
+
+ align:start position:0%
+involvement of other people like so and
+ 
+
+ align:start position:0%
+involvement of other people like so and
+so and so and so with the fact that that
+
+ align:start position:0%
+so and so and so with the fact that that
+ 
+
+ align:start position:0%
+so and so and so with the fact that that
+person had the most experience in this
+
+ align:start position:0%
+person had the most experience in this
+ 
+
+ align:start position:0%
+person had the most experience in this
+kind of a role would that qualify them
+
+ align:start position:0%
+kind of a role would that qualify them
+ 
+
+ align:start position:0%
+kind of a role would that qualify them
+to be the leader would that make them
+
+ align:start position:0%
+to be the leader would that make them
+ 
+
+ align:start position:0%
+to be the leader would that make them
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+leader is one person who clearly is the
+
+ align:start position:0%
+leader is one person who clearly is the
+ 
+
+ align:start position:0%
+leader is one person who clearly is the
+Workhorse on this committee they're
+
+ align:start position:0%
+Workhorse on this committee they're
+ 
+
+ align:start position:0%
+Workhorse on this committee they're
+saying oh I'll take the notes I'll work
+
+ align:start position:0%
+saying oh I'll take the notes I'll work
+ 
+
+ align:start position:0%
+saying oh I'll take the notes I'll work
+the flip chart and they're making very
+
+ align:start position:0%
+the flip chart and they're making very
+ 
+
+ align:start position:0%
+the flip chart and they're making very
+clear that they're taking care of all
+
+ align:start position:0%
+clear that they're taking care of all
+ 
+
+ align:start position:0%
+clear that they're taking care of all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+housekeeping chores and activities
+
+ align:start position:0%
+housekeeping chores and activities
+ 
+
+ align:start position:0%
+housekeeping chores and activities
+almost like a secretary keeping track of
+
+ align:start position:0%
+almost like a secretary keeping track of
+ 
+
+ align:start position:0%
+almost like a secretary keeping track of
+the ideas and offering their own views
+
+ align:start position:0%
+the ideas and offering their own views
+ 
+
+ align:start position:0%
+the ideas and offering their own views
+along the
+
+ align:start position:0%
+along the
+ 
+
+ align:start position:0%
+along the
+way is the person willing to do the most
+
+ align:start position:0%
+way is the person willing to do the most
+ 
+
+ align:start position:0%
+way is the person willing to do the most
+work the leader who's the
+
+ align:start position:0%
+work the leader who's the
+ 
+
+ align:start position:0%
+work the leader who's the
+leader or are there just these
+
+ align:start position:0%
+leader or are there just these
+ 
+
+ align:start position:0%
+leader or are there just these
+leadership
+
+ align:start position:0%
+leadership
+ 
+
+ align:start position:0%
+leadership
+functions and different people can all
+
+ align:start position:0%
+functions and different people can all
+ 
+
+ align:start position:0%
+functions and different people can all
+choose on their own to play different
+
+ align:start position:0%
+choose on their own to play different
+ 
+
+ align:start position:0%
+choose on their own to play different
+functions as long as the rest of the
+
+ align:start position:0%
+functions as long as the rest of the
+ 
+
+ align:start position:0%
+functions as long as the rest of the
+group accepts it if we're in a corporate
+
+ align:start position:0%
+group accepts it if we're in a corporate
+ 
+
+ align:start position:0%
+group accepts it if we're in a corporate
+context I promise you everyone would
+
+ align:start position:0%
+context I promise you everyone would
+ 
+
+ align:start position:0%
+context I promise you everyone would
+know who the leader of the group is
+
+ align:start position:0%
+know who the leader of the group is
+ 
+
+ align:start position:0%
+know who the leader of the group is
+because whoever said there would be a
+
+ align:start position:0%
+because whoever said there would be a
+ 
+
+ align:start position:0%
+because whoever said there would be a
+meeting whoever said there would be a
+
+ align:start position:0%
+meeting whoever said there would be a
+ 
+
+ align:start position:0%
+meeting whoever said there would be a
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+appointed the person who was the head of
+
+ align:start position:0%
+appointed the person who was the head of
+ 
+
+ align:start position:0%
+appointed the person who was the head of
+the group
+
+ align:start position:0%
+the group
+ 
+
+ align:start position:0%
+the group
+right doesn't happen that way most of
+
+ align:start position:0%
+right doesn't happen that way most of
+ 
+
+ align:start position:0%
+right doesn't happen that way most of
+the time I'm talking about when the
+
+ align:start position:0%
+the time I'm talking about when the
+ 
+
+ align:start position:0%
+the time I'm talking about when the
+larger
+
+ align:start position:0%
+larger
+ 
+
+ align:start position:0%
+larger
+network of
+
+ align:start position:0%
+network of
+ 
+
+ align:start position:0%
+network of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+public is
+
+ align:start position:0%
+public is
+ 
+
+ align:start position:0%
+public is
+tapped and trying to organize in cities
+
+ align:start position:0%
+tapped and trying to organize in cities
+ 
+
+ align:start position:0%
+tapped and trying to organize in cities
+trying to organize them don't we need a
+
+ align:start position:0%
+trying to organize them don't we need a
+ 
+
+ align:start position:0%
+trying to organize them don't we need a
+theory of
+
+ align:start position:0%
+theory of
+ 
+
+ align:start position:0%
+theory of
+practice as urban
+
+ align:start position:0%
+practice as urban
+ 
+
+ align:start position:0%
+practice as urban
+planners with regard to how this
+
+ align:start position:0%
+planners with regard to how this
+ 
+
+ align:start position:0%
+planners with regard to how this
+leadership question should be handled in
+
+ align:start position:0%
+leadership question should be handled in
+ 
+
+ align:start position:0%
+leadership question should be handled in
+the public
+
+ align:start position:0%
+the public
+ 
+
+ align:start position:0%
+the public
+Arena just whatever happens mayor says
+
+ align:start position:0%
+Arena just whatever happens mayor says
+ 
+
+ align:start position:0%
+Arena just whatever happens mayor says
+it's fine with me it's a whole group can
+
+ align:start position:0%
+it's fine with me it's a whole group can
+ 
+
+ align:start position:0%
+it's fine with me it's a whole group can
+just collect their suggestions and send
+
+ align:start position:0%
+just collect their suggestions and send
+ 
+
+ align:start position:0%
+just collect their suggestions and send
+them to me that's
+
+ align:start position:0%
+them to me that's
+ 
+
+ align:start position:0%
+them to me that's
+fine as practitioners I think we need a
+
+ align:start position:0%
+fine as practitioners I think we need a
+ 
+
+ align:start position:0%
+fine as practitioners I think we need a
+theory of practice could be our own it
+
+ align:start position:0%
+theory of practice could be our own it
+ 
+
+ align:start position:0%
+theory of practice could be our own it
+could be the MIT theory of leadership
+
+ align:start position:0%
+could be the MIT theory of leadership
+ 
+
+ align:start position:0%
+could be the MIT theory of leadership
+facilitative leadership could be you
+
+ align:start position:0%
+facilitative leadership could be you
+ 
+
+ align:start position:0%
+facilitative leadership could be you
+know your tables Theory but I don't see
+
+ align:start position:0%
+know your tables Theory but I don't see
+ 
+
+ align:start position:0%
+know your tables Theory but I don't see
+how as planners we just wander
+
+ align:start position:0%
+how as planners we just wander
+ 
+
+ align:start position:0%
+how as planners we just wander
+forward and we're going to be in so many
+
+ align:start position:0%
+forward and we're going to be in so many
+ 
+
+ align:start position:0%
+forward and we're going to be in so many
+situations in which OD hoc clusters of
+
+ align:start position:0%
+situations in which OD hoc clusters of
+ 
+
+ align:start position:0%
+situations in which OD hoc clusters of
+people are supposed to be doing the
+
+ align:start position:0%
+people are supposed to be doing the
+ 
+
+ align:start position:0%
+people are supposed to be doing the
+Public's work we're usually supposed to
+
+ align:start position:0%
+Public's work we're usually supposed to
+ 
+
+ align:start position:0%
+Public's work we're usually supposed to
+be involved in such things and I think
+
+ align:start position:0%
+be involved in such things and I think
+ 
+
+ align:start position:0%
+be involved in such things and I think
+the key to that is to see yourself as a
+
+ align:start position:0%
+the key to that is to see yourself as a
+ 
+
+ align:start position:0%
+the key to that is to see yourself as a
+facilitative leader providing a
+
+ align:start position:0%
+facilitative leader providing a
+ 
+
+ align:start position:0%
+facilitative leader providing a
+service a service it's a service model
+
+ align:start position:0%
+service a service it's a service model
+ 
+
+ align:start position:0%
+service a service it's a service model
+of leadership which I think is necessary
+
+ align:start position:0%
+of leadership which I think is necessary
+ 
+
+ align:start position:0%
+of leadership which I think is necessary
+in the public sector but you can
+
+ align:start position:0%
+in the public sector but you can
+ 
+
+ align:start position:0%
+in the public sector but you can
+convince me that that's wrong you have
+
+ align:start position:0%
+convince me that that's wrong you have
+ 
+
+ align:start position:0%
+convince me that that's wrong you have
+plenty of alternative models and that's
+
+ align:start position:0%
+plenty of alternative models and that's
+ 
+
+ align:start position:0%
+plenty of alternative models and that's
+why we're going to be having
+
+ align:start position:0%
+why we're going to be having
+ 
+
+ align:start position:0%
+why we're going to be having
+conversations about this they need to be
+
+ align:start position:0%
+conversations about this they need to be
+ 
+
+ align:start position:0%
+conversations about this they need to be
+empathetic to the interests of the other
+
+ align:start position:0%
+empathetic to the interests of the other
+ 
+
+ align:start position:0%
+empathetic to the interests of the other
+people in the around the
+
+ align:start position:0%
+people in the around the
+ 
+
+ align:start position:0%
+people in the around the
+table if you can't Jin up empathy for
+
+ align:start position:0%
+table if you can't Jin up empathy for
+ 
+
+ align:start position:0%
+table if you can't Jin up empathy for
+the others and their quandaries with
+
+ align:start position:0%
+the others and their quandaries with
+ 
+
+ align:start position:0%
+the others and their quandaries with
+regard to this you'll never be a leader
+
+ align:start position:0%
+regard to this you'll never be a leader
+ 
+
+ align:start position:0%
+regard to this you'll never be a leader
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+group you have to be a capable active
+
+ align:start position:0%
+group you have to be a capable active
+ 
+
+ align:start position:0%
+group you have to be a capable active
+listener if you can't hear how far off
+
+ align:start position:0%
+listener if you can't hear how far off
+ 
+
+ align:start position:0%
+listener if you can't hear how far off
+you are about what's going on by
+
+ align:start position:0%
+you are about what's going on by
+ 
+
+ align:start position:0%
+you are about what's going on by
+listening to people talking to each
+
+ align:start position:0%
+listening to people talking to each
+ 
+
+ align:start position:0%
+listening to people talking to each
+other or to you you won't
+
+ align:start position:0%
+other or to you you won't
+ 
+
+ align:start position:0%
+other or to you you won't
+succeed you have to be able to read the
+
+ align:start position:0%
+succeed you have to be able to read the
+ 
+
+ align:start position:0%
+succeed you have to be able to read the
+group to recognize underlying
+
+ align:start position:0%
+group to recognize underlying
+ 
+
+ align:start position:0%
+group to recognize underlying
+dynamics that let you know more about
+
+ align:start position:0%
+dynamics that let you know more about
+ 
+
+ align:start position:0%
+dynamics that let you know more about
+the interests of the
+
+ align:start position:0%
+the interests of the
+ 
+
+ align:start position:0%
+the interests of the
+participants this is not people raising
+
+ align:start position:0%
+participants this is not people raising
+ 
+
+ align:start position:0%
+participants this is not people raising
+their hand and saying something reading
+
+ align:start position:0%
+their hand and saying something reading
+ 
+
+ align:start position:0%
+their hand and saying something reading
+the group over many occasions Coalition
+
+ align:start position:0%
+the group over many occasions Coalition
+ 
+
+ align:start position:0%
+the group over many occasions Coalition
+building you can't keep treating it like
+
+ align:start position:0%
+building you can't keep treating it like
+ 
+
+ align:start position:0%
+building you can't keep treating it like
+a set of individuals who are only there
+
+ align:start position:0%
+a set of individuals who are only there
+ 
+
+ align:start position:0%
+a set of individuals who are only there
+for themselves you have to help them
+
+ align:start position:0%
+for themselves you have to help them
+ 
+
+ align:start position:0%
+for themselves you have to help them
+begin to form
+
+ align:start position:0%
+begin to form
+ 
+
+ align:start position:0%
+begin to form
+coalitions you cannot function in a
+
+ align:start position:0%
+coalitions you cannot function in a
+ 
+
+ align:start position:0%
+coalitions you cannot function in a
+service role if you cannot put aside
+
+ align:start position:0%
+service role if you cannot put aside
+ 
+
+ align:start position:0%
+service role if you cannot put aside
+your ego you need to be able to take a
+
+ align:start position:0%
+your ego you need to be able to take a
+ 
+
+ align:start position:0%
+your ego you need to be able to take a
+Long View the group needs you to do that
+
+ align:start position:0%
+Long View the group needs you to do that
+ 
+
+ align:start position:0%
+Long View the group needs you to do that
+they're focused on the short term I
+
+ align:start position:0%
+they're focused on the short term I
+ 
+
+ align:start position:0%
+they're focused on the short term I
+would argue the facilitative leader has
+
+ align:start position:0%
+would argue the facilitative leader has
+ 
+
+ align:start position:0%
+would argue the facilitative leader has
+to constantly be thinking about the long
+
+ align:start position:0%
+to constantly be thinking about the long
+ 
+
+ align:start position:0%
+to constantly be thinking about the long
+term you have to be able to write the
+
+ align:start position:0%
+term you have to be able to write the
+ 
+
+ align:start position:0%
+term you have to be able to write the
+group's victory speech you have to be
+
+ align:start position:0%
+group's victory speech you have to be
+ 
+
+ align:start position:0%
+group's victory speech you have to be
+able to draft that as the facilitative
+
+ align:start position:0%
+able to draft that as the facilitative
+ 
+
+ align:start position:0%
+able to draft that as the facilitative
+leader because it has to take count of
+
+ align:start position:0%
+leader because it has to take count of
+ 
+
+ align:start position:0%
+leader because it has to take count of
+how it looks from all of their
+
+ align:start position:0%
+how it looks from all of their
+ 
+
+ align:start position:0%
+how it looks from all of their
+standpoints you have to promote
+
+ align:start position:0%
+standpoints you have to promote
+ 
+
+ align:start position:0%
+standpoints you have to promote
+organizational learning along the way
+
+ align:start position:0%
+organizational learning along the way
+ 
+
+ align:start position:0%
+organizational learning along the way
+what didn't we do well what did we do
+
+ align:start position:0%
+what didn't we do well what did we do
+ 
+
+ align:start position:0%
+what didn't we do well what did we do
+well how would was that just this one
+
+ align:start position:0%
+well how would was that just this one
+ 
+
+ align:start position:0%
+well how would was that just this one
+time or is there something there we can
+
+ align:start position:0%
+time or is there something there we can
+ 
+
+ align:start position:0%
+time or is there something there we can
+change about how we're working so we do
+
+ align:start position:0%
+change about how we're working so we do
+ 
+
+ align:start position:0%
+change about how we're working so we do
+better next time but if someone is not
+
+ align:start position:0%
+better next time but if someone is not
+ 
+
+ align:start position:0%
+better next time but if someone is not
+focused on organizational learning it
+
+ align:start position:0%
+focused on organizational learning it
+ 
+
+ align:start position:0%
+focused on organizational learning it
+will not just fall out
+
+ align:start position:0%
+will not just fall out
+ 
+
+ align:start position:0%
+will not just fall out
+naturally now when I look at that list
+
+ align:start position:0%
+naturally now when I look at that list
+ 
+
+ align:start position:0%
+naturally now when I look at that list
+of let's call them skills not micro
+
+ align:start position:0%
+of let's call them skills not micro
+ 
+
+ align:start position:0%
+of let's call them skills not micro
+skills but capabilities capacities leads
+
+ align:start position:0%
+skills but capabilities capacities leads
+ 
+
+ align:start position:0%
+skills but capabilities capacities leads
+me to the conclusion may lead you to a
+
+ align:start position:0%
+me to the conclusion may lead you to a
+ 
+
+ align:start position:0%
+me to the conclusion may lead you to a
+different conclusion that facilitative
+
+ align:start position:0%
+different conclusion that facilitative
+ 
+
+ align:start position:0%
+different conclusion that facilitative
+leaders are made and not
+
+ align:start position:0%
+leaders are made and not
+ 
+
+ align:start position:0%
+leaders are made and not
+born I believe that the
+
+ align:start position:0%
+born I believe that the
+ 
+
+ align:start position:0%
+born I believe that the
+charismatic
+
+ align:start position:0%
+charismatic
+ 
+
+ align:start position:0%
+charismatic
+leader who provides Vision who provides
+
+ align:start position:0%
+leader who provides Vision who provides
+ 
+
+ align:start position:0%
+leader who provides Vision who provides
+inspiration uh you you might try really
+
+ align:start position:0%
+inspiration uh you you might try really
+ 
+
+ align:start position:0%
+inspiration uh you you might try really
+hard to become that my sense is that
+
+ align:start position:0%
+hard to become that my sense is that
+ 
+
+ align:start position:0%
+hard to become that my sense is that
+carismatic leaders are
+
+ align:start position:0%
+carismatic leaders are
+ 
+
+ align:start position:0%
+carismatic leaders are
+born it's not that they don't do
+
+ align:start position:0%
+born it's not that they don't do
+ 
+
+ align:start position:0%
+born it's not that they don't do
+anything to improve themselves I just
+
+ align:start position:0%
+anything to improve themselves I just
+ 
+
+ align:start position:0%
+anything to improve themselves I just
+don't think you can build yourself up
+
+ align:start position:0%
+don't think you can build yourself up
+ 
+
+ align:start position:0%
+don't think you can build yourself up
+piece by piece to become
+
+ align:start position:0%
+piece by piece to become
+ 
+
+ align:start position:0%
+piece by piece to become
+charismatic I really do think that's
+
+ align:start position:0%
+charismatic I really do think that's
+ 
+
+ align:start position:0%
+charismatic I really do think that's
+either lucky or not lucky to be endowed
+
+ align:start position:0%
+either lucky or not lucky to be endowed
+ 
+
+ align:start position:0%
+either lucky or not lucky to be endowed
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+that ability as an inspirational
+
+ align:start position:0%
+that ability as an inspirational
+ 
+
+ align:start position:0%
+that ability as an inspirational
+leader charismatic leaders I think are
+
+ align:start position:0%
+leader charismatic leaders I think are
+ 
+
+ align:start position:0%
+leader charismatic leaders I think are
+more likely to be born than
+
+ align:start position:0%
+more likely to be born than
+ 
+
+ align:start position:0%
+more likely to be born than
+made paternalistic
+
+ align:start position:0%
+made paternalistic
+ 
+
+ align:start position:0%
+made paternalistic
+leaders that you we can train them I
+
+ align:start position:0%
+leaders that you we can train them I
+ 
+
+ align:start position:0%
+leaders that you we can train them I
+think Sloan and H BS do a great
+
+ align:start position:0%
+think Sloan and H BS do a great
+ 
+
+ align:start position:0%
+think Sloan and H BS do a great
+job I can't deny they've made a whole
+
+ align:start position:0%
+job I can't deny they've made a whole
+ 
+
+ align:start position:0%
+job I can't deny they've made a whole
+lot of people like that I would like to
+
+ align:start position:0%
+lot of people like that I would like to
+ 
+
+ align:start position:0%
+lot of people like that I would like to
+think that if we
+
+ align:start position:0%
+think that if we
+ 
+
+ align:start position:0%
+think that if we
+tried D USP could make a whole lot of
+
+ align:start position:0%
+tried D USP could make a whole lot of
+ 
+
+ align:start position:0%
+tried D USP could make a whole lot of
+facilitative leaders people who are
+
+ align:start position:0%
+facilitative leaders people who are
+ 
+
+ align:start position:0%
+facilitative leaders people who are
+collaborative service providers in the
+
+ align:start position:0%
+collaborative service providers in the
+ 
+
+ align:start position:0%
+collaborative service providers in the
+public sector on this question of our
+
+ align:start position:0%
+public sector on this question of our
+ 
+
+ align:start position:0%
+public sector on this question of our
+facilitative leaders made not born I I
+
+ align:start position:0%
+facilitative leaders made not born I I
+ 
+
+ align:start position:0%
+facilitative leaders made not born I I
+think facilitative leaders can be
+
+ align:start position:0%
+think facilitative leaders can be
+ 
+
+ align:start position:0%
+think facilitative leaders can be
+made and there are people who
+
+ align:start position:0%
+made and there are people who
+ 
+
+ align:start position:0%
+made and there are people who
+when it comes down to it say yeah a
+
+ align:start position:0%
+when it comes down to it say yeah a
+ 
+
+ align:start position:0%
+when it comes down to it say yeah a
+facilitative leader can provide
+
+ align:start position:0%
+facilitative leader can provide
+ 
+
+ align:start position:0%
+facilitative leader can provide
+Direction without taking
+
+ align:start position:0%
+Direction without taking
+ 
+
+ align:start position:0%
+Direction without taking
+control they know that everyone has to
+
+ align:start position:0%
+control they know that everyone has to
+ 
+
+ align:start position:0%
+control they know that everyone has to
+be involved in all the decisions
+
+ align:start position:0%
+be involved in all the decisions
+ 
+
+ align:start position:0%
+be involved in all the decisions
+leadership in the public sector requires
+
+ align:start position:0%
+leadership in the public sector requires
+ 
+
+ align:start position:0%
+leadership in the public sector requires
+different kinds of skills orientation
+
+ align:start position:0%
+different kinds of skills orientation
+ 
+
+ align:start position:0%
+different kinds of skills orientation
+and a different Theory from leadership
+
+ align:start position:0%
+and a different Theory from leadership
+ 
+
+ align:start position:0%
+and a different Theory from leadership
+in private organizational contexts I
+
+ align:start position:0%
+in private organizational contexts I
+ 
+
+ align:start position:0%
+in private organizational contexts I
+counting on the
+
+ align:start position:0%
+counting on the
+ 
+
+ align:start position:0%
+counting on the
+conversation over these uh four weeks uh
+
+ align:start position:0%
+conversation over these uh four weeks uh
+ 
+
+ align:start position:0%
+conversation over these uh four weeks uh
+to maybe make a case the beginning of a
+
+ align:start position:0%
+to maybe make a case the beginning of a
+ 
+
+ align:start position:0%
+to maybe make a case the beginning of a
+case to take to the department and say
+
+ align:start position:0%
+case to take to the department and say
+ 
+
+ align:start position:0%
+case to take to the department and say
+what what exactly are you hoping I'm
+
+ align:start position:0%
+what what exactly are you hoping I'm
+ 
+
+ align:start position:0%
+what what exactly are you hoping I'm
+going to turn out to
+
+ align:start position:0%
+going to turn out to
+ 
+
+ align:start position:0%
+going to turn out to
+be don't tell me planner that do doesn't
+
+ align:start position:0%
+be don't tell me planner that do doesn't
+ 
+
+ align:start position:0%
+be don't tell me planner that do doesn't
+do it it has to be more than
+
+ align:start position:0%
+do it it has to be more than
+ 
+
+ align:start position:0%
+do it it has to be more than
+that so we break for dinner and then um
+
+ align:start position:0%
+that so we break for dinner and then um
+ 
+
+ align:start position:0%
+that so we break for dinner and then um
+I will ask you uh to uh consider some of
+
+ align:start position:0%
+I will ask you uh to uh consider some of
+ 
+
+ align:start position:0%
+I will ask you uh to uh consider some of
+the questions from within what I've
+
+ align:start position:0%
+the questions from within what I've
+ 
+
+ align:start position:0%
+the questions from within what I've
+presented I'm hoping to get from each of
+
+ align:start position:0%
+presented I'm hoping to get from each of
+ 
+
+ align:start position:0%
+presented I'm hoping to get from each of
+you by the end of week four some
+
+ align:start position:0%
+you by the end of week four some
+ 
+
+ align:start position:0%
+you by the end of week four some
+reflection on this proposition that I'm
+
+ align:start position:0%
+reflection on this proposition that I'm
+ 
+
+ align:start position:0%
+reflection on this proposition that I'm
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+offering so public private any
+
+ align:start position:0%
+offering so public private any
+ 
+
+ align:start position:0%
+offering so public private any
+important difference always sometimes
+
+ align:start position:0%
+important difference always sometimes
+ 
+
+ align:start position:0%
+important difference always sometimes
+maybe second question facilitative
+
+ align:start position:0%
+maybe second question facilitative
+ 
+
+ align:start position:0%
+maybe second question facilitative
+leaders are made not born does that
+
+ align:start position:0%
+leaders are made not born does that
+ 
+
+ align:start position:0%
+leaders are made not born does that
+sound right to you and anybody become a
+
+ align:start position:0%
+sound right to you and anybody become a
+ 
+
+ align:start position:0%
+sound right to you and anybody become a
+facilitative leader I mean leader I
+
+ align:start position:0%
+facilitative leader I mean leader I
+ 
+
+ align:start position:0%
+facilitative leader I mean leader I
+don't just mean a facilitative person so
+
+ align:start position:0%
+don't just mean a facilitative person so
+ 
+
+ align:start position:0%
+don't just mean a facilitative person so
+made not born public versus private and
+
+ align:start position:0%
+made not born public versus private and
+ 
+
+ align:start position:0%
+made not born public versus private and
+can you cons really construe leadership
+
+ align:start position:0%
+can you cons really construe leadership
+ 
+
+ align:start position:0%
+can you cons really construe leadership
+as service
+
+ align:start position:0%
+as service
+ 
+
+ align:start position:0%
+as service
+you say I'm a leader I'm providing
+
+ align:start position:0%
+you say I'm a leader I'm providing
+ 
+
+ align:start position:0%
+you say I'm a leader I'm providing
+service that's what I'm doing service in
+
+ align:start position:0%
+service that's what I'm doing service in
+ 
+
+ align:start position:0%
+service that's what I'm doing service in
+the public interest that's the dominant
+
+ align:start position:0%
+the public interest that's the dominant
+ 
+
+ align:start position:0%
+the public interest that's the dominant
+consideration in thinking about
+
+ align:start position:0%
+consideration in thinking about
+ 
+
+ align:start position:0%
+consideration in thinking about
+leadership in the public sector can you
+
+ align:start position:0%
+leadership in the public sector can you
+ 
+
+ align:start position:0%
+leadership in the public sector can you
+imagine yourself in a service role
+
+ align:start position:0%
+imagine yourself in a service role
+ 
+
+ align:start position:0%
+imagine yourself in a service role
+someone who's recognized for the service
+
+ align:start position:0%
+someone who's recognized for the service
+ 
+
+ align:start position:0%
+someone who's recognized for the service
+they provide in the public Arena so I
+
+ align:start position:0%
+they provide in the public Arena so I
+ 
+
+ align:start position:0%
+they provide in the public Arena so I
+offer those three points um see where
+
+ align:start position:0%
+offer those three points um see where
+ 
+
+ align:start position:0%
+offer those three points um see where
+the discussion goes take 20 minut
+
+ align:start position:0%
+the discussion goes take 20 minut
+ 
+
+ align:start position:0%
+the discussion goes take 20 minut
+minutes meet somebody you don't know
+
+ align:start position:0%
+minutes meet somebody you don't know
+ 
+
+ align:start position:0%
+minutes meet somebody you don't know
+talk to someone you do know and you
+
+ align:start position:0%
+talk to someone you do know and you
+ 
+
+ align:start position:0%
+talk to someone you do know and you
+never get to talk
+
+ align:start position:0%
+never get to talk
+ 
+
+ align:start position:0%
+never get to talk
+to one of my managers was like you need
+
+ align:start position:0%
+to one of my managers was like you need
+ 
+
+ align:start position:0%
+to one of my managers was like you need
+to have the confidence to like assert
+
+ align:start position:0%
+to have the confidence to like assert
+ 
+
+ align:start position:0%
+to have the confidence to like assert
+that make a decision and move forward
+
+ align:start position:0%
+that make a decision and move forward
+ 
+
+ align:start position:0%
+that make a decision and move forward
+with it rather than trying to make
+
+ align:start position:0%
+with it rather than trying to make
+ 
+
+ align:start position:0%
+with it rather than trying to make
+everything a collective decision when
+
+ align:start position:0%
+everything a collective decision when
+ 
+
+ align:start position:0%
+everything a collective decision when
+you're like there's a group and I do
+
+ align:start position:0%
+you're like there's a group and I do
+ 
+
+ align:start position:0%
+you're like there's a group and I do
+think there's kind of a gender Dynamic
+
+ align:start position:0%
+think there's kind of a gender Dynamic
+ 
+
+ align:start position:0%
+think there's kind of a gender Dynamic
+involved in that where and I felt like I
+
+ align:start position:0%
+involved in that where and I felt like I
+ 
+
+ align:start position:0%
+involved in that where and I felt like I
+was younger in the office I felt like oh
+
+ align:start position:0%
+was younger in the office I felt like oh
+ 
+
+ align:start position:0%
+was younger in the office I felt like oh
+I should be deferring to all the other
+
+ align:start position:0%
+I should be deferring to all the other
+ 
+
+ align:start position:0%
+I should be deferring to all the other
+people in his group uh in order to make
+
+ align:start position:0%
+people in his group uh in order to make
+ 
+
+ align:start position:0%
+people in his group uh in order to make
+decisions I do think like women maybe
+
+ align:start position:0%
+decisions I do think like women maybe
+ 
+
+ align:start position:0%
+decisions I do think like women maybe
+socialized to be more
+
+ align:start position:0%
+socialized to be more
+ 
+
+ align:start position:0%
+socialized to be more
+facilitated uh rather than like turtle
+
+ align:start position:0%
+facilitated uh rather than like turtle
+ 
+
+ align:start position:0%
+facilitated uh rather than like turtle
+or top down I don't want to say like a
+
+ align:start position:0%
+or top down I don't want to say like a
+ 
+
+ align:start position:0%
+or top down I don't want to say like a
+taping role but it does begin to feel
+
+ align:start position:0%
+taping role but it does begin to feel
+ 
+
+ align:start position:0%
+taping role but it does begin to feel
+like you're nurturing consciences sort
+
+ align:start position:0%
+like you're nurturing consciences sort
+ 
+
+ align:start position:0%
+like you're nurturing consciences sort
+of timing to every news as opposed to
+
+ align:start position:0%
+of timing to every news as opposed to
+ 
+
+ align:start position:0%
+of timing to every news as opposed to
+achieving the best station it kind of
+
+ align:start position:0%
+achieving the best station it kind of
+ 
+
+ align:start position:0%
+achieving the best station it kind of
+feels like hurting cats sometimes and
+
+ align:start position:0%
+feels like hurting cats sometimes and
+ 
+
+ align:start position:0%
+feels like hurting cats sometimes and
+there is a lot of emotional labor
+
+ align:start position:0%
+there is a lot of emotional labor
+ 
+
+ align:start position:0%
+there is a lot of emotional labor
+involved understanding
+
+ align:start position:0%
+involved understanding
+ 
+
+ align:start position:0%
+involved understanding
+social dynamics and power and political
+
+ align:start position:0%
+social dynamics and power and political
+ 
+
+ align:start position:0%
+social dynamics and power and political
+Dynamics sometimes even like I don't
+
+ align:start position:0%
+Dynamics sometimes even like I don't
+ 
+
+ align:start position:0%
+Dynamics sometimes even like I don't
+know like
+
+ align:start position:0%
+know like
+ 
+
+ align:start position:0%
+know like
+babysitting you know it doesn't feel
+
+ align:start position:0%
+babysitting you know it doesn't feel
+ 
+
+ align:start position:0%
+babysitting you know it doesn't feel
+like a sexy leader
+
+ align:start position:0%
+like a sexy leader
+ 
+
+ align:start position:0%
+like a sexy leader
+role like it's definitely not I think if
+
+ align:start position:0%
+role like it's definitely not I think if
+ 
+
+ align:start position:0%
+role like it's definitely not I think if
+you're delivering a product as opposed
+
+ align:start position:0%
+you're delivering a product as opposed
+ 
+
+ align:start position:0%
+you're delivering a product as opposed
+to a service you don't have to have much
+
+ align:start position:0%
+to a service you don't have to have much
+ 
+
+ align:start position:0%
+to a service you don't have to have much
+of it within just Mo drive and ambition
+
+ align:start position:0%
+of it within just Mo drive and ambition
+ 
+
+ align:start position:0%
+of it within just Mo drive and ambition
+but if
+
+ align:start position:0%
+but if
+ 
+
+ align:start position:0%
+but if
+you're leaning into
+
+ align:start position:0%
+you're leaning into
+ 
+
+ align:start position:0%
+you're leaning into
+process which I think is like the nature
+
+ align:start position:0%
+process which I think is like the nature
+ 
+
+ align:start position:0%
+process which I think is like the nature
+of filation like you need to be patient
+
+ align:start position:0%
+of filation like you need to be patient
+ 
+
+ align:start position:0%
+of filation like you need to be patient
+with folks to provide the service I feel
+
+ align:start position:0%
+with folks to provide the service I feel
+ 
+
+ align:start position:0%
+with folks to provide the service I feel
+like this can be very easily under
+
+ align:start position:0%
+like this can be very easily under
+ 
+
+ align:start position:0%
+like this can be very easily under
+appreciated that's kind of service I
+
+ align:start position:0%
+appreciated that's kind of service I
+ 
+
+ align:start position:0%
+appreciated that's kind of service I
+feel like maybe leadership does contain
+
+ align:start position:0%
+feel like maybe leadership does contain
+ 
+
+ align:start position:0%
+feel like maybe leadership does contain
+a meaning of achieving a consensus like
+
+ align:start position:0%
+a meaning of achieving a consensus like
+ 
+
+ align:start position:0%
+a meaning of achieving a consensus like
+we still need to lead people to
+
+ align:start position:0%
+we still need to lead people to
+ 
+
+ align:start position:0%
+we still need to lead people to
+somewhere public sector is trying to
+
+ align:start position:0%
+somewhere public sector is trying to
+ 
+
+ align:start position:0%
+somewhere public sector is trying to
+achieve our best to serve public
+
+ align:start position:0%
+achieve our best to serve public
+ 
+
+ align:start position:0%
+achieve our best to serve public
+interest uh in public different voices
+
+ align:start position:0%
+interest uh in public different voices
+ 
+
+ align:start position:0%
+interest uh in public different voices
+from multi stakeholders but for private
+
+ align:start position:0%
+from multi stakeholders but for private
+ 
+
+ align:start position:0%
+from multi stakeholders but for private
+corporate they have a Clear Vision or a
+
+ align:start position:0%
+corporate they have a Clear Vision or a
+ 
+
+ align:start position:0%
+corporate they have a Clear Vision or a
+clear goal that I want to create this
+
+ align:start position:0%
+clear goal that I want to create this
+ 
+
+ align:start position:0%
+clear goal that I want to create this
+product there is no involvement of the
+
+ align:start position:0%
+product there is no involvement of the
+ 
+
+ align:start position:0%
+product there is no involvement of the
+community in what we are doing the
+
+ align:start position:0%
+community in what we are doing the
+ 
+
+ align:start position:0%
+community in what we are doing the
+corland is different than probably the
+
+ align:start position:0%
+corland is different than probably the
+ 
+
+ align:start position:0%
+corland is different than probably the
+skills that you may need in terms of
+
+ align:start position:0%
+skills that you may need in terms of
+ 
+
+ align:start position:0%
+skills that you may need in terms of
+leadership they may have commonalities
+
+ align:start position:0%
+leadership they may have commonalities
+ 
+
+ align:start position:0%
+leadership they may have commonalities
+but I do believe that there are certain
+
+ align:start position:0%
+but I do believe that there are certain
+ 
+
+ align:start position:0%
+but I do believe that there are certain
+differences my perception is that the
+
+ align:start position:0%
+differences my perception is that the
+ 
+
+ align:start position:0%
+differences my perception is that the
+private sector is it's more it's more
+
+ align:start position:0%
+private sector is it's more it's more
+ 
+
+ align:start position:0%
+private sector is it's more it's more
+Bur fault and it's more based on on
+
+ align:start position:0%
+Bur fault and it's more based on on
+ 
+
+ align:start position:0%
+Bur fault and it's more based on on
+appointments and authori and in the
+
+ align:start position:0%
+appointments and authori and in the
+ 
+
+ align:start position:0%
+appointments and authori and in the
+public sector in my experience you may
+
+ align:start position:0%
+public sector in my experience you may
+ 
+
+ align:start position:0%
+public sector in my experience you may
+need a little more influence in the
+
+ align:start position:0%
+need a little more influence in the
+ 
+
+ align:start position:0%
+need a little more influence in the
+public sector what's more dangerous is
+
+ align:start position:0%
+public sector what's more dangerous is
+ 
+
+ align:start position:0%
+public sector what's more dangerous is
+that you're kind of putting on this
+
+ align:start position:0%
+that you're kind of putting on this
+ 
+
+ align:start position:0%
+that you're kind of putting on this
+facade of like this is the public but
+
+ align:start position:0%
+facade of like this is the public but
+ 
+
+ align:start position:0%
+facade of like this is the public but
+then the mechanisms there don't allow
+
+ align:start position:0%
+then the mechanisms there don't allow
+ 
+
+ align:start position:0%
+then the mechanisms there don't allow
+people to equally come to the table the
+
+ align:start position:0%
+people to equally come to the table the
+ 
+
+ align:start position:0%
+people to equally come to the table the
+of the public and private sectors are
+
+ align:start position:0%
+of the public and private sectors are
+ 
+
+ align:start position:0%
+of the public and private sectors are
+different the the nature of leadership
+
+ align:start position:0%
+different the the nature of leadership
+ 
+
+ align:start position:0%
+different the the nature of leadership
+should be different how do you think
+
+ align:start position:0%
+should be different how do you think
+ 
+
+ align:start position:0%
+should be different how do you think
+like managing people differs the public
+
+ align:start position:0%
+like managing people differs the public
+ 
+
+ align:start position:0%
+like managing people differs the public
+sector in many South European countries
+
+ align:start position:0%
+sector in many South European countries
+ 
+
+ align:start position:0%
+sector in many South European countries
+you have to play a a low profile Asad as
+
+ align:start position:0%
+you have to play a a low profile Asad as
+ 
+
+ align:start position:0%
+you have to play a a low profile Asad as
+no as an individual that wants to Aspire
+
+ align:start position:0%
+no as an individual that wants to Aspire
+ 
+
+ align:start position:0%
+no as an individual that wants to Aspire
+as a leader I I have a heart type here
+
+ align:start position:0%
+as a leader I I have a heart type here
+ 
+
+ align:start position:0%
+as a leader I I have a heart type here
+uh in the US in the US particularly yeah
+
+ align:start position:0%
+uh in the US in the US particularly yeah
+ 
+
+ align:start position:0%
+uh in the US in the US particularly yeah
+I mean I've been working 20 years with
+
+ align:start position:0%
+I mean I've been working 20 years with
+ 
+
+ align:start position:0%
+I mean I've been working 20 years with
+an Anglo Saxon organization that is the
+
+ align:start position:0%
+an Anglo Saxon organization that is the
+ 
+
+ align:start position:0%
+an Anglo Saxon organization that is the
+UN and I think that this doesn't work in
+
+ align:start position:0%
+UN and I think that this doesn't work in
+ 
+
+ align:start position:0%
+UN and I think that this doesn't work in
+other cultures in many cultures I think
+
+ align:start position:0%
+other cultures in many cultures I think
+ 
+
+ align:start position:0%
+other cultures in many cultures I think
+it's very difficult to transpose these
+
+ align:start position:0%
+it's very difficult to transpose these
+ 
+
+ align:start position:0%
+it's very difficult to transpose these
+styles of leadership wholesale but by
+
+ align:start position:0%
+styles of leadership wholesale but by
+ 
+
+ align:start position:0%
+styles of leadership wholesale but by
+developing skills you can eventually
+
+ align:start position:0%
+developing skills you can eventually
+ 
+
+ align:start position:0%
+developing skills you can eventually
+bestowed the power by the community
+
+ align:start position:0%
+bestowed the power by the community
+ 
+
+ align:start position:0%
+bestowed the power by the community
+because they see that you are ready to
+
+ align:start position:0%
+because they see that you are ready to
+ 
+
+ align:start position:0%
+because they see that you are ready to
+show up and you are aligned to their
+
+ align:start position:0%
+show up and you are aligned to their
+ 
+
+ align:start position:0%
+show up and you are aligned to their
+values and that's very important is in
+
+ align:start position:0%
+values and that's very important is in
+ 
+
+ align:start position:0%
+values and that's very important is in
+Japan for example they have a hard time
+
+ align:start position:0%
+Japan for example they have a hard time
+ 
+
+ align:start position:0%
+Japan for example they have a hard time
+partnering and negotiating with
+
+ align:start position:0%
+partnering and negotiating with
+ 
+
+ align:start position:0%
+partnering and negotiating with
+Americans they are self-confident and
+
+ align:start position:0%
+Americans they are self-confident and
+ 
+
+ align:start position:0%
+Americans they are self-confident and
+spoken and and they are bold yes and
+
+ align:start position:0%
+spoken and and they are bold yes and
+ 
+
+ align:start position:0%
+spoken and and they are bold yes and
+this boldness which here is considering
+
+ align:start position:0%
+this boldness which here is considering
+ 
+
+ align:start position:0%
+this boldness which here is considering
+a skill and something positive you are
+
+ align:start position:0%
+a skill and something positive you are
+ 
+
+ align:start position:0%
+a skill and something positive you are
+confident with yourself which don't take
+
+ align:start position:0%
+confident with yourself which don't take
+ 
+
+ align:start position:0%
+confident with yourself which don't take
+me wrong it's not bad in certain
+
+ align:start position:0%
+me wrong it's not bad in certain
+ 
+
+ align:start position:0%
+me wrong it's not bad in certain
+cultures could be considered arrogant
+
+ align:start position:0%
+cultures could be considered arrogant
+ 
+
+ align:start position:0%
+cultures could be considered arrogant
+and it's important to play a more low
+
+ align:start position:0%
+and it's important to play a more low
+ 
+
+ align:start position:0%
+and it's important to play a more low
+profile role so how was that very when
+
+ align:start position:0%
+profile role so how was that very when
+ 
+
+ align:start position:0%
+profile role so how was that very when
+you're in that give it that's that's one
+
+ align:start position:0%
+you're in that give it that's that's one
+ 
+
+ align:start position:0%
+you're in that give it that's that's one
+of the things is is empathy you reading
+
+ align:start position:0%
+of the things is is empathy you reading
+ 
+
+ align:start position:0%
+of the things is is empathy you reading
+the room and you understand that for
+
+ align:start position:0%
+the room and you understand that for
+ 
+
+ align:start position:0%
+the room and you understand that for
+example in the noric countries people
+
+ align:start position:0%
+example in the noric countries people
+ 
+
+ align:start position:0%
+example in the noric countries people
+don't want to shine Ah that's people
+
+ align:start position:0%
+don't want to shine Ah that's people
+ 
+
+ align:start position:0%
+don't want to shine Ah that's people
+don't want to shine the power of the
+
+ align:start position:0%
+don't want to shine the power of the
+ 
+
+ align:start position:0%
+don't want to shine the power of the
+many noric countries is the community
+
+ align:start position:0%
+many noric countries is the community
+ 
+
+ align:start position:0%
+many noric countries is the community
+itself while here in the state I can see
+
+ align:start position:0%
+itself while here in the state I can see
+ 
+
+ align:start position:0%
+itself while here in the state I can see
+that this distinction you can see that
+
+ align:start position:0%
+that this distinction you can see that
+ 
+
+ align:start position:0%
+that this distinction you can see that
+in movies and narrative a leader is
+
+ align:start position:0%
+in movies and narrative a leader is
+ 
+
+ align:start position:0%
+in movies and narrative a leader is
+someone that shine that concept of
+
+ align:start position:0%
+someone that shine that concept of
+ 
+
+ align:start position:0%
+someone that shine that concept of
+leadership doesn't apply every for us
+
+ align:start position:0%
+leadership doesn't apply every for us
+ 
+
+ align:start position:0%
+leadership doesn't apply every for us
+reades working in Japan is perfect but
+
+ align:start position:0%
+reades working in Japan is perfect but
+ 
+
+ align:start position:0%
+reades working in Japan is perfect but
+Americans they always have a CL septum
+
+ align:start position:0%
+Americans they always have a CL septum
+ 
+
+ align:start position:0%
+Americans they always have a CL septum
+communities are are more like silent so
+
+ align:start position:0%
+communities are are more like silent so
+ 
+
+ align:start position:0%
+communities are are more like silent so
+you don't have to discuss and I'm not
+
+ align:start position:0%
+you don't have to discuss and I'm not
+ 
+
+ align:start position:0%
+you don't have to discuss and I'm not
+saying that they are better or worse
+
+ align:start position:0%
+saying that they are better or worse
+ 
+
+ align:start position:0%
+saying that they are better or worse
+there are certain communities that they
+
+ align:start position:0%
+there are certain communities that they
+ 
+
+ align:start position:0%
+there are certain communities that they
+have other value than a
+
+ align:start position:0%
+have other value than a
+ 
+
+ align:start position:0%
+have other value than a
+financials this goes for public Evans I
+
+ align:start position:0%
+financials this goes for public Evans I
+ 
+
+ align:start position:0%
+financials this goes for public Evans I
+think a lot of times you're rewarded for
+
+ align:start position:0%
+think a lot of times you're rewarded for
+ 
+
+ align:start position:0%
+think a lot of times you're rewarded for
+just like doing your Curr job well which
+
+ align:start position:0%
+just like doing your Curr job well which
+ 
+
+ align:start position:0%
+just like doing your Curr job well which
+a lot of just start out as like a
+
+ align:start position:0%
+a lot of just start out as like a
+ 
+
+ align:start position:0%
+a lot of just start out as like a
+technical skill and then you can get
+
+ align:start position:0%
+technical skill and then you can get
+ 
+
+ align:start position:0%
+technical skill and then you can get
+promoted to a manager role of people who
+
+ align:start position:0%
+promoted to a manager role of people who
+ 
+
+ align:start position:0%
+promoted to a manager role of people who
+do that technical skin
+
+ align:start position:0%
+do that technical skin
+ 
+
+ align:start position:0%
+do that technical skin
+but you're not taught how to be a
+
+ align:start position:0%
+but you're not taught how to be a
+ 
+
+ align:start position:0%
+but you're not taught how to be a
+manager how to support people how to
+
+ align:start position:0%
+manager how to support people how to
+ 
+
+ align:start position:0%
+manager how to support people how to
+develop their skills you're just like
+
+ align:start position:0%
+develop their skills you're just like
+ 
+
+ align:start position:0%
+develop their skills you're just like
+really good at that
+
+ align:start position:0%
+really good at that
+ 
+
+ align:start position:0%
+really good at that
+one things like empathy and being a good
+
+ align:start position:0%
+one things like empathy and being a good
+ 
+
+ align:start position:0%
+one things like empathy and being a good
+listener are things that you know might
+
+ align:start position:0%
+listener are things that you know might
+ 
+
+ align:start position:0%
+listener are things that you know might
+get I don't know kind of not embody
+
+ align:start position:0%
+get I don't know kind of not embody
+ 
+
+ align:start position:0%
+get I don't know kind of not embody
+those qualities as much I'd honestly
+
+ align:start position:0%
+those qualities as much I'd honestly
+ 
+
+ align:start position:0%
+those qualities as much I'd honestly
+like love to talk about the like
+
+ align:start position:0%
+like love to talk about the like
+ 
+
+ align:start position:0%
+like love to talk about the like
+efficiency piece in the public sector
+
+ align:start position:0%
+efficiency piece in the public sector
+ 
+
+ align:start position:0%
+efficiency piece in the public sector
+because cost efficiency is usually one
+
+ align:start position:0%
+because cost efficiency is usually one
+ 
+
+ align:start position:0%
+because cost efficiency is usually one
+of the biggest conversations that
+
+ align:start position:0%
+of the biggest conversations that
+ 
+
+ align:start position:0%
+of the biggest conversations that
+efficiency isn't articulated as like
+
+ align:start position:0%
+efficiency isn't articulated as like
+ 
+
+ align:start position:0%
+efficiency isn't articulated as like
+anything come up that anybody felt
+
+ align:start position:0%
+anything come up that anybody felt
+ 
+
+ align:start position:0%
+anything come up that anybody felt
+strongly about on any of those three
+
+ align:start position:0%
+strongly about on any of those three
+ 
+
+ align:start position:0%
+strongly about on any of those three
+issues the concept of leadership as
+
+ align:start position:0%
+issues the concept of leadership as
+ 
+
+ align:start position:0%
+issues the concept of leadership as
+service and we kind of had a maybe this
+
+ align:start position:0%
+service and we kind of had a maybe this
+ 
+
+ align:start position:0%
+service and we kind of had a maybe this
+is a philosophical question about
+
+ align:start position:0%
+is a philosophical question about
+ 
+
+ align:start position:0%
+is a philosophical question about
+whether there's a such thing as like
+
+ align:start position:0%
+whether there's a such thing as like
+ 
+
+ align:start position:0%
+whether there's a such thing as like
+selfless leadership or is everyone
+
+ align:start position:0%
+selfless leadership or is everyone
+ 
+
+ align:start position:0%
+selfless leadership or is everyone
+always at the back of their minds doing
+
+ align:start position:0%
+always at the back of their minds doing
+ 
+
+ align:start position:0%
+always at the back of their minds doing
+something for their own benefit even if
+
+ align:start position:0%
+something for their own benefit even if
+ 
+
+ align:start position:0%
+something for their own benefit even if
+you are facilitating trying to be a
+
+ align:start position:0%
+you are facilitating trying to be a
+ 
+
+ align:start position:0%
+you are facilitating trying to be a
+facilitative leader do you get a little
+
+ align:start position:0%
+facilitative leader do you get a little
+ 
+
+ align:start position:0%
+facilitative leader do you get a little
+ego Rush when you like make something
+
+ align:start position:0%
+ego Rush when you like make something
+ 
+
+ align:start position:0%
+ego Rush when you like make something
+happen you know are we all at dust
+
+ align:start position:0%
+happen you know are we all at dust
+ 
+
+ align:start position:0%
+happen you know are we all at dust
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+we truly want to change the world or
+
+ align:start position:0%
+we truly want to change the world or
+ 
+
+ align:start position:0%
+we truly want to change the world or
+because we think that we're important
+
+ align:start position:0%
+because we think that we're important
+ 
+
+ align:start position:0%
+because we think that we're important
+enough to do that thank you thanks
+
+ align:start position:0%
+enough to do that thank you thanks
+ 
+
+ align:start position:0%
+enough to do that thank you thanks
+Cris those who have some CTIC
+
+ align:start position:0%
+Cris those who have some CTIC
+ 
+
+ align:start position:0%
+Cris those who have some CTIC
+characteristics will naturally be deer
+
+ align:start position:0%
+characteristics will naturally be deer
+ 
+
+ align:start position:0%
+characteristics will naturally be deer
+so we opened up by discussing the
+
+ align:start position:0%
+so we opened up by discussing the
+ 
+
+ align:start position:0%
+so we opened up by discussing the
+question of whether facilitative leaders
+
+ align:start position:0%
+question of whether facilitative leaders
+ 
+
+ align:start position:0%
+question of whether facilitative leaders
+are made or war and uh we talked a
+
+ align:start position:0%
+are made or war and uh we talked a
+ 
+
+ align:start position:0%
+are made or war and uh we talked a
+little bit about the role of gender and
+
+ align:start position:0%
+little bit about the role of gender and
+ 
+
+ align:start position:0%
+little bit about the role of gender and
+race and sexuality in this question just
+
+ align:start position:0%
+race and sexuality in this question just
+ 
+
+ align:start position:0%
+race and sexuality in this question just
+kind of speaking from my experience
+
+ align:start position:0%
+kind of speaking from my experience
+ 
+
+ align:start position:0%
+kind of speaking from my experience
+being a woman in the public sector I
+
+ align:start position:0%
+being a woman in the public sector I
+ 
+
+ align:start position:0%
+being a woman in the public sector I
+found myself deferring to a more
+
+ align:start position:0%
+found myself deferring to a more
+ 
+
+ align:start position:0%
+found myself deferring to a more
+facilitative form of leadership when
+
+ align:start position:0%
+facilitative form of leadership when
+ 
+
+ align:start position:0%
+facilitative form of leadership when
+maybe being a little bit more assertive
+
+ align:start position:0%
+maybe being a little bit more assertive
+ 
+
+ align:start position:0%
+maybe being a little bit more assertive
+or um taking on more of a
+
+ align:start position:0%
+or um taking on more of a
+ 
+
+ align:start position:0%
+or um taking on more of a
+decision-making role would have been
+
+ align:start position:0%
+decision-making role would have been
+ 
+
+ align:start position:0%
+decision-making role would have been
+better um so I think that yeah kind of
+
+ align:start position:0%
+better um so I think that yeah kind of
+ 
+
+ align:start position:0%
+better um so I think that yeah kind of
+thinking about the social dynamics
+
+ align:start position:0%
+thinking about the social dynamics
+ 
+
+ align:start position:0%
+thinking about the social dynamics
+around whether someone is innately
+
+ align:start position:0%
+around whether someone is innately
+ 
+
+ align:start position:0%
+around whether someone is innately
+facilitative is important a lot of the
+
+ align:start position:0%
+facilitative is important a lot of the
+ 
+
+ align:start position:0%
+facilitative is important a lot of the
+time in public settings there's
+
+ align:start position:0%
+time in public settings there's
+ 
+
+ align:start position:0%
+time in public settings there's
+apprehension to take that more
+
+ align:start position:0%
+apprehension to take that more
+ 
+
+ align:start position:0%
+apprehension to take that more
+decision-making position just
+
+ align:start position:0%
+decision-making position just
+ 
+
+ align:start position:0%
+decision-making position just
+because that's maybe not like the the
+
+ align:start position:0%
+because that's maybe not like the the
+ 
+
+ align:start position:0%
+because that's maybe not like the the
+role that we've like historically
+
+ align:start position:0%
+role that we've like historically
+ 
+
+ align:start position:0%
+role that we've like historically
+occupied and so we defer to potentially
+
+ align:start position:0%
+occupied and so we defer to potentially
+ 
+
+ align:start position:0%
+occupied and so we defer to potentially
+more caretaking more
+
+ align:start position:0%
+more caretaking more
+ 
+
+ align:start position:0%
+more caretaking more
+nurturing uh I guess like function in
+
+ align:start position:0%
+nurturing uh I guess like function in
+ 
+
+ align:start position:0%
+nurturing uh I guess like function in
+decision making so we tend to build in
+
+ align:start position:0%
+decision making so we tend to build in
+ 
+
+ align:start position:0%
+decision making so we tend to build in
+consensus rather than delegating respons
+
+ align:start position:0%
+consensus rather than delegating respons
+ 
+
+ align:start position:0%
+consensus rather than delegating respons
+responsibility or asserting expertise in
+
+ align:start position:0%
+responsibility or asserting expertise in
+ 
+
+ align:start position:0%
+responsibility or asserting expertise in
+a realm um because if you don't look
+
+ align:start position:0%
+a realm um because if you don't look
+ 
+
+ align:start position:0%
+a realm um because if you don't look
+like the decision maker often times your
+
+ align:start position:0%
+like the decision maker often times your
+ 
+
+ align:start position:0%
+like the decision maker often times your
+credibility could be reckoned challenged
+
+ align:start position:0%
+credibility could be reckoned challenged
+ 
+
+ align:start position:0%
+credibility could be reckoned challenged
+pushed back against and so the next best
+
+ align:start position:0%
+pushed back against and so the next best
+ 
+
+ align:start position:0%
+pushed back against and so the next best
+thing is often to maybe opt for
+
+ align:start position:0%
+thing is often to maybe opt for
+ 
+
+ align:start position:0%
+thing is often to maybe opt for
+facilitation instead especially in a
+
+ align:start position:0%
+facilitation instead especially in a
+ 
+
+ align:start position:0%
+facilitation instead especially in a
+public setting when when sometimes it
+
+ align:start position:0%
+public setting when when sometimes it
+ 
+
+ align:start position:0%
+public setting when when sometimes it
+can be hard to Corral really cating
+
+ align:start position:0%
+can be hard to Corral really cating
+ 
+
+ align:start position:0%
+can be hard to Corral really cating
+interest okay we have a very interesting
+
+ align:start position:0%
+interest okay we have a very interesting
+ 
+
+ align:start position:0%
+interest okay we have a very interesting
+discussion on we may have in our minds a
+
+ align:start position:0%
+discussion on we may have in our minds a
+ 
+
+ align:start position:0%
+discussion on we may have in our minds a
+concept of leader that perhaps is not
+
+ align:start position:0%
+concept of leader that perhaps is not
+ 
+
+ align:start position:0%
+concept of leader that perhaps is not
+share with other parts of the world and
+
+ align:start position:0%
+share with other parts of the world and
+ 
+
+ align:start position:0%
+share with other parts of the world and
+I think that this is very important
+
+ align:start position:0%
+I think that this is very important
+ 
+
+ align:start position:0%
+I think that this is very important
+where we are defining some of the skills
+
+ align:start position:0%
+where we are defining some of the skills
+ 
+
+ align:start position:0%
+where we are defining some of the skills
+that makes a leader because we are still
+
+ align:start position:0%
+that makes a leader because we are still
+ 
+
+ align:start position:0%
+that makes a leader because we are still
+especially certain communities certain
+
+ align:start position:0%
+especially certain communities certain
+ 
+
+ align:start position:0%
+especially certain communities certain
+societies create a sort of a narrative
+
+ align:start position:0%
+societies create a sort of a narrative
+ 
+
+ align:start position:0%
+societies create a sort of a narrative
+in certain communities what leadership
+
+ align:start position:0%
+in certain communities what leadership
+ 
+
+ align:start position:0%
+in certain communities what leadership
+should be we discuss that leaders are
+
+ align:start position:0%
+should be we discuss that leaders are
+ 
+
+ align:start position:0%
+should be we discuss that leaders are
+made by the legitimacy that the
+
+ align:start position:0%
+made by the legitimacy that the
+ 
+
+ align:start position:0%
+made by the legitimacy that the
+community give to someone what
+
+ align:start position:0%
+community give to someone what
+ 
+
+ align:start position:0%
+community give to someone what
+legitimizes the leader and gives them
+
+ align:start position:0%
+legitimizes the leader and gives them
+ 
+
+ align:start position:0%
+legitimizes the leader and gives them
+that capacity that authority to
+
+ align:start position:0%
+that capacity that authority to
+ 
+
+ align:start position:0%
+that capacity that authority to
+influence all those folks usually we see
+
+ align:start position:0%
+influence all those folks usually we see
+ 
+
+ align:start position:0%
+influence all those folks usually we see
+the arrow going the other way which is
+
+ align:start position:0%
+the arrow going the other way which is
+ 
+
+ align:start position:0%
+the arrow going the other way which is
+the legitimacy of the leader is a
+
+ align:start position:0%
+the legitimacy of the leader is a
+ 
+
+ align:start position:0%
+the legitimacy of the leader is a
+function of the support of the
+
+ align:start position:0%
+function of the support of the
+ 
+
+ align:start position:0%
+function of the support of the
+population in the public Arena so the
+
+ align:start position:0%
+population in the public Arena so the
+ 
+
+ align:start position:0%
+population in the public Arena so the
+arrow goes from the
+
+ align:start position:0%
+arrow goes from the
+ 
+
+ align:start position:0%
+arrow goes from the
+constituency to the leader it all it's
+
+ align:start position:0%
+constituency to the leader it all it's
+ 
+
+ align:start position:0%
+constituency to the leader it all it's
+providing
+
+ align:start position:0%
+providing
+ 
+
+ align:start position:0%
+providing
+legitimacy and yet we're crediting the
+
+ align:start position:0%
+legitimacy and yet we're crediting the
+ 
+
+ align:start position:0%
+legitimacy and yet we're crediting the
+leader with providing Direction and
+
+ align:start position:0%
+leader with providing Direction and
+ 
+
+ align:start position:0%
+leader with providing Direction and
+helping everybody see what they're going
+
+ align:start position:0%
+helping everybody see what they're going
+ 
+
+ align:start position:0%
+helping everybody see what they're going
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+so if we talk about legitimacy and
+
+ align:start position:0%
+so if we talk about legitimacy and
+ 
+
+ align:start position:0%
+so if we talk about legitimacy and
+sources of legitimacy and we talk about
+
+ align:start position:0%
+sources of legitimacy and we talk about
+ 
+
+ align:start position:0%
+sources of legitimacy and we talk about
+Authority and the sources of authority
+
+ align:start position:0%
+Authority and the sources of authority
+ 
+
+ align:start position:0%
+Authority and the sources of authority
+and we can certainly compare public and
+
+ align:start position:0%
+and we can certainly compare public and
+ 
+
+ align:start position:0%
+and we can certainly compare public and
+private there are very different sources
+
+ align:start position:0%
+private there are very different sources
+ 
+
+ align:start position:0%
+private there are very different sources
+of legitimacy sources of authority if we
+
+ align:start position:0%
+of legitimacy sources of authority if we
+ 
+
+ align:start position:0%
+of legitimacy sources of authority if we
+talk about responsibility comparing
+
+ align:start position:0%
+talk about responsibility comparing
+ 
+
+ align:start position:0%
+talk about responsibility comparing
+leaders in the private sector versus
+
+ align:start position:0%
+leaders in the private sector versus
+ 
+
+ align:start position:0%
+leaders in the private sector versus
+leaders in the public sector what's
+
+ align:start position:0%
+leaders in the public sector what's
+ 
+
+ align:start position:0%
+leaders in the public sector what's
+their responsibility clearly this
+
+ align:start position:0%
+their responsibility clearly this
+ 
+
+ align:start position:0%
+their responsibility clearly this
+there's different right so if you begin
+
+ align:start position:0%
+there's different right so if you begin
+ 
+
+ align:start position:0%
+there's different right so if you begin
+to pile up these differences and you say
+
+ align:start position:0%
+to pile up these differences and you say
+ 
+
+ align:start position:0%
+to pile up these differences and you say
+all right so how is this public sector
+
+ align:start position:0%
+all right so how is this public sector
+ 
+
+ align:start position:0%
+all right so how is this public sector
+leader
+
+ align:start position:0%
+leader
+ 
+
+ align:start position:0%
+leader
+leading to get a different source of
+
+ align:start position:0%
+leading to get a different source of
+ 
+
+ align:start position:0%
+leading to get a different source of
+authority different source of legitimacy
+
+ align:start position:0%
+authority different source of legitimacy
+ 
+
+ align:start position:0%
+authority different source of legitimacy
+different nature of responsibility
+
+ align:start position:0%
+different nature of responsibility
+ 
+
+ align:start position:0%
+different nature of responsibility
+forget about the skills they have or
+
+ align:start position:0%
+forget about the skills they have or
+ 
+
+ align:start position:0%
+forget about the skills they have or
+don't have there's a big difference I
+
+ align:start position:0%
+don't have there's a big difference I
+ 
+
+ align:start position:0%
+don't have there's a big difference I
+think now we can say oh you're just
+
+ align:start position:0%
+think now we can say oh you're just
+ 
+
+ align:start position:0%
+think now we can say oh you're just
+saying that because you're looking at it
+
+ align:start position:0%
+saying that because you're looking at it
+ 
+
+ align:start position:0%
+saying that because you're looking at it
+from a a a western perspective or you're
+
+ align:start position:0%
+from a a a western perspective or you're
+ 
+
+ align:start position:0%
+from a a a western perspective or you're
+looking at it from a a US perspective uh
+
+ align:start position:0%
+looking at it from a a US perspective uh
+ 
+
+ align:start position:0%
+looking at it from a a US perspective uh
+and that may be although
+
+ align:start position:0%
+and that may be although
+ 
+
+ align:start position:0%
+and that may be although
+when I look at the sources of legitimacy
+
+ align:start position:0%
+when I look at the sources of legitimacy
+ 
+
+ align:start position:0%
+when I look at the sources of legitimacy
+for leaders in some different countries
+
+ align:start position:0%
+for leaders in some different countries
+ 
+
+ align:start position:0%
+for leaders in some different countries
+I can't find out I can't figure out what
+
+ align:start position:0%
+I can't find out I can't figure out what
+ 
+
+ align:start position:0%
+I can't find out I can't figure out what
+they are I mean people have taken
+
+ align:start position:0%
+they are I mean people have taken
+ 
+
+ align:start position:0%
+they are I mean people have taken
+leadership and it legitimacy wasn't the
+
+ align:start position:0%
+leadership and it legitimacy wasn't the
+ 
+
+ align:start position:0%
+leadership and it legitimacy wasn't the
+issue they sort of took the leadership
+
+ align:start position:0%
+issue they sort of took the leadership
+ 
+
+ align:start position:0%
+issue they sort of took the leadership
+I'm not saying they worked against an
+
+ align:start position:0%
+I'm not saying they worked against an
+ 
+
+ align:start position:0%
+I'm not saying they worked against an
+electoral process in a democratic
+
+ align:start position:0%
+electoral process in a democratic
+ 
+
+ align:start position:0%
+electoral process in a democratic
+context I'm saying but what gave them
+
+ align:start position:0%
+context I'm saying but what gave them
+ 
+
+ align:start position:0%
+context I'm saying but what gave them
+credibility as a leader wasn't just that
+
+ align:start position:0%
+credibility as a leader wasn't just that
+ 
+
+ align:start position:0%
+credibility as a leader wasn't just that
+they were elected my goodness
+
+ align:start position:0%
+they were elected my goodness
+ 
+
+ align:start position:0%
+they were elected my goodness
+that something else gave them
+
+ align:start position:0%
+that something else gave them
+ 
+
+ align:start position:0%
+that something else gave them
+credibility gave them the right to
+
+ align:start position:0%
+credibility gave them the right to
+ 
+
+ align:start position:0%
+credibility gave them the right to
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+Authority and I'm wondering what their
+
+ align:start position:0%
+Authority and I'm wondering what their
+ 
+
+ align:start position:0%
+Authority and I'm wondering what their
+sense of responsibility was I know that
+
+ align:start position:0%
+sense of responsibility was I know that
+ 
+
+ align:start position:0%
+sense of responsibility was I know that
+those three things are different when I
+
+ align:start position:0%
+those three things are different when I
+ 
+
+ align:start position:0%
+those three things are different when I
+talk to and watch leaders in the public
+
+ align:start position:0%
+talk to and watch leaders in the public
+ 
+
+ align:start position:0%
+talk to and watch leaders in the public
+Arena versus leadership in a private
+
+ align:start position:0%
+Arena versus leadership in a private
+ 
+
+ align:start position:0%
+Arena versus leadership in a private
+company and we didn't get to discuss
+
+ align:start position:0%
+company and we didn't get to discuss
+ 
+
+ align:start position:0%
+company and we didn't get to discuss
+what you mean by the public interest
+
+ align:start position:0%
+what you mean by the public interest
+ 
+
+ align:start position:0%
+what you mean by the public interest
+right we're we're presuming the
+
+ align:start position:0%
+right we're we're presuming the
+ 
+
+ align:start position:0%
+right we're we're presuming the
+responsibility partly to the Public's
+
+ align:start position:0%
+responsibility partly to the Public's
+ 
+
+ align:start position:0%
+responsibility partly to the Public's
+interest as part at least of what a
+
+ align:start position:0%
+interest as part at least of what a
+ 
+
+ align:start position:0%
+interest as part at least of what a
+leader in the public sector has to do
+
+ align:start position:0%
+leader in the public sector has to do
+ 
+
+ align:start position:0%
+leader in the public sector has to do
+and then where do they get satisfaction
+
+ align:start position:0%
+and then where do they get satisfaction
+ 
+
+ align:start position:0%
+and then where do they get satisfaction
+the questions that you raised first what
+
+ align:start position:0%
+the questions that you raised first what
+ 
+
+ align:start position:0%
+the questions that you raised first what
+do they think success means and what
+
+ align:start position:0%
+do they think success means and what
+ 
+
+ align:start position:0%
+do they think success means and what
+does it give them what does it generate
+
+ align:start position:0%
+does it give them what does it generate
+ 
+
+ align:start position:0%
+does it give them what does it generate
+for them I said earlier that if you take
+
+ align:start position:0%
+for them I said earlier that if you take
+ 
+
+ align:start position:0%
+for them I said earlier that if you take
+service seriously as a model that you
+
+ align:start position:0%
+service seriously as a model that you
+ 
+
+ align:start position:0%
+service seriously as a model that you
+would include in that ability put your
+
+ align:start position:0%
+would include in that ability put your
+ 
+
+ align:start position:0%
+would include in that ability put your
+ego aside I don't mean you have no ego I
+
+ align:start position:0%
+ego aside I don't mean you have no ego I
+ 
+
+ align:start position:0%
+ego aside I don't mean you have no ego I
+mean the issue is when I rank my
+
+ align:start position:0%
+mean the issue is when I rank my
+ 
+
+ align:start position:0%
+mean the issue is when I rank my
+responsibilities what's first and when
+
+ align:start position:0%
+responsibilities what's first and when
+ 
+
+ align:start position:0%
+responsibilities what's first and when
+there's a tradeoff what's dominant and
+
+ align:start position:0%
+there's a tradeoff what's dominant and
+ 
+
+ align:start position:0%
+there's a tradeoff what's dominant and
+over time
+
+ align:start position:0%
+over time
+ 
+
+ align:start position:0%
+over time
+consistently and my sense is that we've
+
+ align:start position:0%
+consistently and my sense is that we've
+ 
+
+ align:start position:0%
+consistently and my sense is that we've
+got to talk about being an effective
+
+ align:start position:0%
+got to talk about being an effective
+ 
+
+ align:start position:0%
+got to talk about being an effective
+leader who can meet the public
+
+ align:start position:0%
+leader who can meet the public
+ 
+
+ align:start position:0%
+leader who can meet the public
+interest but also this satis action that
+
+ align:start position:0%
+interest but also this satis action that
+ 
+
+ align:start position:0%
+interest but also this satis action that
+comes from being effective in that role
+
+ align:start position:0%
+comes from being effective in that role
+ 
+
+ align:start position:0%
+comes from being effective in that role
+and that's for that person I don't mean
+
+ align:start position:0%
+and that's for that person I don't mean
+ 
+
+ align:start position:0%
+and that's for that person I don't mean
+to erase any of that when I talk about
+
+ align:start position:0%
+to erase any of that when I talk about
+ 
+
+ align:start position:0%
+to erase any of that when I talk about
+Service as the primary model yes people
+
+ align:start position:0%
+Service as the primary model yes people
+ 
+
+ align:start position:0%
+Service as the primary model yes people
+still will
+
+ align:start position:0%
+still will
+ 
+
+ align:start position:0%
+still will
+pursue the things that satisfy them that
+
+ align:start position:0%
+pursue the things that satisfy them that
+ 
+
+ align:start position:0%
+pursue the things that satisfy them that
+they're going to be motivated not just
+
+ align:start position:0%
+they're going to be motivated not just
+ 
+
+ align:start position:0%
+they're going to be motivated not just
+by being in service not just by meeting
+
+ align:start position:0%
+by being in service not just by meeting
+ 
+
+ align:start position:0%
+by being in service not just by meeting
+the public interest but by doing a good
+
+ align:start position:0%
+the public interest but by doing a good
+ 
+
+ align:start position:0%
+the public interest but by doing a good
+job being recognized for that it's just
+
+ align:start position:0%
+job being recognized for that it's just
+ 
+
+ align:start position:0%
+job being recognized for that it's just
+what's got priority when tradeoffs have
+
+ align:start position:0%
+what's got priority when tradeoffs have
+ 
+
+ align:start position:0%
+what's got priority when tradeoffs have
+to be made what's the
+
+ align:start position:0%
+to be made what's the
+ 
+
+ align:start position:0%
+to be made what's the
+primary objective will come back to them
+
+ align:start position:0%
+primary objective will come back to them
+ 
+
+ align:start position:0%
+primary objective will come back to them
+but born versus
+
+ align:start position:0%
+but born versus
+ 
+
+ align:start position:0%
+but born versus
+made public versus private when we make
+
+ align:start position:0%
+made public versus private when we make
+ 
+
+ align:start position:0%
+made public versus private when we make
+these distinctions do we end up with a
+
+ align:start position:0%
+these distinctions do we end up with a
+ 
+
+ align:start position:0%
+these distinctions do we end up with a
+model of a leader that we would admire
+
+ align:start position:0%
+model of a leader that we would admire
+ 
+
+ align:start position:0%
+model of a leader that we would admire
+in any country in the
+
+ align:start position:0%
+in any country in the
+ 
+
+ align:start position:0%
+in any country in the
+world Maybe not maybe there's just
+
+ align:start position:0%
+world Maybe not maybe there's just
+ 
+
+ align:start position:0%
+world Maybe not maybe there's just
+radical differences by culture and
+
+ align:start position:0%
+radical differences by culture and
+ 
+
+ align:start position:0%
+radical differences by culture and
+context and location I'm very prepared
+
+ align:start position:0%
+context and location I'm very prepared
+ 
+
+ align:start position:0%
+context and location I'm very prepared
+to hear that that's a view that's come
+
+ align:start position:0%
+to hear that that's a view that's come
+ 
+
+ align:start position:0%
+to hear that that's a view that's come
+out of everybody the levels of
+
+ align:start position:0%
+out of everybody the levels of
+ 
+
+ align:start position:0%
+out of everybody the levels of
+governance uh Power relationships and
+
+ align:start position:0%
+governance uh Power relationships and
+ 
+
+ align:start position:0%
+governance uh Power relationships and
+power dynamics responsibility and even
+
+ align:start position:0%
+power dynamics responsibility and even
+ 
+
+ align:start position:0%
+power dynamics responsibility and even
+impact that the public and private
+
+ align:start position:0%
+impact that the public and private
+ 
+
+ align:start position:0%
+impact that the public and private
+sector may have they also would be
+
+ align:start position:0%
+sector may have they also would be
+ 
+
+ align:start position:0%
+sector may have they also would be
+reflected on some skills and
+
+ align:start position:0%
+reflected on some skills and
+ 
+
+ align:start position:0%
+reflected on some skills and
+characteristics that we be shared by
+
+ align:start position:0%
+characteristics that we be shared by
+ 
+
+ align:start position:0%
+characteristics that we be shared by
+both of them them there are certain
+
+ align:start position:0%
+both of them them there are certain
+ 
+
+ align:start position:0%
+both of them them there are certain
+characteristics and skills and nuanced
+
+ align:start position:0%
+characteristics and skills and nuanced
+ 
+
+ align:start position:0%
+characteristics and skills and nuanced
+and in even political sense that you
+
+ align:start position:0%
+and in even political sense that you
+ 
+
+ align:start position:0%
+and in even political sense that you
+will need in the public sector more than
+
+ align:start position:0%
+will need in the public sector more than
+ 
+
+ align:start position:0%
+will need in the public sector more than
+in the private sector in order to move
+
+ align:start position:0%
+in the private sector in order to move
+ 
+
+ align:start position:0%
+in the private sector in order to move
+forward initiatives in order to create
+
+ align:start position:0%
+forward initiatives in order to create
+ 
+
+ align:start position:0%
+forward initiatives in order to create
+consensus in order to engage with
+
+ align:start position:0%
+consensus in order to engage with
+ 
+
+ align:start position:0%
+consensus in order to engage with
+different communities um so we thought
+
+ align:start position:0%
+different communities um so we thought
+ 
+
+ align:start position:0%
+different communities um so we thought
+that it could be a little bit more
+
+ align:start position:0%
+that it could be a little bit more
+ 
+
+ align:start position:0%
+that it could be a little bit more
+complex in the public sector and
+
+ align:start position:0%
+complex in the public sector and
+ 
+
+ align:start position:0%
+complex in the public sector and
+therefore those skills must be
+
+ align:start position:0%
+therefore those skills must be
+ 
+
+ align:start position:0%
+therefore those skills must be
+enhanced something that we just
+
+ align:start position:0%
+enhanced something that we just
+ 
+
+ align:start position:0%
+enhanced something that we just
+discussed is the difference in the
+
+ align:start position:0%
+discussed is the difference in the
+ 
+
+ align:start position:0%
+discussed is the difference in the
+public sector versus the private sector
+
+ align:start position:0%
+public sector versus the private sector
+ 
+
+ align:start position:0%
+public sector versus the private sector
+of the accountability measures and how
+
+ align:start position:0%
+of the accountability measures and how
+ 
+
+ align:start position:0%
+of the accountability measures and how
+in a lot of different
+
+ align:start position:0%
+in a lot of different
+ 
+
+ align:start position:0%
+in a lot of different
+contexts across the world the public
+
+ align:start position:0%
+contexts across the world the public
+ 
+
+ align:start position:0%
+contexts across the world the public
+sector a big fault is that you might
+
+ align:start position:0%
+sector a big fault is that you might
+ 
+
+ align:start position:0%
+sector a big fault is that you might
+have a good relationship with people
+
+ align:start position:0%
+have a good relationship with people
+ 
+
+ align:start position:0%
+have a good relationship with people
+that you're interacting with through a
+
+ align:start position:0%
+that you're interacting with through a
+ 
+
+ align:start position:0%
+that you're interacting with through a
+public process but if there is no
+
+ align:start position:0%
+public process but if there is no
+ 
+
+ align:start position:0%
+public process but if there is no
+tangible outcome that people see from
+
+ align:start position:0%
+tangible outcome that people see from
+ 
+
+ align:start position:0%
+tangible outcome that people see from
+their time and efforts people are going
+
+ align:start position:0%
+their time and efforts people are going
+ 
+
+ align:start position:0%
+their time and efforts people are going
+to be frustrated and disempowered by the
+
+ align:start position:0%
+to be frustrated and disempowered by the
+ 
+
+ align:start position:0%
+to be frustrated and disempowered by the
+process and then they'll be much less
+
+ align:start position:0%
+process and then they'll be much less
+ 
+
+ align:start position:0%
+process and then they'll be much less
+likely or even ref used to participate
+
+ align:start position:0%
+likely or even ref used to participate
+ 
+
+ align:start position:0%
+likely or even ref used to participate
+again and in the private sector that is
+
+ align:start position:0%
+again and in the private sector that is
+ 
+
+ align:start position:0%
+again and in the private sector that is
+just not really something that people
+
+ align:start position:0%
+just not really something that people
+ 
+
+ align:start position:0%
+just not really something that people
+have to navigate because the
+
+ align:start position:0%
+have to navigate because the
+ 
+
+ align:start position:0%
+have to navigate because the
+accountability is already built into the
+
+ align:start position:0%
+accountability is already built into the
+ 
+
+ align:start position:0%
+accountability is already built into the
+leadership role and then we talked a
+
+ align:start position:0%
+leadership role and then we talked a
+ 
+
+ align:start position:0%
+leadership role and then we talked a
+little bit about the leaders
+
+ align:start position:0%
+little bit about the leaders
+ 
+
+ align:start position:0%
+little bit about the leaders
+facilitative leaders are made or born
+
+ align:start position:0%
+facilitative leaders are made or born
+ 
+
+ align:start position:0%
+facilitative leaders are made or born
+and I think collectively we did talk
+
+ align:start position:0%
+and I think collectively we did talk
+ 
+
+ align:start position:0%
+and I think collectively we did talk
+about they're mostly made because a lot
+
+ align:start position:0%
+about they're mostly made because a lot
+ 
+
+ align:start position:0%
+about they're mostly made because a lot
+of qualities that you did point out like
+
+ align:start position:0%
+of qualities that you did point out like
+ 
+
+ align:start position:0%
+of qualities that you did point out like
+empathy or active listening or putting
+
+ align:start position:0%
+empathy or active listening or putting
+ 
+
+ align:start position:0%
+empathy or active listening or putting
+your ego aside or organizational
+
+ align:start position:0%
+your ego aside or organizational
+ 
+
+ align:start position:0%
+your ego aside or organizational
+learning I feel like are things you
+
+ align:start position:0%
+learning I feel like are things you
+ 
+
+ align:start position:0%
+learning I feel like are things you
+learn by actually interacting with
+
+ align:start position:0%
+learn by actually interacting with
+ 
+
+ align:start position:0%
+learn by actually interacting with
+people by doing this again and again
+
+ align:start position:0%
+people by doing this again and again
+ 
+
+ align:start position:0%
+people by doing this again and again
+this process we need to stop thinking of
+
+ align:start position:0%
+this process we need to stop thinking of
+ 
+
+ align:start position:0%
+this process we need to stop thinking of
+this one person needs to have all of
+
+ align:start position:0%
+this one person needs to have all of
+ 
+
+ align:start position:0%
+this one person needs to have all of
+these qualities and maybe just think
+
+ align:start position:0%
+these qualities and maybe just think
+ 
+
+ align:start position:0%
+these qualities and maybe just think
+along the lines of how you can continue
+
+ align:start position:0%
+along the lines of how you can continue
+ 
+
+ align:start position:0%
+along the lines of how you can continue
+to do it better thank you okay um we'll
+
+ align:start position:0%
+to do it better thank you okay um we'll
+ 
+
+ align:start position:0%
+to do it better thank you okay um we'll
+meet again same time next week think
+
+ align:start position:0%
+meet again same time next week think
+ 
+
+ align:start position:0%
+meet again same time next week think
+about your own view of what makes a
+
+ align:start position:0%
+about your own view of what makes a
+ 
+
+ align:start position:0%
+about your own view of what makes a
+leader in the public sector successful
+
+ align:start position:0%
+leader in the public sector successful
+ 
+
+ align:start position:0%
+leader in the public sector successful
+okay so do think about that thank you
+
+ align:start position:0%
+okay so do think about that thank you
+ 
+
+ align:start position:0%
+okay so do think about that thank you
+all so much for coming and we'll see you
+
+ align:start position:0%
+all so much for coming and we'll see you
+ 
+
+ align:start position:0%
+all so much for coming and we'll see you
+next week
+
+ align:start position:0%
+next week
+ 
+
+ align:start position:0%
+next week
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
\ No newline at end of file
diff --git a/jisTDmIk3Nw.txt b/jisTDmIk3Nw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8d402b97ce7cdf63e63074155b6f58535cf3e7d0
--- /dev/null
+++ b/jisTDmIk3Nw.txt
@@ -0,0 +1,9779 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a nano tool
+
+ align:start position:0%
+so this is a nano tool
+ 
+
+ align:start position:0%
+so this is a nano tool
+macro principle process two five seven
+
+ align:start position:0%
+macro principle process two five seven
+ 
+
+ align:start position:0%
+macro principle process two five seven
+zero and for undergraduate students and
+
+ align:start position:0%
+zero and for undergraduate students and
+ 
+
+ align:start position:0%
+zero and for undergraduate students and
+257 for graduate student and it's
+
+ align:start position:0%
+257 for graduate student and it's
+ 
+
+ align:start position:0%
+257 for graduate student and it's
+offered every two years so I'm glad to
+
+ align:start position:0%
+offered every two years so I'm glad to
+ 
+
+ align:start position:0%
+offered every two years so I'm glad to
+say this is a probably largest audience
+
+ align:start position:0%
+say this is a probably largest audience
+ 
+
+ align:start position:0%
+say this is a probably largest audience
+I've ever had and so that's a very
+
+ align:start position:0%
+I've ever had and so that's a very
+ 
+
+ align:start position:0%
+I've ever had and so that's a very
+pleased to see the growing popularity
+
+ align:start position:0%
+pleased to see the growing popularity
+ 
+
+ align:start position:0%
+pleased to see the growing popularity
+the last time we did a OpenCourseWare I
+
+ align:start position:0%
+the last time we did a OpenCourseWare I
+ 
+
+ align:start position:0%
+the last time we did a OpenCourseWare I
+think there was a 2004 and that one we
+
+ align:start position:0%
+think there was a 2004 and that one we
+ 
+
+ align:start position:0%
+think there was a 2004 and that one we
+had a voice recording and typewritten
+
+ align:start position:0%
+had a voice recording and typewritten
+ 
+
+ align:start position:0%
+had a voice recording and typewritten
+notes and you can still go to the MIT
+
+ align:start position:0%
+notes and you can still go to the MIT
+ 
+
+ align:start position:0%
+notes and you can still go to the MIT
+OpenCourseWare if you miss a lecture I
+
+ align:start position:0%
+OpenCourseWare if you miss a lecture I
+ 
+
+ align:start position:0%
+OpenCourseWare if you miss a lecture I
+think although we do have changes the
+
+ align:start position:0%
+think although we do have changes the
+ 
+
+ align:start position:0%
+think although we do have changes the
+changes are not dramatic so you can go
+
+ align:start position:0%
+changes are not dramatic so you can go
+ 
+
+ align:start position:0%
+changes are not dramatic so you can go
+there and try to make that up if you
+
+ align:start position:0%
+there and try to make that up if you
+ 
+
+ align:start position:0%
+there and try to make that up if you
+miss any lectures and this semester MIT
+
+ align:start position:0%
+miss any lectures and this semester MIT
+ 
+
+ align:start position:0%
+miss any lectures and this semester MIT
+has a new initiative trying to put a
+
+ align:start position:0%
+has a new initiative trying to put a
+ 
+
+ align:start position:0%
+has a new initiative trying to put a
+course or video online and that's why I
+
+ align:start position:0%
+course or video online and that's why I
+ 
+
+ align:start position:0%
+course or video online and that's why I
+volunteered and also that way people can
+
+ align:start position:0%
+volunteered and also that way people can
+ 
+
+ align:start position:0%
+volunteered and also that way people can
+read my book better it's a hard book to
+
+ align:start position:0%
+read my book better it's a hard book to
+ 
+
+ align:start position:0%
+read my book better it's a hard book to
+read and in addition to my book there
+
+ align:start position:0%
+read and in addition to my book there
+ 
+
+ align:start position:0%
+read and in addition to my book there
+are also a list of books they recommend
+
+ align:start position:0%
+are also a list of books they recommend
+ 
+
+ align:start position:0%
+are also a list of books they recommend
+it because the USC that this course
+
+ align:start position:0%
+it because the USC that this course
+ 
+
+ align:start position:0%
+it because the USC that this course
+really cover a wide range of topics so
+
+ align:start position:0%
+really cover a wide range of topics so
+ 
+
+ align:start position:0%
+really cover a wide range of topics so
+we have given list of references for
+
+ align:start position:0%
+we have given list of references for
+ 
+
+ align:start position:0%
+we have given list of references for
+each subject you can always go to other
+
+ align:start position:0%
+each subject you can always go to other
+ 
+
+ align:start position:0%
+each subject you can always go to other
+books this is not necessary the use is
+
+ align:start position:0%
+books this is not necessary the use is
+ 
+
+ align:start position:0%
+books this is not necessary the use is
+to understand but to say we put it in on
+
+ align:start position:0%
+to understand but to say we put it in on
+ 
+
+ align:start position:0%
+to understand but to say we put it in on
+reserve in the library and with that I
+
+ align:start position:0%
+reserve in the library and with that I
+ 
+
+ align:start position:0%
+reserve in the library and with that I
+think it's pretty much the housekeeping
+
+ align:start position:0%
+think it's pretty much the housekeeping
+ 
+
+ align:start position:0%
+think it's pretty much the housekeeping
+item done and what I'm going to do next
+
+ align:start position:0%
+item done and what I'm going to do next
+ 
+
+ align:start position:0%
+item done and what I'm going to do next
+is to give you some slide this I'm not
+
+ align:start position:0%
+is to give you some slide this I'm not
+ 
+
+ align:start position:0%
+is to give you some slide this I'm not
+going to choose slides every week but
+
+ align:start position:0%
+going to choose slides every week but
+ 
+
+ align:start position:0%
+going to choose slides every week but
+I'm going to give you some slides to to
+
+ align:start position:0%
+I'm going to give you some slides to to
+ 
+
+ align:start position:0%
+I'm going to give you some slides to to
+see what's the scope of this course and
+
+ align:start position:0%
+see what's the scope of this course and
+ 
+
+ align:start position:0%
+see what's the scope of this course and
+some motivation or side so any questions
+
+ align:start position:0%
+some motivation or side so any questions
+ 
+
+ align:start position:0%
+some motivation or side so any questions
+if you look at the title this is nano -
+
+ align:start position:0%
+if you look at the title this is nano -
+ 
+
+ align:start position:0%
+if you look at the title this is nano -
+macro transport process so we'll
+
+ align:start position:0%
+macro transport process so we'll
+ 
+
+ align:start position:0%
+macro transport process so we'll
+emphasize the Nano
+
+ align:start position:0%
+emphasize the Nano
+ 
+
+ align:start position:0%
+emphasize the Nano
+were emphasizing transport we're also
+
+ align:start position:0%
+were emphasizing transport we're also
+ 
+
+ align:start position:0%
+were emphasizing transport we're also
+emphasizing the transition from Nano to
+
+ align:start position:0%
+emphasizing the transition from Nano to
+ 
+
+ align:start position:0%
+emphasizing the transition from Nano to
+macro and so those are they this is a
+
+ align:start position:0%
+macro and so those are they this is a
+ 
+
+ align:start position:0%
+macro and so those are they this is a
+slide from a colleague of mine before
+
+ align:start position:0%
+slide from a colleague of mine before
+ 
+
+ align:start position:0%
+slide from a colleague of mine before
+say and here what we're showing the lens
+
+ align:start position:0%
+say and here what we're showing the lens
+ 
+
+ align:start position:0%
+say and here what we're showing the lens
+skills that's in nature and learn skills
+
+ align:start position:0%
+skills that's in nature and learn skills
+ 
+
+ align:start position:0%
+skills that's in nature and learn skills
+all for what we made artificially I say
+
+ align:start position:0%
+all for what we made artificially I say
+ 
+
+ align:start position:0%
+all for what we made artificially I say
+leisure of course we have the biological
+
+ align:start position:0%
+leisure of course we have the biological
+ 
+
+ align:start position:0%
+leisure of course we have the biological
+side you can say going to from molecules
+
+ align:start position:0%
+side you can say going to from molecules
+ 
+
+ align:start position:0%
+side you can say going to from molecules
+through DNA to bacterial cells and
+
+ align:start position:0%
+through DNA to bacterial cells and
+ 
+
+ align:start position:0%
+through DNA to bacterial cells and
+progressively increase in this scale and
+
+ align:start position:0%
+progressively increase in this scale and
+ 
+
+ align:start position:0%
+progressively increase in this scale and
+then if we look at what people are
+
+ align:start position:0%
+then if we look at what people are
+ 
+
+ align:start position:0%
+then if we look at what people are
+making from for example this
+
+ align:start position:0%
+making from for example this
+ 
+
+ align:start position:0%
+making from for example this
+nanoparticles sometimes we call the
+
+ align:start position:0%
+nanoparticles sometimes we call the
+ 
+
+ align:start position:0%
+nanoparticles sometimes we call the
+quantum dots as small as a few one two
+
+ align:start position:0%
+quantum dots as small as a few one two
+ 
+
+ align:start position:0%
+quantum dots as small as a few one two
+to five nanometers and the two nano
+
+ align:start position:0%
+to five nanometers and the two nano
+ 
+
+ align:start position:0%
+to five nanometers and the two nano
+wires and nano electronics where they
+
+ align:start position:0%
+wires and nano electronics where they
+ 
+
+ align:start position:0%
+wires and nano electronics where they
+this is actually quite a few year old
+
+ align:start position:0%
+this is actually quite a few year old
+ 
+
+ align:start position:0%
+this is actually quite a few year old
+I think the gate length in
+
+ align:start position:0%
+I think the gate length in
+ 
+
+ align:start position:0%
+I think the gate length in
+semiconductors now is just around few
+
+ align:start position:0%
+semiconductors now is just around few
+ 
+
+ align:start position:0%
+semiconductors now is just around few
+tens ten twenty nanometers so those are
+
+ align:start position:0%
+tens ten twenty nanometers so those are
+ 
+
+ align:start position:0%
+tens ten twenty nanometers so those are
+they are making smaller and smaller
+
+ align:start position:0%
+they are making smaller and smaller
+ 
+
+ align:start position:0%
+they are making smaller and smaller
+devices and of course at the end
+
+ align:start position:0%
+devices and of course at the end
+ 
+
+ align:start position:0%
+devices and of course at the end
+whatever interfacing is at the macro
+
+ align:start position:0%
+whatever interfacing is at the macro
+ 
+
+ align:start position:0%
+whatever interfacing is at the macro
+scale so when we go through small scales
+
+ align:start position:0%
+scale so when we go through small scales
+ 
+
+ align:start position:0%
+scale so when we go through small scales
+the questions because you have learned a
+
+ align:start position:0%
+the questions because you have learned a
+ 
+
+ align:start position:0%
+the questions because you have learned a
+lot in the transport theory for example
+
+ align:start position:0%
+lot in the transport theory for example
+ 
+
+ align:start position:0%
+lot in the transport theory for example
+the question is are they valid or not
+
+ align:start position:0%
+the question is are they valid or not
+ 
+
+ align:start position:0%
+the question is are they valid or not
+right and what if they are not valid
+
+ align:start position:0%
+right and what if they are not valid
+ 
+
+ align:start position:0%
+right and what if they are not valid
+what are the alternatives and also we're
+
+ align:start position:0%
+what are the alternatives and also we're
+ 
+
+ align:start position:0%
+what are the alternatives and also we're
+not just looking at the individual
+
+ align:start position:0%
+not just looking at the individual
+ 
+
+ align:start position:0%
+not just looking at the individual
+nanoparticles when you put them together
+
+ align:start position:0%
+nanoparticles when you put them together
+ 
+
+ align:start position:0%
+nanoparticles when you put them together
+and it will macro scale what's the
+
+ align:start position:0%
+and it will macro scale what's the
+ 
+
+ align:start position:0%
+and it will macro scale what's the
+picture here so this is where this
+
+ align:start position:0%
+picture here so this is where this
+ 
+
+ align:start position:0%
+picture here so this is where this
+course is trying to wrestle with and
+
+ align:start position:0%
+course is trying to wrestle with and
+ 
+
+ align:start position:0%
+course is trying to wrestle with and
+that's in fact that most of my research
+
+ align:start position:0%
+that's in fact that most of my research
+ 
+
+ align:start position:0%
+that's in fact that most of my research
+is looking to thinking how we can look
+
+ align:start position:0%
+is looking to thinking how we can look
+ 
+
+ align:start position:0%
+is looking to thinking how we can look
+at this small and then how using the
+
+ align:start position:0%
+at this small and then how using the
+ 
+
+ align:start position:0%
+at this small and then how using the
+small to do the big things particularly
+
+ align:start position:0%
+small to do the big things particularly
+ 
+
+ align:start position:0%
+small to do the big things particularly
+most of the work I'm working on is the
+
+ align:start position:0%
+most of the work I'm working on is the
+ 
+
+ align:start position:0%
+most of the work I'm working on is the
+heat transfer relate to
+
+ align:start position:0%
+heat transfer relate to
+ 
+
+ align:start position:0%
+heat transfer relate to
+energy and energy is an odd skill so how
+
+ align:start position:0%
+energy and energy is an odd skill so how
+ 
+
+ align:start position:0%
+energy and energy is an odd skill so how
+I can take small to go to the large and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me give you two examples that from
+
+ align:start position:0%
+let me give you two examples that from
+ 
+
+ align:start position:0%
+let me give you two examples that from
+research to show that when you go to
+
+ align:start position:0%
+research to show that when you go to
+ 
+
+ align:start position:0%
+research to show that when you go to
+nano scale the classical theory that you
+
+ align:start position:0%
+nano scale the classical theory that you
+ 
+
+ align:start position:0%
+nano scale the classical theory that you
+have learned breaks down and the first
+
+ align:start position:0%
+have learned breaks down and the first
+ 
+
+ align:start position:0%
+have learned breaks down and the first
+example is a heat conduction example
+
+ align:start position:0%
+example is a heat conduction example
+ 
+
+ align:start position:0%
+example is a heat conduction example
+right we we we know in heat conduction
+
+ align:start position:0%
+right we we we know in heat conduction
+ 
+
+ align:start position:0%
+right we we we know in heat conduction
+we have four law and we have a thermal
+
+ align:start position:0%
+we have four law and we have a thermal
+ 
+
+ align:start position:0%
+we have four law and we have a thermal
+conductivity of the materials and this
+
+ align:start position:0%
+conductivity of the materials and this
+ 
+
+ align:start position:0%
+conductivity of the materials and this
+is the why example of nano this is in
+
+ align:start position:0%
+is the why example of nano this is in
+ 
+
+ align:start position:0%
+is the why example of nano this is in
+fact transmission electron microscopy
+
+ align:start position:0%
+fact transmission electron microscopy
+ 
+
+ align:start position:0%
+fact transmission electron microscopy
+image of a layer structure one layer the
+
+ align:start position:0%
+image of a layer structure one layer the
+ 
+
+ align:start position:0%
+image of a layer structure one layer the
+bright layer is silicon the darker layer
+
+ align:start position:0%
+bright layer is silicon the darker layer
+ 
+
+ align:start position:0%
+bright layer is silicon the darker layer
+is germanium so each layer is about two
+
+ align:start position:0%
+is germanium so each layer is about two
+ 
+
+ align:start position:0%
+is germanium so each layer is about two
+nanometers and when you measure thermal
+
+ align:start position:0%
+nanometers and when you measure thermal
+ 
+
+ align:start position:0%
+nanometers and when you measure thermal
+conductivity so you can take a silicon
+
+ align:start position:0%
+conductivity so you can take a silicon
+ 
+
+ align:start position:0%
+conductivity so you can take a silicon
+because the one layer stick on the other
+
+ align:start position:0%
+because the one layer stick on the other
+ 
+
+ align:start position:0%
+because the one layer stick on the other
+is germanium right so you have started
+
+ align:start position:0%
+is germanium right so you have started
+ 
+
+ align:start position:0%
+is germanium right so you have started
+heat transfer it's parallel plates and
+
+ align:start position:0%
+heat transfer it's parallel plates and
+ 
+
+ align:start position:0%
+heat transfer it's parallel plates and
+you can do thermal resistors to see
+
+ align:start position:0%
+you can do thermal resistors to see
+ 
+
+ align:start position:0%
+you can do thermal resistors to see
+what's the factor with thermal
+
+ align:start position:0%
+what's the factor with thermal
+ 
+
+ align:start position:0%
+what's the factor with thermal
+conductivity and you can say if I take a
+
+ align:start position:0%
+conductivity and you can say if I take a
+ 
+
+ align:start position:0%
+conductivity and you can say if I take a
+silicon germanium thermal conductivity I
+
+ align:start position:0%
+silicon germanium thermal conductivity I
+ 
+
+ align:start position:0%
+silicon germanium thermal conductivity I
+will predict that's the equivalent
+
+ align:start position:0%
+will predict that's the equivalent
+ 
+
+ align:start position:0%
+will predict that's the equivalent
+thermal kinetic those open circles but
+
+ align:start position:0%
+thermal kinetic those open circles but
+ 
+
+ align:start position:0%
+thermal kinetic those open circles but
+the experimentally measured dots are
+
+ align:start position:0%
+the experimentally measured dots are
+ 
+
+ align:start position:0%
+the experimentally measured dots are
+order magnitude smaller and in fact we
+
+ align:start position:0%
+order magnitude smaller and in fact we
+ 
+
+ align:start position:0%
+order magnitude smaller and in fact we
+have to go to complete different theory
+
+ align:start position:0%
+have to go to complete different theory
+ 
+
+ align:start position:0%
+have to go to complete different theory
+in this case we have to go to boards my
+
+ align:start position:0%
+in this case we have to go to boards my
+ 
+
+ align:start position:0%
+in this case we have to go to boards my
+equation to predict now so this is a
+
+ align:start position:0%
+equation to predict now so this is a
+ 
+
+ align:start position:0%
+equation to predict now so this is a
+work that we started in 90s and now
+
+ align:start position:0%
+work that we started in 90s and now
+ 
+
+ align:start position:0%
+work that we started in 90s and now
+we're doing quantum calculations on
+
+ align:start position:0%
+we're doing quantum calculations on
+ 
+
+ align:start position:0%
+we're doing quantum calculations on
+those structures right so there's
+
+ align:start position:0%
+those structures right so there's
+ 
+
+ align:start position:0%
+those structures right so there's
+significant departure from the classical
+
+ align:start position:0%
+significant departure from the classical
+ 
+
+ align:start position:0%
+significant departure from the classical
+theory when you go to nano skills and is
+
+ align:start position:0%
+theory when you go to nano skills and is
+ 
+
+ align:start position:0%
+theory when you go to nano skills and is
+another example you learn in thermal
+
+ align:start position:0%
+another example you learn in thermal
+ 
+
+ align:start position:0%
+another example you learn in thermal
+radiation blackbody is the maximum on
+
+ align:start position:0%
+radiation blackbody is the maximum on
+ 
+
+ align:start position:0%
+radiation blackbody is the maximum on
+thermal radiation right but see when we
+
+ align:start position:0%
+thermal radiation right but see when we
+ 
+
+ align:start position:0%
+thermal radiation right but see when we
+go to nano scale when we put two objects
+
+ align:start position:0%
+go to nano scale when we put two objects
+ 
+
+ align:start position:0%
+go to nano scale when we put two objects
+smaller the distance this was an MIT
+
+ align:start position:0%
+smaller the distance this was an MIT
+ 
+
+ align:start position:0%
+smaller the distance this was an MIT
+webpage I really like this they're very
+
+ align:start position:0%
+webpage I really like this they're very
+ 
+
+ align:start position:0%
+webpage I really like this they're very
+creative much less say this is a better
+
+ align:start position:0%
+creative much less say this is a better
+ 
+
+ align:start position:0%
+creative much less say this is a better
+than what we did so that's a
+
+ align:start position:0%
+than what we did so that's a
+ 
+
+ align:start position:0%
+than what we did so that's a
+slow blackbody radiation and that's
+
+ align:start position:0%
+slow blackbody radiation and that's
+ 
+
+ align:start position:0%
+slow blackbody radiation and that's
+usually consider maximum and when we put
+
+ align:start position:0%
+usually consider maximum and when we put
+ 
+
+ align:start position:0%
+usually consider maximum and when we put
+two surfaces down to nano scale right
+
+ align:start position:0%
+two surfaces down to nano scale right
+ 
+
+ align:start position:0%
+two surfaces down to nano scale right
+here is 1 micron 100 nanometer and
+
+ align:start position:0%
+here is 1 micron 100 nanometer and
+ 
+
+ align:start position:0%
+here is 1 micron 100 nanometer and
+attend nanometer we can go beyond the
+
+ align:start position:0%
+attend nanometer we can go beyond the
+ 
+
+ align:start position:0%
+attend nanometer we can go beyond the
+Planck's law by several automatic do
+
+ align:start position:0%
+Planck's law by several automatic do
+ 
+
+ align:start position:0%
+Planck's law by several automatic do
+right when I say we're this is a three
+
+ align:start position:0%
+right when I say we're this is a three
+ 
+
+ align:start position:0%
+right when I say we're this is a three
+order magnitude we're not at the four
+
+ align:start position:0%
+order magnitude we're not at the four
+ 
+
+ align:start position:0%
+order magnitude we're not at the four
+order magnitude and we're look we're
+
+ align:start position:0%
+order magnitude and we're look we're
+ 
+
+ align:start position:0%
+order magnitude and we're look we're
+looking at what happens between that one
+
+ align:start position:0%
+looking at what happens between that one
+ 
+
+ align:start position:0%
+looking at what happens between that one
+nanometer and contact and you see why
+
+ align:start position:0%
+nanometer and contact and you see why
+ 
+
+ align:start position:0%
+nanometer and contact and you see why
+you Cure's right the factor is when I
+
+ align:start position:0%
+you Cure's right the factor is when I
+ 
+
+ align:start position:0%
+you Cure's right the factor is when I
+put many materials together they say
+
+ align:start position:0%
+put many materials together they say
+ 
+
+ align:start position:0%
+put many materials together they say
+it's a really particle when I do Canal
+
+ align:start position:0%
+it's a really particle when I do Canal
+ 
+
+ align:start position:0%
+it's a really particle when I do Canal
+oh it's really the interface dominates
+
+ align:start position:0%
+oh it's really the interface dominates
+ 
+
+ align:start position:0%
+oh it's really the interface dominates
+and so that interface is sometimes the
+
+ align:start position:0%
+and so that interface is sometimes the
+ 
+
+ align:start position:0%
+and so that interface is sometimes the
+contact share each other sometimes they
+
+ align:start position:0%
+contact share each other sometimes they
+ 
+
+ align:start position:0%
+contact share each other sometimes they
+do not so this is a the the connection I
+
+ align:start position:0%
+do not so this is a the the connection I
+ 
+
+ align:start position:0%
+do not so this is a the the connection I
+say how I can take this nanoscale and
+
+ align:start position:0%
+say how I can take this nanoscale and
+ 
+
+ align:start position:0%
+say how I can take this nanoscale and
+you actually go to macro scale so I this
+
+ align:start position:0%
+you actually go to macro scale so I this
+ 
+
+ align:start position:0%
+you actually go to macro scale so I this
+is a propaganda I do nano I say once I
+
+ align:start position:0%
+is a propaganda I do nano I say once I
+ 
+
+ align:start position:0%
+is a propaganda I do nano I say once I
+was asked by graduate students
+
+ align:start position:0%
+was asked by graduate students
+ 
+
+ align:start position:0%
+was asked by graduate students
+summarized research in three words
+
+ align:start position:0%
+summarized research in three words
+ 
+
+ align:start position:0%
+summarized research in three words
+that's like what I came up
+
+ align:start position:0%
+that's like what I came up
+ 
+
+ align:start position:0%
+that's like what I came up
+nano heat energy and what I had
+
+ align:start position:0%
+nano heat energy and what I had
+ 
+
+ align:start position:0%
+nano heat energy and what I had
+benefited over the years is I mean
+
+ align:start position:0%
+benefited over the years is I mean
+ 
+
+ align:start position:0%
+benefited over the years is I mean
+mechanical engineer I'm a mechanical
+
+ align:start position:0%
+mechanical engineer I'm a mechanical
+ 
+
+ align:start position:0%
+mechanical engineer I'm a mechanical
+engineer I always say at the end what I
+
+ align:start position:0%
+engineer I always say at the end what I
+ 
+
+ align:start position:0%
+engineer I always say at the end what I
+do want to be useful right so I think
+
+ align:start position:0%
+do want to be useful right so I think
+ 
+
+ align:start position:0%
+do want to be useful right so I think
+about atoms but I also think about
+
+ align:start position:0%
+about atoms but I also think about
+ 
+
+ align:start position:0%
+about atoms but I also think about
+continue and I see we have few things we
+
+ align:start position:0%
+continue and I see we have few things we
+ 
+
+ align:start position:0%
+continue and I see we have few things we
+can probably claim that that we had
+
+ align:start position:0%
+can probably claim that that we had
+ 
+
+ align:start position:0%
+can probably claim that that we had
+really done some change in the materials
+
+ align:start position:0%
+really done some change in the materials
+ 
+
+ align:start position:0%
+really done some change in the materials
+I gave an example on this thermal
+
+ align:start position:0%
+I gave an example on this thermal
+ 
+
+ align:start position:0%
+I gave an example on this thermal
+connectivity germanium super
+
+ align:start position:0%
+connectivity germanium super
+ 
+
+ align:start position:0%
+connectivity germanium super
+lattice the layer structure and we're
+
+ align:start position:0%
+lattice the layer structure and we're
+ 
+
+ align:start position:0%
+lattice the layer structure and we're
+taking that to make a better thermal
+
+ align:start position:0%
+taking that to make a better thermal
+ 
+
+ align:start position:0%
+taking that to make a better thermal
+actually energy converters because we
+
+ align:start position:0%
+actually energy converters because we
+ 
+
+ align:start position:0%
+actually energy converters because we
+need amateurs with the pool heat
+
+ align:start position:0%
+need amateurs with the pool heat
+ 
+
+ align:start position:0%
+need amateurs with the pool heat
+conduction and that we still need the
+
+ align:start position:0%
+conduction and that we still need the
+ 
+
+ align:start position:0%
+conduction and that we still need the
+electron goes through so this is a very
+
+ align:start position:0%
+electron goes through so this is a very
+ 
+
+ align:start position:0%
+electron goes through so this is a very
+contradictory requirement and currently
+
+ align:start position:0%
+contradictory requirement and currently
+ 
+
+ align:start position:0%
+contradictory requirement and currently
+we're working on on this photon side
+
+ align:start position:0%
+we're working on on this photon side
+ 
+
+ align:start position:0%
+we're working on on this photon side
+that were designing nano structured
+
+ align:start position:0%
+that were designing nano structured
+ 
+
+ align:start position:0%
+that were designing nano structured
+to do user nest material to do solar
+
+ align:start position:0%
+to do user nest material to do solar
+ 
+
+ align:start position:0%
+to do user nest material to do solar
+cells and we have a some of the most
+
+ align:start position:0%
+cells and we have a some of the most
+ 
+
+ align:start position:0%
+cells and we have a some of the most
+conductive liquid just by putting
+
+ align:start position:0%
+conductive liquid just by putting
+ 
+
+ align:start position:0%
+conductive liquid just by putting
+nanoparticles in the liquid and find out
+
+ align:start position:0%
+nanoparticles in the liquid and find out
+ 
+
+ align:start position:0%
+nanoparticles in the liquid and find out
+what's the thermal conductivity in fact
+
+ align:start position:0%
+what's the thermal conductivity in fact
+ 
+
+ align:start position:0%
+what's the thermal conductivity in fact
+at the end that we say I don't want the
+
+ align:start position:0%
+at the end that we say I don't want the
+ 
+
+ align:start position:0%
+at the end that we say I don't want the
+average in nano that's where you
+
+ align:start position:0%
+average in nano that's where you
+ 
+
+ align:start position:0%
+average in nano that's where you
+understand if you understand physics
+
+ align:start position:0%
+understand if you understand physics
+ 
+
+ align:start position:0%
+understand if you understand physics
+another area is nano also right so we
+
+ align:start position:0%
+another area is nano also right so we
+ 
+
+ align:start position:0%
+another area is nano also right so we
+work on people put in a particular into
+
+ align:start position:0%
+work on people put in a particular into
+ 
+
+ align:start position:0%
+work on people put in a particular into
+liquid some say have high thermal
+
+ align:start position:0%
+liquid some say have high thermal
+ 
+
+ align:start position:0%
+liquid some say have high thermal
+conductivity others go to lab they say
+
+ align:start position:0%
+conductivity others go to lab they say
+ 
+
+ align:start position:0%
+conductivity others go to lab they say
+no we can't measure it we struggle for
+
+ align:start position:0%
+no we can't measure it we struggle for
+ 
+
+ align:start position:0%
+no we can't measure it we struggle for
+four years and we should we figure out
+
+ align:start position:0%
+four years and we should we figure out
+ 
+
+ align:start position:0%
+four years and we should we figure out
+we say okay
+
+ align:start position:0%
+we say okay
+ 
+
+ align:start position:0%
+we say okay
+usually what we need is a macro in one
+
+ align:start position:0%
+usually what we need is a macro in one
+ 
+
+ align:start position:0%
+usually what we need is a macro in one
+direction and Natalie in the other
+
+ align:start position:0%
+direction and Natalie in the other
+ 
+
+ align:start position:0%
+direction and Natalie in the other
+direction and that's how we achieve the
+
+ align:start position:0%
+direction and that's how we achieve the
+ 
+
+ align:start position:0%
+direction and that's how we achieve the
+best thermal conductivity and we also
+
+ align:start position:0%
+best thermal conductivity and we also
+ 
+
+ align:start position:0%
+best thermal conductivity and we also
+have most conductive polymers I get a
+
+ align:start position:0%
+have most conductive polymers I get a
+ 
+
+ align:start position:0%
+have most conductive polymers I get a
+call every every every month almost
+
+ align:start position:0%
+call every every every month almost
+ 
+
+ align:start position:0%
+call every every every month almost
+affirming industry to say can we have it
+
+ align:start position:0%
+affirming industry to say can we have it
+ 
+
+ align:start position:0%
+affirming industry to say can we have it
+so the question was polymers plastics
+
+ align:start position:0%
+so the question was polymers plastics
+ 
+
+ align:start position:0%
+so the question was polymers plastics
+are typically pool heat conduction right
+
+ align:start position:0%
+are typically pool heat conduction right
+ 
+
+ align:start position:0%
+are typically pool heat conduction right
+so people always want to make them more
+
+ align:start position:0%
+so people always want to make them more
+ 
+
+ align:start position:0%
+so people always want to make them more
+conductive some most people work is
+
+ align:start position:0%
+conductive some most people work is
+ 
+
+ align:start position:0%
+conductive some most people work is
+making them more electrically conductive
+
+ align:start position:0%
+making them more electrically conductive
+ 
+
+ align:start position:0%
+making them more electrically conductive
+but see when I ask the question I've got
+
+ align:start position:0%
+but see when I ask the question I've got
+ 
+
+ align:start position:0%
+but see when I ask the question I've got
+a call from Intel say can you think
+
+ align:start position:0%
+a call from Intel say can you think
+ 
+
+ align:start position:0%
+a call from Intel say can you think
+about how I can better manage your heat
+
+ align:start position:0%
+about how I can better manage your heat
+ 
+
+ align:start position:0%
+about how I can better manage your heat
+I start thinking of plastics so how I
+
+ align:start position:0%
+I start thinking of plastics so how I
+ 
+
+ align:start position:0%
+I start thinking of plastics so how I
+make them more conductive and if you
+
+ align:start position:0%
+make them more conductive and if you
+ 
+
+ align:start position:0%
+make them more conductive and if you
+look at how people are usually do it
+
+ align:start position:0%
+look at how people are usually do it
+ 
+
+ align:start position:0%
+look at how people are usually do it
+they're putting composite they're
+
+ align:start position:0%
+they're putting composite they're
+ 
+
+ align:start position:0%
+they're putting composite they're
+putting a lot of component and make them
+
+ align:start position:0%
+putting a lot of component and make them
+ 
+
+ align:start position:0%
+putting a lot of component and make them
+averaged speaking a higher conduct
+
+ align:start position:0%
+averaged speaking a higher conduct
+ 
+
+ align:start position:0%
+averaged speaking a higher conduct
+higher heat conduction and when I think
+
+ align:start position:0%
+higher heat conduction and when I think
+ 
+
+ align:start position:0%
+higher heat conduction and when I think
+about this okay of course that's
+
+ align:start position:0%
+about this okay of course that's
+ 
+
+ align:start position:0%
+about this okay of course that's
+approach one of the approach but see the
+
+ align:start position:0%
+approach one of the approach but see the
+ 
+
+ align:start position:0%
+approach one of the approach but see the
+question we ask is a molecule a polymer
+
+ align:start position:0%
+question we ask is a molecule a polymer
+ 
+
+ align:start position:0%
+question we ask is a molecule a polymer
+really a poor heat conductor it's a
+
+ align:start position:0%
+really a poor heat conductor it's a
+ 
+
+ align:start position:0%
+really a poor heat conductor it's a
+molecular champuli hikmah poor heat
+
+ align:start position:0%
+molecular champuli hikmah poor heat
+ 
+
+ align:start position:0%
+molecular champuli hikmah poor heat
+conductor if you think of a polyethylene
+
+ align:start position:0%
+conductor if you think of a polyethylene
+ 
+
+ align:start position:0%
+conductor if you think of a polyethylene
+which is sixty percent of the plastics
+
+ align:start position:0%
+which is sixty percent of the plastics
+ 
+
+ align:start position:0%
+which is sixty percent of the plastics
+and it's a carbon carbon bonding right
+
+ align:start position:0%
+and it's a carbon carbon bonding right
+ 
+
+ align:start position:0%
+and it's a carbon carbon bonding right
+and carbon carbon what's the highest the
+
+ align:start position:0%
+and carbon carbon what's the highest the
+ 
+
+ align:start position:0%
+and carbon carbon what's the highest the
+thermal conductivity mature anyone know
+
+ align:start position:0%
+thermal conductivity mature anyone know
+ 
+
+ align:start position:0%
+thermal conductivity mature anyone know
+diamond carbon-carbon bond right so that
+
+ align:start position:0%
+diamond carbon-carbon bond right so that
+ 
+
+ align:start position:0%
+diamond carbon-carbon bond right so that
+suggests and the molecular chain the
+
+ align:start position:0%
+suggests and the molecular chain the
+ 
+
+ align:start position:0%
+suggests and the molecular chain the
+Russian I should have a high heat
+
+ align:start position:0%
+Russian I should have a high heat
+ 
+
+ align:start position:0%
+Russian I should have a high heat
+thermal conductivity right so you think
+
+ align:start position:0%
+thermal conductivity right so you think
+ 
+
+ align:start position:0%
+thermal conductivity right so you think
+about the nano you single more let
+
+ align:start position:0%
+about the nano you single more let
+ 
+
+ align:start position:0%
+about the nano you single more let
+molecules and in fact I say of course I
+
+ align:start position:0%
+molecules and in fact I say of course I
+ 
+
+ align:start position:0%
+molecules and in fact I say of course I
+can put in most fancy or theory I go to
+
+ align:start position:0%
+can put in most fancy or theory I go to
+ 
+
+ align:start position:0%
+can put in most fancy or theory I go to
+Fermi and he did work in the fifties he
+
+ align:start position:0%
+Fermi and he did work in the fifties he
+ 
+
+ align:start position:0%
+Fermi and he did work in the fifties he
+said one dimensional conductor has the
+
+ align:start position:0%
+said one dimensional conductor has the
+ 
+
+ align:start position:0%
+said one dimensional conductor has the
+infinite thermal conductivity so they
+
+ align:start position:0%
+infinite thermal conductivity so they
+ 
+
+ align:start position:0%
+infinite thermal conductivity so they
+give me a lot of motivation to look into
+
+ align:start position:0%
+give me a lot of motivation to look into
+ 
+
+ align:start position:0%
+give me a lot of motivation to look into
+that and in turn we did succeed in
+
+ align:start position:0%
+that and in turn we did succeed in
+ 
+
+ align:start position:0%
+that and in turn we did succeed in
+actually create the most conductive
+
+ align:start position:0%
+actually create the most conductive
+ 
+
+ align:start position:0%
+actually create the most conductive
+polymer except I seen one single fiber
+
+ align:start position:0%
+polymer except I seen one single fiber
+ 
+
+ align:start position:0%
+polymer except I seen one single fiber
+nano fiber right so I say I got a course
+
+ align:start position:0%
+nano fiber right so I say I got a course
+ 
+
+ align:start position:0%
+nano fiber right so I say I got a course
+every month from company I said you guys
+
+ align:start position:0%
+every month from company I said you guys
+ 
+
+ align:start position:0%
+every month from company I said you guys
+have to wait or you give me money we do
+
+ align:start position:0%
+have to wait or you give me money we do
+ 
+
+ align:start position:0%
+have to wait or you give me money we do
+more research because I need to scale
+
+ align:start position:0%
+more research because I need to scale
+ 
+
+ align:start position:0%
+more research because I need to scale
+this up right because you usually am not
+
+ align:start position:0%
+this up right because you usually am not
+ 
+
+ align:start position:0%
+this up right because you usually am not
+using single nano fiber to put in your
+
+ align:start position:0%
+using single nano fiber to put in your
+ 
+
+ align:start position:0%
+using single nano fiber to put in your
+heat exchangers so that's what I say you
+
+ align:start position:0%
+heat exchangers so that's what I say you
+ 
+
+ align:start position:0%
+heat exchangers so that's what I say you
+need to think of nano you have leather
+
+ align:start position:0%
+need to think of nano you have leather
+ 
+
+ align:start position:0%
+need to think of nano you have leather
+you can generate more new ideas but also
+
+ align:start position:0%
+you can generate more new ideas but also
+ 
+
+ align:start position:0%
+you can generate more new ideas but also
+you to think to how you can go to macro
+
+ align:start position:0%
+you to think to how you can go to macro
+ 
+
+ align:start position:0%
+you to think to how you can go to macro
+and so this when I say what's the matter
+
+ align:start position:0%
+and so this when I say what's the matter
+ 
+
+ align:start position:0%
+and so this when I say what's the matter
+for energy right if you think about
+
+ align:start position:0%
+for energy right if you think about
+ 
+
+ align:start position:0%
+for energy right if you think about
+energy at the end it's molecules that
+
+ align:start position:0%
+energy at the end it's molecules that
+ 
+
+ align:start position:0%
+energy at the end it's molecules that
+you will for mechanical engineer
+
+ align:start position:0%
+you will for mechanical engineer
+ 
+
+ align:start position:0%
+you will for mechanical engineer
+familiar with it's the electrons and
+
+ align:start position:0%
+familiar with it's the electrons and
+ 
+
+ align:start position:0%
+familiar with it's the electrons and
+it's a fold hung delight or its lattice
+
+ align:start position:0%
+it's a fold hung delight or its lattice
+ 
+
+ align:start position:0%
+it's a fold hung delight or its lattice
+vibration fold on but those are the
+
+ align:start position:0%
+vibration fold on but those are the
+ 
+
+ align:start position:0%
+vibration fold on but those are the
+basic energy carrier there some other
+
+ align:start position:0%
+basic energy carrier there some other
+ 
+
+ align:start position:0%
+basic energy carrier there some other
+terms say but let's see those are the
+
+ align:start position:0%
+terms say but let's see those are the
+ 
+
+ align:start position:0%
+terms say but let's see those are the
+basic energy carriers right Woodstock
+
+ align:start position:0%
+basic energy carriers right Woodstock
+ 
+
+ align:start position:0%
+basic energy carriers right Woodstock
+high risk Allen's the mean free path and
+
+ align:start position:0%
+high risk Allen's the mean free path and
+ 
+
+ align:start position:0%
+high risk Allen's the mean free path and
+the wavelengths right so the mean free
+
+ align:start position:0%
+the wavelengths right so the mean free
+ 
+
+ align:start position:0%
+the wavelengths right so the mean free
+path of air molecule will get into that
+
+ align:start position:0%
+path of air molecule will get into that
+ 
+
+ align:start position:0%
+path of air molecule will get into that
+very shown in this room is about a
+
+ align:start position:0%
+very shown in this room is about a
+ 
+
+ align:start position:0%
+very shown in this room is about a
+hundred nanometer and that means they
+
+ align:start position:0%
+hundred nanometer and that means they
+ 
+
+ align:start position:0%
+hundred nanometer and that means they
+travel 100 nanometer and the collided
+
+ align:start position:0%
+travel 100 nanometer and the collided
+ 
+
+ align:start position:0%
+travel 100 nanometer and the collided
+with another molecule and the
+
+ align:start position:0%
+with another molecule and the
+ 
+
+ align:start position:0%
+with another molecule and the
+wavelengths of light visible light
+
+ align:start position:0%
+wavelengths of light visible light
+ 
+
+ align:start position:0%
+wavelengths of light visible light
+how much wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+400 nanometer to 5 a 2 to 700 nanometer
+
+ align:start position:0%
+400 nanometer to 5 a 2 to 700 nanometer
+ 
+
+ align:start position:0%
+400 nanometer to 5 a 2 to 700 nanometer
+ring right
+
+ align:start position:0%
+ring right
+ 
+
+ align:start position:0%
+ring right
+so 1/2 micron and so a lot of this in
+
+ align:start position:0%
+so 1/2 micron and so a lot of this in
+ 
+
+ align:start position:0%
+so 1/2 micron and so a lot of this in
+the nanometer range and if you think
+
+ align:start position:0%
+the nanometer range and if you think
+ 
+
+ align:start position:0%
+the nanometer range and if you think
+about energy fundamentally if you can
+
+ align:start position:0%
+about energy fundamentally if you can
+ 
+
+ align:start position:0%
+about energy fundamentally if you can
+control the energy level of material has
+
+ align:start position:0%
+control the energy level of material has
+ 
+
+ align:start position:0%
+control the energy level of material has
+for example if I make a quantum dots
+
+ align:start position:0%
+for example if I make a quantum dots
+ 
+
+ align:start position:0%
+for example if I make a quantum dots
+that I showed before 5 nanometer spheres
+
+ align:start position:0%
+that I showed before 5 nanometer spheres
+ 
+
+ align:start position:0%
+that I showed before 5 nanometer spheres
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+particles what happens is a electron
+
+ align:start position:0%
+particles what happens is a electron
+ 
+
+ align:start position:0%
+particles what happens is a electron
+quantum mechanics it's a way right and
+
+ align:start position:0%
+quantum mechanics it's a way right and
+ 
+
+ align:start position:0%
+quantum mechanics it's a way right and
+that way we had the wavelength and
+
+ align:start position:0%
+that way we had the wavelength and
+ 
+
+ align:start position:0%
+that way we had the wavelength and
+typical wavelength is you can say let's
+
+ align:start position:0%
+typical wavelength is you can say let's
+ 
+
+ align:start position:0%
+typical wavelength is you can say let's
+say 10 nanometer now a wave of 10
+
+ align:start position:0%
+say 10 nanometer now a wave of 10
+ 
+
+ align:start position:0%
+say 10 nanometer now a wave of 10
+nanometer you try to fit into that 5
+
+ align:start position:0%
+nanometer you try to fit into that 5
+ 
+
+ align:start position:0%
+nanometer you try to fit into that 5
+nanometer quantum dot what happens you
+
+ align:start position:0%
+nanometer quantum dot what happens you
+ 
+
+ align:start position:0%
+nanometer quantum dot what happens you
+squeeze that wave right you squeeze that
+
+ align:start position:0%
+squeeze that wave right you squeeze that
+ 
+
+ align:start position:0%
+squeeze that wave right you squeeze that
+way the energy level will change so if
+
+ align:start position:0%
+way the energy level will change so if
+ 
+
+ align:start position:0%
+way the energy level will change so if
+you look at the professor mu nipple in
+
+ align:start position:0%
+you look at the professor mu nipple in
+ 
+
+ align:start position:0%
+you look at the professor mu nipple in
+this homepage you will see the quantum
+
+ align:start position:0%
+this homepage you will see the quantum
+ 
+
+ align:start position:0%
+this homepage you will see the quantum
+dots of different colors that's because
+
+ align:start position:0%
+dots of different colors that's because
+ 
+
+ align:start position:0%
+dots of different colors that's because
+the energy level changed when you make
+
+ align:start position:0%
+the energy level changed when you make
+ 
+
+ align:start position:0%
+the energy level changed when you make
+the size change so that's the one way
+
+ align:start position:0%
+the size change so that's the one way
+ 
+
+ align:start position:0%
+the size change so that's the one way
+you can control the energy if you
+
+ align:start position:0%
+you can control the energy if you
+ 
+
+ align:start position:0%
+you can control the energy if you
+control the energy now come to
+
+ align:start position:0%
+control the energy now come to
+ 
+
+ align:start position:0%
+control the energy now come to
+mechanical engineering or any
+
+ align:start position:0%
+mechanical engineering or any
+ 
+
+ align:start position:0%
+mechanical engineering or any
+engineering what do you do you control
+
+ align:start position:0%
+engineering what do you do you control
+ 
+
+ align:start position:0%
+engineering what do you do you control
+the thermodynamics right energy is the
+
+ align:start position:0%
+the thermodynamics right energy is the
+ 
+
+ align:start position:0%
+the thermodynamics right energy is the
+most fundamental so you can control
+
+ align:start position:0%
+most fundamental so you can control
+ 
+
+ align:start position:0%
+most fundamental so you can control
+Surma dynamics another is say transport
+
+ align:start position:0%
+Surma dynamics another is say transport
+ 
+
+ align:start position:0%
+Surma dynamics another is say transport
+right if you look at the where the loss
+
+ align:start position:0%
+right if you look at the where the loss
+ 
+
+ align:start position:0%
+right if you look at the where the loss
+is up if you see ok second law Carlos a
+
+ align:start position:0%
+is up if you see ok second law Carlos a
+ 
+
+ align:start position:0%
+is up if you see ok second law Carlos a
+you can get to color efficiency pretty
+
+ align:start position:0%
+you can get to color efficiency pretty
+ 
+
+ align:start position:0%
+you can get to color efficiency pretty
+good if we you can get all color
+
+ align:start position:0%
+good if we you can get all color
+ 
+
+ align:start position:0%
+good if we you can get all color
+efficiency you should all be pleased
+
+ align:start position:0%
+efficiency you should all be pleased
+ 
+
+ align:start position:0%
+efficiency you should all be pleased
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but say we lose about 60% of useful
+
+ align:start position:0%
+but say we lose about 60% of useful
+ 
+
+ align:start position:0%
+but say we lose about 60% of useful
+energy if you look at the energy input
+
+ align:start position:0%
+energy if you look at the energy input
+ 
+
+ align:start position:0%
+energy if you look at the energy input
+output and Carlos say you can get the
+
+ align:start position:0%
+output and Carlos say you can get the
+ 
+
+ align:start position:0%
+output and Carlos say you can get the
+landing portion right so we're were see
+
+ align:start position:0%
+landing portion right so we're were see
+ 
+
+ align:start position:0%
+landing portion right so we're were see
+you can improve the transport if you can
+
+ align:start position:0%
+you can improve the transport if you can
+ 
+
+ align:start position:0%
+you can improve the transport if you can
+control the energy carrier
+
+ align:start position:0%
+control the energy carrier
+ 
+
+ align:start position:0%
+control the energy carrier
+traveling there interaction there
+
+ align:start position:0%
+traveling there interaction there
+ 
+
+ align:start position:0%
+traveling there interaction there
+traveling right so I said the air
+
+ align:start position:0%
+traveling right so I said the air
+ 
+
+ align:start position:0%
+traveling right so I said the air
+molecule is about 100 nanometers they
+
+ align:start position:0%
+molecule is about 100 nanometers they
+ 
+
+ align:start position:0%
+molecule is about 100 nanometers they
+mean free path and that seems so awfully
+
+ align:start position:0%
+mean free path and that seems so awfully
+ 
+
+ align:start position:0%
+mean free path and that seems so awfully
+small but if you open your computer you
+
+ align:start position:0%
+small but if you open your computer you
+ 
+
+ align:start position:0%
+small but if you open your computer you
+look at the hard disk the separation
+
+ align:start position:0%
+look at the hard disk the separation
+ 
+
+ align:start position:0%
+look at the hard disk the separation
+between the disk itself which is routing
+
+ align:start position:0%
+between the disk itself which is routing
+ 
+
+ align:start position:0%
+between the disk itself which is routing
+about 10,000 rpm and the magnetic head
+
+ align:start position:0%
+about 10,000 rpm and the magnetic head
+ 
+
+ align:start position:0%
+about 10,000 rpm and the magnetic head
+is a few nanometers few nanometers in
+
+ align:start position:0%
+is a few nanometers few nanometers in
+ 
+
+ align:start position:0%
+is a few nanometers few nanometers in
+everybody's computer so you go through
+
+ align:start position:0%
+everybody's computer so you go through
+ 
+
+ align:start position:0%
+everybody's computer so you go through
+this describe company and that they have
+
+ align:start position:0%
+this describe company and that they have
+ 
+
+ align:start position:0%
+this describe company and that they have
+give up the Newton because the day it's
+
+ align:start position:0%
+give up the Newton because the day it's
+ 
+
+ align:start position:0%
+give up the Newton because the day it's
+basically how to allow to crash that
+
+ align:start position:0%
+basically how to allow to crash that
+ 
+
+ align:start position:0%
+basically how to allow to crash that
+this hat with the disk right it's a
+
+ align:start position:0%
+this hat with the disk right it's a
+ 
+
+ align:start position:0%
+this hat with the disk right it's a
+fluid mechanics problem and they have
+
+ align:start position:0%
+fluid mechanics problem and they have
+ 
+
+ align:start position:0%
+fluid mechanics problem and they have
+given up a solving the navier-stokes
+
+ align:start position:0%
+given up a solving the navier-stokes
+ 
+
+ align:start position:0%
+given up a solving the navier-stokes
+equation because a full mechanic so
+
+ align:start position:0%
+equation because a full mechanic so
+ 
+
+ align:start position:0%
+equation because a full mechanic so
+that's so nervous Stokes equation they
+
+ align:start position:0%
+that's so nervous Stokes equation they
+ 
+
+ align:start position:0%
+that's so nervous Stokes equation they
+don't use it in there for long time ago
+
+ align:start position:0%
+don't use it in there for long time ago
+ 
+
+ align:start position:0%
+don't use it in there for long time ago
+they give them up and one day they call
+
+ align:start position:0%
+they give them up and one day they call
+ 
+
+ align:start position:0%
+they give them up and one day they call
+me they say we have one nanometer
+
+ align:start position:0%
+me they say we have one nanometer
+ 
+
+ align:start position:0%
+me they say we have one nanometer
+problem so what nano me right at the
+
+ align:start position:0%
+problem so what nano me right at the
+ 
+
+ align:start position:0%
+problem so what nano me right at the
+time I didn't know you in this
+
+ align:start position:0%
+time I didn't know you in this
+ 
+
+ align:start position:0%
+time I didn't know you in this
+separation so why you care about it
+
+ align:start position:0%
+separation so why you care about it
+ 
+
+ align:start position:0%
+separation so why you care about it
+because at the time they're about 20
+
+ align:start position:0%
+because at the time they're about 20
+ 
+
+ align:start position:0%
+because at the time they're about 20
+nanometer separation and they say that's
+
+ align:start position:0%
+nanometer separation and they say that's
+ 
+
+ align:start position:0%
+nanometer separation and they say that's
+already 5 5 percent uncertainty right
+
+ align:start position:0%
+already 5 5 percent uncertainty right
+ 
+
+ align:start position:0%
+already 5 5 percent uncertainty right
+and now they are going beyond they
+
+ align:start position:0%
+and now they are going beyond they
+ 
+
+ align:start position:0%
+and now they are going beyond they
+they're only say there are below 10
+
+ align:start position:0%
+they're only say there are below 10
+ 
+
+ align:start position:0%
+they're only say there are below 10
+nanometers we still didn't figure out
+
+ align:start position:0%
+nanometers we still didn't figure out
+ 
+
+ align:start position:0%
+nanometers we still didn't figure out
+what was that one nanometer problem so
+
+ align:start position:0%
+what was that one nanometer problem so
+ 
+
+ align:start position:0%
+what was that one nanometer problem so
+but their ladder will see so basically
+
+ align:start position:0%
+but their ladder will see so basically
+ 
+
+ align:start position:0%
+but their ladder will see so basically
+using the boundaries and you at this
+
+ align:start position:0%
+using the boundaries and you at this
+ 
+
+ align:start position:0%
+using the boundaries and you at this
+regime you need to go to different laws
+
+ align:start position:0%
+regime you need to go to different laws
+ 
+
+ align:start position:0%
+regime you need to go to different laws
+so what whether we are talking in this
+
+ align:start position:0%
+so what whether we are talking in this
+ 
+
+ align:start position:0%
+so what whether we are talking in this
+course and in this book are really this
+
+ align:start position:0%
+course and in this book are really this
+ 
+
+ align:start position:0%
+course and in this book are really this
+is my view of trying to have a picture
+
+ align:start position:0%
+is my view of trying to have a picture
+ 
+
+ align:start position:0%
+is my view of trying to have a picture
+from nano to they continue and firstly
+
+ align:start position:0%
+from nano to they continue and firstly
+ 
+
+ align:start position:0%
+from nano to they continue and firstly
+you need to understand the basic energy
+
+ align:start position:0%
+you need to understand the basic energy
+ 
+
+ align:start position:0%
+you need to understand the basic energy
+states the energy levels in the material
+
+ align:start position:0%
+states the energy levels in the material
+ 
+
+ align:start position:0%
+states the energy levels in the material
+so that really need need the quantum
+
+ align:start position:0%
+so that really need need the quantum
+ 
+
+ align:start position:0%
+so that really need need the quantum
+mechanics solid state and then I do heat
+
+ align:start position:0%
+mechanics solid state and then I do heat
+ 
+
+ align:start position:0%
+mechanics solid state and then I do heat
+transfers I need to bring in the
+
+ align:start position:0%
+transfers I need to bring in the
+ 
+
+ align:start position:0%
+transfers I need to bring in the
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+that's a statistics sir more energy and
+
+ align:start position:0%
+that's a statistics sir more energy and
+ 
+
+ align:start position:0%
+that's a statistics sir more energy and
+then we need to look at how those energy
+
+ align:start position:0%
+then we need to look at how those energy
+ 
+
+ align:start position:0%
+then we need to look at how those energy
+carrier moves so that's the transport
+
+ align:start position:0%
+carrier moves so that's the transport
+ 
+
+ align:start position:0%
+carrier moves so that's the transport
+and transport that you have continuum
+
+ align:start position:0%
+and transport that you have continuum
+ 
+
+ align:start position:0%
+and transport that you have continuum
+laws you have also the you need to go
+
+ align:start position:0%
+laws you have also the you need to go
+ 
+
+ align:start position:0%
+laws you have also the you need to go
+the long continuum you need to vary
+
+ align:start position:0%
+the long continuum you need to vary
+ 
+
+ align:start position:0%
+the long continuum you need to vary
+whether you need to see in the quantum
+
+ align:start position:0%
+whether you need to see in the quantum
+ 
+
+ align:start position:0%
+whether you need to see in the quantum
+regime where you have to look at the
+
+ align:start position:0%
+regime where you have to look at the
+ 
+
+ align:start position:0%
+regime where you have to look at the
+wave nature or you can forget about it
+
+ align:start position:0%
+wave nature or you can forget about it
+ 
+
+ align:start position:0%
+wave nature or you can forget about it
+right so the what I would like you to
+
+ align:start position:0%
+right so the what I would like you to
+ 
+
+ align:start position:0%
+right so the what I would like you to
+have is to develop that picture say if
+
+ align:start position:0%
+have is to develop that picture say if
+ 
+
+ align:start position:0%
+have is to develop that picture say if
+you have a problem and people come to
+
+ align:start position:0%
+you have a problem and people come to
+ 
+
+ align:start position:0%
+you have a problem and people come to
+you and say well in this regime I'm very
+
+ align:start position:0%
+you and say well in this regime I'm very
+ 
+
+ align:start position:0%
+you and say well in this regime I'm very
+the weather I can still use my the
+
+ align:start position:0%
+the weather I can still use my the
+ 
+
+ align:start position:0%
+the weather I can still use my the
+continuum right if you feel comfortable
+
+ align:start position:0%
+continuum right if you feel comfortable
+ 
+
+ align:start position:0%
+continuum right if you feel comfortable
+to tell them yeah there's no problem
+
+ align:start position:0%
+to tell them yeah there's no problem
+ 
+
+ align:start position:0%
+to tell them yeah there's no problem
+just to go you you may get a ten percent
+
+ align:start position:0%
+just to go you you may get a ten percent
+ 
+
+ align:start position:0%
+just to go you you may get a ten percent
+error twenty percent error but say at
+
+ align:start position:0%
+error twenty percent error but say at
+ 
+
+ align:start position:0%
+error twenty percent error but say at
+least say I want to devote the comfort
+
+ align:start position:0%
+least say I want to devote the comfort
+ 
+
+ align:start position:0%
+least say I want to devote the comfort
+level of when you can use uh say what
+
+ align:start position:0%
+level of when you can use uh say what
+ 
+
+ align:start position:0%
+level of when you can use uh say what
+kind of transport pictures and in fact I
+
+ align:start position:0%
+kind of transport pictures and in fact I
+ 
+
+ align:start position:0%
+kind of transport pictures and in fact I
+say if you look at the book it's a
+
+ align:start position:0%
+say if you look at the book it's a
+ 
+
+ align:start position:0%
+say if you look at the book it's a
+parallel treatment say all four
+
+ align:start position:0%
+parallel treatment say all four
+ 
+
+ align:start position:0%
+parallel treatment say all four
+electrons molecules photons photons
+
+ align:start position:0%
+electrons molecules photons photons
+ 
+
+ align:start position:0%
+electrons molecules photons photons
+right so the that's that's the way I
+
+ align:start position:0%
+right so the that's that's the way I
+ 
+
+ align:start position:0%
+right so the that's that's the way I
+aren't I understand the object the the
+
+ align:start position:0%
+aren't I understand the object the the
+ 
+
+ align:start position:0%
+aren't I understand the object the the
+subjects and I was it I've been always a
+
+ align:start position:0%
+subjects and I was it I've been always a
+ 
+
+ align:start position:0%
+subjects and I was it I've been always a
+mechanical engineer I first learned
+
+ align:start position:0%
+mechanical engineer I first learned
+ 
+
+ align:start position:0%
+mechanical engineer I first learned
+summer radiation photons and of course I
+
+ align:start position:0%
+summer radiation photons and of course I
+ 
+
+ align:start position:0%
+summer radiation photons and of course I
+learned all those continuum theory and
+
+ align:start position:0%
+learned all those continuum theory and
+ 
+
+ align:start position:0%
+learned all those continuum theory and
+it turns out that if you understand that
+
+ align:start position:0%
+it turns out that if you understand that
+ 
+
+ align:start position:0%
+it turns out that if you understand that
+one carrier you can make a rudder it's
+
+ align:start position:0%
+one carrier you can make a rudder it's
+ 
+
+ align:start position:0%
+one carrier you can make a rudder it's
+easy relatively easy analogy for other
+
+ align:start position:0%
+easy relatively easy analogy for other
+ 
+
+ align:start position:0%
+easy relatively easy analogy for other
+carriers and at least in this is
+
+ align:start position:0%
+carriers and at least in this is
+ 
+
+ align:start position:0%
+carriers and at least in this is
+so-called the dilute gas picture they
+
+ align:start position:0%
+so-called the dilute gas picture they
+ 
+
+ align:start position:0%
+so-called the dilute gas picture they
+are all bt behavior a very similar so
+
+ align:start position:0%
+are all bt behavior a very similar so
+ 
+
+ align:start position:0%
+are all bt behavior a very similar so
+this is what I'm most familiar with
+
+ align:start position:0%
+this is what I'm most familiar with
+ 
+
+ align:start position:0%
+this is what I'm most familiar with
+and wave Maxwell equation and by say
+
+ align:start position:0%
+and wave Maxwell equation and by say
+ 
+
+ align:start position:0%
+and wave Maxwell equation and by say
+this is a where most engineers familiar
+
+ align:start position:0%
+this is a where most engineers familiar
+ 
+
+ align:start position:0%
+this is a where most engineers familiar
+with right Ohm's law for alone
+
+ align:start position:0%
+with right Ohm's law for alone
+ 
+
+ align:start position:0%
+with right Ohm's law for alone
+you'll ensure stress and what those are
+
+ align:start position:0%
+you'll ensure stress and what those are
+ 
+
+ align:start position:0%
+you'll ensure stress and what those are
+the continuum right let's see if I go to
+
+ align:start position:0%
+the continuum right let's see if I go to
+ 
+
+ align:start position:0%
+the continuum right let's see if I go to
+photon radiation where if you think
+
+ align:start position:0%
+photon radiation where if you think
+ 
+
+ align:start position:0%
+photon radiation where if you think
+about the full time from the Sun to
+
+ align:start position:0%
+about the full time from the Sun to
+ 
+
+ align:start position:0%
+about the full time from the Sun to
+earth
+
+ align:start position:0%
+earth
+ 
+
+ align:start position:0%
+earth
+you don't go to solve diffusion equation
+
+ align:start position:0%
+you don't go to solve diffusion equation
+ 
+
+ align:start position:0%
+you don't go to solve diffusion equation
+for that now in fact I say this a place
+
+ align:start position:0%
+for that now in fact I say this a place
+ 
+
+ align:start position:0%
+for that now in fact I say this a place
+is just a street trajectory ballistic
+
+ align:start position:0%
+is just a street trajectory ballistic
+ 
+
+ align:start position:0%
+is just a street trajectory ballistic
+right so this will happens if I have a
+
+ align:start position:0%
+right so this will happens if I have a
+ 
+
+ align:start position:0%
+right so this will happens if I have a
+describe I have a disc the example here
+
+ align:start position:0%
+describe I have a disc the example here
+ 
+
+ align:start position:0%
+describe I have a disc the example here
+average speaking the molecule travel 100
+
+ align:start position:0%
+average speaking the molecule travel 100
+ 
+
+ align:start position:0%
+average speaking the molecule travel 100
+nanometer and now the molecule if there
+
+ align:start position:0%
+nanometer and now the molecule if there
+ 
+
+ align:start position:0%
+nanometer and now the molecule if there
+is a molecule in the gap they'll collide
+
+ align:start position:0%
+is a molecule in the gap they'll collide
+ 
+
+ align:start position:0%
+is a molecule in the gap they'll collide
+the wall they don't collide with each
+
+ align:start position:0%
+the wall they don't collide with each
+ 
+
+ align:start position:0%
+the wall they don't collide with each
+other right that's a ballistic transfer
+
+ align:start position:0%
+other right that's a ballistic transfer
+ 
+
+ align:start position:0%
+other right that's a ballistic transfer
+picture so what I want to have is
+
+ align:start position:0%
+picture so what I want to have is
+ 
+
+ align:start position:0%
+picture so what I want to have is
+developing say when I need to think
+
+ align:start position:0%
+developing say when I need to think
+ 
+
+ align:start position:0%
+developing say when I need to think
+about the way we need to think about
+
+ align:start position:0%
+about the way we need to think about
+ 
+
+ align:start position:0%
+about the way we need to think about
+they forget by the way by say still need
+
+ align:start position:0%
+they forget by the way by say still need
+ 
+
+ align:start position:0%
+they forget by the way by say still need
+to see what's the boundary effects and
+
+ align:start position:0%
+to see what's the boundary effects and
+ 
+
+ align:start position:0%
+to see what's the boundary effects and
+they eventually say they continue
+
+ align:start position:0%
+they eventually say they continue
+ 
+
+ align:start position:0%
+they eventually say they continue
+so it's a very the challenge for this is
+
+ align:start position:0%
+so it's a very the challenge for this is
+ 
+
+ align:start position:0%
+so it's a very the challenge for this is
+most of you I know most my students they
+
+ align:start position:0%
+most of you I know most my students they
+ 
+
+ align:start position:0%
+most of you I know most my students they
+are mechanical engineers right with the
+
+ align:start position:0%
+are mechanical engineers right with the
+ 
+
+ align:start position:0%
+are mechanical engineers right with the
+mechanical engineering background and
+
+ align:start position:0%
+mechanical engineering background and
+ 
+
+ align:start position:0%
+mechanical engineering background and
+that's where we're most familiar with
+
+ align:start position:0%
+that's where we're most familiar with
+ 
+
+ align:start position:0%
+that's where we're most familiar with
+most comfortably and what do we add to
+
+ align:start position:0%
+most comfortably and what do we add to
+ 
+
+ align:start position:0%
+most comfortably and what do we add to
+this is a lot of a new subject and the
+
+ align:start position:0%
+this is a lot of a new subject and the
+ 
+
+ align:start position:0%
+this is a lot of a new subject and the
+typically taken many years to build up
+
+ align:start position:0%
+typically taken many years to build up
+ 
+
+ align:start position:0%
+typically taken many years to build up
+but it took myself many years to build
+
+ align:start position:0%
+but it took myself many years to build
+ 
+
+ align:start position:0%
+but it took myself many years to build
+up so I'm very ambitious let's say I
+
+ align:start position:0%
+up so I'm very ambitious let's say I
+ 
+
+ align:start position:0%
+up so I'm very ambitious let's say I
+want to teach you when semester you will
+
+ align:start position:0%
+want to teach you when semester you will
+ 
+
+ align:start position:0%
+want to teach you when semester you will
+be inundated with the terminology okay
+
+ align:start position:0%
+be inundated with the terminology okay
+ 
+
+ align:start position:0%
+be inundated with the terminology okay
+and also by say D at what I'm hoping is
+
+ align:start position:0%
+and also by say D at what I'm hoping is
+ 
+
+ align:start position:0%
+and also by say D at what I'm hoping is
+at the end you gain something you gain
+
+ align:start position:0%
+at the end you gain something you gain
+ 
+
+ align:start position:0%
+at the end you gain something you gain
+that say you can look and say I have a
+
+ align:start position:0%
+that say you can look and say I have a
+ 
+
+ align:start position:0%
+that say you can look and say I have a
+sense of from nano from molecules to the
+
+ align:start position:0%
+sense of from nano from molecules to the
+ 
+
+ align:start position:0%
+sense of from nano from molecules to the
+continued so that's a water we have in
+
+ align:start position:0%
+continued so that's a water we have in
+ 
+
+ align:start position:0%
+continued so that's a water we have in
+the in the general introduction any
+
+ align:start position:0%
+the in the general introduction any
+ 
+
+ align:start position:0%
+the in the general introduction any
+questions I want you feel free to ask
+
+ align:start position:0%
+questions I want you feel free to ask
+ 
+
+ align:start position:0%
+questions I want you feel free to ask
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before I turn off the computer because I
+
+ align:start position:0%
+before I turn off the computer because I
+ 
+
+ align:start position:0%
+before I turn off the computer because I
+I'll do that say every week I actually
+
+ align:start position:0%
+I'll do that say every week I actually
+ 
+
+ align:start position:0%
+I'll do that say every week I actually
+were spend at the end of lecture ten
+
+ align:start position:0%
+were spend at the end of lecture ten
+ 
+
+ align:start position:0%
+were spend at the end of lecture ten
+minutes also to have some relaxation
+
+ align:start position:0%
+minutes also to have some relaxation
+ 
+
+ align:start position:0%
+minutes also to have some relaxation
+time relaxing time and what I wanted to
+
+ align:start position:0%
+time relaxing time and what I wanted to
+ 
+
+ align:start position:0%
+time relaxing time and what I wanted to
+to show you is I don't know how many of
+
+ align:start position:0%
+to show you is I don't know how many of
+ 
+
+ align:start position:0%
+to show you is I don't know how many of
+you go to journals and then most of you
+
+ align:start position:0%
+you go to journals and then most of you
+ 
+
+ align:start position:0%
+you go to journals and then most of you
+are graduate students and you should go
+
+ align:start position:0%
+are graduate students and you should go
+ 
+
+ align:start position:0%
+are graduate students and you should go
+to journal every week if not every day
+
+ align:start position:0%
+to journal every week if not every day
+ 
+
+ align:start position:0%
+to journal every week if not every day
+and just look at what other people are
+
+ align:start position:0%
+and just look at what other people are
+ 
+
+ align:start position:0%
+and just look at what other people are
+doing so ah when you a new graduate
+
+ align:start position:0%
+doing so ah when you a new graduate
+ 
+
+ align:start position:0%
+doing so ah when you a new graduate
+student you don't go to joiner often and
+
+ align:start position:0%
+student you don't go to joiner often and
+ 
+
+ align:start position:0%
+student you don't go to joiner often and
+you go to journal you look at that this
+
+ align:start position:0%
+you go to journal you look at that this
+ 
+
+ align:start position:0%
+you go to journal you look at that this
+is most of this stuff you don't
+
+ align:start position:0%
+is most of this stuff you don't
+ 
+
+ align:start position:0%
+is most of this stuff you don't
+understand other than the ones that if
+
+ align:start position:0%
+understand other than the ones that if
+ 
+
+ align:start position:0%
+understand other than the ones that if
+you heat work on heat transfer you go
+
+ align:start position:0%
+you heat work on heat transfer you go
+ 
+
+ align:start position:0%
+you heat work on heat transfer you go
+journal heat transfer maybe you know
+
+ align:start position:0%
+journal heat transfer maybe you know
+ 
+
+ align:start position:0%
+journal heat transfer maybe you know
+what the people are talking right so ah
+
+ align:start position:0%
+what the people are talking right so ah
+ 
+
+ align:start position:0%
+what the people are talking right so ah
+what might say if I want to start with
+
+ align:start position:0%
+what might say if I want to start with
+ 
+
+ align:start position:0%
+what might say if I want to start with
+the any journal not medical not bad
+
+ align:start position:0%
+the any journal not medical not bad
+ 
+
+ align:start position:0%
+the any journal not medical not bad
+matter go I'm nothing now is there any
+
+ align:start position:0%
+matter go I'm nothing now is there any
+ 
+
+ align:start position:0%
+matter go I'm nothing now is there any
+other journal you tell me and I want to
+
+ align:start position:0%
+other journal you tell me and I want to
+ 
+
+ align:start position:0%
+other journal you tell me and I want to
+say okay where you are this today and
+
+ align:start position:0%
+say okay where you are this today and
+ 
+
+ align:start position:0%
+say okay where you are this today and
+where you are at the end of the semester
+
+ align:start position:0%
+where you are at the end of the semester
+ 
+
+ align:start position:0%
+where you are at the end of the semester
+and my ambition is for you to see look
+
+ align:start position:0%
+and my ambition is for you to see look
+ 
+
+ align:start position:0%
+and my ambition is for you to see look
+at the paper title and 50% you say maybe
+
+ align:start position:0%
+at the paper title and 50% you say maybe
+ 
+
+ align:start position:0%
+at the paper title and 50% you say maybe
+I can take a look maybe as I am NOT
+
+ align:start position:0%
+I can take a look maybe as I am NOT
+ 
+
+ align:start position:0%
+I can take a look maybe as I am NOT
+completely ignorant so give me a name of
+
+ align:start position:0%
+completely ignorant so give me a name of
+ 
+
+ align:start position:0%
+completely ignorant so give me a name of
+a journal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah later ok let's look at take a look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so the Wow for the challenge of later is
+
+ align:start position:0%
+so the Wow for the challenge of later is
+ 
+
+ align:start position:0%
+so the Wow for the challenge of later is
+that now most of them are actually on
+
+ align:start position:0%
+that now most of them are actually on
+ 
+
+ align:start position:0%
+that now most of them are actually on
+biological but but that's fine let's say
+
+ align:start position:0%
+biological but but that's fine let's say
+ 
+
+ align:start position:0%
+biological but but that's fine let's say
+still see what today what's the news
+
+ align:start position:0%
+still see what today what's the news
+ 
+
+ align:start position:0%
+still see what today what's the news
+this week yeah social level one social
+
+ align:start position:0%
+this week yeah social level one social
+ 
+
+ align:start position:0%
+this week yeah social level one social
+network I want to think about the
+
+ align:start position:0%
+network I want to think about the
+ 
+
+ align:start position:0%
+network I want to think about the
+entropy of social network all right I
+
+ align:start position:0%
+entropy of social network all right I
+ 
+
+ align:start position:0%
+entropy of social network all right I
+see I I tell you at the end I only need
+
+ align:start position:0%
+see I I tell you at the end I only need
+ 
+
+ align:start position:0%
+see I I tell you at the end I only need
+you if you if you your career at the end
+
+ align:start position:0%
+you if you if you your career at the end
+ 
+
+ align:start position:0%
+you if you if you your career at the end
+you say ok there are only three words
+
+ align:start position:0%
+you say ok there are only three words
+ 
+
+ align:start position:0%
+you say ok there are only three words
+you need to understand not just nano
+
+ align:start position:0%
+you need to understand not just nano
+ 
+
+ align:start position:0%
+you need to understand not just nano
+heat energy right there are only three
+
+ align:start position:0%
+heat energy right there are only three
+ 
+
+ align:start position:0%
+heat energy right there are only three
+words you need to understand energy
+
+ align:start position:0%
+words you need to understand energy
+ 
+
+ align:start position:0%
+words you need to understand energy
+momentum and entropy okay if you feel
+
+ align:start position:0%
+momentum and entropy okay if you feel
+ 
+
+ align:start position:0%
+momentum and entropy okay if you feel
+comfortable with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look hi Betsy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're at the technical papers dear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+research book hello that those are those
+
+ align:start position:0%
+research book hello that those are those
+ 
+
+ align:start position:0%
+research book hello that those are those
+are the sign this way I want to go more
+
+ align:start position:0%
+are the sign this way I want to go more
+ 
+
+ align:start position:0%
+are the sign this way I want to go more
+into the plasma right what is the plasma
+
+ align:start position:0%
+into the plasma right what is the plasma
+ 
+
+ align:start position:0%
+into the plasma right what is the plasma
+and so when I look at this right quantum
+
+ align:start position:0%
+and so when I look at this right quantum
+ 
+
+ align:start position:0%
+and so when I look at this right quantum
+current the company of mechanical
+
+ align:start position:0%
+current the company of mechanical
+ 
+
+ align:start position:0%
+current the company of mechanical
+oscillator to off recovery mode I look
+
+ align:start position:0%
+oscillator to off recovery mode I look
+ 
+
+ align:start position:0%
+oscillator to off recovery mode I look
+at that paper I haven't read it right
+
+ align:start position:0%
+at that paper I haven't read it right
+ 
+
+ align:start position:0%
+at that paper I haven't read it right
+clearly I'm what I was thinking anybody
+
+ align:start position:0%
+clearly I'm what I was thinking anybody
+ 
+
+ align:start position:0%
+clearly I'm what I was thinking anybody
+will guess what they will be talking
+
+ align:start position:0%
+will guess what they will be talking
+ 
+
+ align:start position:0%
+will guess what they will be talking
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you will say I I don't know okay so
+
+ align:start position:0%
+so you will say I I don't know okay so
+ 
+
+ align:start position:0%
+so you will say I I don't know okay so
+my guess is were probably related to
+
+ align:start position:0%
+my guess is were probably related to
+ 
+
+ align:start position:0%
+my guess is were probably related to
+force momentum of photon right it's a
+
+ align:start position:0%
+force momentum of photon right it's a
+ 
+
+ align:start position:0%
+force momentum of photon right it's a
+mechanical and so it turns out that the
+
+ align:start position:0%
+mechanical and so it turns out that the
+ 
+
+ align:start position:0%
+mechanical and so it turns out that the
+photon has a momentum and then carry
+
+ align:start position:0%
+photon has a momentum and then carry
+ 
+
+ align:start position:0%
+photon has a momentum and then carry
+force once anything has a moment then we
+
+ align:start position:0%
+force once anything has a moment then we
+ 
+
+ align:start position:0%
+force once anything has a moment then we
+can generate force so after your cavity
+
+ align:start position:0%
+can generate force so after your cavity
+ 
+
+ align:start position:0%
+can generate force so after your cavity
+so you will learn this stuff okay so the
+
+ align:start position:0%
+so you will learn this stuff okay so the
+ 
+
+ align:start position:0%
+so you will learn this stuff okay so the
+quantum control I'm not very familiar
+
+ align:start position:0%
+quantum control I'm not very familiar
+ 
+
+ align:start position:0%
+quantum control I'm not very familiar
+but say what I can say is the object
+
+ align:start position:0%
+but say what I can say is the object
+ 
+
+ align:start position:0%
+but say what I can say is the object
+cavity the modes and also the coherency
+
+ align:start position:0%
+cavity the modes and also the coherency
+ 
+
+ align:start position:0%
+cavity the modes and also the coherency
+issue we'll talk not exactly related to
+
+ align:start position:0%
+issue we'll talk not exactly related to
+ 
+
+ align:start position:0%
+issue we'll talk not exactly related to
+photon but related transport right see
+
+ align:start position:0%
+photon but related transport right see
+ 
+
+ align:start position:0%
+photon but related transport right see
+how I can go from that normally the wave
+
+ align:start position:0%
+how I can go from that normally the wave
+ 
+
+ align:start position:0%
+how I can go from that normally the wave
+a coherent state to eventually I can
+
+ align:start position:0%
+a coherent state to eventually I can
+ 
+
+ align:start position:0%
+a coherent state to eventually I can
+forget about the coherence of the waves
+
+ align:start position:0%
+forget about the coherence of the waves
+ 
+
+ align:start position:0%
+forget about the coherence of the waves
+and treating my the particles so the my
+
+ align:start position:0%
+and treating my the particles so the my
+ 
+
+ align:start position:0%
+and treating my the particles so the my
+point is to say at the end of what I'm
+
+ align:start position:0%
+point is to say at the end of what I'm
+ 
+
+ align:start position:0%
+point is to say at the end of what I'm
+hoping is that you open journal like
+
+ align:start position:0%
+hoping is that you open journal like
+ 
+
+ align:start position:0%
+hoping is that you open journal like
+apply physics and nano letters or
+
+ align:start position:0%
+apply physics and nano letters or
+ 
+
+ align:start position:0%
+apply physics and nano letters or
+science a leisure
+
+ align:start position:0%
+science a leisure
+ 
+
+ align:start position:0%
+science a leisure
+you're not scared okay a lot of
+
+ align:start position:0%
+you're not scared okay a lot of
+ 
+
+ align:start position:0%
+you're not scared okay a lot of
+terminologies that the you probably
+
+ align:start position:0%
+terminologies that the you probably
+ 
+
+ align:start position:0%
+terminologies that the you probably
+didn't know and they'll stick to you and
+
+ align:start position:0%
+didn't know and they'll stick to you and
+ 
+
+ align:start position:0%
+didn't know and they'll stick to you and
+threw to you and then maybe you remember
+
+ align:start position:0%
+threw to you and then maybe you remember
+ 
+
+ align:start position:0%
+threw to you and then maybe you remember
+something okay so let's start talking
+
+ align:start position:0%
+something okay so let's start talking
+ 
+
+ align:start position:0%
+something okay so let's start talking
+more details so what I want to start
+
+ align:start position:0%
+more details so what I want to start
+ 
+
+ align:start position:0%
+more details so what I want to start
+with is for you to think about what are
+
+ align:start position:0%
+with is for you to think about what are
+ 
+
+ align:start position:0%
+with is for you to think about what are
+the laws you have learned to see what
+
+ align:start position:0%
+the laws you have learned to see what
+ 
+
+ align:start position:0%
+the laws you have learned to see what
+are they okay I wanted get thee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talked about briefly you just
+
+ align:start position:0%
+so we talked about briefly you just
+ 
+
+ align:start position:0%
+so we talked about briefly you just
+follow my syllabus we show the slides on
+
+ align:start position:0%
+follow my syllabus we show the slides on
+ 
+
+ align:start position:0%
+follow my syllabus we show the slides on
+motivations and scope now let's go to
+
+ align:start position:0%
+motivations and scope now let's go to
+ 
+
+ align:start position:0%
+motivations and scope now let's go to
+classical laws not necessary classical I
+
+ align:start position:0%
+classical laws not necessary classical I
+ 
+
+ align:start position:0%
+classical laws not necessary classical I
+just want to say what have a loss that
+
+ align:start position:0%
+just want to say what have a loss that
+ 
+
+ align:start position:0%
+just want to say what have a loss that
+you think you have learned and
+
+ align:start position:0%
+you think you have learned and
+ 
+
+ align:start position:0%
+you think you have learned and
+particular I like to transport right ok
+
+ align:start position:0%
+particular I like to transport right ok
+ 
+
+ align:start position:0%
+particular I like to transport right ok
+let's start with the conservation so
+
+ align:start position:0%
+let's start with the conservation so
+ 
+
+ align:start position:0%
+let's start with the conservation so
+I'll use this side right we have
+
+ align:start position:0%
+I'll use this side right we have
+ 
+
+ align:start position:0%
+I'll use this side right we have
+conservation what are the conservation
+
+ align:start position:0%
+conservation what are the conservation
+ 
+
+ align:start position:0%
+conservation what are the conservation
+laws ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have mass conservation momentum with
+
+ align:start position:0%
+you have mass conservation momentum with
+ 
+
+ align:start position:0%
+you have mass conservation momentum with
+ardor energy first law other charge so
+
+ align:start position:0%
+ardor energy first law other charge so
+ 
+
+ align:start position:0%
+ardor energy first law other charge so
+charge on what charge transport what a
+
+ align:start position:0%
+charge on what charge transport what a
+ 
+
+ align:start position:0%
+charge on what charge transport what a
+conservation of charge okay yeah that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh parity I'm not familiar with that
+
+ align:start position:0%
+huh parity I'm not familiar with that
+ 
+
+ align:start position:0%
+huh parity I'm not familiar with that
+okay yeah I heard the lane what others
+
+ align:start position:0%
+okay yeah I heard the lane what others
+ 
+
+ align:start position:0%
+okay yeah I heard the lane what others
+know we're not going to touch much on
+
+ align:start position:0%
+know we're not going to touch much on
+ 
+
+ align:start position:0%
+know we're not going to touch much on
+conservation laws Einstein say that
+
+ align:start position:0%
+conservation laws Einstein say that
+ 
+
+ align:start position:0%
+conservation laws Einstein say that
+anything can be broken except the first
+
+ align:start position:0%
+anything can be broken except the first
+ 
+
+ align:start position:0%
+anything can be broken except the first
+and second law so I'm not going to touch
+
+ align:start position:0%
+and second law so I'm not going to touch
+ 
+
+ align:start position:0%
+and second law so I'm not going to touch
+much on okay well say okay even though
+
+ align:start position:0%
+much on okay well say okay even though
+ 
+
+ align:start position:0%
+much on okay well say okay even though
+it's not a conservation by the second
+
+ align:start position:0%
+it's not a conservation by the second
+ 
+
+ align:start position:0%
+it's not a conservation by the second
+law is say you can write the entropy
+
+ align:start position:0%
+law is say you can write the entropy
+ 
+
+ align:start position:0%
+law is say you can write the entropy
+generation you can still write the
+
+ align:start position:0%
+generation you can still write the
+ 
+
+ align:start position:0%
+generation you can still write the
+equation there right so those are the
+
+ align:start position:0%
+equation there right so those are the
+ 
+
+ align:start position:0%
+equation there right so those are the
+things we don't touch much there are
+
+ align:start position:0%
+things we don't touch much there are
+ 
+
+ align:start position:0%
+things we don't touch much there are
+discussions in literature say you can
+
+ align:start position:0%
+discussions in literature say you can
+ 
+
+ align:start position:0%
+discussions in literature say you can
+break the second law that's and mean the
+
+ align:start position:0%
+break the second law that's and mean the
+ 
+
+ align:start position:0%
+break the second law that's and mean the
+time very short time scale and the
+
+ align:start position:0%
+time very short time scale and the
+ 
+
+ align:start position:0%
+time very short time scale and the
+statistical speaking you could have
+
+ align:start position:0%
+statistical speaking you could have
+ 
+
+ align:start position:0%
+statistical speaking you could have
+deviations that's possible and let's
+
+ align:start position:0%
+deviations that's possible and let's
+ 
+
+ align:start position:0%
+deviations that's possible and let's
+look at transport tell me more on the
+
+ align:start position:0%
+look at transport tell me more on the
+ 
+
+ align:start position:0%
+look at transport tell me more on the
+transport laws you learn so let's say
+
+ align:start position:0%
+transport laws you learn so let's say
+ 
+
+ align:start position:0%
+transport laws you learn so let's say
+you learn some of you familiar with the
+
+ align:start position:0%
+you learn some of you familiar with the
+ 
+
+ align:start position:0%
+you learn some of you familiar with the
+heat something from of you may be
+
+ align:start position:0%
+heat something from of you may be
+ 
+
+ align:start position:0%
+heat something from of you may be
+familiar with charge or fluids or mass
+
+ align:start position:0%
+familiar with charge or fluids or mass
+ 
+
+ align:start position:0%
+familiar with charge or fluids or mass
+right tell me they will all see in those
+
+ align:start position:0%
+right tell me they will all see in those
+ 
+
+ align:start position:0%
+right tell me they will all see in those
+disciplines ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do heat right right heat
+
+ align:start position:0%
+okay so let's do heat right right heat
+ 
+
+ align:start position:0%
+okay so let's do heat right right heat
+in the in terms of the laws the Fourier
+
+ align:start position:0%
+in the in terms of the laws the Fourier
+ 
+
+ align:start position:0%
+in the in terms of the laws the Fourier
+law is for heat conduction
+
+ align:start position:0%
+law is for heat conduction
+ 
+
+ align:start position:0%
+law is for heat conduction
+so conduction right I this course I put
+
+ align:start position:0%
+so conduction right I this course I put
+ 
+
+ align:start position:0%
+so conduction right I this course I put
+a prerequisite either to double five
+
+ align:start position:0%
+a prerequisite either to double five
+ 
+
+ align:start position:0%
+a prerequisite either to double five
+level and 2005 from other department is
+
+ align:start position:0%
+level and 2005 from other department is
+ 
+
+ align:start position:0%
+level and 2005 from other department is
+basically heat conduction heat transfer
+
+ align:start position:0%
+basically heat conduction heat transfer
+ 
+
+ align:start position:0%
+basically heat conduction heat transfer
+thermal fluids course and in your
+
+ align:start position:0%
+thermal fluids course and in your
+ 
+
+ align:start position:0%
+thermal fluids course and in your
+department there is also of course nano
+
+ align:start position:0%
+department there is also of course nano
+ 
+
+ align:start position:0%
+department there is also of course nano
+engineering if you take in that this
+
+ align:start position:0%
+engineering if you take in that this
+ 
+
+ align:start position:0%
+engineering if you take in that this
+will be easier because there lot of
+
+ align:start position:0%
+will be easier because there lot of
+ 
+
+ align:start position:0%
+will be easier because there lot of
+there's some overlap but see if not you
+
+ align:start position:0%
+there's some overlap but see if not you
+ 
+
+ align:start position:0%
+there's some overlap but see if not you
+can still survive so heat conduction we
+
+ align:start position:0%
+can still survive so heat conduction we
+ 
+
+ align:start position:0%
+can still survive so heat conduction we
+have the simplest picture when one side
+
+ align:start position:0%
+have the simplest picture when one side
+ 
+
+ align:start position:0%
+have the simplest picture when one side
+is the hot the other side is a call and
+
+ align:start position:0%
+is the hot the other side is a call and
+ 
+
+ align:start position:0%
+is the hot the other side is a call and
+there's a heat flow inside right and the
+
+ align:start position:0%
+there's a heat flow inside right and the
+ 
+
+ align:start position:0%
+there's a heat flow inside right and the
+law of governing the heat conduction I
+
+ align:start position:0%
+law of governing the heat conduction I
+ 
+
+ align:start position:0%
+law of governing the heat conduction I
+write this simplest form is the Fourier
+
+ align:start position:0%
+write this simplest form is the Fourier
+ 
+
+ align:start position:0%
+write this simplest form is the Fourier
+law right Fourier law of heat conduction
+
+ align:start position:0%
+law right Fourier law of heat conduction
+ 
+
+ align:start position:0%
+law right Fourier law of heat conduction
+the heat flux equals thermal
+
+ align:start position:0%
+the heat flux equals thermal
+ 
+
+ align:start position:0%
+the heat flux equals thermal
+conductivity times temperature gradient
+
+ align:start position:0%
+conductivity times temperature gradient
+ 
+
+ align:start position:0%
+conductivity times temperature gradient
+and this is a one dimension that I'm
+
+ align:start position:0%
+and this is a one dimension that I'm
+ 
+
+ align:start position:0%
+and this is a one dimension that I'm
+reading and this is a heat flux the unit
+
+ align:start position:0%
+reading and this is a heat flux the unit
+ 
+
+ align:start position:0%
+reading and this is a heat flux the unit
+here is a watt meter square and the
+
+ align:start position:0%
+here is a watt meter square and the
+ 
+
+ align:start position:0%
+here is a watt meter square and the
+thermal conductivity is a mature
+
+ align:start position:0%
+thermal conductivity is a mature
+ 
+
+ align:start position:0%
+thermal conductivity is a mature
+property at the macro scale we go to
+
+ align:start position:0%
+property at the macro scale we go to
+ 
+
+ align:start position:0%
+property at the macro scale we go to
+Llano you'll find this is no longer
+
+ align:start position:0%
+Llano you'll find this is no longer
+ 
+
+ align:start position:0%
+Llano you'll find this is no longer
+material property because it's structure
+
+ align:start position:0%
+material property because it's structure
+ 
+
+ align:start position:0%
+material property because it's structure
+dependent but the unit of that is a watt
+
+ align:start position:0%
+dependent but the unit of that is a watt
+ 
+
+ align:start position:0%
+dependent but the unit of that is a watt
+per meter per Kelvin and we just said
+
+ align:start position:0%
+per meter per Kelvin and we just said
+ 
+
+ align:start position:0%
+per meter per Kelvin and we just said
+diamond is most conductive heat
+
+ align:start position:0%
+diamond is most conductive heat
+ 
+
+ align:start position:0%
+diamond is most conductive heat
+conducting material and in fact some
+
+ align:start position:0%
+conducting material and in fact some
+ 
+
+ align:start position:0%
+conducting material and in fact some
+people will say is the carbon nanotube
+
+ align:start position:0%
+people will say is the carbon nanotube
+ 
+
+ align:start position:0%
+people will say is the carbon nanotube
+graphene so I thought this is a nano
+
+ align:start position:0%
+graphene so I thought this is a nano
+ 
+
+ align:start position:0%
+graphene so I thought this is a nano
+scale on one side they can go very high
+
+ align:start position:0%
+scale on one side they can go very high
+ 
+
+ align:start position:0%
+scale on one side they can go very high
+and the other side I give example
+
+ align:start position:0%
+and the other side I give example
+ 
+
+ align:start position:0%
+and the other side I give example
+can go very low right so this is one of
+
+ align:start position:0%
+can go very low right so this is one of
+ 
+
+ align:start position:0%
+can go very low right so this is one of
+the knows transport laws and this is a
+
+ align:start position:0%
+the knows transport laws and this is a
+ 
+
+ align:start position:0%
+the knows transport laws and this is a
+this is a conservation law and for this
+
+ align:start position:0%
+this is a conservation law and for this
+ 
+
+ align:start position:0%
+this is a conservation law and for this
+flow what do we call constitutive
+
+ align:start position:0%
+flow what do we call constitutive
+ 
+
+ align:start position:0%
+flow what do we call constitutive
+relation it's a relation between
+
+ align:start position:0%
+relation it's a relation between
+ 
+
+ align:start position:0%
+relation it's a relation between
+temperature and the heat flux right in
+
+ align:start position:0%
+temperature and the heat flux right in
+ 
+
+ align:start position:0%
+temperature and the heat flux right in
+those consider relation many of them
+
+ align:start position:0%
+those consider relation many of them
+ 
+
+ align:start position:0%
+those consider relation many of them
+have their regime of validity and then
+
+ align:start position:0%
+have their regime of validity and then
+ 
+
+ align:start position:0%
+have their regime of validity and then
+you can it slow you can break them okay
+
+ align:start position:0%
+you can it slow you can break them okay
+ 
+
+ align:start position:0%
+you can it slow you can break them okay
+and so since we're doing heat what are
+
+ align:start position:0%
+and so since we're doing heat what are
+ 
+
+ align:start position:0%
+and so since we're doing heat what are
+the other heat loss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's say conversion right so for
+
+ align:start position:0%
+okay let's say conversion right so for
+ 
+
+ align:start position:0%
+okay let's say conversion right so for
+conversion of course for those who now
+
+ align:start position:0%
+conversion of course for those who now
+ 
+
+ align:start position:0%
+conversion of course for those who now
+live in Stokes equation and you'll be to
+
+ align:start position:0%
+live in Stokes equation and you'll be to
+ 
+
+ align:start position:0%
+live in Stokes equation and you'll be to
+this very complicated differential
+
+ align:start position:0%
+this very complicated differential
+ 
+
+ align:start position:0%
+this very complicated differential
+equations but in this simplest picture
+
+ align:start position:0%
+equations but in this simplest picture
+ 
+
+ align:start position:0%
+equations but in this simplest picture
+when we do convection is I have heated a
+
+ align:start position:0%
+when we do convection is I have heated a
+ 
+
+ align:start position:0%
+when we do convection is I have heated a
+surface let's say this is the wall and I
+
+ align:start position:0%
+surface let's say this is the wall and I
+ 
+
+ align:start position:0%
+surface let's say this is the wall and I
+have a fluids and away from the wall the
+
+ align:start position:0%
+have a fluids and away from the wall the
+ 
+
+ align:start position:0%
+have a fluids and away from the wall the
+fluid temperature is ta ambient and then
+
+ align:start position:0%
+fluid temperature is ta ambient and then
+ 
+
+ align:start position:0%
+fluid temperature is ta ambient and then
+I write the law for cooling is the Q
+
+ align:start position:0%
+I write the law for cooling is the Q
+ 
+
+ align:start position:0%
+I write the law for cooling is the Q
+equals h TW minus ta right this is the
+
+ align:start position:0%
+equals h TW minus ta right this is the
+ 
+
+ align:start position:0%
+equals h TW minus ta right this is the
+Luden's law of cooling right Newton's
+
+ align:start position:0%
+Luden's law of cooling right Newton's
+ 
+
+ align:start position:0%
+Luden's law of cooling right Newton's
+law of cooling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and H here is the heat transfer
+
+ align:start position:0%
+and H here is the heat transfer
+ 
+
+ align:start position:0%
+and H here is the heat transfer
+coefficient the unit of H is different
+
+ align:start position:0%
+coefficient the unit of H is different
+ 
+
+ align:start position:0%
+coefficient the unit of H is different
+from K if you look at what we had for
+
+ align:start position:0%
+from K if you look at what we had for
+ 
+
+ align:start position:0%
+from K if you look at what we had for
+fuller law and this is what meter square
+
+ align:start position:0%
+fuller law and this is what meter square
+ 
+
+ align:start position:0%
+fuller law and this is what meter square
+per Kelvin H is not a material property
+
+ align:start position:0%
+per Kelvin H is not a material property
+ 
+
+ align:start position:0%
+per Kelvin H is not a material property
+it depends on how fast is fluid will
+
+ align:start position:0%
+it depends on how fast is fluid will
+ 
+
+ align:start position:0%
+it depends on how fast is fluid will
+Flutie use right and the geometry so
+
+ align:start position:0%
+Flutie use right and the geometry so
+ 
+
+ align:start position:0%
+Flutie use right and the geometry so
+it's so for that you need to go to
+
+ align:start position:0%
+it's so for that you need to go to
+ 
+
+ align:start position:0%
+it's so for that you need to go to
+newest ox equation to solve if the case
+
+ align:start position:0%
+newest ox equation to solve if the case
+ 
+
+ align:start position:0%
+newest ox equation to solve if the case
+is simple if it's case is complicated
+
+ align:start position:0%
+is simple if it's case is complicated
+ 
+
+ align:start position:0%
+is simple if it's case is complicated
+you go to do the experiment right and
+
+ align:start position:0%
+you go to do the experiment right and
+ 
+
+ align:start position:0%
+you go to do the experiment right and
+one thing I want to say remain you if
+
+ align:start position:0%
+one thing I want to say remain you if
+ 
+
+ align:start position:0%
+one thing I want to say remain you if
+you do fluids problem or heat transfer
+
+ align:start position:0%
+you do fluids problem or heat transfer
+ 
+
+ align:start position:0%
+you do fluids problem or heat transfer
+conversion on the war you often invoke a
+
+ align:start position:0%
+conversion on the war you often invoke a
+ 
+
+ align:start position:0%
+conversion on the war you often invoke a
+condition what is that condition now
+
+ align:start position:0%
+condition what is that condition now
+ 
+
+ align:start position:0%
+condition what is that condition now
+asleep right so the molecule the
+
+ align:start position:0%
+asleep right so the molecule the
+ 
+
+ align:start position:0%
+asleep right so the molecule the
+velocity of molecule is zero or equal to
+
+ align:start position:0%
+velocity of molecule is zero or equal to
+ 
+
+ align:start position:0%
+velocity of molecule is zero or equal to
+the velocity of the war and temperature
+
+ align:start position:0%
+the velocity of the war and temperature
+ 
+
+ align:start position:0%
+the velocity of the war and temperature
+you were a temperature of the wall
+
+ align:start position:0%
+you were a temperature of the wall
+ 
+
+ align:start position:0%
+you were a temperature of the wall
+that's the no slip boundary condition
+
+ align:start position:0%
+that's the no slip boundary condition
+ 
+
+ align:start position:0%
+that's the no slip boundary condition
+and area of you learn fluids or heat
+
+ align:start position:0%
+and area of you learn fluids or heat
+ 
+
+ align:start position:0%
+and area of you learn fluids or heat
+transfer notes there but I say that's
+
+ align:start position:0%
+transfer notes there but I say that's
+ 
+
+ align:start position:0%
+transfer notes there but I say that's
+not valid that's not true in fact there
+
+ align:start position:0%
+not valid that's not true in fact there
+ 
+
+ align:start position:0%
+not valid that's not true in fact there
+is always sleep there's always velocity
+
+ align:start position:0%
+is always sleep there's always velocity
+ 
+
+ align:start position:0%
+is always sleep there's always velocity
+and temperature sorry it's just a
+
+ align:start position:0%
+and temperature sorry it's just a
+ 
+
+ align:start position:0%
+and temperature sorry it's just a
+normally it's too small so you can
+
+ align:start position:0%
+normally it's too small so you can
+ 
+
+ align:start position:0%
+normally it's too small so you can
+ignore it and you will see why
+
+ align:start position:0%
+ignore it and you will see why
+ 
+
+ align:start position:0%
+ignore it and you will see why
+downstream okay so conduction convection
+
+ align:start position:0%
+downstream okay so conduction convection
+ 
+
+ align:start position:0%
+downstream okay so conduction convection
+radiation let's look at radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the radiation law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's write both
+
+ align:start position:0%
+okay so let's write both
+ 
+
+ align:start position:0%
+okay so let's write both
+stefan-boltzmann or QE course for
+
+ align:start position:0%
+stefan-boltzmann or QE course for
+ 
+
+ align:start position:0%
+stefan-boltzmann or QE course for
+blackbody Sigma T fourth power right and
+
+ align:start position:0%
+blackbody Sigma T fourth power right and
+ 
+
+ align:start position:0%
+blackbody Sigma T fourth power right and
+the stefan-boltzmann constant the five
+
+ align:start position:0%
+the stefan-boltzmann constant the five
+ 
+
+ align:start position:0%
+the stefan-boltzmann constant the five
+point six seven ten to the minus eight
+
+ align:start position:0%
+point six seven ten to the minus eight
+ 
+
+ align:start position:0%
+point six seven ten to the minus eight
+watt meter square and in this case
+
+ align:start position:0%
+watt meter square and in this case
+ 
+
+ align:start position:0%
+watt meter square and in this case
+because it's not near with temperature
+
+ align:start position:0%
+because it's not near with temperature
+ 
+
+ align:start position:0%
+because it's not near with temperature
+so you have to use Kelvin Kelvin fourth
+
+ align:start position:0%
+so you have to use Kelvin Kelvin fourth
+ 
+
+ align:start position:0%
+so you have to use Kelvin Kelvin fourth
+power and I already commented before we
+
+ align:start position:0%
+power and I already commented before we
+ 
+
+ align:start position:0%
+power and I already commented before we
+can go if we go now we can go way beyond
+
+ align:start position:0%
+can go if we go now we can go way beyond
+ 
+
+ align:start position:0%
+can go if we go now we can go way beyond
+this okay so those are the our heat
+
+ align:start position:0%
+this okay so those are the our heat
+ 
+
+ align:start position:0%
+this okay so those are the our heat
+transfer laws I'm more ambitious I want
+
+ align:start position:0%
+transfer laws I'm more ambitious I want
+ 
+
+ align:start position:0%
+transfer laws I'm more ambitious I want
+to hear more if your electrical engineer
+
+ align:start position:0%
+to hear more if your electrical engineer
+ 
+
+ align:start position:0%
+to hear more if your electrical engineer
+you tell me or Templar engineer what are
+
+ align:start position:0%
+you tell me or Templar engineer what are
+ 
+
+ align:start position:0%
+you tell me or Templar engineer what are
+they transport laws or fluids right
+
+ align:start position:0%
+they transport laws or fluids right
+ 
+
+ align:start position:0%
+they transport laws or fluids right
+these are the ones that I'm familiar
+
+ align:start position:0%
+these are the ones that I'm familiar
+ 
+
+ align:start position:0%
+these are the ones that I'm familiar
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay brief diffusion
+
+ align:start position:0%
+okay brief diffusion
+ 
+
+ align:start position:0%
+okay brief diffusion
+let me simplify it further let's just
+
+ align:start position:0%
+let me simplify it further let's just
+ 
+
+ align:start position:0%
+let me simplify it further let's just
+write Ohm's law well would the right
+
+ align:start position:0%
+write Ohm's law well would the right
+ 
+
+ align:start position:0%
+write Ohm's law well would the right
+drift diffusion okay so ah here I have a
+
+ align:start position:0%
+drift diffusion okay so ah here I have a
+ 
+
+ align:start position:0%
+drift diffusion okay so ah here I have a
+heat and I will have a charge and so
+
+ align:start position:0%
+heat and I will have a charge and so
+ 
+
+ align:start position:0%
+heat and I will have a charge and so
+Ohm's law I really want to write a
+
+ align:start position:0%
+Ohm's law I really want to write a
+ 
+
+ align:start position:0%
+Ohm's law I really want to write a
+differential form so the differential
+
+ align:start position:0%
+differential form so the differential
+ 
+
+ align:start position:0%
+differential form so the differential
+form for almost law is a current density
+
+ align:start position:0%
+form for almost law is a current density
+ 
+
+ align:start position:0%
+form for almost law is a current density
+so here is a flux the write flux is the
+
+ align:start position:0%
+so here is a flux the write flux is the
+ 
+
+ align:start position:0%
+so here is a flux the write flux is the
+heat flux is a watt per meter square and
+
+ align:start position:0%
+heat flux is a watt per meter square and
+ 
+
+ align:start position:0%
+heat flux is a watt per meter square and
+here current density is and per meter
+
+ align:start position:0%
+here current density is and per meter
+ 
+
+ align:start position:0%
+here current density is and per meter
+square okay eCourse
+
+ align:start position:0%
+square okay eCourse
+ 
+
+ align:start position:0%
+square okay eCourse
+electric conductivity times the electric
+
+ align:start position:0%
+electric conductivity times the electric
+ 
+
+ align:start position:0%
+electric conductivity times the electric
+field they write okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the here I have an meter square and
+
+ align:start position:0%
+so the here I have an meter square and
+ 
+
+ align:start position:0%
+so the here I have an meter square and
+here I have Oh immersion in worse ohm
+
+ align:start position:0%
+here I have Oh immersion in worse ohm
+ 
+
+ align:start position:0%
+here I have Oh immersion in worse ohm
+per meter it doesn't look like a
+
+ align:start position:0%
+per meter it doesn't look like a
+ 
+
+ align:start position:0%
+per meter it doesn't look like a
+differential form so I'm going to write
+
+ align:start position:0%
+differential form so I'm going to write
+ 
+
+ align:start position:0%
+differential form so I'm going to write
+it into a differential form the electric
+
+ align:start position:0%
+it into a differential form the electric
+ 
+
+ align:start position:0%
+it into a differential form the electric
+field is the derivative of potential
+
+ align:start position:0%
+field is the derivative of potential
+ 
+
+ align:start position:0%
+field is the derivative of potential
+right so I have Sigma and D Phi DX and I
+
+ align:start position:0%
+right so I have Sigma and D Phi DX and I
+ 
+
+ align:start position:0%
+right so I have Sigma and D Phi DX and I
+have a shoe that mountain sign right so
+
+ align:start position:0%
+have a shoe that mountain sign right so
+ 
+
+ align:start position:0%
+have a shoe that mountain sign right so
+Phi is a electrostatic potential okay so
+
+ align:start position:0%
+Phi is a electrostatic potential okay so
+ 
+
+ align:start position:0%
+Phi is a electrostatic potential okay so
+that's for charge right more we talked
+
+ align:start position:0%
+that's for charge right more we talked
+ 
+
+ align:start position:0%
+that's for charge right more we talked
+about the heat we talked about charge
+
+ align:start position:0%
+about the heat we talked about charge
+ 
+
+ align:start position:0%
+about the heat we talked about charge
+fluid guy tell me
+
+ align:start position:0%
+fluid guy tell me
+ 
+
+ align:start position:0%
+fluid guy tell me
+ah momentum okay Newton sure stress not
+
+ align:start position:0%
+ah momentum okay Newton sure stress not
+ 
+
+ align:start position:0%
+ah momentum okay Newton sure stress not
+related force to the momentum right so
+
+ align:start position:0%
+related force to the momentum right so
+ 
+
+ align:start position:0%
+related force to the momentum right so
+Newton shear stress no shear stress and
+
+ align:start position:0%
+Newton shear stress no shear stress and
+ 
+
+ align:start position:0%
+Newton shear stress no shear stress and
+this is a again if I take a simplest
+
+ align:start position:0%
+this is a again if I take a simplest
+ 
+
+ align:start position:0%
+this is a again if I take a simplest
+picture if I have X I have Y and in the
+
+ align:start position:0%
+picture if I have X I have Y and in the
+ 
+
+ align:start position:0%
+picture if I have X I have Y and in the
+fluids there's a there's shear stress
+
+ align:start position:0%
+fluids there's a there's shear stress
+ 
+
+ align:start position:0%
+fluids there's a there's shear stress
+tau XY right and in the simplest form
+
+ align:start position:0%
+tau XY right and in the simplest form
+ 
+
+ align:start position:0%
+tau XY right and in the simplest form
+tau XY equals mu deal dy were you this
+
+ align:start position:0%
+tau XY equals mu deal dy were you this
+ 
+
+ align:start position:0%
+tau XY equals mu deal dy were you this
+is the velocity yo this is a velocity
+
+ align:start position:0%
+is the velocity yo this is a velocity
+ 
+
+ align:start position:0%
+is the velocity yo this is a velocity
+way right so here we have dynamic
+
+ align:start position:0%
+way right so here we have dynamic
+ 
+
+ align:start position:0%
+way right so here we have dynamic
+viscosity the shear stress is a Newton
+
+ align:start position:0%
+viscosity the shear stress is a Newton
+ 
+
+ align:start position:0%
+viscosity the shear stress is a Newton
+meter square and the dynamic squid with
+
+ align:start position:0%
+meter square and the dynamic squid with
+ 
+
+ align:start position:0%
+meter square and the dynamic squid with
+God is the Newton second meter square
+
+ align:start position:0%
+God is the Newton second meter square
+ 
+
+ align:start position:0%
+God is the Newton second meter square
+okay so we have during shear stress no
+
+ align:start position:0%
+okay so we have during shear stress no
+ 
+
+ align:start position:0%
+okay so we have during shear stress no
+and you can write into more complex
+
+ align:start position:0%
+and you can write into more complex
+ 
+
+ align:start position:0%
+and you can write into more complex
+tensor form 3d I'm always writing the
+
+ align:start position:0%
+tensor form 3d I'm always writing the
+ 
+
+ align:start position:0%
+tensor form 3d I'm always writing the
+same place what what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mess tell me mass transport fix laws
+
+ align:start position:0%
+mess tell me mass transport fix laws
+ 
+
+ align:start position:0%
+mess tell me mass transport fix laws
+right fix roll so mass we have how here
+
+ align:start position:0%
+right fix roll so mass we have how here
+ 
+
+ align:start position:0%
+right fix roll so mass we have how here
+that we have so we have mass diffusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the mass flux equals Rho T and D say
+
+ align:start position:0%
+and the mass flux equals Rho T and D say
+ 
+
+ align:start position:0%
+and the mass flux equals Rho T and D say
+DX right the mass flux here you say is a
+
+ align:start position:0%
+DX right the mass flux here you say is a
+ 
+
+ align:start position:0%
+DX right the mass flux here you say is a
+kilogram per meter square flux is always
+
+ align:start position:0%
+kilogram per meter square flux is always
+ 
+
+ align:start position:0%
+kilogram per meter square flux is always
+a lot at a meter square and the
+
+ align:start position:0%
+a lot at a meter square and the
+ 
+
+ align:start position:0%
+a lot at a meter square and the
+diffusivity 10 or is density diffusivity
+
+ align:start position:0%
+diffusivity 10 or is density diffusivity
+ 
+
+ align:start position:0%
+diffusivity 10 or is density diffusivity
+is a meter square per second and this
+
+ align:start position:0%
+is a meter square per second and this
+ 
+
+ align:start position:0%
+is a meter square per second and this
+say is the mass fraction you can go to
+
+ align:start position:0%
+say is the mass fraction you can go to
+ 
+
+ align:start position:0%
+say is the mass fraction you can go to
+check a unit right so we wrote all this
+
+ align:start position:0%
+check a unit right so we wrote all this
+ 
+
+ align:start position:0%
+check a unit right so we wrote all this
+constitutive equation and in the first
+
+ align:start position:0%
+constitutive equation and in the first
+ 
+
+ align:start position:0%
+constitutive equation and in the first
+homework you would derive so even though
+
+ align:start position:0%
+homework you would derive so even though
+ 
+
+ align:start position:0%
+homework you would derive so even though
+say most of the classes that you'll
+
+ align:start position:0%
+say most of the classes that you'll
+ 
+
+ align:start position:0%
+say most of the classes that you'll
+probably give it but you can use the
+
+ align:start position:0%
+probably give it but you can use the
+ 
+
+ align:start position:0%
+probably give it but you can use the
+simplest picture by counting the numbers
+
+ align:start position:0%
+simplest picture by counting the numbers
+ 
+
+ align:start position:0%
+simplest picture by counting the numbers
+and if you have a gradient of velocity
+
+ align:start position:0%
+and if you have a gradient of velocity
+ 
+
+ align:start position:0%
+and if you have a gradient of velocity
+you have gradient of temperature your
+
+ align:start position:0%
+you have gradient of temperature your
+ 
+
+ align:start position:0%
+you have gradient of temperature your
+gradient see in the you know you're
+
+ align:start position:0%
+gradient see in the you know you're
+ 
+
+ align:start position:0%
+gradient see in the you know you're
+actually a field you will see that this
+
+ align:start position:0%
+actually a field you will see that this
+ 
+
+ align:start position:0%
+actually a field you will see that this
+can be when you go to see the granular
+
+ align:start position:0%
+can be when you go to see the granular
+ 
+
+ align:start position:0%
+can be when you go to see the granular
+picture the those nodes can be easily
+
+ align:start position:0%
+picture the those nodes can be easily
+ 
+
+ align:start position:0%
+picture the those nodes can be easily
+derived and I'll show you in the lecture
+
+ align:start position:0%
+derived and I'll show you in the lecture
+ 
+
+ align:start position:0%
+derived and I'll show you in the lecture
+and let's make sure how to derive it
+
+ align:start position:0%
+and let's make sure how to derive it
+ 
+
+ align:start position:0%
+and let's make sure how to derive it
+okay so we said those are the continuum
+
+ align:start position:0%
+okay so we said those are the continuum
+ 
+
+ align:start position:0%
+okay so we said those are the continuum
+those are the ones at least you feel
+
+ align:start position:0%
+those are the ones at least you feel
+ 
+
+ align:start position:0%
+those are the ones at least you feel
+comfortable and the question we ask is
+
+ align:start position:0%
+comfortable and the question we ask is
+ 
+
+ align:start position:0%
+comfortable and the question we ask is
+when we go to nano the other still valid
+
+ align:start position:0%
+when we go to nano the other still valid
+ 
+
+ align:start position:0%
+when we go to nano the other still valid
+right if they are not valid what
+
+ align:start position:0%
+right if they are not valid what
+ 
+
+ align:start position:0%
+right if they are not valid what
+alternatives we have and to do
+
+ align:start position:0%
+alternatives we have and to do
+ 
+
+ align:start position:0%
+alternatives we have and to do
+that we need to go to granular picture
+
+ align:start position:0%
+that we need to go to granular picture
+ 
+
+ align:start position:0%
+that we need to go to granular picture
+we need to look at the individual chart
+
+ align:start position:0%
+we need to look at the individual chart
+ 
+
+ align:start position:0%
+we need to look at the individual chart
+individual molecules and individual
+
+ align:start position:0%
+individual molecules and individual
+ 
+
+ align:start position:0%
+individual molecules and individual
+photons so what we are going to look at
+
+ align:start position:0%
+photons so what we are going to look at
+ 
+
+ align:start position:0%
+photons so what we are going to look at
+next let's let's look at take a look at
+
+ align:start position:0%
+next let's let's look at take a look at
+ 
+
+ align:start position:0%
+next let's let's look at take a look at
+the simplest microscopic picture for
+
+ align:start position:0%
+the simplest microscopic picture for
+ 
+
+ align:start position:0%
+the simplest microscopic picture for
+this transport okay so let's first look
+
+ align:start position:0%
+this transport okay so let's first look
+ 
+
+ align:start position:0%
+this transport okay so let's first look
+either we talked about heat that's why
+
+ align:start position:0%
+either we talked about heat that's why
+ 
+
+ align:start position:0%
+either we talked about heat that's why
+I'm most familiar with right so let's
+
+ align:start position:0%
+I'm most familiar with right so let's
+ 
+
+ align:start position:0%
+I'm most familiar with right so let's
+first talk about the heat and let's say
+
+ align:start position:0%
+first talk about the heat and let's say
+ 
+
+ align:start position:0%
+first talk about the heat and let's say
+heat conduction so we draw this picture
+
+ align:start position:0%
+heat conduction so we draw this picture
+ 
+
+ align:start position:0%
+heat conduction so we draw this picture
+on one side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is hot the other side is cold we see
+
+ align:start position:0%
+is hot the other side is cold we see
+ 
+
+ align:start position:0%
+is hot the other side is cold we see
+there is a heat flow and now I want to
+
+ align:start position:0%
+there is a heat flow and now I want to
+ 
+
+ align:start position:0%
+there is a heat flow and now I want to
+look at the granular let's say I have a
+
+ align:start position:0%
+look at the granular let's say I have a
+ 
+
+ align:start position:0%
+look at the granular let's say I have a
+box of with molecules let's see the
+
+ align:start position:0%
+box of with molecules let's see the
+ 
+
+ align:start position:0%
+box of with molecules let's see the
+right one side that is the hot the other
+
+ align:start position:0%
+right one side that is the hot the other
+ 
+
+ align:start position:0%
+right one side that is the hot the other
+side is cold let's say we have gas
+
+ align:start position:0%
+side is cold let's say we have gas
+ 
+
+ align:start position:0%
+side is cold let's say we have gas
+molecules inside how heat is actually
+
+ align:start position:0%
+molecules inside how heat is actually
+ 
+
+ align:start position:0%
+molecules inside how heat is actually
+conducted right I'm sorry
+
+ align:start position:0%
+conducted right I'm sorry
+ 
+
+ align:start position:0%
+conducted right I'm sorry
+guess molecule so I take the simplest
+
+ align:start position:0%
+guess molecule so I take the simplest
+ 
+
+ align:start position:0%
+guess molecule so I take the simplest
+guess there's no vibration
+
+ align:start position:0%
+guess there's no vibration
+ 
+
+ align:start position:0%
+guess there's no vibration
+I take Heaney
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this side is hotter right and
+
+ align:start position:0%
+right so this side is hotter right and
+ 
+
+ align:start position:0%
+right so this side is hotter right and
+the gas molecule they do random motion
+
+ align:start position:0%
+the gas molecule they do random motion
+ 
+
+ align:start position:0%
+the gas molecule they do random motion
+and at least say when I say random
+
+ align:start position:0%
+and at least say when I say random
+ 
+
+ align:start position:0%
+and at least say when I say random
+motion about half of them would go this
+
+ align:start position:0%
+motion about half of them would go this
+ 
+
+ align:start position:0%
+motion about half of them would go this
+way and they were collided with the
+
+ align:start position:0%
+way and they were collided with the
+ 
+
+ align:start position:0%
+way and they were collided with the
+whole a higher temperature and what
+
+ align:start position:0%
+whole a higher temperature and what
+ 
+
+ align:start position:0%
+whole a higher temperature and what
+again is it again a higher kinetic
+
+ align:start position:0%
+again is it again a higher kinetic
+ 
+
+ align:start position:0%
+again is it again a higher kinetic
+energy because this is a higher
+
+ align:start position:0%
+energy because this is a higher
+ 
+
+ align:start position:0%
+energy because this is a higher
+temperature when they bounce back they
+
+ align:start position:0%
+temperature when they bounce back they
+ 
+
+ align:start position:0%
+temperature when they bounce back they
+have a higher kinetic energy faster
+
+ align:start position:0%
+have a higher kinetic energy faster
+ 
+
+ align:start position:0%
+have a higher kinetic energy faster
+right so we begin energy when the
+
+ align:start position:0%
+right so we begin energy when the
+ 
+
+ align:start position:0%
+right so we begin energy when the
+collision and they bounce back the lexer
+
+ align:start position:0%
+collision and they bounce back the lexer
+ 
+
+ align:start position:0%
+collision and they bounce back the lexer
+molecule they say will have slightly
+
+ align:start position:0%
+molecule they say will have slightly
+ 
+
+ align:start position:0%
+molecule they say will have slightly
+lower energy so is the two ball
+
+ align:start position:0%
+lower energy so is the two ball
+ 
+
+ align:start position:0%
+lower energy so is the two ball
+collision problem and during that
+
+ align:start position:0%
+collision problem and during that
+ 
+
+ align:start position:0%
+collision problem and during that
+process they'll pass some of the energy
+
+ align:start position:0%
+process they'll pass some of the energy
+ 
+
+ align:start position:0%
+process they'll pass some of the energy
+to the Lexx molecule and the next
+
+ align:start position:0%
+to the Lexx molecule and the next
+ 
+
+ align:start position:0%
+to the Lexx molecule and the next
+molecule against have different chance
+
+ align:start position:0%
+molecule against have different chance
+ 
+
+ align:start position:0%
+molecule against have different chance
+going this way and that way and it's
+
+ align:start position:0%
+going this way and that way and it's
+ 
+
+ align:start position:0%
+going this way and that way and it's
+that diffusion process that he goes from
+
+ align:start position:0%
+that diffusion process that he goes from
+ 
+
+ align:start position:0%
+that diffusion process that he goes from
+hot to the cold right so it's the random
+
+ align:start position:0%
+hot to the cold right so it's the random
+ 
+
+ align:start position:0%
+hot to the cold right so it's the random
+walk and diffusion process and in fact
+
+ align:start position:0%
+walk and diffusion process and in fact
+ 
+
+ align:start position:0%
+walk and diffusion process and in fact
+turns out other than radiation orders
+
+ align:start position:0%
+turns out other than radiation orders
+ 
+
+ align:start position:0%
+turns out other than radiation orders
+are similar process okay and the if this
+
+ align:start position:0%
+are similar process okay and the if this
+ 
+
+ align:start position:0%
+are similar process okay and the if this
+is not an easy picture in the history of
+
+ align:start position:0%
+is not an easy picture in the history of
+ 
+
+ align:start position:0%
+is not an easy picture in the history of
+heat because we a long time ago people
+
+ align:start position:0%
+heat because we a long time ago people
+ 
+
+ align:start position:0%
+heat because we a long time ago people
+have this heat is there something
+
+ align:start position:0%
+have this heat is there something
+ 
+
+ align:start position:0%
+have this heat is there something
+calorie right code when you have to
+
+ align:start position:0%
+calorie right code when you have to
+ 
+
+ align:start position:0%
+calorie right code when you have to
+object touching each other the cholera
+
+ align:start position:0%
+object touching each other the cholera
+ 
+
+ align:start position:0%
+object touching each other the cholera
+flow from one side to the other so when
+
+ align:start position:0%
+flow from one side to the other so when
+ 
+
+ align:start position:0%
+flow from one side to the other so when
+you go to supermarket is do you have the
+
+ align:start position:0%
+you go to supermarket is do you have the
+ 
+
+ align:start position:0%
+you go to supermarket is do you have the
+calories it's a wrong concept we use the
+
+ align:start position:0%
+calories it's a wrong concept we use the
+ 
+
+ align:start position:0%
+calories it's a wrong concept we use the
+terminology today
+
+ align:start position:0%
+terminology today
+ 
+
+ align:start position:0%
+terminology today
+now this is a gas molecule what about
+
+ align:start position:0%
+now this is a gas molecule what about
+ 
+
+ align:start position:0%
+now this is a gas molecule what about
+metal what care is hitting metal so
+
+ align:start position:0%
+metal what care is hitting metal so
+ 
+
+ align:start position:0%
+metal what care is hitting metal so
+electrons right so I put the metal and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the transport picture one side is
+
+ align:start position:0%
+what's the transport picture one side is
+ 
+
+ align:start position:0%
+what's the transport picture one side is
+hot the other side is cold so that's the
+
+ align:start position:0%
+hot the other side is cold so that's the
+ 
+
+ align:start position:0%
+hot the other side is cold so that's the
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+it's the electron now is the gas in the
+
+ align:start position:0%
+it's the electron now is the gas in the
+ 
+
+ align:start position:0%
+it's the electron now is the gas in the
+solid they're bound by the ions but they
+
+ align:start position:0%
+solid they're bound by the ions but they
+ 
+
+ align:start position:0%
+solid they're bound by the ions but they
+actually can know quite a few distance
+
+ align:start position:0%
+actually can know quite a few distance
+ 
+
+ align:start position:0%
+actually can know quite a few distance
+beyond their nitrogen see electron that
+
+ align:start position:0%
+beyond their nitrogen see electron that
+ 
+
+ align:start position:0%
+beyond their nitrogen see electron that
+these are free electrons the electron
+
+ align:start position:0%
+these are free electrons the electron
+ 
+
+ align:start position:0%
+these are free electrons the electron
+actually can move around and again they
+
+ align:start position:0%
+actually can move around and again they
+ 
+
+ align:start position:0%
+actually can move around and again they
+will have a collision distance right we
+
+ align:start position:0%
+will have a collision distance right we
+ 
+
+ align:start position:0%
+will have a collision distance right we
+say the air molecule collision distance
+
+ align:start position:0%
+say the air molecule collision distance
+ 
+
+ align:start position:0%
+say the air molecule collision distance
+is 100 nanometer and the electron
+
+ align:start position:0%
+is 100 nanometer and the electron
+ 
+
+ align:start position:0%
+is 100 nanometer and the electron
+collision distance can be few nanometer
+
+ align:start position:0%
+collision distance can be few nanometer
+ 
+
+ align:start position:0%
+collision distance can be few nanometer
+to you and longer 100 nanometer or you
+
+ align:start position:0%
+to you and longer 100 nanometer or you
+ 
+
+ align:start position:0%
+to you and longer 100 nanometer or you
+micron depends on temperature so it's
+
+ align:start position:0%
+micron depends on temperature so it's
+ 
+
+ align:start position:0%
+micron depends on temperature so it's
+easily amazing they're minutes minutes
+
+ align:start position:0%
+easily amazing they're minutes minutes
+ 
+
+ align:start position:0%
+easily amazing they're minutes minutes
+of atom if you think of one micron how
+
+ align:start position:0%
+of atom if you think of one micron how
+ 
+
+ align:start position:0%
+of atom if you think of one micron how
+many items there and the electron can
+
+ align:start position:0%
+many items there and the electron can
+ 
+
+ align:start position:0%
+many items there and the electron can
+zip through them and no collision so of
+
+ align:start position:0%
+zip through them and no collision so of
+ 
+
+ align:start position:0%
+zip through them and no collision so of
+course at the end there is a collision
+
+ align:start position:0%
+course at the end there is a collision
+ 
+
+ align:start position:0%
+course at the end there is a collision
+so if you think about that case is the
+
+ align:start position:0%
+so if you think about that case is the
+ 
+
+ align:start position:0%
+so if you think about that case is the
+electron power few distance and the
+
+ align:start position:0%
+electron power few distance and the
+ 
+
+ align:start position:0%
+electron power few distance and the
+collide and that's the same process so
+
+ align:start position:0%
+collide and that's the same process so
+ 
+
+ align:start position:0%
+collide and that's the same process so
+it's the electron gas when you can give
+
+ align:start position:0%
+it's the electron gas when you can give
+ 
+
+ align:start position:0%
+it's the electron gas when you can give
+a name like a gas right so it's the
+
+ align:start position:0%
+a name like a gas right so it's the
+ 
+
+ align:start position:0%
+a name like a gas right so it's the
+electron gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and next what about a loam or
+
+ align:start position:0%
+okay and next what about a loam or
+ 
+
+ align:start position:0%
+okay and next what about a loam or
+nonmetal
+
+ align:start position:0%
+nonmetal
+ 
+
+ align:start position:0%
+nonmetal
+diamond ah it's a full-on okay but most
+
+ align:start position:0%
+diamond ah it's a full-on okay but most
+ 
+
+ align:start position:0%
+diamond ah it's a full-on okay but most
+of you probably the first time I heard
+
+ align:start position:0%
+of you probably the first time I heard
+ 
+
+ align:start position:0%
+of you probably the first time I heard
+phonon in fact mother first time I heard
+
+ align:start position:0%
+phonon in fact mother first time I heard
+ 
+
+ align:start position:0%
+phonon in fact mother first time I heard
+full none but I remember when I was a
+
+ align:start position:0%
+full none but I remember when I was a
+ 
+
+ align:start position:0%
+full none but I remember when I was a
+graduate student walking into a electric
+
+ align:start position:0%
+graduate student walking into a electric
+ 
+
+ align:start position:0%
+graduate student walking into a electric
+engineer and they have an open house
+
+ align:start position:0%
+engineer and they have an open house
+ 
+
+ align:start position:0%
+engineer and they have an open house
+they had an open house to their lab show
+
+ align:start position:0%
+they had an open house to their lab show
+ 
+
+ align:start position:0%
+they had an open house to their lab show
+I said work on heat transfer and the guy
+
+ align:start position:0%
+I said work on heat transfer and the guy
+ 
+
+ align:start position:0%
+I said work on heat transfer and the guy
+said oh you work on photons and the most
+
+ align:start position:0%
+said oh you work on photons and the most
+ 
+
+ align:start position:0%
+said oh you work on photons and the most
+mechanical engineer when they work heat
+
+ align:start position:0%
+mechanical engineer when they work heat
+ 
+
+ align:start position:0%
+mechanical engineer when they work heat
+transfer they don't know what it was
+
+ align:start position:0%
+transfer they don't know what it was
+ 
+
+ align:start position:0%
+transfer they don't know what it was
+used for right in some not of you
+
+ align:start position:0%
+used for right in some not of you
+ 
+
+ align:start position:0%
+used for right in some not of you
+probably just to graduate from
+
+ align:start position:0%
+probably just to graduate from
+ 
+
+ align:start position:0%
+probably just to graduate from
+undergraduate degree in mechanical
+
+ align:start position:0%
+undergraduate degree in mechanical
+ 
+
+ align:start position:0%
+undergraduate degree in mechanical
+engineering how many of you have heard
+
+ align:start position:0%
+engineering how many of you have heard
+ 
+
+ align:start position:0%
+engineering how many of you have heard
+the phone long heat transfer course
+
+ align:start position:0%
+the phone long heat transfer course
+ 
+
+ align:start position:0%
+the phone long heat transfer course
+right molarity okay so what is the
+
+ align:start position:0%
+right molarity okay so what is the
+ 
+
+ align:start position:0%
+right molarity okay so what is the
+fullness
+
+ align:start position:0%
+fullness
+ 
+
+ align:start position:0%
+fullness
+I had a once I had a say I was teaching
+
+ align:start position:0%
+I had a once I had a say I was teaching
+ 
+
+ align:start position:0%
+I had a once I had a say I was teaching
+another university and I had a colleague
+
+ align:start position:0%
+another university and I had a colleague
+ 
+
+ align:start position:0%
+another university and I had a colleague
+and he said in my scars and I end he
+
+ align:start position:0%
+and he said in my scars and I end he
+ 
+
+ align:start position:0%
+and he said in my scars and I end he
+said I still don't know what is a phone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you know what is the full huh
+
+ align:start position:0%
+what do you know what is the full huh
+ 
+
+ align:start position:0%
+what do you know what is the full huh
+yes I hope huh vibration it is a
+
+ align:start position:0%
+yes I hope huh vibration it is a
+ 
+
+ align:start position:0%
+yes I hope huh vibration it is a
+vibration yes yeah it's another electron
+
+ align:start position:0%
+vibration yes yeah it's another electron
+ 
+
+ align:start position:0%
+vibration yes yeah it's another electron
+so let's say what is the unknown metal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dielectric let's first concrete right so
+
+ align:start position:0%
+dielectric let's first concrete right so
+ 
+
+ align:start position:0%
+dielectric let's first concrete right so
+what holds the mature together is the
+
+ align:start position:0%
+what holds the mature together is the
+ 
+
+ align:start position:0%
+what holds the mature together is the
+force right and if I think about two
+
+ align:start position:0%
+force right and if I think about two
+ 
+
+ align:start position:0%
+force right and if I think about two
+atoms in a material and the potential
+
+ align:start position:0%
+atoms in a material and the potential
+ 
+
+ align:start position:0%
+atoms in a material and the potential
+between the two atom that's a typical
+
+ align:start position:0%
+between the two atom that's a typical
+ 
+
+ align:start position:0%
+between the two atom that's a typical
+curve is like this this is the
+
+ align:start position:0%
+curve is like this this is the
+ 
+
+ align:start position:0%
+curve is like this this is the
+separation between the two and this is
+
+ align:start position:0%
+separation between the two and this is
+ 
+
+ align:start position:0%
+separation between the two and this is
+the potential energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the minimum point that's
+
+ align:start position:0%
+this is the minimum point that's
+ 
+
+ align:start position:0%
+this is the minimum point that's
+normally their separation distance right
+
+ align:start position:0%
+normally their separation distance right
+ 
+
+ align:start position:0%
+normally their separation distance right
+when the further away the attract each
+
+ align:start position:0%
+when the further away the attract each
+ 
+
+ align:start position:0%
+when the further away the attract each
+other and when they are too close they
+
+ align:start position:0%
+other and when they are too close they
+ 
+
+ align:start position:0%
+other and when they are too close they
+repulse each other because there is
+
+ align:start position:0%
+repulse each other because there is
+ 
+
+ align:start position:0%
+repulse each other because there is
+charging the every atom has a positive
+
+ align:start position:0%
+charging the every atom has a positive
+ 
+
+ align:start position:0%
+charging the every atom has a positive
+charge and negative charge at the end is
+
+ align:start position:0%
+charge and negative charge at the end is
+ 
+
+ align:start position:0%
+charge and negative charge at the end is
+the charge that's the glue for the force
+
+ align:start position:0%
+the charge that's the glue for the force
+ 
+
+ align:start position:0%
+the charge that's the glue for the force
+for the potential of anima - okay and so
+
+ align:start position:0%
+for the potential of anima - okay and so
+ 
+
+ align:start position:0%
+for the potential of anima - okay and so
+that's the force that's the minimum
+
+ align:start position:0%
+that's the force that's the minimum
+ 
+
+ align:start position:0%
+that's the force that's the minimum
+distance and I'll Kurt the potential and
+
+ align:start position:0%
+distance and I'll Kurt the potential and
+ 
+
+ align:start position:0%
+distance and I'll Kurt the potential and
+the force is the force is the gradient
+
+ align:start position:0%
+the force is the force is the gradient
+ 
+
+ align:start position:0%
+the force is the force is the gradient
+of potential you okay right and at this
+
+ align:start position:0%
+of potential you okay right and at this
+ 
+
+ align:start position:0%
+of potential you okay right and at this
+minimum point that first should order
+
+ align:start position:0%
+minimum point that first should order
+ 
+
+ align:start position:0%
+minimum point that first should order
+graded is zero so the I can write they
+
+ align:start position:0%
+graded is zero so the I can write they
+ 
+
+ align:start position:0%
+graded is zero so the I can write they
+in fact I can write the potentially this
+
+ align:start position:0%
+in fact I can write the potentially this
+ 
+
+ align:start position:0%
+in fact I can write the potentially this
+for shoulder if I do the expansion and I
+
+ align:start position:0%
+for shoulder if I do the expansion and I
+ 
+
+ align:start position:0%
+for shoulder if I do the expansion and I
+will write the force roughly the
+
+ align:start position:0%
+will write the force roughly the
+ 
+
+ align:start position:0%
+will write the force roughly the
+potential expansion first order zero the
+
+ align:start position:0%
+potential expansion first order zero the
+ 
+
+ align:start position:0%
+potential expansion first order zero the
+second order give me a linear term
+
+ align:start position:0%
+second order give me a linear term
+ 
+
+ align:start position:0%
+second order give me a linear term
+that's a sprint so the two atoms the
+
+ align:start position:0%
+that's a sprint so the two atoms the
+ 
+
+ align:start position:0%
+that's a sprint so the two atoms the
+petunias your this simply is
+
+ align:start position:0%
+petunias your this simply is
+ 
+
+ align:start position:0%
+petunias your this simply is
+approximation is the spring holding them
+
+ align:start position:0%
+approximation is the spring holding them
+ 
+
+ align:start position:0%
+approximation is the spring holding them
+together okay so when I have a crystal
+
+ align:start position:0%
+together okay so when I have a crystal
+ 
+
+ align:start position:0%
+together okay so when I have a crystal
+like a diamond
+
+ align:start position:0%
+like a diamond
+ 
+
+ align:start position:0%
+like a diamond
+it's a periodic arrangement of atoms so
+
+ align:start position:0%
+it's a periodic arrangement of atoms so
+ 
+
+ align:start position:0%
+it's a periodic arrangement of atoms so
+they have their equilibrium position and
+
+ align:start position:0%
+they have their equilibrium position and
+ 
+
+ align:start position:0%
+they have their equilibrium position and
+they are holding together by this
+
+ align:start position:0%
+they are holding together by this
+ 
+
+ align:start position:0%
+they are holding together by this
+Springs right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this spring now you have you have
+
+ align:start position:0%
+so this spring now you have you have
+ 
+
+ align:start position:0%
+so this spring now you have you have
+this let work you look at it it has
+
+ align:start position:0%
+this let work you look at it it has
+ 
+
+ align:start position:0%
+this let work you look at it it has
+vibration and the vibration has a
+
+ align:start position:0%
+vibration and the vibration has a
+ 
+
+ align:start position:0%
+vibration and the vibration has a
+different frequency right so when we
+
+ align:start position:0%
+different frequency right so when we
+ 
+
+ align:start position:0%
+different frequency right so when we
+have vibration frequency frequency nu
+
+ align:start position:0%
+have vibration frequency frequency nu
+ 
+
+ align:start position:0%
+have vibration frequency frequency nu
+and this is where it has to go to
+
+ align:start position:0%
+and this is where it has to go to
+ 
+
+ align:start position:0%
+and this is where it has to go to
+quantum mechanics and it turns out that
+
+ align:start position:0%
+quantum mechanics and it turns out that
+ 
+
+ align:start position:0%
+quantum mechanics and it turns out that
+the vibrational energy cannot be
+
+ align:start position:0%
+the vibrational energy cannot be
+ 
+
+ align:start position:0%
+the vibrational energy cannot be
+arbitrary and the energy has to be
+
+ align:start position:0%
+arbitrary and the energy has to be
+ 
+
+ align:start position:0%
+arbitrary and the energy has to be
+multiple of n H nu
+
+ align:start position:0%
+multiple of n H nu
+ 
+
+ align:start position:0%
+multiple of n H nu
+the H is the Planck constant 6.6 10
+
+ align:start position:0%
+the H is the Planck constant 6.6 10
+ 
+
+ align:start position:0%
+the H is the Planck constant 6.6 10
+today I only remember if you are a
+
+ align:start position:0%
+today I only remember if you are a
+ 
+
+ align:start position:0%
+today I only remember if you are a
+physicist enough at me this is a H times
+
+ align:start position:0%
+physicist enough at me this is a H times
+ 
+
+ align:start position:0%
+physicist enough at me this is a H times
+SiC jar 10 second because the physicist
+
+ align:start position:0%
+SiC jar 10 second because the physicist
+ 
+
+ align:start position:0%
+SiC jar 10 second because the physicist
+use a Tomica unit it didn't carry this
+
+ align:start position:0%
+use a Tomica unit it didn't carry this
+ 
+
+ align:start position:0%
+use a Tomica unit it didn't carry this
+large negative numbers but I only
+
+ align:start position:0%
+large negative numbers but I only
+ 
+
+ align:start position:0%
+large negative numbers but I only
+remember the SI unit so I carried a
+
+ align:start position:0%
+remember the SI unit so I carried a
+ 
+
+ align:start position:0%
+remember the SI unit so I carried a
+large number smaller Planck constant H
+
+ align:start position:0%
+large number smaller Planck constant H
+ 
+
+ align:start position:0%
+large number smaller Planck constant H
+is Punkins so what what this says is the
+
+ align:start position:0%
+is Punkins so what what this says is the
+ 
+
+ align:start position:0%
+is Punkins so what what this says is the
+basic energy is H nu that's Hong Kong
+
+ align:start position:0%
+basic energy is H nu that's Hong Kong
+ 
+
+ align:start position:0%
+basic energy is H nu that's Hong Kong
+that's a that's the fundamental unit of
+
+ align:start position:0%
+that's a that's the fundamental unit of
+ 
+
+ align:start position:0%
+that's a that's the fundamental unit of
+the vibrational energy and that
+
+ align:start position:0%
+the vibrational energy and that
+ 
+
+ align:start position:0%
+the vibrational energy and that
+fundamental unit is called a fuller it's
+
+ align:start position:0%
+fundamental unit is called a fuller it's
+ 
+
+ align:start position:0%
+fundamental unit is called a fuller it's
+another like a electron has a mass but
+
+ align:start position:0%
+another like a electron has a mass but
+ 
+
+ align:start position:0%
+another like a electron has a mass but
+say it's a very similar to photon photon
+
+ align:start position:0%
+say it's a very similar to photon photon
+ 
+
+ align:start position:0%
+say it's a very similar to photon photon
+don't have a mess
+
+ align:start position:0%
+don't have a mess
+ 
+
+ align:start position:0%
+don't have a mess
+it's turns out the photon has a
+
+ align:start position:0%
+it's turns out the photon has a
+ 
+
+ align:start position:0%
+it's turns out the photon has a
+frequency and the fundamental unit that
+
+ align:start position:0%
+frequency and the fundamental unit that
+ 
+
+ align:start position:0%
+frequency and the fundamental unit that
+you get again is the H nu 4 photon and
+
+ align:start position:0%
+you get again is the H nu 4 photon and
+ 
+
+ align:start position:0%
+you get again is the H nu 4 photon and
+in fact I say eat later and you learned
+
+ align:start position:0%
+in fact I say eat later and you learned
+ 
+
+ align:start position:0%
+in fact I say eat later and you learned
+a plunk relation is the energy is always
+
+ align:start position:0%
+a plunk relation is the energy is always
+ 
+
+ align:start position:0%
+a plunk relation is the energy is always
+related to frequencies through H nu ok
+
+ align:start position:0%
+related to frequencies through H nu ok
+ 
+
+ align:start position:0%
+related to frequencies through H nu ok
+so the photon is the quantized a
+
+ align:start position:0%
+so the photon is the quantized a
+ 
+
+ align:start position:0%
+so the photon is the quantized a
+vibrational energy in the material a
+
+ align:start position:0%
+vibrational energy in the material a
+ 
+
+ align:start position:0%
+vibrational energy in the material a
+photon is a one want i canta of that
+
+ align:start position:0%
+photon is a one want i canta of that
+ 
+
+ align:start position:0%
+photon is a one want i canta of that
+vibration so if you do that
+
+ align:start position:0%
+vibration so if you do that
+ 
+
+ align:start position:0%
+vibration so if you do that
+and going through this is where you will
+
+ align:start position:0%
+and going through this is where you will
+ 
+
+ align:start position:0%
+and going through this is where you will
+have to wait probably until chapter 5
+
+ align:start position:0%
+have to wait probably until chapter 5
+ 
+
+ align:start position:0%
+have to wait probably until chapter 5
+that it will go from the vibrational
+
+ align:start position:0%
+that it will go from the vibrational
+ 
+
+ align:start position:0%
+that it will go from the vibrational
+modes is a wave right we say I
+
+ align:start position:0%
+modes is a wave right we say I
+ 
+
+ align:start position:0%
+modes is a wave right we say I
+originally I treat them as a particles
+
+ align:start position:0%
+originally I treat them as a particles
+ 
+
+ align:start position:0%
+originally I treat them as a particles
+and that as a full-on gas so I go from
+
+ align:start position:0%
+and that as a full-on gas so I go from
+ 
+
+ align:start position:0%
+and that as a full-on gas so I go from
+that wave picture mode to a gas picture
+
+ align:start position:0%
+that wave picture mode to a gas picture
+ 
+
+ align:start position:0%
+that wave picture mode to a gas picture
+in the solid so for the heat conduction
+
+ align:start position:0%
+in the solid so for the heat conduction
+ 
+
+ align:start position:0%
+in the solid so for the heat conduction
+it's the full-on gas in the solid and
+
+ align:start position:0%
+it's the full-on gas in the solid and
+ 
+
+ align:start position:0%
+it's the full-on gas in the solid and
+once I think about the gas is the same
+
+ align:start position:0%
+once I think about the gas is the same
+ 
+
+ align:start position:0%
+once I think about the gas is the same
+picture right when one side is hot that
+
+ align:start position:0%
+picture right when one side is hot that
+ 
+
+ align:start position:0%
+picture right when one side is hot that
+photon gets a lock at the wall the gain
+
+ align:start position:0%
+photon gets a lock at the wall the gain
+ 
+
+ align:start position:0%
+photon gets a lock at the wall the gain
+higher energy to go two legs
+
+ align:start position:0%
+higher energy to go two legs
+ 
+
+ align:start position:0%
+higher energy to go two legs
+so the full-on mean free paths again the
+
+ align:start position:0%
+so the full-on mean free paths again the
+ 
+
+ align:start position:0%
+so the full-on mean free paths again the
+collision between the photons and turns
+
+ align:start position:0%
+collision between the photons and turns
+ 
+
+ align:start position:0%
+collision between the photons and turns
+out that it's a wide range and we're
+
+ align:start position:0%
+out that it's a wide range and we're
+ 
+
+ align:start position:0%
+out that it's a wide range and we're
+doing quantum calculations on this and
+
+ align:start position:0%
+doing quantum calculations on this and
+ 
+
+ align:start position:0%
+doing quantum calculations on this and
+some of them says one nanometer order so
+
+ align:start position:0%
+some of them says one nanometer order so
+ 
+
+ align:start position:0%
+some of them says one nanometer order so
+is what micron
+
+ align:start position:0%
+is what micron
+ 
+
+ align:start position:0%
+is what micron
+okay so for heat conduction that basic
+
+ align:start position:0%
+okay so for heat conduction that basic
+ 
+
+ align:start position:0%
+okay so for heat conduction that basic
+picture is this gas picture and so
+
+ align:start position:0%
+picture is this gas picture and so
+ 
+
+ align:start position:0%
+picture is this gas picture and so
+that's why I'm treating photon electron
+
+ align:start position:0%
+that's why I'm treating photon electron
+ 
+
+ align:start position:0%
+that's why I'm treating photon electron
+and photon and at the end is a photon
+
+ align:start position:0%
+and photon and at the end is a photon
+ 
+
+ align:start position:0%
+and photon and at the end is a photon
+gas and they just say the photon from
+
+ align:start position:0%
+gas and they just say the photon from
+ 
+
+ align:start position:0%
+gas and they just say the photon from
+the Sun when we treated the photon gas
+
+ align:start position:0%
+the Sun when we treated the photon gas
+ 
+
+ align:start position:0%
+the Sun when we treated the photon gas
+but they don't obey the diffusion noise
+
+ align:start position:0%
+but they don't obey the diffusion noise
+ 
+
+ align:start position:0%
+but they don't obey the diffusion noise
+like a full Yolo they go ballistic
+
+ align:start position:0%
+like a full Yolo they go ballistic
+ 
+
+ align:start position:0%
+like a full Yolo they go ballistic
+there's no scatter I'm sure they reach
+
+ align:start position:0%
+there's no scatter I'm sure they reach
+ 
+
+ align:start position:0%
+there's no scatter I'm sure they reach
+the earth okay so that's they are
+
+ align:start position:0%
+the earth okay so that's they are
+ 
+
+ align:start position:0%
+the earth okay so that's they are
+conduction convection what's the
+
+ align:start position:0%
+conduction convection what's the
+ 
+
+ align:start position:0%
+conduction convection what's the
+difference right microscopically sure
+
+ align:start position:0%
+difference right microscopically sure
+ 
+
+ align:start position:0%
+difference right microscopically sure
+for convection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we say okay you have high or and
+
+ align:start position:0%
+right we say okay you have high or and
+ 
+
+ align:start position:0%
+right we say okay you have high or and
+the ambient we gave the Newton law of
+
+ align:start position:0%
+the ambient we gave the Newton law of
+ 
+
+ align:start position:0%
+the ambient we gave the Newton law of
+cooling right so what's the microscopic
+
+ align:start position:0%
+cooling right so what's the microscopic
+ 
+
+ align:start position:0%
+cooling right so what's the microscopic
+picture of conversion what's the
+
+ align:start position:0%
+picture of conversion what's the
+ 
+
+ align:start position:0%
+picture of conversion what's the
+difference from conduction yeah very
+
+ align:start position:0%
+difference from conduction yeah very
+ 
+
+ align:start position:0%
+difference from conduction yeah very
+good answer so what in heat conduction
+
+ align:start position:0%
+good answer so what in heat conduction
+ 
+
+ align:start position:0%
+good answer so what in heat conduction
+is molecules are moving randomly and
+
+ align:start position:0%
+is molecules are moving randomly and
+ 
+
+ align:start position:0%
+is molecules are moving randomly and
+they're moving at a 300 meter per second
+
+ align:start position:0%
+they're moving at a 300 meter per second
+ 
+
+ align:start position:0%
+they're moving at a 300 meter per second
+pretty fast but their average velocity
+
+ align:start position:0%
+pretty fast but their average velocity
+ 
+
+ align:start position:0%
+pretty fast but their average velocity
+vector is zero right so for the
+
+ align:start position:0%
+vector is zero right so for the
+ 
+
+ align:start position:0%
+vector is zero right so for the
+conduction we have the average velocity
+
+ align:start position:0%
+conduction we have the average velocity
+ 
+
+ align:start position:0%
+conduction we have the average velocity
+is zero but for convection this is not
+
+ align:start position:0%
+is zero but for convection this is not
+ 
+
+ align:start position:0%
+is zero but for convection this is not
+zero okay and that is could be one meter
+
+ align:start position:0%
+zero okay and that is could be one meter
+ 
+
+ align:start position:0%
+zero okay and that is could be one meter
+per second two meter per second but we I
+
+ align:start position:0%
+per second two meter per second but we I
+ 
+
+ align:start position:0%
+per second two meter per second but we I
+said that molecules are always doing
+
+ align:start position:0%
+said that molecules are always doing
+ 
+
+ align:start position:0%
+said that molecules are always doing
+random motions 300 meter per second much
+
+ align:start position:0%
+random motions 300 meter per second much
+ 
+
+ align:start position:0%
+random motions 300 meter per second much
+faster right but the you know convection
+
+ align:start position:0%
+faster right but the you know convection
+ 
+
+ align:start position:0%
+faster right but the you know convection
+is the more effective that's because
+
+ align:start position:0%
+is the more effective that's because
+ 
+
+ align:start position:0%
+is the more effective that's because
+they are not a diffusion because when
+
+ align:start position:0%
+they are not a diffusion because when
+ 
+
+ align:start position:0%
+they are not a diffusion because when
+they move from one place to another
+
+ align:start position:0%
+they move from one place to another
+ 
+
+ align:start position:0%
+they move from one place to another
+place they carry all that energy
+
+ align:start position:0%
+place they carry all that energy
+ 
+
+ align:start position:0%
+place they carry all that energy
+directly from one place to other right
+
+ align:start position:0%
+directly from one place to other right
+ 
+
+ align:start position:0%
+directly from one place to other right
+that energy is enthalpy so that's the
+
+ align:start position:0%
+that energy is enthalpy so that's the
+ 
+
+ align:start position:0%
+that energy is enthalpy so that's the
+fundamental difference you still got
+
+ align:start position:0%
+fundamental difference you still got
+ 
+
+ align:start position:0%
+fundamental difference you still got
+this random motion so when you go
+
+ align:start position:0%
+this random motion so when you go
+ 
+
+ align:start position:0%
+this random motion so when you go
+through back to thing about
+
+ align:start position:0%
+through back to thing about
+ 
+
+ align:start position:0%
+through back to thing about
+navier-stocks equation you still have
+
+ align:start position:0%
+navier-stocks equation you still have
+ 
+
+ align:start position:0%
+navier-stocks equation you still have
+heat conduction term there I ran the
+
+ align:start position:0%
+heat conduction term there I ran the
+ 
+
+ align:start position:0%
+heat conduction term there I ran the
+motions there but you got a convective
+
+ align:start position:0%
+motions there but you got a convective
+ 
+
+ align:start position:0%
+motions there but you got a convective
+term okay so that's a convection and in
+
+ align:start position:0%
+term okay so that's a convection and in
+ 
+
+ align:start position:0%
+term okay so that's a convection and in
+fact if you take that and convection is
+
+ align:start position:0%
+fact if you take that and convection is
+ 
+
+ align:start position:0%
+fact if you take that and convection is
+almost the same as conduction except the
+
+ align:start position:0%
+almost the same as conduction except the
+ 
+
+ align:start position:0%
+almost the same as conduction except the
+rather than you just have a Dirac and
+
+ align:start position:0%
+rather than you just have a Dirac and
+ 
+
+ align:start position:0%
+rather than you just have a Dirac and
+moving term so I would say it's
+
+ align:start position:0%
+moving term so I would say it's
+ 
+
+ align:start position:0%
+moving term so I would say it's
+fundamental is not
+
+ align:start position:0%
+fundamental is not
+ 
+
+ align:start position:0%
+fundamental is not
+two new a picture at this skill and then
+
+ align:start position:0%
+two new a picture at this skill and then
+ 
+
+ align:start position:0%
+two new a picture at this skill and then
+we think about radiation right what's
+
+ align:start position:0%
+we think about radiation right what's
+ 
+
+ align:start position:0%
+we think about radiation right what's
+the thermal radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the radiation from a radio with a
+
+ align:start position:0%
+what's the radiation from a radio with a
+ 
+
+ align:start position:0%
+what's the radiation from a radio with a
+difference huh so the radiation from the
+
+ align:start position:0%
+difference huh so the radiation from the
+ 
+
+ align:start position:0%
+difference huh so the radiation from the
+heat source is the photon the radiation
+
+ align:start position:0%
+heat source is the photon the radiation
+ 
+
+ align:start position:0%
+heat source is the photon the radiation
+electromagnetic wave from radio source
+
+ align:start position:0%
+electromagnetic wave from radio source
+ 
+
+ align:start position:0%
+electromagnetic wave from radio source
+we normally don't call the photon it's
+
+ align:start position:0%
+we normally don't call the photon it's
+ 
+
+ align:start position:0%
+we normally don't call the photon it's
+also photon it is all full time and all
+
+ align:start position:0%
+also photon it is all full time and all
+ 
+
+ align:start position:0%
+also photon it is all full time and all
+photon in free space you learn this at
+
+ align:start position:0%
+photon in free space you learn this at
+ 
+
+ align:start position:0%
+photon in free space you learn this at
+high school speed of night witness
+
+ align:start position:0%
+high school speed of night witness
+ 
+
+ align:start position:0%
+high school speed of night witness
+frequency right we channel do turn
+
+ align:start position:0%
+frequency right we channel do turn
+ 
+
+ align:start position:0%
+frequency right we channel do turn
+what's the frequency I turn to nineteen
+
+ align:start position:0%
+what's the frequency I turn to nineteen
+ 
+
+ align:start position:0%
+what's the frequency I turn to nineteen
+point five well I forgot that's
+
+ align:start position:0%
+point five well I forgot that's
+ 
+
+ align:start position:0%
+point five well I forgot that's
+megahertz or kilohertz doe but it
+
+ align:start position:0%
+megahertz or kilohertz doe but it
+ 
+
+ align:start position:0%
+megahertz or kilohertz doe but it
+doesn't matter is a megahertz or killers
+
+ align:start position:0%
+doesn't matter is a megahertz or killers
+ 
+
+ align:start position:0%
+doesn't matter is a megahertz or killers
+I think huh huh anybody remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can so let me just put the Henry
+
+ align:start position:0%
+I can so let me just put the Henry
+ 
+
+ align:start position:0%
+I can so let me just put the Henry
+kilohertz
+
+ align:start position:0%
+kilohertz
+ 
+
+ align:start position:0%
+kilohertz
+I know there are 200 kilohertz range and
+
+ align:start position:0%
+I know there are 200 kilohertz range and
+ 
+
+ align:start position:0%
+I know there are 200 kilohertz range and
+so what's the wavelengths speed outline
+
+ align:start position:0%
+so what's the wavelengths speed outline
+ 
+
+ align:start position:0%
+so what's the wavelengths speed outline
+three ten to the eighth meters per
+
+ align:start position:0%
+three ten to the eighth meters per
+ 
+
+ align:start position:0%
+three ten to the eighth meters per
+second right so that gives me
+
+ align:start position:0%
+second right so that gives me
+ 
+
+ align:start position:0%
+second right so that gives me
+wavelengths 10 to the fifth
+
+ align:start position:0%
+wavelengths 10 to the fifth
+ 
+
+ align:start position:0%
+wavelengths 10 to the fifth
+ten days a kilometer okay so it's a
+
+ align:start position:0%
+ten days a kilometer okay so it's a
+ 
+
+ align:start position:0%
+ten days a kilometer okay so it's a
+photon and the energy is H nu - that's a
+
+ align:start position:0%
+photon and the energy is H nu - that's a
+ 
+
+ align:start position:0%
+photon and the energy is H nu - that's a
+low energy photon and it's generated by
+
+ align:start position:0%
+low energy photon and it's generated by
+ 
+
+ align:start position:0%
+low energy photon and it's generated by
+you know that station right oscillating
+
+ align:start position:0%
+you know that station right oscillating
+ 
+
+ align:start position:0%
+you know that station right oscillating
+current generate this electromagnetic
+
+ align:start position:0%
+current generate this electromagnetic
+ 
+
+ align:start position:0%
+current generate this electromagnetic
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+it's an oscillating current so it's
+
+ align:start position:0%
+it's an oscillating current so it's
+ 
+
+ align:start position:0%
+it's an oscillating current so it's
+artificially you oscillate what's the
+
+ align:start position:0%
+artificially you oscillate what's the
+ 
+
+ align:start position:0%
+artificially you oscillate what's the
+thermal radiation huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the it's a vibration of all frequency
+
+ align:start position:0%
+the it's a vibration of all frequency
+ 
+
+ align:start position:0%
+the it's a vibration of all frequency
+that's the what is that it's okay it is
+
+ align:start position:0%
+that's the what is that it's okay it is
+ 
+
+ align:start position:0%
+that's the what is that it's okay it is
+the color of white radio frequency but
+
+ align:start position:0%
+the color of white radio frequency but
+ 
+
+ align:start position:0%
+the color of white radio frequency but
+there's still oscillating current don't
+
+ align:start position:0%
+there's still oscillating current don't
+ 
+
+ align:start position:0%
+there's still oscillating current don't
+think say all radiation is a thermal
+
+ align:start position:0%
+think say all radiation is a thermal
+ 
+
+ align:start position:0%
+think say all radiation is a thermal
+motion right is this similar generated
+
+ align:start position:0%
+motion right is this similar generated
+ 
+
+ align:start position:0%
+motion right is this similar generated
+oscillating current and think about the
+
+ align:start position:0%
+oscillating current and think about the
+ 
+
+ align:start position:0%
+oscillating current and think about the
+atoms think about electrons one electron
+
+ align:start position:0%
+atoms think about electrons one electron
+ 
+
+ align:start position:0%
+atoms think about electrons one electron
+move around the general corner right so
+
+ align:start position:0%
+move around the general corner right so
+ 
+
+ align:start position:0%
+move around the general corner right so
+it's the cermony random motion generated
+
+ align:start position:0%
+it's the cermony random motion generated
+ 
+
+ align:start position:0%
+it's the cermony random motion generated
+and this is a much smaller oscillator
+
+ align:start position:0%
+and this is a much smaller oscillator
+ 
+
+ align:start position:0%
+and this is a much smaller oscillator
+much faster so if you think about
+
+ align:start position:0%
+much faster so if you think about
+ 
+
+ align:start position:0%
+much faster so if you think about
+wavelength is the 0.5 micron it's the
+
+ align:start position:0%
+wavelength is the 0.5 micron it's the
+ 
+
+ align:start position:0%
+wavelength is the 0.5 micron it's the
+point five ten to the minus six this is
+
+ align:start position:0%
+point five ten to the minus six this is
+ 
+
+ align:start position:0%
+point five ten to the minus six this is
+a ten to the fourteen then right
+
+ align:start position:0%
+a ten to the fourteen then right
+ 
+
+ align:start position:0%
+a ten to the fourteen then right
+frequencies within two fourteen is an
+
+ align:start position:0%
+frequencies within two fourteen is an
+ 
+
+ align:start position:0%
+frequencies within two fourteen is an
+hour longer Henry Kitteridge
+
+ align:start position:0%
+hour longer Henry Kitteridge
+ 
+
+ align:start position:0%
+hour longer Henry Kitteridge
+okay so that's what a difference but
+
+ align:start position:0%
+okay so that's what a difference but
+ 
+
+ align:start position:0%
+okay so that's what a difference but
+let's say in terms of propagation of
+
+ align:start position:0%
+let's say in terms of propagation of
+ 
+
+ align:start position:0%
+let's say in terms of propagation of
+thermal radiation it's actually the same
+
+ align:start position:0%
+thermal radiation it's actually the same
+ 
+
+ align:start position:0%
+thermal radiation it's actually the same
+Maxwell equation it's not different from
+
+ align:start position:0%
+Maxwell equation it's not different from
+ 
+
+ align:start position:0%
+Maxwell equation it's not different from
+what the electrical engineer does is it
+
+ align:start position:0%
+what the electrical engineer does is it
+ 
+
+ align:start position:0%
+what the electrical engineer does is it
+this source that's different
+
+ align:start position:0%
+this source that's different
+ 
+
+ align:start position:0%
+this source that's different
+once they are out the propagation you
+
+ align:start position:0%
+once they are out the propagation you
+ 
+
+ align:start position:0%
+once they are out the propagation you
+write the same equation okay so at the
+
+ align:start position:0%
+write the same equation okay so at the
+ 
+
+ align:start position:0%
+write the same equation okay so at the
+end there are not many equations and so
+
+ align:start position:0%
+end there are not many equations and so
+ 
+
+ align:start position:0%
+end there are not many equations and so
+that's the heat transfer we can go
+
+ align:start position:0%
+that's the heat transfer we can go
+ 
+
+ align:start position:0%
+that's the heat transfer we can go
+either we can pick up another object
+
+ align:start position:0%
+either we can pick up another object
+ 
+
+ align:start position:0%
+either we can pick up another object
+subject to here let's say charge Ohm's
+
+ align:start position:0%
+subject to here let's say charge Ohm's
+ 
+
+ align:start position:0%
+subject to here let's say charge Ohm's
+law right I want show you easily how I
+
+ align:start position:0%
+law right I want show you easily how I
+ 
+
+ align:start position:0%
+law right I want show you easily how I
+can derive Ohm's law and let's look
+
+ align:start position:0%
+can derive Ohm's law and let's look
+ 
+
+ align:start position:0%
+can derive Ohm's law and let's look
+either the charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course I do a lot of hand waving
+
+ align:start position:0%
+and of course I do a lot of hand waving
+ 
+
+ align:start position:0%
+and of course I do a lot of hand waving
+and I have a conductor electrons I have
+
+ align:start position:0%
+and I have a conductor electrons I have
+ 
+
+ align:start position:0%
+and I have a conductor electrons I have
+a protein sure right what's the force on
+
+ align:start position:0%
+a protein sure right what's the force on
+ 
+
+ align:start position:0%
+a protein sure right what's the force on
+the electron anybody remember if I have
+
+ align:start position:0%
+the electron anybody remember if I have
+ 
+
+ align:start position:0%
+the electron anybody remember if I have
+a charge I have protein sure if I my
+
+ align:start position:0%
+a charge I have protein sure if I my
+ 
+
+ align:start position:0%
+a charge I have protein sure if I my
+potential is the e let's say this is the
+
+ align:start position:0%
+potential is the e let's say this is the
+ 
+
+ align:start position:0%
+potential is the e let's say this is the
+X X the ration right the force F X
+
+ align:start position:0%
+X X the ration right the force F X
+ 
+
+ align:start position:0%
+X X the ration right the force F X
+equals charge times the field right so
+
+ align:start position:0%
+equals charge times the field right so
+ 
+
+ align:start position:0%
+equals charge times the field right so
+it's a minus of e times e^x this is what
+
+ align:start position:0%
+it's a minus of e times e^x this is what
+ 
+
+ align:start position:0%
+it's a minus of e times e^x this is what
+I really heat
+
+ align:start position:0%
+I really heat
+ 
+
+ align:start position:0%
+I really heat
+the money sign I often get confused okay
+
+ align:start position:0%
+the money sign I often get confused okay
+ 
+
+ align:start position:0%
+the money sign I often get confused okay
+so I have force and I'm going to write
+
+ align:start position:0%
+so I have force and I'm going to write
+ 
+
+ align:start position:0%
+so I have force and I'm going to write
+this so Newton's second law F equals MA
+
+ align:start position:0%
+this so Newton's second law F equals MA
+ 
+
+ align:start position:0%
+this so Newton's second law F equals MA
+so this is M D V X DT right F equals MA
+
+ align:start position:0%
+so this is M D V X DT right F equals MA
+ 
+
+ align:start position:0%
+so this is M D V X DT right F equals MA
+and it turns out that what the electron
+
+ align:start position:0%
+and it turns out that what the electron
+ 
+
+ align:start position:0%
+and it turns out that what the electron
+does we mentioned before you collide
+
+ align:start position:0%
+does we mentioned before you collide
+ 
+
+ align:start position:0%
+does we mentioned before you collide
+right it can go certain distance then
+
+ align:start position:0%
+right it can go certain distance then
+ 
+
+ align:start position:0%
+right it can go certain distance then
+collide so the acceleration time is
+
+ align:start position:0%
+collide so the acceleration time is
+ 
+
+ align:start position:0%
+collide so the acceleration time is
+between the collision and collide a
+
+ align:start position:0%
+between the collision and collide a
+ 
+
+ align:start position:0%
+between the collision and collide a
+accelerated collide actually so I'm
+
+ align:start position:0%
+accelerated collide actually so I'm
+ 
+
+ align:start position:0%
+accelerated collide actually so I'm
+going to give a hand waving if I do that
+
+ align:start position:0%
+going to give a hand waving if I do that
+ 
+
+ align:start position:0%
+going to give a hand waving if I do that
+integration I say that's how that's the
+
+ align:start position:0%
+integration I say that's how that's the
+ 
+
+ align:start position:0%
+integration I say that's how that's the
+average time between the collision so my
+
+ align:start position:0%
+average time between the collision so my
+ 
+
+ align:start position:0%
+average time between the collision so my
+velocity then is if I integrate this
+
+ align:start position:0%
+velocity then is if I integrate this
+ 
+
+ align:start position:0%
+velocity then is if I integrate this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I gather e epsilon X divided by M times
+
+ align:start position:0%
+I gather e epsilon X divided by M times
+ 
+
+ align:start position:0%
+I gather e epsilon X divided by M times
+tau this is the drift velocity the
+
+ align:start position:0%
+tau this is the drift velocity the
+ 
+
+ align:start position:0%
+tau this is the drift velocity the
+electron at the end is sort of under
+
+ align:start position:0%
+electron at the end is sort of under
+ 
+
+ align:start position:0%
+electron at the end is sort of under
+this field is the moving average
+
+ align:start position:0%
+this field is the moving average
+ 
+
+ align:start position:0%
+this field is the moving average
+velocity of the charge okay
+
+ align:start position:0%
+velocity of the charge okay
+ 
+
+ align:start position:0%
+velocity of the charge okay
+and now if I have this velocity
+
+ align:start position:0%
+and now if I have this velocity
+ 
+
+ align:start position:0%
+and now if I have this velocity
+I can write the current write the
+
+ align:start position:0%
+I can write the current write the
+ 
+
+ align:start position:0%
+I can write the current write the
+current what's card current is just the
+
+ align:start position:0%
+current what's card current is just the
+ 
+
+ align:start position:0%
+current what's card current is just the
+charge per unit time going across
+
+ align:start position:0%
+charge per unit time going across
+ 
+
+ align:start position:0%
+charge per unit time going across
+certain area so if I look at the current
+
+ align:start position:0%
+certain area so if I look at the current
+ 
+
+ align:start position:0%
+certain area so if I look at the current
+right because the VX is the average of
+
+ align:start position:0%
+right because the VX is the average of
+ 
+
+ align:start position:0%
+right because the VX is the average of
+velocity so if I know the charge density
+
+ align:start position:0%
+velocity so if I know the charge density
+ 
+
+ align:start position:0%
+velocity so if I know the charge density
+per unit volume then I write my J equals
+
+ align:start position:0%
+per unit volume then I write my J equals
+ 
+
+ align:start position:0%
+per unit volume then I write my J equals
+take the current write is JX is the
+
+ align:start position:0%
+take the current write is JX is the
+ 
+
+ align:start position:0%
+take the current write is JX is the
+charge that's in Coulomb pants N and
+
+ align:start position:0%
+charge that's in Coulomb pants N and
+ 
+
+ align:start position:0%
+charge that's in Coulomb pants N and
+Hansa a VX that's my current density
+
+ align:start position:0%
+Hansa a VX that's my current density
+ 
+
+ align:start position:0%
+Hansa a VX that's my current density
+right if you look at the unit e anyone
+
+ align:start position:0%
+right if you look at the unit e anyone
+ 
+
+ align:start position:0%
+right if you look at the unit e anyone
+in remember again 1.6 10 to the minus 19
+
+ align:start position:0%
+in remember again 1.6 10 to the minus 19
+ 
+
+ align:start position:0%
+in remember again 1.6 10 to the minus 19
+coulomb okay one charge again I'm
+
+ align:start position:0%
+coulomb okay one charge again I'm
+ 
+
+ align:start position:0%
+coulomb okay one charge again I'm
+awkward I remember SI unit and here is
+
+ align:start position:0%
+awkward I remember SI unit and here is
+ 
+
+ align:start position:0%
+awkward I remember SI unit and here is
+one over meters cubic because that's a
+
+ align:start position:0%
+one over meters cubic because that's a
+ 
+
+ align:start position:0%
+one over meters cubic because that's a
+charge density per unit volume and then
+
+ align:start position:0%
+charge density per unit volume and then
+ 
+
+ align:start position:0%
+charge density per unit volume and then
+you do Lea this is a meter per second
+
+ align:start position:0%
+you do Lea this is a meter per second
+ 
+
+ align:start position:0%
+you do Lea this is a meter per second
+and you get the here is a Coulomb per
+
+ align:start position:0%
+and you get the here is a Coulomb per
+ 
+
+ align:start position:0%
+and you get the here is a Coulomb per
+meter square per second Coulomb per
+
+ align:start position:0%
+meter square per second Coulomb per
+ 
+
+ align:start position:0%
+meter square per second Coulomb per
+meter square is the amp per meter square
+
+ align:start position:0%
+meter square is the amp per meter square
+ 
+
+ align:start position:0%
+meter square is the amp per meter square
+right that's your card in honey so if I
+
+ align:start position:0%
+right that's your card in honey so if I
+ 
+
+ align:start position:0%
+right that's your card in honey so if I
+plug in there what I have the e square
+
+ align:start position:0%
+plug in there what I have the e square
+ 
+
+ align:start position:0%
+plug in there what I have the e square
+and tau M times n times epsilon X that's
+
+ align:start position:0%
+and tau M times n times epsilon X that's
+ 
+
+ align:start position:0%
+and tau M times n times epsilon X that's
+almost all right this is my electric
+
+ align:start position:0%
+almost all right this is my electric
+ 
+
+ align:start position:0%
+almost all right this is my electric
+conductivity this is Sigma you've seen X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do another exam so Howie that have
+
+ align:start position:0%
+let's do another exam so Howie that have
+ 
+
+ align:start position:0%
+let's do another exam so Howie that have
+charged a now to think about force
+
+ align:start position:0%
+charged a now to think about force
+ 
+
+ align:start position:0%
+charged a now to think about force
+noticing about the momentum right the
+
+ align:start position:0%
+noticing about the momentum right the
+ 
+
+ align:start position:0%
+noticing about the momentum right the
+pressure let's say we have heat charge
+
+ align:start position:0%
+pressure let's say we have heat charge
+ 
+
+ align:start position:0%
+pressure let's say we have heat charge
+momentum okay
+
+ align:start position:0%
+momentum okay
+ 
+
+ align:start position:0%
+momentum okay
+what's the pressure when you have a box
+
+ align:start position:0%
+what's the pressure when you have a box
+ 
+
+ align:start position:0%
+what's the pressure when you have a box
+of gas you have pressure what is that
+
+ align:start position:0%
+of gas you have pressure what is that
+ 
+
+ align:start position:0%
+of gas you have pressure what is that
+pressure so this is the gas
+
+ align:start position:0%
+pressure so this is the gas
+ 
+
+ align:start position:0%
+pressure so this is the gas
+I have box of gas inside
+
+ align:start position:0%
+I have box of gas inside
+ 
+
+ align:start position:0%
+I have box of gas inside
+I have Monaco's right they're moving the
+
+ align:start position:0%
+I have Monaco's right they're moving the
+ 
+
+ align:start position:0%
+I have Monaco's right they're moving the
+movement randomly and the pressure is
+
+ align:start position:0%
+movement randomly and the pressure is
+ 
+
+ align:start position:0%
+movement randomly and the pressure is
+when the gas here the war right and they
+
+ align:start position:0%
+when the gas here the war right and they
+ 
+
+ align:start position:0%
+when the gas here the war right and they
+were change the Russian bounce back
+
+ align:start position:0%
+were change the Russian bounce back
+ 
+
+ align:start position:0%
+were change the Russian bounce back
+there's a momentum change the momentum
+
+ align:start position:0%
+there's a momentum change the momentum
+ 
+
+ align:start position:0%
+there's a momentum change the momentum
+change give you the force so I can argue
+
+ align:start position:0%
+change give you the force so I can argue
+ 
+
+ align:start position:0%
+change give you the force so I can argue
+with you inside I don't know what's the
+
+ align:start position:0%
+with you inside I don't know what's the
+ 
+
+ align:start position:0%
+with you inside I don't know what's the
+pressure now you stick up an emitter
+
+ align:start position:0%
+pressure now you stick up an emitter
+ 
+
+ align:start position:0%
+pressure now you stick up an emitter
+there you will measure that momentum
+
+ align:start position:0%
+there you will measure that momentum
+ 
+
+ align:start position:0%
+there you will measure that momentum
+change and you measure the pressure
+
+ align:start position:0%
+change and you measure the pressure
+ 
+
+ align:start position:0%
+change and you measure the pressure
+right okay so here is the of course the
+
+ align:start position:0%
+right okay so here is the of course the
+ 
+
+ align:start position:0%
+right okay so here is the of course the
+force let's say is f x on the wall is a
+
+ align:start position:0%
+force let's say is f x on the wall is a
+ 
+
+ align:start position:0%
+force let's say is f x on the wall is a
+single molecule is the reacts to this
+
+ align:start position:0%
+single molecule is the reacts to this
+ 
+
+ align:start position:0%
+single molecule is the reacts to this
+larger than the romance MV x less than
+
+ align:start position:0%
+larger than the romance MV x less than
+ 
+
+ align:start position:0%
+larger than the romance MV x less than
+zero divided by delta T so that's the
+
+ align:start position:0%
+zero divided by delta T so that's the
+ 
+
+ align:start position:0%
+zero divided by delta T so that's the
+single molecule acting on the wall of
+
+ align:start position:0%
+single molecule acting on the wall of
+ 
+
+ align:start position:0%
+single molecule acting on the wall of
+force right now I want to find the
+
+ align:start position:0%
+force right now I want to find the
+ 
+
+ align:start position:0%
+force right now I want to find the
+pressure in the chamber I have a lot of
+
+ align:start position:0%
+pressure in the chamber I have a lot of
+ 
+
+ align:start position:0%
+pressure in the chamber I have a lot of
+molecules again the density molecular
+
+ align:start position:0%
+molecules again the density molecular
+ 
+
+ align:start position:0%
+molecules again the density molecular
+density n and they are coming towards
+
+ align:start position:0%
+density n and they are coming towards
+ 
+
+ align:start position:0%
+density n and they are coming towards
+their wall and bounce back so let me
+
+ align:start position:0%
+their wall and bounce back so let me
+ 
+
+ align:start position:0%
+their wall and bounce back so let me
+just make my simplest perfecting war so
+
+ align:start position:0%
+just make my simplest perfecting war so
+ 
+
+ align:start position:0%
+just make my simplest perfecting war so
+the coming velocity across the bouncing
+
+ align:start position:0%
+the coming velocity across the bouncing
+ 
+
+ align:start position:0%
+the coming velocity across the bouncing
+back velocity so it's a factor of two
+
+ align:start position:0%
+back velocity so it's a factor of two
+ 
+
+ align:start position:0%
+back velocity so it's a factor of two
+and I have a lot of molecules here this
+
+ align:start position:0%
+and I have a lot of molecules here this
+ 
+
+ align:start position:0%
+and I have a lot of molecules here this
+is molecular density is n 2 random so
+
+ align:start position:0%
+is molecular density is n 2 random so
+ 
+
+ align:start position:0%
+is molecular density is n 2 random so
+half of them coming towards the wall
+
+ align:start position:0%
+half of them coming towards the wall
+ 
+
+ align:start position:0%
+half of them coming towards the wall
+so my is 1/2 and and in terms of the
+
+ align:start position:0%
+so my is 1/2 and and in terms of the
+ 
+
+ align:start position:0%
+so my is 1/2 and and in terms of the
+rate the time comes to steal VX that's
+
+ align:start position:0%
+rate the time comes to steal VX that's
+ 
+
+ align:start position:0%
+rate the time comes to steal VX that's
+the rate that's the really coming and
+
+ align:start position:0%
+the rate that's the really coming and
+ 
+
+ align:start position:0%
+the rate that's the really coming and
+this give me the delta T eyelid and then
+
+ align:start position:0%
+this give me the delta T eyelid and then
+ 
+
+ align:start position:0%
+this give me the delta T eyelid and then
+say I have a 2 MV x I'm assuming like I
+
+ align:start position:0%
+say I have a 2 MV x I'm assuming like I
+ 
+
+ align:start position:0%
+say I have a 2 MV x I'm assuming like I
+said this way X is just reflecting back
+
+ align:start position:0%
+said this way X is just reflecting back
+ 
+
+ align:start position:0%
+said this way X is just reflecting back
+so this will give me pressure again you
+
+ align:start position:0%
+so this will give me pressure again you
+ 
+
+ align:start position:0%
+so this will give me pressure again you
+go to check a unit ok so what I get I
+
+ align:start position:0%
+go to check a unit ok so what I get I
+ 
+
+ align:start position:0%
+go to check a unit ok so what I get I
+get this pressure equals n M way x
+
+ align:start position:0%
+get this pressure equals n M way x
+ 
+
+ align:start position:0%
+get this pressure equals n M way x
+squared right we x squared is the
+
+ align:start position:0%
+squared right we x squared is the
+ 
+
+ align:start position:0%
+squared right we x squared is the
+velocity component in X Direction
+
+ align:start position:0%
+velocity component in X Direction
+ 
+
+ align:start position:0%
+velocity component in X Direction
+squared so it's just 1/3 ruff speaking
+
+ align:start position:0%
+squared so it's just 1/3 ruff speaking
+ 
+
+ align:start position:0%
+squared so it's just 1/3 ruff speaking
+right homogenized
+
+ align:start position:0%
+right homogenized
+ 
+
+ align:start position:0%
+right homogenized
+so is this 1/3 of Y squared ok so what I
+
+ align:start position:0%
+so is this 1/3 of Y squared ok so what I
+ 
+
+ align:start position:0%
+so is this 1/3 of Y squared ok so what I
+have here is n m 1 third way square ok
+
+ align:start position:0%
+have here is n m 1 third way square ok
+ 
+
+ align:start position:0%
+have here is n m 1 third way square ok
+now I want to show you ideal gas flow
+
+ align:start position:0%
+now I want to show you ideal gas flow
+ 
+
+ align:start position:0%
+now I want to show you ideal gas flow
+and V Square and this is you have to go
+
+ align:start position:0%
+and V Square and this is you have to go
+ 
+
+ align:start position:0%
+and V Square and this is you have to go
+you have to wait a little bit but then
+
+ align:start position:0%
+you have to wait a little bit but then
+ 
+
+ align:start position:0%
+you have to wait a little bit but then
+let me give you say the equipartition
+
+ align:start position:0%
+let me give you say the equipartition
+ 
+
+ align:start position:0%
+let me give you say the equipartition
+that's a statistical thermo says here
+
+ align:start position:0%
+that's a statistical thermo says here
+ 
+
+ align:start position:0%
+that's a statistical thermo says here
+equals MV square because it has three we
+
+ align:start position:0%
+equals MV square because it has three we
+ 
+
+ align:start position:0%
+equals MV square because it has three we
+x revise it with a so each of this mode
+
+ align:start position:0%
+x revise it with a so each of this mode
+ 
+
+ align:start position:0%
+x revise it with a so each of this mode
+will give you this board my constant
+
+ align:start position:0%
+will give you this board my constant
+ 
+
+ align:start position:0%
+will give you this board my constant
+times T so this one you wait statistic
+
+ align:start position:0%
+times T so this one you wait statistic
+ 
+
+ align:start position:0%
+times T so this one you wait statistic
+your thermo fundamental result equal
+
+ align:start position:0%
+your thermo fundamental result equal
+ 
+
+ align:start position:0%
+your thermo fundamental result equal
+partition ok so I plug in this would I
+
+ align:start position:0%
+partition ok so I plug in this would I
+ 
+
+ align:start position:0%
+partition ok so I plug in this would I
+have that 1 through 10 so that's 3
+
+ align:start position:0%
+have that 1 through 10 so that's 3
+ 
+
+ align:start position:0%
+have that 1 through 10 so that's 3
+when half kinds of my square is K T KB T
+
+ align:start position:0%
+when half kinds of my square is K T KB T
+ 
+
+ align:start position:0%
+when half kinds of my square is K T KB T
+so what I have here is then is a n KB T
+
+ align:start position:0%
+so what I have here is then is a n KB T
+ 
+
+ align:start position:0%
+so what I have here is then is a n KB T
+and this is ideal gas no still doesn't
+
+ align:start position:0%
+and this is ideal gas no still doesn't
+ 
+
+ align:start position:0%
+and this is ideal gas no still doesn't
+look like ideal gas all right one more
+
+ align:start position:0%
+look like ideal gas all right one more
+ 
+
+ align:start position:0%
+look like ideal gas all right one more
+step and one more step I'll stop here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so n is the number of molecules per
+
+ align:start position:0%
+okay so n is the number of molecules per
+ 
+
+ align:start position:0%
+okay so n is the number of molecules per
+unit volume so I put a plug I multiply a
+
+ align:start position:0%
+unit volume so I put a plug I multiply a
+ 
+
+ align:start position:0%
+unit volume so I put a plug I multiply a
+volume so I have P way equal number of
+
+ align:start position:0%
+volume so I have P way equal number of
+ 
+
+ align:start position:0%
+volume so I have P way equal number of
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+Tambor is my constant times T doesn't
+
+ align:start position:0%
+Tambor is my constant times T doesn't
+ 
+
+ align:start position:0%
+Tambor is my constant times T doesn't
+look like a are yet so I to n divided by
+
+ align:start position:0%
+look like a are yet so I to n divided by
+ 
+
+ align:start position:0%
+look like a are yet so I to n divided by
+n a Avogadro constant and a KBT and this
+
+ align:start position:0%
+n a Avogadro constant and a KBT and this
+ 
+
+ align:start position:0%
+n a Avogadro constant and a KBT and this
+is your R that's your universal gas
+
+ align:start position:0%
+is your R that's your universal gas
+ 
+
+ align:start position:0%
+is your R that's your universal gas
+constant and this is your mole fraction
+
+ align:start position:0%
+constant and this is your mole fraction
+ 
+
+ align:start position:0%
+constant and this is your mole fraction
+mole fraction times you are universal
+
+ align:start position:0%
+mole fraction times you are universal
+ 
+
+ align:start position:0%
+mole fraction times you are universal
+gas constant times T PV equals NRT right
+
+ align:start position:0%
+gas constant times T PV equals NRT right
+ 
+
+ align:start position:0%
+gas constant times T PV equals NRT right
+I do guys know I'm leaving I'm not doing
+
+ align:start position:0%
+I do guys know I'm leaving I'm not doing
+ 
+
+ align:start position:0%
+I do guys know I'm leaving I'm not doing
+rigorously of course okay so uh anyway I
+
+ align:start position:0%
+rigorously of course okay so uh anyway I
+ 
+
+ align:start position:0%
+rigorously of course okay so uh anyway I
+remember knows KB with some number
+
+ align:start position:0%
+remember knows KB with some number
+ 
+
+ align:start position:0%
+remember knows KB with some number
+boards mine consulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.38 ten to the minus 23
+
+ align:start position:0%
+1.38 ten to the minus 23
+ 
+
+ align:start position:0%
+1.38 ten to the minus 23
+jar per Kelvin okay so you go to look at
+
+ align:start position:0%
+jar per Kelvin okay so you go to look at
+ 
+
+ align:start position:0%
+jar per Kelvin okay so you go to look at
+Avogadro's constant right honey is a six
+
+ align:start position:0%
+Avogadro's constant right honey is a six
+ 
+
+ align:start position:0%
+Avogadro's constant right honey is a six
+point six about 16 to 23 to cancel six
+
+ align:start position:0%
+point six about 16 to 23 to cancel six
+ 
+
+ align:start position:0%
+point six about 16 to 23 to cancel six
+times one point three eight give you
+
+ align:start position:0%
+times one point three eight give you
+ 
+
+ align:start position:0%
+times one point three eight give you
+right that's the universal gas comes
+
+ align:start position:0%
+right that's the universal gas comes
+ 
+
+ align:start position:0%
+right that's the universal gas comes
+okay so basically what we're we're going
+
+ align:start position:0%
+okay so basically what we're we're going
+ 
+
+ align:start position:0%
+okay so basically what we're we're going
+is to look at those microscopic picture
+
+ align:start position:0%
+is to look at those microscopic picture
+ 
+
+ align:start position:0%
+is to look at those microscopic picture
+and look at the electrons look at the
+
+ align:start position:0%
+and look at the electrons look at the
+ 
+
+ align:start position:0%
+and look at the electrons look at the
+photons look at molecule photons and
+
+ align:start position:0%
+photons look at molecule photons and
+ 
+
+ align:start position:0%
+photons look at molecule photons and
+come to this n counting how many we have
+
+ align:start position:0%
+come to this n counting how many we have
+ 
+
+ align:start position:0%
+come to this n counting how many we have
+come to how much energy they have and
+
+ align:start position:0%
+come to how much energy they have and
+ 
+
+ align:start position:0%
+come to how much energy they have and
+count how long they travel and with that
+
+ align:start position:0%
+count how long they travel and with that
+ 
+
+ align:start position:0%
+count how long they travel and with that
+you can do all the counting so the host
+
+ align:start position:0%
+you can do all the counting so the host
+ 
+
+ align:start position:0%
+you can do all the counting so the host
+a thread line for the transport is the
+
+ align:start position:0%
+a thread line for the transport is the
+ 
+
+ align:start position:0%
+a thread line for the transport is the
+county in the basically see the
+
+ align:start position:0%
+county in the basically see the
+ 
+
+ align:start position:0%
+county in the basically see the
+microscopic carriers and for that we
+
+ align:start position:0%
+microscopic carriers and for that we
+ 
+
+ align:start position:0%
+microscopic carriers and for that we
+need to go another more detail okay so
+
+ align:start position:0%
+need to go another more detail okay so
+ 
+
+ align:start position:0%
+need to go another more detail okay so
+any questions I will stop here oh yeah I
+
+ align:start position:0%
+any questions I will stop here oh yeah I
+ 
+
+ align:start position:0%
+any questions I will stop here oh yeah I
+send out a questionnaire I would like
+
+ align:start position:0%
+send out a questionnaire I would like
+ 
+
+ align:start position:0%
+send out a questionnaire I would like
+you to feel it and hand back to me so
+
+ align:start position:0%
+you to feel it and hand back to me so
+ 
+
+ align:start position:0%
+you to feel it and hand back to me so
+that I can have some idea what's your
+
+ align:start position:0%
+that I can have some idea what's your
+ 
+
+ align:start position:0%
+that I can have some idea what's your
+background what's the interest okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/kQnA60blp6o.txt b/kQnA60blp6o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2189792113ef7f4e0c7298d2f1df0c3130b88f71
--- /dev/null
+++ b/kQnA60blp6o.txt
@@ -0,0 +1,9091 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu basically you're not going
+
+ align:start position:0%
+ocw.mit.edu basically you're not going
+ 
+
+ align:start position:0%
+ocw.mit.edu basically you're not going
+to be able to use this beetles clip
+
+ align:start position:0%
+to be able to use this beetles clip
+ 
+
+ align:start position:0%
+to be able to use this beetles clip
+unfortunately but can I hear what it
+
+ align:start position:0%
+unfortunately but can I hear what it
+ 
+
+ align:start position:0%
+unfortunately but can I hear what it
+what the song is yes um so the reason
+
+ align:start position:0%
+what the song is yes um so the reason
+ 
+
+ align:start position:0%
+what the song is yes um so the reason
+why um this is under Creative Commons
+
+ align:start position:0%
+why um this is under Creative Commons
+ 
+
+ align:start position:0%
+why um this is under Creative Commons
+which it's a little sketchy I'm not sure
+
+ align:start position:0%
+which it's a little sketchy I'm not sure
+ 
+
+ align:start position:0%
+which it's a little sketchy I'm not sure
+if they legitimately could have done
+
+ align:start position:0%
+if they legitimately could have done
+ 
+
+ align:start position:0%
+if they legitimately could have done
+that but it's because they've
+
+ align:start position:0%
+that but it's because they've
+ 
+
+ align:start position:0%
+that but it's because they've
+transformed it so much to the extent
+
+ align:start position:0%
+transformed it so much to the extent
+ 
+
+ align:start position:0%
+transformed it so much to the extent
+that it's like no longer the original
+
+ align:start position:0%
+that it's like no longer the original
+ 
+
+ align:start position:0%
+that it's like no longer the original
+work right so if you revert it to the
+
+ align:start position:0%
+work right so if you revert it to the
+ 
+
+ align:start position:0%
+work right so if you revert it to the
+original work then you're also reverting
+
+ align:start position:0%
+original work then you're also reverting
+ 
+
+ align:start position:0%
+original work then you're also reverting
+you're like taking away the Creative
+
+ align:start position:0%
+you're like taking away the Creative
+ 
+
+ align:start position:0%
+you're like taking away the Creative
+Commons work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you like this
+
+ align:start position:0%
+um and you like this
+ 
+
+ align:start position:0%
+um and you like this
+instrumental
+
+ align:start position:0%
+instrumental
+ 
+
+ align:start position:0%
+instrumental
+mhm you could find something like this
+
+ align:start position:0%
+mhm you could find something like this
+ 
+
+ align:start position:0%
+mhm you could find something like this
+on CC mixer or free music archive it'll
+
+ align:start position:0%
+on CC mixer or free music archive it'll
+ 
+
+ align:start position:0%
+on CC mixer or free music archive it'll
+take a while and unfortunately I don't
+
+ align:start position:0%
+take a while and unfortunately I don't
+ 
+
+ align:start position:0%
+take a while and unfortunately I don't
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+shortcut that's the problem with music
+
+ align:start position:0%
+shortcut that's the problem with music
+ 
+
+ align:start position:0%
+shortcut that's the problem with music
+is that it's not cataloged very well so
+
+ align:start position:0%
+is that it's not cataloged very well so
+ 
+
+ align:start position:0%
+is that it's not cataloged very well so
+it's time consuming cuz you just have to
+
+ align:start position:0%
+it's time consuming cuz you just have to
+ 
+
+ align:start position:0%
+it's time consuming cuz you just have to
+listen to everything what what would be
+
+ align:start position:0%
+listen to everything what what would be
+ 
+
+ align:start position:0%
+listen to everything what what would be
+like a good like a good mood to search
+
+ align:start position:0%
+like a good like a good mood to search
+ 
+
+ align:start position:0%
+like a good like a good mood to search
+for that or um how I wouldn't
+
+ align:start position:0%
+for that or um how I wouldn't
+ 
+
+ align:start position:0%
+for that or um how I wouldn't
+necessarily search by mood I would
+
+ align:start position:0%
+necessarily search by mood I would
+ 
+
+ align:start position:0%
+necessarily search by mood I would
+search by
+
+ align:start position:0%
+search by
+ 
+
+ align:start position:0%
+search by
+instrumentation okay so have you looked
+
+ align:start position:0%
+instrumentation okay so have you looked
+ 
+
+ align:start position:0%
+instrumentation okay so have you looked
+at any of those links that were up on
+
+ align:start position:0%
+at any of those links that were up on
+ 
+
+ align:start position:0%
+at any of those links that were up on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+syllabus um I mean this is sort of like
+
+ align:start position:0%
+syllabus um I mean this is sort of like
+ 
+
+ align:start position:0%
+syllabus um I mean this is sort of like
+chill Rock basically okay um and that
+
+ align:start position:0%
+chill Rock basically okay um and that
+ 
+
+ align:start position:0%
+chill Rock basically okay um and that
+that may not actually narrow it down um
+
+ align:start position:0%
+that may not actually narrow it down um
+ 
+
+ align:start position:0%
+that may not actually narrow it down um
+go ahead and try to explore other genres
+
+ align:start position:0%
+go ahead and try to explore other genres
+ 
+
+ align:start position:0%
+go ahead and try to explore other genres
+too I unfortunately there's no like
+
+ align:start position:0%
+too I unfortunately there's no like
+ 
+
+ align:start position:0%
+too I unfortunately there's no like
+quick algorithm for finding good music
+
+ align:start position:0%
+quick algorithm for finding good music
+ 
+
+ align:start position:0%
+quick algorithm for finding good music
+that's why it's so timec consuming um
+
+ align:start position:0%
+that's why it's so timec consuming um
+ 
+
+ align:start position:0%
+that's why it's so timec consuming um
+but let me see what you've got cut so
+
+ align:start position:0%
+but let me see what you've got cut so
+ 
+
+ align:start position:0%
+but let me see what you've got cut so
+far okay the video mhm all right do you
+
+ align:start position:0%
+far okay the video mhm all right do you
+ 
+
+ align:start position:0%
+far okay the video mhm all right do you
+mind if I bump up your brightness a
+
+ align:start position:0%
+mind if I bump up your brightness a
+ 
+
+ align:start position:0%
+mind if I bump up your brightness a
+little bit you can see it
+
+ align:start position:0%
+little bit you can see it
+ 
+
+ align:start position:0%
+little bit you can see it
+better um and I'll delete this song for
+
+ align:start position:0%
+better um and I'll delete this song for
+ 
+
+ align:start position:0%
+better um and I'll delete this song for
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi what do snowflakes and cell phones
+
+ align:start position:0%
+hi what do snowflakes and cell phones
+ 
+
+ align:start position:0%
+hi what do snowflakes and cell phones
+have in common well let me start by
+
+ align:start position:0%
+have in common well let me start by
+ 
+
+ align:start position:0%
+have in common well let me start by
+drawing a snowflake
+
+ align:start position:0%
+drawing a snowflake
+ 
+
+ align:start position:0%
+drawing a snowflake
+first first I draw an equilateral
+
+ align:start position:0%
+first first I draw an equilateral
+ 
+
+ align:start position:0%
+first first I draw an equilateral
+triangle divide each side into three
+
+ align:start position:0%
+triangle divide each side into three
+ 
+
+ align:start position:0%
+triangle divide each side into three
+parts and draw another equilateral
+
+ align:start position:0%
+parts and draw another equilateral
+ 
+
+ align:start position:0%
+parts and draw another equilateral
+triangle on top of each one then take
+
+ align:start position:0%
+triangle on top of each one then take
+ 
+
+ align:start position:0%
+triangle on top of each one then take
+out the middle and repeat the process
+
+ align:start position:0%
+out the middle and repeat the process
+ 
+
+ align:start position:0%
+out the middle and repeat the process
+this time with 1 2 3 4 * 3 which is 12
+
+ align:start position:0%
+this time with 1 2 3 4 * 3 which is 12
+ 
+
+ align:start position:0%
+this time with 1 2 3 4 * 3 which is 12
+sides eventually the shape will start
+
+ align:start position:0%
+sides eventually the shape will start
+ 
+
+ align:start position:0%
+sides eventually the shape will start
+looking something like this in
+
+ align:start position:0%
+looking something like this in
+ 
+
+ align:start position:0%
+looking something like this in
+mathematics this is called a
+
+ align:start position:0%
+mathematics this is called a
+ 
+
+ align:start position:0%
+mathematics this is called a
+snowflake if I repeated my process again
+
+ align:start position:0%
+snowflake if I repeated my process again
+ 
+
+ align:start position:0%
+snowflake if I repeated my process again
+and again I would see this same pattern
+
+ align:start position:0%
+and again I would see this same pattern
+ 
+
+ align:start position:0%
+and again I would see this same pattern
+anywhere I looked this is a
+
+ align:start position:0%
+anywhere I looked this is a
+ 
+
+ align:start position:0%
+anywhere I looked this is a
+snowflake this time dra animation I just
+
+ align:start position:0%
+snowflake this time dra animation I just
+ 
+
+ align:start position:0%
+snowflake this time dra animation I just
+such NeverEnding tatters that on any
+
+ align:start position:0%
+such NeverEnding tatters that on any
+ 
+
+ align:start position:0%
+such NeverEnding tatters that on any
+scale on any level of Zoom look roughly
+
+ align:start position:0%
+scale on any level of Zoom look roughly
+ 
+
+ align:start position:0%
+scale on any level of Zoom look roughly
+the same are called
+
+ align:start position:0%
+the same are called
+ 
+
+ align:start position:0%
+the same are called
+fractals computer scientists can program
+
+ align:start position:0%
+fractals computer scientists can program
+ 
+
+ align:start position:0%
+fractals computer scientists can program
+these infinite patterns by repeating
+
+ align:start position:0%
+these infinite patterns by repeating
+ 
+
+ align:start position:0%
+these infinite patterns by repeating
+often simple mathematical process over
+
+ align:start position:0%
+often simple mathematical process over
+ 
+
+ align:start position:0%
+often simple mathematical process over
+and over in the 1990s a radio astronomer
+
+ align:start position:0%
+and over in the 1990s a radio astronomer
+ 
+
+ align:start position:0%
+and over in the 1990s a radio astronomer
+named Nathan Cohen used fractals to
+
+ align:start position:0%
+named Nathan Cohen used fractals to
+ 
+
+ align:start position:0%
+named Nathan Cohen used fractals to
+revolutionize telecommunications at the
+
+ align:start position:0%
+revolutionize telecommunications at the
+ 
+
+ align:start position:0%
+revolutionize telecommunications at the
+time Cohen was having troubles with his
+
+ align:start position:0%
+time Cohen was having troubles with his
+ 
+
+ align:start position:0%
+time Cohen was having troubles with his
+landlord the man wouldn't let him put an
+
+ align:start position:0%
+landlord the man wouldn't let him put an
+ 
+
+ align:start position:0%
+landlord the man wouldn't let him put an
+antenna on his roof so Cohen designed a
+
+ align:start position:0%
+antenna on his roof so Cohen designed a
+ 
+
+ align:start position:0%
+antenna on his roof so Cohen designed a
+more compact fractal radio antenna
+
+ align:start position:0%
+more compact fractal radio antenna
+ 
+
+ align:start position:0%
+more compact fractal radio antenna
+instead the landlord didn't notice it
+
+ align:start position:0%
+instead the landlord didn't notice it
+ 
+
+ align:start position:0%
+instead the landlord didn't notice it
+and it worked better than the ones
+
+ align:start position:0%
+and it worked better than the ones
+ 
+
+ align:start position:0%
+and it worked better than the ones
+before working further colen designed a
+
+ align:start position:0%
+before working further colen designed a
+ 
+
+ align:start position:0%
+before working further colen designed a
+new antenna this time using a fractal
+
+ align:start position:0%
+new antenna this time using a fractal
+ 
+
+ align:start position:0%
+new antenna this time using a fractal
+called the mener
+
+ align:start position:0%
+called the mener
+ 
+
+ align:start position:0%
+called the mener
+sponge the mener sponge is not really
+
+ align:start position:0%
+sponge the mener sponge is not really
+ 
+
+ align:start position:0%
+sponge the mener sponge is not really
+the sponge you be scrubbing your back
+
+ align:start position:0%
+the sponge you be scrubbing your back
+ 
+
+ align:start position:0%
+the sponge you be scrubbing your back
+with but you can still think of it like
+
+ align:start position:0%
+with but you can still think of it like
+ 
+
+ align:start position:0%
+with but you can still think of it like
+that imagine both water and soap getting
+
+ align:start position:0%
+that imagine both water and soap getting
+ 
+
+ align:start position:0%
+that imagine both water and soap getting
+through your spong's holes except the
+
+ align:start position:0%
+through your spong's holes except the
+ 
+
+ align:start position:0%
+through your spong's holes except the
+water is Wi-Fi and the soap is say
+
+ align:start position:0%
+water is Wi-Fi and the soap is say
+ 
+
+ align:start position:0%
+water is Wi-Fi and the soap is say
+glooth how is it the fractal's infinite
+
+ align:start position:0%
+glooth how is it the fractal's infinite
+ 
+
+ align:start position:0%
+glooth how is it the fractal's infinite
+sponginess allows it to receive many
+
+ align:start position:0%
+sponginess allows it to receive many
+ 
+
+ align:start position:0%
+sponginess allows it to receive many
+different frequencies simultaneously
+
+ align:start position:0%
+different frequencies simultaneously
+ 
+
+ align:start position:0%
+different frequencies simultaneously
+before con's invention antennas had to
+
+ align:start position:0%
+before con's invention antennas had to
+ 
+
+ align:start position:0%
+before con's invention antennas had to
+be cut for one frequency and that was
+
+ align:start position:0%
+be cut for one frequency and that was
+ 
+
+ align:start position:0%
+be cut for one frequency and that was
+the only frequency they could operate
+
+ align:start position:0%
+the only frequency they could operate
+ 
+
+ align:start position:0%
+the only frequency they could operate
+that so without con sponge your cell
+
+ align:start position:0%
+that so without con sponge your cell
+ 
+
+ align:start position:0%
+that so without con sponge your cell
+phone would have to look something like
+
+ align:start position:0%
+phone would have to look something like
+ 
+
+ align:start position:0%
+phone would have to look something like
+a hedgehog to receive multiple signals
+
+ align:start position:0%
+a hedgehog to receive multiple signals
+ 
+
+ align:start position:0%
+a hedgehog to receive multiple signals
+including the one your friends use when
+
+ align:start position:0%
+including the one your friends use when
+ 
+
+ align:start position:0%
+including the one your friends use when
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+call Goen later proved that only fractal
+
+ align:start position:0%
+call Goen later proved that only fractal
+ 
+
+ align:start position:0%
+call Goen later proved that only fractal
+shapes could work with such a wide range
+
+ align:start position:0%
+shapes could work with such a wide range
+ 
+
+ align:start position:0%
+shapes could work with such a wide range
+of frequencies today millions of
+
+ align:start position:0%
+of frequencies today millions of
+ 
+
+ align:start position:0%
+of frequencies today millions of
+wireless communication devices laptops
+
+ align:start position:0%
+wireless communication devices laptops
+ 
+
+ align:start position:0%
+wireless communication devices laptops
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+barcodes that was uh I was testing
+
+ align:start position:0%
+barcodes that was uh I was testing
+ 
+
+ align:start position:0%
+barcodes that was uh I was testing
+something okay I was like what was
+
+ align:start position:0%
+something okay I was like what was
+ 
+
+ align:start position:0%
+something okay I was like what was
+happening when you guys were
+
+ align:start position:0%
+happening when you guys were
+ 
+
+ align:start position:0%
+happening when you guys were
+recording yeah I'm going delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that come
+
+ align:start position:0%
+that come
+ 
+
+ align:start position:0%
+that come
+on you here let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go I was like earlier somewhere up there
+
+ align:start position:0%
+go I was like earlier somewhere up there
+ 
+
+ align:start position:0%
+go I was like earlier somewhere up there
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th's genius invention however was not
+
+ align:start position:0%
+th's genius invention however was not
+ 
+
+ align:start position:0%
+th's genius invention however was not
+the first application of fractal in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ah why is it doing you can just do
+
+ align:start position:0%
+the ah why is it doing you can just do
+ 
+
+ align:start position:0%
+the ah why is it doing you can just do
+this and it's around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here guess
+
+ align:start position:0%
+here guess
+ 
+
+ align:start position:0%
+here guess
+it's including laptops and barcode
+
+ align:start position:0%
+it's including laptops and barcode
+ 
+
+ align:start position:0%
+it's including laptops and barcode
+scanners use coen's fractal antenna
+
+ align:start position:0%
+scanners use coen's fractal antenna
+ 
+
+ align:start position:0%
+scanners use coen's fractal antenna
+genius invention however was not the
+
+ align:start position:0%
+genius invention however was not the
+ 
+
+ align:start position:0%
+genius invention however was not the
+first application of fractals in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world turns out Nature has been doing it
+
+ align:start position:0%
+world turns out Nature has been doing it
+ 
+
+ align:start position:0%
+world turns out Nature has been doing it
+the whole time and not just with
+
+ align:start position:0%
+the whole time and not just with
+ 
+
+ align:start position:0%
+the whole time and not just with
+snowflakes natural selection favors the
+
+ align:start position:0%
+snowflakes natural selection favors the
+ 
+
+ align:start position:0%
+snowflakes natural selection favors the
+most efficient systems and organisms
+
+ align:start position:0%
+most efficient systems and organisms
+ 
+
+ align:start position:0%
+most efficient systems and organisms
+often of a fractal shape for example the
+
+ align:start position:0%
+often of a fractal shape for example the
+ 
+
+ align:start position:0%
+often of a fractal shape for example the
+spiral fractal is present in broccoli
+
+ align:start position:0%
+spiral fractal is present in broccoli
+ 
+
+ align:start position:0%
+spiral fractal is present in broccoli
+seashells and hurricanes the fractal
+
+ align:start position:0%
+seashells and hurricanes the fractal
+ 
+
+ align:start position:0%
+seashells and hurricanes the fractal
+tree is relatively easy to program and
+
+ align:start position:0%
+tree is relatively easy to program and
+ 
+
+ align:start position:0%
+tree is relatively easy to program and
+can be used to study river systems blood
+
+ align:start position:0%
+can be used to study river systems blood
+ 
+
+ align:start position:0%
+can be used to study river systems blood
+vessels and lightning bolts so many
+
+ align:start position:0%
+vessels and lightning bolts so many
+ 
+
+ align:start position:0%
+vessels and lightning bolts so many
+natural systems previously thought off
+
+ align:start position:0%
+natural systems previously thought off
+ 
+
+ align:start position:0%
+natural systems previously thought off
+limits to mathematicians can now be
+
+ align:start position:0%
+limits to mathematicians can now be
+ 
+
+ align:start position:0%
+limits to mathematicians can now be
+explained in terms of
+
+ align:start position:0%
+explained in terms of
+ 
+
+ align:start position:0%
+explained in terms of
+fractals th mathematics allows us to
+
+ align:start position:0%
+fractals th mathematics allows us to
+ 
+
+ align:start position:0%
+fractals th mathematics allows us to
+learn Nature's Best Practices and then
+
+ align:start position:0%
+learn Nature's Best Practices and then
+ 
+
+ align:start position:0%
+learn Nature's Best Practices and then
+apply them to solve real world problems
+
+ align:start position:0%
+apply them to solve real world problems
+ 
+
+ align:start position:0%
+apply them to solve real world problems
+much like CO's anten revolutionized the
+
+ align:start position:0%
+much like CO's anten revolutionized the
+ 
+
+ align:start position:0%
+much like CO's anten revolutionized the
+field of telecommunications other
+
+ align:start position:0%
+field of telecommunications other
+ 
+
+ align:start position:0%
+field of telecommunications other
+fractal research is changing medicine
+
+ align:start position:0%
+fractal research is changing medicine
+ 
+
+ align:start position:0%
+fractal research is changing medicine
+weather prediction and building design
+
+ align:start position:0%
+weather prediction and building design
+ 
+
+ align:start position:0%
+weather prediction and building design
+here MIT everywhere in the world look
+
+ align:start position:0%
+here MIT everywhere in the world look
+ 
+
+ align:start position:0%
+here MIT everywhere in the world look
+around you what beautiful pattern do you
+
+ align:start position:0%
+around you what beautiful pattern do you
+ 
+
+ align:start position:0%
+around you what beautiful pattern do you
+see all right that's a good start Good
+
+ align:start position:0%
+see all right that's a good start Good
+ 
+
+ align:start position:0%
+see all right that's a good start Good
+Start um so I think in general the
+
+ align:start position:0%
+Start um so I think in general the
+ 
+
+ align:start position:0%
+Start um so I think in general the
+transitions could be a little bit
+
+ align:start position:0%
+transitions could be a little bit
+ 
+
+ align:start position:0%
+transitions could be a little bit
+tighter um so like right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here when you walk off um well this
+
+ align:start position:0%
+here when you walk off um well this
+ 
+
+ align:start position:0%
+here when you walk off um well this
+hiccup is like really noticeable so
+
+ align:start position:0%
+hiccup is like really noticeable so
+ 
+
+ align:start position:0%
+hiccup is like really noticeable so
+either hide it by having an extreme
+
+ align:start position:0%
+either hide it by having an extreme
+ 
+
+ align:start position:0%
+either hide it by having an extreme
+closeup before you leave um or just get
+
+ align:start position:0%
+closeup before you leave um or just get
+ 
+
+ align:start position:0%
+closeup before you leave um or just get
+rid of this entirely although I know
+
+ align:start position:0%
+rid of this entirely although I know
+ 
+
+ align:start position:0%
+rid of this entirely although I know
+that you did that to show the walkoff so
+
+ align:start position:0%
+that you did that to show the walkoff so
+ 
+
+ align:start position:0%
+that you did that to show the walkoff so
+that you could show walking in and I can
+
+ align:start position:0%
+that you could show walking in and I can
+ 
+
+ align:start position:0%
+that you could show walking in and I can
+connect these were this is actually one
+
+ align:start position:0%
+connect these were this is actually one
+ 
+
+ align:start position:0%
+connect these were this is actually one
+video um I separated so I could speed
+
+ align:start position:0%
+video um I separated so I could speed
+ 
+
+ align:start position:0%
+video um I separated so I could speed
+this up oh okay so this and I guess I'm
+
+ align:start position:0%
+this up oh okay so this and I guess I'm
+ 
+
+ align:start position:0%
+this up oh okay so this and I guess I'm
+just playing around with that I almost
+
+ align:start position:0%
+just playing around with that I almost
+ 
+
+ align:start position:0%
+just playing around with that I almost
+think this happens too quickly though
+
+ align:start position:0%
+think this happens too quickly though
+ 
+
+ align:start position:0%
+think this happens too quickly though
+yeah it's at 140 right now slow back
+
+ align:start position:0%
+yeah it's at 140 right now slow back
+ 
+
+ align:start position:0%
+yeah it's at 140 right now slow back
+down yeah
+
+ align:start position:0%
+down yeah
+ 
+
+ align:start position:0%
+down yeah
+um so let's go scene by scene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this track Creative Commons no it's
+
+ align:start position:0%
+is this track Creative Commons no it's
+ 
+
+ align:start position:0%
+is this track Creative Commons no it's
+Aerosmith I would I would take that
+
+ align:start position:0%
+Aerosmith I would I would take that
+ 
+
+ align:start position:0%
+Aerosmith I would I would take that
+out there's probably um an iMovie sound
+
+ align:start position:0%
+out there's probably um an iMovie sound
+ 
+
+ align:start position:0%
+out there's probably um an iMovie sound
+effect actually that you could use okay
+
+ align:start position:0%
+effect actually that you could use okay
+ 
+
+ align:start position:0%
+effect actually that you could use okay
+um for this part where you're just like
+
+ align:start position:0%
+um for this part where you're just like
+ 
+
+ align:start position:0%
+um for this part where you're just like
+walking around I would digitally zoom
+
+ align:start position:0%
+walking around I would digitally zoom
+ 
+
+ align:start position:0%
+walking around I would digitally zoom
+and close up um cuz otherwise you jump
+
+ align:start position:0%
+and close up um cuz otherwise you jump
+ 
+
+ align:start position:0%
+and close up um cuz otherwise you jump
+to talking all of a sudden but um your
+
+ align:start position:0%
+to talking all of a sudden but um your
+ 
+
+ align:start position:0%
+to talking all of a sudden but um your
+movement wasn't exaggerated enough to
+
+ align:start position:0%
+movement wasn't exaggerated enough to
+ 
+
+ align:start position:0%
+movement wasn't exaggerated enough to
+where you like get the joke that you're
+
+ align:start position:0%
+where you like get the joke that you're
+ 
+
+ align:start position:0%
+where you like get the joke that you're
+talking so you can exaggerate it by
+
+ align:start position:0%
+talking so you can exaggerate it by
+ 
+
+ align:start position:0%
+talking so you can exaggerate it by
+changing the actual framing of the scene
+
+ align:start position:0%
+changing the actual framing of the scene
+ 
+
+ align:start position:0%
+changing the actual framing of the scene
+so would I zoom in when I start talking
+
+ align:start position:0%
+so would I zoom in when I start talking
+ 
+
+ align:start position:0%
+so would I zoom in when I start talking
+um I I would stay zoomed in when you're
+
+ align:start position:0%
+um I I would stay zoomed in when you're
+ 
+
+ align:start position:0%
+um I I would stay zoomed in when you're
+talking and then clean cut to a wider
+
+ align:start position:0%
+talking and then clean cut to a wider
+ 
+
+ align:start position:0%
+talking and then clean cut to a wider
+shot of you afterwards um so basically I
+
+ align:start position:0%
+shot of you afterwards um so basically I
+ 
+
+ align:start position:0%
+shot of you afterwards um so basically I
+would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cut like right there there
+
+ align:start position:0%
+cut like right there there
+ 
+
+ align:start position:0%
+cut like right there there
+okay um I don't remember how my version
+
+ align:start position:0%
+okay um I don't remember how my version
+ 
+
+ align:start position:0%
+okay um I don't remember how my version
+is a little bit different than yours um
+
+ align:start position:0%
+is a little bit different than yours um
+ 
+
+ align:start position:0%
+is a little bit different than yours um
+but I would cut right there and for the
+
+ align:start position:0%
+but I would cut right there and for the
+ 
+
+ align:start position:0%
+but I would cut right there and for the
+proceeding clip I would do you know how
+
+ align:start position:0%
+proceeding clip I would do you know how
+ 
+
+ align:start position:0%
+proceeding clip I would do you know how
+to crop and zoom on CLI um yeah I can
+
+ align:start position:0%
+to crop and zoom on CLI um yeah I can
+ 
+
+ align:start position:0%
+to crop and zoom on CLI um yeah I can
+you just go like that basically
+
+ align:start position:0%
+you just go like that basically
+ 
+
+ align:start position:0%
+you just go like that basically
+um yeah for that now for this I would
+
+ align:start position:0%
+um yeah for that now for this I would
+ 
+
+ align:start position:0%
+um yeah for that now for this I would
+also first this is basically one really
+
+ align:start position:0%
+also first this is basically one really
+ 
+
+ align:start position:0%
+also first this is basically one really
+long shot that is framed the exact same
+
+ align:start position:0%
+long shot that is framed the exact same
+ 
+
+ align:start position:0%
+long shot that is framed the exact same
+way um and it's very
+
+ align:start position:0%
+way um and it's very
+ 
+
+ align:start position:0%
+way um and it's very
+luxury cuz you're literally at a
+
+ align:start position:0%
+luxury cuz you're literally at a
+ 
+
+ align:start position:0%
+luxury cuz you're literally at a
+Blackboard although I I think that that
+
+ align:start position:0%
+Blackboard although I I think that that
+ 
+
+ align:start position:0%
+Blackboard although I I think that that
+was a good setup for you guys given the
+
+ align:start position:0%
+was a good setup for you guys given the
+ 
+
+ align:start position:0%
+was a good setup for you guys given the
+complexity of explaining this but I
+
+ align:start position:0%
+complexity of explaining this but I
+ 
+
+ align:start position:0%
+complexity of explaining this but I
+think you can avoid making it sound too
+
+ align:start position:0%
+think you can avoid making it sound too
+ 
+
+ align:start position:0%
+think you can avoid making it sound too
+chalkboard lexury by cutting in and out
+
+ align:start position:0%
+chalkboard lexury by cutting in and out
+ 
+
+ align:start position:0%
+chalkboard lexury by cutting in and out
+of your frame okay or of your framing so
+
+ align:start position:0%
+of your frame okay or of your framing so
+ 
+
+ align:start position:0%
+of your frame okay or of your framing so
+this is fine first I draw an
+
+ align:start position:0%
+this is fine first I draw an
+ 
+
+ align:start position:0%
+this is fine first I draw an
+equal like right there I would save your
+
+ align:start position:0%
+equal like right there I would save your
+ 
+
+ align:start position:0%
+equal like right there I would save your
+audio but just um cut to a a Clos of
+
+ align:start position:0%
+audio but just um cut to a a Clos of
+ 
+
+ align:start position:0%
+audio but just um cut to a a Clos of
+your hand drawing it does that make
+
+ align:start position:0%
+your hand drawing it does that make
+ 
+
+ align:start position:0%
+your hand drawing it does that make
+sense yeah that makes sense triangle so
+
+ align:start position:0%
+sense yeah that makes sense triangle so
+ 
+
+ align:start position:0%
+sense yeah that makes sense triangle so
+kind of like uh with the phone when I'm
+
+ align:start position:0%
+kind of like uh with the phone when I'm
+ 
+
+ align:start position:0%
+kind of like uh with the phone when I'm
+showing yeah yeah okay I I would do more
+
+ align:start position:0%
+showing yeah yeah okay I I would do more
+ 
+
+ align:start position:0%
+showing yeah yeah okay I I would do more
+of that I think in general um you have
+
+ align:start position:0%
+of that I think in general um you have
+ 
+
+ align:start position:0%
+of that I think in general um you have
+very static shots that are that last for
+
+ align:start position:0%
+very static shots that are that last for
+ 
+
+ align:start position:0%
+very static shots that are that last for
+a long time so you can break that up by
+
+ align:start position:0%
+a long time so you can break that up by
+ 
+
+ align:start position:0%
+a long time so you can break that up by
+um keeping the same track from your one
+
+ align:start position:0%
+um keeping the same track from your one
+ 
+
+ align:start position:0%
+um keeping the same track from your one
+long take M but mixing up the extent to
+
+ align:start position:0%
+long take M but mixing up the extent to
+ 
+
+ align:start position:0%
+long take M but mixing up the extent to
+which you've zoomed in okay yeah that's
+
+ align:start position:0%
+which you've zoomed in okay yeah that's
+ 
+
+ align:start position:0%
+which you've zoomed in okay yeah that's
+what I did with the phone so I can
+
+ align:start position:0%
+what I did with the phone so I can
+ 
+
+ align:start position:0%
+what I did with the phone so I can
+definitely on that I think that would
+
+ align:start position:0%
+definitely on that I think that would
+ 
+
+ align:start position:0%
+definitely on that I think that would
+help with cuz this section's pretty long
+
+ align:start position:0%
+help with cuz this section's pretty long
+ 
+
+ align:start position:0%
+help with cuz this section's pretty long
+like if you just even look at your
+
+ align:start position:0%
+like if you just even look at your
+ 
+
+ align:start position:0%
+like if you just even look at your
+project um this file is this is 32
+
+ align:start position:0%
+project um this file is this is 32
+ 
+
+ align:start position:0%
+project um this file is this is 32
+seconds um which um it's the video is
+
+ align:start position:0%
+seconds um which um it's the video is
+ 
+
+ align:start position:0%
+seconds um which um it's the video is
+about 3 minutes and 40 seconds right now
+
+ align:start position:0%
+about 3 minutes and 40 seconds right now
+ 
+
+ align:start position:0%
+about 3 minutes and 40 seconds right now
+okay I think and then like this part is
+
+ align:start position:0%
+okay I think and then like this part is
+ 
+
+ align:start position:0%
+okay I think and then like this part is
+cuz I inserted the song in the okay okay
+
+ align:start position:0%
+cuz I inserted the song in the okay okay
+ 
+
+ align:start position:0%
+cuz I inserted the song in the okay okay
+great repeated my process again and
+
+ align:start position:0%
+great repeated my process again and
+ 
+
+ align:start position:0%
+great repeated my process again and
+again I would see this same so I guess
+
+ align:start position:0%
+again I would see this same so I guess
+ 
+
+ align:start position:0%
+again I would see this same so I guess
+you could zoom in and repe it I actually
+
+ align:start position:0%
+you could zoom in and repe it I actually
+ 
+
+ align:start position:0%
+you could zoom in and repe it I actually
+I wouldn't um I feel like you're
+
+ align:start position:0%
+I wouldn't um I feel like you're
+ 
+
+ align:start position:0%
+I wouldn't um I feel like you're
+revealing this image too soon in your
+
+ align:start position:0%
+revealing this image too soon in your
+ 
+
+ align:start position:0%
+revealing this image too soon in your
+sentence if I repeated this process over
+
+ align:start position:0%
+sentence if I repeated this process over
+ 
+
+ align:start position:0%
+sentence if I repeated this process over
+and over again I would see this image
+
+ align:start position:0%
+and over again I would see this image
+ 
+
+ align:start position:0%
+and over again I would see this image
+and I wouldn't I almost don't want to
+
+ align:start position:0%
+and I wouldn't I almost don't want to
+ 
+
+ align:start position:0%
+and I wouldn't I almost don't want to
+see that image until you say this image
+
+ align:start position:0%
+see that image until you say this image
+ 
+
+ align:start position:0%
+see that image until you say this image
+okay all right so maybe if you can zoom
+
+ align:start position:0%
+okay all right so maybe if you can zoom
+ 
+
+ align:start position:0%
+okay all right so maybe if you can zoom
+in and frame and crop out the uh fractal
+
+ align:start position:0%
+in and frame and crop out the uh fractal
+ 
+
+ align:start position:0%
+in and frame and crop out the uh fractal
+zoom in until you say this and then at
+
+ align:start position:0%
+zoom in until you say this and then at
+ 
+
+ align:start position:0%
+zoom in until you say this and then at
+this you can either um pan to the
+
+ align:start position:0%
+this you can either um pan to the
+ 
+
+ align:start position:0%
+this you can either um pan to the
+drawing or you can cut to a wide shot
+
+ align:start position:0%
+drawing or you can cut to a wide shot
+ 
+
+ align:start position:0%
+drawing or you can cut to a wide shot
+okay if I repeated my process again and
+
+ align:start position:0%
+okay if I repeated my process again and
+ 
+
+ align:start position:0%
+okay if I repeated my process again and
+again I would see this same pattern
+
+ align:start position:0%
+again I would see this same pattern
+ 
+
+ align:start position:0%
+again I would see this same pattern
+anywhere I
+
+ align:start position:0%
+anywhere I
+ 
+
+ align:start position:0%
+anywhere I
+looked and um anywhere you looked I mean
+
+ align:start position:0%
+looked and um anywhere you looked I mean
+ 
+
+ align:start position:0%
+looked and um anywhere you looked I mean
+if is there a way to like shoot footage
+
+ align:start position:0%
+if is there a way to like shoot footage
+ 
+
+ align:start position:0%
+if is there a way to like shoot footage
+of just close-ups of the snowflake of
+
+ align:start position:0%
+of just close-ups of the snowflake of
+ 
+
+ align:start position:0%
+of just close-ups of the snowflake of
+you like going around the edge of the of
+
+ align:start position:0%
+you like going around the edge of the of
+ 
+
+ align:start position:0%
+you like going around the edge of the of
+the perere the snowflake so that would
+
+ align:start position:0%
+the perere the snowflake so that would
+ 
+
+ align:start position:0%
+the perere the snowflake so that would
+be this part that would be that part
+
+ align:start position:0%
+be this part that would be that part
+ 
+
+ align:start position:0%
+be this part that would be that part
+okay yeah this is a cop snowflake which
+
+ align:start position:0%
+okay yeah this is a cop snowflake which
+ 
+
+ align:start position:0%
+okay yeah this is a cop snowflake which
+this is a software a fractal drawing
+
+ align:start position:0%
+this is a software a fractal drawing
+ 
+
+ align:start position:0%
+this is a software a fractal drawing
+software I'm allowed to like film the
+
+ align:start position:0%
+software I'm allowed to like film the
+ 
+
+ align:start position:0%
+software I'm allowed to like film the
+zoom in on that and then
+
+ align:start position:0%
+zoom in on that and then
+ 
+
+ align:start position:0%
+zoom in on that and then
+use it depends on if the what licensed
+
+ align:start position:0%
+use it depends on if the what licensed
+ 
+
+ align:start position:0%
+use it depends on if the what licensed
+the software is released under and who
+
+ align:start position:0%
+the software is released under and who
+ 
+
+ align:start position:0%
+the software is released under and who
+created that image
+
+ align:start position:0%
+created that image
+ 
+
+ align:start position:0%
+created that image
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so I mean I didn't have to pay for it
+
+ align:start position:0%
+um so I mean I didn't have to pay for it
+ 
+
+ align:start position:0%
+um so I mean I didn't have to pay for it
+or anything oh you created the image no
+
+ align:start position:0%
+or anything oh you created the image no
+ 
+
+ align:start position:0%
+or anything oh you created the image no
+well so kind of it's just a software and
+
+ align:start position:0%
+well so kind of it's just a software and
+ 
+
+ align:start position:0%
+well so kind of it's just a software and
+then you can
+
+ align:start position:0%
+then you can
+ 
+
+ align:start position:0%
+then you can
+do um let's say you draw a
+
+ align:start position:0%
+do um let's say you draw a
+ 
+
+ align:start position:0%
+do um let's say you draw a
+Snowflake and then you can just zoom in
+
+ align:start position:0%
+Snowflake and then you can just zoom in
+ 
+
+ align:start position:0%
+Snowflake and then you can just zoom in
+on it
+
+ align:start position:0%
+on it
+ 
+
+ align:start position:0%
+on it
+oh and then I just free open source
+
+ align:start position:0%
+oh and then I just free open source
+ 
+
+ align:start position:0%
+oh and then I just free open source
+software um yeah it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free you know what you should do is you
+
+ align:start position:0%
+free you know what you should do is you
+ 
+
+ align:start position:0%
+free you know what you should do is you
+should just take a QuickTime recording
+
+ align:start position:0%
+should just take a QuickTime recording
+ 
+
+ align:start position:0%
+should just take a QuickTime recording
+of your screen like what we yeah that
+
+ align:start position:0%
+of your screen like what we yeah that
+ 
+
+ align:start position:0%
+of your screen like what we yeah that
+was that's what I and just like do a
+
+ align:start position:0%
+was that's what I and just like do a
+ 
+
+ align:start position:0%
+was that's what I and just like do a
+quick time recording of you zooming in
+
+ align:start position:0%
+quick time recording of you zooming in
+ 
+
+ align:start position:0%
+quick time recording of you zooming in
+and that's okay to use yeah all right oh
+
+ align:start position:0%
+and that's okay to use yeah all right oh
+ 
+
+ align:start position:0%
+and that's okay to use yeah all right oh
+W this is so trippy
+
+ align:start position:0%
+W this is so trippy
+ 
+
+ align:start position:0%
+W this is so trippy
+ah why my kid stop I don't actually no
+
+ align:start position:0%
+ah why my kid stop I don't actually no
+ 
+
+ align:start position:0%
+ah why my kid stop I don't actually no
+like I haven't worked too much there's
+
+ align:start position:0%
+like I haven't worked too much there's
+ 
+
+ align:start position:0%
+like I haven't worked too much there's
+actually a video of somebody doing that
+
+ align:start position:0%
+actually a video of somebody doing that
+ 
+
+ align:start position:0%
+actually a video of somebody doing that
+which is well done so I may use part of
+
+ align:start position:0%
+which is well done so I may use part of
+ 
+
+ align:start position:0%
+which is well done so I may use part of
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+you I ideally you would make your own
+
+ align:start position:0%
+you I ideally you would make your own
+ 
+
+ align:start position:0%
+you I ideally you would make your own
+video yeah I'll work on it maybe I'll
+
+ align:start position:0%
+video yeah I'll work on it maybe I'll
+ 
+
+ align:start position:0%
+video yeah I'll work on it maybe I'll
+just like track their movements at least
+
+ align:start position:0%
+just like track their movements at least
+ 
+
+ align:start position:0%
+just like track their movements at least
+yeah um cuz I don't know what the
+
+ align:start position:0%
+yeah um cuz I don't know what the
+ 
+
+ align:start position:0%
+yeah um cuz I don't know what the
+details of that would be if you're
+
+ align:start position:0%
+details of that would be if you're
+ 
+
+ align:start position:0%
+details of that would be if you're
+actually allowed to use that video
+
+ align:start position:0%
+actually allowed to use that video
+ 
+
+ align:start position:0%
+actually allowed to use that video
+unless they've specifically released it
+
+ align:start position:0%
+unless they've specifically released it
+ 
+
+ align:start position:0%
+unless they've specifically released it
+under creative commments um
+
+ align:start position:0%
+under creative commments um
+ 
+
+ align:start position:0%
+under creative commments um
+all right here here this is a
+
+ align:start position:0%
+all right here here this is a
+ 
+
+ align:start position:0%
+all right here here this is a
+snowflake this time drawn on a computer
+
+ align:start position:0%
+snowflake this time drawn on a computer
+ 
+
+ align:start position:0%
+snowflake this time drawn on a computer
+such NeverEnding patents that on any
+
+ align:start position:0%
+such NeverEnding patents that on any
+ 
+
+ align:start position:0%
+such NeverEnding patents that on any
+scale on any level of Zoom look roughly
+
+ align:start position:0%
+scale on any level of Zoom look roughly
+ 
+
+ align:start position:0%
+scale on any level of Zoom look roughly
+the same are called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fractals okay this is where you
+
+ align:start position:0%
+fractals okay this is where you
+ 
+
+ align:start position:0%
+fractals okay this is where you
+change your wardrobe all of a
+
+ align:start position:0%
+change your wardrobe all of a
+ 
+
+ align:start position:0%
+change your wardrobe all of a
+sudden
+
+ align:start position:0%
+sudden
+ 
+
+ align:start position:0%
+sudden
+um I ideally that wouldn't
+
+ align:start position:0%
+um I ideally that wouldn't
+ 
+
+ align:start position:0%
+um I ideally that wouldn't
+happen wardrobe changes are okay if it
+
+ align:start position:0%
+happen wardrobe changes are okay if it
+ 
+
+ align:start position:0%
+happen wardrobe changes are okay if it
+makes sense but here it seems like a
+
+ align:start position:0%
+makes sense but here it seems like a
+ 
+
+ align:start position:0%
+makes sense but here it seems like a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+arbitrary
+
+ align:start position:0%
+arbitrary
+ 
+
+ align:start position:0%
+arbitrary
+um but it's not the end of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world does that make sense why that
+
+ align:start position:0%
+world does that make sense why that
+ 
+
+ align:start position:0%
+world does that make sense why that
+seems a little bit weird though cuz it's
+
+ align:start position:0%
+seems a little bit weird though cuz it's
+ 
+
+ align:start position:0%
+seems a little bit weird though cuz it's
+like in your script there's nothing that
+
+ align:start position:0%
+like in your script there's nothing that
+ 
+
+ align:start position:0%
+like in your script there's nothing that
+sort of signifies or identifies that
+
+ align:start position:0%
+sort of signifies or identifies that
+ 
+
+ align:start position:0%
+sort of signifies or identifies that
+you've shot like at a different day or
+
+ align:start position:0%
+you've shot like at a different day or
+ 
+
+ align:start position:0%
+you've shot like at a different day or
+that you're in a location that requires
+
+ align:start position:0%
+that you're in a location that requires
+ 
+
+ align:start position:0%
+that you're in a location that requires
+a different wardrobe you know
+
+ align:start position:0%
+a different wardrobe you know
+ 
+
+ align:start position:0%
+a different wardrobe you know
+mhm
+
+ align:start position:0%
+mhm
+ 
+
+ align:start position:0%
+mhm
+um this is a snowflake this time
+
+ align:start position:0%
+um this is a snowflake this time
+ 
+
+ align:start position:0%
+um this is a snowflake this time
+drawn on a computer such NeverEnding
+
+ align:start position:0%
+drawn on a computer such NeverEnding
+ 
+
+ align:start position:0%
+drawn on a computer such NeverEnding
+patents that on any scale on any level
+
+ align:start position:0%
+patents that on any scale on any level
+ 
+
+ align:start position:0%
+patents that on any scale on any level
+of Zoom look roughly the same are called
+
+ align:start position:0%
+of Zoom look roughly the same are called
+ 
+
+ align:start position:0%
+of Zoom look roughly the same are called
+fractals okay I'm just going to say it
+
+ align:start position:0%
+fractals okay I'm just going to say it
+ 
+
+ align:start position:0%
+fractals okay I'm just going to say it
+how do you pronounce Coke snowflake I
+
+ align:start position:0%
+how do you pronounce Coke snowflake I
+ 
+
+ align:start position:0%
+how do you pronounce Coke snowflake I
+think it's Coke but I don't know I'm
+
+ align:start position:0%
+think it's Coke but I don't know I'm
+ 
+
+ align:start position:0%
+think it's Coke but I don't know I'm
+pretty sure it's c k o c h
+
+ align:start position:0%
+pretty sure it's c k o c h
+ 
+
+ align:start position:0%
+pretty sure it's c k o c h
+right just cuz because
+
+ align:start position:0%
+right just cuz because
+ 
+
+ align:start position:0%
+right just cuz because
+um I would imagine that it's Educators
+
+ align:start position:0%
+um I would imagine that it's Educators
+ 
+
+ align:start position:0%
+um I would imagine that it's Educators
+watching this video but if there
+
+ align:start position:0%
+watching this video but if there
+ 
+
+ align:start position:0%
+watching this video but if there
+are little children watching this one
+
+ align:start position:0%
+are little children watching this one
+ 
+
+ align:start position:0%
+are little children watching this one
+they're going to be some he said
+
+ align:start position:0%
+they're going to be some he said
+ 
+
+ align:start position:0%
+they're going to be some he said
+snowflake com I was actually thinking of
+
+ align:start position:0%
+snowflake com I was actually thinking of
+ 
+
+ align:start position:0%
+snowflake com I was actually thinking of
+um doing cuz the the sound changes so
+
+ align:start position:0%
+um doing cuz the the sound changes so
+ 
+
+ align:start position:0%
+um doing cuz the the sound changes so
+much I was actually thinking of doing a
+
+ align:start position:0%
+much I was actually thinking of doing a
+ 
+
+ align:start position:0%
+much I was actually thinking of doing a
+voice over of this uh because what I
+
+ align:start position:0%
+voice over of this uh because what I
+ 
+
+ align:start position:0%
+voice over of this uh because what I
+found I recorded this part indoors and
+
+ align:start position:0%
+found I recorded this part indoors and
+ 
+
+ align:start position:0%
+found I recorded this part indoors and
+Outdoors and I could match up the sound
+
+ align:start position:0%
+Outdoors and I could match up the sound
+ 
+
+ align:start position:0%
+Outdoors and I could match up the sound
+perfectly okay for what I was moving so
+
+ align:start position:0%
+perfectly okay for what I was moving so
+ 
+
+ align:start position:0%
+perfectly okay for what I was moving so
+if I like do the same thing but
+
+ align:start position:0%
+if I like do the same thing but
+ 
+
+ align:start position:0%
+if I like do the same thing but
+somewhere else I can probably match up
+
+ align:start position:0%
+somewhere else I can probably match up
+ 
+
+ align:start position:0%
+somewhere else I can probably match up
+the sound and change the snowflake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part Helga Von
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Coke yeah I would just look up the
+
+ align:start position:0%
+Coke yeah I would just look up the
+ 
+
+ align:start position:0%
+Coke yeah I would just look up the
+pronunciation of that just to all right
+
+ align:start position:0%
+pronunciation of that just to all right
+ 
+
+ align:start position:0%
+pronunciation of that just to all right
+I will do that just to be careful
+
+ align:start position:0%
+I will do that just to be careful
+ 
+
+ align:start position:0%
+I will do that just to be careful
+um yeah and especially like this is just
+
+ align:start position:0%
+um yeah and especially like this is just
+ 
+
+ align:start position:0%
+um yeah and especially like this is just
+vo stuff anyway so you can easily
+
+ align:start position:0%
+vo stuff anyway so you can easily
+ 
+
+ align:start position:0%
+vo stuff anyway so you can easily
+re-record that M um so wait wait for the
+
+ align:start position:0%
+re-record that M um so wait wait for the
+ 
+
+ align:start position:0%
+re-record that M um so wait wait for the
+reveal here basically do a little more
+
+ align:start position:0%
+reveal here basically do a little more
+ 
+
+ align:start position:0%
+reveal here basically do a little more
+with cutting in and out of close-ups and
+
+ align:start position:0%
+with cutting in and out of close-ups and
+ 
+
+ align:start position:0%
+with cutting in and out of close-ups and
+wide
+
+ align:start position:0%
+wide
+ 
+
+ align:start position:0%
+wide
+shots um oh okay right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fractals so this reveal is a little
+
+ align:start position:0%
+fractals so this reveal is a little
+ 
+
+ align:start position:0%
+fractals so this reveal is a little
+awkward cuz you're not looking at the
+
+ align:start position:0%
+awkward cuz you're not looking at the
+ 
+
+ align:start position:0%
+awkward cuz you're not looking at the
+audience when you're saying the big
+
+ align:start position:0%
+audience when you're saying the big
+ 
+
+ align:start position:0%
+audience when you're saying the big
+reveal and then you have this sort of
+
+ align:start position:0%
+reveal and then you have this sort of
+ 
+
+ align:start position:0%
+reveal and then you have this sort of
+unnatural pause before you start the
+
+ align:start position:0%
+unnatural pause before you start the
+ 
+
+ align:start position:0%
+unnatural pause before you start the
+next sentence I was actually originally
+
+ align:start position:0%
+next sentence I was actually originally
+ 
+
+ align:start position:0%
+next sentence I was actually originally
+intending to save fractals here but I
+
+ align:start position:0%
+intending to save fractals here but I
+ 
+
+ align:start position:0%
+intending to save fractals here but I
+cut it and thought oh cool I'll just say
+
+ align:start position:0%
+cut it and thought oh cool I'll just say
+ 
+
+ align:start position:0%
+cut it and thought oh cool I'll just say
+that but originally it was going to be I
+
+ align:start position:0%
+that but originally it was going to be I
+ 
+
+ align:start position:0%
+that but originally it was going to be I
+finished saying fra and then I type on
+
+ align:start position:0%
+finished saying fra and then I type on
+ 
+
+ align:start position:0%
+finished saying fra and then I type on
+the computer and say okay that'll work a
+
+ align:start position:0%
+the computer and say okay that'll work a
+ 
+
+ align:start position:0%
+the computer and say okay that'll work a
+lot better so I'll I can just redo that
+
+ align:start position:0%
+lot better so I'll I can just redo that
+ 
+
+ align:start position:0%
+lot better so I'll I can just redo that
+okay cool I mean I think it's also um if
+
+ align:start position:0%
+okay cool I mean I think it's also um if
+ 
+
+ align:start position:0%
+okay cool I mean I think it's also um if
+you I think ideally you would say
+
+ align:start position:0%
+you I think ideally you would say
+ 
+
+ align:start position:0%
+you I think ideally you would say
+fractals and then you'd look down at
+
+ align:start position:0%
+fractals and then you'd look down at
+ 
+
+ align:start position:0%
+fractals and then you'd look down at
+your computer but what you're saying now
+
+ align:start position:0%
+your computer but what you're saying now
+ 
+
+ align:start position:0%
+your computer but what you're saying now
+that'll work too yeah yeah and that's
+
+ align:start position:0%
+that'll work too yeah yeah and that's
+ 
+
+ align:start position:0%
+that'll work too yeah yeah and that's
+how we filmed it
+
+ align:start position:0%
+how we filmed it
+ 
+
+ align:start position:0%
+how we filmed it
+so yeah cuz this like Gap in where you
+
+ align:start position:0%
+so yeah cuz this like Gap in where you
+ 
+
+ align:start position:0%
+so yeah cuz this like Gap in where you
+take a breath it sounds fine but it
+
+ align:start position:0%
+take a breath it sounds fine but it
+ 
+
+ align:start position:0%
+take a breath it sounds fine but it
+looks a little awkward computer
+
+ align:start position:0%
+looks a little awkward computer
+ 
+
+ align:start position:0%
+looks a little awkward computer
+scientists can program these infinite
+
+ align:start position:0%
+scientists can program these infinite
+ 
+
+ align:start position:0%
+scientists can program these infinite
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+by um so this is super Overexposed in
+
+ align:start position:0%
+by um so this is super Overexposed in
+ 
+
+ align:start position:0%
+by um so this is super Overexposed in
+the background so I would try to see if
+
+ align:start position:0%
+the background so I would try to see if
+ 
+
+ align:start position:0%
+the background so I would try to see if
+you can bring the exposure down just a
+
+ align:start position:0%
+you can bring the exposure down just a
+ 
+
+ align:start position:0%
+you can bring the exposure down just a
+little bit okay uh I don't remember how
+
+ align:start position:0%
+little bit okay uh I don't remember how
+ 
+
+ align:start position:0%
+little bit okay uh I don't remember how
+to do that on my movie it's it's on this
+
+ align:start position:0%
+to do that on my movie it's it's on this
+ 
+
+ align:start position:0%
+to do that on my movie it's it's on this
+I actually increased the exposure cuz
+
+ align:start position:0%
+I actually increased the exposure cuz
+ 
+
+ align:start position:0%
+I actually increased the exposure cuz
+there were some Shadows but I can play
+
+ align:start position:0%
+there were some Shadows but I can play
+ 
+
+ align:start position:0%
+there were some Shadows but I can play
+around with that yeah I mean the main
+
+ align:start position:0%
+around with that yeah I mean the main
+ 
+
+ align:start position:0%
+around with that yeah I mean the main
+thing is the whites right like you're
+
+ align:start position:0%
+thing is the whites right like you're
+ 
+
+ align:start position:0%
+thing is the whites right like you're
+super blown out in the back in the
+
+ align:start position:0%
+super blown out in the back in the
+ 
+
+ align:start position:0%
+super blown out in the back in the
+window infin patterns but repeating also
+
+ align:start position:0%
+window infin patterns but repeating also
+ 
+
+ align:start position:0%
+window infin patterns but repeating also
+no it was it was different in the
+
+ align:start position:0%
+no it was it was different in the
+ 
+
+ align:start position:0%
+no it was it was different in the
+original um and I don't know if you can
+
+ align:start position:0%
+original um and I don't know if you can
+ 
+
+ align:start position:0%
+original um and I don't know if you can
+if there's a histogram on iMovie but if
+
+ align:start position:0%
+if there's a histogram on iMovie but if
+ 
+
+ align:start position:0%
+if there's a histogram on iMovie but if
+you can somehow just like increase the
+
+ align:start position:0%
+you can somehow just like increase the
+ 
+
+ align:start position:0%
+you can somehow just like increase the
+blacks but don't um blow out the whites
+
+ align:start position:0%
+blacks but don't um blow out the whites
+ 
+
+ align:start position:0%
+blacks but don't um blow out the whites
+that might help if you have weird
+
+ align:start position:0%
+that might help if you have weird
+ 
+
+ align:start position:0%
+that might help if you have weird
+shadows going on I think so it looked
+
+ align:start position:0%
+shadows going on I think so it looked
+ 
+
+ align:start position:0%
+shadows going on I think so it looked
+like this originally I think oh yeah
+
+ align:start position:0%
+like this originally I think oh yeah
+ 
+
+ align:start position:0%
+like this originally I think oh yeah
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+better yeah I don't know I was playing
+
+ align:start position:0%
+better yeah I don't know I was playing
+ 
+
+ align:start position:0%
+better yeah I don't know I was playing
+around with that but that's not the
+
+ align:start position:0%
+around with that but that's not the
+ 
+
+ align:start position:0%
+around with that but that's not the
+final version okay cool but that was the
+
+ align:start position:0%
+final version okay cool but that was the
+ 
+
+ align:start position:0%
+final version okay cool but that was the
+original got it like Communications
+
+ align:start position:0%
+original got it like Communications
+ 
+
+ align:start position:0%
+original got it like Communications
+oh yeah I remember this one also feels
+
+ align:start position:0%
+oh yeah I remember this one also feels
+ 
+
+ align:start position:0%
+oh yeah I remember this one also feels
+pretty long to me computer scientists
+
+ align:start position:0%
+pretty long to me computer scientists
+ 
+
+ align:start position:0%
+pretty long to me computer scientists
+can program these infinite patterns by
+
+ align:start position:0%
+can program these infinite patterns by
+ 
+
+ align:start position:0%
+can program these infinite patterns by
+repeating often simple mathematical
+
+ align:start position:0%
+repeating often simple mathematical
+ 
+
+ align:start position:0%
+repeating often simple mathematical
+process over over and over so for that
+
+ align:start position:0%
+process over over and over so for that
+ 
+
+ align:start position:0%
+process over over and over so for that
+line do you have um footage of you on
+
+ align:start position:0%
+line do you have um footage of you on
+ 
+
+ align:start position:0%
+line do you have um footage of you on
+mat
+
+ align:start position:0%
+mat
+ 
+
+ align:start position:0%
+mat
+lab uh graphing a fractal um I can do
+
+ align:start position:0%
+lab uh graphing a fractal um I can do
+ 
+
+ align:start position:0%
+lab uh graphing a fractal um I can do
+that cuz it would probably be on the
+
+ align:start position:0%
+that cuz it would probably be on the
+ 
+
+ align:start position:0%
+that cuz it would probably be on the
+fractal software and you can just yeah
+
+ align:start position:0%
+fractal software and you can just yeah
+ 
+
+ align:start position:0%
+fractal software and you can just yeah
+even that like just to break it up a
+
+ align:start position:0%
+even that like just to break it up a
+ 
+
+ align:start position:0%
+even that like just to break it up a
+little bit and give them like a visual
+
+ align:start position:0%
+little bit and give them like a visual
+ 
+
+ align:start position:0%
+little bit and give them like a visual
+Association CU this is one of those
+
+ align:start position:0%
+Association CU this is one of those
+ 
+
+ align:start position:0%
+Association CU this is one of those
+times where if you're like again in a
+
+ align:start position:0%
+times where if you're like again in a
+ 
+
+ align:start position:0%
+times where if you're like again in a
+static Place saying the same like a big
+
+ align:start position:0%
+static Place saying the same like a big
+ 
+
+ align:start position:0%
+static Place saying the same like a big
+chunk of words to them it's sort of
+
+ align:start position:0%
+chunk of words to them it's sort of
+ 
+
+ align:start position:0%
+chunk of words to them it's sort of
+easier to tune it out a little bit
+
+ align:start position:0%
+easier to tune it out a little bit
+ 
+
+ align:start position:0%
+easier to tune it out a little bit
+fractals computer scientists can program
+
+ align:start position:0%
+fractals computer scientists can program
+ 
+
+ align:start position:0%
+fractals computer scientists can program
+these infinite patterns by repeating an
+
+ align:start position:0%
+these infinite patterns by repeating an
+ 
+
+ align:start position:0%
+these infinite patterns by repeating an
+often simple mathematical process over
+
+ align:start position:0%
+often simple mathematical process over
+ 
+
+ align:start position:0%
+often simple mathematical process over
+and over in the 1990s yeah and then cut
+
+ align:start position:0%
+and over in the 1990s yeah and then cut
+ 
+
+ align:start position:0%
+and over in the 1990s yeah and then cut
+back out to you when you say cuz that's
+
+ align:start position:0%
+back out to you when you say cuz that's
+ 
+
+ align:start position:0%
+back out to you when you say cuz that's
+like a very separate thought a radio
+
+ align:start position:0%
+like a very separate thought a radio
+ 
+
+ align:start position:0%
+like a very separate thought a radio
+astronomer named Nathan Cohen is there a
+
+ align:start position:0%
+astronomer named Nathan Cohen is there a
+ 
+
+ align:start position:0%
+astronomer named Nathan Cohen is there a
+picture of Nathan Cohen that could like
+
+ align:start position:0%
+picture of Nathan Cohen that could like
+ 
+
+ align:start position:0%
+picture of Nathan Cohen that could like
+pop up on the side I can probably find
+
+ align:start position:0%
+pop up on the side I can probably find
+ 
+
+ align:start position:0%
+pop up on the side I can probably find
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah there is one actually to
+
+ align:start position:0%
+yeah there is one actually to
+ 
+
+ align:start position:0%
+yeah there is one actually to
+revolutionize
+
+ align:start position:0%
+revolutionize
+ 
+
+ align:start position:0%
+revolutionize
+telecomunications oh okay
+
+ align:start position:0%
+telecomunications oh okay
+ 
+
+ align:start position:0%
+telecomunications oh okay
+so halfway through the video you switch
+
+ align:start position:0%
+so halfway through the video you switch
+ 
+
+ align:start position:0%
+so halfway through the video you switch
+to these like Cube turn transitions um I
+
+ align:start position:0%
+to these like Cube turn transitions um I
+ 
+
+ align:start position:0%
+to these like Cube turn transitions um I
+mean this is this personal preference I
+
+ align:start position:0%
+mean this is this personal preference I
+ 
+
+ align:start position:0%
+mean this is this personal preference I
+don't know how you feel about
+
+ align:start position:0%
+don't know how you feel about
+ 
+
+ align:start position:0%
+don't know how you feel about
+transitions um but I feel
+
+ align:start position:0%
+transitions um but I feel
+ 
+
+ align:start position:0%
+transitions um but I feel
+like either keep it all the same mm or
+
+ align:start position:0%
+like either keep it all the same mm or
+ 
+
+ align:start position:0%
+like either keep it all the same mm or
+use like the
+
+ align:start position:0%
+use like the
+ 
+
+ align:start position:0%
+use like the
+little quirkier transitions for you know
+
+ align:start position:0%
+little quirkier transitions for you know
+ 
+
+ align:start position:0%
+little quirkier transitions for you know
+a very pointed reason okay um for this
+
+ align:start position:0%
+a very pointed reason okay um for this
+ 
+
+ align:start position:0%
+a very pointed reason okay um for this
+one I because it was such different
+
+ align:start position:0%
+one I because it was such different
+ 
+
+ align:start position:0%
+one I because it was such different
+locations I use these to tell the story
+
+ align:start position:0%
+locations I use these to tell the story
+ 
+
+ align:start position:0%
+locations I use these to tell the story
+so this is me introducing the story and
+
+ align:start position:0%
+so this is me introducing the story and
+ 
+
+ align:start position:0%
+so this is me introducing the story and
+telling the story so just for that story
+
+ align:start position:0%
+telling the story so just for that story
+ 
+
+ align:start position:0%
+telling the story so just for that story
+I'm using those transitions yeah I think
+
+ align:start position:0%
+I'm using those transitions yeah I think
+ 
+
+ align:start position:0%
+I'm using those transitions yeah I think
+uh if you're going to do that I much
+
+ align:start position:0%
+uh if you're going to do that I much
+ 
+
+ align:start position:0%
+uh if you're going to do that I much
+prefer a push rather than a cube turn
+
+ align:start position:0%
+prefer a push rather than a cube turn
+ 
+
+ align:start position:0%
+prefer a push rather than a cube turn
+Okay um cuz we've we've done that once
+
+ align:start position:0%
+Okay um cuz we've we've done that once
+ 
+
+ align:start position:0%
+Okay um cuz we've we've done that once
+before and again personal preference
+
+ align:start position:0%
+before and again personal preference
+ 
+
+ align:start position:0%
+before and again personal preference
+George had to really sell me on the idea
+
+ align:start position:0%
+George had to really sell me on the idea
+ 
+
+ align:start position:0%
+George had to really sell me on the idea
+cuz I was very opposed to it but instead
+
+ align:start position:0%
+cuz I was very opposed to it but instead
+ 
+
+ align:start position:0%
+cuz I was very opposed to it but instead
+of doing a rotation you just it's a a
+
+ align:start position:0%
+of doing a rotation you just it's a a
+ 
+
+ align:start position:0%
+of doing a rotation you just it's a a
+wipe basically one frame pushes off and
+
+ align:start position:0%
+wipe basically one frame pushes off and
+ 
+
+ align:start position:0%
+wipe basically one frame pushes off and
+reveals the next one okay I think that
+
+ align:start position:0%
+reveals the next one okay I think that
+ 
+
+ align:start position:0%
+reveals the next one okay I think that
+looks a little bit better basically I I
+
+ align:start position:0%
+looks a little bit better basically I I
+ 
+
+ align:start position:0%
+looks a little bit better basically I I
+prefer as subtle of trans uh yeah uh
+
+ align:start position:0%
+prefer as subtle of trans uh yeah uh
+ 
+
+ align:start position:0%
+prefer as subtle of trans uh yeah uh
+transition as possible and the
+
+ align:start position:0%
+transition as possible and the
+ 
+
+ align:start position:0%
+transition as possible and the
+animations are cool but they
+
+ align:start position:0%
+animations are cool but they
+ 
+
+ align:start position:0%
+animations are cool but they
+remind people of like really flashy
+
+ align:start position:0%
+remind people of like really flashy
+ 
+
+ align:start position:0%
+remind people of like really flashy
+homemade videos as opposed to like this
+
+ align:start position:0%
+homemade videos as opposed to like this
+ 
+
+ align:start position:0%
+homemade videos as opposed to like this
+is a very ey
+
+ align:start position:0%
+is a very ey
+ 
+
+ align:start position:0%
+is a very ey
+transition at the time Cen was having
+
+ align:start position:0%
+transition at the time Cen was having
+ 
+
+ align:start position:0%
+transition at the time Cen was having
+troubl with his
+
+ align:start position:0%
+troubl with his
+ 
+
+ align:start position:0%
+troubl with his
+landlord the man would let him put an
+
+ align:start position:0%
+landlord the man would let him put an
+ 
+
+ align:start position:0%
+landlord the man would let him put an
+antenna on his
+
+ align:start position:0%
+antenna on his
+ 
+
+ align:start position:0%
+antenna on his
+roof
+
+ align:start position:0%
+roof
+ 
+
+ align:start position:0%
+roof
+so there are some wait let me listen to
+
+ align:start position:0%
+so there are some wait let me listen to
+ 
+
+ align:start position:0%
+so there are some wait let me listen to
+this again time Cohen was having
+
+ align:start position:0%
+this again time Cohen was having
+ 
+
+ align:start position:0%
+this again time Cohen was having
+troubles with his landlord the man
+
+ align:start position:0%
+troubles with his landlord the man
+ 
+
+ align:start position:0%
+troubles with his landlord the man
+wouldn't let him put an antenna on his
+
+ align:start position:0%
+wouldn't let him put an antenna on his
+ 
+
+ align:start position:0%
+wouldn't let him put an antenna on his
+roof so Cohen designed a more compact
+
+ align:start position:0%
+roof so Cohen designed a more compact
+ 
+
+ align:start position:0%
+roof so Cohen designed a more compact
+fra there I would zoom in mhm cut to a a
+
+ align:start position:0%
+fra there I would zoom in mhm cut to a a
+ 
+
+ align:start position:0%
+fra there I would zoom in mhm cut to a a
+closer framing of that R that's like
+
+ align:start position:0%
+closer framing of that R that's like
+ 
+
+ align:start position:0%
+closer framing of that R that's like
+just the wire antenna instead the
+
+ align:start position:0%
+just the wire antenna instead the
+ 
+
+ align:start position:0%
+just the wire antenna instead the
+landlord didn't notice it and it worked
+
+ align:start position:0%
+landlord didn't notice it and it worked
+ 
+
+ align:start position:0%
+landlord didn't notice it and it worked
+better than the ones before working
+
+ align:start position:0%
+better than the ones before working
+ 
+
+ align:start position:0%
+better than the ones before working
+further and cut back out designed a new
+
+ align:start position:0%
+further and cut back out designed a new
+ 
+
+ align:start position:0%
+further and cut back out designed a new
+antenna this time using a fractal called
+
+ align:start position:0%
+antenna this time using a fractal called
+ 
+
+ align:start position:0%
+antenna this time using a fractal called
+the mener
+
+ align:start position:0%
+the mener
+ 
+
+ align:start position:0%
+the mener
+sponge and again I don't think it's
+
+ align:start position:0%
+sponge and again I don't think it's
+ 
+
+ align:start position:0%
+sponge and again I don't think it's
+necessary to do a rotation and I was
+
+ align:start position:0%
+necessary to do a rotation and I was
+ 
+
+ align:start position:0%
+necessary to do a rotation and I was
+thinking here while the the maybe have
+
+ align:start position:0%
+thinking here while the the maybe have
+ 
+
+ align:start position:0%
+thinking here while the the maybe have
+the mener sponge increase in size and
+
+ align:start position:0%
+the mener sponge increase in size and
+ 
+
+ align:start position:0%
+the mener sponge increase in size and
+then have curtain as a background so
+
+ align:start position:0%
+then have curtain as a background so
+ 
+
+ align:start position:0%
+then have curtain as a background so
+would that be another transition to kind
+
+ align:start position:0%
+would that be another transition to kind
+ 
+
+ align:start position:0%
+would that be another transition to kind
+of have the mener sponge expand and then
+
+ align:start position:0%
+of have the mener sponge expand and then
+ 
+
+ align:start position:0%
+of have the mener sponge expand and then
+have me wipe it off are you drawing your
+
+ align:start position:0%
+have me wipe it off are you drawing your
+ 
+
+ align:start position:0%
+have me wipe it off are you drawing your
+sponge um going to have a model of it
+
+ align:start position:0%
+sponge um going to have a model of it
+ 
+
+ align:start position:0%
+sponge um going to have a model of it
+hopefully your
+
+ align:start position:0%
+hopefully your
+ 
+
+ align:start position:0%
+hopefully your
+sponge so you're going to sorry are you
+
+ align:start position:0%
+sponge so you're going to sorry are you
+ 
+
+ align:start position:0%
+sponge so you're going to sorry are you
+going to refilm the part with with like
+
+ align:start position:0%
+going to refilm the part with with like
+ 
+
+ align:start position:0%
+going to refilm the part with with like
+a model or like no just like a image
+
+ align:start position:0%
+a model or like no just like a image
+ 
+
+ align:start position:0%
+a model or like no just like a image
+model oh okay okay so it would pop up in
+
+ align:start position:0%
+model oh okay okay so it would pop up in
+ 
+
+ align:start position:0%
+model oh okay okay so it would pop up in
+your hand right there so this the way
+
+ align:start position:0%
+your hand right there so this the way
+ 
+
+ align:start position:0%
+your hand right there so this the way
+this is framed um I mean the subject is
+
+ align:start position:0%
+this is framed um I mean the subject is
+ 
+
+ align:start position:0%
+this is framed um I mean the subject is
+really here it's going to be here and
+
+ align:start position:0%
+really here it's going to be here and
+ 
+
+ align:start position:0%
+really here it's going to be here and
+it's so you're so biased I mean this is
+
+ align:start position:0%
+it's so you're so biased I mean this is
+ 
+
+ align:start position:0%
+it's so you're so biased I mean this is
+beautifully framed in terms of like rule
+
+ align:start position:0%
+beautifully framed in terms of like rule
+ 
+
+ align:start position:0%
+beautifully framed in terms of like rule
+of thirds and everything but um because
+
+ align:start position:0%
+of thirds and everything but um because
+ 
+
+ align:start position:0%
+of thirds and everything but um because
+you held your hand out this way um it's
+
+ align:start position:0%
+you held your hand out this way um it's
+ 
+
+ align:start position:0%
+you held your hand out this way um it's
+going to look really F like the visual
+
+ align:start position:0%
+going to look really F like the visual
+ 
+
+ align:start position:0%
+going to look really F like the visual
+balance of that frame is going to look
+
+ align:start position:0%
+balance of that frame is going to look
+ 
+
+ align:start position:0%
+balance of that frame is going to look
+really funny when you're like menend
+
+ align:start position:0%
+really funny when you're like menend
+ 
+
+ align:start position:0%
+really funny when you're like menend
+your sponge and then all of a sudden
+
+ align:start position:0%
+your sponge and then all of a sudden
+ 
+
+ align:start position:0%
+your sponge and then all of a sudden
+this like huge thing gets cut off on the
+
+ align:start position:0%
+this like huge thing gets cut off on the
+ 
+
+ align:start position:0%
+this like huge thing gets cut off on the
+side mhm so either zoom in a little bit
+
+ align:start position:0%
+side mhm so either zoom in a little bit
+ 
+
+ align:start position:0%
+side mhm so either zoom in a little bit
+I mean and ideally you would have held
+
+ align:start position:0%
+I mean and ideally you would have held
+ 
+
+ align:start position:0%
+I mean and ideally you would have held
+out this hand so that it would have been
+
+ align:start position:0%
+out this hand so that it would have been
+ 
+
+ align:start position:0%
+out this hand so that it would have been
+in the midal although the background's
+
+ align:start position:0%
+in the midal although the background's
+ 
+
+ align:start position:0%
+in the midal although the background's
+really distracting so I don't know
+
+ align:start position:0%
+really distracting so I don't know
+ 
+
+ align:start position:0%
+really distracting so I don't know
+if uh mener
+
+ align:start position:0%
+if uh mener
+ 
+
+ align:start position:0%
+if uh mener
+sponge the mener sponge and are you
+
+ align:start position:0%
+sponge the mener sponge and are you
+ 
+
+ align:start position:0%
+sponge the mener sponge and are you
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+hold oh so I'm assuming the mener sponge
+
+ align:start position:0%
+hold oh so I'm assuming the mener sponge
+ 
+
+ align:start position:0%
+hold oh so I'm assuming the mener sponge
+picture will be floating somewhere um it
+
+ align:start position:0%
+picture will be floating somewhere um it
+ 
+
+ align:start position:0%
+picture will be floating somewhere um it
+would be here yeah uh but then I would
+
+ align:start position:0%
+would be here yeah uh but then I would
+ 
+
+ align:start position:0%
+would be here yeah uh but then I would
+get rid of it when I'm talking about the
+
+ align:start position:0%
+get rid of it when I'm talking about the
+ 
+
+ align:start position:0%
+get rid of it when I'm talking about the
+regular
+
+ align:start position:0%
+regular
+ 
+
+ align:start position:0%
+regular
+sponge well here you're here it would
+
+ align:start position:0%
+sponge well here you're here it would
+ 
+
+ align:start position:0%
+sponge well here you're here it would
+still be floating cuz I think when
+
+ align:start position:0%
+still be floating cuz I think when
+ 
+
+ align:start position:0%
+still be floating cuz I think when
+you're say the Menor sponge isn't
+
+ align:start position:0%
+you're say the Menor sponge isn't
+ 
+
+ align:start position:0%
+you're say the Menor sponge isn't
+exactly like a real sponge right but I
+
+ align:start position:0%
+exactly like a real sponge right but I
+ 
+
+ align:start position:0%
+exactly like a real sponge right but I
+think the Menor sponge needs to be shown
+
+ align:start position:0%
+think the Menor sponge needs to be shown
+ 
+
+ align:start position:0%
+think the Menor sponge needs to be shown
+okay um if you're going to show
+
+ align:start position:0%
+okay um if you're going to show
+ 
+
+ align:start position:0%
+okay um if you're going to show
+something show it long enough to where
+
+ align:start position:0%
+something show it long enough to where
+ 
+
+ align:start position:0%
+something show it long enough to where
+the viewer can process it a little bit
+
+ align:start position:0%
+the viewer can process it a little bit
+ 
+
+ align:start position:0%
+the viewer can process it a little bit
+uh otherwise it's like this blip that
+
+ align:start position:0%
+uh otherwise it's like this blip that
+ 
+
+ align:start position:0%
+uh otherwise it's like this blip that
+might distract them
+
+ align:start position:0%
+might distract them
+ 
+
+ align:start position:0%
+might distract them
+sponge
+
+ align:start position:0%
+sponge
+ 
+
+ align:start position:0%
+sponge
+okay your sponge hold did you cut right
+
+ align:start position:0%
+okay your sponge hold did you cut right
+ 
+
+ align:start position:0%
+okay your sponge hold did you cut right
+here or did is there a little bit more I
+
+ align:start position:0%
+here or did is there a little bit more I
+ 
+
+ align:start position:0%
+here or did is there a little bit more I
+think there's a little bit more okay
+
+ align:start position:0%
+think there's a little bit more okay
+ 
+
+ align:start position:0%
+think there's a little bit more okay
+yeah leave hold it just a little bit and
+
+ align:start position:0%
+yeah leave hold it just a little bit and
+ 
+
+ align:start position:0%
+yeah leave hold it just a little bit and
+maybe cut to um again cut to a close-up
+
+ align:start position:0%
+maybe cut to um again cut to a close-up
+ 
+
+ align:start position:0%
+maybe cut to um again cut to a close-up
+shot that can be sort of a work around
+
+ align:start position:0%
+shot that can be sort of a work around
+ 
+
+ align:start position:0%
+shot that can be sort of a work around
+to the weird framing issue otherwise
+
+ align:start position:0%
+to the weird framing issue otherwise
+ 
+
+ align:start position:0%
+to the weird framing issue otherwise
+it's like it's really nicely
+
+ align:start position:0%
+it's like it's really nicely
+ 
+
+ align:start position:0%
+it's like it's really nicely
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+the you can see the men sponge in it pop
+
+ align:start position:0%
+the you can see the men sponge in it pop
+ 
+
+ align:start position:0%
+the you can see the men sponge in it pop
+up right there is not really the sponge
+
+ align:start position:0%
+up right there is not really the sponge
+ 
+
+ align:start position:0%
+up right there is not really the sponge
+you'd be scrubbing your back with but
+
+ align:start position:0%
+you'd be scrubbing your back with but
+ 
+
+ align:start position:0%
+you'd be scrubbing your back with but
+you can still think of it like that
+
+ align:start position:0%
+you can still think of it like that
+ 
+
+ align:start position:0%
+you can still think of it like that
+imagine both water and soap getting
+
+ align:start position:0%
+imagine both water and soap getting
+ 
+
+ align:start position:0%
+imagine both water and soap getting
+through your sponges holes except water
+
+ align:start position:0%
+through your sponges holes except water
+ 
+
+ align:start position:0%
+through your sponges holes except water
+is Wi-Fi and the soap is safe GL yeah so
+
+ align:start position:0%
+is Wi-Fi and the soap is safe GL yeah so
+ 
+
+ align:start position:0%
+is Wi-Fi and the soap is safe GL yeah so
+here the timing of you turning on the
+
+ align:start position:0%
+here the timing of you turning on the
+ 
+
+ align:start position:0%
+here the timing of you turning on the
+water is a little bit weird cuz you turn
+
+ align:start position:0%
+water is a little bit weird cuz you turn
+ 
+
+ align:start position:0%
+water is a little bit weird cuz you turn
+it on like way after you say water and
+
+ align:start position:0%
+it on like way after you say water and
+ 
+
+ align:start position:0%
+it on like way after you say water and
+soap um and I wonder if were you
+
+ align:start position:0%
+soap um and I wonder if were you
+ 
+
+ align:start position:0%
+soap um and I wonder if were you
+planning on doing an animation for this
+
+ align:start position:0%
+planning on doing an animation for this
+ 
+
+ align:start position:0%
+planning on doing an animation for this
+section it like that imagine both water
+
+ align:start position:0%
+section it like that imagine both water
+ 
+
+ align:start position:0%
+section it like that imagine both water
+and soap getting through your sponges
+
+ align:start position:0%
+and soap getting through your sponges
+ 
+
+ align:start position:0%
+and soap getting through your sponges
+holes cuz I feel like this is a a spot
+
+ align:start position:0%
+holes cuz I feel like this is a a spot
+ 
+
+ align:start position:0%
+holes cuz I feel like this is a a spot
+where it actually would be beneficial to
+
+ align:start position:0%
+where it actually would be beneficial to
+ 
+
+ align:start position:0%
+where it actually would be beneficial to
+not even have an overlay but a
+
+ align:start position:0%
+not even have an overlay but a
+ 
+
+ align:start position:0%
+not even have an overlay but a
+completely separate animation of like a
+
+ align:start position:0%
+completely separate animation of like a
+ 
+
+ align:start position:0%
+completely separate animation of like a
+sponge with holes and like H2O and soap
+
+ align:start position:0%
+sponge with holes and like H2O and soap
+ 
+
+ align:start position:0%
+sponge with holes and like H2O and soap
+with arrows pointing like going into the
+
+ align:start position:0%
+with arrows pointing like going into the
+ 
+
+ align:start position:0%
+with arrows pointing like going into the
+sponge holes what do you think
+
+ align:start position:0%
+sponge holes what do you think
+ 
+
+ align:start position:0%
+sponge holes what do you think
+Siri yeah or just to like demonstrate
+
+ align:start position:0%
+Siri yeah or just to like demonstrate
+ 
+
+ align:start position:0%
+Siri yeah or just to like demonstrate
+that concept because you it's easier to
+
+ align:start position:0%
+that concept because you it's easier to
+ 
+
+ align:start position:0%
+that concept because you it's easier to
+understand when you read it than when
+
+ align:start position:0%
+understand when you read it than when
+ 
+
+ align:start position:0%
+understand when you read it than when
+you hear it in a couple seconds yeah and
+
+ align:start position:0%
+you hear it in a couple seconds yeah and
+ 
+
+ align:start position:0%
+you hear it in a couple seconds yeah and
+I think like the this visuals of this
+
+ align:start position:0%
+I think like the this visuals of this
+ 
+
+ align:start position:0%
+I think like the this visuals of this
+again it's a pretty
+
+ align:start position:0%
+again it's a pretty
+ 
+
+ align:start position:0%
+again it's a pretty
+long it's what it's 14 seconds it's
+
+ align:start position:0%
+long it's what it's 14 seconds it's
+ 
+
+ align:start position:0%
+long it's what it's 14 seconds it's
+actually kind of long to have the same
+
+ align:start position:0%
+actually kind of long to have the same
+ 
+
+ align:start position:0%
+actually kind of long to have the same
+sort of still
+
+ align:start position:0%
+sort of still
+ 
+
+ align:start position:0%
+sort of still
+framing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you like how it's framed it's
+
+ align:start position:0%
+um if you like how it's framed it's
+ 
+
+ align:start position:0%
+um if you like how it's framed it's
+another you could also just overlay yeah
+
+ align:start position:0%
+another you could also just overlay yeah
+ 
+
+ align:start position:0%
+another you could also just overlay yeah
+a little like a little arrow pointing in
+
+ align:start position:0%
+a little like a little arrow pointing in
+ 
+
+ align:start position:0%
+a little like a little arrow pointing in
+it's not really cuz you hold it pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+still yeah like you could just have you
+
+ align:start position:0%
+still yeah like you could just have you
+ 
+
+ align:start position:0%
+still yeah like you could just have you
+know H2O and soap with arrows pointing
+
+ align:start position:0%
+know H2O and soap with arrows pointing
+ 
+
+ align:start position:0%
+know H2O and soap with arrows pointing
+into the sponge and like coming out of
+
+ align:start position:0%
+into the sponge and like coming out of
+ 
+
+ align:start position:0%
+into the sponge and like coming out of
+the sponge get into your sponge is hold
+
+ align:start position:0%
+the sponge get into your sponge is hold
+ 
+
+ align:start position:0%
+the sponge get into your sponge is hold
+except the water is Wi-Fi and the soap
+
+ align:start position:0%
+except the water is Wi-Fi and the soap
+ 
+
+ align:start position:0%
+except the water is Wi-Fi and the soap
+is safe Bluetooth yeah but I I almost
+
+ align:start position:0%
+is safe Bluetooth yeah but I I almost
+ 
+
+ align:start position:0%
+is safe Bluetooth yeah but I I almost
+would um you can leave it in for the
+
+ align:start position:0%
+would um you can leave it in for the
+ 
+
+ align:start position:0%
+would um you can leave it in for the
+rough cut and we can see what other
+
+ align:start position:0%
+rough cut and we can see what other
+ 
+
+ align:start position:0%
+rough cut and we can see what other
+people say but the sorry the movement of
+
+ align:start position:0%
+people say but the sorry the movement of
+ 
+
+ align:start position:0%
+people say but the sorry the movement of
+that is is almost distracting because it
+
+ align:start position:0%
+that is is almost distracting because it
+ 
+
+ align:start position:0%
+that is is almost distracting because it
+has nothing to do with what you're
+
+ align:start position:0%
+has nothing to do with what you're
+ 
+
+ align:start position:0%
+has nothing to do with what you're
+saying when you're saying it right do
+
+ align:start position:0%
+saying when you're saying it right do
+ 
+
+ align:start position:0%
+saying when you're saying it right do
+you have another take of this uh all of
+
+ align:start position:0%
+you have another take of this uh all of
+ 
+
+ align:start position:0%
+you have another take of this uh all of
+them are kind of like this the exact
+
+ align:start position:0%
+them are kind of like this the exact
+ 
+
+ align:start position:0%
+them are kind of like this the exact
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+yeah there might be one when I finish
+
+ align:start position:0%
+yeah there might be one when I finish
+ 
+
+ align:start position:0%
+yeah there might be one when I finish
+talking and then turn on the water so I
+
+ align:start position:0%
+talking and then turn on the water so I
+ 
+
+ align:start position:0%
+talking and then turn on the water so I
+could use
+
+ align:start position:0%
+could use
+ 
+
+ align:start position:0%
+could use
+that cuz if you cut it right here and
+
+ align:start position:0%
+that cuz if you cut it right here and
+ 
+
+ align:start position:0%
+that cuz if you cut it right here and
+you didn't turn on the water then that
+
+ align:start position:0%
+you didn't turn on the water then that
+ 
+
+ align:start position:0%
+you didn't turn on the water then that
+would have been that would have been
+
+ align:start position:0%
+would have been that would have been
+ 
+
+ align:start position:0%
+would have been that would have been
+better I think there are versions like
+
+ align:start position:0%
+better I think there are versions like
+ 
+
+ align:start position:0%
+better I think there are versions like
+that that I can
+
+ align:start position:0%
+that that I can
+ 
+
+ align:start position:0%
+that that I can
+use and again this one like I wouldn't
+
+ align:start position:0%
+use and again this one like I wouldn't
+ 
+
+ align:start position:0%
+use and again this one like I wouldn't
+even I wouldn't do a push at all I like
+
+ align:start position:0%
+even I wouldn't do a push at all I like
+ 
+
+ align:start position:0%
+even I wouldn't do a push at all I like
+I really I really think sorry it looks a
+
+ align:start position:0%
+I really I really think sorry it looks a
+ 
+
+ align:start position:0%
+I really I really think sorry it looks a
+lot better when you do as clean
+
+ align:start position:0%
+lot better when you do as clean
+ 
+
+ align:start position:0%
+lot better when you do as clean
+transitions as you can the fractal's
+
+ align:start position:0%
+transitions as you can the fractal's
+ 
+
+ align:start position:0%
+transitions as you can the fractal's
+infinite sponginess allows it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would shave off maybe like a half
+
+ align:start position:0%
+I would shave off maybe like a half
+ 
+
+ align:start position:0%
+I would shave off maybe like a half
+second cuz you like you take a breath
+
+ align:start position:0%
+second cuz you like you take a breath
+ 
+
+ align:start position:0%
+second cuz you like you take a breath
+and then it takes like just a hair
+
+ align:start position:0%
+and then it takes like just a hair
+ 
+
+ align:start position:0%
+and then it takes like just a hair
+before you actually start talking okay I
+
+ align:start position:0%
+before you actually start talking okay I
+ 
+
+ align:start position:0%
+before you actually start talking okay I
+just snip just like the tiniest bit off
+
+ align:start position:0%
+just snip just like the tiniest bit off
+ 
+
+ align:start position:0%
+just snip just like the tiniest bit off
+of the begin those infinite
+
+ align:start position:0%
+of the begin those infinite
+ 
+
+ align:start position:0%
+of the begin those infinite
+sponginess are you planning on doing any
+
+ align:start position:0%
+sponginess are you planning on doing any
+ 
+
+ align:start position:0%
+sponginess are you planning on doing any
+animations to the side allows it to
+
+ align:start position:0%
+animations to the side allows it to
+ 
+
+ align:start position:0%
+animations to the side allows it to
+receive I probably can put them in just
+
+ align:start position:0%
+receive I probably can put them in just
+ 
+
+ align:start position:0%
+receive I probably can put them in just
+sponge there and like signals coming
+
+ align:start position:0%
+sponge there and like signals coming
+ 
+
+ align:start position:0%
+sponge there and like signals coming
+yeah yeah cuz otherwise again like nice
+
+ align:start position:0%
+yeah yeah cuz otherwise again like nice
+ 
+
+ align:start position:0%
+yeah yeah cuz otherwise again like nice
+rule of thirds but you have a bath is
+
+ align:start position:0%
+rule of thirds but you have a bath is
+ 
+
+ align:start position:0%
+rule of thirds but you have a bath is
+that like a bathroom stall yeah yeah so
+
+ align:start position:0%
+that like a bathroom stall yeah yeah so
+ 
+
+ align:start position:0%
+that like a bathroom stall yeah yeah so
+it's like a really awkward visual um but
+
+ align:start position:0%
+it's like a really awkward visual um but
+ 
+
+ align:start position:0%
+it's like a really awkward visual um but
+if it's a good background it's a good
+
+ align:start position:0%
+if it's a good background it's a good
+ 
+
+ align:start position:0%
+if it's a good background it's a good
+background if you wanted to put a
+
+ align:start position:0%
+background if you wanted to put a
+ 
+
+ align:start position:0%
+background if you wanted to put a
+picture of a m sponge receiving like
+
+ align:start position:0%
+picture of a m sponge receiving like
+ 
+
+ align:start position:0%
+picture of a m sponge receiving like
+different signals four con's invention
+
+ align:start position:0%
+different signals four con's invention
+ 
+
+ align:start position:0%
+different signals four con's invention
+antennas had to be cut for one frequency
+
+ align:start position:0%
+antennas had to be cut for one frequency
+ 
+
+ align:start position:0%
+antennas had to be cut for one frequency
+yeah so like show an old antenna and
+
+ align:start position:0%
+yeah so like show an old antenna and
+ 
+
+ align:start position:0%
+yeah so like show an old antenna and
+that was the only frequency they could
+
+ align:start position:0%
+that was the only frequency they could
+ 
+
+ align:start position:0%
+that was the only frequency they could
+operate that so yeah and like right here
+
+ align:start position:0%
+operate that so yeah and like right here
+ 
+
+ align:start position:0%
+operate that so yeah and like right here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+back so without con sponge your cell
+
+ align:start position:0%
+back so without con sponge your cell
+ 
+
+ align:start position:0%
+back so without con sponge your cell
+phone would have to look something like
+
+ align:start position:0%
+phone would have to look something like
+ 
+
+ align:start position:0%
+phone would have to look something like
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+hedgehog I would so you there's like a
+
+ align:start position:0%
+hedgehog I would so you there's like a
+ 
+
+ align:start position:0%
+hedgehog I would so you there's like a
+bit of a hesitation before you say
+
+ align:start position:0%
+bit of a hesitation before you say
+ 
+
+ align:start position:0%
+bit of a hesitation before you say
+without cone sponge and I don't even
+
+ align:start position:0%
+without cone sponge and I don't even
+ 
+
+ align:start position:0%
+without cone sponge and I don't even
+think you need the sew so I would just
+
+ align:start position:0%
+think you need the sew so I would just
+ 
+
+ align:start position:0%
+think you need the sew so I would just
+cut out the paws and the sew and cut
+
+ align:start position:0%
+cut out the paws and the sew and cut
+ 
+
+ align:start position:0%
+cut out the paws and the sew and cut
+straight to without Coen sponge okay um
+
+ align:start position:0%
+straight to without Coen sponge okay um
+ 
+
+ align:start position:0%
+straight to without Coen sponge okay um
+and then to hide that cut you can either
+
+ align:start position:0%
+and then to hide that cut you can either
+ 
+
+ align:start position:0%
+and then to hide that cut you can either
+zoom in a little bit more right there so
+
+ align:start position:0%
+zoom in a little bit more right there so
+ 
+
+ align:start position:0%
+zoom in a little bit more right there so
+okay con sponge your cell phone would
+
+ align:start position:0%
+okay con sponge your cell phone would
+ 
+
+ align:start position:0%
+okay con sponge your cell phone would
+have yeah and like for that since you're
+
+ align:start position:0%
+have yeah and like for that since you're
+ 
+
+ align:start position:0%
+have yeah and like for that since you're
+not going to have the animation I would
+
+ align:start position:0%
+not going to have the animation I would
+ 
+
+ align:start position:0%
+not going to have the animation I would
+I would frame it and zoom in to where
+
+ align:start position:0%
+I would frame it and zoom in to where
+ 
+
+ align:start position:0%
+I would frame it and zoom in to where
+it's just you all right um and the
+
+ align:start position:0%
+it's just you all right um and the
+ 
+
+ align:start position:0%
+it's just you all right um and the
+resolution's going to look a little
+
+ align:start position:0%
+resolution's going to look a little
+ 
+
+ align:start position:0%
+resolution's going to look a little
+funky but I I think it's worth a
+
+ align:start position:0%
+funky but I I think it's worth a
+ 
+
+ align:start position:0%
+funky but I I think it's worth a
+compromise um to do that and it helps
+
+ align:start position:0%
+compromise um to do that and it helps
+ 
+
+ align:start position:0%
+compromise um to do that and it helps
+lead into cuz like start leading the
+
+ align:start position:0%
+lead into cuz like start leading the
+ 
+
+ align:start position:0%
+lead into cuz like start leading the
+viewer into seeing your phone cuz it's
+
+ align:start position:0%
+viewer into seeing your phone cuz it's
+ 
+
+ align:start position:0%
+viewer into seeing your phone cuz it's
+like you're starting out with a wide
+
+ align:start position:0%
+like you're starting out with a wide
+ 
+
+ align:start position:0%
+like you're starting out with a wide
+shot and then now you're on you and then
+
+ align:start position:0%
+shot and then now you're on you and then
+ 
+
+ align:start position:0%
+shot and then now you're on you and then
+you eventually it'll be your phone and
+
+ align:start position:0%
+you eventually it'll be your phone and
+ 
+
+ align:start position:0%
+you eventually it'll be your phone and
+so it's like just a helps the narrative
+
+ align:start position:0%
+so it's like just a helps the narrative
+ 
+
+ align:start position:0%
+so it's like just a helps the narrative
+along look something like a hedgehog to
+
+ align:start position:0%
+along look something like a hedgehog to
+ 
+
+ align:start position:0%
+along look something like a hedgehog to
+rece and again I wouldn't riple I would
+
+ align:start position:0%
+rece and again I wouldn't riple I would
+ 
+
+ align:start position:0%
+rece and again I wouldn't riple I would
+just go
+
+ align:start position:0%
+just go
+ 
+
+ align:start position:0%
+just go
+straight multiple signals including the
+
+ align:start position:0%
+straight multiple signals including the
+ 
+
+ align:start position:0%
+straight multiple signals including the
+one your friends use when they call okay
+
+ align:start position:0%
+one your friends use when they call okay
+ 
+
+ align:start position:0%
+one your friends use when they call okay
+so take at that transition yeah this one
+
+ align:start position:0%
+so take at that transition yeah this one
+ 
+
+ align:start position:0%
+so take at that transition yeah this one
+you could I mean cuz it's such a
+
+ align:start position:0%
+you could I mean cuz it's such a
+ 
+
+ align:start position:0%
+you could I mean cuz it's such a
+different wait is that the end
+
+ align:start position:0%
+different wait is that the end
+ 
+
+ align:start position:0%
+different wait is that the end
+no oh oh the end of the
+
+ align:start position:0%
+no oh oh the end of the
+ 
+
+ align:start position:0%
+no oh oh the end of the
+story yeah maybe you could do a push go
+
+ align:start position:0%
+story yeah maybe you could do a push go
+ 
+
+ align:start position:0%
+story yeah maybe you could do a push go
+later proved that only fractal but it's
+
+ align:start position:0%
+later proved that only fractal but it's
+ 
+
+ align:start position:0%
+later proved that only fractal but it's
+still part of the same story so I I I
+
+ align:start position:0%
+still part of the same story so I I I
+ 
+
+ align:start position:0%
+still part of the same story so I I I
+would say just do a clean cut there too
+
+ align:start position:0%
+would say just do a clean cut there too
+ 
+
+ align:start position:0%
+would say just do a clean cut there too
+okay I like that
+
+ align:start position:0%
+okay I like that
+ 
+
+ align:start position:0%
+okay I like that
+background um but it is a little it's
+
+ align:start position:0%
+background um but it is a little it's
+ 
+
+ align:start position:0%
+background um but it is a little it's
+still a little Overexposed here too
+
+ align:start position:0%
+still a little Overexposed here too
+ 
+
+ align:start position:0%
+still a little Overexposed here too
+bring down just a touch
+
+ align:start position:0%
+bring down just a touch
+ 
+
+ align:start position:0%
+bring down just a touch
+yeah um yeah so clean transition there I
+
+ align:start position:0%
+yeah um yeah so clean transition there I
+ 
+
+ align:start position:0%
+yeah um yeah so clean transition there I
+would cut out this Gap too it's just
+
+ align:start position:0%
+would cut out this Gap too it's just
+ 
+
+ align:start position:0%
+would cut out this Gap too it's just
+like the slightest okay it's too long by
+
+ align:start position:0%
+like the slightest okay it's too long by
+ 
+
+ align:start position:0%
+like the slightest okay it's too long by
+just like the slightest amount of time
+
+ align:start position:0%
+just like the slightest amount of time
+ 
+
+ align:start position:0%
+just like the slightest amount of time
+Cohen later proved that only fractal
+
+ align:start position:0%
+Cohen later proved that only fractal
+ 
+
+ align:start position:0%
+Cohen later proved that only fractal
+shapes could work and that's actually
+
+ align:start position:0%
+shapes could work and that's actually
+ 
+
+ align:start position:0%
+shapes could work and that's actually
+what makes it read
+
+ align:start position:0%
+what makes it read
+ 
+
+ align:start position:0%
+what makes it read
+um sort of newscaster you know like have
+
+ align:start position:0%
+um sort of newscaster you know like have
+ 
+
+ align:start position:0%
+um sort of newscaster you know like have
+you ever seen the special special
+
+ align:start position:0%
+you ever seen the special special
+ 
+
+ align:start position:0%
+you ever seen the special special
+segments you know and the the reporters
+
+ align:start position:0%
+segments you know and the the reporters
+ 
+
+ align:start position:0%
+segments you know and the the reporters
+like on their couch and they're
+
+ align:start position:0%
+like on their couch and they're
+ 
+
+ align:start position:0%
+like on their couch and they're
+like and then this person did this so
+
+ align:start position:0%
+like and then this person did this so
+ 
+
+ align:start position:0%
+like and then this person did this so
+it's it's just like this tiny little
+
+ align:start position:0%
+it's it's just like this tiny little
+ 
+
+ align:start position:0%
+it's it's just like this tiny little
+gaps that make it read that way but if
+
+ align:start position:0%
+gaps that make it read that way but if
+ 
+
+ align:start position:0%
+gaps that make it read that way but if
+you get rid of it then it'll be a lot
+
+ align:start position:0%
+you get rid of it then it'll be a lot
+ 
+
+ align:start position:0%
+you get rid of it then it'll be a lot
+more natural with such a wide range of
+
+ align:start position:0%
+more natural with such a wide range of
+ 
+
+ align:start position:0%
+more natural with such a wide range of
+frequencies today millions of wireless
+
+ align:start position:0%
+frequencies today millions of wireless
+ 
+
+ align:start position:0%
+frequencies today millions of wireless
+communication devices including laptops
+
+ align:start position:0%
+communication devices including laptops
+ 
+
+ align:start position:0%
+communication devices including laptops
+and barcode scanners used Cohen's
+
+ align:start position:0%
+and barcode scanners used Cohen's
+ 
+
+ align:start position:0%
+and barcode scanners used Cohen's
+fractal antenna Cohen's genius invention
+
+ align:start position:0%
+fractal antenna Cohen's genius invention
+ 
+
+ align:start position:0%
+fractal antenna Cohen's genius invention
+however was not the first application of
+
+ align:start position:0%
+however was not the first application of
+ 
+
+ align:start position:0%
+however was not the first application of
+fractals in the world so I'm going to
+
+ align:start position:0%
+fractals in the world so I'm going to
+ 
+
+ align:start position:0%
+fractals in the world so I'm going to
+change that audio as well cuz I think
+
+ align:start position:0%
+change that audio as well cuz I think
+ 
+
+ align:start position:0%
+change that audio as well cuz I think
+that was too Grand and I I have other
+
+ align:start position:0%
+that was too Grand and I I have other
+ 
+
+ align:start position:0%
+that was too Grand and I I have other
+versions that may work better okay I
+
+ align:start position:0%
+versions that may work better okay I
+ 
+
+ align:start position:0%
+versions that may work better okay I
+like this uh camera slow pan off
+
+ align:start position:0%
+like this uh camera slow pan off
+ 
+
+ align:start position:0%
+like this uh camera slow pan off
+actually I yeah we did another version
+
+ align:start position:0%
+actually I yeah we did another version
+ 
+
+ align:start position:0%
+actually I yeah we did another version
+which had also this pan it wasn't as
+
+ align:start position:0%
+which had also this pan it wasn't as
+ 
+
+ align:start position:0%
+which had also this pan it wasn't as
+good but um I said the next sentence
+
+ align:start position:0%
+good but um I said the next sentence
+ 
+
+ align:start position:0%
+good but um I said the next sentence
+after that so it sounds more natural so
+
+ align:start position:0%
+after that so it sounds more natural so
+ 
+
+ align:start position:0%
+after that so it sounds more natural so
+I'm going to see if I
+
+ align:start position:0%
+I'm going to see if I
+ 
+
+ align:start position:0%
+I'm going to see if I
+can trade off the visual for better do
+
+ align:start position:0%
+can trade off the visual for better do
+ 
+
+ align:start position:0%
+can trade off the visual for better do
+you do
+
+ align:start position:0%
+you do
+ 
+
+ align:start position:0%
+you do
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+sorry uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is why this transition is a
+
+ align:start position:0%
+okay so this is why this transition is a
+ 
+
+ align:start position:0%
+okay so this is why this transition is a
+little bit funny here the speed at which
+
+ align:start position:0%
+little bit funny here the speed at which
+ 
+
+ align:start position:0%
+little bit funny here the speed at which
+you're moving the camera when you pan
+
+ align:start position:0%
+you're moving the camera when you pan
+ 
+
+ align:start position:0%
+you're moving the camera when you pan
+off is way faster than when you pan down
+
+ align:start position:0%
+off is way faster than when you pan down
+ 
+
+ align:start position:0%
+off is way faster than when you pan down
+on to you okay so what you could do is
+
+ align:start position:0%
+on to you okay so what you could do is
+ 
+
+ align:start position:0%
+on to you okay so what you could do is
+cut this clip into two and speed up the
+
+ align:start position:0%
+cut this clip into two and speed up the
+ 
+
+ align:start position:0%
+cut this clip into two and speed up the
+first part like you did earlier also is
+
+ align:start position:0%
+first part like you did earlier also is
+ 
+
+ align:start position:0%
+first part like you did earlier also is
+this broccoli it is broccoli there's a
+
+ align:start position:0%
+this broccoli it is broccoli there's a
+ 
+
+ align:start position:0%
+this broccoli it is broccoli there's a
+girl in um then stata I didn't know that
+
+ align:start position:0%
+girl in um then stata I didn't know that
+ 
+
+ align:start position:0%
+girl in um then stata I didn't know that
+was broccoli it looked like bags of
+
+ align:start position:0%
+was broccoli it looked like bags of
+ 
+
+ align:start position:0%
+was broccoli it looked like bags of
+seeds or something and maybe it look
+
+ align:start position:0%
+seeds or something and maybe it look
+ 
+
+ align:start position:0%
+seeds or something and maybe it look
+like broccoli enough like looks like
+
+ align:start position:0%
+like broccoli enough like looks like
+ 
+
+ align:start position:0%
+like broccoli enough like looks like
+cauliflower turns out Nature
+
+ align:start position:0%
+cauliflower turns out Nature
+ 
+
+ align:start position:0%
+cauliflower turns out Nature
+has um it actually may be cauliflower I
+
+ align:start position:0%
+has um it actually may be cauliflower I
+ 
+
+ align:start position:0%
+has um it actually may be cauliflower I
+think I've confused the words when I was
+
+ align:start position:0%
+think I've confused the words when I was
+ 
+
+ align:start position:0%
+think I've confused the words when I was
+filming it so
+
+ align:start position:0%
+filming it so
+ 
+
+ align:start position:0%
+filming it so
+um yeah oh I'm movie I hate
+
+ align:start position:0%
+um yeah oh I'm movie I hate
+ 
+
+ align:start position:0%
+um yeah oh I'm movie I hate
+you okay okay so if you just press here
+
+ align:start position:0%
+you okay okay so if you just press here
+ 
+
+ align:start position:0%
+you okay okay so if you just press here
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+would I mean it's indistinguishable and
+
+ align:start position:0%
+would I mean it's indistinguishable and
+ 
+
+ align:start position:0%
+would I mean it's indistinguishable and
+it looks like bags of stuff almost
+
+ align:start position:0%
+it looks like bags of stuff almost
+ 
+
+ align:start position:0%
+it looks like bags of stuff almost
+um I can still like insert just an image
+
+ align:start position:0%
+um I can still like insert just an image
+ 
+
+ align:start position:0%
+um I can still like insert just an image
+of broccoli so I don't today millions of
+
+ align:start position:0%
+of broccoli so I don't today millions of
+ 
+
+ align:start position:0%
+of broccoli so I don't today millions of
+wireless communication devices including
+
+ align:start position:0%
+wireless communication devices including
+ 
+
+ align:start position:0%
+wireless communication devices including
+laptops and barcode scanners use Cohen's
+
+ align:start position:0%
+laptops and barcode scanners use Cohen's
+ 
+
+ align:start position:0%
+laptops and barcode scanners use Cohen's
+fractal antenna col's genius invention
+
+ align:start position:0%
+fractal antenna col's genius invention
+ 
+
+ align:start position:0%
+fractal antenna col's genius invention
+however was not the first application of
+
+ align:start position:0%
+however was not the first application of
+ 
+
+ align:start position:0%
+however was not the first application of
+fractals in the world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the pan just needs to happen sooner
+
+ align:start position:0%
+yeah the pan just needs to happen sooner
+ 
+
+ align:start position:0%
+yeah the pan just needs to happen sooner
+okay if I would even like speed the pan
+
+ align:start position:0%
+okay if I would even like speed the pan
+ 
+
+ align:start position:0%
+okay if I would even like speed the pan
+off mhm and then speed up the pan down
+
+ align:start position:0%
+off mhm and then speed up the pan down
+ 
+
+ align:start position:0%
+off mhm and then speed up the pan down
+got it right cuz it's like you're
+
+ align:start position:0%
+got it right cuz it's like you're
+ 
+
+ align:start position:0%
+got it right cuz it's like you're
+waiting for the camera to get to to move
+
+ align:start position:0%
+waiting for the camera to get to to move
+ 
+
+ align:start position:0%
+waiting for the camera to get to to move
+off of you K's genius invention however
+
+ align:start position:0%
+off of you K's genius invention however
+ 
+
+ align:start position:0%
+off of you K's genius invention however
+was not the first application of
+
+ align:start position:0%
+was not the first application of
+ 
+
+ align:start position:0%
+was not the first application of
+fractals in the world are you planning
+
+ align:start position:0%
+fractals in the world are you planning
+ 
+
+ align:start position:0%
+fractals in the world are you planning
+on re-shooting any of this for sure
+
+ align:start position:0%
+on re-shooting any of this for sure
+ 
+
+ align:start position:0%
+on re-shooting any of this for sure
+turns out Nature has been doing it the
+
+ align:start position:0%
+turns out Nature has been doing it the
+ 
+
+ align:start position:0%
+turns out Nature has been doing it the
+whole time some SCS like I can one and
+
+ align:start position:0%
+whole time some SCS like I can one and
+ 
+
+ align:start position:0%
+whole time some SCS like I can one and
+the one in theal favors the most
+
+ align:start position:0%
+the one in theal favors the most
+ 
+
+ align:start position:0%
+the one in theal favors the most
+efficient in East Campus um I don't
+
+ align:start position:0%
+efficient in East Campus um I don't
+ 
+
+ align:start position:0%
+efficient in East Campus um I don't
+think that do that fine yeah organisms
+
+ align:start position:0%
+think that do that fine yeah organisms
+ 
+
+ align:start position:0%
+think that do that fine yeah organisms
+often of a fractal shape for example the
+
+ align:start position:0%
+often of a fractal shape for example the
+ 
+
+ align:start position:0%
+often of a fractal shape for example the
+spiral fractal is present in broccoli
+
+ align:start position:0%
+spiral fractal is present in broccoli
+ 
+
+ align:start position:0%
+spiral fractal is present in broccoli
+seashells and H yeah cuz I I think
+
+ align:start position:0%
+seashells and H yeah cuz I I think
+ 
+
+ align:start position:0%
+seashells and H yeah cuz I I think
+especially with this one I mean go ahead
+
+ align:start position:0%
+especially with this one I mean go ahead
+ 
+
+ align:start position:0%
+especially with this one I mean go ahead
+oh I know okay so the broccoli that I
+
+ align:start position:0%
+oh I know okay so the broccoli that I
+ 
+
+ align:start position:0%
+oh I know okay so the broccoli that I
+think the BR the spiral fractles are
+
+ align:start position:0%
+think the BR the spiral fractles are
+ 
+
+ align:start position:0%
+think the BR the spiral fractles are
+most president it's like Romanesco
+
+ align:start position:0%
+most president it's like Romanesco
+ 
+
+ align:start position:0%
+most president it's like Romanesco
+broccoli or something like that that and
+
+ align:start position:0%
+broccoli or something like that that and
+ 
+
+ align:start position:0%
+broccoli or something like that that and
+so like it's a specific type it's a
+
+ align:start position:0%
+so like it's a specific type it's a
+ 
+
+ align:start position:0%
+so like it's a specific type it's a
+specific type and so people might be
+
+ align:start position:0%
+specific type and so people might be
+ 
+
+ align:start position:0%
+specific type and so people might be
+confused when then like look at their
+
+ align:start position:0%
+confused when then like look at their
+ 
+
+ align:start position:0%
+confused when then like look at their
+normal broccoli and like I would show a
+
+ align:start position:0%
+normal broccoli and like I would show a
+ 
+
+ align:start position:0%
+normal broccoli and like I would show a
+picture of the Romanesco broccoli
+
+ align:start position:0%
+picture of the Romanesco broccoli
+ 
+
+ align:start position:0%
+picture of the Romanesco broccoli
+especially cuz I don't think this is
+
+ align:start position:0%
+especially cuz I don't think this is
+ 
+
+ align:start position:0%
+especially cuz I don't think this is
+called like I think this is bags of
+
+ align:start position:0%
+called like I think this is bags of
+ 
+
+ align:start position:0%
+called like I think this is bags of
+barley or Cotton Almost um that would
+
+ align:start position:0%
+barley or Cotton Almost um that would
+ 
+
+ align:start position:0%
+barley or Cotton Almost um that would
+make more sense it's also why the person
+
+ align:start position:0%
+make more sense it's also why the person
+ 
+
+ align:start position:0%
+make more sense it's also why the person
+is up there yeah um and I I think also
+
+ align:start position:0%
+is up there yeah um and I I think also
+ 
+
+ align:start position:0%
+is up there yeah um and I I think also
+it just like doesn't really oh my gosh
+
+ align:start position:0%
+it just like doesn't really oh my gosh
+ 
+
+ align:start position:0%
+it just like doesn't really oh my gosh
+it doesn't look like a fractal whereas
+
+ align:start position:0%
+it doesn't look like a fractal whereas
+ 
+
+ align:start position:0%
+it doesn't look like a fractal whereas
+the the broccoli actually there are
+
+ align:start position:0%
+the the broccoli actually there are
+ 
+
+ align:start position:0%
+the the broccoli actually there are
+visualizations of it where it actually
+
+ align:start position:0%
+visualizations of it where it actually
+ 
+
+ align:start position:0%
+visualizations of it where it actually
+looks like oh I can identify this as a
+
+ align:start position:0%
+looks like oh I can identify this as a
+ 
+
+ align:start position:0%
+looks like oh I can identify this as a
+fractal okay and so it'll just like
+
+ align:start position:0%
+fractal okay and so it'll just like
+ 
+
+ align:start position:0%
+fractal okay and so it'll just like
+it'll be reassuring for your viewer when
+
+ align:start position:0%
+it'll be reassuring for your viewer when
+ 
+
+ align:start position:0%
+it'll be reassuring for your viewer when
+they can see the picture of the broccoli
+
+ align:start position:0%
+they can see the picture of the broccoli
+ 
+
+ align:start position:0%
+they can see the picture of the broccoli
+and be like oh I can totally see how
+
+ align:start position:0%
+and be like oh I can totally see how
+ 
+
+ align:start position:0%
+and be like oh I can totally see how
+that's a fractal rather than be like
+
+ align:start position:0%
+that's a fractal rather than be like
+ 
+
+ align:start position:0%
+that's a fractal rather than be like
+squinting at your background and be like
+
+ align:start position:0%
+squinting at your background and be like
+ 
+
+ align:start position:0%
+squinting at your background and be like
+is that like did I learn anything from
+
+ align:start position:0%
+is that like did I learn anything from
+ 
+
+ align:start position:0%
+is that like did I learn anything from
+this video type thing if you're going to
+
+ align:start position:0%
+this video type thing if you're going to
+ 
+
+ align:start position:0%
+this video type thing if you're going to
+reshoot this part and um like if you
+
+ align:start position:0%
+reshoot this part and um like if you
+ 
+
+ align:start position:0%
+reshoot this part and um like if you
+can't get it this weekend that's okay
+
+ align:start position:0%
+can't get it this weekend that's okay
+ 
+
+ align:start position:0%
+can't get it this weekend that's okay
+remember you still have Wednesday to do
+
+ align:start position:0%
+remember you still have Wednesday to do
+ 
+
+ align:start position:0%
+remember you still have Wednesday to do
+it it mhm
+
+ align:start position:0%
+it it mhm
+ 
+
+ align:start position:0%
+it it mhm
+um I would be careful about the way
+
+ align:start position:0%
+um I would be careful about the way
+ 
+
+ align:start position:0%
+um I would be careful about the way
+you're emphasizing words it's kind of
+
+ align:start position:0%
+you're emphasizing words it's kind of
+ 
+
+ align:start position:0%
+you're emphasizing words it's kind of
+falling a little into the Trap of what
+
+ align:start position:0%
+falling a little into the Trap of what
+ 
+
+ align:start position:0%
+falling a little into the Trap of what
+George was saying about how news
+
+ align:start position:0%
+George was saying about how news
+ 
+
+ align:start position:0%
+George was saying about how news
+presenters emphasize every third word
+
+ align:start position:0%
+presenters emphasize every third word
+ 
+
+ align:start position:0%
+presenters emphasize every third word
+just to sound sort of they're
+
+ align:start position:0%
+just to sound sort of they're
+ 
+
+ align:start position:0%
+just to sound sort of they're
+emphasizing important thoughts but they
+
+ align:start position:0%
+emphasizing important thoughts but they
+ 
+
+ align:start position:0%
+emphasizing important thoughts but they
+don't really make sense where they're
+
+ align:start position:0%
+don't really make sense where they're
+ 
+
+ align:start position:0%
+don't really make sense where they're
+emphasizing the words right um so I
+
+ align:start position:0%
+emphasizing the words right um so I
+ 
+
+ align:start position:0%
+emphasizing the words right um so I
+would just uh try try a few different
+
+ align:start position:0%
+would just uh try try a few different
+ 
+
+ align:start position:0%
+would just uh try try a few different
+types of deliveries one where you're
+
+ align:start position:0%
+types of deliveries one where you're
+ 
+
+ align:start position:0%
+types of deliveries one where you're
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+other word on purpose and then you know
+
+ align:start position:0%
+other word on purpose and then you know
+ 
+
+ align:start position:0%
+other word on purpose and then you know
+do something like completely exaggerated
+
+ align:start position:0%
+do something like completely exaggerated
+ 
+
+ align:start position:0%
+do something like completely exaggerated
+and then try one where you're sort of
+
+ align:start position:0%
+and then try one where you're sort of
+ 
+
+ align:start position:0%
+and then try one where you're sort of
+more natural tone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking I think that's how I usually
+
+ align:start position:0%
+talking I think that's how I usually
+ 
+
+ align:start position:0%
+talking I think that's how I usually
+present like even in real life the whole
+
+ align:start position:0%
+present like even in real life the whole
+ 
+
+ align:start position:0%
+present like even in real life the whole
+time and not just with
+
+ align:start position:0%
+time and not just with
+ 
+
+ align:start position:0%
+time and not just with
+snow fractals in the
+
+ align:start position:0%
+snow fractals in the
+ 
+
+ align:start position:0%
+snow fractals in the
+world remember that you're remember the
+
+ align:start position:0%
+world remember that you're remember the
+ 
+
+ align:start position:0%
+world remember that you're remember the
+e8th grade PhD thing you're talking for
+
+ align:start position:0%
+e8th grade PhD thing you're talking for
+ 
+
+ align:start position:0%
+e8th grade PhD thing you're talking for
+eighth graders but you're not talking
+
+ align:start position:0%
+eighth graders but you're not talking
+ 
+
+ align:start position:0%
+eighth graders but you're not talking
+necessarily to a 10-year-old right so
+
+ align:start position:0%
+necessarily to a 10-year-old right so
+ 
+
+ align:start position:0%
+necessarily to a 10-year-old right so
+how would you say this line turns out
+
+ align:start position:0%
+how would you say this line turns out
+ 
+
+ align:start position:0%
+how would you say this line turns out
+Nature has been doing it the whole time
+
+ align:start position:0%
+Nature has been doing it the whole time
+ 
+
+ align:start position:0%
+Nature has been doing it the whole time
+how would you say that line to like your
+
+ align:start position:0%
+how would you say that line to like your
+ 
+
+ align:start position:0%
+how would you say that line to like your
+professor I mean I wouldn't say this
+
+ align:start position:0%
+professor I mean I wouldn't say this
+ 
+
+ align:start position:0%
+professor I mean I wouldn't say this
+line to my professor um how would you
+
+ align:start position:0%
+line to my professor um how would you
+ 
+
+ align:start position:0%
+line to my professor um how would you
+say that line to uh to Jamie turns out
+
+ align:start position:0%
+say that line to uh to Jamie turns out
+ 
+
+ align:start position:0%
+say that line to uh to Jamie turns out
+Nature has been doing it the whole
+
+ align:start position:0%
+Nature has been doing it the whole
+ 
+
+ align:start position:0%
+Nature has been doing it the whole
+time yeah that's a little bit different
+
+ align:start position:0%
+time yeah that's a little bit different
+ 
+
+ align:start position:0%
+time yeah that's a little bit different
+like turns out Nature's been doing it
+
+ align:start position:0%
+like turns out Nature's been doing it
+ 
+
+ align:start position:0%
+like turns out Nature's been doing it
+the whole time um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I mean it's such a subtle Nuance but
+
+ align:start position:0%
+or I mean it's such a subtle Nuance but
+ 
+
+ align:start position:0%
+or I mean it's such a subtle Nuance but
+it's just something about like laptops
+
+ align:start position:0%
+it's just something about like laptops
+ 
+
+ align:start position:0%
+it's just something about like laptops
+and barcode scanners use Cohen's fractal
+
+ align:start position:0%
+and barcode scanners use Cohen's fractal
+ 
+
+ align:start position:0%
+and barcode scanners use Cohen's fractal
+antenna Cohen's genius invention however
+
+ align:start position:0%
+antenna Cohen's genius invention however
+ 
+
+ align:start position:0%
+antenna Cohen's genius invention however
+was not the first application of fractal
+
+ align:start position:0%
+was not the first application of fractal
+ 
+
+ align:start position:0%
+was not the first application of fractal
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world turns out Nature has been doing it
+
+ align:start position:0%
+world turns out Nature has been doing it
+ 
+
+ align:start position:0%
+world turns out Nature has been doing it
+the whole time I think it's the way you
+
+ align:start position:0%
+the whole time I think it's the way you
+ 
+
+ align:start position:0%
+the whole time I think it's the way you
+say time Nature has been doing it the
+
+ align:start position:0%
+say time Nature has been doing it the
+ 
+
+ align:start position:0%
+say time Nature has been doing it the
+whole time okay I mean it's okay to say
+
+ align:start position:0%
+whole time okay I mean it's okay to say
+ 
+
+ align:start position:0%
+whole time okay I mean it's okay to say
+the whole whole time but it it reads
+
+ align:start position:0%
+the whole whole time but it it reads
+ 
+
+ align:start position:0%
+the whole whole time but it it reads
+like a little Reading Rainbow when the
+
+ align:start position:0%
+like a little Reading Rainbow when the
+ 
+
+ align:start position:0%
+like a little Reading Rainbow when the
+intonation is like that um but again
+
+ align:start position:0%
+intonation is like that um but again
+ 
+
+ align:start position:0%
+intonation is like that um but again
+maybe that's just my personal taste I in
+
+ align:start position:0%
+maybe that's just my personal taste I in
+ 
+
+ align:start position:0%
+maybe that's just my personal taste I in
+general I think your enthusiasm is
+
+ align:start position:0%
+general I think your enthusiasm is
+ 
+
+ align:start position:0%
+general I think your enthusiasm is
+really really good like you're taking a
+
+ align:start position:0%
+really really good like you're taking a
+ 
+
+ align:start position:0%
+really really good like you're taking a
+subject that's inherently a little bit
+
+ align:start position:0%
+subject that's inherently a little bit
+ 
+
+ align:start position:0%
+subject that's inherently a little bit
+hard to visualize it's a little bit
+
+ align:start position:0%
+hard to visualize it's a little bit
+ 
+
+ align:start position:0%
+hard to visualize it's a little bit
+tedious and because you have this
+
+ align:start position:0%
+tedious and because you have this
+ 
+
+ align:start position:0%
+tedious and because you have this
+enthusiastic delivery it's a lot easier
+
+ align:start position:0%
+enthusiastic delivery it's a lot easier
+ 
+
+ align:start position:0%
+enthusiastic delivery it's a lot easier
+to follow along with you which is good
+
+ align:start position:0%
+to follow along with you which is good
+ 
+
+ align:start position:0%
+to follow along with you which is good
+so don't lose any of that energy for
+
+ align:start position:0%
+so don't lose any of that energy for
+ 
+
+ align:start position:0%
+so don't lose any of that energy for
+sure not just with snowflakes natural
+
+ align:start position:0%
+sure not just with snowflakes natural
+ 
+
+ align:start position:0%
+sure not just with snowflakes natural
+selection favors the most efficient
+
+ align:start position:0%
+selection favors the most efficient
+ 
+
+ align:start position:0%
+selection favors the most efficient
+systems and organisms often of a fractal
+
+ align:start position:0%
+systems and organisms often of a fractal
+ 
+
+ align:start position:0%
+systems and organisms often of a fractal
+shape for example the spiral fractal is
+
+ align:start position:0%
+shape for example the spiral fractal is
+ 
+
+ align:start position:0%
+shape for example the spiral fractal is
+present in broccoli
+
+ align:start position:0%
+present in broccoli
+ 
+
+ align:start position:0%
+present in broccoli
+seashells yeah and hurricanes if you
+
+ align:start position:0%
+seashells yeah and hurricanes if you
+ 
+
+ align:start position:0%
+seashells yeah and hurricanes if you
+re-shoot this just make sure that you're
+
+ align:start position:0%
+re-shoot this just make sure that you're
+ 
+
+ align:start position:0%
+re-shoot this just make sure that you're
+framed more in the center and there's
+
+ align:start position:0%
+framed more in the center and there's
+ 
+
+ align:start position:0%
+framed more in the center and there's
+enough room above you to accommodate for
+
+ align:start position:0%
+enough room above you to accommodate for
+ 
+
+ align:start position:0%
+enough room above you to accommodate for
+the animations and this is actually
+
+ align:start position:0%
+the animations and this is actually
+ 
+
+ align:start position:0%
+the animations and this is actually
+something that you could probably if you
+
+ align:start position:0%
+something that you could probably if you
+ 
+
+ align:start position:0%
+something that you could probably if you
+had to you could do on your own you just
+
+ align:start position:0%
+had to you could do on your own you just
+ 
+
+ align:start position:0%
+had to you could do on your own you just
+set up the tripod and flip the screen
+
+ align:start position:0%
+set up the tripod and flip the screen
+ 
+
+ align:start position:0%
+set up the tripod and flip the screen
+around you so you could see you wouldn't
+
+ align:start position:0%
+around you so you could see you wouldn't
+ 
+
+ align:start position:0%
+around you so you could see you wouldn't
+have the pan down but um that's okay the
+
+ align:start position:0%
+have the pan down but um that's okay the
+ 
+
+ align:start position:0%
+have the pan down but um that's okay the
+fractal Tre is relatively easy to
+
+ align:start position:0%
+fractal Tre is relatively easy to
+ 
+
+ align:start position:0%
+fractal Tre is relatively easy to
+program and can be used to study river
+
+ align:start position:0%
+program and can be used to study river
+ 
+
+ align:start position:0%
+program and can be used to study river
+systems blood vessels and lightning
+
+ align:start position:0%
+systems blood vessels and lightning
+ 
+
+ align:start position:0%
+systems blood vessels and lightning
+bolts so many yeah I definitely don't
+
+ align:start position:0%
+bolts so many yeah I definitely don't
+ 
+
+ align:start position:0%
+bolts so many yeah I definitely don't
+think there was enough space there but
+
+ align:start position:0%
+think there was enough space there but
+ 
+
+ align:start position:0%
+think there was enough space there but
+um I wasn't the one
+
+ align:start position:0%
+um I wasn't the one
+ 
+
+ align:start position:0%
+um I wasn't the one
+directing the other thing the other
+
+ align:start position:0%
+directing the other thing the other
+ 
+
+ align:start position:0%
+directing the other thing the other
+thing is like if you end up filming this
+
+ align:start position:0%
+thing is like if you end up filming this
+ 
+
+ align:start position:0%
+thing is like if you end up filming this
+part on your own um you don't
+
+ align:start position:0%
+part on your own um you don't
+ 
+
+ align:start position:0%
+part on your own um you don't
+necessarily have to have a pan down you
+
+ align:start position:0%
+necessarily have to have a pan down you
+ 
+
+ align:start position:0%
+necessarily have to have a pan down you
+could just do a push down transition
+
+ align:start position:0%
+could just do a push down transition
+ 
+
+ align:start position:0%
+could just do a push down transition
+that's where like I feel like a
+
+ align:start position:0%
+that's where like I feel like a
+ 
+
+ align:start position:0%
+that's where like I feel like a
+transition would be okay because you've
+
+ align:start position:0%
+transition would be okay because you've
+ 
+
+ align:start position:0%
+transition would be okay because you've
+got the uh the camera tilt up
+
+ align:start position:0%
+got the uh the camera tilt up
+ 
+
+ align:start position:0%
+got the uh the camera tilt up
+previously um
+
+ align:start position:0%
+previously um
+ 
+
+ align:start position:0%
+previously um
+if you do this again when you look I
+
+ align:start position:0%
+if you do this again when you look I
+ 
+
+ align:start position:0%
+if you do this again when you look I
+would just look up instead of going like
+
+ align:start position:0%
+would just look up instead of going like
+ 
+
+ align:start position:0%
+would just look up instead of going like
+this CU it's like a little bit awkward
+
+ align:start position:0%
+this CU it's like a little bit awkward
+ 
+
+ align:start position:0%
+this CU it's like a little bit awkward
+to go like that okay the natural systems
+
+ align:start position:0%
+to go like that okay the natural systems
+ 
+
+ align:start position:0%
+to go like that okay the natural systems
+previously thought off limits to
+
+ align:start position:0%
+previously thought off limits to
+ 
+
+ align:start position:0%
+previously thought off limits to
+mathematicians can now be explained in
+
+ align:start position:0%
+mathematicians can now be explained in
+ 
+
+ align:start position:0%
+mathematicians can now be explained in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+fractals um I wouldn't move off of the
+
+ align:start position:0%
+fractals um I wouldn't move off of the
+ 
+
+ align:start position:0%
+fractals um I wouldn't move off of the
+scene so quickly like give it one more
+
+ align:start position:0%
+scene so quickly like give it one more
+ 
+
+ align:start position:0%
+scene so quickly like give it one more
+beat before you transition and can be
+
+ align:start position:0%
+beat before you transition and can be
+ 
+
+ align:start position:0%
+beat before you transition and can be
+used to study river systems blood
+
+ align:start position:0%
+used to study river systems blood
+ 
+
+ align:start position:0%
+used to study river systems blood
+vessels and lightning bolts so many
+
+ align:start position:0%
+vessels and lightning bolts so many
+ 
+
+ align:start position:0%
+vessels and lightning bolts so many
+natural systems previously thought off
+
+ align:start position:0%
+natural systems previously thought off
+ 
+
+ align:start position:0%
+natural systems previously thought off
+tree is relatively easy to program and
+
+ align:start position:0%
+tree is relatively easy to program and
+ 
+
+ align:start position:0%
+tree is relatively easy to program and
+can be used to study river systems blood
+
+ align:start position:0%
+can be used to study river systems blood
+ 
+
+ align:start position:0%
+can be used to study river systems blood
+vessels and lightning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bolts and I would wish should this
+
+ align:start position:0%
+bolts and I would wish should this
+ 
+
+ align:start position:0%
+bolts and I would wish should this
+completely I don't previously thought
+
+ align:start position:0%
+completely I don't previously thought
+ 
+
+ align:start position:0%
+completely I don't previously thought
+off limits to mathematicians can now be
+
+ align:start position:0%
+off limits to mathematicians can now be
+ 
+
+ align:start position:0%
+off limits to mathematicians can now be
+explained in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fractals yeah and right here um I would
+
+ align:start position:0%
+fractals yeah and right here um I would
+ 
+
+ align:start position:0%
+fractals yeah and right here um I would
+just cut to immediately you talking cuz
+
+ align:start position:0%
+just cut to immediately you talking cuz
+ 
+
+ align:start position:0%
+just cut to immediately you talking cuz
+the there's like a little bit too long
+
+ align:start position:0%
+the there's like a little bit too long
+ 
+
+ align:start position:0%
+the there's like a little bit too long
+of a pause before you start and bump up
+
+ align:start position:0%
+of a pause before you start and bump up
+ 
+
+ align:start position:0%
+of a pause before you start and bump up
+the um yeah I'll do a voice over for
+
+ align:start position:0%
+the um yeah I'll do a voice over for
+ 
+
+ align:start position:0%
+the um yeah I'll do a voice over for
+this one because there's a lot of to
+
+ align:start position:0%
+this one because there's a lot of to
+ 
+
+ align:start position:0%
+this one because there's a lot of to
+learn Nature's Best Practices and then
+
+ align:start position:0%
+learn Nature's Best Practices and then
+ 
+
+ align:start position:0%
+learn Nature's Best Practices and then
+apply them to solve real world problems
+
+ align:start position:0%
+apply them to solve real world problems
+ 
+
+ align:start position:0%
+apply them to solve real world problems
+much like CO's antenna revolutionized
+
+ align:start position:0%
+much like CO's antenna revolutionized
+ 
+
+ align:start position:0%
+much like CO's antenna revolutionized
+the field of telecommunications other
+
+ align:start position:0%
+the field of telecommunications other
+ 
+
+ align:start position:0%
+the field of telecommunications other
+fral research is changing medicine
+
+ align:start position:0%
+fral research is changing medicine
+ 
+
+ align:start position:0%
+fral research is changing medicine
+weather prediction and building design
+
+ align:start position:0%
+weather prediction and building design
+ 
+
+ align:start position:0%
+weather prediction and building design
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+at and everywhere in the world look
+
+ align:start position:0%
+at and everywhere in the world look
+ 
+
+ align:start position:0%
+at and everywhere in the world look
+around you
+
+ align:start position:0%
+around you
+ 
+
+ align:start position:0%
+around you
+for when you say look around you I would
+
+ align:start position:0%
+for when you say look around you I would
+ 
+
+ align:start position:0%
+for when you say look around you I would
+actually cut back to a closeup of you
+
+ align:start position:0%
+actually cut back to a closeup of you
+ 
+
+ align:start position:0%
+actually cut back to a closeup of you
+look around you what beautiful do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see and just end it a little bit sooner
+
+ align:start position:0%
+see and just end it a little bit sooner
+ 
+
+ align:start position:0%
+see and just end it a little bit sooner
+yeah it's a good start really good start
+
+ align:start position:0%
+yeah it's a good start really good start
+ 
+
+ align:start position:0%
+yeah it's a good start really good start
+um A good rule of thumb we never
+
+ align:start position:0%
+um A good rule of thumb we never
+ 
+
+ align:start position:0%
+um A good rule of thumb we never
+mentioned this um in the editing lecture
+
+ align:start position:0%
+mentioned this um in the editing lecture
+ 
+
+ align:start position:0%
+mentioned this um in the editing lecture
+but like you want to give the end of a
+
+ align:start position:0%
+but like you want to give the end of a
+ 
+
+ align:start position:0%
+but like you want to give the end of a
+scene a little room to breathe so people
+
+ align:start position:0%
+scene a little room to breathe so people
+ 
+
+ align:start position:0%
+scene a little room to breathe so people
+can process like what's going on and
+
+ align:start position:0%
+can process like what's going on and
+ 
+
+ align:start position:0%
+can process like what's going on and
+then at the beginning of a scene you
+
+ align:start position:0%
+then at the beginning of a scene you
+ 
+
+ align:start position:0%
+then at the beginning of a scene you
+want it to be like one or two frames
+
+ align:start position:0%
+want it to be like one or two frames
+ 
+
+ align:start position:0%
+want it to be like one or two frames
+before you start talking so it's like
+
+ align:start position:0%
+before you start talking so it's like
+ 
+
+ align:start position:0%
+before you start talking so it's like
+almost immediately your voice yeah
+
+ align:start position:0%
+almost immediately your voice yeah
+ 
+
+ align:start position:0%
+almost immediately your voice yeah
+that's actually that's a very good point
+
+ align:start position:0%
+that's actually that's a very good point
+ 
+
+ align:start position:0%
+that's actually that's a very good point
+and I should have brought that up during
+
+ align:start position:0%
+and I should have brought that up during
+ 
+
+ align:start position:0%
+and I should have brought that up during
+the editing lecture but I I feel like
+
+ align:start position:0%
+the editing lecture but I I feel like
+ 
+
+ align:start position:0%
+the editing lecture but I I feel like
+the tendency is to do the opposite with
+
+ align:start position:0%
+the tendency is to do the opposite with
+ 
+
+ align:start position:0%
+the tendency is to do the opposite with
+what you've done with the scenes here
+
+ align:start position:0%
+what you've done with the scenes here
+ 
+
+ align:start position:0%
+what you've done with the scenes here
+where you end too soon and then you wait
+
+ align:start position:0%
+where you end too soon and then you wait
+ 
+
+ align:start position:0%
+where you end too soon and then you wait
+too long before you start the next scene
+
+ align:start position:0%
+too long before you start the next scene
+ 
+
+ align:start position:0%
+too long before you start the next scene
+it's like it's counterintuitive but it
+
+ align:start position:0%
+it's like it's counterintuitive but it
+ 
+
+ align:start position:0%
+it's like it's counterintuitive but it
+like it makes it flow better yeah okay
+
+ align:start position:0%
+like it makes it flow better yeah okay
+ 
+
+ align:start position:0%
+like it makes it flow better yeah okay
+but yeah I I mean you're in really good
+
+ align:start position:0%
+but yeah I I mean you're in really good
+ 
+
+ align:start position:0%
+but yeah I I mean you're in really good
+shape for in terms of like pacing um
+
+ align:start position:0%
+shape for in terms of like pacing um
+ 
+
+ align:start position:0%
+shape for in terms of like pacing um
+what you need to do before next week M
+
+ align:start position:0%
+what you need to do before next week M
+ 
+
+ align:start position:0%
+what you need to do before next week M
+so I think that this point it's a matter
+
+ align:start position:0%
+so I think that this point it's a matter
+ 
+
+ align:start position:0%
+so I think that this point it's a matter
+of getting the animations in and the
+
+ align:start position:0%
+of getting the animations in and the
+ 
+
+ align:start position:0%
+of getting the animations in and the
+music um but yeah
+
+ align:start position:0%
+music um but yeah
+ 
+
+ align:start position:0%
+music um but yeah
+fine thank you you're definitely like
+
+ align:start position:0%
+fine thank you you're definitely like
+ 
+
+ align:start position:0%
+fine thank you you're definitely like
+well well on your way on the right track
+
+ align:start position:0%
+well well on your way on the right track
+ 
+
+ align:start position:0%
+well well on your way on the right track
+like to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done this chair
+
+ align:start position:0%
+done this chair
+ 
+
+ align:start position:0%
+done this chair
+is new bear I like leaning back back to
+
+ align:start position:0%
+is new bear I like leaning back back to
+ 
+
+ align:start position:0%
+is new bear I like leaning back back to
+stretch it's like I'm still leaning I'm
+
+ align:start position:0%
+stretch it's like I'm still leaning I'm
+ 
+
+ align:start position:0%
+stretch it's like I'm still leaning I'm
+still leaning this entire room is kind
+
+ align:start position:0%
+still leaning this entire room is kind
+ 
+
+ align:start position:0%
+still leaning this entire room is kind
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half are you guys
+
+ align:start position:0%
+half are you guys
+ 
+
+ align:start position:0%
+half are you guys
+doing thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you I'm choosing which on are choos
+
+ align:start position:0%
+you I'm choosing which on are choos
+ 
+
+ align:start position:0%
+you I'm choosing which on are choos
+you're still cutting and pasting the
+
+ align:start position:0%
+you're still cutting and pasting the
+ 
+
+ align:start position:0%
+you're still cutting and pasting the
+script no no
+
+ align:start position:0%
+script no no
+ 
+
+ align:start position:0%
+script no no
+no oh your your scenes together yeah you
+
+ align:start position:0%
+no oh your your scenes together yeah you
+ 
+
+ align:start position:0%
+no oh your your scenes together yeah you
+guys finished filming everything right
+
+ align:start position:0%
+guys finished filming everything right
+ 
+
+ align:start position:0%
+guys finished filming everything right
+this is nice framing thank you good job
+
+ align:start position:0%
+this is nice framing thank you good job
+ 
+
+ align:start position:0%
+this is nice framing thank you good job
+see you should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know now if you did it again what one
+
+ align:start position:0%
+know now if you did it again what one
+ 
+
+ align:start position:0%
+know now if you did it again what one
+cool thing that you can do and I'm not
+
+ align:start position:0%
+cool thing that you can do and I'm not
+ 
+
+ align:start position:0%
+cool thing that you can do and I'm not
+saying that you need to because
+
+ align:start position:0%
+saying that you need to because
+ 
+
+ align:start position:0%
+saying that you need to because
+um this is fine um but if you had moved
+
+ align:start position:0%
+um this is fine um but if you had moved
+ 
+
+ align:start position:0%
+um this is fine um but if you had moved
+him to the center of that picture so
+
+ align:start position:0%
+him to the center of that picture so
+ 
+
+ align:start position:0%
+him to the center of that picture so
+that and you moved close enough then
+
+ align:start position:0%
+that and you moved close enough then
+ 
+
+ align:start position:0%
+that and you moved close enough then
+this image could basically fill the
+
+ align:start position:0%
+this image could basically fill the
+ 
+
+ align:start position:0%
+this image could basically fill the
+entire background and you wouldn't have
+
+ align:start position:0%
+entire background and you wouldn't have
+ 
+
+ align:start position:0%
+entire background and you wouldn't have
+this weird Gap right oh okay I don't
+
+ align:start position:0%
+this weird Gap right oh okay I don't
+ 
+
+ align:start position:0%
+this weird Gap right oh okay I don't
+know if the image was big enough to do
+
+ align:start position:0%
+know if the image was big enough to do
+ 
+
+ align:start position:0%
+know if the image was big enough to do
+that compared to the size of his the
+
+ align:start position:0%
+that compared to the size of his the
+ 
+
+ align:start position:0%
+that compared to the size of his the
+image was big enough I didn't want to do
+
+ align:start position:0%
+image was big enough I didn't want to do
+ 
+
+ align:start position:0%
+image was big enough I didn't want to do
+that because I didn't want to look like
+
+ align:start position:0%
+that because I didn't want to look like
+ 
+
+ align:start position:0%
+that because I didn't want to look like
+he was in green screen the oh oh that's
+
+ align:start position:0%
+he was in green screen the oh oh that's
+ 
+
+ align:start position:0%
+he was in green screen the oh oh that's
+that's a good point actually um that is
+
+ align:start position:0%
+that's a good point actually um that is
+ 
+
+ align:start position:0%
+that's a good point actually um that is
+a good point that's the reason why I I I
+
+ align:start position:0%
+a good point that's the reason why I I I
+ 
+
+ align:start position:0%
+a good point that's the reason why I I I
+I am I have a bit of OCD so I can't
+
+ align:start position:0%
+I am I have a bit of OCD so I can't
+ 
+
+ align:start position:0%
+I am I have a bit of OCD so I can't
+stand the words on the right
+
+ align:start position:0%
+stand the words on the right
+ 
+
+ align:start position:0%
+stand the words on the right
+actually but I'm fine it's okay it's
+
+ align:start position:0%
+actually but I'm fine it's okay it's
+ 
+
+ align:start position:0%
+actually but I'm fine it's okay it's
+okay yeah it kind of it's blurry enough
+
+ align:start position:0%
+okay yeah it kind of it's blurry enough
+ 
+
+ align:start position:0%
+okay yeah it kind of it's blurry enough
+that it's not distracting because I'm
+
+ align:start position:0%
+that it's not distracting because I'm
+ 
+
+ align:start position:0%
+that it's not distracting because I'm
+not trying to read the words because I
+
+ align:start position:0%
+not trying to read the words because I
+ 
+
+ align:start position:0%
+not trying to read the words because I
+don't think they're like readable yeah I
+
+ align:start position:0%
+don't think they're like readable yeah I
+ 
+
+ align:start position:0%
+don't think they're like readable yeah I
+wish I could have given you guys lights
+
+ align:start position:0%
+wish I could have given you guys lights
+ 
+
+ align:start position:0%
+wish I could have given you guys lights
+cuz that's what happens when you rely on
+
+ align:start position:0%
+cuz that's what happens when you rely on
+ 
+
+ align:start position:0%
+cuz that's what happens when you rely on
+the fluorescent you get some weird
+
+ align:start position:0%
+the fluorescent you get some weird
+ 
+
+ align:start position:0%
+the fluorescent you get some weird
+shadows on your face from overhead yeah
+
+ align:start position:0%
+shadows on your face from overhead yeah
+ 
+
+ align:start position:0%
+shadows on your face from overhead yeah
+um but it looks nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you guys have any specific questions
+
+ align:start position:0%
+do you guys have any specific questions
+ 
+
+ align:start position:0%
+do you guys have any specific questions
+right now or should we just let you let
+
+ align:start position:0%
+right now or should we just let you let
+ 
+
+ align:start position:0%
+right now or should we just let you let
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+work I'm planning to do animation on
+
+ align:start position:0%
+work I'm planning to do animation on
+ 
+
+ align:start position:0%
+work I'm planning to do animation on
+like some uh wait on I didn't see you
+
+ align:start position:0%
+like some uh wait on I didn't see you
+ 
+
+ align:start position:0%
+like some uh wait on I didn't see you
+guys film anything oh I guess I saw you
+
+ align:start position:0%
+guys film anything oh I guess I saw you
+ 
+
+ align:start position:0%
+guys film anything oh I guess I saw you
+guys film that stuff like I I plan to
+
+ align:start position:0%
+guys film that stuff like I I plan to
+ 
+
+ align:start position:0%
+guys film that stuff like I I plan to
+put animation here but yeah that's
+
+ align:start position:0%
+put animation here but yeah that's
+ 
+
+ align:start position:0%
+put animation here but yeah that's
+definitely is that okay that's a good
+
+ align:start position:0%
+definitely is that okay that's a good
+ 
+
+ align:start position:0%
+definitely is that okay that's a good
+surface yeah as long as you keep the
+
+ align:start position:0%
+surface yeah as long as you keep the
+ 
+
+ align:start position:0%
+surface yeah as long as you keep the
+pictures small enough mhm and you can
+
+ align:start position:0%
+pictures small enough mhm and you can
+ 
+
+ align:start position:0%
+pictures small enough mhm and you can
+adjust the size like even after you've
+
+ align:start position:0%
+adjust the size like even after you've
+ 
+
+ align:start position:0%
+adjust the size like even after you've
+done it in After Effects and you've like
+
+ align:start position:0%
+done it in After Effects and you've like
+ 
+
+ align:start position:0%
+done it in After Effects and you've like
+exported it or transferred over to
+
+ align:start position:0%
+exported it or transferred over to
+ 
+
+ align:start position:0%
+exported it or transferred over to
+Premiere you can change the size of
+
+ align:start position:0%
+Premiere you can change the size of
+ 
+
+ align:start position:0%
+Premiere you can change the size of
+it how much faster would that be did you
+
+ align:start position:0%
+it how much faster would that be did you
+ 
+
+ align:start position:0%
+it how much faster would that be did you
+guys use the vi that depends on the
+
+ align:start position:0%
+guys use the vi that depends on the
+ 
+
+ align:start position:0%
+guys use the vi that depends on the
+number of students in the school did you
+
+ align:start position:0%
+number of students in the school did you
+ 
+
+ align:start position:0%
+number of students in the school did you
+use the Vixie let's say there 500
+
+ align:start position:0%
+use the Vixie let's say there 500
+ 
+
+ align:start position:0%
+use the Vixie let's say there 500
+students and we're looking for one Canon
+
+ align:start position:0%
+students and we're looking for one Canon
+ 
+
+ align:start position:0%
+students and we're looking for one Canon
+8 minutes in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theing students so it's like a lot of
+
+ align:start position:0%
+theing students so it's like a lot of
+ 
+
+ align:start position:0%
+theing students so it's like a lot of
+natural 160 minutes with the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it looks really nice I think the
+
+ align:start position:0%
+yeah it looks really nice I think the
+ 
+
+ align:start position:0%
+yeah it looks really nice I think the
+white bed sheets help cuz they're like a
+
+ align:start position:0%
+white bed sheets help cuz they're like a
+ 
+
+ align:start position:0%
+white bed sheets help cuz they're like a
+natural reflector
+
+ align:start position:0%
+natural reflector
+ 
+
+ align:start position:0%
+natural reflector
+yeah really white so they all natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and there was a lot of stuff here
+
+ align:start position:0%
+like and there was a lot of stuff here
+ 
+
+ align:start position:0%
+like and there was a lot of stuff here
+then I threw it away I was like ah cut
+
+ align:start position:0%
+then I threw it away I was like ah cut
+ 
+
+ align:start position:0%
+then I threw it away I was like ah cut
+steady is too
+
+ align:start position:0%
+steady is too
+ 
+
+ align:start position:0%
+steady is too
+much the only thing is um you might want
+
+ align:start position:0%
+much the only thing is um you might want
+ 
+
+ align:start position:0%
+much the only thing is um you might want
+to bring the exposure down just a tiny
+
+ align:start position:0%
+to bring the exposure down just a tiny
+ 
+
+ align:start position:0%
+to bring the exposure down just a tiny
+bit cuz the whites here are really
+
+ align:start position:0%
+bit cuz the whites here are really
+ 
+
+ align:start position:0%
+bit cuz the whites here are really
+peeking pretty high but everything from
+
+ align:start position:0%
+peeking pretty high but everything from
+ 
+
+ align:start position:0%
+peeking pretty high but everything from
+here is so nicely lit that I'm almost
+
+ align:start position:0%
+here is so nicely lit that I'm almost
+ 
+
+ align:start position:0%
+here is so nicely lit that I'm almost
+inclined to just like ah forget it just
+
+ align:start position:0%
+inclined to just like ah forget it just
+ 
+
+ align:start position:0%
+inclined to just like ah forget it just
+keep it the way it
+
+ align:start position:0%
+keep it the way it
+ 
+
+ align:start position:0%
+keep it the way it
+is how do you do that exposure on the in
+
+ align:start position:0%
+is how do you do that exposure on the in
+ 
+
+ align:start position:0%
+is how do you do that exposure on the in
+the editing software you should there
+
+ align:start position:0%
+the editing software you should there
+ 
+
+ align:start position:0%
+the editing software you should there
+should be a way to just like bring down
+
+ align:start position:0%
+should be a way to just like bring down
+ 
+
+ align:start position:0%
+should be a way to just like bring down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+exposure what are you using for your I
+
+ align:start position:0%
+exposure what are you using for your I
+ 
+
+ align:start position:0%
+exposure what are you using for your I
+think the simplest way would be to tap
+
+ align:start position:0%
+think the simplest way would be to tap
+ 
+
+ align:start position:0%
+think the simplest way would be to tap
+the bright eara and then it would
+
+ align:start position:0%
+the bright eara and then it would
+ 
+
+ align:start position:0%
+the bright eara and then it would
+de me on the we the video camera like
+
+ align:start position:0%
+de me on the we the video camera like
+ 
+
+ align:start position:0%
+de me on the we the video camera like
+like on the video itself on the in the
+
+ align:start position:0%
+like on the video itself on the in the
+ 
+
+ align:start position:0%
+like on the video itself on the in the
+touch screen you just tap your shirt
+
+ align:start position:0%
+touch screen you just tap your shirt
+ 
+
+ align:start position:0%
+touch screen you just tap your shirt
+then you will have dimed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on nice job guys
+
+ align:start position:0%
+on nice job guys
+ 
+
+ align:start position:0%
+on nice job guys
+M you just kind of disappeared for a
+
+ align:start position:0%
+M you just kind of disappeared for a
+ 
+
+ align:start position:0%
+M you just kind of disappeared for a
+couple days that you came back with
+
+ align:start position:0%
+couple days that you came back with
+ 
+
+ align:start position:0%
+couple days that you came back with
+really good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+footage I let you guys can just work
+
+ align:start position:0%
+footage I let you guys can just work
+ 
+
+ align:start position:0%
+footage I let you guys can just work
+we'll stay out of the way if you if you
+
+ align:start position:0%
+we'll stay out of the way if you if you
+ 
+
+ align:start position:0%
+we'll stay out of the way if you if you
+have any questions then
+
+ align:start position:0%
+have any questions then
+ 
+
+ align:start position:0%
+have any questions then
+and just go for it yeah and I'll be able
+
+ align:start position:0%
+and just go for it yeah and I'll be able
+ 
+
+ align:start position:0%
+and just go for it yeah and I'll be able
+to answer like any editing questions you
+
+ align:start position:0%
+to answer like any editing questions you
+ 
+
+ align:start position:0%
+to answer like any editing questions you
+have in Premiere this one I would zoom
+
+ align:start position:0%
+have in Premiere this one I would zoom
+ 
+
+ align:start position:0%
+have in Premiere this one I would zoom
+in on you a little bit more cuz you're a
+
+ align:start position:0%
+in on you a little bit more cuz you're a
+ 
+
+ align:start position:0%
+in on you a little bit more cuz you're a
+little low so I would crop in like that
+
+ align:start position:0%
+little low so I would crop in like that
+ 
+
+ align:start position:0%
+little low so I would crop in like that
+yeah to where the top of the frame is
+
+ align:start position:0%
+yeah to where the top of the frame is
+ 
+
+ align:start position:0%
+yeah to where the top of the frame is
+just above your head usually do the rule
+
+ align:start position:0%
+just above your head usually do the rule
+ 
+
+ align:start position:0%
+just above your head usually do the rule
+of thirds with like eyes rather than the
+
+ align:start position:0%
+of thirds with like eyes rather than the
+ 
+
+ align:start position:0%
+of thirds with like eyes rather than the
+top of head type thing and so if you
+
+ align:start position:0%
+top of head type thing and so if you
+ 
+
+ align:start position:0%
+top of head type thing and so if you
+look at your eyes they're kind of in the
+
+ align:start position:0%
+look at your eyes they're kind of in the
+ 
+
+ align:start position:0%
+look at your eyes they're kind of in the
+middle um and so you want to adjust it
+
+ align:start position:0%
+middle um and so you want to adjust it
+ 
+
+ align:start position:0%
+middle um and so you want to adjust it
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little yeah like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closer will let you guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work all for today
+
+ align:start position:0%
+work all for today
+ 
+
+ align:start position:0%
+work all for today
+actually what time is it it's 10 till 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now what the problem is is
+
+ align:start position:0%
+okay okay so now what the problem is is
+ 
+
+ align:start position:0%
+okay okay so now what the problem is is
+illustrator defaults to a brush which we
+
+ align:start position:0%
+illustrator defaults to a brush which we
+ 
+
+ align:start position:0%
+illustrator defaults to a brush which we
+don't want because that will mess up
+
+ align:start position:0%
+don't want because that will mess up
+ 
+
+ align:start position:0%
+don't want because that will mess up
+when we redraw it in After Effects so we
+
+ align:start position:0%
+when we redraw it in After Effects so we
+ 
+
+ align:start position:0%
+when we redraw it in After Effects so we
+select the arrow we want to change brush
+
+ align:start position:0%
+select the arrow we want to change brush
+ 
+
+ align:start position:0%
+select the arrow we want to change brush
+definition to
+
+ align:start position:0%
+definition to
+ 
+
+ align:start position:0%
+definition to
+basic okay um go into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stroke let's
+
+ align:start position:0%
+stroke let's
+ 
+
+ align:start position:0%
+stroke let's
+see why there not more options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you go change the caps and Corners
+
+ align:start position:0%
+there you go change the caps and Corners
+ 
+
+ align:start position:0%
+there you go change the caps and Corners
+to round so it's like nice and smooth
+
+ align:start position:0%
+to round so it's like nice and smooth
+ 
+
+ align:start position:0%
+to round so it's like nice and smooth
+like it looks like a brush basically
+
+ align:start position:0%
+like it looks like a brush basically
+ 
+
+ align:start position:0%
+like it looks like a brush basically
+we're making it look like a brush
+
+ align:start position:0%
+we're making it look like a brush
+ 
+
+ align:start position:0%
+we're making it look like a brush
+without while doing a basic trick and
+
+ align:start position:0%
+without while doing a basic trick and
+ 
+
+ align:start position:0%
+without while doing a basic trick and
+then change it to like whatever weight
+
+ align:start position:0%
+then change it to like whatever weight
+ 
+
+ align:start position:0%
+then change it to like whatever weight
+you want so you want it about that you
+
+ align:start position:0%
+you want so you want it about that you
+ 
+
+ align:start position:0%
+you want so you want it about that you
+can play around like you want a super
+
+ align:start position:0%
+can play around like you want a super
+ 
+
+ align:start position:0%
+can play around like you want a super
+thick or do you want it not so thick um
+
+ align:start position:0%
+thick or do you want it not so thick um
+ 
+
+ align:start position:0%
+thick or do you want it not so thick um
+and then the last thing you need to do
+
+ align:start position:0%
+and then the last thing you need to do
+ 
+
+ align:start position:0%
+and then the last thing you need to do
+before going into After Effects
+
+ align:start position:0%
+before going into After Effects
+ 
+
+ align:start position:0%
+before going into After Effects
+is um go into this layer and so see it
+
+ align:start position:0%
+is um go into this layer and so see it
+ 
+
+ align:start position:0%
+is um go into this layer and so see it
+has like the different parts of the
+
+ align:start position:0%
+has like the different parts of the
+ 
+
+ align:start position:0%
+has like the different parts of the
+arrow you want to highlight everything
+
+ align:start position:0%
+arrow you want to highlight everything
+ 
+
+ align:start position:0%
+arrow you want to highlight everything
+click this drop down menu and click
+
+ align:start position:0%
+click this drop down menu and click
+ 
+
+ align:start position:0%
+click this drop down menu and click
+reverse order because it Stacks it from
+
+ align:start position:0%
+reverse order because it Stacks it from
+ 
+
+ align:start position:0%
+reverse order because it Stacks it from
+the last thing you drew to the first
+
+ align:start position:0%
+the last thing you drew to the first
+ 
+
+ align:start position:0%
+the last thing you drew to the first
+thing you drew and you want it to be
+
+ align:start position:0%
+thing you drew and you want it to be
+ 
+
+ align:start position:0%
+thing you drew and you want it to be
+first thing you drew to last thing you
+
+ align:start position:0%
+first thing you drew to last thing you
+ 
+
+ align:start position:0%
+first thing you drew to last thing you
+drew okay
+
+ align:start position:0%
+drew okay
+ 
+
+ align:start position:0%
+drew okay
+um then you want to save
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and we'll just save it in documents
+
+ align:start position:0%
+this and we'll just save it in documents
+ 
+
+ align:start position:0%
+this and we'll just save it in documents
+for now
+
+ align:start position:0%
+for now
+ 
+
+ align:start position:0%
+for now
+okay and then you open up after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effects if it will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open go this a nice pan Joshua this nice
+
+ align:start position:0%
+open go this a nice pan Joshua this nice
+ 
+
+ align:start position:0%
+open go this a nice pan Joshua this nice
+camera work sorry
+
+ align:start position:0%
+camera work sorry
+ 
+
+ align:start position:0%
+camera work sorry
+what oh I yeah I H I held the tripod to
+
+ align:start position:0%
+what oh I yeah I H I held the tripod to
+ 
+
+ align:start position:0%
+what oh I yeah I H I held the tripod to
+your advice it's good I look really
+
+ align:start position:0%
+your advice it's good I look really
+ 
+
+ align:start position:0%
+your advice it's good I look really
+stupid though but it's really steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I didn't actually hold like that I knew
+
+ align:start position:0%
+I didn't actually hold like that I knew
+ 
+
+ align:start position:0%
+I didn't actually hold like that I knew
+that be it'll be bit okay well if after
+
+ align:start position:0%
+that be it'll be bit okay well if after
+ 
+
+ align:start position:0%
+that be it'll be bit okay well if after
+effects will open and not give us the
+
+ align:start position:0%
+effects will open and not give us the
+ 
+
+ align:start position:0%
+effects will open and not give us the
+color wheel of death then I can show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can also
+
+ align:start position:0%
+I can also
+ 
+
+ align:start position:0%
+I can also
+just oh I can get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I have my computer right it's like
+
+ align:start position:0%
+it I have my computer right it's like
+ 
+
+ align:start position:0%
+it I have my computer right it's like
+open it's about half an hour of video I
+
+ align:start position:0%
+open it's about half an hour of video I
+ 
+
+ align:start position:0%
+open it's about half an hour of video I
+think I don't know okay after effects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hooray okay so we're going to import our
+
+ align:start position:0%
+hooray okay so we're going to import our
+ 
+
+ align:start position:0%
+hooray okay so we're going to import our
+composition as a composition mhm
+
+ align:start position:0%
+composition as a composition mhm
+ 
+
+ align:start position:0%
+composition as a composition mhm
+Right double click it
+
+ align:start position:0%
+Right double click it
+ 
+
+ align:start position:0%
+Right double click it
+um I'm going to set it to a white
+
+ align:start position:0%
+um I'm going to set it to a white
+ 
+
+ align:start position:0%
+um I'm going to set it to a white
+background just so we can see things and
+
+ align:start position:0%
+background just so we can see things and
+ 
+
+ align:start position:0%
+background just so we can see things and
+depending on if you do it on the black
+
+ align:start position:0%
+depending on if you do it on the black
+ 
+
+ align:start position:0%
+depending on if you do it on the black
+portion you might want to set the
+
+ align:start position:0%
+portion you might want to set the
+ 
+
+ align:start position:0%
+portion you might want to set the
+background to Black and have the arrow
+
+ align:start position:0%
+background to Black and have the arrow
+ 
+
+ align:start position:0%
+background to Black and have the arrow
+be in white like depending on what how
+
+ align:start position:0%
+be in white like depending on what how
+ 
+
+ align:start position:0%
+be in white like depending on what how
+you want it to
+
+ align:start position:0%
+you want it to
+ 
+
+ align:start position:0%
+you want it to
+look okay so this is the fun part so
+
+ align:start position:0%
+look okay so this is the fun part so
+ 
+
+ align:start position:0%
+look okay so this is the fun part so
+we're going to turn the arrow layer into
+
+ align:start position:0%
+we're going to turn the arrow layer into
+ 
+
+ align:start position:0%
+we're going to turn the arrow layer into
+shapes and then what we're going to do
+
+ align:start position:0%
+shapes and then what we're going to do
+ 
+
+ align:start position:0%
+shapes and then what we're going to do
+is we're going to
+
+ align:start position:0%
+is we're going to
+ 
+
+ align:start position:0%
+is we're going to
+add a trim paths and basically what that
+
+ align:start position:0%
+add a trim paths and basically what that
+ 
+
+ align:start position:0%
+add a trim paths and basically what that
+means is it's going to draw the line for
+
+ align:start position:0%
+means is it's going to draw the line for
+ 
+
+ align:start position:0%
+means is it's going to draw the line for
+you and then under trim paths we're
+
+ align:start position:0%
+you and then under trim paths we're
+ 
+
+ align:start position:0%
+you and then under trim paths we're
+going to trim multiple shapes
+
+ align:start position:0%
+going to trim multiple shapes
+ 
+
+ align:start position:0%
+going to trim multiple shapes
+individually because that means um so if
+
+ align:start position:0%
+individually because that means um so if
+ 
+
+ align:start position:0%
+individually because that means um so if
+you do it
+
+ align:start position:0%
+you do it
+ 
+
+ align:start position:0%
+you do it
+simultaneously um it'll draw the arrow
+
+ align:start position:0%
+simultaneously um it'll draw the arrow
+ 
+
+ align:start position:0%
+simultaneously um it'll draw the arrow
+like both lines at the same time so
+
+ align:start position:0%
+like both lines at the same time so
+ 
+
+ align:start position:0%
+like both lines at the same time so
+it'll start drawing the long arrow and
+
+ align:start position:0%
+it'll start drawing the long arrow and
+ 
+
+ align:start position:0%
+it'll start drawing the long arrow and
+like The Arrow Head at the same time and
+
+ align:start position:0%
+like The Arrow Head at the same time and
+ 
+
+ align:start position:0%
+like The Arrow Head at the same time and
+we don't want that so change it to
+
+ align:start position:0%
+we don't want that so change it to
+ 
+
+ align:start position:0%
+we don't want that so change it to
+individually um and then wherever you
+
+ align:start position:0%
+individually um and then wherever you
+ 
+
+ align:start position:0%
+individually um and then wherever you
+want it to start you turn the end down
+
+ align:start position:0%
+want it to start you turn the end down
+ 
+
+ align:start position:0%
+want it to start you turn the end down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero set your key frame and say we want
+
+ align:start position:0%
+zero set your key frame and say we want
+ 
+
+ align:start position:0%
+zero set your key frame and say we want
+it to draw in 2 seconds you turn the end
+
+ align:start position:0%
+it to draw in 2 seconds you turn the end
+ 
+
+ align:start position:0%
+it to draw in 2 seconds you turn the end
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+100 and you go back to the beginning and
+
+ align:start position:0%
+100 and you go back to the beginning and
+ 
+
+ align:start position:0%
+100 and you go back to the beginning and
+you press
+
+ align:start position:0%
+you press
+ 
+
+ align:start position:0%
+you press
+space and then I'll draw the
+
+ align:start position:0%
+space and then I'll draw the
+ 
+
+ align:start position:0%
+space and then I'll draw the
+arrow oh in like as much time oh okay is
+
+ align:start position:0%
+arrow oh in like as much time oh okay is
+ 
+
+ align:start position:0%
+arrow oh in like as much time oh okay is
+that like what you wanted to do yeah
+
+ align:start position:0%
+that like what you wanted to do yeah
+ 
+
+ align:start position:0%
+that like what you wanted to do yeah
+yeah okay I want to do arrows yeah and
+
+ align:start position:0%
+yeah okay I want to do arrows yeah and
+ 
+
+ align:start position:0%
+yeah okay I want to do arrows yeah and
+then you can change it like different
+
+ align:start position:0%
+then you can change it like different
+ 
+
+ align:start position:0%
+then you can change it like different
+like there's some lines like I like um
+
+ align:start position:0%
+like there's some lines like I like um
+ 
+
+ align:start position:0%
+like there's some lines like I like um
+writing out handwriting a lot in
+
+ align:start position:0%
+writing out handwriting a lot in
+ 
+
+ align:start position:0%
+writing out handwriting a lot in
+animations um in my videos and so like
+
+ align:start position:0%
+animations um in my videos and so like
+ 
+
+ align:start position:0%
+animations um in my videos and so like
+for example if you want it to pause on
+
+ align:start position:0%
+for example if you want it to pause on
+ 
+
+ align:start position:0%
+for example if you want it to pause on
+this store mhm um you can set it okay so
+
+ align:start position:0%
+this store mhm um you can set it okay so
+ 
+
+ align:start position:0%
+this store mhm um you can set it okay so
+it starts it's like a
+
+ align:start position:0%
+it starts it's like a
+ 
+
+ align:start position:0%
+it starts it's like a
+35% um so you can set a key frame there
+
+ align:start position:0%
+35% um so you can set a key frame there
+ 
+
+ align:start position:0%
+35% um so you can set a key frame there
+at 35% and then you can
+
+ align:start position:0%
+at 35% and then you can
+ 
+
+ align:start position:0%
+at 35% and then you can
+like set another one later on also at
+
+ align:start position:0%
+like set another one later on also at
+ 
+
+ align:start position:0%
+like set another one later on also at
+35% and then what it does is it like
+
+ align:start position:0%
+35% and then what it does is it like
+ 
+
+ align:start position:0%
+35% and then what it does is it like
+pauses at the door hold holds it there
+
+ align:start position:0%
+pauses at the door hold holds it there
+ 
+
+ align:start position:0%
+pauses at the door hold holds it there
+and then it keeps going in the remaining
+
+ align:start position:0%
+and then it keeps going in the remaining
+ 
+
+ align:start position:0%
+and then it keeps going in the remaining
+time okay thank you yeah I don't know if
+
+ align:start position:0%
+time okay thank you yeah I don't know if
+ 
+
+ align:start position:0%
+time okay thank you yeah I don't know if
+you can remember all that but if you if
+
+ align:start position:0%
+you can remember all that but if you if
+ 
+
+ align:start position:0%
+you can remember all that but if you if
+you forget steps of it I can like write
+
+ align:start position:0%
+you forget steps of it I can like write
+ 
+
+ align:start position:0%
+you forget steps of it I can like write
+yeah write me and I'll redo it okay
+
+ align:start position:0%
+yeah write me and I'll redo it okay
+ 
+
+ align:start position:0%
+yeah write me and I'll redo it okay
+thanks
+
+ align:start position:0%
+thanks
+ 
+
+ align:start position:0%
+thanks
+yeah let me know if there's anything
+
+ align:start position:0%
+yeah let me know if there's anything
+ 
+
+ align:start position:0%
+yeah let me know if there's anything
+else you know thank you
\ No newline at end of file
diff --git a/kuht5Nv3Iio.txt b/kuht5Nv3Iio.txt
new file mode 100644
index 0000000000000000000000000000000000000000..98298582636c327d87cbf2ac26cf728e3b57d23d
--- /dev/null
+++ b/kuht5Nv3Iio.txt
@@ -0,0 +1,1027 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu in this demonstration we're
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+ 
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+going to show the influence of an
+
+ align:start position:0%
+going to show the influence of an
+ 
+
+ align:start position:0%
+going to show the influence of an
+optical fiber on the polarization
+
+ align:start position:0%
+optical fiber on the polarization
+ 
+
+ align:start position:0%
+optical fiber on the polarization
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+light this case we're going to use a
+
+ align:start position:0%
+light this case we're going to use a
+ 
+
+ align:start position:0%
+light this case we're going to use a
+normal single mode fiber the
+
+ align:start position:0%
+normal single mode fiber the
+ 
+
+ align:start position:0%
+normal single mode fiber the
+setup is as shown here we have a helium
+
+ align:start position:0%
+setup is as shown here we have a helium
+ 
+
+ align:start position:0%
+setup is as shown here we have a helium
+neon laser here's the beam from the
+
+ align:start position:0%
+neon laser here's the beam from the
+ 
+
+ align:start position:0%
+neon laser here's the beam from the
+laser we reflected by this mirror here
+
+ align:start position:0%
+laser we reflected by this mirror here
+ 
+
+ align:start position:0%
+laser we reflected by this mirror here
+then by another mirror here into a
+
+ align:start position:0%
+then by another mirror here into a
+ 
+
+ align:start position:0%
+then by another mirror here into a
+quarter wave plate and a
+
+ align:start position:0%
+quarter wave plate and a
+ 
+
+ align:start position:0%
+quarter wave plate and a
+polarizer and in this way by rotating
+
+ align:start position:0%
+polarizer and in this way by rotating
+ 
+
+ align:start position:0%
+polarizer and in this way by rotating
+the polarizer here I can select any
+
+ align:start position:0%
+the polarizer here I can select any
+ 
+
+ align:start position:0%
+the polarizer here I can select any
+linear polar ation I want in this region
+
+ align:start position:0%
+linear polar ation I want in this region
+ 
+
+ align:start position:0%
+linear polar ation I want in this region
+then what we do is we take the light
+
+ align:start position:0%
+then what we do is we take the light
+ 
+
+ align:start position:0%
+then what we do is we take the light
+from here we pass it through a short
+
+ align:start position:0%
+from here we pass it through a short
+ 
+
+ align:start position:0%
+from here we pass it through a short
+focal length lens focus it into the
+
+ align:start position:0%
+focal length lens focus it into the
+ 
+
+ align:start position:0%
+focal length lens focus it into the
+fiber to the single mode fiber over here
+
+ align:start position:0%
+fiber to the single mode fiber over here
+ 
+
+ align:start position:0%
+fiber to the single mode fiber over here
+and then the output of the fiber is
+
+ align:start position:0%
+and then the output of the fiber is
+ 
+
+ align:start position:0%
+and then the output of the fiber is
+Again columnated by another short focal
+
+ align:start position:0%
+Again columnated by another short focal
+ 
+
+ align:start position:0%
+Again columnated by another short focal
+length lens and then the output of this
+
+ align:start position:0%
+length lens and then the output of this
+ 
+
+ align:start position:0%
+length lens and then the output of this
+lens then we let go onto onto the screen
+
+ align:start position:0%
+lens then we let go onto onto the screen
+ 
+
+ align:start position:0%
+lens then we let go onto onto the screen
+so this is the basic setup now we're
+
+ align:start position:0%
+so this is the basic setup now we're
+ 
+
+ align:start position:0%
+so this is the basic setup now we're
+ready to look at polarization effects in
+
+ align:start position:0%
+ready to look at polarization effects in
+ 
+
+ align:start position:0%
+ready to look at polarization effects in
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+fibers now first we have to establish
+
+ align:start position:0%
+fibers now first we have to establish
+ 
+
+ align:start position:0%
+fibers now first we have to establish
+the state of
+
+ align:start position:0%
+the state of
+ 
+
+ align:start position:0%
+the state of
+polarization of the light going into the
+
+ align:start position:0%
+polarization of the light going into the
+ 
+
+ align:start position:0%
+polarization of the light going into the
+fiber so what I'm going to do take this
+
+ align:start position:0%
+fiber so what I'm going to do take this
+ 
+
+ align:start position:0%
+fiber so what I'm going to do take this
+polarizer and place it over
+
+ align:start position:0%
+polarizer and place it over
+ 
+
+ align:start position:0%
+polarizer and place it over
+here and then I'll take a card place it
+
+ align:start position:0%
+here and then I'll take a card place it
+ 
+
+ align:start position:0%
+here and then I'll take a card place it
+here and now I want to rotate the
+
+ align:start position:0%
+here and now I want to rotate the
+ 
+
+ align:start position:0%
+here and now I want to rotate the
+polarizer and the the axis the the white
+
+ align:start position:0%
+polarizer and the the axis the the white
+ 
+
+ align:start position:0%
+polarizer and the the axis the the white
+Arrow here indicates the transmission
+
+ align:start position:0%
+Arrow here indicates the transmission
+ 
+
+ align:start position:0%
+Arrow here indicates the transmission
+axis of the polarizer so I can rotate
+
+ align:start position:0%
+axis of the polarizer so I can rotate
+ 
+
+ align:start position:0%
+axis of the polarizer so I can rotate
+polarizer
+
+ align:start position:0%
+polarizer
+ 
+
+ align:start position:0%
+polarizer
+now and then
+
+ align:start position:0%
+now and then
+ 
+
+ align:start position:0%
+now and then
+in this region over here I have null
+
+ align:start position:0%
+in this region over here I have null
+ 
+
+ align:start position:0%
+in this region over here I have null
+which means that the state of the plane
+
+ align:start position:0%
+which means that the state of the plane
+ 
+
+ align:start position:0%
+which means that the state of the plane
+of polarization of light is orthogonal
+
+ align:start position:0%
+of polarization of light is orthogonal
+ 
+
+ align:start position:0%
+of polarization of light is orthogonal
+to this to the direction of this Arrow
+
+ align:start position:0%
+to this to the direction of this Arrow
+ 
+
+ align:start position:0%
+to this to the direction of this Arrow
+right so indeed we have plain polarized
+
+ align:start position:0%
+right so indeed we have plain polarized
+ 
+
+ align:start position:0%
+right so indeed we have plain polarized
+light as indicated by the arrow over
+
+ align:start position:0%
+light as indicated by the arrow over
+ 
+
+ align:start position:0%
+light as indicated by the arrow over
+here which is orthogonal to the one here
+
+ align:start position:0%
+here which is orthogonal to the one here
+ 
+
+ align:start position:0%
+here which is orthogonal to the one here
+all right so now we've established the
+
+ align:start position:0%
+all right so now we've established the
+ 
+
+ align:start position:0%
+all right so now we've established the
+that the state of polarization is linear
+
+ align:start position:0%
+that the state of polarization is linear
+ 
+
+ align:start position:0%
+that the state of polarization is linear
+going in to the to the fiber now let's
+
+ align:start position:0%
+going in to the to the fiber now let's
+ 
+
+ align:start position:0%
+going in to the to the fiber now let's
+look at the polarization of the light
+
+ align:start position:0%
+look at the polarization of the light
+ 
+
+ align:start position:0%
+look at the polarization of the light
+coming out of the fiber again I'm going
+
+ align:start position:0%
+coming out of the fiber again I'm going
+ 
+
+ align:start position:0%
+coming out of the fiber again I'm going
+to take the polarizer and place it over
+
+ align:start position:0%
+to take the polarizer and place it over
+ 
+
+ align:start position:0%
+to take the polarizer and place it over
+here the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output and now let's look at the spot in
+
+ align:start position:0%
+output and now let's look at the spot in
+ 
+
+ align:start position:0%
+output and now let's look at the spot in
+the in the inset here we have the spot
+
+ align:start position:0%
+the in the inset here we have the spot
+ 
+
+ align:start position:0%
+the in the inset here we have the spot
+in the inset now I'm going to rotate
+
+ align:start position:0%
+in the inset now I'm going to rotate
+ 
+
+ align:start position:0%
+in the inset now I'm going to rotate
+rotate the transmission axis of the
+
+ align:start position:0%
+rotate the transmission axis of the
+ 
+
+ align:start position:0%
+rotate the transmission axis of the
+polarizer to see what we
+
+ align:start position:0%
+polarizer to see what we
+ 
+
+ align:start position:0%
+polarizer to see what we
+have gee we have indeed plain polarized
+
+ align:start position:0%
+have gee we have indeed plain polarized
+ 
+
+ align:start position:0%
+have gee we have indeed plain polarized
+light also coming out of the fiber so we
+
+ align:start position:0%
+light also coming out of the fiber so we
+ 
+
+ align:start position:0%
+light also coming out of the fiber so we
+have plain polarized light going in and
+
+ align:start position:0%
+have plain polarized light going in and
+ 
+
+ align:start position:0%
+have plain polarized light going in and
+plain polarized light coming
+
+ align:start position:0%
+plain polarized light coming
+ 
+
+ align:start position:0%
+plain polarized light coming
+out now to
+
+ align:start position:0%
+out now to
+ 
+
+ align:start position:0%
+out now to
+demonstrate what the
+
+ align:start position:0%
+demonstrate what the
+ 
+
+ align:start position:0%
+demonstrate what the
+fiber does to the polarization in a very
+
+ align:start position:0%
+fiber does to the polarization in a very
+ 
+
+ align:start position:0%
+fiber does to the polarization in a very
+dramatic way all I have to do is is
+
+ align:start position:0%
+dramatic way all I have to do is is
+ 
+
+ align:start position:0%
+dramatic way all I have to do is is
+Twist the
+
+ align:start position:0%
+Twist the
+ 
+
+ align:start position:0%
+Twist the
+fiber by by just pushing on it and you
+
+ align:start position:0%
+fiber by by just pushing on it and you
+ 
+
+ align:start position:0%
+fiber by by just pushing on it and you
+can see that now just by applying a
+
+ align:start position:0%
+can see that now just by applying a
+ 
+
+ align:start position:0%
+can see that now just by applying a
+little stress to the fiber now I have
+
+ align:start position:0%
+little stress to the fiber now I have
+ 
+
+ align:start position:0%
+little stress to the fiber now I have
+changed the polarization because now I
+
+ align:start position:0%
+changed the polarization because now I
+ 
+
+ align:start position:0%
+changed the polarization because now I
+have light coming out of the uh of the
+
+ align:start position:0%
+have light coming out of the uh of the
+ 
+
+ align:start position:0%
+have light coming out of the uh of the
+of the polarizer while before it was it
+
+ align:start position:0%
+of the polarizer while before it was it
+ 
+
+ align:start position:0%
+of the polarizer while before it was it
+was null now again I can push the fiber
+
+ align:start position:0%
+was null now again I can push the fiber
+ 
+
+ align:start position:0%
+was null now again I can push the fiber
+around some more I can see I can change
+
+ align:start position:0%
+around some more I can see I can change
+ 
+
+ align:start position:0%
+around some more I can see I can change
+the the amount of light coming through
+
+ align:start position:0%
+the the amount of light coming through
+ 
+
+ align:start position:0%
+the the amount of light coming through
+the polarizer which means that the state
+
+ align:start position:0%
+the polarizer which means that the state
+ 
+
+ align:start position:0%
+the polarizer which means that the state
+of polarization is uh is
+
+ align:start position:0%
+of polarization is uh is
+ 
+
+ align:start position:0%
+of polarization is uh is
+changing just by simply applying simple
+
+ align:start position:0%
+changing just by simply applying simple
+ 
+
+ align:start position:0%
+changing just by simply applying simple
+stress I can apply mechanical stress
+
+ align:start position:0%
+stress I can apply mechanical stress
+ 
+
+ align:start position:0%
+stress I can apply mechanical stress
+like I'm doing now I can uh uh get the
+
+ align:start position:0%
+like I'm doing now I can uh uh get the
+ 
+
+ align:start position:0%
+like I'm doing now I can uh uh get the
+similar effect by heating the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fiber and so on so that the the state of
+
+ align:start position:0%
+fiber and so on so that the the state of
+ 
+
+ align:start position:0%
+fiber and so on so that the the state of
+polarization then can be influenced
+
+ align:start position:0%
+polarization then can be influenced
+ 
+
+ align:start position:0%
+polarization then can be influenced
+quite a bit by by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment the effect of the
+
+ align:start position:0%
+environment the effect of the
+ 
+
+ align:start position:0%
+environment the effect of the
+environment on on the fiber you can see
+
+ align:start position:0%
+environment on on the fiber you can see
+ 
+
+ align:start position:0%
+environment on on the fiber you can see
+here I can make it uh come out very
+
+ align:start position:0%
+here I can make it uh come out very
+ 
+
+ align:start position:0%
+here I can make it uh come out very
+bright through the polarizer when
+
+ align:start position:0%
+bright through the polarizer when
+ 
+
+ align:start position:0%
+bright through the polarizer when
+originally was null here we are can go
+
+ align:start position:0%
+originally was null here we are can go
+ 
+
+ align:start position:0%
+originally was null here we are can go
+null zero which it means PL polarized
+
+ align:start position:0%
+null zero which it means PL polarized
+ 
+
+ align:start position:0%
+null zero which it means PL polarized
+now uh it's some state of polarization
+
+ align:start position:0%
+now uh it's some state of polarization
+ 
+
+ align:start position:0%
+now uh it's some state of polarization
+in fact I'm going to hold it hold the
+
+ align:start position:0%
+in fact I'm going to hold it hold the
+ 
+
+ align:start position:0%
+in fact I'm going to hold it hold the
+fiber in this position and then now I'm
+
+ align:start position:0%
+fiber in this position and then now I'm
+ 
+
+ align:start position:0%
+fiber in this position and then now I'm
+going to go and I'm going to turn the
+
+ align:start position:0%
+going to go and I'm going to turn the
+ 
+
+ align:start position:0%
+going to go and I'm going to turn the
+polarizer to see indeed do I have plain
+
+ align:start position:0%
+polarizer to see indeed do I have plain
+ 
+
+ align:start position:0%
+polarizer to see indeed do I have plain
+polarized light or elliptically
+
+ align:start position:0%
+polarized light or elliptically
+ 
+
+ align:start position:0%
+polarized light or elliptically
+polarized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+light well it's elliptically polarized
+
+ align:start position:0%
+light well it's elliptically polarized
+ 
+
+ align:start position:0%
+light well it's elliptically polarized
+light because I can't I can't know it so
+
+ align:start position:0%
+light because I can't I can't know it so
+ 
+
+ align:start position:0%
+light because I can't I can't know it so
+now I have changed the state of
+
+ align:start position:0%
+now I have changed the state of
+ 
+
+ align:start position:0%
+now I have changed the state of
+polarization then from linear to to
+
+ align:start position:0%
+polarization then from linear to to
+ 
+
+ align:start position:0%
+polarization then from linear to to
+elliptical and again if I
+
+ align:start position:0%
+elliptical and again if I
+ 
+
+ align:start position:0%
+elliptical and again if I
+put uh more stress on the on the fiber
+
+ align:start position:0%
+put uh more stress on the on the fiber
+ 
+
+ align:start position:0%
+put uh more stress on the on the fiber
+let's see now what state polarization I
+
+ align:start position:0%
+let's see now what state polarization I
+ 
+
+ align:start position:0%
+let's see now what state polarization I
+get now again you can see it is
+
+ align:start position:0%
+get now again you can see it is
+ 
+
+ align:start position:0%
+get now again you can see it is
+elliptical because I can't I can't
+
+ align:start position:0%
+elliptical because I can't I can't
+ 
+
+ align:start position:0%
+elliptical because I can't I can't
+knowledge so in in conclusion then the a
+
+ align:start position:0%
+knowledge so in in conclusion then the a
+ 
+
+ align:start position:0%
+knowledge so in in conclusion then the a
+single mode a regular single mode fiber
+
+ align:start position:0%
+single mode a regular single mode fiber
+ 
+
+ align:start position:0%
+single mode a regular single mode fiber
+can change the state of polarization of
+
+ align:start position:0%
+can change the state of polarization of
+ 
+
+ align:start position:0%
+can change the state of polarization of
+light going into it into almost anything
+
+ align:start position:0%
+light going into it into almost anything
+ 
+
+ align:start position:0%
+light going into it into almost anything
+into plain polarized circular polarized
+
+ align:start position:0%
+into plain polarized circular polarized
+ 
+
+ align:start position:0%
+into plain polarized circular polarized
+elliptically polarized and this is
+
+ align:start position:0%
+elliptically polarized and this is
+ 
+
+ align:start position:0%
+elliptically polarized and this is
+influenced greatly by the environment
+
+ align:start position:0%
+influenced greatly by the environment
+ 
+
+ align:start position:0%
+influenced greatly by the environment
+that the fiber is in so it's very
+
+ align:start position:0%
+that the fiber is in so it's very
+ 
+
+ align:start position:0%
+that the fiber is in so it's very
+difficult to maintain then and a a good
+
+ align:start position:0%
+difficult to maintain then and a a good
+ 
+
+ align:start position:0%
+difficult to maintain then and a a good
+state of polarization or a known state
+
+ align:start position:0%
+state of polarization or a known state
+ 
+
+ align:start position:0%
+state of polarization or a known state
+of polarization in a single mode fiber
+
+ align:start position:0%
+of polarization in a single mode fiber
+ 
+
+ align:start position:0%
+of polarization in a single mode fiber
+because of these environmental
+
+ align:start position:0%
+because of these environmental
+ 
+
+ align:start position:0%
+because of these environmental
+disturbances if one wants to maintain
+
+ align:start position:0%
+disturbances if one wants to maintain
+ 
+
+ align:start position:0%
+disturbances if one wants to maintain
+let's say linear polarization one would
+
+ align:start position:0%
+let's say linear polarization one would
+ 
+
+ align:start position:0%
+let's say linear polarization one would
+have to use a polarization maintaining
+
+ align:start position:0%
+have to use a polarization maintaining
+ 
+
+ align:start position:0%
+have to use a polarization maintaining
+fiber
\ No newline at end of file
diff --git a/kyx2QgGkEpc.txt b/kyx2QgGkEpc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d2acb92c850219be9ab86d0b5577f9c8d42a307a
--- /dev/null
+++ b/kyx2QgGkEpc.txt
@@ -0,0 +1,6776 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I thought I would in this
+
+ align:start position:0%
+ocw.mit.edu I thought I would in this
+ 
+
+ align:start position:0%
+ocw.mit.edu I thought I would in this
+last lecture before the break uh speak
+
+ align:start position:0%
+last lecture before the break uh speak
+ 
+
+ align:start position:0%
+last lecture before the break uh speak
+about one specific
+
+ align:start position:0%
+about one specific
+ 
+
+ align:start position:0%
+about one specific
+topic
+
+ align:start position:0%
+topic
+ 
+
+ align:start position:0%
+topic
+uh it's often referred to as a fast Plus
+
+ align:start position:0%
+uh it's often referred to as a fast Plus
+ 
+
+ align:start position:0%
+uh it's often referred to as a fast Plus
+on solver so what does pon mean uh Pon
+
+ align:start position:0%
+on solver so what does pon mean uh Pon
+ 
+
+ align:start position:0%
+on solver so what does pon mean uh Pon
+means lass's equation so this is the 5
+
+ align:start position:0%
+means lass's equation so this is the 5
+ 
+
+ align:start position:0%
+means lass's equation so this is the 5
+point llan it could be some other
+
+ align:start position:0%
+point llan it could be some other
+ 
+
+ align:start position:0%
+point llan it could be some other
+discret LL Matrix but let's take the one
+
+ align:start position:0%
+discret LL Matrix but let's take the one
+ 
+
+ align:start position:0%
+discret LL Matrix but let's take the one
+we know uh so we're in two
+
+ align:start position:0%
+we know uh so we're in two
+ 
+
+ align:start position:0%
+we know uh so we're in two
+dimensions and you use the word poon's
+
+ align:start position:0%
+dimensions and you use the word poon's
+ 
+
+ align:start position:0%
+dimensions and you use the word poon's
+name instead of ll's name when there's a
+
+ align:start position:0%
+name instead of ll's name when there's a
+ 
+
+ align:start position:0%
+name instead of ll's name when there's a
+nonzero right hand side so otherwise
+
+ align:start position:0%
+nonzero right hand side so otherwise
+ 
+
+ align:start position:0%
+nonzero right hand side so otherwise
+it's a solver but
+
+ align:start position:0%
+it's a solver but
+ 
+
+ align:start position:0%
+it's a solver but
+uh here plus okay so remember that right
+
+ align:start position:0%
+uh here plus okay so remember that right
+ 
+
+ align:start position:0%
+uh here plus okay so remember that right
+hand side comes from maybe a right hand
+
+ align:start position:0%
+hand side comes from maybe a right hand
+ 
+
+ align:start position:0%
+hand side comes from maybe a right hand
+side f ofx y in the differential
+
+ align:start position:0%
+side f ofx y in the differential
+ 
+
+ align:start position:0%
+side f ofx y in the differential
+equation but it also comes from uh
+
+ align:start position:0%
+equation but it also comes from uh
+ 
+
+ align:start position:0%
+equation but it also comes from uh
+nonzero boundary conditions because
+
+ align:start position:0%
+nonzero boundary conditions because
+ 
+
+ align:start position:0%
+nonzero boundary conditions because
+nonzero boundary conditions uh when the
+
+ align:start position:0%
+nonzero boundary conditions uh when the
+ 
+
+ align:start position:0%
+nonzero boundary conditions uh when the
+Five Points hit a boundary that known
+
+ align:start position:0%
+Five Points hit a boundary that known
+ 
+
+ align:start position:0%
+Five Points hit a boundary that known
+value is moved over to the right hand
+
+ align:start position:0%
+value is moved over to the right hand
+ 
+
+ align:start position:0%
+value is moved over to the right hand
+side and becomes part of f so f F comes
+
+ align:start position:0%
+side and becomes part of f so f F comes
+ 
+
+ align:start position:0%
+side and becomes part of f so f F comes
+from the nonzero boundary conditions as
+
+ align:start position:0%
+from the nonzero boundary conditions as
+ 
+
+ align:start position:0%
+from the nonzero boundary conditions as
+well as the nonzero right hand side
+
+ align:start position:0%
+well as the nonzero right hand side
+ 
+
+ align:start position:0%
+well as the nonzero right hand side
+okay important problem but special on a
+
+ align:start position:0%
+okay important problem but special on a
+ 
+
+ align:start position:0%
+okay important problem but special on a
+square or a rectangle or a cube or a box
+
+ align:start position:0%
+square or a rectangle or a cube or a box
+ 
+
+ align:start position:0%
+square or a rectangle or a cube or a box
+so we are speaking about special
+
+ align:start position:0%
+so we are speaking about special
+ 
+
+ align:start position:0%
+so we are speaking about special
+geometry I I'll put I today
+
+ align:start position:0%
+geometry I I'll put I today
+ 
+
+ align:start position:0%
+geometry I I'll put I today
+I'll as we've been doing I'll take the
+
+ align:start position:0%
+I'll as we've been doing I'll take the
+ 
+
+ align:start position:0%
+I'll as we've been doing I'll take the
+case on a square
+
+ align:start position:0%
+case on a square
+ 
+
+ align:start position:0%
+case on a square
+and you will see that the whole idea
+
+ align:start position:0%
+and you will see that the whole idea
+ 
+
+ align:start position:0%
+and you will see that the whole idea
+would not fly if we were on some
+
+ align:start position:0%
+would not fly if we were on some
+ 
+
+ align:start position:0%
+would not fly if we were on some
+curved on an ellipse or something like
+
+ align:start position:0%
+curved on an ellipse or something like
+ 
+
+ align:start position:0%
+curved on an ellipse or something like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but a lot of problems on rectangular
+
+ align:start position:0%
+but a lot of problems on rectangular
+ 
+
+ align:start position:0%
+but a lot of problems on rectangular
+domains do appear in
+
+ align:start position:0%
+domains do appear in
+ 
+
+ align:start position:0%
+domains do appear in
+applications or we could use you know I
+
+ align:start position:0%
+applications or we could use you know I
+ 
+
+ align:start position:0%
+applications or we could use you know I
+hope you always think now
+
+ align:start position:0%
+hope you always think now
+ 
+
+ align:start position:0%
+hope you always think now
+about possible preconditioners anytime
+
+ align:start position:0%
+about possible preconditioners anytime
+ 
+
+ align:start position:0%
+about possible preconditioners anytime
+you have something fast it's a candidate
+
+ align:start position:0%
+you have something fast it's a candidate
+ 
+
+ align:start position:0%
+you have something fast it's a candidate
+to be a preconditioner for a real
+
+ align:start position:0%
+to be a preconditioner for a real
+ 
+
+ align:start position:0%
+to be a preconditioner for a real
+problem the real problem might not be on
+
+ align:start position:0%
+problem the real problem might not be on
+ 
+
+ align:start position:0%
+problem the real problem might not be on
+a square or the real problem might not
+
+ align:start position:0%
+a square or the real problem might not
+ 
+
+ align:start position:0%
+a square or the real problem might not
+have the constant coefficient that we
+
+ align:start position:0%
+have the constant coefficient that we
+ 
+
+ align:start position:0%
+have the constant coefficient that we
+have in the in the
+
+ align:start position:0%
+have in the in the
+ 
+
+ align:start position:0%
+have in the in the
+laian in that case you're not solving
+
+ align:start position:0%
+laian in that case you're not solving
+ 
+
+ align:start position:0%
+laian in that case you're not solving
+the exact problem but one that could be
+
+ align:start position:0%
+the exact problem but one that could be
+ 
+
+ align:start position:0%
+the exact problem but one that could be
+reasonably close to it okay now
+
+ align:start position:0%
+reasonably close to it okay now
+ 
+
+ align:start position:0%
+reasonably close to it okay now
+how if so we've discussed the solution
+
+ align:start position:0%
+how if so we've discussed the solution
+ 
+
+ align:start position:0%
+how if so we've discussed the solution
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+problem and actually I have a little
+
+ align:start position:0%
+problem and actually I have a little
+ 
+
+ align:start position:0%
+problem and actually I have a little
+more to say about the movie that is now
+
+ align:start position:0%
+more to say about the movie that is now
+ 
+
+ align:start position:0%
+more to say about the movie that is now
+on the website because I'm quite excited
+
+ align:start position:0%
+on the website because I'm quite excited
+ 
+
+ align:start position:0%
+on the website because I'm quite excited
+about that movie uh let me just before
+
+ align:start position:0%
+about that movie uh let me just before
+ 
+
+ align:start position:0%
+about that movie uh let me just before
+I'll come to the movie in a second let
+
+ align:start position:0%
+I'll come to the movie in a second let
+ 
+
+ align:start position:0%
+I'll come to the movie in a second let
+me just say what today's lecture would
+
+ align:start position:0%
+me just say what today's lecture would
+ 
+
+ align:start position:0%
+me just say what today's lecture would
+be that the the key idea here is that
+
+ align:start position:0%
+be that the the key idea here is that
+ 
+
+ align:start position:0%
+be that the the key idea here is that
+the igen values and igen vectors of this
+
+ align:start position:0%
+the igen values and igen vectors of this
+ 
+
+ align:start position:0%
+the igen values and igen vectors of this
+giant Matrix of order n^2 by N2 size
+
+ align:start position:0%
+giant Matrix of order n^2 by N2 size
+ 
+
+ align:start position:0%
+giant Matrix of order n^2 by N2 size
+it's n^2 by
+
+ align:start position:0%
+it's n^2 by
+ 
+
+ align:start position:0%
+it's n^2 by
+n^2 the igen values and the igen vectors
+
+ align:start position:0%
+n^2 the igen values and the igen vectors
+ 
+
+ align:start position:0%
+n^2 the igen values and the igen vectors
+are known first of all they're
+
+ align:start position:0%
+are known first of all they're
+ 
+
+ align:start position:0%
+are known first of all they're
+known they're the igen vectors are nice
+
+ align:start position:0%
+known they're the igen vectors are nice
+ 
+
+ align:start position:0%
+known they're the igen vectors are nice
+discrete sign functions they're signs
+
+ align:start position:0%
+discrete sign functions they're signs
+ 
+
+ align:start position:0%
+discrete sign functions they're signs
+because I'm assuming zero bound I'm
+
+ align:start position:0%
+because I'm assuming zero bound I'm
+ 
+
+ align:start position:0%
+because I'm assuming zero bound I'm
+assuming zero they come to zero at the
+
+ align:start position:0%
+assuming zero they come to zero at the
+ 
+
+ align:start position:0%
+assuming zero they come to zero at the
+boundaries so that's why I have a sign
+
+ align:start position:0%
+boundaries so that's why I have a sign
+ 
+
+ align:start position:0%
+boundaries so that's why I have a sign
+rather than a
+
+ align:start position:0%
+rather than a
+ 
+
+ align:start position:0%
+rather than a
+cosine that first they're known and
+
+ align:start position:0%
+cosine that first they're known and
+ 
+
+ align:start position:0%
+cosine that first they're known and
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+we can work with them very quickly using
+
+ align:start position:0%
+we can work with them very quickly using
+ 
+
+ align:start position:0%
+we can work with them very quickly using
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fft so the the point is that it it it's
+
+ align:start position:0%
+fft so the the point is that it it it's
+ 
+
+ align:start position:0%
+fft so the the point is that it it it's
+quite exceptional in fact I I don't
+
+ align:start position:0%
+quite exceptional in fact I I don't
+ 
+
+ align:start position:0%
+quite exceptional in fact I I don't
+think I know any comparable examples in
+
+ align:start position:0%
+think I know any comparable examples in
+ 
+
+ align:start position:0%
+think I know any comparable examples in
+which a linear system is solved by using
+
+ align:start position:0%
+which a linear system is solved by using
+ 
+
+ align:start position:0%
+which a linear system is solved by using
+the igen values and igen
+
+ align:start position:0%
+the igen values and igen
+ 
+
+ align:start position:0%
+the igen values and igen
+vectors usually we igen values and igen
+
+ align:start position:0%
+vectors usually we igen values and igen
+ 
+
+ align:start position:0%
+vectors usually we igen values and igen
+vectors they pay off for differential
+
+ align:start position:0%
+vectors they pay off for differential
+ 
+
+ align:start position:0%
+vectors they pay off for differential
+equations that are growing in time then
+
+ align:start position:0%
+equations that are growing in time then
+ 
+
+ align:start position:0%
+equations that are growing in time then
+it is is worth Computing them because
+
+ align:start position:0%
+it is is worth Computing them because
+ 
+
+ align:start position:0%
+it is is worth Computing them because
+then you can just multiply by e to the
+
+ align:start position:0%
+then you can just multiply by e to the
+ 
+
+ align:start position:0%
+then you can just multiply by e to the
+Lambda T and you know what's happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later igen vectors igen values have
+
+ align:start position:0%
+later igen vectors igen values have
+ 
+
+ align:start position:0%
+later igen vectors igen values have
+other purposes but very very rarely are
+
+ align:start position:0%
+other purposes but very very rarely are
+ 
+
+ align:start position:0%
+other purposes but very very rarely are
+they used to solve a linear system I
+
+ align:start position:0%
+they used to solve a linear system I
+ 
+
+ align:start position:0%
+they used to solve a linear system I
+mean it's usually far more
+
+ align:start position:0%
+mean it's usually far more
+ 
+
+ align:start position:0%
+mean it's usually far more
+work and of course it would be
+
+ align:start position:0%
+work and of course it would be
+ 
+
+ align:start position:0%
+work and of course it would be
+incredibly more work if we had to find
+
+ align:start position:0%
+incredibly more work if we had to find
+ 
+
+ align:start position:0%
+incredibly more work if we had to find
+the igen vales and igen vectors but for
+
+ align:start position:0%
+the igen vales and igen vectors but for
+ 
+
+ align:start position:0%
+the igen vales and igen vectors but for
+this problem we know them and also would
+
+ align:start position:0%
+this problem we know them and also would
+ 
+
+ align:start position:0%
+this problem we know them and also would
+be incredibly more work if
+
+ align:start position:0%
+be incredibly more work if
+ 
+
+ align:start position:0%
+be incredibly more work if
+The Matrix of igen
+
+ align:start position:0%
+The Matrix of igen
+ 
+
+ align:start position:0%
+The Matrix of igen
+vectors the basis Matrix the the key
+
+ align:start position:0%
+vectors the basis Matrix the the key
+ 
+
+ align:start position:0%
+vectors the basis Matrix the the key
+Matrix that I I'll denote by
+
+ align:start position:0%
+Matrix that I I'll denote by
+ 
+
+ align:start position:0%
+Matrix that I I'll denote by
+S so the igen vectors go in a Matrix S
+
+ align:start position:0%
+S so the igen vectors go in a Matrix S
+ 
+
+ align:start position:0%
+S so the igen vectors go in a Matrix S
+the igen values go in a matrix Capital
+
+ align:start position:0%
+the igen values go in a matrix Capital
+ 
+
+ align:start position:0%
+the igen values go in a matrix Capital
+Lambda so we know Lambda it's going to
+
+ align:start position:0%
+Lambda so we know Lambda it's going to
+ 
+
+ align:start position:0%
+Lambda so we know Lambda it's going to
+be a simple Matrix just diagonal got
+
+ align:start position:0%
+be a simple Matrix just diagonal got
+ 
+
+ align:start position:0%
+be a simple Matrix just diagonal got
+those n numbers n squar numbers I guess
+
+ align:start position:0%
+those n numbers n squar numbers I guess
+ 
+
+ align:start position:0%
+those n numbers n squar numbers I guess
+cuz we're of size n s but these I
+
+ align:start position:0%
+cuz we're of size n s but these I
+ 
+
+ align:start position:0%
+cuz we're of size n s but these I
+vectors we
+
+ align:start position:0%
+vectors we
+ 
+
+ align:start position:0%
+vectors we
+know so we know them and we can compute
+
+ align:start position:0%
+know so we know them and we can compute
+ 
+
+ align:start position:0%
+know so we know them and we can compute
+quickly with them using the fft or using
+
+ align:start position:0%
+quickly with them using the fft or using
+ 
+
+ align:start position:0%
+quickly with them using the fft or using
+I you might want me to say fast sign
+
+ align:start position:0%
+I you might want me to say fast sign
+ 
+
+ align:start position:0%
+I you might want me to say fast sign
+transform discrete sign transform rather
+
+ align:start position:0%
+transform discrete sign transform rather
+ 
+
+ align:start position:0%
+transform discrete sign transform rather
+than the Fate transform which we think
+
+ align:start position:0%
+than the Fate transform which we think
+ 
+
+ align:start position:0%
+than the Fate transform which we think
+of as doing the complex
+
+ align:start position:0%
+of as doing the complex
+ 
+
+ align:start position:0%
+of as doing the complex
+exponentials so this is this
+
+ align:start position:0%
+exponentials so this is this
+ 
+
+ align:start position:0%
+exponentials so this is this
+small special forier fast forier
+
+ align:start position:0%
+small special forier fast forier
+ 
+
+ align:start position:0%
+small special forier fast forier
+world it's a special so fast for a world
+
+ align:start position:0%
+world it's a special so fast for a world
+ 
+
+ align:start position:0%
+world it's a special so fast for a world
+in which the fft and the related s and
+
+ align:start position:0%
+in which the fft and the related s and
+ 
+
+ align:start position:0%
+in which the fft and the related s and
+cosine uh give us a quick
+
+ align:start position:0%
+cosine uh give us a quick
+ 
+
+ align:start position:0%
+cosine uh give us a quick
+answer faster than elimination because
+
+ align:start position:0%
+answer faster than elimination because
+ 
+
+ align:start position:0%
+answer faster than elimination because
+you you all know it's it's n log n if n
+
+ align:start position:0%
+you you all know it's it's n log n if n
+ 
+
+ align:start position:0%
+you you all know it's it's n log n if n
+is the number of 4A components and
+
+ align:start position:0%
+is the number of 4A components and
+ 
+
+ align:start position:0%
+is the number of 4A components and
+that's hard to
+
+ align:start position:0%
+that's hard to
+ 
+
+ align:start position:0%
+that's hard to
+beat then I'll mention also for the same
+
+ align:start position:0%
+beat then I'll mention also for the same
+ 
+
+ align:start position:0%
+beat then I'll mention also for the same
+problem uh there is another way in which
+
+ align:start position:0%
+problem uh there is another way in which
+ 
+
+ align:start position:0%
+problem uh there is another way in which
+ uh can be
+
+ align:start position:0%
+ uh can be
+ 
+
+ align:start position:0%
+ uh can be
+simplified uh not a forier way just a
+
+ align:start position:0%
+simplified uh not a forier way just a
+ 
+
+ align:start position:0%
+simplified uh not a forier way just a
+direct uh
+
+ align:start position:0%
+direct uh
+ 
+
+ align:start position:0%
+direct uh
+uh combining uh uh neighboring equations
+
+ align:start position:0%
+uh combining uh uh neighboring equations
+ 
+
+ align:start position:0%
+uh combining uh uh neighboring equations
+so that'll be number two okay but mostly
+
+ align:start position:0%
+so that'll be number two okay but mostly
+ 
+
+ align:start position:0%
+so that'll be number two okay but mostly
+the lecture is about number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one the the the best example I know in
+
+ align:start position:0%
+one the the the best example I know in
+ 
+
+ align:start position:0%
+one the the the best example I know in
+which you would use I vectors Ian values
+
+ align:start position:0%
+which you would use I vectors Ian values
+ 
+
+ align:start position:0%
+which you would use I vectors Ian values
+to solve an ordinary linear system and
+
+ align:start position:0%
+to solve an ordinary linear system and
+ 
+
+ align:start position:0%
+to solve an ordinary linear system and
+I'll say in a word just how how you do
+
+ align:start position:0%
+I'll say in a word just how how you do
+ 
+
+ align:start position:0%
+I'll say in a word just how how you do
+it and then what these igen vectors are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay pause time out to say something
+
+ align:start position:0%
+okay pause time out to say something
+ 
+
+ align:start position:0%
+okay pause time out to say something
+about the movie so that movie that's now
+
+ align:start position:0%
+about the movie so that movie that's now
+ 
+
+ align:start position:0%
+about the movie so that movie that's now
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+website
+
+ align:start position:0%
+website
+ 
+
+ align:start position:0%
+website
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+does sparse
+
+ align:start position:0%
+does sparse
+ 
+
+ align:start position:0%
+does sparse
+elimination and the example it takes is
+
+ align:start position:0%
+elimination and the example it takes is
+ 
+
+ align:start position:0%
+elimination and the example it takes is
+k2d and you can make it a 8 s by 8 s 10
+
+ align:start position:0%
+k2d and you can make it a 8 s by 8 s 10
+ 
+
+ align:start position:0%
+k2d and you can make it a 8 s by 8 s 10
+2 by 10 s 20 2 by 20 s uh because it
+
+ align:start position:0%
+2 by 10 s 20 2 by 20 s uh because it
+ 
+
+ align:start position:0%
+2 by 10 s 20 2 by 20 s uh because it
+shows the order that the nodes are
+
+ align:start position:0%
+shows the order that the nodes are
+ 
+
+ align:start position:0%
+shows the order that the nodes are
+eliminated and the graph of no of of
+
+ align:start position:0%
+eliminated and the graph of no of of
+ 
+
+ align:start position:0%
+eliminated and the graph of no of of
+nonzeros in the matrix it's a bit slow
+
+ align:start position:0%
+nonzeros in the matrix it's a bit slow
+ 
+
+ align:start position:0%
+nonzeros in the matrix it's a bit slow
+if you do 20 by 20 you have to go away
+
+ align:start position:0%
+if you do 20 by 20 you have to go away
+ 
+
+ align:start position:0%
+if you do 20 by 20 you have to go away
+for uh um lunch but well maybe not lunch
+
+ align:start position:0%
+for uh um lunch but well maybe not lunch
+ 
+
+ align:start position:0%
+for uh um lunch but well maybe not lunch
+but at least uh coffee uh
+
+ align:start position:0%
+but at least uh coffee uh
+ 
+
+ align:start position:0%
+but at least uh coffee uh
+to before it's done but when it's done
+
+ align:start position:0%
+to before it's done but when it's done
+ 
+
+ align:start position:0%
+to before it's done but when it's done
+it has it counts the number of it shows
+
+ align:start position:0%
+it has it counts the number of it shows
+ 
+
+ align:start position:0%
+it has it counts the number of it shows
+the the uh nonzeros that are in the in
+
+ align:start position:0%
+the the uh nonzeros that are in the in
+ 
+
+ align:start position:0%
+the the uh nonzeros that are in the in
+the final in the in the elimination in
+
+ align:start position:0%
+the final in the in the elimination in
+ 
+
+ align:start position:0%
+the final in the in the elimination in
+the factor L from
+
+ align:start position:0%
+the factor L from
+ 
+
+ align:start position:0%
+the factor L from
+elimination and it counts the number of
+
+ align:start position:0%
+elimination and it counts the number of
+ 
+
+ align:start position:0%
+elimination and it counts the number of
+nonzeros and I was just talking to paron
+
+ align:start position:0%
+nonzeros and I was just talking to paron
+ 
+
+ align:start position:0%
+nonzeros and I was just talking to paron
+about also getting it to count the
+
+ align:start position:0%
+about also getting it to count the
+ 
+
+ align:start position:0%
+about also getting it to count the
+number of actual flops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well why am I interested I'm interested
+
+ align:start position:0%
+well why am I interested I'm interested
+ 
+
+ align:start position:0%
+well why am I interested I'm interested
+because I don't know what
+
+ align:start position:0%
+because I don't know what
+ 
+
+ align:start position:0%
+because I don't know what
+the whether what what power of n those
+
+ align:start position:0%
+the whether what what power of n those
+ 
+
+ align:start position:0%
+the whether what what power of n those
+numbers are going
+
+ align:start position:0%
+numbers are going
+ 
+
+ align:start position:0%
+numbers are going
+like I don't know whether the number of
+
+ align:start position:0%
+like I don't know whether the number of
+ 
+
+ align:start position:0%
+like I don't know whether the number of
+nonzeros and I did 10 20
+
+ align:start position:0%
+nonzeros and I did 10 20
+ 
+
+ align:start position:0%
+nonzeros and I did 10 20
+30 and it looked not too far from the
+
+ align:start position:0%
+30 and it looked not too far from the
+ 
+
+ align:start position:0%
+30 and it looked not too far from the
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+uh uh capital N cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it but but the notes say for nested
+
+ align:start position:0%
+but it but but the notes say for nested
+ 
+
+ align:start position:0%
+but it but but the notes say for nested
+dissection which would be another
+
+ align:start position:0%
+dissection which would be another
+ 
+
+ align:start position:0%
+dissection which would be another
+ordering n s log n so I'm I'm
+
+ align:start position:0%
+ordering n s log n so I'm I'm
+ 
+
+ align:start position:0%
+ordering n s log n so I'm I'm
+uh and of course what power we get
+
+ align:start position:0%
+uh and of course what power we get
+ 
+
+ align:start position:0%
+uh and of course what power we get
+depends on what algorithm we use for
+
+ align:start position:0%
+depends on what algorithm we use for
+ 
+
+ align:start position:0%
+depends on what algorithm we use for
+ordering so nested dissection is one
+
+ align:start position:0%
+ordering so nested dissection is one
+ 
+
+ align:start position:0%
+ordering so nested dissection is one
+ordering which hopefully we could put
+
+ align:start position:0%
+ordering which hopefully we could put
+ 
+
+ align:start position:0%
+ordering which hopefully we could put
+into another
+
+ align:start position:0%
+into another
+ 
+
+ align:start position:0%
+into another
+movie uh the movie now
+
+ align:start position:0%
+movie uh the movie now
+ 
+
+ align:start position:0%
+movie uh the movie now
+has exact minimum degree real MMD which
+
+ align:start position:0%
+has exact minimum degree real MMD which
+ 
+
+ align:start position:0%
+has exact minimum degree real MMD which
+which uh which takes as the next node
+
+ align:start position:0%
+which uh which takes as the next node
+ 
+
+ align:start position:0%
+which uh which takes as the next node
+the one with absolutely the minimum
+
+ align:start position:0%
+the one with absolutely the minimum
+ 
+
+ align:start position:0%
+the one with absolutely the minimum
+degree not just close to
+
+ align:start position:0%
+degree not just close to
+ 
+
+ align:start position:0%
+degree not just close to
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+anyway have a look at that movie uh and
+
+ align:start position:0%
+anyway have a look at that movie uh and
+ 
+
+ align:start position:0%
+anyway have a look at that movie uh and
+uh if you have any
+
+ align:start position:0%
+uh if you have any
+ 
+
+ align:start position:0%
+uh if you have any
+interest see what the what the count
+
+ align:start position:0%
+interest see what the what the count
+ 
+
+ align:start position:0%
+interest see what the what the count
+goes how the count increases as n
+
+ align:start position:0%
+goes how the count increases as n
+ 
+
+ align:start position:0%
+goes how the count increases as n
+increases and also you could you could
+
+ align:start position:0%
+increases and also you could you could
+ 
+
+ align:start position:0%
+increases and also you could you could
+have changed slightly adapt the
+
+ align:start position:0%
+have changed slightly adapt the
+ 
+
+ align:start position:0%
+have changed slightly adapt the
+algorithm that creates the ordering
+
+ align:start position:0%
+algorithm that creates the ordering
+ 
+
+ align:start position:0%
+algorithm that creates the ordering
+creates the permutation and and see what
+
+ align:start position:0%
+creates the permutation and and see what
+ 
+
+ align:start position:0%
+creates the permutation and and see what
+happens there uh there just a lot to do
+
+ align:start position:0%
+happens there uh there just a lot to do
+ 
+
+ align:start position:0%
+happens there uh there just a lot to do
+with that uh and it's a pretty
+
+ align:start position:0%
+with that uh and it's a pretty
+ 
+
+ align:start position:0%
+with that uh and it's a pretty
+fundamental problem actually we're
+
+ align:start position:0%
+fundamental problem actually we're
+ 
+
+ align:start position:0%
+fundamental problem actually we're
+talking there about what what matlab's
+
+ align:start position:0%
+talking there about what what matlab's
+ 
+
+ align:start position:0%
+talking there about what what matlab's
+backslash operation will do for that for
+
+ align:start position:0%
+backslash operation will do for that for
+ 
+
+ align:start position:0%
+backslash operation will do for that for
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+so mat lab's backslash operation will
+
+ align:start position:0%
+so mat lab's backslash operation will
+ 
+
+ align:start position:0%
+so mat lab's backslash operation will
+use elimination it won't use fast Plus
+
+ align:start position:0%
+use elimination it won't use fast Plus
+ 
+
+ align:start position:0%
+use elimination it won't use fast Plus
+on solvers but now let me come to the
+
+ align:start position:0%
+on solvers but now let me come to the
+ 
+
+ align:start position:0%
+on solvers but now let me come to the
+fast Plus on solver okay so I guess the
+
+ align:start position:0%
+fast Plus on solver okay so I guess the
+ 
+
+ align:start position:0%
+fast Plus on solver okay so I guess the
+main point is I have to say what are the
+
+ align:start position:0%
+main point is I have to say what are the
+ 
+
+ align:start position:0%
+main point is I have to say what are the
+igen values and igen vectors and how do
+
+ align:start position:0%
+igen values and igen vectors and how do
+ 
+
+ align:start position:0%
+igen values and igen vectors and how do
+they get used so let me say how do they
+
+ align:start position:0%
+they get used so let me say how do they
+ 
+
+ align:start position:0%
+they get used so let me say how do they
+get used so how can I use igen values
+
+ align:start position:0%
+get used so how can I use igen values
+ 
+
+ align:start position:0%
+get used so how can I use igen values
+and igen vectors to solve a problem like
+
+ align:start position:0%
+and igen vectors to solve a problem like
+ 
+
+ align:start position:0%
+and igen vectors to solve a problem like
+that let me just call it K rather than
+
+ align:start position:0%
+that let me just call it K rather than
+ 
+
+ align:start position:0%
+that let me just call it K rather than
+k2d so k U equal
+
+ align:start position:0%
+k2d so k U equal
+ 
+
+ align:start position:0%
+k2d so k U equal
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+okay by I by I
+
+ align:start position:0%
+okay by I by I
+ 
+
+ align:start position:0%
+okay by I by I
+Vector okay step there's Three Steps
+
+ align:start position:0%
+Vector okay step there's Three Steps
+ 
+
+ align:start position:0%
+Vector okay step there's Three Steps
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+one expand the right hand
+
+ align:start position:0%
+one expand the right hand
+ 
+
+ align:start position:0%
+one expand the right hand
+side as a combination of the igen
+
+ align:start position:0%
+side as a combination of the igen
+ 
+
+ align:start position:0%
+side as a combination of the igen
+vectors okay so
+
+ align:start position:0%
+vectors okay so
+ 
+
+ align:start position:0%
+vectors okay so
+expand F this right hand side Vector as
+
+ align:start position:0%
+expand F this right hand side Vector as
+ 
+
+ align:start position:0%
+expand F this right hand side Vector as
+some some
+
+ align:start position:0%
+some some
+ 
+
+ align:start position:0%
+some some
+combination of the first ion Vector
+
+ align:start position:0%
+combination of the first ion Vector
+ 
+
+ align:start position:0%
+combination of the first ion Vector
+maybe I'm going to call it
+
+ align:start position:0%
+maybe I'm going to call it
+ 
+
+ align:start position:0%
+maybe I'm going to call it
+y1 second I
+
+ align:start position:0%
+y1 second I
+ 
+
+ align:start position:0%
+y1 second I
+Vector n i
+
+ align:start position:0%
+Vector n i
+ 
+
+ align:start position:0%
+Vector n i
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good that mean what do I mean I mean you
+
+ align:start position:0%
+good that mean what do I mean I mean you
+ 
+
+ align:start position:0%
+good that mean what do I mean I mean you
+have to find those C's that's the job
+
+ align:start position:0%
+have to find those C's that's the job
+ 
+
+ align:start position:0%
+have to find those C's that's the job
+there find this find the the
+
+ align:start position:0%
+there find this find the the
+ 
+
+ align:start position:0%
+there find this find the the
+coefficients so that's
+
+ align:start position:0%
+coefficients so that's
+ 
+
+ align:start position:0%
+coefficients so that's
+that's a job a numerical that's a linear
+
+ align:start position:0%
+that's a job a numerical that's a linear
+ 
+
+ align:start position:0%
+that's a job a numerical that's a linear
+system to solve and we'll see what it
+
+ align:start position:0%
+system to solve and we'll see what it
+ 
+
+ align:start position:0%
+system to solve and we'll see what it
+amounts to okay but suppose the right
+
+ align:start position:0%
+amounts to okay but suppose the right
+ 
+
+ align:start position:0%
+amounts to okay but suppose the right
+hand side is a combination of the igen
+
+ align:start position:0%
+hand side is a combination of the igen
+ 
+
+ align:start position:0%
+hand side is a combination of the igen
+vectors how can you use that well step
+
+ align:start position:0%
+vectors how can you use that well step
+ 
+
+ align:start position:0%
+vectors how can you use that well step
+two is the real quick step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divide CI each I'll say each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CI by the ion Vector I can
+
+ align:start position:0%
+CI by the ion Vector I can
+ 
+
+ align:start position:0%
+CI by the ion Vector I can
+value Lambda
+
+ align:start position:0%
+value Lambda
+ 
+
+ align:start position:0%
+value Lambda
+okay so it's byon Vector so I'm assuming
+
+ align:start position:0%
+okay so it's byon Vector so I'm assuming
+ 
+
+ align:start position:0%
+okay so it's byon Vector so I'm assuming
+that K Yi is Lambda I Yi and that we
+
+ align:start position:0%
+that K Yi is Lambda I Yi and that we
+ 
+
+ align:start position:0%
+that K Yi is Lambda I Yi and that we
+know these
+
+ align:start position:0%
+know these
+ 
+
+ align:start position:0%
+know these
+guys all right so this so this is
+
+ align:start position:0%
+guys all right so this so this is
+ 
+
+ align:start position:0%
+guys all right so this so this is
+known and now the question I'm just
+
+ align:start position:0%
+known and now the question I'm just
+ 
+
+ align:start position:0%
+known and now the question I'm just
+saying how do we assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+known so my question now is how do we
+
+ align:start position:0%
+known so my question now is how do we
+ 
+
+ align:start position:0%
+known so my question now is how do we
+use it okay step
+
+ align:start position:0%
+use it okay step
+ 
+
+ align:start position:0%
+use it okay step
+one the idea is going to be right
+
+ align:start position:0%
+one the idea is going to be right
+ 
+
+ align:start position:0%
+one the idea is going to be right
+everything in terms of igen vectors work
+
+ align:start position:0%
+everything in terms of igen vectors work
+ 
+
+ align:start position:0%
+everything in terms of igen vectors work
+with the igen vectors because if I've
+
+ align:start position:0%
+with the igen vectors because if I've
+ 
+
+ align:start position:0%
+with the igen vectors because if I've
+got igen vectors the
+
+ align:start position:0%
+got igen vectors the
+ 
+
+ align:start position:0%
+got igen vectors the
+step is scalar I just divide these
+
+ align:start position:0%
+step is scalar I just divide these
+ 
+
+ align:start position:0%
+step is scalar I just divide these
+numbers by those numbers and then I've
+
+ align:start position:0%
+numbers by those numbers and then I've
+ 
+
+ align:start position:0%
+numbers by those numbers and then I've
+got the
+
+ align:start position:0%
+got the
+ 
+
+ align:start position:0%
+got the
+answer and then
+
+ align:start position:0%
+answer and then
+ 
+
+ align:start position:0%
+answer and then
+construct the correct answer will be U
+
+ align:start position:0%
+construct the correct answer will be U
+ 
+
+ align:start position:0%
+construct the correct answer will be U
+will be C1 over Lambda 1
+
+ align:start position:0%
+will be C1 over Lambda 1
+ 
+
+ align:start position:0%
+will be C1 over Lambda 1
+y1 and C2 over Lambda 2 Y 2 up to CN
+
+ align:start position:0%
+y1 and C2 over Lambda 2 Y 2 up to CN
+ 
+
+ align:start position:0%
+y1 and C2 over Lambda 2 Y 2 up to CN
+over Lambda n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+YN a combination of those same igen
+
+ align:start position:0%
+YN a combination of those same igen
+ 
+
+ align:start position:0%
+YN a combination of those same igen
+vectors with the same coefficients just
+
+ align:start position:0%
+vectors with the same coefficients just
+ 
+
+ align:start position:0%
+vectors with the same coefficients just
+divided by Lambda
+
+ align:start position:0%
+divided by Lambda
+ 
+
+ align:start position:0%
+divided by Lambda
+so but this is of course another
+
+ align:start position:0%
+so but this is of course another
+ 
+
+ align:start position:0%
+so but this is of course another
+numerical job this is like adding up a
+
+ align:start position:0%
+numerical job this is like adding up a
+ 
+
+ align:start position:0%
+numerical job this is like adding up a
+fora Series this is like finding the 4A
+
+ align:start position:0%
+fora Series this is like finding the 4A
+ 
+
+ align:start position:0%
+fora Series this is like finding the 4A
+coefficients this is like reconstructing
+
+ align:start position:0%
+coefficients this is like reconstructing
+ 
+
+ align:start position:0%
+coefficients this is like reconstructing
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+the input only because I've divided by
+
+ align:start position:0%
+the input only because I've divided by
+ 
+
+ align:start position:0%
+the input only because I've divided by
+Lambda I I'm getting the output here is
+
+ align:start position:0%
+Lambda I I'm getting the output here is
+ 
+
+ align:start position:0%
+Lambda I I'm getting the output here is
+U when the input was
+
+ align:start position:0%
+U when the input was
+ 
+
+ align:start position:0%
+U when the input was
+F do you see that that is the correct
+
+ align:start position:0%
+F do you see that that is the correct
+ 
+
+ align:start position:0%
+F do you see that that is the correct
+answer I just all I have to do is check
+
+ align:start position:0%
+answer I just all I have to do is check
+ 
+
+ align:start position:0%
+answer I just all I have to do is check
+that KU equals F so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check that that is that this answer from
+
+ align:start position:0%
+check that that is that this answer from
+ 
+
+ align:start position:0%
+check that that is that this answer from
+step three is is the right answer okay
+
+ align:start position:0%
+step three is is the right answer okay
+ 
+
+ align:start position:0%
+step three is is the right answer okay
+so I multiply by K
+
+ align:start position:0%
+so I multiply by K
+ 
+
+ align:start position:0%
+so I multiply by K
+when I
+
+ align:start position:0%
+when I
+ 
+
+ align:start position:0%
+when I
+multiply y1 by
+
+ align:start position:0%
+multiply y1 by
+ 
+
+ align:start position:0%
+multiply y1 by
+K a factor Lambda 1 appears the igen
+
+ align:start position:0%
+K a factor Lambda 1 appears the igen
+ 
+
+ align:start position:0%
+K a factor Lambda 1 appears the igen
+value it cancels that well that's y
+
+ align:start position:0%
+value it cancels that well that's y
+ 
+
+ align:start position:0%
+value it cancels that well that's y
+divided so it would cancel and I have C1
+
+ align:start position:0%
+divided so it would cancel and I have C1
+ 
+
+ align:start position:0%
+divided so it would cancel and I have C1
+y1 when I multiply this by K ky2 is
+
+ align:start position:0%
+y1 when I multiply this by K ky2 is
+ 
+
+ align:start position:0%
+y1 when I multiply this by K ky2 is
+Lambda 2 Y2 cancel the Lambda 2s and
+
+ align:start position:0%
+Lambda 2 Y2 cancel the Lambda 2s and
+ 
+
+ align:start position:0%
+Lambda 2 Y2 cancel the Lambda 2s and
+you're left with C2
+
+ align:start position:0%
+you're left with C2
+ 
+
+ align:start position:0%
+you're left with C2
+Y2 and so on so when I multipli by K I
+
+ align:start position:0%
+Y2 and so on so when I multipli by K I
+ 
+
+ align:start position:0%
+Y2 and so on so when I multipli by K I
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+F that's it so that's the whole
+
+ align:start position:0%
+F that's it so that's the whole
+ 
+
+ align:start position:0%
+F that's it so that's the whole
+idea written out but
+
+ align:start position:0%
+idea written out but
+ 
+
+ align:start position:0%
+idea written out but
+now what actual computations go into
+
+ align:start position:0%
+now what actual computations go into
+ 
+
+ align:start position:0%
+now what actual computations go into
+steps one and three step two is pretty
+
+ align:start position:0%
+steps one and three step two is pretty
+ 
+
+ align:start position:0%
+steps one and three step two is pretty
+simple well actually this is a good way
+
+ align:start position:0%
+simple well actually this is a good way
+ 
+
+ align:start position:0%
+simple well actually this is a good way
+to look at it I I want to write that
+
+ align:start position:0%
+to look at it I I want to write that
+ 
+
+ align:start position:0%
+to look at it I I want to write that
+same algorithm in Matrix language okay
+
+ align:start position:0%
+same algorithm in Matrix language okay
+ 
+
+ align:start position:0%
+same algorithm in Matrix language okay
+so so in Matrix form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the Matrix of igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors and that's what I'm calling s
+
+ align:start position:0%
+vectors and that's what I'm calling s
+ 
+
+ align:start position:0%
+vectors and that's what I'm calling s
+and it's got the I vectors y1 Y2 YN in
+
+ align:start position:0%
+and it's got the I vectors y1 Y2 YN in
+ 
+
+ align:start position:0%
+and it's got the I vectors y1 Y2 YN in
+its columns and the I value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix the ion value Matrix we need that
+
+ align:start position:0%
+Matrix the ion value Matrix we need that
+ 
+
+ align:start position:0%
+Matrix the ion value Matrix we need that
+a name for that too and that we decided
+
+ align:start position:0%
+a name for that too and that we decided
+ 
+
+ align:start position:0%
+a name for that too and that we decided
+to call Lambda and that's got the igen
+
+ align:start position:0%
+to call Lambda and that's got the igen
+ 
+
+ align:start position:0%
+to call Lambda and that's got the igen
+values on its diagonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so there is this 1806 linear
+
+ align:start position:0%
+so so there is this 1806 linear
+ 
+
+ align:start position:0%
+so so there is this 1806 linear
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+The Matrix of I vectors If I multiply K
+
+ align:start position:0%
+The Matrix of I vectors If I multiply K
+ 
+
+ align:start position:0%
+The Matrix of I vectors If I multiply K
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+S then I'm multiplying K by all its
+
+ align:start position:0%
+S then I'm multiplying K by all its
+ 
+
+ align:start position:0%
+S then I'm multiplying K by all its
+little I
+
+ align:start position:0%
+little I
+ 
+
+ align:start position:0%
+little I
+vectors and K * this gives me Lambda 1
+
+ align:start position:0%
+vectors and K * this gives me Lambda 1
+ 
+
+ align:start position:0%
+vectors and K * this gives me Lambda 1
+y1 K * Y2 gives me Lambda 2 y 2 K YN is
+
+ align:start position:0%
+y1 K * Y2 gives me Lambda 2 y 2 K YN is
+ 
+
+ align:start position:0%
+y1 K * Y2 gives me Lambda 2 y 2 K YN is
+Lambda n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+YN and if I look to see what this is
+
+ align:start position:0%
+YN and if I look to see what this is
+ 
+
+ align:start position:0%
+YN and if I look to see what this is
+this is the same as y1 to YN multiplied
+
+ align:start position:0%
+this is the same as y1 to YN multiplied
+ 
+
+ align:start position:0%
+this is the same as y1 to YN multiplied
+by Lambda if I just multiply on the
+
+ align:start position:0%
+by Lambda if I just multiply on the
+ 
+
+ align:start position:0%
+by Lambda if I just multiply on the
+right by Lambda it will take Lambda 1 *
+
+ align:start position:0%
+right by Lambda it will take Lambda 1 *
+ 
+
+ align:start position:0%
+right by Lambda it will take Lambda 1 *
+the First Column Lambda 2 * the second
+
+ align:start position:0%
+the First Column Lambda 2 * the second
+ 
+
+ align:start position:0%
+the First Column Lambda 2 * the second
+Lambda n * the 3 which is times the last
+
+ align:start position:0%
+Lambda n * the 3 which is times the last
+ 
+
+ align:start position:0%
+Lambda n * the 3 which is times the last
+which is what we want so it's s
+
+ align:start position:0%
+which is what we want so it's s
+ 
+
+ align:start position:0%
+which is what we want so it's s
+Lambda that this is all n i values and
+
+ align:start position:0%
+Lambda that this is all n i values and
+ 
+
+ align:start position:0%
+Lambda that this is all n i values and
+igen vectors in one Matrix equation
+
+ align:start position:0%
+igen vectors in one Matrix equation
+ 
+
+ align:start position:0%
+igen vectors in one Matrix equation
+that's all that is it's just KS equal s
+
+ align:start position:0%
+that's all that is it's just KS equal s
+ 
+
+ align:start position:0%
+that's all that is it's just KS equal s
+Lambda I just
+
+ align:start position:0%
+Lambda I just
+ 
+
+ align:start position:0%
+Lambda I just
+says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this for all I at once all I at the same
+
+ align:start position:0%
+this for all I at once all I at the same
+ 
+
+ align:start position:0%
+this for all I at once all I at the same
+time okay so if I use these
+
+ align:start position:0%
+time okay so if I use these
+ 
+
+ align:start position:0%
+time okay so if I use these
+matrices in describing steps 1 2 3 I
+
+ align:start position:0%
+matrices in describing steps 1 2 3 I
+ 
+
+ align:start position:0%
+matrices in describing steps 1 2 3 I
+I'll see what's happening Matrix
+
+ align:start position:0%
+I'll see what's happening Matrix
+ 
+
+ align:start position:0%
+I'll see what's happening Matrix
+language okay let let me just do that
+
+ align:start position:0%
+language okay let let me just do that
+ 
+
+ align:start position:0%
+language okay let let me just do that
+step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one step one is looking for f as a
+
+ align:start position:0%
+one step one is looking for f as a
+ 
+
+ align:start position:0%
+one step one is looking for f as a
+combination of The Columns of s so step
+
+ align:start position:0%
+combination of The Columns of s so step
+ 
+
+ align:start position:0%
+combination of The Columns of s so step
+one is just f = s *
+
+ align:start position:0%
+one is just f = s *
+ 
+
+ align:start position:0%
+one is just f = s *
+C the vector of
+
+ align:start position:0%
+C the vector of
+ 
+
+ align:start position:0%
+C the vector of
+coefficients multiplies the columns of s
+
+ align:start position:0%
+coefficients multiplies the columns of s
+ 
+
+ align:start position:0%
+coefficients multiplies the columns of s
+and adds to give
+
+ align:start position:0%
+and adds to give
+ 
+
+ align:start position:0%
+and adds to give
+F then step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two which just divide
+
+ align:start position:0%
+two which just divide
+ 
+
+ align:start position:0%
+two which just divide
+divides everything
+
+ align:start position:0%
+divides everything
+ 
+
+ align:start position:0%
+divides everything
+by divides by the lambdas step two is
+
+ align:start position:0%
+by divides by the lambdas step two is
+ 
+
+ align:start position:0%
+by divides by the lambdas step two is
+just creates Lambda
+
+ align:start position:0%
+just creates Lambda
+ 
+
+ align:start position:0%
+just creates Lambda
+inverse s
+
+ align:start position:0%
+inverse s
+ 
+
+ align:start position:0%
+inverse s
+c so I took what I
+
+ align:start position:0%
+c so I took what I
+ 
+
+ align:start position:0%
+c so I took what I
+had oh let's see no uh what am I no the
+
+ align:start position:0%
+had oh let's see no uh what am I no the
+ 
+
+ align:start position:0%
+had oh let's see no uh what am I no the
+Lambda inverse better be multiplying the
+
+ align:start position:0%
+Lambda inverse better be multiplying the
+ 
+
+ align:start position:0%
+Lambda inverse better be multiplying the
+C so okay well actually I can do it all
+
+ align:start position:0%
+C so okay well actually I can do it all
+ 
+
+ align:start position:0%
+C so okay well actually I can do it all
+in well yeah step two so how that's the
+
+ align:start position:0%
+in well yeah step two so how that's the
+ 
+
+ align:start position:0%
+in well yeah step two so how that's the
+easiest step I should be able to do it C
+
+ align:start position:0%
+easiest step I should be able to do it C
+ 
+
+ align:start position:0%
+easiest step I should be able to do it C
+is changed to C is changed to Lambda
+
+ align:start position:0%
+is changed to C is changed to Lambda
+ 
+
+ align:start position:0%
+is changed to C is changed to Lambda
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+C so that c becomes Lambda inverse C
+
+ align:start position:0%
+C so that c becomes Lambda inverse C
+ 
+
+ align:start position:0%
+C so that c becomes Lambda inverse C
+okay and then step three uses
+
+ align:start position:0%
+okay and then step three uses
+ 
+
+ align:start position:0%
+okay and then step three uses
+Lambda inverse C to
+
+ align:start position:0%
+Lambda inverse C to
+ 
+
+ align:start position:0%
+Lambda inverse C to
+construct U so step two that step three
+
+ align:start position:0%
+construct U so step two that step three
+ 
+
+ align:start position:0%
+construct U so step two that step three
+step three is the answer U what is it
+
+ align:start position:0%
+step three is the answer U what is it
+ 
+
+ align:start position:0%
+step three is the answer U what is it
+what do I have here I've got a
+
+ align:start position:0%
+what do I have here I've got a
+ 
+
+ align:start position:0%
+what do I have here I've got a
+combination of these vectors so they are
+
+ align:start position:0%
+combination of these vectors so they are
+ 
+
+ align:start position:0%
+combination of these vectors so they are
+The Columns of s and what are they
+
+ align:start position:0%
+The Columns of s and what are they
+ 
+
+ align:start position:0%
+The Columns of s and what are they
+multiplied by they're multiplied by the
+
+ align:start position:0%
+multiplied by they're multiplied by the
+ 
+
+ align:start position:0%
+multiplied by they're multiplied by the
+C's over lambdas which is what I have
+
+ align:start position:0%
+C's over lambdas which is what I have
+ 
+
+ align:start position:0%
+C's over lambdas which is what I have
+here that's s Lambda inverse C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are the three
+
+ align:start position:0%
+those are the three
+ 
+
+ align:start position:0%
+those are the three
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what what's the work involved here the
+
+ align:start position:0%
+what what's the work involved here the
+ 
+
+ align:start position:0%
+what what's the work involved here the
+work is solving a linear system with the
+
+ align:start position:0%
+work is solving a linear system with the
+ 
+
+ align:start position:0%
+work is solving a linear system with the
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+S here the work is taking a combination
+
+ align:start position:0%
+S here the work is taking a combination
+ 
+
+ align:start position:0%
+S here the work is taking a combination
+of The Columns of s doing a matrix
+
+ align:start position:0%
+of The Columns of s doing a matrix
+ 
+
+ align:start position:0%
+of The Columns of s doing a matrix
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+that's uh those those two steps are
+
+ align:start position:0%
+that's uh those those two steps are
+ 
+
+ align:start position:0%
+that's uh those those two steps are
+usually uh full Scale Matrix operations
+
+ align:start position:0%
+usually uh full Scale Matrix operations
+ 
+
+ align:start position:0%
+usually uh full Scale Matrix operations
+and of course the S the C if I just
+
+ align:start position:0%
+and of course the S the C if I just
+ 
+
+ align:start position:0%
+and of course the S the C if I just
+complete this I'll see that I get the
+
+ align:start position:0%
+complete this I'll see that I get the
+ 
+
+ align:start position:0%
+complete this I'll see that I get the
+right thing that's s Lambda
+
+ align:start position:0%
+right thing that's s Lambda
+ 
+
+ align:start position:0%
+right thing that's s Lambda
+inverse and C is s inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F there is the answer U is s Lambda
+
+ align:start position:0%
+F there is the answer U is s Lambda
+ 
+
+ align:start position:0%
+F there is the answer U is s Lambda
+inverse it's a Lambda inverse there s
+
+ align:start position:0%
+inverse it's a Lambda inverse there s
+ 
+
+ align:start position:0%
+inverse it's a Lambda inverse there s
+inverse F that's that's the correct
+
+ align:start position:0%
+inverse F that's that's the correct
+ 
+
+ align:start position:0%
+inverse F that's that's the correct
+answer in Matrix language right if if uh
+
+ align:start position:0%
+answer in Matrix language right if if uh
+ 
+
+ align:start position:0%
+answer in Matrix language right if if uh
+this is a in this is K inverse that's K
+
+ align:start position:0%
+this is a in this is K inverse that's K
+ 
+
+ align:start position:0%
+this is a in this is K inverse that's K
+inverse K
+
+ align:start position:0%
+inverse K
+ 
+
+ align:start position:0%
+inverse K
+is K is s Lambda s
+
+ align:start position:0%
+is K is s Lambda s
+ 
+
+ align:start position:0%
+is K is s Lambda s
+inverse and if I take the inverse of
+
+ align:start position:0%
+inverse and if I take the inverse of
+ 
+
+ align:start position:0%
+inverse and if I take the inverse of
+that I get S Lambda inverse s inverse to
+
+ align:start position:0%
+that I get S Lambda inverse s inverse to
+ 
+
+ align:start position:0%
+that I get S Lambda inverse s inverse to
+multiply F Well what
+
+ align:start position:0%
+multiply F Well what
+ 
+
+ align:start position:0%
+multiply F Well what
+is I doubt if you're much impressed by
+
+ align:start position:0%
+is I doubt if you're much impressed by
+ 
+
+ align:start position:0%
+is I doubt if you're much impressed by
+this lower board because the upper board
+
+ align:start position:0%
+this lower board because the upper board
+ 
+
+ align:start position:0%
+this lower board because the upper board
+was the same
+
+ align:start position:0%
+was the same
+ 
+
+ align:start position:0%
+was the same
+thing written out took a it took
+
+ align:start position:0%
+thing written out took a it took
+ 
+
+ align:start position:0%
+thing written out took a it took
+uh some indication of what the separate
+
+ align:start position:0%
+uh some indication of what the separate
+ 
+
+ align:start position:0%
+uh some indication of what the separate
+pieces were but it pretty clear Okay
+
+ align:start position:0%
+pieces were but it pretty clear Okay
+ 
+
+ align:start position:0%
+pieces were but it pretty clear Okay
+now what's the the the million dooll
+
+ align:start position:0%
+now what's the the the million dooll
+ 
+
+ align:start position:0%
+now what's the the the million dooll
+question is is it
+
+ align:start position:0%
+question is is it
+ 
+
+ align:start position:0%
+question is is it
+fast and the answer is almost certainly
+
+ align:start position:0%
+fast and the answer is almost certainly
+ 
+
+ align:start position:0%
+fast and the answer is almost certainly
+no but for the particular Matrix
+
+ align:start position:0%
+no but for the particular Matrix
+ 
+
+ align:start position:0%
+no but for the particular Matrix
+S which has good fortune by Good Fortune
+
+ align:start position:0%
+S which has good fortune by Good Fortune
+ 
+
+ align:start position:0%
+S which has good fortune by Good Fortune
+s could also stand for sign the this
+
+ align:start position:0%
+s could also stand for sign the this
+ 
+
+ align:start position:0%
+s could also stand for sign the this
+Matrix of igen vectors for this
+
+ align:start position:0%
+Matrix of igen vectors for this
+ 
+
+ align:start position:0%
+Matrix of igen vectors for this
+particular problem are signs these are
+
+ align:start position:0%
+particular problem are signs these are
+ 
+
+ align:start position:0%
+particular problem are signs these are
+the discrete signs so this is the
+
+ align:start position:0%
+the discrete signs so this is the
+ 
+
+ align:start position:0%
+the discrete signs so this is the
+discrete sign transform that's that's
+
+ align:start position:0%
+discrete sign transform that's that's
+ 
+
+ align:start position:0%
+discrete sign transform that's that's
+what we're doing we're doing the
+
+ align:start position:0%
+what we're doing we're doing the
+ 
+
+ align:start position:0%
+what we're doing we're doing the
+discrete sign
+
+ align:start position:0%
+discrete sign
+ 
+
+ align:start position:0%
+discrete sign
+transform because those discret sign
+
+ align:start position:0%
+transform because those discret sign
+ 
+
+ align:start position:0%
+transform because those discret sign
+vectors are the igen vectors of K okay
+
+ align:start position:0%
+vectors are the igen vectors of K okay
+ 
+
+ align:start position:0%
+vectors are the igen vectors of K okay
+now let
+
+ align:start position:0%
+now let
+ 
+
+ align:start position:0%
+now let
+me let me say what that means first I'm
+
+ align:start position:0%
+me let me say what that means first I'm
+ 
+
+ align:start position:0%
+me let me say what that means first I'm
+thinking of K in 1D so this is my two
+
+ align:start position:0%
+thinking of K in 1D so this is my two
+ 
+
+ align:start position:0%
+thinking of K in 1D so this is my two
+twos and minus 1's and minus 1's
+
+ align:start position:0%
+twos and minus 1's and minus 1's
+ 
+
+ align:start position:0%
+twos and minus 1's and minus 1's
+its ion vectors are discrete signs If I
+
+ align:start position:0%
+its ion vectors are discrete signs If I
+ 
+
+ align:start position:0%
+its ion vectors are discrete signs If I
+multiply that by
+
+ align:start position:0%
+multiply that by
+ 
+
+ align:start position:0%
+multiply that by
+S uh KH s well let me just take the
+
+ align:start position:0%
+S uh KH s well let me just take the
+ 
+
+ align:start position:0%
+S uh KH s well let me just take the
+first one sin H sin 2
+
+ align:start position:0%
+first one sin H sin 2
+ 
+
+ align:start position:0%
+first one sin H sin 2
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+s uh nus one
+
+ align:start position:0%
+s uh nus one
+ 
+
+ align:start position:0%
+s uh nus one
+H that will turn out to be an igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector so this is ky now
+
+ align:start position:0%
+Vector so this is ky now
+ 
+
+ align:start position:0%
+Vector so this is ky now
+ky1 the first igen Vector the igen
+
+ align:start position:0%
+ky1 the first igen Vector the igen
+ 
+
+ align:start position:0%
+ky1 the first igen Vector the igen
+vectors are let me draw them the igen
+
+ align:start position:0%
+vectors are let me draw them the igen
+ 
+
+ align:start position:0%
+vectors are let me draw them the igen
+vectors for for that second difference
+
+ align:start position:0%
+vectors for for that second difference
+ 
+
+ align:start position:0%
+vectors for for that second difference
+Matrix K
+
+ align:start position:0%
+Matrix K
+ 
+
+ align:start position:0%
+Matrix K
+are uh here's the interval 0 to one I
+
+ align:start position:0%
+are uh here's the interval 0 to one I
+ 
+
+ align:start position:0%
+are uh here's the interval 0 to one I
+chop it up in steps of H and I plot I
+
+ align:start position:0%
+chop it up in steps of H and I plot I
+ 
+
+ align:start position:0%
+chop it up in steps of H and I plot I
+take I plot the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign which starts at zero and ends at
+
+ align:start position:0%
+sign which starts at zero and ends at
+ 
+
+ align:start position:0%
+sign which starts at zero and ends at
+zero because those are the boundary
+
+ align:start position:0%
+zero because those are the boundary
+ 
+
+ align:start position:0%
+zero because those are the boundary
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+and here's sin H sin 28 sin 38 sin 48
+
+ align:start position:0%
+and here's sin H sin 28 sin 38 sin 48
+ 
+
+ align:start position:0%
+and here's sin H sin 28 sin 38 sin 48
+sin 5H so for the 5x5
+
+ align:start position:0%
+sin 5H so for the 5x5
+ 
+
+ align:start position:0%
+sin 5H so for the 5x5
+case I maybe I should just be using n
+
+ align:start position:0%
+case I maybe I should just be using n
+ 
+
+ align:start position:0%
+case I maybe I should just be using n
+here or maybe I should even be using
+
+ align:start position:0%
+here or maybe I should even be using
+ 
+
+ align:start position:0%
+here or maybe I should even be using
+capital N so capital N is five in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+good oh what's on the other side of that
+
+ align:start position:0%
+good oh what's on the other side of that
+ 
+
+ align:start position:0%
+good oh what's on the other side of that
+equal sign some value times the same
+
+ align:start position:0%
+equal sign some value times the same
+ 
+
+ align:start position:0%
+equal sign some value times the same
+Vector sin
+
+ align:start position:0%
+Vector sin
+ 
+
+ align:start position:0%
+Vector sin
+H sin 2 H down to S
+
+ align:start position:0%
+H sin 2 H down to S
+ 
+
+ align:start position:0%
+H sin 2 H down to S
+NH and that I value oh let me just write
+
+ align:start position:0%
+NH and that I value oh let me just write
+ 
+
+ align:start position:0%
+NH and that I value oh let me just write
+Lambda one for
+
+ align:start position:0%
+Lambda one for
+ 
+
+ align:start position:0%
+Lambda one for
+it we know what it is the fact that this
+
+ align:start position:0%
+it we know what it is the fact that this
+ 
+
+ align:start position:0%
+it we know what it is the fact that this
+is an igen
+
+ align:start position:0%
+is an igen
+ 
+
+ align:start position:0%
+is an igen
+Vector is
+
+ align:start position:0%
+Vector is
+ 
+
+ align:start position:0%
+Vector is
+just trig you know I I I multiply minus
+
+ align:start position:0%
+just trig you know I I I multiply minus
+ 
+
+ align:start position:0%
+just trig you know I I I multiply minus
+one of that plus two of that minus one
+
+ align:start position:0%
+one of that plus two of that minus one
+ 
+
+ align:start position:0%
+one of that plus two of that minus one
+of sin
+
+ align:start position:0%
+of sin
+ 
+
+ align:start position:0%
+of sin
+3H and I use a little trig
+
+ align:start position:0%
+3H and I use a little trig
+ 
+
+ align:start position:0%
+3H and I use a little trig
+identity so minus that two of that minus
+
+ align:start position:0%
+identity so minus that two of that minus
+ 
+
+ align:start position:0%
+identity so minus that two of that minus
+that turns out to be a multiple of sin 2
+
+ align:start position:0%
+that turns out to be a multiple of sin 2
+ 
+
+ align:start position:0%
+that turns out to be a multiple of sin 2
+H well the two sin 2 H gives us a
+
+ align:start position:0%
+H well the two sin 2 H gives us a
+ 
+
+ align:start position:0%
+H well the two sin 2 H gives us a
+two and then the minus sin H and the
+
+ align:start position:0%
+two and then the minus sin H and the
+ 
+
+ align:start position:0%
+two and then the minus sin H and the
+minus sin 3
+
+ align:start position:0%
+minus sin 3
+ 
+
+ align:start position:0%
+minus sin 3
+H combine into sin 2 H time I think it's
+
+ align:start position:0%
+H combine into sin 2 H time I think it's
+ 
+
+ align:start position:0%
+H combine into sin 2 H time I think it's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+cosine of H or
+
+ align:start position:0%
+cosine of H or
+ 
+
+ align:start position:0%
+cosine of H or
+something it's
+
+ align:start position:0%
+something it's
+ 
+
+ align:start position:0%
+something it's
+that it's that igen Vector that's near
+
+ align:start position:0%
+that it's that igen Vector that's near
+ 
+
+ align:start position:0%
+that it's that igen Vector that's near
+zero because the cosine of H is near one
+
+ align:start position:0%
+zero because the cosine of H is near one
+ 
+
+ align:start position:0%
+zero because the cosine of H is near one
+does that look familiar that a
+
+ align:start position:0%
+does that look familiar that a
+ 
+
+ align:start position:0%
+does that look familiar that a
+combination of s h and sin 3 H should
+
+ align:start position:0%
+combination of s h and sin 3 H should
+ 
+
+ align:start position:0%
+combination of s h and sin 3 H should
+give us twice sin 2 H * some cosine
+
+ align:start position:0%
+give us twice sin 2 H * some cosine
+ 
+
+ align:start position:0%
+give us twice sin 2 H * some cosine
+yeah ele Elementary tra identity
+
+ align:start position:0%
+yeah ele Elementary tra identity
+ 
+
+ align:start position:0%
+yeah ele Elementary tra identity
+okay so those are the igen vectors
+
+ align:start position:0%
+okay so those are the igen vectors
+ 
+
+ align:start position:0%
+okay so those are the igen vectors
+that's the first one the next one would
+
+ align:start position:0%
+that's the first one the next one would
+ 
+
+ align:start position:0%
+that's the first one the next one would
+have H times the K one would have H * K
+
+ align:start position:0%
+have H times the K one would have H * K
+ 
+
+ align:start position:0%
+have H times the K one would have H * K
+instead of just H itself it would take
+
+ align:start position:0%
+instead of just H itself it would take
+ 
+
+ align:start position:0%
+instead of just H itself it would take
+jumps of every K Signs and then uh a
+
+ align:start position:0%
+jumps of every K Signs and then uh a
+ 
+
+ align:start position:0%
+jumps of every K Signs and then uh a
+cosine h k would show up there and this
+
+ align:start position:0%
+cosine h k would show up there and this
+ 
+
+ align:start position:0%
+cosine h k would show up there and this
+would still be an i
+
+ align:start position:0%
+would still be an i
+ 
+
+ align:start position:0%
+would still be an i
+Vector okay um
+
+ align:start position:0%
+Vector okay um
+ 
+
+ align:start position:0%
+Vector okay um
+I'm making a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicit these
+
+ align:start position:0%
+explicit these
+ 
+
+ align:start position:0%
+explicit these
+vectors but the main point is they're
+
+ align:start position:0%
+vectors but the main point is they're
+ 
+
+ align:start position:0%
+vectors but the main point is they're
+signs they're discrete signs at equally
+
+ align:start position:0%
+signs they're discrete signs at equally
+ 
+
+ align:start position:0%
+signs they're discrete signs at equally
+spaced points that's what the real
+
+ align:start position:0%
+spaced points that's what the real
+ 
+
+ align:start position:0%
+spaced points that's what the real
+version of the fft just lives
+
+ align:start position:0%
+version of the fft just lives
+ 
+
+ align:start position:0%
+version of the fft just lives
+on and it would also live on discrete
+
+ align:start position:0%
+on and it would also live on discrete
+ 
+
+ align:start position:0%
+on and it would also live on discrete
+cosiness if we had different boundary
+
+ align:start position:0%
+cosiness if we had different boundary
+ 
+
+ align:start position:0%
+cosiness if we had different boundary
+conditions we could do those too so this
+
+ align:start position:0%
+conditions we could do those too so this
+ 
+
+ align:start position:0%
+conditions we could do those too so this
+isn't the only B this
+
+ align:start position:0%
+isn't the only B this
+ 
+
+ align:start position:0%
+isn't the only B this
+zero these zero boundary conditions are
+
+ align:start position:0%
+zero these zero boundary conditions are
+ 
+
+ align:start position:0%
+zero these zero boundary conditions are
+associated with the name of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derly where zero slopes are associated
+
+ align:start position:0%
+derly where zero slopes are associated
+ 
+
+ align:start position:0%
+derly where zero slopes are associated
+with the name of NOA and both this one
+
+ align:start position:0%
+with the name of NOA and both this one
+ 
+
+ align:start position:0%
+with the name of NOA and both this one
+gives signs noon gives cosiness the fft
+
+ align:start position:0%
+gives signs noon gives cosiness the fft
+ 
+
+ align:start position:0%
+gives signs noon gives cosiness the fft
+deals with both okay so that's
+
+ align:start position:0%
+deals with both okay so that's
+ 
+
+ align:start position:0%
+deals with both okay so that's
+the that's the the fast solution
+
+ align:start position:0%
+the that's the the fast solution
+ 
+
+ align:start position:0%
+the that's the the fast solution
+and it would take n² well oh I have to
+
+ align:start position:0%
+and it would take n² well oh I have to
+ 
+
+ align:start position:0%
+and it would take n² well oh I have to
+go to 2D sorry I I guess I have a little
+
+ align:start position:0%
+go to 2D sorry I I guess I have a little
+ 
+
+ align:start position:0%
+go to 2D sorry I I guess I have a little
+more to say because I have to get from
+
+ align:start position:0%
+more to say because I have to get from
+ 
+
+ align:start position:0%
+more to say because I have to get from
+this onedimensional
+
+ align:start position:0%
+this onedimensional
+ 
+
+ align:start position:0%
+this onedimensional
+second difference to the 5
+
+ align:start position:0%
+second difference to the 5
+ 
+
+ align:start position:0%
+second difference to the 5
+two-dimensional second difference and
+
+ align:start position:0%
+two-dimensional second difference and
+ 
+
+ align:start position:0%
+two-dimensional second difference and
+that's what's going to happen over here
+
+ align:start position:0%
+that's what's going to happen over here
+ 
+
+ align:start position:0%
+that's what's going to happen over here
+uh let me I wrote up
+
+ align:start position:0%
+uh let me I wrote up
+ 
+
+ align:start position:0%
+uh let me I wrote up
+some some stuff about the chroniker
+
+ align:start position:0%
+some some stuff about the chroniker
+ 
+
+ align:start position:0%
+some some stuff about the chroniker
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+which is the Nifty way for these special
+
+ align:start position:0%
+which is the Nifty way for these special
+ 
+
+ align:start position:0%
+which is the Nifty way for these special
+problems to go from 1D to
+
+ align:start position:0%
+problems to go from 1D to
+ 
+
+ align:start position:0%
+problems to go from 1D to
+2D you remember that you remember that
+
+ align:start position:0%
+2D you remember that you remember that
+ 
+
+ align:start position:0%
+2D you remember that you remember that
+the deal that k2d our 2D Matrix was the
+
+ align:start position:0%
+the deal that k2d our 2D Matrix was the
+ 
+
+ align:start position:0%
+the deal that k2d our 2D Matrix was the
+this chroner product
+
+ align:start position:0%
+this chroner product
+ 
+
+ align:start position:0%
+this chroner product
+of of K and I that gave us second
+
+ align:start position:0%
+of of K and I that gave us second
+ 
+
+ align:start position:0%
+of of K and I that gave us second
+differences in One Direction and then we
+
+ align:start position:0%
+differences in One Direction and then we
+ 
+
+ align:start position:0%
+differences in One Direction and then we
+have to add in the chronical product of
+
+ align:start position:0%
+have to add in the chronical product of
+ 
+
+ align:start position:0%
+have to add in the chronical product of
+I and K to get second differences in the
+
+ align:start position:0%
+I and K to get second differences in the
+ 
+
+ align:start position:0%
+I and K to get second differences in the
+other direction and then we better
+
+ align:start position:0%
+other direction and then we better
+ 
+
+ align:start position:0%
+other direction and then we better
+print because that Matrix is going to be
+
+ align:start position:0%
+print because that Matrix is going to be
+ 
+
+ align:start position:0%
+print because that Matrix is going to be
+large I don't want to print
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah what's the point the point is
+
+ align:start position:0%
+it yeah what's the point the point is
+ 
+
+ align:start position:0%
+it yeah what's the point the point is
+that if I know the I vectors of K then I
+
+ align:start position:0%
+that if I know the I vectors of K then I
+ 
+
+ align:start position:0%
+that if I know the I vectors of K then I
+can find the IG the one di if I know the
+
+ align:start position:0%
+can find the IG the one di if I know the
+ 
+
+ align:start position:0%
+can find the IG the one di if I know the
+on Deon vectors I can find the 2 Deon
+
+ align:start position:0%
+on Deon vectors I can find the 2 Deon
+ 
+
+ align:start position:0%
+on Deon vectors I can find the 2 Deon
+vectors and you don't have to know
+
+ align:start position:0%
+vectors and you don't have to know
+ 
+
+ align:start position:0%
+vectors and you don't have to know
+chronic or products to do that all you
+
+ align:start position:0%
+chronic or products to do that all you
+ 
+
+ align:start position:0%
+chronic or products to do that all you
+have to do is just make a sensible guess
+
+ align:start position:0%
+have to do is just make a sensible guess
+ 
+
+ align:start position:0%
+have to do is just make a sensible guess
+so the igen vectors the igen vectors in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2D are so they have a double index K and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L and their
+
+ align:start position:0%
+L and their
+ 
+
+ align:start position:0%
+L and their
+components components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are are signs in One Direction times
+
+ align:start position:0%
+are are signs in One Direction times
+ 
+
+ align:start position:0%
+are are signs in One Direction times
+signs in the other direction so what are
+
+ align:start position:0%
+signs in the other direction so what are
+ 
+
+ align:start position:0%
+signs in the other direction so what are
+those signs is a
+
+ align:start position:0%
+those signs is a
+ 
+
+ align:start position:0%
+those signs is a
+k h I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LH well
+
+ align:start position:0%
+LH well
+ 
+
+ align:start position:0%
+LH well
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+yeah those are the first com those are
+
+ align:start position:0%
+yeah those are the first com those are
+ 
+
+ align:start position:0%
+yeah those are the first com those are
+the first components I guess I have to
+
+ align:start position:0%
+the first components I guess I have to
+ 
+
+ align:start position:0%
+the first components I guess I have to
+tell you what all the components are
+
+ align:start position:0%
+tell you what all the components are
+ 
+
+ align:start position:0%
+tell you what all the components are
+K uh the the seventh component in the X
+
+ align:start position:0%
+K uh the the seventh component in the X
+ 
+
+ align:start position:0%
+K uh the the seventh component in the X
+Direction there'd be a factor 7even so
+
+ align:start position:0%
+Direction there'd be a factor 7even so
+ 
+
+ align:start position:0%
+Direction there'd be a factor 7even so
+say k m h sin l n h this is the
+
+ align:start position:0%
+say k m h sin l n h this is the
+ 
+
+ align:start position:0%
+say k m h sin l n h this is the
+MN
+
+ align:start position:0%
+MN
+ 
+
+ align:start position:0%
+MN
+component
+
+ align:start position:0%
+component
+ 
+
+ align:start position:0%
+component
+of of Y
+
+ align:start position:0%
+of of Y
+ 
+
+ align:start position:0%
+of of Y
+KL of
+
+ align:start position:0%
+KL of
+ 
+
+ align:start position:0%
+KL of
+the right it's just what we had in 1D in
+
+ align:start position:0%
+the right it's just what we had in 1D in
+ 
+
+ align:start position:0%
+the right it's just what we had in 1D in
+1D there was no
+
+ align:start position:0%
+1D there was no
+ 
+
+ align:start position:0%
+1D there was no
+l we just the components were just s kmh
+
+ align:start position:0%
+l we just the components were just s kmh
+ 
+
+ align:start position:0%
+l we just the components were just s kmh
+now we've got two one in the X direction
+
+ align:start position:0%
+now we've got two one in the X direction
+ 
+
+ align:start position:0%
+now we've got two one in the X direction
+we're we're just these are the analoges
+
+ align:start position:0%
+we're we're just these are the analoges
+ 
+
+ align:start position:0%
+we're we're just these are the analoges
+of of the uh uh the The
+
+ align:start position:0%
+of of the uh uh the The
+ 
+
+ align:start position:0%
+of of the uh uh the The
+Continuous case would be
+
+ align:start position:0%
+Continuous case would be
+ 
+
+ align:start position:0%
+Continuous case would be
+s k
+
+ align:start position:0%
+s k
+ 
+
+ align:start position:0%
+s k
+pix
+
+ align:start position:0%
+pix
+ 
+
+ align:start position:0%
+pix
+time sin L Pi
+
+ align:start position:0%
+time sin L Pi
+ 
+
+ align:start position:0%
+time sin L Pi
+y That's the those are the igen vectors
+
+ align:start position:0%
+y That's the those are the igen vectors
+ 
+
+ align:start position:0%
+y That's the those are the igen vectors
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+functions functions of X and Y and the
+
+ align:start position:0%
+functions functions of X and Y and the
+ 
+
+ align:start position:0%
+functions functions of X and Y and the
+point is that once again uh with these
+
+ align:start position:0%
+point is that once again uh with these
+ 
+
+ align:start position:0%
+point is that once again uh with these
+beautiful matrices I can sample the
+
+ align:start position:0%
+beautiful matrices I can sample the
+ 
+
+ align:start position:0%
+beautiful matrices I can sample the
+these at the equally SPAC points and I
+
+ align:start position:0%
+these at the equally SPAC points and I
+ 
+
+ align:start position:0%
+these at the equally SPAC points and I
+get the discrete signs that the fft is
+
+ align:start position:0%
+get the discrete signs that the fft is
+ 
+
+ align:start position:0%
+get the discrete signs that the fft is
+ready to go with
+
+ align:start position:0%
+ready to go with
+ 
+
+ align:start position:0%
+ready to go with
+okay okay I I'm I'm given this much
+
+ align:start position:0%
+okay okay I I'm I'm given this much
+ 
+
+ align:start position:0%
+okay okay I I'm I'm given this much
+detail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the continuous case of course
+
+ align:start position:0%
+because the continuous case of course
+ 
+
+ align:start position:0%
+because the continuous case of course
+our our operators is DC by dx2 and DC by
+
+ align:start position:0%
+our our operators is DC by dx2 and DC by
+ 
+
+ align:start position:0%
+our our operators is DC by dx2 and DC by
+dy^
+
+ align:start position:0%
+dy^
+ 
+
+ align:start position:0%
+dy^
+2 and the
+
+ align:start position:0%
+2 and the
+ 
+
+ align:start position:0%
+2 and the
+whole idea of separating variables of
+
+ align:start position:0%
+whole idea of separating variables of
+ 
+
+ align:start position:0%
+whole idea of separating variables of
+looking for
+
+ align:start position:0%
+looking for
+ 
+
+ align:start position:0%
+looking for
+Solutions youu I I'm really here's the
+
+ align:start position:0%
+Solutions youu I I'm really here's the
+ 
+
+ align:start position:0%
+Solutions youu I I'm really here's the
+igen value problem the continuous value
+
+ align:start position:0%
+igen value problem the continuous value
+ 
+
+ align:start position:0%
+igen value problem the continuous value
+problem the the of U maybe I'd do a
+
+ align:start position:0%
+problem the the of U maybe I'd do a
+ 
+
+ align:start position:0%
+problem the the of U maybe I'd do a
+minus the of U equal Lambda
+
+ align:start position:0%
+minus the of U equal Lambda
+ 
+
+ align:start position:0%
+minus the of U equal Lambda
+U and that's a partial differential
+
+ align:start position:0%
+U and that's a partial differential
+ 
+
+ align:start position:0%
+U and that's a partial differential
+equation usually it's not easy to solve
+
+ align:start position:0%
+equation usually it's not easy to solve
+ 
+
+ align:start position:0%
+equation usually it's not easy to solve
+but if I'm on a
+
+ align:start position:0%
+but if I'm on a
+ 
+
+ align:start position:0%
+but if I'm on a
+square and I have zero boundary
+
+ align:start position:0%
+square and I have zero boundary
+ 
+
+ align:start position:0%
+square and I have zero boundary
+conditions then I've solved it by
+
+ align:start position:0%
+conditions then I've solved it by
+ 
+
+ align:start position:0%
+conditions then I've solved it by
+separation of variables a function of X
+
+ align:start position:0%
+separation of variables a function of X
+ 
+
+ align:start position:0%
+separation of variables a function of X
+time a function of Y right and that
+
+ align:start position:0%
+time a function of Y right and that
+ 
+
+ align:start position:0%
+time a function of Y right and that
+function of X time function of Y is
+
+ align:start position:0%
+function of X time function of Y is
+ 
+
+ align:start position:0%
+function of X time function of Y is
+exactly what chroner product is doing
+
+ align:start position:0%
+exactly what chroner product is doing
+ 
+
+ align:start position:0%
+exactly what chroner product is doing
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's I thought maybe this is a like
+
+ align:start position:0%
+that's I thought maybe this is a like
+ 
+
+ align:start position:0%
+that's I thought maybe this is a like
+good to know when the problem is
+
+ align:start position:0%
+good to know when the problem is
+ 
+
+ align:start position:0%
+good to know when the problem is
+easy and as I say the possibility of
+
+ align:start position:0%
+easy and as I say the possibility of
+ 
+
+ align:start position:0%
+easy and as I say the possibility of
+using the
+
+ align:start position:0%
+using the
+ 
+
+ align:start position:0%
+using the
+easy case on a square for
+
+ align:start position:0%
+easy case on a square for
+ 
+
+ align:start position:0%
+easy case on a square for
+preconditioning a not so easy case is is
+
+ align:start position:0%
+preconditioning a not so easy case is is
+ 
+
+ align:start position:0%
+preconditioning a not so easy case is is
+attractive all right so that's what I
+
+ align:start position:0%
+attractive all right so that's what I
+ 
+
+ align:start position:0%
+attractive all right so that's what I
+wanted to say about number one that's
+
+ align:start position:0%
+wanted to say about number one that's
+ 
+
+ align:start position:0%
+wanted to say about number one that's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+main
+
+ align:start position:0%
+main
+ 
+
+ align:start position:0%
+main
+suggestion and and again the point
+
+ align:start position:0%
+suggestion and and again the point
+ 
+
+ align:start position:0%
+suggestion and and again the point
+was just to take these three simple
+
+ align:start position:0%
+was just to take these three simple
+ 
+
+ align:start position:0%
+was just to take these three simple
+steps provided we know and like the igen
+
+ align:start position:0%
+steps provided we know and like the igen
+ 
+
+ align:start position:0%
+steps provided we know and like the igen
+vectors here we know them and we like
+
+ align:start position:0%
+vectors here we know them and we like
+ 
+
+ align:start position:0%
+vectors here we know them and we like
+them very much because they're those
+
+ align:start position:0%
+them very much because they're those
+ 
+
+ align:start position:0%
+them very much because they're those
+discret signs okay now this the Finish
+
+ align:start position:0%
+discret signs okay now this the Finish
+ 
+
+ align:start position:0%
+discret signs okay now this the Finish
+comes what's up with odd even
+
+ align:start position:0%
+comes what's up with odd even
+ 
+
+ align:start position:0%
+comes what's up with odd even
+reduction I'll use this same 1D problem
+
+ align:start position:0%
+reduction I'll use this same 1D problem
+ 
+
+ align:start position:0%
+reduction I'll use this same 1D problem
+first it it works great in what that's
+
+ align:start position:0%
+first it it works great in what that's
+ 
+
+ align:start position:0%
+first it it works great in what that's
+not good English but it works very well
+
+ align:start position:0%
+not good English but it works very well
+ 
+
+ align:start position:0%
+not good English but it works very well
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1D odd even reduction you'll see it
+
+ align:start position:0%
+1D odd even reduction you'll see it
+ 
+
+ align:start position:0%
+1D odd even reduction you'll see it
+you'll see oh boy simple idea but of
+
+ align:start position:0%
+you'll see oh boy simple idea but of
+ 
+
+ align:start position:0%
+you'll see oh boy simple idea but of
+course don't forget that ordinary
+
+ align:start position:0%
+course don't forget that ordinary
+ 
+
+ align:start position:0%
+course don't forget that ordinary
+elimination is a breeze with a triagonal
+
+ align:start position:0%
+elimination is a breeze with a triagonal
+ 
+
+ align:start position:0%
+elimination is a breeze with a triagonal
+matrix so nothing I could do could be
+
+ align:start position:0%
+matrix so nothing I could do could be
+ 
+
+ align:start position:0%
+matrix so nothing I could do could be
+faster than that but let's see what you
+
+ align:start position:0%
+faster than that but let's see what you
+ 
+
+ align:start position:0%
+faster than that but let's see what you
+can do I just want to write down the
+
+ align:start position:0%
+can do I just want to write down the
+ 
+
+ align:start position:0%
+can do I just want to write down the
+okay keep your keep your eye on this
+
+ align:start position:0%
+okay keep your keep your eye on this
+ 
+
+ align:start position:0%
+okay keep your keep your eye on this
+Matrix uh uh so I'm going to write the
+
+ align:start position:0%
+Matrix uh uh so I'm going to write the
+ 
+
+ align:start position:0%
+Matrix uh uh so I'm going to write the
+I'm going to write out the equations so
+
+ align:start position:0%
+I'm going to write out the equations so
+ 
+
+ align:start position:0%
+I'm going to write out the equations so
+it'll be minus u i - 2 + 2 u i -1 Min -
+
+ align:start position:0%
+it'll be minus u i - 2 + 2 u i -1 Min -
+ 
+
+ align:start position:0%
+it'll be minus u i - 2 + 2 u i -1 Min -
+UI that would be f i -1 that would be
+
+ align:start position:0%
+UI that would be f i -1 that would be
+ 
+
+ align:start position:0%
+UI that would be f i -1 that would be
+equation number I -1 right with a Min -1
+
+ align:start position:0%
+equation number I -1 right with a Min -1
+ 
+
+ align:start position:0%
+equation number I -1 right with a Min -1
+2 minus1 centered there and then the
+
+ align:start position:0%
+2 minus1 centered there and then the
+ 
+
+ align:start position:0%
+2 minus1 centered there and then the
+next one will be a minus u i -1 + 2 UI I
+
+ align:start position:0%
+next one will be a minus u i -1 + 2 UI I
+ 
+
+ align:start position:0%
+next one will be a minus u i -1 + 2 UI I
+better move this guy over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further - u i + 1 that will
+
+ align:start position:0%
+further - u i + 1 that will
+ 
+
+ align:start position:0%
+further - u i + 1 that will
+be fi right that's equation number I and
+
+ align:start position:0%
+be fi right that's equation number I and
+ 
+
+ align:start position:0%
+be fi right that's equation number I and
+now I just want to look at equation
+
+ align:start position:0%
+now I just want to look at equation
+ 
+
+ align:start position:0%
+now I just want to look at equation
+number the next equation - UI + 2 UI + 1
+
+ align:start position:0%
+number the next equation - UI + 2 UI + 1
+ 
+
+ align:start position:0%
+number the next equation - UI + 2 UI + 1
+- u i + 2 is fi +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 so I've written
+
+ align:start position:0%
+1 so I've written
+ 
+
+ align:start position:0%
+1 so I've written
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+three consecutive equations three
+
+ align:start position:0%
+three consecutive equations three
+ 
+
+ align:start position:0%
+three consecutive equations three
+consecutive rows
+
+ align:start position:0%
+consecutive rows
+ 
+
+ align:start position:0%
+consecutive rows
+from my from my
+
+ align:start position:0%
+from my from my
+ 
+
+ align:start position:0%
+from my from my
+uh from my simple Matrix a row the next
+
+ align:start position:0%
+uh from my simple Matrix a row the next
+ 
+
+ align:start position:0%
+uh from my simple Matrix a row the next
+row and the next
+
+ align:start position:0%
+row and the next
+ 
+
+ align:start position:0%
+row and the next
+row so the right hand sides are coming
+
+ align:start position:0%
+row so the right hand sides are coming
+ 
+
+ align:start position:0%
+row so the right hand sides are coming
+in order and the diagonals are there and
+
+ align:start position:0%
+in order and the diagonals are there and
+ 
+
+ align:start position:0%
+in order and the diagonals are there and
+if I look at that do I get any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well there is an idea here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would like
+
+ align:start position:0%
+I would like
+ 
+
+ align:start position:0%
+I would like
+to I'd like to
+
+ align:start position:0%
+to I'd like to
+ 
+
+ align:start position:0%
+to I'd like to
+remove
+
+ align:start position:0%
+remove
+ 
+
+ align:start position:0%
+remove
+these these guys the UI minus ones and
+
+ align:start position:0%
+these these guys the UI minus ones and
+ 
+
+ align:start position:0%
+these these guys the UI minus ones and
+the UI + 1 so that's where this word odd
+
+ align:start position:0%
+the UI + 1 so that's where this word odd
+ 
+
+ align:start position:0%
+the UI + 1 so that's where this word odd
+even reduction is coming in I'm going to
+
+ align:start position:0%
+even reduction is coming in I'm going to
+ 
+
+ align:start position:0%
+even reduction is coming in I'm going to
+reduce this system by keeping only every
+
+ align:start position:0%
+reduce this system by keeping only every
+ 
+
+ align:start position:0%
+reduce this system by keeping only every
+second unknown and
+
+ align:start position:0%
+second unknown and
+ 
+
+ align:start position:0%
+second unknown and
+eliminating those how to do that well
+
+ align:start position:0%
+eliminating those how to do that well
+ 
+
+ align:start position:0%
+eliminating those how to do that well
+you can see how to eliminate if If I
+
+ align:start position:0%
+you can see how to eliminate if If I
+ 
+
+ align:start position:0%
+you can see how to eliminate if If I
+multiply this equation by
+
+ align:start position:0%
+multiply this equation by
+ 
+
+ align:start position:0%
+multiply this equation by
+two so if I multiply that middle
+
+ align:start position:0%
+two so if I multiply that middle
+ 
+
+ align:start position:0%
+two so if I multiply that middle
+equation by two that becomes a four this
+
+ align:start position:0%
+equation by two that becomes a four this
+ 
+
+ align:start position:0%
+equation by two that becomes a four this
+becomes a minus two this becomes a two
+
+ align:start position:0%
+becomes a minus two this becomes a two
+ 
+
+ align:start position:0%
+becomes a minus two this becomes a two
+and now what shall I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+add if I add the equations together I
+
+ align:start position:0%
+add if I add the equations together I
+ 
+
+ align:start position:0%
+add if I add the equations together I
+get min - u i- 2 these cancel that was
+
+ align:start position:0%
+get min - u i- 2 these cancel that was
+ 
+
+ align:start position:0%
+get min - u i- 2 these cancel that was
+the point plus 4 minus a couple so
+
+ align:start position:0%
+the point plus 4 minus a couple so
+ 
+
+ align:start position:0%
+the point plus 4 minus a couple so
+that's 2 UI
+
+ align:start position:0%
+that's 2 UI
+ 
+
+ align:start position:0%
+that's 2 UI
+minus this guy u i- 2 is that sum f i -1
+
+ align:start position:0%
+minus this guy u i- 2 is that sum f i -1
+ 
+
+ align:start position:0%
+minus this guy u i- 2 is that sum f i -1
+to two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fi and fi +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one well sorry it's squeezed down here
+
+ align:start position:0%
+one well sorry it's squeezed down here
+ 
+
+ align:start position:0%
+one well sorry it's squeezed down here
+but this is the the
+
+ align:start position:0%
+but this is the the
+ 
+
+ align:start position:0%
+but this is the the
+point the main point is look at
+
+ align:start position:0%
+point the main point is look at
+ 
+
+ align:start position:0%
+point the main point is look at
+this what what do we
+
+ align:start position:0%
+this what what do we
+ 
+
+ align:start position:0%
+this what what do we
+have we've got a typical
+
+ align:start position:0%
+have we've got a typical
+ 
+
+ align:start position:0%
+have we've got a typical
+equation but now
+
+ align:start position:0%
+equation but now
+ 
+
+ align:start position:0%
+equation but now
+uh We've we've removed half the
+
+ align:start position:0%
+uh We've we've removed half the
+ 
+
+ align:start position:0%
+uh We've we've removed half the
+unknowns the problem is now half size
+
+ align:start position:0%
+unknowns the problem is now half size
+ 
+
+ align:start position:0%
+unknowns the problem is now half size
+we've only got the even numbered
+
+ align:start position:0%
+we've only got the even numbered
+ 
+
+ align:start position:0%
+we've only got the even numbered
+unknowns at a small cost
+
+ align:start position:0%
+unknowns at a small cost
+ 
+
+ align:start position:0%
+unknowns at a small cost
+in updating the right hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sides and the problems cut in
+
+ align:start position:0%
+sides and the problems cut in
+ 
+
+ align:start position:0%
+sides and the problems cut in
+half so that's this odd even
+
+ align:start position:0%
+half so that's this odd even
+ 
+
+ align:start position:0%
+half so that's this odd even
+reduction
+
+ align:start position:0%
+reduction
+ 
+
+ align:start position:0%
+reduction
+and it cuts the problem in half and
+
+ align:start position:0%
+and it cuts the problem in half and
+ 
+
+ align:start position:0%
+and it cuts the problem in half and
+everybody knows right away what to do
+
+ align:start position:0%
+everybody knows right away what to do
+ 
+
+ align:start position:0%
+everybody knows right away what to do
+next the The One Mantra of computer
+
+ align:start position:0%
+next the The One Mantra of computer
+ 
+
+ align:start position:0%
+next the The One Mantra of computer
+science do it
+
+ align:start position:0%
+science do it
+ 
+
+ align:start position:0%
+science do it
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+so that is the same problem on the evens
+
+ align:start position:0%
+so that is the same problem on the evens
+ 
+
+ align:start position:0%
+so that is the same problem on the evens
+we do it again so it's it I should
+
+ align:start position:0%
+we do it again so it's it I should
+ 
+
+ align:start position:0%
+we do it again so it's it I should
+really call it cyclic reduction we just
+
+ align:start position:0%
+really call it cyclic reduction we just
+ 
+
+ align:start position:0%
+really call it cyclic reduction we just
+cycle with this reduction and in the end
+
+ align:start position:0%
+cycle with this reduction and in the end
+ 
+
+ align:start position:0%
+cycle with this reduction and in the end
+we have a 2X two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem that seems pretty smart pretty
+
+ align:start position:0%
+problem that seems pretty smart pretty
+ 
+
+ align:start position:0%
+problem that seems pretty smart pretty
+successful
+
+ align:start position:0%
+successful
+ 
+
+ align:start position:0%
+successful
+move and I guess if we do an operation
+
+ align:start position:0%
+move and I guess if we do an operation
+ 
+
+ align:start position:0%
+move and I guess if we do an operation
+count well I haven't thought that
+
+ align:start position:0%
+count well I haven't thought that
+ 
+
+ align:start position:0%
+count well I haven't thought that
+through what does the operation count
+
+ align:start position:0%
+through what does the operation count
+ 
+
+ align:start position:0%
+through what does the operation count
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like it must be pretty quick right well
+
+ align:start position:0%
+like it must be pretty quick right well
+ 
+
+ align:start position:0%
+like it must be pretty quick right well
+undoubtedly we're solving this linear
+
+ align:start position:0%
+undoubtedly we're solving this linear
+ 
+
+ align:start position:0%
+undoubtedly we're solving this linear
+system in O of n steps
+
+ align:start position:0%
+system in O of n steps
+ 
+
+ align:start position:0%
+system in O of n steps
+well no big surprise to be able to deal
+
+ align:start position:0%
+well no big surprise to be able to deal
+ 
+
+ align:start position:0%
+well no big surprise to be able to deal
+with that Matrix in O of n steps because
+
+ align:start position:0%
+with that Matrix in O of n steps because
+ 
+
+ align:start position:0%
+with that Matrix in O of n steps because
+it's we elimination would take o of n
+
+ align:start position:0%
+it's we elimination would take o of n
+ 
+
+ align:start position:0%
+it's we elimination would take o of n
+steps it's its size n but its bandwidth
+
+ align:start position:0%
+steps it's its size n but its bandwidth
+ 
+
+ align:start position:0%
+steps it's its size n but its bandwidth
+is one so 2 N or something steps would
+
+ align:start position:0%
+is one so 2 N or something steps would
+ 
+
+ align:start position:0%
+is one so 2 N or something steps would
+do it and maybe I don't know how many
+
+ align:start position:0%
+do it and maybe I don't know how many
+ 
+
+ align:start position:0%
+do it and maybe I don't know how many
+steps we have here uh I guess when we
+
+ align:start position:0%
+steps we have here uh I guess when we
+ 
+
+ align:start position:0%
+steps we have here uh I guess when we
+cut it in half that required us to do
+
+ align:start position:0%
+cut it in half that required us to do
+ 
+
+ align:start position:0%
+cut it in half that required us to do
+that much it it's a it's order
+
+ align:start position:0%
+that much it it's a it's order
+ 
+
+ align:start position:0%
+that much it it's a it's order
+in it's order
+
+ align:start position:0%
+in it's order
+ 
+
+ align:start position:0%
+in it's order
+in and
+
+ align:start position:0%
+in and
+ 
+
+ align:start position:0%
+in and
+so the key question is can we do it in
+
+ align:start position:0%
+so the key question is can we do it in
+ 
+
+ align:start position:0%
+so the key question is can we do it in
+2D can we do the same thing in 2D that's
+
+ align:start position:0%
+2D can we do the same thing in 2D that's
+ 
+
+ align:start position:0%
+2D can we do the same thing in 2D that's
+that's so I want to follow that plan in
+
+ align:start position:0%
+that's so I want to follow that plan in
+ 
+
+ align:start position:0%
+that's so I want to follow that plan in
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+Dimensions where now you will
+
+ align:start position:0%
+Dimensions where now you will
+ 
+
+ align:start position:0%
+Dimensions where now you will
+be a whole row at a time so I'm doing
+
+ align:start position:0%
+be a whole row at a time so I'm doing
+ 
+
+ align:start position:0%
+be a whole row at a time so I'm doing
+blocks 2D block
+
+ align:start position:0%
+blocks 2D block
+ 
+
+ align:start position:0%
+blocks 2D block
+2D so can I write down the equations in
+
+ align:start position:0%
+2D so can I write down the equations in
+ 
+
+ align:start position:0%
+2D so can I write down the equations in
+Block 2D for for whole row so UI is the
+
+ align:start position:0%
+Block 2D for for whole row so UI is the
+ 
+
+ align:start position:0%
+Block 2D for for whole row so UI is the
+vector so so now this is the 2D problem
+
+ align:start position:0%
+vector so so now this is the 2D problem
+ 
+
+ align:start position:0%
+vector so so now this is the 2D problem
+so it'll be minus the identity where
+
+ align:start position:0%
+so it'll be minus the identity where
+ 
+
+ align:start position:0%
+so it'll be minus the identity where
+instead of instead of one I have to
+
+ align:start position:0%
+instead of instead of one I have to
+ 
+
+ align:start position:0%
+instead of instead of one I have to
+write the identity U IUS 2 and 2 K right
+
+ align:start position:0%
+write the identity U IUS 2 and 2 K right
+ 
+
+ align:start position:0%
+write the identity U IUS 2 and 2 K right
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+the oh no what is the what is the middle
+
+ align:start position:0%
+the oh no what is the what is the middle
+ 
+
+ align:start position:0%
+the oh no what is the what is the middle
+what's on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the oh let me multiplying
+
+ align:start position:0%
+the oh let me multiplying
+ 
+
+ align:start position:0%
+the oh let me multiplying
+UI UI minus one I want to just say the
+
+ align:start position:0%
+UI UI minus one I want to just say the
+ 
+
+ align:start position:0%
+UI UI minus one I want to just say the
+same thing but I want I have to write
+
+ align:start position:0%
+same thing but I want I have to write
+ 
+
+ align:start position:0%
+same thing but I want I have to write
+down the the N this is going to be n s
+
+ align:start position:0%
+down the the N this is going to be n s
+ 
+
+ align:start position:0%
+down the the N this is going to be n s
+equations n at a time a whole row at a
+
+ align:start position:0%
+equations n at a time a whole row at a
+ 
+
+ align:start position:0%
+equations n at a time a whole row at a
+time and what what's on the diagonal of
+
+ align:start position:0%
+time and what what's on the diagonal of
+ 
+
+ align:start position:0%
+time and what what's on the diagonal of
+k2d not 2K
+
+ align:start position:0%
+k2d not 2K
+ 
+
+ align:start position:0%
+k2d not 2K
+it's um 2 I is it 2 I + K yeah yeah k +
+
+ align:start position:0%
+it's um 2 I is it 2 I + K yeah yeah k +
+ 
+
+ align:start position:0%
+it's um 2 I is it 2 I + K yeah yeah k +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+I isn't that what we have on the
+
+ align:start position:0%
+I isn't that what we have on the
+ 
+
+ align:start position:0%
+I isn't that what we have on the
+diagonal of the K2
+
+ align:start position:0%
+diagonal of the K2
+ 
+
+ align:start position:0%
+diagonal of the K2
+D1 * u i
+
+ align:start position:0%
+D1 * u i
+ 
+
+ align:start position:0%
+D1 * u i
+-1 - i
+
+ align:start position:0%
+-1 - i
+ 
+
+ align:start position:0%
+-1 - i
+u i is equal to
+
+ align:start position:0%
+u i is equal to
+ 
+
+ align:start position:0%
+u i is equal to
+some that's a whole row at a time this
+
+ align:start position:0%
+some that's a whole row at a time this
+ 
+
+ align:start position:0%
+some that's a whole row at a time this
+is these are all vectors with n
+
+ align:start position:0%
+is these are all vectors with n
+ 
+
+ align:start position:0%
+is these are all vectors with n
+components now right right this is the
+
+ align:start position:0%
+components now right right this is the
+ 
+
+ align:start position:0%
+components now right right this is the
+minus I the 2 I and the minus I are the
+
+ align:start position:0%
+minus I the 2 I and the minus I are the
+ 
+
+ align:start position:0%
+minus I the 2 I and the minus I are the
+second differences of one of rows they
+
+ align:start position:0%
+second differences of one of rows they
+ 
+
+ align:start position:0%
+second differences of one of rows they
+they differences in the vertical
+
+ align:start position:0%
+they differences in the vertical
+ 
+
+ align:start position:0%
+they differences in the vertical
+Direction and this K UI is the second
+
+ align:start position:0%
+Direction and this K UI is the second
+ 
+
+ align:start position:0%
+Direction and this K UI is the second
+differences along the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row okay so same equation at the next
+
+ align:start position:0%
+row okay so same equation at the next
+ 
+
+ align:start position:0%
+row okay so same equation at the next
+row so the next row is minus I UI - one
+
+ align:start position:0%
+row so the next row is minus I UI - one
+ 
+
+ align:start position:0%
+row so the next row is minus I UI - one
+2 k + 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UI UI because that's now the diagonal
+
+ align:start position:0%
+UI UI because that's now the diagonal
+ 
+
+ align:start position:0%
+UI UI because that's now the diagonal
+block minus I UI + 1 is f i + 1 and it
+
+ align:start position:0%
+block minus I UI + 1 is f i + 1 and it
+ 
+
+ align:start position:0%
+block minus I UI + 1 is f i + 1 and it
+just take me a second to write this one
+
+ align:start position:0%
+just take me a second to write this one
+ 
+
+ align:start position:0%
+just take me a second to write this one
+this is k + 2
+
+ align:start position:0%
+this is k + 2
+ 
+
+ align:start position:0%
+this is k + 2
+I UI + 1 - I UI + 2 is f i + 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay exactly the
+
+ align:start position:0%
+okay exactly the
+ 
+
+ align:start position:0%
+okay exactly the
+same but
+
+ align:start position:0%
+same but
+ 
+
+ align:start position:0%
+same but
+now a row at a time in 2D okay so what's
+
+ align:start position:0%
+now a row at a time in 2D okay so what's
+ 
+
+ align:start position:0%
+now a row at a time in 2D okay so what's
+the same idea is going to work right
+
+ align:start position:0%
+the same idea is going to work right
+ 
+
+ align:start position:0%
+the same idea is going to work right
+what do I do I want to cancel this so I
+
+ align:start position:0%
+what do I do I want to cancel this so I
+ 
+
+ align:start position:0%
+what do I do I want to cancel this so I
+multiply that row by k + 2
+
+ align:start position:0%
+multiply that row by k + 2
+ 
+
+ align:start position:0%
+multiply that row by k + 2
+I before I multiplied it by two but now
+
+ align:start position:0%
+I before I multiplied it by two but now
+ 
+
+ align:start position:0%
+I before I multiplied it by two but now
+I have to multiply by k + 2
+
+ align:start position:0%
+I have to multiply by k + 2
+ 
+
+ align:start position:0%
+I have to multiply by k + 2
+itimes the row times the row whole row
+
+ align:start position:0%
+itimes the row times the row whole row
+ 
+
+ align:start position:0%
+itimes the row times the row whole row
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+add so when I do that this cancels so I
+
+ align:start position:0%
+add so when I do that this cancels so I
+ 
+
+ align:start position:0%
+add so when I do that this cancels so I
+have minus this this guy wasn't
+
+ align:start position:0%
+have minus this this guy wasn't
+ 
+
+ align:start position:0%
+have minus this this guy wasn't
+affected and this this will cancel right
+
+ align:start position:0%
+affected and this this will cancel right
+ 
+
+ align:start position:0%
+affected and this this will cancel right
+the k+ 2 I will cancel this one just as
+
+ align:start position:0%
+the k+ 2 I will cancel this one just as
+ 
+
+ align:start position:0%
+the k+ 2 I will cancel this one just as
+before this will not be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+affected UI +
+
+ align:start position:0%
+affected UI +
+ 
+
+ align:start position:0%
+affected UI +
+2 and I have some I took I have
+
+ align:start position:0%
+2 and I have some I took I have
+ 
+
+ align:start position:0%
+2 and I have some I took I have
+fi and k + 2 I Fi Fi + 1 and f i + 2 did
+
+ align:start position:0%
+fi and k + 2 I Fi Fi + 1 and f i + 2 did
+ 
+
+ align:start position:0%
+fi and k + 2 I Fi Fi + 1 and f i + 2 did
+I maybe I did that should have been IUS
+
+ align:start position:0%
+I maybe I did that should have been IUS
+ 
+
+ align:start position:0%
+I maybe I did that should have been IUS
+one and this should have been I and this
+
+ align:start position:0%
+one and this should have been I and this
+ 
+
+ align:start position:0%
+one and this should have been I and this
+should have been I + one sorry
+
+ align:start position:0%
+should have been I + one sorry
+ 
+
+ align:start position:0%
+should have been I + one sorry
+to Mis label the
+
+ align:start position:0%
+to Mis label the
+ 
+
+ align:start position:0%
+to Mis label the
+fs but no big deal the point is the left
+
+ align:start position:0%
+fs but no big deal the point is the left
+ 
+
+ align:start position:0%
+fs but no big deal the point is the left
+side and the point is what's in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space what goes in that space well it's
+
+ align:start position:0%
+space what goes in that space well it's
+ 
+
+ align:start position:0%
+space what goes in that space well it's
+Min - i k + 2 i^
+
+ align:start position:0%
+Min - i k + 2 i^
+ 
+
+ align:start position:0%
+Min - i k + 2 i^
+2 - I so this is this
+
+ align:start position:0%
+2 - I so this is this
+ 
+
+ align:start position:0%
+2 - I so this is this
+is k + 2 i^ 2 which before was so
+
+ align:start position:0%
+is k + 2 i^ 2 which before was so
+ 
+
+ align:start position:0%
+is k + 2 i^ 2 which before was so
+easy and then the minus I and the minus
+
+ align:start position:0%
+easy and then the minus I and the minus
+ 
+
+ align:start position:0%
+easy and then the minus I and the minus
+I is min - 2 I is multiplying the UI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that was minus
+
+ align:start position:0%
+yeah that was minus
+ 
+
+ align:start position:0%
+yeah that was minus
+I okay this is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix from OD even
+
+ align:start position:0%
+Matrix from OD even
+ 
+
+ align:start position:0%
+Matrix from OD even
+reduction I I it's just natural to try
+
+ align:start position:0%
+reduction I I it's just natural to try
+ 
+
+ align:start position:0%
+reduction I I it's just natural to try
+the idea and the idea
+
+ align:start position:0%
+the idea and the idea
+ 
+
+ align:start position:0%
+the idea and the idea
+works but not so
+
+ align:start position:0%
+works but not so
+ 
+
+ align:start position:0%
+works but not so
+perfectly because
+
+ align:start position:0%
+perfectly because
+ 
+
+ align:start position:0%
+perfectly because
+previously in
+
+ align:start position:0%
+previously in
+ 
+
+ align:start position:0%
+previously in
+1D that was just gave us the answer
+
+ align:start position:0%
+1D that was just gave us the answer
+ 
+
+ align:start position:0%
+1D that was just gave us the answer
+two it was four 4 - 2 but now in
+
+ align:start position:0%
+two it was four 4 - 2 but now in
+ 
+
+ align:start position:0%
+two it was four 4 - 2 but now in
+2D we have a matrix not surprising but
+
+ align:start position:0%
+2D we have a matrix not surprising but
+ 
+
+ align:start position:0%
+2D we have a matrix not surprising but
+what we don't like is the fact that the
+
+ align:start position:0%
+what we don't like is the fact that the
+ 
+
+ align:start position:0%
+what we don't like is the fact that the
+bandwidth is growing K was Tri diagonal
+
+ align:start position:0%
+bandwidth is growing K was Tri diagonal
+ 
+
+ align:start position:0%
+bandwidth is growing K was Tri diagonal
+but when we Square it it will have five
+
+ align:start position:0%
+but when we Square it it will have five
+ 
+
+ align:start position:0%
+but when we Square it it will have five
+diagonal and when we repeat the odd even
+
+ align:start position:0%
+diagonal and when we repeat the odd even
+ 
+
+ align:start position:0%
+diagonal and when we repeat the odd even
+cycle when we do it again those five
+
+ align:start position:0%
+cycle when we do it again those five
+ 
+
+ align:start position:0%
+cycle when we do it again those five
+diagonals will be nine
+
+ align:start position:0%
+diagonals will be nine
+ 
+
+ align:start position:0%
+diagonals will be nine
+diagonal and
+
+ align:start position:0%
+diagonal and
+ 
+
+ align:start position:0%
+diagonal and
+onwards so
+
+ align:start position:0%
+onwards so
+ 
+
+ align:start position:0%
+onwards so
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+uh I I I'm getting half siize
+
+ align:start position:0%
+uh I I I'm getting half siize
+ 
+
+ align:start position:0%
+uh I I I'm getting half siize
+problems all the odd numbered rows in my
+
+ align:start position:0%
+problems all the odd numbered rows in my
+ 
+
+ align:start position:0%
+problems all the odd numbered rows in my
+Square are are
+
+ align:start position:0%
+Square are are
+ 
+
+ align:start position:0%
+Square are are
+eliminated just this just involves the
+
+ align:start position:0%
+eliminated just this just involves the
+ 
+
+ align:start position:0%
+eliminated just this just involves the
+even numbered rows but the Matrix is
+
+ align:start position:0%
+even numbered rows but the Matrix is
+ 
+
+ align:start position:0%
+even numbered rows but the Matrix is
+not Tri diagonal
+
+ align:start position:0%
+not Tri diagonal
+ 
+
+ align:start position:0%
+not Tri diagonal
+anymore it's growing in bandwidth so the
+
+ align:start position:0%
+anymore it's growing in bandwidth so the
+ 
+
+ align:start position:0%
+anymore it's growing in bandwidth so the
+and then you have to keep track of it so
+
+ align:start position:0%
+and then you have to keep track of it so
+ 
+
+ align:start position:0%
+and then you have to keep track of it so
+the the final conclusion
+
+ align:start position:0%
+the the final conclusion
+ 
+
+ align:start position:0%
+the the final conclusion
+is that this is a pretty good
+
+ align:start position:0%
+is that this is a pretty good
+ 
+
+ align:start position:0%
+is that this is a pretty good
+idea but it's not quite as good as this
+
+ align:start position:0%
+idea but it's not quite as good as this
+ 
+
+ align:start position:0%
+idea but it's not quite as good as this
+one it's not as good as the fft based
+
+ align:start position:0%
+one it's not as good as the fft based
+ 
+
+ align:start position:0%
+one it's not as good as the fft based
+idea also the if you look to see what is
+
+ align:start position:0%
+idea also the if you look to see what is
+ 
+
+ align:start position:0%
+idea also the if you look to see what is
+most efficient see the igon vectors are
+
+ align:start position:0%
+most efficient see the igon vectors are
+ 
+
+ align:start position:0%
+most efficient see the igon vectors are
+still here so I could do three steps of
+
+ align:start position:0%
+still here so I could do three steps of
+ 
+
+ align:start position:0%
+still here so I could do three steps of
+this and then
+
+ align:start position:0%
+this and then
+ 
+
+ align:start position:0%
+this and then
+then go to Fier and that probably is
+
+ align:start position:0%
+then go to Fier and that probably is
+ 
+
+ align:start position:0%
+then go to Fier and that probably is
+about right due so if you really wanted
+
+ align:start position:0%
+about right due so if you really wanted
+ 
+
+ align:start position:0%
+about right due so if you really wanted
+to to polish a um a fast Plus on solver
+
+ align:start position:0%
+to to polish a um a fast Plus on solver
+ 
+
+ align:start position:0%
+to to polish a um a fast Plus on solver
+you could do two or maybe two steps or
+
+ align:start position:0%
+you could do two or maybe two steps or
+ 
+
+ align:start position:0%
+you could do two or maybe two steps or
+three of odd even cyclic
+
+ align:start position:0%
+three of odd even cyclic
+ 
+
+ align:start position:0%
+three of odd even cyclic
+reduction but then your Matrix is
+
+ align:start position:0%
+reduction but then your Matrix is
+ 
+
+ align:start position:0%
+reduction but then your Matrix is
+getting
+
+ align:start position:0%
+getting
+ 
+
+ align:start position:0%
+getting
+messy
+
+ align:start position:0%
+messy
+ 
+
+ align:start position:0%
+messy
+and you switch to the fast Plus solver
+
+ align:start position:0%
+and you switch to the fast Plus solver
+ 
+
+ align:start position:0%
+and you switch to the fast Plus solver
+so it's not quite Pon anymore because
+
+ align:start position:0%
+so it's not quite Pon anymore because
+ 
+
+ align:start position:0%
+so it's not quite Pon anymore because
+it's has a Messier Matrix but it's still
+
+ align:start position:0%
+it's has a Messier Matrix but it's still
+ 
+
+ align:start position:0%
+it's has a Messier Matrix but it's still
+it still has the same ion vectors
+
+ align:start position:0%
+it still has the same ion vectors
+ 
+
+ align:start position:0%
+it still has the same ion vectors
+because we're as long as we stay with
+
+ align:start position:0%
+because we're as long as we stay with
+ 
+
+ align:start position:0%
+because we're as long as we stay with
+the Matrix K we know it's ion vectors
+
+ align:start position:0%
+the Matrix K we know it's ion vectors
+ 
+
+ align:start position:0%
+the Matrix K we know it's ion vectors
+and we know that
+
+ align:start position:0%
+and we know that
+ 
+
+ align:start position:0%
+and we know that
+they're signs and that they're quick to
+
+ align:start position:0%
+they're signs and that they're quick to
+ 
+
+ align:start position:0%
+they're signs and that they're quick to
+work with Okay anyway there you go
+
+ align:start position:0%
+work with Okay anyway there you go
+ 
+
+ align:start position:0%
+work with Okay anyway there you go
+that's a fast algorithm for the for the
+
+ align:start position:0%
+that's a fast algorithm for the for the
+ 
+
+ align:start position:0%
+that's a fast algorithm for the for the
+hour for the lecture before the spring
+
+ align:start position:0%
+hour for the lecture before the spring
+ 
+
+ align:start position:0%
+hour for the lecture before the spring
+break uh so after the break is first of
+
+ align:start position:0%
+break uh so after the break is first of
+ 
+
+ align:start position:0%
+break uh so after the break is first of
+all discussion of
+
+ align:start position:0%
+all discussion of
+ 
+
+ align:start position:0%
+all discussion of
+projects if your project could
+
+ align:start position:0%
+projects if your project could
+ 
+
+ align:start position:0%
+projects if your project could
+include uh page and you could
+
+ align:start position:0%
+include uh page and you could
+ 
+
+ align:start position:0%
+include uh page and you could
+maybe you could email the whole project
+
+ align:start position:0%
+maybe you could email the whole project
+ 
+
+ align:start position:0%
+maybe you could email the whole project
+to Mr Cho maybe also could you email to
+
+ align:start position:0%
+to Mr Cho maybe also could you email to
+ 
+
+ align:start position:0%
+to Mr Cho maybe also could you email to
+me uh a sort of uh summary page
+
+ align:start position:0%
+me uh a sort of uh summary page
+ 
+
+ align:start position:0%
+me uh a sort of uh summary page
+that that tells me what you did so I'll
+
+ align:start position:0%
+that that tells me what you did so I'll
+ 
+
+ align:start position:0%
+that that tells me what you did so I'll
+save the summary pages and I'll have
+
+ align:start position:0%
+save the summary pages and I'll have
+ 
+
+ align:start position:0%
+save the summary pages and I'll have
+from Mr Cho the complete uh project with
+
+ align:start position:0%
+from Mr Cho the complete uh project with
+ 
+
+ align:start position:0%
+from Mr Cho the complete uh project with
+with print out and uh graphs as far as
+
+ align:start position:0%
+with print out and uh graphs as far as
+ 
+
+ align:start position:0%
+with print out and uh graphs as far as
+appropriate and uh so we'll spend some
+
+ align:start position:0%
+appropriate and uh so we'll spend some
+ 
+
+ align:start position:0%
+appropriate and uh so we'll spend some
+time on that and then move to the next
+
+ align:start position:0%
+time on that and then move to the next
+ 
+
+ align:start position:0%
+time on that and then move to the next
+to the the big topic of
+
+ align:start position:0%
+to the the big topic of
+ 
+
+ align:start position:0%
+to the the big topic of
+the of the next month of the next of the
+
+ align:start position:0%
+the of the next month of the next of the
+ 
+
+ align:start position:0%
+the of the next month of the next of the
+rest of the course which is um solving
+
+ align:start position:0%
+rest of the course which is um solving
+ 
+
+ align:start position:0%
+rest of the course which is um solving
+optimization problems minimization
+
+ align:start position:0%
+optimization problems minimization
+ 
+
+ align:start position:0%
+optimization problems minimization
+maximization uh in many
+
+ align:start position:0%
+maximization uh in many
+ 
+
+ align:start position:0%
+maximization uh in many
+variables okay so have a good spring
+
+ align:start position:0%
+variables okay so have a good spring
+ 
+
+ align:start position:0%
+variables okay so have a good spring
+break and uh see you on the Wednesday
+
+ align:start position:0%
+break and uh see you on the Wednesday
+ 
+
+ align:start position:0%
+break and uh see you on the Wednesday
+after so so a week from Wednesday good
\ No newline at end of file
diff --git a/lF-LM9CdiVk.txt b/lF-LM9CdiVk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fdbdd1a90d034a29e33541d9862f52e5a39632a0
--- /dev/null
+++ b/lF-LM9CdiVk.txt
@@ -0,0 +1,859 @@
+align:start position:0%
+ 
+hello everybody
+
+ align:start position:0%
+hello everybody
+ 
+
+ align:start position:0%
+hello everybody
+um so this set of slide is on the
+
+ align:start position:0%
+um so this set of slide is on the
+ 
+
+ align:start position:0%
+um so this set of slide is on the
+organization of this course
+
+ align:start position:0%
+organization of this course
+ 
+
+ align:start position:0%
+organization of this course
+um you know as part of the syllabus i'll
+
+ align:start position:0%
+um you know as part of the syllabus i'll
+ 
+
+ align:start position:0%
+um you know as part of the syllabus i'll
+explain uh how the course is structured
+
+ align:start position:0%
+explain uh how the course is structured
+ 
+
+ align:start position:0%
+explain uh how the course is structured
+how you participate
+
+ align:start position:0%
+how you participate
+ 
+
+ align:start position:0%
+how you participate
+how you've been created um and i give
+
+ align:start position:0%
+how you've been created um and i give
+ 
+
+ align:start position:0%
+how you've been created um and i give
+you some details and you know where to
+
+ align:start position:0%
+you some details and you know where to
+ 
+
+ align:start position:0%
+you some details and you know where to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+proper pointers um to get started
+
+ align:start position:0%
+proper pointers um to get started
+ 
+
+ align:start position:0%
+proper pointers um to get started
+um this class will be taught in an
+
+ align:start position:0%
+um this class will be taught in an
+ 
+
+ align:start position:0%
+um this class will be taught in an
+inverted classroom or flipped
+
+ align:start position:0%
+inverted classroom or flipped
+ 
+
+ align:start position:0%
+inverted classroom or flipped
+classroom setting and it's going to be
+
+ align:start position:0%
+classroom setting and it's going to be
+ 
+
+ align:start position:0%
+classroom setting and it's going to be
+online only
+
+ align:start position:0%
+online only
+ 
+
+ align:start position:0%
+online only
+so we will not have in-person
+
+ align:start position:0%
+so we will not have in-person
+ 
+
+ align:start position:0%
+so we will not have in-person
+opportunities to discuss
+
+ align:start position:0%
+opportunities to discuss
+ 
+
+ align:start position:0%
+opportunities to discuss
+there's a second video where i just
+
+ align:start position:0%
+there's a second video where i just
+ 
+
+ align:start position:0%
+there's a second video where i just
+briefly talk about the strategy of
+
+ align:start position:0%
+briefly talk about the strategy of
+ 
+
+ align:start position:0%
+briefly talk about the strategy of
+the university classroom and and the
+
+ align:start position:0%
+the university classroom and and the
+ 
+
+ align:start position:0%
+the university classroom and and the
+benefits
+
+ align:start position:0%
+benefits
+ 
+
+ align:start position:0%
+benefits
+what you are typically used for as
+
+ align:start position:0%
+what you are typically used for as
+ 
+
+ align:start position:0%
+what you are typically used for as
+lectures is
+
+ align:start position:0%
+lectures is
+ 
+
+ align:start position:0%
+lectures is
+organized solely in short videos um
+
+ align:start position:0%
+organized solely in short videos um
+ 
+
+ align:start position:0%
+organized solely in short videos um
+where i discuss
+
+ align:start position:0%
+where i discuss
+ 
+
+ align:start position:0%
+where i discuss
+concepts or methods um the ideas also
+
+ align:start position:0%
+concepts or methods um the ideas also
+ 
+
+ align:start position:0%
+concepts or methods um the ideas also
+include
+
+ align:start position:0%
+include
+ 
+
+ align:start position:0%
+include
+um a few short questions for you your
+
+ align:start position:0%
+um a few short questions for you your
+ 
+
+ align:start position:0%
+um a few short questions for you your
+own self elimination and we'll pick up
+
+ align:start position:0%
+own self elimination and we'll pick up
+ 
+
+ align:start position:0%
+own self elimination and we'll pick up
+those questions then later
+
+ align:start position:0%
+those questions then later
+ 
+
+ align:start position:0%
+those questions then later
+in visitation sessions so when you meet
+
+ align:start position:0%
+in visitation sessions so when you meet
+ 
+
+ align:start position:0%
+in visitation sessions so when you meet
+tuesdays and thursday
+
+ align:start position:0%
+tuesdays and thursday
+ 
+
+ align:start position:0%
+tuesdays and thursday
+we have time to answer your questions we
+
+ align:start position:0%
+we have time to answer your questions we
+ 
+
+ align:start position:0%
+we have time to answer your questions we
+have time
+
+ align:start position:0%
+have time
+ 
+
+ align:start position:0%
+have time
+to go through those problems
+
+ align:start position:0%
+to go through those problems
+ 
+
+ align:start position:0%
+to go through those problems
+and hopefully have a good discussion the
+
+ align:start position:0%
+and hopefully have a good discussion the
+ 
+
+ align:start position:0%
+and hopefully have a good discussion the
+recitations
+
+ align:start position:0%
+recitations
+ 
+
+ align:start position:0%
+recitations
+are also used for another concept which
+
+ align:start position:0%
+are also used for another concept which
+ 
+
+ align:start position:0%
+are also used for another concept which
+i explained on a later slide
+
+ align:start position:0%
+i explained on a later slide
+ 
+
+ align:start position:0%
+i explained on a later slide
+which is your presentation of a specific
+
+ align:start position:0%
+which is your presentation of a specific
+ 
+
+ align:start position:0%
+which is your presentation of a specific
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+this is part of your homework set
+
+ align:start position:0%
+this is part of your homework set
+ 
+
+ align:start position:0%
+this is part of your homework set
+um is to find a paper to discuss with me
+
+ align:start position:0%
+um is to find a paper to discuss with me
+ 
+
+ align:start position:0%
+um is to find a paper to discuss with me
+whether or not it fits into this that
+
+ align:start position:0%
+whether or not it fits into this that
+ 
+
+ align:start position:0%
+whether or not it fits into this that
+schedule and together with a partner
+
+ align:start position:0%
+schedule and together with a partner
+ 
+
+ align:start position:0%
+schedule and together with a partner
+have a short discussion of this paper
+
+ align:start position:0%
+have a short discussion of this paper
+ 
+
+ align:start position:0%
+have a short discussion of this paper
+so we'll use this tuesday and thursday
+
+ align:start position:0%
+so we'll use this tuesday and thursday
+ 
+
+ align:start position:0%
+so we'll use this tuesday and thursday
+sessions for this purpose
+
+ align:start position:0%
+sessions for this purpose
+ 
+
+ align:start position:0%
+sessions for this purpose
+um in addition there's going to be an
+
+ align:start position:0%
+um in addition there's going to be an
+ 
+
+ align:start position:0%
+um in addition there's going to be an
+office hour on friday so one hour where
+
+ align:start position:0%
+office hour on friday so one hour where
+ 
+
+ align:start position:0%
+office hour on friday so one hour where
+i'm just
+
+ align:start position:0%
+i'm just
+ 
+
+ align:start position:0%
+i'm just
+going to be connected to zoom meeting
+
+ align:start position:0%
+going to be connected to zoom meeting
+ 
+
+ align:start position:0%
+going to be connected to zoom meeting
+you can log in at any time
+
+ align:start position:0%
+you can log in at any time
+ 
+
+ align:start position:0%
+you can log in at any time
+um and we'll discuss whatever you want
+
+ align:start position:0%
+um and we'll discuss whatever you want
+ 
+
+ align:start position:0%
+um and we'll discuss whatever you want
+to talk about um
+
+ align:start position:0%
+to talk about um
+ 
+
+ align:start position:0%
+to talk about um
+for that there's going to be a doodle
+
+ align:start position:0%
+for that there's going to be a doodle
+ 
+
+ align:start position:0%
+for that there's going to be a doodle
+poll which i'll post
+
+ align:start position:0%
+poll which i'll post
+ 
+
+ align:start position:0%
+poll which i'll post
+during the first or at the time of the
+
+ align:start position:0%
+during the first or at the time of the
+ 
+
+ align:start position:0%
+during the first or at the time of the
+first class um and then we
+
+ align:start position:0%
+first class um and then we
+ 
+
+ align:start position:0%
+first class um and then we
+will find the best possible time for
+
+ align:start position:0%
+will find the best possible time for
+ 
+
+ align:start position:0%
+will find the best possible time for
+everybody involved
+
+ align:start position:0%
+everybody involved
+ 
+
+ align:start position:0%
+everybody involved
+um you know the course evaluation or
+
+ align:start position:0%
+um you know the course evaluation or
+ 
+
+ align:start position:0%
+um you know the course evaluation or
+your evaluation in this course will be
+
+ align:start position:0%
+your evaluation in this course will be
+ 
+
+ align:start position:0%
+your evaluation in this course will be
+made up fifty percent out of homework
+
+ align:start position:0%
+made up fifty percent out of homework
+ 
+
+ align:start position:0%
+made up fifty percent out of homework
+because there's going to be
+
+ align:start position:0%
+because there's going to be
+ 
+
+ align:start position:0%
+because there's going to be
+um six psets going to be posted um
+
+ align:start position:0%
+um six psets going to be posted um
+ 
+
+ align:start position:0%
+um six psets going to be posted um
+one will be forgiven so i basically
+
+ align:start position:0%
+one will be forgiven so i basically
+ 
+
+ align:start position:0%
+one will be forgiven so i basically
+count five psets and each
+
+ align:start position:0%
+count five psets and each
+ 
+
+ align:start position:0%
+count five psets and each
+uh will allow you to accumulate
+
+ align:start position:0%
+uh will allow you to accumulate
+ 
+
+ align:start position:0%
+uh will allow you to accumulate
+eight points um the paper presentation i
+
+ align:start position:0%
+eight points um the paper presentation i
+ 
+
+ align:start position:0%
+eight points um the paper presentation i
+was talking
+
+ align:start position:0%
+was talking
+ 
+
+ align:start position:0%
+was talking
+about i will have 20 points
+
+ align:start position:0%
+about i will have 20 points
+ 
+
+ align:start position:0%
+about i will have 20 points
+we are talking about a 20-minute
+
+ align:start position:0%
+we are talking about a 20-minute
+ 
+
+ align:start position:0%
+we are talking about a 20-minute
+presentation of a paper it's really a
+
+ align:start position:0%
+presentation of a paper it's really a
+ 
+
+ align:start position:0%
+presentation of a paper it's really a
+summary of a paper
+
+ align:start position:0%
+summary of a paper
+ 
+
+ align:start position:0%
+summary of a paper
+of your choice together with 10 minutes
+
+ align:start position:0%
+of your choice together with 10 minutes
+ 
+
+ align:start position:0%
+of your choice together with 10 minutes
+of q and a
+
+ align:start position:0%
+of q and a
+ 
+
+ align:start position:0%
+of q and a
+again this has been done in two groups
+
+ align:start position:0%
+again this has been done in two groups
+ 
+
+ align:start position:0%
+again this has been done in two groups
+so you have to split up
+
+ align:start position:0%
+so you have to split up
+ 
+
+ align:start position:0%
+so you have to split up
+the aspect of presenting preparing and
+
+ align:start position:0%
+the aspect of presenting preparing and
+ 
+
+ align:start position:0%
+the aspect of presenting preparing and
+presenting
+
+ align:start position:0%
+presenting
+ 
+
+ align:start position:0%
+presenting
+and then also when it comes to the
+
+ align:start position:0%
+and then also when it comes to the
+ 
+
+ align:start position:0%
+and then also when it comes to the
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+questions and then there's going to be
+
+ align:start position:0%
+questions and then there's going to be
+ 
+
+ align:start position:0%
+questions and then there's going to be
+two short oral exams
+
+ align:start position:0%
+two short oral exams
+ 
+
+ align:start position:0%
+two short oral exams
+this is 20 minutes so the actual exam is
+
+ align:start position:0%
+this is 20 minutes so the actual exam is
+ 
+
+ align:start position:0%
+this is 20 minutes so the actual exam is
+only going to be
+
+ align:start position:0%
+only going to be
+ 
+
+ align:start position:0%
+only going to be
+15 minutes um with the teaching staff so
+
+ align:start position:0%
+15 minutes um with the teaching staff so
+ 
+
+ align:start position:0%
+15 minutes um with the teaching staff so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is justin and myself maybe ask you a
+
+ align:start position:0%
+is justin and myself maybe ask you a
+ 
+
+ align:start position:0%
+is justin and myself maybe ask you a
+couple of questions and just
+
+ align:start position:0%
+couple of questions and just
+ 
+
+ align:start position:0%
+couple of questions and just
+make sure that you are on top of contact
+
+ align:start position:0%
+make sure that you are on top of contact
+ 
+
+ align:start position:0%
+make sure that you are on top of contact
+we discussed in the weeks
+
+ align:start position:0%
+we discussed in the weeks
+ 
+
+ align:start position:0%
+we discussed in the weeks
+prior um so there's two the first one
+
+ align:start position:0%
+prior um so there's two the first one
+ 
+
+ align:start position:0%
+prior um so there's two the first one
+deals with the particle physics context
+
+ align:start position:0%
+deals with the particle physics context
+ 
+
+ align:start position:0%
+deals with the particle physics context
+and the second one with the nuclear
+
+ align:start position:0%
+and the second one with the nuclear
+ 
+
+ align:start position:0%
+and the second one with the nuclear
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+and um experimental methods as well
+
+ align:start position:0%
+and um experimental methods as well
+ 
+
+ align:start position:0%
+and um experimental methods as well
+the grading scheme will not be worse
+
+ align:start position:0%
+the grading scheme will not be worse
+ 
+
+ align:start position:0%
+the grading scheme will not be worse
+than what i'll give you here
+
+ align:start position:0%
+than what i'll give you here
+ 
+
+ align:start position:0%
+than what i'll give you here
+so there is a great divide that's a
+
+ align:start position:0%
+so there is a great divide that's a
+ 
+
+ align:start position:0%
+so there is a great divide that's a
+great divide but a great divide
+
+ align:start position:0%
+great divide but a great divide
+ 
+
+ align:start position:0%
+great divide but a great divide
+at 85 between a and b seventy percent
+
+ align:start position:0%
+at 85 between a and b seventy percent
+ 
+
+ align:start position:0%
+at 85 between a and b seventy percent
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+e and c sixty percent between c and d
+
+ align:start position:0%
+e and c sixty percent between c and d
+ 
+
+ align:start position:0%
+e and c sixty percent between c and d
+and below fifty percent earnest unf i
+
+ align:start position:0%
+and below fifty percent earnest unf i
+ 
+
+ align:start position:0%
+and below fifty percent earnest unf i
+don't think anybody will get into this
+
+ align:start position:0%
+don't think anybody will get into this
+ 
+
+ align:start position:0%
+don't think anybody will get into this
+environment as long as they participate
+
+ align:start position:0%
+environment as long as they participate
+ 
+
+ align:start position:0%
+environment as long as they participate
+you
\ No newline at end of file
diff --git a/lJzybEXmIj0.txt b/lJzybEXmIj0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..236cfefa6b3bc388e0e6bdc6b82827086099e5e9
--- /dev/null
+++ b/lJzybEXmIj0.txt
@@ -0,0 +1,3792 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Welcome
+to Foundations
+
+of Computational
+and Systems Biology.
+
+This course has many numbers.
+
+We'll explain all the
+differences and similarities.
+
+But briefly, there are three
+undergrad course numbers,
+
+which are all similar in
+content, 7.36, 20.390, 6.802.
+
+And then, there are
+four graduate versions.
+
+The 7.91, 20.490, and HST
+versions are all very similar,
+
+basically identical.
+
+But the 6.874 has some
+additional AI content
+
+that we'll discuss in a moment.
+
+So make sure that
+you are registered
+
+for the appropriate
+version of this course.
+
+And please interrupt with
+questions at any time.
+
+The main goal today is to give
+an overview of the course, both
+
+the content as well as
+the mechanics of how
+
+the course will be taught.
+
+And we want to make sure
+that everything is clear.
+
+So this course is
+taught by myself
+
+and Chris Burge from Biology,
+Professor Fraenkel from BE,
+
+and Professor Gifford from EECS.
+
+We have three TAs, Peter
+Freese and Collette Picard,
+
+from Computational and Systems
+Biology, and Tahin, from EECS.
+
+All the TAs have expertise
+in computational biology
+
+as well as other
+quantitative areas
+
+like math, statistics,
+computer science.
+
+So in addition to the lectures
+by the regular instructors,
+
+we will also have guest
+lectures by George Church,
+
+from Harvard, toward
+the end of the semester.
+
+Doug Lauffenburger
+will give a lecture
+
+in the regulatory network
+section of the course.
+
+And we'll have a guest
+lecture from Ron Weiss
+
+on synthetic biology.
+
+And just a note
+that today's lecture
+
+and all the lectures
+this semester
+
+are being recorded by AMPS,
+by MIT's OpenCourseWare.
+
+So the videos, after a
+little bit of editing,
+
+will eventually end
+up on OpenCourseWare.
+
+What are these courses?
+
+So these course numbers are
+the graduate level versions,
+
+which are survey courses
+in computational biology.
+
+Our target audience
+is graduate students
+
+who have a solid
+background and comfort--
+
+or, a solid
+background in biology,
+
+and also, a comfort with
+quantitative approaches.
+
+We don't assume that
+you've programmed before,
+
+but there will be
+some programming
+
+content on the homeworks.
+
+And you will therefore need to
+learn some Python programming.
+
+And the TAs will help with
+that component of the course.
+
+We also have some online
+tutorials on Python programming
+
+that are available.
+
+The undergrad course
+numbers-- this
+
+is an upper level
+undergraduate survey
+
+course in computational biology.
+
+And our target audience are
+upper level undergraduates
+
+with solid biology
+background and comfort
+
+with quantitative approaches.
+
+So there's one key difference
+between the graduate
+
+and undergraduate versions,
+which I'll come to in a moment.
+
+So the goal of this course
+is to develop understanding
+
+of foundational methods in
+computational biology that
+
+will enable you to
+contextualize and understand
+
+a good portion of research
+literature in a growing field.
+
+So if you pick up Science, or
+Nature, or PLOS Computational
+
+Biology and you want
+to read those papers
+
+and understand them,
+after this course,
+
+you will have a better chance.
+
+We're not guaranteeing you'll be
+able to understand all of them.
+
+But you'll be able to recognize,
+perhaps, the category of paper,
+
+the class, and perhaps,
+some of the algorithms
+
+that are involved.
+
+And for the graduate
+version, another goal
+
+is to help you gain exposure
+to research in this field.
+
+So it's actually
+possible to do a smaller
+
+scale computational biology
+research project on your own,
+
+on your laptop-- perhaps,
+on ATHENA-- with relatively
+
+limited computational
+resources and potentially
+
+even discover something new.
+
+And so we want to give
+you that experience.
+
+And that's through
+the project component
+
+that we'll say more
+about in a moment.
+
+So just to make sure that
+everyone's in the right class--
+
+this is not a systems
+biology class.
+
+There are some more
+focused systems
+
+biology classes
+offered on campus.
+
+But we will cover
+some topics that
+
+are important for
+analyzing complex systems.
+
+This is also certainly not
+a synthetic biology course.
+
+Some of the systems methods are
+also used in synthetic biology.
+
+And there will be this
+guest lecturer I mentioned,
+
+Ron Weiss, which will
+cover synthetic biology.
+
+It's also not an
+algorithms class.
+
+We don't assume that
+you have experience
+
+in designing or
+analyzing algorithms.
+
+We'll discuss various
+bioinformatics algorithms.
+
+And you'll have the
+opportunity to implement
+
+at least one bioinformatics
+algorithm on your homework.
+
+But algorithms and not really
+the center of the course.
+
+And there's one
+exception to this,
+
+which is, those of you
+who are taking 6.874
+
+will go to a special
+recitation that
+
+will cover more advanced
+algorithm content.
+
+And there will be special
+homework problems for you
+
+as well.
+
+So that course really does
+have more algorithm content.
+
+So the plan for today
+is that I will just
+
+do a brief, anecdotal history
+of computational and systems
+
+biology.
+
+This is to set the stage and
+the context for the class.
+
+And then we'll spend
+a significant amount
+
+of time reviewing the course
+mechanics, organization,
+
+and content.
+
+Because as you'll see, it's
+a little bit complicated.
+
+But it'll make sense once
+we go over it, hopefully.
+
+So this is my take
+on computational
+
+and systems biology.
+
+Again, it's not a
+scholarly overview.
+
+It doesn't hit everything
+important that happened.
+
+It just gives you
+a flavor of what
+
+was happening in computational
+biology decade by decade.
+
+So first of all,
+where does this field
+
+fall in the academic
+scheme of things?
+
+So I consider
+computational biology
+
+to be actually part of biology.
+
+So in the way that genetics or
+biochemistry are disciplines
+
+that have strategies
+for understanding
+
+biological questions, so
+does computational biology.
+
+You can use it to
+understand a variety
+
+of computational
+questions in gene
+
+regulation, many other areas.
+
+There is also, some
+people make a distinction
+
+that bioinformatics is
+more about building tools
+
+whereas computational biology
+is more about using tools,
+
+for example.
+
+Although many people
+don't-- it's very blurry--
+
+and don't try to-- people
+use them in various ways.
+
+And then, you could
+think of bioinformatics
+
+as being embedded in the larger
+field of informatics, where you
+
+include tools for management
+and analysis of data in general.
+
+And it's certainly true that
+many of the core concepts
+
+and algorithms in bioinformatics
+come from the field,
+
+come from computer science,
+come from other branches
+
+of engineering, from statistics,
+mathematics, and so forth.
+
+So it's really a cross
+disciplinary field.
+
+And then, synthetic biology
+cuts across in the sense
+
+that it's really an
+engineering discipline.
+
+Because you're designing
+and engineering
+
+synthetic molecular
+cellular systems.
+
+But you can also use
+synthetic biology
+
+to help understand natural
+biological systems, of course.
+
+All right, so what was
+happening, decade by decade?
+
+So in the '70s, there
+were not genome sequences
+
+available or large sequence
+databases of any sort.
+
+Except there were starting
+to be some protein sequences.
+
+And early computational
+biologists
+
+focused on comparing proteins,
+understanding their function,
+
+structure, and evolution.
+
+And so in order to
+compare proteins,
+
+you need a protein-- an amino
+acid substitution matrix--
+
+a matrix that describes
+how often one amino acid is
+
+substituted for another.
+
+And Margaret Dayhoff
+was a pioneer
+
+in developing these
+sorts of matrices.
+
+And some of the matrices she
+developed, the PAM series,
+
+are still used today.
+
+And we'll discuss those
+matrices early next week.
+
+So in terms of asking
+evolutionary questions,
+
+two big thinkers were Russ
+Doolittle and Carl Woese,
+
+analyzing both ribosomal RNA
+sequences to study evolution.
+
+And Carl Woese realized,
+looking at these RNA alignments,
+
+that actually, the prokaryotes,
+which had been-- there
+
+was this big split
+between prokaryotes
+
+and eukaryotes was
+sort of a false split--
+
+that actually,
+there was a subgroup
+
+of single-celled
+anuclear organisms
+
+that were closer
+to the eukaryotes--
+
+and named them the Archaea.
+
+So a whole kingdom of life
+was recognized, really,
+
+by sequence analysis.
+
+And Russ Doolittle also
+did a lot of analysis
+
+approaching sequences and came
+up with this molecular clock
+
+idea, or contributed
+to that idea,
+
+to actually build-- instead
+of systematics being based
+
+on phenotypic characteristics,
+do it on a molecular level.
+
+So in the '80s, the
+databases started to expand.
+
+Sequence alignment and
+search became more important.
+
+And various people
+developed fast algorithms
+
+to compare protein and DNA
+sequences and align them.
+
+So the FASTA program
+was widely used.
+
+BLAST-- several of the authors
+of BLAST are shown here--
+
+David Lipman, Pearson, Webb
+Miller, Stephen Altschul.
+
+The statistics for knowing
+when a BLAST search result is
+
+significant were developed
+by Karlin and Altschul.
+
+And there was also progress
+in gapped alignment,
+
+in particularly,
+Smith-Waterman, shown above.
+
+Also progress in RNA
+secondary structure prediction
+
+from Nusinov and Zuker.
+
+We'll talk about all of these
+algorithms during the course.
+
+And there was also development
+of literature databases.
+
+I always liked this picture.
+
+Many of you probably
+used PubMed.
+
+But Al Gore was well coached
+here, by these experts,
+
+in how to use it.
+
+And then, in the '90s,
+computational biology
+
+really started to expand.
+
+It was driven partly
+by the development
+
+of a microarrays, the first
+genome sequences, and questions
+
+like how to identify
+domains in a protein,
+
+how to identify
+genes in the genome.
+
+It was recognized that
+this family of models
+
+from electrical engineering,
+the hidden Markov model,
+
+were quite useful for these sort
+of sequence labeling problems.
+
+That was really pioneered
+by Anders Krogh here,
+
+and David Haussler.
+
+And a variety of
+algorithms were developed
+
+that performed
+these useful tasks.
+
+There was also
+important progress
+
+in the earliest comparative
+genomic approaches,
+
+since you have--
+the first genomes
+
+were sequenced in the mid
+'90s, of free living organisms.
+
+And so you could then start
+to compare these genomes
+
+and learn a lot.
+
+We'll talk a little bit
+about comparative genomics.
+
+And there was important progress
+on predicting protein structure
+
+from primary sequence.
+
+Particularly, David Baker
+made notable progress
+
+on this Rosetta algorithm.
+
+So it's a biophysics
+field, but it's
+
+very much part of
+computational biology as well.
+
+So in the 2000s, definitely,
+genome sequencing
+
+became very fashionable,
+as you can see here.
+
+And the genomes of
+now larger organisms,
+
+including human, it became
+possible to sequence them.
+
+And then, this
+introduced a huge host
+
+of computational challenges
+in assembling the genomes,
+
+annotating the
+genomes, and so forth.
+
+And we'll hear from
+Professor Gifford
+
+about some genome
+assembly topics.
+
+And annotation will
+come up throughout.
+
+Actually, let's
+just mention, this
+
+is Jim Kent, who's the guru
+who did the first human genome
+
+assembly-- at least,
+that was widely used--
+
+and also was involved in UCSC.
+
+And here, Ewan Birney
+has started Ensembl
+
+and continues to run it today.
+
+You know who these other
+people are, probably.
+
+OK.
+
+All right.
+
+So in another phase
+of the last decade,
+
+I would say that much
+of biological research
+
+became more high throughput
+than it was before.
+
+So molecular biology
+had traditionally,
+
+in the '80s and
+'90s, mostly focused
+
+on analysis of individual
+gene or protein products.
+
+But now it became possible,
+and in widespread use,
+
+that you could measure the
+expression of all the genes,
+
+in theory-- using
+microarrays, for example--
+
+and you could start
+to profile all
+
+of the transcripts
+in the cell, all
+
+of the proteins in the
+cell, and so forth.
+
+And then, a variety
+of groups started
+
+to use some of these
+high throughput data
+
+to study various challenges
+in gene expression
+
+to understand how transcription
+works, how splicing works,
+
+how microRNAs work, translation,
+epigenetics, and so forth.
+
+And you'll hear updates on some
+of that work in this course.
+
+Bioimage informatics,
+particularly
+
+for developmental
+biology, became popular.
+
+It continues to be
+a new emerging area.
+
+Systems biology was also really
+born around 2000, roughly.
+
+A very prominent example
+would be the development
+
+of the first gene
+regulatory network
+
+models that describe sea urchin
+development, here, my Eric
+
+Davidson, as well as a whole
+variety of models of other gene
+
+networks in the cell
+that control things like
+
+cell proliferation,
+apoptosis, et cetera.
+
+At the same time, a new
+field of synthetic biology
+
+was born with the development
+of some of the first
+
+completely artificial gene
+networks that would then
+
+program cells to perform
+desired behavior.
+
+So an example would be this
+so-called repressilator,
+
+where you have a network of
+three transcription factors.
+
+Each represses the other.
+
+And then, one of
+them represses GFP.
+
+And you put these into bacteria.
+
+And it causes oscillations
+in GFP, expressions
+
+that are described by these
+differential equations here.
+
+And some of the
+modeling approaches
+
+used in synthetic
+biology will be
+
+covered by Professor Fraenkel
+and Lauffenburger later.
+
+All right.
+
+So late 2000s, early
+2010s, it's still too early
+
+to say, for sure, what the most
+important developments will be.
+
+But certainly, in
+the late 2000s,
+
+next gen sequencing--
+which now probably
+
+should be called second
+generation sequencing,
+
+since there may be
+future generations--
+
+really started to transform
+a whole wide variety
+
+of applications in biology,
+from making genome sequencing--
+
+instead of having to be
+done in the genome center,
+
+now an individual lab can easily
+do microbial genome sequencing.
+
+And when needed,
+it's possible, also,
+
+to do genome sequencing
+of larger organisms.
+
+Transcriptome sequencing
+is now routine.
+
+We'll hear about that.
+
+There are applications
+for mapping protein-DNA
+
+interactions genome
+wide, including
+
+both sequence specific
+transcription factors
+
+as well as more general
+factors like histones,
+
+protein-RNA interactions--
+a method called
+
+CLIP-Seq-- methods for mapping
+all the translated messages,
+
+the methylated sites in
+the genome, open chromatin,
+
+and so forth.
+
+So many people contributed
+to this, obviously.
+
+I'm just mentioning,
+Barbara Wold
+
+was a pioneer in both
+RNA-Seq as well as ChIP-Seq.
+
+And some of the sequencing
+technologies that came out here
+
+are shown here.
+
+And we will discuss those
+at the beginning of lecture
+
+on Thursday.
+
+So I encourage you to
+read this review here,
+
+by Metzger, which covers
+many of the newer sequencing
+
+technologies.
+
+And they're pretty interesting.
+
+As you'll see, there's
+some interesting tricks,
+
+interesting chemistry and
+image analysis tricks.
+
+All right.
+
+So that was not very scholarly.
+
+But if you want a proper
+history, then this guy,
+
+Hallam Stevens, who was a
+History of Science PhD student
+
+at Harvard and
+recently graduated,
+
+wrote this history
+of bioinformatics.
+
+OK.
+
+So let's look at the syllabus.
+
+So also posted on the
+[INAUDIBLE] site is a syllabus.
+
+It looks like this.
+
+This is quite an
+information-rich document.
+
+It has all the lecture
+titles, all the due dates
+
+of all the problem
+sets, and so forth.
+
+So please print yourself a
+copy and familiarize yourself
+
+with it.
+
+So we'll just try to
+look at a high level
+
+first, and then zoom
+in to the details.
+
+So at a high level, if you
+look in this column here,
+
+we've broken the course
+into six different topics.
+
+OK?
+
+So there's Genomic
+Analysis I, that I'll
+
+be teaching, which is more
+classical computational
+
+biology, you could say-- local
+alignment, global alignment,
+
+and so forth.
+
+Then, Genomic Analysis II,
+which Professor Gifford will
+
+be teaching, covers
+some newer methods
+
+that are required
+when you're doing
+
+a lot of second
+generation sequencing--
+
+the standard algorithms
+are not fast enough,
+
+you need better
+algorithms, and so forth.
+
+And then, I will come back and
+give a few lectures on modeling
+
+biological function.
+
+This will have to do with
+sequence motifs, hidden Markov
+
+models, and RNA
+secondary structure.
+
+Professor Fraenkel
+will then do a unit
+
+on proteomics and
+protein structure.
+
+And then, there will
+be an extended unit
+
+on regulatory networks.
+
+Different types of
+regulatory networks
+
+will be covered, with most
+of the lectures by Ernest,
+
+one by David, and one by Doug.
+
+And then, we'll finish up
+with computational genetics,
+
+by David.
+
+And there will also be some
+guest lecturers, one of them
+
+interspersed in
+regulatory networks,
+
+and then two at the end, from
+Ron Weiss and George Church.
+
+So I just wanted to point out
+that in all of these topics,
+
+we will include some discussion
+of motivating question.
+
+So, what are the
+biological questions
+
+that we're seeking to address
+with these approaches.
+
+And there will also
+be some discussion
+
+of the experimental method.
+
+So for example,
+in the first unit,
+
+it's heavy on sequence analysis.
+
+So we'll talk about
+how sequencing is done,
+
+and then, quite a bit
+about the interaction
+
+between the
+experimental technology
+
+and the computational
+analysis, which often involves
+
+statistical methods for
+estimating the error
+
+rate of the experimental
+method, and things like that.
+
+So the emphasis is on
+the computational part,
+
+but we'll have some
+discussion about experiments.
+
+Everyone with me so far?
+
+Any questions?
+
+OK.
+
+All right.
+
+So what are some of these
+motivating questions
+
+that we'll be talking about?
+
+So what are the instructions
+encoded in our genomes?
+
+You can think of the
+genome as a book.
+
+But it's in this very
+strange language.
+
+And we need to understand the
+rules, the code that underlies
+
+a lot of research
+in gene expression.
+
+How are chromosomes organized?
+
+What genes are present-- so
+tools for annotating genomes.
+
+What regulatory
+circuitry is encoded?
+
+You'd like to be able to
+eventually look at a genome,
+
+understand all the
+regulatory elements,
+
+and be able to predict
+that there's some feedback
+
+circuit there that responds to--
+a particular stimulation that
+
+responds to light, or
+nutrient deprivation,
+
+or whatever it might be.
+
+Can the transcriptome be
+predicted from the genome?
+
+This is a longstanding question.
+
+The translatome, if you
+will-- well, let's say,
+
+the proteome can be predicted
+from the transcriptome
+
+in the sense that we
+have a genetic code
+
+and we can look
+up those triplets.
+
+So there's a dream
+that we would be
+
+able to model other
+steps in gene expression
+
+with the precision with which
+the genetic code predicts
+
+translation-- that we'd
+be able to predict where
+
+the polymerase would start
+transcribing, where it will
+
+finish transcribing, how a
+transcript will be spliced,
+
+et cetera-- all the other
+steps in gene expression.
+
+And that motivates a lot
+of work in the field.
+
+Can protein function be
+predicted from sequence?
+
+So this is a very
+classical problem.
+
+But there are a number of new
+and interesting developments
+
+as resolved from a lot of
+this high throughput data
+
+generation, both in
+nucleic acid sequencing
+
+as well as in proteomics.
+
+Can evolutionary history be
+reconstructed from sequence?
+
+Again, this has been a
+longstanding goal of the field.
+
+And a lot of progress
+has been made here.
+
+And now most evolutionary
+classifications
+
+are actually based on molecular
+sequence at some level.
+
+And new species are often
+defined based on sequence.
+
+OK.
+
+Other motivating questions.
+
+So what would you
+need to measure
+
+if you wanted to discover
+the causes of a disease,
+
+the mechanisms of
+existing drugs,
+
+metabolic pathways
+in a micro-organism?
+
+So this is a systems
+biology question.
+
+You've got a new bug.
+
+It causes some disease.
+
+What should you measure?
+
+Should you sequences its genome?
+
+Should you sequence
+its transcriptome?
+
+Should you do proteomics?
+
+What type of proteomics?
+
+Should you perturb the system in
+some way and do a time series?
+
+What are the most
+efficient ways?
+
+What information should
+be gathered, and in what
+
+quantities?
+
+And how should that information
+be integrated in order
+
+to come up with an
+understanding of the physiology
+
+of that organisms
+so that, then, you
+
+can know where to
+intervene, what
+
+would be suitable drug targets?
+
+Yeah.
+
+What kind of modeling
+would help you
+
+to use the data to
+design new therapies,
+
+or even, in a synthetic
+biology context,
+
+to re-engineer organisms
+for new purposes?
+
+So microbes to
+generate-- to produce
+
+fuel, for example, or
+other useful products.
+
+What can we currently measure?
+
+What does each type of
+data mean individually?
+
+What are the strengths
+and weaknesses
+
+of each of the types of
+high throughput approaches
+
+that we have?
+
+And how do we integrate all
+the data we have on a system
+
+to understand the
+functioning of that system?
+
+So these are some of
+the questions that
+
+motivate the latter topics
+on regulatory networks.
+
+OK.
+
+So let's now zoom in
+and look more closely
+
+at the course syllabus.
+
+I've just broken
+it into two halves,
+
+just so it's more readable.
+
+So today we're going over,
+obviously, course mechanics
+
+mostly.
+
+On Thursday, we'll cover
+both some DNA sequencing
+
+technologies and we'll talk
+about local alignment on BLAST.
+
+More on that in a bit.
+
+The 6.8047 recitation--
+6.874, thank you-- recitation
+
+will be on Friday.
+
+The other recitations
+will start next week.
+
+And then, as you can see, we'll
+move through the other topics.
+
+So each of the
+instructors is going
+
+to briefly review their topic.
+
+So I won't go through
+all the titles here.
+
+But please note,
+on the left side
+
+here, that their assignment
+due dates are marked.
+
+OK?
+
+And they're all due at
+noon on the indicated day.
+
+And so some of these
+are problem sets.
+
+So for example,
+problem set 1 will
+
+be due on Thursday,
+February 20 at noon.
+
+And some of the
+other assignments
+
+relate to the project component
+of the course, which we're
+
+going to talk more
+about in a moment.
+
+In particular,
+we're going to ask
+
+you to submit a brief
+statement of your background
+
+and your research interests
+related to forming teams.
+
+So the projects are
+going to be done
+
+in teams of one
+to five students.
+
+And in order to
+facilitate especially
+
+cross disciplinary
+teams-- we'd love
+
+if you interact
+with, maybe, students
+
+in a different grad
+program, or whatever--
+
+you'll post your background.
+
+You know, I'm a
+first year BE student
+
+and I have a background
+in Perl programming,
+
+but never done Python, or
+whatever-- something like that.
+
+And then, I'm interested
+in doing systems biology
+
+modeling in microbial systems,
+or something like that.
+
+And then you can match
+up your interests
+
+with others and form teams.
+
+And then you'll come up
+with your own project ideas
+
+so that the team
+and initial idea
+
+will be due here, February 25th.
+
+Then you'll need to do
+some aims and so forth.
+
+So the project components
+here, these are only for those
+
+taking the grad
+version of the course.
+
+We'll make that clear later.
+
+OK.
+
+So after the first
+three topics here,
+
+taught by myself and David,
+there will be an exam.
+
+More on that later.
+
+And then there will be three
+more topics, mostly taught
+
+by Ernest.
+
+And notice there are additional
+assignments here related
+
+to the project-- so,
+to research strategy--
+
+and the final written report,
+additional problems sets.
+
+We'll have a guest
+lecturer here.
+
+This will be Ron Weiss.
+
+Then, there will
+be the second exam.
+
+Exams are non-cumulative,
+so the second exam
+
+will just cover these three
+topics here predominantly.
+
+And then there will be
+another guest lecturer.
+
+This would be
+George Church here.
+
+And then notice,
+here, presentation.
+
+So those who are doing
+the project component,
+
+those teams will be given--
+assigned a time to present,
+
+to the class, the results
+of their research.
+
+And you'll be graded--
+the presentation will
+
+be part of the overall
+project grade assigned
+
+by the instructors.
+
+But you'll also-- we'll
+also ask all the students
+
+in the class to send comments
+on the presentations.
+
+So you may find that you
+get helpful suggestions
+
+about interpreting your data
+from other people and so forth.
+
+So that'll be a
+required component
+
+of the course for all students,
+to attend the presentations
+
+and comment on them.
+
+And we hope that
+will be a lot of fun.
+
+OK.
+
+So is this the
+right course for me?
+
+So I just wanted to
+let you know you're
+
+fortunate to have a rich
+selection of courses
+
+in computational systems,
+synthetic biology here at MIT.
+
+I've listed many of them.
+
+Probably not all,
+but the ones that I'm
+
+aware of that are
+available on-campus.
+
+757 is really only for
+biology grad students.
+
+But the other courses listed
+here are generally open.
+
+Some are more geared for
+graduate students, some more
+
+undergrads.
+
+Some are more specialized.
+
+So for example, Jeff Gore's
+systems biology course,
+
+it's more focused
+on systems biology
+
+whereas our course covers both
+computational and systems.
+
+So keep that in mind.
+
+Make sure you're
+in the right place,
+
+that this is what you want.
+
+OK.
+
+A few notes on the textbook--
+so there is a textbook.
+
+It's not required.
+
+It's called Understanding
+Bioinformatics
+
+by Zvelebil and Baum.
+
+It's quite good
+on certain topics.
+
+But it really only covers
+about, maybe, a third of what
+
+we cover in the course.
+
+So there is good content
+on local alignment,
+
+global alignment,
+scoring matrices--
+
+the topics of the
+next couple lectures.
+
+And I'll point you
+to those chapters.
+
+But it's very
+important to emphasize
+
+that the content of
+the course is really
+
+what happens in lecture,
+and on the homeworks,
+
+and to some extent, what
+happens in recitation.
+
+And the textbook is just there
+as a backup, if you will,
+
+or for those who
+would like to get more
+
+background on the
+topic or want to read
+
+a different description
+of that topic.
+
+So you decide whether you
+want to purchase the textbook
+
+or not.
+
+It's available at the
+Coop or through Amazon.
+
+Shop around.
+
+You can find it.
+
+It's paperback.
+
+Pretty good general reference
+on a variety of topics,
+
+but it doesn't really have
+much on systems biology.
+
+All right.
+
+Another important reference
+that was developed specifically
+
+for this course a few years
+ago is the probability
+
+and statistics primer.
+
+So you'll notice that
+some of the homeworks,
+
+particularly in the earlier
+parts of the course,
+
+will have significant
+probability and statistics.
+
+And we assume that you have
+some background in this area.
+
+Many of you do.
+
+If you don't, you'll
+need to pick that up.
+
+And this primer was written
+to provide those topics,
+
+in probability especially,
+that are foundational
+
+and most relevant to
+computational biology.
+
+So for example, there
+are some concepts
+
+like p-value, probability
+density function, probability
+
+mass function, cumulative
+distribution function,
+
+and then, common distributions,
+exponential distribution,
+
+Poisson distribution,
+extreme value distribution.
+
+If those are mostly sounding
+familiar to you, that's good.
+
+If they're familiar, but
+you couldn't-- you really
+
+don't-- you get binomial and
+Poisson confused or something,
+
+then, definitely, you want
+to consult this primer.
+
+So I think, looking at the
+lectures and the homeworks,
+
+it should probably
+become pretty clear
+
+which aspects are
+going to be relevant.
+
+And I'll try to point
+those out when possible.
+
+And you can also
+consult your TAs
+
+if you're having trouble with
+the probability and statistics
+
+content.
+
+So we are going to
+focus, here, on, really,
+
+the computational biology,
+bioinformatics content.
+
+And we might briefly review
+a concept from probability,
+
+like, maybe, conditional
+probability when
+
+we talk about Markov chains.
+
+But we're not going to
+spend a lot of time.
+
+So if that's the
+first time you've
+
+seen conditional probability,
+you might be a little bit lost.
+
+So you'd be better off
+reading about it in advance.
+
+OK?
+
+Questions?
+
+No questions?
+
+All right.
+
+Maybe it's that the video
+is intimidating people.
+
+OK.
+
+All right.
+
+The TAs know a lot about
+probability and statistics
+
+and will be able to help you.
+
+OK.
+
+So homework-- so I
+apologize, the font
+
+is a little bit small here.
+
+So I'll try to state it clearly.
+
+So there are going
+to be five problem
+
+sets that are roughly
+one per topic.
+
+Except you'll see p set two
+covers topics two and three.
+
+So it might be a
+little bit longer.
+
+The way we handle students who
+have to travel-- so many of you
+
+might be seniors.
+
+You might be interviewing
+for graduate schools.
+
+Or you might have other
+conflicts with the course.
+
+So rather than
+doing that on a case
+
+by case basis, which, we've
+found, gets very complicated
+
+and is not necessarily fair,
+the way we've set it up
+
+is that the total number of
+points available on the five
+
+homeworks is 120.
+
+OK?
+
+But the maximum score
+that you can get is 100.
+
+So if you, for example,
+were to get 90% on all five
+
+of the homeworks,
+that would be 90%
+
+of 120, which would
+be 108 points.
+
+You would get the
+full 100-- you'd
+
+get 100% on your homework.
+
+That would be a perfect
+score on the homework.
+
+OK?
+
+But because of that-- because
+there's more points available
+
+than you need-- we don't
+allow you to drop homeworks,
+
+or to do an alternate
+assignment, or something
+
+like that.
+
+So the way it works
+is you can basically
+
+miss-- as long as
+you do well on, say,
+
+four of the homeworks--
+you could actually
+
+miss one without
+much of a penalty.
+
+For example, if each of the
+homeworks were worth 24 points
+
+and you got a perfect
+score on four of them,
+
+that would be 96 points.
+
+You would have an almost
+perfect score on your homework
+
+and you could miss
+that fifth homework.
+
+Now of course, we
+don't encourage
+
+you to skip that homework.
+
+We think the homeworks are
+useful and are a good way
+
+to solidify the information
+you've gotten from lecture,
+
+and reading, and so forth.
+
+So It's good to do them.
+
+And doing the homeworks
+will help you and perhaps
+
+prepare you for the exams.
+
+But that's the way we
+handle the homework policy.
+
+Now I should also mention that
+not all the homeworks will
+
+be the same number of points.
+
+We'll apportion the
+points in proportion
+
+to the difficulty and length
+of the homework assignment.
+
+So for example, the
+first homework assignment
+
+is a little bit easier
+than the others.
+
+So it's going to have
+somewhat fewer points.
+
+So late assignments--
+so all the homeworks
+
+are due at noon on
+the indicated day.
+
+And if it's within
+24 hours after that,
+
+you'll be eligible
+for 50% credit.
+
+And beyond that, you don't
+get any points, in part
+
+because the TAs will be posting
+the answers to the homeworks.
+
+OK?
+
+And we want to be able to post
+them promptly so that you'll
+
+get the answers while
+those problems are
+
+fresh in your mind.
+
+Questions about homeworks?
+
+OK.
+
+Good.
+
+So collaboration
+on problem sets--
+
+so we want you to
+do the problem sets.
+
+You can do them independently.
+
+You can work with a friend
+on them, or even in a group,
+
+discuss them together.
+
+But write up your
+solutions independently.
+
+You don't learn
+anything by copying
+
+someone else's solution.
+
+And if the TAs see duplicate
+or near identical solutions,
+
+both of those
+homeworks will get a 0.
+
+OK?
+
+And this occasionally happens.
+
+We don't want this
+to happen to you.
+
+So just avoid that.
+
+So discuss together, but write
+up your solutions separately.
+
+Similarly, with
+programming, if you
+
+have a friend who's a more
+experienced programmer
+
+than you are, by
+all means, ask them
+
+for advice, general things, how
+should I structure my program,
+
+do you know of a function
+that generates a loop,
+
+or whatever it is that you need.
+
+But don't share code
+with anyone else.
+
+OK?
+
+That would be a no-no.
+
+So write up your
+code independently.
+
+And again, the graders will
+be looking for identical code.
+
+And that will be thrown out.
+
+And so we don't want
+to have any misconduct
+
+of that type occurring.
+
+All right.
+
+So recitations-- there are
+three recitation sessions
+
+offered each week,
+Wednesday at 4:00 by Peter,
+
+Thursday at 4:00 by Colette,
+Friday at 4:00 by Tahin.
+
+And that is a special
+recitation that's
+
+required for the 6.874
+students-- David?
+
+Yes-- and has
+additional AI content.
+
+So anyone is welcome to
+go to that recitation.
+
+But those who are
+taking 6.874 must go.
+
+For students registered for the
+other versions of the course,
+
+going to recitation is optional
+but strongly recommended.
+
+Because the TAs will go over
+material from the lectures,
+
+material that's helpful
+for the homeworks
+
+or for studying for exams--
+in the first weeks, Python,
+
+probability as well.
+
+So go to the
+recitations, particularly
+
+if you're having
+trouble in the course.
+
+So Tahin's recitation
+starts this week.
+
+And Peter and Colette's
+will start next week.
+
+Question.
+
+Yes.
+
+AUDIENCE: Are they covering
+the same material, Peter
+
+and Colette?
+
+PROFESSOR: Peter and Colette
+will cover similar material
+
+and Tahin will cover
+different material.
+
+Python instruction-- so
+the first problem set,
+
+which will be
+posted this evening,
+
+doesn't have any
+programming on it.
+
+But if you don't
+have programming,
+
+you need to start
+learning it very soon.
+
+And so there will be a
+significant programming problem
+
+on p set two.
+
+And we'll be posting that
+problem soon-- this week,
+
+some time.
+
+And you'll want to
+look at that and gauge,
+
+how much Python
+do I need to learn
+
+to at least do that problem.
+
+So what is this
+project component
+
+that we've been hearing about?
+
+So here's a more
+concrete description.
+
+So again, this is only
+for the graduate versions
+
+of the course.
+
+So students will--
+basically, we've
+
+structured it so you
+work incrementally
+
+toward the final
+research project
+
+and so that we can offer
+feedback and help along the way
+
+if needed.
+
+So the first assignment
+will be next week.
+
+I think it's on Tuesday.
+
+I'll have more instructions
+on Thursday's lecture.
+
+But all the students
+registered for the grad version
+
+will submit their
+background and interests
+
+for posting on the
+course website.
+
+And then you can
+look at those and try
+
+to find other students who
+have, ideally, similar interests
+
+but perhaps somewhat
+different backgrounds.
+
+It's particularly
+helpful to have
+
+a strong biologist on the team.
+
+And perhaps, a strong
+programmer would help as well.
+
+So then, you will
+choose your teams
+
+and submit a project title
+and one-paragraph summary,
+
+the basic idea of your project.
+
+Now we are not providing a
+menu of research projects.
+
+It's your choice--
+whatever you want
+
+to do, as long as it's related
+to computational and systems
+
+biology.
+
+So it could be analysis of
+some publicly available data.
+
+Could be analysis of
+some data that you
+
+got during your rotation.
+
+Or for those of you who are
+already in labs that you're
+
+actually working
+on, it's totally
+
+fine and encouraged that the
+project be something that's
+
+related to your main PhD work
+if you've started on that.
+
+And it could also be more in
+the modeling, some modeling
+
+with MATLAB or something, if
+you're familiar with that.
+
+But, a variety of possibilities.
+
+We'll have more
+information on this later.
+
+But we want you to form teams.
+
+The teams can work independently
+or with up to four friends
+
+in teams of five.
+
+And if people want
+to have a giant team
+
+to do some really
+challenging project,
+
+then you can come
+and discuss with us.
+
+And we'll see if
+that would work.
+
+So then there's
+the initial title
+
+and one-paragraph summary.
+
+We'll give you a little
+feedback on that.
+
+And then you'll submit an
+actual specific aims document--
+
+so with actual,
+NIH-style, specific aims--
+
+the goal is to understand
+whether this organism has
+
+operons or not, or some actual
+scientific question-- and a bit
+
+about how you will
+undertake that.
+
+And then you'll submit a longer
+two-page research strategy,
+
+which will include,
+specifically,
+
+we will use these data.
+
+We will use this software,
+these statistical
+
+approaches-- that sort of thing.
+
+And then, toward the end of
+the semester, a final written
+
+report will be due
+that'll be five pages.
+
+You'll work on it
+together, but it'll
+
+need to be clear who did what.
+
+You'll need an author
+contribution statement.
+
+So and so did this analysis.
+
+So and so wrote this
+section-- that sort of thing.
+
+And then, as I
+mentioned before, there
+
+will be oral presentations,
+by each team,
+
+on the last two course sessions.
+
+OK?
+
+Questions about the projects?
+
+There's more information on the
+course info document online.
+
+OK?
+
+Good.
+
+Yes, so for those taking 6.874,
+in addition to the project,
+
+there will also be
+additional AI problems
+
+on both the p
+sets-- and the exam?
+
+David?
+
+Yes.
+
+OK.
+
+And they're optional for others.
+
+All right.
+
+Good.
+
+OK.
+
+So how are we going
+to do the exam?
+
+So as I mentioned, there's
+two 80-minute exams.
+
+They're non-cumulative.
+
+So the first exam
+covers, basically,
+
+the first three topics.
+
+The second exam is on
+the last three topics.
+
+They're 80 minutes.
+
+They're during
+normal class time.
+
+There's no final exam.
+
+The grading-- so for those
+taking the undergrad version,
+
+the homeworks will count 36%
+out of the maximum 100 points.
+
+And the exams will count 62%.
+
+And then, this
+peer review, where
+
+there's two days
+where you go, and you
+
+listen to presentations,
+and you submit
+
+comments online counts 2%.
+
+For the graduate
+Bio BE HST versions,
+
+it's 30% homeworks, 48% exams,
+20% project, 2% peer review.
+
+For the EECS version, 6.874,
+25% homework, 48% exams, 20%
+
+project, and then, 5% for
+these extra AI related
+
+problems, and 2% peer review.
+
+And those should add up to 100.
+
+And then, in addition, we
+will reward 1% extra credit
+
+for outstanding
+class participation--
+
+so questions,
+comments during class.
+
+OK.
+
+All right.
+
+So a few announcements
+about topic one.
+
+And then, each of us will review
+the topics that are coming up.
+
+So p set one will
+be posted tonight.
+
+It's due February 20th, at noon.
+
+It involves basic microbiology,
+probability, and statistics.
+
+It'll give you some
+experience with BLAST
+
+and some of the
+statistics associated.
+
+P set two will be
+posted later this week.
+
+So you don't need to, obviously,
+start on p set two yet.
+
+It's not due for several weeks.
+
+But definitely, look at
+the programming problem
+
+to give you an idea
+of what's involved
+
+and what to focus on when
+you're reviewing your Python.
+
+Mentioned the
+probability/stats primer.
+
+Sequencing technology--
+so for Thursday's lecture,
+
+it will be very helpful if you
+read the review, by Metzger,
+
+on next gen sequencing
+technologies.
+
+It's pretty well written.
+
+Covers Illumina,
+454, PACBIO, and
+
+a few other interesting
+sequence technologies.
+
+Other background
+reading-- so we'll
+
+be talking about local
+alignment, global alignment,
+
+statistics, and similarly
+matrices for the next two
+
+lectures.
+
+And chapters four and
+five of the textbook
+
+provide a pretty good
+background on these topics.
+
+I encourage you to take a look.
+
+OK.
+
+So I'm just going to
+briefly review my lectures.
+
+And then we'll have David
+and Ernest do the same.
+
+So sequencing
+technologies will be
+
+the beginning of lecture two.
+
+And then we'll talk about
+local ungapped sequence
+
+alignment-- in
+particular, BLAST.
+
+So BLAST is something
+like the Google search
+
+engine of bioinformatics,
+if you will.
+
+It's one of the most
+widely used tools.
+
+And it's important to understand
+something about how it works,
+
+and in particular,
+how to evaluate
+
+the significance of BLAST
+hits, which are described
+
+by this extreme value
+distribution here.
+
+And then, lecture three, we'll
+talk about global alignment
+
+and introducing gaps
+into sequence alignments.
+
+We'll talk about some
+dynamic programming
+
+algorithms-- Needleman-Wunsch,
+Smith-Waterman.
+
+And in lecture four,
+we'll talk about
+
+comparative genomic analysis
+of gene regulation--
+
+so using sequence similarity
+across genomes two infer
+
+location of regulatory elements
+such as microRNA target
+
+sites, other things like that.
+
+All right.
+
+So I think this is now-- oh
+sorry, a few more lectures.
+
+Then, in the next unit,
+modeling biological function,
+
+I'll talk about the
+problem of motif finding--
+
+so searching a set of sequences
+for a common subsequence,
+
+or similar subsequences,
+that possess
+
+a particular
+biological function,
+
+like binding to a protein.
+
+It's often a complex
+search space.
+
+We'll talk about
+the Gibbs sampling
+
+algorithm and some alternatives.
+
+And then, in lecture
+10, I'll talk
+
+about Markov and hidden
+Markov models, which
+
+have been called the Legos
+of bioinformatics, which
+
+can be used to model a
+variety of linear sequence
+
+labeling problems.
+
+And then, in the last
+lecture of that unit,
+
+I'll talk a little
+bit about protein--
+
+I'm sorry, about RNA--
+secondary structure--
+
+so the base pairing of
+RNAs-- predicting it
+
+from thermodynamic
+tools, as well as
+
+comparative genomic approaches.
+
+And you'll learn
+about the mfold tool
+
+and how you can use
+a diagram like that
+
+to infer that this RNA may have
+different possible structures
+
+that I can fold into,
+like those shown.
+
+All right.
+
+So I'm going to pass
+it off to David here.
+
+PROFESSOR: Thanks
+very much, Chris.
+
+All Right.
+
+So I'm David Gifford.
+
+And I'm delighted to be here.
+
+It's really a
+wonderfully exciting time
+
+in computational biology.
+
+And one of the reasons
+it's so exciting
+
+is shown on this slide, which
+is the production of DNA base
+
+sequence per
+instrument over time.
+
+And as you can see, it's
+just amazingly more efficient
+
+as time goes forward.
+
+And if you think about the
+reciprocal of this curve,
+
+the cost per base is basically
+becoming extraordinarily low.
+
+And this kind of
+instrument allows
+
+us to produce
+hundreds of millions
+
+of sequence reads for
+a single experiment.
+
+And thus do we not only need
+new computational methods
+
+to handle this kind
+of a big data problem,
+
+but we need
+computational methods
+
+to represent the results
+in computational models.
+
+And so we have multiple
+challenges computationally.
+
+Because modern biology
+really can't be done
+
+outside of a
+computational framework.
+
+And to summarise the
+way people have adapted
+
+these high throughput DNA
+sequencing instruments,
+
+I built this small
+figure for you.
+
+And you can see that--
+Professor Burge will
+
+be talking about DNA
+sequencing next time.
+
+And obviously, you
+can use DNA sequencing
+
+to sequence your own
+genomes, or the genomes
+
+of your favorite pet,
+or whatever you like.
+
+And so we'll talk about,
+in lecture six, how
+
+to actually do
+genome sequencing.
+
+And one of the challenges
+in doing genome sequencing
+
+is how to actually find
+what you have sequenced.
+
+And we'll be talking about how
+to map sequence reads as well.
+
+Another way to
+use DNA sequencing
+
+is to take the RNA species
+present in a single cell,
+
+or in a population of
+cells, and convert them
+
+into DNA using
+reverse transcriptase.
+
+Then we can sequence the DNA
+and understand the RNA component
+
+of the cell, which,
+of course, either
+
+can be used as messenger
+RNA to code for protein,
+
+or for structural RNAs, or
+for non-coding RNAs that
+
+have other kinds of functions
+associated with chromatin.
+
+In lecture seven,
+we'll be talking
+
+about protein/DNA interactions,
+which Professor Burge already
+
+mentioned-- the idea
+that we can actually
+
+locate all the regulatory
+factors associated
+
+with the genome using a single
+high throughput experiment.
+
+We do this by isolating the
+proteins and their associated
+
+DNA fragments and
+sequencing the DNA fragments
+
+using this DNA
+sequencing technology.
+
+So briefly, the first
+thing that we'll
+
+look at in lecture five is,
+given a reference genome
+
+sequence and a basket
+of DNA sequence reads,
+
+how do we build
+an efficient index
+
+so that we can either
+map or align those
+
+reads back to the
+reference genome.
+
+That's a very important
+and fundamental problem.
+
+Because if I give you a
+basket of 200 million reads,
+
+we need to build its
+alignment very, very rapidly,
+
+and quickly, and
+accurately, especially
+
+in the context of
+repetitive elements.
+
+Because a genome obviously
+has many repeats in it.
+
+We need to consider how
+our indexing and searching
+
+algorithms are going to handle
+those sorts of elements.
+
+In the next lecture,
+we'll talk about how
+
+to actually sequence a
+genome and assemble it.
+
+So the fundamental way that
+we approach genome sequencing
+
+given today's
+sequencing instruments
+
+is that we take intact
+chromosomes at the top, which,
+
+of course, are hundreds
+of millions of bases long,
+
+and we shatter them into pieces.
+
+And then we sequence
+size selected pieces
+
+in a sequencing instrument.
+
+And then we need to put the
+jigsaw puzzle back together
+
+with a computational assembler.
+
+So we'll be talking about
+assembly algorithms, how
+
+they work, and furthermore,
+how resolve ambiguities
+
+as we put that puzzle
+together, which often arise
+
+in the context of
+repetitive sequence.
+
+And in the next lecture,
+in lecture seven,
+
+we'll be looking at how to
+actually take those little DNA
+
+molecules that are
+associated with proteins
+
+and analyze them to figure out
+where particular proteins are
+
+bound to the genome and how they
+might regulate target genes.
+
+Here we see two
+different occurrences
+
+of OCT4 binding events
+binding proximally
+
+to the SOX2 gene, which
+they are regulating.
+
+So that's the beginning of our
+analysis of DNA sequencing.
+
+And then we'll look at RNA
+sequencing-- once again,
+
+with going through
+a DNA intermediate--
+
+and ask the question,
+how can we look
+
+at the expression
+of particular genes
+
+by mapping RNA sequence
+reads back onto the genome.
+
+And there are two fundamental
+questions we can address here,
+
+which is, what is the level
+of expression of a given gene,
+
+and secondarily, what
+isoforms are being expressed.
+
+The second sets of reads,
+you see up on the screen,
+
+are split reads that
+cross splice junctions.
+
+And so by looking at how
+reads align to the genome,
+
+we can figure out which
+particular axons are included
+
+or excluded from a
+particular transcript.
+
+So that's the beginning of
+the high throughput biology
+
+genomic analysis module.
+
+And I'll be returning to
+talk, later in the term,
+
+about computational genetics,
+which, really, is a way
+
+to summarize everything
+we're learning
+
+in the course into
+an applicable way
+
+to ask fundamental questions
+about genome function, which
+
+Professor Burge
+talked about earlier.
+
+Now we all have about 3
+billion bases in our genomes.
+
+And as you know, you
+differ from the individual
+
+sitting next to you in about
+one in every 1,000 base pairs,
+
+on average.
+
+And so one question
+is, how do we actually
+
+interpret these differences
+between genomes.
+
+And how can we build
+accurate computational models
+
+that allow us to infer
+function from genome sequence?
+
+And that's a pretty
+big challenge.
+
+So we'll start by
+asking questions about,
+
+what parts of the
+genome are active
+
+and how could we annotate them.
+
+So we can use, once again,
+different kinds of sequencing
+
+based assays to identify the
+regions of the genome that
+
+are active in any
+given cellular state.
+
+And furthermore, if we
+look at different cells,
+
+we can tell which
+parts of the genome
+
+are differentially active.
+
+Here you can see
+the active chromatin
+
+during the
+differentiation of an ESL
+
+into a terminal type over
+a 50 kilobase window.
+
+And the regions of the genome
+that are shaded in yellow
+
+represent regions that
+are differentially active.
+
+And so, using this kind of
+DNA seq. data and other data,
+
+we can automatically
+annotate the genome
+
+with where the
+regulatory elements are
+
+and begin to understand what the
+regulatory code of the genome
+
+is.
+
+So once we understand what
+parts of the genome are active,
+
+we can ask questions
+about, how do they
+
+contribute to some
+overall phenotype.
+
+And our next
+lecture, lecture 19,
+
+we'll be looking
+at how we can build
+
+a model of a
+quantitative trait based
+
+upon multiple loci and the
+particular alleles that
+
+are present at that loci.
+
+So here you see an
+example of a bunch
+
+of different
+quantitative trait loci
+
+that are contributing to
+the growth rate of yeast
+
+in a given condition.
+
+So part of our exploration
+during this term
+
+will be to develop
+computational methods
+
+to automatically identify
+regions of the genome that
+
+control such traits and to
+assign them significance.
+
+And finally, we'd like to
+put all this together and ask
+
+a very fundamental
+question, which
+
+is, how do we assign
+variations in the human genome
+
+to differential risk
+for human disease.
+
+And associated questions
+are, how could we
+
+assign those variants to what
+best therapy would be applied
+
+to the disease--
+what therapeutics
+
+might be used, for example.
+
+And here we have
+a bunch of results
+
+from genome wide
+association studies,
+
+starting at the top
+with bipolar disorder.
+
+And at the bottom
+is type 2 diabetes.
+
+And looking along
+the chromosomes,
+
+we're asking which
+locations along the genome
+
+have variants that
+are highly associated
+
+with these particular diseases
+in these so-called Manhattan
+
+plots.
+
+Because the things that
+stick up look like buildings.
+
+And so these sorts of studies
+are yielding very interesting
+
+insights into variants that are
+associated with human disease.
+
+And the next step, of
+course, is to figure out
+
+how to actually prove that
+these variants are causal,
+
+and also, to look
+at mechanisms where
+
+we might be able to address
+what kinds of therapeutics
+
+might be applied to deal
+with these diseases.
+
+So those are my two units.
+
+Once again, high throughput
+genomic analysis,
+
+and secondarily,
+computational genetics.
+
+And finally, if you have
+any questions about 6.874,
+
+I'll be here after lecture.
+
+Feel free to ask me.
+
+Ernest.
+
+PROFESSOR: Thank
+you very much, Dave.
+
+All right.
+
+So in the preceding
+lectures, you'll
+
+have heard a lot about
+the amazing things
+
+we can learn from
+nucleic acid sequencing.
+
+And what we're going to do in
+the latter part of the course
+
+is look at other
+modalities in the cell.
+
+Obviously, there's
+a lot that goes
+
+on inside of cells
+that's not taking place
+
+at the level of DNA/RNA.
+
+And so we're going to start
+to look at proteins, protein
+
+interactions, and ultimately,
+protein interaction networks.
+
+So we'll start with
+the small scale,
+
+looking at intermolecular
+interactions
+
+of the biophysics-- the
+fundamental biophysics
+
+of a protein structure.
+
+Then we'll start to look at
+protein-protein interactions.
+
+And as I said, the final
+level will be networks.
+
+There's been an amazing
+advance in our ability
+
+to predict protein structure.
+
+So it's always been the dream
+of computational biology
+
+to be able to go from
+the sequence of a gene
+
+to the structure of the
+corresponding protein.
+
+And ever since Anfinsen,
+we know that, at least,
+
+that should be theoretically
+possible for a lot of proteins.
+
+But it's been computationally
+virtually intractable
+
+until quite recently.
+
+And a number of
+different approaches
+
+have allowed us to
+predict protein structure.
+
+So this slide
+shows, for example--
+
+I don't know which one's
+which-- but in blue, perhaps,
+
+prediction, and in red, the
+true structure, or the other way
+
+around.
+
+But you can see, it
+doesn't matter very much.
+
+We're getting extremely accurate
+predictions of small protein
+
+structure.
+
+There are a variety
+of approaches here
+
+that live on a spectrum.
+
+On the one hand, there's
+the computational approach
+
+that tries to make special
+purpose hardware to carry out
+
+the calculations for
+protein structure.
+
+And that's been
+wildly successful.
+
+On the other end of
+the extreme, there's
+
+been the crowd sourcing
+approach to have gamers
+
+try to predict
+protein structure.
+
+And that turns out
+to be successful.
+
+And there's a lot of interesting
+computational approaches
+
+in the middle as well.
+
+So we'll explore some of
+these different strategies.
+
+Then, the ability to go from
+just seeing a single protein
+
+structure, how these
+proteins interact.
+
+So now there are
+pretty good algorithms
+
+predicting protein-protein
+interactions as well.
+
+And that allows us, then,
+to figure out not only
+
+how these proteins
+function individually,
+
+but how they begin to
+function as a network.
+
+Now one of the things
+that we've already--
+
+going to be touched on in
+the early parts of the course
+
+are protein-DNA interactions
+through sequencing approaches.
+
+We want to now look at
+them at a regulatory level.
+
+And could you reconstruct
+the regulation of a genome
+
+by predicting the protein-DNA?
+
+And there's been a
+lot of work here.
+
+We talked earlier
+about Eric Davidson's
+
+pioneering approaches, a lot
+of interesting computational
+
+approaches as well, that go from
+the relatively simple models we
+
+saw on those earlier slides to
+these very complicated networks
+
+that you see here.
+
+We'll look at what
+these networks actually
+
+tell us, how much information
+is really encoded in them.
+
+They are certainly
+pretty, whatever they are.
+
+We'll look at other kinds
+of interactions networks.
+
+We'll look at genetic
+interaction networks as well,
+
+and perhaps, some other kinds.
+
+And finally, we'll look
+at computable models.
+
+And what do we mean by that?
+
+We mean model that
+make some kind of very
+
+specific prediction,
+whether it's
+
+a Boolean prediction-- this gene
+will be on or off-- or perhaps,
+
+an even more
+quantitative prediction.
+
+So we'll look at
+logic based modeling,
+
+and probably, Bayesian
+networks as well.
+
+So that's been a very
+whirlwind tour of the course.
+
+Just to go back
+to the mechanics,
+
+make sure you're signed
+up for the right course.
+
+The undergraduate
+versions of the course
+
+do not have a project.
+
+And they certainly do not have
+the artificial intelligence
+
+problems.
+
+Then, there are the graduate
+versions that have the project,
+
+but do not have the AI,
+and finally, the 6.874,
+
+which has both.
+
+So please be sure you're
+in the right class
+
+so you get credit for
+the right assignments.
+
+And finally, if you've got
+any questions about the course
+
+mechanics, we have
+a few minutes.
+
+We can talk about it here,
+in front of everybody.
+
+And then, we'll all be available
+after class, a little bit,
+
+to answer questions.
+
+So please, any questions?
+
+Yes.
+
+AUDIENCE: Can
+undergrads do a project?
+
+PROFESSOR: Can
+undergrads do a project?
+
+Well, they can sign up for the
+graduate version, absolutely.
+
+Other questions?
+
+Yes.
+
+AUDIENCE: Yeah, I actually can't
+make either of those sessions.
+
+PROFESSOR: Well, send an
+email to the staff list
+
+and we'll see what we can do.
+
+Other questions?
+
+Yes.
+
+AUDIENCE: 6.877
+doesn't exist anymore--
+
+Computational Evolutionary
+Biology, the class.
+
+PROFESSOR: Oh, the thing we
+listed as alternative classes?
+
+Sorry.
+
+PROFESSOR: We'll fix that.
+
+AUDIENCE: Really?
+
+I would be so happy.
+
+[LAUGHTER]
+
+PROFESSOR: We'll delete
+it from our slides, yes.
+
+We are powerful, but
+not that powerful.
+
+Other questions,
+comments, critiques?
+
+Yes, in the back.
+
+AUDIENCE: Are each of the
+exams equally weighted?
+
+PROFESSOR: Are each of the
+exams equally weighted?
+
+Yes, they are.
+
+Yes.
+
+AUDIENCE: If we're in 6.874,
+we have the additional AI
+
+problems.
+
+Does that mean that we have
+more questions on the exam,
+
+but just as much
+time to do them?
+
+PROFESSOR: The question
+was, if you're in 6.874
+
+and you have the additional
+AI questions on the exam,
+
+does that mean you
+have more questions,
+
+but the same amount of time.
+
+And I believe the
+answer to that is yes.
+
+PROFESSOR: We may
+revisit that question.
+
+PROFESSOR: We will revisit
+that question at a later date.
+
+But course six students
+are just so much smarter
+
+than everyone else, right?
+
+Yes.
+
+AUDIENCE: Can we switch between
+different versions of the class
+
+by the add deadline?
+
+PROFESSOR: I'm sorry,
+could you say that again?
+
+AUDIENCE: Can we switch
+between versions of the class
+
+by the add deadline?
+
+PROFESSOR: Can you switch
+between different versions
+
+of class by the
+add/drop deadline?
+
+In principle, yes.
+
+But if you haven't
+done the work for that,
+
+then you will be in trouble.
+
+And there may not be
+a smooth mechanism
+
+for making up missed
+work that late.
+
+Because the add/drop
+deadline is rather late.
+
+So I'd encourage you,
+if you're considering
+
+doing the more intensive
+version or not,
+
+sign up for the more
+intensive version.
+
+You can always drop back.
+
+Once we form groups
+though, for the projects,
+
+then, obviously,
+there's an aspect
+
+of letting down your teammates.
+
+So think carefully, now, about
+which one you want to join.
+
+It'll be hard to
+switch between them.
+
+But we'll do whatever
+the registrar requires
+
+us to do in terms
+of allowing it.
+
+Other questions?
+
+Yes.
+
+AUDIENCE: If the course sites,
+can we undergrads access the AI
+
+problems just for
+fun, to look at them?
+
+PROFESSOR: Yes.
+
+If the course sites
+remain separate,
+
+will undergrads be able
+to access the AI problems?
+
+The answer is yes.
+
+Yes.
+
+AUDIENCE: Should
+students in 6.874
+
+attend both presentations?
+
+PROFESSOR: Should
+students in 6.874
+
+attend both presentations?
+
+Not necessary.
+
+You're welcome to
+both if you want.
+
+But the course six recitation
+should be sufficient.
+
+Other questions?
+
+Yes.
+
+AUDIENCE: So what's covered
+in the normal recitations?
+
+PROFESSOR: What's covered
+in the normal recitations?
+
+It'll be reinforcing material
+that's in the lectures.
+
+So the goal is not introduce any
+new material in the course 20,
+
+course seven recitations.
+
+Just to clarify, not to
+introduce any new material.
+
+Other questions?
+
+OK.
+
+Great.
+
+And we'll hang
+around a little bit
+
+to answer any remaining
+questions when they come up.
\ No newline at end of file
diff --git a/lL0oUZGMhXc.txt b/lL0oUZGMhXc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..519d9d1328581d6ca902a76974a791eca4448381
--- /dev/null
+++ b/lL0oUZGMhXc.txt
@@ -0,0 +1,1931 @@
+align:start position:0%
+ 
+okay uh this video is to give you more
+
+ align:start position:0%
+okay uh this video is to give you more
+ 
+
+ align:start position:0%
+okay uh this video is to give you more
+examples of Fier series I'll start with
+
+ align:start position:0%
+examples of Fier series I'll start with
+ 
+
+ align:start position:0%
+examples of Fier series I'll start with
+a function that's odd my odd function
+
+ align:start position:0%
+a function that's odd my odd function
+ 
+
+ align:start position:0%
+a function that's odd my odd function
+means that the on the left side of zero
+
+ align:start position:0%
+means that the on the left side of zero
+ 
+
+ align:start position:0%
+means that the on the left side of zero
+I get the negative of what I have on the
+
+ align:start position:0%
+I get the negative of what I have on the
+ 
+
+ align:start position:0%
+I get the negative of what I have on the
+right side of zero f at Min - x is minus
+
+ align:start position:0%
+right side of zero f at Min - x is minus
+ 
+
+ align:start position:0%
+right side of zero f at Min - x is minus
+F ofx and it's the S function that's odd
+
+ align:start position:0%
+F ofx and it's the S function that's odd
+ 
+
+ align:start position:0%
+F ofx and it's the S function that's odd
+the cosine function is even and we will
+
+ align:start position:0%
+the cosine function is even and we will
+ 
+
+ align:start position:0%
+the cosine function is even and we will
+have no cosine here all the integrals
+
+ align:start position:0%
+have no cosine here all the integrals
+ 
+
+ align:start position:0%
+have no cosine here all the integrals
+that involve cosin will tell us zero for
+
+ align:start position:0%
+that involve cosin will tell us zero for
+ 
+
+ align:start position:0%
+that involve cosin will tell us zero for
+the coefficients a n what we'll get is
+
+ align:start position:0%
+the coefficients a n what we'll get is
+ 
+
+ align:start position:0%
+the coefficients a n what we'll get is
+the co the B coefficients the S
+
+ align:start position:0%
+the co the B coefficients the S
+ 
+
+ align:start position:0%
+the co the B coefficients the S
+functions okay and so you see that I
+
+ align:start position:0%
+functions okay and so you see that I
+ 
+
+ align:start position:0%
+functions okay and so you see that I
+chose a simple odd function minus one or
+
+ align:start position:0%
+chose a simple odd function minus one or
+ 
+
+ align:start position:0%
+chose a simple odd function minus one or
+one which would give a square wave if I
+
+ align:start position:0%
+one which would give a square wave if I
+ 
+
+ align:start position:0%
+one which would give a square wave if I
+keep if I continue it on it will go down
+
+ align:start position:0%
+keep if I continue it on it will go down
+ 
+
+ align:start position:0%
+keep if I continue it on it will go down
+up down up in a square wave pattern okay
+
+ align:start position:0%
+up down up in a square wave pattern okay
+ 
+
+ align:start position:0%
+up down up in a square wave pattern okay
+okay and I'm going to express that as a
+
+ align:start position:0%
+okay and I'm going to express that as a
+ 
+
+ align:start position:0%
+okay and I'm going to express that as a
+combination of s functions smooth waves
+
+ align:start position:0%
+combination of s functions smooth waves
+ 
+
+ align:start position:0%
+combination of s functions smooth waves
+and here was the formula from last time
+
+ align:start position:0%
+and here was the formula from last time
+ 
+
+ align:start position:0%
+and here was the formula from last time
+for the coefficients BK except I have
+
+ align:start position:0%
+for the coefficients BK except I have
+ 
+
+ align:start position:0%
+for the coefficients BK except I have
+now I'm only integrating over half over
+
+ align:start position:0%
+now I'm only integrating over half over
+ 
+
+ align:start position:0%
+now I'm only integrating over half over
+the over the zero to Pi part of the
+
+ align:start position:0%
+the over the zero to Pi part of the
+ 
+
+ align:start position:0%
+the over the zero to Pi part of the
+interval so I and I double it so with so
+
+ align:start position:0%
+interval so I and I double it so with so
+ 
+
+ align:start position:0%
+interval so I and I double it so with so
+that's an odd function that's an odd
+
+ align:start position:0%
+that's an odd function that's an odd
+ 
+
+ align:start position:0%
+that's an odd function that's an odd
+function when I mul mply them I have an
+
+ align:start position:0%
+function when I mul mply them I have an
+ 
+
+ align:start position:0%
+function when I mul mply them I have an
+even function and the integral fromus pi
+
+ align:start position:0%
+even function and the integral fromus pi
+ 
+
+ align:start position:0%
+even function and the integral fromus pi
+to 0 is just the same as the integral
+
+ align:start position:0%
+to 0 is just the same as the integral
+ 
+
+ align:start position:0%
+to 0 is just the same as the integral
+from 0 to Pi so I'll do what only Zer to
+
+ align:start position:0%
+from 0 to Pi so I'll do what only Zer to
+ 
+
+ align:start position:0%
+from 0 to Pi so I'll do what only Zer to
+Pi and and multiply by two okay but my
+
+ align:start position:0%
+Pi and and multiply by two okay but my
+ 
+
+ align:start position:0%
+Pi and and multiply by two okay but my
+function on 0 to Pi is
+
+ align:start position:0%
+function on 0 to Pi is
+ 
+
+ align:start position:0%
+function on 0 to Pi is
+one my my nice Square wave is just plus
+
+ align:start position:0%
+one my my nice Square wave is just plus
+ 
+
+ align:start position:0%
+one my my nice Square wave is just plus
+one there so I'm just integrating sin KX
+
+ align:start position:0%
+one there so I'm just integrating sin KX
+ 
+
+ align:start position:0%
+one there so I'm just integrating sin KX
+DX we can do
+
+ align:start position:0%
+DX we can do
+ 
+
+ align:start position:0%
+DX we can do
+this it's minus cine KX / K right that's
+
+ align:start position:0%
+this it's minus cine KX / K right that's
+ 
+
+ align:start position:0%
+this it's minus cine KX / K right that's
+the integral with the 2 over Pi Factor
+
+ align:start position:0%
+the integral with the 2 over Pi Factor
+ 
+
+ align:start position:0%
+the integral with the 2 over Pi Factor
+now I have to put in
+
+ align:start position:0%
+now I have to put in
+ 
+
+ align:start position:0%
+now I have to put in
+pi and
+
+ align:start position:0%
+pi and
+ 
+
+ align:start position:0%
+pi and
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and put in the limits of integration and
+
+ align:start position:0%
+and put in the limits of integration and
+ 
+
+ align:start position:0%
+and put in the limits of integration and
+get the answer okay so what do I get I
+
+ align:start position:0%
+get the answer okay so what do I get I
+ 
+
+ align:start position:0%
+get the answer okay so what do I get I
+get 2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi for k equal 1 I think I get
+
+ align:start position:0%
+Pi for k equal 1 I think I get
+ 
+
+ align:start position:0%
+Pi for k equal 1 I think I get
+um so K is one the denominator will be
+
+ align:start position:0%
+um so K is one the denominator will be
+ 
+
+ align:start position:0%
+um so K is one the denominator will be
+one and I think the numerator is two yes
+
+ align:start position:0%
+one and I think the numerator is two yes
+ 
+
+ align:start position:0%
+one and I think the numerator is two yes
+when K is zero I get yeah you you when K
+
+ align:start position:0%
+when K is zero I get yeah you you when K
+ 
+
+ align:start position:0%
+when K is zero I get yeah you you when K
+is one I get to two when K is two so
+
+ align:start position:0%
+is one I get to two when K is two so
+ 
+
+ align:start position:0%
+is one I get to two when K is two so
+this is 4 over Pi I figured out as the
+
+ align:start position:0%
+this is 4 over Pi I figured out as the
+ 
+
+ align:start position:0%
+this is 4 over Pi I figured out as the
+first coefficient the coefficient B1 is
+
+ align:start position:0%
+first coefficient the coefficient B1 is
+ 
+
+ align:start position:0%
+first coefficient the coefficient B1 is
+4 over Pi the coefficient B2 now if I
+
+ align:start position:0%
+4 over Pi the coefficient B2 now if I
+ 
+
+ align:start position:0%
+4 over Pi the coefficient B2 now if I
+take k equal to 2 I have a two down
+
+ align:start position:0%
+take k equal to 2 I have a two down
+ 
+
+ align:start position:0%
+take k equal to 2 I have a two down
+below but above I have a zero cuz the
+
+ align:start position:0%
+below but above I have a zero cuz the
+ 
+
+ align:start position:0%
+below but above I have a zero cuz the
+cosine of
+
+ align:start position:0%
+cosine of
+ 
+
+ align:start position:0%
+cosine of
+two Pi is the same as the co cosine of
+
+ align:start position:0%
+two Pi is the same as the co cosine of
+ 
+
+ align:start position:0%
+two Pi is the same as the co cosine of
+0o when I subtract I get nothing so
+
+ align:start position:0%
+0o when I subtract I get nothing so
+ 
+
+ align:start position:0%
+0o when I subtract I get nothing so
+that's zero okay now I go to k = 3 so
+
+ align:start position:0%
+that's zero okay now I go to k = 3 so
+ 
+
+ align:start position:0%
+that's zero okay now I go to k = 3 so
+the k equal 3 will come down here and
+
+ align:start position:0%
+the k equal 3 will come down here and
+ 
+
+ align:start position:0%
+the k equal 3 will come down here and
+now when K is three it turns out I get
+
+ align:start position:0%
+now when K is three it turns out I get
+ 
+
+ align:start position:0%
+now when K is three it turns out I get
+they they don't cancel I reinforce I get
+
+ align:start position:0%
+they they don't cancel I reinforce I get
+ 
+
+ align:start position:0%
+they they don't cancel I reinforce I get
+another two good if you do these and
+
+ align:start position:0%
+another two good if you do these and
+ 
+
+ align:start position:0%
+another two good if you do these and
+when K is four I get a zero again you
+
+ align:start position:0%
+when K is four I get a zero again you
+ 
+
+ align:start position:0%
+when K is four I get a zero again you
+see the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pattern the pattern for the integrals is
+
+ align:start position:0%
+pattern the pattern for the integrals is
+ 
+
+ align:start position:0%
+pattern the pattern for the integrals is
+the K is going 1 2 3 4 5 the this part
+
+ align:start position:0%
+the K is going 1 2 3 4 5 the this part
+ 
+
+ align:start position:0%
+the K is going 1 2 3 4 5 the this part
+gives me a two or a zero or a two or a
+
+ align:start position:0%
+gives me a two or a zero or a two or a
+ 
+
+ align:start position:0%
+gives me a two or a zero or a two or a
+zero in order if you check that you'll
+
+ align:start position:0%
+zero in order if you check that you'll
+ 
+
+ align:start position:0%
+zero in order if you check that you'll
+get it okay so I see that now for for
+
+ align:start position:0%
+get it okay so I see that now for for
+ 
+
+ align:start position:0%
+get it okay so I see that now for for
+this function which is better than the
+
+ align:start position:0%
+this function which is better than the
+ 
+
+ align:start position:0%
+this function which is better than the
+Delta function although it not it's not
+
+ align:start position:0%
+Delta function although it not it's not
+ 
+
+ align:start position:0%
+Delta function although it not it's not
+very smooth it has jumps it's a jump
+
+ align:start position:0%
+very smooth it has jumps it's a jump
+ 
+
+ align:start position:0%
+very smooth it has jumps it's a jump
+function a step function uh I see some
+
+ align:start position:0%
+function a step function uh I see some
+ 
+
+ align:start position:0%
+function a step function uh I see some
+Decay some slow decay in the forier
+
+ align:start position:0%
+Decay some slow decay in the forier
+ 
+
+ align:start position:0%
+Decay some slow decay in the forier
+coefficients there's a this this this uh
+
+ align:start position:0%
+coefficients there's a this this this uh
+ 
+
+ align:start position:0%
+coefficients there's a this this this uh
+Factor K is growing so the the numbers
+
+ align:start position:0%
+Factor K is growing so the the numbers
+ 
+
+ align:start position:0%
+Factor K is growing so the the numbers
+are going to zero but not very fast not
+
+ align:start position:0%
+are going to zero but not very fast not
+ 
+
+ align:start position:0%
+are going to zero but not very fast not
+very fast because my function is not
+
+ align:start position:0%
+very fast because my function is not
+ 
+
+ align:start position:0%
+very fast because my function is not
+very smooth move okay so that's now you
+
+ align:start position:0%
+very smooth move okay so that's now you
+ 
+
+ align:start position:0%
+very smooth move okay so that's now you
+see the so if I use those numbers I'm
+
+ align:start position:0%
+see the so if I use those numbers I'm
+ 
+
+ align:start position:0%
+see the so if I use those numbers I'm
+saying that the square
+
+ align:start position:0%
+saying that the square
+ 
+
+ align:start position:0%
+saying that the square
+wave this this function the the minus1
+
+ align:start position:0%
+wave this this function the the minus1
+ 
+
+ align:start position:0%
+wave this this function the the minus1
+to one
+
+ align:start position:0%
+to one
+ 
+
+ align:start position:0%
+to one
+function is equal to let's see I might
+
+ align:start position:0%
+function is equal to let's see I might
+ 
+
+ align:start position:0%
+function is equal to let's see I might
+as well take that 4 over
+
+ align:start position:0%
+as well take that 4 over
+ 
+
+ align:start position:0%
+as well take that 4 over
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+times 1 so that's 1 sin x
+
+ align:start position:0%
+times 1 so that's 1 sin x
+ 
+
+ align:start position:0%
+times 1 so that's 1 sin x
+0 sin 2
+
+ align:start position:0%
+0 sin 2
+ 
+
+ align:start position:0%
+0 sin 2
+X's there then two 4 Pi sin
+
+ align:start position:0%
+X's there then two 4 Pi sin
+ 
+
+ align:start position:0%
+X's there then two 4 Pi sin
+3x's but with this guy there's a
+
+ align:start position:0%
+3x's but with this guy there's a
+ 
+
+ align:start position:0%
+3x's but with this guy there's a
+three Z Sin
+
+ align:start position:0%
+three Z Sin
+ 
+
+ align:start position:0%
+three Z Sin
+4x's Sin 5x comes in over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five and so
+
+ align:start position:0%
+five and so
+ 
+
+ align:start position:0%
+five and so
+on that's a kind of nice example it it
+
+ align:start position:0%
+on that's a kind of nice example it it
+ 
+
+ align:start position:0%
+on that's a kind of nice example it it
+turns out that that we have just the odd
+
+ align:start position:0%
+turns out that that we have just the odd
+ 
+
+ align:start position:0%
+turns out that that we have just the odd
+frequencies
+
+ align:start position:0%
+frequencies
+ 
+
+ align:start position:0%
+frequencies
+135 in the Square wave and they're
+
+ align:start position:0%
+135 in the Square wave and they're
+ 
+
+ align:start position:0%
+135 in the Square wave and they're
+multiplied by uh 4 over pi and they're
+
+ align:start position:0%
+multiplied by uh 4 over pi and they're
+ 
+
+ align:start position:0%
+multiplied by uh 4 over pi and they're
+divided by the frequency so that's the
+
+ align:start position:0%
+divided by the frequency so that's the
+ 
+
+ align:start position:0%
+divided by the frequency so that's the
+decay all right there's an odd function
+
+ align:start position:0%
+decay all right there's an odd function
+ 
+
+ align:start position:0%
+decay all right there's an odd function
+let me uh why don't I integrate that
+
+ align:start position:0%
+let me uh why don't I integrate that
+ 
+
+ align:start position:0%
+let me uh why don't I integrate that
+function if I want to get an even
+
+ align:start position:0%
+function if I want to get an even
+ 
+
+ align:start position:0%
+function if I want to get an even
+function to show you an even example
+
+ align:start position:0%
+function to show you an even example
+ 
+
+ align:start position:0%
+function to show you an even example
+I'll just integrate that square wave
+
+ align:start position:0%
+I'll just integrate that square wave
+ 
+
+ align:start position:0%
+I'll just integrate that square wave
+what when I integrate that square wave
+
+ align:start position:0%
+what when I integrate that square wave
+ 
+
+ align:start position:0%
+what when I integrate that square wave
+it'll be even maybe I'll start the
+
+ align:start position:0%
+it'll be even maybe I'll start the
+ 
+
+ align:start position:0%
+it'll be even maybe I'll start the
+integral at zero then it goes up at
+
+ align:start position:0%
+integral at zero then it goes up at
+ 
+
+ align:start position:0%
+integral at zero then it goes up at
+one okay and here the integral is
+
+ align:start position:0%
+one okay and here the integral is
+ 
+
+ align:start position:0%
+one okay and here the integral is
+negative so it's coming down so you see
+
+ align:start position:0%
+negative so it's coming down so you see
+ 
+
+ align:start position:0%
+negative so it's coming down so you see
+my it's
+
+ align:start position:0%
+my it's
+ 
+
+ align:start position:0%
+my it's
+a what am I going to call this function
+
+ align:start position:0%
+a what am I going to call this function
+ 
+
+ align:start position:0%
+a what am I going to call this function
+sort of a repeating ramp function it's a
+
+ align:start position:0%
+sort of a repeating ramp function it's a
+ 
+
+ align:start position:0%
+sort of a repeating ramp function it's a
+ramp down and then up down and then up
+
+ align:start position:0%
+ramp down and then up down and then up
+ 
+
+ align:start position:0%
+ramp down and then up down and then up
+but of course from minus pi to Pi that's
+
+ align:start position:0%
+but of course from minus pi to Pi that's
+ 
+
+ align:start position:0%
+but of course from minus pi to Pi that's
+where I'm looking I'm looking between
+
+ align:start position:0%
+where I'm looking I'm looking between
+ 
+
+ align:start position:0%
+where I'm looking I'm looking between
+minus pi and pi and my I see that
+
+ align:start position:0%
+minus pi and pi and my I see that
+ 
+
+ align:start position:0%
+minus pi and pi and my I see that
+function as
+
+ align:start position:0%
+function as
+ 
+
+ align:start position:0%
+function as
+even and what does even mean that means
+
+ align:start position:0%
+even and what does even mean that means
+ 
+
+ align:start position:0%
+even and what does even mean that means
+that my function at
+
+ align:start position:0%
+that my function at
+ 
+
+ align:start position:0%
+that my function at
+minus there's minus X is the same as the
+
+ align:start position:0%
+minus there's minus X is the same as the
+ 
+
+ align:start position:0%
+minus there's minus X is the same as the
+value at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and what that means for 4A series is
+
+ align:start position:0%
+X and what that means for 4A series is
+ 
+
+ align:start position:0%
+X and what that means for 4A series is
+cosiness even functions only have cosine
+
+ align:start position:0%
+cosiness even functions only have cosine
+ 
+
+ align:start position:0%
+cosiness even functions only have cosine
+terms and of course since I'm just
+
+ align:start position:0%
+terms and of course since I'm just
+ 
+
+ align:start position:0%
+terms and of course since I'm just
+integrating I might as well just
+
+ align:start position:0%
+integrating I might as well just
+ 
+
+ align:start position:0%
+integrating I might as well just
+integrate that Series so this is this
+
+ align:start position:0%
+integrate that Series so this is this
+ 
+
+ align:start position:0%
+integrate that Series so this is this
+ramp this repeating ramp function is
+
+ align:start position:0%
+ramp this repeating ramp function is
+ 
+
+ align:start position:0%
+ramp this repeating ramp function is
+going to be 4 over
+
+ align:start position:0%
+going to be 4 over
+ 
+
+ align:start position:0%
+going to be 4 over
+Pi I could figure out the cosine
+
+ align:start position:0%
+Pi I could figure out the cosine
+ 
+
+ align:start position:0%
+Pi I could figure out the cosine
+coefficients the A's patiently but why
+
+ align:start position:0%
+coefficients the A's patiently but why
+ 
+
+ align:start position:0%
+coefficients the A's patiently but why
+should I do that when I can just
+
+ align:start position:0%
+should I do that when I can just
+ 
+
+ align:start position:0%
+should I do that when I can just
+integrate so I'll have the integral of
+
+ align:start position:0%
+integrate so I'll have the integral of
+ 
+
+ align:start position:0%
+integrate so I'll have the integral of
+so the integral of sinx will be minus is
+
+ align:start position:0%
+so the integral of sinx will be minus is
+ 
+
+ align:start position:0%
+so the integral of sinx will be minus is
+the integral of sinx X is minus cine X
+
+ align:start position:0%
+the integral of sinx X is minus cine X
+ 
+
+ align:start position:0%
+the integral of sinx X is minus cine X
+so I'll put the minus there cine
+
+ align:start position:0%
+so I'll put the minus there cine
+ 
+
+ align:start position:0%
+so I'll put the minus there cine
+X over 1 I guess now what's the integral
+
+ align:start position:0%
+X over 1 I guess now what's the integral
+ 
+
+ align:start position:0%
+X over 1 I guess now what's the integral
+of this the integral of sin 3x is a
+
+ align:start position:0%
+of this the integral of sin 3x is a
+ 
+
+ align:start position:0%
+of this the integral of sin 3x is a
+cosine 3x over
+
+ align:start position:0%
+cosine 3x over
+ 
+
+ align:start position:0%
+cosine 3x over
+3 and there's another three and there's
+
+ align:start position:0%
+3 and there's another three and there's
+ 
+
+ align:start position:0%
+3 and there's another three and there's
+a minus sign so I which I've got so I
+
+ align:start position:0%
+a minus sign so I which I've got so I
+ 
+
+ align:start position:0%
+a minus sign so I which I've got so I
+think it's cosine of 3x over 3^ 2ar cuz
+
+ align:start position:0%
+think it's cosine of 3x over 3^ 2ar cuz
+ 
+
+ align:start position:0%
+think it's cosine of 3x over 3^ 2ar cuz
+I have one three there and I get another
+
+ align:start position:0%
+I have one three there and I get another
+ 
+
+ align:start position:0%
+I have one three there and I get another
+three from the integration and similarly
+
+ align:start position:0%
+three from the integration and similarly
+ 
+
+ align:start position:0%
+three from the integration and similarly
+here when I integrate sin 5x I get cos
+
+ align:start position:0%
+here when I integrate sin 5x I get cos
+ 
+
+ align:start position:0%
+here when I integrate sin 5x I get cos
+5x with a five and then I already had
+
+ align:start position:0%
+5x with a five and then I already had
+ 
+
+ align:start position:0%
+5x with a five and then I already had
+one five so 5 squared so there you go
+
+ align:start position:0%
+one five so 5 squared so there you go
+ 
+
+ align:start position:0%
+one five so 5 squared so there you go
+well H there's something in freshman
+
+ align:start position:0%
+well H there's something in freshman
+ 
+
+ align:start position:0%
+well H there's something in freshman
+calculus which I totally forgot the
+
+ align:start position:0%
+calculus which I totally forgot the
+ 
+
+ align:start position:0%
+calculus which I totally forgot the
+constant term so there is a constant
+
+ align:start position:0%
+constant term so there is a constant
+ 
+
+ align:start position:0%
+constant term so there is a constant
+term the average value the a Zer I've
+
+ align:start position:0%
+term the average value the a Zer I've
+ 
+
+ align:start position:0%
+term the average value the a Zer I've
+only found the A1 2 3 4 five I haven't
+
+ align:start position:0%
+only found the A1 2 3 4 five I haven't
+ 
+
+ align:start position:0%
+only found the A1 2 3 4 five I haven't
+found the a z and that would be the
+
+ align:start position:0%
+found the a z and that would be the
+ 
+
+ align:start position:0%
+found the a z and that would be the
+average of that I don't know what's the
+
+ align:start position:0%
+average of that I don't know what's the
+ 
+
+ align:start position:0%
+average of that I don't know what's the
+average of this function it starts it's
+
+ align:start position:0%
+average of this function it starts it's
+ 
+
+ align:start position:0%
+average of this function it starts it's
+goes from zero up to Pi and it seems
+
+ align:start position:0%
+goes from zero up to Pi and it seems
+ 
+
+ align:start position:0%
+goes from zero up to Pi and it seems
+like it's pretty I didn't draw it well
+
+ align:start position:0%
+like it's pretty I didn't draw it well
+ 
+
+ align:start position:0%
+like it's pretty I didn't draw it well
+but halfway I think probably its average
+
+ align:start position:0%
+but halfway I think probably its average
+ 
+
+ align:start position:0%
+but halfway I think probably its average
+is about pi over two
+
+ align:start position:0%
+is about pi over two
+ 
+
+ align:start position:0%
+is about pi over two
+right let's let's hope that's right okay
+
+ align:start position:0%
+right let's let's hope that's right okay
+ 
+
+ align:start position:0%
+right let's let's hope that's right okay
+so let me sneak in the constant term
+
+ align:start position:0%
+so let me sneak in the constant term
+ 
+
+ align:start position:0%
+so let me sneak in the constant term
+here the
+
+ align:start position:0%
+here the
+ 
+
+ align:start position:0%
+here the
+ramp is I think I have the constant term
+
+ align:start position:0%
+ramp is I think I have the constant term
+ 
+
+ align:start position:0%
+ramp is I think I have the constant term
+is Pi / 2 that's the average value it
+
+ align:start position:0%
+is Pi / 2 that's the average value it
+ 
+
+ align:start position:0%
+is Pi / 2 that's the average value it
+would come from the formula and those
+
+ align:start position:0%
+would come from the formula and those
+ 
+
+ align:start position:0%
+would come from the formula and those
+well what do you see
+
+ align:start position:0%
+well what do you see
+ 
+
+ align:start position:0%
+well what do you see
+now that's the other example I wanted
+
+ align:start position:0%
+now that's the other example I wanted
+ 
+
+ align:start position:0%
+now that's the other example I wanted
+you to see you see a faster drop off one
+
+ align:start position:0%
+you to see you see a faster drop off one
+ 
+
+ align:start position:0%
+you to see you see a faster drop off one
+n 25 49 whatever it's dropping off with
+
+ align:start position:0%
+n 25 49 whatever it's dropping off with
+ 
+
+ align:start position:0%
+n 25 49 whatever it's dropping off with
+K squared and the reason it drops off
+
+ align:start position:0%
+K squared and the reason it drops off
+ 
+
+ align:start position:0%
+K squared and the reason it drops off
+faster than this one is
+
+ align:start position:0%
+faster than this one is
+ 
+
+ align:start position:0%
+faster than this one is
+that uh it's smoother this function has
+
+ align:start position:0%
+that uh it's smoother this function has
+ 
+
+ align:start position:0%
+that uh it's smoother this function has
+Corners this function has
+
+ align:start position:0%
+Corners this function has
+ 
+
+ align:start position:0%
+Corners this function has
+jumps so a jump is one level more rough
+
+ align:start position:0%
+jumps so a jump is one level more rough
+ 
+
+ align:start position:0%
+jumps so a jump is one level more rough
+more more noisy than a than a ramp
+
+ align:start position:0%
+more more noisy than a than a ramp
+ 
+
+ align:start position:0%
+more more noisy than a than a ramp
+function the smoother function has
+
+ align:start position:0%
+function the smoother function has
+ 
+
+ align:start position:0%
+function the smoother function has
+faster Decay smooth let me write those
+
+ align:start position:0%
+faster Decay smooth let me write those
+ 
+
+ align:start position:0%
+faster Decay smooth let me write those
+words smooth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function connects with faster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Decay faster drop off of the fora
+
+ align:start position:0%
+Decay faster drop off of the fora
+ 
+
+ align:start position:0%
+Decay faster drop off of the fora
+coefficient it means that the fora
+
+ align:start position:0%
+coefficient it means that the fora
+ 
+
+ align:start position:0%
+coefficient it means that the fora
+series is much more useful fora series
+
+ align:start position:0%
+series is much more useful fora series
+ 
+
+ align:start position:0%
+series is much more useful fora series
+is really terrific for functions that
+
+ align:start position:0%
+is really terrific for functions that
+ 
+
+ align:start position:0%
+is really terrific for functions that
+are smooth because then you only need to
+
+ align:start position:0%
+are smooth because then you only need to
+ 
+
+ align:start position:0%
+are smooth because then you only need to
+keep a few
+
+ align:start position:0%
+keep a few
+ 
+
+ align:start position:0%
+keep a few
+terms for functions that are that have
+
+ align:start position:0%
+terms for functions that are that have
+ 
+
+ align:start position:0%
+terms for functions that are that have
+jumps or Delta functions you have to
+
+ align:start position:0%
+jumps or Delta functions you have to
+ 
+
+ align:start position:0%
+jumps or Delta functions you have to
+keep many many terms and the for a
+
+ align:start position:0%
+keep many many terms and the for a
+ 
+
+ align:start position:0%
+keep many many terms and the for a
+series calculation is much more
+
+ align:start position:0%
+series calculation is much more
+ 
+
+ align:start position:0%
+series calculation is much more
+difficult okay so that's the that's the
+
+ align:start position:0%
+difficult okay so that's the that's the
+ 
+
+ align:start position:0%
+difficult okay so that's the that's the
+second example uh let's see what what uh
+
+ align:start position:0%
+second example uh let's see what what uh
+ 
+
+ align:start position:0%
+second example uh let's see what what uh
+more shall I say we learned something
+
+ align:start position:0%
+more shall I say we learned something
+ 
+
+ align:start position:0%
+more shall I say we learned something
+about integrating and taking the
+
+ align:start position:0%
+about integrating and taking the
+ 
+
+ align:start position:0%
+about integrating and taking the
+derivative so let me end with just two
+
+ align:start position:0%
+derivative so let me end with just two
+ 
+
+ align:start position:0%
+derivative so let me end with just two
+basic rules two basic
+
+ align:start position:0%
+basic rules two basic
+ 
+
+ align:start position:0%
+basic rules two basic
+rules so the
+
+ align:start position:0%
+rules so the
+ 
+
+ align:start position:0%
+rules so the
+rule for derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the 4 series of DF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX and the second will be the rule for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shift what's the 4 a series for f of x
+
+ align:start position:0%
+shift what's the 4 a series for f of x
+ 
+
+ align:start position:0%
+shift what's the 4 a series for f of x
+minus a
+
+ align:start position:0%
+minus a
+ 
+
+ align:start position:0%
+minus a
+shift you you know that that when I
+
+ align:start position:0%
+shift you you know that that when I
+ 
+
+ align:start position:0%
+shift you you know that that when I
+change X to xus D all that does is shift
+
+ align:start position:0%
+change X to xus D all that does is shift
+ 
+
+ align:start position:0%
+change X to xus D all that does is shift
+the graph by a distance D that should do
+
+ align:start position:0%
+the graph by a distance D that should do
+ 
+
+ align:start position:0%
+the graph by a distance D that should do
+something nice to its 48 coefficients so
+
+ align:start position:0%
+something nice to its 48 coefficients so
+ 
+
+ align:start position:0%
+something nice to its 48 coefficients so
+I'm starting with oh I haven't given you
+
+ align:start position:0%
+I'm starting with oh I haven't given you
+ 
+
+ align:start position:0%
+I'm starting with oh I haven't given you
+any practice with the complex case this
+
+ align:start position:0%
+any practice with the complex case this
+ 
+
+ align:start position:0%
+any practice with the complex case this
+would be a good time suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start is f ofx equals the sum of CK the
+
+ align:start position:0%
+start is f ofx equals the sum of CK the
+ 
+
+ align:start position:0%
+start is f ofx equals the sum of CK the
+complex coefficient e to the I KX the
+
+ align:start position:0%
+complex coefficient e to the I KX the
+ 
+
+ align:start position:0%
+complex coefficient e to the I KX the
+complex exponential and you remember
+
+ align:start position:0%
+complex exponential and you remember
+ 
+
+ align:start position:0%
+complex exponential and you remember
+that sum went from minus infinity to
+
+ align:start position:0%
+that sum went from minus infinity to
+ 
+
+ align:start position:0%
+that sum went from minus infinity to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+okay so I have a for series I'm
+
+ align:start position:0%
+okay so I have a for series I'm
+ 
+
+ align:start position:0%
+okay so I have a for series I'm
+imagining I know the coefficients and I
+
+ align:start position:0%
+imagining I know the coefficients and I
+ 
+
+ align:start position:0%
+imagining I know the coefficients and I
+want to say what happens if I take the
+
+ align:start position:0%
+want to say what happens if I take the
+ 
+
+ align:start position:0%
+want to say what happens if I take the
+derivative well just take the derivative
+
+ align:start position:0%
+derivative well just take the derivative
+ 
+
+ align:start position:0%
+derivative well just take the derivative
+you'll have the sum of the derivative
+
+ align:start position:0%
+you'll have the sum of the derivative
+ 
+
+ align:start position:0%
+you'll have the sum of the derivative
+brings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down a factor ik k
+
+ align:start position:0%
+down a factor ik k
+ 
+
+ align:start position:0%
+down a factor ik k
+so that's the rule simple but important
+
+ align:start position:0%
+so that's the rule simple but important
+ 
+
+ align:start position:0%
+so that's the rule simple but important
+that's why frea series is so great
+
+ align:start position:0%
+that's why frea series is so great
+ 
+
+ align:start position:0%
+that's why frea series is so great
+because it you have orthogonality and
+
+ align:start position:0%
+because it you have orthogonality and
+ 
+
+ align:start position:0%
+because it you have orthogonality and
+then you have this simple rule with
+
+ align:start position:0%
+then you have this simple rule with
+ 
+
+ align:start position:0%
+then you have this simple rule with
+derivatives you just it just brings a
+
+ align:start position:0%
+derivatives you just it just brings a
+ 
+
+ align:start position:0%
+derivatives you just it just brings a
+factor i k so the derivative makes your
+
+ align:start position:0%
+factor i k so the derivative makes your
+ 
+
+ align:start position:0%
+factor i k so the derivative makes your
+function noisier and you have larger uh
+
+ align:start position:0%
+function noisier and you have larger uh
+ 
+
+ align:start position:0%
+function noisier and you have larger uh
+coefficients and if I do F of xus D so
+
+ align:start position:0%
+coefficients and if I do F of xus D so
+ 
+
+ align:start position:0%
+coefficients and if I do F of xus D so
+I'll change X to xus D so I'll see that
+
+ align:start position:0%
+I'll change X to xus D so I'll see that
+ 
+
+ align:start position:0%
+I'll change X to xus D so I'll see that
+sum of CK e to the I KX e to the minus i
+
+ align:start position:0%
+sum of CK e to the I KX e to the minus i
+ 
+
+ align:start position:0%
+sum of CK e to the I KX e to the minus i
+k d right I've I've put in x minus D
+
+ align:start position:0%
+k d right I've I've put in x minus D
+ 
+
+ align:start position:0%
+k d right I've I've put in x minus D
+instead of X and here I see that the 48
+
+ align:start position:0%
+instead of X and here I see that the 48
+ 
+
+ align:start position:0%
+instead of X and here I see that the 48
+coefficient for a shifted
+
+ align:start position:0%
+coefficient for a shifted
+ 
+
+ align:start position:0%
+coefficient for a shifted
+function so this the CK was the 48
+
+ align:start position:0%
+function so this the CK was the 48
+ 
+
+ align:start position:0%
+function so this the CK was the 48
+coefficient for f when I shift f it
+
+ align:start position:0%
+coefficient for f when I shift f it
+ 
+
+ align:start position:0%
+coefficient for f when I shift f it
+multiplies that coefficient by uh a
+
+ align:start position:0%
+multiplies that coefficient by uh a
+ 
+
+ align:start position:0%
+multiplies that coefficient by uh a
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+change the magnitude stayed the same
+
+ align:start position:0%
+change the magnitude stayed the same
+ 
+
+ align:start position:0%
+change the magnitude stayed the same
+because that's a number everybody
+
+ align:start position:0%
+because that's a number everybody
+ 
+
+ align:start position:0%
+because that's a number everybody
+recognizes that as a number of magnitude
+
+ align:start position:0%
+recognizes that as a number of magnitude
+ 
+
+ align:start position:0%
+recognizes that as a number of magnitude
+one and just has a phase shift okay
+
+ align:start position:0%
+one and just has a phase shift okay
+ 
+
+ align:start position:0%
+one and just has a phase shift okay
+those are two good rules that show why
+
+ align:start position:0%
+those are two good rules that show why
+ 
+
+ align:start position:0%
+those are two good rules that show why
+you can use 4A Series in differential
+
+ align:start position:0%
+you can use 4A Series in differential
+ 
+
+ align:start position:0%
+you can use 4A Series in differential
+equations and in difference
+
+ align:start position:0%
+equations and in difference
+ 
+
+ align:start position:0%
+equations and in difference
+equations thank you
\ No newline at end of file
diff --git a/lpnY5QVjU5w.txt b/lpnY5QVjU5w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6451cc978cc4f5438a1f4f3a8e680f7f5f058f4e
--- /dev/null
+++ b/lpnY5QVjU5w.txt
@@ -0,0 +1,1611 @@
+align:start position:0%
+ 
+hi everyone welcome back so today I'd
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+ 
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+like to talk about positive definite
+
+ align:start position:0%
+like to talk about positive definite
+ 
+
+ align:start position:0%
+like to talk about positive definite
+matrices and specifically
+
+ align:start position:0%
+matrices and specifically
+ 
+
+ align:start position:0%
+matrices and specifically
+to analyze some several properties of
+
+ align:start position:0%
+to analyze some several properties of
+ 
+
+ align:start position:0%
+to analyze some several properties of
+positive definite matrices and
+
+ align:start position:0%
+positive definite matrices and
+ 
+
+ align:start position:0%
+positive definite matrices and
+specifically we're going to look at why
+
+ align:start position:0%
+specifically we're going to look at why
+ 
+
+ align:start position:0%
+specifically we're going to look at why
+each one of these following statements
+
+ align:start position:0%
+each one of these following statements
+ 
+
+ align:start position:0%
+each one of these following statements
+is true so first off why every positive
+
+ align:start position:0%
+is true so first off why every positive
+ 
+
+ align:start position:0%
+is true so first off why every positive
+definite matrix is invertible why the
+
+ align:start position:0%
+definite matrix is invertible why the
+ 
+
+ align:start position:0%
+definite matrix is invertible why the
+only positive definite projection matrix
+
+ align:start position:0%
+only positive definite projection matrix
+ 
+
+ align:start position:0%
+only positive definite projection matrix
+is the identity matrix if d is a
+
+ align:start position:0%
+is the identity matrix if d is a
+ 
+
+ align:start position:0%
+is the identity matrix if d is a
+diagonal matrix with positive entries
+
+ align:start position:0%
+diagonal matrix with positive entries
+ 
+
+ align:start position:0%
+diagonal matrix with positive entries
+show that it must also be positive
+
+ align:start position:0%
+show that it must also be positive
+ 
+
+ align:start position:0%
+show that it must also be positive
+definite and then lastly if s is a
+
+ align:start position:0%
+definite and then lastly if s is a
+ 
+
+ align:start position:0%
+definite and then lastly if s is a
+symmetric matrix where the determinant s
+
+ align:start position:0%
+symmetric matrix where the determinant s
+ 
+
+ align:start position:0%
+symmetric matrix where the determinant s
+is bigger than 0 show why this might not
+
+ align:start position:0%
+is bigger than 0 show why this might not
+ 
+
+ align:start position:0%
+is bigger than 0 show why this might not
+necessarily imply that it's positive
+
+ align:start position:0%
+necessarily imply that it's positive
+ 
+
+ align:start position:0%
+necessarily imply that it's positive
+definite so I'll let you think about
+
+ align:start position:0%
+definite so I'll let you think about
+ 
+
+ align:start position:0%
+definite so I'll let you think about
+these for a moment and I'll come back in
+
+ align:start position:0%
+these for a moment and I'll come back in
+ 
+
+ align:start position:0%
+these for a moment and I'll come back in
+a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi everyone welcome back okay so let's
+
+ align:start position:0%
+hi everyone welcome back okay so let's
+ 
+
+ align:start position:0%
+hi everyone welcome back okay so let's
+take a look at Part A so Part A is
+
+ align:start position:0%
+take a look at Part A so Part A is
+ 
+
+ align:start position:0%
+take a look at Part A so Part A is
+asking why every positive definite
+
+ align:start position:0%
+asking why every positive definite
+ 
+
+ align:start position:0%
+asking why every positive definite
+definite matrix is invertible well let's
+
+ align:start position:0%
+definite matrix is invertible well let's
+ 
+
+ align:start position:0%
+definite matrix is invertible well let's
+just recall that if a is a matrix and if
+
+ align:start position:0%
+just recall that if a is a matrix and if
+ 
+
+ align:start position:0%
+just recall that if a is a matrix and if
+a is invertible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this necessarily implies that the
+
+ align:start position:0%
+then this necessarily implies that the
+ 
+
+ align:start position:0%
+then this necessarily implies that the
+determinant of a is nonzero and I'm
+
+ align:start position:0%
+determinant of a is nonzero and I'm
+ 
+
+ align:start position:0%
+determinant of a is nonzero and I'm
+going to just write out dead a as the
+
+ align:start position:0%
+going to just write out dead a as the
+ 
+
+ align:start position:0%
+going to just write out dead a as the
+product of the eigenvalues of a okay so
+
+ align:start position:0%
+product of the eigenvalues of a okay so
+ 
+
+ align:start position:0%
+product of the eigenvalues of a okay so
+lambda 1 to lambda n are the eigen
+
+ align:start position:0%
+lambda 1 to lambda n are the eigen
+ 
+
+ align:start position:0%
+lambda 1 to lambda n are the eigen
+values of a okay in addition if a is
+
+ align:start position:0%
+values of a okay in addition if a is
+ 
+
+ align:start position:0%
+values of a okay in addition if a is
+positive definite what does this say
+
+ align:start position:0%
+positive definite what does this say
+ 
+
+ align:start position:0%
+positive definite what does this say
+about the eigenvalues of a well it says
+
+ align:start position:0%
+about the eigenvalues of a well it says
+ 
+
+ align:start position:0%
+about the eigenvalues of a well it says
+that each eigenvalue of a lambda 1
+
+ align:start position:0%
+that each eigenvalue of a lambda 1
+ 
+
+ align:start position:0%
+that each eigenvalue of a lambda 1
+lambda 2 about that dot to lambda n each
+
+ align:start position:0%
+lambda 2 about that dot to lambda n each
+ 
+
+ align:start position:0%
+lambda 2 about that dot to lambda n each
+one of them must be bigger than 0 so
+
+ align:start position:0%
+one of them must be bigger than 0 so
+ 
+
+ align:start position:0%
+one of them must be bigger than 0 so
+this this statement that each eigenvalue
+
+ align:start position:0%
+this this statement that each eigenvalue
+ 
+
+ align:start position:0%
+this this statement that each eigenvalue
+of a is bigger than 0 is completely
+
+ align:start position:0%
+of a is bigger than 0 is completely
+ 
+
+ align:start position:0%
+of a is bigger than 0 is completely
+equivalent to a being positive definite
+
+ align:start position:0%
+equivalent to a being positive definite
+ 
+
+ align:start position:0%
+equivalent to a being positive definite
+for symmetric matrices a ok so if I have
+
+ align:start position:0%
+for symmetric matrices a ok so if I have
+ 
+
+ align:start position:0%
+for symmetric matrices a ok so if I have
+a whole bunch of eigenvalues and each of
+
+ align:start position:0%
+a whole bunch of eigenvalues and each of
+ 
+
+ align:start position:0%
+a whole bunch of eigenvalues and each of
+them are bigger than 0 what does this
+
+ align:start position:0%
+them are bigger than 0 what does this
+ 
+
+ align:start position:0%
+them are bigger than 0 what does this
+say about dead a well I can take the
+
+ align:start position:0%
+say about dead a well I can take the
+ 
+
+ align:start position:0%
+say about dead a well I can take the
+product of all these eigen values and of
+
+ align:start position:0%
+product of all these eigen values and of
+ 
+
+ align:start position:0%
+product of all these eigen values and of
+course the product of a whole bunch of
+
+ align:start position:0%
+course the product of a whole bunch of
+ 
+
+ align:start position:0%
+course the product of a whole bunch of
+positive numbers must also be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if the quantity is positive then it
+
+ align:start position:0%
+so if the quantity is positive then it
+ 
+
+ align:start position:0%
+so if the quantity is positive then it
+certainly can equal 0 so this proves
+
+ align:start position:0%
+certainly can equal 0 so this proves
+ 
+
+ align:start position:0%
+certainly can equal 0 so this proves
+that dead a is not equal to 0 hence a
+
+ align:start position:0%
+that dead a is not equal to 0 hence a
+ 
+
+ align:start position:0%
+that dead a is not equal to 0 hence a
+must be invertible
+
+ align:start position:0%
+must be invertible
+ 
+
+ align:start position:0%
+must be invertible
+okay so for Part B were asked about to
+
+ align:start position:0%
+okay so for Part B were asked about to
+ 
+
+ align:start position:0%
+okay so for Part B were asked about to
+show that the only positive definite
+
+ align:start position:0%
+show that the only positive definite
+ 
+
+ align:start position:0%
+show that the only positive definite
+projection matrix is the identity matrix
+
+ align:start position:0%
+projection matrix is the identity matrix
+ 
+
+ align:start position:0%
+projection matrix is the identity matrix
+okay so again how do we tackle this
+
+ align:start position:0%
+okay so again how do we tackle this
+ 
+
+ align:start position:0%
+okay so again how do we tackle this
+problem we're going to look at the
+
+ align:start position:0%
+problem we're going to look at the
+ 
+
+ align:start position:0%
+problem we're going to look at the
+eigenvalues so remember if P is a
+
+ align:start position:0%
+eigenvalues so remember if P is a
+ 
+
+ align:start position:0%
+eigenvalues so remember if P is a
+projection what does it say about the
+
+ align:start position:0%
+projection what does it say about the
+ 
+
+ align:start position:0%
+projection what does it say about the
+eigenvalues of p well it says that the
+
+ align:start position:0%
+eigenvalues of p well it says that the
+ 
+
+ align:start position:0%
+eigenvalues of p well it says that the
+eigenvalues of p are either 0 or 1 so
+
+ align:start position:0%
+eigenvalues of p are either 0 or 1 so
+ 
+
+ align:start position:0%
+eigenvalues of p are either 0 or 1 so
+this is 0.1 0.2 if P is a projection
+
+ align:start position:0%
+this is 0.1 0.2 if P is a projection
+ 
+
+ align:start position:0%
+this is 0.1 0.2 if P is a projection
+matrix sorry if P is a positive definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does this say about the eigenvalues
+
+ align:start position:0%
+what does this say about the eigenvalues
+ 
+
+ align:start position:0%
+what does this say about the eigenvalues
+of p well as I've noted before it means
+
+ align:start position:0%
+of p well as I've noted before it means
+ 
+
+ align:start position:0%
+of p well as I've noted before it means
+that the eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are bigger than zero so if P is a
+
+ align:start position:0%
+are bigger than zero so if P is a
+ 
+
+ align:start position:0%
+are bigger than zero so if P is a
+projection and it's positive definite
+
+ align:start position:0%
+projection and it's positive definite
+ 
+
+ align:start position:0%
+projection and it's positive definite
+the only possible eigenvalues that are
+
+ align:start position:0%
+the only possible eigenvalues that are
+ 
+
+ align:start position:0%
+the only possible eigenvalues that are
+both 0 and 1 and bigger than 0 are 1 so
+
+ align:start position:0%
+both 0 and 1 and bigger than 0 are 1 so
+ 
+
+ align:start position:0%
+both 0 and 1 and bigger than 0 are 1 so
+the conclusion is that the eigenvalues
+
+ align:start position:0%
+the conclusion is that the eigenvalues
+ 
+
+ align:start position:0%
+the conclusion is that the eigenvalues
+of p must all equal 1 so which matrix
+
+ align:start position:0%
+of p must all equal 1 so which matrix
+ 
+
+ align:start position:0%
+of p must all equal 1 so which matrix
+has eigenvalues 1 and is also symmetric
+
+ align:start position:0%
+has eigenvalues 1 and is also symmetric
+ 
+
+ align:start position:0%
+has eigenvalues 1 and is also symmetric
+well the only matrix that satisfies this
+
+ align:start position:0%
+well the only matrix that satisfies this
+ 
+
+ align:start position:0%
+well the only matrix that satisfies this
+property is the identity matrix now you
+
+ align:start position:0%
+property is the identity matrix now you
+ 
+
+ align:start position:0%
+property is the identity matrix now you
+might ask how do you actually show that
+
+ align:start position:0%
+might ask how do you actually show that
+ 
+
+ align:start position:0%
+might ask how do you actually show that
+well you could argue as follows if p is
+
+ align:start position:0%
+well you could argue as follows if p is
+ 
+
+ align:start position:0%
+well you could argue as follows if p is
+diagonalizable and every symmetric
+
+ align:start position:0%
+diagonalizable and every symmetric
+ 
+
+ align:start position:0%
+diagonalizable and every symmetric
+matrix is diagonalizable so I'm not I'm
+
+ align:start position:0%
+matrix is diagonalizable so I'm not I'm
+ 
+
+ align:start position:0%
+matrix is diagonalizable so I'm not I'm
+not making this up so if P is
+
+ align:start position:0%
+not making this up so if P is
+ 
+
+ align:start position:0%
+not making this up so if P is
+diagonalizable then you can always write
+
+ align:start position:0%
+diagonalizable then you can always write
+ 
+
+ align:start position:0%
+diagonalizable then you can always write
+P as some matrix u times a diagonal
+
+ align:start position:0%
+P as some matrix u times a diagonal
+ 
+
+ align:start position:0%
+P as some matrix u times a diagonal
+matrix and we know in this case the
+
+ align:start position:0%
+matrix and we know in this case the
+ 
+
+ align:start position:0%
+matrix and we know in this case the
+diagonal matrix has eigenvalues 1 so
+
+ align:start position:0%
+diagonal matrix has eigenvalues 1 so
+ 
+
+ align:start position:0%
+diagonal matrix has eigenvalues 1 so
+it's actually the identity matrix times
+
+ align:start position:0%
+it's actually the identity matrix times
+ 
+
+ align:start position:0%
+it's actually the identity matrix times
+the inverse of the eigenvector matrix
+
+ align:start position:0%
+the inverse of the eigenvector matrix
+ 
+
+ align:start position:0%
+the inverse of the eigenvector matrix
+but of course this is just u times u
+
+ align:start position:0%
+but of course this is just u times u
+ 
+
+ align:start position:0%
+but of course this is just u times u
+inverse which then gives me the identity
+
+ align:start position:0%
+inverse which then gives me the identity
+ 
+
+ align:start position:0%
+inverse which then gives me the identity
+at the end so u times the identity times
+
+ align:start position:0%
+at the end so u times the identity times
+ 
+
+ align:start position:0%
+at the end so u times the identity times
+u inverse this is just u times u inverse
+
+ align:start position:0%
+u inverse this is just u times u inverse
+ 
+
+ align:start position:0%
+u inverse this is just u times u inverse
+and of course u and u inverse collapse
+
+ align:start position:0%
+and of course u and u inverse collapse
+ 
+
+ align:start position:0%
+and of course u and u inverse collapse
+back down to the identity so this shows
+
+ align:start position:0%
+back down to the identity so this shows
+ 
+
+ align:start position:0%
+back down to the identity so this shows
+you that the only matrix that has
+
+ align:start position:0%
+you that the only matrix that has
+ 
+
+ align:start position:0%
+you that the only matrix that has
+eigenvalues of 1 is the identity matrix
+
+ align:start position:0%
+eigenvalues of 1 is the identity matrix
+ 
+
+ align:start position:0%
+eigenvalues of 1 is the identity matrix
+so that's just to cross all the T's and
+
+ align:start position:0%
+so that's just to cross all the T's and
+ 
+
+ align:start position:0%
+so that's just to cross all the T's and
+dot all the i's ok for Part C we're
+
+ align:start position:0%
+dot all the i's ok for Part C we're
+ 
+
+ align:start position:0%
+dot all the i's ok for Part C we're
+given D is a diagonal matrix with
+
+ align:start position:0%
+given D is a diagonal matrix with
+ 
+
+ align:start position:0%
+given D is a diagonal matrix with
+positive entries on the diagonal now we
+
+ align:start position:0%
+positive entries on the diagonal now we
+ 
+
+ align:start position:0%
+positive entries on the diagonal now we
+have to show that it's positive definite
+
+ align:start position:0%
+have to show that it's positive definite
+ 
+
+ align:start position:0%
+have to show that it's positive definite
+ok so let me write D as follows I'll
+
+ align:start position:0%
+ok so let me write D as follows I'll
+ 
+
+ align:start position:0%
+ok so let me write D as follows I'll
+just write it like this I'm going to use
+
+ align:start position:0%
+just write it like this I'm going to use
+ 
+
+ align:start position:0%
+just write it like this I'm going to use
+a compact notation
+
+ align:start position:0%
+a compact notation
+ 
+
+ align:start position:0%
+a compact notation
+which is sometimes seen diagonal D 1 D 2
+
+ align:start position:0%
+which is sometimes seen diagonal D 1 D 2
+ 
+
+ align:start position:0%
+which is sometimes seen diagonal D 1 D 2
+DN
+
+ align:start position:0%
+DN
+ 
+
+ align:start position:0%
+DN
+ok so D is a diagonal matrix whose
+
+ align:start position:0%
+ok so D is a diagonal matrix whose
+ 
+
+ align:start position:0%
+ok so D is a diagonal matrix whose
+elements along the diagonal are D 1 D 2
+
+ align:start position:0%
+elements along the diagonal are D 1 D 2
+ 
+
+ align:start position:0%
+elements along the diagonal are D 1 D 2
+D 2 DN ok now what does it mean for a
+
+ align:start position:0%
+D 2 DN ok now what does it mean for a
+ 
+
+ align:start position:0%
+D 2 DN ok now what does it mean for a
+matrix to be positive definite well it
+
+ align:start position:0%
+matrix to be positive definite well it
+ 
+
+ align:start position:0%
+matrix to be positive definite well it
+means that for any X for any vector X X
+
+ align:start position:0%
+means that for any X for any vector X X
+ 
+
+ align:start position:0%
+means that for any X for any vector X X
+I have to look at the product X
+
+ align:start position:0%
+I have to look at the product X
+ 
+
+ align:start position:0%
+I have to look at the product X
+transpose D X and I have to show that
+
+ align:start position:0%
+transpose D X and I have to show that
+ 
+
+ align:start position:0%
+transpose D X and I have to show that
+it's bigger than 0 and I should I should
+
+ align:start position:0%
+it's bigger than 0 and I should I should
+ 
+
+ align:start position:0%
+it's bigger than 0 and I should I should
+qualify this and say that the vector
+
+ align:start position:0%
+qualify this and say that the vector
+ 
+
+ align:start position:0%
+qualify this and say that the vector
+we're looking at is X not equal to 0 so
+
+ align:start position:0%
+we're looking at is X not equal to 0 so
+ 
+
+ align:start position:0%
+we're looking at is X not equal to 0 so
+we're not looking at the 0 vector but
+
+ align:start position:0%
+we're not looking at the 0 vector but
+ 
+
+ align:start position:0%
+we're not looking at the 0 vector but
+for D to be positive definite we have to
+
+ align:start position:0%
+for D to be positive definite we have to
+ 
+
+ align:start position:0%
+for D to be positive definite we have to
+show that X transpose DX is bigger than
+
+ align:start position:0%
+show that X transpose DX is bigger than
+ 
+
+ align:start position:0%
+show that X transpose DX is bigger than
+0 this is just 1 one way to show that
+
+ align:start position:0%
+0 this is just 1 one way to show that
+ 
+
+ align:start position:0%
+0 this is just 1 one way to show that
+it's positive definite it's not the only
+
+ align:start position:0%
+it's positive definite it's not the only
+ 
+
+ align:start position:0%
+it's positive definite it's not the only
+way so if I write X out using components
+
+ align:start position:0%
+way so if I write X out using components
+ 
+
+ align:start position:0%
+way so if I write X out using components
+X 1 X 2 dot dot dot 2 xn and I'll write
+
+ align:start position:0%
+X 1 X 2 dot dot dot 2 xn and I'll write
+ 
+
+ align:start position:0%
+X 1 X 2 dot dot dot 2 xn and I'll write
+it like this then you can work out the
+
+ align:start position:0%
+it like this then you can work out the
+ 
+
+ align:start position:0%
+it like this then you can work out the
+quantity x transpose DX and we see that
+
+ align:start position:0%
+quantity x transpose DX and we see that
+ 
+
+ align:start position:0%
+quantity x transpose DX and we see that
+we get a sum of squares we get D 1 times
+
+ align:start position:0%
+we get a sum of squares we get D 1 times
+ 
+
+ align:start position:0%
+we get a sum of squares we get D 1 times
+X 1 squared plus D 2 D 2 X 2 squared
+
+ align:start position:0%
+X 1 squared plus D 2 D 2 X 2 squared
+ 
+
+ align:start position:0%
+X 1 squared plus D 2 D 2 X 2 squared
+plus dot dot dot plus D n xn squared now
+
+ align:start position:0%
+plus dot dot dot plus D n xn squared now
+ 
+
+ align:start position:0%
+plus dot dot dot plus D n xn squared now
+by definition each coefficient is
+
+ align:start position:0%
+by definition each coefficient is
+ 
+
+ align:start position:0%
+by definition each coefficient is
+positive a sum of a square is positive
+
+ align:start position:0%
+positive a sum of a square is positive
+ 
+
+ align:start position:0%
+positive a sum of a square is positive
+so I'm sorry a product of a positive
+
+ align:start position:0%
+so I'm sorry a product of a positive
+ 
+
+ align:start position:0%
+so I'm sorry a product of a positive
+number with the square is positive and
+
+ align:start position:0%
+number with the square is positive and
+ 
+
+ align:start position:0%
+number with the square is positive and
+then of course a sum of positive numbers
+
+ align:start position:0%
+then of course a sum of positive numbers
+ 
+
+ align:start position:0%
+then of course a sum of positive numbers
+is going to be positive so this means
+
+ align:start position:0%
+is going to be positive so this means
+ 
+
+ align:start position:0%
+is going to be positive so this means
+the whole thing is positive now there's
+
+ align:start position:0%
+the whole thing is positive now there's
+ 
+
+ align:start position:0%
+the whole thing is positive now there's
+other more efficient ways of getting at
+
+ align:start position:0%
+other more efficient ways of getting at
+ 
+
+ align:start position:0%
+other more efficient ways of getting at
+this using other tricks we know for
+
+ align:start position:0%
+this using other tricks we know for
+ 
+
+ align:start position:0%
+this using other tricks we know for
+example if we're given a diagonal matrix
+
+ align:start position:0%
+example if we're given a diagonal matrix
+ 
+
+ align:start position:0%
+example if we're given a diagonal matrix
+we know its eigenvalues are already d 1
+
+ align:start position:0%
+we know its eigenvalues are already d 1
+ 
+
+ align:start position:0%
+we know its eigenvalues are already d 1
+d 2 2 DN
+
+ align:start position:0%
+d 2 2 DN
+ 
+
+ align:start position:0%
+d 2 2 DN
+and we know that a matrix with positive
+
+ align:start position:0%
+and we know that a matrix with positive
+ 
+
+ align:start position:0%
+and we know that a matrix with positive
+eigenvalues is already positive definite
+
+ align:start position:0%
+eigenvalues is already positive definite
+ 
+
+ align:start position:0%
+eigenvalues is already positive definite
+so but this is this is kind of starting
+
+ align:start position:0%
+so but this is this is kind of starting
+ 
+
+ align:start position:0%
+so but this is this is kind of starting
+from from the base to show that it's
+
+ align:start position:0%
+from from the base to show that it's
+ 
+
+ align:start position:0%
+from from the base to show that it's
+positive definite okay and now lastly
+
+ align:start position:0%
+positive definite okay and now lastly
+ 
+
+ align:start position:0%
+positive definite okay and now lastly
+let's look at Part D so s is a symmetric
+
+ align:start position:0%
+let's look at Part D so s is a symmetric
+ 
+
+ align:start position:0%
+let's look at Part D so s is a symmetric
+matrix with Dead s bigger than 0 show
+
+ align:start position:0%
+matrix with Dead s bigger than 0 show
+ 
+
+ align:start position:0%
+matrix with Dead s bigger than 0 show
+that s might not necessarily be positive
+
+ align:start position:0%
+that s might not necessarily be positive
+ 
+
+ align:start position:0%
+that s might not necessarily be positive
+definite so there's lots of counter
+
+ align:start position:0%
+definite so there's lots of counter
+ 
+
+ align:start position:0%
+definite so there's lots of counter
+examples I only need to construct one so
+
+ align:start position:0%
+examples I only need to construct one so
+ 
+
+ align:start position:0%
+examples I only need to construct one so
+I'm looking at s which is a symmetric
+
+ align:start position:0%
+I'm looking at s which is a symmetric
+ 
+
+ align:start position:0%
+I'm looking at s which is a symmetric
+matrix so I'm just going to throw in
+
+ align:start position:0%
+matrix so I'm just going to throw in
+ 
+
+ align:start position:0%
+matrix so I'm just going to throw in
+some numbers on some off diagonals so
+
+ align:start position:0%
+some numbers on some off diagonals so
+ 
+
+ align:start position:0%
+some numbers on some off diagonals so
+I'll just pick one and now I need to
+
+ align:start position:0%
+I'll just pick one and now I need to
+ 
+
+ align:start position:0%
+I'll just pick one and now I need to
+pick some numbers along the diagonal and
+
+ align:start position:0%
+pick some numbers along the diagonal and
+ 
+
+ align:start position:0%
+pick some numbers along the diagonal and
+the easiest way to do it is to pick two
+
+ align:start position:0%
+the easiest way to do it is to pick two
+ 
+
+ align:start position:0%
+the easiest way to do it is to pick two
+negative numbers on the diagonal because
+
+ align:start position:0%
+negative numbers on the diagonal because
+ 
+
+ align:start position:0%
+negative numbers on the diagonal because
+if if there's a negative number on a
+
+ align:start position:0%
+if if there's a negative number on a
+ 
+
+ align:start position:0%
+if if there's a negative number on a
+diagonal then we know S can't be
+
+ align:start position:0%
+diagonal then we know S can't be
+ 
+
+ align:start position:0%
+diagonal then we know S can't be
+positive definite and I'll say more
+
+ align:start position:0%
+positive definite and I'll say more
+ 
+
+ align:start position:0%
+positive definite and I'll say more
+about that in a second so I can just
+
+ align:start position:0%
+about that in a second so I can just
+ 
+
+ align:start position:0%
+about that in a second so I can just
+pick negative 2 and negative 3 so let's
+
+ align:start position:0%
+pick negative 2 and negative 3 so let's
+ 
+
+ align:start position:0%
+pick negative 2 and negative 3 so let's
+quickly check what Dead s is well it's
+
+ align:start position:0%
+quickly check what Dead s is well it's
+ 
+
+ align:start position:0%
+quickly check what Dead s is well it's
+negative 2 times negative 3 minus 1 so
+
+ align:start position:0%
+negative 2 times negative 3 minus 1 so
+ 
+
+ align:start position:0%
+negative 2 times negative 3 minus 1 so
+this gives me 6 minus 1 which is 5 so by
+
+ align:start position:0%
+this gives me 6 minus 1 which is 5 so by
+ 
+
+ align:start position:0%
+this gives me 6 minus 1 which is 5 so by
+construction Dead s is positive which is
+
+ align:start position:0%
+construction Dead s is positive which is
+ 
+
+ align:start position:0%
+construction Dead s is positive which is
+good and then as I mentioned before if
+
+ align:start position:0%
+good and then as I mentioned before if
+ 
+
+ align:start position:0%
+good and then as I mentioned before if
+there's negative elements along the
+
+ align:start position:0%
+there's negative elements along the
+ 
+
+ align:start position:0%
+there's negative elements along the
+diagonal of a matrix that matrix can't
+
+ align:start position:0%
+diagonal of a matrix that matrix can't
+ 
+
+ align:start position:0%
+diagonal of a matrix that matrix can't
+be positive definite well why is that
+
+ align:start position:0%
+be positive definite well why is that
+ 
+
+ align:start position:0%
+be positive definite well why is that
+well suppose I wanted to take a look at
+
+ align:start position:0%
+well suppose I wanted to take a look at
+ 
+
+ align:start position:0%
+well suppose I wanted to take a look at
+this this upper left component negative
+
+ align:start position:0%
+this this upper left component negative
+ 
+
+ align:start position:0%
+this this upper left component negative
+3 and it's negative how do I show that
+
+ align:start position:0%
+3 and it's negative how do I show that
+ 
+
+ align:start position:0%
+3 and it's negative how do I show that
+that implies S is not positive definite
+
+ align:start position:0%
+that implies S is not positive definite
+ 
+
+ align:start position:0%
+that implies S is not positive definite
+well what I can do is I can look at the
+
+ align:start position:0%
+well what I can do is I can look at the
+ 
+
+ align:start position:0%
+well what I can do is I can look at the
+the product X transpose s X and what I
+
+ align:start position:0%
+the product X transpose s X and what I
+ 
+
+ align:start position:0%
+the product X transpose s X and what I
+do is I look at it I just take one value
+
+ align:start position:0%
+do is I look at it I just take one value
+ 
+
+ align:start position:0%
+do is I look at it I just take one value
+of X so we know that this has to be
+
+ align:start position:0%
+of X so we know that this has to be
+ 
+
+ align:start position:0%
+of X so we know that this has to be
+positive for every value of x so I can
+
+ align:start position:0%
+positive for every value of x so I can
+ 
+
+ align:start position:0%
+positive for every value of x so I can
+pick any value I want so I can take X
+
+ align:start position:0%
+pick any value I want so I can take X
+ 
+
+ align:start position:0%
+pick any value I want so I can take X
+say 1 0
+
+ align:start position:0%
+say 1 0
+ 
+
+ align:start position:0%
+say 1 0
+Transpo's and when I do this we end up
+
+ align:start position:0%
+Transpo's and when I do this we end up
+ 
+
+ align:start position:0%
+Transpo's and when I do this we end up
+getting that X transpose s X is equal to
+
+ align:start position:0%
+getting that X transpose s X is equal to
+ 
+
+ align:start position:0%
+getting that X transpose s X is equal to
+negative three so notice how by taking
+
+ align:start position:0%
+negative three so notice how by taking
+ 
+
+ align:start position:0%
+negative three so notice how by taking
+one in the first entry and zero in the
+
+ align:start position:0%
+one in the first entry and zero in the
+ 
+
+ align:start position:0%
+one in the first entry and zero in the
+second entry that picks out the upper
+
+ align:start position:0%
+second entry that picks out the upper
+ 
+
+ align:start position:0%
+second entry that picks out the upper
+left corner negative three if I were to
+
+ align:start position:0%
+left corner negative three if I were to
+ 
+
+ align:start position:0%
+left corner negative three if I were to
+take 0 here and 1 here it would pick out
+
+ align:start position:0%
+take 0 here and 1 here it would pick out
+ 
+
+ align:start position:0%
+take 0 here and 1 here it would pick out
+the negative 2 entry in s so by picking
+
+ align:start position:0%
+the negative 2 entry in s so by picking
+ 
+
+ align:start position:0%
+the negative 2 entry in s so by picking
+one in entry I of a vector X and then
+
+ align:start position:0%
+one in entry I of a vector X and then
+ 
+
+ align:start position:0%
+one in entry I of a vector X and then
+computing this product X transpose SX I
+
+ align:start position:0%
+computing this product X transpose SX I
+ 
+
+ align:start position:0%
+computing this product X transpose SX I
+pick out the i'f element along the
+
+ align:start position:0%
+pick out the i'f element along the
+ 
+
+ align:start position:0%
+pick out the i'f element along the
+diagonal and since that element is
+
+ align:start position:0%
+diagonal and since that element is
+ 
+
+ align:start position:0%
+diagonal and since that element is
+negative this shows me that along the
+
+ align:start position:0%
+negative this shows me that along the
+ 
+
+ align:start position:0%
+negative this shows me that along the
+direction 1 0 the product X transpose SX
+
+ align:start position:0%
+direction 1 0 the product X transpose SX
+ 
+
+ align:start position:0%
+direction 1 0 the product X transpose SX
+is also negative and hence s can't
+
+ align:start position:0%
+is also negative and hence s can't
+ 
+
+ align:start position:0%
+is also negative and hence s can't
+possibly be positive definite ok so just
+
+ align:start position:0%
+possibly be positive definite ok so just
+ 
+
+ align:start position:0%
+possibly be positive definite ok so just
+to summarize we've taken a look at a
+
+ align:start position:0%
+to summarize we've taken a look at a
+ 
+
+ align:start position:0%
+to summarize we've taken a look at a
+couple matrices and a couple different
+
+ align:start position:0%
+couple matrices and a couple different
+ 
+
+ align:start position:0%
+couple matrices and a couple different
+properties of positive definite matrices
+
+ align:start position:0%
+properties of positive definite matrices
+ 
+
+ align:start position:0%
+properties of positive definite matrices
+and notably we've we've used the
+
+ align:start position:0%
+and notably we've we've used the
+ 
+
+ align:start position:0%
+and notably we've we've used the
+eigenvalues to get a handle of positive
+
+ align:start position:0%
+eigenvalues to get a handle of positive
+ 
+
+ align:start position:0%
+eigenvalues to get a handle of positive
+definite matrices and I hope these
+
+ align:start position:0%
+definite matrices and I hope these
+ 
+
+ align:start position:0%
+definite matrices and I hope these
+provide some useful tricks and I'll see
+
+ align:start position:0%
+provide some useful tricks and I'll see
+ 
+
+ align:start position:0%
+provide some useful tricks and I'll see
+you next time
\ No newline at end of file
diff --git a/mqhO9GT8hD4.txt b/mqhO9GT8hD4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..29996cdc0e6f32306a176221515f41678322f687
--- /dev/null
+++ b/mqhO9GT8hD4.txt
@@ -0,0 +1,10699 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so welcome back everybody to ao3
+
+ align:start position:0%
+okay so welcome back everybody to ao3
+ 
+
+ align:start position:0%
+okay so welcome back everybody to ao3
+so before we start the lecture today we
+
+ align:start position:0%
+so before we start the lecture today we
+ 
+
+ align:start position:0%
+so before we start the lecture today we
+will give you a as usual a short review
+
+ align:start position:0%
+will give you a as usual a short review
+ 
+
+ align:start position:0%
+will give you a as usual a short review
+on what we have learned and and also an
+
+ align:start position:0%
+on what we have learned and and also an
+ 
+
+ align:start position:0%
+on what we have learned and and also an
+introduction about what we are going to
+
+ align:start position:0%
+introduction about what we are going to
+ 
+
+ align:start position:0%
+introduction about what we are going to
+learn today so last lecture we were
+
+ align:start position:0%
+learn today so last lecture we were
+ 
+
+ align:start position:0%
+learn today so last lecture we were
+discussing interesting phenomena which
+
+ align:start position:0%
+discussing interesting phenomena which
+ 
+
+ align:start position:0%
+discussing interesting phenomena which
+is seen film interference pattern as you
+
+ align:start position:0%
+is seen film interference pattern as you
+ 
+
+ align:start position:0%
+is seen film interference pattern as you
+can see from this slide we were
+
+ align:start position:0%
+can see from this slide we were
+ 
+
+ align:start position:0%
+can see from this slide we were
+wondering why the soap bubbles are
+
+ align:start position:0%
+wondering why the soap bubbles are
+ 
+
+ align:start position:0%
+wondering why the soap bubbles are
+colorful and in the end of the class we
+
+ align:start position:0%
+colorful and in the end of the class we
+ 
+
+ align:start position:0%
+colorful and in the end of the class we
+actually recognized that the reason why
+
+ align:start position:0%
+actually recognized that the reason why
+ 
+
+ align:start position:0%
+actually recognized that the reason why
+the soap bubbles are colorful is because
+
+ align:start position:0%
+the soap bubbles are colorful is because
+ 
+
+ align:start position:0%
+the soap bubbles are colorful is because
+of the interference phenomena between
+
+ align:start position:0%
+of the interference phenomena between
+ 
+
+ align:start position:0%
+of the interference phenomena between
+the refracted light on the bubble one
+
+ align:start position:0%
+the refracted light on the bubble one
+ 
+
+ align:start position:0%
+the refracted light on the bubble one
+one pass one pass of past is that the
+
+ align:start position:0%
+one pass one pass of past is that the
+ 
+
+ align:start position:0%
+one pass one pass of past is that the
+light goes into the cat will frankly
+
+ align:start position:0%
+light goes into the cat will frankly
+ 
+
+ align:start position:0%
+light goes into the cat will frankly
+direct different from the surface of the
+
+ align:start position:0%
+direct different from the surface of the
+ 
+
+ align:start position:0%
+direct different from the surface of the
+soft film the other possible optical
+
+ align:start position:0%
+soft film the other possible optical
+ 
+
+ align:start position:0%
+soft film the other possible optical
+pass is to get refracted by the inner
+
+ align:start position:0%
+pass is to get refracted by the inner
+ 
+
+ align:start position:0%
+pass is to get refracted by the inner
+surface of the film
+
+ align:start position:0%
+surface of the film
+ 
+
+ align:start position:0%
+surface of the film
+therefore the interference between these
+
+ align:start position:0%
+therefore the interference between these
+ 
+
+ align:start position:0%
+therefore the interference between these
+two paths actually created a colorful
+
+ align:start position:0%
+two paths actually created a colorful
+ 
+
+ align:start position:0%
+two paths actually created a colorful
+pattern and the under the bubble so we
+
+ align:start position:0%
+pattern and the under the bubble so we
+ 
+
+ align:start position:0%
+pattern and the under the bubble so we
+also learned how about how thick is the
+
+ align:start position:0%
+also learned how about how thick is the
+ 
+
+ align:start position:0%
+also learned how about how thick is the
+soft film and I think just a quick
+
+ align:start position:0%
+soft film and I think just a quick
+ 
+
+ align:start position:0%
+soft film and I think just a quick
+reminder actually we concluded that in
+
+ align:start position:0%
+reminder actually we concluded that in
+ 
+
+ align:start position:0%
+reminder actually we concluded that in
+order to see a colorful pattern the
+
+ align:start position:0%
+order to see a colorful pattern the
+ 
+
+ align:start position:0%
+order to see a colorful pattern the
+sickness of the war or say the film
+
+ align:start position:0%
+sickness of the war or say the film
+ 
+
+ align:start position:0%
+sickness of the war or say the film
+should be something like in the order of
+
+ align:start position:0%
+should be something like in the order of
+ 
+
+ align:start position:0%
+should be something like in the order of
+100 narrow meter so that's actually
+
+ align:start position:0%
+100 narrow meter so that's actually
+ 
+
+ align:start position:0%
+100 narrow meter so that's actually
+pretty remarkable because that's already
+
+ align:start position:0%
+pretty remarkable because that's already
+ 
+
+ align:start position:0%
+pretty remarkable because that's already
+in the order of the size of the virus
+
+ align:start position:0%
+in the order of the size of the virus
+ 
+
+ align:start position:0%
+in the order of the size of the virus
+okay so that's actually really cool so
+
+ align:start position:0%
+okay so that's actually really cool so
+ 
+
+ align:start position:0%
+okay so that's actually really cool so
+what are we going to do today
+
+ align:start position:0%
+what are we going to do today
+ 
+
+ align:start position:0%
+what are we going to do today
+what we are going to do today is to
+
+ align:start position:0%
+what we are going to do today is to
+ 
+
+ align:start position:0%
+what we are going to do today is to
+continue the discussion that all kinds
+
+ align:start position:0%
+continue the discussion that all kinds
+ 
+
+ align:start position:0%
+continue the discussion that all kinds
+of different phenomena which can be
+
+ align:start position:0%
+of different phenomena which can be
+ 
+
+ align:start position:0%
+of different phenomena which can be
+experienced by interference we would
+
+ align:start position:0%
+experienced by interference we would
+ 
+
+ align:start position:0%
+experienced by interference we would
+learn interference phenomena with double
+
+ align:start position:0%
+learn interference phenomena with double
+ 
+
+ align:start position:0%
+learn interference phenomena with double
+the experiment and the using of example
+
+ align:start position:0%
+the experiment and the using of example
+ 
+
+ align:start position:0%
+the experiment and the using of example
+laser or water which I have a water tank
+
+ align:start position:0%
+laser or water which I have a water tank
+ 
+
+ align:start position:0%
+laser or water which I have a water tank
+here which I will show you the
+
+ align:start position:0%
+here which I will show you the
+ 
+
+ align:start position:0%
+here which I will show you the
+interference pattern and also the second
+
+ align:start position:0%
+interference pattern and also the second
+ 
+
+ align:start position:0%
+interference pattern and also the second
+thing we are going to learn today is how
+
+ align:start position:0%
+thing we are going to learn today is how
+ 
+
+ align:start position:0%
+thing we are going to learn today is how
+does faceless phase the radii works okay
+
+ align:start position:0%
+does faceless phase the radii works okay
+ 
+
+ align:start position:0%
+does faceless phase the radii works okay
+so but by the end of the lecture today
+
+ align:start position:0%
+so but by the end of the lecture today
+ 
+
+ align:start position:0%
+so but by the end of the lecture today
+usually I would be able to learn why we
+
+ align:start position:0%
+usually I would be able to learn why we
+ 
+
+ align:start position:0%
+usually I would be able to learn why we
+should construct the radar in that way
+
+ align:start position:0%
+should construct the radar in that way
+ 
+
+ align:start position:0%
+should construct the radar in that way
+and how to issue the focus and the
+
+ align:start position:0%
+and how to issue the focus and the
+ 
+
+ align:start position:0%
+and how to issue the focus and the
+electromagnetic wave to work one
+
+ align:start position:0%
+electromagnetic wave to work one
+ 
+
+ align:start position:0%
+electromagnetic wave to work one
+specific direction so that is what we
+
+ align:start position:0%
+specific direction so that is what we
+ 
+
+ align:start position:0%
+specific direction so that is what we
+are going to learn today the third goal
+
+ align:start position:0%
+are going to learn today the third goal
+ 
+
+ align:start position:0%
+are going to learn today the third goal
+is that we are going to make connection
+
+ align:start position:0%
+is that we are going to make connection
+ 
+
+ align:start position:0%
+is that we are going to make connection
+to quantum mechanics from the lecture
+
+ align:start position:0%
+to quantum mechanics from the lecture
+ 
+
+ align:start position:0%
+to quantum mechanics from the lecture
+today all right
+
+ align:start position:0%
+today all right
+ 
+
+ align:start position:0%
+today all right
+so thus immediately get started so
+
+ align:start position:0%
+so thus immediately get started so
+ 
+
+ align:start position:0%
+so thus immediately get started so
+before we start the discussion of double
+
+ align:start position:0%
+before we start the discussion of double
+ 
+
+ align:start position:0%
+before we start the discussion of double
+slit experiment I would like to remind
+
+ align:start position:0%
+slit experiment I would like to remind
+ 
+
+ align:start position:0%
+slit experiment I would like to remind
+everybody about Huygens principle which
+
+ align:start position:0%
+everybody about Huygens principle which
+ 
+
+ align:start position:0%
+everybody about Huygens principle which
+you may already learned it from a o2 or
+
+ align:start position:0%
+you may already learned it from a o2 or
+ 
+
+ align:start position:0%
+you may already learned it from a o2 or
+in high school days so what is actually
+
+ align:start position:0%
+in high school days so what is actually
+ 
+
+ align:start position:0%
+in high school days so what is actually
+this principle so this principle is
+
+ align:start position:0%
+this principle so this principle is
+ 
+
+ align:start position:0%
+this principle so this principle is
+saying that if I take a look at all the
+
+ align:start position:0%
+saying that if I take a look at all the
+ 
+
+ align:start position:0%
+saying that if I take a look at all the
+points okay in the wave front okay
+
+ align:start position:0%
+points okay in the wave front okay
+ 
+
+ align:start position:0%
+points okay in the wave front okay
+basically you can treat all those points
+
+ align:start position:0%
+basically you can treat all those points
+ 
+
+ align:start position:0%
+basically you can treat all those points
+and the wavefront as a point source and
+
+ align:start position:0%
+and the wavefront as a point source and
+ 
+
+ align:start position:0%
+and the wavefront as a point source and
+this point source is actually a point
+
+ align:start position:0%
+this point source is actually a point
+ 
+
+ align:start position:0%
+this point source is actually a point
+source of superior wave and that it's
+
+ align:start position:0%
+source of superior wave and that it's
+ 
+
+ align:start position:0%
+source of superior wave and that it's
+emitted from all the points and the wave
+
+ align:start position:0%
+emitted from all the points and the wave
+ 
+
+ align:start position:0%
+emitted from all the points and the wave
+front so you can see from this slide
+
+ align:start position:0%
+front so you can see from this slide
+ 
+
+ align:start position:0%
+front so you can see from this slide
+basically if we choose to focus on the
+
+ align:start position:0%
+basically if we choose to focus on the
+ 
+
+ align:start position:0%
+basically if we choose to focus on the
+yellow point on the wave prophet you can
+
+ align:start position:0%
+yellow point on the wave prophet you can
+ 
+
+ align:start position:0%
+yellow point on the wave prophet you can
+see that from each point you can
+
+ align:start position:0%
+see that from each point you can
+ 
+
+ align:start position:0%
+see that from each point you can
+actually treat that as a severe achill
+
+ align:start position:0%
+actually treat that as a severe achill
+ 
+
+ align:start position:0%
+actually treat that as a severe achill
+wave point source and then what you will
+
+ align:start position:0%
+wave point source and then what you will
+ 
+
+ align:start position:0%
+wave point source and then what you will
+actually need to do in order to
+
+ align:start position:0%
+actually need to do in order to
+ 
+
+ align:start position:0%
+actually need to do in order to
+calculate will be the total of electric
+
+ align:start position:0%
+calculate will be the total of electric
+ 
+
+ align:start position:0%
+calculate will be the total of electric
+field for example is to add up all those
+
+ align:start position:0%
+field for example is to add up all those
+ 
+
+ align:start position:0%
+field for example is to add up all those
+contribution from
+
+ align:start position:0%
+contribution from
+ 
+
+ align:start position:0%
+contribution from
+point and then you will be able to
+
+ align:start position:0%
+point and then you will be able to
+ 
+
+ align:start position:0%
+point and then you will be able to
+actually explain the interference
+
+ align:start position:0%
+actually explain the interference
+ 
+
+ align:start position:0%
+actually explain the interference
+pattern which we see in the experiment
+
+ align:start position:0%
+pattern which we see in the experiment
+ 
+
+ align:start position:0%
+pattern which we see in the experiment
+you may wonder where is this Huygens
+
+ align:start position:0%
+you may wonder where is this Huygens
+ 
+
+ align:start position:0%
+you may wonder where is this Huygens
+principle coming from and although we
+
+ align:start position:0%
+principle coming from and although we
+ 
+
+ align:start position:0%
+principle coming from and although we
+are not going to derive that directly in
+
+ align:start position:0%
+are not going to derive that directly in
+ 
+
+ align:start position:0%
+are not going to derive that directly in
+the lecture today but I can actually
+
+ align:start position:0%
+the lecture today but I can actually
+ 
+
+ align:start position:0%
+the lecture today but I can actually
+safely tell you that is actually can be
+
+ align:start position:0%
+safely tell you that is actually can be
+ 
+
+ align:start position:0%
+safely tell you that is actually can be
+derived from Maxwell's equation okay I
+
+ align:start position:0%
+derived from Maxwell's equation okay I
+ 
+
+ align:start position:0%
+derived from Maxwell's equation okay I
+think some document which actually shows
+
+ align:start position:0%
+think some document which actually shows
+ 
+
+ align:start position:0%
+think some document which actually shows
+the proof of that principle on the
+
+ align:start position:0%
+the proof of that principle on the
+ 
+
+ align:start position:0%
+the proof of that principle on the
+website for your reference the other
+
+ align:start position:0%
+website for your reference the other
+ 
+
+ align:start position:0%
+website for your reference the other
+thing which you may or you may not know
+
+ align:start position:0%
+thing which you may or you may not know
+ 
+
+ align:start position:0%
+thing which you may or you may not know
+is that we are really lucky so that we
+
+ align:start position:0%
+is that we are really lucky so that we
+ 
+
+ align:start position:0%
+is that we are really lucky so that we
+can use hi this Huygens principle in our
+
+ align:start position:0%
+can use hi this Huygens principle in our
+ 
+
+ align:start position:0%
+can use hi this Huygens principle in our
+universe why is that because if you do
+
+ align:start position:0%
+universe why is that because if you do
+ 
+
+ align:start position:0%
+universe why is that because if you do
+get the mathematical proof of this
+
+ align:start position:0%
+get the mathematical proof of this
+ 
+
+ align:start position:0%
+get the mathematical proof of this
+principle it is because the number of
+
+ align:start position:0%
+principle it is because the number of
+ 
+
+ align:start position:0%
+principle it is because the number of
+time mentioned number of spatial
+
+ align:start position:0%
+time mentioned number of spatial
+ 
+
+ align:start position:0%
+time mentioned number of spatial
+dimension is odd which is true in our
+
+ align:start position:0%
+dimension is odd which is true in our
+ 
+
+ align:start position:0%
+dimension is odd which is true in our
+universe or in my universe also it's
+
+ align:start position:0%
+universe or in my universe also it's
+ 
+
+ align:start position:0%
+universe or in my universe also it's
+yours okay happen to be us as well such
+
+ align:start position:0%
+yours okay happen to be us as well such
+ 
+
+ align:start position:0%
+yours okay happen to be us as well such
+that the Huygens principle issue works
+
+ align:start position:0%
+that the Huygens principle issue works
+ 
+
+ align:start position:0%
+that the Huygens principle issue works
+on the other hand if the number of
+
+ align:start position:0%
+on the other hand if the number of
+ 
+
+ align:start position:0%
+on the other hand if the number of
+dimension is even there's no Huygens
+
+ align:start position:0%
+dimension is even there's no Huygens
+ 
+
+ align:start position:0%
+dimension is even there's no Huygens
+principle actually so elastic pretty
+
+ align:start position:0%
+principle actually so elastic pretty
+ 
+
+ align:start position:0%
+principle actually so elastic pretty
+interesting and we are really lucky that
+
+ align:start position:0%
+interesting and we are really lucky that
+ 
+
+ align:start position:0%
+interesting and we are really lucky that
+it actually works in your universe but I
+
+ align:start position:0%
+it actually works in your universe but I
+ 
+
+ align:start position:0%
+it actually works in your universe but I
+will not go into detail in three so
+
+ align:start position:0%
+will not go into detail in three so
+ 
+
+ align:start position:0%
+will not go into detail in three so
+let's get started with a concrete
+
+ align:start position:0%
+let's get started with a concrete
+ 
+
+ align:start position:0%
+let's get started with a concrete
+example which we would like to further
+
+ align:start position:0%
+example which we would like to further
+ 
+
+ align:start position:0%
+example which we would like to further
+investigate to understand the
+
+ align:start position:0%
+investigate to understand the
+ 
+
+ align:start position:0%
+investigate to understand the
+interference phenomena and also prepare
+
+ align:start position:0%
+interference phenomena and also prepare
+ 
+
+ align:start position:0%
+interference phenomena and also prepare
+ourselves to the understanding of the
+
+ align:start position:0%
+ourselves to the understanding of the
+ 
+
+ align:start position:0%
+ourselves to the understanding of the
+design of elaborate greata okay for
+
+ align:start position:0%
+design of elaborate greata okay for
+ 
+
+ align:start position:0%
+design of elaborate greata okay for
+example all right so suppose I have
+
+ align:start position:0%
+example all right so suppose I have
+ 
+
+ align:start position:0%
+example all right so suppose I have
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+to set up here which content war where
+
+ align:start position:0%
+to set up here which content war where
+ 
+
+ align:start position:0%
+to set up here which content war where
+on the wall there are two sleet a and
+
+ align:start position:0%
+on the wall there are two sleet a and
+ 
+
+ align:start position:0%
+on the wall there are two sleet a and
+the beach the upper one is a a lower
+
+ align:start position:0%
+the beach the upper one is a a lower
+ 
+
+ align:start position:0%
+the beach the upper one is a a lower
+ones P is designed here and from lapping
+
+ align:start position:0%
+ones P is designed here and from lapping
+ 
+
+ align:start position:0%
+ones P is designed here and from lapping
+side there is an insert that
+
+ align:start position:0%
+side there is an insert that
+ 
+
+ align:start position:0%
+side there is an insert that
+prang wave with wavelength lambda which
+
+ align:start position:0%
+prang wave with wavelength lambda which
+ 
+
+ align:start position:0%
+prang wave with wavelength lambda which
+is shown here it's this brain wave print
+
+ align:start position:0%
+is shown here it's this brain wave print
+ 
+
+ align:start position:0%
+is shown here it's this brain wave print
+electromagnetic wave or can be a water
+
+ align:start position:0%
+electromagnetic wave or can be a water
+ 
+
+ align:start position:0%
+electromagnetic wave or can be a water
+wave etc essentially approaching the the
+
+ align:start position:0%
+wave etc essentially approaching the the
+ 
+
+ align:start position:0%
+wave etc essentially approaching the the
+wall with these two three there and we
+
+ align:start position:0%
+wall with these two three there and we
+ 
+
+ align:start position:0%
+wall with these two three there and we
+were wondering what would be the
+
+ align:start position:0%
+were wondering what would be the
+ 
+
+ align:start position:0%
+were wondering what would be the
+resulting pattern on the screen this
+
+ align:start position:0%
+resulting pattern on the screen this
+ 
+
+ align:start position:0%
+resulting pattern on the screen this
+screen is actually pretty far away from
+
+ align:start position:0%
+screen is actually pretty far away from
+ 
+
+ align:start position:0%
+screen is actually pretty far away from
+the experimental set up the wall on the
+
+ align:start position:0%
+the experimental set up the wall on the
+ 
+
+ align:start position:0%
+the experimental set up the wall on the
+left hand side how far is that the
+
+ align:start position:0%
+left hand side how far is that the
+ 
+
+ align:start position:0%
+left hand side how far is that the
+distance between the the screen which
+
+ align:start position:0%
+distance between the the screen which
+ 
+
+ align:start position:0%
+distance between the the screen which
+shows the the resulting interference
+
+ align:start position:0%
+shows the the resulting interference
+ 
+
+ align:start position:0%
+shows the the resulting interference
+pattern in the wall is actually defined
+
+ align:start position:0%
+pattern in the wall is actually defined
+ 
+
+ align:start position:0%
+pattern in the wall is actually defined
+essentially given here is actually
+
+ align:start position:0%
+essentially given here is actually
+ 
+
+ align:start position:0%
+essentially given here is actually
+called L capital L and the immediate in
+
+ align:start position:0%
+called L capital L and the immediate in
+ 
+
+ align:start position:0%
+called L capital L and the immediate in
+this experimental setup L is actually
+
+ align:start position:0%
+this experimental setup L is actually
+ 
+
+ align:start position:0%
+this experimental setup L is actually
+pretty pretty large and there is much
+
+ align:start position:0%
+pretty pretty large and there is much
+ 
+
+ align:start position:0%
+pretty pretty large and there is much
+much larger than the T where T small T
+
+ align:start position:0%
+much larger than the T where T small T
+ 
+
+ align:start position:0%
+much larger than the T where T small T
+is the distance between the two sweets
+
+ align:start position:0%
+is the distance between the two sweets
+ 
+
+ align:start position:0%
+is the distance between the two sweets
+okay so our job now is to understand
+
+ align:start position:0%
+okay so our job now is to understand
+ 
+
+ align:start position:0%
+okay so our job now is to understand
+what would be and do predict what is
+
+ align:start position:0%
+what would be and do predict what is
+ 
+
+ align:start position:0%
+what would be and do predict what is
+going to be the interference pattern
+
+ align:start position:0%
+going to be the interference pattern
+ 
+
+ align:start position:0%
+going to be the interference pattern
+coming from the electromagnetic wave
+
+ align:start position:0%
+coming from the electromagnetic wave
+ 
+
+ align:start position:0%
+coming from the electromagnetic wave
+which pass through point a and point B
+
+ align:start position:0%
+which pass through point a and point B
+ 
+
+ align:start position:0%
+which pass through point a and point B
+okay and what is going to happen over
+
+ align:start position:0%
+okay and what is going to happen over
+ 
+
+ align:start position:0%
+okay and what is going to happen over
+say well be the result which will
+
+ align:start position:0%
+say well be the result which will
+ 
+
+ align:start position:0%
+say well be the result which will
+observe under on the screen okay so the
+
+ align:start position:0%
+observe under on the screen okay so the
+ 
+
+ align:start position:0%
+observe under on the screen okay so the
+first thing which we can do is that okay
+
+ align:start position:0%
+first thing which we can do is that okay
+ 
+
+ align:start position:0%
+first thing which we can do is that okay
+we can now assign observer which is
+
+ align:start position:0%
+we can now assign observer which is
+ 
+
+ align:start position:0%
+we can now assign observer which is
+called p1 of the point of interest on
+
+ align:start position:0%
+called p1 of the point of interest on
+ 
+
+ align:start position:0%
+called p1 of the point of interest on
+the screen which is located here okay
+
+ align:start position:0%
+the screen which is located here okay
+ 
+
+ align:start position:0%
+the screen which is located here okay
+and we can link or say like annette the
+
+ align:start position:0%
+and we can link or say like annette the
+ 
+
+ align:start position:0%
+and we can link or say like annette the
+point a which is location of the first
+
+ align:start position:0%
+point a which is location of the first
+ 
+
+ align:start position:0%
+point a which is location of the first
+lead and the location of the second
+
+ align:start position:0%
+lead and the location of the second
+ 
+
+ align:start position:0%
+lead and the location of the second
+state which is called P we can link
+
+ align:start position:0%
+state which is called P we can link
+ 
+
+ align:start position:0%
+state which is called P we can link
+those points to get a byline and the
+
+ align:start position:0%
+those points to get a byline and the
+ 
+
+ align:start position:0%
+those points to get a byline and the
+data security noted by AP and the PP
+
+ align:start position:0%
+data security noted by AP and the PP
+ 
+
+ align:start position:0%
+data security noted by AP and the PP
+these two lies since we are talking
+
+ align:start position:0%
+these two lies since we are talking
+ 
+
+ align:start position:0%
+these two lies since we are talking
+about L which is actually very very
+
+ align:start position:0%
+about L which is actually very very
+ 
+
+ align:start position:0%
+about L which is actually very very
+large okay I assume that the distance
+
+ align:start position:0%
+large okay I assume that the distance
+ 
+
+ align:start position:0%
+large okay I assume that the distance
+the land scale of the distance between
+
+ align:start position:0%
+the land scale of the distance between
+ 
+
+ align:start position:0%
+the land scale of the distance between
+the wall and the screen is my
+
+ align:start position:0%
+the wall and the screen is my
+ 
+
+ align:start position:0%
+the wall and the screen is my
+much larger than the land scale of the
+
+ align:start position:0%
+much larger than the land scale of the
+ 
+
+ align:start position:0%
+much larger than the land scale of the
+distance between the two sleet which is
+
+ align:start position:0%
+distance between the two sleet which is
+ 
+
+ align:start position:0%
+distance between the two sleet which is
+D therefore I would I can safely assume
+
+ align:start position:0%
+D therefore I would I can safely assume
+ 
+
+ align:start position:0%
+D therefore I would I can safely assume
+that AP and BP almost parallel to each
+
+ align:start position:0%
+that AP and BP almost parallel to each
+ 
+
+ align:start position:0%
+that AP and BP almost parallel to each
+other right and I can also try to
+
+ align:start position:0%
+other right and I can also try to
+ 
+
+ align:start position:0%
+other right and I can also try to
+express the location of the P point by
+
+ align:start position:0%
+express the location of the P point by
+ 
+
+ align:start position:0%
+express the location of the P point by
+using the angle between P P and the
+
+ align:start position:0%
+using the angle between P P and the
+ 
+
+ align:start position:0%
+using the angle between P P and the
+horizontal direction okay and the
+
+ align:start position:0%
+horizontal direction okay and the
+ 
+
+ align:start position:0%
+horizontal direction okay and the
+horizontal Direction is actually showing
+
+ align:start position:0%
+horizontal Direction is actually showing
+ 
+
+ align:start position:0%
+horizontal Direction is actually showing
+us the dash line here and the angle
+
+ align:start position:0%
+us the dash line here and the angle
+ 
+
+ align:start position:0%
+us the dash line here and the angle
+between P P and the horizontal Direction
+
+ align:start position:0%
+between P P and the horizontal Direction
+ 
+
+ align:start position:0%
+between P P and the horizontal Direction
+is called Sita here okay so since AP and
+
+ align:start position:0%
+is called Sita here okay so since AP and
+ 
+
+ align:start position:0%
+is called Sita here okay so since AP and
+BP are almost parallel to each other
+
+ align:start position:0%
+BP are almost parallel to each other
+ 
+
+ align:start position:0%
+BP are almost parallel to each other
+okay I can now calculate what will be
+
+ align:start position:0%
+okay I can now calculate what will be
+ 
+
+ align:start position:0%
+okay I can now calculate what will be
+the optical path length difference
+
+ align:start position:0%
+the optical path length difference
+ 
+
+ align:start position:0%
+the optical path length difference
+between AP and a PP alright so in order
+
+ align:start position:0%
+between AP and a PP alright so in order
+ 
+
+ align:start position:0%
+between AP and a PP alright so in order
+to actually calculate the phase
+
+ align:start position:0%
+to actually calculate the phase
+ 
+
+ align:start position:0%
+to actually calculate the phase
+difference between the electromagnetic
+
+ align:start position:0%
+difference between the electromagnetic
+ 
+
+ align:start position:0%
+difference between the electromagnetic
+native wave coming from sleep a compare
+
+ align:start position:0%
+native wave coming from sleep a compare
+ 
+
+ align:start position:0%
+native wave coming from sleep a compare
+to sleepy I need to calculate again like
+
+ align:start position:0%
+to sleepy I need to calculate again like
+ 
+
+ align:start position:0%
+to sleepy I need to calculate again like
+what we did last time optical path
+
+ align:start position:0%
+what we did last time optical path
+ 
+
+ align:start position:0%
+what we did last time optical path
+length difference okay in this case I
+
+ align:start position:0%
+length difference okay in this case I
+ 
+
+ align:start position:0%
+length difference okay in this case I
+can call the distance between a and P RA
+
+ align:start position:0%
+can call the distance between a and P RA
+ 
+
+ align:start position:0%
+can call the distance between a and P RA
+and I can also call the distance between
+
+ align:start position:0%
+and I can also call the distance between
+ 
+
+ align:start position:0%
+and I can also call the distance between
+P and the P R R P then the optical path
+
+ align:start position:0%
+P and the P R R P then the optical path
+ 
+
+ align:start position:0%
+P and the P R R P then the optical path
+length difference is called R P minus a
+
+ align:start position:0%
+length difference is called R P minus a
+ 
+
+ align:start position:0%
+length difference is called R P minus a
+and we can actually calculate that
+
+ align:start position:0%
+and we can actually calculate that
+ 
+
+ align:start position:0%
+and we can actually calculate that
+because we have already given you the
+
+ align:start position:0%
+because we have already given you the
+ 
+
+ align:start position:0%
+because we have already given you the
+angle between pp and horizontal
+
+ align:start position:0%
+angle between pp and horizontal
+ 
+
+ align:start position:0%
+angle between pp and horizontal
+direction and the basically we can
+
+ align:start position:0%
+direction and the basically we can
+ 
+
+ align:start position:0%
+direction and the basically we can
+safely conclude that okay the path
+
+ align:start position:0%
+safely conclude that okay the path
+ 
+
+ align:start position:0%
+safely conclude that okay the path
+length difference is actually this line
+
+ align:start position:0%
+length difference is actually this line
+ 
+
+ align:start position:0%
+length difference is actually this line
+here therefore I can easily calculate
+
+ align:start position:0%
+here therefore I can easily calculate
+ 
+
+ align:start position:0%
+here therefore I can easily calculate
+and get the optical path length
+
+ align:start position:0%
+and get the optical path length
+ 
+
+ align:start position:0%
+and get the optical path length
+difference the difference between RP and
+
+ align:start position:0%
+difference the difference between RP and
+ 
+
+ align:start position:0%
+difference the difference between RP and
+i2 p t sine-theta okay once we have that
+
+ align:start position:0%
+i2 p t sine-theta okay once we have that
+ 
+
+ align:start position:0%
+i2 p t sine-theta okay once we have that
+it's actually pretty straightforward to
+
+ align:start position:0%
+it's actually pretty straightforward to
+ 
+
+ align:start position:0%
+it's actually pretty straightforward to
+calculate what will be the phase
+
+ align:start position:0%
+calculate what will be the phase
+ 
+
+ align:start position:0%
+calculate what will be the phase
+difference the phase difference between
+
+ align:start position:0%
+difference the phase difference between
+ 
+
+ align:start position:0%
+difference the phase difference between
+the first between the field front coming
+
+ align:start position:0%
+the first between the field front coming
+ 
+
+ align:start position:0%
+the first between the field front coming
+from ously a which I will call it a year
+
+ align:start position:0%
+from ously a which I will call it a year
+ 
+
+ align:start position:0%
+from ously a which I will call it a year
+and the field coming from the streetlamp
+
+ align:start position:0%
+and the field coming from the streetlamp
+ 
+
+ align:start position:0%
+and the field coming from the streetlamp
+sleepy which I will call here the phase
+
+ align:start position:0%
+sleepy which I will call here the phase
+ 
+
+ align:start position:0%
+sleepy which I will call here the phase
+difference as we actually define a lot
+
+ align:start position:0%
+difference as we actually define a lot
+ 
+
+ align:start position:0%
+difference as we actually define a lot
+of time to be Delta Delta can be
+
+ align:start position:0%
+of time to be Delta Delta can be
+ 
+
+ align:start position:0%
+of time to be Delta Delta can be
+calculated by the optical path length
+
+ align:start position:0%
+calculated by the optical path length
+ 
+
+ align:start position:0%
+calculated by the optical path length
+difference piece I see huh right divided
+
+ align:start position:0%
+difference piece I see huh right divided
+ 
+
+ align:start position:0%
+difference piece I see huh right divided
+by lambda which is actually telling you
+
+ align:start position:0%
+by lambda which is actually telling you
+ 
+
+ align:start position:0%
+by lambda which is actually telling you
+how many period have passed okay when
+
+ align:start position:0%
+how many period have passed okay when
+ 
+
+ align:start position:0%
+how many period have passed okay when
+the the light have to issue the overcome
+
+ align:start position:0%
+the the light have to issue the overcome
+ 
+
+ align:start position:0%
+the the light have to issue the overcome
+this also help to pass through this
+
+ align:start position:0%
+this also help to pass through this
+ 
+
+ align:start position:0%
+this also help to pass through this
+optical path length difference and of
+
+ align:start position:0%
+optical path length difference and of
+ 
+
+ align:start position:0%
+optical path length difference and of
+course these need to be multiplied by 2
+
+ align:start position:0%
+course these need to be multiplied by 2
+ 
+
+ align:start position:0%
+course these need to be multiplied by 2
+pi right in order to change the day to
+
+ align:start position:0%
+pi right in order to change the day to
+ 
+
+ align:start position:0%
+pi right in order to change the day to
+from a number of period to face
+
+ align:start position:0%
+from a number of period to face
+ 
+
+ align:start position:0%
+from a number of period to face
+difference therefore you get a phase
+
+ align:start position:0%
+difference therefore you get a phase
+ 
+
+ align:start position:0%
+difference therefore you get a phase
+difference between a P and a PP to be
+
+ align:start position:0%
+difference between a P and a PP to be
+ 
+
+ align:start position:0%
+difference between a P and a PP to be
+Delta equal to D sine theta divided by
+
+ align:start position:0%
+Delta equal to D sine theta divided by
+ 
+
+ align:start position:0%
+Delta equal to D sine theta divided by
+lambda ties to panel okay so you can see
+
+ align:start position:0%
+lambda ties to panel okay so you can see
+ 
+
+ align:start position:0%
+lambda ties to panel okay so you can see
+that all those calculations are pretty
+
+ align:start position:0%
+that all those calculations are pretty
+ 
+
+ align:start position:0%
+that all those calculations are pretty
+straight for maybe you have already seen
+
+ align:start position:0%
+straight for maybe you have already seen
+ 
+
+ align:start position:0%
+straight for maybe you have already seen
+that before in earlier class but what I
+
+ align:start position:0%
+that before in earlier class but what I
+ 
+
+ align:start position:0%
+that before in earlier class but what I
+want to say is that it essentially
+
+ align:start position:0%
+want to say is that it essentially
+ 
+
+ align:start position:0%
+want to say is that it essentially
+because of Huygens principle such that
+
+ align:start position:0%
+because of Huygens principle such that
+ 
+
+ align:start position:0%
+because of Huygens principle such that
+you can expect something which will show
+
+ align:start position:0%
+you can expect something which will show
+ 
+
+ align:start position:0%
+you can expect something which will show
+up at Point P right if you have you if
+
+ align:start position:0%
+up at Point P right if you have you if
+ 
+
+ align:start position:0%
+up at Point P right if you have you if
+you don't have hidings principle what is
+
+ align:start position:0%
+you don't have hidings principle what is
+ 
+
+ align:start position:0%
+you don't have hidings principle what is
+going to happen what is going to happen
+
+ align:start position:0%
+going to happen what is going to happen
+ 
+
+ align:start position:0%
+going to happen what is going to happen
+is that the light passing through this
+
+ align:start position:0%
+is that the light passing through this
+ 
+
+ align:start position:0%
+is that the light passing through this
+lead will just go straight and they will
+
+ align:start position:0%
+lead will just go straight and they will
+ 
+
+ align:start position:0%
+lead will just go straight and they will
+never overlap each other okay so that's
+
+ align:start position:0%
+never overlap each other okay so that's
+ 
+
+ align:start position:0%
+never overlap each other okay so that's
+actually why because of Huygens
+
+ align:start position:0%
+actually why because of Huygens
+ 
+
+ align:start position:0%
+actually why because of Huygens
+principle all the point source are
+
+ align:start position:0%
+principle all the point source are
+ 
+
+ align:start position:0%
+principle all the point source are
+treated as a all the points on the
+
+ align:start position:0%
+treated as a all the points on the
+ 
+
+ align:start position:0%
+treated as a all the points on the
+wavefront are treated as a point source
+
+ align:start position:0%
+wavefront are treated as a point source
+ 
+
+ align:start position:0%
+wavefront are treated as a point source
+of a spherical wave okay so now the
+
+ align:start position:0%
+of a spherical wave okay so now the
+ 
+
+ align:start position:0%
+of a spherical wave okay so now the
+says you why you can expect that
+
+ align:start position:0%
+says you why you can expect that
+ 
+
+ align:start position:0%
+says you why you can expect that
+something will hit the P point which is
+
+ align:start position:0%
+something will hit the P point which is
+ 
+
+ align:start position:0%
+something will hit the P point which is
+because or in this case we have two
+
+ align:start position:0%
+because or in this case we have two
+ 
+
+ align:start position:0%
+because or in this case we have two
+points two point source and if they are
+
+ align:start position:0%
+points two point source and if they are
+ 
+
+ align:start position:0%
+points two point source and if they are
+emitting Supriya Co waves coming from
+
+ align:start position:0%
+emitting Supriya Co waves coming from
+ 
+
+ align:start position:0%
+emitting Supriya Co waves coming from
+this to a point okay so it is really
+
+ align:start position:0%
+this to a point okay so it is really
+ 
+
+ align:start position:0%
+this to a point okay so it is really
+because of Huygens principle which a
+
+ align:start position:0%
+because of Huygens principle which a
+ 
+
+ align:start position:0%
+because of Huygens principle which a
+price here such that we can see the we
+
+ align:start position:0%
+price here such that we can see the we
+ 
+
+ align:start position:0%
+price here such that we can see the we
+can actually see the observed phenomena
+
+ align:start position:0%
+can actually see the observed phenomena
+ 
+
+ align:start position:0%
+can actually see the observed phenomena
+at the P and now we have managed to
+
+ align:start position:0%
+at the P and now we have managed to
+ 
+
+ align:start position:0%
+at the P and now we have managed to
+calculate the phase difference which is
+
+ align:start position:0%
+calculate the phase difference which is
+ 
+
+ align:start position:0%
+calculate the phase difference which is
+Delta P Delta here so what the next
+
+ align:start position:0%
+Delta P Delta here so what the next
+ 
+
+ align:start position:0%
+Delta P Delta here so what the next
+question is what will be the intensity
+
+ align:start position:0%
+question is what will be the intensity
+ 
+
+ align:start position:0%
+question is what will be the intensity
+since we have already calculated the
+
+ align:start position:0%
+since we have already calculated the
+ 
+
+ align:start position:0%
+since we have already calculated the
+phase difference Delta what would be the
+
+ align:start position:0%
+phase difference Delta what would be the
+ 
+
+ align:start position:0%
+phase difference Delta what would be the
+intensity observed at P so for that we
+
+ align:start position:0%
+intensity observed at P so for that we
+ 
+
+ align:start position:0%
+intensity observed at P so for that we
+have already prepared ourselves from the
+
+ align:start position:0%
+have already prepared ourselves from the
+ 
+
+ align:start position:0%
+have already prepared ourselves from the
+last few lectures so now we can actually
+
+ align:start position:0%
+last few lectures so now we can actually
+ 
+
+ align:start position:0%
+last few lectures so now we can actually
+calculate what will be the total e the
+
+ align:start position:0%
+calculate what will be the total e the
+ 
+
+ align:start position:0%
+calculate what will be the total e the
+total e will be equal to a cos P and
+
+ align:start position:0%
+total e will be equal to a cos P and
+ 
+
+ align:start position:0%
+total e will be equal to a cos P and
+here I'm going to use complex notation
+
+ align:start position:0%
+here I'm going to use complex notation
+ 
+
+ align:start position:0%
+here I'm going to use complex notation
+just for simplicity and basically you
+
+ align:start position:0%
+just for simplicity and basically you
+ 
+
+ align:start position:0%
+just for simplicity and basically you
+can rewrite EA and the EP as 0
+
+ align:start position:0%
+can rewrite EA and the EP as 0
+ 
+
+ align:start position:0%
+can rewrite EA and the EP as 0
+exponential I Omega t minus K times R a
+
+ align:start position:0%
+exponential I Omega t minus K times R a
+ 
+
+ align:start position:0%
+exponential I Omega t minus K times R a
++ e 0 exponential I Omega t minus K P
+
+ align:start position:0%
++ e 0 exponential I Omega t minus K P
+ 
+
+ align:start position:0%
++ e 0 exponential I Omega t minus K P
+the first turn is actually telling you
+
+ align:start position:0%
+the first turn is actually telling you
+ 
+
+ align:start position:0%
+the first turn is actually telling you
+the contribution from the first lead
+
+ align:start position:0%
+the contribution from the first lead
+ 
+
+ align:start position:0%
+the contribution from the first lead
+read as the a and the second term is
+
+ align:start position:0%
+read as the a and the second term is
+ 
+
+ align:start position:0%
+read as the a and the second term is
+actually telling you the contribution
+
+ align:start position:0%
+actually telling you the contribution
+ 
+
+ align:start position:0%
+actually telling you the contribution
+from coming France the in this set up
+
+ align:start position:0%
+from coming France the in this set up
+ 
+
+ align:start position:0%
+from coming France the in this set up
+I'm telling you that I have the pram
+
+ align:start position:0%
+I'm telling you that I have the pram
+ 
+
+ align:start position:0%
+I'm telling you that I have the pram
+wave coming from the lap inside of the
+
+ align:start position:0%
+wave coming from the lap inside of the
+ 
+
+ align:start position:0%
+wave coming from the lap inside of the
+experiment and actually hitting the wall
+
+ align:start position:0%
+experiment and actually hitting the wall
+ 
+
+ align:start position:0%
+experiment and actually hitting the wall
+and you can see that from the drawing
+
+ align:start position:0%
+and you can see that from the drawing
+ 
+
+ align:start position:0%
+and you can see that from the drawing
+actually the wave front is actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually telling you that the the
+
+ align:start position:0%
+actually telling you that the the
+ 
+
+ align:start position:0%
+actually telling you that the the
+direction of the electric field is
+
+ align:start position:0%
+direction of the electric field is
+ 
+
+ align:start position:0%
+direction of the electric field is
+actually in the Z direction in my
+
+ align:start position:0%
+actually in the Z direction in my
+ 
+
+ align:start position:0%
+actually in the Z direction in my
+coordinates it and showing on the port
+
+ align:start position:0%
+coordinates it and showing on the port
+ 
+
+ align:start position:0%
+coordinates it and showing on the port
+so basically the the Z Direction is
+
+ align:start position:0%
+so basically the the Z Direction is
+ 
+
+ align:start position:0%
+so basically the the Z Direction is
+actually pointing you to to you guys and
+
+ align:start position:0%
+actually pointing you to to you guys and
+ 
+
+ align:start position:0%
+actually pointing you to to you guys and
+that means the electric field is
+
+ align:start position:0%
+that means the electric field is
+ 
+
+ align:start position:0%
+that means the electric field is
+actually oscillating in this direction
+
+ align:start position:0%
+actually oscillating in this direction
+ 
+
+ align:start position:0%
+actually oscillating in this direction
+okay so therefore I have to be careful
+
+ align:start position:0%
+okay so therefore I have to be careful
+ 
+
+ align:start position:0%
+okay so therefore I have to be careful
+those are vectors so therefore I need to
+
+ align:start position:0%
+those are vectors so therefore I need to
+ 
+
+ align:start position:0%
+those are vectors so therefore I need to
+give the direction and in this case is
+
+ align:start position:0%
+give the direction and in this case is
+ 
+
+ align:start position:0%
+give the direction and in this case is
+actually the Z direction and also you
+
+ align:start position:0%
+actually the Z direction and also you
+ 
+
+ align:start position:0%
+actually the Z direction and also you
+can see that the amplitude is actually
+
+ align:start position:0%
+can see that the amplitude is actually
+ 
+
+ align:start position:0%
+can see that the amplitude is actually
+denoted by E 0 because both I assuming
+
+ align:start position:0%
+denoted by E 0 because both I assuming
+ 
+
+ align:start position:0%
+denoted by E 0 because both I assuming
+that post sleet have the same final
+
+ align:start position:0%
+that post sleet have the same final
+ 
+
+ align:start position:0%
+that post sleet have the same final
+width for the moment I ignore the wheels
+
+ align:start position:0%
+width for the moment I ignore the wheels
+ 
+
+ align:start position:0%
+width for the moment I ignore the wheels
+of the sleep and also they are coming
+
+ align:start position:0%
+of the sleep and also they are coming
+ 
+
+ align:start position:0%
+of the sleep and also they are coming
+from the same a plane wave they are
+
+ align:start position:0%
+from the same a plane wave they are
+ 
+
+ align:start position:0%
+from the same a plane wave they are
+therefore the amplitude so they don't
+
+ align:start position:0%
+therefore the amplitude so they don't
+ 
+
+ align:start position:0%
+therefore the amplitude so they don't
+eat I eat zero okay so now I have the
+
+ align:start position:0%
+eat I eat zero okay so now I have the
+ 
+
+ align:start position:0%
+eat I eat zero okay so now I have the
+expression here and I can now go ahead
+
+ align:start position:0%
+expression here and I can now go ahead
+ 
+
+ align:start position:0%
+expression here and I can now go ahead
+and simplify this expression and rewrite
+
+ align:start position:0%
+and simplify this expression and rewrite
+ 
+
+ align:start position:0%
+and simplify this expression and rewrite
+that in this form so I can now extract
+
+ align:start position:0%
+that in this form so I can now extract
+ 
+
+ align:start position:0%
+that in this form so I can now extract
+the zero and also I extract the common
+
+ align:start position:0%
+the zero and also I extract the common
+ 
+
+ align:start position:0%
+the zero and also I extract the common
+factors here which is a the exponential
+
+ align:start position:0%
+factors here which is a the exponential
+ 
+
+ align:start position:0%
+factors here which is a the exponential
+I Omega T and also a minus k ra I can
+
+ align:start position:0%
+I Omega T and also a minus k ra I can
+ 
+
+ align:start position:0%
+I Omega T and also a minus k ra I can
+actually factorize some some part of the
+
+ align:start position:0%
+actually factorize some some part of the
+ 
+
+ align:start position:0%
+actually factorize some some part of the
+exponential function out so so the
+
+ align:start position:0%
+exponential function out so so the
+ 
+
+ align:start position:0%
+exponential function out so so the
+choice I made is so I factorize our
+
+ align:start position:0%
+choice I made is so I factorize our
+ 
+
+ align:start position:0%
+choice I made is so I factorize our
+exponential I Omega t minus K times R
+
+ align:start position:0%
+exponential I Omega t minus K times R
+ 
+
+ align:start position:0%
+exponential I Omega t minus K times R
+basically I take this out and I get this
+
+ align:start position:0%
+basically I take this out and I get this
+ 
+
+ align:start position:0%
+basically I take this out and I get this
+turn showing here Omega t minus K a I
+
+ align:start position:0%
+turn showing here Omega t minus K a I
+ 
+
+ align:start position:0%
+turn showing here Omega t minus K a I
+take this out then basically what you
+
+ align:start position:0%
+take this out then basically what you
+ 
+
+ align:start position:0%
+take this out then basically what you
+are going to get inside will be 1 plus
+
+ align:start position:0%
+are going to get inside will be 1 plus
+ 
+
+ align:start position:0%
+are going to get inside will be 1 plus
+exponential minus I Delta actually okay
+
+ align:start position:0%
+exponential minus I Delta actually okay
+ 
+
+ align:start position:0%
+exponential minus I Delta actually okay
+why why is that do that because once you
+
+ align:start position:0%
+why why is that do that because once you
+ 
+
+ align:start position:0%
+why why is that do that because once you
+factorize out or take out exponential I
+
+ align:start position:0%
+factorize out or take out exponential I
+ 
+
+ align:start position:0%
+factorize out or take out exponential I
+Omega t minus K are a basically you are
+
+ align:start position:0%
+Omega t minus K are a basically you are
+ 
+
+ align:start position:0%
+Omega t minus K are a basically you are
+left with something proportional to
+
+ align:start position:0%
+left with something proportional to
+ 
+
+ align:start position:0%
+left with something proportional to
+explanation
+
+ align:start position:0%
+explanation
+ 
+
+ align:start position:0%
+explanation
+i - k RP - are a right and that is it
+
+ align:start position:0%
+i - k RP - are a right and that is it
+ 
+
+ align:start position:0%
+i - k RP - are a right and that is it
+should be the optical path length
+
+ align:start position:0%
+should be the optical path length
+ 
+
+ align:start position:0%
+should be the optical path length
+difference here and also of course you
+
+ align:start position:0%
+difference here and also of course you
+ 
+
+ align:start position:0%
+difference here and also of course you
+can always rewrite lam lambda over 2 pi
+
+ align:start position:0%
+can always rewrite lam lambda over 2 pi
+ 
+
+ align:start position:0%
+can always rewrite lam lambda over 2 pi
+right basically you can actually rewrite
+
+ align:start position:0%
+right basically you can actually rewrite
+ 
+
+ align:start position:0%
+right basically you can actually rewrite
+this to be K times B times C right so
+
+ align:start position:0%
+this to be K times B times C right so
+ 
+
+ align:start position:0%
+this to be K times B times C right so
+therefore you can issue the immediately
+
+ align:start position:0%
+therefore you can issue the immediately
+ 
+
+ align:start position:0%
+therefore you can issue the immediately
+identify that the second turn is to
+
+ align:start position:0%
+identify that the second turn is to
+ 
+
+ align:start position:0%
+identify that the second turn is to
+essentially explanation - I do it okay
+
+ align:start position:0%
+essentially explanation - I do it okay
+ 
+
+ align:start position:0%
+essentially explanation - I do it okay
+any questions here okay because sine
+
+ align:start position:0%
+any questions here okay because sine
+ 
+
+ align:start position:0%
+any questions here okay because sine
+theta a T sine theta is just R P - R a
+
+ align:start position:0%
+theta a T sine theta is just R P - R a
+ 
+
+ align:start position:0%
+theta a T sine theta is just R P - R a
+therefore I can safely replace that by
+
+ align:start position:0%
+therefore I can safely replace that by
+ 
+
+ align:start position:0%
+therefore I can safely replace that by
+Delta here okay all right so it seems
+
+ align:start position:0%
+Delta here okay all right so it seems
+ 
+
+ align:start position:0%
+Delta here okay all right so it seems
+everybody is on the same page I can now
+
+ align:start position:0%
+everybody is on the same page I can now
+ 
+
+ align:start position:0%
+everybody is on the same page I can now
+again factorize out not only the Omega t
+
+ align:start position:0%
+again factorize out not only the Omega t
+ 
+
+ align:start position:0%
+again factorize out not only the Omega t
+minus K a turn but I can actually do a
+
+ align:start position:0%
+minus K a turn but I can actually do a
+ 
+
+ align:start position:0%
+minus K a turn but I can actually do a
+chick to factorize out also exponential
+
+ align:start position:0%
+chick to factorize out also exponential
+ 
+
+ align:start position:0%
+chick to factorize out also exponential
+minus I Delta divided by two out and
+
+ align:start position:0%
+minus I Delta divided by two out and
+ 
+
+ align:start position:0%
+minus I Delta divided by two out and
+basically what I'm going to get X
+
+ align:start position:0%
+basically what I'm going to get X
+ 
+
+ align:start position:0%
+basically what I'm going to get X
+exponential I Delta over two Cox
+
+ align:start position:0%
+exponential I Delta over two Cox
+ 
+
+ align:start position:0%
+exponential I Delta over two Cox
+exponential minus I Delta the reason why
+
+ align:start position:0%
+exponential minus I Delta the reason why
+ 
+
+ align:start position:0%
+exponential minus I Delta the reason why
+I'm doing this is because ha now I have
+
+ align:start position:0%
+I'm doing this is because ha now I have
+ 
+
+ align:start position:0%
+I'm doing this is because ha now I have
+this turn identified and this is a
+
+ align:start position:0%
+this turn identified and this is a
+ 
+
+ align:start position:0%
+this turn identified and this is a
+should be just two times cosine they are
+
+ align:start position:0%
+should be just two times cosine they are
+ 
+
+ align:start position:0%
+should be just two times cosine they are
+type / - alright okay so now I'm really
+
+ align:start position:0%
+type / - alright okay so now I'm really
+ 
+
+ align:start position:0%
+type / - alright okay so now I'm really
+pretty close to the intensity so what
+
+ align:start position:0%
+pretty close to the intensity so what
+ 
+
+ align:start position:0%
+pretty close to the intensity so what
+would be the intensity coming out of
+
+ align:start position:0%
+would be the intensity coming out of
+ 
+
+ align:start position:0%
+would be the intensity coming out of
+this electric field that is actually
+
+ align:start position:0%
+this electric field that is actually
+ 
+
+ align:start position:0%
+this electric field that is actually
+going to be average intensity is as we
+
+ align:start position:0%
+going to be average intensity is as we
+ 
+
+ align:start position:0%
+going to be average intensity is as we
+discussed last time in a lecture the
+
+ align:start position:0%
+discussed last time in a lecture the
+ 
+
+ align:start position:0%
+discussed last time in a lecture the
+average intensity is proportional to
+
+ align:start position:0%
+average intensity is proportional to
+ 
+
+ align:start position:0%
+average intensity is proportional to
+square of e vector right in the complex
+
+ align:start position:0%
+square of e vector right in the complex
+ 
+
+ align:start position:0%
+square of e vector right in the complex
+notation how do we evaluate the absolute
+
+ align:start position:0%
+notation how do we evaluate the absolute
+ 
+
+ align:start position:0%
+notation how do we evaluate the absolute
+value of e vector square in the complex
+
+ align:start position:0%
+value of e vector square in the complex
+ 
+
+ align:start position:0%
+value of e vector square in the complex
+notation basically you get basically
+
+ align:start position:0%
+notation basically you get basically
+ 
+
+ align:start position:0%
+notation basically you get basically
+times you stop right where E is actually
+
+ align:start position:0%
+times you stop right where E is actually
+ 
+
+ align:start position:0%
+times you stop right where E is actually
+the amplitude which is the size of the
+
+ align:start position:0%
+the amplitude which is the size of the
+ 
+
+ align:start position:0%
+the amplitude which is the size of the
+impacter the magnitude of the e vector
+
+ align:start position:0%
+impacter the magnitude of the e vector
+ 
+
+ align:start position:0%
+impacter the magnitude of the e vector
+then basically you will see that this
+
+ align:start position:0%
+then basically you will see that this
+ 
+
+ align:start position:0%
+then basically you will see that this
+will be proportional to cosine squared
+
+ align:start position:0%
+will be proportional to cosine squared
+ 
+
+ align:start position:0%
+will be proportional to cosine squared
+Delta by D by 2 right because you can
+
+ align:start position:0%
+Delta by D by 2 right because you can
+ 
+
+ align:start position:0%
+Delta by D by 2 right because you can
+see that if I calculate E star then all
+
+ align:start position:0%
+see that if I calculate E star then all
+ 
+
+ align:start position:0%
+see that if I calculate E star then all
+the terms related to exponential I
+
+ align:start position:0%
+the terms related to exponential I
+ 
+
+ align:start position:0%
+the terms related to exponential I
+something as eudicot cancel right so
+
+ align:start position:0%
+something as eudicot cancel right so
+ 
+
+ align:start position:0%
+something as eudicot cancel right so
+therefore you can see that huh very very
+
+ align:start position:0%
+therefore you can see that huh very very
+ 
+
+ align:start position:0%
+therefore you can see that huh very very
+quickly we can show that the intensity
+
+ align:start position:0%
+quickly we can show that the intensity
+ 
+
+ align:start position:0%
+quickly we can show that the intensity
+will be proportional to cosine square
+
+ align:start position:0%
+will be proportional to cosine square
+ 
+
+ align:start position:0%
+will be proportional to cosine square
+Delta divided by 2 where Delta is the is
+
+ align:start position:0%
+Delta divided by 2 where Delta is the is
+ 
+
+ align:start position:0%
+Delta divided by 2 where Delta is the is
+the phase difference between the first
+
+ align:start position:0%
+the phase difference between the first
+ 
+
+ align:start position:0%
+the phase difference between the first
+pass and the second pass okay any
+
+ align:start position:0%
+pass and the second pass okay any
+ 
+
+ align:start position:0%
+pass and the second pass okay any
+questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so we can see that the intensity is
+
+ align:start position:0%
+ok so we can see that the intensity is
+ 
+
+ align:start position:0%
+ok so we can see that the intensity is
+actually changing really rapidly and as
+
+ align:start position:0%
+actually changing really rapidly and as
+ 
+
+ align:start position:0%
+actually changing really rapidly and as
+a function of Delta right so when I have
+
+ align:start position:0%
+a function of Delta right so when I have
+ 
+
+ align:start position:0%
+a function of Delta right so when I have
+a situation where Delta is equal to zero
+
+ align:start position:0%
+a situation where Delta is equal to zero
+ 
+
+ align:start position:0%
+a situation where Delta is equal to zero
+okay that's actually post a bit and a
+
+ align:start position:0%
+okay that's actually post a bit and a
+ 
+
+ align:start position:0%
+okay that's actually post a bit and a
+stop here a bit and enjoy what we have
+
+ align:start position:0%
+stop here a bit and enjoy what we have
+ 
+
+ align:start position:0%
+stop here a bit and enjoy what we have
+which we learn from here all right so if
+
+ align:start position:0%
+which we learn from here all right so if
+ 
+
+ align:start position:0%
+which we learn from here all right so if
+you have Delta equal to zero what does
+
+ align:start position:0%
+you have Delta equal to zero what does
+ 
+
+ align:start position:0%
+you have Delta equal to zero what does
+that mean that means there is no phase
+
+ align:start position:0%
+that mean that means there is no phase
+ 
+
+ align:start position:0%
+that mean that means there is no phase
+difference between the first and second
+
+ align:start position:0%
+difference between the first and second
+ 
+
+ align:start position:0%
+difference between the first and second
+electric field therefore when you add
+
+ align:start position:0%
+electric field therefore when you add
+ 
+
+ align:start position:0%
+electric field therefore when you add
+them together just a reminder about the
+
+ align:start position:0%
+them together just a reminder about the
+ 
+
+ align:start position:0%
+them together just a reminder about the
+notation we were using before so if you
+
+ align:start position:0%
+notation we were using before so if you
+ 
+
+ align:start position:0%
+notation we were using before so if you
+draw the vector in the complex plane
+
+ align:start position:0%
+draw the vector in the complex plane
+ 
+
+ align:start position:0%
+draw the vector in the complex plane
+what is what you are actually doing is
+
+ align:start position:0%
+what is what you are actually doing is
+ 
+
+ align:start position:0%
+what is what you are actually doing is
+that you are actually adding the a and
+
+ align:start position:0%
+that you are actually adding the a and
+ 
+
+ align:start position:0%
+that you are actually adding the a and
+the e P together in the most efficient
+
+ align:start position:0%
+the e P together in the most efficient
+ 
+
+ align:start position:0%
+the e P together in the most efficient
+way right because the Delta is equal to
+
+ align:start position:0%
+way right because the Delta is equal to
+ 
+
+ align:start position:0%
+way right because the Delta is equal to
+0 the phase difference is equal to zero
+
+ align:start position:0%
+0 the phase difference is equal to zero
+ 
+
+ align:start position:0%
+0 the phase difference is equal to zero
+therefore you are actually adding them
+
+ align:start position:0%
+therefore you are actually adding them
+ 
+
+ align:start position:0%
+therefore you are actually adding them
+in a straight line ok so that is you
+
+ align:start position:0%
+in a straight line ok so that is you
+ 
+
+ align:start position:0%
+in a straight line ok so that is you
+give you the Maxima intensity because
+
+ align:start position:0%
+give you the Maxima intensity because
+ 
+
+ align:start position:0%
+give you the Maxima intensity because
+when Delta is equal to 0 cosine 0 is 1
+
+ align:start position:0%
+when Delta is equal to 0 cosine 0 is 1
+ 
+
+ align:start position:0%
+when Delta is equal to 0 cosine 0 is 1
+right therefore you have reaching the
+
+ align:start position:0%
+right therefore you have reaching the
+ 
+
+ align:start position:0%
+right therefore you have reaching the
+maxima in the intensity so now I can
+
+ align:start position:0%
+maxima in the intensity so now I can
+ 
+
+ align:start position:0%
+maxima in the intensity so now I can
+always increase my Delta until a number
+
+ align:start position:0%
+always increase my Delta until a number
+ 
+
+ align:start position:0%
+always increase my Delta until a number
+which you say should be PI what is going
+
+ align:start position:0%
+which you say should be PI what is going
+ 
+
+ align:start position:0%
+which you say should be PI what is going
+to happen is that if I still use the
+
+ align:start position:0%
+to happen is that if I still use the
+ 
+
+ align:start position:0%
+to happen is that if I still use the
+notation which I was using for the
+
+ align:start position:0%
+notation which I was using for the
+ 
+
+ align:start position:0%
+notation which I was using for the
+complex brand what it does is that huh
+
+ align:start position:0%
+complex brand what it does is that huh
+ 
+
+ align:start position:0%
+complex brand what it does is that huh
+now I am actually completely canceling
+
+ align:start position:0%
+now I am actually completely canceling
+ 
+
+ align:start position:0%
+now I am actually completely canceling
+the electric field because the phase
+
+ align:start position:0%
+the electric field because the phase
+ 
+
+ align:start position:0%
+the electric field because the phase
+difference now is PI right so therefore
+
+ align:start position:0%
+difference now is PI right so therefore
+ 
+
+ align:start position:0%
+difference now is PI right so therefore
+in the complex friend you are adding the
+
+ align:start position:0%
+in the complex friend you are adding the
+ 
+
+ align:start position:0%
+in the complex friend you are adding the
+two vectors in way such that they
+
+ align:start position:0%
+two vectors in way such that they
+ 
+
+ align:start position:0%
+two vectors in way such that they
+completely cancel each other the
+
+ align:start position:0%
+completely cancel each other the
+ 
+
+ align:start position:0%
+completely cancel each other the
+magnitude of the two vectors are the
+
+ align:start position:0%
+magnitude of the two vectors are the
+ 
+
+ align:start position:0%
+magnitude of the two vectors are the
+same right what's shown here which is a
+
+ align:start position:0%
+same right what's shown here which is a
+ 
+
+ align:start position:0%
+same right what's shown here which is a
+easy therefore what you are going to get
+
+ align:start position:0%
+easy therefore what you are going to get
+ 
+
+ align:start position:0%
+easy therefore what you are going to get
+as you each path is going to be zero
+
+ align:start position:0%
+as you each path is going to be zero
+ 
+
+ align:start position:0%
+as you each path is going to be zero
+because they completely cancel okay you
+
+ align:start position:0%
+because they completely cancel okay you
+ 
+
+ align:start position:0%
+because they completely cancel okay you
+can also see that from this formula with
+
+ align:start position:0%
+can also see that from this formula with
+ 
+
+ align:start position:0%
+can also see that from this formula with
+arrived here when Delta is equal to PI
+
+ align:start position:0%
+arrived here when Delta is equal to PI
+ 
+
+ align:start position:0%
+arrived here when Delta is equal to PI
+then essentially cosine PI over 2 then
+
+ align:start position:0%
+then essentially cosine PI over 2 then
+ 
+
+ align:start position:0%
+then essentially cosine PI over 2 then
+you get intensity equal to zero
+
+ align:start position:0%
+you get intensity equal to zero
+ 
+
+ align:start position:0%
+you get intensity equal to zero
+okay everybody accept this alright now I
+
+ align:start position:0%
+okay everybody accept this alright now I
+ 
+
+ align:start position:0%
+okay everybody accept this alright now I
+can still continue and increase Delta
+
+ align:start position:0%
+can still continue and increase Delta
+ 
+
+ align:start position:0%
+can still continue and increase Delta
+for example until two ties to equal to
+
+ align:start position:0%
+for example until two ties to equal to
+ 
+
+ align:start position:0%
+for example until two ties to equal to
+two pi then you are getting this again
+
+ align:start position:0%
+two pi then you are getting this again
+ 
+
+ align:start position:0%
+two pi then you are getting this again
+basically you have EA and EB again line
+
+ align:start position:0%
+basically you have EA and EB again line
+ 
+
+ align:start position:0%
+basically you have EA and EB again line
+up each other and the difference is that
+
+ align:start position:0%
+up each other and the difference is that
+ 
+
+ align:start position:0%
+up each other and the difference is that
+this be actually rotated maybe such as
+
+ align:start position:0%
+this be actually rotated maybe such as
+ 
+
+ align:start position:0%
+this be actually rotated maybe such as
+360 degree and basically you will see
+
+ align:start position:0%
+360 degree and basically you will see
+ 
+
+ align:start position:0%
+360 degree and basically you will see
+that again the intensity become the
+
+ align:start position:0%
+that again the intensity become the
+ 
+
+ align:start position:0%
+that again the intensity become the
+Maxima again okay so that is actually
+
+ align:start position:0%
+Maxima again okay so that is actually
+ 
+
+ align:start position:0%
+Maxima again okay so that is actually
+how we a can actually understand this
+
+ align:start position:0%
+how we a can actually understand this
+ 
+
+ align:start position:0%
+how we a can actually understand this
+result and of course you can also go
+
+ align:start position:0%
+result and of course you can also go
+ 
+
+ align:start position:0%
+result and of course you can also go
+ahead and the plot or simulate this
+
+ align:start position:0%
+ahead and the plot or simulate this
+ 
+
+ align:start position:0%
+ahead and the plot or simulate this
+result in a computer and really draw the
+
+ align:start position:0%
+result in a computer and really draw the
+ 
+
+ align:start position:0%
+result in a computer and really draw the
+amplitude so really Church or the
+
+ align:start position:0%
+amplitude so really Church or the
+ 
+
+ align:start position:0%
+amplitude so really Church or the
+intensity as a function of angle here or
+
+ align:start position:0%
+intensity as a function of angle here or
+ 
+
+ align:start position:0%
+intensity as a function of angle here or
+say the Delta here as you can see from
+
+ align:start position:0%
+say the Delta here as you can see from
+ 
+
+ align:start position:0%
+say the Delta here as you can see from
+here that
+
+ align:start position:0%
+here that
+ 
+
+ align:start position:0%
+here that
+the intensity essentially reaching the
+
+ align:start position:0%
+the intensity essentially reaching the
+ 
+
+ align:start position:0%
+the intensity essentially reaching the
+maximum in the in the in the center why
+
+ align:start position:0%
+maximum in the in the in the center why
+ 
+
+ align:start position:0%
+maximum in the in the in the center why
+is that in the center okay if I I have a
+
+ align:start position:0%
+is that in the center okay if I I have a
+ 
+
+ align:start position:0%
+is that in the center okay if I I have a
+observer here in the center what is
+
+ align:start position:0%
+observer here in the center what is
+ 
+
+ align:start position:0%
+observer here in the center what is
+going to happen is that the past Lance
+
+ align:start position:0%
+going to happen is that the past Lance
+ 
+
+ align:start position:0%
+going to happen is that the past Lance
+optical path length between a P Prime
+
+ align:start position:0%
+optical path length between a P Prime
+ 
+
+ align:start position:0%
+optical path length between a P Prime
+and the PP prong is going to be the same
+
+ align:start position:0%
+and the PP prong is going to be the same
+ 
+
+ align:start position:0%
+and the PP prong is going to be the same
+by symmetry right because this is
+
+ align:start position:0%
+by symmetry right because this is
+ 
+
+ align:start position:0%
+by symmetry right because this is
+actually in the absolute center
+
+ align:start position:0%
+actually in the absolute center
+ 
+
+ align:start position:0%
+actually in the absolute center
+therefore you will expect that Delta is
+
+ align:start position:0%
+therefore you will expect that Delta is
+ 
+
+ align:start position:0%
+therefore you will expect that Delta is
+actually equal to zero okay so that is
+
+ align:start position:0%
+actually equal to zero okay so that is
+ 
+
+ align:start position:0%
+actually equal to zero okay so that is
+actually why you see the Maxima there
+
+ align:start position:0%
+actually why you see the Maxima there
+ 
+
+ align:start position:0%
+actually why you see the Maxima there
+and if you start to move away from there
+
+ align:start position:0%
+and if you start to move away from there
+ 
+
+ align:start position:0%
+and if you start to move away from there
+you will see that the theta
+
+ align:start position:0%
+you will see that the theta
+ 
+
+ align:start position:0%
+you will see that the theta
+start to increase and at some point you
+
+ align:start position:0%
+start to increase and at some point you
+ 
+
+ align:start position:0%
+start to increase and at some point you
+reach your minima which you can see that
+
+ align:start position:0%
+reach your minima which you can see that
+ 
+
+ align:start position:0%
+reach your minima which you can see that
+on the plot and that is actually because
+
+ align:start position:0%
+on the plot and that is actually because
+ 
+
+ align:start position:0%
+on the plot and that is actually because
+now the due to the increasing optical
+
+ align:start position:0%
+now the due to the increasing optical
+ 
+
+ align:start position:0%
+now the due to the increasing optical
+path length difference in the phase
+
+ align:start position:0%
+path length difference in the phase
+ 
+
+ align:start position:0%
+path length difference in the phase
+difference the two electric field is
+
+ align:start position:0%
+difference the two electric field is
+ 
+
+ align:start position:0%
+difference the two electric field is
+starting to cancel each other which
+
+ align:start position:0%
+starting to cancel each other which
+ 
+
+ align:start position:0%
+starting to cancel each other which
+actually produce the black pattern there
+
+ align:start position:0%
+actually produce the black pattern there
+ 
+
+ align:start position:0%
+actually produce the black pattern there
+and finally after a pass
+
+ align:start position:0%
+and finally after a pass
+ 
+
+ align:start position:0%
+and finally after a pass
+Delta equal to PI okay then stop then
+
+ align:start position:0%
+Delta equal to PI okay then stop then
+ 
+
+ align:start position:0%
+Delta equal to PI okay then stop then
+these two electric fields start to work
+
+ align:start position:0%
+these two electric fields start to work
+ 
+
+ align:start position:0%
+these two electric fields start to work
+together again
+
+ align:start position:0%
+together again
+ 
+
+ align:start position:0%
+together again
+alright they're collaborating again and
+
+ align:start position:0%
+alright they're collaborating again and
+ 
+
+ align:start position:0%
+alright they're collaborating again and
+then you can see that again you would
+
+ align:start position:0%
+then you can see that again you would
+ 
+
+ align:start position:0%
+then you can see that again you would
+get another Maxima afterward okay and
+
+ align:start position:0%
+get another Maxima afterward okay and
+ 
+
+ align:start position:0%
+get another Maxima afterward okay and
+here you can see that is actually my
+
+ align:start position:0%
+here you can see that is actually my
+ 
+
+ align:start position:0%
+here you can see that is actually my
+calculation and of course I can do a
+
+ align:start position:0%
+calculation and of course I can do a
+ 
+
+ align:start position:0%
+calculation and of course I can do a
+demonstration to you to really show that
+
+ align:start position:0%
+demonstration to you to really show that
+ 
+
+ align:start position:0%
+demonstration to you to really show that
+is actually what we are going to see
+
+ align:start position:0%
+is actually what we are going to see
+ 
+
+ align:start position:0%
+is actually what we are going to see
+from based on of experiment
+
+ align:start position:0%
+from based on of experiment
+ 
+
+ align:start position:0%
+from based on of experiment
+demonstration we are going to show here
+
+ align:start position:0%
+demonstration we are going to show here
+ 
+
+ align:start position:0%
+demonstration we are going to show here
+so now I'm going to turn the light off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here I have a device which actually
+
+ align:start position:0%
+and here I have a device which actually
+ 
+
+ align:start position:0%
+and here I have a device which actually
+contain a water tank and I need to
+
+ align:start position:0%
+contain a water tank and I need to
+ 
+
+ align:start position:0%
+contain a water tank and I need to
+actually turn this thing up under under
+
+ align:start position:0%
+actually turn this thing up under under
+ 
+
+ align:start position:0%
+actually turn this thing up under under
+water tank I have to vibrator which is
+
+ align:start position:0%
+water tank I have to vibrator which is
+ 
+
+ align:start position:0%
+water tank I have to vibrator which is
+actually acting as point source so
+
+ align:start position:0%
+actually acting as point source so
+ 
+
+ align:start position:0%
+actually acting as point source so
+basically those are vibrator vibrating
+
+ align:start position:0%
+basically those are vibrator vibrating
+ 
+
+ align:start position:0%
+basically those are vibrator vibrating
+up and down to create waves in this tank
+
+ align:start position:0%
+up and down to create waves in this tank
+ 
+
+ align:start position:0%
+up and down to create waves in this tank
+okay so basically you can see that huh
+
+ align:start position:0%
+okay so basically you can see that huh
+ 
+
+ align:start position:0%
+okay so basically you can see that huh
+really you have two point light source
+
+ align:start position:0%
+really you have two point light source
+ 
+
+ align:start position:0%
+really you have two point light source
+and you can see it's a pretty cool wave
+
+ align:start position:0%
+and you can see it's a pretty cool wave
+ 
+
+ align:start position:0%
+and you can see it's a pretty cool wave
+she says she's really generated and
+
+ align:start position:0%
+she says she's really generated and
+ 
+
+ align:start position:0%
+she says she's really generated and
+actually propagating away from the point
+
+ align:start position:0%
+actually propagating away from the point
+ 
+
+ align:start position:0%
+actually propagating away from the point
+source okay and what I can do now you
+
+ align:start position:0%
+source okay and what I can do now you
+ 
+
+ align:start position:0%
+source okay and what I can do now you
+can see that this picture is really
+
+ align:start position:0%
+can see that this picture is really
+ 
+
+ align:start position:0%
+can see that this picture is really
+demanding right because you can see that
+
+ align:start position:0%
+demanding right because you can see that
+ 
+
+ align:start position:0%
+demanding right because you can see that
+wave front is actually moving as a
+
+ align:start position:0%
+wave front is actually moving as a
+ 
+
+ align:start position:0%
+wave front is actually moving as a
+function of time so what I'm going to do
+
+ align:start position:0%
+function of time so what I'm going to do
+ 
+
+ align:start position:0%
+function of time so what I'm going to do
+is to really change the frequency of the
+
+ align:start position:0%
+is to really change the frequency of the
+ 
+
+ align:start position:0%
+is to really change the frequency of the
+light which is actually shining and this
+
+ align:start position:0%
+light which is actually shining and this
+ 
+
+ align:start position:0%
+light which is actually shining and this
+water so that you can actually see the
+
+ align:start position:0%
+water so that you can actually see the
+ 
+
+ align:start position:0%
+water so that you can actually see the
+fix the pattern here and now I am going
+
+ align:start position:0%
+fix the pattern here and now I am going
+ 
+
+ align:start position:0%
+fix the pattern here and now I am going
+to change the light frequency you can
+
+ align:start position:0%
+to change the light frequency you can
+ 
+
+ align:start position:0%
+to change the light frequency you can
+see now I only shine the the water tank
+
+ align:start position:0%
+see now I only shine the the water tank
+ 
+
+ align:start position:0%
+see now I only shine the the water tank
+at the specific time which match the
+
+ align:start position:0%
+at the specific time which match the
+ 
+
+ align:start position:0%
+at the specific time which match the
+speed of the publication of the water
+
+ align:start position:0%
+speed of the publication of the water
+ 
+
+ align:start position:0%
+speed of the publication of the water
+wave and you can see that I've actually
+
+ align:start position:0%
+wave and you can see that I've actually
+ 
+
+ align:start position:0%
+wave and you can see that I've actually
+managed to freeze the wave front
+
+ align:start position:0%
+managed to freeze the wave front
+ 
+
+ align:start position:0%
+managed to freeze the wave front
+you see okay so you can see now really
+
+ align:start position:0%
+you see okay so you can see now really
+ 
+
+ align:start position:0%
+you see okay so you can see now really
+you can see the coming from the source
+
+ align:start position:0%
+you can see the coming from the source
+ 
+
+ align:start position:0%
+you can see the coming from the source
+they are a circular circular wavefront
+
+ align:start position:0%
+they are a circular circular wavefront
+ 
+
+ align:start position:0%
+they are a circular circular wavefront
+which we actually means mimicking the
+
+ align:start position:0%
+which we actually means mimicking the
+ 
+
+ align:start position:0%
+which we actually means mimicking the
+result from Huygens principle and you
+
+ align:start position:0%
+result from Huygens principle and you
+ 
+
+ align:start position:0%
+result from Huygens principle and you
+can see that they are complicated
+
+ align:start position:0%
+can see that they are complicated
+ 
+
+ align:start position:0%
+can see that they are complicated
+interference pattern forming you can see
+
+ align:start position:0%
+interference pattern forming you can see
+ 
+
+ align:start position:0%
+interference pattern forming you can see
+that at some point they have
+
+ align:start position:0%
+that at some point they have
+ 
+
+ align:start position:0%
+that at some point they have
+constructive interference if you focus
+
+ align:start position:0%
+constructive interference if you focus
+ 
+
+ align:start position:0%
+constructive interference if you focus
+on them the central part you can see
+
+ align:start position:0%
+on them the central part you can see
+ 
+
+ align:start position:0%
+on them the central part you can see
+that the Maxima is as you reach there
+
+ align:start position:0%
+that the Maxima is as you reach there
+ 
+
+ align:start position:0%
+that the Maxima is as you reach there
+and the other hand if you move away a
+
+ align:start position:0%
+and the other hand if you move away a
+ 
+
+ align:start position:0%
+and the other hand if you move away a
+little bit away from the center you can
+
+ align:start position:0%
+little bit away from the center you can
+ 
+
+ align:start position:0%
+little bit away from the center you can
+see that really the intensity
+
+ align:start position:0%
+see that really the intensity
+ 
+
+ align:start position:0%
+see that really the intensity
+drop and at some point you you also see
+
+ align:start position:0%
+drop and at some point you you also see
+ 
+
+ align:start position:0%
+drop and at some point you you also see
+that okay again I am changing the
+
+ align:start position:0%
+that okay again I am changing the
+ 
+
+ align:start position:0%
+that okay again I am changing the
+position such that the phase difference
+
+ align:start position:0%
+position such that the phase difference
+ 
+
+ align:start position:0%
+position such that the phase difference
+between the the contribution from source
+
+ align:start position:0%
+between the the contribution from source
+ 
+
+ align:start position:0%
+between the the contribution from source
+a and the P is actually equal to two pi
+
+ align:start position:0%
+a and the P is actually equal to two pi
+ 
+
+ align:start position:0%
+a and the P is actually equal to two pi
+in that case you will be able to see
+
+ align:start position:0%
+in that case you will be able to see
+ 
+
+ align:start position:0%
+in that case you will be able to see
+that the maximum another maximize they
+
+ align:start position:0%
+that the maximum another maximize they
+ 
+
+ align:start position:0%
+that the maximum another maximize they
+should be creative yeah so now we can
+
+ align:start position:0%
+should be creative yeah so now we can
+ 
+
+ align:start position:0%
+should be creative yeah so now we can
+actually also show you that a lot if
+
+ align:start position:0%
+actually also show you that a lot if
+ 
+
+ align:start position:0%
+actually also show you that a lot if
+that have based on that this moriya's
+
+ align:start position:0%
+that have based on that this moriya's
+ 
+
+ align:start position:0%
+that have based on that this moriya's
+pattern let's actually take a look at
+
+ align:start position:0%
+pattern let's actually take a look at
+ 
+
+ align:start position:0%
+pattern let's actually take a look at
+the pajetta here so if i do get from on
+
+ align:start position:0%
+the pajetta here so if i do get from on
+ 
+
+ align:start position:0%
+the pajetta here so if i do get from on
+the individual individual slide which i
+
+ align:start position:0%
+the individual individual slide which i
+ 
+
+ align:start position:0%
+the individual individual slide which i
+have here okay you can see that those i
+
+ align:start position:0%
+have here okay you can see that those i
+ 
+
+ align:start position:0%
+have here okay you can see that those i
+should be like point light source and
+
+ align:start position:0%
+should be like point light source and
+ 
+
+ align:start position:0%
+should be like point light source and
+creating a circular pattern and now I
+
+ align:start position:0%
+creating a circular pattern and now I
+ 
+
+ align:start position:0%
+creating a circular pattern and now I
+can actually overlap with two patterns
+
+ align:start position:0%
+can actually overlap with two patterns
+ 
+
+ align:start position:0%
+can actually overlap with two patterns
+together and you can see that when I
+
+ align:start position:0%
+together and you can see that when I
+ 
+
+ align:start position:0%
+together and you can see that when I
+have these two the center of the two
+
+ align:start position:0%
+have these two the center of the two
+ 
+
+ align:start position:0%
+have these two the center of the two
+circles pretty close to each other you
+
+ align:start position:0%
+circles pretty close to each other you
+ 
+
+ align:start position:0%
+circles pretty close to each other you
+can see that really you have very small
+
+ align:start position:0%
+can see that really you have very small
+ 
+
+ align:start position:0%
+can see that really you have very small
+D in this case you have very a small
+
+ align:start position:0%
+D in this case you have very a small
+ 
+
+ align:start position:0%
+D in this case you have very a small
+distance between source number one and
+
+ align:start position:0%
+distance between source number one and
+ 
+
+ align:start position:0%
+distance between source number one and
+number two then basically based on our
+
+ align:start position:0%
+number two then basically based on our
+ 
+
+ align:start position:0%
+number two then basically based on our
+expression so you can see that Delta is
+
+ align:start position:0%
+expression so you can see that Delta is
+ 
+
+ align:start position:0%
+expression so you can see that Delta is
+equal to D sine theta divided by lambda
+
+ align:start position:0%
+equal to D sine theta divided by lambda
+ 
+
+ align:start position:0%
+equal to D sine theta divided by lambda
+times two pi right and you can actually
+
+ align:start position:0%
+times two pi right and you can actually
+ 
+
+ align:start position:0%
+times two pi right and you can actually
+calculate sine theta will be equal to
+
+ align:start position:0%
+calculate sine theta will be equal to
+ 
+
+ align:start position:0%
+calculate sine theta will be equal to
+Delta divided by K times D okay when
+
+ align:start position:0%
+Delta divided by K times D okay when
+ 
+
+ align:start position:0%
+Delta divided by K times D okay when
+Delta is equal to 2pi this will is equal
+
+ align:start position:0%
+Delta is equal to 2pi this will is equal
+ 
+
+ align:start position:0%
+Delta is equal to 2pi this will is equal
+to PI sorry
+
+ align:start position:0%
+to PI sorry
+ 
+
+ align:start position:0%
+to PI sorry
+when Delta is equal to PI that is going
+
+ align:start position:0%
+when Delta is equal to PI that is going
+ 
+
+ align:start position:0%
+when Delta is equal to PI that is going
+to give you minimum okay where is
+
+ align:start position:0%
+to give you minimum okay where is
+ 
+
+ align:start position:0%
+to give you minimum okay where is
+actually also showing here the minima is
+
+ align:start position:0%
+actually also showing here the minima is
+ 
+
+ align:start position:0%
+actually also showing here the minima is
+shown as the black pattern here okay you
+
+ align:start position:0%
+shown as the black pattern here okay you
+ 
+
+ align:start position:0%
+shown as the black pattern here okay you
+can see from from here
+
+ align:start position:0%
+can see from from here
+ 
+
+ align:start position:0%
+can see from from here
+so what this session formula is showing
+
+ align:start position:0%
+so what this session formula is showing
+ 
+
+ align:start position:0%
+so what this session formula is showing
+you that when I have tea which is very
+
+ align:start position:0%
+you that when I have tea which is very
+ 
+
+ align:start position:0%
+you that when I have tea which is very
+small what is going to happen is that
+
+ align:start position:0%
+small what is going to happen is that
+ 
+
+ align:start position:0%
+small what is going to happen is that
+I'm going to get sine theta to be very
+
+ align:start position:0%
+I'm going to get sine theta to be very
+ 
+
+ align:start position:0%
+I'm going to get sine theta to be very
+large right when P is very very small
+
+ align:start position:0%
+large right when P is very very small
+ 
+
+ align:start position:0%
+large right when P is very very small
+and that can be showing here when I have
+
+ align:start position:0%
+and that can be showing here when I have
+ 
+
+ align:start position:0%
+and that can be showing here when I have
+P which is the distance between the
+
+ align:start position:0%
+P which is the distance between the
+ 
+
+ align:start position:0%
+P which is the distance between the
+center of the these two point source are
+
+ align:start position:0%
+center of the these two point source are
+ 
+
+ align:start position:0%
+center of the these two point source are
+very small you can see that the place
+
+ align:start position:0%
+very small you can see that the place
+ 
+
+ align:start position:0%
+very small you can see that the place
+you get the minima is really far away
+
+ align:start position:0%
+you get the minima is really far away
+ 
+
+ align:start position:0%
+you get the minima is really far away
+from the center which is a shoe here
+
+ align:start position:0%
+from the center which is a shoe here
+ 
+
+ align:start position:0%
+from the center which is a shoe here
+which is a shoe here okay now what I'm
+
+ align:start position:0%
+which is a shoe here okay now what I'm
+ 
+
+ align:start position:0%
+which is a shoe here okay now what I'm
+going to do is to increase the distance
+
+ align:start position:0%
+going to do is to increase the distance
+ 
+
+ align:start position:0%
+going to do is to increase the distance
+between these two stores according to
+
+ align:start position:0%
+between these two stores according to
+ 
+
+ align:start position:0%
+between these two stores according to
+our petition what is going to happen is
+
+ align:start position:0%
+our petition what is going to happen is
+ 
+
+ align:start position:0%
+our petition what is going to happen is
+that the the central maxima will
+
+ align:start position:0%
+that the the central maxima will
+ 
+
+ align:start position:0%
+that the the central maxima will
+decrease the position where you get a
+
+ align:start position:0%
+decrease the position where you get a
+ 
+
+ align:start position:0%
+decrease the position where you get a
+minima will be moving closer to the
+
+ align:start position:0%
+minima will be moving closer to the
+ 
+
+ align:start position:0%
+minima will be moving closer to the
+center right according to that formula
+
+ align:start position:0%
+center right according to that formula
+ 
+
+ align:start position:0%
+center right according to that formula
+because it's proportional to 100 T and
+
+ align:start position:0%
+because it's proportional to 100 T and
+ 
+
+ align:start position:0%
+because it's proportional to 100 T and
+we can do this really carefully to see
+
+ align:start position:0%
+we can do this really carefully to see
+ 
+
+ align:start position:0%
+we can do this really carefully to see
+if I can success succeed and you can see
+
+ align:start position:0%
+if I can success succeed and you can see
+ 
+
+ align:start position:0%
+if I can success succeed and you can see
+that really when I am moving these two
+
+ align:start position:0%
+that really when I am moving these two
+ 
+
+ align:start position:0%
+that really when I am moving these two
+slides away from each other you can see
+
+ align:start position:0%
+slides away from each other you can see
+ 
+
+ align:start position:0%
+slides away from each other you can see
+that the pattern is changing right and
+
+ align:start position:0%
+that the pattern is changing right and
+ 
+
+ align:start position:0%
+that the pattern is changing right and
+the change center Maxima or say this
+
+ align:start position:0%
+the change center Maxima or say this
+ 
+
+ align:start position:0%
+the change center Maxima or say this
+Gaussian like curve there become
+
+ align:start position:0%
+Gaussian like curve there become
+ 
+
+ align:start position:0%
+Gaussian like curve there become
+narrower and narrower okay so that is
+
+ align:start position:0%
+narrower and narrower okay so that is
+ 
+
+ align:start position:0%
+narrower and narrower okay so that is
+actually what we can actually learn from
+
+ align:start position:0%
+actually what we can actually learn from
+ 
+
+ align:start position:0%
+actually what we can actually learn from
+here and our calculation really works
+
+ align:start position:0%
+here and our calculation really works
+ 
+
+ align:start position:0%
+here and our calculation really works
+very well very good so that we have any
+
+ align:start position:0%
+very well very good so that we have any
+ 
+
+ align:start position:0%
+very well very good so that we have any
+questions regarding the demonstration we
+
+ align:start position:0%
+questions regarding the demonstration we
+ 
+
+ align:start position:0%
+questions regarding the demonstration we
+have here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so all those things seems to be
+
+ align:start position:0%
+okay so all those things seems to be
+ 
+
+ align:start position:0%
+okay so all those things seems to be
+pretty straightforward to you and what
+
+ align:start position:0%
+pretty straightforward to you and what
+ 
+
+ align:start position:0%
+pretty straightforward to you and what
+we we are actually now using a position
+
+ align:start position:0%
+we we are actually now using a position
+ 
+
+ align:start position:0%
+we we are actually now using a position
+where we can issue the discuss how we
+
+ align:start position:0%
+where we can issue the discuss how we
+ 
+
+ align:start position:0%
+where we can issue the discuss how we
+actually can understand the rate at
+
+ align:start position:0%
+actually can understand the rate at
+ 
+
+ align:start position:0%
+actually can understand the rate at
+which is how issue radar works so here
+
+ align:start position:0%
+which is how issue radar works so here
+ 
+
+ align:start position:0%
+which is how issue radar works so here
+is actually how great that worked
+
+ align:start position:0%
+is actually how great that worked
+ 
+
+ align:start position:0%
+is actually how great that worked
+suppose you have some unknown object
+
+ align:start position:0%
+suppose you have some unknown object
+ 
+
+ align:start position:0%
+suppose you have some unknown object
+which is like an airplane okay and you
+
+ align:start position:0%
+which is like an airplane okay and you
+ 
+
+ align:start position:0%
+which is like an airplane okay and you
+were we would like to know where is this
+
+ align:start position:0%
+were we would like to know where is this
+ 
+
+ align:start position:0%
+were we would like to know where is this
+object why you do actually is to shoot
+
+ align:start position:0%
+object why you do actually is to shoot
+ 
+
+ align:start position:0%
+object why you do actually is to shoot
+whyever radio waves toward some
+
+ align:start position:0%
+whyever radio waves toward some
+ 
+
+ align:start position:0%
+whyever radio waves toward some
+direction and see if there are something
+
+ align:start position:0%
+direction and see if there are something
+ 
+
+ align:start position:0%
+direction and see if there are something
+coming back right then you know there's
+
+ align:start position:0%
+coming back right then you know there's
+ 
+
+ align:start position:0%
+coming back right then you know there's
+something on the sky because you can
+
+ align:start position:0%
+something on the sky because you can
+ 
+
+ align:start position:0%
+something on the sky because you can
+detect the refracted wave right so so we
+
+ align:start position:0%
+detect the refracted wave right so so we
+ 
+
+ align:start position:0%
+detect the refracted wave right so so we
+shoot this airplane and the something is
+
+ align:start position:0%
+shoot this airplane and the something is
+ 
+
+ align:start position:0%
+shoot this airplane and the something is
+going to come back and now you can say
+
+ align:start position:0%
+going to come back and now you can say
+ 
+
+ align:start position:0%
+going to come back and now you can say
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Atlanta Russia I have something coming
+
+ align:start position:0%
+Atlanta Russia I have something coming
+ 
+
+ align:start position:0%
+Atlanta Russia I have something coming
+back that means there's something there
+
+ align:start position:0%
+back that means there's something there
+ 
+
+ align:start position:0%
+back that means there's something there
+and I can also measure the time it takes
+
+ align:start position:0%
+and I can also measure the time it takes
+ 
+
+ align:start position:0%
+and I can also measure the time it takes
+Werfel for the wave to come back then I
+
+ align:start position:0%
+Werfel for the wave to come back then I
+ 
+
+ align:start position:0%
+Werfel for the wave to come back then I
+know where I should be that object right
+
+ align:start position:0%
+know where I should be that object right
+ 
+
+ align:start position:0%
+know where I should be that object right
+so that's actually pretty
+
+ align:start position:0%
+so that's actually pretty
+ 
+
+ align:start position:0%
+so that's actually pretty
+straightforward thing to do however
+
+ align:start position:0%
+straightforward thing to do however
+ 
+
+ align:start position:0%
+straightforward thing to do however
+there's one difficulty so this is
+
+ align:start position:0%
+there's one difficulty so this is
+ 
+
+ align:start position:0%
+there's one difficulty so this is
+actually the radiation pattern of
+
+ align:start position:0%
+actually the radiation pattern of
+ 
+
+ align:start position:0%
+actually the radiation pattern of
+oscillating dipole which we actually
+
+ align:start position:0%
+oscillating dipole which we actually
+ 
+
+ align:start position:0%
+oscillating dipole which we actually
+learned before so the problem is that
+
+ align:start position:0%
+learned before so the problem is that
+ 
+
+ align:start position:0%
+learned before so the problem is that
+okay what we really need is
+
+ align:start position:0%
+okay what we really need is
+ 
+
+ align:start position:0%
+okay what we really need is
+electromagnetic wave which we should be
+
+ align:start position:0%
+electromagnetic wave which we should be
+ 
+
+ align:start position:0%
+electromagnetic wave which we should be
+very very narrow in angle and the
+
+ align:start position:0%
+very very narrow in angle and the
+ 
+
+ align:start position:0%
+very very narrow in angle and the
+pointing to some specific direction and
+
+ align:start position:0%
+pointing to some specific direction and
+ 
+
+ align:start position:0%
+pointing to some specific direction and
+then I would like to see if I can get
+
+ align:start position:0%
+then I would like to see if I can get
+ 
+
+ align:start position:0%
+then I would like to see if I can get
+some refracted wave coming from that
+
+ align:start position:0%
+some refracted wave coming from that
+ 
+
+ align:start position:0%
+some refracted wave coming from that
+direction okay the problem is that look
+
+ align:start position:0%
+direction okay the problem is that look
+ 
+
+ align:start position:0%
+direction okay the problem is that look
+if I actually some charge up and down
+
+ align:start position:0%
+if I actually some charge up and down
+ 
+
+ align:start position:0%
+if I actually some charge up and down
+the radiation I'm getting is really
+
+ align:start position:0%
+the radiation I'm getting is really
+ 
+
+ align:start position:0%
+the radiation I'm getting is really
+really broad right so it's going to work
+
+ align:start position:0%
+really broad right so it's going to work
+ 
+
+ align:start position:0%
+really broad right so it's going to work
+all kinds of different direction so if
+
+ align:start position:0%
+all kinds of different direction so if
+ 
+
+ align:start position:0%
+all kinds of different direction so if
+you use this to tip at things you are
+
+ align:start position:0%
+you use this to tip at things you are
+ 
+
+ align:start position:0%
+you use this to tip at things you are
+you are always going to get something
+
+ align:start position:0%
+you are always going to get something
+ 
+
+ align:start position:0%
+you are always going to get something
+coming back because
+
+ align:start position:0%
+coming back because
+ 
+
+ align:start position:0%
+coming back because
+essentially shooting the electromagnetic
+
+ align:start position:0%
+essentially shooting the electromagnetic
+ 
+
+ align:start position:0%
+essentially shooting the electromagnetic
+wave it into parent interaction and you
+
+ align:start position:0%
+wave it into parent interaction and you
+ 
+
+ align:start position:0%
+wave it into parent interaction and you
+are not sure anymore where they should
+
+ align:start position:0%
+are not sure anymore where they should
+ 
+
+ align:start position:0%
+are not sure anymore where they should
+be this option you are trying to detail
+
+ align:start position:0%
+be this option you are trying to detail
+ 
+
+ align:start position:0%
+be this option you are trying to detail
+okay so that's a that's actually
+
+ align:start position:0%
+okay so that's a that's actually
+ 
+
+ align:start position:0%
+okay so that's a that's actually
+apparently a problem and what we can
+
+ align:start position:0%
+apparently a problem and what we can
+ 
+
+ align:start position:0%
+apparently a problem and what we can
+actually do is to make use of the
+
+ align:start position:0%
+actually do is to make use of the
+ 
+
+ align:start position:0%
+actually do is to make use of the
+interference phenomena which we can
+
+ align:start position:0%
+interference phenomena which we can
+ 
+
+ align:start position:0%
+interference phenomena which we can
+learn from here to actually try to make
+
+ align:start position:0%
+learn from here to actually try to make
+ 
+
+ align:start position:0%
+learn from here to actually try to make
+sure that the electromagnetic wave is as
+
+ align:start position:0%
+sure that the electromagnetic wave is as
+ 
+
+ align:start position:0%
+sure that the electromagnetic wave is as
+you're pointing to some specific
+
+ align:start position:0%
+you're pointing to some specific
+ 
+
+ align:start position:0%
+you're pointing to some specific
+direction we want we want so that's a
+
+ align:start position:0%
+direction we want we want so that's a
+ 
+
+ align:start position:0%
+direction we want we want so that's a
+should be go ahead and consider a three
+
+ align:start position:0%
+should be go ahead and consider a three
+ 
+
+ align:start position:0%
+should be go ahead and consider a three
+sleep experiment I have this set up I
+
+ align:start position:0%
+sleep experiment I have this set up I
+ 
+
+ align:start position:0%
+sleep experiment I have this set up I
+changed originally I have two slits and
+
+ align:start position:0%
+changed originally I have two slits and
+ 
+
+ align:start position:0%
+changed originally I have two slits and
+now I am shooting three holes under on
+
+ align:start position:0%
+now I am shooting three holes under on
+ 
+
+ align:start position:0%
+now I am shooting three holes under on
+the wall and again I have the distance
+
+ align:start position:0%
+the wall and again I have the distance
+ 
+
+ align:start position:0%
+the wall and again I have the distance
+between the slits to be D and I code
+
+ align:start position:0%
+between the slits to be D and I code
+ 
+
+ align:start position:0%
+between the slits to be D and I code
+this three number one two and three and
+
+ align:start position:0%
+this three number one two and three and
+ 
+
+ align:start position:0%
+this three number one two and three and
+we were wondering what would be the
+
+ align:start position:0%
+we were wondering what would be the
+ 
+
+ align:start position:0%
+we were wondering what would be the
+interference pattern at the on the
+
+ align:start position:0%
+interference pattern at the on the
+ 
+
+ align:start position:0%
+interference pattern at the on the
+screen which is a should be far away
+
+ align:start position:0%
+screen which is a should be far away
+ 
+
+ align:start position:0%
+screen which is a should be far away
+from the from the wall at the distance
+
+ align:start position:0%
+from the from the wall at the distance
+ 
+
+ align:start position:0%
+from the from the wall at the distance
+of L and I'm interested in the intensity
+
+ align:start position:0%
+of L and I'm interested in the intensity
+ 
+
+ align:start position:0%
+of L and I'm interested in the intensity
+at Point P on the screen okay so what I
+
+ align:start position:0%
+at Point P on the screen okay so what I
+ 
+
+ align:start position:0%
+at Point P on the screen okay so what I
+am going to do is to basically repeat
+
+ align:start position:0%
+am going to do is to basically repeat
+ 
+
+ align:start position:0%
+am going to do is to basically repeat
+what we have done in the previous
+
+ align:start position:0%
+what we have done in the previous
+ 
+
+ align:start position:0%
+what we have done in the previous
+example I'm trying to connect one to the
+
+ align:start position:0%
+example I'm trying to connect one to the
+ 
+
+ align:start position:0%
+example I'm trying to connect one to the
+P to P and the 3p basically connect us
+
+ align:start position:0%
+P to P and the 3p basically connect us
+ 
+
+ align:start position:0%
+P to P and the 3p basically connect us
+to lead to the point of interest and on
+
+ align:start position:0%
+to lead to the point of interest and on
+ 
+
+ align:start position:0%
+to lead to the point of interest and on
+the screen and I can actually also if
+
+ align:start position:0%
+the screen and I can actually also if
+ 
+
+ align:start position:0%
+the screen and I can actually also if
+you know this angle this one P to the
+
+ align:start position:0%
+you know this angle this one P to the
+ 
+
+ align:start position:0%
+you know this angle this one P to the
+whole rental direction this angle is
+
+ align:start position:0%
+whole rental direction this angle is
+ 
+
+ align:start position:0%
+whole rental direction this angle is
+called theta my notation then here D I
+
+ align:start position:0%
+called theta my notation then here D I
+ 
+
+ align:start position:0%
+called theta my notation then here D I
+can go ahead and calculate what will be
+
+ align:start position:0%
+can go ahead and calculate what will be
+ 
+
+ align:start position:0%
+can go ahead and calculate what will be
+the optical path length difference
+
+ align:start position:0%
+the optical path length difference
+ 
+
+ align:start position:0%
+the optical path length difference
+between the the light coming from three
+
+ align:start position:0%
+between the the light coming from three
+ 
+
+ align:start position:0%
+between the the light coming from three
+number one seed number two and the C
+
+ align:start position:0%
+number one seed number two and the C
+ 
+
+ align:start position:0%
+number one seed number two and the C
+Lamberth street okay
+
+ align:start position:0%
+Lamberth street okay
+ 
+
+ align:start position:0%
+Lamberth street okay
+in this case okay
+
+ align:start position:0%
+in this case okay
+ 
+
+ align:start position:0%
+in this case okay
+what I'm interested is Delta 1 2 and
+
+ align:start position:0%
+what I'm interested is Delta 1 2 and
+ 
+
+ align:start position:0%
+what I'm interested is Delta 1 2 and
+Delta 1 right since the screen is really
+
+ align:start position:0%
+Delta 1 right since the screen is really
+ 
+
+ align:start position:0%
+Delta 1 right since the screen is really
+far away from the wall
+
+ align:start position:0%
+far away from the wall
+ 
+
+ align:start position:0%
+far away from the wall
+therefore I can actually safely assume
+
+ align:start position:0%
+therefore I can actually safely assume
+ 
+
+ align:start position:0%
+therefore I can actually safely assume
+that this 2 angle is 2 P is actually
+
+ align:start position:0%
+that this 2 angle is 2 P is actually
+ 
+
+ align:start position:0%
+that this 2 angle is 2 P is actually
+Sita because the three lines due to the
+
+ align:start position:0%
+Sita because the three lines due to the
+ 
+
+ align:start position:0%
+Sita because the three lines due to the
+large distance this arrow says she
+
+ align:start position:0%
+large distance this arrow says she
+ 
+
+ align:start position:0%
+large distance this arrow says she
+really really large therefore they are
+
+ align:start position:0%
+really really large therefore they are
+ 
+
+ align:start position:0%
+really really large therefore they are
+actually almost parallel to each other
+
+ align:start position:0%
+actually almost parallel to each other
+ 
+
+ align:start position:0%
+actually almost parallel to each other
+okay so what is going to happen is that
+
+ align:start position:0%
+okay so what is going to happen is that
+ 
+
+ align:start position:0%
+okay so what is going to happen is that
+theta 1 2 which is the phase difference
+
+ align:start position:0%
+theta 1 2 which is the phase difference
+ 
+
+ align:start position:0%
+theta 1 2 which is the phase difference
+between light from the first 3-year
+
+ align:start position:0%
+between light from the first 3-year
+ 
+
+ align:start position:0%
+between light from the first 3-year
+second sleep this egg is going to be
+
+ align:start position:0%
+second sleep this egg is going to be
+ 
+
+ align:start position:0%
+second sleep this egg is going to be
+equal to Delta 1 3 which is the phase
+
+ align:start position:0%
+equal to Delta 1 3 which is the phase
+ 
+
+ align:start position:0%
+equal to Delta 1 3 which is the phase
+difference so a 2 3
+
+ align:start position:0%
+difference so a 2 3
+ 
+
+ align:start position:0%
+difference so a 2 3
+okay it's going to be equal to the phase
+
+ align:start position:0%
+okay it's going to be equal to the phase
+ 
+
+ align:start position:0%
+okay it's going to be equal to the phase
+difference between the seconds 3 and the
+
+ align:start position:0%
+difference between the seconds 3 and the
+ 
+
+ align:start position:0%
+difference between the seconds 3 and the
+light from seconds the answers lead and
+
+ align:start position:0%
+light from seconds the answers lead and
+ 
+
+ align:start position:0%
+light from seconds the answers lead and
+what is the shaitaan' number this number
+
+ align:start position:0%
+what is the shaitaan' number this number
+ 
+
+ align:start position:0%
+what is the shaitaan' number this number
+is going to be equal to t science iike
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's exactly the let's stand as the what
+
+ align:start position:0%
+it's exactly the let's stand as the what
+ 
+
+ align:start position:0%
+it's exactly the let's stand as the what
+we as we get from the first example okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore what is going to happen is
+
+ align:start position:0%
+therefore what is going to happen is
+ 
+
+ align:start position:0%
+therefore what is going to happen is
+that no matter what city I choose ok the
+
+ align:start position:0%
+that no matter what city I choose ok the
+ 
+
+ align:start position:0%
+that no matter what city I choose ok the
+phase difference between nearby sleet is
+
+ align:start position:0%
+phase difference between nearby sleet is
+ 
+
+ align:start position:0%
+phase difference between nearby sleet is
+actually a constant which is actually
+
+ align:start position:0%
+actually a constant which is actually
+ 
+
+ align:start position:0%
+actually a constant which is actually
+this one and I call this phase
+
+ align:start position:0%
+this one and I call this phase
+ 
+
+ align:start position:0%
+this one and I call this phase
+difference Delta I would like to ask you
+
+ align:start position:0%
+difference Delta I would like to ask you
+ 
+
+ align:start position:0%
+difference Delta I would like to ask you
+a question now the question is how do we
+
+ align:start position:0%
+a question now the question is how do we
+ 
+
+ align:start position:0%
+a question now the question is how do we
+choose the Delta here such that I have a
+
+ align:start position:0%
+choose the Delta here such that I have a
+ 
+
+ align:start position:0%
+choose the Delta here such that I have a
+completely destructive interference now
+
+ align:start position:0%
+completely destructive interference now
+ 
+
+ align:start position:0%
+completely destructive interference now
+I have three vectors vector e 1 vector e
+
+ align:start position:0%
+I have three vectors vector e 1 vector e
+ 
+
+ align:start position:0%
+I have three vectors vector e 1 vector e
+2 and the vector history
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the phase difference between a 1 e 2 and
+
+ align:start position:0%
+the phase difference between a 1 e 2 and
+ 
+
+ align:start position:0%
+the phase difference between a 1 e 2 and
+E 3 the nearby phase difference is a
+
+ align:start position:0%
+E 3 the nearby phase difference is a
+ 
+
+ align:start position:0%
+E 3 the nearby phase difference is a
+delta so the question is how do i h the
+
+ align:start position:0%
+delta so the question is how do i h the
+ 
+
+ align:start position:0%
+delta so the question is how do i h the
+company cancel the electric field so
+
+ align:start position:0%
+company cancel the electric field so
+ 
+
+ align:start position:0%
+company cancel the electric field so
+that I have completely destructive
+
+ align:start position:0%
+that I have completely destructive
+ 
+
+ align:start position:0%
+that I have completely destructive
+interference can somebody help me here
+
+ align:start position:0%
+interference can somebody help me here
+ 
+
+ align:start position:0%
+interference can somebody help me here
+he is that you can actually use this
+
+ align:start position:0%
+he is that you can actually use this
+ 
+
+ align:start position:0%
+he is that you can actually use this
+vector sum idea in the complex printer
+
+ align:start position:0%
+vector sum idea in the complex printer
+ 
+
+ align:start position:0%
+vector sum idea in the complex printer
+yes very good so to form a triangle
+
+ align:start position:0%
+yes very good so to form a triangle
+ 
+
+ align:start position:0%
+yes very good so to form a triangle
+right in the complex print right so what
+
+ align:start position:0%
+right in the complex print right so what
+ 
+
+ align:start position:0%
+right in the complex print right so what
+we can do is now choose the the phase
+
+ align:start position:0%
+we can do is now choose the the phase
+ 
+
+ align:start position:0%
+we can do is now choose the the phase
+difference Delta to P such that e 1 e 2
+
+ align:start position:0%
+difference Delta to P such that e 1 e 2
+ 
+
+ align:start position:0%
+difference Delta to P such that e 1 e 2
+and the eastery actually form the
+
+ align:start position:0%
+and the eastery actually form the
+ 
+
+ align:start position:0%
+and the eastery actually form the
+triangle you see what I mean
+
+ align:start position:0%
+triangle you see what I mean
+ 
+
+ align:start position:0%
+triangle you see what I mean
+therefore you can actually already get
+
+ align:start position:0%
+therefore you can actually already get
+ 
+
+ align:start position:0%
+therefore you can actually already get
+what would be the that required the
+
+ align:start position:0%
+what would be the that required the
+ 
+
+ align:start position:0%
+what would be the that required the
+Delta value that required that the other
+
+ align:start position:0%
+Delta value that required that the other
+ 
+
+ align:start position:0%
+Delta value that required that the other
+value is going to be 2pi divided by 3
+
+ align:start position:0%
+value is going to be 2pi divided by 3
+ 
+
+ align:start position:0%
+value is going to be 2pi divided by 3
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so very good so now you are not
+
+ align:start position:0%
+okay so very good so now you are not
+ 
+
+ align:start position:0%
+okay so very good so now you are not
+afraid anymore so how about force to did
+
+ align:start position:0%
+afraid anymore so how about force to did
+ 
+
+ align:start position:0%
+afraid anymore so how about force to did
+experiment I just add another sleep P is
+
+ align:start position:0%
+experiment I just add another sleep P is
+ 
+
+ align:start position:0%
+experiment I just add another sleep P is
+actually the distance between the fourth
+
+ align:start position:0%
+actually the distance between the fourth
+ 
+
+ align:start position:0%
+actually the distance between the fourth
+sleet and the certainty what would be
+
+ align:start position:0%
+sleet and the certainty what would be
+ 
+
+ align:start position:0%
+sleet and the certainty what would be
+the third time required to have
+
+ align:start position:0%
+the third time required to have
+ 
+
+ align:start position:0%
+the third time required to have
+destructive destructive interference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody can help me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good so if you have force to be
+
+ align:start position:0%
+very good so if you have force to be
+ 
+
+ align:start position:0%
+very good so if you have force to be
+based on this intuition which we develop
+
+ align:start position:0%
+based on this intuition which we develop
+ 
+
+ align:start position:0%
+based on this intuition which we develop
+from the complex location vector sum
+
+ align:start position:0%
+from the complex location vector sum
+ 
+
+ align:start position:0%
+from the complex location vector sum
+what is going to happen is that if you
+
+ align:start position:0%
+what is going to happen is that if you
+ 
+
+ align:start position:0%
+what is going to happen is that if you
+have force lead the Delta will be equal
+
+ align:start position:0%
+have force lead the Delta will be equal
+ 
+
+ align:start position:0%
+have force lead the Delta will be equal
+to two pi divided by okay so what does
+
+ align:start position:0%
+to two pi divided by okay so what does
+ 
+
+ align:start position:0%
+to two pi divided by okay so what does
+this tell us
+
+ align:start position:0%
+this tell us
+ 
+
+ align:start position:0%
+this tell us
+so remember the sine theta sine theta is
+
+ align:start position:0%
+so remember the sine theta sine theta is
+ 
+
+ align:start position:0%
+so remember the sine theta sine theta is
+helping you the location where you get a
+
+ align:start position:0%
+helping you the location where you get a
+ 
+
+ align:start position:0%
+helping you the location where you get a
+minimum okay so this is actually the
+
+ align:start position:0%
+minimum okay so this is actually the
+ 
+
+ align:start position:0%
+minimum okay so this is actually the
+power profile or say the intensity
+
+ align:start position:0%
+power profile or say the intensity
+ 
+
+ align:start position:0%
+power profile or say the intensity
+profile okay and the DC side should be
+
+ align:start position:0%
+profile okay and the DC side should be
+ 
+
+ align:start position:0%
+profile okay and the DC side should be
+equal to 0 and this is Asian dota
+
+ align:start position:0%
+equal to 0 and this is Asian dota
+ 
+
+ align:start position:0%
+equal to 0 and this is Asian dota
+okay the preys which you get zero
+
+ align:start position:0%
+okay the preys which you get zero
+ 
+
+ align:start position:0%
+okay the preys which you get zero
+intensity okay is they should be
+
+ align:start position:0%
+intensity okay is they should be
+ 
+
+ align:start position:0%
+intensity okay is they should be
+becoming closer and closer to zero right
+
+ align:start position:0%
+becoming closer and closer to zero right
+ 
+
+ align:start position:0%
+becoming closer and closer to zero right
+because sine theta which is the angle
+
+ align:start position:0%
+because sine theta which is the angle
+ 
+
+ align:start position:0%
+because sine theta which is the angle
+between her interaction and that this
+
+ align:start position:0%
+between her interaction and that this
+ 
+
+ align:start position:0%
+between her interaction and that this
+observer P is proportional to theta when
+
+ align:start position:0%
+observer P is proportional to theta when
+ 
+
+ align:start position:0%
+observer P is proportional to theta when
+you have destructive interference at
+
+ align:start position:0%
+you have destructive interference at
+ 
+
+ align:start position:0%
+you have destructive interference at
+angle which is smaller smaller and
+
+ align:start position:0%
+angle which is smaller smaller and
+ 
+
+ align:start position:0%
+angle which is smaller smaller and
+smaller that means what that means the
+
+ align:start position:0%
+smaller that means what that means the
+ 
+
+ align:start position:0%
+smaller that means what that means the
+central Gaussian like structure is going
+
+ align:start position:0%
+central Gaussian like structure is going
+ 
+
+ align:start position:0%
+central Gaussian like structure is going
+to be becoming narrower and narrower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good so so at this we found
+
+ align:start position:0%
+very good so so at this we found
+ 
+
+ align:start position:0%
+very good so so at this we found
+something interesting
+
+ align:start position:0%
+something interesting
+ 
+
+ align:start position:0%
+something interesting
+now that means huh one idea to get very
+
+ align:start position:0%
+now that means huh one idea to get very
+ 
+
+ align:start position:0%
+now that means huh one idea to get very
+narrow electromagnetic wave pointing to
+
+ align:start position:0%
+narrow electromagnetic wave pointing to
+ 
+
+ align:start position:0%
+narrow electromagnetic wave pointing to
+the interaction is to have a huge number
+
+ align:start position:0%
+the interaction is to have a huge number
+ 
+
+ align:start position:0%
+the interaction is to have a huge number
+of point light source and slit
+
+ align:start position:0%
+of point light source and slit
+ 
+
+ align:start position:0%
+of point light source and slit
+experiment such that I can actually
+
+ align:start position:0%
+experiment such that I can actually
+ 
+
+ align:start position:0%
+experiment such that I can actually
+construct something which is a very
+
+ align:start position:0%
+construct something which is a very
+ 
+
+ align:start position:0%
+construct something which is a very
+narrow in angle and I can use that to
+
+ align:start position:0%
+narrow in angle and I can use that to
+ 
+
+ align:start position:0%
+narrow in angle and I can use that to
+suit the object which I
+
+ align:start position:0%
+suit the object which I
+ 
+
+ align:start position:0%
+suit the object which I
+to be that you see what I mean does that
+
+ align:start position:0%
+to be that you see what I mean does that
+ 
+
+ align:start position:0%
+to be that you see what I mean does that
+make sense okay all right so that's very
+
+ align:start position:0%
+make sense okay all right so that's very
+ 
+
+ align:start position:0%
+make sense okay all right so that's very
+good so now let's actually consider
+
+ align:start position:0%
+good so now let's actually consider
+ 
+
+ align:start position:0%
+good so now let's actually consider
+unsweet interference pattern okay so
+
+ align:start position:0%
+unsweet interference pattern okay so
+ 
+
+ align:start position:0%
+unsweet interference pattern okay so
+suppose now I have not only one two
+
+ align:start position:0%
+suppose now I have not only one two
+ 
+
+ align:start position:0%
+suppose now I have not only one two
+three and the many more until indeed all
+
+ align:start position:0%
+three and the many more until indeed all
+ 
+
+ align:start position:0%
+three and the many more until indeed all
+right I can now go ahead and cut today
+
+ align:start position:0%
+right I can now go ahead and cut today
+ 
+
+ align:start position:0%
+right I can now go ahead and cut today
+the e total which is the total total
+
+ align:start position:0%
+the e total which is the total total
+ 
+
+ align:start position:0%
+the e total which is the total total
+electric field coming from all the speed
+
+ align:start position:0%
+electric field coming from all the speed
+ 
+
+ align:start position:0%
+electric field coming from all the speed
+we have basically this will be equal to
+
+ align:start position:0%
+we have basically this will be equal to
+ 
+
+ align:start position:0%
+we have basically this will be equal to
+e 0 exponential I Omega t minus K R
+
+ align:start position:0%
+e 0 exponential I Omega t minus K R
+ 
+
+ align:start position:0%
+e 0 exponential I Omega t minus K R
+where I define R 1 is roughly capital ah
+
+ align:start position:0%
+where I define R 1 is roughly capital ah
+ 
+
+ align:start position:0%
+where I define R 1 is roughly capital ah
+ok last is actually a contribution from
+
+ align:start position:0%
+ok last is actually a contribution from
+ 
+
+ align:start position:0%
+ok last is actually a contribution from
+suite number one okay and the
+
+ align:start position:0%
+suite number one okay and the
+ 
+
+ align:start position:0%
+suite number one okay and the
+contribution from street number 1 is
+
+ align:start position:0%
+contribution from street number 1 is
+ 
+
+ align:start position:0%
+contribution from street number 1 is
+going to be look like duty looking night
+
+ align:start position:0%
+going to be look like duty looking night
+ 
+
+ align:start position:0%
+going to be look like duty looking night
+exponential I Omega t minus K R minus
+
+ align:start position:0%
+exponential I Omega t minus K R minus
+ 
+
+ align:start position:0%
+exponential I Omega t minus K R minus
+Delta right because there is a phase
+
+ align:start position:0%
+Delta right because there is a phase
+ 
+
+ align:start position:0%
+Delta right because there is a phase
+difference between the light from coming
+
+ align:start position:0%
+difference between the light from coming
+ 
+
+ align:start position:0%
+difference between the light from coming
+from first deep and the second which is
+
+ align:start position:0%
+from first deep and the second which is
+ 
+
+ align:start position:0%
+from first deep and the second which is
+actually dirt all right so what would be
+
+ align:start position:0%
+actually dirt all right so what would be
+ 
+
+ align:start position:0%
+actually dirt all right so what would be
+the third turn so this is actually
+
+ align:start position:0%
+the third turn so this is actually
+ 
+
+ align:start position:0%
+the third turn so this is actually
+coming from see them too well below
+
+ align:start position:0%
+coming from see them too well below
+ 
+
+ align:start position:0%
+coming from see them too well below
+certain exponential I Omega t minus kr -
+
+ align:start position:0%
+certain exponential I Omega t minus kr -
+ 
+
+ align:start position:0%
+certain exponential I Omega t minus kr -
+what - Delta yeah because you can see
+
+ align:start position:0%
+what - Delta yeah because you can see
+ 
+
+ align:start position:0%
+what - Delta yeah because you can see
+that coming from here since the distance
+
+ align:start position:0%
+that coming from here since the distance
+ 
+
+ align:start position:0%
+that coming from here since the distance
+between these has constant which is D
+
+ align:start position:0%
+between these has constant which is D
+ 
+
+ align:start position:0%
+between these has constant which is D
+therefore the the phase difference
+
+ align:start position:0%
+therefore the the phase difference
+ 
+
+ align:start position:0%
+therefore the the phase difference
+between nearby street he said to the
+
+ align:start position:0%
+between nearby street he said to the
+ 
+
+ align:start position:0%
+between nearby street he said to the
+constant therefore I accumulating the
+
+ align:start position:0%
+constant therefore I accumulating the
+ 
+
+ align:start position:0%
+constant therefore I accumulating the
+phase difference now I get to Delta and
+
+ align:start position:0%
+phase difference now I get to Delta and
+ 
+
+ align:start position:0%
+phase difference now I get to Delta and
+this is actually contribution from the
+
+ align:start position:0%
+this is actually contribution from the
+ 
+
+ align:start position:0%
+this is actually contribution from the
+system and etc and ok and antio
+
+ align:start position:0%
+system and etc and ok and antio
+ 
+
+ align:start position:0%
+system and etc and ok and antio
+sleep which is actually going to be
+
+ align:start position:0%
+sleep which is actually going to be
+ 
+
+ align:start position:0%
+sleep which is actually going to be
+exponential I Omega t minus kr minus -1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and summing all those things together
+
+ align:start position:0%
+and summing all those things together
+ 
+
+ align:start position:0%
+and summing all those things together
+and all them in the Z direction okay so
+
+ align:start position:0%
+and all them in the Z direction okay so
+ 
+
+ align:start position:0%
+and all them in the Z direction okay so
+I'm now going to calculate this sum
+
+ align:start position:0%
+I'm now going to calculate this sum
+ 
+
+ align:start position:0%
+I'm now going to calculate this sum
+mention so basically you are getting 0
+
+ align:start position:0%
+mention so basically you are getting 0
+ 
+
+ align:start position:0%
+mention so basically you are getting 0
+exponential I Omega t minus kr I can
+
+ align:start position:0%
+exponential I Omega t minus kr I can
+ 
+
+ align:start position:0%
+exponential I Omega t minus kr I can
+actually factorize this factor out and
+
+ align:start position:0%
+actually factorize this factor out and
+ 
+
+ align:start position:0%
+actually factorize this factor out and
+what I'm going to get is 1 plus
+
+ align:start position:0%
+what I'm going to get is 1 plus
+ 
+
+ align:start position:0%
+what I'm going to get is 1 plus
+exponential minus I Delta plus
+
+ align:start position:0%
+exponential minus I Delta plus
+ 
+
+ align:start position:0%
+exponential minus I Delta plus
+exponential minus exponential minus I 2
+
+ align:start position:0%
+exponential minus exponential minus I 2
+ 
+
+ align:start position:0%
+exponential minus exponential minus I 2
+delta past blah blah blah and visit you
+
+ align:start position:0%
+delta past blah blah blah and visit you
+ 
+
+ align:start position:0%
+delta past blah blah blah and visit you
+I get exponential minus I minus 1 Delta
+
+ align:start position:0%
+I get exponential minus I minus 1 Delta
+ 
+
+ align:start position:0%
+I get exponential minus I minus 1 Delta
+in the first and all those things are
+
+ align:start position:0%
+in the first and all those things are
+ 
+
+ align:start position:0%
+in the first and all those things are
+pointing to the interaction and this I
+
+ align:start position:0%
+pointing to the interaction and this I
+ 
+
+ align:start position:0%
+pointing to the interaction and this I
+know how to actually calculate right
+
+ align:start position:0%
+know how to actually calculate right
+ 
+
+ align:start position:0%
+know how to actually calculate right
+just a reminder basically if you
+
+ align:start position:0%
+just a reminder basically if you
+ 
+
+ align:start position:0%
+just a reminder basically if you
+calculate some mentioned n equal to 0 to
+
+ align:start position:0%
+calculate some mentioned n equal to 0 to
+ 
+
+ align:start position:0%
+calculate some mentioned n equal to 0 to
+n minus 1 R to the N and this will give
+
+ align:start position:0%
+n minus 1 R to the N and this will give
+ 
+
+ align:start position:0%
+n minus 1 R to the N and this will give
+you 1 minus R to the N Peabody PI I
+
+ align:start position:0%
+you 1 minus R to the N Peabody PI I
+ 
+
+ align:start position:0%
+you 1 minus R to the N Peabody PI I
+minus 1 ok so basically I can now go
+
+ align:start position:0%
+minus 1 ok so basically I can now go
+ 
+
+ align:start position:0%
+minus 1 ok so basically I can now go
+ahead and calculate this and this will
+
+ align:start position:0%
+ahead and calculate this and this will
+ 
+
+ align:start position:0%
+ahead and calculate this and this will
+keep you basically this work basically
+
+ align:start position:0%
+keep you basically this work basically
+ 
+
+ align:start position:0%
+keep you basically this work basically
+give you one - ok so are the small R
+
+ align:start position:0%
+give you one - ok so are the small R
+ 
+
+ align:start position:0%
+give you one - ok so are the small R
+here is replaced by exponential minus I
+
+ align:start position:0%
+here is replaced by exponential minus I
+ 
+
+ align:start position:0%
+here is replaced by exponential minus I
+Delta right so therefore we're going to
+
+ align:start position:0%
+Delta right so therefore we're going to
+ 
+
+ align:start position:0%
+Delta right so therefore we're going to
+get is 1 minus exponential minus I Delta
+
+ align:start position:0%
+get is 1 minus exponential minus I Delta
+ 
+
+ align:start position:0%
+get is 1 minus exponential minus I Delta
+and right for the upper part and then I
+
+ align:start position:0%
+and right for the upper part and then I
+ 
+
+ align:start position:0%
+and right for the upper part and then I
+have it's 1 minus exponential minus I
+
+ align:start position:0%
+have it's 1 minus exponential minus I
+ 
+
+ align:start position:0%
+have it's 1 minus exponential minus I
+Delta in the lower part ok so that
+
+ align:start position:0%
+Delta in the lower part ok so that
+ 
+
+ align:start position:0%
+Delta in the lower part ok so that
+actually make use of this formula which
+
+ align:start position:0%
+actually make use of this formula which
+ 
+
+ align:start position:0%
+actually make use of this formula which
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+we simplify this series all right as
+
+ align:start position:0%
+we simplify this series all right as
+ 
+
+ align:start position:0%
+we simplify this series all right as
+usual what I'm going to do is to use the
+
+ align:start position:0%
+usual what I'm going to do is to use the
+ 
+
+ align:start position:0%
+usual what I'm going to do is to use the
+trick similar to what I have done there
+
+ align:start position:0%
+trick similar to what I have done there
+ 
+
+ align:start position:0%
+trick similar to what I have done there
+okay to actually get cosine function out
+
+ align:start position:0%
+okay to actually get cosine function out
+ 
+
+ align:start position:0%
+okay to actually get cosine function out
+of the exponential functions all right
+
+ align:start position:0%
+of the exponential functions all right
+ 
+
+ align:start position:0%
+of the exponential functions all right
+so what I'm going to do is to factorize
+
+ align:start position:0%
+so what I'm going to do is to factorize
+ 
+
+ align:start position:0%
+so what I'm going to do is to factorize
+our x one nation minus I Delta M over
+
+ align:start position:0%
+our x one nation minus I Delta M over
+ 
+
+ align:start position:0%
+our x one nation minus I Delta M over
+two for the upper part so basically I
+
+ align:start position:0%
+two for the upper part so basically I
+ 
+
+ align:start position:0%
+two for the upper part so basically I
+get explanation minus I Delta and
+
+ align:start position:0%
+get explanation minus I Delta and
+ 
+
+ align:start position:0%
+get explanation minus I Delta and
+divided by two exponential I Delta n
+
+ align:start position:0%
+divided by two exponential I Delta n
+ 
+
+ align:start position:0%
+divided by two exponential I Delta n
+divided by two minus exponential minus I
+
+ align:start position:0%
+divided by two minus exponential minus I
+ 
+
+ align:start position:0%
+divided by two minus exponential minus I
+Delta n / - okay this is essentially
+
+ align:start position:0%
+Delta n / - okay this is essentially
+ 
+
+ align:start position:0%
+Delta n / - okay this is essentially
+divided by exponential minus I Delta
+
+ align:start position:0%
+divided by exponential minus I Delta
+ 
+
+ align:start position:0%
+divided by exponential minus I Delta
+over two exponential I Delta over two
+
+ align:start position:0%
+over two exponential I Delta over two
+ 
+
+ align:start position:0%
+over two exponential I Delta over two
+minus exponential minus I Delta two
+
+ align:start position:0%
+minus exponential minus I Delta two
+ 
+
+ align:start position:0%
+minus exponential minus I Delta two
+right the reason I'm doing this is
+
+ align:start position:0%
+right the reason I'm doing this is
+ 
+
+ align:start position:0%
+right the reason I'm doing this is
+because I would like to actually make
+
+ align:start position:0%
+because I would like to actually make
+ 
+
+ align:start position:0%
+because I would like to actually make
+this a cosine function okay any
+
+ align:start position:0%
+this a cosine function okay any
+ 
+
+ align:start position:0%
+this a cosine function okay any
+questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if no question then basically
+
+ align:start position:0%
+okay so if no question then basically
+ 
+
+ align:start position:0%
+okay so if no question then basically
+this expression can be again read
+
+ align:start position:0%
+this expression can be again read
+ 
+
+ align:start position:0%
+this expression can be again read
+written as exponential minus I Delta
+
+ align:start position:0%
+written as exponential minus I Delta
+ 
+
+ align:start position:0%
+written as exponential minus I Delta
+minus 1/2 right because I have this
+
+ align:start position:0%
+minus 1/2 right because I have this
+ 
+
+ align:start position:0%
+minus 1/2 right because I have this
+denominator nominator exponential I
+
+ align:start position:0%
+denominator nominator exponential I
+ 
+
+ align:start position:0%
+denominator nominator exponential I
+Delta n over 2 and the explanation is
+
+ align:start position:0%
+Delta n over 2 and the explanation is
+ 
+
+ align:start position:0%
+Delta n over 2 and the explanation is
+Delta divided by 2 okay
+
+ align:start position:0%
+Delta divided by 2 okay
+ 
+
+ align:start position:0%
+Delta divided by 2 okay
+therefore I can combine them all
+
+ align:start position:0%
+therefore I can combine them all
+ 
+
+ align:start position:0%
+therefore I can combine them all
+together and get this expression and the
+
+ align:start position:0%
+together and get this expression and the
+ 
+
+ align:start position:0%
+together and get this expression and the
+digital exponential minus exponential
+
+ align:start position:0%
+digital exponential minus exponential
+ 
+
+ align:start position:0%
+digital exponential minus exponential
+therefore I'm going to get sign out of
+
+ align:start position:0%
+therefore I'm going to get sign out of
+ 
+
+ align:start position:0%
+therefore I'm going to get sign out of
+it and basically I get sine Delta
+
+ align:start position:0%
+it and basically I get sine Delta
+ 
+
+ align:start position:0%
+it and basically I get sine Delta
+divided by 2 divided by sine Delta ok so
+
+ align:start position:0%
+divided by 2 divided by sine Delta ok so
+ 
+
+ align:start position:0%
+divided by 2 divided by sine Delta ok so
+now I can easily go ahead and calculate
+
+ align:start position:0%
+now I can easily go ahead and calculate
+ 
+
+ align:start position:0%
+now I can easily go ahead and calculate
+what will be the resulting intensity
+
+ align:start position:0%
+what will be the resulting intensity
+ 
+
+ align:start position:0%
+what will be the resulting intensity
+right the resulting intensity is going
+
+ align:start position:0%
+right the resulting intensity is going
+ 
+
+ align:start position:0%
+right the resulting intensity is going
+to be proportional to the square of the
+
+ align:start position:0%
+to be proportional to the square of the
+ 
+
+ align:start position:0%
+to be proportional to the square of the
+electric field right so basically the
+
+ align:start position:0%
+electric field right so basically the
+ 
+
+ align:start position:0%
+electric field right so basically the
+intensity will be proportional to e
+
+ align:start position:0%
+intensity will be proportional to e
+ 
+
+ align:start position:0%
+intensity will be proportional to e
+square and that is actually equal to x
+
+ align:start position:0%
+square and that is actually equal to x
+ 
+
+ align:start position:0%
+square and that is actually equal to x
+star and is compressed conjugate and
+
+ align:start position:0%
+star and is compressed conjugate and
+ 
+
+ align:start position:0%
+star and is compressed conjugate and
+basically you will see that this will be
+
+ align:start position:0%
+basically you will see that this will be
+ 
+
+ align:start position:0%
+basically you will see that this will be
+proportional to sine and Delta divided
+
+ align:start position:0%
+proportional to sine and Delta divided
+ 
+
+ align:start position:0%
+proportional to sine and Delta divided
+by 2 divided by sine Delta 2 squared
+
+ align:start position:0%
+by 2 divided by sine Delta 2 squared
+ 
+
+ align:start position:0%
+by 2 divided by sine Delta 2 squared
+therefore the intensity will be equal to
+
+ align:start position:0%
+therefore the intensity will be equal to
+ 
+
+ align:start position:0%
+therefore the intensity will be equal to
+I 0 times sine and divided by 2 divided
+
+ align:start position:0%
+I 0 times sine and divided by 2 divided
+ 
+
+ align:start position:0%
+I 0 times sine and divided by 2 divided
+by sine PI over 2 and the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so after all this work we have arrived
+
+ align:start position:0%
+so after all this work we have arrived
+ 
+
+ align:start position:0%
+so after all this work we have arrived
+expression which is very hard to to
+
+ align:start position:0%
+expression which is very hard to to
+ 
+
+ align:start position:0%
+expression which is very hard to to
+understand so what I'm going to do to
+
+ align:start position:0%
+understand so what I'm going to do to
+ 
+
+ align:start position:0%
+understand so what I'm going to do to
+help you is to really practice all as a
+
+ align:start position:0%
+help you is to really practice all as a
+ 
+
+ align:start position:0%
+help you is to really practice all as a
+function of Delta on the screen you can
+
+ align:start position:0%
+function of Delta on the screen you can
+ 
+
+ align:start position:0%
+function of Delta on the screen you can
+see there are four plots here
+
+ align:start position:0%
+see there are four plots here
+ 
+
+ align:start position:0%
+see there are four plots here
+the first one is an equal to three the
+
+ align:start position:0%
+the first one is an equal to three the
+ 
+
+ align:start position:0%
+the first one is an equal to three the
+upper lab one is an equal to three so
+
+ align:start position:0%
+upper lab one is an equal to three so
+ 
+
+ align:start position:0%
+upper lab one is an equal to three so
+you can see that the pattern looks like
+
+ align:start position:0%
+you can see that the pattern looks like
+ 
+
+ align:start position:0%
+you can see that the pattern looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so at Delta equal to zero surprise
+
+ align:start position:0%
+so at Delta equal to zero surprise
+ 
+
+ align:start position:0%
+so at Delta equal to zero surprise
+nobody you are going to get maximum
+
+ align:start position:0%
+nobody you are going to get maximum
+ 
+
+ align:start position:0%
+nobody you are going to get maximum
+right because theta is equal to zero you
+
+ align:start position:0%
+right because theta is equal to zero you
+ 
+
+ align:start position:0%
+right because theta is equal to zero you
+are adding in vectors the most efficient
+
+ align:start position:0%
+are adding in vectors the most efficient
+ 
+
+ align:start position:0%
+are adding in vectors the most efficient
+way therefore you are going to get the
+
+ align:start position:0%
+way therefore you are going to get the
+ 
+
+ align:start position:0%
+way therefore you are going to get the
+maximum which is I equal to I 0 okay and
+
+ align:start position:0%
+maximum which is I equal to I 0 okay and
+ 
+
+ align:start position:0%
+maximum which is I equal to I 0 okay and
+if you move a wafer from the center
+
+ align:start position:0%
+if you move a wafer from the center
+ 
+
+ align:start position:0%
+if you move a wafer from the center
+Delta equal to 0 and you see that is a
+
+ align:start position:0%
+Delta equal to 0 and you see that is a
+ 
+
+ align:start position:0%
+Delta equal to 0 and you see that is a
+small bump okay in between then you
+
+ align:start position:0%
+small bump okay in between then you
+ 
+
+ align:start position:0%
+small bump okay in between then you
+continue and continue and you see that
+
+ align:start position:0%
+continue and continue and you see that
+ 
+
+ align:start position:0%
+continue and continue and you see that
+there's another big peak again you see
+
+ align:start position:0%
+there's another big peak again you see
+ 
+
+ align:start position:0%
+there's another big peak again you see
+so that is actually the structure if you
+
+ align:start position:0%
+so that is actually the structure if you
+ 
+
+ align:start position:0%
+so that is actually the structure if you
+prat this result I equal to something
+
+ align:start position:0%
+prat this result I equal to something
+ 
+
+ align:start position:0%
+prat this result I equal to something
+proportional to sine squared this
+
+ align:start position:0%
+proportional to sine squared this
+ 
+
+ align:start position:0%
+proportional to sine squared this
+expression there and that is actually
+
+ align:start position:0%
+expression there and that is actually
+ 
+
+ align:start position:0%
+expression there and that is actually
+what you will get when n is equal to 3
+
+ align:start position:0%
+what you will get when n is equal to 3
+ 
+
+ align:start position:0%
+what you will get when n is equal to 3
+okay and though this is how I remember
+
+ align:start position:0%
+okay and though this is how I remember
+ 
+
+ align:start position:0%
+okay and though this is how I remember
+this pattern okay so when n is equal to
+
+ align:start position:0%
+this pattern okay so when n is equal to
+ 
+
+ align:start position:0%
+this pattern okay so when n is equal to
+3 you have a family of two adult and
+
+ align:start position:0%
+3 you have a family of two adult and
+ 
+
+ align:start position:0%
+3 you have a family of two adult and
+white child right so basically you have
+
+ align:start position:0%
+white child right so basically you have
+ 
+
+ align:start position:0%
+white child right so basically you have
+to peak peak and between then there's a
+
+ align:start position:0%
+to peak peak and between then there's a
+ 
+
+ align:start position:0%
+to peak peak and between then there's a
+smoke okay that's actually how I
+
+ align:start position:0%
+smoke okay that's actually how I
+ 
+
+ align:start position:0%
+smoke okay that's actually how I
+remember this pattern and I think is
+
+ align:start position:0%
+remember this pattern and I think is
+ 
+
+ align:start position:0%
+remember this pattern and I think is
+it's pretty nice right so you can have
+
+ align:start position:0%
+it's pretty nice right so you can have
+ 
+
+ align:start position:0%
+it's pretty nice right so you can have
+an equal to four
+
+ align:start position:0%
+an equal to four
+ 
+
+ align:start position:0%
+an equal to four
+it's a bigger family you have to add out
+
+ align:start position:0%
+it's a bigger family you have to add out
+ 
+
+ align:start position:0%
+it's a bigger family you have to add out
+adults are slimmer okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because they have a lot of work to do
+
+ align:start position:0%
+because they have a lot of work to do
+ 
+
+ align:start position:0%
+because they have a lot of work to do
+then they have to charge all right an
+
+ align:start position:0%
+then they have to charge all right an
+ 
+
+ align:start position:0%
+then they have to charge all right an
+equal to five how many child how many
+
+ align:start position:0%
+equal to five how many child how many
+ 
+
+ align:start position:0%
+equal to five how many child how many
+children do we have three therefore the
+
+ align:start position:0%
+children do we have three therefore the
+ 
+
+ align:start position:0%
+children do we have three therefore the
+you know the adults are really
+
+ align:start position:0%
+you know the adults are really
+ 
+
+ align:start position:0%
+you know the adults are really
+frustrated so they are even swing okay
+
+ align:start position:0%
+frustrated so they are even swing okay
+ 
+
+ align:start position:0%
+frustrated so they are even swing okay
+in a happy way okay making it positive n
+
+ align:start position:0%
+in a happy way okay making it positive n
+ 
+
+ align:start position:0%
+in a happy way okay making it positive n
+equal to six
+
+ align:start position:0%
+equal to six
+ 
+
+ align:start position:0%
+equal to six
+whoa oh my god I have four children in
+
+ align:start position:0%
+whoa oh my god I have four children in
+ 
+
+ align:start position:0%
+whoa oh my god I have four children in
+the family all right so there are three
+
+ align:start position:0%
+the family all right so there are three
+ 
+
+ align:start position:0%
+the family all right so there are three
+two things which we learn from here the
+
+ align:start position:0%
+two things which we learn from here the
+ 
+
+ align:start position:0%
+two things which we learn from here the
+first one is that the damper of peak
+
+ align:start position:0%
+first one is that the damper of peak
+ 
+
+ align:start position:0%
+first one is that the damper of peak
+peak which I will call it principal
+
+ align:start position:0%
+peak which I will call it principal
+ 
+
+ align:start position:0%
+peak which I will call it principal
+Maxima okay the number of a principal
+
+ align:start position:0%
+Maxima okay the number of a principal
+ 
+
+ align:start position:0%
+Maxima okay the number of a principal
+Maxima is actually pretty similar okay
+
+ align:start position:0%
+Maxima is actually pretty similar okay
+ 
+
+ align:start position:0%
+Maxima is actually pretty similar okay
+as a function of Delta but the number of
+
+ align:start position:0%
+as a function of Delta but the number of
+ 
+
+ align:start position:0%
+as a function of Delta but the number of
+secondary Maxima increase as a function
+
+ align:start position:0%
+secondary Maxima increase as a function
+ 
+
+ align:start position:0%
+secondary Maxima increase as a function
+of M value value is actually telling you
+
+ align:start position:0%
+of M value value is actually telling you
+ 
+
+ align:start position:0%
+of M value value is actually telling you
+how many sleet you have in the
+
+ align:start position:0%
+how many sleet you have in the
+ 
+
+ align:start position:0%
+how many sleet you have in the
+experiment and also you can see that the
+
+ align:start position:0%
+experiment and also you can see that the
+ 
+
+ align:start position:0%
+experiment and also you can see that the
+tilta is actually becoming the first
+
+ align:start position:0%
+tilta is actually becoming the first
+ 
+
+ align:start position:0%
+tilta is actually becoming the first
+minima the total value is actually
+
+ align:start position:0%
+minima the total value is actually
+ 
+
+ align:start position:0%
+minima the total value is actually
+decreasing as a function of M L so that
+
+ align:start position:0%
+decreasing as a function of M L so that
+ 
+
+ align:start position:0%
+decreasing as a function of M L so that
+the parents are getting slimmer all
+
+ align:start position:0%
+the parents are getting slimmer all
+ 
+
+ align:start position:0%
+the parents are getting slimmer all
+right so therefore you can see that if I
+
+ align:start position:0%
+right so therefore you can see that if I
+ 
+
+ align:start position:0%
+right so therefore you can see that if I
+would like to have a greater which is as
+
+ align:start position:0%
+would like to have a greater which is as
+ 
+
+ align:start position:0%
+would like to have a greater which is as
+you pointing to a very specific
+
+ align:start position:0%
+you pointing to a very specific
+ 
+
+ align:start position:0%
+you pointing to a very specific
+direction what is actually the choose
+
+ align:start position:0%
+direction what is actually the choose
+ 
+
+ align:start position:0%
+direction what is actually the choose
+choice of M value which we need infinity
+
+ align:start position:0%
+choice of M value which we need infinity
+ 
+
+ align:start position:0%
+choice of M value which we need infinity
+or a very large number okay for sure in
+
+ align:start position:0%
+or a very large number okay for sure in
+ 
+
+ align:start position:0%
+or a very large number okay for sure in
+your life we can add to infinity but now
+
+ align:start position:0%
+your life we can add to infinity but now
+ 
+
+ align:start position:0%
+your life we can add to infinity but now
+we have found a way to actually design
+
+ align:start position:0%
+we have found a way to actually design
+ 
+
+ align:start position:0%
+we have found a way to actually design
+our radar since sine theta is actually
+
+ align:start position:0%
+our radar since sine theta is actually
+ 
+
+ align:start position:0%
+our radar since sine theta is actually
+proportional to Delta therefore what we
+
+ align:start position:0%
+proportional to Delta therefore what we
+ 
+
+ align:start position:0%
+proportional to Delta therefore what we
+actually really need to do is to really
+
+ align:start position:0%
+actually really need to do is to really
+ 
+
+ align:start position:0%
+actually really need to do is to really
+maximize the number of sleet we have so
+
+ align:start position:0%
+maximize the number of sleet we have so
+ 
+
+ align:start position:0%
+maximize the number of sleet we have so
+that actually we can create radar which
+
+ align:start position:0%
+that actually we can create radar which
+ 
+
+ align:start position:0%
+that actually we can create radar which
+we really coin
+
+ align:start position:0%
+we really coin
+ 
+
+ align:start position:0%
+we really coin
+to the direction of the enemy which is
+
+ align:start position:0%
+to the direction of the enemy which is
+ 
+
+ align:start position:0%
+to the direction of the enemy which is
+shown there invading the earth okay and
+
+ align:start position:0%
+shown there invading the earth okay and
+ 
+
+ align:start position:0%
+shown there invading the earth okay and
+we can actually detect it okay so we
+
+ align:start position:0%
+we can actually detect it okay so we
+ 
+
+ align:start position:0%
+we can actually detect it okay so we
+will take a five-minute break before we
+
+ align:start position:0%
+will take a five-minute break before we
+ 
+
+ align:start position:0%
+will take a five-minute break before we
+actually go to the last part of the
+
+ align:start position:0%
+actually go to the last part of the
+ 
+
+ align:start position:0%
+actually go to the last part of the
+course which is the connection to
+
+ align:start position:0%
+course which is the connection to
+ 
+
+ align:start position:0%
+course which is the connection to
+quantum mechanics so we come back at 35
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so welcome back from the break so
+
+ align:start position:0%
+okay so welcome back from the break so
+ 
+
+ align:start position:0%
+okay so welcome back from the break so
+before we move to the connection to
+
+ align:start position:0%
+before we move to the connection to
+ 
+
+ align:start position:0%
+before we move to the connection to
+quantum mechanics I would like to talk
+
+ align:start position:0%
+quantum mechanics I would like to talk
+ 
+
+ align:start position:0%
+quantum mechanics I would like to talk
+some more about what we have learned
+
+ align:start position:0%
+some more about what we have learned
+ 
+
+ align:start position:0%
+some more about what we have learned
+from from the design of the radar
+
+ align:start position:0%
+from from the design of the radar
+ 
+
+ align:start position:0%
+from from the design of the radar
+okay so this is actually what we
+
+ align:start position:0%
+okay so this is actually what we
+ 
+
+ align:start position:0%
+okay so this is actually what we
+actually get the the position of the
+
+ align:start position:0%
+actually get the the position of the
+ 
+
+ align:start position:0%
+actually get the the position of the
+minima the required phase difference
+
+ align:start position:0%
+minima the required phase difference
+ 
+
+ align:start position:0%
+minima the required phase difference
+Delta is actually equal to 2pi divided
+
+ align:start position:0%
+Delta is actually equal to 2pi divided
+ 
+
+ align:start position:0%
+Delta is actually equal to 2pi divided
+by and value right because you have
+
+ align:start position:0%
+by and value right because you have
+ 
+
+ align:start position:0%
+by and value right because you have
+issue the it with this Delta value the
+
+ align:start position:0%
+issue the it with this Delta value the
+ 
+
+ align:start position:0%
+issue the it with this Delta value the
+factors is going to cancel each other
+
+ align:start position:0%
+factors is going to cancel each other
+ 
+
+ align:start position:0%
+factors is going to cancel each other
+and you are going to form something like
+
+ align:start position:0%
+and you are going to form something like
+ 
+
+ align:start position:0%
+and you are going to form something like
+a circle if you choose Delta equal to
+
+ align:start position:0%
+a circle if you choose Delta equal to
+ 
+
+ align:start position:0%
+a circle if you choose Delta equal to
+2pi divided by capital okay
+
+ align:start position:0%
+2pi divided by capital okay
+ 
+
+ align:start position:0%
+2pi divided by capital okay
+and don't forget what is actually total
+
+ align:start position:0%
+and don't forget what is actually total
+ 
+
+ align:start position:0%
+and don't forget what is actually total
+the total is actually T sine theta
+
+ align:start position:0%
+the total is actually T sine theta
+ 
+
+ align:start position:0%
+the total is actually T sine theta
+divided by lambda right okay and and a
+
+ align:start position:0%
+divided by lambda right okay and and a
+ 
+
+ align:start position:0%
+divided by lambda right okay and and a
+times 2pi okay
+
+ align:start position:0%
+times 2pi okay
+ 
+
+ align:start position:0%
+times 2pi okay
+right so therefore you can see that the
+
+ align:start position:0%
+right so therefore you can see that the
+ 
+
+ align:start position:0%
+right so therefore you can see that the
+sine sine theta is actually proportional
+
+ align:start position:0%
+sine sine theta is actually proportional
+ 
+
+ align:start position:0%
+sine sine theta is actually proportional
+to lambda divided by n times D okay and
+
+ align:start position:0%
+to lambda divided by n times D okay and
+ 
+
+ align:start position:0%
+to lambda divided by n times D okay and
+in this case you can see that after you
+
+ align:start position:0%
+in this case you can see that after you
+ 
+
+ align:start position:0%
+in this case you can see that after you
+if you increase n value the resolution
+
+ align:start position:0%
+if you increase n value the resolution
+ 
+
+ align:start position:0%
+if you increase n value the resolution
+or the width of the central principle
+
+ align:start position:0%
+or the width of the central principle
+ 
+
+ align:start position:0%
+or the width of the central principle
+Maxima is going to be decreasing as a
+
+ align:start position:0%
+Maxima is going to be decreasing as a
+ 
+
+ align:start position:0%
+Maxima is going to be decreasing as a
+function of M value you're putting so in
+
+ align:start position:0%
+function of M value you're putting so in
+ 
+
+ align:start position:0%
+function of M value you're putting so in
+short how do I actually design a
+
+ align:start position:0%
+short how do I actually design a
+ 
+
+ align:start position:0%
+short how do I actually design a
+high-resolution radar what I really need
+
+ align:start position:0%
+high-resolution radar what I really need
+ 
+
+ align:start position:0%
+high-resolution radar what I really need
+is to have lambda to be small okay so
+
+ align:start position:0%
+is to have lambda to be small okay so
+ 
+
+ align:start position:0%
+is to have lambda to be small okay so
+that means I need to use high frequency
+
+ align:start position:0%
+that means I need to use high frequency
+ 
+
+ align:start position:0%
+that means I need to use high frequency
+electromagnetic wave I can maximize the
+
+ align:start position:0%
+electromagnetic wave I can maximize the
+ 
+
+ align:start position:0%
+electromagnetic wave I can maximize the
+value I can actually make T very large
+
+ align:start position:0%
+value I can actually make T very large
+ 
+
+ align:start position:0%
+value I can actually make T very large
+that means I'm going to have a very
+
+ align:start position:0%
+that means I'm going to have a very
+ 
+
+ align:start position:0%
+that means I'm going to have a very
+large radar okay a design right then I
+
+ align:start position:0%
+large radar okay a design right then I
+ 
+
+ align:start position:0%
+large radar okay a design right then I
+can have a very good resolution okay so
+
+ align:start position:0%
+can have a very good resolution okay so
+ 
+
+ align:start position:0%
+can have a very good resolution okay so
+we are almost done with radar but
+
+ align:start position:0%
+we are almost done with radar but
+ 
+
+ align:start position:0%
+we are almost done with radar but
+there's a problem
+
+ align:start position:0%
+there's a problem
+ 
+
+ align:start position:0%
+there's a problem
+the problem is that if you look at this
+
+ align:start position:0%
+the problem is that if you look at this
+ 
+
+ align:start position:0%
+the problem is that if you look at this
+if this is actually the position of the
+
+ align:start position:0%
+if this is actually the position of the
+ 
+
+ align:start position:0%
+if this is actually the position of the
+principle minimum okay you will see that
+
+ align:start position:0%
+principle minimum okay you will see that
+ 
+
+ align:start position:0%
+principle minimum okay you will see that
+it's always pointing to the center of
+
+ align:start position:0%
+it's always pointing to the center of
+ 
+
+ align:start position:0%
+it's always pointing to the center of
+the Breda right where the turret is
+
+ align:start position:0%
+the Breda right where the turret is
+ 
+
+ align:start position:0%
+the Breda right where the turret is
+equal to zero okay and then that means I
+
+ align:start position:0%
+equal to zero okay and then that means I
+ 
+
+ align:start position:0%
+equal to zero okay and then that means I
+can only scan in one direction there is
+
+ align:start position:0%
+can only scan in one direction there is
+ 
+
+ align:start position:0%
+can only scan in one direction there is
+a reason why those radar are code faced
+
+ align:start position:0%
+a reason why those radar are code faced
+ 
+
+ align:start position:0%
+a reason why those radar are code faced
+radar that is because now I can actually
+
+ align:start position:0%
+radar that is because now I can actually
+ 
+
+ align:start position:0%
+radar that is because now I can actually
+change the relative face of all those
+
+ align:start position:0%
+change the relative face of all those
+ 
+
+ align:start position:0%
+change the relative face of all those
+point source emitted from the radar so
+
+ align:start position:0%
+point source emitted from the radar so
+ 
+
+ align:start position:0%
+point source emitted from the radar so
+that I can shift the direction of the
+
+ align:start position:0%
+that I can shift the direction of the
+ 
+
+ align:start position:0%
+that I can shift the direction of the
+central principle Maxima okay so what
+
+ align:start position:0%
+central principle Maxima okay so what
+ 
+
+ align:start position:0%
+central principle Maxima okay so what
+what is a shit-ton here is like this so
+
+ align:start position:0%
+what is a shit-ton here is like this so
+ 
+
+ align:start position:0%
+what is a shit-ton here is like this so
+basically I can have introduced before
+
+ align:start position:0%
+basically I can have introduced before
+ 
+
+ align:start position:0%
+basically I can have introduced before
+emitting the electromagnetic wave I can
+
+ align:start position:0%
+emitting the electromagnetic wave I can
+ 
+
+ align:start position:0%
+emitting the electromagnetic wave I can
+introduce a zero additional phase
+
+ align:start position:0%
+introduce a zero additional phase
+ 
+
+ align:start position:0%
+introduce a zero additional phase
+difference and for the second one I
+
+ align:start position:0%
+difference and for the second one I
+ 
+
+ align:start position:0%
+difference and for the second one I
+introduce additional phase difference of
+
+ align:start position:0%
+introduce additional phase difference of
+ 
+
+ align:start position:0%
+introduce additional phase difference of
+Pi okay and for the third one I
+
+ align:start position:0%
+Pi okay and for the third one I
+ 
+
+ align:start position:0%
+Pi okay and for the third one I
+introduce a Titian of phase difference
+
+ align:start position:0%
+introduce a Titian of phase difference
+ 
+
+ align:start position:0%
+introduce a Titian of phase difference
+between the third Street emit out over
+
+ align:start position:0%
+between the third Street emit out over
+ 
+
+ align:start position:0%
+between the third Street emit out over
+say the third emitter in the first
+
+ align:start position:0%
+say the third emitter in the first
+ 
+
+ align:start position:0%
+say the third emitter in the first
+emitter by two Delta and for this
+
+ align:start position:0%
+emitter by two Delta and for this
+ 
+
+ align:start position:0%
+emitter by two Delta and for this
+emitter I introduce the phase difference
+
+ align:start position:0%
+emitter I introduce the phase difference
+ 
+
+ align:start position:0%
+emitter I introduce the phase difference
+of one minus one five okay if I add this
+
+ align:start position:0%
+of one minus one five okay if I add this
+ 
+
+ align:start position:0%
+of one minus one five okay if I add this
+phase difference into the set up what I
+
+ align:start position:0%
+phase difference into the set up what I
+ 
+
+ align:start position:0%
+phase difference into the set up what I
+am going to get is like this so
+
+ align:start position:0%
+am going to get is like this so
+ 
+
+ align:start position:0%
+am going to get is like this so
+basically Delta will become two pi
+
+ align:start position:0%
+basically Delta will become two pi
+ 
+
+ align:start position:0%
+basically Delta will become two pi
+divided by lambda T sine theta minus Phi
+
+ align:start position:0%
+divided by lambda T sine theta minus Phi
+ 
+
+ align:start position:0%
+divided by lambda T sine theta minus Phi
+angle right and this Phi is actually the
+
+ align:start position:0%
+angle right and this Phi is actually the
+ 
+
+ align:start position:0%
+angle right and this Phi is actually the
+artificial Ettie phase difference
+
+ align:start position:0%
+artificial Ettie phase difference
+ 
+
+ align:start position:0%
+artificial Ettie phase difference
+between those source okay and that means
+
+ align:start position:0%
+between those source okay and that means
+ 
+
+ align:start position:0%
+between those source okay and that means
+I were required and this will be T equal
+
+ align:start position:0%
+I were required and this will be T equal
+ 
+
+ align:start position:0%
+I were required and this will be T equal
+to 2 pi right this will be equal to PI
+
+ align:start position:0%
+to 2 pi right this will be equal to PI
+ 
+
+ align:start position:0%
+to 2 pi right this will be equal to PI
+divided by 2 pi divided by
+
+ align:start position:0%
+divided by 2 pi divided by
+ 
+
+ align:start position:0%
+divided by 2 pi divided by
+right such a you have completely
+
+ align:start position:0%
+right such a you have completely
+ 
+
+ align:start position:0%
+right such a you have completely
+destructive interference okay I can now
+
+ align:start position:0%
+destructive interference okay I can now
+ 
+
+ align:start position:0%
+destructive interference okay I can now
+make this Phi to be time dependent for
+
+ align:start position:0%
+make this Phi to be time dependent for
+ 
+
+ align:start position:0%
+make this Phi to be time dependent for
+example is increasing as a function of
+
+ align:start position:0%
+example is increasing as a function of
+ 
+
+ align:start position:0%
+example is increasing as a function of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+pythons T a five times T right then what
+
+ align:start position:0%
+pythons T a five times T right then what
+ 
+
+ align:start position:0%
+pythons T a five times T right then what
+is going to happen is that it's a
+
+ align:start position:0%
+is going to happen is that it's a
+ 
+
+ align:start position:0%
+is going to happen is that it's a
+function of time I'm going to change the
+
+ align:start position:0%
+function of time I'm going to change the
+ 
+
+ align:start position:0%
+function of time I'm going to change the
+D I'm going to change the sine theta
+
+ align:start position:0%
+D I'm going to change the sine theta
+ 
+
+ align:start position:0%
+D I'm going to change the sine theta
+value so that I can get the complete
+
+ align:start position:0%
+value so that I can get the complete
+ 
+
+ align:start position:0%
+value so that I can get the complete
+cancellation two PI over n right so
+
+ align:start position:0%
+cancellation two PI over n right so
+ 
+
+ align:start position:0%
+cancellation two PI over n right so
+effectively I'm changing the angle of
+
+ align:start position:0%
+effectively I'm changing the angle of
+ 
+
+ align:start position:0%
+effectively I'm changing the angle of
+the central principle maximum right by
+
+ align:start position:0%
+the central principle maximum right by
+ 
+
+ align:start position:0%
+the central principle maximum right by
+introducing additional artificial phase
+
+ align:start position:0%
+introducing additional artificial phase
+ 
+
+ align:start position:0%
+introducing additional artificial phase
+difference between all those point
+
+ align:start position:0%
+difference between all those point
+ 
+
+ align:start position:0%
+difference between all those point
+source okay and this is actually the way
+
+ align:start position:0%
+source okay and this is actually the way
+ 
+
+ align:start position:0%
+source okay and this is actually the way
+we can actually rotate the the press we
+
+ align:start position:0%
+we can actually rotate the the press we
+ 
+
+ align:start position:0%
+we can actually rotate the the press we
+are scanning up and down and get a very
+
+ align:start position:0%
+are scanning up and down and get a very
+ 
+
+ align:start position:0%
+are scanning up and down and get a very
+nice result to detect the enemy okay any
+
+ align:start position:0%
+nice result to detect the enemy okay any
+ 
+
+ align:start position:0%
+nice result to detect the enemy okay any
+questions don't okay so now I'm going to
+
+ align:start position:0%
+questions don't okay so now I'm going to
+ 
+
+ align:start position:0%
+questions don't okay so now I'm going to
+move on and it is caused a very
+
+ align:start position:0%
+move on and it is caused a very
+ 
+
+ align:start position:0%
+move on and it is caused a very
+interesting experiment so this very
+
+ align:start position:0%
+interesting experiment so this very
+ 
+
+ align:start position:0%
+interesting experiment so this very
+exciting experiment can ten pedia boards
+
+ align:start position:0%
+exciting experiment can ten pedia boards
+ 
+
+ align:start position:0%
+exciting experiment can ten pedia boards
+and the two-slit okay and we were
+
+ align:start position:0%
+and the two-slit okay and we were
+ 
+
+ align:start position:0%
+and the two-slit okay and we were
+wondering what is going to happen when
+
+ align:start position:0%
+wondering what is going to happen when
+ 
+
+ align:start position:0%
+wondering what is going to happen when
+those opposed specially passed through
+
+ align:start position:0%
+those opposed specially passed through
+ 
+
+ align:start position:0%
+those opposed specially passed through
+the street can anybody tell me what is
+
+ align:start position:0%
+the street can anybody tell me what is
+ 
+
+ align:start position:0%
+the street can anybody tell me what is
+going to happen and while I will be the
+
+ align:start position:0%
+going to happen and while I will be the
+ 
+
+ align:start position:0%
+going to happen and while I will be the
+statistics which were were say the
+
+ align:start position:0%
+statistics which were were say the
+ 
+
+ align:start position:0%
+statistics which were were say the
+which are going to get in the receiver
+
+ align:start position:0%
+which are going to get in the receiver
+ 
+
+ align:start position:0%
+which are going to get in the receiver
+layer anybody can you tell if I shoot a
+
+ align:start position:0%
+layer anybody can you tell if I shoot a
+ 
+
+ align:start position:0%
+layer anybody can you tell if I shoot a
+lot of pass through this I don't be shy
+
+ align:start position:0%
+lot of pass through this I don't be shy
+ 
+
+ align:start position:0%
+lot of pass through this I don't be shy
+right it's easy
+
+ align:start position:0%
+right it's easy
+ 
+
+ align:start position:0%
+right it's easy
+no nobody want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah this surprised nobody right afraid
+
+ align:start position:0%
+yeah this surprised nobody right afraid
+ 
+
+ align:start position:0%
+yeah this surprised nobody right afraid
+of answering questions okay so you can
+
+ align:start position:0%
+of answering questions okay so you can
+ 
+
+ align:start position:0%
+of answering questions okay so you can
+see that they make two piles right no
+
+ align:start position:0%
+see that they make two piles right no
+ 
+
+ align:start position:0%
+see that they make two piles right no
+right okay very good
+
+ align:start position:0%
+right okay very good
+ 
+
+ align:start position:0%
+right okay very good
+so now this is an exciting part
+
+ align:start position:0%
+so now this is an exciting part
+ 
+
+ align:start position:0%
+so now this is an exciting part
+now instead of shooting video boards but
+
+ align:start position:0%
+now instead of shooting video boards but
+ 
+
+ align:start position:0%
+now instead of shooting video boards but
+a boss okay what I'm going to do is to
+
+ align:start position:0%
+a boss okay what I'm going to do is to
+ 
+
+ align:start position:0%
+a boss okay what I'm going to do is to
+shoot electrons so I can actually
+
+ align:start position:0%
+shoot electrons so I can actually
+ 
+
+ align:start position:0%
+shoot electrons so I can actually
+prepare an electron source and he did up
+
+ align:start position:0%
+prepare an electron source and he did up
+ 
+
+ align:start position:0%
+prepare an electron source and he did up
+Saturday is start to emit electron and I
+
+ align:start position:0%
+Saturday is start to emit electron and I
+ 
+
+ align:start position:0%
+Saturday is start to emit electron and I
+have two slits and have then pass
+
+ align:start position:0%
+have two slits and have then pass
+ 
+
+ align:start position:0%
+have two slits and have then pass
+through the slits and I have a screen
+
+ align:start position:0%
+through the slits and I have a screen
+ 
+
+ align:start position:0%
+through the slits and I have a screen
+which actually have a electron detector
+
+ align:start position:0%
+which actually have a electron detector
+ 
+
+ align:start position:0%
+which actually have a electron detector
+to count the number of electron which I
+
+ align:start position:0%
+to count the number of electron which I
+ 
+
+ align:start position:0%
+to count the number of electron which I
+am going to get on the screen now reason
+
+ align:start position:0%
+am going to get on the screen now reason
+ 
+
+ align:start position:0%
+am going to get on the screen now reason
+why I call it single electron source is
+
+ align:start position:0%
+why I call it single electron source is
+ 
+
+ align:start position:0%
+why I call it single electron source is
+because each time I control my
+
+ align:start position:0%
+because each time I control my
+ 
+
+ align:start position:0%
+because each time I control my
+experiment such that you only emit one
+
+ align:start position:0%
+experiment such that you only emit one
+ 
+
+ align:start position:0%
+experiment such that you only emit one
+electron every time okay the question
+
+ align:start position:0%
+electron every time okay the question
+ 
+
+ align:start position:0%
+electron every time okay the question
+I'm trying to ask is well I see some
+
+ align:start position:0%
+I'm trying to ask is well I see some
+ 
+
+ align:start position:0%
+I'm trying to ask is well I see some
+pattern which is actually like like
+
+ align:start position:0%
+pattern which is actually like like
+ 
+
+ align:start position:0%
+pattern which is actually like like
+video board and they form two piles in a
+
+ align:start position:0%
+video board and they form two piles in a
+ 
+
+ align:start position:0%
+video board and they form two piles in a
+pack that's actually option number one
+
+ align:start position:0%
+pack that's actually option number one
+ 
+
+ align:start position:0%
+pack that's actually option number one
+or I'm going to see it is something
+
+ align:start position:0%
+or I'm going to see it is something
+ 
+
+ align:start position:0%
+or I'm going to see it is something
+crazy the electron is going to be
+
+ align:start position:0%
+crazy the electron is going to be
+ 
+
+ align:start position:0%
+crazy the electron is going to be
+interfere going to the interference with
+
+ align:start position:0%
+interfere going to the interference with
+ 
+
+ align:start position:0%
+interfere going to the interference with
+itself and that is actually option
+
+ align:start position:0%
+itself and that is actually option
+ 
+
+ align:start position:0%
+itself and that is actually option
+number two okay the duo of a also is
+
+ align:start position:0%
+number two okay the duo of a also is
+ 
+
+ align:start position:0%
+number two okay the duo of a also is
+that everybody have to choose one okay
+
+ align:start position:0%
+that everybody have to choose one okay
+ 
+
+ align:start position:0%
+that everybody have to choose one okay
+so how many of you think what is going
+
+ align:start position:0%
+so how many of you think what is going
+ 
+
+ align:start position:0%
+so how many of you think what is going
+to happen is number one um I have only
+
+ align:start position:0%
+to happen is number one um I have only
+ 
+
+ align:start position:0%
+to happen is number one um I have only
+one electron okay each time nobody
+
+ align:start position:0%
+one electron okay each time nobody
+ 
+
+ align:start position:0%
+one electron okay each time nobody
+thinks oh wow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe all of you are wrong
+
+ align:start position:0%
+maybe all of you are wrong
+ 
+
+ align:start position:0%
+maybe all of you are wrong
+how about the second options hey some of
+
+ align:start position:0%
+how about the second options hey some of
+ 
+
+ align:start position:0%
+how about the second options hey some of
+us you didn't raise your hand come on
+
+ align:start position:0%
+us you didn't raise your hand come on
+ 
+
+ align:start position:0%
+us you didn't raise your hand come on
+come on okay everybody Wow
+
+ align:start position:0%
+come on okay everybody Wow
+ 
+
+ align:start position:0%
+come on okay everybody Wow
+what is actually happening to your brand
+
+ align:start position:0%
+what is actually happening to your brand
+ 
+
+ align:start position:0%
+what is actually happening to your brand
+my brand is not functional like this
+
+ align:start position:0%
+my brand is not functional like this
+ 
+
+ align:start position:0%
+my brand is not functional like this
+okay so I really hope that I can bring
+
+ align:start position:0%
+okay so I really hope that I can bring
+ 
+
+ align:start position:0%
+okay so I really hope that I can bring
+the experiment to here but unfortunately
+
+ align:start position:0%
+the experiment to here but unfortunately
+ 
+
+ align:start position:0%
+the experiment to here but unfortunately
+that's actually going to be very
+
+ align:start position:0%
+that's actually going to be very
+ 
+
+ align:start position:0%
+that's actually going to be very
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+okay so what I'm going to do is that I'm
+
+ align:start position:0%
+okay so what I'm going to do is that I'm
+ 
+
+ align:start position:0%
+okay so what I'm going to do is that I'm
+going to show you the experimental
+
+ align:start position:0%
+going to show you the experimental
+ 
+
+ align:start position:0%
+going to show you the experimental
+result a video and we are going to see
+
+ align:start position:0%
+result a video and we are going to see
+ 
+
+ align:start position:0%
+result a video and we are going to see
+what is going to happen you see that
+
+ align:start position:0%
+what is going to happen you see that
+ 
+
+ align:start position:0%
+what is going to happen you see that
+they are thoughts popping out what are
+
+ align:start position:0%
+they are thoughts popping out what are
+ 
+
+ align:start position:0%
+they are thoughts popping out what are
+those those are the detective electron
+
+ align:start position:0%
+those those are the detective electron
+ 
+
+ align:start position:0%
+those those are the detective electron
+one by one on screen okay so basically
+
+ align:start position:0%
+one by one on screen okay so basically
+ 
+
+ align:start position:0%
+one by one on screen okay so basically
+you can see that the number of dots are
+
+ align:start position:0%
+you can see that the number of dots are
+ 
+
+ align:start position:0%
+you can see that the number of dots are
+increasing as a function of time
+
+ align:start position:0%
+increasing as a function of time
+ 
+
+ align:start position:0%
+increasing as a function of time
+and I actually speeding up things a bit
+
+ align:start position:0%
+and I actually speeding up things a bit
+ 
+
+ align:start position:0%
+and I actually speeding up things a bit
+so that actually you can see the pattern
+
+ align:start position:0%
+so that actually you can see the pattern
+ 
+
+ align:start position:0%
+so that actually you can see the pattern
+quicker okay so you can see that there
+
+ align:start position:0%
+quicker okay so you can see that there
+ 
+
+ align:start position:0%
+quicker okay so you can see that there
+are more and more thoughts and each time
+
+ align:start position:0%
+are more and more thoughts and each time
+ 
+
+ align:start position:0%
+are more and more thoughts and each time
+you can see that only get one electron
+
+ align:start position:0%
+you can see that only get one electron
+ 
+
+ align:start position:0%
+you can see that only get one electron
+but per image right so you can see now
+
+ align:start position:0%
+but per image right so you can see now
+ 
+
+ align:start position:0%
+but per image right so you can see now
+there are more and more and more and
+
+ align:start position:0%
+there are more and more and more and
+ 
+
+ align:start position:0%
+there are more and more and more and
+more and accumulating more data like
+
+ align:start position:0%
+more and accumulating more data like
+ 
+
+ align:start position:0%
+more and accumulating more data like
+what we actually done in the Large
+
+ align:start position:0%
+what we actually done in the Large
+ 
+
+ align:start position:0%
+what we actually done in the Large
+Hadron Collider with with the collect
+
+ align:start position:0%
+Hadron Collider with with the collect
+ 
+
+ align:start position:0%
+Hadron Collider with with the collect
+more data and we are speeding things up
+
+ align:start position:0%
+more data and we are speeding things up
+ 
+
+ align:start position:0%
+more data and we are speeding things up
+and you can see that Wow
+
+ align:start position:0%
+and you can see that Wow
+ 
+
+ align:start position:0%
+and you can see that Wow
+something is as you develop in what is
+
+ align:start position:0%
+something is as you develop in what is
+ 
+
+ align:start position:0%
+something is as you develop in what is
+that can you see it now you can speaking
+
+ align:start position:0%
+that can you see it now you can speaking
+ 
+
+ align:start position:0%
+that can you see it now you can speaking
+up like a 100 1000 times faster you can
+
+ align:start position:0%
+up like a 100 1000 times faster you can
+ 
+
+ align:start position:0%
+up like a 100 1000 times faster you can
+see what pattern interference pattern
+
+ align:start position:0%
+see what pattern interference pattern
+ 
+
+ align:start position:0%
+see what pattern interference pattern
+what is going on you are not surprised
+
+ align:start position:0%
+what is going on you are not surprised
+ 
+
+ align:start position:0%
+what is going on you are not surprised
+oh my god what is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm so surprised look at this
+
+ align:start position:0%
+I'm so surprised look at this
+ 
+
+ align:start position:0%
+I'm so surprised look at this
+so I have emission of one electron each
+
+ align:start position:0%
+so I have emission of one electron each
+ 
+
+ align:start position:0%
+so I have emission of one electron each
+time and that is actually the four
+
+ align:start position:0%
+time and that is actually the four
+ 
+
+ align:start position:0%
+time and that is actually the four
+snapshot which I took which actually
+
+ align:start position:0%
+snapshot which I took which actually
+ 
+
+ align:start position:0%
+snapshot which I took which actually
+this experiment he touched a group as
+
+ align:start position:0%
+this experiment he touched a group as
+ 
+
+ align:start position:0%
+this experiment he touched a group as
+you did this experiment you can actually
+
+ align:start position:0%
+you did this experiment you can actually
+ 
+
+ align:start position:0%
+you did this experiment you can actually
+click on this link to them more detail
+
+ align:start position:0%
+click on this link to them more detail
+ 
+
+ align:start position:0%
+click on this link to them more detail
+and they've took four snapshots of the
+
+ align:start position:0%
+and they've took four snapshots of the
+ 
+
+ align:start position:0%
+and they've took four snapshots of the
+experiment and you can see that in the
+
+ align:start position:0%
+experiment and you can see that in the
+ 
+
+ align:start position:0%
+experiment and you can see that in the
+beginning you can see clearly each time
+
+ align:start position:0%
+beginning you can see clearly each time
+ 
+
+ align:start position:0%
+beginning you can see clearly each time
+you only get one electron out of the
+
+ align:start position:0%
+you only get one electron out of the
+ 
+
+ align:start position:0%
+you only get one electron out of the
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+okay but as a function of time you are
+
+ align:start position:0%
+okay but as a function of time you are
+ 
+
+ align:start position:0%
+okay but as a function of time you are
+accumulating more and more and you see
+
+ align:start position:0%
+accumulating more and more and you see
+ 
+
+ align:start position:0%
+accumulating more and more and you see
+that clearly there is a pattern forming
+
+ align:start position:0%
+that clearly there is a pattern forming
+ 
+
+ align:start position:0%
+that clearly there is a pattern forming
+which essentially consistent with what
+
+ align:start position:0%
+which essentially consistent with what
+ 
+
+ align:start position:0%
+which essentially consistent with what
+we see in this calculation okay so I
+
+ align:start position:0%
+we see in this calculation okay so I
+ 
+
+ align:start position:0%
+we see in this calculation okay so I
+think that's actually truly amazing and
+
+ align:start position:0%
+think that's actually truly amazing and
+ 
+
+ align:start position:0%
+think that's actually truly amazing and
+what does that mean that means the
+
+ align:start position:0%
+what does that mean that means the
+ 
+
+ align:start position:0%
+what does that mean that means the
+electron is praying with itself it's
+
+ align:start position:0%
+electron is praying with itself it's
+ 
+
+ align:start position:0%
+electron is praying with itself it's
+interfering with itself right that's
+
+ align:start position:0%
+interfering with itself right that's
+ 
+
+ align:start position:0%
+interfering with itself right that's
+really strange what is going to happen
+
+ align:start position:0%
+really strange what is going to happen
+ 
+
+ align:start position:0%
+really strange what is going to happen
+what is what is going on so one single
+
+ align:start position:0%
+what is what is going on so one single
+ 
+
+ align:start position:0%
+what is what is going on so one single
+Elettra passed through posts lead which
+
+ align:start position:0%
+Elettra passed through posts lead which
+ 
+
+ align:start position:0%
+Elettra passed through posts lead which
+is actually the option you choose
+
+ align:start position:0%
+is actually the option you choose
+ 
+
+ align:start position:0%
+is actually the option you choose
+surprise me and then they interfere like
+
+ align:start position:0%
+surprise me and then they interfere like
+ 
+
+ align:start position:0%
+surprise me and then they interfere like
+waves and produce the pattern which we
+
+ align:start position:0%
+waves and produce the pattern which we
+ 
+
+ align:start position:0%
+waves and produce the pattern which we
+see on the screen that is a she's really
+
+ align:start position:0%
+see on the screen that is a she's really
+ 
+
+ align:start position:0%
+see on the screen that is a she's really
+crazy to me what is actually even more
+
+ align:start position:0%
+crazy to me what is actually even more
+ 
+
+ align:start position:0%
+crazy to me what is actually even more
+crazy is this situation so now if I make
+
+ align:start position:0%
+crazy is this situation so now if I make
+ 
+
+ align:start position:0%
+crazy is this situation so now if I make
+measurement in front of the slit okay so
+
+ align:start position:0%
+measurement in front of the slit okay so
+ 
+
+ align:start position:0%
+measurement in front of the slit okay so
+now I put some a dito
+
+ align:start position:0%
+now I put some a dito
+ 
+
+ align:start position:0%
+now I put some a dito
+device when the electron passed through
+
+ align:start position:0%
+device when the electron passed through
+ 
+
+ align:start position:0%
+device when the electron passed through
+one of the sleet I say semi a signal
+
+ align:start position:0%
+one of the sleet I say semi a signal
+ 
+
+ align:start position:0%
+one of the sleet I say semi a signal
+okay so now I can spray this now that
+
+ align:start position:0%
+okay so now I can spray this now that
+ 
+
+ align:start position:0%
+okay so now I can spray this now that
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+sleep the electron is actually going
+
+ align:start position:0%
+sleep the electron is actually going
+ 
+
+ align:start position:0%
+sleep the electron is actually going
+through in the experiment okay
+
+ align:start position:0%
+through in the experiment okay
+ 
+
+ align:start position:0%
+through in the experiment okay
+and the crazy thing is that if I do that
+
+ align:start position:0%
+and the crazy thing is that if I do that
+ 
+
+ align:start position:0%
+and the crazy thing is that if I do that
+then it become two piles okay of course
+
+ align:start position:0%
+then it become two piles okay of course
+ 
+
+ align:start position:0%
+then it become two piles okay of course
+maybe there are some diffraction pattern
+
+ align:start position:0%
+maybe there are some diffraction pattern
+ 
+
+ align:start position:0%
+maybe there are some diffraction pattern
+but the it really changed the pattern of
+
+ align:start position:0%
+but the it really changed the pattern of
+ 
+
+ align:start position:0%
+but the it really changed the pattern of
+the experimental result and that
+
+ align:start position:0%
+the experimental result and that
+ 
+
+ align:start position:0%
+the experimental result and that
+decision is really very strange and we
+
+ align:start position:0%
+decision is really very strange and we
+ 
+
+ align:start position:0%
+decision is really very strange and we
+are going to talk about that briefly in
+
+ align:start position:0%
+are going to talk about that briefly in
+ 
+
+ align:start position:0%
+are going to talk about that briefly in
+the next lecture so before the end I'm
+
+ align:start position:0%
+the next lecture so before the end I'm
+ 
+
+ align:start position:0%
+the next lecture so before the end I'm
+going to show you additional
+
+ align:start position:0%
+going to show you additional
+ 
+
+ align:start position:0%
+going to show you additional
+demonstration which motivate the
+
+ align:start position:0%
+demonstration which motivate the
+ 
+
+ align:start position:0%
+demonstration which motivate the
+discussion what we are going to have in
+
+ align:start position:0%
+discussion what we are going to have in
+ 
+
+ align:start position:0%
+discussion what we are going to have in
+the next lecture so now I can actually
+
+ align:start position:0%
+the next lecture so now I can actually
+ 
+
+ align:start position:0%
+the next lecture so now I can actually
+turn off the light again and also hide
+
+ align:start position:0%
+turn off the light again and also hide
+ 
+
+ align:start position:0%
+turn off the light again and also hide
+the image okay I hope I can find a
+
+ align:start position:0%
+the image okay I hope I can find a
+ 
+
+ align:start position:0%
+the image okay I hope I can find a
+pattern all right so here I have two
+
+ align:start position:0%
+pattern all right so here I have two
+ 
+
+ align:start position:0%
+pattern all right so here I have two
+laser so I'm going to turn up the first
+
+ align:start position:0%
+laser so I'm going to turn up the first
+ 
+
+ align:start position:0%
+laser so I'm going to turn up the first
+laser and this laser is going to pass
+
+ align:start position:0%
+laser and this laser is going to pass
+ 
+
+ align:start position:0%
+laser and this laser is going to pass
+through to a two-slit a tool already
+
+ align:start position:0%
+through to a two-slit a tool already
+ 
+
+ align:start position:0%
+through to a two-slit a tool already
+nearby sleet and and the form
+
+ align:start position:0%
+nearby sleet and and the form
+ 
+
+ align:start position:0%
+nearby sleet and and the form
+interference pattern you can see on the
+
+ align:start position:0%
+interference pattern you can see on the
+ 
+
+ align:start position:0%
+interference pattern you can see on the
+wall I hope you can see I don't know if
+
+ align:start position:0%
+wall I hope you can see I don't know if
+ 
+
+ align:start position:0%
+wall I hope you can see I don't know if
+you can see clearly that you can see
+
+ align:start position:0%
+you can see clearly that you can see
+ 
+
+ align:start position:0%
+you can see clearly that you can see
+there are many many dots nearby dots
+
+ align:start position:0%
+there are many many dots nearby dots
+ 
+
+ align:start position:0%
+there are many many dots nearby dots
+which really shows you the position of
+
+ align:start position:0%
+which really shows you the position of
+ 
+
+ align:start position:0%
+which really shows you the position of
+the principal Maximas right because
+
+ align:start position:0%
+the principal Maximas right because
+ 
+
+ align:start position:0%
+the principal Maximas right because
+these roots the experiment therefore how
+
+ align:start position:0%
+these roots the experiment therefore how
+ 
+
+ align:start position:0%
+these roots the experiment therefore how
+many children do we have in the family
+
+ align:start position:0%
+many children do we have in the family
+ 
+
+ align:start position:0%
+many children do we have in the family
+zero right because they are okay they
+
+ align:start position:0%
+zero right because they are okay they
+ 
+
+ align:start position:0%
+zero right because they are okay they
+just got married
+
+ align:start position:0%
+just got married
+ 
+
+ align:start position:0%
+just got married
+maybe all right so so therefore you will
+
+ align:start position:0%
+maybe all right so so therefore you will
+ 
+
+ align:start position:0%
+maybe all right so so therefore you will
+see only a doubt and that is actually
+
+ align:start position:0%
+see only a doubt and that is actually
+ 
+
+ align:start position:0%
+see only a doubt and that is actually
+the the principal maxi mass you can see
+
+ align:start position:0%
+the the principal maxi mass you can see
+ 
+
+ align:start position:0%
+the the principal maxi mass you can see
+many many nearby thoughts they are
+
+ align:start position:0%
+many many nearby thoughts they are
+ 
+
+ align:start position:0%
+many many nearby thoughts they are
+almost equally bright okay but there is
+
+ align:start position:0%
+almost equally bright okay but there is
+ 
+
+ align:start position:0%
+almost equally bright okay but there is
+something happening to this pattern as
+
+ align:start position:0%
+something happening to this pattern as
+ 
+
+ align:start position:0%
+something happening to this pattern as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+you can see that we wait a second in the
+
+ align:start position:0%
+you can see that we wait a second in the
+ 
+
+ align:start position:0%
+you can see that we wait a second in the
+calculation we get the the max the
+
+ align:start position:0%
+calculation we get the the max the
+ 
+
+ align:start position:0%
+calculation we get the the max the
+principle Maxima should have the same
+
+ align:start position:0%
+principle Maxima should have the same
+ 
+
+ align:start position:0%
+principle Maxima should have the same
+height right that means you are going to
+
+ align:start position:0%
+height right that means you are going to
+ 
+
+ align:start position:0%
+height right that means you are going to
+get exactly the same intensity for all
+
+ align:start position:0%
+get exactly the same intensity for all
+ 
+
+ align:start position:0%
+get exactly the same intensity for all
+the Maximus but that you don't see that
+
+ align:start position:0%
+the Maximus but that you don't see that
+ 
+
+ align:start position:0%
+the Maximus but that you don't see that
+here you can see that if you move away
+
+ align:start position:0%
+here you can see that if you move away
+ 
+
+ align:start position:0%
+here you can see that if you move away
+from the center too much
+
+ align:start position:0%
+from the center too much
+ 
+
+ align:start position:0%
+from the center too much
+the intensity is decreasing you see at
+
+ align:start position:0%
+the intensity is decreasing you see at
+ 
+
+ align:start position:0%
+the intensity is decreasing you see at
+the edge it actually even goes to zero
+
+ align:start position:0%
+the edge it actually even goes to zero
+ 
+
+ align:start position:0%
+the edge it actually even goes to zero
+right what is actually happening
+
+ align:start position:0%
+right what is actually happening
+ 
+
+ align:start position:0%
+right what is actually happening
+something clearly is actually missing in
+
+ align:start position:0%
+something clearly is actually missing in
+ 
+
+ align:start position:0%
+something clearly is actually missing in
+our calculation and that is not missing
+
+ align:start position:0%
+our calculation and that is not missing
+ 
+
+ align:start position:0%
+our calculation and that is not missing
+part is actually the fraction which we
+
+ align:start position:0%
+part is actually the fraction which we
+ 
+
+ align:start position:0%
+part is actually the fraction which we
+will talk about that in the next lecture
+
+ align:start position:0%
+will talk about that in the next lecture
+ 
+
+ align:start position:0%
+will talk about that in the next lecture
+so if you compare this pattern to the
+
+ align:start position:0%
+so if you compare this pattern to the
+ 
+
+ align:start position:0%
+so if you compare this pattern to the
+second demo you can see in the right
+
+ align:start position:0%
+second demo you can see in the right
+ 
+
+ align:start position:0%
+second demo you can see in the right
+hand side setup which I have here which
+
+ align:start position:0%
+hand side setup which I have here which
+ 
+
+ align:start position:0%
+hand side setup which I have here which
+actually give you a projection on the
+
+ align:start position:0%
+actually give you a projection on the
+ 
+
+ align:start position:0%
+actually give you a projection on the
+wall which is actually lower part of the
+
+ align:start position:0%
+wall which is actually lower part of the
+ 
+
+ align:start position:0%
+wall which is actually lower part of the
+result of the demo you can see that this
+
+ align:start position:0%
+result of the demo you can see that this
+ 
+
+ align:start position:0%
+result of the demo you can see that this
+laser actually passed through a singles
+
+ align:start position:0%
+laser actually passed through a singles
+ 
+
+ align:start position:0%
+laser actually passed through a singles
+lead but this lead is actually pretty
+
+ align:start position:0%
+lead but this lead is actually pretty
+ 
+
+ align:start position:0%
+lead but this lead is actually pretty
+white okay and you can see that indeed
+
+ align:start position:0%
+white okay and you can see that indeed
+ 
+
+ align:start position:0%
+white okay and you can see that indeed
+you see the laser coming out but
+
+ align:start position:0%
+you see the laser coming out but
+ 
+
+ align:start position:0%
+you see the laser coming out but
+essentially not as not a single spot and
+
+ align:start position:0%
+essentially not as not a single spot and
+ 
+
+ align:start position:0%
+essentially not as not a single spot and
+he has some kind of pattern which is
+
+ align:start position:0%
+he has some kind of pattern which is
+ 
+
+ align:start position:0%
+he has some kind of pattern which is
+popping out there and it is also related
+
+ align:start position:0%
+popping out there and it is also related
+ 
+
+ align:start position:0%
+popping out there and it is also related
+to interference between infinite number
+
+ align:start position:0%
+to interference between infinite number
+ 
+
+ align:start position:0%
+to interference between infinite number
+of source okay and you can see that the
+
+ align:start position:0%
+of source okay and you can see that the
+ 
+
+ align:start position:0%
+of source okay and you can see that the
+the the pattern seems to really pretty
+
+ align:start position:0%
+the the pattern seems to really pretty
+ 
+
+ align:start position:0%
+the the pattern seems to really pretty
+similar to the pattern we see in the
+
+ align:start position:0%
+similar to the pattern we see in the
+ 
+
+ align:start position:0%
+similar to the pattern we see in the
+upper demo except that the upper demo
+
+ align:start position:0%
+upper demo except that the upper demo
+ 
+
+ align:start position:0%
+upper demo except that the upper demo
+have individual small structure which is
+
+ align:start position:0%
+have individual small structure which is
+ 
+
+ align:start position:0%
+have individual small structure which is
+actually the principal Maxima from the
+
+ align:start position:0%
+actually the principal Maxima from the
+ 
+
+ align:start position:0%
+actually the principal Maxima from the
+two slit interference and we are going
+
+ align:start position:0%
+two slit interference and we are going
+ 
+
+ align:start position:0%
+two slit interference and we are going
+to solve the mystery in the lecture next
+
+ align:start position:0%
+to solve the mystery in the lecture next
+ 
+
+ align:start position:0%
+to solve the mystery in the lecture next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so thank you very much and if you
+
+ align:start position:0%
+okay so thank you very much and if you
+ 
+
+ align:start position:0%
+okay so thank you very much and if you
+have any questions related to the
+
+ align:start position:0%
+have any questions related to the
+ 
+
+ align:start position:0%
+have any questions related to the
+lecture today I will be here to answer
+
+ align:start position:0%
+lecture today I will be here to answer
+ 
+
+ align:start position:0%
+lecture today I will be here to answer
+your question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a demo which we would like to
+
+ align:start position:0%
+so this is a demo which we would like to
+ 
+
+ align:start position:0%
+so this is a demo which we would like to
+show you single sleet and the top of the
+
+ align:start position:0%
+show you single sleet and the top of the
+ 
+
+ align:start position:0%
+show you single sleet and the top of the
+interference pattern okay so the the
+
+ align:start position:0%
+interference pattern okay so the the
+ 
+
+ align:start position:0%
+interference pattern okay so the the
+first scene is the setup so we have a
+
+ align:start position:0%
+first scene is the setup so we have a
+ 
+
+ align:start position:0%
+first scene is the setup so we have a
+laser beam which is actually passing
+
+ align:start position:0%
+laser beam which is actually passing
+ 
+
+ align:start position:0%
+laser beam which is actually passing
+through this this either singly or top
+
+ align:start position:0%
+through this this either singly or top
+ 
+
+ align:start position:0%
+through this this either singly or top
+of the screen and single Co double slit
+
+ align:start position:0%
+of the screen and single Co double slit
+ 
+
+ align:start position:0%
+of the screen and single Co double slit
+experiment and then the laser beam will
+
+ align:start position:0%
+experiment and then the laser beam will
+ 
+
+ align:start position:0%
+experiment and then the laser beam will
+be going through this and interfere and
+
+ align:start position:0%
+be going through this and interfere and
+ 
+
+ align:start position:0%
+be going through this and interfere and
+so interesting pattern and screen and
+
+ align:start position:0%
+so interesting pattern and screen and
+ 
+
+ align:start position:0%
+so interesting pattern and screen and
+there are to set up the lava inside one
+
+ align:start position:0%
+there are to set up the lava inside one
+ 
+
+ align:start position:0%
+there are to set up the lava inside one
+is too sweet interference experiment and
+
+ align:start position:0%
+is too sweet interference experiment and
+ 
+
+ align:start position:0%
+is too sweet interference experiment and
+right hand side is a single slit into
+
+ align:start position:0%
+right hand side is a single slit into
+ 
+
+ align:start position:0%
+right hand side is a single slit into
+diffraction experiment so you can see
+
+ align:start position:0%
+diffraction experiment so you can see
+ 
+
+ align:start position:0%
+diffraction experiment so you can see
+laughs and say one I already turned it
+
+ align:start position:0%
+laughs and say one I already turned it
+ 
+
+ align:start position:0%
+laughs and say one I already turned it
+down the laser beam pass through to
+
+ align:start position:0%
+down the laser beam pass through to
+ 
+
+ align:start position:0%
+down the laser beam pass through to
+sleet and they form company to
+
+ align:start position:0%
+sleet and they form company to
+ 
+
+ align:start position:0%
+sleet and they form company to
+complicated pattern on the screen and
+
+ align:start position:0%
+complicated pattern on the screen and
+ 
+
+ align:start position:0%
+complicated pattern on the screen and
+you can see there are two kinds of
+
+ align:start position:0%
+you can see there are two kinds of
+ 
+
+ align:start position:0%
+you can see there are two kinds of
+structure here the first one is the very
+
+ align:start position:0%
+structure here the first one is the very
+ 
+
+ align:start position:0%
+structure here the first one is the very
+fine structure where you can see that
+
+ align:start position:0%
+fine structure where you can see that
+ 
+
+ align:start position:0%
+fine structure where you can see that
+it's like several dots you know in the
+
+ align:start position:0%
+it's like several dots you know in the
+ 
+
+ align:start position:0%
+it's like several dots you know in the
+in the in the center of the pattern and
+
+ align:start position:0%
+in the in the center of the pattern and
+ 
+
+ align:start position:0%
+in the in the center of the pattern and
+there are larger scale pattern as well
+
+ align:start position:0%
+there are larger scale pattern as well
+ 
+
+ align:start position:0%
+there are larger scale pattern as well
+which you can see that the overall
+
+ align:start position:0%
+which you can see that the overall
+ 
+
+ align:start position:0%
+which you can see that the overall
+intensity of all those little dots are
+
+ align:start position:0%
+intensity of all those little dots are
+ 
+
+ align:start position:0%
+intensity of all those little dots are
+also very thin as a function of distance
+
+ align:start position:0%
+also very thin as a function of distance
+ 
+
+ align:start position:0%
+also very thin as a function of distance
+with respect to the same center
+
+ align:start position:0%
+with respect to the same center
+ 
+
+ align:start position:0%
+with respect to the same center
+so the during the lecture when wondering
+
+ align:start position:0%
+so the during the lecture when wondering
+ 
+
+ align:start position:0%
+so the during the lecture when wondering
+what actually caused this kind of
+
+ align:start position:0%
+what actually caused this kind of
+ 
+
+ align:start position:0%
+what actually caused this kind of
+pattern and the answer is that this is
+
+ align:start position:0%
+pattern and the answer is that this is
+ 
+
+ align:start position:0%
+pattern and the answer is that this is
+action coming from the effect of single
+
+ align:start position:0%
+action coming from the effect of single
+ 
+
+ align:start position:0%
+action coming from the effect of single
+slit interference that the reason why we
+
+ align:start position:0%
+slit interference that the reason why we
+ 
+
+ align:start position:0%
+slit interference that the reason why we
+have this pattern is because the the to
+
+ align:start position:0%
+have this pattern is because the the to
+ 
+
+ align:start position:0%
+have this pattern is because the the to
+sleet is actually not infinitely narrow
+
+ align:start position:0%
+sleet is actually not infinitely narrow
+ 
+
+ align:start position:0%
+sleet is actually not infinitely narrow
+in my setup therefore within a single
+
+ align:start position:0%
+in my setup therefore within a single
+ 
+
+ align:start position:0%
+in my setup therefore within a single
+studied there is already interference
+
+ align:start position:0%
+studied there is already interference
+ 
+
+ align:start position:0%
+studied there is already interference
+pattern are coming out of it
+
+ align:start position:0%
+pattern are coming out of it
+ 
+
+ align:start position:0%
+pattern are coming out of it
+therefore the compound in fact results
+
+ align:start position:0%
+therefore the compound in fact results
+ 
+
+ align:start position:0%
+therefore the compound in fact results
+in a break
+
+ align:start position:0%
+in a break
+ 
+
+ align:start position:0%
+in a break
+Katie structure we see on the screen so
+
+ align:start position:0%
+Katie structure we see on the screen so
+ 
+
+ align:start position:0%
+Katie structure we see on the screen so
+to demonstrate this in fact now I'm
+
+ align:start position:0%
+to demonstrate this in fact now I'm
+ 
+
+ align:start position:0%
+to demonstrate this in fact now I'm
+going to turn on the right hand side set
+
+ align:start position:0%
+going to turn on the right hand side set
+ 
+
+ align:start position:0%
+going to turn on the right hand side set
+up in the right hands I said that I am
+
+ align:start position:0%
+up in the right hands I said that I am
+ 
+
+ align:start position:0%
+up in the right hands I said that I am
+going to have the laser beam which is
+
+ align:start position:0%
+going to have the laser beam which is
+ 
+
+ align:start position:0%
+going to have the laser beam which is
+emitting from here pass through a single
+
+ align:start position:0%
+emitting from here pass through a single
+ 
+
+ align:start position:0%
+emitting from here pass through a single
+sleeve which have happened engineer
+
+ align:start position:0%
+sleeve which have happened engineer
+ 
+
+ align:start position:0%
+sleeve which have happened engineer
+setting up so that they have the same
+
+ align:start position:0%
+setting up so that they have the same
+ 
+
+ align:start position:0%
+setting up so that they have the same
+width between the single slit experiment
+
+ align:start position:0%
+width between the single slit experiment
+ 
+
+ align:start position:0%
+width between the single slit experiment
+and double slit experiment and then you
+
+ align:start position:0%
+and double slit experiment and then you
+ 
+
+ align:start position:0%
+and double slit experiment and then you
+can see after I turn it down after I
+
+ align:start position:0%
+can see after I turn it down after I
+ 
+
+ align:start position:0%
+can see after I turn it down after I
+turn it on you can see that now we have
+
+ align:start position:0%
+turn it on you can see that now we have
+ 
+
+ align:start position:0%
+turn it on you can see that now we have
+two sets of pattern the lower set
+
+ align:start position:0%
+two sets of pattern the lower set
+ 
+
+ align:start position:0%
+two sets of pattern the lower set
+essentially are coming from a single
+
+ align:start position:0%
+essentially are coming from a single
+ 
+
+ align:start position:0%
+essentially are coming from a single
+slit interference experiment and you can
+
+ align:start position:0%
+slit interference experiment and you can
+ 
+
+ align:start position:0%
+slit interference experiment and you can
+see very nicely that first of all it has
+
+ align:start position:0%
+see very nicely that first of all it has
+ 
+
+ align:start position:0%
+see very nicely that first of all it has
+a similar pattern like what we see in
+
+ align:start position:0%
+a similar pattern like what we see in
+ 
+
+ align:start position:0%
+a similar pattern like what we see in
+the double slit experiment secondly you
+
+ align:start position:0%
+the double slit experiment secondly you
+ 
+
+ align:start position:0%
+the double slit experiment secondly you
+can see that basically we carefully tune
+
+ align:start position:0%
+can see that basically we carefully tune
+ 
+
+ align:start position:0%
+can see that basically we carefully tune
+these two experiments so that the
+
+ align:start position:0%
+these two experiments so that the
+ 
+
+ align:start position:0%
+these two experiments so that the
+distance between the sleet and the
+
+ align:start position:0%
+distance between the sleet and the
+ 
+
+ align:start position:0%
+distance between the sleet and the
+screen is roughly the same finally we
+
+ align:start position:0%
+screen is roughly the same finally we
+ 
+
+ align:start position:0%
+screen is roughly the same finally we
+also set it up as I mentioned before
+
+ align:start position:0%
+also set it up as I mentioned before
+ 
+
+ align:start position:0%
+also set it up as I mentioned before
+such that the width of the individual
+
+ align:start position:0%
+such that the width of the individual
+ 
+
+ align:start position:0%
+such that the width of the individual
+sleet in the double slit and a single
+
+ align:start position:0%
+sleet in the double slit and a single
+ 
+
+ align:start position:0%
+sleet in the double slit and a single
+experiment understand and you can see
+
+ align:start position:0%
+experiment understand and you can see
+ 
+
+ align:start position:0%
+experiment understand and you can see
+that with single slit experiment we also
+
+ align:start position:0%
+that with single slit experiment we also
+ 
+
+ align:start position:0%
+that with single slit experiment we also
+see a very similar pattern that you have
+
+ align:start position:0%
+see a very similar pattern that you have
+ 
+
+ align:start position:0%
+see a very similar pattern that you have
+a central maxima you have a high
+
+ align:start position:0%
+a central maxima you have a high
+ 
+
+ align:start position:0%
+a central maxima you have a high
+intensity light going toward the central
+
+ align:start position:0%
+intensity light going toward the central
+ 
+
+ align:start position:0%
+intensity light going toward the central
+of the going to go in toward the center
+
+ align:start position:0%
+of the going to go in toward the center
+ 
+
+ align:start position:0%
+of the going to go in toward the center
+of the pattern and the intensity HD
+
+ align:start position:0%
+of the pattern and the intensity HD
+ 
+
+ align:start position:0%
+of the pattern and the intensity HD
+decrease dramatically really quickly as
+
+ align:start position:0%
+decrease dramatically really quickly as
+ 
+
+ align:start position:0%
+decrease dramatically really quickly as
+a function of distance and also you can
+
+ align:start position:0%
+a function of distance and also you can
+ 
+
+ align:start position:0%
+a function of distance and also you can
+see that the pattern a she matches with
+
+ align:start position:0%
+see that the pattern a she matches with
+ 
+
+ align:start position:0%
+see that the pattern a she matches with
+what you see in the double slit
+
+ align:start position:0%
+what you see in the double slit
+ 
+
+ align:start position:0%
+what you see in the double slit
+experiment very well and that is
+
+ align:start position:0%
+experiment very well and that is
+ 
+
+ align:start position:0%
+experiment very well and that is
+actually pretty remarkable and
+
+ align:start position:0%
+actually pretty remarkable and
+ 
+
+ align:start position:0%
+actually pretty remarkable and
+the front is to experiment we understand
+
+ align:start position:0%
+the front is to experiment we understand
+ 
+
+ align:start position:0%
+the front is to experiment we understand
+why we have also complicated structure
+
+ align:start position:0%
+why we have also complicated structure
+ 
+
+ align:start position:0%
+why we have also complicated structure
+in the double slit experiment not just
+
+ align:start position:0%
+in the double slit experiment not just
+ 
+
+ align:start position:0%
+in the double slit experiment not just
+like many many little Maximas many many
+
+ align:start position:0%
+like many many little Maximas many many
+ 
+
+ align:start position:0%
+like many many little Maximas many many
+little dots but also you have this
+
+ align:start position:0%
+little dots but also you have this
+ 
+
+ align:start position:0%
+little dots but also you have this
+overall modulation in the in the light
+
+ align:start position:0%
+overall modulation in the in the light
+ 
+
+ align:start position:0%
+overall modulation in the in the light
+intensity and that decision mainly
+
+ align:start position:0%
+intensity and that decision mainly
+ 
+
+ align:start position:0%
+intensity and that decision mainly
+coming from the single slit diffraction
+
+ align:start position:0%
+coming from the single slit diffraction
+ 
+
+ align:start position:0%
+coming from the single slit diffraction
+pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/nOb_iQjTy-Q.txt b/nOb_iQjTy-Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a12eb413ebd41b19241130ff5f94fb873c6df3d5
--- /dev/null
+++ b/nOb_iQjTy-Q.txt
@@ -0,0 +1,123 @@
+align:start position:0%
+ 
+a o3 is a very very interesting course
+
+ align:start position:0%
+a o3 is a very very interesting course
+ 
+
+ align:start position:0%
+a o3 is a very very interesting course
+because without wave evaporation will
+
+ align:start position:0%
+because without wave evaporation will
+ 
+
+ align:start position:0%
+because without wave evaporation will
+not be able to even recognize this
+
+ align:start position:0%
+not be able to even recognize this
+ 
+
+ align:start position:0%
+not be able to even recognize this
+universe during this class I decided to
+
+ align:start position:0%
+universe during this class I decided to
+ 
+
+ align:start position:0%
+universe during this class I decided to
+include a lot of demos during my
+
+ align:start position:0%
+include a lot of demos during my
+ 
+
+ align:start position:0%
+include a lot of demos during my
+lectures demonstrations are particularly
+
+ align:start position:0%
+lectures demonstrations are particularly
+ 
+
+ align:start position:0%
+lectures demonstrations are particularly
+useful because we first introduce the
+
+ align:start position:0%
+useful because we first introduce the
+ 
+
+ align:start position:0%
+useful because we first introduce the
+physical situation we are interested
+
+ align:start position:0%
+physical situation we are interested
+ 
+
+ align:start position:0%
+physical situation we are interested
+then we compare our mathematical
+
+ align:start position:0%
+then we compare our mathematical
+ 
+
+ align:start position:0%
+then we compare our mathematical
+solution to reality which is agility
+
+ align:start position:0%
+solution to reality which is agility
+ 
+
+ align:start position:0%
+solution to reality which is agility
+mode I hope you will be able to enjoy
+
+ align:start position:0%
+mode I hope you will be able to enjoy
+ 
+
+ align:start position:0%
+mode I hope you will be able to enjoy
+this free content provided by OCW
+
+ align:start position:0%
+this free content provided by OCW
+ 
+
+ align:start position:0%
+this free content provided by OCW
+including the lecture videos the lecture
+
+ align:start position:0%
+including the lecture videos the lecture
+ 
+
+ align:start position:0%
+including the lecture videos the lecture
+notes and the province of in video from
+
+ align:start position:0%
+notes and the province of in video from
+ 
+
+ align:start position:0%
+notes and the province of in video from
+professor with Busha it's really course
+
+ align:start position:0%
+professor with Busha it's really course
+ 
+
+ align:start position:0%
+professor with Busha it's really course
+you take the course
\ No newline at end of file
diff --git a/nSPZP92vWsE.txt b/nSPZP92vWsE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17d05f2477ba7ebc70c639c81f517b334ce4292f
--- /dev/null
+++ b/nSPZP92vWsE.txt
@@ -0,0 +1,851 @@
+align:start position:0%
+ 
+hi this is richard again and change of
+
+ align:start position:0%
+hi this is richard again and change of
+ 
+
+ align:start position:0%
+hi this is richard again and change of
+pace now from the sequence i'm going to
+
+ align:start position:0%
+pace now from the sequence i'm going to
+ 
+
+ align:start position:0%
+pace now from the sequence i'm going to
+be talking about something called the
+
+ align:start position:0%
+be talking about something called the
+ 
+
+ align:start position:0%
+be talking about something called the
+flaw of averages
+
+ align:start position:0%
+flaw of averages
+ 
+
+ align:start position:0%
+flaw of averages
+what is this
+
+ align:start position:0%
+what is this
+ 
+
+ align:start position:0%
+what is this
+it's a fundamental problem in the design
+
+ align:start position:0%
+it's a fundamental problem in the design
+ 
+
+ align:start position:0%
+it's a fundamental problem in the design
+and evaluating of projects
+
+ align:start position:0%
+and evaluating of projects
+ 
+
+ align:start position:0%
+and evaluating of projects
+and i'm going to take some time to
+
+ align:start position:0%
+and i'm going to take some time to
+ 
+
+ align:start position:0%
+and i'm going to take some time to
+explain it to you and then in the
+
+ align:start position:0%
+explain it to you and then in the
+ 
+
+ align:start position:0%
+explain it to you and then in the
+following session to talk about what its
+
+ align:start position:0%
+following session to talk about what its
+ 
+
+ align:start position:0%
+following session to talk about what its
+implications are
+
+ align:start position:0%
+implications are
+ 
+
+ align:start position:0%
+implications are
+so the flaw consists of or is the
+
+ align:start position:0%
+so the flaw consists of or is the
+ 
+
+ align:start position:0%
+so the flaw consists of or is the
+pattern of designing evaluating projects
+
+ align:start position:0%
+pattern of designing evaluating projects
+ 
+
+ align:start position:0%
+pattern of designing evaluating projects
+based on the average or most likely
+
+ align:start position:0%
+based on the average or most likely
+ 
+
+ align:start position:0%
+based on the average or most likely
+future forecast that is of thinking that
+
+ align:start position:0%
+future forecast that is of thinking that
+ 
+
+ align:start position:0%
+future forecast that is of thinking that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+here's what the forecast is going to be
+
+ align:start position:0%
+here's what the forecast is going to be
+ 
+
+ align:start position:0%
+here's what the forecast is going to be
+or here is our best guess at the
+
+ align:start position:0%
+or here is our best guess at the
+ 
+
+ align:start position:0%
+or here is our best guess at the
+forecast we know it's wrong you've told
+
+ align:start position:0%
+forecast we know it's wrong you've told
+ 
+
+ align:start position:0%
+forecast we know it's wrong you've told
+us so but we're still going to
+
+ align:start position:0%
+us so but we're still going to
+ 
+
+ align:start position:0%
+us so but we're still going to
+analyze it based upon one forecast
+
+ align:start position:0%
+analyze it based upon one forecast
+ 
+
+ align:start position:0%
+analyze it based upon one forecast
+then what often happens is that people
+
+ align:start position:0%
+then what often happens is that people
+ 
+
+ align:start position:0%
+then what often happens is that people
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+take some variation around it plus or
+
+ align:start position:0%
+take some variation around it plus or
+ 
+
+ align:start position:0%
+take some variation around it plus or
+minus 10 say but the fundamental choice
+
+ align:start position:0%
+minus 10 say but the fundamental choice
+ 
+
+ align:start position:0%
+minus 10 say but the fundamental choice
+is that they're
+
+ align:start position:0%
+is that they're
+ 
+
+ align:start position:0%
+is that they're
+looking at it from an average or a
+
+ align:start position:0%
+looking at it from an average or a
+ 
+
+ align:start position:0%
+looking at it from an average or a
+projected
+
+ align:start position:0%
+projected
+ 
+
+ align:start position:0%
+projected
+now what happens is that there is a
+
+ align:start position:0%
+now what happens is that there is a
+ 
+
+ align:start position:0%
+now what happens is that there is a
+fundamental misunderstanding of
+
+ align:start position:0%
+fundamental misunderstanding of
+ 
+
+ align:start position:0%
+fundamental misunderstanding of
+probability and systems behavior when
+
+ align:start position:0%
+probability and systems behavior when
+ 
+
+ align:start position:0%
+probability and systems behavior when
+you do that
+
+ align:start position:0%
+you do that
+ 
+
+ align:start position:0%
+you do that
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me explain the name
+
+ align:start position:0%
+let me explain the name
+ 
+
+ align:start position:0%
+let me explain the name
+it's a pun by somebody sam savage's who
+
+ align:start position:0%
+it's a pun by somebody sam savage's who
+ 
+
+ align:start position:0%
+it's a pun by somebody sam savage's who
+wrote the book in fact called flaw of
+
+ align:start position:0%
+wrote the book in fact called flaw of
+ 
+
+ align:start position:0%
+wrote the book in fact called flaw of
+averages
+
+ align:start position:0%
+averages
+ 
+
+ align:start position:0%
+averages
+it integrates two concepts first concept
+
+ align:start position:0%
+it integrates two concepts first concept
+ 
+
+ align:start position:0%
+it integrates two concepts first concept
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+there is a mistake a flaw
+
+ align:start position:0%
+there is a mistake a flaw
+ 
+
+ align:start position:0%
+there is a mistake a flaw
+f l a w
+
+ align:start position:0%
+f l a w
+ 
+
+ align:start position:0%
+f l a w
+flaw
+
+ align:start position:0%
+flaw
+ 
+
+ align:start position:0%
+flaw
+and it combines that with the concept of
+
+ align:start position:0%
+and it combines that with the concept of
+ 
+
+ align:start position:0%
+and it combines that with the concept of
+the law of averages that means that
+
+ align:start position:0%
+the law of averages that means that
+ 
+
+ align:start position:0%
+the law of averages that means that
+basically things work out on the
+
+ align:start position:0%
+basically things work out on the
+ 
+
+ align:start position:0%
+basically things work out on the
+averages that the pluses balance the
+
+ align:start position:0%
+averages that the pluses balance the
+ 
+
+ align:start position:0%
+averages that the pluses balance the
+minuses and everything works out so that
+
+ align:start position:0%
+minuses and everything works out so that
+ 
+
+ align:start position:0%
+minuses and everything works out so that
+if you design around the average you'll
+
+ align:start position:0%
+if you design around the average you'll
+ 
+
+ align:start position:0%
+if you design around the average you'll
+be okay
+
+ align:start position:0%
+be okay
+ 
+
+ align:start position:0%
+be okay
+that is not correct
+
+ align:start position:0%
+that is not correct
+ 
+
+ align:start position:0%
+that is not correct
+the error
+
+ align:start position:0%
+the error
+ 
+
+ align:start position:0%
+the error
+consists in general of assuming that the
+
+ align:start position:0%
+consists in general of assuming that the
+ 
+
+ align:start position:0%
+consists in general of assuming that the
+analysis based upon average or most like
+
+ align:start position:0%
+analysis based upon average or most like
+ 
+
+ align:start position:0%
+analysis based upon average or most like
+conditions give correct answers this is
+
+ align:start position:0%
+conditions give correct answers this is
+ 
+
+ align:start position:0%
+conditions give correct answers this is
+wrong it's fundamentally wrong and it's
+
+ align:start position:0%
+wrong it's fundamentally wrong and it's
+ 
+
+ align:start position:0%
+wrong it's fundamentally wrong and it's
+not a new discovery it's a very old uh
+
+ align:start position:0%
+not a new discovery it's a very old uh
+ 
+
+ align:start position:0%
+not a new discovery it's a very old uh
+mathematical uh fact
+
+ align:start position:0%
+mathematical uh fact
+ 
+
+ align:start position:0%
+mathematical uh fact
+it's called jensen's law i don't know
+
+ align:start position:0%
+it's called jensen's law i don't know
+ 
+
+ align:start position:0%
+it's called jensen's law i don't know
+why i suppose that somehow
+
+ align:start position:0%
+why i suppose that somehow
+ 
+
+ align:start position:0%
+why i suppose that somehow
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+articulated it but all it says is
+
+ align:start position:0%
+articulated it but all it says is
+ 
+
+ align:start position:0%
+articulated it but all it says is
+that the expected value of something
+
+ align:start position:0%
+that the expected value of something
+ 
+
+ align:start position:0%
+that the expected value of something
+that's variable the expected value of
+
+ align:start position:0%
+that's variable the expected value of
+ 
+
+ align:start position:0%
+that's variable the expected value of
+a function
+
+ align:start position:0%
+a function
+ 
+
+ align:start position:0%
+a function
+that is say the profit from a uh
+
+ align:start position:0%
+that is say the profit from a uh
+ 
+
+ align:start position:0%
+that is say the profit from a uh
+a project or its net present value or
+
+ align:start position:0%
+a project or its net present value or
+ 
+
+ align:start position:0%
+a project or its net present value or
+some measure of goodness
+
+ align:start position:0%
+some measure of goodness
+ 
+
+ align:start position:0%
+some measure of goodness
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+not equal
+
+ align:start position:0%
+not equal
+ 
+
+ align:start position:0%
+not equal
+to that function evaluated using an
+
+ align:start position:0%
+to that function evaluated using an
+ 
+
+ align:start position:0%
+to that function evaluated using an
+expected value
+
+ align:start position:0%
+expected value
+ 
+
+ align:start position:0%
+expected value
+in detail that says if it's a convex
+
+ align:start position:0%
+in detail that says if it's a convex
+ 
+
+ align:start position:0%
+in detail that says if it's a convex
+function but in general it is it applies
+
+ align:start position:0%
+function but in general it is it applies
+ 
+
+ align:start position:0%
+function but in general it is it applies
+in all cases
+
+ align:start position:0%
+in all cases
+ 
+
+ align:start position:0%
+in all cases
+so all practical cases so what it says
+
+ align:start position:0%
+so all practical cases so what it says
+ 
+
+ align:start position:0%
+so all practical cases so what it says
+is if you really want to know the
+
+ align:start position:0%
+is if you really want to know the
+ 
+
+ align:start position:0%
+is if you really want to know the
+average value the expected value of
+
+ align:start position:0%
+average value the expected value of
+ 
+
+ align:start position:0%
+average value the expected value of
+something you cannot do it around the
+
+ align:start position:0%
+something you cannot do it around the
+ 
+
+ align:start position:0%
+something you cannot do it around the
+looking at evaluating it at its most
+
+ align:start position:0%
+looking at evaluating it at its most
+ 
+
+ align:start position:0%
+looking at evaluating it at its most
+likely or average or most probable uh
+
+ align:start position:0%
+likely or average or most probable uh
+ 
+
+ align:start position:0%
+likely or average or most probable uh
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+and for the notation the e of x simply
+
+ align:start position:0%
+and for the notation the e of x simply
+ 
+
+ align:start position:0%
+and for the notation the e of x simply
+means it's the arithmetical average or
+
+ align:start position:0%
+means it's the arithmetical average or
+ 
+
+ align:start position:0%
+means it's the arithmetical average or
+expectation of that
+
+ align:start position:0%
+expectation of that
+ 
+
+ align:start position:0%
+expectation of that
+and in words we're talking about that
+
+ align:start position:0%
+and in words we're talking about that
+ 
+
+ align:start position:0%
+and in words we're talking about that
+the average of all possible outcomes
+
+ align:start position:0%
+the average of all possible outcomes
+ 
+
+ align:start position:0%
+the average of all possible outcomes
+that is what's on the left-hand side
+
+ align:start position:0%
+that is what's on the left-hand side
+ 
+
+ align:start position:0%
+that is what's on the left-hand side
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is not equal to the outcome calculated
+
+ align:start position:0%
+is not equal to the outcome calculated
+ 
+
+ align:start position:0%
+is not equal to the outcome calculated
+by using the average value
+
+ align:start position:0%
+by using the average value
+ 
+
+ align:start position:0%
+by using the average value
+very simple
+
+ align:start position:0%
+very simple
+ 
+
+ align:start position:0%
+very simple
+concept that is
+
+ align:start position:0%
+concept that is
+ 
+
+ align:start position:0%
+concept that is
+put another way that if you really want
+
+ align:start position:0%
+put another way that if you really want
+ 
+
+ align:start position:0%
+put another way that if you really want
+to get the right value you can't
+
+ align:start position:0%
+to get the right value you can't
+ 
+
+ align:start position:0%
+to get the right value you can't
+evaluate it around some most likely or
+
+ align:start position:0%
+evaluate it around some most likely or
+ 
+
+ align:start position:0%
+evaluate it around some most likely or
+most probable or average or median
+
+ align:start position:0%
+most probable or average or median
+ 
+
+ align:start position:0%
+most probable or average or median
+forecast you have to look at the whole
+
+ align:start position:0%
+forecast you have to look at the whole
+ 
+
+ align:start position:0%
+forecast you have to look at the whole
+distribution or some approximation of
+
+ align:start position:0%
+distribution or some approximation of
+ 
+
+ align:start position:0%
+distribution or some approximation of
+the whole
+
+ align:start position:0%
+the whole
+ 
+
+ align:start position:0%
+the whole
+distribution so in words the flaw of
+
+ align:start position:0%
+distribution so in words the flaw of
+ 
+
+ align:start position:0%
+distribution so in words the flaw of
+averages is
+
+ align:start position:0%
+averages is
+ 
+
+ align:start position:0%
+averages is
+the average of all possible outcome
+
+ align:start position:0%
+the average of all possible outcome
+ 
+
+ align:start position:0%
+the average of all possible outcome
+associated with uncertain parameters
+
+ align:start position:0%
+associated with uncertain parameters
+ 
+
+ align:start position:0%
+associated with uncertain parameters
+generally does not equal
+
+ align:start position:0%
+generally does not equal
+ 
+
+ align:start position:0%
+generally does not equal
+the value obtained from using the
+
+ align:start position:0%
+the value obtained from using the
+ 
+
+ align:start position:0%
+the value obtained from using the
+average value of the parameters that's
+
+ align:start position:0%
+average value of the parameters that's
+ 
+
+ align:start position:0%
+average value of the parameters that's
+the flaw of averages in words
\ No newline at end of file
diff --git a/nnssRe5DewE.txt b/nnssRe5DewE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..90874b977ad98d233228e5ee93866d727eb044fc
--- /dev/null
+++ b/nnssRe5DewE.txt
@@ -0,0 +1,1875 @@
+align:start position:0%
+ 
+hi everyone welcome back so today I'd
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+ 
+
+ align:start position:0%
+hi everyone welcome back so today I'd
+like to tackle a problem in Markov
+
+ align:start position:0%
+like to tackle a problem in Markov
+ 
+
+ align:start position:0%
+like to tackle a problem in Markov
+matrices specifically uh we're going to
+
+ align:start position:0%
+matrices specifically uh we're going to
+ 
+
+ align:start position:0%
+matrices specifically uh we're going to
+start with this problem which almost has
+
+ align:start position:0%
+start with this problem which almost has
+ 
+
+ align:start position:0%
+start with this problem which almost has
+a physics origin if we have a particle
+
+ align:start position:0%
+a physics origin if we have a particle
+ 
+
+ align:start position:0%
+a physics origin if we have a particle
+that jumps between positions A and B uh
+
+ align:start position:0%
+that jumps between positions A and B uh
+ 
+
+ align:start position:0%
+that jumps between positions A and B uh
+with the following probabilities I'll
+
+ align:start position:0%
+with the following probabilities I'll
+ 
+
+ align:start position:0%
+with the following probabilities I'll
+just state it if it starts at a and
+
+ align:start position:0%
+just state it if it starts at a and
+ 
+
+ align:start position:0%
+just state it if it starts at a and
+jumps to B with probability 0.4 or it
+
+ align:start position:0%
+jumps to B with probability 0.4 or it
+ 
+
+ align:start position:0%
+jumps to B with probability 0.4 or it
+starts at a and stays at a with
+
+ align:start position:0%
+starts at a and stays at a with
+ 
+
+ align:start position:0%
+starts at a and stays at a with
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+0.6 or if it starts at B then it goes to
+
+ align:start position:0%
+0.6 or if it starts at B then it goes to
+ 
+
+ align:start position:0%
+0.6 or if it starts at B then it goes to
+a with probability 0.2 or stays at B
+
+ align:start position:0%
+a with probability 0.2 or stays at B
+ 
+
+ align:start position:0%
+a with probability 0.2 or stays at B
+with probability
+
+ align:start position:0%
+with probability
+ 
+
+ align:start position:0%
+with probability
+0.8 we'd like to know the evolution of
+
+ align:start position:0%
+0.8 we'd like to know the evolution of
+ 
+
+ align:start position:0%
+0.8 we'd like to know the evolution of
+the probability of this particle over a
+
+ align:start position:0%
+the probability of this particle over a
+ 
+
+ align:start position:0%
+the probability of this particle over a
+long period of time so specifically the
+
+ align:start position:0%
+long period of time so specifically the
+ 
+
+ align:start position:0%
+long period of time so specifically the
+problem we're interested today is if we
+
+ align:start position:0%
+problem we're interested today is if we
+ 
+
+ align:start position:0%
+problem we're interested today is if we
+have a particle and we know that it
+
+ align:start position:0%
+have a particle and we know that it
+ 
+
+ align:start position:0%
+have a particle and we know that it
+starts at position a what is the
+
+ align:start position:0%
+starts at position a what is the
+ 
+
+ align:start position:0%
+starts at position a what is the
+probability that it is at position a and
+
+ align:start position:0%
+probability that it is at position a and
+ 
+
+ align:start position:0%
+probability that it is at position a and
+the probability that it's at position B
+
+ align:start position:0%
+the probability that it's at position B
+ 
+
+ align:start position:0%
+the probability that it's at position B
+after one step after after end steps and
+
+ align:start position:0%
+after one step after after end steps and
+ 
+
+ align:start position:0%
+after one step after after end steps and
+then finally after an infinite number of
+
+ align:start position:0%
+then finally after an infinite number of
+ 
+
+ align:start position:0%
+then finally after an infinite number of
+steps so I'll let you think about this
+
+ align:start position:0%
+steps so I'll let you think about this
+ 
+
+ align:start position:0%
+steps so I'll let you think about this
+problem for a moment and I'll be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back hi everyone welcome back so the
+
+ align:start position:0%
+back hi everyone welcome back so the
+ 
+
+ align:start position:0%
+back hi everyone welcome back so the
+main difficulty with this
+
+ align:start position:0%
+main difficulty with this
+ 
+
+ align:start position:0%
+main difficulty with this
+problem is that it's phrased as a
+
+ align:start position:0%
+problem is that it's phrased as a
+ 
+
+ align:start position:0%
+problem is that it's phrased as a
+physics problem and we need to convert
+
+ align:start position:0%
+physics problem and we need to convert
+ 
+
+ align:start position:0%
+physics problem and we need to convert
+it into some mathematical language to
+
+ align:start position:0%
+it into some mathematical language to
+ 
+
+ align:start position:0%
+it into some mathematical language to
+get a handle on it so specifically what
+
+ align:start position:0%
+get a handle on it so specifically what
+ 
+
+ align:start position:0%
+get a handle on it so specifically what
+we'd like to do is to convert this into
+
+ align:start position:0%
+we'd like to do is to convert this into
+ 
+
+ align:start position:0%
+we'd like to do is to convert this into
+a matrix
+
+ align:start position:0%
+a matrix
+ 
+
+ align:start position:0%
+a matrix
+formalism so what we can do is we can
+
+ align:start position:0%
+formalism so what we can do is we can
+ 
+
+ align:start position:0%
+formalism so what we can do is we can
+write this little graph
+
+ align:start position:0%
+write this little graph
+ 
+
+ align:start position:0%
+write this little graph
+down and describe everything in this
+
+ align:start position:0%
+down and describe everything in this
+ 
+
+ align:start position:0%
+down and describe everything in this
+graph using a
+
+ align:start position:0%
+graph using a
+ 
+
+ align:start position:0%
+graph using a
+matrix so I'm going to call this Matrix
+
+ align:start position:0%
+matrix so I'm going to call this Matrix
+ 
+
+ align:start position:0%
+matrix so I'm going to call this Matrix
+a and I'm going to
+
+ align:start position:0%
+a and I'm going to
+ 
+
+ align:start position:0%
+a and I'm going to
+associate the first row of a with
+
+ align:start position:0%
+associate the first row of a with
+ 
+
+ align:start position:0%
+associate the first row of a with
+particle position a and particle
+
+ align:start position:0%
+particle position a and particle
+ 
+
+ align:start position:0%
+particle position a and particle
+position B and I'll associate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first and second
+
+ align:start position:0%
+the first and second
+ 
+
+ align:start position:0%
+the first and second
+columns with particles positions A and B
+
+ align:start position:0%
+columns with particles positions A and B
+ 
+
+ align:start position:0%
+columns with particles positions A and B
+and then what I'm going to do is I'm
+
+ align:start position:0%
+and then what I'm going to do is I'm
+ 
+
+ align:start position:0%
+and then what I'm going to do is I'm
+going to fill in this Matrix with the
+
+ align:start position:0%
+going to fill in this Matrix with the
+ 
+
+ align:start position:0%
+going to fill in this Matrix with the
+probability uh distributions so
+
+ align:start position:0%
+probability uh distributions so
+ 
+
+ align:start position:0%
+probability uh distributions so
+specifically what's going to go in this
+
+ align:start position:0%
+specifically what's going to go in this
+ 
+
+ align:start position:0%
+specifically what's going to go in this
+top left corner well the number uh
+
+ align:start position:0%
+top left corner well the number uh
+ 
+
+ align:start position:0%
+top left corner well the number uh
+0.6 which represents the probability
+
+ align:start position:0%
+0.6 which represents the probability
+ 
+
+ align:start position:0%
+0.6 which represents the probability
+that I stay at position a given that I
+
+ align:start position:0%
+that I stay at position a given that I
+ 
+
+ align:start position:0%
+that I stay at position a given that I
+start at position
+
+ align:start position:0%
+start at position
+ 
+
+ align:start position:0%
+start at position
+a with going to go here in the bottom
+
+ align:start position:0%
+a with going to go here in the bottom
+ 
+
+ align:start position:0%
+a with going to go here in the bottom
+left hand quarter well we're going to
+
+ align:start position:0%
+left hand quarter well we're going to
+ 
+
+ align:start position:0%
+left hand quarter well we're going to
+put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.4 because this is the probability that
+
+ align:start position:0%
+0.4 because this is the probability that
+ 
+
+ align:start position:0%
+0.4 because this is the probability that
+I wind up at B given that I start at
+
+ align:start position:0%
+I wind up at B given that I start at
+ 
+
+ align:start position:0%
+I wind up at B given that I start at
+a and then lastly we'll fill in these
+
+ align:start position:0%
+a and then lastly we'll fill in these
+ 
+
+ align:start position:0%
+a and then lastly we'll fill in these
+other two
+
+ align:start position:0%
+other two
+ 
+
+ align:start position:0%
+other two
+columns or the the second column with 0.
+
+ align:start position:0%
+columns or the the second column with 0.
+ 
+
+ align:start position:0%
+columns or the the second column with 0.
+a 8 and
+
+ align:start position:0%
+a 8 and
+ 
+
+ align:start position:0%
+a 8 and
+0.2 okay so I'll just State briefly this
+
+ align:start position:0%
+0.2 okay so I'll just State briefly this
+ 
+
+ align:start position:0%
+0.2 okay so I'll just State briefly this
+is what's uh called a Markov MJ Matrix
+
+ align:start position:0%
+is what's uh called a Markov MJ Matrix
+ 
+
+ align:start position:0%
+is what's uh called a Markov MJ Matrix
+and it's called marov because first off
+
+ align:start position:0%
+and it's called marov because first off
+ 
+
+ align:start position:0%
+and it's called marov because first off
+every element is positive or
+
+ align:start position:0%
+every element is positive or
+ 
+
+ align:start position:0%
+every element is positive or
+zero and secondly the sum of each uh the
+
+ align:start position:0%
+zero and secondly the sum of each uh the
+ 
+
+ align:start position:0%
+zero and secondly the sum of each uh the
+sum of the elements in each column is
+
+ align:start position:0%
+sum of the elements in each column is
+ 
+
+ align:start position:0%
+sum of the elements in each column is
+one so if we Note 4 plus 6 is 1 8 plus2
+
+ align:start position:0%
+one so if we Note 4 plus 6 is 1 8 plus2
+ 
+
+ align:start position:0%
+one so if we Note 4 plus 6 is 1 8 plus2
+is 1 and these matrices come up all the
+
+ align:start position:0%
+is 1 and these matrices come up all the
+ 
+
+ align:start position:0%
+is 1 and these matrices come up all the
+time when we're talking about
+
+ align:start position:0%
+time when we're talking about
+ 
+
+ align:start position:0%
+time when we're talking about
+probabilities and the evolution of
+
+ align:start position:0%
+probabilities and the evolution of
+ 
+
+ align:start position:0%
+probabilities and the evolution of
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distributions okay so now once we've
+
+ align:start position:0%
+distributions okay so now once we've
+ 
+
+ align:start position:0%
+distributions okay so now once we've
+encoded this graph uh using this Matrix
+
+ align:start position:0%
+encoded this graph uh using this Matrix
+ 
+
+ align:start position:0%
+encoded this graph uh using this Matrix
+a we now want to tackle this problem
+
+ align:start position:0%
+a we now want to tackle this problem
+ 
+
+ align:start position:0%
+a we now want to tackle this problem
+so I'm going to introduce uh the vector
+
+ align:start position:0%
+so I'm going to introduce uh the vector
+ 
+
+ align:start position:0%
+so I'm going to introduce uh the vector
+p and I'm going to use a subscript zero
+
+ align:start position:0%
+p and I'm going to use a subscript zero
+ 
+
+ align:start position:0%
+p and I'm going to use a subscript zero
+to denote the probability that the
+
+ align:start position:0%
+to denote the probability that the
+ 
+
+ align:start position:0%
+to denote the probability that the
+particle is at time zero so we're told
+
+ align:start position:0%
+particle is at time zero so we're told
+ 
+
+ align:start position:0%
+particle is at time zero so we're told
+that the particle starts at position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so at Time Zero I'm going to use uh
+
+ align:start position:0%
+a so at Time Zero I'm going to use uh
+ 
+
+ align:start position:0%
+a so at Time Zero I'm going to use uh
+the vector 1 Zer
+
+ align:start position:0%
+the vector 1 Zer
+ 
+
+ align:start position:0%
+the vector 1 Zer
+again I'm going to match
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the top component of this Vector with
+
+ align:start position:0%
+the top component of this Vector with
+ 
+
+ align:start position:0%
+the top component of this Vector with
+the top component of this Matrix and the
+
+ align:start position:0%
+the top component of this Matrix and the
+ 
+
+ align:start position:0%
+the top component of this Matrix and the
+first row or First Column of this Matrix
+
+ align:start position:0%
+first row or First Column of this Matrix
+ 
+
+ align:start position:0%
+first row or First Column of this Matrix
+and then likewise the second component
+
+ align:start position:0%
+and then likewise the second component
+ 
+
+ align:start position:0%
+and then likewise the second component
+of this Vector with the second uh row
+
+ align:start position:0%
+of this Vector with the second uh row
+ 
+
+ align:start position:0%
+of this Vector with the second uh row
+and second column of this
+
+ align:start position:0%
+and second column of this
+ 
+
+ align:start position:0%
+and second column of this
+Matrix and we're interested in how does
+
+ align:start position:0%
+Matrix and we're interested in how does
+ 
+
+ align:start position:0%
+Matrix and we're interested in how does
+this probability
+
+ align:start position:0%
+this probability
+ 
+
+ align:start position:0%
+this probability
+evolve uh after uh as the particle takes
+
+ align:start position:0%
+evolve uh after uh as the particle takes
+ 
+
+ align:start position:0%
+evolve uh after uh as the particle takes
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+steps so for one
+
+ align:start position:0%
+steps so for one
+ 
+
+ align:start position:0%
+steps so for one
+step for one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step what's the probability of the
+
+ align:start position:0%
+step what's the probability of the
+ 
+
+ align:start position:0%
+step what's the probability of the
+particle going to be well this is the
+
+ align:start position:0%
+particle going to be well this is the
+ 
+
+ align:start position:0%
+particle going to be well this is the
+beauty of introducing Matrix
+
+ align:start position:0%
+beauty of introducing Matrix
+ 
+
+ align:start position:0%
+beauty of introducing Matrix
+notation I'm going to denote P1 to be
+
+ align:start position:0%
+notation I'm going to denote P1 to be
+ 
+
+ align:start position:0%
+notation I'm going to denote P1 to be
+the probability of the particle after
+
+ align:start position:0%
+the probability of the particle after
+ 
+
+ align:start position:0%
+the probability of the particle after
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+step and we see that we can write this
+
+ align:start position:0%
+step and we see that we can write this
+ 
+
+ align:start position:0%
+step and we see that we can write this
+as the Matrix a multiplied by p 0 like
+
+ align:start position:0%
+as the Matrix a multiplied by p 0 like
+ 
+
+ align:start position:0%
+as the Matrix a multiplied by p 0 like
+this so the answer is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.6 and
+
+ align:start position:0%
+0.6 and
+ 
+
+ align:start position:0%
+0.6 and
+0.4 and I achiev this just by
+
+ align:start position:0%
+0.4 and I achiev this just by
+ 
+
+ align:start position:0%
+0.4 and I achiev this just by
+multiplying this matrix by this
+
+ align:start position:0%
+multiplying this matrix by this
+ 
+
+ align:start position:0%
+multiplying this matrix by this
+Vector okay so this concludes part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now part two is a little
+
+ align:start position:0%
+one now part two is a little
+ 
+
+ align:start position:0%
+one now part two is a little
+trickier so part two is end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps and to tackle this problem we need
+
+ align:start position:0%
+steps and to tackle this problem we need
+ 
+
+ align:start position:0%
+steps and to tackle this problem we need
+to use a little more machinery
+
+ align:start position:0%
+to use a little more machinery
+ 
+
+ align:start position:0%
+to use a little more machinery
+so first off I'm going to note that
+
+ align:start position:0%
+so first off I'm going to note that
+ 
+
+ align:start position:0%
+so first off I'm going to note that
+P1 is a * p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 uh likewise P2 so this is the position
+
+ align:start position:0%
+0 uh likewise P2 so this is the position
+ 
+
+ align:start position:0%
+0 uh likewise P2 so this is the position
+of the probability distribution of the
+
+ align:start position:0%
+of the probability distribution of the
+ 
+
+ align:start position:0%
+of the probability distribution of the
+particle after two steps this is a *
+
+ align:start position:0%
+particle after two steps this is a *
+ 
+
+ align:start position:0%
+particle after two steps this is a *
+P1 which is a^ 2 * p
+
+ align:start position:0%
+P1 which is a^ 2 * p
+ 
+
+ align:start position:0%
+P1 which is a^ 2 * p
+0 and we note that there's a general
+
+ align:start position:0%
+0 and we note that there's a general
+ 
+
+ align:start position:0%
+0 and we note that there's a general
+Trend after n
+
+ align:start position:0%
+Trend after n
+ 
+
+ align:start position:0%
+Trend after n
+steps so PN
+
+ align:start position:0%
+steps so PN
+ 
+
+ align:start position:0%
+steps so PN
+the general trend is it's going to be
+
+ align:start position:0%
+the general trend is it's going to be
+ 
+
+ align:start position:0%
+the general trend is it's going to be
+this Matrix a raised to the nth
+
+ align:start position:0%
+this Matrix a raised to the nth
+ 
+
+ align:start position:0%
+this Matrix a raised to the nth
+power multiplying the vector p
+
+ align:start position:0%
+power multiplying the vector p
+ 
+
+ align:start position:0%
+power multiplying the vector p
+0 so how do we take the nth power of a
+
+ align:start position:0%
+0 so how do we take the nth power of a
+ 
+
+ align:start position:0%
+0 so how do we take the nth power of a
+matrix well this is where we use I
+
+ align:start position:0%
+matrix well this is where we use I
+ 
+
+ align:start position:0%
+matrix well this is where we use I
+vectors and
+
+ align:start position:0%
+vectors and
+ 
+
+ align:start position:0%
+vectors and
+values so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall that we can take any Matrix a
+
+ align:start position:0%
+recall that we can take any Matrix a
+ 
+
+ align:start position:0%
+recall that we can take any Matrix a
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+diagonalizable and write it as U
+
+ align:start position:0%
+diagonalizable and write it as U
+ 
+
+ align:start position:0%
+diagonalizable and write it as U
+du U
+
+ align:start position:0%
+du U
+ 
+
+ align:start position:0%
+du U
+inverse where D is a diagonal matrix and
+
+ align:start position:0%
+inverse where D is a diagonal matrix and
+ 
+
+ align:start position:0%
+inverse where D is a diagonal matrix and
+this Matrix U is a matrix where uh whose
+
+ align:start position:0%
+this Matrix U is a matrix where uh whose
+ 
+
+ align:start position:0%
+this Matrix U is a matrix where uh whose
+columns correspond to the AUG vectors of
+
+ align:start position:0%
+columns correspond to the AUG vectors of
+ 
+
+ align:start position:0%
+columns correspond to the AUG vectors of
+a so for this problem I'm just going to
+
+ align:start position:0%
+a so for this problem I'm just going to
+ 
+
+ align:start position:0%
+a so for this problem I'm just going to
+State what the AUG values and a vectors
+
+ align:start position:0%
+State what the AUG values and a vectors
+ 
+
+ align:start position:0%
+State what the AUG values and a vectors
+are and I'll let you work them
+
+ align:start position:0%
+are and I'll let you work them
+ 
+
+ align:start position:0%
+are and I'll let you work them
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+so because it's a marov
+
+ align:start position:0%
+so because it's a marov
+ 
+
+ align:start position:0%
+so because it's a marov
+matrix we always have an a value which
+
+ align:start position:0%
+matrix we always have an a value which
+ 
+
+ align:start position:0%
+matrix we always have an a value which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one and in this case we have an IG
+
+ align:start position:0%
+one and in this case we have an IG
+ 
+
+ align:start position:0%
+one and in this case we have an IG
+Vector U which is one and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two in addition the second I
+
+ align:start position:0%
+two in addition the second I
+ 
+
+ align:start position:0%
+two in addition the second I
+value is
+
+ align:start position:0%
+value is
+ 
+
+ align:start position:0%
+value is
+0.4 and the a vector corresponding to
+
+ align:start position:0%
+0.4 and the a vector corresponding to
+ 
+
+ align:start position:0%
+0.4 and the a vector corresponding to
+this one is 1 minus one and I'll just
+
+ align:start position:0%
+this one is 1 minus one and I'll just
+ 
+
+ align:start position:0%
+this one is 1 minus one and I'll just
+call these U1 and U2 like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we can now write this big Matrix
+
+ align:start position:0%
+okay we can now write this big Matrix
+ 
+
+ align:start position:0%
+okay we can now write this big Matrix
+U as 1 2 1 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One D is going to be now I have to match
+
+ align:start position:0%
+One D is going to be now I have to match
+ 
+
+ align:start position:0%
+One D is going to be now I have to match
+things up if I'm going to put the first
+
+ align:start position:0%
+things up if I'm going to put the first
+ 
+
+ align:start position:0%
+things up if I'm going to put the first
+Vector in the First
+
+ align:start position:0%
+Vector in the First
+ 
+
+ align:start position:0%
+Vector in the First
+Column we have to stick one in the first
+
+ align:start position:0%
+Column we have to stick one in the first
+ 
+
+ align:start position:0%
+Column we have to stick one in the first
+uh column as well and then
+
+ align:start position:0%
+uh column as well and then
+ 
+
+ align:start position:0%
+uh column as well and then
+0.4 like
+
+ align:start position:0%
+0.4 like
+ 
+
+ align:start position:0%
+0.4 like
+this and then lastly we also have U
+
+ align:start position:0%
+this and then lastly we also have U
+ 
+
+ align:start position:0%
+this and then lastly we also have U
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+which I can just work out to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be uh minus 1/3 one over the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant uh times- one - one - 2 uh n
+
+ align:start position:0%
+determinant uh times- one - one - 2 uh n
+ 
+
+ align:start position:0%
+determinant uh times- one - one - 2 uh n
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which simplifies to this
+
+ align:start position:0%
+which simplifies to this
+ 
+
+ align:start position:0%
+which simplifies to this
+okay so now if we take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and raise it to the power of
+
+ align:start position:0%
+a and raise it to the power of
+ 
+
+ align:start position:0%
+a and raise it to the power of
+n we have this nice identity that all
+
+ align:start position:0%
+n we have this nice identity that all
+ 
+
+ align:start position:0%
+n we have this nice identity that all
+the U and U inverses collapse in the
+
+ align:start position:0%
+the U and U inverses collapse in the
+ 
+
+ align:start position:0%
+the U and U inverses collapse in the
+middle and we're left with
+
+ align:start position:0%
+middle and we're left with
+ 
+
+ align:start position:0%
+middle and we're left with
+u d to the
+
+ align:start position:0%
+u d to the
+ 
+
+ align:start position:0%
+u d to the
+n u inverse p
+
+ align:start position:0%
+n u inverse p
+ 
+
+ align:start position:0%
+n u inverse p
+0 now raising the uh a diagonal matrix
+
+ align:start position:0%
+0 now raising the uh a diagonal matrix
+ 
+
+ align:start position:0%
+0 now raising the uh a diagonal matrix
+to the power of n is a relatively simple
+
+ align:start position:0%
+to the power of n is a relatively simple
+ 
+
+ align:start position:0%
+to the power of n is a relatively simple
+thing to do we just take the aigen
+
+ align:start position:0%
+thing to do we just take the aigen
+ 
+
+ align:start position:0%
+thing to do we just take the aigen
+values and raise them to the power of
+
+ align:start position:0%
+values and raise them to the power of
+ 
+
+ align:start position:0%
+values and raise them to the power of
+n so when we compute this product
+
+ align:start position:0%
+n so when we compute this product
+ 
+
+ align:start position:0%
+n so when we compute this product
+there's a question of what order do we
+
+ align:start position:0%
+there's a question of what order do we
+ 
+
+ align:start position:0%
+there's a question of what order do we
+do things now these are 2x two matrices
+
+ align:start position:0%
+do things now these are 2x two matrices
+ 
+
+ align:start position:0%
+do things now these are 2x two matrices
+so in theory we could just multiply out
+
+ align:start position:0%
+so in theory we could just multiply out
+ 
+
+ align:start position:0%
+so in theory we could just multiply out
+2 X2 Matrix 2 x two Matrix 2 x two
+
+ align:start position:0%
+2 X2 Matrix 2 x two Matrix 2 x two
+ 
+
+ align:start position:0%
+2 X2 Matrix 2 x two Matrix 2 x two
+Matrix and then on a vector which is a
+
+ align:start position:0%
+Matrix and then on a vector which is a
+ 
+
+ align:start position:0%
+Matrix and then on a vector which is a
+2x1 matrix but if you're in a test and
+
+ align:start position:0%
+2x1 matrix but if you're in a test and
+ 
+
+ align:start position:0%
+2x1 matrix but if you're in a test and
+you're cramp for time you want to do as
+
+ align:start position:0%
+you're cramp for time you want to do as
+ 
+
+ align:start position:0%
+you're cramp for time you want to do as
+much as little computations as possible
+
+ align:start position:0%
+much as little computations as possible
+ 
+
+ align:start position:0%
+much as little computations as possible
+so what you want to do is you want to
+
+ align:start position:0%
+so what you want to do is you want to
+ 
+
+ align:start position:0%
+so what you want to do is you want to
+start on the right hand side and then
+
+ align:start position:0%
+start on the right hand side and then
+ 
+
+ align:start position:0%
+start on the right hand side and then
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+backwards so if we do
+
+ align:start position:0%
+backwards so if we do
+ 
+
+ align:start position:0%
+backwards so if we do
+this we end up obtaining one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two this is going to be to the power of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+13 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay so for this last part I'm just
+
+ align:start position:0%
+2 okay so for this last part I'm just
+ 
+
+ align:start position:0%
+2 okay so for this last part I'm just
+going to write down the final answer and
+
+ align:start position:0%
+going to write down the final answer and
+ 
+
+ align:start position:0%
+going to write down the final answer and
+I'll let you work out the multiplication
+
+ align:start position:0%
+I'll let you work out the multiplication
+ 
+
+ align:start position:0%
+I'll let you work out the multiplication
+of matrices
+
+ align:start position:0%
+of matrices
+ 
+
+ align:start position:0%
+of matrices
+so we have for PN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1/3 2 *
+
+ align:start position:0%
+1/3 2 *
+ 
+
+ align:start position:0%
+1/3 2 *
+0.4 to the
+
+ align:start position:0%
+0.4 to the
+ 
+
+ align:start position:0%
+0.4 to the
+n +
+
+ align:start position:0%
+n +
+ 
+
+ align:start position:0%
+n +
+1 minus 2 0.4 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n +
+
+ align:start position:0%
+n +
+ 
+
+ align:start position:0%
+n +
+2 and this is the final Vector for p of
+
+ align:start position:0%
+2 and this is the final Vector for p of
+ 
+
+ align:start position:0%
+2 and this is the final Vector for p of
+n okay so this finishes up part two and
+
+ align:start position:0%
+n okay so this finishes up part two and
+ 
+
+ align:start position:0%
+n okay so this finishes up part two and
+then lastly for part three
+
+ align:start position:0%
+then lastly for part three
+ 
+
+ align:start position:0%
+then lastly for part three
+what happens when n goes to
+
+ align:start position:0%
+what happens when n goes to
+ 
+
+ align:start position:0%
+what happens when n goes to
+Infinity well we have the answer for uh
+
+ align:start position:0%
+Infinity well we have the answer for uh
+ 
+
+ align:start position:0%
+Infinity well we have the answer for uh
+for any n so we can just take the limit
+
+ align:start position:0%
+for any n so we can just take the limit
+ 
+
+ align:start position:0%
+for any n so we can just take the limit
+as n goes to Infinity now specifically
+
+ align:start position:0%
+as n goes to Infinity now specifically
+ 
+
+ align:start position:0%
+as n goes to Infinity now specifically
+as n goes to in Infinity 0.4 raised to
+
+ align:start position:0%
+as n goes to in Infinity 0.4 raised to
+ 
+
+ align:start position:0%
+as n goes to in Infinity 0.4 raised to
+some very large power vanishes so these
+
+ align:start position:0%
+some very large power vanishes so these
+ 
+
+ align:start position:0%
+some very large power vanishes so these
+two terms drop off and at the end of the
+
+ align:start position:0%
+two terms drop off and at the end of the
+ 
+
+ align:start position:0%
+two terms drop off and at the end of the
+day we're left with P
+
+ align:start position:0%
+day we're left with P
+ 
+
+ align:start position:0%
+day we're left with P
+Infinity is
+
+ align:start position:0%
+Infinity is
+ 
+
+ align:start position:0%
+Infinity is
+1/3 1
+
+ align:start position:0%
+1/3 1
+ 
+
+ align:start position:0%
+1/3 1
+2 okay so just to recap we started off
+
+ align:start position:0%
+2 okay so just to recap we started off
+ 
+
+ align:start position:0%
+2 okay so just to recap we started off
+with a a particle uh starting at a and
+
+ align:start position:0%
+with a a particle uh starting at a and
+ 
+
+ align:start position:0%
+with a a particle uh starting at a and
+then after a very long
+
+ align:start position:0%
+then after a very long
+ 
+
+ align:start position:0%
+then after a very long
+time the particle uh winds up with a
+
+ align:start position:0%
+time the particle uh winds up with a
+ 
+
+ align:start position:0%
+time the particle uh winds up with a
+probability distribution which is
+
+ align:start position:0%
+probability distribution which is
+ 
+
+ align:start position:0%
+probability distribution which is
+1/3 1 and
+
+ align:start position:0%
+1/3 1 and
+ 
+
+ align:start position:0%
+1/3 1 and
+two and this is quite characteristic of
+
+ align:start position:0%
+two and this is quite characteristic of
+ 
+
+ align:start position:0%
+two and this is quite characteristic of
+Markov Matrix
+
+ align:start position:0%
+Markov Matrix
+ 
+
+ align:start position:0%
+Markov Matrix
+chains specifically we note that 1/3 one
+
+ align:start position:0%
+chains specifically we note that 1/3 one
+ 
+
+ align:start position:0%
+chains specifically we note that 1/3 one
+two is a multiple of the igen value of
+
+ align:start position:0%
+two is a multiple of the igen value of
+ 
+
+ align:start position:0%
+two is a multiple of the igen value of
+the igen vector corresponding to igen
+
+ align:start position:0%
+the igen vector corresponding to igen
+ 
+
+ align:start position:0%
+the igen vector corresponding to igen
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+one so even though the particle started
+
+ align:start position:0%
+one so even though the particle started
+ 
+
+ align:start position:0%
+one so even though the particle started
+at position a after a long period of
+
+ align:start position:0%
+at position a after a long period of
+ 
+
+ align:start position:0%
+at position a after a long period of
+time it tended to forget where it
+
+ align:start position:0%
+time it tended to forget where it
+ 
+
+ align:start position:0%
+time it tended to forget where it
+started and approached diffused into
+
+ align:start position:0%
+started and approached diffused into
+ 
+
+ align:start position:0%
+started and approached diffused into
+this uniform
+
+ align:start position:0%
+this uniform
+ 
+
+ align:start position:0%
+this uniform
+distribution okay I'd like to finish up
+
+ align:start position:0%
+distribution okay I'd like to finish up
+ 
+
+ align:start position:0%
+distribution okay I'd like to finish up
+here and I'll see you next time
\ No newline at end of file
diff --git a/o3Oog9I25dA.txt b/o3Oog9I25dA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c32c8b761b7c0820c78fc25abd4b8d876a5d058
--- /dev/null
+++ b/o3Oog9I25dA.txt
@@ -0,0 +1,3455 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Are we ready?
+
+So good afternoon.
+
+Just a reminder, this week we
+see each other three times--
+
+today on Wednesday and
+Friday in this other lecture
+
+hall for our mid-term exam.
+
+Today we will finish
+the big chapter
+
+on light-atom interaction.
+
+But we're not getting
+rid of it, because we
+
+will be transitioning
+to an important aspect
+
+of light-atom interaction.
+
+And these are line shifts
+and line broadening.
+
+So today we start the next big
+chapter-- line shifts and line
+
+broadening.
+
+But before I do that, we have to
+finish light-atom interaction.
+
+And I want to come back
+to the rotating wave
+
+approximation revisited.
+
+So I'll revisit the revisit
+of the rotating wave
+
+approximation.
+
+And sometimes when
+I have discussions
+
+with students after
+class, I realize
+
+that something which I
+sort of casually mentioned
+
+is either confusing or
+interesting for you.
+
+And there are two
+aspects I actually
+
+want to come back here.
+
+So several people
+reacted to that,
+
+but some felt it was maybe a
+little bit too complicated.
+
+Or others asked me
+about some details.
+
+So let me come back
+to two aspects.
+
+And I hope you find
+them interesting.
+
+One is when we sorted
+out all those terms,
+
+those [? need two ?] angular
+momentum selection rules.
+
+But I made sort of the
+innocent comment-- well,
+
+if you have omega minus omega
+in a time-dependent Hamiltonian,
+
+one term is responsible
+for absorption,
+
+one is for emission.
+
+And when more than one
+person asked me about it,
+
+I think many more than
+one person in class
+
+would like to know
+more about it.
+
+So therefore, let me spend the
+first few minutes in explaining
+
+why is a time-dependent
+term in the Hamiltonian
+
+with plus or minus
+omega, why is one of them
+
+responsible for
+absorption, and one
+
+is responsible for emission?
+
+Well, we have
+Schrodinger's equation,
+
+which says that the change
+of the amplitude in state one
+
+has a term.
+
+And if it started out with
+population in state two--
+
+let's say perturbation theory,
+we start in state two--
+
+then it is the only term where
+the differential equation,
+
+through an off-diagonal
+matrix element
+
+puts amplitude from
+state two into state one.
+
+So what I'm writing down here
+is just Schrodinger's equation.
+
+And the operator V
+is the drive field
+
+connecting state
+two to state one.
+
+And so if I just
+integrate this equation
+
+for a short time between
+time t and t plus delta t,
+
+and I'm asking, did we
+change the population
+
+of state one, which is
+now our final state?
+
+Well, then you integrate over
+that for time interval delta t.
+
+But now comes the point
+that the initial state has,
+
+in its time-dependent
+wave function,
+
+a vector which is e to
+the minus i omega 2 t.
+
+The final state,
+which I called one,
+
+has-- because it's a complex
+conjugate-- plus omega 1 t.
+
+And let's just
+assume we have here
+
+the proportionality
+to e to the i omega t.
+
+And let me just say omega can
+now be positive and negative.
+
+It will be part of
+the answer whether it
+
+should be positive or negative.
+
+Well, this integral here becomes
+an integral of e to the i,
+
+omega 1 minus omega 2 plus
+omega t integrated with time.
+
+And this is an
+oscillating function,
+
+where if you integrated
+with over time,
+
+it will average to
+zero unless omega
+
+is equal or at least
+close to the frequency
+
+difference between
+initial and excited state.
+
+So actually, what
+you encounter here
+
+is-- well, what I've derived
+for you here is actually,
+
+you can say energy conservation.
+
+I didn't assume it.
+
+It is built into the time
+evolution of the Schrodinger
+
+equation, that you can
+only go from state one
+
+to state two or state two to one
+if the drive term has a Fourier
+
+component omega, which
+makes up for the difference.
+
+Or I'm using different
+language now.
+
+If, through the drive
+term, you provide photons,
+
+you provide quanta of
+energy, where omega fulfills
+
+the equation for
+energy conservation.
+
+And you also see from this
+result, when omega 1 is higher
+
+than omega 2, omega
+has to be negative.
+
+When the reverse is true,
+omega has to be positive.
+
+So that's why I said,
+the e to the plus
+
+i omega t term is
+responsible for absorption.
+
+The e to the minus
+i omega t term
+
+is responsible for
+stimulated emission.
+
+You also see, of
+course-- but I stop here,
+
+because I think you've
+heard it often enough.
+
+If you integrate over
+short time delta t,
+
+this equation has
+to be fulfilled
+
+only to within 1 over delta t.
+
+This is sort of the
+energy-time uncertainty.
+
+For short times,
+the photon energy
+
+does not need to match
+exactly the energy difference.
+
+And you also realize
+when we think
+
+about omega is
+close to resonance,
+
+then e to the i omega
+t does absorption.
+
+But if you're in
+the ground state,
+
+e to the minus i
+omega t, leads now
+
+to a very rapid
+oscillation here,
+
+which is close to [? 2 ?]
+omega oscillation.
+
+And we've discussed that in the
+context of the AC stark shift,
+
+that this gives rise to
+the [? proxy ?] shift.
+
+We've also discussed that this
+term is rapidly oscillating
+
+and it's nothing else than the
+counter-rotating term which
+
+we usually neglect when
+we do the rotating wave
+
+approximation.
+
+So everything we've
+discussed in this context--
+
+counter-rotating term, energy
+conservation, Heisenberg's
+
+uncertainty,
+time-energy uncertainty
+
+actually comes from
+this kind of formalism.
+
+Any question?
+
+Of course, if you quantize
+the electromagnetic field,
+
+then you don't have a drive
+term with e to the i omega t.
+
+You just have a and a
+[? degas ?] for the photons.
+
+And the question, which
+term absorbs a photon
+
+or creates a photon,
+does not exist.
+
+Because you know it whether
+it's a or a [? dega. ?] But
+
+you have the two
+choices, whether you
+
+want to use a fully quantized
+field with photon operators
+
+or whether you want to use
+the time-dependent formalism,
+
+using a semi-classical
+or classical field
+
+in the Schrodinger equation.
+
+The second comment
+I wanted to do
+
+is using the
+semi-classical picture,
+
+I was sort of going with you
+through some examples when
+
+the rotating wave approximation
+is necessary, when not.
+
+When do you have
+counter-rotating terms.
+
+And yes, everything I
+told you is, I think,
+
+is the best possible way
+how you can-- I assume,
+
+because I haven't found a better
+one-- the best possible way
+
+to present it and
+explain it to using
+
+the time-dependent
+electromagnetic field.
+
+But I realized
+after class that it
+
+may be useful to
+quickly state what
+
+I have said in using
+the photon picture.
+
+If we have circular
+polarization,
+
+we have, for given frequency,
+annihilation and creation
+
+operator.
+
+But let's assume that the
+mode we are considering
+
+is right-handed
+circularly polarized,
+
+so the operator creates a
+photon at frequency omega
+
+with this right-handed
+circular polarization.
+
+So that means now if
+we start from a level m
+
+and we have now
+light-atom interaction,
+
+the operator which
+annihilates a photon
+
+with circular polarization
+because of angular momentum
+
+conservation can only
+take us to a level
+
+where the magnetic quantum
+number is n plus 1.
+
+Well, the operator A
+[? dega ?] creates a photon
+
+through stimulated emission.
+
+And so this is now
+our two-level system.
+
+And now we should ask the
+question, in terms of rotating
+
+wave approximation,
+is necessary or not,
+
+are there
+counter-rotating terms?
+
+Well, the counter-rotating terms
+are the non-intuitive terms,
+
+where you start out
+in the lowest state.
+
+But now instead of absorbing
+a photon, you emit a photon.
+
+And the operator for
+emission is this one.
+
+So I can now ask, is
+there another term?
+
+Why don't we stick to the
+blue color for the photons?
+
+That there is a term which
+is driven by the operator
+
+A [? dega ?]
+circularly polarized.
+
+Well, the answer is,
+there may be such a term,
+
+but the state we need has
+now a magnetic quantum
+
+number of m minus 1 because
+of angular momentum selection
+
+rules.
+
+So this here is the
+counter-rotating term,
+
+which you may or may not
+neglect, depending whether you
+
+want to make the rotating
+wave approximation or not.
+
+So therefore, if you got
+a little bit confused
+
+about the different
+cases I considered
+
+at the end of the
+last lecture, then
+
+you may just summarize the
+many examples I gave you
+
+in the lecture just
+as a note which
+
+you should keep in
+the back of your head,
+
+namely-- let me first
+phrase it in words
+
+and then write it down.
+
+If you have circular
+polarization and angular
+
+momentum selection rules,
+then the counter-rotating term
+
+may require a third level and is
+not part of two-level physics.
+
+So if you have a situation where
+the third level does not exist,
+
+you do not have a
+counter-rotating term.
+
+However, in all situations
+I've encountered in the lab,
+
+this third level does exist.
+
+OK.
+
+So let me just write that
+down-- counter-rotating term
+
+for circularly
+polarized radiation
+
+requires a third level
+which may not exist.
+
+And then you don't
+have this term.
+
+But it does exist in most cases.
+
+Anyway, just an additional
+clarification for the topics
+
+we had on Wednesday.
+
+Any questions about that?
+
+Yes.
+
+STUDENT: Are there cases other
+than a spin-1/2 system where it
+
+doesn't exist?
+
+PROFESSOR: Well, I mentioned
+the example last class--
+
+if you do spectroscopy
+of an S2P transition
+
+in the magnetic field
+of a neutron star.
+
+Then the same one
+splitting is so huge
+
+that, well, you can assume that
+this has been shifted so far
+
+away that it has been
+completely suppressed.
+
+Other than that, well, we
+have the trivial situation
+
+which we discussed in NMR.
+
+If you simply have
+spin one half,
+
+then the total number
+of levels is only two,
+
+because we're talking about
+spin up and spin down.
+
+Or I constructed,
+in the last class,
+
+the forbidden transition, a
+doublet S to doublet S state.
+
+So that's two pairs
+of S equals one half.
+
+And then we are
+missing this state
+
+to couple any counter-rotating
+term into the system.
+
+OK.
+
+The next subject is saturation.
+
+Now, in this chapter,
+I want to talk
+
+about saturation in general.
+
+I want to discuss monochromatic
+light but also broadband light.
+
+And I want to introduce
+concepts of saturation intensity
+
+of absorption cross section,
+certain things which
+
+I find extremely useful if I
+want to understand what happens
+
+when light interacts
+with a system.
+
+Just sort of to
+whet your appetite,
+
+I will sort of show you
+that the absorption cross
+
+section of a two-level
+system is independent
+
+whether you have a strong
+or weak transition.
+
+Some people think the
+cross section should be--
+
+but there is a
+difference which is
+
+important between monochromatic
+and broadband light.
+
+But in the end, the
+concepts are very simple.
+
+I should say, sometimes
+I feel it's almost too
+
+simple to present it in class.
+
+On the other hand, if
+I don't present it,
+
+I can't make a few comments
+and guide you through.
+
+So my conclusion
+now is, at least
+
+for now, I show you
+some prepared slides,
+
+and I sort of step you through,
+and make a few annotations,
+
+and point out certain things.
+
+We have already
+partially transitioned
+
+to teach you this material
+through homework assignment.
+
+This week's homework assignment,
+which is due on Wednesday,
+
+is almost completely
+on saturation.
+
+And I will make a few comments
+where what I present you today
+
+is an extension or different
+from what you're learning
+
+in the homework and vice versa.
+
+Yes.
+
+If I wanted to present
+you saturation,
+
+power broadening, and all
+that in the purest form,
+
+I would just preset you with
+the Optical Bloch equations.
+
+We can solve them.
+
+And then we have everything
+we want-- a result which
+
+explains saturation
+and a result which
+
+explains power broadening.
+
+And you do some of
+it in your homework.
+
+However, what I
+want to show here
+
+is that saturation is
+actually a general feature
+
+of a two-level system if you
+have sort of three rates, which
+
+I will explain to you in
+a moment-- very similar
+
+to Einstein's A
+and B coefficient--
+
+that all such systems
+have saturation.
+
+And then you may immediately
+solve the Optical Bloch
+
+creation for
+monochromatic radiation.
+
+But for broadband
+radiation, we usually
+
+don't use the Optical
+Bloch equations,
+
+because for infinitely
+broad light,
+
+there is no coherence
+for which we
+
+need Optical Bloch equations.
+
+If you only have the
+Optical Bloch equations,
+
+you have solved for saturation
+in one limiting case,
+
+and you don't see that
+the concept of saturation
+
+is much broader.
+
+So therefore, let us assume
+that we have a two-level system.
+
+And we have the
+couple two levels
+
+with a rate--
+which you can think
+
+of the rate of absorption, the
+rate of stimulated emission.
+
+And I call the rate
+the unsaturated rate.
+
+In addition, there
+is some dissipation,
+
+some spontaneous decay
+described by gamma.
+
+So Ru is the unsaturated
+rate for absorption
+
+and for stimulated emission.
+
+Of course, you know even before
+you solve those equations
+
+that there must be some
+saturation built in.
+
+If you would look at
+the fraction of atoms
+
+in the excited state and
+you change the laser power,
+
+which means changing
+the unsaturated rate,
+
+things cannot shoot up forever,
+because you cannot put more
+
+than 100% of the population
+into the excited state.
+
+However, the effect that when
+we increase the laser power,
+
+we do upwards absorption
+and downward stimulation--
+
+means you won't even get 100%.
+
+The maximum you can get is 50%.
+
+And what I'm just
+drawing for you is
+
+this is a phenomenon
+of saturation,
+
+and now we want to
+understand the details.
+
+So using this rate
+equation, we are
+
+defining-- this is now a
+definition-- the saturated rate
+
+is the net transfer from A to B.
+
+Because we have an absorption
+and stimulated emission,
+
+the net transfer is the
+[? unsaturated ?] rate
+
+times the population difference.
+
+And this is our saturated rate.
+
+But of course, we normalize
+everything for atom.
+
+So therefore, our saturated
+rate has a rate coefficient S
+
+times the total number of
+atoms, or the total population
+
+in both states.
+
+Eventually, we are
+interested in steady state.
+
+We can immediately
+solve the rate equation
+
+in terms of steady state,
+which is done there.
+
+And we find that for
+those, we can now
+
+eliminate one of the
+states from the equation,
+
+because we have the
+steady state ratio.
+
+And then we find that
+the saturated rate
+
+is gamma over 2 times
+an expression which
+
+involves a saturation parameter.
+
+So in other words, it's just
+almost trivial solutions
+
+of very simple equations,
+which describe the saturation
+
+phenomenon I outlined
+for you at the beginning.
+
+This solution has the
+two limiting cases
+
+which we want to see-- that at
+a very low unsaturated rate,
+
+the saturated rate is the
+unsaturated rate because there
+
+is no saturation.
+
+And secondly, if we would
+go to infinite power,
+
+the saturated rate
+becomes gamma over 2,
+
+because we have equalized
+the population between ground
+
+and excited state.
+
+One half of the atoms
+are in the excited state,
+
+and they dissipate or scatter
+light with the rate gamma.
+
+All right.
+
+Any questions?
+
+We now want to specialize it
+to a situation which we often
+
+encounter, namely
+monochromatic radiation.
+
+And for monochromatic
+radiation, the unsaturated rate
+
+follows-- well, I factored
+out something here.
+
+But it follows the
+normalized line shape,
+
+which is a Lorentzian.
+
+And therefore, our
+unsaturated rate
+
+is proportion to
+the laser power.
+
+But I usually like to express
+the laser power through a Rabi
+
+frequency or the Rabi
+frequency squared.
+
+So our unsaturated rate
+follows this Lorentzian.
+
+And on resonance,
+this part is one.
+
+Our rate is omega Rabi
+squared over comma.
+
+And the definition for the
+saturation parameter of one,
+
+or for the saturation intensity
+is that the unsaturated rate
+
+has to be gamma over 2.
+
+So therefore, by
+omega Rabi squared
+
+over gamma is the
+unsaturated rate,
+
+it should be gamma
+over 2 for saturation,
+
+for saturation parameter of one.
+
+So therefore, our saturation
+pentameter resonance
+
+is given by this expression.
+
+And if you use the
+previous result
+
+and apply it to this
+unsaturated rate,
+
+we find a saturated
+rate which shows now
+
+the new phenomenon
+of power broadening.
+
+Let me illustrate
+it in two ways.
+
+The saturated rate involves
+a saturation parameter,
+
+and the unsaturated
+rate is a Lorentzian.
+
+But this Lorentzian appears
+now in the numerator
+
+and the denominator.
+
+So it appears twice.
+
+But with a one-step
+manipulation,
+
+you can transform it
+into a single Lorentzian.
+
+But this single Lorentzian
+is now power-broadened.
+
+It no longer has
+[? width ?] of gamma
+
+over-- of the natural
+line with gamma.
+
+It has an additional term,
+and this is power broadening.
+
+STUDENT: [INAUDIBLE]?
+
+PROFESSOR: No.
+
+It's still-- the resonance
+is at [? 0 ?] [INAUDIBLE].
+
+The equations are trivial.
+
+It's really just
+substituting one
+
+and getting from an
+expression, simplifying it
+
+to simple Lorentzian.
+
+I just want to
+emphasize the result.
+
+If you drive a
+transition, we have
+
+now-- the [? width ?] of the
+Lorentzian is now gamma over 2
+
+if we have no saturation.
+
+But then if we crank up
+the saturation parameter,
+
+the [? width ?] increases with
+a square root of the power.
+
+That's an important result.
+
+The square root of the
+power leads to broadening.
+
+Now let me give you a
+pictorial description
+
+of what we have done here.
+
+If we start with the Lorentzian
+and we increase the power,
+
+you sort of want to drive
+the system with the stronger
+
+Lorentzian.
+
+But we know we have a
+ceiling, which is saturation.
+
+And of course, when
+you drive it stronger,
+
+you reach the
+ceiling on resonance
+
+earlier than you reach the
+ceiling when you transfer it
+
+away from resonance.
+
+So therefore, if you
+start with the red curve,
+
+crank up the power,
+you will get more
+
+of a factor, more of
+a result in the wings
+
+because you are not
+yet saturated there.
+
+And this graphical construction,
+which I have just sort of
+
+indicated to you, lead now to
+a curve which is broadened,
+
+broader than the
+original Lorentzian.
+
+And this is the reason
+behind power broadening.
+
+I want to mention
+one thing here.
+
+For the classroom
+discussion, I have
+
+assumed that the light-atom
+interaction can be described
+
+by Fermi's golden rule, which
+we know is a limitation.
+
+When the system is,
+in effect, incoherent
+
+or no longer coherent,
+we had a long discussion
+
+about Rabi oscillation,
+Fermi's golden rule
+
+in the last two weeks.
+
+But what I'm doing is
+mathematically correct.
+
+The Optical Bloch
+equation, which
+
+you'll use in your
+homework assignment,
+
+will include the transition
+from Rabi oscillation
+
+towards Fermi's golden rule.
+
+And I'm just considering
+this [? fundamental ?] case.
+
+OK.
+
+I've talked about
+saturation of a transition.
+
+I've mentioned that we
+have defined the saturation
+
+parameter such that when we have
+saturation parameter of one,
+
+we sort of get into
+the non-linear regime
+
+where saturation happens.
+
+And of course, for
+an experimentalist,
+
+the next question is, at what
+intensity does that happen?
+
+This is summarized
+in those equations.
+
+It's as simple as
+possible algebra.
+
+You just combine two equations.
+
+I don't want to do it here.
+
+And we have a result for the
+saturation intensity, which
+
+has two features, which
+I want to point out.
+
+One is [? its case ?]
+with omega cube.
+
+So the higher the frequency
+of your transition is,
+
+the harder it is to saturate.
+
+Of course, it has something
+to do with that in saturation,
+
+you have an
+unsaturated rate, which
+
+is one half of the
+spontaneous emission rate.
+
+And you remember that the
+spontaneous emission rate
+
+was proportional to omega cube.
+
+So that's why we have,
+again, the omega cube factor.
+
+And in addition, the larger--
+actually, it depends.
+
+Sorry.
+
+I made a mistake.
+
+Well, you can write the
+results in several ways.
+
+If you have an intensity
+and you go back to photons,
+
+you get factors of omega.
+
+So when I said omega cubed comes
+from the natural line widths,
+
+yes, it does, but it's
+not the only omega factor.
+
+You can write the
+result actually
+
+that you have a gamma
+squared dependence,
+
+because one gamma comes from
+the matrix element squared
+
+and one comes because you need
+to compete in your excitation
+
+with spontaneous emission.
+
+So anyway, this is
+sort of the result.
+
+And you can calculate it
+for your favorite atom.
+
+And for alkaline
+atoms, we usually find
+
+that the saturation
+intensity is a few milliwatt
+
+per square centimeter
+
+Well, we can now repeat
+some of this exercise
+
+for the broadband case.
+
+In the broadband case,
+the unsaturated rate,
+
+which is the rate for absorption
+in stimulated emission,
+
+following Einstein's treatment
+of the AB coefficient
+
+is used by using
+Einstein's B coefficient
+
+times the spectral intensity.
+
+And now we want the same
+situation as before.
+
+We want to reach saturation.
+
+And saturation happens when
+this is comparable with gamma.
+
+And it's purely a
+definition that we
+
+say it should be gamma over 2.
+
+But we are consistent
+with what we did before.
+
+And if you just
+take this equation
+
+and calculate what the
+saturation intensity is,
+
+well, gamma is nothing else
+than the Einstein A coefficient.
+
+Here we have the
+Einstein B coefficient.
+
+And if we take the ratio
+between the Einstein A and B
+
+coefficient, the matrix
+element, everything
+
+which is specific to
+the atom, cancels out.
+
+And the saturation intensity,
+or the spectral density--
+
+it's the spectral density
+now for broadband--
+
+only depends on speed of light
+and the transition frequency
+
+cube.
+
+And it doesn't make a
+difference whether you
+
+have a two-level system which
+has a strong matrix element
+
+or weak matrix element.
+
+I could explain it to
+you now at this point,
+
+but we want to hold
+the idea that there
+
+is a difference
+between single mode
+
+monochromatic and
+broadband excitation
+
+until I have discussed
+one more concept.
+
+And this is the cross section.
+
+Just to check, are
+there any questions?
+
+Yes, Nancy.
+
+AUDIENCE: So in
+the broadband case,
+
+the line shift
+doesn't matter at all?
+
+Because in the
+monochromatic case,
+
+we had a line shift [INAUDIBLE].
+
+Well, hold your question.
+
+The line shape matters.
+
+I will now discuss what is
+the line shape of the atom.
+
+And the quick answer is, if
+the atom has a line shape,
+
+we have to take the
+atomic line shape
+
+and do a convolution with
+the line of the radiation.
+
+And we have the two
+situations where in one case,
+
+the monochromatic
+light is narrower
+
+than the line
+shape of the atoms.
+
+In the other case, it's broader.
+
+And this difference,
+in the end, will
+
+be responsible for the
+effect that the line widths
+
+of the atom, which is
+the natural line widths,
+
+will cancel out in one
+case and not in the other.
+
+But that's actually the result
+of the next five minutes.
+
+Other questions?
+
+I know this topic
+can get confusing,
+
+because we go from one
+definition to the next.
+
+So let me just summarize.
+
+What I've said so far is
+we [? derive ?] an atom.
+
+We have absorption, we
+have stimulated emission.
+
+And we want to understand
+the phenomenon of saturation.
+
+And based on the effect how
+we define saturation, namely
+
+that the unsaturated
+rate is gamma over 2,
+
+we got some nice results
+for the saturation intensity
+
+and for power broadening
+of a Lorentzian.
+
+So it's pretty much having a
+definition and running with it.
+
+And now we want to
+express the same physics
+
+by using the concept
+of a cross section
+
+for the following reason.
+
+You can do physics, you
+can do atomic physics
+
+without ever thinking
+about a cross section.
+
+You can just say, I have a laser
+beam of a certain intensity,
+
+and I scatter light.
+
+But often, when we
+scatter something--
+
+and you may be familiar,
+from atomic collisions--
+
+you often want to write
+the scattering rate
+
+as a density times cross
+section times relative velocity.
+
+And this sort of has
+this intuitive feeling.
+
+If you have a stream of
+particles in your accelerator
+
+or a stream of photons
+in your laser beam,
+
+you can now hold
+onto the picture
+
+that each atom in your
+target is a little disk.
+
+If the particle of photons hits
+the disk, something happens.
+
+If it misses the
+disk, nothing happens.
+
+And the area of the disk
+is this cross section.
+
+So in other words, we
+want to now understand
+
+how big is the disk of the
+atom which will, so to speak,
+
+cast the shadow, which is
+synonymous with absorption,
+
+when we illuminate those
+atoms with laser light.
+
+So for me, a very
+intuitive quantity.
+
+Anyway, so all we do
+is we have already
+
+discussed the rate
+of excitation,
+
+which is now the
+unsaturated rate.
+
+But now we express
+the unsaturated rate
+
+by the density of photons
+times the cross section.
+
+And the relative velocity
+is the speed of light.
+
+And from this equation, we
+find-- because everything
+
+is known, we have talked about
+that on the last few pages--
+
+we find that the cross section
+is-- and this is the result.
+
+6 pi lambda bar square.
+
+Lambda bar is the wavelengths
+of light divided by 2 pi.
+
+So we find that for
+monochromatic radiation,
+
+the cross sectional
+of a two-level system
+
+is independent of the
+strength of the transition,
+
+independent of the
+matrix element.
+
+It just depends on the
+resonant wavelengths.
+
+Now you would say,
+well, but what is now
+
+the difference between a
+strong and a weak transition?
+
+And this is shown here.
+
+If you take your monochromatic
+laser and you scan it,
+
+you scan it through
+the cross section.
+
+When you are on resonance, you
+have 6 pi lambda bar square.
+
+And the difference between
+a narrow transition
+
+with a small Einstein
+A coefficient
+
+and a strong transition with
+a large Einstein A coefficient
+
+simply means that in
+one case, it's narrower.
+
+In the other case, it's wider.
+
+We talked about the
+phenomenon of saturation.
+
+6 pi lambda bar squared
+is the cross section
+
+in the perturbative limit, or
+the unsaturated cross section.
+
+Of course, if you
+increase the laser power,
+
+you saturation the transition.
+
+The atom will have a smaller
+and smaller cross section.
+
+Actually, that's something
+important you should consider.
+
+When you have an atom and
+you increase the laser power,
+
+you scatter light.
+
+And the scattered light, or
+the absorbed light, saturates.
+
+But with the cross
+section, we want
+
+to know what fraction of the
+laser light is scattered.
+
+And the fraction of the
+laser light scattered
+
+goes to zero, because
+you make your laser
+
+light stronger and stronger.
+
+And the total amount of laser
+light which is scattered
+
+saturates.
+
+So in other words,
+you have a saturation
+
+of the scattered light.
+
+You have a saturation of
+the net transfer of atoms
+
+through the excited state in the
+limit of infinite laser power.
+
+But since the cross section is
+sort of normalized by the laser
+
+power, the cross section has
+this dependence, 1 over 1
+
+plus saturation
+parameter, and goes to 0.
+
+And that means--
+and this is sort
+
+of the language we use-- that
+the transition bleaches out.
+
+If you saturation
+the transition,
+
+the cross section
+becomes smaller.
+
+So when you saturation the
+transition in an absorption
+
+imaging experiment,
+which many of you do,
+
+the shadow is less
+and less black
+
+exactly because the cross
+section is bleaching out.
+
+But the amount of
+light you would scatter
+
+you would observe
+in fluorescence
+
+is not getting
+less, it saturates.
+
+This is sort of just the
+two flip sides of the coin.
+
+If anybody is confused,
+please ask a question.
+
+OK.
+
+So now in this picture,
+we can immediately
+
+understand why we
+have differences
+
+between monochromatic radiation
+and broadband radiation.
+
+If you want to
+saturation a transition
+
+with monochromatic radiation,
+we have our narrow laser.
+
+We absorb with a cross section
+6 pi lambda bar square.
+
+And we have to increase
+the intensity of the laser
+
+until the excitation
+rate equals gamma over 2.
+
+That's our definition
+for saturation.
+
+So therefore, the
+laser intensity
+
+is proportional to
+gamma, because we
+
+have the cross
+section is constant,
+
+but the product of cross
+section and laser intensity
+
+has to be equal to gamma over 2.
+
+However, now consider
+the case that you
+
+use broadband radiation.
+
+The spectrum is
+completely broad.
+
+Now, if an atom has a
+stronger transition,
+
+its cross section is
+wider, and the atom
+
+can sort of absorb a wider
+part of the incident spectrum.
+
+So therefore, if the atom
+has a stronger transition,
+
+it automatically takes, absorbs
+more of your spectral profile.
+
+And therefore, the
+result for the saturation
+
+and for the spectral
+saturation intensity
+
+is independent of
+the matrix element
+
+and the strengths
+of the transition.
+
+In general, if
+you're not in either
+
+of the extreme cases
+of monochromatic light
+
+or broadband light,
+what you have to do
+
+is you have to use
+this cross section
+
+as a function of
+frequency, and convolve it
+
+to a convolution with a
+spectrum of the incident light.
+
+And this is exactly done here.
+
+You take your
+frequency-dependent cross
+
+section.
+
+You do the convolution with the
+spectrum of the incident light.
+
+And if you assume the incident
+light is spectrally very broad,
+
+you simply integrate over
+the Lorentzian line shape
+
+of the cross section.
+
+And then you find
+exactly the same result
+
+as we had two slides ago,
+that the saturation intensity
+
+is independent of the
+strengths of the transition.
+
+OK.
+
+Can you think of a
+very intuitive argument
+
+why for spectrally
+broad radiation,
+
+all the properties of
+the atoms cancel out?
+
+If you think about one physical
+example for, let's say,
+
+black body radiation--
+this is spectrally broad.
+
+So you have an atom in
+a black body cavity.
+
+And the atom experiences
+a very broad spectrum.
+
+For what number of photons,
+black body photons per mode
+
+would we find saturation?
+
+Think about it.
+
+It's a simple criterion you
+can formulate for black body
+
+radiation to saturation
+your transition in terms
+
+of the number of
+photons per mode.
+
+You crank up the
+temperature in your cavity.
+
+How high do you have to
+go with the temperature
+
+in order to saturate an atom
+which is inside your black body
+
+cavity?
+
+AUDIENCE: One photon.
+
+PROFESSOR: Pretty close.
+
+AUDIENCE: 1 over
+[? degenerates. ?]
+
+PROFESSOR:
+[? Degenerates. ?] OK.
+
+No [? degenerates. ?] I
+hate [? degenerates. ?]
+
+That's your private homework
+to put in [? degenerates ?]
+
+afterwards.
+
+The answer I came was
+n equals 1/2, I think.
+
+I run the risk that I'm
+off by a factor of 2 now.
+
+But the argument was that--
+
+AUDIENCE: The rate equals
+[? degeneracy ?] by n by gamma.
+
+So if the rate equals
+gamma over 1/2,
+
+that mean that [? degenerates ?]
+by n equals 1/2.
+
+And if [? degenerates ?]
+equals 1, n equals 1/2.
+
+PROFESSOR: Yes.
+
+OK.
+
+So spontaneous emission, we
+know that spontaneous emission--
+
+from our derivation of
+spontaneous emission--
+
+corresponds to one
+photon per mode.
+
+And our criterion now is that we
+want to have an absorption rate
+
+or stimulated rate
+which is gamma over 2.
+
+So we get sort of 1/2 the effect
+of spontaneous emission when
+
+we have 1/2 a photon per mode.
+
+So therefore, spontaneous
+emission absorption
+
+is proportional to n.
+
+And I think if n
+equals 1/2, then
+
+we have the unsaturated
+rates equal to gamma over 2.
+
+So this is a very
+physical argument.
+
+When we put an atom into
+a black body cavity,
+
+and we have 1/2 a photon
+per mode occupation number,
+
+then we saturate
+any atom we put in.
+
+Because using Einstein's
+argument, we have now the rate
+
+coefficient for
+absorption emission
+
+for stimulated emission
+and absorption is just 1/2
+
+of the rate coefficient
+for spontaneous emission.
+
+And that explains that
+all atomic properties
+
+have to cancel out.
+
+So now question for you.
+
+We talked about the fact that if
+you have hyperfine transitions,
+
+that it would take--
+what was the value?
+
+1,000 years for
+spontaneous emission?
+
+So that we can completely
+neglect spontaneous emission.
+
+On the other hand, we've just
+learned that saturation only
+
+comes from spontaneous emission.
+
+Without spontaneous emission,
+we wouldn't have saturation.
+
+But now I'm telling you
+that any atom should really
+
+be saturated if we put
+it in a black body cavity
+
+where n bar is 1/2.
+
+So what is the story now if we
+put an atom into a black body
+
+cavity, and we are asking
+about, will we saturate?
+
+The hyperfine transition.
+
+Will we eventually
+have-- saturation
+
+means we have [BLOWS AIR], 1/4
+of the atoms in the excited
+
+state, 3/4 in the ground state.
+
+So the delta n has been reduced
+from 1, which it was initially,
+
+to 3/4 minus 1/4, which is 1/2.
+
+What will happen?
+
+I mean, this was almost like
+a thermodynamic argument.
+
+Will we equilibrate and
+saturate hyperfine transitions
+
+in a black body cavity
+based on this argument
+
+that for n bar equals
+1/2, we should really
+
+saturate everything?
+
+AUDIENCE: Yes, but it's
+going to take a long time?
+
+PROFESSOR: Yeah.
+
+So for those conditions,
+if your black body cavity
+
+was n bar equals 1/2, you should
+saturate any two-level system
+
+completely independent
+what gamma is.
+
+And if the gamma is 10
+nanoseconds or 10,000 years,
+
+you will saturate it.
+
+The value of gamma
+has completely
+
+dropped out of the argument.
+
+But of course, if you want to
+reach any kind of equilibrium,
+
+it will take a time scale,
+which is 1 over gamma.
+
+And then we are
+back to 1,000 years.
+
+Questions?
+
+All right.
+
+Then let's conclude this
+chapter and start our discussion
+
+about line shifts
+and line broadening.
+
+I have a problem with
+the tablet computer.
+
+I draw a line, but the computer
+draws a line somewhere else.
+
+So maybe I should just go
+back to this one and then copy
+
+things over.
+
+OK.
+
+Our next big chapter is
+line shifts and broadening.
+
+So the first question
+is motivational.
+
+Why should we be interested
+in line broadening?
+
+Well, the answer
+is almost trivial.
+
+No resonance is
+infinitely narrow.
+
+Whenever we want to interpret
+any result we obtain
+
+spectroscopically, we are not
+observing a delta function,
+
+we are not observing
+a resonance,
+
+we are observing a line shape.
+
+And unless we understand
+the line shape,
+
+we may not accurately find
+the resonance frequency.
+
+You could, of course, assume
+that your line shape is
+
+symmetric, which may be the
+case but is not always the case.
+
+So without understanding
+line broadening,
+
+you cannot interpret
+spectroscopic information.
+
+And eventually, as I
+mentioned in the first chapter
+
+of this course, the art
+of analyzing line shapes
+
+and finding the line center
+is very well advanced.
+
+When we have caesium
+fountain clocks,
+
+the accuracy how you operate the
+clock as a frequency standard
+
+is on the order
+of one microhertz.
+
+But those fountain
+clocks with you toss up
+
+the atoms for one second
+in the atomic fountain,
+
+they fall up and down,
+well, like a rock,
+
+which takes about a second for a
+rock to go up and down a meter.
+
+So therefore, the line width
+is on the order of one Hertz.
+
+So therefore, people have to
+understand any single aspect
+
+of the line shape at the
+level of 10 to the minus 5,
+
+or 10 to the minus 6 to
+have this kind of accuracy.
+
+OK.
+
+So I thought I want to start
+this unit by collecting form
+
+you examples for phenomena which
+cause broadening and shifting
+
+of lines.
+
+And well, my list
+has about 10 of them.
+
+Let's see how many you get.
+
+So what phenomena can lead
+to line shifts and line
+
+broadening?
+
+AUDIENCE: Phonons.
+
+PROFESSOR: Phonons?
+
+In terms of-- OK,
+AC stark effect.
+
+Pardon?
+
+AUDIENCE: Magnetic field noise.
+
+PROFESSOR: Magnetic field noise.
+
+OK.
+
+I tried to-- yes, very good.
+
+OK, yes.
+
+Let me just try to
+group it a little bit
+
+further, because I
+want to discuss it.
+
+So we have external fields.
+
+And external fields can
+have AC stark shifts.
+
+If an external field is noisy,
+we have noise fluctuations.
+
+All right.
+
+Anything else?
+
+AUDIENCE: Doppler shift.
+
+PROFESSOR: Doppler shift.
+
+Yes.
+
+So we have the
+velocity of the atoms.
+
+Doppler shift.
+
+AUDIENCE: Collisions.
+
+PROFESSOR: Collisions.
+
+Very good.
+
+Well, we just talked
+about one thing.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Exactly.
+
+When we have external
+fields, we can
+
+have external fields
+like magnetic fields
+
+or electric fields which
+cause shift and broadening.
+
+And if there's noise,
+additional shifts.
+
+But when we regard those
+fields as drive fields,
+
+they can do power broadening.
+
+Maybe by collisions, I should
+add the keyboard "pressure
+
+broadening."
+
+The higher the pressure
+in your gas cell is,
+
+the more collisions you have and
+the more you have broadening.
+
+Other suggestion?
+
+If you don't have
+any of those effects,
+
+do you measure delta function?
+
+What's the line width?
+
+Will?
+
+STUDENT: [INAUDIBLE].
+
+STUDENT: Spontaneous emission.
+
+PROFESSOR: Spontaneous emission.
+
+Yes.
+
+And if you don't have
+spontaneous emission,
+
+do we then measure
+delta function?
+
+STUDENT: There's
+a Fourier limit.
+
+PROFESSOR: The Fourier limit.
+
+You can call it
+observation time,
+
+or time of light broadening.
+
+If an atom flies
+through your laser beam
+
+and you can interrogate
+it only for a finite time,
+
+you have a broadening due
+to the Fourier theorem.
+
+And this can be called time of
+flight broadening and time of--
+
+or interaction time broadening.
+
+STUDENT: Rotations
+and vibrations?
+
+PROFESSOR: Rotations
+and vibrations.
+
+Not really.
+
+These are more-- then the
+system has more energy levels,
+
+and that's what you
+want to find out.
+
+So maybe I'm more asking,
+how are those energy levels--
+
+how do they appear
+spectroscopically?
+
+Well, I think that's
+pretty complete.
+
+Two external fields.
+
+If you want, you
+can add gravity.
+
+There is a
+gravitational red shift,
+
+which is general relativity.
+
+But anyway, let me look over
+that and try to categorize it.
+
+What we had here actually all
+comes from a finite observation
+
+time.
+
+Either we do not have the atom
+long enough in our laser beam,
+
+and that sets a limit.
+
+Or if you are interested in an
+excited state and the excited
+
+state decays, then
+the atoms themselves
+
+have terminated our
+interrogation time.
+
+The second class
+here, velocity, I
+
+would summarize that we
+have motion of the atom.
+
+It's a form of
+motional broadening.
+
+We will actually discuss,
+when we discuss motion, also
+
+the possibility of having
+atoms in a harmonic oscillator
+
+potential, ions in an ion trap.
+
+So these are now
+trapped particles.
+
+This will actually often give
+rise to a splitting of the line
+
+into side bends.
+
+So we want to discuss that.
+
+I've already mentioned external
+fields, conditional [INAUDIBLE]
+
+interrogation, power broadening.
+
+Some power broadening
+will actually
+
+result into a splitting of
+line into [INAUDIBLE] triplet.
+
+So power will not
+only broaden the line,
+
+it can also split the line.
+
+And we want to discuss that.
+
+And finally, we have the
+effect of atomic interactions.
+
+So for interactions, I think
+we should add something
+
+like mean field shifts,
+which also goes sometimes
+
+by the name of clock shift.
+
+If you're not at zero
+density, your transition
+
+can be shifted by the
+presence of other atoms.
+
+Will?
+
+STUDENT: Isn't collisional
+broadening or pressure
+
+broadening sort of
+just an ensemble
+
+average of a stark effect?
+
+So that's sort of
+an external field?
+
+PROFESSOR: That depends now.
+
+Collisions is one of the richest
+phenomena on the list here.
+
+You're ahead of me.
+
+But in the next few minutes,
+I wanted to actually
+
+see, well, maybe we should--
+those categories are not
+
+mutually exclusive, because
+one part of collisions is.
+
+An atom is in the excited
+state, it collides,
+
+it gets de-excited.
+
+So then collisions
+have no other effect
+
+than sort of give us a
+finite observation time,
+
+where there is an effective
+lifetime, which is just
+
+the time between two collisions.
+
+So it can be this.
+
+There's another
+aspect of collisions,
+
+that every time
+there is a collision,
+
+an atom feels the electric
+field of another atom.
+
+And then we have some form
+of collisional broadening,
+
+because we do some statistical
+averaging over stark effects,
+
+over level shifts.
+
+Now, there is a third
+aspect of collisions,
+
+which is maybe surprising
+to many of you.
+
+And this is actually-- I
+put it here under motion.
+
+It is collisional narrowing,
+or [? diche ?] narrowing.
+
+There's one limiting case
+when you have collisions,
+
+that collisions lead to a
+narrower line and not only
+
+to a broader line.
+
+the reason is a little bit-- if
+you put an atom in a buffer gas
+
+and it collides with
+all the buffer gas atom,
+
+it cannot fly away.
+
+So buffer gas and
+collisions can sort of
+
+help to increase your
+observation time.
+
+But only if the other effects
+of collisions are absent.
+
+So anyway, I thought
+this is a number
+
+of really interesting effects.
+
+And you already see from my
+presentation and discussion
+
+that it makes perfect sense to
+discuss them not one by one,
+
+as they appear in
+other chapters,
+
+but try to have comprehensive
+discussions of those.
+
+Let me talk about one
+classification of those shifts
+
+and broadening.
+
+And one is the distinction
+between homogeneous
+
+and inhomogeneous broadening.
+
+So the picture
+here is that if you
+
+have-- let me just give
+you the cartoon picture.
+
+If you have different atoms,
+atom 1, atom 2, atom 3.
+
+A homogeneous
+broadening situation
+
+is if the line
+has been broadened
+
+for each atom in the same way.
+
+An inhomogeneous
+broadening situation
+
+is that atom 1 has a line
+here, atom 2 has a line here,
+
+atom 3 has a line there.
+
+And if you look at the
+statistical ensemble,
+
+you may find the
+same line widths
+
+as on the left-hand side, but
+the situation and the mechanism
+
+is a very different one.
+
+So the different characteristics
+are that here, we
+
+have a mechanism which
+broadens or widens
+
+the line for each atom.
+
+Whereas here, there is
+maybe not even any line
+
+broadening for the atom.
+
+It's more a random shift
+to individual atoms.
+
+And the widening happens
+for the ensemble.
+
+Another very
+important distinction
+
+is in the left case, if you
+have one powerful laser,
+
+it can talk to all the atoms.
+
+Whereas in the
+right-hand side, you
+
+may have a laser with
+a certain frequency,
+
+and it may only excite one
+group of atoms in your ensemble.
+
+So this is the opposite here.
+
+In many situations do we have
+a physical picture where,
+
+in homogeneous broadening,
+we can understand it
+
+as random interruptions of the
+phase's evolution of the atom.
+
+For instance, through
+spontaneous emission,
+
+or you can see certain
+collisions-- just mean
+
+the phase of the excited
+state is suddenly perturbed.
+
+And therefore, the
+phase is randomized.
+
+So if the physical picture
+is a random interruption
+
+of the phase evolution,
+well, a random interruption
+
+of a phase evolution
+means that there
+
+is an exponential
+decay of coherence.
+
+And the line shape,
+the Fourier transform
+
+of an exponential
+decay is a Lorentzian.
+
+Whereas the physical picture
+behind inhomogeneous broadening
+
+is that you have
+random perturbations.
+
+And if you have many random
+or small perturbations,
+
+they often follow a
+normal distribution,
+
+which is a Gaussian.
+
+There's one other aspect of
+an inhomogeneous broadening.
+
+If it's an inhomogeneous
+broadening,
+
+it is as if the individual
+atom is not broadened,
+
+the individual atom
+is actually sharp,
+
+it has a longer coherence.
+
+And you can-- there
+are techniques to make
+
+that visible.
+
+And one famous technique,
+for those of you
+
+who have heard about it,
+are an echo technique.
+
+So having explained to
+you in a general way
+
+the difference between
+inhomogeneous and homogeneous
+
+broadening, how would you
+classify the line broadening
+
+mechanisms we have
+collected before?
+
+Which one are
+inhomogeneous broadening?
+
+STUDENT: Doppler broadening.
+
+PROFESSOR: Doppler broadening.
+
+We exploit that when we
+do saturation spectroscopy
+
+in the lab, when we just talk
+to one component of the velocity
+
+distribution.
+
+What else?
+
+STUDENT: [INAUDIBLE].
+
+STUDENT: Collisions.
+
+PROFESSOR: Collisions.
+
+That's actually a good one.
+
+Usually, collisions
+are classified
+
+as homogeneous broadening,
+because the simplest
+
+model for collisions
+is collisions
+
+are sort of just hard-core
+collisions which just de-excite
+
+the atom, completely change
+the coherent phase evolution.
+
+And therefore, collisions
+would broaden the transition
+
+for all atoms to a
+line widths which
+
+is 1 over the collision rates.
+
+However-- and this shows that
+the distinction cannot always
+
+be made-- you can actually have
+collision rate which depends
+
+on the velocity.
+
+The faster atoms may have
+a smaller collision cross
+
+section than the slower atoms.
+
+And now you have an
+inhomogeneous aspect
+
+of the collision rate.
+
+And therefore, collision
+rate becomes inhomogeneous.
+
+I mean, the standard example
+for inhomogeneous fields
+
+would-- if you have an
+inhomogeneous magnetic field,
+
+you have stationary atoms--
+well, not in an atomic gas,
+
+but maybe in [INAUDIBLE]
+or in a solid.
+
+And you have an
+inhomogeneous magnetic field.
+
+This is actually
+the standard case
+
+of nuclear magnetic
+resonance, that each atom
+
+possesses at its
+local magnetic field.
+
+And the line shape is
+inhomogeneously broadened.
+
+Colin?
+
+STUDENT: [INAUDIBLE]
+clock shift sometimes,
+
+in some circumstances.
+
+PROFESSOR: If the
+density is constant,
+
+you would actually
+say the mean field is
+
+the same for all
+atoms in the ensemble.
+
+But if you have a
+trapped atom sample
+
+where the density
+drops at the edge,
+
+you may actually
+have a sharper line,
+
+and less broadening, or less
+shift at the edge of the cloud.
+
+Anyway, so I think you have
+all the tools to classify it.
+
+And you see from the
+discussion that sometimes it's
+
+not so obvious.
+
+Or you may have
+a mechanism which
+
+has [? both ?] inhomogeneous
+that it does something
+
+to all atoms.
+
+So for instance, collisions
+broaden all the atoms,
+
+but then different atoms are
+more broadened than others.
+
+So there may be also an
+inhomogeneous aspect.
+
+But finally, let me
+ask you the following.
+
+It seems the first
+items on our list
+
+had sort of a very
+natural explanation
+
+in terms of the Fourier theorem,
+that, well, we only talk
+
+to the atoms for a finite time.
+
+Or the atoms decide not
+to talk to us for longer,
+
+because they
+spontaneously decay.
+
+Now, maybe you want to
+give me some arguments why
+
+some of the other
+mechanisms are actually
+
+also due to some form of
+finite time of interrogation.
+
+Well, if I would say,
+can we regard collisions
+
+as an effect of finite
+observation time?
+
+Well, if I rephrase "observation
+time" to "finite coherence
+
+time," that something interrupts
+the coherent evolution
+
+of the wave function,
+I think we would
+
+say the collision time sets
+a time limit to the coherence
+
+time and therefore,
+should also be regarded
+
+as due to the
+finite time, we can
+
+drive the atom in
+a coherent fashion.
+
+If I take power
+broadening, we just
+
+discussed power broadening.
+
+Well, what is the rate--
+or 1 over the rate
+
+of power broadening?
+
+We just discussed
+that that's maybe
+
+nice to take it
+out of the context.
+
+We discussed before that
+power-broadened line widths
+
+is gamma over 2 times S
+plus 1 square root of it--
+
+the saturation parameter.
+
+But when does power
+broadening happening?
+
+And what is the real time scale
+for what is the physical--
+
+STUDENT: Spontaneous emission.
+
+PROFESSOR: Spontaneous--
+so we had a criterion
+
+that the unsaturated rate has
+to be comparable to gamma.
+
+Let's forget about
+factors of 2 now.
+
+But that means that
+the Rabi frequency
+
+has to be comparable to gamma.
+
+The Rabi frequency tells
+us a time of Rabi flopping.
+
+So actually, power
+broadening can
+
+be understood as a finite
+observation time broadening,
+
+but the atom is leaving
+the excited state
+
+not by spontaneous emission,
+but by stimulated emission.
+
+So in other words,
+stimulated emission
+
+interrupts our ability
+to observe the atoms
+
+in the excited state.
+
+And so again, we see that
+there is a process coming
+
+in which interrupts
+our observation
+
+time of the unperturbed
+atomic levels.
+
+Well, let me go
+one step further.
+
+Let me ask you, do
+you have any idea
+
+how we could discuss
+the Doppler shift as
+
+due to some finite time scale?
+
+You would say, well, yeah,
+that's dimensional analysis.
+
+If you have a broadening, a
+broadening is a frequency,
+
+1 over the frequency
+is the time,
+
+and there is a time
+scale associated
+
+with Doppler broadening.
+
+Sure.
+
+But now my question is,
+what is the physical time
+
+scale with Doppler broadening?
+
+Yes?
+
+STUDENT: [? Collisions. ?]
+
+PROFESSOR: No.
+
+We have an ideal gas without
+any collisions-- just
+
+a [INAUDIBLE] distribution.
+
+You're right.
+
+In practice, yes.
+
+But I try to create an
+idealized situation.
+
+So what is the time scale
+of Doppler broadening?
+
+You may have never
+heard the question.
+
+But this is for me, what
+I want to really teach you
+
+when I teach all these
+different line shifts
+
+and line broadening.
+
+There is a common denominator.
+
+STUDENT: You could think of
+the atom [INAUDIBLE] emission.
+
+And then you would have
+velocity [INAUDIBLE] emission.
+
+PROFESSOR: You're talking
+about recoil shifts,
+
+and the atom is changing
+its velocity due to recoil.
+
+This would something
+in addition,
+
+but it's not necessarily
+the case here.
+
+I give you a physical argument.
+
+If I make the atom heavier
+and heavier and heavier,
+
+the effect of the recoil vanish.
+
+But then I can heat
+up the heavier atom,
+
+that it moves with the same
+velocity as the slow atom.
+
+So there is an effect which
+you can associate just
+
+to the velocity and to
+the velocity distribution.
+
+And that's what I
+want to discuss now.
+
+But there is another
+effect with the recoil.
+
+But I can say the
+recoil is a finite mass
+
+effect, for that purpose.
+
+The mass is sort of my
+handle, whether the recoil
+
+of a singular photon
+is important or not.
+
+Yes?
+
+STUDENT: [INAUDIBLE]?
+
+PROFESSOR: Yes,
+but this is really
+
+a more trivial finite
+observation time.
+
+When you heat the
+wall of the chamber,
+
+it's a collision
+with the chamber.
+
+It means we have only a
+finite interaction size.
+
+Now, let me sort of
+guide you to that.
+
+The secret here is
+when we say, you
+
+have a finite lifetime, a
+finite observation time,
+
+what matters when
+we do spectroscopy
+
+is the time we can observe
+the atoms coherently.
+
+If the atoms de-phase,
+if the atoms get out
+
+of coherence-- for instance,
+if you have collisions--
+
+if collision de-excite
+the atom-- we'll
+
+talk about it later-- it's
+like spontaneous emission.
+
+But then there are
+collisions which
+
+just create a phase
+hiccup, that the excited
+
+state gets a random phase.
+
+So an interruption of the
+phase, an interruption
+
+of the coherent
+evolution is, in effect,
+
+an interruption of us probing
+the atoms in a coherent way.
+
+And then the Fourier transform
+just tells us, this time, or 1
+
+over this time, is the
+line which we observe.
+
+And you would say,
+but how does it
+
+come into play with atoms
+with a velocity distribution?
+
+In the following way.
+
+If you line up several atoms
+and they interact with a laser
+
+beam, some atoms are faster,
+some atoms are slower.
+
+If some of the atoms have
+moved compared to the slower
+
+atoms, one additional
+wavelength,
+
+then your ensemble
+of atoms is no longer
+
+interacting with the laser
+beam in a phase-coherent way.
+
+Because of the
+different velocities,
+
+they are now talking to
+random phases of the laser.
+
+So therefore,
+Doppler broadening is
+
+nothing else as a
+loss of the atoms
+
+to coherently interact with
+a laser, because some of them
+
+have moved an additional
+wavelength in the laser beam.
+
+Well, if that is true-- but what
+happens if the laser beam is
+
+like this, with the wavelengths,
+and the atoms go perpendicular?
+
+What happens then?
+
+STUDENT: There's no Doppler.
+
+PROFESSOR: Then there
+is no Doppler effect.
+
+So what I'm saying
+is fully consistent
+
+with every single thing you
+know about the Doppler effect.
+
+OK.
+
+So I think there's not
+much more we can do today.
+
+But let me give you the
+summary of this discussion.
+
+To the best of my knowledge,
+all line broadening mechanisms
+
+can be described by using the
+concept of coherence time.
+
+And it's a coherence time
+of a correlation function.
+
+It's pretty much the
+correlation function
+
+of the phase which
+the atom experiences.
+
+At t equals 0, it experiences
+one phase of your drive field.
+
+And a later time, how
+long does it stay coherent
+
+with the coherent evolution
+of the phase of your drive
+
+field of a correlation function?
+
+However, in the case
+of inhomogeneous
+
+broadening-- and
+this is what I just
+
+discussed with the
+different atoms
+
+starting together and
+having different velocities.
+
+In the case of
+inhomogeneous broadening,
+
+I have to include in the
+description of the correlation
+
+function ensemble averaging.
+
+So this is our agenda.
+
+On Wednesday, I will
+start to discuss with you
+
+very simple cases.
+
+I sort of like, before I
+introduce correlation function,
+
+we have the
+generalized discussion
+
+to summarize for you the
+phenomenological description
+
+of just Rabi resonance, Ramsey
+resonance, exponential decay,
+
+simple Doppler broadening,
+the recoil effect,
+
+that you have a clear
+physical picture of what
+
+the different phenomena are.
+
+And then we describe them
+with a common language,
+
+with a common
+formalism, which is
+
+a formalism of
+correlation functions.
+
+Any questions?
+
+One obvious
+question-- the chapter
+
+on line shifts and broadening
+will not be on the mid-term.
+
+OK.
+
+See you on Wednesday.
\ No newline at end of file
diff --git a/omdqRLVehrw.txt b/omdqRLVehrw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed60242e7e557acdce2f63f91b21e9cae003501f
--- /dev/null
+++ b/omdqRLVehrw.txt
@@ -0,0 +1,7267 @@
+align:start position:0%
+ 
+the people who are living in cities
+
+ align:start position:0%
+the people who are living in cities
+ 
+
+ align:start position:0%
+the people who are living in cities
+represent a complexity of the human
+
+ align:start position:0%
+represent a complexity of the human
+ 
+
+ align:start position:0%
+represent a complexity of the human
+experience that we've never
+
+ align:start position:0%
+experience that we've never
+ 
+
+ align:start position:0%
+experience that we've never
+organized around if you have a democracy
+
+ align:start position:0%
+organized around if you have a democracy
+ 
+
+ align:start position:0%
+organized around if you have a democracy
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you need your public to be able to be
+
+ align:start position:0%
+you need your public to be able to be
+ 
+
+ align:start position:0%
+you need your public to be able to be
+engaged you need to have a system for
+
+ align:start position:0%
+engaged you need to have a system for
+ 
+
+ align:start position:0%
+engaged you need to have a system for
+doing that
+
+ align:start position:0%
+doing that
+ 
+
+ align:start position:0%
+doing that
+we actually don't have one for that kind
+
+ align:start position:0%
+we actually don't have one for that kind
+ 
+
+ align:start position:0%
+we actually don't have one for that kind
+of problem
+
+ align:start position:0%
+of problem
+ 
+
+ align:start position:0%
+of problem
+today on the podcast we're exploring the
+
+ align:start position:0%
+today on the podcast we're exploring the
+ 
+
+ align:start position:0%
+today on the podcast we're exploring the
+world of civic design
+
+ align:start position:0%
+world of civic design
+ 
+
+ align:start position:0%
+world of civic design
+and reimagining what public engagement
+
+ align:start position:0%
+and reimagining what public engagement
+ 
+
+ align:start position:0%
+and reimagining what public engagement
+in demographically complex communities
+
+ align:start position:0%
+in demographically complex communities
+ 
+
+ align:start position:0%
+in demographically complex communities
+might look like there are no complete
+
+ align:start position:0%
+might look like there are no complete
+ 
+
+ align:start position:0%
+might look like there are no complete
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+you have to learn how to make decisions
+
+ align:start position:0%
+you have to learn how to make decisions
+ 
+
+ align:start position:0%
+you have to learn how to make decisions
+in the midst of ambiguity
+
+ align:start position:0%
+in the midst of ambiguity
+ 
+
+ align:start position:0%
+in the midst of ambiguity
+which means for you internally you have
+
+ align:start position:0%
+which means for you internally you have
+ 
+
+ align:start position:0%
+which means for you internally you have
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+your own dialogue for yourself
+
+ align:start position:0%
+your own dialogue for yourself
+ 
+
+ align:start position:0%
+your own dialogue for yourself
+i'm your host sarah hansen in this
+
+ align:start position:0%
+i'm your host sarah hansen in this
+ 
+
+ align:start position:0%
+i'm your host sarah hansen in this
+episode
+
+ align:start position:0%
+episode
+ 
+
+ align:start position:0%
+episode
+i'm talking with an mit professor who
+
+ align:start position:0%
+i'm talking with an mit professor who
+ 
+
+ align:start position:0%
+i'm talking with an mit professor who
+bravely navigates along the deepest
+
+ align:start position:0%
+bravely navigates along the deepest
+ 
+
+ align:start position:0%
+bravely navigates along the deepest
+rifts in our public discourse
+
+ align:start position:0%
+rifts in our public discourse
+ 
+
+ align:start position:0%
+rifts in our public discourse
+and who works with students and
+
+ align:start position:0%
+and who works with students and
+ 
+
+ align:start position:0%
+and who works with students and
+communities alike
+
+ align:start position:0%
+communities alike
+ 
+
+ align:start position:0%
+communities alike
+to step consciously into these spaces
+
+ align:start position:0%
+to step consciously into these spaces
+ 
+
+ align:start position:0%
+to step consciously into these spaces
+my guest today is professor cesar
+
+ align:start position:0%
+my guest today is professor cesar
+ 
+
+ align:start position:0%
+my guest today is professor cesar
+mcdowell who teaches course
+
+ align:start position:0%
+mcdowell who teaches course
+ 
+
+ align:start position:0%
+mcdowell who teaches course
+11312 engaging community
+
+ align:start position:0%
+11312 engaging community
+ 
+
+ align:start position:0%
+11312 engaging community
+but before we get into our conversation
+
+ align:start position:0%
+but before we get into our conversation
+ 
+
+ align:start position:0%
+but before we get into our conversation
+we wanted to pause to remember
+
+ align:start position:0%
+we wanted to pause to remember
+ 
+
+ align:start position:0%
+we wanted to pause to remember
+that so many of our ocw team members and
+
+ align:start position:0%
+that so many of our ocw team members and
+ 
+
+ align:start position:0%
+that so many of our ocw team members and
+probably many of you
+
+ align:start position:0%
+probably many of you
+ 
+
+ align:start position:0%
+probably many of you
+have lost people that they love over
+
+ align:start position:0%
+have lost people that they love over
+ 
+
+ align:start position:0%
+have lost people that they love over
+this past year
+
+ align:start position:0%
+this past year
+ 
+
+ align:start position:0%
+this past year
+and so we're dedicating this last
+
+ align:start position:0%
+and so we're dedicating this last
+ 
+
+ align:start position:0%
+and so we're dedicating this last
+episode of season two
+
+ align:start position:0%
+episode of season two
+ 
+
+ align:start position:0%
+episode of season two
+to all of our loved ones and to all of
+
+ align:start position:0%
+to all of our loved ones and to all of
+ 
+
+ align:start position:0%
+to all of our loved ones and to all of
+yours and to all of those
+
+ align:start position:0%
+yours and to all of those
+ 
+
+ align:start position:0%
+yours and to all of those
+who carry their light forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professor mcdowell approaches his work
+
+ align:start position:0%
+professor mcdowell approaches his work
+ 
+
+ align:start position:0%
+professor mcdowell approaches his work
+with community engagement like it's an
+
+ align:start position:0%
+with community engagement like it's an
+ 
+
+ align:start position:0%
+with community engagement like it's an
+art form
+
+ align:start position:0%
+art form
+ 
+
+ align:start position:0%
+art form
+in fact he's built an entire design
+
+ align:start position:0%
+in fact he's built an entire design
+ 
+
+ align:start position:0%
+in fact he's built an entire design
+framework for practitioners
+
+ align:start position:0%
+framework for practitioners
+ 
+
+ align:start position:0%
+framework for practitioners
+to shape and facilitate these
+
+ align:start position:0%
+to shape and facilitate these
+ 
+
+ align:start position:0%
+to shape and facilitate these
+engagements but before we get into all
+
+ align:start position:0%
+engagements but before we get into all
+ 
+
+ align:start position:0%
+engagements but before we get into all
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+we need to understand the main problem
+
+ align:start position:0%
+we need to understand the main problem
+ 
+
+ align:start position:0%
+we need to understand the main problem
+his work seeks to address
+
+ align:start position:0%
+his work seeks to address
+ 
+
+ align:start position:0%
+his work seeks to address
+his why if you will things are actually
+
+ align:start position:0%
+his why if you will things are actually
+ 
+
+ align:start position:0%
+his why if you will things are actually
+changing in this country our populations
+
+ align:start position:0%
+changing in this country our populations
+ 
+
+ align:start position:0%
+changing in this country our populations
+are changing
+
+ align:start position:0%
+are changing
+ 
+
+ align:start position:0%
+are changing
+and right now in cities i think we're
+
+ align:start position:0%
+and right now in cities i think we're
+ 
+
+ align:start position:0%
+and right now in cities i think we're
+just saying that
+
+ align:start position:0%
+just saying that
+ 
+
+ align:start position:0%
+just saying that
+we're pronouncing anywhere else right
+
+ align:start position:0%
+we're pronouncing anywhere else right
+ 
+
+ align:start position:0%
+we're pronouncing anywhere else right
+that the people who are living
+
+ align:start position:0%
+that the people who are living
+ 
+
+ align:start position:0%
+that the people who are living
+in cities just happening to represent
+
+ align:start position:0%
+in cities just happening to represent
+ 
+
+ align:start position:0%
+in cities just happening to represent
+a complexity of the human experience
+
+ align:start position:0%
+a complexity of the human experience
+ 
+
+ align:start position:0%
+a complexity of the human experience
+that we've never organized around
+
+ align:start position:0%
+that we've never organized around
+ 
+
+ align:start position:0%
+that we've never organized around
+and if you have a democracy and you need
+
+ align:start position:0%
+and if you have a democracy and you need
+ 
+
+ align:start position:0%
+and if you have a democracy and you need
+your public to be able to
+
+ align:start position:0%
+your public to be able to
+ 
+
+ align:start position:0%
+your public to be able to
+be engaged you need to have a system for
+
+ align:start position:0%
+be engaged you need to have a system for
+ 
+
+ align:start position:0%
+be engaged you need to have a system for
+doing that
+
+ align:start position:0%
+doing that
+ 
+
+ align:start position:0%
+doing that
+we actually don't have one for that kind
+
+ align:start position:0%
+we actually don't have one for that kind
+ 
+
+ align:start position:0%
+we actually don't have one for that kind
+of public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of professor mcdowell's course and
+
+ align:start position:0%
+a lot of professor mcdowell's course and
+ 
+
+ align:start position:0%
+a lot of professor mcdowell's course and
+work center around the idea of democracy
+
+ align:start position:0%
+work center around the idea of democracy
+ 
+
+ align:start position:0%
+work center around the idea of democracy
+but in this episode when we talk about
+
+ align:start position:0%
+but in this episode when we talk about
+ 
+
+ align:start position:0%
+but in this episode when we talk about
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+we're not talking about elections and
+
+ align:start position:0%
+we're not talking about elections and
+ 
+
+ align:start position:0%
+we're not talking about elections and
+voting when professor mcdowell speaks of
+
+ align:start position:0%
+voting when professor mcdowell speaks of
+ 
+
+ align:start position:0%
+voting when professor mcdowell speaks of
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+he's talking about the engagements the
+
+ align:start position:0%
+he's talking about the engagements the
+ 
+
+ align:start position:0%
+he's talking about the engagements the
+communities the conversations
+
+ align:start position:0%
+communities the conversations
+ 
+
+ align:start position:0%
+communities the conversations
+the processes that we have as a public
+
+ align:start position:0%
+the processes that we have as a public
+ 
+
+ align:start position:0%
+the processes that we have as a public
+to come together and make decisions
+
+ align:start position:0%
+to come together and make decisions
+ 
+
+ align:start position:0%
+to come together and make decisions
+and a lot of these processes that we
+
+ align:start position:0%
+and a lot of these processes that we
+ 
+
+ align:start position:0%
+and a lot of these processes that we
+traditionally consider democracy in
+
+ align:start position:0%
+traditionally consider democracy in
+ 
+
+ align:start position:0%
+traditionally consider democracy in
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+are a little outdated i'll tell you what
+
+ align:start position:0%
+are a little outdated i'll tell you what
+ 
+
+ align:start position:0%
+are a little outdated i'll tell you what
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+we don't have a democracy that works for
+
+ align:start position:0%
+we don't have a democracy that works for
+ 
+
+ align:start position:0%
+we don't have a democracy that works for
+who we are i'll give an example
+
+ align:start position:0%
+who we are i'll give an example
+ 
+
+ align:start position:0%
+who we are i'll give an example
+of how we hold on to something as a way
+
+ align:start position:0%
+of how we hold on to something as a way
+ 
+
+ align:start position:0%
+of how we hold on to something as a way
+of thinking about democracy that does
+
+ align:start position:0%
+of thinking about democracy that does
+ 
+
+ align:start position:0%
+of thinking about democracy that does
+not serve as well
+
+ align:start position:0%
+not serve as well
+ 
+
+ align:start position:0%
+not serve as well
+right now if you kind of go back
+
+ align:start position:0%
+right now if you kind of go back
+ 
+
+ align:start position:0%
+right now if you kind of go back
+to the founding of the country and you
+
+ align:start position:0%
+to the founding of the country and you
+ 
+
+ align:start position:0%
+to the founding of the country and you
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+original colonies they weren't the
+
+ align:start position:0%
+original colonies they weren't the
+ 
+
+ align:start position:0%
+original colonies they weren't the
+original colors the people who came and
+
+ align:start position:0%
+original colors the people who came and
+ 
+
+ align:start position:0%
+original colors the people who came and
+occupied the land and created these
+
+ align:start position:0%
+occupied the land and created these
+ 
+
+ align:start position:0%
+occupied the land and created these
+opportunities for themselves here and
+
+ align:start position:0%
+opportunities for themselves here and
+ 
+
+ align:start position:0%
+opportunities for themselves here and
+if you look at those they created this
+
+ align:start position:0%
+if you look at those they created this
+ 
+
+ align:start position:0%
+if you look at those they created this
+thing that we hold as a myth today which
+
+ align:start position:0%
+thing that we hold as a myth today which
+ 
+
+ align:start position:0%
+thing that we hold as a myth today which
+is this thing of the new england town
+
+ align:start position:0%
+is this thing of the new england town
+ 
+
+ align:start position:0%
+is this thing of the new england town
+meeting town hall but if we're really
+
+ align:start position:0%
+meeting town hall but if we're really
+ 
+
+ align:start position:0%
+meeting town hall but if we're really
+serious about looking at that there were
+
+ align:start position:0%
+serious about looking at that there were
+ 
+
+ align:start position:0%
+serious about looking at that there were
+some things that were very true
+
+ align:start position:0%
+some things that were very true
+ 
+
+ align:start position:0%
+some things that were very true
+about that it was mostly open to men
+
+ align:start position:0%
+about that it was mostly open to men
+ 
+
+ align:start position:0%
+about that it was mostly open to men
+who were property owners most of these
+
+ align:start position:0%
+who were property owners most of these
+ 
+
+ align:start position:0%
+who were property owners most of these
+people who are men and property owned is
+
+ align:start position:0%
+people who are men and property owned is
+ 
+
+ align:start position:0%
+people who are men and property owned is
+lived in enclaves that share a religious
+
+ align:start position:0%
+lived in enclaves that share a religious
+ 
+
+ align:start position:0%
+lived in enclaves that share a religious
+belief
+
+ align:start position:0%
+belief
+ 
+
+ align:start position:0%
+belief
+okay so you take that as a core
+
+ align:start position:0%
+okay so you take that as a core
+ 
+
+ align:start position:0%
+okay so you take that as a core
+and you build build processes around
+
+ align:start position:0%
+and you build build processes around
+ 
+
+ align:start position:0%
+and you build build processes around
+that core that allow you to come to
+
+ align:start position:0%
+that core that allow you to come to
+ 
+
+ align:start position:0%
+that core that allow you to come to
+decisions
+
+ align:start position:0%
+decisions
+ 
+
+ align:start position:0%
+decisions
+right over time what we've been doing is
+
+ align:start position:0%
+right over time what we've been doing is
+ 
+
+ align:start position:0%
+right over time what we've been doing is
+saying well
+
+ align:start position:0%
+saying well
+ 
+
+ align:start position:0%
+saying well
+we don't want to be that exclusive we
+
+ align:start position:0%
+we don't want to be that exclusive we
+ 
+
+ align:start position:0%
+we don't want to be that exclusive we
+want to let a few more people in so we
+
+ align:start position:0%
+want to let a few more people in so we
+ 
+
+ align:start position:0%
+want to let a few more people in so we
+modify that a little bit more
+
+ align:start position:0%
+modify that a little bit more
+ 
+
+ align:start position:0%
+modify that a little bit more
+and over time that's what we've been
+
+ align:start position:0%
+and over time that's what we've been
+ 
+
+ align:start position:0%
+and over time that's what we've been
+doing and modifying it more modifying it
+
+ align:start position:0%
+doing and modifying it more modifying it
+ 
+
+ align:start position:0%
+doing and modifying it more modifying it
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+and then you get to something like the
+
+ align:start position:0%
+and then you get to something like the
+ 
+
+ align:start position:0%
+and then you get to something like the
+presidential debates and what do we have
+
+ align:start position:0%
+presidential debates and what do we have
+ 
+
+ align:start position:0%
+presidential debates and what do we have
+what do we say is the way we let the
+
+ align:start position:0%
+what do we say is the way we let the
+ 
+
+ align:start position:0%
+what do we say is the way we let the
+public into this conversation
+
+ align:start position:0%
+public into this conversation
+ 
+
+ align:start position:0%
+public into this conversation
+these televised town halls they have no
+
+ align:start position:0%
+these televised town halls they have no
+ 
+
+ align:start position:0%
+these televised town halls they have no
+reality or connection to the complexity
+
+ align:start position:0%
+reality or connection to the complexity
+ 
+
+ align:start position:0%
+reality or connection to the complexity
+of who we are
+
+ align:start position:0%
+of who we are
+ 
+
+ align:start position:0%
+of who we are
+but we hold on to them as
+
+ align:start position:0%
+but we hold on to them as
+ 
+
+ align:start position:0%
+but we hold on to them as
+our evidence that we are doing
+
+ align:start position:0%
+our evidence that we are doing
+ 
+
+ align:start position:0%
+our evidence that we are doing
+and engaging the public around a
+
+ align:start position:0%
+and engaging the public around a
+ 
+
+ align:start position:0%
+and engaging the public around a
+diaphragm
+
+ align:start position:0%
+diaphragm
+ 
+
+ align:start position:0%
+diaphragm
+so this is what it means we don't have
+
+ align:start position:0%
+so this is what it means we don't have
+ 
+
+ align:start position:0%
+so this is what it means we don't have
+it we actually don't have
+
+ align:start position:0%
+it we actually don't have
+ 
+
+ align:start position:0%
+it we actually don't have
+a functioning infrastructure for
+
+ align:start position:0%
+a functioning infrastructure for
+ 
+
+ align:start position:0%
+a functioning infrastructure for
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+given the complexity of who we are so
+
+ align:start position:0%
+given the complexity of who we are so
+ 
+
+ align:start position:0%
+given the complexity of who we are so
+that's what i mean by it's not just
+
+ align:start position:0%
+that's what i mean by it's not just
+ 
+
+ align:start position:0%
+that's what i mean by it's not just
+about voting
+
+ align:start position:0%
+about voting
+ 
+
+ align:start position:0%
+about voting
+it's the infrastructure that allows
+
+ align:start position:0%
+it's the infrastructure that allows
+ 
+
+ align:start position:0%
+it's the infrastructure that allows
+people to do the work that the public
+
+ align:start position:0%
+people to do the work that the public
+ 
+
+ align:start position:0%
+people to do the work that the public
+has to do
+
+ align:start position:0%
+has to do
+ 
+
+ align:start position:0%
+has to do
+in order for democracy to function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the new infrastructure professor
+
+ align:start position:0%
+the new infrastructure professor
+ 
+
+ align:start position:0%
+the new infrastructure professor
+mcdowell was talking about here
+
+ align:start position:0%
+mcdowell was talking about here
+ 
+
+ align:start position:0%
+mcdowell was talking about here
+involves a shift away from the more
+
+ align:start position:0%
+involves a shift away from the more
+ 
+
+ align:start position:0%
+involves a shift away from the more
+traditional forms of civic engagement
+
+ align:start position:0%
+traditional forms of civic engagement
+ 
+
+ align:start position:0%
+traditional forms of civic engagement
+and participation
+
+ align:start position:0%
+and participation
+ 
+
+ align:start position:0%
+and participation
+professor mcdowell's way involves
+
+ align:start position:0%
+professor mcdowell's way involves
+ 
+
+ align:start position:0%
+professor mcdowell's way involves
+looking at a given situation
+
+ align:start position:0%
+looking at a given situation
+ 
+
+ align:start position:0%
+looking at a given situation
+from multiple perspectives and then
+
+ align:start position:0%
+from multiple perspectives and then
+ 
+
+ align:start position:0%
+from multiple perspectives and then
+spending time to reflect on our own
+
+ align:start position:0%
+spending time to reflect on our own
+ 
+
+ align:start position:0%
+spending time to reflect on our own
+values and the needs of our community
+
+ align:start position:0%
+values and the needs of our community
+ 
+
+ align:start position:0%
+values and the needs of our community
+one point in my life i lived in alaska
+
+ align:start position:0%
+one point in my life i lived in alaska
+ 
+
+ align:start position:0%
+one point in my life i lived in alaska
+we had to love the arctic circle
+
+ align:start position:0%
+we had to love the arctic circle
+ 
+
+ align:start position:0%
+we had to love the arctic circle
+i was associate superintendent of a new
+
+ align:start position:0%
+i was associate superintendent of a new
+ 
+
+ align:start position:0%
+i was associate superintendent of a new
+school system there
+
+ align:start position:0%
+school system there
+ 
+
+ align:start position:0%
+school system there
+that was the size of the state of
+
+ align:start position:0%
+that was the size of the state of
+ 
+
+ align:start position:0%
+that was the size of the state of
+indiana and
+
+ align:start position:0%
+indiana and
+ 
+
+ align:start position:0%
+indiana and
+villages 5 000 people no roads okay so
+
+ align:start position:0%
+villages 5 000 people no roads okay so
+ 
+
+ align:start position:0%
+villages 5 000 people no roads okay so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+that's the context predominantly uh
+
+ align:start position:0%
+that's the context predominantly uh
+ 
+
+ align:start position:0%
+that's the context predominantly uh
+and there's this one instance in the
+
+ align:start position:0%
+and there's this one instance in the
+ 
+
+ align:start position:0%
+and there's this one instance in the
+village where
+
+ align:start position:0%
+village where
+ 
+
+ align:start position:0%
+village where
+we had a teacher who was
+
+ align:start position:0%
+we had a teacher who was
+ 
+
+ align:start position:0%
+we had a teacher who was
+actually not performing very well in
+
+ align:start position:0%
+actually not performing very well in
+ 
+
+ align:start position:0%
+actually not performing very well in
+this school and we were really concerned
+
+ align:start position:0%
+this school and we were really concerned
+ 
+
+ align:start position:0%
+this school and we were really concerned
+the principal was concerned we were
+
+ align:start position:0%
+the principal was concerned we were
+ 
+
+ align:start position:0%
+the principal was concerned we were
+concerned
+
+ align:start position:0%
+concerned
+ 
+
+ align:start position:0%
+concerned
+and the teacher was angry in this
+
+ align:start position:0%
+and the teacher was angry in this
+ 
+
+ align:start position:0%
+and the teacher was angry in this
+predominantly euphemia village and we
+
+ align:start position:0%
+predominantly euphemia village and we
+ 
+
+ align:start position:0%
+predominantly euphemia village and we
+had decided to remove the teacher
+
+ align:start position:0%
+had decided to remove the teacher
+ 
+
+ align:start position:0%
+had decided to remove the teacher
+because this is the best thing for the
+
+ align:start position:0%
+because this is the best thing for the
+ 
+
+ align:start position:0%
+because this is the best thing for the
+kids just wasn't performing well
+
+ align:start position:0%
+kids just wasn't performing well
+ 
+
+ align:start position:0%
+kids just wasn't performing well
+and there was a meeting in the village
+
+ align:start position:0%
+and there was a meeting in the village
+ 
+
+ align:start position:0%
+and there was a meeting in the village
+where we talked about that
+
+ align:start position:0%
+where we talked about that
+ 
+
+ align:start position:0%
+where we talked about that
+and there was a lot of
+
+ align:start position:0%
+and there was a lot of
+ 
+
+ align:start position:0%
+and there was a lot of
+resistance and so uh the superintendent
+
+ align:start position:0%
+resistance and so uh the superintendent
+ 
+
+ align:start position:0%
+resistance and so uh the superintendent
+asked me to kind of go
+
+ align:start position:0%
+asked me to kind of go
+ 
+
+ align:start position:0%
+asked me to kind of go
+and try to find out what's going on and
+
+ align:start position:0%
+and try to find out what's going on and
+ 
+
+ align:start position:0%
+and try to find out what's going on and
+so i went
+
+ align:start position:0%
+so i went
+ 
+
+ align:start position:0%
+so i went
+and these little fellows you can do it i
+
+ align:start position:0%
+and these little fellows you can do it i
+ 
+
+ align:start position:0%
+and these little fellows you can do it i
+talked to almost everyone
+
+ align:start position:0%
+talked to almost everyone
+ 
+
+ align:start position:0%
+talked to almost everyone
+talk to a lot of people in the village
+
+ align:start position:0%
+talk to a lot of people in the village
+ 
+
+ align:start position:0%
+talk to a lot of people in the village
+and here's
+
+ align:start position:0%
+and here's
+ 
+
+ align:start position:0%
+and here's
+what was happening the school was saying
+
+ align:start position:0%
+what was happening the school was saying
+ 
+
+ align:start position:0%
+what was happening the school was saying
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+person is not a good teacher and people
+
+ align:start position:0%
+person is not a good teacher and people
+ 
+
+ align:start position:0%
+person is not a good teacher and people
+were saying this person is a good
+
+ align:start position:0%
+were saying this person is a good
+ 
+
+ align:start position:0%
+were saying this person is a good
+teacher
+
+ align:start position:0%
+teacher
+ 
+
+ align:start position:0%
+teacher
+and we couldn't reconcile but what we
+
+ align:start position:0%
+and we couldn't reconcile but what we
+ 
+
+ align:start position:0%
+and we couldn't reconcile but what we
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+when we started to kind of talk to
+
+ align:start position:0%
+when we started to kind of talk to
+ 
+
+ align:start position:0%
+when we started to kind of talk to
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+is that we were valuing the teacher in
+
+ align:start position:0%
+is that we were valuing the teacher in
+ 
+
+ align:start position:0%
+is that we were valuing the teacher in
+very different ways
+
+ align:start position:0%
+very different ways
+ 
+
+ align:start position:0%
+very different ways
+inside the school the good was really
+
+ align:start position:0%
+inside the school the good was really
+ 
+
+ align:start position:0%
+inside the school the good was really
+applied for the school system the bill
+
+ align:start position:0%
+applied for the school system the bill
+ 
+
+ align:start position:0%
+applied for the school system the bill
+was applied to how well
+
+ align:start position:0%
+was applied to how well
+ 
+
+ align:start position:0%
+was applied to how well
+is this person taking care of the
+
+ align:start position:0%
+is this person taking care of the
+ 
+
+ align:start position:0%
+is this person taking care of the
+educational needs
+
+ align:start position:0%
+educational needs
+ 
+
+ align:start position:0%
+educational needs
+of the children for some of the people
+
+ align:start position:0%
+of the children for some of the people
+ 
+
+ align:start position:0%
+of the children for some of the people
+in the community
+
+ align:start position:0%
+in the community
+ 
+
+ align:start position:0%
+in the community
+teacher was a role good was the value to
+
+ align:start position:0%
+teacher was a role good was the value to
+ 
+
+ align:start position:0%
+teacher was a role good was the value to
+the community
+
+ align:start position:0%
+the community
+ 
+
+ align:start position:0%
+the community
+she was good for the community because
+
+ align:start position:0%
+she was good for the community because
+ 
+
+ align:start position:0%
+she was good for the community because
+of other functions she played in the
+
+ align:start position:0%
+of other functions she played in the
+ 
+
+ align:start position:0%
+of other functions she played in the
+community
+
+ align:start position:0%
+community
+ 
+
+ align:start position:0%
+community
+and so we had this totally different use
+
+ align:start position:0%
+and so we had this totally different use
+ 
+
+ align:start position:0%
+and so we had this totally different use
+of language
+
+ align:start position:0%
+of language
+ 
+
+ align:start position:0%
+of language
+and they knew that if she wasn't there
+
+ align:start position:0%
+and they knew that if she wasn't there
+ 
+
+ align:start position:0%
+and they knew that if she wasn't there
+as a teacher she wouldn't be there
+
+ align:start position:0%
+as a teacher she wouldn't be there
+ 
+
+ align:start position:0%
+as a teacher she wouldn't be there
+because she'd have to leave
+
+ align:start position:0%
+because she'd have to leave
+ 
+
+ align:start position:0%
+because she'd have to leave
+and so other values to the community
+
+ align:start position:0%
+and so other values to the community
+ 
+
+ align:start position:0%
+and so other values to the community
+will be lost
+
+ align:start position:0%
+will be lost
+ 
+
+ align:start position:0%
+will be lost
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+that kind of perspective taking i think
+
+ align:start position:0%
+that kind of perspective taking i think
+ 
+
+ align:start position:0%
+that kind of perspective taking i think
+is so required
+
+ align:start position:0%
+is so required
+ 
+
+ align:start position:0%
+is so required
+and as we find ways to bring people
+
+ align:start position:0%
+and as we find ways to bring people
+ 
+
+ align:start position:0%
+and as we find ways to bring people
+together we have to
+
+ align:start position:0%
+together we have to
+ 
+
+ align:start position:0%
+together we have to
+you know start to construct mechanisms
+
+ align:start position:0%
+you know start to construct mechanisms
+ 
+
+ align:start position:0%
+you know start to construct mechanisms
+that allow people to do that kind of
+
+ align:start position:0%
+that allow people to do that kind of
+ 
+
+ align:start position:0%
+that allow people to do that kind of
+reflection
+
+ align:start position:0%
+reflection
+ 
+
+ align:start position:0%
+reflection
+and that kind of perspective taking in
+
+ align:start position:0%
+and that kind of perspective taking in
+ 
+
+ align:start position:0%
+and that kind of perspective taking in
+relationship to the other
+
+ align:start position:0%
+relationship to the other
+ 
+
+ align:start position:0%
+relationship to the other
+one of the challenges of getting people
+
+ align:start position:0%
+one of the challenges of getting people
+ 
+
+ align:start position:0%
+one of the challenges of getting people
+to practice tuning into different
+
+ align:start position:0%
+to practice tuning into different
+ 
+
+ align:start position:0%
+to practice tuning into different
+perspectives
+
+ align:start position:0%
+perspectives
+ 
+
+ align:start position:0%
+perspectives
+is a physical one in our current
+
+ align:start position:0%
+is a physical one in our current
+ 
+
+ align:start position:0%
+is a physical one in our current
+political climate
+
+ align:start position:0%
+political climate
+ 
+
+ align:start position:0%
+political climate
+how do we even get people with different
+
+ align:start position:0%
+how do we even get people with different
+ 
+
+ align:start position:0%
+how do we even get people with different
+perspectives in the same room
+
+ align:start position:0%
+perspectives in the same room
+ 
+
+ align:start position:0%
+perspectives in the same room
+so we've started this campaign that
+
+ align:start position:0%
+so we've started this campaign that
+ 
+
+ align:start position:0%
+so we've started this campaign that
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+testing out now it's called america's
+
+ align:start position:0%
+testing out now it's called america's
+ 
+
+ align:start position:0%
+testing out now it's called america's
+path forward
+
+ align:start position:0%
+path forward
+ 
+
+ align:start position:0%
+path forward
+in the campaign we're actually reaching
+
+ align:start position:0%
+in the campaign we're actually reaching
+ 
+
+ align:start position:0%
+in the campaign we're actually reaching
+out to people in the public and we're
+
+ align:start position:0%
+out to people in the public and we're
+ 
+
+ align:start position:0%
+out to people in the public and we're
+asking them
+
+ align:start position:0%
+asking them
+ 
+
+ align:start position:0%
+asking them
+to do one thing and say two things
+
+ align:start position:0%
+to do one thing and say two things
+ 
+
+ align:start position:0%
+to do one thing and say two things
+one is to donate the question they have
+
+ align:start position:0%
+one is to donate the question they have
+ 
+
+ align:start position:0%
+one is to donate the question they have
+about the future of america
+
+ align:start position:0%
+about the future of america
+ 
+
+ align:start position:0%
+about the future of america
+and the experience in their life that
+
+ align:start position:0%
+and the experience in their life that
+ 
+
+ align:start position:0%
+and the experience in their life that
+led them to that question
+
+ align:start position:0%
+led them to that question
+ 
+
+ align:start position:0%
+led them to that question
+and then what we do is we bring people
+
+ align:start position:0%
+and then what we do is we bring people
+ 
+
+ align:start position:0%
+and then what we do is we bring people
+who have similar questions
+
+ align:start position:0%
+who have similar questions
+ 
+
+ align:start position:0%
+who have similar questions
+and sometimes not into small
+
+ align:start position:0%
+and sometimes not into small
+ 
+
+ align:start position:0%
+and sometimes not into small
+conversations
+
+ align:start position:0%
+conversations
+ 
+
+ align:start position:0%
+conversations
+in those conversations all people are
+
+ align:start position:0%
+in those conversations all people are
+ 
+
+ align:start position:0%
+in those conversations all people are
+doing is sharing their question
+
+ align:start position:0%
+doing is sharing their question
+ 
+
+ align:start position:0%
+doing is sharing their question
+sharing their experience and what people
+
+ align:start position:0%
+sharing their experience and what people
+ 
+
+ align:start position:0%
+sharing their experience and what people
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+is when they go into these rooms with
+
+ align:start position:0%
+is when they go into these rooms with
+ 
+
+ align:start position:0%
+is when they go into these rooms with
+people who have similar questions
+
+ align:start position:0%
+people who have similar questions
+ 
+
+ align:start position:0%
+people who have similar questions
+they're surprised at who's in the room
+
+ align:start position:0%
+they're surprised at who's in the room
+ 
+
+ align:start position:0%
+they're surprised at who's in the room
+because the thing that they hold as
+
+ align:start position:0%
+because the thing that they hold as
+ 
+
+ align:start position:0%
+because the thing that they hold as
+what's theirs they're realizing well
+
+ align:start position:0%
+what's theirs they're realizing well
+ 
+
+ align:start position:0%
+what's theirs they're realizing well
+there's a different set of people who
+
+ align:start position:0%
+there's a different set of people who
+ 
+
+ align:start position:0%
+there's a different set of people who
+actually hold this too
+
+ align:start position:0%
+actually hold this too
+ 
+
+ align:start position:0%
+actually hold this too
+and then when they hear different
+
+ align:start position:0%
+and then when they hear different
+ 
+
+ align:start position:0%
+and then when they hear different
+experiences they're beginning to realize
+
+ align:start position:0%
+experiences they're beginning to realize
+ 
+
+ align:start position:0%
+experiences they're beginning to realize
+oh this question manifests itself in
+
+ align:start position:0%
+oh this question manifests itself in
+ 
+
+ align:start position:0%
+oh this question manifests itself in
+totally different ways
+
+ align:start position:0%
+totally different ways
+ 
+
+ align:start position:0%
+totally different ways
+right it's the same question but it's
+
+ align:start position:0%
+right it's the same question but it's
+ 
+
+ align:start position:0%
+right it's the same question but it's
+living out differently in our society
+
+ align:start position:0%
+living out differently in our society
+ 
+
+ align:start position:0%
+living out differently in our society
+and for me this is a way of helping the
+
+ align:start position:0%
+and for me this is a way of helping the
+ 
+
+ align:start position:0%
+and for me this is a way of helping the
+public build its own kind of reflection
+
+ align:start position:0%
+public build its own kind of reflection
+ 
+
+ align:start position:0%
+public build its own kind of reflection
+and connection to others and what we're
+
+ align:start position:0%
+and connection to others and what we're
+ 
+
+ align:start position:0%
+and connection to others and what we're
+trying to get people to do
+
+ align:start position:0%
+trying to get people to do
+ 
+
+ align:start position:0%
+trying to get people to do
+at the end of these conversations is to
+
+ align:start position:0%
+at the end of these conversations is to
+ 
+
+ align:start position:0%
+at the end of these conversations is to
+say if you could reframe this question
+
+ align:start position:0%
+say if you could reframe this question
+ 
+
+ align:start position:0%
+say if you could reframe this question
+so that if it was addressed it would
+
+ align:start position:0%
+so that if it was addressed it would
+ 
+
+ align:start position:0%
+so that if it was addressed it would
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+likely attend to the different ways
+
+ align:start position:0%
+likely attend to the different ways
+ 
+
+ align:start position:0%
+likely attend to the different ways
+you're experiencing
+
+ align:start position:0%
+you're experiencing
+ 
+
+ align:start position:0%
+you're experiencing
+how would you reframe the question just
+
+ align:start position:0%
+how would you reframe the question just
+ 
+
+ align:start position:0%
+how would you reframe the question just
+getting people to start to think that
+
+ align:start position:0%
+getting people to start to think that
+ 
+
+ align:start position:0%
+getting people to start to think that
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+holding the public as curious
+
+ align:start position:0%
+holding the public as curious
+ 
+
+ align:start position:0%
+holding the public as curious
+intellectual beings and
+
+ align:start position:0%
+intellectual beings and
+ 
+
+ align:start position:0%
+intellectual beings and
+encouraging them in that to say yes this
+
+ align:start position:0%
+encouraging them in that to say yes this
+ 
+
+ align:start position:0%
+encouraging them in that to say yes this
+is hard work
+
+ align:start position:0%
+is hard work
+ 
+
+ align:start position:0%
+is hard work
+and yes you can do it professor mcdowell
+
+ align:start position:0%
+and yes you can do it professor mcdowell
+ 
+
+ align:start position:0%
+and yes you can do it professor mcdowell
+has worked with a team
+
+ align:start position:0%
+has worked with a team
+ 
+
+ align:start position:0%
+has worked with a team
+to create a tool for having better
+
+ align:start position:0%
+to create a tool for having better
+ 
+
+ align:start position:0%
+to create a tool for having better
+public conversations
+
+ align:start position:0%
+public conversations
+ 
+
+ align:start position:0%
+public conversations
+the tool is called the civic design
+
+ align:start position:0%
+the tool is called the civic design
+ 
+
+ align:start position:0%
+the tool is called the civic design
+framework i was curious about how the
+
+ align:start position:0%
+framework i was curious about how the
+ 
+
+ align:start position:0%
+framework i was curious about how the
+design element
+
+ align:start position:0%
+design element
+ 
+
+ align:start position:0%
+design element
+fits into this kind of community
+
+ align:start position:0%
+fits into this kind of community
+ 
+
+ align:start position:0%
+fits into this kind of community
+engagement work yeah so when i think
+
+ align:start position:0%
+engagement work yeah so when i think
+ 
+
+ align:start position:0%
+engagement work yeah so when i think
+about community engagement and design
+
+ align:start position:0%
+about community engagement and design
+ 
+
+ align:start position:0%
+about community engagement and design
+the reason i put those two together is
+
+ align:start position:0%
+the reason i put those two together is
+ 
+
+ align:start position:0%
+the reason i put those two together is
+to talk about the purposefulness of
+
+ align:start position:0%
+to talk about the purposefulness of
+ 
+
+ align:start position:0%
+to talk about the purposefulness of
+how we go out in the world and create
+
+ align:start position:0%
+how we go out in the world and create
+ 
+
+ align:start position:0%
+how we go out in the world and create
+engagement processes
+
+ align:start position:0%
+engagement processes
+ 
+
+ align:start position:0%
+engagement processes
+and they actually are designed and can
+
+ align:start position:0%
+and they actually are designed and can
+ 
+
+ align:start position:0%
+and they actually are designed and can
+be designed right
+
+ align:start position:0%
+be designed right
+ 
+
+ align:start position:0%
+be designed right
+the main thing i'm trying to get people
+
+ align:start position:0%
+the main thing i'm trying to get people
+ 
+
+ align:start position:0%
+the main thing i'm trying to get people
+to pay attention to is
+
+ align:start position:0%
+to pay attention to is
+ 
+
+ align:start position:0%
+to pay attention to is
+when you're putting together an
+
+ align:start position:0%
+when you're putting together an
+ 
+
+ align:start position:0%
+when you're putting together an
+engagement process
+
+ align:start position:0%
+engagement process
+ 
+
+ align:start position:0%
+engagement process
+you have the ability to construct it for
+
+ align:start position:0%
+you have the ability to construct it for
+ 
+
+ align:start position:0%
+you have the ability to construct it for
+certain kinds
+
+ align:start position:0%
+certain kinds
+ 
+
+ align:start position:0%
+certain kinds
+of outcomes and processes that you want
+
+ align:start position:0%
+of outcomes and processes that you want
+ 
+
+ align:start position:0%
+of outcomes and processes that you want
+to have having and connections you want
+
+ align:start position:0%
+to have having and connections you want
+ 
+
+ align:start position:0%
+to have having and connections you want
+to have happen
+
+ align:start position:0%
+to have happen
+ 
+
+ align:start position:0%
+to have happen
+therefore that's a design challenge
+
+ align:start position:0%
+therefore that's a design challenge
+ 
+
+ align:start position:0%
+therefore that's a design challenge
+right given the population you work
+
+ align:start position:0%
+right given the population you work
+ 
+
+ align:start position:0%
+right given the population you work
+within the issue you're going
+
+ align:start position:0%
+within the issue you're going
+ 
+
+ align:start position:0%
+within the issue you're going
+to follow up with how then do you
+
+ align:start position:0%
+to follow up with how then do you
+ 
+
+ align:start position:0%
+to follow up with how then do you
+construct that the sets of things that
+
+ align:start position:0%
+construct that the sets of things that
+ 
+
+ align:start position:0%
+construct that the sets of things that
+can happen
+
+ align:start position:0%
+can happen
+ 
+
+ align:start position:0%
+can happen
+so that they actually allow you to
+
+ align:start position:0%
+so that they actually allow you to
+ 
+
+ align:start position:0%
+so that they actually allow you to
+bring people not just close together but
+
+ align:start position:0%
+bring people not just close together but
+ 
+
+ align:start position:0%
+bring people not just close together but
+also what i like to say is help people
+
+ align:start position:0%
+also what i like to say is help people
+ 
+
+ align:start position:0%
+also what i like to say is help people
+the public build its muscle for
+
+ align:start position:0%
+the public build its muscle for
+ 
+
+ align:start position:0%
+the public build its muscle for
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+the civic design framework gives us a
+
+ align:start position:0%
+the civic design framework gives us a
+ 
+
+ align:start position:0%
+the civic design framework gives us a
+way into these conversations that are
+
+ align:start position:0%
+way into these conversations that are
+ 
+
+ align:start position:0%
+way into these conversations that are
+central to having a truly functional
+
+ align:start position:0%
+central to having a truly functional
+ 
+
+ align:start position:0%
+central to having a truly functional
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+professor mcdowell teaches the framework
+
+ align:start position:0%
+professor mcdowell teaches the framework
+ 
+
+ align:start position:0%
+professor mcdowell teaches the framework
+to students in 11312
+
+ align:start position:0%
+to students in 11312
+ 
+
+ align:start position:0%
+to students in 11312
+engage in community we really use a
+
+ align:start position:0%
+engage in community we really use a
+ 
+
+ align:start position:0%
+engage in community we really use a
+certain design framework
+
+ align:start position:0%
+certain design framework
+ 
+
+ align:start position:0%
+certain design framework
+as a tool for organizing thinking in
+
+ align:start position:0%
+as a tool for organizing thinking in
+ 
+
+ align:start position:0%
+as a tool for organizing thinking in
+projects
+
+ align:start position:0%
+projects
+ 
+
+ align:start position:0%
+projects
+and the framework really has two
+
+ align:start position:0%
+and the framework really has two
+ 
+
+ align:start position:0%
+and the framework really has two
+components to it
+
+ align:start position:0%
+components to it
+ 
+
+ align:start position:0%
+components to it
+it's based on the notion that part of
+
+ align:start position:0%
+it's based on the notion that part of
+ 
+
+ align:start position:0%
+it's based on the notion that part of
+the issue
+
+ align:start position:0%
+the issue
+ 
+
+ align:start position:0%
+the issue
+of bringing the public in to any
+
+ align:start position:0%
+of bringing the public in to any
+ 
+
+ align:start position:0%
+of bringing the public in to any
+engagement process
+
+ align:start position:0%
+engagement process
+ 
+
+ align:start position:0%
+engagement process
+is we're not clear about what
+
+ align:start position:0%
+is we're not clear about what
+ 
+
+ align:start position:0%
+is we're not clear about what
+conversation we're invited into
+
+ align:start position:0%
+conversation we're invited into
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+our problem in our public discourse in
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+ align:start position:0%
+our problem in our public discourse in
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+ align:start position:0%
+engagement process is we often invite
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+ align:start position:0%
+engagement process is we often invite
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+
+ align:start position:0%
+people into one conversation and then
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+ align:start position:0%
+people into one conversation and then
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+ align:start position:0%
+when they get in the room
+ 
+
+ align:start position:0%
+when they get in the room
+we set them up for another so we will
+
+ align:start position:0%
+we set them up for another so we will
+ 
+
+ align:start position:0%
+we set them up for another so we will
+say to them
+
+ align:start position:0%
+say to them
+ 
+
+ align:start position:0%
+say to them
+come imagine a new sarasota florida
+
+ align:start position:0%
+come imagine a new sarasota florida
+ 
+
+ align:start position:0%
+come imagine a new sarasota florida
+and you go into the room and you have
+
+ align:start position:0%
+and you go into the room and you have
+ 
+
+ align:start position:0%
+and you go into the room and you have
+three choices to make
+
+ align:start position:0%
+three choices to make
+ 
+
+ align:start position:0%
+three choices to make
+so basically you've set people up right
+
+ align:start position:0%
+so basically you've set people up right
+ 
+
+ align:start position:0%
+so basically you've set people up right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+no wonder people are really dissatisfied
+
+ align:start position:0%
+no wonder people are really dissatisfied
+ 
+
+ align:start position:0%
+no wonder people are really dissatisfied
+the other thing why it's important to
+
+ align:start position:0%
+the other thing why it's important to
+ 
+
+ align:start position:0%
+the other thing why it's important to
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+know which kind of conversation you have
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+ align:start position:0%
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+ align:start position:0%
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+each require something different if you
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+ align:start position:0%
+each require something different if you
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+ align:start position:0%
+each require something different if you
+want to be in a framing conversation
+
+ align:start position:0%
+want to be in a framing conversation
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+want to be in a framing conversation
+with someone that's
+
+ align:start position:0%
+with someone that's
+ 
+
+ align:start position:0%
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+totally different you're using really
+
+ align:start position:0%
+totally different you're using really
+ 
+
+ align:start position:0%
+totally different you're using really
+different cognitive structures
+
+ align:start position:0%
+different cognitive structures
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+
+ align:start position:0%
+different cognitive structures
+than if you're in the ideation process
+
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+than if you're in the ideation process
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+ align:start position:0%
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+right because in the ideation process
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+ align:start position:0%
+you're trying to ignite
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+ align:start position:0%
+you're trying to ignite
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+the imagination in a framing
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+ align:start position:0%
+the imagination in a framing
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+
+ align:start position:0%
+conversation you're really trying to
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+ align:start position:0%
+conversation you're really trying to
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+deeply understand
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+ align:start position:0%
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+experience and what's happening in the
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+ align:start position:0%
+experience and what's happening in the
+world so those are very
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+ align:start position:0%
+world so those are very
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+ align:start position:0%
+world so those are very
+different right and so if you don't know
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+ align:start position:0%
+different right and so if you don't know
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+
+ align:start position:0%
+different right and so if you don't know
+what kind of conversation you want to
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+ align:start position:0%
+what kind of conversation you want to
+ 
+
+ align:start position:0%
+what kind of conversation you want to
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+ align:start position:0%
+have in public
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+ align:start position:0%
+have in public
+you're not going to design it the right
+
+ align:start position:0%
+you're not going to design it the right
+ 
+
+ align:start position:0%
+you're not going to design it the right
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+what's really exciting about professor
+
+ align:start position:0%
+what's really exciting about professor
+ 
+
+ align:start position:0%
+what's really exciting about professor
+mcdowell's class
+
+ align:start position:0%
+mcdowell's class
+ 
+
+ align:start position:0%
+mcdowell's class
+is that he doesn't just teach the theory
+
+ align:start position:0%
+is that he doesn't just teach the theory
+ 
+
+ align:start position:0%
+is that he doesn't just teach the theory
+of this civic design framework
+
+ align:start position:0%
+of this civic design framework
+ 
+
+ align:start position:0%
+of this civic design framework
+students are also invited to bring
+
+ align:start position:0%
+students are also invited to bring
+ 
+
+ align:start position:0%
+students are also invited to bring
+forward actual cases
+
+ align:start position:0%
+forward actual cases
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+ align:start position:0%
+forward actual cases
+from the communities with which they are
+
+ align:start position:0%
+from the communities with which they are
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+ align:start position:0%
+from the communities with which they are
+already engaging where they can
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+ align:start position:0%
+already engaging where they can
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+ align:start position:0%
+already engaging where they can
+implement the design
+
+ align:start position:0%
+implement the design
+ 
+
+ align:start position:0%
+implement the design
+framework in real life i always try to
+
+ align:start position:0%
+framework in real life i always try to
+ 
+
+ align:start position:0%
+framework in real life i always try to
+generate this opportunity for students
+
+ align:start position:0%
+generate this opportunity for students
+ 
+
+ align:start position:0%
+generate this opportunity for students
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+here are the things we want to work on
+
+ align:start position:0%
+here are the things we want to work on
+ 
+
+ align:start position:0%
+here are the things we want to work on
+and then to negotiate among themselves
+
+ align:start position:0%
+and then to negotiate among themselves
+ 
+
+ align:start position:0%
+and then to negotiate among themselves
+which ones
+
+ align:start position:0%
+which ones
+ 
+
+ align:start position:0%
+which ones
+they really want to move forward on we
+
+ align:start position:0%
+they really want to move forward on we
+ 
+
+ align:start position:0%
+they really want to move forward on we
+did one in mexico
+
+ align:start position:0%
+did one in mexico
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+ align:start position:0%
+did one in mexico
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+
+ align:start position:0%
+and that one is actually interesting it
+ 
+
+ align:start position:0%
+and that one is actually interesting it
+was a former alum of our department
+
+ align:start position:0%
+was a former alum of our department
+ 
+
+ align:start position:0%
+was a former alum of our department
+who had just stepped into this major
+
+ align:start position:0%
+who had just stepped into this major
+ 
+
+ align:start position:0%
+who had just stepped into this major
+role in the new
+
+ align:start position:0%
+role in the new
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+ align:start position:0%
+role in the new
+government in the town in mexico
+
+ align:start position:0%
+government in the town in mexico
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+
+ align:start position:0%
+government in the town in mexico
+and they had got them through kind of a
+
+ align:start position:0%
+and they had got them through kind of a
+ 
+
+ align:start position:0%
+and they had got them through kind of a
+popular
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+ align:start position:0%
+popular
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+ align:start position:0%
+popular
+you know all grassroots campaign and now
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+ align:start position:0%
+you know all grassroots campaign and now
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+ align:start position:0%
+you know all grassroots campaign and now
+they wanted to figure out how do we
+
+ align:start position:0%
+they wanted to figure out how do we
+ 
+
+ align:start position:0%
+they wanted to figure out how do we
+carry that into
+
+ align:start position:0%
+carry that into
+ 
+
+ align:start position:0%
+carry that into
+a structure into governance that
+
+ align:start position:0%
+a structure into governance that
+ 
+
+ align:start position:0%
+a structure into governance that
+actually allows to get the public
+
+ align:start position:0%
+actually allows to get the public
+ 
+
+ align:start position:0%
+actually allows to get the public
+involved and so the class is really
+
+ align:start position:0%
+involved and so the class is really
+ 
+
+ align:start position:0%
+involved and so the class is really
+helping them through that design so it's
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+ align:start position:0%
+helping them through that design so it's
+ 
+
+ align:start position:0%
+helping them through that design so it's
+always that kind of
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+always that kind of
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+ align:start position:0%
+always that kind of
+some problem some place where people are
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+some problem some place where people are
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+some problem some place where people are
+trying to figure out how to broad and
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+trying to figure out how to broad and
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+trying to figure out how to broad and
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+
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+diversify
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+diversify
+how they're engaging with the public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the realities of collaborating
+
+ align:start position:0%
+one of the realities of collaborating
+ 
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+ align:start position:0%
+one of the realities of collaborating
+with real people in real communities
+
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+with real people in real communities
+ 
+
+ align:start position:0%
+with real people in real communities
+is that practitioners often find
+
+ align:start position:0%
+is that practitioners often find
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+themselves in situations
+
+ align:start position:0%
+themselves in situations
+ 
+
+ align:start position:0%
+themselves in situations
+where solutions are complicated and
+
+ align:start position:0%
+where solutions are complicated and
+ 
+
+ align:start position:0%
+where solutions are complicated and
+sometimes not complete
+
+ align:start position:0%
+sometimes not complete
+ 
+
+ align:start position:0%
+sometimes not complete
+professor mcdowell offered some
+
+ align:start position:0%
+professor mcdowell offered some
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+
+ align:start position:0%
+professor mcdowell offered some
+important words of wisdom for
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+ align:start position:0%
+important words of wisdom for
+ 
+
+ align:start position:0%
+important words of wisdom for
+practitioners new to fieldwork
+
+ align:start position:0%
+practitioners new to fieldwork
+ 
+
+ align:start position:0%
+practitioners new to fieldwork
+i think it's not just this course but in
+
+ align:start position:0%
+i think it's not just this course but in
+ 
+
+ align:start position:0%
+i think it's not just this course but in
+terms of any real practice based course
+
+ align:start position:0%
+terms of any real practice based course
+ 
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+terms of any real practice based course
+that puts you out of
+
+ align:start position:0%
+that puts you out of
+ 
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+ align:start position:0%
+that puts you out of
+the field there are a couple things that
+
+ align:start position:0%
+the field there are a couple things that
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+
+ align:start position:0%
+the field there are a couple things that
+you have to contend with one
+
+ align:start position:0%
+you have to contend with one
+ 
+
+ align:start position:0%
+you have to contend with one
+there are no complete solutions
+
+ align:start position:0%
+there are no complete solutions
+ 
+
+ align:start position:0%
+there are no complete solutions
+right you have to learn how to make
+
+ align:start position:0%
+right you have to learn how to make
+ 
+
+ align:start position:0%
+right you have to learn how to make
+decisions in the midst of ambiguity
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+ align:start position:0%
+decisions in the midst of ambiguity
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+
+ align:start position:0%
+decisions in the midst of ambiguity
+you just you know you have to do it
+
+ align:start position:0%
+you just you know you have to do it
+ 
+
+ align:start position:0%
+you just you know you have to do it
+which means for you
+
+ align:start position:0%
+which means for you
+ 
+
+ align:start position:0%
+which means for you
+internally you have to have your
+
+ align:start position:0%
+internally you have to have your
+ 
+
+ align:start position:0%
+internally you have to have your
+own dialogue to yourself
+
+ align:start position:0%
+own dialogue to yourself
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+ align:start position:0%
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+to understand how you're holding on to
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+ align:start position:0%
+to understand how you're holding on to
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+ align:start position:0%
+to understand how you're holding on to
+the things that you believe
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+the things that you believe
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+even though you're not able to really
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+achieve them
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+achieve them
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+achieve them
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+right within the midst of any one
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+right within the midst of any one
+project or any one initiative but you
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+ align:start position:0%
+project or any one initiative but you
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+
+ align:start position:0%
+project or any one initiative but you
+still
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+ align:start position:0%
+still
+ 
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+ align:start position:0%
+still
+not letting it kind of get to you and
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+ align:start position:0%
+not letting it kind of get to you and
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+ align:start position:0%
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+one of the ways
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+one of the ways
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+we talk about this is i make a real
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+we talk about this is i make a real
+distinction in our class around
+
+ align:start position:0%
+distinction in our class around
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+ align:start position:0%
+distinction in our class around
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+
+ align:start position:0%
+how we talk about things so for example
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+
+ align:start position:0%
+how we talk about things so for example
+you know in our society i'm really good
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+ align:start position:0%
+you know in our society i'm really good
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+ align:start position:0%
+you know in our society i'm really good
+at what i would say this kind of
+
+ align:start position:0%
+at what i would say this kind of
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+at what i would say this kind of
+language of evaluation
+
+ align:start position:0%
+language of evaluation
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+ align:start position:0%
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+you know how well something is not we're
+
+ align:start position:0%
+you know how well something is not we're
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+
+ align:start position:0%
+you know how well something is not we're
+also good in language with critique
+
+ align:start position:0%
+also good in language with critique
+ 
+
+ align:start position:0%
+also good in language with critique
+which is different than the evaluation
+
+ align:start position:0%
+which is different than the evaluation
+ 
+
+ align:start position:0%
+which is different than the evaluation
+and we're really good at this language
+
+ align:start position:0%
+and we're really good at this language
+ 
+
+ align:start position:0%
+and we're really good at this language
+of possibility
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+ align:start position:0%
+of possibility
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+
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+of possibility
+right now really looking into the future
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+ align:start position:0%
+right now really looking into the future
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+right now really looking into the future
+what we're
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+what we're
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+what we're
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+
+ align:start position:0%
+not really good at is talking about the
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+
+ align:start position:0%
+not really good at is talking about the
+reality what i call the language of
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+ align:start position:0%
+reality what i call the language of
+ 
+
+ align:start position:0%
+reality what i call the language of
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+ align:start position:0%
+transition
+ 
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+ align:start position:0%
+transition
+the reality is we have things we want to
+
+ align:start position:0%
+the reality is we have things we want to
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+
+ align:start position:0%
+the reality is we have things we want to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+and as we're trying to do those things
+
+ align:start position:0%
+and as we're trying to do those things
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+ align:start position:0%
+and as we're trying to do those things
+to change systems we want to be
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+ align:start position:0%
+to change systems we want to be
+ 
+
+ align:start position:0%
+to change systems we want to be
+different we
+
+ align:start position:0%
+different we
+ 
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+ align:start position:0%
+different we
+have to support the systems that we're
+
+ align:start position:0%
+have to support the systems that we're
+ 
+
+ align:start position:0%
+have to support the systems that we're
+trying to change
+
+ align:start position:0%
+trying to change
+ 
+
+ align:start position:0%
+trying to change
+and so we live in this in-between space
+
+ align:start position:0%
+and so we live in this in-between space
+ 
+
+ align:start position:0%
+and so we live in this in-between space
+a space called department that's where
+
+ align:start position:0%
+a space called department that's where
+ 
+
+ align:start position:0%
+a space called department that's where
+we live and
+
+ align:start position:0%
+we live and
+ 
+
+ align:start position:0%
+we live and
+in that space we have to learn how to
+
+ align:start position:0%
+in that space we have to learn how to
+ 
+
+ align:start position:0%
+in that space we have to learn how to
+talk to each other and this is why i
+
+ align:start position:0%
+talk to each other and this is why i
+ 
+
+ align:start position:0%
+talk to each other and this is why i
+always use these terms like grace and
+
+ align:start position:0%
+always use these terms like grace and
+ 
+
+ align:start position:0%
+always use these terms like grace and
+stuff like that
+
+ align:start position:0%
+stuff like that
+ 
+
+ align:start position:0%
+stuff like that
+because there's a recognition but that's
+
+ align:start position:0%
+because there's a recognition but that's
+ 
+
+ align:start position:0%
+because there's a recognition but that's
+where you are
+
+ align:start position:0%
+where you are
+ 
+
+ align:start position:0%
+where you are
+so in my class i try to support folks
+
+ align:start position:0%
+so in my class i try to support folks
+ 
+
+ align:start position:0%
+so in my class i try to support folks
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+able to talk about that about what
+
+ align:start position:0%
+able to talk about that about what
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+ align:start position:0%
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+they're living with
+
+ align:start position:0%
+they're living with
+ 
+
+ align:start position:0%
+they're living with
+in the middle what they're having to
+
+ align:start position:0%
+in the middle what they're having to
+ 
+
+ align:start position:0%
+in the middle what they're having to
+hold on to that they don't
+
+ align:start position:0%
+hold on to that they don't
+ 
+
+ align:start position:0%
+hold on to that they don't
+necessarily feel good about but they
+
+ align:start position:0%
+necessarily feel good about but they
+ 
+
+ align:start position:0%
+necessarily feel good about but they
+know they have to do it is they're
+
+ align:start position:0%
+know they have to do it is they're
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+
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+know they have to do it is they're
+trying to do this other thing and to
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+ align:start position:0%
+trying to do this other thing and to
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+ align:start position:0%
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+support them through that kind of
+
+ align:start position:0%
+support them through that kind of
+ 
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+ align:start position:0%
+support them through that kind of
+conversation this is a reflection of the
+
+ align:start position:0%
+conversation this is a reflection of the
+ 
+
+ align:start position:0%
+conversation this is a reflection of the
+transition you're living in and just a
+
+ align:start position:0%
+transition you're living in and just a
+ 
+
+ align:start position:0%
+transition you're living in and just a
+recognition of that and honoring it and
+
+ align:start position:0%
+recognition of that and honoring it and
+ 
+
+ align:start position:0%
+recognition of that and honoring it and
+letting it be okay
+
+ align:start position:0%
+letting it be okay
+ 
+
+ align:start position:0%
+letting it be okay
+right it's almost being able to have
+
+ align:start position:0%
+right it's almost being able to have
+ 
+
+ align:start position:0%
+right it's almost being able to have
+a dialogue of forgiveness with yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i wanted to know what these engagements
+
+ align:start position:0%
+i wanted to know what these engagements
+ 
+
+ align:start position:0%
+i wanted to know what these engagements
+look like in practice
+
+ align:start position:0%
+look like in practice
+ 
+
+ align:start position:0%
+look like in practice
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+
+ align:start position:0%
+so professor mcdowell shared with me one
+ 
+
+ align:start position:0%
+so professor mcdowell shared with me one
+example that took place in my very own
+
+ align:start position:0%
+example that took place in my very own
+ 
+
+ align:start position:0%
+example that took place in my very own
+city of cambridge massachusetts
+
+ align:start position:0%
+city of cambridge massachusetts
+ 
+
+ align:start position:0%
+city of cambridge massachusetts
+the dialogue was around domestic
+
+ align:start position:0%
+the dialogue was around domestic
+ 
+
+ align:start position:0%
+the dialogue was around domestic
+violence and how the city could better
+
+ align:start position:0%
+violence and how the city could better
+ 
+
+ align:start position:0%
+violence and how the city could better
+address the issue
+
+ align:start position:0%
+address the issue
+ 
+
+ align:start position:0%
+address the issue
+and the engagement was simple professor
+
+ align:start position:0%
+and the engagement was simple professor
+ 
+
+ align:start position:0%
+and the engagement was simple professor
+mcdowell and his team
+
+ align:start position:0%
+mcdowell and his team
+ 
+
+ align:start position:0%
+mcdowell and his team
+asked residents of cambridge to donate a
+
+ align:start position:0%
+asked residents of cambridge to donate a
+ 
+
+ align:start position:0%
+asked residents of cambridge to donate a
+question they had about domestic
+
+ align:start position:0%
+question they had about domestic
+ 
+
+ align:start position:0%
+question they had about domestic
+violence
+
+ align:start position:0%
+violence
+ 
+
+ align:start position:0%
+violence
+think about domestic violence that is
+
+ align:start position:0%
+think about domestic violence that is
+ 
+
+ align:start position:0%
+think about domestic violence that is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+a public conversation right there's
+
+ align:start position:0%
+a public conversation right there's
+ 
+
+ align:start position:0%
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+nothing that people talk about
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+nothing that people talk about
+because we have the structure of all you
+
+ align:start position:0%
+because we have the structure of all you
+ 
+
+ align:start position:0%
+because we have the structure of all you
+have to do is donate a question
+
+ align:start position:0%
+have to do is donate a question
+ 
+
+ align:start position:0%
+have to do is donate a question
+a group of young people from cambridge
+
+ align:start position:0%
+a group of young people from cambridge
+ 
+
+ align:start position:0%
+a group of young people from cambridge
+ranch and latin set up a booth
+
+ align:start position:0%
+ranch and latin set up a booth
+ 
+
+ align:start position:0%
+ranch and latin set up a booth
+in harvard square they put up a board
+
+ align:start position:0%
+in harvard square they put up a board
+ 
+
+ align:start position:0%
+in harvard square they put up a board
+and they made cookies and they just
+
+ align:start position:0%
+and they made cookies and they just
+ 
+
+ align:start position:0%
+and they made cookies and they just
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+
+ align:start position:0%
+basically had a thing a cookie for your
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+
+ align:start position:0%
+basically had a thing a cookie for your
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and people would write their question
+
+ align:start position:0%
+and people would write their question
+ 
+
+ align:start position:0%
+and people would write their question
+about the next survives and put on the
+
+ align:start position:0%
+about the next survives and put on the
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+
+ align:start position:0%
+about the next survives and put on the
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+
+ align:start position:0%
+board and get a cookie
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+
+ align:start position:0%
+board and get a cookie
+and then people started having
+
+ align:start position:0%
+and then people started having
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+
+ align:start position:0%
+and then people started having
+conversations
+
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+conversations
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+conversations
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+
+ align:start position:0%
+in public about what's on the board
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+
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+
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+all the questions that came in
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+printed them out very large and
+
+ align:start position:0%
+printed them out very large and
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+printed them out very large and
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+we had a space in cambridge that we
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+all 2000 something questions up on the
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+
+ align:start position:0%
+all 2000 something questions up on the
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+wall
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+
+ align:start position:0%
+wall
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+and we created a public event for people
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+
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+read the questions and sit down and have
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+
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+
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+and then we had people from the public
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+
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+come in and say let's figure out
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+
+ align:start position:0%
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+can we organize these questions and
+
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+
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+certain kinds of themes and issues
+
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+certain kinds of themes and issues
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+
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+certain kinds of themes and issues
+and then we have conversations with
+
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+and then we have conversations with
+ 
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+right so all this is like taking
+
+ align:start position:0%
+right so all this is like taking
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+ align:start position:0%
+right so all this is like taking
+something we don't talk about
+
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+something we don't talk about
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+
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+something we don't talk about
+and creating an opportunity for people
+
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+and creating an opportunity for people
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+
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+and creating an opportunity for people
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+
+ align:start position:0%
+to do it because you're in some sense
+ 
+
+ align:start position:0%
+to do it because you're in some sense
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+
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+
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+
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+
+ align:start position:0%
+right but if you do it in the right way
+ 
+
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+right but if you do it in the right way
+you don't try to tell them what they
+
+ align:start position:0%
+you don't try to tell them what they
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+
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+
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+you just create that opportunity that
+
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+you just create that opportunity that
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+
+ align:start position:0%
+you just create that opportunity that
+equalizes voices
+
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+
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+
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+
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+
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+is incredibly important in professor
+
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+
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+
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+
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+one specific aspect of his design
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+
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+
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+ 
+
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+it's built on the notion of equity and
+
+ align:start position:0%
+it's built on the notion of equity and
+ 
+
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+it's built on the notion of equity and
+it's a concept he calls
+
+ align:start position:0%
+it's a concept he calls
+ 
+
+ align:start position:0%
+it's a concept he calls
+designing for the margins the reason i
+
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+designing for the margins the reason i
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+
+ align:start position:0%
+designing for the margins the reason i
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+
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+margins is
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+
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+
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+our default and everything we do
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+
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+kind of design is designed for the
+
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+kind of design is designed for the
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+
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+kind of design is designed for the
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+
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+middle
+ 
+
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+middle
+where most people are and we do that
+
+ align:start position:0%
+where most people are and we do that
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+
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+where most people are and we do that
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+
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+because we want to scale we want things
+ 
+
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+because we want to scale we want things
+to grow fast we want to make sure we're
+
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+to grow fast we want to make sure we're
+ 
+
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+to grow fast we want to make sure we're
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+
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+
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+those that are in the middle you're
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+
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+
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+
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+
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+
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+further and further out and as
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+
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+further and further out and as
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+
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+other things in our systems fail we end
+ 
+
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+other things in our systems fail we end
+up putting more and more people
+
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+
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+those who are living with the failures
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+
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+those who are living with the failures
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+
+ align:start position:0%
+of the society
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+
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+
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+and so if we're going to attend that
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+
+ align:start position:0%
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+
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+
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+
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+
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+
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+decades ago it created some access and a
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+
+ align:start position:0%
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+
+ align:start position:0%
+but the interesting thing about it is
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+
+ align:start position:0%
+you look at it now and you say well who
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+
+ align:start position:0%
+you look at it now and you say well who
+benefits from that that's a design for
+
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+
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+who uses it well anybody rides a bicycle
+
+ align:start position:0%
+who uses it well anybody rides a bicycle
+ 
+
+ align:start position:0%
+who uses it well anybody rides a bicycle
+pushes a trailer carries a grocery chart
+
+ align:start position:0%
+pushes a trailer carries a grocery chart
+ 
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+pushes a trailer carries a grocery chart
+stroller right strollers right it's all
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+ align:start position:0%
+stroller right strollers right it's all
+ 
+
+ align:start position:0%
+stroller right strollers right it's all
+there right
+
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+but that's not what it was designed for
+
+ align:start position:0%
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+
+ align:start position:0%
+but that's not what it was designed for
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+
+ align:start position:0%
+it was designed for the margin but yet
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+all these central activities that people
+
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+
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+
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+too
+ 
+
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+too
+the interesting thing about it and why
+
+ align:start position:0%
+the interesting thing about it and why
+ 
+
+ align:start position:0%
+the interesting thing about it and why
+i'd actually like to use that example
+
+ align:start position:0%
+i'd actually like to use that example
+ 
+
+ align:start position:0%
+i'd actually like to use that example
+is what have you noticed about
+
+ align:start position:0%
+is what have you noticed about
+ 
+
+ align:start position:0%
+is what have you noticed about
+changes in curb cuts in the last decade
+
+ align:start position:0%
+changes in curb cuts in the last decade
+ 
+
+ align:start position:0%
+changes in curb cuts in the last decade
+they have bumps on them now they have
+
+ align:start position:0%
+they have bumps on them now they have
+ 
+
+ align:start position:0%
+they have bumps on them now they have
+texture to them and they have texture to
+
+ align:start position:0%
+texture to them and they have texture to
+ 
+
+ align:start position:0%
+texture to them and they have texture to
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+because it helps people
+
+ align:start position:0%
+because it helps people
+ 
+
+ align:start position:0%
+because it helps people
+without sight to know they're coming to
+
+ align:start position:0%
+without sight to know they're coming to
+ 
+
+ align:start position:0%
+without sight to know they're coming to
+a corner so the thing about designing
+
+ align:start position:0%
+a corner so the thing about designing
+ 
+
+ align:start position:0%
+a corner so the thing about designing
+for the margins
+
+ align:start position:0%
+for the margins
+ 
+
+ align:start position:0%
+for the margins
+it's not a thing that you achieve it's a
+
+ align:start position:0%
+it's not a thing that you achieve it's a
+ 
+
+ align:start position:0%
+it's not a thing that you achieve it's a
+thing that you're always working at
+
+ align:start position:0%
+thing that you're always working at
+ 
+
+ align:start position:0%
+thing that you're always working at
+because the margins will keep emerging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're anything like me you may be
+
+ align:start position:0%
+if you're anything like me you may be
+ 
+
+ align:start position:0%
+if you're anything like me you may be
+thinking to yourself
+
+ align:start position:0%
+thinking to yourself
+ 
+
+ align:start position:0%
+thinking to yourself
+that this is exactly the kind of work
+
+ align:start position:0%
+that this is exactly the kind of work
+ 
+
+ align:start position:0%
+that this is exactly the kind of work
+that our country
+
+ align:start position:0%
+that our country
+ 
+
+ align:start position:0%
+that our country
+and really our planet could use more of
+
+ align:start position:0%
+and really our planet could use more of
+ 
+
+ align:start position:0%
+and really our planet could use more of
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+more open more connected ways to engage
+
+ align:start position:0%
+more open more connected ways to engage
+ 
+
+ align:start position:0%
+more open more connected ways to engage
+groups of people
+
+ align:start position:0%
+groups of people
+ 
+
+ align:start position:0%
+groups of people
+around complex issues and a design
+
+ align:start position:0%
+around complex issues and a design
+ 
+
+ align:start position:0%
+around complex issues and a design
+framework that allows us to keep working
+
+ align:start position:0%
+framework that allows us to keep working
+ 
+
+ align:start position:0%
+framework that allows us to keep working
+at those issues
+
+ align:start position:0%
+at those issues
+ 
+
+ align:start position:0%
+at those issues
+part of what i love about professor
+
+ align:start position:0%
+part of what i love about professor
+ 
+
+ align:start position:0%
+part of what i love about professor
+mcdowell's work is that it's grounded in
+
+ align:start position:0%
+mcdowell's work is that it's grounded in
+ 
+
+ align:start position:0%
+mcdowell's work is that it's grounded in
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+the hard work of community and community
+
+ align:start position:0%
+the hard work of community and community
+ 
+
+ align:start position:0%
+the hard work of community and community
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+the way that our systems are set up
+
+ align:start position:0%
+the way that our systems are set up
+ 
+
+ align:start position:0%
+the way that our systems are set up
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+they really are designed to keep people
+
+ align:start position:0%
+they really are designed to keep people
+ 
+
+ align:start position:0%
+they really are designed to keep people
+apart to disconnect people from each
+
+ align:start position:0%
+apart to disconnect people from each
+ 
+
+ align:start position:0%
+apart to disconnect people from each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+groups from each other right and they
+
+ align:start position:0%
+groups from each other right and they
+ 
+
+ align:start position:0%
+groups from each other right and they
+draw these false dichotomies
+
+ align:start position:0%
+draw these false dichotomies
+ 
+
+ align:start position:0%
+draw these false dichotomies
+but in reality people live with a much
+
+ align:start position:0%
+but in reality people live with a much
+ 
+
+ align:start position:0%
+but in reality people live with a much
+more complex set of things
+
+ align:start position:0%
+more complex set of things
+ 
+
+ align:start position:0%
+more complex set of things
+right so for example you take the
+
+ align:start position:0%
+right so for example you take the
+ 
+
+ align:start position:0%
+right so for example you take the
+movement from black lives
+
+ align:start position:0%
+movement from black lives
+ 
+
+ align:start position:0%
+movement from black lives
+and you take away that in a very
+
+ align:start position:0%
+and you take away that in a very
+ 
+
+ align:start position:0%
+and you take away that in a very
+powerful way
+
+ align:start position:0%
+powerful way
+ 
+
+ align:start position:0%
+powerful way
+using the notions of defunding the
+
+ align:start position:0%
+using the notions of defunding the
+ 
+
+ align:start position:0%
+using the notions of defunding the
+police you know some of the views
+
+ align:start position:0%
+police you know some of the views
+ 
+
+ align:start position:0%
+police you know some of the views
+and others to change what policing is
+
+ align:start position:0%
+and others to change what policing is
+ 
+
+ align:start position:0%
+and others to change what policing is
+right because
+
+ align:start position:0%
+right because
+ 
+
+ align:start position:0%
+right because
+they have seen the evidence over and
+
+ align:start position:0%
+they have seen the evidence over and
+ 
+
+ align:start position:0%
+they have seen the evidence over and
+over again
+
+ align:start position:0%
+over again
+ 
+
+ align:start position:0%
+over again
+of the devaluing of black lives within
+
+ align:start position:0%
+of the devaluing of black lives within
+ 
+
+ align:start position:0%
+of the devaluing of black lives within
+the midst of the police
+
+ align:start position:0%
+the midst of the police
+ 
+
+ align:start position:0%
+the midst of the police
+however even with that same experience
+
+ align:start position:0%
+however even with that same experience
+ 
+
+ align:start position:0%
+however even with that same experience
+knowledge space you can go into the
+
+ align:start position:0%
+knowledge space you can go into the
+ 
+
+ align:start position:0%
+knowledge space you can go into the
+black community
+
+ align:start position:0%
+black community
+ 
+
+ align:start position:0%
+black community
+and people have very different feelings
+
+ align:start position:0%
+and people have very different feelings
+ 
+
+ align:start position:0%
+and people have very different feelings
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+do we do from the police or not the
+
+ align:start position:0%
+do we do from the police or not the
+ 
+
+ align:start position:0%
+do we do from the police or not the
+trading off of there
+
+ align:start position:0%
+trading off of there
+ 
+
+ align:start position:0%
+trading off of there
+i know there's a risk but that risk is
+
+ align:start position:0%
+i know there's a risk but that risk is
+ 
+
+ align:start position:0%
+i know there's a risk but that risk is
+in here and it's out there and i don't
+
+ align:start position:0%
+in here and it's out there and i don't
+ 
+
+ align:start position:0%
+in here and it's out there and i don't
+know how to balance it
+
+ align:start position:0%
+know how to balance it
+ 
+
+ align:start position:0%
+know how to balance it
+i don't know what to do about that right
+
+ align:start position:0%
+i don't know what to do about that right
+ 
+
+ align:start position:0%
+i don't know what to do about that right
+when we
+
+ align:start position:0%
+when we
+ 
+
+ align:start position:0%
+when we
+put things in our either or then we
+
+ align:start position:0%
+put things in our either or then we
+ 
+
+ align:start position:0%
+put things in our either or then we
+really lose the opportunity
+
+ align:start position:0%
+really lose the opportunity
+ 
+
+ align:start position:0%
+really lose the opportunity
+to really connect people or to create
+
+ align:start position:0%
+to really connect people or to create
+ 
+
+ align:start position:0%
+to really connect people or to create
+some opportunity for people to
+
+ align:start position:0%
+some opportunity for people to
+ 
+
+ align:start position:0%
+some opportunity for people to
+acknowledge what's the complexity that's
+
+ align:start position:0%
+acknowledge what's the complexity that's
+ 
+
+ align:start position:0%
+acknowledge what's the complexity that's
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+and how do you negotiate that in a way
+
+ align:start position:0%
+and how do you negotiate that in a way
+ 
+
+ align:start position:0%
+and how do you negotiate that in a way
+that doesn't leave people behind
+
+ align:start position:0%
+that doesn't leave people behind
+ 
+
+ align:start position:0%
+that doesn't leave people behind
+or leave them to the side i should say
+
+ align:start position:0%
+or leave them to the side i should say
+ 
+
+ align:start position:0%
+or leave them to the side i should say
+and you know you can use policing as
+
+ align:start position:0%
+and you know you can use policing as
+ 
+
+ align:start position:0%
+and you know you can use policing as
+some you can use
+
+ align:start position:0%
+some you can use
+ 
+
+ align:start position:0%
+some you can use
+what's happening in vaccinations there's
+
+ align:start position:0%
+what's happening in vaccinations there's
+ 
+
+ align:start position:0%
+what's happening in vaccinations there's
+another there's a lot of things that are
+
+ align:start position:0%
+another there's a lot of things that are
+ 
+
+ align:start position:0%
+another there's a lot of things that are
+just structured
+
+ align:start position:0%
+just structured
+ 
+
+ align:start position:0%
+just structured
+and the way we talk about them in the
+
+ align:start position:0%
+and the way we talk about them in the
+ 
+
+ align:start position:0%
+and the way we talk about them in the
+public doesn't recognize one thing that
+
+ align:start position:0%
+public doesn't recognize one thing that
+ 
+
+ align:start position:0%
+public doesn't recognize one thing that
+we know is really true
+
+ align:start position:0%
+we know is really true
+ 
+
+ align:start position:0%
+we know is really true
+our values kind of moderate a continuum
+
+ align:start position:0%
+our values kind of moderate a continuum
+ 
+
+ align:start position:0%
+our values kind of moderate a continuum
+and what we're always doing
+
+ align:start position:0%
+and what we're always doing
+ 
+
+ align:start position:0%
+and what we're always doing
+is trading off one for the other we're
+
+ align:start position:0%
+is trading off one for the other we're
+ 
+
+ align:start position:0%
+is trading off one for the other we're
+going back and forth
+
+ align:start position:0%
+going back and forth
+ 
+
+ align:start position:0%
+going back and forth
+right people are looking at things and
+
+ align:start position:0%
+right people are looking at things and
+ 
+
+ align:start position:0%
+right people are looking at things and
+they're looking at that value
+
+ align:start position:0%
+they're looking at that value
+ 
+
+ align:start position:0%
+they're looking at that value
+versus another value versus another
+
+ align:start position:0%
+versus another value versus another
+ 
+
+ align:start position:0%
+versus another value versus another
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+and why that's important for public
+
+ align:start position:0%
+and why that's important for public
+ 
+
+ align:start position:0%
+and why that's important for public
+conversations is if we can step away
+
+ align:start position:0%
+conversations is if we can step away
+ 
+
+ align:start position:0%
+conversations is if we can step away
+from saying
+
+ align:start position:0%
+from saying
+ 
+
+ align:start position:0%
+from saying
+your value is this and mine is that and
+
+ align:start position:0%
+your value is this and mine is that and
+ 
+
+ align:start position:0%
+your value is this and mine is that and
+you can get people in the space to
+
+ align:start position:0%
+you can get people in the space to
+ 
+
+ align:start position:0%
+you can get people in the space to
+realize
+
+ align:start position:0%
+realize
+ 
+
+ align:start position:0%
+realize
+oh this is how you trading off this set
+
+ align:start position:0%
+oh this is how you trading off this set
+ 
+
+ align:start position:0%
+oh this is how you trading off this set
+of values and this is how i'm trading
+
+ align:start position:0%
+of values and this is how i'm trading
+ 
+
+ align:start position:0%
+of values and this is how i'm trading
+them off
+
+ align:start position:0%
+them off
+ 
+
+ align:start position:0%
+them off
+then when you realize that people are
+
+ align:start position:0%
+then when you realize that people are
+ 
+
+ align:start position:0%
+then when you realize that people are
+holding half within the
+
+ align:start position:0%
+holding half within the
+ 
+
+ align:start position:0%
+holding half within the
+same values they really are
+
+ align:start position:0%
+same values they really are
+ 
+
+ align:start position:0%
+same values they really are
+just shifting and weighing them
+
+ align:start position:0%
+just shifting and weighing them
+ 
+
+ align:start position:0%
+just shifting and weighing them
+differently at different times and that
+
+ align:start position:0%
+differently at different times and that
+ 
+
+ align:start position:0%
+differently at different times and that
+creates
+
+ align:start position:0%
+creates
+ 
+
+ align:start position:0%
+creates
+more of an opportunity for people at
+
+ align:start position:0%
+more of an opportunity for people at
+ 
+
+ align:start position:0%
+more of an opportunity for people at
+least to see the other they may not
+
+ align:start position:0%
+least to see the other they may not
+ 
+
+ align:start position:0%
+least to see the other they may not
+agree
+
+ align:start position:0%
+agree
+ 
+
+ align:start position:0%
+agree
+but they begin to see the other and
+
+ align:start position:0%
+but they begin to see the other and
+ 
+
+ align:start position:0%
+but they begin to see the other and
+that's you know
+
+ align:start position:0%
+that's you know
+ 
+
+ align:start position:0%
+that's you know
+in our society where so many groups of
+
+ align:start position:0%
+in our society where so many groups of
+ 
+
+ align:start position:0%
+in our society where so many groups of
+people have been so dehumanized
+
+ align:start position:0%
+people have been so dehumanized
+ 
+
+ align:start position:0%
+people have been so dehumanized
+our first step is to let people be seen
+
+ align:start position:0%
+our first step is to let people be seen
+ 
+
+ align:start position:0%
+our first step is to let people be seen
+through all the social upheaval and the
+
+ align:start position:0%
+through all the social upheaval and the
+ 
+
+ align:start position:0%
+through all the social upheaval and the
+many defining events of 2020
+
+ align:start position:0%
+many defining events of 2020
+ 
+
+ align:start position:0%
+many defining events of 2020
+professor mcdowell has continued to
+
+ align:start position:0%
+professor mcdowell has continued to
+ 
+
+ align:start position:0%
+professor mcdowell has continued to
+spend a lot of his time engaging with
+
+ align:start position:0%
+spend a lot of his time engaging with
+ 
+
+ align:start position:0%
+spend a lot of his time engaging with
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+he often works with smaller class sizes
+
+ align:start position:0%
+he often works with smaller class sizes
+ 
+
+ align:start position:0%
+he often works with smaller class sizes
+so that he can develop the close
+
+ align:start position:0%
+so that he can develop the close
+ 
+
+ align:start position:0%
+so that he can develop the close
+relationships he feels are essential
+
+ align:start position:0%
+relationships he feels are essential
+ 
+
+ align:start position:0%
+relationships he feels are essential
+this kind of close contact allows him to
+
+ align:start position:0%
+this kind of close contact allows him to
+ 
+
+ align:start position:0%
+this kind of close contact allows him to
+see into students lives beyond the
+
+ align:start position:0%
+see into students lives beyond the
+ 
+
+ align:start position:0%
+see into students lives beyond the
+classroom
+
+ align:start position:0%
+classroom
+ 
+
+ align:start position:0%
+classroom
+and he shared with me some insights into
+
+ align:start position:0%
+and he shared with me some insights into
+ 
+
+ align:start position:0%
+and he shared with me some insights into
+what he's seeing and what educators can
+
+ align:start position:0%
+what he's seeing and what educators can
+ 
+
+ align:start position:0%
+what he's seeing and what educators can
+do to help
+
+ align:start position:0%
+do to help
+ 
+
+ align:start position:0%
+do to help
+i think students are dealing with a lot
+
+ align:start position:0%
+i think students are dealing with a lot
+ 
+
+ align:start position:0%
+i think students are dealing with a lot
+right now and it's not just because of
+
+ align:start position:0%
+right now and it's not just because of
+ 
+
+ align:start position:0%
+right now and it's not just because of
+kodi i think our society is in a huge
+
+ align:start position:0%
+kodi i think our society is in a huge
+ 
+
+ align:start position:0%
+kodi i think our society is in a huge
+transition
+
+ align:start position:0%
+transition
+ 
+
+ align:start position:0%
+transition
+you know i can't tell you how many
+
+ align:start position:0%
+you know i can't tell you how many
+ 
+
+ align:start position:0%
+you know i can't tell you how many
+students i have right now
+
+ align:start position:0%
+students i have right now
+ 
+
+ align:start position:0%
+students i have right now
+who don't feel
+
+ align:start position:0%
+who don't feel
+ 
+
+ align:start position:0%
+who don't feel
+connected to their families anymore
+
+ align:start position:0%
+connected to their families anymore
+ 
+
+ align:start position:0%
+connected to their families anymore
+because of what's going on politically
+
+ align:start position:0%
+because of what's going on politically
+ 
+
+ align:start position:0%
+because of what's going on politically
+in this country
+
+ align:start position:0%
+in this country
+ 
+
+ align:start position:0%
+in this country
+that disrupture that people are sitting
+
+ align:start position:0%
+that disrupture that people are sitting
+ 
+
+ align:start position:0%
+that disrupture that people are sitting
+with and so then you ask
+
+ align:start position:0%
+with and so then you ask
+ 
+
+ align:start position:0%
+with and so then you ask
+how do we as educators
+
+ align:start position:0%
+how do we as educators
+ 
+
+ align:start position:0%
+how do we as educators
+know they're sitting with this help them
+
+ align:start position:0%
+know they're sitting with this help them
+ 
+
+ align:start position:0%
+know they're sitting with this help them
+to actually move forward in a way that i
+
+ align:start position:0%
+to actually move forward in a way that i
+ 
+
+ align:start position:0%
+to actually move forward in a way that i
+was going to allow them
+
+ align:start position:0%
+was going to allow them
+ 
+
+ align:start position:0%
+was going to allow them
+to be generative with other people
+
+ align:start position:0%
+to be generative with other people
+ 
+
+ align:start position:0%
+to be generative with other people
+in the communities they work with and
+
+ align:start position:0%
+in the communities they work with and
+ 
+
+ align:start position:0%
+in the communities they work with and
+also find their own path
+
+ align:start position:0%
+also find their own path
+ 
+
+ align:start position:0%
+also find their own path
+and so for me teaching always has to be
+
+ align:start position:0%
+and so for me teaching always has to be
+ 
+
+ align:start position:0%
+and so for me teaching always has to be
+grounded
+
+ align:start position:0%
+grounded
+ 
+
+ align:start position:0%
+grounded
+in a reality you have to be working with
+
+ align:start position:0%
+in a reality you have to be working with
+ 
+
+ align:start position:0%
+in a reality you have to be working with
+others who are actually dealing with the
+
+ align:start position:0%
+others who are actually dealing with the
+ 
+
+ align:start position:0%
+others who are actually dealing with the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+or the issue or who wants to do
+
+ align:start position:0%
+or the issue or who wants to do
+ 
+
+ align:start position:0%
+or the issue or who wants to do
+something and you just have to work with
+
+ align:start position:0%
+something and you just have to work with
+ 
+
+ align:start position:0%
+something and you just have to work with
+them and
+
+ align:start position:0%
+them and
+ 
+
+ align:start position:0%
+them and
+it really is about lifting up and
+
+ align:start position:0%
+it really is about lifting up and
+ 
+
+ align:start position:0%
+it really is about lifting up and
+supporting
+
+ align:start position:0%
+supporting
+ 
+
+ align:start position:0%
+supporting
+people through that process of working
+
+ align:start position:0%
+people through that process of working
+ 
+
+ align:start position:0%
+people through that process of working
+with others and working with yourself
+
+ align:start position:0%
+with others and working with yourself
+ 
+
+ align:start position:0%
+with others and working with yourself
+in some ways a lot of my teaching is yes
+
+ align:start position:0%
+in some ways a lot of my teaching is yes
+ 
+
+ align:start position:0%
+in some ways a lot of my teaching is yes
+it's about social
+
+ align:start position:0%
+it's about social
+ 
+
+ align:start position:0%
+it's about social
+issues but it is also about
+
+ align:start position:0%
+issues but it is also about
+ 
+
+ align:start position:0%
+issues but it is also about
+helping people develop not only just a
+
+ align:start position:0%
+helping people develop not only just a
+ 
+
+ align:start position:0%
+helping people develop not only just a
+theory of practice
+
+ align:start position:0%
+theory of practice
+ 
+
+ align:start position:0%
+theory of practice
+but a reflective strategy for themselves
+
+ align:start position:0%
+but a reflective strategy for themselves
+ 
+
+ align:start position:0%
+but a reflective strategy for themselves
+as they move
+
+ align:start position:0%
+as they move
+ 
+
+ align:start position:0%
+as they move
+through their careers into their lives
+
+ align:start position:0%
+through their careers into their lives
+ 
+
+ align:start position:0%
+through their careers into their lives
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there's a lot of excitement about
+
+ align:start position:0%
+there's a lot of excitement about
+ 
+
+ align:start position:0%
+there's a lot of excitement about
+professor mcdowell's work in teaching
+
+ align:start position:0%
+professor mcdowell's work in teaching
+ 
+
+ align:start position:0%
+professor mcdowell's work in teaching
+so we had some really wonderful listener
+
+ align:start position:0%
+so we had some really wonderful listener
+ 
+
+ align:start position:0%
+so we had some really wonderful listener
+questions sent in for this episode
+
+ align:start position:0%
+questions sent in for this episode
+ 
+
+ align:start position:0%
+questions sent in for this episode
+and we're excited to share two of them
+
+ align:start position:0%
+and we're excited to share two of them
+ 
+
+ align:start position:0%
+and we're excited to share two of them
+with you now
+
+ align:start position:0%
+with you now
+ 
+
+ align:start position:0%
+with you now
+here's one a listener sent in for people
+
+ align:start position:0%
+here's one a listener sent in for people
+ 
+
+ align:start position:0%
+here's one a listener sent in for people
+who are used to having privileged access
+
+ align:start position:0%
+who are used to having privileged access
+ 
+
+ align:start position:0%
+who are used to having privileged access
+to policy discussion and implementation
+
+ align:start position:0%
+to policy discussion and implementation
+ 
+
+ align:start position:0%
+to policy discussion and implementation
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+what habits should we watch out for are
+
+ align:start position:0%
+what habits should we watch out for are
+ 
+
+ align:start position:0%
+what habits should we watch out for are
+there subconscious attitudes or
+
+ align:start position:0%
+there subconscious attitudes or
+ 
+
+ align:start position:0%
+there subconscious attitudes or
+behaviors
+
+ align:start position:0%
+behaviors
+ 
+
+ align:start position:0%
+behaviors
+that get in the way of including
+
+ align:start position:0%
+that get in the way of including
+ 
+
+ align:start position:0%
+that get in the way of including
+historically excluded people
+
+ align:start position:0%
+historically excluded people
+ 
+
+ align:start position:0%
+historically excluded people
+that's a really beautiful question i
+
+ align:start position:0%
+that's a really beautiful question i
+ 
+
+ align:start position:0%
+that's a really beautiful question i
+think the
+
+ align:start position:0%
+think the
+ 
+
+ align:start position:0%
+think the
+number one habit we have to watch out
+
+ align:start position:0%
+number one habit we have to watch out
+ 
+
+ align:start position:0%
+number one habit we have to watch out
+for is a habit that we
+
+ align:start position:0%
+for is a habit that we
+ 
+
+ align:start position:0%
+for is a habit that we
+actually understand the issue
+
+ align:start position:0%
+actually understand the issue
+ 
+
+ align:start position:0%
+actually understand the issue
+right that we fully understand it we
+
+ align:start position:0%
+right that we fully understand it we
+ 
+
+ align:start position:0%
+right that we fully understand it we
+have to make space
+
+ align:start position:0%
+have to make space
+ 
+
+ align:start position:0%
+have to make space
+for people to be able to reframe the
+
+ align:start position:0%
+for people to be able to reframe the
+ 
+
+ align:start position:0%
+for people to be able to reframe the
+issues we understand it
+
+ align:start position:0%
+issues we understand it
+ 
+
+ align:start position:0%
+issues we understand it
+if we hold on to our frame from that
+
+ align:start position:0%
+if we hold on to our frame from that
+ 
+
+ align:start position:0%
+if we hold on to our frame from that
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+we will never really fully be able to
+
+ align:start position:0%
+we will never really fully be able to
+ 
+
+ align:start position:0%
+we will never really fully be able to
+include others
+
+ align:start position:0%
+include others
+ 
+
+ align:start position:0%
+include others
+so for me that's the critical
+
+ align:start position:0%
+so for me that's the critical
+ 
+
+ align:start position:0%
+so for me that's the critical
+issue and that means we have to make
+
+ align:start position:0%
+issue and that means we have to make
+ 
+
+ align:start position:0%
+issue and that means we have to make
+time and space for that
+
+ align:start position:0%
+time and space for that
+ 
+
+ align:start position:0%
+time and space for that
+and that pushes against so much of what
+
+ align:start position:0%
+and that pushes against so much of what
+ 
+
+ align:start position:0%
+and that pushes against so much of what
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+you know these policy areas think about
+
+ align:start position:0%
+you know these policy areas think about
+ 
+
+ align:start position:0%
+you know these policy areas think about
+because we try to do everything we gotta
+
+ align:start position:0%
+because we try to do everything we gotta
+ 
+
+ align:start position:0%
+because we try to do everything we gotta
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+we gotta and i think
+
+ align:start position:0%
+we gotta and i think
+ 
+
+ align:start position:0%
+we gotta and i think
+the mantra should be we're going to do
+
+ align:start position:0%
+the mantra should be we're going to do
+ 
+
+ align:start position:0%
+the mantra should be we're going to do
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+we're not going to get it quite right we
+
+ align:start position:0%
+we're not going to get it quite right we
+ 
+
+ align:start position:0%
+we're not going to get it quite right we
+can take some time
+
+ align:start position:0%
+can take some time
+ 
+
+ align:start position:0%
+can take some time
+to maybe understand a little different
+
+ align:start position:0%
+to maybe understand a little different
+ 
+
+ align:start position:0%
+to maybe understand a little different
+we're going to do something there we're
+
+ align:start position:0%
+we're going to do something there we're
+ 
+
+ align:start position:0%
+we're going to do something there we're
+not gonna get quite right
+
+ align:start position:0%
+not gonna get quite right
+ 
+
+ align:start position:0%
+not gonna get quite right
+we're gonna take time to understand it
+
+ align:start position:0%
+we're gonna take time to understand it
+ 
+
+ align:start position:0%
+we're gonna take time to understand it
+you know it's like
+
+ align:start position:0%
+you know it's like
+ 
+
+ align:start position:0%
+you know it's like
+because that's the reality it is the
+
+ align:start position:0%
+because that's the reality it is the
+ 
+
+ align:start position:0%
+because that's the reality it is the
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+so we have to acknowledge it
+
+ align:start position:0%
+so we have to acknowledge it
+ 
+
+ align:start position:0%
+so we have to acknowledge it
+and to close one more listener question
+
+ align:start position:0%
+and to close one more listener question
+ 
+
+ align:start position:0%
+and to close one more listener question
+one that very well may have been on your
+
+ align:start position:0%
+one that very well may have been on your
+ 
+
+ align:start position:0%
+one that very well may have been on your
+mind while listening
+
+ align:start position:0%
+mind while listening
+ 
+
+ align:start position:0%
+mind while listening
+is it easier or harder to have difficult
+
+ align:start position:0%
+is it easier or harder to have difficult
+ 
+
+ align:start position:0%
+is it easier or harder to have difficult
+conversations
+
+ align:start position:0%
+conversations
+ 
+
+ align:start position:0%
+conversations
+in small groups or large town hall
+
+ align:start position:0%
+in small groups or large town hall
+ 
+
+ align:start position:0%
+in small groups or large town hall
+settings
+
+ align:start position:0%
+settings
+ 
+
+ align:start position:0%
+settings
+how do we scale up dialogues how do you
+
+ align:start position:0%
+how do we scale up dialogues how do you
+ 
+
+ align:start position:0%
+how do we scale up dialogues how do you
+adjust the questions the tone
+
+ align:start position:0%
+adjust the questions the tone
+ 
+
+ align:start position:0%
+adjust the questions the tone
+the pacing to accommodate large and
+
+ align:start position:0%
+the pacing to accommodate large and
+ 
+
+ align:start position:0%
+the pacing to accommodate large and
+diverse audiences
+
+ align:start position:0%
+diverse audiences
+ 
+
+ align:start position:0%
+diverse audiences
+i'm a firm believer in small-scale
+
+ align:start position:0%
+i'm a firm believer in small-scale
+ 
+
+ align:start position:0%
+i'm a firm believer in small-scale
+dialogues
+
+ align:start position:0%
+dialogues
+ 
+
+ align:start position:0%
+dialogues
+to deal with really difficult issues
+
+ align:start position:0%
+to deal with really difficult issues
+ 
+
+ align:start position:0%
+to deal with really difficult issues
+if we try to do it in large scale
+
+ align:start position:0%
+if we try to do it in large scale
+ 
+
+ align:start position:0%
+if we try to do it in large scale
+audience we
+
+ align:start position:0%
+audience we
+ 
+
+ align:start position:0%
+audience we
+one you can't have one voice in there
+
+ align:start position:0%
+one you can't have one voice in there
+ 
+
+ align:start position:0%
+one you can't have one voice in there
+which means you're inevitably silencing
+
+ align:start position:0%
+which means you're inevitably silencing
+ 
+
+ align:start position:0%
+which means you're inevitably silencing
+certain people
+
+ align:start position:0%
+certain people
+ 
+
+ align:start position:0%
+certain people
+and i'm not saying don't do large-scale
+
+ align:start position:0%
+and i'm not saying don't do large-scale
+ 
+
+ align:start position:0%
+and i'm not saying don't do large-scale
+events because it's good sometimes just
+
+ align:start position:0%
+events because it's good sometimes just
+ 
+
+ align:start position:0%
+events because it's good sometimes just
+a certain place to listen
+
+ align:start position:0%
+a certain place to listen
+ 
+
+ align:start position:0%
+a certain place to listen
+and hear and and watch others that's
+
+ align:start position:0%
+and hear and and watch others that's
+ 
+
+ align:start position:0%
+and hear and and watch others that's
+that has value
+
+ align:start position:0%
+that has value
+ 
+
+ align:start position:0%
+that has value
+but the transformational piece for
+
+ align:start position:0%
+but the transformational piece for
+ 
+
+ align:start position:0%
+but the transformational piece for
+everyone i think is
+
+ align:start position:0%
+everyone i think is
+ 
+
+ align:start position:0%
+everyone i think is
+being small space dialogues with others
+
+ align:start position:0%
+being small space dialogues with others
+ 
+
+ align:start position:0%
+being small space dialogues with others
+i think we need work in turning our
+
+ align:start position:0%
+i think we need work in turning our
+ 
+
+ align:start position:0%
+i think we need work in turning our
+technologies and designing our
+
+ align:start position:0%
+technologies and designing our
+ 
+
+ align:start position:0%
+technologies and designing our
+communication systems
+
+ align:start position:0%
+communication systems
+ 
+
+ align:start position:0%
+communication systems
+to support that kind of listening and
+
+ align:start position:0%
+to support that kind of listening and
+ 
+
+ align:start position:0%
+to support that kind of listening and
+conversation and that's not what we have
+
+ align:start position:0%
+conversation and that's not what we have
+ 
+
+ align:start position:0%
+conversation and that's not what we have
+right they're driven by other things and
+
+ align:start position:0%
+right they're driven by other things and
+ 
+
+ align:start position:0%
+right they're driven by other things and
+that's one of the problems with them so
+
+ align:start position:0%
+that's one of the problems with them so
+ 
+
+ align:start position:0%
+that's one of the problems with them so
+i think we can get that if we shift
+
+ align:start position:0%
+i think we can get that if we shift
+ 
+
+ align:start position:0%
+i think we can get that if we shift
+our attention our design attention to
+
+ align:start position:0%
+our attention our design attention to
+ 
+
+ align:start position:0%
+our attention our design attention to
+that and
+
+ align:start position:0%
+that and
+ 
+
+ align:start position:0%
+that and
+the reality around it is all of our
+
+ align:start position:0%
+the reality around it is all of our
+ 
+
+ align:start position:0%
+the reality around it is all of our
+incentives
+
+ align:start position:0%
+incentives
+ 
+
+ align:start position:0%
+incentives
+for creating things like that are in the
+
+ align:start position:0%
+for creating things like that are in the
+ 
+
+ align:start position:0%
+for creating things like that are in the
+opposite direction you know
+
+ align:start position:0%
+opposite direction you know
+ 
+
+ align:start position:0%
+opposite direction you know
+you know it's like it's hard to build
+
+ align:start position:0%
+you know it's like it's hard to build
+ 
+
+ align:start position:0%
+you know it's like it's hard to build
+technologies that are designed for the
+
+ align:start position:0%
+technologies that are designed for the
+ 
+
+ align:start position:0%
+technologies that are designed for the
+largest that are gonna
+
+ align:start position:0%
+largest that are gonna
+ 
+
+ align:start position:0%
+largest that are gonna
+actually scale right because you have
+
+ align:start position:0%
+actually scale right because you have
+ 
+
+ align:start position:0%
+actually scale right because you have
+all these other things going on
+
+ align:start position:0%
+all these other things going on
+ 
+
+ align:start position:0%
+all these other things going on
+it's a challenge i don't think it's a
+
+ align:start position:0%
+it's a challenge i don't think it's a
+ 
+
+ align:start position:0%
+it's a challenge i don't think it's a
+challenge that can be met
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're interested in learning more
+
+ align:start position:0%
+if you're interested in learning more
+ 
+
+ align:start position:0%
+if you're interested in learning more
+about professor cesar mcdowell's work
+
+ align:start position:0%
+about professor cesar mcdowell's work
+ 
+
+ align:start position:0%
+about professor cesar mcdowell's work
+or teaching with his open educational
+
+ align:start position:0%
+or teaching with his open educational
+ 
+
+ align:start position:0%
+or teaching with his open educational
+resources you can check out his course
+
+ align:start position:0%
+resources you can check out his course
+ 
+
+ align:start position:0%
+resources you can check out his course
+11312 engage in community on our mit
+
+ align:start position:0%
+11312 engage in community on our mit
+ 
+
+ align:start position:0%
+11312 engage in community on our mit
+opencourseware website you can also
+
+ align:start position:0%
+opencourseware website you can also
+ 
+
+ align:start position:0%
+opencourseware website you can also
+listen to his podcast
+
+ align:start position:0%
+listen to his podcast
+ 
+
+ align:start position:0%
+listen to his podcast
+we who engage it's available wherever
+
+ align:start position:0%
+we who engage it's available wherever
+ 
+
+ align:start position:0%
+we who engage it's available wherever
+you listen to podcasts
+
+ align:start position:0%
+you listen to podcasts
+ 
+
+ align:start position:0%
+you listen to podcasts
+thanks for tuning in for our second
+
+ align:start position:0%
+thanks for tuning in for our second
+ 
+
+ align:start position:0%
+thanks for tuning in for our second
+season of chalk radio
+
+ align:start position:0%
+season of chalk radio
+ 
+
+ align:start position:0%
+season of chalk radio
+we hope you enjoyed these episodes and
+
+ align:start position:0%
+we hope you enjoyed these episodes and
+ 
+
+ align:start position:0%
+we hope you enjoyed these episodes and
+will consider sharing this
+
+ align:start position:0%
+will consider sharing this
+ 
+
+ align:start position:0%
+will consider sharing this
+or any of our other episodes with a
+
+ align:start position:0%
+or any of our other episodes with a
+ 
+
+ align:start position:0%
+or any of our other episodes with a
+friend family member or colleague
+
+ align:start position:0%
+friend family member or colleague
+ 
+
+ align:start position:0%
+friend family member or colleague
+we have more in store for season three
+
+ align:start position:0%
+we have more in store for season three
+ 
+
+ align:start position:0%
+we have more in store for season three
+and are already working hard to bring
+
+ align:start position:0%
+and are already working hard to bring
+ 
+
+ align:start position:0%
+and are already working hard to bring
+you more episodes
+
+ align:start position:0%
+you more episodes
+ 
+
+ align:start position:0%
+you more episodes
+to inspire your teaching and learning
+
+ align:start position:0%
+to inspire your teaching and learning
+ 
+
+ align:start position:0%
+to inspire your teaching and learning
+when chalk radio
+
+ align:start position:0%
+when chalk radio
+ 
+
+ align:start position:0%
+when chalk radio
+returns in the fall signing off from
+
+ align:start position:0%
+returns in the fall signing off from
+ 
+
+ align:start position:0%
+returns in the fall signing off from
+cambridge massachusetts
+
+ align:start position:0%
+cambridge massachusetts
+ 
+
+ align:start position:0%
+cambridge massachusetts
+i'm sarah hansen from mit open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+courseware
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+passed the car
\ No newline at end of file
diff --git a/pWq8blw9Nhc.txt b/pWq8blw9Nhc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c56f86fc5ff89b355152ff907b4a10307e1a7d45
--- /dev/null
+++ b/pWq8blw9Nhc.txt
@@ -0,0 +1,12763 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+today we are going to start a new topic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so first we talk about the chirophobia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember
+
+ align:start position:0%
+so remember
+ 
+
+ align:start position:0%
+so remember
+say under low range transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+the uh this The Rock spinner field
+
+ align:start position:0%
+the uh this The Rock spinner field
+ 
+
+ align:start position:0%
+the uh this The Rock spinner field
+transforms
+
+ align:start position:0%
+transforms
+ 
+
+ align:start position:0%
+transforms
+as s Lambda
+
+ align:start position:0%
+as s Lambda
+ 
+
+ align:start position:0%
+as s Lambda
+PSI X
+
+ align:start position:0%
+PSI X
+ 
+
+ align:start position:0%
+PSI X
+and the X Prime is the low range
+
+ align:start position:0%
+and the X Prime is the low range
+ 
+
+ align:start position:0%
+and the X Prime is the low range
+transformation of X okay so X Prime
+
+ align:start position:0%
+transformation of X okay so X Prime
+ 
+
+ align:start position:0%
+transformation of X okay so X Prime
+Lambda X on x okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then then the S is uh uh given by
+
+ align:start position:0%
+and then then the S is uh uh given by
+ 
+
+ align:start position:0%
+and then then the S is uh uh given by
+say uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the second one mu is given by
+
+ align:start position:0%
+okay and the second one mu is given by
+ 
+
+ align:start position:0%
+okay and the second one mu is given by
+the commutator of the gamma matrices
+
+ align:start position:0%
+the commutator of the gamma matrices
+ 
+
+ align:start position:0%
+the commutator of the gamma matrices
+so let me just write it down so Sigma
+
+ align:start position:0%
+so let me just write it down so Sigma
+ 
+
+ align:start position:0%
+so let me just write it down so Sigma
+just remind you
+
+ align:start position:0%
+just remind you
+ 
+
+ align:start position:0%
+just remind you
+I divided by four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one natural question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so previously when we derived The Rock
+
+ align:start position:0%
+so previously when we derived The Rock
+ 
+
+ align:start position:0%
+so previously when we derived The Rock
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+we showed that The Rock equation
+
+ align:start position:0%
+we showed that The Rock equation
+ 
+
+ align:start position:0%
+we showed that The Rock equation
+requires actually precise to have four
+
+ align:start position:0%
+requires actually precise to have four
+ 
+
+ align:start position:0%
+requires actually precise to have four
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+but then we showed that the debug
+
+ align:start position:0%
+but then we showed that the debug
+ 
+
+ align:start position:0%
+but then we showed that the debug
+equation is covarent if the side
+
+ align:start position:0%
+equation is covarent if the side
+ 
+
+ align:start position:0%
+equation is covarent if the side
+transform this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so natural question is that whether you
+
+ align:start position:0%
+so natural question is that whether you
+ 
+
+ align:start position:0%
+so natural question is that whether you
+can actually restrict
+
+ align:start position:0%
+can actually restrict
+ 
+
+ align:start position:0%
+can actually restrict
+to a smaller part say to a subset of PSI
+
+ align:start position:0%
+to a smaller part say to a subset of PSI
+ 
+
+ align:start position:0%
+to a smaller part say to a subset of PSI
+whether they still have well-defined low
+
+ align:start position:0%
+whether they still have well-defined low
+ 
+
+ align:start position:0%
+whether they still have well-defined low
+range transformation
+
+ align:start position:0%
+range transformation
+ 
+
+ align:start position:0%
+range transformation
+okay whether they still whether we
+
+ align:start position:0%
+okay whether they still whether we
+ 
+
+ align:start position:0%
+okay whether they still whether we
+actually need to have four components to
+
+ align:start position:0%
+actually need to have four components to
+ 
+
+ align:start position:0%
+actually need to have four components to
+have well-defined four complex
+
+ align:start position:0%
+have well-defined four complex
+ 
+
+ align:start position:0%
+have well-defined four complex
+components you have well-defined level
+
+ align:start position:0%
+components you have well-defined level
+ 
+
+ align:start position:0%
+components you have well-defined level
+and transformation
+
+ align:start position:0%
+and transformation
+ 
+
+ align:start position:0%
+and transformation
+okay and the answer turns out to be
+
+ align:start position:0%
+okay and the answer turns out to be
+ 
+
+ align:start position:0%
+okay and the answer turns out to be
+no you actually don't need to have four
+
+ align:start position:0%
+no you actually don't need to have four
+ 
+
+ align:start position:0%
+no you actually don't need to have four
+complex components to have well-defined
+
+ align:start position:0%
+complex components to have well-defined
+ 
+
+ align:start position:0%
+complex components to have well-defined
+transformation actually uh you can you
+
+ align:start position:0%
+transformation actually uh you can you
+ 
+
+ align:start position:0%
+transformation actually uh you can you
+can reduce it okay and so there are two
+
+ align:start position:0%
+can reduce it okay and so there are two
+ 
+
+ align:start position:0%
+can reduce it okay and so there are two
+ways to reduce it and one is called
+
+ align:start position:0%
+ways to reduce it and one is called
+ 
+
+ align:start position:0%
+ways to reduce it and one is called
+chirophobia and the wine is called the
+
+ align:start position:0%
+chirophobia and the wine is called the
+ 
+
+ align:start position:0%
+chirophobia and the wine is called the
+Myron formula okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so so we first talk about the
+
+ align:start position:0%
+so so so we first talk about the
+ 
+
+ align:start position:0%
+so so so we first talk about the
+chirophobia and one way to do it
+
+ align:start position:0%
+chirophobia and one way to do it
+ 
+
+ align:start position:0%
+chirophobia and one way to do it
+so for this purpose we will look at the
+
+ align:start position:0%
+so for this purpose we will look at the
+ 
+
+ align:start position:0%
+so for this purpose we will look at the
+specific representation
+
+ align:start position:0%
+specific representation
+ 
+
+ align:start position:0%
+specific representation
+of gamma matrices okay consider
+
+ align:start position:0%
+of gamma matrices okay consider
+ 
+
+ align:start position:0%
+of gamma matrices okay consider
+so now I will use the repetition which
+
+ align:start position:0%
+so now I will use the repetition which
+ 
+
+ align:start position:0%
+so now I will use the repetition which
+is different from what you uh us uh uh
+
+ align:start position:0%
+is different from what you uh us uh uh
+ 
+
+ align:start position:0%
+is different from what you uh us uh uh
+so we can see the folding one
+
+ align:start position:0%
+so we can see the folding one
+ 
+
+ align:start position:0%
+so we can see the folding one
+comma zero equal to
+
+ align:start position:0%
+comma zero equal to
+ 
+
+ align:start position:0%
+comma zero equal to
+zero I I zero
+
+ align:start position:0%
+zero I I zero
+ 
+
+ align:start position:0%
+zero I I zero
+comma I
+
+ align:start position:0%
+comma I
+ 
+
+ align:start position:0%
+comma I
+equal to zero minus I single my I I
+
+ align:start position:0%
+equal to zero minus I single my I I
+ 
+
+ align:start position:0%
+equal to zero minus I single my I I
+Sigma I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay so this so this look at this
+
+ align:start position:0%
+zero okay so this so this look at this
+ 
+
+ align:start position:0%
+zero okay so this so this look at this
+choice of gamma matrices okay so I will
+
+ align:start position:0%
+choice of gamma matrices okay so I will
+ 
+
+ align:start position:0%
+choice of gamma matrices okay so I will
+look for this choice to be star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh so so you can also work it out
+
+ align:start position:0%
+and uh so so you can also work it out
+ 
+
+ align:start position:0%
+and uh so so you can also work it out
+you find the sigma
+
+ align:start position:0%
+you find the sigma
+ 
+
+ align:start position:0%
+you find the sigma
+so Sigma 0 I
+
+ align:start position:0%
+so Sigma 0 I
+ 
+
+ align:start position:0%
+so Sigma 0 I
+so so this is the sigma corresponding to
+
+ align:start position:0%
+so so this is the sigma corresponding to
+ 
+
+ align:start position:0%
+so so this is the sigma corresponding to
+the Boost
+
+ align:start position:0%
+the Boost
+ 
+
+ align:start position:0%
+the Boost
+so you find the sigma I you can just do
+
+ align:start position:0%
+so you find the sigma I you can just do
+ 
+
+ align:start position:0%
+so you find the sigma I you can just do
+the commutator
+
+ align:start position:0%
+the commutator
+ 
+
+ align:start position:0%
+the commutator
+from the sigma i x is equal to minus I
+
+ align:start position:0%
+from the sigma i x is equal to minus I
+ 
+
+ align:start position:0%
+from the sigma i x is equal to minus I
+divided by 2
+
+ align:start position:0%
+divided by 2
+ 
+
+ align:start position:0%
+divided by 2
+have this block diagonal form Sigma I
+
+ align:start position:0%
+have this block diagonal form Sigma I
+ 
+
+ align:start position:0%
+have this block diagonal form Sigma I
+zero zero Sigma again the small Sigma is
+
+ align:start position:0%
+zero zero Sigma again the small Sigma is
+ 
+
+ align:start position:0%
+zero zero Sigma again the small Sigma is
+always the poly matrices
+
+ align:start position:0%
+always the poly matrices
+ 
+
+ align:start position:0%
+always the poly matrices
+and then you can also work out the sigma
+
+ align:start position:0%
+and then you can also work out the sigma
+ 
+
+ align:start position:0%
+and then you can also work out the sigma
+J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you find this given by minus one
+
+ align:start position:0%
+then you find this given by minus one
+ 
+
+ align:start position:0%
+then you find this given by minus one
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+some i j k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then Sigma k
+
+ align:start position:0%
+then Sigma k
+ 
+
+ align:start position:0%
+then Sigma k
+zero zero Sigma okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+oh sorry here this is the minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so you find that the uh
+
+ align:start position:0%
+okay so so you find that the uh
+ 
+
+ align:start position:0%
+okay so so you find that the uh
+um they have the following form
+
+ align:start position:0%
+um they have the following form
+ 
+
+ align:start position:0%
+um they have the following form
+so what do You observe about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so do you see something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yes they are blocked diagonal
+
+ align:start position:0%
+yes they are blocked diagonal
+ 
+
+ align:start position:0%
+yes they are blocked diagonal
+so if Sigma is block diagonal then that
+
+ align:start position:0%
+so if Sigma is block diagonal then that
+ 
+
+ align:start position:0%
+so if Sigma is block diagonal then that
+means this s
+
+ align:start position:0%
+means this s
+ 
+
+ align:start position:0%
+means this s
+is also block diagonal
+
+ align:start position:0%
+is also block diagonal
+ 
+
+ align:start position:0%
+is also block diagonal
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so when s is blocked diagonal what does
+
+ align:start position:0%
+so when s is blocked diagonal what does
+ 
+
+ align:start position:0%
+so when s is blocked diagonal what does
+that mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+hmm
+
+ align:start position:0%
+hmm
+ 
+
+ align:start position:0%
+hmm
+exactly so so when the S is block
+
+ align:start position:0%
+exactly so so when the S is block
+ 
+
+ align:start position:0%
+exactly so so when the S is block
+diagonal that means
+
+ align:start position:0%
+diagonal that means
+ 
+
+ align:start position:0%
+diagonal that means
+when I write PSI subscribe four
+
+ align:start position:0%
+when I write PSI subscribe four
+ 
+
+ align:start position:0%
+when I write PSI subscribe four
+components that means that the upper two
+
+ align:start position:0%
+components that means that the upper two
+ 
+
+ align:start position:0%
+components that means that the upper two
+component the lower two components that
+
+ align:start position:0%
+component the lower two components that
+ 
+
+ align:start position:0%
+component the lower two components that
+don't transform to each other
+
+ align:start position:0%
+don't transform to each other
+ 
+
+ align:start position:0%
+don't transform to each other
+okay they only transform within
+
+ align:start position:0%
+okay they only transform within
+ 
+
+ align:start position:0%
+okay they only transform within
+themselves they don't transform to each
+
+ align:start position:0%
+themselves they don't transform to each
+ 
+
+ align:start position:0%
+themselves they don't transform to each
+other okay so so if I choose
+
+ align:start position:0%
+other okay so so if I choose
+ 
+
+ align:start position:0%
+other okay so so if I choose
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+is Lambda
+
+ align:start position:0%
+is Lambda
+ 
+
+ align:start position:0%
+is Lambda
+diagonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+so that means if I write PSI
+
+ align:start position:0%
+so that means if I write PSI
+ 
+
+ align:start position:0%
+so that means if I write PSI
+X into 2
+
+ align:start position:0%
+X into 2
+ 
+
+ align:start position:0%
+X into 2
+2 component Vector okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I delete the upper two component by PSI
+
+ align:start position:0%
+I delete the upper two component by PSI
+ 
+
+ align:start position:0%
+I delete the upper two component by PSI
+L another two components by percent r
+
+ align:start position:0%
+L another two components by percent r
+ 
+
+ align:start position:0%
+L another two components by percent r
+two components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+under low range transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the S Lambda
+
+ align:start position:0%
+on the S Lambda
+ 
+
+ align:start position:0%
+on the S Lambda
+PSI l
+
+ align:start position:0%
+PSI l
+ 
+
+ align:start position:0%
+PSI l
+and PSI R do not mix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they just transform among themselves
+
+ align:start position:0%
+so they just transform among themselves
+ 
+
+ align:start position:0%
+so they just transform among themselves
+and they just trans among themselves so
+
+ align:start position:0%
+and they just trans among themselves so
+ 
+
+ align:start position:0%
+and they just trans among themselves so
+they actually have well-defined the line
+
+ align:start position:0%
+they actually have well-defined the line
+ 
+
+ align:start position:0%
+they actually have well-defined the line
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+as a smaller unit okay you don't need
+
+ align:start position:0%
+as a smaller unit okay you don't need
+ 
+
+ align:start position:0%
+as a smaller unit okay you don't need
+four components to be able to transform
+
+ align:start position:0%
+four components to be able to transform
+ 
+
+ align:start position:0%
+four components to be able to transform
+On The Low End transformation actually
+
+ align:start position:0%
+On The Low End transformation actually
+ 
+
+ align:start position:0%
+On The Low End transformation actually
+these two components already transform
+
+ align:start position:0%
+these two components already transform
+ 
+
+ align:start position:0%
+these two components already transform
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this tells you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the sense that the Lawrence
+
+ align:start position:0%
+in the sense that the Lawrence
+ 
+
+ align:start position:0%
+in the sense that the Lawrence
+covariance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only requires
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two component spindles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you actually don't just by the Learning
+
+ align:start position:0%
+you actually don't just by the Learning
+ 
+
+ align:start position:0%
+you actually don't just by the Learning
+transformation itself we don't actually
+
+ align:start position:0%
+transformation itself we don't actually
+ 
+
+ align:start position:0%
+transformation itself we don't actually
+need four components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I'm going to tell you we actually
+
+ align:start position:0%
+so now I'm going to tell you we actually
+ 
+
+ align:start position:0%
+so now I'm going to tell you we actually
+do this all along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do we do know this all along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um sorry say it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah we have to go to four
+
+ align:start position:0%
+yeah yeah we have to go to four
+ 
+
+ align:start position:0%
+yeah yeah we have to go to four
+components because there's no
+
+ align:start position:0%
+components because there's no
+ 
+
+ align:start position:0%
+components because there's no
+two-dimensional there's no two component
+
+ align:start position:0%
+two-dimensional there's no two component
+ 
+
+ align:start position:0%
+two-dimensional there's no two component
+representation of the gamma matrices
+
+ align:start position:0%
+representation of the gamma matrices
+ 
+
+ align:start position:0%
+representation of the gamma matrices
+but that doesn't say it's a lower end
+
+ align:start position:0%
+but that doesn't say it's a lower end
+ 
+
+ align:start position:0%
+but that doesn't say it's a lower end
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+yeah and to write down the algebra for
+
+ align:start position:0%
+yeah and to write down the algebra for
+ 
+
+ align:start position:0%
+yeah and to write down the algebra for
+the gamma matrices
+
+ align:start position:0%
+the gamma matrices
+ 
+
+ align:start position:0%
+the gamma matrices
+you need four components
+
+ align:start position:0%
+you need four components
+ 
+
+ align:start position:0%
+you need four components
+but we actually knew all along that the
+
+ align:start position:0%
+but we actually knew all along that the
+ 
+
+ align:start position:0%
+but we actually knew all along that the
+two component is enough for the range
+
+ align:start position:0%
+two component is enough for the range
+ 
+
+ align:start position:0%
+two component is enough for the range
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+how do we know how do we actually know
+
+ align:start position:0%
+how do we know how do we actually know
+ 
+
+ align:start position:0%
+how do we know how do we actually know
+all along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have a yeah this is maybe more
+
+ align:start position:0%
+and we have a yeah this is maybe more
+ 
+
+ align:start position:0%
+and we have a yeah this is maybe more
+more complicated we have something much
+
+ align:start position:0%
+more complicated we have something much
+ 
+
+ align:start position:0%
+more complicated we have something much
+simpler yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah exactly so we we already said
+
+ align:start position:0%
+yeah exactly so we we already said
+ 
+
+ align:start position:0%
+yeah exactly so we we already said
+before if you have a mass list case when
+
+ align:start position:0%
+before if you have a mass list case when
+ 
+
+ align:start position:0%
+before if you have a mass list case when
+m equal to zero
+
+ align:start position:0%
+m equal to zero
+ 
+
+ align:start position:0%
+m equal to zero
+and the debug equation reduced to the
+
+ align:start position:0%
+and the debug equation reduced to the
+ 
+
+ align:start position:0%
+and the debug equation reduced to the
+two components
+
+ align:start position:0%
+two components
+ 
+
+ align:start position:0%
+two components
+and uh it's enough to do two components
+
+ align:start position:0%
+and uh it's enough to do two components
+ 
+
+ align:start position:0%
+and uh it's enough to do two components
+and the debug equation is covalent okay
+
+ align:start position:0%
+and the debug equation is covalent okay
+ 
+
+ align:start position:0%
+and the debug equation is covalent okay
+and so that means that actually you
+
+ align:start position:0%
+and so that means that actually you
+ 
+
+ align:start position:0%
+and so that means that actually you
+should be able to do it with two
+
+ align:start position:0%
+should be able to do it with two
+ 
+
+ align:start position:0%
+should be able to do it with two
+components okay because the mass of this
+
+ align:start position:0%
+components okay because the mass of this
+ 
+
+ align:start position:0%
+components okay because the mass of this
+particle they should be able to
+
+ align:start position:0%
+particle they should be able to
+ 
+
+ align:start position:0%
+particle they should be able to
+transform on the lower end
+
+ align:start position:0%
+transform on the lower end
+ 
+
+ align:start position:0%
+transform on the lower end
+transformation and so uh uh yeah and so
+
+ align:start position:0%
+transformation and so uh uh yeah and so
+ 
+
+ align:start position:0%
+transformation and so uh uh yeah and so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+require
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+few components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the mass of this case must also be
+
+ align:start position:0%
+since the mass of this case must also be
+ 
+
+ align:start position:0%
+since the mass of this case must also be
+Lorenz covarian so that a lorenze image
+
+ align:start position:0%
+Lorenz covarian so that a lorenze image
+ 
+
+ align:start position:0%
+Lorenz covarian so that a lorenze image
+itself should only require two
+
+ align:start position:0%
+itself should only require two
+ 
+
+ align:start position:0%
+itself should only require two
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+so it is not the lowest symmetry
+
+ align:start position:0%
+so it is not the lowest symmetry
+ 
+
+ align:start position:0%
+so it is not the lowest symmetry
+actually low rent covariance required
+
+ align:start position:0%
+actually low rent covariance required
+ 
+
+ align:start position:0%
+actually low rent covariance required
+the rock theory to have four component
+
+ align:start position:0%
+the rock theory to have four component
+ 
+
+ align:start position:0%
+the rock theory to have four component
+it is the mass okay
+
+ align:start position:0%
+it is the mass okay
+ 
+
+ align:start position:0%
+it is the mass okay
+so it is the mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass m if you wanted to describe a
+
+ align:start position:0%
+mass m if you wanted to describe a
+ 
+
+ align:start position:0%
+mass m if you wanted to describe a
+massive particle
+
+ align:start position:0%
+massive particle
+ 
+
+ align:start position:0%
+massive particle
+then you must have four components okay
+
+ align:start position:0%
+then you must have four components okay
+ 
+
+ align:start position:0%
+then you must have four components okay
+so so this is the mass which is the key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+okay good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have shown
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this particular representation of
+
+ align:start position:0%
+in this particular representation of
+ 
+
+ align:start position:0%
+in this particular representation of
+gamma matrices for this particular
+
+ align:start position:0%
+gamma matrices for this particular
+ 
+
+ align:start position:0%
+gamma matrices for this particular
+choice of gamma matrices
+
+ align:start position:0%
+choice of gamma matrices
+ 
+
+ align:start position:0%
+choice of gamma matrices
+and then the size transform a block a
+
+ align:start position:0%
+and then the size transform a block a
+ 
+
+ align:start position:0%
+and then the size transform a block a
+block diagonally
+
+ align:start position:0%
+block diagonally
+ 
+
+ align:start position:0%
+block diagonally
+but then we also said
+
+ align:start position:0%
+but then we also said
+ 
+
+ align:start position:0%
+but then we also said
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+not consider different choice of gamma
+
+ align:start position:0%
+not consider different choice of gamma
+ 
+
+ align:start position:0%
+not consider different choice of gamma
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+and this property will not hold
+
+ align:start position:0%
+and this property will not hold
+ 
+
+ align:start position:0%
+and this property will not hold
+okay this property will not hold now the
+
+ align:start position:0%
+okay this property will not hold now the
+ 
+
+ align:start position:0%
+okay this property will not hold now the
+question is that does this even with
+
+ align:start position:0%
+question is that does this even with
+ 
+
+ align:start position:0%
+question is that does this even with
+other gamma matrices can we actually
+
+ align:start position:0%
+other gamma matrices can we actually
+ 
+
+ align:start position:0%
+other gamma matrices can we actually
+reduce PSI to some smaller components
+
+ align:start position:0%
+reduce PSI to some smaller components
+ 
+
+ align:start position:0%
+reduce PSI to some smaller components
+okay the answer is still should still be
+
+ align:start position:0%
+okay the answer is still should still be
+ 
+
+ align:start position:0%
+okay the answer is still should still be
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+because we said that the Oracle or a
+
+ align:start position:0%
+because we said that the Oracle or a
+ 
+
+ align:start position:0%
+because we said that the Oracle or a
+representation of government is there
+
+ align:start position:0%
+representation of government is there
+ 
+
+ align:start position:0%
+representation of government is there
+should be equivalent
+
+ align:start position:0%
+should be equivalent
+ 
+
+ align:start position:0%
+should be equivalent
+so if we can do it in this a choice of
+
+ align:start position:0%
+so if we can do it in this a choice of
+ 
+
+ align:start position:0%
+so if we can do it in this a choice of
+government matrices then we should be
+
+ align:start position:0%
+government matrices then we should be
+ 
+
+ align:start position:0%
+government matrices then we should be
+able to do it in any choice of
+
+ align:start position:0%
+able to do it in any choice of
+ 
+
+ align:start position:0%
+able to do it in any choice of
+government uses okay so so now let's uh
+
+ align:start position:0%
+government uses okay so so now let's uh
+ 
+
+ align:start position:0%
+government uses okay so so now let's uh
+uh let me tell you how to do it for the
+
+ align:start position:0%
+uh let me tell you how to do it for the
+ 
+
+ align:start position:0%
+uh let me tell you how to do it for the
+general government matrices okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you can reduce to two components
+
+ align:start position:0%
+that you can reduce to two components
+ 
+
+ align:start position:0%
+that you can reduce to two components
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all choice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of ground matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just for other choice of government
+
+ align:start position:0%
+just for other choice of government
+ 
+
+ align:start position:0%
+just for other choice of government
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+to separate the side into side L and the
+
+ align:start position:0%
+to separate the side into side L and the
+ 
+
+ align:start position:0%
+to separate the side into side L and the
+percent R is more subtle
+
+ align:start position:0%
+percent R is more subtle
+ 
+
+ align:start position:0%
+percent R is more subtle
+okay you no longer it's just simple the
+
+ align:start position:0%
+okay you no longer it's just simple the
+ 
+
+ align:start position:0%
+okay you no longer it's just simple the
+upper two component no load to component
+
+ align:start position:0%
+upper two component no load to component
+ 
+
+ align:start position:0%
+upper two component no load to component
+so we have to do a little bit work okay
+
+ align:start position:0%
+so we have to do a little bit work okay
+ 
+
+ align:start position:0%
+so we have to do a little bit work okay
+actually we don't need to do much work
+
+ align:start position:0%
+actually we don't need to do much work
+ 
+
+ align:start position:0%
+actually we don't need to do much work
+if you actually find the right trick
+
+ align:start position:0%
+if you actually find the right trick
+ 
+
+ align:start position:0%
+if you actually find the right trick
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the uh so the beautiful trick to do
+
+ align:start position:0%
+and the uh so the beautiful trick to do
+ 
+
+ align:start position:0%
+and the uh so the beautiful trick to do
+this for or for any choice of gamma
+
+ align:start position:0%
+this for or for any choice of gamma
+ 
+
+ align:start position:0%
+this for or for any choice of gamma
+matrices is that you can introduce the
+
+ align:start position:0%
+matrices is that you can introduce the
+ 
+
+ align:start position:0%
+matrices is that you can introduce the
+following object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is called gamma 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go
+
+ align:start position:0%
+let's go
+ 
+
+ align:start position:0%
+let's go
+so gamma 5 is defined to be
+
+ align:start position:0%
+so gamma 5 is defined to be
+ 
+
+ align:start position:0%
+so gamma 5 is defined to be
+I comma 0 comma 1 comma Q comma 3. okay
+
+ align:start position:0%
+I comma 0 comma 1 comma Q comma 3. okay
+ 
+
+ align:start position:0%
+I comma 0 comma 1 comma Q comma 3. okay
+so you take the product of all the gamma
+
+ align:start position:0%
+so you take the product of all the gamma
+ 
+
+ align:start position:0%
+so you take the product of all the gamma
+matrices together
+
+ align:start position:0%
+matrices together
+ 
+
+ align:start position:0%
+matrices together
+and then with a factor of I
+
+ align:start position:0%
+and then with a factor of I
+ 
+
+ align:start position:0%
+and then with a factor of I
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so the I there is for the purpose
+
+ align:start position:0%
+okay so the I there is for the purpose
+ 
+
+ align:start position:0%
+okay so the I there is for the purpose
+that if you you can check yourself
+
+ align:start position:0%
+that if you you can check yourself
+ 
+
+ align:start position:0%
+that if you you can check yourself
+that the gamma 5 is actually a
+
+ align:start position:0%
+that the gamma 5 is actually a
+ 
+
+ align:start position:0%
+that the gamma 5 is actually a
+commission
+
+ align:start position:0%
+commission
+ 
+
+ align:start position:0%
+commission
+so the I is there for this purpose okay
+
+ align:start position:0%
+so the I is there for this purpose okay
+ 
+
+ align:start position:0%
+so the I is there for this purpose okay
+you need I for this to be two
+
+ align:start position:0%
+you need I for this to be two
+ 
+
+ align:start position:0%
+you need I for this to be two
+you also can check yourself
+
+ align:start position:0%
+you also can check yourself
+ 
+
+ align:start position:0%
+you also can check yourself
+the gamma 5 Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to one
+
+ align:start position:0%
+is equal to one
+ 
+
+ align:start position:0%
+is equal to one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this you can
+
+ align:start position:0%
+so so this you can
+ 
+
+ align:start position:0%
+so so this you can
+almost easily understand because it's
+
+ align:start position:0%
+almost easily understand because it's
+ 
+
+ align:start position:0%
+almost easily understand because it's
+all comma zero comma one comma three so
+
+ align:start position:0%
+all comma zero comma one comma three so
+ 
+
+ align:start position:0%
+all comma zero comma one comma three so
+you multiply itself again
+
+ align:start position:0%
+you multiply itself again
+ 
+
+ align:start position:0%
+you multiply itself again
+because any same comma which is a
+
+ align:start position:0%
+because any same comma which is a
+ 
+
+ align:start position:0%
+because any same comma which is a
+multiply either to be one or minus one
+
+ align:start position:0%
+multiply either to be one or minus one
+ 
+
+ align:start position:0%
+multiply either to be one or minus one
+so you multiply them together in the end
+
+ align:start position:0%
+so you multiply them together in the end
+ 
+
+ align:start position:0%
+so you multiply them together in the end
+they can be either one or minus one just
+
+ align:start position:0%
+they can be either one or minus one just
+ 
+
+ align:start position:0%
+they can be either one or minus one just
+ten dots for this choice of Y is one
+
+ align:start position:0%
+ten dots for this choice of Y is one
+ 
+
+ align:start position:0%
+ten dots for this choice of Y is one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um yeah
+
+ align:start position:0%
+so um yeah
+ 
+
+ align:start position:0%
+so um yeah
+and then you can also check
+
+ align:start position:0%
+and then you can also check
+ 
+
+ align:start position:0%
+and then you can also check
+the gamma 5 anti-commute with any
+
+ align:start position:0%
+the gamma 5 anti-commute with any
+ 
+
+ align:start position:0%
+the gamma 5 anti-commute with any
+government matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so mu here is of course from 0 to 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so so this is uh of
+
+ align:start position:0%
+and so so this is uh of
+ 
+
+ align:start position:0%
+and so so this is uh of
+you can see immediately from here
+
+ align:start position:0%
+you can see immediately from here
+ 
+
+ align:start position:0%
+you can see immediately from here
+okay you can give me this from here
+
+ align:start position:0%
+okay you can give me this from here
+ 
+
+ align:start position:0%
+okay you can give me this from here
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+gamma matrices which which on ink
+
+ align:start position:0%
+gamma matrices which which on ink
+ 
+
+ align:start position:0%
+gamma matrices which which on ink
+whose index is not the same the
+
+ align:start position:0%
+whose index is not the same the
+ 
+
+ align:start position:0%
+whose index is not the same the
+anti-computes
+
+ align:start position:0%
+anti-computes
+ 
+
+ align:start position:0%
+anti-computes
+okay so if you
+
+ align:start position:0%
+okay so if you
+ 
+
+ align:start position:0%
+okay so if you
+try to commute this with any gamma
+
+ align:start position:0%
+try to commute this with any gamma
+ 
+
+ align:start position:0%
+try to commute this with any gamma
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+you have three of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah because this runs over all
+
+ align:start position:0%
+yeah yeah because this runs over all
+ 
+
+ align:start position:0%
+yeah yeah because this runs over all
+gamma matrices
+
+ align:start position:0%
+gamma matrices
+ 
+
+ align:start position:0%
+gamma matrices
+so the one which yes if you take with
+
+ align:start position:0%
+so the one which yes if you take with
+ 
+
+ align:start position:0%
+so the one which yes if you take with
+some gamma mu and that particular one
+
+ align:start position:0%
+some gamma mu and that particular one
+ 
+
+ align:start position:0%
+some gamma mu and that particular one
+which is the same as gamma Mia of course
+
+ align:start position:0%
+which is the same as gamma Mia of course
+ 
+
+ align:start position:0%
+which is the same as gamma Mia of course
+compute with common mu but then you have
+
+ align:start position:0%
+compute with common mu but then you have
+ 
+
+ align:start position:0%
+compute with common mu but then you have
+three others but three hours will give
+
+ align:start position:0%
+three others but three hours will give
+ 
+
+ align:start position:0%
+three others but three hours will give
+you minus sign
+
+ align:start position:0%
+you minus sign
+ 
+
+ align:start position:0%
+you minus sign
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you can also check yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comma five have actually have zero Trace
+
+ align:start position:0%
+comma five have actually have zero Trace
+ 
+
+ align:start position:0%
+comma five have actually have zero Trace
+okay and so this I will leave us
+
+ align:start position:0%
+okay and so this I will leave us
+ 
+
+ align:start position:0%
+okay and so this I will leave us
+exercise for yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh which you can do as you did before
+
+ align:start position:0%
+uh which you can do as you did before
+ 
+
+ align:start position:0%
+uh which you can do as you did before
+with other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah in your homework
+
+ align:start position:0%
+um yeah in your homework
+ 
+
+ align:start position:0%
+um yeah in your homework
+yeah similar to the exercise you have
+
+ align:start position:0%
+yeah similar to the exercise you have
+ 
+
+ align:start position:0%
+yeah similar to the exercise you have
+done your homework
+
+ align:start position:0%
+done your homework
+ 
+
+ align:start position:0%
+done your homework
+so now from these properties
+
+ align:start position:0%
+so now from these properties
+ 
+
+ align:start position:0%
+so now from these properties
+okay now we can say the following scenes
+
+ align:start position:0%
+okay now we can say the following scenes
+ 
+
+ align:start position:0%
+okay now we can say the following scenes
+about the gamma 5 Matrix
+
+ align:start position:0%
+about the gamma 5 Matrix
+ 
+
+ align:start position:0%
+about the gamma 5 Matrix
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because gamma 5 squares Square to 1
+
+ align:start position:0%
+because gamma 5 squares Square to 1
+ 
+
+ align:start position:0%
+because gamma 5 squares Square to 1
+and also this is Commission
+
+ align:start position:0%
+and also this is Commission
+ 
+
+ align:start position:0%
+and also this is Commission
+so it's commission means it's eigenvalue
+
+ align:start position:0%
+so it's commission means it's eigenvalue
+ 
+
+ align:start position:0%
+so it's commission means it's eigenvalue
+is all real
+
+ align:start position:0%
+is all real
+ 
+
+ align:start position:0%
+is all real
+okay so it's algorithm is all real
+
+ align:start position:0%
+okay so it's algorithm is all real
+ 
+
+ align:start position:0%
+okay so it's algorithm is all real
+and Gamma 5 Square equal to one that
+
+ align:start position:0%
+and Gamma 5 Square equal to one that
+ 
+
+ align:start position:0%
+and Gamma 5 Square equal to one that
+means his eigenvalue is either by a plus
+
+ align:start position:0%
+means his eigenvalue is either by a plus
+ 
+
+ align:start position:0%
+means his eigenvalue is either by a plus
+or minus one okay so I have eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus minus one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then from the probability that this
+
+ align:start position:0%
+and then from the probability that this
+ 
+
+ align:start position:0%
+and then from the probability that this
+is trace this
+
+ align:start position:0%
+is trace this
+ 
+
+ align:start position:0%
+is trace this
+then tell you the number of the
+
+ align:start position:0%
+then tell you the number of the
+ 
+
+ align:start position:0%
+then tell you the number of the
+eigenvalues which is plus one and the
+
+ align:start position:0%
+eigenvalues which is plus one and the
+ 
+
+ align:start position:0%
+eigenvalues which is plus one and the
+number of minus one they should be the
+
+ align:start position:0%
+number of minus one they should be the
+ 
+
+ align:start position:0%
+number of minus one they should be the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+okay otherwise they won't cancel it
+
+ align:start position:0%
+okay otherwise they won't cancel it
+ 
+
+ align:start position:0%
+okay otherwise they won't cancel it
+won't be trace this and so so each act
+
+ align:start position:0%
+won't be trace this and so so each act
+ 
+
+ align:start position:0%
+won't be trace this and so so each act
+so each again space is two-dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so you have four uh you have
+
+ align:start position:0%
+okay so so you have four uh you have
+ 
+
+ align:start position:0%
+okay so so you have four uh you have
+four outcome values so there's two plus
+
+ align:start position:0%
+four outcome values so there's two plus
+ 
+
+ align:start position:0%
+four outcome values so there's two plus
+one two minus one okay must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since you have eigen values two plus
+
+ align:start position:0%
+so since you have eigen values two plus
+ 
+
+ align:start position:0%
+so since you have eigen values two plus
+one two minus one and then we can
+
+ align:start position:0%
+one two minus one and then we can
+ 
+
+ align:start position:0%
+one two minus one and then we can
+introduce a projector
+
+ align:start position:0%
+introduce a projector
+ 
+
+ align:start position:0%
+introduce a projector
+to project into the eigen space say with
+
+ align:start position:0%
+to project into the eigen space say with
+ 
+
+ align:start position:0%
+to project into the eigen space say with
+plus one besiding Value Plus One all the
+
+ align:start position:0%
+plus one besiding Value Plus One all the
+ 
+
+ align:start position:0%
+plus one besiding Value Plus One all the
+eigenvalue minus one okay so I can
+
+ align:start position:0%
+eigenvalue minus one okay so I can
+ 
+
+ align:start position:0%
+eigenvalue minus one okay so I can
+introduce a projector
+
+ align:start position:0%
+introduce a projector
+ 
+
+ align:start position:0%
+introduce a projector
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+for historical reasons it's called PL
+
+ align:start position:0%
+for historical reasons it's called PL
+ 
+
+ align:start position:0%
+for historical reasons it's called PL
+it's defined to be one half one plus
+
+ align:start position:0%
+it's defined to be one half one plus
+ 
+
+ align:start position:0%
+it's defined to be one half one plus
+gamma five
+
+ align:start position:0%
+gamma five
+ 
+
+ align:start position:0%
+gamma five
+and the pr
+
+ align:start position:0%
+and the pr
+ 
+
+ align:start position:0%
+and the pr
+is well half y minus gamma 5.
+
+ align:start position:0%
+is well half y minus gamma 5.
+ 
+
+ align:start position:0%
+is well half y minus gamma 5.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so this will project into
+
+ align:start position:0%
+so so so this will project into
+ 
+
+ align:start position:0%
+so so so this will project into
+eigenspace
+
+ align:start position:0%
+eigenspace
+ 
+
+ align:start position:0%
+eigenspace
+with the uh uh eigenvalue plus one
+
+ align:start position:0%
+with the uh uh eigenvalue plus one
+ 
+
+ align:start position:0%
+with the uh uh eigenvalue plus one
+and this will project into angular space
+
+ align:start position:0%
+and this will project into angular space
+ 
+
+ align:start position:0%
+and this will project into angular space
+with minus one
+
+ align:start position:0%
+with minus one
+ 
+
+ align:start position:0%
+with minus one
+okay because when you one minus one plus
+
+ align:start position:0%
+okay because when you one minus one plus
+ 
+
+ align:start position:0%
+okay because when you one minus one plus
+uh yeah anyway so so so you can check
+
+ align:start position:0%
+uh yeah anyway so so so you can check
+ 
+
+ align:start position:0%
+uh yeah anyway so so so you can check
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can check they are really
+
+ align:start position:0%
+so you can check they are really
+ 
+
+ align:start position:0%
+so you can check they are really
+projectors so PL square is going to be
+
+ align:start position:0%
+projectors so PL square is going to be
+ 
+
+ align:start position:0%
+projectors so PL square is going to be
+PR Square equal to Y and plpr equal to
+
+ align:start position:0%
+PR Square equal to Y and plpr equal to
+ 
+
+ align:start position:0%
+PR Square equal to Y and plpr equal to
+zero and P L cross PR okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now I introduce
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I can project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Define the projection of PSI L into of
+
+ align:start position:0%
+Define the projection of PSI L into of
+ 
+
+ align:start position:0%
+Define the projection of PSI L into of
+the projection of PSI project to the
+
+ align:start position:0%
+the projection of PSI project to the
+ 
+
+ align:start position:0%
+the projection of PSI project to the
+left a left space okay and PSI R to be
+
+ align:start position:0%
+left a left space okay and PSI R to be
+ 
+
+ align:start position:0%
+left a left space okay and PSI R to be
+the projection to the to the other space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I Define them
+
+ align:start position:0%
+okay I Define them
+ 
+
+ align:start position:0%
+okay I Define them
+and then you can easily see if by
+
+ align:start position:0%
+and then you can easily see if by
+ 
+
+ align:start position:0%
+and then you can easily see if by
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+you can really convince yourself comma
+
+ align:start position:0%
+you can really convince yourself comma
+ 
+
+ align:start position:0%
+you can really convince yourself comma
+five actium size L and the gamma 5 PSI
+
+ align:start position:0%
+five actium size L and the gamma 5 PSI
+ 
+
+ align:start position:0%
+five actium size L and the gamma 5 PSI
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+foreign okay
+
+ align:start position:0%
+foreign okay
+ 
+
+ align:start position:0%
+foreign okay
+so so they project into the outcome
+
+ align:start position:0%
+so so they project into the outcome
+ 
+
+ align:start position:0%
+so so they project into the outcome
+values of plus minus one yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh look sorry
+
+ align:start position:0%
+oh look sorry
+ 
+
+ align:start position:0%
+oh look sorry
+no no this is good good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is a completed Rock okay this
+
+ align:start position:0%
+now this is a completed Rock okay this
+ 
+
+ align:start position:0%
+now this is a completed Rock okay this
+is completely wrong like excuse me
+
+ align:start position:0%
+is completely wrong like excuse me
+ 
+
+ align:start position:0%
+is completely wrong like excuse me
+um Sophia square is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry yeah thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so yeah so so you can check their
+
+ align:start position:0%
+yeah so yeah so so you can check their
+ 
+
+ align:start position:0%
+yeah so yeah so so you can check their
+projectors okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so indeed you see
+
+ align:start position:0%
+so so indeed you see
+ 
+
+ align:start position:0%
+so so indeed you see
+so from here from this definition you
+
+ align:start position:0%
+so from here from this definition you
+ 
+
+ align:start position:0%
+so from here from this definition you
+can check this is true okay just this is
+
+ align:start position:0%
+can check this is true okay just this is
+ 
+
+ align:start position:0%
+can check this is true okay just this is
+a one second check and so so indeed they
+
+ align:start position:0%
+a one second check and so so indeed they
+ 
+
+ align:start position:0%
+a one second check and so so indeed they
+project you to the eigen space of gamma
+
+ align:start position:0%
+project you to the eigen space of gamma
+ 
+
+ align:start position:0%
+project you to the eigen space of gamma
+5 or plus minus one
+
+ align:start position:0%
+5 or plus minus one
+ 
+
+ align:start position:0%
+5 or plus minus one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+then by definition
+
+ align:start position:0%
+then by definition
+ 
+
+ align:start position:0%
+then by definition
+okay so now this percent L opposite R
+
+ align:start position:0%
+okay so now this percent L opposite R
+ 
+
+ align:start position:0%
+okay so now this percent L opposite R
+which is not defined for any choice of
+
+ align:start position:0%
+which is not defined for any choice of
+ 
+
+ align:start position:0%
+which is not defined for any choice of
+gamma matrices
+
+ align:start position:0%
+gamma matrices
+ 
+
+ align:start position:0%
+gamma matrices
+so again they
+
+ align:start position:0%
+so again they
+ 
+
+ align:start position:0%
+so again they
+they have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex component okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so they're
+
+ align:start position:0%
+so they're
+ 
+
+ align:start position:0%
+so they're
+so they call the chiral spinners
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes also called The Wild skin is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is the analog of sale and
+
+ align:start position:0%
+and so this is the analog of sale and
+ 
+
+ align:start position:0%
+and so this is the analog of sale and
+say ah here for the for the general
+
+ align:start position:0%
+say ah here for the for the general
+ 
+
+ align:start position:0%
+say ah here for the for the general
+choice of gamma matrices
+
+ align:start position:0%
+choice of gamma matrices
+ 
+
+ align:start position:0%
+choice of gamma matrices
+so now we will check
+
+ align:start position:0%
+so now we will check
+ 
+
+ align:start position:0%
+so now we will check
+this actually indeed
+
+ align:start position:0%
+this actually indeed
+ 
+
+ align:start position:0%
+this actually indeed
+so now the claim is
+
+ align:start position:0%
+so now the claim is
+ 
+
+ align:start position:0%
+so now the claim is
+defined this way
+
+ align:start position:0%
+defined this way
+ 
+
+ align:start position:0%
+defined this way
+will transform under themselves under
+
+ align:start position:0%
+will transform under themselves under
+ 
+
+ align:start position:0%
+will transform under themselves under
+low range transformation that will not
+
+ align:start position:0%
+low range transformation that will not
+ 
+
+ align:start position:0%
+low range transformation that will not
+be expressed each other
+
+ align:start position:0%
+be expressed each other
+ 
+
+ align:start position:0%
+be expressed each other
+okay so again
+
+ align:start position:0%
+okay so again
+ 
+
+ align:start position:0%
+okay so again
+so Ellen say oh here uh each are four
+
+ align:start position:0%
+so Ellen say oh here uh each are four
+ 
+
+ align:start position:0%
+so Ellen say oh here uh each are four
+components okay
+
+ align:start position:0%
+components okay
+ 
+
+ align:start position:0%
+components okay
+they they just have only two independent
+
+ align:start position:0%
+they they just have only two independent
+ 
+
+ align:start position:0%
+they they just have only two independent
+compact components so they still have
+
+ align:start position:0%
+compact components so they still have
+ 
+
+ align:start position:0%
+compact components so they still have
+four complex components okay and there's
+
+ align:start position:0%
+four complex components okay and there's
+ 
+
+ align:start position:0%
+four complex components okay and there's
+still four component Spinners just
+
+ align:start position:0%
+still four component Spinners just
+ 
+
+ align:start position:0%
+still four component Spinners just
+just there's only two independent ones
+
+ align:start position:0%
+just there's only two independent ones
+ 
+
+ align:start position:0%
+just there's only two independent ones
+which is only two independent modes
+
+ align:start position:0%
+which is only two independent modes
+ 
+
+ align:start position:0%
+which is only two independent modes
+okay so so now let's it's easy to check
+
+ align:start position:0%
+okay so so now let's it's easy to check
+ 
+
+ align:start position:0%
+okay so so now let's it's easy to check
+they actually transform uh to the among
+
+ align:start position:0%
+they actually transform uh to the among
+ 
+
+ align:start position:0%
+they actually transform uh to the among
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+so you can check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the gamma 5
+
+ align:start position:0%
+the gamma 5
+ 
+
+ align:start position:0%
+the gamma 5
+actually commute with Sigma mu mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is even easy to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from here
+
+ align:start position:0%
+so from here
+ 
+
+ align:start position:0%
+so from here
+gamma 5 commute with any gamma mu
+
+ align:start position:0%
+gamma 5 commute with any gamma mu
+ 
+
+ align:start position:0%
+gamma 5 commute with any gamma mu
+okay or any commute with any gamma mu
+
+ align:start position:0%
+okay or any commute with any gamma mu
+ 
+
+ align:start position:0%
+okay or any commute with any gamma mu
+and the second mu is just the the sum of
+
+ align:start position:0%
+and the second mu is just the the sum of
+ 
+
+ align:start position:0%
+and the second mu is just the the sum of
+two the product of two government views
+
+ align:start position:0%
+two the product of two government views
+ 
+
+ align:start position:0%
+two the product of two government views
+have even gamma mute so and the so gamma
+
+ align:start position:0%
+have even gamma mute so and the so gamma
+ 
+
+ align:start position:0%
+have even gamma mute so and the so gamma
+5 will compute with them okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma 5 commutes
+
+ align:start position:0%
+gamma 5 commutes
+ 
+
+ align:start position:0%
+gamma 5 commutes
+with s Lambda because the S Lam they
+
+ align:start position:0%
+with s Lambda because the S Lam they
+ 
+
+ align:start position:0%
+with s Lambda because the S Lam they
+just generally generated by per Sigma mu
+
+ align:start position:0%
+just generally generated by per Sigma mu
+ 
+
+ align:start position:0%
+just generally generated by per Sigma mu
+and then that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to commute with s that means
+
+ align:start position:0%
+so we need to commute with s that means
+ 
+
+ align:start position:0%
+so we need to commute with s that means
+on the transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as we are not on the transformation but
+
+ align:start position:0%
+as we are not on the transformation but
+ 
+
+ align:start position:0%
+as we are not on the transformation but
+as we are not changing the eigenvalues
+
+ align:start position:0%
+as we are not changing the eigenvalues
+ 
+
+ align:start position:0%
+as we are not changing the eigenvalues
+of gamma Phi okay so that means that l
+
+ align:start position:0%
+of gamma Phi okay so that means that l
+ 
+
+ align:start position:0%
+of gamma Phi okay so that means that l
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+as Lambda
+
+ align:start position:0%
+as Lambda
+ 
+
+ align:start position:0%
+as Lambda
+so l
+
+ align:start position:0%
+so l
+ 
+
+ align:start position:0%
+so l
+and the gamma 5 acting upside L Prime
+
+ align:start position:0%
+and the gamma 5 acting upside L Prime
+ 
+
+ align:start position:0%
+and the gamma 5 acting upside L Prime
+is still a gamma l
+
+ align:start position:0%
+is still a gamma l
+ 
+
+ align:start position:0%
+is still a gamma l
+okay so it's still within the same space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the similarly we say R okay
+
+ align:start position:0%
+and the similarly we say R okay
+ 
+
+ align:start position:0%
+and the similarly we say R okay
+so so that tells you the percent L and
+
+ align:start position:0%
+so so that tells you the percent L and
+ 
+
+ align:start position:0%
+so so that tells you the percent L and
+say oh they transform separately
+
+ align:start position:0%
+say oh they transform separately
+ 
+
+ align:start position:0%
+say oh they transform separately
+because of the gamma 5 computes with the
+
+ align:start position:0%
+because of the gamma 5 computes with the
+ 
+
+ align:start position:0%
+because of the gamma 5 computes with the
+original range transformation
+
+ align:start position:0%
+original range transformation
+ 
+
+ align:start position:0%
+original range transformation
+and so each again space they transform
+
+ align:start position:0%
+and so each again space they transform
+ 
+
+ align:start position:0%
+and so each again space they transform
+separately from each other
+
+ align:start position:0%
+separately from each other
+ 
+
+ align:start position:0%
+separately from each other
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can also find in the um
+
+ align:start position:0%
+so you can also find in the um
+ 
+
+ align:start position:0%
+so you can also find in the um
+so in the chiral representation
+
+ align:start position:0%
+so in the chiral representation
+ 
+
+ align:start position:0%
+so in the chiral representation
+you can check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the star that particular choice of
+
+ align:start position:0%
+so the star that particular choice of
+ 
+
+ align:start position:0%
+so the star that particular choice of
+gamma is called the chiral
+
+ align:start position:0%
+gamma is called the chiral
+ 
+
+ align:start position:0%
+gamma is called the chiral
+representation okay
+
+ align:start position:0%
+representation okay
+ 
+
+ align:start position:0%
+representation okay
+because in that uh choice of gamma uh
+
+ align:start position:0%
+because in that uh choice of gamma uh
+ 
+
+ align:start position:0%
+because in that uh choice of gamma uh
+since simplified just have upper two
+
+ align:start position:0%
+since simplified just have upper two
+ 
+
+ align:start position:0%
+since simplified just have upper two
+component the lower two components
+
+ align:start position:0%
+component the lower two components
+ 
+
+ align:start position:0%
+component the lower two components
+so you can check yourself
+
+ align:start position:0%
+so you can check yourself
+ 
+
+ align:start position:0%
+so you can check yourself
+just by working it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the gamma 5
+
+ align:start position:0%
+the gamma 5
+ 
+
+ align:start position:0%
+the gamma 5
+indeed just a block diagonal form
+
+ align:start position:0%
+indeed just a block diagonal form
+ 
+
+ align:start position:0%
+indeed just a block diagonal form
+one zero zero minus one okay
+
+ align:start position:0%
+one zero zero minus one okay
+ 
+
+ align:start position:0%
+one zero zero minus one okay
+so that's why in that case it's very
+
+ align:start position:0%
+so that's why in that case it's very
+ 
+
+ align:start position:0%
+so that's why in that case it's very
+simple okay but but but in other
+
+ align:start position:0%
+simple okay but but but in other
+ 
+
+ align:start position:0%
+simple okay but but but in other
+representation gamma 5 can be more
+
+ align:start position:0%
+representation gamma 5 can be more
+ 
+
+ align:start position:0%
+representation gamma 5 can be more
+complicated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you have a question okay
+
+ align:start position:0%
+yes you have a question okay
+ 
+
+ align:start position:0%
+yes you have a question okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that shows
+
+ align:start position:0%
+that shows
+ 
+
+ align:start position:0%
+that shows
+under which this arbitrary
+
+ align:start position:0%
+under which this arbitrary
+ 
+
+ align:start position:0%
+under which this arbitrary
+representation is equivalent of the
+
+ align:start position:0%
+representation is equivalent of the
+ 
+
+ align:start position:0%
+representation is equivalent of the
+chiral representation from this Market
+
+ align:start position:0%
+chiral representation from this Market
+ 
+
+ align:start position:0%
+chiral representation from this Market
+can we figure out what those
+
+ align:start position:0%
+can we figure out what those
+ 
+
+ align:start position:0%
+can we figure out what those
+that unitary concludes looks like yeah
+
+ align:start position:0%
+that unitary concludes looks like yeah
+ 
+
+ align:start position:0%
+that unitary concludes looks like yeah
+yeah yeah you can yeah yeah it's not
+
+ align:start position:0%
+yeah yeah you can yeah yeah it's not
+ 
+
+ align:start position:0%
+yeah yeah you can yeah yeah it's not
+it's not the unitary transmission just a
+
+ align:start position:0%
+it's not the unitary transmission just a
+ 
+
+ align:start position:0%
+it's not the unitary transmission just a
+similar transformation yeah uh uh uh so
+
+ align:start position:0%
+similar transformation yeah uh uh uh so
+ 
+
+ align:start position:0%
+similar transformation yeah uh uh uh so
+each of them are related by similar
+
+ align:start position:0%
+each of them are related by similar
+ 
+
+ align:start position:0%
+each of them are related by similar
+transformation and indeed uh there's a
+
+ align:start position:0%
+transformation and indeed uh there's a
+ 
+
+ align:start position:0%
+transformation and indeed uh there's a
+gamma 5 uh a comma five in the other
+
+ align:start position:0%
+gamma 5 uh a comma five in the other
+ 
+
+ align:start position:0%
+gamma 5 uh a comma five in the other
+representation are related to this one
+
+ align:start position:0%
+representation are related to this one
+ 
+
+ align:start position:0%
+representation are related to this one
+just by a similar transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I will use that language when I
+
+ align:start position:0%
+yeah so I will use that language when I
+ 
+
+ align:start position:0%
+yeah so I will use that language when I
+talk about my Runner spindle so so in
+
+ align:start position:0%
+talk about my Runner spindle so so in
+ 
+
+ align:start position:0%
+talk about my Runner spindle so so in
+this case it's sufficiently simple I
+
+ align:start position:0%
+this case it's sufficiently simple I
+ 
+
+ align:start position:0%
+this case it's sufficiently simple I
+don't need to use that language
+
+ align:start position:0%
+don't need to use that language
+ 
+
+ align:start position:0%
+don't need to use that language
+yeah but you can use that language yeah
+
+ align:start position:0%
+yeah but you can use that language yeah
+ 
+
+ align:start position:0%
+yeah but you can use that language yeah
+okay so so let's go back to this kind of
+
+ align:start position:0%
+okay so so let's go back to this kind of
+ 
+
+ align:start position:0%
+okay so so let's go back to this kind of
+representation okay and write the debug
+
+ align:start position:0%
+representation okay and write the debug
+ 
+
+ align:start position:0%
+representation okay and write the debug
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+into this chiral representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah on one second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now if you write the wrong
+
+ align:start position:0%
+so so now if you write the wrong
+ 
+
+ align:start position:0%
+so so now if you write the wrong
+equation in terms of PSI L and say oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember the rock equation of the
+
+ align:start position:0%
+so remember the rock equation of the
+ 
+
+ align:start position:0%
+so remember the rock equation of the
+following form like the rock a
+
+ align:start position:0%
+following form like the rock a
+ 
+
+ align:start position:0%
+following form like the rock a
+lagrantian density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then since PSI just equal to the sum
+
+ align:start position:0%
+and then since PSI just equal to the sum
+ 
+
+ align:start position:0%
+and then since PSI just equal to the sum
+of the uh so the PSI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then you can just write this in
+
+ align:start position:0%
+and then you can just write this in
+ 
+
+ align:start position:0%
+and then you can just write this in
+terms of the opposite L on the side R
+
+ align:start position:0%
+terms of the opposite L on the side R
+ 
+
+ align:start position:0%
+terms of the opposite L on the side R
+okay and write this in terms of our
+
+ align:start position:0%
+okay and write this in terms of our
+ 
+
+ align:start position:0%
+okay and write this in terms of our
+personal
+
+ align:start position:0%
+personal
+ 
+
+ align:start position:0%
+personal
+and then you find the cross term the
+
+ align:start position:0%
+and then you find the cross term the
+ 
+
+ align:start position:0%
+and then you find the cross term the
+vanish okay you can also check this
+
+ align:start position:0%
+vanish okay you can also check this
+ 
+
+ align:start position:0%
+vanish okay you can also check this
+explicitly in the chiral representation
+
+ align:start position:0%
+explicitly in the chiral representation
+ 
+
+ align:start position:0%
+explicitly in the chiral representation
+but uh but the expression I'm writing
+
+ align:start position:0%
+but uh but the expression I'm writing
+ 
+
+ align:start position:0%
+but uh but the expression I'm writing
+down is General
+
+ align:start position:0%
+down is General
+ 
+
+ align:start position:0%
+down is General
+okay so you can write it as
+
+ align:start position:0%
+okay so you can write it as
+ 
+
+ align:start position:0%
+okay so you can write it as
+I dagger
+
+ align:start position:0%
+I dagger
+ 
+
+ align:start position:0%
+I dagger
+actual zero
+
+ align:start position:0%
+actual zero
+ 
+
+ align:start position:0%
+actual zero
+I Sigma I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial I
+
+ align:start position:0%
+partial I
+ 
+
+ align:start position:0%
+partial I
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry
+
+ align:start position:0%
+yeah sorry
+ 
+
+ align:start position:0%
+yeah sorry
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh uh uh uh yeah uh actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me first write that I think I
+
+ align:start position:0%
+yeah let me first write that I think I
+ 
+
+ align:start position:0%
+yeah let me first write that I think I
+said something wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so so so so yeah I said something
+
+ align:start position:0%
+so so so so so so yeah I said something
+ 
+
+ align:start position:0%
+so so so so so so yeah I said something
+at least expression only applies to the
+
+ align:start position:0%
+at least expression only applies to the
+ 
+
+ align:start position:0%
+at least expression only applies to the
+chiral representation okay so in
+
+ align:start position:0%
+chiral representation okay so in
+ 
+
+ align:start position:0%
+chiral representation okay so in
+the parallel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compensation of gamma star
+
+ align:start position:0%
+compensation of gamma star
+ 
+
+ align:start position:0%
+compensation of gamma star
+in this space of star and then we have
+
+ align:start position:0%
+in this space of star and then we have
+ 
+
+ align:start position:0%
+in this space of star and then we have
+two components then I can write in this
+
+ align:start position:0%
+two components then I can write in this
+ 
+
+ align:start position:0%
+two components then I can write in this
+side and the percent R into two
+
+ align:start position:0%
+side and the percent R into two
+ 
+
+ align:start position:0%
+side and the percent R into two
+components and then then yeah yeah so so
+
+ align:start position:0%
+components and then then yeah yeah so so
+ 
+
+ align:start position:0%
+components and then then yeah yeah so so
+this just ordinary Sigma matrices okay
+
+ align:start position:0%
+this just ordinary Sigma matrices okay
+ 
+
+ align:start position:0%
+this just ordinary Sigma matrices okay
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is expressed you get okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what you notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you said for m equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's no coupling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+so L and say r
+
+ align:start position:0%
+so L and say r
+ 
+
+ align:start position:0%
+so L and say r
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so the is the mass term which couple
+
+ align:start position:0%
+so so the is the mass term which couple
+ 
+
+ align:start position:0%
+so so the is the mass term which couple
+them together
+
+ align:start position:0%
+them together
+ 
+
+ align:start position:0%
+them together
+okay kelastic term because there's no
+
+ align:start position:0%
+okay kelastic term because there's no
+ 
+
+ align:start position:0%
+okay kelastic term because there's no
+cross term between the upside down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this behavior is actually General
+
+ align:start position:0%
+and this behavior is actually General
+ 
+
+ align:start position:0%
+and this behavior is actually General
+you can write it in arbitrary
+
+ align:start position:0%
+you can write it in arbitrary
+ 
+
+ align:start position:0%
+you can write it in arbitrary
+representations
+
+ align:start position:0%
+representations
+ 
+
+ align:start position:0%
+representations
+and but of course you have to
+
+ align:start position:0%
+and but of course you have to
+ 
+
+ align:start position:0%
+and but of course you have to
+representation I can no longer use this
+
+ align:start position:0%
+representation I can no longer use this
+ 
+
+ align:start position:0%
+representation I can no longer use this
+Sigma I okay and uh so so this in this
+
+ align:start position:0%
+Sigma I okay and uh so so this in this
+ 
+
+ align:start position:0%
+Sigma I okay and uh so so this in this
+particular form
+
+ align:start position:0%
+particular form
+ 
+
+ align:start position:0%
+particular form
+even though this feature is General but
+
+ align:start position:0%
+even though this feature is General but
+ 
+
+ align:start position:0%
+even though this feature is General but
+but this particular form of The Chronic
+
+ align:start position:0%
+but this particular form of The Chronic
+ 
+
+ align:start position:0%
+but this particular form of The Chronic
+term only applies for the current
+
+ align:start position:0%
+term only applies for the current
+ 
+
+ align:start position:0%
+term only applies for the current
+representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so for n equal to zero you don't have
+
+ align:start position:0%
+so so for n equal to zero you don't have
+ 
+
+ align:start position:0%
+so so for n equal to zero you don't have
+a coupling between the upside L and say
+
+ align:start position:0%
+a coupling between the upside L and say
+ 
+
+ align:start position:0%
+a coupling between the upside L and say
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+and then you'll have
+
+ align:start position:0%
+and then you'll have
+ 
+
+ align:start position:0%
+and then you'll have
+to say oh diagonal term and say autumn
+
+ align:start position:0%
+to say oh diagonal term and say autumn
+ 
+
+ align:start position:0%
+to say oh diagonal term and say autumn
+and then they'll give you something else
+
+ align:start position:0%
+and then they'll give you something else
+ 
+
+ align:start position:0%
+and then they'll give you something else
+okay uh so so again this is reduced to
+
+ align:start position:0%
+okay uh so so again this is reduced to
+ 
+
+ align:start position:0%
+okay uh so so again this is reduced to
+our previous statement that the if you
+
+ align:start position:0%
+our previous statement that the if you
+ 
+
+ align:start position:0%
+our previous statement that the if you
+have a master's case you can describe
+
+ align:start position:0%
+have a master's case you can describe
+ 
+
+ align:start position:0%
+have a master's case you can describe
+using a two component spindle okay so
+
+ align:start position:0%
+using a two component spindle okay so
+ 
+
+ align:start position:0%
+using a two component spindle okay so
+here indeed but but here there's also
+
+ align:start position:0%
+here indeed but but here there's also
+ 
+
+ align:start position:0%
+here indeed but but here there's also
+something actual
+
+ align:start position:0%
+something actual
+ 
+
+ align:start position:0%
+something actual
+so what do you see uh something actually
+
+ align:start position:0%
+so what do you see uh something actually
+ 
+
+ align:start position:0%
+so what do you see uh something actually
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I did somebody raise you yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right yeah yeah sorry uh uh uh uh
+
+ align:start position:0%
+right right yeah yeah sorry uh uh uh uh
+ 
+
+ align:start position:0%
+right right yeah yeah sorry uh uh uh uh
+a good question this yeah this
+
+ align:start position:0%
+a good question this yeah this
+ 
+
+ align:start position:0%
+a good question this yeah this
+expression is wrong okay uh I was uh
+
+ align:start position:0%
+expression is wrong okay uh I was uh
+ 
+
+ align:start position:0%
+expression is wrong okay uh I was uh
+somehow I was doing uh uh uh I was
+
+ align:start position:0%
+somehow I was doing uh uh uh I was
+ 
+
+ align:start position:0%
+somehow I was doing uh uh uh I was
+trying to yeah uh uh uh
+
+ align:start position:0%
+trying to yeah uh uh uh
+ 
+
+ align:start position:0%
+trying to yeah uh uh uh
+I remembered I wrote this in the general
+
+ align:start position:0%
+I remembered I wrote this in the general
+ 
+
+ align:start position:0%
+I remembered I wrote this in the general
+basis but then I realized I only wrote
+
+ align:start position:0%
+basis but then I realized I only wrote
+ 
+
+ align:start position:0%
+basis but then I realized I only wrote
+it in that basis yeah in the general
+
+ align:start position:0%
+it in that basis yeah in the general
+ 
+
+ align:start position:0%
+it in that basis yeah in the general
+basis I would have uh PSI 50 L plus
+
+ align:start position:0%
+basis I would have uh PSI 50 L plus
+ 
+
+ align:start position:0%
+basis I would have uh PSI 50 L plus
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+yeah but then I realized I only write
+
+ align:start position:0%
+yeah but then I realized I only write
+ 
+
+ align:start position:0%
+yeah but then I realized I only write
+the galactic term in this in this
+
+ align:start position:0%
+the galactic term in this in this
+ 
+
+ align:start position:0%
+the galactic term in this in this
+specific basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good yeah yeah so they're extracting oh
+
+ align:start position:0%
+good yeah yeah so they're extracting oh
+ 
+
+ align:start position:0%
+good yeah yeah so they're extracting oh
+it does not apply for the Cairo basis
+
+ align:start position:0%
+it does not apply for the Cairo basis
+ 
+
+ align:start position:0%
+it does not apply for the Cairo basis
+but apply for the general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+actually something profound happens
+
+ align:start position:0%
+actually something profound happens
+ 
+
+ align:start position:0%
+actually something profound happens
+because when m equal to zero when you
+
+ align:start position:0%
+because when m equal to zero when you
+ 
+
+ align:start position:0%
+because when m equal to zero when you
+don't have company between side L and
+
+ align:start position:0%
+don't have company between side L and
+ 
+
+ align:start position:0%
+don't have company between side L and
+cosine r
+
+ align:start position:0%
+cosine r
+ 
+
+ align:start position:0%
+cosine r
+you actually get the extra symmetry
+
+ align:start position:0%
+you actually get the extra symmetry
+ 
+
+ align:start position:0%
+you actually get the extra symmetry
+okay so in the drug lagranging
+
+ align:start position:0%
+okay so in the drug lagranging
+ 
+
+ align:start position:0%
+okay so in the drug lagranging
+so in the direct lagranging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as we discussed earlier so we have a U1
+
+ align:start position:0%
+as we discussed earlier so we have a U1
+ 
+
+ align:start position:0%
+as we discussed earlier so we have a U1
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+PSI goes to
+
+ align:start position:0%
+PSI goes to
+ 
+
+ align:start position:0%
+PSI goes to
+exponential IR for PSI okay so this drug
+
+ align:start position:0%
+exponential IR for PSI okay so this drug
+ 
+
+ align:start position:0%
+exponential IR for PSI okay so this drug
+LaGrange is environment under that
+
+ align:start position:0%
+LaGrange is environment under that
+ 
+
+ align:start position:0%
+LaGrange is environment under that
+because the size complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now and say oh they are separate
+
+ align:start position:0%
+but now and say oh they are separate
+ 
+
+ align:start position:0%
+but now and say oh they are separate
+so now I can actually transform
+
+ align:start position:0%
+so now I can actually transform
+ 
+
+ align:start position:0%
+so now I can actually transform
+separately okay so under this
+
+ align:start position:0%
+separately okay so under this
+ 
+
+ align:start position:0%
+separately okay so under this
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transform the same
+
+ align:start position:0%
+transform the same
+ 
+
+ align:start position:0%
+transform the same
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+m equal to zero
+
+ align:start position:0%
+m equal to zero
+ 
+
+ align:start position:0%
+m equal to zero
+I can have set L goes to expression I
+
+ align:start position:0%
+I can have set L goes to expression I
+ 
+
+ align:start position:0%
+I can have set L goes to expression I
+Alpha l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say r
+
+ align:start position:0%
+say r
+ 
+
+ align:start position:0%
+say r
+goes to expansion I Alpha r
+
+ align:start position:0%
+goes to expansion I Alpha r
+ 
+
+ align:start position:0%
+goes to expansion I Alpha r
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because they only couple to themselves
+
+ align:start position:0%
+because they only couple to themselves
+ 
+
+ align:start position:0%
+because they only couple to themselves
+okay and now I have this symmetry
+
+ align:start position:0%
+okay and now I have this symmetry
+ 
+
+ align:start position:0%
+okay and now I have this symmetry
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh uh so so now so here you have UI
+
+ align:start position:0%
+and uh uh so so now so here you have UI
+ 
+
+ align:start position:0%
+and uh uh so so now so here you have UI
+now you have U1 times UI
+
+ align:start position:0%
+now you have U1 times UI
+ 
+
+ align:start position:0%
+now you have U1 times UI
+call the u n times L and U1 R so these
+
+ align:start position:0%
+call the u n times L and U1 R so these
+ 
+
+ align:start position:0%
+call the u n times L and U1 R so these
+are called chiral symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because they transform
+
+ align:start position:0%
+because they transform
+ 
+
+ align:start position:0%
+because they transform
+the left and the right separately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+sized some
+
+ align:start position:0%
+sized some
+ 
+
+ align:start position:0%
+sized some
+no no I can't write it no I can write
+
+ align:start position:0%
+no no I can't write it no I can write
+ 
+
+ align:start position:0%
+no no I can't write it no I can write
+that way just now I'm using the two
+
+ align:start position:0%
+that way just now I'm using the two
+ 
+
+ align:start position:0%
+that way just now I'm using the two
+component form
+
+ align:start position:0%
+component form
+ 
+
+ align:start position:0%
+component form
+when I write two components in the form
+
+ align:start position:0%
+when I write two components in the form
+ 
+
+ align:start position:0%
+when I write two components in the form
+then the right side that way it doesn't
+
+ align:start position:0%
+then the right side that way it doesn't
+ 
+
+ align:start position:0%
+then the right side that way it doesn't
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+yeah because of the sale is the upper
+
+ align:start position:0%
+yeah because of the sale is the upper
+ 
+
+ align:start position:0%
+yeah because of the sale is the upper
+two component of say I is the lower two
+
+ align:start position:0%
+two component of say I is the lower two
+ 
+
+ align:start position:0%
+two component of say I is the lower two
+component yeah
+
+ align:start position:0%
+component yeah
+ 
+
+ align:start position:0%
+component yeah
+yeah yeah I'm using the same notation
+
+ align:start position:0%
+yeah yeah I'm using the same notation
+ 
+
+ align:start position:0%
+yeah yeah I'm using the same notation
+for here for these spaces and so in this
+
+ align:start position:0%
+for here for these spaces and so in this
+ 
+
+ align:start position:0%
+for here for these spaces and so in this
+space it's say and say oh they only have
+
+ align:start position:0%
+space it's say and say oh they only have
+ 
+
+ align:start position:0%
+space it's say and say oh they only have
+two components but in the general case
+
+ align:start position:0%
+two components but in the general case
+ 
+
+ align:start position:0%
+two components but in the general case
+they are four components
+
+ align:start position:0%
+they are four components
+ 
+
+ align:start position:0%
+they are four components
+okay so in the general case I can write
+
+ align:start position:0%
+okay so in the general case I can write
+ 
+
+ align:start position:0%
+okay so in the general case I can write
+PSI equals
+
+ align:start position:0%
+PSI equals
+ 
+
+ align:start position:0%
+PSI equals
+but in this basis I cannot yeah yeah
+
+ align:start position:0%
+but in this basis I cannot yeah yeah
+ 
+
+ align:start position:0%
+but in this basis I cannot yeah yeah
+using this rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um so now you have a do you see
+
+ align:start position:0%
+so um so now you have a do you see
+ 
+
+ align:start position:0%
+so um so now you have a do you see
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+which uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can transform them separately
+
+ align:start position:0%
+you can transform them separately
+ 
+
+ align:start position:0%
+you can transform them separately
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the symmetries are one of the most
+
+ align:start position:0%
+and the symmetries are one of the most
+ 
+
+ align:start position:0%
+and the symmetries are one of the most
+important aspects of physics and they
+
+ align:start position:0%
+important aspects of physics and they
+ 
+
+ align:start position:0%
+important aspects of physics and they
+have very uh important implications Etc
+
+ align:start position:0%
+have very uh important implications Etc
+ 
+
+ align:start position:0%
+have very uh important implications Etc
+and the chiral symmetries are actually
+
+ align:start position:0%
+and the chiral symmetries are actually
+ 
+
+ align:start position:0%
+and the chiral symmetries are actually
+has also very
+
+ align:start position:0%
+has also very
+ 
+
+ align:start position:0%
+has also very
+important effects in uh in particle
+
+ align:start position:0%
+important effects in uh in particle
+ 
+
+ align:start position:0%
+important effects in uh in particle
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+for example the the pions okay the
+
+ align:start position:0%
+for example the the pions okay the
+ 
+
+ align:start position:0%
+for example the the pions okay the
+parents has to do with uh I will not go
+
+ align:start position:0%
+parents has to do with uh I will not go
+ 
+
+ align:start position:0%
+parents has to do with uh I will not go
+into detail and the parents uh they
+
+ align:start position:0%
+into detail and the parents uh they
+ 
+
+ align:start position:0%
+into detail and the parents uh they
+essentially come from uh uh the Kairos
+
+ align:start position:0%
+essentially come from uh uh the Kairos
+ 
+
+ align:start position:0%
+essentially come from uh uh the Kairos
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+there's no parallel there's no piles
+
+ align:start position:0%
+there's no parallel there's no piles
+ 
+
+ align:start position:0%
+there's no parallel there's no piles
+and uh and I actually understanding the
+
+ align:start position:0%
+and uh and I actually understanding the
+ 
+
+ align:start position:0%
+and uh and I actually understanding the
+uh the the how the pions come from the
+
+ align:start position:0%
+uh the the how the pions come from the
+ 
+
+ align:start position:0%
+uh the the how the pions come from the
+chirosimetry ETC there was a Nobel Prize
+
+ align:start position:0%
+chirosimetry ETC there was a Nobel Prize
+ 
+
+ align:start position:0%
+chirosimetry ETC there was a Nobel Prize
+to lambu say a number of years ago which
+
+ align:start position:0%
+to lambu say a number of years ago which
+ 
+
+ align:start position:0%
+to lambu say a number of years ago which
+our colleague Goldstone also made a very
+
+ align:start position:0%
+our colleague Goldstone also made a very
+ 
+
+ align:start position:0%
+our colleague Goldstone also made a very
+important contribution uh to that
+
+ align:start position:0%
+important contribution uh to that
+ 
+
+ align:start position:0%
+important contribution uh to that
+and also nature
+
+ align:start position:0%
+and also nature
+ 
+
+ align:start position:0%
+and also nature
+also interesting about this chiral
+
+ align:start position:0%
+also interesting about this chiral
+ 
+
+ align:start position:0%
+also interesting about this chiral
+symmetry is that they are there so if
+
+ align:start position:0%
+symmetry is that they are there so if
+ 
+
+ align:start position:0%
+symmetry is that they are there so if
+you have a classical message so if you
+
+ align:start position:0%
+you have a classical message so if you
+ 
+
+ align:start position:0%
+you have a classical message so if you
+have a mass list uh a message not
+
+ align:start position:0%
+have a mass list uh a message not
+ 
+
+ align:start position:0%
+have a mass list uh a message not
+grounding then you can have this
+
+ align:start position:0%
+grounding then you can have this
+ 
+
+ align:start position:0%
+grounding then you can have this
+symmetry in the classical level in the
+
+ align:start position:0%
+symmetry in the classical level in the
+ 
+
+ align:start position:0%
+symmetry in the classical level in the
+lagrangian level but once we quantize
+
+ align:start position:0%
+lagrangian level but once we quantize
+ 
+
+ align:start position:0%
+lagrangian level but once we quantize
+this Theory you find the Symmetry go
+
+ align:start position:0%
+this Theory you find the Symmetry go
+ 
+
+ align:start position:0%
+this Theory you find the Symmetry go
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+you have become Anonymous called become
+
+ align:start position:0%
+you have become Anonymous called become
+ 
+
+ align:start position:0%
+you have become Anonymous called become
+alumus symmetry is only present in the
+
+ align:start position:0%
+alumus symmetry is only present in the
+ 
+
+ align:start position:0%
+alumus symmetry is only present in the
+classical level but not uh uh in the
+
+ align:start position:0%
+classical level but not uh uh in the
+ 
+
+ align:start position:0%
+classical level but not uh uh in the
+quantum level and and again that played
+
+ align:start position:0%
+quantum level and and again that played
+ 
+
+ align:start position:0%
+quantum level and and again that played
+very important role in particle physics
+
+ align:start position:0%
+very important role in particle physics
+ 
+
+ align:start position:0%
+very important role in particle physics
+such okay yeah the bottom line is that
+
+ align:start position:0%
+such okay yeah the bottom line is that
+ 
+
+ align:start position:0%
+such okay yeah the bottom line is that
+the chiral symmetry uh is very important
+
+ align:start position:0%
+the chiral symmetry uh is very important
+ 
+
+ align:start position:0%
+the chiral symmetry uh is very important
+in many aspects of the physics okay it's
+
+ align:start position:0%
+in many aspects of the physics okay it's
+ 
+
+ align:start position:0%
+in many aspects of the physics okay it's
+also important in many Smart Systems
+
+ align:start position:0%
+also important in many Smart Systems
+ 
+
+ align:start position:0%
+also important in many Smart Systems
+like liquid helium Etc
+
+ align:start position:0%
+like liquid helium Etc
+ 
+
+ align:start position:0%
+like liquid helium Etc
+so you can also write this symmetry
+
+ align:start position:0%
+so you can also write this symmetry
+ 
+
+ align:start position:0%
+so you can also write this symmetry
+for General gamma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for General gamma you can have your
+
+ align:start position:0%
+so for General gamma you can have your
+ 
+
+ align:start position:0%
+so for General gamma you can have your
+previous symmetry
+
+ align:start position:0%
+previous symmetry
+ 
+
+ align:start position:0%
+previous symmetry
+so so now I'm using the full control in
+
+ align:start position:0%
+so so now I'm using the full control in
+ 
+
+ align:start position:0%
+so so now I'm using the full control in
+the rotation
+
+ align:start position:0%
+the rotation
+ 
+
+ align:start position:0%
+the rotation
+which side here and say ah transformed
+
+ align:start position:0%
+which side here and say ah transformed
+ 
+
+ align:start position:0%
+which side here and say ah transformed
+the same way
+
+ align:start position:0%
+the same way
+ 
+
+ align:start position:0%
+the same way
+and then now you have a low symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comma five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now now you can put the gamma 5
+
+ align:start position:0%
+okay and now now you can put the gamma 5
+ 
+
+ align:start position:0%
+okay and now now you can put the gamma 5
+in the exponents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+any questions on this yes
+
+ align:start position:0%
+any questions on this yes
+ 
+
+ align:start position:0%
+any questions on this yes
+yeah yeah if I tell there's just some
+
+ align:start position:0%
+yeah yeah if I tell there's just some
+ 
+
+ align:start position:0%
+yeah yeah if I tell there's just some
+other constant you have to tell there's
+
+ align:start position:0%
+other constant you have to tell there's
+ 
+
+ align:start position:0%
+other constant you have to tell there's
+just some other constant then you
+
+ align:start position:0%
+just some other constant then you
+ 
+
+ align:start position:0%
+just some other constant then you
+multiply gamma Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the way to understand that these two
+
+ align:start position:0%
+so the way to understand that these two
+ 
+
+ align:start position:0%
+so the way to understand that these two
+are related
+
+ align:start position:0%
+are related
+ 
+
+ align:start position:0%
+are related
+so think about the transformation here
+
+ align:start position:0%
+so think about the transformation here
+ 
+
+ align:start position:0%
+so think about the transformation here
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+we can rewrite a little bit differently
+
+ align:start position:0%
+we can rewrite a little bit differently
+ 
+
+ align:start position:0%
+we can rewrite a little bit differently
+if we can consider
+
+ align:start position:0%
+if we can consider
+ 
+
+ align:start position:0%
+if we can consider
+rewrite this Alpha L and Alpha items in
+
+ align:start position:0%
+rewrite this Alpha L and Alpha items in
+ 
+
+ align:start position:0%
+rewrite this Alpha L and Alpha items in
+terms of the following
+
+ align:start position:0%
+terms of the following
+ 
+
+ align:start position:0%
+terms of the following
+let's consider the two transformation
+
+ align:start position:0%
+let's consider the two transformation
+ 
+
+ align:start position:0%
+let's consider the two transformation
+when transformation PSI L and PSI R
+
+ align:start position:0%
+when transformation PSI L and PSI R
+ 
+
+ align:start position:0%
+when transformation PSI L and PSI R
+transform the same
+
+ align:start position:0%
+transform the same
+ 
+
+ align:start position:0%
+transform the same
+and a lot of the transformation is that
+
+ align:start position:0%
+and a lot of the transformation is that
+ 
+
+ align:start position:0%
+and a lot of the transformation is that
+they transform opposite
+
+ align:start position:0%
+they transform opposite
+ 
+
+ align:start position:0%
+they transform opposite
+okay they transform in the opposite
+
+ align:start position:0%
+okay they transform in the opposite
+ 
+
+ align:start position:0%
+okay they transform in the opposite
+phase okay as I write the alpha and
+
+ align:start position:0%
+phase okay as I write the alpha and
+ 
+
+ align:start position:0%
+phase okay as I write the alpha and
+these writing is like that okay so in
+
+ align:start position:0%
+these writing is like that okay so in
+ 
+
+ align:start position:0%
+these writing is like that okay so in
+this way Epsilon and say R transform the
+
+ align:start position:0%
+this way Epsilon and say R transform the
+ 
+
+ align:start position:0%
+this way Epsilon and say R transform the
+same but so and say are the transform
+
+ align:start position:0%
+same but so and say are the transform
+ 
+
+ align:start position:0%
+same but so and say are the transform
+opposite because they have opposite
+
+ align:start position:0%
+opposite because they have opposite
+ 
+
+ align:start position:0%
+opposite because they have opposite
+eigenvalue on the gamma Phi
+
+ align:start position:0%
+eigenvalue on the gamma Phi
+ 
+
+ align:start position:0%
+eigenvalue on the gamma Phi
+and so this is equivalent to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+good any questions on this
+ 
+
+ align:start position:0%
+good any questions on this
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I think again it's a historical
+
+ align:start position:0%
+um I think again it's a historical
+ 
+
+ align:start position:0%
+um I think again it's a historical
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+um so so people
+
+ align:start position:0%
+um so so people
+ 
+
+ align:start position:0%
+um so so people
+often likely to go to euclidian space
+
+ align:start position:0%
+often likely to go to euclidian space
+ 
+
+ align:start position:0%
+often likely to go to euclidian space
+so when you go to creating space you
+
+ align:start position:0%
+so when you go to creating space you
+ 
+
+ align:start position:0%
+so when you go to creating space you
+continue gamma zero to gamma 4.
+
+ align:start position:0%
+continue gamma zero to gamma 4.
+ 
+
+ align:start position:0%
+continue gamma zero to gamma 4.
+yeah I just uh yeah uh to come before
+
+ align:start position:0%
+yeah I just uh yeah uh to come before
+ 
+
+ align:start position:0%
+yeah I just uh yeah uh to come before
+and then you reserve gamma 4 for that
+
+ align:start position:0%
+and then you reserve gamma 4 for that
+ 
+
+ align:start position:0%
+and then you reserve gamma 4 for that
+yeah then the gamma five is the next one
+
+ align:start position:0%
+yeah then the gamma five is the next one
+ 
+
+ align:start position:0%
+yeah then the gamma five is the next one
+you take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so mostly this case it's
+
+ align:start position:0%
+yeah yeah so mostly this case it's
+ 
+
+ align:start position:0%
+yeah yeah so mostly this case it's
+always special
+
+ align:start position:0%
+always special
+ 
+
+ align:start position:0%
+always special
+and and you will see uh in physics
+
+ align:start position:0%
+and and you will see uh in physics
+ 
+
+ align:start position:0%
+and and you will see uh in physics
+actually the max Space Case actually
+
+ align:start position:0%
+actually the max Space Case actually
+ 
+
+ align:start position:0%
+actually the max Space Case actually
+give you
+
+ align:start position:0%
+give you
+ 
+
+ align:start position:0%
+give you
+very much richer structure normally than
+
+ align:start position:0%
+very much richer structure normally than
+ 
+
+ align:start position:0%
+very much richer structure normally than
+than the uh than the massive particle
+
+ align:start position:0%
+than the uh than the massive particle
+ 
+
+ align:start position:0%
+than the uh than the massive particle
+it's because mathematically it's because
+
+ align:start position:0%
+it's because mathematically it's because
+ 
+
+ align:start position:0%
+it's because mathematically it's because
+of the mass list case uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the Master's case the representation
+
+ align:start position:0%
+in the Master's case the representation
+ 
+
+ align:start position:0%
+in the Master's case the representation
+on the Lawrence group is very different
+
+ align:start position:0%
+on the Lawrence group is very different
+ 
+
+ align:start position:0%
+on the Lawrence group is very different
+from the massive case
+
+ align:start position:0%
+from the massive case
+ 
+
+ align:start position:0%
+from the massive case
+for example if you have worked Fields
+
+ align:start position:0%
+for example if you have worked Fields
+ 
+
+ align:start position:0%
+for example if you have worked Fields
+say for Maxwell fields for the photon
+
+ align:start position:0%
+say for Maxwell fields for the photon
+ 
+
+ align:start position:0%
+say for Maxwell fields for the photon
+mass of its Photon have two
+
+ align:start position:0%
+mass of its Photon have two
+ 
+
+ align:start position:0%
+mass of its Photon have two
+polarizations
+
+ align:start position:0%
+polarizations
+ 
+
+ align:start position:0%
+polarizations
+but if you have a massive Vector say for
+
+ align:start position:0%
+but if you have a massive Vector say for
+ 
+
+ align:start position:0%
+but if you have a massive Vector say for
+the photon is massive then we have three
+
+ align:start position:0%
+the photon is massive then we have three
+ 
+
+ align:start position:0%
+the photon is massive then we have three
+transitions and so and so the message
+
+ align:start position:0%
+transitions and so and so the message
+ 
+
+ align:start position:0%
+transitions and so and so the message
+case the in the massive case are very
+
+ align:start position:0%
+case the in the massive case are very
+ 
+
+ align:start position:0%
+case the in the massive case are very
+very different
+
+ align:start position:0%
+very different
+ 
+
+ align:start position:0%
+very different
+so the formula case is the same so so so
+
+ align:start position:0%
+so the formula case is the same so so so
+ 
+
+ align:start position:0%
+so the formula case is the same so so so
+if you have a massive uh ferment you
+
+ align:start position:0%
+if you have a massive uh ferment you
+ 
+
+ align:start position:0%
+if you have a massive uh ferment you
+have four complex components but if you
+
+ align:start position:0%
+have four complex components but if you
+ 
+
+ align:start position:0%
+have four complex components but if you
+have a massive case then you have two
+
+ align:start position:0%
+have a massive case then you have two
+ 
+
+ align:start position:0%
+have a massive case then you have two
+compounds components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah that's a very interesting
+
+ align:start position:0%
+yeah yeah that's a very interesting
+ 
+
+ align:start position:0%
+yeah yeah that's a very interesting
+question and a lot of subtlety
+
+ align:start position:0%
+question and a lot of subtlety
+ 
+
+ align:start position:0%
+question and a lot of subtlety
+associated with that kind of
+
+ align:start position:0%
+associated with that kind of
+ 
+
+ align:start position:0%
+associated with that kind of
+questions yeah indeed yeah
+
+ align:start position:0%
+questions yeah indeed yeah
+ 
+
+ align:start position:0%
+questions yeah indeed yeah
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and say oh certainly are independent you
+
+ align:start position:0%
+and say oh certainly are independent you
+ 
+
+ align:start position:0%
+and say oh certainly are independent you
+can certainly treat them as independent
+
+ align:start position:0%
+can certainly treat them as independent
+ 
+
+ align:start position:0%
+can certainly treat them as independent
+dynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so let's conclude our discussion
+
+ align:start position:0%
+so so so let's conclude our discussion
+ 
+
+ align:start position:0%
+so so so let's conclude our discussion
+of the Cairo spinners
+
+ align:start position:0%
+of the Cairo spinners
+ 
+
+ align:start position:0%
+of the Cairo spinners
+and now we can talk about my Runner
+
+ align:start position:0%
+and now we can talk about my Runner
+ 
+
+ align:start position:0%
+and now we can talk about my Runner
+spinners
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the direct spinner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we have talked about so far
+
+ align:start position:0%
+which we have talked about so far
+ 
+
+ align:start position:0%
+which we have talked about so far
+is four components so you have four
+
+ align:start position:0%
+is four components so you have four
+ 
+
+ align:start position:0%
+is four components so you have four
+times two real components okay
+
+ align:start position:0%
+times two real components okay
+ 
+
+ align:start position:0%
+times two real components okay
+and then the chiral spindle we talk
+
+ align:start position:0%
+and then the chiral spindle we talk
+ 
+
+ align:start position:0%
+and then the chiral spindle we talk
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially have to come
+
+ align:start position:0%
+essentially have to come
+ 
+
+ align:start position:0%
+essentially have to come
+too complex components it's say two
+
+ align:start position:0%
+too complex components it's say two
+ 
+
+ align:start position:0%
+too complex components it's say two
+times two real component
+
+ align:start position:0%
+times two real component
+ 
+
+ align:start position:0%
+times two real component
+okay two times two will component
+
+ align:start position:0%
+okay two times two will component
+ 
+
+ align:start position:0%
+okay two times two will component
+so the last one I'm going to talk about
+
+ align:start position:0%
+so the last one I'm going to talk about
+ 
+
+ align:start position:0%
+so the last one I'm going to talk about
+is the mayorana
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in which case
+
+ align:start position:0%
+in which case
+ 
+
+ align:start position:0%
+in which case
+I will argue we have four times one
+
+ align:start position:0%
+I will argue we have four times one
+ 
+
+ align:start position:0%
+I will argue we have four times one
+real components so it has four
+
+ align:start position:0%
+real components so it has four
+ 
+
+ align:start position:0%
+real components so it has four
+independent real components okay
+
+ align:start position:0%
+independent real components okay
+ 
+
+ align:start position:0%
+independent real components okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes yeah
+
+ align:start position:0%
+yes yes yeah
+ 
+
+ align:start position:0%
+yes yes yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no no no physically uh electron
+
+ align:start position:0%
+no no no no physically uh electron
+ 
+
+ align:start position:0%
+no no no no physically uh electron
+contain both left and the right yeah so
+
+ align:start position:0%
+contain both left and the right yeah so
+ 
+
+ align:start position:0%
+contain both left and the right yeah so
+for massive particle because they always
+
+ align:start position:0%
+for massive particle because they always
+ 
+
+ align:start position:0%
+for massive particle because they always
+coupled together
+
+ align:start position:0%
+coupled together
+ 
+
+ align:start position:0%
+coupled together
+so the left hand so turning into play
+
+ align:start position:0%
+so the left hand so turning into play
+ 
+
+ align:start position:0%
+so the left hand so turning into play
+Upside upside out turning into percent L
+
+ align:start position:0%
+Upside upside out turning into percent L
+ 
+
+ align:start position:0%
+Upside upside out turning into percent L
+all the time and you cannot for massive
+
+ align:start position:0%
+all the time and you cannot for massive
+ 
+
+ align:start position:0%
+all the time and you cannot for massive
+particle you cannot really separate them
+
+ align:start position:0%
+particle you cannot really separate them
+ 
+
+ align:start position:0%
+particle you cannot really separate them
+but now for mass of this particle
+
+ align:start position:0%
+but now for mass of this particle
+ 
+
+ align:start position:0%
+but now for mass of this particle
+then then say Oh yeah this is a very
+
+ align:start position:0%
+then then say Oh yeah this is a very
+ 
+
+ align:start position:0%
+then then say Oh yeah this is a very
+good question say oh preserved
+
+ align:start position:0%
+good question say oh preserved
+ 
+
+ align:start position:0%
+good question say oh preserved
+so so massive particle is either side oh
+
+ align:start position:0%
+so so massive particle is either side oh
+ 
+
+ align:start position:0%
+so so massive particle is either side oh
+and then and then if you look at their
+
+ align:start position:0%
+and then and then if you look at their
+ 
+
+ align:start position:0%
+and then and then if you look at their
+uh so-called obesity it's either left
+
+ align:start position:0%
+uh so-called obesity it's either left
+ 
+
+ align:start position:0%
+uh so-called obesity it's either left
+handed or right-handed so that's where
+
+ align:start position:0%
+handed or right-handed so that's where
+ 
+
+ align:start position:0%
+handed or right-handed so that's where
+the lamps on say oh come from yeah but
+
+ align:start position:0%
+the lamps on say oh come from yeah but
+ 
+
+ align:start position:0%
+the lamps on say oh come from yeah but
+but for the massive particle you cannot
+
+ align:start position:0%
+but for the massive particle you cannot
+ 
+
+ align:start position:0%
+but for the massive particle you cannot
+make this impression
+
+ align:start position:0%
+make this impression
+ 
+
+ align:start position:0%
+make this impression
+but for the mass of this case it's
+
+ align:start position:0%
+but for the mass of this case it's
+ 
+
+ align:start position:0%
+but for the mass of this case it's
+preserved and then it's generally
+
+ align:start position:0%
+preserved and then it's generally
+ 
+
+ align:start position:0%
+preserved and then it's generally
+left-handed or right-handed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good and now let's talk about the
+
+ align:start position:0%
+okay good and now let's talk about the
+ 
+
+ align:start position:0%
+okay good and now let's talk about the
+last case
+
+ align:start position:0%
+last case
+ 
+
+ align:start position:0%
+last case
+this case which is the you have four
+
+ align:start position:0%
+this case which is the you have four
+ 
+
+ align:start position:0%
+this case which is the you have four
+real components okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so what do you do again we follow the
+
+ align:start position:0%
+so so what do you do again we follow the
+ 
+
+ align:start position:0%
+so so what do you do again we follow the
+similar strategy to see whether it's
+
+ align:start position:0%
+similar strategy to see whether it's
+ 
+
+ align:start position:0%
+similar strategy to see whether it's
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+to have four real components
+
+ align:start position:0%
+to have four real components
+ 
+
+ align:start position:0%
+to have four real components
+again we first uh the idea is that you
+
+ align:start position:0%
+again we first uh the idea is that you
+ 
+
+ align:start position:0%
+again we first uh the idea is that you
+first try to find the special
+
+ align:start position:0%
+first try to find the special
+ 
+
+ align:start position:0%
+first try to find the special
+reputation of gamma matrices
+
+ align:start position:0%
+reputation of gamma matrices
+ 
+
+ align:start position:0%
+reputation of gamma matrices
+so that you can a spindle can be real
+
+ align:start position:0%
+so that you can a spindle can be real
+ 
+
+ align:start position:0%
+so that you can a spindle can be real
+okay and then you try to generalize to
+
+ align:start position:0%
+okay and then you try to generalize to
+ 
+
+ align:start position:0%
+okay and then you try to generalize to
+to any representation of government
+
+ align:start position:0%
+to any representation of government
+ 
+
+ align:start position:0%
+to any representation of government
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if you look at the Rock equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now look at the Rock equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say if we what
+
+ align:start position:0%
+say if we what
+ 
+
+ align:start position:0%
+say if we what
+if I want to find the real
+
+ align:start position:0%
+if I want to find the real
+ 
+
+ align:start position:0%
+if I want to find the real
+spinner
+
+ align:start position:0%
+spinner
+ 
+
+ align:start position:0%
+spinner
+then I ask myself why the real spindle
+
+ align:start position:0%
+then I ask myself why the real spindle
+ 
+
+ align:start position:0%
+then I ask myself why the real spindle
+is compatible with this equation
+
+ align:start position:0%
+is compatible with this equation
+ 
+
+ align:start position:0%
+is compatible with this equation
+okay so like usually a real scale is not
+
+ align:start position:0%
+okay so like usually a real scale is not
+ 
+
+ align:start position:0%
+okay so like usually a real scale is not
+compatible with this equation because I
+
+ align:start position:0%
+compatible with this equation because I
+ 
+
+ align:start position:0%
+compatible with this equation because I
+take a complex conjugate
+
+ align:start position:0%
+take a complex conjugate
+ 
+
+ align:start position:0%
+take a complex conjugate
+and then take a gamma mu star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if PSI is real
+
+ align:start position:0%
+if PSI is real
+ 
+
+ align:start position:0%
+if PSI is real
+then percent has also have to satisfy
+
+ align:start position:0%
+then percent has also have to satisfy
+ 
+
+ align:start position:0%
+then percent has also have to satisfy
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+okay but in general gamma mu is complex
+
+ align:start position:0%
+okay but in general gamma mu is complex
+ 
+
+ align:start position:0%
+okay but in general gamma mu is complex
+as we wrote before
+
+ align:start position:0%
+as we wrote before
+ 
+
+ align:start position:0%
+as we wrote before
+yeah I just erase it for example in this
+
+ align:start position:0%
+yeah I just erase it for example in this
+ 
+
+ align:start position:0%
+yeah I just erase it for example in this
+basis it's complex
+
+ align:start position:0%
+basis it's complex
+ 
+
+ align:start position:0%
+basis it's complex
+okay with complex then these two
+
+ align:start position:0%
+okay with complex then these two
+ 
+
+ align:start position:0%
+okay with complex then these two
+equations are not compatible and then
+
+ align:start position:0%
+equations are not compatible and then
+ 
+
+ align:start position:0%
+equations are not compatible and then
+PSI cannot be real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there's a way out
+
+ align:start position:0%
+but there's a way out
+ 
+
+ align:start position:0%
+but there's a way out
+the way out is that if they exist a
+
+ align:start position:0%
+the way out is that if they exist a
+ 
+
+ align:start position:0%
+the way out is that if they exist a
+reputation
+
+ align:start position:0%
+reputation
+ 
+
+ align:start position:0%
+reputation
+of gamma mu
+
+ align:start position:0%
+of gamma mu
+ 
+
+ align:start position:0%
+of gamma mu
+the question whether they exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they exist a representation of a gamma
+
+ align:start position:0%
+they exist a representation of a gamma
+ 
+
+ align:start position:0%
+they exist a representation of a gamma
+mule so that's gamma mu is real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if this is real
+
+ align:start position:0%
+so if this is real
+ 
+
+ align:start position:0%
+so if this is real
+and then these two equations become the
+
+ align:start position:0%
+and then these two equations become the
+ 
+
+ align:start position:0%
+and then these two equations become the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then this equation becomes the
+
+ align:start position:0%
+okay and then this equation becomes the
+ 
+
+ align:start position:0%
+okay and then this equation becomes the
+same and then and then and then for PSI
+
+ align:start position:0%
+same and then and then and then for PSI
+ 
+
+ align:start position:0%
+same and then and then and then for PSI
+being real is compatible with the rock
+
+ align:start position:0%
+being real is compatible with the rock
+ 
+
+ align:start position:0%
+being real is compatible with the rock
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+okay it's compatible with the rocket
+
+ align:start position:0%
+okay it's compatible with the rocket
+ 
+
+ align:start position:0%
+okay it's compatible with the rocket
+quiz
+
+ align:start position:0%
+quiz
+ 
+
+ align:start position:0%
+quiz
+okay so so now let's
+
+ align:start position:0%
+okay so so now let's
+ 
+
+ align:start position:0%
+okay so so now let's
+so then this becomes
+
+ align:start position:0%
+so then this becomes
+ 
+
+ align:start position:0%
+so then this becomes
+question of trial and arrow okay so you
+
+ align:start position:0%
+question of trial and arrow okay so you
+ 
+
+ align:start position:0%
+question of trial and arrow okay so you
+try to find the representation of gamma
+
+ align:start position:0%
+try to find the representation of gamma
+ 
+
+ align:start position:0%
+try to find the representation of gamma
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+so that it's real okay
+
+ align:start position:0%
+so that it's real okay
+ 
+
+ align:start position:0%
+so that it's real okay
+and then uh uh uh uh it's
+
+ align:start position:0%
+and then uh uh uh uh it's
+ 
+
+ align:start position:0%
+and then uh uh uh uh it's
+attended out you can find it okay and
+
+ align:start position:0%
+attended out you can find it okay and
+ 
+
+ align:start position:0%
+attended out you can find it okay and
+here is the answer
+
+ align:start position:0%
+here is the answer
+ 
+
+ align:start position:0%
+here is the answer
+so let me just write down the answer
+
+ align:start position:0%
+so let me just write down the answer
+ 
+
+ align:start position:0%
+so let me just write down the answer
+I don't know how
+
+ align:start position:0%
+I don't know how
+ 
+
+ align:start position:0%
+I don't know how
+he originally found it by Iran
+
+ align:start position:0%
+he originally found it by Iran
+ 
+
+ align:start position:0%
+he originally found it by Iran
+originally found it
+
+ align:start position:0%
+originally found it
+ 
+
+ align:start position:0%
+originally found it
+but here is the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is four comma matrices
+
+ align:start position:0%
+so this is four comma matrices
+ 
+
+ align:start position:0%
+so this is four comma matrices
+and you can see there are each of them
+
+ align:start position:0%
+and you can see there are each of them
+ 
+
+ align:start position:0%
+and you can see there are each of them
+is real because Sigma 2 is pure
+
+ align:start position:0%
+is real because Sigma 2 is pure
+ 
+
+ align:start position:0%
+is real because Sigma 2 is pure
+imaginary
+
+ align:start position:0%
+imaginary
+ 
+
+ align:start position:0%
+imaginary
+and single one Sigma 3 are real
+
+ align:start position:0%
+and single one Sigma 3 are real
+ 
+
+ align:start position:0%
+and single one Sigma 3 are real
+and so this is purely real and you can
+
+ align:start position:0%
+and so this is purely real and you can
+ 
+
+ align:start position:0%
+and so this is purely real and you can
+check this satisfied the algebra of the
+
+ align:start position:0%
+check this satisfied the algebra of the
+ 
+
+ align:start position:0%
+check this satisfied the algebra of the
+gamma matrices
+
+ align:start position:0%
+gamma matrices
+ 
+
+ align:start position:0%
+gamma matrices
+okay I decided to find the algebra gamma
+
+ align:start position:0%
+okay I decided to find the algebra gamma
+ 
+
+ align:start position:0%
+okay I decided to find the algebra gamma
+Matrix the anti-commute with each other
+
+ align:start position:0%
+Matrix the anti-commute with each other
+ 
+
+ align:start position:0%
+Matrix the anti-commute with each other
+and each of them are a square so each of
+
+ align:start position:0%
+and each of them are a square so each of
+ 
+
+ align:start position:0%
+and each of them are a square so each of
+them square into one and so this three
+
+ align:start position:0%
+them square into one and so this three
+ 
+
+ align:start position:0%
+them square into one and so this three
+squared them into one this square into
+
+ align:start position:0%
+squared them into one this square into
+ 
+
+ align:start position:0%
+squared them into one this square into
+minus one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now this is compatible with the
+
+ align:start position:0%
+so so now this is compatible with the
+ 
+
+ align:start position:0%
+so so now this is compatible with the
+wrong equation but this is actually not
+
+ align:start position:0%
+wrong equation but this is actually not
+ 
+
+ align:start position:0%
+wrong equation but this is actually not
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+we also have to be sure this is
+
+ align:start position:0%
+we also have to be sure this is
+ 
+
+ align:start position:0%
+we also have to be sure this is
+compatible with low range transformation
+
+ align:start position:0%
+compatible with low range transformation
+ 
+
+ align:start position:0%
+compatible with low range transformation
+okay so so now let's check whether this
+
+ align:start position:0%
+okay so so now let's check whether this
+ 
+
+ align:start position:0%
+okay so so now let's check whether this
+compatible with fluorine transformation
+
+ align:start position:0%
+compatible with fluorine transformation
+ 
+
+ align:start position:0%
+compatible with fluorine transformation
+so so now we have this Sigma mu a gamma
+
+ align:start position:0%
+so so now we have this Sigma mu a gamma
+ 
+
+ align:start position:0%
+so so now we have this Sigma mu a gamma
+mu and remember the sigma mu or I just
+
+ align:start position:0%
+mu and remember the sigma mu or I just
+ 
+
+ align:start position:0%
+mu and remember the sigma mu or I just
+raised it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now this is pure imaginary
+
+ align:start position:0%
+so now this is pure imaginary
+ 
+
+ align:start position:0%
+so now this is pure imaginary
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+is also real and the sigma will be pure
+
+ align:start position:0%
+is also real and the sigma will be pure
+ 
+
+ align:start position:0%
+is also real and the sigma will be pure
+imaginary
+
+ align:start position:0%
+imaginary
+ 
+
+ align:start position:0%
+imaginary
+and then that means s Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is now is purely real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this means this is real
+
+ align:start position:0%
+now this means this is real
+ 
+
+ align:start position:0%
+now this means this is real
+and now we are done
+
+ align:start position:0%
+and now we are done
+ 
+
+ align:start position:0%
+and now we are done
+okay that means that if we take the size
+
+ align:start position:0%
+okay that means that if we take the size
+ 
+
+ align:start position:0%
+okay that means that if we take the size
+real
+
+ align:start position:0%
+real
+ 
+
+ align:start position:0%
+real
+then after low range transformation
+
+ align:start position:0%
+then after low range transformation
+ 
+
+ align:start position:0%
+then after low range transformation
+this remains to be real okay and so that
+
+ align:start position:0%
+this remains to be real okay and so that
+ 
+
+ align:start position:0%
+this remains to be real okay and so that
+that means that the uh it's compatible
+
+ align:start position:0%
+that means that the uh it's compatible
+ 
+
+ align:start position:0%
+that means that the uh it's compatible
+with an orange transformation
+
+ align:start position:0%
+with an orange transformation
+ 
+
+ align:start position:0%
+with an orange transformation
+so if we were not compatible with
+
+ align:start position:0%
+so if we were not compatible with
+ 
+
+ align:start position:0%
+so if we were not compatible with
+fluorine transformation then then we
+
+ align:start position:0%
+fluorine transformation then then we
+ 
+
+ align:start position:0%
+fluorine transformation then then we
+will finish okay so so this shows this
+
+ align:start position:0%
+will finish okay so so this shows this
+ 
+
+ align:start position:0%
+will finish okay so so this shows this
+remains real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so such a spinner is called a Myron
+
+ align:start position:0%
+so such a spinner is called a Myron
+ 
+
+ align:start position:0%
+so such a spinner is called a Myron
+spinner okay so it has four real
+
+ align:start position:0%
+spinner okay so it has four real
+ 
+
+ align:start position:0%
+spinner okay so it has four real
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+yeah we wrote there it's four real
+
+ align:start position:0%
+yeah we wrote there it's four real
+ 
+
+ align:start position:0%
+yeah we wrote there it's four real
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so you can contact it
+
+ align:start position:0%
+so you can contact it
+ 
+
+ align:start position:0%
+so you can contact it
+which I think I will give it as an
+
+ align:start position:0%
+which I think I will give it as an
+ 
+
+ align:start position:0%
+which I think I will give it as an
+exercise for you to do okay you can
+
+ align:start position:0%
+exercise for you to do okay you can
+ 
+
+ align:start position:0%
+exercise for you to do okay you can
+quantize it and then in this case then
+
+ align:start position:0%
+quantize it and then in this case then
+ 
+
+ align:start position:0%
+quantize it and then in this case then
+the uh the the the fermions are its own
+
+ align:start position:0%
+the uh the the the fermions are its own
+ 
+
+ align:start position:0%
+the uh the the the fermions are its own
+anti-particle okay it's online the
+
+ align:start position:0%
+anti-particle okay it's online the
+ 
+
+ align:start position:0%
+anti-particle okay it's online the
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+rather than uh rather than for the drug
+
+ align:start position:0%
+rather than uh rather than for the drug
+ 
+
+ align:start position:0%
+rather than uh rather than for the drug
+spinder uh you have particle and
+
+ align:start position:0%
+spinder uh you have particle and
+ 
+
+ align:start position:0%
+spinder uh you have particle and
+anti-particle so this is the analog of
+
+ align:start position:0%
+anti-particle so this is the analog of
+ 
+
+ align:start position:0%
+anti-particle so this is the analog of
+the real scalar uh uh uh in the spinner
+
+ align:start position:0%
+the real scalar uh uh uh in the spinner
+ 
+
+ align:start position:0%
+the real scalar uh uh uh in the spinner
+case okay
+
+ align:start position:0%
+case okay
+ 
+
+ align:start position:0%
+case okay
+so so this was discovered by uh by by
+
+ align:start position:0%
+so so this was discovered by uh by by
+ 
+
+ align:start position:0%
+so so this was discovered by uh by by
+veranda
+
+ align:start position:0%
+veranda
+ 
+
+ align:start position:0%
+veranda
+in 1937 okay
+
+ align:start position:0%
+in 1937 okay
+ 
+
+ align:start position:0%
+in 1937 okay
+and he was very young at the time he was
+
+ align:start position:0%
+and he was very young at the time he was
+ 
+
+ align:start position:0%
+and he was very young at the time he was
+31.
+
+ align:start position:0%
+31.
+ 
+
+ align:start position:0%
+31.
+and uh uh yeah we're brilliant
+
+ align:start position:0%
+and uh uh yeah we're brilliant
+ 
+
+ align:start position:0%
+and uh uh yeah we're brilliant
+physicists completely genius
+
+ align:start position:0%
+physicists completely genius
+ 
+
+ align:start position:0%
+physicists completely genius
+and then in 1938
+
+ align:start position:0%
+and then in 1938
+ 
+
+ align:start position:0%
+and then in 1938
+so he he lived in CCD okay so his
+
+ align:start position:0%
+so he he lived in CCD okay so his
+ 
+
+ align:start position:0%
+so he he lived in CCD okay so his
+hometown was insisted so he bought it
+
+ align:start position:0%
+hometown was insisted so he bought it
+ 
+
+ align:start position:0%
+hometown was insisted so he bought it
+the ship
+
+ align:start position:0%
+the ship
+ 
+
+ align:start position:0%
+the ship
+from labels to to to yeah to seasoning
+
+ align:start position:0%
+from labels to to to yeah to seasoning
+ 
+
+ align:start position:0%
+from labels to to to yeah to seasoning
+and then he just disappeared on the ship
+
+ align:start position:0%
+and then he just disappeared on the ship
+ 
+
+ align:start position:0%
+and then he just disappeared on the ship
+Never sing again okay level thing okay
+
+ align:start position:0%
+Never sing again okay level thing okay
+ 
+
+ align:start position:0%
+Never sing again okay level thing okay
+and uh at the age of 32 okay at the age
+
+ align:start position:0%
+and uh at the age of 32 okay at the age
+ 
+
+ align:start position:0%
+and uh at the age of 32 okay at the age
+of 32 he just disappeared
+
+ align:start position:0%
+of 32 he just disappeared
+ 
+
+ align:start position:0%
+of 32 he just disappeared
+um yeah it's a
+
+ align:start position:0%
+um yeah it's a
+ 
+
+ align:start position:0%
+um yeah it's a
+uh quite
+
+ align:start position:0%
+uh quite
+ 
+
+ align:start position:0%
+uh quite
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah extremely pretty in the physicists
+
+ align:start position:0%
+yeah extremely pretty in the physicists
+ 
+
+ align:start position:0%
+yeah extremely pretty in the physicists
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and the the all kind of stories about
+
+ align:start position:0%
+and the the all kind of stories about
+ 
+
+ align:start position:0%
+and the the all kind of stories about
+his disappearance they may be killed by
+
+ align:start position:0%
+his disappearance they may be killed by
+ 
+
+ align:start position:0%
+his disappearance they may be killed by
+Mafia or maybe suicide Etc but but just
+
+ align:start position:0%
+Mafia or maybe suicide Etc but but just
+ 
+
+ align:start position:0%
+Mafia or maybe suicide Etc but but just
+nobody knows
+
+ align:start position:0%
+nobody knows
+ 
+
+ align:start position:0%
+nobody knows
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we will talk about that yeah
+
+ align:start position:0%
+yeah we will talk about that yeah
+ 
+
+ align:start position:0%
+yeah we will talk about that yeah
+yeah so um
+
+ align:start position:0%
+yeah so um
+ 
+
+ align:start position:0%
+yeah so um
+so now we have chosen a very specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reputation for for gamma matrices
+
+ align:start position:0%
+reputation for for gamma matrices
+ 
+
+ align:start position:0%
+reputation for for gamma matrices
+which side can be chosen to be real okay
+
+ align:start position:0%
+which side can be chosen to be real okay
+ 
+
+ align:start position:0%
+which side can be chosen to be real okay
+but how about for the general
+
+ align:start position:0%
+but how about for the general
+ 
+
+ align:start position:0%
+but how about for the general
+uh for the general or or a
+
+ align:start position:0%
+uh for the general or or a
+ 
+
+ align:start position:0%
+uh for the general or or a
+representation okay so so now now we
+
+ align:start position:0%
+representation okay so so now now we
+ 
+
+ align:start position:0%
+representation okay so so now now we
+talk about the general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Myron spinner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh yeah also let me just make a
+
+ align:start position:0%
+yeah oh yeah also let me just make a
+ 
+
+ align:start position:0%
+yeah oh yeah also let me just make a
+remark my iron spinner of course uh also
+
+ align:start position:0%
+remark my iron spinner of course uh also
+ 
+
+ align:start position:0%
+remark my iron spinner of course uh also
+plays very important role in in modern
+
+ align:start position:0%
+plays very important role in in modern
+ 
+
+ align:start position:0%
+plays very important role in in modern
+day physics
+
+ align:start position:0%
+day physics
+ 
+
+ align:start position:0%
+day physics
+and uh it's uh
+
+ align:start position:0%
+and uh it's uh
+ 
+
+ align:start position:0%
+and uh it's uh
+um say for example people suspect a
+
+ align:start position:0%
+um say for example people suspect a
+ 
+
+ align:start position:0%
+um say for example people suspect a
+neutrino could be uh uh Myron or spinner
+
+ align:start position:0%
+neutrino could be uh uh Myron or spinner
+ 
+
+ align:start position:0%
+neutrino could be uh uh Myron or spinner
+okay so so to check whether the channel
+
+ align:start position:0%
+okay so so to check whether the channel
+ 
+
+ align:start position:0%
+okay so so to check whether the channel
+is my own spinner it's uh uh yeah it's a
+
+ align:start position:0%
+is my own spinner it's uh uh yeah it's a
+ 
+
+ align:start position:0%
+is my own spinner it's uh uh yeah it's a
+very yeah it's a Forefront experimental
+
+ align:start position:0%
+very yeah it's a Forefront experimental
+ 
+
+ align:start position:0%
+very yeah it's a Forefront experimental
+program has been pursued by many years
+
+ align:start position:0%
+program has been pursued by many years
+ 
+
+ align:start position:0%
+program has been pursued by many years
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+nothing in this matter
+
+ align:start position:0%
+nothing in this matter
+ 
+
+ align:start position:0%
+nothing in this matter
+inclined information and my Runner
+
+ align:start position:0%
+inclined information and my Runner
+ 
+
+ align:start position:0%
+inclined information and my Runner
+spindle play a very important role
+
+ align:start position:0%
+spindle play a very important role
+ 
+
+ align:start position:0%
+spindle play a very important role
+and so so in this matter you only have
+
+ align:start position:0%
+and so so in this matter you only have
+ 
+
+ align:start position:0%
+and so so in this matter you only have
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+so electron
+
+ align:start position:0%
+so electron
+ 
+
+ align:start position:0%
+so electron
+and the Byron spin is like half electron
+
+ align:start position:0%
+and the Byron spin is like half electron
+ 
+
+ align:start position:0%
+and the Byron spin is like half electron
+okay because the election have eight
+
+ align:start position:0%
+okay because the election have eight
+ 
+
+ align:start position:0%
+okay because the election have eight
+components right remember and the
+
+ align:start position:0%
+components right remember and the
+ 
+
+ align:start position:0%
+components right remember and the
+Mariana only have four components so so
+
+ align:start position:0%
+Mariana only have four components so so
+ 
+
+ align:start position:0%
+Mariana only have four components so so
+Byron is like a half electron so
+
+ align:start position:0%
+Byron is like a half electron so
+ 
+
+ align:start position:0%
+Byron is like a half electron so
+precisely because it's
+
+ align:start position:0%
+precisely because it's
+ 
+
+ align:start position:0%
+precisely because it's
+heuristic like a half election it has
+
+ align:start position:0%
+heuristic like a half election it has
+ 
+
+ align:start position:0%
+heuristic like a half election it has
+very stable topological properties which
+
+ align:start position:0%
+very stable topological properties which
+ 
+
+ align:start position:0%
+very stable topological properties which
+election a single electron does not have
+
+ align:start position:0%
+election a single electron does not have
+ 
+
+ align:start position:0%
+election a single electron does not have
+and uh and whether you can engineer in
+
+ align:start position:0%
+and uh and whether you can engineer in
+ 
+
+ align:start position:0%
+and uh and whether you can engineer in
+your in your kindness matter systems
+
+ align:start position:0%
+your in your kindness matter systems
+ 
+
+ align:start position:0%
+your in your kindness matter systems
+marijuana spinner then become a Holy
+
+ align:start position:0%
+marijuana spinner then become a Holy
+ 
+
+ align:start position:0%
+marijuana spinner then become a Holy
+Grail because if you can do it and then
+
+ align:start position:0%
+Grail because if you can do it and then
+ 
+
+ align:start position:0%
+Grail because if you can do it and then
+you can do a lot of uh uh yeah uh you
+
+ align:start position:0%
+you can do a lot of uh uh yeah uh you
+ 
+
+ align:start position:0%
+you can do a lot of uh uh yeah uh you
+can achieve more more stable Quantum
+
+ align:start position:0%
+can achieve more more stable Quantum
+ 
+
+ align:start position:0%
+can achieve more more stable Quantum
+computation Etc
+
+ align:start position:0%
+computation Etc
+ 
+
+ align:start position:0%
+computation Etc
+um yeah uh during the last number of
+
+ align:start position:0%
+um yeah uh during the last number of
+ 
+
+ align:start position:0%
+um yeah uh during the last number of
+years there have been various
+
+ align:start position:0%
+years there have been various
+ 
+
+ align:start position:0%
+years there have been various
+experimental reports people say they
+
+ align:start position:0%
+experimental reports people say they
+ 
+
+ align:start position:0%
+experimental reports people say they
+have uh
+
+ align:start position:0%
+have uh
+ 
+
+ align:start position:0%
+have uh
+engineered my Runner spindle in the lab
+
+ align:start position:0%
+engineered my Runner spindle in the lab
+ 
+
+ align:start position:0%
+engineered my Runner spindle in the lab
+which I think has never been fully
+
+ align:start position:0%
+which I think has never been fully
+ 
+
+ align:start position:0%
+which I think has never been fully
+confirmed I think yeah none of them has
+
+ align:start position:0%
+confirmed I think yeah none of them has
+ 
+
+ align:start position:0%
+confirmed I think yeah none of them has
+been fully confirmed
+
+ align:start position:0%
+been fully confirmed
+ 
+
+ align:start position:0%
+been fully confirmed
+anyway so so yeah so uh so now let's
+
+ align:start position:0%
+anyway so so yeah so uh so now let's
+ 
+
+ align:start position:0%
+anyway so so yeah so uh so now let's
+talk about marijuana spinner in in
+
+ align:start position:0%
+talk about marijuana spinner in in
+ 
+
+ align:start position:0%
+talk about marijuana spinner in in
+general basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for General Karma mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea would be the similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the case of the chiral spinner
+
+ align:start position:0%
+to the case of the chiral spinner
+ 
+
+ align:start position:0%
+to the case of the chiral spinner
+for the Carol spinner
+
+ align:start position:0%
+for the Carol spinner
+ 
+
+ align:start position:0%
+for the Carol spinner
+in the Cairo basis is very simple just
+
+ align:start position:0%
+in the Cairo basis is very simple just
+ 
+
+ align:start position:0%
+in the Cairo basis is very simple just
+Apple up and low components
+
+ align:start position:0%
+Apple up and low components
+ 
+
+ align:start position:0%
+Apple up and low components
+so for the Carolina you have to
+
+ align:start position:0%
+so for the Carolina you have to
+ 
+
+ align:start position:0%
+so for the Carolina you have to
+introduce some other structure to
+
+ align:start position:0%
+introduce some other structure to
+ 
+
+ align:start position:0%
+introduce some other structure to
+isolate on episode
+
+ align:start position:0%
+isolate on episode
+ 
+
+ align:start position:0%
+isolate on episode
+okay so you have to uh allow you have
+
+ align:start position:0%
+okay so you have to uh allow you have
+ 
+
+ align:start position:0%
+okay so you have to uh allow you have
+this non-trivial condition okay and the
+
+ align:start position:0%
+this non-trivial condition okay and the
+ 
+
+ align:start position:0%
+this non-trivial condition okay and the
+chirophonium come from this non-trivial
+
+ align:start position:0%
+chirophonium come from this non-trivial
+ 
+
+ align:start position:0%
+chirophonium come from this non-trivial
+condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come from this non-trivial condition
+
+ align:start position:0%
+come from this non-trivial condition
+ 
+
+ align:start position:0%
+come from this non-trivial condition
+so so now the key is that how to find
+
+ align:start position:0%
+so so now the key is that how to find
+ 
+
+ align:start position:0%
+so so now the key is that how to find
+the linear gas condition
+
+ align:start position:0%
+the linear gas condition
+ 
+
+ align:start position:0%
+the linear gas condition
+to to the website to be real
+
+ align:start position:0%
+to to the website to be real
+ 
+
+ align:start position:0%
+to to the website to be real
+in the in the general basis okay because
+
+ align:start position:0%
+in the in the general basis okay because
+ 
+
+ align:start position:0%
+in the in the general basis okay because
+when gamma mu is changed is generally
+
+ align:start position:0%
+when gamma mu is changed is generally
+ 
+
+ align:start position:0%
+when gamma mu is changed is generally
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+clearly you cannot set the side you
+
+ align:start position:0%
+clearly you cannot set the side you
+ 
+
+ align:start position:0%
+clearly you cannot set the side you
+could preside stop okay that does not
+
+ align:start position:0%
+could preside stop okay that does not
+ 
+
+ align:start position:0%
+could preside stop okay that does not
+make sense and you have to find another
+
+ align:start position:0%
+make sense and you have to find another
+ 
+
+ align:start position:0%
+make sense and you have to find another
+equivalent equation to do essentially
+
+ align:start position:0%
+equivalent equation to do essentially
+ 
+
+ align:start position:0%
+equivalent equation to do essentially
+the same thing okay so that's the basic
+
+ align:start position:0%
+the same thing okay so that's the basic
+ 
+
+ align:start position:0%
+the same thing okay so that's the basic
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+okay so so for this purpose
+
+ align:start position:0%
+okay so so for this purpose
+ 
+
+ align:start position:0%
+okay so so for this purpose
+we want to uh
+
+ align:start position:0%
+we want to uh
+ 
+
+ align:start position:0%
+we want to uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now we use that the any gamma Matrix is
+
+ align:start position:0%
+now we use that the any gamma Matrix is
+ 
+
+ align:start position:0%
+now we use that the any gamma Matrix is
+the equivalent to each other up to a
+
+ align:start position:0%
+the equivalent to each other up to a
+ 
+
+ align:start position:0%
+the equivalent to each other up to a
+similar transformation okay so so let's
+
+ align:start position:0%
+similar transformation okay so so let's
+ 
+
+ align:start position:0%
+similar transformation okay so so let's
+delote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this space is by gamma m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then then we have gamma M which is
+
+ align:start position:0%
+and then then we have gamma M which is
+ 
+
+ align:start position:0%
+and then then we have gamma M which is
+the this called Myra basis
+
+ align:start position:0%
+the this called Myra basis
+ 
+
+ align:start position:0%
+the this called Myra basis
+and then any choice of gamma mu then
+
+ align:start position:0%
+and then any choice of gamma mu then
+ 
+
+ align:start position:0%
+and then any choice of gamma mu then
+related to gamma M by a similar
+
+ align:start position:0%
+related to gamma M by a similar
+ 
+
+ align:start position:0%
+related to gamma M by a similar
+transformation that means they exist
+
+ align:start position:0%
+transformation that means they exist
+ 
+
+ align:start position:0%
+transformation that means they exist
+from Matrix C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that the C can take
+
+ align:start position:0%
+that the C can take
+ 
+
+ align:start position:0%
+that the C can take
+any gamma mu into gamma
+
+ align:start position:0%
+any gamma mu into gamma
+ 
+
+ align:start position:0%
+any gamma mu into gamma
+mu n okay so so there must exist C this
+
+ align:start position:0%
+mu n okay so so there must exist C this
+ 
+
+ align:start position:0%
+mu n okay so so there must exist C this
+equation is satisfied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so now given this C then we can easily
+
+ align:start position:0%
+so now given this C then we can easily
+ 
+
+ align:start position:0%
+so now given this C then we can easily
+write down the condition
+
+ align:start position:0%
+write down the condition
+ 
+
+ align:start position:0%
+write down the condition
+for the general basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because under such a change of basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the side you change your basis that
+
+ align:start position:0%
+on the side you change your basis that
+ 
+
+ align:start position:0%
+on the side you change your basis that
+might run a screen in my around the
+
+ align:start position:0%
+might run a screen in my around the
+ 
+
+ align:start position:0%
+might run a screen in my around the
+basis which is real is related to the
+
+ align:start position:0%
+basis which is real is related to the
+ 
+
+ align:start position:0%
+basis which is real is related to the
+spinner in the in the gamma mu basis by
+
+ align:start position:0%
+spinner in the in the gamma mu basis by
+ 
+
+ align:start position:0%
+spinner in the in the gamma mu basis by
+this transformation C
+
+ align:start position:0%
+this transformation C
+ 
+
+ align:start position:0%
+this transformation C
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the C relates to the gamma matrices
+
+ align:start position:0%
+so the C relates to the gamma matrices
+ 
+
+ align:start position:0%
+so the C relates to the gamma matrices
+but C of course also relates to the
+
+ align:start position:0%
+but C of course also relates to the
+ 
+
+ align:start position:0%
+but C of course also relates to the
+spinner you just change your bases okay
+
+ align:start position:0%
+spinner you just change your bases okay
+ 
+
+ align:start position:0%
+spinner you just change your bases okay
+and so so M will be related to psi by C
+
+ align:start position:0%
+and so so M will be related to psi by C
+ 
+
+ align:start position:0%
+and so so M will be related to psi by C
+and now since the same
+
+ align:start position:0%
+and now since the same
+ 
+
+ align:start position:0%
+and now since the same
+is equal to same star
+
+ align:start position:0%
+is equal to same star
+ 
+
+ align:start position:0%
+is equal to same star
+so that means that c
+
+ align:start position:0%
+so that means that c
+ 
+
+ align:start position:0%
+so that means that c
+stops I star should be equal to C
+
+ align:start position:0%
+stops I star should be equal to C
+ 
+
+ align:start position:0%
+stops I star should be equal to C
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+okay so that means
+
+ align:start position:0%
+okay so that means
+ 
+
+ align:start position:0%
+okay so that means
+website star
+
+ align:start position:0%
+website star
+ 
+
+ align:start position:0%
+website star
+should be equal to B PSI
+
+ align:start position:0%
+should be equal to B PSI
+ 
+
+ align:start position:0%
+should be equal to B PSI
+with B
+
+ align:start position:0%
+with B
+ 
+
+ align:start position:0%
+with B
+equal to C minus 1 star C okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that should be the condition which
+
+ align:start position:0%
+so that should be the condition which
+ 
+
+ align:start position:0%
+so that should be the condition which
+you impose in the general basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that should be the condition you
+
+ align:start position:0%
+okay so that should be the condition you
+ 
+
+ align:start position:0%
+okay so that should be the condition you
+should impose in the general basis so so
+
+ align:start position:0%
+should impose in the general basis so so
+ 
+
+ align:start position:0%
+should impose in the general basis so so
+you have to introduce DC
+
+ align:start position:0%
+you have to introduce DC
+ 
+
+ align:start position:0%
+you have to introduce DC
+so if you find the transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the uh between the uh the
+
+ align:start position:0%
+between the uh between the uh the
+ 
+
+ align:start position:0%
+between the uh between the uh the
+general gamma mu and the gamma mu M and
+
+ align:start position:0%
+general gamma mu and the gamma mu M and
+ 
+
+ align:start position:0%
+general gamma mu and the gamma mu M and
+then you can use that to find the B and
+
+ align:start position:0%
+then you can use that to find the B and
+ 
+
+ align:start position:0%
+then you can use that to find the B and
+once you find the B and then you can
+
+ align:start position:0%
+once you find the B and then you can
+ 
+
+ align:start position:0%
+once you find the B and then you can
+find the uh you can impose the Micron
+
+ align:start position:0%
+find the uh you can impose the Micron
+ 
+
+ align:start position:0%
+find the uh you can impose the Micron
+yeah so this is called the Myron
+
+ align:start position:0%
+yeah so this is called the Myron
+ 
+
+ align:start position:0%
+yeah so this is called the Myron
+condition in the general basis
+
+ align:start position:0%
+condition in the general basis
+ 
+
+ align:start position:0%
+condition in the general basis
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's understand the little bit
+
+ align:start position:0%
+so let's understand the little bit
+ 
+
+ align:start position:0%
+so let's understand the little bit
+so actually we can understand B more
+
+ align:start position:0%
+so actually we can understand B more
+ 
+
+ align:start position:0%
+so actually we can understand B more
+directly
+
+ align:start position:0%
+directly
+ 
+
+ align:start position:0%
+directly
+okay so here we express number c but we
+
+ align:start position:0%
+okay so here we express number c but we
+ 
+
+ align:start position:0%
+okay so here we express number c but we
+actually can find the B more directly
+
+ align:start position:0%
+actually can find the B more directly
+ 
+
+ align:start position:0%
+actually can find the B more directly
+we can just take the we can take the
+
+ align:start position:0%
+we can just take the we can take the
+ 
+
+ align:start position:0%
+we can just take the we can take the
+compressed conjugate of this equation
+
+ align:start position:0%
+compressed conjugate of this equation
+ 
+
+ align:start position:0%
+compressed conjugate of this equation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because the gamma
+
+ align:start position:0%
+because the gamma
+ 
+
+ align:start position:0%
+because the gamma
+because gamma mu m is real
+
+ align:start position:0%
+because gamma mu m is real
+ 
+
+ align:start position:0%
+because gamma mu m is real
+so we can also take a complex conjugate
+
+ align:start position:0%
+so we can also take a complex conjugate
+ 
+
+ align:start position:0%
+so we can also take a complex conjugate
+of this equation so that means that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m equal to gamma mu M Star
+
+ align:start position:0%
+m equal to gamma mu M Star
+ 
+
+ align:start position:0%
+m equal to gamma mu M Star
+so if we take complex conjugate of that
+
+ align:start position:0%
+so if we take complex conjugate of that
+ 
+
+ align:start position:0%
+so if we take complex conjugate of that
+equation means that the C star
+
+ align:start position:0%
+equation means that the C star
+ 
+
+ align:start position:0%
+equation means that the C star
+gamma mu C minus one star is equal to C
+
+ align:start position:0%
+gamma mu C minus one star is equal to C
+ 
+
+ align:start position:0%
+gamma mu C minus one star is equal to C
+gamma mu
+
+ align:start position:0%
+gamma mu
+ 
+
+ align:start position:0%
+gamma mu
+C minus 1
+
+ align:start position:0%
+C minus 1
+ 
+
+ align:start position:0%
+C minus 1
+and now again you just
+
+ align:start position:0%
+and now again you just
+ 
+
+ align:start position:0%
+and now again you just
+sorry this star okay
+
+ align:start position:0%
+sorry this star okay
+ 
+
+ align:start position:0%
+sorry this star okay
+so now if we put all the C to this side
+
+ align:start position:0%
+so now if we put all the C to this side
+ 
+
+ align:start position:0%
+so now if we put all the C to this side
+and then we find
+
+ align:start position:0%
+and then we find
+ 
+
+ align:start position:0%
+and then we find
+gamma mu star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from a mu star
+
+ align:start position:0%
+from a mu star
+ 
+
+ align:start position:0%
+from a mu star
+is just equal to B comma mu e minus 1.
+
+ align:start position:0%
+is just equal to B comma mu e minus 1.
+ 
+
+ align:start position:0%
+is just equal to B comma mu e minus 1.
+okay so so you just put this to this
+
+ align:start position:0%
+okay so so you just put this to this
+ 
+
+ align:start position:0%
+okay so so you just put this to this
+side then you just so this becomes B and
+
+ align:start position:0%
+side then you just so this becomes B and
+ 
+
+ align:start position:0%
+side then you just so this becomes B and
+then this becomes B minus one okay
+
+ align:start position:0%
+then this becomes B minus one okay
+ 
+
+ align:start position:0%
+then this becomes B minus one okay
+so so now we see
+
+ align:start position:0%
+so so now we see
+ 
+
+ align:start position:0%
+so so now we see
+that b
+
+ align:start position:0%
+that b
+ 
+
+ align:start position:0%
+that b
+is actually makes sense it is actually
+
+ align:start position:0%
+is actually makes sense it is actually
+ 
+
+ align:start position:0%
+is actually makes sense it is actually
+the Matrix we take a gamma mu to gamma
+
+ align:start position:0%
+the Matrix we take a gamma mu to gamma
+ 
+
+ align:start position:0%
+the Matrix we take a gamma mu to gamma
+mu stock
+
+ align:start position:0%
+mu stock
+ 
+
+ align:start position:0%
+mu stock
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the B is the Matrix uh uh to take
+
+ align:start position:0%
+so the B is the Matrix uh uh to take
+ 
+
+ align:start position:0%
+so the B is the Matrix uh uh to take
+stock okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+good any questions on this
+ 
+
+ align:start position:0%
+good any questions on this
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+well they just general long singular or
+
+ align:start position:0%
+well they just general long singular or
+ 
+
+ align:start position:0%
+well they just general long singular or
+or a matrices
+
+ align:start position:0%
+or a matrices
+ 
+
+ align:start position:0%
+or a matrices
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah just four by four uh non singular
+
+ align:start position:0%
+yeah just four by four uh non singular
+ 
+
+ align:start position:0%
+yeah just four by four uh non singular
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they often can be chosen to be unitary
+
+ align:start position:0%
+they often can be chosen to be unitary
+ 
+
+ align:start position:0%
+they often can be chosen to be unitary
+and but but in principle you don't have
+
+ align:start position:0%
+and but but in principle you don't have
+ 
+
+ align:start position:0%
+and but but in principle you don't have
+to choose them to be used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so now let's double check
+
+ align:start position:0%
+so so now let's double check
+ 
+
+ align:start position:0%
+so so now let's double check
+so let's call this equation star star
+
+ align:start position:0%
+so let's call this equation star star
+ 
+
+ align:start position:0%
+so let's call this equation star star
+so let's check
+
+ align:start position:0%
+so let's check
+ 
+
+ align:start position:0%
+so let's check
+let's start star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we showed that here
+
+ align:start position:0%
+so we showed that here
+ 
+
+ align:start position:0%
+so we showed that here
+in this representation this is
+
+ align:start position:0%
+in this representation this is
+ 
+
+ align:start position:0%
+in this representation this is
+compatible with Romaine transformation
+
+ align:start position:0%
+compatible with Romaine transformation
+ 
+
+ align:start position:0%
+compatible with Romaine transformation
+okay so we still need to check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star star is compatible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the lowering transformation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we mean by by this is compatible
+
+ align:start position:0%
+so what we mean by by this is compatible
+ 
+
+ align:start position:0%
+so what we mean by by this is compatible
+with lowering transformation
+
+ align:start position:0%
+with lowering transformation
+ 
+
+ align:start position:0%
+with lowering transformation
+which means that if we take a PSI
+
+ align:start position:0%
+which means that if we take a PSI
+ 
+
+ align:start position:0%
+which means that if we take a PSI
+which satisfy this condition
+
+ align:start position:0%
+which satisfy this condition
+ 
+
+ align:start position:0%
+which satisfy this condition
+okay so take a side which satisfy that
+
+ align:start position:0%
+okay so take a side which satisfy that
+ 
+
+ align:start position:0%
+okay so take a side which satisfy that
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+take upside which satisfies
+
+ align:start position:0%
+take upside which satisfies
+ 
+
+ align:start position:0%
+take upside which satisfies
+star star
+
+ align:start position:0%
+star star
+ 
+
+ align:start position:0%
+star star
+and then we make a lower end
+
+ align:start position:0%
+and then we make a lower end
+ 
+
+ align:start position:0%
+and then we make a lower end
+transformation PSI Prime equal to S
+
+ align:start position:0%
+transformation PSI Prime equal to S
+ 
+
+ align:start position:0%
+transformation PSI Prime equal to S
+Lambda PSI
+
+ align:start position:0%
+Lambda PSI
+ 
+
+ align:start position:0%
+Lambda PSI
+okay and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PSI Prime should also satisfy that
+
+ align:start position:0%
+PSI Prime should also satisfy that
+ 
+
+ align:start position:0%
+PSI Prime should also satisfy that
+condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start stop okay so that means this is
+
+ align:start position:0%
+start stop okay so that means this is
+ 
+
+ align:start position:0%
+start stop okay so that means this is
+compatible with small engine so it means
+
+ align:start position:0%
+compatible with small engine so it means
+ 
+
+ align:start position:0%
+compatible with small engine so it means
+that the PSI Prime Star
+
+ align:start position:0%
+that the PSI Prime Star
+ 
+
+ align:start position:0%
+that the PSI Prime Star
+should be equal to the same as B
+
+ align:start position:0%
+should be equal to the same as B
+ 
+
+ align:start position:0%
+should be equal to the same as B
+side price okay
+
+ align:start position:0%
+side price okay
+ 
+
+ align:start position:0%
+side price okay
+that means that type uh should set this
+
+ align:start position:0%
+that means that type uh should set this
+ 
+
+ align:start position:0%
+that means that type uh should set this
+upside Prime Star if satisfy that
+
+ align:start position:0%
+upside Prime Star if satisfy that
+ 
+
+ align:start position:0%
+upside Prime Star if satisfy that
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+okay so now let's check that okay now
+
+ align:start position:0%
+okay so now let's check that okay now
+ 
+
+ align:start position:0%
+okay so now let's check that okay now
+let's check this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before checking that you have any
+
+ align:start position:0%
+so before checking that you have any
+ 
+
+ align:start position:0%
+so before checking that you have any
+questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so so first from this equation let's
+
+ align:start position:0%
+so so first from this equation let's
+ 
+
+ align:start position:0%
+so so first from this equation let's
+call it the star star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from this star Cube equation
+
+ align:start position:0%
+from this star Cube equation
+ 
+
+ align:start position:0%
+from this star Cube equation
+so we can find the
+
+ align:start position:0%
+so we can find the
+ 
+
+ align:start position:0%
+so we can find the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can find the
+
+ align:start position:0%
+so we can find the
+ 
+
+ align:start position:0%
+so we can find the
+the p
+
+ align:start position:0%
+the p
+ 
+
+ align:start position:0%
+the p
+when you act on Sigma mu
+
+ align:start position:0%
+when you act on Sigma mu
+ 
+
+ align:start position:0%
+when you act on Sigma mu
+in minus one so that gives you minus
+
+ align:start position:0%
+in minus one so that gives you minus
+ 
+
+ align:start position:0%
+in minus one so that gives you minus
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+okay so this is obvious
+
+ align:start position:0%
+okay so this is obvious
+ 
+
+ align:start position:0%
+okay so this is obvious
+mu is has I there so the minus sign
+
+ align:start position:0%
+mu is has I there so the minus sign
+ 
+
+ align:start position:0%
+mu is has I there so the minus sign
+comes from the I and otherwise the the B
+
+ align:start position:0%
+comes from the I and otherwise the the B
+ 
+
+ align:start position:0%
+comes from the I and otherwise the the B
+taking each comma a gamma Matrix there
+
+ align:start position:0%
+taking each comma a gamma Matrix there
+ 
+
+ align:start position:0%
+taking each comma a gamma Matrix there
+into star okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that means that the S star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+which is given by experiential one half
+
+ align:start position:0%
+which is given by experiential one half
+ 
+
+ align:start position:0%
+which is given by experiential one half
+Omega mu
+
+ align:start position:0%
+Omega mu
+ 
+
+ align:start position:0%
+Omega mu
+Sigma star
+
+ align:start position:0%
+Sigma star
+ 
+
+ align:start position:0%
+Sigma star
+new mu
+
+ align:start position:0%
+new mu
+ 
+
+ align:start position:0%
+new mu
+Sigma mu mu star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is equal to
+
+ align:start position:0%
+now this is equal to
+ 
+
+ align:start position:0%
+now this is equal to
+okay just equal to
+
+ align:start position:0%
+okay just equal to
+ 
+
+ align:start position:0%
+okay just equal to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah you can just uh plug this in okay
+
+ align:start position:0%
+yeah you can just uh plug this in okay
+ 
+
+ align:start position:0%
+yeah you can just uh plug this in okay
+uh probably this in it just become
+
+ align:start position:0%
+uh probably this in it just become
+ 
+
+ align:start position:0%
+uh probably this in it just become
+exponential minus I Omega V mu
+
+ align:start position:0%
+exponential minus I Omega V mu
+ 
+
+ align:start position:0%
+exponential minus I Omega V mu
+or minus I will review
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+Sigma C minus one okay
+
+ align:start position:0%
+Sigma C minus one okay
+ 
+
+ align:start position:0%
+Sigma C minus one okay
+so let me just yeah this Sigma will be
+
+ align:start position:0%
+so let me just yeah this Sigma will be
+ 
+
+ align:start position:0%
+so let me just yeah this Sigma will be
+minus one okay
+
+ align:start position:0%
+minus one okay
+ 
+
+ align:start position:0%
+minus one okay
+so I just inserted the sigma mu star is
+
+ align:start position:0%
+so I just inserted the sigma mu star is
+ 
+
+ align:start position:0%
+so I just inserted the sigma mu star is
+equal to minus that here okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now you can since this B B minus y
+
+ align:start position:0%
+so so now you can since this B B minus y
+ 
+
+ align:start position:0%
+so so now you can since this B B minus y
+is in the expression you can immediately
+
+ align:start position:0%
+is in the expression you can immediately
+ 
+
+ align:start position:0%
+is in the expression you can immediately
+take it down
+
+ align:start position:0%
+take it down
+ 
+
+ align:start position:0%
+take it down
+so that just equal to B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+Lambda V minus 1. okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so because when you expand this in
+
+ align:start position:0%
+so so because when you expand this in
+ 
+
+ align:start position:0%
+so so because when you expand this in
+power series p and B minus one always
+
+ align:start position:0%
+power series p and B minus one always
+ 
+
+ align:start position:0%
+power series p and B minus one always
+cancel accepted the first one and the
+
+ align:start position:0%
+cancel accepted the first one and the
+ 
+
+ align:start position:0%
+cancel accepted the first one and the
+last one okay so we have used this trick
+
+ align:start position:0%
+last one okay so we have used this trick
+ 
+
+ align:start position:0%
+last one okay so we have used this trick
+many times
+
+ align:start position:0%
+many times
+ 
+
+ align:start position:0%
+many times
+yeah and uh and then so so we get a very
+
+ align:start position:0%
+yeah and uh and then so so we get a very
+ 
+
+ align:start position:0%
+yeah and uh and then so so we get a very
+very nice relation that under low range
+
+ align:start position:0%
+very nice relation that under low range
+ 
+
+ align:start position:0%
+very nice relation that under low range
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+so the law low range transformation
+
+ align:start position:0%
+so the law low range transformation
+ 
+
+ align:start position:0%
+so the law low range transformation
+matrix on the compressed conjugation
+
+ align:start position:0%
+matrix on the compressed conjugation
+ 
+
+ align:start position:0%
+matrix on the compressed conjugation
+again is generated by this speed okay
+
+ align:start position:0%
+again is generated by this speed okay
+ 
+
+ align:start position:0%
+again is generated by this speed okay
+related by this B Matrix
+
+ align:start position:0%
+related by this B Matrix
+ 
+
+ align:start position:0%
+related by this B Matrix
+and now it's just immediate okay and so
+
+ align:start position:0%
+and now it's just immediate okay and so
+ 
+
+ align:start position:0%
+and now it's just immediate okay and so
+not just immediate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and not just immediate so so when you
+
+ align:start position:0%
+and not just immediate so so when you
+ 
+
+ align:start position:0%
+and not just immediate so so when you
+have the PSI Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to that let's just take the star
+
+ align:start position:0%
+equal to that let's just take the star
+ 
+
+ align:start position:0%
+equal to that let's just take the star
+of this equation
+
+ align:start position:0%
+of this equation
+ 
+
+ align:start position:0%
+of this equation
+okay so subscribe Prime Star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just equal to S star
+
+ align:start position:0%
+just equal to S star
+ 
+
+ align:start position:0%
+just equal to S star
+Lambda PSI star
+
+ align:start position:0%
+Lambda PSI star
+ 
+
+ align:start position:0%
+Lambda PSI star
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that is equal to
+
+ align:start position:0%
+so that is equal to
+ 
+
+ align:start position:0%
+so that is equal to
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+is Lambda e minus 1 and B as a B plus I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is equal to B
+
+ align:start position:0%
+okay so this is equal to B
+ 
+
+ align:start position:0%
+okay so this is equal to B
+as number
+
+ align:start position:0%
+as number
+ 
+
+ align:start position:0%
+as number
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+okay so this is equal to P5 okay
+
+ align:start position:0%
+okay so this is equal to P5 okay
+ 
+
+ align:start position:0%
+okay so this is equal to P5 okay
+precisely what we were trying to show
+
+ align:start position:0%
+precisely what we were trying to show
+ 
+
+ align:start position:0%
+precisely what we were trying to show
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so now let me give you a
+
+ align:start position:0%
+okay so so now let me give you a
+ 
+
+ align:start position:0%
+okay so so now let me give you a
+specific example of this Matrix
+
+ align:start position:0%
+specific example of this Matrix
+ 
+
+ align:start position:0%
+specific example of this Matrix
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+in the in the uh in uh so so for this my
+
+ align:start position:0%
+in the in the uh in uh so so for this my
+ 
+
+ align:start position:0%
+in the in the uh in uh so so for this my
+wrong representation the B just equal to
+
+ align:start position:0%
+wrong representation the B just equal to
+ 
+
+ align:start position:0%
+wrong representation the B just equal to
+Identity okay so B just equal to
+
+ align:start position:0%
+Identity okay so B just equal to
+ 
+
+ align:start position:0%
+Identity okay so B just equal to
+Identity
+
+ align:start position:0%
+Identity
+ 
+
+ align:start position:0%
+Identity
+in this representation and now let's try
+
+ align:start position:0%
+in this representation and now let's try
+ 
+
+ align:start position:0%
+in this representation and now let's try
+to give you an example of the b in the
+
+ align:start position:0%
+to give you an example of the b in the
+ 
+
+ align:start position:0%
+to give you an example of the b in the
+other representation
+
+ align:start position:0%
+other representation
+ 
+
+ align:start position:0%
+other representation
+so so suppose in the chiral
+
+ align:start position:0%
+so so suppose in the chiral
+ 
+
+ align:start position:0%
+so so suppose in the chiral
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+which I wrote down before
+
+ align:start position:0%
+which I wrote down before
+ 
+
+ align:start position:0%
+which I wrote down before
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah I should not have erased it um yeah
+
+ align:start position:0%
+yeah I should not have erased it um yeah
+ 
+
+ align:start position:0%
+yeah I should not have erased it um yeah
+anyway so so in the current
+
+ align:start position:0%
+anyway so so in the current
+ 
+
+ align:start position:0%
+anyway so so in the current
+representation I wrote down before
+
+ align:start position:0%
+representation I wrote down before
+ 
+
+ align:start position:0%
+representation I wrote down before
+so if you stare at that expression you
+
+ align:start position:0%
+so if you stare at that expression you
+ 
+
+ align:start position:0%
+so if you stare at that expression you
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+that comma zero
+
+ align:start position:0%
+that comma zero
+ 
+
+ align:start position:0%
+that comma zero
+comma 1 and comma two okay zero comma
+
+ align:start position:0%
+comma 1 and comma two okay zero comma
+ 
+
+ align:start position:0%
+comma 1 and comma two okay zero comma
+one comma three are imaginary pure
+
+ align:start position:0%
+one comma three are imaginary pure
+ 
+
+ align:start position:0%
+one comma three are imaginary pure
+imaginary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the gamma Q is real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay comma 2 is real
+
+ align:start position:0%
+okay comma 2 is real
+ 
+
+ align:start position:0%
+okay comma 2 is real
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this pure imaginary means when you
+
+ align:start position:0%
+so this pure imaginary means when you
+ 
+
+ align:start position:0%
+so this pure imaginary means when you
+take the style of them
+
+ align:start position:0%
+take the style of them
+ 
+
+ align:start position:0%
+take the style of them
+you get a minus sign
+
+ align:start position:0%
+you get a minus sign
+ 
+
+ align:start position:0%
+you get a minus sign
+so this one you take a star of them you
+
+ align:start position:0%
+so this one you take a star of them you
+ 
+
+ align:start position:0%
+so this one you take a star of them you
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+just get back to itself
+
+ align:start position:0%
+just get back to itself
+ 
+
+ align:start position:0%
+just get back to itself
+so now if we look at this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if we look at this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we
+
+ align:start position:0%
+so if we
+ 
+
+ align:start position:0%
+so if we
+if this is pure imaginary
+
+ align:start position:0%
+if this is pure imaginary
+ 
+
+ align:start position:0%
+if this is pure imaginary
+you get the star you get the minus
+
+ align:start position:0%
+you get the star you get the minus
+ 
+
+ align:start position:0%
+you get the star you get the minus
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+and then essentially you can imagine
+
+ align:start position:0%
+and then essentially you can imagine
+ 
+
+ align:start position:0%
+and then essentially you can imagine
+cell means
+
+ align:start position:0%
+cell means
+ 
+
+ align:start position:0%
+cell means
+Let It Be actually anti-commute with
+
+ align:start position:0%
+Let It Be actually anti-commute with
+ 
+
+ align:start position:0%
+Let It Be actually anti-commute with
+gamma mu
+
+ align:start position:0%
+gamma mu
+ 
+
+ align:start position:0%
+gamma mu
+okay because you can just bring a B
+
+ align:start position:0%
+okay because you can just bring a B
+ 
+
+ align:start position:0%
+okay because you can just bring a B
+minus one to this side so you just
+
+ align:start position:0%
+minus one to this side so you just
+ 
+
+ align:start position:0%
+minus one to this side so you just
+become gamma mu star b equal to B gamma
+
+ align:start position:0%
+become gamma mu star b equal to B gamma
+ 
+
+ align:start position:0%
+become gamma mu star b equal to B gamma
+mu so so if this is a minus gamma mu
+
+ align:start position:0%
+mu so so if this is a minus gamma mu
+ 
+
+ align:start position:0%
+mu so so if this is a minus gamma mu
+that means B should anti-commute with
+
+ align:start position:0%
+that means B should anti-commute with
+ 
+
+ align:start position:0%
+that means B should anti-commute with
+gamma mu
+
+ align:start position:0%
+gamma mu
+ 
+
+ align:start position:0%
+gamma mu
+okay but if gamma is real that means P
+
+ align:start position:0%
+okay but if gamma is real that means P
+ 
+
+ align:start position:0%
+okay but if gamma is real that means P
+will commute with mu
+
+ align:start position:0%
+will commute with mu
+ 
+
+ align:start position:0%
+will commute with mu
+okay even mu is real then that means B
+
+ align:start position:0%
+okay even mu is real then that means B
+ 
+
+ align:start position:0%
+okay even mu is real then that means B
+should commute with mu
+
+ align:start position:0%
+should commute with mu
+ 
+
+ align:start position:0%
+should commute with mu
+so now in this current basis
+
+ align:start position:0%
+so now in this current basis
+ 
+
+ align:start position:0%
+so now in this current basis
+these three are pure imaginary that
+
+ align:start position:0%
+these three are pure imaginary that
+ 
+
+ align:start position:0%
+these three are pure imaginary that
+means speed leads to anti-commute with
+
+ align:start position:0%
+means speed leads to anti-commute with
+ 
+
+ align:start position:0%
+means speed leads to anti-commute with
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+but this is real mean speed is to
+
+ align:start position:0%
+but this is real mean speed is to
+ 
+
+ align:start position:0%
+but this is real mean speed is to
+commute with this guy then what is p
+
+ align:start position:0%
+commute with this guy then what is p
+ 
+
+ align:start position:0%
+commute with this guy then what is p
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+exactly so B in this case I can only
+
+ align:start position:0%
+exactly so B in this case I can only
+ 
+
+ align:start position:0%
+exactly so B in this case I can only
+be government two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you we can work out what is the
+
+ align:start position:0%
+and then you we can work out what is the
+ 
+
+ align:start position:0%
+and then you we can work out what is the
+viral condition in this basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so essentially this condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means
+
+ align:start position:0%
+so that means
+ 
+
+ align:start position:0%
+so that means
+that the PSI star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should equal to gamma 2
+
+ align:start position:0%
+should equal to gamma 2
+ 
+
+ align:start position:0%
+should equal to gamma 2
+sorry okay
+
+ align:start position:0%
+sorry okay
+ 
+
+ align:start position:0%
+sorry okay
+so that's the myorary condition here
+
+ align:start position:0%
+so that's the myorary condition here
+ 
+
+ align:start position:0%
+so that's the myorary condition here
+so now remember the in the chiral basis
+
+ align:start position:0%
+so now remember the in the chiral basis
+ 
+
+ align:start position:0%
+so now remember the in the chiral basis
+we can write sign in terms of the
+
+ align:start position:0%
+we can write sign in terms of the
+ 
+
+ align:start position:0%
+we can write sign in terms of the
+percent ah
+
+ align:start position:0%
+percent ah
+ 
+
+ align:start position:0%
+percent ah
+so essentially we have this condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so the gamma 2 uh let me write
+
+ align:start position:0%
+okay so so the gamma 2 uh let me write
+ 
+
+ align:start position:0%
+okay so so the gamma 2 uh let me write
+it here explicitly this minus I comma
+
+ align:start position:0%
+it here explicitly this minus I comma
+ 
+
+ align:start position:0%
+it here explicitly this minus I comma
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero minus side Sigma 2.
+
+ align:start position:0%
+zero minus side Sigma 2.
+ 
+
+ align:start position:0%
+zero minus side Sigma 2.
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you look at this condition
+
+ align:start position:0%
+so now if you look at this condition
+ 
+
+ align:start position:0%
+so now if you look at this condition
+this means
+
+ align:start position:0%
+this means
+ 
+
+ align:start position:0%
+this means
+that no longer percent L and say are
+
+ align:start position:0%
+that no longer percent L and say are
+ 
+
+ align:start position:0%
+that no longer percent L and say are
+long independent of each other
+
+ align:start position:0%
+long independent of each other
+ 
+
+ align:start position:0%
+long independent of each other
+so we said L start should be equal to
+
+ align:start position:0%
+so we said L start should be equal to
+ 
+
+ align:start position:0%
+so we said L start should be equal to
+minus I Sigma 2 PSI r
+
+ align:start position:0%
+minus I Sigma 2 PSI r
+ 
+
+ align:start position:0%
+minus I Sigma 2 PSI r
+or equivalent to the percent r
+
+ align:start position:0%
+or equivalent to the percent r
+ 
+
+ align:start position:0%
+or equivalent to the percent r
+equal to I Sigma 2 so L okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or else stop okay so so uh so in this
+
+ align:start position:0%
+or else stop okay so so uh so in this
+ 
+
+ align:start position:0%
+or else stop okay so so uh so in this
+case the side don't have the following
+
+ align:start position:0%
+case the side don't have the following
+ 
+
+ align:start position:0%
+case the side don't have the following
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+so l
+
+ align:start position:0%
+so l
+ 
+
+ align:start position:0%
+so l
+I Sigma 2.
+
+ align:start position:0%
+I Sigma 2.
+ 
+
+ align:start position:0%
+I Sigma 2.
+so Sigma I just can be expressed in
+
+ align:start position:0%
+so Sigma I just can be expressed in
+ 
+
+ align:start position:0%
+so Sigma I just can be expressed in
+terms of Sigma l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is the my Runner spinner
+
+ align:start position:0%
+so so this is the my Runner spinner
+ 
+
+ align:start position:0%
+so so this is the my Runner spinner
+in the Carol basis
+
+ align:start position:0%
+in the Carol basis
+ 
+
+ align:start position:0%
+in the Carol basis
+okay you see there are only four
+
+ align:start position:0%
+okay you see there are only four
+ 
+
+ align:start position:0%
+okay you see there are only four
+independent real components because each
+
+ align:start position:0%
+independent real components because each
+ 
+
+ align:start position:0%
+independent real components because each
+cell is two complex components okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no no here we are imposing this
+
+ align:start position:0%
+no no no here we are imposing this
+ 
+
+ align:start position:0%
+no no no here we are imposing this
+condition right
+
+ align:start position:0%
+condition right
+ 
+
+ align:start position:0%
+condition right
+we're imposing this condition
+
+ align:start position:0%
+we're imposing this condition
+ 
+
+ align:start position:0%
+we're imposing this condition
+yeah yeah this is my random condition we
+
+ align:start position:0%
+yeah yeah this is my random condition we
+ 
+
+ align:start position:0%
+yeah yeah this is my random condition we
+want to impose in this basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah yeah this is yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so this concludes our discussion of the
+
+ align:start position:0%
+so this concludes our discussion of the
+ 
+
+ align:start position:0%
+so this concludes our discussion of the
+marijuana spinner
+
+ align:start position:0%
+marijuana spinner
+ 
+
+ align:start position:0%
+marijuana spinner
+do you have any questions on this
+
+ align:start position:0%
+do you have any questions on this
+ 
+
+ align:start position:0%
+do you have any questions on this
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alternative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I get two commands of fat yeah so here
+
+ align:start position:0%
+I get two commands of fat yeah so here
+ 
+
+ align:start position:0%
+I get two commands of fat yeah so here
+like we have one problem outside and
+
+ align:start position:0%
+like we have one problem outside and
+ 
+
+ align:start position:0%
+like we have one problem outside and
+there's really another one right
+
+ align:start position:0%
+there's really another one right
+ 
+
+ align:start position:0%
+there's really another one right
+I don't quite understand your question
+
+ align:start position:0%
+I don't quite understand your question
+ 
+
+ align:start position:0%
+I don't quite understand your question
+uh say it again uh
+
+ align:start position:0%
+uh say it again uh
+ 
+
+ align:start position:0%
+uh say it again uh
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+all the questions yes so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so for the
+
+ align:start position:0%
+right so so for the
+ 
+
+ align:start position:0%
+right so so for the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the uh uh yeah if we for a format
+
+ align:start position:0%
+for the uh uh yeah if we for a format
+ 
+
+ align:start position:0%
+for the uh uh yeah if we for a format
+it's particle you can just directly be
+
+ align:start position:0%
+it's particle you can just directly be
+ 
+
+ align:start position:0%
+it's particle you can just directly be
+bigger then you don't just have uh you
+
+ align:start position:0%
+bigger then you don't just have uh you
+ 
+
+ align:start position:0%
+bigger then you don't just have uh you
+don't have to think about the percent R
+
+ align:start position:0%
+don't have to think about the percent R
+ 
+
+ align:start position:0%
+don't have to think about the percent R
+and uh uh uh this is just have the same
+
+ align:start position:0%
+and uh uh uh this is just have the same
+ 
+
+ align:start position:0%
+and uh uh uh this is just have the same
+number because Freedom has a mass
+
+ align:start position:0%
+number because Freedom has a mass
+ 
+
+ align:start position:0%
+number because Freedom has a mass
+respond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+good okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so so so let's now go to the
+
+ align:start position:0%
+okay good so so so let's now go to the
+ 
+
+ align:start position:0%
+okay good so so so let's now go to the
+next topic we only have a few minutes so
+
+ align:start position:0%
+next topic we only have a few minutes so
+ 
+
+ align:start position:0%
+next topic we only have a few minutes so
+so we can only just make some general
+
+ align:start position:0%
+so we can only just make some general
+ 
+
+ align:start position:0%
+so we can only just make some general
+comments
+
+ align:start position:0%
+comments
+ 
+
+ align:start position:0%
+comments
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so far mostly we have been talking
+
+ align:start position:0%
+so so far mostly we have been talking
+ 
+
+ align:start position:0%
+so so far mostly we have been talking
+about continuous symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there are also
+
+ align:start position:0%
+but there are also
+ 
+
+ align:start position:0%
+but there are also
+discrete symmetries
+
+ align:start position:0%
+discrete symmetries
+ 
+
+ align:start position:0%
+discrete symmetries
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discrete symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which don't have continuous parameters
+
+ align:start position:0%
+which don't have continuous parameters
+ 
+
+ align:start position:0%
+which don't have continuous parameters
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so continuous symmetry or symmetries
+
+ align:start position:0%
+so continuous symmetry or symmetries
+ 
+
+ align:start position:0%
+so continuous symmetry or symmetries
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah which has
+
+ align:start position:0%
+yeah which has
+ 
+
+ align:start position:0%
+yeah which has
+the translation depends on continuous
+
+ align:start position:0%
+the translation depends on continuous
+ 
+
+ align:start position:0%
+the translation depends on continuous
+parameter okay discrete symmetries you
+
+ align:start position:0%
+parameter okay discrete symmetries you
+ 
+
+ align:start position:0%
+parameter okay discrete symmetries you
+just don't okay uh you don't have
+
+ align:start position:0%
+just don't okay uh you don't have
+ 
+
+ align:start position:0%
+just don't okay uh you don't have
+continuous parameter
+
+ align:start position:0%
+continuous parameter
+ 
+
+ align:start position:0%
+continuous parameter
+so so simple example
+
+ align:start position:0%
+so so simple example
+ 
+
+ align:start position:0%
+so so simple example
+say this imagine we have
+
+ align:start position:0%
+say this imagine we have
+ 
+
+ align:start position:0%
+say this imagine we have
+so this scalar will scalar series we
+
+ align:start position:0%
+so this scalar will scalar series we
+ 
+
+ align:start position:0%
+so this scalar will scalar series we
+considered before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this Series has a
+
+ align:start position:0%
+so this Series has a
+ 
+
+ align:start position:0%
+so this Series has a
+discrete symmetry because this is
+
+ align:start position:0%
+discrete symmetry because this is
+ 
+
+ align:start position:0%
+discrete symmetry because this is
+invariant on the Phi goes to -5
+
+ align:start position:0%
+invariant on the Phi goes to -5
+ 
+
+ align:start position:0%
+invariant on the Phi goes to -5
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so because you see all the terms are
+
+ align:start position:0%
+so because you see all the terms are
+ 
+
+ align:start position:0%
+so because you see all the terms are
+even so using one down the fire go to
+
+ align:start position:0%
+even so using one down the fire go to
+ 
+
+ align:start position:0%
+even so using one down the fire go to
+minus five
+
+ align:start position:0%
+minus five
+ 
+
+ align:start position:0%
+minus five
+and this transformation there's no
+
+ align:start position:0%
+and this transformation there's no
+ 
+
+ align:start position:0%
+and this transformation there's no
+continuous parameter okay so this is a
+
+ align:start position:0%
+continuous parameter okay so this is a
+ 
+
+ align:start position:0%
+continuous parameter okay so this is a
+discrete symmetry
+
+ align:start position:0%
+discrete symmetry
+ 
+
+ align:start position:0%
+discrete symmetry
+and so this is uh so if you do it twice
+
+ align:start position:0%
+and so this is uh so if you do it twice
+ 
+
+ align:start position:0%
+and so this is uh so if you do it twice
+you go back to itself so this is often
+
+ align:start position:0%
+you go back to itself so this is often
+ 
+
+ align:start position:0%
+you go back to itself so this is often
+called the two symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is called the religious
+
+ align:start position:0%
+okay so this is called the religious
+ 
+
+ align:start position:0%
+okay so this is called the religious
+image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they are also space-time discrete
+
+ align:start position:0%
+and they are also space-time discrete
+ 
+
+ align:start position:0%
+and they are also space-time discrete
+symmetries
+
+ align:start position:0%
+symmetries
+ 
+
+ align:start position:0%
+symmetries
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is an internal discrete symmetry
+
+ align:start position:0%
+so this is an internal discrete symmetry
+ 
+
+ align:start position:0%
+so this is an internal discrete symmetry
+of nothing to do with space-time okay
+
+ align:start position:0%
+of nothing to do with space-time okay
+ 
+
+ align:start position:0%
+of nothing to do with space-time okay
+there are also space-time discrete
+
+ align:start position:0%
+there are also space-time discrete
+ 
+
+ align:start position:0%
+there are also space-time discrete
+symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so space time discrete symmetry is
+
+ align:start position:0%
+so space time discrete symmetry is
+ 
+
+ align:start position:0%
+so space time discrete symmetry is
+including say if we consider blinkowsky
+
+ align:start position:0%
+including say if we consider blinkowsky
+ 
+
+ align:start position:0%
+including say if we consider blinkowsky
+space time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can have t goes to minus t
+
+ align:start position:0%
+so you can have t goes to minus t
+ 
+
+ align:start position:0%
+so you can have t goes to minus t
+so you can have so-called time reversal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which corresponding to u t x
+
+ align:start position:0%
+which corresponding to u t x
+ 
+
+ align:start position:0%
+which corresponding to u t x
+goes to minus TX
+
+ align:start position:0%
+goes to minus TX
+ 
+
+ align:start position:0%
+goes to minus TX
+okay you just transform time
+
+ align:start position:0%
+okay you just transform time
+ 
+
+ align:start position:0%
+okay you just transform time
+you can also have the parrot so-called
+
+ align:start position:0%
+you can also have the parrot so-called
+ 
+
+ align:start position:0%
+you can also have the parrot so-called
+parity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you take T you then you revert all the
+
+ align:start position:0%
+you take T you then you revert all the
+ 
+
+ align:start position:0%
+you take T you then you revert all the
+spatial Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so comment that you can ask
+
+ align:start position:0%
+so comment that you can ask
+ 
+
+ align:start position:0%
+so comment that you can ask
+why we actually reverse all the all
+
+ align:start position:0%
+why we actually reverse all the all
+ 
+
+ align:start position:0%
+why we actually reverse all the all
+three directions
+
+ align:start position:0%
+three directions
+ 
+
+ align:start position:0%
+three directions
+how about if I just reverse One
+
+ align:start position:0%
+how about if I just reverse One
+ 
+
+ align:start position:0%
+how about if I just reverse One
+Direction or reverse two directions okay
+
+ align:start position:0%
+Direction or reverse two directions okay
+ 
+
+ align:start position:0%
+Direction or reverse two directions okay
+that seems also to be a discrete
+
+ align:start position:0%
+that seems also to be a discrete
+ 
+
+ align:start position:0%
+that seems also to be a discrete
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+and indeed
+
+ align:start position:0%
+and indeed
+ 
+
+ align:start position:0%
+and indeed
+so if you just uh change the directions
+
+ align:start position:0%
+so if you just uh change the directions
+ 
+
+ align:start position:0%
+so if you just uh change the directions
+in say in the X Direction uh that's also
+
+ align:start position:0%
+in say in the X Direction uh that's also
+ 
+
+ align:start position:0%
+in say in the X Direction uh that's also
+discrete Symmetry and if you only change
+
+ align:start position:0%
+discrete Symmetry and if you only change
+ 
+
+ align:start position:0%
+discrete Symmetry and if you only change
+the direction in both X and the Y
+
+ align:start position:0%
+the direction in both X and the Y
+ 
+
+ align:start position:0%
+the direction in both X and the Y
+Direction that's also a discrete image
+
+ align:start position:0%
+Direction that's also a discrete image
+ 
+
+ align:start position:0%
+Direction that's also a discrete image
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+if you change
+
+ align:start position:0%
+if you change
+ 
+
+ align:start position:0%
+if you change
+if you do a reflection in two directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's equivalent to 90 degree rotation
+
+ align:start position:0%
+that's equivalent to 90 degree rotation
+ 
+
+ align:start position:0%
+that's equivalent to 90 degree rotation
+oh a 100
+
+ align:start position:0%
+oh a 100
+ 
+
+ align:start position:0%
+oh a 100
+180 degree rotation
+
+ align:start position:0%
+180 degree rotation
+ 
+
+ align:start position:0%
+180 degree rotation
+in that plane
+
+ align:start position:0%
+in that plane
+ 
+
+ align:start position:0%
+in that plane
+okay and so that's
+
+ align:start position:0%
+okay and so that's
+ 
+
+ align:start position:0%
+okay and so that's
+it's part of the continuous imagery so
+
+ align:start position:0%
+it's part of the continuous imagery so
+ 
+
+ align:start position:0%
+it's part of the continuous imagery so
+it's not independent discrete image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now when you change all three
+
+ align:start position:0%
+and now when you change all three
+ 
+
+ align:start position:0%
+and now when you change all three
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+compared to change One Direction
+
+ align:start position:0%
+compared to change One Direction
+ 
+
+ align:start position:0%
+compared to change One Direction
+you differ only by changing two
+
+ align:start position:0%
+you differ only by changing two
+ 
+
+ align:start position:0%
+you differ only by changing two
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+so that means changing all three
+
+ align:start position:0%
+so that means changing all three
+ 
+
+ align:start position:0%
+so that means changing all three
+directions I change One Direction they
+
+ align:start position:0%
+directions I change One Direction they
+ 
+
+ align:start position:0%
+directions I change One Direction they
+differ by 180 degree rotation
+
+ align:start position:0%
+differ by 180 degree rotation
+ 
+
+ align:start position:0%
+differ by 180 degree rotation
+okay and so that means that when you
+
+ align:start position:0%
+okay and so that means that when you
+ 
+
+ align:start position:0%
+okay and so that means that when you
+change this is the only Independence
+
+ align:start position:0%
+change this is the only Independence
+ 
+
+ align:start position:0%
+change this is the only Independence
+okay discrete symmetry
+
+ align:start position:0%
+okay discrete symmetry
+ 
+
+ align:start position:0%
+okay discrete symmetry
+okay from the spatial translate from the
+
+ align:start position:0%
+okay from the spatial translate from the
+ 
+
+ align:start position:0%
+okay from the spatial translate from the
+spatial Reflection Point of View
+
+ align:start position:0%
+spatial Reflection Point of View
+ 
+
+ align:start position:0%
+spatial Reflection Point of View
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for complex scalar field
+
+ align:start position:0%
+for complex scalar field
+ 
+
+ align:start position:0%
+for complex scalar field
+so if you consider complex scale of
+
+ align:start position:0%
+so if you consider complex scale of
+ 
+
+ align:start position:0%
+so if you consider complex scale of
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you can see the complex scale
+
+ align:start position:0%
+okay if you can see the complex scale
+ 
+
+ align:start position:0%
+okay if you can see the complex scale
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+then this is no longer a discrete
+
+ align:start position:0%
+then this is no longer a discrete
+ 
+
+ align:start position:0%
+then this is no longer a discrete
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because remember we can rotate Phi by a
+
+ align:start position:0%
+because remember we can rotate Phi by a
+ 
+
+ align:start position:0%
+because remember we can rotate Phi by a
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+when you rotate the file by a face if
+
+ align:start position:0%
+when you rotate the file by a face if
+ 
+
+ align:start position:0%
+when you rotate the file by a face if
+you take that phase to be Pi say
+
+ align:start position:0%
+you take that phase to be Pi say
+ 
+
+ align:start position:0%
+you take that phase to be Pi say
+expansion I Pi then you take to be minus
+
+ align:start position:0%
+expansion I Pi then you take to be minus
+ 
+
+ align:start position:0%
+expansion I Pi then you take to be minus
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+and so so in this case this is part of
+
+ align:start position:0%
+and so so in this case this is part of
+ 
+
+ align:start position:0%
+and so so in this case this is part of
+the continuous symmetry so it's no
+
+ align:start position:0%
+the continuous symmetry so it's no
+ 
+
+ align:start position:0%
+the continuous symmetry so it's no
+longer independent discrete image
+
+ align:start position:0%
+longer independent discrete image
+ 
+
+ align:start position:0%
+longer independent discrete image
+but here there's nevertheless a lot of
+
+ align:start position:0%
+but here there's nevertheless a lot of
+ 
+
+ align:start position:0%
+but here there's nevertheless a lot of
+discrete symmetry
+
+ align:start position:0%
+discrete symmetry
+ 
+
+ align:start position:0%
+discrete symmetry
+can you see what is the other
+
+ align:start position:0%
+can you see what is the other
+ 
+
+ align:start position:0%
+can you see what is the other
+independent discrete symmetry here
+
+ align:start position:0%
+independent discrete symmetry here
+ 
+
+ align:start position:0%
+independent discrete symmetry here
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+good you can take five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to Five Star okay you can exchange five
+
+ align:start position:0%
+to Five Star okay you can exchange five
+ 
+
+ align:start position:0%
+to Five Star okay you can exchange five
+to five stop
+
+ align:start position:0%
+to five stop
+ 
+
+ align:start position:0%
+to five stop
+okay it's like a complex conjugation and
+
+ align:start position:0%
+okay it's like a complex conjugation and
+ 
+
+ align:start position:0%
+okay it's like a complex conjugation and
+this is often called charge conjugation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is because remember uh
+
+ align:start position:0%
+okay this is because remember uh
+ 
+
+ align:start position:0%
+okay this is because remember uh
+heuristically we can simplify uh uh uh
+
+ align:start position:0%
+heuristically we can simplify uh uh uh
+ 
+
+ align:start position:0%
+heuristically we can simplify uh uh uh
+as create
+
+ align:start position:0%
+as create
+ 
+
+ align:start position:0%
+as create
+yeah it's just one of them create the
+
+ align:start position:0%
+yeah it's just one of them create the
+ 
+
+ align:start position:0%
+yeah it's just one of them create the
+particle and the other create the under
+
+ align:start position:0%
+particle and the other create the under
+ 
+
+ align:start position:0%
+particle and the other create the under
+particle and then they have opposite
+
+ align:start position:0%
+particle and then they have opposite
+ 
+
+ align:start position:0%
+particle and then they have opposite
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+okay so this is called the charge
+
+ align:start position:0%
+okay so this is called the charge
+ 
+
+ align:start position:0%
+okay so this is called the charge
+conjugation so this will give a symbol
+
+ align:start position:0%
+conjugation so this will give a symbol
+ 
+
+ align:start position:0%
+conjugation so this will give a symbol
+called t
+
+ align:start position:0%
+called t
+ 
+
+ align:start position:0%
+called t
+script T and this will give a symbol
+
+ align:start position:0%
+script T and this will give a symbol
+ 
+
+ align:start position:0%
+script T and this will give a symbol
+called P script p and this will give a
+
+ align:start position:0%
+called P script p and this will give a
+ 
+
+ align:start position:0%
+called P script p and this will give a
+symbol called Script a c so to go
+
+ align:start position:0%
+symbol called Script a c so to go
+ 
+
+ align:start position:0%
+symbol called Script a c so to go
+together they call cpts images okay CPT
+
+ align:start position:0%
+together they call cpts images okay CPT
+ 
+
+ align:start position:0%
+together they call cpts images okay CPT
+yeah yeah let's stop here
\ No newline at end of file
diff --git a/qGZy1CRoZdE.txt b/qGZy1CRoZdE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f88bdc9e66e3d95f1ed6ad3b8eae5b852129df42
--- /dev/null
+++ b/qGZy1CRoZdE.txt
@@ -0,0 +1,601 @@
+KENDRA PUGH: Hi.
+
+Today, I'd like to talk
+to you about circuits.
+
+Last time, we finished up the
+LTIs, and signals, and
+
+systems, where we learned how to
+both model existing systems
+
+and predict their long-term
+behavior.
+
+But we haven't forayed into how
+to actually create systems
+
+in the physical world.
+
+We've created some amount of
+systems in software and made
+
+some brains for our robots.
+
+But if we want to make something
+in the physical
+
+world, then we probably have to
+come up with ways to model
+
+physical systems or use
+physical components.
+
+That starts our new
+model on circuits.
+
+Circuits are going to be our
+first foray into designing
+
+systems in the physical world,
+also designing systems using
+
+physical components.
+
+It's worth mentioning now that
+the information that you learn
+
+about circuits is good for more
+
+things than even circuits.
+
+You can use basic circuit
+diagrams and properties of
+
+circuits to model all sorts of
+kinds of systems, especially
+
+ones in the human body--
+
+circulatory system, neurological
+system, different
+
+kinds of fluid flow,
+that kind of thing.
+
+In the next few videos, we'll
+go over how to represent
+
+circuits, and also cover some of
+the basic methods by which
+
+people solve circuits.
+
+We'll also introduce an element
+called an op-amp, and
+
+use that element in order to
+enable us to do things like
+
+modularity and abstraction
+from our circuits.
+
+First, let's talk about
+representation.
+
+In the general sense, when you
+come across a circuit diagram,
+
+you're going to see--
+
+at the very broad level--
+
+a bunch of elements and a bunch
+of connections between
+
+the elements.
+
+Those things will form
+loops and nodes.
+
+If you don't actually specify
+the elements, then your
+
+circuit diagram actually
+looks a whole lot
+
+like a block diagram.
+
+And in fact, block diagrams and
+circuit diagrams are very
+
+closely related in part because
+block diagrams are
+
+used to model feedback systems,
+which frequently are
+
+implemented using circuits.
+
+In this course, we're going to
+be focusing on independent
+
+sources and resistors as the
+two major kinds of elements
+
+that we'll use in
+our circuits.
+
+We'll also use things like
+potentiometers, which are
+
+resistors that you can
+adjust, and op-amps.
+
+And we'll look at op-amps
+specifically in a later video.
+
+But I have one drawn up here
+just so you recognize it when
+
+you see it written.
+
+Note that it looks a whole lot
+like the block diagram symbol
+
+for a gain.
+
+And that's intentional, and
+we'll cover that later.
+
+But in the meantime, the other
+sources that we're going to be
+
+using are independent current,
+and voltage sources.
+
+We're going to use resistors
+to adjust the amount of
+
+voltage and current that we're
+actually dealing with and then
+
+sample either the current or
+the voltage at a particular
+
+point in our circuit
+to get the desired
+
+values that we're after.
+
+On a circuit diagram, when
+you're interested in the
+
+voltage drop across a particular
+element, you'll
+
+indicate it by putting a
+plus and minus sign.
+
+This also indicates
+the directionality
+
+of the voltage drop.
+
+Likewise, when you're interested
+in the current
+
+flowing through a particular
+element, you'll usually see an
+
+indication of it by labeling the
+current i, and then maybe
+
+i with some sort of subscript,
+and an arrow indicating the
+
+direction of current flow
+through that element so that
+
+you avoid making sign errors
+with the person that might be
+
+reading or writing
+your diagram.
+
+A quick note here.
+
+This is the reason that
+electrical engineers use j to
+
+symbolize values in
+the complex plane.
+
+It's because i is used
+in particular
+
+for values of current.
+
+Let's review Kirchhoff's voltage
+laws and Kirchhoff's
+
+current laws.
+
+You've probably covered this
+in 8.02, electricity and
+
+magnetism, or possibly in
+an AP physics class.
+
+But we're going to go over
+it really fast right now.
+
+Kirchhoff's voltage law is that
+the voltage drop around a
+
+loop is equal to 0.
+
+Or if you take the voltage drop
+across a particular loop
+
+in your circuit, the sum
+of those voltage drop
+
+is going to be 0.
+
+Let's demonstrate
+on this diagram.
+
+Or, I'll demonstrate
+on this diagram.
+
+Say the voltage drop
+across this element
+
+is equal to V, right?
+
+Doesn't matter what it is.
+
+We're going to stick
+with that.
+
+The voltage drop across these
+elements, if I were to move
+
+around this loop, is
+going to sum to 0.
+
+Note that if I'm tracing out
+my voltage drop across this
+
+loop, I'm actually moving
+through this voltage source in
+
+the direction opposite of
+its indicated potential.
+
+So when I move through this
+voltage source, I'm going to
+
+account for its value as
+negative V. As I work my way
+
+around the rest of the circuit,
+the voltage drop
+
+across these elements is
+going to sum to V.
+
+This is true for all loops
+in my circuit.
+
+So any loop that includes V, the
+elements I encounter as a
+
+consequence of moving around
+that loop are going to have
+
+voltage drop equal and opposite
+to the value I get by
+
+moving through V in
+this direction.
+
+This loop counts, too, but it
+doesn't include V. All this
+
+loop tells me is that the
+voltage drop across this
+
+element is equivalent
+to the voltage
+
+drop across this element.
+
+Or, the voltage drop in this
+direction across that element
+
+is equal to the voltage
+drop in this
+
+direction across this element.
+
+That's Kirchhoff's
+voltage law.
+
+Kirchhoff's current law is that
+the current flow into a
+
+particular node is equal to 0.
+
+Or, if you take all of the
+current flows in and out of a
+
+particular node and sum them,
+they should sum to 0.
+
+I've actually got the
+same set up here.
+
+I'm not going to use
+a current divider.
+
+I'm interested in the current
+flowing over this element.
+
+It's actually the same as the
+current flowing over this
+
+element because resistance
+doesn't change current,
+
+resistors flowing through
+a resistor should
+
+not change the current.
+
+So this is still the same i.
+
+Here's my node.
+
+The current flowing in this
+direction and in this
+
+direction, if I took the linear
+combination of these
+
+two currents, they would be
+equal in value to the current
+
+flowing into this node.
+
+When I'm looking at the current
+flowing through a
+
+particular node, I
+pick a direction.
+
+It's usually arbitrary.
+
+I pick a direction.
+
+It's arbitrary which
+direction I pick.
+
+Typically, you pick currents
+flowing into the
+
+node as being positive.
+
+I sum up all the currents, and
+I set that equal to 0.
+
+So in this case--.
+
+Or--
+
+pretty simple.
+
+Let's practice on this
+particular circuit.
+
+One thing to note is that when
+you're solving circuits in the
+
+general sense, both when you
+want TA help and when you're
+
+solving for a mid-term and want
+partial credit, you want
+
+to label all of your nodes, all
+of your elements, and all
+
+of the currents that you're
+interested in solving.
+
+See, I've got my voltage drop
+across this resistor, this
+
+resistor, and this resistor
+labeled, as well as these
+
+currents, which I'll also
+be solving for.
+
+The first thing that I would
+do when approaching this
+
+problem is attempt to reduce
+this circuit to something that
+
+is a little bit simpler.
+
+The first thing that I'm going
+to do is try to figure out how
+
+to change these two resistors
+in parallel into a single
+
+resistor and still have
+an equivalent circuit.
+
+That'll allow me to
+solve for I1.
+
+There will be 0 nodes
+in my system.
+
+I'll just have one
+single loop.
+
+And the current through the
+system will just be V/R.
+
+So if I'm just looking at these
+two resistors, I have
+
+resistors in parallel.
+
+In the general sense, the way
+to solve for resistors in
+
+parallel is to take
+the inverse of the
+
+sum of their inverses.
+
+When you only have two
+resistors, you can typically
+
+cheat by saying that this
+is equal to their
+
+product over their sum.
+
+I'm going to redraw my current
+understanding of the circuit.
+
+The other stuff that I've saved
+myself is that because
+
+these resistors are
+in parallel,
+
+they're a current divider.
+
+They take the current in and
+divide it two ways determined
+
+by the ratio between
+these two values.
+
+The thing I'm actually
+interested in expressing is
+
+that V2 and V3 are
+the same value.
+
+When you have a current divider,
+the voltage drop
+
+across all elements in the
+current divider are the same.
+
+So the value of V here is going
+to be both V2 and V3.
+
+2R plus 6/5 R. I'm going to
+go with 16/5 R for now.
+
+I've solved for I.
+
+At this point, I have a voltage
+divider, which means
+
+that the current flowing through
+this part of the
+
+system is going to
+be the same.
+
+But the voltage drop across
+this element versus this
+
+element is going to be
+proportional to the ratio
+
+between these two values.
+
+V1 is going to be the amount
+of the total resistance in
+
+this simple circuit that this
+resistor contributes over the
+
+entire resistance
+in the system.
+
+Or, 10/5 R over 16/5 R, which is
+10/16 R, or 5/8 R. Or, it's
+
+going to be 5/8 V.
+
+Same thing happens with V2.
+
+Note that these two values
+should sum to V in order to
+
+maintain Kirchoff's
+voltage law.
+
+We've also found V3.
+
+So the two things that we have
+to find are I2 and I3.
+
+Here, I've just done
+Kirchoff's current
+
+law for this node.
+
+Because I'm working with a
+current divider, I can break
+
+up the total current flowing
+into that node into the number
+
+of parts equal to the sum
+of these values and then
+
+distribute them.
+
+And then, that's
+[? inappropriate ?]
+
+given that less resistance
+means more current.
+
+What do I mean by that?
+
+Well, I mean that here my
+current is equal to 5/16 V
+
+over R. I2 is going to be equal
+to this value over the
+
+sum of these two values
+times I1.
+
+Likewise--.
+
+And just to simplify--.
+
+That concludes my tutorial
+on circuits.
+
+Next time, we'll talk about
+other ways we can solve this
+
+circuit, and then we'll end
+up talking about op-amps.
\ No newline at end of file
diff --git a/rChKr66KG-c.txt b/rChKr66KG-c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fcfef9d9b200618f9d1c2ca7b059eb668234503b
--- /dev/null
+++ b/rChKr66KG-c.txt
@@ -0,0 +1,12059 @@
+align:start position:0%
+ 
+Hey everyone.
+
+ align:start position:0%
+Hey everyone.
+ 
+
+ align:start position:0%
+Hey everyone.
+Um, today and this week we are going to
+
+ align:start position:0%
+Um, today and this week we are going to
+ 
+
+ align:start position:0%
+Um, today and this week we are going to
+talk about the a connection between
+
+ align:start position:0%
+talk about the a connection between
+ 
+
+ align:start position:0%
+talk about the a connection between
+homogeneous dynamics and projection
+
+ align:start position:0%
+homogeneous dynamics and projection
+ 
+
+ align:start position:0%
+homogeneous dynamics and projection
+theory. Um today is by the way the first
+
+ align:start position:0%
+theory. Um today is by the way the first
+ 
+
+ align:start position:0%
+theory. Um today is by the way the first
+day of the Simon's lectures. Marina
+
+ align:start position:0%
+day of the Simon's lectures. Marina
+ 
+
+ align:start position:0%
+day of the Simon's lectures. Marina
+Vioska is giving them this year and
+
+ align:start position:0%
+Vioska is giving them this year and
+ 
+
+ align:start position:0%
+Vioska is giving them this year and
+she's going to be talking about sphere
+
+ align:start position:0%
+she's going to be talking about sphere
+ 
+
+ align:start position:0%
+she's going to be talking about sphere
+packing and um I got interested in this
+
+ align:start position:0%
+packing and um I got interested in this
+ 
+
+ align:start position:0%
+packing and um I got interested in this
+two years ago when Alon Lynen Strauss
+
+ align:start position:0%
+two years ago when Alon Lynen Strauss
+ 
+
+ align:start position:0%
+two years ago when Alon Lynen Strauss
+came to give the Simon's lectures and he
+
+ align:start position:0%
+came to give the Simon's lectures and he
+ 
+
+ align:start position:0%
+came to give the Simon's lectures and he
+was talking about homogeneous dynamics
+
+ align:start position:0%
+was talking about homogeneous dynamics
+ 
+
+ align:start position:0%
+was talking about homogeneous dynamics
+and he explained a little bit this
+
+ align:start position:0%
+and he explained a little bit this
+ 
+
+ align:start position:0%
+and he explained a little bit this
+connection with projection theory and I
+
+ align:start position:0%
+connection with projection theory and I
+ 
+
+ align:start position:0%
+connection with projection theory and I
+have been trying to understand it since
+
+ align:start position:0%
+have been trying to understand it since
+ 
+
+ align:start position:0%
+have been trying to understand it since
+then. um and uh it's uh it's a pretty
+
+ align:start position:0%
+then. um and uh it's uh it's a pretty
+ 
+
+ align:start position:0%
+then. um and uh it's uh it's a pretty
+geometric visual thing. So I brought
+
+ align:start position:0%
+geometric visual thing. So I brought
+ 
+
+ align:start position:0%
+geometric visual thing. So I brought
+some tools with me and the goal of the
+
+ align:start position:0%
+some tools with me and the goal of the
+ 
+
+ align:start position:0%
+some tools with me and the goal of the
+class is to try to understand visually
+
+ align:start position:0%
+class is to try to understand visually
+ 
+
+ align:start position:0%
+class is to try to understand visually
+geometrically uh how homogeneous
+
+ align:start position:0%
+geometrically uh how homogeneous
+ 
+
+ align:start position:0%
+geometrically uh how homogeneous
+dynamics is related to projection
+
+ align:start position:0%
+dynamics is related to projection
+ 
+
+ align:start position:0%
+dynamics is related to projection
+theory. Um
+
+ align:start position:0%
+theory. Um
+ 
+
+ align:start position:0%
+theory. Um
+okay so let's let's first say uh a
+
+ align:start position:0%
+okay so let's let's first say uh a
+ 
+
+ align:start position:0%
+okay so let's let's first say uh a
+little bit what what is homogeneous
+
+ align:start position:0%
+little bit what what is homogeneous
+ 
+
+ align:start position:0%
+little bit what what is homogeneous
+dynamics.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So we're going to uh be working
+
+ align:start position:0%
+Okay. So we're going to uh be working
+ 
+
+ align:start position:0%
+Okay. So we're going to uh be working
+with spaces that have a lot of
+
+ align:start position:0%
+with spaces that have a lot of
+ 
+
+ align:start position:0%
+with spaces that have a lot of
+symmetries. And so the spaces will come
+
+ align:start position:0%
+symmetries. And so the spaces will come
+ 
+
+ align:start position:0%
+symmetries. And so the spaces will come
+from a league group. So G will be a
+
+ align:start position:0%
+from a league group. So G will be a
+ 
+
+ align:start position:0%
+from a league group. So G will be a
+league group. Um for example, SLNR
+
+ align:start position:0%
+league group. Um for example, SLNR
+ 
+
+ align:start position:0%
+league group. Um for example, SLNR
+and inside of G there'll be a discrete
+
+ align:start position:0%
+and inside of G there'll be a discrete
+ 
+
+ align:start position:0%
+and inside of G there'll be a discrete
+subgroup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So EG,
+
+ align:start position:0%
+So EG,
+ 
+
+ align:start position:0%
+So EG,
+SLN Z.
+
+ align:start position:0%
+SLN Z.
+ 
+
+ align:start position:0%
+SLN Z.
+And then we're going to be studying the
+
+ align:start position:0%
+And then we're going to be studying the
+ 
+
+ align:start position:0%
+And then we're going to be studying the
+quotient space G mod gamma.
+
+ align:start position:0%
+quotient space G mod gamma.
+ 
+
+ align:start position:0%
+quotient space G mod gamma.
+So this is called a homogeneous space.
+
+ align:start position:0%
+So this is called a homogeneous space.
+ 
+
+ align:start position:0%
+So this is called a homogeneous space.
+So we'll see it has a lot of symmetries.
+
+ align:start position:0%
+So we'll see it has a lot of symmetries.
+ 
+
+ align:start position:0%
+So we'll see it has a lot of symmetries.
+Um and so the homogeneous and
+
+ align:start position:0%
+Um and so the homogeneous and
+ 
+
+ align:start position:0%
+Um and so the homogeneous and
+homogeneous dynamics is we're acting on
+
+ align:start position:0%
+homogeneous dynamics is we're acting on
+ 
+
+ align:start position:0%
+homogeneous dynamics is we're acting on
+this homogeneous space.
+
+ align:start position:0%
+this homogeneous space.
+ 
+
+ align:start position:0%
+this homogeneous space.
+Okay. Now what does dynamics mean? Um
+
+ align:start position:0%
+Okay. Now what does dynamics mean? Um
+ 
+
+ align:start position:0%
+Okay. Now what does dynamics mean? Um
+suppose that H is a subgroup of G
+
+ align:start position:0%
+suppose that H is a subgroup of G
+ 
+
+ align:start position:0%
+suppose that H is a subgroup of G
+and then if X is a point in G mod gamma
+
+ align:start position:0%
+and then if X is a point in G mod gamma
+ 
+
+ align:start position:0%
+and then if X is a point in G mod gamma
+then we can look at H dox. So H acts on
+
+ align:start position:0%
+then we can look at H dox. So H acts on
+ 
+
+ align:start position:0%
+then we can look at H dox. So H acts on
+G mod gamma. So you can talk about H dox
+
+ align:start position:0%
+G mod gamma. So you can talk about H dox
+ 
+
+ align:start position:0%
+G mod gamma. So you can talk about H dox
+that's called an orbit. And the question
+
+ align:start position:0%
+that's called an orbit. And the question
+ 
+
+ align:start position:0%
+that's called an orbit. And the question
+is to describe the orbits.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let's make a picture. Um so in
+
+ align:start position:0%
+Okay. So let's make a picture. Um so in
+ 
+
+ align:start position:0%
+Okay. So let's make a picture. Um so in
+actual group GR
+
+ align:start position:0%
+actual group GR
+ 
+
+ align:start position:0%
+actual group GR
+G this um there might be some group
+
+ align:start position:0%
+G this um there might be some group
+ 
+
+ align:start position:0%
+G this um there might be some group
+element and then um you could take a
+
+ align:start position:0%
+element and then um you could take a
+ 
+
+ align:start position:0%
+element and then um you could take a
+co-et
+
+ align:start position:0%
+co-et
+ 
+
+ align:start position:0%
+co-et
+h.g and that h might be non-compact so
+
+ align:start position:0%
+h.g and that h might be non-compact so
+ 
+
+ align:start position:0%
+h.g and that h might be non-compact so
+that might go on forever but somehow
+
+ align:start position:0%
+that might go on forever but somehow
+ 
+
+ align:start position:0%
+that might go on forever but somehow
+it's not that complicated. Yeah. for
+
+ align:start position:0%
+it's not that complicated. Yeah. for
+ 
+
+ align:start position:0%
+it's not that complicated. Yeah. for
+taking the quotient gamma
+
+ align:start position:0%
+taking the quotient gamma
+ 
+
+ align:start position:0%
+taking the quotient gamma
+is what are the conditions for gamma to
+
+ align:start position:0%
+is what are the conditions for gamma to
+ 
+
+ align:start position:0%
+is what are the conditions for gamma to
+be a normal subgroup fill out this
+
+ align:start position:0%
+be a normal subgroup fill out this
+ 
+
+ align:start position:0%
+be a normal subgroup fill out this
+question. So this so this object is not
+
+ align:start position:0%
+question. So this so this object is not
+ 
+
+ align:start position:0%
+question. So this so this object is not
+a group
+
+ align:start position:0%
+a group
+ 
+
+ align:start position:0%
+a group
+>> it's just a space
+
+ align:start position:0%
+>> it's just a space
+ 
+
+ align:start position:0%
+>> it's just a space
+>> right so gamma is a so so the question
+
+ align:start position:0%
+>> right so gamma is a so so the question
+ 
+
+ align:start position:0%
+>> right so gamma is a so so the question
+was about whether whether gamma is
+
+ align:start position:0%
+was about whether whether gamma is
+ 
+
+ align:start position:0%
+was about whether whether gamma is
+normal um and the answer is gamma
+
+ align:start position:0%
+normal um and the answer is gamma
+ 
+
+ align:start position:0%
+normal um and the answer is gamma
+doesn't have to be normal so this this
+
+ align:start position:0%
+doesn't have to be normal so this this
+ 
+
+ align:start position:0%
+doesn't have to be normal so this this
+is not a normal subgroup of this that
+
+ align:start position:0%
+is not a normal subgroup of this that
+ 
+
+ align:start position:0%
+is not a normal subgroup of this that
+means that this is not a group but it's
+
+ align:start position:0%
+means that this is not a group but it's
+ 
+
+ align:start position:0%
+means that this is not a group but it's
+still a space
+
+ align:start position:0%
+still a space
+ 
+
+ align:start position:0%
+still a space
+okay um so gm mod gamma oh and I I I'll
+
+ align:start position:0%
+okay um so gm mod gamma oh and I I I'll
+ 
+
+ align:start position:0%
+okay um so gm mod gamma oh and I I I'll
+put something else so gmod gamma uh
+
+ align:start position:0%
+put something else so gmod gamma uh
+ 
+
+ align:start position:0%
+put something else so gmod gamma uh
+where we'll assume that the volume of or
+
+ align:start position:0%
+where we'll assume that the volume of or
+ 
+
+ align:start position:0%
+where we'll assume that the volume of or
+we'll be interested in cases where the
+
+ align:start position:0%
+we'll be interested in cases where the
+ 
+
+ align:start position:0%
+we'll be interested in cases where the
+volume of G mod gamma is finite. So the
+
+ align:start position:0%
+volume of G mod gamma is finite. So the
+ 
+
+ align:start position:0%
+volume of G mod gamma is finite. So the
+volume of G is infinite but the volume
+
+ align:start position:0%
+volume of G is infinite but the volume
+ 
+
+ align:start position:0%
+volume of G is infinite but the volume
+of G mod gamma is finite. So G mod gamma
+
+ align:start position:0%
+of G mod gamma is finite. So G mod gamma
+ 
+
+ align:start position:0%
+of G mod gamma is finite. So G mod gamma
+looks sort of like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and so then there's a point X in
+
+ align:start position:0%
+Um, and so then there's a point X in
+ 
+
+ align:start position:0%
+Um, and so then there's a point X in
+there and the orbit goes through X, but
+
+ align:start position:0%
+there and the orbit goes through X, but
+ 
+
+ align:start position:0%
+there and the orbit goes through X, but
+then it wraps around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the picture looks a lot more
+
+ align:start position:0%
+and the picture looks a lot more
+ 
+
+ align:start position:0%
+and the picture looks a lot more
+complicated already. And we want to
+
+ align:start position:0%
+complicated already. And we want to
+ 
+
+ align:start position:0%
+complicated already. And we want to
+understand what what does this do? Is it
+
+ align:start position:0%
+understand what what does this do? Is it
+ 
+
+ align:start position:0%
+understand what what does this do? Is it
+um is it going to wrap back on itself
+
+ align:start position:0%
+um is it going to wrap back on itself
+ 
+
+ align:start position:0%
+um is it going to wrap back on itself
+and just just go around over and over
+
+ align:start position:0%
+and just just go around over and over
+ 
+
+ align:start position:0%
+and just just go around over and over
+again the same thing? Or is it going to
+
+ align:start position:0%
+again the same thing? Or is it going to
+ 
+
+ align:start position:0%
+again the same thing? Or is it going to
+evenly distribute all over G mod gamma
+
+ align:start position:0%
+evenly distribute all over G mod gamma
+ 
+
+ align:start position:0%
+evenly distribute all over G mod gamma
+or or something else?
+
+ align:start position:0%
+or or something else?
+ 
+
+ align:start position:0%
+or or something else?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So to make it concrete, I'd like to
+
+ align:start position:0%
+So to make it concrete, I'd like to
+ 
+
+ align:start position:0%
+So to make it concrete, I'd like to
+begin with a with a very simple warm-up
+
+ align:start position:0%
+begin with a with a very simple warm-up
+ 
+
+ align:start position:0%
+begin with a with a very simple warm-up
+um which is with a commutative group. So
+
+ align:start position:0%
+um which is with a commutative group. So
+ 
+
+ align:start position:0%
+um which is with a commutative group. So
+it's it's simpler than that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So uh so I think the simplest
+
+ align:start position:0%
+Okay. So uh so I think the simplest
+ 
+
+ align:start position:0%
+Okay. So uh so I think the simplest
+example of this is that G could be R2
+
+ align:start position:0%
+example of this is that G could be R2
+ 
+
+ align:start position:0%
+example of this is that G could be R2
+and then gamma could be Z2. So G mod
+
+ align:start position:0%
+and then gamma could be Z2. So G mod
+ 
+
+ align:start position:0%
+and then gamma could be Z2. So G mod
+gamma is uh R2 mod Z2. It's a Tors.
+
+ align:start position:0%
+gamma is uh R2 mod Z2. It's a Tors.
+ 
+
+ align:start position:0%
+gamma is uh R2 mod Z2. It's a Tors.
+All right. And H is going to be a
+
+ align:start position:0%
+All right. And H is going to be a
+ 
+
+ align:start position:0%
+All right. And H is going to be a
+subgroup of G. And let's say it's like a
+
+ align:start position:0%
+subgroup of G. And let's say it's like a
+ 
+
+ align:start position:0%
+subgroup of G. And let's say it's like a
+one parameter subgroup.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll do a couple of examples. H could be
+
+ align:start position:0%
+I'll do a couple of examples. H could be
+ 
+
+ align:start position:0%
+I'll do a couple of examples. H could be
+the subgroup T2 T
+
+ align:start position:0%
+the subgroup T2 T
+ 
+
+ align:start position:0%
+the subgroup T2 T
+and R there's a subgroup of R2 and if we
+
+ align:start position:0%
+and R there's a subgroup of R2 and if we
+ 
+
+ align:start position:0%
+and R there's a subgroup of R2 and if we
+do this what happens um so I'll
+
+ align:start position:0%
+do this what happens um so I'll
+ 
+
+ align:start position:0%
+do this what happens um so I'll
+visualize G mod gamma as a square with
+
+ align:start position:0%
+visualize G mod gamma as a square with
+ 
+
+ align:start position:0%
+visualize G mod gamma as a square with
+sides identified
+
+ align:start position:0%
+sides identified
+ 
+
+ align:start position:0%
+sides identified
+um and if I were to take so let's say X
+
+ align:start position:0%
+um and if I were to take so let's say X
+ 
+
+ align:start position:0%
+um and if I were to take so let's say X
+knot is like is just gamma which is an
+
+ align:start position:0%
+knot is like is just gamma which is an
+ 
+
+ align:start position:0%
+knot is like is just gamma which is an
+element of G by gamma it's like you you
+
+ align:start position:0%
+element of G by gamma it's like you you
+ 
+
+ align:start position:0%
+element of G by gamma it's like you you
+take the identity in G and push down.
+
+ align:start position:0%
+take the identity in G and push down.
+ 
+
+ align:start position:0%
+take the identity in G and push down.
+Um, okay. So, what does the orbit
+
+ align:start position:0%
+Um, okay. So, what does the orbit
+ 
+
+ align:start position:0%
+Um, okay. So, what does the orbit
+through x knot look like? Well, it's
+
+ align:start position:0%
+through x knot look like? Well, it's
+ 
+
+ align:start position:0%
+through x knot look like? Well, it's
+this line of slope 2 looks like that
+
+ align:start position:0%
+this line of slope 2 looks like that
+ 
+
+ align:start position:0%
+this line of slope 2 looks like that
+and then it comes back where it started
+
+ align:start position:0%
+and then it comes back where it started
+ 
+
+ align:start position:0%
+and then it comes back where it started
+and it just keeps going like that. Okay.
+
+ align:start position:0%
+and it just keeps going like that. Okay.
+ 
+
+ align:start position:0%
+and it just keeps going like that. Okay.
+And actually, it wouldn't be it's a
+
+ align:start position:0%
+And actually, it wouldn't be it's a
+ 
+
+ align:start position:0%
+And actually, it wouldn't be it's a
+little harder to draw accurately, but it
+
+ align:start position:0%
+little harder to draw accurately, but it
+ 
+
+ align:start position:0%
+little harder to draw accurately, but it
+wouldn't be different if you started at
+
+ align:start position:0%
+wouldn't be different if you started at
+ 
+
+ align:start position:0%
+wouldn't be different if you started at
+any other point. So x if you start at
+
+ align:start position:0%
+any other point. So x if you start at
+ 
+
+ align:start position:0%
+any other point. So x if you start at
+any point x then if I were to add 1
+
+ align:start position:0%
+any point x then if I were to add 1
+ 
+
+ align:start position:0%
+any point x then if I were to add 1
+comma 2 that would be equal to x in r2
+
+ align:start position:0%
+comma 2 that would be equal to x in r2
+ 
+
+ align:start position:0%
+comma 2 that would be equal to x in r2
+z2
+
+ align:start position:0%
+z2
+ 
+
+ align:start position:0%
+z2
+and so actually every orbit is periodic.
+
+ align:start position:0%
+and so actually every orbit is periodic.
+ 
+
+ align:start position:0%
+and so actually every orbit is periodic.
+So the conclusion in example one is that
+
+ align:start position:0%
+So the conclusion in example one is that
+ 
+
+ align:start position:0%
+So the conclusion in example one is that
+h dox is periodic
+
+ align:start position:0%
+h dox is periodic
+ 
+
+ align:start position:0%
+h dox is periodic
+for every x.
+
+ align:start position:0%
+for every x.
+ 
+
+ align:start position:0%
+for every x.
+Okay. Example two, I'll take a different
+
+ align:start position:0%
+Okay. Example two, I'll take a different
+ 
+
+ align:start position:0%
+Okay. Example two, I'll take a different
+one parameter subgroup t comma
+
+ align:start position:0%
+one parameter subgroup t comma
+ 
+
+ align:start position:0%
+one parameter subgroup t comma
+square<unk> of 2t
+
+ align:start position:0%
+square<unk> of 2t
+ 
+
+ align:start position:0%
+square<unk> of 2t
+t.
+
+ align:start position:0%
+t.
+ 
+
+ align:start position:0%
+t.
+Okay. So now what happens?
+
+ align:start position:0%
+Okay. So now what happens?
+ 
+
+ align:start position:0%
+Okay. So now what happens?
+Well, if I if I again start at x knot is
+
+ align:start position:0%
+Well, if I if I again start at x knot is
+ 
+
+ align:start position:0%
+Well, if I if I again start at x knot is
+the identity. Um now I'm going up at
+
+ align:start position:0%
+the identity. Um now I'm going up at
+ 
+
+ align:start position:0%
+the identity. Um now I'm going up at
+slope square<unk> of two
+
+ align:start position:0%
+slope square<unk> of two
+ 
+
+ align:start position:0%
+slope square<unk> of two
+the top and keep going at slope square
+
+ align:start position:0%
+the top and keep going at slope square
+ 
+
+ align:start position:0%
+the top and keep going at slope square
+root of two. And this time this will
+
+ align:start position:0%
+root of two. And this time this will
+ 
+
+ align:start position:0%
+root of two. And this time this will
+this will never close up because uh the
+
+ align:start position:0%
+this will never close up because uh the
+ 
+
+ align:start position:0%
+this will never close up because uh the
+slope is irrational. Um and in fact this
+
+ align:start position:0%
+slope is irrational. Um and in fact this
+ 
+
+ align:start position:0%
+slope is irrational. Um and in fact this
+this orbit will be dense and even evenly
+
+ align:start position:0%
+this orbit will be dense and even evenly
+ 
+
+ align:start position:0%
+this orbit will be dense and even evenly
+distributed.
+
+ align:start position:0%
+distributed.
+ 
+
+ align:start position:0%
+distributed.
+So now what happens is that h dox
+
+ align:start position:0%
+So now what happens is that h dox
+ 
+
+ align:start position:0%
+So now what happens is that h dox
+is dense
+
+ align:start position:0%
+is dense
+ 
+
+ align:start position:0%
+is dense
+for every x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. I won't do a proof right now. Um
+
+ align:start position:0%
+Okay. I won't do a proof right now. Um
+ 
+
+ align:start position:0%
+Okay. I won't do a proof right now. Um
+but um I'll make a remark there. So
+
+ align:start position:0%
+but um I'll make a remark there. So
+ 
+
+ align:start position:0%
+but um I'll make a remark there. So
+there are several proofs but there's
+
+ align:start position:0%
+there are several proofs but there's
+ 
+
+ align:start position:0%
+there are several proofs but there's
+there's a nice proof using for analysis
+
+ align:start position:0%
+there's a nice proof using for analysis
+ 
+
+ align:start position:0%
+there's a nice proof using for analysis
+that we might talk about later if we if
+
+ align:start position:0%
+that we might talk about later if we if
+ 
+
+ align:start position:0%
+that we might talk about later if we if
+we feel like it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Questions or comments so far?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So we've seen two things that
+
+ align:start position:0%
+Okay. So we've seen two things that
+ 
+
+ align:start position:0%
+Okay. So we've seen two things that
+could happen. The orbit could be
+
+ align:start position:0%
+could happen. The orbit could be
+ 
+
+ align:start position:0%
+could happen. The orbit could be
+periodic and the orbit could be dense.
+
+ align:start position:0%
+periodic and the orbit could be dense.
+ 
+
+ align:start position:0%
+periodic and the orbit could be dense.
+uh and we haven't yet seen other things
+
+ align:start position:0%
+uh and we haven't yet seen other things
+ 
+
+ align:start position:0%
+uh and we haven't yet seen other things
+but we might wonder about whether other
+
+ align:start position:0%
+but we might wonder about whether other
+ 
+
+ align:start position:0%
+but we might wonder about whether other
+things could happen and now we can shift
+
+ align:start position:0%
+things could happen and now we can shift
+ 
+
+ align:start position:0%
+things could happen and now we can shift
+to a more complicated non-communive
+
+ align:start position:0%
+to a more complicated non-communive
+ 
+
+ align:start position:0%
+to a more complicated non-communive
+group like SL2R
+
+ align:start position:0%
+group like SL2R
+ 
+
+ align:start position:0%
+group like SL2R
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Now let's say G is SL2R
+
+ align:start position:0%
+so Now let's say G is SL2R
+ 
+
+ align:start position:0%
+so Now let's say G is SL2R
+and gamma is SL2Z.
+
+ align:start position:0%
+and gamma is SL2Z.
+ 
+
+ align:start position:0%
+and gamma is SL2Z.
+Okay. And um there's there are multiple
+
+ align:start position:0%
+Okay. And um there's there are multiple
+ 
+
+ align:start position:0%
+Okay. And um there's there are multiple
+reasons for looking at these quotients G
+
+ align:start position:0%
+reasons for looking at these quotients G
+ 
+
+ align:start position:0%
+reasons for looking at these quotients G
+mod gamma but one of them that comes up
+
+ align:start position:0%
+mod gamma but one of them that comes up
+ 
+
+ align:start position:0%
+mod gamma but one of them that comes up
+for this particular example is that
+
+ align:start position:0%
+for this particular example is that
+ 
+
+ align:start position:0%
+for this particular example is that
+these parameterize lises.
+
+ align:start position:0%
+these parameterize lises.
+ 
+
+ align:start position:0%
+these parameterize lises.
+So gamma is this space of latises
+
+ align:start position:0%
+So gamma is this space of latises
+ 
+
+ align:start position:0%
+So gamma is this space of latises
+in R2
+
+ align:start position:0%
+in R2
+ 
+
+ align:start position:0%
+in R2
+with the property latticees lambda in R2
+
+ align:start position:0%
+with the property latticees lambda in R2
+ 
+
+ align:start position:0%
+with the property latticees lambda in R2
+with the property that the area of R2
+
+ align:start position:0%
+with the property that the area of R2
+ 
+
+ align:start position:0%
+with the property that the area of R2
+mod lambda is one.
+
+ align:start position:0%
+mod lambda is one.
+ 
+
+ align:start position:0%
+mod lambda is one.
+Um so let's do a proof sketch.
+
+ align:start position:0%
+Um so let's do a proof sketch.
+ 
+
+ align:start position:0%
+Um so let's do a proof sketch.
+So um any such lattice we can write as G
+
+ align:start position:0%
+So um any such lattice we can write as G
+ 
+
+ align:start position:0%
+So um any such lattice we can write as G
+times the lattice Z ^2 where G is an
+
+ align:start position:0%
+times the lattice Z ^2 where G is an
+ 
+
+ align:start position:0%
+times the lattice Z ^2 where G is an
+SL2R.
+
+ align:start position:0%
+SL2R.
+ 
+
+ align:start position:0%
+SL2R.
+So you can make any lattice by starting
+
+ align:start position:0%
+So you can make any lattice by starting
+ 
+
+ align:start position:0%
+So you can make any lattice by starting
+with with Z ^ squ and applying a a
+
+ align:start position:0%
+with with Z ^ squ and applying a a
+ 
+
+ align:start position:0%
+with with Z ^ squ and applying a a
+linear transformation. Okay. However
+
+ align:start position:0%
+linear transformation. Okay. However
+ 
+
+ align:start position:0%
+linear transformation. Okay. However
+there's more than one G that gives you
+
+ align:start position:0%
+there's more than one G that gives you
+ 
+
+ align:start position:0%
+there's more than one G that gives you
+the same lambda. So um if H is in SL2Z
+
+ align:start position:0%
+the same lambda. So um if H is in SL2Z
+ 
+
+ align:start position:0%
+the same lambda. So um if H is in SL2Z
+then HZ2 is Z2 and therefore G * HZ2 is
+
+ align:start position:0%
+then HZ2 is Z2 and therefore G * HZ2 is
+ 
+
+ align:start position:0%
+then HZ2 is Z2 and therefore G * HZ2 is
+G * Z2 and these guys give you the same
+
+ align:start position:0%
+G * Z2 and these guys give you the same
+ 
+
+ align:start position:0%
+G * Z2 and these guys give you the same
+lice. So the space of lises is G modulo
+
+ align:start position:0%
+lice. So the space of lises is G modulo
+ 
+
+ align:start position:0%
+lice. So the space of lises is G modulo
+SL2Z.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Now, this uh space of lises G
+
+ align:start position:0%
+All right. Now, this uh space of lises G
+ 
+
+ align:start position:0%
+All right. Now, this uh space of lises G
+mod gamma is not compact. Um and I will
+
+ align:start position:0%
+mod gamma is not compact. Um and I will
+ 
+
+ align:start position:0%
+mod gamma is not compact. Um and I will
+give you an example of a sequence of
+
+ align:start position:0%
+give you an example of a sequence of
+ 
+
+ align:start position:0%
+give you an example of a sequence of
+lises that don't converge to anything.
+
+ align:start position:0%
+lises that don't converge to anything.
+ 
+
+ align:start position:0%
+lises that don't converge to anything.
+Don't have a subsequence that converge
+
+ align:start position:0%
+Don't have a subsequence that converge
+ 
+
+ align:start position:0%
+Don't have a subsequence that converge
+to anything. So example we could take
+
+ align:start position:0%
+to anything. So example we could take
+ 
+
+ align:start position:0%
+to anything. So example we could take
+lambdaepsilon
+
+ align:start position:0%
+lambdaepsilon
+ 
+
+ align:start position:0%
+lambdaepsilon
+to be epsilon z direct sum epsilon
+
+ align:start position:0%
+to be epsilon z direct sum epsilon
+ 
+
+ align:start position:0%
+to be epsilon z direct sum epsilon
+inverse z.
+
+ align:start position:0%
+inverse z.
+ 
+
+ align:start position:0%
+inverse z.
+So this is a lattice which is very
+
+ align:start position:0%
+So this is a lattice which is very
+ 
+
+ align:start position:0%
+So this is a lattice which is very
+skinny in one direction and very tall in
+
+ align:start position:0%
+skinny in one direction and very tall in
+ 
+
+ align:start position:0%
+skinny in one direction and very tall in
+the other direction and has co- volume
+
+ align:start position:0%
+the other direction and has co- volume
+ 
+
+ align:start position:0%
+the other direction and has co- volume
+one and as epsilon goes to zero this is
+
+ align:start position:0%
+one and as epsilon goes to zero this is
+ 
+
+ align:start position:0%
+one and as epsilon goes to zero this is
+not going to converge to anything. So
+
+ align:start position:0%
+not going to converge to anything. So
+ 
+
+ align:start position:0%
+not going to converge to anything. So
+the space of lises is not compact
+
+ align:start position:0%
+the space of lises is not compact
+ 
+
+ align:start position:0%
+the space of lises is not compact
+and this is the only reason that the
+
+ align:start position:0%
+and this is the only reason that the
+ 
+
+ align:start position:0%
+and this is the only reason that the
+space of lises is not compact. So a
+
+ align:start position:0%
+space of lises is not compact. So a
+ 
+
+ align:start position:0%
+space of lises is not compact. So a
+definition k epsilon is a subset of g
+
+ align:start position:0%
+definition k epsilon is a subset of g
+ 
+
+ align:start position:0%
+definition k epsilon is a subset of g
+mod gamma.
+
+ align:start position:0%
+mod gamma.
+ 
+
+ align:start position:0%
+mod gamma.
+Kepsilon is defined to be the set of
+
+ align:start position:0%
+Kepsilon is defined to be the set of
+ 
+
+ align:start position:0%
+Kepsilon is defined to be the set of
+lises. So that the minimum over nonzero
+
+ align:start position:0%
+lises. So that the minimum over nonzero
+ 
+
+ align:start position:0%
+lises. So that the minimum over nonzero
+v in our lattice of the size v is at
+
+ align:start position:0%
+v in our lattice of the size v is at
+ 
+
+ align:start position:0%
+v in our lattice of the size v is at
+least epsilon is greater than or equal
+
+ align:start position:0%
+least epsilon is greater than or equal
+ 
+
+ align:start position:0%
+least epsilon is greater than or equal
+to let's say epsilon.
+
+ align:start position:0%
+to let's say epsilon.
+ 
+
+ align:start position:0%
+to let's say epsilon.
+Okay. And there's a a proposition which
+
+ align:start position:0%
+Okay. And there's a a proposition which
+ 
+
+ align:start position:0%
+Okay. And there's a a proposition which
+is called the moler criterion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that says for every epsilon bigger than
+
+ align:start position:0%
+that says for every epsilon bigger than
+ 
+
+ align:start position:0%
+that says for every epsilon bigger than
+zero kepsilon is compact.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so um so a picture of of G mod gamma
+
+ align:start position:0%
+Um so um so a picture of of G mod gamma
+ 
+
+ align:start position:0%
+Um so um so a picture of of G mod gamma
+it's something like this. G mod gamma is
+
+ align:start position:0%
+it's something like this. G mod gamma is
+ 
+
+ align:start position:0%
+it's something like this. G mod gamma is
+threedimensional so it's um not super
+
+ align:start position:0%
+threedimensional so it's um not super
+ 
+
+ align:start position:0%
+threedimensional so it's um not super
+easy to draw. Um but over here so this
+
+ align:start position:0%
+easy to draw. Um but over here so this
+ 
+
+ align:start position:0%
+easy to draw. Um but over here so this
+would be G mod gamma. There's this
+
+ align:start position:0%
+would be G mod gamma. There's this
+ 
+
+ align:start position:0%
+would be G mod gamma. There's this
+non-compact part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you make a cut off maybe here and
+
+ align:start position:0%
+and you make a cut off maybe here and
+ 
+
+ align:start position:0%
+and you make a cut off maybe here and
+this stuff is K epsilon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um so I won't prove this in
+
+ align:start position:0%
+Okay. Um so I won't prove this in
+ 
+
+ align:start position:0%
+Okay. Um so I won't prove this in
+detail. This is not super difficult. If
+
+ align:start position:0%
+detail. This is not super difficult. If
+ 
+
+ align:start position:0%
+detail. This is not super difficult. If
+you think about uh two vectors that
+
+ align:start position:0%
+you think about uh two vectors that
+ 
+
+ align:start position:0%
+you think about uh two vectors that
+generate lambda, um if there if we're in
+
+ align:start position:0%
+generate lambda, um if there if we're in
+ 
+
+ align:start position:0%
+generate lambda, um if there if we're in
+k epsilon, the vectors definitely cannot
+
+ align:start position:0%
+k epsilon, the vectors definitely cannot
+ 
+
+ align:start position:0%
+k epsilon, the vectors definitely cannot
+be too close to zero. And you can also
+
+ align:start position:0%
+be too close to zero. And you can also
+ 
+
+ align:start position:0%
+be too close to zero. And you can also
+always find two vectors that are not too
+
+ align:start position:0%
+always find two vectors that are not too
+ 
+
+ align:start position:0%
+always find two vectors that are not too
+giant because the area of the thing is
+
+ align:start position:0%
+giant because the area of the thing is
+ 
+
+ align:start position:0%
+giant because the area of the thing is
+one. This gives you sort of a compact
+
+ align:start position:0%
+one. This gives you sort of a compact
+ 
+
+ align:start position:0%
+one. This gives you sort of a compact
+set of choices of these two vectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so it gives a little bit of
+
+ align:start position:0%
+Okay, so it gives a little bit of
+ 
+
+ align:start position:0%
+Okay, so it gives a little bit of
+intuition about what the space gamma
+
+ align:start position:0%
+intuition about what the space gamma
+ 
+
+ align:start position:0%
+intuition about what the space gamma
+looks like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now, inside of there, we have some
+
+ align:start position:0%
+Okay. Now, inside of there, we have some
+ 
+
+ align:start position:0%
+Okay. Now, inside of there, we have some
+interesting one parameter subgroups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of of G of SL2R.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, one of them is the unipotent
+
+ align:start position:0%
+So, one of them is the unipotent
+ 
+
+ align:start position:0%
+So, one of them is the unipotent
+subgroup. So, that's the set of 1 T 01
+
+ align:start position:0%
+subgroup. So, that's the set of 1 T 01
+ 
+
+ align:start position:0%
+subgroup. So, that's the set of 1 T 01
+T and R. And the other one is the
+
+ align:start position:0%
+T and R. And the other one is the
+ 
+
+ align:start position:0%
+T and R. And the other one is the
+diagonal subgroup. So this is I'll call
+
+ align:start position:0%
+diagonal subgroup. So this is I'll call
+ 
+
+ align:start position:0%
+diagonal subgroup. So this is I'll call
+this so it's the set of u t. So this
+
+ align:start position:0%
+this so it's the set of u t. So this
+ 
+
+ align:start position:0%
+this so it's the set of u t. So this
+matrix is u subt and there's the
+
+ align:start position:0%
+matrix is u subt and there's the
+ 
+
+ align:start position:0%
+matrix is u subt and there's the
+diagonal subgroup e to the r e to the
+
+ align:start position:0%
+diagonal subgroup e to the r e to the
+ 
+
+ align:start position:0%
+diagonal subgroup e to the r e to the
+minus r 0
+
+ align:start position:0%
+minus r 0
+ 
+
+ align:start position:0%
+minus r 0
+little r the reals and this I'll call
+
+ align:start position:0%
+little r the reals and this I'll call
+ 
+
+ align:start position:0%
+little r the reals and this I'll call
+the set of a sub r. So this matrix here
+
+ align:start position:0%
+the set of a sub r. So this matrix here
+ 
+
+ align:start position:0%
+the set of a sub r. So this matrix here
+is called a sub r. Okay. So those are
+
+ align:start position:0%
+is called a sub r. Okay. So those are
+ 
+
+ align:start position:0%
+is called a sub r. Okay. So those are
+one parameter subgroups. And now we can
+
+ align:start position:0%
+one parameter subgroups. And now we can
+ 
+
+ align:start position:0%
+one parameter subgroups. And now we can
+ask our question about what the orbits
+
+ align:start position:0%
+ask our question about what the orbits
+ 
+
+ align:start position:0%
+ask our question about what the orbits
+look like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+cool. So, um, so there's a theorem that
+
+ align:start position:0%
+cool. So, um, so there's a theorem that
+ 
+
+ align:start position:0%
+cool. So, um, so there's a theorem that
+goes back to the 1930s. Headed in the
+
+ align:start position:0%
+goes back to the 1930s. Headed in the
+ 
+
+ align:start position:0%
+goes back to the 1930s. Headed in the
+1930s,
+
+ align:start position:0%
+1930s,
+ 
+
+ align:start position:0%
+1930s,
+he said that a U orbit
+
+ align:start position:0%
+he said that a U orbit
+ 
+
+ align:start position:0%
+he said that a U orbit
+is either
+
+ align:start position:0%
+is either
+ 
+
+ align:start position:0%
+is either
+periodic
+
+ align:start position:0%
+periodic
+ 
+
+ align:start position:0%
+periodic
+or dense.
+
+ align:start position:0%
+or dense.
+ 
+
+ align:start position:0%
+or dense.
+Okay. And but in contrast there's a
+
+ align:start position:0%
+Okay. And but in contrast there's a
+ 
+
+ align:start position:0%
+Okay. And but in contrast there's a
+guess I'll also call it a theorem. I
+
+ align:start position:0%
+guess I'll also call it a theorem. I
+ 
+
+ align:start position:0%
+guess I'll also call it a theorem. I
+don't know who proved this when um that
+
+ align:start position:0%
+don't know who proved this when um that
+ 
+
+ align:start position:0%
+don't know who proved this when um that
+uh d orbit does not have to be
+
+ align:start position:0%
+uh d orbit does not have to be
+ 
+
+ align:start position:0%
+uh d orbit does not have to be
+maybe neither
+
+ align:start position:0%
+maybe neither
+ 
+
+ align:start position:0%
+maybe neither
+periodic
+
+ align:start position:0%
+periodic
+ 
+
+ align:start position:0%
+periodic
+nor dense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let me say something more than
+
+ align:start position:0%
+Okay, let me say something more than
+ 
+
+ align:start position:0%
+Okay, let me say something more than
+that about how these d orbits can be
+
+ align:start position:0%
+that about how these d orbits can be
+ 
+
+ align:start position:0%
+that about how these d orbits can be
+really quite complicated. So here's G
+
+ align:start position:0%
+really quite complicated. So here's G
+ 
+
+ align:start position:0%
+really quite complicated. So here's G
+mod gamma and inside of G mod gamma pick
+
+ align:start position:0%
+mod gamma and inside of G mod gamma pick
+ 
+
+ align:start position:0%
+mod gamma and inside of G mod gamma pick
+out three small balls that are not too
+
+ align:start position:0%
+out three small balls that are not too
+ 
+
+ align:start position:0%
+out three small balls that are not too
+close together. So B1, B2, B3 are small
+
+ align:start position:0%
+close together. So B1, B2, B3 are small
+ 
+
+ align:start position:0%
+close together. So B1, B2, B3 are small
+balls.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Then for any sequence of ones and
+
+ align:start position:0%
+Okay. Then for any sequence of ones and
+ 
+
+ align:start position:0%
+Okay. Then for any sequence of ones and
+twos.
+
+ align:start position:0%
+twos.
+ 
+
+ align:start position:0%
+twos.
+So for example the sequence 1 one two
+
+ align:start position:0%
+So for example the sequence 1 one two
+ 
+
+ align:start position:0%
+So for example the sequence 1 one two
+one two one two two two one any sequence
+
+ align:start position:0%
+one two one two two two one any sequence
+ 
+
+ align:start position:0%
+one two one two two two one any sequence
+um there exists an x in gamma
+
+ align:start position:0%
+um there exists an x in gamma
+ 
+
+ align:start position:0%
+um there exists an x in gamma
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+the d- orbit of x
+
+ align:start position:0%
+the d- orbit of x
+ 
+
+ align:start position:0%
+the d- orbit of x
+never hits b3
+
+ align:start position:0%
+never hits b3
+ 
+
+ align:start position:0%
+never hits b3
+and the d- orbit of x hits b1 and b2
+
+ align:start position:0%
+and the d- orbit of x hits b1 and b2
+ 
+
+ align:start position:0%
+and the d- orbit of x hits b1 and b2
+many times.
+
+ align:start position:0%
+many times.
+ 
+
+ align:start position:0%
+many times.
+in this sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, what must this orbit look like?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, let's see. So, first it hits B1 and
+
+ align:start position:0%
+Um, let's see. So, first it hits B1 and
+ 
+
+ align:start position:0%
+Um, let's see. So, first it hits B1 and
+it goes through there. Then it goes
+
+ align:start position:0%
+it goes through there. Then it goes
+ 
+
+ align:start position:0%
+it goes through there. Then it goes
+around and it the next thing it hits is
+
+ align:start position:0%
+around and it the next thing it hits is
+ 
+
+ align:start position:0%
+around and it the next thing it hits is
+also B1.
+
+ align:start position:0%
+also B1.
+ 
+
+ align:start position:0%
+also B1.
+And it goes around and the next thing it
+
+ align:start position:0%
+And it goes around and the next thing it
+ 
+
+ align:start position:0%
+And it goes around and the next thing it
+hits is B2. and it keeps going and the
+
+ align:start position:0%
+hits is B2. and it keeps going and the
+ 
+
+ align:start position:0%
+hits is B2. and it keeps going and the
+next thing it hits is B1 and so on
+
+ align:start position:0%
+next thing it hits is B1 and so on
+ 
+
+ align:start position:0%
+next thing it hits is B1 and so on
+and it never touches B3.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this orbit apparently is not
+
+ align:start position:0%
+Okay, so this orbit apparently is not
+ 
+
+ align:start position:0%
+Okay, so this orbit apparently is not
+dense because it never intersects B3 and
+
+ align:start position:0%
+dense because it never intersects B3 and
+ 
+
+ align:start position:0%
+dense because it never intersects B3 and
+it is not periodic if this sequence is
+
+ align:start position:0%
+it is not periodic if this sequence is
+ 
+
+ align:start position:0%
+it is not periodic if this sequence is
+not periodic. So it's something else.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, so d orbits can do this
+
+ align:start position:0%
+Okay. So, so d orbits can do this
+ 
+
+ align:start position:0%
+Okay. So, so d orbits can do this
+somewhat crazy thing, somewhat chaotic
+
+ align:start position:0%
+somewhat crazy thing, somewhat chaotic
+ 
+
+ align:start position:0%
+somewhat crazy thing, somewhat chaotic
+thing that we're anyway. Um, but U
+
+ align:start position:0%
+thing that we're anyway. Um, but U
+ 
+
+ align:start position:0%
+thing that we're anyway. Um, but U
+orbits can't. U orbits can be periodic.
+
+ align:start position:0%
+orbits can't. U orbits can be periodic.
+ 
+
+ align:start position:0%
+orbits can't. U orbits can be periodic.
+Um so if you were to take
+
+ align:start position:0%
+Um so if you were to take
+ 
+
+ align:start position:0%
+Um so if you were to take
+u of x knot um
+
+ align:start position:0%
+u of x knot um
+ 
+
+ align:start position:0%
+u of x knot um
+uh this is periodic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason is um so if you take so x
+
+ align:start position:0%
+and the reason is um so if you take so x
+ 
+
+ align:start position:0%
+and the reason is um so if you take so x
+so x knot corresponds to the matrix 1
+
+ align:start position:0%
+so x knot corresponds to the matrix 1
+ 
+
+ align:start position:0%
+so x knot corresponds to the matrix 1
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh times time s 2z
+
+ align:start position:0%
+uh times time s 2z
+ 
+
+ align:start position:0%
+uh times time s 2z
+so now if I were to take one one tx knot
+
+ align:start position:0%
+so now if I were to take one one tx knot
+ 
+
+ align:start position:0%
+so now if I were to take one one tx knot
+that's equal to x knot in gy gamma.
+
+ align:start position:0%
+that's equal to x knot in gy gamma.
+ 
+
+ align:start position:0%
+that's equal to x knot in gy gamma.
+Uh if t is an integer.
+
+ align:start position:0%
+Uh if t is an integer.
+ 
+
+ align:start position:0%
+Uh if t is an integer.
+So that's a periodic orbit. It makes a
+
+ align:start position:0%
+So that's a periodic orbit. It makes a
+ 
+
+ align:start position:0%
+So that's a periodic orbit. It makes a
+closed circle in in gm mod gamma.
+
+ align:start position:0%
+closed circle in in gm mod gamma.
+ 
+
+ align:start position:0%
+closed circle in in gm mod gamma.
+Um okay. Uh but if you were to start
+
+ align:start position:0%
+Um okay. Uh but if you were to start
+ 
+
+ align:start position:0%
+Um okay. Uh but if you were to start
+with a kind of weird looking choice of x
+
+ align:start position:0%
+with a kind of weird looking choice of x
+ 
+
+ align:start position:0%
+with a kind of weird looking choice of x
+knot um and you were to do this then it
+
+ align:start position:0%
+knot um and you were to do this then it
+ 
+
+ align:start position:0%
+knot um and you were to do this then it
+won't there won't be any obvious
+
+ align:start position:0%
+won't there won't be any obvious
+ 
+
+ align:start position:0%
+won't there won't be any obvious
+periodicity.
+
+ align:start position:0%
+periodicity.
+ 
+
+ align:start position:0%
+periodicity.
+Um so for most
+
+ align:start position:0%
+Um so for most
+ 
+
+ align:start position:0%
+Um so for most
+for most x so that's that's let's that's
+
+ align:start position:0%
+for most x so that's that's let's that's
+ 
+
+ align:start position:0%
+for most x so that's that's let's that's
+let's let's suppose now x is uh <unk>2
+
+ align:start position:0%
+let's let's suppose now x is uh <unk>2
+ 
+
+ align:start position:0%
+let's let's suppose now x is uh <unk>2
+01 over <unk>2
+
+ align:start position:0%
+01 over <unk>2
+ 
+
+ align:start position:0%
+01 over <unk>2
+okay so now what happens when we and
+
+ align:start position:0%
+okay so now what happens when we and
+ 
+
+ align:start position:0%
+okay so now what happens when we and
+then times sl2z
+
+ align:start position:0%
+then times sl2z
+ 
+
+ align:start position:0%
+then times sl2z
+so now what is
+
+ align:start position:0%
+so now what is
+ 
+
+ align:start position:0%
+so now what is
+ut of x that's one t <unk>20 one over
+
+ align:start position:0%
+ut of x that's one t <unk>20 one over
+ 
+
+ align:start position:0%
+ut of x that's one t <unk>20 one over
+<unk>2
+
+ align:start position:0%
+<unk>2
+ 
+
+ align:start position:0%
+<unk>2
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+okay. So, that'll be <unk>2,
+
+ align:start position:0%
+okay. So, that'll be <unk>2,
+ 
+
+ align:start position:0%
+okay. So, that'll be <unk>2,
+that'll be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+<unk>2, that'll be t over <unk>2.
+
+ align:start position:0%
+<unk>2, that'll be t over <unk>2.
+ 
+
+ align:start position:0%
+<unk>2, that'll be t over <unk>2.
+Um, this will be zero.
+
+ align:start position:0%
+Um, this will be zero.
+ 
+
+ align:start position:0%
+Um, this will be zero.
+This will be 1 over <unk>2.
+
+ align:start position:0%
+This will be 1 over <unk>2.
+ 
+
+ align:start position:0%
+This will be 1 over <unk>2.
+And
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh, that one might be periodic. I think
+
+ align:start position:0%
+oh, that one might be periodic. I think
+ 
+
+ align:start position:0%
+oh, that one might be periodic. I think
+I picked the wrong example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Yeah. Okay. Sorry. Um that was
+
+ align:start position:0%
+Yeah. Yeah. Okay. Sorry. Um that was
+ 
+
+ align:start position:0%
+Yeah. Yeah. Okay. Sorry. Um that was
+unhelpful.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, so to see why they're not all
+
+ align:start position:0%
+Okay. So, so to see why they're not all
+ 
+
+ align:start position:0%
+Okay. So, so to see why they're not all
+periodic, let's let's instead try to
+
+ align:start position:0%
+periodic, let's let's instead try to
+ 
+
+ align:start position:0%
+periodic, let's let's instead try to
+visualize what is happening to the
+
+ align:start position:0%
+visualize what is happening to the
+ 
+
+ align:start position:0%
+visualize what is happening to the
+lattice.
+
+ align:start position:0%
+lattice.
+ 
+
+ align:start position:0%
+lattice.
+So a point uh a point x corresponds to a
+
+ align:start position:0%
+So a point uh a point x corresponds to a
+ 
+
+ align:start position:0%
+So a point uh a point x corresponds to a
+lice
+
+ align:start position:0%
+lice
+ 
+
+ align:start position:0%
+lice
+uh lambda x.
+
+ align:start position:0%
+uh lambda x.
+ 
+
+ align:start position:0%
+uh lambda x.
+And if you think about what what is
+
+ align:start position:0%
+And if you think about what what is
+ 
+
+ align:start position:0%
+And if you think about what what is
+happening if you take gx
+
+ align:start position:0%
+happening if you take gx
+ 
+
+ align:start position:0%
+happening if you take gx
+that corresponds to the lice
+
+ align:start position:0%
+that corresponds to the lice
+ 
+
+ align:start position:0%
+that corresponds to the lice
+g of lambda of x. So g is in sl2r. It
+
+ align:start position:0%
+g of lambda of x. So g is in sl2r. It
+ 
+
+ align:start position:0%
+g of lambda of x. So g is in sl2r. It
+acts on r2. It moves a lattice to
+
+ align:start position:0%
+acts on r2. It moves a lattice to
+ 
+
+ align:start position:0%
+acts on r2. It moves a lattice to
+another lattice and that's what the
+
+ align:start position:0%
+another lattice and that's what the
+ 
+
+ align:start position:0%
+another lattice and that's what the
+action is.
+
+ align:start position:0%
+action is.
+ 
+
+ align:start position:0%
+action is.
+Okay. And so now G is going to be UT.
+
+ align:start position:0%
+Okay. And so now G is going to be UT.
+ 
+
+ align:start position:0%
+Okay. And so now G is going to be UT.
+And the way UT acts on R2 is by
+
+ align:start position:0%
+And the way UT acts on R2 is by
+ 
+
+ align:start position:0%
+And the way UT acts on R2 is by
+shearing.
+
+ align:start position:0%
+shearing.
+ 
+
+ align:start position:0%
+shearing.
+So UT acts on R2
+
+ align:start position:0%
+So UT acts on R2
+ 
+
+ align:start position:0%
+So UT acts on R2
+um by shearing. So I'll I'll do it this
+
+ align:start position:0%
+um by shearing. So I'll I'll do it this
+ 
+
+ align:start position:0%
+um by shearing. So I'll I'll do it this
+way.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'll draw some points in R2. And
+
+ align:start position:0%
+So I'll draw some points in R2. And
+ 
+
+ align:start position:0%
+So I'll draw some points in R2. And
+perhaps coincidentally, these points
+
+ align:start position:0%
+perhaps coincidentally, these points
+ 
+
+ align:start position:0%
+perhaps coincidentally, these points
+come from a lattice. Um, and then I'll
+
+ align:start position:0%
+come from a lattice. Um, and then I'll
+ 
+
+ align:start position:0%
+come from a lattice. Um, and then I'll
+illustrate what UT does. Um, so if this
+
+ align:start position:0%
+illustrate what UT does. Um, so if this
+ 
+
+ align:start position:0%
+illustrate what UT does. Um, so if this
+is the point P, then this over here is
+
+ align:start position:0%
+is the point P, then this over here is
+ 
+
+ align:start position:0%
+is the point P, then this over here is
+UT of P.
+
+ align:start position:0%
+UT of P.
+ 
+
+ align:start position:0%
+UT of P.
+It's a shearing motion. And so the
+
+ align:start position:0%
+It's a shearing motion. And so the
+ 
+
+ align:start position:0%
+It's a shearing motion. And so the
+shearing motion moves everybody
+
+ align:start position:0%
+shearing motion moves everybody
+ 
+
+ align:start position:0%
+shearing motion moves everybody
+horizontally. And it moves you
+
+ align:start position:0%
+horizontally. And it moves you
+ 
+
+ align:start position:0%
+horizontally. And it moves you
+horizontally, but at an amount
+
+ align:start position:0%
+horizontally, but at an amount
+ 
+
+ align:start position:0%
+horizontally, but at an amount
+proportional to your height. So this one
+
+ align:start position:0%
+proportional to your height. So this one
+ 
+
+ align:start position:0%
+proportional to your height. So this one
+moves horizontally, but a bit less. And
+
+ align:start position:0%
+moves horizontally, but a bit less. And
+ 
+
+ align:start position:0%
+moves horizontally, but a bit less. And
+this one moves horizontally and a bit
+
+ align:start position:0%
+this one moves horizontally and a bit
+ 
+
+ align:start position:0%
+this one moves horizontally and a bit
+more.
+
+ align:start position:0%
+more.
+ 
+
+ align:start position:0%
+more.
+Okay. Now what would it mean? So this so
+
+ align:start position:0%
+Okay. Now what would it mean? So this so
+ 
+
+ align:start position:0%
+Okay. Now what would it mean? So this so
+so you start with a lattice and when we
+
+ align:start position:0%
+so you start with a lattice and when we
+ 
+
+ align:start position:0%
+so you start with a lattice and when we
+apply this uniport orbit to the lattice
+
+ align:start position:0%
+apply this uniport orbit to the lattice
+ 
+
+ align:start position:0%
+apply this uniport orbit to the lattice
+every point in the lattice is shearing.
+
+ align:start position:0%
+every point in the lattice is shearing.
+ 
+
+ align:start position:0%
+every point in the lattice is shearing.
+What would it mean if the orbit was
+
+ align:start position:0%
+What would it mean if the orbit was
+ 
+
+ align:start position:0%
+What would it mean if the orbit was
+periodic? Well, it would mean that this
+
+ align:start position:0%
+periodic? Well, it would mean that this
+ 
+
+ align:start position:0%
+periodic? Well, it would mean that this
+point this lattice point is shearing
+
+ align:start position:0%
+point this lattice point is shearing
+ 
+
+ align:start position:0%
+point this lattice point is shearing
+along and eventually it reaches another
+
+ align:start position:0%
+along and eventually it reaches another
+ 
+
+ align:start position:0%
+along and eventually it reaches another
+lattice point.
+
+ align:start position:0%
+lattice point.
+ 
+
+ align:start position:0%
+lattice point.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+if ux is periodic,
+
+ align:start position:0%
+if ux is periodic,
+ 
+
+ align:start position:0%
+if ux is periodic,
+um that implies that each
+
+ align:start position:0%
+um that implies that each
+ 
+
+ align:start position:0%
+um that implies that each
+lattice point
+
+ align:start position:0%
+lattice point
+ 
+
+ align:start position:0%
+lattice point
+is at the same height
+
+ align:start position:0%
+is at the same height
+ 
+
+ align:start position:0%
+is at the same height
+as another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lattice point,
+
+ align:start position:0%
+lattice point,
+ 
+
+ align:start position:0%
+lattice point,
+right? So there must be another lattice
+
+ align:start position:0%
+right? So there must be another lattice
+ 
+
+ align:start position:0%
+right? So there must be another lattice
+point somewhere over here.
+
+ align:start position:0%
+point somewhere over here.
+ 
+
+ align:start position:0%
+point somewhere over here.
+Okay, but now think about this. This
+
+ align:start position:0%
+Okay, but now think about this. This
+ 
+
+ align:start position:0%
+Okay, but now think about this. This
+difference is also in our lattice
+
+ align:start position:0%
+difference is also in our lattice
+ 
+
+ align:start position:0%
+difference is also in our lattice
+because a lattice is a subgroup
+
+ align:start position:0%
+because a lattice is a subgroup
+ 
+
+ align:start position:0%
+because a lattice is a subgroup
+and this distance is is horizontal. So
+
+ align:start position:0%
+and this distance is is horizontal. So
+ 
+
+ align:start position:0%
+and this distance is is horizontal. So
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+um if and only if um there exists if and
+
+ align:start position:0%
+um if and only if um there exists if and
+ 
+
+ align:start position:0%
+um if and only if um there exists if and
+only if lambda of x contains a vector of
+
+ align:start position:0%
+only if lambda of x contains a vector of
+ 
+
+ align:start position:0%
+only if lambda of x contains a vector of
+the form x1 comma 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So most lises don't contain a vector on
+
+ align:start position:0%
+So most lises don't contain a vector on
+ 
+
+ align:start position:0%
+So most lises don't contain a vector on
+the x-axis. So u * x is usually not
+
+ align:start position:0%
+the x-axis. So u * x is usually not
+ 
+
+ align:start position:0%
+the x-axis. So u * x is usually not
+periodic.
+
+ align:start position:0%
+periodic.
+ 
+
+ align:start position:0%
+periodic.
+And then um the difficult theorem is
+
+ align:start position:0%
+And then um the difficult theorem is
+ 
+
+ align:start position:0%
+And then um the difficult theorem is
+that in that situation u * x is dense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+cool. So this is the situation in SL2
+
+ align:start position:0%
+cool. So this is the situation in SL2
+ 
+
+ align:start position:0%
+cool. So this is the situation in SL2
+and the situation in other league groups
+
+ align:start position:0%
+and the situation in other league groups
+ 
+
+ align:start position:0%
+and the situation in other league groups
+say SLNR for larger N is more difficult
+
+ align:start position:0%
+say SLNR for larger N is more difficult
+ 
+
+ align:start position:0%
+say SLNR for larger N is more difficult
+and more recent but there are similar
+
+ align:start position:0%
+and more recent but there are similar
+ 
+
+ align:start position:0%
+and more recent but there are similar
+theorems. Um so for SL3R
+
+ align:start position:0%
+theorems. Um so for SL3R
+ 
+
+ align:start position:0%
+theorems. Um so for SL3R
+uh for SL3R Margulus and Donnie in the
+
+ align:start position:0%
+uh for SL3R Margulus and Donnie in the
+ 
+
+ align:start position:0%
+uh for SL3R Margulus and Donnie in the
+1980s proved an analog of this theorem
+
+ align:start position:0%
+1980s proved an analog of this theorem
+ 
+
+ align:start position:0%
+1980s proved an analog of this theorem
+and then for all the SLNR and and all
+
+ align:start position:0%
+and then for all the SLNR and and all
+ 
+
+ align:start position:0%
+and then for all the SLNR and and all
+the groups Ratner around 1990 proved an
+
+ align:start position:0%
+the groups Ratner around 1990 proved an
+ 
+
+ align:start position:0%
+the groups Ratner around 1990 proved an
+analog of this theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um cool.
+
+ align:start position:0%
+Um cool.
+ 
+
+ align:start position:0%
+Um cool.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+so that's a little summary of some kinds
+
+ align:start position:0%
+so that's a little summary of some kinds
+ 
+
+ align:start position:0%
+so that's a little summary of some kinds
+of theorems.
+
+ align:start position:0%
+of theorems.
+ 
+
+ align:start position:0%
+of theorems.
+There's some motivations for this.
+
+ align:start position:0%
+There's some motivations for this.
+ 
+
+ align:start position:0%
+There's some motivations for this.
+There's some motivation from Yeah.
+
+ align:start position:0%
+There's some motivation from Yeah.
+ 
+
+ align:start position:0%
+There's some motivation from Yeah.
+>> Just a kind of a question about the link
+
+ align:start position:0%
+>> Just a kind of a question about the link
+ 
+
+ align:start position:0%
+>> Just a kind of a question about the link
+between the lises and the elements of
+
+ align:start position:0%
+between the lises and the elements of
+ 
+
+ align:start position:0%
+between the lises and the elements of
+the uh quotient group. Um so up up there
+
+ align:start position:0%
+the uh quotient group. Um so up up there
+ 
+
+ align:start position:0%
+the uh quotient group. Um so up up there
+in the definition of kp epsilon there's
+
+ align:start position:0%
+in the definition of kp epsilon there's
+ 
+
+ align:start position:0%
+in the definition of kp epsilon there's
+kind of what looks like some sort of
+
+ align:start position:0%
+kind of what looks like some sort of
+ 
+
+ align:start position:0%
+kind of what looks like some sort of
+norm the minimum size of v or the
+
+ align:start position:0%
+norm the minimum size of v or the
+ 
+
+ align:start position:0%
+norm the minimum size of v or the
+non-zero vector v in the does that
+
+ align:start position:0%
+non-zero vector v in the does that
+ 
+
+ align:start position:0%
+non-zero vector v in the does that
+generate the same topology as the the
+
+ align:start position:0%
+generate the same topology as the the
+ 
+
+ align:start position:0%
+generate the same topology as the the
+quotient topology from so
+
+ align:start position:0%
+quotient topology from so
+ 
+
+ align:start position:0%
+quotient topology from so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question is about the topology of
+
+ align:start position:0%
+so the question is about the topology of
+ 
+
+ align:start position:0%
+so the question is about the topology of
+gmod gamma and how the topology of gmod
+
+ align:start position:0%
+gmod gamma and how the topology of gmod
+ 
+
+ align:start position:0%
+gmod gamma and how the topology of gmod
+gamma plays with this definition of
+
+ align:start position:0%
+gamma plays with this definition of
+ 
+
+ align:start position:0%
+gamma plays with this definition of
+Kepsilon.
+
+ align:start position:0%
+Kepsilon.
+ 
+
+ align:start position:0%
+Kepsilon.
+Yeah. Um in a moment we'll put a metric
+
+ align:start position:0%
+Yeah. Um in a moment we'll put a metric
+ 
+
+ align:start position:0%
+Yeah. Um in a moment we'll put a metric
+on G mod gamma and that's what its
+
+ align:start position:0%
+on G mod gamma and that's what its
+ 
+
+ align:start position:0%
+on G mod gamma and that's what its
+topology is. It's a manifold. It has um
+
+ align:start position:0%
+topology is. It's a manifold. It has um
+ 
+
+ align:start position:0%
+topology is. It's a manifold. It has um
+topology manifold. Um and um this thing
+
+ align:start position:0%
+topology manifold. Um and um this thing
+ 
+
+ align:start position:0%
+topology manifold. Um and um this thing
+here is a continuous function on on our
+
+ align:start position:0%
+here is a continuous function on on our
+ 
+
+ align:start position:0%
+here is a continuous function on on our
+um on our uh space of lises.
+
+ align:start position:0%
+um on our uh space of lises.
+ 
+
+ align:start position:0%
+um on our uh space of lises.
+Another way to say what the topology is
+
+ align:start position:0%
+Another way to say what the topology is
+ 
+
+ align:start position:0%
+Another way to say what the topology is
+is you know if you describe a lattice as
+
+ align:start position:0%
+is you know if you describe a lattice as
+ 
+
+ align:start position:0%
+is you know if you describe a lattice as
+the span of two particular vectors if
+
+ align:start position:0%
+the span of two particular vectors if
+ 
+
+ align:start position:0%
+the span of two particular vectors if
+you slightly perturb those particular
+
+ align:start position:0%
+you slightly perturb those particular
+ 
+
+ align:start position:0%
+you slightly perturb those particular
+vectors that will be a slight change in
+
+ align:start position:0%
+vectors that will be a slight change in
+ 
+
+ align:start position:0%
+vectors that will be a slight change in
+the in the space of latises
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> is is that definition similar anyway to
+
+ align:start position:0%
+>> is is that definition similar anyway to
+ 
+
+ align:start position:0%
+>> is is that definition similar anyway to
+have a minimum I guess you're right not
+
+ align:start position:0%
+have a minimum I guess you're right not
+ 
+
+ align:start position:0%
+have a minimum I guess you're right not
+quite thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So when I introduced homogeneous
+
+ align:start position:0%
+Okay. So when I introduced homogeneous
+ 
+
+ align:start position:0%
+Okay. So when I introduced homogeneous
+dynamics, I mentioned some application
+
+ align:start position:0%
+dynamics, I mentioned some application
+ 
+
+ align:start position:0%
+dynamics, I mentioned some application
+in number theory. The uh uh connection
+
+ align:start position:0%
+in number theory. The uh uh connection
+ 
+
+ align:start position:0%
+in number theory. The uh uh connection
+to the Oenheim Davenport conjecture
+
+ align:start position:0%
+to the Oenheim Davenport conjecture
+ 
+
+ align:start position:0%
+to the Oenheim Davenport conjecture
+which is about the values of quadratic
+
+ align:start position:0%
+which is about the values of quadratic
+ 
+
+ align:start position:0%
+which is about the values of quadratic
+forms. Um and it's a nice that that's a
+
+ align:start position:0%
+forms. Um and it's a nice that that's a
+ 
+
+ align:start position:0%
+forms. Um and it's a nice that that's a
+nice connection. I feel like we already
+
+ align:start position:0%
+nice connection. I feel like we already
+ 
+
+ align:start position:0%
+nice connection. I feel like we already
+talked about a little bit and if you
+
+ align:start position:0%
+talked about a little bit and if you
+ 
+
+ align:start position:0%
+talked about a little bit and if you
+wanted to read about it, it's also easy
+
+ align:start position:0%
+wanted to read about it, it's also easy
+ 
+
+ align:start position:0%
+wanted to read about it, it's also easy
+to read about it. Um, so I wanted to
+
+ align:start position:0%
+to read about it. Um, so I wanted to
+ 
+
+ align:start position:0%
+to read about it. Um, so I wanted to
+spend the class time on um, uh, yeah.
+
+ align:start position:0%
+spend the class time on um, uh, yeah.
+ 
+
+ align:start position:0%
+spend the class time on um, uh, yeah.
+Okay. So I wanted So okay, so I wanted
+
+ align:start position:0%
+Okay. So I wanted So okay, so I wanted
+ 
+
+ align:start position:0%
+Okay. So I wanted So okay, so I wanted
+to spend the class time on trying to get
+
+ align:start position:0%
+to spend the class time on trying to get
+ 
+
+ align:start position:0%
+to spend the class time on trying to get
+intuition for why something like this
+
+ align:start position:0%
+intuition for why something like this
+ 
+
+ align:start position:0%
+intuition for why something like this
+would be true and also maybe why
+
+ align:start position:0%
+would be true and also maybe why
+ 
+
+ align:start position:0%
+would be true and also maybe why
+something like this would be false. And
+
+ align:start position:0%
+something like this would be false. And
+ 
+
+ align:start position:0%
+something like this would be false. And
+um, there are many different ways of
+
+ align:start position:0%
+um, there are many different ways of
+ 
+
+ align:start position:0%
+um, there are many different ways of
+thinking about homogeneous dynamics.
+
+ align:start position:0%
+thinking about homogeneous dynamics.
+ 
+
+ align:start position:0%
+thinking about homogeneous dynamics.
+There's a big literature, but I want to
+
+ align:start position:0%
+There's a big literature, but I want to
+ 
+
+ align:start position:0%
+There's a big literature, but I want to
+highlight the way of of connecting it to
+
+ align:start position:0%
+highlight the way of of connecting it to
+ 
+
+ align:start position:0%
+highlight the way of of connecting it to
+projection theory. Um, and that's not
+
+ align:start position:0%
+projection theory. Um, and that's not
+ 
+
+ align:start position:0%
+projection theory. Um, and that's not
+one of the classical ways. It's actually
+
+ align:start position:0%
+one of the classical ways. It's actually
+ 
+
+ align:start position:0%
+one of the classical ways. It's actually
+not super easy to find in the
+
+ align:start position:0%
+not super easy to find in the
+ 
+
+ align:start position:0%
+not super easy to find in the
+literature. Um the the
+
+ align:start position:0%
+literature. Um the the
+ 
+
+ align:start position:0%
+literature. Um the the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so it appears in these recent works
+
+ align:start position:0%
+um so it appears in these recent works
+ 
+
+ align:start position:0%
+um so it appears in these recent works
+of Lynden Strauss and Mohammadi and
+
+ align:start position:0%
+of Lynden Strauss and Mohammadi and
+ 
+
+ align:start position:0%
+of Lynden Strauss and Mohammadi and
+their collaborators and they're trying
+
+ align:start position:0%
+their collaborators and they're trying
+ 
+
+ align:start position:0%
+their collaborators and they're trying
+they're doing you know the cutting edge
+
+ align:start position:0%
+they're doing you know the cutting edge
+ 
+
+ align:start position:0%
+they're doing you know the cutting edge
+of homogeneous dynamics and the
+
+ align:start position:0%
+of homogeneous dynamics and the
+ 
+
+ align:start position:0%
+of homogeneous dynamics and the
+particular problem they're trying to
+
+ align:start position:0%
+particular problem they're trying to
+ 
+
+ align:start position:0%
+particular problem they're trying to
+solve is to do first of all these
+
+ align:start position:0%
+solve is to do first of all these
+ 
+
+ align:start position:0%
+solve is to do first of all these
+higherdimensional things that Margulus
+
+ align:start position:0%
+higherdimensional things that Margulus
+ 
+
+ align:start position:0%
+higherdimensional things that Margulus
+and Ratner and Donnie were doing and
+
+ align:start position:0%
+and Ratner and Donnie were doing and
+ 
+
+ align:start position:0%
+and Ratner and Donnie were doing and
+second of all instead of having a
+
+ align:start position:0%
+second of all instead of having a
+ 
+
+ align:start position:0%
+second of all instead of having a
+qualitative theorem like this to have a
+
+ align:start position:0%
+qualitative theorem like this to have a
+ 
+
+ align:start position:0%
+qualitative theorem like this to have a
+quantitative theorem that says If you're
+
+ align:start position:0%
+quantitative theorem that says If you're
+ 
+
+ align:start position:0%
+quantitative theorem that says If you're
+not approximately periodic for some
+
+ align:start position:0%
+not approximately periodic for some
+ 
+
+ align:start position:0%
+not approximately periodic for some
+length, then you're, you know,
+
+ align:start position:0%
+length, then you're, you know,
+ 
+
+ align:start position:0%
+length, then you're, you know,
+quantitatively
+
+ align:start position:0%
+quantitatively
+ 
+
+ align:start position:0%
+quantitatively
+uh dense.
+
+ align:start position:0%
+uh dense.
+ 
+
+ align:start position:0%
+uh dense.
+Um, okay. And at that point, the they
+
+ align:start position:0%
+Um, okay. And at that point, the they
+ 
+
+ align:start position:0%
+Um, okay. And at that point, the they
+had they ran into some things that the
+
+ align:start position:0%
+had they ran into some things that the
+ 
+
+ align:start position:0%
+had they ran into some things that the
+many interesting classical techniques
+
+ align:start position:0%
+many interesting classical techniques
+ 
+
+ align:start position:0%
+many interesting classical techniques
+did could not do or could not obviously
+
+ align:start position:0%
+did could not do or could not obviously
+ 
+
+ align:start position:0%
+did could not do or could not obviously
+do and they invented this new technique,
+
+ align:start position:0%
+do and they invented this new technique,
+ 
+
+ align:start position:0%
+do and they invented this new technique,
+this connection to projection theory.
+
+ align:start position:0%
+this connection to projection theory.
+ 
+
+ align:start position:0%
+this connection to projection theory.
+But in hindsight, you could also look
+
+ align:start position:0%
+But in hindsight, you could also look
+ 
+
+ align:start position:0%
+But in hindsight, you could also look
+back at the oldest theorems, the oldest
+
+ align:start position:0%
+back at the oldest theorems, the oldest
+ 
+
+ align:start position:0%
+back at the oldest theorems, the oldest
+theorems like this one, and you could
+
+ align:start position:0%
+theorems like this one, and you could
+ 
+
+ align:start position:0%
+theorems like this one, and you could
+approach it using projection theory. And
+
+ align:start position:0%
+approach it using projection theory. And
+ 
+
+ align:start position:0%
+approach it using projection theory. And
+it may not be the best approach to this
+
+ align:start position:0%
+it may not be the best approach to this
+ 
+
+ align:start position:0%
+it may not be the best approach to this
+theorem. It's certainly not the only
+
+ align:start position:0%
+theorem. It's certainly not the only
+ 
+
+ align:start position:0%
+theorem. It's certainly not the only
+approach to this theorem, but but uh but
+
+ align:start position:0%
+approach to this theorem, but but uh but
+ 
+
+ align:start position:0%
+approach to this theorem, but but uh but
+it's a it's a way of looking at it and
+
+ align:start position:0%
+it's a it's a way of looking at it and
+ 
+
+ align:start position:0%
+it's a it's a way of looking at it and
+and quite a visual way of looking at at
+
+ align:start position:0%
+and quite a visual way of looking at at
+ 
+
+ align:start position:0%
+and quite a visual way of looking at at
+what's going on. So the goal of the
+
+ align:start position:0%
+what's going on. So the goal of the
+ 
+
+ align:start position:0%
+what's going on. So the goal of the
+class is to try to explain um uh
+
+ align:start position:0%
+class is to try to explain um uh
+ 
+
+ align:start position:0%
+class is to try to explain um uh
+uh the how projection theory could help
+
+ align:start position:0%
+uh the how projection theory could help
+ 
+
+ align:start position:0%
+uh the how projection theory could help
+to understand something like this.
+
+ align:start position:0%
+to understand something like this.
+ 
+
+ align:start position:0%
+to understand something like this.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. Um great. So we're going to do
+
+ align:start position:0%
+Okay. Um great. So we're going to do
+ 
+
+ align:start position:0%
+Okay. Um great. So we're going to do
+some geometry. So next we we need to
+
+ align:start position:0%
+some geometry. So next we we need to
+ 
+
+ align:start position:0%
+some geometry. So next we we need to
+think about the geometry on the space G
+
+ align:start position:0%
+think about the geometry on the space G
+ 
+
+ align:start position:0%
+think about the geometry on the space G
+mod gamma. Um and um
+
+ align:start position:0%
+mod gamma. Um and um
+ 
+
+ align:start position:0%
+mod gamma. Um and um
+uh and how that geometry interacts with
+
+ align:start position:0%
+uh and how that geometry interacts with
+ 
+
+ align:start position:0%
+uh and how that geometry interacts with
+the action.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oops.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So geometry of gamma.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+first we'll talk about the right action
+
+ align:start position:0%
+first we'll talk about the right action
+ 
+
+ align:start position:0%
+first we'll talk about the right action
+of G on itself.
+
+ align:start position:0%
+of G on itself.
+ 
+
+ align:start position:0%
+of G on itself.
+Right? So if G is in G, there's a right
+
+ align:start position:0%
+Right? So if G is in G, there's a right
+ 
+
+ align:start position:0%
+Right? So if G is in G, there's a right
+action which is a map from G to itself.
+
+ align:start position:0%
+action which is a map from G to itself.
+ 
+
+ align:start position:0%
+action which is a map from G to itself.
+And the right action G of H is H. and
+
+ align:start position:0%
+And the right action G of H is H. and
+ 
+
+ align:start position:0%
+And the right action G of H is H. and
+you multiply by G on the right side. So
+
+ align:start position:0%
+you multiply by G on the right side. So
+ 
+
+ align:start position:0%
+you multiply by G on the right side. So
+these groups don't commute. So it's, you
+
+ align:start position:0%
+these groups don't commute. So it's, you
+ 
+
+ align:start position:0%
+these groups don't commute. So it's, you
+know, it matters which side you put it
+
+ align:start position:0%
+know, it matters which side you put it
+ 
+
+ align:start position:0%
+know, it matters which side you put it
+on. And actually you have to be quite
+
+ align:start position:0%
+on. And actually you have to be quite
+ 
+
+ align:start position:0%
+on. And actually you have to be quite
+quite careful in this story.
+
+ align:start position:0%
+quite careful in this story.
+ 
+
+ align:start position:0%
+quite careful in this story.
+Okay. So that's a map from from G to
+
+ align:start position:0%
+Okay. So that's a map from from G to
+ 
+
+ align:start position:0%
+Okay. So that's a map from from G to
+itself.
+
+ align:start position:0%
+itself.
+ 
+
+ align:start position:0%
+itself.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+now we're going to use that to start to
+
+ align:start position:0%
+now we're going to use that to start to
+ 
+
+ align:start position:0%
+now we're going to use that to start to
+put a geometry on G. Going to have a
+
+ align:start position:0%
+put a geometry on G. Going to have a
+ 
+
+ align:start position:0%
+put a geometry on G. Going to have a
+right invariant
+
+ align:start position:0%
+right invariant
+ 
+
+ align:start position:0%
+right invariant
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+M.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, how does this work? Um, so, so what
+
+ align:start position:0%
+So, how does this work? Um, so, so what
+ 
+
+ align:start position:0%
+So, how does this work? Um, so, so what
+does that mean? So, M is going to be a
+
+ align:start position:0%
+does that mean? So, M is going to be a
+ 
+
+ align:start position:0%
+does that mean? So, M is going to be a
+Romanian metric
+
+ align:start position:0%
+Romanian metric
+ 
+
+ align:start position:0%
+Romanian metric
+on G and for every G and G, we have this
+
+ align:start position:0%
+on G and for every G and G, we have this
+ 
+
+ align:start position:0%
+on G and for every G and G, we have this
+right action G. So, that's a map from
+
+ align:start position:0%
+right action G. So, that's a map from
+ 
+
+ align:start position:0%
+right action G. So, that's a map from
+our group with its metric to itself. And
+
+ align:start position:0%
+our group with its metric to itself. And
+ 
+
+ align:start position:0%
+our group with its metric to itself. And
+this is for every G and G, this is an
+
+ align:start position:0%
+this is for every G and G, this is an
+ 
+
+ align:start position:0%
+this is for every G and G, this is an
+isometry.
+
+ align:start position:0%
+isometry.
+ 
+
+ align:start position:0%
+isometry.
+That's what it that's what it means to
+
+ align:start position:0%
+That's what it that's what it means to
+ 
+
+ align:start position:0%
+That's what it that's what it means to
+have a right invariant metric. Where do
+
+ align:start position:0%
+have a right invariant metric. Where do
+ 
+
+ align:start position:0%
+have a right invariant metric. Where do
+they come from? Um the idea is that
+
+ align:start position:0%
+they come from? Um the idea is that
+ 
+
+ align:start position:0%
+they come from? Um the idea is that
+we'll put a metric at the origin and
+
+ align:start position:0%
+we'll put a metric at the origin and
+ 
+
+ align:start position:0%
+we'll put a metric at the origin and
+then we'll use R subg to help define the
+
+ align:start position:0%
+then we'll use R subg to help define the
+ 
+
+ align:start position:0%
+then we'll use R subg to help define the
+metric at every other place.
+
+ align:start position:0%
+metric at every other place.
+ 
+
+ align:start position:0%
+metric at every other place.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So um a lot of what we'll say here
+
+ align:start position:0%
+Okay. So um a lot of what we'll say here
+ 
+
+ align:start position:0%
+Okay. So um a lot of what we'll say here
+works for any group but to be concrete
+
+ align:start position:0%
+works for any group but to be concrete
+ 
+
+ align:start position:0%
+works for any group but to be concrete
+I'm going to stick to the group SL2R
+
+ align:start position:0%
+I'm going to stick to the group SL2R
+ 
+
+ align:start position:0%
+I'm going to stick to the group SL2R
+the tangent space at the origin. So E E
+
+ align:start position:0%
+the tangent space at the origin. So E E
+ 
+
+ align:start position:0%
+the tangent space at the origin. So E E
+is or the the identity I was using the
+
+ align:start position:0%
+is or the the identity I was using the
+ 
+
+ align:start position:0%
+is or the the identity I was using the
+word origin I should say identity T is E
+
+ align:start position:0%
+word origin I should say identity T is E
+ 
+
+ align:start position:0%
+word origin I should say identity T is E
+is the identity in the group. The
+
+ align:start position:0%
+is the identity in the group. The
+ 
+
+ align:start position:0%
+is the identity in the group. The
+tangent space in the identity of this
+
+ align:start position:0%
+tangent space in the identity of this
+ 
+
+ align:start position:0%
+tangent space in the identity of this
+group is the space of matrices A B C D
+
+ align:start position:0%
+group is the space of matrices A B C D
+ 
+
+ align:start position:0%
+group is the space of matrices A B C D
+with A + D equal to Z.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so this is not a deep factor. This is
+
+ align:start position:0%
+Um so this is not a deep factor. This is
+ 
+
+ align:start position:0%
+Um so this is not a deep factor. This is
+so SL2R is matrices A B C D where A D
+
+ align:start position:0%
+so SL2R is matrices A B C D where A D
+ 
+
+ align:start position:0%
+so SL2R is matrices A B C D where A D
+minus BC equals 1 and the identity is a
+
+ align:start position:0%
+minus BC equals 1 and the identity is a
+ 
+
+ align:start position:0%
+minus BC equals 1 and the identity is a
+is a matrix that's sitting in there in
+
+ align:start position:0%
+is a matrix that's sitting in there in
+ 
+
+ align:start position:0%
+is a matrix that's sitting in there in
+R4. So it's the the group is a
+
+ align:start position:0%
+R4. So it's the the group is a
+ 
+
+ align:start position:0%
+R4. So it's the the group is a
+threedimensional manifold in R4 and this
+
+ align:start position:0%
+threedimensional manifold in R4 and this
+ 
+
+ align:start position:0%
+threedimensional manifold in R4 and this
+is just its tangent space in the usual
+
+ align:start position:0%
+is just its tangent space in the usual
+ 
+
+ align:start position:0%
+is just its tangent space in the usual
+sense.
+
+ align:start position:0%
+sense.
+ 
+
+ align:start position:0%
+sense.
+Okay. So that's it tangent space. So now
+
+ align:start position:0%
+Okay. So that's it tangent space. So now
+ 
+
+ align:start position:0%
+Okay. So that's it tangent space. So now
+m is going to be a metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on t and I can specify it by by
+
+ align:start position:0%
+on t and I can specify it by by
+ 
+
+ align:start position:0%
+on t and I can specify it by by
+specifying who an orthonormal basis and
+
+ align:start position:0%
+specifying who an orthonormal basis and
+ 
+
+ align:start position:0%
+specifying who an orthonormal basis and
+this choice doesn't matter super a lot
+
+ align:start position:0%
+this choice doesn't matter super a lot
+ 
+
+ align:start position:0%
+this choice doesn't matter super a lot
+but um but there's a convenient choice.
+
+ align:start position:0%
+but um but there's a convenient choice.
+ 
+
+ align:start position:0%
+but um but there's a convenient choice.
+So my orthonormal basis
+
+ align:start position:0%
+So my orthonormal basis
+ 
+
+ align:start position:0%
+So my orthonormal basis
+of Mn is going to be 0 1 0 0. So which
+
+ align:start position:0%
+of Mn is going to be 0 1 0 0. So which
+ 
+
+ align:start position:0%
+of Mn is going to be 0 1 0 0. So which
+I'll call u 0 0 1 0 which I'll call u
+
+ align:start position:0%
+I'll call u 0 0 1 0 which I'll call u
+ 
+
+ align:start position:0%
+I'll call u 0 0 1 0 which I'll call u
+tilda and then uh 1 / <unk>2 0 - 1 /2
+
+ align:start position:0%
+tilda and then uh 1 / <unk>2 0 - 1 /2
+ 
+
+ align:start position:0%
+tilda and then uh 1 / <unk>2 0 - 1 /2
+which I'll call D.
+
+ align:start position:0%
+which I'll call D.
+ 
+
+ align:start position:0%
+which I'll call D.
+um these root twos are not actually
+
+ align:start position:0%
+um these root twos are not actually
+ 
+
+ align:start position:0%
+um these root twos are not actually
+important but this this orthonormal
+
+ align:start position:0%
+important but this this orthonormal
+ 
+
+ align:start position:0%
+important but this this orthonormal
+basis happens to be the orthoral basis
+
+ align:start position:0%
+basis happens to be the orthoral basis
+ 
+
+ align:start position:0%
+basis happens to be the orthoral basis
+that corresponds to the metric where you
+
+ align:start position:0%
+that corresponds to the metric where you
+ 
+
+ align:start position:0%
+that corresponds to the metric where you
+just take the metric on R4 and restrict
+
+ align:start position:0%
+just take the metric on R4 and restrict
+ 
+
+ align:start position:0%
+just take the metric on R4 and restrict
+it to to uh this subspace.
+
+ align:start position:0%
+it to to uh this subspace.
+ 
+
+ align:start position:0%
+it to to uh this subspace.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now how will we define the metric
+
+ align:start position:0%
+So now how will we define the metric
+ 
+
+ align:start position:0%
+So now how will we define the metric
+elsewhere?
+
+ align:start position:0%
+elsewhere?
+ 
+
+ align:start position:0%
+elsewhere?
+So now suppose G is in our group. Um
+
+ align:start position:0%
+So now suppose G is in our group. Um
+ 
+
+ align:start position:0%
+So now suppose G is in our group. Um
+R subg
+
+ align:start position:0%
+R subg
+ 
+
+ align:start position:0%
+R subg
+of the identity is G. It's easy to check
+
+ align:start position:0%
+of the identity is G. It's easy to check
+ 
+
+ align:start position:0%
+of the identity is G. It's easy to check
+from the definition of R subg.
+
+ align:start position:0%
+from the definition of R subg.
+ 
+
+ align:start position:0%
+from the definition of R subg.
+And therefore R subg defines a map from
+
+ align:start position:0%
+And therefore R subg defines a map from
+ 
+
+ align:start position:0%
+And therefore R subg defines a map from
+T tangent space E of G to the tangent
+
+ align:start position:0%
+T tangent space E of G to the tangent
+ 
+
+ align:start position:0%
+T tangent space E of G to the tangent
+space G of G. And this map is an
+
+ align:start position:0%
+space G of G. And this map is an
+ 
+
+ align:start position:0%
+space G of G. And this map is an
+isomeorphism.
+
+ align:start position:0%
+isomeorphism.
+ 
+
+ align:start position:0%
+isomeorphism.
+We have a metric over here. We use this
+
+ align:start position:0%
+We have a metric over here. We use this
+ 
+
+ align:start position:0%
+We have a metric over here. We use this
+map to define a metric over there.
+
+ align:start position:0%
+map to define a metric over there.
+ 
+
+ align:start position:0%
+map to define a metric over there.
+So now we define
+
+ align:start position:0%
+So now we define
+ 
+
+ align:start position:0%
+So now we define
+mg which is a a metric or inner product
+
+ align:start position:0%
+mg which is a a metric or inner product
+ 
+
+ align:start position:0%
+mg which is a a metric or inner product
+MG on TG.
+
+ align:start position:0%
+MG on TG.
+ 
+
+ align:start position:0%
+MG on TG.
+So that
+
+ align:start position:0%
+So that
+ 
+
+ align:start position:0%
+So that
+RG goes from T E G comma M KN to T G
+
+ align:start position:0%
+RG goes from T E G comma M KN to T G
+ 
+
+ align:start position:0%
+RG goes from T E G comma M KN to T G
+comma MG. So that that's an isometry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then it's an exercise to check
+
+ align:start position:0%
+Okay. And then it's an exercise to check
+ 
+
+ align:start position:0%
+Okay. And then it's an exercise to check
+that this thing we just defined is right
+
+ align:start position:0%
+that this thing we just defined is right
+ 
+
+ align:start position:0%
+that this thing we just defined is right
+invariant. So So
+
+ align:start position:0%
+invariant. So So
+ 
+
+ align:start position:0%
+invariant. So So
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+that all of these maps are isometries
+
+ align:start position:0%
+that all of these maps are isometries
+ 
+
+ align:start position:0%
+that all of these maps are isometries
+everywhere.
+
+ align:start position:0%
+everywhere.
+ 
+
+ align:start position:0%
+everywhere.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So now because m is right
+
+ align:start position:0%
+right. So now because m is right
+ 
+
+ align:start position:0%
+right. So now because m is right
+invariant
+
+ align:start position:0%
+invariant
+ 
+
+ align:start position:0%
+invariant
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we we get a metric it it sends to a
+
+ align:start position:0%
+we we get a metric it it sends to a
+ 
+
+ align:start position:0%
+we we get a metric it it sends to a
+metric m on g mod g.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So how does that work? Um so we have
+
+ align:start position:0%
+So how does that work? Um so we have
+ 
+
+ align:start position:0%
+So how does that work? Um so we have
+like all of G have a projection map pi
+
+ align:start position:0%
+like all of G have a projection map pi
+ 
+
+ align:start position:0%
+like all of G have a projection map pi
+to G mod gamma. We have a point X and G
+
+ align:start position:0%
+to G mod gamma. We have a point X and G
+ 
+
+ align:start position:0%
+to G mod gamma. We have a point X and G
+mod gamma. And X has many pre-im images.
+
+ align:start position:0%
+mod gamma. And X has many pre-im images.
+ 
+
+ align:start position:0%
+mod gamma. And X has many pre-im images.
+Um so X is equal to say little G *
+
+ align:start position:0%
+Um so X is equal to say little G *
+ 
+
+ align:start position:0%
+Um so X is equal to say little G *
+little G little little H* gamma.
+
+ align:start position:0%
+little G little little H* gamma.
+ 
+
+ align:start position:0%
+little G little little H* gamma.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the pre-image of X is these many
+
+ align:start position:0%
+so the pre-image of X is these many
+ 
+
+ align:start position:0%
+so the pre-image of X is these many
+different points. Okay. Now I have a
+
+ align:start position:0%
+different points. Okay. Now I have a
+ 
+
+ align:start position:0%
+different points. Okay. Now I have a
+metric upstairs and I'd like to try to
+
+ align:start position:0%
+metric upstairs and I'd like to try to
+ 
+
+ align:start position:0%
+metric upstairs and I'd like to try to
+define a metric downstairs in a natural
+
+ align:start position:0%
+define a metric downstairs in a natural
+ 
+
+ align:start position:0%
+define a metric downstairs in a natural
+way. So I'd like to define a metric
+
+ align:start position:0%
+way. So I'd like to define a metric
+ 
+
+ align:start position:0%
+way. So I'd like to define a metric
+here. So for each of these lifts
+
+ align:start position:0%
+here. So for each of these lifts
+ 
+
+ align:start position:0%
+here. So for each of these lifts
+upstairs, I can take the metric there
+
+ align:start position:0%
+upstairs, I can take the metric there
+ 
+
+ align:start position:0%
+upstairs, I can take the metric there
+and I can use the map pi and I can
+
+ align:start position:0%
+and I can use the map pi and I can
+ 
+
+ align:start position:0%
+and I can use the map pi and I can
+produce a metric over here.
+
+ align:start position:0%
+produce a metric over here.
+ 
+
+ align:start position:0%
+produce a metric over here.
+There's no canonical choice of which of
+
+ align:start position:0%
+There's no canonical choice of which of
+ 
+
+ align:start position:0%
+There's no canonical choice of which of
+these purple points in the pre-image I
+
+ align:start position:0%
+these purple points in the pre-image I
+ 
+
+ align:start position:0%
+these purple points in the pre-image I
+should use. But because our metric
+
+ align:start position:0%
+should use. But because our metric
+ 
+
+ align:start position:0%
+should use. But because our metric
+upstairs is right invariant, they all
+
+ align:start position:0%
+upstairs is right invariant, they all
+ 
+
+ align:start position:0%
+upstairs is right invariant, they all
+give the same answer. And so there's a
+
+ align:start position:0%
+give the same answer. And so there's a
+ 
+
+ align:start position:0%
+give the same answer. And so there's a
+coherent choice.
+
+ align:start position:0%
+coherent choice.
+ 
+
+ align:start position:0%
+coherent choice.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So that gives us a metric on GMO gap.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So now have also a left action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of G on G.
+
+ align:start position:0%
+of G on G.
+ 
+
+ align:start position:0%
+of G on G.
+Okay. So if G is in G, the left action
+
+ align:start position:0%
+Okay. So if G is in G, the left action
+ 
+
+ align:start position:0%
+Okay. So if G is in G, the left action
+of G is also a map from G to itself.
+
+ align:start position:0%
+of G is also a map from G to itself.
+ 
+
+ align:start position:0%
+of G is also a map from G to itself.
+Left action G of H is G inverse on the
+
+ align:start position:0%
+Left action G of H is G inverse on the
+ 
+
+ align:start position:0%
+Left action G of H is G inverse on the
+left H. So the word left and left action
+
+ align:start position:0%
+left H. So the word left and left action
+ 
+
+ align:start position:0%
+left H. So the word left and left action
+is because the the thing that comes from
+
+ align:start position:0%
+is because the the thing that comes from
+ 
+
+ align:start position:0%
+is because the the thing that comes from
+G is over here. Um the inverse is not
+
+ align:start position:0%
+G is over here. Um the inverse is not
+ 
+
+ align:start position:0%
+G is over here. Um the inverse is not
+super important in our discussion today,
+
+ align:start position:0%
+super important in our discussion today,
+ 
+
+ align:start position:0%
+super important in our discussion today,
+but it causes this to behave correctly
+
+ align:start position:0%
+but it causes this to behave correctly
+ 
+
+ align:start position:0%
+but it causes this to behave correctly
+when you compose elements in the group.
+
+ align:start position:0%
+when you compose elements in the group.
+ 
+
+ align:start position:0%
+when you compose elements in the group.
+And so it's traditional to do this.
+
+ align:start position:0%
+And so it's traditional to do this.
+ 
+
+ align:start position:0%
+And so it's traditional to do this.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Right.
+
+ align:start position:0%
+Right.
+ 
+
+ align:start position:0%
+Right.
+So um
+
+ align:start position:0%
+So um
+ 
+
+ align:start position:0%
+So um
+SLG
+
+ align:start position:0%
+SLG
+ 
+
+ align:start position:0%
+SLG
+is not
+
+ align:start position:0%
+is not
+ 
+
+ align:start position:0%
+is not
+an isometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of our group with our right invariant
+
+ align:start position:0%
+of our group with our right invariant
+ 
+
+ align:start position:0%
+of our group with our right invariant
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+and that's very important. It's very
+
+ align:start position:0%
+and that's very important. It's very
+ 
+
+ align:start position:0%
+and that's very important. It's very
+important to our whole discussion to
+
+ align:start position:0%
+important to our whole discussion to
+ 
+
+ align:start position:0%
+important to our whole discussion to
+understand um geometrically how this
+
+ align:start position:0%
+understand um geometrically how this
+ 
+
+ align:start position:0%
+understand um geometrically how this
+operation uh affects this space. Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's see what happens. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So, it's easiest to see what
+
+ align:start position:0%
+right. So, it's easiest to see what
+ 
+
+ align:start position:0%
+right. So, it's easiest to see what
+happens around the identity and you can
+
+ align:start position:0%
+happens around the identity and you can
+ 
+
+ align:start position:0%
+happens around the identity and you can
+do it starting at other points too.
+
+ align:start position:0%
+do it starting at other points too.
+ 
+
+ align:start position:0%
+do it starting at other points too.
+So here's the identity and here's some G
+
+ align:start position:0%
+So here's the identity and here's some G
+ 
+
+ align:start position:0%
+So here's the identity and here's some G
+and I have a map the left action by G
+
+ align:start position:0%
+and I have a map the left action by G
+ 
+
+ align:start position:0%
+and I have a map the left action by G
+inverse that takes the identity over
+
+ align:start position:0%
+inverse that takes the identity over
+ 
+
+ align:start position:0%
+inverse that takes the identity over
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+And now this action it's not clear from
+
+ align:start position:0%
+And now this action it's not clear from
+ 
+
+ align:start position:0%
+And now this action it's not clear from
+what we've said whether it preserves the
+
+ align:start position:0%
+what we've said whether it preserves the
+ 
+
+ align:start position:0%
+what we've said whether it preserves the
+metric. In fact it distorts the metric.
+
+ align:start position:0%
+metric. In fact it distorts the metric.
+ 
+
+ align:start position:0%
+metric. In fact it distorts the metric.
+Um but how can we figure out what what
+
+ align:start position:0%
+Um but how can we figure out what what
+ 
+
+ align:start position:0%
+Um but how can we figure out what what
+this mapping is doing to the metric?
+
+ align:start position:0%
+this mapping is doing to the metric?
+ 
+
+ align:start position:0%
+this mapping is doing to the metric?
+Well, our metric was defined to be right
+
+ align:start position:0%
+Well, our metric was defined to be right
+ 
+
+ align:start position:0%
+Well, our metric was defined to be right
+invariant. So there's a map going the
+
+ align:start position:0%
+invariant. So there's a map going the
+ 
+
+ align:start position:0%
+invariant. So there's a map going the
+other direction. The right uh action by
+
+ align:start position:0%
+other direction. The right uh action by
+ 
+
+ align:start position:0%
+other direction. The right uh action by
+G inverse that takes G back to the
+
+ align:start position:0%
+G inverse that takes G back to the
+ 
+
+ align:start position:0%
+G inverse that takes G back to the
+identity. And this one we do understand
+
+ align:start position:0%
+identity. And this one we do understand
+ 
+
+ align:start position:0%
+identity. And this one we do understand
+what it does to the metric. It's an
+
+ align:start position:0%
+what it does to the metric. It's an
+ 
+
+ align:start position:0%
+what it does to the metric. It's an
+isometry.
+
+ align:start position:0%
+isometry.
+ 
+
+ align:start position:0%
+isometry.
+So if I want to understand what this map
+
+ align:start position:0%
+So if I want to understand what this map
+ 
+
+ align:start position:0%
+So if I want to understand what this map
+did to the metric, it's a reasonable
+
+ align:start position:0%
+did to the metric, it's a reasonable
+ 
+
+ align:start position:0%
+did to the metric, it's a reasonable
+idea to look at this and then this.
+
+ align:start position:0%
+idea to look at this and then this.
+ 
+
+ align:start position:0%
+idea to look at this and then this.
+That part is an isometry. So all of the
+
+ align:start position:0%
+That part is an isometry. So all of the
+ 
+
+ align:start position:0%
+That part is an isometry. So all of the
+distortion of the metric came from this
+
+ align:start position:0%
+distortion of the metric came from this
+ 
+
+ align:start position:0%
+distortion of the metric came from this
+part.
+
+ align:start position:0%
+part.
+ 
+
+ align:start position:0%
+part.
+Um and this composition is going to be a
+
+ align:start position:0%
+Um and this composition is going to be a
+ 
+
+ align:start position:0%
+Um and this composition is going to be a
+little easier to understand.
+
+ align:start position:0%
+little easier to understand.
+ 
+
+ align:start position:0%
+little easier to understand.
+Okay. So what happens if I if I do this?
+
+ align:start position:0%
+Okay. So what happens if I if I do this?
+ 
+
+ align:start position:0%
+Okay. So what happens if I if I do this?
+If I take a left action by G inverse and
+
+ align:start position:0%
+If I take a left action by G inverse and
+ 
+
+ align:start position:0%
+If I take a left action by G inverse and
+a right action by G inverse and I apply
+
+ align:start position:0%
+a right action by G inverse and I apply
+ 
+
+ align:start position:0%
+a right action by G inverse and I apply
+it to H.
+
+ align:start position:0%
+it to H.
+ 
+
+ align:start position:0%
+it to H.
+These these guys uh commute with each
+
+ align:start position:0%
+These these guys uh commute with each
+ 
+
+ align:start position:0%
+These these guys uh commute with each
+other. We'll see when we write it out.
+
+ align:start position:0%
+other. We'll see when we write it out.
+ 
+
+ align:start position:0%
+other. We'll see when we write it out.
+So, um, I don't have to be super careful
+
+ align:start position:0%
+So, um, I don't have to be super careful
+ 
+
+ align:start position:0%
+So, um, I don't have to be super careful
+what order to write them in. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> What's that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, I guess I should really write it
+
+ align:start position:0%
+>> Yeah, I guess I should really write it
+ 
+
+ align:start position:0%
+>> Yeah, I guess I should really write it
+in the other order, although it doesn't
+
+ align:start position:0%
+in the other order, although it doesn't
+ 
+
+ align:start position:0%
+in the other order, although it doesn't
+matter.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I want you to imagine I started with
+
+ align:start position:0%
+So, I want you to imagine I started with
+ 
+
+ align:start position:0%
+So, I want you to imagine I started with
+E or maybe somebody else near E. I
+
+ align:start position:0%
+E or maybe somebody else near E. I
+ 
+
+ align:start position:0%
+E or maybe somebody else near E. I
+applied left G inverse and then I
+
+ align:start position:0%
+applied left G inverse and then I
+ 
+
+ align:start position:0%
+applied left G inverse and then I
+applied right G inverse and we're gonna
+
+ align:start position:0%
+applied right G inverse and we're gonna
+ 
+
+ align:start position:0%
+applied right G inverse and we're gonna
+see what happens.
+
+ align:start position:0%
+see what happens.
+ 
+
+ align:start position:0%
+see what happens.
+Okay. So just from the formulas this is
+
+ align:start position:0%
+Okay. So just from the formulas this is
+ 
+
+ align:start position:0%
+Okay. So just from the formulas this is
+right action of G inverse of GH
+
+ align:start position:0%
+right action of G inverse of GH
+ 
+
+ align:start position:0%
+right action of G inverse of GH
+and that's GHG inverse. So actually it's
+
+ align:start position:0%
+and that's GHG inverse. So actually it's
+ 
+
+ align:start position:0%
+and that's GHG inverse. So actually it's
+something natural and important. It's
+
+ align:start position:0%
+something natural and important. It's
+ 
+
+ align:start position:0%
+something natural and important. It's
+conjugating.
+
+ align:start position:0%
+conjugating.
+ 
+
+ align:start position:0%
+conjugating.
+So I'll call this uh C subg of H
+
+ align:start position:0%
+So I'll call this uh C subg of H
+ 
+
+ align:start position:0%
+So I'll call this uh C subg of H
+conjugating by G of H.
+
+ align:start position:0%
+conjugating by G of H.
+ 
+
+ align:start position:0%
+conjugating by G of H.
+Okay, cool. So conjugating by H then
+
+ align:start position:0%
+Okay, cool. So conjugating by H then
+ 
+
+ align:start position:0%
+Okay, cool. So conjugating by H then
+induces a map from the tangent space of
+
+ align:start position:0%
+induces a map from the tangent space of
+ 
+
+ align:start position:0%
+induces a map from the tangent space of
+E to itself.
+
+ align:start position:0%
+E to itself.
+ 
+
+ align:start position:0%
+E to itself.
+Right? So so conjugating by G is a map
+
+ align:start position:0%
+Right? So so conjugating by G is a map
+ 
+
+ align:start position:0%
+Right? So so conjugating by G is a map
+from the group to itself and it sends
+
+ align:start position:0%
+from the group to itself and it sends
+ 
+
+ align:start position:0%
+from the group to itself and it sends
+the identity to the identity and
+
+ align:start position:0%
+the identity to the identity and
+ 
+
+ align:start position:0%
+the identity to the identity and
+therefore it sends the tangent space to
+
+ align:start position:0%
+therefore it sends the tangent space to
+ 
+
+ align:start position:0%
+therefore it sends the tangent space to
+the tangent space. All right. And uh we
+
+ align:start position:0%
+the tangent space. All right. And uh we
+ 
+
+ align:start position:0%
+the tangent space. All right. And uh we
+can see what we we can write we can
+
+ align:start position:0%
+can see what we we can write we can
+ 
+
+ align:start position:0%
+can see what we we can write we can
+write this down and we can see what it
+
+ align:start position:0%
+write this down and we can see what it
+ 
+
+ align:start position:0%
+write this down and we can see what it
+does. Um and
+
+ align:start position:0%
+does. Um and
+ 
+
+ align:start position:0%
+does. Um and
+um if if this thing is distorting the
+
+ align:start position:0%
+um if if this thing is distorting the
+ 
+
+ align:start position:0%
+um if if this thing is distorting the
+geometry it means that this thing was
+
+ align:start position:0%
+geometry it means that this thing was
+ 
+
+ align:start position:0%
+geometry it means that this thing was
+distorting the geometry and in exactly
+
+ align:start position:0%
+distorting the geometry and in exactly
+ 
+
+ align:start position:0%
+distorting the geometry and in exactly
+the same way.
+
+ align:start position:0%
+the same way.
+ 
+
+ align:start position:0%
+the same way.
+So we could say it's you could say more
+
+ align:start position:0%
+So we could say it's you could say more
+ 
+
+ align:start position:0%
+So we could say it's you could say more
+than this but the singular values
+
+ align:start position:0%
+than this but the singular values
+ 
+
+ align:start position:0%
+than this but the singular values
+of LG inverse are equal to the singular
+
+ align:start position:0%
+of LG inverse are equal to the singular
+ 
+
+ align:start position:0%
+of LG inverse are equal to the singular
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+of um CG.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So what you know what they
+
+ align:start position:0%
+All right. So what you know what they
+ 
+
+ align:start position:0%
+All right. So what you know what they
+are depends on G. So I'm going to pick a
+
+ align:start position:0%
+are depends on G. So I'm going to pick a
+ 
+
+ align:start position:0%
+are depends on G. So I'm going to pick a
+nice G and we're actually going to
+
+ align:start position:0%
+nice G and we're actually going to
+ 
+
+ align:start position:0%
+nice G and we're actually going to
+compute them to see how the geometry is
+
+ align:start position:0%
+compute them to see how the geometry is
+ 
+
+ align:start position:0%
+compute them to see how the geometry is
+being distorted. All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So the interesting uh G's are
+
+ align:start position:0%
+right. So the interesting uh G's are
+ 
+
+ align:start position:0%
+right. So the interesting uh G's are
+going to be from those one parameter
+
+ align:start position:0%
+going to be from those one parameter
+ 
+
+ align:start position:0%
+going to be from those one parameter
+subgroups up there. And the one that
+
+ align:start position:0%
+subgroups up there. And the one that
+ 
+
+ align:start position:0%
+subgroups up there. And the one that
+looks up looks the nicest and where this
+
+ align:start position:0%
+looks up looks the nicest and where this
+ 
+
+ align:start position:0%
+looks up looks the nicest and where this
+is calculation is the most important is
+
+ align:start position:0%
+is calculation is the most important is
+ 
+
+ align:start position:0%
+is calculation is the most important is
+for that diagonal matrix A R. So we're
+
+ align:start position:0%
+for that diagonal matrix A R. So we're
+ 
+
+ align:start position:0%
+for that diagonal matrix A R. So we're
+going to compute what that does.
+
+ align:start position:0%
+going to compute what that does.
+ 
+
+ align:start position:0%
+going to compute what that does.
+Okay. So I'm going to look at C A R
+
+ align:start position:0%
+Okay. So I'm going to look at C A R
+ 
+
+ align:start position:0%
+Okay. So I'm going to look at C A R
+that goes from the tangent space to
+
+ align:start position:0%
+that goes from the tangent space to
+ 
+
+ align:start position:0%
+that goes from the tangent space to
+itself.
+
+ align:start position:0%
+itself.
+ 
+
+ align:start position:0%
+itself.
+Um so the tangent space is the set of
+
+ align:start position:0%
+Um so the tangent space is the set of
+ 
+
+ align:start position:0%
+Um so the tangent space is the set of
+matrices a b c d with a + d equals zero.
+
+ align:start position:0%
+matrices a b c d with a + d equals zero.
+ 
+
+ align:start position:0%
+matrices a b c d with a + d equals zero.
+Let's call this matrix m
+
+ align:start position:0%
+Let's call this matrix m
+ 
+
+ align:start position:0%
+Let's call this matrix m
+and we're
+
+ align:start position:0%
+and we're
+ 
+
+ align:start position:0%
+and we're
+so c a r of m is a r m a r inverse.
+
+ align:start position:0%
+so c a r of m is a r m a r inverse.
+ 
+
+ align:start position:0%
+so c a r of m is a r m a r inverse.
+So that's e to the r e to the minus r a
+
+ align:start position:0%
+So that's e to the r e to the minus r a
+ 
+
+ align:start position:0%
+So that's e to the r e to the minus r a
+b c d e to the minus r e to the r.
+
+ align:start position:0%
+b c d e to the minus r e to the r.
+ 
+
+ align:start position:0%
+b c d e to the minus r e to the r.
+Right? So this is a sub r. That's just
+
+ align:start position:0%
+Right? So this is a sub r. That's just
+ 
+
+ align:start position:0%
+Right? So this is a sub r. That's just
+the definition. This is a sub r inverse.
+
+ align:start position:0%
+the definition. This is a sub r inverse.
+ 
+
+ align:start position:0%
+the definition. This is a sub r inverse.
+So I switched the minus signs.
+
+ align:start position:0%
+So I switched the minus signs.
+ 
+
+ align:start position:0%
+So I switched the minus signs.
+Okay? So
+
+ align:start position:0%
+Okay? So
+ 
+
+ align:start position:0%
+Okay? So
+I did this very carefully. Uh it's not
+
+ align:start position:0%
+I did this very carefully. Uh it's not
+ 
+
+ align:start position:0%
+I did this very carefully. Uh it's not
+super instructive to watch me do it very
+
+ align:start position:0%
+super instructive to watch me do it very
+ 
+
+ align:start position:0%
+super instructive to watch me do it very
+carefully. So I'm just going to write
+
+ align:start position:0%
+carefully. So I'm just going to write
+ 
+
+ align:start position:0%
+carefully. So I'm just going to write
+down the answer.
+
+ align:start position:0%
+down the answer.
+ 
+
+ align:start position:0%
+down the answer.
+It's a d e 2 r b eus 2 r c.
+
+ align:start position:0%
+It's a d e 2 r b eus 2 r c.
+ 
+
+ align:start position:0%
+It's a d e 2 r b eus 2 r c.
+So this conjugation what it does is it
+
+ align:start position:0%
+So this conjugation what it does is it
+ 
+
+ align:start position:0%
+So this conjugation what it does is it
+doesn't change the diagonal. It
+
+ align:start position:0%
+doesn't change the diagonal. It
+ 
+
+ align:start position:0%
+doesn't change the diagonal. It
+magnifies
+
+ align:start position:0%
+magnifies
+ 
+
+ align:start position:0%
+magnifies
+this component and it uh demagnifies
+
+ align:start position:0%
+this component and it uh demagnifies
+ 
+
+ align:start position:0%
+this component and it uh demagnifies
+that component. So that happens to be
+
+ align:start position:0%
+that component. So that happens to be
+ 
+
+ align:start position:0%
+that component. So that happens to be
+something we can describe really nicely
+
+ align:start position:0%
+something we can describe really nicely
+ 
+
+ align:start position:0%
+something we can describe really nicely
+in the orthonormal basis that I picked.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So,
+
+ align:start position:0%
+All right. So,
+ 
+
+ align:start position:0%
+All right. So,
+C A R of U.
+
+ align:start position:0%
+C A R of U.
+ 
+
+ align:start position:0%
+C A R of U.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+is E 2R U.
+
+ align:start position:0%
+is E 2R U.
+ 
+
+ align:start position:0%
+is E 2R U.
+C A R of utilda is E to the minus 2 R U
+
+ align:start position:0%
+C A R of utilda is E to the minus 2 R U
+ 
+
+ align:start position:0%
+C A R of utilda is E to the minus 2 R U
+tilda and C A R D is D.
+
+ align:start position:0%
+tilda and C A R D is D.
+ 
+
+ align:start position:0%
+tilda and C A R D is D.
+This conjugation behaves really nicely
+
+ align:start position:0%
+This conjugation behaves really nicely
+ 
+
+ align:start position:0%
+This conjugation behaves really nicely
+in this basis. But you can see that it
+
+ align:start position:0%
+in this basis. But you can see that it
+ 
+
+ align:start position:0%
+in this basis. But you can see that it
+does not preserve the metric. It
+
+ align:start position:0%
+does not preserve the metric. It
+ 
+
+ align:start position:0%
+does not preserve the metric. It
+stretches that one. it compresses that
+
+ align:start position:0%
+stretches that one. it compresses that
+ 
+
+ align:start position:0%
+stretches that one. it compresses that
+one and it preserves that one.
+
+ align:start position:0%
+one and it preserves that one.
+ 
+
+ align:start position:0%
+one and it preserves that one.
+Okay. So the conclusion from this is
+
+ align:start position:0%
+Okay. So the conclusion from this is
+ 
+
+ align:start position:0%
+Okay. So the conclusion from this is
+that l a r inverse
+
+ align:start position:0%
+that l a r inverse
+ 
+
+ align:start position:0%
+that l a r inverse
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+of u
+
+ align:start position:0%
+of u
+ 
+
+ align:start position:0%
+of u
+the length of that is e 2r
+
+ align:start position:0%
+the length of that is e 2r
+ 
+
+ align:start position:0%
+the length of that is e 2r
+l a r inverse of u tilda has length e to
+
+ align:start position:0%
+l a r inverse of u tilda has length e to
+ 
+
+ align:start position:0%
+l a r inverse of u tilda has length e to
+the minus 2r
+
+ align:start position:0%
+the minus 2r
+ 
+
+ align:start position:0%
+the minus 2r
+l a r inverse of d has length one and uh
+
+ align:start position:0%
+l a r inverse of d has length one and uh
+ 
+
+ align:start position:0%
+l a r inverse of d has length one and uh
+it also preserved angles right so We
+
+ align:start position:0%
+it also preserved angles right so We
+ 
+
+ align:start position:0%
+it also preserved angles right so We
+just stretched things but we didn't tilt
+
+ align:start position:0%
+just stretched things but we didn't tilt
+ 
+
+ align:start position:0%
+just stretched things but we didn't tilt
+anything. So
+
+ align:start position:0%
+anything. So
+ 
+
+ align:start position:0%
+anything. So
+l a r inverse of u of ut tilda and of d
+
+ align:start position:0%
+l a r inverse of u of ut tilda and of d
+ 
+
+ align:start position:0%
+l a r inverse of u of ut tilda and of d
+are orthogonal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this describes how the left action by
+
+ align:start position:0%
+So this describes how the left action by
+ 
+
+ align:start position:0%
+So this describes how the left action by
+this matrix is distorting the geometry
+
+ align:start position:0%
+this matrix is distorting the geometry
+ 
+
+ align:start position:0%
+this matrix is distorting the geometry
+of the space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And we also can make some kind of
+
+ align:start position:0%
+Okay. And we also can make some kind of
+ 
+
+ align:start position:0%
+Okay. And we also can make some kind of
+picture. Um
+
+ align:start position:0%
+picture. Um
+ 
+
+ align:start position:0%
+picture. Um
+so suppose this is a quote unquote cube
+
+ align:start position:0%
+so suppose this is a quote unquote cube
+ 
+
+ align:start position:0%
+so suppose this is a quote unquote cube
+in G. Um where this is the
+
+ align:start position:0%
+in G. Um where this is the
+ 
+
+ align:start position:0%
+in G. Um where this is the
+U direction this is the utilda direction
+
+ align:start position:0%
+U direction this is the utilda direction
+ 
+
+ align:start position:0%
+U direction this is the utilda direction
+and the direction into the board is the
+
+ align:start position:0%
+and the direction into the board is the
+ 
+
+ align:start position:0%
+and the direction into the board is the
+D direction. So what will happen to it
+
+ align:start position:0%
+D direction. So what will happen to it
+ 
+
+ align:start position:0%
+D direction. So what will happen to it
+when we do this? Um the U direction gets
+
+ align:start position:0%
+when we do this? Um the U direction gets
+ 
+
+ align:start position:0%
+when we do this? Um the U direction gets
+really long the utild direction gets
+
+ align:start position:0%
+really long the utild direction gets
+ 
+
+ align:start position:0%
+really long the utild direction gets
+really short other direction is
+
+ align:start position:0%
+really short other direction is
+ 
+
+ align:start position:0%
+really short other direction is
+preserved. So it looks kind of like
+
+ align:start position:0%
+preserved. So it looks kind of like
+ 
+
+ align:start position:0%
+preserved. So it looks kind of like
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um, one thing that you can notice from
+
+ align:start position:0%
+Um, one thing that you can notice from
+ 
+
+ align:start position:0%
+Um, one thing that you can notice from
+the picture and from the calculation is
+
+ align:start position:0%
+the picture and from the calculation is
+ 
+
+ align:start position:0%
+the picture and from the calculation is
+that um, while L inverse distorts
+
+ align:start position:0%
+that um, while L inverse distorts
+ 
+
+ align:start position:0%
+that um, while L inverse distorts
+lengths, distorts the metric,
+
+ align:start position:0%
+lengths, distorts the metric,
+ 
+
+ align:start position:0%
+lengths, distorts the metric,
+it nevertheless preserves the volume.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's how the left action uh
+
+ align:start position:0%
+Okay. So that's how the left action uh
+ 
+
+ align:start position:0%
+Okay. So that's how the left action uh
+distorts the geometry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And we also have a left action.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of G on G mod gamma,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And so how does that work? Um
+
+ align:start position:0%
+right? And so how does that work? Um
+ 
+
+ align:start position:0%
+right? And so how does that work? Um
+well, LG of H gamma is just G inverse H
+
+ align:start position:0%
+well, LG of H gamma is just G inverse H
+ 
+
+ align:start position:0%
+well, LG of H gamma is just G inverse H
+gamma
+
+ align:start position:0%
+gamma
+ 
+
+ align:start position:0%
+gamma
+because the gamma is on the right and
+
+ align:start position:0%
+because the gamma is on the right and
+ 
+
+ align:start position:0%
+because the gamma is on the right and
+this guy is on the left. They sort of
+
+ align:start position:0%
+this guy is on the left. They sort of
+ 
+
+ align:start position:0%
+this guy is on the left. They sort of
+don't interfere with each other. And so
+
+ align:start position:0%
+don't interfere with each other. And so
+ 
+
+ align:start position:0%
+don't interfere with each other. And so
+this is an actual group action.
+
+ align:start position:0%
+this is an actual group action.
+ 
+
+ align:start position:0%
+this is an actual group action.
+Um so LG maps
+
+ align:start position:0%
+Um so LG maps
+ 
+
+ align:start position:0%
+Um so LG maps
+G mod gamma to itself
+
+ align:start position:0%
+G mod gamma to itself
+ 
+
+ align:start position:0%
+G mod gamma to itself
+and it is a bjection.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It distorts the metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it preserves
+
+ align:start position:0%
+but it preserves
+ 
+
+ align:start position:0%
+but it preserves
+the ball.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And maybe I should say we just
+
+ align:start position:0%
+Okay. And maybe I should say we just
+ 
+
+ align:start position:0%
+Okay. And maybe I should say we just
+computed this carefully for a particular
+
+ align:start position:0%
+computed this carefully for a particular
+ 
+
+ align:start position:0%
+computed this carefully for a particular
+element G which is these diagonal
+
+ align:start position:0%
+element G which is these diagonal
+ 
+
+ align:start position:0%
+element G which is these diagonal
+elements. You could take any G there
+
+ align:start position:0%
+elements. You could take any G there
+ 
+
+ align:start position:0%
+elements. You could take any G there
+don't doesn't have to be diagonal. It
+
+ align:start position:0%
+don't doesn't have to be diagonal. It
+ 
+
+ align:start position:0%
+don't doesn't have to be diagonal. It
+will distort the metric in some
+
+ align:start position:0%
+will distort the metric in some
+ 
+
+ align:start position:0%
+will distort the metric in some
+different way. Every G is different but
+
+ align:start position:0%
+different way. Every G is different but
+ 
+
+ align:start position:0%
+different way. Every G is different but
+they all preserve the volume. We didn't
+
+ align:start position:0%
+they all preserve the volume. We didn't
+ 
+
+ align:start position:0%
+they all preserve the volume. We didn't
+really prove that because I just did one
+
+ align:start position:0%
+really prove that because I just did one
+ 
+
+ align:start position:0%
+really prove that because I just did one
+example but it's true.
+
+ align:start position:0%
+example but it's true.
+ 
+
+ align:start position:0%
+example but it's true.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Are you able to show that by showing
+
+ align:start position:0%
+>> Are you able to show that by showing
+ 
+
+ align:start position:0%
+>> Are you able to show that by showing
+like that in a second? uh the u u of t
+
+ align:start position:0%
+like that in a second? uh the u u of t
+ 
+
+ align:start position:0%
+like that in a second? uh the u u of t
+one parameter subgroup um does it change
+
+ align:start position:0%
+one parameter subgroup um does it change
+ 
+
+ align:start position:0%
+one parameter subgroup um does it change
+the volume and like do those two two one
+
+ align:start position:0%
+the volume and like do those two two one
+ 
+
+ align:start position:0%
+the volume and like do those two two one
+prime subgroups generate a g of pump
+
+ align:start position:0%
+prime subgroups generate a g of pump
+ 
+
+ align:start position:0%
+prime subgroups generate a g of pump
+>> yeah so the question was if we wanted to
+
+ align:start position:0%
+>> yeah so the question was if we wanted to
+ 
+
+ align:start position:0%
+>> yeah so the question was if we wanted to
+to check that it preserve that that
+
+ align:start position:0%
+to check that it preserve that that
+ 
+
+ align:start position:0%
+to check that it preserve that that
+every G preserves the volume it would be
+
+ align:start position:0%
+every G preserves the volume it would be
+ 
+
+ align:start position:0%
+every G preserves the volume it would be
+enough to check a few G's that generate
+
+ align:start position:0%
+enough to check a few G's that generate
+ 
+
+ align:start position:0%
+enough to check a few G's that generate
+it um and um yeah so so we could if we
+
+ align:start position:0%
+it um and um yeah so so we could if we
+ 
+
+ align:start position:0%
+it um and um yeah so so we could if we
+did the computation with the potent one
+
+ align:start position:0%
+did the computation with the potent one
+ 
+
+ align:start position:0%
+did the computation with the potent one
+that would basically finish the job okay
+
+ align:start position:0%
+that would basically finish the job okay
+ 
+
+ align:start position:0%
+that would basically finish the job okay
+so it's not that difficult um we also
+
+ align:start position:0%
+so it's not that difficult um we also
+ 
+
+ align:start position:0%
+so it's not that difficult um we also
+could just describe the G as you know
+
+ align:start position:0%
+could just describe the G as you know
+ 
+
+ align:start position:0%
+could just describe the G as you know
+ABC D
+
+ align:start position:0%
+ABC D
+ 
+
+ align:start position:0%
+ABC D
+um and and then the computation a little
+
+ align:start position:0%
+um and and then the computation a little
+ 
+
+ align:start position:0%
+um and and then the computation a little
+messy but could just check once and for
+
+ align:start position:0%
+messy but could just check once and for
+ 
+
+ align:start position:0%
+messy but could just check once and for
+all. There's probably a better way of
+
+ align:start position:0%
+all. There's probably a better way of
+ 
+
+ align:start position:0%
+all. There's probably a better way of
+doing it but it's not my part of that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now we can say um
+
+ align:start position:0%
+Okay. So now we can say um
+ 
+
+ align:start position:0%
+Okay. So now we can say um
+all right.
+
+ align:start position:0%
+all right.
+ 
+
+ align:start position:0%
+all right.
+So now important and interesting part of
+
+ align:start position:0%
+So now important and interesting part of
+ 
+
+ align:start position:0%
+So now important and interesting part of
+this story is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what is the difference between the
+
+ align:start position:0%
+what is the difference between the
+ 
+
+ align:start position:0%
+what is the difference between the
+unitary ones and the diagonal ones?
+
+ align:start position:0%
+unitary ones and the diagonal ones?
+ 
+
+ align:start position:0%
+unitary ones and the diagonal ones?
+And there are many different answers to
+
+ align:start position:0%
+And there are many different answers to
+ 
+
+ align:start position:0%
+And there are many different answers to
+this. Um, we could come back to it
+
+ align:start position:0%
+this. Um, we could come back to it
+ 
+
+ align:start position:0%
+this. Um, we could come back to it
+multiple times,
+
+ align:start position:0%
+multiple times,
+ 
+
+ align:start position:0%
+multiple times,
+but I'm gonna mention one way of looking
+
+ align:start position:0%
+but I'm gonna mention one way of looking
+ 
+
+ align:start position:0%
+but I'm gonna mention one way of looking
+at it which will start to get us to the
+
+ align:start position:0%
+at it which will start to get us to the
+ 
+
+ align:start position:0%
+at it which will start to get us to the
+projection theory.
+
+ align:start position:0%
+projection theory.
+ 
+
+ align:start position:0%
+projection theory.
+Um, so there's a special feature of
+
+ align:start position:0%
+Um, so there's a special feature of
+ 
+
+ align:start position:0%
+Um, so there's a special feature of
+unitary matrices that we saw also maybe
+
+ align:start position:0%
+unitary matrices that we saw also maybe
+ 
+
+ align:start position:0%
+unitary matrices that we saw also maybe
+by coincidence, but it also came up when
+
+ align:start position:0%
+by coincidence, but it also came up when
+ 
+
+ align:start position:0%
+by coincidence, but it also came up when
+we were talking about SL2 of FP, which
+
+ align:start position:0%
+we were talking about SL2 of FP, which
+ 
+
+ align:start position:0%
+we were talking about SL2 of FP, which
+what we saw there basically is that
+
+ align:start position:0%
+what we saw there basically is that
+ 
+
+ align:start position:0%
+what we saw there basically is that
+something cool happens when you
+
+ align:start position:0%
+something cool happens when you
+ 
+
+ align:start position:0%
+something cool happens when you
+conjugate a unitary matrix by a diagonal
+
+ align:start position:0%
+conjugate a unitary matrix by a diagonal
+ 
+
+ align:start position:0%
+conjugate a unitary matrix by a diagonal
+matrix. And that that is a special
+
+ align:start position:0%
+matrix. And that that is a special
+ 
+
+ align:start position:0%
+matrix. And that that is a special
+feature of unitary matrices and it
+
+ align:start position:0%
+feature of unitary matrices and it
+ 
+
+ align:start position:0%
+feature of unitary matrices and it
+really helps to understand.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So what is special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+unitary
+
+ align:start position:0%
+unitary
+ 
+
+ align:start position:0%
+unitary
+matrices?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So there's a computation that if I
+
+ align:start position:0%
+Okay. So there's a computation that if I
+ 
+
+ align:start position:0%
+Okay. So there's a computation that if I
+take a unitary matrix and I conjugate it
+
+ align:start position:0%
+take a unitary matrix and I conjugate it
+ 
+
+ align:start position:0%
+take a unitary matrix and I conjugate it
+by a diagonal matrix. So I have e to the
+
+ align:start position:0%
+by a diagonal matrix. So I have e to the
+ 
+
+ align:start position:0%
+by a diagonal matrix. So I have e to the
+r e to the minus r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potent.
+
+ align:start position:0%
+potent.
+ 
+
+ align:start position:0%
+potent.
+>> Uni potent. Yeah, thanks.
+
+ align:start position:0%
+>> Uni potent. Yeah, thanks.
+ 
+
+ align:start position:0%
+>> Uni potent. Yeah, thanks.
+>> Yes, thank you. Uni potent.
+
+ align:start position:0%
+>> Yes, thank you. Uni potent.
+ 
+
+ align:start position:0%
+>> Yes, thank you. Uni potent.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so if you multiply this out, you get
+
+ align:start position:0%
+so if you multiply this out, you get
+ 
+
+ align:start position:0%
+so if you multiply this out, you get
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+So if you're interested in a uni potent
+
+ align:start position:0%
+So if you're interested in a uni potent
+ 
+
+ align:start position:0%
+So if you're interested in a uni potent
+matrix UT where this T is really large,
+
+ align:start position:0%
+matrix UT where this T is really large,
+ 
+
+ align:start position:0%
+matrix UT where this T is really large,
+you can get at it by starting with U1
+
+ align:start position:0%
+you can get at it by starting with U1
+ 
+
+ align:start position:0%
+you can get at it by starting with U1
+and conjugating it by one of these
+
+ align:start position:0%
+and conjugating it by one of these
+ 
+
+ align:start position:0%
+and conjugating it by one of these
+diagonal matrices.
+
+ align:start position:0%
+diagonal matrices.
+ 
+
+ align:start position:0%
+diagonal matrices.
+Um so let's let's say U0 T. This is a
+
+ align:start position:0%
+Um so let's let's say U0 T. This is a
+ 
+
+ align:start position:0%
+Um so let's let's say U0 T. This is a
+set of unitary matrices. This is UT
+
+ align:start position:0%
+set of unitary matrices. This is UT
+ 
+
+ align:start position:0%
+set of unitary matrices. This is UT
+t goes from zero to t. And so to
+
+ align:start position:0%
+t goes from zero to t. And so to
+ 
+
+ align:start position:0%
+t goes from zero to t. And so to
+understand an orbit we you know our goal
+
+ align:start position:0%
+understand an orbit we you know our goal
+ 
+
+ align:start position:0%
+understand an orbit we you know our goal
+is to understand
+
+ align:start position:0%
+is to understand
+ 
+
+ align:start position:0%
+is to understand
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+u 0t of x where t is large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and because of this slick little formula
+
+ align:start position:0%
+and because of this slick little formula
+ 
+
+ align:start position:0%
+and because of this slick little formula
+we can write u0 t x.
+
+ align:start position:0%
+we can write u0 t x.
+ 
+
+ align:start position:0%
+we can write u0 t x.
+So let's let's say
+
+ align:start position:0%
+So let's let's say
+ 
+
+ align:start position:0%
+So let's let's say
+um we can write it as
+
+ align:start position:0%
+um we can write it as
+ 
+
+ align:start position:0%
+um we can write it as
+a r
+
+ align:start position:0%
+a r
+ 
+
+ align:start position:0%
+a r
+u01
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a - r of x
+
+ align:start position:0%
+a - r of x
+ 
+
+ align:start position:0%
+a - r of x
+where e 2r t.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Why is this helpful? So this here is
+
+ align:start position:0%
+Why is this helpful? So this here is
+ 
+
+ align:start position:0%
+Why is this helpful? So this here is
+just some point in uh in G mod gamma.
+
+ align:start position:0%
+just some point in uh in G mod gamma.
+ 
+
+ align:start position:0%
+just some point in uh in G mod gamma.
+It's not the point we started with. It's
+
+ align:start position:0%
+It's not the point we started with. It's
+ 
+
+ align:start position:0%
+It's not the point we started with. It's
+some other point but it's just a point.
+
+ align:start position:0%
+some other point but it's just a point.
+ 
+
+ align:start position:0%
+some other point but it's just a point.
+This here is a short unitary orbit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um short unitary orbit isn't so
+
+ align:start position:0%
+Um short unitary orbit isn't so
+ 
+
+ align:start position:0%
+Um short unitary orbit isn't so
+intimidating to to draw. And then all
+
+ align:start position:0%
+intimidating to to draw. And then all
+ 
+
+ align:start position:0%
+intimidating to to draw. And then all
+the action is here. And the question is
+
+ align:start position:0%
+the action is here. And the question is
+ 
+
+ align:start position:0%
+the action is here. And the question is
+what does this uh map do to a short
+
+ align:start position:0%
+what does this uh map do to a short
+ 
+
+ align:start position:0%
+what does this uh map do to a short
+unitary orbit?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so if we make a picture,
+
+ align:start position:0%
+Okay, so if we make a picture,
+ 
+
+ align:start position:0%
+Okay, so if we make a picture,
+here's our G mod gamma. Here's our new
+
+ align:start position:0%
+here's our G mod gamma. Here's our new
+ 
+
+ align:start position:0%
+here's our G mod gamma. Here's our new
+starting point a minus rx.
+
+ align:start position:0%
+starting point a minus rx.
+ 
+
+ align:start position:0%
+starting point a minus rx.
+Here's our orbit. It's not very long. It
+
+ align:start position:0%
+Here's our orbit. It's not very long. It
+ 
+
+ align:start position:0%
+Here's our orbit. It's not very long. It
+doesn't wrap around yet, so it's not
+
+ align:start position:0%
+doesn't wrap around yet, so it's not
+ 
+
+ align:start position:0%
+doesn't wrap around yet, so it's not
+that intimidating. That's um this guy
+
+ align:start position:0%
+that intimidating. That's um this guy
+ 
+
+ align:start position:0%
+that intimidating. That's um this guy
+short unitary orbit. Okay. And now we're
+
+ align:start position:0%
+short unitary orbit. Okay. And now we're
+ 
+
+ align:start position:0%
+short unitary orbit. Okay. And now we're
+going to take this map of Gamma to
+
+ align:start position:0%
+going to take this map of Gamma to
+ 
+
+ align:start position:0%
+going to take this map of Gamma to
+itself and we're going to apply it and
+
+ align:start position:0%
+itself and we're going to apply it and
+ 
+
+ align:start position:0%
+itself and we're going to apply it and
+we want to see what happens to this blue
+
+ align:start position:0%
+we want to see what happens to this blue
+ 
+
+ align:start position:0%
+we want to see what happens to this blue
+thing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Again, uni potent. Thanks short.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thanks.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And we can also make a remark a r
+
+ align:start position:0%
+Okay. And we can also make a remark a r
+ 
+
+ align:start position:0%
+Okay. And we can also make a remark a r
+is a subgroup. So a r is like a1 to the
+
+ align:start position:0%
+is a subgroup. So a r is like a1 to the
+ 
+
+ align:start position:0%
+is a subgroup. So a r is like a1 to the
+r or a little r to the big r over little
+
+ align:start position:0%
+r or a little r to the big r over little
+ 
+
+ align:start position:0%
+r or a little r to the big r over little
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+big r little over r is a natural number.
+
+ align:start position:0%
+big r little over r is a natural number.
+ 
+
+ align:start position:0%
+big r little over r is a natural number.
+So we don't have to do this all at once.
+
+ align:start position:0%
+So we don't have to do this all at once.
+ 
+
+ align:start position:0%
+So we don't have to do this all at once.
+We could take a less dramatic map of gi
+
+ align:start position:0%
+We could take a less dramatic map of gi
+ 
+
+ align:start position:0%
+We could take a less dramatic map of gi
+gamma to itself and we repeat that over
+
+ align:start position:0%
+gamma to itself and we repeat that over
+ 
+
+ align:start position:0%
+gamma to itself and we repeat that over
+and over again. We want to see what
+
+ align:start position:0%
+and over again. We want to see what
+ 
+
+ align:start position:0%
+and over again. We want to see what
+happens to this thing. Right?
+
+ align:start position:0%
+happens to this thing. Right?
+ 
+
+ align:start position:0%
+happens to this thing. Right?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. So we are led to try so we led to
+
+ align:start position:0%
+Okay. So we are led to try so we led to
+ 
+
+ align:start position:0%
+Okay. So we are led to try so we led to
+a goal which is to try to understand
+
+ align:start position:0%
+a goal which is to try to understand
+ 
+
+ align:start position:0%
+a goal which is to try to understand
+and visualize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the action of a little r and ga
+
+ align:start position:0%
+the action of a little r and ga
+ 
+
+ align:start position:0%
+the action of a little r and ga
+and if we understand that really well we
+
+ align:start position:0%
+and if we understand that really well we
+ 
+
+ align:start position:0%
+and if we understand that really well we
+should be able to understand this orbit.
+
+ align:start position:0%
+should be able to understand this orbit.
+ 
+
+ align:start position:0%
+should be able to understand this orbit.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, how might we try to get a
+
+ align:start position:0%
+All right. So, how might we try to get a
+ 
+
+ align:start position:0%
+All right. So, how might we try to get a
+handle on this? Let's look at a
+
+ align:start position:0%
+handle on this? Let's look at a
+ 
+
+ align:start position:0%
+handle on this? Let's look at a
+fundamental domain. So, f is a
+
+ align:start position:0%
+fundamental domain. So, f is a
+ 
+
+ align:start position:0%
+fundamental domain. So, f is a
+fundamental domain of gamma.
+
+ align:start position:0%
+fundamental domain of gamma.
+ 
+
+ align:start position:0%
+fundamental domain of gamma.
+So, f is a subset just of g. And I'll
+
+ align:start position:0%
+So, f is a subset just of g. And I'll
+ 
+
+ align:start position:0%
+So, f is a subset just of g. And I'll
+draw it as a cube. It's not literally a
+
+ align:start position:0%
+draw it as a cube. It's not literally a
+ 
+
+ align:start position:0%
+draw it as a cube. It's not literally a
+cube.
+
+ align:start position:0%
+cube.
+ 
+
+ align:start position:0%
+cube.
+um uh god gamma is not compact. So f
+
+ align:start position:0%
+um uh god gamma is not compact. So f
+ 
+
+ align:start position:0%
+um uh god gamma is not compact. So f
+cannot be compact. So it should have
+
+ align:start position:0%
+cannot be compact. So it should have
+ 
+
+ align:start position:0%
+cannot be compact. So it should have
+like a little tail that's going off to
+
+ align:start position:0%
+like a little tail that's going off to
+ 
+
+ align:start position:0%
+like a little tail that's going off to
+infinity. Um but for what I'm about to
+
+ align:start position:0%
+infinity. Um but for what I'm about to
+ 
+
+ align:start position:0%
+infinity. Um but for what I'm about to
+say that's not super important.
+
+ align:start position:0%
+say that's not super important.
+ 
+
+ align:start position:0%
+say that's not super important.
+And actually by the way the whole story
+
+ align:start position:0%
+And actually by the way the whole story
+ 
+
+ align:start position:0%
+And actually by the way the whole story
+also makes sense for gamas that are
+
+ align:start position:0%
+also makes sense for gamas that are
+ 
+
+ align:start position:0%
+also makes sense for gamas that are
+co-compact and then you would this
+
+ align:start position:0%
+co-compact and then you would this
+ 
+
+ align:start position:0%
+co-compact and then you would this
+picture would be better. Okay. So now uh
+
+ align:start position:0%
+picture would be better. Okay. So now uh
+ 
+
+ align:start position:0%
+picture would be better. Okay. So now uh
+we'd like to understand what a does. So
+
+ align:start position:0%
+we'd like to understand what a does. So
+ 
+
+ align:start position:0%
+we'd like to understand what a does. So
+the first step is I'm going to apply AR.
+
+ align:start position:0%
+the first step is I'm going to apply AR.
+ 
+
+ align:start position:0%
+the first step is I'm going to apply AR.
+And we just thought about what AR does
+
+ align:start position:0%
+And we just thought about what AR does
+ 
+
+ align:start position:0%
+And we just thought about what AR does
+geometrically, how it distorts the
+
+ align:start position:0%
+geometrically, how it distorts the
+ 
+
+ align:start position:0%
+geometrically, how it distorts the
+geometry. Um we were looking at what it
+
+ align:start position:0%
+geometry. Um we were looking at what it
+ 
+
+ align:start position:0%
+geometry. Um we were looking at what it
+does to the metric, but it's very
+
+ align:start position:0%
+does to the metric, but it's very
+ 
+
+ align:start position:0%
+does to the metric, but it's very
+similar to what it does to like a unit
+
+ align:start position:0%
+similar to what it does to like a unit
+ 
+
+ align:start position:0%
+similar to what it does to like a unit
+cube. Um so this thing um is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a r of of um of f which is
+
+ align:start position:0%
+so this is a r of of um of f which is
+ 
+
+ align:start position:0%
+so this is a r of of um of f which is
+still sitting in the group g. It got
+
+ align:start position:0%
+still sitting in the group g. It got
+ 
+
+ align:start position:0%
+still sitting in the group g. It got
+longer in one way shorter in another
+
+ align:start position:0%
+longer in one way shorter in another
+ 
+
+ align:start position:0%
+longer in one way shorter in another
+way. The real thing would have more
+
+ align:start position:0%
+way. The real thing would have more
+ 
+
+ align:start position:0%
+way. The real thing would have more
+dimensions than this but just to give
+
+ align:start position:0%
+dimensions than this but just to give
+ 
+
+ align:start position:0%
+dimensions than this but just to give
+the idea.
+
+ align:start position:0%
+the idea.
+ 
+
+ align:start position:0%
+the idea.
+Okay. Now the next thing that happens is
+
+ align:start position:0%
+Okay. Now the next thing that happens is
+ 
+
+ align:start position:0%
+Okay. Now the next thing that happens is
+we have to apply the quotient map. So pi
+
+ align:start position:0%
+we have to apply the quotient map. So pi
+ 
+
+ align:start position:0%
+we have to apply the quotient map. So pi
+is the map from G to G mod gamma.
+
+ align:start position:0%
+is the map from G to G mod gamma.
+ 
+
+ align:start position:0%
+is the map from G to G mod gamma.
+Um and when we do that I'll visualize G
+
+ align:start position:0%
+Um and when we do that I'll visualize G
+ 
+
+ align:start position:0%
+Um and when we do that I'll visualize G
+mod gamma again as this fundamental
+
+ align:start position:0%
+mod gamma again as this fundamental
+ 
+
+ align:start position:0%
+mod gamma again as this fundamental
+domain. And what happens is that this
+
+ align:start position:0%
+domain. And what happens is that this
+ 
+
+ align:start position:0%
+domain. And what happens is that this
+thing is going to kind of wrap around
+
+ align:start position:0%
+thing is going to kind of wrap around
+ 
+
+ align:start position:0%
+thing is going to kind of wrap around
+the fundamental domain.
+
+ align:start position:0%
+the fundamental domain.
+ 
+
+ align:start position:0%
+the fundamental domain.
+Okay. So it will look something like
+
+ align:start position:0%
+Okay. So it will look something like
+ 
+
+ align:start position:0%
+Okay. So it will look something like
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+There it'll go in there. Um
+
+ align:start position:0%
+There it'll go in there. Um
+ 
+
+ align:start position:0%
+There it'll go in there. Um
+okay it's very difficult to draw this
+
+ align:start position:0%
+okay it's very difficult to draw this
+ 
+
+ align:start position:0%
+okay it's very difficult to draw this
+well um this map from the fundamental
+
+ align:start position:0%
+well um this map from the fundamental
+ 
+
+ align:start position:0%
+well um this map from the fundamental
+domain to itself is going to be of
+
+ align:start position:0%
+domain to itself is going to be of
+ 
+
+ align:start position:0%
+domain to itself is going to be of
+ejection right so somehow this is going
+
+ align:start position:0%
+ejection right so somehow this is going
+ 
+
+ align:start position:0%
+ejection right so somehow this is going
+to wrap around it's going to cover every
+
+ align:start position:0%
+to wrap around it's going to cover every
+ 
+
+ align:start position:0%
+to wrap around it's going to cover every
+point exactly once uh it's like a some
+
+ align:start position:0%
+point exactly once uh it's like a some
+ 
+
+ align:start position:0%
+point exactly once uh it's like a some
+sort of beautiful jigsaw puzzle I don't
+
+ align:start position:0%
+sort of beautiful jigsaw puzzle I don't
+ 
+
+ align:start position:0%
+sort of beautiful jigsaw puzzle I don't
+know how to draw that so I'll just do
+
+ align:start position:0%
+know how to draw that so I'll just do
+ 
+
+ align:start position:0%
+know how to draw that so I'll just do
+I'll just have this come out here and
+
+ align:start position:0%
+I'll just have this come out here and
+ 
+
+ align:start position:0%
+I'll just have this come out here and
+I'll do sort of a dot dot dot
+
+ align:start position:0%
+I'll do sort of a dot dot dot
+ 
+
+ align:start position:0%
+I'll do sort of a dot dot dot
+okay and then I don't know if We were
+
+ align:start position:0%
+okay and then I don't know if We were
+ 
+
+ align:start position:0%
+okay and then I don't know if We were
+visualizing if we had something of
+
+ align:start position:0%
+visualizing if we had something of
+ 
+
+ align:start position:0%
+visualizing if we had something of
+interest eventually it would be some
+
+ align:start position:0%
+interest eventually it would be some
+ 
+
+ align:start position:0%
+interest eventually it would be some
+unipotent orbits but maybe initially
+
+ align:start position:0%
+unipotent orbits but maybe initially
+ 
+
+ align:start position:0%
+unipotent orbits but maybe initially
+we're interested in what happens to
+
+ align:start position:0%
+we're interested in what happens to
+ 
+
+ align:start position:0%
+we're interested in what happens to
+that. So in the first step
+
+ align:start position:0%
+that. So in the first step
+ 
+
+ align:start position:0%
+that. So in the first step
+it did this
+
+ align:start position:0%
+it did this
+ 
+
+ align:start position:0%
+it did this
+and then in the next step we see this
+
+ align:start position:0%
+and then in the next step we see this
+ 
+
+ align:start position:0%
+and then in the next step we see this
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+somewhere over here we see this. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Cool. Um all right. So
+
+ align:start position:0%
+Cool. Um all right. So
+ 
+
+ align:start position:0%
+Cool. Um all right. So
+>> yeah,
+
+ align:start position:0%
+>> yeah,
+ 
+
+ align:start position:0%
+>> yeah,
+>> why does the map have to be a bjection?
+
+ align:start position:0%
+>> why does the map have to be a bjection?
+ 
+
+ align:start position:0%
+>> why does the map have to be a bjection?
+Like why can't the projection map sort
+
+ align:start position:0%
+Like why can't the projection map sort
+ 
+
+ align:start position:0%
+Like why can't the projection map sort
+of not be injective?
+
+ align:start position:0%
+of not be injective?
+ 
+
+ align:start position:0%
+of not be injective?
+>> Yeah. So the question is um why is this
+
+ align:start position:0%
+>> Yeah. So the question is um why is this
+ 
+
+ align:start position:0%
+>> Yeah. So the question is um why is this
+map a bjection?
+
+ align:start position:0%
+map a bjection?
+ 
+
+ align:start position:0%
+map a bjection?
+Um so we were saying so this this uh I
+
+ align:start position:0%
+Um so we were saying so this this uh I
+ 
+
+ align:start position:0%
+Um so we were saying so this this uh I
+guess is actually there um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um right? So we said earlier that the
+
+ align:start position:0%
+um right? So we said earlier that the
+ 
+
+ align:start position:0%
+um right? So we said earlier that the
+left action of G god gamma goes to
+
+ align:start position:0%
+left action of G god gamma goes to
+ 
+
+ align:start position:0%
+left action of G god gamma goes to
+itself as a bjection
+
+ align:start position:0%
+itself as a bjection
+ 
+
+ align:start position:0%
+itself as a bjection
+and if we believe that then if we start
+
+ align:start position:0%
+and if we believe that then if we start
+ 
+
+ align:start position:0%
+and if we believe that then if we start
+with the fundamental domain we have one
+
+ align:start position:0%
+with the fundamental domain we have one
+ 
+
+ align:start position:0%
+with the fundamental domain we have one
+representative of each point in G mod
+
+ align:start position:0%
+representative of each point in G mod
+ 
+
+ align:start position:0%
+representative of each point in G mod
+gamma and then we end up in back in G
+
+ align:start position:0%
+gamma and then we end up in back in G
+ 
+
+ align:start position:0%
+gamma and then we end up in back in G
+mod gamma we should cover everything
+
+ align:start position:0%
+mod gamma we should cover everything
+ 
+
+ align:start position:0%
+mod gamma we should cover everything
+exactly once if this is a bjection.
+
+ align:start position:0%
+exactly once if this is a bjection.
+ 
+
+ align:start position:0%
+exactly once if this is a bjection.
+Okay. Now why was this a bjection? So
+
+ align:start position:0%
+Okay. Now why was this a bjection? So
+ 
+
+ align:start position:0%
+Okay. Now why was this a bjection? So
+what is this map? It's the map H gamma
+
+ align:start position:0%
+what is this map? It's the map H gamma
+ 
+
+ align:start position:0%
+what is this map? It's the map H gamma
+goes to G inverse H gamma.
+
+ align:start position:0%
+goes to G inverse H gamma.
+ 
+
+ align:start position:0%
+goes to G inverse H gamma.
+So why is this a bjection? Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So uh it's injective that means
+
+ align:start position:0%
+right. So uh it's injective that means
+ 
+
+ align:start position:0%
+right. So uh it's injective that means
+that if H1
+
+ align:start position:0%
+that if H1
+ 
+
+ align:start position:0%
+that if H1
+G inverse H1 gamma is equal to G inverse
+
+ align:start position:0%
+G inverse H1 gamma is equal to G inverse
+ 
+
+ align:start position:0%
+G inverse H1 gamma is equal to G inverse
+H2 gamma then um H1 gamma equals H2
+
+ align:start position:0%
+H2 gamma then um H1 gamma equals H2
+ 
+
+ align:start position:0%
+H2 gamma then um H1 gamma equals H2
+gamma. That's what it means for it to be
+
+ align:start position:0%
+gamma. That's what it means for it to be
+ 
+
+ align:start position:0%
+gamma. That's what it means for it to be
+injective.
+
+ align:start position:0%
+injective.
+ 
+
+ align:start position:0%
+injective.
+So is this clear?
+
+ align:start position:0%
+So is this clear?
+ 
+
+ align:start position:0%
+So is this clear?
+Yeah. You multiply on both sides by G.
+
+ align:start position:0%
+Yeah. You multiply on both sides by G.
+ 
+
+ align:start position:0%
+Yeah. You multiply on both sides by G.
+Okay. Serjective.
+
+ align:start position:0%
+Okay. Serjective.
+ 
+
+ align:start position:0%
+Okay. Serjective.
+That means that um
+
+ align:start position:0%
+That means that um
+ 
+
+ align:start position:0%
+That means that um
+for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+every H2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in in G there exists H1 in G. So that G
+
+ align:start position:0%
+in in G there exists H1 in G. So that G
+ 
+
+ align:start position:0%
+in in G there exists H1 in G. So that G
+inverse H1 gamma is H2 gamma.
+
+ align:start position:0%
+inverse H1 gamma is H2 gamma.
+ 
+
+ align:start position:0%
+inverse H1 gamma is H2 gamma.
+So yeah, we set these equal and solve
+
+ align:start position:0%
+So yeah, we set these equal and solve
+ 
+
+ align:start position:0%
+So yeah, we set these equal and solve
+for G.
+
+ align:start position:0%
+for G.
+ 
+
+ align:start position:0%
+for G.
+>> I guess that convertibility.
+
+ align:start position:0%
+>> I guess that convertibility.
+ 
+
+ align:start position:0%
+>> I guess that convertibility.
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. Um,
+
+ align:start position:0%
+>> Yeah. Um,
+ 
+
+ align:start position:0%
+>> Yeah. Um,
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+I have to say I went through this too
+
+ align:start position:0%
+I have to say I went through this too
+ 
+
+ align:start position:0%
+I have to say I went through this too
+when I when I drew these pictures. I
+
+ align:start position:0%
+when I when I drew these pictures. I
+ 
+
+ align:start position:0%
+when I when I drew these pictures. I
+asked myself like, is this actually
+
+ align:start position:0%
+asked myself like, is this actually
+ 
+
+ align:start position:0%
+asked myself like, is this actually
+going to like fold up and cover
+
+ align:start position:0%
+going to like fold up and cover
+ 
+
+ align:start position:0%
+going to like fold up and cover
+everything exactly once? And then I was
+
+ align:start position:0%
+everything exactly once? And then I was
+ 
+
+ align:start position:0%
+everything exactly once? And then I was
+like, is it really vigive?
+
+ align:start position:0%
+like, is it really vigive?
+ 
+
+ align:start position:0%
+like, is it really vigive?
+Yeah, it should happen.
+
+ align:start position:0%
+Yeah, it should happen.
+ 
+
+ align:start position:0%
+Yeah, it should happen.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+I guess you can make easier fun examples
+
+ align:start position:0%
+I guess you can make easier fun examples
+ 
+
+ align:start position:0%
+I guess you can make easier fun examples
+where that are more linear. So you just
+
+ align:start position:0%
+where that are more linear. So you just
+ 
+
+ align:start position:0%
+where that are more linear. So you just
+have like a matrix acting on R2 mod Z2
+
+ align:start position:0%
+have like a matrix acting on R2 mod Z2
+ 
+
+ align:start position:0%
+have like a matrix acting on R2 mod Z2
+or something like that. Um and then the
+
+ align:start position:0%
+or something like that. Um and then the
+ 
+
+ align:start position:0%
+or something like that. Um and then the
+fundamental domain is a square and you
+
+ align:start position:0%
+fundamental domain is a square and you
+ 
+
+ align:start position:0%
+fundamental domain is a square and you
+can draw what happens to it and you can
+
+ align:start position:0%
+can draw what happens to it and you can
+ 
+
+ align:start position:0%
+can draw what happens to it and you can
+look up. So this was inspired by the by
+
+ align:start position:0%
+look up. So this was inspired by the by
+ 
+
+ align:start position:0%
+look up. So this was inspired by the by
+that example. They called that the cat
+
+ align:start position:0%
+that example. They called that the cat
+ 
+
+ align:start position:0%
+that example. They called that the cat
+map, a particular map. And instead of a
+
+ align:start position:0%
+map, a particular map. And instead of a
+ 
+
+ align:start position:0%
+map, a particular map. And instead of a
+smiley face, they draw a cat. They've
+
+ align:start position:0%
+smiley face, they draw a cat. They've
+ 
+
+ align:start position:0%
+smiley face, they draw a cat. They've
+better artistic skills than me. You can
+
+ align:start position:0%
+better artistic skills than me. You can
+ 
+
+ align:start position:0%
+better artistic skills than me. You can
+Google that and see some nice pictures
+
+ align:start position:0%
+Google that and see some nice pictures
+ 
+
+ align:start position:0%
+Google that and see some nice pictures
+like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, cool. Okay. So here, so so this um
+
+ align:start position:0%
+Okay, cool. Okay. So here, so so this um
+ 
+
+ align:start position:0%
+Okay, cool. Okay. So here, so so this um
+this thing LG LL with with this diagonal
+
+ align:start position:0%
+this thing LG LL with with this diagonal
+ 
+
+ align:start position:0%
+this thing LG LL with with this diagonal
+action, they've broken it into two
+
+ align:start position:0%
+action, they've broken it into two
+ 
+
+ align:start position:0%
+action, they've broken it into two
+steps. And out of these two steps, I
+
+ align:start position:0%
+steps. And out of these two steps, I
+ 
+
+ align:start position:0%
+steps. And out of these two steps, I
+find this one quite confusing.
+
+ align:start position:0%
+find this one quite confusing.
+ 
+
+ align:start position:0%
+find this one quite confusing.
+uh it's difficult to write this down
+
+ align:start position:0%
+uh it's difficult to write this down
+ 
+
+ align:start position:0%
+uh it's difficult to write this down
+sufficiently accurately and then to say
+
+ align:start position:0%
+sufficiently accurately and then to say
+ 
+
+ align:start position:0%
+sufficiently accurately and then to say
+what happened here and and you know did
+
+ align:start position:0%
+what happened here and and you know did
+ 
+
+ align:start position:0%
+what happened here and and you know did
+this come back over here over there when
+
+ align:start position:0%
+this come back over here over there when
+ 
+
+ align:start position:0%
+this come back over here over there when
+it wrapped you know where did it wrap
+
+ align:start position:0%
+it wrapped you know where did it wrap
+ 
+
+ align:start position:0%
+it wrapped you know where did it wrap
+and that all of that seems very
+
+ align:start position:0%
+and that all of that seems very
+ 
+
+ align:start position:0%
+and that all of that seems very
+intimidating to me so very difficult to
+
+ align:start position:0%
+intimidating to me so very difficult to
+ 
+
+ align:start position:0%
+intimidating to me so very difficult to
+write down in a clean way but this first
+
+ align:start position:0%
+write down in a clean way but this first
+ 
+
+ align:start position:0%
+write down in a clean way but this first
+step is not so bad right
+
+ align:start position:0%
+step is not so bad right
+ 
+
+ align:start position:0%
+step is not so bad right
+um and so we're going to try to
+
+ align:start position:0%
+um and so we're going to try to
+ 
+
+ align:start position:0%
+um and so we're going to try to
+understand the first step very well and
+
+ align:start position:0%
+understand the first step very well and
+ 
+
+ align:start position:0%
+understand the first step very well and
+use that to see how much we can figure
+
+ align:start position:0%
+use that to see how much we can figure
+ 
+
+ align:start position:0%
+use that to see how much we can figure
+out about the about this map um LG
+
+ align:start position:0%
+out about the about this map um LG
+ 
+
+ align:start position:0%
+out about the about this map um LG
+acting on our homogeneous space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now the object that we want to
+
+ align:start position:0%
+Okay. Now the object that we want to
+ 
+
+ align:start position:0%
+Okay. Now the object that we want to
+follow is not a smiley face but a
+
+ align:start position:0%
+follow is not a smiley face but a
+ 
+
+ align:start position:0%
+follow is not a smiley face but a
+unipotent orbit.
+
+ align:start position:0%
+unipotent orbit.
+ 
+
+ align:start position:0%
+unipotent orbit.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+let's see here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. This we can erase all of it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I erased something that is
+
+ align:start position:0%
+Okay. So I erased something that is
+ 
+
+ align:start position:0%
+Okay. So I erased something that is
+useful for us. So recall we worked out
+
+ align:start position:0%
+useful for us. So recall we worked out
+ 
+
+ align:start position:0%
+useful for us. So recall we worked out
+um that the left map by a r inverse we
+
+ align:start position:0%
+um that the left map by a r inverse we
+ 
+
+ align:start position:0%
+um that the left map by a r inverse we
+found its singular values and singular
+
+ align:start position:0%
+found its singular values and singular
+ 
+
+ align:start position:0%
+found its singular values and singular
+vectors. So in the u direction um the
+
+ align:start position:0%
+vectors. So in the u direction um the
+ 
+
+ align:start position:0%
+vectors. So in the u direction um the
+length of this is e to the 2r
+
+ align:start position:0%
+length of this is e to the 2r
+ 
+
+ align:start position:0%
+length of this is e to the 2r
+and in the utilda direction the length
+
+ align:start position:0%
+and in the utilda direction the length
+ 
+
+ align:start position:0%
+and in the utilda direction the length
+is eus 2 r
+
+ align:start position:0%
+is eus 2 r
+ 
+
+ align:start position:0%
+is eus 2 r
+and in the diagonal direction the length
+
+ align:start position:0%
+and in the diagonal direction the length
+ 
+
+ align:start position:0%
+and in the diagonal direction the length
+is one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+so this is this is if we're thinking of
+
+ align:start position:0%
+so this is this is if we're thinking of
+ 
+
+ align:start position:0%
+so this is this is if we're thinking of
+l a r inverse from t e g to t a
+
+ align:start position:0%
+l a r inverse from t e g to t a
+ 
+
+ align:start position:0%
+l a r inverse from t e g to t a
+right and this little u
+
+ align:start position:0%
+right and this little u
+ 
+
+ align:start position:0%
+right and this little u
+this is also the tangent direction
+
+ align:start position:0%
+this is also the tangent direction
+ 
+
+ align:start position:0%
+this is also the tangent direction
+of our group u.
+
+ align:start position:0%
+of our group u.
+ 
+
+ align:start position:0%
+of our group u.
+So that group is going to get stretched
+
+ align:start position:0%
+So that group is going to get stretched
+ 
+
+ align:start position:0%
+So that group is going to get stretched
+which is the same thing we saw in the
+
+ align:start position:0%
+which is the same thing we saw in the
+ 
+
+ align:start position:0%
+which is the same thing we saw in the
+computation over there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step one so if we start with a single
+
+ align:start position:0%
+step one so if we start with a single
+ 
+
+ align:start position:0%
+step one so if we start with a single
+unipotent orbit starts at some point we
+
+ align:start position:0%
+unipotent orbit starts at some point we
+ 
+
+ align:start position:0%
+unipotent orbit starts at some point we
+have like this.
+
+ align:start position:0%
+have like this.
+ 
+
+ align:start position:0%
+have like this.
+So that's u01 of some point x. What
+
+ align:start position:0%
+So that's u01 of some point x. What
+ 
+
+ align:start position:0%
+So that's u01 of some point x. What
+happens when we apply L?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Well, this thing is going to get
+
+ align:start position:0%
+Okay. Well, this thing is going to get
+ 
+
+ align:start position:0%
+Okay. Well, this thing is going to get
+tall and skinny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the direction that got stretched is
+
+ align:start position:0%
+and the direction that got stretched is
+ 
+
+ align:start position:0%
+and the direction that got stretched is
+the direction of this orbit. So now
+
+ align:start position:0%
+the direction of this orbit. So now
+ 
+
+ align:start position:0%
+the direction of this orbit. So now
+we're going to have a long orbit
+
+ align:start position:0%
+we're going to have a long orbit
+ 
+
+ align:start position:0%
+we're going to have a long orbit
+and the height of this thing is e to the
+
+ align:start position:0%
+and the height of this thing is e to the
+ 
+
+ align:start position:0%
+and the height of this thing is e to the
+2R. Then we're going to quotient.
+
+ align:start position:0%
+2R. Then we're going to quotient.
+ 
+
+ align:start position:0%
+2R. Then we're going to quotient.
+Um, so when we quotient, I don't know
+
+ align:start position:0%
+Um, so when we quotient, I don't know
+ 
+
+ align:start position:0%
+Um, so when we quotient, I don't know
+exactly where it's going to go,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it will go along. It'll go out the
+
+ align:start position:0%
+but it will go along. It'll go out the
+ 
+
+ align:start position:0%
+but it will go along. It'll go out the
+top and come in the bottom somewhere.
+
+ align:start position:0%
+top and come in the bottom somewhere.
+ 
+
+ align:start position:0%
+top and come in the bottom somewhere.
+And then we'll have a bunch of these. So
+
+ align:start position:0%
+And then we'll have a bunch of these. So
+ 
+
+ align:start position:0%
+And then we'll have a bunch of these. So
+we'll have like
+
+ align:start position:0%
+we'll have like
+ 
+
+ align:start position:0%
+we'll have like
+e to the 2 r
+
+ align:start position:0%
+e to the 2 r
+ 
+
+ align:start position:0%
+e to the 2 r
+u orbits of length one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I have no idea where they are. So,
+
+ align:start position:0%
+and I have no idea where they are. So,
+ 
+
+ align:start position:0%
+and I have no idea where they are. So,
+we haven't made any progress yet on our
+
+ align:start position:0%
+we haven't made any progress yet on our
+ 
+
+ align:start position:0%
+we haven't made any progress yet on our
+main question, which is to see if these
+
+ align:start position:0%
+main question, which is to see if these
+ 
+
+ align:start position:0%
+main question, which is to see if these
+are distributing kind of evenly.
+
+ align:start position:0%
+are distributing kind of evenly.
+ 
+
+ align:start position:0%
+are distributing kind of evenly.
+Um, but now we can start again.
+
+ align:start position:0%
+Um, but now we can start again.
+ 
+
+ align:start position:0%
+Um, but now we can start again.
+Move this over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, now we have a bunch of unipotent
+
+ align:start position:0%
+So, now we have a bunch of unipotent
+ 
+
+ align:start position:0%
+So, now we have a bunch of unipotent
+orbits
+
+ align:start position:0%
+orbits
+ 
+
+ align:start position:0%
+orbits
+and we're going to stretch them out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, what happens when we stretch them
+
+ align:start position:0%
+Now, what happens when we stretch them
+ 
+
+ align:start position:0%
+Now, what happens when we stretch them
+out this time?
+
+ align:start position:0%
+out this time?
+ 
+
+ align:start position:0%
+out this time?
+Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. So, each one of them got longer.
+
+ align:start position:0%
+okay. So, each one of them got longer.
+ 
+
+ align:start position:0%
+okay. So, each one of them got longer.
+It's going to go from the bottom to the
+
+ align:start position:0%
+It's going to go from the bottom to the
+ 
+
+ align:start position:0%
+It's going to go from the bottom to the
+top.
+
+ align:start position:0%
+top.
+ 
+
+ align:start position:0%
+top.
+But also, um,
+
+ align:start position:0%
+But also, um,
+ 
+
+ align:start position:0%
+But also, um,
+there's also some compression which is
+
+ align:start position:0%
+there's also some compression which is
+ 
+
+ align:start position:0%
+there's also some compression which is
+kind of in this direction. And that
+
+ align:start position:0%
+kind of in this direction. And that
+ 
+
+ align:start position:0%
+kind of in this direction. And that
+could potentially cause some orbits to
+
+ align:start position:0%
+could potentially cause some orbits to
+ 
+
+ align:start position:0%
+could potentially cause some orbits to
+get closer together or not. And this is
+
+ align:start position:0%
+get closer together or not. And this is
+ 
+
+ align:start position:0%
+get closer together or not. And this is
+the part that we have to understand
+
+ align:start position:0%
+the part that we have to understand
+ 
+
+ align:start position:0%
+the part that we have to understand
+really carefully.
+
+ align:start position:0%
+really carefully.
+ 
+
+ align:start position:0%
+really carefully.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+>> All right.
+
+ align:start position:0%
+>> All right.
+ 
+
+ align:start position:0%
+>> All right.
+>> So this box is some small box.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. So this Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. That's right. That's right. So
+
+ align:start position:0%
+>> Yeah. That's right. That's right. So
+ 
+
+ align:start position:0%
+>> Yeah. That's right. That's right. So
+this this box here is a fundamental
+
+ align:start position:0%
+this this box here is a fundamental
+ 
+
+ align:start position:0%
+this this box here is a fundamental
+domain.
+
+ align:start position:0%
+domain.
+ 
+
+ align:start position:0%
+domain.
+So it's scale one
+
+ align:start position:0%
+So it's scale one
+ 
+
+ align:start position:0%
+So it's scale one
+and sure it could be around the
+
+ align:start position:0%
+and sure it could be around the
+ 
+
+ align:start position:0%
+and sure it could be around the
+identity. Thing I most want to convey in
+
+ align:start position:0%
+identity. Thing I most want to convey in
+ 
+
+ align:start position:0%
+identity. Thing I most want to convey in
+this class is a feeling for how this map
+
+ align:start position:0%
+this class is a feeling for how this map
+ 
+
+ align:start position:0%
+this class is a feeling for how this map
+is like twisting and distorting these
+
+ align:start position:0%
+is like twisting and distorting these
+ 
+
+ align:start position:0%
+is like twisting and distorting these
+curves. All right. And so I'm going to
+
+ align:start position:0%
+curves. All right. And so I'm going to
+ 
+
+ align:start position:0%
+curves. All right. And so I'm going to
+try to make a really big picture of it
+
+ align:start position:0%
+try to make a really big picture of it
+ 
+
+ align:start position:0%
+try to make a really big picture of it
+there. I also brought with me some um
+
+ align:start position:0%
+there. I also brought with me some um
+ 
+
+ align:start position:0%
+there. I also brought with me some um
+props.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So, I'm going to sort of visualize our
+
+ align:start position:0%
+So, I'm going to sort of visualize our
+ 
+
+ align:start position:0%
+So, I'm going to sort of visualize our
+fundamental domain or maybe a piece of
+
+ align:start position:0%
+fundamental domain or maybe a piece of
+ 
+
+ align:start position:0%
+fundamental domain or maybe a piece of
+it as a cylinder. And now I'm going to
+
+ align:start position:0%
+it as a cylinder. And now I'm going to
+ 
+
+ align:start position:0%
+it as a cylinder. And now I'm going to
+draw some unipotent orbits in different
+
+ align:start position:0%
+draw some unipotent orbits in different
+ 
+
+ align:start position:0%
+draw some unipotent orbits in different
+colors. And they all go from the bottom
+
+ align:start position:0%
+colors. And they all go from the bottom
+ 
+
+ align:start position:0%
+colors. And they all go from the bottom
+to the top.
+
+ align:start position:0%
+to the top.
+ 
+
+ align:start position:0%
+to the top.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe I'll draw three of them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now what happens to this picture?
+
+ align:start position:0%
+Okay. Now what happens to this picture?
+ 
+
+ align:start position:0%
+Okay. Now what happens to this picture?
+So, first of all, it's going to stretch
+
+ align:start position:0%
+So, first of all, it's going to stretch
+ 
+
+ align:start position:0%
+So, first of all, it's going to stretch
+that way. That part's not that hard to
+
+ align:start position:0%
+that way. That part's not that hard to
+ 
+
+ align:start position:0%
+that way. That part's not that hard to
+imagine. It would go off the board, so
+
+ align:start position:0%
+imagine. It would go off the board, so
+ 
+
+ align:start position:0%
+imagine. It would go off the board, so
+I'm not going to emphasize that. Then
+
+ align:start position:0%
+I'm not going to emphasize that. Then
+ 
+
+ align:start position:0%
+I'm not going to emphasize that. Then
+each one of these uh slices, so we have
+
+ align:start position:0%
+each one of these uh slices, so we have
+ 
+
+ align:start position:0%
+each one of these uh slices, so we have
+some sort of slices. Let's say this is
+
+ align:start position:0%
+some sort of slices. Let's say this is
+ 
+
+ align:start position:0%
+some sort of slices. Let's say this is
+tals 0 up to tals 1. Other t's in the
+
+ align:start position:0%
+tals 0 up to tals 1. Other t's in the
+ 
+
+ align:start position:0%
+tals 0 up to tals 1. Other t's in the
+middle. Each one of these slices, one
+
+ align:start position:0%
+middle. Each one of these slices, one
+ 
+
+ align:start position:0%
+middle. Each one of these slices, one
+direction is going to be squished and
+
+ align:start position:0%
+direction is going to be squished and
+ 
+
+ align:start position:0%
+direction is going to be squished and
+the other direction is going to stay the
+
+ align:start position:0%
+the other direction is going to stay the
+ 
+
+ align:start position:0%
+the other direction is going to stay the
+same.
+
+ align:start position:0%
+same.
+ 
+
+ align:start position:0%
+same.
+So let's say that at t = 1 cross-section
+
+ align:start position:0%
+So let's say that at t = 1 cross-section
+ 
+
+ align:start position:0%
+So let's say that at t = 1 cross-section
+of this picture, I see a triangle
+
+ align:start position:0%
+of this picture, I see a triangle
+ 
+
+ align:start position:0%
+of this picture, I see a triangle
+that looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And there's going to be some direction
+
+ align:start position:0%
+And there's going to be some direction
+ 
+
+ align:start position:0%
+And there's going to be some direction
+that gets compressed.
+
+ align:start position:0%
+that gets compressed.
+ 
+
+ align:start position:0%
+that gets compressed.
+When I apply l inverse, if that
+
+ align:start position:0%
+When I apply l inverse, if that
+ 
+
+ align:start position:0%
+When I apply l inverse, if that
+direction gets compressed, the output is
+
+ align:start position:0%
+direction gets compressed, the output is
+ 
+
+ align:start position:0%
+direction gets compressed, the output is
+going to look like so.
+
+ align:start position:0%
+going to look like so.
+ 
+
+ align:start position:0%
+going to look like so.
+And that has been actually worked out so
+
+ align:start position:0%
+And that has been actually worked out so
+ 
+
+ align:start position:0%
+And that has been actually worked out so
+that this blue and yellow get kind of
+
+ align:start position:0%
+that this blue and yellow get kind of
+ 
+
+ align:start position:0%
+that this blue and yellow get kind of
+squished together.
+
+ align:start position:0%
+squished together.
+ 
+
+ align:start position:0%
+squished together.
+And the orange is still there.
+
+ align:start position:0%
+And the orange is still there.
+ 
+
+ align:start position:0%
+And the orange is still there.
+And at t equals 0,
+
+ align:start position:0%
+And at t equals 0,
+ 
+
+ align:start position:0%
+And at t equals 0,
+if I look at the bottom disc, I have the
+
+ align:start position:0%
+if I look at the bottom disc, I have the
+ 
+
+ align:start position:0%
+if I look at the bottom disc, I have the
+same picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And there's some direction that's going
+
+ align:start position:0%
+And there's some direction that's going
+ 
+
+ align:start position:0%
+And there's some direction that's going
+to be compressed.
+
+ align:start position:0%
+to be compressed.
+ 
+
+ align:start position:0%
+to be compressed.
+And it's not the same direction. I'll do
+
+ align:start position:0%
+And it's not the same direction. I'll do
+ 
+
+ align:start position:0%
+And it's not the same direction. I'll do
+somewhat arbitrarily that one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That one. Okay. So,
+
+ align:start position:0%
+That one. Okay. So,
+ 
+
+ align:start position:0%
+That one. Okay. So,
+compress that way. That will look sort
+
+ align:start position:0%
+compress that way. That will look sort
+ 
+
+ align:start position:0%
+compress that way. That will look sort
+of like so. And the blue point will be
+
+ align:start position:0%
+of like so. And the blue point will be
+ 
+
+ align:start position:0%
+of like so. And the blue point will be
+over here. And the yellow and orange
+
+ align:start position:0%
+over here. And the yellow and orange
+ 
+
+ align:start position:0%
+over here. And the yellow and orange
+point will be somewhat close together.
+
+ align:start position:0%
+point will be somewhat close together.
+ 
+
+ align:start position:0%
+point will be somewhat close together.
+Okay. And as you look at all the
+
+ align:start position:0%
+Okay. And as you look at all the
+ 
+
+ align:start position:0%
+Okay. And as you look at all the
+intermediate heights, you'll have a
+
+ align:start position:0%
+intermediate heights, you'll have a
+ 
+
+ align:start position:0%
+intermediate heights, you'll have a
+similar picture. But this compression
+
+ align:start position:0%
+similar picture. But this compression
+ 
+
+ align:start position:0%
+similar picture. But this compression
+direction is going to be changing
+
+ align:start position:0%
+direction is going to be changing
+ 
+
+ align:start position:0%
+direction is going to be changing
+continuously as you go up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. All right. So I'm not sure if this
+
+ align:start position:0%
+Okay. All right. So I'm not sure if this
+ 
+
+ align:start position:0%
+Okay. All right. So I'm not sure if this
+will be helpful, but I brought several
+
+ align:start position:0%
+will be helpful, but I brought several
+ 
+
+ align:start position:0%
+will be helpful, but I brought several
+props to try to illustrate this
+
+ align:start position:0%
+props to try to illustrate this
+ 
+
+ align:start position:0%
+props to try to illustrate this
+important process. So if you imagine
+
+ align:start position:0%
+important process. So if you imagine
+ 
+
+ align:start position:0%
+important process. So if you imagine
+that you have a bunch of unipotent
+
+ align:start position:0%
+that you have a bunch of unipotent
+ 
+
+ align:start position:0%
+that you have a bunch of unipotent
+orbits in your homogeneous space like so
+
+ align:start position:0%
+orbits in your homogeneous space like so
+ 
+
+ align:start position:0%
+orbits in your homogeneous space like so
+and we apply a okay first of all they
+
+ align:start position:0%
+and we apply a okay first of all they
+ 
+
+ align:start position:0%
+and we apply a okay first of all they
+will stretch this way and second of all
+
+ align:start position:0%
+will stretch this way and second of all
+ 
+
+ align:start position:0%
+will stretch this way and second of all
+there will be some compression. So maybe
+
+ align:start position:0%
+there will be some compression. So maybe
+ 
+
+ align:start position:0%
+there will be some compression. So maybe
+at the top they might get smooshed
+
+ align:start position:0%
+at the top they might get smooshed
+ 
+
+ align:start position:0%
+at the top they might get smooshed
+together this way and at the bottom they
+
+ align:start position:0%
+together this way and at the bottom they
+ 
+
+ align:start position:0%
+together this way and at the bottom they
+might get smooshed together sort of a
+
+ align:start position:0%
+might get smooshed together sort of a
+ 
+
+ align:start position:0%
+might get smooshed together sort of a
+different way sort of like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+um if this piece of Play-Doh is this
+
+ align:start position:0%
+um if this piece of Play-Doh is this
+ 
+
+ align:start position:0%
+um if this piece of Play-Doh is this
+cylinder here what's going to happen to
+
+ align:start position:0%
+cylinder here what's going to happen to
+ 
+
+ align:start position:0%
+cylinder here what's going to happen to
+it when we apply the map? Well, it's
+
+ align:start position:0%
+it when we apply the map? Well, it's
+ 
+
+ align:start position:0%
+it when we apply the map? Well, it's
+going to get taller
+
+ align:start position:0%
+going to get taller
+ 
+
+ align:start position:0%
+going to get taller
+and it's going to get squished and maybe
+
+ align:start position:0%
+and it's going to get squished and maybe
+ 
+
+ align:start position:0%
+and it's going to get squished and maybe
+the top will get squished sort of that
+
+ align:start position:0%
+the top will get squished sort of that
+ 
+
+ align:start position:0%
+the top will get squished sort of that
+way, but the bottom will get squished
+
+ align:start position:0%
+way, but the bottom will get squished
+ 
+
+ align:start position:0%
+way, but the bottom will get squished
+sort of that way and in the middle it'll
+
+ align:start position:0%
+sort of that way and in the middle it'll
+ 
+
+ align:start position:0%
+sort of that way and in the middle it'll
+get squished some direction sort of in
+
+ align:start position:0%
+get squished some direction sort of in
+ 
+
+ align:start position:0%
+get squished some direction sort of in
+the middle and that will if I had done
+
+ align:start position:0%
+the middle and that will if I had done
+ 
+
+ align:start position:0%
+the middle and that will if I had done
+it carefully practiced it at home it
+
+ align:start position:0%
+it carefully practiced it at home it
+ 
+
+ align:start position:0%
+it carefully practiced it at home it
+produces something that's sort of like a
+
+ align:start position:0%
+produces something that's sort of like a
+ 
+
+ align:start position:0%
+produces something that's sort of like a
+helix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let me say briefly why this is
+
+ align:start position:0%
+Okay, so let me say briefly why this is
+ 
+
+ align:start position:0%
+Okay, so let me say briefly why this is
+relevant. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then if we have time, if we feel
+
+ align:start position:0%
+and then if we have time, if we feel
+ 
+
+ align:start position:0%
+and then if we have time, if we feel
+like it, we could try to do some
+
+ align:start position:0%
+like it, we could try to do some
+ 
+
+ align:start position:0%
+like it, we could try to do some
+computations with matrices to check it.
+
+ align:start position:0%
+computations with matrices to check it.
+ 
+
+ align:start position:0%
+computations with matrices to check it.
+Okay. So, why is this relevant? Well, if
+
+ align:start position:0%
+Okay. So, why is this relevant? Well, if
+ 
+
+ align:start position:0%
+Okay. So, why is this relevant? Well, if
+you had a, you know, a situation like
+
+ align:start position:0%
+you had a, you know, a situation like
+ 
+
+ align:start position:0%
+you had a, you know, a situation like
+this,
+
+ align:start position:0%
+this,
+ 
+
+ align:start position:0%
+this,
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah. Okay, let's go back up here.
+
+ align:start position:0%
+yeah. Okay, let's go back up here.
+ 
+
+ align:start position:0%
+yeah. Okay, let's go back up here.
+So, this guy is really tall. We're going
+
+ align:start position:0%
+So, this guy is really tall. We're going
+ 
+
+ align:start position:0%
+So, this guy is really tall. We're going
+to cut it into a sequence of pieces that
+
+ align:start position:0%
+to cut it into a sequence of pieces that
+ 
+
+ align:start position:0%
+to cut it into a sequence of pieces that
+each have height one. And then each one
+
+ align:start position:0%
+each have height one. And then each one
+ 
+
+ align:start position:0%
+each have height one. And then each one
+of these pieces is going to fold back
+
+ align:start position:0%
+of these pieces is going to fold back
+ 
+
+ align:start position:0%
+of these pieces is going to fold back
+in.
+
+ align:start position:0%
+in.
+ 
+
+ align:start position:0%
+in.
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So over here there is a an unused color.
+
+ align:start position:0%
+So over here there is a an unused color.
+ 
+
+ align:start position:0%
+So over here there is a an unused color.
+There's a purple piece over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. That purple piece is going to fold
+
+ align:start position:0%
+Okay. That purple piece is going to fold
+ 
+
+ align:start position:0%
+Okay. That purple piece is going to fold
+back in over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Can you see that?
+
+ align:start position:0%
+Can you see that?
+ 
+
+ align:start position:0%
+Can you see that?
+All right. And then there are a bunch of
+
+ align:start position:0%
+All right. And then there are a bunch of
+ 
+
+ align:start position:0%
+All right. And then there are a bunch of
+other pieces in different colors. Those
+
+ align:start position:0%
+other pieces in different colors. Those
+ 
+
+ align:start position:0%
+other pieces in different colors. Those
+other pieces will somehow get slotted in
+
+ align:start position:0%
+other pieces will somehow get slotted in
+ 
+
+ align:start position:0%
+other pieces will somehow get slotted in
+in an order that I don't understand at
+
+ align:start position:0%
+in an order that I don't understand at
+ 
+
+ align:start position:0%
+in an order that I don't understand at
+all, but they'll all go somewhere.
+
+ align:start position:0%
+all, but they'll all go somewhere.
+ 
+
+ align:start position:0%
+all, but they'll all go somewhere.
+All right. Now, inside of this purple
+
+ align:start position:0%
+All right. Now, inside of this purple
+ 
+
+ align:start position:0%
+All right. Now, inside of this purple
+piece, so over here we have uh a yellow
+
+ align:start position:0%
+piece, so over here we have uh a yellow
+ 
+
+ align:start position:0%
+piece, so over here we have uh a yellow
+orbit, a blue orbit, and an orange
+
+ align:start position:0%
+orbit, a blue orbit, and an orange
+ 
+
+ align:start position:0%
+orbit, a blue orbit, and an orange
+orbit. Let's just focus on those three.
+
+ align:start position:0%
+orbit. Let's just focus on those three.
+ 
+
+ align:start position:0%
+orbit. Let's just focus on those three.
+They aren't all are going to pass
+
+ align:start position:0%
+They aren't all are going to pass
+ 
+
+ align:start position:0%
+They aren't all are going to pass
+through here. And we could have
+
+ align:start position:0%
+through here. And we could have
+ 
+
+ align:start position:0%
+through here. And we could have
+um the blue orbit and the orange orbit
+
+ align:start position:0%
+um the blue orbit and the orange orbit
+ 
+
+ align:start position:0%
+um the blue orbit and the orange orbit
+and the yellow orbit all kind of spread
+
+ align:start position:0%
+and the yellow orbit all kind of spread
+ 
+
+ align:start position:0%
+and the yellow orbit all kind of spread
+out from each other. Or we could be that
+
+ align:start position:0%
+out from each other. Or we could be that
+ 
+
+ align:start position:0%
+out from each other. Or we could be that
+they are smooshed together close to each
+
+ align:start position:0%
+they are smooshed together close to each
+ 
+
+ align:start position:0%
+they are smooshed together close to each
+other.
+
+ align:start position:0%
+other.
+ 
+
+ align:start position:0%
+other.
+Anyway, whatever happens here, this is
+
+ align:start position:0%
+Anyway, whatever happens here, this is
+ 
+
+ align:start position:0%
+Anyway, whatever happens here, this is
+just slotted in over here. So that will
+
+ align:start position:0%
+just slotted in over here. So that will
+ 
+
+ align:start position:0%
+just slotted in over here. So that will
+tell us how they're spaced over here.
+
+ align:start position:0%
+tell us how they're spaced over here.
+ 
+
+ align:start position:0%
+tell us how they're spaced over here.
+Okay. So um
+
+ align:start position:0%
+Okay. So um
+ 
+
+ align:start position:0%
+Okay. So um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+when we have something like this that
+
+ align:start position:0%
+when we have something like this that
+ 
+
+ align:start position:0%
+when we have something like this that
+will produce two unit length unipotent
+
+ align:start position:0%
+will produce two unit length unipotent
+ 
+
+ align:start position:0%
+will produce two unit length unipotent
+orbits over here in this purple thing
+
+ align:start position:0%
+orbits over here in this purple thing
+ 
+
+ align:start position:0%
+orbits over here in this purple thing
+that are really close to each other and
+
+ align:start position:0%
+that are really close to each other and
+ 
+
+ align:start position:0%
+that are really close to each other and
+that that phenomenon is the enemy of the
+
+ align:start position:0%
+that that phenomenon is the enemy of the
+ 
+
+ align:start position:0%
+that that phenomenon is the enemy of the
+unipotent orbit spreading out. Unipot
+
+ align:start position:0%
+unipotent orbit spreading out. Unipot
+ 
+
+ align:start position:0%
+unipotent orbit spreading out. Unipot
+orbit is definitely going to be really
+
+ align:start position:0%
+orbit is definitely going to be really
+ 
+
+ align:start position:0%
+orbit is definitely going to be really
+long but it may not spread out because
+
+ align:start position:0%
+long but it may not spread out because
+ 
+
+ align:start position:0%
+long but it may not spread out because
+it may have many segments that are
+
+ align:start position:0%
+it may have many segments that are
+ 
+
+ align:start position:0%
+it may have many segments that are
+really close to each other.
+
+ align:start position:0%
+really close to each other.
+ 
+
+ align:start position:0%
+really close to each other.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+so let me scribe.
+
+ align:start position:0%
+so let me scribe.
+ 
+
+ align:start position:0%
+so let me scribe.
+So to prove
+
+ align:start position:0%
+So to prove
+ 
+
+ align:start position:0%
+So to prove
+that u 0t of x spreads out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that coincidences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this type are rare.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And why are they rare? Well,
+
+ align:start position:0%
+Okay. And why are they rare? Well,
+ 
+
+ align:start position:0%
+Okay. And why are they rare? Well,
+they're rare because this compression
+
+ align:start position:0%
+they're rare because this compression
+ 
+
+ align:start position:0%
+they're rare because this compression
+angle is rotating smoothly as we vary t.
+
+ align:start position:0%
+angle is rotating smoothly as we vary t.
+ 
+
+ align:start position:0%
+angle is rotating smoothly as we vary t.
+And so even though there may be one
+
+ align:start position:0%
+And so even though there may be one
+ 
+
+ align:start position:0%
+And so even though there may be one
+projection that smooshes a lot of things
+
+ align:start position:0%
+projection that smooshes a lot of things
+ 
+
+ align:start position:0%
+projection that smooshes a lot of things
+together,
+
+ align:start position:0%
+together,
+ 
+
+ align:start position:0%
+together,
+we have learned in this course that if
+
+ align:start position:0%
+we have learned in this course that if
+ 
+
+ align:start position:0%
+we have learned in this course that if
+you look at the projection in all
+
+ align:start position:0%
+you look at the projection in all
+ 
+
+ align:start position:0%
+you look at the projection in all
+different directions, most of them do
+
+ align:start position:0%
+different directions, most of them do
+ 
+
+ align:start position:0%
+different directions, most of them do
+not smoosh things together very much.
+
+ align:start position:0%
+not smoosh things together very much.
+ 
+
+ align:start position:0%
+not smoosh things together very much.
+And that forces this unipotent orbit to
+
+ align:start position:0%
+And that forces this unipotent orbit to
+ 
+
+ align:start position:0%
+And that forces this unipotent orbit to
+spread out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sorry for so confused. Why does like the
+
+ align:start position:0%
+Sorry for so confused. Why does like the
+ 
+
+ align:start position:0%
+Sorry for so confused. Why does like the
+direction get like compressed change
+
+ align:start position:0%
+direction get like compressed change
+ 
+
+ align:start position:0%
+direction get like compressed change
+like from that picture after you apply L
+
+ align:start position:0%
+like from that picture after you apply L
+ 
+
+ align:start position:0%
+like from that picture after you apply L
+A R inverse it's always
+
+ align:start position:0%
+A R inverse it's always
+ 
+
+ align:start position:0%
+A R inverse it's always
+get long and
+
+ align:start position:0%
+get long and
+ 
+
+ align:start position:0%
+get long and
+and get
+
+ align:start position:0%
+and get
+ 
+
+ align:start position:0%
+and get
+another direction gets
+
+ align:start position:0%
+another direction gets
+ 
+
+ align:start position:0%
+another direction gets
+>> Yeah. Yeah. Okay. All right. So the
+
+ align:start position:0%
+>> Yeah. Yeah. Okay. All right. So the
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Okay. All right. So the
+question is why does this happen? And in
+
+ align:start position:0%
+question is why does this happen? And in
+ 
+
+ align:start position:0%
+question is why does this happen? And in
+fact there was a point that the picture
+
+ align:start position:0%
+fact there was a point that the picture
+ 
+
+ align:start position:0%
+fact there was a point that the picture
+that I drew up there sort of makes it
+
+ align:start position:0%
+that I drew up there sort of makes it
+ 
+
+ align:start position:0%
+that I drew up there sort of makes it
+look like it doesn't happen.
+
+ align:start position:0%
+look like it doesn't happen.
+ 
+
+ align:start position:0%
+look like it doesn't happen.
+Right.
+
+ align:start position:0%
+Right.
+ 
+
+ align:start position:0%
+Right.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So in my picture I this is not exactly
+
+ align:start position:0%
+So in my picture I this is not exactly
+ 
+
+ align:start position:0%
+So in my picture I this is not exactly
+accurate but but I I drew it as though
+
+ align:start position:0%
+accurate but but I I drew it as though
+ 
+
+ align:start position:0%
+accurate but but I I drew it as though
+this map was just a linear map that
+
+ align:start position:0%
+this map was just a linear map that
+ 
+
+ align:start position:0%
+this map was just a linear map that
+takes a cube to a rectangular solid. and
+
+ align:start position:0%
+takes a cube to a rectangular solid. and
+ 
+
+ align:start position:0%
+takes a cube to a rectangular solid. and
+I drew it as though well I tried to show
+
+ align:start position:0%
+I drew it as though well I tried to show
+ 
+
+ align:start position:0%
+I drew it as though well I tried to show
+that this would okay so these unipotent
+
+ align:start position:0%
+that this would okay so these unipotent
+ 
+
+ align:start position:0%
+that this would okay so these unipotent
+orbits are more or less vertical.
+
+ align:start position:0%
+orbits are more or less vertical.
+ 
+
+ align:start position:0%
+orbits are more or less vertical.
+All right so here's what so here's what
+
+ align:start position:0%
+All right so here's what so here's what
+ 
+
+ align:start position:0%
+All right so here's what so here's what
+wouldn't work. So if the unipotent
+
+ align:start position:0%
+wouldn't work. So if the unipotent
+ 
+
+ align:start position:0%
+wouldn't work. So if the unipotent
+orbits were literally vertical and if
+
+ align:start position:0%
+orbits were literally vertical and if
+ 
+
+ align:start position:0%
+orbits were literally vertical and if
+this map was literally a linear map then
+
+ align:start position:0%
+this map was literally a linear map then
+ 
+
+ align:start position:0%
+this map was literally a linear map then
+this would not happen the compression
+
+ align:start position:0%
+this would not happen the compression
+ 
+
+ align:start position:0%
+this would not happen the compression
+direction would be the same at every
+
+ align:start position:0%
+direction would be the same at every
+ 
+
+ align:start position:0%
+direction would be the same at every
+height.
+
+ align:start position:0%
+height.
+ 
+
+ align:start position:0%
+height.
+All right. So, um I think you have to
+
+ align:start position:0%
+All right. So, um I think you have to
+ 
+
+ align:start position:0%
+All right. So, um I think you have to
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+pick
+
+ align:start position:0%
+pick
+ 
+
+ align:start position:0%
+pick
+um this this this Lee group is like, you
+
+ align:start position:0%
+um this this this Lee group is like, you
+ 
+
+ align:start position:0%
+um this this this Lee group is like, you
+know, it's a sub manifold of R4, but if
+
+ align:start position:0%
+know, it's a sub manifold of R4, but if
+ 
+
+ align:start position:0%
+know, it's a sub manifold of R4, but if
+you want to represent it in coordinates
+
+ align:start position:0%
+you want to represent it in coordinates
+ 
+
+ align:start position:0%
+you want to represent it in coordinates
+in three dimensions, you have to make a
+
+ align:start position:0%
+in three dimensions, you have to make a
+ 
+
+ align:start position:0%
+in three dimensions, you have to make a
+choice. There's not a completely
+
+ align:start position:0%
+choice. There's not a completely
+ 
+
+ align:start position:0%
+choice. There's not a completely
+canonical choice.
+
+ align:start position:0%
+canonical choice.
+ 
+
+ align:start position:0%
+canonical choice.
+So, um, we could make the choice that,
+
+ align:start position:0%
+So, um, we could make the choice that,
+ 
+
+ align:start position:0%
+So, um, we could make the choice that,
+um, the unipotent orbits were literally
+
+ align:start position:0%
+um, the unipotent orbits were literally
+ 
+
+ align:start position:0%
+um, the unipotent orbits were literally
+vertical.
+
+ align:start position:0%
+vertical.
+ 
+
+ align:start position:0%
+vertical.
+And if we did that, this picture would
+
+ align:start position:0%
+And if we did that, this picture would
+ 
+
+ align:start position:0%
+And if we did that, this picture would
+not be right anymore. Um, if if we did
+
+ align:start position:0%
+not be right anymore. Um, if if we did
+ 
+
+ align:start position:0%
+not be right anymore. Um, if if we did
+that, then this would have a bit of a
+
+ align:start position:0%
+that, then this would have a bit of a
+ 
+
+ align:start position:0%
+that, then this would have a bit of a
+twist. This would be more this would be
+
+ align:start position:0%
+twist. This would be more this would be
+ 
+
+ align:start position:0%
+twist. This would be more this would be
+like a helixy thing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Or another way of looking at it is I
+
+ align:start position:0%
+Or another way of looking at it is I
+ 
+
+ align:start position:0%
+Or another way of looking at it is I
+think we could choose coordinates in
+
+ align:start position:0%
+think we could choose coordinates in
+ 
+
+ align:start position:0%
+think we could choose coordinates in
+such a way that um this map was pretty
+
+ align:start position:0%
+such a way that um this map was pretty
+ 
+
+ align:start position:0%
+such a way that um this map was pretty
+close to a linear map but then these
+
+ align:start position:0%
+close to a linear map but then these
+ 
+
+ align:start position:0%
+close to a linear map but then these
+unipotent orbits would not be vertical
+
+ align:start position:0%
+unipotent orbits would not be vertical
+ 
+
+ align:start position:0%
+unipotent orbits would not be vertical
+and instead they would kind of spiral a
+
+ align:start position:0%
+and instead they would kind of spiral a
+ 
+
+ align:start position:0%
+and instead they would kind of spiral a
+little bit as you went up
+
+ align:start position:0%
+little bit as you went up
+ 
+
+ align:start position:0%
+little bit as you went up
+and so the angle between two unipotent
+
+ align:start position:0%
+and so the angle between two unipotent
+ 
+
+ align:start position:0%
+and so the angle between two unipotent
+guys would be changing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now at some point
+
+ align:start position:0%
+Okay. Now at some point
+ 
+
+ align:start position:0%
+Okay. Now at some point
+you know why do you believe that?
+
+ align:start position:0%
+you know why do you believe that?
+ 
+
+ align:start position:0%
+you know why do you believe that?
+So at some point we should do a
+
+ align:start position:0%
+So at some point we should do a
+ 
+
+ align:start position:0%
+So at some point we should do a
+computation right. Um I don't think I'll
+
+ align:start position:0%
+computation right. Um I don't think I'll
+ 
+
+ align:start position:0%
+computation right. Um I don't think I'll
+do it in the last two minutes but I'll
+
+ align:start position:0%
+do it in the last two minutes but I'll
+ 
+
+ align:start position:0%
+do it in the last two minutes but I'll
+just say what you should do.
+
+ align:start position:0%
+just say what you should do.
+ 
+
+ align:start position:0%
+just say what you should do.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we figured out which direction is
+
+ align:start position:0%
+we figured out which direction is
+ 
+
+ align:start position:0%
+we figured out which direction is
+compressing. Um we could have written it
+
+ align:start position:0%
+compressing. Um we could have written it
+ 
+
+ align:start position:0%
+compressing. Um we could have written it
+down a little bit more clearly but if if
+
+ align:start position:0%
+down a little bit more clearly but if if
+ 
+
+ align:start position:0%
+down a little bit more clearly but if if
+you trace through our thoughts today at
+
+ align:start position:0%
+you trace through our thoughts today at
+ 
+
+ align:start position:0%
+you trace through our thoughts today at
+any point in the homogeneous space if
+
+ align:start position:0%
+any point in the homogeneous space if
+ 
+
+ align:start position:0%
+any point in the homogeneous space if
+you ask which is the tangent direction
+
+ align:start position:0%
+you ask which is the tangent direction
+ 
+
+ align:start position:0%
+you ask which is the tangent direction
+that's going to get compressed when you
+
+ align:start position:0%
+that's going to get compressed when you
+ 
+
+ align:start position:0%
+that's going to get compressed when you
+apply L we have a formula for it.
+
+ align:start position:0%
+apply L we have a formula for it.
+ 
+
+ align:start position:0%
+apply L we have a formula for it.
+Okay. And then we can also say if you
+
+ align:start position:0%
+Okay. And then we can also say if you
+ 
+
+ align:start position:0%
+Okay. And then we can also say if you
+have two nearby unipotent orbits and
+
+ align:start position:0%
+have two nearby unipotent orbits and
+ 
+
+ align:start position:0%
+have two nearby unipotent orbits and
+down here at the bottom there's like a a
+
+ align:start position:0%
+down here at the bottom there's like a a
+ 
+
+ align:start position:0%
+down here at the bottom there's like a a
+little vector between them as you go up
+
+ align:start position:0%
+little vector between them as you go up
+ 
+
+ align:start position:0%
+little vector between them as you go up
+the orbit what what happens to that
+
+ align:start position:0%
+the orbit what what happens to that
+ 
+
+ align:start position:0%
+the orbit what what happens to that
+vector. There's a formula for that too.
+
+ align:start position:0%
+vector. There's a formula for that too.
+ 
+
+ align:start position:0%
+vector. There's a formula for that too.
+If you compare these two formulas you
+
+ align:start position:0%
+If you compare these two formulas you
+ 
+
+ align:start position:0%
+If you compare these two formulas you
+will see that they don't match. So that
+
+ align:start position:0%
+will see that they don't match. So that
+ 
+
+ align:start position:0%
+will see that they don't match. So that
+the the if if this direction initially
+
+ align:start position:0%
+the the if if this direction initially
+ 
+
+ align:start position:0%
+the the if if this direction initially
+was the compression direction
+
+ align:start position:0%
+was the compression direction
+ 
+
+ align:start position:0%
+was the compression direction
+compression direction if you follow it
+
+ align:start position:0%
+compression direction if you follow it
+ 
+
+ align:start position:0%
+compression direction if you follow it
+up you don't get the compression
+
+ align:start position:0%
+up you don't get the compression
+ 
+
+ align:start position:0%
+up you don't get the compression
+direction up here and you you can
+
+ align:start position:0%
+direction up here and you you can
+ 
+
+ align:start position:0%
+direction up here and you you can
+compute it all with matrices.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah
+
+ align:start position:0%
+>> Yeah
+ 
+
+ align:start position:0%
+>> Yeah
+>> this just kind of saying is a curvature
+
+ align:start position:0%
+>> this just kind of saying is a curvature
+ 
+
+ align:start position:0%
+>> this just kind of saying is a curvature
+tensor that's not zero any from the
+
+ align:start position:0%
+tensor that's not zero any from the
+ 
+
+ align:start position:0%
+tensor that's not zero any from the
+guess one of the two one parameter
+
+ align:start position:0%
+guess one of the two one parameter
+ 
+
+ align:start position:0%
+guess one of the two one parameter
+groups.
+
+ align:start position:0%
+groups.
+ 
+
+ align:start position:0%
+groups.
+Yeah, the question is is is this saying
+
+ align:start position:0%
+Yeah, the question is is is this saying
+ 
+
+ align:start position:0%
+Yeah, the question is is is this saying
+that this there's some kind of curvature
+
+ align:start position:0%
+that this there's some kind of curvature
+ 
+
+ align:start position:0%
+that this there's some kind of curvature
+tensor that doesn't vanish? Maybe it's
+
+ align:start position:0%
+tensor that doesn't vanish? Maybe it's
+ 
+
+ align:start position:0%
+tensor that doesn't vanish? Maybe it's
+it's not the remon curvature tensor, but
+
+ align:start position:0%
+it's not the remon curvature tensor, but
+ 
+
+ align:start position:0%
+it's not the remon curvature tensor, but
+uh it might be something in that spirit.
+
+ align:start position:0%
+uh it might be something in that spirit.
+ 
+
+ align:start position:0%
+uh it might be something in that spirit.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> The picture kind of makes it seem like
+
+ align:start position:0%
+>> The picture kind of makes it seem like
+ 
+
+ align:start position:0%
+>> The picture kind of makes it seem like
+it stretches.
+
+ align:start position:0%
+it stretches.
+ 
+
+ align:start position:0%
+it stretches.
+It's not periodic. Is there something
+
+ align:start position:0%
+It's not periodic. Is there something
+ 
+
+ align:start position:0%
+It's not periodic. Is there something
+I'm missing?
+
+ align:start position:0%
+I'm missing?
+ 
+
+ align:start position:0%
+I'm missing?
+Yeah, great question. Okay, the question
+
+ align:start position:0%
+Yeah, great question. Okay, the question
+ 
+
+ align:start position:0%
+Yeah, great question. Okay, the question
+was this appears to be a proof sketch
+
+ align:start position:0%
+was this appears to be a proof sketch
+ 
+
+ align:start position:0%
+was this appears to be a proof sketch
+that every orbit of the uniport group is
+
+ align:start position:0%
+that every orbit of the uniport group is
+ 
+
+ align:start position:0%
+that every orbit of the uniport group is
+uh evenly distributed and we saw at the
+
+ align:start position:0%
+uh evenly distributed and we saw at the
+ 
+
+ align:start position:0%
+uh evenly distributed and we saw at the
+beginning that that is not true. So what
+
+ align:start position:0%
+beginning that that is not true. So what
+ 
+
+ align:start position:0%
+beginning that that is not true. So what
+did we what did we do wrong?
+
+ align:start position:0%
+did we what did we do wrong?
+ 
+
+ align:start position:0%
+did we what did we do wrong?
+Okay. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right. So this orbit we can write
+
+ align:start position:0%
+all right. So this orbit we can write
+ 
+
+ align:start position:0%
+all right. So this orbit we can write
+this way.
+
+ align:start position:0%
+this way.
+ 
+
+ align:start position:0%
+this way.
+All right. Actually, so let me say that
+
+ align:start position:0%
+All right. Actually, so let me say that
+ 
+
+ align:start position:0%
+All right. Actually, so let me say that
+the the shortest answer to your
+
+ align:start position:0%
+the the shortest answer to your
+ 
+
+ align:start position:0%
+the the shortest answer to your
+question, the key thing is that the cusp
+
+ align:start position:0%
+question, the key thing is that the cusp
+ 
+
+ align:start position:0%
+question, the key thing is that the cusp
+of the homogeneous space is really
+
+ align:start position:0%
+of the homogeneous space is really
+ 
+
+ align:start position:0%
+of the homogeneous space is really
+important here. And we were neglecting
+
+ align:start position:0%
+important here. And we were neglecting
+ 
+
+ align:start position:0%
+important here. And we were neglecting
+the cusp. Um so you know the the cusp
+
+ align:start position:0%
+the cusp. Um so you know the the cusp
+ 
+
+ align:start position:0%
+the cusp. Um so you know the the cusp
+produces a piece of the fundamental
+
+ align:start position:0%
+produces a piece of the fundamental
+ 
+
+ align:start position:0%
+produces a piece of the fundamental
+domain that's really skinny and it
+
+ align:start position:0%
+domain that's really skinny and it
+ 
+
+ align:start position:0%
+domain that's really skinny and it
+doesn't look like the rest of it. And
+
+ align:start position:0%
+doesn't look like the rest of it. And
+ 
+
+ align:start position:0%
+doesn't look like the rest of it. And
+when something's in the cusp, it doesn't
+
+ align:start position:0%
+when something's in the cusp, it doesn't
+ 
+
+ align:start position:0%
+when something's in the cusp, it doesn't
+apply.
+
+ align:start position:0%
+apply.
+ 
+
+ align:start position:0%
+apply.
+Um and so actually Hedland proved
+
+ align:start position:0%
+Um and so actually Hedland proved
+ 
+
+ align:start position:0%
+Um and so actually Hedland proved
+another theorem which is that if you
+
+ align:start position:0%
+another theorem which is that if you
+ 
+
+ align:start position:0%
+another theorem which is that if you
+take a a co-compact subgroup gamma then
+
+ align:start position:0%
+take a a co-compact subgroup gamma then
+ 
+
+ align:start position:0%
+take a a co-compact subgroup gamma then
+in Gmod gamma every unipotent orbit uh
+
+ align:start position:0%
+in Gmod gamma every unipotent orbit uh
+ 
+
+ align:start position:0%
+in Gmod gamma every unipotent orbit uh
+is is dense and this is a sketch of the
+
+ align:start position:0%
+is is dense and this is a sketch of the
+ 
+
+ align:start position:0%
+is is dense and this is a sketch of the
+proof of that theorem.
+
+ align:start position:0%
+proof of that theorem.
+ 
+
+ align:start position:0%
+proof of that theorem.
+Okay. But now what goes wrong um is that
+
+ align:start position:0%
+Okay. But now what goes wrong um is that
+ 
+
+ align:start position:0%
+Okay. But now what goes wrong um is that
+this a minus rx
+
+ align:start position:0%
+this a minus rx
+ 
+
+ align:start position:0%
+this a minus rx
+could be very far in the cusp and then
+
+ align:start position:0%
+could be very far in the cusp and then
+ 
+
+ align:start position:0%
+could be very far in the cusp and then
+our whole analysis is wrong. So what
+
+ align:start position:0%
+our whole analysis is wrong. So what
+ 
+
+ align:start position:0%
+our whole analysis is wrong. So what
+what we've roughly shown is that either
+
+ align:start position:0%
+what we've roughly shown is that either
+ 
+
+ align:start position:0%
+what we've roughly shown is that either
+our orbit is very well distributed or a
+
+ align:start position:0%
+our orbit is very well distributed or a
+ 
+
+ align:start position:0%
+our orbit is very well distributed or a
+minus rx is deep in the cusp.
+
+ align:start position:0%
+minus rx is deep in the cusp.
+ 
+
+ align:start position:0%
+minus rx is deep in the cusp.
+And if you unwind what that means about
+
+ align:start position:0%
+And if you unwind what that means about
+ 
+
+ align:start position:0%
+And if you unwind what that means about
+x, it means that it's very close to
+
+ align:start position:0%
+x, it means that it's very close to
+ 
+
+ align:start position:0%
+x, it means that it's very close to
+being a periodic or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool. Okay. So, we'll talk a little more
+
+ align:start position:0%
+cool. Okay. So, we'll talk a little more
+ 
+
+ align:start position:0%
+cool. Okay. So, we'll talk a little more
+about homogeneous dynamics on Thursday.
+
+ align:start position:0%
+about homogeneous dynamics on Thursday.
+ 
+
+ align:start position:0%
+about homogeneous dynamics on Thursday.
+I'm not sure exactly what we'll say.
+
+ align:start position:0%
+I'm not sure exactly what we'll say.
+ 
+
+ align:start position:0%
+I'm not sure exactly what we'll say.
+Maybe we'll fill in some things.
\ No newline at end of file
diff --git a/rUis1mSzwyA.txt b/rUis1mSzwyA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3745303e1c6e68b1ed801652258a857d9c67ea8d
--- /dev/null
+++ b/rUis1mSzwyA.txt
@@ -0,0 +1,2563 @@
+align:start position:0%
+ 
+Welcome back to recitation. In this
+
+ align:start position:0%
+Welcome back to recitation. In this
+ 
+
+ align:start position:0%
+Welcome back to recitation. In this
+video, I want to talk to you about a
+
+ align:start position:0%
+video, I want to talk to you about a
+ 
+
+ align:start position:0%
+video, I want to talk to you about a
+another test for convergence we have for
+
+ align:start position:0%
+another test for convergence we have for
+ 
+
+ align:start position:0%
+another test for convergence we have for
+series that you haven't really spent any
+
+ align:start position:0%
+series that you haven't really spent any
+ 
+
+ align:start position:0%
+series that you haven't really spent any
+time looking at this particular one and
+
+ align:start position:0%
+time looking at this particular one and
+ 
+
+ align:start position:0%
+time looking at this particular one and
+it's pretty helpful and also will help
+
+ align:start position:0%
+it's pretty helpful and also will help
+ 
+
+ align:start position:0%
+it's pretty helpful and also will help
+us understand something about tailaylor
+
+ align:start position:0%
+us understand something about tailaylor
+ 
+
+ align:start position:0%
+us understand something about tailaylor
+series which I'll do in another video.
+
+ align:start position:0%
+series which I'll do in another video.
+ 
+
+ align:start position:0%
+series which I'll do in another video.
+So this is the ratio test and you'll
+
+ align:start position:0%
+So this is the ratio test and you'll
+ 
+
+ align:start position:0%
+So this is the ratio test and you'll
+understand the name of this test
+
+ align:start position:0%
+understand the name of this test
+ 
+
+ align:start position:0%
+understand the name of this test
+momentarily. So we're going to start
+
+ align:start position:0%
+momentarily. So we're going to start
+ 
+
+ align:start position:0%
+momentarily. So we're going to start
+with a series. Sorry, we're going to
+
+ align:start position:0%
+with a series. Sorry, we're going to
+ 
+
+ align:start position:0%
+with a series. Sorry, we're going to
+start with the series that we'll just
+
+ align:start position:0%
+start with the series that we'll just
+ 
+
+ align:start position:0%
+start with the series that we'll just
+say we'll call each term a
+
+ align:start position:0%
+say we'll call each term a
+ 
+
+ align:start position:0%
+say we'll call each term a
+subn. And I'm not going to tell you
+
+ align:start position:0%
+subn. And I'm not going to tell you
+ 
+
+ align:start position:0%
+subn. And I'm not going to tell you
+where it end starts because it doesn't
+
+ align:start position:0%
+where it end starts because it doesn't
+ 
+
+ align:start position:0%
+where it end starts because it doesn't
+matter. It's really going to only matter
+
+ align:start position:0%
+matter. It's really going to only matter
+ 
+
+ align:start position:0%
+matter. It's really going to only matter
+what's happening out at infinity. And to
+
+ align:start position:0%
+what's happening out at infinity. And to
+ 
+
+ align:start position:0%
+what's happening out at infinity. And to
+make things simpler, we're going to let
+
+ align:start position:0%
+make things simpler, we're going to let
+ 
+
+ align:start position:0%
+make things simpler, we're going to let
+all the terms be positive.
+
+ align:start position:0%
+all the terms be positive.
+ 
+
+ align:start position:0%
+all the terms be positive.
+Okay, you if they're not positive, you
+
+ align:start position:0%
+Okay, you if they're not positive, you
+ 
+
+ align:start position:0%
+Okay, you if they're not positive, you
+can take the absolute value of all the
+
+ align:start position:0%
+can take the absolute value of all the
+ 
+
+ align:start position:0%
+can take the absolute value of all the
+terms and still make some conclusions in
+
+ align:start position:0%
+terms and still make some conclusions in
+ 
+
+ align:start position:0%
+terms and still make some conclusions in
+terms of absolute convergence. So that's
+
+ align:start position:0%
+terms of absolute convergence. So that's
+ 
+
+ align:start position:0%
+terms of absolute convergence. So that's
+just a little sidebar, but let's just
+
+ align:start position:0%
+just a little sidebar, but let's just
+ 
+
+ align:start position:0%
+just a little sidebar, but let's just
+deal with all the terms positive, so we
+
+ align:start position:0%
+deal with all the terms positive, so we
+ 
+
+ align:start position:0%
+deal with all the terms positive, so we
+don't have to worry about anything. And
+
+ align:start position:0%
+don't have to worry about anything. And
+ 
+
+ align:start position:0%
+don't have to worry about anything. And
+now what does the ratio test say? Well,
+
+ align:start position:0%
+now what does the ratio test say? Well,
+ 
+
+ align:start position:0%
+now what does the ratio test say? Well,
+the ratio test says that we first we
+
+ align:start position:0%
+the ratio test says that we first we
+ 
+
+ align:start position:0%
+the ratio test says that we first we
+consider a certain ratio, the limit as n
+
+ align:start position:0%
+consider a certain ratio, the limit as n
+ 
+
+ align:start position:0%
+consider a certain ratio, the limit as n
+goes to infinity of a subn plus one over
+
+ align:start position:0%
+goes to infinity of a subn plus one over
+ 
+
+ align:start position:0%
+goes to infinity of a subn plus one over
+a subn. Okay, so we consider this limit.
+
+ align:start position:0%
+a subn. Okay, so we consider this limit.
+ 
+
+ align:start position:0%
+a subn. Okay, so we consider this limit.
+Well, that's your ratio. What is this
+
+ align:start position:0%
+Well, that's your ratio. What is this
+ 
+
+ align:start position:0%
+Well, that's your ratio. What is this
+doing? This is taking a term and it's
+
+ align:start position:0%
+doing? This is taking a term and it's
+ 
+
+ align:start position:0%
+doing? This is taking a term and it's
+dividing by the previous term. You do
+
+ align:start position:0%
+dividing by the previous term. You do
+ 
+
+ align:start position:0%
+dividing by the previous term. You do
+that for all of the values for n as n
+
+ align:start position:0%
+that for all of the values for n as n
+ 
+
+ align:start position:0%
+that for all of the values for n as n
+goes to infinity and you look at the
+
+ align:start position:0%
+goes to infinity and you look at the
+ 
+
+ align:start position:0%
+goes to infinity and you look at the
+limit if if it exists. Okay, if the
+
+ align:start position:0%
+limit if if it exists. Okay, if the
+ 
+
+ align:start position:0%
+limit if if it exists. Okay, if the
+limit doesn't exist, then you can't use
+
+ align:start position:0%
+limit doesn't exist, then you can't use
+ 
+
+ align:start position:0%
+limit doesn't exist, then you can't use
+this test. So sometimes that will
+
+ align:start position:0%
+this test. So sometimes that will
+ 
+
+ align:start position:0%
+this test. So sometimes that will
+happen. But if the limit exists, you can
+
+ align:start position:0%
+happen. But if the limit exists, you can
+ 
+
+ align:start position:0%
+happen. But if the limit exists, you can
+use this test and you say it equals L.
+
+ align:start position:0%
+use this test and you say it equals L.
+ 
+
+ align:start position:0%
+use this test and you say it equals L.
+And then you have the following
+
+ align:start position:0%
+And then you have the following
+ 
+
+ align:start position:0%
+And then you have the following
+conclusions you can make. So here are
+
+ align:start position:0%
+conclusions you can make. So here are
+ 
+
+ align:start position:0%
+conclusions you can make. So here are
+the conclusions. There's three of them.
+
+ align:start position:0%
+the conclusions. There's three of them.
+ 
+
+ align:start position:0%
+the conclusions. There's three of them.
+So if L is less than
+
+ align:start position:0%
+So if L is less than
+ 
+
+ align:start position:0%
+So if L is less than
+one, then the series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges. Okay, that's nice. It's good.
+
+ align:start position:0%
+converges. Okay, that's nice. It's good.
+ 
+
+ align:start position:0%
+converges. Okay, that's nice. It's good.
+If L is bigger than
+
+ align:start position:0%
+If L is bigger than
+ 
+
+ align:start position:0%
+If L is bigger than
+one, the series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diverges. Okay, that's another good
+
+ align:start position:0%
+diverges. Okay, that's another good
+ 
+
+ align:start position:0%
+diverges. Okay, that's another good
+thing. And then the last one is if L
+
+ align:start position:0%
+thing. And then the last one is if L
+ 
+
+ align:start position:0%
+thing. And then the last one is if L
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+1, you can't conclude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything. So I I will try and convince
+
+ align:start position:0%
+anything. So I I will try and convince
+ 
+
+ align:start position:0%
+anything. So I I will try and convince
+you of that fact with a few examples
+
+ align:start position:0%
+you of that fact with a few examples
+ 
+
+ align:start position:0%
+you of that fact with a few examples
+later. But uh but let's look at this. So
+
+ align:start position:0%
+later. But uh but let's look at this. So
+ 
+
+ align:start position:0%
+later. But uh but let's look at this. So
+you look at the ratio and if the ratio
+
+ align:start position:0%
+you look at the ratio and if the ratio
+ 
+
+ align:start position:0%
+you look at the ratio and if the ratio
+is less than one then you actually can
+
+ align:start position:0%
+is less than one then you actually can
+ 
+
+ align:start position:0%
+is less than one then you actually can
+conclude the series converges and if the
+
+ align:start position:0%
+conclude the series converges and if the
+ 
+
+ align:start position:0%
+conclude the series converges and if the
+ratio is bigger than one you can
+
+ align:start position:0%
+ratio is bigger than one you can
+ 
+
+ align:start position:0%
+ratio is bigger than one you can
+conclude that the series diverges. So
+
+ align:start position:0%
+conclude that the series diverges. So
+ 
+
+ align:start position:0%
+conclude that the series diverges. So
+let me just give you a little
+
+ align:start position:0%
+let me just give you a little
+ 
+
+ align:start position:0%
+let me just give you a little
+understanding of why this one is true
+
+ align:start position:0%
+understanding of why this one is true
+ 
+
+ align:start position:0%
+understanding of why this one is true
+and then the same kind of logic can be
+
+ align:start position:0%
+and then the same kind of logic can be
+ 
+
+ align:start position:0%
+and then the same kind of logic can be
+used for this second one. So we'll try
+
+ align:start position:0%
+used for this second one. So we'll try
+ 
+
+ align:start position:0%
+used for this second one. So we'll try
+and understand just at least a little
+
+ align:start position:0%
+and understand just at least a little
+ 
+
+ align:start position:0%
+and understand just at least a little
+bit why when L is less than one the
+
+ align:start position:0%
+bit why when L is less than one the
+ 
+
+ align:start position:0%
+bit why when L is less than one the
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+converges. Okay. So let me just start
+
+ align:start position:0%
+converges. Okay. So let me just start
+ 
+
+ align:start position:0%
+converges. Okay. So let me just start
+writing here. So if L is less than one
+
+ align:start position:0%
+writing here. So if L is less than one
+ 
+
+ align:start position:0%
+writing here. So if L is less than one
+then this means that we have that a sub
+
+ align:start position:0%
+then this means that we have that a sub
+ 
+
+ align:start position:0%
+then this means that we have that a sub
+n plus one over a subn as n goes to
+
+ align:start position:0%
+n plus one over a subn as n goes to
+ 
+
+ align:start position:0%
+n plus one over a subn as n goes to
+infinity is equal to l which is less
+
+ align:start position:0%
+infinity is equal to l which is less
+ 
+
+ align:start position:0%
+infinity is equal to l which is less
+than one. Right? So we can pick
+
+ align:start position:0%
+than one. Right? So we can pick
+ 
+
+ align:start position:0%
+than one. Right? So we can pick
+something between l and one. We can pick
+
+ align:start position:0%
+something between l and one. We can pick
+ 
+
+ align:start position:0%
+something between l and one. We can pick
+a number between l and one because l is
+
+ align:start position:0%
+a number between l and one because l is
+ 
+
+ align:start position:0%
+a number between l and one because l is
+strictly less than one. And so what I'm
+
+ align:start position:0%
+strictly less than one. And so what I'm
+ 
+
+ align:start position:0%
+strictly less than one. And so what I'm
+going to do is I'm going to say I'm
+
+ align:start position:0%
+going to do is I'm going to say I'm
+ 
+
+ align:start position:0%
+going to do is I'm going to say I'm
+going to call this thing r. Some number
+
+ align:start position:0%
+going to call this thing r. Some number
+ 
+
+ align:start position:0%
+going to call this thing r. Some number
+between l and one. Okay. So what does
+
+ align:start position:0%
+between l and one. Okay. So what does
+ 
+
+ align:start position:0%
+between l and one. Okay. So what does
+that mean? That means
+
+ align:start position:0%
+that mean? That means
+ 
+
+ align:start position:0%
+that mean? That means
+that for large n we have a sub n + one
+
+ align:start position:0%
+that for large n we have a sub n + one
+ 
+
+ align:start position:0%
+that for large n we have a sub n + one
+over a subn. Sorry, that looks like I'm
+
+ align:start position:0%
+over a subn. Sorry, that looks like I'm
+ 
+
+ align:start position:0%
+over a subn. Sorry, that looks like I'm
+adding one to the a subn. That's a
+
+ align:start position:0%
+adding one to the a subn. That's a
+ 
+
+ align:start position:0%
+adding one to the a subn. That's a
+subscript. a sub n plus one over a subn
+
+ align:start position:0%
+subscript. a sub n plus one over a subn
+ 
+
+ align:start position:0%
+subscript. a sub n plus one over a subn
+is less than some fixed r. So I'm
+
+ align:start position:0%
+is less than some fixed r. So I'm
+ 
+
+ align:start position:0%
+is less than some fixed r. So I'm
+picking a value r between l and one. And
+
+ align:start position:0%
+picking a value r between l and one. And
+ 
+
+ align:start position:0%
+picking a value r between l and one. And
+then this is true for all large n. And
+
+ align:start position:0%
+then this is true for all large n. And
+ 
+
+ align:start position:0%
+then this is true for all large n. And
+when you're doing math, sometimes people
+
+ align:start position:0%
+when you're doing math, sometimes people
+ 
+
+ align:start position:0%
+when you're doing math, sometimes people
+say for n, you know, bigger than or
+
+ align:start position:0%
+say for n, you know, bigger than or
+ 
+
+ align:start position:0%
+say for n, you know, bigger than or
+equal to some fixed value. Basically, if
+
+ align:start position:0%
+equal to some fixed value. Basically, if
+ 
+
+ align:start position:0%
+equal to some fixed value. Basically, if
+you go far enough out in the sequence,
+
+ align:start position:0%
+you go far enough out in the sequence,
+ 
+
+ align:start position:0%
+you go far enough out in the sequence,
+then all the values bigger than some
+
+ align:start position:0%
+then all the values bigger than some
+ 
+
+ align:start position:0%
+then all the values bigger than some
+fixed one have this ratio. Okay, but
+
+ align:start position:0%
+fixed one have this ratio. Okay, but
+ 
+
+ align:start position:0%
+fixed one have this ratio. Okay, but
+let's get fancy with this. This we can
+
+ align:start position:0%
+let's get fancy with this. This we can
+ 
+
+ align:start position:0%
+let's get fancy with this. This we can
+rewrite as r the n +1 over r the n.
+
+ align:start position:0%
+rewrite as r the n +1 over r the n.
+ 
+
+ align:start position:0%
+rewrite as r the n +1 over r the n.
+Right? This is just r. And now if I do a
+
+ align:start position:0%
+Right? This is just r. And now if I do a
+ 
+
+ align:start position:0%
+Right? This is just r. And now if I do a
+little moving around, what do I see? I
+
+ align:start position:0%
+little moving around, what do I see? I
+ 
+
+ align:start position:0%
+little moving around, what do I see? I
+see that uh a sub n +1 over r the n +1
+
+ align:start position:0%
+see that uh a sub n +1 over r the n +1
+ 
+
+ align:start position:0%
+see that uh a sub n +1 over r the n +1
+is less than a subn / r the n. Now this
+
+ align:start position:0%
+is less than a subn / r the n. Now this
+ 
+
+ align:start position:0%
+is less than a subn / r the n. Now this
+might be weird. What did I do? I just
+
+ align:start position:0%
+might be weird. What did I do? I just
+ 
+
+ align:start position:0%
+might be weird. What did I do? I just
+multiplied through by the a subn and I
+
+ align:start position:0%
+multiplied through by the a subn and I
+ 
+
+ align:start position:0%
+multiplied through by the a subn and I
+divided by the r subn plus one. I get
+
+ align:start position:0%
+divided by the r subn plus one. I get
+ 
+
+ align:start position:0%
+divided by the r subn plus one. I get
+this thing and then I see that this
+
+ align:start position:0%
+this thing and then I see that this
+ 
+
+ align:start position:0%
+this thing and then I see that this
+ratio as n goes to infinity the ratio
+
+ align:start position:0%
+ratio as n goes to infinity the ratio
+ 
+
+ align:start position:0%
+ratio as n goes to infinity the ratio
+between a subn and r to the n is
+
+ align:start position:0%
+between a subn and r to the n is
+ 
+
+ align:start position:0%
+between a subn and r to the n is
+decreasing. It's a decreasing because
+
+ align:start position:0%
+decreasing. It's a decreasing because
+ 
+
+ align:start position:0%
+decreasing. It's a decreasing because
+the next term it's
+
+ align:start position:0%
+the next term it's
+ 
+
+ align:start position:0%
+the next term it's
+smaller. Right? And so the point is that
+
+ align:start position:0%
+smaller. Right? And so the point is that
+ 
+
+ align:start position:0%
+smaller. Right? And so the point is that
+if I go far enough out, if I start say
+
+ align:start position:0%
+if I go far enough out, if I start say
+ 
+
+ align:start position:0%
+if I go far enough out, if I start say
+past this n, if I go far enough out,
+
+ align:start position:0%
+past this n, if I go far enough out,
+ 
+
+ align:start position:0%
+past this n, if I go far enough out,
+then I always have that a subn is less
+
+ align:start position:0%
+then I always have that a subn is less
+ 
+
+ align:start position:0%
+then I always have that a subn is less
+than some constant times r the n. Okay,
+
+ align:start position:0%
+than some constant times r the n. Okay,
+ 
+
+ align:start position:0%
+than some constant times r the n. Okay,
+so this means this this is implies a
+
+ align:start position:0%
+so this means this this is implies a
+ 
+
+ align:start position:0%
+so this means this this is implies a
+subn is always less than some constant
+
+ align:start position:0%
+subn is always less than some constant
+ 
+
+ align:start position:0%
+subn is always less than some constant
+times r the
+
+ align:start position:0%
+times r the
+ 
+
+ align:start position:0%
+times r the
+n.
+
+ align:start position:0%
+n.
+ 
+
+ align:start position:0%
+n.
+Right? And now what do we do? We do our
+
+ align:start position:0%
+Right? And now what do we do? We do our
+ 
+
+ align:start position:0%
+Right? And now what do we do? We do our
+comparison test. Okay, we do our
+
+ align:start position:0%
+comparison test. Okay, we do our
+ 
+
+ align:start position:0%
+comparison test. Okay, we do our
+comparison test. This is what's going to
+
+ align:start position:0%
+comparison test. This is what's going to
+ 
+
+ align:start position:0%
+comparison test. This is what's going to
+tell us that the series converges. Now
+
+ align:start position:0%
+tell us that the series converges. Now
+ 
+
+ align:start position:0%
+tell us that the series converges. Now
+again, this isn't necessarily true all
+
+ align:start position:0%
+again, this isn't necessarily true all
+ 
+
+ align:start position:0%
+again, this isn't necessarily true all
+the way through the series, but it's
+
+ align:start position:0%
+the way through the series, but it's
+ 
+
+ align:start position:0%
+the way through the series, but it's
+true when you're far enough out after
+
+ align:start position:0%
+true when you're far enough out after
+ 
+
+ align:start position:0%
+true when you're far enough out after
+this n knot. And if a series converges
+
+ align:start position:0%
+this n knot. And if a series converges
+ 
+
+ align:start position:0%
+this n knot. And if a series converges
+at the end, the beginning is just a
+
+ align:start position:0%
+at the end, the beginning is just a
+ 
+
+ align:start position:0%
+at the end, the beginning is just a
+finite sum. So we don't have to worry
+
+ align:start position:0%
+finite sum. So we don't have to worry
+ 
+
+ align:start position:0%
+finite sum. So we don't have to worry
+about what's going on at the beginning.
+
+ align:start position:0%
+about what's going on at the beginning.
+ 
+
+ align:start position:0%
+about what's going on at the beginning.
+So again, we're at this place. We want
+
+ align:start position:0%
+So again, we're at this place. We want
+ 
+
+ align:start position:0%
+So again, we're at this place. We want
+to know what happens to the sum of a
+
+ align:start position:0%
+to know what happens to the sum of a
+ 
+
+ align:start position:0%
+to know what happens to the sum of a
+subn of all the terms a subn. Well, we
+
+ align:start position:0%
+subn of all the terms a subn. Well, we
+ 
+
+ align:start position:0%
+subn of all the terms a subn. Well, we
+know that's going to be less than k
+
+ align:start position:0%
+know that's going to be less than k
+ 
+
+ align:start position:0%
+know that's going to be less than k
+times the sum of r the n, right? because
+
+ align:start position:0%
+times the sum of r the n, right? because
+ 
+
+ align:start position:0%
+times the sum of r the n, right? because
+each a subn is less than some constant
+
+ align:start position:0%
+each a subn is less than some constant
+ 
+
+ align:start position:0%
+each a subn is less than some constant
+times r the n. Now why does this
+
+ align:start position:0%
+times r the n. Now why does this
+ 
+
+ align:start position:0%
+times r the n. Now why does this
+converge? What do we know about
+
+ align:start position:0%
+converge? What do we know about
+ 
+
+ align:start position:0%
+converge? What do we know about
+r? r we chose we said it's between l and
+
+ align:start position:0%
+r? r we chose we said it's between l and
+ 
+
+ align:start position:0%
+r? r we chose we said it's between l and
+one. In particular it's less than one.
+
+ align:start position:0%
+one. In particular it's less than one.
+ 
+
+ align:start position:0%
+one. In particular it's less than one.
+This is a geometric series. Geometric
+
+ align:start position:0%
+This is a geometric series. Geometric
+ 
+
+ align:start position:0%
+This is a geometric series. Geometric
+series when r is less than one we know
+
+ align:start position:0%
+series when r is less than one we know
+ 
+
+ align:start position:0%
+series when r is less than one we know
+it it converges. And so this one
+
+ align:start position:0%
+it it converges. And so this one
+ 
+
+ align:start position:0%
+it it converges. And so this one
+converges. So then this one
+
+ align:start position:0%
+converges. So then this one
+ 
+
+ align:start position:0%
+converges. So then this one
+converges. So that's the logic behind
+
+ align:start position:0%
+converges. So that's the logic behind
+ 
+
+ align:start position:0%
+converges. So that's the logic behind
+it. We're going to now you know we're
+
+ align:start position:0%
+it. We're going to now you know we're
+ 
+
+ align:start position:0%
+it. We're going to now you know we're
+going to now use it. But I want to point
+
+ align:start position:0%
+going to now use it. But I want to point
+ 
+
+ align:start position:0%
+going to now use it. But I want to point
+out that uh that if you liked that you
+
+ align:start position:0%
+out that uh that if you liked that you
+ 
+
+ align:start position:0%
+out that uh that if you liked that you
+can come back over here and you can do
+
+ align:start position:0%
+can come back over here and you can do
+ 
+
+ align:start position:0%
+can come back over here and you can do
+the same kind of reasoning for why if L
+
+ align:start position:0%
+the same kind of reasoning for why if L
+ 
+
+ align:start position:0%
+the same kind of reasoning for why if L
+is bigger than one a subn the this
+
+ align:start position:0%
+is bigger than one a subn the this
+ 
+
+ align:start position:0%
+is bigger than one a subn the this
+series the sum of the A subn diverges
+
+ align:start position:0%
+series the sum of the A subn diverges
+ 
+
+ align:start position:0%
+series the sum of the A subn diverges
+and that's going to come down to now you
+
+ align:start position:0%
+and that's going to come down to now you
+ 
+
+ align:start position:0%
+and that's going to come down to now you
+choose an R that's between L and one but
+
+ align:start position:0%
+choose an R that's between L and one but
+ 
+
+ align:start position:0%
+choose an R that's between L and one but
+it has to be bigger than one. Okay. And
+
+ align:start position:0%
+it has to be bigger than one. Okay. And
+ 
+
+ align:start position:0%
+it has to be bigger than one. Okay. And
+then you can uh you can look at that or
+
+ align:start position:0%
+then you can uh you can look at that or
+ 
+
+ align:start position:0%
+then you can uh you can look at that or
+maybe R has to be bigger than L. I have
+
+ align:start position:0%
+maybe R has to be bigger than L. I have
+ 
+
+ align:start position:0%
+maybe R has to be bigger than L. I have
+I didn't even work that one out all the
+
+ align:start position:0%
+I didn't even work that one out all the
+ 
+
+ align:start position:0%
+I didn't even work that one out all the
+way but uh but you can do it. you put an
+
+ align:start position:0%
+way but uh but you can do it. you put an
+ 
+
+ align:start position:0%
+way but uh but you can do it. you put an
+R in there somewhere and the same kind
+
+ align:start position:0%
+R in there somewhere and the same kind
+ 
+
+ align:start position:0%
+R in there somewhere and the same kind
+of logic because the R will be bigger
+
+ align:start position:0%
+of logic because the R will be bigger
+ 
+
+ align:start position:0%
+of logic because the R will be bigger
+than one, you're going to get to a place
+
+ align:start position:0%
+than one, you're going to get to a place
+ 
+
+ align:start position:0%
+than one, you're going to get to a place
+where probably the inequality sign is
+
+ align:start position:0%
+where probably the inequality sign is
+ 
+
+ align:start position:0%
+where probably the inequality sign is
+going to go the opposite way, right? And
+
+ align:start position:0%
+going to go the opposite way, right? And
+ 
+
+ align:start position:0%
+going to go the opposite way, right? And
+then you'll have a series that diverges
+
+ align:start position:0%
+then you'll have a series that diverges
+ 
+
+ align:start position:0%
+then you'll have a series that diverges
+and the other one will be bigger than
+
+ align:start position:0%
+and the other one will be bigger than
+ 
+
+ align:start position:0%
+and the other one will be bigger than
+that one. And so that's how the logic is
+
+ align:start position:0%
+that one. And so that's how the logic is
+ 
+
+ align:start position:0%
+that one. And so that's how the logic is
+going to work. So you have to figure out
+
+ align:start position:0%
+going to work. So you have to figure out
+ 
+
+ align:start position:0%
+going to work. So you have to figure out
+where the r goes, but I guarantee you'll
+
+ align:start position:0%
+where the r goes, but I guarantee you'll
+ 
+
+ align:start position:0%
+where the r goes, but I guarantee you'll
+want the r bigger than one. And then you
+
+ align:start position:0%
+want the r bigger than one. And then you
+ 
+
+ align:start position:0%
+want the r bigger than one. And then you
+can you'll have to have the inequality
+
+ align:start position:0%
+can you'll have to have the inequality
+ 
+
+ align:start position:0%
+can you'll have to have the inequality
+signs be opposite what they are here.
+
+ align:start position:0%
+signs be opposite what they are here.
+ 
+
+ align:start position:0%
+signs be opposite what they are here.
+Okay? You'll see they're going to be
+
+ align:start position:0%
+Okay? You'll see they're going to be
+ 
+
+ align:start position:0%
+Okay? You'll see they're going to be
+opposite there.
+
+ align:start position:0%
+opposite there.
+ 
+
+ align:start position:0%
+opposite there.
+Okay, now let's get some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples. Okay, example one. Let's look
+
+ align:start position:0%
+examples. Okay, example one. Let's look
+ 
+
+ align:start position:0%
+examples. Okay, example one. Let's look
+at some that we know and then let's look
+
+ align:start position:0%
+at some that we know and then let's look
+ 
+
+ align:start position:0%
+at some that we know and then let's look
+at some that we don't know. Okay, so
+
+ align:start position:0%
+at some that we don't know. Okay, so
+ 
+
+ align:start position:0%
+at some that we don't know. Okay, so
+let's look for example first at 1 overn.
+
+ align:start position:0%
+let's look for example first at 1 overn.
+ 
+
+ align:start position:0%
+let's look for example first at 1 overn.
+All right, and let's use the ratio test
+
+ align:start position:0%
+All right, and let's use the ratio test
+ 
+
+ align:start position:0%
+All right, and let's use the ratio test
+on one overn. Maybe this seems funny
+
+ align:start position:0%
+on one overn. Maybe this seems funny
+ 
+
+ align:start position:0%
+on one overn. Maybe this seems funny
+because what do we know about it? We
+
+ align:start position:0%
+because what do we know about it? We
+ 
+
+ align:start position:0%
+because what do we know about it? We
+know it diverges, right? But let's check
+
+ align:start position:0%
+know it diverges, right? But let's check
+ 
+
+ align:start position:0%
+know it diverges, right? But let's check
+if this tells us the limit as n goes to
+
+ align:start position:0%
+if this tells us the limit as n goes to
+ 
+
+ align:start position:0%
+if this tells us the limit as n goes to
+infinity of well what's the n + 1st term
+
+ align:start position:0%
+infinity of well what's the n + 1st term
+ 
+
+ align:start position:0%
+infinity of well what's the n + 1st term
+of this? It's going to be 1 / n + 1. And
+
+ align:start position:0%
+of this? It's going to be 1 / n + 1. And
+ 
+
+ align:start position:0%
+of this? It's going to be 1 / n + 1. And
+what's the nth term of this? It's going
+
+ align:start position:0%
+what's the nth term of this? It's going
+ 
+
+ align:start position:0%
+what's the nth term of this? It's going
+to be 1 / n. And so we get it's the
+
+ align:start position:0%
+to be 1 / n. And so we get it's the
+ 
+
+ align:start position:0%
+to be 1 / n. And so we get it's the
+limit as n goes to
+
+ align:start position:0%
+limit as n goes to
+ 
+
+ align:start position:0%
+limit as n goes to
+infinity of n / n + 1 and that equals 1.
+
+ align:start position:0%
+infinity of n / n + 1 and that equals 1.
+ 
+
+ align:start position:0%
+infinity of n / n + 1 and that equals 1.
+Hm. So this one didn't work. This one
+
+ align:start position:0%
+Hm. So this one didn't work. This one
+ 
+
+ align:start position:0%
+Hm. So this one didn't work. This one
+didn't tell us anything. And okay, but
+
+ align:start position:0%
+didn't tell us anything. And okay, but
+ 
+
+ align:start position:0%
+didn't tell us anything. And okay, but
+we know this one diverges. So we know
+
+ align:start position:0%
+we know this one diverges. So we know
+ 
+
+ align:start position:0%
+we know this one diverges. So we know
+that that this makes us think well maybe
+
+ align:start position:0%
+that that this makes us think well maybe
+ 
+
+ align:start position:0%
+that that this makes us think well maybe
+when L is one then we know it diverges.
+
+ align:start position:0%
+when L is one then we know it diverges.
+ 
+
+ align:start position:0%
+when L is one then we know it diverges.
+But just to make sure we don't make that
+
+ align:start position:0%
+But just to make sure we don't make that
+ 
+
+ align:start position:0%
+But just to make sure we don't make that
+conclusion, we don't draw that
+
+ align:start position:0%
+conclusion, we don't draw that
+ 
+
+ align:start position:0%
+conclusion, we don't draw that
+conclusion. Let's look at 1 over n^2.
+
+ align:start position:0%
+conclusion. Let's look at 1 over n^2.
+ 
+
+ align:start position:0%
+conclusion. Let's look at 1 over n^2.
+And what are the terms there? A sub n
+
+ align:start position:0%
+And what are the terms there? A sub n
+ 
+
+ align:start position:0%
+And what are the terms there? A sub n
+plus1 and a subn. The limit as n goes to
+
+ align:start position:0%
+plus1 and a subn. The limit as n goes to
+ 
+
+ align:start position:0%
+plus1 and a subn. The limit as n goes to
+infinity. Well, the n plus first term is
+
+ align:start position:0%
+infinity. Well, the n plus first term is
+ 
+
+ align:start position:0%
+infinity. Well, the n plus first term is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+be 1 over n plus oneity squared. And the
+
+ align:start position:0%
+be 1 over n plus oneity squared. And the
+ 
+
+ align:start position:0%
+be 1 over n plus oneity squared. And the
+nth term is going to be 1 over n^2,
+
+ align:start position:0%
+nth term is going to be 1 over n^2,
+ 
+
+ align:start position:0%
+nth term is going to be 1 over n^2,
+which is going to be the limit as n goes
+
+ align:start position:0%
+which is going to be the limit as n goes
+ 
+
+ align:start position:0%
+which is going to be the limit as n goes
+to infinity of
+
+ align:start position:0%
+to infinity of
+ 
+
+ align:start position:0%
+to infinity of
+n^2 over n
+
+ align:start position:0%
+n^2 over n
+ 
+
+ align:start position:0%
+n^2 over n
++1^2, which is also equal to one. And
+
+ align:start position:0%
++1^2, which is also equal to one. And
+ 
+
+ align:start position:0%
++1^2, which is also equal to one. And
+what do we know about this one? This one
+
+ align:start position:0%
+what do we know about this one? This one
+ 
+
+ align:start position:0%
+what do we know about this one? This one
+converges. So this one gave us the L is
+
+ align:start position:0%
+converges. So this one gave us the L is
+ 
+
+ align:start position:0%
+converges. So this one gave us the L is
+equal to 1 and but we know this one
+
+ align:start position:0%
+equal to 1 and but we know this one
+ 
+
+ align:start position:0%
+equal to 1 and but we know this one
+diverges. And this one gave us L is
+
+ align:start position:0%
+diverges. And this one gave us L is
+ 
+
+ align:start position:0%
+diverges. And this one gave us L is
+equal to one. and we know it converges.
+
+ align:start position:0%
+equal to one. and we know it converges.
+ 
+
+ align:start position:0%
+equal to one. and we know it converges.
+So we know that when L equals 1, we
+
+ align:start position:0%
+So we know that when L equals 1, we
+ 
+
+ align:start position:0%
+So we know that when L equals 1, we
+really cannot conclude convergence or
+
+ align:start position:0%
+really cannot conclude convergence or
+ 
+
+ align:start position:0%
+really cannot conclude convergence or
+divergence. Okay, L equals 1 doesn't let
+
+ align:start position:0%
+divergence. Okay, L equals 1 doesn't let
+ 
+
+ align:start position:0%
+divergence. Okay, L equals 1 doesn't let
+us draw any conclusions. But now let's
+
+ align:start position:0%
+us draw any conclusions. But now let's
+ 
+
+ align:start position:0%
+us draw any conclusions. But now let's
+see something where you know we can draw
+
+ align:start position:0%
+see something where you know we can draw
+ 
+
+ align:start position:0%
+see something where you know we can draw
+a conclusion because it'd be no fun if
+
+ align:start position:0%
+a conclusion because it'd be no fun if
+ 
+
+ align:start position:0%
+a conclusion because it'd be no fun if
+this test never told us
+
+ align:start position:0%
+this test never told us
+ 
+
+ align:start position:0%
+this test never told us
+anything. It probably wouldn't be be a
+
+ align:start position:0%
+anything. It probably wouldn't be be a
+ 
+
+ align:start position:0%
+anything. It probably wouldn't be be a
+test then. So let's try this one. Let's
+
+ align:start position:0%
+test then. So let's try this one. Let's
+ 
+
+ align:start position:0%
+test then. So let's try this one. Let's
+try um 4 to the n over n * 3 the n.
+
+ align:start position:0%
+try um 4 to the n over n * 3 the n.
+ 
+
+ align:start position:0%
+try um 4 to the n over n * 3 the n.
+Let's see what that one does.
+
+ align:start position:0%
+Let's see what that one does.
+ 
+
+ align:start position:0%
+Let's see what that one does.
+All right. So, let's see what is We need
+
+ align:start position:0%
+All right. So, let's see what is We need
+ 
+
+ align:start position:0%
+All right. So, let's see what is We need
+the limit as n goes to infinity. We need
+
+ align:start position:0%
+the limit as n goes to infinity. We need
+ 
+
+ align:start position:0%
+the limit as n goes to infinity. We need
+the n plus first term. So, let's plug in
+
+ align:start position:0%
+the n plus first term. So, let's plug in
+ 
+
+ align:start position:0%
+the n plus first term. So, let's plug in
+n + one for all of these. And I'm
+
+ align:start position:0%
+n + one for all of these. And I'm
+ 
+
+ align:start position:0%
+n + one for all of these. And I'm
+actually going to do a little trick here
+
+ align:start position:0%
+actually going to do a little trick here
+ 
+
+ align:start position:0%
+actually going to do a little trick here
+and I'll I'll explain it as I go. 4 n +
+
+ align:start position:0%
+and I'll I'll explain it as I go. 4 n +
+ 
+
+ align:start position:0%
+and I'll I'll explain it as I go. 4 n +
+1 over n +1 3 n +1. I'm going to
+
+ align:start position:0%
+1 over n +1 3 n +1. I'm going to
+ 
+
+ align:start position:0%
+1 over n +1 3 n +1. I'm going to
+multiply by 1 over a subn because
+
+ align:start position:0%
+multiply by 1 over a subn because
+ 
+
+ align:start position:0%
+multiply by 1 over a subn because
+sometimes that's a lot easier to do. I
+
+ align:start position:0%
+sometimes that's a lot easier to do. I
+ 
+
+ align:start position:0%
+sometimes that's a lot easier to do. I
+could have done it on these other ones
+
+ align:start position:0%
+could have done it on these other ones
+ 
+
+ align:start position:0%
+could have done it on these other ones
+maybe, but now I'm going to do it on
+
+ align:start position:0%
+maybe, but now I'm going to do it on
+ 
+
+ align:start position:0%
+maybe, but now I'm going to do it on
+this one. So, this is actually what the
+
+ align:start position:0%
+this one. So, this is actually what the
+ 
+
+ align:start position:0%
+this one. So, this is actually what the
+a subn is going to look like, right? I
+
+ align:start position:0%
+a subn is going to look like, right? I
+ 
+
+ align:start position:0%
+a subn is going to look like, right? I
+had to put in n plus one to get a sub n
+
+ align:start position:0%
+had to put in n plus one to get a sub n
+ 
+
+ align:start position:0%
+had to put in n plus one to get a sub n
+plus one. This is a subn. I'm going to
+
+ align:start position:0%
+plus one. This is a subn. I'm going to
+ 
+
+ align:start position:0%
+plus one. This is a subn. I'm going to
+write down 1 / a subn. And that's going
+
+ align:start position:0%
+write down 1 / a subn. And that's going
+ 
+
+ align:start position:0%
+write down 1 / a subn. And that's going
+to give me n * 3 the n over 4 the n. And
+
+ align:start position:0%
+to give me n * 3 the n over 4 the n. And
+ 
+
+ align:start position:0%
+to give me n * 3 the n over 4 the n. And
+now let's start simplifying. I have 3
+
+ align:start position:0%
+now let's start simplifying. I have 3
+ 
+
+ align:start position:0%
+now let's start simplifying. I have 3
+the n over 3 n + 1. I'm left with just a
+
+ align:start position:0%
+the n over 3 n + 1. I'm left with just a
+ 
+
+ align:start position:0%
+the n over 3 n + 1. I'm left with just a
+three there. four to the n and four to
+
+ align:start position:0%
+three there. four to the n and four to
+ 
+
+ align:start position:0%
+three there. four to the n and four to
+the n plus one. I'm up with just a four
+
+ align:start position:0%
+the n plus one. I'm up with just a four
+ 
+
+ align:start position:0%
+the n plus one. I'm up with just a four
+there. And now the limit as n goes to
+
+ align:start position:0%
+there. And now the limit as n goes to
+ 
+
+ align:start position:0%
+there. And now the limit as n goes to
+infinity. Let's just rewrite it so I
+
+ align:start position:0%
+infinity. Let's just rewrite it so I
+ 
+
+ align:start position:0%
+infinity. Let's just rewrite it so I
+know what it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is. Let's see. I have 4 n over 3 * n +
+
+ align:start position:0%
+is. Let's see. I have 4 n over 3 * n +
+ 
+
+ align:start position:0%
+is. Let's see. I have 4 n over 3 * n +
+1. Well, the four and the three I can
+
+ align:start position:0%
+1. Well, the four and the three I can
+ 
+
+ align:start position:0%
+1. Well, the four and the three I can
+actually just pull out. But what do I
+
+ align:start position:0%
+actually just pull out. But what do I
+ 
+
+ align:start position:0%
+actually just pull out. But what do I
+have here? n over n plus one. The limit
+
+ align:start position:0%
+have here? n over n plus one. The limit
+ 
+
+ align:start position:0%
+have here? n over n plus one. The limit
+as n goes to infinity of that that
+
+ align:start position:0%
+as n goes to infinity of that that
+ 
+
+ align:start position:0%
+as n goes to infinity of that that
+equals to
+
+ align:start position:0%
+equals to
+ 
+
+ align:start position:0%
+equals to
+4/3. That's bigger than one. So that
+
+ align:start position:0%
+4/3. That's bigger than one. So that
+ 
+
+ align:start position:0%
+4/3. That's bigger than one. So that
+actually diverges.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And I have one more example. And
+
+ align:start position:0%
+Okay. And I have one more example. And
+ 
+
+ align:start position:0%
+Okay. And I have one more example. And
+I'm almost out of space. And let me
+
+ align:start position:0%
+I'm almost out of space. And let me
+ 
+
+ align:start position:0%
+I'm almost out of space. And let me
+actually come over here and figure out
+
+ align:start position:0%
+actually come over here and figure out
+ 
+
+ align:start position:0%
+actually come over here and figure out
+what example I wanted. Ah, sorry about
+
+ align:start position:0%
+what example I wanted. Ah, sorry about
+ 
+
+ align:start position:0%
+what example I wanted. Ah, sorry about
+that. I knew I had one more.
+
+ align:start position:0%
+that. I knew I had one more.
+ 
+
+ align:start position:0%
+that. I knew I had one more.
+Okay. N to the 10th over 10 to the n. So
+
+ align:start position:0%
+Okay. N to the 10th over 10 to the n. So
+ 
+
+ align:start position:0%
+Okay. N to the 10th over 10 to the n. So
+this is kind of an interesting one
+
+ align:start position:0%
+this is kind of an interesting one
+ 
+
+ align:start position:0%
+this is kind of an interesting one
+because you have you have an exponential
+
+ align:start position:0%
+because you have you have an exponential
+ 
+
+ align:start position:0%
+because you have you have an exponential
+and then you have a power of n. So let's
+
+ align:start position:0%
+and then you have a power of n. So let's
+ 
+
+ align:start position:0%
+and then you have a power of n. So let's
+look at this one. So we need to consider
+
+ align:start position:0%
+look at this one. So we need to consider
+ 
+
+ align:start position:0%
+look at this one. So we need to consider
+limit as n goes to infinity. So I put in
+
+ align:start position:0%
+limit as n goes to infinity. So I put in
+ 
+
+ align:start position:0%
+limit as n goes to infinity. So I put in
+n+1 first. n +1 to the 10th over 10 n
+
+ align:start position:0%
+n+1 first. n +1 to the 10th over 10 n
+ 
+
+ align:start position:0%
+n+1 first. n +1 to the 10th over 10 n
++1. And then I'm going to just remember
+
+ align:start position:0%
++1. And then I'm going to just remember
+ 
+
+ align:start position:0%
++1. And then I'm going to just remember
+do times 1 over a subn. So I'm going to
+
+ align:start position:0%
+do times 1 over a subn. So I'm going to
+ 
+
+ align:start position:0%
+do times 1 over a subn. So I'm going to
+have 10 the n over n the 10th. So again,
+
+ align:start position:0%
+have 10 the n over n the 10th. So again,
+ 
+
+ align:start position:0%
+have 10 the n over n the 10th. So again,
+I took a subn. I did one over that.
+
+ align:start position:0%
+I took a subn. I did one over that.
+ 
+
+ align:start position:0%
+I took a subn. I did one over that.
+That's just the reciprocal. And now
+
+ align:start position:0%
+That's just the reciprocal. And now
+ 
+
+ align:start position:0%
+That's just the reciprocal. And now
+let's start dividing if I'm allowed to
+
+ align:start position:0%
+let's start dividing if I'm allowed to
+ 
+
+ align:start position:0%
+let's start dividing if I'm allowed to
+divide. Yeah, I've got 10 to the n there
+
+ align:start position:0%
+divide. Yeah, I've got 10 to the n there
+ 
+
+ align:start position:0%
+divide. Yeah, I've got 10 to the n there
+and 10 the n plus one there. So that
+
+ align:start position:0%
+and 10 the n plus one there. So that
+ 
+
+ align:start position:0%
+and 10 the n plus one there. So that
+gives me a single 10 in the denominator.
+
+ align:start position:0%
+gives me a single 10 in the denominator.
+ 
+
+ align:start position:0%
+gives me a single 10 in the denominator.
+And so now I really have the limit as n
+
+ align:start position:0%
+And so now I really have the limit as n
+ 
+
+ align:start position:0%
+And so now I really have the limit as n
+goes to infinity of 1 / 10 times n + 1
+
+ align:start position:0%
+goes to infinity of 1 / 10 times n + 1
+ 
+
+ align:start position:0%
+goes to infinity of 1 / 10 times n + 1
+10th over n
+
+ align:start position:0%
+10th over n
+ 
+
+ align:start position:0%
+10th over n
+10th. Well, that's equal to n plus one
+
+ align:start position:0%
+10th. Well, that's equal to n plus one
+ 
+
+ align:start position:0%
+10th. Well, that's equal to n plus one
+to the 10th over n the 10th. You might
+
+ align:start position:0%
+to the 10th over n the 10th. You might
+ 
+
+ align:start position:0%
+to the 10th over n the 10th. You might
+start to get nervous and think, "Oh my
+
+ align:start position:0%
+start to get nervous and think, "Oh my
+ 
+
+ align:start position:0%
+start to get nervous and think, "Oh my
+gosh, this is these powers are getting
+
+ align:start position:0%
+gosh, this is these powers are getting
+ 
+
+ align:start position:0%
+gosh, this is these powers are getting
+really big. It might make a difference
+
+ align:start position:0%
+really big. It might make a difference
+ 
+
+ align:start position:0%
+really big. It might make a difference
+that that one is there." It doesn't make
+
+ align:start position:0%
+that that one is there." It doesn't make
+ 
+
+ align:start position:0%
+that that one is there." It doesn't make
+a difference that that one is there
+
+ align:start position:0%
+a difference that that one is there
+ 
+
+ align:start position:0%
+a difference that that one is there
+because if you actually expand this out,
+
+ align:start position:0%
+because if you actually expand this out,
+ 
+
+ align:start position:0%
+because if you actually expand this out,
+the leading term is just n to the 10th.
+
+ align:start position:0%
+the leading term is just n to the 10th.
+ 
+
+ align:start position:0%
+the leading term is just n to the 10th.
+And we we uh know that the the highest
+
+ align:start position:0%
+And we we uh know that the the highest
+ 
+
+ align:start position:0%
+And we we uh know that the the highest
+order is going or the highest degree is
+
+ align:start position:0%
+order is going or the highest degree is
+ 
+
+ align:start position:0%
+order is going or the highest degree is
+going to win out. So, it's going to be
+
+ align:start position:0%
+going to win out. So, it's going to be
+ 
+
+ align:start position:0%
+going to win out. So, it's going to be
+an n to the 10th over n to the tenth is
+
+ align:start position:0%
+an n to the 10th over n to the tenth is
+ 
+
+ align:start position:0%
+an n to the 10th over n to the tenth is
+how it's going to behave in the limit.
+
+ align:start position:0%
+how it's going to behave in the limit.
+ 
+
+ align:start position:0%
+how it's going to behave in the limit.
+So, this part's just going to go to one.
+
+ align:start position:0%
+So, this part's just going to go to one.
+ 
+
+ align:start position:0%
+So, this part's just going to go to one.
+So, I get one/10enth. Oh, that's less
+
+ align:start position:0%
+So, I get one/10enth. Oh, that's less
+ 
+
+ align:start position:0%
+So, I get one/10enth. Oh, that's less
+than one. Yay. So this
+
+ align:start position:0%
+than one. Yay. So this
+ 
+
+ align:start position:0%
+than one. Yay. So this
+series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges. Okay. So we had one that
+
+ align:start position:0%
+converges. Okay. So we had one that
+ 
+
+ align:start position:0%
+converges. Okay. So we had one that
+diverges, one that converges, and a few
+
+ align:start position:0%
+diverges, one that converges, and a few
+ 
+
+ align:start position:0%
+diverges, one that converges, and a few
+where we couldn't get conclusions by
+
+ align:start position:0%
+where we couldn't get conclusions by
+ 
+
+ align:start position:0%
+where we couldn't get conclusions by
+this test. And one point I want to make
+
+ align:start position:0%
+this test. And one point I want to make
+ 
+
+ align:start position:0%
+this test. And one point I want to make
+about this is that um in some cases you
+
+ align:start position:0%
+about this is that um in some cases you
+ 
+
+ align:start position:0%
+about this is that um in some cases you
+have the integral test already. And
+
+ align:start position:0%
+have the integral test already. And
+ 
+
+ align:start position:0%
+have the integral test already. And
+sometimes that's that's easy and that
+
+ align:start position:0%
+sometimes that's that's easy and that
+ 
+
+ align:start position:0%
+sometimes that's that's easy and that
+helps you. In the case of these examples
+
+ align:start position:0%
+helps you. In the case of these examples
+ 
+
+ align:start position:0%
+helps you. In the case of these examples
+where we couldn't tell where L was equal
+
+ align:start position:0%
+where we couldn't tell where L was equal
+ 
+
+ align:start position:0%
+where we couldn't tell where L was equal
+to one, the integral test is going to
+
+ align:start position:0%
+to one, the integral test is going to
+ 
+
+ align:start position:0%
+to one, the integral test is going to
+tell you something. But in this case,
+
+ align:start position:0%
+tell you something. But in this case,
+ 
+
+ align:start position:0%
+tell you something. But in this case,
+it's a little bit harder to deal with um
+
+ align:start position:0%
+it's a little bit harder to deal with um
+ 
+
+ align:start position:0%
+it's a little bit harder to deal with um
+to deal with this as an integral test.
+
+ align:start position:0%
+to deal with this as an integral test.
+ 
+
+ align:start position:0%
+to deal with this as an integral test.
+You can still do it, but it's a little
+
+ align:start position:0%
+You can still do it, but it's a little
+ 
+
+ align:start position:0%
+You can still do it, but it's a little
+bit harder. And so, this maybe is a
+
+ align:start position:0%
+bit harder. And so, this maybe is a
+ 
+
+ align:start position:0%
+bit harder. And so, this maybe is a
+little bit quicker way to deal with
+
+ align:start position:0%
+little bit quicker way to deal with
+ 
+
+ align:start position:0%
+little bit quicker way to deal with
+these types of types of problems. And
+
+ align:start position:0%
+these types of types of problems. And
+ 
+
+ align:start position:0%
+these types of types of problems. And
+the big thing we're going to do is in
+
+ align:start position:0%
+the big thing we're going to do is in
+ 
+
+ align:start position:0%
+the big thing we're going to do is in
+the next video on the ratio test, I'm
+
+ align:start position:0%
+the next video on the ratio test, I'm
+ 
+
+ align:start position:0%
+the next video on the ratio test, I'm
+going to show you how you can use this
+
+ align:start position:0%
+going to show you how you can use this
+ 
+
+ align:start position:0%
+going to show you how you can use this
+to determine the radius of convergence
+
+ align:start position:0%
+to determine the radius of convergence
+ 
+
+ align:start position:0%
+to determine the radius of convergence
+for these tailaylor series. So, that's
+
+ align:start position:0%
+for these tailaylor series. So, that's
+ 
+
+ align:start position:0%
+for these tailaylor series. So, that's
+actually going to be uh kind of exciting
+
+ align:start position:0%
+actually going to be uh kind of exciting
+ 
+
+ align:start position:0%
+actually going to be uh kind of exciting
+and that'll be in our next video.
\ No newline at end of file
diff --git a/re2cL2GfUfM.txt b/re2cL2GfUfM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cab04d96106fd88e533f73bf6678e75f148374a6
--- /dev/null
+++ b/re2cL2GfUfM.txt
@@ -0,0 +1,9392 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so welcome to the last lecture of
+
+ align:start position:0%
+yeah so welcome to the last lecture of
+ 
+
+ align:start position:0%
+yeah so welcome to the last lecture of
+the class uh today we're going to talk
+
+ align:start position:0%
+the class uh today we're going to talk
+ 
+
+ align:start position:0%
+the class uh today we're going to talk
+about where all this material
+
+ align:start position:0%
+about where all this material
+ 
+
+ align:start position:0%
+about where all this material
+particularly goes from here so for
+
+ align:start position:0%
+particularly goes from here so for
+ 
+
+ align:start position:0%
+particularly goes from here so for
+instance how this material applies to
+
+ align:start position:0%
+instance how this material applies to
+ 
+
+ align:start position:0%
+instance how this material applies to
+18102 a little bit of 18101 901 for sure
+
+ align:start position:0%
+18102 a little bit of 18101 901 for sure
+ 
+
+ align:start position:0%
+18102 a little bit of 18101 901 for sure
+and a little bit of 152. if those
+
+ align:start position:0%
+and a little bit of 152. if those
+ 
+
+ align:start position:0%
+and a little bit of 152. if those
+numbers don't mean anything to you right
+
+ align:start position:0%
+numbers don't mean anything to you right
+ 
+
+ align:start position:0%
+numbers don't mean anything to you right
+now that's totally fair I'm going to
+
+ align:start position:0%
+now that's totally fair I'm going to
+ 
+
+ align:start position:0%
+now that's totally fair I'm going to
+write out what the number and the title
+
+ align:start position:0%
+write out what the number and the title
+ 
+
+ align:start position:0%
+write out what the number and the title
+of it is but Loosely speaking that's the
+
+ align:start position:0%
+of it is but Loosely speaking that's the
+ 
+
+ align:start position:0%
+of it is but Loosely speaking that's the
+general plan for today but before we do
+
+ align:start position:0%
+general plan for today but before we do
+ 
+
+ align:start position:0%
+general plan for today but before we do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+I want to introduce just a little bit of
+
+ align:start position:0%
+I want to introduce just a little bit of
+ 
+
+ align:start position:0%
+I want to introduce just a little bit of
+brief history to metric spaces in the
+
+ align:start position:0%
+brief history to metric spaces in the
+ 
+
+ align:start position:0%
+brief history to metric spaces in the
+first place because I think that there's
+
+ align:start position:0%
+first place because I think that there's
+ 
+
+ align:start position:0%
+first place because I think that there's
+this weird notion that all those
+
+ align:start position:0%
+this weird notion that all those
+ 
+
+ align:start position:0%
+this weird notion that all those
+mathematical tools just pop up but in
+
+ align:start position:0%
+mathematical tools just pop up but in
+ 
+
+ align:start position:0%
+mathematical tools just pop up but in
+fact everyone sort of knew each other in
+
+ align:start position:0%
+fact everyone sort of knew each other in
+ 
+
+ align:start position:0%
+fact everyone sort of knew each other in
+the field which I think is really cool
+
+ align:start position:0%
+the field which I think is really cool
+ 
+
+ align:start position:0%
+the field which I think is really cool
+um so firstly
+
+ align:start position:0%
+um so firstly
+ 
+
+ align:start position:0%
+um so firstly
+the main thing to know is that in the
+
+ align:start position:0%
+the main thing to know is that in the
+ 
+
+ align:start position:0%
+the main thing to know is that in the
+early 1900s
+
+ align:start position:0%
+early 1900s
+ 
+
+ align:start position:0%
+early 1900s
+mathematics was far less axiomatized
+
+ align:start position:0%
+mathematics was far less axiomatized
+ 
+
+ align:start position:0%
+mathematics was far less axiomatized
+like it was far more localized in each
+
+ align:start position:0%
+like it was far more localized in each
+ 
+
+ align:start position:0%
+like it was far more localized in each
+field like oh in this field who's
+
+ align:start position:0%
+field like oh in this field who's
+ 
+
+ align:start position:0%
+field like oh in this field who's
+studying this type of function we can
+
+ align:start position:0%
+studying this type of function we can
+ 
+
+ align:start position:0%
+studying this type of function we can
+study you know what this means for the
+
+ align:start position:0%
+study you know what this means for the
+ 
+
+ align:start position:0%
+study you know what this means for the
+entire space what does being lip shits
+
+ align:start position:0%
+entire space what does being lip shits
+ 
+
+ align:start position:0%
+entire space what does being lip shits
+mean what does
+
+ align:start position:0%
+mean what does
+ 
+
+ align:start position:0%
+mean what does
+um what is a vector space things like
+
+ align:start position:0%
+um what is a vector space things like
+ 
+
+ align:start position:0%
+um what is a vector space things like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um but because of this a bunch of
+
+ align:start position:0%
+um but because of this a bunch of
+ 
+
+ align:start position:0%
+um but because of this a bunch of
+different people had all different types
+
+ align:start position:0%
+different people had all different types
+ 
+
+ align:start position:0%
+different people had all different types
+of convergence they just weren't unified
+
+ align:start position:0%
+of convergence they just weren't unified
+ 
+
+ align:start position:0%
+of convergence they just weren't unified
+and now this is fine but it makes it
+
+ align:start position:0%
+and now this is fine but it makes it
+ 
+
+ align:start position:0%
+and now this is fine but it makes it
+difficult to see if it's something
+
+ align:start position:0%
+difficult to see if it's something
+ 
+
+ align:start position:0%
+difficult to see if it's something
+that's true specifically about the space
+
+ align:start position:0%
+that's true specifically about the space
+ 
+
+ align:start position:0%
+that's true specifically about the space
+or if it's something true in higher
+
+ align:start position:0%
+or if it's something true in higher
+ 
+
+ align:start position:0%
+or if it's something true in higher
+generality
+
+ align:start position:0%
+generality
+ 
+
+ align:start position:0%
+generality
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in 1906
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fresh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invented metric spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the reason I think this is
+
+ align:start position:0%
+um the reason I think this is
+ 
+
+ align:start position:0%
+um the reason I think this is
+particularly interesting is because this
+
+ align:start position:0%
+particularly interesting is because this
+ 
+
+ align:start position:0%
+particularly interesting is because this
+this concept is one that he introduced
+
+ align:start position:0%
+this concept is one that he introduced
+ 
+
+ align:start position:0%
+this concept is one that he introduced
+in his PhD dissertation
+
+ align:start position:0%
+in his PhD dissertation
+ 
+
+ align:start position:0%
+in his PhD dissertation
+so he went throughout his PhD
+
+ align:start position:0%
+so he went throughout his PhD
+ 
+
+ align:start position:0%
+so he went throughout his PhD
+course load and then created metric
+
+ align:start position:0%
+course load and then created metric
+ 
+
+ align:start position:0%
+course load and then created metric
+spaces in his dissertation
+
+ align:start position:0%
+spaces in his dissertation
+ 
+
+ align:start position:0%
+spaces in his dissertation
+very very powerful tool and as we've
+
+ align:start position:0%
+very very powerful tool and as we've
+ 
+
+ align:start position:0%
+very very powerful tool and as we've
+seen in this class so far it unified all
+
+ align:start position:0%
+seen in this class so far it unified all
+ 
+
+ align:start position:0%
+seen in this class so far it unified all
+these different types of convergence at
+
+ align:start position:0%
+these different types of convergence at
+ 
+
+ align:start position:0%
+these different types of convergence at
+once no longer did people have to State
+
+ align:start position:0%
+once no longer did people have to State
+ 
+
+ align:start position:0%
+once no longer did people have to State
+convergence in their field and improve
+
+ align:start position:0%
+convergence in their field and improve
+ 
+
+ align:start position:0%
+convergence in their field and improve
+all the properties they can simply State
+
+ align:start position:0%
+all the properties they can simply State
+ 
+
+ align:start position:0%
+all the properties they can simply State
+the distance on it and then State what
+
+ align:start position:0%
+the distance on it and then State what
+ 
+
+ align:start position:0%
+the distance on it and then State what
+convergence means if it is in fact a
+
+ align:start position:0%
+convergence means if it is in fact a
+ 
+
+ align:start position:0%
+convergence means if it is in fact a
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+so uh this in particular really Unified
+
+ align:start position:0%
+so uh this in particular really Unified
+ 
+
+ align:start position:0%
+so uh this in particular really Unified
+Notions of convergence
+
+ align:start position:0%
+Notions of convergence
+ 
+
+ align:start position:0%
+Notions of convergence
+and other types of like open sets and
+
+ align:start position:0%
+and other types of like open sets and
+ 
+
+ align:start position:0%
+and other types of like open sets and
+things like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in particular
+
+ align:start position:0%
+so in particular
+ 
+
+ align:start position:0%
+so in particular
+this lets you prove facts about metric
+
+ align:start position:0%
+this lets you prove facts about metric
+ 
+
+ align:start position:0%
+this lets you prove facts about metric
+spaces and then stated about your space
+
+ align:start position:0%
+spaces and then stated about your space
+ 
+
+ align:start position:0%
+spaces and then stated about your space
+that's the main idea
+
+ align:start position:0%
+that's the main idea
+ 
+
+ align:start position:0%
+that's the main idea
+and then later on
+
+ align:start position:0%
+and then later on
+ 
+
+ align:start position:0%
+and then later on
+in 1914
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a mathematician known as housedorf which
+
+ align:start position:0%
+a mathematician known as housedorf which
+ 
+
+ align:start position:0%
+a mathematician known as housedorf which
+will be a familiar name if you've done
+
+ align:start position:0%
+will be a familiar name if you've done
+ 
+
+ align:start position:0%
+will be a familiar name if you've done
+topology
+
+ align:start position:0%
+topology
+ 
+
+ align:start position:0%
+topology
+a popularized metric spaces
+
+ align:start position:0%
+a popularized metric spaces
+ 
+
+ align:start position:0%
+a popularized metric spaces
+so in particular he wrote this book
+
+ align:start position:0%
+so in particular he wrote this book
+ 
+
+ align:start position:0%
+so in particular he wrote this book
+called principles of set theory
+
+ align:start position:0%
+called principles of set theory
+ 
+
+ align:start position:0%
+called principles of set theory
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and in this book he was able to define
+
+ align:start position:0%
+and in this book he was able to define
+ 
+
+ align:start position:0%
+and in this book he was able to define
+or this book was very very popular and
+
+ align:start position:0%
+or this book was very very popular and
+ 
+
+ align:start position:0%
+or this book was very very popular and
+in it he includes metric spaces so it
+
+ align:start position:0%
+in it he includes metric spaces so it
+ 
+
+ align:start position:0%
+in it he includes metric spaces so it
+made it more and more popular but in
+
+ align:start position:0%
+made it more and more popular but in
+ 
+
+ align:start position:0%
+made it more and more popular but in
+fact he did quite a bit more than that
+
+ align:start position:0%
+fact he did quite a bit more than that
+ 
+
+ align:start position:0%
+fact he did quite a bit more than that
+in this book in this book he introduced
+
+ align:start position:0%
+in this book in this book he introduced
+ 
+
+ align:start position:0%
+in this book in this book he introduced
+topological spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and topological spaces are of course
+
+ align:start position:0%
+and topological spaces are of course
+ 
+
+ align:start position:0%
+and topological spaces are of course
+what is studied in introduction to
+
+ align:start position:0%
+what is studied in introduction to
+ 
+
+ align:start position:0%
+what is studied in introduction to
+topology 8901
+
+ align:start position:0%
+topology 8901
+ 
+
+ align:start position:0%
+topology 8901
+now throughout today I'm going to use
+
+ align:start position:0%
+now throughout today I'm going to use
+ 
+
+ align:start position:0%
+now throughout today I'm going to use
+this diagram
+
+ align:start position:0%
+this diagram
+ 
+
+ align:start position:0%
+this diagram
+where what I'm going to talk about
+
+ align:start position:0%
+where what I'm going to talk about
+ 
+
+ align:start position:0%
+where what I'm going to talk about
+is this idea that topological space is
+
+ align:start position:0%
+is this idea that topological space is
+ 
+
+ align:start position:0%
+is this idea that topological space is
+are more General than metric spaces
+
+ align:start position:0%
+are more General than metric spaces
+ 
+
+ align:start position:0%
+are more General than metric spaces
+uh let me write this down topological
+
+ align:start position:0%
+uh let me write this down topological
+ 
+
+ align:start position:0%
+uh let me write this down topological
+spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way to see this is that the
+
+ align:start position:0%
+the way to see this is that the
+ 
+
+ align:start position:0%
+the way to see this is that the
+definition of a topology which we'll get
+
+ align:start position:0%
+definition of a topology which we'll get
+ 
+
+ align:start position:0%
+definition of a topology which we'll get
+to in a moment is simply a definition of
+
+ align:start position:0%
+to in a moment is simply a definition of
+ 
+
+ align:start position:0%
+to in a moment is simply a definition of
+what it means to be open
+
+ align:start position:0%
+what it means to be open
+ 
+
+ align:start position:0%
+what it means to be open
+and of course we have a notion of what
+
+ align:start position:0%
+and of course we have a notion of what
+ 
+
+ align:start position:0%
+and of course we have a notion of what
+it means to be open under the metric you
+
+ align:start position:0%
+it means to be open under the metric you
+ 
+
+ align:start position:0%
+it means to be open under the metric you
+can just cover it with Epsilon balls and
+
+ align:start position:0%
+can just cover it with Epsilon balls and
+ 
+
+ align:start position:0%
+can just cover it with Epsilon balls and
+everything's fine
+
+ align:start position:0%
+everything's fine
+ 
+
+ align:start position:0%
+everything's fine
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+topological spaces are for more General
+
+ align:start position:0%
+topological spaces are for more General
+ 
+
+ align:start position:0%
+topological spaces are for more General
+than metric spaces and there's quite a
+
+ align:start position:0%
+than metric spaces and there's quite a
+ 
+
+ align:start position:0%
+than metric spaces and there's quite a
+bit to study here
+
+ align:start position:0%
+bit to study here
+ 
+
+ align:start position:0%
+bit to study here
+so let me
+
+ align:start position:0%
+so let me
+ 
+
+ align:start position:0%
+so let me
+introduce what the definition is of a
+
+ align:start position:0%
+introduce what the definition is of a
+ 
+
+ align:start position:0%
+introduce what the definition is of a
+topological space
+
+ align:start position:0%
+topological space
+ 
+
+ align:start position:0%
+topological space
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a topological space is simply a set that
+
+ align:start position:0%
+a topological space is simply a set that
+ 
+
+ align:start position:0%
+a topological space is simply a set that
+has a topology on it
+
+ align:start position:0%
+has a topology on it
+ 
+
+ align:start position:0%
+has a topology on it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and I'll Define what it means to be a
+
+ align:start position:0%
+and I'll Define what it means to be a
+ 
+
+ align:start position:0%
+and I'll Define what it means to be a
+topology in a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+a topology t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a set X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a collection of subsets of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that I
+
+ align:start position:0%
+such that I
+ 
+
+ align:start position:0%
+such that I
+won
+
+ align:start position:0%
+won
+ 
+
+ align:start position:0%
+won
+the empty set and the entire met or not
+
+ align:start position:0%
+the empty set and the entire met or not
+ 
+
+ align:start position:0%
+the empty set and the entire met or not
+metric space the entire set is in your
+
+ align:start position:0%
+metric space the entire set is in your
+ 
+
+ align:start position:0%
+metric space the entire set is in your
+topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+if I let T I be
+
+ align:start position:0%
+if I let T I be
+ 
+
+ align:start position:0%
+if I let T I be
+a set or a collection of subsets of t
+
+ align:start position:0%
+a set or a collection of subsets of t
+ 
+
+ align:start position:0%
+a set or a collection of subsets of t
+then the arbitrary Union of them
+
+ align:start position:0%
+then the arbitrary Union of them
+ 
+
+ align:start position:0%
+then the arbitrary Union of them
+t i is in t
+
+ align:start position:0%
+t i is in t
+ 
+
+ align:start position:0%
+t i is in t
+and three
+
+ align:start position:0%
+and three
+ 
+
+ align:start position:0%
+and three
+the finite intersection
+
+ align:start position:0%
+the finite intersection
+ 
+
+ align:start position:0%
+the finite intersection
+of open sets TI
+
+ align:start position:0%
+of open sets TI
+ 
+
+ align:start position:0%
+of open sets TI
+rnt
+
+ align:start position:0%
+rnt
+ 
+
+ align:start position:0%
+rnt
+so again just reiterate a topology is
+
+ align:start position:0%
+so again just reiterate a topology is
+ 
+
+ align:start position:0%
+so again just reiterate a topology is
+just a collection of subsets of the
+
+ align:start position:0%
+just a collection of subsets of the
+ 
+
+ align:start position:0%
+just a collection of subsets of the
+metric Space X or not metric space the
+
+ align:start position:0%
+metric Space X or not metric space the
+ 
+
+ align:start position:0%
+metric Space X or not metric space the
+set X
+
+ align:start position:0%
+set X
+ 
+
+ align:start position:0%
+set X
+such that the empty set and the entirety
+
+ align:start position:0%
+such that the empty set and the entirety
+ 
+
+ align:start position:0%
+such that the empty set and the entirety
+of the set is in the topology
+
+ align:start position:0%
+of the set is in the topology
+ 
+
+ align:start position:0%
+of the set is in the topology
+uh arbitrary unions of points of
+
+ align:start position:0%
+uh arbitrary unions of points of
+ 
+
+ align:start position:0%
+uh arbitrary unions of points of
+anthropology are in the topology and
+
+ align:start position:0%
+anthropology are in the topology and
+ 
+
+ align:start position:0%
+anthropology are in the topology and
+finite intersections are as well
+
+ align:start position:0%
+finite intersections are as well
+ 
+
+ align:start position:0%
+finite intersections are as well
+and notice that these are the same as
+
+ align:start position:0%
+and notice that these are the same as
+ 
+
+ align:start position:0%
+and notice that these are the same as
+the topological properties of open sets
+
+ align:start position:0%
+the topological properties of open sets
+ 
+
+ align:start position:0%
+the topological properties of open sets
+we defined in metric spaces which is a
+
+ align:start position:0%
+we defined in metric spaces which is a
+ 
+
+ align:start position:0%
+we defined in metric spaces which is a
+good thing because this is what we would
+
+ align:start position:0%
+good thing because this is what we would
+ 
+
+ align:start position:0%
+good thing because this is what we would
+want to have if in fact metric spaces
+
+ align:start position:0%
+want to have if in fact metric spaces
+ 
+
+ align:start position:0%
+want to have if in fact metric spaces
+are more specific than topological
+
+ align:start position:0%
+are more specific than topological
+ 
+
+ align:start position:0%
+are more specific than topological
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+and what is the topological space well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a topological space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is simply a set with a topology on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll just write with t right T is the
+
+ align:start position:0%
+so I'll just write with t right T is the
+ 
+
+ align:start position:0%
+so I'll just write with t right T is the
+topology
+
+ align:start position:0%
+topology
+ 
+
+ align:start position:0%
+topology
+so with these three properties we have
+
+ align:start position:0%
+so with these three properties we have
+ 
+
+ align:start position:0%
+so with these three properties we have
+Notions of openness in particular in
+
+ align:start position:0%
+Notions of openness in particular in
+ 
+
+ align:start position:0%
+Notions of openness in particular in
+fact one can define an apology
+
+ align:start position:0%
+fact one can define an apology
+ 
+
+ align:start position:0%
+fact one can define an apology
+this is more of a terminology thing
+
+ align:start position:0%
+this is more of a terminology thing
+ 
+
+ align:start position:0%
+this is more of a terminology thing
+a set is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say a set a inside a topological
+
+ align:start position:0%
+let's say a set a inside a topological
+ 
+
+ align:start position:0%
+let's say a set a inside a topological
+Space X
+
+ align:start position:0%
+Space X
+ 
+
+ align:start position:0%
+Space X
+is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a is in the topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enclosed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x minus a
+
+ align:start position:0%
+if x minus a
+ 
+
+ align:start position:0%
+if x minus a
+is in the topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies that the complement of a
+
+ align:start position:0%
+which implies that the complement of a
+ 
+
+ align:start position:0%
+which implies that the complement of a
+closed set is open
+
+ align:start position:0%
+closed set is open
+ 
+
+ align:start position:0%
+closed set is open
+so that's an equivalent definition
+
+ align:start position:0%
+so that's an equivalent definition
+ 
+
+ align:start position:0%
+so that's an equivalent definition
+but yeah these are properties of what
+
+ align:start position:0%
+but yeah these are properties of what
+ 
+
+ align:start position:0%
+but yeah these are properties of what
+are known as open sets and this much
+
+ align:start position:0%
+are known as open sets and this much
+ 
+
+ align:start position:0%
+are known as open sets and this much
+much more general setting
+
+ align:start position:0%
+much more general setting
+ 
+
+ align:start position:0%
+much more general setting
+now you might be asking yourself like
+
+ align:start position:0%
+now you might be asking yourself like
+ 
+
+ align:start position:0%
+now you might be asking yourself like
+why should we particularly
+
+ align:start position:0%
+why should we particularly
+ 
+
+ align:start position:0%
+why should we particularly
+care like this is a very abstract
+
+ align:start position:0%
+care like this is a very abstract
+ 
+
+ align:start position:0%
+care like this is a very abstract
+definition right but I'll remind you
+
+ align:start position:0%
+definition right but I'll remind you
+ 
+
+ align:start position:0%
+definition right but I'll remind you
+that when we first started talking about
+
+ align:start position:0%
+that when we first started talking about
+ 
+
+ align:start position:0%
+that when we first started talking about
+metric spaces we had a very very general
+
+ align:start position:0%
+metric spaces we had a very very general
+ 
+
+ align:start position:0%
+metric spaces we had a very very general
+somewhat abstract definition
+
+ align:start position:0%
+somewhat abstract definition
+ 
+
+ align:start position:0%
+somewhat abstract definition
+right it's one that at first seems not
+
+ align:start position:0%
+right it's one that at first seems not
+ 
+
+ align:start position:0%
+right it's one that at first seems not
+too bad it's just the topological
+
+ align:start position:0%
+too bad it's just the topological
+ 
+
+ align:start position:0%
+too bad it's just the topological
+properties of open sets we've already
+
+ align:start position:0%
+properties of open sets we've already
+ 
+
+ align:start position:0%
+properties of open sets we've already
+discussed but with this generality we
+
+ align:start position:0%
+discussed but with this generality we
+ 
+
+ align:start position:0%
+discussed but with this generality we
+can prove quite a bit more
+
+ align:start position:0%
+can prove quite a bit more
+ 
+
+ align:start position:0%
+can prove quite a bit more
+so to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah I already noted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the topology
+
+ align:start position:0%
+the topology
+ 
+
+ align:start position:0%
+the topology
+on a metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is simply the simply unions of Epsilon
+
+ align:start position:0%
+is simply the simply unions of Epsilon
+ 
+
+ align:start position:0%
+is simply the simply unions of Epsilon
+bottles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're in a topology class this would
+
+ align:start position:0%
+if you're in a topology class this would
+ 
+
+ align:start position:0%
+if you're in a topology class this would
+say this would be the same as having a
+
+ align:start position:0%
+say this would be the same as having a
+ 
+
+ align:start position:0%
+say this would be the same as having a
+basis of Epsilon balls for the topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I'll leave it there for now
+
+ align:start position:0%
+but I'll leave it there for now
+ 
+
+ align:start position:0%
+but I'll leave it there for now
+and in fact
+
+ align:start position:0%
+and in fact
+ 
+
+ align:start position:0%
+and in fact
+when does when is the topological space
+
+ align:start position:0%
+when does when is the topological space
+ 
+
+ align:start position:0%
+when does when is the topological space
+in fact a metric space
+
+ align:start position:0%
+in fact a metric space
+ 
+
+ align:start position:0%
+in fact a metric space
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+known as a mechanical space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a topological space
+
+ align:start position:0%
+so a topological space
+ 
+
+ align:start position:0%
+so a topological space
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+is betrayable if there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there exists
+
+ align:start position:0%
+if there exists
+ 
+
+ align:start position:0%
+if there exists
+a metric d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inducing the topology on x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here the topology on a metric space
+
+ align:start position:0%
+so here the topology on a metric space
+ 
+
+ align:start position:0%
+so here the topology on a metric space
+is induced by these Epsilon balls in
+
+ align:start position:0%
+is induced by these Epsilon balls in
+ 
+
+ align:start position:0%
+is induced by these Epsilon balls in
+more generality a topological space is
+
+ align:start position:0%
+more generality a topological space is
+ 
+
+ align:start position:0%
+more generality a topological space is
+metrizable if there exists a metric
+
+ align:start position:0%
+metrizable if there exists a metric
+ 
+
+ align:start position:0%
+metrizable if there exists a metric
+inducing that topology
+
+ align:start position:0%
+inducing that topology
+ 
+
+ align:start position:0%
+inducing that topology
+and now this notion of inducing is one
+
+ align:start position:0%
+and now this notion of inducing is one
+ 
+
+ align:start position:0%
+and now this notion of inducing is one
+that I'll leave for 18901 but I just
+
+ align:start position:0%
+that I'll leave for 18901 but I just
+ 
+
+ align:start position:0%
+that I'll leave for 18901 but I just
+bring it up now because as I mentioned
+
+ align:start position:0%
+bring it up now because as I mentioned
+ 
+
+ align:start position:0%
+bring it up now because as I mentioned
+on our second day not every topological
+
+ align:start position:0%
+on our second day not every topological
+ 
+
+ align:start position:0%
+on our second day not every topological
+space is metrizable not every set that
+
+ align:start position:0%
+space is metrizable not every set that
+ 
+
+ align:start position:0%
+space is metrizable not every set that
+you're considering is going to be as
+
+ align:start position:0%
+you're considering is going to be as
+ 
+
+ align:start position:0%
+you're considering is going to be as
+nice as a metric space even though we
+
+ align:start position:0%
+nice as a metric space even though we
+ 
+
+ align:start position:0%
+nice as a metric space even though we
+can put a metric on any space it doesn't
+
+ align:start position:0%
+can put a metric on any space it doesn't
+ 
+
+ align:start position:0%
+can put a metric on any space it doesn't
+mean that it gives us actually good
+
+ align:start position:0%
+mean that it gives us actually good
+ 
+
+ align:start position:0%
+mean that it gives us actually good
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+so having a tradability is deeply
+
+ align:start position:0%
+so having a tradability is deeply
+ 
+
+ align:start position:0%
+so having a tradability is deeply
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's let's take this time real quick to
+
+ align:start position:0%
+let's let's take this time real quick to
+ 
+
+ align:start position:0%
+let's let's take this time real quick to
+define the Notions of convergence and
+
+ align:start position:0%
+define the Notions of convergence and
+ 
+
+ align:start position:0%
+define the Notions of convergence and
+open sets and continuity in terms of the
+
+ align:start position:0%
+open sets and continuity in terms of the
+ 
+
+ align:start position:0%
+open sets and continuity in terms of the
+topology just like we did on our first
+
+ align:start position:0%
+topology just like we did on our first
+ 
+
+ align:start position:0%
+topology just like we did on our first
+day right we Define what a metric was
+
+ align:start position:0%
+day right we Define what a metric was
+ 
+
+ align:start position:0%
+day right we Define what a metric was
+and then we defined all of the terms we
+
+ align:start position:0%
+and then we defined all of the terms we
+ 
+
+ align:start position:0%
+and then we defined all of the terms we
+were used to in terms of that metric
+
+ align:start position:0%
+were used to in terms of that metric
+ 
+
+ align:start position:0%
+were used to in terms of that metric
+and so we're going to do the same now
+
+ align:start position:0%
+and so we're going to do the same now
+ 
+
+ align:start position:0%
+and so we're going to do the same now
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+a neighborhood
+
+ align:start position:0%
+a neighborhood
+ 
+
+ align:start position:0%
+a neighborhood
+I should write this out the first time
+
+ align:start position:0%
+I should write this out the first time
+ 
+
+ align:start position:0%
+I should write this out the first time
+a neighborhood
+
+ align:start position:0%
+a neighborhood
+ 
+
+ align:start position:0%
+a neighborhood
+of a point x
+
+ align:start position:0%
+of a point x
+ 
+
+ align:start position:0%
+of a point x
+inside your set X
+
+ align:start position:0%
+inside your set X
+ 
+
+ align:start position:0%
+inside your set X
+is simply an open set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U containing X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why do I bring this up because our
+
+ align:start position:0%
+why do I bring this up because our
+ 
+
+ align:start position:0%
+why do I bring this up because our
+Definition of convergence and of end of
+
+ align:start position:0%
+Definition of convergence and of end of
+ 
+
+ align:start position:0%
+Definition of convergence and of end of
+continuity will depend on this
+
+ align:start position:0%
+continuity will depend on this
+ 
+
+ align:start position:0%
+continuity will depend on this
+definition of a neighborhood
+
+ align:start position:0%
+definition of a neighborhood
+ 
+
+ align:start position:0%
+definition of a neighborhood
+so two a sequence xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges to a point x
+
+ align:start position:0%
+converges to a point x
+ 
+
+ align:start position:0%
+converges to a point x
+if for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all but finitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x i
+
+ align:start position:0%
+x i
+ 
+
+ align:start position:0%
+x i
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+X I are not in the neighborhood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now recall that this is the same
+
+ align:start position:0%
+now recall that this is the same
+ 
+
+ align:start position:0%
+now recall that this is the same
+definition that we had for metric spaces
+
+ align:start position:0%
+definition that we had for metric spaces
+ 
+
+ align:start position:0%
+definition that we had for metric spaces
+right we had the Dilemma that a sequence
+
+ align:start position:0%
+right we had the Dilemma that a sequence
+ 
+
+ align:start position:0%
+right we had the Dilemma that a sequence
+converges to a point x if and only if
+
+ align:start position:0%
+converges to a point x if and only if
+ 
+
+ align:start position:0%
+converges to a point x if and only if
+for every Epsilon ball around it
+
+ align:start position:0%
+for every Epsilon ball around it
+ 
+
+ align:start position:0%
+for every Epsilon ball around it
+um all but finally many terms are
+
+ align:start position:0%
+um all but finally many terms are
+ 
+
+ align:start position:0%
+um all but finally many terms are
+outside of it which was a pretty Direct
+
+ align:start position:0%
+outside of it which was a pretty Direct
+ 
+
+ align:start position:0%
+outside of it which was a pretty Direct
+blema
+
+ align:start position:0%
+blema
+ 
+
+ align:start position:0%
+blema
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is how we Define convergence
+
+ align:start position:0%
+so this is how we Define convergence
+ 
+
+ align:start position:0%
+so this is how we Define convergence
+for topological space
+
+ align:start position:0%
+for topological space
+ 
+
+ align:start position:0%
+for topological space
+three we also state
+
+ align:start position:0%
+three we also state
+ 
+
+ align:start position:0%
+three we also state
+thinks about continuity if I have a
+
+ align:start position:0%
+thinks about continuity if I have a
+ 
+
+ align:start position:0%
+thinks about continuity if I have a
+function f from a topological space y to
+
+ align:start position:0%
+function f from a topological space y to
+ 
+
+ align:start position:0%
+function f from a topological space y to
+or sorry X to y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll say that the topologies are on
+
+ align:start position:0%
+and I'll say that the topologies are on
+ 
+
+ align:start position:0%
+and I'll say that the topologies are on
+that the topologies are called TX and Ty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I should write this out continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+for every single open set
+
+ align:start position:0%
+for every single open set
+ 
+
+ align:start position:0%
+for every single open set
+T and Ty
+
+ align:start position:0%
+T and Ty
+ 
+
+ align:start position:0%
+T and Ty
+F inverse
+
+ align:start position:0%
+F inverse
+ 
+
+ align:start position:0%
+F inverse
+of T is in TX
+
+ align:start position:0%
+of T is in TX
+ 
+
+ align:start position:0%
+of T is in TX
+in other words the inverse images of
+
+ align:start position:0%
+in other words the inverse images of
+ 
+
+ align:start position:0%
+in other words the inverse images of
+open sets uh
+
+ align:start position:0%
+open sets uh
+ 
+
+ align:start position:0%
+open sets uh
+the inverse images of open sets remain
+
+ align:start position:0%
+the inverse images of open sets remain
+ 
+
+ align:start position:0%
+the inverse images of open sets remain
+open which is as we've shown as well the
+
+ align:start position:0%
+open which is as we've shown as well the
+ 
+
+ align:start position:0%
+open which is as we've shown as well the
+same definition of continuity we can
+
+ align:start position:0%
+same definition of continuity we can
+ 
+
+ align:start position:0%
+same definition of continuity we can
+have for metric spaces so all of this is
+
+ align:start position:0%
+have for metric spaces so all of this is
+ 
+
+ align:start position:0%
+have for metric spaces so all of this is
+still very very related to what we've
+
+ align:start position:0%
+still very very related to what we've
+ 
+
+ align:start position:0%
+still very very related to what we've
+been talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you might wonder why we even study
+
+ align:start position:0%
+so you might wonder why we even study
+ 
+
+ align:start position:0%
+so you might wonder why we even study
+metric spaces at all then right because
+
+ align:start position:0%
+metric spaces at all then right because
+ 
+
+ align:start position:0%
+metric spaces at all then right because
+topological spaces are much much more
+
+ align:start position:0%
+topological spaces are much much more
+ 
+
+ align:start position:0%
+topological spaces are much much more
+General if I can prove a fact about a
+
+ align:start position:0%
+General if I can prove a fact about a
+ 
+
+ align:start position:0%
+General if I can prove a fact about a
+topological space I will have proven it
+
+ align:start position:0%
+topological space I will have proven it
+ 
+
+ align:start position:0%
+topological space I will have proven it
+for my metric space as well
+
+ align:start position:0%
+for my metric space as well
+ 
+
+ align:start position:0%
+for my metric space as well
+and the short answer to that is in my
+
+ align:start position:0%
+and the short answer to that is in my
+ 
+
+ align:start position:0%
+and the short answer to that is in my
+opinion why would the same answer to why
+
+ align:start position:0%
+opinion why would the same answer to why
+ 
+
+ align:start position:0%
+opinion why would the same answer to why
+would you study real analysis after
+
+ align:start position:0%
+would you study real analysis after
+ 
+
+ align:start position:0%
+would you study real analysis after
+calculus right in theory real analysis
+
+ align:start position:0%
+calculus right in theory real analysis
+ 
+
+ align:start position:0%
+calculus right in theory real analysis
+shows all the facts you need to know
+
+ align:start position:0%
+shows all the facts you need to know
+ 
+
+ align:start position:0%
+shows all the facts you need to know
+about calculus
+
+ align:start position:0%
+about calculus
+ 
+
+ align:start position:0%
+about calculus
+it proves in more generality but
+
+ align:start position:0%
+it proves in more generality but
+ 
+
+ align:start position:0%
+it proves in more generality but
+but you gain a lot of intuition from
+
+ align:start position:0%
+but you gain a lot of intuition from
+ 
+
+ align:start position:0%
+but you gain a lot of intuition from
+dealing with Calculus in the first place
+
+ align:start position:0%
+dealing with Calculus in the first place
+ 
+
+ align:start position:0%
+dealing with Calculus in the first place
+right before you prove the mean value
+
+ align:start position:0%
+right before you prove the mean value
+ 
+
+ align:start position:0%
+right before you prove the mean value
+theorem abstractly it makes sense to
+
+ align:start position:0%
+theorem abstractly it makes sense to
+ 
+
+ align:start position:0%
+theorem abstractly it makes sense to
+have an idea of what's Happening
+
+ align:start position:0%
+have an idea of what's Happening
+ 
+
+ align:start position:0%
+have an idea of what's Happening
+um before you even do so
+
+ align:start position:0%
+um before you even do so
+ 
+
+ align:start position:0%
+um before you even do so
+so very similarly here having intuition
+
+ align:start position:0%
+so very similarly here having intuition
+ 
+
+ align:start position:0%
+so very similarly here having intuition
+about metrics and metrics bases provides
+
+ align:start position:0%
+about metrics and metrics bases provides
+ 
+
+ align:start position:0%
+about metrics and metrics bases provides
+a lot of intuition about topological
+
+ align:start position:0%
+a lot of intuition about topological
+ 
+
+ align:start position:0%
+a lot of intuition about topological
+spaces even though most topological
+
+ align:start position:0%
+spaces even though most topological
+ 
+
+ align:start position:0%
+spaces even though most topological
+spaces are not metric spaces right it
+
+ align:start position:0%
+spaces are not metric spaces right it
+ 
+
+ align:start position:0%
+spaces are not metric spaces right it
+still gives you the framework to move
+
+ align:start position:0%
+still gives you the framework to move
+ 
+
+ align:start position:0%
+still gives you the framework to move
+forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too for this reason that's that's
+
+ align:start position:0%
+too for this reason that's that's
+ 
+
+ align:start position:0%
+too for this reason that's that's
+essentially why whenever I could I would
+
+ align:start position:0%
+essentially why whenever I could I would
+ 
+
+ align:start position:0%
+essentially why whenever I could I would
+draw pictures of what's Happening as a
+
+ align:start position:0%
+draw pictures of what's Happening as a
+ 
+
+ align:start position:0%
+draw pictures of what's Happening as a
+like blob
+
+ align:start position:0%
+like blob
+ 
+
+ align:start position:0%
+like blob
+um because then you get the intuition of
+
+ align:start position:0%
+um because then you get the intuition of
+ 
+
+ align:start position:0%
+um because then you get the intuition of
+oh how can I start to problem solve via
+
+ align:start position:0%
+oh how can I start to problem solve via
+ 
+
+ align:start position:0%
+oh how can I start to problem solve via
+a diagram
+
+ align:start position:0%
+a diagram
+ 
+
+ align:start position:0%
+a diagram
+um it just gives you that right frame of
+
+ align:start position:0%
+um it just gives you that right frame of
+ 
+
+ align:start position:0%
+um it just gives you that right frame of
+mind to move forward
+
+ align:start position:0%
+mind to move forward
+ 
+
+ align:start position:0%
+mind to move forward
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now that being said metric spaces
+
+ align:start position:0%
+now that being said metric spaces
+ 
+
+ align:start position:0%
+now that being said metric spaces
+because they're much more specific than
+
+ align:start position:0%
+because they're much more specific than
+ 
+
+ align:start position:0%
+because they're much more specific than
+topological spaces are an ABS or our
+
+ align:start position:0%
+topological spaces are an ABS or our
+ 
+
+ align:start position:0%
+topological spaces are an ABS or our
+current area of research topological
+
+ align:start position:0%
+current area of research topological
+ 
+
+ align:start position:0%
+current area of research topological
+spaces are mostly done being researched
+
+ align:start position:0%
+spaces are mostly done being researched
+ 
+
+ align:start position:0%
+spaces are mostly done being researched
+I mean topologies of not a closed field
+
+ align:start position:0%
+I mean topologies of not a closed field
+ 
+
+ align:start position:0%
+I mean topologies of not a closed field
+but Point set topology the the basic
+
+ align:start position:0%
+but Point set topology the the basic
+ 
+
+ align:start position:0%
+but Point set topology the the basic
+framework is not as much of an active
+
+ align:start position:0%
+framework is not as much of an active
+ 
+
+ align:start position:0%
+framework is not as much of an active
+area of research and Metric spaces on
+
+ align:start position:0%
+area of research and Metric spaces on
+ 
+
+ align:start position:0%
+area of research and Metric spaces on
+the other hand very much so are
+
+ align:start position:0%
+the other hand very much so are
+ 
+
+ align:start position:0%
+the other hand very much so are
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that is yet another answer to the
+
+ align:start position:0%
+that is yet another answer to the
+ 
+
+ align:start position:0%
+that is yet another answer to the
+question of why should I care about
+
+ align:start position:0%
+question of why should I care about
+ 
+
+ align:start position:0%
+question of why should I care about
+metric spaces if I could talk about
+
+ align:start position:0%
+metric spaces if I could talk about
+ 
+
+ align:start position:0%
+metric spaces if I could talk about
+topological spaces
+
+ align:start position:0%
+topological spaces
+ 
+
+ align:start position:0%
+topological spaces
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now we're going to talk about
+
+ align:start position:0%
+so now we're going to talk about
+ 
+
+ align:start position:0%
+so now we're going to talk about
+18102 unless you have some questions on
+
+ align:start position:0%
+18102 unless you have some questions on
+ 
+
+ align:start position:0%
+18102 unless you have some questions on
+the material I've talked about today
+
+ align:start position:0%
+the material I've talked about today
+ 
+
+ align:start position:0%
+the material I've talked about today
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+generate down 18901 I didn't I meant to
+
+ align:start position:0%
+generate down 18901 I didn't I meant to
+ 
+
+ align:start position:0%
+generate down 18901 I didn't I meant to
+do so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the sort of material that's
+
+ align:start position:0%
+so this is the sort of material that's
+ 
+
+ align:start position:0%
+so this is the sort of material that's
+covered
+
+ align:start position:0%
+covered
+ 
+
+ align:start position:0%
+covered
+in one of the first lectures of 18901
+
+ align:start position:0%
+in one of the first lectures of 18901
+ 
+
+ align:start position:0%
+in one of the first lectures of 18901
+introduction to topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functional analysis
+
+ align:start position:0%
+functional analysis
+ 
+
+ align:start position:0%
+functional analysis
+or intro to functional analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functional analysis is all about
+
+ align:start position:0%
+functional analysis is all about
+ 
+
+ align:start position:0%
+functional analysis is all about
+studying what are known as Norm spaces
+
+ align:start position:0%
+studying what are known as Norm spaces
+ 
+
+ align:start position:0%
+studying what are known as Norm spaces
+and we've already talked about them
+
+ align:start position:0%
+and we've already talked about them
+ 
+
+ align:start position:0%
+and we've already talked about them
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Norm spaces are just a subset of metric
+
+ align:start position:0%
+Norm spaces are just a subset of metric
+ 
+
+ align:start position:0%
+Norm spaces are just a subset of metric
+spaces we talked about this in like
+
+ align:start position:0%
+spaces we talked about this in like
+ 
+
+ align:start position:0%
+spaces we talked about this in like
+lecture three
+
+ align:start position:0%
+lecture three
+ 
+
+ align:start position:0%
+lecture three
+it's slightly more specific than metric
+
+ align:start position:0%
+it's slightly more specific than metric
+ 
+
+ align:start position:0%
+it's slightly more specific than metric
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+for Norm spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is simply a set with a norm on it
+
+ align:start position:0%
+is simply a set with a norm on it
+ 
+
+ align:start position:0%
+is simply a set with a norm on it
+or a vector space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a norm on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denoted with absolute value bars
+
+ align:start position:0%
+denoted with absolute value bars
+ 
+
+ align:start position:0%
+denoted with absolute value bars
+and specifically here the three
+
+ align:start position:0%
+and specifically here the three
+ 
+
+ align:start position:0%
+and specifically here the three
+properties we want again are a positive
+
+ align:start position:0%
+properties we want again are a positive
+ 
+
+ align:start position:0%
+properties we want again are a positive
+definiteness we want the norm to be
+
+ align:start position:0%
+definiteness we want the norm to be
+ 
+
+ align:start position:0%
+definiteness we want the norm to be
+bigger than zero or if it's equal to
+
+ align:start position:0%
+bigger than zero or if it's equal to
+ 
+
+ align:start position:0%
+bigger than zero or if it's equal to
+zero for the point B zero itself
+
+ align:start position:0%
+zero for the point B zero itself
+ 
+
+ align:start position:0%
+zero for the point B zero itself
+um positive definiteness absolute
+
+ align:start position:0%
+um positive definiteness absolute
+ 
+
+ align:start position:0%
+um positive definiteness absolute
+homogeneity and the triangle inequality
+
+ align:start position:0%
+homogeneity and the triangle inequality
+ 
+
+ align:start position:0%
+homogeneity and the triangle inequality
+these are the three properties we want
+
+ align:start position:0%
+these are the three properties we want
+ 
+
+ align:start position:0%
+these are the three properties we want
+to abnorm spaces and on the homework
+
+ align:start position:0%
+to abnorm spaces and on the homework
+ 
+
+ align:start position:0%
+to abnorm spaces and on the homework
+you've already shown that a metric
+
+ align:start position:0%
+you've already shown that a metric
+ 
+
+ align:start position:0%
+you've already shown that a metric
+induced by the norm is is in fact a
+
+ align:start position:0%
+induced by the norm is is in fact a
+ 
+
+ align:start position:0%
+induced by the norm is is in fact a
+metric so Norm spaces are generalization
+
+ align:start position:0%
+metric so Norm spaces are generalization
+ 
+
+ align:start position:0%
+metric so Norm spaces are generalization
+of metric spaces
+
+ align:start position:0%
+of metric spaces
+ 
+
+ align:start position:0%
+of metric spaces
+okay now with this definition of a norm
+
+ align:start position:0%
+okay now with this definition of a norm
+ 
+
+ align:start position:0%
+okay now with this definition of a norm
+we can yet again redefine all of our
+
+ align:start position:0%
+we can yet again redefine all of our
+ 
+
+ align:start position:0%
+we can yet again redefine all of our
+Notions of convergence in neighborhoods
+
+ align:start position:0%
+Notions of convergence in neighborhoods
+ 
+
+ align:start position:0%
+Notions of convergence in neighborhoods
+and continuity as we've done before
+
+ align:start position:0%
+and continuity as we've done before
+ 
+
+ align:start position:0%
+and continuity as we've done before
+so I'll quickly do so
+
+ align:start position:0%
+so I'll quickly do so
+ 
+
+ align:start position:0%
+so I'll quickly do so
+the way to do it
+
+ align:start position:0%
+the way to do it
+ 
+
+ align:start position:0%
+the way to do it
+is to just write it in terms of the
+
+ align:start position:0%
+is to just write it in terms of the
+ 
+
+ align:start position:0%
+is to just write it in terms of the
+metric right
+
+ align:start position:0%
+metric right
+ 
+
+ align:start position:0%
+metric right
+a sequence xn converges to X in a norm
+
+ align:start position:0%
+a sequence xn converges to X in a norm
+ 
+
+ align:start position:0%
+a sequence xn converges to X in a norm
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if for all Epsilon bigger than zero
+
+ align:start position:0%
+if for all Epsilon bigger than zero
+ 
+
+ align:start position:0%
+if for all Epsilon bigger than zero
+zero exists in n
+
+ align:start position:0%
+zero exists in n
+ 
+
+ align:start position:0%
+zero exists in n
+in the natural numbers
+
+ align:start position:0%
+in the natural numbers
+ 
+
+ align:start position:0%
+in the natural numbers
+such that for all n bigger than or equal
+
+ align:start position:0%
+such that for all n bigger than or equal
+ 
+
+ align:start position:0%
+such that for all n bigger than or equal
+to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the distance
+
+ align:start position:0%
+the distance
+ 
+
+ align:start position:0%
+the distance
+between x n and X
+
+ align:start position:0%
+between x n and X
+ 
+
+ align:start position:0%
+between x n and X
+is less than Epsilon this is the
+
+ align:start position:0%
+is less than Epsilon this is the
+ 
+
+ align:start position:0%
+is less than Epsilon this is the
+definition in terms of the metric space
+
+ align:start position:0%
+definition in terms of the metric space
+ 
+
+ align:start position:0%
+definition in terms of the metric space
+but recall that we can Define this
+
+ align:start position:0%
+but recall that we can Define this
+ 
+
+ align:start position:0%
+but recall that we can Define this
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+in terms of the norm
+
+ align:start position:0%
+in terms of the norm
+ 
+
+ align:start position:0%
+in terms of the norm
+so if you're in a class like functional
+
+ align:start position:0%
+so if you're in a class like functional
+ 
+
+ align:start position:0%
+so if you're in a class like functional
+analysis you'll probably just use this
+
+ align:start position:0%
+analysis you'll probably just use this
+ 
+
+ align:start position:0%
+analysis you'll probably just use this
+notation as opposed to going to the
+
+ align:start position:0%
+notation as opposed to going to the
+ 
+
+ align:start position:0%
+notation as opposed to going to the
+metric one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but this is the definition of
+
+ align:start position:0%
+um but this is the definition of
+ 
+
+ align:start position:0%
+um but this is the definition of
+convergence in an arm space and again we
+
+ align:start position:0%
+convergence in an arm space and again we
+ 
+
+ align:start position:0%
+convergence in an arm space and again we
+want all these definitions to be
+
+ align:start position:0%
+want all these definitions to be
+ 
+
+ align:start position:0%
+want all these definitions to be
+compatible so if it feels like
+
+ align:start position:0%
+compatible so if it feels like
+ 
+
+ align:start position:0%
+compatible so if it feels like
+repetition there's a good reason why it
+
+ align:start position:0%
+repetition there's a good reason why it
+ 
+
+ align:start position:0%
+repetition there's a good reason why it
+does it's just
+
+ align:start position:0%
+does it's just
+ 
+
+ align:start position:0%
+does it's just
+we want a new definition but one that
+
+ align:start position:0%
+we want a new definition but one that
+ 
+
+ align:start position:0%
+we want a new definition but one that
+still works with the broader setting of
+
+ align:start position:0%
+still works with the broader setting of
+ 
+
+ align:start position:0%
+still works with the broader setting of
+metric spaces so that we don't have to
+
+ align:start position:0%
+metric spaces so that we don't have to
+ 
+
+ align:start position:0%
+metric spaces so that we don't have to
+redo all of our work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+um of course we can Define Koji
+
+ align:start position:0%
+um of course we can Define Koji
+ 
+
+ align:start position:0%
+um of course we can Define Koji
+sequences in the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simply one such such that for all
+
+ align:start position:0%
+simply one such such that for all
+ 
+
+ align:start position:0%
+simply one such such that for all
+Epsilon bigger than zero
+
+ align:start position:0%
+Epsilon bigger than zero
+ 
+
+ align:start position:0%
+Epsilon bigger than zero
+there exists an n in the natural numbers
+
+ align:start position:0%
+there exists an n in the natural numbers
+ 
+
+ align:start position:0%
+there exists an n in the natural numbers
+such that for all n and M bigger than or
+
+ align:start position:0%
+such that for all n and M bigger than or
+ 
+
+ align:start position:0%
+such that for all n and M bigger than or
+equal to n
+
+ align:start position:0%
+equal to n
+ 
+
+ align:start position:0%
+equal to n
+is the distance between xn and x m
+
+ align:start position:0%
+is the distance between xn and x m
+ 
+
+ align:start position:0%
+is the distance between xn and x m
+is less than Epsilon
+
+ align:start position:0%
+is less than Epsilon
+ 
+
+ align:start position:0%
+is less than Epsilon
+so this is the definition of cushy
+
+ align:start position:0%
+so this is the definition of cushy
+ 
+
+ align:start position:0%
+so this is the definition of cushy
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+and finally we Define a set to be open
+
+ align:start position:0%
+and finally we Define a set to be open
+ 
+
+ align:start position:0%
+and finally we Define a set to be open
+if and only if we can find a ball of
+
+ align:start position:0%
+if and only if we can find a ball of
+ 
+
+ align:start position:0%
+if and only if we can find a ball of
+radius Epsilon around each point
+
+ align:start position:0%
+radius Epsilon around each point
+ 
+
+ align:start position:0%
+radius Epsilon around each point
+so three
+
+ align:start position:0%
+so three
+ 
+
+ align:start position:0%
+so three
+a subset a inside of x
+
+ align:start position:0%
+a subset a inside of x
+ 
+
+ align:start position:0%
+a subset a inside of x
+is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if for all X and A
+
+ align:start position:0%
+if for all X and A
+ 
+
+ align:start position:0%
+if for all X and A
+there exists an Epsilon bigger than zero
+
+ align:start position:0%
+there exists an Epsilon bigger than zero
+ 
+
+ align:start position:0%
+there exists an Epsilon bigger than zero
+such that the ball of radius Epsilon
+
+ align:start position:0%
+such that the ball of radius Epsilon
+ 
+
+ align:start position:0%
+such that the ball of radius Epsilon
+around X
+
+ align:start position:0%
+around X
+ 
+
+ align:start position:0%
+around X
+is contained in a and in terms of the
+
+ align:start position:0%
+is contained in a and in terms of the
+ 
+
+ align:start position:0%
+is contained in a and in terms of the
+norm
+
+ align:start position:0%
+norm
+ 
+
+ align:start position:0%
+norm
+this is the set of Y such that the norm
+
+ align:start position:0%
+this is the set of Y such that the norm
+ 
+
+ align:start position:0%
+this is the set of Y such that the norm
+distance between x minus y is less than
+
+ align:start position:0%
+distance between x minus y is less than
+ 
+
+ align:start position:0%
+distance between x minus y is less than
+Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so precisely the same as in a metric
+
+ align:start position:0%
+so precisely the same as in a metric
+ 
+
+ align:start position:0%
+so precisely the same as in a metric
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um now
+
+ align:start position:0%
+um now
+ 
+
+ align:start position:0%
+um now
+to this point as I was talking about
+
+ align:start position:0%
+to this point as I was talking about
+ 
+
+ align:start position:0%
+to this point as I was talking about
+last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so again a set is open if and only if
+
+ align:start position:0%
+so again a set is open if and only if
+ 
+
+ align:start position:0%
+so again a set is open if and only if
+for all X and A there exists a ball of
+
+ align:start position:0%
+for all X and A there exists a ball of
+ 
+
+ align:start position:0%
+for all X and A there exists a ball of
+radius Epsilon that's contained in a
+
+ align:start position:0%
+radius Epsilon that's contained in a
+ 
+
+ align:start position:0%
+radius Epsilon that's contained in a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just to continue off where we left off
+
+ align:start position:0%
+just to continue off where we left off
+ 
+
+ align:start position:0%
+just to continue off where we left off
+last time in terms of lecture five
+
+ align:start position:0%
+last time in terms of lecture five
+ 
+
+ align:start position:0%
+last time in terms of lecture five
+um we started introducing completions of
+
+ align:start position:0%
+um we started introducing completions of
+ 
+
+ align:start position:0%
+um we started introducing completions of
+metric spaces because koshy completeness
+
+ align:start position:0%
+metric spaces because koshy completeness
+ 
+
+ align:start position:0%
+metric spaces because koshy completeness
+is very very important so much so in the
+
+ align:start position:0%
+is very very important so much so in the
+ 
+
+ align:start position:0%
+is very very important so much so in the
+setting of functional analysis that we
+
+ align:start position:0%
+setting of functional analysis that we
+ 
+
+ align:start position:0%
+setting of functional analysis that we
+have a name for it
+
+ align:start position:0%
+have a name for it
+ 
+
+ align:start position:0%
+have a name for it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a bond like space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a norm space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's kosher complete essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that it's complete with respect to
+
+ align:start position:0%
+is that it's complete with respect to
+ 
+
+ align:start position:0%
+is that it's complete with respect to
+the metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because again we have a notion of koshy
+
+ align:start position:0%
+because again we have a notion of koshy
+ 
+
+ align:start position:0%
+because again we have a notion of koshy
+completeness in terms of metric spaces
+
+ align:start position:0%
+completeness in terms of metric spaces
+ 
+
+ align:start position:0%
+completeness in terms of metric spaces
+so we want it to be compatible
+
+ align:start position:0%
+so we want it to be compatible
+ 
+
+ align:start position:0%
+so we want it to be compatible
+and as we talked about last time you can
+
+ align:start position:0%
+and as we talked about last time you can
+ 
+
+ align:start position:0%
+and as we talked about last time you can
+take the completion of a norm space to
+
+ align:start position:0%
+take the completion of a norm space to
+ 
+
+ align:start position:0%
+take the completion of a norm space to
+get a buttock space
+
+ align:start position:0%
+get a buttock space
+ 
+
+ align:start position:0%
+get a buttock space
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+bottom spaces are slightly more General
+
+ align:start position:0%
+bottom spaces are slightly more General
+ 
+
+ align:start position:0%
+bottom spaces are slightly more General
+or sorry slightly more specific than a
+
+ align:start position:0%
+or sorry slightly more specific than a
+ 
+
+ align:start position:0%
+or sorry slightly more specific than a
+normal space but the tools that we use
+
+ align:start position:0%
+normal space but the tools that we use
+ 
+
+ align:start position:0%
+normal space but the tools that we use
+are very very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in particular as an example of ebonics
+
+ align:start position:0%
+in particular as an example of ebonics
+ 
+
+ align:start position:0%
+in particular as an example of ebonics
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+you can show that c Infinity of a metric
+
+ align:start position:0%
+you can show that c Infinity of a metric
+ 
+
+ align:start position:0%
+you can show that c Infinity of a metric
+space m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or even a normal space
+
+ align:start position:0%
+or even a normal space
+ 
+
+ align:start position:0%
+or even a normal space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is a bionic space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about this last time but the
+
+ align:start position:0%
+we talked about this last time but the
+ 
+
+ align:start position:0%
+we talked about this last time but the
+proof is essentially the same as in this
+
+ align:start position:0%
+proof is essentially the same as in this
+ 
+
+ align:start position:0%
+proof is essentially the same as in this
+sense of continuity where again this is
+
+ align:start position:0%
+sense of continuity where again this is
+ 
+
+ align:start position:0%
+sense of continuity where again this is
+the set of functions F that are
+
+ align:start position:0%
+the set of functions F that are
+ 
+
+ align:start position:0%
+the set of functions F that are
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this inbounded so the separamum over M
+
+ align:start position:0%
+this inbounded so the separamum over M
+ 
+
+ align:start position:0%
+this inbounded so the separamum over M
+and M
+
+ align:start position:0%
+and M
+ 
+
+ align:start position:0%
+and M
+of f of M
+
+ align:start position:0%
+of f of M
+ 
+
+ align:start position:0%
+of f of M
+sorry F of
+
+ align:start position:0%
+sorry F of
+ 
+
+ align:start position:0%
+sorry F of
+m is less than infinity
+
+ align:start position:0%
+m is less than infinity
+ 
+
+ align:start position:0%
+m is less than infinity
+so you can show that this is a buttock
+
+ align:start position:0%
+so you can show that this is a buttock
+ 
+
+ align:start position:0%
+so you can show that this is a buttock
+space there's a few other classic
+
+ align:start position:0%
+space there's a few other classic
+ 
+
+ align:start position:0%
+space there's a few other classic
+examples like RN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CN
+
+ align:start position:0%
+CN
+ 
+
+ align:start position:0%
+CN
+instead of continuous spaces or C naught
+
+ align:start position:0%
+instead of continuous spaces or C naught
+ 
+
+ align:start position:0%
+instead of continuous spaces or C naught
+a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but most of them are based off of these
+
+ align:start position:0%
+but most of them are based off of these
+ 
+
+ align:start position:0%
+but most of them are based off of these
+four these are the few key ones to have
+
+ align:start position:0%
+four these are the few key ones to have
+ 
+
+ align:start position:0%
+four these are the few key ones to have
+in mind and these are so useful that it
+
+ align:start position:0%
+in mind and these are so useful that it
+ 
+
+ align:start position:0%
+in mind and these are so useful that it
+makes sense to use these as our main
+
+ align:start position:0%
+makes sense to use these as our main
+ 
+
+ align:start position:0%
+makes sense to use these as our main
+sense of note intuition
+
+ align:start position:0%
+sense of note intuition
+ 
+
+ align:start position:0%
+sense of note intuition
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact we even have weirder examples of
+
+ align:start position:0%
+in fact we even have weirder examples of
+ 
+
+ align:start position:0%
+in fact we even have weirder examples of
+buttock spaces though and I'll introduce
+
+ align:start position:0%
+buttock spaces though and I'll introduce
+ 
+
+ align:start position:0%
+buttock spaces though and I'll introduce
+one of them now
+
+ align:start position:0%
+one of them now
+ 
+
+ align:start position:0%
+one of them now
+where specifically
+
+ align:start position:0%
+where specifically
+ 
+
+ align:start position:0%
+where specifically
+you're interested in the Dual of the
+
+ align:start position:0%
+you're interested in the Dual of the
+ 
+
+ align:start position:0%
+you're interested in the Dual of the
+vector space Have you heard of the
+
+ align:start position:0%
+vector space Have you heard of the
+ 
+
+ align:start position:0%
+vector space Have you heard of the
+notion of dual before
+
+ align:start position:0%
+notion of dual before
+ 
+
+ align:start position:0%
+notion of dual before
+no worries yeah it's totally fair in the
+
+ align:start position:0%
+no worries yeah it's totally fair in the
+ 
+
+ align:start position:0%
+no worries yeah it's totally fair in the
+case of Norm spaces it's not too bad
+
+ align:start position:0%
+case of Norm spaces it's not too bad
+ 
+
+ align:start position:0%
+case of Norm spaces it's not too bad
+it's the set of functionals
+
+ align:start position:0%
+it's the set of functionals
+ 
+
+ align:start position:0%
+it's the set of functionals
+a functional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a linear map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say t
+
+ align:start position:0%
+let's say t
+ 
+
+ align:start position:0%
+let's say t
+from your Norm Space X into the real
+
+ align:start position:0%
+from your Norm Space X into the real
+ 
+
+ align:start position:0%
+from your Norm Space X into the real
+numbers or complex numbers if you prefer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's just a linear map from your Norm
+
+ align:start position:0%
+so it's just a linear map from your Norm
+ 
+
+ align:start position:0%
+so it's just a linear map from your Norm
+space into the real numbers of the
+
+ align:start position:0%
+space into the real numbers of the
+ 
+
+ align:start position:0%
+space into the real numbers of the
+complex numbers and in fact this is the
+
+ align:start position:0%
+complex numbers and in fact this is the
+ 
+
+ align:start position:0%
+complex numbers and in fact this is the
+definition of a dual of a vector space
+
+ align:start position:0%
+definition of a dual of a vector space
+ 
+
+ align:start position:0%
+definition of a dual of a vector space
+in general this replace x with the
+
+ align:start position:0%
+in general this replace x with the
+ 
+
+ align:start position:0%
+in general this replace x with the
+vector space
+
+ align:start position:0%
+vector space
+ 
+
+ align:start position:0%
+vector space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and in fact you can show that the set of
+
+ align:start position:0%
+and in fact you can show that the set of
+ 
+
+ align:start position:0%
+and in fact you can show that the set of
+functionals are robotic space but to do
+
+ align:start position:0%
+functionals are robotic space but to do
+ 
+
+ align:start position:0%
+functionals are robotic space but to do
+so we need to introduce a norm
+
+ align:start position:0%
+so we need to introduce a norm
+ 
+
+ align:start position:0%
+so we need to introduce a norm
+right in order to even have the
+
+ align:start position:0%
+right in order to even have the
+ 
+
+ align:start position:0%
+right in order to even have the
+possibility of defining or showing that
+
+ align:start position:0%
+possibility of defining or showing that
+ 
+
+ align:start position:0%
+possibility of defining or showing that
+a space is a bionic space you need to
+
+ align:start position:0%
+a space is a bionic space you need to
+ 
+
+ align:start position:0%
+a space is a bionic space you need to
+have a notion of a norm
+
+ align:start position:0%
+have a notion of a norm
+ 
+
+ align:start position:0%
+have a notion of a norm
+so the norm on it
+
+ align:start position:0%
+so the norm on it
+ 
+
+ align:start position:0%
+so the norm on it
+the norm on T known as the operator Norm
+
+ align:start position:0%
+the norm on T known as the operator Norm
+ 
+
+ align:start position:0%
+the norm on T known as the operator Norm
+is simply the supremum
+
+ align:start position:0%
+is simply the supremum
+ 
+
+ align:start position:0%
+is simply the supremum
+over X in
+
+ align:start position:0%
+over X in
+ 
+
+ align:start position:0%
+over X in
+X in capital x what's the norm of x
+
+ align:start position:0%
+X in capital x what's the norm of x
+ 
+
+ align:start position:0%
+X in capital x what's the norm of x
+equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of T of x
+
+ align:start position:0%
+of T of x
+ 
+
+ align:start position:0%
+of T of x
+so it's just the largest image sorry
+
+ align:start position:0%
+so it's just the largest image sorry
+ 
+
+ align:start position:0%
+so it's just the largest image sorry
+this upper bound of points on the ball
+
+ align:start position:0%
+this upper bound of points on the ball
+ 
+
+ align:start position:0%
+this upper bound of points on the ball
+of radius one
+
+ align:start position:0%
+of radius one
+ 
+
+ align:start position:0%
+of radius one
+around X
+
+ align:start position:0%
+around X
+ 
+
+ align:start position:0%
+around X
+that's what the definition of the
+
+ align:start position:0%
+that's what the definition of the
+ 
+
+ align:start position:0%
+that's what the definition of the
+operator Norm is and you can show the
+
+ align:start position:0%
+operator Norm is and you can show the
+ 
+
+ align:start position:0%
+operator Norm is and you can show the
+disinfectant a norm homogeneity is not
+
+ align:start position:0%
+disinfectant a norm homogeneity is not
+ 
+
+ align:start position:0%
+disinfectant a norm homogeneity is not
+too bad the triangle inequality is where
+
+ align:start position:0%
+too bad the triangle inequality is where
+ 
+
+ align:start position:0%
+too bad the triangle inequality is where
+things get worse
+
+ align:start position:0%
+things get worse
+ 
+
+ align:start position:0%
+things get worse
+as always but homogeneity and positive
+
+ align:start position:0%
+as always but homogeneity and positive
+ 
+
+ align:start position:0%
+as always but homogeneity and positive
+definiteness are nearly immediate so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+with this Norm
+
+ align:start position:0%
+with this Norm
+ 
+
+ align:start position:0%
+with this Norm
+then you can show that the set of
+
+ align:start position:0%
+then you can show that the set of
+ 
+
+ align:start position:0%
+then you can show that the set of
+functionals is ebonic space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why is this important
+
+ align:start position:0%
+and why is this important
+ 
+
+ align:start position:0%
+and why is this important
+because it turns out that studying your
+
+ align:start position:0%
+because it turns out that studying your
+ 
+
+ align:start position:0%
+because it turns out that studying your
+Norm space is pretty much analogous to
+
+ align:start position:0%
+Norm space is pretty much analogous to
+ 
+
+ align:start position:0%
+Norm space is pretty much analogous to
+studying your dual space
+
+ align:start position:0%
+studying your dual space
+ 
+
+ align:start position:0%
+studying your dual space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so studying this at a functionals you
+
+ align:start position:0%
+so studying this at a functionals you
+ 
+
+ align:start position:0%
+so studying this at a functionals you
+can redefine continuity you can redefine
+
+ align:start position:0%
+can redefine continuity you can redefine
+ 
+
+ align:start position:0%
+can redefine continuity you can redefine
+open sets things like that you can show
+
+ align:start position:0%
+open sets things like that you can show
+ 
+
+ align:start position:0%
+open sets things like that you can show
+all of these properties but for
+
+ align:start position:0%
+all of these properties but for
+ 
+
+ align:start position:0%
+all of these properties but for
+functionals as
+
+ align:start position:0%
+functionals as
+ 
+
+ align:start position:0%
+functionals as
+um as a specific example
+
+ align:start position:0%
+um as a specific example
+ 
+
+ align:start position:0%
+um as a specific example
+and the fact that operators are bubonic
+
+ align:start position:0%
+and the fact that operators are bubonic
+ 
+
+ align:start position:0%
+and the fact that operators are bubonic
+space is particularly really helpful
+
+ align:start position:0%
+space is particularly really helpful
+ 
+
+ align:start position:0%
+space is particularly really helpful
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now I want to know one more example of a
+
+ align:start position:0%
+now I want to know one more example of a
+ 
+
+ align:start position:0%
+now I want to know one more example of a
+norm space before I move aurobonic yeah
+
+ align:start position:0%
+norm space before I move aurobonic yeah
+ 
+
+ align:start position:0%
+norm space before I move aurobonic yeah
+I want to give one more example of a
+
+ align:start position:0%
+I want to give one more example of a
+ 
+
+ align:start position:0%
+I want to give one more example of a
+norm space before I move on which is one
+
+ align:start position:0%
+norm space before I move on which is one
+ 
+
+ align:start position:0%
+norm space before I move on which is one
+that I briefly talked about before
+
+ align:start position:0%
+that I briefly talked about before
+ 
+
+ align:start position:0%
+that I briefly talked about before
+uh let me I'll write up here
+
+ align:start position:0%
+uh let me I'll write up here
+ 
+
+ align:start position:0%
+uh let me I'll write up here
+because we're done with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifically
+
+ align:start position:0%
+specifically
+ 
+
+ align:start position:0%
+specifically
+you can study what are known as inner
+
+ align:start position:0%
+you can study what are known as inner
+ 
+
+ align:start position:0%
+you can study what are known as inner
+product spaces which is something which
+
+ align:start position:0%
+product spaces which is something which
+ 
+
+ align:start position:0%
+product spaces which is something which
+is a title that I which is a word I
+
+ align:start position:0%
+is a title that I which is a word I
+ 
+
+ align:start position:0%
+is a title that I which is a word I
+introduced last time
+
+ align:start position:0%
+introduced last time
+ 
+
+ align:start position:0%
+introduced last time
+but I'll Define right now
+
+ align:start position:0%
+but I'll Define right now
+ 
+
+ align:start position:0%
+but I'll Define right now
+it's basically the same concept as a
+
+ align:start position:0%
+it's basically the same concept as a
+ 
+
+ align:start position:0%
+it's basically the same concept as a
+norm space and a metric space you just
+
+ align:start position:0%
+norm space and a metric space you just
+ 
+
+ align:start position:0%
+norm space and a metric space you just
+introduce an inner product on your set
+
+ align:start position:0%
+introduce an inner product on your set
+ 
+
+ align:start position:0%
+introduce an inner product on your set
+and your inner product you can think of
+
+ align:start position:0%
+and your inner product you can think of
+ 
+
+ align:start position:0%
+and your inner product you can think of
+like a DOT product on RN
+
+ align:start position:0%
+like a DOT product on RN
+ 
+
+ align:start position:0%
+like a DOT product on RN
+create the dot having the dot product
+
+ align:start position:0%
+create the dot having the dot product
+ 
+
+ align:start position:0%
+create the dot having the dot product
+was very very helpful in our end because
+
+ align:start position:0%
+was very very helpful in our end because
+ 
+
+ align:start position:0%
+was very very helpful in our end because
+that lets you define things like
+
+ align:start position:0%
+that lets you define things like
+ 
+
+ align:start position:0%
+that lets you define things like
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+which is part of the reason why we
+
+ align:start position:0%
+which is part of the reason why we
+ 
+
+ align:start position:0%
+which is part of the reason why we
+introduced Norms in the first place
+
+ align:start position:0%
+introduced Norms in the first place
+ 
+
+ align:start position:0%
+introduced Norms in the first place
+is to introduce a notion of magnitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in inner products base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+a vector space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+an inner product defined on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and specifically we want this inner
+
+ align:start position:0%
+and specifically we want this inner
+ 
+
+ align:start position:0%
+and specifically we want this inner
+product as usual to have three main
+
+ align:start position:0%
+product as usual to have three main
+ 
+
+ align:start position:0%
+product as usual to have three main
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+the three properties are
+
+ align:start position:0%
+the three properties are
+ 
+
+ align:start position:0%
+the three properties are
+and I'm going to assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to assume that the inner
+
+ align:start position:0%
+I'm going to assume that the inner
+ 
+
+ align:start position:0%
+I'm going to assume that the inner
+product takes in two points in x
+
+ align:start position:0%
+product takes in two points in x
+ 
+
+ align:start position:0%
+product takes in two points in x
+and spits out a real number
+
+ align:start position:0%
+and spits out a real number
+ 
+
+ align:start position:0%
+and spits out a real number
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so the three properties
+
+ align:start position:0%
+so the three properties
+ 
+
+ align:start position:0%
+so the three properties
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+symmetry the inner product of X and Y
+
+ align:start position:0%
+symmetry the inner product of X and Y
+ 
+
+ align:start position:0%
+symmetry the inner product of X and Y
+should be the same as Y and X
+
+ align:start position:0%
+should be the same as Y and X
+ 
+
+ align:start position:0%
+should be the same as Y and X
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+linearity
+
+ align:start position:0%
+linearity
+ 
+
+ align:start position:0%
+linearity
+the inner product of a X plus b y and a
+
+ align:start position:0%
+the inner product of a X plus b y and a
+ 
+
+ align:start position:0%
+the inner product of a X plus b y and a
+product with z
+
+ align:start position:0%
+product with z
+ 
+
+ align:start position:0%
+product with z
+is the same as a x inner product C plus
+
+ align:start position:0%
+is the same as a x inner product C plus
+ 
+
+ align:start position:0%
+is the same as a x inner product C plus
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+y inter product C so this is linearity
+
+ align:start position:0%
+y inter product C so this is linearity
+ 
+
+ align:start position:0%
+y inter product C so this is linearity
+and lastly we want
+
+ align:start position:0%
+and lastly we want
+ 
+
+ align:start position:0%
+and lastly we want
+positive definiteness but it's slightly
+
+ align:start position:0%
+positive definiteness but it's slightly
+ 
+
+ align:start position:0%
+positive definiteness but it's slightly
+weirder
+
+ align:start position:0%
+weirder
+ 
+
+ align:start position:0%
+weirder
+If X is not zero then the inner product
+
+ align:start position:0%
+If X is not zero then the inner product
+ 
+
+ align:start position:0%
+If X is not zero then the inner product
+of X with itself is bigger than zero
+
+ align:start position:0%
+of X with itself is bigger than zero
+ 
+
+ align:start position:0%
+of X with itself is bigger than zero
+it's not an if and only if statement
+
+ align:start position:0%
+it's not an if and only if statement
+ 
+
+ align:start position:0%
+it's not an if and only if statement
+because of course we have Notions of
+
+ align:start position:0%
+because of course we have Notions of
+ 
+
+ align:start position:0%
+because of course we have Notions of
+orthogonality
+
+ align:start position:0%
+orthogonality
+ 
+
+ align:start position:0%
+orthogonality
+uh from real and out sorry from RN
+
+ align:start position:0%
+uh from real and out sorry from RN
+ 
+
+ align:start position:0%
+uh from real and out sorry from RN
+but if it's not zero the inner product
+
+ align:start position:0%
+but if it's not zero the inner product
+ 
+
+ align:start position:0%
+but if it's not zero the inner product
+should be non-zero
+
+ align:start position:0%
+should be non-zero
+ 
+
+ align:start position:0%
+should be non-zero
+uh these are the three properties of an
+
+ align:start position:0%
+uh these are the three properties of an
+ 
+
+ align:start position:0%
+uh these are the three properties of an
+inner product space and the reason I
+
+ align:start position:0%
+inner product space and the reason I
+ 
+
+ align:start position:0%
+inner product space and the reason I
+bring this up right now is because you
+
+ align:start position:0%
+bring this up right now is because you
+ 
+
+ align:start position:0%
+bring this up right now is because you
+can show
+
+ align:start position:0%
+can show
+ 
+
+ align:start position:0%
+can show
+uh consider
+
+ align:start position:0%
+uh consider
+ 
+
+ align:start position:0%
+uh consider
+just as we did in calculus
+
+ align:start position:0%
+just as we did in calculus
+ 
+
+ align:start position:0%
+just as we did in calculus
+you can consider
+
+ align:start position:0%
+you can consider
+ 
+
+ align:start position:0%
+you can consider
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the inner product of X and X to the
+
+ align:start position:0%
+the inner product of X and X to the
+ 
+
+ align:start position:0%
+the inner product of X and X to the
+one-half this makes sense because it's
+
+ align:start position:0%
+one-half this makes sense because it's
+ 
+
+ align:start position:0%
+one-half this makes sense because it's
+positive so taking the square roots
+
+ align:start position:0%
+positive so taking the square roots
+ 
+
+ align:start position:0%
+positive so taking the square roots
+totally fine
+
+ align:start position:0%
+totally fine
+ 
+
+ align:start position:0%
+totally fine
+what you can show
+
+ align:start position:0%
+what you can show
+ 
+
+ align:start position:0%
+what you can show
+is that this induces a norm on x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way that you show this
+
+ align:start position:0%
+the way that you show this
+ 
+
+ align:start position:0%
+the way that you show this
+so in other words
+
+ align:start position:0%
+so in other words
+ 
+
+ align:start position:0%
+so in other words
+induces
+
+ align:start position:0%
+induces
+ 
+
+ align:start position:0%
+induces
+Norm
+
+ align:start position:0%
+Norm
+ 
+
+ align:start position:0%
+Norm
+so what you would want to show is that
+
+ align:start position:0%
+so what you would want to show is that
+ 
+
+ align:start position:0%
+so what you would want to show is that
+given an inner product space if I look
+
+ align:start position:0%
+given an inner product space if I look
+ 
+
+ align:start position:0%
+given an inner product space if I look
+at the square root of x in the product
+
+ align:start position:0%
+at the square root of x in the product
+ 
+
+ align:start position:0%
+at the square root of x in the product
+itself you would want to show that this
+
+ align:start position:0%
+itself you would want to show that this
+ 
+
+ align:start position:0%
+itself you would want to show that this
+implies you have the three properties
+
+ align:start position:0%
+implies you have the three properties
+ 
+
+ align:start position:0%
+implies you have the three properties
+you want for a norm space just as we did
+
+ align:start position:0%
+you want for a norm space just as we did
+ 
+
+ align:start position:0%
+you want for a norm space just as we did
+in the proof of metric spaces
+
+ align:start position:0%
+in the proof of metric spaces
+ 
+
+ align:start position:0%
+in the proof of metric spaces
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+really important this is this shows up
+
+ align:start position:0%
+really important this is this shows up
+ 
+
+ align:start position:0%
+really important this is this shows up
+all the time in fact in quantum
+
+ align:start position:0%
+all the time in fact in quantum
+ 
+
+ align:start position:0%
+all the time in fact in quantum
+mechanics if you're
+
+ align:start position:0%
+mechanics if you're
+ 
+
+ align:start position:0%
+mechanics if you're
+uh is that some part of math and physics
+
+ align:start position:0%
+uh is that some part of math and physics
+ 
+
+ align:start position:0%
+uh is that some part of math and physics
+that you're interested in
+
+ align:start position:0%
+that you're interested in
+ 
+
+ align:start position:0%
+that you're interested in
+uh and in fact
+
+ align:start position:0%
+uh and in fact
+ 
+
+ align:start position:0%
+uh and in fact
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+I should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can go should complete it as usual
+
+ align:start position:0%
+we can go should complete it as usual
+ 
+
+ align:start position:0%
+we can go should complete it as usual
+once we have that our inner product
+
+ align:start position:0%
+once we have that our inner product
+ 
+
+ align:start position:0%
+once we have that our inner product
+induces a norm we know that it then
+
+ align:start position:0%
+induces a norm we know that it then
+ 
+
+ align:start position:0%
+induces a norm we know that it then
+induces a metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the one thing we don't know is if it's a
+
+ align:start position:0%
+the one thing we don't know is if it's a
+ 
+
+ align:start position:0%
+the one thing we don't know is if it's a
+bionic space or not and that's totally
+
+ align:start position:0%
+bionic space or not and that's totally
+ 
+
+ align:start position:0%
+bionic space or not and that's totally
+fine we can just coach you complete it
+
+ align:start position:0%
+fine we can just coach you complete it
+ 
+
+ align:start position:0%
+fine we can just coach you complete it
+and get what is known as a Hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a Hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a koshy complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inner product space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you can view it as a completion you
+
+ align:start position:0%
+um you can view it as a completion you
+ 
+
+ align:start position:0%
+um you can view it as a completion you
+can also view it as just the definition
+
+ align:start position:0%
+can also view it as just the definition
+ 
+
+ align:start position:0%
+can also view it as just the definition
+and here koshy completeness is with
+
+ align:start position:0%
+and here koshy completeness is with
+ 
+
+ align:start position:0%
+and here koshy completeness is with
+respect to the metric that's induced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I'm going to rearrange this diagram
+
+ align:start position:0%
+um I'm going to rearrange this diagram
+ 
+
+ align:start position:0%
+um I'm going to rearrange this diagram
+real quick because not every inner
+
+ align:start position:0%
+real quick because not every inner
+ 
+
+ align:start position:0%
+real quick because not every inner
+product space is a bionic space but it
+
+ align:start position:0%
+product space is a bionic space but it
+ 
+
+ align:start position:0%
+product space is a bionic space but it
+is a subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so specifically you can have
+
+ align:start position:0%
+so specifically you can have
+ 
+
+ align:start position:0%
+so specifically you can have
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inner product spaces
+
+ align:start position:0%
+inner product spaces
+ 
+
+ align:start position:0%
+inner product spaces
+are a subset of Norm spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Hobart spaces
+
+ align:start position:0%
+and Hobart spaces
+ 
+
+ align:start position:0%
+and Hobart spaces
+are inner product spaces that are koshy
+
+ align:start position:0%
+are inner product spaces that are koshy
+ 
+
+ align:start position:0%
+are inner product spaces that are koshy
+complete so therefore our bionic spaces
+
+ align:start position:0%
+complete so therefore our bionic spaces
+ 
+
+ align:start position:0%
+complete so therefore our bionic spaces
+this is the end of my diagram no more no
+
+ align:start position:0%
+this is the end of my diagram no more no
+ 
+
+ align:start position:0%
+this is the end of my diagram no more no
+more drawing squares all the way down
+
+ align:start position:0%
+more drawing squares all the way down
+ 
+
+ align:start position:0%
+more drawing squares all the way down
+but um I just wanted to show all these
+
+ align:start position:0%
+but um I just wanted to show all these
+ 
+
+ align:start position:0%
+but um I just wanted to show all these
+ideas are deeply related and each one of
+
+ align:start position:0%
+ideas are deeply related and each one of
+ 
+
+ align:start position:0%
+ideas are deeply related and each one of
+them is interesting to study was in its
+
+ align:start position:0%
+them is interesting to study was in its
+ 
+
+ align:start position:0%
+them is interesting to study was in its
+own respect now granted all the center
+
+ align:start position:0%
+own respect now granted all the center
+ 
+
+ align:start position:0%
+own respect now granted all the center
+squares Norm spaces spawning spaces and
+
+ align:start position:0%
+squares Norm spaces spawning spaces and
+ 
+
+ align:start position:0%
+squares Norm spaces spawning spaces and
+inner product spaces these are mostly
+
+ align:start position:0%
+inner product spaces these are mostly
+ 
+
+ align:start position:0%
+inner product spaces these are mostly
+talked about in functional analysis
+
+ align:start position:0%
+talked about in functional analysis
+ 
+
+ align:start position:0%
+talked about in functional analysis
+which roughly makes sense because you
+
+ align:start position:0%
+which roughly makes sense because you
+ 
+
+ align:start position:0%
+which roughly makes sense because you
+need Vector spaces in order to move
+
+ align:start position:0%
+need Vector spaces in order to move
+ 
+
+ align:start position:0%
+need Vector spaces in order to move
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+um but yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because again functional analysis is
+
+ align:start position:0%
+because again functional analysis is
+ 
+
+ align:start position:0%
+because again functional analysis is
+done on arm spaces and more specifically
+
+ align:start position:0%
+done on arm spaces and more specifically
+ 
+
+ align:start position:0%
+done on arm spaces and more specifically
+usually product spaces
+
+ align:start position:0%
+usually product spaces
+ 
+
+ align:start position:0%
+usually product spaces
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+I want to know one small application to
+
+ align:start position:0%
+I want to know one small application to
+ 
+
+ align:start position:0%
+I want to know one small application to
+18 and 101 and then I'm going to talk
+
+ align:start position:0%
+18 and 101 and then I'm going to talk
+ 
+
+ align:start position:0%
+18 and 101 and then I'm going to talk
+about the application to differential
+
+ align:start position:0%
+about the application to differential
+ 
+
+ align:start position:0%
+about the application to differential
+equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in 18101
+
+ align:start position:0%
+in 18101
+ 
+
+ align:start position:0%
+in 18101
+analysis and manifolds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in your studying of course manifolds
+
+ align:start position:0%
+in your studying of course manifolds
+ 
+
+ align:start position:0%
+in your studying of course manifolds
+now what is a manifold
+
+ align:start position:0%
+now what is a manifold
+ 
+
+ align:start position:0%
+now what is a manifold
+a manifold is just some smooth enough
+
+ align:start position:0%
+a manifold is just some smooth enough
+ 
+
+ align:start position:0%
+a manifold is just some smooth enough
+blob and you can picture it in euclidean
+
+ align:start position:0%
+blob and you can picture it in euclidean
+ 
+
+ align:start position:0%
+blob and you can picture it in euclidean
+space it's a to be even more specific a
+
+ align:start position:0%
+space it's a to be even more specific a
+ 
+
+ align:start position:0%
+space it's a to be even more specific a
+picture you have like an orange the main
+
+ align:start position:0%
+picture you have like an orange the main
+ 
+
+ align:start position:0%
+picture you have like an orange the main
+properties that we like about an orange
+
+ align:start position:0%
+properties that we like about an orange
+ 
+
+ align:start position:0%
+properties that we like about an orange
+or sphere is that locally it looks that
+
+ align:start position:0%
+or sphere is that locally it looks that
+ 
+
+ align:start position:0%
+or sphere is that locally it looks that
+right just like it is in calculus a
+
+ align:start position:0%
+right just like it is in calculus a
+ 
+
+ align:start position:0%
+right just like it is in calculus a
+function locally looks like a line in
+
+ align:start position:0%
+function locally looks like a line in
+ 
+
+ align:start position:0%
+function locally looks like a line in
+higher generality a manifold is just a
+
+ align:start position:0%
+higher generality a manifold is just a
+ 
+
+ align:start position:0%
+higher generality a manifold is just a
+space that locally looks flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the reason I bring this up is because
+
+ align:start position:0%
+um the reason I bring this up is because
+ 
+
+ align:start position:0%
+um the reason I bring this up is because
+in the definition of a manifold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you assume
+
+ align:start position:0%
+you assume
+ 
+
+ align:start position:0%
+you assume
+or at least you define a manifold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you assume it is metrizable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a space where it's a metric on it
+
+ align:start position:0%
+it's a space where it's a metric on it
+ 
+
+ align:start position:0%
+it's a space where it's a metric on it
+or at least a metric that induces the
+
+ align:start position:0%
+or at least a metric that induces the
+ 
+
+ align:start position:0%
+or at least a metric that induces the
+norm
+
+ align:start position:0%
+norm
+ 
+
+ align:start position:0%
+norm
+so why is this so important right why do
+
+ align:start position:0%
+so why is this so important right why do
+ 
+
+ align:start position:0%
+so why is this so important right why do
+we study my child's ability in our
+
+ align:start position:0%
+we study my child's ability in our
+ 
+
+ align:start position:0%
+we study my child's ability in our
+manifold well we want there to be a
+
+ align:start position:0%
+manifold well we want there to be a
+ 
+
+ align:start position:0%
+manifold well we want there to be a
+notion of distance on our manifold which
+
+ align:start position:0%
+notion of distance on our manifold which
+ 
+
+ align:start position:0%
+notion of distance on our manifold which
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+the reason why metrics ability I bring
+
+ align:start position:0%
+the reason why metrics ability I bring
+ 
+
+ align:start position:0%
+the reason why metrics ability I bring
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+is because in reality when you're
+
+ align:start position:0%
+is because in reality when you're
+ 
+
+ align:start position:0%
+is because in reality when you're
+studying matricable spaces you don't
+
+ align:start position:0%
+studying matricable spaces you don't
+ 
+
+ align:start position:0%
+studying matricable spaces you don't
+often care what the metric is sometimes
+
+ align:start position:0%
+often care what the metric is sometimes
+ 
+
+ align:start position:0%
+often care what the metric is sometimes
+you do sometimes you want to say oh once
+
+ align:start position:0%
+you do sometimes you want to say oh once
+ 
+
+ align:start position:0%
+you do sometimes you want to say oh once
+you know they're exist symmetric then x
+
+ align:start position:0%
+you know they're exist symmetric then x
+ 
+
+ align:start position:0%
+you know they're exist symmetric then x
+y and z
+
+ align:start position:0%
+y and z
+ 
+
+ align:start position:0%
+y and z
+but most of the time you just use the
+
+ align:start position:0%
+but most of the time you just use the
+ 
+
+ align:start position:0%
+but most of the time you just use the
+properties of the open sets
+
+ align:start position:0%
+properties of the open sets
+ 
+
+ align:start position:0%
+properties of the open sets
+so most of the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just want to use the fact that balls
+
+ align:start position:0%
+you just want to use the fact that balls
+ 
+
+ align:start position:0%
+you just want to use the fact that balls
+of radius Epsilon
+
+ align:start position:0%
+of radius Epsilon
+ 
+
+ align:start position:0%
+of radius Epsilon
+are open
+
+ align:start position:0%
+are open
+ 
+
+ align:start position:0%
+are open
+in doing so lets you define smooth
+
+ align:start position:0%
+in doing so lets you define smooth
+ 
+
+ align:start position:0%
+in doing so lets you define smooth
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it lets you define integration it lets
+
+ align:start position:0%
+it lets you define integration it lets
+ 
+
+ align:start position:0%
+it lets you define integration it lets
+you define
+
+ align:start position:0%
+you define
+ 
+
+ align:start position:0%
+you define
+I had one more thing I mentioned it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can Define integration and you can
+
+ align:start position:0%
+you can Define integration and you can
+ 
+
+ align:start position:0%
+you can Define integration and you can
+define a vector fields
+
+ align:start position:0%
+define a vector fields
+ 
+
+ align:start position:0%
+define a vector fields
+as you might have seen in 1802
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all this is just letting us do calculus
+
+ align:start position:0%
+all this is just letting us do calculus
+ 
+
+ align:start position:0%
+all this is just letting us do calculus
+on weirder shapes right doing calculus
+
+ align:start position:0%
+on weirder shapes right doing calculus
+ 
+
+ align:start position:0%
+on weirder shapes right doing calculus
+on a sphere doing calculus on a smooth
+
+ align:start position:0%
+on a sphere doing calculus on a smooth
+ 
+
+ align:start position:0%
+on a sphere doing calculus on a smooth
+enough tree things like that
+
+ align:start position:0%
+enough tree things like that
+ 
+
+ align:start position:0%
+enough tree things like that
+but really all we really need is that
+
+ align:start position:0%
+but really all we really need is that
+ 
+
+ align:start position:0%
+but really all we really need is that
+the balls of radius Epsilon are open to
+
+ align:start position:0%
+the balls of radius Epsilon are open to
+ 
+
+ align:start position:0%
+the balls of radius Epsilon are open to
+start doing so
+
+ align:start position:0%
+start doing so
+ 
+
+ align:start position:0%
+start doing so
+so sometimes in 18101 you won't see how
+
+ align:start position:0%
+so sometimes in 18101 you won't see how
+ 
+
+ align:start position:0%
+so sometimes in 18101 you won't see how
+metrics come up in particular but the
+
+ align:start position:0%
+metrics come up in particular but the
+ 
+
+ align:start position:0%
+metrics come up in particular but the
+intuition is still there right you still
+
+ align:start position:0%
+intuition is still there right you still
+ 
+
+ align:start position:0%
+intuition is still there right you still
+want to have a notion of distance on
+
+ align:start position:0%
+want to have a notion of distance on
+ 
+
+ align:start position:0%
+want to have a notion of distance on
+your manifold
+
+ align:start position:0%
+your manifold
+ 
+
+ align:start position:0%
+your manifold
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+that's all I'll say about 18101 because
+
+ align:start position:0%
+that's all I'll say about 18101 because
+ 
+
+ align:start position:0%
+that's all I'll say about 18101 because
+of course it takes like a month to
+
+ align:start position:0%
+of course it takes like a month to
+ 
+
+ align:start position:0%
+of course it takes like a month to
+actually get into manifold Theory
+
+ align:start position:0%
+actually get into manifold Theory
+ 
+
+ align:start position:0%
+actually get into manifold Theory
+because you're redefining multivariable
+
+ align:start position:0%
+because you're redefining multivariable
+ 
+
+ align:start position:0%
+because you're redefining multivariable
+calculus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I'll leave that there for now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+the last example I want to talk about
+
+ align:start position:0%
+the last example I want to talk about
+ 
+
+ align:start position:0%
+the last example I want to talk about
+today is specifically the application to
+
+ align:start position:0%
+today is specifically the application to
+ 
+
+ align:start position:0%
+today is specifically the application to
+differential equations
+
+ align:start position:0%
+differential equations
+ 
+
+ align:start position:0%
+differential equations
+and we already briefly talked about this
+
+ align:start position:0%
+and we already briefly talked about this
+ 
+
+ align:start position:0%
+and we already briefly talked about this
+right last time we talked about
+
+ align:start position:0%
+right last time we talked about
+ 
+
+ align:start position:0%
+right last time we talked about
+um integral operators
+
+ align:start position:0%
+um integral operators
+ 
+
+ align:start position:0%
+um integral operators
+specifically as an application of the
+
+ align:start position:0%
+specifically as an application of the
+ 
+
+ align:start position:0%
+specifically as an application of the
+Bonnet fixed Point theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me just write this down
+
+ align:start position:0%
+let me just write this down
+ 
+
+ align:start position:0%
+let me just write this down
+last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we considered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Odes of the form
+
+ align:start position:0%
+Odes of the form
+ 
+
+ align:start position:0%
+Odes of the form
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what was it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G of x
+
+ align:start position:0%
+G of x
+ 
+
+ align:start position:0%
+G of x
+plus the integral from A to B
+
+ align:start position:0%
+plus the integral from A to B
+ 
+
+ align:start position:0%
+plus the integral from A to B
+k x y
+
+ align:start position:0%
+k x y
+ 
+
+ align:start position:0%
+k x y
+f of x
+
+ align:start position:0%
+f of x
+ 
+
+ align:start position:0%
+f of x
+sorry F of y d y
+
+ align:start position:0%
+sorry F of y d y
+ 
+
+ align:start position:0%
+sorry F of y d y
+so last time we considered pde that
+
+ align:start position:0%
+so last time we considered pde that
+ 
+
+ align:start position:0%
+so last time we considered pde that
+leads to this nice integral operator
+
+ align:start position:0%
+leads to this nice integral operator
+ 
+
+ align:start position:0%
+leads to this nice integral operator
+if this is unfamiliar that's totally
+
+ align:start position:0%
+if this is unfamiliar that's totally
+ 
+
+ align:start position:0%
+if this is unfamiliar that's totally
+fair but I'm just bringing up the fact
+
+ align:start position:0%
+fair but I'm just bringing up the fact
+ 
+
+ align:start position:0%
+fair but I'm just bringing up the fact
+that we've already seen one small
+
+ align:start position:0%
+that we've already seen one small
+ 
+
+ align:start position:0%
+that we've already seen one small
+application of demonic fixed Point
+
+ align:start position:0%
+application of demonic fixed Point
+ 
+
+ align:start position:0%
+application of demonic fixed Point
+theorem to differential equations
+
+ align:start position:0%
+theorem to differential equations
+ 
+
+ align:start position:0%
+theorem to differential equations
+but in fact you can use differential
+
+ align:start position:0%
+but in fact you can use differential
+ 
+
+ align:start position:0%
+but in fact you can use differential
+equations to motivate the notion of
+
+ align:start position:0%
+equations to motivate the notion of
+ 
+
+ align:start position:0%
+equations to motivate the notion of
+compact sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I should have written
+
+ align:start position:0%
+oh I should have written
+ 
+
+ align:start position:0%
+oh I should have written
+eighteen one five two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intro
+
+ align:start position:0%
+intro
+ 
+
+ align:start position:0%
+intro
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+partial differential equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can use the notion
+
+ align:start position:0%
+so we can use the notion
+ 
+
+ align:start position:0%
+so we can use the notion
+or we can use
+
+ align:start position:0%
+or we can use
+ 
+
+ align:start position:0%
+or we can use
+ode or pde
+
+ align:start position:0%
+ode or pde
+ 
+
+ align:start position:0%
+ode or pde
+to motivate
+
+ align:start position:0%
+to motivate
+ 
+
+ align:start position:0%
+to motivate
+compact sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me just briefly explain why this
+
+ align:start position:0%
+and let me just briefly explain why this
+ 
+
+ align:start position:0%
+and let me just briefly explain why this
+is the case
+
+ align:start position:0%
+is the case
+ 
+
+ align:start position:0%
+is the case
+so picture
+
+ align:start position:0%
+so picture
+ 
+
+ align:start position:0%
+so picture
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+picture some subset Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of set subset Omega
+
+ align:start position:0%
+some of set subset Omega
+ 
+
+ align:start position:0%
+some of set subset Omega
+of R2
+
+ align:start position:0%
+of R2
+ 
+
+ align:start position:0%
+of R2
+and picture this as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a metal sheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I just have some subset out here
+
+ align:start position:0%
+so I just have some subset out here
+ 
+
+ align:start position:0%
+so I just have some subset out here
+Omega I'm going to assume it's nice and
+
+ align:start position:0%
+Omega I'm going to assume it's nice and
+ 
+
+ align:start position:0%
+Omega I'm going to assume it's nice and
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and I want to consider it as a metal
+
+ align:start position:0%
+and I want to consider it as a metal
+ 
+
+ align:start position:0%
+and I want to consider it as a metal
+sheet why do I do that because from here
+
+ align:start position:0%
+sheet why do I do that because from here
+ 
+
+ align:start position:0%
+sheet why do I do that because from here
+let's say I just heat up one tiny
+
+ align:start position:0%
+let's say I just heat up one tiny
+ 
+
+ align:start position:0%
+let's say I just heat up one tiny
+portion of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say I take a little blow torch and
+
+ align:start position:0%
+let's say I take a little blow torch and
+ 
+
+ align:start position:0%
+let's say I take a little blow torch and
+I heat it up right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to know how the temperature is
+
+ align:start position:0%
+we want to know how the temperature is
+ 
+
+ align:start position:0%
+we want to know how the temperature is
+affected by this in particular
+
+ align:start position:0%
+affected by this in particular
+ 
+
+ align:start position:0%
+affected by this in particular
+the temperature
+
+ align:start position:0%
+the temperature
+ 
+
+ align:start position:0%
+the temperature
+let's say that you
+
+ align:start position:0%
+let's say that you
+ 
+
+ align:start position:0%
+let's say that you
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+x y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x y
+
+ align:start position:0%
+at x y
+ 
+
+ align:start position:0%
+at x y
+in Omega
+
+ align:start position:0%
+in Omega
+ 
+
+ align:start position:0%
+in Omega
+what you can derive using physics or
+
+ align:start position:0%
+what you can derive using physics or
+ 
+
+ align:start position:0%
+what you can derive using physics or
+using um
+
+ align:start position:0%
+using um
+ 
+
+ align:start position:0%
+using um
+just differential uh looking at it from
+
+ align:start position:0%
+just differential uh looking at it from
+ 
+
+ align:start position:0%
+just differential uh looking at it from
+a differential viewpoint
+
+ align:start position:0%
+a differential viewpoint
+ 
+
+ align:start position:0%
+a differential viewpoint
+you can Define
+
+ align:start position:0%
+you can Define
+ 
+
+ align:start position:0%
+you can Define
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you can show that the heat equation that
+
+ align:start position:0%
+you can show that the heat equation that
+ 
+
+ align:start position:0%
+you can show that the heat equation that
+you'll get from heating up this tiny
+
+ align:start position:0%
+you'll get from heating up this tiny
+ 
+
+ align:start position:0%
+you'll get from heating up this tiny
+spot is of the form derivative of U
+
+ align:start position:0%
+spot is of the form derivative of U
+ 
+
+ align:start position:0%
+spot is of the form derivative of U
+with respect to X twice
+
+ align:start position:0%
+with respect to X twice
+ 
+
+ align:start position:0%
+with respect to X twice
+plus derivative
+
+ align:start position:0%
+plus derivative
+ 
+
+ align:start position:0%
+plus derivative
+of U with respect to y
+
+ align:start position:0%
+of U with respect to y
+ 
+
+ align:start position:0%
+of U with respect to y
+twice this is known as the heat equation
+
+ align:start position:0%
+twice this is known as the heat equation
+ 
+
+ align:start position:0%
+twice this is known as the heat equation
+and in fact
+
+ align:start position:0%
+and in fact
+ 
+
+ align:start position:0%
+and in fact
+if it reaches
+
+ align:start position:0%
+if it reaches
+ 
+
+ align:start position:0%
+if it reaches
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if we let this metal sheet reach
+
+ align:start position:0%
+if we let this metal sheet reach
+ 
+
+ align:start position:0%
+if we let this metal sheet reach
+equilibrium if we let the blowtorch heat
+
+ align:start position:0%
+equilibrium if we let the blowtorch heat
+ 
+
+ align:start position:0%
+equilibrium if we let the blowtorch heat
+dissipate to all over the metal sheet
+
+ align:start position:0%
+dissipate to all over the metal sheet
+ 
+
+ align:start position:0%
+dissipate to all over the metal sheet
+then you'll get that this equation is
+
+ align:start position:0%
+then you'll get that this equation is
+ 
+
+ align:start position:0%
+then you'll get that this equation is
+equal to zero which is the differential
+
+ align:start position:0%
+equal to zero which is the differential
+ 
+
+ align:start position:0%
+equal to zero which is the differential
+equation that we're particularly
+
+ align:start position:0%
+equation that we're particularly
+ 
+
+ align:start position:0%
+equation that we're particularly
+interested in if I have a solution of
+
+ align:start position:0%
+interested in if I have a solution of
+ 
+
+ align:start position:0%
+interested in if I have a solution of
+this form what what do I know
+
+ align:start position:0%
+this form what what do I know
+ 
+
+ align:start position:0%
+this form what what do I know
+this is in fact so important this this
+
+ align:start position:0%
+this is in fact so important this this
+ 
+
+ align:start position:0%
+this is in fact so important this this
+operator that we just call it the
+
+ align:start position:0%
+operator that we just call it the
+ 
+
+ align:start position:0%
+operator that we just call it the
+laplacian of you if you've heard of that
+
+ align:start position:0%
+laplacian of you if you've heard of that
+ 
+
+ align:start position:0%
+laplacian of you if you've heard of that
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+where the laplacian is just the
+
+ align:start position:0%
+where the laplacian is just the
+ 
+
+ align:start position:0%
+where the laplacian is just the
+derivatives squared applied each time
+
+ align:start position:0%
+derivatives squared applied each time
+ 
+
+ align:start position:0%
+derivatives squared applied each time
+and summing over them
+
+ align:start position:0%
+and summing over them
+ 
+
+ align:start position:0%
+and summing over them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the question is what if I only know
+
+ align:start position:0%
+so the question is what if I only know
+ 
+
+ align:start position:0%
+so the question is what if I only know
+the temperature at the boundary
+
+ align:start position:0%
+the temperature at the boundary
+ 
+
+ align:start position:0%
+the temperature at the boundary
+so here the boundary is just
+
+ align:start position:0%
+so here the boundary is just
+ 
+
+ align:start position:0%
+so here the boundary is just
+we could just draw it out pictorially
+
+ align:start position:0%
+we could just draw it out pictorially
+ 
+
+ align:start position:0%
+we could just draw it out pictorially
+it's the point
+
+ align:start position:0%
+it's the point
+ 
+
+ align:start position:0%
+it's the point
+it's just along the edge
+
+ align:start position:0%
+it's just along the edge
+ 
+
+ align:start position:0%
+it's just along the edge
+suppose just along the edge I knew the
+
+ align:start position:0%
+suppose just along the edge I knew the
+ 
+
+ align:start position:0%
+suppose just along the edge I knew the
+temperature and that's all I knew so
+
+ align:start position:0%
+temperature and that's all I knew so
+ 
+
+ align:start position:0%
+temperature and that's all I knew so
+f equals U
+
+ align:start position:0%
+f equals U
+ 
+
+ align:start position:0%
+f equals U
+on Boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we denote the boundary as partial
+
+ align:start position:0%
+and we denote the boundary as partial
+ 
+
+ align:start position:0%
+and we denote the boundary as partial
+Omega this is just how we Define that's
+
+ align:start position:0%
+Omega this is just how we Define that's
+ 
+
+ align:start position:0%
+Omega this is just how we Define that's
+just the notation that's used
+
+ align:start position:0%
+just the notation that's used
+ 
+
+ align:start position:0%
+just the notation that's used
+the question is is given this equation
+
+ align:start position:0%
+the question is is given this equation
+ 
+
+ align:start position:0%
+the question is is given this equation
+is true and given that I know the
+
+ align:start position:0%
+is true and given that I know the
+ 
+
+ align:start position:0%
+is true and given that I know the
+temperature values along the boundary
+
+ align:start position:0%
+temperature values along the boundary
+ 
+
+ align:start position:0%
+temperature values along the boundary
+does their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist or I should just write out
+
+ align:start position:0%
+exist or I should just write out
+ 
+
+ align:start position:0%
+exist or I should just write out
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+a u
+
+ align:start position:0%
+a u
+ 
+
+ align:start position:0%
+a u
+satisfying this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so specifically does there exist to you
+
+ align:start position:0%
+so specifically does there exist to you
+ 
+
+ align:start position:0%
+so specifically does there exist to you
+such that the laplacian of U is zero and
+
+ align:start position:0%
+such that the laplacian of U is zero and
+ 
+
+ align:start position:0%
+such that the laplacian of U is zero and
+such that U is the function when
+
+ align:start position:0%
+such that U is the function when
+ 
+
+ align:start position:0%
+such that U is the function when
+restricted to the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is this will be what I call q1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the question is quite a bit difficult to
+
+ align:start position:0%
+the question is quite a bit difficult to
+ 
+
+ align:start position:0%
+the question is quite a bit difficult to
+answer at least immediately in fact
+
+ align:start position:0%
+answer at least immediately in fact
+ 
+
+ align:start position:0%
+answer at least immediately in fact
+that's how most pde questions go like
+
+ align:start position:0%
+that's how most pde questions go like
+ 
+
+ align:start position:0%
+that's how most pde questions go like
+it's particularly difficult to show
+
+ align:start position:0%
+it's particularly difficult to show
+ 
+
+ align:start position:0%
+it's particularly difficult to show
+existence of a solution
+
+ align:start position:0%
+existence of a solution
+ 
+
+ align:start position:0%
+existence of a solution
+but we can perhaps think about it more
+
+ align:start position:0%
+but we can perhaps think about it more
+ 
+
+ align:start position:0%
+but we can perhaps think about it more
+physically What If instead of viewing it
+
+ align:start position:0%
+physically What If instead of viewing it
+ 
+
+ align:start position:0%
+physically What If instead of viewing it
+in terms of its temperature which can be
+
+ align:start position:0%
+in terms of its temperature which can be
+ 
+
+ align:start position:0%
+in terms of its temperature which can be
+a little bit weird we try to minimize
+
+ align:start position:0%
+a little bit weird we try to minimize
+ 
+
+ align:start position:0%
+a little bit weird we try to minimize
+the energy right if we minimize the
+
+ align:start position:0%
+the energy right if we minimize the
+ 
+
+ align:start position:0%
+the energy right if we minimize the
+energy then maybe then we'll have
+
+ align:start position:0%
+energy then maybe then we'll have
+ 
+
+ align:start position:0%
+energy then maybe then we'll have
+reached
+
+ align:start position:0%
+reached
+ 
+
+ align:start position:0%
+reached
+thermal equilibrium
+
+ align:start position:0%
+thermal equilibrium
+ 
+
+ align:start position:0%
+thermal equilibrium
+and this is exactly what mathematicians
+
+ align:start position:0%
+and this is exactly what mathematicians
+ 
+
+ align:start position:0%
+and this is exactly what mathematicians
+did at the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry one second
+
+ align:start position:0%
+sorry one second
+ 
+
+ align:start position:0%
+sorry one second
+oh I should note this this question is
+
+ align:start position:0%
+oh I should note this this question is
+ 
+
+ align:start position:0%
+oh I should note this this question is
+known as the dear slay problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you would have saw or you've likely seen
+
+ align:start position:0%
+you would have saw or you've likely seen
+ 
+
+ align:start position:0%
+you would have saw or you've likely seen
+a discrete version of this if you've
+
+ align:start position:0%
+a discrete version of this if you've
+ 
+
+ align:start position:0%
+a discrete version of this if you've
+done 18701 on the first problem set
+
+ align:start position:0%
+done 18701 on the first problem set
+ 
+
+ align:start position:0%
+done 18701 on the first problem set
+sometimes professors include it
+
+ align:start position:0%
+sometimes professors include it
+ 
+
+ align:start position:0%
+sometimes professors include it
+sometimes they don't it's totally fair
+
+ align:start position:0%
+sometimes they don't it's totally fair
+ 
+
+ align:start position:0%
+sometimes they don't it's totally fair
+if not
+
+ align:start position:0%
+if not
+ 
+
+ align:start position:0%
+if not
+um but yeah the first question is does
+
+ align:start position:0%
+um but yeah the first question is does
+ 
+
+ align:start position:0%
+um but yeah the first question is does
+there exist to you satisfying this and
+
+ align:start position:0%
+there exist to you satisfying this and
+ 
+
+ align:start position:0%
+there exist to you satisfying this and
+mathematicians at the time just try to
+
+ align:start position:0%
+mathematicians at the time just try to
+ 
+
+ align:start position:0%
+mathematicians at the time just try to
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+the energy so defined
+
+ align:start position:0%
+the energy so defined
+ 
+
+ align:start position:0%
+the energy so defined
+the energy of a function U
+
+ align:start position:0%
+the energy of a function U
+ 
+
+ align:start position:0%
+the energy of a function U
+to be one half times the integral over
+
+ align:start position:0%
+to be one half times the integral over
+ 
+
+ align:start position:0%
+to be one half times the integral over
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+of the gradient of U
+
+ align:start position:0%
+of the gradient of U
+ 
+
+ align:start position:0%
+of the gradient of U
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+d a where a is the area differential on
+
+ align:start position:0%
+d a where a is the area differential on
+ 
+
+ align:start position:0%
+d a where a is the area differential on
+a on Omega
+
+ align:start position:0%
+a on Omega
+ 
+
+ align:start position:0%
+a on Omega
+this is known as the energy of the
+
+ align:start position:0%
+this is known as the energy of the
+ 
+
+ align:start position:0%
+this is known as the energy of the
+function U you can think about it as
+
+ align:start position:0%
+function U you can think about it as
+ 
+
+ align:start position:0%
+function U you can think about it as
+like the heat energy
+
+ align:start position:0%
+like the heat energy
+ 
+
+ align:start position:0%
+like the heat energy
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but now the question is is if I minimize
+
+ align:start position:0%
+but now the question is is if I minimize
+ 
+
+ align:start position:0%
+but now the question is is if I minimize
+this is it a solution delivered to the
+
+ align:start position:0%
+this is it a solution delivered to the
+ 
+
+ align:start position:0%
+this is it a solution delivered to the
+differential equation
+
+ align:start position:0%
+differential equation
+ 
+
+ align:start position:0%
+differential equation
+and that's what mathematicians in
+
+ align:start position:0%
+and that's what mathematicians in
+ 
+
+ align:start position:0%
+and that's what mathematicians in
+particular did they said
+
+ align:start position:0%
+particular did they said
+ 
+
+ align:start position:0%
+particular did they said
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question two
+
+ align:start position:0%
+question two
+ 
+
+ align:start position:0%
+question two
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U specifically U
+
+ align:start position:0%
+U specifically U
+ 
+
+ align:start position:0%
+U specifically U
+in D in C2 because we want to be able to
+
+ align:start position:0%
+in D in C2 because we want to be able to
+ 
+
+ align:start position:0%
+in D in C2 because we want to be able to
+differentiate it twice
+
+ align:start position:0%
+differentiate it twice
+ 
+
+ align:start position:0%
+differentiate it twice
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+energy of U
+
+ align:start position:0%
+energy of U
+ 
+
+ align:start position:0%
+energy of U
+is equal to the infamous of the energy
+
+ align:start position:0%
+is equal to the infamous of the energy
+ 
+
+ align:start position:0%
+is equal to the infamous of the energy
+so it's equal to
+
+ align:start position:0%
+so it's equal to
+ 
+
+ align:start position:0%
+so it's equal to
+e if
+
+ align:start position:0%
+e if
+ 
+
+ align:start position:0%
+e if
+where e is defined as Z
+
+ align:start position:0%
+where e is defined as Z
+ 
+
+ align:start position:0%
+where e is defined as Z
+Infamous of the energy
+
+ align:start position:0%
+Infamous of the energy
+ 
+
+ align:start position:0%
+Infamous of the energy
+so just take the infamous this assume
+
+ align:start position:0%
+so just take the infamous this assume
+ 
+
+ align:start position:0%
+so just take the infamous this assume
+that I know that in the end the energy
+
+ align:start position:0%
+that I know that in the end the energy
+ 
+
+ align:start position:0%
+that I know that in the end the energy
+should be insert value here does there
+
+ align:start position:0%
+should be insert value here does there
+ 
+
+ align:start position:0%
+should be insert value here does there
+exist to you that minimizes that energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll come back to these questions in
+
+ align:start position:0%
+and I'll come back to these questions in
+ 
+
+ align:start position:0%
+and I'll come back to these questions in
+a moment but the thing I want to know is
+
+ align:start position:0%
+a moment but the thing I want to know is
+ 
+
+ align:start position:0%
+a moment but the thing I want to know is
+that what mathematicians did is they
+
+ align:start position:0%
+that what mathematicians did is they
+ 
+
+ align:start position:0%
+that what mathematicians did is they
+said oh if there exists a function in U
+
+ align:start position:0%
+said oh if there exists a function in U
+ 
+
+ align:start position:0%
+said oh if there exists a function in U
+that satisfies this
+
+ align:start position:0%
+that satisfies this
+ 
+
+ align:start position:0%
+that satisfies this
+then it'll solve the dirichlet problem
+
+ align:start position:0%
+then it'll solve the dirichlet problem
+ 
+
+ align:start position:0%
+then it'll solve the dirichlet problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but the issue here
+
+ align:start position:0%
+but the issue here
+ 
+
+ align:start position:0%
+but the issue here
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+sorry let me just read through this one
+
+ align:start position:0%
+sorry let me just read through this one
+ 
+
+ align:start position:0%
+sorry let me just read through this one
+more time so what I'm trying to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the issue here is that we still have to
+
+ align:start position:0%
+the issue here is that we still have to
+ 
+
+ align:start position:0%
+the issue here is that we still have to
+find this function right the question of
+
+ align:start position:0%
+find this function right the question of
+ 
+
+ align:start position:0%
+find this function right the question of
+existence is finding one that works and
+
+ align:start position:0%
+existence is finding one that works and
+ 
+
+ align:start position:0%
+existence is finding one that works and
+what was done
+
+ align:start position:0%
+what was done
+ 
+
+ align:start position:0%
+what was done
+is they were taking sequences of
+
+ align:start position:0%
+is they were taking sequences of
+ 
+
+ align:start position:0%
+is they were taking sequences of
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+so what was done
+
+ align:start position:0%
+so what was done
+ 
+
+ align:start position:0%
+so what was done
+is you would study functions u n
+
+ align:start position:0%
+is you would study functions u n
+ 
+
+ align:start position:0%
+is you would study functions u n
+converging to U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you would construct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u n
+
+ align:start position:0%
+u n
+ 
+
+ align:start position:0%
+u n
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u n would convert to the function U that
+
+ align:start position:0%
+u n would convert to the function U that
+ 
+
+ align:start position:0%
+u n would convert to the function U that
+you wanted
+
+ align:start position:0%
+you wanted
+ 
+
+ align:start position:0%
+you wanted
+and once this was done you would get
+
+ align:start position:0%
+and once this was done you would get
+ 
+
+ align:start position:0%
+and once this was done you would get
+that the energy of u n converges to the
+
+ align:start position:0%
+that the energy of u n converges to the
+ 
+
+ align:start position:0%
+that the energy of u n converges to the
+energy of U the proof of this fact just
+
+ align:start position:0%
+energy of U the proof of this fact just
+ 
+
+ align:start position:0%
+energy of U the proof of this fact just
+follows from taking the limit right here
+
+ align:start position:0%
+follows from taking the limit right here
+ 
+
+ align:start position:0%
+follows from taking the limit right here
+and applying uniform continuity
+
+ align:start position:0%
+and applying uniform continuity
+ 
+
+ align:start position:0%
+and applying uniform continuity
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um but yeah this was the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this idea
+
+ align:start position:0%
+and this idea
+ 
+
+ align:start position:0%
+and this idea
+did not work
+
+ align:start position:0%
+did not work
+ 
+
+ align:start position:0%
+did not work
+weirdly Why didn't it work
+
+ align:start position:0%
+weirdly Why didn't it work
+ 
+
+ align:start position:0%
+weirdly Why didn't it work
+because even if there exists a sequence
+
+ align:start position:0%
+because even if there exists a sequence
+ 
+
+ align:start position:0%
+because even if there exists a sequence
+of these functions in C2
+
+ align:start position:0%
+of these functions in C2
+ 
+
+ align:start position:0%
+of these functions in C2
+that converges to you how do we know
+
+ align:start position:0%
+that converges to you how do we know
+ 
+
+ align:start position:0%
+that converges to you how do we know
+that U is C2
+
+ align:start position:0%
+that U is C2
+ 
+
+ align:start position:0%
+that U is C2
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is you
+
+ align:start position:0%
+is you
+ 
+
+ align:start position:0%
+is you
+in C2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer isn't is not directly yes
+
+ align:start position:0%
+the answer isn't is not directly yes
+ 
+
+ align:start position:0%
+the answer isn't is not directly yes
+because the C2 functions are not
+
+ align:start position:0%
+because the C2 functions are not
+ 
+
+ align:start position:0%
+because the C2 functions are not
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+are there not a bionic space or yeah
+
+ align:start position:0%
+are there not a bionic space or yeah
+ 
+
+ align:start position:0%
+are there not a bionic space or yeah
+it's an autobotic space
+
+ align:start position:0%
+it's an autobotic space
+ 
+
+ align:start position:0%
+it's an autobotic space
+the way that you can see this
+
+ align:start position:0%
+the way that you can see this
+ 
+
+ align:start position:0%
+the way that you can see this
+so not necessarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way that you see that it's
+
+ align:start position:0%
+the way that you see that it's
+ 
+
+ align:start position:0%
+the way that you see that it's
+non-compact is you just consider the
+
+ align:start position:0%
+non-compact is you just consider the
+ 
+
+ align:start position:0%
+non-compact is you just consider the
+sequence xn x to the n
+
+ align:start position:0%
+sequence xn x to the n
+ 
+
+ align:start position:0%
+sequence xn x to the n
+as your un each of these is
+
+ align:start position:0%
+as your un each of these is
+ 
+
+ align:start position:0%
+as your un each of these is
+differentiable twice
+
+ align:start position:0%
+differentiable twice
+ 
+
+ align:start position:0%
+differentiable twice
+um but U.N
+
+ align:start position:0%
+um but U.N
+ 
+
+ align:start position:0%
+um but U.N
+will converge Point wise to 1
+
+ align:start position:0%
+will converge Point wise to 1
+ 
+
+ align:start position:0%
+will converge Point wise to 1
+or sorry to U of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to one when X is not equal when X
+
+ align:start position:0%
+equal to one when X is not equal when X
+ 
+
+ align:start position:0%
+equal to one when X is not equal when X
+is in
+
+ align:start position:0%
+is in
+ 
+
+ align:start position:0%
+is in
+zero to one
+
+ align:start position:0%
+zero to one
+ 
+
+ align:start position:0%
+zero to one
+and zero otherwise
+
+ align:start position:0%
+and zero otherwise
+ 
+
+ align:start position:0%
+and zero otherwise
+I.E if it's equal to zero
+
+ align:start position:0%
+I.E if it's equal to zero
+ 
+
+ align:start position:0%
+I.E if it's equal to zero
+and this is not twice differentiable
+
+ align:start position:0%
+and this is not twice differentiable
+ 
+
+ align:start position:0%
+and this is not twice differentiable
+it's not differentiable at the point
+
+ align:start position:0%
+it's not differentiable at the point
+ 
+
+ align:start position:0%
+it's not differentiable at the point
+zero it's discontinuous
+
+ align:start position:0%
+zero it's discontinuous
+ 
+
+ align:start position:0%
+zero it's discontinuous
+so the issue is that this function
+
+ align:start position:0%
+so the issue is that this function
+ 
+
+ align:start position:0%
+so the issue is that this function
+wasn't in C2 necessarily
+
+ align:start position:0%
+wasn't in C2 necessarily
+ 
+
+ align:start position:0%
+wasn't in C2 necessarily
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as the way that you see that this isn't
+
+ align:start position:0%
+as the way that you see that this isn't
+ 
+
+ align:start position:0%
+as the way that you see that this isn't
+compact recall is by the fact that this
+
+ align:start position:0%
+compact recall is by the fact that this
+ 
+
+ align:start position:0%
+compact recall is by the fact that this
+would imply that it's not sequentially
+
+ align:start position:0%
+would imply that it's not sequentially
+ 
+
+ align:start position:0%
+would imply that it's not sequentially
+compact
+
+ align:start position:0%
+compact
+ 
+
+ align:start position:0%
+compact
+now what else could we do
+
+ align:start position:0%
+now what else could we do
+ 
+
+ align:start position:0%
+now what else could we do
+well mathematicians then also showed
+
+ align:start position:0%
+well mathematicians then also showed
+ 
+
+ align:start position:0%
+well mathematicians then also showed
+that if the sequence of u n
+
+ align:start position:0%
+that if the sequence of u n
+ 
+
+ align:start position:0%
+that if the sequence of u n
+is instead in C1
+
+ align:start position:0%
+is instead in C1
+ 
+
+ align:start position:0%
+is instead in C1
+does that work
+
+ align:start position:0%
+does that work
+ 
+
+ align:start position:0%
+does that work
+and what they were able to show is that
+
+ align:start position:0%
+and what they were able to show is that
+ 
+
+ align:start position:0%
+and what they were able to show is that
+if the sequence is in C1 and such and
+
+ align:start position:0%
+if the sequence is in C1 and such and
+ 
+
+ align:start position:0%
+if the sequence is in C1 and such and
+the submit point Sorry if U1 was in C1
+
+ align:start position:0%
+the submit point Sorry if U1 was in C1
+ 
+
+ align:start position:0%
+the submit point Sorry if U1 was in C1
+and this limit existed then you can show
+
+ align:start position:0%
+and this limit existed then you can show
+ 
+
+ align:start position:0%
+and this limit existed then you can show
+that U was in C2 so retroactively we'd
+
+ align:start position:0%
+that U was in C2 so retroactively we'd
+ 
+
+ align:start position:0%
+that U was in C2 so retroactively we'd
+be done
+
+ align:start position:0%
+be done
+ 
+
+ align:start position:0%
+be done
+but the issue
+
+ align:start position:0%
+but the issue
+ 
+
+ align:start position:0%
+but the issue
+is again sorry not that U was in C2 but
+
+ align:start position:0%
+is again sorry not that U was in C2 but
+ 
+
+ align:start position:0%
+is again sorry not that U was in C2 but
+that each of the UNS would be in C2
+
+ align:start position:0%
+that each of the UNS would be in C2
+ 
+
+ align:start position:0%
+that each of the UNS would be in C2
+the issue is that again C1 is not
+
+ align:start position:0%
+the issue is that again C1 is not
+ 
+
+ align:start position:0%
+the issue is that again C1 is not
+compact so we're still not done
+
+ align:start position:0%
+compact so we're still not done
+ 
+
+ align:start position:0%
+compact so we're still not done
+now in the end we were able to solve
+
+ align:start position:0%
+now in the end we were able to solve
+ 
+
+ align:start position:0%
+now in the end we were able to solve
+this problem
+
+ align:start position:0%
+this problem
+ 
+
+ align:start position:0%
+this problem
+um with techniques that are quite beyond
+
+ align:start position:0%
+um with techniques that are quite beyond
+ 
+
+ align:start position:0%
+um with techniques that are quite beyond
+the scope of this class it's sometimes
+
+ align:start position:0%
+the scope of this class it's sometimes
+ 
+
+ align:start position:0%
+the scope of this class it's sometimes
+talked about in 18102
+
+ align:start position:0%
+talked about in 18102
+ 
+
+ align:start position:0%
+talked about in 18102
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+18 and 102 sometimes it's talked about
+
+ align:start position:0%
+18 and 102 sometimes it's talked about
+ 
+
+ align:start position:0%
+18 and 102 sometimes it's talked about
+there it's talked about in the lecture
+
+ align:start position:0%
+there it's talked about in the lecture
+ 
+
+ align:start position:0%
+there it's talked about in the lecture
+notes that are on ocw so if you want to
+
+ align:start position:0%
+notes that are on ocw so if you want to
+ 
+
+ align:start position:0%
+notes that are on ocw so if you want to
+read more about that there but that's
+
+ align:start position:0%
+read more about that there but that's
+ 
+
+ align:start position:0%
+read more about that there but that's
+like the very very last lecture so it's
+
+ align:start position:0%
+like the very very last lecture so it's
+ 
+
+ align:start position:0%
+like the very very last lecture so it's
+difficult yes but interesting
+
+ align:start position:0%
+difficult yes but interesting
+ 
+
+ align:start position:0%
+difficult yes but interesting
+nonetheless
+
+ align:start position:0%
+nonetheless
+ 
+
+ align:start position:0%
+nonetheless
+but it's an interesting question how
+
+ align:start position:0%
+but it's an interesting question how
+ 
+
+ align:start position:0%
+but it's an interesting question how
+should we be approaching these problems
+
+ align:start position:0%
+should we be approaching these problems
+ 
+
+ align:start position:0%
+should we be approaching these problems
+should we be approaching them physically
+
+ align:start position:0%
+should we be approaching them physically
+ 
+
+ align:start position:0%
+should we be approaching them physically
+or should we be approaching them super
+
+ align:start position:0%
+or should we be approaching them super
+ 
+
+ align:start position:0%
+or should we be approaching them super
+rigorously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answer
+
+ align:start position:0%
+and the answer
+ 
+
+ align:start position:0%
+and the answer
+is unclear right like it makes sense
+
+ align:start position:0%
+is unclear right like it makes sense
+ 
+
+ align:start position:0%
+is unclear right like it makes sense
+there's no direct answer to this
+
+ align:start position:0%
+there's no direct answer to this
+ 
+
+ align:start position:0%
+there's no direct answer to this
+question this gave us the framework to
+
+ align:start position:0%
+question this gave us the framework to
+ 
+
+ align:start position:0%
+question this gave us the framework to
+think about compactness even though the
+
+ align:start position:0%
+think about compactness even though the
+ 
+
+ align:start position:0%
+think about compactness even though the
+solution didn't work
+
+ align:start position:0%
+solution didn't work
+ 
+
+ align:start position:0%
+solution didn't work
+it motivated the development of compact
+
+ align:start position:0%
+it motivated the development of compact
+ 
+
+ align:start position:0%
+it motivated the development of compact
+sets for metric spaces right we have the
+
+ align:start position:0%
+sets for metric spaces right we have the
+ 
+
+ align:start position:0%
+sets for metric spaces right we have the
+C1 and C2 are metric spaces we want to
+
+ align:start position:0%
+C1 and C2 are metric spaces we want to
+ 
+
+ align:start position:0%
+C1 and C2 are metric spaces we want to
+understand if limit points are in your
+
+ align:start position:0%
+understand if limit points are in your
+ 
+
+ align:start position:0%
+understand if limit points are in your
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+and even though it wasn't the case for
+
+ align:start position:0%
+and even though it wasn't the case for
+ 
+
+ align:start position:0%
+and even though it wasn't the case for
+C1 and C2 it still developed all this
+
+ align:start position:0%
+C1 and C2 it still developed all this
+ 
+
+ align:start position:0%
+C1 and C2 it still developed all this
+terminology that as you've already seen
+
+ align:start position:0%
+terminology that as you've already seen
+ 
+
+ align:start position:0%
+terminology that as you've already seen
+is very very important
+
+ align:start position:0%
+is very very important
+ 
+
+ align:start position:0%
+is very very important
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah they were able to solve this
+
+ align:start position:0%
+yeah they were able to solve this
+ 
+
+ align:start position:0%
+yeah they were able to solve this
+problem eventually just using much
+
+ align:start position:0%
+problem eventually just using much
+ 
+
+ align:start position:0%
+problem eventually just using much
+different techniques
+
+ align:start position:0%
+different techniques
+ 
+
+ align:start position:0%
+different techniques
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's all I've prepared for today I
+
+ align:start position:0%
+that's all I've prepared for today I
+ 
+
+ align:start position:0%
+that's all I've prepared for today I
+mean this was mostly just a broad
+
+ align:start position:0%
+mean this was mostly just a broad
+ 
+
+ align:start position:0%
+mean this was mostly just a broad
+overview of where the material goes from
+
+ align:start position:0%
+overview of where the material goes from
+ 
+
+ align:start position:0%
+overview of where the material goes from
+here this the intuition that comes from
+
+ align:start position:0%
+here this the intuition that comes from
+ 
+
+ align:start position:0%
+here this the intuition that comes from
+metric spaces shows up all the time
+
+ align:start position:0%
+metric spaces shows up all the time
+ 
+
+ align:start position:0%
+metric spaces shows up all the time
+like for instance in foia analysis you
+
+ align:start position:0%
+like for instance in foia analysis you
+ 
+
+ align:start position:0%
+like for instance in foia analysis you
+want to understand a foyer series
+
+ align:start position:0%
+want to understand a foyer series
+ 
+
+ align:start position:0%
+want to understand a foyer series
+converts sheer function and in which
+
+ align:start position:0%
+converts sheer function and in which
+ 
+
+ align:start position:0%
+converts sheer function and in which
+sense and in that way it's related to
+
+ align:start position:0%
+sense and in that way it's related to
+ 
+
+ align:start position:0%
+sense and in that way it's related to
+metric spaces
+
+ align:start position:0%
+metric spaces
+ 
+
+ align:start position:0%
+metric spaces
+we've talked about how it applies to
+
+ align:start position:0%
+we've talked about how it applies to
+ 
+
+ align:start position:0%
+we've talked about how it applies to
+manifold Theory we've talked about
+
+ align:start position:0%
+manifold Theory we've talked about
+ 
+
+ align:start position:0%
+manifold Theory we've talked about
+functional analysis topology
+
+ align:start position:0%
+functional analysis topology
+ 
+
+ align:start position:0%
+functional analysis topology
+differential equations these are like
+
+ align:start position:0%
+differential equations these are like
+ 
+
+ align:start position:0%
+differential equations these are like
+five major applications of the material
+
+ align:start position:0%
+five major applications of the material
+ 
+
+ align:start position:0%
+five major applications of the material
+but the intuition that you gain for
+
+ align:start position:0%
+but the intuition that you gain for
+ 
+
+ align:start position:0%
+but the intuition that you gain for
+metric spaces will continue to work
+
+ align:start position:0%
+metric spaces will continue to work
+ 
+
+ align:start position:0%
+metric spaces will continue to work
+throughout your time at MIT so for
+
+ align:start position:0%
+throughout your time at MIT so for
+ 
+
+ align:start position:0%
+throughout your time at MIT so for
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+um in general proving things
+
+ align:start position:0%
+um in general proving things
+ 
+
+ align:start position:0%
+um in general proving things
+axiomatically are functions that satisfy
+
+ align:start position:0%
+axiomatically are functions that satisfy
+ 
+
+ align:start position:0%
+axiomatically are functions that satisfy
+certain properties like Norms inner
+
+ align:start position:0%
+certain properties like Norms inner
+ 
+
+ align:start position:0%
+certain properties like Norms inner
+products and metrics
+
+ align:start position:0%
+products and metrics
+ 
+
+ align:start position:0%
+products and metrics
+is a useful skill but even more in
+
+ align:start position:0%
+is a useful skill but even more in
+ 
+
+ align:start position:0%
+is a useful skill but even more in
+particular I think a class like this and
+
+ align:start position:0%
+particular I think a class like this and
+ 
+
+ align:start position:0%
+particular I think a class like this and
+the class like
+
+ align:start position:0%
+the class like
+ 
+
+ align:start position:0%
+the class like
+real analysis is interesting because of
+
+ align:start position:0%
+real analysis is interesting because of
+ 
+
+ align:start position:0%
+real analysis is interesting because of
+all these different subsets and bigger
+
+ align:start position:0%
+all these different subsets and bigger
+ 
+
+ align:start position:0%
+all these different subsets and bigger
+subsets or bigger subsets is the
+
+ align:start position:0%
+subsets or bigger subsets is the
+ 
+
+ align:start position:0%
+subsets or bigger subsets is the
+terminology right we started off with
+
+ align:start position:0%
+terminology right we started off with
+ 
+
+ align:start position:0%
+terminology right we started off with
+studying euclidean space which was just
+
+ align:start position:0%
+studying euclidean space which was just
+ 
+
+ align:start position:0%
+studying euclidean space which was just
+a tiny little Dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the set of metric spaces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there's obviously much more to be
+
+ align:start position:0%
+but there's obviously much more to be
+ 
+
+ align:start position:0%
+but there's obviously much more to be
+done here we talked about metric spaces
+
+ align:start position:0%
+done here we talked about metric spaces
+ 
+
+ align:start position:0%
+done here we talked about metric spaces
+but it makes sense to start right in the
+
+ align:start position:0%
+but it makes sense to start right in the
+ 
+
+ align:start position:0%
+but it makes sense to start right in the
+middle right and then work your way out
+
+ align:start position:0%
+middle right and then work your way out
+ 
+
+ align:start position:0%
+middle right and then work your way out
+work your way out towards topological
+
+ align:start position:0%
+work your way out towards topological
+ 
+
+ align:start position:0%
+work your way out towards topological
+spaces and then work your or potentially
+
+ align:start position:0%
+spaces and then work your or potentially
+ 
+
+ align:start position:0%
+spaces and then work your or potentially
+also work your way towards Norm spaces
+
+ align:start position:0%
+also work your way towards Norm spaces
+ 
+
+ align:start position:0%
+also work your way towards Norm spaces
+and bionic spaces in whichever order you
+
+ align:start position:0%
+and bionic spaces in whichever order you
+ 
+
+ align:start position:0%
+and bionic spaces in whichever order you
+choose but the main important thing the
+
+ align:start position:0%
+choose but the main important thing the
+ 
+
+ align:start position:0%
+choose but the main important thing the
+main reason I've been teaching this
+
+ align:start position:0%
+main reason I've been teaching this
+ 
+
+ align:start position:0%
+main reason I've been teaching this
+class for two years
+
+ align:start position:0%
+class for two years
+ 
+
+ align:start position:0%
+class for two years
+is to highlight you know the fact that
+
+ align:start position:0%
+is to highlight you know the fact that
+ 
+
+ align:start position:0%
+is to highlight you know the fact that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is is to give you the tools to be able
+
+ align:start position:0%
+is is to give you the tools to be able
+ 
+
+ align:start position:0%
+is is to give you the tools to be able
+to move forward into studying
+
+ align:start position:0%
+to move forward into studying
+ 
+
+ align:start position:0%
+to move forward into studying
+topological spaces in our spaces with
+
+ align:start position:0%
+topological spaces in our spaces with
+ 
+
+ align:start position:0%
+topological spaces in our spaces with
+some amount of intuition as much as
+
+ align:start position:0%
+some amount of intuition as much as
+ 
+
+ align:start position:0%
+some amount of intuition as much as
+that's possible
+
+ align:start position:0%
+that's possible
+ 
+
+ align:start position:0%
+that's possible
+okay so unless you have any questions
+
+ align:start position:0%
+okay so unless you have any questions
+ 
+
+ align:start position:0%
+okay so unless you have any questions
+well n 30 or 25 minutes early
\ No newline at end of file
diff --git a/sldnB9DVjUk.txt b/sldnB9DVjUk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1129d362982f6b4f65cc223771fc938b3ae0a1a
--- /dev/null
+++ b/sldnB9DVjUk.txt
@@ -0,0 +1,459 @@
+align:start position:0%
+ 
+So, so there are a couple challenges
+
+ align:start position:0%
+So, so there are a couple challenges
+ 
+
+ align:start position:0%
+So, so there are a couple challenges
+that you need to to think about when
+
+ align:start position:0%
+that you need to to think about when
+ 
+
+ align:start position:0%
+that you need to to think about when
+you're using this approach. One is it's
+
+ align:start position:0%
+you're using this approach. One is it's
+ 
+
+ align:start position:0%
+you're using this approach. One is it's
+important to explain to the students
+
+ align:start position:0%
+important to explain to the students
+ 
+
+ align:start position:0%
+important to explain to the students
+what's going on. Uh if you just start
+
+ align:start position:0%
+what's going on. Uh if you just start
+ 
+
+ align:start position:0%
+what's going on. Uh if you just start
+doing this and say this is what we're
+
+ align:start position:0%
+doing this and say this is what we're
+ 
+
+ align:start position:0%
+doing this and say this is what we're
+going to do and don't tell the students
+
+ align:start position:0%
+going to do and don't tell the students
+ 
+
+ align:start position:0%
+going to do and don't tell the students
+why you're going to do it, u that's
+
+ align:start position:0%
+why you're going to do it, u that's
+ 
+
+ align:start position:0%
+why you're going to do it, u that's
+problematic. Um I think it's important
+
+ align:start position:0%
+problematic. Um I think it's important
+ 
+
+ align:start position:0%
+problematic. Um I think it's important
+to think of the students as partners. Um
+
+ align:start position:0%
+to think of the students as partners. Um
+ 
+
+ align:start position:0%
+to think of the students as partners. Um
+explain what's going on. They're much
+
+ align:start position:0%
+explain what's going on. They're much
+ 
+
+ align:start position:0%
+explain what's going on. They're much
+more likely to u buy into it and and um
+
+ align:start position:0%
+more likely to u buy into it and and um
+ 
+
+ align:start position:0%
+more likely to u buy into it and and um
+u and maybe get used to the new
+
+ align:start position:0%
+u and maybe get used to the new
+ 
+
+ align:start position:0%
+u and maybe get used to the new
+approach. One of the things I do is I
+
+ align:start position:0%
+approach. One of the things I do is I
+ 
+
+ align:start position:0%
+approach. One of the things I do is I
+present some data um because it's MIT
+
+ align:start position:0%
+present some data um because it's MIT
+ 
+
+ align:start position:0%
+present some data um because it's MIT
+and students are persuaded by data and
+
+ align:start position:0%
+and students are persuaded by data and
+ 
+
+ align:start position:0%
+and students are persuaded by data and
+what the data says is that generally the
+
+ align:start position:0%
+what the data says is that generally the
+ 
+
+ align:start position:0%
+what the data says is that generally the
+more active a learning exercise the more
+
+ align:start position:0%
+more active a learning exercise the more
+ 
+
+ align:start position:0%
+more active a learning exercise the more
+that students learn. And there's there's
+
+ align:start position:0%
+that students learn. And there's there's
+ 
+
+ align:start position:0%
+that students learn. And there's there's
+some really good data in the literature
+
+ align:start position:0%
+some really good data in the literature
+ 
+
+ align:start position:0%
+some really good data in the literature
+uh that shows that. So um I explain to
+
+ align:start position:0%
+uh that shows that. So um I explain to
+ 
+
+ align:start position:0%
+uh that shows that. So um I explain to
+students that the reason I'm doing this
+
+ align:start position:0%
+students that the reason I'm doing this
+ 
+
+ align:start position:0%
+students that the reason I'm doing this
+uh is to increase their level of
+
+ align:start position:0%
+uh is to increase their level of
+ 
+
+ align:start position:0%
+uh is to increase their level of
+understanding especially at the
+
+ align:start position:0%
+understanding especially at the
+ 
+
+ align:start position:0%
+understanding especially at the
+conceptual level uh as a as opposed to
+
+ align:start position:0%
+conceptual level uh as a as opposed to
+ 
+
+ align:start position:0%
+conceptual level uh as a as opposed to
+the uh analytic level of just doing a
+
+ align:start position:0%
+the uh analytic level of just doing a
+ 
+
+ align:start position:0%
+the uh analytic level of just doing a
+problem using the the equations. I've
+
+ align:start position:0%
+problem using the the equations. I've
+ 
+
+ align:start position:0%
+problem using the the equations. I've
+never had a restation like this before
+
+ align:start position:0%
+never had a restation like this before
+ 
+
+ align:start position:0%
+never had a restation like this before
+actually working on problems with
+
+ align:start position:0%
+actually working on problems with
+ 
+
+ align:start position:0%
+actually working on problems with
+everybody else and kind of going through
+
+ align:start position:0%
+everybody else and kind of going through
+ 
+
+ align:start position:0%
+everybody else and kind of going through
+it and struggling through it. Um but
+
+ align:start position:0%
+it and struggling through it. Um but
+ 
+
+ align:start position:0%
+it and struggling through it. Um but
+eventually understanding a lot better
+
+ align:start position:0%
+eventually understanding a lot better
+ 
+
+ align:start position:0%
+eventually understanding a lot better
+what was done in lecture through I guess
+
+ align:start position:0%
+what was done in lecture through I guess
+ 
+
+ align:start position:0%
+what was done in lecture through I guess
+a more hands-on approach.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do the students like this? Well, I I
+
+ align:start position:0%
+Do the students like this? Well, I I
+ 
+
+ align:start position:0%
+Do the students like this? Well, I I
+have a little bit of feedback. I I do
+
+ align:start position:0%
+have a little bit of feedback. I I do
+ 
+
+ align:start position:0%
+have a little bit of feedback. I I do
+think that initially they're
+
+ align:start position:0%
+think that initially they're
+ 
+
+ align:start position:0%
+think that initially they're
+apprehensive. Um they're not used to
+
+ align:start position:0%
+apprehensive. Um they're not used to
+ 
+
+ align:start position:0%
+apprehensive. Um they're not used to
+being so uh exposed uh in the classroom.
+
+ align:start position:0%
+being so uh exposed uh in the classroom.
+ 
+
+ align:start position:0%
+being so uh exposed uh in the classroom.
+They can hide. Usually, they don't want
+
+ align:start position:0%
+They can hide. Usually, they don't want
+ 
+
+ align:start position:0%
+They can hide. Usually, they don't want
+to answer a question. They don't raise
+
+ align:start position:0%
+to answer a question. They don't raise
+ 
+
+ align:start position:0%
+to answer a question. They don't raise
+their hands. Uh but in a situation like
+
+ align:start position:0%
+their hands. Uh but in a situation like
+ 
+
+ align:start position:0%
+their hands. Uh but in a situation like
+this, everyone's answer is visible. So,
+
+ align:start position:0%
+this, everyone's answer is visible. So,
+ 
+
+ align:start position:0%
+this, everyone's answer is visible. So,
+initially I do think they're a little
+
+ align:start position:0%
+initially I do think they're a little
+ 
+
+ align:start position:0%
+initially I do think they're a little
+bit um uncomfortable. I think they get
+
+ align:start position:0%
+bit um uncomfortable. I think they get
+ 
+
+ align:start position:0%
+bit um uncomfortable. I think they get
+comfortable very quickly and get um used
+
+ align:start position:0%
+comfortable very quickly and get um used
+ 
+
+ align:start position:0%
+comfortable very quickly and get um used
+to it. Um at the end of the day, at the
+
+ align:start position:0%
+to it. Um at the end of the day, at the
+ 
+
+ align:start position:0%
+to it. Um at the end of the day, at the
+end of the class, uh when they evaluate
+
+ align:start position:0%
+end of the class, uh when they evaluate
+ 
+
+ align:start position:0%
+end of the class, uh when they evaluate
+it, um I've found that students really
+
+ align:start position:0%
+it, um I've found that students really
+ 
+
+ align:start position:0%
+it, um I've found that students really
+like uh this approach that they like
+
+ align:start position:0%
+like uh this approach that they like
+ 
+
+ align:start position:0%
+like uh this approach that they like
+this sort of recitation
+
+ align:start position:0%
+this sort of recitation
+ 
+
+ align:start position:0%
+this sort of recitation
+uh much more than conventional
+
+ align:start position:0%
+uh much more than conventional
+ 
+
+ align:start position:0%
+uh much more than conventional
+recitations and um often comment about
+
+ align:start position:0%
+recitations and um often comment about
+ 
+
+ align:start position:0%
+recitations and um often comment about
+that uh in the course evaluation. So uh
+
+ align:start position:0%
+that uh in the course evaluation. So uh
+ 
+
+ align:start position:0%
+that uh in the course evaluation. So uh
+even though there might be a little bit
+
+ align:start position:0%
+even though there might be a little bit
+ 
+
+ align:start position:0%
+even though there might be a little bit
+of initial reluctance uh I think uh most
+
+ align:start position:0%
+of initial reluctance uh I think uh most
+ 
+
+ align:start position:0%
+of initial reluctance uh I think uh most
+students would really like this
+
+ align:start position:0%
+students would really like this
+ 
+
+ align:start position:0%
+students would really like this
+approach.
\ No newline at end of file
diff --git a/txKXRtlrFfI.txt b/txKXRtlrFfI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..59980af9b2d9ce7fe7deb70a68d462aeda39f4d4
--- /dev/null
+++ b/txKXRtlrFfI.txt
@@ -0,0 +1,8787 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's go ahead and get started hope
+
+ align:start position:0%
+okay let's go ahead and get started hope
+ 
+
+ align:start position:0%
+okay let's go ahead and get started hope
+everybody saw the correction to a typo
+
+ align:start position:0%
+everybody saw the correction to a typo
+ 
+
+ align:start position:0%
+everybody saw the correction to a typo
+in homework one that was posted on
+
+ align:start position:0%
+in homework one that was posted on
+ 
+
+ align:start position:0%
+in homework one that was posted on
+stellar last night and sent out gee
+
+ align:start position:0%
+stellar last night and sent out gee
+ 
+
+ align:start position:0%
+stellar last night and sent out gee
+that's gonna happen from time to time we
+
+ align:start position:0%
+that's gonna happen from time to time we
+ 
+
+ align:start position:0%
+that's gonna happen from time to time we
+have four course staff that review all
+
+ align:start position:0%
+have four course staff that review all
+ 
+
+ align:start position:0%
+have four course staff that review all
+the problems we try to look through it
+
+ align:start position:0%
+the problems we try to look through it
+ 
+
+ align:start position:0%
+the problems we try to look through it
+for any issues or ambiguities but from
+
+ align:start position:0%
+for any issues or ambiguities but from
+ 
+
+ align:start position:0%
+for any issues or ambiguities but from
+time to time we'll miss something and
+
+ align:start position:0%
+time to time we'll miss something and
+ 
+
+ align:start position:0%
+time to time we'll miss something and
+try to make a correction the t's gave a
+
+ align:start position:0%
+try to make a correction the t's gave a
+ 
+
+ align:start position:0%
+try to make a correction the t's gave a
+hint that would let you solve the
+
+ align:start position:0%
+hint that would let you solve the
+ 
+
+ align:start position:0%
+hint that would let you solve the
+problem as written but that's more
+
+ align:start position:0%
+problem as written but that's more
+ 
+
+ align:start position:0%
+problem as written but that's more
+difficult than what we had intended for
+
+ align:start position:0%
+difficult than what we had intended for
+ 
+
+ align:start position:0%
+difficult than what we had intended for
+you guys wouldn't want to give you a
+
+ align:start position:0%
+you guys wouldn't want to give you a
+ 
+
+ align:start position:0%
+you guys wouldn't want to give you a
+homework assignment that's punishing we
+
+ align:start position:0%
+homework assignment that's punishing we
+ 
+
+ align:start position:0%
+homework assignment that's punishing we
+want to give you an assignment that'll
+
+ align:start position:0%
+want to give you an assignment that'll
+ 
+
+ align:start position:0%
+want to give you an assignment that'll
+help you learn some people in this class
+
+ align:start position:0%
+help you learn some people in this class
+ 
+
+ align:start position:0%
+help you learn some people in this class
+are very good at programming apparently
+
+ align:start position:0%
+are very good at programming apparently
+ 
+
+ align:start position:0%
+are very good at programming apparently
+already completed that problem with the
+
+ align:start position:0%
+already completed that problem with the
+ 
+
+ align:start position:0%
+already completed that problem with the
+hint but it's easier as originally
+
+ align:start position:0%
+hint but it's easier as originally
+ 
+
+ align:start position:0%
+hint but it's easier as originally
+intended and the correction resets that
+
+ align:start position:0%
+intended and the correction resets that
+ 
+
+ align:start position:0%
+intended and the correction resets that
+so maybe you'll see the distinction
+
+ align:start position:0%
+so maybe you'll see the distinction
+ 
+
+ align:start position:0%
+so maybe you'll see the distinction
+between those things and understand why
+
+ align:start position:0%
+between those things and understand why
+ 
+
+ align:start position:0%
+between those things and understand why
+one version of the problem is much
+
+ align:start position:0%
+one version of the problem is much
+ 
+
+ align:start position:0%
+one version of the problem is much
+easier than another but we try to
+
+ align:start position:0%
+easier than another but we try to
+ 
+
+ align:start position:0%
+easier than another but we try to
+respond as quickly as possible when when
+
+ align:start position:0%
+respond as quickly as possible when when
+ 
+
+ align:start position:0%
+respond as quickly as possible when when
+we notice a typo like that so we can set
+
+ align:start position:0%
+we notice a typo like that so we can set
+ 
+
+ align:start position:0%
+we notice a typo like that so we can set
+you guys on the right course okay so
+
+ align:start position:0%
+you guys on the right course okay so
+ 
+
+ align:start position:0%
+you guys on the right course okay so
+we've got two lectures left discussing
+
+ align:start position:0%
+we've got two lectures left discussing
+ 
+
+ align:start position:0%
+we've got two lectures left discussing
+linear algebra but before we move on to
+
+ align:start position:0%
+linear algebra but before we move on to
+ 
+
+ align:start position:0%
+linear algebra but before we move on to
+other topics we're still going to talk
+
+ align:start position:0%
+other topics we're still going to talk
+ 
+
+ align:start position:0%
+other topics we're still going to talk
+about transformations of matrices we
+
+ align:start position:0%
+about transformations of matrices we
+ 
+
+ align:start position:0%
+about transformations of matrices we
+looked at one type of transformation we
+
+ align:start position:0%
+looked at one type of transformation we
+ 
+
+ align:start position:0%
+looked at one type of transformation we
+can utilize for solving systems of
+
+ align:start position:0%
+can utilize for solving systems of
+ 
+
+ align:start position:0%
+can utilize for solving systems of
+equations today we'll look at another
+
+ align:start position:0%
+equations today we'll look at another
+ 
+
+ align:start position:0%
+equations today we'll look at another
+one the eigenvalue decomposition and on
+
+ align:start position:0%
+one the eigenvalue decomposition and on
+ 
+
+ align:start position:0%
+one the eigenvalue decomposition and on
+Monday we'll look at another one called
+
+ align:start position:0%
+Monday we'll look at another one called
+ 
+
+ align:start position:0%
+Monday we'll look at another one called
+the singular value decomposition before
+
+ align:start position:0%
+the singular value decomposition before
+ 
+
+ align:start position:0%
+the singular value decomposition before
+jumping right in I want to take a minute
+
+ align:start position:0%
+jumping right in I want to take a minute
+ 
+
+ align:start position:0%
+jumping right in I want to take a minute
+and see if there any any questions that
+
+ align:start position:0%
+and see if there any any questions that
+ 
+
+ align:start position:0%
+and see if there any any questions that
+I can answer anything that's been
+
+ align:start position:0%
+I can answer anything that's been
+ 
+
+ align:start position:0%
+I can answer anything that's been
+unclear so far that I can try to
+
+ align:start position:0%
+unclear so far that I can try to
+ 
+
+ align:start position:0%
+unclear so far that I can try to
+reemphasize or focus on for you I was
+
+ align:start position:0%
+reemphasize or focus on for you I was
+ 
+
+ align:start position:0%
+reemphasize or focus on for you I was
+told the office hours are really well
+
+ align:start position:0%
+told the office hours are really well
+ 
+
+ align:start position:0%
+told the office hours are really well
+attended so hopefully you're getting an
+
+ align:start position:0%
+attended so hopefully you're getting an
+ 
+
+ align:start position:0%
+attended so hopefully you're getting an
+opportunity to ask any pressing
+
+ align:start position:0%
+opportunity to ask any pressing
+ 
+
+ align:start position:0%
+opportunity to ask any pressing
+questions during the office hours or
+
+ align:start position:0%
+questions during the office hours or
+ 
+
+ align:start position:0%
+questions during the office hours or
+your meeting with the instructors after
+
+ align:start position:0%
+your meeting with the instructors after
+ 
+
+ align:start position:0%
+your meeting with the instructors after
+class to ask anything that was unclear
+
+ align:start position:0%
+class to ask anything that was unclear
+ 
+
+ align:start position:0%
+class to ask anything that was unclear
+we want to make sure that we're
+
+ align:start position:0%
+we want to make sure that we're
+ 
+
+ align:start position:0%
+we want to make sure that we're
+answering those questions in a timely
+
+ align:start position:0%
+answering those questions in a timely
+ 
+
+ align:start position:0%
+answering those questions in a timely
+fashion this course moves at a pretty
+
+ align:start position:0%
+fashion this course moves at a pretty
+ 
+
+ align:start position:0%
+fashion this course moves at a pretty
+quick pace we don't want anyone to get
+
+ align:start position:0%
+quick pace we don't want anyone to get
+ 
+
+ align:start position:0%
+quick pace we don't want anyone to get
+left behind speaking of getting left
+
+ align:start position:0%
+left behind speaking of getting left
+ 
+
+ align:start position:0%
+left behind speaking of getting left
+behind we ran out of time a little bit
+
+ align:start position:0%
+behind we ran out of time a little bit
+ 
+
+ align:start position:0%
+behind we ran out of time a little bit
+at the end of lecture
+
+ align:start position:0%
+at the end of lecture
+ 
+
+ align:start position:0%
+at the end of lecture
+on Wednesday that's okay there were a
+
+ align:start position:0%
+on Wednesday that's okay there were a
+ 
+
+ align:start position:0%
+on Wednesday that's okay there were a
+lot of good questions that came up
+
+ align:start position:0%
+lot of good questions that came up
+ 
+
+ align:start position:0%
+lot of good questions that came up
+during class and one topic that we
+
+ align:start position:0%
+during class and one topic that we
+ 
+
+ align:start position:0%
+during class and one topic that we
+didn't get to discuss is formal systems
+
+ align:start position:0%
+didn't get to discuss is formal systems
+ 
+
+ align:start position:0%
+didn't get to discuss is formal systems
+for doing reordering in systems of
+
+ align:start position:0%
+for doing reordering in systems of
+ 
+
+ align:start position:0%
+for doing reordering in systems of
+equations we saw that reordering is
+
+ align:start position:0%
+equations we saw that reordering is
+ 
+
+ align:start position:0%
+equations we saw that reordering is
+important in fact it's it's essential
+
+ align:start position:0%
+important in fact it's it's essential
+ 
+
+ align:start position:0%
+important in fact it's it's essential
+for solving certain problems via
+
+ align:start position:0%
+for solving certain problems via
+ 
+
+ align:start position:0%
+for solving certain problems via
+Gaussian elimination you won't be able
+
+ align:start position:0%
+Gaussian elimination you won't be able
+ 
+
+ align:start position:0%
+Gaussian elimination you won't be able
+to solve them either you'll incur large
+
+ align:start position:0%
+to solve them either you'll incur large
+ 
+
+ align:start position:0%
+to solve them either you'll incur large
+numerical error because you didn't do
+
+ align:start position:0%
+numerical error because you didn't do
+ 
+
+ align:start position:0%
+numerical error because you didn't do
+pivoting we'd like to do pivoting in
+
+ align:start position:0%
+pivoting we'd like to do pivoting in
+ 
+
+ align:start position:0%
+pivoting we'd like to do pivoting in
+order to minimize the numerical error or
+
+ align:start position:0%
+order to minimize the numerical error or
+ 
+
+ align:start position:0%
+order to minimize the numerical error or
+you need to reorder in order to minimize
+
+ align:start position:0%
+you need to reorder in order to minimize
+ 
+
+ align:start position:0%
+you need to reorder in order to minimize
+filling as an example I I've solved a
+
+ align:start position:0%
+filling as an example I I've solved a
+ 
+
+ align:start position:0%
+filling as an example I I've solved a
+research problem where there was
+
+ align:start position:0%
+research problem where there was
+ 
+
+ align:start position:0%
+research problem where there was
+something like 40 million equations and
+
+ align:start position:0%
+something like 40 million equations and
+ 
+
+ align:start position:0%
+something like 40 million equations and
+unknowns a system of partial
+
+ align:start position:0%
+unknowns a system of partial
+ 
+
+ align:start position:0%
+unknowns a system of partial
+differential equations and if you
+
+ align:start position:0%
+differential equations and if you
+ 
+
+ align:start position:0%
+differential equations and if you
+reorder those equations then you can
+
+ align:start position:0%
+reorder those equations then you can
+ 
+
+ align:start position:0%
+reorder those equations then you can
+solve via Gaussian elimination pretty
+
+ align:start position:0%
+solve via Gaussian elimination pretty
+ 
+
+ align:start position:0%
+solve via Gaussian elimination pretty
+readily but if you don't well my PC had
+
+ align:start position:0%
+readily but if you don't well my PC had
+ 
+
+ align:start position:0%
+readily but if you don't well my PC had
+like 192 gigabytes of RAM and the matrix
+
+ align:start position:0%
+like 192 gigabytes of RAM and the matrix
+ 
+
+ align:start position:0%
+like 192 gigabytes of RAM and the matrix
+fills the you know the elimination on
+
+ align:start position:0%
+fills the you know the elimination on
+ 
+
+ align:start position:0%
+fills the you know the elimination on
+that matrix will fill the memory of that
+
+ align:start position:0%
+that matrix will fill the memory of that
+ 
+
+ align:start position:0%
+that matrix will fill the memory of that
+PC up in 20 minutes and you'll be stuck
+
+ align:start position:0%
+PC up in 20 minutes and you'll be stuck
+ 
+
+ align:start position:0%
+PC up in 20 minutes and you'll be stuck
+it won't proceed after that okay so it's
+
+ align:start position:0%
+it won't proceed after that okay so it's
+ 
+
+ align:start position:0%
+it won't proceed after that okay so it's
+the difference between getting a
+
+ align:start position:0%
+the difference between getting a
+ 
+
+ align:start position:0%
+the difference between getting a
+solution and writing a publication about
+
+ align:start position:0%
+solution and writing a publication about
+ 
+
+ align:start position:0%
+solution and writing a publication about
+the research problem you're interested
+
+ align:start position:0%
+the research problem you're interested
+ 
+
+ align:start position:0%
+the research problem you're interested
+in and not so how do you do reordering
+
+ align:start position:0%
+in and not so how do you do reordering
+ 
+
+ align:start position:0%
+in and not so how do you do reordering
+well we use a process called permutation
+
+ align:start position:0%
+well we use a process called permutation
+ 
+
+ align:start position:0%
+well we use a process called permutation
+there's a certain class of matrix called
+
+ align:start position:0%
+there's a certain class of matrix called
+ 
+
+ align:start position:0%
+there's a certain class of matrix called
+a permutation matrix that can its action
+
+ align:start position:0%
+a permutation matrix that can its action
+ 
+
+ align:start position:0%
+a permutation matrix that can its action
+multiplying another matrix can swap rows
+
+ align:start position:0%
+multiplying another matrix can swap rows
+ 
+
+ align:start position:0%
+multiplying another matrix can swap rows
+or columns and here's an example of a
+
+ align:start position:0%
+or columns and here's an example of a
+ 
+
+ align:start position:0%
+or columns and here's an example of a
+permutation matrix whose intention is to
+
+ align:start position:0%
+permutation matrix whose intention is to
+ 
+
+ align:start position:0%
+permutation matrix whose intention is to
+swap Row one and two of a matrix okay so
+
+ align:start position:0%
+swap Row one and two of a matrix okay so
+ 
+
+ align:start position:0%
+swap Row one and two of a matrix okay so
+here it looks like identity except
+
+ align:start position:0%
+here it looks like identity except
+ 
+
+ align:start position:0%
+here it looks like identity except
+rather than having one run on the first
+
+ align:start position:0%
+rather than having one run on the first
+ 
+
+ align:start position:0%
+rather than having one run on the first
+two elements of the diagonal I have 0 1
+
+ align:start position:0%
+two elements of the diagonal I have 0 1
+ 
+
+ align:start position:0%
+two elements of the diagonal I have 0 1
+and 1 0 here's an example where I take
+
+ align:start position:0%
+and 1 0 here's an example where I take
+ 
+
+ align:start position:0%
+and 1 0 here's an example where I take
+that sort of a matrix which should swap
+
+ align:start position:0%
+that sort of a matrix which should swap
+ 
+
+ align:start position:0%
+that sort of a matrix which should swap
+rows one and two and I multiply it by a
+
+ align:start position:0%
+rows one and two and I multiply it by a
+ 
+
+ align:start position:0%
+rows one and two and I multiply it by a
+vector if you do this matrix vector
+
+ align:start position:0%
+vector if you do this matrix vector
+ 
+
+ align:start position:0%
+vector if you do this matrix vector
+multiplication you'll see initially the
+
+ align:start position:0%
+multiplication you'll see initially the
+ 
+
+ align:start position:0%
+multiplication you'll see initially the
+vector was X 1 X 2 X 3 but the product
+
+ align:start position:0%
+vector was X 1 X 2 X 3 but the product
+ 
+
+ align:start position:0%
+vector was X 1 X 2 X 3 but the product
+will be X 2 X 1 X 3 it swapped two rows
+
+ align:start position:0%
+will be X 2 X 1 X 3 it swapped two rows
+ 
+
+ align:start position:0%
+will be X 2 X 1 X 3 it swapped two rows
+in that vector course a vector is just
+
+ align:start position:0%
+in that vector course a vector is just
+ 
+
+ align:start position:0%
+in that vector course a vector is just
+matrix right it's an N by 1 matrix so P
+
+ align:start position:0%
+matrix right it's an N by 1 matrix so P
+ 
+
+ align:start position:0%
+matrix right it's an N by 1 matrix so P
+times a is the same as a matrix whose
+
+ align:start position:0%
+times a is the same as a matrix whose
+ 
+
+ align:start position:0%
+times a is the same as a matrix whose
+columns are P times each of
+
+ align:start position:0%
+columns are P times each of
+ 
+
+ align:start position:0%
+columns are P times each of
+columns of a that's what this notation
+
+ align:start position:0%
+columns of a that's what this notation
+ 
+
+ align:start position:0%
+columns of a that's what this notation
+indicates here and we know that P times
+
+ align:start position:0%
+indicates here and we know that P times
+ 
+
+ align:start position:0%
+indicates here and we know that P times
+a vector which is the column from a will
+
+ align:start position:0%
+a vector which is the column from a will
+ 
+
+ align:start position:0%
+a vector which is the column from a will
+swap two rows in a right so the product
+
+ align:start position:0%
+swap two rows in a right so the product
+ 
+
+ align:start position:0%
+swap two rows in a right so the product
+here will be all the rows of a at the
+
+ align:start position:0%
+here will be all the rows of a at the
+ 
+
+ align:start position:0%
+here will be all the rows of a at the
+different rows of a a superscript R with
+
+ align:start position:0%
+different rows of a a superscript R with
+ 
+
+ align:start position:0%
+different rows of a a superscript R with
+Row 1 into swapped with each other right
+
+ align:start position:0%
+Row 1 into swapped with each other right
+ 
+
+ align:start position:0%
+Row 1 into swapped with each other right
+so permutation multiplication by the
+
+ align:start position:0%
+so permutation multiplication by the
+ 
+
+ align:start position:0%
+so permutation multiplication by the
+special special type of matrix of
+
+ align:start position:0%
+special special type of matrix of
+ 
+
+ align:start position:0%
+special special type of matrix of
+permutation matrix does reordering of
+
+ align:start position:0%
+permutation matrix does reordering of
+ 
+
+ align:start position:0%
+permutation matrix does reordering of
+rows if I want to swap columns I
+
+ align:start position:0%
+rows if I want to swap columns I
+ 
+
+ align:start position:0%
+rows if I want to swap columns I
+multiply my matrix from the right by P
+
+ align:start position:0%
+multiply my matrix from the right by P
+ 
+
+ align:start position:0%
+multiply my matrix from the right by P
+transpose okay so if I want to swap
+
+ align:start position:0%
+transpose okay so if I want to swap
+ 
+
+ align:start position:0%
+transpose okay so if I want to swap
+column 1 in 2 I multiply a from the
+
+ align:start position:0%
+column 1 in 2 I multiply a from the
+ 
+
+ align:start position:0%
+column 1 in 2 I multiply a from the
+right by P transpose how can I show that
+
+ align:start position:0%
+right by P transpose how can I show that
+ 
+
+ align:start position:0%
+right by P transpose how can I show that
+that swaps columns well a times P
+
+ align:start position:0%
+that swaps columns well a times P
+ 
+
+ align:start position:0%
+that swaps columns well a times P
+transpose is the same as P times a
+
+ align:start position:0%
+transpose is the same as P times a
+ 
+
+ align:start position:0%
+transpose is the same as P times a
+transpose transpose P swaps rows so it's
+
+ align:start position:0%
+transpose transpose P swaps rows so it's
+ 
+
+ align:start position:0%
+transpose transpose P swaps rows so it's
+swapping rows of a transpose which is
+
+ align:start position:0%
+swapping rows of a transpose which is
+ 
+
+ align:start position:0%
+swapping rows of a transpose which is
+like swapping columns of a ok so we had
+
+ align:start position:0%
+like swapping columns of a ok so we had
+ 
+
+ align:start position:0%
+like swapping columns of a ok so we had
+some identities associated with matrix
+
+ align:start position:0%
+some identities associated with matrix
+ 
+
+ align:start position:0%
+some identities associated with matrix
+matrix multiplication and there
+
+ align:start position:0%
+matrix multiplication and there
+ 
+
+ align:start position:0%
+matrix multiplication and there
+transposes and you can use that to work
+
+ align:start position:0%
+transposes and you can use that to work
+ 
+
+ align:start position:0%
+transposes and you can use that to work
+out how this permutation matrix will
+
+ align:start position:0%
+out how this permutation matrix will
+ 
+
+ align:start position:0%
+out how this permutation matrix will
+swap columns instead of rows if I
+
+ align:start position:0%
+swap columns instead of rows if I
+ 
+
+ align:start position:0%
+swap columns instead of rows if I
+multiply from the right instead of the
+
+ align:start position:0%
+multiply from the right instead of the
+ 
+
+ align:start position:0%
+multiply from the right instead of the
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's an important concept to know
+
+ align:start position:0%
+here's an important concept to know
+ 
+
+ align:start position:0%
+here's an important concept to know
+permutation matrices are would refer to
+
+ align:start position:0%
+permutation matrices are would refer to
+ 
+
+ align:start position:0%
+permutation matrices are would refer to
+as unitary matrices their transpose is
+
+ align:start position:0%
+as unitary matrices their transpose is
+ 
+
+ align:start position:0%
+as unitary matrices their transpose is
+also their inverse so P times P
+
+ align:start position:0%
+also their inverse so P times P
+ 
+
+ align:start position:0%
+also their inverse so P times P
+transpose is identity if I swap the rows
+
+ align:start position:0%
+transpose is identity if I swap the rows
+ 
+
+ align:start position:0%
+transpose is identity if I swap the rows
+and then I swap them back I get back
+
+ align:start position:0%
+and then I swap them back I get back
+ 
+
+ align:start position:0%
+and then I swap them back I get back
+what I had before ok so there are lots
+
+ align:start position:0%
+what I had before ok so there are lots
+ 
+
+ align:start position:0%
+what I had before ok so there are lots
+of matrices that have this property that
+
+ align:start position:0%
+of matrices that have this property that
+ 
+
+ align:start position:0%
+of matrices that have this property that
+they're unitary we'll see some today ok
+
+ align:start position:0%
+they're unitary we'll see some today ok
+ 
+
+ align:start position:0%
+they're unitary we'll see some today ok
+but permutation matrices are one class
+
+ align:start position:0%
+but permutation matrices are one class
+ 
+
+ align:start position:0%
+but permutation matrices are one class
+maybe the simplest class of unitary
+
+ align:start position:0%
+maybe the simplest class of unitary
+ 
+
+ align:start position:0%
+maybe the simplest class of unitary
+matrices they're just doing row or
+
+ align:start position:0%
+matrices they're just doing row or
+ 
+
+ align:start position:0%
+matrices they're just doing row or
+column swaps right that's their job
+
+ align:start position:0%
+column swaps right that's their job
+ 
+
+ align:start position:0%
+column swaps right that's their job
+and so if I have some reordering of the
+
+ align:start position:0%
+and so if I have some reordering of the
+ 
+
+ align:start position:0%
+and so if I have some reordering of the
+equations or rows of my system of
+
+ align:start position:0%
+equations or rows of my system of
+ 
+
+ align:start position:0%
+equations or rows of my system of
+equations that I want that's going to be
+
+ align:start position:0%
+equations that I want that's going to be
+ 
+
+ align:start position:0%
+equations that I want that's going to be
+indicated by a permutation matrix say p1
+
+ align:start position:0%
+indicated by a permutation matrix say p1
+ 
+
+ align:start position:0%
+indicated by a permutation matrix say p1
+and I would multiply my entire system of
+
+ align:start position:0%
+and I would multiply my entire system of
+ 
+
+ align:start position:0%
+and I would multiply my entire system of
+both sides of my system of equations by
+
+ align:start position:0%
+both sides of my system of equations by
+ 
+
+ align:start position:0%
+both sides of my system of equations by
+p1 that would reorder the rows if I have
+
+ align:start position:0%
+p1 that would reorder the rows if I have
+ 
+
+ align:start position:0%
+p1 that would reorder the rows if I have
+some reordering of the columns or the
+
+ align:start position:0%
+some reordering of the columns or the
+ 
+
+ align:start position:0%
+some reordering of the columns or the
+unknowns in my problem I'm going to use
+
+ align:start position:0%
+unknowns in my problem I'm going to use
+ 
+
+ align:start position:0%
+unknowns in my problem I'm going to use
+a similar permutation matrix p2 of
+
+ align:start position:0%
+a similar permutation matrix p2 of
+ 
+
+ align:start position:0%
+a similar permutation matrix p2 of
+course p2 transpose times p2 is identity
+
+ align:start position:0%
+course p2 transpose times p2 is identity
+ 
+
+ align:start position:0%
+course p2 transpose times p2 is identity
+so this product here does not
+
+ align:start position:0%
+so this product here does not
+ 
+
+ align:start position:0%
+so this product here does not
+thing to the system of equations it just
+
+ align:start position:0%
+thing to the system of equations it just
+ 
+
+ align:start position:0%
+thing to the system of equations it just
+swaps the unknown so there's a formal
+
+ align:start position:0%
+swaps the unknown so there's a formal
+ 
+
+ align:start position:0%
+swaps the unknown so there's a formal
+system for doing this sort of swapping
+
+ align:start position:0%
+system for doing this sort of swapping
+ 
+
+ align:start position:0%
+system for doing this sort of swapping
+there are a couple other slides that are
+
+ align:start position:0%
+there are a couple other slides that are
+ 
+
+ align:start position:0%
+there are a couple other slides that are
+in your notes from last time that you
+
+ align:start position:0%
+in your notes from last time that you
+ 
+
+ align:start position:0%
+in your notes from last time that you
+can look at and I'm happy to answer
+
+ align:start position:0%
+can look at and I'm happy to answer
+ 
+
+ align:start position:0%
+can look at and I'm happy to answer
+questions on we don't would have time to
+
+ align:start position:0%
+questions on we don't would have time to
+ 
+
+ align:start position:0%
+questions on we don't would have time to
+go into detail but it's it discusses the
+
+ align:start position:0%
+go into detail but it's it discusses the
+ 
+
+ align:start position:0%
+go into detail but it's it discusses the
+actual methodology the simplest possible
+
+ align:start position:0%
+actual methodology the simplest possible
+ 
+
+ align:start position:0%
+actual methodology the simplest possible
+methodology for doing this kind of
+
+ align:start position:0%
+methodology for doing this kind of
+ 
+
+ align:start position:0%
+methodology for doing this kind of
+reordering or swapping so this is a form
+
+ align:start position:0%
+reordering or swapping so this is a form
+ 
+
+ align:start position:0%
+reordering or swapping so this is a form
+of preconditioning okay it's
+
+ align:start position:0%
+of preconditioning okay it's
+ 
+
+ align:start position:0%
+of preconditioning okay it's
+preconditioning design if it's
+
+ align:start position:0%
+preconditioning design if it's
+ 
+
+ align:start position:0%
+preconditioning design if it's
+preconditioning for pivoting it's
+
+ align:start position:0%
+preconditioning for pivoting it's
+ 
+
+ align:start position:0%
+preconditioning for pivoting it's
+designed to minimize numerical error if
+
+ align:start position:0%
+designed to minimize numerical error if
+ 
+
+ align:start position:0%
+designed to minimize numerical error if
+it's preconditioning in order to
+
+ align:start position:0%
+it's preconditioning in order to
+ 
+
+ align:start position:0%
+it's preconditioning in order to
+minimize fill-in instead right that's
+
+ align:start position:0%
+minimize fill-in instead right that's
+ 
+
+ align:start position:0%
+minimize fill-in instead right that's
+meant to make the problem solvable on
+
+ align:start position:0%
+meant to make the problem solvable on
+ 
+
+ align:start position:0%
+meant to make the problem solvable on
+your computer but it's a form of
+
+ align:start position:0%
+your computer but it's a form of
+ 
+
+ align:start position:0%
+your computer but it's a form of
+preconditioning a system of equations
+
+ align:start position:0%
+preconditioning a system of equations
+ 
+
+ align:start position:0%
+preconditioning a system of equations
+and we discuss preconditioning before
+
+ align:start position:0%
+and we discuss preconditioning before
+ 
+
+ align:start position:0%
+and we discuss preconditioning before
+okay so now we know how to solve systems
+
+ align:start position:0%
+okay so now we know how to solve systems
+ 
+
+ align:start position:0%
+okay so now we know how to solve systems
+of equations it's always done via
+
+ align:start position:0%
+of equations it's always done via
+ 
+
+ align:start position:0%
+of equations it's always done via
+Gaussian elimination if we want an exact
+
+ align:start position:0%
+Gaussian elimination if we want an exact
+ 
+
+ align:start position:0%
+Gaussian elimination if we want an exact
+solution there are lots of variants on
+
+ align:start position:0%
+solution there are lots of variants on
+ 
+
+ align:start position:0%
+solution there are lots of variants on
+Gaussian elimination that we can utilize
+
+ align:start position:0%
+Gaussian elimination that we can utilize
+ 
+
+ align:start position:0%
+Gaussian elimination that we can utilize
+you're studying one of them in your
+
+ align:start position:0%
+you're studying one of them in your
+ 
+
+ align:start position:0%
+you're studying one of them in your
+homework assignment now where you know
+
+ align:start position:0%
+homework assignment now where you know
+ 
+
+ align:start position:0%
+homework assignment now where you know
+the matrix is banded with some bandwidth
+
+ align:start position:0%
+the matrix is banded with some bandwidth
+ 
+
+ align:start position:0%
+the matrix is banded with some bandwidth
+so you don't do elimination on an entire
+
+ align:start position:0%
+so you don't do elimination on an entire
+ 
+
+ align:start position:0%
+so you don't do elimination on an entire
+full matrix you do it on a sparse matrix
+
+ align:start position:0%
+full matrix you do it on a sparse matrix
+ 
+
+ align:start position:0%
+full matrix you do it on a sparse matrix
+whose structure you understand we
+
+ align:start position:0%
+whose structure you understand we
+ 
+
+ align:start position:0%
+whose structure you understand we
+discussed sparse matrices and a little
+
+ align:start position:0%
+discussed sparse matrices and a little
+ 
+
+ align:start position:0%
+discussed sparse matrices and a little
+bit about reordering and now permutation
+
+ align:start position:0%
+bit about reordering and now permutation
+ 
+
+ align:start position:0%
+bit about reordering and now permutation
+I feel like my diffusion example last
+
+ align:start position:0%
+I feel like my diffusion example last
+ 
+
+ align:start position:0%
+I feel like my diffusion example last
+time wasn't wasn't especially clear so
+
+ align:start position:0%
+time wasn't wasn't especially clear so
+ 
+
+ align:start position:0%
+time wasn't wasn't especially clear so
+let me give you a different example of
+
+ align:start position:0%
+let me give you a different example of
+ 
+
+ align:start position:0%
+let me give you a different example of
+diffusion hey you guys know Plinko have
+
+ align:start position:0%
+diffusion hey you guys know Plinko have
+ 
+
+ align:start position:0%
+diffusion hey you guys know Plinko have
+you seen the price is right right this
+
+ align:start position:0%
+you seen the price is right right this
+ 
+
+ align:start position:0%
+you seen the price is right right this
+is a game where you drop a chip into a
+
+ align:start position:0%
+is a game where you drop a chip into a
+ 
+
+ align:start position:0%
+is a game where you drop a chip into a
+board with pegs in it it's a model of
+
+ align:start position:0%
+board with pegs in it it's a model of
+ 
+
+ align:start position:0%
+board with pegs in it it's a model of
+diffusion okay
+
+ align:start position:0%
+diffusion okay
+ 
+
+ align:start position:0%
+diffusion okay
+the Plinko chip falls from level to
+
+ align:start position:0%
+the Plinko chip falls from level to
+ 
+
+ align:start position:0%
+the Plinko chip falls from level to
+level it hits a peg and it can go left
+
+ align:start position:0%
+level it hits a peg and it can go left
+ 
+
+ align:start position:0%
+level it hits a peg and it can go left
+or it can go right with equal
+
+ align:start position:0%
+or it can go right with equal
+ 
+
+ align:start position:0%
+or it can go right with equal
+probability okay so the Plinko chip
+
+ align:start position:0%
+probability okay so the Plinko chip
+ 
+
+ align:start position:0%
+probability okay so the Plinko chip
+diffuses as it falls down this guy's
+
+ align:start position:0%
+diffuses as it falls down this guy's
+ 
+
+ align:start position:0%
+diffuses as it falls down this guy's
+excited they just won $10,000 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a sparse matrix that describes
+
+ align:start position:0%
+there's a sparse matrix that describes
+ 
+
+ align:start position:0%
+there's a sparse matrix that describes
+how the probability of finding the
+
+ align:start position:0%
+how the probability of finding the
+ 
+
+ align:start position:0%
+how the probability of finding the
+Plinko chip in a certain in a certain
+
+ align:start position:0%
+Plinko chip in a certain in a certain
+ 
+
+ align:start position:0%
+Plinko chip in a certain in a certain
+cell evolves from level to level okay it
+
+ align:start position:0%
+cell evolves from level to level okay it
+ 
+
+ align:start position:0%
+cell evolves from level to level okay it
+works the same way the cellular automata
+
+ align:start position:0%
+works the same way the cellular automata
+ 
+
+ align:start position:0%
+works the same way the cellular automata
+model I showed you last time works right
+
+ align:start position:0%
+model I showed you last time works right
+ 
+
+ align:start position:0%
+model I showed you last time works right
+if the chip is in a particular cell then
+
+ align:start position:0%
+if the chip is in a particular cell then
+ 
+
+ align:start position:0%
+if the chip is in a particular cell then
+at the next level there's a 50/50 chance
+
+ align:start position:0%
+at the next level there's a 50/50 chance
+ 
+
+ align:start position:0%
+at the next level there's a 50/50 chance
+that I'll go to the left or I'll go to
+
+ align:start position:0%
+that I'll go to the left or I'll go to
+ 
+
+ align:start position:0%
+that I'll go to the left or I'll go to
+the right it looks like this right if
+
+ align:start position:0%
+the right it looks like this right if
+ 
+
+ align:start position:0%
+the right it looks like this right if
+the chip is here there's a 50/50 chance
+
+ align:start position:0%
+the chip is here there's a 50/50 chance
+ 
+
+ align:start position:0%
+the chip is here there's a 50/50 chance
+I'll go here or I'll go there so if the
+
+ align:start position:0%
+I'll go here or I'll go there so if the
+ 
+
+ align:start position:0%
+I'll go here or I'll go there so if the
+probability was one that I was in this
+
+ align:start position:0%
+probability was one that I was in this
+ 
+
+ align:start position:0%
+probability was one that I was in this
+cell then at the next level it'll be a
+
+ align:start position:0%
+cell then at the next level it'll be a
+ 
+
+ align:start position:0%
+cell then at the next level it'll be a
+half and a half and at the next level
+
+ align:start position:0%
+half and a half and at the next level
+ 
+
+ align:start position:0%
+half and a half and at the next level
+those halves will split again so the
+
+ align:start position:0%
+those halves will split again so the
+ 
+
+ align:start position:0%
+those halves will split again so the
+probability right that I'm in a
+
+ align:start position:0%
+probability right that I'm in a
+ 
+
+ align:start position:0%
+probability right that I'm in a
+particular cell at level I is this P I
+
+ align:start position:0%
+particular cell at level I is this P I
+ 
+
+ align:start position:0%
+particular cell at level I is this P I
+and the probability that I'm in a
+
+ align:start position:0%
+and the probability that I'm in a
+ 
+
+ align:start position:0%
+and the probability that I'm in a
+particular cell level I plus one is this
+
+ align:start position:0%
+particular cell level I plus one is this
+ 
+
+ align:start position:0%
+particular cell level I plus one is this
+P I plus one and there's some sparse
+
+ align:start position:0%
+P I plus one and there's some sparse
+ 
+
+ align:start position:0%
+P I plus one and there's some sparse
+matrix a which spreads that probability
+
+ align:start position:0%
+matrix a which spreads that probability
+ 
+
+ align:start position:0%
+matrix a which spreads that probability
+out it splits it into my neighbors 50/50
+
+ align:start position:0%
+out it splits it into my neighbors 50/50
+ 
+
+ align:start position:0%
+out it splits it into my neighbors 50/50
+okay here's a simulation of Plinko okay
+
+ align:start position:0%
+okay here's a simulation of Plinko okay
+ 
+
+ align:start position:0%
+okay here's a simulation of Plinko okay
+so I started with the probability one in
+
+ align:start position:0%
+so I started with the probability one in
+ 
+
+ align:start position:0%
+so I started with the probability one in
+the center cell and as I go through
+
+ align:start position:0%
+the center cell and as I go through
+ 
+
+ align:start position:0%
+the center cell and as I go through
+different levels right I get split 50/50
+
+ align:start position:0%
+different levels right I get split 50/50
+ 
+
+ align:start position:0%
+different levels right I get split 50/50
+right you see a binomial or almost
+
+ align:start position:0%
+right you see a binomial or almost
+ 
+
+ align:start position:0%
+right you see a binomial or almost
+Gaussian distribution spread as I go
+
+ align:start position:0%
+Gaussian distribution spread as I go
+ 
+
+ align:start position:0%
+Gaussian distribution spread as I go
+through more and more levels until it's
+
+ align:start position:0%
+through more and more levels until it's
+ 
+
+ align:start position:0%
+through more and more levels until it's
+equally probable that I could wind up in
+
+ align:start position:0%
+equally probable that I could wind up in
+ 
+
+ align:start position:0%
+equally probable that I could wind up in
+any one of the cells okay you can think
+
+ align:start position:0%
+any one of the cells okay you can think
+ 
+
+ align:start position:0%
+any one of the cells okay you can think
+about it this way right the probability
+
+ align:start position:0%
+about it this way right the probability
+ 
+
+ align:start position:0%
+about it this way right the probability
+at level I plus one okay that the chip
+
+ align:start position:0%
+at level I plus one okay that the chip
+ 
+
+ align:start position:0%
+at level I plus one okay that the chip
+is in so n is inherited 50/50 from its
+
+ align:start position:0%
+is in so n is inherited 50/50 from its
+ 
+
+ align:start position:0%
+is in so n is inherited 50/50 from its
+two neighbors right there's some
+
+ align:start position:0%
+two neighbors right there's some
+ 
+
+ align:start position:0%
+two neighbors right there's some
+probability that was in these two
+
+ align:start position:0%
+probability that was in these two
+ 
+
+ align:start position:0%
+probability that was in these two
+neighbors I would inherit that that
+
+ align:start position:0%
+neighbors I would inherit that that
+ 
+
+ align:start position:0%
+neighbors I would inherit that that
+probably but half of that probability
+
+ align:start position:0%
+probably but half of that probability
+ 
+
+ align:start position:0%
+probably but half of that probability
+will be split by these pegs the sparse
+
+ align:start position:0%
+will be split by these pegs the sparse
+ 
+
+ align:start position:0%
+will be split by these pegs the sparse
+matrix that represents this operation
+
+ align:start position:0%
+matrix that represents this operation
+ 
+
+ align:start position:0%
+matrix that represents this operation
+has two diagonals okay and on each of
+
+ align:start position:0%
+has two diagonals okay and on each of
+ 
+
+ align:start position:0%
+has two diagonals okay and on each of
+those diagonals is a half and you can
+
+ align:start position:0%
+those diagonals is a half and you can
+ 
+
+ align:start position:0%
+those diagonals is a half and you can
+build that matrix using the SP diag skom
+
+ align:start position:0%
+build that matrix using the SP diag skom
+ 
+
+ align:start position:0%
+build that matrix using the SP diag skom
+and it says that there's going to be two
+
+ align:start position:0%
+and it says that there's going to be two
+ 
+
+ align:start position:0%
+and it says that there's going to be two
+diagonal components okay which are equal
+
+ align:start position:0%
+diagonal components okay which are equal
+ 
+
+ align:start position:0%
+diagonal components okay which are equal
+to 1/2 and their position is going to be
+
+ align:start position:0%
+to 1/2 and their position is going to be
+ 
+
+ align:start position:0%
+to 1/2 and their position is going to be
+one on either side of the central
+
+ align:start position:0%
+one on either side of the central
+ 
+
+ align:start position:0%
+one on either side of the central
+diagonal okay that's going to indicate
+
+ align:start position:0%
+diagonal okay that's going to indicate
+ 
+
+ align:start position:0%
+diagonal okay that's going to indicate
+that I passed this probability 50/50 to
+
+ align:start position:0%
+that I passed this probability 50/50 to
+ 
+
+ align:start position:0%
+that I passed this probability 50/50 to
+each of my neighbors and then successive
+
+ align:start position:0%
+each of my neighbors and then successive
+ 
+
+ align:start position:0%
+each of my neighbors and then successive
+multiplications by a will split this
+
+ align:start position:0%
+multiplications by a will split this
+ 
+
+ align:start position:0%
+multiplications by a will split this
+probability and we'll see this
+
+ align:start position:0%
+probability and we'll see this
+ 
+
+ align:start position:0%
+probability and we'll see this
+simulation that tells us how probable it
+
+ align:start position:0%
+simulation that tells us how probable it
+ 
+
+ align:start position:0%
+simulation that tells us how probable it
+is to find the Plinko chip in a
+
+ align:start position:0%
+is to find the Plinko chip in a
+ 
+
+ align:start position:0%
+is to find the Plinko chip in a
+particular column yes yeah so in
+
+ align:start position:0%
+particular column yes yeah so in
+ 
+
+ align:start position:0%
+particular column yes yeah so in
+diffusion in general well okay that
+
+ align:start position:0%
+diffusion in general well okay that
+ 
+
+ align:start position:0%
+diffusion in general well okay that
+that's that's fair enough this is this
+
+ align:start position:0%
+that's that's fair enough this is this
+ 
+
+ align:start position:0%
+that's that's fair enough this is this
+is one particular model of the Plinko
+
+ align:start position:0%
+is one particular model of the Plinko
+ 
+
+ align:start position:0%
+is one particular model of the Plinko
+board which sort of imagines alternating
+
+ align:start position:0%
+board which sort of imagines alternating
+ 
+
+ align:start position:0%
+board which sort of imagines alternating
+alternating cells that I'm falling
+
+ align:start position:0%
+alternating cells that I'm falling
+ 
+
+ align:start position:0%
+alternating cells that I'm falling
+through we could construct an
+
+ align:start position:0%
+through we could construct an
+ 
+
+ align:start position:0%
+through we could construct an
+alternative model if we wanted to that
+
+ align:start position:0%
+alternative model if we wanted to that
+ 
+
+ align:start position:0%
+alternative model if we wanted to that
+didn't didn't have that part of the
+
+ align:start position:0%
+didn't didn't have that part of the
+ 
+
+ align:start position:0%
+didn't didn't have that part of the
+picture okay so that's a matrix that
+
+ align:start position:0%
+picture okay so that's a matrix that
+ 
+
+ align:start position:0%
+picture okay so that's a matrix that
+looks like this right the central
+
+ align:start position:0%
+looks like this right the central
+ 
+
+ align:start position:0%
+looks like this right the central
+diagonal is 0
+
+ align:start position:0%
+diagonal is 0
+ 
+
+ align:start position:0%
+diagonal is 0
+most of the off diagonal components here
+
+ align:start position:0%
+most of the off diagonal components here
+ 
+
+ align:start position:0%
+most of the off diagonal components here
+are 0 and 1 above and one below I get a
+
+ align:start position:0%
+are 0 and 1 above and one below I get a
+ 
+
+ align:start position:0%
+are 0 and 1 above and one below I get a
+half and a half and if I'm careful
+
+ align:start position:0%
+half and a half and if I'm careful
+ 
+
+ align:start position:0%
+half and a half and if I'm careful
+somebody mentioned I need boundary
+
+ align:start position:0%
+somebody mentioned I need boundary
+ 
+
+ align:start position:0%
+somebody mentioned I need boundary
+conditions when the Plinko chip gets to
+
+ align:start position:0%
+conditions when the Plinko chip gets to
+ 
+
+ align:start position:0%
+conditions when the Plinko chip gets to
+the edge right it doesn't fall out of
+
+ align:start position:0%
+the edge right it doesn't fall out of
+ 
+
+ align:start position:0%
+the edge right it doesn't fall out of
+the doesn't fall out of the game it gets
+
+ align:start position:0%
+the doesn't fall out of the game it gets
+ 
+
+ align:start position:0%
+the doesn't fall out of the game it gets
+reflected back in so maybe we have to
+
+ align:start position:0%
+reflected back in so maybe we have to
+ 
+
+ align:start position:0%
+reflected back in so maybe we have to
+choose some special values for a couple
+
+ align:start position:0%
+choose some special values for a couple
+ 
+
+ align:start position:0%
+choose some special values for a couple
+of elements of this matrix but this is a
+
+ align:start position:0%
+of elements of this matrix but this is a
+ 
+
+ align:start position:0%
+of elements of this matrix but this is a
+sparse matrix okay it has a sparse
+
+ align:start position:0%
+sparse matrix okay it has a sparse
+ 
+
+ align:start position:0%
+sparse matrix okay it has a sparse
+structure it models a diffusion problem
+
+ align:start position:0%
+structure it models a diffusion problem
+ 
+
+ align:start position:0%
+structure it models a diffusion problem
+just like we saw before most of physics
+
+ align:start position:0%
+just like we saw before most of physics
+ 
+
+ align:start position:0%
+just like we saw before most of physics
+is local like this right and just need
+
+ align:start position:0%
+is local like this right and just need
+ 
+
+ align:start position:0%
+is local like this right and just need
+to know what's going on with my
+
+ align:start position:0%
+to know what's going on with my
+ 
+
+ align:start position:0%
+to know what's going on with my
+neighbors and I spread the probability
+
+ align:start position:0%
+neighbors and I spread the probability
+ 
+
+ align:start position:0%
+neighbors and I spread the probability
+out I get this nice diffusion problem so
+
+ align:start position:0%
+out I get this nice diffusion problem so
+ 
+
+ align:start position:0%
+out I get this nice diffusion problem so
+it looks like this I here's something to
+
+ align:start position:0%
+it looks like this I here's something to
+ 
+
+ align:start position:0%
+it looks like this I here's something to
+notice right after many levels or cycles
+
+ align:start position:0%
+notice right after many levels or cycles
+ 
+
+ align:start position:0%
+notice right after many levels or cycles
+I multiply by a many many times this
+
+ align:start position:0%
+I multiply by a many many times this
+ 
+
+ align:start position:0%
+I multiply by a many many times this
+probability distribution always seems to
+
+ align:start position:0%
+probability distribution always seems to
+ 
+
+ align:start position:0%
+probability distribution always seems to
+flatten out it becomes uniform it turns
+
+ align:start position:0%
+flatten out it becomes uniform it turns
+ 
+
+ align:start position:0%
+flatten out it becomes uniform it turns
+out there are even special distributions
+
+ align:start position:0%
+out there are even special distributions
+ 
+
+ align:start position:0%
+out there are even special distributions
+for which a times a times that
+
+ align:start position:0%
+for which a times a times that
+ 
+
+ align:start position:0%
+for which a times a times that
+distribution is equal to that
+
+ align:start position:0%
+distribution is equal to that
+ 
+
+ align:start position:0%
+distribution is equal to that
+distribution you can see it at the end
+
+ align:start position:0%
+distribution you can see it at the end
+ 
+
+ align:start position:0%
+distribution you can see it at the end
+here this is one of those special
+
+ align:start position:0%
+here this is one of those special
+ 
+
+ align:start position:0%
+here this is one of those special
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+where the probability is equal in every
+
+ align:start position:0%
+where the probability is equal in every
+ 
+
+ align:start position:0%
+where the probability is equal in every
+other cell right and at the next level
+
+ align:start position:0%
+other cell right and at the next level
+ 
+
+ align:start position:0%
+other cell right and at the next level
+it all gets passed down that's one
+
+ align:start position:0%
+it all gets passed down that's one
+ 
+
+ align:start position:0%
+it all gets passed down that's one
+multiplication by it all gets spread by
+
+ align:start position:0%
+multiplication by it all gets spread by
+ 
+
+ align:start position:0%
+multiplication by it all gets spread by
+50% and the next multiplication
+
+ align:start position:0%
+50% and the next multiplication
+ 
+
+ align:start position:0%
+50% and the next multiplication
+everything gets spread by 50% again and
+
+ align:start position:0%
+everything gets spread by 50% again and
+ 
+
+ align:start position:0%
+everything gets spread by 50% again and
+I recover the same distribution that I
+
+ align:start position:0%
+I recover the same distribution that I
+ 
+
+ align:start position:0%
+I recover the same distribution that I
+had before this uniform distribution
+
+ align:start position:0%
+had before this uniform distribution
+ 
+
+ align:start position:0%
+had before this uniform distribution
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's a special distribution for which
+
+ align:start position:0%
+that's a special distribution for which
+ 
+
+ align:start position:0%
+that's a special distribution for which
+a times a a times P is equal to P and
+
+ align:start position:0%
+a times a a times P is equal to P and
+ 
+
+ align:start position:0%
+a times a a times P is equal to P and
+this distribution is one of the
+
+ align:start position:0%
+this distribution is one of the
+ 
+
+ align:start position:0%
+this distribution is one of the
+eigenvectors of this matrix a times a
+
+ align:start position:0%
+eigenvectors of this matrix a times a
+ 
+
+ align:start position:0%
+eigenvectors of this matrix a times a
+okay it's a particular vector that when
+
+ align:start position:0%
+okay it's a particular vector that when
+ 
+
+ align:start position:0%
+okay it's a particular vector that when
+I multiply it by this matrix a a okay I
+
+ align:start position:0%
+I multiply it by this matrix a a okay I
+ 
+
+ align:start position:0%
+I multiply it by this matrix a a okay I
+get that vector back okay it happens to
+
+ align:start position:0%
+get that vector back okay it happens to
+ 
+
+ align:start position:0%
+get that vector back okay it happens to
+be unstretched so this vector points in
+
+ align:start position:0%
+be unstretched so this vector points in
+ 
+
+ align:start position:0%
+be unstretched so this vector points in
+some direction I transform it by the
+
+ align:start position:0%
+some direction I transform it by the
+ 
+
+ align:start position:0%
+some direction I transform it by the
+matrix and I get back something the
+
+ align:start position:0%
+matrix and I get back something the
+ 
+
+ align:start position:0%
+matrix and I get back something the
+points in the same direction okay that's
+
+ align:start position:0%
+points in the same direction okay that's
+ 
+
+ align:start position:0%
+points in the same direction okay that's
+the definition of this thing called an
+
+ align:start position:0%
+the definition of this thing called an
+ 
+
+ align:start position:0%
+the definition of this thing called an
+eigenvector okay and this will be the
+
+ align:start position:0%
+eigenvector okay and this will be the
+ 
+
+ align:start position:0%
+eigenvector okay and this will be the
+subject that we we focus on today so
+
+ align:start position:0%
+subject that we we focus on today so
+ 
+
+ align:start position:0%
+subject that we we focus on today so
+eigenvectors of a matrix they're special
+
+ align:start position:0%
+eigenvectors of a matrix they're special
+ 
+
+ align:start position:0%
+eigenvectors of a matrix they're special
+vectors that are stretched on
+
+ align:start position:0%
+vectors that are stretched on
+ 
+
+ align:start position:0%
+vectors that are stretched on
+multiplication by the matrix okay so
+
+ align:start position:0%
+multiplication by the matrix okay so
+ 
+
+ align:start position:0%
+multiplication by the matrix okay so
+they're transformed but they're only
+
+ align:start position:0%
+they're transformed but they're only
+ 
+
+ align:start position:0%
+they're transformed but they're only
+transformed into a stretched form of
+
+ align:start position:0%
+transformed into a stretched form of
+ 
+
+ align:start position:0%
+transformed into a stretched form of
+whatever they were before they point in
+
+ align:start position:0%
+whatever they were before they point in
+ 
+
+ align:start position:0%
+whatever they were before they point in
+a direction you transform them by the
+
+ align:start position:0%
+a direction you transform them by the
+ 
+
+ align:start position:0%
+a direction you transform them by the
+matrix and you get something in the
+
+ align:start position:0%
+matrix and you get something in the
+ 
+
+ align:start position:0%
+matrix and you get something in the
+points in the same direction but it's
+
+ align:start position:0%
+points in the same direction but it's
+ 
+
+ align:start position:0%
+points in the same direction but it's
+stretched before we saw the amount of
+
+ align:start position:0%
+stretched before we saw the amount of
+ 
+
+ align:start position:0%
+stretched before we saw the amount of
+stretch the previous example we saw the
+
+ align:start position:0%
+stretch the previous example we saw the
+ 
+
+ align:start position:0%
+stretch the previous example we saw the
+amount of stretch was one okay it wasn't
+
+ align:start position:0%
+amount of stretch was one okay it wasn't
+ 
+
+ align:start position:0%
+amount of stretch was one okay it wasn't
+stretched at all you just get back the
+
+ align:start position:0%
+stretched at all you just get back the
+ 
+
+ align:start position:0%
+stretched at all you just get back the
+same vector you had before but in
+
+ align:start position:0%
+same vector you had before but in
+ 
+
+ align:start position:0%
+same vector you had before but in
+principle it could come back with any
+
+ align:start position:0%
+principle it could come back with any
+ 
+
+ align:start position:0%
+principle it could come back with any
+length okay for a real n by n matrix
+
+ align:start position:0%
+length okay for a real n by n matrix
+ 
+
+ align:start position:0%
+length okay for a real n by n matrix
+there will be I in vectors and eigen
+
+ align:start position:0%
+there will be I in vectors and eigen
+ 
+
+ align:start position:0%
+there will be I in vectors and eigen
+values which are the amount of stretch
+
+ align:start position:0%
+values which are the amount of stretch
+ 
+
+ align:start position:0%
+values which are the amount of stretch
+which are complex numbers okay
+
+ align:start position:0%
+which are complex numbers okay
+ 
+
+ align:start position:0%
+which are complex numbers okay
+and finding eigen vector eigen value
+
+ align:start position:0%
+and finding eigen vector eigen value
+ 
+
+ align:start position:0%
+and finding eigen vector eigen value
+pairs involves solving and equations
+
+ align:start position:0%
+pairs involves solving and equations
+ 
+
+ align:start position:0%
+pairs involves solving and equations
+okay we'd like to know what these
+
+ align:start position:0%
+okay we'd like to know what these
+ 
+
+ align:start position:0%
+okay we'd like to know what these
+eigenvectors and eigenvalues are they're
+
+ align:start position:0%
+eigenvectors and eigenvalues are they're
+ 
+
+ align:start position:0%
+eigenvectors and eigenvalues are they're
+nonlinear because they depend on both
+
+ align:start position:0%
+nonlinear because they depend on both
+ 
+
+ align:start position:0%
+nonlinear because they depend on both
+the value and the vector the product of
+
+ align:start position:0%
+the value and the vector the product of
+ 
+
+ align:start position:0%
+the value and the vector the product of
+the two for n plus 1 unknowns we don't
+
+ align:start position:0%
+the two for n plus 1 unknowns we don't
+ 
+
+ align:start position:0%
+the two for n plus 1 unknowns we don't
+know how to solve nonlinear equations
+
+ align:start position:0%
+know how to solve nonlinear equations
+ 
+
+ align:start position:0%
+know how to solve nonlinear equations
+yet so we're
+
+ align:start position:0%
+yet so we're
+ 
+
+ align:start position:0%
+yet so we're
+kind of might seem like we're we're in a
+
+ align:start position:0%
+kind of might seem like we're we're in a
+ 
+
+ align:start position:0%
+kind of might seem like we're we're in a
+rough spot but I'll show you that we're
+
+ align:start position:0%
+rough spot but I'll show you that we're
+ 
+
+ align:start position:0%
+rough spot but I'll show you that we're
+not okay but because there's n equations
+
+ align:start position:0%
+not okay but because there's n equations
+ 
+
+ align:start position:0%
+not okay but because there's n equations
+for n plus 1 unknowns that means
+
+ align:start position:0%
+for n plus 1 unknowns that means
+ 
+
+ align:start position:0%
+for n plus 1 unknowns that means
+eigenvectors are not unique if w is an
+
+ align:start position:0%
+eigenvectors are not unique if w is an
+ 
+
+ align:start position:0%
+eigenvectors are not unique if w is an
+eigenvector then any other vector the
+
+ align:start position:0%
+eigenvector then any other vector the
+ 
+
+ align:start position:0%
+eigenvector then any other vector the
+points in that same direction it's also
+
+ align:start position:0%
+points in that same direction it's also
+ 
+
+ align:start position:0%
+points in that same direction it's also
+an eigenvector right it also gets
+
+ align:start position:0%
+an eigenvector right it also gets
+ 
+
+ align:start position:0%
+an eigenvector right it also gets
+stretched by this factor lambda so we
+
+ align:start position:0%
+stretched by this factor lambda so we
+ 
+
+ align:start position:0%
+stretched by this factor lambda so we
+can never say what an eigenvector is
+
+ align:start position:0%
+can never say what an eigenvector is
+ 
+
+ align:start position:0%
+can never say what an eigenvector is
+uniquely we only prescribe its direction
+
+ align:start position:0%
+uniquely we only prescribe its direction
+ 
+
+ align:start position:0%
+uniquely we only prescribe its direction
+okay whatever its magnitude is we don't
+
+ align:start position:0%
+okay whatever its magnitude is we don't
+ 
+
+ align:start position:0%
+okay whatever its magnitude is we don't
+care we just care about its direction
+
+ align:start position:0%
+care we just care about its direction
+ 
+
+ align:start position:0%
+care we just care about its direction
+the amount of stretch however is unique
+
+ align:start position:0%
+the amount of stretch however is unique
+ 
+
+ align:start position:0%
+the amount of stretch however is unique
+okay it's associated with that direction
+
+ align:start position:0%
+okay it's associated with that direction
+ 
+
+ align:start position:0%
+okay it's associated with that direction
+so you have an amount of stretch and you
+
+ align:start position:0%
+so you have an amount of stretch and you
+ 
+
+ align:start position:0%
+so you have an amount of stretch and you
+have a direction and that describes the
+
+ align:start position:0%
+have a direction and that describes the
+ 
+
+ align:start position:0%
+have a direction and that describes the
+eigenvalue eigenvector pair okay this is
+
+ align:start position:0%
+eigenvalue eigenvector pair okay this is
+ 
+
+ align:start position:0%
+eigenvalue eigenvector pair okay this is
+clear
+
+ align:start position:0%
+clear
+ 
+
+ align:start position:0%
+clear
+you've heard of eigenvalues and
+
+ align:start position:0%
+you've heard of eigenvalues and
+ 
+
+ align:start position:0%
+you've heard of eigenvalues and
+eigenvectors before so how do you find
+
+ align:start position:0%
+eigenvectors before so how do you find
+ 
+
+ align:start position:0%
+eigenvectors before so how do you find
+eigenvalues okay they seem like special
+
+ align:start position:0%
+eigenvalues okay they seem like special
+ 
+
+ align:start position:0%
+eigenvalues okay they seem like special
+sorts of solutions associated with
+
+ align:start position:0%
+sorts of solutions associated with
+ 
+
+ align:start position:0%
+sorts of solutions associated with
+matrix and if we understood them then we
+
+ align:start position:0%
+matrix and if we understood them then we
+ 
+
+ align:start position:0%
+matrix and if we understood them then we
+can do a transformation so I'll explain
+
+ align:start position:0%
+can do a transformation so I'll explain
+ 
+
+ align:start position:0%
+can do a transformation so I'll explain
+that in a minute but how do you actually
+
+ align:start position:0%
+that in a minute but how do you actually
+ 
+
+ align:start position:0%
+that in a minute but how do you actually
+find these things these eigenvalues well
+
+ align:start position:0%
+find these things these eigenvalues well
+ 
+
+ align:start position:0%
+find these things these eigenvalues well
+I've got to solve an equation a times w
+
+ align:start position:0%
+I've got to solve an equation a times w
+ 
+
+ align:start position:0%
+I've got to solve an equation a times w
+equals lambda times W which can be
+
+ align:start position:0%
+equals lambda times W which can be
+ 
+
+ align:start position:0%
+equals lambda times W which can be
+transformed into a minus lambda identity
+
+ align:start position:0%
+transformed into a minus lambda identity
+ 
+
+ align:start position:0%
+transformed into a minus lambda identity
+times w equals 0 and so the solution to
+
+ align:start position:0%
+times w equals 0 and so the solution to
+ 
+
+ align:start position:0%
+times w equals 0 and so the solution to
+this equation is either W is equal to 0
+
+ align:start position:0%
+this equation is either W is equal to 0
+ 
+
+ align:start position:0%
+this equation is either W is equal to 0
+that's one possible solution to this
+
+ align:start position:0%
+that's one possible solution to this
+ 
+
+ align:start position:0%
+that's one possible solution to this
+problem or the eigenvector W belongs to
+
+ align:start position:0%
+problem or the eigenvector W belongs to
+ 
+
+ align:start position:0%
+problem or the eigenvector W belongs to
+the null space of this matrix it's one
+
+ align:start position:0%
+the null space of this matrix it's one
+ 
+
+ align:start position:0%
+the null space of this matrix it's one
+of those special vectors that when it
+
+ align:start position:0%
+of those special vectors that when it
+ 
+
+ align:start position:0%
+of those special vectors that when it
+multiplies this matrix gives back 0
+
+ align:start position:0%
+multiplies this matrix gives back 0
+ 
+
+ align:start position:0%
+multiplies this matrix gives back 0
+right it gets projected out on
+
+ align:start position:0%
+right it gets projected out on
+ 
+
+ align:start position:0%
+right it gets projected out on
+transformation by this matrix well this
+
+ align:start position:0%
+transformation by this matrix well this
+ 
+
+ align:start position:0%
+transformation by this matrix well this
+this solution doesn't seem very useful
+
+ align:start position:0%
+this solution doesn't seem very useful
+ 
+
+ align:start position:0%
+this solution doesn't seem very useful
+to us right it's trivial ok so let's go
+
+ align:start position:0%
+to us right it's trivial ok so let's go
+ 
+
+ align:start position:0%
+to us right it's trivial ok so let's go
+with this idea that W belongs to the
+
+ align:start position:0%
+with this idea that W belongs to the
+ 
+
+ align:start position:0%
+with this idea that W belongs to the
+null space of a minus lambda I that
+
+ align:start position:0%
+null space of a minus lambda I that
+ 
+
+ align:start position:0%
+null space of a minus lambda I that
+means a minus lambda I must be a
+
+ align:start position:0%
+means a minus lambda I must be a
+ 
+
+ align:start position:0%
+means a minus lambda I must be a
+singular matrix whatever it is right and
+
+ align:start position:0%
+singular matrix whatever it is right and
+ 
+
+ align:start position:0%
+singular matrix whatever it is right and
+if it's singular then the determinant of
+
+ align:start position:0%
+if it's singular then the determinant of
+ 
+
+ align:start position:0%
+if it's singular then the determinant of
+a minus lambda I must be equal to 0 so
+
+ align:start position:0%
+a minus lambda I must be equal to 0 so
+ 
+
+ align:start position:0%
+a minus lambda I must be equal to 0 so
+if this is true and it should be
+
+ align:start position:0%
+if this is true and it should be
+ 
+
+ align:start position:0%
+if this is true and it should be
+true if we don't want a trivial solution
+
+ align:start position:0%
+true if we don't want a trivial solution
+ 
+
+ align:start position:0%
+true if we don't want a trivial solution
+then the determinant of a minus lambda I
+
+ align:start position:0%
+then the determinant of a minus lambda I
+ 
+
+ align:start position:0%
+then the determinant of a minus lambda I
+is equal to zero so if we can compute
+
+ align:start position:0%
+is equal to zero so if we can compute
+ 
+
+ align:start position:0%
+is equal to zero so if we can compute
+that determinant and solve for lambda
+
+ align:start position:0%
+that determinant and solve for lambda
+ 
+
+ align:start position:0%
+that determinant and solve for lambda
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+then we'll know the eigenvalue well it
+
+ align:start position:0%
+then we'll know the eigenvalue well it
+ 
+
+ align:start position:0%
+then we'll know the eigenvalue well it
+turns out that the determinant of a
+
+ align:start position:0%
+turns out that the determinant of a
+ 
+
+ align:start position:0%
+turns out that the determinant of a
+matrix like a minus lambda I is a
+
+ align:start position:0%
+matrix like a minus lambda I is a
+ 
+
+ align:start position:0%
+matrix like a minus lambda I is a
+polynomial okay in terms of lambda it's
+
+ align:start position:0%
+polynomial okay in terms of lambda it's
+ 
+
+ align:start position:0%
+polynomial okay in terms of lambda it's
+a polynomial of degree and called the
+
+ align:start position:0%
+a polynomial of degree and called the
+ 
+
+ align:start position:0%
+a polynomial of degree and called the
+characteristic polynomial and the end
+
+ align:start position:0%
+characteristic polynomial and the end
+ 
+
+ align:start position:0%
+characteristic polynomial and the end
+roots of this characteristic polynomial
+
+ align:start position:0%
+roots of this characteristic polynomial
+ 
+
+ align:start position:0%
+roots of this characteristic polynomial
+are called the eigenvalues of the matrix
+
+ align:start position:0%
+are called the eigenvalues of the matrix
+ 
+
+ align:start position:0%
+are called the eigenvalues of the matrix
+so there n possible lambdas for which a
+
+ align:start position:0%
+so there n possible lambdas for which a
+ 
+
+ align:start position:0%
+so there n possible lambdas for which a
+minus lambda I becomes singular it has a
+
+ align:start position:0%
+minus lambda I becomes singular it has a
+ 
+
+ align:start position:0%
+minus lambda I becomes singular it has a
+null space and associated with those
+
+ align:start position:0%
+null space and associated with those
+ 
+
+ align:start position:0%
+null space and associated with those
+values are eigen vectors vectors that
+
+ align:start position:0%
+values are eigen vectors vectors that
+ 
+
+ align:start position:0%
+values are eigen vectors vectors that
+live in that null space so this
+
+ align:start position:0%
+live in that null space so this
+ 
+
+ align:start position:0%
+live in that null space so this
+polynomial we could compute it for any
+
+ align:start position:0%
+polynomial we could compute it for any
+ 
+
+ align:start position:0%
+polynomial we could compute it for any
+matrix we could compute this thing in
+
+ align:start position:0%
+matrix we could compute this thing in
+ 
+
+ align:start position:0%
+matrix we could compute this thing in
+principle right and we might even be
+
+ align:start position:0%
+principle right and we might even be
+ 
+
+ align:start position:0%
+principle right and we might even be
+able to factor it right into this form
+
+ align:start position:0%
+able to factor it right into this form
+ 
+
+ align:start position:0%
+able to factor it right into this form
+and then lambda 1 lambda 2 lambda in
+
+ align:start position:0%
+and then lambda 1 lambda 2 lambda in
+ 
+
+ align:start position:0%
+and then lambda 1 lambda 2 lambda in
+this factorized form are all the
+
+ align:start position:0%
+this factorized form are all the
+ 
+
+ align:start position:0%
+this factorized form are all the
+possible eigenvalues associated with our
+
+ align:start position:0%
+possible eigenvalues associated with our
+ 
+
+ align:start position:0%
+possible eigenvalues associated with our
+matrix a they're all the possible
+
+ align:start position:0%
+matrix a they're all the possible
+ 
+
+ align:start position:0%
+matrix a they're all the possible
+amounts of stretch that can be imparted
+
+ align:start position:0%
+amounts of stretch that can be imparted
+ 
+
+ align:start position:0%
+amounts of stretch that can be imparted
+to particular eigenvectors we don't know
+
+ align:start position:0%
+to particular eigenvectors we don't know
+ 
+
+ align:start position:0%
+to particular eigenvectors we don't know
+those vectors yet right we'll find them
+
+ align:start position:0%
+those vectors yet right we'll find them
+ 
+
+ align:start position:0%
+those vectors yet right we'll find them
+in a second but we know the amounts of
+
+ align:start position:0%
+in a second but we know the amounts of
+ 
+
+ align:start position:0%
+in a second but we know the amounts of
+stretch that can be imparted by this
+
+ align:start position:0%
+stretch that can be imparted by this
+ 
+
+ align:start position:0%
+stretch that can be imparted by this
+matrix okay any questions so far let's
+
+ align:start position:0%
+matrix okay any questions so far let's
+ 
+
+ align:start position:0%
+matrix okay any questions so far let's
+do an example okay here's a matrix minus
+
+ align:start position:0%
+do an example okay here's a matrix minus
+ 
+
+ align:start position:0%
+do an example okay here's a matrix minus
+2 1 3 and it's zeros everywhere else and
+
+ align:start position:0%
+2 1 3 and it's zeros everywhere else and
+ 
+
+ align:start position:0%
+2 1 3 and it's zeros everywhere else and
+we'd like to find the eigenvalues of
+
+ align:start position:0%
+we'd like to find the eigenvalues of
+ 
+
+ align:start position:0%
+we'd like to find the eigenvalues of
+this matrix so we need to know a minus
+
+ align:start position:0%
+this matrix so we need to know a minus
+ 
+
+ align:start position:0%
+this matrix so we need to know a minus
+lambda I and it's determinant so here's
+
+ align:start position:0%
+lambda I and it's determinant so here's
+ 
+
+ align:start position:0%
+lambda I and it's determinant so here's
+a minus lambda I we just subtract lambda
+
+ align:start position:0%
+a minus lambda I we just subtract lambda
+ 
+
+ align:start position:0%
+a minus lambda I we just subtract lambda
+from each of the diagonals and the
+
+ align:start position:0%
+from each of the diagonals and the
+ 
+
+ align:start position:0%
+from each of the diagonals and the
+determinate well here is just the
+
+ align:start position:0%
+determinate well here is just the
+ 
+
+ align:start position:0%
+determinate well here is just the
+product of the diagonal elements that's
+
+ align:start position:0%
+product of the diagonal elements that's
+ 
+
+ align:start position:0%
+product of the diagonal elements that's
+the determinant of a diagonal matrix
+
+ align:start position:0%
+the determinant of a diagonal matrix
+ 
+
+ align:start position:0%
+the determinant of a diagonal matrix
+like this the product of the diagonal
+
+ align:start position:0%
+like this the product of the diagonal
+ 
+
+ align:start position:0%
+like this the product of the diagonal
+elements so it's minus 2 minus lambda
+
+ align:start position:0%
+elements so it's minus 2 minus lambda
+ 
+
+ align:start position:0%
+elements so it's minus 2 minus lambda
+times 1 minus lambda times 3 minus
+
+ align:start position:0%
+times 1 minus lambda times 3 minus
+ 
+
+ align:start position:0%
+times 1 minus lambda times 3 minus
+lambda and the determinant this has to
+
+ align:start position:0%
+lambda and the determinant this has to
+ 
+
+ align:start position:0%
+lambda and the determinant this has to
+be equal to 0 so the amounts of stretch
+
+ align:start position:0%
+be equal to 0 so the amounts of stretch
+ 
+
+ align:start position:0%
+be equal to 0 so the amounts of stretch
+the eigenvalues imparted by this matrix
+
+ align:start position:0%
+the eigenvalues imparted by this matrix
+ 
+
+ align:start position:0%
+the eigenvalues imparted by this matrix
+are minus 2
+
+ align:start position:0%
+are minus 2
+ 
+
+ align:start position:0%
+are minus 2
+and three okay we found the eigenvalues
+
+ align:start position:0%
+and three okay we found the eigenvalues
+ 
+
+ align:start position:0%
+and three okay we found the eigenvalues
+here's another matrix can you work out
+
+ align:start position:0%
+here's another matrix can you work out
+ 
+
+ align:start position:0%
+here's another matrix can you work out
+the eigenvalues of this matrix
+
+ align:start position:0%
+the eigenvalues of this matrix
+ 
+
+ align:start position:0%
+the eigenvalues of this matrix
+let's take 90 seconds you can work with
+
+ align:start position:0%
+let's take 90 seconds you can work with
+ 
+
+ align:start position:0%
+let's take 90 seconds you can work with
+your neighbors see if you can figure out
+
+ align:start position:0%
+your neighbors see if you can figure out
+ 
+
+ align:start position:0%
+your neighbors see if you can figure out
+the eigenvalues of that matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody's cooperating today I'm going to
+
+ align:start position:0%
+nobody's cooperating today I'm going to
+ 
+
+ align:start position:0%
+nobody's cooperating today I'm going to
+do it myself it's okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay were you finding never want to want
+
+ align:start position:0%
+okay were you finding never want to want
+ 
+
+ align:start position:0%
+okay were you finding never want to want
+to guess what are the eigenvalues good
+
+ align:start position:0%
+to guess what are the eigenvalues good
+ 
+
+ align:start position:0%
+to guess what are the eigenvalues good
+okay so we need to compute the
+
+ align:start position:0%
+okay so we need to compute the
+ 
+
+ align:start position:0%
+okay so we need to compute the
+determinant of a minus lambda hi that'll
+
+ align:start position:0%
+determinant of a minus lambda hi that'll
+ 
+
+ align:start position:0%
+determinant of a minus lambda hi that'll
+be minus 2 minus lambda times minus 2
+
+ align:start position:0%
+be minus 2 minus lambda times minus 2
+ 
+
+ align:start position:0%
+be minus 2 minus lambda times minus 2
+minus lambda minus 1 you can solve this
+
+ align:start position:0%
+minus lambda minus 1 you can solve this
+ 
+
+ align:start position:0%
+minus lambda minus 1 you can solve this
+to find that lambda equals minus 3 or
+
+ align:start position:0%
+to find that lambda equals minus 3 or
+ 
+
+ align:start position:0%
+to find that lambda equals minus 3 or
+minus 1 these little checks are useful
+
+ align:start position:0%
+minus 1 these little checks are useful
+ 
+
+ align:start position:0%
+minus 1 these little checks are useful
+if you couldn't do this that's okay but
+
+ align:start position:0%
+if you couldn't do this that's okay but
+ 
+
+ align:start position:0%
+if you couldn't do this that's okay but
+you should try to practice this on your
+
+ align:start position:0%
+you should try to practice this on your
+ 
+
+ align:start position:0%
+you should try to practice this on your
+own to make sure you can here's some
+
+ align:start position:0%
+own to make sure you can here's some
+ 
+
+ align:start position:0%
+own to make sure you can here's some
+more examples so the elements of a
+
+ align:start position:0%
+more examples so the elements of a
+ 
+
+ align:start position:0%
+more examples so the elements of a
+diagonal matrix are always the
+
+ align:start position:0%
+diagonal matrix are always the
+ 
+
+ align:start position:0%
+diagonal matrix are always the
+eigenvalues because the determinant of a
+
+ align:start position:0%
+eigenvalues because the determinant of a
+ 
+
+ align:start position:0%
+eigenvalues because the determinant of a
+diagonal matrix is the product of the
+
+ align:start position:0%
+diagonal matrix is the product of the
+ 
+
+ align:start position:0%
+diagonal matrix is the product of the
+diagonal elements okay so these diagonal
+
+ align:start position:0%
+diagonal elements okay so these diagonal
+ 
+
+ align:start position:0%
+diagonal elements okay so these diagonal
+values here are the roots of the secular
+
+ align:start position:0%
+values here are the roots of the secular
+ 
+
+ align:start position:0%
+values here are the roots of the secular
+characteristic polynomial they are the
+
+ align:start position:0%
+characteristic polynomial they are the
+ 
+
+ align:start position:0%
+characteristic polynomial they are the
+eigenvalues it turns out the diagonal
+
+ align:start position:0%
+eigenvalues it turns out the diagonal
+ 
+
+ align:start position:0%
+eigenvalues it turns out the diagonal
+elements of a triangular matrix are
+
+ align:start position:0%
+elements of a triangular matrix are
+ 
+
+ align:start position:0%
+elements of a triangular matrix are
+eigenvalues too okay this should seem
+
+ align:start position:0%
+eigenvalues too okay this should seem
+ 
+
+ align:start position:0%
+eigenvalues too okay this should seem
+familiar to you we talked about easy to
+
+ align:start position:0%
+familiar to you we talked about easy to
+ 
+
+ align:start position:0%
+familiar to you we talked about easy to
+solve systems of equations right
+
+ align:start position:0%
+solve systems of equations right
+ 
+
+ align:start position:0%
+solve systems of equations right
+diagonal systems of equations are easy
+
+ align:start position:0%
+diagonal systems of equations are easy
+ 
+
+ align:start position:0%
+diagonal systems of equations are easy
+to solve right triangular systems of
+
+ align:start position:0%
+to solve right triangular systems of
+ 
+
+ align:start position:0%
+to solve right triangular systems of
+equations are easy to sell it's also
+
+ align:start position:0%
+equations are easy to sell it's also
+ 
+
+ align:start position:0%
+equations are easy to sell it's also
+easy to find their eigenvalues okay so
+
+ align:start position:0%
+easy to find their eigenvalues okay so
+ 
+
+ align:start position:0%
+easy to find their eigenvalues okay so
+the diagonal elements here are the
+
+ align:start position:0%
+the diagonal elements here are the
+ 
+
+ align:start position:0%
+the diagonal elements here are the
+eigenvalues of the triangular matrix and
+
+ align:start position:0%
+eigenvalues of the triangular matrix and
+ 
+
+ align:start position:0%
+eigenvalues of the triangular matrix and
+eigenvalues have certain properties that
+
+ align:start position:0%
+eigenvalues have certain properties that
+ 
+
+ align:start position:0%
+eigenvalues have certain properties that
+can be inferred from the properties of
+
+ align:start position:0%
+can be inferred from the properties of
+ 
+
+ align:start position:0%
+can be inferred from the properties of
+polynomials right since they are the
+
+ align:start position:0%
+polynomials right since they are the
+ 
+
+ align:start position:0%
+polynomials right since they are the
+roots to a polynomial if we know
+
+ align:start position:0%
+roots to a polynomial if we know
+ 
+
+ align:start position:0%
+roots to a polynomial if we know
+certain things that should be true of
+
+ align:start position:0%
+certain things that should be true of
+ 
+
+ align:start position:0%
+certain things that should be true of
+those polynomial roots that has to be
+
+ align:start position:0%
+those polynomial roots that has to be
+ 
+
+ align:start position:0%
+those polynomial roots that has to be
+true of the eigenvalues themselves so if
+
+ align:start position:0%
+true of the eigenvalues themselves so if
+ 
+
+ align:start position:0%
+true of the eigenvalues themselves so if
+we have a matrix which is real valued
+
+ align:start position:0%
+we have a matrix which is real valued
+ 
+
+ align:start position:0%
+we have a matrix which is real valued
+then we know that we're gonna have this
+
+ align:start position:0%
+then we know that we're gonna have this
+ 
+
+ align:start position:0%
+then we know that we're gonna have this
+polynomial of degree n which is also
+
+ align:start position:0%
+polynomial of degree n which is also
+ 
+
+ align:start position:0%
+polynomial of degree n which is also
+real valued okay it can have no more
+
+ align:start position:0%
+real valued okay it can have no more
+ 
+
+ align:start position:0%
+real valued okay it can have no more
+than n roots right and so a can have no
+
+ align:start position:0%
+than n roots right and so a can have no
+ 
+
+ align:start position:0%
+than n roots right and so a can have no
+more than n distinct eigenvalues okay
+
+ align:start position:0%
+more than n distinct eigenvalues okay
+ 
+
+ align:start position:0%
+more than n distinct eigenvalues okay
+the eigen values like the factors of the
+
+ align:start position:0%
+the eigen values like the factors of the
+ 
+
+ align:start position:0%
+the eigen values like the factors of the
+polynomial don't have to be distinct
+
+ align:start position:0%
+polynomial don't have to be distinct
+ 
+
+ align:start position:0%
+polynomial don't have to be distinct
+though okay you could have multiplicity
+
+ align:start position:0%
+though okay you could have multiplicity
+ 
+
+ align:start position:0%
+though okay you could have multiplicity
+in the roots of the polynomial so it's
+
+ align:start position:0%
+in the roots of the polynomial so it's
+ 
+
+ align:start position:0%
+in the roots of the polynomial so it's
+possible that lambda 1 here is an
+
+ align:start position:0%
+possible that lambda 1 here is an
+ 
+
+ align:start position:0%
+possible that lambda 1 here is an
+eigenvalue twice okay that's referred to
+
+ align:start position:0%
+eigenvalue twice okay that's referred to
+ 
+
+ align:start position:0%
+eigenvalue twice okay that's referred to
+as algebraic multiplicity we'll come
+
+ align:start position:0%
+as algebraic multiplicity we'll come
+ 
+
+ align:start position:0%
+as algebraic multiplicity we'll come
+back to that idea in a second because
+
+ align:start position:0%
+back to that idea in a second because
+ 
+
+ align:start position:0%
+back to that idea in a second because
+the polynomial is real valued it means
+
+ align:start position:0%
+the polynomial is real valued it means
+ 
+
+ align:start position:0%
+the polynomial is real valued it means
+that the eigenvalues could be real or
+
+ align:start position:0%
+that the eigenvalues could be real or
+ 
+
+ align:start position:0%
+that the eigenvalues could be real or
+complex just like the roots of a real
+
+ align:start position:0%
+complex just like the roots of a real
+ 
+
+ align:start position:0%
+complex just like the roots of a real
+valued polynomial but complex
+
+ align:start position:0%
+valued polynomial but complex
+ 
+
+ align:start position:0%
+valued polynomial but complex
+eigenvalues always appear as conjugate
+
+ align:start position:0%
+eigenvalues always appear as conjugate
+ 
+
+ align:start position:0%
+eigenvalues always appear as conjugate
+pairs okay if there is a complex
+
+ align:start position:0%
+pairs okay if there is a complex
+ 
+
+ align:start position:0%
+pairs okay if there is a complex
+eigenvalue then necessarily right it's
+
+ align:start position:0%
+eigenvalue then necessarily right it's
+ 
+
+ align:start position:0%
+eigenvalue then necessarily right it's
+complex conjugate is also an eigenvalue
+
+ align:start position:0%
+complex conjugate is also an eigenvalue
+ 
+
+ align:start position:0%
+complex conjugate is also an eigenvalue
+here's a couple other properties so the
+
+ align:start position:0%
+here's a couple other properties so the
+ 
+
+ align:start position:0%
+here's a couple other properties so the
+determinant of a matrix is the product
+
+ align:start position:0%
+determinant of a matrix is the product
+ 
+
+ align:start position:0%
+determinant of a matrix is the product
+of the eigenvalues we talked once about
+
+ align:start position:0%
+of the eigenvalues we talked once about
+ 
+
+ align:start position:0%
+of the eigenvalues we talked once about
+the trace of the matrix which is the sum
+
+ align:start position:0%
+the trace of the matrix which is the sum
+ 
+
+ align:start position:0%
+the trace of the matrix which is the sum
+of its diagonal elements the trace of
+
+ align:start position:0%
+of its diagonal elements the trace of
+ 
+
+ align:start position:0%
+of its diagonal elements the trace of
+the matrix is also the sum of the
+
+ align:start position:0%
+the matrix is also the sum of the
+ 
+
+ align:start position:0%
+the matrix is also the sum of the
+eigenvalues these can sometimes come in
+
+ align:start position:0%
+eigenvalues these can sometimes come in
+ 
+
+ align:start position:0%
+eigenvalues these can sometimes come in
+handy not often but sometimes here's an
+
+ align:start position:0%
+handy not often but sometimes here's an
+ 
+
+ align:start position:0%
+handy not often but sometimes here's an
+example I talked about before so a
+
+ align:start position:0%
+example I talked about before so a
+ 
+
+ align:start position:0%
+example I talked about before so a
+series of chemical reactions so we have
+
+ align:start position:0%
+series of chemical reactions so we have
+ 
+
+ align:start position:0%
+series of chemical reactions so we have
+a batch a batch reactor we load some
+
+ align:start position:0%
+a batch a batch reactor we load some
+ 
+
+ align:start position:0%
+a batch a batch reactor we load some
+material in and we want to know how the
+
+ align:start position:0%
+material in and we want to know how the
+ 
+
+ align:start position:0%
+material in and we want to know how the
+concentrations of a B C and D vary as a
+
+ align:start position:0%
+concentrations of a B C and D vary as a
+ 
+
+ align:start position:0%
+concentrations of a B C and D vary as a
+function of time and so a transforms
+
+ align:start position:0%
+function of time and so a transforms
+ 
+
+ align:start position:0%
+function of time and so a transforms
+into B B and C are in equilibrium C and
+
+ align:start position:0%
+into B B and C are in equilibrium C and
+ 
+
+ align:start position:0%
+into B B and C are in equilibrium C and
+D are in equilibrium and our
+
+ align:start position:0%
+D are in equilibrium and our
+ 
+
+ align:start position:0%
+D are in equilibrium and our
+conservation equation for material is
+
+ align:start position:0%
+conservation equation for material is
+ 
+
+ align:start position:0%
+conservation equation for material is
+here this rate matrix we'd like to
+
+ align:start position:0%
+here this rate matrix we'd like to
+ 
+
+ align:start position:0%
+here this rate matrix we'd like to
+understand what the characteristic
+
+ align:start position:0%
+understand what the characteristic
+ 
+
+ align:start position:0%
+understand what the characteristic
+polynomial of that is the eigenvalues of
+
+ align:start position:0%
+polynomial of that is the eigenvalues of
+ 
+
+ align:start position:0%
+polynomial of that is the eigenvalues of
+that matrix are going to tell us
+
+ align:start position:0%
+that matrix are going to tell us
+ 
+
+ align:start position:0%
+that matrix are going to tell us
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+about how different rate processes about
+
+ align:start position:0%
+about how different rate processes about
+ 
+
+ align:start position:0%
+about how different rate processes about
+evolve in time you can imagine right
+
+ align:start position:0%
+evolve in time you can imagine right
+ 
+
+ align:start position:0%
+evolve in time you can imagine right
+just just using units okay on this side
+
+ align:start position:0%
+just just using units okay on this side
+ 
+
+ align:start position:0%
+just just using units okay on this side
+we have concentration overtime on this
+
+ align:start position:0%
+we have concentration overtime on this
+ 
+
+ align:start position:0%
+we have concentration overtime on this
+side we have concentration and the rate
+
+ align:start position:0%
+side we have concentration and the rate
+ 
+
+ align:start position:0%
+side we have concentration and the rate
+matrix has units of rate or one over
+
+ align:start position:0%
+matrix has units of rate or one over
+ 
+
+ align:start position:0%
+matrix has units of rate or one over
+time so the eigenvalues also have units
+
+ align:start position:0%
+time so the eigenvalues also have units
+ 
+
+ align:start position:0%
+time so the eigenvalues also have units
+of rate and they tell us the rate at
+
+ align:start position:0%
+of rate and they tell us the rate at
+ 
+
+ align:start position:0%
+of rate and they tell us the rate at
+which different transformations between
+
+ align:start position:0%
+which different transformations between
+ 
+
+ align:start position:0%
+which different transformations between
+these materials occur and so if we want
+
+ align:start position:0%
+these materials occur and so if we want
+ 
+
+ align:start position:0%
+these materials occur and so if we want
+to find the characteristic polynomial of
+
+ align:start position:0%
+to find the characteristic polynomial of
+ 
+
+ align:start position:0%
+to find the characteristic polynomial of
+this matrix and we need to compute the
+
+ align:start position:0%
+this matrix and we need to compute the
+ 
+
+ align:start position:0%
+this matrix and we need to compute the
+determinant of this matrix minus lambda
+
+ align:start position:0%
+determinant of this matrix minus lambda
+ 
+
+ align:start position:0%
+determinant of this matrix minus lambda
+I so subtract lambda from each of the
+
+ align:start position:0%
+I so subtract lambda from each of the
+ 
+
+ align:start position:0%
+I so subtract lambda from each of the
+diagonals even though this is a four by
+
+ align:start position:0%
+diagonals even though this is a four by
+ 
+
+ align:start position:0%
+diagonals even though this is a four by
+four matrix its determinate is easy to
+
+ align:start position:0%
+four matrix its determinate is easy to
+ 
+
+ align:start position:0%
+four matrix its determinate is easy to
+compute because it's full of zeros I'm
+
+ align:start position:0%
+compute because it's full of zeros I'm
+ 
+
+ align:start position:0%
+compute because it's full of zeros I'm
+not going to compute it for you here
+
+ align:start position:0%
+not going to compute it for you here
+ 
+
+ align:start position:0%
+not going to compute it for you here
+it'll turn out that the characteristic
+
+ align:start position:0%
+it'll turn out that the characteristic
+ 
+
+ align:start position:0%
+it'll turn out that the characteristic
+polynomial looks like this you should
+
+ align:start position:0%
+polynomial looks like this you should
+ 
+
+ align:start position:0%
+polynomial looks like this you should
+actually try to do this determinant and
+
+ align:start position:0%
+actually try to do this determinant and
+ 
+
+ align:start position:0%
+actually try to do this determinant and
+show that the polynomial works out to be
+
+ align:start position:0%
+show that the polynomial works out to be
+ 
+
+ align:start position:0%
+show that the polynomial works out to be
+this but knowing that this is the
+
+ align:start position:0%
+this but knowing that this is the
+ 
+
+ align:start position:0%
+this but knowing that this is the
+characteristic polynomial what are the
+
+ align:start position:0%
+characteristic polynomial what are the
+ 
+
+ align:start position:0%
+characteristic polynomial what are the
+eigenvalues of the rete matrix if that's
+
+ align:start position:0%
+eigenvalues of the rete matrix if that's
+ 
+
+ align:start position:0%
+eigenvalues of the rete matrix if that's
+the characteristic polynomial what are
+
+ align:start position:0%
+the characteristic polynomial what are
+ 
+
+ align:start position:0%
+the characteristic polynomial what are
+the eigenvalues or tell me some of the
+
+ align:start position:0%
+the eigenvalues or tell me some of the
+ 
+
+ align:start position:0%
+the eigenvalues or tell me some of the
+eigen values of the rate matrix zero
+
+ align:start position:0%
+eigen values of the rate matrix zero
+ 
+
+ align:start position:0%
+eigen values of the rate matrix zero
+zero is an eigen value lambda equals 0
+
+ align:start position:0%
+zero is an eigen value lambda equals 0
+ 
+
+ align:start position:0%
+zero is an eigen value lambda equals 0
+is a solution ok minus k1 is another
+
+ align:start position:0%
+is a solution ok minus k1 is another
+ 
+
+ align:start position:0%
+is a solution ok minus k1 is another
+solution what is this solution this
+
+ align:start position:0%
+solution what is this solution this
+ 
+
+ align:start position:0%
+solution what is this solution this
+eigenvalue zero correspond to what's up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but yeah physically it's a rate process
+
+ align:start position:0%
+but yeah physically it's a rate process
+ 
+
+ align:start position:0%
+but yeah physically it's a rate process
+with zero rate okay steady state ok so
+
+ align:start position:0%
+with zero rate okay steady state ok so
+ 
+
+ align:start position:0%
+with zero rate okay steady state ok so
+the zero eigenvalue is going to
+
+ align:start position:0%
+the zero eigenvalue is going to
+ 
+
+ align:start position:0%
+the zero eigenvalue is going to
+correspond to the steady state the
+
+ align:start position:0%
+correspond to the steady state the
+ 
+
+ align:start position:0%
+correspond to the steady state the
+eigenvector associated with that
+
+ align:start position:0%
+eigenvector associated with that
+ 
+
+ align:start position:0%
+eigenvector associated with that
+eigenvalue should correspond to the
+
+ align:start position:0%
+eigenvalue should correspond to the
+ 
+
+ align:start position:0%
+eigenvalue should correspond to the
+steady state solution okay and what this
+
+ align:start position:0%
+steady state solution okay and what this
+ 
+
+ align:start position:0%
+steady state solution okay and what this
+came one this eigenvalue minus k1 this
+
+ align:start position:0%
+came one this eigenvalue minus k1 this
+ 
+
+ align:start position:0%
+came one this eigenvalue minus k1 this
+is a rate process with rate k1 what
+
+ align:start position:0%
+is a rate process with rate k1 what
+ 
+
+ align:start position:0%
+is a rate process with rate k1 what
+physical process does that represent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's something evolving in time now
+
+ align:start position:0%
+it's something evolving in time now
+ 
+
+ align:start position:0%
+it's something evolving in time now
+right so that's the transformation of a
+
+ align:start position:0%
+right so that's the transformation of a
+ 
+
+ align:start position:0%
+right so that's the transformation of a
+into B and the eigenvector should
+
+ align:start position:0%
+into B and the eigenvector should
+ 
+
+ align:start position:0%
+into B and the eigenvector should
+reflect that transformation okay we'll
+
+ align:start position:0%
+reflect that transformation okay we'll
+ 
+
+ align:start position:0%
+reflect that transformation okay we'll
+see what those eigenvectors are in a
+
+ align:start position:0%
+see what those eigenvectors are in a
+ 
+
+ align:start position:0%
+see what those eigenvectors are in a
+minute okay but these eigenvalues can be
+
+ align:start position:0%
+minute okay but these eigenvalues can be
+ 
+
+ align:start position:0%
+minute okay but these eigenvalues can be
+interpreted in terms of physical
+
+ align:start position:0%
+interpreted in terms of physical
+ 
+
+ align:start position:0%
+interpreted in terms of physical
+is this quadratic solution here has some
+
+ align:start position:0%
+is this quadratic solution here has some
+ 
+
+ align:start position:0%
+is this quadratic solution here has some
+some eigenvalue I don't know what it is
+
+ align:start position:0%
+some eigenvalue I don't know what it is
+ 
+
+ align:start position:0%
+some eigenvalue I don't know what it is
+okay you use the quadratic formula you
+
+ align:start position:0%
+okay you use the quadratic formula you
+ 
+
+ align:start position:0%
+okay you use the quadratic formula you
+can find it but it involves K 2 K 3 K 4
+
+ align:start position:0%
+can find it but it involves K 2 K 3 K 4
+ 
+
+ align:start position:0%
+can find it but it involves K 2 K 3 K 4
+and this is a typo it should be K 5 ok
+
+ align:start position:0%
+and this is a typo it should be K 5 ok
+ 
+
+ align:start position:0%
+and this is a typo it should be K 5 ok
+and so that says something about the
+
+ align:start position:0%
+and so that says something about the
+ 
+
+ align:start position:0%
+and so that says something about the
+inter conversion between B C and D okay
+
+ align:start position:0%
+inter conversion between B C and D okay
+ 
+
+ align:start position:0%
+inter conversion between B C and D okay
+and the rate processes that occur is we
+
+ align:start position:0%
+and the rate processes that occur is we
+ 
+
+ align:start position:0%
+and the rate processes that occur is we
+convert from B to C to D alright is that
+
+ align:start position:0%
+convert from B to C to D alright is that
+ 
+
+ align:start position:0%
+convert from B to C to D alright is that
+too fast do you want to write somewhere
+
+ align:start position:0%
+too fast do you want to write somewhere
+ 
+
+ align:start position:0%
+too fast do you want to write somewhere
+on this slide before I go on are you
+
+ align:start position:0%
+on this slide before I go on are you
+ 
+
+ align:start position:0%
+on this slide before I go on are you
+okay have any questions about this okay
+
+ align:start position:0%
+okay have any questions about this okay
+ 
+
+ align:start position:0%
+okay have any questions about this okay
+given an eigen value a particular eigen
+
+ align:start position:0%
+given an eigen value a particular eigen
+ 
+
+ align:start position:0%
+given an eigen value a particular eigen
+value what's the corresponding
+
+ align:start position:0%
+value what's the corresponding
+ 
+
+ align:start position:0%
+value what's the corresponding
+eigenvector
+
+ align:start position:0%
+eigenvector
+ 
+
+ align:start position:0%
+eigenvector
+we know the eigenvector isn't uniquely
+
+ align:start position:0%
+we know the eigenvector isn't uniquely
+ 
+
+ align:start position:0%
+we know the eigenvector isn't uniquely
+specified it belongs to the null space
+
+ align:start position:0%
+specified it belongs to the null space
+ 
+
+ align:start position:0%
+specified it belongs to the null space
+of this matrix a minus lambda I times
+
+ align:start position:0%
+of this matrix a minus lambda I times
+ 
+
+ align:start position:0%
+of this matrix a minus lambda I times
+identity even though it's not unique we
+
+ align:start position:0%
+identity even though it's not unique we
+ 
+
+ align:start position:0%
+identity even though it's not unique we
+might still try to find it using
+
+ align:start position:0%
+might still try to find it using
+ 
+
+ align:start position:0%
+might still try to find it using
+Gaussian elimination right so we may try
+
+ align:start position:0%
+Gaussian elimination right so we may try
+ 
+
+ align:start position:0%
+Gaussian elimination right so we may try
+to take may try to solve the equation a
+
+ align:start position:0%
+to take may try to solve the equation a
+ 
+
+ align:start position:0%
+to take may try to solve the equation a
+minus lambda I times identity multiplied
+
+ align:start position:0%
+minus lambda I times identity multiplied
+ 
+
+ align:start position:0%
+minus lambda I times identity multiplied
+by W equals 0 using Gaussian elimination
+
+ align:start position:0%
+by W equals 0 using Gaussian elimination
+ 
+
+ align:start position:0%
+by W equals 0 using Gaussian elimination
+but because it's not unique at some
+
+ align:start position:0%
+but because it's not unique at some
+ 
+
+ align:start position:0%
+but because it's not unique at some
+point we'll run out of rows to eliminate
+
+ align:start position:0%
+point we'll run out of rows to eliminate
+ 
+
+ align:start position:0%
+point we'll run out of rows to eliminate
+right there's a null space to this
+
+ align:start position:0%
+right there's a null space to this
+ 
+
+ align:start position:0%
+right there's a null space to this
+matrix right we won't be able to
+
+ align:start position:0%
+matrix right we won't be able to
+ 
+
+ align:start position:0%
+matrix right we won't be able to
+eliminate everything its rank we'd say
+
+ align:start position:0%
+eliminate everything its rank we'd say
+ 
+
+ align:start position:0%
+eliminate everything its rank we'd say
+it's rank deficient right so we'll be
+
+ align:start position:0%
+it's rank deficient right so we'll be
+ 
+
+ align:start position:0%
+it's rank deficient right so we'll be
+able to eliminate up to some R the rank
+
+ align:start position:0%
+able to eliminate up to some R the rank
+ 
+
+ align:start position:0%
+able to eliminate up to some R the rank
+of this matrix and then all the
+
+ align:start position:0%
+of this matrix and then all the
+ 
+
+ align:start position:0%
+of this matrix and then all the
+components below are essentially free or
+
+ align:start position:0%
+components below are essentially free or
+ 
+
+ align:start position:0%
+components below are essentially free or
+arbitrarily specified there are no
+
+ align:start position:0%
+arbitrarily specified there are no
+ 
+
+ align:start position:0%
+arbitrarily specified there are no
+equations to say with those components
+
+ align:start position:0%
+equations to say with those components
+ 
+
+ align:start position:0%
+equations to say with those components
+of the eigen vector R the number of all
+
+ align:start position:0%
+of the eigen vector R the number of all
+ 
+
+ align:start position:0%
+of the eigen vector R the number of all
+0 rows is called the geometric
+
+ align:start position:0%
+0 rows is called the geometric
+ 
+
+ align:start position:0%
+0 rows is called the geometric
+multiplicity of the eigen value sorry
+
+ align:start position:0%
+multiplicity of the eigen value sorry
+ 
+
+ align:start position:0%
+multiplicity of the eigen value sorry
+geometric is missing here it's the
+
+ align:start position:0%
+geometric is missing here it's the
+ 
+
+ align:start position:0%
+geometric is missing here it's the
+number of components of the eigenvector
+
+ align:start position:0%
+number of components of the eigenvector
+ 
+
+ align:start position:0%
+number of components of the eigenvector
+that can be freely specified the
+
+ align:start position:0%
+that can be freely specified the
+ 
+
+ align:start position:0%
+that can be freely specified the
+geometric multiplicity might be one
+
+ align:start position:0%
+geometric multiplicity might be one
+ 
+
+ align:start position:0%
+geometric multiplicity might be one
+that's like saying that the
+
+ align:start position:0%
+that's like saying that the
+ 
+
+ align:start position:0%
+that's like saying that the
+I can vectors are all pointing in the
+
+ align:start position:0%
+I can vectors are all pointing in the
+ 
+
+ align:start position:0%
+I can vectors are all pointing in the
+same direction but can have an arbitrary
+
+ align:start position:0%
+same direction but can have an arbitrary
+ 
+
+ align:start position:0%
+same direction but can have an arbitrary
+magnitude it might have geometric
+
+ align:start position:0%
+magnitude it might have geometric
+ 
+
+ align:start position:0%
+magnitude it might have geometric
+multiplicity two which means the
+
+ align:start position:0%
+multiplicity two which means the
+ 
+
+ align:start position:0%
+multiplicity two which means the
+eigenvectors associated with this
+
+ align:start position:0%
+eigenvectors associated with this
+ 
+
+ align:start position:0%
+eigenvectors associated with this
+eigenvalue live in some plane and any
+
+ align:start position:0%
+eigenvalue live in some plane and any
+ 
+
+ align:start position:0%
+eigenvalue live in some plane and any
+vector from that plane is a
+
+ align:start position:0%
+vector from that plane is a
+ 
+
+ align:start position:0%
+vector from that plane is a
+corresponding eigenvector okay may have
+
+ align:start position:0%
+corresponding eigenvector okay may have
+ 
+
+ align:start position:0%
+corresponding eigenvector okay may have
+a higher geometric multiplicity
+
+ align:start position:0%
+a higher geometric multiplicity
+ 
+
+ align:start position:0%
+a higher geometric multiplicity
+associated with it okay so let's try
+
+ align:start position:0%
+associated with it okay so let's try
+ 
+
+ align:start position:0%
+associated with it okay so let's try
+something here let's try to find the
+
+ align:start position:0%
+something here let's try to find the
+ 
+
+ align:start position:0%
+something here let's try to find the
+eigenvectors of this matrix I told you
+
+ align:start position:0%
+eigenvectors of this matrix I told you
+ 
+
+ align:start position:0%
+eigenvectors of this matrix I told you
+what the eigenvalues were they were the
+
+ align:start position:0%
+what the eigenvalues were they were the
+ 
+
+ align:start position:0%
+what the eigenvalues were they were the
+diagonal values here so they're -2 1 & 3
+
+ align:start position:0%
+diagonal values here so they're -2 1 & 3
+ 
+
+ align:start position:0%
+diagonal values here so they're -2 1 & 3
+let's look for the eigen vector
+
+ align:start position:0%
+let's look for the eigen vector
+ 
+
+ align:start position:0%
+let's look for the eigen vector
+corresponding to this eigenvalue so I
+
+ align:start position:0%
+corresponding to this eigenvalue so I
+ 
+
+ align:start position:0%
+corresponding to this eigenvalue so I
+want to solve this equation write a
+
+ align:start position:0%
+want to solve this equation write a
+ 
+
+ align:start position:0%
+want to solve this equation write a
+minus this particular lambda which is
+
+ align:start position:0%
+minus this particular lambda which is
+ 
+
+ align:start position:0%
+minus this particular lambda which is
+minus 2 times identity equals 0 so I got
+
+ align:start position:0%
+minus 2 times identity equals 0 so I got
+ 
+
+ align:start position:0%
+minus 2 times identity equals 0 so I got
+to do Gaussian elimination on this
+
+ align:start position:0%
+to do Gaussian elimination on this
+ 
+
+ align:start position:0%
+to do Gaussian elimination on this
+matrix it's already eliminated for me
+
+ align:start position:0%
+matrix it's already eliminated for me
+ 
+
+ align:start position:0%
+matrix it's already eliminated for me
+right I have one row which is all zeros
+
+ align:start position:0%
+right I have one row which is all zeros
+ 
+
+ align:start position:0%
+right I have one row which is all zeros
+which says the first component of my
+
+ align:start position:0%
+which says the first component of my
+ 
+
+ align:start position:0%
+which says the first component of my
+eigen the first component of my
+
+ align:start position:0%
+eigen the first component of my
+ 
+
+ align:start position:0%
+eigen the first component of my
+eigenvector can be freely specified the
+
+ align:start position:0%
+eigenvector can be freely specified the
+ 
+
+ align:start position:0%
+eigenvector can be freely specified the
+other two components have to be 0 3
+
+ align:start position:0%
+other two components have to be 0 3
+ 
+
+ align:start position:0%
+other two components have to be 0 3
+times the second component of my
+
+ align:start position:0%
+times the second component of my
+ 
+
+ align:start position:0%
+times the second component of my
+eigenvector is 0 5 times the third
+
+ align:start position:0%
+eigenvector is 0 5 times the third
+ 
+
+ align:start position:0%
+eigenvector is 0 5 times the third
+component is 0 so the other two
+
+ align:start position:0%
+component is 0 so the other two
+ 
+
+ align:start position:0%
+component is 0 so the other two
+components have to be 0 but the first
+
+ align:start position:0%
+components have to be 0 but the first
+ 
+
+ align:start position:0%
+components have to be 0 but the first
+component is freely specified so the
+
+ align:start position:0%
+component is freely specified so the
+ 
+
+ align:start position:0%
+component is freely specified so the
+eigen vector associated with this
+
+ align:start position:0%
+eigen vector associated with this
+ 
+
+ align:start position:0%
+eigen vector associated with this
+eigenvalue is 1 0 0 if I take a vector
+
+ align:start position:0%
+eigenvalue is 1 0 0 if I take a vector
+ 
+
+ align:start position:0%
+eigenvalue is 1 0 0 if I take a vector
+which points in the X direction in r3
+
+ align:start position:0%
+which points in the X direction in r3
+ 
+
+ align:start position:0%
+which points in the X direction in r3
+and I multiply it by this matrix it gets
+
+ align:start position:0%
+and I multiply it by this matrix it gets
+ 
+
+ align:start position:0%
+and I multiply it by this matrix it gets
+stretched by minus 2 so I points in the
+
+ align:start position:0%
+stretched by minus 2 so I points in the
+ 
+
+ align:start position:0%
+stretched by minus 2 so I points in the
+other direction and I stretch out by a
+
+ align:start position:0%
+other direction and I stretch out by a
+ 
+
+ align:start position:0%
+other direction and I stretch out by a
+factor of 2 you can guess then what the
+
+ align:start position:0%
+factor of 2 you can guess then what the
+ 
+
+ align:start position:0%
+factor of 2 you can guess then what the
+other eigen vectors are what's the
+
+ align:start position:0%
+other eigen vectors are what's the
+ 
+
+ align:start position:0%
+other eigen vectors are what's the
+eigenvector associated with this
+
+ align:start position:0%
+eigenvector associated with this
+ 
+
+ align:start position:0%
+eigenvector associated with this
+eigenvalue here 0 1 0 or anything
+
+ align:start position:0%
+eigenvalue here 0 1 0 or anything
+ 
+
+ align:start position:0%
+eigenvalue here 0 1 0 or anything
+proportional to that what's the
+
+ align:start position:0%
+proportional to that what's the
+ 
+
+ align:start position:0%
+proportional to that what's the
+eigenvector associated with this
+
+ align:start position:0%
+eigenvector associated with this
+ 
+
+ align:start position:0%
+eigenvector associated with this
+eigenvalue 0 0 1 or anything
+
+ align:start position:0%
+eigenvalue 0 0 1 or anything
+ 
+
+ align:start position:0%
+eigenvalue 0 0 1 or anything
+proportional to it all these
+
+ align:start position:0%
+proportional to it all these
+ 
+
+ align:start position:0%
+proportional to it all these
+eigenvectors have a geometric
+
+ align:start position:0%
+eigenvectors have a geometric
+ 
+
+ align:start position:0%
+eigenvectors have a geometric
+multiplicity of 1 right I can just
+
+ align:start position:0%
+multiplicity of 1 right I can just
+ 
+
+ align:start position:0%
+multiplicity of 1 right I can just
+specify some scalar variant on them and
+
+ align:start position:0%
+specify some scalar variant on them and
+ 
+
+ align:start position:0%
+specify some scalar variant on them and
+they'll transform into themselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's a problem you can try okay
+
+ align:start position:0%
+okay here's a problem you can try okay
+ 
+
+ align:start position:0%
+okay here's a problem you can try okay
+here's our series of chemical reactions
+
+ align:start position:0%
+here's our series of chemical reactions
+ 
+
+ align:start position:0%
+here's our series of chemical reactions
+again and we want to know the
+
+ align:start position:0%
+again and we want to know the
+ 
+
+ align:start position:0%
+again and we want to know the
+eigenvector of the rate matrix having
+
+ align:start position:0%
+eigenvector of the rate matrix having
+ 
+
+ align:start position:0%
+eigenvector of the rate matrix having
+eigenvalue zero this should correspond
+
+ align:start position:0%
+eigenvalue zero this should correspond
+ 
+
+ align:start position:0%
+eigenvalue zero this should correspond
+to the steady-state solution of our
+
+ align:start position:0%
+to the steady-state solution of our
+ 
+
+ align:start position:0%
+to the steady-state solution of our
+ordinary differential equation here so
+
+ align:start position:0%
+ordinary differential equation here so
+ 
+
+ align:start position:0%
+ordinary differential equation here so
+you've got to do elimination on this
+
+ align:start position:0%
+you've got to do elimination on this
+ 
+
+ align:start position:0%
+you've got to do elimination on this
+matrix okay can you do that can you find
+
+ align:start position:0%
+matrix okay can you do that can you find
+ 
+
+ align:start position:0%
+matrix okay can you do that can you find
+this eigenvector try it out with your
+
+ align:start position:0%
+this eigenvector try it out with your
+ 
+
+ align:start position:0%
+this eigenvector try it out with your
+neighbors see if you can do it okay and
+
+ align:start position:0%
+neighbors see if you can do it okay and
+ 
+
+ align:start position:0%
+neighbors see if you can do it okay and
+then we'll compare compare results this
+
+ align:start position:0%
+then we'll compare compare results this
+ 
+
+ align:start position:0%
+then we'll compare compare results this
+would just be a quick test of
+
+ align:start position:0%
+would just be a quick test of
+ 
+
+ align:start position:0%
+would just be a quick test of
+understanding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are you guys able to do this sort of
+
+ align:start position:0%
+are you guys able to do this sort of
+ 
+
+ align:start position:0%
+are you guys able to do this sort of
+maybe right here's here's the answer
+
+ align:start position:0%
+maybe right here's here's the answer
+ 
+
+ align:start position:0%
+maybe right here's here's the answer
+okay or an answer for the eigenvector
+
+ align:start position:0%
+okay or an answer for the eigenvector
+ 
+
+ align:start position:0%
+okay or an answer for the eigenvector
+it's not unique right it's got some some
+
+ align:start position:0%
+it's not unique right it's got some some
+ 
+
+ align:start position:0%
+it's not unique right it's got some some
+constant out in front of it so you do
+
+ align:start position:0%
+constant out in front of it so you do
+ 
+
+ align:start position:0%
+constant out in front of it so you do
+Gaussian elimination here so subtract or
+
+ align:start position:0%
+Gaussian elimination here so subtract or
+ 
+
+ align:start position:0%
+Gaussian elimination here so subtract or
+add the first row to the second row
+
+ align:start position:0%
+add the first row to the second row
+ 
+
+ align:start position:0%
+add the first row to the second row
+you'll eliminate this zero right and
+
+ align:start position:0%
+you'll eliminate this zero right and
+ 
+
+ align:start position:0%
+you'll eliminate this zero right and
+then add the second row to the third row
+
+ align:start position:0%
+then add the second row to the third row
+ 
+
+ align:start position:0%
+then add the second row to the third row
+you'll eliminate this k2 you have to do
+
+ align:start position:0%
+you'll eliminate this k2 you have to do
+ 
+
+ align:start position:0%
+you'll eliminate this k2 you have to do
+a little bit more work to do elimination
+
+ align:start position:0%
+a little bit more work to do elimination
+ 
+
+ align:start position:0%
+a little bit more work to do elimination
+of k4 here but that's not a big deal
+
+ align:start position:0%
+of k4 here but that's not a big deal
+ 
+
+ align:start position:0%
+of k4 here but that's not a big deal
+okay again you'll add the third row to
+
+ align:start position:0%
+okay again you'll add the third row to
+ 
+
+ align:start position:0%
+okay again you'll add the third row to
+the fourth row and eliminate that and
+
+ align:start position:0%
+the fourth row and eliminate that and
+ 
+
+ align:start position:0%
+the fourth row and eliminate that and
+you'll also wind up eliminating this k5
+
+ align:start position:0%
+you'll also wind up eliminating this k5
+ 
+
+ align:start position:0%
+you'll also wind up eliminating this k5
+so the last row here will be all zeros
+
+ align:start position:0%
+so the last row here will be all zeros
+ 
+
+ align:start position:0%
+so the last row here will be all zeros
+okay and that means the last component
+
+ align:start position:0%
+okay and that means the last component
+ 
+
+ align:start position:0%
+okay and that means the last component
+of our eigenvector is freely specifiable
+
+ align:start position:0%
+of our eigenvector is freely specifiable
+ 
+
+ align:start position:0%
+of our eigenvector is freely specifiable
+can be anything we want so I set it as
+
+ align:start position:0%
+can be anything we want so I set it as
+ 
+
+ align:start position:0%
+can be anything we want so I set it as
+one and then I did back substitution to
+
+ align:start position:0%
+one and then I did back substitution to
+ 
+
+ align:start position:0%
+one and then I did back substitution to
+determine all the other components right
+
+ align:start position:0%
+determine all the other components right
+ 
+
+ align:start position:0%
+determine all the other components right
+that's the way to do this and here's
+
+ align:start position:0%
+that's the way to do this and here's
+ 
+
+ align:start position:0%
+that's the way to do this and here's
+what the eigenvector looks like when
+
+ align:start position:0%
+what the eigenvector looks like when
+ 
+
+ align:start position:0%
+what the eigenvector looks like when
+you're done the steady-state solution
+
+ align:start position:0%
+you're done the steady-state solution
+ 
+
+ align:start position:0%
+you're done the steady-state solution
+has no a in it of course a it's just
+
+ align:start position:0%
+has no a in it of course a it's just
+ 
+
+ align:start position:0%
+has no a in it of course a it's just
+eliminated by forward reactions so if we
+
+ align:start position:0%
+eliminated by forward reactions so if we
+ 
+
+ align:start position:0%
+eliminated by forward reactions so if we
+let this run out to infinite there
+
+ align:start position:0%
+let this run out to infinite there
+ 
+
+ align:start position:0%
+let this run out to infinite there
+should be no way and that's what happens
+
+ align:start position:0%
+should be no way and that's what happens
+ 
+
+ align:start position:0%
+should be no way and that's what happens
+okay but there's equilibria between B C
+
+ align:start position:0%
+okay but there's equilibria between B C
+ 
+
+ align:start position:0%
+okay but there's equilibria between B C
+and D okay and the steady state solution
+
+ align:start position:0%
+and D okay and the steady state solution
+ 
+
+ align:start position:0%
+and D okay and the steady state solution
+reflects that equilibria we have to pick
+
+ align:start position:0%
+reflects that equilibria we have to pick
+ 
+
+ align:start position:0%
+reflects that equilibria we have to pick
+what this constant out in front is and
+
+ align:start position:0%
+what this constant out in front is and
+ 
+
+ align:start position:0%
+what this constant out in front is and
+we discussed this before actually right
+
+ align:start position:0%
+we discussed this before actually right
+ 
+
+ align:start position:0%
+we discussed this before actually right
+you would pick that based on how much
+
+ align:start position:0%
+you would pick that based on how much
+ 
+
+ align:start position:0%
+you would pick that based on how much
+material was initially in the reactor
+
+ align:start position:0%
+material was initially in the reactor
+ 
+
+ align:start position:0%
+material was initially in the reactor
+I'm gonna have an overall mass balance
+
+ align:start position:0%
+I'm gonna have an overall mass balance
+ 
+
+ align:start position:0%
+I'm gonna have an overall mass balance
+and that's missing from this system of
+
+ align:start position:0%
+and that's missing from this system of
+ 
+
+ align:start position:0%
+and that's missing from this system of
+equations right mass conservation is
+
+ align:start position:0%
+equations right mass conservation is
+ 
+
+ align:start position:0%
+equations right mass conservation is
+looking of a null space for this rate
+
+ align:start position:0%
+looking of a null space for this rate
+ 
+
+ align:start position:0%
+looking of a null space for this rate
+rate matrix in the first place make
+
+ align:start position:0%
+rate matrix in the first place make
+ 
+
+ align:start position:0%
+rate matrix in the first place make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+try this example out okay see if we can
+
+ align:start position:0%
+try this example out okay see if we can
+ 
+
+ align:start position:0%
+try this example out okay see if we can
+see if we work through the details and I
+
+ align:start position:0%
+see if we work through the details and I
+ 
+
+ align:start position:0%
+see if we work through the details and I
+think it's useful to be able to do these
+
+ align:start position:0%
+think it's useful to be able to do these
+ 
+
+ align:start position:0%
+think it's useful to be able to do these
+sorts of things quickly here's some
+
+ align:start position:0%
+sorts of things quickly here's some
+ 
+
+ align:start position:0%
+sorts of things quickly here's some
+simpler problems okay so here's a matrix
+
+ align:start position:0%
+simpler problems okay so here's a matrix
+ 
+
+ align:start position:0%
+simpler problems okay so here's a matrix
+it's not a very good matrix matrices
+
+ align:start position:0%
+it's not a very good matrix matrices
+ 
+
+ align:start position:0%
+it's not a very good matrix matrices
+can't be good or bad it's not
+
+ align:start position:0%
+can't be good or bad it's not
+ 
+
+ align:start position:0%
+can't be good or bad it's not
+particularly interesting but it's all
+
+ align:start position:0%
+particularly interesting but it's all
+ 
+
+ align:start position:0%
+particularly interesting but it's all
+zeros okay so what are its eigenvalue
+
+ align:start position:0%
+zeros okay so what are its eigenvalue
+ 
+
+ align:start position:0%
+zeros okay so what are its eigenvalue
+it's just a zero okay right the diagonal
+
+ align:start position:0%
+it's just a zero okay right the diagonal
+ 
+
+ align:start position:0%
+it's just a zero okay right the diagonal
+elements are the eigenvalues and they're
+
+ align:start position:0%
+elements are the eigenvalues and they're
+ 
+
+ align:start position:0%
+elements are the eigenvalues and they're
+zero right that eigenvalue has algebraic
+
+ align:start position:0%
+zero right that eigenvalue has algebraic
+ 
+
+ align:start position:0%
+zero right that eigenvalue has algebraic
+multiplicity two okay it's a double root
+
+ align:start position:0%
+multiplicity two okay it's a double root
+ 
+
+ align:start position:0%
+multiplicity two okay it's a double root
+of the secular characteristic polynomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you give me the eigenvectors okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you give me I can vectors of this
+
+ align:start position:0%
+can you give me I can vectors of this
+ 
+
+ align:start position:0%
+can you give me I can vectors of this
+matrix can give me linearly independent
+
+ align:start position:0%
+matrix can give me linearly independent
+ 
+
+ align:start position:0%
+matrix can give me linearly independent
+eigen yeah okay okay good
+
+ align:start position:0%
+eigen yeah okay okay good
+ 
+
+ align:start position:0%
+eigen yeah okay okay good
+so this is this is a very ambiguous sort
+
+ align:start position:0%
+so this is this is a very ambiguous sort
+ 
+
+ align:start position:0%
+so this is this is a very ambiguous sort
+of problem or question right any vector
+
+ align:start position:0%
+of problem or question right any vector
+ 
+
+ align:start position:0%
+of problem or question right any vector
+I multiply by a here it's gonna be
+
+ align:start position:0%
+I multiply by a here it's gonna be
+ 
+
+ align:start position:0%
+I multiply by a here it's gonna be
+stretched by zero cuz a by its very
+
+ align:start position:0%
+stretched by zero cuz a by its very
+ 
+
+ align:start position:0%
+stretched by zero cuz a by its very
+nature is all zeros okay all those
+
+ align:start position:0%
+nature is all zeros okay all those
+ 
+
+ align:start position:0%
+nature is all zeros okay all those
+vectors live in a plane okay so any
+
+ align:start position:0%
+vectors live in a plane okay so any
+ 
+
+ align:start position:0%
+vectors live in a plane okay so any
+vector from that plane is gonna be
+
+ align:start position:0%
+vector from that plane is gonna be
+ 
+
+ align:start position:0%
+vector from that plane is gonna be
+transformed in this way the eigenvector
+
+ align:start position:0%
+transformed in this way the eigenvector
+ 
+
+ align:start position:0%
+transformed in this way the eigenvector
+corresponding to eigenvalue zero as
+
+ align:start position:0%
+corresponding to eigenvalue zero as
+ 
+
+ align:start position:0%
+corresponding to eigenvalue zero as
+geometric multiplicity two because i can
+
+ align:start position:0%
+geometric multiplicity two because i can
+ 
+
+ align:start position:0%
+geometric multiplicity two because i can
+freely specify two of its components oh
+
+ align:start position:0%
+freely specify two of its components oh
+ 
+
+ align:start position:0%
+freely specify two of its components oh
+my goodness i what so fast people just
+
+ align:start position:0%
+my goodness i what so fast people just
+ 
+
+ align:start position:0%
+my goodness i what so fast people just
+do it this way okay algebraic
+
+ align:start position:0%
+do it this way okay algebraic
+ 
+
+ align:start position:0%
+do it this way okay algebraic
+multiplicity two geometric multiplicity
+
+ align:start position:0%
+multiplicity two geometric multiplicity
+ 
+
+ align:start position:0%
+multiplicity two geometric multiplicity
+two i can pick two vectors they can be
+
+ align:start position:0%
+two i can pick two vectors they can be
+ 
+
+ align:start position:0%
+two i can pick two vectors they can be
+any two i want in principle right it has
+
+ align:start position:0%
+any two i want in principle right it has
+ 
+
+ align:start position:0%
+any two i want in principle right it has
+geometric multiplicity two okay here's
+
+ align:start position:0%
+geometric multiplicity two okay here's
+ 
+
+ align:start position:0%
+geometric multiplicity two okay here's
+another matrix it's a little more
+
+ align:start position:0%
+another matrix it's a little more
+ 
+
+ align:start position:0%
+another matrix it's a little more
+interesting than the last one I stuck a
+
+ align:start position:0%
+interesting than the last one I stuck a
+ 
+
+ align:start position:0%
+interesting than the last one I stuck a
+one in there instead okay again right
+
+ align:start position:0%
+one in there instead okay again right
+ 
+
+ align:start position:0%
+one in there instead okay again right
+the the eigen values are zero it's a
+
+ align:start position:0%
+the the eigen values are zero it's a
+ 
+
+ align:start position:0%
+the the eigen values are zero it's a
+double root so it has algebraic
+
+ align:start position:0%
+double root so it has algebraic
+ 
+
+ align:start position:0%
+double root so it has algebraic
+multiplicity two but you can convince
+
+ align:start position:0%
+multiplicity two but you can convince
+ 
+
+ align:start position:0%
+multiplicity two but you can convince
+yourself that there's only one direction
+
+ align:start position:0%
+yourself that there's only one direction
+ 
+
+ align:start position:0%
+yourself that there's only one direction
+that transforms that squeezed down to
+
+ align:start position:0%
+that transforms that squeezed down to
+ 
+
+ align:start position:0%
+that transforms that squeezed down to
+zero right there's only one vector
+
+ align:start position:0%
+zero right there's only one vector
+ 
+
+ align:start position:0%
+zero right there's only one vector
+direction right that lives in the null
+
+ align:start position:0%
+direction right that lives in the null
+ 
+
+ align:start position:0%
+direction right that lives in the null
+space of a minus lambda I lives in the
+
+ align:start position:0%
+space of a minus lambda I lives in the
+ 
+
+ align:start position:0%
+space of a minus lambda I lives in the
+null space of a and that's vectors
+
+ align:start position:0%
+null space of a and that's vectors
+ 
+
+ align:start position:0%
+null space of a and that's vectors
+parallel to one zero so the eigenvector
+
+ align:start position:0%
+parallel to one zero so the eigenvector
+ 
+
+ align:start position:0%
+parallel to one zero so the eigenvector
+associated with that eigenvalue zero as
+
+ align:start position:0%
+associated with that eigenvalue zero as
+ 
+
+ align:start position:0%
+associated with that eigenvalue zero as
+geometric multiplicity 1 instead of
+
+ align:start position:0%
+geometric multiplicity 1 instead of
+ 
+
+ align:start position:0%
+geometric multiplicity 1 instead of
+geometric multiplicity two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now here's an example for you to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you find the eigenvalues and some
+
+ align:start position:0%
+can you find the eigenvalues and some
+ 
+
+ align:start position:0%
+can you find the eigenvalues and some
+linearly independent eigenvectors of
+
+ align:start position:0%
+linearly independent eigenvectors of
+ 
+
+ align:start position:0%
+linearly independent eigenvectors of
+this matrix which looks like the one we
+
+ align:start position:0%
+this matrix which looks like the one we
+ 
+
+ align:start position:0%
+this matrix which looks like the one we
+just looked at but now it's three by
+
+ align:start position:0%
+just looked at but now it's three by
+ 
+
+ align:start position:0%
+just looked at but now it's three by
+three instead of two by two and if you
+
+ align:start position:0%
+three instead of two by two and if you
+ 
+
+ align:start position:0%
+three instead of two by two and if you
+find those eigenvalues and eigenvectors
+
+ align:start position:0%
+find those eigenvalues and eigenvectors
+ 
+
+ align:start position:0%
+find those eigenvalues and eigenvectors
+what are the algebraic and geometric
+
+ align:start position:0%
+what are the algebraic and geometric
+ 
+
+ align:start position:0%
+what are the algebraic and geometric
+multiplicity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we has must had a rough week you really
+
+ align:start position:0%
+we has must had a rough week you really
+ 
+
+ align:start position:0%
+we has must had a rough week you really
+you're usually much more talkative and
+
+ align:start position:0%
+you're usually much more talkative and
+ 
+
+ align:start position:0%
+you're usually much more talkative and
+energetic than this well what are the
+
+ align:start position:0%
+energetic than this well what are the
+ 
+
+ align:start position:0%
+energetic than this well what are the
+eigenvalues here yeah they all turn out
+
+ align:start position:0%
+eigenvalues here yeah they all turn out
+ 
+
+ align:start position:0%
+eigenvalues here yeah they all turn out
+to be zero okay so that's an algebraic
+
+ align:start position:0%
+to be zero okay so that's an algebraic
+ 
+
+ align:start position:0%
+to be zero okay so that's an algebraic
+multiplicity of three it'll turn out
+
+ align:start position:0%
+multiplicity of three it'll turn out
+ 
+
+ align:start position:0%
+multiplicity of three it'll turn out
+there are two vectors two vector
+
+ align:start position:0%
+there are two vectors two vector
+ 
+
+ align:start position:0%
+there are two vectors two vector
+directions that I can specify it will
+
+ align:start position:0%
+directions that I can specify it will
+ 
+
+ align:start position:0%
+directions that I can specify it will
+both be squeezed down to zero in fact
+
+ align:start position:0%
+both be squeezed down to zero in fact
+ 
+
+ align:start position:0%
+both be squeezed down to zero in fact
+any vector from the XY plane it will
+
+ align:start position:0%
+any vector from the XY plane it will
+ 
+
+ align:start position:0%
+any vector from the XY plane it will
+also be squeezed down to zero so this
+
+ align:start position:0%
+also be squeezed down to zero so this
+ 
+
+ align:start position:0%
+also be squeezed down to zero so this
+has algebraic multiplicity three and
+
+ align:start position:0%
+has algebraic multiplicity three and
+ 
+
+ align:start position:0%
+has algebraic multiplicity three and
+geometric multiplicity two okay I'm
+
+ align:start position:0%
+geometric multiplicity two okay I'm
+ 
+
+ align:start position:0%
+geometric multiplicity two okay I'm
+gonna explain why this is important in a
+
+ align:start position:0%
+gonna explain why this is important in a
+ 
+
+ align:start position:0%
+gonna explain why this is important in a
+second but understanding that this can
+
+ align:start position:0%
+second but understanding that this can
+ 
+
+ align:start position:0%
+second but understanding that this can
+happen is is gonna be useful for you
+
+ align:start position:0%
+happen is is gonna be useful for you
+ 
+
+ align:start position:0%
+happen is is gonna be useful for you
+okay so if an eigenvalue is distinct
+
+ align:start position:0%
+okay so if an eigenvalue is distinct
+ 
+
+ align:start position:0%
+okay so if an eigenvalue is distinct
+right then as algebraic multiplicity one
+
+ align:start position:0%
+right then as algebraic multiplicity one
+ 
+
+ align:start position:0%
+right then as algebraic multiplicity one
+okay it's the only eigenvalue with that
+
+ align:start position:0%
+okay it's the only eigenvalue with that
+ 
+
+ align:start position:0%
+okay it's the only eigenvalue with that
+value it's the only time that amount of
+
+ align:start position:0%
+value it's the only time that amount of
+ 
+
+ align:start position:0%
+value it's the only time that amount of
+stretch is imparted and there will be
+
+ align:start position:0%
+stretch is imparted and there will be
+ 
+
+ align:start position:0%
+stretch is imparted and there will be
+only one corresponding eigenvector okay
+
+ align:start position:0%
+only one corresponding eigenvector okay
+ 
+
+ align:start position:0%
+only one corresponding eigenvector okay
+there will be direction and an amount of
+
+ align:start position:0%
+there will be direction and an amount of
+ 
+
+ align:start position:0%
+there will be direction and an amount of
+stretch if a night I can value has
+
+ align:start position:0%
+stretch if a night I can value has
+ 
+
+ align:start position:0%
+stretch if a night I can value has
+algebraic multiplicity M well you just
+
+ align:start position:0%
+algebraic multiplicity M well you just
+ 
+
+ align:start position:0%
+algebraic multiplicity M well you just
+saw that the geometric multiplicity okay
+
+ align:start position:0%
+saw that the geometric multiplicity okay
+ 
+
+ align:start position:0%
+saw that the geometric multiplicity okay
+which is the dimension of the null space
+
+ align:start position:0%
+which is the dimension of the null space
+ 
+
+ align:start position:0%
+which is the dimension of the null space
+of a minus lambda I right it's the
+
+ align:start position:0%
+of a minus lambda I right it's the
+ 
+
+ align:start position:0%
+of a minus lambda I right it's the
+dimension of the space spanned by no
+
+ align:start position:0%
+dimension of the space spanned by no
+ 
+
+ align:start position:0%
+dimension of the space spanned by no
+vectors of a minus lambda I it's going
+
+ align:start position:0%
+vectors of a minus lambda I it's going
+ 
+
+ align:start position:0%
+vectors of a minus lambda I it's going
+to be bigger than 1 or equal to 1 and
+
+ align:start position:0%
+to be bigger than 1 or equal to 1 and
+ 
+
+ align:start position:0%
+to be bigger than 1 or equal to 1 and
+it's going to be smaller or equal to M
+
+ align:start position:0%
+it's going to be smaller or equal to M
+ 
+
+ align:start position:0%
+it's going to be smaller or equal to M
+and we saw different variants on values
+
+ align:start position:0%
+and we saw different variants on values
+ 
+
+ align:start position:0%
+and we saw different variants on values
+that sit in this range so there could be
+
+ align:start position:0%
+that sit in this range so there could be
+ 
+
+ align:start position:0%
+that sit in this range so there could be
+as many as M linearly independent eigen
+
+ align:start position:0%
+as many as M linearly independent eigen
+ 
+
+ align:start position:0%
+as many as M linearly independent eigen
+vectors okay and there may be fewer so
+
+ align:start position:0%
+vectors okay and there may be fewer so
+ 
+
+ align:start position:0%
+vectors okay and there may be fewer so
+geometric multiplicity it's the number
+
+ align:start position:0%
+geometric multiplicity it's the number
+ 
+
+ align:start position:0%
+geometric multiplicity it's the number
+of linearly independent eigenvectors
+
+ align:start position:0%
+of linearly independent eigenvectors
+ 
+
+ align:start position:0%
+of linearly independent eigenvectors
+associated with an eigenvalue it's the
+
+ align:start position:0%
+associated with an eigenvalue it's the
+ 
+
+ align:start position:0%
+associated with an eigenvalue it's the
+dimension of the null space of this
+
+ align:start position:0%
+dimension of the null space of this
+ 
+
+ align:start position:0%
+dimension of the null space of this
+matrix problems for which the geometric
+
+ align:start position:0%
+matrix problems for which the geometric
+ 
+
+ align:start position:0%
+matrix problems for which the geometric
+and algebraic multiplicity are the same
+
+ align:start position:0%
+and algebraic multiplicity are the same
+ 
+
+ align:start position:0%
+and algebraic multiplicity are the same
+okay for all the eigenvalues and
+
+ align:start position:0%
+okay for all the eigenvalues and
+ 
+
+ align:start position:0%
+okay for all the eigenvalues and
+eigenvectors
+
+ align:start position:0%
+eigenvectors
+ 
+
+ align:start position:0%
+eigenvectors
+all those pairs are nice because the
+
+ align:start position:0%
+all those pairs are nice because the
+ 
+
+ align:start position:0%
+all those pairs are nice because the
+matrix then is said to have a complete
+
+ align:start position:0%
+matrix then is said to have a complete
+ 
+
+ align:start position:0%
+matrix then is said to have a complete
+set of eigenvectors okay there's enough
+
+ align:start position:0%
+set of eigenvectors okay there's enough
+ 
+
+ align:start position:0%
+set of eigenvectors okay there's enough
+eigenvectors in the problem that they
+
+ align:start position:0%
+eigenvectors in the problem that they
+ 
+
+ align:start position:0%
+eigenvectors in the problem that they
+describe the span of of our vector space
+
+ align:start position:0%
+describe the span of of our vector space
+ 
+
+ align:start position:0%
+describe the span of of our vector space
+RN right that our matrix is doing
+
+ align:start position:0%
+RN right that our matrix is doing
+ 
+
+ align:start position:0%
+RN right that our matrix is doing
+transformations between if we have
+
+ align:start position:0%
+transformations between if we have
+ 
+
+ align:start position:0%
+transformations between if we have
+geometric multiplicity that's smaller
+
+ align:start position:0%
+geometric multiplicity that's smaller
+ 
+
+ align:start position:0%
+geometric multiplicity that's smaller
+than the algebraic multiplicity then
+
+ align:start position:0%
+than the algebraic multiplicity then
+ 
+
+ align:start position:0%
+than the algebraic multiplicity then
+some of these stretched or we can't
+
+ align:start position:0%
+some of these stretched or we can't
+ 
+
+ align:start position:0%
+some of these stretched or we can't
+stretch in all possible directions in RN
+
+ align:start position:0%
+stretch in all possible directions in RN
+ 
+
+ align:start position:0%
+stretch in all possible directions in RN
+there's going to be a direction that
+
+ align:start position:0%
+there's going to be a direction that
+ 
+
+ align:start position:0%
+there's going to be a direction that
+might be left out we want to be able to
+
+ align:start position:0%
+might be left out we want to be able to
+ 
+
+ align:start position:0%
+might be left out we want to be able to
+do a type of transformation called in an
+
+ align:start position:0%
+do a type of transformation called in an
+ 
+
+ align:start position:0%
+do a type of transformation called in an
+eigen decomposition I'm going to show
+
+ align:start position:0%
+eigen decomposition I'm going to show
+ 
+
+ align:start position:0%
+eigen decomposition I'm going to show
+you that in a second it's useful for
+
+ align:start position:0%
+you that in a second it's useful for
+ 
+
+ align:start position:0%
+you that in a second it's useful for
+solving systems of equations or for
+
+ align:start position:0%
+solving systems of equations or for
+ 
+
+ align:start position:0%
+solving systems of equations or for
+transforming systems of ordinary
+
+ align:start position:0%
+transforming systems of ordinary
+ 
+
+ align:start position:0%
+transforming systems of ordinary
+differential equations linear ordinary
+
+ align:start position:0%
+differential equations linear ordinary
+ 
+
+ align:start position:0%
+differential equations linear ordinary
+differential equations okay but we're
+
+ align:start position:0%
+differential equations okay but we're
+ 
+
+ align:start position:0%
+differential equations okay but we're
+only going to be do able to do that when
+
+ align:start position:0%
+only going to be do able to do that when
+ 
+
+ align:start position:0%
+only going to be do able to do that when
+we have this complete set of eigen
+
+ align:start position:0%
+we have this complete set of eigen
+ 
+
+ align:start position:0%
+we have this complete set of eigen
+vectors when we don't have that complete
+
+ align:start position:0%
+vectors when we don't have that complete
+ 
+
+ align:start position:0%
+vectors when we don't have that complete
+set we're gonna have to do other sorts
+
+ align:start position:0%
+set we're gonna have to do other sorts
+ 
+
+ align:start position:0%
+set we're gonna have to do other sorts
+of transformations you have a problem in
+
+ align:start position:0%
+of transformations you have a problem in
+ 
+
+ align:start position:0%
+of transformations you have a problem in
+your homework now I think that has this
+
+ align:start position:0%
+your homework now I think that has this
+ 
+
+ align:start position:0%
+your homework now I think that has this
+this sort of a hang-up associated with
+
+ align:start position:0%
+this sort of a hang-up associated with
+ 
+
+ align:start position:0%
+this sort of a hang-up associated with
+us the second problem in your homework
+
+ align:start position:0%
+us the second problem in your homework
+ 
+
+ align:start position:0%
+us the second problem in your homework
+set it's something to think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a matrix with a complete set of
+
+ align:start position:0%
+for a matrix with a complete set of
+ 
+
+ align:start position:0%
+for a matrix with a complete set of
+eigenvectors we can write the following
+
+ align:start position:0%
+eigenvectors we can write the following
+ 
+
+ align:start position:0%
+eigenvectors we can write the following
+a time's the matrix W is equal to W
+
+ align:start position:0%
+a time's the matrix W is equal to W
+ 
+
+ align:start position:0%
+a time's the matrix W is equal to W
+times the matrix lambda let me tell you
+
+ align:start position:0%
+times the matrix lambda let me tell you
+ 
+
+ align:start position:0%
+times the matrix lambda let me tell you
+what W and lambda are so W is a matrix
+
+ align:start position:0%
+what W and lambda are so W is a matrix
+ 
+
+ align:start position:0%
+what W and lambda are so W is a matrix
+whose columns are made up of this all of
+
+ align:start position:0%
+whose columns are made up of this all of
+ 
+
+ align:start position:0%
+whose columns are made up of this all of
+these eigenvectors okay
+
+ align:start position:0%
+these eigenvectors okay
+ 
+
+ align:start position:0%
+these eigenvectors okay
+and lambda is a matrix whose diagonal
+
+ align:start position:0%
+and lambda is a matrix whose diagonal
+ 
+
+ align:start position:0%
+and lambda is a matrix whose diagonal
+values are each of the corresponding
+
+ align:start position:0%
+values are each of the corresponding
+ 
+
+ align:start position:0%
+values are each of the corresponding
+eigen values associated with those
+
+ align:start position:0%
+eigen values associated with those
+ 
+
+ align:start position:0%
+eigen values associated with those
+eigenvectors this write is nothing more
+
+ align:start position:0%
+eigenvectors this write is nothing more
+ 
+
+ align:start position:0%
+eigenvectors this write is nothing more
+than a restatement of the original
+
+ align:start position:0%
+than a restatement of the original
+ 
+
+ align:start position:0%
+than a restatement of the original
+eigenvalue problem write a W is lambda W
+
+ align:start position:0%
+eigenvalue problem write a W is lambda W
+ 
+
+ align:start position:0%
+eigenvalue problem write a W is lambda W
+but now each eigenvalue has a
+
+ align:start position:0%
+but now each eigenvalue has a
+ 
+
+ align:start position:0%
+but now each eigenvalue has a
+corresponding particular eigenvector and
+
+ align:start position:0%
+corresponding particular eigenvector and
+ 
+
+ align:start position:0%
+corresponding particular eigenvector and
+we've stacked those equations up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make this statement about matrix matrix
+
+ align:start position:0%
+make this statement about matrix matrix
+ 
+
+ align:start position:0%
+make this statement about matrix matrix
+multiplication so we've taken each of
+
+ align:start position:0%
+multiplication so we've taken each of
+ 
+
+ align:start position:0%
+multiplication so we've taken each of
+these WS over here we've just made them
+
+ align:start position:0%
+these WS over here we've just made them
+ 
+
+ align:start position:0%
+these WS over here we've just made them
+the columns of a particular matrix but
+
+ align:start position:0%
+the columns of a particular matrix but
+ 
+
+ align:start position:0%
+the columns of a particular matrix but
+it's nothing more than a restatement of
+
+ align:start position:0%
+it's nothing more than a restatement of
+ 
+
+ align:start position:0%
+it's nothing more than a restatement of
+the fundamental eigenvalue problem we've
+
+ align:start position:0%
+the fundamental eigenvalue problem we've
+ 
+
+ align:start position:0%
+the fundamental eigenvalue problem we've
+posed at the beginning here but what's
+
+ align:start position:0%
+posed at the beginning here but what's
+ 
+
+ align:start position:0%
+posed at the beginning here but what's
+nice is if I have this complete set of
+
+ align:start position:0%
+nice is if I have this complete set of
+ 
+
+ align:start position:0%
+nice is if I have this complete set of
+eigen vectors then W has an inverse that
+
+ align:start position:0%
+eigen vectors then W has an inverse that
+ 
+
+ align:start position:0%
+eigen vectors then W has an inverse that
+I can write down ok so another way it's
+
+ align:start position:0%
+I can write down ok so another way it's
+ 
+
+ align:start position:0%
+I can write down ok so another way it's
+a state this same equation is that
+
+ align:start position:0%
+a state this same equation is that
+ 
+
+ align:start position:0%
+a state this same equation is that
+lambda the eigen values can be found
+
+ align:start position:0%
+lambda the eigen values can be found
+ 
+
+ align:start position:0%
+lambda the eigen values can be found
+okay from this matrix product W inverse
+
+ align:start position:0%
+okay from this matrix product W inverse
+ 
+
+ align:start position:0%
+okay from this matrix product W inverse
+times a times W and under these
+
+ align:start position:0%
+times a times W and under these
+ 
+
+ align:start position:0%
+times a times W and under these
+circumstances we say the matrix can be
+
+ align:start position:0%
+circumstances we say the matrix can be
+ 
+
+ align:start position:0%
+circumstances we say the matrix can be
+diagonalized there's a transformation
+
+ align:start position:0%
+diagonalized there's a transformation
+ 
+
+ align:start position:0%
+diagonalized there's a transformation
+from a to a diagonal form that's good
+
+ align:start position:0%
+from a to a diagonal form that's good
+ 
+
+ align:start position:0%
+from a to a diagonal form that's good
+for us right we know diagonal of systems
+
+ align:start position:0%
+for us right we know diagonal of systems
+ 
+
+ align:start position:0%
+for us right we know diagonal of systems
+of equations are easy to solve so if I
+
+ align:start position:0%
+of equations are easy to solve so if I
+ 
+
+ align:start position:0%
+of equations are easy to solve so if I
+knew what the eigenvectors wore then I
+
+ align:start position:0%
+knew what the eigenvectors wore then I
+ 
+
+ align:start position:0%
+knew what the eigenvectors wore then I
+could transform my equation to this
+
+ align:start position:0%
+could transform my equation to this
+ 
+
+ align:start position:0%
+could transform my equation to this
+diagonal form and I could solve systems
+
+ align:start position:0%
+diagonal form and I could solve systems
+ 
+
+ align:start position:0%
+diagonal form and I could solve systems
+of equations really easily of course we
+
+ align:start position:0%
+of equations really easily of course we
+ 
+
+ align:start position:0%
+of equations really easily of course we
+just saw that knowing what those
+
+ align:start position:0%
+just saw that knowing what those
+ 
+
+ align:start position:0%
+just saw that knowing what those
+eigenvectors are requires solving
+
+ align:start position:0%
+eigenvectors are requires solving
+ 
+
+ align:start position:0%
+eigenvectors are requires solving
+systems of equations anyway so the
+
+ align:start position:0%
+systems of equations anyway so the
+ 
+
+ align:start position:0%
+systems of equations anyway so the
+problem of finding the eigenvectors is
+
+ align:start position:0%
+problem of finding the eigenvectors is
+ 
+
+ align:start position:0%
+problem of finding the eigenvectors is
+as hard as the problem of solving a
+
+ align:start position:0%
+as hard as the problem of solving a
+ 
+
+ align:start position:0%
+as hard as the problem of solving a
+system of equations okay
+
+ align:start position:0%
+system of equations okay
+ 
+
+ align:start position:0%
+system of equations okay
+but in principle I can do this sort of
+
+ align:start position:0%
+but in principle I can do this sort of
+ 
+
+ align:start position:0%
+but in principle I can do this sort of
+transformation equivalently the matrix a
+
+ align:start position:0%
+transformation equivalently the matrix a
+ 
+
+ align:start position:0%
+transformation equivalently the matrix a
+can be written as W times lambda times W
+
+ align:start position:0%
+can be written as W times lambda times W
+ 
+
+ align:start position:0%
+can be written as W times lambda times W
+inverse these are all equivalent ways of
+
+ align:start position:0%
+inverse these are all equivalent ways of
+ 
+
+ align:start position:0%
+inverse these are all equivalent ways of
+writing this fundamental relationship up
+
+ align:start position:0%
+writing this fundamental relationship up
+ 
+
+ align:start position:0%
+writing this fundamental relationship up
+here when the inverse of W exists so
+
+ align:start position:0%
+here when the inverse of W exists so
+ 
+
+ align:start position:0%
+here when the inverse of W exists so
+this means that if I know the
+
+ align:start position:0%
+this means that if I know the
+ 
+
+ align:start position:0%
+this means that if I know the
+eigenvalues and eigenvectors I can
+
+ align:start position:0%
+eigenvalues and eigenvectors I can
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors I can
+easily reconstruct my equation right if
+
+ align:start position:0%
+easily reconstruct my equation right if
+ 
+
+ align:start position:0%
+easily reconstruct my equation right if
+I know the eigen vectors in a then I can
+
+ align:start position:0%
+I know the eigen vectors in a then I can
+ 
+
+ align:start position:0%
+I know the eigen vectors in a then I can
+easily diagonalize my system of
+
+ align:start position:0%
+easily diagonalize my system of
+ 
+
+ align:start position:0%
+easily diagonalize my system of
+equations right so this is a useful sort
+
+ align:start position:0%
+equations right so this is a useful sort
+ 
+
+ align:start position:0%
+equations right so this is a useful sort
+of transformation to do we haven't
+
+ align:start position:0%
+of transformation to do we haven't
+ 
+
+ align:start position:0%
+of transformation to do we haven't
+talked about how it's done in the
+
+ align:start position:0%
+talked about how it's done in the
+ 
+
+ align:start position:0%
+talked about how it's done in the
+computer ok we've talked about how you
+
+ align:start position:0%
+computer ok we've talked about how you
+ 
+
+ align:start position:0%
+computer ok we've talked about how you
+would do it by hand these are ways you
+
+ align:start position:0%
+would do it by hand these are ways you
+ 
+
+ align:start position:0%
+would do it by hand these are ways you
+could do it by hand the computer won't
+
+ align:start position:0%
+could do it by hand the computer won't
+ 
+
+ align:start position:0%
+could do it by hand the computer won't
+do Gaussian elimination for each of
+
+ align:start position:0%
+do Gaussian elimination for each of
+ 
+
+ align:start position:0%
+do Gaussian elimination for each of
+those eigenvectors independently right
+
+ align:start position:0%
+those eigenvectors independently right
+ 
+
+ align:start position:0%
+those eigenvectors independently right
+that's an order each elimination
+
+ align:start position:0%
+that's an order each elimination
+ 
+
+ align:start position:0%
+that's an order each elimination
+procedure is order n cubed right and you
+
+ align:start position:0%
+procedure is order n cubed right and you
+ 
+
+ align:start position:0%
+procedure is order n cubed right and you
+got to do that for n eigenvectors so
+
+ align:start position:0%
+got to do that for n eigenvectors so
+ 
+
+ align:start position:0%
+got to do that for n eigenvectors so
+that's n to the fourth operations that's
+
+ align:start position:0%
+that's n to the fourth operations that's
+ 
+
+ align:start position:0%
+that's n to the fourth operations that's
+pretty slow there's an alternative way
+
+ align:start position:0%
+pretty slow there's an alternative way
+ 
+
+ align:start position:0%
+pretty slow there's an alternative way
+of doing it that's beyond the scope of
+
+ align:start position:0%
+of doing it that's beyond the scope of
+ 
+
+ align:start position:0%
+of doing it that's beyond the scope of
+this class called
+
+ align:start position:0%
+this class called
+ 
+
+ align:start position:0%
+this class called
+it's called the Linksys algorithm okay
+
+ align:start position:0%
+it's called the Linksys algorithm okay
+ 
+
+ align:start position:0%
+it's called the Linksys algorithm okay
+and it's a
+
+ align:start position:0%
+and it's a
+ 
+
+ align:start position:0%
+and it's a
+it's what's referred to as a Krylov
+
+ align:start position:0%
+it's what's referred to as a Krylov
+ 
+
+ align:start position:0%
+it's what's referred to as a Krylov
+subspace method a sort of iterative
+
+ align:start position:0%
+subspace method a sort of iterative
+ 
+
+ align:start position:0%
+subspace method a sort of iterative
+method where you take products of your
+
+ align:start position:0%
+method where you take products of your
+ 
+
+ align:start position:0%
+method where you take products of your
+matrix with certain vectors and from
+
+ align:start position:0%
+matrix with certain vectors and from
+ 
+
+ align:start position:0%
+matrix with certain vectors and from
+those products and for what the
+
+ align:start position:0%
+those products and for what the
+ 
+
+ align:start position:0%
+those products and for what the
+eigenvectors and eigenvalues are okay so
+
+ align:start position:0%
+eigenvectors and eigenvalues are okay so
+ 
+
+ align:start position:0%
+eigenvectors and eigenvalues are okay so
+that's the way computer is going to do
+
+ align:start position:0%
+that's the way computer is going to do
+ 
+
+ align:start position:0%
+that's the way computer is going to do
+it that's going to be an order n-cubed
+
+ align:start position:0%
+it that's going to be an order n-cubed
+ 
+
+ align:start position:0%
+it that's going to be an order n-cubed
+sort of calculation to find all the
+
+ align:start position:0%
+sort of calculation to find all the
+ 
+
+ align:start position:0%
+sort of calculation to find all the
+eigenvalues and eigenvectors it's hard
+
+ align:start position:0%
+eigenvalues and eigenvectors it's hard
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors it's hard
+to solving a system of equations but
+
+ align:start position:0%
+to solving a system of equations but
+ 
+
+ align:start position:0%
+to solving a system of equations but
+sometimes you want these things here's
+
+ align:start position:0%
+sometimes you want these things here's
+ 
+
+ align:start position:0%
+sometimes you want these things here's
+an example of how this eigen
+
+ align:start position:0%
+an example of how this eigen
+ 
+
+ align:start position:0%
+an example of how this eigen
+decomposition could be useful to you if
+
+ align:start position:0%
+decomposition could be useful to you if
+ 
+
+ align:start position:0%
+decomposition could be useful to you if
+you did it so we know the matrix a can
+
+ align:start position:0%
+you did it so we know the matrix a can
+ 
+
+ align:start position:0%
+you did it so we know the matrix a can
+be represented as W lambda W inverse
+
+ align:start position:0%
+be represented as W lambda W inverse
+ 
+
+ align:start position:0%
+be represented as W lambda W inverse
+times x equals B this is our transformed
+
+ align:start position:0%
+times x equals B this is our transformed
+ 
+
+ align:start position:0%
+times x equals B this is our transformed
+system of equations here we've just
+
+ align:start position:0%
+system of equations here we've just
+ 
+
+ align:start position:0%
+system of equations here we've just
+substituted for a if I multiply both
+
+ align:start position:0%
+substituted for a if I multiply both
+ 
+
+ align:start position:0%
+substituted for a if I multiply both
+sides of this equation by W inverse then
+
+ align:start position:0%
+sides of this equation by W inverse then
+ 
+
+ align:start position:0%
+sides of this equation by W inverse then
+I've got lambda times the quantity W
+
+ align:start position:0%
+I've got lambda times the quantity W
+ 
+
+ align:start position:0%
+I've got lambda times the quantity W
+inverse X is equal to W inverse B now if
+
+ align:start position:0%
+inverse X is equal to W inverse B now if
+ 
+
+ align:start position:0%
+inverse X is equal to W inverse B now if
+I call this quantity in parentheses Y
+
+ align:start position:0%
+I call this quantity in parentheses Y
+ 
+
+ align:start position:0%
+I call this quantity in parentheses Y
+then I have an easy to solve system of
+
+ align:start position:0%
+then I have an easy to solve system of
+ 
+
+ align:start position:0%
+then I have an easy to solve system of
+equations for y okay y is equal to
+
+ align:start position:0%
+equations for y okay y is equal to
+ 
+
+ align:start position:0%
+equations for y okay y is equal to
+lambda inverse times e but lambda
+
+ align:start position:0%
+lambda inverse times e but lambda
+ 
+
+ align:start position:0%
+lambda inverse times e but lambda
+inverse is just one over each of the
+
+ align:start position:0%
+inverse is just one over each of the
+ 
+
+ align:start position:0%
+inverse is just one over each of the
+diagonal components of lambda lambda is
+
+ align:start position:0%
+diagonal components of lambda lambda is
+ 
+
+ align:start position:0%
+diagonal components of lambda lambda is
+a diagonal matrix then all I need to do
+
+ align:start position:0%
+a diagonal matrix then all I need to do
+ 
+
+ align:start position:0%
+a diagonal matrix then all I need to do
+ooh
+
+ align:start position:0%
+ooh
+ 
+
+ align:start position:0%
+ooh
+typo there's an equal sign missing here
+
+ align:start position:0%
+typo there's an equal sign missing here
+ 
+
+ align:start position:0%
+typo there's an equal sign missing here
+sorry for that and now all I need to do
+
+ align:start position:0%
+sorry for that and now all I need to do
+ 
+
+ align:start position:0%
+sorry for that and now all I need to do
+a substitute for what I called Y and
+
+ align:start position:0%
+a substitute for what I called Y and
+ 
+
+ align:start position:0%
+a substitute for what I called Y and
+what I called C so Y was W inverse times
+
+ align:start position:0%
+what I called C so Y was W inverse times
+ 
+
+ align:start position:0%
+what I called C so Y was W inverse times
+X that's equal to lambda inverse times W
+
+ align:start position:0%
+X that's equal to lambda inverse times W
+ 
+
+ align:start position:0%
+X that's equal to lambda inverse times W
+inverse times B and so I multiply both
+
+ align:start position:0%
+inverse times B and so I multiply both
+ 
+
+ align:start position:0%
+inverse times B and so I multiply both
+sides of this equation by W and I get X
+
+ align:start position:0%
+sides of this equation by W and I get X
+ 
+
+ align:start position:0%
+sides of this equation by W and I get X
+is W land inverse W inverse B okay so if
+
+ align:start position:0%
+is W land inverse W inverse B okay so if
+ 
+
+ align:start position:0%
+is W land inverse W inverse B okay so if
+I knew the eigenvalues and eigenvectors
+
+ align:start position:0%
+I knew the eigenvalues and eigenvectors
+ 
+
+ align:start position:0%
+I knew the eigenvalues and eigenvectors
+they can really easily solve a system of
+
+ align:start position:0%
+they can really easily solve a system of
+ 
+
+ align:start position:0%
+they can really easily solve a system of
+equations I did this decomposition right
+
+ align:start position:0%
+equations I did this decomposition right
+ 
+
+ align:start position:0%
+equations I did this decomposition right
+I could solve many systems of equations
+
+ align:start position:0%
+I could solve many systems of equations
+ 
+
+ align:start position:0%
+I could solve many systems of equations
+right they're simple to solve with just
+
+ align:start position:0%
+right they're simple to solve with just
+ 
+
+ align:start position:0%
+right they're simple to solve with just
+matrix matrix multiplication
+
+ align:start position:0%
+matrix matrix multiplication
+ 
+
+ align:start position:0%
+matrix matrix multiplication
+how is W inverse computed ok well W
+
+ align:start position:0%
+how is W inverse computed ok well W
+ 
+
+ align:start position:0%
+how is W inverse computed ok well W
+inverse transpose are actually the eigen
+
+ align:start position:0%
+inverse transpose are actually the eigen
+ 
+
+ align:start position:0%
+inverse transpose are actually the eigen
+vectors of a transpose you may have to
+
+ align:start position:0%
+vectors of a transpose you may have to
+ 
+
+ align:start position:0%
+vectors of a transpose you may have to
+compute this matrix explicitly but there
+
+ align:start position:0%
+compute this matrix explicitly but there
+ 
+
+ align:start position:0%
+compute this matrix explicitly but there
+are times when we deal with so-called
+
+ align:start position:0%
+are times when we deal with so-called
+ 
+
+ align:start position:0%
+are times when we deal with so-called
+symmetric matrices ones for which they
+
+ align:start position:0%
+symmetric matrices ones for which they
+ 
+
+ align:start position:0%
+symmetric matrices ones for which they
+are equal to their transpose and if
+
+ align:start position:0%
+are equal to their transpose and if
+ 
+
+ align:start position:0%
+are equal to their transpose and if
+that's the case and if you take all of
+
+ align:start position:0%
+that's the case and if you take all of
+ 
+
+ align:start position:0%
+that's the case and if you take all of
+your eigen vectors and you normalize
+
+ align:start position:0%
+your eigen vectors and you normalize
+ 
+
+ align:start position:0%
+your eigen vectors and you normalize
+them so they're of length 1
+
+ align:start position:0%
+them so they're of length 1
+ 
+
+ align:start position:0%
+them so they're of length 1
+Euclidean norm is one then it'll turn
+
+ align:start position:0%
+Euclidean norm is one then it'll turn
+ 
+
+ align:start position:0%
+Euclidean norm is one then it'll turn
+out the W inverse is precisely equal to
+
+ align:start position:0%
+out the W inverse is precisely equal to
+ 
+
+ align:start position:0%
+out the W inverse is precisely equal to
+W transpose right and so the eigenvalue
+
+ align:start position:0%
+W transpose right and so the eigenvalue
+ 
+
+ align:start position:0%
+W transpose right and so the eigenvalue
+matrix will be unitary you'll have this
+
+ align:start position:0%
+matrix will be unitary you'll have this
+ 
+
+ align:start position:0%
+matrix will be unitary you'll have this
+property where its transpose is its
+
+ align:start position:0%
+property where its transpose is its
+ 
+
+ align:start position:0%
+property where its transpose is its
+inverse so this becomes trivial to do
+
+ align:start position:0%
+inverse so this becomes trivial to do
+ 
+
+ align:start position:0%
+inverse so this becomes trivial to do
+then this process of W inverse not
+
+ align:start position:0%
+then this process of W inverse not
+ 
+
+ align:start position:0%
+then this process of W inverse not
+always true that this is the case right
+
+ align:start position:0%
+always true that this is the case right
+ 
+
+ align:start position:0%
+always true that this is the case right
+it is true when we deal with problems
+
+ align:start position:0%
+it is true when we deal with problems
+ 
+
+ align:start position:0%
+it is true when we deal with problems
+that have symmetric matrices associated
+
+ align:start position:0%
+that have symmetric matrices associated
+ 
+
+ align:start position:0%
+that have symmetric matrices associated
+with them it pops up in a lot of cases
+
+ align:start position:0%
+with them it pops up in a lot of cases
+ 
+
+ align:start position:0%
+with them it pops up in a lot of cases
+you can prove I might ask you to show
+
+ align:start position:0%
+you can prove I might ask you to show
+ 
+
+ align:start position:0%
+you can prove I might ask you to show
+this some time that the eigenvectors of
+
+ align:start position:0%
+this some time that the eigenvectors of
+ 
+
+ align:start position:0%
+this some time that the eigenvectors of
+the symmetric matrix are orthogonal okay
+
+ align:start position:0%
+the symmetric matrix are orthogonal okay
+ 
+
+ align:start position:0%
+the symmetric matrix are orthogonal okay
+that they satisfy this property that I
+
+ align:start position:0%
+that they satisfy this property that I
+ 
+
+ align:start position:0%
+that they satisfy this property that I
+take the dot product between two
+
+ align:start position:0%
+take the dot product between two
+ 
+
+ align:start position:0%
+take the dot product between two
+different eigenvectors and it'll be
+
+ align:start position:0%
+different eigenvectors and it'll be
+ 
+
+ align:start position:0%
+different eigenvectors and it'll be
+equal to zero unless those are the same
+
+ align:start position:0%
+equal to zero unless those are the same
+ 
+
+ align:start position:0%
+equal to zero unless those are the same
+eigen vector that's a property
+
+ align:start position:0%
+eigen vector that's a property
+ 
+
+ align:start position:0%
+eigen vector that's a property
+associated with symmetric matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're also useful when analyzing
+
+ align:start position:0%
+they're also useful when analyzing
+ 
+
+ align:start position:0%
+they're also useful when analyzing
+systems of ordinary differential
+
+ align:start position:0%
+systems of ordinary differential
+ 
+
+ align:start position:0%
+systems of ordinary differential
+equations so here I've got a
+
+ align:start position:0%
+equations so here I've got a
+ 
+
+ align:start position:0%
+equations so here I've got a
+differential equation write a vector X
+
+ align:start position:0%
+differential equation write a vector X
+ 
+
+ align:start position:0%
+differential equation write a vector X
+dot so the time derivative of X is equal
+
+ align:start position:0%
+dot so the time derivative of X is equal
+ 
+
+ align:start position:0%
+dot so the time derivative of X is equal
+to a times X and if I substitute write
+
+ align:start position:0%
+to a times X and if I substitute write
+ 
+
+ align:start position:0%
+to a times X and if I substitute write
+my eigen decomposition so W lambda W
+
+ align:start position:0%
+my eigen decomposition so W lambda W
+ 
+
+ align:start position:0%
+my eigen decomposition so W lambda W
+inverse and I defined a new unknown Y
+
+ align:start position:0%
+inverse and I defined a new unknown Y
+ 
+
+ align:start position:0%
+inverse and I defined a new unknown Y
+instead of X then I can diagonalize that
+
+ align:start position:0%
+instead of X then I can diagonalize that
+ 
+
+ align:start position:0%
+instead of X then I can diagonalize that
+system of equations so you see y dot is
+
+ align:start position:0%
+system of equations so you see y dot is
+ 
+
+ align:start position:0%
+system of equations so you see y dot is
+equal to lambda times y or each
+
+ align:start position:0%
+equal to lambda times y or each
+ 
+
+ align:start position:0%
+equal to lambda times y or each
+component of Y is decoupled from all of
+
+ align:start position:0%
+component of Y is decoupled from all of
+ 
+
+ align:start position:0%
+component of Y is decoupled from all of
+the others each of them satisfies their
+
+ align:start position:0%
+the others each of them satisfies their
+ 
+
+ align:start position:0%
+the others each of them satisfies their
+own ordinary differential equation
+
+ align:start position:0%
+own ordinary differential equation
+ 
+
+ align:start position:0%
+own ordinary differential equation
+that's not coupled to any of the others
+
+ align:start position:0%
+that's not coupled to any of the others
+ 
+
+ align:start position:0%
+that's not coupled to any of the others
+right and it has a simple first order
+
+ align:start position:0%
+right and it has a simple first order
+ 
+
+ align:start position:0%
+right and it has a simple first order
+rate constant which is the eigenvalue
+
+ align:start position:0%
+rate constant which is the eigenvalue
+ 
+
+ align:start position:0%
+rate constant which is the eigenvalue
+right associated with that particular
+
+ align:start position:0%
+right associated with that particular
+ 
+
+ align:start position:0%
+right associated with that particular
+eigen direction so this system of Odie's
+
+ align:start position:0%
+eigen direction so this system of Odie's
+ 
+
+ align:start position:0%
+eigen direction so this system of Odie's
+is decoupled and it's easy to solve you
+
+ align:start position:0%
+is decoupled and it's easy to solve you
+ 
+
+ align:start position:0%
+is decoupled and it's easy to solve you
+know the solution right it's an
+
+ align:start position:0%
+know the solution right it's an
+ 
+
+ align:start position:0%
+know the solution right it's an
+exponential and that can be quite handy
+
+ align:start position:0%
+exponential and that can be quite handy
+ 
+
+ align:start position:0%
+exponential and that can be quite handy
+when we're looking at different sorts of
+
+ align:start position:0%
+when we're looking at different sorts of
+ 
+
+ align:start position:0%
+when we're looking at different sorts of
+chemical rate processes that correspond
+
+ align:start position:0%
+chemical rate processes that correspond
+ 
+
+ align:start position:0%
+chemical rate processes that correspond
+to linear differential equations we'll
+
+ align:start position:0%
+to linear differential equations we'll
+ 
+
+ align:start position:0%
+to linear differential equations we'll
+talk about nonlinear systems and
+
+ align:start position:0%
+talk about nonlinear systems and
+ 
+
+ align:start position:0%
+talk about nonlinear systems and
+nonlinear differential equations later
+
+ align:start position:0%
+nonlinear differential equations later
+ 
+
+ align:start position:0%
+nonlinear differential equations later
+in this term and you'll find out that
+
+ align:start position:0%
+in this term and you'll find out that
+ 
+
+ align:start position:0%
+in this term and you'll find out that
+this same sort of analysis can be quite
+
+ align:start position:0%
+this same sort of analysis can be quite
+ 
+
+ align:start position:0%
+this same sort of analysis can be quite
+useful there
+
+ align:start position:0%
+useful there
+ 
+
+ align:start position:0%
+useful there
+so will linearize those equations and
+
+ align:start position:0%
+so will linearize those equations and
+ 
+
+ align:start position:0%
+so will linearize those equations and
+will ask it sir linear in their
+
+ align:start position:0%
+will ask it sir linear in their
+ 
+
+ align:start position:0%
+will ask it sir linear in their
+linearized form what are these different
+
+ align:start position:0%
+linearized form what are these different
+ 
+
+ align:start position:0%
+linearized form what are these different
+rate constants how big are they
+
+ align:start position:0%
+rate constants how big are they
+ 
+
+ align:start position:0%
+rate constants how big are they
+they might determine what we need to do
+
+ align:start position:0%
+they might determine what we need to do
+ 
+
+ align:start position:0%
+they might determine what we need to do
+in order to integrate those equations
+
+ align:start position:0%
+in order to integrate those equations
+ 
+
+ align:start position:0%
+in order to integrate those equations
+numerically there's there many times
+
+ align:start position:0%
+numerically there's there many times
+ 
+
+ align:start position:0%
+numerically there's there many times
+when there's not a complete set of
+
+ align:start position:0%
+when there's not a complete set of
+ 
+
+ align:start position:0%
+when there's not a complete set of
+eigenvectors okay that happens and then
+
+ align:start position:0%
+eigenvectors okay that happens and then
+ 
+
+ align:start position:0%
+eigenvectors okay that happens and then
+the matrix can't be diagonalized in this
+
+ align:start position:0%
+the matrix can't be diagonalized in this
+ 
+
+ align:start position:0%
+the matrix can't be diagonalized in this
+way there's some components that can't
+
+ align:start position:0%
+way there's some components that can't
+ 
+
+ align:start position:0%
+way there's some components that can't
+be decoupled from each other that's what
+
+ align:start position:0%
+be decoupled from each other that's what
+ 
+
+ align:start position:0%
+be decoupled from each other that's what
+this diagonalization does right it
+
+ align:start position:0%
+this diagonalization does right it
+ 
+
+ align:start position:0%
+this diagonalization does right it
+splits up these different stretching
+
+ align:start position:0%
+splits up these different stretching
+ 
+
+ align:start position:0%
+splits up these different stretching
+directions from each other but there's
+
+ align:start position:0%
+directions from each other but there's
+ 
+
+ align:start position:0%
+directions from each other but there's
+some directions that can't be decoupled
+
+ align:start position:0%
+some directions that can't be decoupled
+ 
+
+ align:start position:0%
+some directions that can't be decoupled
+from each other anymore and then there
+
+ align:start position:0%
+from each other anymore and then there
+ 
+
+ align:start position:0%
+from each other anymore and then there
+are other transformations one can do so
+
+ align:start position:0%
+are other transformations one can do so
+ 
+
+ align:start position:0%
+are other transformations one can do so
+there's an almost diagonal form that you
+
+ align:start position:0%
+there's an almost diagonal form that you
+ 
+
+ align:start position:0%
+there's an almost diagonal form that you
+can transform into called the Jordan
+
+ align:start position:0%
+can transform into called the Jordan
+ 
+
+ align:start position:0%
+can transform into called the Jordan
+normal form okay there are other
+
+ align:start position:0%
+normal form okay there are other
+ 
+
+ align:start position:0%
+normal form okay there are other
+transformations that one can do like
+
+ align:start position:0%
+transformations that one can do like
+ 
+
+ align:start position:0%
+transformations that one can do like
+called for example sure decomposition
+
+ align:start position:0%
+called for example sure decomposition
+ 
+
+ align:start position:0%
+called for example sure decomposition
+which is a transformation into an upper
+
+ align:start position:0%
+which is a transformation into an upper
+ 
+
+ align:start position:0%
+which is a transformation into an upper
+triangular form for this matrix we'll
+
+ align:start position:0%
+triangular form for this matrix we'll
+ 
+
+ align:start position:0%
+triangular form for this matrix we'll
+talk next time about the singular value
+
+ align:start position:0%
+talk next time about the singular value
+ 
+
+ align:start position:0%
+talk next time about the singular value
+decomposition right which is another
+
+ align:start position:0%
+decomposition right which is another
+ 
+
+ align:start position:0%
+decomposition right which is another
+sort of transformation one can do when
+
+ align:start position:0%
+sort of transformation one can do when
+ 
+
+ align:start position:0%
+sort of transformation one can do when
+we don't have these complete sets of
+
+ align:start position:0%
+we don't have these complete sets of
+ 
+
+ align:start position:0%
+we don't have these complete sets of
+eigenvectors but this concludes our
+
+ align:start position:0%
+eigenvectors but this concludes our
+ 
+
+ align:start position:0%
+eigenvectors but this concludes our
+discussion of eigenvalues and
+
+ align:start position:0%
+discussion of eigenvalues and
+ 
+
+ align:start position:0%
+discussion of eigenvalues and
+eigenvectors you'll get a chance to
+
+ align:start position:0%
+eigenvectors you'll get a chance to
+ 
+
+ align:start position:0%
+eigenvectors you'll get a chance to
+practice these things on your next two
+
+ align:start position:0%
+practice these things on your next two
+ 
+
+ align:start position:0%
+practice these things on your next two
+homework assignments actually so it'll
+
+ align:start position:0%
+homework assignments actually so it'll
+ 
+
+ align:start position:0%
+homework assignments actually so it'll
+it'll come up in a couple of different
+
+ align:start position:0%
+it'll come up in a couple of different
+ 
+
+ align:start position:0%
+it'll come up in a couple of different
+circumstances I would really encourage
+
+ align:start position:0%
+circumstances I would really encourage
+ 
+
+ align:start position:0%
+circumstances I would really encourage
+you to try to try to solve some of these
+
+ align:start position:0%
+you to try to try to solve some of these
+ 
+
+ align:start position:0%
+you to try to try to solve some of these
+example problems that were in here right
+
+ align:start position:0%
+example problems that were in here right
+ 
+
+ align:start position:0%
+example problems that were in here right
+solving by hand can be useful make sure
+
+ align:start position:0%
+solving by hand can be useful make sure
+ 
+
+ align:start position:0%
+solving by hand can be useful make sure
+you can work through the steps and
+
+ align:start position:0%
+you can work through the steps and
+ 
+
+ align:start position:0%
+you can work through the steps and
+understand where these different where
+
+ align:start position:0%
+understand where these different where
+ 
+
+ align:start position:0%
+understand where these different where
+these different concepts come into play
+
+ align:start position:0%
+these different concepts come into play
+ 
+
+ align:start position:0%
+these different concepts come into play
+in terms of determining what the
+
+ align:start position:0%
+in terms of determining what the
+ 
+
+ align:start position:0%
+in terms of determining what the
+eigenvalues and eigenvectors are all
+
+ align:start position:0%
+eigenvalues and eigenvectors are all
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors are all
+right have a great weekend see on Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/uHUA6M1OEwk.txt b/uHUA6M1OEwk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4070434db6b4be83b8faec801a5d6bd96978e052
--- /dev/null
+++ b/uHUA6M1OEwk.txt
@@ -0,0 +1,15851 @@
+align:start position:0%
+ 
+welcome back to fintech shaping the
+
+ align:start position:0%
+welcome back to fintech shaping the
+ 
+
+ align:start position:0%
+welcome back to fintech shaping the
+world of finance today we're going to
+
+ align:start position:0%
+world of finance today we're going to
+ 
+
+ align:start position:0%
+world of finance today we're going to
+review
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+developments in finance and technology
+
+ align:start position:0%
+developments in finance and technology
+ 
+
+ align:start position:0%
+developments in finance and technology
+related to capital markets and since
+
+ align:start position:0%
+related to capital markets and since
+ 
+
+ align:start position:0%
+related to capital markets and since
+there's so many pieces of capital
+
+ align:start position:0%
+there's so many pieces of capital
+ 
+
+ align:start position:0%
+there's so many pieces of capital
+markets i've chosen to take the time to
+
+ align:start position:0%
+markets i've chosen to take the time to
+ 
+
+ align:start position:0%
+markets i've chosen to take the time to
+dig more deeply into two areas
+
+ align:start position:0%
+dig more deeply into two areas
+ 
+
+ align:start position:0%
+dig more deeply into two areas
+online brokerage or really mobile
+
+ align:start position:0%
+online brokerage or really mobile
+ 
+
+ align:start position:0%
+online brokerage or really mobile
+brokerage applications
+
+ align:start position:0%
+brokerage applications
+ 
+
+ align:start position:0%
+brokerage applications
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+wealth advising through robo advising
+
+ align:start position:0%
+wealth advising through robo advising
+ 
+
+ align:start position:0%
+wealth advising through robo advising
+but we'll touch upon
+
+ align:start position:0%
+but we'll touch upon
+ 
+
+ align:start position:0%
+but we'll touch upon
+the broader capital markets
+
+ align:start position:0%
+the broader capital markets
+ 
+
+ align:start position:0%
+the broader capital markets
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+as a little touch on crypto currencies
+
+ align:start position:0%
+as a little touch on crypto currencies
+ 
+
+ align:start position:0%
+as a little touch on crypto currencies
+because some of the most successful
+
+ align:start position:0%
+because some of the most successful
+ 
+
+ align:start position:0%
+because some of the most successful
+financial technology companies
+
+ align:start position:0%
+financial technology companies
+ 
+
+ align:start position:0%
+financial technology companies
+in the capital markets have actually
+
+ align:start position:0%
+in the capital markets have actually
+ 
+
+ align:start position:0%
+in the capital markets have actually
+been crypto exchanges in some of the
+
+ align:start position:0%
+been crypto exchanges in some of the
+ 
+
+ align:start position:0%
+been crypto exchanges in some of the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+endeavors around crypto markets
+
+ align:start position:0%
+endeavors around crypto markets
+ 
+
+ align:start position:0%
+endeavors around crypto markets
+so if i just take a moment just to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+share share my screen and share some
+
+ align:start position:0%
+share share my screen and share some
+ 
+
+ align:start position:0%
+share share my screen and share some
+slides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll uh
+
+ align:start position:0%
+and we'll uh
+ 
+
+ align:start position:0%
+and we'll uh
+we'll get going here um online brokerage
+
+ align:start position:0%
+we'll get going here um online brokerage
+ 
+
+ align:start position:0%
+we'll get going here um online brokerage
+this is not a new tradition it goes back
+
+ align:start position:0%
+this is not a new tradition it goes back
+ 
+
+ align:start position:0%
+this is not a new tradition it goes back
+actually several decades
+
+ align:start position:0%
+actually several decades
+ 
+
+ align:start position:0%
+actually several decades
+and so then the question is sort of
+
+ align:start position:0%
+and so then the question is sort of
+ 
+
+ align:start position:0%
+and so then the question is sort of
+what's happened here in the last six or
+
+ align:start position:0%
+what's happened here in the last six or
+ 
+
+ align:start position:0%
+what's happened here in the last six or
+eight years what's happened that this
+
+ align:start position:0%
+eight years what's happened that this
+ 
+
+ align:start position:0%
+eight years what's happened that this
+startup robin hood and others have
+
+ align:start position:0%
+startup robin hood and others have
+ 
+
+ align:start position:0%
+startup robin hood and others have
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+just toppled over the last remaining
+
+ align:start position:0%
+just toppled over the last remaining
+ 
+
+ align:start position:0%
+just toppled over the last remaining
+bits of of the commission structure
+
+ align:start position:0%
+bits of of the commission structure
+ 
+
+ align:start position:0%
+bits of of the commission structure
+that we've had
+
+ align:start position:0%
+that we've had
+ 
+
+ align:start position:0%
+that we've had
+robo advising and then capital markets
+
+ align:start position:0%
+robo advising and then capital markets
+ 
+
+ align:start position:0%
+robo advising and then capital markets
+fintech startups more generally we'll
+
+ align:start position:0%
+fintech startups more generally we'll
+ 
+
+ align:start position:0%
+fintech startups more generally we'll
+we'll have to do a quick survey there
+
+ align:start position:0%
+we'll have to do a quick survey there
+ 
+
+ align:start position:0%
+we'll have to do a quick survey there
+and then a little discussion of what's
+
+ align:start position:0%
+and then a little discussion of what's
+ 
+
+ align:start position:0%
+and then a little discussion of what's
+happening in crypto exchanges and
+
+ align:start position:0%
+happening in crypto exchanges and
+ 
+
+ align:start position:0%
+happening in crypto exchanges and
+decentralized finance because it's
+
+ align:start position:0%
+decentralized finance because it's
+ 
+
+ align:start position:0%
+decentralized finance because it's
+really the question will that will that
+
+ align:start position:0%
+really the question will that will that
+ 
+
+ align:start position:0%
+really the question will that will that
+actually transform finance or will it
+
+ align:start position:0%
+actually transform finance or will it
+ 
+
+ align:start position:0%
+actually transform finance or will it
+stay as it is right now a more narrow
+
+ align:start position:0%
+stay as it is right now a more narrow
+ 
+
+ align:start position:0%
+stay as it is right now a more narrow
+niche though still a 200 billion dollar
+
+ align:start position:0%
+niche though still a 200 billion dollar
+ 
+
+ align:start position:0%
+niche though still a 200 billion dollar
+asset class
+
+ align:start position:0%
+asset class
+ 
+
+ align:start position:0%
+asset class
+environment but will some of those
+
+ align:start position:0%
+environment but will some of those
+ 
+
+ align:start position:0%
+environment but will some of those
+technologies come into
+
+ align:start position:0%
+technologies come into
+ 
+
+ align:start position:0%
+technologies come into
+mainstream finance
+
+ align:start position:0%
+mainstream finance
+ 
+
+ align:start position:0%
+mainstream finance
+so the readings again were mostly
+
+ align:start position:0%
+so the readings again were mostly
+ 
+
+ align:start position:0%
+so the readings again were mostly
+focused around those two areas robo
+
+ align:start position:0%
+focused around those two areas robo
+ 
+
+ align:start position:0%
+focused around those two areas robo
+advising and online brokerage and how
+
+ align:start position:0%
+advising and online brokerage and how
+ 
+
+ align:start position:0%
+advising and online brokerage and how
+robinhood has transformed the industry
+
+ align:start position:0%
+robinhood has transformed the industry
+ 
+
+ align:start position:0%
+robinhood has transformed the industry
+and how charles schwab and others
+
+ align:start position:0%
+and how charles schwab and others
+ 
+
+ align:start position:0%
+and how charles schwab and others
+entered into by the late part of 2019
+
+ align:start position:0%
+entered into by the late part of 2019
+ 
+
+ align:start position:0%
+entered into by the late part of 2019
+what's some call the new broker wars in
+
+ align:start position:0%
+what's some call the new broker wars in
+ 
+
+ align:start position:0%
+what's some call the new broker wars in
+part because of this financial
+
+ align:start position:0%
+part because of this financial
+ 
+
+ align:start position:0%
+part because of this financial
+technology along the way
+
+ align:start position:0%
+technology along the way
+ 
+
+ align:start position:0%
+technology along the way
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so just some uh uh lively questions but
+
+ align:start position:0%
+so just some uh uh lively questions but
+ 
+
+ align:start position:0%
+so just some uh uh lively questions but
+a way to get us going here and hopefully
+
+ align:start position:0%
+a way to get us going here and hopefully
+ 
+
+ align:start position:0%
+a way to get us going here and hopefully
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+somebody wants to chime in
+
+ align:start position:0%
+somebody wants to chime in
+ 
+
+ align:start position:0%
+somebody wants to chime in
+how did online brokers emerge
+
+ align:start position:0%
+how did online brokers emerge
+ 
+
+ align:start position:0%
+how did online brokers emerge
+during an earlier fintech development
+
+ align:start position:0%
+during an earlier fintech development
+ 
+
+ align:start position:0%
+during an earlier fintech development
+period during the
+
+ align:start position:0%
+period during the
+ 
+
+ align:start position:0%
+period during the
+80s 90s that sort of internet
+
+ align:start position:0%
+80s 90s that sort of internet
+ 
+
+ align:start position:0%
+80s 90s that sort of internet
+technology fintech technology area
+
+ align:start position:0%
+technology fintech technology area
+ 
+
+ align:start position:0%
+technology fintech technology area
+and then how robin hood's transformed
+
+ align:start position:0%
+and then how robin hood's transformed
+ 
+
+ align:start position:0%
+and then how robin hood's transformed
+maybe this more recent era um
+
+ align:start position:0%
+maybe this more recent era um
+ 
+
+ align:start position:0%
+maybe this more recent era um
+romaine does anybody want to
+
+ align:start position:0%
+romaine does anybody want to
+ 
+
+ align:start position:0%
+romaine does anybody want to
+dive in at all
+
+ align:start position:0%
+dive in at all
+ 
+
+ align:start position:0%
+dive in at all
+let's see who will be the first
+
+ align:start position:0%
+let's see who will be the first
+ 
+
+ align:start position:0%
+let's see who will be the first
+volunteer today
+
+ align:start position:0%
+volunteer today
+ 
+
+ align:start position:0%
+volunteer today
+i mean everybody will we'll be talking
+
+ align:start position:0%
+i mean everybody will we'll be talking
+ 
+
+ align:start position:0%
+i mean everybody will we'll be talking
+about this for the whole class but i
+
+ align:start position:0%
+about this for the whole class but i
+ 
+
+ align:start position:0%
+about this for the whole class but i
+just if anybody wants to sort of offer
+
+ align:start position:0%
+just if anybody wants to sort of offer
+ 
+
+ align:start position:0%
+just if anybody wants to sort of offer
+their thoughts to start and we have
+
+ align:start position:0%
+their thoughts to start and we have
+ 
+
+ align:start position:0%
+their thoughts to start and we have
+michael
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so when i think the earlier than
+
+ align:start position:0%
+yeah so when i think the earlier than
+ 
+
+ align:start position:0%
+yeah so when i think the earlier than
+tech stars i think just
+
+ align:start position:0%
+tech stars i think just
+ 
+
+ align:start position:0%
+tech stars i think just
+taking advantage of the internet i'm
+
+ align:start position:0%
+taking advantage of the internet i'm
+ 
+
+ align:start position:0%
+taking advantage of the internet i'm
+thinking kind of
+
+ align:start position:0%
+thinking kind of
+ 
+
+ align:start position:0%
+thinking kind of
+like paypal just
+
+ align:start position:0%
+like paypal just
+ 
+
+ align:start position:0%
+like paypal just
+ways you can do online payments and
+
+ align:start position:0%
+ways you can do online payments and
+ 
+
+ align:start position:0%
+ways you can do online payments and
+online interfaces for
+
+ align:start position:0%
+online interfaces for
+ 
+
+ align:start position:0%
+online interfaces for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+are not sorry not island broke or
+
+ align:start position:0%
+are not sorry not island broke or
+ 
+
+ align:start position:0%
+are not sorry not island broke or
+something uh
+
+ align:start position:0%
+something uh
+ 
+
+ align:start position:0%
+something uh
+e-trade but ways to make it without
+
+ align:start position:0%
+e-trade but ways to make it without
+ 
+
+ align:start position:0%
+e-trade but ways to make it without
+having to call somebody on the phone
+
+ align:start position:0%
+having to call somebody on the phone
+ 
+
+ align:start position:0%
+having to call somebody on the phone
+um i guess it was probably more
+
+ align:start position:0%
+um i guess it was probably more
+ 
+
+ align:start position:0%
+um i guess it was probably more
+inaccessible when you actually had to
+
+ align:start position:0%
+inaccessible when you actually had to
+ 
+
+ align:start position:0%
+inaccessible when you actually had to
+interact with the broker directly or in
+
+ align:start position:0%
+interact with the broker directly or in
+ 
+
+ align:start position:0%
+interact with the broker directly or in
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+robin hood
+
+ align:start position:0%
+robin hood
+ 
+
+ align:start position:0%
+robin hood
+definitely was more starting to take the
+
+ align:start position:0%
+definitely was more starting to take the
+ 
+
+ align:start position:0%
+definitely was more starting to take the
+mobile first approach starting detective
+
+ align:start position:0%
+mobile first approach starting detective
+ 
+
+ align:start position:0%
+mobile first approach starting detective
+weaknesses of
+
+ align:start position:0%
+weaknesses of
+ 
+
+ align:start position:0%
+weaknesses of
+the larger platforms such as user
+
+ align:start position:0%
+the larger platforms such as user
+ 
+
+ align:start position:0%
+the larger platforms such as user
+interface make it more accessible for
+
+ align:start position:0%
+interface make it more accessible for
+ 
+
+ align:start position:0%
+interface make it more accessible for
+somebody to really just
+
+ align:start position:0%
+somebody to really just
+ 
+
+ align:start position:0%
+somebody to really just
+uh trade from anywhere and then also the
+
+ align:start position:0%
+uh trade from anywhere and then also the
+ 
+
+ align:start position:0%
+uh trade from anywhere and then also the
+fee structure was a huge part of that
+
+ align:start position:0%
+fee structure was a huge part of that
+ 
+
+ align:start position:0%
+fee structure was a huge part of that
+too for trading
+
+ align:start position:0%
+too for trading
+ 
+
+ align:start position:0%
+too for trading
+yeah but i'm glad i'm actually glad
+
+ align:start position:0%
+yeah but i'm glad i'm actually glad
+ 
+
+ align:start position:0%
+yeah but i'm glad i'm actually glad
+michael raised paypal because there's
+
+ align:start position:0%
+michael raised paypal because there's
+ 
+
+ align:start position:0%
+michael raised paypal because there's
+analogies and that's what this class is
+
+ align:start position:0%
+analogies and that's what this class is
+ 
+
+ align:start position:0%
+analogies and that's what this class is
+really about it's finding what's
+
+ align:start position:0%
+really about it's finding what's
+ 
+
+ align:start position:0%
+really about it's finding what's
+happening from a strategic point of view
+
+ align:start position:0%
+happening from a strategic point of view
+ 
+
+ align:start position:0%
+happening from a strategic point of view
+i mean we're teaching finance technology
+
+ align:start position:0%
+i mean we're teaching finance technology
+ 
+
+ align:start position:0%
+i mean we're teaching finance technology
+the intersection but about the
+
+ align:start position:0%
+the intersection but about the
+ 
+
+ align:start position:0%
+the intersection but about the
+strategies and there's a lot of parallel
+
+ align:start position:0%
+strategies and there's a lot of parallel
+ 
+
+ align:start position:0%
+strategies and there's a lot of parallel
+there we were in the 1990s
+
+ align:start position:0%
+there we were in the 1990s
+ 
+
+ align:start position:0%
+there we were in the 1990s
+some of it even started a little earlier
+
+ align:start position:0%
+some of it even started a little earlier
+ 
+
+ align:start position:0%
+some of it even started a little earlier
+and online brokerage started e-trade
+
+ align:start position:0%
+and online brokerage started e-trade
+ 
+
+ align:start position:0%
+and online brokerage started e-trade
+ameritrade we will dive into a number of
+
+ align:start position:0%
+ameritrade we will dive into a number of
+ 
+
+ align:start position:0%
+ameritrade we will dive into a number of
+these companies similar to paypal
+
+ align:start position:0%
+these companies similar to paypal
+ 
+
+ align:start position:0%
+these companies similar to paypal
+starting in 1998 so i thank you michael
+
+ align:start position:0%
+starting in 1998 so i thank you michael
+ 
+
+ align:start position:0%
+starting in 1998 so i thank you michael
+for pulling that together
+
+ align:start position:0%
+for pulling that together
+ 
+
+ align:start position:0%
+for pulling that together
+paypal starting in 1998 that earlier
+
+ align:start position:0%
+paypal starting in 1998 that earlier
+ 
+
+ align:start position:0%
+paypal starting in 1998 that earlier
+wave the internet
+
+ align:start position:0%
+wave the internet
+ 
+
+ align:start position:0%
+wave the internet
+access
+
+ align:start position:0%
+access
+ 
+
+ align:start position:0%
+access
+rather than through bricks and mortar or
+
+ align:start position:0%
+rather than through bricks and mortar or
+ 
+
+ align:start position:0%
+rather than through bricks and mortar or
+physical checks or an old credit card
+
+ align:start position:0%
+physical checks or an old credit card
+ 
+
+ align:start position:0%
+physical checks or an old credit card
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+vis-a-vis the payment systems and paypal
+
+ align:start position:0%
+vis-a-vis the payment systems and paypal
+ 
+
+ align:start position:0%
+vis-a-vis the payment systems and paypal
+online brokerage starts emerges does it
+
+ align:start position:0%
+online brokerage starts emerges does it
+ 
+
+ align:start position:0%
+online brokerage starts emerges does it
+does it take off not entirely but over
+
+ align:start position:0%
+does it take off not entirely but over
+ 
+
+ align:start position:0%
+does it take off not entirely but over
+time it's a big story in the capital
+
+ align:start position:0%
+time it's a big story in the capital
+ 
+
+ align:start position:0%
+time it's a big story in the capital
+markets especially retail investing
+
+ align:start position:0%
+markets especially retail investing
+ 
+
+ align:start position:0%
+markets especially retail investing
+and then we get to this other period a
+
+ align:start position:0%
+and then we get to this other period a
+ 
+
+ align:start position:0%
+and then we get to this other period a
+new form of technology largely about
+
+ align:start position:0%
+new form of technology largely about
+ 
+
+ align:start position:0%
+new form of technology largely about
+mobile phones but not entirely about
+
+ align:start position:0%
+mobile phones but not entirely about
+ 
+
+ align:start position:0%
+mobile phones but not entirely about
+mobile phones also related to open api
+
+ align:start position:0%
+mobile phones also related to open api
+ 
+
+ align:start position:0%
+mobile phones also related to open api
+and access to the data
+
+ align:start position:0%
+and access to the data
+ 
+
+ align:start position:0%
+and access to the data
+robinhood comes along and also in the
+
+ align:start position:0%
+robinhood comes along and also in the
+ 
+
+ align:start position:0%
+robinhood comes along and also in the
+payment area we've talked about this
+
+ align:start position:0%
+payment area we've talked about this
+ 
+
+ align:start position:0%
+payment area we've talked about this
+already a few classes ago a lot of these
+
+ align:start position:0%
+already a few classes ago a lot of these
+ 
+
+ align:start position:0%
+already a few classes ago a lot of these
+payment startups
+
+ align:start position:0%
+payment startups
+ 
+
+ align:start position:0%
+payment startups
+and robinhood gen
+
+ align:start position:0%
+and robinhood gen
+ 
+
+ align:start position:0%
+and robinhood gen
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+further transforms
+
+ align:start position:0%
+further transforms
+ 
+
+ align:start position:0%
+further transforms
+in industry
+
+ align:start position:0%
+in industry
+ 
+
+ align:start position:0%
+in industry
+and by night and by 2019 robin hood had
+
+ align:start position:0%
+and by night and by 2019 robin hood had
+ 
+
+ align:start position:0%
+and by night and by 2019 robin hood had
+almost as many members online through
+
+ align:start position:0%
+almost as many members online through
+ 
+
+ align:start position:0%
+almost as many members online through
+their mobile app with just a handful of
+
+ align:start position:0%
+their mobile app with just a handful of
+ 
+
+ align:start position:0%
+their mobile app with just a handful of
+years as e-trade
+
+ align:start position:0%
+years as e-trade
+ 
+
+ align:start position:0%
+years as e-trade
+or many of the brokerage firms
+
+ align:start position:0%
+or many of the brokerage firms
+ 
+
+ align:start position:0%
+or many of the brokerage firms
+so it's it's it's got that parallels and
+
+ align:start position:0%
+so it's it's it's got that parallels and
+ 
+
+ align:start position:0%
+so it's it's it's got that parallels and
+we're going to dive into how robinhood
+
+ align:start position:0%
+we're going to dive into how robinhood
+ 
+
+ align:start position:0%
+we're going to dive into how robinhood
+pressed further
+
+ align:start position:0%
+pressed further
+ 
+
+ align:start position:0%
+pressed further
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and i'm wondering michael do you have a
+
+ align:start position:0%
+and i'm wondering michael do you have a
+ 
+
+ align:start position:0%
+and i'm wondering michael do you have a
+robinhood account
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah but i haven't really used this
+
+ align:start position:0%
+yeah but i haven't really used this
+ 
+
+ align:start position:0%
+yeah but i haven't really used this
+since i started paying them
+
+ align:start position:0%
+since i started paying them
+ 
+
+ align:start position:0%
+since i started paying them
+oh no no i understand why you might not
+
+ align:start position:0%
+oh no no i understand why you might not
+ 
+
+ align:start position:0%
+oh no no i understand why you might not
+be investing while you're at school and
+
+ align:start position:0%
+be investing while you're at school and
+ 
+
+ align:start position:0%
+be investing while you're at school and
+why you might not have the money to do
+
+ align:start position:0%
+why you might not have the money to do
+ 
+
+ align:start position:0%
+why you might not have the money to do
+it but you actually have a robinhood
+
+ align:start position:0%
+it but you actually have a robinhood
+ 
+
+ align:start position:0%
+it but you actually have a robinhood
+account uh and while it's hard to
+
+ align:start position:0%
+account uh and while it's hard to
+ 
+
+ align:start position:0%
+account uh and while it's hard to
+do it by a show of hands but i imagine
+
+ align:start position:0%
+do it by a show of hands but i imagine
+ 
+
+ align:start position:0%
+do it by a show of hands but i imagine
+that many other students in the class
+
+ align:start position:0%
+that many other students in the class
+ 
+
+ align:start position:0%
+that many other students in the class
+have downloaded the app
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then a little bit different area that
+
+ align:start position:0%
+so then a little bit different area that
+ 
+
+ align:start position:0%
+so then a little bit different area that
+we're going to be chatting about is robo
+
+ align:start position:0%
+we're going to be chatting about is robo
+ 
+
+ align:start position:0%
+we're going to be chatting about is robo
+advising
+
+ align:start position:0%
+advising
+ 
+
+ align:start position:0%
+advising
+how has that transformed the provision
+
+ align:start position:0%
+how has that transformed the provision
+ 
+
+ align:start position:0%
+how has that transformed the provision
+of retail investment management and how
+
+ align:start position:0%
+of retail investment management and how
+ 
+
+ align:start position:0%
+of retail investment management and how
+has big finance reacted and i'm
+
+ align:start position:0%
+has big finance reacted and i'm
+ 
+
+ align:start position:0%
+has big finance reacted and i'm
+wondering
+
+ align:start position:0%
+wondering
+ 
+
+ align:start position:0%
+wondering
+if romain if anybody wants to just take
+
+ align:start position:0%
+if romain if anybody wants to just take
+ 
+
+ align:start position:0%
+if romain if anybody wants to just take
+a a high-level
+
+ align:start position:0%
+a a high-level
+ 
+
+ align:start position:0%
+a a high-level
+hit at that i hope so we had great
+
+ align:start position:0%
+hit at that i hope so we had great
+ 
+
+ align:start position:0%
+hit at that i hope so we had great
+papers on the topic
+
+ align:start position:0%
+papers on the topic
+ 
+
+ align:start position:0%
+papers on the topic
+any volunteers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wei
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh sure so um i guess from the robot
+
+ align:start position:0%
+uh sure so um i guess from the robot
+ 
+
+ align:start position:0%
+uh sure so um i guess from the robot
+advisor perspective is sort of uh i
+
+ align:start position:0%
+advisor perspective is sort of uh i
+ 
+
+ align:start position:0%
+advisor perspective is sort of uh i
+personally feel um a help to transform
+
+ align:start position:0%
+personally feel um a help to transform
+ 
+
+ align:start position:0%
+personally feel um a help to transform
+people's behavior from like you know
+
+ align:start position:0%
+people's behavior from like you know
+ 
+
+ align:start position:0%
+people's behavior from like you know
+going to some kind of financial advisors
+
+ align:start position:0%
+going to some kind of financial advisors
+ 
+
+ align:start position:0%
+going to some kind of financial advisors
+to actually you know going through more
+
+ align:start position:0%
+to actually you know going through more
+ 
+
+ align:start position:0%
+to actually you know going through more
+like electronic platforms um whereas um
+
+ align:start position:0%
+like electronic platforms um whereas um
+ 
+
+ align:start position:0%
+like electronic platforms um whereas um
+you know traditionally
+
+ align:start position:0%
+you know traditionally
+ 
+
+ align:start position:0%
+you know traditionally
+especially for maybe on the younger
+
+ align:start position:0%
+especially for maybe on the younger
+ 
+
+ align:start position:0%
+especially for maybe on the younger
+generations who are a lot more used to
+
+ align:start position:0%
+generations who are a lot more used to
+ 
+
+ align:start position:0%
+generations who are a lot more used to
+like doing things online i think global
+
+ align:start position:0%
+like doing things online i think global
+ 
+
+ align:start position:0%
+like doing things online i think global
+advisors provide them a new way to um to
+
+ align:start position:0%
+advisors provide them a new way to um to
+ 
+
+ align:start position:0%
+advisors provide them a new way to um to
+construct their
+
+ align:start position:0%
+construct their
+ 
+
+ align:start position:0%
+construct their
+financial portfolios rather than going
+
+ align:start position:0%
+financial portfolios rather than going
+ 
+
+ align:start position:0%
+financial portfolios rather than going
+to financial advisor so
+
+ align:start position:0%
+to financial advisor so
+ 
+
+ align:start position:0%
+to financial advisor so
+it's definitely um
+
+ align:start position:0%
+it's definitely um
+ 
+
+ align:start position:0%
+it's definitely um
+feeling like
+
+ align:start position:0%
+feeling like
+ 
+
+ align:start position:0%
+feeling like
+um it's gonna take advice out of the
+
+ align:start position:0%
+um it's gonna take advice out of the
+ 
+
+ align:start position:0%
+um it's gonna take advice out of the
+existing financial advisors um which are
+
+ align:start position:0%
+existing financial advisors um which are
+ 
+
+ align:start position:0%
+existing financial advisors um which are
+probably where we're talking about from
+
+ align:start position:0%
+probably where we're talking about from
+ 
+
+ align:start position:0%
+probably where we're talking about from
+the retail asset manager perspective
+
+ align:start position:0%
+the retail asset manager perspective
+ 
+
+ align:start position:0%
+the retail asset manager perspective
+some of them are trying to i feel like
+
+ align:start position:0%
+some of them are trying to i feel like
+ 
+
+ align:start position:0%
+some of them are trying to i feel like
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+emerge or create new platforms or either
+
+ align:start position:0%
+emerge or create new platforms or either
+ 
+
+ align:start position:0%
+emerge or create new platforms or either
+you know buying some of the existing
+
+ align:start position:0%
+you know buying some of the existing
+ 
+
+ align:start position:0%
+you know buying some of the existing
+platforms or um kind of like having some
+
+ align:start position:0%
+platforms or um kind of like having some
+ 
+
+ align:start position:0%
+platforms or um kind of like having some
+kind of interaction with them so uh the
+
+ align:start position:0%
+kind of interaction with them so uh the
+ 
+
+ align:start position:0%
+kind of interaction with them so uh the
+existing uh the asset managers are
+
+ align:start position:0%
+existing uh the asset managers are
+ 
+
+ align:start position:0%
+existing uh the asset managers are
+definitely i feel like um looking more
+
+ align:start position:0%
+definitely i feel like um looking more
+ 
+
+ align:start position:0%
+definitely i feel like um looking more
+into how to incorporate more like um
+
+ align:start position:0%
+into how to incorporate more like um
+ 
+
+ align:start position:0%
+into how to incorporate more like um
+tools um to sort of compete with robot
+
+ align:start position:0%
+tools um to sort of compete with robot
+ 
+
+ align:start position:0%
+tools um to sort of compete with robot
+advisors right so
+
+ align:start position:0%
+advisors right so
+ 
+
+ align:start position:0%
+advisors right so
+robo advising the ability to have
+
+ align:start position:0%
+robo advising the ability to have
+ 
+
+ align:start position:0%
+robo advising the ability to have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+an application on your laptop or on your
+
+ align:start position:0%
+an application on your laptop or on your
+ 
+
+ align:start position:0%
+an application on your laptop or on your
+phones of course
+
+ align:start position:0%
+phones of course
+ 
+
+ align:start position:0%
+phones of course
+uh robo advising having an application
+
+ align:start position:0%
+uh robo advising having an application
+ 
+
+ align:start position:0%
+uh robo advising having an application
+rather than having a human but having
+
+ align:start position:0%
+rather than having a human but having
+ 
+
+ align:start position:0%
+rather than having a human but having
+analytics embedded in a program give you
+
+ align:start position:0%
+analytics embedded in a program give you
+ 
+
+ align:start position:0%
+analytics embedded in a program give you
+advice about asset allocation investing
+
+ align:start position:0%
+advice about asset allocation investing
+ 
+
+ align:start position:0%
+advice about asset allocation investing
+and the like
+
+ align:start position:0%
+and the like
+ 
+
+ align:start position:0%
+and the like
+and then secondly
+
+ align:start position:0%
+and then secondly
+ 
+
+ align:start position:0%
+and then secondly
+as you said big finance and big finance
+
+ align:start position:0%
+as you said big finance and big finance
+ 
+
+ align:start position:0%
+as you said big finance and big finance
+in this case is asset managers generally
+
+ align:start position:0%
+in this case is asset managers generally
+ 
+
+ align:start position:0%
+in this case is asset managers generally
+but also the brokerage firms reacting
+
+ align:start position:0%
+but also the brokerage firms reacting
+ 
+
+ align:start position:0%
+but also the brokerage firms reacting
+what do they do
+
+ align:start position:0%
+what do they do
+ 
+
+ align:start position:0%
+what do they do
+there's one other thing that's similar
+
+ align:start position:0%
+there's one other thing that's similar
+ 
+
+ align:start position:0%
+there's one other thing that's similar
+to what we see on online brokerage and
+
+ align:start position:0%
+to what we see on online brokerage and
+ 
+
+ align:start position:0%
+to what we see on online brokerage and
+robinhood
+
+ align:start position:0%
+robinhood
+ 
+
+ align:start position:0%
+robinhood
+and that's about costs
+
+ align:start position:0%
+and that's about costs
+ 
+
+ align:start position:0%
+and that's about costs
+it's not just about a delivery system
+
+ align:start position:0%
+it's not just about a delivery system
+ 
+
+ align:start position:0%
+it's not just about a delivery system
+it's not just about mobile phones but
+
+ align:start position:0%
+it's not just about mobile phones but
+ 
+
+ align:start position:0%
+it's not just about mobile phones but
+it's also about a cost point and a price
+
+ align:start position:0%
+it's also about a cost point and a price
+ 
+
+ align:start position:0%
+it's also about a cost point and a price
+point and we'll dive into that a little
+
+ align:start position:0%
+point and we'll dive into that a little
+ 
+
+ align:start position:0%
+point and we'll dive into that a little
+bit but robo advisors giving
+
+ align:start position:0%
+bit but robo advisors giving
+ 
+
+ align:start position:0%
+bit but robo advisors giving
+access to financial advice at lower cost
+
+ align:start position:0%
+access to financial advice at lower cost
+ 
+
+ align:start position:0%
+access to financial advice at lower cost
+maybe in the sort of range of 20 to 50
+
+ align:start position:0%
+maybe in the sort of range of 20 to 50
+ 
+
+ align:start position:0%
+maybe in the sort of range of 20 to 50
+basis points a year
+
+ align:start position:0%
+basis points a year
+ 
+
+ align:start position:0%
+basis points a year
+asset management the whole field of
+
+ align:start position:0%
+asset management the whole field of
+ 
+
+ align:start position:0%
+asset management the whole field of
+asset management the business of asset
+
+ align:start position:0%
+asset management the business of asset
+ 
+
+ align:start position:0%
+asset management the business of asset
+management is accumulating assets under
+
+ align:start position:0%
+management is accumulating assets under
+ 
+
+ align:start position:0%
+management is accumulating assets under
+management
+
+ align:start position:0%
+management
+ 
+
+ align:start position:0%
+management
+and if you accumulate a hundred million
+
+ align:start position:0%
+and if you accumulate a hundred million
+ 
+
+ align:start position:0%
+and if you accumulate a hundred million
+dollars of assets under management and
+
+ align:start position:0%
+dollars of assets under management and
+ 
+
+ align:start position:0%
+dollars of assets under management and
+charge one percent fee that's one
+
+ align:start position:0%
+charge one percent fee that's one
+ 
+
+ align:start position:0%
+charge one percent fee that's one
+million dollars of revenue if you only
+
+ align:start position:0%
+million dollars of revenue if you only
+ 
+
+ align:start position:0%
+million dollars of revenue if you only
+charge a quarter of a point that's only
+
+ align:start position:0%
+charge a quarter of a point that's only
+ 
+
+ align:start position:0%
+charge a quarter of a point that's only
+250 000 of revenues now of course you
+
+ align:start position:0%
+250 000 of revenues now of course you
+ 
+
+ align:start position:0%
+250 000 of revenues now of course you
+can multiply it because none of these
+
+ align:start position:0%
+can multiply it because none of these
+ 
+
+ align:start position:0%
+can multiply it because none of these
+firms really want to just be at 100
+
+ align:start position:0%
+firms really want to just be at 100
+ 
+
+ align:start position:0%
+firms really want to just be at 100
+million dollars of assets under
+
+ align:start position:0%
+million dollars of assets under
+ 
+
+ align:start position:0%
+million dollars of assets under
+management and the biggest the black
+
+ align:start position:0%
+management and the biggest the black
+ 
+
+ align:start position:0%
+management and the biggest the black
+rocks of the world are at five six seven
+
+ align:start position:0%
+rocks of the world are at five six seven
+ 
+
+ align:start position:0%
+rocks of the world are at five six seven
+trillion dollars of assets under
+
+ align:start position:0%
+trillion dollars of assets under
+ 
+
+ align:start position:0%
+trillion dollars of assets under
+management but the robo advisors have
+
+ align:start position:0%
+management but the robo advisors have
+ 
+
+ align:start position:0%
+management but the robo advisors have
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+tucked in here at a lower cost point
+
+ align:start position:0%
+tucked in here at a lower cost point
+ 
+
+ align:start position:0%
+tucked in here at a lower cost point
+and that true that is also true on the
+
+ align:start position:0%
+and that true that is also true on the
+ 
+
+ align:start position:0%
+and that true that is also true on the
+online brokerage side
+
+ align:start position:0%
+online brokerage side
+ 
+
+ align:start position:0%
+online brokerage side
+so it's delivery mechanisms it's user
+
+ align:start position:0%
+so it's delivery mechanisms it's user
+ 
+
+ align:start position:0%
+so it's delivery mechanisms it's user
+interfaces it's service
+
+ align:start position:0%
+interfaces it's service
+ 
+
+ align:start position:0%
+interfaces it's service
+and it's also
+
+ align:start position:0%
+and it's also
+ 
+
+ align:start position:0%
+and it's also
+costs and and thus price points
+
+ align:start position:0%
+costs and and thus price points
+ 
+
+ align:start position:0%
+costs and and thus price points
+in essence can you do something better
+
+ align:start position:0%
+in essence can you do something better
+ 
+
+ align:start position:0%
+in essence can you do something better
+quicker cheaper that's that's kind of a
+
+ align:start position:0%
+quicker cheaper that's that's kind of a
+ 
+
+ align:start position:0%
+quicker cheaper that's that's kind of a
+very simplistic way to think about it
+
+ align:start position:0%
+very simplistic way to think about it
+ 
+
+ align:start position:0%
+very simplistic way to think about it
+but um any other fintech trends i mean
+
+ align:start position:0%
+but um any other fintech trends i mean
+ 
+
+ align:start position:0%
+but um any other fintech trends i mean
+there's a lot going on in the capital
+
+ align:start position:0%
+there's a lot going on in the capital
+ 
+
+ align:start position:0%
+there's a lot going on in the capital
+markets that uh romaine you want to see
+
+ align:start position:0%
+markets that uh romaine you want to see
+ 
+
+ align:start position:0%
+markets that uh romaine you want to see
+if somebody wants to just sort of
+
+ align:start position:0%
+if somebody wants to just sort of
+ 
+
+ align:start position:0%
+if somebody wants to just sort of
+capture a couple of the other trends uh
+
+ align:start position:0%
+capture a couple of the other trends uh
+ 
+
+ align:start position:0%
+capture a couple of the other trends uh
+beyond these two
+
+ align:start position:0%
+beyond these two
+ 
+
+ align:start position:0%
+beyond these two
+on the retail side
+
+ align:start position:0%
+on the retail side
+ 
+
+ align:start position:0%
+on the retail side
+any volunteers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come on guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nikhil go ahead
+
+ align:start position:0%
+nikhil go ahead
+ 
+
+ align:start position:0%
+nikhil go ahead
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry i was muted um i thought something
+
+ align:start position:0%
+sorry i was muted um i thought something
+ 
+
+ align:start position:0%
+sorry i was muted um i thought something
+interesting was both robinhood and
+
+ align:start position:0%
+interesting was both robinhood and
+ 
+
+ align:start position:0%
+interesting was both robinhood and
+wealthfront are moving towards cash
+
+ align:start position:0%
+wealthfront are moving towards cash
+ 
+
+ align:start position:0%
+wealthfront are moving towards cash
+management so they entered the market
+
+ align:start position:0%
+management so they entered the market
+ 
+
+ align:start position:0%
+management so they entered the market
+from like you know
+
+ align:start position:0%
+from like you know
+ 
+
+ align:start position:0%
+from like you know
+the stock side of things and robo
+
+ align:start position:0%
+the stock side of things and robo
+ 
+
+ align:start position:0%
+the stock side of things and robo
+advisor side of things but they seem to
+
+ align:start position:0%
+advisor side of things but they seem to
+ 
+
+ align:start position:0%
+advisor side of things but they seem to
+converge to cash management as the next
+
+ align:start position:0%
+converge to cash management as the next
+ 
+
+ align:start position:0%
+converge to cash management as the next
+uh product to roll out
+
+ align:start position:0%
+uh product to roll out
+ 
+
+ align:start position:0%
+uh product to roll out
+so that's a big trend
+
+ align:start position:0%
+so that's a big trend
+ 
+
+ align:start position:0%
+so that's a big trend
+yeah and look even better mint which
+
+ align:start position:0%
+yeah and look even better mint which
+ 
+
+ align:start position:0%
+yeah and look even better mint which
+we'll talk about in the revo advising
+
+ align:start position:0%
+we'll talk about in the revo advising
+ 
+
+ align:start position:0%
+we'll talk about in the revo advising
+space betterment is starting to enter
+
+ align:start position:0%
+space betterment is starting to enter
+ 
+
+ align:start position:0%
+space betterment is starting to enter
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+the challenger bank area
+
+ align:start position:0%
+the challenger bank area
+ 
+
+ align:start position:0%
+the challenger bank area
+i mean they're not the only ones you
+
+ align:start position:0%
+i mean they're not the only ones you
+ 
+
+ align:start position:0%
+i mean they're not the only ones you
+have transferwise from the payment side
+
+ align:start position:0%
+have transferwise from the payment side
+ 
+
+ align:start position:0%
+have transferwise from the payment side
+entering into the challenger bank side
+
+ align:start position:0%
+entering into the challenger bank side
+ 
+
+ align:start position:0%
+entering into the challenger bank side
+but absolutely some of these platforms
+
+ align:start position:0%
+but absolutely some of these platforms
+ 
+
+ align:start position:0%
+but absolutely some of these platforms
+are then spreading out so you could be
+
+ align:start position:0%
+are then spreading out so you could be
+ 
+
+ align:start position:0%
+are then spreading out so you could be
+robo advisor first and then move into
+
+ align:start position:0%
+robo advisor first and then move into
+ 
+
+ align:start position:0%
+robo advisor first and then move into
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+other trends because of data
+
+ align:start position:0%
+other trends because of data
+ 
+
+ align:start position:0%
+other trends because of data
+we'll see there's a lot of startups
+
+ align:start position:0%
+we'll see there's a lot of startups
+ 
+
+ align:start position:0%
+we'll see there's a lot of startups
+dozens of startups in the fintech space
+
+ align:start position:0%
+dozens of startups in the fintech space
+ 
+
+ align:start position:0%
+dozens of startups in the fintech space
+around data around infrastructure about
+
+ align:start position:0%
+around data around infrastructure about
+ 
+
+ align:start position:0%
+around data around infrastructure about
+what many
+
+ align:start position:0%
+what many
+ 
+
+ align:start position:0%
+what many
+uh investors think of as the back office
+
+ align:start position:0%
+uh investors think of as the back office
+ 
+
+ align:start position:0%
+uh investors think of as the back office
+side of things that are connecting
+
+ align:start position:0%
+side of things that are connecting
+ 
+
+ align:start position:0%
+side of things that are connecting
+exchanges
+
+ align:start position:0%
+exchanges
+ 
+
+ align:start position:0%
+exchanges
+with the public
+
+ align:start position:0%
+with the public
+ 
+
+ align:start position:0%
+with the public
+there are many startups around asset
+
+ align:start position:0%
+there are many startups around asset
+ 
+
+ align:start position:0%
+there are many startups around asset
+management and trying to
+
+ align:start position:0%
+management and trying to
+ 
+
+ align:start position:0%
+management and trying to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+help asset management out and this would
+
+ align:start position:0%
+help asset management out and this would
+ 
+
+ align:start position:0%
+help asset management out and this would
+be big wholesale uh institutional asset
+
+ align:start position:0%
+be big wholesale uh institutional asset
+ 
+
+ align:start position:0%
+be big wholesale uh institutional asset
+management and not just the retail side
+
+ align:start position:0%
+management and not just the retail side
+ 
+
+ align:start position:0%
+management and not just the retail side
+so let's sort of dive into a little bit
+
+ align:start position:0%
+so let's sort of dive into a little bit
+ 
+
+ align:start position:0%
+so let's sort of dive into a little bit
+the history of uh
+
+ align:start position:0%
+the history of uh
+ 
+
+ align:start position:0%
+the history of uh
+online uh company landscape and think
+
+ align:start position:0%
+online uh company landscape and think
+ 
+
+ align:start position:0%
+online uh company landscape and think
+about this for for a moment um who
+
+ align:start position:0%
+about this for for a moment um who
+ 
+
+ align:start position:0%
+about this for for a moment um who
+really started out this whole thing and
+
+ align:start position:0%
+really started out this whole thing and
+ 
+
+ align:start position:0%
+really started out this whole thing and
+i put some of the foundation dates and
+
+ align:start position:0%
+i put some of the foundation dates and
+ 
+
+ align:start position:0%
+i put some of the foundation dates and
+the number of customers these are the
+
+ align:start position:0%
+the number of customers these are the
+ 
+
+ align:start position:0%
+the number of customers these are the
+figures i could get from time to time i
+
+ align:start position:0%
+figures i could get from time to time i
+ 
+
+ align:start position:0%
+figures i could get from time to time i
+wasn't able to online to find a figure
+
+ align:start position:0%
+wasn't able to online to find a figure
+ 
+
+ align:start position:0%
+wasn't able to online to find a figure
+but charles schwab
+
+ align:start position:0%
+but charles schwab
+ 
+
+ align:start position:0%
+but charles schwab
+and td ameritrade you might think of
+
+ align:start position:0%
+and td ameritrade you might think of
+ 
+
+ align:start position:0%
+and td ameritrade you might think of
+them as ameritrade both started back in
+
+ align:start position:0%
+them as ameritrade both started back in
+ 
+
+ align:start position:0%
+them as ameritrade both started back in
+the early 1970s i mean it actually
+
+ align:start position:0%
+the early 1970s i mean it actually
+ 
+
+ align:start position:0%
+the early 1970s i mean it actually
+pre-internet the idea was a lower cost
+
+ align:start position:0%
+pre-internet the idea was a lower cost
+ 
+
+ align:start position:0%
+pre-internet the idea was a lower cost
+brokerage but what was happening in the
+
+ align:start position:0%
+brokerage but what was happening in the
+ 
+
+ align:start position:0%
+brokerage but what was happening in the
+early 1970s
+
+ align:start position:0%
+early 1970s
+ 
+
+ align:start position:0%
+early 1970s
+a really important part of this saga
+
+ align:start position:0%
+a really important part of this saga
+ 
+
+ align:start position:0%
+a really important part of this saga
+is out of the 1960s there was a movement
+
+ align:start position:0%
+is out of the 1960s there was a movement
+ 
+
+ align:start position:0%
+is out of the 1960s there was a movement
+that was ultimately captured in
+
+ align:start position:0%
+that was ultimately captured in
+ 
+
+ align:start position:0%
+that was ultimately captured in
+congressional action in the u.s the u.s
+
+ align:start position:0%
+congressional action in the u.s the u.s
+ 
+
+ align:start position:0%
+congressional action in the u.s the u.s
+congress got involved the securities and
+
+ align:start position:0%
+congress got involved the securities and
+ 
+
+ align:start position:0%
+congress got involved the securities and
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+got involved
+
+ align:start position:0%
+got involved
+ 
+
+ align:start position:0%
+got involved
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+repeal
+
+ align:start position:0%
+repeal
+ 
+
+ align:start position:0%
+repeal
+fixed commission rates you see for
+
+ align:start position:0%
+fixed commission rates you see for
+ 
+
+ align:start position:0%
+fixed commission rates you see for
+decades
+
+ align:start position:0%
+decades
+ 
+
+ align:start position:0%
+decades
+the new york stock exchange had fixed
+
+ align:start position:0%
+the new york stock exchange had fixed
+ 
+
+ align:start position:0%
+the new york stock exchange had fixed
+commission rates set by the members of
+
+ align:start position:0%
+commission rates set by the members of
+ 
+
+ align:start position:0%
+commission rates set by the members of
+the new york stock exchange
+
+ align:start position:0%
+the new york stock exchange
+ 
+
+ align:start position:0%
+the new york stock exchange
+and the institutional world the larger
+
+ align:start position:0%
+and the institutional world the larger
+ 
+
+ align:start position:0%
+and the institutional world the larger
+broke the larger
+
+ align:start position:0%
+broke the larger
+ 
+
+ align:start position:0%
+broke the larger
+investors
+
+ align:start position:0%
+investors
+ 
+
+ align:start position:0%
+investors
+wanted discounts wanted cheaper rates
+
+ align:start position:0%
+wanted discounts wanted cheaper rates
+ 
+
+ align:start position:0%
+wanted discounts wanted cheaper rates
+and in the early 1970s this was this
+
+ align:start position:0%
+and in the early 1970s this was this
+ 
+
+ align:start position:0%
+and in the early 1970s this was this
+movement to
+
+ align:start position:0%
+movement to
+ 
+
+ align:start position:0%
+movement to
+free that up not to have fixed set rates
+
+ align:start position:0%
+free that up not to have fixed set rates
+ 
+
+ align:start position:0%
+free that up not to have fixed set rates
+by the new york stock exchange
+
+ align:start position:0%
+by the new york stock exchange
+ 
+
+ align:start position:0%
+by the new york stock exchange
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+around this time schwab
+
+ align:start position:0%
+around this time schwab
+ 
+
+ align:start position:0%
+around this time schwab
+ameritrade started later
+
+ align:start position:0%
+ameritrade started later
+ 
+
+ align:start position:0%
+ameritrade started later
+affiliated with toronto dominion bank
+
+ align:start position:0%
+affiliated with toronto dominion bank
+ 
+
+ align:start position:0%
+affiliated with toronto dominion bank
+and thus the td
+
+ align:start position:0%
+and thus the td
+ 
+
+ align:start position:0%
+and thus the td
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+50 some years later about 12 million
+
+ align:start position:0%
+50 some years later about 12 million
+ 
+
+ align:start position:0%
+50 some years later about 12 million
+users
+
+ align:start position:0%
+users
+ 
+
+ align:start position:0%
+users
+e-trade starts in the 80s
+
+ align:start position:0%
+e-trade starts in the 80s
+ 
+
+ align:start position:0%
+e-trade starts in the 80s
+first trade later interactive broker is
+
+ align:start position:0%
+first trade later interactive broker is
+ 
+
+ align:start position:0%
+first trade later interactive broker is
+a remarkable company uh
+
+ align:start position:0%
+a remarkable company uh
+ 
+
+ align:start position:0%
+a remarkable company uh
+more on the institutional side little
+
+ align:start position:0%
+more on the institutional side little
+ 
+
+ align:start position:0%
+more on the institutional side little
+less than a million
+
+ align:start position:0%
+less than a million
+ 
+
+ align:start position:0%
+less than a million
+and and so forth monex
+
+ align:start position:0%
+and and so forth monex
+ 
+
+ align:start position:0%
+and and so forth monex
+bought trade station but monex from the
+
+ align:start position:0%
+bought trade station but monex from the
+ 
+
+ align:start position:0%
+bought trade station but monex from the
+90s and even trade station earlier
+
+ align:start position:0%
+90s and even trade station earlier
+ 
+
+ align:start position:0%
+90s and even trade station earlier
+each of these companies were chipping
+
+ align:start position:0%
+each of these companies were chipping
+ 
+
+ align:start position:0%
+each of these companies were chipping
+away a little bit of the old
+
+ align:start position:0%
+away a little bit of the old
+ 
+
+ align:start position:0%
+away a little bit of the old
+concept of brokers and there were many
+
+ align:start position:0%
+concept of brokers and there were many
+ 
+
+ align:start position:0%
+concept of brokers and there were many
+challenges in the 1990s into the knots
+
+ align:start position:0%
+challenges in the 1990s into the knots
+ 
+
+ align:start position:0%
+challenges in the 1990s into the knots
+between schwab and ameritrade and
+
+ align:start position:0%
+between schwab and ameritrade and
+ 
+
+ align:start position:0%
+between schwab and ameritrade and
+e-trade and traditional firms like
+
+ align:start position:0%
+e-trade and traditional firms like
+ 
+
+ align:start position:0%
+e-trade and traditional firms like
+merrill lynch and the like
+
+ align:start position:0%
+merrill lynch and the like
+ 
+
+ align:start position:0%
+merrill lynch and the like
+the asset managers themselves the big
+
+ align:start position:0%
+the asset managers themselves the big
+ 
+
+ align:start position:0%
+the asset managers themselves the big
+asset managers like fidelity and
+
+ align:start position:0%
+asset managers like fidelity and
+ 
+
+ align:start position:0%
+asset managers like fidelity and
+vanguard predate all of this
+
+ align:start position:0%
+vanguard predate all of this
+ 
+
+ align:start position:0%
+vanguard predate all of this
+but fidelity and vanguard also were sort
+
+ align:start position:0%
+but fidelity and vanguard also were sort
+ 
+
+ align:start position:0%
+but fidelity and vanguard also were sort
+of saying how can we in addition to
+
+ align:start position:0%
+of saying how can we in addition to
+ 
+
+ align:start position:0%
+of saying how can we in addition to
+wealth management offer online brokerage
+
+ align:start position:0%
+wealth management offer online brokerage
+ 
+
+ align:start position:0%
+wealth management offer online brokerage
+and as we all know if you have an
+
+ align:start position:0%
+and as we all know if you have an
+ 
+
+ align:start position:0%
+and as we all know if you have an
+account with fidelity or vanguard or for
+
+ align:start position:0%
+account with fidelity or vanguard or for
+ 
+
+ align:start position:0%
+account with fidelity or vanguard or for
+that matter with t rowe price or other
+
+ align:start position:0%
+that matter with t rowe price or other
+ 
+
+ align:start position:0%
+that matter with t rowe price or other
+large asset managers in the u.s
+
+ align:start position:0%
+large asset managers in the u.s
+ 
+
+ align:start position:0%
+large asset managers in the u.s
+some point in time in the last
+
+ align:start position:0%
+some point in time in the last
+ 
+
+ align:start position:0%
+some point in time in the last
+20-ish years some starting in the
+
+ align:start position:0%
+20-ish years some starting in the
+ 
+
+ align:start position:0%
+20-ish years some starting in the
+mid-90s some waiting all the way until
+
+ align:start position:0%
+mid-90s some waiting all the way until
+ 
+
+ align:start position:0%
+mid-90s some waiting all the way until
+the late naughts they started to say
+
+ align:start position:0%
+the late naughts they started to say
+ 
+
+ align:start position:0%
+the late naughts they started to say
+they're going to compete with
+
+ align:start position:0%
+they're going to compete with
+ 
+
+ align:start position:0%
+they're going to compete with
+traditional
+
+ align:start position:0%
+traditional
+ 
+
+ align:start position:0%
+traditional
+wall street the merrill lynches and so
+
+ align:start position:0%
+wall street the merrill lynches and so
+ 
+
+ align:start position:0%
+wall street the merrill lynches and so
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+and they were going to compete by
+
+ align:start position:0%
+and they were going to compete by
+ 
+
+ align:start position:0%
+and they were going to compete by
+offering an online ability to buy and
+
+ align:start position:0%
+offering an online ability to buy and
+ 
+
+ align:start position:0%
+offering an online ability to buy and
+sell stocks
+
+ align:start position:0%
+sell stocks
+ 
+
+ align:start position:0%
+sell stocks
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+got into the business it's not that the
+
+ align:start position:0%
+got into the business it's not that the
+ 
+
+ align:start position:0%
+got into the business it's not that the
+big banks uh
+
+ align:start position:0%
+big banks uh
+ 
+
+ align:start position:0%
+big banks uh
+didn't notice and everything and some of
+
+ align:start position:0%
+didn't notice and everything and some of
+ 
+
+ align:start position:0%
+didn't notice and everything and some of
+them even in the last few years started
+
+ align:start position:0%
+them even in the last few years started
+ 
+
+ align:start position:0%
+them even in the last few years started
+uh sort of discount retail of packages
+
+ align:start position:0%
+uh sort of discount retail of packages
+ 
+
+ align:start position:0%
+uh sort of discount retail of packages
+merrill lynch which i keep mentioning
+
+ align:start position:0%
+merrill lynch which i keep mentioning
+ 
+
+ align:start position:0%
+merrill lynch which i keep mentioning
+merrill lynch edge
+
+ align:start position:0%
+merrill lynch edge
+ 
+
+ align:start position:0%
+merrill lynch edge
+uh 2010 was a product after merrill
+
+ align:start position:0%
+uh 2010 was a product after merrill
+ 
+
+ align:start position:0%
+uh 2010 was a product after merrill
+lynch was bought by bank of america bank
+
+ align:start position:0%
+lynch was bought by bank of america bank
+ 
+
+ align:start position:0%
+lynch was bought by bank of america bank
+of america is thinking okay
+
+ align:start position:0%
+of america is thinking okay
+ 
+
+ align:start position:0%
+of america is thinking okay
+it's post-crisis they buy merrill lynch
+
+ align:start position:0%
+it's post-crisis they buy merrill lynch
+ 
+
+ align:start position:0%
+it's post-crisis they buy merrill lynch
+merrill lynch has this
+
+ align:start position:0%
+merrill lynch has this
+ 
+
+ align:start position:0%
+merrill lynch has this
+remarkable multiple thousand person
+
+ align:start position:0%
+remarkable multiple thousand person
+ 
+
+ align:start position:0%
+remarkable multiple thousand person
+uh organization
+
+ align:start position:0%
+uh organization
+ 
+
+ align:start position:0%
+uh organization
+um uh brokers but they do edge to be
+
+ align:start position:0%
+um uh brokers but they do edge to be
+ 
+
+ align:start position:0%
+um uh brokers but they do edge to be
+online
+
+ align:start position:0%
+online
+ 
+
+ align:start position:0%
+online
+and even ali
+
+ align:start position:0%
+and even ali
+ 
+
+ align:start position:0%
+and even ali
+back alley finance
+
+ align:start position:0%
+back alley finance
+ 
+
+ align:start position:0%
+back alley finance
+which started in the auto lending
+
+ align:start position:0%
+which started in the auto lending
+ 
+
+ align:start position:0%
+which started in the auto lending
+business was that first challenger bank
+
+ align:start position:0%
+business was that first challenger bank
+ 
+
+ align:start position:0%
+business was that first challenger bank
+in 2009 by 2016
+
+ align:start position:0%
+in 2009 by 2016
+ 
+
+ align:start position:0%
+in 2009 by 2016
+is sort of saying we can get into this
+
+ align:start position:0%
+is sort of saying we can get into this
+ 
+
+ align:start position:0%
+is sort of saying we can get into this
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+online four million members
+
+ align:start position:0%
+online four million members
+ 
+
+ align:start position:0%
+online four million members
+but where are we on the startups
+
+ align:start position:0%
+but where are we on the startups
+ 
+
+ align:start position:0%
+but where are we on the startups
+the startups robin hood in 2013 and all
+
+ align:start position:0%
+the startups robin hood in 2013 and all
+ 
+
+ align:start position:0%
+the startups robin hood in 2013 and all
+this package of startups in the last few
+
+ align:start position:0%
+this package of startups in the last few
+ 
+
+ align:start position:0%
+this package of startups in the last few
+years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really have transformed things
+
+ align:start position:0%
+really have transformed things
+ 
+
+ align:start position:0%
+really have transformed things
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what i was saying is these fintech
+
+ align:start position:0%
+what i was saying is these fintech
+ 
+
+ align:start position:0%
+what i was saying is these fintech
+startups
+
+ align:start position:0%
+startups
+ 
+
+ align:start position:0%
+startups
+primarily we think of robinhood but
+
+ align:start position:0%
+primarily we think of robinhood but
+ 
+
+ align:start position:0%
+primarily we think of robinhood but
+there's a bunch of others with with uh
+
+ align:start position:0%
+there's a bunch of others with with uh
+ 
+
+ align:start position:0%
+there's a bunch of others with with uh
+in other markets like free trade and
+
+ align:start position:0%
+in other markets like free trade and
+ 
+
+ align:start position:0%
+in other markets like free trade and
+tastyworks and weibull
+
+ align:start position:0%
+tastyworks and weibull
+ 
+
+ align:start position:0%
+tastyworks and weibull
+have come along
+
+ align:start position:0%
+have come along
+ 
+
+ align:start position:0%
+have come along
+partly because of mobile phones
+
+ align:start position:0%
+partly because of mobile phones
+ 
+
+ align:start position:0%
+partly because of mobile phones
+partly because
+
+ align:start position:0%
+partly because
+ 
+
+ align:start position:0%
+partly because
+even the schwabs and ameritrades were
+
+ align:start position:0%
+even the schwabs and ameritrades were
+ 
+
+ align:start position:0%
+even the schwabs and ameritrades were
+still charging
+
+ align:start position:0%
+still charging
+ 
+
+ align:start position:0%
+still charging
+you know whether it was a few pennies a
+
+ align:start position:0%
+you know whether it was a few pennies a
+ 
+
+ align:start position:0%
+you know whether it was a few pennies a
+share but still charging three four five
+
+ align:start position:0%
+share but still charging three four five
+ 
+
+ align:start position:0%
+share but still charging three four five
+cents a share and so forth
+
+ align:start position:0%
+cents a share and so forth
+ 
+
+ align:start position:0%
+cents a share and so forth
+um user interface and costs
+
+ align:start position:0%
+um user interface and costs
+ 
+
+ align:start position:0%
+um user interface and costs
+provided some uh opportunity to move in
+
+ align:start position:0%
+provided some uh opportunity to move in
+ 
+
+ align:start position:0%
+provided some uh opportunity to move in
+so i'm going to just talk a little bit
+
+ align:start position:0%
+so i'm going to just talk a little bit
+ 
+
+ align:start position:0%
+so i'm going to just talk a little bit
+about the the large companies the
+
+ align:start position:0%
+about the the large companies the
+ 
+
+ align:start position:0%
+about the the large companies the
+e-trades and ameritrades and fidelities
+
+ align:start position:0%
+e-trades and ameritrades and fidelities
+ 
+
+ align:start position:0%
+e-trades and ameritrades and fidelities
+and the like for a moment
+
+ align:start position:0%
+and the like for a moment
+ 
+
+ align:start position:0%
+and the like for a moment
+because part of it is about mobile
+
+ align:start position:0%
+because part of it is about mobile
+ 
+
+ align:start position:0%
+because part of it is about mobile
+trading
+
+ align:start position:0%
+trading
+ 
+
+ align:start position:0%
+trading
+and they each in this this this uh
+
+ align:start position:0%
+and they each in this this this uh
+ 
+
+ align:start position:0%
+and they each in this this this uh
+chart that i was able to get from
+
+ align:start position:0%
+chart that i was able to get from
+ 
+
+ align:start position:0%
+chart that i was able to get from
+stockbrokers.com
+
+ align:start position:0%
+stockbrokers.com
+ 
+
+ align:start position:0%
+stockbrokers.com
+comparison was just like what are the
+
+ align:start position:0%
+comparison was just like what are the
+ 
+
+ align:start position:0%
+comparison was just like what are the
+apps what is that user interface and
+
+ align:start position:0%
+apps what is that user interface and
+ 
+
+ align:start position:0%
+apps what is that user interface and
+this was one example but better believe
+
+ align:start position:0%
+this was one example but better believe
+ 
+
+ align:start position:0%
+this was one example but better believe
+that whether you're merrill lynch edge
+
+ align:start position:0%
+that whether you're merrill lynch edge
+ 
+
+ align:start position:0%
+that whether you're merrill lynch edge
+or your uh robin hood you're also
+
+ align:start position:0%
+or your uh robin hood you're also
+ 
+
+ align:start position:0%
+or your uh robin hood you're also
+thinking about do i interface well with
+
+ align:start position:0%
+thinking about do i interface well with
+ 
+
+ align:start position:0%
+thinking about do i interface well with
+an iphone and android and so forth an
+
+ align:start position:0%
+an iphone and android and so forth an
+ 
+
+ align:start position:0%
+an iphone and android and so forth an
+apple watch i have to sort of have that
+
+ align:start position:0%
+apple watch i have to sort of have that
+ 
+
+ align:start position:0%
+apple watch i have to sort of have that
+connectivity and that technology
+
+ align:start position:0%
+connectivity and that technology
+ 
+
+ align:start position:0%
+connectivity and that technology
+to be ready and used on all of these and
+
+ align:start position:0%
+to be ready and used on all of these and
+ 
+
+ align:start position:0%
+to be ready and used on all of these and
+you can run your eye through
+
+ align:start position:0%
+you can run your eye through
+ 
+
+ align:start position:0%
+you can run your eye through
+uh can i have trading on each of these
+
+ align:start position:0%
+uh can i have trading on each of these
+ 
+
+ align:start position:0%
+uh can i have trading on each of these
+products mutual funds and particularly
+
+ align:start position:0%
+products mutual funds and particularly
+ 
+
+ align:start position:0%
+products mutual funds and particularly
+electronic trading often is around etfs
+
+ align:start position:0%
+electronic trading often is around etfs
+ 
+
+ align:start position:0%
+electronic trading often is around etfs
+but not only etfs and as the
+
+ align:start position:0%
+but not only etfs and as the
+ 
+
+ align:start position:0%
+but not only etfs and as the
+cryptocurrency space came up a number of
+
+ align:start position:0%
+cryptocurrency space came up a number of
+ 
+
+ align:start position:0%
+cryptocurrency space came up a number of
+them said well can we trade
+
+ align:start position:0%
+them said well can we trade
+ 
+
+ align:start position:0%
+them said well can we trade
+cryptocurrencies as well not the
+
+ align:start position:0%
+cryptocurrencies as well not the
+ 
+
+ align:start position:0%
+cryptocurrencies as well not the
+e-trades and ameritrades but the robin
+
+ align:start position:0%
+e-trades and ameritrades but the robin
+ 
+
+ align:start position:0%
+e-trades and ameritrades but the robin
+hoods and the and the disruptors were
+
+ align:start position:0%
+hoods and the and the disruptors were
+ 
+
+ align:start position:0%
+hoods and the and the disruptors were
+into that
+
+ align:start position:0%
+into that
+ 
+
+ align:start position:0%
+into that
+uh space so it's just sort of a little
+
+ align:start position:0%
+uh space so it's just sort of a little
+ 
+
+ align:start position:0%
+uh space so it's just sort of a little
+bit of a comparison in how some folks
+
+ align:start position:0%
+bit of a comparison in how some folks
+ 
+
+ align:start position:0%
+bit of a comparison in how some folks
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+um recent developments are really
+
+ align:start position:0%
+um recent developments are really
+ 
+
+ align:start position:0%
+um recent developments are really
+important and the biggest one was late
+
+ align:start position:0%
+important and the biggest one was late
+ 
+
+ align:start position:0%
+important and the biggest one was late
+in 2019
+
+ align:start position:0%
+in 2019
+ 
+
+ align:start position:0%
+in 2019
+what's called sort of the broker wars
+
+ align:start position:0%
+what's called sort of the broker wars
+ 
+
+ align:start position:0%
+what's called sort of the broker wars
+what happened start was
+
+ align:start position:0%
+what happened start was
+ 
+
+ align:start position:0%
+what happened start was
+at the start was
+
+ align:start position:0%
+at the start was
+ 
+
+ align:start position:0%
+at the start was
+robin hood was eating into this six
+
+ align:start position:0%
+robin hood was eating into this six
+ 
+
+ align:start position:0%
+robin hood was eating into this six
+seven eight million members now maybe 10
+
+ align:start position:0%
+seven eight million members now maybe 10
+ 
+
+ align:start position:0%
+seven eight million members now maybe 10
+million members and as we saw the
+
+ align:start position:0%
+million members and as we saw the
+ 
+
+ align:start position:0%
+million members and as we saw the
+earlier numbers schwab and ameritrader
+
+ align:start position:0%
+earlier numbers schwab and ameritrader
+ 
+
+ align:start position:0%
+earlier numbers schwab and ameritrader
+are only about 12 million
+
+ align:start position:0%
+are only about 12 million
+ 
+
+ align:start position:0%
+are only about 12 million
+and as that was happening
+
+ align:start position:0%
+and as that was happening
+ 
+
+ align:start position:0%
+and as that was happening
+ibkr which is that
+
+ align:start position:0%
+ibkr which is that
+ 
+
+ align:start position:0%
+ibkr which is that
+smaller but remarkable company uh
+
+ align:start position:0%
+smaller but remarkable company uh
+ 
+
+ align:start position:0%
+smaller but remarkable company uh
+institutional brokers
+
+ align:start position:0%
+institutional brokers
+ 
+
+ align:start position:0%
+institutional brokers
+in september of 2019 said they were
+
+ align:start position:0%
+in september of 2019 said they were
+ 
+
+ align:start position:0%
+in september of 2019 said they were
+going to go to free brokerage
+
+ align:start position:0%
+going to go to free brokerage
+ 
+
+ align:start position:0%
+going to go to free brokerage
+for some of their accounts it wasn't 100
+
+ align:start position:0%
+for some of their accounts it wasn't 100
+ 
+
+ align:start position:0%
+for some of their accounts it wasn't 100
+but they were going to go
+
+ align:start position:0%
+but they were going to go
+ 
+
+ align:start position:0%
+but they were going to go
+and within weeks
+
+ align:start position:0%
+and within weeks
+ 
+
+ align:start position:0%
+and within weeks
+early in october 2019 schwab finally
+
+ align:start position:0%
+early in october 2019 schwab finally
+ 
+
+ align:start position:0%
+early in october 2019 schwab finally
+said zero commission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what's fascinating i think is this
+
+ align:start position:0%
+now what's fascinating i think is this
+ 
+
+ align:start position:0%
+now what's fascinating i think is this
+is the challenge that we're in
+
+ align:start position:0%
+is the challenge that we're in
+ 
+
+ align:start position:0%
+is the challenge that we're in
+we're in the challenge of are there
+
+ align:start position:0%
+we're in the challenge of are there
+ 
+
+ align:start position:0%
+we're in the challenge of are there
+financial services that will move to
+
+ align:start position:0%
+financial services that will move to
+ 
+
+ align:start position:0%
+financial services that will move to
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+top line pricing
+
+ align:start position:0%
+top line pricing
+ 
+
+ align:start position:0%
+top line pricing
+and what we've found whether it's in
+
+ align:start position:0%
+and what we've found whether it's in
+ 
+
+ align:start position:0%
+and what we've found whether it's in
+facebook or many many online
+
+ align:start position:0%
+facebook or many many online
+ 
+
+ align:start position:0%
+facebook or many many online
+applications
+
+ align:start position:0%
+applications
+ 
+
+ align:start position:0%
+applications
+and outside of the financial world it's
+
+ align:start position:0%
+and outside of the financial world it's
+ 
+
+ align:start position:0%
+and outside of the financial world it's
+a zero fee environment and then the
+
+ align:start position:0%
+a zero fee environment and then the
+ 
+
+ align:start position:0%
+a zero fee environment and then the
+business model is earning money some
+
+ align:start position:0%
+business model is earning money some
+ 
+
+ align:start position:0%
+business model is earning money some
+other way in facebook's case
+
+ align:start position:0%
+other way in facebook's case
+ 
+
+ align:start position:0%
+other way in facebook's case
+it's about marketing and advertising
+
+ align:start position:0%
+it's about marketing and advertising
+ 
+
+ align:start position:0%
+it's about marketing and advertising
+90-plus percent of their revenue is
+
+ align:start position:0%
+90-plus percent of their revenue is
+ 
+
+ align:start position:0%
+90-plus percent of their revenue is
+really about advertising and marketing
+
+ align:start position:0%
+really about advertising and marketing
+ 
+
+ align:start position:0%
+really about advertising and marketing
+if you look at that business model that
+
+ align:start position:0%
+if you look at that business model that
+ 
+
+ align:start position:0%
+if you look at that business model that
+remarkable business model
+
+ align:start position:0%
+remarkable business model
+ 
+
+ align:start position:0%
+remarkable business model
+but it may be on the data it may be
+
+ align:start position:0%
+but it may be on the data it may be
+ 
+
+ align:start position:0%
+but it may be on the data it may be
+cross-selling and marketing it may be on
+
+ align:start position:0%
+cross-selling and marketing it may be on
+ 
+
+ align:start position:0%
+cross-selling and marketing it may be on
+the data it may be somewhere else we're
+
+ align:start position:0%
+the data it may be somewhere else we're
+ 
+
+ align:start position:0%
+the data it may be somewhere else we're
+going to talk about the revenue model of
+
+ align:start position:0%
+going to talk about the revenue model of
+ 
+
+ align:start position:0%
+going to talk about the revenue model of
+robinhood in a moment
+
+ align:start position:0%
+robinhood in a moment
+ 
+
+ align:start position:0%
+robinhood in a moment
+but charles schwab reacted
+
+ align:start position:0%
+but charles schwab reacted
+ 
+
+ align:start position:0%
+but charles schwab reacted
+e-trade td ameritrade all within one
+
+ align:start position:0%
+e-trade td ameritrade all within one
+ 
+
+ align:start position:0%
+e-trade td ameritrade all within one
+week went to zero commission
+
+ align:start position:0%
+week went to zero commission
+ 
+
+ align:start position:0%
+week went to zero commission
+and in fact it led to schwab being able
+
+ align:start position:0%
+and in fact it led to schwab being able
+ 
+
+ align:start position:0%
+and in fact it led to schwab being able
+to do the next thing
+
+ align:start position:0%
+to do the next thing
+ 
+
+ align:start position:0%
+to do the next thing
+which was
+
+ align:start position:0%
+which was
+ 
+
+ align:start position:0%
+which was
+announce the purchase of ameritrade
+
+ align:start position:0%
+announce the purchase of ameritrade
+ 
+
+ align:start position:0%
+announce the purchase of ameritrade
+with collapsing revenues at ameritrade
+
+ align:start position:0%
+with collapsing revenues at ameritrade
+ 
+
+ align:start position:0%
+with collapsing revenues at ameritrade
+schwab could actually say we're we they
+
+ align:start position:0%
+schwab could actually say we're we they
+ 
+
+ align:start position:0%
+schwab could actually say we're we they
+made them an offer purchased for 26
+
+ align:start position:0%
+made them an offer purchased for 26
+ 
+
+ align:start position:0%
+made them an offer purchased for 26
+billion morgan stanley wasn't going to
+
+ align:start position:0%
+billion morgan stanley wasn't going to
+ 
+
+ align:start position:0%
+billion morgan stanley wasn't going to
+be out dawn and early in 2020 morgan
+
+ align:start position:0%
+be out dawn and early in 2020 morgan
+ 
+
+ align:start position:0%
+be out dawn and early in 2020 morgan
+stanley one of the most venerable old
+
+ align:start position:0%
+stanley one of the most venerable old
+ 
+
+ align:start position:0%
+stanley one of the most venerable old
+line investment banks all dating all the
+
+ align:start position:0%
+line investment banks all dating all the
+ 
+
+ align:start position:0%
+line investment banks all dating all the
+way back to james to jp morgan him
+
+ align:start position:0%
+way back to james to jp morgan him
+ 
+
+ align:start position:0%
+way back to james to jp morgan him
+himself
+
+ align:start position:0%
+himself
+ 
+
+ align:start position:0%
+himself
+the industrialist that uh though he's
+
+ align:start position:0%
+the industrialist that uh though he's
+ 
+
+ align:start position:0%
+the industrialist that uh though he's
+departed this world many decades ago
+
+ align:start position:0%
+departed this world many decades ago
+ 
+
+ align:start position:0%
+departed this world many decades ago
+has his name on morgan stanley and jp
+
+ align:start position:0%
+has his name on morgan stanley and jp
+ 
+
+ align:start position:0%
+has his name on morgan stanley and jp
+morgan chase
+
+ align:start position:0%
+morgan chase
+ 
+
+ align:start position:0%
+morgan chase
+morgan stanley buys e-trade earlier this
+
+ align:start position:0%
+morgan stanley buys e-trade earlier this
+ 
+
+ align:start position:0%
+morgan stanley buys e-trade earlier this
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+if you would have told the morgan
+
+ align:start position:0%
+if you would have told the morgan
+ 
+
+ align:start position:0%
+if you would have told the morgan
+stanley executives when e-trade started
+
+ align:start position:0%
+stanley executives when e-trade started
+ 
+
+ align:start position:0%
+stanley executives when e-trade started
+30 years ago that some time
+
+ align:start position:0%
+30 years ago that some time
+ 
+
+ align:start position:0%
+30 years ago that some time
+they would in their future buy each
+
+ align:start position:0%
+they would in their future buy each
+ 
+
+ align:start position:0%
+they would in their future buy each
+right they would have sort of scratched
+
+ align:start position:0%
+right they would have sort of scratched
+ 
+
+ align:start position:0%
+right they would have sort of scratched
+their head and said really
+
+ align:start position:0%
+their head and said really
+ 
+
+ align:start position:0%
+their head and said really
+we're going to be a retail online
+
+ align:start position:0%
+we're going to be a retail online
+ 
+
+ align:start position:0%
+we're going to be a retail online
+brokerage firm
+
+ align:start position:0%
+brokerage firm
+ 
+
+ align:start position:0%
+brokerage firm
+so it's sort of an interesting change in
+
+ align:start position:0%
+so it's sort of an interesting change in
+ 
+
+ align:start position:0%
+so it's sort of an interesting change in
+in this world
+
+ align:start position:0%
+in this world
+ 
+
+ align:start position:0%
+in this world
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what's the long road what's the long
+
+ align:start position:0%
+what's the long road what's the long
+ 
+
+ align:start position:0%
+what's the long road what's the long
+road of commissions
+
+ align:start position:0%
+road of commissions
+ 
+
+ align:start position:0%
+road of commissions
+this this is the
+
+ align:start position:0%
+this this is the
+ 
+
+ align:start position:0%
+this this is the
+a much earlier chart but if you look at
+
+ align:start position:0%
+a much earlier chart but if you look at
+ 
+
+ align:start position:0%
+a much earlier chart but if you look at
+this gray line this commission rate
+
+ align:start position:0%
+this gray line this commission rate
+ 
+
+ align:start position:0%
+this gray line this commission rate
+from 25 cents a share down to about 3
+
+ align:start position:0%
+from 25 cents a share down to about 3
+ 
+
+ align:start position:0%
+from 25 cents a share down to about 3
+cents a share
+
+ align:start position:0%
+cents a share
+ 
+
+ align:start position:0%
+cents a share
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+2008 or 9. i think this chart cuts off
+
+ align:start position:0%
+2008 or 9. i think this chart cuts off
+ 
+
+ align:start position:0%
+2008 or 9. i think this chart cuts off
+around 2008
+
+ align:start position:0%
+around 2008
+ 
+
+ align:start position:0%
+around 2008
+this long march of competition
+
+ align:start position:0%
+this long march of competition
+ 
+
+ align:start position:0%
+this long march of competition
+in part is because of volumes as you can
+
+ align:start position:0%
+in part is because of volumes as you can
+ 
+
+ align:start position:0%
+in part is because of volumes as you can
+see on this that volumes were going up
+
+ align:start position:0%
+see on this that volumes were going up
+ 
+
+ align:start position:0%
+see on this that volumes were going up
+and commissions were going down
+
+ align:start position:0%
+and commissions were going down
+ 
+
+ align:start position:0%
+and commissions were going down
+so some of it is just efficiency
+
+ align:start position:0%
+so some of it is just efficiency
+ 
+
+ align:start position:0%
+so some of it is just efficiency
+but it's also this competition that was
+
+ align:start position:0%
+but it's also this competition that was
+ 
+
+ align:start position:0%
+but it's also this competition that was
+coming in from e-trade and ameritrade on
+
+ align:start position:0%
+coming in from e-trade and ameritrade on
+ 
+
+ align:start position:0%
+coming in from e-trade and ameritrade on
+the retail side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but robin hood sort of entered a world
+
+ align:start position:0%
+but robin hood sort of entered a world
+ 
+
+ align:start position:0%
+but robin hood sort of entered a world
+that still had three four five cents
+
+ align:start position:0%
+that still had three four five cents
+ 
+
+ align:start position:0%
+that still had three four five cents
+commission
+
+ align:start position:0%
+commission
+ 
+
+ align:start position:0%
+commission
+robin hood initially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did an online app that was easy
+
+ align:start position:0%
+did an online app that was easy
+ 
+
+ align:start position:0%
+did an online app that was easy
+with a mobile phone
+
+ align:start position:0%
+with a mobile phone
+ 
+
+ align:start position:0%
+with a mobile phone
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+start an account
+
+ align:start position:0%
+start an account
+ 
+
+ align:start position:0%
+start an account
+but what they also did is they said
+
+ align:start position:0%
+but what they also did is they said
+ 
+
+ align:start position:0%
+but what they also did is they said
+we'll do it for free their business
+
+ align:start position:0%
+we'll do it for free their business
+ 
+
+ align:start position:0%
+we'll do it for free their business
+model from 2013 on we'll do it for free
+
+ align:start position:0%
+model from 2013 on we'll do it for free
+ 
+
+ align:start position:0%
+model from 2013 on we'll do it for free
+and how did they do that what's the
+
+ align:start position:0%
+and how did they do that what's the
+ 
+
+ align:start position:0%
+and how did they do that what's the
+revenue model behind that anybody want
+
+ align:start position:0%
+revenue model behind that anybody want
+ 
+
+ align:start position:0%
+revenue model behind that anybody want
+to take a i'm going to pause romaine i
+
+ align:start position:0%
+to take a i'm going to pause romaine i
+ 
+
+ align:start position:0%
+to take a i'm going to pause romaine i
+will answer this question i'm just
+
+ align:start position:0%
+will answer this question i'm just
+ 
+
+ align:start position:0%
+will answer this question i'm just
+saying romaine who
+
+ align:start position:0%
+saying romaine who
+ 
+
+ align:start position:0%
+saying romaine who
+amongst the class would think
+
+ align:start position:0%
+amongst the class would think
+ 
+
+ align:start position:0%
+amongst the class would think
+how could you be so bold as a startup
+
+ align:start position:0%
+how could you be so bold as a startup
+ 
+
+ align:start position:0%
+how could you be so bold as a startup
+venture capitalist you start
+
+ align:start position:0%
+venture capitalist you start
+ 
+
+ align:start position:0%
+venture capitalist you start
+uh entrepreneurial effort free online
+
+ align:start position:0%
+uh entrepreneurial effort free online
+ 
+
+ align:start position:0%
+uh entrepreneurial effort free online
+brokerage from day one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+volunteers victor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um i guess that you can either make a
+
+ align:start position:0%
+um i guess that you can either make a
+ 
+
+ align:start position:0%
+um i guess that you can either make a
+profit on the
+
+ align:start position:0%
+profit on the
+ 
+
+ align:start position:0%
+profit on the
+on lending money to traders so they can
+
+ align:start position:0%
+on lending money to traders so they can
+ 
+
+ align:start position:0%
+on lending money to traders so they can
+so they can purchase stock
+
+ align:start position:0%
+so they can purchase stock
+ 
+
+ align:start position:0%
+so they can purchase stock
+and you can also use some high frequency
+
+ align:start position:0%
+and you can also use some high frequency
+ 
+
+ align:start position:0%
+and you can also use some high frequency
+trading as some people said that robin
+
+ align:start position:0%
+trading as some people said that robin
+ 
+
+ align:start position:0%
+trading as some people said that robin
+food is doing in order to before you
+
+ align:start position:0%
+food is doing in order to before you
+ 
+
+ align:start position:0%
+food is doing in order to before you
+sell you actually go through a
+
+ align:start position:0%
+sell you actually go through a
+ 
+
+ align:start position:0%
+sell you actually go through a
+intermediary that you make a profit out
+
+ align:start position:0%
+intermediary that you make a profit out
+ 
+
+ align:start position:0%
+intermediary that you make a profit out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+okay so victor's raised two things i'm
+
+ align:start position:0%
+okay so victor's raised two things i'm
+ 
+
+ align:start position:0%
+okay so victor's raised two things i'm
+going to focus on the second was the
+
+ align:start position:0%
+going to focus on the second was the
+ 
+
+ align:start position:0%
+going to focus on the second was the
+relationship of these
+
+ align:start position:0%
+relationship of these
+ 
+
+ align:start position:0%
+relationship of these
+mobile
+
+ align:start position:0%
+mobile
+ 
+
+ align:start position:0%
+mobile
+uh platforms robin hood in particularly
+
+ align:start position:0%
+uh platforms robin hood in particularly
+ 
+
+ align:start position:0%
+uh platforms robin hood in particularly
+and high frequency trading
+
+ align:start position:0%
+and high frequency trading
+ 
+
+ align:start position:0%
+and high frequency trading
+what robin hood
+
+ align:start position:0%
+what robin hood
+ 
+
+ align:start position:0%
+what robin hood
+knew was that a feature of the capital
+
+ align:start position:0%
+knew was that a feature of the capital
+ 
+
+ align:start position:0%
+knew was that a feature of the capital
+markets was that there were firms that
+
+ align:start position:0%
+markets was that there were firms that
+ 
+
+ align:start position:0%
+markets was that there were firms that
+would pay for order flow
+
+ align:start position:0%
+would pay for order flow
+ 
+
+ align:start position:0%
+would pay for order flow
+they would pay a very modest amount
+
+ align:start position:0%
+they would pay a very modest amount
+ 
+
+ align:start position:0%
+they would pay a very modest amount
+maybe a penny a share
+
+ align:start position:0%
+maybe a penny a share
+ 
+
+ align:start position:0%
+maybe a penny a share
+but they would pay
+
+ align:start position:0%
+but they would pay
+ 
+
+ align:start position:0%
+but they would pay
+just to receive the order flow and this
+
+ align:start position:0%
+just to receive the order flow and this
+ 
+
+ align:start position:0%
+just to receive the order flow and this
+is a feature
+
+ align:start position:0%
+is a feature
+ 
+
+ align:start position:0%
+is a feature
+of the competitive
+
+ align:start position:0%
+of the competitive
+ 
+
+ align:start position:0%
+of the competitive
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+the competitive exchange markets in the
+
+ align:start position:0%
+the competitive exchange markets in the
+ 
+
+ align:start position:0%
+the competitive exchange markets in the
+u.s we have 50 to 70 individual
+
+ align:start position:0%
+u.s we have 50 to 70 individual
+ 
+
+ align:start position:0%
+u.s we have 50 to 70 individual
+exchanges we think of the new york stock
+
+ align:start position:0%
+exchanges we think of the new york stock
+ 
+
+ align:start position:0%
+exchanges we think of the new york stock
+exchange we think about nasdaq and so
+
+ align:start position:0%
+exchange we think about nasdaq and so
+ 
+
+ align:start position:0%
+exchange we think about nasdaq and so
+forth but there are many other
+
+ align:start position:0%
+forth but there are many other
+ 
+
+ align:start position:0%
+forth but there are many other
+electronic markets where
+
+ align:start position:0%
+electronic markets where
+ 
+
+ align:start position:0%
+electronic markets where
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+transactions occur
+
+ align:start position:0%
+transactions occur
+ 
+
+ align:start position:0%
+transactions occur
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and and and some people call them the
+
+ align:start position:0%
+and and and some people call them the
+ 
+
+ align:start position:0%
+and and and some people call them the
+the dark markets
+
+ align:start position:0%
+the dark markets
+ 
+
+ align:start position:0%
+the dark markets
+but all of those markets might pay for
+
+ align:start position:0%
+but all of those markets might pay for
+ 
+
+ align:start position:0%
+but all of those markets might pay for
+order flow and then individual trading
+
+ align:start position:0%
+order flow and then individual trading
+ 
+
+ align:start position:0%
+order flow and then individual trading
+shops high frequency trading shops might
+
+ align:start position:0%
+shops high frequency trading shops might
+ 
+
+ align:start position:0%
+shops high frequency trading shops might
+pay for order flow what that means is
+
+ align:start position:0%
+pay for order flow what that means is
+ 
+
+ align:start position:0%
+pay for order flow what that means is
+they want it they want to have a first
+
+ align:start position:0%
+they want it they want to have a first
+ 
+
+ align:start position:0%
+they want it they want to have a first
+look they want to have those orders and
+
+ align:start position:0%
+look they want to have those orders and
+ 
+
+ align:start position:0%
+look they want to have those orders and
+to route them through their
+
+ align:start position:0%
+to route them through their
+ 
+
+ align:start position:0%
+to route them through their
+algorithms and into their either
+
+ align:start position:0%
+algorithms and into their either
+ 
+
+ align:start position:0%
+algorithms and into their either
+exchange engines if it's an exchange
+
+ align:start position:0%
+exchange engines if it's an exchange
+ 
+
+ align:start position:0%
+exchange engines if it's an exchange
+that's paying for order flow or a high
+
+ align:start position:0%
+that's paying for order flow or a high
+ 
+
+ align:start position:0%
+that's paying for order flow or a high
+frequency trading shop that's paying for
+
+ align:start position:0%
+frequency trading shop that's paying for
+ 
+
+ align:start position:0%
+frequency trading shop that's paying for
+order flow
+
+ align:start position:0%
+order flow
+ 
+
+ align:start position:0%
+order flow
+and the exchanges have different
+
+ align:start position:0%
+and the exchanges have different
+ 
+
+ align:start position:0%
+and the exchanges have different
+fee structures depending upon whether
+
+ align:start position:0%
+fee structures depending upon whether
+ 
+
+ align:start position:0%
+fee structures depending upon whether
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+make a bid or offer or you take a bitter
+
+ align:start position:0%
+make a bid or offer or you take a bitter
+ 
+
+ align:start position:0%
+make a bid or offer or you take a bitter
+offer you will sometimes hear this
+
+ align:start position:0%
+offer you will sometimes hear this
+ 
+
+ align:start position:0%
+offer you will sometimes hear this
+called maker and taker rates
+
+ align:start position:0%
+called maker and taker rates
+ 
+
+ align:start position:0%
+called maker and taker rates
+making a bitter offer
+
+ align:start position:0%
+making a bitter offer
+ 
+
+ align:start position:0%
+making a bitter offer
+putting a resting bid or a resting offer
+
+ align:start position:0%
+putting a resting bid or a resting offer
+ 
+
+ align:start position:0%
+putting a resting bid or a resting offer
+into a an exchange engine
+
+ align:start position:0%
+into a an exchange engine
+ 
+
+ align:start position:0%
+into a an exchange engine
+is more valuable for the exchange
+
+ align:start position:0%
+is more valuable for the exchange
+ 
+
+ align:start position:0%
+is more valuable for the exchange
+because it brings other orders into the
+
+ align:start position:0%
+because it brings other orders into the
+ 
+
+ align:start position:0%
+because it brings other orders into the
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+so what robinhood figured out was
+
+ align:start position:0%
+so what robinhood figured out was
+ 
+
+ align:start position:0%
+so what robinhood figured out was
+they could
+
+ align:start position:0%
+they could
+ 
+
+ align:start position:0%
+they could
+offer the retail public something for
+
+ align:start position:0%
+offer the retail public something for
+ 
+
+ align:start position:0%
+offer the retail public something for
+free
+
+ align:start position:0%
+free
+ 
+
+ align:start position:0%
+free
+because they entered into two or three
+
+ align:start position:0%
+because they entered into two or three
+ 
+
+ align:start position:0%
+because they entered into two or three
+major contracts with hedge funds with
+
+ align:start position:0%
+major contracts with hedge funds with
+ 
+
+ align:start position:0%
+major contracts with hedge funds with
+high frequency trading shops saying we
+
+ align:start position:0%
+high frequency trading shops saying we
+ 
+
+ align:start position:0%
+high frequency trading shops saying we
+will we will enter into something where
+
+ align:start position:0%
+will we will enter into something where
+ 
+
+ align:start position:0%
+will we will enter into something where
+we're selling you the order flow
+
+ align:start position:0%
+we're selling you the order flow
+ 
+
+ align:start position:0%
+we're selling you the order flow
+for a modest amount i don't know the
+
+ align:start position:0%
+for a modest amount i don't know the
+ 
+
+ align:start position:0%
+for a modest amount i don't know the
+exact amount but let's call it a penny a
+
+ align:start position:0%
+exact amount but let's call it a penny a
+ 
+
+ align:start position:0%
+exact amount but let's call it a penny a
+share
+
+ align:start position:0%
+share
+ 
+
+ align:start position:0%
+share
+inside the pricing of the three or so
+
+ align:start position:0%
+inside the pricing of the three or so
+ 
+
+ align:start position:0%
+inside the pricing of the three or so
+cents to five cents that the online
+
+ align:start position:0%
+cents to five cents that the online
+ 
+
+ align:start position:0%
+cents to five cents that the online
+brokers were charging but still
+
+ align:start position:0%
+brokers were charging but still
+ 
+
+ align:start position:0%
+brokers were charging but still
+very valuable over time for robinhood
+
+ align:start position:0%
+very valuable over time for robinhood
+ 
+
+ align:start position:0%
+very valuable over time for robinhood
+and then bingo
+
+ align:start position:0%
+and then bingo
+ 
+
+ align:start position:0%
+and then bingo
+six or eight million members later
+
+ align:start position:0%
+six or eight million members later
+ 
+
+ align:start position:0%
+six or eight million members later
+account holders later and a good user
+
+ align:start position:0%
+account holders later and a good user
+ 
+
+ align:start position:0%
+account holders later and a good user
+face
+
+ align:start position:0%
+face
+ 
+
+ align:start position:0%
+face
+we get into the broker wars where others
+
+ align:start position:0%
+we get into the broker wars where others
+ 
+
+ align:start position:0%
+we get into the broker wars where others
+drop their rates as well and so then i
+
+ align:start position:0%
+drop their rates as well and so then i
+ 
+
+ align:start position:0%
+drop their rates as well and so then i
+go to this interesting
+
+ align:start position:0%
+go to this interesting
+ 
+
+ align:start position:0%
+go to this interesting
+zero commission model chart
+
+ align:start position:0%
+zero commission model chart
+ 
+
+ align:start position:0%
+zero commission model chart
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that sort of talks about well how could
+
+ align:start position:0%
+that sort of talks about well how could
+ 
+
+ align:start position:0%
+that sort of talks about well how could
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+the cost of financial advice be zero
+
+ align:start position:0%
+the cost of financial advice be zero
+ 
+
+ align:start position:0%
+the cost of financial advice be zero
+well it's because of everything else and
+
+ align:start position:0%
+well it's because of everything else and
+ 
+
+ align:start position:0%
+well it's because of everything else and
+the everything else model whether it's
+
+ align:start position:0%
+the everything else model whether it's
+ 
+
+ align:start position:0%
+the everything else model whether it's
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+morgan stanley and e trade
+
+ align:start position:0%
+morgan stanley and e trade
+ 
+
+ align:start position:0%
+morgan stanley and e trade
+whether it's for
+
+ align:start position:0%
+whether it's for
+ 
+
+ align:start position:0%
+whether it's for
+schwab charles schwab or whether it's
+
+ align:start position:0%
+schwab charles schwab or whether it's
+ 
+
+ align:start position:0%
+schwab charles schwab or whether it's
+for robin hood
+
+ align:start position:0%
+for robin hood
+ 
+
+ align:start position:0%
+for robin hood
+as victor said this is everything else
+
+ align:start position:0%
+as victor said this is everything else
+ 
+
+ align:start position:0%
+as victor said this is everything else
+that might be
+
+ align:start position:0%
+that might be
+ 
+
+ align:start position:0%
+that might be
+valuable for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picking up payment for order flow is the
+
+ align:start position:0%
+picking up payment for order flow is the
+ 
+
+ align:start position:0%
+picking up payment for order flow is the
+third one on this list but margin
+
+ align:start position:0%
+third one on this list but margin
+ 
+
+ align:start position:0%
+third one on this list but margin
+interest maintenance fees transaction
+
+ align:start position:0%
+interest maintenance fees transaction
+ 
+
+ align:start position:0%
+interest maintenance fees transaction
+fees sort of saying once you have a
+
+ align:start position:0%
+fees sort of saying once you have a
+ 
+
+ align:start position:0%
+fees sort of saying once you have a
+client
+
+ align:start position:0%
+client
+ 
+
+ align:start position:0%
+client
+there's a lot of other revenues that can
+
+ align:start position:0%
+there's a lot of other revenues that can
+ 
+
+ align:start position:0%
+there's a lot of other revenues that can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+garnered so once facebook has your
+
+ align:start position:0%
+garnered so once facebook has your
+ 
+
+ align:start position:0%
+garnered so once facebook has your
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+there are other revenues that facebook
+
+ align:start position:0%
+there are other revenues that facebook
+ 
+
+ align:start position:0%
+there are other revenues that facebook
+can garner
+
+ align:start position:0%
+can garner
+ 
+
+ align:start position:0%
+can garner
+but in the brokerage space
+
+ align:start position:0%
+but in the brokerage space
+ 
+
+ align:start position:0%
+but in the brokerage space
+this is very well known this was known
+
+ align:start position:0%
+this is very well known this was known
+ 
+
+ align:start position:0%
+this is very well known this was known
+in the 1960s and 1970s
+
+ align:start position:0%
+in the 1960s and 1970s
+ 
+
+ align:start position:0%
+in the 1960s and 1970s
+when the large investment banks would
+
+ align:start position:0%
+when the large investment banks would
+ 
+
+ align:start position:0%
+when the large investment banks would
+think if i have a relationship with this
+
+ align:start position:0%
+think if i have a relationship with this
+ 
+
+ align:start position:0%
+think if i have a relationship with this
+big insurance company
+
+ align:start position:0%
+big insurance company
+ 
+
+ align:start position:0%
+big insurance company
+i can earn money in other ways it's what
+
+ align:start position:0%
+i can earn money in other ways it's what
+ 
+
+ align:start position:0%
+i can earn money in other ways it's what
+led in part in the early 1970s to break
+
+ align:start position:0%
+led in part in the early 1970s to break
+ 
+
+ align:start position:0%
+led in part in the early 1970s to break
+the old decades-old fixed commission
+
+ align:start position:0%
+the old decades-old fixed commission
+ 
+
+ align:start position:0%
+the old decades-old fixed commission
+rates because large investment banks
+
+ align:start position:0%
+rates because large investment banks
+ 
+
+ align:start position:0%
+rates because large investment banks
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+discount and lower their rates for large
+
+ align:start position:0%
+discount and lower their rates for large
+ 
+
+ align:start position:0%
+discount and lower their rates for large
+institutions not for the retail public
+
+ align:start position:0%
+institutions not for the retail public
+ 
+
+ align:start position:0%
+institutions not for the retail public
+but for large institutions that was 50
+
+ align:start position:0%
+but for large institutions that was 50
+ 
+
+ align:start position:0%
+but for large institutions that was 50
+years ago
+
+ align:start position:0%
+years ago
+ 
+
+ align:start position:0%
+years ago
+but that was also because there's all
+
+ align:start position:0%
+but that was also because there's all
+ 
+
+ align:start position:0%
+but that was also because there's all
+this revenue potential as this little
+
+ align:start position:0%
+this revenue potential as this little
+ 
+
+ align:start position:0%
+this revenue potential as this little
+graphic says beneath
+
+ align:start position:0%
+graphic says beneath
+ 
+
+ align:start position:0%
+graphic says beneath
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+uh romaine questions if i can pause a
+
+ align:start position:0%
+uh romaine questions if i can pause a
+ 
+
+ align:start position:0%
+uh romaine questions if i can pause a
+little bit because it's about the
+
+ align:start position:0%
+little bit because it's about the
+ 
+
+ align:start position:0%
+little bit because it's about the
+business models of
+
+ align:start position:0%
+business models of
+ 
+
+ align:start position:0%
+business models of
+brokerage and the business models of
+
+ align:start position:0%
+brokerage and the business models of
+ 
+
+ align:start position:0%
+brokerage and the business models of
+investment banking
+
+ align:start position:0%
+investment banking
+ 
+
+ align:start position:0%
+investment banking
+let's wait a few seconds so people
+
+ align:start position:0%
+let's wait a few seconds so people
+ 
+
+ align:start position:0%
+let's wait a few seconds so people
+worldwide lived at goldman sachs for 18
+
+ align:start position:0%
+worldwide lived at goldman sachs for 18
+ 
+
+ align:start position:0%
+worldwide lived at goldman sachs for 18
+years even though that feels like
+
+ align:start position:0%
+years even though that feels like
+ 
+
+ align:start position:0%
+years even though that feels like
+another era
+
+ align:start position:0%
+another era
+ 
+
+ align:start position:0%
+another era
+so we have a few questions let's take
+
+ align:start position:0%
+so we have a few questions let's take
+ 
+
+ align:start position:0%
+so we have a few questions let's take
+luke and then hassan
+
+ align:start position:0%
+luke and then hassan
+ 
+
+ align:start position:0%
+luke and then hassan
+so i have one quick question um when it
+
+ align:start position:0%
+so i have one quick question um when it
+ 
+
+ align:start position:0%
+so i have one quick question um when it
+comes to traders or trading platforms
+
+ align:start position:0%
+comes to traders or trading platforms
+ 
+
+ align:start position:0%
+comes to traders or trading platforms
+banks usually make money by holding
+
+ align:start position:0%
+banks usually make money by holding
+ 
+
+ align:start position:0%
+banks usually make money by holding
+deposits
+
+ align:start position:0%
+deposits
+ 
+
+ align:start position:0%
+deposits
+uh in daily basis because that's a
+
+ align:start position:0%
+uh in daily basis because that's a
+ 
+
+ align:start position:0%
+uh in daily basis because that's a
+revenue to the firm
+
+ align:start position:0%
+revenue to the firm
+ 
+
+ align:start position:0%
+revenue to the firm
+it's especially hard to do so in u.s
+
+ align:start position:0%
+it's especially hard to do so in u.s
+ 
+
+ align:start position:0%
+it's especially hard to do so in u.s
+when interest rate is near zero but in
+
+ align:start position:0%
+when interest rate is near zero but in
+ 
+
+ align:start position:0%
+when interest rate is near zero but in
+emerging markets such as
+
+ align:start position:0%
+emerging markets such as
+ 
+
+ align:start position:0%
+emerging markets such as
+korea china or india they basically make
+
+ align:start position:0%
+korea china or india they basically make
+ 
+
+ align:start position:0%
+korea china or india they basically make
+the revenue if you have somebody's money
+
+ align:start position:0%
+the revenue if you have somebody's money
+ 
+
+ align:start position:0%
+the revenue if you have somebody's money
+and you can lend it out in that interest
+
+ align:start position:0%
+and you can lend it out in that interest
+ 
+
+ align:start position:0%
+and you can lend it out in that interest
+margin of positive
+
+ align:start position:0%
+margin of positive
+ 
+
+ align:start position:0%
+margin of positive
+how do platforms like these e-trade or
+
+ align:start position:0%
+how do platforms like these e-trade or
+ 
+
+ align:start position:0%
+how do platforms like these e-trade or
+robinhood make money when they transfer
+
+ align:start position:0%
+robinhood make money when they transfer
+ 
+
+ align:start position:0%
+robinhood make money when they transfer
+the money from a deposit
+
+ align:start position:0%
+the money from a deposit
+ 
+
+ align:start position:0%
+the money from a deposit
+to their account and takes two three
+
+ align:start position:0%
+to their account and takes two three
+ 
+
+ align:start position:0%
+to their account and takes two three
+days and they can make money out of it
+
+ align:start position:0%
+days and they can make money out of it
+ 
+
+ align:start position:0%
+days and they can make money out of it
+besides these hedge fund deals that you
+
+ align:start position:0%
+besides these hedge fund deals that you
+ 
+
+ align:start position:0%
+besides these hedge fund deals that you
+have explained
+
+ align:start position:0%
+have explained
+ 
+
+ align:start position:0%
+have explained
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a great question so the classic
+
+ align:start position:0%
+a great question so the classic
+ 
+
+ align:start position:0%
+a great question so the classic
+what i would call a commercial bank
+
+ align:start position:0%
+what i would call a commercial bank
+ 
+
+ align:start position:0%
+what i would call a commercial bank
+model is exactly what luke said
+
+ align:start position:0%
+model is exactly what luke said
+ 
+
+ align:start position:0%
+model is exactly what luke said
+to pot there's a net interest spread
+
+ align:start position:0%
+to pot there's a net interest spread
+ 
+
+ align:start position:0%
+to pot there's a net interest spread
+between the depositors money and what
+
+ align:start position:0%
+between the depositors money and what
+ 
+
+ align:start position:0%
+between the depositors money and what
+you lend it out and whether you're a
+
+ align:start position:0%
+you lend it out and whether you're a
+ 
+
+ align:start position:0%
+you lend it out and whether you're a
+trillion dollar bank or a hundred
+
+ align:start position:0%
+trillion dollar bank or a hundred
+ 
+
+ align:start position:0%
+trillion dollar bank or a hundred
+million dollar bank it's basically that
+
+ align:start position:0%
+million dollar bank it's basically that
+ 
+
+ align:start position:0%
+million dollar bank it's basically that
+spread between the depositors money and
+
+ align:start position:0%
+spread between the depositors money and
+ 
+
+ align:start position:0%
+spread between the depositors money and
+what you're lending out that model's
+
+ align:start position:0%
+what you're lending out that model's
+ 
+
+ align:start position:0%
+what you're lending out that model's
+been around for
+
+ align:start position:0%
+been around for
+ 
+
+ align:start position:0%
+been around for
+centuries
+
+ align:start position:0%
+centuries
+ 
+
+ align:start position:0%
+centuries
+uh and as luke said it's a little bit
+
+ align:start position:0%
+uh and as luke said it's a little bit
+ 
+
+ align:start position:0%
+uh and as luke said it's a little bit
+more challenging in different interest
+
+ align:start position:0%
+more challenging in different interest
+ 
+
+ align:start position:0%
+more challenging in different interest
+rate environments but that's been there
+
+ align:start position:0%
+rate environments but that's been there
+ 
+
+ align:start position:0%
+rate environments but that's been there
+the brokerage business traditionally was
+
+ align:start position:0%
+the brokerage business traditionally was
+ 
+
+ align:start position:0%
+the brokerage business traditionally was
+making money on commissions and
+
+ align:start position:0%
+making money on commissions and
+ 
+
+ align:start position:0%
+making money on commissions and
+commissions was a big part of that
+
+ align:start position:0%
+commissions was a big part of that
+ 
+
+ align:start position:0%
+commissions was a big part of that
+revenue model all the way through the
+
+ align:start position:0%
+revenue model all the way through the
+ 
+
+ align:start position:0%
+revenue model all the way through the
+1960s and 70s but there's other pieces
+
+ align:start position:0%
+1960s and 70s but there's other pieces
+ 
+
+ align:start position:0%
+1960s and 70s but there's other pieces
+of it as well
+
+ align:start position:0%
+of it as well
+ 
+
+ align:start position:0%
+of it as well
+beyond just the commission of as we saw
+
+ align:start position:0%
+beyond just the commission of as we saw
+ 
+
+ align:start position:0%
+beyond just the commission of as we saw
+in that chart 25 cents a share long ago
+
+ align:start position:0%
+in that chart 25 cents a share long ago
+ 
+
+ align:start position:0%
+in that chart 25 cents a share long ago
+or three or five cents a share more
+
+ align:start position:0%
+or three or five cents a share more
+ 
+
+ align:start position:0%
+or three or five cents a share more
+recently
+
+ align:start position:0%
+recently
+ 
+
+ align:start position:0%
+recently
+beyond that it's also
+
+ align:start position:0%
+beyond that it's also
+ 
+
+ align:start position:0%
+beyond that it's also
+when you buy and sell securities you
+
+ align:start position:0%
+when you buy and sell securities you
+ 
+
+ align:start position:0%
+when you buy and sell securities you
+there is what's known as a bid offer
+
+ align:start position:0%
+there is what's known as a bid offer
+ 
+
+ align:start position:0%
+there is what's known as a bid offer
+spread the difference between the bid
+
+ align:start position:0%
+spread the difference between the bid
+ 
+
+ align:start position:0%
+spread the difference between the bid
+side and where somebody's offering it
+
+ align:start position:0%
+side and where somebody's offering it
+ 
+
+ align:start position:0%
+side and where somebody's offering it
+and a market maker can be in the middle
+
+ align:start position:0%
+and a market maker can be in the middle
+ 
+
+ align:start position:0%
+and a market maker can be in the middle
+and provide liquidity to the market get
+
+ align:start position:0%
+and provide liquidity to the market get
+ 
+
+ align:start position:0%
+and provide liquidity to the market get
+paid for taking risk
+
+ align:start position:0%
+paid for taking risk
+ 
+
+ align:start position:0%
+paid for taking risk
+it's it's a risk return business
+
+ align:start position:0%
+it's it's a risk return business
+ 
+
+ align:start position:0%
+it's it's a risk return business
+but first luke is the bid offer spread
+
+ align:start position:0%
+but first luke is the bid offer spread
+ 
+
+ align:start position:0%
+but first luke is the bid offer spread
+just being in the flow
+
+ align:start position:0%
+just being in the flow
+ 
+
+ align:start position:0%
+just being in the flow
+in robinhood's case robin who had said
+
+ align:start position:0%
+in robinhood's case robin who had said
+ 
+
+ align:start position:0%
+in robinhood's case robin who had said
+we don't have the balance sheet
+
+ align:start position:0%
+we don't have the balance sheet
+ 
+
+ align:start position:0%
+we don't have the balance sheet
+we're not going to pay for the bid ass
+
+ align:start position:0%
+we're not going to pay for the bid ass
+ 
+
+ align:start position:0%
+we're not going to pay for the bid ass
+spread but we will enter into
+
+ align:start position:0%
+spread but we will enter into
+ 
+
+ align:start position:0%
+spread but we will enter into
+transactions with high frequency trading
+
+ align:start position:0%
+transactions with high frequency trading
+ 
+
+ align:start position:0%
+transactions with high frequency trading
+shops and effectively
+
+ align:start position:0%
+shops and effectively
+ 
+
+ align:start position:0%
+shops and effectively
+give them access to this flow of
+
+ align:start position:0%
+give them access to this flow of
+ 
+
+ align:start position:0%
+give them access to this flow of
+transactions and so that's payment for
+
+ align:start position:0%
+transactions and so that's payment for
+ 
+
+ align:start position:0%
+transactions and so that's payment for
+order flow
+
+ align:start position:0%
+order flow
+ 
+
+ align:start position:0%
+order flow
+and the high frequency trading shops are
+
+ align:start position:0%
+and the high frequency trading shops are
+ 
+
+ align:start position:0%
+and the high frequency trading shops are
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+trying to tap into that bid offer spread
+
+ align:start position:0%
+trying to tap into that bid offer spread
+ 
+
+ align:start position:0%
+trying to tap into that bid offer spread
+so that's a that's a dominant part of it
+
+ align:start position:0%
+so that's a that's a dominant part of it
+ 
+
+ align:start position:0%
+so that's a that's a dominant part of it
+in addition just to name one other but
+
+ align:start position:0%
+in addition just to name one other but
+ 
+
+ align:start position:0%
+in addition just to name one other but
+there are many others in addition
+
+ align:start position:0%
+there are many others in addition
+ 
+
+ align:start position:0%
+there are many others in addition
+charles schwab and others merrill lynch
+
+ align:start position:0%
+charles schwab and others merrill lynch
+ 
+
+ align:start position:0%
+charles schwab and others merrill lynch
+figured this out decades ago
+
+ align:start position:0%
+figured this out decades ago
+ 
+
+ align:start position:0%
+figured this out decades ago
+once you have that customer relationship
+
+ align:start position:0%
+once you have that customer relationship
+ 
+
+ align:start position:0%
+once you have that customer relationship
+that customer relationship will come to
+
+ align:start position:0%
+that customer relationship will come to
+ 
+
+ align:start position:0%
+that customer relationship will come to
+you for other things and and they will
+
+ align:start position:0%
+you for other things and and they will
+ 
+
+ align:start position:0%
+you for other things and and they will
+come to you to do margin lending which
+
+ align:start position:0%
+come to you to do margin lending which
+ 
+
+ align:start position:0%
+come to you to do margin lending which
+is a form of borrowing
+
+ align:start position:0%
+is a form of borrowing
+ 
+
+ align:start position:0%
+is a form of borrowing
+and so you have maybe them
+
+ align:start position:0%
+and so you have maybe them
+ 
+
+ align:start position:0%
+and so you have maybe them
+that that customer there who you can
+
+ align:start position:0%
+that that customer there who you can
+ 
+
+ align:start position:0%
+that that customer there who you can
+actually use your balance sheet and lend
+
+ align:start position:0%
+actually use your balance sheet and lend
+ 
+
+ align:start position:0%
+actually use your balance sheet and lend
+them money usually what's called margin
+
+ align:start position:0%
+them money usually what's called margin
+ 
+
+ align:start position:0%
+them money usually what's called margin
+lending so
+
+ align:start position:0%
+lending so
+ 
+
+ align:start position:0%
+lending so
+i'm just mentioning two of them bit ass
+
+ align:start position:0%
+i'm just mentioning two of them bit ass
+ 
+
+ align:start position:0%
+i'm just mentioning two of them bit ass
+spread
+
+ align:start position:0%
+spread
+ 
+
+ align:start position:0%
+spread
+robin hood was not taking that
+
+ align:start position:0%
+robin hood was not taking that
+ 
+
+ align:start position:0%
+robin hood was not taking that
+themselves they were selling that access
+
+ align:start position:0%
+themselves they were selling that access
+ 
+
+ align:start position:0%
+themselves they were selling that access
+and then the relationship that you can
+
+ align:start position:0%
+and then the relationship that you can
+ 
+
+ align:start position:0%
+and then the relationship that you can
+have on using your balance sheet and
+
+ align:start position:0%
+have on using your balance sheet and
+ 
+
+ align:start position:0%
+have on using your balance sheet and
+lending money
+
+ align:start position:0%
+lending money
+ 
+
+ align:start position:0%
+lending money
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+can you tell us a little bit about the
+
+ align:start position:0%
+can you tell us a little bit about the
+ 
+
+ align:start position:0%
+can you tell us a little bit about the
+kickbacks in the presentation what's
+
+ align:start position:0%
+kickbacks in the presentation what's
+ 
+
+ align:start position:0%
+kickbacks in the presentation what's
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+can you tell us a little bit about the
+
+ align:start position:0%
+can you tell us a little bit about the
+ 
+
+ align:start position:0%
+can you tell us a little bit about the
+kickbacks in the presentation you have
+
+ align:start position:0%
+kickbacks in the presentation you have
+ 
+
+ align:start position:0%
+kickbacks in the presentation you have
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+these are not my words these are jason
+
+ align:start position:0%
+these are not my words these are jason
+ 
+
+ align:start position:0%
+these are not my words these are jason
+wank of
+
+ align:start position:0%
+wank of
+ 
+
+ align:start position:0%
+wank of
+altrus but altruist but
+
+ align:start position:0%
+altrus but altruist but
+ 
+
+ align:start position:0%
+altrus but altruist but
+in essence there's so many different
+
+ align:start position:0%
+in essence there's so many different
+ 
+
+ align:start position:0%
+in essence there's so many different
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh you might take a customer's order
+
+ align:start position:0%
+uh you might take a customer's order
+ 
+
+ align:start position:0%
+uh you might take a customer's order
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+and and sell access to that
+
+ align:start position:0%
+and and sell access to that
+ 
+
+ align:start position:0%
+and and sell access to that
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+you might
+
+ align:start position:0%
+you might
+ 
+
+ align:start position:0%
+you might
+be the front-end model you could be i'm
+
+ align:start position:0%
+be the front-end model you could be i'm
+ 
+
+ align:start position:0%
+be the front-end model you could be i'm
+not saying robinhood or schwab are doing
+
+ align:start position:0%
+not saying robinhood or schwab are doing
+ 
+
+ align:start position:0%
+not saying robinhood or schwab are doing
+this but you can be that front-end model
+
+ align:start position:0%
+this but you can be that front-end model
+ 
+
+ align:start position:0%
+this but you can be that front-end model
+and then somebody else will pay you pay
+
+ align:start position:0%
+and then somebody else will pay you pay
+ 
+
+ align:start position:0%
+and then somebody else will pay you pay
+the schwab pay the robin hood
+
+ align:start position:0%
+the schwab pay the robin hood
+ 
+
+ align:start position:0%
+the schwab pay the robin hood
+and so i think what jason wenk who wrote
+
+ align:start position:0%
+and so i think what jason wenk who wrote
+ 
+
+ align:start position:0%
+and so i think what jason wenk who wrote
+this is calling about a kickback but
+
+ align:start position:0%
+this is calling about a kickback but
+ 
+
+ align:start position:0%
+this is calling about a kickback but
+it's it's a a sort of
+
+ align:start position:0%
+it's it's a a sort of
+ 
+
+ align:start position:0%
+it's it's a a sort of
+a contractual arrangement to be have
+
+ align:start position:0%
+a contractual arrangement to be have
+ 
+
+ align:start position:0%
+a contractual arrangement to be have
+access to that customer and that order
+
+ align:start position:0%
+access to that customer and that order
+ 
+
+ align:start position:0%
+access to that customer and that order
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+i safely assume that they're selling our
+
+ align:start position:0%
+i safely assume that they're selling our
+ 
+
+ align:start position:0%
+i safely assume that they're selling our
+data as well as google is doing
+
+ align:start position:0%
+data as well as google is doing
+ 
+
+ align:start position:0%
+data as well as google is doing
+so data is really important and data is
+
+ align:start position:0%
+so data is really important and data is
+ 
+
+ align:start position:0%
+so data is really important and data is
+really important for multiple reasons
+
+ align:start position:0%
+really important for multiple reasons
+ 
+
+ align:start position:0%
+really important for multiple reasons
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+the better data you have the better
+
+ align:start position:0%
+the better data you have the better
+ 
+
+ align:start position:0%
+the better data you have the better
+trading algorithms you can create
+
+ align:start position:0%
+trading algorithms you can create
+ 
+
+ align:start position:0%
+trading algorithms you can create
+so part of the payment for order flow is
+
+ align:start position:0%
+so part of the payment for order flow is
+ 
+
+ align:start position:0%
+so part of the payment for order flow is
+to capture bids spread part of the
+
+ align:start position:0%
+to capture bids spread part of the
+ 
+
+ align:start position:0%
+to capture bids spread part of the
+payment for order flow
+
+ align:start position:0%
+payment for order flow
+ 
+
+ align:start position:0%
+payment for order flow
+is the data so that you can build your
+
+ align:start position:0%
+is the data so that you can build your
+ 
+
+ align:start position:0%
+is the data so that you can build your
+algorithms you have more data for your
+
+ align:start position:0%
+algorithms you have more data for your
+ 
+
+ align:start position:0%
+algorithms you have more data for your
+machine learning absolutely there's also
+
+ align:start position:0%
+machine learning absolutely there's also
+ 
+
+ align:start position:0%
+machine learning absolutely there's also
+other relevant data but
+
+ align:start position:0%
+other relevant data but
+ 
+
+ align:start position:0%
+other relevant data but
+fundamentally the data is to be a better
+
+ align:start position:0%
+fundamentally the data is to be a better
+ 
+
+ align:start position:0%
+fundamentally the data is to be a better
+market maker and a better investor i
+
+ align:start position:0%
+market maker and a better investor i
+ 
+
+ align:start position:0%
+market maker and a better investor i
+think romaine there was somebody else
+
+ align:start position:0%
+think romaine there was somebody else
+ 
+
+ align:start position:0%
+think romaine there was somebody else
+that still had a question before i go on
+
+ align:start position:0%
+that still had a question before i go on
+ 
+
+ align:start position:0%
+that still had a question before i go on
+yes hassan
+
+ align:start position:0%
+yes hassan
+ 
+
+ align:start position:0%
+yes hassan
+hi professor yeah my question is about
+
+ align:start position:0%
+hi professor yeah my question is about
+ 
+
+ align:start position:0%
+hi professor yeah my question is about
+the bird ask
+
+ align:start position:0%
+the bird ask
+ 
+
+ align:start position:0%
+the bird ask
+margin
+
+ align:start position:0%
+margin
+ 
+
+ align:start position:0%
+margin
+and i'm just wondering i mean uh
+
+ align:start position:0%
+and i'm just wondering i mean uh
+ 
+
+ align:start position:0%
+and i'm just wondering i mean uh
+so for instance like like um robin hood
+
+ align:start position:0%
+so for instance like like um robin hood
+ 
+
+ align:start position:0%
+so for instance like like um robin hood
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+so because they had many customers they
+
+ align:start position:0%
+so because they had many customers they
+ 
+
+ align:start position:0%
+so because they had many customers they
+could get better deals and
+
+ align:start position:0%
+could get better deals and
+ 
+
+ align:start position:0%
+could get better deals and
+they could benefit from the from from
+
+ align:start position:0%
+they could benefit from the from from
+ 
+
+ align:start position:0%
+they could benefit from the from from
+from the flow of customers that they
+
+ align:start position:0%
+from the flow of customers that they
+ 
+
+ align:start position:0%
+from the flow of customers that they
+have is this how they make money i'm
+
+ align:start position:0%
+have is this how they make money i'm
+ 
+
+ align:start position:0%
+have is this how they make money i'm
+just wondering well so actually the way
+
+ align:start position:0%
+just wondering well so actually the way
+ 
+
+ align:start position:0%
+just wondering well so actually the way
+they made money is they were getting
+
+ align:start position:0%
+they made money is they were getting
+ 
+
+ align:start position:0%
+they made money is they were getting
+paid for that flow because their
+
+ align:start position:0%
+paid for that flow because their
+ 
+
+ align:start position:0%
+paid for that flow because their
+business model early on and others like
+
+ align:start position:0%
+business model early on and others like
+ 
+
+ align:start position:0%
+business model early on and others like
+them now said we will go to the
+
+ align:start position:0%
+them now said we will go to the
+ 
+
+ align:start position:0%
+them now said we will go to the
+investing public and zero commission
+
+ align:start position:0%
+investing public and zero commission
+ 
+
+ align:start position:0%
+investing public and zero commission
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh somebody else will pay us
+
+ align:start position:0%
+uh somebody else will pay us
+ 
+
+ align:start position:0%
+uh somebody else will pay us
+a fraction of a penny at this point in
+
+ align:start position:0%
+a fraction of a penny at this point in
+ 
+
+ align:start position:0%
+a fraction of a penny at this point in
+time would be enough but a fraction of a
+
+ align:start position:0%
+time would be enough but a fraction of a
+ 
+
+ align:start position:0%
+time would be enough but a fraction of a
+penny
+
+ align:start position:0%
+penny
+ 
+
+ align:start position:0%
+penny
+that other party would pay us
+
+ align:start position:0%
+that other party would pay us
+ 
+
+ align:start position:0%
+that other party would pay us
+to in essence
+
+ align:start position:0%
+to in essence
+ 
+
+ align:start position:0%
+to in essence
+route those transactions to the stock
+
+ align:start position:0%
+route those transactions to the stock
+ 
+
+ align:start position:0%
+route those transactions to the stock
+exchanges
+
+ align:start position:0%
+exchanges
+ 
+
+ align:start position:0%
+exchanges
+and so one company that does pay for
+
+ align:start position:0%
+and so one company that does pay for
+ 
+
+ align:start position:0%
+and so one company that does pay for
+order flow is a large
+
+ align:start position:0%
+order flow is a large
+ 
+
+ align:start position:0%
+order flow is a large
+hedge fund high frequency shop from
+
+ align:start position:0%
+hedge fund high frequency shop from
+ 
+
+ align:start position:0%
+hedge fund high frequency shop from
+chicago called citadel
+
+ align:start position:0%
+chicago called citadel
+ 
+
+ align:start position:0%
+chicago called citadel
+which uh i don't know its current size
+
+ align:start position:0%
+which uh i don't know its current size
+ 
+
+ align:start position:0%
+which uh i don't know its current size
+but it used to be about a 20 billion
+
+ align:start position:0%
+but it used to be about a 20 billion
+ 
+
+ align:start position:0%
+but it used to be about a 20 billion
+dollar hedge fund asset management
+
+ align:start position:0%
+dollar hedge fund asset management
+ 
+
+ align:start position:0%
+dollar hedge fund asset management
+shop
+
+ align:start position:0%
+shop
+ 
+
+ align:start position:0%
+shop
+and a very active in high frequency
+
+ align:start position:0%
+and a very active in high frequency
+ 
+
+ align:start position:0%
+and a very active in high frequency
+trading it's very public that it is
+
+ align:start position:0%
+trading it's very public that it is
+ 
+
+ align:start position:0%
+trading it's very public that it is
+and so citadel is one of those vendors
+
+ align:start position:0%
+and so citadel is one of those vendors
+ 
+
+ align:start position:0%
+and so citadel is one of those vendors
+on the other side of the robin hood app
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then they find a way as we were
+
+ align:start position:0%
+and then they find a way as we were
+ 
+
+ align:start position:0%
+and then they find a way as we were
+talking with luke they find the citadels
+
+ align:start position:0%
+talking with luke they find the citadels
+ 
+
+ align:start position:0%
+talking with luke they find the citadels
+of the world not just citadel they find
+
+ align:start position:0%
+of the world not just citadel they find
+ 
+
+ align:start position:0%
+of the world not just citadel they find
+that that order flow is then valuable
+
+ align:start position:0%
+that that order flow is then valuable
+ 
+
+ align:start position:0%
+that that order flow is then valuable
+for them
+
+ align:start position:0%
+for them
+ 
+
+ align:start position:0%
+for them
+they're routing some of it to this the
+
+ align:start position:0%
+they're routing some of it to this the
+ 
+
+ align:start position:0%
+they're routing some of it to this the
+stock exchange and that could still be
+
+ align:start position:0%
+stock exchange and that could still be
+ 
+
+ align:start position:0%
+stock exchange and that could still be
+worth something they're putting it into
+
+ align:start position:0%
+worth something they're putting it into
+ 
+
+ align:start position:0%
+worth something they're putting it into
+their analytics they then get better
+
+ align:start position:0%
+their analytics they then get better
+ 
+
+ align:start position:0%
+their analytics they then get better
+sophisticated machine learning on the
+
+ align:start position:0%
+sophisticated machine learning on the
+ 
+
+ align:start position:0%
+sophisticated machine learning on the
+analytics
+
+ align:start position:0%
+analytics
+ 
+
+ align:start position:0%
+analytics
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that order flow is also something
+
+ align:start position:0%
+and that order flow is also something
+ 
+
+ align:start position:0%
+and that order flow is also something
+that can be very valuable to an operator
+
+ align:start position:0%
+that can be very valuable to an operator
+ 
+
+ align:start position:0%
+that can be very valuable to an operator
+of a dark market one of these small uh
+
+ align:start position:0%
+of a dark market one of these small uh
+ 
+
+ align:start position:0%
+of a dark market one of these small uh
+electronic markets because you're all
+
+ align:start position:0%
+electronic markets because you're all
+ 
+
+ align:start position:0%
+electronic markets because you're all
+competing if there's 60 or 70 of these
+
+ align:start position:0%
+competing if there's 60 or 70 of these
+ 
+
+ align:start position:0%
+competing if there's 60 or 70 of these
+small dark markets they're all competing
+
+ align:start position:0%
+small dark markets they're all competing
+ 
+
+ align:start position:0%
+small dark markets they're all competing
+for volume
+
+ align:start position:0%
+for volume
+ 
+
+ align:start position:0%
+for volume
+and market share and then all of a
+
+ align:start position:0%
+and market share and then all of a
+ 
+
+ align:start position:0%
+and market share and then all of a
+sudden robin hood has not just
+
+ align:start position:0%
+sudden robin hood has not just
+ 
+
+ align:start position:0%
+sudden robin hood has not just
+a few hundred thousand customers but
+
+ align:start position:0%
+a few hundred thousand customers but
+ 
+
+ align:start position:0%
+a few hundred thousand customers but
+they have five or ten million customers
+
+ align:start position:0%
+they have five or ten million customers
+ 
+
+ align:start position:0%
+they have five or ten million customers
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you know they can provide a lot of order
+
+ align:start position:0%
+you know they can provide a lot of order
+ 
+
+ align:start position:0%
+you know they can provide a lot of order
+flow and a lot of market coverage
+
+ align:start position:0%
+flow and a lot of market coverage
+ 
+
+ align:start position:0%
+flow and a lot of market coverage
+for somebody on the other side
+
+ align:start position:0%
+for somebody on the other side
+ 
+
+ align:start position:0%
+for somebody on the other side
+now as it relates to schwab
+
+ align:start position:0%
+now as it relates to schwab
+ 
+
+ align:start position:0%
+now as it relates to schwab
+schwab and some of the earlier online
+
+ align:start position:0%
+schwab and some of the earlier online
+ 
+
+ align:start position:0%
+schwab and some of the earlier online
+brokers they got into the business of
+
+ align:start position:0%
+brokers they got into the business of
+ 
+
+ align:start position:0%
+brokers they got into the business of
+collecting assets under management they
+
+ align:start position:0%
+collecting assets under management they
+ 
+
+ align:start position:0%
+collecting assets under management they
+got into the asset under management
+
+ align:start position:0%
+got into the asset under management
+ 
+
+ align:start position:0%
+got into the asset under management
+custodial side of the business as well
+
+ align:start position:0%
+custodial side of the business as well
+ 
+
+ align:start position:0%
+custodial side of the business as well
+there's a lot of other revenue streams
+
+ align:start position:0%
+there's a lot of other revenue streams
+ 
+
+ align:start position:0%
+there's a lot of other revenue streams
+transaction fees account maintenance
+
+ align:start position:0%
+transaction fees account maintenance
+ 
+
+ align:start position:0%
+transaction fees account maintenance
+fees
+
+ align:start position:0%
+fees
+ 
+
+ align:start position:0%
+fees
+and even advisory fees uh in in those
+
+ align:start position:0%
+and even advisory fees uh in in those
+ 
+
+ align:start position:0%
+and even advisory fees uh in in those
+shops
+
+ align:start position:0%
+shops
+ 
+
+ align:start position:0%
+shops
+and i think you'll see merging i want to
+
+ align:start position:0%
+and i think you'll see merging i want to
+ 
+
+ align:start position:0%
+and i think you'll see merging i want to
+move on now to wealth management i think
+
+ align:start position:0%
+move on now to wealth management i think
+ 
+
+ align:start position:0%
+move on now to wealth management i think
+you'll see merging
+
+ align:start position:0%
+you'll see merging
+ 
+
+ align:start position:0%
+you'll see merging
+uh between the wealth management fees
+
+ align:start position:0%
+uh between the wealth management fees
+ 
+
+ align:start position:0%
+uh between the wealth management fees
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+brokerage fees
+
+ align:start position:0%
+brokerage fees
+ 
+
+ align:start position:0%
+brokerage fees
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which is exactly what we've seen over
+
+ align:start position:0%
+which is exactly what we've seen over
+ 
+
+ align:start position:0%
+which is exactly what we've seen over
+time in the traditional brokerage field
+
+ align:start position:0%
+time in the traditional brokerage field
+ 
+
+ align:start position:0%
+time in the traditional brokerage field
+the traditional brokerage field for
+
+ align:start position:0%
+the traditional brokerage field for
+ 
+
+ align:start position:0%
+the traditional brokerage field for
+decades a broker earned commissions and
+
+ align:start position:0%
+decades a broker earned commissions and
+ 
+
+ align:start position:0%
+decades a broker earned commissions and
+then they started by the late 1990s
+
+ align:start position:0%
+then they started by the late 1990s
+ 
+
+ align:start position:0%
+then they started by the late 1990s
+with some support from the regulators to
+
+ align:start position:0%
+with some support from the regulators to
+ 
+
+ align:start position:0%
+with some support from the regulators to
+change their revenue models the
+
+ align:start position:0%
+change their revenue models the
+ 
+
+ align:start position:0%
+change their revenue models the
+traditional merrill lynch broker from
+
+ align:start position:0%
+traditional merrill lynch broker from
+ 
+
+ align:start position:0%
+traditional merrill lynch broker from
+the 1930s to the 1980s was a
+
+ align:start position:0%
+the 1930s to the 1980s was a
+ 
+
+ align:start position:0%
+the 1930s to the 1980s was a
+commission-based broker but by the 1990s
+
+ align:start position:0%
+commission-based broker but by the 1990s
+ 
+
+ align:start position:0%
+commission-based broker but by the 1990s
+they started to charge advisory fees
+
+ align:start position:0%
+they started to charge advisory fees
+ 
+
+ align:start position:0%
+they started to charge advisory fees
+meaning for instance maybe one percent
+
+ align:start position:0%
+meaning for instance maybe one percent
+ 
+
+ align:start position:0%
+meaning for instance maybe one percent
+of the assets that you left with them
+
+ align:start position:0%
+of the assets that you left with them
+ 
+
+ align:start position:0%
+of the assets that you left with them
+and if you leave a million dollars if
+
+ align:start position:0%
+and if you leave a million dollars if
+ 
+
+ align:start position:0%
+and if you leave a million dollars if
+you're wealthy enough to have that
+
+ align:start position:0%
+you're wealthy enough to have that
+ 
+
+ align:start position:0%
+you're wealthy enough to have that
+million dollars that means they're
+
+ align:start position:0%
+million dollars that means they're
+ 
+
+ align:start position:0%
+million dollars that means they're
+earning ten thousand dollars a year
+
+ align:start position:0%
+earning ten thousand dollars a year
+ 
+
+ align:start position:0%
+earning ten thousand dollars a year
+of on your account
+
+ align:start position:0%
+of on your account
+ 
+
+ align:start position:0%
+of on your account
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you obviously had more that would
+
+ align:start position:0%
+if you obviously had more that would
+ 
+
+ align:start position:0%
+if you obviously had more that would
+even be better for merrill lynch and
+
+ align:start position:0%
+even be better for merrill lynch and
+ 
+
+ align:start position:0%
+even be better for merrill lynch and
+worse for you because you'd be leaving
+
+ align:start position:0%
+worse for you because you'd be leaving
+ 
+
+ align:start position:0%
+worse for you because you'd be leaving
+them a lot of money to just
+
+ align:start position:0%
+them a lot of money to just
+ 
+
+ align:start position:0%
+them a lot of money to just
+be a custodian for your
+
+ align:start position:0%
+be a custodian for your
+ 
+
+ align:start position:0%
+be a custodian for your
+account largely and to give you advice
+
+ align:start position:0%
+account largely and to give you advice
+ 
+
+ align:start position:0%
+account largely and to give you advice
+from time to time
+
+ align:start position:0%
+from time to time
+ 
+
+ align:start position:0%
+from time to time
+and that's kind of the setup
+
+ align:start position:0%
+and that's kind of the setup
+ 
+
+ align:start position:0%
+and that's kind of the setup
+for the next discussion uh romaine any
+
+ align:start position:0%
+for the next discussion uh romaine any
+ 
+
+ align:start position:0%
+for the next discussion uh romaine any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+nope all good
+
+ align:start position:0%
+nope all good
+ 
+
+ align:start position:0%
+nope all good
+so robo advisory and hassan sort of
+
+ align:start position:0%
+so robo advisory and hassan sort of
+ 
+
+ align:start position:0%
+so robo advisory and hassan sort of
+helped me set this up i'm gonna do the
+
+ align:start position:0%
+helped me set this up i'm gonna do the
+ 
+
+ align:start position:0%
+helped me set this up i'm gonna do the
+same sort of landscape we have the same
+
+ align:start position:0%
+same sort of landscape we have the same
+ 
+
+ align:start position:0%
+same sort of landscape we have the same
+groups retail brokers asset managers and
+
+ align:start position:0%
+groups retail brokers asset managers and
+ 
+
+ align:start position:0%
+groups retail brokers asset managers and
+the banks
+
+ align:start position:0%
+the banks
+ 
+
+ align:start position:0%
+the banks
+advisory work brokerage advisory was
+
+ align:start position:0%
+advisory work brokerage advisory was
+ 
+
+ align:start position:0%
+advisory work brokerage advisory was
+largely for many decades the domain of
+
+ align:start position:0%
+largely for many decades the domain of
+ 
+
+ align:start position:0%
+largely for many decades the domain of
+investment banks and broker-dealers
+
+ align:start position:0%
+investment banks and broker-dealers
+ 
+
+ align:start position:0%
+investment banks and broker-dealers
+merrill lynch smith barney payne weber
+
+ align:start position:0%
+merrill lynch smith barney payne weber
+ 
+
+ align:start position:0%
+merrill lynch smith barney payne weber
+many many companies
+
+ align:start position:0%
+many many companies
+ 
+
+ align:start position:0%
+many many companies
+across the land small and large and they
+
+ align:start position:0%
+across the land small and large and they
+ 
+
+ align:start position:0%
+across the land small and large and they
+were a commission-based business by the
+
+ align:start position:0%
+were a commission-based business by the
+ 
+
+ align:start position:0%
+were a commission-based business by the
+1990s as i mentioned they started to
+
+ align:start position:0%
+1990s as i mentioned they started to
+ 
+
+ align:start position:0%
+1990s as i mentioned they started to
+move to a financial advisory
+
+ align:start position:0%
+move to a financial advisory
+ 
+
+ align:start position:0%
+move to a financial advisory
+commission
+
+ align:start position:0%
+commission
+ 
+
+ align:start position:0%
+commission
+number and i can't remember exactly what
+
+ align:start position:0%
+number and i can't remember exactly what
+ 
+
+ align:start position:0%
+number and i can't remember exactly what
+year it was in the 1990s even the
+
+ align:start position:0%
+year it was in the 1990s even the
+ 
+
+ align:start position:0%
+year it was in the 1990s even the
+securities and exchange commission
+
+ align:start position:0%
+securities and exchange commission
+ 
+
+ align:start position:0%
+securities and exchange commission
+changed some roles to facilitate some of
+
+ align:start position:0%
+changed some roles to facilitate some of
+ 
+
+ align:start position:0%
+changed some roles to facilitate some of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the big asset managers coming from the
+
+ align:start position:0%
+the big asset managers coming from the
+ 
+
+ align:start position:0%
+the big asset managers coming from the
+other side the big asset managers
+
+ align:start position:0%
+other side the big asset managers
+ 
+
+ align:start position:0%
+other side the big asset managers
+managing pension money and managing
+
+ align:start position:0%
+managing pension money and managing
+ 
+
+ align:start position:0%
+managing pension money and managing
+uh big pools of money through mutual
+
+ align:start position:0%
+uh big pools of money through mutual
+ 
+
+ align:start position:0%
+uh big pools of money through mutual
+funds also started to get into the
+
+ align:start position:0%
+funds also started to get into the
+ 
+
+ align:start position:0%
+funds also started to get into the
+retail advisory space
+
+ align:start position:0%
+retail advisory space
+ 
+
+ align:start position:0%
+retail advisory space
+and thirdly you had the brokers the
+
+ align:start position:0%
+and thirdly you had the brokers the
+ 
+
+ align:start position:0%
+and thirdly you had the brokers the
+schwabs and so forth
+
+ align:start position:0%
+schwabs and so forth
+ 
+
+ align:start position:0%
+schwabs and so forth
+now i've put some names here like
+
+ align:start position:0%
+now i've put some names here like
+ 
+
+ align:start position:0%
+now i've put some names here like
+charles schwab intelligent portfolios
+
+ align:start position:0%
+charles schwab intelligent portfolios
+ 
+
+ align:start position:0%
+charles schwab intelligent portfolios
+which is a more recent
+
+ align:start position:0%
+which is a more recent
+ 
+
+ align:start position:0%
+which is a more recent
+uh rollout that that branding
+
+ align:start position:0%
+uh rollout that that branding
+ 
+
+ align:start position:0%
+uh rollout that that branding
+intelligent portfolios or td americas
+
+ align:start position:0%
+intelligent portfolios or td americas
+ 
+
+ align:start position:0%
+intelligent portfolios or td americas
+ameritrades essential portfolios
+
+ align:start position:0%
+ameritrades essential portfolios
+ 
+
+ align:start position:0%
+ameritrades essential portfolios
+more recent rollout for them and they've
+
+ align:start position:0%
+more recent rollout for them and they've
+ 
+
+ align:start position:0%
+more recent rollout for them and they've
+been reacting
+
+ align:start position:0%
+been reacting
+ 
+
+ align:start position:0%
+been reacting
+to this crowd
+
+ align:start position:0%
+to this crowd
+ 
+
+ align:start position:0%
+to this crowd
+this this remarkable
+
+ align:start position:0%
+this this remarkable
+ 
+
+ align:start position:0%
+this this remarkable
+entrepreneurial
+
+ align:start position:0%
+entrepreneurial
+ 
+
+ align:start position:0%
+entrepreneurial
+mobile app
+
+ align:start position:0%
+mobile app
+ 
+
+ align:start position:0%
+mobile app
+robo advisors
+
+ align:start position:0%
+robo advisors
+ 
+
+ align:start position:0%
+robo advisors
+and what betterment and and and these
+
+ align:start position:0%
+and what betterment and and and these
+ 
+
+ align:start position:0%
+and what betterment and and and these
+companies span the globe
+
+ align:start position:0%
+companies span the globe
+ 
+
+ align:start position:0%
+companies span the globe
+in europe us
+
+ align:start position:0%
+in europe us
+ 
+
+ align:start position:0%
+in europe us
+in asia but what bettermen or nutmag
+
+ align:start position:0%
+in asia but what bettermen or nutmag
+ 
+
+ align:start position:0%
+in asia but what bettermen or nutmag
+and others are doing is they're saying
+
+ align:start position:0%
+and others are doing is they're saying
+ 
+
+ align:start position:0%
+and others are doing is they're saying
+we can give more financial inclusion and
+
+ align:start position:0%
+we can give more financial inclusion and
+ 
+
+ align:start position:0%
+we can give more financial inclusion and
+we can do it in a better user interface
+
+ align:start position:0%
+we can do it in a better user interface
+ 
+
+ align:start position:0%
+we can do it in a better user interface
+and a lower cost structure
+
+ align:start position:0%
+and a lower cost structure
+ 
+
+ align:start position:0%
+and a lower cost structure
+by and large the asset management fees
+
+ align:start position:0%
+by and large the asset management fees
+ 
+
+ align:start position:0%
+by and large the asset management fees
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+an account in the traditional brokerage
+
+ align:start position:0%
+an account in the traditional brokerage
+ 
+
+ align:start position:0%
+an account in the traditional brokerage
+environment was hovering close to one
+
+ align:start position:0%
+environment was hovering close to one
+ 
+
+ align:start position:0%
+environment was hovering close to one
+percent there was some price compression
+
+ align:start position:0%
+percent there was some price compression
+ 
+
+ align:start position:0%
+percent there was some price compression
+some of it was coming down into the
+
+ align:start position:0%
+some of it was coming down into the
+ 
+
+ align:start position:0%
+some of it was coming down into the
+three-quarters of a percent to one
+
+ align:start position:0%
+three-quarters of a percent to one
+ 
+
+ align:start position:0%
+three-quarters of a percent to one
+percent area that means again
+
+ align:start position:0%
+percent area that means again
+ 
+
+ align:start position:0%
+percent area that means again
+if you were fortunate enough to have
+
+ align:start position:0%
+if you were fortunate enough to have
+ 
+
+ align:start position:0%
+if you were fortunate enough to have
+let's just say that you had
+
+ align:start position:0%
+let's just say that you had
+ 
+
+ align:start position:0%
+let's just say that you had
+uh 500 000
+
+ align:start position:0%
+uh 500 000
+ 
+
+ align:start position:0%
+uh 500 000
+and you were able to have somebody
+
+ align:start position:0%
+and you were able to have somebody
+ 
+
+ align:start position:0%
+and you were able to have somebody
+invest it for you or advise you
+
+ align:start position:0%
+invest it for you or advise you
+ 
+
+ align:start position:0%
+invest it for you or advise you
+one percent of 500 000 is 5 000 that's
+
+ align:start position:0%
+one percent of 500 000 is 5 000 that's
+ 
+
+ align:start position:0%
+one percent of 500 000 is 5 000 that's
+400 a month that you were paying in
+
+ align:start position:0%
+400 a month that you were paying in
+ 
+
+ align:start position:0%
+400 a month that you were paying in
+essence for somebody to give you
+
+ align:start position:0%
+essence for somebody to give you
+ 
+
+ align:start position:0%
+essence for somebody to give you
+occasional advice and be your custodian
+
+ align:start position:0%
+occasional advice and be your custodian
+ 
+
+ align:start position:0%
+occasional advice and be your custodian
+for your electronic securities because
+
+ align:start position:0%
+for your electronic securities because
+ 
+
+ align:start position:0%
+for your electronic securities because
+everything was digital by this point in
+
+ align:start position:0%
+everything was digital by this point in
+ 
+
+ align:start position:0%
+everything was digital by this point in
+time it was no longer those earlier days
+
+ align:start position:0%
+time it was no longer those earlier days
+ 
+
+ align:start position:0%
+time it was no longer those earlier days
+where you had physical certificates
+
+ align:start position:0%
+where you had physical certificates
+ 
+
+ align:start position:0%
+where you had physical certificates
+this group came along and said maybe we
+
+ align:start position:0%
+this group came along and said maybe we
+ 
+
+ align:start position:0%
+this group came along and said maybe we
+could do it at a different price point a
+
+ align:start position:0%
+could do it at a different price point a
+ 
+
+ align:start position:0%
+could do it at a different price point a
+better user interface maybe better
+
+ align:start position:0%
+better user interface maybe better
+ 
+
+ align:start position:0%
+better user interface maybe better
+analytics and service
+
+ align:start position:0%
+analytics and service
+ 
+
+ align:start position:0%
+analytics and service
+generally somewhere between 30 to 50
+
+ align:start position:0%
+generally somewhere between 30 to 50
+ 
+
+ align:start position:0%
+generally somewhere between 30 to 50
+basis points or a quarter to a half a
+
+ align:start position:0%
+basis points or a quarter to a half a
+ 
+
+ align:start position:0%
+basis points or a quarter to a half a
+percent that same
+
+ align:start position:0%
+percent that same
+ 
+
+ align:start position:0%
+percent that same
+that same sort of 500 000 if you were to
+
+ align:start position:0%
+that same sort of 500 000 if you were to
+ 
+
+ align:start position:0%
+that same sort of 500 000 if you were to
+have that 500 all of a sudden doesn't
+
+ align:start position:0%
+have that 500 all of a sudden doesn't
+ 
+
+ align:start position:0%
+have that 500 all of a sudden doesn't
+cost you 5 000 or 4 000 a year but it's
+
+ align:start position:0%
+cost you 5 000 or 4 000 a year but it's
+ 
+
+ align:start position:0%
+cost you 5 000 or 4 000 a year but it's
+costing maybe 1500 a year 100 a month
+
+ align:start position:0%
+costing maybe 1500 a year 100 a month
+ 
+
+ align:start position:0%
+costing maybe 1500 a year 100 a month
+now you don't get a bill for the 100 a
+
+ align:start position:0%
+now you don't get a bill for the 100 a
+ 
+
+ align:start position:0%
+now you don't get a bill for the 100 a
+month it's just comes out each
+
+ align:start position:0%
+month it's just comes out each
+ 
+
+ align:start position:0%
+month it's just comes out each
+each month out of your uh
+
+ align:start position:0%
+each month out of your uh
+ 
+
+ align:start position:0%
+each month out of your uh
+account
+
+ align:start position:0%
+account
+ 
+
+ align:start position:0%
+account
+and it's charged as as a fee per se
+
+ align:start position:0%
+and it's charged as as a fee per se
+ 
+
+ align:start position:0%
+and it's charged as as a fee per se
+but there's a there's generally a
+
+ align:start position:0%
+but there's a there's generally a
+ 
+
+ align:start position:0%
+but there's a there's generally a
+different price point
+
+ align:start position:0%
+different price point
+ 
+
+ align:start position:0%
+different price point
+we haven't gone all the way that we went
+
+ align:start position:0%
+we haven't gone all the way that we went
+ 
+
+ align:start position:0%
+we haven't gone all the way that we went
+with online brokerage to mobile
+
+ align:start position:0%
+with online brokerage to mobile
+ 
+
+ align:start position:0%
+with online brokerage to mobile
+brokerage to zero accounts zero fees but
+
+ align:start position:0%
+brokerage to zero accounts zero fees but
+ 
+
+ align:start position:0%
+brokerage to zero accounts zero fees but
+one of the great pressures that have
+
+ align:start position:0%
+one of the great pressures that have
+ 
+
+ align:start position:0%
+one of the great pressures that have
+happened here as well which is off this
+
+ align:start position:0%
+happened here as well which is off this
+ 
+
+ align:start position:0%
+happened here as well which is off this
+page
+
+ align:start position:0%
+page
+ 
+
+ align:start position:0%
+page
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+asset management fees have been coming
+
+ align:start position:0%
+asset management fees have been coming
+ 
+
+ align:start position:0%
+asset management fees have been coming
+down as well
+
+ align:start position:0%
+down as well
+ 
+
+ align:start position:0%
+down as well
+and particularly around the product
+
+ align:start position:0%
+and particularly around the product
+ 
+
+ align:start position:0%
+and particularly around the product
+called exchange traded funds and to
+
+ align:start position:0%
+called exchange traded funds and to
+ 
+
+ align:start position:0%
+called exchange traded funds and to
+understand the field of robo advisors i
+
+ align:start position:0%
+understand the field of robo advisors i
+ 
+
+ align:start position:0%
+understand the field of robo advisors i
+just want to mention something about
+
+ align:start position:0%
+just want to mention something about
+ 
+
+ align:start position:0%
+just want to mention something about
+exchange traded funds which is an
+
+ align:start position:0%
+exchange traded funds which is an
+ 
+
+ align:start position:0%
+exchange traded funds which is an
+invention of the late 1990s
+
+ align:start position:0%
+invention of the late 1990s
+ 
+
+ align:start position:0%
+invention of the late 1990s
+that was a fintech of its time
+
+ align:start position:0%
+that was a fintech of its time
+ 
+
+ align:start position:0%
+that was a fintech of its time
+that somebody came up with the idea i
+
+ align:start position:0%
+that somebody came up with the idea i
+ 
+
+ align:start position:0%
+that somebody came up with the idea i
+can have a mutual fund
+
+ align:start position:0%
+can have a mutual fund
+ 
+
+ align:start position:0%
+can have a mutual fund
+i can have a mutual fund that invests in
+
+ align:start position:0%
+i can have a mutual fund that invests in
+ 
+
+ align:start position:0%
+i can have a mutual fund that invests in
+the entire market
+
+ align:start position:0%
+the entire market
+ 
+
+ align:start position:0%
+the entire market
+and i can do it at a low cost
+
+ align:start position:0%
+and i can do it at a low cost
+ 
+
+ align:start position:0%
+and i can do it at a low cost
+and i could package it through a
+
+ align:start position:0%
+and i could package it through a
+ 
+
+ align:start position:0%
+and i could package it through a
+security so let me unpack that
+
+ align:start position:0%
+security so let me unpack that
+ 
+
+ align:start position:0%
+security so let me unpack that
+the first innovation was an innovation
+
+ align:start position:0%
+the first innovation was an innovation
+ 
+
+ align:start position:0%
+the first innovation was an innovation
+of the early 1970s
+
+ align:start position:0%
+of the early 1970s
+ 
+
+ align:start position:0%
+of the early 1970s
+jack bogle who was the key innovator
+
+ align:start position:0%
+jack bogle who was the key innovator
+ 
+
+ align:start position:0%
+jack bogle who was the key innovator
+behind vanguard said wouldn't it be
+
+ align:start position:0%
+behind vanguard said wouldn't it be
+ 
+
+ align:start position:0%
+behind vanguard said wouldn't it be
+great if we gave america at the time a
+
+ align:start position:0%
+great if we gave america at the time a
+ 
+
+ align:start position:0%
+great if we gave america at the time a
+product they can invest in the whole
+
+ align:start position:0%
+product they can invest in the whole
+ 
+
+ align:start position:0%
+product they can invest in the whole
+stock market a little bit of each
+
+ align:start position:0%
+stock market a little bit of each
+ 
+
+ align:start position:0%
+stock market a little bit of each
+company and we're not going to manage it
+
+ align:start position:0%
+company and we're not going to manage it
+ 
+
+ align:start position:0%
+company and we're not going to manage it
+for them we're just going to
+
+ align:start position:0%
+for them we're just going to
+ 
+
+ align:start position:0%
+for them we're just going to
+algorithmically arithmetically pick a
+
+ align:start position:0%
+algorithmically arithmetically pick a
+ 
+
+ align:start position:0%
+algorithmically arithmetically pick a
+little bit of every stock and it was
+
+ align:start position:0%
+little bit of every stock and it was
+ 
+
+ align:start position:0%
+little bit of every stock and it was
+called an index fund we take it for
+
+ align:start position:0%
+called an index fund we take it for
+ 
+
+ align:start position:0%
+called an index fund we take it for
+granted but that was kind of an
+
+ align:start position:0%
+granted but that was kind of an
+ 
+
+ align:start position:0%
+granted but that was kind of an
+innovation a remarkable innovation of
+
+ align:start position:0%
+innovation a remarkable innovation of
+ 
+
+ align:start position:0%
+innovation a remarkable innovation of
+the 1970s
+
+ align:start position:0%
+the 1970s
+ 
+
+ align:start position:0%
+the 1970s
+everybody could have a piece of the
+
+ align:start position:0%
+everybody could have a piece of the
+ 
+
+ align:start position:0%
+everybody could have a piece of the
+stock market at a low cost and to this
+
+ align:start position:0%
+stock market at a low cost and to this
+ 
+
+ align:start position:0%
+stock market at a low cost and to this
+day vanguard is still not a publicly
+
+ align:start position:0%
+day vanguard is still not a publicly
+ 
+
+ align:start position:0%
+day vanguard is still not a publicly
+traded for-profit company it's a mutual
+
+ align:start position:0%
+traded for-profit company it's a mutual
+ 
+
+ align:start position:0%
+traded for-profit company it's a mutual
+company vanguard is held and owned by
+
+ align:start position:0%
+company vanguard is held and owned by
+ 
+
+ align:start position:0%
+company vanguard is held and owned by
+its mutual funds that are held known by
+
+ align:start position:0%
+its mutual funds that are held known by
+ 
+
+ align:start position:0%
+its mutual funds that are held known by
+us if we're part of vanguard
+
+ align:start position:0%
+us if we're part of vanguard
+ 
+
+ align:start position:0%
+us if we're part of vanguard
+that innovation then led to an
+
+ align:start position:0%
+that innovation then led to an
+ 
+
+ align:start position:0%
+that innovation then led to an
+innovation in the 1990s that said what
+
+ align:start position:0%
+innovation in the 1990s that said what
+ 
+
+ align:start position:0%
+innovation in the 1990s that said what
+can we do to make this even more
+
+ align:start position:0%
+can we do to make this even more
+ 
+
+ align:start position:0%
+can we do to make this even more
+efficient what if we take a index mutual
+
+ align:start position:0%
+efficient what if we take a index mutual
+ 
+
+ align:start position:0%
+efficient what if we take a index mutual
+fund
+
+ align:start position:0%
+fund
+ 
+
+ align:start position:0%
+fund
+and take the interest in the mutual
+
+ align:start position:0%
+and take the interest in the mutual
+ 
+
+ align:start position:0%
+and take the interest in the mutual
+funds and make those securities take a
+
+ align:start position:0%
+funds and make those securities take a
+ 
+
+ align:start position:0%
+funds and make those securities take a
+look took a little change in some
+
+ align:start position:0%
+look took a little change in some
+ 
+
+ align:start position:0%
+look took a little change in some
+regulations but all of a sudden we had
+
+ align:start position:0%
+regulations but all of a sudden we had
+ 
+
+ align:start position:0%
+regulations but all of a sudden we had
+this thing called exchange traded funds
+
+ align:start position:0%
+this thing called exchange traded funds
+ 
+
+ align:start position:0%
+this thing called exchange traded funds
+these low-cost ways to participate in
+
+ align:start position:0%
+these low-cost ways to participate in
+ 
+
+ align:start position:0%
+these low-cost ways to participate in
+the stock market the bond market
+
+ align:start position:0%
+the stock market the bond market
+ 
+
+ align:start position:0%
+the stock market the bond market
+some in in the gold and silver markets
+
+ align:start position:0%
+some in in the gold and silver markets
+ 
+
+ align:start position:0%
+some in in the gold and silver markets
+exchange traded funds
+
+ align:start position:0%
+exchange traded funds
+ 
+
+ align:start position:0%
+exchange traded funds
+all of these robo advisors in their sort
+
+ align:start position:0%
+all of these robo advisors in their sort
+ 
+
+ align:start position:0%
+all of these robo advisors in their sort
+of packaging
+
+ align:start position:0%
+of packaging
+ 
+
+ align:start position:0%
+of packaging
+have sort of said we can we can get you
+
+ align:start position:0%
+have sort of said we can we can get you
+ 
+
+ align:start position:0%
+have sort of said we can we can get you
+into this and get you out of this into
+
+ align:start position:0%
+into this and get you out of this into
+ 
+
+ align:start position:0%
+into this and get you out of this into
+this market or out of this market and
+
+ align:start position:0%
+this market or out of this market and
+ 
+
+ align:start position:0%
+this market or out of this market and
+use exchange traded funds
+
+ align:start position:0%
+use exchange traded funds
+ 
+
+ align:start position:0%
+use exchange traded funds
+the second big innovation for robo
+
+ align:start position:0%
+the second big innovation for robo
+ 
+
+ align:start position:0%
+the second big innovation for robo
+advisors
+
+ align:start position:0%
+advisors
+ 
+
+ align:start position:0%
+advisors
+of course is everything we talked about
+
+ align:start position:0%
+of course is everything we talked about
+ 
+
+ align:start position:0%
+of course is everything we talked about
+out of artificial intelligence and
+
+ align:start position:0%
+out of artificial intelligence and
+ 
+
+ align:start position:0%
+out of artificial intelligence and
+natural language
+
+ align:start position:0%
+natural language
+ 
+
+ align:start position:0%
+natural language
+programming processing
+
+ align:start position:0%
+programming processing
+ 
+
+ align:start position:0%
+programming processing
+the ability to take voice or to take
+
+ align:start position:0%
+the ability to take voice or to take
+ 
+
+ align:start position:0%
+the ability to take voice or to take
+digital
+
+ align:start position:0%
+digital
+ 
+
+ align:start position:0%
+digital
+and transfer that into
+
+ align:start position:0%
+and transfer that into
+ 
+
+ align:start position:0%
+and transfer that into
+machine language computer language and
+
+ align:start position:0%
+machine language computer language and
+ 
+
+ align:start position:0%
+machine language computer language and
+and the reverse so robo advisors
+
+ align:start position:0%
+and the reverse so robo advisors
+ 
+
+ align:start position:0%
+and the reverse so robo advisors
+came along at a point in time where you
+
+ align:start position:0%
+came along at a point in time where you
+ 
+
+ align:start position:0%
+came along at a point in time where you
+could basically automate us humans a bit
+
+ align:start position:0%
+could basically automate us humans a bit
+ 
+
+ align:start position:0%
+could basically automate us humans a bit
+not entirely not entirely but we could
+
+ align:start position:0%
+not entirely not entirely but we could
+ 
+
+ align:start position:0%
+not entirely not entirely but we could
+you know step back humans step back and
+
+ align:start position:0%
+you know step back humans step back and
+ 
+
+ align:start position:0%
+you know step back humans step back and
+robo advice goes in
+
+ align:start position:0%
+robo advice goes in
+ 
+
+ align:start position:0%
+robo advice goes in
+and you could do it at a lower price
+
+ align:start position:0%
+and you could do it at a lower price
+ 
+
+ align:start position:0%
+and you could do it at a lower price
+point and the third innovation was
+
+ align:start position:0%
+point and the third innovation was
+ 
+
+ align:start position:0%
+point and the third innovation was
+basically some simple analytics some
+
+ align:start position:0%
+basically some simple analytics some
+ 
+
+ align:start position:0%
+basically some simple analytics some
+simple analytics not machine learning
+
+ align:start position:0%
+simple analytics not machine learning
+ 
+
+ align:start position:0%
+simple analytics not machine learning
+but simple analytics on
+
+ align:start position:0%
+but simple analytics on
+ 
+
+ align:start position:0%
+but simple analytics on
+portfolio and asset allocation
+
+ align:start position:0%
+portfolio and asset allocation
+ 
+
+ align:start position:0%
+portfolio and asset allocation
+some of it's related to if you're in
+
+ align:start position:0%
+some of it's related to if you're in
+ 
+
+ align:start position:0%
+some of it's related to if you're in
+your 20s and you're saving for
+
+ align:start position:0%
+your 20s and you're saving for
+ 
+
+ align:start position:0%
+your 20s and you're saving for
+retirement you could take more risk you
+
+ align:start position:0%
+retirement you could take more risk you
+ 
+
+ align:start position:0%
+retirement you could take more risk you
+could have a higher equity share versus
+
+ align:start position:0%
+could have a higher equity share versus
+ 
+
+ align:start position:0%
+could have a higher equity share versus
+a bond share if you're in your 60s and
+
+ align:start position:0%
+a bond share if you're in your 60s and
+ 
+
+ align:start position:0%
+a bond share if you're in your 60s and
+you're about to retire you should be
+
+ align:start position:0%
+you're about to retire you should be
+ 
+
+ align:start position:0%
+you're about to retire you should be
+more stable a little less risk maybe
+
+ align:start position:0%
+more stable a little less risk maybe
+ 
+
+ align:start position:0%
+more stable a little less risk maybe
+more bonds and less
+
+ align:start position:0%
+more bonds and less
+ 
+
+ align:start position:0%
+more bonds and less
+equities some of it's that simple
+
+ align:start position:0%
+equities some of it's that simple
+ 
+
+ align:start position:0%
+equities some of it's that simple
+but they were able to basically
+
+ align:start position:0%
+but they were able to basically
+ 
+
+ align:start position:0%
+but they were able to basically
+take that
+
+ align:start position:0%
+take that
+ 
+
+ align:start position:0%
+take that
+and so the betterment started and they
+
+ align:start position:0%
+and so the betterment started and they
+ 
+
+ align:start position:0%
+and so the betterment started and they
+could find
+
+ align:start position:0%
+could find
+ 
+
+ align:start position:0%
+could find
+really readily available software
+
+ align:start position:0%
+really readily available software
+ 
+
+ align:start position:0%
+really readily available software
+for asset allocation they could use
+
+ align:start position:0%
+for asset allocation they could use
+ 
+
+ align:start position:0%
+for asset allocation they could use
+products like exchange traded funds
+
+ align:start position:0%
+products like exchange traded funds
+ 
+
+ align:start position:0%
+products like exchange traded funds
+mobile phones were around already so
+
+ align:start position:0%
+mobile phones were around already so
+ 
+
+ align:start position:0%
+mobile phones were around already so
+they had a good platform
+
+ align:start position:0%
+they had a good platform
+ 
+
+ align:start position:0%
+they had a good platform
+and they sort of say all right we'll go
+
+ align:start position:0%
+and they sort of say all right we'll go
+ 
+
+ align:start position:0%
+and they sort of say all right we'll go
+to a lower fee point
+
+ align:start position:0%
+to a lower fee point
+ 
+
+ align:start position:0%
+to a lower fee point
+and all of a sudden we start to see a
+
+ align:start position:0%
+and all of a sudden we start to see a
+ 
+
+ align:start position:0%
+and all of a sudden we start to see a
+real change of things
+
+ align:start position:0%
+real change of things
+ 
+
+ align:start position:0%
+real change of things
+questions remain
+
+ align:start position:0%
+questions remain
+ 
+
+ align:start position:0%
+questions remain
+while we wait for questions on this
+
+ align:start position:0%
+while we wait for questions on this
+ 
+
+ align:start position:0%
+while we wait for questions on this
+topic we have a question in the chat
+
+ align:start position:0%
+topic we have a question in the chat
+ 
+
+ align:start position:0%
+topic we have a question in the chat
+about robinhood's business model from
+
+ align:start position:0%
+about robinhood's business model from
+ 
+
+ align:start position:0%
+about robinhood's business model from
+george
+
+ align:start position:0%
+george
+ 
+
+ align:start position:0%
+george
+do you see robin hood and other startups
+
+ align:start position:0%
+do you see robin hood and other startups
+ 
+
+ align:start position:0%
+do you see robin hood and other startups
+starting their own high frequency
+
+ align:start position:0%
+starting their own high frequency
+ 
+
+ align:start position:0%
+starting their own high frequency
+trading operations instead of selling
+
+ align:start position:0%
+trading operations instead of selling
+ 
+
+ align:start position:0%
+trading operations instead of selling
+the order flows and then devin asked
+
+ align:start position:0%
+the order flows and then devin asked
+ 
+
+ align:start position:0%
+the order flows and then devin asked
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+maybe citadel or any other hedge fund
+
+ align:start position:0%
+maybe citadel or any other hedge fund
+ 
+
+ align:start position:0%
+maybe citadel or any other hedge fund
+should just buy roblox right
+
+ align:start position:0%
+should just buy roblox right
+ 
+
+ align:start position:0%
+should just buy roblox right
+these are two uh really great questions
+
+ align:start position:0%
+these are two uh really great questions
+ 
+
+ align:start position:0%
+these are two uh really great questions
+about the future i think that
+
+ align:start position:0%
+about the future i think that
+ 
+
+ align:start position:0%
+about the future i think that
+in both ways will
+
+ align:start position:0%
+in both ways will
+ 
+
+ align:start position:0%
+in both ways will
+will the
+
+ align:start position:0%
+will the
+ 
+
+ align:start position:0%
+will the
+um front-end platform and that's really
+
+ align:start position:0%
+um front-end platform and that's really
+ 
+
+ align:start position:0%
+um front-end platform and that's really
+in a sense robin hood and even in this
+
+ align:start position:0%
+in a sense robin hood and even in this
+ 
+
+ align:start position:0%
+in a sense robin hood and even in this
+robo advisor space the betterments of
+
+ align:start position:0%
+robo advisor space the betterments of
+ 
+
+ align:start position:0%
+robo advisor space the betterments of
+the world is a front-end user interface
+
+ align:start position:0%
+the world is a front-end user interface
+ 
+
+ align:start position:0%
+the world is a front-end user interface
+platform that tend not to have balance
+
+ align:start position:0%
+platform that tend not to have balance
+ 
+
+ align:start position:0%
+platform that tend not to have balance
+sheets
+
+ align:start position:0%
+sheets
+ 
+
+ align:start position:0%
+sheets
+and they tend to let somebody else
+
+ align:start position:0%
+and they tend to let somebody else
+ 
+
+ align:start position:0%
+and they tend to let somebody else
+handle that capital markets risk behind
+
+ align:start position:0%
+handle that capital markets risk behind
+ 
+
+ align:start position:0%
+handle that capital markets risk behind
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um but the question here is do i see
+
+ align:start position:0%
+um but the question here is do i see
+ 
+
+ align:start position:0%
+um but the question here is do i see
+the front end sort of building balance
+
+ align:start position:0%
+the front end sort of building balance
+ 
+
+ align:start position:0%
+the front end sort of building balance
+sheet and moving into the capital market
+
+ align:start position:0%
+sheet and moving into the capital market
+ 
+
+ align:start position:0%
+sheet and moving into the capital market
+side and do i see the capital market
+
+ align:start position:0%
+side and do i see the capital market
+ 
+
+ align:start position:0%
+side and do i see the capital market
+side the sort of balance sheet
+
+ align:start position:0%
+side the sort of balance sheet
+ 
+
+ align:start position:0%
+side the sort of balance sheet
+risk-taking moving into the front-end
+
+ align:start position:0%
+risk-taking moving into the front-end
+ 
+
+ align:start position:0%
+risk-taking moving into the front-end
+side and we don't know but history tells
+
+ align:start position:0%
+side and we don't know but history tells
+ 
+
+ align:start position:0%
+side and we don't know but history tells
+us that tends to happen at some point
+
+ align:start position:0%
+us that tends to happen at some point
+ 
+
+ align:start position:0%
+us that tends to happen at some point
+that there's some
+
+ align:start position:0%
+that there's some
+ 
+
+ align:start position:0%
+that there's some
+sort of um
+
+ align:start position:0%
+sort of um
+ 
+
+ align:start position:0%
+sort of um
+what you might call sort of uh vertical
+
+ align:start position:0%
+what you might call sort of uh vertical
+ 
+
+ align:start position:0%
+what you might call sort of uh vertical
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh integration and if you really think
+
+ align:start position:0%
+uh integration and if you really think
+ 
+
+ align:start position:0%
+uh integration and if you really think
+about um
+
+ align:start position:0%
+about um
+ 
+
+ align:start position:0%
+about um
+these slices on this page the jp morgan
+
+ align:start position:0%
+these slices on this page the jp morgan
+ 
+
+ align:start position:0%
+these slices on this page the jp morgan
+building you invest in 2018 or mayoral
+
+ align:start position:0%
+building you invest in 2018 or mayoral
+ 
+
+ align:start position:0%
+building you invest in 2018 or mayoral
+edge in an earlier time and if i go back
+
+ align:start position:0%
+edge in an earlier time and if i go back
+ 
+
+ align:start position:0%
+edge in an earlier time and if i go back
+to the brokerage side there they're
+
+ align:start position:0%
+to the brokerage side there they're
+ 
+
+ align:start position:0%
+to the brokerage side there they're
+named products there too
+
+ align:start position:0%
+named products there too
+ 
+
+ align:start position:0%
+named products there too
+that's balance sheet coupled with front
+
+ align:start position:0%
+that's balance sheet coupled with front
+ 
+
+ align:start position:0%
+that's balance sheet coupled with front
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+that's that's the fully integrated model
+
+ align:start position:0%
+that's that's the fully integrated model
+ 
+
+ align:start position:0%
+that's that's the fully integrated model
+but then if you look at the asset
+
+ align:start position:0%
+but then if you look at the asset
+ 
+
+ align:start position:0%
+but then if you look at the asset
+managers the asset managers the black
+
+ align:start position:0%
+managers the asset managers the black
+ 
+
+ align:start position:0%
+managers the asset managers the black
+rocks of the world are not actually
+
+ align:start position:0%
+rocks of the world are not actually
+ 
+
+ align:start position:0%
+rocks of the world are not actually
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+acting as a principal they're acting as
+
+ align:start position:0%
+acting as a principal they're acting as
+ 
+
+ align:start position:0%
+acting as a principal they're acting as
+an advisor a pure advisor pure agency
+
+ align:start position:0%
+an advisor a pure advisor pure agency
+ 
+
+ align:start position:0%
+an advisor a pure advisor pure agency
+business so one of the things is do you
+
+ align:start position:0%
+business so one of the things is do you
+ 
+
+ align:start position:0%
+business so one of the things is do you
+just want to stay as an agent or do you
+
+ align:start position:0%
+just want to stay as an agent or do you
+ 
+
+ align:start position:0%
+just want to stay as an agent or do you
+actually want to
+
+ align:start position:0%
+actually want to
+ 
+
+ align:start position:0%
+actually want to
+invest your capital in the markets and
+
+ align:start position:0%
+invest your capital in the markets and
+ 
+
+ align:start position:0%
+invest your capital in the markets and
+that big business decision
+
+ align:start position:0%
+that big business decision
+ 
+
+ align:start position:0%
+that big business decision
+separates some of the asset managers
+
+ align:start position:0%
+separates some of the asset managers
+ 
+
+ align:start position:0%
+separates some of the asset managers
+and then as you mentioned the high
+
+ align:start position:0%
+and then as you mentioned the high
+ 
+
+ align:start position:0%
+and then as you mentioned the high
+frequency traders
+
+ align:start position:0%
+frequency traders
+ 
+
+ align:start position:0%
+frequency traders
+uh i think that if robinhood is going to
+
+ align:start position:0%
+uh i think that if robinhood is going to
+ 
+
+ align:start position:0%
+uh i think that if robinhood is going to
+be bought it could be bought by high
+
+ align:start position:0%
+be bought it could be bought by high
+ 
+
+ align:start position:0%
+be bought it could be bought by high
+frequency trading shop but the the
+
+ align:start position:0%
+frequency trading shop but the the
+ 
+
+ align:start position:0%
+frequency trading shop but the the
+challenge there the challenge there is
+
+ align:start position:0%
+challenge there the challenge there is
+ 
+
+ align:start position:0%
+challenge there the challenge there is
+will they still get as big a customer
+
+ align:start position:0%
+will they still get as big a customer
+ 
+
+ align:start position:0%
+will they still get as big a customer
+base i mean 10 million customers
+
+ align:start position:0%
+base i mean 10 million customers
+ 
+
+ align:start position:0%
+base i mean 10 million customers
+or is robinhood more valuable
+
+ align:start position:0%
+or is robinhood more valuable
+ 
+
+ align:start position:0%
+or is robinhood more valuable
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+one of the large banks to buy or one of
+
+ align:start position:0%
+one of the large banks to buy or one of
+ 
+
+ align:start position:0%
+one of the large banks to buy or one of
+the large asset managers i think if you
+
+ align:start position:0%
+the large asset managers i think if you
+ 
+
+ align:start position:0%
+the large asset managers i think if you
+look out three to five years it's quite
+
+ align:start position:0%
+look out three to five years it's quite
+ 
+
+ align:start position:0%
+look out three to five years it's quite
+likely that robin hood
+
+ align:start position:0%
+likely that robin hood
+ 
+
+ align:start position:0%
+likely that robin hood
+gets soup you know merged up into
+
+ align:start position:0%
+gets soup you know merged up into
+ 
+
+ align:start position:0%
+gets soup you know merged up into
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+as you saw morgan stanley buying e-trade
+
+ align:start position:0%
+as you saw morgan stanley buying e-trade
+ 
+
+ align:start position:0%
+as you saw morgan stanley buying e-trade
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+another question
+
+ align:start position:0%
+another question
+ 
+
+ align:start position:0%
+another question
+yes let's go with camilo
+
+ align:start position:0%
+yes let's go with camilo
+ 
+
+ align:start position:0%
+yes let's go with camilo
+and then i'm going to sort of do a few
+
+ align:start position:0%
+and then i'm going to sort of do a few
+ 
+
+ align:start position:0%
+and then i'm going to sort of do a few
+more slides here on
+
+ align:start position:0%
+more slides here on
+ 
+
+ align:start position:0%
+more slides here on
+roboadvisors
+
+ align:start position:0%
+roboadvisors
+ 
+
+ align:start position:0%
+roboadvisors
+um hi gary i
+
+ align:start position:0%
+um hi gary i
+ 
+
+ align:start position:0%
+um hi gary i
+wonder why um platforms such as acorns
+
+ align:start position:0%
+wonder why um platforms such as acorns
+ 
+
+ align:start position:0%
+wonder why um platforms such as acorns
+and betterment that you were just
+
+ align:start position:0%
+and betterment that you were just
+ 
+
+ align:start position:0%
+and betterment that you were just
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+i have like a like a mixed business
+
+ align:start position:0%
+i have like a like a mixed business
+ 
+
+ align:start position:0%
+i have like a like a mixed business
+model because in in
+
+ align:start position:0%
+model because in in
+ 
+
+ align:start position:0%
+model because in in
+in one way they are a robot advisor
+
+ align:start position:0%
+in one way they are a robot advisor
+ 
+
+ align:start position:0%
+in one way they are a robot advisor
+business model but but then they have
+
+ align:start position:0%
+business model but but then they have
+ 
+
+ align:start position:0%
+business model but but then they have
+savings and checking accounts correct
+
+ align:start position:0%
+savings and checking accounts correct
+ 
+
+ align:start position:0%
+savings and checking accounts correct
+you're stepping a foot like into a
+
+ align:start position:0%
+you're stepping a foot like into a
+ 
+
+ align:start position:0%
+you're stepping a foot like into a
+banking model what's the reason to merge
+
+ align:start position:0%
+banking model what's the reason to merge
+ 
+
+ align:start position:0%
+banking model what's the reason to merge
+the two spaces into one i think because
+
+ align:start position:0%
+the two spaces into one i think because
+ 
+
+ align:start position:0%
+the two spaces into one i think because
+they have the front-end customer
+
+ align:start position:0%
+they have the front-end customer
+ 
+
+ align:start position:0%
+they have the front-end customer
+relationship and they have some trust
+
+ align:start position:0%
+relationship and they have some trust
+ 
+
+ align:start position:0%
+relationship and they have some trust
+and and this sort of helps set something
+
+ align:start position:0%
+and and this sort of helps set something
+ 
+
+ align:start position:0%
+and and this sort of helps set something
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is a chart on users
+
+ align:start position:0%
+this is a chart on users
+ 
+
+ align:start position:0%
+this is a chart on users
+just and and it's got some predictions
+
+ align:start position:0%
+just and and it's got some predictions
+ 
+
+ align:start position:0%
+just and and it's got some predictions
+here we don't know if these predictions
+
+ align:start position:0%
+here we don't know if these predictions
+ 
+
+ align:start position:0%
+here we don't know if these predictions
+were hold but if you see the use of robo
+
+ align:start position:0%
+were hold but if you see the use of robo
+ 
+
+ align:start position:0%
+were hold but if you see the use of robo
+advisors it's just getting much more
+
+ align:start position:0%
+advisors it's just getting much more
+ 
+
+ align:start position:0%
+advisors it's just getting much more
+comfortable that folks are being and
+
+ align:start position:0%
+comfortable that folks are being and
+ 
+
+ align:start position:0%
+comfortable that folks are being and
+this this i believe also includes the
+
+ align:start position:0%
+this this i believe also includes the
+ 
+
+ align:start position:0%
+this this i believe also includes the
+robo advisors at the big shops as well
+
+ align:start position:0%
+robo advisors at the big shops as well
+ 
+
+ align:start position:0%
+robo advisors at the big shops as well
+as the startups but just as if you have
+
+ align:start position:0%
+as the startups but just as if you have
+ 
+
+ align:start position:0%
+as the startups but just as if you have
+that user interface and remember we
+
+ align:start position:0%
+that user interface and remember we
+ 
+
+ align:start position:0%
+that user interface and remember we
+talked about challenger banks as well
+
+ align:start position:0%
+talked about challenger banks as well
+ 
+
+ align:start position:0%
+talked about challenger banks as well
+camilo the challenger banks last session
+
+ align:start position:0%
+camilo the challenger banks last session
+ 
+
+ align:start position:0%
+camilo the challenger banks last session
+a lot of it's about trust as well
+
+ align:start position:0%
+a lot of it's about trust as well
+ 
+
+ align:start position:0%
+a lot of it's about trust as well
+once you have that user interface
+
+ align:start position:0%
+once you have that user interface
+ 
+
+ align:start position:0%
+once you have that user interface
+there's a certain trust and frankly
+
+ align:start position:0%
+there's a certain trust and frankly
+ 
+
+ align:start position:0%
+there's a certain trust and frankly
+stickiness to it so if betterment which
+
+ align:start position:0%
+stickiness to it so if betterment which
+ 
+
+ align:start position:0%
+stickiness to it so if betterment which
+is looking to become a challenger bank
+
+ align:start position:0%
+is looking to become a challenger bank
+ 
+
+ align:start position:0%
+is looking to become a challenger bank
+can use that customer relationship
+
+ align:start position:0%
+can use that customer relationship
+ 
+
+ align:start position:0%
+can use that customer relationship
+then you can build the platform and back
+
+ align:start position:0%
+then you can build the platform and back
+ 
+
+ align:start position:0%
+then you can build the platform and back
+to the the economics of platforms the
+
+ align:start position:0%
+to the the economics of platforms the
+ 
+
+ align:start position:0%
+to the the economics of platforms the
+economics of platforms is as you layer
+
+ align:start position:0%
+economics of platforms is as you layer
+ 
+
+ align:start position:0%
+economics of platforms is as you layer
+activities on top of a platform and if
+
+ align:start position:0%
+activities on top of a platform and if
+ 
+
+ align:start position:0%
+activities on top of a platform and if
+you can grow your user base
+
+ align:start position:0%
+you can grow your user base
+ 
+
+ align:start position:0%
+you can grow your user base
+you get more data you get more
+
+ align:start position:0%
+you get more data you get more
+ 
+
+ align:start position:0%
+you get more data you get more
+centrality there's not going to be 10
+
+ align:start position:0%
+centrality there's not going to be 10
+ 
+
+ align:start position:0%
+centrality there's not going to be 10
+years from now
+
+ align:start position:0%
+years from now
+ 
+
+ align:start position:0%
+years from now
+this many advisory platforms and in fact
+
+ align:start position:0%
+this many advisory platforms and in fact
+ 
+
+ align:start position:0%
+this many advisory platforms and in fact
+in the blue the advisory platforms i
+
+ align:start position:0%
+in the blue the advisory platforms i
+ 
+
+ align:start position:0%
+in the blue the advisory platforms i
+picked the ones that are large there's
+
+ align:start position:0%
+picked the ones that are large there's
+ 
+
+ align:start position:0%
+picked the ones that are large there's
+50 to 100 others that i haven't listed
+
+ align:start position:0%
+50 to 100 others that i haven't listed
+ 
+
+ align:start position:0%
+50 to 100 others that i haven't listed
+so there's going to be consolidation as
+
+ align:start position:0%
+so there's going to be consolidation as
+ 
+
+ align:start position:0%
+so there's going to be consolidation as
+sure as where we're here
+
+ align:start position:0%
+sure as where we're here
+ 
+
+ align:start position:0%
+sure as where we're here
+uh at this moment there's going to be
+
+ align:start position:0%
+uh at this moment there's going to be
+ 
+
+ align:start position:0%
+uh at this moment there's going to be
+consolidation in this space and so
+
+ align:start position:0%
+consolidation in this space and so
+ 
+
+ align:start position:0%
+consolidation in this space and so
+they're trying to build a
+
+ align:start position:0%
+they're trying to build a
+ 
+
+ align:start position:0%
+they're trying to build a
+classic platform economics build
+
+ align:start position:0%
+classic platform economics build
+ 
+
+ align:start position:0%
+classic platform economics build
+activities build user bases um
+
+ align:start position:0%
+activities build user bases um
+ 
+
+ align:start position:0%
+activities build user bases um
+and and and this is assets under
+
+ align:start position:0%
+and and and this is assets under
+ 
+
+ align:start position:0%
+and and and this is assets under
+management the same uh uh website uh
+
+ align:start position:0%
+management the same uh uh website uh
+ 
+
+ align:start position:0%
+management the same uh uh website uh
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+behind this but as of a few days ago
+
+ align:start position:0%
+behind this but as of a few days ago
+ 
+
+ align:start position:0%
+behind this but as of a few days ago
+just a sense of what are the assets this
+
+ align:start position:0%
+just a sense of what are the assets this
+ 
+
+ align:start position:0%
+just a sense of what are the assets this
+is in billions
+
+ align:start position:0%
+is in billions
+ 
+
+ align:start position:0%
+is in billions
+so uh in 2020 well 1.2
+
+ align:start position:0%
+so uh in 2020 well 1.2
+ 
+
+ align:start position:0%
+so uh in 2020 well 1.2
+trillion dollars of assets under
+
+ align:start position:0%
+trillion dollars of assets under
+ 
+
+ align:start position:0%
+trillion dollars of assets under
+management somehow associated with robo
+
+ align:start position:0%
+management somehow associated with robo
+ 
+
+ align:start position:0%
+management somehow associated with robo
+advisors so
+
+ align:start position:0%
+advisors so
+ 
+
+ align:start position:0%
+advisors so
+even a quarter percent fee on this
+
+ align:start position:0%
+even a quarter percent fee on this
+ 
+
+ align:start position:0%
+even a quarter percent fee on this
+starts to be a real revenue model
+
+ align:start position:0%
+starts to be a real revenue model
+ 
+
+ align:start position:0%
+starts to be a real revenue model
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+possible evolution i sort of like
+
+ align:start position:0%
+possible evolution i sort of like
+ 
+
+ align:start position:0%
+possible evolution i sort of like
+thinking about where could this go in
+
+ align:start position:0%
+thinking about where could this go in
+ 
+
+ align:start position:0%
+thinking about where could this go in
+the future
+
+ align:start position:0%
+the future
+ 
+
+ align:start position:0%
+the future
+i mean where did robo advising start all
+
+ align:start position:0%
+i mean where did robo advising start all
+ 
+
+ align:start position:0%
+i mean where did robo advising start all
+the way on the left it's just an online
+
+ align:start position:0%
+the way on the left it's just an online
+ 
+
+ align:start position:0%
+the way on the left it's just an online
+questionnaire about asset allocation
+
+ align:start position:0%
+questionnaire about asset allocation
+ 
+
+ align:start position:0%
+questionnaire about asset allocation
+largely and an online questionnaire a
+
+ align:start position:0%
+largely and an online questionnaire a
+ 
+
+ align:start position:0%
+largely and an online questionnaire a
+mobile questionnaire about products
+
+ align:start position:0%
+mobile questionnaire about products
+ 
+
+ align:start position:0%
+mobile questionnaire about products
+and risk
+
+ align:start position:0%
+and risk
+ 
+
+ align:start position:0%
+and risk
+risk and how and then usually a list of
+
+ align:start position:0%
+risk and how and then usually a list of
+ 
+
+ align:start position:0%
+risk and how and then usually a list of
+exchange traded funds some bonds some
+
+ align:start position:0%
+exchange traded funds some bonds some
+ 
+
+ align:start position:0%
+exchange traded funds some bonds some
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+but very
+
+ align:start position:0%
+but very
+ 
+
+ align:start position:0%
+but very
+accessible broadening financial
+
+ align:start position:0%
+accessible broadening financial
+ 
+
+ align:start position:0%
+accessible broadening financial
+inclusion for lower rates and it helps a
+
+ align:start position:0%
+inclusion for lower rates and it helps a
+ 
+
+ align:start position:0%
+inclusion for lower rates and it helps a
+lot of people a lot of investors sleep
+
+ align:start position:0%
+lot of people a lot of investors sleep
+ 
+
+ align:start position:0%
+lot of people a lot of investors sleep
+well at night it lowers their
+
+ align:start position:0%
+well at night it lowers their
+ 
+
+ align:start position:0%
+well at night it lowers their
+uncertainty i'm getting some good advice
+
+ align:start position:0%
+uncertainty i'm getting some good advice
+ 
+
+ align:start position:0%
+uncertainty i'm getting some good advice
+about asset allocation some risk some
+
+ align:start position:0%
+about asset allocation some risk some
+ 
+
+ align:start position:0%
+about asset allocation some risk some
+life events but could it move further
+
+ align:start position:0%
+life events but could it move further
+ 
+
+ align:start position:0%
+life events but could it move further
+that's the question can it move further
+
+ align:start position:0%
+that's the question can it move further
+ 
+
+ align:start position:0%
+that's the question can it move further
+and exactly like camilla said and luke's
+
+ align:start position:0%
+and exactly like camilla said and luke's
+ 
+
+ align:start position:0%
+and exactly like camilla said and luke's
+earlier question about other revenues
+
+ align:start position:0%
+earlier question about other revenues
+ 
+
+ align:start position:0%
+earlier question about other revenues
+can robo advisor like betterment say
+
+ align:start position:0%
+can robo advisor like betterment say
+ 
+
+ align:start position:0%
+can robo advisor like betterment say
+well we'll actually be the fund manager
+
+ align:start position:0%
+well we'll actually be the fund manager
+ 
+
+ align:start position:0%
+well we'll actually be the fund manager
+we'll start to actually manage the funds
+
+ align:start position:0%
+we'll start to actually manage the funds
+ 
+
+ align:start position:0%
+we'll start to actually manage the funds
+rather than just doing these low-cost
+
+ align:start position:0%
+rather than just doing these low-cost
+ 
+
+ align:start position:0%
+rather than just doing these low-cost
+etfs
+
+ align:start position:0%
+etfs
+ 
+
+ align:start position:0%
+etfs
+and maybe we'll start to actually do
+
+ align:start position:0%
+and maybe we'll start to actually do
+ 
+
+ align:start position:0%
+and maybe we'll start to actually do
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+with regard to risk-based portfolio
+
+ align:start position:0%
+with regard to risk-based portfolio
+ 
+
+ align:start position:0%
+with regard to risk-based portfolio
+allocation maybe we'll start in this
+
+ align:start position:0%
+allocation maybe we'll start in this
+ 
+
+ align:start position:0%
+allocation maybe we'll start in this
+third column do a little bit of
+
+ align:start position:0%
+third column do a little bit of
+ 
+
+ align:start position:0%
+third column do a little bit of
+algorithms maybe in fact will start to
+
+ align:start position:0%
+algorithms maybe in fact will start to
+ 
+
+ align:start position:0%
+algorithms maybe in fact will start to
+do trading and be a principal as a
+
+ align:start position:0%
+do trading and be a principal as a
+ 
+
+ align:start position:0%
+do trading and be a principal as a
+rather than just an agent and an advisor
+
+ align:start position:0%
+rather than just an agent and an advisor
+ 
+
+ align:start position:0%
+rather than just an agent and an advisor
+uh and the like so you know there's
+
+ align:start position:0%
+uh and the like so you know there's
+ 
+
+ align:start position:0%
+uh and the like so you know there's
+there's gonna be more
+
+ align:start position:0%
+there's gonna be more
+ 
+
+ align:start position:0%
+there's gonna be more
+sophisticated algorithmic ai or machine
+
+ align:start position:0%
+sophisticated algorithmic ai or machine
+ 
+
+ align:start position:0%
+sophisticated algorithmic ai or machine
+learning but i don't think it's going to
+
+ align:start position:0%
+learning but i don't think it's going to
+ 
+
+ align:start position:0%
+learning but i don't think it's going to
+be highly sophisticated machine learning
+
+ align:start position:0%
+be highly sophisticated machine learning
+ 
+
+ align:start position:0%
+be highly sophisticated machine learning
+because there's a certain
+
+ align:start position:0%
+because there's a certain
+ 
+
+ align:start position:0%
+because there's a certain
+commoditization about the advice
+
+ align:start position:0%
+commoditization about the advice
+ 
+
+ align:start position:0%
+commoditization about the advice
+but it is quite possible as we move
+
+ align:start position:0%
+but it is quite possible as we move
+ 
+
+ align:start position:0%
+but it is quite possible as we move
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+somebody will figure out what risk i
+
+ align:start position:0%
+somebody will figure out what risk i
+ 
+
+ align:start position:0%
+somebody will figure out what risk i
+should take versus somebody else andrew
+
+ align:start position:0%
+should take versus somebody else andrew
+ 
+
+ align:start position:0%
+should take versus somebody else andrew
+lowe a faculty member at mit
+
+ align:start position:0%
+lowe a faculty member at mit
+ 
+
+ align:start position:0%
+lowe a faculty member at mit
+thinks that you can take
+
+ align:start position:0%
+thinks that you can take
+ 
+
+ align:start position:0%
+thinks that you can take
+machine learning and embed it in even an
+
+ align:start position:0%
+machine learning and embed it in even an
+ 
+
+ align:start position:0%
+machine learning and embed it in even an
+index fund that you could have
+
+ align:start position:0%
+index fund that you could have
+ 
+
+ align:start position:0%
+index fund that you could have
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+of an index fund what andy talks about
+
+ align:start position:0%
+of an index fund what andy talks about
+ 
+
+ align:start position:0%
+of an index fund what andy talks about
+is called the freakout factor that we
+
+ align:start position:0%
+is called the freakout factor that we
+ 
+
+ align:start position:0%
+is called the freakout factor that we
+all have different risk profiles when
+
+ align:start position:0%
+all have different risk profiles when
+ 
+
+ align:start position:0%
+all have different risk profiles when
+the stock market goes out down
+
+ align:start position:0%
+the stock market goes out down
+ 
+
+ align:start position:0%
+the stock market goes out down
+how likely are we to quote as he says
+
+ align:start position:0%
+how likely are we to quote as he says
+ 
+
+ align:start position:0%
+how likely are we to quote as he says
+freak out
+
+ align:start position:0%
+freak out
+ 
+
+ align:start position:0%
+freak out
+and want to sell
+
+ align:start position:0%
+and want to sell
+ 
+
+ align:start position:0%
+and want to sell
+and that we could based upon other
+
+ align:start position:0%
+and that we could based upon other
+ 
+
+ align:start position:0%
+and that we could based upon other
+aspects of our lives sort of put that
+
+ align:start position:0%
+aspects of our lives sort of put that
+ 
+
+ align:start position:0%
+aspects of our lives sort of put that
+into a machine learning model and have
+
+ align:start position:0%
+into a machine learning model and have
+ 
+
+ align:start position:0%
+into a machine learning model and have
+it automatically adjust
+
+ align:start position:0%
+it automatically adjust
+ 
+
+ align:start position:0%
+it automatically adjust
+up and down
+
+ align:start position:0%
+up and down
+ 
+
+ align:start position:0%
+up and down
+um questions before i think i'm going to
+
+ align:start position:0%
+um questions before i think i'm going to
+ 
+
+ align:start position:0%
+um questions before i think i'm going to
+go to the broadly the capital markets
+
+ align:start position:0%
+go to the broadly the capital markets
+ 
+
+ align:start position:0%
+go to the broadly the capital markets
+piece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm pausing here for a second but we've
+
+ align:start position:0%
+i'm pausing here for a second but we've
+ 
+
+ align:start position:0%
+i'm pausing here for a second but we've
+sort of covered the online brokerage
+
+ align:start position:0%
+sort of covered the online brokerage
+ 
+
+ align:start position:0%
+sort of covered the online brokerage
+robo advisor there's two big pieces as
+
+ align:start position:0%
+robo advisor there's two big pieces as
+ 
+
+ align:start position:0%
+robo advisor there's two big pieces as
+sort of captured by robin hood and
+
+ align:start position:0%
+sort of captured by robin hood and
+ 
+
+ align:start position:0%
+sort of captured by robin hood and
+betterment might be the two companies
+
+ align:start position:0%
+betterment might be the two companies
+ 
+
+ align:start position:0%
+betterment might be the two companies
+that that are
+
+ align:start position:0%
+that that are
+ 
+
+ align:start position:0%
+that that are
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+the leads of the pack but they're not
+
+ align:start position:0%
+the leads of the pack but they're not
+ 
+
+ align:start position:0%
+the leads of the pack but they're not
+alone and in the in the wealth
+
+ align:start position:0%
+alone and in the in the wealth
+ 
+
+ align:start position:0%
+alone and in the in the wealth
+management side it's much more um evenly
+
+ align:start position:0%
+management side it's much more um evenly
+ 
+
+ align:start position:0%
+management side it's much more um evenly
+split whereas in the mobile side in the
+
+ align:start position:0%
+split whereas in the mobile side in the
+ 
+
+ align:start position:0%
+split whereas in the mobile side in the
+mobile brokerage side robin hood seemed
+
+ align:start position:0%
+mobile brokerage side robin hood seemed
+ 
+
+ align:start position:0%
+mobile brokerage side robin hood seemed
+to have really
+
+ align:start position:0%
+to have really
+ 
+
+ align:start position:0%
+to have really
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+punched high and done well
+
+ align:start position:0%
+punched high and done well
+ 
+
+ align:start position:0%
+punched high and done well
+the only question we have gary is from
+
+ align:start position:0%
+the only question we have gary is from
+ 
+
+ align:start position:0%
+the only question we have gary is from
+the chat from luke what kind of u.s
+
+ align:start position:0%
+the chat from luke what kind of u.s
+ 
+
+ align:start position:0%
+the chat from luke what kind of u.s
+regulation is deterring the likes of
+
+ align:start position:0%
+regulation is deterring the likes of
+ 
+
+ align:start position:0%
+regulation is deterring the likes of
+robin hood to expand globally
+
+ align:start position:0%
+robin hood to expand globally
+ 
+
+ align:start position:0%
+robin hood to expand globally
+or to attract capital from abroad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+this is a highly regulated space in both
+
+ align:start position:0%
+this is a highly regulated space in both
+ 
+
+ align:start position:0%
+this is a highly regulated space in both
+the advisory side and the brokerage side
+
+ align:start position:0%
+the advisory side and the brokerage side
+ 
+
+ align:start position:0%
+the advisory side and the brokerage side
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and robin hood would certainly
+
+ align:start position:0%
+and robin hood would certainly
+ 
+
+ align:start position:0%
+and robin hood would certainly
+need to be aware of that and registered
+
+ align:start position:0%
+need to be aware of that and registered
+ 
+
+ align:start position:0%
+need to be aware of that and registered
+appropriately
+
+ align:start position:0%
+appropriately
+ 
+
+ align:start position:0%
+appropriately
+as a broker-dealer here in the u.s
+
+ align:start position:0%
+as a broker-dealer here in the u.s
+ 
+
+ align:start position:0%
+as a broker-dealer here in the u.s
+and and then on the asset management
+
+ align:start position:0%
+and and then on the asset management
+ 
+
+ align:start position:0%
+and and then on the asset management
+side there's a little bit different
+
+ align:start position:0%
+side there's a little bit different
+ 
+
+ align:start position:0%
+side there's a little bit different
+regulations but also uh regulated here
+
+ align:start position:0%
+regulations but also uh regulated here
+ 
+
+ align:start position:0%
+regulations but also uh regulated here
+attracting capital
+
+ align:start position:0%
+attracting capital
+ 
+
+ align:start position:0%
+attracting capital
+from overseas if the capital is just
+
+ align:start position:0%
+from overseas if the capital is just
+ 
+
+ align:start position:0%
+from overseas if the capital is just
+investing in robin hood in one of their
+
+ align:start position:0%
+investing in robin hood in one of their
+ 
+
+ align:start position:0%
+investing in robin hood in one of their
+venture rounds you know bcd rounds
+
+ align:start position:0%
+venture rounds you know bcd rounds
+ 
+
+ align:start position:0%
+venture rounds you know bcd rounds
+because these are probably private
+
+ align:start position:0%
+because these are probably private
+ 
+
+ align:start position:0%
+because these are probably private
+placements
+
+ align:start position:0%
+placements
+ 
+
+ align:start position:0%
+placements
+largely speaking other than the usual
+
+ align:start position:0%
+largely speaking other than the usual
+ 
+
+ align:start position:0%
+largely speaking other than the usual
+regulations around
+
+ align:start position:0%
+regulations around
+ 
+
+ align:start position:0%
+regulations around
+sanctions and any money laundering would
+
+ align:start position:0%
+sanctions and any money laundering would
+ 
+
+ align:start position:0%
+sanctions and any money laundering would
+be straightforward if it's actually
+
+ align:start position:0%
+be straightforward if it's actually
+ 
+
+ align:start position:0%
+be straightforward if it's actually
+customers using the platform customers
+
+ align:start position:0%
+customers using the platform customers
+ 
+
+ align:start position:0%
+customers using the platform customers
+using the platform then a robinhood
+
+ align:start position:0%
+using the platform then a robinhood
+ 
+
+ align:start position:0%
+using the platform then a robinhood
+would have to be aware of the
+
+ align:start position:0%
+would have to be aware of the
+ 
+
+ align:start position:0%
+would have to be aware of the
+regulations in that jurisdiction whether
+
+ align:start position:0%
+regulations in that jurisdiction whether
+ 
+
+ align:start position:0%
+regulations in that jurisdiction whether
+it's the regulations in europe or in in
+
+ align:start position:0%
+it's the regulations in europe or in in
+ 
+
+ align:start position:0%
+it's the regulations in europe or in in
+your home country luke and korea that
+
+ align:start position:0%
+your home country luke and korea that
+ 
+
+ align:start position:0%
+your home country luke and korea that
+they'd those customer facing
+
+ align:start position:0%
+they'd those customer facing
+ 
+
+ align:start position:0%
+they'd those customer facing
+applications robin hood korea
+
+ align:start position:0%
+applications robin hood korea
+ 
+
+ align:start position:0%
+applications robin hood korea
+would have to think do they register as
+
+ align:start position:0%
+would have to think do they register as
+ 
+
+ align:start position:0%
+would have to think do they register as
+a broker dealer in korea or japan and
+
+ align:start position:0%
+a broker dealer in korea or japan and
+ 
+
+ align:start position:0%
+a broker dealer in korea or japan and
+the like as they
+
+ align:start position:0%
+the like as they
+ 
+
+ align:start position:0%
+the like as they
+they are in fact just a mobile
+
+ align:start position:0%
+they are in fact just a mobile
+ 
+
+ align:start position:0%
+they are in fact just a mobile
+application for a traditional um
+
+ align:start position:0%
+application for a traditional um
+ 
+
+ align:start position:0%
+application for a traditional um
+investment uh brokerage firm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again sort of trying to capture capital
+
+ align:start position:0%
+again sort of trying to capture capital
+ 
+
+ align:start position:0%
+again sort of trying to capture capital
+markets capital markets is a vast
+
+ align:start position:0%
+markets capital markets is a vast
+ 
+
+ align:start position:0%
+markets capital markets is a vast
+uh array of activities from
+
+ align:start position:0%
+uh array of activities from
+ 
+
+ align:start position:0%
+uh array of activities from
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+accessing capital to trading platforms
+
+ align:start position:0%
+accessing capital to trading platforms
+ 
+
+ align:start position:0%
+accessing capital to trading platforms
+and the like and this this slide from
+
+ align:start position:0%
+and the like and this this slide from
+ 
+
+ align:start position:0%
+and the like and this this slide from
+mckinsey just sort of captures an
+
+ align:start position:0%
+mckinsey just sort of captures an
+ 
+
+ align:start position:0%
+mckinsey just sort of captures an
+earlier stage of where where is fintech
+
+ align:start position:0%
+earlier stage of where where is fintech
+ 
+
+ align:start position:0%
+earlier stage of where where is fintech
+in each of these
+
+ align:start position:0%
+in each of these
+ 
+
+ align:start position:0%
+in each of these
+and and i'm not going to go through each
+
+ align:start position:0%
+and and i'm not going to go through each
+ 
+
+ align:start position:0%
+and and i'm not going to go through each
+of these buckets but part of why i have
+
+ align:start position:0%
+of these buckets but part of why i have
+ 
+
+ align:start position:0%
+of these buckets but part of why i have
+this is it's so
+
+ align:start position:0%
+this is it's so
+ 
+
+ align:start position:0%
+this is it's so
+many little buckets we talked about two
+
+ align:start position:0%
+many little buckets we talked about two
+ 
+
+ align:start position:0%
+many little buckets we talked about two
+on the retail side
+
+ align:start position:0%
+on the retail side
+ 
+
+ align:start position:0%
+on the retail side
+they're crowd funding platforms
+
+ align:start position:0%
+they're crowd funding platforms
+ 
+
+ align:start position:0%
+they're crowd funding platforms
+literally platforms that help
+
+ align:start position:0%
+literally platforms that help
+ 
+
+ align:start position:0%
+literally platforms that help
+companies raise money there's trade
+
+ align:start position:0%
+companies raise money there's trade
+ 
+
+ align:start position:0%
+companies raise money there's trade
+execution and i'm going to talk about a
+
+ align:start position:0%
+execution and i'm going to talk about a
+ 
+
+ align:start position:0%
+execution and i'm going to talk about a
+couple in a minute
+
+ align:start position:0%
+couple in a minute
+ 
+
+ align:start position:0%
+couple in a minute
+decentralized trading platforms like in
+
+ align:start position:0%
+decentralized trading platforms like in
+ 
+
+ align:start position:0%
+decentralized trading platforms like in
+cryptocurrencies but also centralized
+
+ align:start position:0%
+cryptocurrencies but also centralized
+ 
+
+ align:start position:0%
+cryptocurrencies but also centralized
+trading platforms and cryptocurrencies
+
+ align:start position:0%
+trading platforms and cryptocurrencies
+ 
+
+ align:start position:0%
+trading platforms and cryptocurrencies
+but even in the last few years a firm
+
+ align:start position:0%
+but even in the last few years a firm
+ 
+
+ align:start position:0%
+but even in the last few years a firm
+called iex is a startup in trade
+
+ align:start position:0%
+called iex is a startup in trade
+ 
+
+ align:start position:0%
+called iex is a startup in trade
+execution it's a new trading platform
+
+ align:start position:0%
+execution it's a new trading platform
+ 
+
+ align:start position:0%
+execution it's a new trading platform
+there's post-trade services there's a
+
+ align:start position:0%
+there's post-trade services there's a
+ 
+
+ align:start position:0%
+there's post-trade services there's a
+lot of infrastructure and operations
+
+ align:start position:0%
+lot of infrastructure and operations
+ 
+
+ align:start position:0%
+lot of infrastructure and operations
+the capital markets are vast
+
+ align:start position:0%
+the capital markets are vast
+ 
+
+ align:start position:0%
+the capital markets are vast
+multi-trillion dollar uh business
+
+ align:start position:0%
+multi-trillion dollar uh business
+ 
+
+ align:start position:0%
+multi-trillion dollar uh business
+globally in terms of
+
+ align:start position:0%
+globally in terms of
+ 
+
+ align:start position:0%
+globally in terms of
+uh revenues so
+
+ align:start position:0%
+uh revenues so
+ 
+
+ align:start position:0%
+uh revenues so
+i'm just going to quickly sort of touch
+
+ align:start position:0%
+i'm just going to quickly sort of touch
+ 
+
+ align:start position:0%
+i'm just going to quickly sort of touch
+upon some
+
+ align:start position:0%
+upon some
+ 
+
+ align:start position:0%
+upon some
+in in these next couple of slides you
+
+ align:start position:0%
+in in these next couple of slides you
+ 
+
+ align:start position:0%
+in in these next couple of slides you
+can see i picked some like dozen or so
+
+ align:start position:0%
+can see i picked some like dozen or so
+ 
+
+ align:start position:0%
+can see i picked some like dozen or so
+firms that were just one's icon of like
+
+ align:start position:0%
+firms that were just one's icon of like
+ 
+
+ align:start position:0%
+firms that were just one's icon of like
+to watch and follow we can take any
+
+ align:start position:0%
+to watch and follow we can take any
+ 
+
+ align:start position:0%
+to watch and follow we can take any
+questions about uh
+
+ align:start position:0%
+questions about uh
+ 
+
+ align:start position:0%
+questions about uh
+each of these but there are a number of
+
+ align:start position:0%
+each of these but there are a number of
+ 
+
+ align:start position:0%
+each of these but there are a number of
+them in the wealth management space and
+
+ align:start position:0%
+them in the wealth management space and
+ 
+
+ align:start position:0%
+them in the wealth management space and
+one of the things in wealth management
+
+ align:start position:0%
+one of the things in wealth management
+ 
+
+ align:start position:0%
+one of the things in wealth management
+we talked about like betterment is
+
+ align:start position:0%
+we talked about like betterment is
+ 
+
+ align:start position:0%
+we talked about like betterment is
+facing the retail public but there are
+
+ align:start position:0%
+facing the retail public but there are
+ 
+
+ align:start position:0%
+facing the retail public but there are
+startups that are in the wealth
+
+ align:start position:0%
+startups that are in the wealth
+ 
+
+ align:start position:0%
+startups that are in the wealth
+management space facing financial
+
+ align:start position:0%
+management space facing financial
+ 
+
+ align:start position:0%
+management space facing financial
+advisors these tens of thousands of
+
+ align:start position:0%
+advisors these tens of thousands of
+ 
+
+ align:start position:0%
+advisors these tens of thousands of
+financial advisors
+
+ align:start position:0%
+financial advisors
+ 
+
+ align:start position:0%
+financial advisors
+want better software
+
+ align:start position:0%
+want better software
+ 
+
+ align:start position:0%
+want better software
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+add a and a number of others are
+
+ align:start position:0%
+add a and a number of others are
+ 
+
+ align:start position:0%
+add a and a number of others are
+actually platforms for the financial
+
+ align:start position:0%
+actually platforms for the financial
+ 
+
+ align:start position:0%
+actually platforms for the financial
+advisors that financial advisor that's
+
+ align:start position:0%
+advisors that financial advisor that's
+ 
+
+ align:start position:0%
+advisors that financial advisor that's
+trying to build a business
+
+ align:start position:0%
+trying to build a business
+ 
+
+ align:start position:0%
+trying to build a business
+wants
+
+ align:start position:0%
+wants
+ 
+
+ align:start position:0%
+wants
+software and access to the capital
+
+ align:start position:0%
+software and access to the capital
+ 
+
+ align:start position:0%
+software and access to the capital
+market so it's an interface between the
+
+ align:start position:0%
+market so it's an interface between the
+ 
+
+ align:start position:0%
+market so it's an interface between the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+there's a bunch that are in um
+
+ align:start position:0%
+there's a bunch that are in um
+ 
+
+ align:start position:0%
+there's a bunch that are in um
+in the area of
+
+ align:start position:0%
+in the area of
+ 
+
+ align:start position:0%
+in the area of
+collateral management and infrastructure
+
+ align:start position:0%
+collateral management and infrastructure
+ 
+
+ align:start position:0%
+collateral management and infrastructure
+uh cloud margin uh literally cl
+
+ align:start position:0%
+uh cloud margin uh literally cl
+ 
+
+ align:start position:0%
+uh cloud margin uh literally cl
+collateral management means the the
+
+ align:start position:0%
+collateral management means the the
+ 
+
+ align:start position:0%
+collateral management means the the
+collateral that you're moving on
+
+ align:start position:0%
+collateral that you're moving on
+ 
+
+ align:start position:0%
+collateral that you're moving on
+derivatives in the institutional market
+
+ align:start position:0%
+derivatives in the institutional market
+ 
+
+ align:start position:0%
+derivatives in the institutional market
+or collateral that you're moving even as
+
+ align:start position:0%
+or collateral that you're moving even as
+ 
+
+ align:start position:0%
+or collateral that you're moving even as
+it relates to loans
+
+ align:start position:0%
+it relates to loans
+ 
+
+ align:start position:0%
+it relates to loans
+why not start a platform that might be a
+
+ align:start position:0%
+why not start a platform that might be a
+ 
+
+ align:start position:0%
+why not start a platform that might be a
+little better for collateral management
+
+ align:start position:0%
+little better for collateral management
+ 
+
+ align:start position:0%
+little better for collateral management
+and take some of the back office cost
+
+ align:start position:0%
+and take some of the back office cost
+ 
+
+ align:start position:0%
+and take some of the back office cost
+out of it
+
+ align:start position:0%
+out of it
+ 
+
+ align:start position:0%
+out of it
+and not to be outdone you could have
+
+ align:start position:0%
+and not to be outdone you could have
+ 
+
+ align:start position:0%
+and not to be outdone you could have
+digital fixed income brokers as well as
+
+ align:start position:0%
+digital fixed income brokers as well as
+ 
+
+ align:start position:0%
+digital fixed income brokers as well as
+equity brokers what we were talking
+
+ align:start position:0%
+equity brokers what we were talking
+ 
+
+ align:start position:0%
+equity brokers what we were talking
+about earlier was the stock market and
+
+ align:start position:0%
+about earlier was the stock market and
+ 
+
+ align:start position:0%
+about earlier was the stock market and
+this company called
+
+ align:start position:0%
+this company called
+ 
+
+ align:start position:0%
+this company called
+uh elephant
+
+ align:start position:0%
+uh elephant
+ 
+
+ align:start position:0%
+uh elephant
+i mentioned iex started in 2012.
+
+ align:start position:0%
+i mentioned iex started in 2012.
+ 
+
+ align:start position:0%
+i mentioned iex started in 2012.
+it's to be a competitive stock market to
+
+ align:start position:0%
+it's to be a competitive stock market to
+ 
+
+ align:start position:0%
+it's to be a competitive stock market to
+nasdaq new york stock exchange started
+
+ align:start position:0%
+nasdaq new york stock exchange started
+ 
+
+ align:start position:0%
+nasdaq new york stock exchange started
+by a bunch of
+
+ align:start position:0%
+by a bunch of
+ 
+
+ align:start position:0%
+by a bunch of
+buy side institutions for instance
+
+ align:start position:0%
+buy side institutions for instance
+ 
+
+ align:start position:0%
+buy side institutions for instance
+and and sometimes it's just research
+
+ align:start position:0%
+and and sometimes it's just research
+ 
+
+ align:start position:0%
+and and sometimes it's just research
+pitch book
+
+ align:start position:0%
+pitch book
+ 
+
+ align:start position:0%
+pitch book
+and others like pitch book put together
+
+ align:start position:0%
+and others like pitch book put together
+ 
+
+ align:start position:0%
+and others like pitch book put together
+a remarkable data base on the financial
+
+ align:start position:0%
+a remarkable data base on the financial
+ 
+
+ align:start position:0%
+a remarkable data base on the financial
+business of venture capital for instance
+
+ align:start position:0%
+business of venture capital for instance
+ 
+
+ align:start position:0%
+business of venture capital for instance
+so it could be a lot of different spaces
+
+ align:start position:0%
+so it could be a lot of different spaces
+ 
+
+ align:start position:0%
+so it could be a lot of different spaces
+back to sort of thinking about the
+
+ align:start position:0%
+back to sort of thinking about the
+ 
+
+ align:start position:0%
+back to sort of thinking about the
+different aspects of capital markets
+
+ align:start position:0%
+different aspects of capital markets
+ 
+
+ align:start position:0%
+different aspects of capital markets
+crowdfunding platforms trade execution
+
+ align:start position:0%
+crowdfunding platforms trade execution
+ 
+
+ align:start position:0%
+crowdfunding platforms trade execution
+the post-trade side of it
+
+ align:start position:0%
+the post-trade side of it
+ 
+
+ align:start position:0%
+the post-trade side of it
+i don't do this to be like a full course
+
+ align:start position:0%
+i don't do this to be like a full course
+ 
+
+ align:start position:0%
+i don't do this to be like a full course
+on capital markets but it's to sort of
+
+ align:start position:0%
+on capital markets but it's to sort of
+ 
+
+ align:start position:0%
+on capital markets but it's to sort of
+open your sort of uh thinking to
+
+ align:start position:0%
+open your sort of uh thinking to
+ 
+
+ align:start position:0%
+open your sort of uh thinking to
+it's not just the retail interface it's
+
+ align:start position:0%
+it's not just the retail interface it's
+ 
+
+ align:start position:0%
+it's not just the retail interface it's
+not just
+
+ align:start position:0%
+not just
+ 
+
+ align:start position:0%
+not just
+using a mobile phone good data good user
+
+ align:start position:0%
+using a mobile phone good data good user
+ 
+
+ align:start position:0%
+using a mobile phone good data good user
+delivery and lower cost and that's
+
+ align:start position:0%
+delivery and lower cost and that's
+ 
+
+ align:start position:0%
+delivery and lower cost and that's
+really the robinhood betterment side
+
+ align:start position:0%
+really the robinhood betterment side
+ 
+
+ align:start position:0%
+really the robinhood betterment side
+it's also a lot of taking the paper
+
+ align:start position:0%
+it's also a lot of taking the paper
+ 
+
+ align:start position:0%
+it's also a lot of taking the paper
+flows out of it old
+
+ align:start position:0%
+flows out of it old
+ 
+
+ align:start position:0%
+flows out of it old
+processes out of the back office
+
+ align:start position:0%
+processes out of the back office
+ 
+
+ align:start position:0%
+processes out of the back office
+and trying to
+
+ align:start position:0%
+and trying to
+ 
+
+ align:start position:0%
+and trying to
+sort of provide a service to the capital
+
+ align:start position:0%
+sort of provide a service to the capital
+ 
+
+ align:start position:0%
+sort of provide a service to the capital
+markets in a better way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+romaine any uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any hands raised anyone has a question
+
+ align:start position:0%
+any hands raised anyone has a question
+ 
+
+ align:start position:0%
+any hands raised anyone has a question
+on this topic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no i think we can let me just close out
+
+ align:start position:0%
+no i think we can let me just close out
+ 
+
+ align:start position:0%
+no i think we can let me just close out
+crypto markets a bit and and some of you
+
+ align:start position:0%
+crypto markets a bit and and some of you
+ 
+
+ align:start position:0%
+crypto markets a bit and and some of you
+take the crypto finance course or it may
+
+ align:start position:0%
+take the crypto finance course or it may
+ 
+
+ align:start position:0%
+take the crypto finance course or it may
+be a little bit repetitive but let me
+
+ align:start position:0%
+be a little bit repetitive but let me
+ 
+
+ align:start position:0%
+be a little bit repetitive but let me
+just say
+
+ align:start position:0%
+just say
+ 
+
+ align:start position:0%
+just say
+one thing that's interesting is this
+
+ align:start position:0%
+one thing that's interesting is this
+ 
+
+ align:start position:0%
+one thing that's interesting is this
+crypto market came along
+
+ align:start position:0%
+crypto market came along
+ 
+
+ align:start position:0%
+crypto market came along
+is there a question here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+luke has his hand raised let me let me
+
+ align:start position:0%
+luke has his hand raised let me let me
+ 
+
+ align:start position:0%
+luke has his hand raised let me let me
+hold luke because he's he's had a lot
+
+ align:start position:0%
+hold luke because he's he's had a lot
+ 
+
+ align:start position:0%
+hold luke because he's he's had a lot
+here so let me just say something crypto
+
+ align:start position:0%
+here so let me just say something crypto
+ 
+
+ align:start position:0%
+here so let me just say something crypto
+markets and then we'll take we'll
+
+ align:start position:0%
+markets and then we'll take we'll
+ 
+
+ align:start position:0%
+markets and then we'll take we'll
+definitely take luke's question but
+
+ align:start position:0%
+definitely take luke's question but
+ 
+
+ align:start position:0%
+definitely take luke's question but
+the crypto
+
+ align:start position:0%
+the crypto
+ 
+
+ align:start position:0%
+the crypto
+markets came along about a dozen years
+
+ align:start position:0%
+markets came along about a dozen years
+ 
+
+ align:start position:0%
+markets came along about a dozen years
+ago and by an early stage of these
+
+ align:start position:0%
+ago and by an early stage of these
+ 
+
+ align:start position:0%
+ago and by an early stage of these
+markets somebody said how can you buy
+
+ align:start position:0%
+markets somebody said how can you buy
+ 
+
+ align:start position:0%
+markets somebody said how can you buy
+and sell bitcoin
+
+ align:start position:0%
+and sell bitcoin
+ 
+
+ align:start position:0%
+and sell bitcoin
+and they created exchanges a new form of
+
+ align:start position:0%
+and they created exchanges a new form of
+ 
+
+ align:start position:0%
+and they created exchanges a new form of
+exchange not for equities not for bonds
+
+ align:start position:0%
+exchange not for equities not for bonds
+ 
+
+ align:start position:0%
+exchange not for equities not for bonds
+not for foreign currencies or fiat
+
+ align:start position:0%
+not for foreign currencies or fiat
+ 
+
+ align:start position:0%
+not for foreign currencies or fiat
+currencies but cryptocurrencies and
+
+ align:start position:0%
+currencies but cryptocurrencies and
+ 
+
+ align:start position:0%
+currencies but cryptocurrencies and
+these exchanges act as agents matching
+
+ align:start position:0%
+these exchanges act as agents matching
+ 
+
+ align:start position:0%
+these exchanges act as agents matching
+buyers and sellers like traditional
+
+ align:start position:0%
+buyers and sellers like traditional
+ 
+
+ align:start position:0%
+buyers and sellers like traditional
+exchanges
+
+ align:start position:0%
+exchanges
+ 
+
+ align:start position:0%
+exchanges
+but they also act as market makers we
+
+ align:start position:0%
+but they also act as market makers we
+ 
+
+ align:start position:0%
+but they also act as market makers we
+talked earlier about capturing bid air
+
+ align:start position:0%
+talked earlier about capturing bid air
+ 
+
+ align:start position:0%
+talked earlier about capturing bid air
+spread
+
+ align:start position:0%
+spread
+ 
+
+ align:start position:0%
+spread
+these exchanges could also buy and sell
+
+ align:start position:0%
+these exchanges could also buy and sell
+ 
+
+ align:start position:0%
+these exchanges could also buy and sell
+from customers not all of them do but
+
+ align:start position:0%
+from customers not all of them do but
+ 
+
+ align:start position:0%
+from customers not all of them do but
+they could traditional exchanges did not
+
+ align:start position:0%
+they could traditional exchanges did not
+ 
+
+ align:start position:0%
+they could traditional exchanges did not
+and they also acted as a custody and
+
+ align:start position:0%
+and they also acted as a custody and
+ 
+
+ align:start position:0%
+and they also acted as a custody and
+held your funds and even to this day if
+
+ align:start position:0%
+held your funds and even to this day if
+ 
+
+ align:start position:0%
+held your funds and even to this day if
+you trade on a crypto exchange you're
+
+ align:start position:0%
+you trade on a crypto exchange you're
+ 
+
+ align:start position:0%
+you trade on a crypto exchange you're
+moving your asset through the use of
+
+ align:start position:0%
+moving your asset through the use of
+ 
+
+ align:start position:0%
+moving your asset through the use of
+what's called a private key
+
+ align:start position:0%
+what's called a private key
+ 
+
+ align:start position:0%
+what's called a private key
+but you're moving your asset to the
+
+ align:start position:0%
+but you're moving your asset to the
+ 
+
+ align:start position:0%
+but you're moving your asset to the
+crypto exchange and they're the custody
+
+ align:start position:0%
+crypto exchange and they're the custody
+ 
+
+ align:start position:0%
+crypto exchange and they're the custody
+they're the custodian
+
+ align:start position:0%
+they're the custodian
+ 
+
+ align:start position:0%
+they're the custodian
+the public
+
+ align:start position:0%
+the public
+ 
+
+ align:start position:0%
+the public
+has direct access and this is a very
+
+ align:start position:0%
+has direct access and this is a very
+ 
+
+ align:start position:0%
+has direct access and this is a very
+different model than traditional
+
+ align:start position:0%
+different model than traditional
+ 
+
+ align:start position:0%
+different model than traditional
+exchanges and the question will be will
+
+ align:start position:0%
+exchanges and the question will be will
+ 
+
+ align:start position:0%
+exchanges and the question will be will
+this come to traditional
+
+ align:start position:0%
+this come to traditional
+ 
+
+ align:start position:0%
+this come to traditional
+markets and that's why i wanted to focus
+
+ align:start position:0%
+markets and that's why i wanted to focus
+ 
+
+ align:start position:0%
+markets and that's why i wanted to focus
+on this minute in traditional markets
+
+ align:start position:0%
+on this minute in traditional markets
+ 
+
+ align:start position:0%
+on this minute in traditional markets
+built upon a business model that's
+
+ align:start position:0%
+built upon a business model that's
+ 
+
+ align:start position:0%
+built upon a business model that's
+multiple centuries old
+
+ align:start position:0%
+multiple centuries old
+ 
+
+ align:start position:0%
+multiple centuries old
+you and i are not members directly of
+
+ align:start position:0%
+you and i are not members directly of
+ 
+
+ align:start position:0%
+you and i are not members directly of
+the new york stock exchange we have to
+
+ align:start position:0%
+the new york stock exchange we have to
+ 
+
+ align:start position:0%
+the new york stock exchange we have to
+go through somebody to get to the new
+
+ align:start position:0%
+go through somebody to get to the new
+ 
+
+ align:start position:0%
+go through somebody to get to the new
+york stock exchange that's called a
+
+ align:start position:0%
+york stock exchange that's called a
+ 
+
+ align:start position:0%
+york stock exchange that's called a
+broker it's called a member of the new
+
+ align:start position:0%
+broker it's called a member of the new
+ 
+
+ align:start position:0%
+broker it's called a member of the new
+york stock exchange or the london stock
+
+ align:start position:0%
+york stock exchange or the london stock
+ 
+
+ align:start position:0%
+york stock exchange or the london stock
+exchange or the shanghai stock exchange
+
+ align:start position:0%
+exchange or the shanghai stock exchange
+ 
+
+ align:start position:0%
+exchange or the shanghai stock exchange
+but in these markets in these crypto
+
+ align:start position:0%
+but in these markets in these crypto
+ 
+
+ align:start position:0%
+but in these markets in these crypto
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+everybody can access directly the
+
+ align:start position:0%
+everybody can access directly the
+ 
+
+ align:start position:0%
+everybody can access directly the
+markets the markets actually
+
+ align:start position:0%
+markets the markets actually
+ 
+
+ align:start position:0%
+markets the markets actually
+interestingly have to have a much more
+
+ align:start position:0%
+interestingly have to have a much more
+ 
+
+ align:start position:0%
+interestingly have to have a much more
+robust
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+api for the retail public the new york
+
+ align:start position:0%
+api for the retail public the new york
+ 
+
+ align:start position:0%
+api for the retail public the new york
+stock exchange and london stock exchange
+
+ align:start position:0%
+stock exchange and london stock exchange
+ 
+
+ align:start position:0%
+stock exchange and london stock exchange
+have to have a robust api
+
+ align:start position:0%
+have to have a robust api
+ 
+
+ align:start position:0%
+have to have a robust api
+application program interface for
+
+ align:start position:0%
+application program interface for
+ 
+
+ align:start position:0%
+application program interface for
+institutions and it has to be very high
+
+ align:start position:0%
+institutions and it has to be very high
+ 
+
+ align:start position:0%
+institutions and it has to be very high
+volume very resilient
+
+ align:start position:0%
+volume very resilient
+ 
+
+ align:start position:0%
+volume very resilient
+but it can be limited to
+
+ align:start position:0%
+but it can be limited to
+ 
+
+ align:start position:0%
+but it can be limited to
+hundreds or at most a couple thousands
+
+ align:start position:0%
+hundreds or at most a couple thousands
+ 
+
+ align:start position:0%
+hundreds or at most a couple thousands
+of users even if the volumes are high
+
+ align:start position:0%
+of users even if the volumes are high
+ 
+
+ align:start position:0%
+of users even if the volumes are high
+these exchanges have to be open to
+
+ align:start position:0%
+these exchanges have to be open to
+ 
+
+ align:start position:0%
+these exchanges have to be open to
+millions of people from their home
+
+ align:start position:0%
+millions of people from their home
+ 
+
+ align:start position:0%
+millions of people from their home
+laptops and mobile phones a very
+
+ align:start position:0%
+laptops and mobile phones a very
+ 
+
+ align:start position:0%
+laptops and mobile phones a very
+different architecture where it's
+
+ align:start position:0%
+different architecture where it's
+ 
+
+ align:start position:0%
+different architecture where it's
+disintermediated the broker dealers and
+
+ align:start position:0%
+disintermediated the broker dealers and
+ 
+
+ align:start position:0%
+disintermediated the broker dealers and
+the question i have
+
+ align:start position:0%
+the question i have
+ 
+
+ align:start position:0%
+the question i have
+which is unanswerable right now will
+
+ align:start position:0%
+which is unanswerable right now will
+ 
+
+ align:start position:0%
+which is unanswerable right now will
+this be something moving forward will we
+
+ align:start position:0%
+this be something moving forward will we
+ 
+
+ align:start position:0%
+this be something moving forward will we
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+a direct access model at any exchange
+
+ align:start position:0%
+a direct access model at any exchange
+ 
+
+ align:start position:0%
+a direct access model at any exchange
+around the globe or will we stay in the
+
+ align:start position:0%
+around the globe or will we stay in the
+ 
+
+ align:start position:0%
+around the globe or will we stay in the
+intermediate access there's a lot of
+
+ align:start position:0%
+intermediate access there's a lot of
+ 
+
+ align:start position:0%
+intermediate access there's a lot of
+regulatory reasons we'd stay in the
+
+ align:start position:0%
+regulatory reasons we'd stay in the
+ 
+
+ align:start position:0%
+regulatory reasons we'd stay in the
+intermediate access there's some
+
+ align:start position:0%
+intermediate access there's some
+ 
+
+ align:start position:0%
+intermediate access there's some
+competitive reasons brokers wouldn't
+
+ align:start position:0%
+competitive reasons brokers wouldn't
+ 
+
+ align:start position:0%
+competitive reasons brokers wouldn't
+want to have folks going directly
+
+ align:start position:0%
+want to have folks going directly
+ 
+
+ align:start position:0%
+want to have folks going directly
+but on the other hand the technology now
+
+ align:start position:0%
+but on the other hand the technology now
+ 
+
+ align:start position:0%
+but on the other hand the technology now
+exists that you could go directly
+
+ align:start position:0%
+exists that you could go directly
+ 
+
+ align:start position:0%
+exists that you could go directly
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+these markets by the way are not well
+
+ align:start position:0%
+these markets by the way are not well
+ 
+
+ align:start position:0%
+these markets by the way are not well
+regulated and they're rife with fraud
+
+ align:start position:0%
+regulated and they're rife with fraud
+ 
+
+ align:start position:0%
+regulated and they're rife with fraud
+and scams and and manipulation so i just
+
+ align:start position:0%
+and scams and and manipulation so i just
+ 
+
+ align:start position:0%
+and scams and and manipulation so i just
+want to mention that i see a few hands
+
+ align:start position:0%
+want to mention that i see a few hands
+ 
+
+ align:start position:0%
+want to mention that i see a few hands
+in addition to luke's head so maybe we
+
+ align:start position:0%
+in addition to luke's head so maybe we
+ 
+
+ align:start position:0%
+in addition to luke's head so maybe we
+should pause
+
+ align:start position:0%
+should pause
+ 
+
+ align:start position:0%
+should pause
+yes carlos
+
+ align:start position:0%
+yes carlos
+ 
+
+ align:start position:0%
+yes carlos
+and and we'd have to get loots too right
+
+ align:start position:0%
+and and we'd have to get loots too right
+ 
+
+ align:start position:0%
+and and we'd have to get loots too right
+carlos all right
+
+ align:start position:0%
+carlos all right
+ 
+
+ align:start position:0%
+carlos all right
+so so what do you think would happen if
+
+ align:start position:0%
+so so what do you think would happen if
+ 
+
+ align:start position:0%
+so so what do you think would happen if
+the big banks started holding more
+
+ align:start position:0%
+the big banks started holding more
+ 
+
+ align:start position:0%
+the big banks started holding more
+crypto in their balance sheets right if
+
+ align:start position:0%
+crypto in their balance sheets right if
+ 
+
+ align:start position:0%
+crypto in their balance sheets right if
+they if they start acting as market
+
+ align:start position:0%
+they if they start acting as market
+ 
+
+ align:start position:0%
+they if they start acting as market
+makers in crypto markets then would it
+
+ align:start position:0%
+makers in crypto markets then would it
+ 
+
+ align:start position:0%
+makers in crypto markets then would it
+for example under current regulation
+
+ align:start position:0%
+for example under current regulation
+ 
+
+ align:start position:0%
+for example under current regulation
+would this asset go under dodd-frank as
+
+ align:start position:0%
+would this asset go under dodd-frank as
+ 
+
+ align:start position:0%
+would this asset go under dodd-frank as
+well and therefore limit proprietary
+
+ align:start position:0%
+well and therefore limit proprietary
+ 
+
+ align:start position:0%
+well and therefore limit proprietary
+trading or do you think it would be
+
+ align:start position:0%
+trading or do you think it would be
+ 
+
+ align:start position:0%
+trading or do you think it would be
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+there's a lot of questions in there
+
+ align:start position:0%
+there's a lot of questions in there
+ 
+
+ align:start position:0%
+there's a lot of questions in there
+the large banks around the globe today
+
+ align:start position:0%
+the large banks around the globe today
+ 
+
+ align:start position:0%
+the large banks around the globe today
+have not been active uh in this asset
+
+ align:start position:0%
+have not been active uh in this asset
+ 
+
+ align:start position:0%
+have not been active uh in this asset
+class the asset class is about 225
+
+ align:start position:0%
+class the asset class is about 225
+ 
+
+ align:start position:0%
+class the asset class is about 225
+billion dollars as of this morning
+
+ align:start position:0%
+billion dollars as of this morning
+ 
+
+ align:start position:0%
+billion dollars as of this morning
+which is small the worldwide capital
+
+ align:start position:0%
+which is small the worldwide capital
+ 
+
+ align:start position:0%
+which is small the worldwide capital
+markets are
+
+ align:start position:0%
+markets are
+ 
+
+ align:start position:0%
+markets are
+between three and 400 trillion when you
+
+ align:start position:0%
+between three and 400 trillion when you
+ 
+
+ align:start position:0%
+between three and 400 trillion when you
+add equities and bonds worldwide
+
+ align:start position:0%
+add equities and bonds worldwide
+ 
+
+ align:start position:0%
+add equities and bonds worldwide
+and debt
+
+ align:start position:0%
+and debt
+ 
+
+ align:start position:0%
+and debt
+so this is quite small in comparison but
+
+ align:start position:0%
+so this is quite small in comparison but
+ 
+
+ align:start position:0%
+so this is quite small in comparison but
+for regulatory reasons and for customer
+
+ align:start position:0%
+for regulatory reasons and for customer
+ 
+
+ align:start position:0%
+for regulatory reasons and for customer
+interest reasons large banks haven't
+
+ align:start position:0%
+interest reasons large banks haven't
+ 
+
+ align:start position:0%
+interest reasons large banks haven't
+really gone in if they were to get in to
+
+ align:start position:0%
+really gone in if they were to get in to
+ 
+
+ align:start position:0%
+really gone in if they were to get in to
+you answer your question on the
+
+ align:start position:0%
+you answer your question on the
+ 
+
+ align:start position:0%
+you answer your question on the
+regulatory side
+
+ align:start position:0%
+regulatory side
+ 
+
+ align:start position:0%
+regulatory side
+yes it would be just like any other
+
+ align:start position:0%
+yes it would be just like any other
+ 
+
+ align:start position:0%
+yes it would be just like any other
+asset they have any commodity so if you
+
+ align:start position:0%
+asset they have any commodity so if you
+ 
+
+ align:start position:0%
+asset they have any commodity so if you
+hold bitcoin you might think if you're
+
+ align:start position:0%
+hold bitcoin you might think if you're
+ 
+
+ align:start position:0%
+hold bitcoin you might think if you're
+jp morgan
+
+ align:start position:0%
+jp morgan
+ 
+
+ align:start position:0%
+jp morgan
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'm now holding it
+
+ align:start position:0%
+i'm now holding it
+ 
+
+ align:start position:0%
+i'm now holding it
+uh i'm barclays bank i'm now holding it
+
+ align:start position:0%
+uh i'm barclays bank i'm now holding it
+ 
+
+ align:start position:0%
+uh i'm barclays bank i'm now holding it
+what regulations if it's bitcoin it
+
+ align:start position:0%
+what regulations if it's bitcoin it
+ 
+
+ align:start position:0%
+what regulations if it's bitcoin it
+would be very similar to the regulations
+
+ align:start position:0%
+would be very similar to the regulations
+ 
+
+ align:start position:0%
+would be very similar to the regulations
+around holding gold or silver
+
+ align:start position:0%
+around holding gold or silver
+ 
+
+ align:start position:0%
+around holding gold or silver
+uh maybe
+
+ align:start position:0%
+uh maybe
+ 
+
+ align:start position:0%
+uh maybe
+you would hold gold or silver
+
+ align:start position:0%
+you would hold gold or silver
+ 
+
+ align:start position:0%
+you would hold gold or silver
+uh futures or contracts but holding gold
+
+ align:start position:0%
+uh futures or contracts but holding gold
+ 
+
+ align:start position:0%
+uh futures or contracts but holding gold
+silver and um to the extent that there
+
+ align:start position:0%
+silver and um to the extent that there
+ 
+
+ align:start position:0%
+silver and um to the extent that there
+was a uh you mentioned dodd-frank
+
+ align:start position:0%
+was a uh you mentioned dodd-frank
+ 
+
+ align:start position:0%
+was a uh you mentioned dodd-frank
+uh if there were any rules and
+
+ align:start position:0%
+uh if there were any rules and
+ 
+
+ align:start position:0%
+uh if there were any rules and
+regulations out of dodd-frank that were
+
+ align:start position:0%
+regulations out of dodd-frank that were
+ 
+
+ align:start position:0%
+regulations out of dodd-frank that were
+generally applicable the trading
+
+ align:start position:0%
+generally applicable the trading
+ 
+
+ align:start position:0%
+generally applicable the trading
+accounts that would be applicable to
+
+ align:start position:0%
+accounts that would be applicable to
+ 
+
+ align:start position:0%
+accounts that would be applicable to
+these trading accounts the one big
+
+ align:start position:0%
+these trading accounts the one big
+ 
+
+ align:start position:0%
+these trading accounts the one big
+challenge for big institutions is
+
+ align:start position:0%
+challenge for big institutions is
+ 
+
+ align:start position:0%
+challenge for big institutions is
+custody
+
+ align:start position:0%
+custody
+ 
+
+ align:start position:0%
+custody
+custody has been a challenge
+
+ align:start position:0%
+custody has been a challenge
+ 
+
+ align:start position:0%
+custody has been a challenge
+and what's interesting is fidelity one
+
+ align:start position:0%
+and what's interesting is fidelity one
+ 
+
+ align:start position:0%
+and what's interesting is fidelity one
+of the largest asset managers of the
+
+ align:start position:0%
+of the largest asset managers of the
+ 
+
+ align:start position:0%
+of the largest asset managers of the
+world started something called fidelity
+
+ align:start position:0%
+world started something called fidelity
+ 
+
+ align:start position:0%
+world started something called fidelity
+digital asset holding
+
+ align:start position:0%
+digital asset holding
+ 
+
+ align:start position:0%
+digital asset holding
+i believe that's the name
+
+ align:start position:0%
+i believe that's the name
+ 
+
+ align:start position:0%
+i believe that's the name
+where they are providing a custody
+
+ align:start position:0%
+where they are providing a custody
+ 
+
+ align:start position:0%
+where they are providing a custody
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+coinbase which is a large crypto
+
+ align:start position:0%
+coinbase which is a large crypto
+ 
+
+ align:start position:0%
+coinbase which is a large crypto
+exchange has a custody solution the
+
+ align:start position:0%
+exchange has a custody solution the
+ 
+
+ align:start position:0%
+exchange has a custody solution the
+owner of the new york stock exchange
+
+ align:start position:0%
+owner of the new york stock exchange
+ 
+
+ align:start position:0%
+owner of the new york stock exchange
+intercontinental exchange started backed
+
+ align:start position:0%
+intercontinental exchange started backed
+ 
+
+ align:start position:0%
+intercontinental exchange started backed
+the akkt
+
+ align:start position:0%
+the akkt
+ 
+
+ align:start position:0%
+the akkt
+backed as trading crypto markets but
+
+ align:start position:0%
+backed as trading crypto markets but
+ 
+
+ align:start position:0%
+backed as trading crypto markets but
+also providing a custody solution and
+
+ align:start position:0%
+also providing a custody solution and
+ 
+
+ align:start position:0%
+also providing a custody solution and
+why i'm focusing on custody is one of
+
+ align:start position:0%
+why i'm focusing on custody is one of
+ 
+
+ align:start position:0%
+why i'm focusing on custody is one of
+the challenges in this small asset class
+
+ align:start position:0%
+the challenges in this small asset class
+ 
+
+ align:start position:0%
+the challenges in this small asset class
+is how to hold the digital asset
+
+ align:start position:0%
+is how to hold the digital asset
+ 
+
+ align:start position:0%
+is how to hold the digital asset
+in the traditional markets in the
+
+ align:start position:0%
+in the traditional markets in the
+ 
+
+ align:start position:0%
+in the traditional markets in the
+traditional markets
+
+ align:start position:0%
+traditional markets
+ 
+
+ align:start position:0%
+traditional markets
+there are centralized
+
+ align:start position:0%
+there are centralized
+ 
+
+ align:start position:0%
+there are centralized
+organizations
+
+ align:start position:0%
+organizations
+ 
+
+ align:start position:0%
+organizations
+uh that operate as clearing houses but
+
+ align:start position:0%
+uh that operate as clearing houses but
+ 
+
+ align:start position:0%
+uh that operate as clearing houses but
+also as the ultimate digital custodian
+
+ align:start position:0%
+also as the ultimate digital custodian
+ 
+
+ align:start position:0%
+also as the ultimate digital custodian
+in the u.s it's called dtcc
+
+ align:start position:0%
+in the u.s it's called dtcc
+ 
+
+ align:start position:0%
+in the u.s it's called dtcc
+uh in other countries different names
+
+ align:start position:0%
+uh in other countries different names
+ 
+
+ align:start position:0%
+uh in other countries different names
+but how do you make sure that the the
+
+ align:start position:0%
+but how do you make sure that the the
+ 
+
+ align:start position:0%
+but how do you make sure that the the
+in essence the cryptocurrency isn't
+
+ align:start position:0%
+in essence the cryptocurrency isn't
+ 
+
+ align:start position:0%
+in essence the cryptocurrency isn't
+stolen and for these crypto exchanges
+
+ align:start position:0%
+stolen and for these crypto exchanges
+ 
+
+ align:start position:0%
+stolen and for these crypto exchanges
+have had lots of stolen
+
+ align:start position:0%
+have had lots of stolen
+ 
+
+ align:start position:0%
+have had lots of stolen
+cryptocurrency because once you steal
+
+ align:start position:0%
+cryptocurrency because once you steal
+ 
+
+ align:start position:0%
+cryptocurrency because once you steal
+what's called the private key the
+
+ align:start position:0%
+what's called the private key the
+ 
+
+ align:start position:0%
+what's called the private key the
+effectively the password
+
+ align:start position:0%
+effectively the password
+ 
+
+ align:start position:0%
+effectively the password
+you have the digital asset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what was luke's question earlier uh
+
+ align:start position:0%
+what was luke's question earlier uh
+ 
+
+ align:start position:0%
+what was luke's question earlier uh
+speaking of cryptocurrency
+
+ align:start position:0%
+speaking of cryptocurrency
+ 
+
+ align:start position:0%
+speaking of cryptocurrency
+i know you teach in uh age four the
+
+ align:start position:0%
+i know you teach in uh age four the
+ 
+
+ align:start position:0%
+i know you teach in uh age four the
+cryptocurrency class which i don't have
+
+ align:start position:0%
+cryptocurrency class which i don't have
+ 
+
+ align:start position:0%
+cryptocurrency class which i don't have
+the luxury of taking but the first year
+
+ align:start position:0%
+the luxury of taking but the first year
+ 
+
+ align:start position:0%
+the luxury of taking but the first year
+you have the opportunity to take next
+
+ align:start position:0%
+you have the opportunity to take next
+ 
+
+ align:start position:0%
+you have the opportunity to take next
+semester or next year
+
+ align:start position:0%
+semester or next year
+ 
+
+ align:start position:0%
+semester or next year
+my question is
+
+ align:start position:0%
+my question is
+ 
+
+ align:start position:0%
+my question is
+then is that because of the security
+
+ align:start position:0%
+then is that because of the security
+ 
+
+ align:start position:0%
+then is that because of the security
+that robin hood does not implement
+
+ align:start position:0%
+that robin hood does not implement
+ 
+
+ align:start position:0%
+that robin hood does not implement
+um customers the option to buy
+
+ align:start position:0%
+um customers the option to buy
+ 
+
+ align:start position:0%
+um customers the option to buy
+u.s equity with bitcoin overseas because
+
+ align:start position:0%
+u.s equity with bitcoin overseas because
+ 
+
+ align:start position:0%
+u.s equity with bitcoin overseas because
+they would allow them to jump over its
+
+ align:start position:0%
+they would allow them to jump over its
+ 
+
+ align:start position:0%
+they would allow them to jump over its
+respective nations effects regulations
+
+ align:start position:0%
+respective nations effects regulations
+ 
+
+ align:start position:0%
+respective nations effects regulations
+i.e
+
+ align:start position:0%
+i.e
+ 
+
+ align:start position:0%
+i.e
+chinese customers or creating customers
+
+ align:start position:0%
+chinese customers or creating customers
+ 
+
+ align:start position:0%
+chinese customers or creating customers
+who wants to invest in
+
+ align:start position:0%
+who wants to invest in
+ 
+
+ align:start position:0%
+who wants to invest in
+you know ong buy low sale high with
+
+ align:start position:0%
+you know ong buy low sale high with
+ 
+
+ align:start position:0%
+you know ong buy low sale high with
+i'm going to answer briefly i think the
+
+ align:start position:0%
+i'm going to answer briefly i think the
+ 
+
+ align:start position:0%
+i'm going to answer briefly i think the
+regulation
+
+ align:start position:0%
+regulation
+ 
+
+ align:start position:0%
+regulation
+for any one platform like robinhood
+
+ align:start position:0%
+for any one platform like robinhood
+ 
+
+ align:start position:0%
+for any one platform like robinhood
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+cryptocurrencies is a bit challenging
+
+ align:start position:0%
+cryptocurrencies is a bit challenging
+ 
+
+ align:start position:0%
+cryptocurrencies is a bit challenging
+because in many jurisdictions and many
+
+ align:start position:0%
+because in many jurisdictions and many
+ 
+
+ align:start position:0%
+because in many jurisdictions and many
+jurisdictions
+
+ align:start position:0%
+jurisdictions
+ 
+
+ align:start position:0%
+jurisdictions
+we have not gotten to a place where you
+
+ align:start position:0%
+we have not gotten to a place where you
+ 
+
+ align:start position:0%
+we have not gotten to a place where you
+can feel confident we have a robust
+
+ align:start position:0%
+can feel confident we have a robust
+ 
+
+ align:start position:0%
+can feel confident we have a robust
+uh investor protection regime on
+
+ align:start position:0%
+uh investor protection regime on
+ 
+
+ align:start position:0%
+uh investor protection regime on
+cryptocurrency and in fact in most
+
+ align:start position:0%
+cryptocurrency and in fact in most
+ 
+
+ align:start position:0%
+cryptocurrency and in fact in most
+jurisdictions it's pretty shaky it's
+
+ align:start position:0%
+jurisdictions it's pretty shaky it's
+ 
+
+ align:start position:0%
+jurisdictions it's pretty shaky it's
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+undeveloped i'm talking about investor
+
+ align:start position:0%
+undeveloped i'm talking about investor
+ 
+
+ align:start position:0%
+undeveloped i'm talking about investor
+protection so robin hood may have made a
+
+ align:start position:0%
+protection so robin hood may have made a
+ 
+
+ align:start position:0%
+protection so robin hood may have made a
+choice look if you're going to trade
+
+ align:start position:0%
+choice look if you're going to trade
+ 
+
+ align:start position:0%
+choice look if you're going to trade
+you're going to trade fiat currency
+
+ align:start position:0%
+you're going to trade fiat currency
+ 
+
+ align:start position:0%
+you're going to trade fiat currency
+versus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buying and selling stocks and that would
+
+ align:start position:0%
+buying and selling stocks and that would
+ 
+
+ align:start position:0%
+buying and selling stocks and that would
+be an appropriate business decision that
+
+ align:start position:0%
+be an appropriate business decision that
+ 
+
+ align:start position:0%
+be an appropriate business decision that
+they made until there's a much more
+
+ align:start position:0%
+they made until there's a much more
+ 
+
+ align:start position:0%
+they made until there's a much more
+robust and satisfactory
+
+ align:start position:0%
+robust and satisfactory
+ 
+
+ align:start position:0%
+robust and satisfactory
+uh both investor protection and also
+
+ align:start position:0%
+uh both investor protection and also
+ 
+
+ align:start position:0%
+uh both investor protection and also
+guarding against illicit activity
+
+ align:start position:0%
+guarding against illicit activity
+ 
+
+ align:start position:0%
+guarding against illicit activity
+cryptocurrency started and emanated out
+
+ align:start position:0%
+cryptocurrency started and emanated out
+ 
+
+ align:start position:0%
+cryptocurrency started and emanated out
+of a little bit of an off the grid
+
+ align:start position:0%
+of a little bit of an off the grid
+ 
+
+ align:start position:0%
+of a little bit of an off the grid
+cipher punk
+
+ align:start position:0%
+cipher punk
+ 
+
+ align:start position:0%
+cipher punk
+uh movement and i used the word
+
+ align:start position:0%
+uh movement and i used the word
+ 
+
+ align:start position:0%
+uh movement and i used the word
+accurately cypherpunk was a mailing list
+
+ align:start position:0%
+accurately cypherpunk was a mailing list
+ 
+
+ align:start position:0%
+accurately cypherpunk was a mailing list
+that satoshi nakamoto uploaded that
+
+ align:start position:0%
+that satoshi nakamoto uploaded that
+ 
+
+ align:start position:0%
+that satoshi nakamoto uploaded that
+eight-page paper on 12 years ago
+
+ align:start position:0%
+eight-page paper on 12 years ago
+ 
+
+ align:start position:0%
+eight-page paper on 12 years ago
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+though you can track bitcoin
+
+ align:start position:0%
+though you can track bitcoin
+ 
+
+ align:start position:0%
+though you can track bitcoin
+transactions
+
+ align:start position:0%
+transactions
+ 
+
+ align:start position:0%
+transactions
+a lot of use of bitcoin and other
+
+ align:start position:0%
+a lot of use of bitcoin and other
+ 
+
+ align:start position:0%
+a lot of use of bitcoin and other
+cryptocurrencies has been to avoid the
+
+ align:start position:0%
+cryptocurrencies has been to avoid the
+ 
+
+ align:start position:0%
+cryptocurrencies has been to avoid the
+censorship and the watchful eyes of the
+
+ align:start position:0%
+censorship and the watchful eyes of the
+ 
+
+ align:start position:0%
+censorship and the watchful eyes of the
+official sector
+
+ align:start position:0%
+official sector
+ 
+
+ align:start position:0%
+official sector
+and so i i would imagine i'm not i've
+
+ align:start position:0%
+and so i i would imagine i'm not i've
+ 
+
+ align:start position:0%
+and so i i would imagine i'm not i've
+not talked to robin hood that they would
+
+ align:start position:0%
+not talked to robin hood that they would
+ 
+
+ align:start position:0%
+not talked to robin hood that they would
+be aware of that and they would just
+
+ align:start position:0%
+be aware of that and they would just
+ 
+
+ align:start position:0%
+be aware of that and they would just
+feel
+
+ align:start position:0%
+feel
+ 
+
+ align:start position:0%
+feel
+as a as both a legal matter and as for
+
+ align:start position:0%
+as a as both a legal matter and as for
+ 
+
+ align:start position:0%
+as a as both a legal matter and as for
+reputational reasons better not to go
+
+ align:start position:0%
+reputational reasons better not to go
+ 
+
+ align:start position:0%
+reputational reasons better not to go
+there and unless there's a more robust
+
+ align:start position:0%
+there and unless there's a more robust
+ 
+
+ align:start position:0%
+there and unless there's a more robust
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+support for that system
+
+ align:start position:0%
+support for that system
+ 
+
+ align:start position:0%
+support for that system
+and nadia had her hand up for a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nadia
+
+ align:start position:0%
+nadia
+ 
+
+ align:start position:0%
+nadia
+uh yeah actually i have two questions on
+
+ align:start position:0%
+uh yeah actually i have two questions on
+ 
+
+ align:start position:0%
+uh yeah actually i have two questions on
+wealth management fintech so the first
+
+ align:start position:0%
+wealth management fintech so the first
+ 
+
+ align:start position:0%
+wealth management fintech so the first
+question what do you think more
+
+ align:start position:0%
+question what do you think more
+ 
+
+ align:start position:0%
+question what do you think more
+important for wealth management fintech
+
+ align:start position:0%
+important for wealth management fintech
+ 
+
+ align:start position:0%
+important for wealth management fintech
+to grow is it the inclusion part meaning
+
+ align:start position:0%
+to grow is it the inclusion part meaning
+ 
+
+ align:start position:0%
+to grow is it the inclusion part meaning
+like low minimum deposit or the user
+
+ align:start position:0%
+like low minimum deposit or the user
+ 
+
+ align:start position:0%
+like low minimum deposit or the user
+experience part that is for the first
+
+ align:start position:0%
+experience part that is for the first
+ 
+
+ align:start position:0%
+experience part that is for the first
+questions and for the second question
+
+ align:start position:0%
+questions and for the second question
+ 
+
+ align:start position:0%
+questions and for the second question
+given the growth of cash management
+
+ align:start position:0%
+given the growth of cash management
+ 
+
+ align:start position:0%
+given the growth of cash management
+feature like wealthfront do you think
+
+ align:start position:0%
+feature like wealthfront do you think
+ 
+
+ align:start position:0%
+feature like wealthfront do you think
+now customers prefer a simpler product
+
+ align:start position:0%
+now customers prefer a simpler product
+ 
+
+ align:start position:0%
+now customers prefer a simpler product
+rather than more complicated product
+
+ align:start position:0%
+rather than more complicated product
+ 
+
+ align:start position:0%
+rather than more complicated product
+so there's a lot there nadia i'm not
+
+ align:start position:0%
+so there's a lot there nadia i'm not
+ 
+
+ align:start position:0%
+so there's a lot there nadia i'm not
+sure but
+
+ align:start position:0%
+sure but
+ 
+
+ align:start position:0%
+sure but
+but i think that the betterments and the
+
+ align:start position:0%
+but i think that the betterments and the
+ 
+
+ align:start position:0%
+but i think that the betterments and the
+and the robo advisors
+
+ align:start position:0%
+and the robo advisors
+ 
+
+ align:start position:0%
+and the robo advisors
+i can't separate the two when you're
+
+ align:start position:0%
+i can't separate the two when you're
+ 
+
+ align:start position:0%
+i can't separate the two when you're
+saying is it more about user interface
+
+ align:start position:0%
+saying is it more about user interface
+ 
+
+ align:start position:0%
+saying is it more about user interface
+is it more about pricing
+
+ align:start position:0%
+is it more about pricing
+ 
+
+ align:start position:0%
+is it more about pricing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+maybe somebody better than i could but i
+
+ align:start position:0%
+maybe somebody better than i could but i
+ 
+
+ align:start position:0%
+maybe somebody better than i could but i
+think it's about both i really do think
+
+ align:start position:0%
+think it's about both i really do think
+ 
+
+ align:start position:0%
+think it's about both i really do think
+that i think that they have provided
+
+ align:start position:0%
+that i think that they have provided
+ 
+
+ align:start position:0%
+that i think that they have provided
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a lower price point which
+
+ align:start position:0%
+a lower price point which
+ 
+
+ align:start position:0%
+a lower price point which
+is really important but if it were only
+
+ align:start position:0%
+is really important but if it were only
+ 
+
+ align:start position:0%
+is really important but if it were only
+that if somebody had just put out an
+
+ align:start position:0%
+that if somebody had just put out an
+ 
+
+ align:start position:0%
+that if somebody had just put out an
+advertisement i'm going to give you
+
+ align:start position:0%
+advertisement i'm going to give you
+ 
+
+ align:start position:0%
+advertisement i'm going to give you
+wealth advice for a quarter of a point i
+
+ align:start position:0%
+wealth advice for a quarter of a point i
+ 
+
+ align:start position:0%
+wealth advice for a quarter of a point i
+don't think you could have gotten
+
+ align:start position:0%
+don't think you could have gotten
+ 
+
+ align:start position:0%
+don't think you could have gotten
+adoption i think you had to have that
+
+ align:start position:0%
+adoption i think you had to have that
+ 
+
+ align:start position:0%
+adoption i think you had to have that
+user interface and i i think the two of
+
+ align:start position:0%
+user interface and i i think the two of
+ 
+
+ align:start position:0%
+user interface and i i think the two of
+them together
+
+ align:start position:0%
+them together
+ 
+
+ align:start position:0%
+them together
+uh are really important so it's not just
+
+ align:start position:0%
+uh are really important so it's not just
+ 
+
+ align:start position:0%
+uh are really important so it's not just
+doing something cheaper
+
+ align:start position:0%
+doing something cheaper
+ 
+
+ align:start position:0%
+doing something cheaper
+because a lot of people could say listen
+
+ align:start position:0%
+because a lot of people could say listen
+ 
+
+ align:start position:0%
+because a lot of people could say listen
+i'll give you wealth advice for a
+
+ align:start position:0%
+i'll give you wealth advice for a
+ 
+
+ align:start position:0%
+i'll give you wealth advice for a
+quarter of a point i think the user
+
+ align:start position:0%
+quarter of a point i think the user
+ 
+
+ align:start position:0%
+quarter of a point i think the user
+experience uh
+
+ align:start position:0%
+experience uh
+ 
+
+ align:start position:0%
+experience uh
+you know these are very private matters
+
+ align:start position:0%
+you know these are very private matters
+ 
+
+ align:start position:0%
+you know these are very private matters
+sometimes it's just frankly a little
+
+ align:start position:0%
+sometimes it's just frankly a little
+ 
+
+ align:start position:0%
+sometimes it's just frankly a little
+easier it's interesting to just kind of
+
+ align:start position:0%
+easier it's interesting to just kind of
+ 
+
+ align:start position:0%
+easier it's interesting to just kind of
+go to a drop down menu answer some
+
+ align:start position:0%
+go to a drop down menu answer some
+ 
+
+ align:start position:0%
+go to a drop down menu answer some
+questions feel that i'm getting the
+
+ align:start position:0%
+questions feel that i'm getting the
+ 
+
+ align:start position:0%
+questions feel that i'm getting the
+advice feel that i'm yes getting low
+
+ align:start position:0%
+advice feel that i'm yes getting low
+ 
+
+ align:start position:0%
+advice feel that i'm yes getting low
+cost etfs and low cost advisory fees but
+
+ align:start position:0%
+cost etfs and low cost advisory fees but
+ 
+
+ align:start position:0%
+cost etfs and low cost advisory fees but
+i think the user experience goes hand in
+
+ align:start position:0%
+i think the user experience goes hand in
+ 
+
+ align:start position:0%
+i think the user experience goes hand in
+hand and i can't easily separate them
+
+ align:start position:0%
+hand and i can't easily separate them
+ 
+
+ align:start position:0%
+hand and i can't easily separate them
+let me just try to wrap up and and then
+
+ align:start position:0%
+let me just try to wrap up and and then
+ 
+
+ align:start position:0%
+let me just try to wrap up and and then
+and then nadia remind me the second half
+
+ align:start position:0%
+and then nadia remind me the second half
+ 
+
+ align:start position:0%
+and then nadia remind me the second half
+of your question
+
+ align:start position:0%
+of your question
+ 
+
+ align:start position:0%
+of your question
+as as i wrap up because i want to make a
+
+ align:start position:0%
+as as i wrap up because i want to make a
+ 
+
+ align:start position:0%
+as as i wrap up because i want to make a
+we only have about three minutes so i
+
+ align:start position:0%
+we only have about three minutes so i
+ 
+
+ align:start position:0%
+we only have about three minutes so i
+want to just make a point
+
+ align:start position:0%
+want to just make a point
+ 
+
+ align:start position:0%
+want to just make a point
+beyond these crypto exchanges um there's
+
+ align:start position:0%
+beyond these crypto exchanges um there's
+ 
+
+ align:start position:0%
+beyond these crypto exchanges um there's
+a bunch of crypto lending and borrowing
+
+ align:start position:0%
+a bunch of crypto lending and borrowing
+ 
+
+ align:start position:0%
+a bunch of crypto lending and borrowing
+and why i raise this is this market just
+
+ align:start position:0%
+and why i raise this is this market just
+ 
+
+ align:start position:0%
+and why i raise this is this market just
+like the capital markets is starting to
+
+ align:start position:0%
+like the capital markets is starting to
+ 
+
+ align:start position:0%
+like the capital markets is starting to
+say can i lend to crypto can i borrow
+
+ align:start position:0%
+say can i lend to crypto can i borrow
+ 
+
+ align:start position:0%
+say can i lend to crypto can i borrow
+crypto
+
+ align:start position:0%
+crypto
+ 
+
+ align:start position:0%
+crypto
+and why would you do that
+
+ align:start position:0%
+and why would you do that
+ 
+
+ align:start position:0%
+and why would you do that
+same reason in the capital markets you
+
+ align:start position:0%
+same reason in the capital markets you
+ 
+
+ align:start position:0%
+same reason in the capital markets you
+lend and borrow stocks sometimes because
+
+ align:start position:0%
+lend and borrow stocks sometimes because
+ 
+
+ align:start position:0%
+lend and borrow stocks sometimes because
+you want to buy the stocks on margin or
+
+ align:start position:0%
+you want to buy the stocks on margin or
+ 
+
+ align:start position:0%
+you want to buy the stocks on margin or
+sometimes you lend it because you need
+
+ align:start position:0%
+sometimes you lend it because you need
+ 
+
+ align:start position:0%
+sometimes you lend it because you need
+to borrow against your assets to do
+
+ align:start position:0%
+to borrow against your assets to do
+ 
+
+ align:start position:0%
+to borrow against your assets to do
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+so these markets are developing that way
+
+ align:start position:0%
+so these markets are developing that way
+ 
+
+ align:start position:0%
+so these markets are developing that way
+but the thing that i wanted to mention
+
+ align:start position:0%
+but the thing that i wanted to mention
+ 
+
+ align:start position:0%
+but the thing that i wanted to mention
+was this question of decentralized
+
+ align:start position:0%
+was this question of decentralized
+ 
+
+ align:start position:0%
+was this question of decentralized
+finance versus centralized finance
+
+ align:start position:0%
+finance versus centralized finance
+ 
+
+ align:start position:0%
+finance versus centralized finance
+centralized traditional finance
+
+ align:start position:0%
+centralized traditional finance
+ 
+
+ align:start position:0%
+centralized traditional finance
+this is a slide that i i sort of created
+
+ align:start position:0%
+this is a slide that i i sort of created
+ 
+
+ align:start position:0%
+this is a slide that i i sort of created
+in the last eight months
+
+ align:start position:0%
+in the last eight months
+ 
+
+ align:start position:0%
+in the last eight months
+has proprietary software central
+
+ align:start position:0%
+has proprietary software central
+ 
+
+ align:start position:0%
+has proprietary software central
+clearing all the attributes that i list
+
+ align:start position:0%
+clearing all the attributes that i list
+ 
+
+ align:start position:0%
+clearing all the attributes that i list
+here the question is
+
+ align:start position:0%
+here the question is
+ 
+
+ align:start position:0%
+here the question is
+is there a market just like we talked
+
+ align:start position:0%
+is there a market just like we talked
+ 
+
+ align:start position:0%
+is there a market just like we talked
+about in lending for peer-to-peer
+
+ align:start position:0%
+about in lending for peer-to-peer
+ 
+
+ align:start position:0%
+about in lending for peer-to-peer
+decentralized finance
+
+ align:start position:0%
+decentralized finance
+ 
+
+ align:start position:0%
+decentralized finance
+and what we found in lending club and
+
+ align:start position:0%
+and what we found in lending club and
+ 
+
+ align:start position:0%
+and what we found in lending club and
+other companies
+
+ align:start position:0%
+other companies
+ 
+
+ align:start position:0%
+other companies
+they really haven't stayed decentralized
+
+ align:start position:0%
+they really haven't stayed decentralized
+ 
+
+ align:start position:0%
+they really haven't stayed decentralized
+they started with this concept that will
+
+ align:start position:0%
+they started with this concept that will
+ 
+
+ align:start position:0%
+they started with this concept that will
+be peers lending to peers and then what
+
+ align:start position:0%
+be peers lending to peers and then what
+ 
+
+ align:start position:0%
+be peers lending to peers and then what
+we've found is they've become more
+
+ align:start position:0%
+we've found is they've become more
+ 
+
+ align:start position:0%
+we've found is they've become more
+marketplace platforms and platform
+
+ align:start position:0%
+marketplace platforms and platform
+ 
+
+ align:start position:0%
+marketplace platforms and platform
+economics have taken over but there's
+
+ align:start position:0%
+economics have taken over but there's
+ 
+
+ align:start position:0%
+economics have taken over but there's
+been this question
+
+ align:start position:0%
+been this question
+ 
+
+ align:start position:0%
+been this question
+can there be an open source software
+
+ align:start position:0%
+can there be an open source software
+ 
+
+ align:start position:0%
+can there be an open source software
+built on blockchain technology that's
+
+ align:start position:0%
+built on blockchain technology that's
+ 
+
+ align:start position:0%
+built on blockchain technology that's
+truly peer-to-peer and you will hear
+
+ align:start position:0%
+truly peer-to-peer and you will hear
+ 
+
+ align:start position:0%
+truly peer-to-peer and you will hear
+this time and again it's a business
+
+ align:start position:0%
+this time and again it's a business
+ 
+
+ align:start position:0%
+this time and again it's a business
+concept that i i just want to prepare
+
+ align:start position:0%
+concept that i i just want to prepare
+ 
+
+ align:start position:0%
+concept that i i just want to prepare
+you for
+
+ align:start position:0%
+you for
+ 
+
+ align:start position:0%
+you for
+decentralized finance versus traditional
+
+ align:start position:0%
+decentralized finance versus traditional
+ 
+
+ align:start position:0%
+decentralized finance versus traditional
+finance
+
+ align:start position:0%
+finance
+ 
+
+ align:start position:0%
+finance
+usually used in the context of
+
+ align:start position:0%
+usually used in the context of
+ 
+
+ align:start position:0%
+usually used in the context of
+blockchain technology and the advocates
+
+ align:start position:0%
+blockchain technology and the advocates
+ 
+
+ align:start position:0%
+blockchain technology and the advocates
+say blockchain technology facilitates
+
+ align:start position:0%
+say blockchain technology facilitates
+ 
+
+ align:start position:0%
+say blockchain technology facilitates
+we can get rid of the big banks
+
+ align:start position:0%
+we can get rid of the big banks
+ 
+
+ align:start position:0%
+we can get rid of the big banks
+that is what they might say that's what
+
+ align:start position:0%
+that is what they might say that's what
+ 
+
+ align:start position:0%
+that is what they might say that's what
+satoshi nakamoto wrote in some of the
+
+ align:start position:0%
+satoshi nakamoto wrote in some of the
+ 
+
+ align:start position:0%
+satoshi nakamoto wrote in some of the
+early emails and and so forth that we
+
+ align:start position:0%
+early emails and and so forth that we
+ 
+
+ align:start position:0%
+early emails and and so forth that we
+can disintermediate both banks and
+
+ align:start position:0%
+can disintermediate both banks and
+ 
+
+ align:start position:0%
+can disintermediate both banks and
+central banks around cryptocurrency
+
+ align:start position:0%
+central banks around cryptocurrency
+ 
+
+ align:start position:0%
+central banks around cryptocurrency
+and the like
+
+ align:start position:0%
+and the like
+ 
+
+ align:start position:0%
+and the like
+that's the that's the dream but the
+
+ align:start position:0%
+that's the that's the dream but the
+ 
+
+ align:start position:0%
+that's the that's the dream but the
+question is whether network economics
+
+ align:start position:0%
+question is whether network economics
+ 
+
+ align:start position:0%
+question is whether network economics
+whether there's a reason in capital
+
+ align:start position:0%
+whether there's a reason in capital
+ 
+
+ align:start position:0%
+whether there's a reason in capital
+markets and finance that you have sort
+
+ align:start position:0%
+markets and finance that you have sort
+ 
+
+ align:start position:0%
+markets and finance that you have sort
+of a hub and spoke approach rather than
+
+ align:start position:0%
+of a hub and spoke approach rather than
+ 
+
+ align:start position:0%
+of a hub and spoke approach rather than
+a decentralized approach when i say hub
+
+ align:start position:0%
+a decentralized approach when i say hub
+ 
+
+ align:start position:0%
+a decentralized approach when i say hub
+and spoke the new york stock exchange or
+
+ align:start position:0%
+and spoke the new york stock exchange or
+ 
+
+ align:start position:0%
+and spoke the new york stock exchange or
+london stock exchange isn't sort of in
+
+ align:start position:0%
+london stock exchange isn't sort of in
+ 
+
+ align:start position:0%
+london stock exchange isn't sort of in
+the middle of the market
+
+ align:start position:0%
+the middle of the market
+ 
+
+ align:start position:0%
+the middle of the market
+the the banks back to luke earlier
+
+ align:start position:0%
+the the banks back to luke earlier
+ 
+
+ align:start position:0%
+the the banks back to luke earlier
+question are sitting there collecting a
+
+ align:start position:0%
+question are sitting there collecting a
+ 
+
+ align:start position:0%
+question are sitting there collecting a
+net interest margin and why london club
+
+ align:start position:0%
+net interest margin and why london club
+ 
+
+ align:start position:0%
+net interest margin and why london club
+is moved into a marketplace platform
+
+ align:start position:0%
+is moved into a marketplace platform
+ 
+
+ align:start position:0%
+is moved into a marketplace platform
+rather than that peer-to-peer
+
+ align:start position:0%
+rather than that peer-to-peer
+ 
+
+ align:start position:0%
+rather than that peer-to-peer
+and so this debate and this business
+
+ align:start position:0%
+and so this debate and this business
+ 
+
+ align:start position:0%
+and so this debate and this business
+concept is a relatively important one
+
+ align:start position:0%
+concept is a relatively important one
+ 
+
+ align:start position:0%
+concept is a relatively important one
+and it and it basically goes well beyond
+
+ align:start position:0%
+and it and it basically goes well beyond
+ 
+
+ align:start position:0%
+and it and it basically goes well beyond
+cryptocurrencies and i wanted to mention
+
+ align:start position:0%
+cryptocurrencies and i wanted to mention
+ 
+
+ align:start position:0%
+cryptocurrencies and i wanted to mention
+it but in cryptocurrencies and this is
+
+ align:start position:0%
+it but in cryptocurrencies and this is
+ 
+
+ align:start position:0%
+it but in cryptocurrencies and this is
+my last little bit
+
+ align:start position:0%
+my last little bit
+ 
+
+ align:start position:0%
+my last little bit
+is that there are d5 platforms
+
+ align:start position:0%
+is that there are d5 platforms
+ 
+
+ align:start position:0%
+is that there are d5 platforms
+decentralized finance where you can peer
+
+ align:start position:0%
+decentralized finance where you can peer
+ 
+
+ align:start position:0%
+decentralized finance where you can peer
+to peer
+
+ align:start position:0%
+to peer
+ 
+
+ align:start position:0%
+to peer
+use a crypto exchange binance idex unit
+
+ align:start position:0%
+use a crypto exchange binance idex unit
+ 
+
+ align:start position:0%
+use a crypto exchange binance idex unit
+swap others basically say we're not
+
+ align:start position:0%
+swap others basically say we're not
+ 
+
+ align:start position:0%
+swap others basically say we're not
+going to have a central exchange or more
+
+ align:start position:0%
+going to have a central exchange or more
+ 
+
+ align:start position:0%
+going to have a central exchange or more
+technically a central limit order book
+
+ align:start position:0%
+technically a central limit order book
+ 
+
+ align:start position:0%
+technically a central limit order book
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+noddy and i could trade and later nadia
+
+ align:start position:0%
+noddy and i could trade and later nadia
+ 
+
+ align:start position:0%
+noddy and i could trade and later nadia
+could trade with luke and camillo could
+
+ align:start position:0%
+could trade with luke and camillo could
+ 
+
+ align:start position:0%
+could trade with luke and camillo could
+trade with somebody else but it's not
+
+ align:start position:0%
+trade with somebody else but it's not
+ 
+
+ align:start position:0%
+trade with somebody else but it's not
+all centralized
+
+ align:start position:0%
+all centralized
+ 
+
+ align:start position:0%
+all centralized
+and similarly there's platforms maker
+
+ align:start position:0%
+and similarly there's platforms maker
+ 
+
+ align:start position:0%
+and similarly there's platforms maker
+dow and compound and synthenex are the
+
+ align:start position:0%
+dow and compound and synthenex are the
+ 
+
+ align:start position:0%
+dow and compound and synthenex are the
+three big ones that are trying to do
+
+ align:start position:0%
+three big ones that are trying to do
+ 
+
+ align:start position:0%
+three big ones that are trying to do
+that on crypto lending and borrowing
+
+ align:start position:0%
+that on crypto lending and borrowing
+ 
+
+ align:start position:0%
+that on crypto lending and borrowing
+there's even prediction marking markets
+
+ align:start position:0%
+there's even prediction marking markets
+ 
+
+ align:start position:0%
+there's even prediction marking markets
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that are trying to say nadia can trade
+
+ align:start position:0%
+that are trying to say nadia can trade
+ 
+
+ align:start position:0%
+that are trying to say nadia can trade
+with luke and make a bet
+
+ align:start position:0%
+with luke and make a bet
+ 
+
+ align:start position:0%
+with luke and make a bet
+now the regulatory environment for these
+
+ align:start position:0%
+now the regulatory environment for these
+ 
+
+ align:start position:0%
+now the regulatory environment for these
+prediction markets is highly uh
+
+ align:start position:0%
+prediction markets is highly uh
+ 
+
+ align:start position:0%
+prediction markets is highly uh
+challenged and and and they might be
+
+ align:start position:0%
+challenged and and and they might be
+ 
+
+ align:start position:0%
+challenged and and and they might be
+doing things that are not uh strictly
+
+ align:start position:0%
+doing things that are not uh strictly
+ 
+
+ align:start position:0%
+doing things that are not uh strictly
+within the law but these decentralized
+
+ align:start position:0%
+within the law but these decentralized
+ 
+
+ align:start position:0%
+within the law but these decentralized
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+are very small
+
+ align:start position:0%
+are very small
+ 
+
+ align:start position:0%
+are very small
+none of these projects are really big
+
+ align:start position:0%
+none of these projects are really big
+ 
+
+ align:start position:0%
+none of these projects are really big
+but some of these projects have a few
+
+ align:start position:0%
+but some of these projects have a few
+ 
+
+ align:start position:0%
+but some of these projects have a few
+billion dollars in their crypto lending
+
+ align:start position:0%
+billion dollars in their crypto lending
+ 
+
+ align:start position:0%
+billion dollars in their crypto lending
+and borrowing some of these exchanges
+
+ align:start position:0%
+and borrowing some of these exchanges
+ 
+
+ align:start position:0%
+and borrowing some of these exchanges
+have a few hundred thousand dollars a
+
+ align:start position:0%
+have a few hundred thousand dollars a
+ 
+
+ align:start position:0%
+have a few hundred thousand dollars a
+day of trading they're not big
+
+ align:start position:0%
+day of trading they're not big
+ 
+
+ align:start position:0%
+day of trading they're not big
+but back it raises this central question
+
+ align:start position:0%
+but back it raises this central question
+ 
+
+ align:start position:0%
+but back it raises this central question
+of traditional finance versus
+
+ align:start position:0%
+of traditional finance versus
+ 
+
+ align:start position:0%
+of traditional finance versus
+decentralized finance and i just wanted
+
+ align:start position:0%
+decentralized finance and i just wanted
+ 
+
+ align:start position:0%
+decentralized finance and i just wanted
+to capture that before we uh signed off
+
+ align:start position:0%
+to capture that before we uh signed off
+ 
+
+ align:start position:0%
+to capture that before we uh signed off
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/uc4xJsi99bk.txt b/uc4xJsi99bk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb856a0882487d81d7773777643d549bb0699fd1
--- /dev/null
+++ b/uc4xJsi99bk.txt
@@ -0,0 +1,2587 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I want to explain to you where the
+
+ align:start position:0%
+I want to explain to you where the
+ 
+
+ align:start position:0%
+I want to explain to you where the
+coefficients we saw in Simpsons rule
+
+ align:start position:0%
+coefficients we saw in Simpsons rule
+ 
+
+ align:start position:0%
+coefficients we saw in Simpsons rule
+actually come from so what I'm going to
+
+ align:start position:0%
+actually come from so what I'm going to
+ 
+
+ align:start position:0%
+actually come from so what I'm going to
+do is take this curve that I have and
+
+ align:start position:0%
+do is take this curve that I have and
+ 
+
+ align:start position:0%
+do is take this curve that I have and
+show you what the picture of Simpson's
+
+ align:start position:0%
+show you what the picture of Simpson's
+ 
+
+ align:start position:0%
+show you what the picture of Simpson's
+rule does and then I'm actually going to
+
+ align:start position:0%
+rule does and then I'm actually going to
+ 
+
+ align:start position:0%
+rule does and then I'm actually going to
+determine explicitly where the
+
+ align:start position:0%
+determine explicitly where the
+ 
+
+ align:start position:0%
+determine explicitly where the
+coefficients come from so let's look at
+
+ align:start position:0%
+coefficients come from so let's look at
+ 
+
+ align:start position:0%
+coefficients come from so let's look at
+this picture first
+
+ align:start position:0%
+this picture first
+ 
+
+ align:start position:0%
+this picture first
+the picture I have here this white is
+
+ align:start position:0%
+the picture I have here this white is
+ 
+
+ align:start position:0%
+the picture I have here this white is
+going to the white curve is going to be
+
+ align:start position:0%
+going to the white curve is going to be
+ 
+
+ align:start position:0%
+going to the white curve is going to be
+my yal f ofx function and so if you
+
+ align:start position:0%
+my yal f ofx function and so if you
+ 
+
+ align:start position:0%
+my yal f ofx function and so if you
+remember what Simpson's rule is saying
+
+ align:start position:0%
+remember what Simpson's rule is saying
+ 
+
+ align:start position:0%
+remember what Simpson's rule is saying
+you have to have you have to have two uh
+
+ align:start position:0%
+you have to have you have to have two uh
+ 
+
+ align:start position:0%
+you have to have you have to have two uh
+two Delta X's so in this case h is equal
+
+ align:start position:0%
+two Delta X's so in this case h is equal
+ 
+
+ align:start position:0%
+two Delta X's so in this case h is equal
+to Delta X so what Simpson's rule is
+
+ align:start position:0%
+to Delta X so what Simpson's rule is
+ 
+
+ align:start position:0%
+to Delta X so what Simpson's rule is
+saying is I can find approximate the
+
+ align:start position:0%
+saying is I can find approximate the
+ 
+
+ align:start position:0%
+saying is I can find approximate the
+area under this curve from minus H to H
+
+ align:start position:0%
+area under this curve from minus H to H
+ 
+
+ align:start position:0%
+area under this curve from minus H to H
+by a certain expression and the
+
+ align:start position:0%
+by a certain expression and the
+ 
+
+ align:start position:0%
+by a certain expression and the
+expression is oh I said Delta X is equal
+
+ align:start position:0%
+expression is oh I said Delta X is equal
+ 
+
+ align:start position:0%
+expression is oh I said Delta X is equal
+to H so let me write H over 3 * y0 + 4
+
+ align:start position:0%
+to H so let me write H over 3 * y0 + 4
+ 
+
+ align:start position:0%
+to H so let me write H over 3 * y0 + 4
+y1 plus
+
+ align:start position:0%
+y1 plus
+ 
+
+ align:start position:0%
+y1 plus
+Y2 oh y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so that's what you got that's what you
+
+ align:start position:0%
+2 so that's what you got that's what you
+ 
+
+ align:start position:0%
+2 so that's what you got that's what you
+saw in the lecture that this is where
+
+ align:start position:0%
+saw in the lecture that this is where
+ 
+
+ align:start position:0%
+saw in the lecture that this is where
+what the coefficients are so I want to
+
+ align:start position:0%
+what the coefficients are so I want to
+ 
+
+ align:start position:0%
+what the coefficients are so I want to
+explain why this is a one why that's a
+
+ align:start position:0%
+explain why this is a one why that's a
+ 
+
+ align:start position:0%
+explain why this is a one why that's a
+four why that's a one and where that
+
+ align:start position:0%
+four why that's a one and where that
+ 
+
+ align:start position:0%
+four why that's a one and where that
+three comes from the picture is not
+
+ align:start position:0%
+three comes from the picture is not
+ 
+
+ align:start position:0%
+three comes from the picture is not
+going to explain it but the picture will
+
+ align:start position:0%
+going to explain it but the picture will
+ 
+
+ align:start position:0%
+going to explain it but the picture will
+help us understand how to go so what
+
+ align:start position:0%
+help us understand how to go so what
+ 
+
+ align:start position:0%
+help us understand how to go so what
+Simpsons rule does is it takes those
+
+ align:start position:0%
+Simpsons rule does is it takes those
+ 
+
+ align:start position:0%
+Simpsons rule does is it takes those
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+points so the xot Y knot the X1 y1 and
+
+ align:start position:0%
+points so the xot Y knot the X1 y1 and
+ 
+
+ align:start position:0%
+points so the xot Y knot the X1 y1 and
+the X2 Y2 that are on the function or on
+
+ align:start position:0%
+the X2 Y2 that are on the function or on
+ 
+
+ align:start position:0%
+the X2 Y2 that are on the function or on
+the curve y equals F ofx and it finds a
+
+ align:start position:0%
+the curve y equals F ofx and it finds a
+ 
+
+ align:start position:0%
+the curve y equals F ofx and it finds a
+parabola through those three points so
+
+ align:start position:0%
+parabola through those three points so
+ 
+
+ align:start position:0%
+parabola through those three points so
+I'm going to do my best to draw what
+
+ align:start position:0%
+I'm going to do my best to draw what
+ 
+
+ align:start position:0%
+I'm going to do my best to draw what
+looks like a parabola through those
+
+ align:start position:0%
+looks like a parabola through those
+ 
+
+ align:start position:0%
+looks like a parabola through those
+three points something I'll draw it
+
+ align:start position:0%
+three points something I'll draw it
+ 
+
+ align:start position:0%
+three points something I'll draw it
+lightly first and then I'll fill it in
+
+ align:start position:0%
+lightly first and then I'll fill it in
+ 
+
+ align:start position:0%
+lightly first and then I'll fill it in
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+along these lines
+
+ align:start position:0%
+along these lines
+ 
+
+ align:start position:0%
+along these lines
+something like that that's a sort of
+
+ align:start position:0%
+something like that that's a sort of
+ 
+
+ align:start position:0%
+something like that that's a sort of
+looks like a parabola and so the idea is
+
+ align:start position:0%
+looks like a parabola and so the idea is
+ 
+
+ align:start position:0%
+looks like a parabola and so the idea is
+Simpsons rule is saying I can find the
+
+ align:start position:0%
+Simpsons rule is saying I can find the
+ 
+
+ align:start position:0%
+Simpsons rule is saying I can find the
+area under the blue
+
+ align:start position:0%
+area under the blue
+ 
+
+ align:start position:0%
+area under the blue
+curve so I can find the area under the
+
+ align:start position:0%
+curve so I can find the area under the
+ 
+
+ align:start position:0%
+curve so I can find the area under the
+blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve so this is a function we'll call
+
+ align:start position:0%
+curve so this is a function we'll call
+ 
+
+ align:start position:0%
+curve so this is a function we'll call
+this yal P of
+
+ align:start position:0%
+this yal P of
+ 
+
+ align:start position:0%
+this yal P of
+X and that's what you were actually told
+
+ align:start position:0%
+X and that's what you were actually told
+ 
+
+ align:start position:0%
+X and that's what you were actually told
+about in in lecture that you're
+
+ align:start position:0%
+about in in lecture that you're
+ 
+
+ align:start position:0%
+about in in lecture that you're
+approximating your function yal f ofx by
+
+ align:start position:0%
+approximating your function yal f ofx by
+ 
+
+ align:start position:0%
+approximating your function yal f ofx by
+a quadratic function that goes through
+
+ align:start position:0%
+a quadratic function that goes through
+ 
+
+ align:start position:0%
+a quadratic function that goes through
+the values X Y not X1 y1 and X2 Y2 and
+
+ align:start position:0%
+the values X Y not X1 y1 and X2 Y2 and
+ 
+
+ align:start position:0%
+the values X Y not X1 y1 and X2 Y2 and
+then you find the area under that uh
+
+ align:start position:0%
+then you find the area under that uh
+ 
+
+ align:start position:0%
+then you find the area under that uh
+Parabola between minus H and H now this
+
+ align:start position:0%
+Parabola between minus H and H now this
+ 
+
+ align:start position:0%
+Parabola between minus H and H now this
+picture you might say Christine this
+
+ align:start position:0%
+picture you might say Christine this
+ 
+
+ align:start position:0%
+picture you might say Christine this
+looks really like a bad estimate this
+
+ align:start position:0%
+looks really like a bad estimate this
+ 
+
+ align:start position:0%
+looks really like a bad estimate this
+looks kind of stupid maybe you should
+
+ align:start position:0%
+looks kind of stupid maybe you should
+ 
+
+ align:start position:0%
+looks kind of stupid maybe you should
+have picked a different function to
+
+ align:start position:0%
+have picked a different function to
+ 
+
+ align:start position:0%
+have picked a different function to
+estimate this and I did this one because
+
+ align:start position:0%
+estimate this and I did this one because
+ 
+
+ align:start position:0%
+estimate this and I did this one because
+I wanted to be sort of zoomed out far
+
+ align:start position:0%
+I wanted to be sort of zoomed out far
+ 
+
+ align:start position:0%
+I wanted to be sort of zoomed out far
+and to show you to give you a little
+
+ align:start position:0%
+and to show you to give you a little
+ 
+
+ align:start position:0%
+and to show you to give you a little
+intuition about what happens when we
+
+ align:start position:0%
+intuition about what happens when we
+ 
+
+ align:start position:0%
+intuition about what happens when we
+make H smaller notice that if I cut the
+
+ align:start position:0%
+make H smaller notice that if I cut the
+ 
+
+ align:start position:0%
+make H smaller notice that if I cut the
+size of H in half so if I started with
+
+ align:start position:0%
+size of H in half so if I started with
+ 
+
+ align:start position:0%
+size of H in half so if I started with
+here was minus H to H what would my
+
+ align:start position:0%
+here was minus H to H what would my
+ 
+
+ align:start position:0%
+here was minus H to H what would my
+three points be my three points would be
+
+ align:start position:0%
+three points be my three points would be
+ 
+
+ align:start position:0%
+three points be my three points would be
+this point y1 and Y2 would be right here
+
+ align:start position:0%
+this point y1 and Y2 would be right here
+ 
+
+ align:start position:0%
+this point y1 and Y2 would be right here
+well the quadratic through those points
+
+ align:start position:0%
+well the quadratic through those points
+ 
+
+ align:start position:0%
+well the quadratic through those points
+is much closer to the actual function
+
+ align:start position:0%
+is much closer to the actual function
+ 
+
+ align:start position:0%
+is much closer to the actual function
+and if I cut that in half again I'd have
+
+ align:start position:0%
+and if I cut that in half again I'd have
+ 
+
+ align:start position:0%
+and if I cut that in half again I'd have
+points here here and here something like
+
+ align:start position:0%
+points here here and here something like
+ 
+
+ align:start position:0%
+points here here and here something like
+that and those that starts to look
+
+ align:start position:0%
+that and those that starts to look
+ 
+
+ align:start position:0%
+that and those that starts to look
+almost exactly like a quadratic so if I
+
+ align:start position:0%
+almost exactly like a quadratic so if I
+ 
+
+ align:start position:0%
+almost exactly like a quadratic so if I
+found the area under under this or if I
+
+ align:start position:0%
+found the area under under this or if I
+ 
+
+ align:start position:0%
+found the area under under this or if I
+wanted to estimate the area under this
+
+ align:start position:0%
+wanted to estimate the area under this
+ 
+
+ align:start position:0%
+wanted to estimate the area under this
+piece of the curve using a quadratic
+
+ align:start position:0%
+piece of the curve using a quadratic
+ 
+
+ align:start position:0%
+piece of the curve using a quadratic
+through those three points they would be
+
+ align:start position:0%
+through those three points they would be
+ 
+
+ align:start position:0%
+through those three points they would be
+very close so don't be alarmed by
+
+ align:start position:0%
+very close so don't be alarmed by
+ 
+
+ align:start position:0%
+very close so don't be alarmed by
+Simpsons rule as an approximation based
+
+ align:start position:0%
+Simpsons rule as an approximation based
+ 
+
+ align:start position:0%
+Simpsons rule as an approximation based
+on this large
+
+ align:start position:0%
+on this large
+ 
+
+ align:start position:0%
+on this large
+picture so now what do we have to do
+
+ align:start position:0%
+picture so now what do we have to do
+ 
+
+ align:start position:0%
+picture so now what do we have to do
+remember what's our goal our goal is to
+
+ align:start position:0%
+remember what's our goal our goal is to
+ 
+
+ align:start position:0%
+remember what's our goal our goal is to
+figure out where the coefficients come
+
+ align:start position:0%
+figure out where the coefficients come
+ 
+
+ align:start position:0%
+figure out where the coefficients come
+from so what I actually need to do is I
+
+ align:start position:0%
+from so what I actually need to do is I
+ 
+
+ align:start position:0%
+from so what I actually need to do is I
+need to evaluate a certain uh integral
+
+ align:start position:0%
+need to evaluate a certain uh integral
+ 
+
+ align:start position:0%
+need to evaluate a certain uh integral
+or I need to I need to integrate a
+
+ align:start position:0%
+or I need to I need to integrate a
+ 
+
+ align:start position:0%
+or I need to I need to integrate a
+certain function I need to integrate P
+
+ align:start position:0%
+certain function I need to integrate P
+ 
+
+ align:start position:0%
+certain function I need to integrate P
+of X so what I'm going to be finding
+
+ align:start position:0%
+of X so what I'm going to be finding
+ 
+
+ align:start position:0%
+of X so what I'm going to be finding
+through the rest of this video is the
+
+ align:start position:0%
+through the rest of this video is the
+ 
+
+ align:start position:0%
+through the rest of this video is the
+integral from minus H to H of P of X
+
+ align:start position:0%
+integral from minus H to H of P of X
+ 
+
+ align:start position:0%
+integral from minus H to H of P of X
+DX and my goal is to show that this
+
+ align:start position:0%
+DX and my goal is to show that this
+ 
+
+ align:start position:0%
+DX and my goal is to show that this
+integral is equal to this expression I
+
+ align:start position:0%
+integral is equal to this expression I
+ 
+
+ align:start position:0%
+integral is equal to this expression I
+want to show that these are equal that's
+
+ align:start position:0%
+want to show that these are equal that's
+ 
+
+ align:start position:0%
+want to show that these are equal that's
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal so let's get down to it well what
+
+ align:start position:0%
+goal so let's get down to it well what
+ 
+
+ align:start position:0%
+goal so let's get down to it well what
+do I know what's the only thing I know
+
+ align:start position:0%
+do I know what's the only thing I know
+ 
+
+ align:start position:0%
+do I know what's the only thing I know
+right away about P of x I know I'm
+
+ align:start position:0%
+right away about P of x I know I'm
+ 
+
+ align:start position:0%
+right away about P of x I know I'm
+choosing it to be a quadratic function
+
+ align:start position:0%
+choosing it to be a quadratic function
+ 
+
+ align:start position:0%
+choosing it to be a quadratic function
+and I know it goes through three certain
+
+ align:start position:0%
+and I know it goes through three certain
+ 
+
+ align:start position:0%
+and I know it goes through three certain
+points right I'll write down what the
+
+ align:start position:0%
+points right I'll write down what the
+ 
+
+ align:start position:0%
+points right I'll write down what the
+three points are when we need them but
+
+ align:start position:0%
+three points are when we need them but
+ 
+
+ align:start position:0%
+three points are when we need them but
+first let's just say in general let's
+
+ align:start position:0%
+first let's just say in general let's
+ 
+
+ align:start position:0%
+first let's just say in general let's
+take let's take this integral for a
+
+ align:start position:0%
+take let's take this integral for a
+ 
+
+ align:start position:0%
+take let's take this integral for a
+general quadratic and see how much
+
+ align:start position:0%
+general quadratic and see how much
+ 
+
+ align:start position:0%
+general quadratic and see how much
+information we actually need so let me
+
+ align:start position:0%
+information we actually need so let me
+ 
+
+ align:start position:0%
+information we actually need so let me
+come over
+
+ align:start position:0%
+come over
+ 
+
+ align:start position:0%
+come over
+here actually let me say first what do I
+
+ align:start position:0%
+here actually let me say first what do I
+ 
+
+ align:start position:0%
+here actually let me say first what do I
+mean by General
+
+ align:start position:0%
+mean by General
+ 
+
+ align:start position:0%
+mean by General
+quadratic I mean something of the form
+
+ align:start position:0%
+quadratic I mean something of the form
+ 
+
+ align:start position:0%
+quadratic I mean something of the form
+big a capital A x^2 Plus BX plus C so
+
+ align:start position:0%
+big a capital A x^2 Plus BX plus C so
+ 
+
+ align:start position:0%
+big a capital A x^2 Plus BX plus C so
+I'm not filling in values for these
+
+ align:start position:0%
+I'm not filling in values for these
+ 
+
+ align:start position:0%
+I'm not filling in values for these
+coefficients yet those coefficients are
+
+ align:start position:0%
+coefficients yet those coefficients are
+ 
+
+ align:start position:0%
+coefficients yet those coefficients are
+coming exactly from my three points xot
+
+ align:start position:0%
+coming exactly from my three points xot
+ 
+
+ align:start position:0%
+coming exactly from my three points xot
+y KN X1 y1 and X2 Y2 so let's just let's
+
+ align:start position:0%
+y KN X1 y1 and X2 Y2 so let's just let's
+ 
+
+ align:start position:0%
+y KN X1 y1 and X2 Y2 so let's just let's
+just integrate that from minus H to H
+
+ align:start position:0%
+just integrate that from minus H to H
+ 
+
+ align:start position:0%
+just integrate that from minus H to H
+first and see what kind of information
+
+ align:start position:0%
+first and see what kind of information
+ 
+
+ align:start position:0%
+first and see what kind of information
+we need so if I come over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what do I get when I actually
+
+ align:start position:0%
+so what do I get when I actually
+ 
+
+ align:start position:0%
+so what do I get when I actually
+integrate this well I get ax 3r over
+
+ align:start position:0%
+integrate this well I get ax 3r over
+ 
+
+ align:start position:0%
+integrate this well I get ax 3r over
+3 plus bx^ 2 over
+
+ align:start position:0%
+3 plus bx^ 2 over
+ 
+
+ align:start position:0%
+3 plus bx^ 2 over
+2 plus CX and then I have to evaluate
+
+ align:start position:0%
+2 plus CX and then I have to evaluate
+ 
+
+ align:start position:0%
+2 plus CX and then I have to evaluate
+from minus H to
+
+ align:start position:0%
+from minus H to
+ 
+
+ align:start position:0%
+from minus H to
+H well if you uh if you were thinking
+
+ align:start position:0%
+H well if you uh if you were thinking
+ 
+
+ align:start position:0%
+H well if you uh if you were thinking
+about this it shouldn't be surprising
+
+ align:start position:0%
+about this it shouldn't be surprising
+ 
+
+ align:start position:0%
+about this it shouldn't be surprising
+that when I do this there's not going to
+
+ align:start position:0%
+that when I do this there's not going to
+ 
+
+ align:start position:0%
+that when I do this there's not going to
+be a b term why is that well these two
+
+ align:start position:0%
+be a b term why is that well these two
+ 
+
+ align:start position:0%
+be a b term why is that well these two
+functions are even ax s and C are even
+
+ align:start position:0%
+functions are even ax s and C are even
+ 
+
+ align:start position:0%
+functions are even ax s and C are even
+functions and I'm integrating over
+
+ align:start position:0%
+functions and I'm integrating over
+ 
+
+ align:start position:0%
+functions and I'm integrating over
+something that's symmetric about the Y
+
+ align:start position:0%
+something that's symmetric about the Y
+ 
+
+ align:start position:0%
+something that's symmetric about the Y
+AIS I'm going from minus H to H so if
+
+ align:start position:0%
+AIS I'm going from minus H to H so if
+ 
+
+ align:start position:0%
+AIS I'm going from minus H to H so if
+you think about ax2 and I'm going from
+
+ align:start position:0%
+you think about ax2 and I'm going from
+ 
+
+ align:start position:0%
+you think about ax2 and I'm going from
+minus H to H I'm finding the area under
+
+ align:start position:0%
+minus H to H I'm finding the area under
+ 
+
+ align:start position:0%
+minus H to H I'm finding the area under
+a quadratic from minus H to H it's going
+
+ align:start position:0%
+a quadratic from minus H to H it's going
+ 
+
+ align:start position:0%
+a quadratic from minus H to H it's going
+to be twice the area from 0 to
+
+ align:start position:0%
+to be twice the area from 0 to
+ 
+
+ align:start position:0%
+to be twice the area from 0 to
+H but BX that's a line with slope B if I
+
+ align:start position:0%
+H but BX that's a line with slope B if I
+ 
+
+ align:start position:0%
+H but BX that's a line with slope B if I
+want to if I wanted to integrate BX from
+
+ align:start position:0%
+want to if I wanted to integrate BX from
+ 
+
+ align:start position:0%
+want to if I wanted to integrate BX from
+minus H to H that's the area the signed
+
+ align:start position:0%
+minus H to H that's the area the signed
+ 
+
+ align:start position:0%
+minus H to H that's the area the signed
+area under the curve of a line BX fromus
+
+ align:start position:0%
+area under the curve of a line BX fromus
+ 
+
+ align:start position:0%
+area under the curve of a line BX fromus
+H to H if I just draw a quick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture what does that look like it's a
+
+ align:start position:0%
+picture what does that look like it's a
+ 
+
+ align:start position:0%
+picture what does that look like it's a
+symmetric it's symmetric with respect to
+
+ align:start position:0%
+symmetric it's symmetric with respect to
+ 
+
+ align:start position:0%
+symmetric it's symmetric with respect to
+a rotation there so the I'd have this
+
+ align:start position:0%
+a rotation there so the I'd have this
+ 
+
+ align:start position:0%
+a rotation there so the I'd have this
+signed area this is the curve yal
+
+ align:start position:0%
+signed area this is the curve yal
+ 
+
+ align:start position:0%
+signed area this is the curve yal
+BX from minus H to H I get this area is
+
+ align:start position:0%
+BX from minus H to H I get this area is
+ 
+
+ align:start position:0%
+BX from minus H to H I get this area is
+negative and this area is positive and
+
+ align:start position:0%
+negative and this area is positive and
+ 
+
+ align:start position:0%
+negative and this area is positive and
+they're equal so what I'm about to do
+
+ align:start position:0%
+they're equal so what I'm about to do
+ 
+
+ align:start position:0%
+they're equal so what I'm about to do
+you shouldn't be surprised there won't
+
+ align:start position:0%
+you shouldn't be surprised there won't
+ 
+
+ align:start position:0%
+you shouldn't be surprised there won't
+be a b term so what do we actually get
+
+ align:start position:0%
+be a b term so what do we actually get
+ 
+
+ align:start position:0%
+be a b term so what do we actually get
+when we evaluate this we get 2 a h cubed
+
+ align:start position:0%
+when we evaluate this we get 2 a h cubed
+ 
+
+ align:start position:0%
+when we evaluate this we get 2 a h cubed
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+3 + 2 c
+
+ align:start position:0%
+3 + 2 c
+ 
+
+ align:start position:0%
+3 + 2 c
+h so that's what we get you can actually
+
+ align:start position:0%
+h so that's what we get you can actually
+ 
+
+ align:start position:0%
+h so that's what we get you can actually
+work it all out putting in all the hes
+
+ align:start position:0%
+work it all out putting in all the hes
+ 
+
+ align:start position:0%
+work it all out putting in all the hes
+and see that but I knew I was going to
+
+ align:start position:0%
+and see that but I knew I was going to
+ 
+
+ align:start position:0%
+and see that but I knew I was going to
+have double what was here when I
+
+ align:start position:0%
+have double what was here when I
+ 
+
+ align:start position:0%
+have double what was here when I
+evaluated at H and nothing from the B
+
+ align:start position:0%
+evaluated at H and nothing from the B
+ 
+
+ align:start position:0%
+evaluated at H and nothing from the B
+term so we're getting
+
+ align:start position:0%
+term so we're getting
+ 
+
+ align:start position:0%
+term so we're getting
+closer we're getting closer we might not
+
+ align:start position:0%
+closer we're getting closer we might not
+ 
+
+ align:start position:0%
+closer we're getting closer we might not
+look like we're getting closer but we're
+
+ align:start position:0%
+look like we're getting closer but we're
+ 
+
+ align:start position:0%
+look like we're getting closer but we're
+getting closer so let's simplify this
+
+ align:start position:0%
+getting closer so let's simplify this
+ 
+
+ align:start position:0%
+getting closer so let's simplify this
+expression a little bit what I actually
+
+ align:start position:0%
+expression a little bit what I actually
+ 
+
+ align:start position:0%
+expression a little bit what I actually
+what I ultimately need to to do is I
+
+ align:start position:0%
+what I ultimately need to to do is I
+ 
+
+ align:start position:0%
+what I ultimately need to to do is I
+need to figure out C and I need to
+
+ align:start position:0%
+need to figure out C and I need to
+ 
+
+ align:start position:0%
+need to figure out C and I need to
+figure out something over here I need to
+
+ align:start position:0%
+figure out something over here I need to
+ 
+
+ align:start position:0%
+figure out something over here I need to
+actually figure out ah s and let me
+
+ align:start position:0%
+actually figure out ah s and let me
+ 
+
+ align:start position:0%
+actually figure out ah s and let me
+explain why I need to figure out ah squ
+
+ align:start position:0%
+explain why I need to figure out ah squ
+ 
+
+ align:start position:0%
+explain why I need to figure out ah squ
+in the end if I if I come over back to
+
+ align:start position:0%
+in the end if I if I come over back to
+ 
+
+ align:start position:0%
+in the end if I if I come over back to
+what I want to show let me even box it
+
+ align:start position:0%
+what I want to show let me even box it
+ 
+
+ align:start position:0%
+what I want to show let me even box it
+so we see it I want to
+
+ align:start position:0%
+so we see it I want to
+ 
+
+ align:start position:0%
+so we see it I want to
+show that this integral which I've
+
+ align:start position:0%
+show that this integral which I've
+ 
+
+ align:start position:0%
+show that this integral which I've
+started to calculate is equal to H over
+
+ align:start position:0%
+started to calculate is equal to H over
+ 
+
+ align:start position:0%
+started to calculate is equal to H over
+3times this quantity so I want to keep
+
+ align:start position:0%
+3times this quantity so I want to keep
+ 
+
+ align:start position:0%
+3times this quantity so I want to keep
+one H around but I want the other any
+
+ align:start position:0%
+one H around but I want the other any
+ 
+
+ align:start position:0%
+one H around but I want the other any
+other powers of H to not be there when
+
+ align:start position:0%
+other powers of H to not be there when
+ 
+
+ align:start position:0%
+other powers of H to not be there when
+I'm done right I need one power of H
+
+ align:start position:0%
+I'm done right I need one power of H
+ 
+
+ align:start position:0%
+I'm done right I need one power of H
+there in fact I need an H over3 there so
+
+ align:start position:0%
+there in fact I need an H over3 there so
+ 
+
+ align:start position:0%
+there in fact I need an H over3 there so
+I think what I'll do is I'll start off
+
+ align:start position:0%
+I think what I'll do is I'll start off
+ 
+
+ align:start position:0%
+I think what I'll do is I'll start off
+and I'll and I'll pull out an H over
+
+ align:start position:0%
+and I'll and I'll pull out an H over
+ 
+
+ align:start position:0%
+and I'll and I'll pull out an H over
+three and then I'll try and figure out
+
+ align:start position:0%
+three and then I'll try and figure out
+ 
+
+ align:start position:0%
+three and then I'll try and figure out
+if I can get the rest of my expression
+
+ align:start position:0%
+if I can get the rest of my expression
+ 
+
+ align:start position:0%
+if I can get the rest of my expression
+to look like what's in the parenthesis
+
+ align:start position:0%
+to look like what's in the parenthesis
+ 
+
+ align:start position:0%
+to look like what's in the parenthesis
+that's really ultimately what I'd like
+
+ align:start position:0%
+that's really ultimately what I'd like
+ 
+
+ align:start position:0%
+that's really ultimately what I'd like
+to do so let's come back over
+
+ align:start position:0%
+to do so let's come back over
+ 
+
+ align:start position:0%
+to do so let's come back over
+here I'm going to pull out an H over
+
+ align:start position:0%
+here I'm going to pull out an H over
+ 
+
+ align:start position:0%
+here I'm going to pull out an H over
+three from both of these and we're going
+
+ align:start position:0%
+three from both of these and we're going
+ 
+
+ align:start position:0%
+three from both of these and we're going
+to see what we end up with okay so if I
+
+ align:start position:0%
+to see what we end up with okay so if I
+ 
+
+ align:start position:0%
+to see what we end up with okay so if I
+pull out an H over3 here what do I end
+
+ align:start position:0%
+pull out an H over3 here what do I end
+ 
+
+ align:start position:0%
+pull out an H over3 here what do I end
+up with this is easy that's two a h^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and this one's a little bit trickier
+
+ align:start position:0%
+2 and this one's a little bit trickier
+ 
+
+ align:start position:0%
+2 and this one's a little bit trickier
+but I have to multiply by 3 over 3 to
+
+ align:start position:0%
+but I have to multiply by 3 over 3 to
+ 
+
+ align:start position:0%
+but I have to multiply by 3 over 3 to
+get a three there so I end up with 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C okay let's make sure I didn't make any
+
+ align:start position:0%
+C okay let's make sure I didn't make any
+ 
+
+ align:start position:0%
+C okay let's make sure I didn't make any
+mistakes If I multiply through here I
+
+ align:start position:0%
+mistakes If I multiply through here I
+ 
+
+ align:start position:0%
+mistakes If I multiply through here I
+get 2 ah cubed over 3 If I multiply
+
+ align:start position:0%
+get 2 ah cubed over 3 If I multiply
+ 
+
+ align:start position:0%
+get 2 ah cubed over 3 If I multiply
+through here I get 2 H C looking good so
+
+ align:start position:0%
+through here I get 2 H C looking good so
+ 
+
+ align:start position:0%
+through here I get 2 H C looking good so
+far now I have to figure out a and C or
+
+ align:start position:0%
+far now I have to figure out a and C or
+ 
+
+ align:start position:0%
+far now I have to figure out a and C or
+a squ and C what C is pretty easy to
+
+ align:start position:0%
+a squ and C what C is pretty easy to
+ 
+
+ align:start position:0%
+a squ and C what C is pretty easy to
+find let's think about why that is I
+
+ align:start position:0%
+find let's think about why that is I
+ 
+
+ align:start position:0%
+find let's think about why that is I
+have this polom the polom was equal to
+
+ align:start position:0%
+have this polom the polom was equal to
+ 
+
+ align:start position:0%
+have this polom the polom was equal to
+if we come over here and we look again
+
+ align:start position:0%
+if we come over here and we look again
+ 
+
+ align:start position:0%
+if we come over here and we look again
+it's ax^2 plus BX plus C and the
+
+ align:start position:0%
+it's ax^2 plus BX plus C and the
+ 
+
+ align:start position:0%
+it's ax^2 plus BX plus C and the
+polinomial has to go through those three
+
+ align:start position:0%
+polinomial has to go through those three
+ 
+
+ align:start position:0%
+polinomial has to go through those three
+points I had so when X is
+
+ align:start position:0%
+points I had so when X is
+ 
+
+ align:start position:0%
+points I had so when X is
+zero P of Z is C so let's come back and
+
+ align:start position:0%
+zero P of Z is C so let's come back and
+ 
+
+ align:start position:0%
+zero P of Z is C so let's come back and
+look at our picture when X is
+
+ align:start position:0%
+look at our picture when X is
+ 
+
+ align:start position:0%
+look at our picture when X is
+zero what's the output on the on the
+
+ align:start position:0%
+zero what's the output on the on the
+ 
+
+ align:start position:0%
+zero what's the output on the on the
+white curve it's y1 so C is exactly y1
+
+ align:start position:0%
+white curve it's y1 so C is exactly y1
+ 
+
+ align:start position:0%
+white curve it's y1 so C is exactly y1
+how am I going to find ah2 well what I
+
+ align:start position:0%
+how am I going to find ah2 well what I
+ 
+
+ align:start position:0%
+how am I going to find ah2 well what I
+need to do is use these other two points
+
+ align:start position:0%
+need to do is use these other two points
+ 
+
+ align:start position:0%
+need to do is use these other two points
+I'm going to evaluate the function P of
+
+ align:start position:0%
+I'm going to evaluate the function P of
+ 
+
+ align:start position:0%
+I'm going to evaluate the function P of
+X at minus H and its output has to be y
+
+ align:start position:0%
+X at minus H and its output has to be y
+ 
+
+ align:start position:0%
+X at minus H and its output has to be y
+z and I'm going to evaluate the function
+
+ align:start position:0%
+z and I'm going to evaluate the function
+ 
+
+ align:start position:0%
+z and I'm going to evaluate the function
+P of X at H and its output has to be Y2
+
+ align:start position:0%
+P of X at H and its output has to be Y2
+ 
+
+ align:start position:0%
+P of X at H and its output has to be Y2
+so we're going to come over to the other
+
+ align:start position:0%
+so we're going to come over to the other
+ 
+
+ align:start position:0%
+so we're going to come over to the other
+side but that's really what we're doing
+
+ align:start position:0%
+side but that's really what we're doing
+ 
+
+ align:start position:0%
+side but that's really what we're doing
+next so let's come over
+
+ align:start position:0%
+next so let's come over
+ 
+
+ align:start position:0%
+next so let's come over
+here and let's evaluate P of H
+
+ align:start position:0%
+here and let's evaluate P of H
+ 
+
+ align:start position:0%
+here and let's evaluate P of H
+and P of minus
+
+ align:start position:0%
+and P of minus
+ 
+
+ align:start position:0%
+and P of minus
+H so P of
+
+ align:start position:0%
+H so P of
+ 
+
+ align:start position:0%
+H so P of
+H is a h^ 2 plus b
+
+ align:start position:0%
+H is a h^ 2 plus b
+ 
+
+ align:start position:0%
+H is a h^ 2 plus b
+h plus C and P of minus H is uh a^
+
+ align:start position:0%
+h plus C and P of minus H is uh a^
+ 
+
+ align:start position:0%
+h plus C and P of minus H is uh a^
+2 minus
+
+ align:start position:0%
+2 minus
+ 
+
+ align:start position:0%
+2 minus
+BH plus
+
+ align:start position:0%
+BH plus
+ 
+
+ align:start position:0%
+BH plus
+C okay what else again we said this this
+
+ align:start position:0%
+C okay what else again we said this this
+ 
+
+ align:start position:0%
+C okay what else again we said this this
+one has to be Y2 the output and this one
+
+ align:start position:0%
+one has to be Y2 the output and this one
+ 
+
+ align:start position:0%
+one has to be Y2 the output and this one
+has to be y z because the output at H
+
+ align:start position:0%
+has to be y z because the output at H
+ 
+
+ align:start position:0%
+has to be y z because the output at H
+has to agree with the output of the
+
+ align:start position:0%
+has to agree with the output of the
+ 
+
+ align:start position:0%
+has to agree with the output of the
+function f ofx and its output at H was
+
+ align:start position:0%
+function f ofx and its output at H was
+ 
+
+ align:start position:0%
+function f ofx and its output at H was
+Y2 the output at minus h of of P has to
+
+ align:start position:0%
+Y2 the output at minus h of of P has to
+ 
+
+ align:start position:0%
+Y2 the output at minus h of of P has to
+be the same as the output a minus h of F
+
+ align:start position:0%
+be the same as the output a minus h of F
+ 
+
+ align:start position:0%
+be the same as the output a minus h of F
+and that was Y Z now this might not look
+
+ align:start position:0%
+and that was Y Z now this might not look
+ 
+
+ align:start position:0%
+and that was Y Z now this might not look
+fun yet but what if I add these two
+
+ align:start position:0%
+fun yet but what if I add these two
+ 
+
+ align:start position:0%
+fun yet but what if I add these two
+things together what happens I get 2 a h
+
+ align:start position:0%
+things together what happens I get 2 a h
+ 
+
+ align:start position:0%
+things together what happens I get 2 a h
+2 these drop out and then I get plus 2 C
+
+ align:start position:0%
+2 these drop out and then I get plus 2 C
+ 
+
+ align:start position:0%
+2 these drop out and then I get plus 2 C
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+y0 +
+
+ align:start position:0%
+y0 +
+ 
+
+ align:start position:0%
+y0 +
+Y2 I'm getting closer I'm getting much
+
+ align:start position:0%
+Y2 I'm getting closer I'm getting much
+ 
+
+ align:start position:0%
+Y2 I'm getting closer I'm getting much
+closer because now notice what I have I
+
+ align:start position:0%
+closer because now notice what I have I
+ 
+
+ align:start position:0%
+closer because now notice what I have I
+have 2 ah squ I can isolate that and
+
+ align:start position:0%
+have 2 ah squ I can isolate that and
+ 
+
+ align:start position:0%
+have 2 ah squ I can isolate that and
+that's something that I want to figure
+
+ align:start position:0%
+that's something that I want to figure
+ 
+
+ align:start position:0%
+that's something that I want to figure
+out I want to figure out 2 A2 so let's
+
+ align:start position:0%
+out I want to figure out 2 A2 so let's
+ 
+
+ align:start position:0%
+out I want to figure out 2 A2 so let's
+figure out what that
+
+ align:start position:0%
+figure out what that
+ 
+
+ align:start position:0%
+figure out what that
+is 2
+
+ align:start position:0%
+is 2
+ 
+
+ align:start position:0%
+is 2
+ah2 is equal to
+
+ align:start position:0%
+ah2 is equal to
+ 
+
+ align:start position:0%
+ah2 is equal to
+y0 + Y
+
+ align:start position:0%
+y0 + Y
+ 
+
+ align:start position:0%
+y0 + Y
+2 minus well what did we say C was C was
+
+ align:start position:0%
+2 minus well what did we say C was C was
+ 
+
+ align:start position:0%
+2 minus well what did we say C was C was
+the output at at xal 0 which is y1 so
+
+ align:start position:0%
+the output at at xal 0 which is y1 so
+ 
+
+ align:start position:0%
+the output at at xal 0 which is y1 so
+it's minus 2 C which isus 2 y1 so now
+
+ align:start position:0%
+it's minus 2 C which isus 2 y1 so now
+ 
+
+ align:start position:0%
+it's minus 2 C which isus 2 y1 so now
+we're very close we're very close to
+
+ align:start position:0%
+we're very close we're very close to
+ 
+
+ align:start position:0%
+we're very close we're very close to
+getting what we want and that's good
+
+ align:start position:0%
+getting what we want and that's good
+ 
+
+ align:start position:0%
+getting what we want and that's good
+because I'm almost out of room so let's
+
+ align:start position:0%
+because I'm almost out of room so let's
+ 
+
+ align:start position:0%
+because I'm almost out of room so let's
+take that expression we were working on
+
+ align:start position:0%
+take that expression we were working on
+ 
+
+ align:start position:0%
+take that expression we were working on
+this expression right here and let's
+
+ align:start position:0%
+this expression right here and let's
+ 
+
+ align:start position:0%
+this expression right here and let's
+start to fill in what we get we get H
+
+ align:start position:0%
+start to fill in what we get we get H
+ 
+
+ align:start position:0%
+start to fill in what we get we get H
+over3 time 2 ah^ 2 which is
+
+ align:start position:0%
+over3 time 2 ah^ 2 which is
+ 
+
+ align:start position:0%
+over3 time 2 ah^ 2 which is
+y+ Y 2
+
+ align:start position:0%
+y+ Y 2
+ 
+
+ align:start position:0%
+y+ Y 2
+- 2 y1 and then I have to add 6 C now
+
+ align:start position:0%
+- 2 y1 and then I have to add 6 C now
+ 
+
+ align:start position:0%
+- 2 y1 and then I have to add 6 C now
+what's c c is y1 so I'm going to add six
+
+ align:start position:0%
+what's c c is y1 so I'm going to add six
+ 
+
+ align:start position:0%
+what's c c is y1 so I'm going to add six
+y1 and if I simplify
+
+ align:start position:0%
+y1 and if I simplify
+ 
+
+ align:start position:0%
+y1 and if I simplify
+that I get y
+
+ align:start position:0%
+that I get y
+ 
+
+ align:start position:0%
+that I get y
+z Bingo Plus 4 y1 + Y
+
+ align:start position:0%
+z Bingo Plus 4 y1 + Y
+ 
+
+ align:start position:0%
+z Bingo Plus 4 y1 + Y
+2 and that's what we wanted so let me
+
+ align:start position:0%
+2 and that's what we wanted so let me
+ 
+
+ align:start position:0%
+2 and that's what we wanted so let me
+take us through kind of where where all
+
+ align:start position:0%
+take us through kind of where where all
+ 
+
+ align:start position:0%
+take us through kind of where where all
+this came from again what the big pieces
+
+ align:start position:0%
+this came from again what the big pieces
+ 
+
+ align:start position:0%
+this came from again what the big pieces
+were and uh and we'll see now we
+
+ align:start position:0%
+were and uh and we'll see now we
+ 
+
+ align:start position:0%
+were and uh and we'll see now we
+understand how we How We Do Simpsons
+
+ align:start position:0%
+understand how we How We Do Simpsons
+ 
+
+ align:start position:0%
+understand how we How We Do Simpsons
+rule in these small chunks of Simpsons
+
+ align:start position:0%
+rule in these small chunks of Simpsons
+ 
+
+ align:start position:0%
+rule in these small chunks of Simpsons
+rule so let's come back to the very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beginning okay in the very beginning
+
+ align:start position:0%
+beginning okay in the very beginning
+ 
+
+ align:start position:0%
+beginning okay in the very beginning
+what we had was a function f ofx that
+
+ align:start position:0%
+what we had was a function f ofx that
+ 
+
+ align:start position:0%
+what we had was a function f ofx that
+was the white curve yals F ofx was the
+
+ align:start position:0%
+was the white curve yals F ofx was the
+ 
+
+ align:start position:0%
+was the white curve yals F ofx was the
+white curve and then I found a quadratic
+
+ align:start position:0%
+white curve and then I found a quadratic
+ 
+
+ align:start position:0%
+white curve and then I found a quadratic
+that went through minus h y 0 y1 and H
+
+ align:start position:0%
+that went through minus h y 0 y1 and H
+ 
+
+ align:start position:0%
+that went through minus h y 0 y1 and H
+Y2 went through those three points and I
+
+ align:start position:0%
+Y2 went through those three points and I
+ 
+
+ align:start position:0%
+Y2 went through those three points and I
+called that quadratic P of x
+
+ align:start position:0%
+called that quadratic P of x
+ 
+
+ align:start position:0%
+called that quadratic P of x
+and then what I was doing we know
+
+ align:start position:0%
+and then what I was doing we know
+ 
+
+ align:start position:0%
+and then what I was doing we know
+Simpson rule says find the area under
+
+ align:start position:0%
+Simpson rule says find the area under
+ 
+
+ align:start position:0%
+Simpson rule says find the area under
+the curve of P of X between minus H and
+
+ align:start position:0%
+the curve of P of X between minus H and
+ 
+
+ align:start position:0%
+the curve of P of X between minus H and
+H so what I did was I came over here and
+
+ align:start position:0%
+H so what I did was I came over here and
+ 
+
+ align:start position:0%
+H so what I did was I came over here and
+I said okay P of X integral of P of x
+
+ align:start position:0%
+I said okay P of X integral of P of x
+ 
+
+ align:start position:0%
+I said okay P of X integral of P of x
+from minus H to H I wrote P of X in a
+
+ align:start position:0%
+from minus H to H I wrote P of X in a
+ 
+
+ align:start position:0%
+from minus H to H I wrote P of X in a
+very general
+
+ align:start position:0%
+very general
+ 
+
+ align:start position:0%
+very general
+form and then I actually found an
+
+ align:start position:0%
+form and then I actually found an
+ 
+
+ align:start position:0%
+form and then I actually found an
+integral I came through and after after
+
+ align:start position:0%
+integral I came through and after after
+ 
+
+ align:start position:0%
+integral I came through and after after
+writing it out calculating the integral
+
+ align:start position:0%
+writing it out calculating the integral
+ 
+
+ align:start position:0%
+writing it out calculating the integral
+I got to this expression this is
+
+ align:start position:0%
+I got to this expression this is
+ 
+
+ align:start position:0%
+I got to this expression this is
+actually the integral of P of x fromus h
+
+ align:start position:0%
+actually the integral of P of x fromus h
+ 
+
+ align:start position:0%
+actually the integral of P of x fromus h
+to H so that's area under the curve of P
+
+ align:start position:0%
+to H so that's area under the curve of P
+ 
+
+ align:start position:0%
+to H so that's area under the curve of P
+of x from minus H to H is that and now I
+
+ align:start position:0%
+of x from minus H to H is that and now I
+ 
+
+ align:start position:0%
+of x from minus H to H is that and now I
+had to figure this out how to how to
+
+ align:start position:0%
+had to figure this out how to how to
+ 
+
+ align:start position:0%
+had to figure this out how to how to
+write this in terms of the outputs of f
+
+ align:start position:0%
+write this in terms of the outputs of f
+ 
+
+ align:start position:0%
+write this in terms of the outputs of f
+ofx which were y z y1 and Y2 those were
+
+ align:start position:0%
+ofx which were y z y1 and Y2 those were
+ 
+
+ align:start position:0%
+ofx which were y z y1 and Y2 those were
+the ones we were interested in so I
+
+ align:start position:0%
+the ones we were interested in so I
+ 
+
+ align:start position:0%
+the ones we were interested in so I
+ultimately knew I wanted an H over3 in
+
+ align:start position:0%
+ultimately knew I wanted an H over3 in
+ 
+
+ align:start position:0%
+ultimately knew I wanted an H over3 in
+front I knew I wanted my my integral of
+
+ align:start position:0%
+front I knew I wanted my my integral of
+ 
+
+ align:start position:0%
+front I knew I wanted my my integral of
+my quadratic to be H over3 time
+
+ align:start position:0%
+my quadratic to be H over3 time
+ 
+
+ align:start position:0%
+my quadratic to be H over3 time
+something so I pulled out an h
+
+ align:start position:0%
+something so I pulled out an h
+ 
+
+ align:start position:0%
+something so I pulled out an h
+over3 and then I looked at what this
+
+ align:start position:0%
+over3 and then I looked at what this
+ 
+
+ align:start position:0%
+over3 and then I looked at what this
+expression was and if I could get this
+
+ align:start position:0%
+expression was and if I could get this
+ 
+
+ align:start position:0%
+expression was and if I could get this
+expression to look like the inside of
+
+ align:start position:0%
+expression to look like the inside of
+ 
+
+ align:start position:0%
+expression to look like the inside of
+what I wanted which which was y0 + 4 y1
+
+ align:start position:0%
+what I wanted which which was y0 + 4 y1
+ 
+
+ align:start position:0%
+what I wanted which which was y0 + 4 y1
++ Y2 I was in business and so then I
+
+ align:start position:0%
++ Y2 I was in business and so then I
+ 
+
+ align:start position:0%
++ Y2 I was in business and so then I
+used outputs that I knew for p of x to
+
+ align:start position:0%
+used outputs that I knew for p of x to
+ 
+
+ align:start position:0%
+used outputs that I knew for p of x to
+find 2 a h^2 and to find C I know P of H
+
+ align:start position:0%
+find 2 a h^2 and to find C I know P of H
+ 
+
+ align:start position:0%
+find 2 a h^2 and to find C I know P of H
+is the output of the F ofx function at
+
+ align:start position:0%
+is the output of the F ofx function at
+ 
+
+ align:start position:0%
+is the output of the F ofx function at
+the far right which was Y2 and I knew P
+
+ align:start position:0%
+the far right which was Y2 and I knew P
+ 
+
+ align:start position:0%
+the far right which was Y2 and I knew P
+of minus H was the output of the F ofx
+
+ align:start position:0%
+of minus H was the output of the F ofx
+ 
+
+ align:start position:0%
+of minus H was the output of the F ofx
+function at the far left that's y z I
+
+ align:start position:0%
+function at the far left that's y z I
+ 
+
+ align:start position:0%
+function at the far left that's y z I
+actually then evaluate P at H and minus
+
+ align:start position:0%
+actually then evaluate P at H and minus
+ 
+
+ align:start position:0%
+actually then evaluate P at H and minus
+H and when I add those together I get my
+
+ align:start position:0%
+H and when I add those together I get my
+ 
+
+ align:start position:0%
+H and when I add those together I get my
+2 a h^2 in terms of y z y1 and Y2 that
+
+ align:start position:0%
+2 a h^2 in terms of y z y1 and Y2 that
+ 
+
+ align:start position:0%
+2 a h^2 in terms of y z y1 and Y2 that
+let me do this in terms of y z y1 and Y2
+
+ align:start position:0%
+let me do this in terms of y z y1 and Y2
+ 
+
+ align:start position:0%
+let me do this in terms of y z y1 and Y2
+because I also knew C was y1 we talked
+
+ align:start position:0%
+because I also knew C was y1 we talked
+ 
+
+ align:start position:0%
+because I also knew C was y1 we talked
+about that as well C had to be y1 so I
+
+ align:start position:0%
+about that as well C had to be y1 so I
+ 
+
+ align:start position:0%
+about that as well C had to be y1 so I
+can then do the substitution I need
+
+ align:start position:0%
+can then do the substitution I need
+ 
+
+ align:start position:0%
+can then do the substitution I need
+right here and show where the
+
+ align:start position:0%
+right here and show where the
+ 
+
+ align:start position:0%
+right here and show where the
+coefficients and Simpsons R come from so
+
+ align:start position:0%
+coefficients and Simpsons R come from so
+ 
+
+ align:start position:0%
+coefficients and Simpsons R come from so
+hopefully that was informative for you
+
+ align:start position:0%
+hopefully that was informative for you
+ 
+
+ align:start position:0%
+hopefully that was informative for you
+and I think I'll stop there
\ No newline at end of file
diff --git a/uz7GkOzULm8.txt b/uz7GkOzULm8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d9b91b67640dc25dea7b75e6c2f44f1f769567d0
--- /dev/null
+++ b/uz7GkOzULm8.txt
@@ -0,0 +1,9760 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we we study group theory not to
+
+ align:start position:0%
+So we we study group theory not to
+ 
+
+ align:start position:0%
+So we we study group theory not to
+admire group theory but to use it to
+
+ align:start position:0%
+admire group theory but to use it to
+ 
+
+ align:start position:0%
+admire group theory but to use it to
+make sense of spectra and usually when
+
+ align:start position:0%
+make sense of spectra and usually when
+ 
+
+ align:start position:0%
+make sense of spectra and usually when
+it's taught it's taught as a separate
+
+ align:start position:0%
+it's taught it's taught as a separate
+ 
+
+ align:start position:0%
+it's taught it's taught as a separate
+and beautiful object. And the the goal
+
+ align:start position:0%
+and beautiful object. And the the goal
+ 
+
+ align:start position:0%
+and beautiful object. And the the goal
+of trying to uh uh uh use it to ask the
+
+ align:start position:0%
+of trying to uh uh uh use it to ask the
+ 
+
+ align:start position:0%
+of trying to uh uh uh use it to ask the
+kinds of questions that we would want
+
+ align:start position:0%
+kinds of questions that we would want
+ 
+
+ align:start position:0%
+kinds of questions that we would want
+answers to as practicing spectroscopist
+
+ align:start position:0%
+answers to as practicing spectroscopist
+ 
+
+ align:start position:0%
+answers to as practicing spectroscopist
+is usually hidden. And so what do we
+
+ align:start position:0%
+is usually hidden. And so what do we
+ 
+
+ align:start position:0%
+is usually hidden. And so what do we
+want to ask? We would like to know from
+
+ align:start position:0%
+want to ask? We would like to know from
+ 
+
+ align:start position:0%
+want to ask? We would like to know from
+how a spectrum appears what it tells us
+
+ align:start position:0%
+how a spectrum appears what it tells us
+ 
+
+ align:start position:0%
+how a spectrum appears what it tells us
+qualitatively about the molecule. And uh
+
+ align:start position:0%
+qualitatively about the molecule. And uh
+ 
+
+ align:start position:0%
+qualitatively about the molecule. And uh
+as much as possible I'm going to be
+
+ align:start position:0%
+as much as possible I'm going to be
+ 
+
+ align:start position:0%
+as much as possible I'm going to be
+trying to address that. And one of the
+
+ align:start position:0%
+trying to address that. And one of the
+ 
+
+ align:start position:0%
+trying to address that. And one of the
+most important techniques
+
+ align:start position:0%
+most important techniques
+ 
+
+ align:start position:0%
+most important techniques
+is creating a reducible representation
+
+ align:start position:0%
+is creating a reducible representation
+ 
+
+ align:start position:0%
+is creating a reducible representation
+uh using cartoon-like ideas and reducing
+
+ align:start position:0%
+uh using cartoon-like ideas and reducing
+ 
+
+ align:start position:0%
+uh using cartoon-like ideas and reducing
+it. So that we can figure out what are
+
+ align:start position:0%
+it. So that we can figure out what are
+ 
+
+ align:start position:0%
+it. So that we can figure out what are
+the vibrations of the molecule. And then
+
+ align:start position:0%
+the vibrations of the molecule. And then
+ 
+
+ align:start position:0%
+the vibrations of the molecule. And then
+we find out what are their
+
+ align:start position:0%
+we find out what are their
+ 
+
+ align:start position:0%
+we find out what are their
+symmetries and then we find out what
+
+ align:start position:0%
+symmetries and then we find out what
+ 
+
+ align:start position:0%
+symmetries and then we find out what
+will their spectral look like because a
+
+ align:start position:0%
+will their spectral look like because a
+ 
+
+ align:start position:0%
+will their spectral look like because a
+given vibrational symmetry implies a
+
+ align:start position:0%
+given vibrational symmetry implies a
+ 
+
+ align:start position:0%
+given vibrational symmetry implies a
+certain uh rotational structure in the
+
+ align:start position:0%
+certain uh rotational structure in the
+ 
+
+ align:start position:0%
+certain uh rotational structure in the
+spectrum. And there
+
+ align:start position:0%
+spectrum. And there
+ 
+
+ align:start position:0%
+spectrum. And there
+are beautiful examples in the literature
+
+ align:start position:0%
+are beautiful examples in the literature
+ 
+
+ align:start position:0%
+are beautiful examples in the literature
+of the use of this kind of logic to
+
+ align:start position:0%
+of the use of this kind of logic to
+ 
+
+ align:start position:0%
+of the use of this kind of logic to
+decide on the shape of a molecule. And
+
+ align:start position:0%
+decide on the shape of a molecule. And
+ 
+
+ align:start position:0%
+decide on the shape of a molecule. And
+uh we will soon be starting talking uh
+
+ align:start position:0%
+uh we will soon be starting talking uh
+ 
+
+ align:start position:0%
+uh we will soon be starting talking uh
+in a case study way of electronic
+
+ align:start position:0%
+in a case study way of electronic
+ 
+
+ align:start position:0%
+in a case study way of electronic
+spectra. And one of the most beautiful
+
+ align:start position:0%
+spectra. And one of the most beautiful
+ 
+
+ align:start position:0%
+spectra. And one of the most beautiful
+things that happened uh about uh 60
+
+ align:start position:0%
+things that happened uh about uh 60
+ 
+
+ align:start position:0%
+things that happened uh about uh 60
+years ago was the proof that
+
+ align:start position:0%
+years ago was the proof that
+ 
+
+ align:start position:0%
+years ago was the proof that
+acetylene is undergoes a qualitative
+
+ align:start position:0%
+acetylene is undergoes a qualitative
+ 
+
+ align:start position:0%
+acetylene is undergoes a qualitative
+change in geometric structure upon
+
+ align:start position:0%
+change in geometric structure upon
+ 
+
+ align:start position:0%
+change in geometric structure upon
+exitation from the ground state to the
+
+ align:start position:0%
+exitation from the ground state to the
+ 
+
+ align:start position:0%
+exitation from the ground state to the
+electronically excited state and that
+
+ align:start position:0%
+electronically excited state and that
+ 
+
+ align:start position:0%
+electronically excited state and that
+this could be proven uh by the selective
+
+ align:start position:0%
+this could be proven uh by the selective
+ 
+
+ align:start position:0%
+this could be proven uh by the selective
+use of group theory. A similar thing
+
+ align:start position:0%
+use of group theory. A similar thing
+ 
+
+ align:start position:0%
+use of group theory. A similar thing
+happens with firmaldahhide although the
+
+ align:start position:0%
+happens with firmaldahhide although the
+ 
+
+ align:start position:0%
+happens with firmaldahhide although the
+change in structure is not so dramatic
+
+ align:start position:0%
+change in structure is not so dramatic
+ 
+
+ align:start position:0%
+change in structure is not so dramatic
+and it's more subtle and that is
+
+ align:start position:0%
+and it's more subtle and that is
+ 
+
+ align:start position:0%
+and it's more subtle and that is
+formaldahhide in the ground state is
+
+ align:start position:0%
+formaldahhide in the ground state is
+ 
+
+ align:start position:0%
+formaldahhide in the ground state is
+planer and in the excited state it's
+
+ align:start position:0%
+planer and in the excited state it's
+ 
+
+ align:start position:0%
+planer and in the excited state it's
+bent but the barrier to planerity is
+
+ align:start position:0%
+bent but the barrier to planerity is
+ 
+
+ align:start position:0%
+bent but the barrier to planerity is
+very low and so uh one uses group theory
+
+ align:start position:0%
+very low and so uh one uses group theory
+ 
+
+ align:start position:0%
+very low and so uh one uses group theory
+to look at the spectrum and you see two
+
+ align:start position:0%
+to look at the spectrum and you see two
+ 
+
+ align:start position:0%
+to look at the spectrum and you see two
+different answers depending on whether
+
+ align:start position:0%
+different answers depending on whether
+ 
+
+ align:start position:0%
+different answers depending on whether
+you're looking at low vibrational levels
+
+ align:start position:0%
+you're looking at low vibrational levels
+ 
+
+ align:start position:0%
+you're looking at low vibrational levels
+or higher vibrational levels. So
+
+ align:start position:0%
+or higher vibrational levels. So
+ 
+
+ align:start position:0%
+or higher vibrational levels. So
+um I hope that I will be able to give
+
+ align:start position:0%
+um I hope that I will be able to give
+ 
+
+ align:start position:0%
+um I hope that I will be able to give
+enough tools so that you can you can see
+
+ align:start position:0%
+enough tools so that you can you can see
+ 
+
+ align:start position:0%
+enough tools so that you can you can see
+how we get the qualitative information
+
+ align:start position:0%
+how we get the qualitative information
+ 
+
+ align:start position:0%
+how we get the qualitative information
+quickly.
+
+ align:start position:0%
+quickly.
+ 
+
+ align:start position:0%
+quickly.
+Okay. So here is a character table and
+
+ align:start position:0%
+Okay. So here is a character table and
+ 
+
+ align:start position:0%
+Okay. So here is a character table and
+the reason I chose D3 is
+
+ align:start position:0%
+the reason I chose D3 is
+ 
+
+ align:start position:0%
+the reason I chose D3 is
+because it's not C2V
+
+ align:start position:0%
+because it's not C2V
+ 
+
+ align:start position:0%
+because it's not C2V
+uh and everybody can do C2V and there
+
+ align:start position:0%
+uh and everybody can do C2V and there
+ 
+
+ align:start position:0%
+uh and everybody can do C2V and there
+isn't much there. And this is one of the
+
+ align:start position:0%
+isn't much there. And this is one of the
+ 
+
+ align:start position:0%
+isn't much there. And this is one of the
+smallest group that has degenerate
+
+ align:start position:0%
+smallest group that has degenerate
+ 
+
+ align:start position:0%
+smallest group that has degenerate
+representations. And so
+
+ align:start position:0%
+representations. And so
+ 
+
+ align:start position:0%
+representations. And so
+it's degenerate
+
+ align:start position:0%
+it's degenerate
+ 
+
+ align:start position:0%
+it's degenerate
+representation. Well, uh you can see how
+
+ align:start position:0%
+representation. Well, uh you can see how
+ 
+
+ align:start position:0%
+representation. Well, uh you can see how
+well prepared I am. So um this is
+
+ align:start position:0%
+well prepared I am. So um this is
+ 
+
+ align:start position:0%
+well prepared I am. So um this is
+sufficient to uh illustrate as much of
+
+ align:start position:0%
+sufficient to uh illustrate as much of
+ 
+
+ align:start position:0%
+sufficient to uh illustrate as much of
+the complexity of group theory as I
+
+ align:start position:0%
+the complexity of group theory as I
+ 
+
+ align:start position:0%
+the complexity of group theory as I
+would hope we'd need. Now, so we have a
+
+ align:start position:0%
+would hope we'd need. Now, so we have a
+ 
+
+ align:start position:0%
+would hope we'd need. Now, so we have a
+character table and these are uh the
+
+ align:start position:0%
+character table and these are uh the
+ 
+
+ align:start position:0%
+character table and these are uh the
+irreducible
+
+ align:start position:0%
+irreducible
+ 
+
+ align:start position:0%
+irreducible
+representations and the first thing to
+
+ align:start position:0%
+representations and the first thing to
+ 
+
+ align:start position:0%
+representations and the first thing to
+notice is that the symmetry operations
+
+ align:start position:0%
+notice is that the symmetry operations
+ 
+
+ align:start position:0%
+notice is that the symmetry operations
+are arranged according to
+
+ align:start position:0%
+are arranged according to
+ 
+
+ align:start position:0%
+are arranged according to
+classes. I told you what a class is and
+
+ align:start position:0%
+classes. I told you what a class is and
+ 
+
+ align:start position:0%
+classes. I told you what a class is and
+how to find all the uh members of a
+
+ align:start position:0%
+how to find all the uh members of a
+ 
+
+ align:start position:0%
+how to find all the uh members of a
+class. But you can um
+
+ align:start position:0%
+class. But you can um
+ 
+
+ align:start position:0%
+class. But you can um
+yeah and uh uh so there's one two three
+
+ align:start position:0%
+yeah and uh uh so there's one two three
+ 
+
+ align:start position:0%
+yeah and uh uh so there's one two three
+four five six classes and these are the
+
+ align:start position:0%
+four five six classes and these are the
+ 
+
+ align:start position:0%
+four five six classes and these are the
+irreducible representations and there's
+
+ align:start position:0%
+irreducible representations and there's
+ 
+
+ align:start position:0%
+irreducible representations and there's
+six of them. The character tables are
+
+ align:start position:0%
+six of them. The character tables are
+ 
+
+ align:start position:0%
+six of them. The character tables are
+always square when they're arranged
+
+ align:start position:0%
+always square when they're arranged
+ 
+
+ align:start position:0%
+always square when they're arranged
+according to classes. There's the same
+
+ align:start position:0%
+according to classes. There's the same
+ 
+
+ align:start position:0%
+according to classes. There's the same
+number of classes as there are
+
+ align:start position:0%
+number of classes as there are
+ 
+
+ align:start position:0%
+number of classes as there are
+irreducible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representations. Okay. Now uh the
+
+ align:start position:0%
+representations. Okay. Now uh the
+ 
+
+ align:start position:0%
+representations. Okay. Now uh the
+irreducible representations the
+
+ align:start position:0%
+irreducible representations the
+ 
+
+ align:start position:0%
+irreducible representations the
+characters for them are like a set of
+
+ align:start position:0%
+characters for them are like a set of
+ 
+
+ align:start position:0%
+characters for them are like a set of
+normal well not they're not normalized
+
+ align:start position:0%
+normal well not they're not normalized
+ 
+
+ align:start position:0%
+normal well not they're not normalized
+here but they're like uh they're
+
+ align:start position:0%
+here but they're like uh they're
+ 
+
+ align:start position:0%
+here but they're like uh they're
+orthogonal vectors and they are norm
+
+ align:start position:0%
+orthogonal vectors and they are norm
+ 
+
+ align:start position:0%
+orthogonal vectors and they are norm
+normalizable in the sense that if you
+
+ align:start position:0%
+normalizable in the sense that if you
+ 
+
+ align:start position:0%
+normalizable in the sense that if you
+recognize that each element appears the
+
+ align:start position:0%
+recognize that each element appears the
+ 
+
+ align:start position:0%
+recognize that each element appears the
+number times that there are members in a
+
+ align:start position:0%
+number times that there are members in a
+ 
+
+ align:start position:0%
+number times that there are members in a
+class and you divide by the order of the
+
+ align:start position:0%
+class and you divide by the order of the
+ 
+
+ align:start position:0%
+class and you divide by the order of the
+group then they are normalized.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, one can
+
+ align:start position:0%
+So, one can
+ 
+
+ align:start position:0%
+So, one can
+always generate a character table by
+
+ align:start position:0%
+always generate a character table by
+ 
+
+ align:start position:0%
+always generate a character table by
+knowing the dimension of the the uh
+
+ align:start position:0%
+knowing the dimension of the the uh
+ 
+
+ align:start position:0%
+knowing the dimension of the the uh
+um usually what you would do is you'd
+
+ align:start position:0%
+um usually what you would do is you'd
+ 
+
+ align:start position:0%
+um usually what you would do is you'd
+find out how many classes there are and
+
+ align:start position:0%
+find out how many classes there are and
+ 
+
+ align:start position:0%
+find out how many classes there are and
+then you say okay I need six I need that
+
+ align:start position:0%
+then you say okay I need six I need that
+ 
+
+ align:start position:0%
+then you say okay I need six I need that
+number of irreducible
+
+ align:start position:0%
+number of irreducible
+ 
+
+ align:start position:0%
+number of irreducible
+representations and uh uh it doesn't
+
+ align:start position:0%
+representations and uh uh it doesn't
+ 
+
+ align:start position:0%
+representations and uh uh it doesn't
+take much to recognize that you're going
+
+ align:start position:0%
+take much to recognize that you're going
+ 
+
+ align:start position:0%
+take much to recognize that you're going
+to have uh two doubly degenerate
+
+ align:start position:0%
+to have uh two doubly degenerate
+ 
+
+ align:start position:0%
+to have uh two doubly degenerate
+represent and so you and and you start
+
+ align:start position:0%
+represent and so you and and you start
+ 
+
+ align:start position:0%
+represent and so you and and you start
+with the totally symmetric guy and you
+
+ align:start position:0%
+with the totally symmetric guy and you
+ 
+
+ align:start position:0%
+with the totally symmetric guy and you
+write as many orthogonal vectors as you
+
+ align:start position:0%
+write as many orthogonal vectors as you
+ 
+
+ align:start position:0%
+write as many orthogonal vectors as you
+can knowing some rules and you could
+
+ align:start position:0%
+can knowing some rules and you could
+ 
+
+ align:start position:0%
+can knowing some rules and you could
+generate this and then after you've done
+
+ align:start position:0%
+generate this and then after you've done
+ 
+
+ align:start position:0%
+generate this and then after you've done
+that you say oh well now how do I put
+
+ align:start position:0%
+that you say oh well now how do I put
+ 
+
+ align:start position:0%
+that you say oh well now how do I put
+the different labels on these things
+
+ align:start position:0%
+the different labels on these things
+ 
+
+ align:start position:0%
+the different labels on these things
+what are the characteristic features
+
+ align:start position:0%
+what are the characteristic features
+ 
+
+ align:start position:0%
+what are the characteristic features
+that are associated with each label and
+
+ align:start position:0%
+that are associated with each label and
+ 
+
+ align:start position:0%
+that are associated with each label and
+u I thought I knew that uh until I
+
+ align:start position:0%
+u I thought I knew that uh until I
+ 
+
+ align:start position:0%
+u I thought I knew that uh until I
+discovered that uh uh my rule about C
+
+ align:start position:0%
+discovered that uh uh my rule about C
+ 
+
+ align:start position:0%
+discovered that uh uh my rule about C
+sigma V was wrong. Uh but
+
+ align:start position:0%
+sigma V was wrong. Uh but
+ 
+
+ align:start position:0%
+sigma V was wrong. Uh but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in addition to I mean you don't
+
+ align:start position:0%
+okay in addition to I mean you don't
+ 
+
+ align:start position:0%
+okay in addition to I mean you don't
+need to generate all of these uh
+
+ align:start position:0%
+need to generate all of these uh
+ 
+
+ align:start position:0%
+need to generate all of these uh
+characters because there there unless
+
+ align:start position:0%
+characters because there there unless
+ 
+
+ align:start position:0%
+characters because there there unless
+you're on a desert island and you don't
+
+ align:start position:0%
+you're on a desert island and you don't
+ 
+
+ align:start position:0%
+you're on a desert island and you don't
+have a book uh the character tables are
+
+ align:start position:0%
+have a book uh the character tables are
+ 
+
+ align:start position:0%
+have a book uh the character tables are
+ubiquitous. They're all they're
+
+ align:start position:0%
+ubiquitous. They're all they're
+ 
+
+ align:start position:0%
+ubiquitous. They're all they're
+everywhere. And uh uh so mostly what we
+
+ align:start position:0%
+everywhere. And uh uh so mostly what we
+ 
+
+ align:start position:0%
+everywhere. And uh uh so mostly what we
+want to do is know how to use these
+
+ align:start position:0%
+want to do is know how to use these
+ 
+
+ align:start position:0%
+want to do is know how to use these
+things. Okay. The character tables are
+
+ align:start position:0%
+things. Okay. The character tables are
+ 
+
+ align:start position:0%
+things. Okay. The character tables are
+dressed up with extra symbols in columns
+
+ align:start position:0%
+dressed up with extra symbols in columns
+ 
+
+ align:start position:0%
+dressed up with extra symbols in columns
+on the right and more over here. And
+
+ align:start position:0%
+on the right and more over here. And
+ 
+
+ align:start position:0%
+on the right and more over here. And
+these are what you need for describing
+
+ align:start position:0%
+these are what you need for describing
+ 
+
+ align:start position:0%
+these are what you need for describing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the uh selection rules for electric
+
+ align:start position:0%
+the uh selection rules for electric
+ 
+
+ align:start position:0%
+the uh selection rules for electric
+dipole transitions. And the thing that I
+
+ align:start position:0%
+dipole transitions. And the thing that I
+ 
+
+ align:start position:0%
+dipole transitions. And the thing that I
+didn't put over here are for ramen
+
+ align:start position:0%
+didn't put over here are for ramen
+ 
+
+ align:start position:0%
+didn't put over here are for ramen
+transitions. These are also uh things
+
+ align:start position:0%
+transitions. These are also uh things
+ 
+
+ align:start position:0%
+transitions. These are also uh things
+the uh x y and z tell you about p
+
+ align:start position:0%
+the uh x y and z tell you about p
+ 
+
+ align:start position:0%
+the uh x y and z tell you about p
+orbitals. These tell you about d
+
+ align:start position:0%
+orbitals. These tell you about d
+ 
+
+ align:start position:0%
+orbitals. These tell you about d
+orbitals. So there's all sorts of things
+
+ align:start position:0%
+orbitals. So there's all sorts of things
+ 
+
+ align:start position:0%
+orbitals. So there's all sorts of things
+that you can use these
+
+ align:start position:0%
+that you can use these
+ 
+
+ align:start position:0%
+that you can use these
+character tables for.
+
+ align:start position:0%
+character tables for.
+ 
+
+ align:start position:0%
+character tables for.
+Okay. So one of the first things we want
+
+ align:start position:0%
+Okay. So one of the first things we want
+ 
+
+ align:start position:0%
+Okay. So one of the first things we want
+to do is to
+
+ align:start position:0%
+to do is to
+ 
+
+ align:start position:0%
+to do is to
+discover how I mean suppose someone
+
+ align:start position:0%
+discover how I mean suppose someone
+ 
+
+ align:start position:0%
+discover how I mean suppose someone
+gives you a character table like this
+
+ align:start position:0%
+gives you a character table like this
+ 
+
+ align:start position:0%
+gives you a character table like this
+without these things. Uh to discover how
+
+ align:start position:0%
+without these things. Uh to discover how
+ 
+
+ align:start position:0%
+without these things. Uh to discover how
+rotations and translations what what do
+
+ align:start position:0%
+rotations and translations what what do
+ 
+
+ align:start position:0%
+rotations and translations what what do
+they correspond what character what
+
+ align:start position:0%
+they correspond what character what
+ 
+
+ align:start position:0%
+they correspond what character what
+irreducible representations do they
+
+ align:start position:0%
+irreducible representations do they
+ 
+
+ align:start position:0%
+irreducible representations do they
+correspond to? And so you always want to
+
+ align:start position:0%
+correspond to? And so you always want to
+ 
+
+ align:start position:0%
+correspond to? And so you always want to
+draw a
+
+ align:start position:0%
+draw a
+ 
+
+ align:start position:0%
+draw a
+cartoon and you want to know how to use
+
+ align:start position:0%
+cartoon and you want to know how to use
+ 
+
+ align:start position:0%
+cartoon and you want to know how to use
+these cartoons. And uh this is true for
+
+ align:start position:0%
+these cartoons. And uh this is true for
+ 
+
+ align:start position:0%
+these cartoons. And uh this is true for
+CNPI group theory as well as point group
+
+ align:start position:0%
+CNPI group theory as well as point group
+ 
+
+ align:start position:0%
+CNPI group theory as well as point group
+theory. And there are some very
+
+ align:start position:0%
+theory. And there are some very
+ 
+
+ align:start position:0%
+theory. And there are some very
+beautiful uh uh cartoons uh for
+
+ align:start position:0%
+beautiful uh uh cartoons uh for
+ 
+
+ align:start position:0%
+beautiful uh uh cartoons uh for
+classifying uh
+
+ align:start position:0%
+classifying uh
+ 
+
+ align:start position:0%
+classifying uh
+uh uh things according to irreducible
+
+ align:start position:0%
+uh uh things according to irreducible
+ 
+
+ align:start position:0%
+uh uh things according to irreducible
+representation in Bunker and Jensen. But
+
+ align:start position:0%
+representation in Bunker and Jensen. But
+ 
+
+ align:start position:0%
+representation in Bunker and Jensen. But
+I mean
+
+ align:start position:0%
+I mean
+ 
+
+ align:start position:0%
+I mean
+suppose we have an axis
+
+ align:start position:0%
+suppose we have an axis
+ 
+
+ align:start position:0%
+suppose we have an axis
+system x y
+
+ align:start position:0%
+system x y
+ 
+
+ align:start position:0%
+system x y
+z and uh uh we would like to uh so here
+
+ align:start position:0%
+z and uh uh we would like to uh so here
+ 
+
+ align:start position:0%
+z and uh uh we would like to uh so here
+we have a vector uh pointing in the in
+
+ align:start position:0%
+we have a vector uh pointing in the in
+ 
+
+ align:start position:0%
+we have a vector uh pointing in the in
+the z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction and uh so we'd like to know
+
+ align:start position:0%
+direction and uh so we'd like to know
+ 
+
+ align:start position:0%
+direction and uh so we'd like to know
+what the various symmetry operations do
+
+ align:start position:0%
+what the various symmetry operations do
+ 
+
+ align:start position:0%
+what the various symmetry operations do
+to a vector pointing in the Z direction.
+
+ align:start position:0%
+to a vector pointing in the Z direction.
+ 
+
+ align:start position:0%
+to a vector pointing in the Z direction.
+And so the first thing is the identity
+
+ align:start position:0%
+And so the first thing is the identity
+ 
+
+ align:start position:0%
+And so the first thing is the identity
+operation leaves it alone. A
+
+ align:start position:0%
+operation leaves it alone. A
+ 
+
+ align:start position:0%
+operation leaves it alone. A
+rotation by
+
+ align:start position:0%
+rotation by
+ 
+
+ align:start position:0%
+rotation by
+uh um about the the Z-axis leaves
+
+ align:start position:0%
+uh um about the the Z-axis leaves
+ 
+
+ align:start position:0%
+uh um about the the Z-axis leaves
+alone. It's still pointing I mean
+
+ align:start position:0%
+alone. It's still pointing I mean
+ 
+
+ align:start position:0%
+alone. It's still pointing I mean
+uh so the issue would be is it pointing
+
+ align:start position:0%
+uh so the issue would be is it pointing
+ 
+
+ align:start position:0%
+uh so the issue would be is it pointing
+this way, that way or this way. And so
+
+ align:start position:0%
+this way, that way or this way. And so
+ 
+
+ align:start position:0%
+this way, that way or this way. And so
+that you could have uh all right so C2
+
+ align:start position:0%
+that you could have uh all right so C2
+ 
+
+ align:start position:0%
+that you could have uh all right so C2
+perpendicular to the symmetry axis well
+
+ align:start position:0%
+perpendicular to the symmetry axis well
+ 
+
+ align:start position:0%
+perpendicular to the symmetry axis well
+that turns it over so that's minus one
+
+ align:start position:0%
+that turns it over so that's minus one
+ 
+
+ align:start position:0%
+that turns it over so that's minus one
+uh sigma h well that that's a reflection
+
+ align:start position:0%
+uh sigma h well that that's a reflection
+ 
+
+ align:start position:0%
+uh sigma h well that that's a reflection
+in this plane that turns it over minus
+
+ align:start position:0%
+in this plane that turns it over minus
+ 
+
+ align:start position:0%
+in this plane that turns it over minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh s3 well that leaves it alone for the
+
+ align:start position:0%
+uh s3 well that leaves it alone for the
+ 
+
+ align:start position:0%
+uh s3 well that leaves it alone for the
+rotation part and turns it over for the
+
+ align:start position:0%
+rotation part and turns it over for the
+ 
+
+ align:start position:0%
+rotation part and turns it over for the
+other part and sigma v that's a
+
+ align:start position:0%
+other part and sigma v that's a
+ 
+
+ align:start position:0%
+other part and sigma v that's a
+reflection
+
+ align:start position:0%
+reflection
+ 
+
+ align:start position:0%
+reflection
+in a plane containing the z-axis that
+
+ align:start position:0%
+in a plane containing the z-axis that
+ 
+
+ align:start position:0%
+in a plane containing the z-axis that
+leaves it alone. So here are the six uh
+
+ align:start position:0%
+leaves it alone. So here are the six uh
+ 
+
+ align:start position:0%
+leaves it alone. So here are the six uh
+things that happens to a translation in
+
+ align:start position:0%
+things that happens to a translation in
+ 
+
+ align:start position:0%
+things that happens to a translation in
+the Z direction. And so we look for an
+
+ align:start position:0%
+the Z direction. And so we look for an
+ 
+
+ align:start position:0%
+the Z direction. And so we look for an
+irreducible representation that uh
+
+ align:start position:0%
+irreducible representation that uh
+ 
+
+ align:start position:0%
+irreducible representation that uh
+behaves that way. And uh it's not that
+
+ align:start position:0%
+behaves that way. And uh it's not that
+ 
+
+ align:start position:0%
+behaves that way. And uh it's not that
+one. It must
+
+ align:start position:0%
+one. It must
+ 
+
+ align:start position:0%
+one. It must
+be one
+
+ align:start position:0%
+be one
+ 
+
+ align:start position:0%
+be one
+one this one a2 double prime. And
+
+ align:start position:0%
+one this one a2 double prime. And
+ 
+
+ align:start position:0%
+one this one a2 double prime. And
+uh and that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. And so I suggest that you uh do
+
+ align:start position:0%
+right. And so I suggest that you uh do
+ 
+
+ align:start position:0%
+right. And so I suggest that you uh do
+the same thing for a vector pointing in
+
+ align:start position:0%
+the same thing for a vector pointing in
+ 
+
+ align:start position:0%
+the same thing for a vector pointing in
+that direction and see how that behaves.
+
+ align:start position:0%
+that direction and see how that behaves.
+ 
+
+ align:start position:0%
+that direction and see how that behaves.
+And what you end up discovering is if
+
+ align:start position:0%
+And what you end up discovering is if
+ 
+
+ align:start position:0%
+And what you end up discovering is if
+you have a vector pointing in the x
+
+ align:start position:0%
+you have a vector pointing in the x
+ 
+
+ align:start position:0%
+you have a vector pointing in the x
+direction, it gets mixed with a vector
+
+ align:start position:0%
+direction, it gets mixed with a vector
+ 
+
+ align:start position:0%
+direction, it gets mixed with a vector
+pointing in the y direction. And uh you
+
+ align:start position:0%
+pointing in the y direction. And uh you
+ 
+
+ align:start position:0%
+pointing in the y direction. And uh you
+find that xy together behave as e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime. So then there's rotations.
+
+ align:start position:0%
+prime. So then there's rotations.
+ 
+
+ align:start position:0%
+prime. So then there's rotations.
+Suppose we have a
+
+ align:start position:0%
+Suppose we have a
+ 
+
+ align:start position:0%
+Suppose we have a
+rotation about the
+
+ align:start position:0%
+rotation about the
+ 
+
+ align:start position:0%
+rotation about the
+Z-axis. And now we ask, well, what do
+
+ align:start position:0%
+Z-axis. And now we ask, well, what do
+ 
+
+ align:start position:0%
+Z-axis. And now we ask, well, what do
+the various symmetry operations do to
+
+ align:start position:0%
+the various symmetry operations do to
+ 
+
+ align:start position:0%
+the various symmetry operations do to
+that that uh object? And
+
+ align:start position:0%
+that that uh object? And
+ 
+
+ align:start position:0%
+that that uh object? And
+so a rotation the identity does nothing.
+
+ align:start position:0%
+so a rotation the identity does nothing.
+ 
+
+ align:start position:0%
+so a rotation the identity does nothing.
+Uh C3 does nothing.
+
+ align:start position:0%
+Uh C3 does nothing.
+ 
+
+ align:start position:0%
+Uh C3 does nothing.
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh C2
+
+ align:start position:0%
+uh C2
+ 
+
+ align:start position:0%
+uh C2
+perpendicular. Well, that's going to uh
+
+ align:start position:0%
+perpendicular. Well, that's going to uh
+ 
+
+ align:start position:0%
+perpendicular. Well, that's going to uh
+uh take now this is harder for hard for
+
+ align:start position:0%
+uh take now this is harder for hard for
+ 
+
+ align:start position:0%
+uh take now this is harder for hard for
+me to see.
+
+ align:start position:0%
+me to see.
+ 
+
+ align:start position:0%
+me to see.
+Uh it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will reverses it and uh uh so you have
+
+ align:start position:0%
+will reverses it and uh uh so you have
+ 
+
+ align:start position:0%
+will reverses it and uh uh so you have
+to practice a little bit. So you do this
+
+ align:start position:0%
+to practice a little bit. So you do this
+ 
+
+ align:start position:0%
+to practice a little bit. So you do this
+and you discover that the rotation about
+
+ align:start position:0%
+and you discover that the rotation about
+ 
+
+ align:start position:0%
+and you discover that the rotation about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+z-axis g belongs to a2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime. And so
+
+ align:start position:0%
+prime. And so
+ 
+
+ align:start position:0%
+prime. And so
+uh you you can uh uh dress up the
+
+ align:start position:0%
+uh you you can uh uh dress up the
+ 
+
+ align:start position:0%
+uh you you can uh uh dress up the
+character table with these symbols which
+
+ align:start position:0%
+character table with these symbols which
+ 
+
+ align:start position:0%
+character table with these symbols which
+are useful for telling you about
+
+ align:start position:0%
+are useful for telling you about
+ 
+
+ align:start position:0%
+are useful for telling you about
+uh selection rules.
+
+ align:start position:0%
+uh selection rules.
+ 
+
+ align:start position:0%
+uh selection rules.
+um and we'll see how that works out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, one of the things you're going
+
+ align:start position:0%
+Okay. So, one of the things you're going
+ 
+
+ align:start position:0%
+Okay. So, one of the things you're going
+to want to do
+
+ align:start position:0%
+to want to do
+ 
+
+ align:start position:0%
+to want to do
+is compute the character of a direct
+
+ align:start position:0%
+is compute the character of a direct
+ 
+
+ align:start position:0%
+is compute the character of a direct
+product of two characters. So, we have a
+
+ align:start position:0%
+product of two characters. So, we have a
+ 
+
+ align:start position:0%
+product of two characters. So, we have a
+character for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so what do you do?
+
+ align:start position:0%
+uh so what do you do?
+ 
+
+ align:start position:0%
+uh so what do you do?
+uh you just multiply element by element
+
+ align:start position:0%
+uh you just multiply element by element
+ 
+
+ align:start position:0%
+uh you just multiply element by element
+and get a new vector
+
+ align:start position:0%
+and get a new vector
+ 
+
+ align:start position:0%
+and get a new vector
+uh and uh so for example if we did E
+
+ align:start position:0%
+uh and uh so for example if we did E
+ 
+
+ align:start position:0%
+uh and uh so for example if we did E
+prime times uh EP
+
+ align:start position:0%
+prime times uh EP
+ 
+
+ align:start position:0%
+prime times uh EP
+prime what are we going to get well
+
+ align:start position:0%
+prime what are we going to get well
+ 
+
+ align:start position:0%
+prime what are we going to get well
+we're going to get four in the first
+
+ align:start position:0%
+we're going to get four in the first
+ 
+
+ align:start position:0%
+we're going to get four in the first
+position and then lots of other stuff
+
+ align:start position:0%
+position and then lots of other stuff
+ 
+
+ align:start position:0%
+position and then lots of other stuff
+and one of the things you know is that
+
+ align:start position:0%
+and one of the things you know is that
+ 
+
+ align:start position:0%
+and one of the things you know is that
+prime times double-p prime is double
+
+ align:start position:0%
+prime times double-p prime is double
+ 
+
+ align:start position:0%
+prime times double-p prime is double
+prime and 1 * uh 2 is 2 and uh so there
+
+ align:start position:0%
+prime and 1 * uh 2 is 2 and uh so there
+ 
+
+ align:start position:0%
+prime and 1 * uh 2 is 2 and uh so there
+are a lot of things a * b is b and uh uh
+
+ align:start position:0%
+are a lot of things a * b is b and uh uh
+ 
+
+ align:start position:0%
+are a lot of things a * b is b and uh uh
+g * u is u and so uh you know
+
+ align:start position:0%
+g * u is u and so uh you know
+ 
+
+ align:start position:0%
+g * u is u and so uh you know
+immediately that this is going to be is
+
+ align:start position:0%
+immediately that this is going to be is
+ 
+
+ align:start position:0%
+immediately that this is going to be is
+going to consist of nothing but uh
+
+ align:start position:0%
+going to consist of nothing but uh
+ 
+
+ align:start position:0%
+going to consist of nothing but uh
+irreducible representations that are
+
+ align:start position:0%
+irreducible representations that are
+ 
+
+ align:start position:0%
+irreducible representations that are
+double
+
+ align:start position:0%
+double
+ 
+
+ align:start position:0%
+double
+prime and uh uh and so on. Okay, so you
+
+ align:start position:0%
+prime and uh uh and so on. Okay, so you
+ 
+
+ align:start position:0%
+prime and uh uh and so on. Okay, so you
+do this out and you get 4 1 0 -4 -1
+
+ align:start position:0%
+do this out and you get 4 1 0 -4 -1
+ 
+
+ align:start position:0%
+do this out and you get 4 1 0 -4 -1
+0. Okay, so now we've taken uh a direct
+
+ align:start position:0%
+0. Okay, so now we've taken uh a direct
+ 
+
+ align:start position:0%
+0. Okay, so now we've taken uh a direct
+product of two e representations and we
+
+ align:start position:0%
+product of two e representations and we
+ 
+
+ align:start position:0%
+product of two e representations and we
+have something that has four in the
+
+ align:start position:0%
+have something that has four in the
+ 
+
+ align:start position:0%
+have something that has four in the
+first position. This is reducible
+
+ align:start position:0%
+first position. This is reducible
+ 
+
+ align:start position:0%
+first position. This is reducible
+because the highest order uh irreducible
+
+ align:start position:0%
+because the highest order uh irreducible
+ 
+
+ align:start position:0%
+because the highest order uh irreducible
+representations are of order two. So we
+
+ align:start position:0%
+representations are of order two. So we
+ 
+
+ align:start position:0%
+representations are of order two. So we
+know that we have to take this apart
+
+ align:start position:0%
+know that we have to take this apart
+ 
+
+ align:start position:0%
+know that we have to take this apart
+into different irreducible
+
+ align:start position:0%
+into different irreducible
+ 
+
+ align:start position:0%
+into different irreducible
+representations. And what do we do?
+
+ align:start position:0%
+representations. And what do we do?
+ 
+
+ align:start position:0%
+representations. And what do we do?
+Well, we ask, well, how does this vector
+
+ align:start position:0%
+Well, we ask, well, how does this vector
+ 
+
+ align:start position:0%
+Well, we ask, well, how does this vector
+project or how do each of these vectors
+
+ align:start position:0%
+project or how do each of these vectors
+ 
+
+ align:start position:0%
+project or how do each of these vectors
+project on
+
+ align:start position:0%
+project on
+ 
+
+ align:start position:0%
+project on
+this? And again, this is where you make
+
+ align:start position:0%
+this? And again, this is where you make
+ 
+
+ align:start position:0%
+this? And again, this is where you make
+the mistake. You have to remember that
+
+ align:start position:0%
+the mistake. You have to remember that
+ 
+
+ align:start position:0%
+the mistake. You have to remember that
+we're we we're describing vectors that
+
+ align:start position:0%
+we're we we're describing vectors that
+ 
+
+ align:start position:0%
+we're we we're describing vectors that
+are associated with one thing for each
+
+ align:start position:0%
+are associated with one thing for each
+ 
+
+ align:start position:0%
+are associated with one thing for each
+symmetry operation, but we've condensed
+
+ align:start position:0%
+symmetry operation, but we've condensed
+ 
+
+ align:start position:0%
+symmetry operation, but we've condensed
+them according to classes. And so when
+
+ align:start position:0%
+them according to classes. And so when
+ 
+
+ align:start position:0%
+them according to classes. And so when
+you when you attempt to reduce this, you
+
+ align:start position:0%
+you when you attempt to reduce this, you
+ 
+
+ align:start position:0%
+you when you attempt to reduce this, you
+have to multiply
+
+ align:start position:0%
+have to multiply
+ 
+
+ align:start position:0%
+have to multiply
+uh the uh by the number of elements in a
+
+ align:start position:0%
+uh the uh by the number of elements in a
+ 
+
+ align:start position:0%
+uh the uh by the number of elements in a
+class.
+
+ align:start position:0%
+class.
+ 
+
+ align:start position:0%
+class.
+So I've done the reduction and uh so you
+
+ align:start position:0%
+So I've done the reduction and uh so you
+ 
+
+ align:start position:0%
+So I've done the reduction and uh so you
+discover that this gives rise to
+
+ align:start position:0%
+discover that this gives rise to
+ 
+
+ align:start position:0%
+discover that this gives rise to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+e I can't even read what's in my notes.
+
+ align:start position:0%
+e I can't even read what's in my notes.
+ 
+
+ align:start position:0%
+e I can't even read what's in my notes.
+Is that a prime or a double prime? That
+
+ align:start position:0%
+Is that a prime or a double prime? That
+ 
+
+ align:start position:0%
+Is that a prime or a double prime? That
+looks like a double prime. It has to be
+
+ align:start position:0%
+looks like a double prime. It has to be
+ 
+
+ align:start position:0%
+looks like a double prime. It has to be
+a d. I said it was going to be a double
+
+ align:start position:0%
+a d. I said it was going to be a double
+ 
+
+ align:start position:0%
+a d. I said it was going to be a double
+prime. E double prime and a one double
+
+ align:start position:0%
+prime. E double prime and a one double
+ 
+
+ align:start position:0%
+prime. E double prime and a one double
+prime and
+
+ align:start position:0%
+prime and
+ 
+
+ align:start position:0%
+prime and
+a two double prime. So I mean one way to
+
+ align:start position:0%
+a two double prime. So I mean one way to
+ 
+
+ align:start position:0%
+a two double prime. So I mean one way to
+do this is you multiply this reducible
+
+ align:start position:0%
+do this is you multiply this reducible
+ 
+
+ align:start position:0%
+do this is you multiply this reducible
+character by each of these. But if you
+
+ align:start position:0%
+character by each of these. But if you
+ 
+
+ align:start position:0%
+character by each of these. But if you
+have some shortcuts, you don't have to
+
+ align:start position:0%
+have some shortcuts, you don't have to
+ 
+
+ align:start position:0%
+have some shortcuts, you don't have to
+do each of them. You just do the ones
+
+ align:start position:0%
+do each of them. You just do the ones
+ 
+
+ align:start position:0%
+do each of them. You just do the ones
+that you think are going to be
+
+ align:start position:0%
+that you think are going to be
+ 
+
+ align:start position:0%
+that you think are going to be
+important. And so this didn't require
+
+ align:start position:0%
+important. And so this didn't require
+ 
+
+ align:start position:0%
+important. And so this didn't require
+six uh direct products. You could have
+
+ align:start position:0%
+six uh direct products. You could have
+ 
+
+ align:start position:0%
+six uh direct products. You could have
+gotten it very quickly just with three
+
+ align:start position:0%
+gotten it very quickly just with three
+ 
+
+ align:start position:0%
+gotten it very quickly just with three
+and in fact you could have gotten it
+
+ align:start position:0%
+and in fact you could have gotten it
+ 
+
+ align:start position:0%
+and in fact you could have gotten it
+with two because then you would know
+
+ align:start position:0%
+with two because then you would know
+ 
+
+ align:start position:0%
+with two because then you would know
+whether there's something left
+
+ align:start position:0%
+whether there's something left
+ 
+
+ align:start position:0%
+whether there's something left
+over. So anyway this is this is the main
+
+ align:start position:0%
+over. So anyway this is this is the main
+ 
+
+ align:start position:0%
+over. So anyway this is this is the main
+thing you get a reducible representation
+
+ align:start position:0%
+thing you get a reducible representation
+ 
+
+ align:start position:0%
+thing you get a reducible representation
+and you and you reduce it and there all
+
+ align:start position:0%
+and you and you reduce it and there all
+ 
+
+ align:start position:0%
+and you and you reduce it and there all
+it happens again and again in various
+
+ align:start position:0%
+it happens again and again in various
+ 
+
+ align:start position:0%
+it happens again and again in various
+applications. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, and this
+
+ align:start position:0%
+So, and this
+ 
+
+ align:start position:0%
+So, and this
+is this is one of the things that I
+
+ align:start position:0%
+is this is one of the things that I
+ 
+
+ align:start position:0%
+is this is one of the things that I
+really love about group theory. Uh
+
+ align:start position:0%
+really love about group theory. Uh
+ 
+
+ align:start position:0%
+really love about group theory. Uh
+dressing up a molecule with
+
+ align:start position:0%
+dressing up a molecule with
+ 
+
+ align:start position:0%
+dressing up a molecule with
+uh things that represent the internal
+
+ align:start position:0%
+uh things that represent the internal
+ 
+
+ align:start position:0%
+uh things that represent the internal
+coordinates or anything you want and
+
+ align:start position:0%
+coordinates or anything you want and
+ 
+
+ align:start position:0%
+coordinates or anything you want and
+finding which irreducible
+
+ align:start position:0%
+finding which irreducible
+ 
+
+ align:start position:0%
+finding which irreducible
+representations do the things you picked
+
+ align:start position:0%
+representations do the things you picked
+ 
+
+ align:start position:0%
+representations do the things you picked
+out span. And so you can you can be so
+
+ align:start position:0%
+out span. And so you can you can be so
+ 
+
+ align:start position:0%
+out span. And so you can you can be so
+suppose we have a molecule which is a D3
+
+ align:start position:0%
+suppose we have a molecule which is a D3
+ 
+
+ align:start position:0%
+suppose we have a molecule which is a D3
+molecule that's planer and symmetric and
+
+ align:start position:0%
+molecule that's planer and symmetric and
+ 
+
+ align:start position:0%
+molecule that's planer and symmetric and
+so boron triricchloride is the the
+
+ align:start position:0%
+so boron triricchloride is the the
+ 
+
+ align:start position:0%
+so boron triricchloride is the the
+molecule that everybody talks about but
+
+ align:start position:0%
+molecule that everybody talks about but
+ 
+
+ align:start position:0%
+molecule that everybody talks about but
+uh CO3 double minus is the same thing
+
+ align:start position:0%
+uh CO3 double minus is the same thing
+ 
+
+ align:start position:0%
+uh CO3 double minus is the same thing
+any you know there's there's a bunch of
+
+ align:start position:0%
+any you know there's there's a bunch of
+ 
+
+ align:start position:0%
+any you know there's there's a bunch of
+these molecules and so one of the things
+
+ align:start position:0%
+these molecules and so one of the things
+ 
+
+ align:start position:0%
+these molecules and so one of the things
+you can do is attach XYZ Z
+
+ align:start position:0%
+you can do is attach XYZ Z
+ 
+
+ align:start position:0%
+you can do is attach XYZ Z
+coordinates to each of the atoms. So we
+
+ align:start position:0%
+coordinates to each of the atoms. So we
+ 
+
+ align:start position:0%
+coordinates to each of the atoms. So we
+have we have four atoms. So we have four
+
+ align:start position:0%
+have we have four atoms. So we have four
+ 
+
+ align:start position:0%
+have we have four atoms. So we have four
+* 3 uh um uh cartisian
+
+ align:start position:0%
+* 3 uh um uh cartisian
+ 
+
+ align:start position:0%
+* 3 uh um uh cartisian
+coordinates. So we're we're going to get
+
+ align:start position:0%
+coordinates. So we're we're going to get
+ 
+
+ align:start position:0%
+coordinates. So we're we're going to get
+a 12dimensional irreducible
+
+ align:start position:0%
+a 12dimensional irreducible
+ 
+
+ align:start position:0%
+a 12dimensional irreducible
+representation reducible representation
+
+ align:start position:0%
+representation reducible representation
+ 
+
+ align:start position:0%
+representation reducible representation
+by just uh applying each of the symmetry
+
+ align:start position:0%
+by just uh applying each of the symmetry
+ 
+
+ align:start position:0%
+by just uh applying each of the symmetry
+operations to these cartisian
+
+ align:start position:0%
+operations to these cartisian
+ 
+
+ align:start position:0%
+operations to these cartisian
+coordinates.
+
+ align:start position:0%
+coordinates.
+ 
+
+ align:start position:0%
+coordinates.
+And so you got 12 coordinates and you do
+
+ align:start position:0%
+And so you got 12 coordinates and you do
+ 
+
+ align:start position:0%
+And so you got 12 coordinates and you do
+nothing. Uh you ask well how many have
+
+ align:start position:0%
+nothing. Uh you ask well how many have
+ 
+
+ align:start position:0%
+nothing. Uh you ask well how many have
+been you
+
+ align:start position:0%
+been you
+ 
+
+ align:start position:0%
+been you
+know everything is left alone. The the
+
+ align:start position:0%
+know everything is left alone. The the
+ 
+
+ align:start position:0%
+know everything is left alone. The the
+matrix that did that was a matrix which
+
+ align:start position:0%
+matrix that did that was a matrix which
+ 
+
+ align:start position:0%
+matrix that did that was a matrix which
+has ones along the diagonal and traces
+
+ align:start position:0%
+has ones along the diagonal and traces
+ 
+
+ align:start position:0%
+has ones along the diagonal and traces
+12.
+
+ align:start position:0%
+12.
+ 
+
+ align:start position:0%
+12.
+Uh the next thing is C3 and C3
+
+ align:start position:0%
+Uh the next thing is C3 and C3
+ 
+
+ align:start position:0%
+Uh the next thing is C3 and C3
+perpendicular to plane permutes the
+
+ align:start position:0%
+perpendicular to plane permutes the
+ 
+
+ align:start position:0%
+perpendicular to plane permutes the
+uh the end
+
+ align:start position:0%
+uh the end
+ 
+
+ align:start position:0%
+uh the end
+atoms and so you don't care about that.
+
+ align:start position:0%
+atoms and so you don't care about that.
+ 
+
+ align:start position:0%
+atoms and so you don't care about that.
+So this is so easy you know you the only
+
+ align:start position:0%
+So this is so easy you know you the only
+ 
+
+ align:start position:0%
+So this is so easy you know you the only
+thing you worry about is what happens
+
+ align:start position:0%
+thing you worry about is what happens
+ 
+
+ align:start position:0%
+thing you worry about is what happens
+when you do a C3 for the atom that the
+
+ align:start position:0%
+when you do a C3 for the atom that the
+ 
+
+ align:start position:0%
+when you do a C3 for the atom that the
+C3 axis goes through. And there's a
+
+ align:start position:0%
+C3 axis goes through. And there's a
+ 
+
+ align:start position:0%
+C3 axis goes through. And there's a
+little trigonometry involved and uh uh
+
+ align:start position:0%
+little trigonometry involved and uh uh
+ 
+
+ align:start position:0%
+little trigonometry involved and uh uh
+you discover that that has a trace of
+
+ align:start position:0%
+you discover that that has a trace of
+ 
+
+ align:start position:0%
+you discover that that has a trace of
+zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, and then uh C2 perpendicular uh and
+
+ align:start position:0%
+So, and then uh C2 perpendicular uh and
+ 
+
+ align:start position:0%
+So, and then uh C2 perpendicular uh and
+there's u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there's three perpendicular C2s. And
+
+ align:start position:0%
+uh there's three perpendicular C2s. And
+ 
+
+ align:start position:0%
+uh there's three perpendicular C2s. And
+so those are a C2
+
+ align:start position:0%
+so those are a C2
+ 
+
+ align:start position:0%
+so those are a C2
+uh that contains each of the atoms.
+
+ align:start position:0%
+uh that contains each of the atoms.
+ 
+
+ align:start position:0%
+uh that contains each of the atoms.
+These are permuted. And so they're gone.
+
+ align:start position:0%
+These are permuted. And so they're gone.
+ 
+
+ align:start position:0%
+These are permuted. And so they're gone.
+And now uh the what happens when you
+
+ align:start position:0%
+And now uh the what happens when you
+ 
+
+ align:start position:0%
+And now uh the what happens when you
+rotate about this axis is you take uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you leave one of the coordinates
+
+ align:start position:0%
+um you leave one of the coordinates
+ 
+
+ align:start position:0%
+um you leave one of the coordinates
+alone and you reverse the direction of
+
+ align:start position:0%
+alone and you reverse the direction of
+ 
+
+ align:start position:0%
+alone and you reverse the direction of
+the other two. And so the trace for each
+
+ align:start position:0%
+the other two. And so the trace for each
+ 
+
+ align:start position:0%
+the other two. And so the trace for each
+of these is minus1. And so we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus2. And uh so sigma h sigma h
+
+ align:start position:0%
+minus2. And uh so sigma h sigma h
+ 
+
+ align:start position:0%
+minus2. And uh so sigma h sigma h
+everybody is involved nobody gets goes
+
+ align:start position:0%
+everybody is involved nobody gets goes
+ 
+
+ align:start position:0%
+everybody is involved nobody gets goes
+away but two of the axes are in the
+
+ align:start position:0%
+away but two of the axes are in the
+ 
+
+ align:start position:0%
+away but two of the axes are in the
+plane and one is perpendicular and so 2
+
+ align:start position:0%
+plane and one is perpendicular and so 2
+ 
+
+ align:start position:0%
+plane and one is perpendicular and so 2
+- one for each atom 2 - 1 * 4 is
+
+ align:start position:0%
+- one for each atom 2 - 1 * 4 is
+ 
+
+ align:start position:0%
+- one for each atom 2 - 1 * 4 is
+four and so
+
+ align:start position:0%
+four and so
+ 
+
+ align:start position:0%
+four and so
+on. So you you generate this reducible
+
+ align:start position:0%
+on. So you you generate this reducible
+ 
+
+ align:start position:0%
+on. So you you generate this reducible
+representation that contains everything
+
+ align:start position:0%
+representation that contains everything
+ 
+
+ align:start position:0%
+representation that contains everything
+that this molecule can do which will be
+
+ align:start position:0%
+that this molecule can do which will be
+ 
+
+ align:start position:0%
+that this molecule can do which will be
+3 n minus 6
+
+ align:start position:0%
+3 n minus 6
+ 
+
+ align:start position:0%
+3 n minus 6
+vibrations, three translations and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotations. Well, we got three
+
+ align:start position:0%
+rotations. Well, we got three
+ 
+
+ align:start position:0%
+rotations. Well, we got three
+translations and three rotations here.
+
+ align:start position:0%
+translations and three rotations here.
+ 
+
+ align:start position:0%
+translations and three rotations here.
+And so what we do is we reduce this and
+
+ align:start position:0%
+And so what we do is we reduce this and
+ 
+
+ align:start position:0%
+And so what we do is we reduce this and
+that gives us all of the reducible rep
+
+ align:start position:0%
+that gives us all of the reducible rep
+ 
+
+ align:start position:0%
+that gives us all of the reducible rep
+irreducible representation spanned by
+
+ align:start position:0%
+irreducible representation spanned by
+ 
+
+ align:start position:0%
+irreducible representation spanned by
+this cartisian representation.
+
+ align:start position:0%
+this cartisian representation.
+ 
+
+ align:start position:0%
+this cartisian representation.
+and then we
+
+ align:start position:0%
+and then we
+ 
+
+ align:start position:0%
+and then we
+remove uh the ones that we have to
+
+ align:start position:0%
+remove uh the ones that we have to
+ 
+
+ align:start position:0%
+remove uh the ones that we have to
+because those aren't vibrations and
+
+ align:start position:0%
+because those aren't vibrations and
+ 
+
+ align:start position:0%
+because those aren't vibrations and
+we're left with something else.
+
+ align:start position:0%
+we're left with something else.
+ 
+
+ align:start position:0%
+we're left with something else.
+So we can determine very quickly that
+
+ align:start position:0%
+So we can determine very quickly that
+ 
+
+ align:start position:0%
+So we can determine very quickly that
+the vibrations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+generate
+
+ align:start position:0%
+generate
+ 
+
+ align:start position:0%
+generate
+uh the a one
+
+ align:start position:0%
+uh the a one
+ 
+
+ align:start position:0%
+uh the a one
+prime two e prime and uh one a two
+
+ align:start position:0%
+prime two e prime and uh one a two
+ 
+
+ align:start position:0%
+prime two e prime and uh one a two
+double prime. Okay, that's four, five,
+
+ align:start position:0%
+double prime. Okay, that's four, five,
+ 
+
+ align:start position:0%
+double prime. Okay, that's four, five,
+six, the right number of uh degrees of
+
+ align:start position:0%
+six, the right number of uh degrees of
+ 
+
+ align:start position:0%
+six, the right number of uh degrees of
+freedom.
+
+ align:start position:0%
+freedom.
+ 
+
+ align:start position:0%
+freedom.
+So this D3 molecule gives rise to a
+
+ align:start position:0%
+So this D3 molecule gives rise to a
+ 
+
+ align:start position:0%
+So this D3 molecule gives rise to a
+total of four normal
+
+ align:start position:0%
+total of four normal
+ 
+
+ align:start position:0%
+total of four normal
+modes. The generacy is is six the but
+
+ align:start position:0%
+modes. The generacy is is six the but
+ 
+
+ align:start position:0%
+modes. The generacy is is six the but
+they're only
+
+ align:start position:0%
+they're only
+ 
+
+ align:start position:0%
+they're only
+four and not uh not six. And uh it might
+
+ align:start position:0%
+four and not uh not six. And uh it might
+ 
+
+ align:start position:0%
+four and not uh not six. And uh it might
+be a useful question to ask well can we
+
+ align:start position:0%
+be a useful question to ask well can we
+ 
+
+ align:start position:0%
+be a useful question to ask well can we
+distinguish between stretches and bends
+
+ align:start position:0%
+distinguish between stretches and bends
+ 
+
+ align:start position:0%
+distinguish between stretches and bends
+or can we uh uh divide this up in some
+
+ align:start position:0%
+or can we uh uh divide this up in some
+ 
+
+ align:start position:0%
+or can we uh uh divide this up in some
+uh useful way. So we could take a
+
+ align:start position:0%
+uh useful way. So we could take a
+ 
+
+ align:start position:0%
+uh useful way. So we could take a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+representation and just say okay what
+
+ align:start position:0%
+representation and just say okay what
+ 
+
+ align:start position:0%
+representation and just say okay what
+about that? What about the
+
+ align:start position:0%
+about that? What about the
+ 
+
+ align:start position:0%
+about that? What about the
+stretches and what did the group theory
+
+ align:start position:0%
+stretches and what did the group theory
+ 
+
+ align:start position:0%
+stretches and what did the group theory
+do for this
+
+ align:start position:0%
+do for this
+ 
+
+ align:start position:0%
+do for this
+three-dimensional reducible
+
+ align:start position:0%
+three-dimensional reducible
+ 
+
+ align:start position:0%
+three-dimensional reducible
+representation? What what did you do
+
+ align:start position:0%
+representation? What what did you do
+ 
+
+ align:start position:0%
+representation? What what did you do
+with your razor? I I took away the
+
+ align:start position:0%
+with your razor? I I took away the
+ 
+
+ align:start position:0%
+with your razor? I I took away the
+cartisian axes and instead of having 12
+
+ align:start position:0%
+cartisian axes and instead of having 12
+ 
+
+ align:start position:0%
+cartisian axes and instead of having 12
+things that we're we're messing with now
+
+ align:start position:0%
+things that we're we're messing with now
+ 
+
+ align:start position:0%
+things that we're we're messing with now
+we have three things. Or I could also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say three. Now these are not linearly
+
+ align:start position:0%
+say three. Now these are not linearly
+ 
+
+ align:start position:0%
+say three. Now these are not linearly
+independent but you know that they can't
+
+ align:start position:0%
+independent but you know that they can't
+ 
+
+ align:start position:0%
+independent but you know that they can't
+all increase. That would be the totally
+
+ align:start position:0%
+all increase. That would be the totally
+ 
+
+ align:start position:0%
+all increase. That would be the totally
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+representation. So you know that they're
+
+ align:start position:0%
+representation. So you know that they're
+ 
+
+ align:start position:0%
+representation. So you know that they're
+two linearly independent
+
+ align:start position:0%
+two linearly independent
+ 
+
+ align:start position:0%
+two linearly independent
+uh things you can do with the angles. So
+
+ align:start position:0%
+uh things you can do with the angles. So
+ 
+
+ align:start position:0%
+uh things you can do with the angles. So
+but it's much more convenient to use
+
+ align:start position:0%
+but it's much more convenient to use
+ 
+
+ align:start position:0%
+but it's much more convenient to use
+this. And so you get a you get three uh
+
+ align:start position:0%
+this. And so you get a you get three uh
+ 
+
+ align:start position:0%
+this. And so you get a you get three uh
+a total um you you have a
+
+ align:start position:0%
+a total um you you have a
+ 
+
+ align:start position:0%
+a total um you you have a
+three-dimensional reducible
+
+ align:start position:0%
+three-dimensional reducible
+ 
+
+ align:start position:0%
+three-dimensional reducible
+representation and you take away a1
+
+ align:start position:0%
+representation and you take away a1
+ 
+
+ align:start position:0%
+representation and you take away a1
+prime and that tells you about the
+
+ align:start position:0%
+prime and that tells you about the
+ 
+
+ align:start position:0%
+prime and that tells you about the
+inplane
+
+ align:start position:0%
+inplane
+ 
+
+ align:start position:0%
+inplane
+bends. You could also uh take a
+
+ align:start position:0%
+bends. You could also uh take a
+ 
+
+ align:start position:0%
+bends. You could also uh take a
+representation where here's the plane of
+
+ align:start position:0%
+representation where here's the plane of
+ 
+
+ align:start position:0%
+representation where here's the plane of
+the molecule and we just put a uh z the
+
+ align:start position:0%
+the molecule and we just put a uh z the
+ 
+
+ align:start position:0%
+the molecule and we just put a uh z the
+z-axis through the center atom on
+
+ align:start position:0%
+z-axis through the center atom on
+ 
+
+ align:start position:0%
+z-axis through the center atom on
+dimensional and we ask well what is
+
+ align:start position:0%
+dimensional and we ask well what is
+ 
+
+ align:start position:0%
+dimensional and we ask well what is
+that? that'll be the out of plane bend
+
+ align:start position:0%
+that? that'll be the out of plane bend
+ 
+
+ align:start position:0%
+that? that'll be the out of plane bend
+and that'll correspond to one of the
+
+ align:start position:0%
+and that'll correspond to one of the
+ 
+
+ align:start position:0%
+and that'll correspond to one of the
+irreducible represent. So as long as if
+
+ align:start position:0%
+irreducible represent. So as long as if
+ 
+
+ align:start position:0%
+irreducible represent. So as long as if
+you can draw a cartoon-like object that
+
+ align:start position:0%
+you can draw a cartoon-like object that
+ 
+
+ align:start position:0%
+you can draw a cartoon-like object that
+enables you to sort the vibrations
+
+ align:start position:0%
+enables you to sort the vibrations
+ 
+
+ align:start position:0%
+enables you to sort the vibrations
+uh you can begin to discover uh what is
+
+ align:start position:0%
+uh you can begin to discover uh what is
+ 
+
+ align:start position:0%
+uh you can begin to discover uh what is
+in each of these uh normal modes.
+
+ align:start position:0%
+in each of these uh normal modes.
+ 
+
+ align:start position:0%
+in each of these uh normal modes.
+Now when you have only one of a
+
+ align:start position:0%
+Now when you have only one of a
+ 
+
+ align:start position:0%
+Now when you have only one of a
+particular symmetry species, you can be
+
+ align:start position:0%
+particular symmetry species, you can be
+ 
+
+ align:start position:0%
+particular symmetry species, you can be
+pretty sure that there is a unique
+
+ align:start position:0%
+pretty sure that there is a unique
+ 
+
+ align:start position:0%
+pretty sure that there is a unique
+conclusion about what that is that you
+
+ align:start position:0%
+conclusion about what that is that you
+ 
+
+ align:start position:0%
+conclusion about what that is that you
+can get from these cartoons. When
+
+ align:start position:0%
+can get from these cartoons. When
+ 
+
+ align:start position:0%
+can get from these cartoons. When
+there's more than one of a particular
+
+ align:start position:0%
+there's more than one of a particular
+ 
+
+ align:start position:0%
+there's more than one of a particular
+species, it tells you it's pretty likely
+
+ align:start position:0%
+species, it tells you it's pretty likely
+ 
+
+ align:start position:0%
+species, it tells you it's pretty likely
+that there won't be a segregation of
+
+ align:start position:0%
+that there won't be a segregation of
+ 
+
+ align:start position:0%
+that there won't be a segregation of
+stretches and
+
+ align:start position:0%
+stretches and
+ 
+
+ align:start position:0%
+stretches and
+bends. So, uh, this is beautiful because
+
+ align:start position:0%
+bends. So, uh, this is beautiful because
+ 
+
+ align:start position:0%
+bends. So, uh, this is beautiful because
+you didn't do anything. We didn't solve
+
+ align:start position:0%
+you didn't do anything. We didn't solve
+ 
+
+ align:start position:0%
+you didn't do anything. We didn't solve
+the GF matrix problem. We don't know
+
+ align:start position:0%
+the GF matrix problem. We don't know
+ 
+
+ align:start position:0%
+the GF matrix problem. We don't know
+what the S vectors are. Yet we we know
+
+ align:start position:0%
+what the S vectors are. Yet we we know
+ 
+
+ align:start position:0%
+what the S vectors are. Yet we we know
+what are the allowed symmetries of all
+
+ align:start position:0%
+what are the allowed symmetries of all
+ 
+
+ align:start position:0%
+what are the allowed symmetries of all
+of the vibrations and we know whe
+
+ align:start position:0%
+of the vibrations and we know whe
+ 
+
+ align:start position:0%
+of the vibrations and we know whe
+whether some of them are pure stretches
+
+ align:start position:0%
+whether some of them are pure stretches
+ 
+
+ align:start position:0%
+whether some of them are pure stretches
+and some of them are pure bends and even
+
+ align:start position:0%
+and some of them are pure bends and even
+ 
+
+ align:start position:0%
+and some of them are pure bends and even
+qualitatively what kind of
+
+ align:start position:0%
+qualitatively what kind of
+ 
+
+ align:start position:0%
+qualitatively what kind of
+bends. And you don't have to do any you
+
+ align:start position:0%
+bends. And you don't have to do any you
+ 
+
+ align:start position:0%
+bends. And you don't have to do any you
+don't have to be careful to avoid an
+
+ align:start position:0%
+don't have to be careful to avoid an
+ 
+
+ align:start position:0%
+don't have to be careful to avoid an
+overcomplete cartoon because you can
+
+ align:start position:0%
+overcomplete cartoon because you can
+ 
+
+ align:start position:0%
+overcomplete cartoon because you can
+very quickly project out the piece that
+
+ align:start position:0%
+very quickly project out the piece that
+ 
+
+ align:start position:0%
+very quickly project out the piece that
+that was uh was uh associated with being
+
+ align:start position:0%
+that was uh was uh associated with being
+ 
+
+ align:start position:0%
+that was uh was uh associated with being
+overcomplete and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fantastic. And so once we have uh sorted
+
+ align:start position:0%
+fantastic. And so once we have uh sorted
+ 
+
+ align:start position:0%
+fantastic. And so once we have uh sorted
+things out, I mean in this case we have
+
+ align:start position:0%
+things out, I mean in this case we have
+ 
+
+ align:start position:0%
+things out, I mean in this case we have
+a one prime is a pure
+
+ align:start position:0%
+a one prime is a pure
+ 
+
+ align:start position:0%
+a one prime is a pure
+symmetric stretch. Well, that's pretty
+
+ align:start position:0%
+symmetric stretch. Well, that's pretty
+ 
+
+ align:start position:0%
+symmetric stretch. Well, that's pretty
+obvious because you know a symmetric
+
+ align:start position:0%
+obvious because you know a symmetric
+ 
+
+ align:start position:0%
+obvious because you know a symmetric
+stretch you can look at that you could
+
+ align:start position:0%
+stretch you can look at that you could
+ 
+
+ align:start position:0%
+stretch you can look at that you could
+say well that's got to be totally
+
+ align:start position:0%
+say well that's got to be totally
+ 
+
+ align:start position:0%
+say well that's got to be totally
+symmetric. And uh what's harder to say
+
+ align:start position:0%
+symmetric. And uh what's harder to say
+ 
+
+ align:start position:0%
+symmetric. And uh what's harder to say
+is well that's all it could be that
+
+ align:start position:0%
+is well that's all it could be that
+ 
+
+ align:start position:0%
+is well that's all it could be that
+there's nothing else. But there's only
+
+ align:start position:0%
+there's nothing else. But there's only
+ 
+
+ align:start position:0%
+there's nothing else. But there's only
+one of them. And so it had damn well
+
+ align:start position:0%
+one of them. And so it had damn well
+ 
+
+ align:start position:0%
+one of them. And so it had damn well
+better be the symmetric stretch. And
+
+ align:start position:0%
+better be the symmetric stretch. And
+ 
+
+ align:start position:0%
+better be the symmetric stretch. And
+then uh the a two double prime is a
+
+ align:start position:0%
+then uh the a two double prime is a
+ 
+
+ align:start position:0%
+then uh the a two double prime is a
+pure out of plane
+
+ align:start position:0%
+pure out of plane
+ 
+
+ align:start position:0%
+pure out of plane
+bend. And uh uh and so the two e prime
+
+ align:start position:0%
+bend. And uh uh and so the two e prime
+ 
+
+ align:start position:0%
+bend. And uh uh and so the two e prime
+representations are mixtures of
+
+ align:start position:0%
+representations are mixtures of
+ 
+
+ align:start position:0%
+representations are mixtures of
+stretches and bends.
+
+ align:start position:0%
+stretches and bends.
+ 
+
+ align:start position:0%
+stretches and bends.
+And uh one of the nice things about them
+
+ align:start position:0%
+And uh one of the nice things about them
+ 
+
+ align:start position:0%
+And uh one of the nice things about them
+is when you have a doubly degenerate
+
+ align:start position:0%
+is when you have a doubly degenerate
+ 
+
+ align:start position:0%
+is when you have a doubly degenerate
+representation, you can often draw a
+
+ align:start position:0%
+representation, you can often draw a
+ 
+
+ align:start position:0%
+representation, you can often draw a
+picture that uh that suggests the
+
+ align:start position:0%
+picture that uh that suggests the
+ 
+
+ align:start position:0%
+picture that uh that suggests the
+molecule is doing something that looks
+
+ align:start position:0%
+molecule is doing something that looks
+ 
+
+ align:start position:0%
+molecule is doing something that looks
+like uh an angular momentum. So here's a
+
+ align:start position:0%
+like uh an angular momentum. So here's a
+ 
+
+ align:start position:0%
+like uh an angular momentum. So here's a
+a picture and what I've done is I've
+
+ align:start position:0%
+a picture and what I've done is I've
+ 
+
+ align:start position:0%
+a picture and what I've done is I've
+made one of the angles
+
+ align:start position:0%
+made one of the angles
+ 
+
+ align:start position:0%
+made one of the angles
+small and now I'm going to draw the same
+
+ align:start position:0%
+small and now I'm going to draw the same
+ 
+
+ align:start position:0%
+small and now I'm going to draw the same
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+uh except that now I'm going to uh make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u this
+
+ align:start position:0%
+u this
+ 
+
+ align:start position:0%
+u this
+angle
+
+ align:start position:0%
+angle
+ 
+
+ align:start position:0%
+angle
+small and then another picture that
+
+ align:start position:0%
+small and then another picture that
+ 
+
+ align:start position:0%
+small and then another picture that
+makes this
+
+ align:start position:0%
+makes this
+ 
+
+ align:start position:0%
+makes this
+angle small. I may So what you have is a
+
+ align:start position:0%
+angle small. I may So what you have is a
+ 
+
+ align:start position:0%
+angle small. I may So what you have is a
+uh a distortion of the structure that
+
+ align:start position:0%
+uh a distortion of the structure that
+ 
+
+ align:start position:0%
+uh a distortion of the structure that
+looks like it's
+
+ align:start position:0%
+looks like it's
+ 
+
+ align:start position:0%
+looks like it's
+rotating. That's called pseudo rotation.
+
+ align:start position:0%
+rotating. That's called pseudo rotation.
+ 
+
+ align:start position:0%
+rotating. That's called pseudo rotation.
+And you can do the same sort of thing
+
+ align:start position:0%
+And you can do the same sort of thing
+ 
+
+ align:start position:0%
+And you can do the same sort of thing
+with the stretches. You can say, okay,
+
+ align:start position:0%
+with the stretches. You can say, okay,
+ 
+
+ align:start position:0%
+with the stretches. You can say, okay,
+I've got a a stretch where I've
+
+ align:start position:0%
+I've got a a stretch where I've
+ 
+
+ align:start position:0%
+I've got a a stretch where I've
+elongated this guy. And then the next
+
+ align:start position:0%
+elongated this guy. And then the next
+ 
+
+ align:start position:0%
+elongated this guy. And then the next
+cartoon I've got a a stretch where I've
+
+ align:start position:0%
+cartoon I've got a a stretch where I've
+ 
+
+ align:start position:0%
+cartoon I've got a a stretch where I've
+elongated that guy. And then the next
+
+ align:start position:0%
+elongated that guy. And then the next
+ 
+
+ align:start position:0%
+elongated that guy. And then the next
+one I've got a stretch where I've
+
+ align:start position:0%
+one I've got a stretch where I've
+ 
+
+ align:start position:0%
+one I've got a stretch where I've
+elongated this guy. So it looks like the
+
+ align:start position:0%
+elongated this guy. So it looks like the
+ 
+
+ align:start position:0%
+elongated this guy. So it looks like the
+molecule is rotating again. And you can
+
+ align:start position:0%
+molecule is rotating again. And you can
+ 
+
+ align:start position:0%
+molecule is rotating again. And you can
+go in both senses. That's why it's a
+
+ align:start position:0%
+go in both senses. That's why it's a
+ 
+
+ align:start position:0%
+go in both senses. That's why it's a
+doubly degenerate
+
+ align:start position:0%
+doubly degenerate
+ 
+
+ align:start position:0%
+doubly degenerate
+representation. So you have a kind of
+
+ align:start position:0%
+representation. So you have a kind of
+ 
+
+ align:start position:0%
+representation. So you have a kind of
+vibrational angular momentum which isn't
+
+ align:start position:0%
+vibrational angular momentum which isn't
+ 
+
+ align:start position:0%
+vibrational angular momentum which isn't
+an angular momentum. And there's two
+
+ align:start position:0%
+an angular momentum. And there's two
+ 
+
+ align:start position:0%
+an angular momentum. And there's two
+senses. And so those are called pseudo
+
+ align:start position:0%
+senses. And so those are called pseudo
+ 
+
+ align:start position:0%
+senses. And so those are called pseudo
+rotation. And that's uh an interesting
+
+ align:start position:0%
+rotation. And that's uh an interesting
+ 
+
+ align:start position:0%
+rotation. And that's uh an interesting
+thing. You mean in both senses you could
+
+ align:start position:0%
+thing. You mean in both senses you could
+ 
+
+ align:start position:0%
+thing. You mean in both senses you could
+be stretch and bending? Well, you can
+
+ align:start position:0%
+be stretch and bending? Well, you can
+ 
+
+ align:start position:0%
+be stretch and bending? Well, you can
+mix them together, too. But I mean, just
+
+ align:start position:0%
+mix them together, too. But I mean, just
+ 
+
+ align:start position:0%
+mix them together, too. But I mean, just
+have these two pictures. You can have
+
+ align:start position:0%
+have these two pictures. You can have
+ 
+
+ align:start position:0%
+have these two pictures. You can have
+first this one, then this one, then that
+
+ align:start position:0%
+first this one, then this one, then that
+ 
+
+ align:start position:0%
+first this one, then this one, then that
+one, or you can have uh first this one,
+
+ align:start position:0%
+one, or you can have uh first this one,
+ 
+
+ align:start position:0%
+one, or you can have uh first this one,
+and then somebody that's distorted in
+
+ align:start position:0%
+and then somebody that's distorted in
+ 
+
+ align:start position:0%
+and then somebody that's distorted in
+that direction. So, you can have the
+
+ align:start position:0%
+that direction. So, you can have the
+ 
+
+ align:start position:0%
+that direction. So, you can have the
+distortion going around this way, or you
+
+ align:start position:0%
+distortion going around this way, or you
+ 
+
+ align:start position:0%
+distortion going around this way, or you
+can have the distortion going around
+
+ align:start position:0%
+can have the distortion going around
+ 
+
+ align:start position:0%
+can have the distortion going around
+that way. Couldn't you also have one
+
+ align:start position:0%
+that way. Couldn't you also have one
+ 
+
+ align:start position:0%
+that way. Couldn't you also have one
+distortion going in one direction and
+
+ align:start position:0%
+distortion going in one direction and
+ 
+
+ align:start position:0%
+distortion going in one direction and
+another distortion going in another
+
+ align:start position:0%
+another distortion going in another
+ 
+
+ align:start position:0%
+another distortion going in another
+direction? Sure, you can have any linear
+
+ align:start position:0%
+direction? Sure, you can have any linear
+ 
+
+ align:start position:0%
+direction? Sure, you can have any linear
+com you have a doubly you can take any
+
+ align:start position:0%
+com you have a doubly you can take any
+ 
+
+ align:start position:0%
+com you have a doubly you can take any
+linear combination of them. Uh but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it it turns out that often when there
+
+ align:start position:0%
+um it it turns out that often when there
+ 
+
+ align:start position:0%
+um it it turns out that often when there
+are these pictures that that say okay
+
+ align:start position:0%
+are these pictures that that say okay
+ 
+
+ align:start position:0%
+are these pictures that that say okay
+there's a distortion that's moving
+
+ align:start position:0%
+there's a distortion that's moving
+ 
+
+ align:start position:0%
+there's a distortion that's moving
+around the molecule without the molecule
+
+ align:start position:0%
+around the molecule without the molecule
+ 
+
+ align:start position:0%
+around the molecule without the molecule
+rotating. It's like an angular momentum
+
+ align:start position:0%
+rotating. It's like an angular momentum
+ 
+
+ align:start position:0%
+rotating. It's like an angular momentum
+and you you use ideas of angular
+
+ align:start position:0%
+and you you use ideas of angular
+ 
+
+ align:start position:0%
+and you you use ideas of angular
+momentum to get splittings in the
+
+ align:start position:0%
+momentum to get splittings in the
+ 
+
+ align:start position:0%
+momentum to get splittings in the
+spectrum. That's a little bit beyond my
+
+ align:start position:0%
+spectrum. That's a little bit beyond my
+ 
+
+ align:start position:0%
+spectrum. That's a little bit beyond my
+pay grade right now because I don't
+
+ align:start position:0%
+pay grade right now because I don't
+ 
+
+ align:start position:0%
+pay grade right now because I don't
+understand that well enough to lecture.
+
+ align:start position:0%
+understand that well enough to lecture.
+ 
+
+ align:start position:0%
+understand that well enough to lecture.
+Okay. So now we have determined the
+
+ align:start position:0%
+Okay. So now we have determined the
+ 
+
+ align:start position:0%
+Okay. So now we have determined the
+irreducible representations and now what
+
+ align:start position:0%
+irreducible representations and now what
+ 
+
+ align:start position:0%
+irreducible representations and now what
+we want to do is find out well what's
+
+ align:start position:0%
+we want to do is find out well what's
+ 
+
+ align:start position:0%
+we want to do is find out well what's
+the spect what are the spectra going to
+
+ align:start position:0%
+the spect what are the spectra going to
+ 
+
+ align:start position:0%
+the spect what are the spectra going to
+look like? Can we tell whether uh this
+
+ align:start position:0%
+look like? Can we tell whether uh this
+ 
+
+ align:start position:0%
+look like? Can we tell whether uh this
+molecule B C3 is planer or something
+
+ align:start position:0%
+molecule B C3 is planer or something
+ 
+
+ align:start position:0%
+molecule B C3 is planer or something
+else? And so
+
+ align:start position:0%
+else? And so
+ 
+
+ align:start position:0%
+else? And so
+uh if it's planer, it's obviously an
+
+ align:start position:0%
+uh if it's planer, it's obviously an
+ 
+
+ align:start position:0%
+uh if it's planer, it's obviously an
+oblate
+
+ align:start position:0%
+oblate
+ 
+
+ align:start position:0%
+oblate
+top. If it's distorted from
+
+ align:start position:0%
+top. If it's distorted from
+ 
+
+ align:start position:0%
+top. If it's distorted from
+planer, it can be oblate or prolate. But
+
+ align:start position:0%
+planer, it can be oblate or prolate. But
+ 
+
+ align:start position:0%
+planer, it can be oblate or prolate. But
+it so we have
+
+ align:start position:0%
+it so we have
+ 
+
+ align:start position:0%
+it so we have
+D3H and then we have
+
+ align:start position:0%
+D3H and then we have
+ 
+
+ align:start position:0%
+D3H and then we have
+C3V oblate or
+
+ align:start position:0%
+C3V oblate or
+ 
+
+ align:start position:0%
+C3V oblate or
+prolate limits and then there are lower
+
+ align:start position:0%
+prolate limits and then there are lower
+ 
+
+ align:start position:0%
+prolate limits and then there are lower
+symmetry still and so what you often do
+
+ align:start position:0%
+symmetry still and so what you often do
+ 
+
+ align:start position:0%
+symmetry still and so what you often do
+when you don't know what the symmetry of
+
+ align:start position:0%
+when you don't know what the symmetry of
+ 
+
+ align:start position:0%
+when you don't know what the symmetry of
+a molecule will be is you say okay there
+
+ align:start position:0%
+a molecule will be is you say okay there
+ 
+
+ align:start position:0%
+a molecule will be is you say okay there
+are reasonable there's a reasonable
+
+ align:start position:0%
+are reasonable there's a reasonable
+ 
+
+ align:start position:0%
+are reasonable there's a reasonable
+sequence of
+
+ align:start position:0%
+sequence of
+ 
+
+ align:start position:0%
+sequence of
+possibilities and I do the group theory
+
+ align:start position:0%
+possibilities and I do the group theory
+ 
+
+ align:start position:0%
+possibilities and I do the group theory
+for each of them and I look for features
+
+ align:start position:0%
+for each of them and I look for features
+ 
+
+ align:start position:0%
+for each of them and I look for features
+in the group theory that will say this
+
+ align:start position:0%
+in the group theory that will say this
+ 
+
+ align:start position:0%
+in the group theory that will say this
+is where I can tell the spectrum
+
+ align:start position:0%
+is where I can tell the spectrum
+ 
+
+ align:start position:0%
+is where I can tell the spectrum
+uh I can tell from the spectrum what
+
+ align:start position:0%
+uh I can tell from the spectrum what
+ 
+
+ align:start position:0%
+uh I can tell from the spectrum what
+which point group the molecule belongs
+
+ align:start position:0%
+which point group the molecule belongs
+ 
+
+ align:start position:0%
+which point group the molecule belongs
+to and it's that's kind of neat and uh
+
+ align:start position:0%
+to and it's that's kind of neat and uh
+ 
+
+ align:start position:0%
+to and it's that's kind of neat and uh
+um and uh I wish I could do this
+
+ align:start position:0%
+um and uh I wish I could do this
+ 
+
+ align:start position:0%
+um and uh I wish I could do this
+smoothly and cleanly to impress you with
+
+ align:start position:0%
+smoothly and cleanly to impress you with
+ 
+
+ align:start position:0%
+smoothly and cleanly to impress you with
+how h how uh informative it is but let's
+
+ align:start position:0%
+how h how uh informative it is but let's
+ 
+
+ align:start position:0%
+how h how uh informative it is but let's
+see what we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the thing that makes transitions
+
+ align:start position:0%
+So the thing that makes transitions
+ 
+
+ align:start position:0%
+So the thing that makes transitions
+occur occur is the dipole moment
+
+ align:start position:0%
+occur occur is the dipole moment
+ 
+
+ align:start position:0%
+occur occur is the dipole moment
+function and uh uh this dipole moment is
+
+ align:start position:0%
+function and uh uh this dipole moment is
+ 
+
+ align:start position:0%
+function and uh uh this dipole moment is
+a function of the coordinates and uh
+
+ align:start position:0%
+a function of the coordinates and uh
+ 
+
+ align:start position:0%
+a function of the coordinates and uh
+it's a vector and we can write it
+
+ align:start position:0%
+it's a vector and we can write it
+ 
+
+ align:start position:0%
+it's a vector and we can write it
+as a sum of components where we classify
+
+ align:start position:0%
+as a sum of components where we classify
+ 
+
+ align:start position:0%
+as a sum of components where we classify
+the components according to the uh
+
+ align:start position:0%
+the components according to the uh
+ 
+
+ align:start position:0%
+the components according to the uh
+inertial axis
+
+ align:start position:0%
+inertial axis
+ 
+
+ align:start position:0%
+inertial axis
+system. Okay. And so we're interested in
+
+ align:start position:0%
+system. Okay. And so we're interested in
+ 
+
+ align:start position:0%
+system. Okay. And so we're interested in
+uh this vector and we're resolving it
+
+ align:start position:0%
+uh this vector and we're resolving it
+ 
+
+ align:start position:0%
+uh this vector and we're resolving it
+according to the uh three principal axis
+
+ align:start position:0%
+according to the uh three principal axis
+ 
+
+ align:start position:0%
+according to the uh three principal axis
+components. These are unit vectors. And
+
+ align:start position:0%
+components. These are unit vectors. And
+ 
+
+ align:start position:0%
+components. These are unit vectors. And
+so we have the equilibrium geometry
+
+ align:start position:0%
+so we have the equilibrium geometry
+ 
+
+ align:start position:0%
+so we have the equilibrium geometry
+uh the a component of the equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometry. And then we have the first
+
+ align:start position:0%
+geometry. And then we have the first
+ 
+
+ align:start position:0%
+geometry. And then we have the first
+term in the power series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion at equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+etc. Okay. And so these are the
+
+ align:start position:0%
+etc. Okay. And so these are the
+ 
+
+ align:start position:0%
+etc. Okay. And so these are the
+permanent dipole moments along the uh
+
+ align:start position:0%
+permanent dipole moments along the uh
+ 
+
+ align:start position:0%
+permanent dipole moments along the uh
+the principal axis system. And and
+
+ align:start position:0%
+the principal axis system. And and
+ 
+
+ align:start position:0%
+the principal axis system. And and
+uh and for this molecule you know at
+
+ align:start position:0%
+uh and for this molecule you know at
+ 
+
+ align:start position:0%
+uh and for this molecule you know at
+least in
+
+ align:start position:0%
+least in
+ 
+
+ align:start position:0%
+least in
+um in D38 you know that all of those are
+
+ align:start position:0%
+um in D38 you know that all of those are
+ 
+
+ align:start position:0%
+um in D38 you know that all of those are
+zero. These are the things that gives
+
+ align:start position:0%
+zero. These are the things that gives
+ 
+
+ align:start position:0%
+zero. These are the things that gives
+rise to a pure rotation spectrum.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And uh so if the various geometries
+
+ align:start position:0%
+And uh so if the various geometries
+ 
+
+ align:start position:0%
+And uh so if the various geometries
+uh uh will have some nonzero permanent
+
+ align:start position:0%
+uh uh will have some nonzero permanent
+ 
+
+ align:start position:0%
+uh uh will have some nonzero permanent
+dipole moments, one can resolve the
+
+ align:start position:0%
+dipole moments, one can resolve the
+ 
+
+ align:start position:0%
+dipole moments, one can resolve the
+question simply by looking at the
+
+ align:start position:0%
+question simply by looking at the
+ 
+
+ align:start position:0%
+question simply by looking at the
+rotational
+
+ align:start position:0%
+rotational
+ 
+
+ align:start position:0%
+rotational
+spectrum. But usually the interesting
+
+ align:start position:0%
+spectrum. But usually the interesting
+ 
+
+ align:start position:0%
+spectrum. But usually the interesting
+stuff and there's much more information
+
+ align:start position:0%
+stuff and there's much more information
+ 
+
+ align:start position:0%
+stuff and there's much more information
+coming from the vibrational spectrum. So
+
+ align:start position:0%
+coming from the vibrational spectrum. So
+ 
+
+ align:start position:0%
+coming from the vibrational spectrum. So
+these are controlling the intensities of
+
+ align:start position:0%
+these are controlling the intensities of
+ 
+
+ align:start position:0%
+these are controlling the intensities of
+the vibrational spectrum and uh uh they
+
+ align:start position:0%
+the vibrational spectrum and uh uh they
+ 
+
+ align:start position:0%
+the vibrational spectrum and uh uh they
+so what is this? This is some this m is
+
+ align:start position:0%
+so what is this? This is some this m is
+ 
+
+ align:start position:0%
+so what is this? This is some this m is
+the the result of an integral or this
+
+ align:start position:0%
+the the result of an integral or this
+ 
+
+ align:start position:0%
+the the result of an integral or this
+partial derivative of m is the result of
+
+ align:start position:0%
+partial derivative of m is the result of
+ 
+
+ align:start position:0%
+partial derivative of m is the result of
+an electronic integral. So we know that
+
+ align:start position:0%
+an electronic integral. So we know that
+ 
+
+ align:start position:0%
+an electronic integral. So we know that
+this quantity partial
+
+ align:start position:0%
+this quantity partial
+ 
+
+ align:start position:0%
+this quantity partial
+m a b c
+
+ align:start position:0%
+m a b c
+ 
+
+ align:start position:0%
+m a b c
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+dqi is an
+
+ align:start position:0%
+dqi is an
+ 
+
+ align:start position:0%
+dqi is an
+integral that contains the partial
+
+ align:start position:0%
+integral that contains the partial
+ 
+
+ align:start position:0%
+integral that contains the partial
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+qi. It contains zi
+
+ align:start position:0%
+qi. It contains zi
+ 
+
+ align:start position:0%
+qi. It contains zi
+star the j electronic state
+
+ align:start position:0%
+star the j electronic state
+ 
+
+ align:start position:0%
+star the j electronic state
+and a b or c and si star s j d. So we
+
+ align:start position:0%
+and a b or c and si star s j d. So we
+ 
+
+ align:start position:0%
+and a b or c and si star s j d. So we
+want this integral to be non zero. Now
+
+ align:start position:0%
+want this integral to be non zero. Now
+ 
+
+ align:start position:0%
+want this integral to be non zero. Now
+this is a vibrational spectrum. So the
+
+ align:start position:0%
+this is a vibrational spectrum. So the
+ 
+
+ align:start position:0%
+this is a vibrational spectrum. So the
+electronic wave function is the same. We
+
+ align:start position:0%
+electronic wave function is the same. We
+ 
+
+ align:start position:0%
+electronic wave function is the same. We
+we use the so this is automatically
+
+ align:start position:0%
+we use the so this is automatically
+ 
+
+ align:start position:0%
+we use the so this is automatically
+totally symmetric.
+
+ align:start position:0%
+totally symmetric.
+ 
+
+ align:start position:0%
+totally symmetric.
+This has the symmetry of the i normal
+
+ align:start position:0%
+This has the symmetry of the i normal
+ 
+
+ align:start position:0%
+This has the symmetry of the i normal
+coordinate and this has the symmetry of
+
+ align:start position:0%
+coordinate and this has the symmetry of
+ 
+
+ align:start position:0%
+coordinate and this has the symmetry of
+uh rx r y or rz but we have to make a
+
+ align:start position:0%
+uh rx r y or rz but we have to make a
+ 
+
+ align:start position:0%
+uh rx r y or rz but we have to make a
+correspondence
+
+ align:start position:0%
+correspondence
+ 
+
+ align:start position:0%
+correspondence
+xyz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+abc and that correspondence you know
+
+ align:start position:0%
+abc and that correspondence you know
+ 
+
+ align:start position:0%
+abc and that correspondence you know
+there are often many
+
+ align:start position:0%
+there are often many
+ 
+
+ align:start position:0%
+there are often many
+different or several different geometric
+
+ align:start position:0%
+different or several different geometric
+ 
+
+ align:start position:0%
+different or several different geometric
+forms that are consistent with uh a
+
+ align:start position:0%
+forms that are consistent with uh a
+ 
+
+ align:start position:0%
+forms that are consistent with uh a
+particular point group. And so you have
+
+ align:start position:0%
+particular point group. And so you have
+ 
+
+ align:start position:0%
+particular point group. And so you have
+to worry about how does uh how do the
+
+ align:start position:0%
+to worry about how does uh how do the
+ 
+
+ align:start position:0%
+to worry about how does uh how do the
+cartisian coordinates in which in terms
+
+ align:start position:0%
+cartisian coordinates in which in terms
+ 
+
+ align:start position:0%
+cartisian coordinates in which in terms
+of which the point group is expressed
+
+ align:start position:0%
+of which the point group is expressed
+ 
+
+ align:start position:0%
+of which the point group is expressed
+how do they map onto the principal
+
+ align:start position:0%
+how do they map onto the principal
+ 
+
+ align:start position:0%
+how do they map onto the principal
+inertial components? Josh, did you mean
+
+ align:start position:0%
+inertial components? Josh, did you mean
+ 
+
+ align:start position:0%
+inertial components? Josh, did you mean
+x y and z instead of rx r y rz in the
+
+ align:start position:0%
+x y and z instead of rx r y rz in the
+ 
+
+ align:start position:0%
+x y and z instead of rx r y rz in the
+middle of that integral there?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You said those map to RX, R Y, and RZ.
+
+ align:start position:0%
+You said those map to RX, R Y, and RZ.
+ 
+
+ align:start position:0%
+You said those map to RX, R Y, and RZ.
+Do you really mean X, Y, and Z? These
+
+ align:start position:0%
+Do you really mean X, Y, and Z? These
+ 
+
+ align:start position:0%
+Do you really mean X, Y, and Z? These
+are rotations. I I haven't I haven't
+
+ align:start position:0%
+are rotations. I I haven't I haven't
+ 
+
+ align:start position:0%
+are rotations. I I haven't I haven't
+thought about this in fighting detail
+
+ align:start position:0%
+thought about this in fighting detail
+ 
+
+ align:start position:0%
+thought about this in fighting detail
+for 12 years. It was my impression that
+
+ align:start position:0%
+for 12 years. It was my impression that
+ 
+
+ align:start position:0%
+for 12 years. It was my impression that
+I want RX, R Y, and RZ here, but I might
+
+ align:start position:0%
+I want RX, R Y, and RZ here, but I might
+ 
+
+ align:start position:0%
+I want RX, R Y, and RZ here, but I might
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+wrong. So,
+
+ align:start position:0%
+wrong. So,
+ 
+
+ align:start position:0%
+wrong. So,
+uh, so it's a good question. I can't
+
+ align:start position:0%
+uh, so it's a good question. I can't
+ 
+
+ align:start position:0%
+uh, so it's a good question. I can't
+answer it. uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so what we want is since these have
+
+ align:start position:0%
+uh so what we want is since these have
+ 
+
+ align:start position:0%
+uh so what we want is since these have
+the same belong to the same irreducible
+
+ align:start position:0%
+the same belong to the same irreducible
+ 
+
+ align:start position:0%
+the same belong to the same irreducible
+representation we in order for this
+
+ align:start position:0%
+representation we in order for this
+ 
+
+ align:start position:0%
+representation we in order for this
+integral to be non zero we want the
+
+ align:start position:0%
+integral to be non zero we want the
+ 
+
+ align:start position:0%
+integral to be non zero we want the
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+coordinate
+
+ align:start position:0%
+coordinate
+ 
+
+ align:start position:0%
+coordinate
+and whatever symmetry species these are
+
+ align:start position:0%
+and whatever symmetry species these are
+ 
+
+ align:start position:0%
+and whatever symmetry species these are
+supposed to refer to to be the
+
+ align:start position:0%
+supposed to refer to to be the
+ 
+
+ align:start position:0%
+supposed to refer to to be the
+same and uh uh so let's think about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's it's X, Y, and Z. It is X, Y,
+
+ align:start position:0%
+um it's it's X, Y, and Z. It is X, Y,
+ 
+
+ align:start position:0%
+um it's it's X, Y, and Z. It is X, Y,
+and Z. So, this then tells us which one
+
+ align:start position:0%
+and Z. So, this then tells us which one
+ 
+
+ align:start position:0%
+and Z. So, this then tells us which one
+of these survives, and that determines
+
+ align:start position:0%
+of these survives, and that determines
+ 
+
+ align:start position:0%
+of these survives, and that determines
+the rotational
+
+ align:start position:0%
+the rotational
+ 
+
+ align:start position:0%
+the rotational
+structure. Thank you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I stared at this a long time last night
+
+ align:start position:0%
+I stared at this a long time last night
+ 
+
+ align:start position:0%
+I stared at this a long time last night
+and I thought I I had it, but that was
+
+ align:start position:0%
+and I thought I I had it, but that was
+ 
+
+ align:start position:0%
+and I thought I I had it, but that was
+the one thing. Okay. So we're we're
+
+ align:start position:0%
+the one thing. Okay. So we're we're
+ 
+
+ align:start position:0%
+the one thing. Okay. So we're we're
+Okay. So now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we
+
+ align:start position:0%
+uh we
+ 
+
+ align:start position:0%
+uh we
+can we know that
+
+ align:start position:0%
+can we know that
+ 
+
+ align:start position:0%
+can we know that
+uh the derivative with respect to
+
+ align:start position:0%
+uh the derivative with respect to
+ 
+
+ align:start position:0%
+uh the derivative with respect to
+qi that's the same uh symmetry species
+
+ align:start position:0%
+qi that's the same uh symmetry species
+ 
+
+ align:start position:0%
+qi that's the same uh symmetry species
+as qi. And so we uh we then look at the
+
+ align:start position:0%
+as qi. And so we uh we then look at the
+ 
+
+ align:start position:0%
+as qi. And so we uh we then look at the
+transition moment uh
+
+ align:start position:0%
+transition moment uh
+ 
+
+ align:start position:0%
+transition moment uh
+uh the the three possibilities for the
+
+ align:start position:0%
+uh the the three possibilities for the
+ 
+
+ align:start position:0%
+uh the the three possibilities for the
+transition moment. And uh this so the
+
+ align:start position:0%
+transition moment. And uh this so the
+ 
+
+ align:start position:0%
+transition moment. And uh this so the
+normal mode the normal coordinate here
+
+ align:start position:0%
+normal mode the normal coordinate here
+ 
+
+ align:start position:0%
+normal mode the normal coordinate here
+has to correspond to one of these three
+
+ align:start position:0%
+has to correspond to one of these three
+ 
+
+ align:start position:0%
+has to correspond to one of these three
+and those that then determines what are
+
+ align:start position:0%
+and those that then determines what are
+ 
+
+ align:start position:0%
+and those that then determines what are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+u what are the allowed transitions and
+
+ align:start position:0%
+u what are the allowed transitions and
+ 
+
+ align:start position:0%
+u what are the allowed transitions and
+how does their rotational uh structure
+
+ align:start position:0%
+how does their rotational uh structure
+ 
+
+ align:start position:0%
+how does their rotational uh structure
+uh behave. So we have um we
+
+ align:start position:0%
+uh behave. So we have um we
+ 
+
+ align:start position:0%
+uh behave. So we have um we
+have three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetries and we have E prime twice.
+
+ align:start position:0%
+symmetries and we have E prime twice.
+ 
+
+ align:start position:0%
+symmetries and we have E prime twice.
+And
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there is no symbol opposite A1 prime.
+
+ align:start position:0%
+so there is no symbol opposite A1 prime.
+ 
+
+ align:start position:0%
+so there is no symbol opposite A1 prime.
+And so this is
+
+ align:start position:0%
+And so this is
+ 
+
+ align:start position:0%
+And so this is
+vibrational forbidden.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The fundamental for this mode is a
+
+ align:start position:0%
+The fundamental for this mode is a
+ 
+
+ align:start position:0%
+The fundamental for this mode is a
+transition between a totally symmetric
+
+ align:start position:0%
+transition between a totally symmetric
+ 
+
+ align:start position:0%
+transition between a totally symmetric
+level and another totally symmetric
+
+ align:start position:0%
+level and another totally symmetric
+ 
+
+ align:start position:0%
+level and another totally symmetric
+level. And there is no x y or z opposite
+
+ align:start position:0%
+level. And there is no x y or z opposite
+ 
+
+ align:start position:0%
+level. And there is no x y or z opposite
+that corresponds to totally symmetric.
+
+ align:start position:0%
+that corresponds to totally symmetric.
+ 
+
+ align:start position:0%
+that corresponds to totally symmetric.
+So this guy this mode is not going to
+
+ align:start position:0%
+So this guy this mode is not going to
+ 
+
+ align:start position:0%
+So this guy this mode is not going to
+appear in the infrared.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This
+
+ align:start position:0%
+This
+ 
+
+ align:start position:0%
+This
+one uh is
+
+ align:start position:0%
+one uh is
+ 
+
+ align:start position:0%
+one uh is
+uh a to double prime that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z. So that is going to appear and e
+
+ align:start position:0%
+z. So that is going to appear and e
+ 
+
+ align:start position:0%
+z. So that is going to appear and e
+prime e prime is here and uh uh that's
+
+ align:start position:0%
+prime e prime is here and uh uh that's
+ 
+
+ align:start position:0%
+prime e prime is here and uh uh that's
+xy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have in the spectrum we have one
+
+ align:start position:0%
+So we have in the spectrum we have one
+ 
+
+ align:start position:0%
+So we have in the spectrum we have one
+normal mode that's going to be
+
+ align:start position:0%
+normal mode that's going to be
+ 
+
+ align:start position:0%
+normal mode that's going to be
+zpolarized or is going to have
+
+ align:start position:0%
+zpolarized or is going to have
+ 
+
+ align:start position:0%
+zpolarized or is going to have
+rotational structure that's associated
+
+ align:start position:0%
+rotational structure that's associated
+ 
+
+ align:start position:0%
+rotational structure that's associated
+with a z
+
+ align:start position:0%
+with a z
+ 
+
+ align:start position:0%
+with a z
+dipole a zch changing dipole and and two
+
+ align:start position:0%
+dipole a zch changing dipole and and two
+ 
+
+ align:start position:0%
+dipole a zch changing dipole and and two
+doubly degenerate vibrations that uh are
+
+ align:start position:0%
+doubly degenerate vibrations that uh are
+ 
+
+ align:start position:0%
+doubly degenerate vibrations that uh are
+going to uh be associated with the
+
+ align:start position:0%
+going to uh be associated with the
+ 
+
+ align:start position:0%
+going to uh be associated with the
+perpendicular. Okay. So now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for for
+
+ align:start position:0%
+for for
+ 
+
+ align:start position:0%
+for for
+this the caxis is the z-axis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for a for a symmetric
+
+ align:start position:0%
+So for a for a symmetric
+ 
+
+ align:start position:0%
+So for a for a symmetric
+top which is oblate the symmetry axis is
+
+ align:start position:0%
+top which is oblate the symmetry axis is
+ 
+
+ align:start position:0%
+top which is oblate the symmetry axis is
+going to be uh so that that's the
+
+ align:start position:0%
+going to be uh so that that's the
+ 
+
+ align:start position:0%
+going to be uh so that that's the
+highest order rotation and that's going
+
+ align:start position:0%
+highest order rotation and that's going
+ 
+
+ align:start position:0%
+highest order rotation and that's going
+to be the C inertial axis for an for a
+
+ align:start position:0%
+to be the C inertial axis for an for a
+ 
+
+ align:start position:0%
+to be the C inertial axis for an for a
+prolate top the symmetry axis is going
+
+ align:start position:0%
+prolate top the symmetry axis is going
+ 
+
+ align:start position:0%
+prolate top the symmetry axis is going
+to be uh
+
+ align:start position:0%
+to be uh
+ 
+
+ align:start position:0%
+to be uh
+uh the A axis and that would be
+
+ align:start position:0%
+uh the A axis and that would be
+ 
+
+ align:start position:0%
+uh the A axis and that would be
+Z. Okay, but we don't have a prolate top
+
+ align:start position:0%
+Z. Okay, but we don't have a prolate top
+ 
+
+ align:start position:0%
+Z. Okay, but we don't have a prolate top
+here. It's fairly hard to make this have
+
+ align:start position:0%
+here. It's fairly hard to make this have
+ 
+
+ align:start position:0%
+here. It's fairly hard to make this have
+a shape that looks like a prolate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+top. Okay,
+
+ align:start position:0%
+top. Okay,
+ 
+
+ align:start position:0%
+top. Okay,
+so C is equal to Z. And it doesn't
+
+ align:start position:0%
+so C is equal to Z. And it doesn't
+ 
+
+ align:start position:0%
+so C is equal to Z. And it doesn't
+matter whether X is A or X is B. And in
+
+ align:start position:0%
+matter whether X is A or X is B. And in
+ 
+
+ align:start position:0%
+matter whether X is A or X is B. And in
+many case because this a doubly
+
+ align:start position:0%
+many case because this a doubly
+ 
+
+ align:start position:0%
+many case because this a doubly
+degenerate group, doubly degenerate
+
+ align:start position:0%
+degenerate group, doubly degenerate
+ 
+
+ align:start position:0%
+degenerate group, doubly degenerate
+irreducible representation.
+
+ align:start position:0%
+irreducible representation.
+ 
+
+ align:start position:0%
+irreducible representation.
+There's almost always a problem about
+
+ align:start position:0%
+There's almost always a problem about
+ 
+
+ align:start position:0%
+There's almost always a problem about
+ambiguity about uh what do x and y
+
+ align:start position:0%
+ambiguity about uh what do x and y
+ 
+
+ align:start position:0%
+ambiguity about uh what do x and y
+correspond to and the only cases in
+
+ align:start position:0%
+correspond to and the only cases in
+ 
+
+ align:start position:0%
+correspond to and the only cases in
+which you have problems is when you have
+
+ align:start position:0%
+which you have problems is when you have
+ 
+
+ align:start position:0%
+which you have problems is when you have
+b1 and b2 irreducible
+
+ align:start position:0%
+b1 and b2 irreducible
+ 
+
+ align:start position:0%
+b1 and b2 irreducible
+representations and that happens in c2v
+
+ align:start position:0%
+representations and that happens in c2v
+ 
+
+ align:start position:0%
+representations and that happens in c2v
+and there needs to be a convention about
+
+ align:start position:0%
+and there needs to be a convention about
+ 
+
+ align:start position:0%
+and there needs to be a convention about
+which is going to be x and which is
+
+ align:start position:0%
+which is going to be x and which is
+ 
+
+ align:start position:0%
+which is going to be x and which is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+Y and uh I believe X is out of the plane
+
+ align:start position:0%
+Y and uh I believe X is out of the plane
+ 
+
+ align:start position:0%
+Y and uh I believe X is out of the plane
+of a planer molecule and uh but that
+
+ align:start position:0%
+of a planer molecule and uh but that
+ 
+
+ align:start position:0%
+of a planer molecule and uh but that
+there there is an agreement on that and
+
+ align:start position:0%
+there there is an agreement on that and
+ 
+
+ align:start position:0%
+there there is an agreement on that and
+I uh and I always forget it. I used to
+
+ align:start position:0%
+I uh and I always forget it. I used to
+ 
+
+ align:start position:0%
+I uh and I always forget it. I used to
+not forget it. I'm too old to remember
+
+ align:start position:0%
+not forget it. I'm too old to remember
+ 
+
+ align:start position:0%
+not forget it. I'm too old to remember
+these things. Yes, I have a question.
+
+ align:start position:0%
+these things. Yes, I have a question.
+ 
+
+ align:start position:0%
+these things. Yes, I have a question.
+Yes. Um why do you use the molecule
+
+ align:start position:0%
+Yes. Um why do you use the molecule
+ 
+
+ align:start position:0%
+Yes. Um why do you use the molecule
+fixed axes instead of the lab fixed
+
+ align:start position:0%
+fixed axes instead of the lab fixed
+ 
+
+ align:start position:0%
+fixed axes instead of the lab fixed
+axis?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I guess the dipole moment is in a
+
+ align:start position:0%
+well I guess the dipole moment is in a
+ 
+
+ align:start position:0%
+well I guess the dipole moment is in a
+particular direction in the molecule.
+
+ align:start position:0%
+particular direction in the molecule.
+ 
+
+ align:start position:0%
+particular direction in the molecule.
+That's correct. And so you know once we
+
+ align:start position:0%
+That's correct. And so you know once we
+ 
+
+ align:start position:0%
+That's correct. And so you know once we
+uh we get rotations rotate rotational
+
+ align:start position:0%
+uh we get rotations rotate rotational
+ 
+
+ align:start position:0%
+uh we get rotations rotate rotational
+wave functions are really the
+
+ align:start position:0%
+wave functions are really the
+ 
+
+ align:start position:0%
+wave functions are really the
+transformation between the laboratory
+
+ align:start position:0%
+transformation between the laboratory
+ 
+
+ align:start position:0%
+transformation between the laboratory
+and the body.
+
+ align:start position:0%
+and the body.
+ 
+
+ align:start position:0%
+and the body.
+and and so the information once we
+
+ align:start position:0%
+and and so the information once we
+ 
+
+ align:start position:0%
+and and so the information once we
+specify where the dipole is in the
+
+ align:start position:0%
+specify where the dipole is in the
+ 
+
+ align:start position:0%
+specify where the dipole is in the
+laboratory in the molecule then uh the
+
+ align:start position:0%
+laboratory in the molecule then uh the
+ 
+
+ align:start position:0%
+laboratory in the molecule then uh the
+rotational selection rules give you know
+
+ align:start position:0%
+rotational selection rules give you know
+ 
+
+ align:start position:0%
+rotational selection rules give you know
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um tell us about the relationship
+
+ align:start position:0%
+um tell us about the relationship
+ 
+
+ align:start position:0%
+um tell us about the relationship
+between the laboratory and the body.
+
+ align:start position:0%
+between the laboratory and the body.
+ 
+
+ align:start position:0%
+between the laboratory and the body.
+Okay. Now uh we don't care
+
+ align:start position:0%
+Okay. Now uh we don't care
+ 
+
+ align:start position:0%
+Okay. Now uh we don't care
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+polarization along the x y and z axes in
+
+ align:start position:0%
+polarization along the x y and z axes in
+ 
+
+ align:start position:0%
+polarization along the x y and z axes in
+the laboratory but we do care about how
+
+ align:start position:0%
+the laboratory but we do care about how
+ 
+
+ align:start position:0%
+the laboratory but we do care about how
+the transition moment in the body
+
+ align:start position:0%
+the transition moment in the body
+ 
+
+ align:start position:0%
+the transition moment in the body
+frame. Yes. Okay. So uh it's a good
+
+ align:start position:0%
+frame. Yes. Okay. So uh it's a good
+ 
+
+ align:start position:0%
+frame. Yes. Okay. So uh it's a good
+question but I think that uh I think
+
+ align:start position:0%
+question but I think that uh I think
+ 
+
+ align:start position:0%
+question but I think that uh I think
+I've answered it in a fairly primitive
+
+ align:start position:0%
+I've answered it in a fairly primitive
+ 
+
+ align:start position:0%
+I've answered it in a fairly primitive
+way.
+
+ align:start position:0%
+way.
+ 
+
+ align:start position:0%
+way.
+Okay. All right.
+
+ align:start position:0%
+Okay. All right.
+ 
+
+ align:start position:0%
+Okay. All right.
+So for D3H we have four uh modes three
+
+ align:start position:0%
+So for D3H we have four uh modes three
+ 
+
+ align:start position:0%
+So for D3H we have four uh modes three
+of which are um infrared
+
+ align:start position:0%
+of which are um infrared
+ 
+
+ align:start position:0%
+of which are um infrared
+active and
+
+ align:start position:0%
+active and
+ 
+
+ align:start position:0%
+active and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um if I had filled out this table I
+
+ align:start position:0%
+um if I had filled out this table I
+ 
+
+ align:start position:0%
+um if I had filled out this table I
+think we would have found that uh the
+
+ align:start position:0%
+think we would have found that uh the
+ 
+
+ align:start position:0%
+think we would have found that uh the
+other one is ramen active and there is a
+
+ align:start position:0%
+other one is ramen active and there is a
+ 
+
+ align:start position:0%
+other one is ramen active and there is a
+general rule about uh complime mentarity
+
+ align:start position:0%
+general rule about uh complime mentarity
+ 
+
+ align:start position:0%
+general rule about uh complime mentarity
+or there's a rule and uh in certain
+
+ align:start position:0%
+or there's a rule and uh in certain
+ 
+
+ align:start position:0%
+or there's a rule and uh in certain
+symmetry species if it's now I better
+
+ align:start position:0%
+symmetry species if it's now I better
+ 
+
+ align:start position:0%
+symmetry species if it's now I better
+not say that I don't know uh but often
+
+ align:start position:0%
+not say that I don't know uh but often
+ 
+
+ align:start position:0%
+not say that I don't know uh but often
+you get if there's a mode that's
+
+ align:start position:0%
+you get if there's a mode that's
+ 
+
+ align:start position:0%
+you get if there's a mode that's
+forbidden infrared uh chances are it
+
+ align:start position:0%
+forbidden infrared uh chances are it
+ 
+
+ align:start position:0%
+forbidden infrared uh chances are it
+will be allowed rama but even so I mean
+
+ align:start position:0%
+will be allowed rama but even so I mean
+ 
+
+ align:start position:0%
+will be allowed rama but even so I mean
+if you have too many irreducible
+
+ align:start position:0%
+if you have too many irreducible
+ 
+
+ align:start position:0%
+if you have too many irreducible
+representations there's there's you know
+
+ align:start position:0%
+representations there's there's you know
+ 
+
+ align:start position:0%
+representations there's there's you know
+there uh there's uh no guarantee that
+
+ align:start position:0%
+there uh there's uh no guarantee that
+ 
+
+ align:start position:0%
+there uh there's uh no guarantee that
+all modes will be allowed both taking
+
+ align:start position:0%
+all modes will be allowed both taking
+ 
+
+ align:start position:0%
+all modes will be allowed both taking
+together infrared and ramen. So let's
+
+ align:start position:0%
+together infrared and ramen. So let's
+ 
+
+ align:start position:0%
+together infrared and ramen. So let's
+just uh be careful about do these um
+
+ align:start position:0%
+just uh be careful about do these um
+ 
+
+ align:start position:0%
+just uh be careful about do these um
+labels about the polarizability also
+
+ align:start position:0%
+labels about the polarizability also
+ 
+
+ align:start position:0%
+labels about the polarizability also
+tell you about the quadripole.
+
+ align:start position:0%
+tell you about the quadripole.
+ 
+
+ align:start position:0%
+tell you about the quadripole.
+Yes. Yes.
+
+ align:start position:0%
+Yes. Yes.
+ 
+
+ align:start position:0%
+Yes. Yes.
+Um and uh so these tell you about
+
+ align:start position:0%
+Um and uh so these tell you about
+ 
+
+ align:start position:0%
+Um and uh so these tell you about
+electric dipole. These tell you about
+
+ align:start position:0%
+electric dipole. These tell you about
+ 
+
+ align:start position:0%
+electric dipole. These tell you about
+magnetic dipole. Then there's a
+
+ align:start position:0%
+magnetic dipole. Then there's a
+ 
+
+ align:start position:0%
+magnetic dipole. Then there's a
+quadripole. There's all sorts of things.
+
+ align:start position:0%
+quadripole. There's all sorts of things.
+ 
+
+ align:start position:0%
+quadripole. There's all sorts of things.
+So uh you learn to use whichever symbol
+
+ align:start position:0%
+So uh you learn to use whichever symbol
+ 
+
+ align:start position:0%
+So uh you learn to use whichever symbol
+symbols are relevant to the kind of
+
+ align:start position:0%
+symbols are relevant to the kind of
+ 
+
+ align:start position:0%
+symbols are relevant to the kind of
+spectroscopy you're doing. Uh okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so one of the important things
+
+ align:start position:0%
+So, so one of the important things
+ 
+
+ align:start position:0%
+So, so one of the important things
+is here is a transition that is
+
+ align:start position:0%
+is here is a transition that is
+ 
+
+ align:start position:0%
+is here is a transition that is
+polarized in the body along the symmetry
+
+ align:start position:0%
+polarized in the body along the symmetry
+ 
+
+ align:start position:0%
+polarized in the body along the symmetry
+axis. And so we call that
+
+ align:start position:0%
+axis. And so we call that
+ 
+
+ align:start position:0%
+axis. And so we call that
+parallel and here is something polarized
+
+ align:start position:0%
+parallel and here is something polarized
+ 
+
+ align:start position:0%
+parallel and here is something polarized
+perpendicular to the symmetry axis and
+
+ align:start position:0%
+perpendicular to the symmetry axis and
+ 
+
+ align:start position:0%
+perpendicular to the symmetry axis and
+we call that perpendicular. And this is
+
+ align:start position:0%
+we call that perpendicular. And this is
+ 
+
+ align:start position:0%
+we call that perpendicular. And this is
+all the difference in the world as far
+
+ align:start position:0%
+all the difference in the world as far
+ 
+
+ align:start position:0%
+all the difference in the world as far
+as the rotational structure of the bands
+
+ align:start position:0%
+as the rotational structure of the bands
+ 
+
+ align:start position:0%
+as the rotational structure of the bands
+is going to be. And we saw that for
+
+ align:start position:0%
+is going to be. And we saw that for
+ 
+
+ align:start position:0%
+is going to be. And we saw that for
+diatomic molecules we had transitions
+
+ align:start position:0%
+diatomic molecules we had transitions
+ 
+
+ align:start position:0%
+diatomic molecules we had transitions
+that were parallel delta omega equals z
+
+ align:start position:0%
+that were parallel delta omega equals z
+ 
+
+ align:start position:0%
+that were parallel delta omega equals z
+and they don't have q
+
+ align:start position:0%
+and they don't have q
+ 
+
+ align:start position:0%
+and they don't have q
+branches and or they have really weak q
+
+ align:start position:0%
+branches and or they have really weak q
+ 
+
+ align:start position:0%
+branches and or they have really weak q
+branches. Um and perpendicular
+
+ align:start position:0%
+branches. Um and perpendicular
+ 
+
+ align:start position:0%
+branches. Um and perpendicular
+transitions they have delta omega plus
+
+ align:start position:0%
+transitions they have delta omega plus
+ 
+
+ align:start position:0%
+transitions they have delta omega plus
+or minus one. They have strong q
+
+ align:start position:0%
+or minus one. They have strong q
+ 
+
+ align:start position:0%
+or minus one. They have strong q
+branches. And so this is going to be
+
+ align:start position:0%
+branches. And so this is going to be
+ 
+
+ align:start position:0%
+branches. And so this is going to be
+delta k equals z. This is going to be
+
+ align:start position:0%
+delta k equals z. This is going to be
+ 
+
+ align:start position:0%
+delta k equals z. This is going to be
+delta k equals plus or minus one. This
+
+ align:start position:0%
+delta k equals plus or minus one. This
+ 
+
+ align:start position:0%
+delta k equals plus or minus one. This
+is going to have no q weak q branches.
+
+ align:start position:0%
+is going to have no q weak q branches.
+ 
+
+ align:start position:0%
+is going to have no q weak q branches.
+is going to have strong cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges.
+
+ align:start position:0%
+edges.
+ 
+
+ align:start position:0%
+edges.
+Okay. So, the traditional way
+
+ align:start position:0%
+Okay. So, the traditional way
+ 
+
+ align:start position:0%
+Okay. So, the traditional way
+of making sense of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what you're going to see in the
+
+ align:start position:0%
+uh what you're going to see in the
+ 
+
+ align:start position:0%
+uh what you're going to see in the
+spectrum. There's all the textbooks have
+
+ align:start position:0%
+spectrum. There's all the textbooks have
+ 
+
+ align:start position:0%
+spectrum. There's all the textbooks have
+to do with uh an ordinary uh um
+
+ align:start position:0%
+to do with uh an ordinary uh um
+ 
+
+ align:start position:0%
+to do with uh an ordinary uh um
+lowresolution spectrum which you would
+
+ align:start position:0%
+lowresolution spectrum which you would
+ 
+
+ align:start position:0%
+lowresolution spectrum which you would
+re record using a spectrograph rather
+
+ align:start position:0%
+re record using a spectrograph rather
+ 
+
+ align:start position:0%
+re record using a spectrograph rather
+than a
+
+ align:start position:0%
+than a
+ 
+
+ align:start position:0%
+than a
+laser. And so I'll start with that. But
+
+ align:start position:0%
+laser. And so I'll start with that. But
+ 
+
+ align:start position:0%
+laser. And so I'll start with that. But
+you should think when you're doing laser
+
+ align:start position:0%
+you should think when you're doing laser
+ 
+
+ align:start position:0%
+you should think when you're doing laser
+spectroscopy
+
+ align:start position:0%
+spectroscopy
+ 
+
+ align:start position:0%
+spectroscopy
+uh it's usually difficult to tune the
+
+ align:start position:0%
+uh it's usually difficult to tune the
+ 
+
+ align:start position:0%
+uh it's usually difficult to tune the
+laser over a lot of spectrum and often
+
+ align:start position:0%
+laser over a lot of spectrum and often
+ 
+
+ align:start position:0%
+laser over a lot of spectrum and often
+you want to get the answer about what is
+
+ align:start position:0%
+you want to get the answer about what is
+ 
+
+ align:start position:0%
+you want to get the answer about what is
+the uh uh what is the um assignment of
+
+ align:start position:0%
+the uh uh what is the um assignment of
+ 
+
+ align:start position:0%
+the uh uh what is the um assignment of
+the spectrum? What is the symmetry of
+
+ align:start position:0%
+the spectrum? What is the symmetry of
+ 
+
+ align:start position:0%
+the spectrum? What is the symmetry of
+the molecule based on a limited amount
+
+ align:start position:0%
+the molecule based on a limited amount
+ 
+
+ align:start position:0%
+the molecule based on a limited amount
+of spectroscopic observation and the
+
+ align:start position:0%
+of spectroscopic observation and the
+ 
+
+ align:start position:0%
+of spectroscopic observation and the
+kinds of questions you ask would be
+
+ align:start position:0%
+kinds of questions you ask would be
+ 
+
+ align:start position:0%
+kinds of questions you ask would be
+different. this would be a legitimate
+
+ align:start position:0%
+different. this would be a legitimate
+ 
+
+ align:start position:0%
+different. this would be a legitimate
+kind of problem but I haven't completely
+
+ align:start position:0%
+kind of problem but I haven't completely
+ 
+
+ align:start position:0%
+kind of problem but I haven't completely
+formulated it. So I will draw the
+
+ align:start position:0%
+formulated it. So I will draw the
+ 
+
+ align:start position:0%
+formulated it. So I will draw the
+pictures the traditional pictures but
+
+ align:start position:0%
+pictures the traditional pictures but
+ 
+
+ align:start position:0%
+pictures the traditional pictures but
+um uh you should you should think about
+
+ align:start position:0%
+um uh you should you should think about
+ 
+
+ align:start position:0%
+um uh you should you should think about
+well what would you know how would you
+
+ align:start position:0%
+well what would you know how would you
+ 
+
+ align:start position:0%
+well what would you know how would you
+use group theory to get a little bit of
+
+ align:start position:0%
+use group theory to get a little bit of
+ 
+
+ align:start position:0%
+use group theory to get a little bit of
+spectrum and decide from a little bit of
+
+ align:start position:0%
+spectrum and decide from a little bit of
+ 
+
+ align:start position:0%
+spectrum and decide from a little bit of
+spectrum what the molecule is doing.
+
+ align:start position:0%
+spectrum what the molecule is doing.
+ 
+
+ align:start position:0%
+spectrum what the molecule is doing.
+Okay, so remember when we talked about
+
+ align:start position:0%
+Okay, so remember when we talked about
+ 
+
+ align:start position:0%
+Okay, so remember when we talked about
+infrared spectra of
+
+ align:start position:0%
+infrared spectra of
+ 
+
+ align:start position:0%
+infrared spectra of
+molecules, we drew this sort of double
+
+ align:start position:0%
+molecules, we drew this sort of double
+ 
+
+ align:start position:0%
+molecules, we drew this sort of double
+hump pattern. And so if we have red on
+
+ align:start position:0%
+hump pattern. And so if we have red on
+ 
+
+ align:start position:0%
+hump pattern. And so if we have red on
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right, so this would be the R branch and
+
+ align:start position:0%
+right, so this would be the R branch and
+ 
+
+ align:start position:0%
+right, so this would be the R branch and
+this would be the P branch.
+
+ align:start position:0%
+this would be the P branch.
+ 
+
+ align:start position:0%
+this would be the P branch.
+And uh uh if it were a perpendicular
+
+ align:start position:0%
+And uh uh if it were a perpendicular
+ 
+
+ align:start position:0%
+And uh uh if it were a perpendicular
+transition which which was kind of hard
+
+ align:start position:0%
+transition which which was kind of hard
+ 
+
+ align:start position:0%
+transition which which was kind of hard
+to imagine for a diatomic molecule but
+
+ align:start position:0%
+to imagine for a diatomic molecule but
+ 
+
+ align:start position:0%
+to imagine for a diatomic molecule but
+there uh then you would have a Q branch
+
+ align:start position:0%
+there uh then you would have a Q branch
+ 
+
+ align:start position:0%
+there uh then you would have a Q branch
+here. So that there is a gap near the
+
+ align:start position:0%
+here. So that there is a gap near the
+ 
+
+ align:start position:0%
+here. So that there is a gap near the
+origin of the band and if there is going
+
+ align:start position:0%
+origin of the band and if there is going
+ 
+
+ align:start position:0%
+origin of the band and if there is going
+to be a Q branch it'll be close to it
+
+ align:start position:0%
+to be a Q branch it'll be close to it
+ 
+
+ align:start position:0%
+to be a Q branch it'll be close to it
+and the R and P branches are always
+
+ align:start position:0%
+and the R and P branches are always
+ 
+
+ align:start position:0%
+and the R and P branches are always
+spread out and the Q branch is always
+
+ align:start position:0%
+spread out and the Q branch is always
+ 
+
+ align:start position:0%
+spread out and the Q branch is always
+compressed. So this is sort of a model
+
+ align:start position:0%
+compressed. So this is sort of a model
+ 
+
+ align:start position:0%
+compressed. So this is sort of a model
+for what we would have for polyatomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecules. So
+
+ align:start position:0%
+molecules. So
+ 
+
+ align:start position:0%
+molecules. So
+uh if we have a parallel type
+
+ align:start position:0%
+uh if we have a parallel type
+ 
+
+ align:start position:0%
+uh if we have a parallel type
+transition so
+
+ align:start position:0%
+transition so
+ 
+
+ align:start position:0%
+transition so
+parallel means delta k symmetry whatever
+
+ align:start position:0%
+parallel means delta k symmetry whatever
+ 
+
+ align:start position:0%
+parallel means delta k symmetry whatever
+it is oblate or prolate is equal to
+
+ align:start position:0%
+it is oblate or prolate is equal to
+ 
+
+ align:start position:0%
+it is oblate or prolate is equal to
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+So we have uh
+
+ align:start position:0%
+So we have uh
+ 
+
+ align:start position:0%
+So we have uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one um one say we have k equals z and
+
+ align:start position:0%
+one um one say we have k equals z and
+ 
+
+ align:start position:0%
+one um one say we have k equals z and
+then we have k equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and so for k equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so in k equals 0 we have a stack
+
+ align:start position:0%
+um yeah so in k equals 0 we have a stack
+ 
+
+ align:start position:0%
+um yeah so in k equals 0 we have a stack
+of rotational levels. In K equals 1, we
+
+ align:start position:0%
+of rotational levels. In K equals 1, we
+ 
+
+ align:start position:0%
+of rotational levels. In K equals 1, we
+have a stack of rotational levels. And
+
+ align:start position:0%
+have a stack of rotational levels. And
+ 
+
+ align:start position:0%
+have a stack of rotational levels. And
+so, uh, we're going K=0 lower state to K
+
+ align:start position:0%
+so, uh, we're going K=0 lower state to K
+ 
+
+ align:start position:0%
+so, uh, we're going K=0 lower state to K
+equals Z upper state. Rotational levels.
+
+ align:start position:0%
+equals Z upper state. Rotational levels.
+ 
+
+ align:start position:0%
+equals Z upper state. Rotational levels.
+The rotational, uh, the the J structure
+
+ align:start position:0%
+The rotational, uh, the the J structure
+ 
+
+ align:start position:0%
+The rotational, uh, the the J structure
+of a given K is pretty much the same
+
+ align:start position:0%
+of a given K is pretty much the same
+ 
+
+ align:start position:0%
+of a given K is pretty much the same
+from one vibrational level to another
+
+ align:start position:0%
+from one vibrational level to another
+ 
+
+ align:start position:0%
+from one vibrational level to another
+and from one K stack to the next, except
+
+ align:start position:0%
+and from one K stack to the next, except
+ 
+
+ align:start position:0%
+and from one K stack to the next, except
+that the lowest few J's are missing for
+
+ align:start position:0%
+that the lowest few J's are missing for
+ 
+
+ align:start position:0%
+that the lowest few J's are missing for
+K not equal to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so if you're going to be doing a
+
+ align:start position:0%
+And so if you're going to be doing a
+ 
+
+ align:start position:0%
+And so if you're going to be doing a
+laser
+
+ align:start position:0%
+laser
+ 
+
+ align:start position:0%
+laser
+experiment, one thing you could do is
+
+ align:start position:0%
+experiment, one thing you could do is
+ 
+
+ align:start position:0%
+experiment, one thing you could do is
+make sure the molecule is really
+
+ align:start position:0%
+make sure the molecule is really
+ 
+
+ align:start position:0%
+make sure the molecule is really
+cold. And so that clears away a lot of
+
+ align:start position:0%
+cold. And so that clears away a lot of
+ 
+
+ align:start position:0%
+cold. And so that clears away a lot of
+the rubble. And then you would be
+
+ align:start position:0%
+the rubble. And then you would be
+ 
+
+ align:start position:0%
+the rubble. And then you would be
+looking to see where what is the lowest
+
+ align:start position:0%
+looking to see where what is the lowest
+ 
+
+ align:start position:0%
+looking to see where what is the lowest
+J you have in a particular series of
+
+ align:start position:0%
+J you have in a particular series of
+ 
+
+ align:start position:0%
+J you have in a particular series of
+lines, which you do by combination
+
+ align:start position:0%
+lines, which you do by combination
+ 
+
+ align:start position:0%
+lines, which you do by combination
+differences. And just rotational cold.
+
+ align:start position:0%
+differences. And just rotational cold.
+ 
+
+ align:start position:0%
+differences. And just rotational cold.
+Yeah, you that would be one way to do
+
+ align:start position:0%
+Yeah, you that would be one way to do
+ 
+
+ align:start position:0%
+Yeah, you that would be one way to do
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Um now one really important thing is
+
+ align:start position:0%
+Um now one really important thing is
+ 
+
+ align:start position:0%
+Um now one really important thing is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh for a prolate
+
+ align:start position:0%
+uh for a prolate
+ 
+
+ align:start position:0%
+uh for a prolate
+top the J structure is smaller than the
+
+ align:start position:0%
+top the J structure is smaller than the
+ 
+
+ align:start position:0%
+top the J structure is smaller than the
+K structure. For an oblate top the J
+
+ align:start position:0%
+K structure. For an oblate top the J
+ 
+
+ align:start position:0%
+K structure. For an oblate top the J
+structure is larger than the K
+
+ align:start position:0%
+structure is larger than the K
+ 
+
+ align:start position:0%
+structure is larger than the K
+structure.
+
+ align:start position:0%
+structure.
+ 
+
+ align:start position:0%
+structure.
+But for both kinds of tops, if you have
+
+ align:start position:0%
+But for both kinds of tops, if you have
+ 
+
+ align:start position:0%
+But for both kinds of tops, if you have
+a parallel
+
+ align:start position:0%
+a parallel
+ 
+
+ align:start position:0%
+a parallel
+transition, the the 0ero to zero
+
+ align:start position:0%
+transition, the the 0ero to zero
+ 
+
+ align:start position:0%
+transition, the the 0ero to zero
+transition and the one to one
+
+ align:start position:0%
+transition and the one to one
+ 
+
+ align:start position:0%
+transition and the one to one
+transitions are going to be almost on
+
+ align:start position:0%
+transitions are going to be almost on
+ 
+
+ align:start position:0%
+transitions are going to be almost on
+top of each
+
+ align:start position:0%
+top of each
+ 
+
+ align:start position:0%
+top of each
+other. For symmetric tops, uh you can
+
+ align:start position:0%
+other. For symmetric tops, uh you can
+ 
+
+ align:start position:0%
+other. For symmetric tops, uh you can
+observe multiple KS, but you can't
+
+ align:start position:0%
+observe multiple KS, but you can't
+ 
+
+ align:start position:0%
+observe multiple KS, but you can't
+observe transitions between them and
+
+ align:start position:0%
+observe transitions between them and
+ 
+
+ align:start position:0%
+observe transitions between them and
+they all stack up. And so for a parallel
+
+ align:start position:0%
+they all stack up. And so for a parallel
+ 
+
+ align:start position:0%
+they all stack up. And so for a parallel
+type transition, all of the different
+
+ align:start position:0%
+type transition, all of the different
+ 
+
+ align:start position:0%
+type transition, all of the different
+uh K subbands look roughly like this.
+
+ align:start position:0%
+uh K subbands look roughly like this.
+ 
+
+ align:start position:0%
+uh K subbands look roughly like this.
+They have this double hump structure.
+
+ align:start position:0%
+They have this double hump structure.
+ 
+
+ align:start position:0%
+They have this double hump structure.
+There's missing stuff in the
+
+ align:start position:0%
+There's missing stuff in the
+ 
+
+ align:start position:0%
+There's missing stuff in the
+middle. And there could be a Q line. The
+
+ align:start position:0%
+middle. And there could be a Q line. The
+ 
+
+ align:start position:0%
+middle. And there could be a Q line. The
+Q- line is generally weak. But it turns
+
+ align:start position:0%
+Q- line is generally weak. But it turns
+ 
+
+ align:start position:0%
+Q- line is generally weak. But it turns
+out that when K is not equal to zero,
+
+ align:start position:0%
+out that when K is not equal to zero,
+ 
+
+ align:start position:0%
+out that when K is not equal to zero,
+there will be one moderately strong Q
+
+ align:start position:0%
+there will be one moderately strong Q
+ 
+
+ align:start position:0%
+there will be one moderately strong Q
+line Q for J is equal to
+
+ align:start position:0%
+line Q for J is equal to
+ 
+
+ align:start position:0%
+line Q for J is equal to
+K. And so the
+
+ align:start position:0%
+K. And so the
+ 
+
+ align:start position:0%
+K. And so the
+parallel bands have the appearance more
+
+ align:start position:0%
+parallel bands have the appearance more
+ 
+
+ align:start position:0%
+parallel bands have the appearance more
+or less just like this, as if it was
+
+ align:start position:0%
+or less just like this, as if it was
+ 
+
+ align:start position:0%
+or less just like this, as if it was
+just a simple diatomic, except that
+
+ align:start position:0%
+just a simple diatomic, except that
+ 
+
+ align:start position:0%
+just a simple diatomic, except that
+there's a lot of lines. And so you see
+
+ align:start position:0%
+there's a lot of lines. And so you see
+ 
+
+ align:start position:0%
+there's a lot of lines. And so you see
+this this simple double hump and a and a
+
+ align:start position:0%
+this this simple double hump and a and a
+ 
+
+ align:start position:0%
+this this simple double hump and a and a
+little bit of a a spike
+
+ align:start position:0%
+little bit of a a spike
+ 
+
+ align:start position:0%
+little bit of a a spike
+here. So one of the bands is going to
+
+ align:start position:0%
+here. So one of the bands is going to
+ 
+
+ align:start position:0%
+here. So one of the bands is going to
+look like this. And perpendicular
+
+ align:start position:0%
+look like this. And perpendicular
+ 
+
+ align:start position:0%
+look like this. And perpendicular
+transitions, those are going to be
+
+ align:start position:0%
+transitions, those are going to be
+ 
+
+ align:start position:0%
+transitions, those are going to be
+transitions where you go from kals 0 to
+
+ align:start position:0%
+transitions where you go from kals 0 to
+ 
+
+ align:start position:0%
+transitions where you go from kals 0 to
+k= 1. uh and uh uh k
+
+ align:start position:0%
+k= 1. uh and uh uh k
+ 
+
+ align:start position:0%
+k= 1. uh and uh uh k
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um k= 1 to k equals z and things like
+
+ align:start position:0%
+um k= 1 to k equals z and things like
+ 
+
+ align:start position:0%
+um k= 1 to k equals z and things like
+that. So there's going to be a whole
+
+ align:start position:0%
+that. So there's going to be a whole
+ 
+
+ align:start position:0%
+that. So there's going to be a whole
+bunch of bands. This time each of them
+
+ align:start position:0%
+bunch of bands. This time each of them
+ 
+
+ align:start position:0%
+bunch of bands. This time each of them
+is going to have a big spike here
+
+ align:start position:0%
+is going to have a big spike here
+ 
+
+ align:start position:0%
+is going to have a big spike here
+because the Q branches are strong. And
+
+ align:start position:0%
+because the Q branches are strong. And
+ 
+
+ align:start position:0%
+because the Q branches are strong. And
+so the question is how do these bands
+
+ align:start position:0%
+so the question is how do these bands
+ 
+
+ align:start position:0%
+so the question is how do these bands
+how are they
+
+ align:start position:0%
+how are they
+ 
+
+ align:start position:0%
+how are they
+arranged? And they're arranged uh
+
+ align:start position:0%
+arranged? And they're arranged uh
+ 
+
+ align:start position:0%
+arranged? And they're arranged uh
+basically you have uh for a prolate top
+
+ align:start position:0%
+basically you have uh for a prolate top
+ 
+
+ align:start position:0%
+basically you have uh for a prolate top
+you have uh c k
+
+ align:start position:0%
+you have uh c k
+ 
+
+ align:start position:0%
+you have uh c k
+squared and so uh you'll have a
+
+ align:start position:0%
+squared and so uh you'll have a
+ 
+
+ align:start position:0%
+squared and so uh you'll have a
+transition that goes uh from zero to one
+
+ align:start position:0%
+transition that goes uh from zero to one
+ 
+
+ align:start position:0%
+transition that goes uh from zero to one
+and from one to two and from two to
+
+ align:start position:0%
+and from one to two and from two to
+ 
+
+ align:start position:0%
+and from one to two and from two to
+three. 0 to one is going to be one is
+
+ align:start position:0%
+three. 0 to one is going to be one is
+ 
+
+ align:start position:0%
+three. 0 to one is going to be one is
+going to be zero. Uh so so
+
+ align:start position:0%
+going to be zero. Uh so so
+ 
+
+ align:start position:0%
+going to be zero. Uh so so
+let's let's just draw this arrow like
+
+ align:start position:0%
+let's let's just draw this arrow like
+ 
+
+ align:start position:0%
+let's let's just draw this arrow like
+that. So this will be 1^ 2 - 0 1 a 1
+
+ align:start position:0%
+that. So this will be 1^ 2 - 0 1 a 1
+ 
+
+ align:start position:0%
+that. So this will be 1^ 2 - 0 1 a 1
+C and this is going to start at 4 - 1 is
+
+ align:start position:0%
+C and this is going to start at 4 - 1 is
+ 
+
+ align:start position:0%
+C and this is going to start at 4 - 1 is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+C 9 - 4 is 5 C. So what you're going to
+
+ align:start position:0%
+C 9 - 4 is 5 C. So what you're going to
+ 
+
+ align:start position:0%
+C 9 - 4 is 5 C. So what you're going to
+see is a series of subbands separated in
+
+ align:start position:0%
+see is a series of subbands separated in
+ 
+
+ align:start position:0%
+see is a series of subbands separated in
+intervals of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2C. So
+
+ align:start position:0%
+2C. So
+ 
+
+ align:start position:0%
+2C. So
+um and you can go 0ero to one or you can
+
+ align:start position:0%
+um and you can go 0ero to one or you can
+ 
+
+ align:start position:0%
+um and you can go 0ero to one or you can
+do uh you can go in the opposite
+
+ align:start position:0%
+do uh you can go in the opposite
+ 
+
+ align:start position:0%
+do uh you can go in the opposite
+direction. And so there'll be bands uh
+
+ align:start position:0%
+direction. And so there'll be bands uh
+ 
+
+ align:start position:0%
+direction. And so there'll be bands uh
+uh there'll be subbands with Q branches
+
+ align:start position:0%
+uh there'll be subbands with Q branches
+ 
+
+ align:start position:0%
+uh there'll be subbands with Q branches
+going one way and Q branches going the
+
+ align:start position:0%
+going one way and Q branches going the
+ 
+
+ align:start position:0%
+going one way and Q branches going the
+other way. And so what do we do? How do
+
+ align:start position:0%
+other way. And so what do we do? How do
+ 
+
+ align:start position:0%
+other way. And so what do we do? How do
+we denote those transitions?
+
+ align:start position:0%
+we denote those transitions?
+ 
+
+ align:start position:0%
+we denote those transitions?
+So we have a
+
+ align:start position:0%
+So we have a
+ 
+
+ align:start position:0%
+So we have a
+notation delta
+
+ align:start position:0%
+notation delta
+ 
+
+ align:start position:0%
+notation delta
+J delta
+
+ align:start position:0%
+J delta
+ 
+
+ align:start position:0%
+J delta
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+initial and we put J
+
+ align:start position:0%
+initial and we put J
+ 
+
+ align:start position:0%
+initial and we put J
+here. So that's how we denote the uh the
+
+ align:start position:0%
+here. So that's how we denote the uh the
+ 
+
+ align:start position:0%
+here. So that's how we denote the uh the
+name of a rotational line. So we use PQ
+
+ align:start position:0%
+name of a rotational line. So we use PQ
+ 
+
+ align:start position:0%
+name of a rotational line. So we use PQ
+and R for delta J. We use PQ and R for
+
+ align:start position:0%
+and R for delta J. We use PQ and R for
+ 
+
+ align:start position:0%
+and R for delta J. We use PQ and R for
+delta K.
+
+ align:start position:0%
+delta K.
+ 
+
+ align:start position:0%
+delta K.
+We specify the number of the initial K
+
+ align:start position:0%
+We specify the number of the initial K
+ 
+
+ align:start position:0%
+We specify the number of the initial K
+and the initial J. The double prime is
+
+ align:start position:0%
+and the initial J. The double prime is
+ 
+
+ align:start position:0%
+and the initial J. The double prime is
+not a symmetry label. It's initial state
+
+ align:start position:0%
+not a symmetry label. It's initial state
+ 
+
+ align:start position:0%
+not a symmetry label. It's initial state
+lower state. I'm sorry, lower state.
+
+ align:start position:0%
+lower state. I'm sorry, lower state.
+ 
+
+ align:start position:0%
+lower state. I'm sorry, lower state.
+Double prime lower
+
+ align:start position:0%
+Double prime lower
+ 
+
+ align:start position:0%
+Double prime lower
+state, single prime, upper state. So
+
+ align:start position:0%
+state, single prime, upper state. So
+ 
+
+ align:start position:0%
+state, single prime, upper state. So
+this is a a very convenient notation
+
+ align:start position:0%
+this is a a very convenient notation
+ 
+
+ align:start position:0%
+this is a a very convenient notation
+that will enable you to label every
+
+ align:start position:0%
+that will enable you to label every
+ 
+
+ align:start position:0%
+that will enable you to label every
+line. Okay? And
+
+ align:start position:0%
+line. Okay? And
+ 
+
+ align:start position:0%
+line. Okay? And
+uh so what you can discover I mean if
+
+ align:start position:0%
+uh so what you can discover I mean if
+ 
+
+ align:start position:0%
+uh so what you can discover I mean if
+you if you're doing relatively low
+
+ align:start position:0%
+you if you're doing relatively low
+ 
+
+ align:start position:0%
+you if you're doing relatively low
+resolution spectroscopy the thing that's
+
+ align:start position:0%
+resolution spectroscopy the thing that's
+ 
+
+ align:start position:0%
+resolution spectroscopy the thing that's
+going to stand out is the Q
+
+ align:start position:0%
+going to stand out is the Q
+ 
+
+ align:start position:0%
+going to stand out is the Q
+branches. And so there'll be a series of
+
+ align:start position:0%
+branches. And so there'll be a series of
+ 
+
+ align:start position:0%
+branches. And so there'll be a series of
+equally spaced Q branches associated
+
+ align:start position:0%
+equally spaced Q branches associated
+ 
+
+ align:start position:0%
+equally spaced Q branches associated
+with each of these K transitions.
+
+ align:start position:0%
+with each of these K transitions.
+ 
+
+ align:start position:0%
+with each of these K transitions.
+And uh
+
+ align:start position:0%
+And uh
+ 
+
+ align:start position:0%
+And uh
+uh so uh on page seven at the top I show
+
+ align:start position:0%
+uh so uh on page seven at the top I show
+ 
+
+ align:start position:0%
+uh so uh on page seven at the top I show
+a bunch of spectra
+
+ align:start position:0%
+a bunch of spectra
+ 
+
+ align:start position:0%
+a bunch of spectra
+uh each like this but the whole spectrum
+
+ align:start position:0%
+uh each like this but the whole spectrum
+ 
+
+ align:start position:0%
+uh each like this but the whole spectrum
+shifted in steps of 2C this way and that
+
+ align:start position:0%
+shifted in steps of 2C this way and that
+ 
+
+ align:start position:0%
+shifted in steps of 2C this way and that
+way. And then I just take those spectrum
+
+ align:start position:0%
+way. And then I just take those spectrum
+ 
+
+ align:start position:0%
+way. And then I just take those spectrum
+and add them together and I see a series
+
+ align:start position:0%
+and add them together and I see a series
+ 
+
+ align:start position:0%
+and add them together and I see a series
+of equally spaced cube branches with a
+
+ align:start position:0%
+of equally spaced cube branches with a
+ 
+
+ align:start position:0%
+of equally spaced cube branches with a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+trash. And so that provides you with the
+
+ align:start position:0%
+trash. And so that provides you with the
+ 
+
+ align:start position:0%
+trash. And so that provides you with the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the signature of a perpendicular
+
+ align:start position:0%
+the signature of a perpendicular
+ 
+
+ align:start position:0%
+the signature of a perpendicular
+transition in a symmetric top. This
+
+ align:start position:0%
+transition in a symmetric top. This
+ 
+
+ align:start position:0%
+transition in a symmetric top. This
+series of strong Q branch spikes. And uh
+
+ align:start position:0%
+series of strong Q branch spikes. And uh
+ 
+
+ align:start position:0%
+series of strong Q branch spikes. And uh
+whereas a parallel
+
+ align:start position:0%
+whereas a parallel
+ 
+
+ align:start position:0%
+whereas a parallel
+transition has uh just a single uh hot
+
+ align:start position:0%
+transition has uh just a single uh hot
+ 
+
+ align:start position:0%
+transition has uh just a single uh hot
+spot in the middle, not quite so
+
+ align:start position:0%
+spot in the middle, not quite so
+ 
+
+ align:start position:0%
+spot in the middle, not quite so
+compact. Uh but uh um and since the Q
+
+ align:start position:0%
+compact. Uh but uh um and since the Q
+ 
+
+ align:start position:0%
+compact. Uh but uh um and since the Q
+branches are relatively weak, that hot
+
+ align:start position:0%
+branches are relatively weak, that hot
+ 
+
+ align:start position:0%
+branches are relatively weak, that hot
+spot in the middle is uh not
+
+ align:start position:0%
+spot in the middle is uh not
+ 
+
+ align:start position:0%
+spot in the middle is uh not
+overwhelmingly stronger than the other
+
+ align:start position:0%
+overwhelmingly stronger than the other
+ 
+
+ align:start position:0%
+overwhelmingly stronger than the other
+lines. Um but because they tend to be a
+
+ align:start position:0%
+lines. Um but because they tend to be a
+ 
+
+ align:start position:0%
+lines. Um but because they tend to be a
+little bit closer together, it's still
+
+ align:start position:0%
+little bit closer together, it's still
+ 
+
+ align:start position:0%
+little bit closer together, it's still
+pretty prominent in the spectrum. Okay.
+
+ align:start position:0%
+pretty prominent in the spectrum. Okay.
+ 
+
+ align:start position:0%
+pretty prominent in the spectrum. Okay.
+What time how much time do I have?
+
+ align:start position:0%
+What time how much time do I have?
+ 
+
+ align:start position:0%
+What time how much time do I have?
+Negative four minutes. Negative4
+
+ align:start position:0%
+Negative four minutes. Negative4
+ 
+
+ align:start position:0%
+Negative four minutes. Negative4
+minutes. That's not true.
+
+ align:start position:0%
+minutes. That's not true.
+ 
+
+ align:start position:0%
+minutes. That's not true.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. So, uh there are a whole bunch of
+
+ align:start position:0%
+Okay. So, uh there are a whole bunch of
+ 
+
+ align:start position:0%
+Okay. So, uh there are a whole bunch of
+pictures that you can draw for the
+
+ align:start position:0%
+pictures that you can draw for the
+ 
+
+ align:start position:0%
+pictures that you can draw for the
+various symmetry types of transitions.
+
+ align:start position:0%
+various symmetry types of transitions.
+ 
+
+ align:start position:0%
+various symmetry types of transitions.
+Now, if you say it's not D3H, it's
+
+ align:start position:0%
+Now, if you say it's not D3H, it's
+ 
+
+ align:start position:0%
+Now, if you say it's not D3H, it's
+C3V. C3V still has E
+
+ align:start position:0%
+C3V. C3V still has E
+ 
+
+ align:start position:0%
+C3V. C3V still has E
+representations, but it's a group of
+
+ align:start position:0%
+representations, but it's a group of
+ 
+
+ align:start position:0%
+representations, but it's a group of
+order six instead of 12.
+
+ align:start position:0%
+order six instead of 12.
+ 
+
+ align:start position:0%
+order six instead of 12.
+And uh
+
+ align:start position:0%
+And uh
+ 
+
+ align:start position:0%
+And uh
+um and but you can still
+
+ align:start position:0%
+um and but you can still
+ 
+
+ align:start position:0%
+um and but you can still
+uh you can still do all of this stuff.
+
+ align:start position:0%
+uh you can still do all of this stuff.
+ 
+
+ align:start position:0%
+uh you can still do all of this stuff.
+But then uh there's two possible C3Vs.
+
+ align:start position:0%
+But then uh there's two possible C3Vs.
+ 
+
+ align:start position:0%
+But then uh there's two possible C3Vs.
+There's a C3V where it's a prolate top
+
+ align:start position:0%
+There's a C3V where it's a prolate top
+ 
+
+ align:start position:0%
+There's a C3V where it's a prolate top
+and there's a C3V where it's uh it's
+
+ align:start position:0%
+and there's a C3V where it's uh it's
+ 
+
+ align:start position:0%
+and there's a C3V where it's uh it's
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+oblate and so and they will have
+
+ align:start position:0%
+oblate and so and they will have
+ 
+
+ align:start position:0%
+oblate and so and they will have
+different looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectra primarily because a an oblate
+
+ align:start position:0%
+spectra primarily because a an oblate
+ 
+
+ align:start position:0%
+spectra primarily because a an oblate
+top is going to have a CO is going to
+
+ align:start position:0%
+top is going to have a CO is going to
+ 
+
+ align:start position:0%
+top is going to have a CO is going to
+have K structure which is really small
+
+ align:start position:0%
+have K structure which is really small
+ 
+
+ align:start position:0%
+have K structure which is really small
+compared to
+
+ align:start position:0%
+compared to
+ 
+
+ align:start position:0%
+compared to
+rotation and the prolate top will have K
+
+ align:start position:0%
+rotation and the prolate top will have K
+ 
+
+ align:start position:0%
+rotation and the prolate top will have K
+structure which is large compared to the
+
+ align:start position:0%
+structure which is large compared to the
+ 
+
+ align:start position:0%
+structure which is large compared to the
+J structure. So there's all sorts of
+
+ align:start position:0%
+J structure. So there's all sorts of
+ 
+
+ align:start position:0%
+J structure. So there's all sorts of
+wonderful things you can do. Now uh on
+
+ align:start position:0%
+wonderful things you can do. Now uh on
+ 
+
+ align:start position:0%
+wonderful things you can do. Now uh on
+page nine in the middle there is a
+
+ align:start position:0%
+page nine in the middle there is a
+ 
+
+ align:start position:0%
+page nine in the middle there is a
+uh a little piece of a somewhat higher
+
+ align:start position:0%
+uh a little piece of a somewhat higher
+ 
+
+ align:start position:0%
+uh a little piece of a somewhat higher
+resolution spectrum which shows
+
+ align:start position:0%
+resolution spectrum which shows
+ 
+
+ align:start position:0%
+resolution spectrum which shows
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+uh K structure. So this is a a parallel
+
+ align:start position:0%
+uh K structure. So this is a a parallel
+ 
+
+ align:start position:0%
+uh K structure. So this is a a parallel
+type band and the caption is the K
+
+ align:start position:0%
+type band and the caption is the K
+ 
+
+ align:start position:0%
+type band and the caption is the K
+structure of two rotational lines in the
+
+ align:start position:0%
+structure of two rotational lines in the
+ 
+
+ align:start position:0%
+structure of two rotational lines in the
+CH3BR new3
+
+ align:start position:0%
+CH3BR new3
+ 
+
+ align:start position:0%
+CH3BR new3
+mode. Okay, there's all sorts of
+
+ align:start position:0%
+mode. Okay, there's all sorts of
+ 
+
+ align:start position:0%
+mode. Okay, there's all sorts of
+wonderful stuff here. First of all, two
+
+ align:start position:0%
+wonderful stuff here. First of all, two
+ 
+
+ align:start position:0%
+wonderful stuff here. First of all, two
+rotational lines that means two changes
+
+ align:start position:0%
+rotational lines that means two changes
+ 
+
+ align:start position:0%
+rotational lines that means two changes
+in J. P17 is J equ= 17 downstairs to J
+
+ align:start position:0%
+in J. P17 is J equ= 17 downstairs to J
+ 
+
+ align:start position:0%
+in J. P17 is J equ= 17 downstairs to J
+equ= 16 upstairs and P8 is the next one
+
+ align:start position:0%
+equ= 16 upstairs and P8 is the next one
+ 
+
+ align:start position:0%
+equ= 16 upstairs and P8 is the next one
+up. And there's a whole bunch of labels
+
+ align:start position:0%
+up. And there's a whole bunch of labels
+ 
+
+ align:start position:0%
+up. And there's a whole bunch of labels
+on that corresponding to the different
+
+ align:start position:0%
+on that corresponding to the different
+ 
+
+ align:start position:0%
+on that corresponding to the different
+case. This being an oblate top uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u it's not an oblate top. This being a
+
+ align:start position:0%
+u it's not an oblate top. This being a
+ 
+
+ align:start position:0%
+u it's not an oblate top. This being a
+parallel type transition. It's a prolate
+
+ align:start position:0%
+parallel type transition. It's a prolate
+ 
+
+ align:start position:0%
+parallel type transition. It's a prolate
+top because the hydrogens's are light
+
+ align:start position:0%
+top because the hydrogens's are light
+ 
+
+ align:start position:0%
+top because the hydrogens's are light
+and there's one bromine. uh if it were C
+
+ align:start position:0%
+and there's one bromine. uh if it were C
+ 
+
+ align:start position:0%
+and there's one bromine. uh if it were C
+B uh
+
+ align:start position:0%
+B uh
+ 
+
+ align:start position:0%
+B uh
+CBR3H probably oblate but uh uh the
+
+ align:start position:0%
+CBR3H probably oblate but uh uh the
+ 
+
+ align:start position:0%
+CBR3H probably oblate but uh uh the
+different rotational transitions for the
+
+ align:start position:0%
+different rotational transitions for the
+ 
+
+ align:start position:0%
+different rotational transitions for the
+different Ks are clustered
+
+ align:start position:0%
+different Ks are clustered
+ 
+
+ align:start position:0%
+different Ks are clustered
+together and and so uh that that is a
+
+ align:start position:0%
+together and and so uh that that is a
+ 
+
+ align:start position:0%
+together and and so uh that that is a
+would be a characteristic structure for
+
+ align:start position:0%
+would be a characteristic structure for
+ 
+
+ align:start position:0%
+would be a characteristic structure for
+a parallel type transition and uh um so
+
+ align:start position:0%
+a parallel type transition and uh um so
+ 
+
+ align:start position:0%
+a parallel type transition and uh um so
+anyway you you do this group theory and
+
+ align:start position:0%
+anyway you you do this group theory and
+ 
+
+ align:start position:0%
+anyway you you do this group theory and
+you try to find what's going to be
+
+ align:start position:0%
+you try to find what's going to be
+ 
+
+ align:start position:0%
+you try to find what's going to be
+different for one symmetry species
+
+ align:start position:0%
+different for one symmetry species
+ 
+
+ align:start position:0%
+different for one symmetry species
+versus another. And one of the commonest
+
+ align:start position:0%
+versus another. And one of the commonest
+ 
+
+ align:start position:0%
+versus another. And one of the commonest
+things is the number of discrete bands
+
+ align:start position:0%
+things is the number of discrete bands
+ 
+
+ align:start position:0%
+things is the number of discrete bands
+that you can see for the molecule
+
+ align:start position:0%
+that you can see for the molecule
+ 
+
+ align:start position:0%
+that you can see for the molecule
+depends on the symmet on the qualitative
+
+ align:start position:0%
+depends on the symmet on the qualitative
+ 
+
+ align:start position:0%
+depends on the symmet on the qualitative
+structure. And so
+
+ align:start position:0%
+structure. And so
+ 
+
+ align:start position:0%
+structure. And so
+uh if you observe
+
+ align:start position:0%
+uh if you observe
+ 
+
+ align:start position:0%
+uh if you observe
+uh if it's D3H there are going to be
+
+ align:start position:0%
+uh if it's D3H there are going to be
+ 
+
+ align:start position:0%
+uh if it's D3H there are going to be
+three allowed
+
+ align:start position:0%
+three allowed
+ 
+
+ align:start position:0%
+three allowed
+uh vibrational
+
+ align:start position:0%
+uh vibrational
+ 
+
+ align:start position:0%
+uh vibrational
+fundamentals. If it's a lower symmetry
+
+ align:start position:0%
+fundamentals. If it's a lower symmetry
+ 
+
+ align:start position:0%
+fundamentals. If it's a lower symmetry
+there will be a different number. Then
+
+ align:start position:0%
+there will be a different number. Then
+ 
+
+ align:start position:0%
+there will be a different number. Then
+there's the question of parallel versus
+
+ align:start position:0%
+there's the question of parallel versus
+ 
+
+ align:start position:0%
+there's the question of parallel versus
+perpendicular. And so you can tell from
+
+ align:start position:0%
+perpendicular. And so you can tell from
+ 
+
+ align:start position:0%
+perpendicular. And so you can tell from
+the nature of the band. Then there's
+
+ align:start position:0%
+the nature of the band. Then there's
+ 
+
+ align:start position:0%
+the nature of the band. Then there's
+this business of asymmetry splittings.
+
+ align:start position:0%
+this business of asymmetry splittings.
+ 
+
+ align:start position:0%
+this business of asymmetry splittings.
+You have a particular uh J K A K J and K
+
+ align:start position:0%
+You have a particular uh J K A K J and K
+ 
+
+ align:start position:0%
+You have a particular uh J K A K J and K
+A there's two KC's associated with that.
+
+ align:start position:0%
+A there's two KC's associated with that.
+ 
+
+ align:start position:0%
+A there's two KC's associated with that.
+And we
+
+ align:start position:0%
+And we
+ 
+
+ align:start position:0%
+And we
+know just from consideration of the
+
+ align:start position:0%
+know just from consideration of the
+ 
+
+ align:start position:0%
+know just from consideration of the
+rotational constants the A, B and C that
+
+ align:start position:0%
+rotational constants the A, B and C that
+ 
+
+ align:start position:0%
+rotational constants the A, B and C that
+the one where K A + KC is equal to J is
+
+ align:start position:0%
+the one where K A + KC is equal to J is
+ 
+
+ align:start position:0%
+the one where K A + KC is equal to J is
+higher than the one where K A plus KC is
+
+ align:start position:0%
+higher than the one where K A plus KC is
+ 
+
+ align:start position:0%
+higher than the one where K A plus KC is
+is equal to J + one. And so that is
+
+ align:start position:0%
+is equal to J + one. And so that is
+ 
+
+ align:start position:0%
+is equal to J + one. And so that is
+always going to be there. And depending
+
+ align:start position:0%
+always going to be there. And depending
+ 
+
+ align:start position:0%
+always going to be there. And depending
+on the symmetry of the vibrational level
+
+ align:start position:0%
+on the symmetry of the vibrational level
+ 
+
+ align:start position:0%
+on the symmetry of the vibrational level
+you will uh
+
+ align:start position:0%
+you will uh
+ 
+
+ align:start position:0%
+you will uh
+uh you will have transitions selectively
+
+ align:start position:0%
+uh you will have transitions selectively
+ 
+
+ align:start position:0%
+uh you will have transitions selectively
+into the upper or lower that you can
+
+ align:start position:0%
+into the upper or lower that you can
+ 
+
+ align:start position:0%
+into the upper or lower that you can
+tell the difference and that uh I didn't
+
+ align:start position:0%
+tell the difference and that uh I didn't
+ 
+
+ align:start position:0%
+tell the difference and that uh I didn't
+say that very well but that turns out to
+
+ align:start position:0%
+say that very well but that turns out to
+ 
+
+ align:start position:0%
+say that very well but that turns out to
+be a really important marker because
+
+ align:start position:0%
+be a really important marker because
+ 
+
+ align:start position:0%
+be a really important marker because
+this ordering of the J KC levels is an
+
+ align:start position:0%
+this ordering of the J KC levels is an
+ 
+
+ align:start position:0%
+this ordering of the J KC levels is an
+inertial effect as opposed to some
+
+ align:start position:0%
+inertial effect as opposed to some
+ 
+
+ align:start position:0%
+inertial effect as opposed to some
+accident in diatomic molecules lambda
+
+ align:start position:0%
+accident in diatomic molecules lambda
+ 
+
+ align:start position:0%
+accident in diatomic molecules lambda
+double is an accident. But this is
+
+ align:start position:0%
+double is an accident. But this is
+ 
+
+ align:start position:0%
+double is an accident. But this is
+something that you can depend on.
+
+ align:start position:0%
+something that you can depend on.
+ 
+
+ align:start position:0%
+something that you can depend on.
+There's another thing and that's nuclear
+
+ align:start position:0%
+There's another thing and that's nuclear
+ 
+
+ align:start position:0%
+There's another thing and that's nuclear
+statistical weights that if you're
+
+ align:start position:0%
+statistical weights that if you're
+ 
+
+ align:start position:0%
+statistical weights that if you're
+permuting identical atoms, you're going
+
+ align:start position:0%
+permuting identical atoms, you're going
+ 
+
+ align:start position:0%
+permuting identical atoms, you're going
+to have to worry about the permutation
+
+ align:start position:0%
+to have to worry about the permutation
+ 
+
+ align:start position:0%
+to have to worry about the permutation
+symmetry. And so there'll be ortho
+
+ align:start position:0%
+symmetry. And so there'll be ortho
+ 
+
+ align:start position:0%
+symmetry. And so there'll be ortho
+levels and parallel levels there. There
+
+ align:start position:0%
+levels and parallel levels there. There
+ 
+
+ align:start position:0%
+levels and parallel levels there. There
+will be uh intensities that alternate or
+
+ align:start position:0%
+will be uh intensities that alternate or
+ 
+
+ align:start position:0%
+will be uh intensities that alternate or
+do something as a function of J and K
+
+ align:start position:0%
+do something as a function of J and K
+ 
+
+ align:start position:0%
+do something as a function of J and K
+that is uniquely recognizable. Now I'm
+
+ align:start position:0%
+that is uniquely recognizable. Now I'm
+ 
+
+ align:start position:0%
+that is uniquely recognizable. Now I'm
+never going to talk about the nuclear
+
+ align:start position:0%
+never going to talk about the nuclear
+ 
+
+ align:start position:0%
+never going to talk about the nuclear
+statistical weights uh in in this course
+
+ align:start position:0%
+statistical weights uh in in this course
+ 
+
+ align:start position:0%
+statistical weights uh in in this course
+but that is a really important feature
+
+ align:start position:0%
+but that is a really important feature
+ 
+
+ align:start position:0%
+but that is a really important feature
+and it's especially important
+
+ align:start position:0%
+and it's especially important
+ 
+
+ align:start position:0%
+and it's especially important
+uh it's best dealt with in CNPI group
+
+ align:start position:0%
+uh it's best dealt with in CNPI group
+ 
+
+ align:start position:0%
+uh it's best dealt with in CNPI group
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+uh because it forces you to to make
+
+ align:start position:0%
+uh because it forces you to to make
+ 
+
+ align:start position:0%
+uh because it forces you to to make
+cartoon
+
+ align:start position:0%
+cartoon
+ 
+
+ align:start position:0%
+cartoon
+representations of the things that where
+
+ align:start position:0%
+representations of the things that where
+ 
+
+ align:start position:0%
+representations of the things that where
+you can build ortho and parasates states
+
+ align:start position:0%
+you can build ortho and parasates states
+ 
+
+ align:start position:0%
+you can build ortho and parasates states
+that with definite nuclear symmetry And
+
+ align:start position:0%
+that with definite nuclear symmetry And
+ 
+
+ align:start position:0%
+that with definite nuclear symmetry And
+I mean I can challenge you. How do you
+
+ align:start position:0%
+I mean I can challenge you. How do you
+ 
+
+ align:start position:0%
+I mean I can challenge you. How do you
+classify the levels of acetylene where
+
+ align:start position:0%
+classify the levels of acetylene where
+ 
+
+ align:start position:0%
+classify the levels of acetylene where
+you got two identical bzons and two
+
+ align:start position:0%
+you got two identical bzons and two
+ 
+
+ align:start position:0%
+you got two identical bzons and two
+identical fermians? And you know that's
+
+ align:start position:0%
+identical fermians? And you know that's
+ 
+
+ align:start position:0%
+identical fermians? And you know that's
+a non-starter. You don't know what to do
+
+ align:start position:0%
+a non-starter. You don't know what to do
+ 
+
+ align:start position:0%
+a non-starter. You don't know what to do
+until you develop a uh a generalization
+
+ align:start position:0%
+until you develop a uh a generalization
+ 
+
+ align:start position:0%
+until you develop a uh a generalization
+and you say okay I need two structures.
+
+ align:start position:0%
+and you say okay I need two structures.
+ 
+
+ align:start position:0%
+and you say okay I need two structures.
+I need to label them one two one a b2
+
+ align:start position:0%
+I need to label them one two one a b2
+ 
+
+ align:start position:0%
+I need to label them one two one a b2
+and one b a2 and then I can build states
+
+ align:start position:0%
+and one b a2 and then I can build states
+ 
+
+ align:start position:0%
+and one b a2 and then I can build states
+that have the right out of linear
+
+ align:start position:0%
+that have the right out of linear
+ 
+
+ align:start position:0%
+that have the right out of linear
+combinations of those two structures I
+
+ align:start position:0%
+combinations of those two structures I
+ 
+
+ align:start position:0%
+combinations of those two structures I
+can build the states and then I can
+
+ align:start position:0%
+can build the states and then I can
+ 
+
+ align:start position:0%
+can build the states and then I can
+classify them according to whether
+
+ align:start position:0%
+classify them according to whether
+ 
+
+ align:start position:0%
+classify them according to whether
+they're like ortho or parah so that's
+
+ align:start position:0%
+they're like ortho or parah so that's
+ 
+
+ align:start position:0%
+they're like ortho or parah so that's
+something that I I wish I could talk
+
+ align:start position:0%
+something that I I wish I could talk
+ 
+
+ align:start position:0%
+something that I I wish I could talk
+about but I want to I I want to move to
+
+ align:start position:0%
+about but I want to I I want to move to
+ 
+
+ align:start position:0%
+about but I want to I I want to move to
+electronics electronic transitions and
+
+ align:start position:0%
+electronics electronic transitions and
+ 
+
+ align:start position:0%
+electronics electronic transitions and
+that can only be dealt with in a case
+
+ align:start position:0%
+that can only be dealt with in a case
+ 
+
+ align:start position:0%
+that can only be dealt with in a case
+study way. And so we're that's but
+
+ align:start position:0%
+study way. And so we're that's but
+ 
+
+ align:start position:0%
+study way. And so we're that's but
+basically what we're going to be doing
+
+ align:start position:0%
+basically what we're going to be doing
+ 
+
+ align:start position:0%
+basically what we're going to be doing
+for the rest of
+
+ align:start position:0%
+for the rest of
+ 
+
+ align:start position:0%
+for the rest of
+580. So
+
+ align:start position:0%
+580. So
+ 
+
+ align:start position:0%
+580. So
+uh thank you for being patient with my
+
+ align:start position:0%
+uh thank you for being patient with my
+ 
+
+ align:start position:0%
+uh thank you for being patient with my
+lack
+
+ align:start position:0%
+lack
+ 
+
+ align:start position:0%
+lack
+of precision on this topic, but it's a
+
+ align:start position:0%
+of precision on this topic, but it's a
+ 
+
+ align:start position:0%
+of precision on this topic, but it's a
+fun topic and you should explore it. And
+
+ align:start position:0%
+fun topic and you should explore it. And
+ 
+
+ align:start position:0%
+fun topic and you should explore it. And
+I I was thinking about a molecule the
+
+ align:start position:0%
+I I was thinking about a molecule the
+ 
+
+ align:start position:0%
+I I was thinking about a molecule the
+you know and so you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um trimethyl cyclopropenyl was our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+candidate. Uh but it I I don't think I'm
+
+ align:start position:0%
+candidate. Uh but it I I don't think I'm
+ 
+
+ align:start position:0%
+candidate. Uh but it I I don't think I'm
+going to ask you to do anything like
+
+ align:start position:0%
+going to ask you to do anything like
+ 
+
+ align:start position:0%
+going to ask you to do anything like
+that. But it's a good molecule because
+
+ align:start position:0%
+that. But it's a good molecule because
+ 
+
+ align:start position:0%
+that. But it's a good molecule because
+it, you know, it's basically this
+
+ align:start position:0%
+it, you know, it's basically this
+ 
+
+ align:start position:0%
+it, you know, it's basically this
+molecule but it's got some hair.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. I had a really quick question
+
+ align:start position:0%
+Okay. I had a really quick question
+ 
+
+ align:start position:0%
+Okay. I had a really quick question
+maybe. Yes. Pseudo rotation.
+
+ align:start position:0%
+maybe. Yes. Pseudo rotation.
+ 
+
+ align:start position:0%
+maybe. Yes. Pseudo rotation.
+If you are an observer, yes, you
+
+ align:start position:0%
+If you are an observer, yes, you
+ 
+
+ align:start position:0%
+If you are an observer, yes, you
+presumably can't tell the difference
+
+ align:start position:0%
+presumably can't tell the difference
+ 
+
+ align:start position:0%
+presumably can't tell the difference
+between rotation and pseudo rotation
+
+ align:start position:0%
+between rotation and pseudo rotation
+ 
+
+ align:start position:0%
+between rotation and pseudo rotation
+if the molecule is really symmetric,
+
+ align:start position:0%
+if the molecule is really symmetric,
+ 
+
+ align:start position:0%
+if the molecule is really symmetric,
+right? So, well, what are you observing?
+
+ align:start position:0%
+right? So, well, what are you observing?
+ 
+
+ align:start position:0%
+right? So, well, what are you observing?
+You're Well, you're not watching the
+
+ align:start position:0%
+You're Well, you're not watching the
+ 
+
+ align:start position:0%
+You're Well, you're not watching the
+molecule move. You're not looking at the
+
+ align:start position:0%
+molecule move. You're not looking at the
+ 
+
+ align:start position:0%
+molecule move. You're not looking at the
+wave function. You're looking at the
+
+ align:start position:0%
+wave function. You're looking at the
+ 
+
+ align:start position:0%
+wave function. You're looking at the
+spectrum.
+
+ align:start position:0%
+spectrum.
+ 
+
+ align:start position:0%
+spectrum.
+Right? So, that that was sort of what I
+
+ align:start position:0%
+Right? So, that that was sort of what I
+ 
+
+ align:start position:0%
+Right? So, that that was sort of what I
+was about to ask. Yeah. If this let's
+
+ align:start position:0%
+was about to ask. Yeah. If this let's
+ 
+
+ align:start position:0%
+was about to ask. Yeah. If this let's
+say that I
+
+ align:start position:0%
+say that I
+ 
+
+ align:start position:0%
+say that I
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+apply a some time varying field to the
+
+ align:start position:0%
+apply a some time varying field to the
+ 
+
+ align:start position:0%
+apply a some time varying field to the
+molecule that ought to induce pseudo
+
+ align:start position:0%
+molecule that ought to induce pseudo
+ 
+
+ align:start position:0%
+molecule that ought to induce pseudo
+rose pseudo rotation if one can imagine
+
+ align:start position:0%
+rose pseudo rotation if one can imagine
+ 
+
+ align:start position:0%
+rose pseudo rotation if one can imagine
+such a thing. Maybe one can't because
+
+ align:start position:0%
+such a thing. Maybe one can't because
+ 
+
+ align:start position:0%
+such a thing. Maybe one can't because
+it's totally symmetric. I think that
+
+ align:start position:0%
+it's totally symmetric. I think that
+ 
+
+ align:start position:0%
+it's totally symmetric. I think that
+would be hard. But one of the things
+
+ align:start position:0%
+would be hard. But one of the things
+ 
+
+ align:start position:0%
+would be hard. But one of the things
+that you do have is when a molecule is
+
+ align:start position:0%
+that you do have is when a molecule is
+ 
+
+ align:start position:0%
+that you do have is when a molecule is
+rotating that distinguishes left
+
+ align:start position:0%
+rotating that distinguishes left
+ 
+
+ align:start position:0%
+rotating that distinguishes left
+rotation and right. So that you you end
+
+ align:start position:0%
+rotation and right. So that you you end
+ 
+
+ align:start position:0%
+rotation and right. So that you you end
+up as soon as the molecule has is
+
+ align:start position:0%
+up as soon as the molecule has is
+ 
+
+ align:start position:0%
+up as soon as the molecule has is
+rotating about an axis that splits
+
+ align:start position:0%
+rotating about an axis that splits
+ 
+
+ align:start position:0%
+rotating about an axis that splits
+these or cans split these pseudorotating
+
+ align:start position:0%
+these or cans split these pseudorotating
+ 
+
+ align:start position:0%
+these or cans split these pseudorotating
+states in a way that is is uh
+
+ align:start position:0%
+states in a way that is is uh
+ 
+
+ align:start position:0%
+states in a way that is is uh
+understandable. Now Dick Lord who uh was
+
+ align:start position:0%
+understandable. Now Dick Lord who uh was
+ 
+
+ align:start position:0%
+understandable. Now Dick Lord who uh was
+you know the
+
+ align:start position:0%
+you know the
+ 
+
+ align:start position:0%
+you know the
+uh my predecessor as a spectroscopist at
+
+ align:start position:0%
+uh my predecessor as a spectroscopist at
+ 
+
+ align:start position:0%
+uh my predecessor as a spectroscopist at
+MIT and uh he made his uh career on
+
+ align:start position:0%
+MIT and uh he made his uh career on
+ 
+
+ align:start position:0%
+MIT and uh he made his uh career on
+pseudo rotation for ring puckering
+
+ align:start position:0%
+pseudo rotation for ring puckering
+ 
+
+ align:start position:0%
+pseudo rotation for ring puckering
+motions so that you would you know you'd
+
+ align:start position:0%
+motions so that you would you know you'd
+ 
+
+ align:start position:0%
+motions so that you would you know you'd
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+a let's say cycllohexene and so you have
+
+ align:start position:0%
+a let's say cycllohexene and so you have
+ 
+
+ align:start position:0%
+a let's say cycllohexene and so you have
+this chair but this chair and boat
+
+ align:start position:0%
+this chair but this chair and boat
+ 
+
+ align:start position:0%
+this chair but this chair and boat
+confirmation and
+
+ align:start position:0%
+confirmation and
+ 
+
+ align:start position:0%
+confirmation and
+yeah and so there are all sorts of
+
+ align:start position:0%
+yeah and so there are all sorts of
+ 
+
+ align:start position:0%
+yeah and so there are all sorts of
+wonderful things like that but um as
+
+ align:start position:0%
+wonderful things like that but um as
+ 
+
+ align:start position:0%
+wonderful things like that but um as
+soon as you introduce rotation then uh
+
+ align:start position:0%
+soon as you introduce rotation then uh
+ 
+
+ align:start position:0%
+soon as you introduce rotation then uh
+the left and right the counter and uh
+
+ align:start position:0%
+the left and right the counter and uh
+ 
+
+ align:start position:0%
+the left and right the counter and uh
+clockwise and counterclockwise rotations
+
+ align:start position:0%
+clockwise and counterclockwise rotations
+ 
+
+ align:start position:0%
+clockwise and counterclockwise rotations
+get distinguished in terms of
+
+ align:start position:0%
+get distinguished in terms of
+ 
+
+ align:start position:0%
+get distinguished in terms of
+corololis effects and so but it's that's
+
+ align:start position:0%
+corololis effects and so but it's that's
+ 
+
+ align:start position:0%
+corololis effects and so but it's that's
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+complicated Okay.
\ No newline at end of file
diff --git a/vVfI1wTp0Jg.txt b/vVfI1wTp0Jg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c1da1fb70149f2ea06b3495450997b7320c116d
--- /dev/null
+++ b/vVfI1wTp0Jg.txt
@@ -0,0 +1,11427 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So last time uh we were
+
+ align:start position:0%
+All right. So last time uh we were
+ 
+
+ align:start position:0%
+All right. So last time uh we were
+talking about tissue engineering
+
+ align:start position:0%
+talking about tissue engineering
+ 
+
+ align:start position:0%
+talking about tissue engineering
+scaffolds and what we're going to talk
+
+ align:start position:0%
+scaffolds and what we're going to talk
+ 
+
+ align:start position:0%
+scaffolds and what we're going to talk
+about today still has to do with tissue
+
+ align:start position:0%
+about today still has to do with tissue
+ 
+
+ align:start position:0%
+about today still has to do with tissue
+engineering scaffolds but we're going to
+
+ align:start position:0%
+engineering scaffolds but we're going to
+ 
+
+ align:start position:0%
+engineering scaffolds but we're going to
+look at it from a different perspective.
+
+ align:start position:0%
+look at it from a different perspective.
+ 
+
+ align:start position:0%
+look at it from a different perspective.
+So last time we were looking more at
+
+ align:start position:0%
+So last time we were looking more at
+ 
+
+ align:start position:0%
+So last time we were looking more at
+sort of a clinical perspective and
+
+ align:start position:0%
+sort of a clinical perspective and
+ 
+
+ align:start position:0%
+sort of a clinical perspective and
+looking at those osteochondrial
+
+ align:start position:0%
+looking at those osteochondrial
+ 
+
+ align:start position:0%
+looking at those osteochondrial
+scaffolds for repairing small defects in
+
+ align:start position:0%
+scaffolds for repairing small defects in
+ 
+
+ align:start position:0%
+scaffolds for repairing small defects in
+cartilage. And today what we're going to
+
+ align:start position:0%
+cartilage. And today what we're going to
+ 
+
+ align:start position:0%
+cartilage. And today what we're going to
+talk about are how cells how biological
+
+ align:start position:0%
+talk about are how cells how biological
+ 
+
+ align:start position:0%
+talk about are how cells how biological
+cells interact with the scaffolds. And
+
+ align:start position:0%
+cells interact with the scaffolds. And
+ 
+
+ align:start position:0%
+cells interact with the scaffolds. And
+there's various kinds of interactions.
+
+ align:start position:0%
+there's various kinds of interactions.
+ 
+
+ align:start position:0%
+there's various kinds of interactions.
+So we're going to go through a bunch of
+
+ align:start position:0%
+So we're going to go through a bunch of
+ 
+
+ align:start position:0%
+So we're going to go through a bunch of
+these. So the first one I'm going to
+
+ align:start position:0%
+these. So the first one I'm going to
+ 
+
+ align:start position:0%
+these. So the first one I'm going to
+talk about is degradation of the
+
+ align:start position:0%
+talk about is degradation of the
+ 
+
+ align:start position:0%
+talk about is degradation of the
+scaffolds. Uh then we'll talk about cell
+
+ align:start position:0%
+scaffolds. Uh then we'll talk about cell
+ 
+
+ align:start position:0%
+scaffolds. Uh then we'll talk about cell
+attachment, cell morphology. So the
+
+ align:start position:0%
+attachment, cell morphology. So the
+ 
+
+ align:start position:0%
+attachment, cell morphology. So the
+shape of the cells in the shape of the
+
+ align:start position:0%
+shape of the cells in the shape of the
+ 
+
+ align:start position:0%
+shape of the cells in the shape of the
+pores in the scaffold can affect the the
+
+ align:start position:0%
+pores in the scaffold can affect the the
+ 
+
+ align:start position:0%
+pores in the scaffold can affect the the
+way the biological cells what shape they
+
+ align:start position:0%
+way the biological cells what shape they
+ 
+
+ align:start position:0%
+way the biological cells what shape they
+have. Uh biological cells can also
+
+ align:start position:0%
+have. Uh biological cells can also
+ 
+
+ align:start position:0%
+have. Uh biological cells can also
+contract the scaffold and apply
+
+ align:start position:0%
+contract the scaffold and apply
+ 
+
+ align:start position:0%
+contract the scaffold and apply
+mechanical forces. So we're going to
+
+ align:start position:0%
+mechanical forces. So we're going to
+ 
+
+ align:start position:0%
+mechanical forces. So we're going to
+talk about that. um the stiffness of the
+
+ align:start position:0%
+talk about that. um the stiffness of the
+ 
+
+ align:start position:0%
+talk about that. um the stiffness of the
+scaffold and the pore size can affect
+
+ align:start position:0%
+scaffold and the pore size can affect
+ 
+
+ align:start position:0%
+scaffold and the pore size can affect
+the speed of cell migration and the
+
+ align:start position:0%
+the speed of cell migration and the
+ 
+
+ align:start position:0%
+the speed of cell migration and the
+stiffness of the scaffold can affect the
+
+ align:start position:0%
+stiffness of the scaffold can affect the
+ 
+
+ align:start position:0%
+stiffness of the scaffold can affect the
+different differentiation of cells. So
+
+ align:start position:0%
+different differentiation of cells. So
+ 
+
+ align:start position:0%
+different differentiation of cells. So
+from one cell type to another. So I
+
+ align:start position:0%
+from one cell type to another. So I
+ 
+
+ align:start position:0%
+from one cell type to another. So I
+thought today I'd talk about that. This
+
+ align:start position:0%
+thought today I'd talk about that. This
+ 
+
+ align:start position:0%
+thought today I'd talk about that. This
+probably won't take the whole hour. The
+
+ align:start position:0%
+probably won't take the whole hour. The
+ 
+
+ align:start position:0%
+probably won't take the whole hour. The
+next topic is on energy absorption in
+
+ align:start position:0%
+next topic is on energy absorption in
+ 
+
+ align:start position:0%
+next topic is on energy absorption in
+foams and so we'll probably start that
+
+ align:start position:0%
+foams and so we'll probably start that
+ 
+
+ align:start position:0%
+foams and so we'll probably start that
+uh towards the end of the lecture. Okay.
+
+ align:start position:0%
+uh towards the end of the lecture. Okay.
+ 
+
+ align:start position:0%
+uh towards the end of the lecture. Okay.
+So the idea here is that we're looking
+
+ align:start position:0%
+So the idea here is that we're looking
+ 
+
+ align:start position:0%
+So the idea here is that we're looking
+at how scaffolds are being used really
+
+ align:start position:0%
+at how scaffolds are being used really
+ 
+
+ align:start position:0%
+at how scaffolds are being used really
+to provide a 3D environment to
+
+ align:start position:0%
+to provide a 3D environment to
+ 
+
+ align:start position:0%
+to provide a 3D environment to
+characterize the behavior of cells and
+
+ align:start position:0%
+characterize the behavior of cells and
+ 
+
+ align:start position:0%
+characterize the behavior of cells and
+in particular how the cells interact
+
+ align:start position:0%
+in particular how the cells interact
+ 
+
+ align:start position:0%
+in particular how the cells interact
+with their environment. So let me just
+
+ align:start position:0%
+with their environment. So let me just
+ 
+
+ align:start position:0%
+with their environment. So let me just
+write that down.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So how the cell behavior is affected by
+
+ align:start position:0%
+So how the cell behavior is affected by
+ 
+
+ align:start position:0%
+So how the cell behavior is affected by
+the substrate it's on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So the first thing we're going to
+
+ align:start position:0%
+Okay. So the first thing we're going to
+ 
+
+ align:start position:0%
+Okay. So the first thing we're going to
+talk about is scaffold degradation. And
+
+ align:start position:0%
+talk about is scaffold degradation. And
+ 
+
+ align:start position:0%
+talk about is scaffold degradation. And
+if you think of the native extracellular
+
+ align:start position:0%
+if you think of the native extracellular
+ 
+
+ align:start position:0%
+if you think of the native extracellular
+matrix, the cells secrete enzymes which
+
+ align:start position:0%
+matrix, the cells secrete enzymes which
+ 
+
+ align:start position:0%
+matrix, the cells secrete enzymes which
+resorb that matrix and then they also
+
+ align:start position:0%
+resorb that matrix and then they also
+ 
+
+ align:start position:0%
+resorb that matrix and then they also
+deposit new matrix. So it was kind of
+
+ align:start position:0%
+deposit new matrix. So it was kind of
+ 
+
+ align:start position:0%
+deposit new matrix. So it was kind of
+like what we were talking about with the
+
+ align:start position:0%
+like what we were talking about with the
+ 
+
+ align:start position:0%
+like what we were talking about with the
+bone. The bone is always being resorbed
+
+ align:start position:0%
+bone. The bone is always being resorbed
+ 
+
+ align:start position:0%
+bone. The bone is always being resorbed
+and deposited. And if there's a balance
+
+ align:start position:0%
+and deposited. And if there's a balance
+ 
+
+ align:start position:0%
+and deposited. And if there's a balance
+between that those two, then the density
+
+ align:start position:0%
+between that those two, then the density
+ 
+
+ align:start position:0%
+between that those two, then the density
+of the bone stays the same. And if the
+
+ align:start position:0%
+of the bone stays the same. And if the
+ 
+
+ align:start position:0%
+of the bone stays the same. And if the
+if one of the rates gets out of whack,
+
+ align:start position:0%
+if one of the rates gets out of whack,
+ 
+
+ align:start position:0%
+if one of the rates gets out of whack,
+then you get osteoporosis and you lose
+
+ align:start position:0%
+then you get osteoporosis and you lose
+ 
+
+ align:start position:0%
+then you get osteoporosis and you lose
+bone mass. So the idea is is that in
+
+ align:start position:0%
+bone mass. So the idea is is that in
+ 
+
+ align:start position:0%
+bone mass. So the idea is is that in
+just a native extracellular matrix
+
+ align:start position:0%
+just a native extracellular matrix
+ 
+
+ align:start position:0%
+just a native extracellular matrix
+the enzymes are producing the cells are
+
+ align:start position:0%
+the enzymes are producing the cells are
+ 
+
+ align:start position:0%
+the enzymes are producing the cells are
+producing enzymes that degrade the
+
+ align:start position:0%
+producing enzymes that degrade the
+ 
+
+ align:start position:0%
+producing enzymes that degrade the
+scaffold and those enzymes are also
+
+ align:start position:0%
+scaffold and those enzymes are also
+ 
+
+ align:start position:0%
+scaffold and those enzymes are also
+going to degrade the tissue engineering
+
+ align:start position:0%
+going to degrade the tissue engineering
+ 
+
+ align:start position:0%
+going to degrade the tissue engineering
+scaffolds as well and you want to be
+
+ align:start position:0%
+scaffolds as well and you want to be
+ 
+
+ align:start position:0%
+scaffolds as well and you want to be
+able to control the rate of degradation
+
+ align:start position:0%
+able to control the rate of degradation
+ 
+
+ align:start position:0%
+able to control the rate of degradation
+versus the rate at which the native
+
+ align:start position:0%
+versus the rate at which the native
+ 
+
+ align:start position:0%
+versus the rate at which the native
+extracellular matrix gets deposited.
+
+ align:start position:0%
+extracellular matrix gets deposited.
+ 
+
+ align:start position:0%
+extracellular matrix gets deposited.
+Excuse me. Sorry. So you can kind of
+
+ align:start position:0%
+Excuse me. Sorry. So you can kind of
+ 
+
+ align:start position:0%
+Excuse me. Sorry. So you can kind of
+imagine if the um tissue engineering
+
+ align:start position:0%
+imagine if the um tissue engineering
+ 
+
+ align:start position:0%
+imagine if the um tissue engineering
+scaffold did not resorb quickly enough,
+
+ align:start position:0%
+scaffold did not resorb quickly enough,
+ 
+
+ align:start position:0%
+scaffold did not resorb quickly enough,
+you'd have scaffold there and the cells
+
+ align:start position:0%
+you'd have scaffold there and the cells
+ 
+
+ align:start position:0%
+you'd have scaffold there and the cells
+would be trying to put down their own
+
+ align:start position:0%
+would be trying to put down their own
+ 
+
+ align:start position:0%
+would be trying to put down their own
+extracellular matrix and there wouldn't
+
+ align:start position:0%
+extracellular matrix and there wouldn't
+ 
+
+ align:start position:0%
+extracellular matrix and there wouldn't
+be kind of a place to put it. And if it
+
+ align:start position:0%
+be kind of a place to put it. And if it
+ 
+
+ align:start position:0%
+be kind of a place to put it. And if it
+resorbs too quickly, then the cells
+
+ align:start position:0%
+resorbs too quickly, then the cells
+ 
+
+ align:start position:0%
+resorbs too quickly, then the cells
+don't have something to attach to. So
+
+ align:start position:0%
+don't have something to attach to. So
+ 
+
+ align:start position:0%
+don't have something to attach to. So
+there has to be a sort of balance
+
+ align:start position:0%
+there has to be a sort of balance
+ 
+
+ align:start position:0%
+there has to be a sort of balance
+between the rate at which the enzymes
+
+ align:start position:0%
+between the rate at which the enzymes
+ 
+
+ align:start position:0%
+between the rate at which the enzymes
+are resorbing the tissue engineering
+
+ align:start position:0%
+are resorbing the tissue engineering
+ 
+
+ align:start position:0%
+are resorbing the tissue engineering
+scaffold versus the rate at which the
+
+ align:start position:0%
+scaffold versus the rate at which the
+ 
+
+ align:start position:0%
+scaffold versus the rate at which the
+cells are depositing their own
+
+ align:start position:0%
+cells are depositing their own
+ 
+
+ align:start position:0%
+cells are depositing their own
+extracellular matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in the native extracellular matrix,
+
+ align:start position:0%
+So in the native extracellular matrix,
+ 
+
+ align:start position:0%
+So in the native extracellular matrix,
+the enzymes produced by the cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are resorbing the extracellular matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the cells are also synthesizing
+
+ align:start position:0%
+And then the cells are also synthesizing
+ 
+
+ align:start position:0%
+And then the cells are also synthesizing
+synthesize.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So they synthesize ECM to replace it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the cells are also going to degrade
+
+ align:start position:0%
+So the cells are also going to degrade
+ 
+
+ align:start position:0%
+So the cells are also going to degrade
+the tissue engineering scaffold that you
+
+ align:start position:0%
+the tissue engineering scaffold that you
+ 
+
+ align:start position:0%
+the tissue engineering scaffold that you
+put in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the length of time that the scaffold
+
+ align:start position:0%
+And the length of time that the scaffold
+ 
+
+ align:start position:0%
+And the length of time that the scaffold
+is insoluble so that it remains in the
+
+ align:start position:0%
+is insoluble so that it remains in the
+ 
+
+ align:start position:0%
+is insoluble so that it remains in the
+body as a solid um is called the
+
+ align:start position:0%
+body as a solid um is called the
+ 
+
+ align:start position:0%
+body as a solid um is called the
+resonance time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so then we require the um scaffold
+
+ align:start position:0%
+And so then we require the um scaffold
+ 
+
+ align:start position:0%
+And so then we require the um scaffold
+degradation to occur over a time that
+
+ align:start position:0%
+degradation to occur over a time that
+ 
+
+ align:start position:0%
+degradation to occur over a time that
+balances with the new ECM synthesis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so the scaffold residence time must
+
+ align:start position:0%
+And so the scaffold residence time must
+ 
+
+ align:start position:0%
+And so the scaffold residence time must
+be about equal to the time required to
+
+ align:start position:0%
+be about equal to the time required to
+ 
+
+ align:start position:0%
+be about equal to the time required to
+make new native extracellular matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the degradation rate depends on the
+
+ align:start position:0%
+So the degradation rate depends on the
+ 
+
+ align:start position:0%
+So the degradation rate depends on the
+composition of the scaffold, on how much
+
+ align:start position:0%
+composition of the scaffold, on how much
+ 
+
+ align:start position:0%
+composition of the scaffold, on how much
+cross-linking there is, and on the
+
+ align:start position:0%
+cross-linking there is, and on the
+ 
+
+ align:start position:0%
+cross-linking there is, and on the
+relative density. Obviously, the more
+
+ align:start position:0%
+relative density. Obviously, the more
+ 
+
+ align:start position:0%
+relative density. Obviously, the more
+scaffold there is, the longer it's going
+
+ align:start position:0%
+scaffold there is, the longer it's going
+ 
+
+ align:start position:0%
+scaffold there is, the longer it's going
+to take to degrade it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And with uh synthetic polymers, you can
+
+ align:start position:0%
+And with uh synthetic polymers, you can
+ 
+
+ align:start position:0%
+And with uh synthetic polymers, you can
+vary the molecular weight of the
+
+ align:start position:0%
+vary the molecular weight of the
+ 
+
+ align:start position:0%
+vary the molecular weight of the
+polymer. And sometimes if you have
+
+ align:start position:0%
+polymer. And sometimes if you have
+ 
+
+ align:start position:0%
+polymer. And sometimes if you have
+co-olymers, one may degrade faster than
+
+ align:start position:0%
+co-olymers, one may degrade faster than
+ 
+
+ align:start position:0%
+co-olymers, one may degrade faster than
+the other. And you can uh control the
+
+ align:start position:0%
+the other. And you can uh control the
+ 
+
+ align:start position:0%
+the other. And you can uh control the
+balance of how much of each co-olymer
+
+ align:start position:0%
+balance of how much of each co-olymer
+ 
+
+ align:start position:0%
+balance of how much of each co-olymer
+you have.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And for
+
+ align:start position:0%
+And for
+ 
+
+ align:start position:0%
+And for
+um na natural proteins like collagen
+
+ align:start position:0%
+um na natural proteins like collagen
+ 
+
+ align:start position:0%
+um na natural proteins like collagen
+you can control the amount of
+
+ align:start position:0%
+you can control the amount of
+ 
+
+ align:start position:0%
+you can control the amount of
+cross-linking.
+
+ align:start position:0%
+cross-linking.
+ 
+
+ align:start position:0%
+cross-linking.
+So you can do the cross-linking by
+
+ align:start position:0%
+So you can do the cross-linking by
+ 
+
+ align:start position:0%
+So you can do the cross-linking by
+various techniques. There's what's
+
+ align:start position:0%
+various techniques. There's what's
+ 
+
+ align:start position:0%
+various techniques. There's what's
+called physical methods. There's
+
+ align:start position:0%
+called physical methods. There's
+ 
+
+ align:start position:0%
+called physical methods. There's
+something called dehydrothermal
+
+ align:start position:0%
+something called dehydrothermal
+ 
+
+ align:start position:0%
+something called dehydrothermal
+treatment where you heat the collagen up
+
+ align:start position:0%
+treatment where you heat the collagen up
+ 
+
+ align:start position:0%
+treatment where you heat the collagen up
+to 105 degrees C in um a vacuum in a dry
+
+ align:start position:0%
+to 105 degrees C in um a vacuum in a dry
+ 
+
+ align:start position:0%
+to 105 degrees C in um a vacuum in a dry
+environment. and uh that eliminates
+
+ align:start position:0%
+environment. and uh that eliminates
+ 
+
+ align:start position:0%
+environment. and uh that eliminates
+water and causes more cross-linking.
+
+ align:start position:0%
+water and causes more cross-linking.
+ 
+
+ align:start position:0%
+water and causes more cross-linking.
+There's a UV treatment, ultraviolet
+
+ align:start position:0%
+There's a UV treatment, ultraviolet
+ 
+
+ align:start position:0%
+There's a UV treatment, ultraviolet
+light treatment you can use. And there's
+
+ align:start position:0%
+light treatment you can use. And there's
+ 
+
+ align:start position:0%
+light treatment you can use. And there's
+also chemical cross linkers you can use.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hello
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's different um chemical methods
+
+ align:start position:0%
+So there's different um chemical methods
+ 
+
+ align:start position:0%
+So there's different um chemical methods
+you can also use to cross-link the um
+
+ align:start position:0%
+you can also use to cross-link the um
+ 
+
+ align:start position:0%
+you can also use to cross-link the um
+the collagen.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, the next thing I wanted to talk
+
+ align:start position:0%
+So, the next thing I wanted to talk
+ 
+
+ align:start position:0%
+So, the next thing I wanted to talk
+about was cell adhesion.
+
+ align:start position:0%
+about was cell adhesion.
+ 
+
+ align:start position:0%
+about was cell adhesion.
+And uh maybe I should just wait a minute
+
+ align:start position:0%
+And uh maybe I should just wait a minute
+ 
+
+ align:start position:0%
+And uh maybe I should just wait a minute
+for people to catch up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Are we just about there?
+
+ align:start position:0%
+Are we just about there?
+ 
+
+ align:start position:0%
+Are we just about there?
+So this next slide shows a sort of
+
+ align:start position:0%
+So this next slide shows a sort of
+ 
+
+ align:start position:0%
+So this next slide shows a sort of
+schematic of how a cell would adhere to
+
+ align:start position:0%
+schematic of how a cell would adhere to
+ 
+
+ align:start position:0%
+schematic of how a cell would adhere to
+a substrate. So down at the bottom here,
+
+ align:start position:0%
+a substrate. So down at the bottom here,
+ 
+
+ align:start position:0%
+a substrate. So down at the bottom here,
+all these little squiggly lines are
+
+ align:start position:0%
+all these little squiggly lines are
+ 
+
+ align:start position:0%
+all these little squiggly lines are
+representing the extracellular matrix in
+
+ align:start position:0%
+representing the extracellular matrix in
+ 
+
+ align:start position:0%
+representing the extracellular matrix in
+the native tissue or you might think of
+
+ align:start position:0%
+the native tissue or you might think of
+ 
+
+ align:start position:0%
+the native tissue or you might think of
+it as a as a say a collagen scaffold.
+
+ align:start position:0%
+it as a as a say a collagen scaffold.
+ 
+
+ align:start position:0%
+it as a as a say a collagen scaffold.
+But here we have the the ECM and this
+
+ align:start position:0%
+But here we have the the ECM and this
+ 
+
+ align:start position:0%
+But here we have the the ECM and this
+little blob here is our cell. This is
+
+ align:start position:0%
+little blob here is our cell. This is
+ 
+
+ align:start position:0%
+little blob here is our cell. This is
+the nucleus of the cell here, the little
+
+ align:start position:0%
+the nucleus of the cell here, the little
+ 
+
+ align:start position:0%
+the nucleus of the cell here, the little
+green blob in the middle. And the cell
+
+ align:start position:0%
+green blob in the middle. And the cell
+ 
+
+ align:start position:0%
+green blob in the middle. And the cell
+is attached to the ECM through something
+
+ align:start position:0%
+is attached to the ECM through something
+ 
+
+ align:start position:0%
+is attached to the ECM through something
+called focal adhesion points. And this
+
+ align:start position:0%
+called focal adhesion points. And this
+ 
+
+ align:start position:0%
+called focal adhesion points. And this
+schematic here is sort of a blowup of
+
+ align:start position:0%
+schematic here is sort of a blowup of
+ 
+
+ align:start position:0%
+schematic here is sort of a blowup of
+that focal adhesion. And at the focal
+
+ align:start position:0%
+that focal adhesion. And at the focal
+ 
+
+ align:start position:0%
+that focal adhesion. And at the focal
+adhesion, there's proteins called
+
+ align:start position:0%
+adhesion, there's proteins called
+ 
+
+ align:start position:0%
+adhesion, there's proteins called
+integrans. And integrans pass across the
+
+ align:start position:0%
+integrans. And integrans pass across the
+ 
+
+ align:start position:0%
+integrans. And integrans pass across the
+cell membrane. So the idea is the integr
+
+ align:start position:0%
+cell membrane. So the idea is the integr
+ 
+
+ align:start position:0%
+cell membrane. So the idea is the integr
+lians on the extracellular matrix and
+
+ align:start position:0%
+lians on the extracellular matrix and
+ 
+
+ align:start position:0%
+lians on the extracellular matrix and
+then they also attach to the submembrane
+
+ align:start position:0%
+then they also attach to the submembrane
+ 
+
+ align:start position:0%
+then they also attach to the submembrane
+plaque within the cell and then that
+
+ align:start position:0%
+plaque within the cell and then that
+ 
+
+ align:start position:0%
+plaque within the cell and then that
+plaque attaches to the cytokeleton. like
+
+ align:start position:0%
+plaque attaches to the cytokeleton. like
+ 
+
+ align:start position:0%
+plaque attaches to the cytokeleton. like
+things like actin filaments within the
+
+ align:start position:0%
+things like actin filaments within the
+ 
+
+ align:start position:0%
+things like actin filaments within the
+cell. So this is what kind of attaches
+
+ align:start position:0%
+cell. So this is what kind of attaches
+ 
+
+ align:start position:0%
+cell. So this is what kind of attaches
+the cell as a whole to the extracellular
+
+ align:start position:0%
+the cell as a whole to the extracellular
+ 
+
+ align:start position:0%
+the cell as a whole to the extracellular
+matrix is these focal adhesion sites
+
+ align:start position:0%
+matrix is these focal adhesion sites
+ 
+
+ align:start position:0%
+matrix is these focal adhesion sites
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+And um
+
+ align:start position:0%
+And um
+ 
+
+ align:start position:0%
+And um
+different kinds of cell behaviors
+
+ align:start position:0%
+different kinds of cell behaviors
+ 
+
+ align:start position:0%
+different kinds of cell behaviors
+obviously things like cell attachment
+
+ align:start position:0%
+obviously things like cell attachment
+ 
+
+ align:start position:0%
+obviously things like cell attachment
+but also things like cell migration are
+
+ align:start position:0%
+but also things like cell migration are
+ 
+
+ align:start position:0%
+but also things like cell migration are
+affected by those focal adhesions there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have that the cells attach
+
+ align:start position:0%
+so we have that the cells attach
+ 
+
+ align:start position:0%
+so we have that the cells attach
+to the ECM.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They're focal adhesions
+
+ align:start position:0%
+They're focal adhesions
+ 
+
+ align:start position:0%
+They're focal adhesions
+ad.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And sometimes you see those referred to
+
+ align:start position:0%
+And sometimes you see those referred to
+ 
+
+ align:start position:0%
+And sometimes you see those referred to
+just as FA.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And at the adhesion point the cell has
+
+ align:start position:0%
+And at the adhesion point the cell has
+ 
+
+ align:start position:0%
+And at the adhesion point the cell has
+integr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+membrane proteins. So they go across the
+
+ align:start position:0%
+membrane proteins. So they go across the
+ 
+
+ align:start position:0%
+membrane proteins. So they go across the
+membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+they bind to lians on the ECM.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the other end of the integrin
+
+ align:start position:0%
+And then the other end of the integrin
+ 
+
+ align:start position:0%
+And then the other end of the integrin
+is attached to the submembrane plaque
+
+ align:start position:0%
+is attached to the submembrane plaque
+ 
+
+ align:start position:0%
+is attached to the submembrane plaque
+within the cell.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that connects to the
+
+ align:start position:0%
+and then that connects to the
+ 
+
+ align:start position:0%
+and then that connects to the
+cytokeleton.
+
+ align:start position:0%
+cytokeleton.
+ 
+
+ align:start position:0%
+cytokeleton.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then different kinds of cell
+
+ align:start position:0%
+and then different kinds of cell
+ 
+
+ align:start position:0%
+and then different kinds of cell
+behaviors.
+
+ align:start position:0%
+behaviors.
+ 
+
+ align:start position:0%
+behaviors.
+So for example, things like adhesion
+
+ align:start position:0%
+So for example, things like adhesion
+ 
+
+ align:start position:0%
+So for example, things like adhesion
+and proliferation and migration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that cell contraction. We're going
+
+ align:start position:0%
+and that cell contraction. We're going
+ 
+
+ align:start position:0%
+and that cell contraction. We're going
+to talk more about that in a minute.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They all depend in part on this adhesion
+
+ align:start position:0%
+They all depend in part on this adhesion
+ 
+
+ align:start position:0%
+They all depend in part on this adhesion
+between the cells and the extracellular
+
+ align:start position:0%
+between the cells and the extracellular
+ 
+
+ align:start position:0%
+between the cells and the extracellular
+matrix.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the biological activity depends of
+
+ align:start position:0%
+And the biological activity depends of
+ 
+
+ align:start position:0%
+And the biological activity depends of
+how much um binding how many binding
+
+ align:start position:0%
+how much um binding how many binding
+ 
+
+ align:start position:0%
+how much um binding how many binding
+sites there are. So if you think of the
+
+ align:start position:0%
+sites there are. So if you think of the
+ 
+
+ align:start position:0%
+sites there are. So if you think of the
+extracellular matrix, it's got these
+
+ align:start position:0%
+extracellular matrix, it's got these
+ 
+
+ align:start position:0%
+extracellular matrix, it's got these
+lians and it depends on the density of
+
+ align:start position:0%
+lians and it depends on the density of
+ 
+
+ align:start position:0%
+lians and it depends on the density of
+binding sites, how much interaction you
+
+ align:start position:0%
+binding sites, how much interaction you
+ 
+
+ align:start position:0%
+binding sites, how much interaction you
+can get. So things like uh how much cell
+
+ align:start position:0%
+can get. So things like uh how much cell
+ 
+
+ align:start position:0%
+can get. So things like uh how much cell
+attachment you can get depends in part
+
+ align:start position:0%
+attachment you can get depends in part
+ 
+
+ align:start position:0%
+attachment you can get depends in part
+on just how many of these binding sites
+
+ align:start position:0%
+on just how many of these binding sites
+ 
+
+ align:start position:0%
+on just how many of these binding sites
+you've got for the cells to attach to.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that density of the binding sites or
+
+ align:start position:0%
+And that density of the binding sites or
+ 
+
+ align:start position:0%
+And that density of the binding sites or
+the density of the lians depends on the
+
+ align:start position:0%
+the density of the lians depends on the
+ 
+
+ align:start position:0%
+the density of the lians depends on the
+composition of the scaffold but also on
+
+ align:start position:0%
+composition of the scaffold but also on
+ 
+
+ align:start position:0%
+composition of the scaffold but also on
+the surface area per unit volume of the
+
+ align:start position:0%
+the surface area per unit volume of the
+ 
+
+ align:start position:0%
+the surface area per unit volume of the
+scaffold.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you think of first just the
+
+ align:start position:0%
+So if you think of first just the
+ 
+
+ align:start position:0%
+So if you think of first just the
+composition if you have uh native
+
+ align:start position:0%
+composition if you have uh native
+ 
+
+ align:start position:0%
+composition if you have uh native
+proteins like collagen they have binding
+
+ align:start position:0%
+proteins like collagen they have binding
+ 
+
+ align:start position:0%
+proteins like collagen they have binding
+sites themselves they have native
+
+ align:start position:0%
+sites themselves they have native
+ 
+
+ align:start position:0%
+sites themselves they have native
+binding binding sites. But if you think
+
+ align:start position:0%
+binding binding sites. But if you think
+ 
+
+ align:start position:0%
+binding binding sites. But if you think
+of synthetic polymers like um the
+
+ align:start position:0%
+of synthetic polymers like um the
+ 
+
+ align:start position:0%
+of synthetic polymers like um the
+resorbable suture type of polymers that
+
+ align:start position:0%
+resorbable suture type of polymers that
+ 
+
+ align:start position:0%
+resorbable suture type of polymers that
+we talked about, they don't have binding
+
+ align:start position:0%
+we talked about, they don't have binding
+ 
+
+ align:start position:0%
+we talked about, they don't have binding
+sites and you have to coat the scaffold
+
+ align:start position:0%
+sites and you have to coat the scaffold
+ 
+
+ align:start position:0%
+sites and you have to coat the scaffold
+with some sort of um adhesive protein.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the surface area per unit
+
+ align:start position:0%
+And then the surface area per unit
+ 
+
+ align:start position:0%
+And then the surface area per unit
+volume of the scaffold is related to the
+
+ align:start position:0%
+volume of the scaffold is related to the
+ 
+
+ align:start position:0%
+volume of the scaffold is related to the
+pore size and the relative density.
+
+ align:start position:0%
+pore size and the relative density.
+ 
+
+ align:start position:0%
+pore size and the relative density.
+So that's called the specific surface
+
+ align:start position:0%
+So that's called the specific surface
+ 
+
+ align:start position:0%
+So that's called the specific surface
+area,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the surface area per unit volume.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if you think of having some scaffold
+
+ align:start position:0%
+And if you think of having some scaffold
+ 
+
+ align:start position:0%
+And if you think of having some scaffold
+that's kind of like an open cell foam,
+
+ align:start position:0%
+that's kind of like an open cell foam,
+ 
+
+ align:start position:0%
+that's kind of like an open cell foam,
+you can roughly calculate what the
+
+ align:start position:0%
+you can roughly calculate what the
+ 
+
+ align:start position:0%
+you can roughly calculate what the
+surface area per unit volume is. So say
+
+ align:start position:0%
+surface area per unit volume is. So say
+ 
+
+ align:start position:0%
+surface area per unit volume is. So say
+each strut was a cylinder, then the
+
+ align:start position:0%
+each strut was a cylinder, then the
+ 
+
+ align:start position:0%
+each strut was a cylinder, then the
+surface area of each cylinder is going
+
+ align:start position:0%
+surface area of each cylinder is going
+ 
+
+ align:start position:0%
+surface area of each cylinder is going
+to be 2 pi rl. If each one has a radius
+
+ align:start position:0%
+to be 2 pi rl. If each one has a radius
+ 
+
+ align:start position:0%
+to be 2 pi rl. If each one has a radius
+r and a length l, say we had n of them,
+
+ align:start position:0%
+r and a length l, say we had n of them,
+ 
+
+ align:start position:0%
+r and a length l, say we had n of them,
+that would be your surface area. And the
+
+ align:start position:0%
+that would be your surface area. And the
+ 
+
+ align:start position:0%
+that would be your surface area. And the
+volume of the whole scaffold or one cell
+
+ align:start position:0%
+volume of the whole scaffold or one cell
+ 
+
+ align:start position:0%
+volume of the whole scaffold or one cell
+would go as l cubed. the length of each
+
+ align:start position:0%
+would go as l cubed. the length of each
+ 
+
+ align:start position:0%
+would go as l cubed. the length of each
+strut cubed. So if we just forget about
+
+ align:start position:0%
+strut cubed. So if we just forget about
+ 
+
+ align:start position:0%
+strut cubed. So if we just forget about
+all the constants here, forget about n,
+
+ align:start position:0%
+all the constants here, forget about n,
+ 
+
+ align:start position:0%
+all the constants here, forget about n,
+this just goes as r
+
+ align:start position:0%
+this just goes as r
+ 
+
+ align:start position:0%
+this just goes as r
+* 1 / l and that goes as the relative
+
+ align:start position:0%
+* 1 / l and that goes as the relative
+ 
+
+ align:start position:0%
+* 1 / l and that goes as the relative
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+to the 1/2 power * 1 over the pore size.
+
+ align:start position:0%
+to the 1/2 power * 1 over the pore size.
+ 
+
+ align:start position:0%
+to the 1/2 power * 1 over the pore size.
+So the specific surface area depends on
+
+ align:start position:0%
+So the specific surface area depends on
+ 
+
+ align:start position:0%
+So the specific surface area depends on
+the relative density and on the pore
+
+ align:start position:0%
+the relative density and on the pore
+ 
+
+ align:start position:0%
+the relative density and on the pore
+size.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if you have a tetraky decahedral
+
+ align:start position:0%
+And if you have a tetraky decahedral
+ 
+
+ align:start position:0%
+And if you have a tetraky decahedral
+cell, this is you can work out exactly
+
+ align:start position:0%
+cell, this is you can work out exactly
+ 
+
+ align:start position:0%
+cell, this is you can work out exactly
+what that relationship is. It's sort of
+
+ align:start position:0%
+what that relationship is. It's sort of
+ 
+
+ align:start position:0%
+what that relationship is. It's sort of
+a model and that gives you the
+
+ align:start position:0%
+a model and that gives you the
+ 
+
+ align:start position:0%
+a model and that gives you the
+relationship there. Uh and in this
+
+ align:start position:0%
+relationship there. Uh and in this
+ 
+
+ align:start position:0%
+relationship there. Uh and in this
+particular case, I think the relative
+
+ align:start position:0%
+particular case, I think the relative
+ 
+
+ align:start position:0%
+particular case, I think the relative
+density was 0.5%. And so it's a constant
+
+ align:start position:0%
+density was 0.5%. And so it's a constant
+ 
+
+ align:start position:0%
+density was 0.5%. And so it's a constant
+over the cell size. So one of the things
+
+ align:start position:0%
+over the cell size. So one of the things
+ 
+
+ align:start position:0%
+over the cell size. So one of the things
+um we did in my group was look at how
+
+ align:start position:0%
+um we did in my group was look at how
+ 
+
+ align:start position:0%
+um we did in my group was look at how
+cell attachment varied with this
+
+ align:start position:0%
+cell attachment varied with this
+ 
+
+ align:start position:0%
+cell attachment varied with this
+specific surface area. So we seated
+
+ align:start position:0%
+specific surface area. So we seated
+ 
+
+ align:start position:0%
+specific surface area. So we seated
+cells onto scaffolds of different pore
+
+ align:start position:0%
+cells onto scaffolds of different pore
+ 
+
+ align:start position:0%
+cells onto scaffolds of different pore
+sizes. We kept the relative density
+
+ align:start position:0%
+sizes. We kept the relative density
+ 
+
+ align:start position:0%
+sizes. We kept the relative density
+constant and we changed the pore sizes.
+
+ align:start position:0%
+constant and we changed the pore sizes.
+ 
+
+ align:start position:0%
+constant and we changed the pore sizes.
+Remember I said when when we make these
+
+ align:start position:0%
+Remember I said when when we make these
+ 
+
+ align:start position:0%
+Remember I said when when we make these
+scaffolds by freeze drying, we can
+
+ align:start position:0%
+scaffolds by freeze drying, we can
+ 
+
+ align:start position:0%
+scaffolds by freeze drying, we can
+control the pore size by controlling the
+
+ align:start position:0%
+control the pore size by controlling the
+ 
+
+ align:start position:0%
+control the pore size by controlling the
+freezing temperature. And we we see
+
+ align:start position:0%
+freezing temperature. And we we see
+ 
+
+ align:start position:0%
+freezing temperature. And we we see
+there's just a linear relationship
+
+ align:start position:0%
+there's just a linear relationship
+ 
+
+ align:start position:0%
+there's just a linear relationship
+between how many cells attach or the
+
+ align:start position:0%
+between how many cells attach or the
+ 
+
+ align:start position:0%
+between how many cells attach or the
+percentage of the cells that were seated
+
+ align:start position:0%
+percentage of the cells that were seated
+ 
+
+ align:start position:0%
+percentage of the cells that were seated
+that attach and the specific surface
+
+ align:start position:0%
+that attach and the specific surface
+ 
+
+ align:start position:0%
+that attach and the specific surface
+area. And here we used MC3T3 cells. It's
+
+ align:start position:0%
+area. And here we used MC3T3 cells. It's
+ 
+
+ align:start position:0%
+area. And here we used MC3T3 cells. It's
+a sort of a standard cell line that you
+
+ align:start position:0%
+a sort of a standard cell line that you
+ 
+
+ align:start position:0%
+a sort of a standard cell line that you
+can get. So Fergle O'Brien was the
+
+ align:start position:0%
+can get. So Fergle O'Brien was the
+ 
+
+ align:start position:0%
+can get. So Fergle O'Brien was the
+posttock in my group who who did that.
+
+ align:start position:0%
+posttock in my group who who did that.
+ 
+
+ align:start position:0%
+posttock in my group who who did that.
+Uh so I'll just say we find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell attachment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is proportional to the specific surface
+
+ align:start position:0%
+is proportional to the specific surface
+ 
+
+ align:start position:0%
+is proportional to the specific surface
+area.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's the cell attachment.
+
+ align:start position:0%
+That's the cell attachment.
+ 
+
+ align:start position:0%
+That's the cell attachment.
+So you can see how the scaffold design
+
+ align:start position:0%
+So you can see how the scaffold design
+ 
+
+ align:start position:0%
+So you can see how the scaffold design
+is going to affect how the cells attach.
+
+ align:start position:0%
+is going to affect how the cells attach.
+ 
+
+ align:start position:0%
+is going to affect how the cells attach.
+So there's some relationship between
+
+ align:start position:0%
+So there's some relationship between
+ 
+
+ align:start position:0%
+So there's some relationship between
+them there. Another thing people have
+
+ align:start position:0%
+them there. Another thing people have
+ 
+
+ align:start position:0%
+them there. Another thing people have
+looked at is cell morphology. And so if
+
+ align:start position:0%
+looked at is cell morphology. And so if
+ 
+
+ align:start position:0%
+looked at is cell morphology. And so if
+you change the sort of orientation of
+
+ align:start position:0%
+you change the sort of orientation of
+ 
+
+ align:start position:0%
+you change the sort of orientation of
+the pores, how does that change the
+
+ align:start position:0%
+the pores, how does that change the
+ 
+
+ align:start position:0%
+the pores, how does that change the
+orientation of the cells? So this was a
+
+ align:start position:0%
+orientation of the cells? So this was a
+ 
+
+ align:start position:0%
+orientation of the cells? So this was a
+study done in another group. So here we
+
+ align:start position:0%
+study done in another group. So here we
+ 
+
+ align:start position:0%
+study done in another group. So here we
+have kind of randomly oriented fibers
+
+ align:start position:0%
+have kind of randomly oriented fibers
+ 
+
+ align:start position:0%
+have kind of randomly oriented fibers
+that make up the scaffold. And here
+
+ align:start position:0%
+that make up the scaffold. And here
+ 
+
+ align:start position:0%
+that make up the scaffold. And here
+they're not perfectly oriented this way,
+
+ align:start position:0%
+they're not perfectly oriented this way,
+ 
+
+ align:start position:0%
+they're not perfectly oriented this way,
+but more or less. And then these are
+
+ align:start position:0%
+but more or less. And then these are
+ 
+
+ align:start position:0%
+but more or less. And then these are
+cells that have been seated onto them.
+
+ align:start position:0%
+cells that have been seated onto them.
+ 
+
+ align:start position:0%
+cells that have been seated onto them.
+So the green staining is the cells. And
+
+ align:start position:0%
+So the green staining is the cells. And
+ 
+
+ align:start position:0%
+So the green staining is the cells. And
+you can see if the scaffold is random,
+
+ align:start position:0%
+you can see if the scaffold is random,
+ 
+
+ align:start position:0%
+you can see if the scaffold is random,
+the cells themselves sort of line up
+
+ align:start position:0%
+the cells themselves sort of line up
+ 
+
+ align:start position:0%
+the cells themselves sort of line up
+with that fiber structure and become
+
+ align:start position:0%
+with that fiber structure and become
+ 
+
+ align:start position:0%
+with that fiber structure and become
+more or less random. And if the scaffold
+
+ align:start position:0%
+more or less random. And if the scaffold
+ 
+
+ align:start position:0%
+more or less random. And if the scaffold
+has fibers that are aligned, then the
+
+ align:start position:0%
+has fibers that are aligned, then the
+ 
+
+ align:start position:0%
+has fibers that are aligned, then the
+cells they also line up and be aligned.
+
+ align:start position:0%
+cells they also line up and be aligned.
+ 
+
+ align:start position:0%
+cells they also line up and be aligned.
+So the morphology of the cells can be
+
+ align:start position:0%
+So the morphology of the cells can be
+ 
+
+ align:start position:0%
+So the morphology of the cells can be
+affected by the orientation of the
+
+ align:start position:0%
+affected by the orientation of the
+ 
+
+ align:start position:0%
+affected by the orientation of the
+scaffold pores.
+
+ align:start position:0%
+scaffold pores.
+ 
+
+ align:start position:0%
+scaffold pores.
+My battery must be getting dead. Also
+
+ align:start position:0%
+My battery must be getting dead. Also
+ 
+
+ align:start position:0%
+My battery must be getting dead. Also
+the cell morphology can be affected by
+
+ align:start position:0%
+the cell morphology can be affected by
+ 
+
+ align:start position:0%
+the cell morphology can be affected by
+the stiffness of the cells or the
+
+ align:start position:0%
+the stiffness of the cells or the
+ 
+
+ align:start position:0%
+the stiffness of the cells or the
+stiffness of the substrate. So this this
+
+ align:start position:0%
+stiffness of the substrate. So this this
+ 
+
+ align:start position:0%
+stiffness of the substrate. So this this
+is a substrate um here this was a
+
+ align:start position:0%
+is a substrate um here this was a
+ 
+
+ align:start position:0%
+is a substrate um here this was a
+PEG fibbrronogen hydrogel and they
+
+ align:start position:0%
+PEG fibbrronogen hydrogel and they
+ 
+
+ align:start position:0%
+PEG fibbrronogen hydrogel and they
+varied the cross-linking of this
+
+ align:start position:0%
+varied the cross-linking of this
+ 
+
+ align:start position:0%
+varied the cross-linking of this
+hydrogel. So they got different moduli
+
+ align:start position:0%
+hydrogel. So they got different moduli
+ 
+
+ align:start position:0%
+hydrogel. So they got different moduli
+for the hydrogel. So these numbers here
+
+ align:start position:0%
+for the hydrogel. So these numbers here
+ 
+
+ align:start position:0%
+for the hydrogel. So these numbers here
+are all the stiffnesses of the four
+
+ align:start position:0%
+are all the stiffnesses of the four
+ 
+
+ align:start position:0%
+are all the stiffnesses of the four
+different hydrogels. And you can see the
+
+ align:start position:0%
+different hydrogels. And you can see the
+ 
+
+ align:start position:0%
+different hydrogels. And you can see the
+cell morphology changes from being kind
+
+ align:start position:0%
+cell morphology changes from being kind
+ 
+
+ align:start position:0%
+cell morphology changes from being kind
+of a spread out thing on the least stiff
+
+ align:start position:0%
+of a spread out thing on the least stiff
+ 
+
+ align:start position:0%
+of a spread out thing on the least stiff
+um substrate to being just a little
+
+ align:start position:0%
+um substrate to being just a little
+ 
+
+ align:start position:0%
+um substrate to being just a little
+spherical or circular blob on the most
+
+ align:start position:0%
+spherical or circular blob on the most
+ 
+
+ align:start position:0%
+spherical or circular blob on the most
+stiff substrate. So the cells respond to
+
+ align:start position:0%
+stiff substrate. So the cells respond to
+ 
+
+ align:start position:0%
+stiff substrate. So the cells respond to
+the substrate and so how the cells
+
+ align:start position:0%
+the substrate and so how the cells
+ 
+
+ align:start position:0%
+the substrate and so how the cells
+behave depends in part on their
+
+ align:start position:0%
+behave depends in part on their
+ 
+
+ align:start position:0%
+behave depends in part on their
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+to hit that. So I wanted to also talk
+
+ align:start position:0%
+to hit that. So I wanted to also talk
+ 
+
+ align:start position:0%
+to hit that. So I wanted to also talk
+about uh wound contraction and talk
+
+ align:start position:0%
+about uh wound contraction and talk
+ 
+
+ align:start position:0%
+about uh wound contraction and talk
+about how cells contract scaffolds as
+
+ align:start position:0%
+about how cells contract scaffolds as
+ 
+
+ align:start position:0%
+about how cells contract scaffolds as
+well. So one of the things people have
+
+ align:start position:0%
+well. So one of the things people have
+ 
+
+ align:start position:0%
+well. So one of the things people have
+found um when they look at say skin and
+
+ align:start position:0%
+found um when they look at say skin and
+ 
+
+ align:start position:0%
+found um when they look at say skin and
+regeneration of skin. So say you had um
+
+ align:start position:0%
+regeneration of skin. So say you had um
+ 
+
+ align:start position:0%
+regeneration of skin. So say you had um
+somebody with a burn and you know that
+
+ align:start position:0%
+somebody with a burn and you know that
+ 
+
+ align:start position:0%
+somebody with a burn and you know that
+the surgeons will clean the burn out and
+
+ align:start position:0%
+the surgeons will clean the burn out and
+ 
+
+ align:start position:0%
+the surgeons will clean the burn out and
+then what'll happen as it heals uh is
+
+ align:start position:0%
+then what'll happen as it heals uh is
+ 
+
+ align:start position:0%
+then what'll happen as it heals uh is
+scar tissue will form and the scar
+
+ align:start position:0%
+scar tissue will form and the scar
+ 
+
+ align:start position:0%
+scar tissue will form and the scar
+tissue forms in conjunction with the
+
+ align:start position:0%
+tissue forms in conjunction with the
+ 
+
+ align:start position:0%
+tissue forms in conjunction with the
+wound contracting. So cells will
+
+ align:start position:0%
+wound contracting. So cells will
+ 
+
+ align:start position:0%
+wound contracting. So cells will
+actually migrate into the wound bed and
+
+ align:start position:0%
+actually migrate into the wound bed and
+ 
+
+ align:start position:0%
+actually migrate into the wound bed and
+they'll pull the edges of the wound
+
+ align:start position:0%
+they'll pull the edges of the wound
+ 
+
+ align:start position:0%
+they'll pull the edges of the wound
+together to try to close the wound. And
+
+ align:start position:0%
+together to try to close the wound. And
+ 
+
+ align:start position:0%
+together to try to close the wound. And
+they won't close it completely but
+
+ align:start position:0%
+they won't close it completely but
+ 
+
+ align:start position:0%
+they won't close it completely but
+they'll partially close it and that's
+
+ align:start position:0%
+they'll partially close it and that's
+ 
+
+ align:start position:0%
+they'll partially close it and that's
+called wound contraction. And that is
+
+ align:start position:0%
+called wound contraction. And that is
+ 
+
+ align:start position:0%
+called wound contraction. And that is
+thought to be associated with the
+
+ align:start position:0%
+thought to be associated with the
+ 
+
+ align:start position:0%
+thought to be associated with the
+formation of scar tissue. So the cells
+
+ align:start position:0%
+formation of scar tissue. So the cells
+ 
+
+ align:start position:0%
+formation of scar tissue. So the cells
+can actually apply mechanical loads and
+
+ align:start position:0%
+can actually apply mechanical loads and
+ 
+
+ align:start position:0%
+can actually apply mechanical loads and
+they can contract the wound. And one of
+
+ align:start position:0%
+they can contract the wound. And one of
+ 
+
+ align:start position:0%
+they can contract the wound. And one of
+the things that professor Yianos found
+
+ align:start position:0%
+the things that professor Yianos found
+ 
+
+ align:start position:0%
+the things that professor Yianos found
+was that if you use one of his collagen
+
+ align:start position:0%
+was that if you use one of his collagen
+ 
+
+ align:start position:0%
+was that if you use one of his collagen
+gag scaffolds, you can inhibit that
+
+ align:start position:0%
+gag scaffolds, you can inhibit that
+ 
+
+ align:start position:0%
+gag scaffolds, you can inhibit that
+wound contraction. And if you can
+
+ align:start position:0%
+wound contraction. And if you can
+ 
+
+ align:start position:0%
+wound contraction. And if you can
+prevent the wound contraction from
+
+ align:start position:0%
+prevent the wound contraction from
+ 
+
+ align:start position:0%
+prevent the wound contraction from
+occurring, you also prevent the
+
+ align:start position:0%
+occurring, you also prevent the
+ 
+
+ align:start position:0%
+occurring, you also prevent the
+formation of the scar tissue and that
+
+ align:start position:0%
+formation of the scar tissue and that
+ 
+
+ align:start position:0%
+formation of the scar tissue and that
+allows normal dermis to form. So you get
+
+ align:start position:0%
+allows normal dermis to form. So you get
+ 
+
+ align:start position:0%
+allows normal dermis to form. So you get
+normal skin.
+
+ align:start position:0%
+normal skin.
+ 
+
+ align:start position:0%
+normal skin.
+So this this photograph here is of
+
+ align:start position:0%
+So this this photograph here is of
+ 
+
+ align:start position:0%
+So this this photograph here is of
+somebody who had burns over their entire
+
+ align:start position:0%
+somebody who had burns over their entire
+ 
+
+ align:start position:0%
+somebody who had burns over their entire
+torso and they put this tissue
+
+ align:start position:0%
+torso and they put this tissue
+ 
+
+ align:start position:0%
+torso and they put this tissue
+engineering scaffold on this part at the
+
+ align:start position:0%
+engineering scaffold on this part at the
+ 
+
+ align:start position:0%
+engineering scaffold on this part at the
+bottom but not on that part at the top.
+
+ align:start position:0%
+bottom but not on that part at the top.
+ 
+
+ align:start position:0%
+bottom but not on that part at the top.
+And you can see you know these sort of
+
+ align:start position:0%
+And you can see you know these sort of
+ 
+
+ align:start position:0%
+And you can see you know these sort of
+uh sort of lines here are contraure
+
+ align:start position:0%
+uh sort of lines here are contraure
+ 
+
+ align:start position:0%
+uh sort of lines here are contraure
+lines from the uh scar formation. And
+
+ align:start position:0%
+lines from the uh scar formation. And
+ 
+
+ align:start position:0%
+lines from the uh scar formation. And
+you can see this skin down here is is
+
+ align:start position:0%
+you can see this skin down here is is
+ 
+
+ align:start position:0%
+you can see this skin down here is is
+relatively normal. And in fact, when
+
+ align:start position:0%
+relatively normal. And in fact, when
+ 
+
+ align:start position:0%
+relatively normal. And in fact, when
+people look at the hisytologology of the
+
+ align:start position:0%
+people look at the hisytologology of the
+ 
+
+ align:start position:0%
+people look at the hisytologology of the
+skin that forms using these scaffolds,
+
+ align:start position:0%
+skin that forms using these scaffolds,
+ 
+
+ align:start position:0%
+skin that forms using these scaffolds,
+they find that it is pretty much the
+
+ align:start position:0%
+they find that it is pretty much the
+ 
+
+ align:start position:0%
+they find that it is pretty much the
+same as normal dermis, it doesn't have
+
+ align:start position:0%
+same as normal dermis, it doesn't have
+ 
+
+ align:start position:0%
+same as normal dermis, it doesn't have
+sweat glands and it doesn't have hair
+
+ align:start position:0%
+sweat glands and it doesn't have hair
+ 
+
+ align:start position:0%
+sweat glands and it doesn't have hair
+follicles. So, you can't sweat from that
+
+ align:start position:0%
+follicles. So, you can't sweat from that
+ 
+
+ align:start position:0%
+follicles. So, you can't sweat from that
+skin and you don't grow hair. But apart
+
+ align:start position:0%
+skin and you don't grow hair. But apart
+ 
+
+ align:start position:0%
+skin and you don't grow hair. But apart
+from that, it's more or less normal uh
+
+ align:start position:0%
+from that, it's more or less normal uh
+ 
+
+ align:start position:0%
+from that, it's more or less normal uh
+dermis. So, this observation that the if
+
+ align:start position:0%
+dermis. So, this observation that the if
+ 
+
+ align:start position:0%
+dermis. So, this observation that the if
+you can inhibit the wound contraction,
+
+ align:start position:0%
+you can inhibit the wound contraction,
+ 
+
+ align:start position:0%
+you can inhibit the wound contraction,
+you can prevent scar formation and you
+
+ align:start position:0%
+you can prevent scar formation and you
+ 
+
+ align:start position:0%
+you can prevent scar formation and you
+can get normal dermis to form. That's
+
+ align:start position:0%
+can get normal dermis to form. That's
+ 
+
+ align:start position:0%
+can get normal dermis to form. That's
+led to some interest in just seeing how
+
+ align:start position:0%
+led to some interest in just seeing how
+ 
+
+ align:start position:0%
+led to some interest in just seeing how
+is it that the cells do this contractile
+
+ align:start position:0%
+is it that the cells do this contractile
+ 
+
+ align:start position:0%
+is it that the cells do this contractile
+process. And so, oops, I keep hitting
+
+ align:start position:0%
+process. And so, oops, I keep hitting
+ 
+
+ align:start position:0%
+process. And so, oops, I keep hitting
+the thing and my battery's dead. Um, so
+
+ align:start position:0%
+the thing and my battery's dead. Um, so
+ 
+
+ align:start position:0%
+the thing and my battery's dead. Um, so
+one of the things people have done is
+
+ align:start position:0%
+one of the things people have done is
+ 
+
+ align:start position:0%
+one of the things people have done is
+they've just taken what's called free
+
+ align:start position:0%
+they've just taken what's called free
+ 
+
+ align:start position:0%
+they've just taken what's called free
+floating scaffold, they've just taken
+
+ align:start position:0%
+floating scaffold, they've just taken
+ 
+
+ align:start position:0%
+floating scaffold, they've just taken
+little discs of scaffold and put it in a
+
+ align:start position:0%
+little discs of scaffold and put it in a
+ 
+
+ align:start position:0%
+little discs of scaffold and put it in a
+cell culture medium in a petri dish and
+
+ align:start position:0%
+cell culture medium in a petri dish and
+ 
+
+ align:start position:0%
+cell culture medium in a petri dish and
+they find that if you put say
+
+ align:start position:0%
+they find that if you put say
+ 
+
+ align:start position:0%
+they find that if you put say
+fiberblasts on it, the fiberblasts will
+
+ align:start position:0%
+fiberblasts on it, the fiberblasts will
+ 
+
+ align:start position:0%
+fiberblasts on it, the fiberblasts will
+contract that scaffold. And people have
+
+ align:start position:0%
+contract that scaffold. And people have
+ 
+
+ align:start position:0%
+contract that scaffold. And people have
+measured how much the diameter of the
+
+ align:start position:0%
+measured how much the diameter of the
+ 
+
+ align:start position:0%
+measured how much the diameter of the
+scaffold changes. And so they've kind of
+
+ align:start position:0%
+scaffold changes. And so they've kind of
+ 
+
+ align:start position:0%
+scaffold changes. And so they've kind of
+measured this contraction just by it's
+
+ align:start position:0%
+measured this contraction just by it's
+ 
+
+ align:start position:0%
+measured this contraction just by it's
+almost like measuring a strain. uh and
+
+ align:start position:0%
+almost like measuring a strain. uh and
+ 
+
+ align:start position:0%
+almost like measuring a strain. uh and
+what we wanted to do is we wanted to try
+
+ align:start position:0%
+what we wanted to do is we wanted to try
+ 
+
+ align:start position:0%
+what we wanted to do is we wanted to try
+to measure the forces that were
+
+ align:start position:0%
+to measure the forces that were
+ 
+
+ align:start position:0%
+to measure the forces that were
+involved. So we first developed
+
+ align:start position:0%
+involved. So we first developed
+ 
+
+ align:start position:0%
+involved. So we first developed
+something called a cell force monitor
+
+ align:start position:0%
+something called a cell force monitor
+ 
+
+ align:start position:0%
+something called a cell force monitor
+and I'll I'll show you that. And then we
+
+ align:start position:0%
+and I'll I'll show you that. And then we
+ 
+
+ align:start position:0%
+and I'll I'll show you that. And then we
+um tried to calculate how much an
+
+ align:start position:0%
+um tried to calculate how much an
+ 
+
+ align:start position:0%
+um tried to calculate how much an
+individual cell could apply in terms of
+
+ align:start position:0%
+individual cell could apply in terms of
+ 
+
+ align:start position:0%
+individual cell could apply in terms of
+the force. So oops. So we used this
+
+ align:start position:0%
+the force. So oops. So we used this
+ 
+
+ align:start position:0%
+the force. So oops. So we used this
+scaffold here. This is the same collagen
+
+ align:start position:0%
+scaffold here. This is the same collagen
+ 
+
+ align:start position:0%
+scaffold here. This is the same collagen
+um gag scaffold I showed you before.
+
+ align:start position:0%
+um gag scaffold I showed you before.
+ 
+
+ align:start position:0%
+um gag scaffold I showed you before.
+And here's the cell force monitor. So
+
+ align:start position:0%
+And here's the cell force monitor. So
+ 
+
+ align:start position:0%
+And here's the cell force monitor. So
+that's that's just a schematic of
+
+ align:start position:0%
+that's that's just a schematic of
+ 
+
+ align:start position:0%
+that's that's just a schematic of
+holding a piece of the scaffold between
+
+ align:start position:0%
+holding a piece of the scaffold between
+ 
+
+ align:start position:0%
+holding a piece of the scaffold between
+two clamps. Uh so here it is kind of in
+
+ align:start position:0%
+two clamps. Uh so here it is kind of in
+ 
+
+ align:start position:0%
+two clamps. Uh so here it is kind of in
+elevation view. And then I'll just build
+
+ align:start position:0%
+elevation view. And then I'll just build
+ 
+
+ align:start position:0%
+elevation view. And then I'll just build
+the whole thing up so you can see how it
+
+ align:start position:0%
+the whole thing up so you can see how it
+ 
+
+ align:start position:0%
+the whole thing up so you can see how it
+works. So there's a it's on a base
+
+ align:start position:0%
+works. So there's a it's on a base
+ 
+
+ align:start position:0%
+works. So there's a it's on a base
+plate. It's attached to a horizontal
+
+ align:start position:0%
+plate. It's attached to a horizontal
+ 
+
+ align:start position:0%
+plate. It's attached to a horizontal
+stage that's adjustable. Then there's a
+
+ align:start position:0%
+stage that's adjustable. Then there's a
+ 
+
+ align:start position:0%
+stage that's adjustable. Then there's a
+a very thin beam here. So this is
+
+ align:start position:0%
+a very thin beam here. So this is
+ 
+
+ align:start position:0%
+a very thin beam here. So this is
+another adjustable stage here. And
+
+ align:start position:0%
+another adjustable stage here. And
+ 
+
+ align:start position:0%
+another adjustable stage here. And
+there's a very thin beam here. And
+
+ align:start position:0%
+there's a very thin beam here. And
+ 
+
+ align:start position:0%
+there's a very thin beam here. And
+that's attached to one end of this
+
+ align:start position:0%
+that's attached to one end of this
+ 
+
+ align:start position:0%
+that's attached to one end of this
+clamp. And here's the matrix. And this
+
+ align:start position:0%
+clamp. And here's the matrix. And this
+ 
+
+ align:start position:0%
+clamp. And here's the matrix. And this
+is attached to this other adjustable
+
+ align:start position:0%
+is attached to this other adjustable
+ 
+
+ align:start position:0%
+is attached to this other adjustable
+stage here. And then oop then we um have
+
+ align:start position:0%
+stage here. And then oop then we um have
+ 
+
+ align:start position:0%
+stage here. And then oop then we um have
+a proximity sensor. So what's going to
+
+ align:start position:0%
+a proximity sensor. So what's going to
+ 
+
+ align:start position:0%
+a proximity sensor. So what's going to
+happen is uh this is fixed over here.
+
+ align:start position:0%
+happen is uh this is fixed over here.
+ 
+
+ align:start position:0%
+happen is uh this is fixed over here.
+The scaffold is going to contract with
+
+ align:start position:0%
+The scaffold is going to contract with
+ 
+
+ align:start position:0%
+The scaffold is going to contract with
+the cells contracting the you know just
+
+ align:start position:0%
+the cells contracting the you know just
+ 
+
+ align:start position:0%
+the cells contracting the you know just
+applying these contractile forces. This
+
+ align:start position:0%
+applying these contractile forces. This
+ 
+
+ align:start position:0%
+applying these contractile forces. This
+beam here is going to bend and the
+
+ align:start position:0%
+beam here is going to bend and the
+ 
+
+ align:start position:0%
+beam here is going to bend and the
+proximity sensor is going to tell us how
+
+ align:start position:0%
+proximity sensor is going to tell us how
+ 
+
+ align:start position:0%
+proximity sensor is going to tell us how
+much it's bent. So we can measure how
+
+ align:start position:0%
+much it's bent. So we can measure how
+ 
+
+ align:start position:0%
+much it's bent. So we can measure how
+much that's bent. If we know how much
+
+ align:start position:0%
+much that's bent. If we know how much
+ 
+
+ align:start position:0%
+much that's bent. If we know how much
+that's bent and we calibrate the beam,
+
+ align:start position:0%
+that's bent and we calibrate the beam,
+ 
+
+ align:start position:0%
+that's bent and we calibrate the beam,
+we can figure out the force in the beam.
+
+ align:start position:0%
+we can figure out the force in the beam.
+ 
+
+ align:start position:0%
+we can figure out the force in the beam.
+Okay? So we can figure out how much is
+
+ align:start position:0%
+Okay? So we can figure out how much is
+ 
+
+ align:start position:0%
+Okay? So we can figure out how much is
+the total force that the cells are
+
+ align:start position:0%
+the total force that the cells are
+ 
+
+ align:start position:0%
+the total force that the cells are
+contracting with. And then this just is
+
+ align:start position:0%
+contracting with. And then this just is
+ 
+
+ align:start position:0%
+contracting with. And then this just is
+a little silicone well with some culture
+
+ align:start position:0%
+a little silicone well with some culture
+ 
+
+ align:start position:0%
+a little silicone well with some culture
+medium. So that's the whole setup there.
+
+ align:start position:0%
+medium. So that's the whole setup there.
+ 
+
+ align:start position:0%
+medium. So that's the whole setup there.
+Toby Fryman was a student who did that
+
+ align:start position:0%
+Toby Fryman was a student who did that
+ 
+
+ align:start position:0%
+Toby Fryman was a student who did that
+who's married to Professor Van Vleet and
+
+ align:start position:0%
+who's married to Professor Van Vleet and
+ 
+
+ align:start position:0%
+who's married to Professor Van Vleet and
+I have a very big soft spot for both of
+
+ align:start position:0%
+I have a very big soft spot for both of
+ 
+
+ align:start position:0%
+I have a very big soft spot for both of
+them. So um so anyway that's the setup
+
+ align:start position:0%
+them. So um so anyway that's the setup
+ 
+
+ align:start position:0%
+them. So um so anyway that's the setup
+and the thing that Toby measured was uh
+
+ align:start position:0%
+and the thing that Toby measured was uh
+ 
+
+ align:start position:0%
+and the thing that Toby measured was uh
+the force by measuring how much that
+
+ align:start position:0%
+the force by measuring how much that
+ 
+
+ align:start position:0%
+the force by measuring how much that
+beam deflected and he measured the force
+
+ align:start position:0%
+beam deflected and he measured the force
+ 
+
+ align:start position:0%
+beam deflected and he measured the force
+over time and he found that if he put uh
+
+ align:start position:0%
+over time and he found that if he put uh
+ 
+
+ align:start position:0%
+over time and he found that if he put uh
+say a certain number of fiberblasts onto
+
+ align:start position:0%
+say a certain number of fiberblasts onto
+ 
+
+ align:start position:0%
+say a certain number of fiberblasts onto
+the scaffold the force would uh increase
+
+ align:start position:0%
+the scaffold the force would uh increase
+ 
+
+ align:start position:0%
+the scaffold the force would uh increase
+and then reach an asmtoic point and you
+
+ align:start position:0%
+and then reach an asmtoic point and you
+ 
+
+ align:start position:0%
+and then reach an asmtoic point and you
+could describe these curves by this
+
+ align:start position:0%
+could describe these curves by this
+ 
+
+ align:start position:0%
+could describe these curves by this
+equation here. Here's the asmtoic force
+
+ align:start position:0%
+equation here. Here's the asmtoic force
+ 
+
+ align:start position:0%
+equation here. Here's the asmtoic force
+and it's a one minus exponential of
+
+ align:start position:0%
+and it's a one minus exponential of
+ 
+
+ align:start position:0%
+and it's a one minus exponential of
+minus time over a time constant tow. And
+
+ align:start position:0%
+minus time over a time constant tow. And
+ 
+
+ align:start position:0%
+minus time over a time constant tow. And
+then this is this number here is the
+
+ align:start position:0%
+then this is this number here is the
+ 
+
+ align:start position:0%
+then this is this number here is the
+number of fiberblasts that were attached
+
+ align:start position:0%
+number of fiberblasts that were attached
+ 
+
+ align:start position:0%
+number of fiberblasts that were attached
+at 22 hours. So he ran these tests for
+
+ align:start position:0%
+at 22 hours. So he ran these tests for
+ 
+
+ align:start position:0%
+at 22 hours. So he ran these tests for
+22 hours and when he was finished he
+
+ align:start position:0%
+22 hours and when he was finished he
+ 
+
+ align:start position:0%
+22 hours and when he was finished he
+could um count the number of cells that
+
+ align:start position:0%
+could um count the number of cells that
+ 
+
+ align:start position:0%
+could um count the number of cells that
+were attached to the scaffolds. So you
+
+ align:start position:0%
+were attached to the scaffolds. So you
+ 
+
+ align:start position:0%
+were attached to the scaffolds. So you
+would just wash off any cells that
+
+ align:start position:0%
+would just wash off any cells that
+ 
+
+ align:start position:0%
+would just wash off any cells that
+weren't attached uh and you can do a
+
+ align:start position:0%
+weren't attached uh and you can do a
+ 
+
+ align:start position:0%
+weren't attached uh and you can do a
+counting of of how many cells are left.
+
+ align:start position:0%
+counting of of how many cells are left.
+ 
+
+ align:start position:0%
+counting of of how many cells are left.
+And one of the things that he found was
+
+ align:start position:0%
+And one of the things that he found was
+ 
+
+ align:start position:0%
+And one of the things that he found was
+that if you plot that asmtoic force, if
+
+ align:start position:0%
+that if you plot that asmtoic force, if
+ 
+
+ align:start position:0%
+that if you plot that asmtoic force, if
+you plot sort of this force over here
+
+ align:start position:0%
+you plot sort of this force over here
+ 
+
+ align:start position:0%
+you plot sort of this force over here
+against the number of cells that were
+
+ align:start position:0%
+against the number of cells that were
+ 
+
+ align:start position:0%
+against the number of cells that were
+attached, you just get a linear
+
+ align:start position:0%
+attached, you just get a linear
+ 
+
+ align:start position:0%
+attached, you just get a linear
+relationship. And the slope of that is
+
+ align:start position:0%
+relationship. And the slope of that is
+ 
+
+ align:start position:0%
+relationship. And the slope of that is
+roughly the force per cell. And that's
+
+ align:start position:0%
+roughly the force per cell. And that's
+ 
+
+ align:start position:0%
+roughly the force per cell. And that's
+about one nanon.
+
+ align:start position:0%
+about one nanon.
+ 
+
+ align:start position:0%
+about one nanon.
+Now, this is a little deceptive because
+
+ align:start position:0%
+Now, this is a little deceptive because
+ 
+
+ align:start position:0%
+Now, this is a little deceptive because
+not all the cells are contracting and
+
+ align:start position:0%
+not all the cells are contracting and
+ 
+
+ align:start position:0%
+not all the cells are contracting and
+not all the cells are lined up in one
+
+ align:start position:0%
+not all the cells are lined up in one
+ 
+
+ align:start position:0%
+not all the cells are lined up in one
+direction. So there's cells in different
+
+ align:start position:0%
+direction. So there's cells in different
+ 
+
+ align:start position:0%
+direction. So there's cells in different
+orientations but just as a sort of order
+
+ align:start position:0%
+orientations but just as a sort of order
+ 
+
+ align:start position:0%
+orientations but just as a sort of order
+of magnitude the cells are applying
+
+ align:start position:0%
+of magnitude the cells are applying
+ 
+
+ align:start position:0%
+of magnitude the cells are applying
+something like one nan per cell. So
+
+ align:start position:0%
+something like one nan per cell. So
+ 
+
+ align:start position:0%
+something like one nan per cell. So
+that's the effect of the cell number.
+
+ align:start position:0%
+that's the effect of the cell number.
+ 
+
+ align:start position:0%
+that's the effect of the cell number.
+Another thing he did was he looked at
+
+ align:start position:0%
+Another thing he did was he looked at
+ 
+
+ align:start position:0%
+Another thing he did was he looked at
+what happens if you change the stiffness
+
+ align:start position:0%
+what happens if you change the stiffness
+ 
+
+ align:start position:0%
+what happens if you change the stiffness
+of that beam. If you make that beam in
+
+ align:start position:0%
+of that beam. If you make that beam in
+ 
+
+ align:start position:0%
+of that beam. If you make that beam in
+the device different stiffnesses how do
+
+ align:start position:0%
+the device different stiffnesses how do
+ 
+
+ align:start position:0%
+the device different stiffnesses how do
+the cells react? And so these
+
+ align:start position:0%
+the cells react? And so these
+ 
+
+ align:start position:0%
+the cells react? And so these
+stiffnesses here are
+
+ align:start position:0%
+stiffnesses here are
+ 
+
+ align:start position:0%
+stiffnesses here are
+the stiffness of of the system. So
+
+ align:start position:0%
+the stiffness of of the system. So
+ 
+
+ align:start position:0%
+the stiffness of of the system. So
+there's seven newtons per meter up to
+
+ align:start position:0%
+there's seven newtons per meter up to
+ 
+
+ align:start position:0%
+there's seven newtons per meter up to
+10. So there's a factor of a little over
+
+ align:start position:0%
+10. So there's a factor of a little over
+ 
+
+ align:start position:0%
+10. So there's a factor of a little over
+10 difference. And you can see the
+
+ align:start position:0%
+10 difference. And you can see the
+ 
+
+ align:start position:0%
+10 difference. And you can see the
+displacement per cell changes. The the
+
+ align:start position:0%
+displacement per cell changes. The the
+ 
+
+ align:start position:0%
+displacement per cell changes. The the
+stiffer the system is, the less the um
+
+ align:start position:0%
+stiffer the system is, the less the um
+ 
+
+ align:start position:0%
+stiffer the system is, the less the um
+cells can displace it. Uh but if you
+
+ align:start position:0%
+cells can displace it. Uh but if you
+ 
+
+ align:start position:0%
+cells can displace it. Uh but if you
+then plot the force per cell, you find
+
+ align:start position:0%
+then plot the force per cell, you find
+ 
+
+ align:start position:0%
+then plot the force per cell, you find
+that the force per cell is about the
+
+ align:start position:0%
+that the force per cell is about the
+ 
+
+ align:start position:0%
+that the force per cell is about the
+same. So you develop this about the same
+
+ align:start position:0%
+same. So you develop this about the same
+ 
+
+ align:start position:0%
+same. So you develop this about the same
+force. So that kind of suggests the
+
+ align:start position:0%
+force. So that kind of suggests the
+ 
+
+ align:start position:0%
+force. So that kind of suggests the
+cells are capable of applying a certain
+
+ align:start position:0%
+cells are capable of applying a certain
+ 
+
+ align:start position:0%
+cells are capable of applying a certain
+amount of force and not any more force,
+
+ align:start position:0%
+amount of force and not any more force,
+ 
+
+ align:start position:0%
+amount of force and not any more force,
+no larger force. So he did that. Um then
+
+ align:start position:0%
+no larger force. So he did that. Um then
+ 
+
+ align:start position:0%
+no larger force. So he did that. Um then
+we were interested in what was the
+
+ align:start position:0%
+we were interested in what was the
+ 
+
+ align:start position:0%
+we were interested in what was the
+mechanism of this? How were the cells
+
+ align:start position:0%
+mechanism of this? How were the cells
+ 
+
+ align:start position:0%
+mechanism of this? How were the cells
+applying this force? Because I was kind
+
+ align:start position:0%
+applying this force? Because I was kind
+ 
+
+ align:start position:0%
+applying this force? Because I was kind
+of surprised to find out the cells even
+
+ align:start position:0%
+of surprised to find out the cells even
+ 
+
+ align:start position:0%
+of surprised to find out the cells even
+could apply forces. So, we were
+
+ align:start position:0%
+could apply forces. So, we were
+ 
+
+ align:start position:0%
+could apply forces. So, we were
+interested in understanding the um
+
+ align:start position:0%
+interested in understanding the um
+ 
+
+ align:start position:0%
+interested in understanding the um
+mechanism of this. And one of the things
+
+ align:start position:0%
+mechanism of this. And one of the things
+ 
+
+ align:start position:0%
+mechanism of this. And one of the things
+we knew that we didn't quite figure out
+
+ align:start position:0%
+we knew that we didn't quite figure out
+ 
+
+ align:start position:0%
+we knew that we didn't quite figure out
+how this all worked together was we knew
+
+ align:start position:0%
+how this all worked together was we knew
+ 
+
+ align:start position:0%
+how this all worked together was we knew
+that the cells elongated. If you just
+
+ align:start position:0%
+that the cells elongated. If you just
+ 
+
+ align:start position:0%
+that the cells elongated. If you just
+take a substrate, like even just a 2D
+
+ align:start position:0%
+take a substrate, like even just a 2D
+ 
+
+ align:start position:0%
+take a substrate, like even just a 2D
+substrate, you put cells on it, they'll
+
+ align:start position:0%
+substrate, you put cells on it, they'll
+ 
+
+ align:start position:0%
+substrate, you put cells on it, they'll
+be rounded to start out with and over
+
+ align:start position:0%
+be rounded to start out with and over
+ 
+
+ align:start position:0%
+be rounded to start out with and over
+time, over a few hours, they'll spread.
+
+ align:start position:0%
+time, over a few hours, they'll spread.
+ 
+
+ align:start position:0%
+time, over a few hours, they'll spread.
+And that's pretty standard. Many types
+
+ align:start position:0%
+And that's pretty standard. Many types
+ 
+
+ align:start position:0%
+And that's pretty standard. Many types
+of cells will do that. So we knew the
+
+ align:start position:0%
+of cells will do that. So we knew the
+ 
+
+ align:start position:0%
+of cells will do that. So we knew the
+cells were starting off as rounded and
+
+ align:start position:0%
+cells were starting off as rounded and
+ 
+
+ align:start position:0%
+cells were starting off as rounded and
+they were spreading. So the cells are
+
+ align:start position:0%
+they were spreading. So the cells are
+ 
+
+ align:start position:0%
+they were spreading. So the cells are
+getting longer, but our whole scaffolds
+
+ align:start position:0%
+getting longer, but our whole scaffolds
+ 
+
+ align:start position:0%
+getting longer, but our whole scaffolds
+getting shorter. And so it wasn't
+
+ align:start position:0%
+getting shorter. And so it wasn't
+ 
+
+ align:start position:0%
+getting shorter. And so it wasn't
+obvious how was the cells getting
+
+ align:start position:0%
+obvious how was the cells getting
+ 
+
+ align:start position:0%
+obvious how was the cells getting
+longer, but the scaffolds getting
+
+ align:start position:0%
+longer, but the scaffolds getting
+ 
+
+ align:start position:0%
+longer, but the scaffolds getting
+shorter. And so the next thing we
+
+ align:start position:0%
+shorter. And so the next thing we
+ 
+
+ align:start position:0%
+shorter. And so the next thing we
+thought we would do is just watch the
+
+ align:start position:0%
+thought we would do is just watch the
+ 
+
+ align:start position:0%
+thought we would do is just watch the
+cells and see what they did. Uh and so
+
+ align:start position:0%
+cells and see what they did. Uh and so
+ 
+
+ align:start position:0%
+cells and see what they did. Uh and so
+we measured the um aspect ratio of the
+
+ align:start position:0%
+we measured the um aspect ratio of the
+ 
+
+ align:start position:0%
+we measured the um aspect ratio of the
+cells at different time points. And we
+
+ align:start position:0%
+cells at different time points. And we
+ 
+
+ align:start position:0%
+cells at different time points. And we
+did this by just uh uh impregnating the
+
+ align:start position:0%
+did this by just uh uh impregnating the
+ 
+
+ align:start position:0%
+did this by just uh uh impregnating the
+scaffold and the cells at different time
+
+ align:start position:0%
+scaffold and the cells at different time
+ 
+
+ align:start position:0%
+scaffold and the cells at different time
+points uh with a resin. and then using a
+
+ align:start position:0%
+points uh with a resin. and then using a
+ 
+
+ align:start position:0%
+points uh with a resin. and then using a
+stain and then using digital image
+
+ align:start position:0%
+stain and then using digital image
+ 
+
+ align:start position:0%
+stain and then using digital image
+analysis.
+
+ align:start position:0%
+analysis.
+ 
+
+ align:start position:0%
+analysis.
+So what we found was that the fiber
+
+ align:start position:0%
+So what we found was that the fiber
+ 
+
+ align:start position:0%
+So what we found was that the fiber
+fiberblast morphology looked like this.
+
+ align:start position:0%
+fiberblast morphology looked like this.
+ 
+
+ align:start position:0%
+fiberblast morphology looked like this.
+So the the long thready things are the
+
+ align:start position:0%
+So the the long thready things are the
+ 
+
+ align:start position:0%
+So the the long thready things are the
+scaffold and these little blobs here are
+
+ align:start position:0%
+scaffold and these little blobs here are
+ 
+
+ align:start position:0%
+scaffold and these little blobs here are
+the fiberblasts or the cells. So here at
+
+ align:start position:0%
+the fiberblasts or the cells. So here at
+ 
+
+ align:start position:0%
+the fiberblasts or the cells. So here at
+time zero you can see like I said the
+
+ align:start position:0%
+time zero you can see like I said the
+ 
+
+ align:start position:0%
+time zero you can see like I said the
+cells are pretty rounded. They're not
+
+ align:start position:0%
+cells are pretty rounded. They're not
+ 
+
+ align:start position:0%
+cells are pretty rounded. They're not
+very spread out. Here at 8 hours you can
+
+ align:start position:0%
+very spread out. Here at 8 hours you can
+ 
+
+ align:start position:0%
+very spread out. Here at 8 hours you can
+see like here's a cell that's gotten
+
+ align:start position:0%
+see like here's a cell that's gotten
+ 
+
+ align:start position:0%
+see like here's a cell that's gotten
+longer. Here's another one. This guy
+
+ align:start position:0%
+longer. Here's another one. This guy
+ 
+
+ align:start position:0%
+longer. Here's another one. This guy
+here is still rounded. It's not doing
+
+ align:start position:0%
+here is still rounded. It's not doing
+ 
+
+ align:start position:0%
+here is still rounded. It's not doing
+much. 22 hours again some of the cells
+
+ align:start position:0%
+much. 22 hours again some of the cells
+ 
+
+ align:start position:0%
+much. 22 hours again some of the cells
+are are quite elongated. Some of them
+
+ align:start position:0%
+are are quite elongated. Some of them
+ 
+
+ align:start position:0%
+are are quite elongated. Some of them
+are still not that elongated, so they
+
+ align:start position:0%
+are still not that elongated, so they
+ 
+
+ align:start position:0%
+are still not that elongated, so they
+don't all become active. But one of the
+
+ align:start position:0%
+don't all become active. But one of the
+ 
+
+ align:start position:0%
+don't all become active. But one of the
+things we noticed, if you look at this
+
+ align:start position:0%
+things we noticed, if you look at this
+ 
+
+ align:start position:0%
+things we noticed, if you look at this
+image here, you can see these cells are
+
+ align:start position:0%
+image here, you can see these cells are
+ 
+
+ align:start position:0%
+image here, you can see these cells are
+attached at one end and at the other
+
+ align:start position:0%
+attached at one end and at the other
+ 
+
+ align:start position:0%
+attached at one end and at the other
+end, but they're not attached in the
+
+ align:start position:0%
+end, but they're not attached in the
+ 
+
+ align:start position:0%
+end, but they're not attached in the
+middle. There's sort of a gap between
+
+ align:start position:0%
+middle. There's sort of a gap between
+ 
+
+ align:start position:0%
+middle. There's sort of a gap between
+the cell and the strut. And this is
+
+ align:start position:0%
+the cell and the strut. And this is
+ 
+
+ align:start position:0%
+the cell and the strut. And this is
+another example here. Here's a cell
+
+ align:start position:0%
+another example here. Here's a cell
+ 
+
+ align:start position:0%
+another example here. Here's a cell
+here. And this is the strut, the
+
+ align:start position:0%
+here. And this is the strut, the
+ 
+
+ align:start position:0%
+here. And this is the strut, the
+collagen gag strut that it's attached
+
+ align:start position:0%
+collagen gag strut that it's attached
+ 
+
+ align:start position:0%
+collagen gag strut that it's attached
+to. And you can see it's attached at the
+
+ align:start position:0%
+to. And you can see it's attached at the
+ 
+
+ align:start position:0%
+to. And you can see it's attached at the
+two ends, but not in the middle. And
+
+ align:start position:0%
+two ends, but not in the middle. And
+ 
+
+ align:start position:0%
+two ends, but not in the middle. And
+this starts to explain um how it is that
+
+ align:start position:0%
+this starts to explain um how it is that
+ 
+
+ align:start position:0%
+this starts to explain um how it is that
+the cells are elongating but the
+
+ align:start position:0%
+the cells are elongating but the
+ 
+
+ align:start position:0%
+the cells are elongating but the
+scaffolds getting shorter. It it's that
+
+ align:start position:0%
+scaffolds getting shorter. It it's that
+ 
+
+ align:start position:0%
+scaffolds getting shorter. It it's that
+the cells are just attached at two ends.
+
+ align:start position:0%
+the cells are just attached at two ends.
+ 
+
+ align:start position:0%
+the cells are just attached at two ends.
+And the cells are sort of moving along a
+
+ align:start position:0%
+And the cells are sort of moving along a
+ 
+
+ align:start position:0%
+And the cells are sort of moving along a
+strut and they're attached at the two
+
+ align:start position:0%
+strut and they're attached at the two
+ 
+
+ align:start position:0%
+strut and they're attached at the two
+ends. And if you think of the cells
+
+ align:start position:0%
+ends. And if you think of the cells
+ 
+
+ align:start position:0%
+ends. And if you think of the cells
+attached through those focal adhesion
+
+ align:start position:0%
+attached through those focal adhesion
+ 
+
+ align:start position:0%
+attached through those focal adhesion
+points, they're applying sort of tension
+
+ align:start position:0%
+points, they're applying sort of tension
+ 
+
+ align:start position:0%
+points, they're applying sort of tension
+to the cell. Uh and the actin filaments
+
+ align:start position:0%
+to the cell. Uh and the actin filaments
+ 
+
+ align:start position:0%
+to the cell. Uh and the actin filaments
+in the cell are in tension. Obviously
+
+ align:start position:0%
+in the cell are in tension. Obviously
+ 
+
+ align:start position:0%
+in the cell are in tension. Obviously
+filaments can't be in compression.
+
+ align:start position:0%
+filaments can't be in compression.
+ 
+
+ align:start position:0%
+filaments can't be in compression.
+They're only going to be in tension. And
+
+ align:start position:0%
+They're only going to be in tension. And
+ 
+
+ align:start position:0%
+They're only going to be in tension. And
+what happens is that puts the strut into
+
+ align:start position:0%
+what happens is that puts the strut into
+ 
+
+ align:start position:0%
+what happens is that puts the strut into
+compression. And if the strut's in
+
+ align:start position:0%
+compression. And if the strut's in
+ 
+
+ align:start position:0%
+compression. And if the strut's in
+compression, at some point it's going to
+
+ align:start position:0%
+compression, at some point it's going to
+ 
+
+ align:start position:0%
+compression, at some point it's going to
+buckle. And you can see this strut here
+
+ align:start position:0%
+buckle. And you can see this strut here
+ 
+
+ align:start position:0%
+buckle. And you can see this strut here
+has basically buckled under that cell.
+
+ align:start position:0%
+has basically buckled under that cell.
+ 
+
+ align:start position:0%
+has basically buckled under that cell.
+And so if the cells are getting longer
+
+ align:start position:0%
+And so if the cells are getting longer
+ 
+
+ align:start position:0%
+And so if the cells are getting longer
+and they're buckling the um the struts,
+
+ align:start position:0%
+and they're buckling the um the struts,
+ 
+
+ align:start position:0%
+and they're buckling the um the struts,
+then that's going to shorten the struts
+
+ align:start position:0%
+then that's going to shorten the struts
+ 
+
+ align:start position:0%
+then that's going to shorten the struts
+and the whole scaffold is going to get
+
+ align:start position:0%
+and the whole scaffold is going to get
+ 
+
+ align:start position:0%
+and the whole scaffold is going to get
+shorter.
+
+ align:start position:0%
+shorter.
+ 
+
+ align:start position:0%
+shorter.
+Oops. And so then Toby plotted the
+
+ align:start position:0%
+Oops. And so then Toby plotted the
+ 
+
+ align:start position:0%
+Oops. And so then Toby plotted the
+aspect ratio of the cells. So that is a
+
+ align:start position:0%
+aspect ratio of the cells. So that is a
+ 
+
+ align:start position:0%
+aspect ratio of the cells. So that is a
+measure of their elongation against the
+
+ align:start position:0%
+measure of their elongation against the
+ 
+
+ align:start position:0%
+measure of their elongation against the
+time. And again he found one of these
+
+ align:start position:0%
+time. And again he found one of these
+ 
+
+ align:start position:0%
+time. And again he found one of these
+curves with the same kind of form as the
+
+ align:start position:0%
+curves with the same kind of form as the
+ 
+
+ align:start position:0%
+curves with the same kind of form as the
+curve for the force development. And he
+
+ align:start position:0%
+curve for the force development. And he
+ 
+
+ align:start position:0%
+curve for the force development. And he
+found the time constant here for the
+
+ align:start position:0%
+found the time constant here for the
+ 
+
+ align:start position:0%
+found the time constant here for the
+change in the aspect ratio was about 5
+
+ align:start position:0%
+change in the aspect ratio was about 5
+ 
+
+ align:start position:0%
+change in the aspect ratio was about 5
+hours. And for the development of the
+
+ align:start position:0%
+hours. And for the development of the
+ 
+
+ align:start position:0%
+hours. And for the development of the
+force it was about 5.7 hours. So the
+
+ align:start position:0%
+force it was about 5.7 hours. So the
+ 
+
+ align:start position:0%
+force it was about 5.7 hours. So the
+time constant for sort of the elongation
+
+ align:start position:0%
+time constant for sort of the elongation
+ 
+
+ align:start position:0%
+time constant for sort of the elongation
+of the cells more or less matches up
+
+ align:start position:0%
+of the cells more or less matches up
+ 
+
+ align:start position:0%
+of the cells more or less matches up
+with the time constant for developing
+
+ align:start position:0%
+with the time constant for developing
+ 
+
+ align:start position:0%
+with the time constant for developing
+the force.
+
+ align:start position:0%
+the force.
+ 
+
+ align:start position:0%
+the force.
+Uh so that's kind of what that says and
+
+ align:start position:0%
+Uh so that's kind of what that says and
+ 
+
+ align:start position:0%
+Uh so that's kind of what that says and
+that suggests there's a link between the
+
+ align:start position:0%
+that suggests there's a link between the
+ 
+
+ align:start position:0%
+that suggests there's a link between the
+elongation of the cell population and
+
+ align:start position:0%
+elongation of the cell population and
+ 
+
+ align:start position:0%
+elongation of the cell population and
+the macroscopic contraction of the
+
+ align:start position:0%
+the macroscopic contraction of the
+ 
+
+ align:start position:0%
+the macroscopic contraction of the
+population. So then we wanted to take it
+
+ align:start position:0%
+population. So then we wanted to take it
+ 
+
+ align:start position:0%
+population. So then we wanted to take it
+one step further and we wanted to look
+
+ align:start position:0%
+one step further and we wanted to look
+ 
+
+ align:start position:0%
+one step further and we wanted to look
+at what the cells were doing live like
+
+ align:start position:0%
+at what the cells were doing live like
+ 
+
+ align:start position:0%
+at what the cells were doing live like
+as they were doing it. So Toby devised
+
+ align:start position:0%
+as they were doing it. So Toby devised
+ 
+
+ align:start position:0%
+as they were doing it. So Toby devised
+this little schematic thing here. So he
+
+ align:start position:0%
+this little schematic thing here. So he
+ 
+
+ align:start position:0%
+this little schematic thing here. So he
+had just an optical microscope. He had a
+
+ align:start position:0%
+had just an optical microscope. He had a
+ 
+
+ align:start position:0%
+had just an optical microscope. He had a
+um a microscope slide with a fairly
+
+ align:start position:0%
+um a microscope slide with a fairly
+ 
+
+ align:start position:0%
+um a microscope slide with a fairly
+thick um well in it so that we could put
+
+ align:start position:0%
+thick um well in it so that we could put
+ 
+
+ align:start position:0%
+thick um well in it so that we could put
+culture medium in the well. We put a
+
+ align:start position:0%
+culture medium in the well. We put a
+ 
+
+ align:start position:0%
+culture medium in the well. We put a
+cell seated matrix in here and he had a
+
+ align:start position:0%
+cell seated matrix in here and he had a
+ 
+
+ align:start position:0%
+cell seated matrix in here and he had a
+heated stage here and then he took
+
+ align:start position:0%
+heated stage here and then he took
+ 
+
+ align:start position:0%
+heated stage here and then he took
+little videos of what the cells were
+
+ align:start position:0%
+little videos of what the cells were
+ 
+
+ align:start position:0%
+little videos of what the cells were
+doing and this required some patience
+
+ align:start position:0%
+doing and this required some patience
+ 
+
+ align:start position:0%
+doing and this required some patience
+because as you could see not all the
+
+ align:start position:0%
+because as you could see not all the
+ 
+
+ align:start position:0%
+because as you could see not all the
+cells did anything. Some of them just
+
+ align:start position:0%
+cells did anything. Some of them just
+ 
+
+ align:start position:0%
+cells did anything. Some of them just
+sat there and did nothing. So he would
+
+ align:start position:0%
+sat there and did nothing. So he would
+ 
+
+ align:start position:0%
+sat there and did nothing. So he would
+set this up for a day and watch a cell
+
+ align:start position:0%
+set this up for a day and watch a cell
+ 
+
+ align:start position:0%
+set this up for a day and watch a cell
+and it would do nothing and then he
+
+ align:start position:0%
+and it would do nothing and then he
+ 
+
+ align:start position:0%
+and it would do nothing and then he
+would have to find another cell. But he
+
+ align:start position:0%
+would have to find another cell. But he
+ 
+
+ align:start position:0%
+would have to find another cell. But he
+did find some cells that um were
+
+ align:start position:0%
+did find some cells that um were
+ 
+
+ align:start position:0%
+did find some cells that um were
+responsible for the contraction and that
+
+ align:start position:0%
+responsible for the contraction and that
+ 
+
+ align:start position:0%
+responsible for the contraction and that
+was was kind of neat. So here's the
+
+ align:start position:0%
+was was kind of neat. So here's the
+ 
+
+ align:start position:0%
+was was kind of neat. So here's the
+scaffold again. All these little bits
+
+ align:start position:0%
+scaffold again. All these little bits
+ 
+
+ align:start position:0%
+scaffold again. All these little bits
+here of the scaffold. This is a strut of
+
+ align:start position:0%
+here of the scaffold. This is a strut of
+ 
+
+ align:start position:0%
+here of the scaffold. This is a strut of
+the scaffold and this is a fiberblast
+
+ align:start position:0%
+the scaffold and this is a fiberblast
+ 
+
+ align:start position:0%
+the scaffold and this is a fiberblast
+parked on the scaffold. And uh this has
+
+ align:start position:0%
+parked on the scaffold. And uh this has
+ 
+
+ align:start position:0%
+parked on the scaffold. And uh this has
+a little video here. And you can see
+
+ align:start position:0%
+a little video here. And you can see
+ 
+
+ align:start position:0%
+a little video here. And you can see
+what's happening is this strut here is
+
+ align:start position:0%
+what's happening is this strut here is
+ 
+
+ align:start position:0%
+what's happening is this strut here is
+starting to buckle. And you can see
+
+ align:start position:0%
+starting to buckle. And you can see
+ 
+
+ align:start position:0%
+starting to buckle. And you can see
+these two sides here. Those two things
+
+ align:start position:0%
+these two sides here. Those two things
+ 
+
+ align:start position:0%
+these two sides here. Those two things
+are coming closer together. So they
+
+ align:start position:0%
+are coming closer together. So they
+ 
+
+ align:start position:0%
+are coming closer together. So they
+originally were this piece here and that
+
+ align:start position:0%
+originally were this piece here and that
+ 
+
+ align:start position:0%
+originally were this piece here and that
+piece there. And now they're at that
+
+ align:start position:0%
+piece there. And now they're at that
+ 
+
+ align:start position:0%
+piece there. And now they're at that
+point there. And then if I let it go a
+
+ align:start position:0%
+point there. And then if I let it go a
+ 
+
+ align:start position:0%
+point there. And then if I let it go a
+little bit longer, you know, it
+
+ align:start position:0%
+little bit longer, you know, it
+ 
+
+ align:start position:0%
+little bit longer, you know, it
+continues to do that process. And then
+
+ align:start position:0%
+continues to do that process. And then
+ 
+
+ align:start position:0%
+continues to do that process. And then
+the final thing, this kind of smooshed
+
+ align:start position:0%
+the final thing, this kind of smooshed
+ 
+
+ align:start position:0%
+the final thing, this kind of smooshed
+up mess here is these two things having
+
+ align:start position:0%
+up mess here is these two things having
+ 
+
+ align:start position:0%
+up mess here is these two things having
+been brought completely together. And
+
+ align:start position:0%
+been brought completely together. And
+ 
+
+ align:start position:0%
+been brought completely together. And
+this strut here is some strut down over
+
+ align:start position:0%
+this strut here is some strut down over
+ 
+
+ align:start position:0%
+this strut here is some strut down over
+here. So you can see how the cells are
+
+ align:start position:0%
+here. So you can see how the cells are
+ 
+
+ align:start position:0%
+here. So you can see how the cells are
+elongating and and causing contraction
+
+ align:start position:0%
+elongating and and causing contraction
+ 
+
+ align:start position:0%
+elongating and and causing contraction
+of the scaffold. Here's a series of
+
+ align:start position:0%
+of the scaffold. Here's a series of
+ 
+
+ align:start position:0%
+of the scaffold. Here's a series of
+stills taken from another video that he
+
+ align:start position:0%
+stills taken from another video that he
+ 
+
+ align:start position:0%
+stills taken from another video that he
+did. So this sort of square thing is the
+
+ align:start position:0%
+did. So this sort of square thing is the
+ 
+
+ align:start position:0%
+did. So this sort of square thing is the
+scaffold. So B is the scaffold. And A,
+
+ align:start position:0%
+scaffold. So B is the scaffold. And A,
+ 
+
+ align:start position:0%
+scaffold. So B is the scaffold. And A,
+this little blob here is the fiberblast.
+
+ align:start position:0%
+this little blob here is the fiberblast.
+ 
+
+ align:start position:0%
+this little blob here is the fiberblast.
+And you can see even from this image to
+
+ align:start position:0%
+And you can see even from this image to
+ 
+
+ align:start position:0%
+And you can see even from this image to
+this one, you can see that the
+
+ align:start position:0%
+this one, you can see that the
+ 
+
+ align:start position:0%
+this one, you can see that the
+fiberblast has spread a little. You see
+
+ align:start position:0%
+fiberblast has spread a little. You see
+ 
+
+ align:start position:0%
+fiberblast has spread a little. You see
+how it's kind of oozed out along the
+
+ align:start position:0%
+how it's kind of oozed out along the
+ 
+
+ align:start position:0%
+how it's kind of oozed out along the
+scaffold there. And eventually it
+
+ align:start position:0%
+scaffold there. And eventually it
+ 
+
+ align:start position:0%
+scaffold there. And eventually it
+attaches over here. And you can see that
+
+ align:start position:0%
+attaches over here. And you can see that
+ 
+
+ align:start position:0%
+attaches over here. And you can see that
+it's buckled this strut underneath it.
+
+ align:start position:0%
+it's buckled this strut underneath it.
+ 
+
+ align:start position:0%
+it's buckled this strut underneath it.
+And here it's a little bit more
+
+ align:start position:0%
+And here it's a little bit more
+ 
+
+ align:start position:0%
+And here it's a little bit more
+deformed. It then grabs on down here
+
+ align:start position:0%
+deformed. It then grabs on down here
+ 
+
+ align:start position:0%
+deformed. It then grabs on down here
+somewhere and it deforms it even more.
+
+ align:start position:0%
+somewhere and it deforms it even more.
+ 
+
+ align:start position:0%
+somewhere and it deforms it even more.
+So you can see that's more deformed. And
+
+ align:start position:0%
+So you can see that's more deformed. And
+ 
+
+ align:start position:0%
+So you can see that's more deformed. And
+then Toby put um alcohol on the um on
+
+ align:start position:0%
+then Toby put um alcohol on the um on
+ 
+
+ align:start position:0%
+then Toby put um alcohol on the um on
+the whole thing which kills the cells
+
+ align:start position:0%
+the whole thing which kills the cells
+ 
+
+ align:start position:0%
+the whole thing which kills the cells
+and then the cell lets go and you can
+
+ align:start position:0%
+and then the cell lets go and you can
+ 
+
+ align:start position:0%
+and then the cell lets go and you can
+see you recover some of the deformation.
+
+ align:start position:0%
+see you recover some of the deformation.
+ 
+
+ align:start position:0%
+see you recover some of the deformation.
+You don't recover all of it but you
+
+ align:start position:0%
+You don't recover all of it but you
+ 
+
+ align:start position:0%
+You don't recover all of it but you
+recover some of it. Uh this was another
+
+ align:start position:0%
+recover some of it. Uh this was another
+ 
+
+ align:start position:0%
+recover some of it. Uh this was another
+example and this was kind of interesting
+
+ align:start position:0%
+example and this was kind of interesting
+ 
+
+ align:start position:0%
+example and this was kind of interesting
+here. There was a a scaffold uh junction
+
+ align:start position:0%
+here. There was a a scaffold uh junction
+ 
+
+ align:start position:0%
+here. There was a a scaffold uh junction
+where there were three struts that came
+
+ align:start position:0%
+where there were three struts that came
+ 
+
+ align:start position:0%
+where there were three struts that came
+together a little bit like a strut and
+
+ align:start position:0%
+together a little bit like a strut and
+ 
+
+ align:start position:0%
+together a little bit like a strut and
+there was a little cell right there and
+
+ align:start position:0%
+there was a little cell right there and
+ 
+
+ align:start position:0%
+there was a little cell right there and
+you can see the cell elongates. You see
+
+ align:start position:0%
+you can see the cell elongates. You see
+ 
+
+ align:start position:0%
+you can see the cell elongates. You see
+how this sort of elongated and it's
+
+ align:start position:0%
+how this sort of elongated and it's
+ 
+
+ align:start position:0%
+how this sort of elongated and it's
+grabbing on up here somewhere. But the
+
+ align:start position:0%
+grabbing on up here somewhere. But the
+ 
+
+ align:start position:0%
+grabbing on up here somewhere. But the
+amount of force the cell was kind of
+
+ align:start position:0%
+amount of force the cell was kind of
+ 
+
+ align:start position:0%
+amount of force the cell was kind of
+pulling with um must have been less than
+
+ align:start position:0%
+pulling with um must have been less than
+ 
+
+ align:start position:0%
+pulling with um must have been less than
+the or rather must have been more than
+
+ align:start position:0%
+the or rather must have been more than
+ 
+
+ align:start position:0%
+the or rather must have been more than
+the force of the focal adhesion because
+
+ align:start position:0%
+the force of the focal adhesion because
+ 
+
+ align:start position:0%
+the force of the focal adhesion because
+what happens was eventually the focal
+
+ align:start position:0%
+what happens was eventually the focal
+ 
+
+ align:start position:0%
+what happens was eventually the focal
+adhesion let go and the cell kind of
+
+ align:start position:0%
+adhesion let go and the cell kind of
+ 
+
+ align:start position:0%
+adhesion let go and the cell kind of
+bounces back and ends up over here. So
+
+ align:start position:0%
+bounces back and ends up over here. So
+ 
+
+ align:start position:0%
+bounces back and ends up over here. So
+the cell has kind of snapped back onto
+
+ align:start position:0%
+the cell has kind of snapped back onto
+ 
+
+ align:start position:0%
+the cell has kind of snapped back onto
+the other focal adhesion over here. And
+
+ align:start position:0%
+the other focal adhesion over here. And
+ 
+
+ align:start position:0%
+the other focal adhesion over here. And
+here it's rounded again. And here it
+
+ align:start position:0%
+here it's rounded again. And here it
+ 
+
+ align:start position:0%
+here it's rounded again. And here it
+elongates again. And then this focal
+
+ align:start position:0%
+elongates again. And then this focal
+ 
+
+ align:start position:0%
+elongates again. And then this focal
+heed lets go. And now it's moved back
+
+ align:start position:0%
+heed lets go. And now it's moved back
+ 
+
+ align:start position:0%
+heed lets go. And now it's moved back
+over to there. So that these these
+
+ align:start position:0%
+over to there. So that these these
+ 
+
+ align:start position:0%
+over to there. So that these these
+struts here are so stiff. They're much
+
+ align:start position:0%
+struts here are so stiff. They're much
+ 
+
+ align:start position:0%
+struts here are so stiff. They're much
+stiffer. I think partly because they're
+
+ align:start position:0%
+stiffer. I think partly because they're
+ 
+
+ align:start position:0%
+stiffer. I think partly because they're
+triangulated and it looks like they're
+
+ align:start position:0%
+triangulated and it looks like they're
+ 
+
+ align:start position:0%
+triangulated and it looks like they're
+just shorter and thicker. Uh that this
+
+ align:start position:0%
+just shorter and thicker. Uh that this
+ 
+
+ align:start position:0%
+just shorter and thicker. Uh that this
+the cell isn't being able to deform
+
+ align:start position:0%
+the cell isn't being able to deform
+ 
+
+ align:start position:0%
+the cell isn't being able to deform
+those, but it's sort of elongating and
+
+ align:start position:0%
+those, but it's sort of elongating and
+ 
+
+ align:start position:0%
+those, but it's sort of elongating and
+then the focal adhesion is letting go.
+
+ align:start position:0%
+then the focal adhesion is letting go.
+ 
+
+ align:start position:0%
+then the focal adhesion is letting go.
+So this is a little schematic of of what
+
+ align:start position:0%
+So this is a little schematic of of what
+ 
+
+ align:start position:0%
+So this is a little schematic of of what
+we think's going on. So the cell starts
+
+ align:start position:0%
+we think's going on. So the cell starts
+ 
+
+ align:start position:0%
+we think's going on. So the cell starts
+out, you know, with some elongation
+
+ align:start position:0%
+out, you know, with some elongation
+ 
+
+ align:start position:0%
+out, you know, with some elongation
+here. It's attached at that point. It's
+
+ align:start position:0%
+here. It's attached at that point. It's
+ 
+
+ align:start position:0%
+here. It's attached at that point. It's
+attached at that point there. And and
+
+ align:start position:0%
+attached at that point there. And and
+ 
+
+ align:start position:0%
+attached at that point there. And and
+the cell is getting longer. And if you
+
+ align:start position:0%
+the cell is getting longer. And if you
+ 
+
+ align:start position:0%
+the cell is getting longer. And if you
+think about it, as the cell is getting
+
+ align:start position:0%
+think about it, as the cell is getting
+ 
+
+ align:start position:0%
+think about it, as the cell is getting
+longer, if you think about the oiler
+
+ align:start position:0%
+longer, if you think about the oiler
+ 
+
+ align:start position:0%
+longer, if you think about the oiler
+buckling formula, the buckling load goes
+
+ align:start position:0%
+buckling formula, the buckling load goes
+ 
+
+ align:start position:0%
+buckling formula, the buckling load goes
+as 1 over L^2. So the the longer the
+
+ align:start position:0%
+as 1 over L^2. So the the longer the
+ 
+
+ align:start position:0%
+as 1 over L^2. So the the longer the
+length of this piece of uh the strut of
+
+ align:start position:0%
+length of this piece of uh the strut of
+ 
+
+ align:start position:0%
+length of this piece of uh the strut of
+the scaffold underneath the cell is, the
+
+ align:start position:0%
+the scaffold underneath the cell is, the
+ 
+
+ align:start position:0%
+the scaffold underneath the cell is, the
+smaller the load it takes to actually
+
+ align:start position:0%
+smaller the load it takes to actually
+ 
+
+ align:start position:0%
+smaller the load it takes to actually
+cause it to buckle. So at some point it
+
+ align:start position:0%
+cause it to buckle. So at some point it
+ 
+
+ align:start position:0%
+cause it to buckle. So at some point it
+buckles like this. And this is just a
+
+ align:start position:0%
+buckles like this. And this is just a
+ 
+
+ align:start position:0%
+buckles like this. And this is just a
+little force diagram. So the actin
+
+ align:start position:0%
+little force diagram. So the actin
+ 
+
+ align:start position:0%
+little force diagram. So the actin
+fibers are in tension and the matrix
+
+ align:start position:0%
+fibers are in tension and the matrix
+ 
+
+ align:start position:0%
+fibers are in tension and the matrix
+strut is in compression. Sometimes we
+
+ align:start position:0%
+strut is in compression. Sometimes we
+ 
+
+ align:start position:0%
+strut is in compression. Sometimes we
+saw um some bending. So you could see if
+
+ align:start position:0%
+saw um some bending. So you could see if
+ 
+
+ align:start position:0%
+saw um some bending. So you could see if
+a cell was spanning between two struts,
+
+ align:start position:0%
+a cell was spanning between two struts,
+ 
+
+ align:start position:0%
+a cell was spanning between two struts,
+you could get the cell bending the
+
+ align:start position:0%
+you could get the cell bending the
+ 
+
+ align:start position:0%
+you could get the cell bending the
+struts as well. That was another
+
+ align:start position:0%
+struts as well. That was another
+ 
+
+ align:start position:0%
+struts as well. That was another
+possibility.
+
+ align:start position:0%
+possibility.
+ 
+
+ align:start position:0%
+possibility.
+And so uh we think that the cell
+
+ align:start position:0%
+And so uh we think that the cell
+ 
+
+ align:start position:0%
+And so uh we think that the cell
+elongation was related to the
+
+ align:start position:0%
+elongation was related to the
+ 
+
+ align:start position:0%
+elongation was related to the
+contraction. The time constants for the
+
+ align:start position:0%
+contraction. The time constants for the
+ 
+
+ align:start position:0%
+contraction. The time constants for the
+two things were almost the same. And as
+
+ align:start position:0%
+two things were almost the same. And as
+ 
+
+ align:start position:0%
+two things were almost the same. And as
+the cell elongates there's a gap between
+
+ align:start position:0%
+the cell elongates there's a gap between
+ 
+
+ align:start position:0%
+the cell elongates there's a gap between
+the um cell and the matrix on the
+
+ align:start position:0%
+the um cell and the matrix on the
+ 
+
+ align:start position:0%
+the um cell and the matrix on the
+central portion and the cell is adhered
+
+ align:start position:0%
+central portion and the cell is adhered
+ 
+
+ align:start position:0%
+central portion and the cell is adhered
+at the periphery at the adhesion points
+
+ align:start position:0%
+at the periphery at the adhesion points
+ 
+
+ align:start position:0%
+at the periphery at the adhesion points
+and then the tensel forces in these
+
+ align:start position:0%
+and then the tensel forces in these
+ 
+
+ align:start position:0%
+and then the tensel forces in these
+actin filaments inside the cell induce
+
+ align:start position:0%
+actin filaments inside the cell induce
+ 
+
+ align:start position:0%
+actin filaments inside the cell induce
+compression in the strut and that causes
+
+ align:start position:0%
+compression in the strut and that causes
+ 
+
+ align:start position:0%
+compression in the strut and that causes
+buckling
+
+ align:start position:0%
+buckling
+ 
+
+ align:start position:0%
+buckling
+and then Toby graduated and then I got
+
+ align:start position:0%
+and then Toby graduated and then I got
+ 
+
+ align:start position:0%
+and then Toby graduated and then I got
+another student Brendan and Brendan saw
+
+ align:start position:0%
+another student Brendan and Brendan saw
+ 
+
+ align:start position:0%
+another student Brendan and Brendan saw
+saw what Toby did and he wanted to do a
+
+ align:start position:0%
+saw what Toby did and he wanted to do a
+ 
+
+ align:start position:0%
+saw what Toby did and he wanted to do a
+little more with that. Uh Brendan was
+
+ align:start position:0%
+little more with that. Uh Brendan was
+ 
+
+ align:start position:0%
+little more with that. Uh Brendan was
+also involved with that osteocchondrial
+
+ align:start position:0%
+also involved with that osteocchondrial
+ 
+
+ align:start position:0%
+also involved with that osteocchondrial
+project that I talked about last time.
+
+ align:start position:0%
+project that I talked about last time.
+ 
+
+ align:start position:0%
+project that I talked about last time.
+Then Brendan did this other thing as
+
+ align:start position:0%
+Then Brendan did this other thing as
+ 
+
+ align:start position:0%
+Then Brendan did this other thing as
+well for his project. So he wanted to
+
+ align:start position:0%
+well for his project. So he wanted to
+ 
+
+ align:start position:0%
+well for his project. So he wanted to
+measure the force of an individual cell.
+
+ align:start position:0%
+measure the force of an individual cell.
+ 
+
+ align:start position:0%
+measure the force of an individual cell.
+So when we had that cell force monitor
+
+ align:start position:0%
+So when we had that cell force monitor
+ 
+
+ align:start position:0%
+So when we had that cell force monitor
+that was sort of the total force of all
+
+ align:start position:0%
+that was sort of the total force of all
+ 
+
+ align:start position:0%
+that was sort of the total force of all
+the cells in that one direction, but
+
+ align:start position:0%
+the cells in that one direction, but
+ 
+
+ align:start position:0%
+the cells in that one direction, but
+Brendan wanted to know if he could
+
+ align:start position:0%
+Brendan wanted to know if he could
+ 
+
+ align:start position:0%
+Brendan wanted to know if he could
+measure the force of a single cell. And
+
+ align:start position:0%
+measure the force of a single cell. And
+ 
+
+ align:start position:0%
+measure the force of a single cell. And
+now that we knew that the contractile
+
+ align:start position:0%
+now that we knew that the contractile
+ 
+
+ align:start position:0%
+now that we knew that the contractile
+process was related to buckling, we
+
+ align:start position:0%
+process was related to buckling, we
+ 
+
+ align:start position:0%
+process was related to buckling, we
+thought well we could just use Oilers's
+
+ align:start position:0%
+thought well we could just use Oilers's
+ 
+
+ align:start position:0%
+thought well we could just use Oilers's
+formula if we knew what the modulus of
+
+ align:start position:0%
+formula if we knew what the modulus of
+ 
+
+ align:start position:0%
+formula if we knew what the modulus of
+the solid was uh and we knew what the
+
+ align:start position:0%
+the solid was uh and we knew what the
+ 
+
+ align:start position:0%
+the solid was uh and we knew what the
+dimensions of the struts were. So that
+
+ align:start position:0%
+dimensions of the struts were. So that
+ 
+
+ align:start position:0%
+dimensions of the struts were. So that
+would allow us to calculate the
+
+ align:start position:0%
+would allow us to calculate the
+ 
+
+ align:start position:0%
+would allow us to calculate the
+contractile force of a single
+
+ align:start position:0%
+contractile force of a single
+ 
+
+ align:start position:0%
+contractile force of a single
+fiberblast.
+
+ align:start position:0%
+fiberblast.
+ 
+
+ align:start position:0%
+fiberblast.
+So I think I've shown you this thing
+
+ align:start position:0%
+So I think I've shown you this thing
+ 
+
+ align:start position:0%
+So I think I've shown you this thing
+here. So Brendan was the one who did
+
+ align:start position:0%
+here. So Brendan was the one who did
+ 
+
+ align:start position:0%
+here. So Brendan was the one who did
+these experiments. He um cut a single
+
+ align:start position:0%
+these experiments. He um cut a single
+ 
+
+ align:start position:0%
+these experiments. He um cut a single
+strut out of the scaffold and the single
+
+ align:start position:0%
+strut out of the scaffold and the single
+ 
+
+ align:start position:0%
+strut out of the scaffold and the single
+strut is about 100 microns long. He then
+
+ align:start position:0%
+strut is about 100 microns long. He then
+ 
+
+ align:start position:0%
+strut is about 100 microns long. He then
+you know he used a microscope to do
+
+ align:start position:0%
+you know he used a microscope to do
+ 
+
+ align:start position:0%
+you know he used a microscope to do
+this. He then glued it onto a glass
+
+ align:start position:0%
+this. He then glued it onto a glass
+ 
+
+ align:start position:0%
+this. He then glued it onto a glass
+slide and he used the atomic force
+
+ align:start position:0%
+slide and he used the atomic force
+ 
+
+ align:start position:0%
+slide and he used the atomic force
+microscope probe to bend the strut like
+
+ align:start position:0%
+microscope probe to bend the strut like
+ 
+
+ align:start position:0%
+microscope probe to bend the strut like
+a cantal lever beam and he measured the
+
+ align:start position:0%
+a cantal lever beam and he measured the
+ 
+
+ align:start position:0%
+a cantal lever beam and he measured the
+you know measured this displacement here
+
+ align:start position:0%
+you know measured this displacement here
+ 
+
+ align:start position:0%
+you know measured this displacement here
+and from that he could back out what the
+
+ align:start position:0%
+and from that he could back out what the
+ 
+
+ align:start position:0%
+and from that he could back out what the
+modulus of the solid was. Uh he did
+
+ align:start position:0%
+modulus of the solid was. Uh he did
+ 
+
+ align:start position:0%
+modulus of the solid was. Uh he did
+these tests in the dry state but we
+
+ align:start position:0%
+these tests in the dry state but we
+ 
+
+ align:start position:0%
+these tests in the dry state but we
+could extrapolate to the wet state from
+
+ align:start position:0%
+could extrapolate to the wet state from
+ 
+
+ align:start position:0%
+could extrapolate to the wet state from
+looking at the behavior of the whole
+
+ align:start position:0%
+looking at the behavior of the whole
+ 
+
+ align:start position:0%
+looking at the behavior of the whole
+scaffold. So we had a modulus for the um
+
+ align:start position:0%
+scaffold. So we had a modulus for the um
+ 
+
+ align:start position:0%
+scaffold. So we had a modulus for the um
+wet scaffold solid.
+
+ align:start position:0%
+wet scaffold solid.
+ 
+
+ align:start position:0%
+wet scaffold solid.
+And then uh this is our formula for
+
+ align:start position:0%
+And then uh this is our formula for
+ 
+
+ align:start position:0%
+And then uh this is our formula for
+oiler buckling here. So that's just the
+
+ align:start position:0%
+oiler buckling here. So that's just the
+ 
+
+ align:start position:0%
+oiler buckling here. So that's just the
+standard formula. Um I had had a a
+
+ align:start position:0%
+standard formula. Um I had had a a
+ 
+
+ align:start position:0%
+standard formula. Um I had had a a
+student from civil engineering who
+
+ align:start position:0%
+student from civil engineering who
+ 
+
+ align:start position:0%
+student from civil engineering who
+looked at hydrostatic loading of a
+
+ align:start position:0%
+looked at hydrostatic loading of a
+ 
+
+ align:start position:0%
+looked at hydrostatic loading of a
+tetraky decahaedral cell and he looked
+
+ align:start position:0%
+tetraky decahaedral cell and he looked
+ 
+
+ align:start position:0%
+tetraky decahaedral cell and he looked
+at buckling. If you had a sort of a
+
+ align:start position:0%
+at buckling. If you had a sort of a
+ 
+
+ align:start position:0%
+at buckling. If you had a sort of a
+tetraky decaedral cell and you loaded it
+
+ align:start position:0%
+tetraky decaedral cell and you loaded it
+ 
+
+ align:start position:0%
+tetraky decaedral cell and you loaded it
+in all three directions, he looked at
+
+ align:start position:0%
+in all three directions, he looked at
+ 
+
+ align:start position:0%
+in all three directions, he looked at
+the buckling and he had calculated that
+
+ align:start position:0%
+the buckling and he had calculated that
+ 
+
+ align:start position:0%
+the buckling and he had calculated that
+the end constraint factor, the n squared
+
+ align:start position:0%
+the end constraint factor, the n squared
+ 
+
+ align:start position:0%
+the end constraint factor, the n squared
+was 34. So we had some idea of what that
+
+ align:start position:0%
+was 34. So we had some idea of what that
+ 
+
+ align:start position:0%
+was 34. So we had some idea of what that
+n squared value should be, although it's
+
+ align:start position:0%
+n squared value should be, although it's
+ 
+
+ align:start position:0%
+n squared value should be, although it's
+somewhat of a an estimate. Um I had a
+
+ align:start position:0%
+somewhat of a an estimate. Um I had a
+ 
+
+ align:start position:0%
+somewhat of a an estimate. Um I had a
+Europe student who took Toby's images
+
+ align:start position:0%
+Europe student who took Toby's images
+ 
+
+ align:start position:0%
+Europe student who took Toby's images
+and measured the dimensions of the
+
+ align:start position:0%
+and measured the dimensions of the
+ 
+
+ align:start position:0%
+and measured the dimensions of the
+struts. So he measured the diameter and
+
+ align:start position:0%
+struts. So he measured the diameter and
+ 
+
+ align:start position:0%
+struts. So he measured the diameter and
+the thickness of the struts and from
+
+ align:start position:0%
+the thickness of the struts and from
+ 
+
+ align:start position:0%
+the thickness of the struts and from
+that we just plugged everything into the
+
+ align:start position:0%
+that we just plugged everything into the
+ 
+
+ align:start position:0%
+that we just plugged everything into the
+oiler formula and we found that the
+
+ align:start position:0%
+oiler formula and we found that the
+ 
+
+ align:start position:0%
+oiler formula and we found that the
+average single cell force is somewhere
+
+ align:start position:0%
+average single cell force is somewhere
+ 
+
+ align:start position:0%
+average single cell force is somewhere
+between about 11 and 41 nanons. So
+
+ align:start position:0%
+between about 11 and 41 nanons. So
+ 
+
+ align:start position:0%
+between about 11 and 41 nanons. So
+something like 26 nanons. So it would
+
+ align:start position:0%
+something like 26 nanons. So it would
+ 
+
+ align:start position:0%
+something like 26 nanons. So it would
+make sense that it's more than the one
+
+ align:start position:0%
+make sense that it's more than the one
+ 
+
+ align:start position:0%
+make sense that it's more than the one
+nan per cell because not all of those
+
+ align:start position:0%
+nan per cell because not all of those
+ 
+
+ align:start position:0%
+nan per cell because not all of those
+cells were active and they weren't all
+
+ align:start position:0%
+cells were active and they weren't all
+ 
+
+ align:start position:0%
+cells were active and they weren't all
+going in the same direction. So Brendan
+
+ align:start position:0%
+going in the same direction. So Brendan
+ 
+
+ align:start position:0%
+going in the same direction. So Brendan
+Harley and Matt Wong did that part of
+
+ align:start position:0%
+Harley and Matt Wong did that part of
+ 
+
+ align:start position:0%
+Harley and Matt Wong did that part of
+the project.
+
+ align:start position:0%
+the project.
+ 
+
+ align:start position:0%
+the project.
+Then um
+
+ align:start position:0%
+Then um
+ 
+
+ align:start position:0%
+Then um
+okay so that's the contraction. Are we
+
+ align:start position:0%
+okay so that's the contraction. Are we
+ 
+
+ align:start position:0%
+okay so that's the contraction. Are we
+good with contraction? So it's kind of
+
+ align:start position:0%
+good with contraction? So it's kind of
+ 
+
+ align:start position:0%
+good with contraction? So it's kind of
+interesting that the cells will contract
+
+ align:start position:0%
+interesting that the cells will contract
+ 
+
+ align:start position:0%
+interesting that the cells will contract
+and we can measure some forces.
+
+ align:start position:0%
+and we can measure some forces.
+ 
+
+ align:start position:0%
+and we can measure some forces.
+So the next type of interaction between
+
+ align:start position:0%
+So the next type of interaction between
+ 
+
+ align:start position:0%
+So the next type of interaction between
+the cells and the scaffolds that I
+
+ align:start position:0%
+the cells and the scaffolds that I
+ 
+
+ align:start position:0%
+the cells and the scaffolds that I
+wanted to talk about is cell migration.
+
+ align:start position:0%
+wanted to talk about is cell migration.
+ 
+
+ align:start position:0%
+wanted to talk about is cell migration.
+And these are some studies from the
+
+ align:start position:0%
+And these are some studies from the
+ 
+
+ align:start position:0%
+And these are some studies from the
+literature. So the these are two
+
+ align:start position:0%
+literature. So the these are two
+ 
+
+ align:start position:0%
+literature. So the these are two
+different studies but the the top one
+
+ align:start position:0%
+different studies but the the top one
+ 
+
+ align:start position:0%
+different studies but the the top one
+here they've measured migration rate as
+
+ align:start position:0%
+here they've measured migration rate as
+ 
+
+ align:start position:0%
+here they've measured migration rate as
+a function of the cross-linking
+
+ align:start position:0%
+a function of the cross-linking
+ 
+
+ align:start position:0%
+a function of the cross-linking
+treatment of a scaffold and uh de
+
+ align:start position:0%
+treatment of a scaffold and uh de
+ 
+
+ align:start position:0%
+treatment of a scaffold and uh de
+decreasing stiffness goes this way. And
+
+ align:start position:0%
+decreasing stiffness goes this way. And
+ 
+
+ align:start position:0%
+decreasing stiffness goes this way. And
+so they're seeing that the speed of
+
+ align:start position:0%
+so they're seeing that the speed of
+ 
+
+ align:start position:0%
+so they're seeing that the speed of
+migration this is in millimeters per
+
+ align:start position:0%
+migration this is in millimeters per
+ 
+
+ align:start position:0%
+migration this is in millimeters per
+day. The cells don't move too quickly.
+
+ align:start position:0%
+day. The cells don't move too quickly.
+ 
+
+ align:start position:0%
+day. The cells don't move too quickly.
+They go millimeters per day. Um but you
+
+ align:start position:0%
+They go millimeters per day. Um but you
+ 
+
+ align:start position:0%
+They go millimeters per day. Um but you
+can see that this the migration speed
+
+ align:start position:0%
+can see that this the migration speed
+ 
+
+ align:start position:0%
+can see that this the migration speed
+the speed at which the cells can move
+
+ align:start position:0%
+the speed at which the cells can move
+ 
+
+ align:start position:0%
+the speed at which the cells can move
+depends on the stiffness of the scaffold
+
+ align:start position:0%
+depends on the stiffness of the scaffold
+ 
+
+ align:start position:0%
+depends on the stiffness of the scaffold
+that they're attached to. And in this
+
+ align:start position:0%
+that they're attached to. And in this
+ 
+
+ align:start position:0%
+that they're attached to. And in this
+study on the bottom here, what they did
+
+ align:start position:0%
+study on the bottom here, what they did
+ 
+
+ align:start position:0%
+study on the bottom here, what they did
+was they had a just a flat 2D substrate,
+
+ align:start position:0%
+was they had a just a flat 2D substrate,
+ 
+
+ align:start position:0%
+was they had a just a flat 2D substrate,
+just a sort of flat polymer. And what
+
+ align:start position:0%
+just a sort of flat polymer. And what
+ 
+
+ align:start position:0%
+just a sort of flat polymer. And what
+they did was they cross-lin one part of
+
+ align:start position:0%
+they did was they cross-lin one part of
+ 
+
+ align:start position:0%
+they did was they cross-lin one part of
+the polymer more than the other part of
+
+ align:start position:0%
+the polymer more than the other part of
+ 
+
+ align:start position:0%
+the polymer more than the other part of
+the polymer. So over here, this was the
+
+ align:start position:0%
+the polymer. So over here, this was the
+ 
+
+ align:start position:0%
+the polymer. So over here, this was the
+the less crosslength, that was the soft
+
+ align:start position:0%
+the less crosslength, that was the soft
+ 
+
+ align:start position:0%
+the less crosslength, that was the soft
+part. And this was the more highly
+
+ align:start position:0%
+part. And this was the more highly
+ 
+
+ align:start position:0%
+part. And this was the more highly
+cross-length, this was the stiffer part.
+
+ align:start position:0%
+cross-length, this was the stiffer part.
+ 
+
+ align:start position:0%
+cross-length, this was the stiffer part.
+And they found if they put a cell on the
+
+ align:start position:0%
+And they found if they put a cell on the
+ 
+
+ align:start position:0%
+And they found if they put a cell on the
+soft part, it would migrate onto the
+
+ align:start position:0%
+soft part, it would migrate onto the
+ 
+
+ align:start position:0%
+soft part, it would migrate onto the
+stiff part. But if they put a cell on
+
+ align:start position:0%
+stiff part. But if they put a cell on
+ 
+
+ align:start position:0%
+stiff part. But if they put a cell on
+the stiff part, it would start going
+
+ align:start position:0%
+the stiff part, it would start going
+ 
+
+ align:start position:0%
+the stiff part, it would start going
+this way towards the soft part. But when
+
+ align:start position:0%
+this way towards the soft part. But when
+ 
+
+ align:start position:0%
+this way towards the soft part. But when
+it got to the interface, it would just
+
+ align:start position:0%
+it got to the interface, it would just
+ 
+
+ align:start position:0%
+it got to the interface, it would just
+spread out along the interface and it
+
+ align:start position:0%
+spread out along the interface and it
+ 
+
+ align:start position:0%
+spread out along the interface and it
+wouldn't go into the into the soft part.
+
+ align:start position:0%
+wouldn't go into the into the soft part.
+ 
+
+ align:start position:0%
+wouldn't go into the into the soft part.
+So the cells were somehow sensing the
+
+ align:start position:0%
+So the cells were somehow sensing the
+ 
+
+ align:start position:0%
+So the cells were somehow sensing the
+stiffness of the substrate. And for some
+
+ align:start position:0%
+stiffness of the substrate. And for some
+ 
+
+ align:start position:0%
+stiffness of the substrate. And for some
+reason, I don't know what, but for some
+
+ align:start position:0%
+reason, I don't know what, but for some
+ 
+
+ align:start position:0%
+reason, I don't know what, but for some
+reason, these particular cells seem to
+
+ align:start position:0%
+reason, these particular cells seem to
+ 
+
+ align:start position:0%
+reason, these particular cells seem to
+prefer being on the stiff substrate. So
+
+ align:start position:0%
+prefer being on the stiff substrate. So
+ 
+
+ align:start position:0%
+prefer being on the stiff substrate. So
+this is just really showing that there's
+
+ align:start position:0%
+this is just really showing that there's
+ 
+
+ align:start position:0%
+this is just really showing that there's
+some interaction between the substrate
+
+ align:start position:0%
+some interaction between the substrate
+ 
+
+ align:start position:0%
+some interaction between the substrate
+stiffness and the way the cells are
+
+ align:start position:0%
+stiffness and the way the cells are
+ 
+
+ align:start position:0%
+stiffness and the way the cells are
+behaving and migrating. And then um
+
+ align:start position:0%
+behaving and migrating. And then um
+ 
+
+ align:start position:0%
+behaving and migrating. And then um
+Brendan
+
+ align:start position:0%
+Brendan
+ 
+
+ align:start position:0%
+Brendan
+also wanted to study this and he got
+
+ align:start position:0%
+also wanted to study this and he got
+ 
+
+ align:start position:0%
+also wanted to study this and he got
+some of the collagen gag scaffold. He
+
+ align:start position:0%
+some of the collagen gag scaffold. He
+ 
+
+ align:start position:0%
+some of the collagen gag scaffold. He
+made some of the scaffold and he stained
+
+ align:start position:0%
+made some of the scaffold and he stained
+ 
+
+ align:start position:0%
+made some of the scaffold and he stained
+that with a a stain that made it turn
+
+ align:start position:0%
+that with a a stain that made it turn
+ 
+
+ align:start position:0%
+that with a a stain that made it turn
+red. So these lines here, all the red uh
+
+ align:start position:0%
+red. So these lines here, all the red uh
+ 
+
+ align:start position:0%
+red. So these lines here, all the red uh
+struts in the scaffold and then he put
+
+ align:start position:0%
+struts in the scaffold and then he put
+ 
+
+ align:start position:0%
+struts in the scaffold and then he put
+fiberblasts onto the scaffold and he
+
+ align:start position:0%
+fiberblasts onto the scaffold and he
+ 
+
+ align:start position:0%
+fiberblasts onto the scaffold and he
+stained them green. So all these little
+
+ align:start position:0%
+stained them green. So all these little
+ 
+
+ align:start position:0%
+stained them green. So all these little
+blobs here that are green are the cells.
+
+ align:start position:0%
+blobs here that are green are the cells.
+ 
+
+ align:start position:0%
+blobs here that are green are the cells.
+And then he used confocal microscopy.
+
+ align:start position:0%
+And then he used confocal microscopy.
+ 
+
+ align:start position:0%
+And then he used confocal microscopy.
+And the confocal microscopy allowed him
+
+ align:start position:0%
+And the confocal microscopy allowed him
+ 
+
+ align:start position:0%
+And the confocal microscopy allowed him
+to look at a certain volume of the
+
+ align:start position:0%
+to look at a certain volume of the
+ 
+
+ align:start position:0%
+to look at a certain volume of the
+scaffold. And he had some software that
+
+ align:start position:0%
+scaffold. And he had some software that
+ 
+
+ align:start position:0%
+scaffold. And he had some software that
+would track the centrid of each cell as
+
+ align:start position:0%
+would track the centrid of each cell as
+ 
+
+ align:start position:0%
+would track the centrid of each cell as
+it moved through the scaffold. And so he
+
+ align:start position:0%
+it moved through the scaffold. And so he
+ 
+
+ align:start position:0%
+it moved through the scaffold. And so he
+had a a thing he called spot tracking.
+
+ align:start position:0%
+had a a thing he called spot tracking.
+ 
+
+ align:start position:0%
+had a a thing he called spot tracking.
+So each of these little spheres here
+
+ align:start position:0%
+So each of these little spheres here
+ 
+
+ align:start position:0%
+So each of these little spheres here
+corresponds to a cell. And the white box
+
+ align:start position:0%
+corresponds to a cell. And the white box
+ 
+
+ align:start position:0%
+corresponds to a cell. And the white box
+is kind of the volume of material that
+
+ align:start position:0%
+is kind of the volume of material that
+ 
+
+ align:start position:0%
+is kind of the volume of material that
+you could see in the scaffold. And this
+
+ align:start position:0%
+you could see in the scaffold. And this
+ 
+
+ align:start position:0%
+you could see in the scaffold. And this
+color scale here really uh corresponds
+
+ align:start position:0%
+color scale here really uh corresponds
+ 
+
+ align:start position:0%
+color scale here really uh corresponds
+to time. So I've forgotten which RAM it
+
+ align:start position:0%
+to time. So I've forgotten which RAM it
+ 
+
+ align:start position:0%
+to time. So I've forgotten which RAM it
+is. I think blue is the original you
+
+ align:start position:0%
+is. I think blue is the original you
+ 
+
+ align:start position:0%
+is. I think blue is the original you
+know time zero and then you know red is
+
+ align:start position:0%
+know time zero and then you know red is
+ 
+
+ align:start position:0%
+know time zero and then you know red is
+maybe 5 seconds and yellow is 10
+
+ align:start position:0%
+maybe 5 seconds and yellow is 10
+ 
+
+ align:start position:0%
+maybe 5 seconds and yellow is 10
+seconds. The different colors correspond
+
+ align:start position:0%
+seconds. The different colors correspond
+ 
+
+ align:start position:0%
+seconds. The different colors correspond
+to different times. So he could track
+
+ align:start position:0%
+to different times. So he could track
+ 
+
+ align:start position:0%
+to different times. So he could track
+the path of each cell and also what the
+
+ align:start position:0%
+the path of each cell and also what the
+ 
+
+ align:start position:0%
+the path of each cell and also what the
+position was at different time points.
+
+ align:start position:0%
+position was at different time points.
+ 
+
+ align:start position:0%
+position was at different time points.
+So he knew what the position was at
+
+ align:start position:0%
+So he knew what the position was at
+ 
+
+ align:start position:0%
+So he knew what the position was at
+different time points and obviously from
+
+ align:start position:0%
+different time points and obviously from
+ 
+
+ align:start position:0%
+different time points and obviously from
+that he could get the uh speed of the
+
+ align:start position:0%
+that he could get the uh speed of the
+ 
+
+ align:start position:0%
+that he could get the uh speed of the
+scaffold. And he did these he did these
+
+ align:start position:0%
+scaffold. And he did these he did these
+ 
+
+ align:start position:0%
+scaffold. And he did these he did these
+experiments on scaffolds of different
+
+ align:start position:0%
+experiments on scaffolds of different
+ 
+
+ align:start position:0%
+experiments on scaffolds of different
+stiffnesses as well as different pore
+
+ align:start position:0%
+stiffnesses as well as different pore
+ 
+
+ align:start position:0%
+stiffnesses as well as different pore
+size. And here you can see the the cell
+
+ align:start position:0%
+size. And here you can see the the cell
+ 
+
+ align:start position:0%
+size. And here you can see the the cell
+speed. He's measuring it in microns per
+
+ align:start position:0%
+speed. He's measuring it in microns per
+ 
+
+ align:start position:0%
+speed. He's measuring it in microns per
+hour. Now the cell speed increases at
+
+ align:start position:0%
+hour. Now the cell speed increases at
+ 
+
+ align:start position:0%
+hour. Now the cell speed increases at
+first and then decreases um with the
+
+ align:start position:0%
+first and then decreases um with the
+ 
+
+ align:start position:0%
+first and then decreases um with the
+strut stiffness. So we don't know
+
+ align:start position:0%
+strut stiffness. So we don't know
+ 
+
+ align:start position:0%
+strut stiffness. So we don't know
+exactly why this is but there is is an
+
+ align:start position:0%
+exactly why this is but there is is an
+ 
+
+ align:start position:0%
+exactly why this is but there is is an
+effect between the stiffness of the
+
+ align:start position:0%
+effect between the stiffness of the
+ 
+
+ align:start position:0%
+effect between the stiffness of the
+scaffold and the migration speed. And
+
+ align:start position:0%
+scaffold and the migration speed. And
+ 
+
+ align:start position:0%
+scaffold and the migration speed. And
+another thing he did was he looked at
+
+ align:start position:0%
+another thing he did was he looked at
+ 
+
+ align:start position:0%
+another thing he did was he looked at
+how the cell speed varies with the pore
+
+ align:start position:0%
+how the cell speed varies with the pore
+ 
+
+ align:start position:0%
+how the cell speed varies with the pore
+size. And as the pore size um gets
+
+ align:start position:0%
+size. And as the pore size um gets
+ 
+
+ align:start position:0%
+size. And as the pore size um gets
+smaller, the speed goes up. And we're
+
+ align:start position:0%
+smaller, the speed goes up. And we're
+ 
+
+ align:start position:0%
+smaller, the speed goes up. And we're
+not entirely sure why that is, but I
+
+ align:start position:0%
+not entirely sure why that is, but I
+ 
+
+ align:start position:0%
+not entirely sure why that is, but I
+think that might be related to this
+
+ align:start position:0%
+think that might be related to this
+ 
+
+ align:start position:0%
+think that might be related to this
+binding site thing too. So as this as
+
+ align:start position:0%
+binding site thing too. So as this as
+ 
+
+ align:start position:0%
+binding site thing too. So as this as
+this as the pore size goes down, the
+
+ align:start position:0%
+this as the pore size goes down, the
+ 
+
+ align:start position:0%
+this as the pore size goes down, the
+number of binding sites is going to go
+
+ align:start position:0%
+number of binding sites is going to go
+ 
+
+ align:start position:0%
+number of binding sites is going to go
+up. And if you think of the cells
+
+ align:start position:0%
+up. And if you think of the cells
+ 
+
+ align:start position:0%
+up. And if you think of the cells
+migrating by having these adhesion sites
+
+ align:start position:0%
+migrating by having these adhesion sites
+ 
+
+ align:start position:0%
+migrating by having these adhesion sites
+and the adhesion sites are just at the
+
+ align:start position:0%
+and the adhesion sites are just at the
+ 
+
+ align:start position:0%
+and the adhesion sites are just at the
+ends of the cells and you know the cells
+
+ align:start position:0%
+ends of the cells and you know the cells
+ 
+
+ align:start position:0%
+ends of the cells and you know the cells
+kind of putting out a a little um
+
+ align:start position:0%
+kind of putting out a a little um
+ 
+
+ align:start position:0%
+kind of putting out a a little um
+extension and then looking for somewhere
+
+ align:start position:0%
+extension and then looking for somewhere
+ 
+
+ align:start position:0%
+extension and then looking for somewhere
+else it can bind. The more binding sites
+
+ align:start position:0%
+else it can bind. The more binding sites
+ 
+
+ align:start position:0%
+else it can bind. The more binding sites
+there are the faster it's going to find
+
+ align:start position:0%
+there are the faster it's going to find
+ 
+
+ align:start position:0%
+there are the faster it's going to find
+a binding site and the faster I think
+
+ align:start position:0%
+a binding site and the faster I think
+ 
+
+ align:start position:0%
+a binding site and the faster I think
+it's going to move on. So I think that
+
+ align:start position:0%
+it's going to move on. So I think that
+ 
+
+ align:start position:0%
+it's going to move on. So I think that
+the cell speed depends on pore size at
+
+ align:start position:0%
+the cell speed depends on pore size at
+ 
+
+ align:start position:0%
+the cell speed depends on pore size at
+least in part because of the increase in
+
+ align:start position:0%
+least in part because of the increase in
+ 
+
+ align:start position:0%
+least in part because of the increase in
+the binding sites with smaller um pore
+
+ align:start position:0%
+the binding sites with smaller um pore
+ 
+
+ align:start position:0%
+the binding sites with smaller um pore
+sizes. So that's the pore size and the
+
+ align:start position:0%
+sizes. So that's the pore size and the
+ 
+
+ align:start position:0%
+sizes. So that's the pore size and the
+migration.
+
+ align:start position:0%
+migration.
+ 
+
+ align:start position:0%
+migration.
+And then the last thing I wanted to talk
+
+ align:start position:0%
+And then the last thing I wanted to talk
+ 
+
+ align:start position:0%
+And then the last thing I wanted to talk
+about was cell differentiation. And this
+
+ align:start position:0%
+about was cell differentiation. And this
+ 
+
+ align:start position:0%
+about was cell differentiation. And this
+is a stud study by Angler. And one of
+
+ align:start position:0%
+is a stud study by Angler. And one of
+ 
+
+ align:start position:0%
+is a stud study by Angler. And one of
+the things he found was he put memal
+
+ align:start position:0%
+the things he found was he put memal
+ 
+
+ align:start position:0%
+the things he found was he put memal
+stem cells on 2D substrates just flat 2D
+
+ align:start position:0%
+stem cells on 2D substrates just flat 2D
+ 
+
+ align:start position:0%
+stem cells on 2D substrates just flat 2D
+substrates of different stiffnesses. And
+
+ align:start position:0%
+substrates of different stiffnesses. And
+ 
+
+ align:start position:0%
+substrates of different stiffnesses. And
+again he could control the stiffness by
+
+ align:start position:0%
+again he could control the stiffness by
+ 
+
+ align:start position:0%
+again he could control the stiffness by
+cross-linking. And what he's showing up
+
+ align:start position:0%
+cross-linking. And what he's showing up
+ 
+
+ align:start position:0%
+cross-linking. And what he's showing up
+here in the first bit is that uh he's
+
+ align:start position:0%
+here in the first bit is that uh he's
+ 
+
+ align:start position:0%
+here in the first bit is that uh he's
+looking at sort of the stiffness of
+
+ align:start position:0%
+looking at sort of the stiffness of
+ 
+
+ align:start position:0%
+looking at sort of the stiffness of
+tissues of different kinds. So here's
+
+ align:start position:0%
+tissues of different kinds. So here's
+ 
+
+ align:start position:0%
+tissues of different kinds. So here's
+brain type tissue uh something like 1
+
+ align:start position:0%
+brain type tissue uh something like 1
+ 
+
+ align:start position:0%
+brain type tissue uh something like 1
+kilopascal. Muscle might be something
+
+ align:start position:0%
+kilopascal. Muscle might be something
+ 
+
+ align:start position:0%
+kilopascal. Muscle might be something
+like 10 kilopascal and collaginous bone.
+
+ align:start position:0%
+like 10 kilopascal and collaginous bone.
+ 
+
+ align:start position:0%
+like 10 kilopascal and collaginous bone.
+This is sort of the osteoid that is the
+
+ align:start position:0%
+This is sort of the osteoid that is the
+ 
+
+ align:start position:0%
+This is sort of the osteoid that is the
+precursor of bone not the bone itself is
+
+ align:start position:0%
+precursor of bone not the bone itself is
+ 
+
+ align:start position:0%
+precursor of bone not the bone itself is
+about 100 kilopascals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And what he did was he put these
+
+ align:start position:0%
+And what he did was he put these
+ 
+
+ align:start position:0%
+And what he did was he put these
+messenymal stem cells. So here's his
+
+ align:start position:0%
+messenymal stem cells. So here's his
+ 
+
+ align:start position:0%
+messenymal stem cells. So here's his
+cell onto his substrate and he varied
+
+ align:start position:0%
+cell onto his substrate and he varied
+ 
+
+ align:start position:0%
+cell onto his substrate and he varied
+the stiffness of the substrate and then
+
+ align:start position:0%
+the stiffness of the substrate and then
+ 
+
+ align:start position:0%
+the stiffness of the substrate and then
+he looked at the shape of the cells. So
+
+ align:start position:0%
+he looked at the shape of the cells. So
+ 
+
+ align:start position:0%
+he looked at the shape of the cells. So
+here's the the least stiff substrate. So
+
+ align:start position:0%
+here's the the least stiff substrate. So
+ 
+
+ align:start position:0%
+here's the the least stiff substrate. So
+between 0.1 and 1 kilopascals and here's
+
+ align:start position:0%
+between 0.1 and 1 kilopascals and here's
+ 
+
+ align:start position:0%
+between 0.1 and 1 kilopascals and here's
+4 hours, 24 hours, 96 hours. And these
+
+ align:start position:0%
+4 hours, 24 hours, 96 hours. And these
+ 
+
+ align:start position:0%
+4 hours, 24 hours, 96 hours. And these
+cells formed uh sort of long uh
+
+ align:start position:0%
+cells formed uh sort of long uh
+ 
+
+ align:start position:0%
+cells formed uh sort of long uh
+processes extending beyond the cell body
+
+ align:start position:0%
+processes extending beyond the cell body
+ 
+
+ align:start position:0%
+processes extending beyond the cell body
+and they looked kind of like neurons. So
+
+ align:start position:0%
+and they looked kind of like neurons. So
+ 
+
+ align:start position:0%
+and they looked kind of like neurons. So
+they he called those neuronlike. Then
+
+ align:start position:0%
+they he called those neuronlike. Then
+ 
+
+ align:start position:0%
+they he called those neuronlike. Then
+there's an intermediate stiffness of
+
+ align:start position:0%
+there's an intermediate stiffness of
+ 
+
+ align:start position:0%
+there's an intermediate stiffness of
+substrate here. And these cells um
+
+ align:start position:0%
+substrate here. And these cells um
+ 
+
+ align:start position:0%
+substrate here. And these cells um
+became even more elongated and became
+
+ align:start position:0%
+became even more elongated and became
+ 
+
+ align:start position:0%
+became even more elongated and became
+something like a muscle cell myoblast
+
+ align:start position:0%
+something like a muscle cell myoblast
+ 
+
+ align:start position:0%
+something like a muscle cell myoblast
+like. And then cells that were put onto
+
+ align:start position:0%
+like. And then cells that were put onto
+ 
+
+ align:start position:0%
+like. And then cells that were put onto
+a scaff or onto a substrate that was
+
+ align:start position:0%
+a scaff or onto a substrate that was
+ 
+
+ align:start position:0%
+a scaff or onto a substrate that was
+between about 25 and 40 kilopascals,
+
+ align:start position:0%
+between about 25 and 40 kilopascals,
+ 
+
+ align:start position:0%
+between about 25 and 40 kilopascals,
+they developed a shape that was
+
+ align:start position:0%
+they developed a shape that was
+ 
+
+ align:start position:0%
+they developed a shape that was
+something like an osteoblast, like a
+
+ align:start position:0%
+something like an osteoblast, like a
+ 
+
+ align:start position:0%
+something like an osteoblast, like a
+bone cell.
+
+ align:start position:0%
+bone cell.
+ 
+
+ align:start position:0%
+bone cell.
+So, one of the things he was looking at
+
+ align:start position:0%
+So, one of the things he was looking at
+ 
+
+ align:start position:0%
+So, one of the things he was looking at
+here was how the stiffness of the
+
+ align:start position:0%
+here was how the stiffness of the
+ 
+
+ align:start position:0%
+here was how the stiffness of the
+substrate affected how a stem cell might
+
+ align:start position:0%
+substrate affected how a stem cell might
+ 
+
+ align:start position:0%
+substrate affected how a stem cell might
+differentiate into different cell types.
+
+ align:start position:0%
+differentiate into different cell types.
+ 
+
+ align:start position:0%
+differentiate into different cell types.
+And another thing, oops, I keep
+
+ align:start position:0%
+And another thing, oops, I keep
+ 
+
+ align:start position:0%
+And another thing, oops, I keep
+forgetting my button doesn't work.
+
+ align:start position:0%
+forgetting my button doesn't work.
+ 
+
+ align:start position:0%
+forgetting my button doesn't work.
+Another thing that he did was he looked
+
+ align:start position:0%
+Another thing that he did was he looked
+ 
+
+ align:start position:0%
+Another thing that he did was he looked
+at different cell markers and he found
+
+ align:start position:0%
+at different cell markers and he found
+ 
+
+ align:start position:0%
+at different cell markers and he found
+that the cells were expressing um
+
+ align:start position:0%
+that the cells were expressing um
+ 
+
+ align:start position:0%
+that the cells were expressing um
+markers uh that were
+
+ align:start position:0%
+markers uh that were
+ 
+
+ align:start position:0%
+markers uh that were
+sort of corresponding to the types of
+
+ align:start position:0%
+sort of corresponding to the types of
+ 
+
+ align:start position:0%
+sort of corresponding to the types of
+tissue. So I don't I I couldn't tell you
+
+ align:start position:0%
+tissue. So I don't I I couldn't tell you
+ 
+
+ align:start position:0%
+tissue. So I don't I I couldn't tell you
+the names of all these things and what
+
+ align:start position:0%
+the names of all these things and what
+ 
+
+ align:start position:0%
+the names of all these things and what
+they are, but I think uh the red here is
+
+ align:start position:0%
+they are, but I think uh the red here is
+ 
+
+ align:start position:0%
+they are, but I think uh the red here is
+expressing more of a particular marker.
+
+ align:start position:0%
+expressing more of a particular marker.
+ 
+
+ align:start position:0%
+expressing more of a particular marker.
+And I think these ones were related to
+
+ align:start position:0%
+And I think these ones were related to
+ 
+
+ align:start position:0%
+And I think these ones were related to
+nerve tissue. These ones here were
+
+ align:start position:0%
+nerve tissue. These ones here were
+ 
+
+ align:start position:0%
+nerve tissue. These ones here were
+related more to muscle tissue. And these
+
+ align:start position:0%
+related more to muscle tissue. And these
+ 
+
+ align:start position:0%
+related more to muscle tissue. And these
+ones here were related more to bone
+
+ align:start position:0%
+ones here were related more to bone
+ 
+
+ align:start position:0%
+ones here were related more to bone
+tissue. So the things the cells were
+
+ align:start position:0%
+tissue. So the things the cells were
+ 
+
+ align:start position:0%
+tissue. So the things the cells were
+expressing also seem to correspond to
+
+ align:start position:0%
+expressing also seem to correspond to
+ 
+
+ align:start position:0%
+expressing also seem to correspond to
+the different types of tissue uh that
+
+ align:start position:0%
+the different types of tissue uh that
+ 
+
+ align:start position:0%
+the different types of tissue uh that
+they were kind of corresponding to.
+
+ align:start position:0%
+they were kind of corresponding to.
+ 
+
+ align:start position:0%
+they were kind of corresponding to.
+So I'm just going to end this part by
+
+ align:start position:0%
+So I'm just going to end this part by
+ 
+
+ align:start position:0%
+So I'm just going to end this part by
+going through a little summary here. So
+
+ align:start position:0%
+going through a little summary here. So
+ 
+
+ align:start position:0%
+going through a little summary here. So
+what I've tried to show you today is
+
+ align:start position:0%
+what I've tried to show you today is
+ 
+
+ align:start position:0%
+what I've tried to show you today is
+different um types of cell behavior that
+
+ align:start position:0%
+different um types of cell behavior that
+ 
+
+ align:start position:0%
+different um types of cell behavior that
+are affected by the scaffold and they're
+
+ align:start position:0%
+are affected by the scaffold and they're
+ 
+
+ align:start position:0%
+are affected by the scaffold and they're
+affected by things like the number of
+
+ align:start position:0%
+affected by things like the number of
+ 
+
+ align:start position:0%
+affected by things like the number of
+binding sites by the pore size by the
+
+ align:start position:0%
+binding sites by the pore size by the
+ 
+
+ align:start position:0%
+binding sites by the pore size by the
+stiffness of the scaffold. So we started
+
+ align:start position:0%
+stiffness of the scaffold. So we started
+ 
+
+ align:start position:0%
+stiffness of the scaffold. So we started
+with the cell attachment. We saw that
+
+ align:start position:0%
+with the cell attachment. We saw that
+ 
+
+ align:start position:0%
+with the cell attachment. We saw that
+the cell attachment increases linearly
+
+ align:start position:0%
+the cell attachment increases linearly
+ 
+
+ align:start position:0%
+the cell attachment increases linearly
+with a specific surface area. We saw
+
+ align:start position:0%
+with a specific surface area. We saw
+ 
+
+ align:start position:0%
+with a specific surface area. We saw
+that the cell morphology depends on the
+
+ align:start position:0%
+that the cell morphology depends on the
+ 
+
+ align:start position:0%
+that the cell morphology depends on the
+orientation of the pores and that kind
+
+ align:start position:0%
+orientation of the pores and that kind
+ 
+
+ align:start position:0%
+orientation of the pores and that kind
+of makes sense. They're going to line up
+
+ align:start position:0%
+of makes sense. They're going to line up
+ 
+
+ align:start position:0%
+of makes sense. They're going to line up
+with the pores. We talked about the
+
+ align:start position:0%
+with the pores. We talked about the
+ 
+
+ align:start position:0%
+with the pores. We talked about the
+contraction behavior. So the cells bind
+
+ align:start position:0%
+contraction behavior. So the cells bind
+ 
+
+ align:start position:0%
+contraction behavior. So the cells bind
+at the periphery, the cells elongate and
+
+ align:start position:0%
+at the periphery, the cells elongate and
+ 
+
+ align:start position:0%
+at the periphery, the cells elongate and
+that causes this buckling and you can
+
+ align:start position:0%
+that causes this buckling and you can
+ 
+
+ align:start position:0%
+that causes this buckling and you can
+calculate the buckling forces. It's
+
+ align:start position:0%
+calculate the buckling forces. It's
+ 
+
+ align:start position:0%
+calculate the buckling forces. It's
+around uh 10 to 40 nanons.
+
+ align:start position:0%
+around uh 10 to 40 nanons.
+ 
+
+ align:start position:0%
+around uh 10 to 40 nanons.
+We looked at the cell migration speed
+
+ align:start position:0%
+We looked at the cell migration speed
+ 
+
+ align:start position:0%
+We looked at the cell migration speed
+that increases with the stiffness of 1D
+
+ align:start position:0%
+that increases with the stiffness of 1D
+ 
+
+ align:start position:0%
+that increases with the stiffness of 1D
+fibers. And uh we looked at cell
+
+ align:start position:0%
+fibers. And uh we looked at cell
+ 
+
+ align:start position:0%
+fibers. And uh we looked at cell
+migration in the collagen gag scaffolds.
+
+ align:start position:0%
+migration in the collagen gag scaffolds.
+ 
+
+ align:start position:0%
+migration in the collagen gag scaffolds.
+So that depends on the stiffness and the
+
+ align:start position:0%
+So that depends on the stiffness and the
+ 
+
+ align:start position:0%
+So that depends on the stiffness and the
+pore size. And then there was this final
+
+ align:start position:0%
+pore size. And then there was this final
+ 
+
+ align:start position:0%
+pore size. And then there was this final
+study on the cell differentiation.
+
+ align:start position:0%
+study on the cell differentiation.
+ 
+
+ align:start position:0%
+study on the cell differentiation.
+So I wasn't going to write any notes on
+
+ align:start position:0%
+So I wasn't going to write any notes on
+ 
+
+ align:start position:0%
+So I wasn't going to write any notes on
+this because the slides I think pretty
+
+ align:start position:0%
+this because the slides I think pretty
+ 
+
+ align:start position:0%
+this because the slides I think pretty
+much explain it. So I was just going to
+
+ align:start position:0%
+much explain it. So I was just going to
+ 
+
+ align:start position:0%
+much explain it. So I was just going to
+put the slides on the website at the end
+
+ align:start position:0%
+put the slides on the website at the end
+ 
+
+ align:start position:0%
+put the slides on the website at the end
+after today's lecture. So are we good
+
+ align:start position:0%
+after today's lecture. So are we good
+ 
+
+ align:start position:0%
+after today's lecture. So are we good
+with how cells and the scaffolds or this
+
+ align:start position:0%
+with how cells and the scaffolds or this
+ 
+
+ align:start position:0%
+with how cells and the scaffolds or this
+the environments kind of interact?
+
+ align:start position:0%
+the environments kind of interact?
+ 
+
+ align:start position:0%
+the environments kind of interact?
+because I think it's not so obvious that
+
+ align:start position:0%
+because I think it's not so obvious that
+ 
+
+ align:start position:0%
+because I think it's not so obvious that
+the sort of actual mechanical
+
+ align:start position:0%
+the sort of actual mechanical
+ 
+
+ align:start position:0%
+the sort of actual mechanical
+environment makes a sense makes a
+
+ align:start position:0%
+environment makes a sense makes a
+ 
+
+ align:start position:0%
+environment makes a sense makes a
+difference. Like people think of you
+
+ align:start position:0%
+difference. Like people think of you
+ 
+
+ align:start position:0%
+difference. Like people think of you
+know um sort of the chemical the
+
+ align:start position:0%
+know um sort of the chemical the
+ 
+
+ align:start position:0%
+know um sort of the chemical the
+biochemical environment that obviously
+
+ align:start position:0%
+biochemical environment that obviously
+ 
+
+ align:start position:0%
+biochemical environment that obviously
+affects the cells but people don't think
+
+ align:start position:0%
+affects the cells but people don't think
+ 
+
+ align:start position:0%
+affects the cells but people don't think
+at first that something like the um the
+
+ align:start position:0%
+at first that something like the um the
+ 
+
+ align:start position:0%
+at first that something like the um the
+sort of structure of the pores the pore
+
+ align:start position:0%
+sort of structure of the pores the pore
+ 
+
+ align:start position:0%
+sort of structure of the pores the pore
+size or the orientation of the pores or
+
+ align:start position:0%
+size or the orientation of the pores or
+ 
+
+ align:start position:0%
+size or the orientation of the pores or
+the mechanical properties are going to
+
+ align:start position:0%
+the mechanical properties are going to
+ 
+
+ align:start position:0%
+the mechanical properties are going to
+affect how the cells behave but in fact
+
+ align:start position:0%
+affect how the cells behave but in fact
+ 
+
+ align:start position:0%
+affect how the cells behave but in fact
+they do. So that's it. Oh and this is
+
+ align:start position:0%
+they do. So that's it. Oh and this is
+ 
+
+ align:start position:0%
+they do. So that's it. Oh and this is
+all various people who worked with me on
+
+ align:start position:0%
+all various people who worked with me on
+ 
+
+ align:start position:0%
+all various people who worked with me on
+these projects. That was a lot of fun.
+
+ align:start position:0%
+these projects. That was a lot of fun.
+ 
+
+ align:start position:0%
+these projects. That was a lot of fun.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+hang on a sec here. What's this all
+
+ align:start position:0%
+hang on a sec here. What's this all
+ 
+
+ align:start position:0%
+hang on a sec here. What's this all
+about? Can I get rid of that? Go away.
+
+ align:start position:0%
+about? Can I get rid of that? Go away.
+ 
+
+ align:start position:0%
+about? Can I get rid of that? Go away.
+There we go. Okay, so are we good with
+
+ align:start position:0%
+There we go. Okay, so are we good with
+ 
+
+ align:start position:0%
+There we go. Okay, so are we good with
+cells and um substrates?
+
+ align:start position:0%
+cells and um substrates?
+ 
+
+ align:start position:0%
+cells and um substrates?
+Yeah. Okay.
+
+ align:start position:0%
+Yeah. Okay.
+ 
+
+ align:start position:0%
+Yeah. Okay.
+So, let me let's just take a little
+
+ align:start position:0%
+So, let me let's just take a little
+ 
+
+ align:start position:0%
+So, let me let's just take a little
+moment and I'll rub the board off and
+
+ align:start position:0%
+moment and I'll rub the board off and
+ 
+
+ align:start position:0%
+moment and I'll rub the board off and
+then we can start the next bit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's the end of the sort of
+
+ align:start position:0%
+Okay, so that's the end of the sort of
+ 
+
+ align:start position:0%
+Okay, so that's the end of the sort of
+medical material stuff. So we talked
+
+ align:start position:0%
+medical material stuff. So we talked
+ 
+
+ align:start position:0%
+medical material stuff. So we talked
+about the bone, we talked about the
+
+ align:start position:0%
+about the bone, we talked about the
+ 
+
+ align:start position:0%
+about the bone, we talked about the
+tissue engineering scaffolds, and then
+
+ align:start position:0%
+tissue engineering scaffolds, and then
+ 
+
+ align:start position:0%
+tissue engineering scaffolds, and then
+we talked about the cell scaffold
+
+ align:start position:0%
+we talked about the cell scaffold
+ 
+
+ align:start position:0%
+we talked about the cell scaffold
+interactions. So now we're going to go
+
+ align:start position:0%
+interactions. So now we're going to go
+ 
+
+ align:start position:0%
+interactions. So now we're going to go
+back to more engineering topics.
+
+ align:start position:0%
+back to more engineering topics.
+ 
+
+ align:start position:0%
+back to more engineering topics.
+And the next thing I wanted to talk
+
+ align:start position:0%
+And the next thing I wanted to talk
+ 
+
+ align:start position:0%
+And the next thing I wanted to talk
+about was energy absorption in foams. So
+
+ align:start position:0%
+about was energy absorption in foams. So
+ 
+
+ align:start position:0%
+about was energy absorption in foams. So
+foams are very widely used for energy
+
+ align:start position:0%
+foams are very widely used for energy
+ 
+
+ align:start position:0%
+foams are very widely used for energy
+absorption applications. Things like
+
+ align:start position:0%
+absorption applications. Things like
+ 
+
+ align:start position:0%
+absorption applications. Things like
+bicycle helmets, different kinds of
+
+ align:start position:0%
+bicycle helmets, different kinds of
+ 
+
+ align:start position:0%
+bicycle helmets, different kinds of
+helmets. You buy a new computer, it
+
+ align:start position:0%
+helmets. You buy a new computer, it
+ 
+
+ align:start position:0%
+helmets. You buy a new computer, it
+comes in foam packaging. And the reason
+
+ align:start position:0%
+comes in foam packaging. And the reason
+ 
+
+ align:start position:0%
+comes in foam packaging. And the reason
+foams are used so much is they're
+
+ align:start position:0%
+foams are used so much is they're
+ 
+
+ align:start position:0%
+foams are used so much is they're
+extremely good at absorbing energy from
+
+ align:start position:0%
+extremely good at absorbing energy from
+ 
+
+ align:start position:0%
+extremely good at absorbing energy from
+impacts. And in fact, they're better
+
+ align:start position:0%
+impacts. And in fact, they're better
+ 
+
+ align:start position:0%
+impacts. And in fact, they're better
+than the solid that they're made from.
+
+ align:start position:0%
+than the solid that they're made from.
+ 
+
+ align:start position:0%
+than the solid that they're made from.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+let's just look at this curve here for a
+
+ align:start position:0%
+let's just look at this curve here for a
+ 
+
+ align:start position:0%
+let's just look at this curve here for a
+minute. So, here's a stress strain curve
+
+ align:start position:0%
+minute. So, here's a stress strain curve
+ 
+
+ align:start position:0%
+minute. So, here's a stress strain curve
+in compression for the foam. And the the
+
+ align:start position:0%
+in compression for the foam. And the the
+ 
+
+ align:start position:0%
+in compression for the foam. And the the
+material that it's made from would have
+
+ align:start position:0%
+material that it's made from would have
+ 
+
+ align:start position:0%
+material that it's made from would have
+a a stiffness something like this,
+
+ align:start position:0%
+a a stiffness something like this,
+ 
+
+ align:start position:0%
+a a stiffness something like this,
+right? It'd be much much stiffer than
+
+ align:start position:0%
+right? It'd be much much stiffer than
+ 
+
+ align:start position:0%
+right? It'd be much much stiffer than
+the foam. And if you think about how
+
+ align:start position:0%
+the foam. And if you think about how
+ 
+
+ align:start position:0%
+the foam. And if you think about how
+much energy you can absorb, the energy
+
+ align:start position:0%
+much energy you can absorb, the energy
+ 
+
+ align:start position:0%
+much energy you can absorb, the energy
+you can absorb is just the area under
+
+ align:start position:0%
+you can absorb is just the area under
+ 
+
+ align:start position:0%
+you can absorb is just the area under
+the stress strain curve. That's the
+
+ align:start position:0%
+the stress strain curve. That's the
+ 
+
+ align:start position:0%
+the stress strain curve. That's the
+energy you can absorb in a given volume
+
+ align:start position:0%
+energy you can absorb in a given volume
+ 
+
+ align:start position:0%
+energy you can absorb in a given volume
+of foam. And so
+
+ align:start position:0%
+of foam. And so
+ 
+
+ align:start position:0%
+of foam. And so
+when you're thinking about these energy
+
+ align:start position:0%
+when you're thinking about these energy
+ 
+
+ align:start position:0%
+when you're thinking about these energy
+absorption problems, it's not just that
+
+ align:start position:0%
+absorption problems, it's not just that
+ 
+
+ align:start position:0%
+absorption problems, it's not just that
+you need to absorb a certain energy, you
+
+ align:start position:0%
+you need to absorb a certain energy, you
+ 
+
+ align:start position:0%
+you need to absorb a certain energy, you
+need to absorb it without exceeding a
+
+ align:start position:0%
+need to absorb it without exceeding a
+ 
+
+ align:start position:0%
+need to absorb it without exceeding a
+certain peak stress. So whatever it is
+
+ align:start position:0%
+certain peak stress. So whatever it is
+ 
+
+ align:start position:0%
+certain peak stress. So whatever it is
+you're trying to protect, at some point
+
+ align:start position:0%
+you're trying to protect, at some point
+ 
+
+ align:start position:0%
+you're trying to protect, at some point
+it's going to break, right? You and this
+
+ align:start position:0%
+it's going to break, right? You and this
+ 
+
+ align:start position:0%
+it's going to break, right? You and this
+is what you want to avoid. You want to
+
+ align:start position:0%
+is what you want to avoid. You want to
+ 
+
+ align:start position:0%
+is what you want to avoid. You want to
+avoid it breaking. So you don't want to
+
+ align:start position:0%
+avoid it breaking. So you don't want to
+ 
+
+ align:start position:0%
+avoid it breaking. So you don't want to
+have a stress bigger than the stress
+
+ align:start position:0%
+have a stress bigger than the stress
+ 
+
+ align:start position:0%
+have a stress bigger than the stress
+that's going to break whatever it is,
+
+ align:start position:0%
+that's going to break whatever it is,
+ 
+
+ align:start position:0%
+that's going to break whatever it is,
+your computer or your head or whatever.
+
+ align:start position:0%
+your computer or your head or whatever.
+ 
+
+ align:start position:0%
+your computer or your head or whatever.
+So say you have a given uh peak stress
+
+ align:start position:0%
+So say you have a given uh peak stress
+ 
+
+ align:start position:0%
+So say you have a given uh peak stress
+that you can tolerate here. And we've
+
+ align:start position:0%
+that you can tolerate here. And we've
+ 
+
+ align:start position:0%
+that you can tolerate here. And we've
+normalized things by the solid modulus,
+
+ align:start position:0%
+normalized things by the solid modulus,
+ 
+
+ align:start position:0%
+normalized things by the solid modulus,
+but just say that's a peak stress here.
+
+ align:start position:0%
+but just say that's a peak stress here.
+ 
+
+ align:start position:0%
+but just say that's a peak stress here.
+The foam is going to absorb this amount
+
+ align:start position:0%
+The foam is going to absorb this amount
+ 
+
+ align:start position:0%
+The foam is going to absorb this amount
+of energy up here, this whole little
+
+ align:start position:0%
+of energy up here, this whole little
+ 
+
+ align:start position:0%
+of energy up here, this whole little
+shaded region. And the solid is going to
+
+ align:start position:0%
+shaded region. And the solid is going to
+ 
+
+ align:start position:0%
+shaded region. And the solid is going to
+absorb that little teeny weeny bit in
+
+ align:start position:0%
+absorb that little teeny weeny bit in
+ 
+
+ align:start position:0%
+absorb that little teeny weeny bit in
+there. So, what you want to do is absorb
+
+ align:start position:0%
+there. So, what you want to do is absorb
+ 
+
+ align:start position:0%
+there. So, what you want to do is absorb
+the energy without exceeding a certain
+
+ align:start position:0%
+the energy without exceeding a certain
+ 
+
+ align:start position:0%
+the energy without exceeding a certain
+peak stress. And the foam is always
+
+ align:start position:0%
+peak stress. And the foam is always
+ 
+
+ align:start position:0%
+peak stress. And the foam is always
+going to be better than the solid that
+
+ align:start position:0%
+going to be better than the solid that
+ 
+
+ align:start position:0%
+going to be better than the solid that
+it's um made from. There's a couple
+
+ align:start position:0%
+it's um made from. There's a couple
+ 
+
+ align:start position:0%
+it's um made from. There's a couple
+other things that make the foams good
+
+ align:start position:0%
+other things that make the foams good
+ 
+
+ align:start position:0%
+other things that make the foams good
+because they're more or less isotropic.
+
+ align:start position:0%
+because they're more or less isotropic.
+ 
+
+ align:start position:0%
+because they're more or less isotropic.
+Maybe not perfectly, but roughly they
+
+ align:start position:0%
+Maybe not perfectly, but roughly they
+ 
+
+ align:start position:0%
+Maybe not perfectly, but roughly they
+have the same properties in all
+
+ align:start position:0%
+have the same properties in all
+ 
+
+ align:start position:0%
+have the same properties in all
+directions. Sometimes you don't know
+
+ align:start position:0%
+directions. Sometimes you don't know
+ 
+
+ align:start position:0%
+directions. Sometimes you don't know
+what direction the impact's going to
+
+ align:start position:0%
+what direction the impact's going to
+ 
+
+ align:start position:0%
+what direction the impact's going to
+come from. And so if you got the same
+
+ align:start position:0%
+come from. And so if you got the same
+ 
+
+ align:start position:0%
+come from. And so if you got the same
+properties in all directions are roughly
+
+ align:start position:0%
+properties in all directions are roughly
+ 
+
+ align:start position:0%
+properties in all directions are roughly
+the same, that's a good thing. Uh you
+
+ align:start position:0%
+the same, that's a good thing. Uh you
+ 
+
+ align:start position:0%
+the same, that's a good thing. Uh you
+also want the pro the protective thing
+
+ align:start position:0%
+also want the pro the protective thing
+ 
+
+ align:start position:0%
+also want the pro the protective thing
+to be light. Like if you're paying for
+
+ align:start position:0%
+to be light. Like if you're paying for
+ 
+
+ align:start position:0%
+to be light. Like if you're paying for
+shipping for your computer or whatever,
+
+ align:start position:0%
+shipping for your computer or whatever,
+ 
+
+ align:start position:0%
+shipping for your computer or whatever,
+the fact that the packaging is light
+
+ align:start position:0%
+the fact that the packaging is light
+ 
+
+ align:start position:0%
+the fact that the packaging is light
+makes the shipping is is easier. If you
+
+ align:start position:0%
+makes the shipping is is easier. If you
+ 
+
+ align:start position:0%
+makes the shipping is is easier. If you
+have a helmet for your head, you don't
+
+ align:start position:0%
+have a helmet for your head, you don't
+ 
+
+ align:start position:0%
+have a helmet for your head, you don't
+want some big heavy thing. you want
+
+ align:start position:0%
+want some big heavy thing. you want
+ 
+
+ align:start position:0%
+want some big heavy thing. you want
+something fairly light and foams are
+
+ align:start position:0%
+something fairly light and foams are
+ 
+
+ align:start position:0%
+something fairly light and foams are
+cheap. So the fact that they're roughly
+
+ align:start position:0%
+cheap. So the fact that they're roughly
+ 
+
+ align:start position:0%
+cheap. So the fact that they're roughly
+isotropic, they're light, they're cheap,
+
+ align:start position:0%
+isotropic, they're light, they're cheap,
+ 
+
+ align:start position:0%
+isotropic, they're light, they're cheap,
+this all helps as well. But from a
+
+ align:start position:0%
+this all helps as well. But from a
+ 
+
+ align:start position:0%
+this all helps as well. But from a
+mechanical point of view, foams are very
+
+ align:start position:0%
+mechanical point of view, foams are very
+ 
+
+ align:start position:0%
+mechanical point of view, foams are very
+good at absorbing energy. And so what
+
+ align:start position:0%
+good at absorbing energy. And so what
+ 
+
+ align:start position:0%
+good at absorbing energy. And so what
+we're going to do uh in the next like
+
+ align:start position:0%
+we're going to do uh in the next like
+ 
+
+ align:start position:0%
+we're going to do uh in the next like
+the rest of this lecture and and on
+
+ align:start position:0%
+the rest of this lecture and and on
+ 
+
+ align:start position:0%
+the rest of this lecture and and on
+Wednesday, we're going to see how we can
+
+ align:start position:0%
+Wednesday, we're going to see how we can
+ 
+
+ align:start position:0%
+Wednesday, we're going to see how we can
+convert these stress strain curves into
+
+ align:start position:0%
+convert these stress strain curves into
+ 
+
+ align:start position:0%
+convert these stress strain curves into
+what are called energy absorption
+
+ align:start position:0%
+what are called energy absorption
+ 
+
+ align:start position:0%
+what are called energy absorption
+diagrams. We're going to look at some
+
+ align:start position:0%
+diagrams. We're going to look at some
+ 
+
+ align:start position:0%
+diagrams. We're going to look at some
+energy absorption diagrams that we just
+
+ align:start position:0%
+energy absorption diagrams that we just
+ 
+
+ align:start position:0%
+energy absorption diagrams that we just
+measure from the stress strain curves
+
+ align:start position:0%
+measure from the stress strain curves
+ 
+
+ align:start position:0%
+measure from the stress strain curves
+and we're going to look at how we can
+
+ align:start position:0%
+and we're going to look at how we can
+ 
+
+ align:start position:0%
+and we're going to look at how we can
+predict the energy absorption diagrams
+
+ align:start position:0%
+predict the energy absorption diagrams
+ 
+
+ align:start position:0%
+predict the energy absorption diagrams
+as well.
+
+ align:start position:0%
+as well.
+ 
+
+ align:start position:0%
+as well.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So the main idea here is that the impact
+
+ align:start position:0%
+So the main idea here is that the impact
+ 
+
+ align:start position:0%
+So the main idea here is that the impact
+protection
+
+ align:start position:0%
+protection
+ 
+
+ align:start position:0%
+protection
+has to absorb the energy from the impact
+
+ align:start position:0%
+has to absorb the energy from the impact
+ 
+
+ align:start position:0%
+has to absorb the energy from the impact
+but without exceeding a certain peak
+
+ align:start position:0%
+but without exceeding a certain peak
+ 
+
+ align:start position:0%
+but without exceeding a certain peak
+stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the direction of loading may not be
+
+ align:start position:0%
+So the direction of loading may not be
+ 
+
+ align:start position:0%
+So the direction of loading may not be
+predictable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And foams are good because they're
+
+ align:start position:0%
+And foams are good because they're
+ 
+
+ align:start position:0%
+And foams are good because they're
+roughly isotropic.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So they would have the same energy
+
+ align:start position:0%
+So they would have the same energy
+ 
+
+ align:start position:0%
+So they would have the same energy
+absorption capacity from any direction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And foams are also light and cheap.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We can say for a given peak stress,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the foam is always going to absorb more
+
+ align:start position:0%
+the foam is always going to absorb more
+ 
+
+ align:start position:0%
+the foam is always going to absorb more
+energy than the solid it's made from.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So other things that make foams good are
+
+ align:start position:0%
+So other things that make foams good are
+ 
+
+ align:start position:0%
+So other things that make foams good are
+that they have a capacity to undergo
+
+ align:start position:0%
+that they have a capacity to undergo
+ 
+
+ align:start position:0%
+that they have a capacity to undergo
+large deformations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they do that at roughly constant
+
+ align:start position:0%
+and they do that at roughly constant
+ 
+
+ align:start position:0%
+and they do that at roughly constant
+stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that if you look at the stress strain
+
+ align:start position:0%
+So that if you look at the stress strain
+ 
+
+ align:start position:0%
+So that if you look at the stress strain
+curve for the foam,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to be able to absorb all
+
+ align:start position:0%
+you're going to be able to absorb all
+ 
+
+ align:start position:0%
+you're going to be able to absorb all
+this energy under here. And these
+
+ align:start position:0%
+this energy under here. And these
+ 
+
+ align:start position:0%
+this energy under here. And these
+strains that the foam might go to might
+
+ align:start position:0%
+strains that the foam might go to might
+ 
+
+ align:start position:0%
+strains that the foam might go to might
+be 08 to 0.9. So huge strains on an
+
+ align:start position:0%
+be 08 to 0.9. So huge strains on an
+ 
+
+ align:start position:0%
+be 08 to 0.9. So huge strains on an
+engineering uh scale.
+
+ align:start position:0%
+engineering uh scale.
+ 
+
+ align:start position:0%
+engineering uh scale.
+And then this is your your energy you
+
+ align:start position:0%
+And then this is your your energy you
+ 
+
+ align:start position:0%
+And then this is your your energy you
+would absorb is that area under the
+
+ align:start position:0%
+would absorb is that area under the
+ 
+
+ align:start position:0%
+would absorb is that area under the
+stress strain curve.
+
+ align:start position:0%
+stress strain curve.
+ 
+
+ align:start position:0%
+stress strain curve.
+So I wanted to say something about
+
+ align:start position:0%
+So I wanted to say something about
+ 
+
+ align:start position:0%
+So I wanted to say something about
+strain rates too.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So typically we're going to be talking
+
+ align:start position:0%
+So typically we're going to be talking
+ 
+
+ align:start position:0%
+So typically we're going to be talking
+about problems of impact and an impact
+
+ align:start position:0%
+about problems of impact and an impact
+ 
+
+ align:start position:0%
+about problems of impact and an impact
+the strain rates are typically on the
+
+ align:start position:0%
+the strain rates are typically on the
+ 
+
+ align:start position:0%
+the strain rates are typically on the
+order of 10 to 100 per second something
+
+ align:start position:0%
+order of 10 to 100 per second something
+ 
+
+ align:start position:0%
+order of 10 to 100 per second something
+like that. We're not going to talk about
+
+ align:start position:0%
+like that. We're not going to talk about
+ 
+
+ align:start position:0%
+like that. We're not going to talk about
+things like blast. If you have a blast
+
+ align:start position:0%
+things like blast. If you have a blast
+ 
+
+ align:start position:0%
+things like blast. If you have a blast
+loading then you have to take inertial
+
+ align:start position:0%
+loading then you have to take inertial
+ 
+
+ align:start position:0%
+loading then you have to take inertial
+effects into account. And blast involves
+
+ align:start position:0%
+effects into account. And blast involves
+ 
+
+ align:start position:0%
+effects into account. And blast involves
+strain rates which are you know a
+
+ align:start position:0%
+strain rates which are you know a
+ 
+
+ align:start position:0%
+strain rates which are you know a
+thousand to 10,000 per second much much
+
+ align:start position:0%
+thousand to 10,000 per second much much
+ 
+
+ align:start position:0%
+thousand to 10,000 per second much much
+higher. So, we're going to talk about uh
+
+ align:start position:0%
+higher. So, we're going to talk about uh
+ 
+
+ align:start position:0%
+higher. So, we're going to talk about uh
+strain rates that are about 10 to 100
+
+ align:start position:0%
+strain rates that are about 10 to 100
+ 
+
+ align:start position:0%
+strain rates that are about 10 to 100
+per second, maybe a bit more than that.
+
+ align:start position:0%
+per second, maybe a bit more than that.
+ 
+
+ align:start position:0%
+per second, maybe a bit more than that.
+And for instance, you can you can
+
+ align:start position:0%
+And for instance, you can you can
+ 
+
+ align:start position:0%
+And for instance, you can you can
+roughly estimate what one of these
+
+ align:start position:0%
+roughly estimate what one of these
+ 
+
+ align:start position:0%
+roughly estimate what one of these
+impact rates would be. Say you had
+
+ align:start position:0%
+impact rates would be. Say you had
+ 
+
+ align:start position:0%
+impact rates would be. Say you had
+something that you dropped from a height
+
+ align:start position:0%
+something that you dropped from a height
+ 
+
+ align:start position:0%
+something that you dropped from a height
+of 1 meter.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then the velocity on impact
+
+ align:start position:0%
+Then the velocity on impact
+ 
+
+ align:start position:0%
+Then the velocity on impact
+is just if you just equate the potential
+
+ align:start position:0%
+is just if you just equate the potential
+ 
+
+ align:start position:0%
+is just if you just equate the potential
+energy with the kinetic energy, the
+
+ align:start position:0%
+energy with the kinetic energy, the
+ 
+
+ align:start position:0%
+energy with the kinetic energy, the
+velocity on impact is just the<unk> of 2
+
+ align:start position:0%
+velocity on impact is just the<unk> of 2
+ 
+
+ align:start position:0%
+velocity on impact is just the<unk> of 2
+gh. So g is the gravity acceleration and
+
+ align:start position:0%
+gh. So g is the gravity acceleration and
+ 
+
+ align:start position:0%
+gh. So g is the gravity acceleration and
+h is the height. So that's the<unk> of 2
+
+ align:start position:0%
+h is the height. So that's the<unk> of 2
+ 
+
+ align:start position:0%
+h is the height. So that's the<unk> of 2
+* 9.81 m/s
+
+ align:start position:0%
+* 9.81 m/s
+ 
+
+ align:start position:0%
+* 9.81 m/s
+* 1 meter and that comes out to 4.4
+
+ align:start position:0%
+* 1 meter and that comes out to 4.4
+ 
+
+ align:start position:0%
+* 1 meter and that comes out to 4.4
+m/s.
+
+ align:start position:0%
+m/s.
+ 
+
+ align:start position:0%
+m/s.
+And say you had some foam packaging that
+
+ align:start position:0%
+And say you had some foam packaging that
+ 
+
+ align:start position:0%
+And say you had some foam packaging that
+was 100 mil millimeters thick.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then you could say roughly that the
+
+ align:start position:0%
+Then you could say roughly that the
+ 
+
+ align:start position:0%
+Then you could say roughly that the
+strain rate will be approximately equal
+
+ align:start position:0%
+strain rate will be approximately equal
+ 
+
+ align:start position:0%
+strain rate will be approximately equal
+to that velocity over the thickness.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So 4.4 m/s
+
+ align:start position:0%
+So 4.4 m/s
+ 
+
+ align:start position:0%
+So 4.4 m/s
+over 0.1 m
+
+ align:start position:0%
+over 0.1 m
+ 
+
+ align:start position:0%
+over 0.1 m
+that' be 44 per second. Okay. So it's
+
+ align:start position:0%
+that' be 44 per second. Okay. So it's
+ 
+
+ align:start position:0%
+that' be 44 per second. Okay. So it's
+somewhere in that kind of range.
+
+ align:start position:0%
+somewhere in that kind of range.
+ 
+
+ align:start position:0%
+somewhere in that kind of range.
+Obviously the thickness could be a
+
+ align:start position:0%
+Obviously the thickness could be a
+ 
+
+ align:start position:0%
+Obviously the thickness could be a
+little bit smaller, could be bigger, but
+
+ align:start position:0%
+little bit smaller, could be bigger, but
+ 
+
+ align:start position:0%
+little bit smaller, could be bigger, but
+it's in that ballpark. And if you do
+
+ align:start position:0%
+it's in that ballpark. And if you do
+ 
+
+ align:start position:0%
+it's in that ballpark. And if you do
+tests on servo controlled inrons or you
+
+ align:start position:0%
+tests on servo controlled inrons or you
+ 
+
+ align:start position:0%
+tests on servo controlled inrons or you
+do a drop hammer test, you can get
+
+ align:start position:0%
+do a drop hammer test, you can get
+ 
+
+ align:start position:0%
+do a drop hammer test, you can get
+strain rates in that ballpark.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, we're talking about impact and
+
+ align:start position:0%
+Okay. So, we're talking about impact and
+ 
+
+ align:start position:0%
+Okay. So, we're talking about impact and
+not not blast.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So most of the energy that's absorbed is
+
+ align:start position:0%
+So most of the energy that's absorbed is
+ 
+
+ align:start position:0%
+So most of the energy that's absorbed is
+really absorbed in that stress plateau.
+
+ align:start position:0%
+really absorbed in that stress plateau.
+ 
+
+ align:start position:0%
+really absorbed in that stress plateau.
+So if you think of the stress strain
+
+ align:start position:0%
+So if you think of the stress strain
+ 
+
+ align:start position:0%
+So if you think of the stress strain
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+um most of the area under the stress
+
+ align:start position:0%
+um most of the area under the stress
+ 
+
+ align:start position:0%
+um most of the area under the stress
+strain curve comes from the area from
+
+ align:start position:0%
+strain curve comes from the area from
+ 
+
+ align:start position:0%
+strain curve comes from the area from
+underneath the stress plateau. So the
+
+ align:start position:0%
+underneath the stress plateau. So the
+ 
+
+ align:start position:0%
+underneath the stress plateau. So the
+mechanisms of absorbing the energy are
+
+ align:start position:0%
+mechanisms of absorbing the energy are
+ 
+
+ align:start position:0%
+mechanisms of absorbing the energy are
+going to be mechanisms that are
+
+ align:start position:0%
+going to be mechanisms that are
+ 
+
+ align:start position:0%
+going to be mechanisms that are
+associated with a plateau stress. So for
+
+ align:start position:0%
+associated with a plateau stress. So for
+ 
+
+ align:start position:0%
+associated with a plateau stress. So for
+elastoic foams, we've got elastic
+
+ align:start position:0%
+elastoic foams, we've got elastic
+ 
+
+ align:start position:0%
+elastoic foams, we've got elastic
+buckling of the cells.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And one of the sort of advantages or
+
+ align:start position:0%
+And one of the sort of advantages or
+ 
+
+ align:start position:0%
+And one of the sort of advantages or
+disadvantages depending on what you want
+
+ align:start position:0%
+disadvantages depending on what you want
+ 
+
+ align:start position:0%
+disadvantages depending on what you want
+uh of this is that the deformation is
+
+ align:start position:0%
+uh of this is that the deformation is
+ 
+
+ align:start position:0%
+uh of this is that the deformation is
+recoverable and you're going to have
+
+ align:start position:0%
+recoverable and you're going to have
+ 
+
+ align:start position:0%
+recoverable and you're going to have
+rebound. So if you have a an object and
+
+ align:start position:0%
+rebound. So if you have a an object and
+ 
+
+ align:start position:0%
+rebound. So if you have a an object and
+you drop it onto an elastimeic foam,
+
+ align:start position:0%
+you drop it onto an elastimeic foam,
+ 
+
+ align:start position:0%
+you drop it onto an elastimeic foam,
+it's going to kind of bounce around like
+
+ align:start position:0%
+it's going to kind of bounce around like
+ 
+
+ align:start position:0%
+it's going to kind of bounce around like
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the elastic deformation is going to
+
+ align:start position:0%
+So the elastic deformation is going to
+ 
+
+ align:start position:0%
+So the elastic deformation is going to
+be recovered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you're going to get rebound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you have a foam that has a plastic
+
+ align:start position:0%
+If you have a foam that has a plastic
+ 
+
+ align:start position:0%
+If you have a foam that has a plastic
+yield point or is brittle, then the
+
+ align:start position:0%
+yield point or is brittle, then the
+ 
+
+ align:start position:0%
+yield point or is brittle, then the
+deformation is going to be largely from
+
+ align:start position:0%
+deformation is going to be largely from
+ 
+
+ align:start position:0%
+deformation is going to be largely from
+dissipating plastic work or work of
+
+ align:start position:0%
+dissipating plastic work or work of
+ 
+
+ align:start position:0%
+dissipating plastic work or work of
+fracture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And in that case, there's no rebound.
+
+ align:start position:0%
+And in that case, there's no rebound.
+ 
+
+ align:start position:0%
+And in that case, there's no rebound.
+But once you've loaded it, you've
+
+ align:start position:0%
+But once you've loaded it, you've
+ 
+
+ align:start position:0%
+But once you've loaded it, you've
+crushed the thing and you've permanently
+
+ align:start position:0%
+crushed the thing and you've permanently
+ 
+
+ align:start position:0%
+crushed the thing and you've permanently
+deformed it and you can't use it again.
+
+ align:start position:0%
+deformed it and you can't use it again.
+ 
+
+ align:start position:0%
+deformed it and you can't use it again.
+So sometimes if you ride your bicycle
+
+ align:start position:0%
+So sometimes if you ride your bicycle
+ 
+
+ align:start position:0%
+So sometimes if you ride your bicycle
+like I do, if you have a helmet, you
+
+ align:start position:0%
+like I do, if you have a helmet, you
+ 
+
+ align:start position:0%
+like I do, if you have a helmet, you
+should wear your bicycle helmet. If you
+
+ align:start position:0%
+should wear your bicycle helmet. If you
+ 
+
+ align:start position:0%
+should wear your bicycle helmet. If you
+have a problem, if you, you know, have
+
+ align:start position:0%
+have a problem, if you, you know, have
+ 
+
+ align:start position:0%
+have a problem, if you, you know, have
+an accident and your helmet gets
+
+ align:start position:0%
+an accident and your helmet gets
+ 
+
+ align:start position:0%
+an accident and your helmet gets
+smooshed, that's it. You have to throw
+
+ align:start position:0%
+smooshed, that's it. You have to throw
+ 
+
+ align:start position:0%
+smooshed, that's it. You have to throw
+your helmet away. You can't use it
+
+ align:start position:0%
+your helmet away. You can't use it
+ 
+
+ align:start position:0%
+your helmet away. You can't use it
+again. And this is why It doesn't get
+
+ align:start position:0%
+again. And this is why It doesn't get
+ 
+
+ align:start position:0%
+again. And this is why It doesn't get
+smooshed. If you hit your head at all,
+
+ align:start position:0%
+smooshed. If you hit your head at all,
+ 
+
+ align:start position:0%
+smooshed. If you hit your head at all,
+you should get a new helmet. Exactly.
+
+ align:start position:0%
+you should get a new helmet. Exactly.
+ 
+
+ align:start position:0%
+you should get a new helmet. Exactly.
+You need like four years. Yeah. You need
+
+ align:start position:0%
+You need like four years. Yeah. You need
+ 
+
+ align:start position:0%
+You need like four years. Yeah. You need
+a new helmet. Yeah. You So, go ahead.
+
+ align:start position:0%
+a new helmet. Yeah. You So, go ahead.
+ 
+
+ align:start position:0%
+a new helmet. Yeah. You So, go ahead.
+Talk about helmets because I'm I'm on a
+
+ align:start position:0%
+Talk about helmets because I'm I'm on a
+ 
+
+ align:start position:0%
+Talk about helmets because I'm I'm on a
+helmet conversion thing. Yes. You got to
+
+ align:start position:0%
+helmet conversion thing. Yes. You got to
+ 
+
+ align:start position:0%
+helmet conversion thing. Yes. You got to
+wear your helmet and you should change
+
+ align:start position:0%
+wear your helmet and you should change
+ 
+
+ align:start position:0%
+wear your helmet and you should change
+it every now and then. Anything else
+
+ align:start position:0%
+it every now and then. Anything else
+ 
+
+ align:start position:0%
+it every now and then. Anything else
+you'd like to add about bicycle helmet
+
+ align:start position:0%
+you'd like to add about bicycle helmet
+ 
+
+ align:start position:0%
+you'd like to add about bicycle helmet
+safety? No. Absolutely. You got to wear
+
+ align:start position:0%
+safety? No. Absolutely. You got to wear
+ 
+
+ align:start position:0%
+safety? No. Absolutely. You got to wear
+a helmet. So, I know several people who
+
+ align:start position:0%
+a helmet. So, I know several people who
+ 
+
+ align:start position:0%
+a helmet. So, I know several people who
+would have had their heads smooshed had
+
+ align:start position:0%
+would have had their heads smooshed had
+ 
+
+ align:start position:0%
+would have had their heads smooshed had
+they not been wearing their helmet. So,
+
+ align:start position:0%
+they not been wearing their helmet. So,
+ 
+
+ align:start position:0%
+they not been wearing their helmet. So,
+you have to wear a helmet.
+
+ align:start position:0%
+you have to wear a helmet.
+ 
+
+ align:start position:0%
+you have to wear a helmet.
+Uh let's see. Okay,
+
+ align:start position:0%
+Uh let's see. Okay,
+ 
+
+ align:start position:0%
+Uh let's see. Okay,
+if you think about natural cellular
+
+ align:start position:0%
+if you think about natural cellular
+ 
+
+ align:start position:0%
+if you think about natural cellular
+materials, things like wood,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they often have cell walls that are
+
+ align:start position:0%
+they often have cell walls that are
+ 
+
+ align:start position:0%
+they often have cell walls that are
+fiber composites and you can dissipate
+
+ align:start position:0%
+fiber composites and you can dissipate
+ 
+
+ align:start position:0%
+fiber composites and you can dissipate
+energy by mechanisms related to the
+
+ align:start position:0%
+energy by mechanisms related to the
+ 
+
+ align:start position:0%
+energy by mechanisms related to the
+fiber nature. So by things like uh fiber
+
+ align:start position:0%
+fiber nature. So by things like uh fiber
+ 
+
+ align:start position:0%
+fiber nature. So by things like uh fiber
+pull out and fracture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you can also have open cell
+
+ align:start position:0%
+And then you can also have open cell
+ 
+
+ align:start position:0%
+And then you can also have open cell
+foams with fluids. You can have fluid
+
+ align:start position:0%
+foams with fluids. You can have fluid
+ 
+
+ align:start position:0%
+foams with fluids. You can have fluid
+within the cells.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if the cells are open cells,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the fluid effect is really only going
+
+ align:start position:0%
+uh the fluid effect is really only going
+ 
+
+ align:start position:0%
+uh the fluid effect is really only going
+to be important if the cells are
+
+ align:start position:0%
+to be important if the cells are
+ 
+
+ align:start position:0%
+to be important if the cells are
+extremely small or the fluid is
+
+ align:start position:0%
+extremely small or the fluid is
+ 
+
+ align:start position:0%
+extremely small or the fluid is
+particularly viscous or the strain rates
+
+ align:start position:0%
+particularly viscous or the strain rates
+ 
+
+ align:start position:0%
+particularly viscous or the strain rates
+are very high.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in most cases, the fluid effects
+
+ align:start position:0%
+So in most cases, the fluid effects
+ 
+
+ align:start position:0%
+So in most cases, the fluid effects
+aren't important in open cell phones,
+
+ align:start position:0%
+aren't important in open cell phones,
+ 
+
+ align:start position:0%
+aren't important in open cell phones,
+but for example, you could try to make
+
+ align:start position:0%
+but for example, you could try to make
+ 
+
+ align:start position:0%
+but for example, you could try to make
+an open cell foam that was had more
+
+ align:start position:0%
+an open cell foam that was had more
+ 
+
+ align:start position:0%
+an open cell foam that was had more
+energy absorption by putting a fluid
+
+ align:start position:0%
+energy absorption by putting a fluid
+ 
+
+ align:start position:0%
+energy absorption by putting a fluid
+into it. So you could put like glycerin
+
+ align:start position:0%
+into it. So you could put like glycerin
+ 
+
+ align:start position:0%
+into it. So you could put like glycerin
+into the fluid and that would increase
+
+ align:start position:0%
+into the fluid and that would increase
+ 
+
+ align:start position:0%
+into the fluid and that would increase
+how much energy you absorb. Or you could
+
+ align:start position:0%
+how much energy you absorb. Or you could
+ 
+
+ align:start position:0%
+how much energy you absorb. Or you could
+put this honey into it that would make
+
+ align:start position:0%
+put this honey into it that would make
+ 
+
+ align:start position:0%
+put this honey into it that would make
+it more energy absorption.
+
+ align:start position:0%
+it more energy absorption.
+ 
+
+ align:start position:0%
+it more energy absorption.
+And in closed cell foams,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may have a a an effect of the gas
+
+ align:start position:0%
+you may have a a an effect of the gas
+ 
+
+ align:start position:0%
+you may have a a an effect of the gas
+within the cells, but it's really only
+
+ align:start position:0%
+within the cells, but it's really only
+ 
+
+ align:start position:0%
+within the cells, but it's really only
+going to be significant if you have
+
+ align:start position:0%
+going to be significant if you have
+ 
+
+ align:start position:0%
+going to be significant if you have
+elastic foams where the cell faces don't
+
+ align:start position:0%
+elastic foams where the cell faces don't
+ 
+
+ align:start position:0%
+elastic foams where the cell faces don't
+rupture. If the cell faces rupture, then
+
+ align:start position:0%
+rupture. If the cell faces rupture, then
+ 
+
+ align:start position:0%
+rupture. If the cell faces rupture, then
+the gas is just going to flow out of
+
+ align:start position:0%
+the gas is just going to flow out of
+ 
+
+ align:start position:0%
+the gas is just going to flow out of
+them and that's not going to do much.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the next step is I want to go from
+
+ align:start position:0%
+So the next step is I want to go from
+ 
+
+ align:start position:0%
+So the next step is I want to go from
+having the stress strain curve that
+
+ align:start position:0%
+having the stress strain curve that
+ 
+
+ align:start position:0%
+having the stress strain curve that
+we've become very familiar with and make
+
+ align:start position:0%
+we've become very familiar with and make
+ 
+
+ align:start position:0%
+we've become very familiar with and make
+some something with that that is a
+
+ align:start position:0%
+some something with that that is a
+ 
+
+ align:start position:0%
+some something with that that is a
+little easier. easier to see graphically
+
+ align:start position:0%
+little easier. easier to see graphically
+ 
+
+ align:start position:0%
+little easier. easier to see graphically
+that shows how much energy we can
+
+ align:start position:0%
+that shows how much energy we can
+ 
+
+ align:start position:0%
+that shows how much energy we can
+absorb. And remember what I said what
+
+ align:start position:0%
+absorb. And remember what I said what
+ 
+
+ align:start position:0%
+absorb. And remember what I said what
+we're really interested in is absorbing
+
+ align:start position:0%
+we're really interested in is absorbing
+ 
+
+ align:start position:0%
+we're really interested in is absorbing
+a certain amount of energy without
+
+ align:start position:0%
+a certain amount of energy without
+ 
+
+ align:start position:0%
+a certain amount of energy without
+exceeding a certain peak stress. So what
+
+ align:start position:0%
+exceeding a certain peak stress. So what
+ 
+
+ align:start position:0%
+exceeding a certain peak stress. So what
+I'm going to do is plot another plot
+
+ align:start position:0%
+I'm going to do is plot another plot
+ 
+
+ align:start position:0%
+I'm going to do is plot another plot
+that's based on that. That's going to be
+
+ align:start position:0%
+that's based on that. That's going to be
+ 
+
+ align:start position:0%
+that's based on that. That's going to be
+the energy absorbed. So W is going to be
+
+ align:start position:0%
+the energy absorbed. So W is going to be
+ 
+
+ align:start position:0%
+the energy absorbed. So W is going to be
+the energy absorbed per unit volume.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I'm going to plot that against the
+
+ align:start position:0%
+And I'm going to plot that against the
+ 
+
+ align:start position:0%
+And I'm going to plot that against the
+peak stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, we're going to look at three
+
+ align:start position:0%
+Okay. So, we're going to look at three
+ 
+
+ align:start position:0%
+Okay. So, we're going to look at three
+different regimes here. We're going to
+
+ align:start position:0%
+different regimes here. We're going to
+ 
+
+ align:start position:0%
+different regimes here. We're going to
+look at what happens in the linear
+
+ align:start position:0%
+look at what happens in the linear
+ 
+
+ align:start position:0%
+look at what happens in the linear
+elastic part. what happens in the stress
+
+ align:start position:0%
+elastic part. what happens in the stress
+ 
+
+ align:start position:0%
+elastic part. what happens in the stress
+plateau and then what happens in the
+
+ align:start position:0%
+plateau and then what happens in the
+ 
+
+ align:start position:0%
+plateau and then what happens in the
+densification part. So let's think about
+
+ align:start position:0%
+densification part. So let's think about
+ 
+
+ align:start position:0%
+densification part. So let's think about
+the um elastimeic or the elastic regime
+
+ align:start position:0%
+the um elastimeic or the elastic regime
+ 
+
+ align:start position:0%
+the um elastimeic or the elastic regime
+first. And
+
+ align:start position:0%
+first. And
+ 
+
+ align:start position:0%
+first. And
+if I moved up, say I moved up to some
+
+ align:start position:0%
+if I moved up, say I moved up to some
+ 
+
+ align:start position:0%
+if I moved up, say I moved up to some
+point right there with a little x is on
+
+ align:start position:0%
+point right there with a little x is on
+ 
+
+ align:start position:0%
+point right there with a little x is on
+the stress strain curve, then the amount
+
+ align:start position:0%
+the stress strain curve, then the amount
+ 
+
+ align:start position:0%
+the stress strain curve, then the amount
+of energy I absorbed would just be equal
+
+ align:start position:0%
+of energy I absorbed would just be equal
+ 
+
+ align:start position:0%
+of energy I absorbed would just be equal
+to this little bit here, right? And if I
+
+ align:start position:0%
+to this little bit here, right? And if I
+ 
+
+ align:start position:0%
+to this little bit here, right? And if I
+moved up and then the peak stress would
+
+ align:start position:0%
+moved up and then the peak stress would
+ 
+
+ align:start position:0%
+moved up and then the peak stress would
+be this peak stress there. Call that
+
+ align:start position:0%
+be this peak stress there. Call that
+ 
+
+ align:start position:0%
+be this peak stress there. Call that
+sigma sigma p1 and w1. And if I moved up
+
+ align:start position:0%
+sigma sigma p1 and w1. And if I moved up
+ 
+
+ align:start position:0%
+sigma sigma p1 and w1. And if I moved up
+over here, I'd be at W2
+
+ align:start position:0%
+over here, I'd be at W2
+ 
+
+ align:start position:0%
+over here, I'd be at W2
+and that'd be sigma P2, right? And if I
+
+ align:start position:0%
+and that'd be sigma P2, right? And if I
+ 
+
+ align:start position:0%
+and that'd be sigma P2, right? And if I
+know the modulus, I know what that
+
+ align:start position:0%
+know the modulus, I know what that
+ 
+
+ align:start position:0%
+know the modulus, I know what that
+relationship is. And I get a
+
+ align:start position:0%
+relationship is. And I get a
+ 
+
+ align:start position:0%
+relationship is. And I get a
+relationship. And these are going to be
+
+ align:start position:0%
+relationship. And these are going to be
+ 
+
+ align:start position:0%
+relationship. And these are going to be
+I'm going to do this on log scales here.
+
+ align:start position:0%
+I'm going to do this on log scales here.
+ 
+
+ align:start position:0%
+I'm going to do this on log scales here.
+This is going to be log and that's going
+
+ align:start position:0%
+This is going to be log and that's going
+ 
+
+ align:start position:0%
+This is going to be log and that's going
+to be log. Um I'm going to get in that
+
+ align:start position:0%
+to be log. Um I'm going to get in that
+ 
+
+ align:start position:0%
+to be log. Um I'm going to get in that
+linear elastic regime, the energy is
+
+ align:start position:0%
+linear elastic regime, the energy is
+ 
+
+ align:start position:0%
+linear elastic regime, the energy is
+going to go as the peak stress squared.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over two times the modulus of the foam.
+
+ align:start position:0%
+over two times the modulus of the foam.
+ 
+
+ align:start position:0%
+over two times the modulus of the foam.
+Remember energy is a half stress time
+
+ align:start position:0%
+Remember energy is a half stress time
+ 
+
+ align:start position:0%
+Remember energy is a half stress time
+strain.
+
+ align:start position:0%
+strain.
+ 
+
+ align:start position:0%
+strain.
+And I can say the strain is sigma p over
+
+ align:start position:0%
+And I can say the strain is sigma p over
+ 
+
+ align:start position:0%
+And I can say the strain is sigma p over
+e. So it's a half sigma p ^2 over e.
+
+ align:start position:0%
+e. So it's a half sigma p ^2 over e.
+ 
+
+ align:start position:0%
+e. So it's a half sigma p ^2 over e.
+So on my log plot here, this is just
+
+ align:start position:0%
+So on my log plot here, this is just
+ 
+
+ align:start position:0%
+So on my log plot here, this is just
+going to be a straight line like that.
+
+ align:start position:0%
+going to be a straight line like that.
+ 
+
+ align:start position:0%
+going to be a straight line like that.
+And then I'm going to get to this value
+
+ align:start position:0%
+And then I'm going to get to this value
+ 
+
+ align:start position:0%
+And then I'm going to get to this value
+here. I'm going to get to my um collapse
+
+ align:start position:0%
+here. I'm going to get to my um collapse
+ 
+
+ align:start position:0%
+here. I'm going to get to my um collapse
+stress here.
+
+ align:start position:0%
+stress here.
+ 
+
+ align:start position:0%
+stress here.
+So let's call that sigma star. And at
+
+ align:start position:0%
+So let's call that sigma star. And at
+ 
+
+ align:start position:0%
+So let's call that sigma star. And at
+that point, I'm going to as the more I
+
+ align:start position:0%
+that point, I'm going to as the more I
+ 
+
+ align:start position:0%
+that point, I'm going to as the more I
+go along here, for every point I go
+
+ align:start position:0%
+go along here, for every point I go
+ 
+
+ align:start position:0%
+go along here, for every point I go
+along like that, I'm going to absorb
+
+ align:start position:0%
+along like that, I'm going to absorb
+ 
+
+ align:start position:0%
+along like that, I'm going to absorb
+more and more energy, but the stress
+
+ align:start position:0%
+more and more energy, but the stress
+ 
+
+ align:start position:0%
+more and more energy, but the stress
+isn't going to go up at all. Right? So
+
+ align:start position:0%
+isn't going to go up at all. Right? So
+ 
+
+ align:start position:0%
+isn't going to go up at all. Right? So
+then this thing here is going to go like
+
+ align:start position:0%
+then this thing here is going to go like
+ 
+
+ align:start position:0%
+then this thing here is going to go like
+that because I'm absorbing more and more
+
+ align:start position:0%
+that because I'm absorbing more and more
+ 
+
+ align:start position:0%
+that because I'm absorbing more and more
+energy, but the stress just stays the
+
+ align:start position:0%
+energy, but the stress just stays the
+ 
+
+ align:start position:0%
+energy, but the stress just stays the
+same. So this is good news if we want to
+
+ align:start position:0%
+same. So this is good news if we want to
+ 
+
+ align:start position:0%
+same. So this is good news if we want to
+if we want to absorb energy. And then
+
+ align:start position:0%
+if we want to absorb energy. And then
+ 
+
+ align:start position:0%
+if we want to absorb energy. And then
+once I get to the densification point,
+
+ align:start position:0%
+once I get to the densification point,
+ 
+
+ align:start position:0%
+once I get to the densification point,
+then it's going to do the opposite
+
+ align:start position:0%
+then it's going to do the opposite
+ 
+
+ align:start position:0%
+then it's going to do the opposite
+thing. If I go, you know, as I go along
+
+ align:start position:0%
+thing. If I go, you know, as I go along
+ 
+
+ align:start position:0%
+thing. If I go, you know, as I go along
+here, at each increment, I'm not
+
+ align:start position:0%
+here, at each increment, I'm not
+ 
+
+ align:start position:0%
+here, at each increment, I'm not
+absorbing that much more energy, but the
+
+ align:start position:0%
+absorbing that much more energy, but the
+ 
+
+ align:start position:0%
+absorbing that much more energy, but the
+stress is going up. So, at some point,
+
+ align:start position:0%
+stress is going up. So, at some point,
+ 
+
+ align:start position:0%
+stress is going up. So, at some point,
+it kind of turns and starts to look like
+
+ align:start position:0%
+it kind of turns and starts to look like
+ 
+
+ align:start position:0%
+it kind of turns and starts to look like
+that. Okay? So, this part here
+
+ align:start position:0%
+that. Okay? So, this part here
+ 
+
+ align:start position:0%
+that. Okay? So, this part here
+corresponds to linear elasticity.
+
+ align:start position:0%
+corresponds to linear elasticity.
+ 
+
+ align:start position:0%
+corresponds to linear elasticity.
+This bit here
+
+ align:start position:0%
+This bit here
+ 
+
+ align:start position:0%
+This bit here
+corresponds to the stress plateau. And
+
+ align:start position:0%
+corresponds to the stress plateau. And
+ 
+
+ align:start position:0%
+corresponds to the stress plateau. And
+this bit here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponds to densification. Okay.
+
+ align:start position:0%
+corresponds to densification. Okay.
+ 
+
+ align:start position:0%
+corresponds to densification. Okay.
+And the point where I would like to be
+
+ align:start position:0%
+And the point where I would like to be
+ 
+
+ align:start position:0%
+And the point where I would like to be
+is right here because here I'm going to
+
+ align:start position:0%
+is right here because here I'm going to
+ 
+
+ align:start position:0%
+is right here because here I'm going to
+absorb the most energy possible for the
+
+ align:start position:0%
+absorb the most energy possible for the
+ 
+
+ align:start position:0%
+absorb the most energy possible for the
+the peak stress. So you can think of
+
+ align:start position:0%
+the peak stress. So you can think of
+ 
+
+ align:start position:0%
+the peak stress. So you can think of
+that as sort of an optimum point and I'm
+
+ align:start position:0%
+that as sort of an optimum point and I'm
+ 
+
+ align:start position:0%
+that as sort of an optimum point and I'm
+going to refer to that as a shoulder.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's kind of the shoulder
+
+ align:start position:0%
+because it's kind of the shoulder
+ 
+
+ align:start position:0%
+because it's kind of the shoulder
+between where the curve bends over
+
+ align:start position:0%
+between where the curve bends over
+ 
+
+ align:start position:0%
+between where the curve bends over
+again. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I've only got a couple minutes left,
+
+ align:start position:0%
+um I've only got a couple minutes left,
+ 
+
+ align:start position:0%
+um I've only got a couple minutes left,
+but let me just show you uh one thing
+
+ align:start position:0%
+but let me just show you uh one thing
+ 
+
+ align:start position:0%
+but let me just show you uh one thing
+and then we'll talk about this more next
+
+ align:start position:0%
+and then we'll talk about this more next
+ 
+
+ align:start position:0%
+and then we'll talk about this more next
+time. So, I've just done this for one
+
+ align:start position:0%
+time. So, I've just done this for one
+ 
+
+ align:start position:0%
+time. So, I've just done this for one
+relative density, but if you look at the
+
+ align:start position:0%
+relative density, but if you look at the
+ 
+
+ align:start position:0%
+relative density, but if you look at the
+screen, you could imagine I would have
+
+ align:start position:0%
+screen, you could imagine I would have
+ 
+
+ align:start position:0%
+screen, you could imagine I would have
+stress strain curves for lots of
+
+ align:start position:0%
+stress strain curves for lots of
+ 
+
+ align:start position:0%
+stress strain curves for lots of
+different relative densities. And let's
+
+ align:start position:0%
+different relative densities. And let's
+ 
+
+ align:start position:0%
+different relative densities. And let's
+say these are all at the same
+
+ align:start position:0%
+say these are all at the same
+ 
+
+ align:start position:0%
+say these are all at the same
+temperature and all at the same strain
+
+ align:start position:0%
+temperature and all at the same strain
+ 
+
+ align:start position:0%
+temperature and all at the same strain
+rate. And I could draw a curve that
+
+ align:start position:0%
+rate. And I could draw a curve that
+ 
+
+ align:start position:0%
+rate. And I could draw a curve that
+looks like that for each stress strain
+
+ align:start position:0%
+looks like that for each stress strain
+ 
+
+ align:start position:0%
+looks like that for each stress strain
+curve. And if I did that, I get a family
+
+ align:start position:0%
+curve. And if I did that, I get a family
+ 
+
+ align:start position:0%
+curve. And if I did that, I get a family
+of them. Right? So, this is our energy
+
+ align:start position:0%
+of them. Right? So, this is our energy
+ 
+
+ align:start position:0%
+of them. Right? So, this is our energy
+absorbed here. I've normalized it by
+
+ align:start position:0%
+absorbed here. I've normalized it by
+ 
+
+ align:start position:0%
+absorbed here. I've normalized it by
+dividing by the solid modulus. This is
+
+ align:start position:0%
+dividing by the solid modulus. This is
+ 
+
+ align:start position:0%
+dividing by the solid modulus. This is
+our peak stress here. And I've
+
+ align:start position:0%
+our peak stress here. And I've
+ 
+
+ align:start position:0%
+our peak stress here. And I've
+normalized that by dividing by the solid
+
+ align:start position:0%
+normalized that by dividing by the solid
+ 
+
+ align:start position:0%
+normalized that by dividing by the solid
+modulus. And then I've got a sort of
+
+ align:start position:0%
+modulus. And then I've got a sort of
+ 
+
+ align:start position:0%
+modulus. And then I've got a sort of
+family of these things, right? They all
+
+ align:start position:0%
+family of these things, right? They all
+ 
+
+ align:start position:0%
+family of these things, right? They all
+have the same shape, but they shift
+
+ align:start position:0%
+have the same shape, but they shift
+ 
+
+ align:start position:0%
+have the same shape, but they shift
+depending on the relative density. And
+
+ align:start position:0%
+depending on the relative density. And
+ 
+
+ align:start position:0%
+depending on the relative density. And
+then the thing that makes life good is
+
+ align:start position:0%
+then the thing that makes life good is
+ 
+
+ align:start position:0%
+then the thing that makes life good is
+that these shoulder points you can
+
+ align:start position:0%
+that these shoulder points you can
+ 
+
+ align:start position:0%
+that these shoulder points you can
+connect with a line. And you can mark
+
+ align:start position:0%
+connect with a line. And you can mark
+ 
+
+ align:start position:0%
+connect with a line. And you can mark
+off the relative density for those
+
+ align:start position:0%
+off the relative density for those
+ 
+
+ align:start position:0%
+off the relative density for those
+shoulder points on each line. And then
+
+ align:start position:0%
+shoulder points on each line. And then
+ 
+
+ align:start position:0%
+shoulder points on each line. And then
+the last step you can do is you can just
+
+ align:start position:0%
+the last step you can do is you can just
+ 
+
+ align:start position:0%
+the last step you can do is you can just
+plot these lines. And you can repeat
+
+ align:start position:0%
+plot these lines. And you can repeat
+ 
+
+ align:start position:0%
+plot these lines. And you can repeat
+this for different strain rates. So this
+
+ align:start position:0%
+this for different strain rates. So this
+ 
+
+ align:start position:0%
+this for different strain rates. So this
+would be a a family of those these guys
+
+ align:start position:0%
+would be a a family of those these guys
+ 
+
+ align:start position:0%
+would be a a family of those these guys
+here. There's a family of those lines at
+
+ align:start position:0%
+here. There's a family of those lines at
+ 
+
+ align:start position:0%
+here. There's a family of those lines at
+different strain rates and then you
+
+ align:start position:0%
+different strain rates and then you
+ 
+
+ align:start position:0%
+different strain rates and then you
+would join up the points that correspond
+
+ align:start position:0%
+would join up the points that correspond
+ 
+
+ align:start position:0%
+would join up the points that correspond
+to each relative density. So you can
+
+ align:start position:0%
+to each relative density. So you can
+ 
+
+ align:start position:0%
+to each relative density. So you can
+make a drawing that looks like this that
+
+ align:start position:0%
+make a drawing that looks like this that
+ 
+
+ align:start position:0%
+make a drawing that looks like this that
+kind of summarizes the the most energy
+
+ align:start position:0%
+kind of summarizes the the most energy
+ 
+
+ align:start position:0%
+kind of summarizes the the most energy
+you could absorb for a certain peak
+
+ align:start position:0%
+you could absorb for a certain peak
+ 
+
+ align:start position:0%
+you could absorb for a certain peak
+stress for foams of different relative
+
+ align:start position:0%
+stress for foams of different relative
+ 
+
+ align:start position:0%
+stress for foams of different relative
+densities tested at different strain
+
+ align:start position:0%
+densities tested at different strain
+ 
+
+ align:start position:0%
+densities tested at different strain
+rates. You could do it for different
+
+ align:start position:0%
+rates. You could do it for different
+ 
+
+ align:start position:0%
+rates. You could do it for different
+temperatures if you wanted to. So next
+
+ align:start position:0%
+temperatures if you wanted to. So next
+ 
+
+ align:start position:0%
+temperatures if you wanted to. So next
+time we'll talk about that, but I'm I'm
+
+ align:start position:0%
+time we'll talk about that, but I'm I'm
+ 
+
+ align:start position:0%
+time we'll talk about that, but I'm I'm
+going to stop there for today. Okay, are
+
+ align:start position:0%
+going to stop there for today. Okay, are
+ 
+
+ align:start position:0%
+going to stop there for today. Okay, are
+we good?
\ No newline at end of file
diff --git a/w2HASHQ8nYw.txt b/w2HASHQ8nYw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0329637e64385de8969e5108b8cabf04a5e985ba
--- /dev/null
+++ b/w2HASHQ8nYw.txt
@@ -0,0 +1,11493 @@
+align:start position:0%
+ 
+so thank you very much for the
+
+ align:start position:0%
+so thank you very much for the
+ 
+
+ align:start position:0%
+so thank you very much for the
+opportunity of the presentation
+
+ align:start position:0%
+opportunity of the presentation
+ 
+
+ align:start position:0%
+opportunity of the presentation
+so today i will be presenting about the
+
+ align:start position:0%
+so today i will be presenting about the
+ 
+
+ align:start position:0%
+so today i will be presenting about the
+ganges water conflicts between india and
+
+ align:start position:0%
+ganges water conflicts between india and
+ 
+
+ align:start position:0%
+ganges water conflicts between india and
+bangladesh which is actually one of the
+
+ align:start position:0%
+bangladesh which is actually one of the
+ 
+
+ align:start position:0%
+bangladesh which is actually one of the
+major boon of contents that's happening
+
+ align:start position:0%
+major boon of contents that's happening
+ 
+
+ align:start position:0%
+major boon of contents that's happening
+between the two neighboring countries
+
+ align:start position:0%
+between the two neighboring countries
+ 
+
+ align:start position:0%
+between the two neighboring countries
+so i would be speaking about
+
+ align:start position:0%
+so i would be speaking about
+ 
+
+ align:start position:0%
+so i would be speaking about
+it is basically it follows three
+
+ align:start position:0%
+it is basically it follows three
+ 
+
+ align:start position:0%
+it is basically it follows three
+three flows the first part would speak
+
+ align:start position:0%
+three flows the first part would speak
+ 
+
+ align:start position:0%
+three flows the first part would speak
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+from where the problem originated and
+
+ align:start position:0%
+from where the problem originated and
+ 
+
+ align:start position:0%
+from where the problem originated and
+the second part would say that uh what
+
+ align:start position:0%
+the second part would say that uh what
+ 
+
+ align:start position:0%
+the second part would say that uh what
+is the present condition and the third
+
+ align:start position:0%
+is the present condition and the third
+ 
+
+ align:start position:0%
+is the present condition and the third
+part we'll discuss uh which i think
+
+ align:start position:0%
+part we'll discuss uh which i think
+ 
+
+ align:start position:0%
+part we'll discuss uh which i think
+would be the most relevant part for our
+
+ align:start position:0%
+would be the most relevant part for our
+ 
+
+ align:start position:0%
+would be the most relevant part for our
+class that is the water diplomacy part
+
+ align:start position:0%
+class that is the water diplomacy part
+ 
+
+ align:start position:0%
+class that is the water diplomacy part
+on how we can actually approach that
+
+ align:start position:0%
+on how we can actually approach that
+ 
+
+ align:start position:0%
+on how we can actually approach that
+problem and how we can uh
+
+ align:start position:0%
+problem and how we can uh
+ 
+
+ align:start position:0%
+problem and how we can uh
+try to find a solution
+
+ align:start position:0%
+try to find a solution
+ 
+
+ align:start position:0%
+try to find a solution
+so let me go to the next slide
+
+ align:start position:0%
+so let me go to the next slide
+ 
+
+ align:start position:0%
+so let me go to the next slide
+so i would be putting a little bit of
+
+ align:start position:0%
+so i would be putting a little bit of
+ 
+
+ align:start position:0%
+so i would be putting a little bit of
+disclaimer uh some part of my discussion
+
+ align:start position:0%
+disclaimer uh some part of my discussion
+ 
+
+ align:start position:0%
+disclaimer uh some part of my discussion
+might not match with bangladesh
+
+ align:start position:0%
+might not match with bangladesh
+ 
+
+ align:start position:0%
+might not match with bangladesh
+government's official view so i would
+
+ align:start position:0%
+government's official view so i would
+ 
+
+ align:start position:0%
+government's official view so i would
+this is important because
+
+ align:start position:0%
+this is important because
+ 
+
+ align:start position:0%
+this is important because
+because of years of training because i'm
+
+ align:start position:0%
+because of years of training because i'm
+ 
+
+ align:start position:0%
+because of years of training because i'm
+not an academic because of years of
+
+ align:start position:0%
+not an academic because of years of
+ 
+
+ align:start position:0%
+not an academic because of years of
+training uh two things happens the first
+
+ align:start position:0%
+training uh two things happens the first
+ 
+
+ align:start position:0%
+training uh two things happens the first
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+subconsciously and i have found it even
+
+ align:start position:0%
+subconsciously and i have found it even
+ 
+
+ align:start position:0%
+subconsciously and i have found it even
+when i've taken classes in japan or in
+
+ align:start position:0%
+when i've taken classes in japan or in
+ 
+
+ align:start position:0%
+when i've taken classes in japan or in
+the us that's uh automatically i
+
+ align:start position:0%
+the us that's uh automatically i
+ 
+
+ align:start position:0%
+the us that's uh automatically i
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+reflect the views of a typical
+
+ align:start position:0%
+reflect the views of a typical
+ 
+
+ align:start position:0%
+reflect the views of a typical
+bangladeshi bureaucrat the particular
+
+ align:start position:0%
+bangladeshi bureaucrat the particular
+ 
+
+ align:start position:0%
+bangladeshi bureaucrat the particular
+government's a point of view it is very
+
+ align:start position:0%
+government's a point of view it is very
+ 
+
+ align:start position:0%
+government's a point of view it is very
+i had to train myself to i mean stay
+
+ align:start position:0%
+i had to train myself to i mean stay
+ 
+
+ align:start position:0%
+i had to train myself to i mean stay
+away from that view and try to match
+
+ align:start position:0%
+away from that view and try to match
+ 
+
+ align:start position:0%
+away from that view and try to match
+with the academic standard and come up
+
+ align:start position:0%
+with the academic standard and come up
+ 
+
+ align:start position:0%
+with the academic standard and come up
+with as much as objective point of view
+
+ align:start position:0%
+with as much as objective point of view
+ 
+
+ align:start position:0%
+with as much as objective point of view
+as possible so here
+
+ align:start position:0%
+as possible so here
+ 
+
+ align:start position:0%
+as possible so here
+i would try deliberately i mean
+
+ align:start position:0%
+i would try deliberately i mean
+ 
+
+ align:start position:0%
+i would try deliberately i mean
+not to match the typical stuffs that is
+
+ align:start position:0%
+not to match the typical stuffs that is
+ 
+
+ align:start position:0%
+not to match the typical stuffs that is
+saved by the bangladesh government or
+
+ align:start position:0%
+saved by the bangladesh government or
+ 
+
+ align:start position:0%
+saved by the bangladesh government or
+any government
+
+ align:start position:0%
+any government
+ 
+
+ align:start position:0%
+any government
+per se so that is one thing so
+
+ align:start position:0%
+per se so that is one thing so
+ 
+
+ align:start position:0%
+per se so that is one thing so
+and the second part is uh the political
+
+ align:start position:0%
+and the second part is uh the political
+ 
+
+ align:start position:0%
+and the second part is uh the political
+history because although it's a
+
+ align:start position:0%
+history because although it's a
+ 
+
+ align:start position:0%
+history because although it's a
+treaty it's a river treaty but it is
+
+ align:start position:0%
+treaty it's a river treaty but it is
+ 
+
+ align:start position:0%
+treaty it's a river treaty but it is
+very sensitive both for bangladesh and
+
+ align:start position:0%
+very sensitive both for bangladesh and
+ 
+
+ align:start position:0%
+very sensitive both for bangladesh and
+india and the political history between
+
+ align:start position:0%
+india and the political history between
+ 
+
+ align:start position:0%
+india and the political history between
+bangladesh and india has a sort of
+
+ align:start position:0%
+bangladesh and india has a sort of
+ 
+
+ align:start position:0%
+bangladesh and india has a sort of
+influence in this whole discussion so
+
+ align:start position:0%
+influence in this whole discussion so
+ 
+
+ align:start position:0%
+influence in this whole discussion so
+knowingly or unknowingly sometimes that
+
+ align:start position:0%
+knowingly or unknowingly sometimes that
+ 
+
+ align:start position:0%
+knowingly or unknowingly sometimes that
+political history will
+
+ align:start position:0%
+political history will
+ 
+
+ align:start position:0%
+political history will
+visit us in my
+
+ align:start position:0%
+visit us in my
+ 
+
+ align:start position:0%
+visit us in my
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+presentation so
+
+ align:start position:0%
+presentation so
+ 
+
+ align:start position:0%
+presentation so
+with these two disclaimers i start my
+
+ align:start position:0%
+with these two disclaimers i start my
+ 
+
+ align:start position:0%
+with these two disclaimers i start my
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+first a little bit of history and
+
+ align:start position:0%
+first a little bit of history and
+ 
+
+ align:start position:0%
+first a little bit of history and
+geography
+
+ align:start position:0%
+geography
+ 
+
+ align:start position:0%
+geography
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you all know about the indian
+
+ align:start position:0%
+you all know about the indian
+ 
+
+ align:start position:0%
+you all know about the indian
+subcontinent that there are many
+
+ align:start position:0%
+subcontinent that there are many
+ 
+
+ align:start position:0%
+subcontinent that there are many
+countries it was basically under the
+
+ align:start position:0%
+countries it was basically under the
+ 
+
+ align:start position:0%
+countries it was basically under the
+british rule for 200 years and before
+
+ align:start position:0%
+british rule for 200 years and before
+ 
+
+ align:start position:0%
+british rule for 200 years and before
+that it was 600 years under the mughals
+
+ align:start position:0%
+that it was 600 years under the mughals
+ 
+
+ align:start position:0%
+that it was 600 years under the mughals
+of the or the muslims
+
+ align:start position:0%
+of the or the muslims
+ 
+
+ align:start position:0%
+of the or the muslims
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+before 1947 at the left most the huge
+
+ align:start position:0%
+before 1947 at the left most the huge
+ 
+
+ align:start position:0%
+before 1947 at the left most the huge
+map that you see total blue
+
+ align:start position:0%
+map that you see total blue
+ 
+
+ align:start position:0%
+map that you see total blue
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+situation of indian subcontinent and in
+
+ align:start position:0%
+situation of indian subcontinent and in
+ 
+
+ align:start position:0%
+situation of indian subcontinent and in
+1947 uh right after the second world war
+
+ align:start position:0%
+1947 uh right after the second world war
+ 
+
+ align:start position:0%
+1947 uh right after the second world war
+the indian subcontinent was divided into
+
+ align:start position:0%
+the indian subcontinent was divided into
+ 
+
+ align:start position:0%
+the indian subcontinent was divided into
+two and that is after the partition in
+
+ align:start position:0%
+two and that is after the partition in
+ 
+
+ align:start position:0%
+two and that is after the partition in
+1947 you can see the green part still
+
+ align:start position:0%
+1947 you can see the green part still
+ 
+
+ align:start position:0%
+1947 you can see the green part still
+stays
+
+ align:start position:0%
+stays
+ 
+
+ align:start position:0%
+stays
+the india the the present-day india and
+
+ align:start position:0%
+the india the the present-day india and
+ 
+
+ align:start position:0%
+the india the the present-day india and
+the orange part deep orange part that is
+
+ align:start position:0%
+the orange part deep orange part that is
+ 
+
+ align:start position:0%
+the orange part deep orange part that is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+on the upper side it's west pakistan and
+
+ align:start position:0%
+on the upper side it's west pakistan and
+ 
+
+ align:start position:0%
+on the upper side it's west pakistan and
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+lower side this small country it's east
+
+ align:start position:0%
+lower side this small country it's east
+ 
+
+ align:start position:0%
+lower side this small country it's east
+pakistan which is the modern-day
+
+ align:start position:0%
+pakistan which is the modern-day
+ 
+
+ align:start position:0%
+pakistan which is the modern-day
+bangladesh
+
+ align:start position:0%
+bangladesh
+ 
+
+ align:start position:0%
+bangladesh
+so in 1971
+
+ align:start position:0%
+so in 1971
+ 
+
+ align:start position:0%
+so in 1971
+we had a
+
+ align:start position:0%
+we had a
+ 
+
+ align:start position:0%
+we had a
+we had a war against the western part of
+
+ align:start position:0%
+we had a war against the western part of
+ 
+
+ align:start position:0%
+we had a war against the western part of
+western part of pakistan uh it was
+
+ align:start position:0%
+western part of pakistan uh it was
+ 
+
+ align:start position:0%
+western part of pakistan uh it was
+actually very natural you see that there
+
+ align:start position:0%
+actually very natural you see that there
+ 
+
+ align:start position:0%
+actually very natural you see that there
+is like almost
+
+ align:start position:0%
+is like almost
+ 
+
+ align:start position:0%
+is like almost
+2000 miles gap between the two parts so
+
+ align:start position:0%
+2000 miles gap between the two parts so
+ 
+
+ align:start position:0%
+2000 miles gap between the two parts so
+it was sort of obvious for many reasons
+
+ align:start position:0%
+it was sort of obvious for many reasons
+ 
+
+ align:start position:0%
+it was sort of obvious for many reasons
+so in 1971 uh this
+
+ align:start position:0%
+so in 1971 uh this
+ 
+
+ align:start position:0%
+so in 1971 uh this
+first one single country that is india
+
+ align:start position:0%
+first one single country that is india
+ 
+
+ align:start position:0%
+first one single country that is india
+second india and pakistan and after 71
+
+ align:start position:0%
+second india and pakistan and after 71
+ 
+
+ align:start position:0%
+second india and pakistan and after 71
+it became three countries that is india
+
+ align:start position:0%
+it became three countries that is india
+ 
+
+ align:start position:0%
+it became three countries that is india
+pakistan and bangladesh
+
+ align:start position:0%
+pakistan and bangladesh
+ 
+
+ align:start position:0%
+pakistan and bangladesh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is the case
+
+ align:start position:0%
+this is the case
+ 
+
+ align:start position:0%
+this is the case
+and here uh
+
+ align:start position:0%
+and here uh
+ 
+
+ align:start position:0%
+and here uh
+i'm bringing this little bit of a little
+
+ align:start position:0%
+i'm bringing this little bit of a little
+ 
+
+ align:start position:0%
+i'm bringing this little bit of a little
+bit of history to explain the
+
+ align:start position:0%
+bit of history to explain the
+ 
+
+ align:start position:0%
+bit of history to explain the
+relationship dynamics of bangladesh
+
+ align:start position:0%
+relationship dynamics of bangladesh
+ 
+
+ align:start position:0%
+relationship dynamics of bangladesh
+india because without bringing the real
+
+ align:start position:0%
+india because without bringing the real
+ 
+
+ align:start position:0%
+india because without bringing the real
+estate dynamics between bangladesh and
+
+ align:start position:0%
+estate dynamics between bangladesh and
+ 
+
+ align:start position:0%
+estate dynamics between bangladesh and
+india it is
+
+ align:start position:0%
+india it is
+ 
+
+ align:start position:0%
+india it is
+kind of tough to understand that how and
+
+ align:start position:0%
+kind of tough to understand that how and
+ 
+
+ align:start position:0%
+kind of tough to understand that how and
+why this treaty is so sensitive
+
+ align:start position:0%
+why this treaty is so sensitive
+ 
+
+ align:start position:0%
+why this treaty is so sensitive
+so here we can see that in 1916 december
+
+ align:start position:0%
+so here we can see that in 1916 december
+ 
+
+ align:start position:0%
+so here we can see that in 1916 december
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+you can see this is the surrender
+
+ align:start position:0%
+you can see this is the surrender
+ 
+
+ align:start position:0%
+you can see this is the surrender
+ceremony this is the surrender ceremony
+
+ align:start position:0%
+ceremony this is the surrender ceremony
+ 
+
+ align:start position:0%
+ceremony this is the surrender ceremony
+of the occupying force in 16 december
+
+ align:start position:0%
+of the occupying force in 16 december
+ 
+
+ align:start position:0%
+of the occupying force in 16 december
+and in the left side three million uh
+
+ align:start position:0%
+and in the left side three million uh
+ 
+
+ align:start position:0%
+and in the left side three million uh
+people that is the official number
+
+ align:start position:0%
+people that is the official number
+ 
+
+ align:start position:0%
+people that is the official number
+bangladesh claims uh it is disputed but
+
+ align:start position:0%
+bangladesh claims uh it is disputed but
+ 
+
+ align:start position:0%
+bangladesh claims uh it is disputed but
+uh this is the official number that it
+
+ align:start position:0%
+uh this is the official number that it
+ 
+
+ align:start position:0%
+uh this is the official number that it
+was killed so there was
+
+ align:start position:0%
+was killed so there was
+ 
+
+ align:start position:0%
+was killed so there was
+we said that there has been genocide and
+
+ align:start position:0%
+we said that there has been genocide and
+ 
+
+ align:start position:0%
+we said that there has been genocide and
+murder which happens almost in all the
+
+ align:start position:0%
+murder which happens almost in all the
+ 
+
+ align:start position:0%
+murder which happens almost in all the
+words so this is the surrender ceremony
+
+ align:start position:0%
+words so this is the surrender ceremony
+ 
+
+ align:start position:0%
+words so this is the surrender ceremony
+and there is an interesting fact you
+
+ align:start position:0%
+and there is an interesting fact you
+ 
+
+ align:start position:0%
+and there is an interesting fact you
+will see
+
+ align:start position:0%
+will see
+ 
+
+ align:start position:0%
+will see
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+in the left side someone who is signing
+
+ align:start position:0%
+in the left side someone who is signing
+ 
+
+ align:start position:0%
+in the left side someone who is signing
+for bangladesh this is an indian indian
+
+ align:start position:0%
+for bangladesh this is an indian indian
+ 
+
+ align:start position:0%
+for bangladesh this is an indian indian
+general uh general jagat singh aurora so
+
+ align:start position:0%
+general uh general jagat singh aurora so
+ 
+
+ align:start position:0%
+general uh general jagat singh aurora so
+you can understand the historical
+
+ align:start position:0%
+you can understand the historical
+ 
+
+ align:start position:0%
+you can understand the historical
+connection between india and bangladesh
+
+ align:start position:0%
+connection between india and bangladesh
+ 
+
+ align:start position:0%
+connection between india and bangladesh
+it's very deep and it used to be
+
+ align:start position:0%
+it's very deep and it used to be
+ 
+
+ align:start position:0%
+it's very deep and it used to be
+during the liberation war
+
+ align:start position:0%
+during the liberation war
+ 
+
+ align:start position:0%
+during the liberation war
+india india directly helped us
+
+ align:start position:0%
+india india directly helped us
+ 
+
+ align:start position:0%
+india india directly helped us
+militarily and later after the
+
+ align:start position:0%
+militarily and later after the
+ 
+
+ align:start position:0%
+militarily and later after the
+independence which both the parties
+
+ align:start position:0%
+independence which both the parties
+ 
+
+ align:start position:0%
+independence which both the parties
+considered that both india and
+
+ align:start position:0%
+considered that both india and
+ 
+
+ align:start position:0%
+considered that both india and
+bangladesh should be very friendly
+
+ align:start position:0%
+bangladesh should be very friendly
+ 
+
+ align:start position:0%
+bangladesh should be very friendly
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+after the after the independence that
+
+ align:start position:0%
+after the after the independence that
+ 
+
+ align:start position:0%
+after the after the independence that
+actually changed and major anti-indian
+
+ align:start position:0%
+actually changed and major anti-indian
+ 
+
+ align:start position:0%
+actually changed and major anti-indian
+sentiment has been present there and one
+
+ align:start position:0%
+sentiment has been present there and one
+ 
+
+ align:start position:0%
+sentiment has been present there and one
+of the reasons this happened is that
+
+ align:start position:0%
+of the reasons this happened is that
+ 
+
+ align:start position:0%
+of the reasons this happened is that
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+pharah
+
+ align:start position:0%
+pharah
+ 
+
+ align:start position:0%
+pharah
+dam which has created serious trouble
+
+ align:start position:0%
+dam which has created serious trouble
+ 
+
+ align:start position:0%
+dam which has created serious trouble
+for bangladesh and for that gradually
+
+ align:start position:0%
+for bangladesh and for that gradually
+ 
+
+ align:start position:0%
+for bangladesh and for that gradually
+there has been some treaties and it was
+
+ align:start position:0%
+there has been some treaties and it was
+ 
+
+ align:start position:0%
+there has been some treaties and it was
+so serious uh that let me explain the
+
+ align:start position:0%
+so serious uh that let me explain the
+ 
+
+ align:start position:0%
+so serious uh that let me explain the
+basin a little bit first so i would be
+
+ align:start position:0%
+basin a little bit first so i would be
+ 
+
+ align:start position:0%
+basin a little bit first so i would be
+reading from an article by either roman
+
+ align:start position:0%
+reading from an article by either roman
+ 
+
+ align:start position:0%
+reading from an article by either roman
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is the dangerous water basin you
+
+ align:start position:0%
+this is the dangerous water basin you
+ 
+
+ align:start position:0%
+this is the dangerous water basin you
+can see that from here the
+
+ align:start position:0%
+can see that from here the
+ 
+
+ align:start position:0%
+can see that from here the
+the ganges is coming and coming and
+
+ align:start position:0%
+the ganges is coming and coming and
+ 
+
+ align:start position:0%
+the ganges is coming and coming and
+coming and it is entering from the
+
+ align:start position:0%
+coming and it is entering from the
+ 
+
+ align:start position:0%
+coming and it is entering from the
+hugely hugely falls in the
+
+ align:start position:0%
+hugely hugely falls in the
+ 
+
+ align:start position:0%
+hugely hugely falls in the
+west bengal so previously before the
+
+ align:start position:0%
+west bengal so previously before the
+ 
+
+ align:start position:0%
+west bengal so previously before the
+partition uh bengal was uh united so
+
+ align:start position:0%
+partition uh bengal was uh united so
+ 
+
+ align:start position:0%
+partition uh bengal was uh united so
+there was no east bengal or west bengal
+
+ align:start position:0%
+there was no east bengal or west bengal
+ 
+
+ align:start position:0%
+there was no east bengal or west bengal
+so after after the partition uh one part
+
+ align:start position:0%
+so after after the partition uh one part
+ 
+
+ align:start position:0%
+so after after the partition uh one part
+of bengal fall into india we speak the
+
+ align:start position:0%
+of bengal fall into india we speak the
+ 
+
+ align:start position:0%
+of bengal fall into india we speak the
+same language our culture is almost same
+
+ align:start position:0%
+same language our culture is almost same
+ 
+
+ align:start position:0%
+same language our culture is almost same
+the religion is a little bit different
+
+ align:start position:0%
+the religion is a little bit different
+ 
+
+ align:start position:0%
+the religion is a little bit different
+religion uh the hindu majority is in the
+
+ align:start position:0%
+religion uh the hindu majority is in the
+ 
+
+ align:start position:0%
+religion uh the hindu majority is in the
+western part the west bengal and the
+
+ align:start position:0%
+western part the west bengal and the
+ 
+
+ align:start position:0%
+western part the west bengal and the
+muslim regulations in the eastern part
+
+ align:start position:0%
+muslim regulations in the eastern part
+ 
+
+ align:start position:0%
+muslim regulations in the eastern part
+because the partition happened for the
+
+ align:start position:0%
+because the partition happened for the
+ 
+
+ align:start position:0%
+because the partition happened for the
+two nations theory that the muslims will
+
+ align:start position:0%
+two nations theory that the muslims will
+ 
+
+ align:start position:0%
+two nations theory that the muslims will
+be living in pakistan and the hindus and
+
+ align:start position:0%
+be living in pakistan and the hindus and
+ 
+
+ align:start position:0%
+be living in pakistan and the hindus and
+other villages will be living in india
+
+ align:start position:0%
+other villages will be living in india
+ 
+
+ align:start position:0%
+other villages will be living in india
+so that was the theory but that didn't
+
+ align:start position:0%
+so that was the theory but that didn't
+ 
+
+ align:start position:0%
+so that was the theory but that didn't
+work so
+
+ align:start position:0%
+work so
+ 
+
+ align:start position:0%
+work so
+here when when we speak about this uh uh
+
+ align:start position:0%
+here when when we speak about this uh uh
+ 
+
+ align:start position:0%
+here when when we speak about this uh uh
+ganges uh water basin we would speak
+
+ align:start position:0%
+ganges uh water basin we would speak
+ 
+
+ align:start position:0%
+ganges uh water basin we would speak
+about the ganges river the ganges river
+
+ align:start position:0%
+about the ganges river the ganges river
+ 
+
+ align:start position:0%
+about the ganges river the ganges river
+originates in the central himalayan at
+
+ align:start position:0%
+originates in the central himalayan at
+ 
+
+ align:start position:0%
+originates in the central himalayan at
+the altitude of uh seven uh seven
+
+ align:start position:0%
+the altitude of uh seven uh seven
+ 
+
+ align:start position:0%
+the altitude of uh seven uh seven
+thousand ten meters and extends into the
+
+ align:start position:0%
+thousand ten meters and extends into the
+ 
+
+ align:start position:0%
+thousand ten meters and extends into the
+alluvial
+
+ align:start position:0%
+alluvial
+ 
+
+ align:start position:0%
+alluvial
+gangetic plains and drains into the
+
+ align:start position:0%
+gangetic plains and drains into the
+ 
+
+ align:start position:0%
+gangetic plains and drains into the
+indian ocean at the bay of bengal
+
+ align:start position:0%
+indian ocean at the bay of bengal
+ 
+
+ align:start position:0%
+indian ocean at the bay of bengal
+the ganges is a trans-boundary river
+
+ align:start position:0%
+the ganges is a trans-boundary river
+ 
+
+ align:start position:0%
+the ganges is a trans-boundary river
+which has a total length of
+
+ align:start position:0%
+which has a total length of
+ 
+
+ align:start position:0%
+which has a total length of
+approximately uh 2600 kilometer and a
+
+ align:start position:0%
+approximately uh 2600 kilometer and a
+ 
+
+ align:start position:0%
+approximately uh 2600 kilometer and a
+total catchment area of
+
+ align:start position:0%
+total catchment area of
+ 
+
+ align:start position:0%
+total catchment area of
+1 million eighty seven thousand square
+
+ align:start position:0%
+1 million eighty seven thousand square
+ 
+
+ align:start position:0%
+1 million eighty seven thousand square
+kilometer
+
+ align:start position:0%
+kilometer
+ 
+
+ align:start position:0%
+kilometer
+the river basin spreads occurred across
+
+ align:start position:0%
+the river basin spreads occurred across
+ 
+
+ align:start position:0%
+the river basin spreads occurred across
+india nepal china and bangladesh where
+
+ align:start position:0%
+india nepal china and bangladesh where
+ 
+
+ align:start position:0%
+india nepal china and bangladesh where
+india shares the major portion which is
+
+ align:start position:0%
+india shares the major portion which is
+ 
+
+ align:start position:0%
+india shares the major portion which is
+79 percent of the total basin area and
+
+ align:start position:0%
+79 percent of the total basin area and
+ 
+
+ align:start position:0%
+79 percent of the total basin area and
+in contrast bangladesh is the furthest
+
+ align:start position:0%
+in contrast bangladesh is the furthest
+ 
+
+ align:start position:0%
+in contrast bangladesh is the furthest
+downstream country of the basin and
+
+ align:start position:0%
+downstream country of the basin and
+ 
+
+ align:start position:0%
+downstream country of the basin and
+shares only about four percent of the
+
+ align:start position:0%
+shares only about four percent of the
+ 
+
+ align:start position:0%
+shares only about four percent of the
+base in area which nevertheless
+
+ align:start position:0%
+base in area which nevertheless
+ 
+
+ align:start position:0%
+base in area which nevertheless
+represents 37 percent of the total area
+
+ align:start position:0%
+represents 37 percent of the total area
+ 
+
+ align:start position:0%
+represents 37 percent of the total area
+of bangladesh
+
+ align:start position:0%
+of bangladesh
+ 
+
+ align:start position:0%
+of bangladesh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the hydrological cycle and water
+
+ align:start position:0%
+the hydrological cycle and water
+ 
+
+ align:start position:0%
+the hydrological cycle and water
+resources of the ganges basin are
+
+ align:start position:0%
+resources of the ganges basin are
+ 
+
+ align:start position:0%
+resources of the ganges basin are
+governed by
+
+ align:start position:0%
+governed by
+ 
+
+ align:start position:0%
+governed by
+a southwest moonsoon are characterized
+
+ align:start position:0%
+a southwest moonsoon are characterized
+ 
+
+ align:start position:0%
+a southwest moonsoon are characterized
+by high temperature heavy rainfall
+
+ align:start position:0%
+by high temperature heavy rainfall
+ 
+
+ align:start position:0%
+by high temperature heavy rainfall
+strong seasonal variations the region is
+
+ align:start position:0%
+strong seasonal variations the region is
+ 
+
+ align:start position:0%
+strong seasonal variations the region is
+characterized by flooding in the wet
+
+ align:start position:0%
+characterized by flooding in the wet
+ 
+
+ align:start position:0%
+characterized by flooding in the wet
+season which is due to october
+
+ align:start position:0%
+season which is due to october
+ 
+
+ align:start position:0%
+season which is due to october
+and water scarcity in the dry season
+
+ align:start position:0%
+and water scarcity in the dry season
+ 
+
+ align:start position:0%
+and water scarcity in the dry season
+which is november to may and during the
+
+ align:start position:0%
+which is november to may and during the
+ 
+
+ align:start position:0%
+which is november to may and during the
+muslim season there is an abundance of
+
+ align:start position:0%
+muslim season there is an abundance of
+ 
+
+ align:start position:0%
+muslim season there is an abundance of
+water but during non-muslim season a
+
+ align:start position:0%
+water but during non-muslim season a
+ 
+
+ align:start position:0%
+water but during non-muslim season a
+lower precipitation causes a reduced
+
+ align:start position:0%
+lower precipitation causes a reduced
+ 
+
+ align:start position:0%
+lower precipitation causes a reduced
+flow in the basin the insufficient
+
+ align:start position:0%
+flow in the basin the insufficient
+ 
+
+ align:start position:0%
+flow in the basin the insufficient
+supply of water in the downstream during
+
+ align:start position:0%
+supply of water in the downstream during
+ 
+
+ align:start position:0%
+supply of water in the downstream during
+the dry season causes significant
+
+ align:start position:0%
+the dry season causes significant
+ 
+
+ align:start position:0%
+the dry season causes significant
+socio-economic impacts
+
+ align:start position:0%
+socio-economic impacts
+ 
+
+ align:start position:0%
+socio-economic impacts
+through disruption to the agriculture
+
+ align:start position:0%
+through disruption to the agriculture
+ 
+
+ align:start position:0%
+through disruption to the agriculture
+fisheries forestry and navigation of
+
+ align:start position:0%
+fisheries forestry and navigation of
+ 
+
+ align:start position:0%
+fisheries forestry and navigation of
+this of this region so here
+
+ align:start position:0%
+this of this region so here
+ 
+
+ align:start position:0%
+this of this region so here
+we can see a little bit more details of
+
+ align:start position:0%
+we can see a little bit more details of
+ 
+
+ align:start position:0%
+we can see a little bit more details of
+the close-up that the ganges river that
+
+ align:start position:0%
+the close-up that the ganges river that
+ 
+
+ align:start position:0%
+the close-up that the ganges river that
+is he entering here is the farah kadam
+
+ align:start position:0%
+is he entering here is the farah kadam
+ 
+
+ align:start position:0%
+is he entering here is the farah kadam
+and here it's it's it's
+
+ align:start position:0%
+and here it's it's it's
+ 
+
+ align:start position:0%
+and here it's it's it's
+ganges entire enter bangladesh
+
+ align:start position:0%
+ganges entire enter bangladesh
+ 
+
+ align:start position:0%
+ganges entire enter bangladesh
+through the the west bengal the hoogly
+
+ align:start position:0%
+through the the west bengal the hoogly
+ 
+
+ align:start position:0%
+through the the west bengal the hoogly
+area river and it enters and it becomes
+
+ align:start position:0%
+area river and it enters and it becomes
+ 
+
+ align:start position:0%
+area river and it enters and it becomes
+pogba which is the biggest river in
+
+ align:start position:0%
+pogba which is the biggest river in
+ 
+
+ align:start position:0%
+pogba which is the biggest river in
+bangladesh also which is the
+
+ align:start position:0%
+bangladesh also which is the
+ 
+
+ align:start position:0%
+bangladesh also which is the
+economically most significant river in
+
+ align:start position:0%
+economically most significant river in
+ 
+
+ align:start position:0%
+economically most significant river in
+bangladesh
+
+ align:start position:0%
+bangladesh
+ 
+
+ align:start position:0%
+bangladesh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the impact you can see in the next
+
+ align:start position:0%
+the impact you can see in the next
+ 
+
+ align:start position:0%
+the impact you can see in the next
+picture you can see that in the in the
+
+ align:start position:0%
+picture you can see that in the in the
+ 
+
+ align:start position:0%
+picture you can see that in the in the
+lower part which means this part this
+
+ align:start position:0%
+lower part which means this part this
+ 
+
+ align:start position:0%
+lower part which means this part this
+whole part this this ganges delta the
+
+ align:start position:0%
+whole part this this ganges delta the
+ 
+
+ align:start position:0%
+whole part this this ganges delta the
+lower part the
+
+ align:start position:0%
+lower part the
+ 
+
+ align:start position:0%
+lower part the
+the ganges river when it enters
+
+ align:start position:0%
+the ganges river when it enters
+ 
+
+ align:start position:0%
+the ganges river when it enters
+bangladesh it becomes pogba and
+
+ align:start position:0%
+bangladesh it becomes pogba and
+ 
+
+ align:start position:0%
+bangladesh it becomes pogba and
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+change in the flow or any climatic
+
+ align:start position:0%
+change in the flow or any climatic
+ 
+
+ align:start position:0%
+change in the flow or any climatic
+change or any man-made change has
+
+ align:start position:0%
+change or any man-made change has
+ 
+
+ align:start position:0%
+change or any man-made change has
+serious impact in the lower region of
+
+ align:start position:0%
+serious impact in the lower region of
+ 
+
+ align:start position:0%
+serious impact in the lower region of
+the southern part of bangladesh and
+
+ align:start position:0%
+the southern part of bangladesh and
+ 
+
+ align:start position:0%
+the southern part of bangladesh and
+i actually have seen uh directly because
+
+ align:start position:0%
+i actually have seen uh directly because
+ 
+
+ align:start position:0%
+i actually have seen uh directly because
+uh my home hometown is actually in the
+
+ align:start position:0%
+uh my home hometown is actually in the
+ 
+
+ align:start position:0%
+uh my home hometown is actually in the
+bhagavata area which is in this region
+
+ align:start position:0%
+bhagavata area which is in this region
+ 
+
+ align:start position:0%
+bhagavata area which is in this region
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+although it's like anecdotal experience
+
+ align:start position:0%
+although it's like anecdotal experience
+ 
+
+ align:start position:0%
+although it's like anecdotal experience
+but i can actually see that like our uh
+
+ align:start position:0%
+but i can actually see that like our uh
+ 
+
+ align:start position:0%
+but i can actually see that like our uh
+village area it was
+
+ align:start position:0%
+village area it was
+ 
+
+ align:start position:0%
+village area it was
+it was actually very uh full of flora
+
+ align:start position:0%
+it was actually very uh full of flora
+ 
+
+ align:start position:0%
+it was actually very uh full of flora
+and funa but with time it actually
+
+ align:start position:0%
+and funa but with time it actually
+ 
+
+ align:start position:0%
+and funa but with time it actually
+reduced and now that when i go to go to
+
+ align:start position:0%
+reduced and now that when i go to go to
+ 
+
+ align:start position:0%
+reduced and now that when i go to go to
+the village after like five or ten years
+
+ align:start position:0%
+the village after like five or ten years
+ 
+
+ align:start position:0%
+the village after like five or ten years
+we see that it has totally changed so
+
+ align:start position:0%
+we see that it has totally changed so
+ 
+
+ align:start position:0%
+we see that it has totally changed so
+this actually matches with the academic
+
+ align:start position:0%
+this actually matches with the academic
+ 
+
+ align:start position:0%
+this actually matches with the academic
+articles that i've read here so
+
+ align:start position:0%
+articles that i've read here so
+ 
+
+ align:start position:0%
+articles that i've read here so
+what are the major water diplomacy
+
+ align:start position:0%
+what are the major water diplomacy
+ 
+
+ align:start position:0%
+what are the major water diplomacy
+events between bangladesh india since
+
+ align:start position:0%
+events between bangladesh india since
+ 
+
+ align:start position:0%
+events between bangladesh india since
+1971 as you know that
+
+ align:start position:0%
+1971 as you know that
+ 
+
+ align:start position:0%
+1971 as you know that
+in 1971 bangladesh became independent
+
+ align:start position:0%
+in 1971 bangladesh became independent
+ 
+
+ align:start position:0%
+in 1971 bangladesh became independent
+and india had direct help india debate
+
+ align:start position:0%
+and india had direct help india debate
+ 
+
+ align:start position:0%
+and india had direct help india debate
+contribution towards that so in 1972
+
+ align:start position:0%
+contribution towards that so in 1972
+ 
+
+ align:start position:0%
+contribution towards that so in 1972
+right after uh bangladesh became
+
+ align:start position:0%
+right after uh bangladesh became
+ 
+
+ align:start position:0%
+right after uh bangladesh became
+independent in 1971 december and in 1972
+
+ align:start position:0%
+independent in 1971 december and in 1972
+ 
+
+ align:start position:0%
+independent in 1971 december and in 1972
+the bangladesh father of the nation
+
+ align:start position:0%
+the bangladesh father of the nation
+ 
+
+ align:start position:0%
+the bangladesh father of the nation
+straight medieval roman and indian prime
+
+ align:start position:0%
+straight medieval roman and indian prime
+ 
+
+ align:start position:0%
+straight medieval roman and indian prime
+minister uh indira gandhi they sat down
+
+ align:start position:0%
+minister uh indira gandhi they sat down
+ 
+
+ align:start position:0%
+minister uh indira gandhi they sat down
+water was actually an issue back then
+
+ align:start position:0%
+water was actually an issue back then
+ 
+
+ align:start position:0%
+water was actually an issue back then
+what was actually an issue back then
+
+ align:start position:0%
+what was actually an issue back then
+ 
+
+ align:start position:0%
+what was actually an issue back then
+between india and pakistan uh especially
+
+ align:start position:0%
+between india and pakistan uh especially
+ 
+
+ align:start position:0%
+between india and pakistan uh especially
+this far far akadam the ganges river
+
+ align:start position:0%
+this far far akadam the ganges river
+ 
+
+ align:start position:0%
+this far far akadam the ganges river
+water sharing treaty so
+
+ align:start position:0%
+water sharing treaty so
+ 
+
+ align:start position:0%
+water sharing treaty so
+for the first time this actually sat
+
+ align:start position:0%
+for the first time this actually sat
+ 
+
+ align:start position:0%
+for the first time this actually sat
+down immediately after uh immediately
+
+ align:start position:0%
+down immediately after uh immediately
+ 
+
+ align:start position:0%
+down immediately after uh immediately
+after the independence in 1972 which
+
+ align:start position:0%
+after the independence in 1972 which
+ 
+
+ align:start position:0%
+after the independence in 1972 which
+actually shows that how important it is
+
+ align:start position:0%
+actually shows that how important it is
+ 
+
+ align:start position:0%
+actually shows that how important it is
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+for the region to maintain the peace and
+
+ align:start position:0%
+for the region to maintain the peace and
+ 
+
+ align:start position:0%
+for the region to maintain the peace and
+tranquility between the two countries so
+
+ align:start position:0%
+tranquility between the two countries so
+ 
+
+ align:start position:0%
+tranquility between the two countries so
+the first joint water commission between
+
+ align:start position:0%
+the first joint water commission between
+ 
+
+ align:start position:0%
+the first joint water commission between
+india and bangladesh was established in
+
+ align:start position:0%
+india and bangladesh was established in
+ 
+
+ align:start position:0%
+india and bangladesh was established in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this newly made joint water commission
+
+ align:start position:0%
+this newly made joint water commission
+ 
+
+ align:start position:0%
+this newly made joint water commission
+between india and bangladesh actually
+
+ align:start position:0%
+between india and bangladesh actually
+ 
+
+ align:start position:0%
+between india and bangladesh actually
+tried to survey and they tried to
+
+ align:start position:0%
+tried to survey and they tried to
+ 
+
+ align:start position:0%
+tried to survey and they tried to
+determine what are the course of actions
+
+ align:start position:0%
+determine what are the course of actions
+ 
+
+ align:start position:0%
+determine what are the course of actions
+that can be taken because for decades
+
+ align:start position:0%
+that can be taken because for decades
+ 
+
+ align:start position:0%
+that can be taken because for decades
+decades for india pakistan rivalry no
+
+ align:start position:0%
+decades for india pakistan rivalry no
+ 
+
+ align:start position:0%
+decades for india pakistan rivalry no
+development actually happened so in 1974
+
+ align:start position:0%
+development actually happened so in 1974
+ 
+
+ align:start position:0%
+development actually happened so in 1974
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it was declared by that commission that
+
+ align:start position:0%
+it was declared by that commission that
+ 
+
+ align:start position:0%
+it was declared by that commission that
+there was this joint declaration to
+
+ align:start position:0%
+there was this joint declaration to
+ 
+
+ align:start position:0%
+there was this joint declaration to
+resolve water sharing issues the
+
+ align:start position:0%
+resolve water sharing issues the
+ 
+
+ align:start position:0%
+resolve water sharing issues the
+existing issues that were there but in
+
+ align:start position:0%
+existing issues that were there but in
+ 
+
+ align:start position:0%
+existing issues that were there but in
+1975 uh bangladesh
+
+ align:start position:0%
+1975 uh bangladesh
+ 
+
+ align:start position:0%
+1975 uh bangladesh
+was killed with his family and there was
+
+ align:start position:0%
+was killed with his family and there was
+ 
+
+ align:start position:0%
+was killed with his family and there was
+a kudeta and the military took over so
+
+ align:start position:0%
+a kudeta and the military took over so
+ 
+
+ align:start position:0%
+a kudeta and the military took over so
+in 1976 uh india unilaterally withdrew
+
+ align:start position:0%
+in 1976 uh india unilaterally withdrew
+ 
+
+ align:start position:0%
+in 1976 uh india unilaterally withdrew
+from this declaration
+
+ align:start position:0%
+from this declaration
+ 
+
+ align:start position:0%
+from this declaration
+so after uh after this happened in 1977
+
+ align:start position:0%
+so after uh after this happened in 1977
+ 
+
+ align:start position:0%
+so after uh after this happened in 1977
+there was this temporary five-year
+
+ align:start position:0%
+there was this temporary five-year
+ 
+
+ align:start position:0%
+there was this temporary five-year
+treaty which ended in 1982
+
+ align:start position:0%
+treaty which ended in 1982
+ 
+
+ align:start position:0%
+treaty which ended in 1982
+uh which started in 1977 during the
+
+ align:start position:0%
+uh which started in 1977 during the
+ 
+
+ align:start position:0%
+uh which started in 1977 during the
+bangladesh national party regime which
+
+ align:start position:0%
+bangladesh national party regime which
+ 
+
+ align:start position:0%
+bangladesh national party regime which
+is the which is uh historically
+
+ align:start position:0%
+is the which is uh historically
+ 
+
+ align:start position:0%
+is the which is uh historically
+considered as anti-india
+
+ align:start position:0%
+considered as anti-india
+ 
+
+ align:start position:0%
+considered as anti-india
+so in 1982 it was not renewed and after
+
+ align:start position:0%
+so in 1982 it was not renewed and after
+ 
+
+ align:start position:0%
+so in 1982 it was not renewed and after
+that after long break in 1996 uh there
+
+ align:start position:0%
+that after long break in 1996 uh there
+ 
+
+ align:start position:0%
+that after long break in 1996 uh there
+was this treaty between india and
+
+ align:start position:0%
+was this treaty between india and
+ 
+
+ align:start position:0%
+was this treaty between india and
+bangladesh which is a ganges water
+
+ align:start position:0%
+bangladesh which is a ganges water
+ 
+
+ align:start position:0%
+bangladesh which is a ganges water
+sharing treaty between bangladesh india
+
+ align:start position:0%
+sharing treaty between bangladesh india
+ 
+
+ align:start position:0%
+sharing treaty between bangladesh india
+which was signed by
+
+ align:start position:0%
+which was signed by
+ 
+
+ align:start position:0%
+which was signed by
+uh dev gorda the veteran prime minister
+
+ align:start position:0%
+uh dev gorda the veteran prime minister
+ 
+
+ align:start position:0%
+uh dev gorda the veteran prime minister
+of india and the present prime minister
+
+ align:start position:0%
+of india and the present prime minister
+ 
+
+ align:start position:0%
+of india and the present prime minister
+of bangladesh uh sheikh hasina
+
+ align:start position:0%
+of bangladesh uh sheikh hasina
+ 
+
+ align:start position:0%
+of bangladesh uh sheikh hasina
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is more or less the major
+
+ align:start position:0%
+this is more or less the major
+ 
+
+ align:start position:0%
+this is more or less the major
+developments and there is this uh
+
+ align:start position:0%
+developments and there is this uh
+ 
+
+ align:start position:0%
+developments and there is this uh
+interesting uh interesting uh fact that
+
+ align:start position:0%
+interesting uh interesting uh fact that
+ 
+
+ align:start position:0%
+interesting uh interesting uh fact that
+is there
+
+ align:start position:0%
+is there
+ 
+
+ align:start position:0%
+is there
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+from india to bangladesh 54 rivers
+
+ align:start position:0%
+from india to bangladesh 54 rivers
+ 
+
+ align:start position:0%
+from india to bangladesh 54 rivers
+actually come and bangladesh is in the
+
+ align:start position:0%
+actually come and bangladesh is in the
+ 
+
+ align:start position:0%
+actually come and bangladesh is in the
+downstream and india is in the upstream
+
+ align:start position:0%
+downstream and india is in the upstream
+ 
+
+ align:start position:0%
+downstream and india is in the upstream
+54 rivers from india bangladesh is a
+
+ align:start position:0%
+54 rivers from india bangladesh is a
+ 
+
+ align:start position:0%
+54 rivers from india bangladesh is a
+rivalry country there is like hundreds
+
+ align:start position:0%
+rivalry country there is like hundreds
+ 
+
+ align:start position:0%
+rivalry country there is like hundreds
+of rivers 54 of them actually comes from
+
+ align:start position:0%
+of rivers 54 of them actually comes from
+ 
+
+ align:start position:0%
+of rivers 54 of them actually comes from
+india and it is spread in bangladesh
+
+ align:start position:0%
+india and it is spread in bangladesh
+ 
+
+ align:start position:0%
+india and it is spread in bangladesh
+throughout just like a net
+
+ align:start position:0%
+throughout just like a net
+ 
+
+ align:start position:0%
+throughout just like a net
+but unfortunately so far there has been
+
+ align:start position:0%
+but unfortunately so far there has been
+ 
+
+ align:start position:0%
+but unfortunately so far there has been
+only one treaty uh one proper treaty
+
+ align:start position:0%
+only one treaty uh one proper treaty
+ 
+
+ align:start position:0%
+only one treaty uh one proper treaty
+which is the
+
+ align:start position:0%
+which is the
+ 
+
+ align:start position:0%
+which is the
+the ganges water treaty we treat sharing
+
+ align:start position:0%
+the ganges water treaty we treat sharing
+ 
+
+ align:start position:0%
+the ganges water treaty we treat sharing
+and out of uh for last quarter century
+
+ align:start position:0%
+and out of uh for last quarter century
+ 
+
+ align:start position:0%
+and out of uh for last quarter century
+there has been no treaty and
+
+ align:start position:0%
+there has been no treaty and
+ 
+
+ align:start position:0%
+there has been no treaty and
+another water treaty that this water
+
+ align:start position:0%
+another water treaty that this water
+ 
+
+ align:start position:0%
+another water treaty that this water
+treaty there has been many talks but
+
+ align:start position:0%
+treaty there has been many talks but
+ 
+
+ align:start position:0%
+treaty there has been many talks but
+still there has been no development so
+
+ align:start position:0%
+still there has been no development so
+ 
+
+ align:start position:0%
+still there has been no development so
+we can actually understand that why we
+
+ align:start position:0%
+we can actually understand that why we
+ 
+
+ align:start position:0%
+we can actually understand that why we
+are speaking about this ganges water
+
+ align:start position:0%
+are speaking about this ganges water
+ 
+
+ align:start position:0%
+are speaking about this ganges water
+sharing treaty and and its significance
+
+ align:start position:0%
+sharing treaty and and its significance
+ 
+
+ align:start position:0%
+sharing treaty and and its significance
+so what do we find in 1996 what a treaty
+
+ align:start position:0%
+so what do we find in 1996 what a treaty
+ 
+
+ align:start position:0%
+so what do we find in 1996 what a treaty
+between bangladesh and india
+
+ align:start position:0%
+between bangladesh and india
+ 
+
+ align:start position:0%
+between bangladesh and india
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this was the treaty this is the very
+
+ align:start position:0%
+this was the treaty this is the very
+ 
+
+ align:start position:0%
+this was the treaty this is the very
+very minimum that treaty was there uh
+
+ align:start position:0%
+very minimum that treaty was there uh
+ 
+
+ align:start position:0%
+very minimum that treaty was there uh
+the the first uh the first the the first
+
+ align:start position:0%
+the the first uh the first the the first
+ 
+
+ align:start position:0%
+the the first uh the first the the first
+uh the sharings the sharing calculation
+
+ align:start position:0%
+uh the sharings the sharing calculation
+ 
+
+ align:start position:0%
+uh the sharings the sharing calculation
+was like this uh 70 000 accusex or less
+
+ align:start position:0%
+was like this uh 70 000 accusex or less
+ 
+
+ align:start position:0%
+was like this uh 70 000 accusex or less
+water when it's available uh 50 will go
+
+ align:start position:0%
+water when it's available uh 50 will go
+ 
+
+ align:start position:0%
+water when it's available uh 50 will go
+to india 50 percent will go to
+
+ align:start position:0%
+to india 50 percent will go to
+ 
+
+ align:start position:0%
+to india 50 percent will go to
+bangladesh if it's between 70 000 to 75
+
+ align:start position:0%
+bangladesh if it's between 70 000 to 75
+ 
+
+ align:start position:0%
+bangladesh if it's between 70 000 to 75
+000 the india will maintain the balance
+
+ align:start position:0%
+000 the india will maintain the balance
+ 
+
+ align:start position:0%
+000 the india will maintain the balance
+of the flow and the the bangladesh will
+
+ align:start position:0%
+of the flow and the the bangladesh will
+ 
+
+ align:start position:0%
+of the flow and the the bangladesh will
+have remaining at 35 000
+
+ align:start position:0%
+have remaining at 35 000
+ 
+
+ align:start position:0%
+have remaining at 35 000
+and 75 000 q6 or more when when there is
+
+ align:start position:0%
+and 75 000 q6 or more when when there is
+ 
+
+ align:start position:0%
+and 75 000 q6 or more when when there is
+water availability uh 40 000 q6 will go
+
+ align:start position:0%
+water availability uh 40 000 q6 will go
+ 
+
+ align:start position:0%
+water availability uh 40 000 q6 will go
+to india and bangladesh will maintain
+
+ align:start position:0%
+to india and bangladesh will maintain
+ 
+
+ align:start position:0%
+to india and bangladesh will maintain
+balance of the flow so that was the uh
+
+ align:start position:0%
+balance of the flow so that was the uh
+ 
+
+ align:start position:0%
+balance of the flow so that was the uh
+basic uh that was the very basic and the
+
+ align:start position:0%
+basic uh that was the very basic and the
+ 
+
+ align:start position:0%
+basic uh that was the very basic and the
+very minimum of the water sharing water
+
+ align:start position:0%
+very minimum of the water sharing water
+ 
+
+ align:start position:0%
+very minimum of the water sharing water
+treaty between bangladesh and india so
+
+ align:start position:0%
+treaty between bangladesh and india so
+ 
+
+ align:start position:0%
+treaty between bangladesh and india so
+what are the real scenario i mean this
+
+ align:start position:0%
+what are the real scenario i mean this
+ 
+
+ align:start position:0%
+what are the real scenario i mean this
+is the treaty that we have got but what
+
+ align:start position:0%
+is the treaty that we have got but what
+ 
+
+ align:start position:0%
+is the treaty that we have got but what
+is the real scenario so here we can see
+
+ align:start position:0%
+is the real scenario so here we can see
+ 
+
+ align:start position:0%
+is the real scenario so here we can see
+the real scenario that bangladesh has
+
+ align:start position:0%
+the real scenario that bangladesh has
+ 
+
+ align:start position:0%
+the real scenario that bangladesh has
+been frequently deprived of its minimum
+
+ align:start position:0%
+been frequently deprived of its minimum
+ 
+
+ align:start position:0%
+been frequently deprived of its minimum
+share during the most critical periods
+
+ align:start position:0%
+share during the most critical periods
+ 
+
+ align:start position:0%
+share during the most critical periods
+of the dry season and which has caused
+
+ align:start position:0%
+of the dry season and which has caused
+ 
+
+ align:start position:0%
+of the dry season and which has caused
+the loss of agricultural land we created
+
+ align:start position:0%
+the loss of agricultural land we created
+ 
+
+ align:start position:0%
+the loss of agricultural land we created
+problem in salination the wellness of
+
+ align:start position:0%
+problem in salination the wellness of
+ 
+
+ align:start position:0%
+problem in salination the wellness of
+the people has decreased and which has
+
+ align:start position:0%
+the people has decreased and which has
+ 
+
+ align:start position:0%
+the people has decreased and which has
+created uh such a huge issue that in
+
+ align:start position:0%
+created uh such a huge issue that in
+ 
+
+ align:start position:0%
+created uh such a huge issue that in
+every election that bangladesh happens
+
+ align:start position:0%
+every election that bangladesh happens
+ 
+
+ align:start position:0%
+every election that bangladesh happens
+this repeatedly comes
+
+ align:start position:0%
+this repeatedly comes
+ 
+
+ align:start position:0%
+this repeatedly comes
+and during the march 24 to 31 the 10-day
+
+ align:start position:0%
+and during the march 24 to 31 the 10-day
+ 
+
+ align:start position:0%
+and during the march 24 to 31 the 10-day
+cycle in in the year 2010 the actual
+
+ align:start position:0%
+cycle in in the year 2010 the actual
+ 
+
+ align:start position:0%
+cycle in in the year 2010 the actual
+release to bangladesh was 44 lower than
+
+ align:start position:0%
+release to bangladesh was 44 lower than
+ 
+
+ align:start position:0%
+release to bangladesh was 44 lower than
+the indicated release and in 2016 the
+
+ align:start position:0%
+the indicated release and in 2016 the
+ 
+
+ align:start position:0%
+the indicated release and in 2016 the
+situation became even worse than that
+
+ align:start position:0%
+situation became even worse than that
+ 
+
+ align:start position:0%
+situation became even worse than that
+even worse the actual release during
+
+ align:start position:0%
+even worse the actual release during
+ 
+
+ align:start position:0%
+even worse the actual release during
+march 20 to 31 was 47 percent lower than
+
+ align:start position:0%
+march 20 to 31 was 47 percent lower than
+ 
+
+ align:start position:0%
+march 20 to 31 was 47 percent lower than
+the indicative share followed by a
+
+ align:start position:0%
+the indicative share followed by a
+ 
+
+ align:start position:0%
+the indicative share followed by a
+further 34 percent and 49 percent
+
+ align:start position:0%
+further 34 percent and 49 percent
+ 
+
+ align:start position:0%
+further 34 percent and 49 percent
+decrease of flows during the other
+
+ align:start position:0%
+decrease of flows during the other
+ 
+
+ align:start position:0%
+decrease of flows during the other
+alternate critical periods so we can see
+
+ align:start position:0%
+alternate critical periods so we can see
+ 
+
+ align:start position:0%
+alternate critical periods so we can see
+that whatever
+
+ align:start position:0%
+that whatever
+ 
+
+ align:start position:0%
+that whatever
+that is written there in the treaty uh
+
+ align:start position:0%
+that is written there in the treaty uh
+ 
+
+ align:start position:0%
+that is written there in the treaty uh
+unfortunately this is not
+
+ align:start position:0%
+unfortunately this is not
+ 
+
+ align:start position:0%
+unfortunately this is not
+the real scenario is very very different
+
+ align:start position:0%
+the real scenario is very very different
+ 
+
+ align:start position:0%
+the real scenario is very very different
+uh which is why i mean
+
+ align:start position:0%
+uh which is why i mean
+ 
+
+ align:start position:0%
+uh which is why i mean
+we have to look into this issues very
+
+ align:start position:0%
+we have to look into this issues very
+ 
+
+ align:start position:0%
+we have to look into this issues very
+seriously and we have to decide because
+
+ align:start position:0%
+seriously and we have to decide because
+ 
+
+ align:start position:0%
+seriously and we have to decide because
+this is going to end in 2025
+
+ align:start position:0%
+this is going to end in 2025
+ 
+
+ align:start position:0%
+this is going to end in 2025
+this is 2021 and to
+
+ align:start position:0%
+this is 2021 and to
+ 
+
+ align:start position:0%
+this is 2021 and to
+if it is not renewed uh a very different
+
+ align:start position:0%
+if it is not renewed uh a very different
+ 
+
+ align:start position:0%
+if it is not renewed uh a very different
+scenario might happen we don't know what
+
+ align:start position:0%
+scenario might happen we don't know what
+ 
+
+ align:start position:0%
+scenario might happen we don't know what
+is going to happen but now is actually
+
+ align:start position:0%
+is going to happen but now is actually
+ 
+
+ align:start position:0%
+is going to happen but now is actually
+the perfect time to think about this
+
+ align:start position:0%
+the perfect time to think about this
+ 
+
+ align:start position:0%
+the perfect time to think about this
+particular scenario and think of
+
+ align:start position:0%
+particular scenario and think of
+ 
+
+ align:start position:0%
+particular scenario and think of
+different possibilities especially
+
+ align:start position:0%
+different possibilities especially
+ 
+
+ align:start position:0%
+different possibilities especially
+especially from the conflict resolution
+
+ align:start position:0%
+especially from the conflict resolution
+ 
+
+ align:start position:0%
+especially from the conflict resolution
+point of view
+
+ align:start position:0%
+point of view
+ 
+
+ align:start position:0%
+point of view
+and what are the
+
+ align:start position:0%
+and what are the
+ 
+
+ align:start position:0%
+and what are the
+problems with the treaty that we can see
+
+ align:start position:0%
+problems with the treaty that we can see
+ 
+
+ align:start position:0%
+problems with the treaty that we can see
+that it underestimated the impact of
+
+ align:start position:0%
+that it underestimated the impact of
+ 
+
+ align:start position:0%
+that it underestimated the impact of
+climate variability the frequency of low
+
+ align:start position:0%
+climate variability the frequency of low
+ 
+
+ align:start position:0%
+climate variability the frequency of low
+flow events and increased water
+
+ align:start position:0%
+flow events and increased water
+ 
+
+ align:start position:0%
+flow events and increased water
+extractions upstream
+
+ align:start position:0%
+extractions upstream
+ 
+
+ align:start position:0%
+extractions upstream
+and the future climate change and higher
+
+ align:start position:0%
+and the future climate change and higher
+ 
+
+ align:start position:0%
+and the future climate change and higher
+upstream water demand were not predicted
+
+ align:start position:0%
+upstream water demand were not predicted
+ 
+
+ align:start position:0%
+upstream water demand were not predicted
+and also in several locations neither
+
+ align:start position:0%
+and also in several locations neither
+ 
+
+ align:start position:0%
+and also in several locations neither
+bangladesh this is very interesting that
+
+ align:start position:0%
+bangladesh this is very interesting that
+ 
+
+ align:start position:0%
+bangladesh this is very interesting that
+i was speaking about the problem that is
+
+ align:start position:0%
+i was speaking about the problem that is
+ 
+
+ align:start position:0%
+i was speaking about the problem that is
+that bangladesh is facing but uh
+
+ align:start position:0%
+that bangladesh is facing but uh
+ 
+
+ align:start position:0%
+that bangladesh is facing but uh
+a few articles actually indicated that
+
+ align:start position:0%
+a few articles actually indicated that
+ 
+
+ align:start position:0%
+a few articles actually indicated that
+the treaty was made in such a way that
+
+ align:start position:0%
+the treaty was made in such a way that
+ 
+
+ align:start position:0%
+the treaty was made in such a way that
+in several occasions uh not only once
+
+ align:start position:0%
+in several occasions uh not only once
+ 
+
+ align:start position:0%
+in several occasions uh not only once
+not only twice but several locations
+
+ align:start position:0%
+not only twice but several locations
+ 
+
+ align:start position:0%
+not only twice but several locations
+neither bangladesh nor india was able to
+
+ align:start position:0%
+neither bangladesh nor india was able to
+ 
+
+ align:start position:0%
+neither bangladesh nor india was able to
+receive their respective shares as i
+
+ align:start position:0%
+receive their respective shares as i
+ 
+
+ align:start position:0%
+receive their respective shares as i
+stipulated as stipulated in the treaty
+
+ align:start position:0%
+stipulated as stipulated in the treaty
+ 
+
+ align:start position:0%
+stipulated as stipulated in the treaty
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some other other problems that can
+
+ align:start position:0%
+some other other problems that can
+ 
+
+ align:start position:0%
+some other other problems that can
+discuss with the treaty is that
+
+ align:start position:0%
+discuss with the treaty is that
+ 
+
+ align:start position:0%
+discuss with the treaty is that
+bangladesh frequently did not receive
+
+ align:start position:0%
+bangladesh frequently did not receive
+ 
+
+ align:start position:0%
+bangladesh frequently did not receive
+its fair share during the most critical
+
+ align:start position:0%
+its fair share during the most critical
+ 
+
+ align:start position:0%
+its fair share during the most critical
+periods of the dry season when water
+
+ align:start position:0%
+periods of the dry season when water
+ 
+
+ align:start position:0%
+periods of the dry season when water
+demand is relatively high in both
+
+ align:start position:0%
+demand is relatively high in both
+ 
+
+ align:start position:0%
+demand is relatively high in both
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+and there was no guarantee clause for
+
+ align:start position:0%
+and there was no guarantee clause for
+ 
+
+ align:start position:0%
+and there was no guarantee clause for
+bangladesh in no guarantee cluster of
+
+ align:start position:0%
+bangladesh in no guarantee cluster of
+ 
+
+ align:start position:0%
+bangladesh in no guarantee cluster of
+bangladesh which would ensure that
+
+ align:start position:0%
+bangladesh which would ensure that
+ 
+
+ align:start position:0%
+bangladesh which would ensure that
+i mean although there is treaty but if
+
+ align:start position:0%
+i mean although there is treaty but if
+ 
+
+ align:start position:0%
+i mean although there is treaty but if
+bangladesh does not get
+
+ align:start position:0%
+bangladesh does not get
+ 
+
+ align:start position:0%
+bangladesh does not get
+there is no guarantee uh that is insured
+
+ align:start position:0%
+there is no guarantee uh that is insured
+ 
+
+ align:start position:0%
+there is no guarantee uh that is insured
+for bangladesh so that became another
+
+ align:start position:0%
+for bangladesh so that became another
+ 
+
+ align:start position:0%
+for bangladesh so that became another
+major problem and the opponents of the
+
+ align:start position:0%
+major problem and the opponents of the
+ 
+
+ align:start position:0%
+major problem and the opponents of the
+current government they used to say
+
+ align:start position:0%
+current government they used to say
+ 
+
+ align:start position:0%
+current government they used to say
+things like uh there is no guarantee
+
+ align:start position:0%
+things like uh there is no guarantee
+ 
+
+ align:start position:0%
+things like uh there is no guarantee
+which means this is get just to show off
+
+ align:start position:0%
+which means this is get just to show off
+ 
+
+ align:start position:0%
+which means this is get just to show off
+so which also created huge political
+
+ align:start position:0%
+so which also created huge political
+ 
+
+ align:start position:0%
+so which also created huge political
+turmoil in bangladesh scenario and it is
+
+ align:start position:0%
+turmoil in bangladesh scenario and it is
+ 
+
+ align:start position:0%
+turmoil in bangladesh scenario and it is
+evident that the advanced hydrological
+
+ align:start position:0%
+evident that the advanced hydrological
+ 
+
+ align:start position:0%
+evident that the advanced hydrological
+models were not used and
+
+ align:start position:0%
+models were not used and
+ 
+
+ align:start position:0%
+models were not used and
+because if there was uh i mean there was
+
+ align:start position:0%
+because if there was uh i mean there was
+ 
+
+ align:start position:0%
+because if there was uh i mean there was
+advanced hydrological models were not if
+
+ align:start position:0%
+advanced hydrological models were not if
+ 
+
+ align:start position:0%
+advanced hydrological models were not if
+our advanced hydrological models are
+
+ align:start position:0%
+our advanced hydrological models are
+ 
+
+ align:start position:0%
+our advanced hydrological models are
+used uh the prediction would not be i
+
+ align:start position:0%
+used uh the prediction would not be i
+ 
+
+ align:start position:0%
+used uh the prediction would not be i
+mean creating so much trouble uh if if
+
+ align:start position:0%
+mean creating so much trouble uh if if
+ 
+
+ align:start position:0%
+mean creating so much trouble uh if if
+there was uh
+
+ align:start position:0%
+there was uh
+ 
+
+ align:start position:0%
+there was uh
+if there was deliberate error then maybe
+
+ align:start position:0%
+if there was deliberate error then maybe
+ 
+
+ align:start position:0%
+if there was deliberate error then maybe
+one side would be benefited and one side
+
+ align:start position:0%
+one side would be benefited and one side
+ 
+
+ align:start position:0%
+one side would be benefited and one side
+uh would not be benefited but
+
+ align:start position:0%
+uh would not be benefited but
+ 
+
+ align:start position:0%
+uh would not be benefited but
+unfortunately the standard was set in
+
+ align:start position:0%
+unfortunately the standard was set in
+ 
+
+ align:start position:0%
+unfortunately the standard was set in
+such a way it shows that none of the
+
+ align:start position:0%
+such a way it shows that none of the
+ 
+
+ align:start position:0%
+such a way it shows that none of the
+countries several times do not get what
+
+ align:start position:0%
+countries several times do not get what
+ 
+
+ align:start position:0%
+countries several times do not get what
+they are supposed to get according to
+
+ align:start position:0%
+they are supposed to get according to
+ 
+
+ align:start position:0%
+they are supposed to get according to
+the treaty so uh some of the authors
+
+ align:start position:0%
+the treaty so uh some of the authors
+ 
+
+ align:start position:0%
+the treaty so uh some of the authors
+like said islam he actually questioned
+
+ align:start position:0%
+like said islam he actually questioned
+ 
+
+ align:start position:0%
+like said islam he actually questioned
+the the hydrological models that has
+
+ align:start position:0%
+the the hydrological models that has
+ 
+
+ align:start position:0%
+the the hydrological models that has
+been used to
+
+ align:start position:0%
+been used to
+ 
+
+ align:start position:0%
+been used to
+deal with the treaty and he also claimed
+
+ align:start position:0%
+deal with the treaty and he also claimed
+ 
+
+ align:start position:0%
+deal with the treaty and he also claimed
+that the advanced models finally used
+
+ align:start position:0%
+that the advanced models finally used
+ 
+
+ align:start position:0%
+that the advanced models finally used
+which is why
+
+ align:start position:0%
+which is why
+ 
+
+ align:start position:0%
+which is why
+the treaty is in the pen and paper but
+
+ align:start position:0%
+the treaty is in the pen and paper but
+ 
+
+ align:start position:0%
+the treaty is in the pen and paper but
+in real in reality the
+
+ align:start position:0%
+in real in reality the
+ 
+
+ align:start position:0%
+in real in reality the
+the quantitative
+
+ align:start position:0%
+the quantitative
+ 
+
+ align:start position:0%
+the quantitative
+distribution of water has not take place
+
+ align:start position:0%
+distribution of water has not take place
+ 
+
+ align:start position:0%
+distribution of water has not take place
+properly
+
+ align:start position:0%
+properly
+ 
+
+ align:start position:0%
+properly
+so this is uh we can see uh there are
+
+ align:start position:0%
+so this is uh we can see uh there are
+ 
+
+ align:start position:0%
+so this is uh we can see uh there are
+some picture two pictures actually that
+
+ align:start position:0%
+some picture two pictures actually that
+ 
+
+ align:start position:0%
+some picture two pictures actually that
+i've picked that what happened during
+
+ align:start position:0%
+i've picked that what happened during
+ 
+
+ align:start position:0%
+i've picked that what happened during
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+what happened during the dry season so
+
+ align:start position:0%
+what happened during the dry season so
+ 
+
+ align:start position:0%
+what happened during the dry season so
+bangladesh is a country which is uh
+
+ align:start position:0%
+bangladesh is a country which is uh
+ 
+
+ align:start position:0%
+bangladesh is a country which is uh
+which is i mean which used to be full of
+
+ align:start position:0%
+which is i mean which used to be full of
+ 
+
+ align:start position:0%
+which is i mean which used to be full of
+blessings from the nature a lot of i
+
+ align:start position:0%
+blessings from the nature a lot of i
+ 
+
+ align:start position:0%
+blessings from the nature a lot of i
+mean you wouldn't see dry lands very
+
+ align:start position:0%
+mean you wouldn't see dry lands very
+ 
+
+ align:start position:0%
+mean you wouldn't see dry lands very
+often but after after this marriage
+
+ align:start position:0%
+often but after after this marriage
+ 
+
+ align:start position:0%
+often but after after this marriage
+actually happened and during the dry
+
+ align:start position:0%
+actually happened and during the dry
+ 
+
+ align:start position:0%
+actually happened and during the dry
+season this actually happened and
+
+ align:start position:0%
+season this actually happened and
+ 
+
+ align:start position:0%
+season this actually happened and
+what happened is the poor farmers i mean
+
+ align:start position:0%
+what happened is the poor farmers i mean
+ 
+
+ align:start position:0%
+what happened is the poor farmers i mean
+many of them actually
+
+ align:start position:0%
+many of them actually
+ 
+
+ align:start position:0%
+many of them actually
+lost their lands and they had to i mean
+
+ align:start position:0%
+lost their lands and they had to i mean
+ 
+
+ align:start position:0%
+lost their lands and they had to i mean
+some of them actually there has been
+
+ align:start position:0%
+some of them actually there has been
+ 
+
+ align:start position:0%
+some of them actually there has been
+cases that some of them could not even
+
+ align:start position:0%
+cases that some of them could not even
+ 
+
+ align:start position:0%
+cases that some of them could not even
+survive physically they couldn't survive
+
+ align:start position:0%
+survive physically they couldn't survive
+ 
+
+ align:start position:0%
+survive physically they couldn't survive
+and many of them in those areas they
+
+ align:start position:0%
+and many of them in those areas they
+ 
+
+ align:start position:0%
+and many of them in those areas they
+left their lands and they came to the
+
+ align:start position:0%
+left their lands and they came to the
+ 
+
+ align:start position:0%
+left their lands and they came to the
+capital city and which is why after they
+
+ align:start position:0%
+capital city and which is why after they
+ 
+
+ align:start position:0%
+capital city and which is why after they
+came to the capital city they didn't
+
+ align:start position:0%
+came to the capital city they didn't
+ 
+
+ align:start position:0%
+came to the capital city they didn't
+know anything about agriculture but they
+
+ align:start position:0%
+know anything about agriculture but they
+ 
+
+ align:start position:0%
+know anything about agriculture but they
+started to find a job they didn't find
+
+ align:start position:0%
+started to find a job they didn't find
+ 
+
+ align:start position:0%
+started to find a job they didn't find
+it so they tried to
+
+ align:start position:0%
+it so they tried to
+ 
+
+ align:start position:0%
+it so they tried to
+do other things which they didn't work
+
+ align:start position:0%
+do other things which they didn't work
+ 
+
+ align:start position:0%
+do other things which they didn't work
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+at one point what happened that crime
+
+ align:start position:0%
+at one point what happened that crime
+ 
+
+ align:start position:0%
+at one point what happened that crime
+rate increased very high because these
+
+ align:start position:0%
+rate increased very high because these
+ 
+
+ align:start position:0%
+rate increased very high because these
+people they cannot survive in their area
+
+ align:start position:0%
+people they cannot survive in their area
+ 
+
+ align:start position:0%
+people they cannot survive in their area
+and they come to the capital city or the
+
+ align:start position:0%
+and they come to the capital city or the
+ 
+
+ align:start position:0%
+and they come to the capital city or the
+big cities and they start coming they
+
+ align:start position:0%
+big cities and they start coming they
+ 
+
+ align:start position:0%
+big cities and they start coming they
+start a career in crime
+
+ align:start position:0%
+start a career in crime
+ 
+
+ align:start position:0%
+start a career in crime
+so that is how actually indirectly even
+
+ align:start position:0%
+so that is how actually indirectly even
+ 
+
+ align:start position:0%
+so that is how actually indirectly even
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+even with the crime perspective even the
+
+ align:start position:0%
+even with the crime perspective even the
+ 
+
+ align:start position:0%
+even with the crime perspective even the
+law enforcement perspective uh this
+
+ align:start position:0%
+law enforcement perspective uh this
+ 
+
+ align:start position:0%
+law enforcement perspective uh this
+faraka is actually affecting bangladesh
+
+ align:start position:0%
+faraka is actually affecting bangladesh
+ 
+
+ align:start position:0%
+faraka is actually affecting bangladesh
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's uh let's see the ground realities
+
+ align:start position:0%
+let's uh let's see the ground realities
+ 
+
+ align:start position:0%
+let's uh let's see the ground realities
+so now that we will we will enter in the
+
+ align:start position:0%
+so now that we will we will enter in the
+ 
+
+ align:start position:0%
+so now that we will we will enter in the
+into the third part of our presentation
+
+ align:start position:0%
+into the third part of our presentation
+ 
+
+ align:start position:0%
+into the third part of our presentation
+which is the uh which is that the water
+
+ align:start position:0%
+which is the uh which is that the water
+ 
+
+ align:start position:0%
+which is the uh which is that the water
+diplomacy part so let us check out some
+
+ align:start position:0%
+diplomacy part so let us check out some
+ 
+
+ align:start position:0%
+diplomacy part so let us check out some
+of the ground realities the first of all
+
+ align:start position:0%
+of the ground realities the first of all
+ 
+
+ align:start position:0%
+of the ground realities the first of all
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+india has economic political
+
+ align:start position:0%
+india has economic political
+ 
+
+ align:start position:0%
+india has economic political
+geographical and military advantage and
+
+ align:start position:0%
+geographical and military advantage and
+ 
+
+ align:start position:0%
+geographical and military advantage and
+not only that uh
+
+ align:start position:0%
+not only that uh
+ 
+
+ align:start position:0%
+not only that uh
+it has been
+
+ align:start position:0%
+it has been
+ 
+
+ align:start position:0%
+it has been
+very few i mean for last last almost 15
+
+ align:start position:0%
+very few i mean for last last almost 15
+ 
+
+ align:start position:0%
+very few i mean for last last almost 15
+years the present government is
+
+ align:start position:0%
+years the present government is
+ 
+
+ align:start position:0%
+years the present government is
+in the power and they have very strong
+
+ align:start position:0%
+in the power and they have very strong
+ 
+
+ align:start position:0%
+in the power and they have very strong
+tie with indians and
+
+ align:start position:0%
+tie with indians and
+ 
+
+ align:start position:0%
+tie with indians and
+many of the many of the political
+
+ align:start position:0%
+many of the many of the political
+ 
+
+ align:start position:0%
+many of the many of the political
+experts they say that without india's
+
+ align:start position:0%
+experts they say that without india's
+ 
+
+ align:start position:0%
+experts they say that without india's
+support and backing this government
+
+ align:start position:0%
+support and backing this government
+ 
+
+ align:start position:0%
+support and backing this government
+would wouldn't probably survive so some
+
+ align:start position:0%
+would wouldn't probably survive so some
+ 
+
+ align:start position:0%
+would wouldn't probably survive so some
+of the political scientists they
+
+ align:start position:0%
+of the political scientists they
+ 
+
+ align:start position:0%
+of the political scientists they
+actually come up with that that sort of
+
+ align:start position:0%
+actually come up with that that sort of
+ 
+
+ align:start position:0%
+actually come up with that that sort of
+analysis so i mean whether this is true
+
+ align:start position:0%
+analysis so i mean whether this is true
+ 
+
+ align:start position:0%
+analysis so i mean whether this is true
+or false there is a separate issue but
+
+ align:start position:0%
+or false there is a separate issue but
+ 
+
+ align:start position:0%
+or false there is a separate issue but
+uh one thing that is clear that a huge
+
+ align:start position:0%
+uh one thing that is clear that a huge
+ 
+
+ align:start position:0%
+uh one thing that is clear that a huge
+uh huge population a i mean a major
+
+ align:start position:0%
+uh huge population a i mean a major
+ 
+
+ align:start position:0%
+uh huge population a i mean a major
+population group they actually believe
+
+ align:start position:0%
+population group they actually believe
+ 
+
+ align:start position:0%
+population group they actually believe
+this and once they believe this they
+
+ align:start position:0%
+this and once they believe this they
+ 
+
+ align:start position:0%
+this and once they believe this they
+automatically have the anti-india
+
+ align:start position:0%
+automatically have the anti-india
+ 
+
+ align:start position:0%
+automatically have the anti-india
+sentiment and india by cashing out on
+
+ align:start position:0%
+sentiment and india by cashing out on
+ 
+
+ align:start position:0%
+sentiment and india by cashing out on
+this sentiment even the political
+
+ align:start position:0%
+this sentiment even the political
+ 
+
+ align:start position:0%
+this sentiment even the political
+leaders they also get paranoid they also
+
+ align:start position:0%
+leaders they also get paranoid they also
+ 
+
+ align:start position:0%
+leaders they also get paranoid they also
+think that if we try to take any
+
+ align:start position:0%
+think that if we try to take any
+ 
+
+ align:start position:0%
+think that if we try to take any
+decision that does not directly go in
+
+ align:start position:0%
+decision that does not directly go in
+ 
+
+ align:start position:0%
+decision that does not directly go in
+favor of india maybe india will try to
+
+ align:start position:0%
+favor of india maybe india will try to
+ 
+
+ align:start position:0%
+favor of india maybe india will try to
+pressure pressure the bangladesh
+
+ align:start position:0%
+pressure pressure the bangladesh
+ 
+
+ align:start position:0%
+pressure pressure the bangladesh
+politics and the bangladesh political
+
+ align:start position:0%
+politics and the bangladesh political
+ 
+
+ align:start position:0%
+politics and the bangladesh political
+leaders will
+
+ align:start position:0%
+leaders will
+ 
+
+ align:start position:0%
+leaders will
+lose their seat so with this fear uh
+
+ align:start position:0%
+lose their seat so with this fear uh
+ 
+
+ align:start position:0%
+lose their seat so with this fear uh
+very very little instance said there
+
+ align:start position:0%
+very very little instance said there
+ 
+
+ align:start position:0%
+very very little instance said there
+that bangladesh actually confronted
+
+ align:start position:0%
+that bangladesh actually confronted
+ 
+
+ align:start position:0%
+that bangladesh actually confronted
+india and i'm sure that this situation
+
+ align:start position:0%
+india and i'm sure that this situation
+ 
+
+ align:start position:0%
+india and i'm sure that this situation
+is not uncommon in other parts of the
+
+ align:start position:0%
+is not uncommon in other parts of the
+ 
+
+ align:start position:0%
+is not uncommon in other parts of the
+world so
+
+ align:start position:0%
+world so
+ 
+
+ align:start position:0%
+world so
+also like in 1971
+
+ align:start position:0%
+also like in 1971
+ 
+
+ align:start position:0%
+also like in 1971
+india was directly supporting bangladesh
+
+ align:start position:0%
+india was directly supporting bangladesh
+ 
+
+ align:start position:0%
+india was directly supporting bangladesh
+to become independent their their
+
+ align:start position:0%
+to become independent their their
+ 
+
+ align:start position:0%
+to become independent their their
+soldiers actually died with our freedom
+
+ align:start position:0%
+soldiers actually died with our freedom
+ 
+
+ align:start position:0%
+soldiers actually died with our freedom
+fighters so what happened that
+
+ align:start position:0%
+fighters so what happened that
+ 
+
+ align:start position:0%
+fighters so what happened that
+when the war ended immediately there was
+
+ align:start position:0%
+when the war ended immediately there was
+ 
+
+ align:start position:0%
+when the war ended immediately there was
+a there was a joint joint commission
+
+ align:start position:0%
+a there was a joint joint commission
+ 
+
+ align:start position:0%
+a there was a joint joint commission
+initiated but uh
+
+ align:start position:0%
+initiated but uh
+ 
+
+ align:start position:0%
+initiated but uh
+it is very unlikely that that sort of
+
+ align:start position:0%
+it is very unlikely that that sort of
+ 
+
+ align:start position:0%
+it is very unlikely that that sort of
+warmth of relationship between the two
+
+ align:start position:0%
+warmth of relationship between the two
+ 
+
+ align:start position:0%
+warmth of relationship between the two
+countries is going to come back in the
+
+ align:start position:0%
+countries is going to come back in the
+ 
+
+ align:start position:0%
+countries is going to come back in the
+near future and even there is a strong
+
+ align:start position:0%
+near future and even there is a strong
+ 
+
+ align:start position:0%
+near future and even there is a strong
+political will there is animosity uh
+
+ align:start position:0%
+political will there is animosity uh
+ 
+
+ align:start position:0%
+political will there is animosity uh
+both from bangladesh bangladesh side and
+
+ align:start position:0%
+both from bangladesh bangladesh side and
+ 
+
+ align:start position:0%
+both from bangladesh bangladesh side and
+indian side and as i say that there is
+
+ align:start position:0%
+indian side and as i say that there is
+ 
+
+ align:start position:0%
+indian side and as i say that there is
+very strong anti-indian sentiment
+
+ align:start position:0%
+very strong anti-indian sentiment
+ 
+
+ align:start position:0%
+very strong anti-indian sentiment
+currently waving in bangladesh and this
+
+ align:start position:0%
+currently waving in bangladesh and this
+ 
+
+ align:start position:0%
+currently waving in bangladesh and this
+feelings is mutual due to the political
+
+ align:start position:0%
+feelings is mutual due to the political
+ 
+
+ align:start position:0%
+feelings is mutual due to the political
+scenario both in india and bangladesh
+
+ align:start position:0%
+scenario both in india and bangladesh
+ 
+
+ align:start position:0%
+scenario both in india and bangladesh
+the present present government in india
+
+ align:start position:0%
+the present present government in india
+ 
+
+ align:start position:0%
+the present present government in india
+they try to
+
+ align:start position:0%
+they try to
+ 
+
+ align:start position:0%
+they try to
+they are a populist government and there
+
+ align:start position:0%
+they are a populist government and there
+ 
+
+ align:start position:0%
+they are a populist government and there
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+us versus them this sentiment is being
+
+ align:start position:0%
+us versus them this sentiment is being
+ 
+
+ align:start position:0%
+us versus them this sentiment is being
+very very much played in india and also
+
+ align:start position:0%
+very very much played in india and also
+ 
+
+ align:start position:0%
+very very much played in india and also
+in bangladesh so these are the ground
+
+ align:start position:0%
+in bangladesh so these are the ground
+ 
+
+ align:start position:0%
+in bangladesh so these are the ground
+abilities so what are the things that we
+
+ align:start position:0%
+abilities so what are the things that we
+ 
+
+ align:start position:0%
+abilities so what are the things that we
+can do that is uh what that is i'm
+
+ align:start position:0%
+can do that is uh what that is i'm
+ 
+
+ align:start position:0%
+can do that is uh what that is i'm
+trying to try to portray the
+
+ align:start position:0%
+trying to try to portray the
+ 
+
+ align:start position:0%
+trying to try to portray the
+the first water diplomacy approach that
+
+ align:start position:0%
+the first water diplomacy approach that
+ 
+
+ align:start position:0%
+the first water diplomacy approach that
+i try to try to find is the finding
+
+ align:start position:0%
+i try to try to find is the finding
+ 
+
+ align:start position:0%
+i try to try to find is the finding
+common grounds what are the common
+
+ align:start position:0%
+common grounds what are the common
+ 
+
+ align:start position:0%
+common grounds what are the common
+grounds uh that we can say because
+
+ align:start position:0%
+grounds uh that we can say because
+ 
+
+ align:start position:0%
+grounds uh that we can say because
+bangladesh actually stand no chance by
+
+ align:start position:0%
+bangladesh actually stand no chance by
+ 
+
+ align:start position:0%
+bangladesh actually stand no chance by
+confronting india saying that you have
+
+ align:start position:0%
+confronting india saying that you have
+ 
+
+ align:start position:0%
+confronting india saying that you have
+to give us india would you say that like
+
+ align:start position:0%
+to give us india would you say that like
+ 
+
+ align:start position:0%
+to give us india would you say that like
+well we wouldn't give you do whatever
+
+ align:start position:0%
+well we wouldn't give you do whatever
+ 
+
+ align:start position:0%
+well we wouldn't give you do whatever
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+so here this international water
+
+ align:start position:0%
+so here this international water
+ 
+
+ align:start position:0%
+so here this international water
+management institute so from there i
+
+ align:start position:0%
+management institute so from there i
+ 
+
+ align:start position:0%
+management institute so from there i
+actually i actually
+
+ align:start position:0%
+actually i actually
+ 
+
+ align:start position:0%
+actually i actually
+brought this and so these the issues
+
+ align:start position:0%
+brought this and so these the issues
+ 
+
+ align:start position:0%
+brought this and so these the issues
+that we can see that low dry season
+
+ align:start position:0%
+that we can see that low dry season
+ 
+
+ align:start position:0%
+that we can see that low dry season
+fresh water flow the increasing
+
+ align:start position:0%
+fresh water flow the increasing
+ 
+
+ align:start position:0%
+fresh water flow the increasing
+siltation accumulation of sediments
+
+ align:start position:0%
+siltation accumulation of sediments
+ 
+
+ align:start position:0%
+siltation accumulation of sediments
+water resources along the areas of the
+
+ align:start position:0%
+water resources along the areas of the
+ 
+
+ align:start position:0%
+water resources along the areas of the
+river basin are depleting the small
+
+ align:start position:0%
+river basin are depleting the small
+ 
+
+ align:start position:0%
+river basin are depleting the small
+rivers and the distributor is getting
+
+ align:start position:0%
+rivers and the distributor is getting
+ 
+
+ align:start position:0%
+rivers and the distributor is getting
+dried and disconnected a reduced length
+
+ align:start position:0%
+dried and disconnected a reduced length
+ 
+
+ align:start position:0%
+dried and disconnected a reduced length
+of waterways used for negotiation and
+
+ align:start position:0%
+of waterways used for negotiation and
+ 
+
+ align:start position:0%
+of waterways used for negotiation and
+reverberate erosion formation of
+
+ align:start position:0%
+reverberate erosion formation of
+ 
+
+ align:start position:0%
+reverberate erosion formation of
+formation of dry lands and the
+
+ align:start position:0%
+formation of dry lands and the
+ 
+
+ align:start position:0%
+formation of dry lands and the
+socio-economic vulnerabilities so the
+
+ align:start position:0%
+socio-economic vulnerabilities so the
+ 
+
+ align:start position:0%
+socio-economic vulnerabilities so the
+problems that has been there gorham is
+
+ align:start position:0%
+problems that has been there gorham is
+ 
+
+ align:start position:0%
+problems that has been there gorham is
+actually a variant of a variant of the
+
+ align:start position:0%
+actually a variant of a variant of the
+ 
+
+ align:start position:0%
+actually a variant of a variant of the
+genghis river on the middle side inside
+
+ align:start position:0%
+genghis river on the middle side inside
+ 
+
+ align:start position:0%
+genghis river on the middle side inside
+of the bangladesh and howard river is in
+
+ align:start position:0%
+of the bangladesh and howard river is in
+ 
+
+ align:start position:0%
+of the bangladesh and howard river is in
+the west bengal another river so
+
+ align:start position:0%
+the west bengal another river so
+ 
+
+ align:start position:0%
+the west bengal another river so
+these common issues that is actually
+
+ align:start position:0%
+these common issues that is actually
+ 
+
+ align:start position:0%
+these common issues that is actually
+there both between india and bangladesh
+
+ align:start position:0%
+there both between india and bangladesh
+ 
+
+ align:start position:0%
+there both between india and bangladesh
+so the joint water commission that we
+
+ align:start position:0%
+so the joint water commission that we
+ 
+
+ align:start position:0%
+so the joint water commission that we
+have and in our water diplomacy syllabus
+
+ align:start position:0%
+have and in our water diplomacy syllabus
+ 
+
+ align:start position:0%
+have and in our water diplomacy syllabus
+what we have studied in various times
+
+ align:start position:0%
+what we have studied in various times
+ 
+
+ align:start position:0%
+what we have studied in various times
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+an emphasis on joint water community and
+
+ align:start position:0%
+an emphasis on joint water community and
+ 
+
+ align:start position:0%
+an emphasis on joint water community and
+finding the common ground and finding
+
+ align:start position:0%
+finding the common ground and finding
+ 
+
+ align:start position:0%
+finding the common ground and finding
+the common challenges uh is very much
+
+ align:start position:0%
+the common challenges uh is very much
+ 
+
+ align:start position:0%
+the common challenges uh is very much
+stressed in water diplomacy so i think
+
+ align:start position:0%
+stressed in water diplomacy so i think
+ 
+
+ align:start position:0%
+stressed in water diplomacy so i think
+these are the issues that happens both
+
+ align:start position:0%
+these are the issues that happens both
+ 
+
+ align:start position:0%
+these are the issues that happens both
+for india and bangladesh during the
+
+ align:start position:0%
+for india and bangladesh during the
+ 
+
+ align:start position:0%
+for india and bangladesh during the
+during the
+
+ align:start position:0%
+during the
+ 
+
+ align:start position:0%
+during the
+dry seasons in in west bengal and in in
+
+ align:start position:0%
+dry seasons in in west bengal and in in
+ 
+
+ align:start position:0%
+dry seasons in in west bengal and in in
+bangladesh so these are the things that
+
+ align:start position:0%
+bangladesh so these are the things that
+ 
+
+ align:start position:0%
+bangladesh so these are the things that
+that both the parties can discuss and
+
+ align:start position:0%
+that both the parties can discuss and
+ 
+
+ align:start position:0%
+that both the parties can discuss and
+they can try to share some common ground
+
+ align:start position:0%
+they can try to share some common ground
+ 
+
+ align:start position:0%
+they can try to share some common ground
+which they which can be exported and
+
+ align:start position:0%
+which they which can be exported and
+ 
+
+ align:start position:0%
+which they which can be exported and
+that is how the treaty can be uh
+
+ align:start position:0%
+that is how the treaty can be uh
+ 
+
+ align:start position:0%
+that is how the treaty can be uh
+the treaty can be uh i mean upgraded so
+
+ align:start position:0%
+the treaty can be uh i mean upgraded so
+ 
+
+ align:start position:0%
+the treaty can be uh i mean upgraded so
+another water diplomacy approach is the
+
+ align:start position:0%
+another water diplomacy approach is the
+ 
+
+ align:start position:0%
+another water diplomacy approach is the
+indicating india's own problems with
+
+ align:start position:0%
+indicating india's own problems with
+ 
+
+ align:start position:0%
+indicating india's own problems with
+farakka this is a 2017 newspaper article
+
+ align:start position:0%
+farakka this is a 2017 newspaper article
+ 
+
+ align:start position:0%
+farakka this is a 2017 newspaper article
+with some references so there is this
+
+ align:start position:0%
+with some references so there is this
+ 
+
+ align:start position:0%
+with some references so there is this
+indian chief engineer he actually
+
+ align:start position:0%
+indian chief engineer he actually
+ 
+
+ align:start position:0%
+indian chief engineer he actually
+discussed when this plan was happening
+
+ align:start position:0%
+discussed when this plan was happening
+ 
+
+ align:start position:0%
+discussed when this plan was happening
+in 1961
+
+ align:start position:0%
+in 1961
+ 
+
+ align:start position:0%
+in 1961
+so he actually uh pointed out some
+
+ align:start position:0%
+so he actually uh pointed out some
+ 
+
+ align:start position:0%
+so he actually uh pointed out some
+various problems for example the drought
+
+ align:start position:0%
+various problems for example the drought
+ 
+
+ align:start position:0%
+various problems for example the drought
+and the climate change these are the
+
+ align:start position:0%
+and the climate change these are the
+ 
+
+ align:start position:0%
+and the climate change these are the
+things he he actually uh pointed out to
+
+ align:start position:0%
+things he he actually uh pointed out to
+ 
+
+ align:start position:0%
+things he he actually uh pointed out to
+the indian government he's a he's a
+
+ align:start position:0%
+the indian government he's a he's a
+ 
+
+ align:start position:0%
+the indian government he's a he's a
+bengali guy krishna
+
+ align:start position:0%
+bengali guy krishna
+ 
+
+ align:start position:0%
+bengali guy krishna
+so he actually pointed out those
+
+ align:start position:0%
+so he actually pointed out those
+ 
+
+ align:start position:0%
+so he actually pointed out those
+problems but back then
+
+ align:start position:0%
+problems but back then
+ 
+
+ align:start position:0%
+problems but back then
+his carrier took us he was a chief
+
+ align:start position:0%
+his carrier took us he was a chief
+ 
+
+ align:start position:0%
+his carrier took us he was a chief
+engineer
+
+ align:start position:0%
+engineer
+ 
+
+ align:start position:0%
+engineer
+on the west bengal side then this far
+
+ align:start position:0%
+on the west bengal side then this far
+ 
+
+ align:start position:0%
+on the west bengal side then this far
+academy was happening and when he
+
+ align:start position:0%
+academy was happening and when he
+ 
+
+ align:start position:0%
+academy was happening and when he
+indicated those problems for example the
+
+ align:start position:0%
+indicated those problems for example the
+ 
+
+ align:start position:0%
+indicated those problems for example the
+different parts of public tools for the
+
+ align:start position:0%
+different parts of public tools for the
+ 
+
+ align:start position:0%
+different parts of public tools for the
+districts and we have the the flooding
+
+ align:start position:0%
+districts and we have the the flooding
+ 
+
+ align:start position:0%
+districts and we have the the flooding
+the drought and the change of
+
+ align:start position:0%
+the drought and the change of
+ 
+
+ align:start position:0%
+the drought and the change of
+biodiversity and the salinity issues and
+
+ align:start position:0%
+biodiversity and the salinity issues and
+ 
+
+ align:start position:0%
+biodiversity and the salinity issues and
+also the annual seed silk region
+
+ align:start position:0%
+also the annual seed silk region
+ 
+
+ align:start position:0%
+also the annual seed silk region
+from 6.4 million uh
+
+ align:start position:0%
+from 6.4 million uh
+ 
+
+ align:start position:0%
+from 6.4 million uh
+cubic meter to 21.8 million uh cubic
+
+ align:start position:0%
+cubic meter to 21.8 million uh cubic
+ 
+
+ align:start position:0%
+cubic meter to 21.8 million uh cubic
+meter till 2003 so this sort of things
+
+ align:start position:0%
+meter till 2003 so this sort of things
+ 
+
+ align:start position:0%
+meter till 2003 so this sort of things
+happened and these were actually
+
+ align:start position:0%
+happened and these were actually
+ 
+
+ align:start position:0%
+happened and these were actually
+predicted so
+
+ align:start position:0%
+predicted so
+ 
+
+ align:start position:0%
+predicted so
+this problem not only it's from an
+
+ align:start position:0%
+this problem not only it's from an
+ 
+
+ align:start position:0%
+this problem not only it's from an
+academic report this was so serious that
+
+ align:start position:0%
+academic report this was so serious that
+ 
+
+ align:start position:0%
+academic report this was so serious that
+the bihar
+
+ align:start position:0%
+the bihar
+ 
+
+ align:start position:0%
+the bihar
+in the bihar area
+
+ align:start position:0%
+in the bihar area
+ 
+
+ align:start position:0%
+in the bihar area
+some very influential politicians the
+
+ align:start position:0%
+some very influential politicians the
+ 
+
+ align:start position:0%
+some very influential politicians the
+chief ministers and they actually saved
+
+ align:start position:0%
+chief ministers and they actually saved
+ 
+
+ align:start position:0%
+chief ministers and they actually saved
+the central government that why don't
+
+ align:start position:0%
+the central government that why don't
+ 
+
+ align:start position:0%
+the central government that why don't
+you i mean demolish the farakadam so the
+
+ align:start position:0%
+you i mean demolish the farakadam so the
+ 
+
+ align:start position:0%
+you i mean demolish the farakadam so the
+way bangladesh wants a solution for this
+
+ align:start position:0%
+way bangladesh wants a solution for this
+ 
+
+ align:start position:0%
+way bangladesh wants a solution for this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+even some parts of india
+
+ align:start position:0%
+even some parts of india
+ 
+
+ align:start position:0%
+even some parts of india
+there actually wants the same so when
+
+ align:start position:0%
+there actually wants the same so when
+ 
+
+ align:start position:0%
+there actually wants the same so when
+there would be a discussion maybe from
+
+ align:start position:0%
+there would be a discussion maybe from
+ 
+
+ align:start position:0%
+there would be a discussion maybe from
+bangladesh's perspective this india's
+
+ align:start position:0%
+bangladesh's perspective this india's
+ 
+
+ align:start position:0%
+bangladesh's perspective this india's
+own interest can be exploited uh and
+
+ align:start position:0%
+own interest can be exploited uh and
+ 
+
+ align:start position:0%
+own interest can be exploited uh and
+come come to a middle ground
+
+ align:start position:0%
+come come to a middle ground
+ 
+
+ align:start position:0%
+come come to a middle ground
+and this is something which bangladesh
+
+ align:start position:0%
+and this is something which bangladesh
+ 
+
+ align:start position:0%
+and this is something which bangladesh
+repeatedly failed that india became
+
+ align:start position:0%
+repeatedly failed that india became
+ 
+
+ align:start position:0%
+repeatedly failed that india became
+repeatedly successful bangladesh since
+
+ align:start position:0%
+repeatedly successful bangladesh since
+ 
+
+ align:start position:0%
+repeatedly successful bangladesh since
+uh after the uh 1982 uh where after 1982
+
+ align:start position:0%
+uh after the uh 1982 uh where after 1982
+ 
+
+ align:start position:0%
+uh after the uh 1982 uh where after 1982
+when the
+
+ align:start position:0%
+when the
+ 
+
+ align:start position:0%
+when the
+when the
+
+ align:start position:0%
+when the
+ 
+
+ align:start position:0%
+when the
+another party which is uh historically
+
+ align:start position:0%
+another party which is uh historically
+ 
+
+ align:start position:0%
+another party which is uh historically
+considered as anti-india they came to
+
+ align:start position:0%
+considered as anti-india they came to
+ 
+
+ align:start position:0%
+considered as anti-india they came to
+power they tried to internationalize the
+
+ align:start position:0%
+power they tried to internationalize the
+ 
+
+ align:start position:0%
+power they tried to internationalize the
+faraka situation they tried to i mean
+
+ align:start position:0%
+faraka situation they tried to i mean
+ 
+
+ align:start position:0%
+faraka situation they tried to i mean
+the sarp was built and then this issue
+
+ align:start position:0%
+the sarp was built and then this issue
+ 
+
+ align:start position:0%
+the sarp was built and then this issue
+was taken but india was actually
+
+ align:start position:0%
+was taken but india was actually
+ 
+
+ align:start position:0%
+was taken but india was actually
+stressing that no this is a bilateral
+
+ align:start position:0%
+stressing that no this is a bilateral
+ 
+
+ align:start position:0%
+stressing that no this is a bilateral
+issue but if you look at the basin you
+
+ align:start position:0%
+issue but if you look at the basin you
+ 
+
+ align:start position:0%
+issue but if you look at the basin you
+will see that there is china bhutan
+
+ align:start position:0%
+will see that there is china bhutan
+ 
+
+ align:start position:0%
+will see that there is china bhutan
+nepal and bangladesh well bhutan and
+
+ align:start position:0%
+nepal and bangladesh well bhutan and
+ 
+
+ align:start position:0%
+nepal and bangladesh well bhutan and
+nepal their cases exactly like
+
+ align:start position:0%
+nepal their cases exactly like
+ 
+
+ align:start position:0%
+nepal their cases exactly like
+bangladesh but
+
+ align:start position:0%
+bangladesh but
+ 
+
+ align:start position:0%
+bangladesh but
+the surprising new scenario is that now
+
+ align:start position:0%
+the surprising new scenario is that now
+ 
+
+ align:start position:0%
+the surprising new scenario is that now
+that china has global aspirations
+
+ align:start position:0%
+that china has global aspirations
+ 
+
+ align:start position:0%
+that china has global aspirations
+china
+
+ align:start position:0%
+china
+ 
+
+ align:start position:0%
+china
+more than once they came out with with
+
+ align:start position:0%
+more than once they came out with with
+ 
+
+ align:start position:0%
+more than once they came out with with
+the tista river which is another river
+
+ align:start position:0%
+the tista river which is another river
+ 
+
+ align:start position:0%
+the tista river which is another river
+in the northern part of bangladesh they
+
+ align:start position:0%
+in the northern part of bangladesh they
+ 
+
+ align:start position:0%
+in the northern part of bangladesh they
+came up with the proposal that we would
+
+ align:start position:0%
+came up with the proposal that we would
+ 
+
+ align:start position:0%
+came up with the proposal that we would
+help you with the technology and the
+
+ align:start position:0%
+help you with the technology and the
+ 
+
+ align:start position:0%
+help you with the technology and the
+money so that you can build another
+
+ align:start position:0%
+money so that you can build another
+ 
+
+ align:start position:0%
+money so that you can build another
+branch on another side so
+
+ align:start position:0%
+branch on another side so
+ 
+
+ align:start position:0%
+branch on another side so
+this became another bargaining chip for
+
+ align:start position:0%
+this became another bargaining chip for
+ 
+
+ align:start position:0%
+this became another bargaining chip for
+the chief for bangladesh
+
+ align:start position:0%
+the chief for bangladesh
+ 
+
+ align:start position:0%
+the chief for bangladesh
+that using the the china factor i would
+
+ align:start position:0%
+that using the the china factor i would
+ 
+
+ align:start position:0%
+that using the the china factor i would
+i'm using the china factor and building
+
+ align:start position:0%
+i'm using the china factor and building
+ 
+
+ align:start position:0%
+i'm using the china factor and building
+an international uh the
+
+ align:start position:0%
+an international uh the
+ 
+
+ align:start position:0%
+an international uh the
+the joint commission is the joint
+
+ align:start position:0%
+the joint commission is the joint
+ 
+
+ align:start position:0%
+the joint commission is the joint
+commission can be international it needs
+
+ align:start position:0%
+commission can be international it needs
+ 
+
+ align:start position:0%
+commission can be international it needs
+not to be bilateral it can be
+
+ align:start position:0%
+not to be bilateral it can be
+ 
+
+ align:start position:0%
+not to be bilateral it can be
+international bringing china since the
+
+ align:start position:0%
+international bringing china since the
+ 
+
+ align:start position:0%
+international bringing china since the
+china is actually trying to provide
+
+ align:start position:0%
+china is actually trying to provide
+ 
+
+ align:start position:0%
+china is actually trying to provide
+bangladesh some with some new options
+
+ align:start position:0%
+bangladesh some with some new options
+ 
+
+ align:start position:0%
+bangladesh some with some new options
+and uh they are actually saying that
+
+ align:start position:0%
+and uh they are actually saying that
+ 
+
+ align:start position:0%
+and uh they are actually saying that
+china's water weapon that is the word
+
+ align:start position:0%
+china's water weapon that is the word
+ 
+
+ align:start position:0%
+china's water weapon that is the word
+they have used so
+
+ align:start position:0%
+they have used so
+ 
+
+ align:start position:0%
+they have used so
+the this is uh this is this is the
+
+ align:start position:0%
+the this is uh this is this is the
+ 
+
+ align:start position:0%
+the this is uh this is this is the
+concept that i've borrowed from uh the
+
+ align:start position:0%
+concept that i've borrowed from uh the
+ 
+
+ align:start position:0%
+concept that i've borrowed from uh the
+cipher stumps are the the slams
+
+ align:start position:0%
+cipher stumps are the the slams
+ 
+
+ align:start position:0%
+cipher stumps are the the slams
+uh the bringing other bargaining chips
+
+ align:start position:0%
+uh the bringing other bargaining chips
+ 
+
+ align:start position:0%
+uh the bringing other bargaining chips
+that is not usually uh considered for
+
+ align:start position:0%
+that is not usually uh considered for
+ 
+
+ align:start position:0%
+that is not usually uh considered for
+example uh this is bangladesh on the on
+
+ align:start position:0%
+example uh this is bangladesh on the on
+ 
+
+ align:start position:0%
+example uh this is bangladesh on the on
+the left side the west bengal is there
+
+ align:start position:0%
+the left side the west bengal is there
+ 
+
+ align:start position:0%
+the left side the west bengal is there
+you can see the jharkhand bihar and this
+
+ align:start position:0%
+you can see the jharkhand bihar and this
+ 
+
+ align:start position:0%
+you can see the jharkhand bihar and this
+is nepal bhutan this is bangladesh and
+
+ align:start position:0%
+is nepal bhutan this is bangladesh and
+ 
+
+ align:start position:0%
+is nepal bhutan this is bangladesh and
+you see a huge part of india is actually
+
+ align:start position:0%
+you see a huge part of india is actually
+ 
+
+ align:start position:0%
+you see a huge part of india is actually
+there and the majority of the border is
+
+ align:start position:0%
+there and the majority of the border is
+ 
+
+ align:start position:0%
+there and the majority of the border is
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+is with bangladesh and there is
+
+ align:start position:0%
+is with bangladesh and there is
+ 
+
+ align:start position:0%
+is with bangladesh and there is
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+sentiment there is strong sentiment
+
+ align:start position:0%
+sentiment there is strong sentiment
+ 
+
+ align:start position:0%
+sentiment there is strong sentiment
+against against the central indian
+
+ align:start position:0%
+against against the central indian
+ 
+
+ align:start position:0%
+against against the central indian
+government because it is very much i
+
+ align:start position:0%
+government because it is very much i
+ 
+
+ align:start position:0%
+government because it is very much i
+mean it is called the seven sisters and
+
+ align:start position:0%
+mean it is called the seven sisters and
+ 
+
+ align:start position:0%
+mean it is called the seven sisters and
+the seven sisters uh well
+
+ align:start position:0%
+the seven sisters uh well
+ 
+
+ align:start position:0%
+the seven sisters uh well
+this is far from the central government
+
+ align:start position:0%
+this is far from the central government
+ 
+
+ align:start position:0%
+this is far from the central government
+and which is why the control is very
+
+ align:start position:0%
+and which is why the control is very
+ 
+
+ align:start position:0%
+and which is why the control is very
+much i mean not as strong as delhi or
+
+ align:start position:0%
+much i mean not as strong as delhi or
+ 
+
+ align:start position:0%
+much i mean not as strong as delhi or
+the nearby states so and many of these
+
+ align:start position:0%
+the nearby states so and many of these
+ 
+
+ align:start position:0%
+the nearby states so and many of these
+states they actually want independence
+
+ align:start position:0%
+states they actually want independence
+ 
+
+ align:start position:0%
+states they actually want independence
+of their own and
+
+ align:start position:0%
+of their own and
+ 
+
+ align:start position:0%
+of their own and
+which is why and even when uh
+
+ align:start position:0%
+which is why and even when uh
+ 
+
+ align:start position:0%
+which is why and even when uh
+at present bangladesh and india has a
+
+ align:start position:0%
+at present bangladesh and india has a
+ 
+
+ align:start position:0%
+at present bangladesh and india has a
+very strong tie because of the
+
+ align:start position:0%
+very strong tie because of the
+ 
+
+ align:start position:0%
+very strong tie because of the
+historical results the present prime
+
+ align:start position:0%
+historical results the present prime
+ 
+
+ align:start position:0%
+historical results the present prime
+minister he when his whole family was uh
+
+ align:start position:0%
+minister he when his whole family was uh
+ 
+
+ align:start position:0%
+minister he when his whole family was uh
+killed uh for six years he actually
+
+ align:start position:0%
+killed uh for six years he actually
+ 
+
+ align:start position:0%
+killed uh for six years he actually
+lived under the indian production so it
+
+ align:start position:0%
+lived under the indian production so it
+ 
+
+ align:start position:0%
+lived under the indian production so it
+is considered that she would probably
+
+ align:start position:0%
+is considered that she would probably
+ 
+
+ align:start position:0%
+is considered that she would probably
+never go against the interest of india
+
+ align:start position:0%
+never go against the interest of india
+ 
+
+ align:start position:0%
+never go against the interest of india
+but when anti-indian sentiment
+
+ align:start position:0%
+but when anti-indian sentiment
+ 
+
+ align:start position:0%
+but when anti-indian sentiment
+comes with a new political party there
+
+ align:start position:0%
+comes with a new political party there
+ 
+
+ align:start position:0%
+comes with a new political party there
+is always threat
+
+ align:start position:0%
+is always threat
+ 
+
+ align:start position:0%
+is always threat
+that this part of india would be very
+
+ align:start position:0%
+that this part of india would be very
+ 
+
+ align:start position:0%
+that this part of india would be very
+much tumultuous there will be terrorism
+
+ align:start position:0%
+much tumultuous there will be terrorism
+ 
+
+ align:start position:0%
+much tumultuous there will be terrorism
+and many of the
+
+ align:start position:0%
+and many of the
+ 
+
+ align:start position:0%
+and many of the
+terrorist leaders many of the
+
+ align:start position:0%
+terrorist leaders many of the
+ 
+
+ align:start position:0%
+terrorist leaders many of the
+nationalist leaders of those parties
+
+ align:start position:0%
+nationalist leaders of those parties
+ 
+
+ align:start position:0%
+nationalist leaders of those parties
+they actually i mean they used to
+
+ align:start position:0%
+they actually i mean they used to
+ 
+
+ align:start position:0%
+they actually i mean they used to
+operate from bangladesh and one famous
+
+ align:start position:0%
+operate from bangladesh and one famous
+ 
+
+ align:start position:0%
+operate from bangladesh and one famous
+incident that i can say that in 2004 uh
+
+ align:start position:0%
+incident that i can say that in 2004 uh
+ 
+
+ align:start position:0%
+incident that i can say that in 2004 uh
+10 trucks 10 truckloads of uh 10
+
+ align:start position:0%
+10 trucks 10 truckloads of uh 10
+ 
+
+ align:start position:0%
+10 trucks 10 truckloads of uh 10
+truckload of
+
+ align:start position:0%
+truckload of
+ 
+
+ align:start position:0%
+truckload of
+most advanced military weapons were
+
+ align:start position:0%
+most advanced military weapons were
+ 
+
+ align:start position:0%
+most advanced military weapons were
+passing towards bangladesh but uh
+
+ align:start position:0%
+passing towards bangladesh but uh
+ 
+
+ align:start position:0%
+passing towards bangladesh but uh
+it it was a fluke that it was caught so
+
+ align:start position:0%
+it it was a fluke that it was caught so
+ 
+
+ align:start position:0%
+it it was a fluke that it was caught so
+it became a huge case so
+
+ align:start position:0%
+it became a huge case so
+ 
+
+ align:start position:0%
+it became a huge case so
+i mean it can be a huge trouble for
+
+ align:start position:0%
+i mean it can be a huge trouble for
+ 
+
+ align:start position:0%
+i mean it can be a huge trouble for
+india so this particular issue can
+
+ align:start position:0%
+india so this particular issue can
+ 
+
+ align:start position:0%
+india so this particular issue can
+actually can be brought in the
+
+ align:start position:0%
+actually can be brought in the
+ 
+
+ align:start position:0%
+actually can be brought in the
+negotiation table by uh say by saying
+
+ align:start position:0%
+negotiation table by uh say by saying
+ 
+
+ align:start position:0%
+negotiation table by uh say by saying
+that well uh we would provide you full
+
+ align:start position:0%
+that well uh we would provide you full
+ 
+
+ align:start position:0%
+that well uh we would provide you full
+support with safety and security of your
+
+ align:start position:0%
+support with safety and security of your
+ 
+
+ align:start position:0%
+support with safety and security of your
+uh the seven sisters part uh in exchange
+
+ align:start position:0%
+uh the seven sisters part uh in exchange
+ 
+
+ align:start position:0%
+uh the seven sisters part uh in exchange
+uh maybe we can discuss about the the
+
+ align:start position:0%
+uh maybe we can discuss about the the
+ 
+
+ align:start position:0%
+uh maybe we can discuss about the the
+sharing of the water treaty so this is
+
+ align:start position:0%
+sharing of the water treaty so this is
+ 
+
+ align:start position:0%
+sharing of the water treaty so this is
+another this is one bargaining chip
+
+ align:start position:0%
+another this is one bargaining chip
+ 
+
+ align:start position:0%
+another this is one bargaining chip
+which i think can be exported i i tried
+
+ align:start position:0%
+which i think can be exported i i tried
+ 
+
+ align:start position:0%
+which i think can be exported i i tried
+to see that check the literature but uh
+
+ align:start position:0%
+to see that check the literature but uh
+ 
+
+ align:start position:0%
+to see that check the literature but uh
+so far i haven't seen that bangladesh
+
+ align:start position:0%
+so far i haven't seen that bangladesh
+ 
+
+ align:start position:0%
+so far i haven't seen that bangladesh
+has went through that path and another
+
+ align:start position:0%
+has went through that path and another
+ 
+
+ align:start position:0%
+has went through that path and another
+another uh
+
+ align:start position:0%
+another uh
+ 
+
+ align:start position:0%
+another uh
+cheap can be
+
+ align:start position:0%
+cheap can be
+ 
+
+ align:start position:0%
+cheap can be
+there are some articles from the indian
+
+ align:start position:0%
+there are some articles from the indian
+ 
+
+ align:start position:0%
+there are some articles from the indian
+sides they actually claim that the
+
+ align:start position:0%
+sides they actually claim that the
+ 
+
+ align:start position:0%
+sides they actually claim that the
+bengal bengal means the west bengal they
+
+ align:start position:0%
+bengal bengal means the west bengal they
+ 
+
+ align:start position:0%
+bengal bengal means the west bengal they
+need pista and the tista we have a
+
+ align:start position:0%
+need pista and the tista we have a
+ 
+
+ align:start position:0%
+need pista and the tista we have a
+barrage in this we have we have a
+
+ align:start position:0%
+barrage in this we have we have a
+ 
+
+ align:start position:0%
+barrage in this we have we have a
+diamond pista and still uh there has
+
+ align:start position:0%
+diamond pista and still uh there has
+ 
+
+ align:start position:0%
+diamond pista and still uh there has
+been many talks but so far there has
+
+ align:start position:0%
+been many talks but so far there has
+ 
+
+ align:start position:0%
+been many talks but so far there has
+been no treaty so
+
+ align:start position:0%
+been no treaty so
+ 
+
+ align:start position:0%
+been no treaty so
+i mean although we are speaking about
+
+ align:start position:0%
+i mean although we are speaking about
+ 
+
+ align:start position:0%
+i mean although we are speaking about
+the advancement of gandhi's treaty the
+
+ align:start position:0%
+the advancement of gandhi's treaty the
+ 
+
+ align:start position:0%
+the advancement of gandhi's treaty the
+upgradation of genji's treaty maybe uh
+
+ align:start position:0%
+upgradation of genji's treaty maybe uh
+ 
+
+ align:start position:0%
+upgradation of genji's treaty maybe uh
+the tista river to get some advantage in
+
+ align:start position:0%
+the tista river to get some advantage in
+ 
+
+ align:start position:0%
+the tista river to get some advantage in
+ganges river treaty bangladesh actually
+
+ align:start position:0%
+ganges river treaty bangladesh actually
+ 
+
+ align:start position:0%
+ganges river treaty bangladesh actually
+can think of discussing with india
+
+ align:start position:0%
+can think of discussing with india
+ 
+
+ align:start position:0%
+can think of discussing with india
+whether they can bring this uh this
+
+ align:start position:0%
+whether they can bring this uh this
+ 
+
+ align:start position:0%
+whether they can bring this uh this
+tista river treaty treaty with them as
+
+ align:start position:0%
+tista river treaty treaty with them as
+ 
+
+ align:start position:0%
+tista river treaty treaty with them as
+well tista is very sensitive because
+
+ align:start position:0%
+well tista is very sensitive because
+ 
+
+ align:start position:0%
+well tista is very sensitive because
+tista is actually it has originated in
+
+ align:start position:0%
+tista is actually it has originated in
+ 
+
+ align:start position:0%
+tista is actually it has originated in
+sikkim which is very close to china and
+
+ align:start position:0%
+sikkim which is very close to china and
+ 
+
+ align:start position:0%
+sikkim which is very close to china and
+this is the river especially for which
+
+ align:start position:0%
+this is the river especially for which
+ 
+
+ align:start position:0%
+this is the river especially for which
+the chinese the chinese actually offered
+
+ align:start position:0%
+the chinese the chinese actually offered
+ 
+
+ align:start position:0%
+the chinese the chinese actually offered
+bangladesh a technical support to bring
+
+ align:start position:0%
+bangladesh a technical support to bring
+ 
+
+ align:start position:0%
+bangladesh a technical support to bring
+bring further dams and by doing that
+
+ align:start position:0%
+bring further dams and by doing that
+ 
+
+ align:start position:0%
+bring further dams and by doing that
+changing the course of the river so it
+
+ align:start position:0%
+changing the course of the river so it
+ 
+
+ align:start position:0%
+changing the course of the river so it
+became a very serious issue between
+
+ align:start position:0%
+became a very serious issue between
+ 
+
+ align:start position:0%
+became a very serious issue between
+bangladesh and india and the diplomatic
+
+ align:start position:0%
+bangladesh and india and the diplomatic
+ 
+
+ align:start position:0%
+bangladesh and india and the diplomatic
+diplomatic talks are still going on so
+
+ align:start position:0%
+diplomatic talks are still going on so
+ 
+
+ align:start position:0%
+diplomatic talks are still going on so
+these are actually the steps that we can
+
+ align:start position:0%
+these are actually the steps that we can
+ 
+
+ align:start position:0%
+these are actually the steps that we can
+think of
+
+ align:start position:0%
+think of
+ 
+
+ align:start position:0%
+think of
+using as the bargaining chips so that
+
+ align:start position:0%
+using as the bargaining chips so that
+ 
+
+ align:start position:0%
+using as the bargaining chips so that
+a new joint commission can be made and
+
+ align:start position:0%
+a new joint commission can be made and
+ 
+
+ align:start position:0%
+a new joint commission can be made and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the things like climate change and other
+
+ align:start position:0%
+the things like climate change and other
+ 
+
+ align:start position:0%
+the things like climate change and other
+the other problems which was not
+
+ align:start position:0%
+the other problems which was not
+ 
+
+ align:start position:0%
+the other problems which was not
+considered in 1996 can be considered now
+
+ align:start position:0%
+considered in 1996 can be considered now
+ 
+
+ align:start position:0%
+considered in 1996 can be considered now
+because uh in 30 35 years
+
+ align:start position:0%
+because uh in 30 35 years
+ 
+
+ align:start position:0%
+because uh in 30 35 years
+in 30 almost 30 years the technology has
+
+ align:start position:0%
+in 30 almost 30 years the technology has
+ 
+
+ align:start position:0%
+in 30 almost 30 years the technology has
+changed the gps has come and many other
+
+ align:start position:0%
+changed the gps has come and many other
+ 
+
+ align:start position:0%
+changed the gps has come and many other
+the scientific scenario has changed so
+
+ align:start position:0%
+the scientific scenario has changed so
+ 
+
+ align:start position:0%
+the scientific scenario has changed so
+maybe by bringing all these things
+
+ align:start position:0%
+maybe by bringing all these things
+ 
+
+ align:start position:0%
+maybe by bringing all these things
+together a solution a better solution
+
+ align:start position:0%
+together a solution a better solution
+ 
+
+ align:start position:0%
+together a solution a better solution
+can be saved and
+
+ align:start position:0%
+can be saved and
+ 
+
+ align:start position:0%
+can be saved and
+before i finish with all the criticisms
+
+ align:start position:0%
+before i finish with all the criticisms
+ 
+
+ align:start position:0%
+before i finish with all the criticisms
+i would actually uh i would actually
+
+ align:start position:0%
+i would actually uh i would actually
+ 
+
+ align:start position:0%
+i would actually uh i would actually
+again say that which i i feel and i also
+
+ align:start position:0%
+again say that which i i feel and i also
+ 
+
+ align:start position:0%
+again say that which i i feel and i also
+read from the ahmed's article
+
+ align:start position:0%
+read from the ahmed's article
+ 
+
+ align:start position:0%
+read from the ahmed's article
+that this this ganges water treaty is
+
+ align:start position:0%
+that this this ganges water treaty is
+ 
+
+ align:start position:0%
+that this this ganges water treaty is
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+uh it is not perfect it is definitely
+
+ align:start position:0%
+uh it is not perfect it is definitely
+ 
+
+ align:start position:0%
+uh it is not perfect it is definitely
+not perfect
+
+ align:start position:0%
+not perfect
+ 
+
+ align:start position:0%
+not perfect
+but if it was not there the situation
+
+ align:start position:0%
+but if it was not there the situation
+ 
+
+ align:start position:0%
+but if it was not there the situation
+for both the countries would probably
+
+ align:start position:0%
+for both the countries would probably
+ 
+
+ align:start position:0%
+for both the countries would probably
+worse
+
+ align:start position:0%
+worse
+ 
+
+ align:start position:0%
+worse
+so the treaty should be there and we
+
+ align:start position:0%
+so the treaty should be there and we
+ 
+
+ align:start position:0%
+so the treaty should be there and we
+should try our best to
+
+ align:start position:0%
+should try our best to
+ 
+
+ align:start position:0%
+should try our best to
+we have four years maybe we can try our
+
+ align:start position:0%
+we have four years maybe we can try our
+ 
+
+ align:start position:0%
+we have four years maybe we can try our
+best to think of the
+
+ align:start position:0%
+best to think of the
+ 
+
+ align:start position:0%
+best to think of the
+the advancement of the treaty the the
+
+ align:start position:0%
+the advancement of the treaty the the
+ 
+
+ align:start position:0%
+the advancement of the treaty the the
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+addressing the
+
+ align:start position:0%
+addressing the
+ 
+
+ align:start position:0%
+addressing the
+addressing the limitations that we are
+
+ align:start position:0%
+addressing the limitations that we are
+ 
+
+ align:start position:0%
+addressing the limitations that we are
+currently facing thank you very much if
+
+ align:start position:0%
+currently facing thank you very much if
+ 
+
+ align:start position:0%
+currently facing thank you very much if
+you have any comments and if you have
+
+ align:start position:0%
+you have any comments and if you have
+ 
+
+ align:start position:0%
+you have any comments and if you have
+any questions i'd like to answer them
+
+ align:start position:0%
+any questions i'd like to answer them
+ 
+
+ align:start position:0%
+any questions i'd like to answer them
+thank you very much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you um for the nice presentation
+
+ align:start position:0%
+thank you um for the nice presentation
+ 
+
+ align:start position:0%
+thank you um for the nice presentation
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so um now i would like to ask um
+
+ align:start position:0%
+so um now i would like to ask um
+ 
+
+ align:start position:0%
+so um now i would like to ask um
+others to make comments like aaron and
+
+ align:start position:0%
+others to make comments like aaron and
+ 
+
+ align:start position:0%
+others to make comments like aaron and
+jemma do you have any comments or
+
+ align:start position:0%
+jemma do you have any comments or
+ 
+
+ align:start position:0%
+jemma do you have any comments or
+feedback
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you mushroom for a really great
+
+ align:start position:0%
+thank you mushroom for a really great
+ 
+
+ align:start position:0%
+thank you mushroom for a really great
+presentation i i learned a lot um
+
+ align:start position:0%
+presentation i i learned a lot um
+ 
+
+ align:start position:0%
+presentation i i learned a lot um
+i really appreciated how much sort of
+
+ align:start position:0%
+i really appreciated how much sort of
+ 
+
+ align:start position:0%
+i really appreciated how much sort of
+geographic and geopolitical context
+
+ align:start position:0%
+geographic and geopolitical context
+ 
+
+ align:start position:0%
+geographic and geopolitical context
+you've brought in i thought that was
+
+ align:start position:0%
+you've brought in i thought that was
+ 
+
+ align:start position:0%
+you've brought in i thought that was
+really helpful
+
+ align:start position:0%
+really helpful
+ 
+
+ align:start position:0%
+really helpful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and i really
+
+ align:start position:0%
+and i really
+ 
+
+ align:start position:0%
+and i really
+liked the sort of back third of your
+
+ align:start position:0%
+liked the sort of back third of your
+ 
+
+ align:start position:0%
+liked the sort of back third of your
+presentation where you really kind of
+
+ align:start position:0%
+presentation where you really kind of
+ 
+
+ align:start position:0%
+presentation where you really kind of
+thought through all of the water
+
+ align:start position:0%
+thought through all of the water
+ 
+
+ align:start position:0%
+thought through all of the water
+diplomacy framework elements um
+
+ align:start position:0%
+diplomacy framework elements um
+ 
+
+ align:start position:0%
+diplomacy framework elements um
+so yeah great job i think my
+
+ align:start position:0%
+so yeah great job i think my
+ 
+
+ align:start position:0%
+so yeah great job i think my
+feedback um as you're thinking about
+
+ align:start position:0%
+feedback um as you're thinking about
+ 
+
+ align:start position:0%
+feedback um as you're thinking about
+writing your paper
+
+ align:start position:0%
+writing your paper
+ 
+
+ align:start position:0%
+writing your paper
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+i was a little confused at times about
+
+ align:start position:0%
+i was a little confused at times about
+ 
+
+ align:start position:0%
+i was a little confused at times about
+sort of how the treaty has failed to be
+
+ align:start position:0%
+sort of how the treaty has failed to be
+ 
+
+ align:start position:0%
+sort of how the treaty has failed to be
+implemented thinking about like
+
+ align:start position:0%
+implemented thinking about like
+ 
+
+ align:start position:0%
+implemented thinking about like
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+most
+
+ align:start position:0%
+most
+ 
+
+ align:start position:0%
+most
+most specifically around like how
+
+ align:start position:0%
+most specifically around like how
+ 
+
+ align:start position:0%
+most specifically around like how
+neither country is able to receive
+
+ align:start position:0%
+neither country is able to receive
+ 
+
+ align:start position:0%
+neither country is able to receive
+um their respective share as it was
+
+ align:start position:0%
+um their respective share as it was
+ 
+
+ align:start position:0%
+um their respective share as it was
+stipulated in the treaty is that
+
+ align:start position:0%
+stipulated in the treaty is that
+ 
+
+ align:start position:0%
+stipulated in the treaty is that
+technical problem is that a diplomatic
+
+ align:start position:0%
+technical problem is that a diplomatic
+ 
+
+ align:start position:0%
+technical problem is that a diplomatic
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i think you could maybe identify like
+
+ align:start position:0%
+i think you could maybe identify like
+ 
+
+ align:start position:0%
+i think you could maybe identify like
+where the specific sort of limitations
+
+ align:start position:0%
+where the specific sort of limitations
+ 
+
+ align:start position:0%
+where the specific sort of limitations
+or weaknesses of the treaty are in terms
+
+ align:start position:0%
+or weaknesses of the treaty are in terms
+ 
+
+ align:start position:0%
+or weaknesses of the treaty are in terms
+of how that actually is sort of
+
+ align:start position:0%
+of how that actually is sort of
+ 
+
+ align:start position:0%
+of how that actually is sort of
+manifested um
+
+ align:start position:0%
+manifested um
+ 
+
+ align:start position:0%
+manifested um
+on the ground
+
+ align:start position:0%
+on the ground
+ 
+
+ align:start position:0%
+on the ground
+so that's one thing to keep in mind um
+
+ align:start position:0%
+so that's one thing to keep in mind um
+ 
+
+ align:start position:0%
+so that's one thing to keep in mind um
+yeah i don't know if you could talk
+
+ align:start position:0%
+yeah i don't know if you could talk
+ 
+
+ align:start position:0%
+yeah i don't know if you could talk
+about that at all like are there sort of
+
+ align:start position:0%
+about that at all like are there sort of
+ 
+
+ align:start position:0%
+about that at all like are there sort of
+technical flaws or
+
+ align:start position:0%
+technical flaws or
+ 
+
+ align:start position:0%
+technical flaws or
+political flaws um that might be sort of
+
+ align:start position:0%
+political flaws um that might be sort of
+ 
+
+ align:start position:0%
+political flaws um that might be sort of
+helpful to understand
+
+ align:start position:0%
+helpful to understand
+ 
+
+ align:start position:0%
+helpful to understand
+uh well uh the technical flaws uh i i
+
+ align:start position:0%
+uh well uh the technical flaws uh i i
+ 
+
+ align:start position:0%
+uh well uh the technical flaws uh i i
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+accept my limitation i'm not really a
+
+ align:start position:0%
+accept my limitation i'm not really a
+ 
+
+ align:start position:0%
+accept my limitation i'm not really a
+technical guy i tried to read some
+
+ align:start position:0%
+technical guy i tried to read some
+ 
+
+ align:start position:0%
+technical guy i tried to read some
+technical papers and i actually read one
+
+ align:start position:0%
+technical papers and i actually read one
+ 
+
+ align:start position:0%
+technical papers and i actually read one
+of professor on animation's paper which
+
+ align:start position:0%
+of professor on animation's paper which
+ 
+
+ align:start position:0%
+of professor on animation's paper which
+gave me some insight so the one
+
+ align:start position:0%
+gave me some insight so the one
+ 
+
+ align:start position:0%
+gave me some insight so the one
+technical paper that i read they said
+
+ align:start position:0%
+technical paper that i read they said
+ 
+
+ align:start position:0%
+technical paper that i read they said
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in last thirty last two decades almost
+
+ align:start position:0%
+in last thirty last two decades almost
+ 
+
+ align:start position:0%
+in last thirty last two decades almost
+last two decades
+
+ align:start position:0%
+last two decades
+ 
+
+ align:start position:0%
+last two decades
+f very few
+
+ align:start position:0%
+f very few
+ 
+
+ align:start position:0%
+f very few
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+very few papers or very few research has
+
+ align:start position:0%
+very few papers or very few research has
+ 
+
+ align:start position:0%
+very few papers or very few research has
+been done to actually trying to quantify
+
+ align:start position:0%
+been done to actually trying to quantify
+ 
+
+ align:start position:0%
+been done to actually trying to quantify
+the quantify the
+
+ align:start position:0%
+the quantify the
+ 
+
+ align:start position:0%
+the quantify the
+the amount of water that has been there
+
+ align:start position:0%
+the amount of water that has been there
+ 
+
+ align:start position:0%
+the amount of water that has been there
+one of the reasons was there but
+
+ align:start position:0%
+one of the reasons was there but
+ 
+
+ align:start position:0%
+one of the reasons was there but
+initially the historical data was not
+
+ align:start position:0%
+initially the historical data was not
+ 
+
+ align:start position:0%
+initially the historical data was not
+there for example in first five years
+
+ align:start position:0%
+there for example in first five years
+ 
+
+ align:start position:0%
+there for example in first five years
+probably i mean first one or two years
+
+ align:start position:0%
+probably i mean first one or two years
+ 
+
+ align:start position:0%
+probably i mean first one or two years
+the the type of precision that you need
+
+ align:start position:0%
+the the type of precision that you need
+ 
+
+ align:start position:0%
+the the type of precision that you need
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to predict that what is going to happen
+
+ align:start position:0%
+to predict that what is going to happen
+ 
+
+ align:start position:0%
+to predict that what is going to happen
+through the history now that we have it
+
+ align:start position:0%
+through the history now that we have it
+ 
+
+ align:start position:0%
+through the history now that we have it
+fortunately because it has been it has
+
+ align:start position:0%
+fortunately because it has been it has
+ 
+
+ align:start position:0%
+fortunately because it has been it has
+been quite long so uh the research has
+
+ align:start position:0%
+been quite long so uh the research has
+ 
+
+ align:start position:0%
+been quite long so uh the research has
+uh already started so maybe i will try
+
+ align:start position:0%
+uh already started so maybe i will try
+ 
+
+ align:start position:0%
+uh already started so maybe i will try
+to put that
+
+ align:start position:0%
+to put that
+ 
+
+ align:start position:0%
+to put that
+and the diplomatic
+
+ align:start position:0%
+and the diplomatic
+ 
+
+ align:start position:0%
+and the diplomatic
+the diplomatic problems that you are
+
+ align:start position:0%
+the diplomatic problems that you are
+ 
+
+ align:start position:0%
+the diplomatic problems that you are
+saying that uh
+
+ align:start position:0%
+saying that uh
+ 
+
+ align:start position:0%
+saying that uh
+one major problem that i can say i mean
+
+ align:start position:0%
+one major problem that i can say i mean
+ 
+
+ align:start position:0%
+one major problem that i can say i mean
+since this is an i would never say this
+
+ align:start position:0%
+since this is an i would never say this
+ 
+
+ align:start position:0%
+since this is an i would never say this
+outside the classroom
+
+ align:start position:0%
+outside the classroom
+ 
+
+ align:start position:0%
+outside the classroom
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+for example uh
+
+ align:start position:0%
+for example uh
+ 
+
+ align:start position:0%
+for example uh
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+it has a national policy
+
+ align:start position:0%
+it has a national policy
+ 
+
+ align:start position:0%
+it has a national policy
+the government changes
+
+ align:start position:0%
+the government changes
+ 
+
+ align:start position:0%
+the government changes
+but the policy
+
+ align:start position:0%
+but the policy
+ 
+
+ align:start position:0%
+but the policy
+the the main theme of the policy remains
+
+ align:start position:0%
+the the main theme of the policy remains
+ 
+
+ align:start position:0%
+the the main theme of the policy remains
+maybe some sides changes but if you have
+
+ align:start position:0%
+maybe some sides changes but if you have
+ 
+
+ align:start position:0%
+maybe some sides changes but if you have
+to change the main theme of the policy
+
+ align:start position:0%
+to change the main theme of the policy
+ 
+
+ align:start position:0%
+to change the main theme of the policy
+for example u.s has a defense policy
+
+ align:start position:0%
+for example u.s has a defense policy
+ 
+
+ align:start position:0%
+for example u.s has a defense policy
+right us as a defense policy that we
+
+ align:start position:0%
+right us as a defense policy that we
+ 
+
+ align:start position:0%
+right us as a defense policy that we
+would do this we will do that how we
+
+ align:start position:0%
+would do this we will do that how we
+ 
+
+ align:start position:0%
+would do this we will do that how we
+would do that maybe that can be
+
+ align:start position:0%
+would do that maybe that can be
+ 
+
+ align:start position:0%
+would do that maybe that can be
+discussed
+
+ align:start position:0%
+discussed
+ 
+
+ align:start position:0%
+discussed
+and maybe different different
+
+ align:start position:0%
+and maybe different different
+ 
+
+ align:start position:0%
+and maybe different different
+governments can do it in a different way
+
+ align:start position:0%
+governments can do it in a different way
+ 
+
+ align:start position:0%
+governments can do it in a different way
+so in india of course indian democracy
+
+ align:start position:0%
+so in india of course indian democracy
+ 
+
+ align:start position:0%
+so in india of course indian democracy
+is not as strong as the u.s or the uk
+
+ align:start position:0%
+is not as strong as the u.s or the uk
+ 
+
+ align:start position:0%
+is not as strong as the u.s or the uk
+but in india
+
+ align:start position:0%
+but in india
+ 
+
+ align:start position:0%
+but in india
+in some basic factors for example the
+
+ align:start position:0%
+in some basic factors for example the
+ 
+
+ align:start position:0%
+in some basic factors for example the
+the defense or whether they would share
+
+ align:start position:0%
+the defense or whether they would share
+ 
+
+ align:start position:0%
+the defense or whether they would share
+this or that they also have some sort of
+
+ align:start position:0%
+this or that they also have some sort of
+ 
+
+ align:start position:0%
+this or that they also have some sort of
+policy they also have some sort of
+
+ align:start position:0%
+policy they also have some sort of
+ 
+
+ align:start position:0%
+policy they also have some sort of
+strict policy that even though the
+
+ align:start position:0%
+strict policy that even though the
+ 
+
+ align:start position:0%
+strict policy that even though the
+political
+
+ align:start position:0%
+political
+ 
+
+ align:start position:0%
+political
+government changes uh this uh this
+
+ align:start position:0%
+government changes uh this uh this
+ 
+
+ align:start position:0%
+government changes uh this uh this
+doesn't change much and they strongly
+
+ align:start position:0%
+doesn't change much and they strongly
+ 
+
+ align:start position:0%
+doesn't change much and they strongly
+uphold the constitution and one of the
+
+ align:start position:0%
+uphold the constitution and one of the
+ 
+
+ align:start position:0%
+uphold the constitution and one of the
+reasons is that there has not been in
+
+ align:start position:0%
+reasons is that there has not been in
+ 
+
+ align:start position:0%
+reasons is that there has not been in
+the history of india more than 60 years
+
+ align:start position:0%
+the history of india more than 60 years
+ 
+
+ align:start position:0%
+the history of india more than 60 years
+from 47 to 2021 more than 60 years uh no
+
+ align:start position:0%
+from 47 to 2021 more than 60 years uh no
+ 
+
+ align:start position:0%
+from 47 to 2021 more than 60 years uh no
+military
+
+ align:start position:0%
+military
+ 
+
+ align:start position:0%
+military
+takeover was there and because of india
+
+ align:start position:0%
+takeover was there and because of india
+ 
+
+ align:start position:0%
+takeover was there and because of india
+is so huge military takeover is actually
+
+ align:start position:0%
+is so huge military takeover is actually
+ 
+
+ align:start position:0%
+is so huge military takeover is actually
+not not very much feasible but in
+
+ align:start position:0%
+not not very much feasible but in
+ 
+
+ align:start position:0%
+not not very much feasible but in
+bangladesh it's a country 50 years of
+
+ align:start position:0%
+bangladesh it's a country 50 years of
+ 
+
+ align:start position:0%
+bangladesh it's a country 50 years of
+age
+
+ align:start position:0%
+age
+ 
+
+ align:start position:0%
+age
+out of 50 years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more than 15 years there were military
+
+ align:start position:0%
+more than 15 years there were military
+ 
+
+ align:start position:0%
+more than 15 years there were military
+governments and i would be very blunt
+
+ align:start position:0%
+governments and i would be very blunt
+ 
+
+ align:start position:0%
+governments and i would be very blunt
+here at present we also have some sort
+
+ align:start position:0%
+here at present we also have some sort
+ 
+
+ align:start position:0%
+here at present we also have some sort
+of autocratic government and the system
+
+ align:start position:0%
+of autocratic government and the system
+ 
+
+ align:start position:0%
+of autocratic government and the system
+has become such that uh i mean it is
+
+ align:start position:0%
+has become such that uh i mean it is
+ 
+
+ align:start position:0%
+has become such that uh i mean it is
+very tough for bangladesh to come out
+
+ align:start position:0%
+very tough for bangladesh to come out
+ 
+
+ align:start position:0%
+very tough for bangladesh to come out
+from this political so when you speak of
+
+ align:start position:0%
+from this political so when you speak of
+ 
+
+ align:start position:0%
+from this political so when you speak of
+diplomacy we have some wonderful
+
+ align:start position:0%
+diplomacy we have some wonderful
+ 
+
+ align:start position:0%
+diplomacy we have some wonderful
+diplomats really well trained diplomats
+
+ align:start position:0%
+diplomats really well trained diplomats
+ 
+
+ align:start position:0%
+diplomats really well trained diplomats
+but the decision actually comes from the
+
+ align:start position:0%
+but the decision actually comes from the
+ 
+
+ align:start position:0%
+but the decision actually comes from the
+politicians i would not blame them they
+
+ align:start position:0%
+politicians i would not blame them they
+ 
+
+ align:start position:0%
+politicians i would not blame them they
+definitely have their point of view but
+
+ align:start position:0%
+definitely have their point of view but
+ 
+
+ align:start position:0%
+definitely have their point of view but
+uh due to this lack of political culture
+
+ align:start position:0%
+uh due to this lack of political culture
+ 
+
+ align:start position:0%
+uh due to this lack of political culture
+of having a straight aim
+
+ align:start position:0%
+of having a straight aim
+ 
+
+ align:start position:0%
+of having a straight aim
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+it is like i mean uh total one
+
+ align:start position:0%
+it is like i mean uh total one
+ 
+
+ align:start position:0%
+it is like i mean uh total one
+government comes so far before the five
+
+ align:start position:0%
+government comes so far before the five
+ 
+
+ align:start position:0%
+government comes so far before the five
+or ten years one policy was going uh the
+
+ align:start position:0%
+or ten years one policy was going uh the
+ 
+
+ align:start position:0%
+or ten years one policy was going uh the
+government changes it goes backwards so
+
+ align:start position:0%
+government changes it goes backwards so
+ 
+
+ align:start position:0%
+government changes it goes backwards so
+it's zig zag zigzag so
+
+ align:start position:0%
+it's zig zag zigzag so
+ 
+
+ align:start position:0%
+it's zig zag zigzag so
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+it is it is an issue but uh thank you
+
+ align:start position:0%
+it is it is an issue but uh thank you
+ 
+
+ align:start position:0%
+it is it is an issue but uh thank you
+very much for the
+
+ align:start position:0%
+very much for the
+ 
+
+ align:start position:0%
+very much for the
+for the input because i would try to
+
+ align:start position:0%
+for the input because i would try to
+ 
+
+ align:start position:0%
+for the input because i would try to
+address these things especially uh
+
+ align:start position:0%
+address these things especially uh
+ 
+
+ align:start position:0%
+address these things especially uh
+specifically maybe i wouldn't be
+
+ align:start position:0%
+specifically maybe i wouldn't be
+ 
+
+ align:start position:0%
+specifically maybe i wouldn't be
+speaking too much about diplomacy
+
+ align:start position:0%
+speaking too much about diplomacy
+ 
+
+ align:start position:0%
+speaking too much about diplomacy
+because i work for the government and
+
+ align:start position:0%
+because i work for the government and
+ 
+
+ align:start position:0%
+because i work for the government and
+they read those papers and
+
+ align:start position:0%
+they read those papers and
+ 
+
+ align:start position:0%
+they read those papers and
+but the technical uh technical part
+
+ align:start position:0%
+but the technical uh technical part
+ 
+
+ align:start position:0%
+but the technical uh technical part
+maybe i will seek help from larry and
+
+ align:start position:0%
+maybe i will seek help from larry and
+ 
+
+ align:start position:0%
+maybe i will seek help from larry and
+professor gein uh to include more the
+
+ align:start position:0%
+professor gein uh to include more the
+ 
+
+ align:start position:0%
+professor gein uh to include more the
+technical parts in in my paper thank you
+
+ align:start position:0%
+technical parts in in my paper thank you
+ 
+
+ align:start position:0%
+technical parts in in my paper thank you
+very much
+
+ align:start position:0%
+very much
+ 
+
+ align:start position:0%
+very much
+hi mushroom um i also wanna echo i
+
+ align:start position:0%
+hi mushroom um i also wanna echo i
+ 
+
+ align:start position:0%
+hi mushroom um i also wanna echo i
+learned that huge amount of presentation
+
+ align:start position:0%
+learned that huge amount of presentation
+ 
+
+ align:start position:0%
+learned that huge amount of presentation
+the question the question i have and
+
+ align:start position:0%
+the question the question i have and
+ 
+
+ align:start position:0%
+the question the question i have and
+perhaps you address this somewhat but i
+
+ align:start position:0%
+perhaps you address this somewhat but i
+ 
+
+ align:start position:0%
+perhaps you address this somewhat but i
+like to speak more to it maybe i missed
+
+ align:start position:0%
+like to speak more to it maybe i missed
+ 
+
+ align:start position:0%
+like to speak more to it maybe i missed
+it but is does the current does the
+
+ align:start position:0%
+it but is does the current does the
+ 
+
+ align:start position:0%
+it but is does the current does the
+current treaty have
+
+ align:start position:0%
+current treaty have
+ 
+
+ align:start position:0%
+current treaty have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+like how does it manage water
+
+ align:start position:0%
+like how does it manage water
+ 
+
+ align:start position:0%
+like how does it manage water
+measurement uh and and the processes for
+
+ align:start position:0%
+measurement uh and and the processes for
+ 
+
+ align:start position:0%
+measurement uh and and the processes for
+actually determining how much water
+
+ align:start position:0%
+actually determining how much water
+ 
+
+ align:start position:0%
+actually determining how much water
+there is different times of year and how
+
+ align:start position:0%
+there is different times of year and how
+ 
+
+ align:start position:0%
+there is different times of year and how
+much water there is over time because
+
+ align:start position:0%
+much water there is over time because
+ 
+
+ align:start position:0%
+much water there is over time because
+you talked about the ways in which the
+
+ align:start position:0%
+you talked about the ways in which the
+ 
+
+ align:start position:0%
+you talked about the ways in which the
+amount of water has
+
+ align:start position:0%
+amount of water has
+ 
+
+ align:start position:0%
+amount of water has
+has changed partially as a result of
+
+ align:start position:0%
+has changed partially as a result of
+ 
+
+ align:start position:0%
+has changed partially as a result of
+droughts and and the different
+
+ align:start position:0%
+droughts and and the different
+ 
+
+ align:start position:0%
+droughts and and the different
+pieces of infrastructure that have been
+
+ align:start position:0%
+pieces of infrastructure that have been
+ 
+
+ align:start position:0%
+pieces of infrastructure that have been
+built um but i'm interested in in
+
+ align:start position:0%
+built um but i'm interested in in
+ 
+
+ align:start position:0%
+built um but i'm interested in in
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+if there's any
+
+ align:start position:0%
+if there's any
+ 
+
+ align:start position:0%
+if there's any
+ongoing uh collaboration or
+
+ align:start position:0%
+ongoing uh collaboration or
+ 
+
+ align:start position:0%
+ongoing uh collaboration or
+shared effort or even even individual uh
+
+ align:start position:0%
+shared effort or even even individual uh
+ 
+
+ align:start position:0%
+shared effort or even even individual uh
+kind of national efforts to
+
+ align:start position:0%
+kind of national efforts to
+ 
+
+ align:start position:0%
+kind of national efforts to
+quantify how the water
+
+ align:start position:0%
+quantify how the water
+ 
+
+ align:start position:0%
+quantify how the water
+both quantity and quality is changing
+
+ align:start position:0%
+both quantity and quality is changing
+ 
+
+ align:start position:0%
+both quantity and quality is changing
+over time
+
+ align:start position:0%
+over time
+ 
+
+ align:start position:0%
+over time
+well i do not know very details of the
+
+ align:start position:0%
+well i do not know very details of the
+ 
+
+ align:start position:0%
+well i do not know very details of the
+technicalities but i can give you some
+
+ align:start position:0%
+technicalities but i can give you some
+ 
+
+ align:start position:0%
+technicalities but i can give you some
+very basics which is there on the treaty
+
+ align:start position:0%
+very basics which is there on the treaty
+ 
+
+ align:start position:0%
+very basics which is there on the treaty
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the geography of the two regions is more
+
+ align:start position:0%
+the geography of the two regions is more
+ 
+
+ align:start position:0%
+the geography of the two regions is more
+or less same
+
+ align:start position:0%
+or less same
+ 
+
+ align:start position:0%
+or less same
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the west bengal and and bangladesh so
+
+ align:start position:0%
+the west bengal and and bangladesh so
+ 
+
+ align:start position:0%
+the west bengal and and bangladesh so
+although we are speaking of india india
+
+ align:start position:0%
+although we are speaking of india india
+ 
+
+ align:start position:0%
+although we are speaking of india india
+is a very big country right so 28 states
+
+ align:start position:0%
+is a very big country right so 28 states
+ 
+
+ align:start position:0%
+is a very big country right so 28 states
+but ultimately uh bangladesh and
+
+ align:start position:0%
+but ultimately uh bangladesh and
+ 
+
+ align:start position:0%
+but ultimately uh bangladesh and
+bangladesh shares with west bengal from
+
+ align:start position:0%
+bangladesh shares with west bengal from
+ 
+
+ align:start position:0%
+bangladesh shares with west bengal from
+where this the ganges river comes so
+
+ align:start position:0%
+where this the ganges river comes so
+ 
+
+ align:start position:0%
+where this the ganges river comes so
+i mean by studying the
+
+ align:start position:0%
+i mean by studying the
+ 
+
+ align:start position:0%
+i mean by studying the
+by studying bangladesh or by studying
+
+ align:start position:0%
+by studying bangladesh or by studying
+ 
+
+ align:start position:0%
+by studying bangladesh or by studying
+west bengal
+
+ align:start position:0%
+west bengal
+ 
+
+ align:start position:0%
+west bengal
+a very basic idea actually
+
+ align:start position:0%
+a very basic idea actually
+ 
+
+ align:start position:0%
+a very basic idea actually
+can be found for example the dry season
+
+ align:start position:0%
+can be found for example the dry season
+ 
+
+ align:start position:0%
+can be found for example the dry season
+in bangladesh from january to may it is
+
+ align:start position:0%
+in bangladesh from january to may it is
+ 
+
+ align:start position:0%
+in bangladesh from january to may it is
+same in west bengal
+
+ align:start position:0%
+same in west bengal
+ 
+
+ align:start position:0%
+same in west bengal
+and and and the
+
+ align:start position:0%
+and and and the
+ 
+
+ align:start position:0%
+and and and the
+under the west season in bangladesh
+
+ align:start position:0%
+under the west season in bangladesh
+ 
+
+ align:start position:0%
+under the west season in bangladesh
+which which falls up to december so
+
+ align:start position:0%
+which which falls up to december so
+ 
+
+ align:start position:0%
+which which falls up to december so
+from from july to december that is also
+
+ align:start position:0%
+from from july to december that is also
+ 
+
+ align:start position:0%
+from from july to december that is also
+that is also same same in
+
+ align:start position:0%
+that is also same same in
+ 
+
+ align:start position:0%
+that is also same same in
+both the parties so
+
+ align:start position:0%
+both the parties so
+ 
+
+ align:start position:0%
+both the parties so
+the join the joint committee they
+
+ align:start position:0%
+the join the joint committee they
+ 
+
+ align:start position:0%
+the join the joint committee they
+probably use some hydraulic models to
+
+ align:start position:0%
+probably use some hydraulic models to
+ 
+
+ align:start position:0%
+probably use some hydraulic models to
+to actually uh set the
+
+ align:start position:0%
+to actually uh set the
+ 
+
+ align:start position:0%
+to actually uh set the
+amount of water for example it is uh
+
+ align:start position:0%
+amount of water for example it is uh
+ 
+
+ align:start position:0%
+amount of water for example it is uh
+70 000
+
+ align:start position:0%
+70 000
+ 
+
+ align:start position:0%
+70 000
+cubics the the basic standard is the
+
+ align:start position:0%
+cubics the the basic standard is the
+ 
+
+ align:start position:0%
+cubics the the basic standard is the
+first one is as if if there is 70 000 uh
+
+ align:start position:0%
+first one is as if if there is 70 000 uh
+ 
+
+ align:start position:0%
+first one is as if if there is 70 000 uh
+cubic seconds
+
+ align:start position:0%
+cubic seconds
+ 
+
+ align:start position:0%
+cubic seconds
+q sec the the
+
+ align:start position:0%
+q sec the the
+ 
+
+ align:start position:0%
+q sec the the
+the unit is q sec if seventy thousand q
+
+ align:start position:0%
+the unit is q sec if seventy thousand q
+ 
+
+ align:start position:0%
+the unit is q sec if seventy thousand q
+sec is there both the countries will
+
+ align:start position:0%
+sec is there both the countries will
+ 
+
+ align:start position:0%
+sec is there both the countries will
+share fifty percent fifty fifty percent
+
+ align:start position:0%
+share fifty percent fifty fifty percent
+ 
+
+ align:start position:0%
+share fifty percent fifty fifty percent
+so the uh this is how they have made and
+
+ align:start position:0%
+so the uh this is how they have made and
+ 
+
+ align:start position:0%
+so the uh this is how they have made and
+from seventy to seventy five uh so there
+
+ align:start position:0%
+from seventy to seventy five uh so there
+ 
+
+ align:start position:0%
+from seventy to seventy five uh so there
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+the the balance ratio would be for india
+
+ align:start position:0%
+the the balance ratio would be for india
+ 
+
+ align:start position:0%
+the the balance ratio would be for india
+and bangladesh would get a minimum at 34
+
+ align:start position:0%
+and bangladesh would get a minimum at 34
+ 
+
+ align:start position:0%
+and bangladesh would get a minimum at 34
+000 q6 and
+
+ align:start position:0%
+000 q6 and
+ 
+
+ align:start position:0%
+000 q6 and
+if it's 75 to 75 and above above then
+
+ align:start position:0%
+if it's 75 to 75 and above above then
+ 
+
+ align:start position:0%
+if it's 75 to 75 and above above then
+the same kind of
+
+ align:start position:0%
+the same kind of
+ 
+
+ align:start position:0%
+the same kind of
+ratio is there
+
+ align:start position:0%
+ratio is there
+ 
+
+ align:start position:0%
+ratio is there
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this much is there for example you
+
+ align:start position:0%
+this much is there for example you
+ 
+
+ align:start position:0%
+this much is there for example you
+mentioned that there have been years in
+
+ align:start position:0%
+mentioned that there have been years in
+ 
+
+ align:start position:0%
+mentioned that there have been years in
+which neither side has gotten the
+
+ align:start position:0%
+which neither side has gotten the
+ 
+
+ align:start position:0%
+which neither side has gotten the
+amounts they've been allocated has there
+
+ align:start position:0%
+amounts they've been allocated has there
+ 
+
+ align:start position:0%
+amounts they've been allocated has there
+have been any ongoing efforts to you
+
+ align:start position:0%
+have been any ongoing efforts to you
+ 
+
+ align:start position:0%
+have been any ongoing efforts to you
+know if there's if there's under 70 000
+
+ align:start position:0%
+know if there's if there's under 70 000
+ 
+
+ align:start position:0%
+know if there's if there's under 70 000
+to quantify how much is flowing
+
+ align:start position:0%
+to quantify how much is flowing
+ 
+
+ align:start position:0%
+to quantify how much is flowing
+um and yes
+
+ align:start position:0%
+um and yes
+ 
+
+ align:start position:0%
+um and yes
+i i think that bangladesh we have we
+
+ align:start position:0%
+i i think that bangladesh we have we
+ 
+
+ align:start position:0%
+i i think that bangladesh we have we
+have an agency bangladesh indian water
+
+ align:start position:0%
+have an agency bangladesh indian water
+ 
+
+ align:start position:0%
+have an agency bangladesh indian water
+trust
+
+ align:start position:0%
+trust
+ 
+
+ align:start position:0%
+trust
+england water authority we have
+
+ align:start position:0%
+england water authority we have
+ 
+
+ align:start position:0%
+england water authority we have
+bangladesh water development board so
+
+ align:start position:0%
+bangladesh water development board so
+ 
+
+ align:start position:0%
+bangladesh water development board so
+they actually conduct some scientific
+
+ align:start position:0%
+they actually conduct some scientific
+ 
+
+ align:start position:0%
+they actually conduct some scientific
+studies and based on those
+
+ align:start position:0%
+studies and based on those
+ 
+
+ align:start position:0%
+studies and based on those
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i would be i would be honest with you
+
+ align:start position:0%
+i would be i would be honest with you
+ 
+
+ align:start position:0%
+i would be i would be honest with you
+that those the government organizations
+
+ align:start position:0%
+that those the government organizations
+ 
+
+ align:start position:0%
+that those the government organizations
+i mean for example the scientists uh
+
+ align:start position:0%
+i mean for example the scientists uh
+ 
+
+ align:start position:0%
+i mean for example the scientists uh
+scientists who have that sort of
+
+ align:start position:0%
+scientists who have that sort of
+ 
+
+ align:start position:0%
+scientists who have that sort of
+expertise
+
+ align:start position:0%
+expertise
+ 
+
+ align:start position:0%
+expertise
+the bangladesh
+
+ align:start position:0%
+the bangladesh
+ 
+
+ align:start position:0%
+the bangladesh
+those organizations are not really the
+
+ align:start position:0%
+those organizations are not really the
+ 
+
+ align:start position:0%
+those organizations are not really the
+most lucrative jobs for them
+
+ align:start position:0%
+most lucrative jobs for them
+ 
+
+ align:start position:0%
+most lucrative jobs for them
+so we do what we can and sometimes we we
+
+ align:start position:0%
+so we do what we can and sometimes we we
+ 
+
+ align:start position:0%
+so we do what we can and sometimes we we
+bring foreign from consultants and with
+
+ align:start position:0%
+bring foreign from consultants and with
+ 
+
+ align:start position:0%
+bring foreign from consultants and with
+those uh some studies studies are made
+
+ align:start position:0%
+those uh some studies studies are made
+ 
+
+ align:start position:0%
+those uh some studies studies are made
+and based on that actually uh this this
+
+ align:start position:0%
+and based on that actually uh this this
+ 
+
+ align:start position:0%
+and based on that actually uh this this
+sort of distributions are made but then
+
+ align:start position:0%
+sort of distributions are made but then
+ 
+
+ align:start position:0%
+sort of distributions are made but then
+again uh
+
+ align:start position:0%
+again uh
+ 
+
+ align:start position:0%
+again uh
+there are flaws in this uh uh um
+
+ align:start position:0%
+there are flaws in this uh uh um
+ 
+
+ align:start position:0%
+there are flaws in this uh uh um
+i think in terms of um
+
+ align:start position:0%
+i think in terms of um
+ 
+
+ align:start position:0%
+i think in terms of um
+measurement uh the joint river
+
+ align:start position:0%
+measurement uh the joint river
+ 
+
+ align:start position:0%
+measurement uh the joint river
+commission um is um so there is joint
+
+ align:start position:0%
+commission um is um so there is joint
+ 
+
+ align:start position:0%
+commission um is um so there is joint
+collaboration between india and uh
+
+ align:start position:0%
+collaboration between india and uh
+ 
+
+ align:start position:0%
+collaboration between india and uh
+bangladesh
+
+ align:start position:0%
+bangladesh
+ 
+
+ align:start position:0%
+bangladesh
+river commission is responsible for
+
+ align:start position:0%
+river commission is responsible for
+ 
+
+ align:start position:0%
+river commission is responsible for
+measuring the things so in in terms of
+
+ align:start position:0%
+measuring the things so in in terms of
+ 
+
+ align:start position:0%
+measuring the things so in in terms of
+theory both the indian side there is a
+
+ align:start position:0%
+theory both the indian side there is a
+ 
+
+ align:start position:0%
+theory both the indian side there is a
+joint rival commission and in the
+
+ align:start position:0%
+joint rival commission and in the
+ 
+
+ align:start position:0%
+joint rival commission and in the
+bangladesh side there is a joint river
+
+ align:start position:0%
+bangladesh side there is a joint river
+ 
+
+ align:start position:0%
+bangladesh side there is a joint river
+commission so both parties
+
+ align:start position:0%
+commission so both parties
+ 
+
+ align:start position:0%
+commission so both parties
+they um in terms of in theoretically
+
+ align:start position:0%
+they um in terms of in theoretically
+ 
+
+ align:start position:0%
+they um in terms of in theoretically
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+measure and in terms of um
+
+ align:start position:0%
+measure and in terms of um
+ 
+
+ align:start position:0%
+measure and in terms of um
+dry season period they measure the flow
+
+ align:start position:0%
+dry season period they measure the flow
+ 
+
+ align:start position:0%
+dry season period they measure the flow
+and they agree on that so i think in
+
+ align:start position:0%
+and they agree on that so i think in
+ 
+
+ align:start position:0%
+and they agree on that so i think in
+terms of agreement they do have this
+
+ align:start position:0%
+terms of agreement they do have this
+ 
+
+ align:start position:0%
+terms of agreement they do have this
+kind of things but
+
+ align:start position:0%
+kind of things but
+ 
+
+ align:start position:0%
+kind of things but
+in reality this kind of collaboration
+
+ align:start position:0%
+in reality this kind of collaboration
+ 
+
+ align:start position:0%
+in reality this kind of collaboration
+although they exist but
+
+ align:start position:0%
+although they exist but
+ 
+
+ align:start position:0%
+although they exist but
+this kind of enforcement is they rely
+
+ align:start position:0%
+this kind of enforcement is they rely
+ 
+
+ align:start position:0%
+this kind of enforcement is they rely
+only on the indian side that
+
+ align:start position:0%
+only on the indian side that
+ 
+
+ align:start position:0%
+only on the indian side that
+maybe they don't regularly go to the
+
+ align:start position:0%
+maybe they don't regularly go to the
+ 
+
+ align:start position:0%
+maybe they don't regularly go to the
+faraka point to measure the things but
+
+ align:start position:0%
+faraka point to measure the things but
+ 
+
+ align:start position:0%
+faraka point to measure the things but
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+the the way that india and john river
+
+ align:start position:0%
+the the way that india and john river
+ 
+
+ align:start position:0%
+the the way that india and john river
+commission communicate to the bangladesh
+
+ align:start position:0%
+commission communicate to the bangladesh
+ 
+
+ align:start position:0%
+commission communicate to the bangladesh
+joint river commission they agree on
+
+ align:start position:0%
+joint river commission they agree on
+ 
+
+ align:start position:0%
+joint river commission they agree on
+that kind of measurement so that's the
+
+ align:start position:0%
+that kind of measurement so that's the
+ 
+
+ align:start position:0%
+that kind of measurement so that's the
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+i was actually looking for some articles
+
+ align:start position:0%
+i was actually looking for some articles
+ 
+
+ align:start position:0%
+i was actually looking for some articles
+uh whether the
+
+ align:start position:0%
+uh whether the
+ 
+
+ align:start position:0%
+uh whether the
+the state water department i'm not sure
+
+ align:start position:0%
+the state water department i'm not sure
+ 
+
+ align:start position:0%
+the state water department i'm not sure
+that whether
+
+ align:start position:0%
+that whether
+ 
+
+ align:start position:0%
+that whether
+the indian states have separate
+
+ align:start position:0%
+the indian states have separate
+ 
+
+ align:start position:0%
+the indian states have separate
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+departments or not or whether it's a
+
+ align:start position:0%
+departments or not or whether it's a
+ 
+
+ align:start position:0%
+departments or not or whether it's a
+it's a federal i'm not sure so i try to
+
+ align:start position:0%
+it's a federal i'm not sure so i try to
+ 
+
+ align:start position:0%
+it's a federal i'm not sure so i try to
+find whether there is any collaboration
+
+ align:start position:0%
+find whether there is any collaboration
+ 
+
+ align:start position:0%
+find whether there is any collaboration
+between not only the state level but
+
+ align:start position:0%
+between not only the state level but
+ 
+
+ align:start position:0%
+between not only the state level but
+also the
+
+ align:start position:0%
+also the
+ 
+
+ align:start position:0%
+also the
+not only the not only the federal level
+
+ align:start position:0%
+not only the not only the federal level
+ 
+
+ align:start position:0%
+not only the not only the federal level
+but also the
+
+ align:start position:0%
+but also the
+ 
+
+ align:start position:0%
+but also the
+state uh the the west bengal state and
+
+ align:start position:0%
+state uh the the west bengal state and
+ 
+
+ align:start position:0%
+state uh the the west bengal state and
+and bangladesh but uh probably i i i
+
+ align:start position:0%
+and bangladesh but uh probably i i i
+ 
+
+ align:start position:0%
+and bangladesh but uh probably i i i
+i probably missed i didn't find in such
+
+ align:start position:0%
+i probably missed i didn't find in such
+ 
+
+ align:start position:0%
+i probably missed i didn't find in such
+collaboration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is there any other feedback that um
+
+ align:start position:0%
+so is there any other feedback that um
+ 
+
+ align:start position:0%
+so is there any other feedback that um
+you would like to
+
+ align:start position:0%
+you would like to
+ 
+
+ align:start position:0%
+you would like to
+bring like councilman or um
+
+ align:start position:0%
+bring like councilman or um
+ 
+
+ align:start position:0%
+bring like councilman or um
+a spline
+
+ align:start position:0%
+a spline
+ 
+
+ align:start position:0%
+a spline
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+mesh roof congratulations presentation i
+
+ align:start position:0%
+mesh roof congratulations presentation i
+ 
+
+ align:start position:0%
+mesh roof congratulations presentation i
+learned a lot from you today thank you
+
+ align:start position:0%
+learned a lot from you today thank you
+ 
+
+ align:start position:0%
+learned a lot from you today thank you
+um especially the visual was very rich
+
+ align:start position:0%
+um especially the visual was very rich
+ 
+
+ align:start position:0%
+um especially the visual was very rich
+your presentation i just have one quick
+
+ align:start position:0%
+your presentation i just have one quick
+ 
+
+ align:start position:0%
+your presentation i just have one quick
+suggestion because you said that you are
+
+ align:start position:0%
+suggestion because you said that you are
+ 
+
+ align:start position:0%
+suggestion because you said that you are
+not going to mention a lot about the
+
+ align:start position:0%
+not going to mention a lot about the
+ 
+
+ align:start position:0%
+not going to mention a lot about the
+diplomacy because you are part of the
+
+ align:start position:0%
+diplomacy because you are part of the
+ 
+
+ align:start position:0%
+diplomacy because you are part of the
+government
+
+ align:start position:0%
+government
+ 
+
+ align:start position:0%
+government
+but if you re when you read the the
+
+ align:start position:0%
+but if you re when you read the the
+ 
+
+ align:start position:0%
+but if you re when you read the the
+larry's book that specifically page one
+
+ align:start position:0%
+larry's book that specifically page one
+ 
+
+ align:start position:0%
+larry's book that specifically page one
+three three one 133
+
+ align:start position:0%
+three three one 133
+ 
+
+ align:start position:0%
+three three one 133
+he mentioned about that
+
+ align:start position:0%
+he mentioned about that
+ 
+
+ align:start position:0%
+he mentioned about that
+water manager and his stakeholder can
+
+ align:start position:0%
+water manager and his stakeholder can
+ 
+
+ align:start position:0%
+water manager and his stakeholder can
+approach
+
+ align:start position:0%
+approach
+ 
+
+ align:start position:0%
+approach
+uh to the to the conflict using the
+
+ align:start position:0%
+uh to the to the conflict using the
+ 
+
+ align:start position:0%
+uh to the to the conflict using the
+traditional way or they can use the
+
+ align:start position:0%
+traditional way or they can use the
+ 
+
+ align:start position:0%
+traditional way or they can use the
+non-zero sum approach and i think that's
+
+ align:start position:0%
+non-zero sum approach and i think that's
+ 
+
+ align:start position:0%
+non-zero sum approach and i think that's
+very interesting if you can
+
+ align:start position:0%
+very interesting if you can
+ 
+
+ align:start position:0%
+very interesting if you can
+include in your in your final paper
+
+ align:start position:0%
+include in your in your final paper
+ 
+
+ align:start position:0%
+include in your in your final paper
+yeah specifically they talk about the
+
+ align:start position:0%
+yeah specifically they talk about the
+ 
+
+ align:start position:0%
+yeah specifically they talk about the
+water management
+
+ align:start position:0%
+water management
+ 
+
+ align:start position:0%
+water management
+that's following two category categories
+
+ align:start position:0%
+that's following two category categories
+ 
+
+ align:start position:0%
+that's following two category categories
+a high
+
+ align:start position:0%
+a high
+ 
+
+ align:start position:0%
+a high
+can enforce a decision or the other
+
+ align:start position:0%
+can enforce a decision or the other
+ 
+
+ align:start position:0%
+can enforce a decision or the other
+parties themselves can negotiate a
+
+ align:start position:0%
+parties themselves can negotiate a
+ 
+
+ align:start position:0%
+parties themselves can negotiate a
+settlement
+
+ align:start position:0%
+settlement
+ 
+
+ align:start position:0%
+settlement
+that formal third help to implement i
+
+ align:start position:0%
+that formal third help to implement i
+ 
+
+ align:start position:0%
+that formal third help to implement i
+think this this chapter is very
+
+ align:start position:0%
+think this this chapter is very
+ 
+
+ align:start position:0%
+think this this chapter is very
+interesting for your presentation thank
+
+ align:start position:0%
+interesting for your presentation thank
+ 
+
+ align:start position:0%
+interesting for your presentation thank
+you very much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you very much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+thanks for the presentation um
+
+ align:start position:0%
+thanks for the presentation um
+ 
+
+ align:start position:0%
+thanks for the presentation um
+i'm hoping
+
+ align:start position:0%
+i'm hoping
+ 
+
+ align:start position:0%
+i'm hoping
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+synthesize
+
+ align:start position:0%
+synthesize
+ 
+
+ align:start position:0%
+synthesize
+the diplomacy discussion in the final
+
+ align:start position:0%
+the diplomacy discussion in the final
+ 
+
+ align:start position:0%
+the diplomacy discussion in the final
+version of the paper
+
+ align:start position:0%
+version of the paper
+ 
+
+ align:start position:0%
+version of the paper
+and it would be wonderful
+
+ align:start position:0%
+and it would be wonderful
+ 
+
+ align:start position:0%
+and it would be wonderful
+if you had a one page
+
+ align:start position:0%
+if you had a one page
+ 
+
+ align:start position:0%
+if you had a one page
+introduction
+
+ align:start position:0%
+introduction
+ 
+
+ align:start position:0%
+introduction
+to your discussion about diplomacy
+
+ align:start position:0%
+to your discussion about diplomacy
+ 
+
+ align:start position:0%
+to your discussion about diplomacy
+that highlighted
+
+ align:start position:0%
+that highlighted
+ 
+
+ align:start position:0%
+that highlighted
+two or three ideas
+
+ align:start position:0%
+two or three ideas
+ 
+
+ align:start position:0%
+two or three ideas
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's new or different
+
+ align:start position:0%
+what's new or different
+ 
+
+ align:start position:0%
+what's new or different
+with regard to diplomacy
+
+ align:start position:0%
+with regard to diplomacy
+ 
+
+ align:start position:0%
+with regard to diplomacy
+that could be tried that hasn't been
+
+ align:start position:0%
+that could be tried that hasn't been
+ 
+
+ align:start position:0%
+that could be tried that hasn't been
+tried
+
+ align:start position:0%
+tried
+ 
+
+ align:start position:0%
+tried
+without going into all the explanation
+
+ align:start position:0%
+without going into all the explanation
+ 
+
+ align:start position:0%
+without going into all the explanation
+in this summary
+
+ align:start position:0%
+in this summary
+ 
+
+ align:start position:0%
+in this summary
+of how this would be done
+
+ align:start position:0%
+of how this would be done
+ 
+
+ align:start position:0%
+of how this would be done
+but to just highlight
+
+ align:start position:0%
+but to just highlight
+ 
+
+ align:start position:0%
+but to just highlight
+you talking about bargaining chips
+
+ align:start position:0%
+you talking about bargaining chips
+ 
+
+ align:start position:0%
+you talking about bargaining chips
+you're talking about linking other
+
+ align:start position:0%
+you're talking about linking other
+ 
+
+ align:start position:0%
+you're talking about linking other
+issues it's it's a lot
+
+ align:start position:0%
+issues it's it's a lot
+ 
+
+ align:start position:0%
+issues it's it's a lot
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+pick two or three things
+
+ align:start position:0%
+pick two or three things
+ 
+
+ align:start position:0%
+pick two or three things
+that you want to suggest that are new
+
+ align:start position:0%
+that you want to suggest that are new
+ 
+
+ align:start position:0%
+that you want to suggest that are new
+and say
+
+ align:start position:0%
+and say
+ 
+
+ align:start position:0%
+and say
+i think the focus should shift to
+
+ align:start position:0%
+i think the focus should shift to
+ 
+
+ align:start position:0%
+i think the focus should shift to
+involving
+
+ align:start position:0%
+involving
+ 
+
+ align:start position:0%
+involving
+all of the states
+
+ align:start position:0%
+all of the states
+ 
+
+ align:start position:0%
+all of the states
+and not just the national governments
+
+ align:start position:0%
+and not just the national governments
+ 
+
+ align:start position:0%
+and not just the national governments
+okay if that's
+
+ align:start position:0%
+okay if that's
+ 
+
+ align:start position:0%
+okay if that's
+if that's one of your proposals
+
+ align:start position:0%
+if that's one of your proposals
+ 
+
+ align:start position:0%
+if that's one of your proposals
+then state that as a as an
+
+ align:start position:0%
+then state that as a as an
+ 
+
+ align:start position:0%
+then state that as a as an
+a a new emphasis
+
+ align:start position:0%
+a a new emphasis
+ 
+
+ align:start position:0%
+a a new emphasis
+that should that might change the whole
+
+ align:start position:0%
+that should that might change the whole
+ 
+
+ align:start position:0%
+that should that might change the whole
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+if you think as aaron was implying
+
+ align:start position:0%
+if you think as aaron was implying
+ 
+
+ align:start position:0%
+if you think as aaron was implying
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+a new approach to joint measurement
+
+ align:start position:0%
+a new approach to joint measurement
+ 
+
+ align:start position:0%
+a new approach to joint measurement
+would provide
+
+ align:start position:0%
+would provide
+ 
+
+ align:start position:0%
+would provide
+timely and believable information in a
+
+ align:start position:0%
+timely and believable information in a
+ 
+
+ align:start position:0%
+timely and believable information in a
+different way
+
+ align:start position:0%
+different way
+ 
+
+ align:start position:0%
+different way
+and that with that information
+
+ align:start position:0%
+and that with that information
+ 
+
+ align:start position:0%
+and that with that information
+new joint management
+
+ align:start position:0%
+new joint management
+ 
+
+ align:start position:0%
+new joint management
+under different sets of circumstances
+
+ align:start position:0%
+under different sets of circumstances
+ 
+
+ align:start position:0%
+under different sets of circumstances
+would be improved
+
+ align:start position:0%
+would be improved
+ 
+
+ align:start position:0%
+would be improved
+even if the treaty isn't changed
+
+ align:start position:0%
+even if the treaty isn't changed
+ 
+
+ align:start position:0%
+even if the treaty isn't changed
+then say that
+
+ align:start position:0%
+then say that
+ 
+
+ align:start position:0%
+then say that
+but not more than two or three ideas
+
+ align:start position:0%
+but not more than two or three ideas
+ 
+
+ align:start position:0%
+but not more than two or three ideas
+that could be expressed in a couple of
+
+ align:start position:0%
+that could be expressed in a couple of
+ 
+
+ align:start position:0%
+that could be expressed in a couple of
+sentences
+
+ align:start position:0%
+sentences
+ 
+
+ align:start position:0%
+sentences
+as the
+
+ align:start position:0%
+as the
+ 
+
+ align:start position:0%
+as the
+contribution
+
+ align:start position:0%
+contribution
+ 
+
+ align:start position:0%
+contribution
+to your discussion about diplomacy
+
+ align:start position:0%
+to your discussion about diplomacy
+ 
+
+ align:start position:0%
+to your discussion about diplomacy
+because otherwise it's too much
+
+ align:start position:0%
+because otherwise it's too much
+ 
+
+ align:start position:0%
+because otherwise it's too much
+okay it's impossible
+
+ align:start position:0%
+okay it's impossible
+ 
+
+ align:start position:0%
+okay it's impossible
+to follow all the different lines of
+
+ align:start position:0%
+to follow all the different lines of
+ 
+
+ align:start position:0%
+to follow all the different lines of
+diplomacy that are implied by the
+
+ align:start position:0%
+diplomacy that are implied by the
+ 
+
+ align:start position:0%
+diplomacy that are implied by the
+different maps and the different
+
+ align:start position:0%
+different maps and the different
+ 
+
+ align:start position:0%
+different maps and the different
+bargaining chips and
+
+ align:start position:0%
+bargaining chips and
+ 
+
+ align:start position:0%
+bargaining chips and
+the different relationships and what
+
+ align:start position:0%
+the different relationships and what
+ 
+
+ align:start position:0%
+the different relationships and what
+might be done and
+
+ align:start position:0%
+might be done and
+ 
+
+ align:start position:0%
+might be done and
+it's it's just too much
+
+ align:start position:0%
+it's it's just too much
+ 
+
+ align:start position:0%
+it's it's just too much
+just choose
+
+ align:start position:0%
+just choose
+ 
+
+ align:start position:0%
+just choose
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+no more than three but even those two
+
+ align:start position:0%
+no more than three but even those two
+ 
+
+ align:start position:0%
+no more than three but even those two
+uh ideas about changed diplomacy and
+
+ align:start position:0%
+uh ideas about changed diplomacy and
+ 
+
+ align:start position:0%
+uh ideas about changed diplomacy and
+highlight those okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i know that you have lots of other stuff
+
+ align:start position:0%
+i know that you have lots of other stuff
+ 
+
+ align:start position:0%
+i know that you have lots of other stuff
+but i think for the paper
+
+ align:start position:0%
+but i think for the paper
+ 
+
+ align:start position:0%
+but i think for the paper
+the power of the paper will be improved
+
+ align:start position:0%
+the power of the paper will be improved
+ 
+
+ align:start position:0%
+the power of the paper will be improved
+if you zero in
+
+ align:start position:0%
+if you zero in
+ 
+
+ align:start position:0%
+if you zero in
+on just a couple of ideas about changes
+
+ align:start position:0%
+on just a couple of ideas about changes
+ 
+
+ align:start position:0%
+on just a couple of ideas about changes
+in the diplomacy
+
+ align:start position:0%
+in the diplomacy
+ 
+
+ align:start position:0%
+in the diplomacy
+going forward that haven't been given
+
+ align:start position:0%
+going forward that haven't been given
+ 
+
+ align:start position:0%
+going forward that haven't been given
+enough or the right attention in the
+
+ align:start position:0%
+enough or the right attention in the
+ 
+
+ align:start position:0%
+enough or the right attention in the
+past
+
+ align:start position:0%
+past
+ 
+
+ align:start position:0%
+past
+professor in that case maybe i will try
+
+ align:start position:0%
+professor in that case maybe i will try
+ 
+
+ align:start position:0%
+professor in that case maybe i will try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+speak about
+
+ align:start position:0%
+speak about
+ 
+
+ align:start position:0%
+speak about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+i mean one point that i that i said
+
+ align:start position:0%
+i mean one point that i that i said
+ 
+
+ align:start position:0%
+i mean one point that i that i said
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+instead of three or two i will just
+
+ align:start position:0%
+instead of three or two i will just
+ 
+
+ align:start position:0%
+instead of three or two i will just
+focus on one
+
+ align:start position:0%
+focus on one
+ 
+
+ align:start position:0%
+focus on one
+that is the
+
+ align:start position:0%
+that is the
+ 
+
+ align:start position:0%
+that is the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bargaining chips the alternate
+
+ align:start position:0%
+bargaining chips the alternate
+ 
+
+ align:start position:0%
+bargaining chips the alternate
+bargaining chips maybe i can choose just
+
+ align:start position:0%
+bargaining chips maybe i can choose just
+ 
+
+ align:start position:0%
+bargaining chips maybe i can choose just
+this one and go deeper on that what do
+
+ align:start position:0%
+this one and go deeper on that what do
+ 
+
+ align:start position:0%
+this one and go deeper on that what do
+you think i i think that
+
+ align:start position:0%
+you think i i think that
+ 
+
+ align:start position:0%
+you think i i think that
+there are different bargaining chips
+
+ align:start position:0%
+there are different bargaining chips
+ 
+
+ align:start position:0%
+there are different bargaining chips
+that are more or less attractive to one
+
+ align:start position:0%
+that are more or less attractive to one
+ 
+
+ align:start position:0%
+that are more or less attractive to one
+country or another and that instead of
+
+ align:start position:0%
+country or another and that instead of
+ 
+
+ align:start position:0%
+country or another and that instead of
+saying bargaining chips is one thing
+
+ align:start position:0%
+saying bargaining chips is one thing
+ 
+
+ align:start position:0%
+saying bargaining chips is one thing
+i would specify the bargaining cheap
+
+ align:start position:0%
+i would specify the bargaining cheap
+ 
+
+ align:start position:0%
+i would specify the bargaining cheap
+pick one bargain in chicago which ones
+
+ align:start position:0%
+pick one bargain in chicago which ones
+ 
+
+ align:start position:0%
+pick one bargain in chicago which ones
+which i mean i thought the idea that you
+
+ align:start position:0%
+which i mean i thought the idea that you
+ 
+
+ align:start position:0%
+which i mean i thought the idea that you
+have all these states they're not happy
+
+ align:start position:0%
+have all these states they're not happy
+ 
+
+ align:start position:0%
+have all these states they're not happy
+with their own national government
+
+ align:start position:0%
+with their own national government
+ 
+
+ align:start position:0%
+with their own national government
+it's possible
+
+ align:start position:0%
+it's possible
+ 
+
+ align:start position:0%
+it's possible
+that a negotiation involving those
+
+ align:start position:0%
+that a negotiation involving those
+ 
+
+ align:start position:0%
+that a negotiation involving those
+states could change what gets talked
+
+ align:start position:0%
+states could change what gets talked
+ 
+
+ align:start position:0%
+states could change what gets talked
+about and shift the balance of power and
+
+ align:start position:0%
+about and shift the balance of power and
+ 
+
+ align:start position:0%
+about and shift the balance of power and
+provide an opportunity for a
+
+ align:start position:0%
+provide an opportunity for a
+ 
+
+ align:start position:0%
+provide an opportunity for a
+sub-regional piece
+
+ align:start position:0%
+sub-regional piece
+ 
+
+ align:start position:0%
+sub-regional piece
+of the treaty to go ahead
+
+ align:start position:0%
+of the treaty to go ahead
+ 
+
+ align:start position:0%
+of the treaty to go ahead
+so that's about bargaining chips but
+
+ align:start position:0%
+so that's about bargaining chips but
+ 
+
+ align:start position:0%
+so that's about bargaining chips but
+it's about the involvement of
+
+ align:start position:0%
+it's about the involvement of
+ 
+
+ align:start position:0%
+it's about the involvement of
+sub-national units on the india side
+
+ align:start position:0%
+sub-national units on the india side
+ 
+
+ align:start position:0%
+sub-national units on the india side
+and why their involvement could make a
+
+ align:start position:0%
+and why their involvement could make a
+ 
+
+ align:start position:0%
+and why their involvement could make a
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+so i'm i'm really saying
+
+ align:start position:0%
+so i'm i'm really saying
+ 
+
+ align:start position:0%
+so i'm i'm really saying
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+just talk about things at the level of
+
+ align:start position:0%
+just talk about things at the level of
+ 
+
+ align:start position:0%
+just talk about things at the level of
+bargaining chips it's too
+
+ align:start position:0%
+bargaining chips it's too
+ 
+
+ align:start position:0%
+bargaining chips it's too
+broad
+
+ align:start position:0%
+broad
+ 
+
+ align:start position:0%
+broad
+pick a couple of bargaining ships that
+
+ align:start position:0%
+pick a couple of bargaining ships that
+ 
+
+ align:start position:0%
+pick a couple of bargaining ships that
+you think are most promising and say who
+
+ align:start position:0%
+you think are most promising and say who
+ 
+
+ align:start position:0%
+you think are most promising and say who
+should do what
+
+ align:start position:0%
+should do what
+ 
+
+ align:start position:0%
+should do what
+with this new bargaining chip that might
+
+ align:start position:0%
+with this new bargaining chip that might
+ 
+
+ align:start position:0%
+with this new bargaining chip that might
+lead to
+
+ align:start position:0%
+lead to
+ 
+
+ align:start position:0%
+lead to
+either a new treaty or
+
+ align:start position:0%
+either a new treaty or
+ 
+
+ align:start position:0%
+either a new treaty or
+better administration of the existing
+
+ align:start position:0%
+better administration of the existing
+ 
+
+ align:start position:0%
+better administration of the existing
+treaty
+
+ align:start position:0%
+treaty
+ 
+
+ align:start position:0%
+treaty
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+a completely different kind of treaty
+
+ align:start position:0%
+a completely different kind of treaty
+ 
+
+ align:start position:0%
+a completely different kind of treaty
+i mean not keep the one you have
+
+ align:start position:0%
+i mean not keep the one you have
+ 
+
+ align:start position:0%
+i mean not keep the one you have
+and in addition
+
+ align:start position:0%
+and in addition
+ 
+
+ align:start position:0%
+and in addition
+adopt maybe a new treaty about this
+
+ align:start position:0%
+adopt maybe a new treaty about this
+ 
+
+ align:start position:0%
+adopt maybe a new treaty about this
+additional river
+
+ align:start position:0%
+additional river
+ 
+
+ align:start position:0%
+additional river
+maybe that's what opens things but but
+
+ align:start position:0%
+maybe that's what opens things but but
+ 
+
+ align:start position:0%
+maybe that's what opens things but but
+take specific bargaining chips and make
+
+ align:start position:0%
+take specific bargaining chips and make
+ 
+
+ align:start position:0%
+take specific bargaining chips and make
+them into your recommendations okay
+
+ align:start position:0%
+them into your recommendations okay
+ 
+
+ align:start position:0%
+them into your recommendations okay
+okay thank you yeah so in line with
+
+ align:start position:0%
+okay thank you yeah so in line with
+ 
+
+ align:start position:0%
+okay thank you yeah so in line with
+larry's succession so my suggestion
+
+ align:start position:0%
+larry's succession so my suggestion
+ 
+
+ align:start position:0%
+larry's succession so my suggestion
+would be um
+
+ align:start position:0%
+would be um
+ 
+
+ align:start position:0%
+would be um
+so you mentioned only the estate versus
+
+ align:start position:0%
+so you mentioned only the estate versus
+ 
+
+ align:start position:0%
+so you mentioned only the estate versus
+state um
+
+ align:start position:0%
+state um
+ 
+
+ align:start position:0%
+state um
+diplomacy but you know the um india's
+
+ align:start position:0%
+diplomacy but you know the um india's
+ 
+
+ align:start position:0%
+diplomacy but you know the um india's
+water um resource responsibility is
+
+ align:start position:0%
+water um resource responsibility is
+ 
+
+ align:start position:0%
+water um resource responsibility is
+given to the um
+
+ align:start position:0%
+given to the um
+ 
+
+ align:start position:0%
+given to the um
+uh is given to the estate i mean not
+
+ align:start position:0%
+uh is given to the estate i mean not
+ 
+
+ align:start position:0%
+uh is given to the estate i mean not
+federal state so um most uh
+
+ align:start position:0%
+federal state so um most uh
+ 
+
+ align:start position:0%
+federal state so um most uh
+mass of the water power is given to the
+
+ align:start position:0%
+mass of the water power is given to the
+ 
+
+ align:start position:0%
+mass of the water power is given to the
+state i mean west bengal state has the
+
+ align:start position:0%
+state i mean west bengal state has the
+ 
+
+ align:start position:0%
+state i mean west bengal state has the
+power for managing water resources
+
+ align:start position:0%
+power for managing water resources
+ 
+
+ align:start position:0%
+power for managing water resources
+in the west bengal so the central
+
+ align:start position:0%
+in the west bengal so the central
+ 
+
+ align:start position:0%
+in the west bengal so the central
+government cannot intervene anything
+
+ align:start position:0%
+government cannot intervene anything
+ 
+
+ align:start position:0%
+government cannot intervene anything
+regarding the
+
+ align:start position:0%
+regarding the
+ 
+
+ align:start position:0%
+regarding the
+decision of the west bengal's water
+
+ align:start position:0%
+decision of the west bengal's water
+ 
+
+ align:start position:0%
+decision of the west bengal's water
+resources uh issues so in that case um
+
+ align:start position:0%
+resources uh issues so in that case um
+ 
+
+ align:start position:0%
+resources uh issues so in that case um
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+one of the key stakeholders would be the
+
+ align:start position:0%
+one of the key stakeholders would be the
+ 
+
+ align:start position:0%
+one of the key stakeholders would be the
+west bengal and i i mean you know the
+
+ align:start position:0%
+west bengal and i i mean you know the
+ 
+
+ align:start position:0%
+west bengal and i i mean you know the
+how how the um this the water treaty
+
+ align:start position:0%
+how how the um this the water treaty
+ 
+
+ align:start position:0%
+how how the um this the water treaty
+didn't work although the central
+
+ align:start position:0%
+didn't work although the central
+ 
+
+ align:start position:0%
+didn't work although the central
+government
+
+ align:start position:0%
+government
+ 
+
+ align:start position:0%
+government
+was agreed with the bangladesh
+
+ align:start position:0%
+was agreed with the bangladesh
+ 
+
+ align:start position:0%
+was agreed with the bangladesh
+government but because of the
+
+ align:start position:0%
+government but because of the
+ 
+
+ align:start position:0%
+government but because of the
+west bengal government uh it didn't
+
+ align:start position:0%
+west bengal government uh it didn't
+ 
+
+ align:start position:0%
+west bengal government uh it didn't
+happen so i think this um as larry
+
+ align:start position:0%
+happen so i think this um as larry
+ 
+
+ align:start position:0%
+happen so i think this um as larry
+mentioned if we can incorporate or you
+
+ align:start position:0%
+mentioned if we can incorporate or you
+ 
+
+ align:start position:0%
+mentioned if we can incorporate or you
+can incorporate the um
+
+ align:start position:0%
+can incorporate the um
+ 
+
+ align:start position:0%
+can incorporate the um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the state as as a stakeholders
+
+ align:start position:0%
+the state as as a stakeholders
+ 
+
+ align:start position:0%
+the state as as a stakeholders
+maybe that can also uh important and uh
+
+ align:start position:0%
+maybe that can also uh important and uh
+ 
+
+ align:start position:0%
+maybe that can also uh important and uh
+i think that is essential not important
+
+ align:start position:0%
+i think that is essential not important
+ 
+
+ align:start position:0%
+i think that is essential not important
+because without a study you cannot
+
+ align:start position:0%
+because without a study you cannot
+ 
+
+ align:start position:0%
+because without a study you cannot
+negotiate with the central
+
+ align:start position:0%
+negotiate with the central
+ 
+
+ align:start position:0%
+negotiate with the central
+government
+
+ align:start position:0%
+government
+ 
+
+ align:start position:0%
+government
+so this is on point and in terms of um
+
+ align:start position:0%
+so this is on point and in terms of um
+ 
+
+ align:start position:0%
+so this is on point and in terms of um
+identifying issues already if you um
+
+ align:start position:0%
+identifying issues already if you um
+ 
+
+ align:start position:0%
+identifying issues already if you um
+ask some of the people's key peoples uh
+
+ align:start position:0%
+ask some of the people's key peoples uh
+ 
+
+ align:start position:0%
+ask some of the people's key peoples uh
+they need to be easier for um
+
+ align:start position:0%
+they need to be easier for um
+ 
+
+ align:start position:0%
+they need to be easier for um
+you so you already identified several
+
+ align:start position:0%
+you so you already identified several
+ 
+
+ align:start position:0%
+you so you already identified several
+issues one of the issues is the um is
+
+ align:start position:0%
+issues one of the issues is the um is
+ 
+
+ align:start position:0%
+issues one of the issues is the um is
+bangladesh is concerned regarding the
+
+ align:start position:0%
+bangladesh is concerned regarding the
+ 
+
+ align:start position:0%
+bangladesh is concerned regarding the
+climate sense and its impact on the
+
+ align:start position:0%
+climate sense and its impact on the
+ 
+
+ align:start position:0%
+climate sense and its impact on the
+future uh river flow
+
+ align:start position:0%
+future uh river flow
+ 
+
+ align:start position:0%
+future uh river flow
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so this is one of the key aspect but
+
+ align:start position:0%
+so this is one of the key aspect but
+ 
+
+ align:start position:0%
+so this is one of the key aspect but
+also other respect for the new soul game
+
+ align:start position:0%
+also other respect for the new soul game
+ 
+
+ align:start position:0%
+also other respect for the new soul game
+um you already mentioned the
+
+ align:start position:0%
+um you already mentioned the
+ 
+
+ align:start position:0%
+um you already mentioned the
+incorporating how the seven sisters and
+
+ align:start position:0%
+incorporating how the seven sisters and
+ 
+
+ align:start position:0%
+incorporating how the seven sisters and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the transit
+
+ align:start position:0%
+the transit
+ 
+
+ align:start position:0%
+the transit
+bangladesh can help achieving this um
+
+ align:start position:0%
+bangladesh can help achieving this um
+ 
+
+ align:start position:0%
+bangladesh can help achieving this um
+this uh yeah the the new
+
+ align:start position:0%
+this uh yeah the the new
+ 
+
+ align:start position:0%
+this uh yeah the the new
+uh water treaty that that incorporates
+
+ align:start position:0%
+uh water treaty that that incorporates
+ 
+
+ align:start position:0%
+uh water treaty that that incorporates
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+the future uh ensuring future
+
+ align:start position:0%
+the future uh ensuring future
+ 
+
+ align:start position:0%
+the future uh ensuring future
+reward flow but but also
+
+ align:start position:0%
+reward flow but but also
+ 
+
+ align:start position:0%
+reward flow but but also
+you know the last few years there was a
+
+ align:start position:0%
+you know the last few years there was a
+ 
+
+ align:start position:0%
+you know the last few years there was a
+discussion for developing a um paris in
+
+ align:start position:0%
+discussion for developing a um paris in
+ 
+
+ align:start position:0%
+discussion for developing a um paris in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ganges in the within the bangladesh part
+
+ align:start position:0%
+ganges in the within the bangladesh part
+ 
+
+ align:start position:0%
+ganges in the within the bangladesh part
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+india um denied and with india opposed
+
+ align:start position:0%
+india um denied and with india opposed
+ 
+
+ align:start position:0%
+india um denied and with india opposed
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+plan has been
+
+ align:start position:0%
+plan has been
+ 
+
+ align:start position:0%
+plan has been
+uh heard the deep sea base the deep sea
+
+ align:start position:0%
+uh heard the deep sea base the deep sea
+ 
+
+ align:start position:0%
+uh heard the deep sea base the deep sea
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+not deep sea uh berries in the uh
+
+ align:start position:0%
+not deep sea uh berries in the uh
+ 
+
+ align:start position:0%
+not deep sea uh berries in the uh
+yeah the freshwater flow
+
+ align:start position:0%
+yeah the freshwater flow
+ 
+
+ align:start position:0%
+yeah the freshwater flow
+uh berries in the bangladesh to store uh
+
+ align:start position:0%
+uh berries in the bangladesh to store uh
+ 
+
+ align:start position:0%
+uh berries in the bangladesh to store uh
+fresh water for for
+
+ align:start position:0%
+fresh water for for
+ 
+
+ align:start position:0%
+fresh water for for
+for uh southwest part of the bangladesh
+
+ align:start position:0%
+for uh southwest part of the bangladesh
+ 
+
+ align:start position:0%
+for uh southwest part of the bangladesh
+so this kind of option clear creation
+
+ align:start position:0%
+so this kind of option clear creation
+ 
+
+ align:start position:0%
+so this kind of option clear creation
+can be helpful for for treaty
+
+ align:start position:0%
+can be helpful for for treaty
+ 
+
+ align:start position:0%
+can be helpful for for treaty
+negotiations so i i
+
+ align:start position:0%
+negotiations so i i
+ 
+
+ align:start position:0%
+negotiations so i i
+believe if you can ask some of the
+
+ align:start position:0%
+believe if you can ask some of the
+ 
+
+ align:start position:0%
+believe if you can ask some of the
+people's that i already mentioned to you
+
+ align:start position:0%
+people's that i already mentioned to you
+ 
+
+ align:start position:0%
+people's that i already mentioned to you
+if you interview them i think you can
+
+ align:start position:0%
+if you interview them i think you can
+ 
+
+ align:start position:0%
+if you interview them i think you can
+have more much more insight but for the
+
+ align:start position:0%
+have more much more insight but for the
+ 
+
+ align:start position:0%
+have more much more insight but for the
+paper you might not consider them given
+
+ align:start position:0%
+paper you might not consider them given
+ 
+
+ align:start position:0%
+paper you might not consider them given
+the time limit but as larry mentioned if
+
+ align:start position:0%
+the time limit but as larry mentioned if
+ 
+
+ align:start position:0%
+the time limit but as larry mentioned if
+you consider only two or three specific
+
+ align:start position:0%
+you consider only two or three specific
+ 
+
+ align:start position:0%
+you consider only two or three specific
+points that can be helpful for
+
+ align:start position:0%
+points that can be helpful for
+ 
+
+ align:start position:0%
+points that can be helpful for
+incorporating someone could be the
+
+ align:start position:0%
+incorporating someone could be the
+ 
+
+ align:start position:0%
+incorporating someone could be the
+climate sense other
+
+ align:start position:0%
+climate sense other
+ 
+
+ align:start position:0%
+climate sense other
+uh could be the engaging stakeholders
+
+ align:start position:0%
+uh could be the engaging stakeholders
+ 
+
+ align:start position:0%
+uh could be the engaging stakeholders
+like state level
+
+ align:start position:0%
+like state level
+ 
+
+ align:start position:0%
+like state level
+stakeholders and and the interacting
+
+ align:start position:0%
+stakeholders and and the interacting
+ 
+
+ align:start position:0%
+stakeholders and and the interacting
+with the um seven system for the transit
+
+ align:start position:0%
+with the um seven system for the transit
+ 
+
+ align:start position:0%
+with the um seven system for the transit
+and how this can help
+
+ align:start position:0%
+and how this can help
+ 
+
+ align:start position:0%
+and how this can help
+treaty negotiations so this kind of
+
+ align:start position:0%
+treaty negotiations so this kind of
+ 
+
+ align:start position:0%
+treaty negotiations so this kind of
+uh this is specific aspects you can
+
+ align:start position:0%
+uh this is specific aspects you can
+ 
+
+ align:start position:0%
+uh this is specific aspects you can
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+thank you very much
\ No newline at end of file
diff --git a/wbEFsypvVQI.txt b/wbEFsypvVQI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..87946303d9a3ee64c2017311c488bc822b9231bc
--- /dev/null
+++ b/wbEFsypvVQI.txt
@@ -0,0 +1,9403 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+down.
+
+ align:start position:0%
+down.
+ 
+
+ align:start position:0%
+down.
+Hey
+
+ align:start position:0%
+Hey
+ 
+
+ align:start position:0%
+Hey
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hi, in this lecture I'd like to continue
+
+ align:start position:0%
+Hi, in this lecture I'd like to continue
+ 
+
+ align:start position:0%
+Hi, in this lecture I'd like to continue
+with describing function analysis that
+
+ align:start position:0%
+with describing function analysis that
+ 
+
+ align:start position:0%
+with describing function analysis that
+we introduced last time.
+
+ align:start position:0%
+we introduced last time.
+ 
+
+ align:start position:0%
+we introduced last time.
+And for the first example, I'd like to
+
+ align:start position:0%
+And for the first example, I'd like to
+ 
+
+ align:start position:0%
+And for the first example, I'd like to
+consider a system where we can actually
+
+ align:start position:0%
+consider a system where we can actually
+ 
+
+ align:start position:0%
+consider a system where we can actually
+get an exact answer by just tracing
+
+ align:start position:0%
+get an exact answer by just tracing
+ 
+
+ align:start position:0%
+get an exact answer by just tracing
+through the operation of the system even
+
+ align:start position:0%
+through the operation of the system even
+ 
+
+ align:start position:0%
+through the operation of the system even
+though it is a nonlinear system.
+
+ align:start position:0%
+though it is a nonlinear system.
+ 
+
+ align:start position:0%
+though it is a nonlinear system.
+Consequently, we really wouldn't use
+
+ align:start position:0%
+Consequently, we really wouldn't use
+ 
+
+ align:start position:0%
+Consequently, we really wouldn't use
+describing function analysis for this
+
+ align:start position:0%
+describing function analysis for this
+ 
+
+ align:start position:0%
+describing function analysis for this
+particular system since we can we can
+
+ align:start position:0%
+particular system since we can we can
+ 
+
+ align:start position:0%
+particular system since we can we can
+get an exact answer by actually what
+
+ align:start position:0%
+get an exact answer by actually what
+ 
+
+ align:start position:0%
+get an exact answer by actually what
+amounts to a far simpler technique. Uh
+
+ align:start position:0%
+amounts to a far simpler technique. Uh
+ 
+
+ align:start position:0%
+amounts to a far simpler technique. Uh
+however, I think it's a good example of
+
+ align:start position:0%
+however, I think it's a good example of
+ 
+
+ align:start position:0%
+however, I think it's a good example of
+how well the describing function
+
+ align:start position:0%
+how well the describing function
+ 
+
+ align:start position:0%
+how well the describing function
+analysis supports the exact answer even
+
+ align:start position:0%
+analysis supports the exact answer even
+ 
+
+ align:start position:0%
+analysis supports the exact answer even
+in a situation where at least one of the
+
+ align:start position:0%
+in a situation where at least one of the
+ 
+
+ align:start position:0%
+in a situation where at least one of the
+assumptions used to used in describing
+
+ align:start position:0%
+assumptions used to used in describing
+ 
+
+ align:start position:0%
+assumptions used to used in describing
+function analysis is rather compromised.
+
+ align:start position:0%
+function analysis is rather compromised.
+ 
+
+ align:start position:0%
+function analysis is rather compromised.
+There's a fairly popular circuit that's
+
+ align:start position:0%
+There's a fairly popular circuit that's
+ 
+
+ align:start position:0%
+There's a fairly popular circuit that's
+used for function generators, the sorts
+
+ align:start position:0%
+used for function generators, the sorts
+ 
+
+ align:start position:0%
+used for function generators, the sorts
+of of equipment that one uses as signal
+
+ align:start position:0%
+of of equipment that one uses as signal
+ 
+
+ align:start position:0%
+of of equipment that one uses as signal
+sources in a laboratory very frequently.
+
+ align:start position:0%
+sources in a laboratory very frequently.
+ 
+
+ align:start position:0%
+sources in a laboratory very frequently.
+And that system or that technique is
+
+ align:start position:0%
+And that system or that technique is
+ 
+
+ align:start position:0%
+And that system or that technique is
+shown in the first viewraph. What we do
+
+ align:start position:0%
+shown in the first viewraph. What we do
+ 
+
+ align:start position:0%
+shown in the first viewraph. What we do
+is take a Schmidt trigger here. I've
+
+ align:start position:0%
+is take a Schmidt trigger here. I've
+ 
+
+ align:start position:0%
+is take a Schmidt trigger here. I've
+shown one that's normalized
+
+ align:start position:0%
+shown one that's normalized
+ 
+
+ align:start position:0%
+shown one that's normalized
+uh and combine it in a negative feedback
+
+ align:start position:0%
+uh and combine it in a negative feedback
+ 
+
+ align:start position:0%
+uh and combine it in a negative feedback
+loop, the inversion indicated here with
+
+ align:start position:0%
+loop, the inversion indicated here with
+ 
+
+ align:start position:0%
+loop, the inversion indicated here with
+an integrator. The Schmidt trigger uh
+
+ align:start position:0%
+an integrator. The Schmidt trigger uh
+ 
+
+ align:start position:0%
+an integrator. The Schmidt trigger uh
+has rather interesting nonlinear
+
+ align:start position:0%
+has rather interesting nonlinear
+ 
+
+ align:start position:0%
+has rather interesting nonlinear
+characteristics. And of course the way
+
+ align:start position:0%
+characteristics. And of course the way
+ 
+
+ align:start position:0%
+characteristics. And of course the way
+it works is suppose we started for
+
+ align:start position:0%
+it works is suppose we started for
+ 
+
+ align:start position:0%
+it works is suppose we started for
+example at this point uh if we made the
+
+ align:start position:0%
+example at this point uh if we made the
+ 
+
+ align:start position:0%
+example at this point uh if we made the
+signal VA the input to the Schmidt
+
+ align:start position:0%
+signal VA the input to the Schmidt
+ 
+
+ align:start position:0%
+signal VA the input to the Schmidt
+trigger negative we could continue going
+
+ align:start position:0%
+trigger negative we could continue going
+ 
+
+ align:start position:0%
+trigger negative we could continue going
+negative as far as we wish to uh the
+
+ align:start position:0%
+negative as far as we wish to uh the
+ 
+
+ align:start position:0%
+negative as far as we wish to uh the
+output of the Schmidt trigger would
+
+ align:start position:0%
+output of the Schmidt trigger would
+ 
+
+ align:start position:0%
+output of the Schmidt trigger would
+remain minus1. Now as we make VA change
+
+ align:start position:0%
+remain minus1. Now as we make VA change
+ 
+
+ align:start position:0%
+remain minus1. Now as we make VA change
+in a positive direction when we get to a
+
+ align:start position:0%
+in a positive direction when we get to a
+ 
+
+ align:start position:0%
+in a positive direction when we get to a
+trigger point in this case at plus one
+
+ align:start position:0%
+trigger point in this case at plus one
+ 
+
+ align:start position:0%
+trigger point in this case at plus one
+the output would abruptly switch to +
+
+ align:start position:0%
+the output would abruptly switch to +
+ 
+
+ align:start position:0%
+the output would abruptly switch to +
+one further increases in the voltage VA
+
+ align:start position:0%
+one further increases in the voltage VA
+ 
+
+ align:start position:0%
+one further increases in the voltage VA
+positive changes in the voltage VA don't
+
+ align:start position:0%
+positive changes in the voltage VA don't
+ 
+
+ align:start position:0%
+positive changes in the voltage VA don't
+change the state of the Schmidt trigger
+
+ align:start position:0%
+change the state of the Schmidt trigger
+ 
+
+ align:start position:0%
+change the state of the Schmidt trigger
+and what we have to do is go back go
+
+ align:start position:0%
+and what we have to do is go back go
+ 
+
+ align:start position:0%
+and what we have to do is go back go
+past the original switching point and in
+
+ align:start position:0%
+past the original switching point and in
+ 
+
+ align:start position:0%
+past the original switching point and in
+fact change VA to minus one before the
+
+ align:start position:0%
+fact change VA to minus one before the
+ 
+
+ align:start position:0%
+fact change VA to minus one before the
+Schmidt trigger once again changes
+
+ align:start position:0%
+Schmidt trigger once again changes
+ 
+
+ align:start position:0%
+Schmidt trigger once again changes
+state, it then flips down and so forth.
+
+ align:start position:0%
+state, it then flips down and so forth.
+ 
+
+ align:start position:0%
+state, it then flips down and so forth.
+Uh again, once we've reached the state
+
+ align:start position:0%
+Uh again, once we've reached the state
+ 
+
+ align:start position:0%
+Uh again, once we've reached the state
+with the output at minus one, further
+
+ align:start position:0%
+with the output at minus one, further
+ 
+
+ align:start position:0%
+with the output at minus one, further
+negative changes in VA don't change the
+
+ align:start position:0%
+negative changes in VA don't change the
+ 
+
+ align:start position:0%
+negative changes in VA don't change the
+state. We have to get back up to a level
+
+ align:start position:0%
+state. We have to get back up to a level
+ 
+
+ align:start position:0%
+state. We have to get back up to a level
+of plus one for the input voltage before
+
+ align:start position:0%
+of plus one for the input voltage before
+ 
+
+ align:start position:0%
+of plus one for the input voltage before
+the circuit once again changes state.
+
+ align:start position:0%
+the circuit once again changes state.
+ 
+
+ align:start position:0%
+the circuit once again changes state.
+The operation then of the oscillator is
+
+ align:start position:0%
+The operation then of the oscillator is
+ 
+
+ align:start position:0%
+The operation then of the oscillator is
+fairly easily seen. This is a circuit
+
+ align:start position:0%
+fairly easily seen. This is a circuit
+ 
+
+ align:start position:0%
+fairly easily seen. This is a circuit
+that has really two modes of energy
+
+ align:start position:0%
+that has really two modes of energy
+ 
+
+ align:start position:0%
+that has really two modes of energy
+storage, if you will. We have the
+
+ align:start position:0%
+storage, if you will. We have the
+ 
+
+ align:start position:0%
+storage, if you will. We have the
+integrator, but we also have the Schmidt
+
+ align:start position:0%
+integrator, but we also have the Schmidt
+ 
+
+ align:start position:0%
+integrator, but we also have the Schmidt
+trigger which has memory. And so we
+
+ align:start position:0%
+trigger which has memory. And so we
+ 
+
+ align:start position:0%
+trigger which has memory. And so we
+really have two initial conditions to
+
+ align:start position:0%
+really have two initial conditions to
+ 
+
+ align:start position:0%
+really have two initial conditions to
+specify. One being the initial voltage
+
+ align:start position:0%
+specify. One being the initial voltage
+ 
+
+ align:start position:0%
+specify. One being the initial voltage
+out of the integrator at some time and
+
+ align:start position:0%
+out of the integrator at some time and
+ 
+
+ align:start position:0%
+out of the integrator at some time and
+the second one being the state of the
+
+ align:start position:0%
+the second one being the state of the
+ 
+
+ align:start position:0%
+the second one being the state of the
+Schmidt trigger. Let's suppose for
+
+ align:start position:0%
+Schmidt trigger. Let's suppose for
+ 
+
+ align:start position:0%
+Schmidt trigger. Let's suppose for
+example we're at a at this point on the
+
+ align:start position:0%
+example we're at a at this point on the
+ 
+
+ align:start position:0%
+example we're at a at this point on the
+Schmidt trigger characteristics. the
+
+ align:start position:0%
+Schmidt trigger characteristics. the
+ 
+
+ align:start position:0%
+Schmidt trigger characteristics. the
+voltage VA which is the voltage out of
+
+ align:start position:0%
+voltage VA which is the voltage out of
+ 
+
+ align:start position:0%
+voltage VA which is the voltage out of
+the integrator
+
+ align:start position:0%
+the integrator
+ 
+
+ align:start position:0%
+the integrator
+equal to zero and the output of the
+
+ align:start position:0%
+equal to zero and the output of the
+ 
+
+ align:start position:0%
+equal to zero and the output of the
+Schmidt trigger at minus one. There's of
+
+ align:start position:0%
+Schmidt trigger at minus one. There's of
+ 
+
+ align:start position:0%
+Schmidt trigger at minus one. There's of
+course two possible values that the
+
+ align:start position:0%
+course two possible values that the
+ 
+
+ align:start position:0%
+course two possible values that the
+output of the Schmidt trigger VB can
+
+ align:start position:0%
+output of the Schmidt trigger VB can
+ 
+
+ align:start position:0%
+output of the Schmidt trigger VB can
+take on. Uh let's assume it's in the
+
+ align:start position:0%
+take on. Uh let's assume it's in the
+ 
+
+ align:start position:0%
+take on. Uh let's assume it's in the
+state where the output is minus1.
+
+ align:start position:0%
+state where the output is minus1.
+ 
+
+ align:start position:0%
+state where the output is minus1.
+Uh if that's the case, what we would
+
+ align:start position:0%
+Uh if that's the case, what we would
+ 
+
+ align:start position:0%
+Uh if that's the case, what we would
+find out is that we apply a negative
+
+ align:start position:0%
+find out is that we apply a negative
+ 
+
+ align:start position:0%
+find out is that we apply a negative
+signal to the integrator. Uh we have a
+
+ align:start position:0%
+signal to the integrator. Uh we have a
+ 
+
+ align:start position:0%
+signal to the integrator. Uh we have a
+minus one volt applied to the
+
+ align:start position:0%
+minus one volt applied to the
+ 
+
+ align:start position:0%
+minus one volt applied to the
+integrator. Consequently, since the
+
+ align:start position:0%
+integrator. Consequently, since the
+ 
+
+ align:start position:0%
+integrator. Consequently, since the
+integrator includes an inversion, why
+
+ align:start position:0%
+integrator includes an inversion, why
+ 
+
+ align:start position:0%
+integrator includes an inversion, why
+the output of the integrator would
+
+ align:start position:0%
+the output of the integrator would
+ 
+
+ align:start position:0%
+the output of the integrator would
+change in a positive direction. So we
+
+ align:start position:0%
+change in a positive direction. So we
+ 
+
+ align:start position:0%
+change in a positive direction. So we
+walk along the characteristics starting
+
+ align:start position:0%
+walk along the characteristics starting
+ 
+
+ align:start position:0%
+walk along the characteristics starting
+at this point with the output of the
+
+ align:start position:0%
+at this point with the output of the
+ 
+
+ align:start position:0%
+at this point with the output of the
+integrator zero its input minus1 volt
+
+ align:start position:0%
+integrator zero its input minus1 volt
+ 
+
+ align:start position:0%
+integrator zero its input minus1 volt
+we'd integrate the minus1 volt or
+
+ align:start position:0%
+we'd integrate the minus1 volt or
+ 
+
+ align:start position:0%
+we'd integrate the minus1 volt or
+actually integrate the negative of that
+
+ align:start position:0%
+actually integrate the negative of that
+ 
+
+ align:start position:0%
+actually integrate the negative of that
+walk along the characteristics to this
+
+ align:start position:0%
+walk along the characteristics to this
+ 
+
+ align:start position:0%
+walk along the characteristics to this
+point. At this point the circuit would
+
+ align:start position:0%
+point. At this point the circuit would
+ 
+
+ align:start position:0%
+point. At this point the circuit would
+switch. We'd now have plus one volt
+
+ align:start position:0%
+switch. We'd now have plus one volt
+ 
+
+ align:start position:0%
+switch. We'd now have plus one volt
+applied to the integrator. Uh as a
+
+ align:start position:0%
+applied to the integrator. Uh as a
+ 
+
+ align:start position:0%
+applied to the integrator. Uh as a
+consequence the output of the integrator
+
+ align:start position:0%
+consequence the output of the integrator
+ 
+
+ align:start position:0%
+consequence the output of the integrator
+would be a negative ramp. plus one volt.
+
+ align:start position:0%
+would be a negative ramp. plus one volt.
+ 
+
+ align:start position:0%
+would be a negative ramp. plus one volt.
+The inversion provided by the
+
+ align:start position:0%
+The inversion provided by the
+ 
+
+ align:start position:0%
+The inversion provided by the
+integrator, the output of the integrator
+
+ align:start position:0%
+integrator, the output of the integrator
+ 
+
+ align:start position:0%
+integrator, the output of the integrator
+would be a negative ramp. VA would start
+
+ align:start position:0%
+would be a negative ramp. VA would start
+ 
+
+ align:start position:0%
+would be a negative ramp. VA would start
+to change in a negative direction. We'd
+
+ align:start position:0%
+to change in a negative direction. We'd
+ 
+
+ align:start position:0%
+to change in a negative direction. We'd
+walk back along the characteristics in
+
+ align:start position:0%
+walk back along the characteristics in
+ 
+
+ align:start position:0%
+walk back along the characteristics in
+this direction. Once again, when we get
+
+ align:start position:0%
+this direction. Once again, when we get
+ 
+
+ align:start position:0%
+this direction. Once again, when we get
+to this point, switch and the circuit
+
+ align:start position:0%
+to this point, switch and the circuit
+ 
+
+ align:start position:0%
+to this point, switch and the circuit
+then follows this trajectory in the VAB
+
+ align:start position:0%
+then follows this trajectory in the VAB
+ 
+
+ align:start position:0%
+then follows this trajectory in the VAB
+plane associated with the the Schmidt
+
+ align:start position:0%
+plane associated with the the Schmidt
+ 
+
+ align:start position:0%
+plane associated with the the Schmidt
+trigger.
+
+ align:start position:0%
+trigger.
+ 
+
+ align:start position:0%
+trigger.
+We can get an exact solution in that
+
+ align:start position:0%
+We can get an exact solution in that
+ 
+
+ align:start position:0%
+We can get an exact solution in that
+case. Of course, let's look at the
+
+ align:start position:0%
+case. Of course, let's look at the
+ 
+
+ align:start position:0%
+case. Of course, let's look at the
+waveforms.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Remember that VA is the output from the
+
+ align:start position:0%
+Remember that VA is the output from the
+ 
+
+ align:start position:0%
+Remember that VA is the output from the
+integrator. Uh VB is the output from the
+
+ align:start position:0%
+integrator. Uh VB is the output from the
+ 
+
+ align:start position:0%
+integrator. Uh VB is the output from the
+Schmidt trigger. And we've started at
+
+ align:start position:0%
+Schmidt trigger. And we've started at
+ 
+
+ align:start position:0%
+Schmidt trigger. And we've started at
+the initial condition that I mentioned
+
+ align:start position:0%
+the initial condition that I mentioned
+ 
+
+ align:start position:0%
+the initial condition that I mentioned
+earlier. In particular, uh the voltage
+
+ align:start position:0%
+earlier. In particular, uh the voltage
+ 
+
+ align:start position:0%
+earlier. In particular, uh the voltage
+VB being minus1 volt, the voltage VA
+
+ align:start position:0%
+VB being minus1 volt, the voltage VA
+ 
+
+ align:start position:0%
+VB being minus1 volt, the voltage VA
+being zero. Uh we integrate the minus1
+
+ align:start position:0%
+being zero. Uh we integrate the minus1
+ 
+
+ align:start position:0%
+being zero. Uh we integrate the minus1
+volt or actually the negative of that.
+
+ align:start position:0%
+volt or actually the negative of that.
+ 
+
+ align:start position:0%
+volt or actually the negative of that.
+uh the slope associated with VA
+
+ align:start position:0%
+uh the slope associated with VA
+ 
+
+ align:start position:0%
+uh the slope associated with VA
+therefore is 1 volt per second. At time
+
+ align:start position:0%
+therefore is 1 volt per second. At time
+ 
+
+ align:start position:0%
+therefore is 1 volt per second. At time
+t = 1 second the output of the
+
+ align:start position:0%
+t = 1 second the output of the
+ 
+
+ align:start position:0%
+t = 1 second the output of the
+integrator reaches + one volt. At that
+
+ align:start position:0%
+integrator reaches + one volt. At that
+ 
+
+ align:start position:0%
+integrator reaches + one volt. At that
+instant the schmidt trigger switches its
+
+ align:start position:0%
+instant the schmidt trigger switches its
+ 
+
+ align:start position:0%
+instant the schmidt trigger switches its
+output becomes + one volt. Uh we
+
+ align:start position:0%
+output becomes + one volt. Uh we
+ 
+
+ align:start position:0%
+output becomes + one volt. Uh we
+integrate that or the negative of that.
+
+ align:start position:0%
+integrate that or the negative of that.
+ 
+
+ align:start position:0%
+integrate that or the negative of that.
+The output of the integrator is now a
+
+ align:start position:0%
+The output of the integrator is now a
+ 
+
+ align:start position:0%
+The output of the integrator is now a
+negative ramp. uh that
+
+ align:start position:0%
+negative ramp. uh that
+ 
+
+ align:start position:0%
+negative ramp. uh that
+time lasts for a total of 2 seconds from
+
+ align:start position:0%
+time lasts for a total of 2 seconds from
+ 
+
+ align:start position:0%
+time lasts for a total of 2 seconds from
+t = 1 to t = 3. Since the slope or the
+
+ align:start position:0%
+t = 1 to t = 3. Since the slope or the
+ 
+
+ align:start position:0%
+t = 1 to t = 3. Since the slope or the
+magnitude of the slope at the output of
+
+ align:start position:0%
+magnitude of the slope at the output of
+ 
+
+ align:start position:0%
+magnitude of the slope at the output of
+the integrator is two is 1 volt per
+
+ align:start position:0%
+the integrator is two is 1 volt per
+ 
+
+ align:start position:0%
+the integrator is two is 1 volt per
+second, we have to undergo a total
+
+ align:start position:0%
+second, we have to undergo a total
+ 
+
+ align:start position:0%
+second, we have to undergo a total
+change of 2 volts before the circuit
+
+ align:start position:0%
+change of 2 volts before the circuit
+ 
+
+ align:start position:0%
+change of 2 volts before the circuit
+switches once again and then the
+
+ align:start position:0%
+switches once again and then the
+ 
+
+ align:start position:0%
+switches once again and then the
+operation continues. So here, as I say,
+
+ align:start position:0%
+operation continues. So here, as I say,
+ 
+
+ align:start position:0%
+operation continues. So here, as I say,
+we're we're able to get an exact
+
+ align:start position:0%
+we're we're able to get an exact
+ 
+
+ align:start position:0%
+we're we're able to get an exact
+solution for this particular system. The
+
+ align:start position:0%
+solution for this particular system. The
+ 
+
+ align:start position:0%
+solution for this particular system. The
+reason for the popularity of this
+
+ align:start position:0%
+reason for the popularity of this
+ 
+
+ align:start position:0%
+reason for the popularity of this
+technique as a function generator is
+
+ align:start position:0%
+technique as a function generator is
+ 
+
+ align:start position:0%
+technique as a function generator is
+that it's quite an easy circuit to
+
+ align:start position:0%
+that it's quite an easy circuit to
+ 
+
+ align:start position:0%
+that it's quite an easy circuit to
+implement. The Schmidt trigger can be
+
+ align:start position:0%
+implement. The Schmidt trigger can be
+ 
+
+ align:start position:0%
+implement. The Schmidt trigger can be
+done with a comparator of of some sort
+
+ align:start position:0%
+done with a comparator of of some sort
+ 
+
+ align:start position:0%
+done with a comparator of of some sort
+and the integrator uh of course uses an
+
+ align:start position:0%
+and the integrator uh of course uses an
+ 
+
+ align:start position:0%
+and the integrator uh of course uses an
+operational ampl amplifier with a
+
+ align:start position:0%
+operational ampl amplifier with a
+ 
+
+ align:start position:0%
+operational ampl amplifier with a
+capacitor in the feedback path and a
+
+ align:start position:0%
+capacitor in the feedback path and a
+ 
+
+ align:start position:0%
+capacitor in the feedback path and a
+resistor as the input element to
+
+ align:start position:0%
+resistor as the input element to
+ 
+
+ align:start position:0%
+resistor as the input element to
+mechanize the integration. The nice part
+
+ align:start position:0%
+mechanize the integration. The nice part
+ 
+
+ align:start position:0%
+mechanize the integration. The nice part
+about it is that the frequency of this
+
+ align:start position:0%
+about it is that the frequency of this
+ 
+
+ align:start position:0%
+about it is that the frequency of this
+configuration can be changed by
+
+ align:start position:0%
+configuration can be changed by
+ 
+
+ align:start position:0%
+configuration can be changed by
+adjusting a single component. Uh
+
+ align:start position:0%
+adjusting a single component. Uh
+ 
+
+ align:start position:0%
+adjusting a single component. Uh
+typically what's done is a potentiometer
+
+ align:start position:0%
+typically what's done is a potentiometer
+ 
+
+ align:start position:0%
+typically what's done is a potentiometer
+is used to adjust scale factor on the
+
+ align:start position:0%
+is used to adjust scale factor on the
+ 
+
+ align:start position:0%
+is used to adjust scale factor on the
+integrator. It'll be at least part of
+
+ align:start position:0%
+integrator. It'll be at least part of
+ 
+
+ align:start position:0%
+integrator. It'll be at least part of
+the input resistor to the integrator
+
+ align:start position:0%
+the input resistor to the integrator
+ 
+
+ align:start position:0%
+the input resistor to the integrator
+will consist of a potentiometer
+
+ align:start position:0%
+will consist of a potentiometer
+ 
+
+ align:start position:0%
+will consist of a potentiometer
+and in that way we can change the scale
+
+ align:start position:0%
+and in that way we can change the scale
+ 
+
+ align:start position:0%
+and in that way we can change the scale
+factor associated with the integrator in
+
+ align:start position:0%
+factor associated with the integrator in
+ 
+
+ align:start position:0%
+factor associated with the integrator in
+a smooth fashion and that changes the
+
+ align:start position:0%
+a smooth fashion and that changes the
+ 
+
+ align:start position:0%
+a smooth fashion and that changes the
+overall operating frequency of the
+
+ align:start position:0%
+overall operating frequency of the
+ 
+
+ align:start position:0%
+overall operating frequency of the
+system. uh the large changes in
+
+ align:start position:0%
+system. uh the large changes in
+ 
+
+ align:start position:0%
+system. uh the large changes in
+frequency are typically accomplished by
+
+ align:start position:0%
+frequency are typically accomplished by
+ 
+
+ align:start position:0%
+frequency are typically accomplished by
+decade switching or or in some other
+
+ align:start position:0%
+decade switching or or in some other
+ 
+
+ align:start position:0%
+decade switching or or in some other
+sequence switching the feedback
+
+ align:start position:0%
+sequence switching the feedback
+ 
+
+ align:start position:0%
+sequence switching the feedback
+capacitor associated with the
+
+ align:start position:0%
+capacitor associated with the
+ 
+
+ align:start position:0%
+capacitor associated with the
+operational amplifier. So this
+
+ align:start position:0%
+operational amplifier. So this
+ 
+
+ align:start position:0%
+operational amplifier. So this
+particular oscillator has the advantage
+
+ align:start position:0%
+particular oscillator has the advantage
+ 
+
+ align:start position:0%
+particular oscillator has the advantage
+that you can tune it by changing a
+
+ align:start position:0%
+that you can tune it by changing a
+ 
+
+ align:start position:0%
+that you can tune it by changing a
+single element. That's in contrast to
+
+ align:start position:0%
+single element. That's in contrast to
+ 
+
+ align:start position:0%
+single element. That's in contrast to
+most syosoidal oscillators where
+
+ align:start position:0%
+most syosoidal oscillators where
+ 
+
+ align:start position:0%
+most syosoidal oscillators where
+typically at least two elements have to
+
+ align:start position:0%
+typically at least two elements have to
+ 
+
+ align:start position:0%
+typically at least two elements have to
+be changed simultaneously to tune a
+
+ align:start position:0%
+be changed simultaneously to tune a
+ 
+
+ align:start position:0%
+be changed simultaneously to tune a
+syosoidal oscillator. Furthermore, the
+
+ align:start position:0%
+syosoidal oscillator. Furthermore, the
+ 
+
+ align:start position:0%
+syosoidal oscillator. Furthermore, the
+topology gives us both a triangle wave
+
+ align:start position:0%
+topology gives us both a triangle wave
+ 
+
+ align:start position:0%
+topology gives us both a triangle wave
+and a square wave. The square wave, of
+
+ align:start position:0%
+and a square wave. The square wave, of
+ 
+
+ align:start position:0%
+and a square wave. The square wave, of
+course, coming out of the Schmidt
+
+ align:start position:0%
+course, coming out of the Schmidt
+ 
+
+ align:start position:0%
+course, coming out of the Schmidt
+trigger, the triangle wave coming off
+
+ align:start position:0%
+trigger, the triangle wave coming off
+ 
+
+ align:start position:0%
+trigger, the triangle wave coming off
+the integrator. And those are two of the
+
+ align:start position:0%
+the integrator. And those are two of the
+ 
+
+ align:start position:0%
+the integrator. And those are two of the
+waveforms that one frequently wants in a
+
+ align:start position:0%
+waveforms that one frequently wants in a
+ 
+
+ align:start position:0%
+waveforms that one frequently wants in a
+function generator. Uh we're also
+
+ align:start position:0%
+function generator. Uh we're also
+ 
+
+ align:start position:0%
+function generator. Uh we're also
+relatively easily able to get a fairly
+
+ align:start position:0%
+relatively easily able to get a fairly
+ 
+
+ align:start position:0%
+relatively easily able to get a fairly
+good approximation to a sine wave.
+
+ align:start position:0%
+good approximation to a sine wave.
+ 
+
+ align:start position:0%
+good approximation to a sine wave.
+What's typically done in in this sort of
+
+ align:start position:0%
+What's typically done in in this sort of
+ 
+
+ align:start position:0%
+What's typically done in in this sort of
+a circuit is to take the triangle wave
+
+ align:start position:0%
+a circuit is to take the triangle wave
+ 
+
+ align:start position:0%
+a circuit is to take the triangle wave
+and go through a nonlinear network that
+
+ align:start position:0%
+and go through a nonlinear network that
+ 
+
+ align:start position:0%
+and go through a nonlinear network that
+approximates a a sine wave as a series
+
+ align:start position:0%
+approximates a a sine wave as a series
+ 
+
+ align:start position:0%
+approximates a a sine wave as a series
+of straight lines. I talk about that
+
+ align:start position:0%
+of straight lines. I talk about that
+ 
+
+ align:start position:0%
+of straight lines. I talk about that
+sort of approximation in chapter 12 and
+
+ align:start position:0%
+sort of approximation in chapter 12 and
+ 
+
+ align:start position:0%
+sort of approximation in chapter 12 and
+go through an example of how one might
+
+ align:start position:0%
+go through an example of how one might
+ 
+
+ align:start position:0%
+go through an example of how one might
+design a nonlinear network that converts
+
+ align:start position:0%
+design a nonlinear network that converts
+ 
+
+ align:start position:0%
+design a nonlinear network that converts
+a triangle wave to an approximate sine
+
+ align:start position:0%
+a triangle wave to an approximate sine
+ 
+
+ align:start position:0%
+a triangle wave to an approximate sine
+wave. So by incorporating one of those
+
+ align:start position:0%
+wave. So by incorporating one of those
+ 
+
+ align:start position:0%
+wave. So by incorporating one of those
+circuits in addition to the basic
+
+ align:start position:0%
+circuits in addition to the basic
+ 
+
+ align:start position:0%
+circuits in addition to the basic
+function generator or oscillator loop,
+
+ align:start position:0%
+function generator or oscillator loop,
+ 
+
+ align:start position:0%
+function generator or oscillator loop,
+we're able to build a function generator
+
+ align:start position:0%
+we're able to build a function generator
+ 
+
+ align:start position:0%
+we're able to build a function generator
+that provides the three most frequently
+
+ align:start position:0%
+that provides the three most frequently
+ 
+
+ align:start position:0%
+that provides the three most frequently
+wanted waveforms for test purposes. I
+
+ align:start position:0%
+wanted waveforms for test purposes. I
+ 
+
+ align:start position:0%
+wanted waveforms for test purposes. I
+have one of these circuits running.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um what we have here again is the same
+
+ align:start position:0%
+Um what we have here again is the same
+ 
+
+ align:start position:0%
+Um what we have here again is the same
+power supply we've been using
+
+ align:start position:0%
+power supply we've been using
+ 
+
+ align:start position:0%
+power supply we've been using
+throughout. We have a storebought
+
+ align:start position:0%
+throughout. We have a storebought
+ 
+
+ align:start position:0%
+throughout. We have a storebought
+function generator that actually uses
+
+ align:start position:0%
+function generator that actually uses
+ 
+
+ align:start position:0%
+function generator that actually uses
+this technique. Uh this is one built by
+
+ align:start position:0%
+this technique. Uh this is one built by
+ 
+
+ align:start position:0%
+this technique. Uh this is one built by
+Cronheight that that uses basically the
+
+ align:start position:0%
+Cronheight that that uses basically the
+ 
+
+ align:start position:0%
+Cronheight that that uses basically the
+kind of a technique that I've described.
+
+ align:start position:0%
+kind of a technique that I've described.
+ 
+
+ align:start position:0%
+kind of a technique that I've described.
+It's a three function three waveform
+
+ align:start position:0%
+It's a three function three waveform
+ 
+
+ align:start position:0%
+It's a three function three waveform
+function generator. It generates a
+
+ align:start position:0%
+function generator. It generates a
+ 
+
+ align:start position:0%
+function generator. It generates a
+triangle wave, a square wave, and a sine
+
+ align:start position:0%
+triangle wave, a square wave, and a sine
+ 
+
+ align:start position:0%
+triangle wave, a square wave, and a sine
+wave by shaping the triangle wave. It
+
+ align:start position:0%
+wave by shaping the triangle wave. It
+ 
+
+ align:start position:0%
+wave by shaping the triangle wave. It
+also has a few more frills that allow
+
+ align:start position:0%
+also has a few more frills that allow
+ 
+
+ align:start position:0%
+also has a few more frills that allow
+you to adjust symmetry of the square
+
+ align:start position:0%
+you to adjust symmetry of the square
+ 
+
+ align:start position:0%
+you to adjust symmetry of the square
+wave and and so forth and get pulse type
+
+ align:start position:0%
+wave and and so forth and get pulse type
+ 
+
+ align:start position:0%
+wave and and so forth and get pulse type
+waveforms. And it has an ability to to
+
+ align:start position:0%
+waveforms. And it has an ability to to
+ 
+
+ align:start position:0%
+waveforms. And it has an ability to to
+voltage control the oscillator. But the
+
+ align:start position:0%
+voltage control the oscillator. But the
+ 
+
+ align:start position:0%
+voltage control the oscillator. But the
+the basic loop is that that I've
+
+ align:start position:0%
+the basic loop is that that I've
+ 
+
+ align:start position:0%
+the basic loop is that that I've
+described, the integrator plus the
+
+ align:start position:0%
+described, the integrator plus the
+ 
+
+ align:start position:0%
+described, the integrator plus the
+Schmidt trigger. This is actually used
+
+ align:start position:0%
+Schmidt trigger. This is actually used
+ 
+
+ align:start position:0%
+Schmidt trigger. This is actually used
+only as a test signal source to display
+
+ align:start position:0%
+only as a test signal source to display
+ 
+
+ align:start position:0%
+only as a test signal source to display
+the characteristics of the Schmidt
+
+ align:start position:0%
+the characteristics of the Schmidt
+ 
+
+ align:start position:0%
+the characteristics of the Schmidt
+trigger in our own function generator.
+
+ align:start position:0%
+trigger in our own function generator.
+ 
+
+ align:start position:0%
+trigger in our own function generator.
+Uh here is the our homebuilt function
+
+ align:start position:0%
+Uh here is the our homebuilt function
+ 
+
+ align:start position:0%
+Uh here is the our homebuilt function
+generator. We actually use an integrated
+
+ align:start position:0%
+generator. We actually use an integrated
+ 
+
+ align:start position:0%
+generator. We actually use an integrated
+circuit comparator to provide the
+
+ align:start position:0%
+circuit comparator to provide the
+ 
+
+ align:start position:0%
+circuit comparator to provide the
+Schmidt trigger function. Here's an
+
+ align:start position:0%
+Schmidt trigger function. Here's an
+ 
+
+ align:start position:0%
+Schmidt trigger function. Here's an
+operational amplifier. uh this is the
+
+ align:start position:0%
+operational amplifier. uh this is the
+ 
+
+ align:start position:0%
+operational amplifier. uh this is the
+amplifier that is mechani that
+
+ align:start position:0%
+amplifier that is mechani that
+ 
+
+ align:start position:0%
+amplifier that is mechani that
+mechanizes the integration. This is the
+
+ align:start position:0%
+mechanizes the integration. This is the
+ 
+
+ align:start position:0%
+mechanizes the integration. This is the
+capacitor used for the integration and
+
+ align:start position:0%
+capacitor used for the integration and
+ 
+
+ align:start position:0%
+capacitor used for the integration and
+and this is the resistor or at least
+
+ align:start position:0%
+and this is the resistor or at least
+ 
+
+ align:start position:0%
+and this is the resistor or at least
+part of the resistor. We also have a
+
+ align:start position:0%
+part of the resistor. We also have a
+ 
+
+ align:start position:0%
+part of the resistor. We also have a
+potentiometer that allows us to change
+
+ align:start position:0%
+potentiometer that allows us to change
+ 
+
+ align:start position:0%
+potentiometer that allows us to change
+the total input resistance to the
+
+ align:start position:0%
+the total input resistance to the
+ 
+
+ align:start position:0%
+the total input resistance to the
+integrator and that's what we use to
+
+ align:start position:0%
+integrator and that's what we use to
+ 
+
+ align:start position:0%
+integrator and that's what we use to
+change the frequency of operation and
+
+ align:start position:0%
+change the frequency of operation and
+ 
+
+ align:start position:0%
+change the frequency of operation and
+then of course various output signals
+
+ align:start position:0%
+then of course various output signals
+ 
+
+ align:start position:0%
+then of course various output signals
+are displayed on the oscilloscope.
+
+ align:start position:0%
+are displayed on the oscilloscope.
+ 
+
+ align:start position:0%
+are displayed on the oscilloscope.
+Uh what we are showing now
+
+ align:start position:0%
+Uh what we are showing now
+ 
+
+ align:start position:0%
+Uh what we are showing now
+are simply the characteristics
+
+ align:start position:0%
+are simply the characteristics
+ 
+
+ align:start position:0%
+are simply the characteristics
+associated with the Schmidt trigger. And
+
+ align:start position:0%
+associated with the Schmidt trigger. And
+ 
+
+ align:start position:0%
+associated with the Schmidt trigger. And
+here in order to do this we apply a
+
+ align:start position:0%
+here in order to do this we apply a
+ 
+
+ align:start position:0%
+here in order to do this we apply a
+triangular sweep to the input of the
+
+ align:start position:0%
+triangular sweep to the input of the
+ 
+
+ align:start position:0%
+triangular sweep to the input of the
+Schmidt trigger from the function
+
+ align:start position:0%
+Schmidt trigger from the function
+ 
+
+ align:start position:0%
+Schmidt trigger from the function
+generator. Uh we use that same sweep on
+
+ align:start position:0%
+generator. Uh we use that same sweep on
+ 
+
+ align:start position:0%
+generator. Uh we use that same sweep on
+the horizontal axis of the oscilloscope.
+
+ align:start position:0%
+the horizontal axis of the oscilloscope.
+ 
+
+ align:start position:0%
+the horizontal axis of the oscilloscope.
+Uh we also then look at the output of
+
+ align:start position:0%
+Uh we also then look at the output of
+ 
+
+ align:start position:0%
+Uh we also then look at the output of
+the Schmidt trigger on the vertical axis
+
+ align:start position:0%
+the Schmidt trigger on the vertical axis
+ 
+
+ align:start position:0%
+the Schmidt trigger on the vertical axis
+of the oscilloscope and we see on the
+
+ align:start position:0%
+of the oscilloscope and we see on the
+ 
+
+ align:start position:0%
+of the oscilloscope and we see on the
+oscillos oscilloscope screen the Schmidt
+
+ align:start position:0%
+oscillos oscilloscope screen the Schmidt
+ 
+
+ align:start position:0%
+oscillos oscilloscope screen the Schmidt
+trigger characteristics. Uh presumably
+
+ align:start position:0%
+trigger characteristics. Uh presumably
+ 
+
+ align:start position:0%
+trigger characteristics. Uh presumably
+the there's a very rapid transition here
+
+ align:start position:0%
+the there's a very rapid transition here
+ 
+
+ align:start position:0%
+the there's a very rapid transition here
+in a positive direction, a very rapid
+
+ align:start position:0%
+in a positive direction, a very rapid
+ 
+
+ align:start position:0%
+in a positive direction, a very rapid
+negative transition here. We don't
+
+ align:start position:0%
+negative transition here. We don't
+ 
+
+ align:start position:0%
+negative transition here. We don't
+actually see those, but we do see the
+
+ align:start position:0%
+actually see those, but we do see the
+ 
+
+ align:start position:0%
+actually see those, but we do see the
+flat portion of the characteristics.
+
+ align:start position:0%
+flat portion of the characteristics.
+ 
+
+ align:start position:0%
+flat portion of the characteristics.
+Here's the input signal going positive,
+
+ align:start position:0%
+Here's the input signal going positive,
+ 
+
+ align:start position:0%
+Here's the input signal going positive,
+then reversing, going negative. The
+
+ align:start position:0%
+then reversing, going negative. The
+ 
+
+ align:start position:0%
+then reversing, going negative. The
+Schmidt trigger flips. So, we're tracing
+
+ align:start position:0%
+Schmidt trigger flips. So, we're tracing
+ 
+
+ align:start position:0%
+Schmidt trigger flips. So, we're tracing
+out the characteristics that we expect
+
+ align:start position:0%
+out the characteristics that we expect
+ 
+
+ align:start position:0%
+out the characteristics that we expect
+from the Schmidt trigger. Uh, I can
+
+ align:start position:0%
+from the Schmidt trigger. Uh, I can
+ 
+
+ align:start position:0%
+from the Schmidt trigger. Uh, I can
+convince you that it's actually going
+
+ align:start position:0%
+convince you that it's actually going
+ 
+
+ align:start position:0%
+convince you that it's actually going
+around uh in the correct direction by
+
+ align:start position:0%
+around uh in the correct direction by
+ 
+
+ align:start position:0%
+around uh in the correct direction by
+simply slowing down the sweep. Uh, let's
+
+ align:start position:0%
+simply slowing down the sweep. Uh, let's
+ 
+
+ align:start position:0%
+simply slowing down the sweep. Uh, let's
+see. There we begin to see it. And let's
+
+ align:start position:0%
+see. There we begin to see it. And let's
+ 
+
+ align:start position:0%
+see. There we begin to see it. And let's
+go even a little bit slower. And then we
+
+ align:start position:0%
+go even a little bit slower. And then we
+ 
+
+ align:start position:0%
+go even a little bit slower. And then we
+can follow the dot. And here we very
+
+ align:start position:0%
+can follow the dot. And here we very
+ 
+
+ align:start position:0%
+can follow the dot. And here we very
+clearly see the pattern being traced out
+
+ align:start position:0%
+clearly see the pattern being traced out
+ 
+
+ align:start position:0%
+clearly see the pattern being traced out
+by the the Schmidt trigger.
+
+ align:start position:0%
+by the the Schmidt trigger.
+ 
+
+ align:start position:0%
+by the the Schmidt trigger.
+the positive going input now it's going
+
+ align:start position:0%
+the positive going input now it's going
+ 
+
+ align:start position:0%
+the positive going input now it's going
+negative switches once again passes the
+
+ align:start position:0%
+negative switches once again passes the
+ 
+
+ align:start position:0%
+negative switches once again passes the
+original transition point before it
+
+ align:start position:0%
+original transition point before it
+ 
+
+ align:start position:0%
+original transition point before it
+switches to the positive state so that's
+
+ align:start position:0%
+switches to the positive state so that's
+ 
+
+ align:start position:0%
+switches to the positive state so that's
+simply the characteristics from the
+
+ align:start position:0%
+simply the characteristics from the
+ 
+
+ align:start position:0%
+simply the characteristics from the
+Schmidt trigger and as I say that's
+
+ align:start position:0%
+Schmidt trigger and as I say that's
+ 
+
+ align:start position:0%
+Schmidt trigger and as I say that's
+mechanized using a commercially
+
+ align:start position:0%
+mechanized using a commercially
+ 
+
+ align:start position:0%
+mechanized using a commercially
+available integrated circuit comparator
+
+ align:start position:0%
+available integrated circuit comparator
+ 
+
+ align:start position:0%
+available integrated circuit comparator
+now let's complete the the loop and look
+
+ align:start position:0%
+now let's complete the the loop and look
+ 
+
+ align:start position:0%
+now let's complete the the loop and look
+at some of the signals uh first I'll
+
+ align:start position:0%
+at some of the signals uh first I'll
+ 
+
+ align:start position:0%
+at some of the signals uh first I'll
+disable the function generator the
+
+ align:start position:0%
+disable the function generator the
+ 
+
+ align:start position:0%
+disable the function generator the
+external one that we were driving the
+
+ align:start position:0%
+external one that we were driving the
+ 
+
+ align:start position:0%
+external one that we were driving the
+system with.
+
+ align:start position:0%
+system with.
+ 
+
+ align:start position:0%
+system with.
+And I'll apply that signal to a second
+
+ align:start position:0%
+And I'll apply that signal to a second
+ 
+
+ align:start position:0%
+And I'll apply that signal to a second
+axis on the uh oscilloscope. This is
+
+ align:start position:0%
+axis on the uh oscilloscope. This is
+ 
+
+ align:start position:0%
+axis on the uh oscilloscope. This is
+actually now the input signal to the
+
+ align:start position:0%
+actually now the input signal to the
+ 
+
+ align:start position:0%
+actually now the input signal to the
+Schmidt trigger or equivalently the
+
+ align:start position:0%
+Schmidt trigger or equivalently the
+ 
+
+ align:start position:0%
+Schmidt trigger or equivalently the
+output of the integrator. Once we close
+
+ align:start position:0%
+output of the integrator. Once we close
+ 
+
+ align:start position:0%
+output of the integrator. Once we close
+the loop, this switch simply closes the
+
+ align:start position:0%
+the loop, this switch simply closes the
+ 
+
+ align:start position:0%
+the loop, this switch simply closes the
+loop with the switch in the position
+
+ align:start position:0%
+loop with the switch in the position
+ 
+
+ align:start position:0%
+loop with the switch in the position
+shown is it disables the loop so that
+
+ align:start position:0%
+shown is it disables the loop so that
+ 
+
+ align:start position:0%
+shown is it disables the loop so that
+we're able to easily plot the Schmidt
+
+ align:start position:0%
+we're able to easily plot the Schmidt
+ 
+
+ align:start position:0%
+we're able to easily plot the Schmidt
+trigger characteristics when we close
+
+ align:start position:0%
+trigger characteristics when we close
+ 
+
+ align:start position:0%
+trigger characteristics when we close
+the loop. Why the circuit oscillates and
+
+ align:start position:0%
+the loop. Why the circuit oscillates and
+ 
+
+ align:start position:0%
+the loop. Why the circuit oscillates and
+we can look at it uh on a time base.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh and here now uh is the
+
+ align:start position:0%
+Uh and here now uh is the
+ 
+
+ align:start position:0%
+Uh and here now uh is the
+square wave coming out of our function
+
+ align:start position:0%
+square wave coming out of our function
+ 
+
+ align:start position:0%
+square wave coming out of our function
+generator. Uh let's look at it uh on
+
+ align:start position:0%
+generator. Uh let's look at it uh on
+ 
+
+ align:start position:0%
+generator. Uh let's look at it uh on
+that time scale possibly and let me
+
+ align:start position:0%
+that time scale possibly and let me
+ 
+
+ align:start position:0%
+that time scale possibly and let me
+lower the amplitude of that a little bit
+
+ align:start position:0%
+lower the amplitude of that a little bit
+ 
+
+ align:start position:0%
+lower the amplitude of that a little bit
+so that we can duplicate the picture
+
+ align:start position:0%
+so that we can duplicate the picture
+ 
+
+ align:start position:0%
+so that we can duplicate the picture
+that we had earlier in the view graph.
+
+ align:start position:0%
+that we had earlier in the view graph.
+ 
+
+ align:start position:0%
+that we had earlier in the view graph.
+Uh we'll now switch the second trace
+
+ align:start position:0%
+Uh we'll now switch the second trace
+ 
+
+ align:start position:0%
+Uh we'll now switch the second trace
+onto the oscilloscope screen so that we
+
+ align:start position:0%
+onto the oscilloscope screen so that we
+ 
+
+ align:start position:0%
+onto the oscilloscope screen so that we
+can simultaneously see the triangle wave
+
+ align:start position:0%
+can simultaneously see the triangle wave
+ 
+
+ align:start position:0%
+can simultaneously see the triangle wave
+and the square wave that our our
+
+ align:start position:0%
+and the square wave that our our
+ 
+
+ align:start position:0%
+and the square wave that our our
+function generator is is making. And we
+
+ align:start position:0%
+function generator is is making. And we
+ 
+
+ align:start position:0%
+function generator is is making. And we
+notice the basically the picture I
+
+ align:start position:0%
+notice the basically the picture I
+ 
+
+ align:start position:0%
+notice the basically the picture I
+showed before. If we change phase, we
+
+ align:start position:0%
+showed before. If we change phase, we
+ 
+
+ align:start position:0%
+showed before. If we change phase, we
+can get very nearly the picture that we
+
+ align:start position:0%
+can get very nearly the picture that we
+ 
+
+ align:start position:0%
+can get very nearly the picture that we
+showed before.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Something like that. Notice the the
+
+ align:start position:0%
+Something like that. Notice the the
+ 
+
+ align:start position:0%
+Something like that. Notice the the
+phasing
+
+ align:start position:0%
+phasing
+ 
+
+ align:start position:0%
+phasing
+when the square wave into the integrator
+
+ align:start position:0%
+when the square wave into the integrator
+ 
+
+ align:start position:0%
+when the square wave into the integrator
+is negative. This is the signal out of
+
+ align:start position:0%
+is negative. This is the signal out of
+ 
+
+ align:start position:0%
+is negative. This is the signal out of
+the Schmidt trigger. Uh the integrator
+
+ align:start position:0%
+the Schmidt trigger. Uh the integrator
+ 
+
+ align:start position:0%
+the Schmidt trigger. Uh the integrator
+is integrating in a positive direction.
+
+ align:start position:0%
+is integrating in a positive direction.
+ 
+
+ align:start position:0%
+is integrating in a positive direction.
+There's an aversion inversion associated
+
+ align:start position:0%
+There's an aversion inversion associated
+ 
+
+ align:start position:0%
+There's an aversion inversion associated
+with the integrator. Uh we then get to
+
+ align:start position:0%
+with the integrator. Uh we then get to
+ 
+
+ align:start position:0%
+with the integrator. Uh we then get to
+the positive peak. The Schmidt trigger
+
+ align:start position:0%
+the positive peak. The Schmidt trigger
+ 
+
+ align:start position:0%
+the positive peak. The Schmidt trigger
+now switches uh applies a positive
+
+ align:start position:0%
+now switches uh applies a positive
+ 
+
+ align:start position:0%
+now switches uh applies a positive
+voltage to the integrator. Uh the
+
+ align:start position:0%
+voltage to the integrator. Uh the
+ 
+
+ align:start position:0%
+voltage to the integrator. Uh the
+integrator now integrates in the
+
+ align:start position:0%
+integrator now integrates in the
+ 
+
+ align:start position:0%
+integrator now integrates in the
+negative direction and so forth. And as
+
+ align:start position:0%
+negative direction and so forth. And as
+ 
+
+ align:start position:0%
+negative direction and so forth. And as
+I mentioned, one of the advantages of
+
+ align:start position:0%
+I mentioned, one of the advantages of
+ 
+
+ align:start position:0%
+I mentioned, one of the advantages of
+this configuration is that we're able to
+
+ align:start position:0%
+this configuration is that we're able to
+ 
+
+ align:start position:0%
+this configuration is that we're able to
+very easily change the frequency of
+
+ align:start position:0%
+very easily change the frequency of
+ 
+
+ align:start position:0%
+very easily change the frequency of
+oscillation by simply changing a
+
+ align:start position:0%
+oscillation by simply changing a
+ 
+
+ align:start position:0%
+oscillation by simply changing a
+potentiometer. And all this is doing is
+
+ align:start position:0%
+potentiometer. And all this is doing is
+ 
+
+ align:start position:0%
+potentiometer. And all this is doing is
+changing the value of an input resistor
+
+ align:start position:0%
+changing the value of an input resistor
+ 
+
+ align:start position:0%
+changing the value of an input resistor
+or the input resistor associated with
+
+ align:start position:0%
+or the input resistor associated with
+ 
+
+ align:start position:0%
+or the input resistor associated with
+the integrator. And here we see
+
+ align:start position:0%
+the integrator. And here we see
+ 
+
+ align:start position:0%
+the integrator. And here we see
+uh we can run uh from something like
+
+ align:start position:0%
+uh we can run uh from something like
+ 
+
+ align:start position:0%
+uh we can run uh from something like
+we're at at 50 microsconds per division
+
+ align:start position:0%
+we're at at 50 microsconds per division
+ 
+
+ align:start position:0%
+we're at at 50 microsconds per division
+now. So that's something like 4
+
+ align:start position:0%
+now. So that's something like 4
+ 
+
+ align:start position:0%
+now. So that's something like 4
+kilhertz.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And here we've increased by just about a
+
+ align:start position:0%
+And here we've increased by just about a
+ 
+
+ align:start position:0%
+And here we've increased by just about a
+decade. We're at five microsconds per
+
+ align:start position:0%
+decade. We're at five microsconds per
+ 
+
+ align:start position:0%
+decade. We're at five microsconds per
+division. So that's running at about 40
+
+ align:start position:0%
+division. So that's running at about 40
+ 
+
+ align:start position:0%
+division. So that's running at about 40
+kHz. So we're able to get very easily
+
+ align:start position:0%
+kHz. So we're able to get very easily
+ 
+
+ align:start position:0%
+kHz. So we're able to get very easily
+that sort of change
+
+ align:start position:0%
+that sort of change
+ 
+
+ align:start position:0%
+that sort of change
+in frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by adjusting a single component and an
+
+ align:start position:0%
+by adjusting a single component and an
+ 
+
+ align:start position:0%
+by adjusting a single component and an
+easily adjustable component.
+
+ align:start position:0%
+easily adjustable component.
+ 
+
+ align:start position:0%
+easily adjustable component.
+potentiometer as opposed to an energy
+
+ align:start position:0%
+potentiometer as opposed to an energy
+ 
+
+ align:start position:0%
+potentiometer as opposed to an energy
+storage element that has to be tuned.
+
+ align:start position:0%
+storage element that has to be tuned.
+ 
+
+ align:start position:0%
+storage element that has to be tuned.
+And as I mentioned, then the typically
+
+ align:start position:0%
+And as I mentioned, then the typically
+ 
+
+ align:start position:0%
+And as I mentioned, then the typically
+the capacitor will be switched in
+
+ align:start position:0%
+the capacitor will be switched in
+ 
+
+ align:start position:0%
+the capacitor will be switched in
+possibly decade steps in order to change
+
+ align:start position:0%
+possibly decade steps in order to change
+ 
+
+ align:start position:0%
+possibly decade steps in order to change
+the basic frequency of operation.
+
+ align:start position:0%
+the basic frequency of operation.
+ 
+
+ align:start position:0%
+the basic frequency of operation.
+Something like this where there are a
+
+ align:start position:0%
+Something like this where there are a
+ 
+
+ align:start position:0%
+Something like this where there are a
+series of decade steps available on the
+
+ align:start position:0%
+series of decade steps available on the
+ 
+
+ align:start position:0%
+series of decade steps available on the
+commercial function generator.
+
+ align:start position:0%
+commercial function generator.
+ 
+
+ align:start position:0%
+commercial function generator.
+Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as I mentioned, this is a circuit where
+
+ align:start position:0%
+as I mentioned, this is a circuit where
+ 
+
+ align:start position:0%
+as I mentioned, this is a circuit where
+we can very easily
+
+ align:start position:0%
+we can very easily
+ 
+
+ align:start position:0%
+we can very easily
+get an exact solution to its behavior.
+
+ align:start position:0%
+get an exact solution to its behavior.
+ 
+
+ align:start position:0%
+get an exact solution to its behavior.
+And so, it'd be a little bit silly to
+
+ align:start position:0%
+And so, it'd be a little bit silly to
+ 
+
+ align:start position:0%
+And so, it'd be a little bit silly to
+actually use this is to actually use
+
+ align:start position:0%
+actually use this is to actually use
+ 
+
+ align:start position:0%
+actually use this is to actually use
+describing functions to analyze this
+
+ align:start position:0%
+describing functions to analyze this
+ 
+
+ align:start position:0%
+describing functions to analyze this
+circuit since describing functions are
+
+ align:start position:0%
+circuit since describing functions are
+ 
+
+ align:start position:0%
+circuit since describing functions are
+of course an approximation. But let's go
+
+ align:start position:0%
+of course an approximation. But let's go
+ 
+
+ align:start position:0%
+of course an approximation. But let's go
+ahead anyway just by by way of
+
+ align:start position:0%
+ahead anyway just by by way of
+ 
+
+ align:start position:0%
+ahead anyway just by by way of
+illustration.
+
+ align:start position:0%
+illustration.
+ 
+
+ align:start position:0%
+illustration.
+the let's look at the behavior of an
+
+ align:start position:0%
+the let's look at the behavior of an
+ 
+
+ align:start position:0%
+the let's look at the behavior of an
+element that has hysteresis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Here I've assumed uh general
+
+ align:start position:0%
+Here I've assumed uh general
+ 
+
+ align:start position:0%
+Here I've assumed uh general
+characteristics with an an output
+
+ align:start position:0%
+characteristics with an an output
+ 
+
+ align:start position:0%
+characteristics with an an output
+amplitude of e subn or minus e subn and
+
+ align:start position:0%
+amplitude of e subn or minus e subn and
+ 
+
+ align:start position:0%
+amplitude of e subn or minus e subn and
+uh an input amplitude switching points
+
+ align:start position:0%
+uh an input amplitude switching points
+ 
+
+ align:start position:0%
+uh an input amplitude switching points
+of plus and minus e subn.
+
+ align:start position:0%
+of plus and minus e subn.
+ 
+
+ align:start position:0%
+of plus and minus e subn.
+And as we normally do in describing
+
+ align:start position:0%
+And as we normally do in describing
+ 
+
+ align:start position:0%
+And as we normally do in describing
+function analysis, we assume that the
+
+ align:start position:0%
+function analysis, we assume that the
+ 
+
+ align:start position:0%
+function analysis, we assume that the
+input signal to our nonlinearity
+
+ align:start position:0%
+input signal to our nonlinearity
+ 
+
+ align:start position:0%
+input signal to our nonlinearity
+uh the voltage applied as its input uh
+
+ align:start position:0%
+uh the voltage applied as its input uh
+ 
+
+ align:start position:0%
+uh the voltage applied as its input uh
+is a sinosoid of peak amplitude E.
+
+ align:start position:0%
+is a sinosoid of peak amplitude E.
+ 
+
+ align:start position:0%
+is a sinosoid of peak amplitude E.
+And what we note of course is that the
+
+ align:start position:0%
+And what we note of course is that the
+ 
+
+ align:start position:0%
+And what we note of course is that the
+output of the signal is of output of the
+
+ align:start position:0%
+output of the signal is of output of the
+ 
+
+ align:start position:0%
+output of the signal is of output of the
+Schmidt trigger or the element with
+
+ align:start position:0%
+Schmidt trigger or the element with
+ 
+
+ align:start position:0%
+Schmidt trigger or the element with
+hysteresis is a square wave.
+
+ align:start position:0%
+hysteresis is a square wave.
+ 
+
+ align:start position:0%
+hysteresis is a square wave.
+uh the peak amplitude of the square wave
+
+ align:start position:0%
+uh the peak amplitude of the square wave
+ 
+
+ align:start position:0%
+uh the peak amplitude of the square wave
+is e subn
+
+ align:start position:0%
+is e subn
+ 
+
+ align:start position:0%
+is e subn
+or minus e subn in the other state
+
+ align:start position:0%
+or minus e subn in the other state
+ 
+
+ align:start position:0%
+or minus e subn in the other state
+uh and the switching point occurs when
+
+ align:start position:0%
+uh and the switching point occurs when
+ 
+
+ align:start position:0%
+uh and the switching point occurs when
+the input saw gets up to a level of e
+
+ align:start position:0%
+the input saw gets up to a level of e
+ 
+
+ align:start position:0%
+the input saw gets up to a level of e
+subm.
+
+ align:start position:0%
+subm.
+ 
+
+ align:start position:0%
+subm.
+Notice that this is an example of an
+
+ align:start position:0%
+Notice that this is an example of an
+ 
+
+ align:start position:0%
+Notice that this is an example of an
+element whose characteristics are
+
+ align:start position:0%
+element whose characteristics are
+ 
+
+ align:start position:0%
+element whose characteristics are
+frequency independent. We nowhere in in
+
+ align:start position:0%
+frequency independent. We nowhere in in
+ 
+
+ align:start position:0%
+frequency independent. We nowhere in in
+this development how to specify the
+
+ align:start position:0%
+this development how to specify the
+ 
+
+ align:start position:0%
+this development how to specify the
+frequency of operation of the schmidt
+
+ align:start position:0%
+frequency of operation of the schmidt
+ 
+
+ align:start position:0%
+frequency of operation of the schmidt
+trigger. uh so its characteristics are
+
+ align:start position:0%
+trigger. uh so its characteristics are
+ 
+
+ align:start position:0%
+trigger. uh so its characteristics are
+frequency independent yet it provides a
+
+ align:start position:0%
+frequency independent yet it provides a
+ 
+
+ align:start position:0%
+frequency independent yet it provides a
+phase shift. So here we have a slightly
+
+ align:start position:0%
+phase shift. So here we have a slightly
+ 
+
+ align:start position:0%
+phase shift. So here we have a slightly
+more complicated nonlinearity than we we
+
+ align:start position:0%
+more complicated nonlinearity than we we
+ 
+
+ align:start position:0%
+more complicated nonlinearity than we we
+saw in the past. The phase shift sort of
+
+ align:start position:0%
+saw in the past. The phase shift sort of
+ 
+
+ align:start position:0%
+saw in the past. The phase shift sort of
+reflects the fact that the element has
+
+ align:start position:0%
+reflects the fact that the element has
+ 
+
+ align:start position:0%
+reflects the fact that the element has
+memory. Uh in this case the phase shift
+
+ align:start position:0%
+memory. Uh in this case the phase shift
+ 
+
+ align:start position:0%
+memory. Uh in this case the phase shift
+though in contrast to most of our our
+
+ align:start position:0%
+though in contrast to most of our our
+ 
+
+ align:start position:0%
+though in contrast to most of our our
+linear elements that have energy storage
+
+ align:start position:0%
+linear elements that have energy storage
+ 
+
+ align:start position:0%
+linear elements that have energy storage
+where the phase shift is a function of
+
+ align:start position:0%
+where the phase shift is a function of
+ 
+
+ align:start position:0%
+where the phase shift is a function of
+operating frequency. In this case it's a
+
+ align:start position:0%
+operating frequency. In this case it's a
+ 
+
+ align:start position:0%
+operating frequency. In this case it's a
+function of driving amplitude.
+
+ align:start position:0%
+function of driving amplitude.
+ 
+
+ align:start position:0%
+function of driving amplitude.
+We can see that because the switching
+
+ align:start position:0%
+We can see that because the switching
+ 
+
+ align:start position:0%
+We can see that because the switching
+point occurs um when the input syosoid
+
+ align:start position:0%
+point occurs um when the input syosoid
+ 
+
+ align:start position:0%
+point occurs um when the input syosoid
+reaches a level of plus or minus E subm
+
+ align:start position:0%
+reaches a level of plus or minus E subm
+ 
+
+ align:start position:0%
+reaches a level of plus or minus E subm
+that tells us that if the input signal
+
+ align:start position:0%
+that tells us that if the input signal
+ 
+
+ align:start position:0%
+that tells us that if the input signal
+is very very large if E is a very large
+
+ align:start position:0%
+is very very large if E is a very large
+ 
+
+ align:start position:0%
+is very very large if E is a very large
+number so that the signal is is nearly
+
+ align:start position:0%
+number so that the signal is is nearly
+ 
+
+ align:start position:0%
+number so that the signal is is nearly
+vertical on this scale uh we go to a
+
+ align:start position:0%
+vertical on this scale uh we go to a
+ 
+
+ align:start position:0%
+vertical on this scale uh we go to a
+level E subm very shortly after time T
+
+ align:start position:0%
+level E subm very shortly after time T
+ 
+
+ align:start position:0%
+level E subm very shortly after time T
+equals Z and under those conditions, the
+
+ align:start position:0%
+equals Z and under those conditions, the
+ 
+
+ align:start position:0%
+equals Z and under those conditions, the
+output square wave would have zero
+
+ align:start position:0%
+output square wave would have zero
+ 
+
+ align:start position:0%
+output square wave would have zero
+crossings very nearly synchronized with
+
+ align:start position:0%
+crossings very nearly synchronized with
+ 
+
+ align:start position:0%
+crossings very nearly synchronized with
+those of the input signal.
+
+ align:start position:0%
+those of the input signal.
+ 
+
+ align:start position:0%
+those of the input signal.
+Conversely, as we get a smaller value
+
+ align:start position:0%
+Conversely, as we get a smaller value
+ 
+
+ align:start position:0%
+Conversely, as we get a smaller value
+for E, the output signal lags behind the
+
+ align:start position:0%
+for E, the output signal lags behind the
+ 
+
+ align:start position:0%
+for E, the output signal lags behind the
+input signal and eventually reaches a a
+
+ align:start position:0%
+input signal and eventually reaches a a
+ 
+
+ align:start position:0%
+input signal and eventually reaches a a
+maximum negative phase shift of 90
+
+ align:start position:0%
+maximum negative phase shift of 90
+ 
+
+ align:start position:0%
+maximum negative phase shift of 90
+degrees when E is exactly equal to E
+
+ align:start position:0%
+degrees when E is exactly equal to E
+ 
+
+ align:start position:0%
+degrees when E is exactly equal to E
+subm. When E is equal to E subm,
+
+ align:start position:0%
+subm. When E is equal to E subm,
+ 
+
+ align:start position:0%
+subm. When E is equal to E subm,
+switching occurs right at the peak and
+
+ align:start position:0%
+switching occurs right at the peak and
+ 
+
+ align:start position:0%
+switching occurs right at the peak and
+at the minimum of the sine wave. And in
+
+ align:start position:0%
+at the minimum of the sine wave. And in
+ 
+
+ align:start position:0%
+at the minimum of the sine wave. And in
+that case, the output square wave is
+
+ align:start position:0%
+that case, the output square wave is
+ 
+
+ align:start position:0%
+that case, the output square wave is
+phase shifted by 90° relative to the
+
+ align:start position:0%
+phase shifted by 90° relative to the
+ 
+
+ align:start position:0%
+phase shifted by 90° relative to the
+input sinosoid. If we keep track of the
+
+ align:start position:0%
+input sinosoid. If we keep track of the
+ 
+
+ align:start position:0%
+input sinosoid. If we keep track of the
+trigonometry involved, the amount of
+
+ align:start position:0%
+trigonometry involved, the amount of
+ 
+
+ align:start position:0%
+trigonometry involved, the amount of
+negative phase shift, this angle uh
+
+ align:start position:0%
+negative phase shift, this angle uh
+ 
+
+ align:start position:0%
+negative phase shift, this angle uh
+alpha, the amount of negative phase
+
+ align:start position:0%
+alpha, the amount of negative phase
+ 
+
+ align:start position:0%
+alpha, the amount of negative phase
+shift is simply equal to the arc sign of
+
+ align:start position:0%
+shift is simply equal to the arc sign of
+ 
+
+ align:start position:0%
+shift is simply equal to the arc sign of
+E subm over E. Of course, the
+
+ align:start position:0%
+E subm over E. Of course, the
+ 
+
+ align:start position:0%
+E subm over E. Of course, the
+characteristics of the Schmidt trigger
+
+ align:start position:0%
+characteristics of the Schmidt trigger
+ 
+
+ align:start position:0%
+characteristics of the Schmidt trigger
+are cyclical only uh if E subm exceeds
+
+ align:start position:0%
+are cyclical only uh if E subm exceeds
+ 
+
+ align:start position:0%
+are cyclical only uh if E subm exceeds
+E. If if the or if E exceeds E subm, I'm
+
+ align:start position:0%
+E. If if the or if E exceeds E subm, I'm
+ 
+
+ align:start position:0%
+E. If if the or if E exceeds E subm, I'm
+sorry. If the value of E is smaller than
+
+ align:start position:0%
+sorry. If the value of E is smaller than
+ 
+
+ align:start position:0%
+sorry. If the value of E is smaller than
+E subm, the Schmidt trigger will remain
+
+ align:start position:0%
+E subm, the Schmidt trigger will remain
+ 
+
+ align:start position:0%
+E subm, the Schmidt trigger will remain
+trapped in one of these two states and
+
+ align:start position:0%
+trapped in one of these two states and
+ 
+
+ align:start position:0%
+trapped in one of these two states and
+and we really don't know without further
+
+ align:start position:0%
+and we really don't know without further
+ 
+
+ align:start position:0%
+and we really don't know without further
+information about its initial conditions
+
+ align:start position:0%
+information about its initial conditions
+ 
+
+ align:start position:0%
+information about its initial conditions
+which state it's in. Uh so for normal
+
+ align:start position:0%
+which state it's in. Uh so for normal
+ 
+
+ align:start position:0%
+which state it's in. Uh so for normal
+operation uh the magnitude of the test
+
+ align:start position:0%
+operation uh the magnitude of the test
+ 
+
+ align:start position:0%
+operation uh the magnitude of the test
+sin you saw has to be at least as large
+
+ align:start position:0%
+sin you saw has to be at least as large
+ 
+
+ align:start position:0%
+sin you saw has to be at least as large
+as E subm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The describing function associated with
+
+ align:start position:0%
+The describing function associated with
+ 
+
+ align:start position:0%
+The describing function associated with
+that element G subd of E is once again
+
+ align:start position:0%
+that element G subd of E is once again
+ 
+
+ align:start position:0%
+that element G subd of E is once again
+the output amplitude or the amplitude of
+
+ align:start position:0%
+the output amplitude or the amplitude of
+ 
+
+ align:start position:0%
+the output amplitude or the amplitude of
+the fundamental component of the output
+
+ align:start position:0%
+the fundamental component of the output
+ 
+
+ align:start position:0%
+the fundamental component of the output
+signal which is of course 4 over pi * E
+
+ align:start position:0%
+signal which is of course 4 over pi * E
+ 
+
+ align:start position:0%
+signal which is of course 4 over pi * E
+subn. The output's a square wave. The
+
+ align:start position:0%
+subn. The output's a square wave. The
+ 
+
+ align:start position:0%
+subn. The output's a square wave. The
+fundamental component is 4 over pi * the
+
+ align:start position:0%
+fundamental component is 4 over pi * the
+ 
+
+ align:start position:0%
+fundamental component is 4 over pi * the
+peak value. So that's 4 over pi * e
+
+ align:start position:0%
+peak value. So that's 4 over pi * e
+ 
+
+ align:start position:0%
+peak value. So that's 4 over pi * e
+subn. We then divide by the magnitude of
+
+ align:start position:0%
+subn. We then divide by the magnitude of
+ 
+
+ align:start position:0%
+subn. We then divide by the magnitude of
+the input signal to get the gain in a
+
+ align:start position:0%
+the input signal to get the gain in a
+ 
+
+ align:start position:0%
+the input signal to get the gain in a
+describing function sense of the
+
+ align:start position:0%
+describing function sense of the
+ 
+
+ align:start position:0%
+describing function sense of the
+element. So this is the magnitude
+
+ align:start position:0%
+element. So this is the magnitude
+ 
+
+ align:start position:0%
+element. So this is the magnitude
+portion of the describing function. The
+
+ align:start position:0%
+portion of the describing function. The
+ 
+
+ align:start position:0%
+portion of the describing function. The
+angle as we mentioned in connection with
+
+ align:start position:0%
+angle as we mentioned in connection with
+ 
+
+ align:start position:0%
+angle as we mentioned in connection with
+the view graph is the is minus the arc
+
+ align:start position:0%
+the view graph is the is minus the arc
+ 
+
+ align:start position:0%
+the view graph is the is minus the arc
+sign of e subm over e. And that
+
+ align:start position:0%
+sign of e subm over e. And that
+ 
+
+ align:start position:0%
+sign of e subm over e. And that
+expression is of course only valid for
+
+ align:start position:0%
+expression is of course only valid for
+ 
+
+ align:start position:0%
+expression is of course only valid for
+the input test amplitude exceeding the
+
+ align:start position:0%
+the input test amplitude exceeding the
+ 
+
+ align:start position:0%
+the input test amplitude exceeding the
+switching magnitude.
+
+ align:start position:0%
+switching magnitude.
+ 
+
+ align:start position:0%
+switching magnitude.
+uh let's to keep so that we don't have
+
+ align:start position:0%
+uh let's to keep so that we don't have
+ 
+
+ align:start position:0%
+uh let's to keep so that we don't have
+to keep track of all the factors of e
+
+ align:start position:0%
+to keep track of all the factors of e
+ 
+
+ align:start position:0%
+to keep track of all the factors of e
+subm and e sub e subn and so forth.
+
+ align:start position:0%
+subm and e sub e subn and so forth.
+ 
+
+ align:start position:0%
+subm and e sub e subn and so forth.
+Let's go ahead and and simply normalize
+
+ align:start position:0%
+Let's go ahead and and simply normalize
+ 
+
+ align:start position:0%
+Let's go ahead and and simply normalize
+and assume that e subm and e subn are
+
+ align:start position:0%
+and assume that e subm and e subn are
+ 
+
+ align:start position:0%
+and assume that e subm and e subn are
+both equal to one.
+
+ align:start position:0%
+both equal to one.
+ 
+
+ align:start position:0%
+both equal to one.
+Uh our describing function then of
+
+ align:start position:0%
+Uh our describing function then of
+ 
+
+ align:start position:0%
+Uh our describing function then of
+course is simply 4 over pi e the same
+
+ align:start position:0%
+course is simply 4 over pi e the same
+ 
+
+ align:start position:0%
+course is simply 4 over pi e the same
+one as we had with the infinite gain
+
+ align:start position:0%
+one as we had with the infinite gain
+ 
+
+ align:start position:0%
+one as we had with the infinite gain
+limiter. As a matter of fact, uh, of
+
+ align:start position:0%
+limiter. As a matter of fact, uh, of
+ 
+
+ align:start position:0%
+limiter. As a matter of fact, uh, of
+course, this is valid only for E greater
+
+ align:start position:0%
+course, this is valid only for E greater
+ 
+
+ align:start position:0%
+course, this is valid only for E greater
+than one, but the same expression
+
+ align:start position:0%
+than one, but the same expression
+ 
+
+ align:start position:0%
+than one, but the same expression
+because the output signal is the same in
+
+ align:start position:0%
+because the output signal is the same in
+ 
+
+ align:start position:0%
+because the output signal is the same in
+magnitude as that of the infinite gain
+
+ align:start position:0%
+magnitude as that of the infinite gain
+ 
+
+ align:start position:0%
+magnitude as that of the infinite gain
+limiter once E is larger than one. And
+
+ align:start position:0%
+limiter once E is larger than one. And
+ 
+
+ align:start position:0%
+limiter once E is larger than one. And
+the angle under these conditions is
+
+ align:start position:0%
+the angle under these conditions is
+ 
+
+ align:start position:0%
+the angle under these conditions is
+simply minus the arc sign of 1 over E.
+
+ align:start position:0%
+simply minus the arc sign of 1 over E.
+ 
+
+ align:start position:0%
+simply minus the arc sign of 1 over E.
+Well, we can then calculate the
+
+ align:start position:0%
+Well, we can then calculate the
+ 
+
+ align:start position:0%
+Well, we can then calculate the
+reciprocal or minus the reciprocal of 1
+
+ align:start position:0%
+reciprocal or minus the reciprocal of 1
+ 
+
+ align:start position:0%
+reciprocal or minus the reciprocal of 1
+/ GD of E, which is of course what we
+
+ align:start position:0%
+/ GD of E, which is of course what we
+ 
+
+ align:start position:0%
+/ GD of E, which is of course what we
+need for our construction
+
+ align:start position:0%
+need for our construction
+ 
+
+ align:start position:0%
+need for our construction
+uh our our describing function analysis.
+
+ align:start position:0%
+uh our our describing function analysis.
+ 
+
+ align:start position:0%
+uh our our describing function analysis.
+The reciprocal of the magnitude is
+
+ align:start position:0%
+The reciprocal of the magnitude is
+ 
+
+ align:start position:0%
+The reciprocal of the magnitude is
+simply pi E / 4. Then we have to get the
+
+ align:start position:0%
+simply pi E / 4. Then we have to get the
+ 
+
+ align:start position:0%
+simply pi E / 4. Then we have to get the
+angle. We have a minus sign. So that
+
+ align:start position:0%
+angle. We have a minus sign. So that
+ 
+
+ align:start position:0%
+angle. We have a minus sign. So that
+gives us minus 180°. is the inversion
+
+ align:start position:0%
+gives us minus 180°. is the inversion
+ 
+
+ align:start position:0%
+gives us minus 180°. is the inversion
+associated with a minus sign gives us
+
+ align:start position:0%
+associated with a minus sign gives us
+ 
+
+ align:start position:0%
+associated with a minus sign gives us
+the minus 180°.
+
+ align:start position:0%
+the minus 180°.
+ 
+
+ align:start position:0%
+the minus 180°.
+Uh we since we're taking 1 / gd of e and
+
+ align:start position:0%
+Uh we since we're taking 1 / gd of e and
+ 
+
+ align:start position:0%
+Uh we since we're taking 1 / gd of e and
+the angle associated with gd of e is
+
+ align:start position:0%
+the angle associated with gd of e is
+ 
+
+ align:start position:0%
+the angle associated with gd of e is
+minus the ark sign of 1 over e when we
+
+ align:start position:0%
+minus the ark sign of 1 over e when we
+ 
+
+ align:start position:0%
+minus the ark sign of 1 over e when we
+take the reciprocal of that we simply
+
+ align:start position:0%
+take the reciprocal of that we simply
+ 
+
+ align:start position:0%
+take the reciprocal of that we simply
+change the sign and we get the si gn and
+
+ align:start position:0%
+change the sign and we get the si gn and
+ 
+
+ align:start position:0%
+change the sign and we get the si gn and
+we get plus the ark sign of 1 / e. So
+
+ align:start position:0%
+we get plus the ark sign of 1 / e. So
+ 
+
+ align:start position:0%
+we get plus the ark sign of 1 / e. So
+the total angle associated with minus 1
+
+ align:start position:0%
+the total angle associated with minus 1
+ 
+
+ align:start position:0%
+the total angle associated with minus 1
+/ GD of E is minus 180° plus the ark
+
+ align:start position:0%
+/ GD of E is minus 180° plus the ark
+ 
+
+ align:start position:0%
+/ GD of E is minus 180° plus the ark
+sign of 1 over E.
+
+ align:start position:0%
+sign of 1 over E.
+ 
+
+ align:start position:0%
+sign of 1 over E.
+We can use that information
+
+ align:start position:0%
+We can use that information
+ 
+
+ align:start position:0%
+We can use that information
+as part of our describing function
+
+ align:start position:0%
+as part of our describing function
+ 
+
+ align:start position:0%
+as part of our describing function
+construction.
+
+ align:start position:0%
+construction.
+ 
+
+ align:start position:0%
+construction.
+Here we have minus1 over GD of E. We're
+
+ align:start position:0%
+Here we have minus1 over GD of E. We're
+ 
+
+ align:start position:0%
+Here we have minus1 over GD of E. We're
+showing this of course as we always do
+
+ align:start position:0%
+showing this of course as we always do
+ 
+
+ align:start position:0%
+showing this of course as we always do
+in a gain phase plane. the angle running
+
+ align:start position:0%
+in a gain phase plane. the angle running
+ 
+
+ align:start position:0%
+in a gain phase plane. the angle running
+from minus 45 degrees in this case to
+
+ align:start position:0%
+from minus 45 degrees in this case to
+ 
+
+ align:start position:0%
+from minus 45 degrees in this case to
+minus 180 degrees.
+
+ align:start position:0%
+minus 180 degrees.
+ 
+
+ align:start position:0%
+minus 180 degrees.
+Uh here's our minus one over GD of E
+
+ align:start position:0%
+Uh here's our minus one over GD of E
+ 
+
+ align:start position:0%
+Uh here's our minus one over GD of E
+for very large values of E. We said that
+
+ align:start position:0%
+for very large values of E. We said that
+ 
+
+ align:start position:0%
+for very large values of E. We said that
+the phase shift associated with uh the
+
+ align:start position:0%
+the phase shift associated with uh the
+ 
+
+ align:start position:0%
+the phase shift associated with uh the
+describe with the element with
+
+ align:start position:0%
+describe with the element with
+ 
+
+ align:start position:0%
+describe with the element with
+hysteresis was very nearly 0 degrees.
+
+ align:start position:0%
+hysteresis was very nearly 0 degrees.
+ 
+
+ align:start position:0%
+hysteresis was very nearly 0 degrees.
+Consequently, minus one over GD of E
+
+ align:start position:0%
+Consequently, minus one over GD of E
+ 
+
+ align:start position:0%
+Consequently, minus one over GD of E
+would approach minus 180 degrees for
+
+ align:start position:0%
+would approach minus 180 degrees for
+ 
+
+ align:start position:0%
+would approach minus 180 degrees for
+very large values of E. Uh, as E drops
+
+ align:start position:0%
+very large values of E. Uh, as E drops
+ 
+
+ align:start position:0%
+very large values of E. Uh, as E drops
+down, we remember that the angle from
+
+ align:start position:0%
+down, we remember that the angle from
+ 
+
+ align:start position:0%
+down, we remember that the angle from
+our earlier development is minus 180°
+
+ align:start position:0%
+our earlier development is minus 180°
+ 
+
+ align:start position:0%
+our earlier development is minus 180°
+plus the arc sign of 1 over E. as as the
+
+ align:start position:0%
+plus the arc sign of 1 over E. as as the
+ 
+
+ align:start position:0%
+plus the arc sign of 1 over E. as as the
+amplitude E gets smaller as we reduce
+
+ align:start position:0%
+amplitude E gets smaller as we reduce
+ 
+
+ align:start position:0%
+amplitude E gets smaller as we reduce
+the magnitude of our test signal, why uh
+
+ align:start position:0%
+the magnitude of our test signal, why uh
+ 
+
+ align:start position:0%
+the magnitude of our test signal, why uh
+we eventually get a net plus 90° from
+
+ align:start position:0%
+we eventually get a net plus 90° from
+ 
+
+ align:start position:0%
+we eventually get a net plus 90° from
+the uh minus or from the 1 / GD of E
+
+ align:start position:0%
+the uh minus or from the 1 / GD of E
+ 
+
+ align:start position:0%
+the uh minus or from the 1 / GD of E
+that added to the - 180° uh gives us a
+
+ align:start position:0%
+that added to the - 180° uh gives us a
+ 
+
+ align:start position:0%
+that added to the - 180° uh gives us a
+net - 90°. So the minus one over GD of E
+
+ align:start position:0%
+net - 90°. So the minus one over GD of E
+ 
+
+ align:start position:0%
+net - 90°. So the minus one over GD of E
+curve goes like so. This is the
+
+ align:start position:0%
+curve goes like so. This is the
+ 
+
+ align:start position:0%
+curve goes like so. This is the
+direction of increasing E.
+
+ align:start position:0%
+direction of increasing E.
+ 
+
+ align:start position:0%
+direction of increasing E.
+And here we have the transfer function
+
+ align:start position:0%
+And here we have the transfer function
+ 
+
+ align:start position:0%
+And here we have the transfer function
+in gain phase form for the linear
+
+ align:start position:0%
+in gain phase form for the linear
+ 
+
+ align:start position:0%
+in gain phase form for the linear
+element. This is an integrator whose
+
+ align:start position:0%
+element. This is an integrator whose
+ 
+
+ align:start position:0%
+element. This is an integrator whose
+value is normalized once again or whose
+
+ align:start position:0%
+value is normalized once again or whose
+ 
+
+ align:start position:0%
+value is normalized once again or whose
+time constant is normalized to unity. Uh
+
+ align:start position:0%
+time constant is normalized to unity. Uh
+ 
+
+ align:start position:0%
+time constant is normalized to unity. Uh
+so we simply have one over S or one over
+
+ align:start position:0%
+so we simply have one over S or one over
+ 
+
+ align:start position:0%
+so we simply have one over S or one over
+J omega for syosoidal exitation. That's
+
+ align:start position:0%
+J omega for syosoidal exitation. That's
+ 
+
+ align:start position:0%
+J omega for syosoidal exitation. That's
+simply a vertical line here. Uh and
+
+ align:start position:0%
+simply a vertical line here. Uh and
+ 
+
+ align:start position:0%
+simply a vertical line here. Uh and
+The phase shift associated with that is
+
+ align:start position:0%
+The phase shift associated with that is
+ 
+
+ align:start position:0%
+The phase shift associated with that is
+always - 90 degrees. This is the
+
+ align:start position:0%
+always - 90 degrees. This is the
+ 
+
+ align:start position:0%
+always - 90 degrees. This is the
+direction of increasing omega. We notice
+
+ align:start position:0%
+direction of increasing omega. We notice
+ 
+
+ align:start position:0%
+direction of increasing omega. We notice
+that there is an intersection. It's not
+
+ align:start position:0%
+that there is an intersection. It's not
+ 
+
+ align:start position:0%
+that there is an intersection. It's not
+as clean an intersection as we had uh uh
+
+ align:start position:0%
+as clean an intersection as we had uh uh
+ 
+
+ align:start position:0%
+as clean an intersection as we had uh uh
+in our other example of of this sort of
+
+ align:start position:0%
+in our other example of of this sort of
+ 
+
+ align:start position:0%
+in our other example of of this sort of
+thing. When we when we looked at the
+
+ align:start position:0%
+thing. When we when we looked at the
+ 
+
+ align:start position:0%
+thing. When we when we looked at the
+phase shift oscillator with the infinite
+
+ align:start position:0%
+phase shift oscillator with the infinite
+ 
+
+ align:start position:0%
+phase shift oscillator with the infinite
+gain limiter, we found a very very clean
+
+ align:start position:0%
+gain limiter, we found a very very clean
+ 
+
+ align:start position:0%
+gain limiter, we found a very very clean
+intersection. And in that case the curve
+
+ align:start position:0%
+intersection. And in that case the curve
+ 
+
+ align:start position:0%
+intersection. And in that case the curve
+that represented the linear portion of
+
+ align:start position:0%
+that represented the linear portion of
+ 
+
+ align:start position:0%
+that represented the linear portion of
+the system crossed the minus1 over GD of
+
+ align:start position:0%
+the system crossed the minus1 over GD of
+ 
+
+ align:start position:0%
+the system crossed the minus1 over GD of
+E curve went through it. Uh there was
+
+ align:start position:0%
+E curve went through it. Uh there was
+ 
+
+ align:start position:0%
+E curve went through it. Uh there was
+they they were nearly perpendicular at
+
+ align:start position:0%
+they they were nearly perpendicular at
+ 
+
+ align:start position:0%
+they they were nearly perpendicular at
+the crossing point or at least made an
+
+ align:start position:0%
+the crossing point or at least made an
+ 
+
+ align:start position:0%
+the crossing point or at least made an
+appreciable angle with respect to each
+
+ align:start position:0%
+appreciable angle with respect to each
+ 
+
+ align:start position:0%
+appreciable angle with respect to each
+other and we could very easily determine
+
+ align:start position:0%
+other and we could very easily determine
+ 
+
+ align:start position:0%
+other and we could very easily determine
+the frequency of oscillation and the
+
+ align:start position:0%
+the frequency of oscillation and the
+ 
+
+ align:start position:0%
+the frequency of oscillation and the
+amplitude. There seem to be little
+
+ align:start position:0%
+amplitude. There seem to be little
+ 
+
+ align:start position:0%
+amplitude. There seem to be little
+ambiguity here. The curves are are
+
+ align:start position:0%
+ambiguity here. The curves are are
+ 
+
+ align:start position:0%
+ambiguity here. The curves are are
+perpendicular but there's a little
+
+ align:start position:0%
+perpendicular but there's a little
+ 
+
+ align:start position:0%
+perpendicular but there's a little
+question. The curve uh never really
+
+ align:start position:0%
+question. The curve uh never really
+ 
+
+ align:start position:0%
+question. The curve uh never really
+crosses. they intersect but but the two
+
+ align:start position:0%
+crosses. they intersect but but the two
+ 
+
+ align:start position:0%
+crosses. they intersect but but the two
+curves never really cross.
+
+ align:start position:0%
+curves never really cross.
+ 
+
+ align:start position:0%
+curves never really cross.
+Uh we might expect there was something a
+
+ align:start position:0%
+Uh we might expect there was something a
+ 
+
+ align:start position:0%
+Uh we might expect there was something a
+little bit funny about that. We'll see
+
+ align:start position:0%
+little bit funny about that. We'll see
+ 
+
+ align:start position:0%
+little bit funny about that. We'll see
+that there is uh some significant error
+
+ align:start position:0%
+that there is uh some significant error
+ 
+
+ align:start position:0%
+that there is uh some significant error
+in the analysis in this case. Uh but
+
+ align:start position:0%
+in the analysis in this case. Uh but
+ 
+
+ align:start position:0%
+in the analysis in this case. Uh but
+let's let's proceed anyway. We notice
+
+ align:start position:0%
+let's let's proceed anyway. We notice
+ 
+
+ align:start position:0%
+let's let's proceed anyway. We notice
+that the curves intersect for a value of
+
+ align:start position:0%
+that the curves intersect for a value of
+ 
+
+ align:start position:0%
+that the curves intersect for a value of
+e equal to one
+
+ align:start position:0%
+e equal to one
+ 
+
+ align:start position:0%
+e equal to one
+and we can use that information to
+
+ align:start position:0%
+and we can use that information to
+ 
+
+ align:start position:0%
+and we can use that information to
+determine the frequency at the
+
+ align:start position:0%
+determine the frequency at the
+ 
+
+ align:start position:0%
+determine the frequency at the
+intersection.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Notice that at E= 1 or 4 E= 1, the
+
+ align:start position:0%
+Notice that at E= 1 or 4 E= 1, the
+ 
+
+ align:start position:0%
+Notice that at E= 1 or 4 E= 1, the
+magnitude of 1 / GD of E is simply pi
+
+ align:start position:0%
+magnitude of 1 / GD of E is simply pi
+ 
+
+ align:start position:0%
+magnitude of 1 / GD of E is simply pi
+over 4. But since there's an oscillation
+
+ align:start position:0%
+over 4. But since there's an oscillation
+ 
+
+ align:start position:0%
+over 4. But since there's an oscillation
+or an intersection with the transfer
+
+ align:start position:0%
+or an intersection with the transfer
+ 
+
+ align:start position:0%
+or an intersection with the transfer
+function associated with the linear
+
+ align:start position:0%
+function associated with the linear
+ 
+
+ align:start position:0%
+function associated with the linear
+elements why we conclude that one over
+
+ align:start position:0%
+elements why we conclude that one over
+ 
+
+ align:start position:0%
+elements why we conclude that one over
+omega is the magnitude of of the uh
+
+ align:start position:0%
+omega is the magnitude of of the uh
+ 
+
+ align:start position:0%
+omega is the magnitude of of the uh
+transfer function of the linear portion
+
+ align:start position:0%
+transfer function of the linear portion
+ 
+
+ align:start position:0%
+transfer function of the linear portion
+of the system the integrator uh we
+
+ align:start position:0%
+of the system the integrator uh we
+ 
+
+ align:start position:0%
+of the system the integrator uh we
+conclude that at the intersection the
+
+ align:start position:0%
+conclude that at the intersection the
+ 
+
+ align:start position:0%
+conclude that at the intersection the
+value of 1 / g d of e pi over4 is equal
+
+ align:start position:0%
+value of 1 / g d of e pi over4 is equal
+ 
+
+ align:start position:0%
+value of 1 / g d of e pi over4 is equal
+to 1 over the frequency of oscillation.
+
+ align:start position:0%
+to 1 over the frequency of oscillation.
+ 
+
+ align:start position:0%
+to 1 over the frequency of oscillation.
+And we'd of course determine the
+
+ align:start position:0%
+And we'd of course determine the
+ 
+
+ align:start position:0%
+And we'd of course determine the
+frequency of oscillation from the linear
+
+ align:start position:0%
+frequency of oscillation from the linear
+ 
+
+ align:start position:0%
+frequency of oscillation from the linear
+elements curve. And that tells us that
+
+ align:start position:0%
+elements curve. And that tells us that
+ 
+
+ align:start position:0%
+elements curve. And that tells us that
+omega oscillation is 4 over pi.
+
+ align:start position:0%
+omega oscillation is 4 over pi.
+ 
+
+ align:start position:0%
+omega oscillation is 4 over pi.
+Uh if we convert that to from radians/s
+
+ align:start position:0%
+Uh if we convert that to from radians/s
+ 
+
+ align:start position:0%
+Uh if we convert that to from radians/s
+to hertz, uh we divide by 2 pi and using
+
+ align:start position:0%
+to hertz, uh we divide by 2 pi and using
+ 
+
+ align:start position:0%
+to hertz, uh we divide by 2 pi and using
+a pretty good engineering approximation
+
+ align:start position:0%
+a pretty good engineering approximation
+ 
+
+ align:start position:0%
+a pretty good engineering approximation
+that pi^ 2 is just about equal to 10. uh
+
+ align:start position:0%
+that pi^ 2 is just about equal to 10. uh
+ 
+
+ align:start position:0%
+that pi^ 2 is just about equal to 10. uh
+we end up with about 1/5if of a hertz
+
+ align:start position:0%
+we end up with about 1/5if of a hertz
+ 
+
+ align:start position:0%
+we end up with about 1/5if of a hertz
+for the frequency of of oscillation as
+
+ align:start position:0%
+for the frequency of of oscillation as
+ 
+
+ align:start position:0%
+for the frequency of of oscillation as
+predicted by our describing function
+
+ align:start position:0%
+predicted by our describing function
+ 
+
+ align:start position:0%
+predicted by our describing function
+analysis.
+
+ align:start position:0%
+analysis.
+ 
+
+ align:start position:0%
+analysis.
+Now we know from our exact analysis that
+
+ align:start position:0%
+Now we know from our exact analysis that
+ 
+
+ align:start position:0%
+Now we know from our exact analysis that
+the exact frequency of oscillation is
+
+ align:start position:0%
+the exact frequency of oscillation is
+ 
+
+ align:start position:0%
+the exact frequency of oscillation is
+about a quarter or is exactly a quarter
+
+ align:start position:0%
+about a quarter or is exactly a quarter
+ 
+
+ align:start position:0%
+about a quarter or is exactly a quarter
+of a hertz. So that gives us an
+
+ align:start position:0%
+of a hertz. So that gives us an
+ 
+
+ align:start position:0%
+of a hertz. So that gives us an
+indication of the error associated with
+
+ align:start position:0%
+indication of the error associated with
+ 
+
+ align:start position:0%
+indication of the error associated with
+the analysis. In this case
+
+ align:start position:0%
+the analysis. In this case
+ 
+
+ align:start position:0%
+the analysis. In this case
+we uh can also look at the amplitude. We
+
+ align:start position:0%
+we uh can also look at the amplitude. We
+ 
+
+ align:start position:0%
+we uh can also look at the amplitude. We
+recognize of course that the actual
+
+ align:start position:0%
+recognize of course that the actual
+ 
+
+ align:start position:0%
+recognize of course that the actual
+signal at the input to the nonlinear
+
+ align:start position:0%
+signal at the input to the nonlinear
+ 
+
+ align:start position:0%
+signal at the input to the nonlinear
+element which is of course where our
+
+ align:start position:0%
+element which is of course where our
+ 
+
+ align:start position:0%
+element which is of course where our
+describing function analysis tells us uh
+
+ align:start position:0%
+describing function analysis tells us uh
+ 
+
+ align:start position:0%
+describing function analysis tells us uh
+amplitude the actual signal at that
+
+ align:start position:0%
+amplitude the actual signal at that
+ 
+
+ align:start position:0%
+amplitude the actual signal at that
+point is a triangular wave with a peak
+
+ align:start position:0%
+point is a triangular wave with a peak
+ 
+
+ align:start position:0%
+point is a triangular wave with a peak
+value of of one for our normalized
+
+ align:start position:0%
+value of of one for our normalized
+ 
+
+ align:start position:0%
+value of of one for our normalized
+system.
+
+ align:start position:0%
+system.
+ 
+
+ align:start position:0%
+system.
+Our analysis tells us that E should be
+
+ align:start position:0%
+Our analysis tells us that E should be
+ 
+
+ align:start position:0%
+Our analysis tells us that E should be
+equal to one. We notice that the
+
+ align:start position:0%
+equal to one. We notice that the
+ 
+
+ align:start position:0%
+equal to one. We notice that the
+intersection occurs for a value of E
+
+ align:start position:0%
+intersection occurs for a value of E
+ 
+
+ align:start position:0%
+intersection occurs for a value of E
+equal to one. However, that E in that
+
+ align:start position:0%
+equal to one. However, that E in that
+ 
+
+ align:start position:0%
+equal to one. However, that E in that
+analysis uh is predicting the value of
+
+ align:start position:0%
+analysis uh is predicting the value of
+ 
+
+ align:start position:0%
+analysis uh is predicting the value of
+the fundamental component of the signal.
+
+ align:start position:0%
+the fundamental component of the signal.
+ 
+
+ align:start position:0%
+the fundamental component of the signal.
+For a triangle wave, the fundamental
+
+ align:start position:0%
+For a triangle wave, the fundamental
+ 
+
+ align:start position:0%
+For a triangle wave, the fundamental
+component is actually about 8/10 of its
+
+ align:start position:0%
+component is actually about 8/10 of its
+ 
+
+ align:start position:0%
+component is actually about 8/10 of its
+peak value. So again, uh depending on
+
+ align:start position:0%
+peak value. So again, uh depending on
+ 
+
+ align:start position:0%
+peak value. So again, uh depending on
+how we interpret the magnitude part of
+
+ align:start position:0%
+how we interpret the magnitude part of
+ 
+
+ align:start position:0%
+how we interpret the magnitude part of
+the analysis, there's a roughly 20%
+
+ align:start position:0%
+the analysis, there's a roughly 20%
+ 
+
+ align:start position:0%
+the analysis, there's a roughly 20%
+error. the uh describing function
+
+ align:start position:0%
+error. the uh describing function
+ 
+
+ align:start position:0%
+error. the uh describing function
+analysis predicts an amplitude of 08 for
+
+ align:start position:0%
+analysis predicts an amplitude of 08 for
+ 
+
+ align:start position:0%
+analysis predicts an amplitude of 08 for
+the fundamental uh or of one for the
+
+ align:start position:0%
+the fundamental uh or of one for the
+ 
+
+ align:start position:0%
+the fundamental uh or of one for the
+fundamental component of the signal into
+
+ align:start position:0%
+fundamental component of the signal into
+ 
+
+ align:start position:0%
+fundamental component of the signal into
+the nonlinearity. The actual fundamental
+
+ align:start position:0%
+the nonlinearity. The actual fundamental
+ 
+
+ align:start position:0%
+the nonlinearity. The actual fundamental
+component is about 08. The reason is
+
+ align:start position:0%
+component is about 08. The reason is
+ 
+
+ align:start position:0%
+component is about 08. The reason is
+that there are at least one of the
+
+ align:start position:0%
+that there are at least one of the
+ 
+
+ align:start position:0%
+that there are at least one of the
+difficulties with the analysis aside
+
+ align:start position:0%
+difficulties with the analysis aside
+ 
+
+ align:start position:0%
+difficulties with the analysis aside
+from the fact that there's not a a good
+
+ align:start position:0%
+from the fact that there's not a a good
+ 
+
+ align:start position:0%
+from the fact that there's not a a good
+clean crossing kind of intersection in
+
+ align:start position:0%
+clean crossing kind of intersection in
+ 
+
+ align:start position:0%
+clean crossing kind of intersection in
+the gain phase plane is that the
+
+ align:start position:0%
+the gain phase plane is that the
+ 
+
+ align:start position:0%
+the gain phase plane is that the
+there's considerably more harmonic
+
+ align:start position:0%
+there's considerably more harmonic
+ 
+
+ align:start position:0%
+there's considerably more harmonic
+distortion in this case than there was
+
+ align:start position:0%
+distortion in this case than there was
+ 
+
+ align:start position:0%
+distortion in this case than there was
+in our earlier example. Uh the signal of
+
+ align:start position:0%
+in our earlier example. Uh the signal of
+ 
+
+ align:start position:0%
+in our earlier example. Uh the signal of
+course into the nonlinearity in this
+
+ align:start position:0%
+course into the nonlinearity in this
+ 
+
+ align:start position:0%
+course into the nonlinearity in this
+case is a triangle wave. The harmonic or
+
+ align:start position:0%
+case is a triangle wave. The harmonic or
+ 
+
+ align:start position:0%
+case is a triangle wave. The harmonic or
+the forier series for a triangle wave
+
+ align:start position:0%
+the forier series for a triangle wave
+ 
+
+ align:start position:0%
+the forier series for a triangle wave
+includes only odd harmonics and they
+
+ align:start position:0%
+includes only odd harmonics and they
+ 
+
+ align:start position:0%
+includes only odd harmonics and they
+drop off as the square of the order of
+
+ align:start position:0%
+drop off as the square of the order of
+ 
+
+ align:start position:0%
+drop off as the square of the order of
+the harmonic. So the uh third harmonic
+
+ align:start position:0%
+the harmonic. So the uh third harmonic
+ 
+
+ align:start position:0%
+the harmonic. So the uh third harmonic
+the magnitude of the third harmonic is
+
+ align:start position:0%
+the magnitude of the third harmonic is
+ 
+
+ align:start position:0%
+the magnitude of the third harmonic is
+about 1 nth or 11% of the magnitude of
+
+ align:start position:0%
+about 1 nth or 11% of the magnitude of
+ 
+
+ align:start position:0%
+about 1 nth or 11% of the magnitude of
+the fundamental. The fifth harmonic is
+
+ align:start position:0%
+the fundamental. The fifth harmonic is
+ 
+
+ align:start position:0%
+the fundamental. The fifth harmonic is
+about 4% of the magnitude of the
+
+ align:start position:0%
+about 4% of the magnitude of the
+ 
+
+ align:start position:0%
+about 4% of the magnitude of the
+fundamental and so forth. So there's
+
+ align:start position:0%
+fundamental and so forth. So there's
+ 
+
+ align:start position:0%
+fundamental and so forth. So there's
+significant harmonic distortion in this
+
+ align:start position:0%
+significant harmonic distortion in this
+ 
+
+ align:start position:0%
+significant harmonic distortion in this
+case. uh we have a triangle wave rather
+
+ align:start position:0%
+case. uh we have a triangle wave rather
+ 
+
+ align:start position:0%
+case. uh we have a triangle wave rather
+than an approximate syosoid at the input
+
+ align:start position:0%
+than an approximate syosoid at the input
+ 
+
+ align:start position:0%
+than an approximate syosoid at the input
+to the nonlinearity and again that leads
+
+ align:start position:0%
+to the nonlinearity and again that leads
+ 
+
+ align:start position:0%
+to the nonlinearity and again that leads
+to some errors but I think in in spite
+
+ align:start position:0%
+to some errors but I think in in spite
+ 
+
+ align:start position:0%
+to some errors but I think in in spite
+of the very large uh amount of harmonic
+
+ align:start position:0%
+of the very large uh amount of harmonic
+ 
+
+ align:start position:0%
+of the very large uh amount of harmonic
+distortion in this case the linear
+
+ align:start position:0%
+distortion in this case the linear
+ 
+
+ align:start position:0%
+distortion in this case the linear
+elements are low pass but only single
+
+ align:start position:0%
+elements are low pass but only single
+ 
+
+ align:start position:0%
+elements are low pass but only single
+order uh we still get a reasonable
+
+ align:start position:0%
+order uh we still get a reasonable
+ 
+
+ align:start position:0%
+order uh we still get a reasonable
+approximation if we didn't have a better
+
+ align:start position:0%
+approximation if we didn't have a better
+ 
+
+ align:start position:0%
+approximation if we didn't have a better
+way of solving this system I think we'd
+
+ align:start position:0%
+way of solving this system I think we'd
+ 
+
+ align:start position:0%
+way of solving this system I think we'd
+probably be be very happy to settle for
+
+ align:start position:0%
+probably be be very happy to settle for
+ 
+
+ align:start position:0%
+probably be be very happy to settle for
+20% kinds of errors
+
+ align:start position:0%
+20% kinds of errors
+ 
+
+ align:start position:0%
+20% kinds of errors
+I'd like to consider uh another aspect
+
+ align:start position:0%
+I'd like to consider uh another aspect
+ 
+
+ align:start position:0%
+I'd like to consider uh another aspect
+of nonlinear system behavior that again
+
+ align:start position:0%
+of nonlinear system behavior that again
+ 
+
+ align:start position:0%
+of nonlinear system behavior that again
+we can uh
+
+ align:start position:0%
+we can uh
+ 
+
+ align:start position:0%
+we can uh
+begin to interpret in terms of
+
+ align:start position:0%
+begin to interpret in terms of
+ 
+
+ align:start position:0%
+begin to interpret in terms of
+describing functions. Let's consider a
+
+ align:start position:0%
+describing functions. Let's consider a
+ 
+
+ align:start position:0%
+describing functions. Let's consider a
+loop of the following form. Uh we have
+
+ align:start position:0%
+loop of the following form. Uh we have
+ 
+
+ align:start position:0%
+loop of the following form. Uh we have
+an input and an output some linear
+
+ align:start position:0%
+an input and an output some linear
+ 
+
+ align:start position:0%
+an input and an output some linear
+elements and then reflecting uh one of
+
+ align:start position:0%
+elements and then reflecting uh one of
+ 
+
+ align:start position:0%
+elements and then reflecting uh one of
+the harsh realities of the real world.
+
+ align:start position:0%
+the harsh realities of the real world.
+ 
+
+ align:start position:0%
+the harsh realities of the real world.
+We have saturation somewhere in the
+
+ align:start position:0%
+We have saturation somewhere in the
+ 
+
+ align:start position:0%
+We have saturation somewhere in the
+loop. uh we simply have an element
+
+ align:start position:0%
+loop. uh we simply have an element
+ 
+
+ align:start position:0%
+loop. uh we simply have an element
+that's maybe the output of an amplifier
+
+ align:start position:0%
+that's maybe the output of an amplifier
+ 
+
+ align:start position:0%
+that's maybe the output of an amplifier
+or the uh maximum capability of a motor
+
+ align:start position:0%
+or the uh maximum capability of a motor
+ 
+
+ align:start position:0%
+or the uh maximum capability of a motor
+or or anything else that that has a a
+
+ align:start position:0%
+or or anything else that that has a a
+ 
+
+ align:start position:0%
+or or anything else that that has a a
+finite dynamic range sort of a thing
+
+ align:start position:0%
+finite dynamic range sort of a thing
+ 
+
+ align:start position:0%
+finite dynamic range sort of a thing
+where uh again we've normalized things
+
+ align:start position:0%
+where uh again we've normalized things
+ 
+
+ align:start position:0%
+where uh again we've normalized things
+we get a a slope of one in this region
+
+ align:start position:0%
+we get a a slope of one in this region
+ 
+
+ align:start position:0%
+we get a a slope of one in this region
+the input and the output of the
+
+ align:start position:0%
+the input and the output of the
+ 
+
+ align:start position:0%
+the input and the output of the
+nonlinearity are equal but when the
+
+ align:start position:0%
+nonlinearity are equal but when the
+ 
+
+ align:start position:0%
+nonlinearity are equal but when the
+input exceeds one or is more negative
+
+ align:start position:0%
+input exceeds one or is more negative
+ 
+
+ align:start position:0%
+input exceeds one or is more negative
+than minus one we assume that the
+
+ align:start position:0%
+than minus one we assume that the
+ 
+
+ align:start position:0%
+than minus one we assume that the
+element saturates and and its output is
+
+ align:start position:0%
+element saturates and and its output is
+ 
+
+ align:start position:0%
+element saturates and and its output is
+bounded at plus or minus one. Well,
+
+ align:start position:0%
+bounded at plus or minus one. Well,
+ 
+
+ align:start position:0%
+bounded at plus or minus one. Well,
+we'll actually calculate the describing
+
+ align:start position:0%
+we'll actually calculate the describing
+ 
+
+ align:start position:0%
+we'll actually calculate the describing
+function for this element exactly next
+
+ align:start position:0%
+function for this element exactly next
+ 
+
+ align:start position:0%
+function for this element exactly next
+time. But I we can estimate important
+
+ align:start position:0%
+time. But I we can estimate important
+ 
+
+ align:start position:0%
+time. But I we can estimate important
+features of it as follows. Uh G subd of
+
+ align:start position:0%
+features of it as follows. Uh G subd of
+ 
+
+ align:start position:0%
+features of it as follows. Uh G subd of
+E is simply one at an angle of zero uh
+
+ align:start position:0%
+E is simply one at an angle of zero uh
+ 
+
+ align:start position:0%
+E is simply one at an angle of zero uh
+when E is less than one. For E less than
+
+ align:start position:0%
+when E is less than one. For E less than
+ 
+
+ align:start position:0%
+when E is less than one. For E less than
+one, we don't encounter saturation. Uh
+
+ align:start position:0%
+one, we don't encounter saturation. Uh
+ 
+
+ align:start position:0%
+one, we don't encounter saturation. Uh
+and and so the input and the output are
+
+ align:start position:0%
+and and so the input and the output are
+ 
+
+ align:start position:0%
+and and so the input and the output are
+identical.
+
+ align:start position:0%
+identical.
+ 
+
+ align:start position:0%
+identical.
+G subd of E approaches uh 4 over pi E
+
+ align:start position:0%
+G subd of E approaches uh 4 over pi E
+ 
+
+ align:start position:0%
+G subd of E approaches uh 4 over pi E
+for very very large values of E. When we
+
+ align:start position:0%
+for very very large values of E. When we
+ 
+
+ align:start position:0%
+for very very large values of E. When we
+get when we put in a very large value of
+
+ align:start position:0%
+get when we put in a very large value of
+ 
+
+ align:start position:0%
+get when we put in a very large value of
+of test signal to the nonlinear element
+
+ align:start position:0%
+of test signal to the nonlinear element
+ 
+
+ align:start position:0%
+of test signal to the nonlinear element
+uh the nonlinear the output of the
+
+ align:start position:0%
+uh the nonlinear the output of the
+ 
+
+ align:start position:0%
+uh the nonlinear the output of the
+nonlinear element is basically a square
+
+ align:start position:0%
+nonlinear element is basically a square
+ 
+
+ align:start position:0%
+nonlinear element is basically a square
+wave. It spends very a very short period
+
+ align:start position:0%
+wave. It spends very a very short period
+ 
+
+ align:start position:0%
+wave. It spends very a very short period
+of time in the transition region. And so
+
+ align:start position:0%
+of time in the transition region. And so
+ 
+
+ align:start position:0%
+of time in the transition region. And so
+when we have a very large value for our
+
+ align:start position:0%
+when we have a very large value for our
+ 
+
+ align:start position:0%
+when we have a very large value for our
+test signal, we get essentially a square
+
+ align:start position:0%
+test signal, we get essentially a square
+ 
+
+ align:start position:0%
+test signal, we get essentially a square
+wave out. The magnitude of the
+
+ align:start position:0%
+wave out. The magnitude of the
+ 
+
+ align:start position:0%
+wave out. The magnitude of the
+fundamental component of that square
+
+ align:start position:0%
+fundamental component of that square
+ 
+
+ align:start position:0%
+fundamental component of that square
+wave is 4 over pi. Uh we divide by by e
+
+ align:start position:0%
+wave is 4 over pi. Uh we divide by by e
+ 
+
+ align:start position:0%
+wave is 4 over pi. Uh we divide by by e
+and we get the magnitude of our
+
+ align:start position:0%
+and we get the magnitude of our
+ 
+
+ align:start position:0%
+and we get the magnitude of our
+describing function as 4 over pi e. If
+
+ align:start position:0%
+describing function as 4 over pi e. If
+ 
+
+ align:start position:0%
+describing function as 4 over pi e. If
+we plot that it it looks something as
+
+ align:start position:0%
+we plot that it it looks something as
+ 
+
+ align:start position:0%
+we plot that it it looks something as
+follows. Uh we have a a magnitude of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for amplitudes smaller than one.
+
+ align:start position:0%
+for amplitudes smaller than one.
+ 
+
+ align:start position:0%
+for amplitudes smaller than one.
+uh for very large values of test signal
+
+ align:start position:0%
+uh for very large values of test signal
+ 
+
+ align:start position:0%
+uh for very large values of test signal
+amplitude the characteristics become
+
+ align:start position:0%
+amplitude the characteristics become
+ 
+
+ align:start position:0%
+amplitude the characteristics become
+hyperbolic inversely proportional to E
+
+ align:start position:0%
+hyperbolic inversely proportional to E
+ 
+
+ align:start position:0%
+hyperbolic inversely proportional to E
+uh and the transition occurs at an
+
+ align:start position:0%
+uh and the transition occurs at an
+ 
+
+ align:start position:0%
+uh and the transition occurs at an
+amplitude of one. As soon as we get up
+
+ align:start position:0%
+amplitude of one. As soon as we get up
+ 
+
+ align:start position:0%
+amplitude of one. As soon as we get up
+to an amplitude of one, we begin to get
+
+ align:start position:0%
+to an amplitude of one, we begin to get
+ 
+
+ align:start position:0%
+to an amplitude of one, we begin to get
+some clipping out of the saturating
+
+ align:start position:0%
+some clipping out of the saturating
+ 
+
+ align:start position:0%
+some clipping out of the saturating
+element and so the gain of our nonlinear
+
+ align:start position:0%
+element and so the gain of our nonlinear
+ 
+
+ align:start position:0%
+element and so the gain of our nonlinear
+nonlinear element begins to drop off.
+
+ align:start position:0%
+nonlinear element begins to drop off.
+ 
+
+ align:start position:0%
+nonlinear element begins to drop off.
+Well, a potential difficulty exists if
+
+ align:start position:0%
+Well, a potential difficulty exists if
+ 
+
+ align:start position:0%
+Well, a potential difficulty exists if
+we combine that sort of a nonlinearity
+
+ align:start position:0%
+we combine that sort of a nonlinearity
+ 
+
+ align:start position:0%
+we combine that sort of a nonlinearity
+and virtually all physical systems
+
+ align:start position:0%
+and virtually all physical systems
+ 
+
+ align:start position:0%
+and virtually all physical systems
+include saturation for appropriately
+
+ align:start position:0%
+include saturation for appropriately
+ 
+
+ align:start position:0%
+include saturation for appropriately
+large signal levels. Of course, uh with
+
+ align:start position:0%
+large signal levels. Of course, uh with
+ 
+
+ align:start position:0%
+large signal levels. Of course, uh with
+a particular kind of of dynamics
+
+ align:start position:0%
+a particular kind of of dynamics
+ 
+
+ align:start position:0%
+a particular kind of of dynamics
+associated with the linear portions of
+
+ align:start position:0%
+associated with the linear portions of
+ 
+
+ align:start position:0%
+associated with the linear portions of
+the loop. Let's consider an a of j omega
+
+ align:start position:0%
+the loop. Let's consider an a of j omega
+ 
+
+ align:start position:0%
+the loop. Let's consider an a of j omega
+that might have the form shown here. uh
+
+ align:start position:0%
+that might have the form shown here. uh
+ 
+
+ align:start position:0%
+that might have the form shown here. uh
+possibly a constant value at DC. Then a
+
+ align:start position:0%
+possibly a constant value at DC. Then a
+ 
+
+ align:start position:0%
+possibly a constant value at DC. Then a
+long region where the gain versus
+
+ align:start position:0%
+long region where the gain versus
+ 
+
+ align:start position:0%
+long region where the gain versus
+frequency characteristic the bodie plot
+
+ align:start position:0%
+frequency characteristic the bodie plot
+ 
+
+ align:start position:0%
+frequency characteristic the bodie plot
+associated with a of j omega falls off
+
+ align:start position:0%
+associated with a of j omega falls off
+ 
+
+ align:start position:0%
+associated with a of j omega falls off
+more rapidly than 1 / s uh possibly 1
+
+ align:start position:0%
+more rapidly than 1 / s uh possibly 1
+ 
+
+ align:start position:0%
+more rapidly than 1 / s uh possibly 1
+over s squared in this region. Uh we
+
+ align:start position:0%
+over s squared in this region. Uh we
+ 
+
+ align:start position:0%
+over s squared in this region. Uh we
+then might break back in the vicinity of
+
+ align:start position:0%
+then might break back in the vicinity of
+ 
+
+ align:start position:0%
+then might break back in the vicinity of
+crossover. If this is uh the unity gain
+
+ align:start position:0%
+crossover. If this is uh the unity gain
+ 
+
+ align:start position:0%
+crossover. If this is uh the unity gain
+point in the vicinity of crossover, we
+
+ align:start position:0%
+point in the vicinity of crossover, we
+ 
+
+ align:start position:0%
+point in the vicinity of crossover, we
+might break back to a one overs slope
+
+ align:start position:0%
+might break back to a one overs slope
+ 
+
+ align:start position:0%
+might break back to a one overs slope
+and then usually at higher frequencies
+
+ align:start position:0%
+and then usually at higher frequencies
+ 
+
+ align:start position:0%
+and then usually at higher frequencies
+something else happens. We get
+
+ align:start position:0%
+something else happens. We get
+ 
+
+ align:start position:0%
+something else happens. We get
+additional modes of energy storage
+
+ align:start position:0%
+additional modes of energy storage
+ 
+
+ align:start position:0%
+additional modes of energy storage
+become important and the characteristics
+
+ align:start position:0%
+become important and the characteristics
+ 
+
+ align:start position:0%
+become important and the characteristics
+once again fall off rapidly. The angle
+
+ align:start position:0%
+once again fall off rapidly. The angle
+ 
+
+ align:start position:0%
+once again fall off rapidly. The angle
+associated with that sort of transfer
+
+ align:start position:0%
+associated with that sort of transfer
+ 
+
+ align:start position:0%
+associated with that sort of transfer
+function is something in this case would
+
+ align:start position:0%
+function is something in this case would
+ 
+
+ align:start position:0%
+function is something in this case would
+start at 0 degrees. If there was a very
+
+ align:start position:0%
+start at 0 degrees. If there was a very
+ 
+
+ align:start position:0%
+start at 0 degrees. If there was a very
+long 1 over s^2 region, the angle
+
+ align:start position:0%
+long 1 over s^2 region, the angle
+ 
+
+ align:start position:0%
+long 1 over s^2 region, the angle
+somewhere in that 1 over s^2 region
+
+ align:start position:0%
+somewhere in that 1 over s^2 region
+ 
+
+ align:start position:0%
+somewhere in that 1 over s^2 region
+would drop down very very close to minus
+
+ align:start position:0%
+would drop down very very close to minus
+ 
+
+ align:start position:0%
+would drop down very very close to minus
+180°.
+
+ align:start position:0%
+180°.
+ 
+
+ align:start position:0%
+180°.
+We'd then come back up reflecting the
+
+ align:start position:0%
+We'd then come back up reflecting the
+ 
+
+ align:start position:0%
+We'd then come back up reflecting the
+zero and the 1 / s slope again depending
+
+ align:start position:0%
+zero and the 1 / s slope again depending
+ 
+
+ align:start position:0%
+zero and the 1 / s slope again depending
+on the duration of the 1 over s slope we
+
+ align:start position:0%
+on the duration of the 1 over s slope we
+ 
+
+ align:start position:0%
+on the duration of the 1 over s slope we
+might approach - 90° in here and then
+
+ align:start position:0%
+might approach - 90° in here and then
+ 
+
+ align:start position:0%
+might approach - 90° in here and then
+conceivably the the angle gets
+
+ align:start position:0%
+conceivably the the angle gets
+ 
+
+ align:start position:0%
+conceivably the the angle gets
+progressively more negative at higher
+
+ align:start position:0%
+progressively more negative at higher
+ 
+
+ align:start position:0%
+progressively more negative at higher
+frequencies. We've seen these general
+
+ align:start position:0%
+frequencies. We've seen these general
+ 
+
+ align:start position:0%
+frequencies. We've seen these general
+sorts of characteristics before in in at
+
+ align:start position:0%
+sorts of characteristics before in in at
+ 
+
+ align:start position:0%
+sorts of characteristics before in in at
+least two two examples that we've looked
+
+ align:start position:0%
+least two two examples that we've looked
+ 
+
+ align:start position:0%
+least two two examples that we've looked
+at. One was lag compensation where we
+
+ align:start position:0%
+at. One was lag compensation where we
+ 
+
+ align:start position:0%
+at. One was lag compensation where we
+ended up with a 1 over s squared region
+
+ align:start position:0%
+ended up with a 1 over s squared region
+ 
+
+ align:start position:0%
+ended up with a 1 over s squared region
+in the loop transmission of our system.
+
+ align:start position:0%
+in the loop transmission of our system.
+ 
+
+ align:start position:0%
+in the loop transmission of our system.
+And again, you recall that there was a
+
+ align:start position:0%
+And again, you recall that there was a
+ 
+
+ align:start position:0%
+And again, you recall that there was a
+dip in the phase. It wasn't quite this
+
+ align:start position:0%
+dip in the phase. It wasn't quite this
+ 
+
+ align:start position:0%
+dip in the phase. It wasn't quite this
+pronounced, but it did dip down and then
+
+ align:start position:0%
+pronounced, but it did dip down and then
+ 
+
+ align:start position:0%
+pronounced, but it did dip down and then
+recover somewhat in the vicinity of
+
+ align:start position:0%
+recover somewhat in the vicinity of
+ 
+
+ align:start position:0%
+recover somewhat in the vicinity of
+crossover because we had taken the
+
+ align:start position:0%
+crossover because we had taken the
+ 
+
+ align:start position:0%
+crossover because we had taken the
+precaution of locating the zero
+
+ align:start position:0%
+precaution of locating the zero
+ 
+
+ align:start position:0%
+precaution of locating the zero
+associated with the lag network back
+
+ align:start position:0%
+associated with the lag network back
+ 
+
+ align:start position:0%
+associated with the lag network back
+fairly far from crossover.
+
+ align:start position:0%
+fairly far from crossover.
+ 
+
+ align:start position:0%
+fairly far from crossover.
+Another case where we didn't actually
+
+ align:start position:0%
+Another case where we didn't actually
+ 
+
+ align:start position:0%
+Another case where we didn't actually
+draw the bodie plot in great detail, but
+
+ align:start position:0%
+draw the bodie plot in great detail, but
+ 
+
+ align:start position:0%
+draw the bodie plot in great detail, but
+we spoke about it was our operational
+
+ align:start position:0%
+we spoke about it was our operational
+ 
+
+ align:start position:0%
+we spoke about it was our operational
+amplifier example when we use two- pole
+
+ align:start position:0%
+amplifier example when we use two- pole
+ 
+
+ align:start position:0%
+amplifier example when we use two- pole
+compensation. And again we get a a curve
+
+ align:start position:0%
+compensation. And again we get a a curve
+ 
+
+ align:start position:0%
+compensation. And again we get a a curve
+for the openloop gain of the operational
+
+ align:start position:0%
+for the openloop gain of the operational
+ 
+
+ align:start position:0%
+for the openloop gain of the operational
+amplifier that's very much like this
+
+ align:start position:0%
+amplifier that's very much like this
+ 
+
+ align:start position:0%
+amplifier that's very much like this
+when we use two- pole compensation. We
+
+ align:start position:0%
+when we use two- pole compensation. We
+ 
+
+ align:start position:0%
+when we use two- pole compensation. We
+have the DC gain of the amplifier. Uh we
+
+ align:start position:0%
+have the DC gain of the amplifier. Uh we
+ 
+
+ align:start position:0%
+have the DC gain of the amplifier. Uh we
+then get into a long 1 over s^ squ
+
+ align:start position:0%
+then get into a long 1 over s^ squ
+ 
+
+ align:start position:0%
+then get into a long 1 over s^ squ
+region. In the case of of our
+
+ align:start position:0%
+region. In the case of of our
+ 
+
+ align:start position:0%
+region. In the case of of our
+operational amplifier that 1 overs
+
+ align:start position:0%
+operational amplifier that 1 overs
+ 
+
+ align:start position:0%
+operational amplifier that 1 overs
+squared region might uh last for a
+
+ align:start position:0%
+squared region might uh last for a
+ 
+
+ align:start position:0%
+squared region might uh last for a
+factor of 100 in frequency or something
+
+ align:start position:0%
+factor of 100 in frequency or something
+ 
+
+ align:start position:0%
+factor of 100 in frequency or something
+like that. And then we had a zero uh so
+
+ align:start position:0%
+like that. And then we had a zero uh so
+ 
+
+ align:start position:0%
+like that. And then we had a zero uh so
+that we went through unity gain or unity
+
+ align:start position:0%
+that we went through unity gain or unity
+ 
+
+ align:start position:0%
+that we went through unity gain or unity
+loop transmission magnitude with a slope
+
+ align:start position:0%
+loop transmission magnitude with a slope
+ 
+
+ align:start position:0%
+loop transmission magnitude with a slope
+of 1 overs in that example. But again
+
+ align:start position:0%
+of 1 overs in that example. But again
+ 
+
+ align:start position:0%
+of 1 overs in that example. But again
+we'd anticipate that the phase curve
+
+ align:start position:0%
+we'd anticipate that the phase curve
+ 
+
+ align:start position:0%
+we'd anticipate that the phase curve
+might look something like this. It
+
+ align:start position:0%
+might look something like this. It
+ 
+
+ align:start position:0%
+might look something like this. It
+particularly if there was a 100 to1
+
+ align:start position:0%
+particularly if there was a 100 to1
+ 
+
+ align:start position:0%
+particularly if there was a 100 to1
+ratio between these frequencies we would
+
+ align:start position:0%
+ratio between these frequencies we would
+ 
+
+ align:start position:0%
+ratio between these frequencies we would
+get down quite close to minus 180° over
+
+ align:start position:0%
+get down quite close to minus 180° over
+ 
+
+ align:start position:0%
+get down quite close to minus 180° over
+some range of frequencies. Now, we feel
+
+ align:start position:0%
+some range of frequencies. Now, we feel
+ 
+
+ align:start position:0%
+some range of frequencies. Now, we feel
+that the system should be perfectly well
+
+ align:start position:0%
+that the system should be perfectly well
+ 
+
+ align:start position:0%
+that the system should be perfectly well
+behaved because we note that as we've
+
+ align:start position:0%
+behaved because we note that as we've
+ 
+
+ align:start position:0%
+behaved because we note that as we've
+arranged things, here's the crossover
+
+ align:start position:0%
+arranged things, here's the crossover
+ 
+
+ align:start position:0%
+arranged things, here's the crossover
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+and we have plenty of phase margin.
+
+ align:start position:0%
+and we have plenty of phase margin.
+ 
+
+ align:start position:0%
+and we have plenty of phase margin.
+There's there's no problem as I've drawn
+
+ align:start position:0%
+There's there's no problem as I've drawn
+ 
+
+ align:start position:0%
+There's there's no problem as I've drawn
+things. And in fact, that's what we hope
+
+ align:start position:0%
+things. And in fact, that's what we hope
+ 
+
+ align:start position:0%
+things. And in fact, that's what we hope
+for when we use lag compensation or
+
+ align:start position:0%
+for when we use lag compensation or
+ 
+
+ align:start position:0%
+for when we use lag compensation or
+possibly two- pole compensation. They're
+
+ align:start position:0%
+possibly two- pole compensation. They're
+ 
+
+ align:start position:0%
+possibly two- pole compensation. They're
+really variations on the same theme. Uh
+
+ align:start position:0%
+really variations on the same theme. Uh
+ 
+
+ align:start position:0%
+really variations on the same theme. Uh
+we hope that the system crosses over in
+
+ align:start position:0%
+we hope that the system crosses over in
+ 
+
+ align:start position:0%
+we hope that the system crosses over in
+a region where the slope is minus one
+
+ align:start position:0%
+a region where the slope is minus one
+ 
+
+ align:start position:0%
+a region where the slope is minus one
+over s or one over frequency.
+
+ align:start position:0%
+over s or one over frequency.
+ 
+
+ align:start position:0%
+over s or one over frequency.
+uh and in that region we certainly hope
+
+ align:start position:0%
+uh and in that region we certainly hope
+ 
+
+ align:start position:0%
+uh and in that region we certainly hope
+that we have adequate phase margin. The
+
+ align:start position:0%
+that we have adequate phase margin. The
+ 
+
+ align:start position:0%
+that we have adequate phase margin. The
+difficulty comes uh or a potential
+
+ align:start position:0%
+difficulty comes uh or a potential
+ 
+
+ align:start position:0%
+difficulty comes uh or a potential
+difficulty exists if there is a
+
+ align:start position:0%
+difficulty exists if there is a
+ 
+
+ align:start position:0%
+difficulty exists if there is a
+saturating element included in the loop
+
+ align:start position:0%
+saturating element included in the loop
+ 
+
+ align:start position:0%
+saturating element included in the loop
+because consider the loop transmission
+
+ align:start position:0%
+because consider the loop transmission
+ 
+
+ align:start position:0%
+because consider the loop transmission
+in a describing function sense or the
+
+ align:start position:0%
+in a describing function sense or the
+ 
+
+ align:start position:0%
+in a describing function sense or the
+magnitude of the loop transmission for
+
+ align:start position:0%
+magnitude of the loop transmission for
+ 
+
+ align:start position:0%
+magnitude of the loop transmission for
+the normalized saturating element that
+
+ align:start position:0%
+the normalized saturating element that
+ 
+
+ align:start position:0%
+the normalized saturating element that
+we showed in this example. uh for small
+
+ align:start position:0%
+we showed in this example. uh for small
+ 
+
+ align:start position:0%
+we showed in this example. uh for small
+signals the magnitude of the gain
+
+ align:start position:0%
+signals the magnitude of the gain
+ 
+
+ align:start position:0%
+signals the magnitude of the gain
+associated with a nonlinear element the
+
+ align:start position:0%
+associated with a nonlinear element the
+ 
+
+ align:start position:0%
+associated with a nonlinear element the
+magnitude of the describing function is
+
+ align:start position:0%
+magnitude of the describing function is
+ 
+
+ align:start position:0%
+magnitude of the describing function is
+one and that's fine for small signals
+
+ align:start position:0%
+one and that's fine for small signals
+ 
+
+ align:start position:0%
+one and that's fine for small signals
+this is the sort of of loop transmission
+
+ align:start position:0%
+this is the sort of of loop transmission
+ 
+
+ align:start position:0%
+this is the sort of of loop transmission
+plot in a describing function sense that
+
+ align:start position:0%
+plot in a describing function sense that
+ 
+
+ align:start position:0%
+plot in a describing function sense that
+we have and we have a perfectly well-
+
+ align:start position:0%
+we have and we have a perfectly well-
+ 
+
+ align:start position:0%
+we have and we have a perfectly well-
+behaved system it's stability is
+
+ align:start position:0%
+behaved system it's stability is
+ 
+
+ align:start position:0%
+behaved system it's stability is
+determined by by what happens out here
+
+ align:start position:0%
+determined by by what happens out here
+ 
+
+ align:start position:0%
+determined by by what happens out here
+the and we can certainly arrange things
+
+ align:start position:0%
+the and we can certainly arrange things
+ 
+
+ align:start position:0%
+the and we can certainly arrange things
+to have acceptable phase margin in that
+
+ align:start position:0%
+to have acceptable phase margin in that
+ 
+
+ align:start position:0%
+to have acceptable phase margin in that
+region but now let's put a big signal
+
+ align:start position:0%
+region but now let's put a big signal
+ 
+
+ align:start position:0%
+region but now let's put a big signal
+into the system uh such that we get the
+
+ align:start position:0%
+into the system uh such that we get the
+ 
+
+ align:start position:0%
+into the system uh such that we get the
+signal at this point larger than one to
+
+ align:start position:0%
+signal at this point larger than one to
+ 
+
+ align:start position:0%
+signal at this point larger than one to
+have a peak value larger than one. The
+
+ align:start position:0%
+have a peak value larger than one. The
+ 
+
+ align:start position:0%
+have a peak value larger than one. The
+element saturates its gain and the
+
+ align:start position:0%
+element saturates its gain and the
+ 
+
+ align:start position:0%
+element saturates its gain and the
+describing function sense begins to drop
+
+ align:start position:0%
+describing function sense begins to drop
+ 
+
+ align:start position:0%
+describing function sense begins to drop
+and now the effect of the gain dropping
+
+ align:start position:0%
+and now the effect of the gain dropping
+ 
+
+ align:start position:0%
+and now the effect of the gain dropping
+is to push down
+
+ align:start position:0%
+is to push down
+ 
+
+ align:start position:0%
+is to push down
+our describing function loop
+
+ align:start position:0%
+our describing function loop
+ 
+
+ align:start position:0%
+our describing function loop
+transmission.
+
+ align:start position:0%
+transmission.
+ 
+
+ align:start position:0%
+transmission.
+uh maybe something like that
+
+ align:start position:0%
+uh maybe something like that
+ 
+
+ align:start position:0%
+uh maybe something like that
+for large signals. And now we begin to
+
+ align:start position:0%
+for large signals. And now we begin to
+ 
+
+ align:start position:0%
+for large signals. And now we begin to
+cross over
+
+ align:start position:0%
+cross over
+ 
+
+ align:start position:0%
+cross over
+in a region that has very very limited
+
+ align:start position:0%
+in a region that has very very limited
+ 
+
+ align:start position:0%
+in a region that has very very limited
+phase margin.
+
+ align:start position:0%
+phase margin.
+ 
+
+ align:start position:0%
+phase margin.
+And if we assume that we drove the
+
+ align:start position:0%
+And if we assume that we drove the
+ 
+
+ align:start position:0%
+And if we assume that we drove the
+system some way such that the signal at
+
+ align:start position:0%
+system some way such that the signal at
+ 
+
+ align:start position:0%
+system some way such that the signal at
+this point were even larger uh we might
+
+ align:start position:0%
+this point were even larger uh we might
+ 
+
+ align:start position:0%
+this point were even larger uh we might
+be able to cross over it at this very
+
+ align:start position:0%
+be able to cross over it at this very
+ 
+
+ align:start position:0%
+be able to cross over it at this very
+unfortunate point. Uh now this sort of
+
+ align:start position:0%
+unfortunate point. Uh now this sort of
+ 
+
+ align:start position:0%
+unfortunate point. Uh now this sort of
+an analysis is is very very difficult to
+
+ align:start position:0%
+an analysis is is very very difficult to
+ 
+
+ align:start position:0%
+an analysis is is very very difficult to
+make exact and and what do we what do we
+
+ align:start position:0%
+make exact and and what do we what do we
+ 
+
+ align:start position:0%
+make exact and and what do we what do we
+really mean by a large signal and what
+
+ align:start position:0%
+really mean by a large signal and what
+ 
+
+ align:start position:0%
+really mean by a large signal and what
+do we really mean by by saturation or
+
+ align:start position:0%
+do we really mean by by saturation or
+ 
+
+ align:start position:0%
+do we really mean by by saturation or
+hard saturation and so forth. But we get
+
+ align:start position:0%
+hard saturation and so forth. But we get
+ 
+
+ align:start position:0%
+hard saturation and so forth. But we get
+the feeling that if we excited this sort
+
+ align:start position:0%
+the feeling that if we excited this sort
+ 
+
+ align:start position:0%
+the feeling that if we excited this sort
+of a system with large signals drove the
+
+ align:start position:0%
+of a system with large signals drove the
+ 
+
+ align:start position:0%
+of a system with large signals drove the
+system into saturation it certainly
+
+ align:start position:0%
+system into saturation it certainly
+ 
+
+ align:start position:0%
+system into saturation it certainly
+might be possible that the stability
+
+ align:start position:0%
+might be possible that the stability
+ 
+
+ align:start position:0%
+might be possible that the stability
+would deteriorate as a result of that.
+
+ align:start position:0%
+would deteriorate as a result of that.
+ 
+
+ align:start position:0%
+would deteriorate as a result of that.
+Well, we have an example of that
+
+ align:start position:0%
+Well, we have an example of that
+ 
+
+ align:start position:0%
+Well, we have an example of that
+here. Once again, we have the test
+
+ align:start position:0%
+here. Once again, we have the test
+ 
+
+ align:start position:0%
+here. Once again, we have the test
+vehicle that we have have used so often.
+
+ align:start position:0%
+vehicle that we have have used so often.
+ 
+
+ align:start position:0%
+vehicle that we have have used so often.
+Uh we have our operational amplifier. In
+
+ align:start position:0%
+Uh we have our operational amplifier. In
+ 
+
+ align:start position:0%
+Uh we have our operational amplifier. In
+this case, we have the ability to
+
+ align:start position:0%
+this case, we have the ability to
+ 
+
+ align:start position:0%
+this case, we have the ability to
+compensate this operational amplifier uh
+
+ align:start position:0%
+compensate this operational amplifier uh
+ 
+
+ align:start position:0%
+compensate this operational amplifier uh
+either with 1 overs single pole or with
+
+ align:start position:0%
+either with 1 overs single pole or with
+ 
+
+ align:start position:0%
+either with 1 overs single pole or with
+two- pole compensation.
+
+ align:start position:0%
+two- pole compensation.
+ 
+
+ align:start position:0%
+two- pole compensation.
+Uh we have a buffer amplifier. If you
+
+ align:start position:0%
+Uh we have a buffer amplifier. If you
+ 
+
+ align:start position:0%
+Uh we have a buffer amplifier. If you
+recall, we used the same configuration
+
+ align:start position:0%
+recall, we used the same configuration
+ 
+
+ align:start position:0%
+recall, we used the same configuration
+before when we were looking at 1 overs
+
+ align:start position:0%
+before when we were looking at 1 overs
+ 
+
+ align:start position:0%
+before when we were looking at 1 overs
+compensation. Uh, and we we are actually
+
+ align:start position:0%
+compensation. Uh, and we we are actually
+ 
+
+ align:start position:0%
+compensation. Uh, and we we are actually
+using an inverting configuration.
+
+ align:start position:0%
+using an inverting configuration.
+ 
+
+ align:start position:0%
+using an inverting configuration.
+There's another buffer amplifier here
+
+ align:start position:0%
+There's another buffer amplifier here
+ 
+
+ align:start position:0%
+There's another buffer amplifier here
+that allows us to look at the error
+
+ align:start position:0%
+that allows us to look at the error
+ 
+
+ align:start position:0%
+that allows us to look at the error
+signal, the input signal to the
+
+ align:start position:0%
+signal, the input signal to the
+ 
+
+ align:start position:0%
+signal, the input signal to the
+amplifier, although we won't really use
+
+ align:start position:0%
+amplifier, although we won't really use
+ 
+
+ align:start position:0%
+amplifier, although we won't really use
+that in this demonstration. And again we
+
+ align:start position:0%
+that in this demonstration. And again we
+ 
+
+ align:start position:0%
+that in this demonstration. And again we
+have the familiar generator that allows
+
+ align:start position:0%
+have the familiar generator that allows
+ 
+
+ align:start position:0%
+have the familiar generator that allows
+us to apply test inputs the power supply
+
+ align:start position:0%
+us to apply test inputs the power supply
+ 
+
+ align:start position:0%
+us to apply test inputs the power supply
+and an oscilloscope to observe the step
+
+ align:start position:0%
+and an oscilloscope to observe the step
+ 
+
+ align:start position:0%
+and an oscilloscope to observe the step
+response or uh other responses of our
+
+ align:start position:0%
+response or uh other responses of our
+ 
+
+ align:start position:0%
+response or uh other responses of our
+system.
+
+ align:start position:0%
+system.
+ 
+
+ align:start position:0%
+system.
+And what we're looking at now is the
+
+ align:start position:0%
+And what we're looking at now is the
+ 
+
+ align:start position:0%
+And what we're looking at now is the
+small signal step response. This is in
+
+ align:start position:0%
+small signal step response. This is in
+ 
+
+ align:start position:0%
+small signal step response. This is in
+the linear region. We have a signal
+
+ align:start position:0%
+the linear region. We have a signal
+ 
+
+ align:start position:0%
+the linear region. We have a signal
+level uh of of something on the order of
+
+ align:start position:0%
+level uh of of something on the order of
+ 
+
+ align:start position:0%
+level uh of of something on the order of
+50 or 100 millolts. We're at 20 millolts
+
+ align:start position:0%
+50 or 100 millolts. We're at 20 millolts
+ 
+
+ align:start position:0%
+50 or 100 millolts. We're at 20 millolts
+per division. So we have quite a small
+
+ align:start position:0%
+per division. So we have quite a small
+ 
+
+ align:start position:0%
+per division. So we have quite a small
+amplitude signal applied to our system
+
+ align:start position:0%
+amplitude signal applied to our system
+ 
+
+ align:start position:0%
+amplitude signal applied to our system
+and right now we're running with one
+
+ align:start position:0%
+and right now we're running with one
+ 
+
+ align:start position:0%
+and right now we're running with one
+overs compensation and we notice quite a
+
+ align:start position:0%
+overs compensation and we notice quite a
+ 
+
+ align:start position:0%
+overs compensation and we notice quite a
+well- behaved transient response. Uh 10
+
+ align:start position:0%
+well- behaved transient response. Uh 10
+ 
+
+ align:start position:0%
+well- behaved transient response. Uh 10
+to 90% rise time of several hundred
+
+ align:start position:0%
+to 90% rise time of several hundred
+ 
+
+ align:start position:0%
+to 90% rise time of several hundred
+nconds. We're at 200 nconds per vertical
+
+ align:start position:0%
+nconds. We're at 200 nconds per vertical
+ 
+
+ align:start position:0%
+nconds. We're at 200 nconds per vertical
+division. A very well- behaved kind of
+
+ align:start position:0%
+division. A very well- behaved kind of
+ 
+
+ align:start position:0%
+division. A very well- behaved kind of
+transient response.
+
+ align:start position:0%
+transient response.
+ 
+
+ align:start position:0%
+transient response.
+If we go to 1 over s^ squ compensation,
+
+ align:start position:0%
+If we go to 1 over s^ squ compensation,
+ 
+
+ align:start position:0%
+If we go to 1 over s^ squ compensation,
+we get very much the same kind of of
+
+ align:start position:0%
+we get very much the same kind of of
+ 
+
+ align:start position:0%
+we get very much the same kind of of
+picture. Uh we notice uh we mentioned
+
+ align:start position:0%
+picture. Uh we notice uh we mentioned
+ 
+
+ align:start position:0%
+picture. Uh we notice uh we mentioned
+this I think in connection with 1 over
+
+ align:start position:0%
+this I think in connection with 1 over
+ 
+
+ align:start position:0%
+this I think in connection with 1 over
+s^2 compensation before. Here we're at 1
+
+ align:start position:0%
+s^2 compensation before. Here we're at 1
+ 
+
+ align:start position:0%
+s^2 compensation before. Here we're at 1
+/ s. Here we're at 1 over s^ squ. Uh you
+
+ align:start position:0%
+/ s. Here we're at 1 over s^ squ. Uh you
+ 
+
+ align:start position:0%
+/ s. Here we're at 1 over s^ squ. Uh you
+recall that the zero uh associated with
+
+ align:start position:0%
+recall that the zero uh associated with
+ 
+
+ align:start position:0%
+recall that the zero uh associated with
+1 over s^2 compensation
+
+ align:start position:0%
+1 over s^2 compensation
+ 
+
+ align:start position:0%
+1 over s^2 compensation
+uh introduces a a long tail to the
+
+ align:start position:0%
+uh introduces a a long tail to the
+ 
+
+ align:start position:0%
+uh introduces a a long tail to the
+transient response. If you do a root
+
+ align:start position:0%
+transient response. If you do a root
+ 
+
+ align:start position:0%
+transient response. If you do a root
+locus plot for this sort of an
+
+ align:start position:0%
+locus plot for this sort of an
+ 
+
+ align:start position:0%
+locus plot for this sort of an
+amplifier, you find out that it includes
+
+ align:start position:0%
+amplifier, you find out that it includes
+ 
+
+ align:start position:0%
+amplifier, you find out that it includes
+a relatively low frequency pole zero
+
+ align:start position:0%
+a relatively low frequency pole zero
+ 
+
+ align:start position:0%
+a relatively low frequency pole zero
+doulet. The zero being the zero
+
+ align:start position:0%
+doulet. The zero being the zero
+ 
+
+ align:start position:0%
+doulet. The zero being the zero
+associated uh with the two- pole
+
+ align:start position:0%
+associated uh with the two- pole
+ 
+
+ align:start position:0%
+associated uh with the two- pole
+compensation and the pole being one of
+
+ align:start position:0%
+compensation and the pole being one of
+ 
+
+ align:start position:0%
+compensation and the pole being one of
+the system poles that in a root locus
+
+ align:start position:0%
+the system poles that in a root locus
+ 
+
+ align:start position:0%
+the system poles that in a root locus
+analysis moves close to that zero for
+
+ align:start position:0%
+analysis moves close to that zero for
+ 
+
+ align:start position:0%
+analysis moves close to that zero for
+large values of a not fnot. Uh that pole
+
+ align:start position:0%
+large values of a not fnot. Uh that pole
+ 
+
+ align:start position:0%
+large values of a not fnot. Uh that pole
+zero dlet gives us a a tail with quite a
+
+ align:start position:0%
+zero dlet gives us a a tail with quite a
+ 
+
+ align:start position:0%
+zero dlet gives us a a tail with quite a
+long settling time compared to the basic
+
+ align:start position:0%
+long settling time compared to the basic
+ 
+
+ align:start position:0%
+long settling time compared to the basic
+dynamics of the system. We see that
+
+ align:start position:0%
+dynamics of the system. We see that
+ 
+
+ align:start position:0%
+dynamics of the system. We see that
+prolonged settling time here. But that
+
+ align:start position:0%
+prolonged settling time here. But that
+ 
+
+ align:start position:0%
+prolonged settling time here. But that
+really isn't a stability problem. The
+
+ align:start position:0%
+really isn't a stability problem. The
+ 
+
+ align:start position:0%
+really isn't a stability problem. The
+percentage overshoot, at least if we
+
+ align:start position:0%
+percentage overshoot, at least if we
+ 
+
+ align:start position:0%
+percentage overshoot, at least if we
+measure it from sort of the initial
+
+ align:start position:0%
+measure it from sort of the initial
+ 
+
+ align:start position:0%
+measure it from sort of the initial
+value of this tail, the kind of of
+
+ align:start position:0%
+value of this tail, the kind of of
+ 
+
+ align:start position:0%
+value of this tail, the kind of of
+overshoot that we or the percent
+
+ align:start position:0%
+overshoot that we or the percent
+ 
+
+ align:start position:0%
+overshoot that we or the percent
+overshoot we get is very much the same
+
+ align:start position:0%
+overshoot we get is very much the same
+ 
+
+ align:start position:0%
+overshoot we get is very much the same
+in the 1 / s case and in the the 1 / s
+
+ align:start position:0%
+in the 1 / s case and in the the 1 / s
+ 
+
+ align:start position:0%
+in the 1 / s case and in the the 1 / s
+squared case.
+
+ align:start position:0%
+squared case.
+ 
+
+ align:start position:0%
+squared case.
+But now let's look at what happens if we
+
+ align:start position:0%
+But now let's look at what happens if we
+ 
+
+ align:start position:0%
+But now let's look at what happens if we
+look at the large signal behavior of the
+
+ align:start position:0%
+look at the large signal behavior of the
+ 
+
+ align:start position:0%
+look at the large signal behavior of the
+amplifier.
+
+ align:start position:0%
+amplifier.
+ 
+
+ align:start position:0%
+amplifier.
+Uh what I'm going to do now is simply up
+
+ align:start position:0%
+Uh what I'm going to do now is simply up
+ 
+
+ align:start position:0%
+Uh what I'm going to do now is simply up
+the amplitude of the input square wave
+
+ align:start position:0%
+the amplitude of the input square wave
+ 
+
+ align:start position:0%
+the amplitude of the input square wave
+that we're driving this with. Let me get
+
+ align:start position:0%
+that we're driving this with. Let me get
+ 
+
+ align:start position:0%
+that we're driving this with. Let me get
+to a more convenient scale. Uh the
+
+ align:start position:0%
+to a more convenient scale. Uh the
+ 
+
+ align:start position:0%
+to a more convenient scale. Uh the
+amplifier at its output saturates at
+
+ align:start position:0%
+amplifier at its output saturates at
+ 
+
+ align:start position:0%
+amplifier at its output saturates at
+voltage levels a little bit in excess of
+
+ align:start position:0%
+voltage levels a little bit in excess of
+ 
+
+ align:start position:0%
+voltage levels a little bit in excess of
+plus or minus 10 volts. Let me apply a
+
+ align:start position:0%
+plus or minus 10 volts. Let me apply a
+ 
+
+ align:start position:0%
+plus or minus 10 volts. Let me apply a
+signal uh which actually never exceeds
+
+ align:start position:0%
+signal uh which actually never exceeds
+ 
+
+ align:start position:0%
+signal uh which actually never exceeds
+plus and minus 10 volts. We now have 1
+
+ align:start position:0%
+plus and minus 10 volts. We now have 1
+ 
+
+ align:start position:0%
+plus and minus 10 volts. We now have 1
+overs compensation.
+
+ align:start position:0%
+overs compensation.
+ 
+
+ align:start position:0%
+overs compensation.
+Uh, let me slow down things just a
+
+ align:start position:0%
+Uh, let me slow down things just a
+ 
+
+ align:start position:0%
+Uh, let me slow down things just a
+little bit.
+
+ align:start position:0%
+little bit.
+ 
+
+ align:start position:0%
+little bit.
+We're looking at the response to a
+
+ align:start position:0%
+We're looking at the response to a
+ 
+
+ align:start position:0%
+We're looking at the response to a
+square wave applied to our inverter
+
+ align:start position:0%
+square wave applied to our inverter
+ 
+
+ align:start position:0%
+square wave applied to our inverter
+and see if we can center things.
+
+ align:start position:0%
+and see if we can center things.
+ 
+
+ align:start position:0%
+and see if we can center things.
+All right. Now we have
+
+ align:start position:0%
+All right. Now we have
+ 
+
+ align:start position:0%
+All right. Now we have
+uh a full scale basically full scale at
+
+ align:start position:0%
+uh a full scale basically full scale at
+ 
+
+ align:start position:0%
+uh a full scale basically full scale at
+the output signal applied to our
+
+ align:start position:0%
+the output signal applied to our
+ 
+
+ align:start position:0%
+the output signal applied to our
+inverting amplifier. What we notice is
+
+ align:start position:0%
+inverting amplifier. What we notice is
+ 
+
+ align:start position:0%
+inverting amplifier. What we notice is
+that we get a trapezoidal sort of a
+
+ align:start position:0%
+that we get a trapezoidal sort of a
+ 
+
+ align:start position:0%
+that we get a trapezoidal sort of a
+waveform.
+
+ align:start position:0%
+waveform.
+ 
+
+ align:start position:0%
+waveform.
+Uh the reason for that is really a a
+
+ align:start position:0%
+Uh the reason for that is really a a
+ 
+
+ align:start position:0%
+Uh the reason for that is really a a
+process known as slooh rate limiting
+
+ align:start position:0%
+process known as slooh rate limiting
+ 
+
+ align:start position:0%
+process known as slooh rate limiting
+associated with the operational
+
+ align:start position:0%
+associated with the operational
+ 
+
+ align:start position:0%
+associated with the operational
+amplifier. We notice that these lines
+
+ align:start position:0%
+amplifier. We notice that these lines
+ 
+
+ align:start position:0%
+amplifier. We notice that these lines
+look very very nearly uh constant slope
+
+ align:start position:0%
+look very very nearly uh constant slope
+ 
+
+ align:start position:0%
+look very very nearly uh constant slope
+lines on the oscilloscope face. And I I
+
+ align:start position:0%
+lines on the oscilloscope face. And I I
+ 
+
+ align:start position:0%
+lines on the oscilloscope face. And I I
+talk about that I believe in chapter
+
+ align:start position:0%
+talk about that I believe in chapter
+ 
+
+ align:start position:0%
+talk about that I believe in chapter
+nine and in chapter 13 of the text. Uh
+
+ align:start position:0%
+nine and in chapter 13 of the text. Uh
+ 
+
+ align:start position:0%
+nine and in chapter 13 of the text. Uh
+the process really is the uh first stage
+
+ align:start position:0%
+the process really is the uh first stage
+ 
+
+ align:start position:0%
+the process really is the uh first stage
+input current going into the capacitor
+
+ align:start position:0%
+input current going into the capacitor
+ 
+
+ align:start position:0%
+input current going into the capacitor
+that's used for minor loop compensation.
+
+ align:start position:0%
+that's used for minor loop compensation.
+ 
+
+ align:start position:0%
+that's used for minor loop compensation.
+And basically the slooh rate is
+
+ align:start position:0%
+And basically the slooh rate is
+ 
+
+ align:start position:0%
+And basically the slooh rate is
+determined by the ratio of that
+
+ align:start position:0%
+determined by the ratio of that
+ 
+
+ align:start position:0%
+determined by the ratio of that
+capacitor to the current that the first
+
+ align:start position:0%
+capacitor to the current that the first
+ 
+
+ align:start position:0%
+capacitor to the current that the first
+stage can either apply or absorb from
+
+ align:start position:0%
+stage can either apply or absorb from
+ 
+
+ align:start position:0%
+stage can either apply or absorb from
+the compensating capacitor. And if you
+
+ align:start position:0%
+the compensating capacitor. And if you
+ 
+
+ align:start position:0%
+the compensating capacitor. And if you
+go through that calculation with the
+
+ align:start position:0%
+go through that calculation with the
+ 
+
+ align:start position:0%
+go through that calculation with the
+compensating elements that we're using,
+
+ align:start position:0%
+compensating elements that we're using,
+ 
+
+ align:start position:0%
+compensating elements that we're using,
+you find a very good match between the
+
+ align:start position:0%
+you find a very good match between the
+ 
+
+ align:start position:0%
+you find a very good match between the
+ratio of of the compensating capacitor
+
+ align:start position:0%
+ratio of of the compensating capacitor
+ 
+
+ align:start position:0%
+ratio of of the compensating capacitor
+size to that current and the slope that
+
+ align:start position:0%
+size to that current and the slope that
+ 
+
+ align:start position:0%
+size to that current and the slope that
+we actually observe. So that's the basic
+
+ align:start position:0%
+we actually observe. So that's the basic
+ 
+
+ align:start position:0%
+we actually observe. So that's the basic
+mechanism. It's not a an output
+
+ align:start position:0%
+mechanism. It's not a an output
+ 
+
+ align:start position:0%
+mechanism. It's not a an output
+amplitude limiting. For example, we
+
+ align:start position:0%
+amplitude limiting. For example, we
+ 
+
+ align:start position:0%
+amplitude limiting. For example, we
+never get to uh the plus or minus 12
+
+ align:start position:0%
+never get to uh the plus or minus 12
+ 
+
+ align:start position:0%
+never get to uh the plus or minus 12
+volts roughly that the amplifier can
+
+ align:start position:0%
+volts roughly that the amplifier can
+ 
+
+ align:start position:0%
+volts roughly that the amplifier can
+supply. So, it's not a a basic uh output
+
+ align:start position:0%
+supply. So, it's not a a basic uh output
+ 
+
+ align:start position:0%
+supply. So, it's not a a basic uh output
+voltage level saturation problem, but
+
+ align:start position:0%
+voltage level saturation problem, but
+ 
+
+ align:start position:0%
+voltage level saturation problem, but
+rather some kind of an internal
+
+ align:start position:0%
+rather some kind of an internal
+ 
+
+ align:start position:0%
+rather some kind of an internal
+saturation mechanism that that has to do
+
+ align:start position:0%
+saturation mechanism that that has to do
+ 
+
+ align:start position:0%
+saturation mechanism that that has to do
+with with uh limited current driving
+
+ align:start position:0%
+with with uh limited current driving
+ 
+
+ align:start position:0%
+with with uh limited current driving
+basically charging a capacitor. If we
+
+ align:start position:0%
+basically charging a capacitor. If we
+ 
+
+ align:start position:0%
+basically charging a capacitor. If we
+examine what happens as the amplifier
+
+ align:start position:0%
+examine what happens as the amplifier
+ 
+
+ align:start position:0%
+examine what happens as the amplifier
+comes out of saturation, we put in a a
+
+ align:start position:0%
+comes out of saturation, we put in a a
+ 
+
+ align:start position:0%
+comes out of saturation, we put in a a
+full amplitude step. It takes quite a
+
+ align:start position:0%
+full amplitude step. It takes quite a
+ 
+
+ align:start position:0%
+full amplitude step. It takes quite a
+while to slo. We're five microsconds per
+
+ align:start position:0%
+while to slo. We're five microsconds per
+ 
+
+ align:start position:0%
+while to slo. We're five microsconds per
+division. So, these transitions are are
+
+ align:start position:0%
+division. So, these transitions are are
+ 
+
+ align:start position:0%
+division. So, these transitions are are
+taking uh 10 microsconds. It's sloowing
+
+ align:start position:0%
+taking uh 10 microsconds. It's sloowing
+ 
+
+ align:start position:0%
+taking uh 10 microsconds. It's sloowing
+at a couple of volts per microscond.
+
+ align:start position:0%
+at a couple of volts per microscond.
+ 
+
+ align:start position:0%
+at a couple of volts per microscond.
+We're going through a total 20 volt
+
+ align:start position:0%
+We're going through a total 20 volt
+ 
+
+ align:start position:0%
+We're going through a total 20 volt
+excursion in in 10 uh 10 microsconds. So
+
+ align:start position:0%
+excursion in in 10 uh 10 microsconds. So
+ 
+
+ align:start position:0%
+excursion in in 10 uh 10 microsconds. So
+the amplifier is sloowing at a couple of
+
+ align:start position:0%
+the amplifier is sloowing at a couple of
+ 
+
+ align:start position:0%
+the amplifier is sloowing at a couple of
+volts per microscond right in here and
+
+ align:start position:0%
+volts per microscond right in here and
+ 
+
+ align:start position:0%
+volts per microscond right in here and
+right here we get out of of uh limiting
+
+ align:start position:0%
+right here we get out of of uh limiting
+ 
+
+ align:start position:0%
+right here we get out of of uh limiting
+with the the amplifier enters its linear
+
+ align:start position:0%
+with the the amplifier enters its linear
+ 
+
+ align:start position:0%
+with the the amplifier enters its linear
+region. I mean the transition is of
+
+ align:start position:0%
+region. I mean the transition is of
+ 
+
+ align:start position:0%
+region. I mean the transition is of
+course not not abrupt but uh the
+
+ align:start position:0%
+course not not abrupt but uh the
+ 
+
+ align:start position:0%
+course not not abrupt but uh the
+amplifier re-enters its linear region in
+
+ align:start position:0%
+amplifier re-enters its linear region in
+ 
+
+ align:start position:0%
+amplifier re-enters its linear region in
+these places and we can get a little
+
+ align:start position:0%
+these places and we can get a little
+ 
+
+ align:start position:0%
+these places and we can get a little
+feeling for the trans for the nature of
+
+ align:start position:0%
+feeling for the trans for the nature of
+ 
+
+ align:start position:0%
+feeling for the trans for the nature of
+that recovery.
+
+ align:start position:0%
+that recovery.
+ 
+
+ align:start position:0%
+that recovery.
+Uh if I I can't quite get it all on the
+
+ align:start position:0%
+Uh if I I can't quite get it all on the
+ 
+
+ align:start position:0%
+Uh if I I can't quite get it all on the
+on the screen but you see just a little
+
+ align:start position:0%
+on the screen but you see just a little
+ 
+
+ align:start position:0%
+on the screen but you see just a little
+bit of overshoot. Of course we're still
+
+ align:start position:0%
+bit of overshoot. Of course we're still
+ 
+
+ align:start position:0%
+bit of overshoot. Of course we're still
+at one volt per division. So we have a a
+
+ align:start position:0%
+at one volt per division. So we have a a
+ 
+
+ align:start position:0%
+at one volt per division. So we have a a
+little bit of overshoot. The amplifier
+
+ align:start position:0%
+little bit of overshoot. The amplifier
+ 
+
+ align:start position:0%
+little bit of overshoot. The amplifier
+enters its linear region somewhere right
+
+ align:start position:0%
+enters its linear region somewhere right
+ 
+
+ align:start position:0%
+enters its linear region somewhere right
+in here and just a little tiny bit of
+
+ align:start position:0%
+in here and just a little tiny bit of
+ 
+
+ align:start position:0%
+in here and just a little tiny bit of
+overshoot. Uh we see the same general
+
+ align:start position:0%
+overshoot. Uh we see the same general
+ 
+
+ align:start position:0%
+overshoot. Uh we see the same general
+kind of a thing on the negative wave
+
+ align:start position:0%
+kind of a thing on the negative wave
+ 
+
+ align:start position:0%
+kind of a thing on the negative wave
+form. Again the amplifier enters its
+
+ align:start position:0%
+form. Again the amplifier enters its
+ 
+
+ align:start position:0%
+form. Again the amplifier enters its
+linear region and just a a little bit of
+
+ align:start position:0%
+linear region and just a a little bit of
+ 
+
+ align:start position:0%
+linear region and just a a little bit of
+overshoot fast recovery at least
+
+ align:start position:0%
+overshoot fast recovery at least
+ 
+
+ align:start position:0%
+overshoot fast recovery at least
+compared to the five microcond per
+
+ align:start position:0%
+compared to the five microcond per
+ 
+
+ align:start position:0%
+compared to the five microcond per
+division time scale that we have here.
+
+ align:start position:0%
+division time scale that we have here.
+ 
+
+ align:start position:0%
+division time scale that we have here.
+Now this is the situation with one overs
+
+ align:start position:0%
+Now this is the situation with one overs
+ 
+
+ align:start position:0%
+Now this is the situation with one overs
+compensation. There is a slooh rate
+
+ align:start position:0%
+compensation. There is a slooh rate
+ 
+
+ align:start position:0%
+compensation. There is a slooh rate
+problem but the amplifier is certainly
+
+ align:start position:0%
+problem but the amplifier is certainly
+ 
+
+ align:start position:0%
+problem but the amplifier is certainly
+very well behaved in terms of stability.
+
+ align:start position:0%
+very well behaved in terms of stability.
+ 
+
+ align:start position:0%
+very well behaved in terms of stability.
+There's a little bit of overshoot as it
+
+ align:start position:0%
+There's a little bit of overshoot as it
+ 
+
+ align:start position:0%
+There's a little bit of overshoot as it
+comes into the linear region, but very
+
+ align:start position:0%
+comes into the linear region, but very
+ 
+
+ align:start position:0%
+comes into the linear region, but very
+nicely behaved.
+
+ align:start position:0%
+nicely behaved.
+ 
+
+ align:start position:0%
+nicely behaved.
+Now, let's look at at what happens to
+
+ align:start position:0%
+Now, let's look at at what happens to
+ 
+
+ align:start position:0%
+Now, let's look at at what happens to
+the waveform if we uh use 1 / s^ squ
+
+ align:start position:0%
+the waveform if we uh use 1 / s^ squ
+ 
+
+ align:start position:0%
+the waveform if we uh use 1 / s^ squ
+compensation.
+
+ align:start position:0%
+compensation.
+ 
+
+ align:start position:0%
+compensation.
+We notice things get quite dramatically
+
+ align:start position:0%
+We notice things get quite dramatically
+ 
+
+ align:start position:0%
+We notice things get quite dramatically
+worse. Uh here again, we don't have
+
+ align:start position:0%
+worse. Uh here again, we don't have
+ 
+
+ align:start position:0%
+worse. Uh here again, we don't have
+quite straight line sloowing or quite
+
+ align:start position:0%
+quite straight line sloowing or quite
+ 
+
+ align:start position:0%
+quite straight line sloowing or quite
+constant velocity sloowing. Uh again, if
+
+ align:start position:0%
+constant velocity sloowing. Uh again, if
+ 
+
+ align:start position:0%
+constant velocity sloowing. Uh again, if
+you chase through the analysis, that's
+
+ align:start position:0%
+you chase through the analysis, that's
+ 
+
+ align:start position:0%
+you chase through the analysis, that's
+reasonable. at least should be partially
+
+ align:start position:0%
+reasonable. at least should be partially
+ 
+
+ align:start position:0%
+reasonable. at least should be partially
+parabolic and uh uh there's a little bit
+
+ align:start position:0%
+parabolic and uh uh there's a little bit
+ 
+
+ align:start position:0%
+parabolic and uh uh there's a little bit
+of that. Um but now what happens is here
+
+ align:start position:0%
+of that. Um but now what happens is here
+ 
+
+ align:start position:0%
+of that. Um but now what happens is here
+the amplifier should be entering its
+
+ align:start position:0%
+the amplifier should be entering its
+ 
+
+ align:start position:0%
+the amplifier should be entering its
+linear region but it doesn't. We or or
+
+ align:start position:0%
+linear region but it doesn't. We or or
+ 
+
+ align:start position:0%
+linear region but it doesn't. We or or
+it it whips right through the linear
+
+ align:start position:0%
+it it whips right through the linear
+ 
+
+ align:start position:0%
+it it whips right through the linear
+region. You get a massive overshoot. The
+
+ align:start position:0%
+region. You get a massive overshoot. The
+ 
+
+ align:start position:0%
+region. You get a massive overshoot. The
+output gets up uh about 3 or 4 volts
+
+ align:start position:0%
+output gets up uh about 3 or 4 volts
+ 
+
+ align:start position:0%
+output gets up uh about 3 or 4 volts
+above final value. This point is 10
+
+ align:start position:0%
+above final value. This point is 10
+ 
+
+ align:start position:0%
+above final value. This point is 10
+volts. We hit a peak of 13 or 14 volts
+
+ align:start position:0%
+volts. We hit a peak of 13 or 14 volts
+ 
+
+ align:start position:0%
+volts. We hit a peak of 13 or 14 volts
+here. similar in the other direction. We
+
+ align:start position:0%
+here. similar in the other direction. We
+ 
+
+ align:start position:0%
+here. similar in the other direction. We
+bang very close to the negative supply.
+
+ align:start position:0%
+bang very close to the negative supply.
+ 
+
+ align:start position:0%
+bang very close to the negative supply.
+Uh so a very tortured kind of a kind of
+
+ align:start position:0%
+Uh so a very tortured kind of a kind of
+ 
+
+ align:start position:0%
+Uh so a very tortured kind of a kind of
+a recovery. Uh and finally we reach
+
+ align:start position:0%
+a recovery. Uh and finally we reach
+ 
+
+ align:start position:0%
+a recovery. Uh and finally we reach
+final value. Uh but but it's a a very
+
+ align:start position:0%
+final value. Uh but but it's a a very
+ 
+
+ align:start position:0%
+final value. Uh but but it's a a very
+tortured sort of a recovery. Uh the same
+
+ align:start position:0%
+tortured sort of a recovery. Uh the same
+ 
+
+ align:start position:0%
+tortured sort of a recovery. Uh the same
+kind of thing happens uh even for
+
+ align:start position:0%
+kind of thing happens uh even for
+ 
+
+ align:start position:0%
+kind of thing happens uh even for
+syosoidal uh behavior. Let's go to a a
+
+ align:start position:0%
+syosoidal uh behavior. Let's go to a a
+ 
+
+ align:start position:0%
+syosoidal uh behavior. Let's go to a a
+somewhat lower frequency and rather than
+
+ align:start position:0%
+somewhat lower frequency and rather than
+ 
+
+ align:start position:0%
+somewhat lower frequency and rather than
+use a a square wave which of course
+
+ align:start position:0%
+use a a square wave which of course
+ 
+
+ align:start position:0%
+use a a square wave which of course
+forces us into slooh rate limiting on
+
+ align:start position:0%
+forces us into slooh rate limiting on
+ 
+
+ align:start position:0%
+forces us into slooh rate limiting on
+the transitions.
+
+ align:start position:0%
+the transitions.
+ 
+
+ align:start position:0%
+the transitions.
+Let's look at the syosoidal behavior.
+
+ align:start position:0%
+Let's look at the syosoidal behavior.
+ 
+
+ align:start position:0%
+Let's look at the syosoidal behavior.
+Let me just lower the amplitude a little
+
+ align:start position:0%
+Let me just lower the amplitude a little
+ 
+
+ align:start position:0%
+Let me just lower the amplitude a little
+bit. And here we're running at a
+
+ align:start position:0%
+bit. And here we're running at a
+ 
+
+ align:start position:0%
+bit. And here we're running at a
+frequency that's low enough uh that's uh
+
+ align:start position:0%
+frequency that's low enough uh that's uh
+ 
+
+ align:start position:0%
+frequency that's low enough uh that's uh
+let's see we're at 50 micros per
+
+ align:start position:0%
+let's see we're at 50 micros per
+ 
+
+ align:start position:0%
+let's see we're at 50 micros per
+division. So that's a couple of
+
+ align:start position:0%
+division. So that's a couple of
+ 
+
+ align:start position:0%
+division. So that's a couple of
+kilhertz. That's low enough so that
+
+ align:start position:0%
+kilhertz. That's low enough so that
+ 
+
+ align:start position:0%
+kilhertz. That's low enough so that
+we're not slooh rate limiting. But now
+
+ align:start position:0%
+we're not slooh rate limiting. But now
+ 
+
+ align:start position:0%
+we're not slooh rate limiting. But now
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+increase the operating frequency.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh we're now up to about 20 kHz.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's continue.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We have to go up one more notch on the
+
+ align:start position:0%
+We have to go up one more notch on the
+ 
+
+ align:start position:0%
+We have to go up one more notch on the
+function generator.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now we begin to get some
+
+ align:start position:0%
+Okay. Now we begin to get some
+ 
+
+ align:start position:0%
+Okay. Now we begin to get some
+noticeable distortion. Uh here we have a
+
+ align:start position:0%
+noticeable distortion. Uh here we have a
+ 
+
+ align:start position:0%
+noticeable distortion. Uh here we have a
+pretty good sine wave.
+
+ align:start position:0%
+pretty good sine wave.
+ 
+
+ align:start position:0%
+pretty good sine wave.
+Here we begin to see some distortion.
+
+ align:start position:0%
+Here we begin to see some distortion.
+ 
+
+ align:start position:0%
+Here we begin to see some distortion.
+Let's look at that again. Here we're
+
+ align:start position:0%
+Let's look at that again. Here we're
+ 
+
+ align:start position:0%
+Let's look at that again. Here we're
+going up in frequency.
+
+ align:start position:0%
+going up in frequency.
+ 
+
+ align:start position:0%
+going up in frequency.
+And notice a rather abrupt change in
+
+ align:start position:0%
+And notice a rather abrupt change in
+ 
+
+ align:start position:0%
+And notice a rather abrupt change in
+characteristics. I haven't increased the
+
+ align:start position:0%
+characteristics. I haven't increased the
+ 
+
+ align:start position:0%
+characteristics. I haven't increased the
+frequency any further. I increased them
+
+ align:start position:0%
+frequency any further. I increased them
+ 
+
+ align:start position:0%
+frequency any further. I increased them
+until there was this sort of a jump. Now
+
+ align:start position:0%
+until there was this sort of a jump. Now
+ 
+
+ align:start position:0%
+until there was this sort of a jump. Now
+I'll back down.
+
+ align:start position:0%
+I'll back down.
+ 
+
+ align:start position:0%
+I'll back down.
+Notice a completely different behavior.
+
+ align:start position:0%
+Notice a completely different behavior.
+ 
+
+ align:start position:0%
+Notice a completely different behavior.
+the amplitude gets bigger and bigger and
+
+ align:start position:0%
+the amplitude gets bigger and bigger and
+ 
+
+ align:start position:0%
+the amplitude gets bigger and bigger and
+now all of a sudden pops back to the
+
+ align:start position:0%
+now all of a sudden pops back to the
+ 
+
+ align:start position:0%
+now all of a sudden pops back to the
+original linear case. Let's go through
+
+ align:start position:0%
+original linear case. Let's go through
+ 
+
+ align:start position:0%
+original linear case. Let's go through
+the cycle one more time. I'll increase
+
+ align:start position:0%
+the cycle one more time. I'll increase
+ 
+
+ align:start position:0%
+the cycle one more time. I'll increase
+frequency.
+
+ align:start position:0%
+frequency.
+ 
+
+ align:start position:0%
+frequency.
+Uh we're at about uh
+
+ align:start position:0%
+Uh we're at about uh
+ 
+
+ align:start position:0%
+Uh we're at about uh
+60 kHz right now.
+
+ align:start position:0%
+60 kHz right now.
+ 
+
+ align:start position:0%
+60 kHz right now.
+Things get distorted and all of a sudden
+
+ align:start position:0%
+Things get distorted and all of a sudden
+ 
+
+ align:start position:0%
+Things get distorted and all of a sudden
+pop. Uh that occurs in this particular
+
+ align:start position:0%
+pop. Uh that occurs in this particular
+ 
+
+ align:start position:0%
+pop. Uh that occurs in this particular
+amplifier at about 75 kHz.
+
+ align:start position:0%
+amplifier at about 75 kHz.
+ 
+
+ align:start position:0%
+amplifier at about 75 kHz.
+Uh that transition to a new state. I'll
+
+ align:start position:0%
+Uh that transition to a new state. I'll
+ 
+
+ align:start position:0%
+Uh that transition to a new state. I'll
+now lower the frequency.
+
+ align:start position:0%
+now lower the frequency.
+ 
+
+ align:start position:0%
+now lower the frequency.
+We get a state that never existed on the
+
+ align:start position:0%
+We get a state that never existed on the
+ 
+
+ align:start position:0%
+We get a state that never existed on the
+way up
+
+ align:start position:0%
+way up
+ 
+
+ align:start position:0%
+way up
+and now it pops and that transition
+
+ align:start position:0%
+and now it pops and that transition
+ 
+
+ align:start position:0%
+and now it pops and that transition
+occurs at about 55 kHz. So there's a
+
+ align:start position:0%
+occurs at about 55 kHz. So there's a
+ 
+
+ align:start position:0%
+occurs at about 55 kHz. So there's a
+hysteresus in the frequency
+
+ align:start position:0%
+hysteresus in the frequency
+ 
+
+ align:start position:0%
+hysteresus in the frequency
+characteristics. The width of the
+
+ align:start position:0%
+characteristics. The width of the
+ 
+
+ align:start position:0%
+characteristics. The width of the
+hysteresus is about 20 kHz.
+
+ align:start position:0%
+hysteresus is about 20 kHz.
+ 
+
+ align:start position:0%
+hysteresus is about 20 kHz.
+Uh that phenomenon is is called jump
+
+ align:start position:0%
+Uh that phenomenon is is called jump
+ 
+
+ align:start position:0%
+Uh that phenomenon is is called jump
+resonance. I've I had read about it. I
+
+ align:start position:0%
+resonance. I've I had read about it. I
+ 
+
+ align:start position:0%
+resonance. I've I had read about it. I
+I'd never observed it until I started
+
+ align:start position:0%
+I'd never observed it until I started
+ 
+
+ align:start position:0%
+I'd never observed it until I started
+playing with this particular
+
+ align:start position:0%
+playing with this particular
+ 
+
+ align:start position:0%
+playing with this particular
+configuration and then I found it in
+
+ align:start position:0%
+configuration and then I found it in
+ 
+
+ align:start position:0%
+configuration and then I found it in
+other 1 over s^ squ kinds of systems. I
+
+ align:start position:0%
+other 1 over s^ squ kinds of systems. I
+ 
+
+ align:start position:0%
+other 1 over s^ squ kinds of systems. I
+originally thought it was just an
+
+ align:start position:0%
+originally thought it was just an
+ 
+
+ align:start position:0%
+originally thought it was just an
+academic exercise. You can make up
+
+ align:start position:0%
+academic exercise. You can make up
+ 
+
+ align:start position:0%
+academic exercise. You can make up
+virtually impossible problems in
+
+ align:start position:0%
+virtually impossible problems in
+ 
+
+ align:start position:0%
+virtually impossible problems in
+describing function analysis that that
+
+ align:start position:0%
+describing function analysis that that
+ 
+
+ align:start position:0%
+describing function analysis that that
+deal with jump resonance. But here's an
+
+ align:start position:0%
+deal with jump resonance. But here's an
+ 
+
+ align:start position:0%
+deal with jump resonance. But here's an
+example of a of a jump resonance that
+
+ align:start position:0%
+example of a of a jump resonance that
+ 
+
+ align:start position:0%
+example of a of a jump resonance that
+that actually does exist.
+
+ align:start position:0%
+that actually does exist.
+ 
+
+ align:start position:0%
+that actually does exist.
+there's a possibility of of having even
+
+ align:start position:0%
+there's a possibility of of having even
+ 
+
+ align:start position:0%
+there's a possibility of of having even
+more severe problems with this sort of a
+
+ align:start position:0%
+more severe problems with this sort of a
+ 
+
+ align:start position:0%
+more severe problems with this sort of a
+of an amplifier or this sort of a
+
+ align:start position:0%
+of an amplifier or this sort of a
+ 
+
+ align:start position:0%
+of an amplifier or this sort of a
+system. Uh suppose we had a rolloff that
+
+ align:start position:0%
+system. Uh suppose we had a rolloff that
+ 
+
+ align:start position:0%
+system. Uh suppose we had a rolloff that
+was even greater than 1 / s^ squ. Here
+
+ align:start position:0%
+was even greater than 1 / s^ squ. Here
+ 
+
+ align:start position:0%
+was even greater than 1 / s^ squ. Here
+we have a 1 over s^ squ roll off the
+
+ align:start position:0%
+we have a 1 over s^ squ roll off the
+ 
+
+ align:start position:0%
+we have a 1 over s^ squ roll off the
+angle gets down close to minus 180°. If
+
+ align:start position:0%
+angle gets down close to minus 180°. If
+ 
+
+ align:start position:0%
+angle gets down close to minus 180°. If
+this rolloff included a portion that
+
+ align:start position:0%
+this rolloff included a portion that
+ 
+
+ align:start position:0%
+this rolloff included a portion that
+were more rapid than 1 over s^ squ, it's
+
+ align:start position:0%
+were more rapid than 1 over s^ squ, it's
+ 
+
+ align:start position:0%
+were more rapid than 1 over s^ squ, it's
+conceivable that over some portion or
+
+ align:start position:0%
+conceivable that over some portion or
+ 
+
+ align:start position:0%
+conceivable that over some portion or
+for some frequencies the angle would
+
+ align:start position:0%
+for some frequencies the angle would
+ 
+
+ align:start position:0%
+for some frequencies the angle would
+actually drop down below minus 180°
+
+ align:start position:0%
+actually drop down below minus 180°
+ 
+
+ align:start position:0%
+actually drop down below minus 180°
+something like so.
+
+ align:start position:0%
+something like so.
+ 
+
+ align:start position:0%
+something like so.
+Uh now again we could hope to have the
+
+ align:start position:0%
+Uh now again we could hope to have the
+ 
+
+ align:start position:0%
+Uh now again we could hope to have the
+characteristics arranged so that there
+
+ align:start position:0%
+characteristics arranged so that there
+ 
+
+ align:start position:0%
+characteristics arranged so that there
+was perfectly adequate phase margin at
+
+ align:start position:0%
+was perfectly adequate phase margin at
+ 
+
+ align:start position:0%
+was perfectly adequate phase margin at
+crossover in the absence of saturation.
+
+ align:start position:0%
+crossover in the absence of saturation.
+ 
+
+ align:start position:0%
+crossover in the absence of saturation.
+But if the system saturated uh and the
+
+ align:start position:0%
+But if the system saturated uh and the
+ 
+
+ align:start position:0%
+But if the system saturated uh and the
+curve in the in a describing function
+
+ align:start position:0%
+curve in the in a describing function
+ 
+
+ align:start position:0%
+curve in the in a describing function
+sense moved down because of lowered gain
+
+ align:start position:0%
+sense moved down because of lowered gain
+ 
+
+ align:start position:0%
+sense moved down because of lowered gain
+as I've shown things we'd actually cross
+
+ align:start position:0%
+as I've shown things we'd actually cross
+ 
+
+ align:start position:0%
+as I've shown things we'd actually cross
+over in a region of negative phase
+
+ align:start position:0%
+over in a region of negative phase
+ 
+
+ align:start position:0%
+over in a region of negative phase
+margin and that sounds uh as though
+
+ align:start position:0%
+margin and that sounds uh as though
+ 
+
+ align:start position:0%
+margin and that sounds uh as though
+there's certainly the potential for very
+
+ align:start position:0%
+there's certainly the potential for very
+ 
+
+ align:start position:0%
+there's certainly the potential for very
+bad performance in that situation. uh we
+
+ align:start position:0%
+bad performance in that situation. uh we
+ 
+
+ align:start position:0%
+bad performance in that situation. uh we
+can look at the same thing in a gain
+
+ align:start position:0%
+can look at the same thing in a gain
+ 
+
+ align:start position:0%
+can look at the same thing in a gain
+phase plane do our conventional
+
+ align:start position:0%
+phase plane do our conventional
+ 
+
+ align:start position:0%
+phase plane do our conventional
+describing function analysis a the
+
+ align:start position:0%
+describing function analysis a the
+ 
+
+ align:start position:0%
+describing function analysis a the
+same kind of curves this sort of a
+
+ align:start position:0%
+same kind of curves this sort of a
+ 
+
+ align:start position:0%
+same kind of curves this sort of a
+magnitude curve and combined with this
+
+ align:start position:0%
+magnitude curve and combined with this
+ 
+
+ align:start position:0%
+magnitude curve and combined with this
+kind of a phase curve in gain phase
+
+ align:start position:0%
+kind of a phase curve in gain phase
+ 
+
+ align:start position:0%
+kind of a phase curve in gain phase
+coordinates of course starts out uh the
+
+ align:start position:0%
+coordinates of course starts out uh the
+ 
+
+ align:start position:0%
+coordinates of course starts out uh the
+the magnitude is always decreasing the
+
+ align:start position:0%
+the magnitude is always decreasing the
+ 
+
+ align:start position:0%
+the magnitude is always decreasing the
+phase goes down more negative than minus
+
+ align:start position:0%
+phase goes down more negative than minus
+ 
+
+ align:start position:0%
+phase goes down more negative than minus
+180° over a range of frequencies omega
+
+ align:start position:0%
+180° over a range of frequencies omega
+ 
+
+ align:start position:0%
+180° over a range of frequencies omega
+is a parameter along the curve
+
+ align:start position:0%
+is a parameter along the curve
+ 
+
+ align:start position:0%
+is a parameter along the curve
+eventually recovers the value is more
+
+ align:start position:0%
+eventually recovers the value is more
+ 
+
+ align:start position:0%
+eventually recovers the value is more
+positive than minus 180°. Hopefully that
+
+ align:start position:0%
+positive than minus 180°. Hopefully that
+ 
+
+ align:start position:0%
+positive than minus 180°. Hopefully that
+occurs in the vicinity of the unity gain
+
+ align:start position:0%
+occurs in the vicinity of the unity gain
+ 
+
+ align:start position:0%
+occurs in the vicinity of the unity gain
+frequency so that we have a system that
+
+ align:start position:0%
+frequency so that we have a system that
+ 
+
+ align:start position:0%
+frequency so that we have a system that
+has positive phase margin. If we then
+
+ align:start position:0%
+has positive phase margin. If we then
+ 
+
+ align:start position:0%
+has positive phase margin. If we then
+construct minus1 over GD of E for this
+
+ align:start position:0%
+construct minus1 over GD of E for this
+ 
+
+ align:start position:0%
+construct minus1 over GD of E for this
+particular nonlinearity the saturation
+
+ align:start position:0%
+particular nonlinearity the saturation
+ 
+
+ align:start position:0%
+particular nonlinearity the saturation
+uh we get a curve remember GD of E has a
+
+ align:start position:0%
+uh we get a curve remember GD of E has a
+ 
+
+ align:start position:0%
+uh we get a curve remember GD of E has a
+magnitude of one for amplitudes less
+
+ align:start position:0%
+magnitude of one for amplitudes less
+ 
+
+ align:start position:0%
+magnitude of one for amplitudes less
+than one applied to the nonlinearity the
+
+ align:start position:0%
+than one applied to the nonlinearity the
+ 
+
+ align:start position:0%
+than one applied to the nonlinearity the
+magnitude of GD of E goes down as E
+
+ align:start position:0%
+magnitude of GD of E goes down as E
+ 
+
+ align:start position:0%
+magnitude of GD of E goes down as E
+increases uh so one over GD of E goes up
+
+ align:start position:0%
+increases uh so one over GD of E goes up
+ 
+
+ align:start position:0%
+increases uh so one over GD of E goes up
+so we get a construction like this this
+
+ align:start position:0%
+so we get a construction like this this
+ 
+
+ align:start position:0%
+so we get a construction like this this
+being the direction of increasing E, we
+
+ align:start position:0%
+being the direction of increasing E, we
+ 
+
+ align:start position:0%
+being the direction of increasing E, we
+see that there's two intersections with
+
+ align:start position:0%
+see that there's two intersections with
+ 
+
+ align:start position:0%
+see that there's two intersections with
+the curve that corresponds to the linear
+
+ align:start position:0%
+the curve that corresponds to the linear
+ 
+
+ align:start position:0%
+the curve that corresponds to the linear
+portion of the system. Uh there's a a
+
+ align:start position:0%
+portion of the system. Uh there's a a
+ 
+
+ align:start position:0%
+portion of the system. Uh there's a a
+question what does this mean? Does this
+
+ align:start position:0%
+question what does this mean? Does this
+ 
+
+ align:start position:0%
+question what does this mean? Does this
+system oscillate? Uh there's two
+
+ align:start position:0%
+system oscillate? Uh there's two
+ 
+
+ align:start position:0%
+system oscillate? Uh there's two
+intersections. If it oscillates, how do
+
+ align:start position:0%
+intersections. If it oscillates, how do
+ 
+
+ align:start position:0%
+intersections. If it oscillates, how do
+we determine the parameters of the
+
+ align:start position:0%
+we determine the parameters of the
+ 
+
+ align:start position:0%
+we determine the parameters of the
+oscillation? Which of those
+
+ align:start position:0%
+oscillation? Which of those
+ 
+
+ align:start position:0%
+oscillation? Which of those
+intersections
+
+ align:start position:0%
+intersections
+ 
+
+ align:start position:0%
+intersections
+are which intersection controls the
+
+ align:start position:0%
+are which intersection controls the
+ 
+
+ align:start position:0%
+are which intersection controls the
+oscillation? Which dominates the
+
+ align:start position:0%
+oscillation? Which dominates the
+ 
+
+ align:start position:0%
+oscillation? Which dominates the
+characteristics of the oscillation? This
+
+ align:start position:0%
+characteristics of the oscillation? This
+ 
+
+ align:start position:0%
+characteristics of the oscillation? This
+sort of a system is called a
+
+ align:start position:0%
+sort of a system is called a
+ 
+
+ align:start position:0%
+sort of a system is called a
+conditionally stable one. And next time
+
+ align:start position:0%
+conditionally stable one. And next time
+ 
+
+ align:start position:0%
+conditionally stable one. And next time
+we're going to go through the analysis
+
+ align:start position:0%
+we're going to go through the analysis
+ 
+
+ align:start position:0%
+we're going to go through the analysis
+of this sort of a system and illustrate
+
+ align:start position:0%
+of this sort of a system and illustrate
+ 
+
+ align:start position:0%
+of this sort of a system and illustrate
+it with an example. Thank you.
\ No newline at end of file
diff --git a/xqmb6D2CpRc.txt b/xqmb6D2CpRc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..634c7496f99cbb8b5c4931fd5333be7c157f8b82
--- /dev/null
+++ b/xqmb6D2CpRc.txt
@@ -0,0 +1,763 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+GREG HUTKO: Hi, and welcome
+back to the 14.01
+
+problem-solving videos.
+
+Today I'm going to do Fall
+2010 Problem Set 7,
+
+Problem Number 2.
+
+And we're going to work through
+both parts A and B to
+
+begin with, so I'm
+going to read the
+
+beginning part of the problem.
+
+Suppose Napster's considering
+selling music via email.
+
+There are two types of users,
+students and non-students.
+
+Each non-student has an inverse
+demand function of 200
+
+minus x and each student has an
+inverse demand function of
+
+160 minus x, where x is the
+number of songs delivered by
+
+email, p is measured in cents.
+
+The marginal cost to Napster of
+sending an additional song
+
+via email is 0.
+
+Suppose Napster can identify all
+users as either students
+
+or non-students.
+
+If Napster offers a fixed number
+of songs per year to
+
+each person, what is the profit
+maximizing level of
+
+songs offered to a student
+and a non-student.
+
+In other words, what is the
+equilibrium level of output
+
+for each type of person under
+first degree price
+
+discrimination?
+
+Part B is going to ask us, given
+the equilibrium level of
+
+outputs that we've calculated,
+what is the dollar price
+
+charged to students and
+non-students per year?
+
+Now what this problem is really
+asking us about, it's
+
+asking us about a situation
+in economics
+
+called a two-part tariff.
+
+Now in some cases, when you have
+two groups of consumers
+
+that have differing demand
+functions, a monopolist can
+
+actually capture the
+vast majority of
+
+the consumer surplus.
+
+Or in most cases, all the
+consumer surplus if he can
+
+differentiate between
+the two groups.
+
+So in this case, Napster is
+probably going to set up a
+
+situation where they can
+differentiate between students
+
+and non-students.
+
+So if they can discriminate by a
+student by having them enter
+
+their school ID or their school
+email address, then
+
+they'd be able to do the
+situation that we're doing for
+
+parts A and B.
+
+The two parts of a two-part
+tariff, the first part is an
+
+access fee that's equal to
+the consumer surplus.
+
+So you can say to a consumer,
+sure, you can have this set
+
+bundle of songs, this
+set number of songs.
+
+But you're going to have to
+pay all of the potential
+
+benefit that it would
+bring you.
+
+So if it's going to bring you
+160 units of benefit, we're
+
+going to take that from you and
+we're going to give it to
+
+the producers instead.
+
+The second part, in addition
+to the access fee, the
+
+producer has to decide the
+price per unit when the
+
+consumer is consuming
+the bundle.
+
+And they also have to decide
+how many songs to bundle.
+
+The way the producer makes this
+decision is by setting
+
+the price per unit equal to the
+marginal cost. So they're
+
+basically going to say, I'm
+going to throw in as many
+
+songs into this bundle, get you
+using as many of the songs
+
+as possible, or listening to
+the songs as possible.
+
+But I'm going to only thrown
+in as many songs until it
+
+starts costing me more than it
+could potentially bring me by
+
+capturing your consumer
+surplus.
+
+So we're going to set the price
+per unit equal to the
+
+marginal cost equal to
+0 in this problem.
+
+Now looking at our graph, I've
+tossed up the demand curves
+
+for the student and
+the non-students.
+
+And what's going to happen
+in this problem is in the
+
+equilibrium case, our supply
+curve is actually straight
+
+along the x-axis because our
+marginal cost is equal to 0.
+
+So if this was a competitive
+equilibrium, the producer's
+
+surplus would be equal to 0.
+
+But what we're going to do
+in this case, or what the
+
+producers are going to do in
+this case, is they're going to
+
+say I can bundle for the
+students 160 songs, so that
+
+the quantity produced is here.
+
+I'm going to charge you the
+marginal cost equal to 0 for
+
+each song you listen to.
+
+But then I'm going to come back
+and I'm going to make you
+
+pay all of your consumer surplus
+each year to download
+
+those 160 songs.
+
+So again, I went to
+the marginal cost,
+
+which is right at 0.
+
+Then I set the price
+where it intersects
+
+with the demand curve.
+
+And then again, I said that
+we're going to charge an
+
+access fee equal to that area.
+
+The same thing is going to
+happen to the non-students.
+
+In addition to charging the
+consumer surplus for A, we're
+
+going to make a larger bundle
+with 200 songs, so that we can
+
+capture this additional consumer
+surplus out here.
+
+And I'm going to break this area
+up into two pieces called
+
+B and C. And you'll
+see why I'm doing
+
+that in just a second.
+
+So for part A, how big are we
+going to make the bundles for
+
+the students and the
+non-students?
+
+The bundle for the students is
+going to be equal to 160.
+
+And the bundle for the
+non-students is going to be
+
+equal to 200.
+
+Now for part B, we know that
+we're going to charge a price
+
+per unit equal to 0.
+
+We just need to calculate what
+the access fee for each of
+
+these groups is going to be.
+
+And so the access fee for the
+group of students who have a
+
+song bundle of 160 is just
+going to be the area of
+
+triangle A. So their fee is
+going to be consumer surplus
+
+of students, which is equal to
+A, which is going to be equal
+
+to 1/2 times 160 squared.
+
+So we're going to charge the
+consumers a fee that's going
+
+to be equal to 12,800.
+
+And a common mistake on this
+problem would be to just have
+
+this answer and put
+dollars here.
+
+But if you look back on the
+problem it said that all
+
+prices are given in cents.
+
+So we know that the fee
+for the students
+
+is going to be $128.
+
+And now we know that the fee for
+the non-students is going
+
+to be higher because their
+consumer surplus is greater
+
+when they have a
+bundle of 200.
+
+So the fee for the non-students
+is just going to
+
+be the consumer surplus
+of the non-students.
+
+And that's going to be the area
+of A plus B plus C. Which
+
+again, that's going to
+just be equal to
+
+1/2 times 200 squared.
+
+So in this case, our fee for the
+non-students is going to
+
+be equal to $200.
+
+So when the monopolist has a way
+of telling who's a student
+
+and who's a non-student, then
+they can charge the
+
+non-students a higher price
+because their demand curve is
+
+further up and they're willing
+to pay for more
+
+songs within a bundle.
+
+Part B is going to ask us, or
+part C, moving on to part C.
+
+It's going to ask us, what's
+the maximum price that
+
+students are willing to
+pay for this bundle?
+
+So for the 160 song bundle,
+we're asked, what's the
+
+maximum price students
+are willing to pay?
+
+Well, if we charge them a
+price higher than their
+
+consumer surplus of $128, then
+they're just going to drop out
+
+of the market.
+
+They're going to say, I'm not
+going to even buy this bundle.
+
+You're taking away all of
+the benefit and then
+
+an extra one penny.
+
+It's worth it for me to just go
+someplace else and take my
+
+money elsewhere.
+
+So the answer to part C, the
+maximum price you can charge a
+
+consumer in a student for the
+160 song bundle is just the
+
+$128 that we calculated
+before.
+
+Part D brings up an interesting
+implication,
+
+however, for the non-students
+who can look over and see the
+
+maximum price that we're
+charging the students for
+
+their bundle.
+
+Part D says, what is the gross
+consumer surplus that
+
+non-students enjoy if they
+consume 160 songs per year at
+
+the price from C?
+
+What is the net consumer
+surplus?
+
+So gross consumer surplus is
+just going to be the situation
+
+that we had before.
+
+In this case, we're looking
+at this point here.
+
+We're dealing with
+the non-students.
+
+They're going to now be
+consuming the 160 song bundle.
+
+The consumer surplus for this
+group of students is going to
+
+be both A and B. So working with
+part C, we know that the
+
+gross consumer surplus for the
+non-students when they're
+
+consuming 160 songs is going
+to be the area of A plus B.
+
+And we know that the net
+consumer surplus, they're
+
+going to be charged a fee
+equal to A. So the net
+
+consumer surplus is just going
+to be what we calculate for
+
+the gross consumer surplus
+minus the fee
+
+the area of A, 128.
+
+So even though the non-students
+will get no
+
+consumer surplus in net if
+they go with the 200 song
+
+bundle, maybe if they go with
+the 160 song bundle, they'll
+
+be left over with some
+consumer surplus.
+
+Now to calculate the area of A
+plus B, all we're going to do
+
+is we're going to say that we
+know the area of A plus B plus
+
+C. Now we're just going to
+subtract out the area of C.
+
+And if we were to go back to
+our demand curve for the
+
+non-students, plugging in the
+quantity of 160 into that
+
+demand curve, we would find
+that it intersects
+
+this axis at 40.
+
+So the area of A plus B plus C
+is going to be equal to 200.
+
+And then the area of C is going
+to be equal to 1/2 times
+
+40 squared.
+
+And so that means that the gross
+consumer surplus for a
+
+non-student is going to
+be equal to $192.
+
+So that's the area of A
+plus B in our diagram.
+
+Now to find the net consumer
+surplus, we're just going to
+
+subtract out 128.
+
+And we're going to find that the
+net consumer surplus for a
+
+non-student who's consuming
+160 songs is going
+
+to be equal to $64.
+
+So if the monopolist was still
+to price the same prices that
+
+they had before, if they were
+to make the 160 song bundle
+
+$128 and the 200 song bundle
+$200, in that case, all of the
+
+non-students would look at their
+two choices between the
+
+bundles and they'd say, even
+though this non-student bundle
+
+is targeted towards me, I'm
+better off in net consumer
+
+surplus if I go with
+the bundle that's
+
+targeted toward students.
+
+But now the monopolists
+aren't going to be
+
+stupid in this situation.
+
+They're going to go back and
+they're going to think, well,
+
+if you're going to go and buy
+the non-student bundle, then
+
+what I have to do is I
+have to make sure--
+
+if you're going to go back and
+buy the student bundle, I have
+
+to make sure that the
+non-student bundle gives you a
+
+higher net consumer surplus, so
+that you're still willing
+
+to buy the non-student bundle
+with 200 songs.
+
+Part B asks us, what is the
+maximum price Napster can
+
+charge for 200 songs per year
+if it offers 160 songs per
+
+year at the highest price that
+students are willing to pay?
+
+And so simply put, what they
+can charge for the 200 song
+
+bundle is they can charge for
+an area of A and C. So we're
+
+going to subtract out.
+
+We have to leave the
+non-students with at least
+
+enough consumer surplus
+for the area of B.
+
+We know from our previous
+problems, we know that the
+
+area of A is just going to be
+equal to 1/2 times 160 squared
+
+plus 1/2 times 40 squared.
+
+This is the area of A and this
+is the area of C. So we can
+
+find that the maximum fee
+is going to be $136.
+
+The other way of calculating
+this is to just say, well, I
+
+know that the non-students are
+starting off with 200 hours of
+
+consumer surplus.
+
+I know that I need to leave
+them with at least $64 of
+
+consumer surplus.
+
+So you can just think
+intuitively.
+
+You know the maximum price
+is going to be $136.
+
+And so what we're really going
+to look at in this situation
+
+where they can't discriminate
+between the students and the
+
+non-students, this is the price
+that they're going to be
+
+able to charge for the
+200 song bundle.
+
+For the 160 song bundle, they
+can charge the maximum price
+
+the students are
+willing to pay.
+
+And if we were in a scenario
+where there were only two
+
+customers in this market, one
+non-student and one student,
+
+then we could calculate the
+overall profits for the
+
+monopolist. And so in this
+scenario, the overall profits
+
+are going to be $264.
+
+The last part of this problem
+is going to give you another
+
+scenario that the monopolist
+might consider.
+
+The last part of these problems
+is going to ask you
+
+to look at, what happens if
+instead of designing a student
+
+bundle that has 160 songs, what
+happens if we design a
+
+student bundle that instead is
+only going to have 140 songs?
+
+And again, when you're designing
+this bundle, you're
+
+going to have to plan the prices
+so that only students
+
+will want the 140 song bundle
+and only non-students are
+
+going to want the
+200 song bundle.
+
+And the process is going
+to be the same.
+
+So we're going to stop
+here on this problem.
+
+And just to summarize what we
+looked at here, we looked at
+
+the consequences and the
+implications of having a
+
+price-discriminating monopolist.
+When you can
+
+actually discriminate, you can
+capture all the consumer
+
+surplus and you can charge
+different prices to different
+
+groups in the market.
+
+But when you can't discriminate,
+what you have to
+
+do is you have to make packages,
+bundle them and
+
+price them, so that the
+consumers will discriminate
+
+themselves by picking the bundle
+that gives them the
+
+highest net consumer surplus.
+
+I hope you found this part
+of the problem helpful.
+
+And go ahead and continue
+through with part I and check
+
+your answers against
+the solution.
\ No newline at end of file
diff --git a/xzUOJ-uQ8F0.txt b/xzUOJ-uQ8F0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..809c96d41b582c3b8567100dc8ad1ced38ca1dc6
--- /dev/null
+++ b/xzUOJ-uQ8F0.txt
@@ -0,0 +1,6706 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+OpenCourseWare under a Creative Commons
+
+ align:start position:0%
+OpenCourseWare under a Creative Commons
+ 
+
+ align:start position:0%
+OpenCourseWare under a Creative Commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and MIT opencourseware in general is
+
+ align:start position:0%
+and MIT opencourseware in general is
+ 
+
+ align:start position:0%
+and MIT opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specific problem and it's just it's a
+
+ align:start position:0%
+specific problem and it's just it's a
+ 
+
+ align:start position:0%
+specific problem and it's just it's a
+pure least squares linear least squares
+
+ align:start position:0%
+pure least squares linear least squares
+ 
+
+ align:start position:0%
+pure least squares linear least squares
+problem but it's got two terms so we're
+
+ align:start position:0%
+problem but it's got two terms so we're
+ 
+
+ align:start position:0%
+problem but it's got two terms so we're
+used to minimizing au minus B squared
+
+ align:start position:0%
+used to minimizing au minus B squared
+ 
+
+ align:start position:0%
+used to minimizing au minus B squared
+that gives us the least square solution
+
+ align:start position:0%
+that gives us the least square solution
+ 
+
+ align:start position:0%
+that gives us the least square solution
+u hat to linear system and usually the
+
+ align:start position:0%
+u hat to linear system and usually the
+ 
+
+ align:start position:0%
+u hat to linear system and usually the
+reason we have to go to the least
+
+ align:start position:0%
+reason we have to go to the least
+ 
+
+ align:start position:0%
+reason we have to go to the least
+squares thing is that there's no exact
+
+ align:start position:0%
+squares thing is that there's no exact
+ 
+
+ align:start position:0%
+squares thing is that there's no exact
+solution probably a has more equations
+
+ align:start position:0%
+solution probably a has more equations
+ 
+
+ align:start position:0%
+solution probably a has more equations
+than unknowns a is long and thin and
+
+ align:start position:0%
+than unknowns a is long and thin and
+ 
+
+ align:start position:0%
+than unknowns a is long and thin and
+there's no exact solution so we look for
+
+ align:start position:0%
+there's no exact solution so we look for
+ 
+
+ align:start position:0%
+there's no exact solution so we look for
+the best solution and call it u hat okay
+
+ align:start position:0%
+the best solution and call it u hat okay
+ 
+
+ align:start position:0%
+the best solution and call it u hat okay
+but there are a lot of problems in which
+
+ align:start position:0%
+but there are a lot of problems in which
+ 
+
+ align:start position:0%
+but there are a lot of problems in which
+a second square appears there's also a
+
+ align:start position:0%
+a second square appears there's also a
+ 
+
+ align:start position:0%
+a second square appears there's also a
+bu equal D hiding in the background and
+
+ align:start position:0%
+bu equal D hiding in the background and
+ 
+
+ align:start position:0%
+bu equal D hiding in the background and
+and so we really have like two sets of
+
+ align:start position:0%
+and so we really have like two sets of
+ 
+
+ align:start position:0%
+and so we really have like two sets of
+equations now typically and we multiply
+
+ align:start position:0%
+equations now typically and we multiply
+ 
+
+ align:start position:0%
+equations now typically and we multiply
+that second square by some factor alpha
+
+ align:start position:0%
+that second square by some factor alpha
+ 
+
+ align:start position:0%
+that second square by some factor alpha
+and the wise choice of alpha is usually
+
+ align:start position:0%
+and the wise choice of alpha is usually
+ 
+
+ align:start position:0%
+and the wise choice of alpha is usually
+a big part of the problem and I want to
+
+ align:start position:0%
+a big part of the problem and I want to
+ 
+
+ align:start position:0%
+a big part of the problem and I want to
+speak about some of the applications of
+
+ align:start position:0%
+speak about some of the applications of
+ 
+
+ align:start position:0%
+speak about some of the applications of
+this area so from the point of view of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the normal equations the the system that
+
+ align:start position:0%
+the normal equations the the system that
+ 
+
+ align:start position:0%
+the normal equations the the system that
+you actually solve you could say no
+
+ align:start position:0%
+you actually solve you could say no
+ 
+
+ align:start position:0%
+you actually solve you could say no
+problem well if we knew how to do this
+
+ align:start position:0%
+problem well if we knew how to do this
+ 
+
+ align:start position:0%
+problem well if we knew how to do this
+then we certainly can do both of them
+
+ align:start position:0%
+then we certainly can do both of them
+ 
+
+ align:start position:0%
+then we certainly can do both of them
+together because instead of a transpose
+
+ align:start position:0%
+together because instead of a transpose
+ 
+
+ align:start position:0%
+together because instead of a transpose
+a showing up will now have a transpose a
+
+ align:start position:0%
+a showing up will now have a transpose a
+ 
+
+ align:start position:0%
+a showing up will now have a transpose a
+plus alpha B transpose B that'll be the
+
+ align:start position:0%
+plus alpha B transpose B that'll be the
+ 
+
+ align:start position:0%
+plus alpha B transpose B that'll be the
+positive definite coefficient matrix on
+
+ align:start position:0%
+positive definite coefficient matrix on
+ 
+
+ align:start position:0%
+positive definite coefficient matrix on
+the left side and then on the right side
+
+ align:start position:0%
+the left side and then on the right side
+ 
+
+ align:start position:0%
+the left side and then on the right side
+instead of just the usual a transpose B
+
+ align:start position:0%
+instead of just the usual a transpose B
+ 
+
+ align:start position:0%
+instead of just the usual a transpose B
+this term is all
+
+ align:start position:0%
+this term is all
+ 
+
+ align:start position:0%
+this term is all
+so going to give us an alpha B transpose
+
+ align:start position:0%
+so going to give us an alpha B transpose
+ 
+
+ align:start position:0%
+so going to give us an alpha B transpose
+D III all I'm saying is we don't need
+
+ align:start position:0%
+D III all I'm saying is we don't need
+ 
+
+ align:start position:0%
+D III all I'm saying is we don't need
+any new mathematics to reach the this
+
+ align:start position:0%
+any new mathematics to reach the this
+ 
+
+ align:start position:0%
+any new mathematics to reach the this
+normal equation with the sort of the two
+
+ align:start position:0%
+normal equation with the sort of the two
+ 
+
+ align:start position:0%
+normal equation with the sort of the two
+term normal equation and another way to
+
+ align:start position:0%
+term normal equation and another way to
+ 
+
+ align:start position:0%
+term normal equation and another way to
+think of it exactly the same thing is
+
+ align:start position:0%
+think of it exactly the same thing is
+ 
+
+ align:start position:0%
+think of it exactly the same thing is
+we're looking at the least squares
+
+ align:start position:0%
+we're looking at the least squares
+ 
+
+ align:start position:0%
+we're looking at the least squares
+problem where the two matrices a and B
+
+ align:start position:0%
+problem where the two matrices a and B
+ 
+
+ align:start position:0%
+problem where the two matrices a and B
+both are multiplying U and we have two
+
+ align:start position:0%
+both are multiplying U and we have two
+ 
+
+ align:start position:0%
+both are multiplying U and we have two
+bits of data B and D and all we're doing
+
+ align:start position:0%
+bits of data B and D and all we're doing
+ 
+
+ align:start position:0%
+bits of data B and D and all we're doing
+is the usual thing but with a weight in
+
+ align:start position:0%
+is the usual thing but with a weight in
+ 
+
+ align:start position:0%
+is the usual thing but with a weight in
+here and the weight is the identity
+
+ align:start position:0%
+here and the weight is the identity
+ 
+
+ align:start position:0%
+here and the weight is the identity
+matrix for the a part and it's alpha
+
+ align:start position:0%
+matrix for the a part and it's alpha
+ 
+
+ align:start position:0%
+matrix for the a part and it's alpha
+times the identity matrix for the B part
+
+ align:start position:0%
+times the identity matrix for the B part
+ 
+
+ align:start position:0%
+times the identity matrix for the B part
+so this is our this is our C right this
+
+ align:start position:0%
+so this is our this is our C right this
+ 
+
+ align:start position:0%
+so this is our this is our C right this
+is our our our C just to say that really
+
+ align:start position:0%
+is our our our C just to say that really
+ 
+
+ align:start position:0%
+is our our our C just to say that really
+the notation that we've created the
+
+ align:start position:0%
+the notation that we've created the
+ 
+
+ align:start position:0%
+the notation that we've created the
+formula the the formulation we have is
+
+ align:start position:0%
+formula the the formulation we have is
+ 
+
+ align:start position:0%
+formula the the formulation we have is
+allows us to take this step so C appears
+
+ align:start position:0%
+allows us to take this step so C appears
+ 
+
+ align:start position:0%
+allows us to take this step so C appears
+here and a transpose CB C appears over
+
+ align:start position:0%
+here and a transpose CB C appears over
+ 
+
+ align:start position:0%
+here and a transpose CB C appears over
+here to just just as always okay now so
+
+ align:start position:0%
+here to just just as always okay now so
+ 
+
+ align:start position:0%
+here to just just as always okay now so
+but there's important questions and of
+
+ align:start position:0%
+but there's important questions and of
+ 
+
+ align:start position:0%
+but there's important questions and of
+course all it was the first important
+
+ align:start position:0%
+course all it was the first important
+ 
+
+ align:start position:0%
+course all it was the first important
+question in applied math is what problem
+
+ align:start position:0%
+question in applied math is what problem
+ 
+
+ align:start position:0%
+question in applied math is what problem
+are you solving what was it why have we
+
+ align:start position:0%
+are you solving what was it why have we
+ 
+
+ align:start position:0%
+are you solving what was it why have we
+produced this class of problems and I
+
+ align:start position:0%
+produced this class of problems and I
+ 
+
+ align:start position:0%
+produced this class of problems and I
+have two answers let me just let me just
+
+ align:start position:0%
+have two answers let me just let me just
+ 
+
+ align:start position:0%
+have two answers let me just let me just
+mention first so we are sure what the
+
+ align:start position:0%
+mention first so we are sure what the
+ 
+
+ align:start position:0%
+mention first so we are sure what the
+shape of these matrices is a as always
+
+ align:start position:0%
+shape of these matrices is a as always
+ 
+
+ align:start position:0%
+shape of these matrices is a as always
+has more rows than columns of course u
+
+ align:start position:0%
+has more rows than columns of course u
+ 
+
+ align:start position:0%
+has more rows than columns of course u
+is n by 1 it's just a comic but a has
+
+ align:start position:0%
+is n by 1 it's just a comic but a has
+ 
+
+ align:start position:0%
+is n by 1 it's just a comic but a has
+too many equations too many rows for us
+
+ align:start position:0%
+too many equations too many rows for us
+ 
+
+ align:start position:0%
+too many equations too many rows for us
+to get an exact solution B on the other
+
+ align:start position:0%
+to get an exact solution B on the other
+ 
+
+ align:start position:0%
+to get an exact solution B on the other
+hand has to as few rows it says it might
+
+ align:start position:0%
+hand has to as few rows it says it might
+ 
+
+ align:start position:0%
+hand has to as few rows it says it might
+even only have one whoa it's very common
+
+ align:start position:0%
+even only have one whoa it's very common
+ 
+
+ align:start position:0%
+even only have one whoa it's very common
+to add on one constraint
+
+ align:start position:0%
+to add on one constraint
+ 
+
+ align:start position:0%
+to add on one constraint
+or one term in regularizing the
+
+ align:start position:0%
+or one term in regularizing the
+ 
+
+ align:start position:0%
+or one term in regularizing the
+situation anyway P is relatively small
+
+ align:start position:0%
+situation anyway P is relatively small
+ 
+
+ align:start position:0%
+situation anyway P is relatively small
+but so the the total matrix a B is has M
+
+ align:start position:0%
+but so the the total matrix a B is has M
+ 
+
+ align:start position:0%
+but so the the total matrix a B is has M
+plus P rows and the same n columns and
+
+ align:start position:0%
+plus P rows and the same n columns and
+ 
+
+ align:start position:0%
+plus P rows and the same n columns and
+and we're ready to go but but the two
+
+ align:start position:0%
+and we're ready to go but but the two
+ 
+
+ align:start position:0%
+and we're ready to go but but the two
+parts are are different somehow they
+
+ align:start position:0%
+parts are are different somehow they
+ 
+
+ align:start position:0%
+parts are are different somehow they
+come from different for different
+
+ align:start position:0%
+come from different for different
+ 
+
+ align:start position:0%
+come from different for different
+reasons and and now I wrote down here
+
+ align:start position:0%
+reasons and and now I wrote down here
+ 
+
+ align:start position:0%
+reasons and and now I wrote down here
+two places they come from and those and
+
+ align:start position:0%
+two places they come from and those and
+ 
+
+ align:start position:0%
+two places they come from and those and
+these are big applications of applied
+
+ align:start position:0%
+these are big applications of applied
+ 
+
+ align:start position:0%
+these are big applications of applied
+math and and and one of them produces
+
+ align:start position:0%
+math and and and one of them produces
+ 
+
+ align:start position:0%
+math and and and one of them produces
+small coefficients alpha and what's
+
+ align:start position:0%
+small coefficients alpha and what's
+ 
+
+ align:start position:0%
+small coefficients alpha and what's
+what's the purpose of the be u minus D
+
+ align:start position:0%
+what's the purpose of the be u minus D
+ 
+
+ align:start position:0%
+what's the purpose of the be u minus D
+term in that case with just a small
+
+ align:start position:0%
+term in that case with just a small
+ 
+
+ align:start position:0%
+term in that case with just a small
+alpha its purpose is usually that the
+
+ align:start position:0%
+alpha its purpose is usually that the
+ 
+
+ align:start position:0%
+alpha its purpose is usually that the
+problem is that the a transpose a part
+
+ align:start position:0%
+problem is that the a transpose a part
+ 
+
+ align:start position:0%
+problem is that the a transpose a part
+is nearly singular or singular so that
+
+ align:start position:0%
+is nearly singular or singular so that
+ 
+
+ align:start position:0%
+is nearly singular or singular so that
+the usual normal equations without the B
+
+ align:start position:0%
+the usual normal equations without the B
+ 
+
+ align:start position:0%
+the usual normal equations without the B
+would be in trouble and this of course
+
+ align:start position:0%
+would be in trouble and this of course
+ 
+
+ align:start position:0%
+would be in trouble and this of course
+happens pretty often so the idea of
+
+ align:start position:0%
+happens pretty often so the idea of
+ 
+
+ align:start position:0%
+happens pretty often so the idea of
+regularization is get some control of
+
+ align:start position:0%
+regularization is get some control of
+ 
+
+ align:start position:0%
+regularization is get some control of
+the solution by putting in another term
+
+ align:start position:0%
+the solution by putting in another term
+ 
+
+ align:start position:0%
+the solution by putting in another term
+that for that that keeps some control
+
+ align:start position:0%
+that for that that keeps some control
+ 
+
+ align:start position:0%
+that for that that keeps some control
+over you and stops it from just taking
+
+ align:start position:0%
+over you and stops it from just taking
+ 
+
+ align:start position:0%
+over you and stops it from just taking
+off as the as would happen with where
+
+ align:start position:0%
+off as the as would happen with where
+ 
+
+ align:start position:0%
+off as the as would happen with where
+the original normal equations would have
+
+ align:start position:0%
+the original normal equations would have
+ 
+
+ align:start position:0%
+the original normal equations would have
+a very large u hat so we're just like
+
+ align:start position:0%
+a very large u hat so we're just like
+ 
+
+ align:start position:0%
+a very large u hat so we're just like
+adding a little steady part that that
+
+ align:start position:0%
+adding a little steady part that that
+ 
+
+ align:start position:0%
+adding a little steady part that that
+keeps it a bit under control and so the
+
+ align:start position:0%
+keeps it a bit under control and so the
+ 
+
+ align:start position:0%
+keeps it a bit under control and so the
+a transpose a is a nearly singular in
+
+ align:start position:0%
+a transpose a is a nearly singular in
+ 
+
+ align:start position:0%
+a transpose a is a nearly singular in
+ill-posed problem so we make them you
+
+ align:start position:0%
+ill-posed problem so we make them you
+ 
+
+ align:start position:0%
+ill-posed problem so we make them you
+know it's like giving aspirin to an
+
+ align:start position:0%
+know it's like giving aspirin to an
+ 
+
+ align:start position:0%
+know it's like giving aspirin to an
+ill-posed problem right you don't fix it
+
+ align:start position:0%
+ill-posed problem right you don't fix it
+ 
+
+ align:start position:0%
+ill-posed problem right you don't fix it
+but you it can it can operate okay and
+
+ align:start position:0%
+but you it can it can operate okay and
+ 
+
+ align:start position:0%
+but you it can it can operate okay and
+where the ill-posed problems come from
+
+ align:start position:0%
+where the ill-posed problems come from
+ 
+
+ align:start position:0%
+where the ill-posed problems come from
+and I just want
+
+ align:start position:0%
+and I just want
+ 
+
+ align:start position:0%
+and I just want
+to say that I I think the fundamental
+
+ align:start position:0%
+to say that I I think the fundamental
+ 
+
+ align:start position:0%
+to say that I I think the fundamental
+ill-posed problem in science is given
+
+ align:start position:0%
+ill-posed problem in science is given
+ 
+
+ align:start position:0%
+ill-posed problem in science is given
+positions suppose we know that a mass
+
+ align:start position:0%
+positions suppose we know that a mass
+ 
+
+ align:start position:0%
+positions suppose we know that a mass
+let's say is in certain positions at
+
+ align:start position:0%
+let's say is in certain positions at
+ 
+
+ align:start position:0%
+let's say is in certain positions at
+certain times find the velocity so we
+
+ align:start position:0%
+certain times find the velocity so we
+ 
+
+ align:start position:0%
+certain times find the velocity so we
+often in in applications have some way
+
+ align:start position:0%
+often in in applications have some way
+ 
+
+ align:start position:0%
+often in in applications have some way
+to know position and want to know
+
+ align:start position:0%
+to know position and want to know
+ 
+
+ align:start position:0%
+to know position and want to know
+velocity and and maybe you realize that
+
+ align:start position:0%
+velocity and and maybe you realize that
+ 
+
+ align:start position:0%
+velocity and and maybe you realize that
+that problem is not well posed because
+
+ align:start position:0%
+that problem is not well posed because
+ 
+
+ align:start position:0%
+that problem is not well posed because
+velocity takes the derivative and if you
+
+ align:start position:0%
+velocity takes the derivative and if you
+ 
+
+ align:start position:0%
+velocity takes the derivative and if you
+take the derivative that's not a good
+
+ align:start position:0%
+take the derivative that's not a good
+ 
+
+ align:start position:0%
+take the derivative that's not a good
+operator to to invert that taking the
+
+ align:start position:0%
+operator to to invert that taking the
+ 
+
+ align:start position:0%
+operator to to invert that taking the
+derivative is makes things very rough
+
+ align:start position:0%
+derivative is makes things very rough
+ 
+
+ align:start position:0%
+derivative is makes things very rough
+and well let's say so you know all sorts
+
+ align:start position:0%
+and well let's say so you know all sorts
+ 
+
+ align:start position:0%
+and well let's say so you know all sorts
+of cases where we're looking for the
+
+ align:start position:0%
+of cases where we're looking for the
+ 
+
+ align:start position:0%
+of cases where we're looking for the
+we're looking for the for the velocity
+
+ align:start position:0%
+we're looking for the for the velocity
+ 
+
+ align:start position:0%
+we're looking for the for the velocity
+and we only have positions one that I
+
+ align:start position:0%
+and we only have positions one that I
+ 
+
+ align:start position:0%
+and we only have positions one that I
+think about is from GPS so GPS uses
+
+ align:start position:0%
+think about is from GPS so GPS uses
+ 
+
+ align:start position:0%
+think about is from GPS so GPS uses
+space-based satellites as you'll know to
+
+ align:start position:0%
+space-based satellites as you'll know to
+ 
+
+ align:start position:0%
+space-based satellites as you'll know to
+give you very accurate positions and
+
+ align:start position:0%
+give you very accurate positions and
+ 
+
+ align:start position:0%
+give you very accurate positions and
+somehow out of those positions you get
+
+ align:start position:0%
+somehow out of those positions you get
+ 
+
+ align:start position:0%
+somehow out of those positions you get
+accurate pretty accurate but not of
+
+ align:start position:0%
+accurate pretty accurate but not of
+ 
+
+ align:start position:0%
+accurate pretty accurate but not of
+course as accurate as the positions but
+
+ align:start position:0%
+course as accurate as the positions but
+ 
+
+ align:start position:0%
+course as accurate as the positions but
+you get decent velocities and how and
+
+ align:start position:0%
+you get decent velocities and how and
+ 
+
+ align:start position:0%
+you get decent velocities and how and
+and and and and so there's an example
+
+ align:start position:0%
+and and and and so there's an example
+ 
+
+ align:start position:0%
+and and and and so there's an example
+where you want to know the motion of
+
+ align:start position:0%
+where you want to know the motion of
+ 
+
+ align:start position:0%
+where you want to know the motion of
+course ask for the acceleration would be
+
+ align:start position:0%
+course ask for the acceleration would be
+ 
+
+ align:start position:0%
+course ask for the acceleration would be
+asking for yet another derivative and
+
+ align:start position:0%
+asking for yet another derivative and
+ 
+
+ align:start position:0%
+asking for yet another derivative and
+you see where the why the derivative is
+
+ align:start position:0%
+you see where the why the derivative is
+ 
+
+ align:start position:0%
+you see where the why the derivative is
+an ill-posed thing I wanna let me just
+
+ align:start position:0%
+an ill-posed thing I wanna let me just
+ 
+
+ align:start position:0%
+an ill-posed thing I wanna let me just
+say ahead of time I'm going to make
+
+ align:start position:0%
+say ahead of time I'm going to make
+ 
+
+ align:start position:0%
+say ahead of time I'm going to make
+today's lecture about direction number
+
+ align:start position:0%
+today's lecture about direction number
+ 
+
+ align:start position:0%
+today's lecture about direction number
+two not the ill-posed problem so I'm
+
+ align:start position:0%
+two not the ill-posed problem so I'm
+ 
+
+ align:start position:0%
+two not the ill-posed problem so I'm
+just like throwing in some comments
+
+ align:start position:0%
+just like throwing in some comments
+ 
+
+ align:start position:0%
+just like throwing in some comments
+about the ill-posed problem
+
+ align:start position:0%
+about the ill-posed problem
+ 
+
+ align:start position:0%
+about the ill-posed problem
+have a weekend to think about those and
+
+ align:start position:0%
+have a weekend to think about those and
+ 
+
+ align:start position:0%
+have a weekend to think about those and
+then next week
+
+ align:start position:0%
+then next week
+ 
+
+ align:start position:0%
+then next week
+I'll come back to this ill-posed problem
+
+ align:start position:0%
+I'll come back to this ill-posed problem
+ 
+
+ align:start position:0%
+I'll come back to this ill-posed problem
+and specifically they often come from
+
+ align:start position:0%
+and specifically they often come from
+ 
+
+ align:start position:0%
+and specifically they often come from
+inverse problems is a big source of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imposed ill-posed problems that need
+
+ align:start position:0%
+imposed ill-posed problems that need
+ 
+
+ align:start position:0%
+imposed ill-posed problems that need
+regularization it's just a very large
+
+ align:start position:0%
+regularization it's just a very large
+ 
+
+ align:start position:0%
+regularization it's just a very large
+class of equations I'm just gonna say
+
+ align:start position:0%
+class of equations I'm just gonna say
+ 
+
+ align:start position:0%
+class of equations I'm just gonna say
+about the derivative example I mean
+
+ align:start position:0%
+about the derivative example I mean
+ 
+
+ align:start position:0%
+about the derivative example I mean
+where why is why is that so unstable
+
+ align:start position:0%
+where why is why is that so unstable
+ 
+
+ align:start position:0%
+where why is why is that so unstable
+well from the point of view of finite
+
+ align:start position:0%
+well from the point of view of finite
+ 
+
+ align:start position:0%
+well from the point of view of finite
+differences how do we if we have
+
+ align:start position:0%
+differences how do we if we have
+ 
+
+ align:start position:0%
+differences how do we if we have
+positions how do you estimate velocities
+
+ align:start position:0%
+positions how do you estimate velocities
+ 
+
+ align:start position:0%
+positions how do you estimate velocities
+you take a difference quotient right you
+
+ align:start position:0%
+you take a difference quotient right you
+ 
+
+ align:start position:0%
+you take a difference quotient right you
+you take the position at this time the
+
+ align:start position:0%
+you take the position at this time the
+ 
+
+ align:start position:0%
+you take the position at this time the
+position at a closeby time and you
+
+ align:start position:0%
+position at a closeby time and you
+ 
+
+ align:start position:0%
+position at a closeby time and you
+divide by delta T that's a reasonable
+
+ align:start position:0%
+divide by delta T that's a reasonable
+ 
+
+ align:start position:0%
+divide by delta T that's a reasonable
+start but dividing by delta T that small
+
+ align:start position:0%
+start but dividing by delta T that small
+ 
+
+ align:start position:0%
+start but dividing by delta T that small
+number is producing big numbers if
+
+ align:start position:0%
+number is producing big numbers if
+ 
+
+ align:start position:0%
+number is producing big numbers if
+you're any errors in the position are
+
+ align:start position:0%
+you're any errors in the position are
+ 
+
+ align:start position:0%
+you're any errors in the position are
+multiplied by that 1 over delta T and
+
+ align:start position:0%
+multiplied by that 1 over delta T and
+ 
+
+ align:start position:0%
+multiplied by that 1 over delta T and
+blown up and similarly in frequency
+
+ align:start position:0%
+blown up and similarly in frequency
+ 
+
+ align:start position:0%
+blown up and similarly in frequency
+space where the functions that we think
+
+ align:start position:0%
+space where the functions that we think
+ 
+
+ align:start position:0%
+space where the functions that we think
+about are the functions like e to the I
+
+ align:start position:0%
+about are the functions like e to the I
+ 
+
+ align:start position:0%
+about are the functions like e to the I
+KT the derivative brings down the factor
+
+ align:start position:0%
+KT the derivative brings down the factor
+ 
+
+ align:start position:0%
+KT the derivative brings down the factor
+K so high oscillations that's the point
+
+ align:start position:0%
+K so high oscillations that's the point
+ 
+
+ align:start position:0%
+K so high oscillations that's the point
+ASSA Latorre functions can be pretty
+
+ align:start position:0%
+ASSA Latorre functions can be pretty
+ 
+
+ align:start position:0%
+ASSA Latorre functions can be pretty
+small but their derivative can be
+
+ align:start position:0%
+small but their derivative can be
+ 
+
+ align:start position:0%
+small but their derivative can be
+enormous so it's at oscillations which
+
+ align:start position:0%
+enormous so it's at oscillations which
+ 
+
+ align:start position:0%
+enormous so it's at oscillations which
+is often associated with noise in the
+
+ align:start position:0%
+is often associated with noise in the
+ 
+
+ align:start position:0%
+is often associated with noise in the
+measurements you know noisy measurements
+
+ align:start position:0%
+measurements you know noisy measurements
+ 
+
+ align:start position:0%
+measurements you know noisy measurements
+are are jumpy and when we go to take
+
+ align:start position:0%
+are are jumpy and when we go to take
+ 
+
+ align:start position:0%
+are are jumpy and when we go to take
+their derivative or their finite
+
+ align:start position:0%
+their derivative or their finite
+ 
+
+ align:start position:0%
+their derivative or their finite
+differences we get big answers anyway
+
+ align:start position:0%
+differences we get big answers anyway
+ 
+
+ align:start position:0%
+differences we get big answers anyway
+that's that for me that's the model
+
+ align:start position:0%
+that's that for me that's the model
+ 
+
+ align:start position:0%
+that's that for me that's the model
+problem the the model ill-posed problem
+
+ align:start position:0%
+problem the the model ill-posed problem
+ 
+
+ align:start position:0%
+problem the the model ill-posed problem
+to find velocities and how to do it I
+
+ align:start position:0%
+to find velocities and how to do it I
+ 
+
+ align:start position:0%
+to find velocities and how to do it I
+mean a lot of thought is gone
+
+ align:start position:0%
+mean a lot of thought is gone
+ 
+
+ align:start position:0%
+mean a lot of thought is gone
+to that let me leave it there and come
+
+ align:start position:0%
+to that let me leave it there and come
+ 
+
+ align:start position:0%
+to that let me leave it there and come
+back to it but just I say all this just
+
+ align:start position:0%
+back to it but just I say all this just
+ 
+
+ align:start position:0%
+back to it but just I say all this just
+to emphasize its importance
+
+ align:start position:0%
+to emphasize its importance
+ 
+
+ align:start position:0%
+to emphasize its importance
+not that we'll completely solve it
+
+ align:start position:0%
+not that we'll completely solve it
+ 
+
+ align:start position:0%
+not that we'll completely solve it
+actually for GPS or for any other thing
+
+ align:start position:0%
+actually for GPS or for any other thing
+ 
+
+ align:start position:0%
+actually for GPS or for any other thing
+it's it's just all we can do is medicate
+
+ align:start position:0%
+it's it's just all we can do is medicate
+ 
+
+ align:start position:0%
+it's it's just all we can do is medicate
+it okay now this is one that we can
+
+ align:start position:0%
+it okay now this is one that we can
+ 
+
+ align:start position:0%
+it okay now this is one that we can
+really solve so this is a different
+
+ align:start position:0%
+really solve so this is a different
+ 
+
+ align:start position:0%
+really solve so this is a different
+application entirely here in this
+
+ align:start position:0%
+application entirely here in this
+ 
+
+ align:start position:0%
+application entirely here in this
+application this second term bu equal D
+
+ align:start position:0%
+application this second term bu equal D
+ 
+
+ align:start position:0%
+application this second term bu equal D
+is something important something that we
+
+ align:start position:0%
+is something important something that we
+ 
+
+ align:start position:0%
+is something important something that we
+want to enforce it's a constraint you
+
+ align:start position:0%
+want to enforce it's a constraint you
+ 
+
+ align:start position:0%
+want to enforce it's a constraint you
+could say and one way to enforce it
+
+ align:start position:0%
+could say and one way to enforce it
+ 
+
+ align:start position:0%
+could say and one way to enforce it
+which fits this pattern is to take out
+
+ align:start position:0%
+which fits this pattern is to take out
+ 
+
+ align:start position:0%
+which fits this pattern is to take out
+for very large right when we take alpha
+
+ align:start position:0%
+for very large right when we take alpha
+ 
+
+ align:start position:0%
+for very large right when we take alpha
+large we're putting a really heavy
+
+ align:start position:0%
+large we're putting a really heavy
+ 
+
+ align:start position:0%
+large we're putting a really heavy
+weight on that bu minus d squared and
+
+ align:start position:0%
+weight on that bu minus d squared and
+ 
+
+ align:start position:0%
+weight on that bu minus d squared and
+when we minimize that weight will force
+
+ align:start position:0%
+when we minimize that weight will force
+ 
+
+ align:start position:0%
+when we minimize that weight will force
+bu to be pretty close to D and yet at
+
+ align:start position:0%
+bu to be pretty close to D and yet at
+ 
+
+ align:start position:0%
+bu to be pretty close to D and yet at
+the st. but of course bu equal D doesn't
+
+ align:start position:0%
+the st. but of course bu equal D doesn't
+ 
+
+ align:start position:0%
+the st. but of course bu equal D doesn't
+determine you everybody's got that
+
+ align:start position:0%
+determine you everybody's got that
+ 
+
+ align:start position:0%
+determine you everybody's got that
+picture clear from bu equal D has many
+
+ align:start position:0%
+picture clear from bu equal D has many
+ 
+
+ align:start position:0%
+picture clear from bu equal D has many
+solutions and so they're the real
+
+ align:start position:0%
+solutions and so they're the real
+ 
+
+ align:start position:0%
+solutions and so they're the real
+problem that we're trying to solve is
+
+ align:start position:0%
+problem that we're trying to solve is
+ 
+
+ align:start position:0%
+problem that we're trying to solve is
+enforce bu equal D but among those
+
+ align:start position:0%
+enforce bu equal D but among those
+ 
+
+ align:start position:0%
+enforce bu equal D but among those
+solutions pick the one that minimizes
+
+ align:start position:0%
+solutions pick the one that minimizes
+ 
+
+ align:start position:0%
+solutions pick the one that minimizes
+the first square au minus B squared so
+
+ align:start position:0%
+the first square au minus B squared so
+ 
+
+ align:start position:0%
+the first square au minus B squared so
+you see the difference you're trying to
+
+ align:start position:0%
+you see the difference you're trying to
+ 
+
+ align:start position:0%
+you see the difference you're trying to
+enforce something that that the physics
+
+ align:start position:0%
+enforce something that that the physics
+ 
+
+ align:start position:0%
+enforce something that that the physics
+or the geometry or whatever source says
+
+ align:start position:0%
+or the geometry or whatever source says
+ 
+
+ align:start position:0%
+or the geometry or whatever source says
+it has to be true and you can do it and
+
+ align:start position:0%
+it has to be true and you can do it and
+ 
+
+ align:start position:0%
+it has to be true and you can do it and
+you're left with lots of options and
+
+ align:start position:0%
+you're left with lots of options and
+ 
+
+ align:start position:0%
+you're left with lots of options and
+then the combined problem attempts to
+
+ align:start position:0%
+then the combined problem attempts to
+ 
+
+ align:start position:0%
+then the combined problem attempts to
+pick your right you okay so that's the
+
+ align:start position:0%
+pick your right you okay so that's the
+ 
+
+ align:start position:0%
+pick your right you okay so that's the
+application number two that I want to
+
+ align:start position:0%
+application number two that I want to
+ 
+
+ align:start position:0%
+application number two that I want to
+speak about today and actually what I
+
+ align:start position:0%
+speak about today and actually what I
+ 
+
+ align:start position:0%
+speak about today and actually what I
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+I want to give several ways to do it
+
+ align:start position:0%
+I want to give several ways to do it
+ 
+
+ align:start position:0%
+I want to give several ways to do it
+it's a very important problem and one
+
+ align:start position:0%
+it's a very important problem and one
+ 
+
+ align:start position:0%
+it's a very important problem and one
+way will be to actually solve bu equal D
+
+ align:start position:0%
+way will be to actually solve bu equal D
+ 
+
+ align:start position:0%
+way will be to actually solve bu equal D
+find those solutions and you may say
+
+ align:start position:0%
+find those solutions and you may say
+ 
+
+ align:start position:0%
+find those solutions and you may say
+well that's what we learned in linear
+
+ align:start position:0%
+well that's what we learned in linear
+ 
+
+ align:start position:0%
+well that's what we learned in linear
+algebra that's the very foundation of
+
+ align:start position:0%
+algebra that's the very foundation of
+ 
+
+ align:start position:0%
+algebra that's the very foundation of
+linear algebra is to is there's a
+
+ align:start position:0%
+linear algebra is to is there's a
+ 
+
+ align:start position:0%
+linear algebra is to is there's a
+particular solution right or there
+
+ align:start position:0%
+particular solution right or there
+ 
+
+ align:start position:0%
+particular solution right or there
+there's a not every solution is of this
+
+ align:start position:0%
+there's a not every solution is of this
+ 
+
+ align:start position:0%
+there's a not every solution is of this
+form particular plus a null space
+
+ align:start position:0%
+form particular plus a null space
+ 
+
+ align:start position:0%
+form particular plus a null space
+maybe I'll just point to the start of
+
+ align:start position:0%
+maybe I'll just point to the start of
+ 
+
+ align:start position:0%
+maybe I'll just point to the start of
+that approach so I want to solve bu
+
+ align:start position:0%
+that approach so I want to solve bu
+ 
+
+ align:start position:0%
+that approach so I want to solve bu
+equal D I'll come back to that to this
+
+ align:start position:0%
+equal D I'll come back to that to this
+ 
+
+ align:start position:0%
+equal D I'll come back to that to this
+method after dealing with the least
+
+ align:start position:0%
+method after dealing with the least
+ 
+
+ align:start position:0%
+method after dealing with the least
+squares I approach but here's a here's
+
+ align:start position:0%
+squares I approach but here's a here's
+ 
+
+ align:start position:0%
+squares I approach but here's a here's
+really the direct approach that if I
+
+ align:start position:0%
+really the direct approach that if I
+ 
+
+ align:start position:0%
+really the direct approach that if I
+solve bu equal D then there's a
+
+ align:start position:0%
+solve bu equal D then there's a
+ 
+
+ align:start position:0%
+solve bu equal D then there's a
+particular solution that solves it and
+
+ align:start position:0%
+particular solution that solves it and
+ 
+
+ align:start position:0%
+particular solution that solves it and
+then there's you can always add on the
+
+ align:start position:0%
+then there's you can always add on the
+ 
+
+ align:start position:0%
+then there's you can always add on the
+general solution which is sorry add on
+
+ align:start position:0%
+general solution which is sorry add on
+ 
+
+ align:start position:0%
+general solution which is sorry add on
+the null space solution the solution of
+
+ align:start position:0%
+the null space solution the solution of
+ 
+
+ align:start position:0%
+the null space solution the solution of
+BU equals zero and the BU equals zero
+
+ align:start position:0%
+BU equals zero and the BU equals zero
+ 
+
+ align:start position:0%
+BU equals zero and the BU equals zero
+has lots of solutions so we have we
+
+ align:start position:0%
+has lots of solutions so we have we
+ 
+
+ align:start position:0%
+has lots of solutions so we have we
+would have to find them okay that's I
+
+ align:start position:0%
+would have to find them okay that's I
+ 
+
+ align:start position:0%
+would have to find them okay that's I
+mean that's what 1806 would naturally do
+
+ align:start position:0%
+mean that's what 1806 would naturally do
+ 
+
+ align:start position:0%
+mean that's what 1806 would naturally do
+but actually never I'm ashamed to say
+
+ align:start position:0%
+but actually never I'm ashamed to say
+ 
+
+ align:start position:0%
+but actually never I'm ashamed to say
+I'd enjoy it in 1806 I never actually
+
+ align:start position:0%
+I'd enjoy it in 1806 I never actually
+ 
+
+ align:start position:0%
+I'd enjoy it in 1806 I never actually
+said how I would scientifically compute
+
+ align:start position:0%
+said how I would scientifically compute
+ 
+
+ align:start position:0%
+said how I would scientifically compute
+in a stable way the solutions okay so I
+
+ align:start position:0%
+in a stable way the solutions okay so I
+ 
+
+ align:start position:0%
+in a stable way the solutions okay so I
+think that will be important but that's
+
+ align:start position:0%
+think that will be important but that's
+ 
+
+ align:start position:0%
+think that will be important but that's
+not the only way to do it that's called
+
+ align:start position:0%
+not the only way to do it that's called
+ 
+
+ align:start position:0%
+not the only way to do it that's called
+the null space method and sometimes it's
+
+ align:start position:0%
+the null space method and sometimes it's
+ 
+
+ align:start position:0%
+the null space method and sometimes it's
+the right choice sometimes not this
+
+ align:start position:0%
+the right choice sometimes not this
+ 
+
+ align:start position:0%
+the right choice sometimes not this
+would be called the the heavyweight
+
+ align:start position:0%
+would be called the the heavyweight
+ 
+
+ align:start position:0%
+would be called the the heavyweight
+method right and put on a very
+
+ align:start position:0%
+method right and put on a very
+ 
+
+ align:start position:0%
+method right and put on a very
+heavyweight and Stan to solve a standard
+
+ align:start position:0%
+heavyweight and Stan to solve a standard
+ 
+
+ align:start position:0%
+heavyweight and Stan to solve a standard
+problem okay so let me follow that one
+
+ align:start position:0%
+problem okay so let me follow that one
+ 
+
+ align:start position:0%
+problem okay so let me follow that one
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+and then there'll be a third method and
+
+ align:start position:0%
+and then there'll be a third method and
+ 
+
+ align:start position:0%
+and then there'll be a third method and
+maybe there's going to be space on the
+
+ align:start position:0%
+maybe there's going to be space on the
+ 
+
+ align:start position:0%
+maybe there's going to be space on the
+middle blackboard for it
+
+ align:start position:0%
+middle blackboard for it
+ 
+
+ align:start position:0%
+middle blackboard for it
+and what will the third method be that
+
+ align:start position:0%
+and what will the third method be that
+ 
+
+ align:start position:0%
+and what will the third method be that
+will be used on the grounds multiplayer
+
+ align:start position:0%
+will be used on the grounds multiplayer
+ 
+
+ align:start position:0%
+will be used on the grounds multiplayer
+this thing is a constraint I'll enforce
+
+ align:start position:0%
+this thing is a constraint I'll enforce
+ 
+
+ align:start position:0%
+this thing is a constraint I'll enforce
+it by Allah groans multiplier okay
+
+ align:start position:0%
+it by Allah groans multiplier okay
+ 
+
+ align:start position:0%
+it by Allah groans multiplier okay
+that's that's coming next what I'm the
+
+ align:start position:0%
+that's that's coming next what I'm the
+ 
+
+ align:start position:0%
+that's that's coming next what I'm the
+way I'm enforcing it right now is by a
+
+ align:start position:0%
+way I'm enforcing it right now is by a
+ 
+
+ align:start position:0%
+way I'm enforcing it right now is by a
+heavyweight okay so that one reason for
+
+ align:start position:0%
+heavyweight okay so that one reason for
+ 
+
+ align:start position:0%
+heavyweight okay so that one reason for
+this the popularity of this method is
+
+ align:start position:0%
+this the popularity of this method is
+ 
+
+ align:start position:0%
+this the popularity of this method is
+you don't have to do any new thinking
+
+ align:start position:0%
+you don't have to do any new thinking
+ 
+
+ align:start position:0%
+you don't have to do any new thinking
+you've you just create this these
+
+ align:start position:0%
+you've you just create this these
+ 
+
+ align:start position:0%
+you've you just create this these
+equations and solve them where the other
+
+ align:start position:0%
+equations and solve them where the other
+ 
+
+ align:start position:0%
+equations and solve them where the other
+methods maybe ask us to think separately
+
+ align:start position:0%
+methods maybe ask us to think separately
+ 
+
+ align:start position:0%
+methods maybe ask us to think separately
+about the constraint here we don't have
+
+ align:start position:0%
+about the constraint here we don't have
+ 
+
+ align:start position:0%
+about the constraint here we don't have
+to think separately we just create this
+
+ align:start position:0%
+to think separately we just create this
+ 
+
+ align:start position:0%
+to think separately we just create this
+normal equation we solve it and we get
+
+ align:start position:0%
+normal equation we solve it and we get
+ 
+
+ align:start position:0%
+normal equation we solve it and we get
+an answer you hat maybe I should call it
+
+ align:start position:0%
+an answer you hat maybe I should call it
+ 
+
+ align:start position:0%
+an answer you hat maybe I should call it
+u hat alpha because it depends on the
+
+ align:start position:0%
+u hat alpha because it depends on the
+ 
+
+ align:start position:0%
+u hat alpha because it depends on the
+weight alpha certainly which we hope is
+
+ align:start position:0%
+weight alpha certainly which we hope is
+ 
+
+ align:start position:0%
+weight alpha certainly which we hope is
+near the exact solution the exact
+
+ align:start position:0%
+near the exact solution the exact
+ 
+
+ align:start position:0%
+near the exact solution the exact
+solution being the one that exactly
+
+ align:start position:0%
+solution being the one that exactly
+ 
+
+ align:start position:0%
+solution being the one that exactly
+solves bu equal D because you you had
+
+ align:start position:0%
+solves bu equal D because you you had
+ 
+
+ align:start position:0%
+solves bu equal D because you you had
+alpha will not exactly solve bu equal D
+
+ align:start position:0%
+alpha will not exactly solve bu equal D
+ 
+
+ align:start position:0%
+alpha will not exactly solve bu equal D
+but we can find solutions that do and
+
+ align:start position:0%
+but we can find solutions that do and
+ 
+
+ align:start position:0%
+but we can find solutions that do and
+then among those we can minimize au
+
+ align:start position:0%
+then among those we can minimize au
+ 
+
+ align:start position:0%
+then among those we can minimize au
+minus P squared okay okay so just a word
+
+ align:start position:0%
+minus P squared okay okay so just a word
+ 
+
+ align:start position:0%
+minus P squared okay okay so just a word
+about the this weighted heavyweight and
+
+ align:start position:0%
+about the this weighted heavyweight and
+ 
+
+ align:start position:0%
+about the this weighted heavyweight and
+that's it okay well first an interesting
+
+ align:start position:0%
+that's it okay well first an interesting
+ 
+
+ align:start position:0%
+that's it okay well first an interesting
+point a point that I think is sort of
+
+ align:start position:0%
+point a point that I think is sort of
+ 
+
+ align:start position:0%
+point a point that I think is sort of
+interesting if I I want to let alpha go
+
+ align:start position:0%
+interesting if I I want to let alpha go
+ 
+
+ align:start position:0%
+interesting if I I want to let alpha go
+to infinity and see what happens right
+
+ align:start position:0%
+to infinity and see what happens right
+ 
+
+ align:start position:0%
+to infinity and see what happens right
+everybody figures that as alpha goes to
+
+ align:start position:0%
+everybody figures that as alpha goes to
+ 
+
+ align:start position:0%
+everybody figures that as alpha goes to
+infinity I'm going to get the right
+
+ align:start position:0%
+infinity I'm going to get the right
+ 
+
+ align:start position:0%
+infinity I'm going to get the right
+answer because this alpha goes to
+
+ align:start position:0%
+answer because this alpha goes to
+ 
+
+ align:start position:0%
+answer because this alpha goes to
+infinity it's going to more and more
+
+ align:start position:0%
+infinity it's going to more and more
+ 
+
+ align:start position:0%
+infinity it's going to more and more
+enforce the constraint bu equal D and
+
+ align:start position:0%
+enforce the constraint bu equal D and
+ 
+
+ align:start position:0%
+enforce the constraint bu equal D and
+then with that constraint enforce the
+
+ align:start position:0%
+then with that constraint enforce the
+ 
+
+ align:start position:0%
+then with that constraint enforce the
+other part of it we'll find the best U
+
+ align:start position:0%
+other part of it we'll find the best U
+ 
+
+ align:start position:0%
+other part of it we'll find the best U
+and that's that's great but let all four
+
+ align:start position:0%
+and that's that's great but let all four
+ 
+
+ align:start position:0%
+and that's that's great but let all four
+go to infinity in this equation and what
+
+ align:start position:0%
+go to infinity in this equation and what
+ 
+
+ align:start position:0%
+go to infinity in this equation and what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+so this is just like a side comment just
+
+ align:start position:0%
+so this is just like a side comment just
+ 
+
+ align:start position:0%
+so this is just like a side comment just
+to say alpha you know taking a limit you
+
+ align:start position:0%
+to say alpha you know taking a limit you
+ 
+
+ align:start position:0%
+to say alpha you know taking a limit you
+got to think about it doing it right
+
+ align:start position:0%
+got to think about it doing it right
+ 
+
+ align:start position:0%
+got to think about it doing it right
+because well let's see if I let alpha go
+
+ align:start position:0%
+because well let's see if I let alpha go
+ 
+
+ align:start position:0%
+because well let's see if I let alpha go
+to infinity as it is
+
+ align:start position:0%
+to infinity as it is
+ 
+
+ align:start position:0%
+to infinity as it is
+that'll be infinite that'll be infinite
+
+ align:start position:0%
+that'll be infinite that'll be infinite
+ 
+
+ align:start position:0%
+that'll be infinite that'll be infinite
+I won't know what's going on let me
+
+ align:start position:0%
+I won't know what's going on let me
+ 
+
+ align:start position:0%
+I won't know what's going on let me
+divide by alpha before I let alpha go to
+
+ align:start position:0%
+divide by alpha before I let alpha go to
+ 
+
+ align:start position:0%
+divide by alpha before I let alpha go to
+infinity so if I just divide everything
+
+ align:start position:0%
+infinity so if I just divide everything
+ 
+
+ align:start position:0%
+infinity so if I just divide everything
+by alpha can I do that with a eraser
+
+ align:start position:0%
+by alpha can I do that with a eraser
+ 
+
+ align:start position:0%
+by alpha can I do that with a eraser
+here divided by alpha so there's a 1
+
+ align:start position:0%
+here divided by alpha so there's a 1
+ 
+
+ align:start position:0%
+here divided by alpha so there's a 1
+over alpha here I divide this by alpha
+
+ align:start position:0%
+over alpha here I divide this by alpha
+ 
+
+ align:start position:0%
+over alpha here I divide this by alpha
+and this has a 1 over alpha there and
+
+ align:start position:0%
+and this has a 1 over alpha there and
+ 
+
+ align:start position:0%
+and this has a 1 over alpha there and
+now if I let alpha go to infinity I get
+
+ align:start position:0%
+now if I let alpha go to infinity I get
+ 
+
+ align:start position:0%
+now if I let alpha go to infinity I get
+something sensible this goes to 0 right
+
+ align:start position:0%
+something sensible this goes to 0 right
+ 
+
+ align:start position:0%
+something sensible this goes to 0 right
+alpha going to infinity getting bigger
+
+ align:start position:0%
+alpha going to infinity getting bigger
+ 
+
+ align:start position:0%
+alpha going to infinity getting bigger
+and bigger this goes to 0 so what do I
+
+ align:start position:0%
+and bigger this goes to 0 so what do I
+ 
+
+ align:start position:0%
+and bigger this goes to 0 so what do I
+get in the limit I get that this equals
+
+ align:start position:0%
+get in the limit I get that this equals
+ 
+
+ align:start position:0%
+get in the limit I get that this equals
+this in the limit so shall I put that up
+
+ align:start position:0%
+this in the limit so shall I put that up
+ 
+
+ align:start position:0%
+this in the limit so shall I put that up
+here well now put it here because I I
+
+ align:start position:0%
+here well now put it here because I I
+ 
+
+ align:start position:0%
+here well now put it here because I I
+don't like it frankly if I if so I'll
+
+ align:start position:0%
+don't like it frankly if I if so I'll
+ 
+
+ align:start position:0%
+don't like it frankly if I if so I'll
+just squeeze it in this little spot and
+
+ align:start position:0%
+just squeeze it in this little spot and
+ 
+
+ align:start position:0%
+just squeeze it in this little spot and
+if I then alpha go to 0 and to infinity
+
+ align:start position:0%
+if I then alpha go to 0 and to infinity
+ 
+
+ align:start position:0%
+if I then alpha go to 0 and to infinity
+so 1 over alpha goes to 0 I get B
+
+ align:start position:0%
+so 1 over alpha goes to 0 I get B
+ 
+
+ align:start position:0%
+so 1 over alpha goes to 0 I get B
+transpose B you have infinity shall I
+
+ align:start position:0%
+transpose B you have infinity shall I
+ 
+
+ align:start position:0%
+transpose B you have infinity shall I
+call it equals B transpose D and I guess
+
+ align:start position:0%
+call it equals B transpose D and I guess
+ 
+
+ align:start position:0%
+call it equals B transpose D and I guess
+what I want to say is from that I don't
+
+ align:start position:0%
+what I want to say is from that I don't
+ 
+
+ align:start position:0%
+what I want to say is from that I don't
+learn a whole lot because B transpose B
+
+ align:start position:0%
+learn a whole lot because B transpose B
+ 
+
+ align:start position:0%
+learn a whole lot because B transpose B
+is a singular matrix B transpose B is a
+
+ align:start position:0%
+is a singular matrix B transpose B is a
+ 
+
+ align:start position:0%
+is a singular matrix B transpose B is a
+matrix of only rank P it's it's very
+
+ align:start position:0%
+matrix of only rank P it's it's very
+ 
+
+ align:start position:0%
+matrix of only rank P it's it's very
+singular right we had this crazy shape
+
+ align:start position:0%
+singular right we had this crazy shape
+ 
+
+ align:start position:0%
+singular right we had this crazy shape
+long and thin B transpose B will be tall
+
+ align:start position:0%
+long and thin B transpose B will be tall
+ 
+
+ align:start position:0%
+long and thin B transpose B will be tall
+B transpose B will be a large matrix but
+
+ align:start position:0%
+B transpose B will be a large matrix but
+ 
+
+ align:start position:0%
+B transpose B will be a large matrix but
+its rank will only be P it's a it's an N
+
+ align:start position:0%
+its rank will only be P it's a it's an N
+ 
+
+ align:start position:0%
+its rank will only be P it's a it's an N
+by n matrix of rank P and it's singular
+
+ align:start position:0%
+by n matrix of rank P and it's singular
+ 
+
+ align:start position:0%
+by n matrix of rank P and it's singular
+and and who knows what's going on here
+
+ align:start position:0%
+and and who knows what's going on here
+ 
+
+ align:start position:0%
+and and who knows what's going on here
+so I guess all I want that
+
+ align:start position:0%
+so I guess all I want that
+ 
+
+ align:start position:0%
+so I guess all I want that
+little sight issue was simply to say
+
+ align:start position:0%
+little sight issue was simply to say
+ 
+
+ align:start position:0%
+little sight issue was simply to say
+that you can't just let alpha go to
+
+ align:start position:0%
+that you can't just let alpha go to
+ 
+
+ align:start position:0%
+that you can't just let alpha go to
+infinity and the central equation there
+
+ align:start position:0%
+infinity and the central equation there
+ 
+
+ align:start position:0%
+infinity and the central equation there
+and expect to see what's happening okay
+
+ align:start position:0%
+and expect to see what's happening okay
+ 
+
+ align:start position:0%
+and expect to see what's happening okay
+so somehow there's more to it than that
+
+ align:start position:0%
+so somehow there's more to it than that
+ 
+
+ align:start position:0%
+so somehow there's more to it than that
+so let me put alpha back where it
+
+ align:start position:0%
+so let me put alpha back where it
+ 
+
+ align:start position:0%
+so let me put alpha back where it
+belongs and look and think again okay
+
+ align:start position:0%
+belongs and look and think again okay
+ 
+
+ align:start position:0%
+belongs and look and think again okay
+think again
+
+ align:start position:0%
+think again
+ 
+
+ align:start position:0%
+think again
+okay and I guess by thinking again I'm
+
+ align:start position:0%
+okay and I guess by thinking again I'm
+ 
+
+ align:start position:0%
+okay and I guess by thinking again I'm
+going to I'm gonna I might as well think
+
+ align:start position:0%
+going to I'm gonna I might as well think
+ 
+
+ align:start position:0%
+going to I'm gonna I might as well think
+in terms of this this way of writing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because I recognize this right this is
+
+ align:start position:0%
+because I recognize this right this is
+ 
+
+ align:start position:0%
+because I recognize this right this is
+exactly the framework that that we've
+
+ align:start position:0%
+exactly the framework that that we've
+ 
+
+ align:start position:0%
+exactly the framework that that we've
+developed and what is the what is the so
+
+ align:start position:0%
+developed and what is the what is the so
+ 
+
+ align:start position:0%
+developed and what is the what is the so
+this is the least squares problem you
+
+ align:start position:0%
+this is the least squares problem you
+ 
+
+ align:start position:0%
+this is the least squares problem you
+remember the this I I just want to write
+
+ align:start position:0%
+remember the this I I just want to write
+ 
+
+ align:start position:0%
+remember the this I I just want to write
+down the saddle point matrix that goes
+
+ align:start position:0%
+down the saddle point matrix that goes
+ 
+
+ align:start position:0%
+down the saddle point matrix that goes
+with this least squares problem what is
+
+ align:start position:0%
+with this least squares problem what is
+ 
+
+ align:start position:0%
+with this least squares problem what is
+the saddle point matrix do you remember
+
+ align:start position:0%
+the saddle point matrix do you remember
+ 
+
+ align:start position:0%
+the saddle point matrix do you remember
+the saddle point matrix s is it has up
+
+ align:start position:0%
+the saddle point matrix s is it has up
+ 
+
+ align:start position:0%
+the saddle point matrix s is it has up
+here it everybody remembers that okay so
+
+ align:start position:0%
+here it everybody remembers that okay so
+ 
+
+ align:start position:0%
+here it everybody remembers that okay so
+now I've got to I've got an A and a B
+
+ align:start position:0%
+now I've got to I've got an A and a B
+ 
+
+ align:start position:0%
+now I've got to I've got an A and a B
+here so that they're going to be on top
+
+ align:start position:0%
+here so that they're going to be on top
+ 
+
+ align:start position:0%
+here so that they're going to be on top
+it's gonna be a little bit larger then I
+
+ align:start position:0%
+it's gonna be a little bit larger then I
+ 
+
+ align:start position:0%
+it's gonna be a little bit larger then I
+have my usual zero block and I have my
+
+ align:start position:0%
+have my usual zero block and I have my
+ 
+
+ align:start position:0%
+have my usual zero block and I have my
+usual a transpose B transpose block and
+
+ align:start position:0%
+usual a transpose B transpose block and
+ 
+
+ align:start position:0%
+usual a transpose B transpose block and
+what block goes there that's the C
+
+ align:start position:0%
+what block goes there that's the C
+ 
+
+ align:start position:0%
+what block goes there that's the C
+inverse right that's this unit right
+
+ align:start position:0%
+inverse right that's this unit right
+ 
+
+ align:start position:0%
+inverse right that's this unit right
+we're now we're now it's our usual C
+
+ align:start position:0%
+we're now we're now it's our usual C
+ 
+
+ align:start position:0%
+we're now we're now it's our usual C
+inverse a a transpose zero that we're
+
+ align:start position:0%
+inverse a a transpose zero that we're
+ 
+
+ align:start position:0%
+inverse a a transpose zero that we're
+totally accustomed to but now a has
+
+ align:start position:0%
+totally accustomed to but now a has
+ 
+
+ align:start position:0%
+totally accustomed to but now a has
+grown into a B zero is still zero that
+
+ align:start position:0%
+grown into a B zero is still zero that
+ 
+
+ align:start position:0%
+grown into a B zero is still zero that
+transpose is still the transpose and up
+
+ align:start position:0%
+transpose is still the transpose and up
+ 
+
+ align:start position:0%
+transpose is still the transpose and up
+here is C inverse and since C was this C
+
+ align:start position:0%
+here is C inverse and since C was this C
+ 
+
+ align:start position:0%
+here is C inverse and since C was this C
+inverse will be the identity and the
+
+ align:start position:0%
+inverse will be the identity and the
+ 
+
+ align:start position:0%
+inverse will be the identity and the
+identity over alpha
+
+ align:start position:0%
+identity over alpha
+ 
+
+ align:start position:0%
+identity over alpha
+okay so that's my s alpha you could say
+
+ align:start position:0%
+okay so that's my s alpha you could say
+ 
+
+ align:start position:0%
+okay so that's my s alpha you could say
+and now I'm prepared to let so my
+
+ align:start position:0%
+and now I'm prepared to let so my
+ 
+
+ align:start position:0%
+and now I'm prepared to let so my
+equation is s alpha what's what's the
+
+ align:start position:0%
+equation is s alpha what's what's the
+ 
+
+ align:start position:0%
+equation is s alpha what's what's the
+written as a Bloch equation what what
+
+ align:start position:0%
+written as a Bloch equation what what
+ 
+
+ align:start position:0%
+written as a Bloch equation what what
+are the pieces of it U is the is the guy
+
+ align:start position:0%
+are the pieces of it U is the is the guy
+ 
+
+ align:start position:0%
+are the pieces of it U is the is the guy
+that I'm looking for that u hat alpha
+
+ align:start position:0%
+that I'm looking for that u hat alpha
+ 
+
+ align:start position:0%
+that I'm looking for that u hat alpha
+and there was a LaGrant a buyer that
+
+ align:start position:0%
+and there was a LaGrant a buyer that
+ 
+
+ align:start position:0%
+and there was a LaGrant a buyer that
+came in you remember that's how we got
+
+ align:start position:0%
+came in you remember that's how we got
+ 
+
+ align:start position:0%
+came in you remember that's how we got
+to a block form from a from a scalar
+
+ align:start position:0%
+to a block form from a from a scalar
+ 
+
+ align:start position:0%
+to a block form from a from a scalar
+form and the I guess I usually called it
+
+ align:start position:0%
+form and the I guess I usually called it
+ 
+
+ align:start position:0%
+form and the I guess I usually called it
+W so stay with W for here okay so that's
+
+ align:start position:0%
+W so stay with W for here okay so that's
+ 
+
+ align:start position:0%
+W so stay with W for here okay so that's
+what multiply is w u and it's what gives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see I think it gives a B and it
+
+ align:start position:0%
+let's see I think it gives a B and it
+ 
+
+ align:start position:0%
+let's see I think it gives a B and it
+gives a D from this a U and B you and I
+
+ align:start position:0%
+gives a D from this a U and B you and I
+ 
+
+ align:start position:0%
+gives a D from this a U and B you and I
+think here it gives a 0 because we don't
+
+ align:start position:0%
+think here it gives a 0 because we don't
+ 
+
+ align:start position:0%
+think here it gives a 0 because we don't
+have okay what am I doing here I'm just
+
+ align:start position:0%
+have okay what am I doing here I'm just
+ 
+
+ align:start position:0%
+have okay what am I doing here I'm just
+writing the problem in a way where I can
+
+ align:start position:0%
+writing the problem in a way where I can
+ 
+
+ align:start position:0%
+writing the problem in a way where I can
+let alpha go to zero and see the limit
+
+ align:start position:0%
+let alpha go to zero and see the limit
+ 
+
+ align:start position:0%
+let alpha go to zero and see the limit
+so let alpha go to sorry but alpha go to
+
+ align:start position:0%
+so let alpha go to sorry but alpha go to
+ 
+
+ align:start position:0%
+so let alpha go to sorry but alpha go to
+infinity this is heavyweight part so
+
+ align:start position:0%
+infinity this is heavyweight part so
+ 
+
+ align:start position:0%
+infinity this is heavyweight part so
+this will go to 0 so this approaches the
+
+ align:start position:0%
+this will go to 0 so this approaches the
+ 
+
+ align:start position:0%
+this will go to 0 so this approaches the
+S infinity W infinity we could call it u
+
+ align:start position:0%
+S infinity W infinity we could call it u
+ 
+
+ align:start position:0%
+S infinity W infinity we could call it u
+hat infinity is now well you see what
+
+ align:start position:0%
+hat infinity is now well you see what
+ 
+
+ align:start position:0%
+hat infinity is now well you see what
+the limit is that's zero in that block
+
+ align:start position:0%
+the limit is that's zero in that block
+ 
+
+ align:start position:0%
+the limit is that's zero in that block
+this is a this is B this is a transpose
+
+ align:start position:0%
+this is a this is B this is a transpose
+ 
+
+ align:start position:0%
+this is a this is B this is a transpose
+this is B transpose this is our usual
+
+ align:start position:0%
+this is B transpose this is our usual
+ 
+
+ align:start position:0%
+this is B transpose this is our usual
+zero block multiplying our same W
+
+ align:start position:0%
+zero block multiplying our same W
+ 
+
+ align:start position:0%
+zero block multiplying our same W
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+you had infinity equaling our same be d
+
+ align:start position:0%
+you had infinity equaling our same be d
+ 
+
+ align:start position:0%
+you had infinity equaling our same be d
+and zero this is the limiting equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's great
+
+ align:start position:0%
+and it's great
+ 
+
+ align:start position:0%
+and it's great
+that's the this is the equation that our
+
+ align:start position:0%
+that's the this is the equation that our
+ 
+
+ align:start position:0%
+that's the this is the equation that our
+that determines that limit as alpha goes
+
+ align:start position:0%
+that determines that limit as alpha goes
+ 
+
+ align:start position:0%
+that determines that limit as alpha goes
+to infinity that determines the best
+
+ align:start position:0%
+to infinity that determines the best
+ 
+
+ align:start position:0%
+to infinity that determines the best
+view yeah this is the problem that we
+
+ align:start position:0%
+view yeah this is the problem that we
+ 
+
+ align:start position:0%
+view yeah this is the problem that we
+would really we really want to solve
+
+ align:start position:0%
+would really we really want to solve
+ 
+
+ align:start position:0%
+would really we really want to solve
+yeah yeah maybe that's what I should say
+
+ align:start position:0%
+yeah yeah maybe that's what I should say
+ 
+
+ align:start position:0%
+yeah yeah maybe that's what I should say
+this is the problem do you see the
+
+ align:start position:0%
+this is the problem do you see the
+ 
+
+ align:start position:0%
+this is the problem do you see the
+constraint bu equal D in here from this
+
+ align:start position:0%
+constraint bu equal D in here from this
+ 
+
+ align:start position:0%
+constraint bu equal D in here from this
+from this middle block row that says
+
+ align:start position:0%
+from this middle block row that says
+ 
+
+ align:start position:0%
+from this middle block row that says
+zero zero bu hat is D so that we've
+
+ align:start position:0%
+zero zero bu hat is D so that we've
+ 
+
+ align:start position:0%
+zero zero bu hat is D so that we've
+introduced the constraint the first part
+
+ align:start position:0%
+introduced the constraint the first part
+ 
+
+ align:start position:0%
+introduced the constraint the first part
+is W infinity with an au infinity that's
+
+ align:start position:0%
+is W infinity with an au infinity that's
+ 
+
+ align:start position:0%
+is W infinity with an au infinity that's
+the usual error term the thing that we
+
+ align:start position:0%
+the usual error term the thing that we
+ 
+
+ align:start position:0%
+the usual error term the thing that we
+probably can't make 0 and then this is
+
+ align:start position:0%
+probably can't make 0 and then this is
+ 
+
+ align:start position:0%
+probably can't make 0 and then this is
+the usual way groans Mulder higher term
+
+ align:start position:0%
+the usual way groans Mulder higher term
+ 
+
+ align:start position:0%
+the usual way groans Mulder higher term
+from there so I've spoken pretty quickly
+
+ align:start position:0%
+from there so I've spoken pretty quickly
+ 
+
+ align:start position:0%
+from there so I've spoken pretty quickly
+here and and I let me just conclude this
+
+ align:start position:0%
+here and and I let me just conclude this
+ 
+
+ align:start position:0%
+here and and I let me just conclude this
+is the limit equation is the correct
+
+ align:start position:0%
+is the limit equation is the correct
+ 
+
+ align:start position:0%
+is the limit equation is the correct
+limit equation it's the limit equation
+
+ align:start position:0%
+limit equation it's the limit equation
+ 
+
+ align:start position:0%
+limit equation it's the limit equation
+that we want to solve one way or another
+
+ align:start position:0%
+that we want to solve one way or another
+ 
+
+ align:start position:0%
+that we want to solve one way or another
+and taking alpha large is one way to get
+
+ align:start position:0%
+and taking alpha large is one way to get
+ 
+
+ align:start position:0%
+and taking alpha large is one way to get
+near the answer but we'll look at other
+
+ align:start position:0%
+near the answer but we'll look at other
+ 
+
+ align:start position:0%
+near the answer but we'll look at other
+ways now so this is this is this is
+
+ align:start position:0%
+ways now so this is this is this is
+ 
+
+ align:start position:0%
+ways now so this is this is this is
+really the correct equation to solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going the the the saddle point like
+
+ align:start position:0%
+going the the the saddle point like
+ 
+
+ align:start position:0%
+going the the the saddle point like
+Ron's multiplier rule okay okay so let
+
+ align:start position:0%
+Ron's multiplier rule okay okay so let
+ 
+
+ align:start position:0%
+Ron's multiplier rule okay okay so let
+me summarize what I've done so far so
+
+ align:start position:0%
+me summarize what I've done so far so
+ 
+
+ align:start position:0%
+me summarize what I've done so far so
+I'm my problem is when bu equal D is a
+
+ align:start position:0%
+I'm my problem is when bu equal D is a
+ 
+
+ align:start position:0%
+I'm my problem is when bu equal D is a
+fixed is a constraint that I would like
+
+ align:start position:0%
+fixed is a constraint that I would like
+ 
+
+ align:start position:0%
+fixed is a constraint that I would like
+to satisfy and one way to do it is to
+
+ align:start position:0%
+to satisfy and one way to do it is to
+ 
+
+ align:start position:0%
+to satisfy and one way to do it is to
+take alpha you know pretty near the
+
+ align:start position:0%
+take alpha you know pretty near the
+ 
+
+ align:start position:0%
+take alpha you know pretty near the
+largest number that the Machine will
+
+ align:start position:0%
+largest number that the Machine will
+ 
+
+ align:start position:0%
+largest number that the Machine will
+hold
+
+ align:start position:0%
+hold
+ 
+
+ align:start position:0%
+hold
+say 10 to the 15th put a really heavy
+
+ align:start position:0%
+say 10 to the 15th put a really heavy
+ 
+
+ align:start position:0%
+say 10 to the 15th put a really heavy
+weight on this but of course when you
+
+ align:start position:0%
+weight on this but of course when you
+ 
+
+ align:start position:0%
+weight on this but of course when you
+let alpha be 10 to the 15th I mean you
+
+ align:start position:0%
+let alpha be 10 to the 15th I mean you
+ 
+
+ align:start position:0%
+let alpha be 10 to the 15th I mean you
+can see that there's like some possible
+
+ align:start position:0%
+can see that there's like some possible
+ 
+
+ align:start position:0%
+can see that there's like some possible
+problems here when you let alpha have an
+
+ align:start position:0%
+problems here when you let alpha have an
+ 
+
+ align:start position:0%
+problems here when you let alpha have an
+enormous weight you're really tilting
+
+ align:start position:0%
+enormous weight you're really tilting
+ 
+
+ align:start position:0%
+enormous weight you're really tilting
+this matrix so strongly you know you
+
+ align:start position:0%
+this matrix so strongly you know you
+ 
+
+ align:start position:0%
+this matrix so strongly you know you
+couldn't let it be 10 to the 20th in
+
+ align:start position:0%
+couldn't let it be 10 to the 20th in
+ 
+
+ align:start position:0%
+couldn't let it be 10 to the 20th in
+single precision or you'd you'd wipe out
+
+ align:start position:0%
+single precision or you'd you'd wipe out
+ 
+
+ align:start position:0%
+single precision or you'd you'd wipe out
+a transpose a so it's a balance here so
+
+ align:start position:0%
+a transpose a so it's a balance here so
+ 
+
+ align:start position:0%
+a transpose a so it's a balance here so
+so I guess probably a lot of numerical
+
+ align:start position:0%
+so I guess probably a lot of numerical
+ 
+
+ align:start position:0%
+so I guess probably a lot of numerical
+analysts would say wrong way to do it
+
+ align:start position:0%
+analysts would say wrong way to do it
+ 
+
+ align:start position:0%
+analysts would say wrong way to do it
+the right way is solve this equation or
+
+ align:start position:0%
+the right way is solve this equation or
+ 
+
+ align:start position:0%
+the right way is solve this equation or
+else do it
+
+ align:start position:0%
+else do it
+ 
+
+ align:start position:0%
+else do it
+this other way but a lot of people with
+
+ align:start position:0%
+this other way but a lot of people with
+ 
+
+ align:start position:0%
+this other way but a lot of people with
+codes say ok you you know you're you're
+
+ align:start position:0%
+codes say ok you you know you're you're
+ 
+
+ align:start position:0%
+codes say ok you you know you're you're
+gonna be a nervous Nellie I'm just gonna
+
+ align:start position:0%
+gonna be a nervous Nellie I'm just gonna
+ 
+
+ align:start position:0%
+gonna be a nervous Nellie I'm just gonna
+use my code that's quite normal
+
+ align:start position:0%
+use my code that's quite normal
+ 
+
+ align:start position:0%
+use my code that's quite normal
+quite human response ok so this and this
+
+ align:start position:0%
+quite human response ok so this and this
+ 
+
+ align:start position:0%
+quite human response ok so this and this
+will frequently succeed ok so that's one
+
+ align:start position:0%
+will frequently succeed ok so that's one
+ 
+
+ align:start position:0%
+will frequently succeed ok so that's one
+method to do it not the method that the
+
+ align:start position:0%
+method to do it not the method that the
+ 
+
+ align:start position:0%
+method to do it not the method that the
+professionals in numerical analysis
+
+ align:start position:0%
+professionals in numerical analysis
+ 
+
+ align:start position:0%
+professionals in numerical analysis
+maybe I'm thinking for example the book
+
+ align:start position:0%
+maybe I'm thinking for example the book
+ 
+
+ align:start position:0%
+maybe I'm thinking for example the book
+by Golub van loan if you know that book
+
+ align:start position:0%
+by Golub van loan if you know that book
+ 
+
+ align:start position:0%
+by Golub van loan if you know that book
+that that's that would discuss this
+
+ align:start position:0%
+that that's that would discuss this
+ 
+
+ align:start position:0%
+that that's that would discuss this
+problem and it would actually discuss
+
+ align:start position:0%
+problem and it would actually discuss
+ 
+
+ align:start position:0%
+problem and it would actually discuss
+this third method of this null space
+
+ align:start position:0%
+this third method of this null space
+ 
+
+ align:start position:0%
+this third method of this null space
+method of solving it ok maybe I'll just
+
+ align:start position:0%
+method of solving it ok maybe I'll just
+ 
+
+ align:start position:0%
+method of solving it ok maybe I'll just
+go to that null space method and I so so
+
+ align:start position:0%
+go to that null space method and I so so
+ 
+
+ align:start position:0%
+go to that null space method and I so so
+this was one way another way is solve bu
+
+ align:start position:0%
+this was one way another way is solve bu
+ 
+
+ align:start position:0%
+this was one way another way is solve bu
+equal D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remember remember again we only have
+
+ align:start position:0%
+and remember remember again we only have
+ 
+
+ align:start position:0%
+and remember remember again we only have
+P equations we have n unknowns so
+
+ align:start position:0%
+P equations we have n unknowns so
+ 
+
+ align:start position:0%
+P equations we have n unknowns so
+there's going to be freedom in the
+
+ align:start position:0%
+there's going to be freedom in the
+ 
+
+ align:start position:0%
+there's going to be freedom in the
+solution so so there's we have to
+
+ align:start position:0%
+solution so so there's we have to
+ 
+
+ align:start position:0%
+solution so so there's we have to
+identify a particular solution there's a
+
+ align:start position:0%
+identify a particular solution there's a
+ 
+
+ align:start position:0%
+identify a particular solution there's a
+lot of freedom in that particular
+
+ align:start position:0%
+lot of freedom in that particular
+ 
+
+ align:start position:0%
+lot of freedom in that particular
+solution and then we can add to it and
+
+ align:start position:0%
+solution and then we can add to it and
+ 
+
+ align:start position:0%
+solution and then we can add to it and
+this is going to the null space is going
+
+ align:start position:0%
+this is going to the null space is going
+ 
+
+ align:start position:0%
+this is going to the null space is going
+to be n minus P dimensions n minus P
+
+ align:start position:0%
+to be n minus P dimensions n minus P
+ 
+
+ align:start position:0%
+to be n minus P dimensions n minus P
+degrees of freedom in in the null space
+
+ align:start position:0%
+degrees of freedom in in the null space
+ 
+
+ align:start position:0%
+degrees of freedom in in the null space
+it's that's the dimension of the null
+
+ align:start position:0%
+it's that's the dimension of the null
+ 
+
+ align:start position:0%
+it's that's the dimension of the null
+space n minus P I'm assuming that B has
+
+ align:start position:0%
+space n minus P I'm assuming that B has
+ 
+
+ align:start position:0%
+space n minus P I'm assuming that B has
+full rank P but P is a small number
+
+ align:start position:0%
+full rank P but P is a small number
+ 
+
+ align:start position:0%
+full rank P but P is a small number
+compared to where okay so how do you
+
+ align:start position:0%
+compared to where okay so how do you
+ 
+
+ align:start position:0%
+compared to where okay so how do you
+find a particular solution how do you
+
+ align:start position:0%
+find a particular solution how do you
+ 
+
+ align:start position:0%
+find a particular solution how do you
+find the null space solution as I said
+
+ align:start position:0%
+find the null space solution as I said
+ 
+
+ align:start position:0%
+find the null space solution as I said
+that's what I should be explaining in
+
+ align:start position:0%
+that's what I should be explaining in
+ 
+
+ align:start position:0%
+that's what I should be explaining in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course we do it in 1806 but we do
+
+ align:start position:0%
+and of course we do it in 1806 but we do
+ 
+
+ align:start position:0%
+and of course we do it in 1806 but we do
+it with a three by three matrix and we
+
+ align:start position:0%
+it with a three by three matrix and we
+ 
+
+ align:start position:0%
+it with a three by three matrix and we
+practically you know we do it by hand
+
+ align:start position:0%
+practically you know we do it by hand
+ 
+
+ align:start position:0%
+practically you know we do it by hand
+we're here we're talking about matrices
+
+ align:start position:0%
+we're here we're talking about matrices
+ 
+
+ align:start position:0%
+we're here we're talking about matrices
+of order thousands or millions we don't
+
+ align:start position:0%
+of order thousands or millions we don't
+ 
+
+ align:start position:0%
+of order thousands or millions we don't
+do those by hand and we better not do it
+
+ align:start position:0%
+do those by hand and we better not do it
+ 
+
+ align:start position:0%
+do those by hand and we better not do it
+in an unstable way so the question is
+
+ align:start position:0%
+in an unstable way so the question is
+ 
+
+ align:start position:0%
+in an unstable way so the question is
+what's a good way to do it and really
+
+ align:start position:0%
+what's a good way to do it and really
+ 
+
+ align:start position:0%
+what's a good way to do it and really
+the heart of modern numerical analysis
+
+ align:start position:0%
+the heart of modern numerical analysis
+ 
+
+ align:start position:0%
+the heart of modern numerical analysis
+is orthogonalize stuff get orthogonal
+
+ align:start position:0%
+is orthogonalize stuff get orthogonal
+ 
+
+ align:start position:0%
+is orthogonalize stuff get orthogonal
+vectors because if you have orthogonal
+
+ align:start position:0%
+vectors because if you have orthogonal
+ 
+
+ align:start position:0%
+vectors because if you have orthogonal
+vectors they don't get out of scale they
+
+ align:start position:0%
+vectors they don't get out of scale they
+ 
+
+ align:start position:0%
+vectors they don't get out of scale they
+the the numbers involved don't become
+
+ align:start position:0%
+the the numbers involved don't become
+ 
+
+ align:start position:0%
+the the numbers involved don't become
+unstable and the standard
+
+ align:start position:0%
+unstable and the standard
+ 
+
+ align:start position:0%
+unstable and the standard
+orthogonalization process is
+
+ align:start position:0%
+orthogonalization process is
+ 
+
+ align:start position:0%
+orthogonalization process is
+gram-schmidt that's right those are the
+
+ align:start position:0%
+gram-schmidt that's right those are the
+ 
+
+ align:start position:0%
+gram-schmidt that's right those are the
+words we all think of if I have a bunch
+
+ align:start position:0%
+words we all think of if I have a bunch
+ 
+
+ align:start position:0%
+words we all think of if I have a bunch
+of vectors I have to make them
+
+ align:start position:0%
+of vectors I have to make them
+ 
+
+ align:start position:0%
+of vectors I have to make them
+orthogonal I want to make them
+
+ align:start position:0%
+orthogonal I want to make them
+ 
+
+ align:start position:0%
+orthogonal I want to make them
+orthogonal then I use well gram-schmidt
+
+ align:start position:0%
+orthogonal then I use well gram-schmidt
+ 
+
+ align:start position:0%
+orthogonal then I use well gram-schmidt
+is what we think of but actually MATLAB
+
+ align:start position:0%
+is what we think of but actually MATLAB
+ 
+
+ align:start position:0%
+is what we think of but actually MATLAB
+doesn't use gram-schmidt doesn't use the
+
+ align:start position:0%
+doesn't use gram-schmidt doesn't use the
+ 
+
+ align:start position:0%
+doesn't use gram-schmidt doesn't use the
+usual grams gram schmidt as they as gram
+
+ align:start position:0%
+usual grams gram schmidt as they as gram
+ 
+
+ align:start position:0%
+usual grams gram schmidt as they as gram
+and schmidt thought of it
+
+ align:start position:0%
+and schmidt thought of it
+ 
+
+ align:start position:0%
+and schmidt thought of it
+Grint MATLAB goes a different route to
+
+ align:start position:0%
+Grint MATLAB goes a different route to
+ 
+
+ align:start position:0%
+Grint MATLAB goes a different route to
+the same conclusion so let me just
+
+ align:start position:0%
+the same conclusion so let me just
+ 
+
+ align:start position:0%
+the same conclusion so let me just
+remind you what what gram-schmidt
+
+ align:start position:0%
+remind you what what gram-schmidt
+ 
+
+ align:start position:0%
+remind you what what gram-schmidt
+produced and and let me put in the name
+
+ align:start position:0%
+produced and and let me put in the name
+ 
+
+ align:start position:0%
+produced and and let me put in the name
+of the numerical analysts long after
+
+ align:start position:0%
+of the numerical analysts long after
+ 
+
+ align:start position:0%
+of the numerical analysts long after
+Graham and Schmidt its householder it
+
+ align:start position:0%
+Graham and Schmidt its householder it
+ 
+
+ align:start position:0%
+Graham and Schmidt its householder it
+was a guy from Tennessee with good ideas
+
+ align:start position:0%
+was a guy from Tennessee with good ideas
+ 
+
+ align:start position:0%
+was a guy from Tennessee with good ideas
+so he had another way to the same
+
+ align:start position:0%
+so he had another way to the same
+ 
+
+ align:start position:0%
+so he had another way to the same
+concludes same answer which is this
+
+ align:start position:0%
+concludes same answer which is this
+ 
+
+ align:start position:0%
+concludes same answer which is this
+factorization so we take our matrix
+
+ align:start position:0%
+factorization so we take our matrix
+ 
+
+ align:start position:0%
+factorization so we take our matrix
+often it's a in in 1806 and we factor it
+
+ align:start position:0%
+often it's a in in 1806 and we factor it
+ 
+
+ align:start position:0%
+often it's a in in 1806 and we factor it
+we we want to orthogonalize its columns
+
+ align:start position:0%
+we we want to orthogonalize its columns
+ 
+
+ align:start position:0%
+we we want to orthogonalize its columns
+so the columns of a get orthogonalize
+
+ align:start position:0%
+so the columns of a get orthogonalize
+ 
+
+ align:start position:0%
+so the columns of a get orthogonalize
+into the columns of q so this is this is
+
+ align:start position:0%
+into the columns of q so this is this is
+ 
+
+ align:start position:0%
+into the columns of q so this is this is
+the guy then that we this has the
+
+ align:start position:0%
+the guy then that we this has the
+ 
+
+ align:start position:0%
+the guy then that we this has the
+orthogonal columns and then of course
+
+ align:start position:0%
+orthogonal columns and then of course
+ 
+
+ align:start position:0%
+orthogonal columns and then of course
+there's some connection between the
+
+ align:start position:0%
+there's some connection between the
+ 
+
+ align:start position:0%
+there's some connection between the
+original columns and the orthogonal
+
+ align:start position:0%
+original columns and the orthogonal
+ 
+
+ align:start position:0%
+original columns and the orthogonal
+columns and the connection is by a
+
+ align:start position:0%
+columns and the connection is by a
+ 
+
+ align:start position:0%
+columns and the connection is by a
+triangular matrix our upper triangular
+
+ align:start position:0%
+triangular matrix our upper triangular
+ 
+
+ align:start position:0%
+triangular matrix our upper triangular
+upper triangular
+
+ align:start position:0%
+upper triangular
+ 
+
+ align:start position:0%
+upper triangular
+I don't know if you remember that from
+
+ align:start position:0%
+I don't know if you remember that from
+ 
+
+ align:start position:0%
+I don't know if you remember that from
+1806 it kind of what I you typically do
+
+ align:start position:0%
+1806 it kind of what I you typically do
+ 
+
+ align:start position:0%
+1806 it kind of what I you typically do
+as I explained gram-schmidt the usual as
+
+ align:start position:0%
+as I explained gram-schmidt the usual as
+ 
+
+ align:start position:0%
+as I explained gram-schmidt the usual as
+they knew it and then at the last minute
+
+ align:start position:0%
+they knew it and then at the last minute
+ 
+
+ align:start position:0%
+they knew it and then at the last minute
+I pull Q&R out as a way to express the
+
+ align:start position:0%
+I pull Q&R out as a way to express the
+ 
+
+ align:start position:0%
+I pull Q&R out as a way to express the
+result okay so it's it's the result we
+
+ align:start position:0%
+result okay so it's it's the result we
+ 
+
+ align:start position:0%
+result okay so it's it's the result we
+want and not the particular gram-schmidt
+
+ align:start position:0%
+want and not the particular gram-schmidt
+ 
+
+ align:start position:0%
+want and not the particular gram-schmidt
+way to get there and householder produce
+
+ align:start position:0%
+way to get there and householder produce
+ 
+
+ align:start position:0%
+way to get there and householder produce
+is a better way to get there okay but
+
+ align:start position:0%
+is a better way to get there okay but
+ 
+
+ align:start position:0%
+is a better way to get there okay but
+the main point is that if a matrix has
+
+ align:start position:0%
+the main point is that if a matrix has
+ 
+
+ align:start position:0%
+the main point is that if a matrix has
+independent columns or even if it hasn't
+
+ align:start position:0%
+independent columns or even if it hasn't
+ 
+
+ align:start position:0%
+independent columns or even if it hasn't
+but if it has independent columns and we
+
+ align:start position:0%
+but if it has independent columns and we
+ 
+
+ align:start position:0%
+but if it has independent columns and we
+know what everything about it
+
+ align:start position:0%
+know what everything about it
+ 
+
+ align:start position:0%
+know what everything about it
+that we can factor it in we can
+
+ align:start position:0%
+that we can factor it in we can
+ 
+
+ align:start position:0%
+that we can factor it in we can
+orthogonalize those columns in fact we
+
+ align:start position:0%
+orthogonalize those columns in fact we
+ 
+
+ align:start position:0%
+orthogonalize those columns in fact we
+can here's what I'm leading to this B
+
+ align:start position:0%
+can here's what I'm leading to this B
+ 
+
+ align:start position:0%
+can here's what I'm leading to this B
+transpose I'm remembering has this shape
+
+ align:start position:0%
+transpose I'm remembering has this shape
+ 
+
+ align:start position:0%
+transpose I'm remembering has this shape
+because B was at that shape so so it's B
+
+ align:start position:0%
+because B was at that shape so so it's B
+ 
+
+ align:start position:0%
+because B was at that shape so so it's B
+transpose that I'm going to do grams
+
+ align:start position:0%
+transpose that I'm going to do grams
+ 
+
+ align:start position:0%
+transpose that I'm going to do grams
+that I'm going to do gram-schmidt
+
+ align:start position:0%
+that I'm going to do gram-schmidt
+ 
+
+ align:start position:0%
+that I'm going to do gram-schmidt
+householder use so this will be the
+
+ align:start position:0%
+householder use so this will be the
+ 
+
+ align:start position:0%
+householder use so this will be the
+command in MATLAB is Q are equals
+
+ align:start position:0%
+command in MATLAB is Q are equals
+ 
+
+ align:start position:0%
+command in MATLAB is Q are equals
+it's gram-schmidt it could be we could
+
+ align:start position:0%
+it's gram-schmidt it could be we could
+ 
+
+ align:start position:0%
+it's gram-schmidt it could be we could
+have used the letters G and s but since
+
+ align:start position:0%
+have used the letters G and s but since
+ 
+
+ align:start position:0%
+have used the letters G and s but since
+we don't use their actual method anymore
+
+ align:start position:0%
+we don't use their actual method anymore
+ 
+
+ align:start position:0%
+we don't use their actual method anymore
+we could use the letter h h for a
+
+ align:start position:0%
+we could use the letter h h for a
+ 
+
+ align:start position:0%
+we could use the letter h h for a
+householder or something but it's QR of
+
+ align:start position:0%
+householder or something but it's QR of
+ 
+
+ align:start position:0%
+householder or something but it's QR of
+in this case b transpose is what we want
+
+ align:start position:0%
+in this case b transpose is what we want
+ 
+
+ align:start position:0%
+in this case b transpose is what we want
+okay so what what that very frequently
+
+ align:start position:0%
+okay so what what that very frequently
+ 
+
+ align:start position:0%
+okay so what what that very frequently
+used command in matlab produces is q and
+
+ align:start position:0%
+used command in matlab produces is q and
+ 
+
+ align:start position:0%
+used command in matlab produces is q and
+r and it produces a square matrix q
+
+ align:start position:0%
+r and it produces a square matrix q
+ 
+
+ align:start position:0%
+r and it produces a square matrix q
+where these columns the columns of of
+
+ align:start position:0%
+where these columns the columns of of
+ 
+
+ align:start position:0%
+where these columns the columns of of
+the first part q1 transpose are our
+
+ align:start position:0%
+the first part q1 transpose are our
+ 
+
+ align:start position:0%
+the first part q1 transpose are our
+orthogonalize versions of these columns
+
+ align:start position:0%
+orthogonalize versions of these columns
+ 
+
+ align:start position:0%
+orthogonalize versions of these columns
+and the are that it just tells us the
+
+ align:start position:0%
+and the are that it just tells us the
+ 
+
+ align:start position:0%
+and the are that it just tells us the
+connection between then it also produces
+
+ align:start position:0%
+connection between then it also produces
+ 
+
+ align:start position:0%
+connection between then it also produces
+and this is handy as you'll see the
+
+ align:start position:0%
+and this is handy as you'll see the
+ 
+
+ align:start position:0%
+and this is handy as you'll see the
+algorithm also produces n minus P more
+
+ align:start position:0%
+algorithm also produces n minus P more
+ 
+
+ align:start position:0%
+algorithm also produces n minus P more
+columns that are orthogonal to these
+
+ align:start position:0%
+columns that are orthogonal to these
+ 
+
+ align:start position:0%
+columns that are orthogonal to these
+guys so it produces a complete
+
+ align:start position:0%
+guys so it produces a complete
+ 
+
+ align:start position:0%
+guys so it produces a complete
+orthonormal basis a complete set of n
+
+ align:start position:0%
+orthonormal basis a complete set of n
+ 
+
+ align:start position:0%
+orthonormal basis a complete set of n
+columns altogether q1 transpose has the
+
+ align:start position:0%
+columns altogether q1 transpose has the
+ 
+
+ align:start position:0%
+columns altogether q1 transpose has the
+columns that we that really that are
+
+ align:start position:0%
+columns that we that really that are
+ 
+
+ align:start position:0%
+columns that we that really that are
+associated with these columns and then
+
+ align:start position:0%
+associated with these columns and then
+ 
+
+ align:start position:0%
+associated with these columns and then
+there will be these are going to be
+
+ align:start position:0%
+there will be these are going to be
+ 
+
+ align:start position:0%
+there will be these are going to be
+associated with a null space and of
+
+ align:start position:0%
+associated with a null space and of
+ 
+
+ align:start position:0%
+associated with a null space and of
+course so out of this I see that
+
+ align:start position:0%
+course so out of this I see that
+ 
+
+ align:start position:0%
+course so out of this I see that
+actually B transpose is Q 1 transpose
+
+ align:start position:0%
+actually B transpose is Q 1 transpose
+ 
+
+ align:start position:0%
+actually B transpose is Q 1 transpose
+are so we're doing a you could say this
+
+ align:start position:0%
+are so we're doing a you could say this
+ 
+
+ align:start position:0%
+are so we're doing a you could say this
+is the reduced factorization with only P
+
+ align:start position:0%
+is the reduced factorization with only P
+ 
+
+ align:start position:0%
+is the reduced factorization with only P
+columns and this is the full picture
+
+ align:start position:0%
+columns and this is the full picture
+ 
+
+ align:start position:0%
+columns and this is the full picture
+with the other n minus P columns that
+
+ align:start position:0%
+with the other n minus P columns that
+ 
+
+ align:start position:0%
+with the other n minus P columns that
+are orthogonal and the reason that's
+
+ align:start position:0%
+are orthogonal and the reason that's
+ 
+
+ align:start position:0%
+are orthogonal and the reason that's
+handy is they tell us about the null
+
+ align:start position:0%
+handy is they tell us about the null
+ 
+
+ align:start position:0%
+handy is they tell us about the null
+space so now I want to identify out of
+
+ align:start position:0%
+space so now I want to identify out of
+ 
+
+ align:start position:0%
+space so now I want to identify out of
+this a particular solution and the
+
+ align:start position:0%
+this a particular solution and the
+ 
+
+ align:start position:0%
+this a particular solution and the
+general null space solution okay so so
+
+ align:start position:0%
+general null space solution okay so so
+ 
+
+ align:start position:0%
+general null space solution okay so so
+what are those so a project so a
+
+ align:start position:0%
+what are those so a project so a
+ 
+
+ align:start position:0%
+what are those so a project so a
+particular solution is going to be from
+
+ align:start position:0%
+particular solution is going to be from
+ 
+
+ align:start position:0%
+particular solution is going to be from
+the use use this part so so let's see I
+
+ align:start position:0%
+the use use this part so so let's see I
+ 
+
+ align:start position:0%
+the use use this part so so let's see I
+want a particular solution so maybe I
+
+ align:start position:0%
+want a particular solution so maybe I
+ 
+
+ align:start position:0%
+want a particular solution so maybe I
+better so be transposing that is R
+
+ align:start position:0%
+better so be transposing that is R
+ 
+
+ align:start position:0%
+better so be transposing that is R
+transpose Q what okay so now I'm
+
+ align:start position:0%
+transpose Q what okay so now I'm
+ 
+
+ align:start position:0%
+transpose Q what okay so now I'm
+prepared to solve yeah so now it's all
+
+ align:start position:0%
+prepared to solve yeah so now it's all
+ 
+
+ align:start position:0%
+prepared to solve yeah so now it's all
+step one is the particular solution I
+
+ align:start position:0%
+step one is the particular solution I
+ 
+
+ align:start position:0%
+step one is the particular solution I
+want to get B u particular equal D okay
+
+ align:start position:0%
+want to get B u particular equal D okay
+ 
+
+ align:start position:0%
+want to get B u particular equal D okay
+alright but now I know B I've been
+
+ align:start position:0%
+alright but now I know B I've been
+ 
+
+ align:start position:0%
+alright but now I know B I've been
+nicely factored so this is our transpose
+
+ align:start position:0%
+nicely factored so this is our transpose
+ 
+
+ align:start position:0%
+nicely factored so this is our transpose
+Q 1 u particular equal D so now comes
+
+ align:start position:0%
+Q 1 u particular equal D so now comes
+ 
+
+ align:start position:0%
+Q 1 u particular equal D so now comes
+the computation that the code has to do
+
+ align:start position:0%
+the computation that the code has to do
+ 
+
+ align:start position:0%
+the computation that the code has to do
+it has to invert that to get Q one times
+
+ align:start position:0%
+it has to invert that to get Q one times
+ 
+
+ align:start position:0%
+it has to invert that to get Q one times
+u particular equals our inverse
+
+ align:start position:0%
+u particular equals our inverse
+ 
+
+ align:start position:0%
+u particular equals our inverse
+transpose D so it had to solve a
+
+ align:start position:0%
+transpose D so it had to solve a
+ 
+
+ align:start position:0%
+transpose D so it had to solve a
+triangular system but of course a
+
+ align:start position:0%
+triangular system but of course a
+ 
+
+ align:start position:0%
+triangular system but of course a
+triangular system is quick to solve
+
+ align:start position:0%
+triangular system is quick to solve
+ 
+
+ align:start position:0%
+triangular system is quick to solve
+that's a good port here and then this
+
+ align:start position:0%
+that's a good port here and then this
+ 
+
+ align:start position:0%
+that's a good port here and then this
+final step to get u particular I have to
+
+ align:start position:0%
+final step to get u particular I have to
+ 
+
+ align:start position:0%
+final step to get u particular I have to
+put the inverse of that guy over there
+
+ align:start position:0%
+put the inverse of that guy over there
+ 
+
+ align:start position:0%
+put the inverse of that guy over there
+but that's because this has orthogonal
+
+ align:start position:0%
+but that's because this has orthogonal
+ 
+
+ align:start position:0%
+but that's because this has orthogonal
+columns that's just Q 1 transpose so
+
+ align:start position:0%
+columns that's just Q 1 transpose so
+ 
+
+ align:start position:0%
+columns that's just Q 1 transpose so
+there we go
+
+ align:start position:0%
+there we go
+ 
+
+ align:start position:0%
+there we go
+that's the inverse ax bar so that's what
+
+ align:start position:0%
+that's the inverse ax bar so that's what
+ 
+
+ align:start position:0%
+that's the inverse ax bar so that's what
+I should have done in 1806 I never did
+
+ align:start position:0%
+I should have done in 1806 I never did
+ 
+
+ align:start position:0%
+I should have done in 1806 I never did
+and and you get to see it what is the
+
+ align:start position:0%
+and and you get to see it what is the
+ 
+
+ align:start position:0%
+and and you get to see it what is the
+what's the what's a convenient
+
+ align:start position:0%
+what's the what's a convenient
+ 
+
+ align:start position:0%
+what's the what's a convenient
+particular solution everybody knows we
+
+ align:start position:0%
+particular solution everybody knows we
+ 
+
+ align:start position:0%
+particular solution everybody knows we
+got a whole whole collection of
+
+ align:start position:0%
+got a whole whole collection of
+ 
+
+ align:start position:0%
+got a whole whole collection of
+particular solutions we want to choose
+
+ align:start position:0%
+particular solutions we want to choose
+ 
+
+ align:start position:0%
+particular solutions we want to choose
+one that's that's that's nice and stable
+
+ align:start position:0%
+one that's that's that's nice and stable
+ 
+
+ align:start position:0%
+one that's that's that's nice and stable
+and the reason it's stable is that it
+
+ align:start position:0%
+and the reason it's stable is that it
+ 
+
+ align:start position:0%
+and the reason it's stable is that it
+works with orthogonal columns
+
+ align:start position:0%
+works with orthogonal columns
+ 
+
+ align:start position:0%
+works with orthogonal columns
+orthonormal even and triangular matrix
+
+ align:start position:0%
+orthonormal even and triangular matrix
+ 
+
+ align:start position:0%
+orthonormal even and triangular matrix
+whose for which linear systems are
+
+ align:start position:0%
+whose for which linear systems are
+ 
+
+ align:start position:0%
+whose for which linear systems are
+highly accurate okay so that's the
+
+ align:start position:0%
+highly accurate okay so that's the
+ 
+
+ align:start position:0%
+highly accurate okay so that's the
+particular solution now what's the null
+
+ align:start position:0%
+particular solution now what's the null
+ 
+
+ align:start position:0%
+particular solution now what's the null
+space solution what are the general
+
+ align:start position:0%
+space solution what are the general
+ 
+
+ align:start position:0%
+space solution what are the general
+solutions to a null space part one of
+
+ align:start position:0%
+solutions to a null space part one of
+ 
+
+ align:start position:0%
+solutions to a null space part one of
+the solutions to those well I could just
+
+ align:start position:0%
+the solutions to those well I could just
+ 
+
+ align:start position:0%
+the solutions to those well I could just
+go down the same steps this is our
+
+ align:start position:0%
+go down the same steps this is our
+ 
+
+ align:start position:0%
+go down the same steps this is our
+transpose q 1u null space equals 0 I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplied both sides this is a nice
+
+ align:start position:0%
+multiplied both sides this is a nice
+ 
+
+ align:start position:0%
+multiplied both sides this is a nice
+square invertible matrix i multiply by
+
+ align:start position:0%
+square invertible matrix i multiply by
+ 
+
+ align:start position:0%
+square invertible matrix i multiply by
+its inverse kills that so now I have q1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the the q1 is is really the heart
+
+ align:start position:0%
+times the the q1 is is really the heart
+ 
+
+ align:start position:0%
+times the the q1 is is really the heart
+of B so what vectors are perpendicular
+
+ align:start position:0%
+of B so what vectors are perpendicular
+ 
+
+ align:start position:0%
+of B so what vectors are perpendicular
+to q1 if I I hope I've got this right
+
+ align:start position:0%
+to q1 if I I hope I've got this right
+ 
+
+ align:start position:0%
+to q1 if I I hope I've got this right
+it's it's easy to mix up a transpose in
+
+ align:start position:0%
+it's it's easy to mix up a transpose in
+ 
+
+ align:start position:0%
+it's it's easy to mix up a transpose in
+the process so let me just pause to be
+
+ align:start position:0%
+the process so let me just pause to be
+ 
+
+ align:start position:0%
+the process so let me just pause to be
+sure I'm doing it correctly okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I hope did I check that I'd get it
+
+ align:start position:0%
+okay I hope did I check that I'd get it
+ 
+
+ align:start position:0%
+okay I hope did I check that I'd get it
+right yes okay so be is yep be yeah I
+
+ align:start position:0%
+right yes okay so be is yep be yeah I
+ 
+
+ align:start position:0%
+right yes okay so be is yep be yeah I
+could have written about what B is here
+
+ align:start position:0%
+could have written about what B is here
+ 
+
+ align:start position:0%
+could have written about what B is here
+since I have a factorization for I have
+
+ align:start position:0%
+since I have a factorization for I have
+ 
+
+ align:start position:0%
+since I have a factorization for I have
+B transpose as a product B is R 0 Q 1 Q
+
+ align:start position:0%
+B transpose as a product B is R 0 Q 1 Q
+ 
+
+ align:start position:0%
+B transpose as a product B is R 0 Q 1 Q
+2 okay okay
+
+ align:start position:0%
+2 okay okay
+ 
+
+ align:start position:0%
+2 okay okay
+and I'm looking for B you know I want I
+
+ align:start position:0%
+and I'm looking for B you know I want I
+ 
+
+ align:start position:0%
+and I'm looking for B you know I want I
+want to multiply by u null and get zero
+
+ align:start position:0%
+want to multiply by u null and get zero
+ 
+
+ align:start position:0%
+want to multiply by u null and get zero
+okay so so what should you know be you
+
+ align:start position:0%
+okay so so what should you know be you
+ 
+
+ align:start position:0%
+okay so so what should you know be you
+know should be the the the things okay
+
+ align:start position:0%
+know should be the the the things okay
+ 
+
+ align:start position:0%
+know should be the the the things okay
+this part is giving us a zero so this is
+
+ align:start position:0%
+this part is giving us a zero so this is
+ 
+
+ align:start position:0%
+this part is giving us a zero so this is
+this is like gone so really yeah you see
+
+ align:start position:0%
+this is like gone so really yeah you see
+ 
+
+ align:start position:0%
+this is like gone so really yeah you see
+that the two are the same
+
+ align:start position:0%
+that the two are the same
+ 
+
+ align:start position:0%
+that the two are the same
+what what is yeah so what vectors are
+
+ align:start position:0%
+what what is yeah so what vectors are
+ 
+
+ align:start position:0%
+what what is yeah so what vectors are
+perpendicular to to the to those the
+
+ align:start position:0%
+perpendicular to to the to those the
+ 
+
+ align:start position:0%
+perpendicular to to the to those the
+answer is the you know is a combination
+
+ align:start position:0%
+answer is the you know is a combination
+ 
+
+ align:start position:0%
+answer is the you know is a combination
+of the columns of Q 2 transpose its the
+
+ align:start position:0%
+of the columns of Q 2 transpose its the
+ 
+
+ align:start position:0%
+of the columns of Q 2 transpose its the
+Q 2 part that's telling us about the
+
+ align:start position:0%
+Q 2 part that's telling us about the
+ 
+
+ align:start position:0%
+Q 2 part that's telling us about the
+null space it's the kid was the q1 part
+
+ align:start position:0%
+null space it's the kid was the q1 part
+ 
+
+ align:start position:0%
+null space it's the kid was the q1 part
+that gave the particular solution it's
+
+ align:start position:0%
+that gave the particular solution it's
+ 
+
+ align:start position:0%
+that gave the particular solution it's
+the q2 part that gives the general
+
+ align:start position:0%
+the q2 part that gives the general
+ 
+
+ align:start position:0%
+the q2 part that gives the general
+solution in other words you know is q2
+
+ align:start position:0%
+solution in other words you know is q2
+ 
+
+ align:start position:0%
+solution in other words you know is q2
+transpose times any vector let me call
+
+ align:start position:0%
+transpose times any vector let me call
+ 
+
+ align:start position:0%
+transpose times any vector let me call
+it Z this is n easy and easy okay
+
+ align:start position:0%
+it Z this is n easy and easy okay
+ 
+
+ align:start position:0%
+it Z this is n easy and easy okay
+now this this has my n minus P degrees
+
+ align:start position:0%
+now this this has my n minus P degrees
+ 
+
+ align:start position:0%
+now this this has my n minus P degrees
+of freedom great or you
+
+ align:start position:0%
+of freedom great or you
+ 
+
+ align:start position:0%
+of freedom great or you
+okay sorry I'm trying to do quite a bit
+
+ align:start position:0%
+okay sorry I'm trying to do quite a bit
+ 
+
+ align:start position:0%
+okay sorry I'm trying to do quite a bit
+here I'm trying to say how you actually
+
+ align:start position:0%
+here I'm trying to say how you actually
+ 
+
+ align:start position:0%
+here I'm trying to say how you actually
+solve rectangular systems when you when
+
+ align:start position:0%
+solve rectangular systems when you when
+ 
+
+ align:start position:0%
+solve rectangular systems when you when
+they have not you know they're they're
+
+ align:start position:0%
+they have not you know they're they're
+ 
+
+ align:start position:0%
+they have not you know they're they're
+not determinate they they have there are
+
+ align:start position:0%
+not determinate they they have there are
+ 
+
+ align:start position:0%
+not determinate they they have there are
+many solutions this is a good particular
+
+ align:start position:0%
+many solutions this is a good particular
+ 
+
+ align:start position:0%
+many solutions this is a good particular
+solution to find and this is a good way
+
+ align:start position:0%
+solution to find and this is a good way
+ 
+
+ align:start position:0%
+solution to find and this is a good way
+to find the general solution the null
+
+ align:start position:0%
+to find the general solution the null
+ 
+
+ align:start position:0%
+to find the general solution the null
+space solution is as a combination of
+
+ align:start position:0%
+space solution is as a combination of
+ 
+
+ align:start position:0%
+space solution is as a combination of
+these these the other columns okay all
+
+ align:start position:0%
+these these the other columns okay all
+ 
+
+ align:start position:0%
+these these the other columns okay all
+right now we're done
+
+ align:start position:0%
+right now we're done
+ 
+
+ align:start position:0%
+right now we're done
+really because I now know what you looks
+
+ align:start position:0%
+really because I now know what you looks
+ 
+
+ align:start position:0%
+really because I now know what you looks
+like you looks like this part which I've
+
+ align:start position:0%
+like you looks like this part which I've
+ 
+
+ align:start position:0%
+like you looks like this part which I've
+computed and this part which has the
+
+ align:start position:0%
+computed and this part which has the
+ 
+
+ align:start position:0%
+computed and this part which has the
+freedom so now let me put those two
+
+ align:start position:0%
+freedom so now let me put those two
+ 
+
+ align:start position:0%
+freedom so now let me put those two
+parts together so now I want to minimize
+
+ align:start position:0%
+parts together so now I want to minimize
+ 
+
+ align:start position:0%
+parts together so now I want to minimize
+minimize so I'm I'm near the end here au
+
+ align:start position:0%
+minimize so I'm I'm near the end here au
+ 
+
+ align:start position:0%
+minimize so I'm I'm near the end here au
+minus B but a u is u particular and I
+
+ align:start position:0%
+minus B but a u is u particular and I
+ 
+
+ align:start position:0%
+minus B but a u is u particular and I
+had you particularly R Q 1 transpose R
+
+ align:start position:0%
+had you particularly R Q 1 transpose R
+ 
+
+ align:start position:0%
+had you particularly R Q 1 transpose R
+minus transpose D that's you particular
+
+ align:start position:0%
+minus transpose D that's you particular
+ 
+
+ align:start position:0%
+minus transpose D that's you particular
+plus you know and that's this this you
+
+ align:start position:0%
+plus you know and that's this this you
+ 
+
+ align:start position:0%
+plus you know and that's this this you
+know was also here you know was any q2
+
+ align:start position:0%
+know was also here you know was any q2
+ 
+
+ align:start position:0%
+know was also here you know was any q2
+transpose Z right that all that is you
+
+ align:start position:0%
+transpose Z right that all that is you
+ 
+
+ align:start position:0%
+transpose Z right that all that is you
+au minus B okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up to possibly screwing up on some
+
+ align:start position:0%
+up to possibly screwing up on some
+ 
+
+ align:start position:0%
+up to possibly screwing up on some
+transposes this is the right message so
+
+ align:start position:0%
+transposes this is the right message so
+ 
+
+ align:start position:0%
+transposes this is the right message so
+this is the purty so this is a fixed
+
+ align:start position:0%
+this is the purty so this is a fixed
+ 
+
+ align:start position:0%
+this is the purty so this is a fixed
+solution let me it's just I just want to
+
+ align:start position:0%
+solution let me it's just I just want to
+ 
+
+ align:start position:0%
+solution let me it's just I just want to
+write that in a different way
+
+ align:start position:0%
+write that in a different way
+ 
+
+ align:start position:0%
+write that in a different way
+minimize a q transpose z it's it's not
+
+ align:start position:0%
+minimize a q transpose z it's it's not
+ 
+
+ align:start position:0%
+minimize a q transpose z it's it's not
+we're minimizing over the Z's say you
+
+ align:start position:0%
+we're minimizing over the Z's say you
+ 
+
+ align:start position:0%
+we're minimizing over the Z's say you
+had n n components but somehow P of them
+
+ align:start position:0%
+had n n components but somehow P of them
+ 
+
+ align:start position:0%
+had n n components but somehow P of them
+were P degrees of freedom were used up
+
+ align:start position:0%
+were P degrees of freedom were used up
+ 
+
+ align:start position:0%
+were P degrees of freedom were used up
+by the constraint bu equal D and we have
+
+ align:start position:0%
+by the constraint bu equal D and we have
+ 
+
+ align:start position:0%
+by the constraint bu equal D and we have
+the N minus P true degrees of freedom
+
+ align:start position:0%
+the N minus P true degrees of freedom
+ 
+
+ align:start position:0%
+the N minus P true degrees of freedom
+are in the Z so there's this - the the B
+
+ align:start position:0%
+are in the Z so there's this - the the B
+ 
+
+ align:start position:0%
+are in the Z so there's this - the the B
+this is all known stuff a q1 transpose R
+
+ align:start position:0%
+this is all known stuff a q1 transpose R
+ 
+
+ align:start position:0%
+this is all known stuff a q1 transpose R
+- transpose d squared ok I'm there so
+
+ align:start position:0%
+- transpose d squared ok I'm there so
+ 
+
+ align:start position:0%
+- transpose d squared ok I'm there so
+this is this is our this is a standard
+
+ align:start position:0%
+this is this is our this is a standard
+ 
+
+ align:start position:0%
+this is this is our this is a standard
+minimization problem minimize so I call
+
+ align:start position:0%
+minimization problem minimize so I call
+ 
+
+ align:start position:0%
+minimization problem minimize so I call
+this a tilde z and I'll call all this
+
+ align:start position:0%
+this a tilde z and I'll call all this
+ 
+
+ align:start position:0%
+this a tilde z and I'll call all this
+stuff B tilde and the solution is found
+
+ align:start position:0%
+stuff B tilde and the solution is found
+ 
+
+ align:start position:0%
+stuff B tilde and the solution is found
+from the normal equations a trans a
+
+ align:start position:0%
+from the normal equations a trans a
+ 
+
+ align:start position:0%
+from the normal equations a trans a
+tilde transpose a tilde times the best
+
+ align:start position:0%
+tilde transpose a tilde times the best
+ 
+
+ align:start position:0%
+tilde transpose a tilde times the best
+zi the I'll put a hat on it to emphasize
+
+ align:start position:0%
+zi the I'll put a hat on it to emphasize
+ 
+
+ align:start position:0%
+zi the I'll put a hat on it to emphasize
+that it's the great one is a tilde
+
+ align:start position:0%
+that it's the great one is a tilde
+ 
+
+ align:start position:0%
+that it's the great one is a tilde
+transpose B tilde ok finish that process
+
+ align:start position:0%
+transpose B tilde ok finish that process
+ 
+
+ align:start position:0%
+transpose B tilde ok finish that process
+without leaving myself a lot of time for
+
+ align:start position:0%
+without leaving myself a lot of time for
+ 
+
+ align:start position:0%
+without leaving myself a lot of time for
+the other method conclusion here that
+
+ align:start position:0%
+the other method conclusion here that
+ 
+
+ align:start position:0%
+the other method conclusion here that
+after you've done the QR step the QR
+
+ align:start position:0%
+after you've done the QR step the QR
+ 
+
+ align:start position:0%
+after you've done the QR step the QR
+command and then after you've solved a
+
+ align:start position:0%
+command and then after you've solved a
+ 
+
+ align:start position:0%
+command and then after you've solved a
+linear system with the r transpose and
+
+ align:start position:0%
+linear system with the r transpose and
+ 
+
+ align:start position:0%
+linear system with the r transpose and
+you've multiplied by Q's and you've
+
+ align:start position:0%
+you've multiplied by Q's and you've
+ 
+
+ align:start position:0%
+you've multiplied by Q's and you've
+ended up with this problem with a new
+
+ align:start position:0%
+ended up with this problem with a new
+ 
+
+ align:start position:0%
+ended up with this problem with a new
+matrix a
+
+ align:start position:0%
+matrix a
+ 
+
+ align:start position:0%
+matrix a
+till then B tilde then you just do the
+
+ align:start position:0%
+till then B tilde then you just do the
+ 
+
+ align:start position:0%
+till then B tilde then you just do the
+normal equation so it's really the the
+
+ align:start position:0%
+normal equation so it's really the the
+ 
+
+ align:start position:0%
+normal equation so it's really the the
+the web will have the the code that
+
+ align:start position:0%
+the web will have the the code that
+ 
+
+ align:start position:0%
+the web will have the the code that
+takes those steps reaches its conclusion
+
+ align:start position:0%
+takes those steps reaches its conclusion
+ 
+
+ align:start position:0%
+takes those steps reaches its conclusion
+solves it
+
+ align:start position:0%
+solves it
+ 
+
+ align:start position:0%
+solves it
+okay so that's the null space method and
+
+ align:start position:0%
+okay so that's the null space method and
+ 
+
+ align:start position:0%
+okay so that's the null space method and
+it would be a method of choice when so Z
+
+ align:start position:0%
+it would be a method of choice when so Z
+ 
+
+ align:start position:0%
+it would be a method of choice when so Z
+has P minus n components n minus P
+
+ align:start position:0%
+has P minus n components n minus P
+ 
+
+ align:start position:0%
+has P minus n components n minus P
+components if P is near in then there
+
+ align:start position:0%
+components if P is near in then there
+ 
+
+ align:start position:0%
+components if P is near in then there
+are not many Z's and this is highly
+
+ align:start position:0%
+are not many Z's and this is highly
+ 
+
+ align:start position:0%
+are not many Z's and this is highly
+efficient okay so that the null space
+
+ align:start position:0%
+efficient okay so that the null space
+ 
+
+ align:start position:0%
+efficient okay so that the null space
+method is one way to go can I just in
+
+ align:start position:0%
+method is one way to go can I just in
+ 
+
+ align:start position:0%
+method is one way to go can I just in
+the remaining minutes go back to the the
+
+ align:start position:0%
+the remaining minutes go back to the the
+ 
+
+ align:start position:0%
+the remaining minutes go back to the the
+Lagrange multiplier idea so what's the
+
+ align:start position:0%
+Lagrange multiplier idea so what's the
+ 
+
+ align:start position:0%
+Lagrange multiplier idea so what's the
+Lagrangian player idea so the other so
+
+ align:start position:0%
+Lagrangian player idea so the other so
+ 
+
+ align:start position:0%
+Lagrangian player idea so the other so
+let me write the problem again as like
+
+ align:start position:0%
+let me write the problem again as like
+ 
+
+ align:start position:0%
+let me write the problem again as like
+wrongs we like it minimize au minus B
+
+ align:start position:0%
+wrongs we like it minimize au minus B
+ 
+
+ align:start position:0%
+wrongs we like it minimize au minus B
+squared subject to bu equal D that's the
+
+ align:start position:0%
+squared subject to bu equal D that's the
+ 
+
+ align:start position:0%
+squared subject to bu equal D that's the
+problem we're solving I should have
+
+ align:start position:0%
+problem we're solving I should have
+ 
+
+ align:start position:0%
+problem we're solving I should have
+written it earlier this is let me put a
+
+ align:start position:0%
+written it earlier this is let me put a
+ 
+
+ align:start position:0%
+written it earlier this is let me put a
+star here because this is our problem
+
+ align:start position:0%
+star here because this is our problem
+ 
+
+ align:start position:0%
+star here because this is our problem
+okay so one way or tackle it was put
+
+ align:start position:0%
+okay so one way or tackle it was put
+ 
+
+ align:start position:0%
+okay so one way or tackle it was put
+that take that constraint give it a
+
+ align:start position:0%
+that take that constraint give it a
+ 
+
+ align:start position:0%
+that take that constraint give it a
+heavyweight that was method 1 method 2
+
+ align:start position:0%
+heavyweight that was method 1 method 2
+ 
+
+ align:start position:0%
+heavyweight that was method 1 method 2
+was solve this constraint in full detail
+
+ align:start position:0%
+was solve this constraint in full detail
+ 
+
+ align:start position:0%
+was solve this constraint in full detail
+get the Z's that remain as degrees of
+
+ align:start position:0%
+get the Z's that remain as degrees of
+ 
+
+ align:start position:0%
+get the Z's that remain as degrees of
+freedom plug in U particular plus u null
+
+ align:start position:0%
+freedom plug in U particular plus u null
+ 
+
+ align:start position:0%
+freedom plug in U particular plus u null
+space into here and then you have a
+
+ align:start position:0%
+space into here and then you have a
+ 
+
+ align:start position:0%
+space into here and then you have a
+problem in the Z that's method 2 now so
+
+ align:start position:0%
+problem in the Z that's method 2 now so
+ 
+
+ align:start position:0%
+problem in the Z that's method 2 now so
+method 3 is like wrong so method 3 would
+
+ align:start position:0%
+method 3 is like wrong so method 3 would
+ 
+
+ align:start position:0%
+method 3 is like wrong so method 3 would
+say okay what does the groans do L we
+
+ align:start position:0%
+say okay what does the groans do L we
+ 
+
+ align:start position:0%
+say okay what does the groans do L we
+call it the Lagrangian he takes this au
+
+ align:start position:0%
+call it the Lagrangian he takes this au
+ 
+
+ align:start position:0%
+call it the Lagrangian he takes this au
+minus B squared and adds to it some
+
+ align:start position:0%
+minus B squared and adds to it some
+ 
+
+ align:start position:0%
+minus B squared and adds to it some
+LaGrant applier and I'll use maybe the
+
+ align:start position:0%
+LaGrant applier and I'll use maybe the
+ 
+
+ align:start position:0%
+LaGrant applier and I'll use maybe the
+standard lambda times the
+
+ align:start position:0%
+standard lambda times the
+ 
+
+ align:start position:0%
+standard lambda times the
+you bu - d right that's the grounders
+
+ align:start position:0%
+you bu - d right that's the grounders
+ 
+
+ align:start position:0%
+you bu - d right that's the grounders
+idea you recognize Lagrange's idea take
+
+ align:start position:0%
+idea you recognize Lagrange's idea take
+ 
+
+ align:start position:0%
+idea you recognize Lagrange's idea take
+the constraint multiply it by a
+
+ align:start position:0%
+the constraint multiply it by a
+ 
+
+ align:start position:0%
+the constraint multiply it by a
+multiplier in fact this is P constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so P lambdas lambda is a vector of P
+
+ align:start position:0%
+so so P lambdas lambda is a vector of P
+ 
+
+ align:start position:0%
+so so P lambdas lambda is a vector of P
+multipliers P multiply not just a single
+
+ align:start position:0%
+multipliers P multiply not just a single
+ 
+
+ align:start position:0%
+multipliers P multiply not just a single
+one because we've got P constraints and
+
+ align:start position:0%
+one because we've got P constraints and
+ 
+
+ align:start position:0%
+one because we've got P constraints and
+now what does lagron jus he sets the
+
+ align:start position:0%
+now what does lagron jus he sets the
+ 
+
+ align:start position:0%
+now what does lagron jus he sets the
+derivative the LD lambda well so let me
+
+ align:start position:0%
+derivative the LD lambda well so let me
+ 
+
+ align:start position:0%
+derivative the LD lambda well so let me
+do the d LD you first
+
+ align:start position:0%
+do the d LD you first
+ 
+
+ align:start position:0%
+do the d LD you first
+he sets the LD you to zero and the LD
+
+ align:start position:0%
+he sets the LD you to zero and the LD
+ 
+
+ align:start position:0%
+he sets the LD you to zero and the LD
+lambda 2 0 I could have started out with
+
+ align:start position:0%
+lambda 2 0 I could have started out with
+ 
+
+ align:start position:0%
+lambda 2 0 I could have started out with
+this method cuz it's gonna be it's gonna
+
+ align:start position:0%
+this method cuz it's gonna be it's gonna
+ 
+
+ align:start position:0%
+this method cuz it's gonna be it's gonna
+lead us to the equations faster what
+
+ align:start position:0%
+lead us to the equations faster what
+ 
+
+ align:start position:0%
+lead us to the equations faster what
+equations do we get from D LD u equal 0
+
+ align:start position:0%
+equations do we get from D LD u equal 0
+ 
+
+ align:start position:0%
+equations do we get from D LD u equal 0
+what's the what's the gradient with
+
+ align:start position:0%
+what's the what's the gradient with
+ 
+
+ align:start position:0%
+what's the what's the gradient with
+respect to you
+
+ align:start position:0%
+respect to you
+ 
+
+ align:start position:0%
+respect to you
+that gives us a transpose au oh they're
+
+ align:start position:0%
+that gives us a transpose au oh they're
+ 
+
+ align:start position:0%
+that gives us a transpose au oh they're
+probably we want to have here so that
+
+ align:start position:0%
+probably we want to have here so that
+ 
+
+ align:start position:0%
+probably we want to have here so that
+the numbers come out right we get a
+
+ align:start position:0%
+the numbers come out right we get a
+ 
+
+ align:start position:0%
+the numbers come out right we get a
+transpose au and another you part will
+
+ align:start position:0%
+transpose au and another you part will
+ 
+
+ align:start position:0%
+transpose au and another you part will
+be the B will be the B lambda that are
+
+ align:start position:0%
+be the B will be the B lambda that are
+ 
+
+ align:start position:0%
+be the B will be the B lambda that are
+taking the derivative of U will produce
+
+ align:start position:0%
+taking the derivative of U will produce
+ 
+
+ align:start position:0%
+taking the derivative of U will produce
+a a B transpose lambda out of that yep a
+
+ align:start position:0%
+a a B transpose lambda out of that yep a
+ 
+
+ align:start position:0%
+a a B transpose lambda out of that yep a
+B transpose lambda out of that and then
+
+ align:start position:0%
+B transpose lambda out of that and then
+ 
+
+ align:start position:0%
+B transpose lambda out of that and then
+in here will be a linear term in you
+
+ align:start position:0%
+in here will be a linear term in you
+ 
+
+ align:start position:0%
+in here will be a linear term in you
+that we might as well put on the
+
+ align:start position:0%
+that we might as well put on the
+ 
+
+ align:start position:0%
+that we might as well put on the
+right-hand side as a transpose B
+
+ align:start position:0%
+right-hand side as a transpose B
+ 
+
+ align:start position:0%
+right-hand side as a transpose B
+familiar okay and what about the LD
+
+ align:start position:0%
+familiar okay and what about the LD
+ 
+
+ align:start position:0%
+familiar okay and what about the LD
+lambda well that's just our constraint
+
+ align:start position:0%
+lambda well that's just our constraint
+ 
+
+ align:start position:0%
+lambda well that's just our constraint
+be u equals D right when I take the I
+
+ align:start position:0%
+be u equals D right when I take the I
+ 
+
+ align:start position:0%
+be u equals D right when I take the I
+always having built in the constraint
+
+ align:start position:0%
+always having built in the constraint
+ 
+
+ align:start position:0%
+always having built in the constraint
+when I take the derivative the specter
+
+ align:start position:0%
+when I take the derivative the specter
+ 
+
+ align:start position:0%
+when I take the derivative the specter
+lambda the constraint just comes back
+
+ align:start position:0%
+lambda the constraint just comes back
+ 
+
+ align:start position:0%
+lambda the constraint just comes back
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+now method 3 solve that system and I
+
+ align:start position:0%
+now method 3 solve that system and I
+ 
+
+ align:start position:0%
+now method 3 solve that system and I
+guess what I wanted to what I want to
+
+ align:start position:0%
+guess what I wanted to what I want to
+ 
+
+ align:start position:0%
+guess what I wanted to what I want to
+say in the remaining 30 seconds is that
+
+ align:start position:0%
+say in the remaining 30 seconds is that
+ 
+
+ align:start position:0%
+say in the remaining 30 seconds is that
+solving this system is the same as this
+
+ align:start position:0%
+solving this system is the same as this
+ 
+
+ align:start position:0%
+solving this system is the same as this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+those two are this are exactly the same
+
+ align:start position:0%
+those two are this are exactly the same
+ 
+
+ align:start position:0%
+those two are this are exactly the same
+I can get so that's a system with three
+
+ align:start position:0%
+I can get so that's a system with three
+ 
+
+ align:start position:0%
+I can get so that's a system with three
+parts but I can as always so maybe I can
+
+ align:start position:0%
+parts but I can as always so maybe I can
+ 
+
+ align:start position:0%
+parts but I can as always so maybe I can
+even get there can I can you see that if
+
+ align:start position:0%
+even get there can I can you see that if
+ 
+
+ align:start position:0%
+even get there can I can you see that if
+I take this part and I subtract a
+
+ align:start position:0%
+I take this part and I subtract a
+ 
+
+ align:start position:0%
+I take this part and I subtract a
+transpose times the top row from the
+
+ align:start position:0%
+transpose times the top row from the
+ 
+
+ align:start position:0%
+transpose times the top row from the
+bottom row that will give me what will
+
+ align:start position:0%
+bottom row that will give me what will
+ 
+
+ align:start position:0%
+bottom row that will give me what will
+that give me you know let me just hope
+
+ align:start position:0%
+that give me you know let me just hope
+ 
+
+ align:start position:0%
+that give me you know let me just hope
+that it works
+
+ align:start position:0%
+that it works
+ 
+
+ align:start position:0%
+that it works
+well I won't actually the time is up
+
+ align:start position:0%
+well I won't actually the time is up
+ 
+
+ align:start position:0%
+well I won't actually the time is up
+it's asking too much to do even what
+
+ align:start position:0%
+it's asking too much to do even what
+ 
+
+ align:start position:0%
+it's asking too much to do even what
+this one piece of linear algebra they
+
+ align:start position:0%
+this one piece of linear algebra they
+ 
+
+ align:start position:0%
+this one piece of linear algebra they
+can be in the in the notes so so this
+
+ align:start position:0%
+can be in the in the notes so so this
+ 
+
+ align:start position:0%
+can be in the in the notes so so this
+system that we got as the correct limit
+
+ align:start position:0%
+system that we got as the correct limit
+ 
+
+ align:start position:0%
+system that we got as the correct limit
+equation is exactly the same one that
+
+ align:start position:0%
+equation is exactly the same one that
+ 
+
+ align:start position:0%
+equation is exactly the same one that
+lagron skits so that's one way this is a
+
+ align:start position:0%
+lagron skits so that's one way this is a
+ 
+
+ align:start position:0%
+lagron skits so that's one way this is a
+system with and plus P unknowns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the price you pay for going
+
+ align:start position:0%
+that's the price you pay for going
+ 
+
+ align:start position:0%
+that's the price you pay for going
+Lagrange's route you add piano this was
+
+ align:start position:0%
+Lagrange's route you add piano this was
+ 
+
+ align:start position:0%
+Lagrange's route you add piano this was
+a system with and minus P unknowns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's because you're using the
+
+ align:start position:0%
+that's because you're using the
+ 
+
+ align:start position:0%
+that's because you're using the
+constraints to reduce the problem and
+
+ align:start position:0%
+constraints to reduce the problem and
+ 
+
+ align:start position:0%
+constraints to reduce the problem and
+the original method one was a method
+
+ align:start position:0%
+the original method one was a method
+ 
+
+ align:start position:0%
+the original method one was a method
+with and unknowns the unknowns of U so
+
+ align:start position:0%
+with and unknowns the unknowns of U so
+ 
+
+ align:start position:0%
+with and unknowns the unknowns of U so
+you have the choice and n plus P that
+
+ align:start position:0%
+you have the choice and n plus P that
+ 
+
+ align:start position:0%
+you have the choice and n plus P that
+lagron should like and n minus P that
+
+ align:start position:0%
+lagron should like and n minus P that
+ 
+
+ align:start position:0%
+lagron should like and n minus P that
+ghaliban loan would prefer and usually
+
+ align:start position:0%
+ghaliban loan would prefer and usually
+ 
+
+ align:start position:0%
+ghaliban loan would prefer and usually
+it's method 2 or method 3 in is
+
+ align:start position:0%
+it's method 2 or method 3 in is
+ 
+
+ align:start position:0%
+it's method 2 or method 3 in is
+recommended but method 1 often used okay
+
+ align:start position:0%
+recommended but method 1 often used okay
+ 
+
+ align:start position:0%
+recommended but method 1 often used okay
+so that's the lecture on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this point that's today and next week
+
+ align:start position:0%
+at this point that's today and next week
+ 
+
+ align:start position:0%
+at this point that's today and next week
+comes the whole class of problems like
+
+ align:start position:0%
+comes the whole class of problems like
+ 
+
+ align:start position:0%
+comes the whole class of problems like
+finding velocities from displacements
+
+ align:start position:0%
+finding velocities from displacements
+ 
+
+ align:start position:0%
+finding velocities from displacements
+where alpha is a small parameter and
+
+ align:start position:0%
+where alpha is a small parameter and
+ 
+
+ align:start position:0%
+where alpha is a small parameter and
+then after that come discussions of the
+
+ align:start position:0%
+then after that come discussions of the
+ 
+
+ align:start position:0%
+then after that come discussions of the
+projects the part of the completed
+
+ align:start position:0%
+projects the part of the completed
+ 
+
+ align:start position:0%
+projects the part of the completed
+project ones and the upcoming extensions
+
+ align:start position:0%
+project ones and the upcoming extensions
+ 
+
+ align:start position:0%
+project ones and the upcoming extensions
+in the project tubes okay see you next
+
+ align:start position:0%
+in the project tubes okay see you next
+ 
+
+ align:start position:0%
+in the project tubes okay see you next
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+Thanks
\ No newline at end of file
diff --git a/y7lV5jwK27E.txt b/y7lV5jwK27E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1dbd745bb948f22948c08294fead85a47a478c5d
--- /dev/null
+++ b/y7lV5jwK27E.txt
@@ -0,0 +1,453 @@
+Hi.
+
+Today, we're going to do a
+really fun problem called
+
+geniuses and chocolates.
+
+And what this problem is
+exercising is your knowledge
+
+of properties of probability
+laws.
+
+So let me just clarify
+what I mean by that.
+
+Hopefully, by this point, you
+have already learned what the
+
+axioms of probability are.
+
+And properties of probability
+laws are essentially any rules
+
+that you can derive
+from those axioms.
+
+So take for example the fact
+that the probability of A
+
+union B is equal to the
+probability of A plus the
+
+probability of B minus the
+probability of the
+
+intersection.
+
+That's an example of a property
+of a probability law.
+
+So enough with the preamble.
+
+Let's see what the problem
+is asking us.
+
+In this problem, we have
+a class of students.
+
+And we're told that 60% of the
+students are geniuses.
+
+70% of the students
+love chocolate.
+
+So I would be in
+that category.
+
+And 40% fall into
+both categories.
+
+And our job is to determine
+the probability that a
+
+randomly selected student is
+neither a genius nor a
+
+chocolate lover.
+
+So first I just want to write
+down the information that
+
+we're given in the problem
+statement.
+
+So if you let G denote the event
+that a randomly selected
+
+student is a genius then the
+problem statement tells us
+
+that the probability of
+G is equal to 0.6.
+
+Similarly, if we let C denote
+the event that a randomly
+
+selected student is a chocolate
+lover, then we have
+
+that the probability of
+C is equal to 0.7.
+
+Lastly, we are told that the
+probability a randomly
+
+selected student falls into
+both categories is 0.4.
+
+And the way we can express
+that using the notation
+
+already on the board is
+probability of G intersect C
+
+is equal to 0.4.
+
+OK, now one way of approaching
+this problem is to essentially
+
+use this information and sort of
+massage it using properties
+
+of probability laws to
+get to our answer.
+
+Instead, I'm going to take a
+different approach, which I
+
+think will be helpful.
+
+So namely, we're going
+to use something
+
+called a Venn diagram.
+
+Now a Venn diagram is just a
+tool that's really useful for
+
+telling you how different sets
+relate to each other and how
+
+their corresponding
+probabilities
+
+relate to each other.
+
+So the way you usually draw this
+is you draw a rectangle,
+
+which denotes your sample space,
+which of course, we
+
+call omega.
+
+And then you draw two
+intersecting circles.
+
+So one to represent our geniuses
+and one to represent
+
+our chocolate lovers.
+
+And the reason why I drew them
+intersecting is because we
+
+know that there are 40% of the
+students in our class are both
+
+geniuses and chocolate lovers.
+
+OK, and the way you sort of
+interpret this diagram is the
+
+space outside these two circles
+correspond to students
+
+who are neither geniuses
+nor chocolate lovers.
+
+And so just keep in mind that
+the probability corresponding
+
+to these students on the
+outside, that's actually what
+
+we're looking for.
+
+Similarly, students in this
+little shape, this tear drop
+
+in the middle, those would
+correspond to geniuses and
+
+chocolate lovers.
+
+You probably get the idea.
+
+So this is our Venn diagram.
+
+Now I'm going to give you guys
+a second trick if you will.
+
+And that is to work
+with partitions.
+
+So I believe you've seen
+partitions in lecture by now.
+
+And a partition is essentially a
+way of cutting up the sample
+
+space into pieces.
+
+But you need two properties
+to be true.
+
+So the pieces that you cut up
+your sample space into, they
+
+need to be disjoint, so
+they can't overlap.
+
+So for instance, G and C are
+not disjoint because they
+
+overlap in this tear
+drop region.
+
+Now the second thing that a
+partition has to satisfy is
+
+that if you put all the pieces
+together, they have to
+
+comprise the entire
+sample space.
+
+So I'm just going to put these
+labels down on my graph.
+
+X, Y, Z, and W. So X is
+everything outside the two
+
+circles but inside
+the rectangle.
+
+And just note, again, that what
+we're actually trying to
+
+solve in this problem is the
+probability of X, the
+
+probability that you're neither
+genius, because you're
+
+not in this circle, and you're
+not a chocolate lover, because
+
+you're not in this circle.
+
+So Y I'm using to refer
+to this sort of
+
+crescent moon shape.
+
+Z, I'm using to refer
+to this tear drop.
+
+And W, I'm using to refer
+to this shape.
+
+So, hopefully, you agree that
+X, Y, Z, and W form a
+
+partition because they
+don't overlap.
+
+So they are disjoint.
+
+And together they form omega.
+
+So now we're ready to
+do some computation.
+
+The first step is to sort of
+get the information we have
+
+written down here in terms
+of these new labels.
+
+So hopefully, you guys buy that
+G is just the union of Y
+
+and Z. And because Y and Z are
+disjoint, we get that the
+
+probability of the union is the
+sum of the probabilities.
+
+And, of course, we have from
+before that this is 0.6.
+
+Similarly, we have that the
+probability of C is equal to
+
+the probability of Z union W.
+And, again, using the fact
+
+that these two guys are
+disjoint, you get this
+
+expression.
+
+And that is equal to 0.7.
+
+OK, and the last piece of
+information, G intersects C
+
+corresponds to Z, or our tear
+drop, and so we have that the
+
+probability of Z is
+equal to 0.4.
+
+And now, if you notice,
+probability of Z shows up in
+
+these two equations.
+
+So we can just plug it in.
+
+So plug in 0.4 into
+this equation.
+
+We get P of Y plus 0.4 is 0.6.
+
+So that implies that
+P of Y is 0.2.
+
+That's just algebra.
+
+And similarly we have point.
+
+0.4 plus P of W is
+equal to 0.7.
+
+So that implies that
+P of W is 0.3.
+
+Again, that's just algebra.
+
+So now we're doing really well
+because we have a lot of
+
+information.
+
+We know the probability of Y,
+the probability of Z, the
+
+probability of W. But remember
+we're going for, we're trying
+
+to find the probability of X. So
+the way we finally put all
+
+this information together to
+solve for X is we use the
+
+axiom that tells us that 1 is
+equal to the probability of
+
+the sample space.
+
+And then, again, we're going
+to use sort of this really
+
+helpful fact that X, Y, Z, and W
+form a partition of omega to
+
+go ahead and write this as
+probability of X plus
+
+probability of Y plus
+probability,
+
+oops, I made a mistake.
+
+Hopefully, you guys
+caught that.
+
+It's really, oh, no.
+
+I'm right.
+
+Never mind.
+
+Probability of X plus
+probability of Y plus
+
+probability of Z plus
+probability of W. And now we
+
+can go ahead and plug-in the
+values that we solved for
+
+previously.
+
+So we get probability of X plus
+0.2 plus 0.4 plus 0.3.
+
+These guys sum to 0.9.
+
+So, again, just simple
+arithmetic, we get that the
+
+probability of X is
+equal to 0.1.
+
+So we're done because we've
+successfully found that the
+
+probability that a randomly
+selected student is neither a
+
+genius nor a chocolate
+lover is 0.1.
+
+So this was a fairly
+straightforward problem.
+
+But there are some important
+takeaways.
+
+The first one is that
+Venn diagrams are
+
+a really nice tool.
+
+Whenever the problem is asking
+you how different sets relate
+
+to each other or how different
+probabilities relate to each
+
+other, you should probably draw
+Venn diagram because it
+
+will help you.
+
+And the second takeaway is that
+it's frequently useful to
+
+divide your sample space into
+a partition mainly because
+
+sort of the pieces
+that compose a
+
+partition are disjoint.
+
+So we will be back soon to
+solve more problems.
\ No newline at end of file
diff --git a/yD0_EQLxHcw.txt b/yD0_EQLxHcw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e6f81a7f374e34adf3fe226a336569e983abd613
--- /dev/null
+++ b/yD0_EQLxHcw.txt
@@ -0,0 +1,1937 @@
+I'd like to talk.
+Thank you.
+
+One of the things I'd like to
+give a little insight into today
+
+is the mathematical basis for
+hearing.
+
+For example,
+if a musical tone,
+
+a pure musical tone would
+consist of a pure oscillation in
+
+terms of the vibration of the
+air.
+
+It would be a pure oscillation.
+So, [SINGS],
+
+and if you superimpose upon
+that, suppose you sing a triad,
+
+[SINGS], those are three tones.
+Each has its own period of
+
+oscillation, and then another
+one, which is the top one,
+
+which is even faster.
+The higher it is,
+
+the faster the thing.
+Anyway, what you hear,
+
+then, is the sum of those
+things.
+
+So, C plus E plus G,
+let's say, what you hear is the
+
+wave form.
+It's periodics,
+
+still, but it's a mess.
+I don't know,
+
+I can't draw it.
+So, this is periodic,
+
+but a mess, some sort of mess.
+Now, of course,
+
+if you hear the three tones
+together, most people,
+
+if they are not tone deaf,
+anyway, can hear the three
+
+tones that make up that.
+So, in other words,
+
+if this is the function which
+is the sum of those three,
+
+some sort of messy function,
+f of t,
+
+you're able to do Fourier
+analysis on it,
+
+and break it up.
+You're able to take that f of
+
+t, and somehow mentally express
+it as the sum of three pure
+
+oscillations.
+That's Fourier analysis.
+
+We've been doing it with an
+infinite series,
+
+but it's okay.
+It's still Fourier analysis if
+
+you do it with just three.
+So, in other words,
+
+the f of t is going to
+be the sum of,
+
+let's say, sine,
+I don't know,
+
+it's going to be the sign of
+one frequency plus the sine of
+
+another frequency plus the sine
+of a third, maybe with
+
+coefficients here.
+So, somehow,
+
+since you were born,
+you have been able to take the
+
+f of t,
+and express it as the sum of
+
+the three signs.
+And, here, therefore,
+
+the three tones that make up
+the triad.
+
+Now, the question is,
+how did you do that Fourier
+
+analysis?
+In other words,
+
+does your brain have a little
+integrator in it,
+
+which calculates the
+coefficients of that series?
+
+Of course, the answer is no.
+It has to do something else.
+
+So, one of the things I'd like
+to aim at in this lecture is
+
+just briefly explaining what,
+in fact, actually happens to do
+
+that.
+Now, to do that,
+
+we'll have to make some little
+detours, as always.
+
+So, first I'm going to,
+throughout the lecture,
+
+in fact, I gave you last time a
+couple of shortcuts for
+
+calculating Fourier series based
+on evenness and oddness,
+
+and also some expansion of the
+idea of Fourier series where we
+
+use the different,
+but things didn't have to be
+
+periodic or period two pi,
+but it can have an arbitrary
+
+period, 2L, and we could still
+get a Fourier expansion for it.
+
+Let me, therefore,
+begin just as a problem,
+
+another type of shortcut
+exercise, to do a Fourier
+
+calculation, which we are going
+to be later in the period to
+
+explain the music problem.
+So, let's suppose we're
+
+starting with the function,
+f of t,
+
+which is a real square wave,
+and I'll make its period
+
+different from the one,
+not two pi.
+
+So, suppose we had a function
+like this.
+
+So, this is one,
+and this is one.
+
+So, the height is one,
+and this point is one as well.
+
+And then, it's periodic ever
+after that.
+
+I'll tell you what,
+let's do like the electrical
+
+engineers do and put these
+vertical lines there even though
+
+they don't exist.
+Okay, so the height is one and
+
+it goes over.
+The half period is one.
+
+This really is a square wave.
+I mean, it's really a square,
+
+not what they usually call a
+square wave.
+
+So, my question is,
+what's its Fourier series?
+
+Well, it's neither even nor
+odd.
+
+That's a little dismaying.
+It sounds like we're going to
+
+have to calculate an's and bn's.
+So, the shortcuts I gave you
+
+last time don't seem to be
+applicable.
+
+Now, of course,
+nor is the period two pi,
+
+but that shouldn't be too bad.
+In fact, you ought to look for
+
+an expansion in terms of things
+that look like sine of n,
+
+well, what should it be?
+
+Since L is equal to one,
+the half period is equal to
+
+one.
+Remember, the period is 2L,
+
+not L.
+It's n pi over L,
+
+but if L is one,
+we should be looking for an
+
+expansion in terms of functions
+that look like this.
+
+Now, since we've already done
+the work for the official square
+
+way, which looks something like
+this, what you always try to do
+
+is reduce these things to
+problems that you've already
+
+solved.
+This is a legitimate one,
+
+since I solved it in lecture
+for you.
+
+So, we can consider it as
+something we know.
+
+So, I observed that since I am
+very lazy, that if I lower this
+
+function by one half,
+it will become an odd function.
+
+Now it's an odd function.
+Okay, I just cut the work in
+
+half.
+So, let's call this function,
+
+let's call this,
+I don't know,
+
+S of t.
+The green one is the one we
+
+wanted to start with.
+So, f of t is a green
+
+function.
+But, I can improve things even
+
+more because the function that
+we calculated in the lecture is
+
+a lot like this salmon function.
+That's why I called it S.
+
+But, the difference is that the
+function we calculated with this
+
+one.
+In the first place,
+
+it went down further.
+It went not to negative one
+
+half, which is where that one
+goes.
+
+But, it went down to negative
+one, and then went up here to
+
+plus one.
+And, it went over to pi.
+
+So, it came down again,
+but not, but at the point,
+
+pi.
+And here, negative pi went up
+
+again.
+Okay, let me remind you what
+
+this one was.
+Suppose we call it,
+
+O doesn't look good,
+I don't know,
+
+how about g of u?
+Let's, for a secret reason,
+
+call the variable u this time,
+okay?
+
+So, the previous knowledge that
+I'm relying on was that I
+
+derived the Fourier series for
+you by an orthodox calculation.
+
+And, it's not too hard to do
+because this is an odd function.
+
+And therefore,
+you only have to calculate the
+
+bn's.
+And, half of them turn out to
+
+be zero, although you don't know
+that in advance.
+
+But anyway, the answer was four
+over pi times the sum
+
+of just the odd ones,
+the sine of n u,
+
+and that you had to 
+divide by n.
+
+So, this is the expansion of g,
+this function,
+
+g of u, the Fourier expansion
+of this function.
+
+Since it's an odd function,
+it only involves the signs.
+
+There's no funny stuff here
+because the period is now two
+
+pi.
+And, this came from the first
+
+lecture on Fourier series,
+or from the book,
+
+wherever you want it,
+or solutions to the notes.
+
+There are lots of sources for
+that.
+
+The solution's in the notes.
+Okay, now, that looks so much
+
+like the salmon function,
+---
+
+-- I ought to be able to
+convert one into the other.
+
+Now, I will do that by
+shrinking the axis.
+
+But, since this can get rather
+confusing, what I'll do is
+
+overlay this.
+What I prefer to do is I think
+
+u, okay, I'm changing,
+I'm keeping the thing the same.
+
+But, I'm going to change the
+name of the variable,
+
+the t, in such a way that on
+the t-axis, this becomes the
+
+point, one.
+If I do that,
+
+then this function will turn
+exactly into that one,
+
+except it will go not from
+minus a half to a half,
+
+but it will go from negative
+one to one, since I haven't done
+
+anything to the vertical axis.
+So, how I do that?
+
+What's the relation between u
+and t?
+
+Well, u is equal to pi times t,
+or the other way around.
+
+You know that it's going to be
+approximately this.
+
+Try one, and then check that it
+works.
+
+When t is equal to one,
+u is pi, which is what it's
+
+supposed to be.
+So, this is the relation
+
+between the two.
+And therefore,
+
+without further ado,
+I can say that,
+
+let's write the relation
+between them.
+
+f of t is what I want.
+Well, what's f of t if I
+
+subtract one half of that?
+So, that's going to be equal to
+
+the salmon function plus one
+half, right, or the salmon
+
+function is f of t lowered by
+one half.
+
+One thing is the same as the
+other.
+
+And, what's the relation
+between this salmon function and
+
+the orange function?
+Well, the salmon function is,
+
+so, let's convert,
+so, S of t -- it's more
+
+convenient, as I wrote the
+formula g of u.
+
+Let's start it from that end.
+If I start from g of u,
+
+what do I have to do to convert
+it into S of-- into the salmon
+
+function?
+Well, take one half of it.
+
+So, if I put them all together,
+the conclusion is that f of t
+
+is equal to one half
+plus S of t,
+
+which is one half of g of u,
+
+but u is pi t.
+So, it's four pi,
+
+four over pi times the sum of
+the sine of n.
+
+And, for u, I will write pi t
+
+divided by n.
+And, sorry, I forgot to say
+
+that sum is only over the odd
+values of n, not all values of
+
+n.
+So, the sum over n odd of that,
+
+and, of course,
+the two will cancel that.
+
+So, here we have,
+in other words,
+
+just by this business of
+shrinking or just stretching or
+
+shrinking the axis,
+lowering it and squishing it
+
+that way a little bit.
+We get from this Fourier
+
+series, we get that one just by
+this geometric procedure.
+
+I'd like you to be able to do
+that because it saves a lot of
+
+time.
+Okay, so let's put this answer
+
+up in, I'm going to need it in a
+minute, but I don't really want
+
+to recopy it.
+So, let me handle it by
+
+erasing.
+So, let's call that plus two
+
+over pi,
+and there is our formula for
+
+that green function that we
+wrote before.
+
+So, I'll put that in green.
+So, we'll have a color-coded
+
+lecture again.
+Now, what we're going to be
+
+doing ultimately,
+to getting at the music problem
+
+that I posed at the beginning of
+the lecture, is we want to
+
+solve, and this is what a study
+of Fourier series has been
+
+aiming at, to solve second-order
+linear equations with constant
+
+coefficients were the right-hand
+side was a more general function
+
+than the kind we've been
+handling.
+
+So, now, in order to simplify,
+and we don't have a lot of time
+
+in the course,
+I'd have to take another day to
+
+make more complicated
+calculations,
+
+which I don't want to do since
+you will learn a lot from them,
+
+anyway.
+I think you will find you've
+
+had enough calculation by the
+time Friday morning rolls
+
+around.
+So, let's look at the undamped
+
+case, which is simpler,
+or undamped spring,
+
+or undamped anything because it
+doesn't have that extra term,
+
+which requires extra
+calculations.
+
+So, I'll follow the book now
+and some of the notes and the
+
+visuals, and called the
+independent variable-- the
+
+dependent variable I'm going to
+call x now.
+
+And, the independent variable
+is, as usual,
+
+time.
+So, this is going to be,
+
+in general, f of t,
+and I'm going to use it by
+
+calculating example,
+this is the actual f of t I'm
+
+going to be using.
+But, the general problem for a
+
+general f of t is to solve this,
+or at least to find a
+
+particular solution.
+That's what most of the work
+
+is, because we already know how
+from that to get the general
+
+solution by adding the solution
+to the reduced equation,
+
+the associated homogeneous
+equation.
+
+So, all our work has been,
+this past couple of weeks,
+
+in how you find a particular
+solution.
+
+Now, the case in which we know
+what to do is,
+
+so we can find our particular
+solution.
+
+Let's call that x sub p.
+
+We could find x sub p if the
+right hand side is cosine omega,
+
+well, in general,
+an exponential,
+
+but since we are not going to
+use complex exponentials today,
+
+all these things are real.
+And I'd like to keep them real.
+
+If it's either cosine omega t
+or sine omega t,
+
+or some multiple of that by
+
+linearity, it's just as good.
+We already know how to find the
+
+thing, and to find a particular
+solution.
+
+So, the procedure is use
+complex exponentials,
+
+and that magic formula I gave
+you.
+
+But, right now,
+just to save a little time,
+
+since I already did that on the
+lecture on resonance,
+
+I solved it explicitly for
+that, and you've had adequate
+
+practice I think in the problem
+sets.
+
+Let's simply write down the
+answer that comes out of that.
+
+The answer for the particular
+solution is cosine omega t
+
+or sine omega t.
+
+That's the top.
+And, it's over a constant.
+
+And, the constant is omega
+naught squared.
+
+That's the natural frequency
+which comes from the system,
+
+minus the imposed frequency,
+the driving frequency that the
+
+system, the spring or whatever
+it is, undamped spring,
+
+is being driven with.
+Okay, understand the notation.
+
+Cosine this over that,
+or sine, depending on whether
+
+you started driving it with
+cosine or sine.
+
+So, this is from the lecture,
+if you like,
+
+from the lecture on resonance,
+but again it's,
+
+I hope by now,
+a familiar fact.
+
+Let me remind you what this had
+to do with resonance.
+
+Then, the observation was that
+if omega, the driving frequency
+
+is very close to the natural
+frequency, then this is close to
+
+that.
+The denominator is almost zero,
+
+and that makes the amplitude of
+the response very,
+
+very large.
+And, that was the phenomenon of
+
+resonance.
+Okay, now what I'd like to do
+
+is apply those formulas to
+finding out what happens for a
+
+general f(t),
+or in particular this one.
+
+So, in general,
+I'll keep using the notation,
+
+f of t,
+even though I've sorted used it
+
+for that.
+But in general,
+
+what's the situation?
+If f of t is a sine series,
+
+cosine series,
+all right, let's do everything.
+
+Suppose it's,
+in other words,
+
+the procedure is,
+take your f of t,
+
+expand it in a Fourier series.
+Well, doesn't that assume it's
+
+periodic?
+Yes, sort of.
+
+So, suppose it's a Fourier
+series.
+
+I'll make a very general
+Fourier series,
+
+write it this way:
+cosine (omega)n t,
+
+and then the sine terms,
+
+sine (omega)n t
+from one to infinity where
+
+the omegas are,
+omega n is short for that.
+
+Well, it's going to have the n
+in it, of course,
+
+but I want, now,
+to make the general period to
+
+be 2L.
+So, it would be n pi over L.
+
+Of course, if L is equal to
+
+one, then it's n pi.
+Or, if L equals pi,
+
+those are the two most popular
+cases, by far.
+
+Then, it's simply n itself,
+the driving frequency.
+
+But, this would be the general
+case, n pi over L
+
+if the period is the period of f
+of t is 2L.
+
+So, that's what the Fourier
+series looks like.
+
+Okay, then the particular
+solution will be what?
+
+Well, I got these formulas.
+In other words,
+
+what I'm using is superposition
+principle.
+
+If it's just this,
+then I know what the answer is
+
+for the particular solution,
+the response.
+
+So, if you make a sum of these
+things, a sum of these inputs,
+
+you are going to get a sum of
+the responses by superposition.
+
+So, let's write out the ones we
+are absolutely certain of.
+
+What's the response to here?
+Well, it's (a)n cosine omega n
+
+t. The only thing is,
+
+now it's divided by omega
+naught squared.
+
+This constant has changed,
+and the same thing here.
+
+Of course, by linearity,
+if this is multiplied by a,
+
+then the answer is multiplied
+by, the response is also
+
+multiplied by a.
+So, the same thing happens
+
+here.
+Here, it's (b)n and over,
+
+again, omega naught squared
+minus omega times the sine of
+
+omega t.
+
+So, in other words,
+as soon as you have the Fourier
+
+expansion, the Fourier series
+for the input,
+
+you automatically get this by
+just writing it down the Fourier
+
+series for the response.
+That's the fundamental idea of
+
+Fourier series,
+at least applied in this
+
+context.
+They have many other contexts,
+
+approximations,
+so on and so forth.
+
+But, that's the idea here.
+All right, what about that
+
+constant term?
+Well, this formula still works
+
+if omega equals zero.
+If omega equals zero,
+
+then this is the constant,
+one.
+
+The formula is still correct.
+Omega is zero here.
+
+The only thing you have to
+remember is that the original
+
+thing is written in this form.
+So, the response will be,
+
+what will it be?
+Well, it's one divided by omega
+
+naught squared,
+if I'm in the case omega zero
+
+is equal to zero.
+So, it's a zero divided by two
+
+omega naught squared.
+And, as you will see,
+
+it looks just like the others.
+You're just taking omega,
+
+and making it equal to zero for
+that particular case.
+
+Sorry, this should be omega n's
+all the way through here.
+
+All right, well,
+let's apply this to the green
+
+function.
+So, what have we got?
+
+We have its Fourier series.
+So, if the green function is,
+
+if the input in other words is
+this square wave,
+
+the green square wave,
+so in your notes,
+
+this guy, this particular f of
+t is the input.
+
+And, the equation is x double
+prime plus omega naught squared
+
+x equals f of t.
+
+Then, the response is,
+well, I can't draw you a
+
+picture of the response because
+I don't know what the Fourier
+
+series actually looks like.
+But, let's at least write down
+
+what the Fourier series is.
+The Fourier series will be,
+
+well, what is it?
+It's one half.
+
+The constant out front is one
+half, except it's one over two
+
+omega naught squared.
+
+So, this is my function,
+f of t.
+
+That's the general formula for
+how the input is related to the
+
+response.
+And, I'm applying it to this
+
+particular function,
+f of t.
+
+And, the answer is plus.
+Well, my Fourier series
+
+involves only odd sums,
+only the summation over odd,
+
+and only of the sign.
+So, it is going to be two over
+
+pi,
+sorry, so it's going to be two
+
+over pi out front.
+That constant will carry along
+
+by linearity.
+And, I'm going to sum over odd,
+
+n odd values only.
+The basic thing in the upstairs
+
+is going to be the sine of omega
+n t.
+
+But, what is (omega)n?
+Well, (omega)n is n pi.
+
+So, it's n pi t.
+And, how about the bottom?
+
+The bottom is going to be omega
+naught squared minus omega n
+
+squared.
+
+And, this is my (omega)n,
+minus n pi squared.
+
+What's that?
+
+Well, I don't know.
+All I could do would be to
+
+calculate it.
+You could put it on MATLAB and
+
+ask MATLAB to calculate and plot
+for you the first few terms,
+
+and get some vague idea of what
+it looks like.
+
+That's nice,
+but it's not what's interesting
+
+to do.
+What's interesting to do is to
+
+look at the size of the
+coefficients.
+
+And, again, rather than do it
+in the abstract,
+
+let's take a specific value.
+Let's suppose that the natural
+
+frequency of the system,
+in other words,
+
+the frequency at which that
+little spring wants to go
+
+vibrate back and forth,
+whatever you got vibrating.
+
+Let's suppose the natural
+frequency that's omega naught is
+
+ten for the sake of
+definiteness,
+
+as they say.
+Okay, if that's ten,
+
+all I want to do is calculate
+in the crudest possible way what
+
+a few of these terms are.
+So, the response is,
+
+so let's see,
+we've got to give that a name.
+
+The response is (x)p of t.
+
+What's (x)p of t?
+I'm just going to calculate it
+
+very approximately.
+This means, you know,
+
+throwing caution to the winds
+because I don't have a
+
+calculator with me.
+And, I want you to look at this
+
+thing without a calculator.
+The first term is one over 200.
+
+Okay, that's the only term I
+
+can get exactly right.
+[LAUGHTER] Or,
+
+I could if I could calculate.
+I suppose it's 0.005,
+
+right?
+That's the constant term.
+
+Okay, so the next term,
+let's see, two over pi is two
+
+thirds.
+I'll keep that in mind,
+
+right?
+Plus two thirds,
+
+0.6, let's say,
+that's an indication of the
+
+accuracy with which these things
+are going to be performed.
+
+I think in Texas for a long
+while, the legislature declared
+
+pi to be three,
+anyways.
+
+One of those states did it to
+save calculation time.
+
+I'm not kidding,
+by the way.
+
+All right, so what's the first
+term?
+
+If n equals one,
+I have the sine of pi t.
+
+That's the n equals one term.
+
+What's the denominator like?
+That's about 100 minus 9
+
+squared. Let's say it's 91,
+
+sine t over 91.
+What's the next term?
+
+Sine of three pi t, remember,
+
+I am omitting,
+I'm only using the odd values
+
+of n because those are the only
+ones that enter into the Fourier
+
+expansion for this function,
+which is at the bottom of
+
+everything.
+All right, what's the sine
+
+three pi t?
+Well, now, I've got 100 minus
+
+three pi, --
+-- that's 9 squared is 81.
+
+So, no, what am I doing?
+So, we have 100 minus three
+
+times pi is 9,
+squared.
+
+Well, let's say a little more.
+Let's say 85.
+
+So, that's 15.
+How bout the next one?
+
+Well, it's sine 5 pi t.
+
+I think I'll stop here as soon
+as we do this one because at
+
+this point it's clear what's
+happening.
+
+This is 100 squared minus,
+that's 15 squared is 225,
+
+so that's about 125 with a
+negative sign.
+
+So, minus this divided by 125.
+And, after this they are going
+
+to get really quite small
+because the next one will be
+
+seven pi squared.
+That's 400, and this is
+
+becoming negligible.
+So, what's happening?
+
+So, it's approximately,
+in other words,
+
+0.005 plus the next coefficient
+is, let's see,
+
+6/10, let's say 100,
+sine pi t.
+
+And, what comes next?
+Well, it's now 1/20th.
+
+It's about a 20th.
+Let's call that 0.005 sine
+
+three pi t,
+and now so small,
+
+minus 0.01, let's say times
+this last one,
+
+sine 5 pi t.
+What you find,
+
+in other words,
+is that the frequencies which
+
+make up the response do not
+occur with the same amplitude.
+
+What happens is that this
+amplitude is roughly five times
+
+larger than any of the
+neighboring ones.
+
+And after that,
+it's a lot larger than the ones
+
+that come later.
+In other words,
+
+the main frequency which occurs
+in the response is the frequency
+
+three pi.
+What's happened is,
+
+in other words,
+near resonance has occurred.
+
+So, if omega is ten,
+very near resonance,
+
+that is, it's not too close,
+but it's not too far away
+
+either, occurs for the frequency
+three pi in the input.
+
+Now, where's the frequency
+three pi in the input?
+
+It isn't there.
+It's just that green thing.
+
+Where in that is the frequency
+three pi?
+
+I can't answer that for you,
+but that's the function of
+
+Fourier series,
+to say that you can decompose
+
+that green function into a sum
+of frequencies,
+
+as it were, and the Fourier
+coefficients tell you how much
+
+frequency goes into each of
+those f of t's.
+
+Now, so, f of t is decomposed
+into the sum of frequencies by
+
+the Fourier analysis.
+But, the system isn't going to
+
+respond equally to all those
+frequencies.
+
+It's going to pick out and
+favor the one which is closest
+
+to its natural frequency.
+So, what's happened,
+
+these frequencies,
+the frequencies and their
+
+relative importance in f of t
+are hidden,
+
+as it were.
+They're hidden because we can't
+
+see them unless you do the
+Fourier analysis,
+
+and look at the size of the
+coefficients.
+
+But, the system can pick out.
+The system picks out and
+
+favors, picks out for resonance,
+or resonates with,
+
+resonates with the frequencies
+closest to its natural
+
+frequency.
+Well, suppose the system had
+
+natural frequency,
+not ten.
+
+This is a put up job.
+Suppose it had natural
+
+frequency five.
+Well, in that case,
+
+none of them are close to the
+hidden frequencies in f of t,
+
+and there would be no
+resonance.
+
+But, because of the particular
+value I gave here,
+
+I gave the value ten,
+it's able to pick out n equals
+
+three as the most important,
+the corresponding three pi as
+
+the most important frequency in
+the input, and respond to that.
+
+Okay, so this is the way we
+hear, give or take a few
+
+thousand pages.
+So, what does the ear do?
+
+How does the ear,
+so, it's got that thing,
+
+messy curve,
+which I erased,
+
+which has a secret,
+which just has three hidden
+
+frequencies.
+Okay, from now on I hand wave,
+
+right, like they do in other
+subjects.
+
+So, we got our frequency.
+So, it's got a [SINGS].
+
+That's one frequency.
+[SINGS] And,
+
+what goes in there is the sum
+of those three,
+
+and the ear has to do something
+to say out of all the
+
+frequencies in the world,
+I'm going to respond to that
+
+one, that one,
+and that one,
+
+and send a signal to the brain,
+which the brain,
+
+then, will interpret as a
+beautiful triad.
+
+Okay, so what happens is that
+the ear, I don't talk
+
+physiology, and I never will
+again.
+
+I know nothing about it,
+but anyway, the ear,
+
+when you get far enough in
+there, there are little three
+
+bones, bang, bang,
+bang; this is the eardrum,
+
+and then there's the part which
+has wax.
+
+Then, there's the eardrum which
+vibrates, at least if there is
+
+not too much wax in your ear.
+And then, the vibrations go
+
+through three little bones which
+send the vibrations to the inner
+
+ear, which nobody ever sees.
+And, the inner ear,
+
+then, is filled with thick
+fluid and a membrane,
+
+and the last bone hits up
+against the membrane,
+
+and the membrane vibrates.
+And, that makes the fluid
+
+vibrate.
+Okay, good.
+
+So, it's vibrating according to
+the function f of t.
+
+Well, what then?
+Well, that's the marvelous
+
+part.
+It's almost impossible to
+
+believe, but there is this,
+sort of like a snail thing
+
+inside.
+I've forgotten the name.
+
+It's cochlea.
+And, it has these hairs.
+
+They are not hairs really.
+I don't know what else to call
+
+them. They're not hairs.
+
+But, there are things so long,
+you know, they stick up.
+
+And, there are 20,000 of them.
+And, they are of different
+
+lengths.
+And, each one is tuned to a
+
+certain frequency.
+Each one has a certain natural
+
+frequency, and they are all
+different, and they are all
+
+graded, just like a bunch of
+organ pipes.
+
+And, when that complicated wave
+hits, the complicated wave hits,
+
+each one resonates to a hidden
+frequency in the wave,
+
+which is closest to its natural
+frequency.
+
+Now, most of them won't be
+resonating at all.
+
+Only the ones close to the
+frequency [SINGS],
+
+they'll resonate,
+and the nearby guys will
+
+resonate, too,
+because they will be nearby,
+
+almost have the same natural
+frequency.
+
+And, over here,
+there will be a few which
+
+resonate to [SINGS],
+and finally over here a few
+
+which go [SINGS],
+and each of those little hairs,
+
+little groups of hairs will
+signal, send that signal to the
+
+auditory nerve somehow or other,
+which will then carry these
+
+three inputs to the brain,
+and the brain,
+
+then, will interpret that as
+you are hearing [SINGS].
+
+So, the Fourier analysis is
+done by resonance.
+
+You here resonance because each
+of these things has a certain
+
+natural frequency which is able,
+then, to pick out a resonant
+
+frequency in the input.
+I'd like to finish our work on
+
+Fourier series.
+So, for homework I'm asking you
+
+to do something similar.
+Taken an input.
+
+I gave you a frequency here,
+a different omega naught,
+
+a different input,
+as you by means of this Fourier
+
+analysis to find out which it
+will resonate,
+
+which of the hidden frequencies
+in the input the system will
+
+resonate to, just so you can
+work it out yourself and do it.
+
+Now, I'd like to first try to
+match up what I just did by this
+
+formula with what's in your
+book, since your book handles
+
+the identical problem but a
+little differently,
+
+and it's essentially the same.
+But I think I'd better say
+
+something about it.
+So, the book's method,
+
+and to the extent which any of
+these problems are worked out in
+
+the notes, the notes do this,
+too.
+
+Use substitution.
+Base uses differentiation of
+
+Fourier series term by term.
+The work is almost exactly the
+
+same as here.
+And, it has a slight advantage,
+
+that it allows you,
+the book's method has a slight
+
+advantage that it allows you to
+forget this formula.
+
+You don't have to know this
+formula.
+
+It will come out in the wash.
+Now, for some of you,
+
+that may be of colossal
+importance, in which case,
+
+by all means,
+use the book's method,
+
+term by term.
+So, it requires no knowledge of
+
+this formula because after all,
+I base this solution,
+
+I simply wrote down the
+solution and I based it on the
+
+fact that I was able to write
+down immediately the solution to
+
+this and put as being that
+response.
+
+And for that,
+I had to remember it,
+
+or be willing to use complex
+exponentials quickly to remind
+
+myself.
+There's very,
+
+very little difference between
+the two.
+
+Even if you have to re-derive
+that formula,
+
+the two take almost about the
+same length of time.
+
+But anyway, the idea is simply
+this.
+
+With the book,
+you assume.
+
+In other words,
+you take your function,
+
+f of t.
+You expand it in a Fourier
+
+series.
+Of course, which signs and
+
+cosines you use will depend upon
+what the period is.
+
+So, you assume the solution of
+the form-- Well,
+
+if I, for example,
+carried out in this particular
+
+case, I don't know if I will do
+all the work,
+
+but it would be natural to
+assume a solution of the form,
+
+since the input looks like the
+green guy.
+
+Assume a solution which looks
+the same.
+
+In other words,
+it will have a constant term
+
+because the input does.
+But all the rest of the terms
+
+will be sines.
+So, it will be something like
+
+(c)n times the sine of n pi t.
+
+The only question is,
+what are the (c)n's?
+
+Well, I found one method up
+there.
+
+But, the general method is just
+plug-in.
+
+Substitute into the ODE.
+Substitute into the ODE.
+
+You differentiate this twice to
+do it.
+
+So, I'll do the double
+differentiation and I won't stop
+
+the lecture there,
+but I will stop the calculation
+
+there because it has nothing new
+to offer.
+
+And, this is the way all the
+calculations in the books and
+
+the solutions and the notes are
+carried out.
+
+So, I don't think you'll have
+any trouble.
+
+Well, this term vanishes.
+This term becomes what?
+
+If I differentiate this twice,
+I get summation,
+
+so, this is one to infinity
+because I don't know which of
+
+these are actually going to
+appear.
+
+Summation one to infinity,
+(c)n times, well,
+
+if you differentiate the sine
+twice, you get negative sine,
+
+right?
+Do it once: you get cosine.
+
+Second time:
+you get negative sine.
+
+But, each time you will get
+this extra factor n pi from the
+
+chain rule.
+And so, the answer will be
+
+negative (c)n times n pi squared
+times the sine of n pi t.
+
+And so, the procedure is,
+
+very simply,
+you substitute (x)p double
+
+prime into the differential
+equation.
+
+In other words,
+if you do it,
+
+we will multiply this by omega
+naught squared.
+
+And, you add them.
+And then, on the left-hand
+
+side, you are going to get a sum
+of terms, sine n pi t
+
+times coefficients
+involving the (c)n's.
+
+And, on the right,
+so, you're going to get a sum
+
+involving the (c)n's,
+and the sines n pi t,
+
+and on the right,
+you're going to get the Fourier
+
+series for f of t,
+which is exactly the same kind
+
+of expression.
+The only difference is,
+
+now the sines have come with
+definite coefficients.
+
+And then, you simply click the
+coefficients on the left and the
+
+coefficients on the right,
+and figure out what the (c)n's
+
+are.
+So, by equating coefficients,
+
+you get the (c)n's.
+Would you like me to carry it
+
+out?
+Yeah, okay, I was going to do
+
+something else,
+but I wouldn't have time to do
+
+it anyway.
+So, why don't I take two
+
+minutes to complete the
+calculation just so you can see
+
+you get the same answer?
+All right, what do we get?
+
+If you add them up,
+you get c naught,
+
+out front, plus (c)n is
+multiplied by what?
+
+Well, from the top it's
+multiplied by omega naught
+
+squared.
+On the bottom,
+
+it's multiplied by n 
+pi squared.
+
+Ah-ha, where have I seen that
+combination?
+
+The sum is equal to,
+sorry, one half plus what is
+
+it, sum over n odd of sine n pi
+t over n.
+
+So, the conclusion is that--
+I'm sorry, it should be c naught
+
+times omega naught squared.
+
+So, what's the conclusion?
+If c zero is one over two omega
+
+naught squared,
+
+and that (c)n,
+only for n odd,
+
+the others will be even.
+The others will be zero.
+
+The (c)n is going to be equal
+to two over pi here.
+
+So, it's going to be two pi,
+
+two over pi times one over n
+times one over omega naught
+
+squared minus n over
+pi squared.
+
+This is terrible,
+
+which is the same answer we got
+before, I hope.
+
+Did I cover it up?
+Same answer.
+
+So, that answer at the
+left-hand end of the board is
+
+the same one.
+I've calculated,
+
+in other words,
+what the c zeros are.
+
+And, I got the same answer as
+before.
\ No newline at end of file
diff --git a/ybCsMYk5xMg.txt b/ybCsMYk5xMg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8fc1c18d5dc6f67c634b41305b8aef7800d73177
--- /dev/null
+++ b/ybCsMYk5xMg.txt
@@ -0,0 +1,3329 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation, or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Let's start.
+
+Are there any questions?
+
+We would like to have a
+perspective for this really
+
+common observation that if you
+have a gas that is initially
+
+in one half of a box, and
+the other half is empty,
+
+and some kind of a partition
+is removed so that the gas can
+
+expand, and it can
+flow, and eventually we
+
+will reach another
+equilibrium state where
+
+the gas occupies more chambers.
+
+How do we describe
+this observation?
+
+We can certainly characterize
+it thermodynamically
+
+from the perspectives
+of atoms and molecules.
+
+We said that if I
+want to describe
+
+the configuration of the gas
+before it starts, and also
+
+throughout the expansion,
+I would basically
+
+have to look at all sets
+of coordinates and momenta
+
+that make up this particle.
+
+There would be some
+point in this [? six ?],
+
+and I mention our
+phase space, that
+
+would correspond to where
+this particle was originally.
+
+We can certainly follow
+the dynamics of this point,
+
+but is that useful?
+
+Normally, I could
+start with billions
+
+of different types of
+boxes, or the same box
+
+in a different
+instance of time, and I
+
+would have totally different
+initial conditions.
+
+The initial
+conditions presumably
+
+can be characterized to a
+density in this phase space.
+
+You can look at some volume
+and see how it changes,
+
+and how many points
+you have there,
+
+and define this
+phase space density
+
+row of all of the
+Q's and P's, and it
+
+works as a function of time.
+
+One way of looking at how it
+works as a function of time
+
+is to look at this box
+and where this box will
+
+be in some other
+instance of time.
+
+Essentially then, we are
+following a kind of evolution
+
+that goes along this streamline.
+
+Basically, the derivative
+that we are going to look at
+
+involves changes both
+explicitly in the time variable,
+
+and also increasingly
+to the changes
+
+of all of the
+coordinates and momenta,
+
+according to the Hamiltonian
+that governs the system.
+
+I have to do, essentially,
+a sum over all coordinates.
+
+I would have the
+change in coordinate i,
+
+Qi dot, dot, d row by dQi.
+
+Then I would have Pi, dot-- I
+guess these are all vectors--
+
+d row by dPi.
+
+There are six end coordinates
+that implicitly depend on time.
+
+In principle, if I am
+following along the streamline,
+
+I have to look at
+all of these things.
+
+The characteristic of evolution,
+according to some Hamiltonian,
+
+was that this volume of
+phase space does not change.
+
+Secondly, we could
+characterize, once we
+
+wrote Qi dot, as dH by dP,
+and the i dot as the H by dQ.
+
+This combination of derivatives
+essentially could be captured,
+
+and be written as 0 by
+dt is the Poisson bracket
+
+of H and [? P. ?]
+
+One of the things,
+however, that we emphasize
+
+is that as far as evolution
+according to a Hamiltonian
+
+and this set of
+dynamics is concerned,
+
+the situation is completely
+reversible in time
+
+so that some
+intermediate process,
+
+if I were to reverse all of
+the momenta, then the gas
+
+would basically come back
+to the initial position.
+
+That's true.
+
+There is nothing to do about it.
+
+That kind of seems to
+go against the intuition
+
+that we have from
+thermodynamics.
+
+We said, well, in
+practical situations,
+
+I really don't care about
+all the six end pieces
+
+of information that
+are embedded currently
+
+in this full phase
+space density.
+
+If I'm really trying
+to physically describe
+
+this gas expanding,
+typically the things
+
+that I'm interested in are
+that at some intermediate time,
+
+whether the particles
+have reached
+
+this point or that
+point, and what
+
+is this streamline velocity
+that I'm seeing before the thing
+
+relaxes, presumably,
+eventually into zero velocity?
+
+There's a lot of
+things that I would
+
+need to characterize
+this relaxation process,
+
+but that is still
+much, much, much
+
+less than all of the information
+that is currently encoded
+
+in all of these six end
+coordinates and momenta.
+
+We said that for things that
+I'm really interested in,
+
+what I could, for
+example, look at,
+
+is a density that involves
+only one particle.
+
+What I can do is to
+then integrate over
+
+all of the positions and
+coordinates of particles
+
+that I'm not interested in.
+
+I'm sort of repeating this to
+introduce some notation so as
+
+to not to repeat all of
+these integration variables,
+
+so I will call dVi the phase
+place contribution of particle
+
+i.
+
+What I may be interested in
+is that this is something
+
+that, if I integrate
+over P1 and Q1,
+
+it is clearly
+normalized to unity
+
+because my row, by definition,
+was normalized to unity.
+
+Typically we may be
+interested in something else
+
+that I call F1, P1
+Q1 P, which is simply
+
+n times this-- n times
+the integral product
+
+out i2 to n, dVi, the full row.
+
+Why we do that is
+because typically you
+
+are interested or used
+to calculating things
+
+in [? terms ?] of
+a number density,
+
+like how many particles are
+within some small volume here,
+
+defining the density so
+that when I integrate over
+
+the entire volume
+of f1, I would get
+
+the total number of
+particles, for example.
+
+That's the kind of normalization
+that people have used for f.
+
+More generally,
+we also introduced
+
+fs, which depended on
+coordinates representing
+
+s sets of points, or s
+particles, if you like,
+
+that was normalized to be--
+
+We said, OK, what I'm really
+interested in, in order
+
+to calculate the properties of
+the gases it expands in terms
+
+of things that I'm
+able to measure, is f1.
+
+Let's write down the
+time evolution of f1.
+
+Actually, we said,
+let's write down
+
+the time evolution
+of fs, along with it.
+
+So there's the time
+evolution of fs.
+
+If I were to go
+along this stream,
+
+it would be the fs
+by dt, and then I
+
+would have contributions
+that would correspond
+
+to a the changes in
+coordinates of these particles.
+
+In order to progress
+along this direction,
+
+we said, let's define
+the total Hamiltonian.
+
+We will have a simple form,
+and certainly for the gas,
+
+it would be a good
+representation.
+
+I have the kinetic energies
+of all of the particles.
+
+I have the box that confines
+the particles, or some other one
+
+particle potential, if you like,
+but I will write in this much.
+
+Then you have the interactions
+between all pairs of particles.
+
+Let's write it as sum over i,
+less than j, V of Qi minus Qj.
+
+This depends on n set of
+particles, coordinates,
+
+and momenta.
+
+Then we said that for purposes
+of manipulations that you have
+
+to deal with, since
+there are s coordinates
+
+that are appearing here
+whose time derivatives I have
+
+to look at, I'm going
+to simply rewrite
+
+this as the
+contribution that comes
+
+from those s particles,
+the contribution that comes
+
+from the remaining
+n minus s particles,
+
+and some kind of [? term ?]
+that covers the two
+
+sets of particles.
+
+This, actually, I didn't quite
+need here until the next stage
+
+because what I write
+here could, presumably,
+
+be sufficiently general,
+like we have here some n
+
+running from 1 to s.
+
+Let me be consistent
+with my S's.
+
+Then I have Qn, dot, dFs by
+dQn, plus Pn, dot, dFs by dPn.
+
+If I just look at the
+coordinates that appear here,
+
+and say, following this
+as they move in time,
+
+there is the explicit
+time dependence
+
+on all of the implicit
+time dependence,
+
+this would be the
+total derivative moving
+
+along the streamline.
+
+Qn dot I know is
+simply the momentum.
+
+It is the H by dPn.
+
+The H by dPn I have from
+this formula over here.
+
+It is simply Pn divided by m.
+
+It's the velocity--
+momentum divided by mass.
+
+This is the velocity
+of the particle.
+
+Pn dot, the rate of
+change of momentum
+
+is the force that is
+acting on the particle.
+
+What I need to do is to take
+the derivatives of various terms
+
+here.
+
+So I have minus dU by dPn.
+
+What is this?
+
+This is essentially the
+force that the particle
+
+feels from the
+external potential.
+
+If you are in the
+box in this room,
+
+It is zero until you
+hit the edge of the box.
+
+I will call this Fn to represent
+external potential that
+
+is acting on the system.
+
+What else is there?
+
+I have the force that will
+come from the interaction
+
+with all other [? guys. ?] I
+will write here a sum over m,
+
+dV of Qm minus Qn,
+by dQn-- dU by dQm.
+
+I'm sorry.
+
+What is this?
+
+This Is basically the
+sum of the forces that
+
+is exerted by the n
+particle on the m particle.
+
+Define it in this fashion.
+
+If this was the entire
+story, what I would have had
+
+here is a group of
+s particles that
+
+are dominated by
+their own dynamics.
+
+If there is no other
+particle involved,
+
+they basically have to
+satisfy the Liouville equation
+
+that I have written, now
+appropriate to s particles.
+
+Of course, we know that
+that's not the entire story
+
+because there are
+all these other terms
+
+involving the interactions
+with particles that I have not
+
+included.
+
+That's the whole
+essence of the story.
+
+Let's say I want to think
+about one or two particles.
+
+There is the interaction
+between the two particles,
+
+and they would be evolving
+according to some trajectories.
+
+But there are all of
+these other particles
+
+in the gas in this room
+that will collide with them.
+
+So those conditions
+are not something
+
+that we had in the
+Liouville equation,
+
+with everything considered.
+
+Here, I have to
+include the effect
+
+of all of those other particles.
+
+We saw that the
+way that it appears
+
+is that I have to imagine that
+there's another particle whose
+
+coordinates and
+momenta are captured
+
+through some volume for
+the s plus 1 particle.
+
+This s plus 1
+particle can interact
+
+with any of the particles
+that are in the set
+
+that I have on the other side.
+
+There is an index
+that runs from 1 to s.
+
+What I would have here is the
+force that will come from this
+
+s plus 1 particle, acting on
+particle n the same way that
+
+this force was deriving
+the change of the momentum,
+
+this force will derive the
+change of the momentum of-- I
+
+guess I put an m here--
+
+The thing that I
+have to put here
+
+is now a density that also
+keeps track of the probability
+
+to find the s plus 1 particle
+in the location in phase place
+
+that I need to
+integrate with both.
+
+I have to integrate
+over all positions.
+
+One particle is moving along
+a straight line by itself,
+
+let's say.
+
+Then there are all of the
+other particles in the system.
+
+I have to ask, what is
+the possibility that there
+
+is a second particle with
+some particular momentum
+
+and coordinate that I
+will be interacting with.
+
+This is the general set up
+of these D-B-G-K-Y hierarchy
+
+of equations.
+
+At this stage, we
+really have just
+
+rewritten what we had for
+the Liouville equation.
+
+We said, I'm really, really
+interested only one particle
+
+[? thing, ?] row one and F1.
+
+Let's focus on that.
+
+Let's write those
+equations in more detail
+
+In the first equation, I
+have that the explicit time
+
+dependence, plus the time
+dependence of the position
+
+coordinate, plus the time
+dependence of the momentum
+
+coordinate, which is driven
+by the external force,
+
+acting on this one
+particle density, which
+
+is dependent on
+p1, q1 at time t.
+
+On the right hand
+side of the equation.
+
+I need to worry about a second
+particle with momenta P2
+
+at position Q2 that
+will, therefore,
+
+be able to exert a force.
+
+Once I know the position,
+I can calculate the force
+
+that particle exerts.
+
+What was my notation?
+
+The order was 2 and
+1, dotted by d by dP1.
+
+I need now f2, p1, q2 at time t.
+
+We say, well, this
+is unfortunate.
+
+I have to worry about
+dependence on F2,
+
+but maybe I can get
+away with things
+
+by estimating
+order of magnitudes
+
+of the various terms.
+
+What is the left hand
+side set of operations?
+
+The left hand side
+set of operations
+
+describes essentially one
+particle moving by itself.
+
+If that particle has to cross
+a distance of this order of L,
+
+and I tell you that the typical
+velocity of these particles
+
+is off the order of V, then
+that time scale is going
+
+to be of the order of L
+over V. The operations
+
+here will give me
+a V over L, which
+
+is what we call the
+inverse of Tau u.
+
+This is a reasonably
+long macroscopic time.
+
+OK, that's fine.
+
+How big is the right hand side?
+
+We said that the
+right hand side has
+
+something to do with collisions.
+
+I have a particle in my system.
+
+Let's say that particle has
+some characteristic dimension
+
+that we call d.
+
+This particle is moving with
+velocity V. Alternatively,
+
+you can think of this
+particle as being stationary,
+
+and all the other
+particles are coming at it
+
+with some velocity V.
+
+If I say that the density
+of these particles is n,
+
+then the typical time for which,
+as I shoot these particles,
+
+they will hit this
+target is related
+
+to V squared and V, the
+volume of particles.
+
+Over time t, I have to
+consider this times V tau x.
+
+V tau xn V squared should
+be of the order of one.
+
+This gave us a
+formula for tau x.
+
+The inverse of tau
+x that controls
+
+what's happening on this
+side is n V squared V.
+
+Is the term on the right
+hand side more important,
+
+or the term on the
+left hand side?
+
+The term on the
+right hand side has
+
+to do with the two body term.
+
+There's a particle
+that is moving,
+
+and then there's
+another particle
+
+with a slightly different
+velocity that it is behind it.
+
+In the absence of
+collisions, these particles
+
+would just go along
+a straight line.
+
+They would bounce off the
+walls, but the magnitude
+
+of their energy,
+and hence, velocity,
+
+would not change from
+these elastic collisions.
+
+But if the particles
+can catch up
+
+and interact, which is governed
+by V2, V on the other side,
+
+then what happens is that the
+particles, when they interact,
+
+would collide and
+go different ways.
+
+Quickly, their velocities,
+and momenta, and everything
+
+would get mixed up.
+
+How rapidly that happens depends
+on this collision distance,
+
+which is much less than
+the size of the system,
+
+and, therefore, the term that
+you have on the right hand
+
+side in magnitude is
+much larger than what
+
+is happening on
+the left hand side.
+
+There is no way in
+order to describe
+
+the relaxation of the gas
+that I can neglect collisions
+
+between gas particles.
+
+If I neglect collisions
+between gas particles,
+
+there is no reason why
+the kinetic energies
+
+of individual particles
+should change.
+
+They would stay
+the same forever.
+
+I have to keep this.
+
+Let's go and look at the second
+equation in the hierarchy.
+
+What do you have?
+
+You have d by dT, P1 over m d
+by d Q1, P2 over m, P d by d Q2.
+
+Then we have F1 d
+by d Q1, plus F2, d
+
+by d Q2 coming from
+the external potential.
+
+Then we have the force
+that the involves
+
+the collision between
+particles one and two.
+
+When I write down the
+Hamiltonian for two particles,
+
+there is going to be
+already for two particles
+
+and interactions between them.
+
+That's where the
+F1 2 comes from.
+
+F1 2 changes d by the
+momentum of particle one.
+
+I should write, it's
+2 1 that changes
+
+momentum of particle two.
+
+But as 2 1 is simply minus F1
+2, I can put the two of them
+
+together in this fashion.
+
+This acting on F2 is
+then equal to something
+
+like integral over V3, F3 1,
+d by dP1, plus F3 2, d by dP2.
+
+[INAUDIBLE] on F3 P1
+and Q3 [INAUDIBLE].
+
+Are we going to do this forever?
+
+Well, we said, let's
+take another look
+
+at the magnitude of
+the various terms.
+
+This term on the
+right hand side still
+
+involves a collision that
+involves a third particle.
+
+I have to find that
+third particle,
+
+so I need to have,
+essentially, a third particle
+
+within some
+characteristic volume,
+
+so I have something
+that is of that order.
+
+Whereas on the
+left hand side now,
+
+I have a term that
+from all perspectives,
+
+looks like the kinds of terms
+that I had before except
+
+that it involves the collision
+between two particles.
+
+What it describes is the
+duration that collision.
+
+We said this is of the
+order of 1 over tau
+
+c, which replaces
+the n over there
+
+with some characteristic
+dimension.
+
+Suddenly, this term is very big.
+
+We should be able to use that.
+
+There was a question.
+
+AUDIENCE: On the left hand
+side of both of your equations,
+
+for F1 and F2, shouldn't
+all the derivatives that
+
+are multiplied by your
+forces be derivatives
+
+of the effects of momentum?
+[INAUDIBLE] the coordinates?
+
+[INAUDIBLE] reasons?
+
+PROFESSOR: Let's go back here.
+
+I have a function that
+depends on P, Q, and t.
+
+Then there's the explicit
+time derivative, d by dt.
+
+Then there is the Q dot here,
+which will go by d by dQ.
+
+Then there's the P dot term
+that will go by d by dP.
+
+All of things have to be there.
+
+I should have derivatives
+in respect to momenta,
+
+and derivatives with
+respect to coordinate.
+
+Dimensions are, of
+course, important.
+
+Somewhat, what I write
+for this and for this
+
+should make up for that.
+
+As I have written it now,
+it's obvious, of course.
+
+This has dimensions of Q
+over T. The Q's cancel.
+
+I would have one over
+T. D over Dps cancel.
+
+I have 1 over P. Here,
+dimensionality is correct.
+
+I have to just make sure
+I haven't made a mistake.
+
+Q dot is a velocity.
+
+Velocity is momentum
+divided by mass.
+
+So that should
+dimensionally work out.
+
+P dot is a force.
+
+Everything here is force.
+
+In a reasonable coordinate--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: What did I do here?
+
+I made mistakes?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Why didn't
+you say that in a way
+
+that-- If I don't
+understand the question,
+
+please correct me before I
+spend another five minutes.
+
+Hopefully, this is now
+free of these deficiencies.
+
+This there is very big.
+
+Now, compared to the
+right hand side in fact,
+
+we said that the
+right hand side is
+
+smaller by a factor that
+measures how many particles
+
+are within an
+interaction volume.
+
+And for a typical
+gas, this would
+
+be a number that's of the
+order of 10 to the minus 4.
+
+Using 10 to the minus
+4 being this small,
+
+we are going to set the
+right hand side to zero.
+
+Now, I don't have to
+write the equation for F2.
+
+I'll answer a question here that
+may arise, which is ultimately,
+
+we will do sufficient
+manipulations
+
+so that we end up with a
+particular equation, known
+
+as the Boltzmann
+Equation, that we
+
+will show does not obey
+the time reversibility
+
+that we wrote over here.
+
+Clearly, that is built in to the
+various approximations I make.
+
+The first question
+is, the approximation
+
+that I've made here,
+did I destroy this time
+
+reversibility?
+
+The answer is no.
+
+You can look at this
+set of equations,
+
+and do the manipulations
+necessary to see
+
+what happens if P goes to minus
+P. You will find that you will
+
+be able to reverse your
+trajectory without any problem.
+
+Yes?
+
+AUDIENCE: Given that it
+is only an interaction
+
+from our left side
+that's very big,
+
+that's the reason why we can
+ignore the stuff on the right.
+
+Why is it that we
+are then keeping
+
+all of the other terms that
+were even smaller before?
+
+PROFESSOR: I will ignore them.
+
+Sure.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: There was the
+question of time reversibility.
+
+This term here has to do
+with three particles coming
+
+together, and how
+that would modify what
+
+we have for just
+two-body collisions.
+
+In principle, there
+is some probability
+
+to have three particles
+coming together
+
+and some combined interactions.
+
+You can imagine some
+fictitious model,
+
+which in addition to these
+two-body interactions,
+
+you cook up some body
+interaction so that it
+
+precisely cancels what
+would have happened
+
+when three particles
+come together.
+
+We can write a computer
+program in which
+
+we have two body conditions.
+
+But if three bodies come
+close enough to each other,
+
+they essentially become ghosts
+and pass through each other.
+
+That computer program
+would be fully reversible.
+
+That's why sort of
+dropping this there
+
+is not causing any
+problems at this point.
+
+What is it that you
+have included so far?
+
+What we have is a situation
+where the change in F1
+
+is governed by a
+process in which I
+
+have a particle that I
+describe on the left hand
+
+side with momentum one, and
+it collides with some particle
+
+that I'm integrating over, but
+in some particular instance
+
+of integration, has momentum P2.
+
+Presumably they come
+close enough to each other
+
+so that afterwards, the
+momenta have changed over so
+
+that I have some P1 prime,
+and I have some P2 prime.
+
+We want to make sure that we
+characterize these correctly.
+
+There was a question about
+while this term is big,
+
+these kinds of terms are small.
+
+Why should I basically
+bother to keep them?
+
+It is reasonable.
+
+What we are following here are
+particles in my picture that
+
+were ejected by the
+first box, and they
+
+collide into each
+other, or they were
+
+colliding in the first box.
+
+As long as you are away from
+the [? vols ?] of the container,
+
+you really don't care
+about these terms.
+
+They don't really
+moved very rapidly.
+
+This is the process of
+collision of two particles,
+
+and it's also the same process
+that is described over here.
+
+Somehow, I should be able
+to simplify the collision
+
+process that is going on
+here with the knowledge
+
+that the evolution
+of two particles
+
+is now completely deterministic.
+
+This equation by itself
+says, take two particles
+
+as if they are the only
+thing in the universe,
+
+and they would follow some
+completely deterministic
+
+trajectory, that if you
+put lots of them together,
+
+is captured through
+this density.
+
+Let's see whether we can
+massage this equation
+
+to look like this equation.
+
+Well, the force term, we
+have, except that here we
+
+have dP by P1 here.
+
+We have d by dP
+1 minus d by dP2.
+
+So let's do this.
+
+Minus d by dP2, acting on F2.
+
+Did I do something wrong?
+
+The answer is no, because I
+added the complete derivative
+
+over something that
+I'm integrating over.
+
+This is perfectly
+legitimate mathematics.
+
+This part now looks like this.
+
+I have to find what is the
+most important term that
+
+matches this.
+
+Again, let's think
+about this procedure.
+
+What I have to make
+sure of is what
+
+is the extent of the
+collision, and how important is
+
+the collision?
+
+If I have one
+particle moving here,
+
+and another particle off there,
+they will pass each other.
+
+Nothing interesting
+could happen.
+
+The important thing is how
+close they come together.
+
+It Is kind of
+important that I keep
+
+track of the relative
+coordinate, Q,
+
+which is Q2 minus Q1,
+as opposed to the center
+
+of mass coordinate, which
+is just Q1 plus Q2 over 2.
+
+That kind of also
+indicates maybe it's
+
+a good thing for me to
+look at this entire process
+
+in the center of mass frame.
+
+So this is the lab frame.
+
+If I were to look at this
+same picture in the center
+
+of mass frame,
+what would I have?
+
+In the center of mass frame, I
+would have the initial particle
+
+coming with P1 prime, P1
+minus P center of mass.
+
+The other particle that
+you are interacting with
+
+comes with P2 minus
+P center of mass.
+
+I actually drew these
+vectors that are hopefully
+
+equal and opposite,
+because you know
+
+that in the center of
+mass, one of them, in fact,
+
+would be P1 minus P2 over 2.
+
+The other would be
+P2 minus P1 over 2.
+
+They would, indeed,
+in the center of mass
+
+be equal and opposite momenta.
+
+Along the direction
+of these objects,
+
+I can look at how close
+they come together.
+
+I can look at some
+coordinate that I
+
+will call A, which measures
+the separation between them
+
+at some instant of time.
+
+Then there's another
+pair of coordinates
+
+that I could put into a vector
+that tells me how head to head
+
+they are.
+
+If I think about they're
+being on the center of mass,
+
+two things that are
+approaching each other,
+
+they can either
+approach head on-- that
+
+would correspond
+to be equal to 0--
+
+or they could be slightly
+off a head-on collision.
+
+There is a so-called
+impact parameter
+
+B, which is a measure
+of this addition fact.
+
+Why is that going to
+be relevant to us?
+
+Again, we said that there
+are parts of this expression
+
+that all of the
+order of this term,
+
+they're kind of
+not that important.
+
+If I think about the collision,
+and what the collision does,
+
+I will have forces that
+are significant when
+
+I am within this
+range of interactions,
+
+D. I really have to look at
+what happens when the two
+
+things come close to each other.
+
+It Is only when this relative
+parameter A has approached D
+
+that these particles
+will start to deviate
+
+from their straight
+line trajectory,
+
+and presumably go, to say in
+this case, P2 prime minus P
+
+center of mass.
+
+This one occurs
+[? and ?] will go,
+
+and eventually P1 prime
+minus P center of mass.
+
+These deviations will
+occur over a distance
+
+that is of the order of
+this collision and D.
+
+The important changes that
+occur in various densities,
+
+in various
+potentials, et cetera,
+
+are all taking place when this
+relative coordinate is small.
+
+Things become big when the
+relative coordinate is small.
+
+They are big as a function
+of the relative coordinate.
+
+In order to get big
+things, what I need to do
+
+is to replace these
+d by dQ's with
+
+the corresponding
+derivatives with respect
+
+to the center of mass.
+
+One of them would come
+be the minus sign.
+
+The other would come
+be the plus sign.
+
+It doesn't matter
+which is which.
+
+It depends on the
+definition, whether I
+
+make Q2 minus Q1,
+or Q1 minus Q2.
+
+We see that the big
+terms are the force that
+
+changes the momenta
+and the variations
+
+that you have over these
+relative coordinates.
+
+What I can do now
+is to replace this
+
+by equating the two big
+terms that I have over here.
+
+The two big terms
+are P2 minus P1
+
+over m, dotted by d by dQ of F2.
+
+There is some other
+approximation that I did.
+
+As was told to me before,
+this is the biggest term,
+
+and there is the
+part of this that
+
+is big and compensates for that.
+
+But there are all these
+other bunches of terms.
+
+There's also this d by dt.
+
+What I have done
+over here is to look
+
+at this slightly coarser
+perspective on time.
+
+Increasing all the equations
+that I have over there
+
+tells me everything
+about particles
+
+approaching each
+other and going away.
+
+I can follow through
+the mechanics
+
+precisely everything
+that is happening, even
+
+in the vicinity
+of this collision.
+
+If I have two squishy balls,
+and I run my hand through them
+
+properly, I can
+see how the things
+
+get squished then released.
+
+There's a lot of
+information, but again, a lot
+
+of information
+that I don't really
+
+care to know as far as
+the properties of this gas
+
+expansion process is concerned.
+
+What you have done is to forget
+about the detailed variations
+
+in time and space that
+are taking place here.
+
+We're going to shortly make
+that even more explicit
+
+by noting the following.
+
+This integration over
+here is an integration
+
+over phase space of
+the second particle.
+
+I had written before d
+cubed, P2, d cubed, Q2,
+
+but I can change
+coordinates and look
+
+at the relative
+coordinate, Q, over here.
+
+What I'm asking is,
+I have one particle
+
+moving through the gas.
+
+What is the chance that
+the second particle comes
+
+with momentum P2, and the
+appropriate relative distance
+
+Q, and I integrate over both the
+P and the relative distance Q?
+
+This is the quantity
+that I have to integrate.
+
+Let's do one more
+calculation, and then we
+
+will try to give a
+physical perspective.
+
+In this picture of the center
+of mass, what did I do?
+
+I do replaced the coordinate, Q,
+with a part that was the impact
+
+parameter, which
+had two components,
+
+and a part that was
+the relative distance.
+
+What was this relative distance?
+
+The relative
+distance was measured
+
+along this line that was
+giving me the closest approach.
+
+What is the direction
+of this line?
+
+The direction of this
+line is P1 minus P2.
+
+This is P1 minus P2 over 2.
+
+It doesn't matter.
+
+The direction is P1 minus P2.
+
+What I'm doing here is I am
+taking the derivative precisely
+
+along this line of
+constant approach.
+
+I'm taking a derivative, and
+I'm integrating along that.
+
+If I were to rewrite the
+whole thing, what do I have?
+
+I have d by dt, plus P1 over m,
+d by dQ1, plus F1, d by dP1--
+
+don't make a mistake--
+acting on F1, P1, Q1, t.
+
+What do I have to write
+on the right hand side?
+
+I have an integral
+over the momentum
+
+of this particle with which
+I'm going to make a collision.
+
+I have an integral over
+the impact parameter
+
+that tells me the distance
+of closest approach.
+
+I have to do the
+magnitude of P2 minus P1
+
+over n, which is
+really the magnitude
+
+of the relative velocity
+of the two particles.
+
+I can write it as P2
+minus P1, or P1 minus P2.
+
+These are, of course, vectors.
+
+and I look at the modulus.
+
+I have the integral
+of the derivative.
+
+Very simply, I will
+write the answer
+
+as F2 that is evaluated
+at some large distance,
+
+plus infinity minus F2
+evaluated at minus infinity.
+
+I have infinity.
+
+In principle, I have
+to integrate over F2
+
+from minus infinity
+to plus infinity.
+
+But once I am beyond
+the range of where
+
+the interaction changes,
+then the two particles
+
+just move away forever.
+
+They will never see each other.
+
+Really, what I should write here
+is F2 of-- after the collision,
+
+I have P1 prime, P2
+prime, at some Q plus,
+
+minus F2, P1, P2, at
+some position minus.
+
+What I need to do is to
+do the integration when
+
+I'm far away from the
+collision, or wait
+
+until I am far
+after the collision.
+
+Really, I have to just
+integrate slightly below, after,
+
+and before the collision occurs.
+
+In principle, if I
+just go a few d's
+
+in one direction or
+the other direction,
+
+this should be enough.
+
+Let's see physically
+what this describes.
+
+There is a connection
+between this
+
+and this thing that I
+had over here, in fact.
+
+This equation on the left
+hand side, if it was zero,
+
+it would describe
+one particle that
+
+is just moving by itself until
+it hits the wall, at which
+
+point it basically
+reverses its trajectory,
+
+and otherwise goes forward.
+
+But what you have on
+the right hand side
+
+says that suddenly
+there could be
+
+another particle with
+which I interact.
+
+Then I change my direction.
+
+I need to know the
+probability, given
+
+that I'm moving
+with velocity P1,
+
+that there is a second
+particle with P2 that
+
+comes close enough.
+
+There is this additional factor.
+
+From what does this
+additional factor come?
+
+It's the same factor
+that we have over here.
+
+It is, if you have a
+target of size d squared,
+
+and we have a set of
+bullets with a density of n,
+
+the number of collisions that
+I get depends both on density
+
+and how fast these things go.
+
+The time between collisions, if
+you like, is proportional to n,
+
+and it is also related to
+V. That's what this is.
+
+I need some kind of a time
+between the collisions
+
+that I make.
+
+I have already
+specified that I'm
+
+only interested in the
+set of particles that
+
+have momentum P2 for this
+particular [? point in ?]
+
+integration, and that they
+have this kind of area or cross
+
+section.
+
+So I replace this
+V squared and V
+
+with the relative coordinates.
+
+This is the corresponding
+thing to V squared,
+
+and this is really a
+two particle density.
+
+This is a subtraction.
+
+The addition is
+because it is true
+
+that I'm going with velocity P1,
+and practically, any collisions
+
+that are significant
+will move me off kilter.
+
+So there has to be a
+subtraction for the channel that
+
+was described by P1
+because of this collision.
+
+This then, is the
+addition, because it
+
+says that it could be that
+there is no particle going
+
+in the horizontal direction.
+
+I was actually coming along
+the vertical direction.
+
+Because of the
+collision, I suddenly
+
+was shifted to move
+along this direction.
+
+The addition comes from having
+particles that would correspond
+
+to momenta that somehow,
+if I were in some sense
+
+to reverse this, and
+then put a minus sign,
+
+a reverse collision
+would create something
+
+that was along the
+direction of P1.
+
+Here I also made
+several approximations.
+
+I said, what is chief among
+them is that basically I
+
+ignored the details of the
+process that is taking place
+
+at scale the order of
+d, so I have thrown away
+
+some amount of detail
+and information.
+
+It is, again, legitimate
+to say, is this
+
+the stage at which you
+made an approximation
+
+so that the time
+reversibility was lost?
+
+The answer is still no.
+
+If you are careful enough with
+making precise definitions
+
+of what these Q's are before
+and after the collision,
+
+and follow what happens if you
+were to reverse everything,
+
+you'll find that the
+equations is fully reversible.
+
+Even at this stage, I have
+not made any transition.
+
+I have made approximations,
+but I haven't made something
+
+to be time irreversible.
+
+That comes at the
+next stage where
+
+we make the so-called
+assumption of molecular chaos.
+
+The assumption is
+that what's the chance
+
+that I have a particle
+here and a particle there?
+
+You would say, it's
+a chance that I
+
+have one here and one there.
+
+You say that if two of
+any P1, P2, Q1, Q2, t
+
+is the same thing as the product
+of F1, P1, Q1, t, F1, P2, Q2,
+
+t.
+
+Of course, this assumption
+is generally varied.
+
+If I were to look
+at the probability
+
+that I have two particles
+as a function of, let's say,
+
+the relative
+separation, I certainly
+
+expect that if
+they are far away,
+
+the density should be the
+product of the one particle
+
+densities.
+
+But you would say that if the
+two particles come to distances
+
+that are closer than
+their separation d,
+
+then the probability and
+the range of interaction d--
+
+and let's say the
+interaction is highly
+
+repulsive like hardcore-- then
+the probability should go to 0.
+
+Clearly, you can
+make this assumption,
+
+but up to some degree.
+
+Part of the reason we
+went through this process
+
+was to indeed make sure that
+we are integrating things
+
+at the locations where
+the particles are
+
+far away from each other.
+
+I said that the range of
+that integration over A
+
+would be someplace
+where they are
+
+far apart after the
+collision, and far apart
+
+before the collision.
+
+You have an
+assumption like that,
+
+which is, in
+principle, something
+
+that I can insert into that.
+
+Having to make a distinction
+between the arguments that
+
+are appearing in this equation
+is kind of not so pleasant.
+
+What you are going to do is
+to make another assumption.
+
+Make sure that everything is
+evaluated at the same point.
+
+What we will eventually now have
+is the equation that d by dt,
+
+plus P1 over n, d by dQ1,
+plus F1, dot, d by dP1,
+
+acting on F1, on
+the left hand side,
+
+is, on the right hand side,
+equal to all collisions
+
+in the particle of
+momentum P2, approaching
+
+at all possible cross
+sections, calculating
+
+the flux of the
+incoming particle
+
+that corresponds to
+that channel, which
+
+is proportional to V2 minus V1.
+
+Then here, we subtract the
+collision of the two particles.
+
+We write that as F1 of
+P1 at this location,
+
+Q1, t, F1 of t2 at the
+same location Q1, t.
+
+Then add F1 prime, P1 prime, Q1
+t, F1 prime, P2 prime, Q2, t.
+
+In order to make the
+equation eventually
+
+manageable, what you
+did is to evaluate all
+
+off the coordinates that
+we have on the right hand
+
+side at the same location, which
+is the same Q1 that you specify
+
+on the left hand side.
+
+That immediately means
+that what you have done
+
+is you have changed the
+resolution with which you
+
+are looking at space.
+
+You have kind of washed
+out the difference
+
+between here and here.
+
+Your resolution has to
+put this whole area that
+
+is of the order of d squared
+or d cubed in three dimensions
+
+into one pixel.
+
+You have changed the
+resolution that you have.
+
+You are not looking at things
+at this [? fine ?] [? state. ?]
+
+You are losing additional
+information here
+
+through this change of
+the resolution in space.
+
+You have also lost
+some information
+
+in making the assumption that
+the two [? point ?] densities
+
+are completely within always
+as the product one particle
+
+densities.
+
+Both of those things
+correspond to taking something
+
+that is very precise
+and deterministic,
+
+and making it kind of vague
+and a little undefined.
+
+It's not surprising then,
+that if you have in some sense
+
+changed the precision of
+your computer-- let's say,
+
+that is running the particles
+forward-- at some point,
+
+you've changed the resolution.
+
+Then you can't
+really run backward.
+
+In fact, to sort of precisely
+be able to run the equations
+
+forward and backward,
+you would need
+
+to keep resolution
+at all levels.
+
+Here, we have sort of removed
+some amount of resolution.
+
+We have a very good guess
+that the equation that you
+
+have over here no longer
+respects time reversal
+
+inversions that you
+had originally posed.
+
+Our next task is to prove
+that you need this equation.
+
+It goes in one particular
+direction in time,
+
+and cannot be drawn
+backward, as opposed to all
+
+of the predecessors that I
+had written up to this point.
+
+Are there any questions?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes, Q prime
+and Q1, not Q1 prime.
+
+There is no dash.
+
+AUDIENCE: Oh, I see.
+
+It is Q1.
+
+PROFESSOR: Yes, it is.
+
+Look at this equation.
+
+On the left hand side,
+what are the arguments?
+
+The arguments are P1 and Q1.
+
+What is it that I have
+on the other side?
+
+I still have P1 and Q1.
+
+I have introduced
+P1 and b, which
+
+is simply an impact parameter.
+
+What I will do is
+I will evaluate
+
+all of these things, always
+at the same location, Q1.
+
+Then I have P1 and P2.
+
+That's part of my story of
+the change in resolution.
+
+When I write here Q1,
+and you say Q1 prime,
+
+but what is Q1 prime?
+
+Is it Q1 plus b?
+
+Is it Q1 minus b?
+
+Something like this
+I'm going to ignore.
+
+It's also legitimate,
+and you should
+
+ask, what is P1
+prime and Q2 prime?
+
+What are they?
+
+What I have to do, is I
+have to run on the computer
+
+or otherwise, the
+equations for what
+
+happens if I have P1
+and P2 come together
+
+at an impact parameter
+that is set by me.
+
+I then integrate
+the equations, and I
+
+find that deterministically,
+that collision will
+
+lead to some P1
+prime and P2 prime.
+
+P1 prime and P2 prime are
+some complicated functions
+
+of P1, P2, and b.
+
+Given that you know two
+particles are approaching
+
+each other at distance d with
+momenta P1 P2, in principle,
+
+you can integrate
+Newton's equations,
+
+and figure out with what
+momenta they end up.
+
+This equation, in fact, hides a
+very, very complicated function
+
+here, which describes
+P1 prime and P2 prime
+
+as a function of P1 and P2.
+
+If you really needed all of
+the details of that function,
+
+you would surely be in trouble.
+
+Fortunately, we don't.
+
+As we shall see shortly, you
+can kind of get a lot of mileage
+
+without knowing that.
+
+Yes, what is your question?
+
+AUDIENCE: There
+was an assumption
+
+that all the interactions
+between different molecules
+
+are central potentials
+[INAUDIBLE].
+
+Does the force of the
+direction between two particles
+
+lie along the [INAUDIBLE]?
+
+PROFESSOR: For the things that
+I have written, yes it does.
+
+I should have been more precise.
+
+I should have put
+absolute value here.
+
+AUDIENCE: You have
+particles moving
+
+along one line
+towards each other,
+
+and b is some arbitrary vector.
+
+You have two directions,
+so you define a plane.
+
+Opposite direction particles
+stay at the same plane.
+
+Have you reduced--
+
+PROFESSOR: Particles
+stay in the same plane?
+
+AUDIENCE: If the two particles
+were moving towards each other,
+
+and also you have
+in the integral
+
+your input parameter,
+which one is [INAUDIBLE].
+
+There's two directions.
+
+All particles align,
+and all b's align.
+
+They form a plane.
+
+[? Opposite ?] direction
+particles [? stand ?] in the--
+
+PROFESSOR: Yes, they
+stand in the same plane.
+
+AUDIENCE: My
+question is, what is
+
+[INAUDIBLE] use the
+integral on the right
+
+from a two-dimensional
+integral [? in v ?]
+
+into employing central symmetry?
+
+PROFESSOR: Yes, you could.
+
+You could, in principle, write
+this as b db, if you like,
+
+if that's what you want.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes, you
+could do that if you
+
+have simple enough potential.
+
+Let's show that this equation
+leads to irreversibility.
+
+That you are going to do here.
+
+This, by the way, is called
+the Boltzmann equation.
+
+There's an associated
+Boltzmann H-Theorem,
+
+which restates the following--
+If F of P1, Q1, and t
+
+satisfies the above
+Boltzmann equation,
+
+then there is a quantity H that
+always decreases in time, where
+
+H is the integral over P
+and Q of F1, log of F1.
+
+The composition of
+irreversibility,
+
+as we saw in thermal
+dynamics, was
+
+that there was a
+quantity entropy that
+
+was always increasing.
+
+If you have calculated
+for this system,
+
+entropy before for the half
+box, and entropy afterwards
+
+for the space both boxes
+occupy, the second one
+
+would certainly be larger.
+
+This H is a quantity like
+that, except that when
+
+it is defined this
+way, it always
+
+decreases as a function of time.
+
+But it certainly is very
+much related to entropy.
+
+You may have asked,
+why did Boltzmann
+
+come across such
+a function, which
+
+is F log F, except that
+actually right now,
+
+you should know
+why you write this.
+
+When we were dealing
+with probabilities,
+
+we introduced the entropy of the
+probability distribution, which
+
+was related to something
+like sum over iPi, log of Pi,
+
+with a minus sign.
+
+Up to this factor
+of normalization N,
+
+this F1 really is a
+one-particle probability.
+
+After this normalization
+N, you have
+
+a one-particle probability,
+the probability
+
+that you have occupation
+of one-particle free space.
+
+This occupation of
+one-particle phase space
+
+is changing as a
+function of time.
+
+What this statement says is
+that if the one-particle density
+
+evolves in time according
+to this equation,
+
+the corresponding
+minus entropy decreases
+
+as a function of time.
+
+Let's see if that's the case.
+
+To prove that, let's do this.
+
+We have the formula for H, so
+let's calculate the H by dt.
+
+I have an integral
+over the phase space
+
+of particle one, the particle
+that I just called one.
+
+I could have
+labeled it anything.
+
+After integration, H is
+only a function of time.
+
+I have to take the
+time derivative.
+
+The time derivative
+can act on F1.
+
+Then I will get the F1
+by dt, times log F1.
+
+Or I will have F1 times
+the derivative of log F1.
+
+The derivative of log F1
+would be dF1 by dt, and then 1
+
+over F1.
+
+Then I multiply by F1.
+
+This term is simply 1.
+
+AUDIENCE: Don't you want to
+write the full derivative,
+
+F1 with respect [INAUDIBLE]?
+
+PROFESSOR: I thought we
+did that with this before.
+
+If you have something that
+I am summing over lots
+
+of [? points, ?] and these
+[? points ?] can be positioned,
+
+then I have S at location
+one, S at location two,
+
+S at location three,
+discretized versions of x.
+
+If I take the time
+derivative, I take
+
+the time derivative
+of this, plus this,
+
+plus this, which are
+partial derivatives.
+
+If I actually take the
+time derivative here,
+
+I get the integral d cubed P1,
+d cubed Q1, the time derivative.
+
+This would be that
+partial dF1 by dt
+
+is the time derivative
+of n, which is 0.
+
+The number of particles
+does not change.
+
+Indeed, I realize that 1
+integrated against dF1 by dt
+
+is the same thing that's here.
+
+This term gives you 0.
+
+All I need to worry
+about is integrating
+
+log F against the Fydt.
+
+I have an integral over P1 and
+Q1 of log F against the Fydt.
+
+We have said that F1 satisfies
+the Boltzmann equation.
+
+So the F1 by dt, if I
+were to rearrange it,
+
+I have the F1 by dt.
+
+I take this part to the
+other side of the equation.
+
+This part is also
+the Poisson bracket
+
+of a one-particle H with F1.
+
+If I take it to
+the other side, it
+
+will be the Poisson
+bracket of H with F1.
+
+Then there is this
+whole thing that
+
+involves the collision
+of two particles.
+
+So I define whatever is
+on the right hand side
+
+to be some collision
+operator that acts on two
+
+[? powers ?] of F1.
+
+This is plus a collision
+operator, F1, F1.
+
+What I do is I
+replace this dF1 by dt
+
+with the Poisson bracket of H,
+or H1, if you like, with F1.
+
+The collision operator I will
+shortly write explicitly.
+
+But for the time being, let
+me just write it as C of F1.
+
+There is a first
+term in this sum--
+
+let's call it number one--
+which I claim to be 0.
+
+Typically, when you
+get these integrations
+
+with Poisson brackets,
+you would get 0.
+
+Let's explicitly show that.
+
+I have an integral over
+P1 and Q1 of log of F1,
+
+and this Poisson
+bracket of H1 and F1,
+
+which is essentially
+these terms.
+
+Alternatively, I could write
+it as dH1 by dQ1, dF1 by dt1,
+
+minus the H1 by
+dt1, dF1, by dQ1.
+
+I've explicitly written this
+form for the one-particle
+
+in terms of the Hamiltonian.
+
+The advantage of
+that is that now I
+
+can start doing
+integrations by parts.
+
+I'm taking derivatives
+with respect to P,
+
+but I have integrations
+with respect to P here.
+
+I could take the F1 out.
+
+I will have a minus.
+
+I have an integral, P1, Q1.
+
+I took F1 out.
+
+Then this d by dP1 acts on
+everything that came before it.
+
+It can act on the H1.
+
+I would get d2 H1 with
+respect to dP1, dQ1.
+
+Or it could act on the
+log of F1, in which case
+
+I will get set dH1 by dQ1.
+
+Then I would have d
+by dP acting on log
+
+of F, which would
+give me dF1 by dP1,
+
+then the derivative of the
+log, which is 1 over F1.
+
+This is only the first term.
+
+I also have this term, with
+which I will do the same thing.
+
+AUDIENCE: [INAUDIBLE] The
+second derivative [INAUDIBLE]
+
+should be multiplied
+by log of F.
+
+PROFESSOR: Yes, it should be.
+
+It is Log F1.
+
+Thank you.
+
+For the next term, I have F1.
+
+I have d2 H1, and the other
+order of derivatives, dQ1, dP1.
+
+Now I'll make sure I
+write down the log of F1.
+
+Then I have dH1
+with respect to dQ1.
+
+Then I have a dot product with
+the derivative of log F, which
+
+is the derivative of F1 with
+respect to Q1 and 1 over F1.
+
+Here are the terms
+that are proportional
+
+to the second derivative.
+
+The order of the
+derivatives does not matter.
+
+One often is positive.
+
+One often is negative,
+so they cancel out.
+
+Then I have these
+additional terms.
+
+For the additional
+terms, you'll note
+
+that the F1 and the
+1 over F1 cancels.
+
+These are just a product
+of two first derivatives.
+
+I will apply the five
+parts process one more time
+
+to get rid of the derivative
+that is acting on F1.
+
+The answer becomes plus
+d cubed P1, d cubed Q1.
+
+Then I have F1, d2 H1, dP1,
+dQ1, minus d2 H1, dQ1, dP1.
+
+These two cancel each other
+out, and the answer is 0.
+
+So that first term vanishes.
+
+Now for the second term,
+number two, what I have
+
+is the first term vanished.
+
+So I have the H by dt.
+
+It is the integral
+over P1 and Q1.
+
+I have log of F1.
+
+F1 is a function of
+P1, and Q1, and t.
+
+I will focus, and make sure I
+write the argument of momentum,
+
+for reasons that will
+become shortly apparent.
+
+I have to multiply with
+the collision term.
+
+The collision term
+involves integrations
+
+over a second particle,
+over an impact parameter,
+
+a relative velocity, once I
+have defined what P2 and P1 are.
+
+I have a subtraction
+of F evaluated at P1,
+
+F evaluated at
+P2, plus addition,
+
+F evaluated at P1 prime,
+F evaluated at P2 prime.
+
+Eventually, this whole thing
+is only a function of time.
+
+There are a whole bunch of
+arguments appearing here,
+
+but all of those arguments
+are being integrated over.
+
+In particular, I have arguments
+that are indexed by P1 and P2.
+
+These are dummy
+variables of integration.
+
+If I have a function
+of x and y that I'm
+
+integrating over x and
+y, I can call x "z."
+
+I can call y "t."
+
+I would integrate
+over z and t, and I
+
+would have the same answer.
+
+I would have exactly
+the same answer
+
+if I were to call all of the
+dummy integration variable that
+
+is indexed 1, "2."
+
+Any dummy variable
+that is indexed 2,
+
+if I rename it and call it 1,
+the integral would not change.
+
+If I do that, what do I have?
+
+I have integral
+over Q-- actually,
+
+let's get of the
+integration number on Q.
+
+It really doesn't matter.
+
+I have the integrals
+over P1 and P1.
+
+I have to integrate over
+both sets of momenta.
+
+I have to integrate over
+the cross section, which
+
+is relative between 1 and 2.
+
+I have V2 minus V1, rather
+than V1 minus V2, rather than
+
+V2 minus V1.
+
+The absolute value
+doesn't matter.
+
+If I were to replace these
+indices with an absolute value,
+
+[? or do a ?] V2 minus V1
+goes to minus V1 minus V2.
+
+The absolute value
+does not change.
+
+Here, what do I have?
+
+I have minus F of P1.
+
+It becomes F of P2, F of
+P1, plus F of P2 prime,
+
+f of P1 prime.
+
+They are a product.
+
+It doesn't really matter in
+which order I write them.
+
+The only thing
+that really matters
+
+is that the argument was
+previously called F1 of P1
+
+for the log, and now it
+will be called F1 of P2.
+
+Just its name changed.
+
+If I take this, and the
+first way of writing things,
+
+which are really two ways of
+writing the same integral,
+
+and just average them, I will
+get 1/2 an integral d cubed Q,
+
+d cubed P1, d cubed P2,
+d2 b, and V2 minus V1.
+
+I will have F1 of P1, F1 of
+P2, plus F1 of P1 prime, F1
+
+of P2 prime.
+
+Then in one term, I
+had log of F1 of P1,
+
+and I averaged it
+with the other way
+
+of writing things, which was
+log of F-- let's put the two
+
+logs together, multiplied by F1.
+
+So the sum of the
+two logs I wrote,
+
+that's a log of the product.
+
+I just rewrote that equation.
+
+If you like, I symmetrized It
+with respect to index 1 and 2.
+
+So the log of 1,
+that previously had
+
+one argument through
+this symmetrization,
+
+became one half
+of the sum of it.
+
+The next thing one has to
+think about, what I want to do,
+
+is to replace primed and
+unprimed coordinates.
+
+What I would
+eventually write down
+
+is d cubed P1 prime, d cubed P2
+prime, d2 b, V2 prime minus V1
+
+prime, minus F1 of P1 prime,
+F1 of P2 prime, plus F1 of P1,
+
+F1 of P2.
+
+Then log of F1 of P1
+prime, F1 of P2 prime.
+
+I've symmetrized originally
+the indices 1 and 2
+
+that were not quite
+symmetric, and I end up
+
+with an expression that has
+variables P1, P2, and functions
+
+P1 prime and P2 prime, which
+are not quite symmetric again,
+
+because I have F's evaluated
+for P's, but not for P primes.
+
+What does this mean?
+
+This mathematical expression
+that I have written down here
+
+actually is not correct,
+because what this amounts to,
+
+is to change variables
+of integration.
+
+In the expression
+that I have up here,
+
+P1 and P2 are variables
+of integration.
+
+P1 prime and P2 prime are
+some complicated functions
+
+of P1 and P2.
+
+P1 prime is some complicated
+function that I don't know.
+
+P1, P2, and V, for which I
+need to solve in principle,
+
+is Newton's equation.
+
+This is similarly for P2 prime.
+
+What I have done
+is I have changed
+
+from my original variables
+to these functions.
+
+When I write things over here,
+now P1 prime and P2 prime
+
+are the integration variables.
+
+P1 and P2 are supposed
+to be regarded
+
+as functions of P1
+prime and P2 prime.
+
+You say, well, what
+does that mean?
+
+You can't simply
+take an integral dx,
+
+let's say F of some function of
+x, and replace this function.
+
+You can't call it
+a new variable,
+
+and do integral dx prime.
+
+You have to multiply with the
+Jacobian of the transformation
+
+that takes you from the P
+variables to the new variables.
+
+My claim is that this
+Jacobian of the integration
+
+is, in fact, the unit.
+
+The reason is as follows.
+
+These equations that have
+to be integrated to give me
+
+the correlation are
+time reversible.
+
+If I give you two momenta, and
+I know what the outcomes are,
+
+I can write the
+equations backward,
+
+and I will have the
+opposite momenta go back
+
+to minus the original momenta.
+
+Up to a factor of minus, you
+can see that this equation has
+
+this character, that P1, P2
+go to P1 prime, P2 prime, then
+
+minus P1 prime, minus P2
+prime, go to P1, and P2.
+
+If you sort of
+follow that, and say
+
+that you do the
+transformation twice,
+
+you have to get back up
+to where a sign actually
+
+disappears to where you want.
+
+You have to multiply
+by two Jacobians,
+
+and you get the same unit.
+
+You can convince yourself that
+this Jacobian has to be unit.
+
+Next time, I guess we'll
+take it from there.
+
+I will explain this
+stuff a little bit more,
+
+and show that this implies what
+we had said about the Boltzmann
+
+equation.
\ No newline at end of file
diff --git a/z8HKWUWS-lA.txt b/z8HKWUWS-lA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1aba4e59e5fb4eb2b218c998701c0387a6daf400
--- /dev/null
+++ b/z8HKWUWS-lA.txt
@@ -0,0 +1,12920 @@
+align:start position:0%
+ 
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+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Last week we talked about the key
+
+ align:start position:0%
+Last week we talked about the key
+ 
+
+ align:start position:0%
+Last week we talked about the key
+components of a proof. Propositions,
+
+ align:start position:0%
+components of a proof. Propositions,
+ 
+
+ align:start position:0%
+components of a proof. Propositions,
+axioms, and logical deductions. And as
+
+ align:start position:0%
+axioms, and logical deductions. And as
+ 
+
+ align:start position:0%
+axioms, and logical deductions. And as
+you probably talked about during
+
+ align:start position:0%
+you probably talked about during
+ 
+
+ align:start position:0%
+you probably talked about during
+recitation,
+
+ align:start position:0%
+recitation,
+ 
+
+ align:start position:0%
+recitation,
+we're not going to worry too much about
+
+ align:start position:0%
+we're not going to worry too much about
+ 
+
+ align:start position:0%
+we're not going to worry too much about
+what axioms or logical deductions that
+
+ align:start position:0%
+what axioms or logical deductions that
+ 
+
+ align:start position:0%
+what axioms or logical deductions that
+you use. Anything that is reasonable is
+
+ align:start position:0%
+you use. Anything that is reasonable is
+ 
+
+ align:start position:0%
+you use. Anything that is reasonable is
+fine by us. We're not going to ask you
+
+ align:start position:0%
+fine by us. We're not going to ask you
+ 
+
+ align:start position:0%
+fine by us. We're not going to ask you
+to know what modus ponins is or to label
+
+ align:start position:0%
+to know what modus ponins is or to label
+ 
+
+ align:start position:0%
+to know what modus ponins is or to label
+some law when you make a logical
+
+ align:start position:0%
+some law when you make a logical
+ 
+
+ align:start position:0%
+some law when you make a logical
+deduction. Just, you know, be
+
+ align:start position:0%
+deduction. Just, you know, be
+ 
+
+ align:start position:0%
+deduction. Just, you know, be
+reasonable. any fact you knew coming
+
+ align:start position:0%
+reasonable. any fact you knew coming
+ 
+
+ align:start position:0%
+reasonable. any fact you knew coming
+into this course about mathematics
+
+ align:start position:0%
+into this course about mathematics
+ 
+
+ align:start position:0%
+into this course about mathematics
+probably close enough to use as an
+
+ align:start position:0%
+probably close enough to use as an
+ 
+
+ align:start position:0%
+probably close enough to use as an
+axiom. You want to make sure your axioms
+
+ align:start position:0%
+axiom. You want to make sure your axioms
+ 
+
+ align:start position:0%
+axiom. You want to make sure your axioms
+are consistent. Uh but that's okay. Now
+
+ align:start position:0%
+are consistent. Uh but that's okay. Now
+ 
+
+ align:start position:0%
+are consistent. Uh but that's okay. Now
+the exception to this would be is say
+
+ align:start position:0%
+the exception to this would be is say
+ 
+
+ align:start position:0%
+the exception to this would be is say
+we're on an exam and we ask you to prove
+
+ align:start position:0%
+we're on an exam and we ask you to prove
+ 
+
+ align:start position:0%
+we're on an exam and we ask you to prove
+some proposition P. Well, you can't say
+
+ align:start position:0%
+some proposition P. Well, you can't say
+ 
+
+ align:start position:0%
+some proposition P. Well, you can't say
+I already knew P. It's an axiom check.
+
+ align:start position:0%
+I already knew P. It's an axiom check.
+ 
+
+ align:start position:0%
+I already knew P. It's an axiom check.
+That's not so good. We're asking you to
+
+ align:start position:0%
+That's not so good. We're asking you to
+ 
+
+ align:start position:0%
+That's not so good. We're asking you to
+prove it from some more elementary
+
+ align:start position:0%
+prove it from some more elementary
+ 
+
+ align:start position:0%
+prove it from some more elementary
+facts.
+
+ align:start position:0%
+facts.
+ 
+
+ align:start position:0%
+facts.
+Okay. It's also you don't want to be
+
+ align:start position:0%
+Okay. It's also you don't want to be
+ 
+
+ align:start position:0%
+Okay. It's also you don't want to be
+making wild leaps of faith or saying
+
+ align:start position:0%
+making wild leaps of faith or saying
+ 
+
+ align:start position:0%
+making wild leaps of faith or saying
+it's obvious that unless it really is
+
+ align:start position:0%
+it's obvious that unless it really is
+ 
+
+ align:start position:0%
+it's obvious that unless it really is
+obvious. That kind of stuff can get you
+
+ align:start position:0%
+obvious. That kind of stuff can get you
+ 
+
+ align:start position:0%
+obvious. That kind of stuff can get you
+in trouble. Much better to sort of
+
+ align:start position:0%
+in trouble. Much better to sort of
+ 
+
+ align:start position:0%
+in trouble. Much better to sort of
+explain the reasoning in the proof.
+
+ align:start position:0%
+explain the reasoning in the proof.
+ 
+
+ align:start position:0%
+explain the reasoning in the proof.
+Now, the proofs that we covered last
+
+ align:start position:0%
+Now, the proofs that we covered last
+ 
+
+ align:start position:0%
+Now, the proofs that we covered last
+week in recitation and the problem set
+
+ align:start position:0%
+week in recitation and the problem set
+ 
+
+ align:start position:0%
+week in recitation and the problem set
+were all examples of what are called
+
+ align:start position:0%
+were all examples of what are called
+ 
+
+ align:start position:0%
+were all examples of what are called
+direct proofs. You start with some
+
+ align:start position:0%
+direct proofs. You start with some
+ 
+
+ align:start position:0%
+direct proofs. You start with some
+axioms. You have some theorems you knew
+
+ align:start position:0%
+axioms. You have some theorems you knew
+ 
+
+ align:start position:0%
+axioms. You have some theorems you knew
+before or you proved along the way and
+
+ align:start position:0%
+before or you proved along the way and
+ 
+
+ align:start position:0%
+before or you proved along the way and
+you make logical deductions until you
+
+ align:start position:0%
+you make logical deductions until you
+ 
+
+ align:start position:0%
+you make logical deductions until you
+get to where you want to go. The theorem
+
+ align:start position:0%
+get to where you want to go. The theorem
+ 
+
+ align:start position:0%
+get to where you want to go. The theorem
+We're going to start today with an
+
+ align:start position:0%
+We're going to start today with an
+ 
+
+ align:start position:0%
+We're going to start today with an
+indirect proof. For example, a proof by
+
+ align:start position:0%
+indirect proof. For example, a proof by
+ 
+
+ align:start position:0%
+indirect proof. For example, a proof by
+contradiction. And this is a little bit
+
+ align:start position:0%
+contradiction. And this is a little bit
+ 
+
+ align:start position:0%
+contradiction. And this is a little bit
+different. In a proof by contradiction,
+
+ align:start position:0%
+different. In a proof by contradiction,
+ 
+
+ align:start position:0%
+different. In a proof by contradiction,
+you assume the opposite of what you're
+
+ align:start position:0%
+you assume the opposite of what you're
+ 
+
+ align:start position:0%
+you assume the opposite of what you're
+trying to prove.
+
+ align:start position:0%
+trying to prove.
+ 
+
+ align:start position:0%
+trying to prove.
+Then you just take steps forward,
+
+ align:start position:0%
+Then you just take steps forward,
+ 
+
+ align:start position:0%
+Then you just take steps forward,
+logical deductions forward until you
+
+ align:start position:0%
+logical deductions forward until you
+ 
+
+ align:start position:0%
+logical deductions forward until you
+arrive at a contradiction. Something
+
+ align:start position:0%
+arrive at a contradiction. Something
+ 
+
+ align:start position:0%
+arrive at a contradiction. Something
+where you prove false equals true.
+
+ align:start position:0%
+where you prove false equals true.
+ 
+
+ align:start position:0%
+where you prove false equals true.
+Now, if you can ever get to the point
+
+ align:start position:0%
+Now, if you can ever get to the point
+ 
+
+ align:start position:0%
+Now, if you can ever get to the point
+where you prove something is false
+
+ align:start position:0%
+where you prove something is false
+ 
+
+ align:start position:0%
+where you prove something is false
+that's and true, that means what you
+
+ align:start position:0%
+that's and true, that means what you
+ 
+
+ align:start position:0%
+that's and true, that means what you
+assumed at the start had to be wrong.
+
+ align:start position:0%
+assumed at the start had to be wrong.
+ 
+
+ align:start position:0%
+assumed at the start had to be wrong.
+Namely, the that what you're trying to
+
+ align:start position:0%
+Namely, the that what you're trying to
+ 
+
+ align:start position:0%
+Namely, the that what you're trying to
+prove has to be true. So, let's let's
+
+ align:start position:0%
+prove has to be true. So, let's let's
+ 
+
+ align:start position:0%
+prove has to be true. So, let's let's
+write that down because it can be a
+
+ align:start position:0%
+write that down because it can be a
+ 
+
+ align:start position:0%
+write that down because it can be a
+little confusing the first time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So to prove
+
+ align:start position:0%
+So to prove
+ 
+
+ align:start position:0%
+So to prove
+a proposition P is true,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it's false.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In other words, that not P is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you use that hypothesis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Namely, that P is false
+
+ align:start position:0%
+Namely, that P is false
+ 
+
+ align:start position:0%
+Namely, that P is false
+to derive
+
+ align:start position:0%
+to derive
+ 
+
+ align:start position:0%
+to derive
+a falsehood. In other words, you prove a
+
+ align:start position:0%
+a falsehood. In other words, you prove a
+ 
+
+ align:start position:0%
+a falsehood. In other words, you prove a
+falsehood is true. And this is called
+
+ align:start position:0%
+falsehood is true. And this is called
+ 
+
+ align:start position:0%
+falsehood is true. And this is called
+deriving a contradiction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so it must be that in fact P is not
+
+ align:start position:0%
+And so it must be that in fact P is not
+ 
+
+ align:start position:0%
+And so it must be that in fact P is not
+false. Namely that it's true.
+
+ align:start position:0%
+false. Namely that it's true.
+ 
+
+ align:start position:0%
+false. Namely that it's true.
+Now this works because if you can prove
+
+ align:start position:0%
+Now this works because if you can prove
+ 
+
+ align:start position:0%
+Now this works because if you can prove
+if not P
+
+ align:start position:0%
+if not P
+ 
+
+ align:start position:0%
+if not P
+implies false is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, from last time,
+
+ align:start position:0%
+Well, from last time,
+ 
+
+ align:start position:0%
+Well, from last time,
+the only way this is a true statement
+
+ align:start position:0%
+the only way this is a true statement
+ 
+
+ align:start position:0%
+the only way this is a true statement
+is if this is false, namely P is true.
+
+ align:start position:0%
+is if this is false, namely P is true.
+ 
+
+ align:start position:0%
+is if this is false, namely P is true.
+All right, so we can conclude that P is
+
+ align:start position:0%
+All right, so we can conclude that P is
+ 
+
+ align:start position:0%
+All right, so we can conclude that P is
+true if we can show that not P implies a
+
+ align:start position:0%
+true if we can show that not P implies a
+ 
+
+ align:start position:0%
+true if we can show that not P implies a
+falsehood.
+
+ align:start position:0%
+falsehood.
+ 
+
+ align:start position:0%
+falsehood.
+Any questions about that? It's sort of a
+
+ align:start position:0%
+Any questions about that? It's sort of a
+ 
+
+ align:start position:0%
+Any questions about that? It's sort of a
+lot of sort of notation and if you until
+
+ align:start position:0%
+lot of sort of notation and if you until
+ 
+
+ align:start position:0%
+lot of sort of notation and if you until
+you've seen it, it can be confusing.
+
+ align:start position:0%
+you've seen it, it can be confusing.
+ 
+
+ align:start position:0%
+you've seen it, it can be confusing.
+So maybe we should do do an example.
+
+ align:start position:0%
+So maybe we should do do an example.
+ 
+
+ align:start position:0%
+So maybe we should do do an example.
+Let's prove
+
+ align:start position:0%
+Let's prove
+ 
+
+ align:start position:0%
+Let's prove
+that square<unk> of two is irrational.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is irrational.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, everybody knows what an irrational
+
+ align:start position:0%
+Okay, everybody knows what an irrational
+ 
+
+ align:start position:0%
+Okay, everybody knows what an irrational
+number is.
+
+ align:start position:0%
+number is.
+ 
+
+ align:start position:0%
+number is.
+That's something that can't be expressed
+
+ align:start position:0%
+That's something that can't be expressed
+ 
+
+ align:start position:0%
+That's something that can't be expressed
+as the ratio of integers.
+
+ align:start position:0%
+as the ratio of integers.
+ 
+
+ align:start position:0%
+as the ratio of integers.
+Okay. And probably most people already
+
+ align:start position:0%
+Okay. And probably most people already
+ 
+
+ align:start position:0%
+Okay. And probably most people already
+know that. How many people have not seen
+
+ align:start position:0%
+know that. How many people have not seen
+ 
+
+ align:start position:0%
+know that. How many people have not seen
+a proof that square root of two is
+
+ align:start position:0%
+a proof that square root of two is
+ 
+
+ align:start position:0%
+a proof that square root of two is
+irrational before?
+
+ align:start position:0%
+irrational before?
+ 
+
+ align:start position:0%
+irrational before?
+All right. So, most of you have seen a
+
+ align:start position:0%
+All right. So, most of you have seen a
+ 
+
+ align:start position:0%
+All right. So, most of you have seen a
+proof of that. Good. You know, if you
+
+ align:start position:0%
+proof of that. Good. You know, if you
+ 
+
+ align:start position:0%
+proof of that. Good. You know, if you
+try to do a direct proof of this, it's
+
+ align:start position:0%
+try to do a direct proof of this, it's
+ 
+
+ align:start position:0%
+try to do a direct proof of this, it's
+pretty hard. How do you show there's no
+
+ align:start position:0%
+pretty hard. How do you show there's no
+ 
+
+ align:start position:0%
+pretty hard. How do you show there's no
+way to represent the square root of two
+
+ align:start position:0%
+way to represent the square root of two
+ 
+
+ align:start position:0%
+way to represent the square root of two
+as as integers a over b. But it's very
+
+ align:start position:0%
+as as integers a over b. But it's very
+ 
+
+ align:start position:0%
+as as integers a over b. But it's very
+easy if we do a proof by contradiction.
+
+ align:start position:0%
+easy if we do a proof by contradiction.
+ 
+
+ align:start position:0%
+easy if we do a proof by contradiction.
+Now, when you're doing a proof by
+
+ align:start position:0%
+Now, when you're doing a proof by
+ 
+
+ align:start position:0%
+Now, when you're doing a proof by
+contradiction, always start off by
+
+ align:start position:0%
+contradiction, always start off by
+ 
+
+ align:start position:0%
+contradiction, always start off by
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+by contradiction. Write that down.
+
+ align:start position:0%
+by contradiction. Write that down.
+ 
+
+ align:start position:0%
+by contradiction. Write that down.
+And then what you do next is you say,
+
+ align:start position:0%
+And then what you do next is you say,
+ 
+
+ align:start position:0%
+And then what you do next is you say,
+I'm going to assume
+
+ align:start position:0%
+I'm going to assume
+ 
+
+ align:start position:0%
+I'm going to assume
+for the purpose of contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+not P that P is false. when not P is
+
+ align:start position:0%
+not P that P is false. when not P is
+ 
+
+ align:start position:0%
+not P that P is false. when not P is
+true. In this case that would be<unk> of
+
+ align:start position:0%
+true. In this case that would be<unk> of
+ 
+
+ align:start position:0%
+true. In this case that would be<unk> of
+two is rational.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in this case,
+
+ align:start position:0%
+So in this case,
+ 
+
+ align:start position:0%
+So in this case,
+here's what we're trying to prove.
+
+ align:start position:0%
+here's what we're trying to prove.
+ 
+
+ align:start position:0%
+here's what we're trying to prove.
+That's P.
+
+ align:start position:0%
+That's P.
+ 
+
+ align:start position:0%
+That's P.
+I'm going to assume not P, namely that
+
+ align:start position:0%
+I'm going to assume not P, namely that
+ 
+
+ align:start position:0%
+I'm going to assume not P, namely that
+square root of two is a rational number.
+
+ align:start position:0%
+square root of two is a rational number.
+ 
+
+ align:start position:0%
+square root of two is a rational number.
+Then I'm going to get a contradiction or
+
+ align:start position:0%
+Then I'm going to get a contradiction or
+ 
+
+ align:start position:0%
+Then I'm going to get a contradiction or
+a falsehood. And then I'm going to know
+
+ align:start position:0%
+a falsehood. And then I'm going to know
+ 
+
+ align:start position:0%
+a falsehood. And then I'm going to know
+that P was true after all.
+
+ align:start position:0%
+that P was true after all.
+ 
+
+ align:start position:0%
+that P was true after all.
+All right. So let's see where this leads
+
+ align:start position:0%
+All right. So let's see where this leads
+ 
+
+ align:start position:0%
+All right. So let's see where this leads
+us.
+
+ align:start position:0%
+us.
+ 
+
+ align:start position:0%
+us.
+Well, if two is rational, then we can
+
+ align:start position:0%
+Well, if two is rational, then we can
+ 
+
+ align:start position:0%
+Well, if two is rational, then we can
+express it as a over b, where a over b
+
+ align:start position:0%
+express it as a over b, where a over b
+ 
+
+ align:start position:0%
+express it as a over b, where a over b
+is a fraction in lowest terms.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That means a and b have no common
+
+ align:start position:0%
+That means a and b have no common
+ 
+
+ align:start position:0%
+That means a and b have no common
+divisor.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then I can square both sides
+
+ align:start position:0%
+And then I can square both sides
+ 
+
+ align:start position:0%
+And then I can square both sides
+and I get 2 is a^2 over b^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then I multiply by b^2 and I get 2 b^2 =
+
+ align:start position:0%
+Then I multiply by b^2 and I get 2 b^2 =
+ 
+
+ align:start position:0%
+Then I multiply by b^2 and I get 2 b^2 =
+a^2.
+
+ align:start position:0%
+a^2.
+ 
+
+ align:start position:0%
+a^2.
+And what does that imply about a?
+
+ align:start position:0%
+And what does that imply about a?
+ 
+
+ align:start position:0%
+And what does that imply about a?
+What can you tell me about a if it
+
+ align:start position:0%
+What can you tell me about a if it
+ 
+
+ align:start position:0%
+What can you tell me about a if it
+equals a square is 2 b^2?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Anything special about a? Can it be can
+
+ align:start position:0%
+Anything special about a? Can it be can
+ 
+
+ align:start position:0%
+Anything special about a? Can it be can
+a be anything?
+
+ align:start position:0%
+a be anything?
+ 
+
+ align:start position:0%
+a be anything?
+A squ is even right because 2 B square
+
+ align:start position:0%
+A squ is even right because 2 B square
+ 
+
+ align:start position:0%
+A squ is even right because 2 B square
+is an even number. So A squ is even. And
+
+ align:start position:0%
+is an even number. So A squ is even. And
+ 
+
+ align:start position:0%
+is an even number. So A squ is even. And
+what does that mean about A?
+
+ align:start position:0%
+what does that mean about A?
+ 
+
+ align:start position:0%
+what does that mean about A?
+A is even. A square is even then A is
+
+ align:start position:0%
+A is even. A square is even then A is
+ 
+
+ align:start position:0%
+A is even. A square is even then A is
+even.
+
+ align:start position:0%
+even.
+ 
+
+ align:start position:0%
+even.
+So A is even.
+
+ align:start position:0%
+So A is even.
+ 
+
+ align:start position:0%
+So A is even.
+All right. So we can write that as two
+
+ align:start position:0%
+All right. So we can write that as two
+ 
+
+ align:start position:0%
+All right. So we can write that as two
+divides a. That's the divide symbol.
+
+ align:start position:0%
+divides a. That's the divide symbol.
+ 
+
+ align:start position:0%
+divides a. That's the divide symbol.
+You'll see a lot of that next week.
+
+ align:start position:0%
+You'll see a lot of that next week.
+ 
+
+ align:start position:0%
+You'll see a lot of that next week.
+All right. If a is even, what do I know
+
+ align:start position:0%
+All right. If a is even, what do I know
+ 
+
+ align:start position:0%
+All right. If a is even, what do I know
+about a squared? I know more than just
+
+ align:start position:0%
+about a squared? I know more than just
+ 
+
+ align:start position:0%
+about a squared? I know more than just
+it's even.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What is it? It's a multiple of
+
+ align:start position:0%
+What is it? It's a multiple of
+ 
+
+ align:start position:0%
+What is it? It's a multiple of
+four. Yeah. So that means that four
+
+ align:start position:0%
+four. Yeah. So that means that four
+ 
+
+ align:start position:0%
+four. Yeah. So that means that four
+divides a 2. A^2 is 2 b^ 2. So that
+
+ align:start position:0%
+divides a 2. A^2 is 2 b^ 2. So that
+ 
+
+ align:start position:0%
+divides a 2. A^2 is 2 b^ 2. So that
+means that 4 divides 2 b ^ 2. Divide
+
+ align:start position:0%
+means that 4 divides 2 b ^ 2. Divide
+ 
+
+ align:start position:0%
+means that 4 divides 2 b ^ 2. Divide
+each side by two means 2 divides b^ 2.
+
+ align:start position:0%
+each side by two means 2 divides b^ 2.
+ 
+
+ align:start position:0%
+each side by two means 2 divides b^ 2.
+What does that imply about b?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B is even.
+
+ align:start position:0%
+B is even.
+ 
+
+ align:start position:0%
+B is even.
+All right, B is even. Good.
+
+ align:start position:0%
+All right, B is even. Good.
+ 
+
+ align:start position:0%
+All right, B is even. Good.
+Well, I've got A is even and B is even.
+
+ align:start position:0%
+Well, I've got A is even and B is even.
+ 
+
+ align:start position:0%
+Well, I've got A is even and B is even.
+I got a contradiction here somewhere.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, A over B was not a fraction in
+
+ align:start position:0%
+Yeah, A over B was not a fraction in
+ 
+
+ align:start position:0%
+Yeah, A over B was not a fraction in
+lowest terms because both A and B are
+
+ align:start position:0%
+lowest terms because both A and B are
+ 
+
+ align:start position:0%
+lowest terms because both A and B are
+even.
+
+ align:start position:0%
+even.
+ 
+
+ align:start position:0%
+even.
+All right. So that implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a over b is not
+
+ align:start position:0%
+a over b is not
+ 
+
+ align:start position:0%
+a over b is not
+in lowest terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+gives a contradiction.
+
+ align:start position:0%
+gives a contradiction.
+ 
+
+ align:start position:0%
+gives a contradiction.
+Now you'll see that written lots of
+
+ align:start position:0%
+Now you'll see that written lots of
+ 
+
+ align:start position:0%
+Now you'll see that written lots of
+ways. One is you can say a
+
+ align:start position:0%
+ways. One is you can say a
+ 
+
+ align:start position:0%
+ways. One is you can say a
+contradiction. Sometimes you'll see just
+
+ align:start position:0%
+contradiction. Sometimes you'll see just
+ 
+
+ align:start position:0%
+contradiction. Sometimes you'll see just
+this sharp symbol written and that means
+
+ align:start position:0%
+this sharp symbol written and that means
+ 
+
+ align:start position:0%
+this sharp symbol written and that means
+you got to a contradiction because here
+
+ align:start position:0%
+you got to a contradiction because here
+ 
+
+ align:start position:0%
+you got to a contradiction because here
+we had it being in lowest terms and here
+
+ align:start position:0%
+we had it being in lowest terms and here
+ 
+
+ align:start position:0%
+we had it being in lowest terms and here
+we have it not in lowest terms. You
+
+ align:start position:0%
+we have it not in lowest terms. You
+ 
+
+ align:start position:0%
+we have it not in lowest terms. You
+can't have both at the same time. So you
+
+ align:start position:0%
+can't have both at the same time. So you
+ 
+
+ align:start position:0%
+can't have both at the same time. So you
+got a contradiction
+
+ align:start position:0%
+got a contradiction
+ 
+
+ align:start position:0%
+got a contradiction
+and that means we've now proved that
+
+ align:start position:0%
+and that means we've now proved that
+ 
+
+ align:start position:0%
+and that means we've now proved that
+this assumption was wrong. Square root
+
+ align:start position:0%
+this assumption was wrong. Square root
+ 
+
+ align:start position:0%
+this assumption was wrong. Square root
+of two is not irrational is not
+
+ align:start position:0%
+of two is not irrational is not
+ 
+
+ align:start position:0%
+of two is not irrational is not
+rational. So it must be irrational.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. And then we put a little box
+
+ align:start position:0%
+All right. And then we put a little box
+ 
+
+ align:start position:0%
+All right. And then we put a little box
+here at the end or sometimes you'll see
+
+ align:start position:0%
+here at the end or sometimes you'll see
+ 
+
+ align:start position:0%
+here at the end or sometimes you'll see
+a check. Sometimes you'll see QED that
+
+ align:start position:0%
+a check. Sometimes you'll see QED that
+ 
+
+ align:start position:0%
+a check. Sometimes you'll see QED that
+says the proof's done now.
+
+ align:start position:0%
+says the proof's done now.
+ 
+
+ align:start position:0%
+says the proof's done now.
+It's over. Any questions
+
+ align:start position:0%
+It's over. Any questions
+ 
+
+ align:start position:0%
+It's over. Any questions
+about that proof? We're going to do a
+
+ align:start position:0%
+about that proof? We're going to do a
+ 
+
+ align:start position:0%
+about that proof? We're going to do a
+lot of proofs by contradiction. Uh
+
+ align:start position:0%
+lot of proofs by contradiction. Uh
+ 
+
+ align:start position:0%
+lot of proofs by contradiction. Uh
+actually there's an interesting story
+
+ align:start position:0%
+actually there's an interesting story
+ 
+
+ align:start position:0%
+actually there's an interesting story
+behind this proof. As far as we know, it
+
+ align:start position:0%
+behind this proof. As far as we know, it
+ 
+
+ align:start position:0%
+behind this proof. As far as we know, it
+was first discovered by the Pythagoreans
+
+ align:start position:0%
+was first discovered by the Pythagoreans
+ 
+
+ align:start position:0%
+was first discovered by the Pythagoreans
+way back when in ancient Greece. And the
+
+ align:start position:0%
+way back when in ancient Greece. And the
+ 
+
+ align:start position:0%
+way back when in ancient Greece. And the
+Pythagoreans were a religious society
+
+ align:start position:0%
+Pythagoreans were a religious society
+ 
+
+ align:start position:0%
+Pythagoreans were a religious society
+started by Pythagoras of Pythagoras
+
+ align:start position:0%
+started by Pythagoras of Pythagoras
+ 
+
+ align:start position:0%
+started by Pythagoras of Pythagoras
+theorem fame. Now, it sounds weird
+
+ align:start position:0%
+theorem fame. Now, it sounds weird
+ 
+
+ align:start position:0%
+theorem fame. Now, it sounds weird
+today, but back then in ancient Greece,
+
+ align:start position:0%
+today, but back then in ancient Greece,
+ 
+
+ align:start position:0%
+today, but back then in ancient Greece,
+math was a religion. All right? Every
+
+ align:start position:0%
+math was a religion. All right? Every
+ 
+
+ align:start position:0%
+math was a religion. All right? Every
+once in a while, you'll see somebody
+
+ align:start position:0%
+once in a while, you'll see somebody
+ 
+
+ align:start position:0%
+once in a while, you'll see somebody
+around MIT and you'll think, "Ah, he
+
+ align:start position:0%
+around MIT and you'll think, "Ah, he
+ 
+
+ align:start position:0%
+around MIT and you'll think, "Ah, he
+must think math is a religion." Uh, but
+
+ align:start position:0%
+must think math is a religion." Uh, but
+ 
+
+ align:start position:0%
+must think math is a religion." Uh, but
+back then, it really was. And it was
+
+ align:start position:0%
+back then, it really was. And it was
+ 
+
+ align:start position:0%
+back then, it really was. And it was
+ruled by gods because this is ancient
+
+ align:start position:0%
+ruled by gods because this is ancient
+ 
+
+ align:start position:0%
+ruled by gods because this is ancient
+Greece. And there were two key gods in
+
+ align:start position:0%
+Greece. And there were two key gods in
+ 
+
+ align:start position:0%
+Greece. And there were two key gods in
+this religion, Apiron and Peros. Now,
+
+ align:start position:0%
+this religion, Apiron and Peros. Now,
+ 
+
+ align:start position:0%
+this religion, Apiron and Peros. Now,
+Aperon was the bad god and he was the
+
+ align:start position:0%
+Aperon was the bad god and he was the
+ 
+
+ align:start position:0%
+Aperon was the bad god and he was the
+god of infinity because infinity was
+
+ align:start position:0%
+god of infinity because infinity was
+ 
+
+ align:start position:0%
+god of infinity because infinity was
+considered all that was bad. And if I
+
+ align:start position:0%
+considered all that was bad. And if I
+ 
+
+ align:start position:0%
+considered all that was bad. And if I
+don't think we'll do a lot with infinity
+
+ align:start position:0%
+don't think we'll do a lot with infinity
+ 
+
+ align:start position:0%
+don't think we'll do a lot with infinity
+this term, but if we do, you'll
+
+ align:start position:0%
+this term, but if we do, you'll
+ 
+
+ align:start position:0%
+this term, but if we do, you'll
+appreciate why that's the case. And uh
+
+ align:start position:0%
+appreciate why that's the case. And uh
+ 
+
+ align:start position:0%
+appreciate why that's the case. And uh
+Peros was the good god. He was the god
+
+ align:start position:0%
+Peros was the good god. He was the god
+ 
+
+ align:start position:0%
+Peros was the good god. He was the god
+of the finite world and represented
+
+ align:start position:0%
+of the finite world and represented
+ 
+
+ align:start position:0%
+of the finite world and represented
+everything that was good to the ancient
+
+ align:start position:0%
+everything that was good to the ancient
+ 
+
+ align:start position:0%
+everything that was good to the ancient
+Greeks.
+
+ align:start position:0%
+Greeks.
+ 
+
+ align:start position:0%
+Greeks.
+Now, one of their main axioms or beliefs
+
+ align:start position:0%
+Now, one of their main axioms or beliefs
+ 
+
+ align:start position:0%
+Now, one of their main axioms or beliefs
+was that there were no irrational
+
+ align:start position:0%
+was that there were no irrational
+ 
+
+ align:start position:0%
+was that there were no irrational
+numbers. They just didn't exist.
+
+ align:start position:0%
+numbers. They just didn't exist.
+ 
+
+ align:start position:0%
+numbers. They just didn't exist.
+Now, the reason is they didn't like
+
+ align:start position:0%
+Now, the reason is they didn't like
+ 
+
+ align:start position:0%
+Now, the reason is they didn't like
+irrational numbers. They were bad
+
+ align:start position:0%
+irrational numbers. They were bad
+ 
+
+ align:start position:0%
+irrational numbers. They were bad
+because, well, they're infinite. You
+
+ align:start position:0%
+because, well, they're infinite. You
+ 
+
+ align:start position:0%
+because, well, they're infinite. You
+can't write them as a decimal without
+
+ align:start position:0%
+can't write them as a decimal without
+ 
+
+ align:start position:0%
+can't write them as a decimal without
+repeating forever. You know, just an
+
+ align:start position:0%
+repeating forever. You know, just an
+ 
+
+ align:start position:0%
+repeating forever. You know, just an
+infinite sort of decimal representation.
+
+ align:start position:0%
+infinite sort of decimal representation.
+ 
+
+ align:start position:0%
+infinite sort of decimal representation.
+They liked rational numbers, you know,
+
+ align:start position:0%
+They liked rational numbers, you know,
+ 
+
+ align:start position:0%
+They liked rational numbers, you know,
+like 17th. That's a good number because
+
+ align:start position:0%
+like 17th. That's a good number because
+ 
+
+ align:start position:0%
+like 17th. That's a good number because
+you can write it as 0.14
+
+ align:start position:0%
+you can write it as 0.14
+ 
+
+ align:start position:0%
+you can write it as 0.14
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+repeating.
+
+ align:start position:0%
+repeating.
+ 
+
+ align:start position:0%
+repeating.
+So rational numbers are finite in that
+
+ align:start position:0%
+So rational numbers are finite in that
+ 
+
+ align:start position:0%
+So rational numbers are finite in that
+you can always find the repeating
+
+ align:start position:0%
+you can always find the repeating
+ 
+
+ align:start position:0%
+you can always find the repeating
+pattern of finite length. Irrational
+
+ align:start position:0%
+pattern of finite length. Irrational
+ 
+
+ align:start position:0%
+pattern of finite length. Irrational
+numbers are not. They're infinite in
+
+ align:start position:0%
+numbers are not. They're infinite in
+ 
+
+ align:start position:0%
+numbers are not. They're infinite in
+that sense of the the ancient Greeks. So
+
+ align:start position:0%
+that sense of the the ancient Greeks. So
+ 
+
+ align:start position:0%
+that sense of the the ancient Greeks. So
+they said there were no irrational
+
+ align:start position:0%
+they said there were no irrational
+ 
+
+ align:start position:0%
+they said there were no irrational
+numbers. That was an early axiom.
+
+ align:start position:0%
+numbers. That was an early axiom.
+ 
+
+ align:start position:0%
+numbers. That was an early axiom.
+Now they also had an axiom that said
+
+ align:start position:0%
+Now they also had an axiom that said
+ 
+
+ align:start position:0%
+Now they also had an axiom that said
+that every
+
+ align:start position:0%
+that every
+ 
+
+ align:start position:0%
+that every
+length of a line was finite therefore
+
+ align:start position:0%
+length of a line was finite therefore
+ 
+
+ align:start position:0%
+length of a line was finite therefore
+rational. Right? You know the ancient
+
+ align:start position:0%
+rational. Right? You know the ancient
+ 
+
+ align:start position:0%
+rational. Right? You know the ancient
+Greeks were good with the uh compass and
+
+ align:start position:0%
+Greeks were good with the uh compass and
+ 
+
+ align:start position:0%
+Greeks were good with the uh compass and
+drawing lines and straight edges and
+
+ align:start position:0%
+drawing lines and straight edges and
+ 
+
+ align:start position:0%
+drawing lines and straight edges and
+stuff. So they said any line that you
+
+ align:start position:0%
+stuff. So they said any line that you
+ 
+
+ align:start position:0%
+stuff. So they said any line that you
+can construct has a finite length to it.
+
+ align:start position:0%
+can construct has a finite length to it.
+ 
+
+ align:start position:0%
+can construct has a finite length to it.
+So therefore it has a rational length.
+
+ align:start position:0%
+So therefore it has a rational length.
+ 
+
+ align:start position:0%
+So therefore it has a rational length.
+That was axiom number two.
+
+ align:start position:0%
+That was axiom number two.
+ 
+
+ align:start position:0%
+That was axiom number two.
+Now they were good geometers. So they
+
+ align:start position:0%
+Now they were good geometers. So they
+ 
+
+ align:start position:0%
+Now they were good geometers. So they
+knew of course they they developed the
+
+ align:start position:0%
+knew of course they they developed the
+ 
+
+ align:start position:0%
+knew of course they they developed the
+Pythagorean theorem that if you took a
+
+ align:start position:0%
+Pythagorean theorem that if you took a
+ 
+
+ align:start position:0%
+Pythagorean theorem that if you took a
+triangle and you had side lengths one
+
+ align:start position:0%
+triangle and you had side lengths one
+ 
+
+ align:start position:0%
+triangle and you had side lengths one
+the length of the hypotenuse was
+
+ align:start position:0%
+the length of the hypotenuse was
+ 
+
+ align:start position:0%
+the length of the hypotenuse was
+hypotenuse was <unk>2.
+
+ align:start position:0%
+hypotenuse was <unk>2.
+ 
+
+ align:start position:0%
+hypotenuse was <unk>2.
+Therefore they had a theorem that said
+
+ align:start position:0%
+Therefore they had a theorem that said
+ 
+
+ align:start position:0%
+Therefore they had a theorem that said
+<unk>2 was rational because you got the
+
+ align:start position:0%
+<unk>2 was rational because you got the
+ 
+
+ align:start position:0%
+<unk>2 was rational because you got the
+two axims there. Right?
+
+ align:start position:0%
+two axims there. Right?
+ 
+
+ align:start position:0%
+two axims there. Right?
+Now eventually they discovered a proof
+
+ align:start position:0%
+Now eventually they discovered a proof
+ 
+
+ align:start position:0%
+Now eventually they discovered a proof
+like that that it wasn't rational. It
+
+ align:start position:0%
+like that that it wasn't rational. It
+ 
+
+ align:start position:0%
+like that that it wasn't rational. It
+was irrational. Now this caused quite a
+
+ align:start position:0%
+was irrational. Now this caused quite a
+ 
+
+ align:start position:0%
+was irrational. Now this caused quite a
+stir. First, it meant that their axioms
+
+ align:start position:0%
+stir. First, it meant that their axioms
+ 
+
+ align:start position:0%
+stir. First, it meant that their axioms
+were inconsistent. Every theorem they'd
+
+ align:start position:0%
+were inconsistent. Every theorem they'd
+ 
+
+ align:start position:0%
+were inconsistent. Every theorem they'd
+proved was now suspect.
+
+ align:start position:0%
+proved was now suspect.
+ 
+
+ align:start position:0%
+proved was now suspect.
+Why don't you have inconsistent axioms?
+
+ align:start position:0%
+Why don't you have inconsistent axioms?
+ 
+
+ align:start position:0%
+Why don't you have inconsistent axioms?
+Even worse, the devil is in their midst.
+
+ align:start position:0%
+Even worse, the devil is in their midst.
+ 
+
+ align:start position:0%
+Even worse, the devil is in their midst.
+Square root two is infinite is the bad
+
+ align:start position:0%
+Square root two is infinite is the bad
+ 
+
+ align:start position:0%
+Square root two is infinite is the bad
+god. And this is the most basic length
+
+ align:start position:0%
+god. And this is the most basic length
+ 
+
+ align:start position:0%
+god. And this is the most basic length
+they had besides one. All right? So,
+
+ align:start position:0%
+they had besides one. All right? So,
+ 
+
+ align:start position:0%
+they had besides one. All right? So,
+that's a very bad thing. Sort of like,
+
+ align:start position:0%
+that's a very bad thing. Sort of like,
+ 
+
+ align:start position:0%
+that's a very bad thing. Sort of like,
+you know, today we were to wake up and
+
+ align:start position:0%
+you know, today we were to wake up and
+ 
+
+ align:start position:0%
+you know, today we were to wake up and
+discover that, you know, there were only
+
+ align:start position:0%
+discover that, you know, there were only
+ 
+
+ align:start position:0%
+discover that, you know, there were only
+nine commandments and the tenth was
+
+ align:start position:0%
+nine commandments and the tenth was
+ 
+
+ align:start position:0%
+nine commandments and the tenth was
+planted there by the devil and you're
+
+ align:start position:0%
+planted there by the devil and you're
+ 
+
+ align:start position:0%
+planted there by the devil and you're
+not sure which one maybe, you know, that
+
+ align:start position:0%
+not sure which one maybe, you know, that
+ 
+
+ align:start position:0%
+not sure which one maybe, you know, that
+would be a big mess sacrilege.
+
+ align:start position:0%
+would be a big mess sacrilege.
+ 
+
+ align:start position:0%
+would be a big mess sacrilege.
+Well, so what were they to do? This is a
+
+ align:start position:0%
+Well, so what were they to do? This is a
+ 
+
+ align:start position:0%
+Well, so what were they to do? This is a
+disaster of major proportions. So they
+
+ align:start position:0%
+disaster of major proportions. So they
+ 
+
+ align:start position:0%
+disaster of major proportions. So they
+covered it up and they denied the
+
+ align:start position:0%
+covered it up and they denied the
+ 
+
+ align:start position:0%
+covered it up and they denied the
+result. So they didn't want to publish
+
+ align:start position:0%
+result. So they didn't want to publish
+ 
+
+ align:start position:0%
+result. So they didn't want to publish
+that proof. So they kept on saying
+
+ align:start position:0%
+that proof. So they kept on saying
+ 
+
+ align:start position:0%
+that proof. So they kept on saying
+square root two was rational.
+
+ align:start position:0%
+square root two was rational.
+ 
+
+ align:start position:0%
+square root two was rational.
+But then according to legend there was a
+
+ align:start position:0%
+But then according to legend there was a
+ 
+
+ align:start position:0%
+But then according to legend there was a
+deep throat somebody who let out the
+
+ align:start position:0%
+deep throat somebody who let out the
+ 
+
+ align:start position:0%
+deep throat somebody who let out the
+word and the proof that square root two
+
+ align:start position:0%
+word and the proof that square root two
+ 
+
+ align:start position:0%
+word and the proof that square root two
+was irrational because that would be
+
+ align:start position:0%
+was irrational because that would be
+ 
+
+ align:start position:0%
+was irrational because that would be
+very destabilizing for the society and
+
+ align:start position:0%
+very destabilizing for the society and
+ 
+
+ align:start position:0%
+very destabilizing for the society and
+so they killed him. Uh this is the
+
+ align:start position:0%
+so they killed him. Uh this is the
+ 
+
+ align:start position:0%
+so they killed him. Uh this is the
+legend. Uh now hard to imagine getting
+
+ align:start position:0%
+legend. Uh now hard to imagine getting
+ 
+
+ align:start position:0%
+legend. Uh now hard to imagine getting
+killed over the irrationality of two but
+
+ align:start position:0%
+killed over the irrationality of two but
+ 
+
+ align:start position:0%
+killed over the irrationality of two but
+uh all right we're going to do a lot
+
+ align:start position:0%
+uh all right we're going to do a lot
+ 
+
+ align:start position:0%
+uh all right we're going to do a lot
+more of of these kind of proofs in
+
+ align:start position:0%
+more of of these kind of proofs in
+ 
+
+ align:start position:0%
+more of of these kind of proofs in
+homework and and throughout the term.
+
+ align:start position:0%
+homework and and throughout the term.
+ 
+
+ align:start position:0%
+homework and and throughout the term.
+The next proof I want to show you is uh
+
+ align:start position:0%
+The next proof I want to show you is uh
+ 
+
+ align:start position:0%
+The next proof I want to show you is uh
+one of my favorite proof techniques. one
+
+ align:start position:0%
+one of my favorite proof techniques. one
+ 
+
+ align:start position:0%
+one of my favorite proof techniques. one
+of my favorite proofs and that is a
+
+ align:start position:0%
+of my favorite proofs and that is a
+ 
+
+ align:start position:0%
+of my favorite proofs and that is a
+false proof. And we're gonna see a lot
+
+ align:start position:0%
+false proof. And we're gonna see a lot
+ 
+
+ align:start position:0%
+false proof. And we're gonna see a lot
+of these during the term too. And if we
+
+ align:start position:0%
+of these during the term too. And if we
+ 
+
+ align:start position:0%
+of these during the term too. And if we
+could bring the screens down.
+
+ align:start position:0%
+could bring the screens down.
+ 
+
+ align:start position:0%
+could bring the screens down.
+Somebody back there to Yeah. Great.
+
+ align:start position:0%
+Somebody back there to Yeah. Great.
+ 
+
+ align:start position:0%
+Somebody back there to Yeah. Great.
+Bring the screens down. I'm going to and
+
+ align:start position:0%
+Bring the screens down. I'm going to and
+ 
+
+ align:start position:0%
+Bring the screens down. I'm going to and
+then turn this on for me. So I'm going
+
+ align:start position:0%
+then turn this on for me. So I'm going
+ 
+
+ align:start position:0%
+then turn this on for me. So I'm going
+to prove to you that 90 is bigger than
+
+ align:start position:0%
+to prove to you that 90 is bigger than
+ 
+
+ align:start position:0%
+to prove to you that 90 is bigger than
+92.
+
+ align:start position:0%
+92.
+ 
+
+ align:start position:0%
+92.
+All right. And that hopefully is not
+
+ align:start position:0%
+All right. And that hopefully is not
+ 
+
+ align:start position:0%
+All right. And that hopefully is not
+really true. Um but you know, watch this
+
+ align:start position:0%
+really true. Um but you know, watch this
+ 
+
+ align:start position:0%
+really true. Um but you know, watch this
+proof and see if uh you see any problems
+
+ align:start position:0%
+proof and see if uh you see any problems
+ 
+
+ align:start position:0%
+proof and see if uh you see any problems
+with it. All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right, the proof by PowerPoint. Right
+
+ align:start position:0%
+right, the proof by PowerPoint. Right
+ 
+
+ align:start position:0%
+right, the proof by PowerPoint. Right
+away, you should be suspicious.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to take two triangles with
+
+ align:start position:0%
+I'm going to take two triangles with
+ 
+
+ align:start position:0%
+I'm going to take two triangles with
+total area 90 and put them together and
+
+ align:start position:0%
+total area 90 and put them together and
+ 
+
+ align:start position:0%
+total area 90 and put them together and
+then divide them up into four triangles
+
+ align:start position:0%
+then divide them up into four triangles
+ 
+
+ align:start position:0%
+then divide them up into four triangles
+with area greater than 92.
+
+ align:start position:0%
+with area greater than 92.
+ 
+
+ align:start position:0%
+with area greater than 92.
+And by the conservation of area axiom,
+
+ align:start position:0%
+And by the conservation of area axiom,
+ 
+
+ align:start position:0%
+And by the conservation of area axiom,
+which you want to be maybe thinking
+
+ align:start position:0%
+which you want to be maybe thinking
+ 
+
+ align:start position:0%
+which you want to be maybe thinking
+about, this will imply an area of 90 is
+
+ align:start position:0%
+about, this will imply an area of 90 is
+ 
+
+ align:start position:0%
+about, this will imply an area of 90 is
+larger than area of 92. and therefore
+
+ align:start position:0%
+larger than area of 92. and therefore
+ 
+
+ align:start position:0%
+larger than area of 92. and therefore
+that 90 is bigger than 92.
+
+ align:start position:0%
+that 90 is bigger than 92.
+ 
+
+ align:start position:0%
+that 90 is bigger than 92.
+All right, those are my triangles. They
+
+ align:start position:0%
+All right, those are my triangles. They
+ 
+
+ align:start position:0%
+All right, those are my triangles. They
+are right triangles 9 by 10.
+
+ align:start position:0%
+are right triangles 9 by 10.
+ 
+
+ align:start position:0%
+are right triangles 9 by 10.
+If I put them together, I get a 9 by10
+
+ align:start position:0%
+If I put them together, I get a 9 by10
+ 
+
+ align:start position:0%
+If I put them together, I get a 9 by10
+rectangle.
+
+ align:start position:0%
+rectangle.
+ 
+
+ align:start position:0%
+rectangle.
+Of course, it has area 90. 9 * 10.
+
+ align:start position:0%
+Of course, it has area 90. 9 * 10.
+ 
+
+ align:start position:0%
+Of course, it has area 90. 9 * 10.
+Now I'm going to slide these triangles
+
+ align:start position:0%
+Now I'm going to slide these triangles
+ 
+
+ align:start position:0%
+Now I'm going to slide these triangles
+across their u uh diagonal so that I get
+
+ align:start position:0%
+across their u uh diagonal so that I get
+ 
+
+ align:start position:0%
+across their u uh diagonal so that I get
+instead of having 10 on the side I'm
+
+ align:start position:0%
+instead of having 10 on the side I'm
+ 
+
+ align:start position:0%
+instead of having 10 on the side I'm
+going to slide it so I get a two and an
+
+ align:start position:0%
+going to slide it so I get a two and an
+ 
+
+ align:start position:0%
+going to slide it so I get a two and an
+eight. Okay, I had 10 there before now
+
+ align:start position:0%
+eight. Okay, I had 10 there before now
+ 
+
+ align:start position:0%
+eight. Okay, I had 10 there before now
+it's two and eight. And then you see
+
+ align:start position:0%
+it's two and eight. And then you see
+ 
+
+ align:start position:0%
+it's two and eight. And then you see
+I've got this I can cut off along the
+
+ align:start position:0%
+I've got this I can cut off along the
+ 
+
+ align:start position:0%
+I've got this I can cut off along the
+dotted line and as you can see that
+
+ align:start position:0%
+dotted line and as you can see that
+ 
+
+ align:start position:0%
+dotted line and as you can see that
+dotted line we haven't won't comput it
+
+ align:start position:0%
+dotted line we haven't won't comput it
+ 
+
+ align:start position:0%
+dotted line we haven't won't comput it
+exactly but it's a little bit bigger
+
+ align:start position:0%
+exactly but it's a little bit bigger
+ 
+
+ align:start position:0%
+exactly but it's a little bit bigger
+than two right it's a little bit longer
+
+ align:start position:0%
+than two right it's a little bit longer
+ 
+
+ align:start position:0%
+than two right it's a little bit longer
+than that two there you could see that.
+
+ align:start position:0%
+than that two there you could see that.
+ 
+
+ align:start position:0%
+than that two there you could see that.
+All right. So, I'll call it two plus
+
+ align:start position:0%
+All right. So, I'll call it two plus
+ 
+
+ align:start position:0%
+All right. So, I'll call it two plus
+bigger than two. Now, I slice off along
+
+ align:start position:0%
+bigger than two. Now, I slice off along
+ 
+
+ align:start position:0%
+bigger than two. Now, I slice off along
+the dotted line.
+
+ align:start position:0%
+the dotted line.
+ 
+
+ align:start position:0%
+the dotted line.
+And now I'm going to put those two
+
+ align:start position:0%
+And now I'm going to put those two
+ 
+
+ align:start position:0%
+And now I'm going to put those two
+triangles together. And I create a
+
+ align:start position:0%
+triangles together. And I create a
+ 
+
+ align:start position:0%
+triangles together. And I create a
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+2 by two little more than two. Now, the
+
+ align:start position:0%
+2 by two little more than two. Now, the
+ 
+
+ align:start position:0%
+2 by two little more than two. Now, the
+area of the little rectangle is bigger
+
+ align:start position:0%
+area of the little rectangle is bigger
+ 
+
+ align:start position:0%
+area of the little rectangle is bigger
+than four because I got two * something
+
+ align:start position:0%
+than four because I got two * something
+ 
+
+ align:start position:0%
+than four because I got two * something
+bigger than two. And you can see here I
+
+ align:start position:0%
+bigger than two. And you can see here I
+ 
+
+ align:start position:0%
+bigger than two. And you can see here I
+have the eight left over and I have 9 +
+
+ align:start position:0%
+have the eight left over and I have 9 +
+ 
+
+ align:start position:0%
+have the eight left over and I have 9 +
+2 plus means it's a little bit bigger
+
+ align:start position:0%
+2 plus means it's a little bit bigger
+ 
+
+ align:start position:0%
+2 plus means it's a little bit bigger
+than 11 by 8. I got area bigger than 88.
+
+ align:start position:0%
+than 11 by 8. I got area bigger than 88.
+ 
+
+ align:start position:0%
+than 11 by 8. I got area bigger than 88.
+add them up, I got area bigger than 92.
+
+ align:start position:0%
+add them up, I got area bigger than 92.
+ 
+
+ align:start position:0%
+add them up, I got area bigger than 92.
+So, I started with 90 and I created more
+
+ align:start position:0%
+So, I started with 90 and I created more
+ 
+
+ align:start position:0%
+So, I started with 90 and I created more
+than 92.
+
+ align:start position:0%
+than 92.
+ 
+
+ align:start position:0%
+than 92.
+All right. What's the problem here?
+
+ align:start position:0%
+All right. What's the problem here?
+ 
+
+ align:start position:0%
+All right. What's the problem here?
+I mean, this would be good if I could do
+
+ align:start position:0%
+I mean, this would be good if I could do
+ 
+
+ align:start position:0%
+I mean, this would be good if I could do
+it. I'd get some gold, you know, bars of
+
+ align:start position:0%
+it. I'd get some gold, you know, bars of
+ 
+
+ align:start position:0%
+it. I'd get some gold, you know, bars of
+gold and, you know, cut them up and do
+
+ align:start position:0%
+gold and, you know, cut them up and do
+ 
+
+ align:start position:0%
+gold and, you know, cut them up and do
+the game and I'd make more gold. That
+
+ align:start position:0%
+the game and I'd make more gold. That
+ 
+
+ align:start position:0%
+the game and I'd make more gold. That
+would be pretty good if I could do that.
+
+ align:start position:0%
+would be pretty good if I could do that.
+ 
+
+ align:start position:0%
+would be pretty good if I could do that.
+Is it the conservation of area axiom?
+
+ align:start position:0%
+Is it the conservation of area axiom?
+ 
+
+ align:start position:0%
+Is it the conservation of area axiom?
+Did I assume something there that was
+
+ align:start position:0%
+Did I assume something there that was
+ 
+
+ align:start position:0%
+Did I assume something there that was
+too powerful? That if I manipulate the
+
+ align:start position:0%
+too powerful? That if I manipulate the
+ 
+
+ align:start position:0%
+too powerful? That if I manipulate the
+area of rectangles like this that the
+
+ align:start position:0%
+area of rectangles like this that the
+ 
+
+ align:start position:0%
+area of rectangles like this that the
+area needs to be the same?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+My bigger ones aren't closed. Well,
+
+ align:start position:0%
+My bigger ones aren't closed. Well,
+ 
+
+ align:start position:0%
+My bigger ones aren't closed. Well,
+let's see. I don't know. Let's go back
+
+ align:start position:0%
+let's see. I don't know. Let's go back
+ 
+
+ align:start position:0%
+let's see. I don't know. Let's go back
+and see how I made those bigger ones.
+
+ align:start position:0%
+and see how I made those bigger ones.
+ 
+
+ align:start position:0%
+and see how I made those bigger ones.
+All right. I got my triangles, right?
+
+ align:start position:0%
+All right. I got my triangles, right?
+ 
+
+ align:start position:0%
+All right. I got my triangles, right?
+I'm just chopping along the line there.
+
+ align:start position:0%
+I'm just chopping along the line there.
+ 
+
+ align:start position:0%
+I'm just chopping along the line there.
+And I got two plus and nine.
+
+ align:start position:0%
+And I got two plus and nine.
+ 
+
+ align:start position:0%
+And I got two plus and nine.
+That's Those are rectangles.
+
+ align:start position:0%
+That's Those are rectangles.
+ 
+
+ align:start position:0%
+That's Those are rectangles.
+They look like rectangles.
+
+ align:start position:0%
+They look like rectangles.
+ 
+
+ align:start position:0%
+They look like rectangles.
+Yeah. Uh yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, it looks bigger than two,
+
+ align:start position:0%
+Well, it looks bigger than two,
+ 
+
+ align:start position:0%
+Well, it looks bigger than two,
+doesn't it?
+
+ align:start position:0%
+doesn't it?
+ 
+
+ align:start position:0%
+doesn't it?
+Yeah. Two plus is Well, two bigger than
+
+ align:start position:0%
+Yeah. Two plus is Well, two bigger than
+ 
+
+ align:start position:0%
+Yeah. Two plus is Well, two bigger than
+two is bigger than two, but yeah, maybe
+
+ align:start position:0%
+two is bigger than two, but yeah, maybe
+ 
+
+ align:start position:0%
+two is bigger than two, but yeah, maybe
+that should have been a two minus. Would
+
+ align:start position:0%
+that should have been a two minus. Would
+ 
+
+ align:start position:0%
+that should have been a two minus. Would
+that change anything?
+
+ align:start position:0%
+that change anything?
+ 
+
+ align:start position:0%
+that change anything?
+Yeah. If if that had been a 2 minus,
+
+ align:start position:0%
+Yeah. If if that had been a 2 minus,
+ 
+
+ align:start position:0%
+Yeah. If if that had been a 2 minus,
+then we'd have area less than four, area
+
+ align:start position:0%
+then we'd have area less than four, area
+ 
+
+ align:start position:0%
+then we'd have area less than four, area
+less than 88, and then 90 would be less
+
+ align:start position:0%
+less than 88, and then 90 would be less
+ 
+
+ align:start position:0%
+less than 88, and then 90 would be less
+than 92. That would be okay. But it sure
+
+ align:start position:0%
+than 92. That would be okay. But it sure
+ 
+
+ align:start position:0%
+than 92. That would be okay. But it sure
+as heck looks bigger than the two plus
+
+ align:start position:0%
+as heck looks bigger than the two plus
+ 
+
+ align:start position:0%
+as heck looks bigger than the two plus
+looks bigger than the two, doesn't it? I
+
+ align:start position:0%
+looks bigger than the two, doesn't it? I
+ 
+
+ align:start position:0%
+looks bigger than the two, doesn't it? I
+don't know. Do they got distortion out
+
+ align:start position:0%
+don't know. Do they got distortion out
+ 
+
+ align:start position:0%
+don't know. Do they got distortion out
+there?
+
+ align:start position:0%
+there?
+ 
+
+ align:start position:0%
+there?
+I guarantee you if I measured on my
+
+ align:start position:0%
+I guarantee you if I measured on my
+ 
+
+ align:start position:0%
+I guarantee you if I measured on my
+screen, that two plus is bigger than the
+
+ align:start position:0%
+screen, that two plus is bigger than the
+ 
+
+ align:start position:0%
+screen, that two plus is bigger than the
+length of the two.
+
+ align:start position:0%
+length of the two.
+ 
+
+ align:start position:0%
+length of the two.
+I guarantee you we can we can take we
+
+ align:start position:0%
+I guarantee you we can we can take we
+ 
+
+ align:start position:0%
+I guarantee you we can we can take we
+can take a a ruler on my screen and the
+
+ align:start position:0%
+can take a a ruler on my screen and the
+ 
+
+ align:start position:0%
+can take a a ruler on my screen and the
+two plus will be longer on the ruler
+
+ align:start position:0%
+two plus will be longer on the ruler
+ 
+
+ align:start position:0%
+two plus will be longer on the ruler
+than the two that I guarantee you. But
+
+ align:start position:0%
+than the two that I guarantee you. But
+ 
+
+ align:start position:0%
+than the two that I guarantee you. But
+you're on the right track.
+
+ align:start position:0%
+you're on the right track.
+ 
+
+ align:start position:0%
+you're on the right track.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+that is really 1.8.
+
+ align:start position:0%
+that is really 1.8.
+ 
+
+ align:start position:0%
+that is really 1.8.
+Good.
+
+ align:start position:0%
+Good.
+ 
+
+ align:start position:0%
+Good.
+All right. Now, how did you But I but it
+
+ align:start position:0%
+All right. Now, how did you But I but it
+ 
+
+ align:start position:0%
+All right. Now, how did you But I but it
+is true. If I measured on my screen,
+
+ align:start position:0%
+is true. If I measured on my screen,
+ 
+
+ align:start position:0%
+is true. If I measured on my screen,
+it's bigger. Yeah.
+
+ align:start position:0%
+it's bigger. Yeah.
+ 
+
+ align:start position:0%
+it's bigger. Yeah.
+So So are are the triangles like drawn
+
+ align:start position:0%
+So So are are the triangles like drawn
+ 
+
+ align:start position:0%
+So So are are the triangles like drawn
+to scale? It's like on SAT they always
+
+ align:start position:0%
+to scale? It's like on SAT they always
+ 
+
+ align:start position:0%
+to scale? It's like on SAT they always
+say not to scale, right?
+
+ align:start position:0%
+say not to scale, right?
+ 
+
+ align:start position:0%
+say not to scale, right?
+Yeah. Yeah. They're not drawn to scale.
+
+ align:start position:0%
+Yeah. Yeah. They're not drawn to scale.
+ 
+
+ align:start position:0%
+Yeah. Yeah. They're not drawn to scale.
+In fact, if I go back to the beginning,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it says 9 by 10.
+
+ align:start position:0%
+it says 9 by 10.
+ 
+
+ align:start position:0%
+it says 9 by 10.
+But in fact, if I measure the nine, it's
+
+ align:start position:0%
+But in fact, if I measure the nine, it's
+ 
+
+ align:start position:0%
+But in fact, if I measure the nine, it's
+bigger than the 10.
+
+ align:start position:0%
+bigger than the 10.
+ 
+
+ align:start position:0%
+bigger than the 10.
+All right?
+
+ align:start position:0%
+All right?
+ 
+
+ align:start position:0%
+All right?
+So, this is one of the big problems of
+
+ align:start position:0%
+So, this is one of the big problems of
+ 
+
+ align:start position:0%
+So, this is one of the big problems of
+proofs by picture because looking at it,
+
+ align:start position:0%
+proofs by picture because looking at it,
+ 
+
+ align:start position:0%
+proofs by picture because looking at it,
+you're not thinking which is bigger,
+
+ align:start position:0%
+you're not thinking which is bigger,
+ 
+
+ align:start position:0%
+you're not thinking which is bigger,
+nine or 10 up there. You the 10's bigger
+
+ align:start position:0%
+nine or 10 up there. You the 10's bigger
+ 
+
+ align:start position:0%
+nine or 10 up there. You the 10's bigger
+even though it's not. It's shorter. But
+
+ align:start position:0%
+even though it's not. It's shorter. But
+ 
+
+ align:start position:0%
+even though it's not. It's shorter. But
+when you get down into the proof, well,
+
+ align:start position:0%
+when you get down into the proof, well,
+ 
+
+ align:start position:0%
+when you get down into the proof, well,
+clearly the two plus was bigger than the
+
+ align:start position:0%
+clearly the two plus was bigger than the
+ 
+
+ align:start position:0%
+clearly the two plus was bigger than the
+two because it looks that way. It is on
+
+ align:start position:0%
+two because it looks that way. It is on
+ 
+
+ align:start position:0%
+two because it looks that way. It is on
+the paper. All right. In fact, you go
+
+ align:start position:0%
+the paper. All right. In fact, you go
+ 
+
+ align:start position:0%
+the paper. All right. In fact, you go
+computer, you're probably right. It's
+
+ align:start position:0%
+computer, you're probably right. It's
+ 
+
+ align:start position:0%
+computer, you're probably right. It's
+1.8, not 2 plus. But that's how the
+
+ align:start position:0%
+1.8, not 2 plus. But that's how the
+ 
+
+ align:start position:0%
+1.8, not 2 plus. But that's how the
+error crept in and how it was drawn and
+
+ align:start position:0%
+error crept in and how it was drawn and
+ 
+
+ align:start position:0%
+error crept in and how it was drawn and
+then you're going along with the proof
+
+ align:start position:0%
+then you're going along with the proof
+ 
+
+ align:start position:0%
+then you're going along with the proof
+and everything else is just fine. So,
+
+ align:start position:0%
+and everything else is just fine. So,
+ 
+
+ align:start position:0%
+and everything else is just fine. So,
+the mistake is right up front. I drew it
+
+ align:start position:0%
+the mistake is right up front. I drew it
+ 
+
+ align:start position:0%
+the mistake is right up front. I drew it
+wrong. Okay. Uh, and this happens. You
+
+ align:start position:0%
+wrong. Okay. Uh, and this happens. You
+ 
+
+ align:start position:0%
+wrong. Okay. Uh, and this happens. You
+do graph, we'll talk about graph in a
+
+ align:start position:0%
+do graph, we'll talk about graph in a
+ 
+
+ align:start position:0%
+do graph, we'll talk about graph in a
+couple weeks. Over and over again,
+
+ align:start position:0%
+couple weeks. Over and over again,
+ 
+
+ align:start position:0%
+couple weeks. Over and over again,
+people do this. They draw it looks like
+
+ align:start position:0%
+people do this. They draw it looks like
+ 
+
+ align:start position:0%
+people do this. They draw it looks like
+this. You accept that and then you're
+
+ align:start position:0%
+this. You accept that and then you're
+ 
+
+ align:start position:0%
+this. You accept that and then you're
+dead. Everything else there's no hope.
+
+ align:start position:0%
+dead. Everything else there's no hope.
+ 
+
+ align:start position:0%
+dead. Everything else there's no hope.
+Every everybody clear what went wrong in
+
+ align:start position:0%
+Every everybody clear what went wrong in
+ 
+
+ align:start position:0%
+Every everybody clear what went wrong in
+this picture? How we got off track? This
+
+ align:start position:0%
+this picture? How we got off track? This
+ 
+
+ align:start position:0%
+this picture? How we got off track? This
+is sort of a nasty one.
+
+ align:start position:0%
+is sort of a nasty one.
+ 
+
+ align:start position:0%
+is sort of a nasty one.
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+now one of the nice things about proofs
+
+ align:start position:0%
+now one of the nice things about proofs
+ 
+
+ align:start position:0%
+now one of the nice things about proofs
+is that when there is a bug, if you
+
+ align:start position:0%
+is that when there is a bug, if you
+ 
+
+ align:start position:0%
+is that when there is a bug, if you
+really write it out step by step and
+
+ align:start position:0%
+really write it out step by step and
+ 
+
+ align:start position:0%
+really write it out step by step and
+there's a bug, you can go back and find
+
+ align:start position:0%
+there's a bug, you can go back and find
+ 
+
+ align:start position:0%
+there's a bug, you can go back and find
+it. Uh, and so this I didn't sort of
+
+ align:start position:0%
+it. Uh, and so this I didn't sort of
+ 
+
+ align:start position:0%
+it. Uh, and so this I didn't sort of
+really write it out very well step by
+
+ align:start position:0%
+really write it out very well step by
+ 
+
+ align:start position:0%
+really write it out very well step by
+step and it was harder harder to find
+
+ align:start position:0%
+step and it was harder harder to find
+ 
+
+ align:start position:0%
+step and it was harder harder to find
+now. All right, so if we can pull the
+
+ align:start position:0%
+now. All right, so if we can pull the
+ 
+
+ align:start position:0%
+now. All right, so if we can pull the
+screens up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thanks.
+
+ align:start position:0%
+Thanks.
+ 
+
+ align:start position:0%
+Thanks.
+Okay, so for the rest of today and the
+
+ align:start position:0%
+Okay, so for the rest of today and the
+ 
+
+ align:start position:0%
+Okay, so for the rest of today and the
+rest of this week, we're going to talk
+
+ align:start position:0%
+rest of this week, we're going to talk
+ 
+
+ align:start position:0%
+rest of this week, we're going to talk
+about a different kind of proof
+
+ align:start position:0%
+about a different kind of proof
+ 
+
+ align:start position:0%
+about a different kind of proof
+technique, which is induction.
+
+ align:start position:0%
+technique, which is induction.
+ 
+
+ align:start position:0%
+technique, which is induction.
+Now, induction is by far the most
+
+ align:start position:0%
+Now, induction is by far the most
+ 
+
+ align:start position:0%
+Now, induction is by far the most
+powerful and commonly used proof
+
+ align:start position:0%
+powerful and commonly used proof
+ 
+
+ align:start position:0%
+powerful and commonly used proof
+technique in computer science. If
+
+ align:start position:0%
+technique in computer science. If
+ 
+
+ align:start position:0%
+technique in computer science. If
+there's one thing that you should know
+
+ align:start position:0%
+there's one thing that you should know
+ 
+
+ align:start position:0%
+there's one thing that you should know
+by the time you're done with this class,
+
+ align:start position:0%
+by the time you're done with this class,
+ 
+
+ align:start position:0%
+by the time you're done with this class,
+it's how to do a proof by induction. In
+
+ align:start position:0%
+it's how to do a proof by induction. In
+ 
+
+ align:start position:0%
+it's how to do a proof by induction. In
+fact, if there's one thing you will know
+
+ align:start position:0%
+fact, if there's one thing you will know
+ 
+
+ align:start position:0%
+fact, if there's one thing you will know
+by the time we're done with this class
+
+ align:start position:0%
+by the time we're done with this class
+ 
+
+ align:start position:0%
+by the time we're done with this class
+is how to do a proof by induction. And
+
+ align:start position:0%
+is how to do a proof by induction. And
+ 
+
+ align:start position:0%
+is how to do a proof by induction. And
+in some sense, when we get to grading
+
+ align:start position:0%
+in some sense, when we get to grading
+ 
+
+ align:start position:0%
+in some sense, when we get to grading
+the final, how we measure ourselves as
+
+ align:start position:0%
+the final, how we measure ourselves as
+ 
+
+ align:start position:0%
+the final, how we measure ourselves as
+instructors, the first test is, can you
+
+ align:start position:0%
+instructors, the first test is, can you
+ 
+
+ align:start position:0%
+instructors, the first test is, can you
+do the proof byinduction question and do
+
+ align:start position:0%
+do the proof byinduction question and do
+ 
+
+ align:start position:0%
+do the proof byinduction question and do
+a good proof there? You will see it on
+
+ align:start position:0%
+a good proof there? You will see it on
+ 
+
+ align:start position:0%
+a good proof there? You will see it on
+the midterm and the final, probably in
+
+ align:start position:0%
+the midterm and the final, probably in
+ 
+
+ align:start position:0%
+the midterm and the final, probably in
+multiple instances.
+
+ align:start position:0%
+multiple instances.
+ 
+
+ align:start position:0%
+multiple instances.
+Now, just to make sure you become
+
+ align:start position:0%
+Now, just to make sure you become
+ 
+
+ align:start position:0%
+Now, just to make sure you become
+intimately familiar with induction,
+
+ align:start position:0%
+intimately familiar with induction,
+ 
+
+ align:start position:0%
+intimately familiar with induction,
+we're going to do over a dozen proofs
+
+ align:start position:0%
+we're going to do over a dozen proofs
+ 
+
+ align:start position:0%
+we're going to do over a dozen proofs
+with induction in class and and many
+
+ align:start position:0%
+with induction in class and and many
+ 
+
+ align:start position:0%
+with induction in class and and many
+more in homework over the next five to
+
+ align:start position:0%
+more in homework over the next five to
+ 
+
+ align:start position:0%
+more in homework over the next five to
+six weeks.
+
+ align:start position:0%
+six weeks.
+ 
+
+ align:start position:0%
+six weeks.
+You'll probably be dreaming about
+
+ align:start position:0%
+You'll probably be dreaming about
+ 
+
+ align:start position:0%
+You'll probably be dreaming about
+induction if we're successful here uh
+
+ align:start position:0%
+induction if we're successful here uh
+ 
+
+ align:start position:0%
+induction if we're successful here uh
+soon. The good news is that induction is
+
+ align:start position:0%
+soon. The good news is that induction is
+ 
+
+ align:start position:0%
+soon. The good news is that induction is
+very easy once you get your mind around
+
+ align:start position:0%
+very easy once you get your mind around
+ 
+
+ align:start position:0%
+very easy once you get your mind around
+it and get some practice. It it really
+
+ align:start position:0%
+it and get some practice. It it really
+ 
+
+ align:start position:0%
+it and get some practice. It it really
+is not a hard thing. Uh in fact,
+
+ align:start position:0%
+is not a hard thing. Uh in fact,
+ 
+
+ align:start position:0%
+is not a hard thing. Uh in fact,
+induction is really just an axiom.
+
+ align:start position:0%
+induction is really just an axiom.
+ 
+
+ align:start position:0%
+induction is really just an axiom.
+So let me state it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let PN
+
+ align:start position:0%
+Let PN
+ 
+
+ align:start position:0%
+Let PN
+be a predicate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if P of zero is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for all natural numbers n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P of N implies P of N + one
+
+ align:start position:0%
+P of N implies P of N + one
+ 
+
+ align:start position:0%
+P of N implies P of N + one
+is true.
+
+ align:start position:0%
+is true.
+ 
+
+ align:start position:0%
+is true.
+So here I'm saying that this is true for
+
+ align:start position:0%
+So here I'm saying that this is true for
+ 
+
+ align:start position:0%
+So here I'm saying that this is true for
+all N.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n
+
+ align:start position:0%
+for all n
+ 
+
+ align:start position:0%
+for all n
+natural numbers
+
+ align:start position:0%
+natural numbers
+ 
+
+ align:start position:0%
+natural numbers
+p of n is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Another way of saying this
+
+ align:start position:0%
+All right. Another way of saying this
+ 
+
+ align:start position:0%
+All right. Another way of saying this
+without the for alls there is that if
+
+ align:start position:0%
+without the for alls there is that if
+ 
+
+ align:start position:0%
+without the for alls there is that if
+P 0 is true, if P 0 implies P1 is true,
+
+ align:start position:0%
+P 0 is true, if P 0 implies P1 is true,
+ 
+
+ align:start position:0%
+P 0 is true, if P 0 implies P1 is true,
+if P2 sorry P1 implies P2 is true and so
+
+ align:start position:0%
+if P2 sorry P1 implies P2 is true and so
+ 
+
+ align:start position:0%
+if P2 sorry P1 implies P2 is true and so
+on forever
+
+ align:start position:0%
+on forever
+ 
+
+ align:start position:0%
+on forever
+then P of N is true for all N. So then
+
+ align:start position:0%
+then P of N is true for all N. So then
+ 
+
+ align:start position:0%
+then P of N is true for all N. So then
+P 0,
+
+ align:start position:0%
+P 0,
+ 
+
+ align:start position:0%
+P 0,
+P1,
+
+ align:start position:0%
+P1,
+ 
+
+ align:start position:0%
+P1,
+P2
+
+ align:start position:0%
+P2
+ 
+
+ align:start position:0%
+P2
+forever are true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+now you can sort of see why this is a
+
+ align:start position:0%
+now you can sort of see why this is a
+ 
+
+ align:start position:0%
+now you can sort of see why this is a
+reasonable axiom
+
+ align:start position:0%
+reasonable axiom
+ 
+
+ align:start position:0%
+reasonable axiom
+because if P 0 is true and P 0 implies
+
+ align:start position:0%
+because if P 0 is true and P 0 implies
+ 
+
+ align:start position:0%
+because if P 0 is true and P 0 implies
+P1 then by that modus ponus thing or one
+
+ align:start position:0%
+P1 then by that modus ponus thing or one
+ 
+
+ align:start position:0%
+P1 then by that modus ponus thing or one
+of the logical deductions we know P1 is
+
+ align:start position:0%
+of the logical deductions we know P1 is
+ 
+
+ align:start position:0%
+of the logical deductions we know P1 is
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+and if P1 is true and P1 implies P2 is
+
+ align:start position:0%
+and if P1 is true and P1 implies P2 is
+ 
+
+ align:start position:0%
+and if P1 is true and P1 implies P2 is
+true then we know by the same reasoning
+
+ align:start position:0%
+true then we know by the same reasoning
+ 
+
+ align:start position:0%
+true then we know by the same reasoning
+P2 is
+
+ align:start position:0%
+P2 is
+ 
+
+ align:start position:0%
+P2 is
+and so on forever. Now the reason it
+
+ align:start position:0%
+and so on forever. Now the reason it
+ 
+
+ align:start position:0%
+and so on forever. Now the reason it
+becomes an axiom is that and so on
+
+ align:start position:0%
+becomes an axiom is that and so on
+ 
+
+ align:start position:0%
+becomes an axiom is that and so on
+forever part of it. That's why we need
+
+ align:start position:0%
+forever part of it. That's why we need
+ 
+
+ align:start position:0%
+forever part of it. That's why we need
+it as an axiom.
+
+ align:start position:0%
+it as an axiom.
+ 
+
+ align:start position:0%
+it as an axiom.
+Uh you can sort of view this as a series
+
+ align:start position:0%
+Uh you can sort of view this as a series
+ 
+
+ align:start position:0%
+Uh you can sort of view this as a series
+of dominoes.
+
+ align:start position:0%
+of dominoes.
+ 
+
+ align:start position:0%
+of dominoes.
+You know, I got a domino for each N.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And each domino knocks over the next in
+
+ align:start position:0%
+And each domino knocks over the next in
+ 
+
+ align:start position:0%
+And each domino knocks over the next in
+terms of truth. Knocking over
+
+ align:start position:0%
+terms of truth. Knocking over
+ 
+
+ align:start position:0%
+terms of truth. Knocking over
+corresponds to truth here. And if I know
+
+ align:start position:0%
+corresponds to truth here. And if I know
+ 
+
+ align:start position:0%
+corresponds to truth here. And if I know
+P 0 is true, that means I knock over P
+
+ align:start position:0%
+P 0 is true, that means I knock over P
+ 
+
+ align:start position:0%
+P 0 is true, that means I knock over P
+0. P 0 implies P1 means P1 goes down. P1
+
+ align:start position:0%
+0. P 0 implies P1 means P1 goes down. P1
+ 
+
+ align:start position:0%
+0. P 0 implies P1 means P1 goes down. P1
+implies P2 means P2 goes down, and so
+
+ align:start position:0%
+implies P2 means P2 goes down, and so
+ 
+
+ align:start position:0%
+implies P2 means P2 goes down, and so
+forth. All right. Pretty pretty basic.
+
+ align:start position:0%
+forth. All right. Pretty pretty basic.
+ 
+
+ align:start position:0%
+forth. All right. Pretty pretty basic.
+Um, raise your hand if you think you
+
+ align:start position:0%
+Um, raise your hand if you think you
+ 
+
+ align:start position:0%
+Um, raise your hand if you think you
+don't have a lot of experience with
+
+ align:start position:0%
+don't have a lot of experience with
+ 
+
+ align:start position:0%
+don't have a lot of experience with
+induction.
+
+ align:start position:0%
+induction.
+ 
+
+ align:start position:0%
+induction.
+All right. Yeah, that's yeah, that's
+
+ align:start position:0%
+All right. Yeah, that's yeah, that's
+ 
+
+ align:start position:0%
+All right. Yeah, that's yeah, that's
+pretty pretty typical. About a third to
+
+ align:start position:0%
+pretty pretty typical. About a third to
+ 
+
+ align:start position:0%
+pretty pretty typical. About a third to
+a half of you. So, we're gonna we're
+
+ align:start position:0%
+a half of you. So, we're gonna we're
+ 
+
+ align:start position:0%
+a half of you. So, we're gonna we're
+going to change that. Um, let's do a
+
+ align:start position:0%
+going to change that. Um, let's do a
+ 
+
+ align:start position:0%
+going to change that. Um, let's do a
+simple proof using induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's prove that for all n bigger
+
+ align:start position:0%
+So let's prove that for all n bigger
+ 
+
+ align:start position:0%
+So let's prove that for all n bigger
+than or equal to zero again natural
+
+ align:start position:0%
+than or equal to zero again natural
+ 
+
+ align:start position:0%
+than or equal to zero again natural
+numbers that 1 + 2 + 3
+
+ align:start position:0%
+numbers that 1 + 2 + 3
+ 
+
+ align:start position:0%
+numbers that 1 + 2 + 3
++ n equals n * n + one over two.
+
+ align:start position:0%
++ n equals n * n + one over two.
+ 
+
+ align:start position:0%
++ n equals n * n + one over two.
+This is actually a useful thing to
+
+ align:start position:0%
+This is actually a useful thing to
+ 
+
+ align:start position:0%
+This is actually a useful thing to
+remember. We're going to use this all
+
+ align:start position:0%
+remember. We're going to use this all
+ 
+
+ align:start position:0%
+remember. We're going to use this all
+term this identity.
+
+ align:start position:0%
+term this identity.
+ 
+
+ align:start position:0%
+term this identity.
+Now the first thing before we prove it I
+
+ align:start position:0%
+Now the first thing before we prove it I
+ 
+
+ align:start position:0%
+Now the first thing before we prove it I
+want to make sure we understand this
+
+ align:start position:0%
+want to make sure we understand this
+ 
+
+ align:start position:0%
+want to make sure we understand this
+this dot dot dot notation because it is
+
+ align:start position:0%
+this dot dot dot notation because it is
+ 
+
+ align:start position:0%
+this dot dot dot notation because it is
+the source of a lot of errors. What it
+
+ align:start position:0%
+the source of a lot of errors. What it
+ 
+
+ align:start position:0%
+the source of a lot of errors. What it
+means is that you need to fill in the
+
+ align:start position:0%
+means is that you need to fill in the
+ 
+
+ align:start position:0%
+means is that you need to fill in the
+pattern here
+
+ align:start position:0%
+pattern here
+ 
+
+ align:start position:0%
+pattern here
+which is vague.
+
+ align:start position:0%
+which is vague.
+ 
+
+ align:start position:0%
+which is vague.
+What it means in this case is you fill
+
+ align:start position:0%
+What it means in this case is you fill
+ 
+
+ align:start position:0%
+What it means in this case is you fill
+in four five six all the way up to n
+
+ align:start position:0%
+in four five six all the way up to n
+ 
+
+ align:start position:0%
+in four five six all the way up to n
+minus one and then n. That's what it
+
+ align:start position:0%
+minus one and then n. That's what it
+ 
+
+ align:start position:0%
+minus one and then n. That's what it
+means. Figure out the pattern and fill
+
+ align:start position:0%
+means. Figure out the pattern and fill
+ 
+
+ align:start position:0%
+means. Figure out the pattern and fill
+it in. Pretty risky thing. Uh now in
+
+ align:start position:0%
+it in. Pretty risky thing. Uh now in
+ 
+
+ align:start position:0%
+it in. Pretty risky thing. Uh now in
+this case because that's so vague
+
+ align:start position:0%
+this case because that's so vague
+ 
+
+ align:start position:0%
+this case because that's so vague
+there's other terminology we use for
+
+ align:start position:0%
+there's other terminology we use for
+ 
+
+ align:start position:0%
+there's other terminology we use for
+this. For example we would use
+
+ align:start position:0%
+this. For example we would use
+ 
+
+ align:start position:0%
+this. For example we would use
+a big sigma capital sigma i = 0 to n of
+
+ align:start position:0%
+a big sigma capital sigma i = 0 to n of
+ 
+
+ align:start position:0%
+a big sigma capital sigma i = 0 to n of
+i. That means the sum of i where i is
+
+ align:start position:0%
+i. That means the sum of i where i is
+ 
+
+ align:start position:0%
+i. That means the sum of i where i is
+the integers from 0 to n inclusive.
+
+ align:start position:0%
+the integers from 0 to n inclusive.
+ 
+
+ align:start position:0%
+the integers from 0 to n inclusive.
+Actually let me put one here.
+
+ align:start position:0%
+Actually let me put one here.
+ 
+
+ align:start position:0%
+Actually let me put one here.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Another way to write this,
+
+ align:start position:0%
+Another way to write this,
+ 
+
+ align:start position:0%
+Another way to write this,
+these are all equivalent ways to write
+
+ align:start position:0%
+these are all equivalent ways to write
+ 
+
+ align:start position:0%
+these are all equivalent ways to write
+it, is you could put one less than equal
+
+ align:start position:0%
+it, is you could put one less than equal
+ 
+
+ align:start position:0%
+it, is you could put one less than equal
+to I less than equal to N of I. So you
+
+ align:start position:0%
+to I less than equal to N of I. So you
+ 
+
+ align:start position:0%
+to I less than equal to N of I. So you
+could put summing I over the range from
+
+ align:start position:0%
+could put summing I over the range from
+ 
+
+ align:start position:0%
+could put summing I over the range from
+1 to N or you could write it on the
+
+ align:start position:0%
+1 to N or you could write it on the
+ 
+
+ align:start position:0%
+1 to N or you could write it on the
+bottom if you want.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So these are four different ways of
+
+ align:start position:0%
+So these are four different ways of
+ 
+
+ align:start position:0%
+So these are four different ways of
+writing the same thing, the sum of the
+
+ align:start position:0%
+writing the same thing, the sum of the
+ 
+
+ align:start position:0%
+writing the same thing, the sum of the
+natural numbers from one to n. And we'll
+
+ align:start position:0%
+natural numbers from one to n. And we'll
+ 
+
+ align:start position:0%
+natural numbers from one to n. And we'll
+use them all during the term.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Now, there's some special
+
+ align:start position:0%
+All right. Now, there's some special
+ 
+
+ align:start position:0%
+All right. Now, there's some special
+cases that make this a little more
+
+ align:start position:0%
+cases that make this a little more
+ 
+
+ align:start position:0%
+cases that make this a little more
+interesting. What if n equals 1?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I've got 1 + 2 plus dot dot dot plus n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do you suppose it equals if n
+
+ align:start position:0%
+What do you suppose it equals if n
+ 
+
+ align:start position:0%
+What do you suppose it equals if n
+equals 1?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One. Because we're summing the numbers
+
+ align:start position:0%
+One. Because we're summing the numbers
+ 
+
+ align:start position:0%
+One. Because we're summing the numbers
+from one to one. That's just one, the
+
+ align:start position:0%
+from one to one. That's just one, the
+ 
+
+ align:start position:0%
+from one to one. That's just one, the
+number one. There is no two.
+
+ align:start position:0%
+number one. There is no two.
+ 
+
+ align:start position:0%
+number one. There is no two.
+And there aren't two copies of one. So
+
+ align:start position:0%
+And there aren't two copies of one. So
+ 
+
+ align:start position:0%
+And there aren't two copies of one. So
+this notation is very ambiguous. You see
+
+ align:start position:0%
+this notation is very ambiguous. You see
+ 
+
+ align:start position:0%
+this notation is very ambiguous. You see
+a two here in the sum. If n is one, you
+
+ align:start position:0%
+a two here in the sum. If n is one, you
+ 
+
+ align:start position:0%
+a two here in the sum. If n is one, you
+see a one here and a one here. Right? So
+
+ align:start position:0%
+see a one here and a one here. Right? So
+ 
+
+ align:start position:0%
+see a one here and a one here. Right? So
+you got to be careful. I guarantee you
+
+ align:start position:0%
+you got to be careful. I guarantee you
+ 
+
+ align:start position:0%
+you got to be careful. I guarantee you
+you'll make a mistake with this. In
+
+ align:start position:0%
+you'll make a mistake with this. In
+ 
+
+ align:start position:0%
+you'll make a mistake with this. In
+fact, I'm going to show you another
+
+ align:start position:0%
+fact, I'm going to show you another
+ 
+
+ align:start position:0%
+fact, I'm going to show you another
+false proof later where this comes into
+
+ align:start position:0%
+false proof later where this comes into
+ 
+
+ align:start position:0%
+false proof later where this comes into
+play. Um, what about if n is less than
+
+ align:start position:0%
+play. Um, what about if n is less than
+ 
+
+ align:start position:0%
+play. Um, what about if n is less than
+equal to zero?
+
+ align:start position:0%
+equal to zero?
+ 
+
+ align:start position:0%
+equal to zero?
+What is it then?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Any thoughts?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Zero. There are no integers to sum.
+
+ align:start position:0%
+Zero. There are no integers to sum.
+ 
+
+ align:start position:0%
+Zero. There are no integers to sum.
+No one, no two, no n because you never
+
+ align:start position:0%
+No one, no two, no n because you never
+ 
+
+ align:start position:0%
+No one, no two, no n because you never
+get started because you're sorry. N is
+
+ align:start position:0%
+get started because you're sorry. N is
+ 
+
+ align:start position:0%
+get started because you're sorry. N is
+less equal to zero because you're
+
+ align:start position:0%
+less equal to zero because you're
+ 
+
+ align:start position:0%
+less equal to zero because you're
+summing from one to zero. Zero's below.
+
+ align:start position:0%
+summing from one to zero. Zero's below.
+ 
+
+ align:start position:0%
+summing from one to zero. Zero's below.
+You never doesn't include anything. So
+
+ align:start position:0%
+You never doesn't include anything. So
+ 
+
+ align:start position:0%
+You never doesn't include anything. So
+these are the conventions to keep in
+
+ align:start position:0%
+these are the conventions to keep in
+ 
+
+ align:start position:0%
+these are the conventions to keep in
+mind um with the edge cases here. All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right, it's easy enough to check that
+
+ align:start position:0%
+right, it's easy enough to check that
+ 
+
+ align:start position:0%
+right, it's easy enough to check that
+the theorem is true for certain values
+
+ align:start position:0%
+the theorem is true for certain values
+ 
+
+ align:start position:0%
+the theorem is true for certain values
+of n. For example, n= 4. I've got 1 + 2
+
+ align:start position:0%
+of n. For example, n= 4. I've got 1 + 2
+ 
+
+ align:start position:0%
+of n. For example, n= 4. I've got 1 + 2
++ 3 + 4. That's 10. And 10= 4 * 5 / 2
+
+ align:start position:0%
++ 3 + 4. That's 10. And 10= 4 * 5 / 2
+ 
+
+ align:start position:0%
++ 3 + 4. That's 10. And 10= 4 * 5 / 2
+plugging in the formula. So for any
+
+ align:start position:0%
+plugging in the formula. So for any
+ 
+
+ align:start position:0%
+plugging in the formula. So for any
+value of n, you could check this formula
+
+ align:start position:0%
+value of n, you could check this formula
+ 
+
+ align:start position:0%
+value of n, you could check this formula
+is true. proving it's true for all n you
+
+ align:start position:0%
+is true. proving it's true for all n you
+ 
+
+ align:start position:0%
+is true. proving it's true for all n you
+know is a takes a little more effort
+
+ align:start position:0%
+know is a takes a little more effort
+ 
+
+ align:start position:0%
+know is a takes a little more effort
+unless you use induction. So let's let's
+
+ align:start position:0%
+unless you use induction. So let's let's
+ 
+
+ align:start position:0%
+unless you use induction. So let's let's
+do that.
+
+ align:start position:0%
+do that.
+ 
+
+ align:start position:0%
+do that.
+So prove the theorem. Now whenever
+
+ align:start position:0%
+So prove the theorem. Now whenever
+ 
+
+ align:start position:0%
+So prove the theorem. Now whenever
+you're using a proof by induction first
+
+ align:start position:0%
+you're using a proof by induction first
+ 
+
+ align:start position:0%
+you're using a proof by induction first
+thing you do is you write down by
+
+ align:start position:0%
+thing you do is you write down by
+ 
+
+ align:start position:0%
+thing you do is you write down by
+induction.
+
+ align:start position:0%
+induction.
+ 
+
+ align:start position:0%
+induction.
+So we know what you're going to do.
+
+ align:start position:0%
+So we know what you're going to do.
+ 
+
+ align:start position:0%
+So we know what you're going to do.
+And the first thing you next thing you
+
+ align:start position:0%
+And the first thing you next thing you
+ 
+
+ align:start position:0%
+And the first thing you next thing you
+need to do is figure out what's your
+
+ align:start position:0%
+need to do is figure out what's your
+ 
+
+ align:start position:0%
+need to do is figure out what's your
+predicate.
+
+ align:start position:0%
+predicate.
+ 
+
+ align:start position:0%
+predicate.
+What's your your inductive hypothesis?
+
+ align:start position:0%
+What's your your inductive hypothesis?
+ 
+
+ align:start position:0%
+What's your your inductive hypothesis?
+What's P?
+
+ align:start position:0%
+What's P?
+ 
+
+ align:start position:0%
+What's P?
+All right. So, usually P will be the
+
+ align:start position:0%
+All right. So, usually P will be the
+ 
+
+ align:start position:0%
+All right. So, usually P will be the
+thing you're trying to prove, namely
+
+ align:start position:0%
+thing you're trying to prove, namely
+ 
+
+ align:start position:0%
+thing you're trying to prove, namely
+that 1 plus 2 plus 3 up to N is N * N +
+
+ align:start position:0%
+that 1 plus 2 plus 3 up to N is N * N +
+ 
+
+ align:start position:0%
+that 1 plus 2 plus 3 up to N is N * N +
+1 over two. And you you state that you
+
+ align:start position:0%
+1 over two. And you you state that you
+ 
+
+ align:start position:0%
+1 over two. And you you state that you
+say let P of N
+
+ align:start position:0%
+say let P of N
+ 
+
+ align:start position:0%
+say let P of N
+be the proposition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the predicate that
+
+ align:start position:0%
+the predicate that
+ 
+
+ align:start position:0%
+the predicate that
+the sum I = 1 to N of I equals N * N + 1
+
+ align:start position:0%
+the sum I = 1 to N of I equals N * N + 1
+ 
+
+ align:start position:0%
+the sum I = 1 to N of I equals N * N + 1
+/2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. All right. And once you've
+
+ align:start position:0%
+All right. All right. And once you've
+ 
+
+ align:start position:0%
+All right. All right. And once you've
+got that established, now we're going to
+
+ align:start position:0%
+got that established, now we're going to
+ 
+
+ align:start position:0%
+got that established, now we're going to
+go verify
+
+ align:start position:0%
+go verify
+ 
+
+ align:start position:0%
+go verify
+that P 0 is true and that P uh N implies
+
+ align:start position:0%
+that P 0 is true and that P uh N implies
+ 
+
+ align:start position:0%
+that P 0 is true and that P uh N implies
+PN plus one.
+
+ align:start position:0%
+PN plus one.
+ 
+
+ align:start position:0%
+PN plus one.
+All right. So always have to write this
+
+ align:start position:0%
+All right. So always have to write this
+ 
+
+ align:start position:0%
+All right. So always have to write this
+down. The next thing to do is to check
+
+ align:start position:0%
+down. The next thing to do is to check
+ 
+
+ align:start position:0%
+down. The next thing to do is to check
+what's called the base case P 0. So
+
+ align:start position:0%
+what's called the base case P 0. So
+ 
+
+ align:start position:0%
+what's called the base case P 0. So
+let's do that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So we write down base case.
+
+ align:start position:0%
+All right. So we write down base case.
+ 
+
+ align:start position:0%
+All right. So we write down base case.
+Some people call it the basis step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have to check that P 0 is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, what's the sum of i = 1 to 0 of i
+
+ align:start position:0%
+Well, what's the sum of i = 1 to 0 of i
+ 
+
+ align:start position:0%
+Well, what's the sum of i = 1 to 0 of i
+zero? There are no terms in this sum.
+
+ align:start position:0%
+zero? There are no terms in this sum.
+ 
+
+ align:start position:0%
+zero? There are no terms in this sum.
+And if I look over there, n * n + 1 /2,
+
+ align:start position:0%
+And if I look over there, n * n + 1 /2,
+ 
+
+ align:start position:0%
+And if I look over there, n * n + 1 /2,
+if n is zero,
+
+ align:start position:0%
+if n is zero,
+ 
+
+ align:start position:0%
+if n is zero,
+it equals zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're done with the base case. We've
+
+ align:start position:0%
+So, we're done with the base case. We've
+ 
+
+ align:start position:0%
+So, we're done with the base case. We've
+now proved that p 0 is true.
+
+ align:start position:0%
+now proved that p 0 is true.
+ 
+
+ align:start position:0%
+now proved that p 0 is true.
+And the second part is called the
+
+ align:start position:0%
+And the second part is called the
+ 
+
+ align:start position:0%
+And the second part is called the
+inductive step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And here we have to show for n greater
+
+ align:start position:0%
+And here we have to show for n greater
+ 
+
+ align:start position:0%
+And here we have to show for n greater
+than equal to zero we need to show that
+
+ align:start position:0%
+than equal to zero we need to show that
+ 
+
+ align:start position:0%
+than equal to zero we need to show that
+pn implies pn plus one is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, how do we show an implication is
+
+ align:start position:0%
+Now, how do we show an implication is
+ 
+
+ align:start position:0%
+Now, how do we show an implication is
+true?
+
+ align:start position:0%
+true?
+ 
+
+ align:start position:0%
+true?
+How do I show this is true? What am I
+
+ align:start position:0%
+How do I show this is true? What am I
+ 
+
+ align:start position:0%
+How do I show this is true? What am I
+going to do to show that's true in
+
+ align:start position:0%
+going to do to show that's true in
+ 
+
+ align:start position:0%
+going to do to show that's true in
+general? Yeah,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. Because an implication is true in
+
+ align:start position:0%
+right. Because an implication is true in
+ 
+
+ align:start position:0%
+right. Because an implication is true in
+every case except for true implies
+
+ align:start position:0%
+every case except for true implies
+ 
+
+ align:start position:0%
+every case except for true implies
+false. So if if PN is false, we're done.
+
+ align:start position:0%
+false. So if if PN is false, we're done.
+ 
+
+ align:start position:0%
+false. So if if PN is false, we're done.
+This implication is true. The only case
+
+ align:start position:0%
+This implication is true. The only case
+ 
+
+ align:start position:0%
+This implication is true. The only case
+we have to worry about is P of N is
+
+ align:start position:0%
+we have to worry about is P of N is
+ 
+
+ align:start position:0%
+we have to worry about is P of N is
+true. So we assume P of N is true. And
+
+ align:start position:0%
+true. So we assume P of N is true. And
+ 
+
+ align:start position:0%
+true. So we assume P of N is true. And
+now we confirm that that means PN plus
+
+ align:start position:0%
+now we confirm that that means PN plus
+ 
+
+ align:start position:0%
+now we confirm that that means PN plus
+one is true.
+
+ align:start position:0%
+one is true.
+ 
+
+ align:start position:0%
+one is true.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So we write that down. Assume
+
+ align:start position:0%
+So we write that down. Assume
+ 
+
+ align:start position:0%
+So we write that down. Assume
+PN is true.
+
+ align:start position:0%
+PN is true.
+ 
+
+ align:start position:0%
+PN is true.
+And you might also write down for
+
+ align:start position:0%
+And you might also write down for
+ 
+
+ align:start position:0%
+And you might also write down for
+purposes of induction
+
+ align:start position:0%
+purposes of induction
+ 
+
+ align:start position:0%
+purposes of induction
+or purposes of it verifying the
+
+ align:start position:0%
+or purposes of it verifying the
+ 
+
+ align:start position:0%
+or purposes of it verifying the
+inductive hypothesis
+
+ align:start position:0%
+inductive hypothesis
+ 
+
+ align:start position:0%
+inductive hypothesis
+just to let us know why you're assuming
+
+ align:start position:0%
+just to let us know why you're assuming
+ 
+
+ align:start position:0%
+just to let us know why you're assuming
+it. In other words, you're not assuming
+
+ align:start position:0%
+it. In other words, you're not assuming
+ 
+
+ align:start position:0%
+it. In other words, you're not assuming
+PN is true for purposes of
+
+ align:start position:0%
+PN is true for purposes of
+ 
+
+ align:start position:0%
+PN is true for purposes of
+contradiction.
+
+ align:start position:0%
+contradiction.
+ 
+
+ align:start position:0%
+contradiction.
+You're assuming it for purposes of
+
+ align:start position:0%
+You're assuming it for purposes of
+ 
+
+ align:start position:0%
+You're assuming it for purposes of
+induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, let's do that. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right that means in this case
+
+ align:start position:0%
+all right that means in this case
+ 
+
+ align:start position:0%
+all right that means in this case
+i.e we assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 + 2 plus up to n equals
+
+ align:start position:0%
+1 + 2 plus up to n equals
+ 
+
+ align:start position:0%
+1 + 2 plus up to n equals
+n * n + 1 / 2.
+
+ align:start position:0%
+n * n + 1 / 2.
+ 
+
+ align:start position:0%
+n * n + 1 / 2.
+And we need to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the n+1 case is true. Namely 1 + 2
+
+ align:start position:0%
+that the n+1 case is true. Namely 1 + 2
+ 
+
+ align:start position:0%
+that the n+1 case is true. Namely 1 + 2
++
+
+ align:start position:0%
++
+ 
+
+ align:start position:0%
++
+n + 1
+
+ align:start position:0%
+n + 1
+ 
+
+ align:start position:0%
+n + 1
+equ=
+
+ align:start position:0%
+equ=
+ 
+
+ align:start position:0%
+equ=
+n +1 * n + 2
+
+ align:start position:0%
+n +1 * n + 2
+ 
+
+ align:start position:0%
+n +1 * n + 2
+/ 2.
+
+ align:start position:0%
+/ 2.
+ 
+
+ align:start position:0%
+/ 2.
+All right. You know, it's sort of weird
+
+ align:start position:0%
+All right. You know, it's sort of weird
+ 
+
+ align:start position:0%
+All right. You know, it's sort of weird
+and this does confuse people that aren't
+
+ align:start position:0%
+and this does confuse people that aren't
+ 
+
+ align:start position:0%
+and this does confuse people that aren't
+familiar to you yet familiar with
+
+ align:start position:0%
+familiar to you yet familiar with
+ 
+
+ align:start position:0%
+familiar to you yet familiar with
+induction. It looks like we just assumed
+
+ align:start position:0%
+induction. It looks like we just assumed
+ 
+
+ align:start position:0%
+induction. It looks like we just assumed
+what we're trying to prove.
+
+ align:start position:0%
+what we're trying to prove.
+ 
+
+ align:start position:0%
+what we're trying to prove.
+We're trying to prove this is true for
+
+ align:start position:0%
+We're trying to prove this is true for
+ 
+
+ align:start position:0%
+We're trying to prove this is true for
+all n and we just assumed it, but we're
+
+ align:start position:0%
+all n and we just assumed it, but we're
+ 
+
+ align:start position:0%
+all n and we just assumed it, but we're
+assuming it in the context of
+
+ align:start position:0%
+assuming it in the context of
+ 
+
+ align:start position:0%
+assuming it in the context of
+establishing
+
+ align:start position:0%
+establishing
+ 
+
+ align:start position:0%
+establishing
+this implication is true. And then we
+
+ align:start position:0%
+this implication is true. And then we
+ 
+
+ align:start position:0%
+this implication is true. And then we
+apply the induction axiom to conclude PN
+
+ align:start position:0%
+apply the induction axiom to conclude PN
+ 
+
+ align:start position:0%
+apply the induction axiom to conclude PN
+is true for all n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, let's rewrite this as 1 + 2 +
+
+ align:start position:0%
+Well, let's rewrite this as 1 + 2 +
+ 
+
+ align:start position:0%
+Well, let's rewrite this as 1 + 2 +
+n + n + 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because I've assumed PN, I can rewrite
+
+ align:start position:0%
+Because I've assumed PN, I can rewrite
+ 
+
+ align:start position:0%
+Because I've assumed PN, I can rewrite
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+as n +1 / 2.
+
+ align:start position:0%
+as n +1 / 2.
+ 
+
+ align:start position:0%
+as n +1 / 2.
+And now
+
+ align:start position:0%
+And now
+ 
+
+ align:start position:0%
+And now
+plus n plus one out here.
+
+ align:start position:0%
+plus n plus one out here.
+ 
+
+ align:start position:0%
+plus n plus one out here.
+That equals
+
+ align:start position:0%
+That equals
+ 
+
+ align:start position:0%
+That equals
+well I got n^2
+
+ align:start position:0%
+well I got n^2
+ 
+
+ align:start position:0%
+well I got n^2
++ n here over 2
+
+ align:start position:0%
++ n here over 2
+ 
+
+ align:start position:0%
++ n here over 2
++ 2 n + 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. And that equals
+
+ align:start position:0%
+All right. And that equals
+ 
+
+ align:start position:0%
+All right. And that equals
+n +1 * n +2 over two which is what we're
+
+ align:start position:0%
+n +1 * n +2 over two which is what we're
+ 
+
+ align:start position:0%
+n +1 * n +2 over two which is what we're
+trying to show.
+
+ align:start position:0%
+trying to show.
+ 
+
+ align:start position:0%
+trying to show.
+So we've completed now the inductive
+
+ align:start position:0%
+So we've completed now the inductive
+ 
+
+ align:start position:0%
+So we've completed now the inductive
+step. We have shown that for all n PN
+
+ align:start position:0%
+step. We have shown that for all n PN
+ 
+
+ align:start position:0%
+step. We have shown that for all n PN
+implies PN plus one for all n bigger
+
+ align:start position:0%
+implies PN plus one for all n bigger
+ 
+
+ align:start position:0%
+implies PN plus one for all n bigger
+than equal to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about that? So the proof is done.
+
+ align:start position:0%
+about that? So the proof is done.
+ 
+
+ align:start position:0%
+about that? So the proof is done.
+We've done everything we need to imply
+
+ align:start position:0%
+We've done everything we need to imply
+ 
+
+ align:start position:0%
+We've done everything we need to imply
+induction. We got P 0 is true and PN
+
+ align:start position:0%
+induction. We got P 0 is true and PN
+ 
+
+ align:start position:0%
+induction. We got P 0 is true and PN
+implies PN plus one for all n bigger
+
+ align:start position:0%
+implies PN plus one for all n bigger
+ 
+
+ align:start position:0%
+implies PN plus one for all n bigger
+than equal to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+induction helped us prove theorem.
+
+ align:start position:0%
+induction helped us prove theorem.
+ 
+
+ align:start position:0%
+induction helped us prove theorem.
+Did it help us understand why theorem is
+
+ align:start position:0%
+Did it help us understand why theorem is
+ 
+
+ align:start position:0%
+Did it help us understand why theorem is
+true?
+
+ align:start position:0%
+true?
+ 
+
+ align:start position:0%
+true?
+Do you have any feel for why the theorem
+
+ align:start position:0%
+Do you have any feel for why the theorem
+ 
+
+ align:start position:0%
+Do you have any feel for why the theorem
+is true after seeing the proof?
+
+ align:start position:0%
+is true after seeing the proof?
+ 
+
+ align:start position:0%
+is true after seeing the proof?
+Not really.
+
+ align:start position:0%
+Not really.
+ 
+
+ align:start position:0%
+Not really.
+No, I don't think you know sometimes
+
+ align:start position:0%
+No, I don't think you know sometimes
+ 
+
+ align:start position:0%
+No, I don't think you know sometimes
+induction will give you an
+
+ align:start position:0%
+induction will give you an
+ 
+
+ align:start position:0%
+induction will give you an
+understanding, sometimes it won't. Here
+
+ align:start position:0%
+understanding, sometimes it won't. Here
+ 
+
+ align:start position:0%
+understanding, sometimes it won't. Here
+you got no understanding of why the
+
+ align:start position:0%
+you got no understanding of why the
+ 
+
+ align:start position:0%
+you got no understanding of why the
+theorem is true, which is sort of
+
+ align:start position:0%
+theorem is true, which is sort of
+ 
+
+ align:start position:0%
+theorem is true, which is sort of
+unfortunate.
+
+ align:start position:0%
+unfortunate.
+ 
+
+ align:start position:0%
+unfortunate.
+Did induction help you figure out
+
+ align:start position:0%
+Did induction help you figure out
+ 
+
+ align:start position:0%
+Did induction help you figure out
+the answer to the sum? Namely, say you
+
+ align:start position:0%
+the answer to the sum? Namely, say you
+ 
+
+ align:start position:0%
+the answer to the sum? Namely, say you
+were trying to derive this answer from
+
+ align:start position:0%
+were trying to derive this answer from
+ 
+
+ align:start position:0%
+were trying to derive this answer from
+this sum. Did induction give you the
+
+ align:start position:0%
+this sum. Did induction give you the
+ 
+
+ align:start position:0%
+this sum. Did induction give you the
+answer?
+
+ align:start position:0%
+answer?
+ 
+
+ align:start position:0%
+answer?
+No. You had to know the answer, namely
+
+ align:start position:0%
+No. You had to know the answer, namely
+ 
+
+ align:start position:0%
+No. You had to know the answer, namely
+this, in order to prove it was true.
+
+ align:start position:0%
+this, in order to prove it was true.
+ 
+
+ align:start position:0%
+this, in order to prove it was true.
+Now later we'll see examples where
+
+ align:start position:0%
+Now later we'll see examples where
+ 
+
+ align:start position:0%
+Now later we'll see examples where
+induction actually can give you the
+
+ align:start position:0%
+induction actually can give you the
+ 
+
+ align:start position:0%
+induction actually can give you the
+answer. But often it does not. Often
+
+ align:start position:0%
+answer. But often it does not. Often
+ 
+
+ align:start position:0%
+answer. But often it does not. Often
+induction gives you no hints, no answer,
+
+ align:start position:0%
+induction gives you no hints, no answer,
+ 
+
+ align:start position:0%
+induction gives you no hints, no answer,
+just proves that it's right once you had
+
+ align:start position:0%
+just proves that it's right once you had
+ 
+
+ align:start position:0%
+just proves that it's right once you had
+the clever idea that oh maybe that's the
+
+ align:start position:0%
+the clever idea that oh maybe that's the
+ 
+
+ align:start position:0%
+the clever idea that oh maybe that's the
+answer.
+
+ align:start position:0%
+answer.
+ 
+
+ align:start position:0%
+answer.
+All right, you'll see that with things
+
+ align:start position:0%
+All right, you'll see that with things
+ 
+
+ align:start position:0%
+All right, you'll see that with things
+like the beaver flu problem. All right,
+
+ align:start position:0%
+like the beaver flu problem. All right,
+ 
+
+ align:start position:0%
+like the beaver flu problem. All right,
+that you know figuring out the inductive
+
+ align:start position:0%
+that you know figuring out the inductive
+ 
+
+ align:start position:0%
+that you know figuring out the inductive
+hypothesis or the answer you know the
+
+ align:start position:0%
+hypothesis or the answer you know the
+ 
+
+ align:start position:0%
+hypothesis or the answer you know the
+details of it is hard but once you do it
+
+ align:start position:0%
+details of it is hard but once you do it
+ 
+
+ align:start position:0%
+details of it is hard but once you do it
+then applying the induction not so hard
+
+ align:start position:0%
+then applying the induction not so hard
+ 
+
+ align:start position:0%
+then applying the induction not so hard
+but it gives you a concrete proof.
+
+ align:start position:0%
+but it gives you a concrete proof.
+ 
+
+ align:start position:0%
+but it gives you a concrete proof.
+Okay, let's do another one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fact we're just going to spend the rest
+
+ align:start position:0%
+Fact we're just going to spend the rest
+ 
+
+ align:start position:0%
+Fact we're just going to spend the rest
+of today doing induction proofs. up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all natural numbers n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 divides n cubed minus n means n cub -
+
+ align:start position:0%
+3 divides n cubed minus n means n cub -
+ 
+
+ align:start position:0%
+3 divides n cubed minus n means n cub -
+n is a multiple of three. For example, n
+
+ align:start position:0%
+n is a multiple of three. For example, n
+ 
+
+ align:start position:0%
+n is a multiple of three. For example, n
+is five.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 divides 125 - 5
+
+ align:start position:0%
+3 divides 125 - 5
+ 
+
+ align:start position:0%
+3 divides 125 - 5
+because it's 120.
+
+ align:start position:0%
+because it's 120.
+ 
+
+ align:start position:0%
+because it's 120.
+Let's prove that.
+
+ align:start position:0%
+Let's prove that.
+ 
+
+ align:start position:0%
+Let's prove that.
+And we're going to use induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do you suppose PN's going to be?
+
+ align:start position:0%
+What do you suppose PN's going to be?
+ 
+
+ align:start position:0%
+What do you suppose PN's going to be?
+What's my predicate or my inductive
+
+ align:start position:0%
+What's my predicate or my inductive
+ 
+
+ align:start position:0%
+What's my predicate or my inductive
+hypothesis here?
+
+ align:start position:0%
+hypothesis here?
+ 
+
+ align:start position:0%
+hypothesis here?
+Any thoughts?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah, that's you. Go ahead.
+
+ align:start position:0%
+Yeah, that's you. Go ahead.
+ 
+
+ align:start position:0%
+Yeah, that's you. Go ahead.
+Yeah. First thing you always want to try
+
+ align:start position:0%
+Yeah. First thing you always want to try
+ 
+
+ align:start position:0%
+Yeah. First thing you always want to try
+is you assume that as your induction
+
+ align:start position:0%
+is you assume that as your induction
+ 
+
+ align:start position:0%
+is you assume that as your induction
+hypothesis.
+
+ align:start position:0%
+hypothesis.
+ 
+
+ align:start position:0%
+hypothesis.
+So we say let PN
+
+ align:start position:0%
+So we say let PN
+ 
+
+ align:start position:0%
+So we say let PN
+be 3ides
+
+ align:start position:0%
+be 3ides
+ 
+
+ align:start position:0%
+be 3ides
+n cub minus n.
+
+ align:start position:0%
+n cub minus n.
+ 
+
+ align:start position:0%
+n cub minus n.
+What's the next thing we do in our
+
+ align:start position:0%
+What's the next thing we do in our
+ 
+
+ align:start position:0%
+What's the next thing we do in our
+proof?
+
+ align:start position:0%
+proof?
+ 
+
+ align:start position:0%
+proof?
+Base case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always easy to forget but not a good
+
+ align:start position:0%
+always easy to forget but not a good
+ 
+
+ align:start position:0%
+always easy to forget but not a good
+idea.
+
+ align:start position:0%
+idea.
+ 
+
+ align:start position:0%
+idea.
+Base case is n equals 0 and sure enough
+
+ align:start position:0%
+Base case is n equals 0 and sure enough
+ 
+
+ align:start position:0%
+Base case is n equals 0 and sure enough
+3 divides 0 - 0. So that's done.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What's the next step we do?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What is it next step?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inductive step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for that we're going to need to show
+
+ align:start position:0%
+and for that we're going to need to show
+ 
+
+ align:start position:0%
+and for that we're going to need to show
+for n bigger than equal to zero we want
+
+ align:start position:0%
+for n bigger than equal to zero we want
+ 
+
+ align:start position:0%
+for n bigger than equal to zero we want
+to show PN implies PN + one is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So to do that we assume PN is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In other words, we assume
+
+ align:start position:0%
+In other words, we assume
+ 
+
+ align:start position:0%
+In other words, we assume
+that 3 divides n cubus n. And we're
+
+ align:start position:0%
+that 3 divides n cubus n. And we're
+ 
+
+ align:start position:0%
+that 3 divides n cubus n. And we're
+trying to show that it 3 divides n + 1
+
+ align:start position:0%
+trying to show that it 3 divides n + 1
+ 
+
+ align:start position:0%
+trying to show that it 3 divides n + 1
+cub - n + 1. So we we take a look at we
+
+ align:start position:0%
+cub - n + 1. So we we take a look at we
+ 
+
+ align:start position:0%
+cub - n + 1. So we we take a look at we
+examine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n +1 cubed minus n +1 and we want to
+
+ align:start position:0%
+n +1 cubed minus n +1 and we want to
+ 
+
+ align:start position:0%
+n +1 cubed minus n +1 and we want to
+show it's a multiple of three.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, let's expand that out.
+
+ align:start position:0%
+Well, let's expand that out.
+ 
+
+ align:start position:0%
+Well, let's expand that out.
+This is n cub + 3 n 2 + 3 n + 1 and I
+
+ align:start position:0%
+This is n cub + 3 n 2 + 3 n + 1 and I
+ 
+
+ align:start position:0%
+This is n cub + 3 n 2 + 3 n + 1 and I
+subtract off n + 1.
+
+ align:start position:0%
+subtract off n + 1.
+ 
+
+ align:start position:0%
+subtract off n + 1.
+So I get n cub + 3 n^2
+
+ align:start position:0%
+So I get n cub + 3 n^2
+ 
+
+ align:start position:0%
+So I get n cub + 3 n^2
++ 2 n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is this a multiple of three?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I need to show that's a multiple of
+
+ align:start position:0%
+I need to show that's a multiple of
+ 
+
+ align:start position:0%
+I need to show that's a multiple of
+three and then I'd be all done.
+
+ align:start position:0%
+three and then I'd be all done.
+ 
+
+ align:start position:0%
+three and then I'd be all done.
+Is it a multiple of three?
+
+ align:start position:0%
+Is it a multiple of three?
+ 
+
+ align:start position:0%
+Is it a multiple of three?
+Beats me.
+
+ align:start position:0%
+Beats me.
+ 
+
+ align:start position:0%
+Beats me.
+It doesn't look like a multiple of three
+
+ align:start position:0%
+It doesn't look like a multiple of three
+ 
+
+ align:start position:0%
+It doesn't look like a multiple of three
+necessarily.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So maybe we need to massage it a little
+
+ align:start position:0%
+So maybe we need to massage it a little
+ 
+
+ align:start position:0%
+So maybe we need to massage it a little
+bit. I I do know that this is a multiple
+
+ align:start position:0%
+bit. I I do know that this is a multiple
+ 
+
+ align:start position:0%
+bit. I I do know that this is a multiple
+of three. I can use that fact. And in
+
+ align:start position:0%
+of three. I can use that fact. And in
+ 
+
+ align:start position:0%
+of three. I can use that fact. And in
+proofs by induction, you always want to
+
+ align:start position:0%
+proofs by induction, you always want to
+ 
+
+ align:start position:0%
+proofs by induction, you always want to
+if you're not making use of that fact,
+
+ align:start position:0%
+if you're not making use of that fact,
+ 
+
+ align:start position:0%
+if you're not making use of that fact,
+then you're not really making use of
+
+ align:start position:0%
+then you're not really making use of
+ 
+
+ align:start position:0%
+then you're not really making use of
+induction. Sort of a warning sign. So I
+
+ align:start position:0%
+induction. Sort of a warning sign. So I
+ 
+
+ align:start position:0%
+induction. Sort of a warning sign. So I
+want to use this fact to prove this.
+
+ align:start position:0%
+want to use this fact to prove this.
+ 
+
+ align:start position:0%
+want to use this fact to prove this.
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+let's do a get a minus n in here.
+
+ align:start position:0%
+let's do a get a minus n in here.
+ 
+
+ align:start position:0%
+let's do a get a minus n in here.
+This equals nub - n + 3 n^2 plus well if
+
+ align:start position:0%
+This equals nub - n + 3 n^2 plus well if
+ 
+
+ align:start position:0%
+This equals nub - n + 3 n^2 plus well if
+I subtracted an n I got to add an n + 3
+
+ align:start position:0%
+I subtracted an n I got to add an n + 3
+ 
+
+ align:start position:0%
+I subtracted an n I got to add an n + 3
+n.
+
+ align:start position:0%
+n.
+ 
+
+ align:start position:0%
+n.
+So I've rewritten it now. Is it clear?
+
+ align:start position:0%
+So I've rewritten it now. Is it clear?
+ 
+
+ align:start position:0%
+So I've rewritten it now. Is it clear?
+Now it's clear. Very simple because
+
+ align:start position:0%
+Now it's clear. Very simple because
+ 
+
+ align:start position:0%
+Now it's clear. Very simple because
+three divides this by pn. Three divides
+
+ align:start position:0%
+three divides this by pn. Three divides
+ 
+
+ align:start position:0%
+three divides this by pn. Three divides
+that and three divides that. So this is
+
+ align:start position:0%
+that and three divides that. So this is
+ 
+
+ align:start position:0%
+that and three divides that. So this is
+a multiple of three.
+
+ align:start position:0%
+a multiple of three.
+ 
+
+ align:start position:0%
+a multiple of three.
+All right. because I've got 3 divides 3
+
+ align:start position:0%
+All right. because I've got 3 divides 3
+ 
+
+ align:start position:0%
+All right. because I've got 3 divides 3
+n^ 2 3 divides 3 n and 3 divides n cub
+
+ align:start position:0%
+n^ 2 3 divides 3 n and 3 divides n cub
+ 
+
+ align:start position:0%
+n^ 2 3 divides 3 n and 3 divides n cub
+minus n by
+
+ align:start position:0%
+minus n by
+ 
+
+ align:start position:0%
+minus n by
+pn or you could say by the inductive
+
+ align:start position:0%
+pn or you could say by the inductive
+ 
+
+ align:start position:0%
+pn or you could say by the inductive
+hypothesis
+
+ align:start position:0%
+hypothesis
+ 
+
+ align:start position:0%
+hypothesis
+pn is the inductive hypothesis another
+
+ align:start position:0%
+pn is the inductive hypothesis another
+ 
+
+ align:start position:0%
+pn is the inductive hypothesis another
+name for it so therefore three divides
+
+ align:start position:0%
+name for it so therefore three divides
+ 
+
+ align:start position:0%
+name for it so therefore three divides
+that which means three divides this
+
+ align:start position:0%
+that which means three divides this
+ 
+
+ align:start position:0%
+that which means three divides this
+so that means three divides n + 1 cubed
+
+ align:start position:0%
+so that means three divides n + 1 cubed
+ 
+
+ align:start position:0%
+so that means three divides n + 1 cubed
+- n + one and we are done
+
+ align:start position:0%
+- n + one and we are done
+ 
+
+ align:start position:0%
+- n + one and we are done
+with the proof by induction.
+
+ align:start position:0%
+with the proof by induction.
+ 
+
+ align:start position:0%
+with the proof by induction.
+Any questions about that one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the key steps in induction are always
+
+ align:start position:0%
+So the key steps in induction are always
+ 
+
+ align:start position:0%
+So the key steps in induction are always
+the same. You write down proof by
+
+ align:start position:0%
+the same. You write down proof by
+ 
+
+ align:start position:0%
+the same. You write down proof by
+induction. You identify your predicate.
+
+ align:start position:0%
+induction. You identify your predicate.
+ 
+
+ align:start position:0%
+induction. You identify your predicate.
+You do the base case. Usually that
+
+ align:start position:0%
+You do the base case. Usually that
+ 
+
+ align:start position:0%
+You do the base case. Usually that
+equals zero, but it could be something
+
+ align:start position:0%
+equals zero, but it could be something
+ 
+
+ align:start position:0%
+equals zero, but it could be something
+else. And then you do your inductive
+
+ align:start position:0%
+else. And then you do your inductive
+ 
+
+ align:start position:0%
+else. And then you do your inductive
+step.
+
+ align:start position:0%
+step.
+ 
+
+ align:start position:0%
+step.
+Now in general you could start your
+
+ align:start position:0%
+Now in general you could start your
+ 
+
+ align:start position:0%
+Now in general you could start your
+induction don't start it at zero you
+
+ align:start position:0%
+induction don't start it at zero you
+ 
+
+ align:start position:0%
+induction don't start it at zero you
+could start it at some value B some
+
+ align:start position:0%
+could start it at some value B some
+ 
+
+ align:start position:0%
+could start it at some value B some
+integer B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's take a look at that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you could have for the base case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could have P of B is true not P of
+
+ align:start position:0%
+you could have P of B is true not P of
+ 
+
+ align:start position:0%
+you could have P of B is true not P of
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+And then for your induction step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you would have for all n bigger than
+
+ align:start position:0%
+you would have for all n bigger than
+ 
+
+ align:start position:0%
+you would have for all n bigger than
+equal to B,
+
+ align:start position:0%
+equal to B,
+ 
+
+ align:start position:0%
+equal to B,
+PN implies PN plus one.
+
+ align:start position:0%
+PN implies PN plus one.
+ 
+
+ align:start position:0%
+PN implies PN plus one.
+And then your conclusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that for all n bigger than equal to
+
+ align:start position:0%
+is that for all n bigger than equal to
+ 
+
+ align:start position:0%
+is that for all n bigger than equal to
+b, pn is true.
+
+ align:start position:0%
+b, pn is true.
+ 
+
+ align:start position:0%
+b, pn is true.
+So inductions don't always have to start
+
+ align:start position:0%
+So inductions don't always have to start
+ 
+
+ align:start position:0%
+So inductions don't always have to start
+at zero. You can pick where you start.
+
+ align:start position:0%
+at zero. You can pick where you start.
+ 
+
+ align:start position:0%
+at zero. You can pick where you start.
+Just make sure that you verify the
+
+ align:start position:0%
+Just make sure that you verify the
+ 
+
+ align:start position:0%
+Just make sure that you verify the
+starting point and you verify the
+
+ align:start position:0%
+starting point and you verify the
+ 
+
+ align:start position:0%
+starting point and you verify the
+implication for all n at that starting
+
+ align:start position:0%
+implication for all n at that starting
+ 
+
+ align:start position:0%
+implication for all n at that starting
+point and beyond.
+
+ align:start position:0%
+point and beyond.
+ 
+
+ align:start position:0%
+point and beyond.
+All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right, let's now
+
+ align:start position:0%
+right, let's now
+ 
+
+ align:start position:0%
+right, let's now
+do a false proof using induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We're going to prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all horses are the same color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oops.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's go through the process.
+
+ align:start position:0%
+So let's go through the process.
+ 
+
+ align:start position:0%
+So let's go through the process.
+So the proof we write down by induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now we need our induction hypothesis the
+
+ align:start position:0%
+Now we need our induction hypothesis the
+ 
+
+ align:start position:0%
+Now we need our induction hypothesis the
+predicate.
+
+ align:start position:0%
+predicate.
+ 
+
+ align:start position:0%
+predicate.
+So we're going to let that be
+
+ align:start position:0%
+So we're going to let that be
+ 
+
+ align:start position:0%
+So we're going to let that be
+we can't let it be this. Why can't this
+
+ align:start position:0%
+we can't let it be this. Why can't this
+ 
+
+ align:start position:0%
+we can't let it be this. Why can't this
+be our predicate? All horses are the
+
+ align:start position:0%
+be our predicate? All horses are the
+ 
+
+ align:start position:0%
+be our predicate? All horses are the
+same color. What's wrong with making
+
+ align:start position:0%
+same color. What's wrong with making
+ 
+
+ align:start position:0%
+same color. What's wrong with making
+that be the induction hypothesis?
+
+ align:start position:0%
+that be the induction hypothesis?
+ 
+
+ align:start position:0%
+that be the induction hypothesis?
+You can't plug anything into it. There's
+
+ align:start position:0%
+You can't plug anything into it. There's
+ 
+
+ align:start position:0%
+You can't plug anything into it. There's
+no number here. I got to have a number
+
+ align:start position:0%
+no number here. I got to have a number
+ 
+
+ align:start position:0%
+no number here. I got to have a number
+to an N to induct on. So, what I'm going
+
+ align:start position:0%
+to an N to induct on. So, what I'm going
+ 
+
+ align:start position:0%
+to an N to induct on. So, what I'm going
+to say is that
+
+ align:start position:0%
+to say is that
+ 
+
+ align:start position:0%
+to say is that
+in any set
+
+ align:start position:0%
+in any set
+ 
+
+ align:start position:0%
+in any set
+of n horses,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's make n bigger than equal to
+
+ align:start position:0%
+and let's make n bigger than equal to
+ 
+
+ align:start position:0%
+and let's make n bigger than equal to
+one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The horses
+
+ align:start position:0%
+The horses
+ 
+
+ align:start position:0%
+The horses
+are all the same color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Now, if I prove this is true
+
+ align:start position:0%
+All right. Now, if I prove this is true
+ 
+
+ align:start position:0%
+All right. Now, if I prove this is true
+for all n, well, then all horses are the
+
+ align:start position:0%
+for all n, well, then all horses are the
+ 
+
+ align:start position:0%
+for all n, well, then all horses are the
+same color because in any set of n
+
+ align:start position:0%
+same color because in any set of n
+ 
+
+ align:start position:0%
+same color because in any set of n
+horses, they're all the same color. So,
+
+ align:start position:0%
+horses, they're all the same color. So,
+ 
+
+ align:start position:0%
+horses, they're all the same color. So,
+all horses must be the same color.
+
+ align:start position:0%
+all horses must be the same color.
+ 
+
+ align:start position:0%
+all horses must be the same color.
+What's the next thing I do? What's the
+
+ align:start position:0%
+What's the next thing I do? What's the
+ 
+
+ align:start position:0%
+What's the next thing I do? What's the
+next step?
+
+ align:start position:0%
+next step?
+ 
+
+ align:start position:0%
+next step?
+base case.
+
+ align:start position:0%
+base case.
+ 
+
+ align:start position:0%
+base case.
+Now, what am I going to use as my base
+
+ align:start position:0%
+Now, what am I going to use as my base
+ 
+
+ align:start position:0%
+Now, what am I going to use as my base
+case here?
+
+ align:start position:0%
+case here?
+ 
+
+ align:start position:0%
+case here?
+One one horse. Okay. Or n equals one.
+
+ align:start position:0%
+One one horse. Okay. Or n equals one.
+ 
+
+ align:start position:0%
+One one horse. Okay. Or n equals one.
+So, p of one. That would say that in any
+
+ align:start position:0%
+So, p of one. That would say that in any
+ 
+
+ align:start position:0%
+So, p of one. That would say that in any
+set of one horses, the horses are all
+
+ align:start position:0%
+set of one horses, the horses are all
+ 
+
+ align:start position:0%
+set of one horses, the horses are all
+the same color. Well, that's true. I got
+
+ align:start position:0%
+the same color. Well, that's true. I got
+ 
+
+ align:start position:0%
+the same color. Well, that's true. I got
+one horse. It's the same color as
+
+ align:start position:0%
+one horse. It's the same color as
+ 
+
+ align:start position:0%
+one horse. It's the same color as
+itself. So, that's easy. It's true
+
+ align:start position:0%
+itself. So, that's easy. It's true
+ 
+
+ align:start position:0%
+itself. So, that's easy. It's true
+since just one horse.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. What's the next step
+
+ align:start position:0%
+All right. What's the next step
+ 
+
+ align:start position:0%
+All right. What's the next step
+of the proof? What's the next thing I
+
+ align:start position:0%
+of the proof? What's the next thing I
+ 
+
+ align:start position:0%
+of the proof? What's the next thing I
+do? Inductive step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I've got a I am going to assume
+
+ align:start position:0%
+So I've got a I am going to assume
+ 
+
+ align:start position:0%
+So I've got a I am going to assume
+that PN is true
+
+ align:start position:0%
+that PN is true
+ 
+
+ align:start position:0%
+that PN is true
+to prove
+
+ align:start position:0%
+to prove
+ 
+
+ align:start position:0%
+to prove
+PN and show PS PN plus one is true.
+
+ align:start position:0%
+PN and show PS PN plus one is true.
+ 
+
+ align:start position:0%
+PN and show PS PN plus one is true.
+All right. So I'm going to assume that
+
+ align:start position:0%
+All right. So I'm going to assume that
+ 
+
+ align:start position:0%
+All right. So I'm going to assume that
+in any set of n horses, the horses are
+
+ align:start position:0%
+in any set of n horses, the horses are
+ 
+
+ align:start position:0%
+in any set of n horses, the horses are
+all the same color that I start with.
+
+ align:start position:0%
+all the same color that I start with.
+ 
+
+ align:start position:0%
+all the same color that I start with.
+And now I look at a set of n plus one
+
+ align:start position:0%
+And now I look at a set of n plus one
+ 
+
+ align:start position:0%
+And now I look at a set of n plus one
+horses.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we consider
+
+ align:start position:0%
+So we consider
+ 
+
+ align:start position:0%
+So we consider
+a set of n plus1 horses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's call those horses h1, h2,
+
+ align:start position:0%
+and let's call those horses h1, h2,
+ 
+
+ align:start position:0%
+and let's call those horses h1, h2,
+hn plus1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do I know about
+
+ align:start position:0%
+What do I know about
+ 
+
+ align:start position:0%
+What do I know about
+horses H1 to HN?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They're the same color because PN is
+
+ align:start position:0%
+They're the same color because PN is
+ 
+
+ align:start position:0%
+They're the same color because PN is
+true. They are a set of N horses by P1.
+
+ align:start position:0%
+true. They are a set of N horses by P1.
+ 
+
+ align:start position:0%
+true. They are a set of N horses by P1.
+They're all the same color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Uh, also
+
+ align:start position:0%
+All right. Uh, also
+ 
+
+ align:start position:0%
+All right. Uh, also
+what do I know about H2, H3,
+
+ align:start position:0%
+what do I know about H2, H3,
+ 
+
+ align:start position:0%
+what do I know about H2, H3,
+and HN plus one?
+
+ align:start position:0%
+and HN plus one?
+ 
+
+ align:start position:0%
+and HN plus one?
+All the same color because they're a set
+
+ align:start position:0%
+All the same color because they're a set
+ 
+
+ align:start position:0%
+All the same color because they're a set
+of N horses.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since H
+
+ align:start position:0%
+since H
+ 
+
+ align:start position:0%
+since H
+the color of H1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals the color of those guys.
+
+ align:start position:0%
+equals the color of those guys.
+ 
+
+ align:start position:0%
+equals the color of those guys.
+H2
+
+ align:start position:0%
+H2
+ 
+
+ align:start position:0%
+H2
+to HN. I know H1 is the same color as
+
+ align:start position:0%
+to HN. I know H1 is the same color as
+ 
+
+ align:start position:0%
+to HN. I know H1 is the same color as
+these guys. I also know that HN plus one
+
+ align:start position:0%
+these guys. I also know that HN plus one
+ 
+
+ align:start position:0%
+these guys. I also know that HN plus one
+is the same color as those guys.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That means that H1 is the same color as
+
+ align:start position:0%
+That means that H1 is the same color as
+ 
+
+ align:start position:0%
+That means that H1 is the same color as
+HN plus one.
+
+ align:start position:0%
+HN plus one.
+ 
+
+ align:start position:0%
+HN plus one.
+And all n plus one are the same color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's PN plus one.
+
+ align:start position:0%
+and that's PN plus one.
+ 
+
+ align:start position:0%
+and that's PN plus one.
+That implies PN plus one
+
+ align:start position:0%
+That implies PN plus one
+ 
+
+ align:start position:0%
+That implies PN plus one
+and I'm done.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now a few years ago we assigned this
+
+ align:start position:0%
+Now a few years ago we assigned this
+ 
+
+ align:start position:0%
+Now a few years ago we assigned this
+problem as homework and we asked
+
+ align:start position:0%
+problem as homework and we asked
+ 
+
+ align:start position:0%
+problem as homework and we asked
+students to figure out what went wrong
+
+ align:start position:0%
+students to figure out what went wrong
+ 
+
+ align:start position:0%
+students to figure out what went wrong
+as the problem. Why why doesn't this
+
+ align:start position:0%
+as the problem. Why why doesn't this
+ 
+
+ align:start position:0%
+as the problem. Why why doesn't this
+work? And uh the responses were a little
+
+ align:start position:0%
+work? And uh the responses were a little
+ 
+
+ align:start position:0%
+work? And uh the responses were a little
+discouraging.
+
+ align:start position:0%
+discouraging.
+ 
+
+ align:start position:0%
+discouraging.
+Half the class responded effectively as
+
+ align:start position:0%
+Half the class responded effectively as
+ 
+
+ align:start position:0%
+Half the class responded effectively as
+follows. This example just goes to show
+
+ align:start position:0%
+follows. This example just goes to show
+ 
+
+ align:start position:0%
+follows. This example just goes to show
+that induction doesn't always work.
+
+ align:start position:0%
+that induction doesn't always work.
+ 
+
+ align:start position:0%
+that induction doesn't always work.
+A third of the class said I always knew
+
+ align:start position:0%
+A third of the class said I always knew
+ 
+
+ align:start position:0%
+A third of the class said I always knew
+that you can't trust mathematics. this
+
+ align:start position:0%
+that you can't trust mathematics. this
+ 
+
+ align:start position:0%
+that you can't trust mathematics. this
+example just proves it.
+
+ align:start position:0%
+example just proves it.
+ 
+
+ align:start position:0%
+example just proves it.
+That that really hurt, you know, and
+
+ align:start position:0%
+That that really hurt, you know, and
+ 
+
+ align:start position:0%
+That that really hurt, you know, and
+most of the rest were something similar
+
+ align:start position:0%
+most of the rest were something similar
+ 
+
+ align:start position:0%
+most of the rest were something similar
+to that. Uh not exactly what we were
+
+ align:start position:0%
+to that. Uh not exactly what we were
+ 
+
+ align:start position:0%
+to that. Uh not exactly what we were
+looking for in the homework. So now we
+
+ align:start position:0%
+looking for in the homework. So now we
+ 
+
+ align:start position:0%
+looking for in the homework. So now we
+we don't leave it to homework. We do it
+
+ align:start position:0%
+we don't leave it to homework. We do it
+ 
+
+ align:start position:0%
+we don't leave it to homework. We do it
+in class. Um what's the flaw here?
+
+ align:start position:0%
+in class. Um what's the flaw here?
+ 
+
+ align:start position:0%
+in class. Um what's the flaw here?
+What what is it?
+
+ align:start position:0%
+What what is it?
+ 
+
+ align:start position:0%
+What what is it?
+P of N. What's wrong with P of N?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No, that's this is a real assumption. In
+
+ align:start position:0%
+No, that's this is a real assumption. In
+ 
+
+ align:start position:0%
+No, that's this is a real assumption. In
+any set of n horses
+
+ align:start position:0%
+any set of n horses
+ 
+
+ align:start position:0%
+any set of n horses
+depends on n, the horses are all the
+
+ align:start position:0%
+depends on n, the horses are all the
+ 
+
+ align:start position:0%
+depends on n, the horses are all the
+same color. That is a proposition
+
+ align:start position:0%
+same color. That is a proposition
+ 
+
+ align:start position:0%
+same color. That is a proposition
+because it depends on n. It's a
+
+ align:start position:0%
+because it depends on n. It's a
+ 
+
+ align:start position:0%
+because it depends on n. It's a
+predicate. It's true or it's false.
+
+ align:start position:0%
+predicate. It's true or it's false.
+ 
+
+ align:start position:0%
+predicate. It's true or it's false.
+Now, we know it's false because you
+
+ align:start position:0%
+Now, we know it's false because you
+ 
+
+ align:start position:0%
+Now, we know it's false because you
+could get a set of couple of horses with
+
+ align:start position:0%
+could get a set of couple of horses with
+ 
+
+ align:start position:0%
+could get a set of couple of horses with
+different color, but it is a
+
+ align:start position:0%
+different color, but it is a
+ 
+
+ align:start position:0%
+different color, but it is a
+proposition. Yeah. Way back there.
+
+ align:start position:0%
+proposition. Yeah. Way back there.
+ 
+
+ align:start position:0%
+proposition. Yeah. Way back there.
+P for like a certain set of forces.
+
+ align:start position:0%
+P for like a certain set of forces.
+ 
+
+ align:start position:0%
+P for like a certain set of forces.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+So even though it was the same number of
+
+ align:start position:0%
+So even though it was the same number of
+ 
+
+ align:start position:0%
+So even though it was the same number of
+forces was the same number, it was a
+
+ align:start position:0%
+forces was the same number, it was a
+ 
+
+ align:start position:0%
+forces was the same number, it was a
+different set of forces. So it's not
+
+ align:start position:0%
+different set of forces. So it's not
+ 
+
+ align:start position:0%
+different set of forces. So it's not
+something you can assume anymore. That's
+
+ align:start position:0%
+something you can assume anymore. That's
+ 
+
+ align:start position:0%
+something you can assume anymore. That's
+a great point. I did gloss over
+
+ align:start position:0%
+a great point. I did gloss over
+ 
+
+ align:start position:0%
+a great point. I did gloss over
+something here because in the predicate
+
+ align:start position:0%
+something here because in the predicate
+ 
+
+ align:start position:0%
+something here because in the predicate
+I've got in any set. So there's really a
+
+ align:start position:0%
+I've got in any set. So there's really a
+ 
+
+ align:start position:0%
+I've got in any set. So there's really a
+for all sets sitting out here. So I got
+
+ align:start position:0%
+for all sets sitting out here. So I got
+ 
+
+ align:start position:0%
+for all sets sitting out here. So I got
+to be careful that I establish that when
+
+ align:start position:0%
+to be careful that I establish that when
+ 
+
+ align:start position:0%
+to be careful that I establish that when
+I'm trying to prove PN implies PN plus
+
+ align:start position:0%
+I'm trying to prove PN implies PN plus
+ 
+
+ align:start position:0%
+I'm trying to prove PN implies PN plus
+one. So to establish PN plus one here, I
+
+ align:start position:0%
+one. So to establish PN plus one here, I
+ 
+
+ align:start position:0%
+one. So to establish PN plus one here, I
+assume PN, which means in any set of N
+
+ align:start position:0%
+assume PN, which means in any set of N
+ 
+
+ align:start position:0%
+assume PN, which means in any set of N
+horses, they're all the same color that
+
+ align:start position:0%
+horses, they're all the same color that
+ 
+
+ align:start position:0%
+horses, they're all the same color that
+I'm given. That's PN. I've got to look
+
+ align:start position:0%
+I'm given. That's PN. I've got to look
+ 
+
+ align:start position:0%
+I'm given. That's PN. I've got to look
+at any set of N plus1 horses. So
+
+ align:start position:0%
+at any set of N plus1 horses. So
+ 
+
+ align:start position:0%
+at any set of N plus1 horses. So
+consider any set, not a set, any set of
+
+ align:start position:0%
+consider any set, not a set, any set of
+ 
+
+ align:start position:0%
+consider any set, not a set, any set of
+N plus1 horses. So you pick any set you
+
+ align:start position:0%
+N plus1 horses. So you pick any set you
+ 
+
+ align:start position:0%
+N plus1 horses. So you pick any set you
+want. Call them this H1 through HN plus
+
+ align:start position:0%
+want. Call them this H1 through HN plus
+ 
+
+ align:start position:0%
+want. Call them this H1 through HN plus
+one. Well, then the first n are a set of
+
+ align:start position:0%
+one. Well, then the first n are a set of
+ 
+
+ align:start position:0%
+one. Well, then the first n are a set of
+n horses, so I can apply PN. Therefore,
+
+ align:start position:0%
+n horses, so I can apply PN. Therefore,
+ 
+
+ align:start position:0%
+n horses, so I can apply PN. Therefore,
+they have the same color. The last n
+
+ align:start position:0%
+they have the same color. The last n
+ 
+
+ align:start position:0%
+they have the same color. The last n
+horses in the set are a set of n horses,
+
+ align:start position:0%
+horses in the set are a set of n horses,
+ 
+
+ align:start position:0%
+horses in the set are a set of n horses,
+so I can apply PN. So, these guys all
+
+ align:start position:0%
+so I can apply PN. So, these guys all
+ 
+
+ align:start position:0%
+so I can apply PN. So, these guys all
+have the same color, and I'm on my merry
+
+ align:start position:0%
+have the same color, and I'm on my merry
+ 
+
+ align:start position:0%
+have the same color, and I'm on my merry
+way here. So, you're right. I had to do
+
+ align:start position:0%
+way here. So, you're right. I had to do
+ 
+
+ align:start position:0%
+way here. So, you're right. I had to do
+a little bit more work, but I can do
+
+ align:start position:0%
+a little bit more work, but I can do
+ 
+
+ align:start position:0%
+a little bit more work, but I can do
+that work, and I still get a proof.
+
+ align:start position:0%
+that work, and I still get a proof.
+ 
+
+ align:start position:0%
+that work, and I still get a proof.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+good question. There's a problem with a
+
+ align:start position:0%
+good question. There's a problem with a
+ 
+
+ align:start position:0%
+good question. There's a problem with a
+base case. So my base case was here n
+
+ align:start position:0%
+base case. So my base case was here n
+ 
+
+ align:start position:0%
+base case. So my base case was here n
+equals 1
+
+ align:start position:0%
+equals 1
+ 
+
+ align:start position:0%
+equals 1
+in any set of one horse the horses let's
+
+ align:start position:0%
+in any set of one horse the horses let's
+ 
+
+ align:start position:0%
+in any set of one horse the horses let's
+say in the set just to be really
+
+ align:start position:0%
+say in the set just to be really
+ 
+
+ align:start position:0%
+say in the set just to be really
+careful
+
+ align:start position:0%
+careful
+ 
+
+ align:start position:0%
+careful
+are all the same color. No in any set of
+
+ align:start position:0%
+are all the same color. No in any set of
+ 
+
+ align:start position:0%
+are all the same color. No in any set of
+one horses is only one horse. So it's
+
+ align:start position:0%
+one horses is only one horse. So it's
+ 
+
+ align:start position:0%
+one horses is only one horse. So it's
+the same color as itself. Yeah,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+N plus one is not the same as n. Yeah.
+
+ align:start position:0%
+N plus one is not the same as n. Yeah.
+ 
+
+ align:start position:0%
+N plus one is not the same as n. Yeah.
+That's set. You can't have the same
+
+ align:start position:0%
+That's set. You can't have the same
+ 
+
+ align:start position:0%
+That's set. You can't have the same
+assumption because it's not um a set of
+
+ align:start position:0%
+assumption because it's not um a set of
+ 
+
+ align:start position:0%
+assumption because it's not um a set of
+n horses. It's a set of n plus one.
+
+ align:start position:0%
+n horses. It's a set of n plus one.
+ 
+
+ align:start position:0%
+n horses. It's a set of n plus one.
+Well, let's see. So, you're you're
+
+ align:start position:0%
+Well, let's see. So, you're you're
+ 
+
+ align:start position:0%
+Well, let's see. So, you're you're
+arguing I made a mistake here, right?
+
+ align:start position:0%
+arguing I made a mistake here, right?
+ 
+
+ align:start position:0%
+arguing I made a mistake here, right?
+Well, I've got horses, horse two, three
+
+ align:start position:0%
+Well, I've got horses, horse two, three
+ 
+
+ align:start position:0%
+Well, I've got horses, horse two, three
+up to n plus one. How many horses are in
+
+ align:start position:0%
+up to n plus one. How many horses are in
+ 
+
+ align:start position:0%
+up to n plus one. How many horses are in
+this set here?
+
+ align:start position:0%
+this set here?
+ 
+
+ align:start position:0%
+this set here?
+Oh, in that set.
+
+ align:start position:0%
+Oh, in that set.
+ 
+
+ align:start position:0%
+Oh, in that set.
+In this set, how many horses are there?
+
+ align:start position:0%
+In this set, how many horses are there?
+ 
+
+ align:start position:0%
+In this set, how many horses are there?
+N.
+
+ align:start position:0%
+N.
+ 
+
+ align:start position:0%
+N.
+N. So I can apply P of N to this set
+
+ align:start position:0%
+N. So I can apply P of N to this set
+ 
+
+ align:start position:0%
+N. So I can apply P of N to this set
+just the same as that set because P of N
+
+ align:start position:0%
+just the same as that set because P of N
+ 
+
+ align:start position:0%
+just the same as that set because P of N
+is any set of N horses. Well, I'm
+
+ align:start position:0%
+is any set of N horses. Well, I'm
+ 
+
+ align:start position:0%
+is any set of N horses. Well, I'm
+picking this one now and applying PN to
+
+ align:start position:0%
+picking this one now and applying PN to
+ 
+
+ align:start position:0%
+picking this one now and applying PN to
+it. And so therefore, they're all the
+
+ align:start position:0%
+it. And so therefore, they're all the
+ 
+
+ align:start position:0%
+it. And so therefore, they're all the
+same color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+H1, H2, dot dot dot.
+
+ align:start position:0%
+H1, H2, dot dot dot.
+ 
+
+ align:start position:0%
+H1, H2, dot dot dot.
+Yes,
+
+ align:start position:0%
+Yes,
+ 
+
+ align:start position:0%
+Yes,
+because it does work if there's two or
+
+ align:start position:0%
+because it does work if there's two or
+ 
+
+ align:start position:0%
+because it does work if there's two or
+more, but you didn't prove it was just
+
+ align:start position:0%
+more, but you didn't prove it was just
+ 
+
+ align:start position:0%
+more, but you didn't prove it was just
+one or one from one to two, I guess.
+
+ align:start position:0%
+one or one from one to two, I guess.
+ 
+
+ align:start position:0%
+one or one from one to two, I guess.
+Exactly. Remember I told you that dot
+
+ align:start position:0%
+Exactly. Remember I told you that dot
+ 
+
+ align:start position:0%
+Exactly. Remember I told you that dot
+dot dot. so reasonable, so easy to use,
+
+ align:start position:0%
+dot dot. so reasonable, so easy to use,
+ 
+
+ align:start position:0%
+dot dot. so reasonable, so easy to use,
+everybody uses it was going to catch us
+
+ align:start position:0%
+everybody uses it was going to catch us
+ 
+
+ align:start position:0%
+everybody uses it was going to catch us
+up. The bug is in the dot dot dot and in
+
+ align:start position:0%
+up. The bug is in the dot dot dot and in
+ 
+
+ align:start position:0%
+up. The bug is in the dot dot dot and in
+particular, it's has to do with the case
+
+ align:start position:0%
+particular, it's has to do with the case
+ 
+
+ align:start position:0%
+particular, it's has to do with the case
+n equal two. So there's two ways to look
+
+ align:start position:0%
+n equal two. So there's two ways to look
+ 
+
+ align:start position:0%
+n equal two. So there's two ways to look
+at the bug dot dot dot or we didn't
+
+ align:start position:0%
+at the bug dot dot dot or we didn't
+ 
+
+ align:start position:0%
+at the bug dot dot dot or we didn't
+completely do all the inductive steps.
+
+ align:start position:0%
+completely do all the inductive steps.
+ 
+
+ align:start position:0%
+completely do all the inductive steps.
+So let's look at the case actually it's
+
+ align:start position:0%
+So let's look at the case actually it's
+ 
+
+ align:start position:0%
+So let's look at the case actually it's
+the case n equals 1
+
+ align:start position:0%
+the case n equals 1
+ 
+
+ align:start position:0%
+the case n equals 1
+here in this inductive step did I prove
+
+ align:start position:0%
+here in this inductive step did I prove
+ 
+
+ align:start position:0%
+here in this inductive step did I prove
+p1 implies p2
+
+ align:start position:0%
+p1 implies p2
+ 
+
+ align:start position:0%
+p1 implies p2
+let's just double check that worked for
+
+ align:start position:0%
+let's just double check that worked for
+ 
+
+ align:start position:0%
+let's just double check that worked for
+n equals 1
+
+ align:start position:0%
+n equals 1
+ 
+
+ align:start position:0%
+n equals 1
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n equals 1 I've got a set of
+
+ align:start position:0%
+n equals 1 I've got a set of
+ 
+
+ align:start position:0%
+n equals 1 I've got a set of
+two horses This becomes two. So I've got
+
+ align:start position:0%
+two horses This becomes two. So I've got
+ 
+
+ align:start position:0%
+two horses This becomes two. So I've got
+H1 H2
+
+ align:start position:0%
+H1 H2
+ 
+
+ align:start position:0%
+H1 H2
+there. Nothing in the dot dot dot. It's
+
+ align:start position:0%
+there. Nothing in the dot dot dot. It's
+ 
+
+ align:start position:0%
+there. Nothing in the dot dot dot. It's
+just H1 and H2.
+
+ align:start position:0%
+just H1 and H2.
+ 
+
+ align:start position:0%
+just H1 and H2.
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+this becomes
+
+ align:start position:0%
+this becomes
+ 
+
+ align:start position:0%
+this becomes
+H1.
+
+ align:start position:0%
+H1.
+ 
+
+ align:start position:0%
+H1.
+So sure enough, H1 is the same color as
+
+ align:start position:0%
+So sure enough, H1 is the same color as
+ 
+
+ align:start position:0%
+So sure enough, H1 is the same color as
+itself. This becomes what does this
+
+ align:start position:0%
+itself. This becomes what does this
+ 
+
+ align:start position:0%
+itself. This becomes what does this
+become? This set of horses. What is it
+
+ align:start position:0%
+become? This set of horses. What is it
+ 
+
+ align:start position:0%
+become? This set of horses. What is it
+really? H2.
+
+ align:start position:0%
+really? H2.
+ 
+
+ align:start position:0%
+really? H2.
+All right. So, I've got the color of H1
+
+ align:start position:0%
+All right. So, I've got the color of H1
+ 
+
+ align:start position:0%
+All right. So, I've got the color of H1
+equals the color of
+
+ align:start position:0%
+equals the color of
+ 
+
+ align:start position:0%
+equals the color of
+Oh, man. This is so hard to see this
+
+ align:start position:0%
+Oh, man. This is so hard to see this
+ 
+
+ align:start position:0%
+Oh, man. This is so hard to see this
+bug. I I I wrote down H2 dot dot dot to
+
+ align:start position:0%
+bug. I I I wrote down H2 dot dot dot to
+ 
+
+ align:start position:0%
+bug. I I I wrote down H2 dot dot dot to
+HN because
+
+ align:start position:0%
+HN because
+ 
+
+ align:start position:0%
+HN because
+take out H1.
+
+ align:start position:0%
+take out H1.
+ 
+
+ align:start position:0%
+take out H1.
+What's left? It's what's left is H2
+
+ align:start position:0%
+What's left? It's what's left is H2
+ 
+
+ align:start position:0%
+What's left? It's what's left is H2
+through HN. But this set is only H1.
+
+ align:start position:0%
+through HN. But this set is only H1.
+ 
+
+ align:start position:0%
+through HN. But this set is only H1.
+What's really left here? What is this
+
+ align:start position:0%
+What's really left here? What is this
+ 
+
+ align:start position:0%
+What's really left here? What is this
+set?
+
+ align:start position:0%
+set?
+ 
+
+ align:start position:0%
+set?
+What is this set?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H2H1. No,
+
+ align:start position:0%
+H2H1. No,
+ 
+
+ align:start position:0%
+H2H1. No,
+there's you see what is the whole set?
+
+ align:start position:0%
+there's you see what is the whole set?
+ 
+
+ align:start position:0%
+there's you see what is the whole set?
+H1 dot dot dot HN. What is the whole
+
+ align:start position:0%
+H1 dot dot dot HN. What is the whole
+ 
+
+ align:start position:0%
+H1 dot dot dot HN. What is the whole
+thing? It's just H1.
+
+ align:start position:0%
+thing? It's just H1.
+ 
+
+ align:start position:0%
+thing? It's just H1.
+Pull out H1 and look at the rest of it.
+
+ align:start position:0%
+Pull out H1 and look at the rest of it.
+ 
+
+ align:start position:0%
+Pull out H1 and look at the rest of it.
+How many horses are are here?
+
+ align:start position:0%
+How many horses are are here?
+ 
+
+ align:start position:0%
+How many horses are are here?
+Zero horses.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is the empty set. There are no
+
+ align:start position:0%
+This is the empty set. There are no
+ 
+
+ align:start position:0%
+This is the empty set. There are no
+horses here to compare to.
+
+ align:start position:0%
+horses here to compare to.
+ 
+
+ align:start position:0%
+horses here to compare to.
+Even though I got a I got an H2, I got
+
+ align:start position:0%
+Even though I got a I got an H2, I got
+ 
+
+ align:start position:0%
+Even though I got a I got an H2, I got
+an HN. I got dot dot dot. Because
+
+ align:start position:0%
+an HN. I got dot dot dot. Because
+ 
+
+ align:start position:0%
+an HN. I got dot dot dot. Because
+generally if n's big,
+
+ align:start position:0%
+generally if n's big,
+ 
+
+ align:start position:0%
+generally if n's big,
+this has n minus one horses are here.
+
+ align:start position:0%
+this has n minus one horses are here.
+ 
+
+ align:start position:0%
+this has n minus one horses are here.
+There's n total. I got n minus one right
+
+ align:start position:0%
+There's n total. I got n minus one right
+ 
+
+ align:start position:0%
+There's n total. I got n minus one right
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+But n minus one is zero. There are no
+
+ align:start position:0%
+But n minus one is zero. There are no
+ 
+
+ align:start position:0%
+But n minus one is zero. There are no
+horses here. And so this bridge in the
+
+ align:start position:0%
+horses here. And so this bridge in the
+ 
+
+ align:start position:0%
+horses here. And so this bridge in the
+equality totally breaks,
+
+ align:start position:0%
+equality totally breaks,
+ 
+
+ align:start position:0%
+equality totally breaks,
+right? I got color of h1 equals
+
+ align:start position:0%
+right? I got color of h1 equals
+ 
+
+ align:start position:0%
+right? I got color of h1 equals
+there's no information here equals the
+
+ align:start position:0%
+there's no information here equals the
+ 
+
+ align:start position:0%
+there's no information here equals the
+color of h2. There's no equality here.
+
+ align:start position:0%
+color of h2. There's no equality here.
+ 
+
+ align:start position:0%
+color of h2. There's no equality here.
+There's no horses in this set. All
+
+ align:start position:0%
+There's no horses in this set. All
+ 
+
+ align:start position:0%
+There's no horses in this set. All
+because of that dot dot dot. Do you see
+
+ align:start position:0%
+because of that dot dot dot. Do you see
+ 
+
+ align:start position:0%
+because of that dot dot dot. Do you see
+where the problem is by using the dot
+
+ align:start position:0%
+where the problem is by using the dot
+ 
+
+ align:start position:0%
+where the problem is by using the dot
+dot dot for the case n equals one? It
+
+ align:start position:0%
+dot dot for the case n equals one? It
+ 
+
+ align:start position:0%
+dot dot for the case n equals one? It
+was true for every other case of n. n=
+
+ align:start position:0%
+was true for every other case of n. n=
+ 
+
+ align:start position:0%
+was true for every other case of n. n=
+2, n= 3, it's all true. All right. In
+
+ align:start position:0%
+2, n= 3, it's all true. All right. In
+ 
+
+ align:start position:0%
+2, n= 3, it's all true. All right. In
+fact, what we proved, we proved the base
+
+ align:start position:0%
+fact, what we proved, we proved the base
+ 
+
+ align:start position:0%
+fact, what we proved, we proved the base
+case of P1 is true. This is an argument
+
+ align:start position:0%
+case of P1 is true. This is an argument
+ 
+
+ align:start position:0%
+case of P1 is true. This is an argument
+that P2 implies P3. That is true.
+
+ align:start position:0%
+that P2 implies P3. That is true.
+ 
+
+ align:start position:0%
+that P2 implies P3. That is true.
+P3
+
+ align:start position:0%
+P3
+ 
+
+ align:start position:0%
+P3
+implies P4. That is true. and so forth.
+
+ align:start position:0%
+implies P4. That is true. and so forth.
+ 
+
+ align:start position:0%
+implies P4. That is true. and so forth.
+We prove for all n bigger than equal to
+
+ align:start position:0%
+We prove for all n bigger than equal to
+ 
+
+ align:start position:0%
+We prove for all n bigger than equal to
+two PN implies PN plus one. That we
+
+ align:start position:0%
+two PN implies PN plus one. That we
+ 
+
+ align:start position:0%
+two PN implies PN plus one. That we
+proved. What is the one missing
+
+ align:start position:0%
+proved. What is the one missing
+ 
+
+ align:start position:0%
+proved. What is the one missing
+implication? We did not prove
+
+ align:start position:0%
+implication? We did not prove
+ 
+
+ align:start position:0%
+implication? We did not prove
+the missing link P1 implies P2.
+
+ align:start position:0%
+the missing link P1 implies P2.
+ 
+
+ align:start position:0%
+the missing link P1 implies P2.
+We did not prove that. Now, is that
+
+ align:start position:0%
+We did not prove that. Now, is that
+ 
+
+ align:start position:0%
+We did not prove that. Now, is that
+true?
+
+ align:start position:0%
+true?
+ 
+
+ align:start position:0%
+true?
+No. any you can find a set of two horses
+
+ align:start position:0%
+No. any you can find a set of two horses
+ 
+
+ align:start position:0%
+No. any you can find a set of two horses
+that are not the same color and just
+
+ align:start position:0%
+that are not the same color and just
+ 
+
+ align:start position:0%
+that are not the same color and just
+because every horse is the same color as
+
+ align:start position:0%
+because every horse is the same color as
+ 
+
+ align:start position:0%
+because every horse is the same color as
+itself does not give you that that was
+
+ align:start position:0%
+itself does not give you that that was
+ 
+
+ align:start position:0%
+itself does not give you that that was
+missing in this proof. And so we have to
+
+ align:start position:0%
+missing in this proof. And so we have to
+ 
+
+ align:start position:0%
+missing in this proof. And so we have to
+be really careful when you're doing
+
+ align:start position:0%
+be really careful when you're doing
+ 
+
+ align:start position:0%
+be really careful when you're doing
+these proofs that you establish the
+
+ align:start position:0%
+these proofs that you establish the
+ 
+
+ align:start position:0%
+these proofs that you establish the
+inductive step for all n bigger than
+
+ align:start position:0%
+inductive step for all n bigger than
+ 
+
+ align:start position:0%
+inductive step for all n bigger than
+equal to the base case. And then make
+
+ align:start position:0%
+equal to the base case. And then make
+ 
+
+ align:start position:0%
+equal to the base case. And then make
+sure if you're going to use this really
+
+ align:start position:0%
+sure if you're going to use this really
+ 
+
+ align:start position:0%
+sure if you're going to use this really
+convenient dot dot dot notation that you
+
+ align:start position:0%
+convenient dot dot dot notation that you
+ 
+
+ align:start position:0%
+convenient dot dot dot notation that you
+don't wind up here saying, "Oh, this is
+
+ align:start position:0%
+don't wind up here saying, "Oh, this is
+ 
+
+ align:start position:0%
+don't wind up here saying, "Oh, this is
+horses H2 through HN when there's no
+
+ align:start position:0%
+horses H2 through HN when there's no
+ 
+
+ align:start position:0%
+horses H2 through HN when there's no
+horses there
+
+ align:start position:0%
+horses there
+ 
+
+ align:start position:0%
+horses there
+because N's one."
+
+ align:start position:0%
+because N's one."
+ 
+
+ align:start position:0%
+because N's one."
+Any questions about this? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Great question. All right, let's fix the
+
+ align:start position:0%
+Great question. All right, let's fix the
+ 
+
+ align:start position:0%
+Great question. All right, let's fix the
+proof. Start with a base case of P of
+
+ align:start position:0%
+proof. Start with a base case of P of
+ 
+
+ align:start position:0%
+proof. Start with a base case of P of
+two. And now I've got all this done. And
+
+ align:start position:0%
+two. And now I've got all this done. And
+ 
+
+ align:start position:0%
+two. And now I've got all this done. And
+so therefore that's another proof.
+
+ align:start position:0%
+so therefore that's another proof.
+ 
+
+ align:start position:0%
+so therefore that's another proof.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say it again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The pro this is still the same. In any
+
+ align:start position:0%
+The pro this is still the same. In any
+ 
+
+ align:start position:0%
+The pro this is still the same. In any
+set of n bigger than equal to two
+
+ align:start position:0%
+set of n bigger than equal to two
+ 
+
+ align:start position:0%
+set of n bigger than equal to two
+horses, all the horses in the set are
+
+ align:start position:0%
+horses, all the horses in the set are
+ 
+
+ align:start position:0%
+horses, all the horses in the set are
+the same color. That's what he's saying.
+
+ align:start position:0%
+the same color. That's what he's saying.
+ 
+
+ align:start position:0%
+the same color. That's what he's saying.
+And he's saying, hey, look, the proof
+
+ align:start position:0%
+And he's saying, hey, look, the proof
+ 
+
+ align:start position:0%
+And he's saying, hey, look, the proof
+worked here. The inductive step is just
+
+ align:start position:0%
+worked here. The inductive step is just
+ 
+
+ align:start position:0%
+worked here. The inductive step is just
+fine. P2 does imply P3. Yeah. base isn't
+
+ align:start position:0%
+fine. P2 does imply P3. Yeah. base isn't
+ 
+
+ align:start position:0%
+fine. P2 does imply P3. Yeah. base isn't
+true. So
+
+ align:start position:0%
+true. So
+ 
+
+ align:start position:0%
+true. So
+that's right. The base case fails.
+
+ align:start position:0%
+that's right. The base case fails.
+ 
+
+ align:start position:0%
+that's right. The base case fails.
+All right. That's why you've always got
+
+ align:start position:0%
+All right. That's why you've always got
+ 
+
+ align:start position:0%
+All right. That's why you've always got
+to check the base case.
+
+ align:start position:0%
+to check the base case.
+ 
+
+ align:start position:0%
+to check the base case.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That is correct. That's a great point.
+
+ align:start position:0%
+That is correct. That's a great point.
+ 
+
+ align:start position:0%
+That is correct. That's a great point.
+We have given a proof that if you look
+
+ align:start position:0%
+We have given a proof that if you look
+ 
+
+ align:start position:0%
+We have given a proof that if you look
+at any pair of horses and they're the
+
+ align:start position:0%
+at any pair of horses and they're the
+ 
+
+ align:start position:0%
+at any pair of horses and they're the
+same color, then all horses are the same
+
+ align:start position:0%
+same color, then all horses are the same
+ 
+
+ align:start position:0%
+same color, then all horses are the same
+color. That's true.
+
+ align:start position:0%
+color. That's true.
+ 
+
+ align:start position:0%
+color. That's true.
+That is true. Of course, there are pairs
+
+ align:start position:0%
+That is true. Of course, there are pairs
+ 
+
+ align:start position:0%
+That is true. Of course, there are pairs
+of horses that aren't the same color.
+
+ align:start position:0%
+of horses that aren't the same color.
+ 
+
+ align:start position:0%
+of horses that aren't the same color.
+So, the base case would fail. So, always
+
+ align:start position:0%
+So, the base case would fail. So, always
+ 
+
+ align:start position:0%
+So, the base case would fail. So, always
+check the base case. You can prove some
+
+ align:start position:0%
+check the base case. You can prove some
+ 
+
+ align:start position:0%
+check the base case. You can prove some
+great stuff if you don't check the base
+
+ align:start position:0%
+great stuff if you don't check the base
+ 
+
+ align:start position:0%
+great stuff if you don't check the base
+case,
+
+ align:start position:0%
+case,
+ 
+
+ align:start position:0%
+case,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+All right. Any any other questions about
+
+ align:start position:0%
+All right. Any any other questions about
+ 
+
+ align:start position:0%
+All right. Any any other questions about
+that? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Yeah. Yeah, as long as it's an
+
+ align:start position:0%
+Yeah. Yeah. Yeah, as long as it's an
+ 
+
+ align:start position:0%
+Yeah. Yeah. Yeah, as long as it's an
+integer and as long as you prove PN
+
+ align:start position:0%
+integer and as long as you prove PN
+ 
+
+ align:start position:0%
+integer and as long as you prove PN
+implies PN plus one starting there all
+
+ align:start position:0%
+implies PN plus one starting there all
+ 
+
+ align:start position:0%
+implies PN plus one starting there all
+the way out. Yeah, you can start at
+
+ align:start position:0%
+the way out. Yeah, you can start at
+ 
+
+ align:start position:0%
+the way out. Yeah, you can start at
+negative numbers if you want. Usually
+
+ align:start position:0%
+negative numbers if you want. Usually
+ 
+
+ align:start position:0%
+negative numbers if you want. Usually
+there's not many cases where that comes
+
+ align:start position:0%
+there's not many cases where that comes
+ 
+
+ align:start position:0%
+there's not many cases where that comes
+up you want to, but you can. Nothing
+
+ align:start position:0%
+up you want to, but you can. Nothing
+ 
+
+ align:start position:0%
+up you want to, but you can. Nothing
+wrong with that.
+
+ align:start position:0%
+wrong with that.
+ 
+
+ align:start position:0%
+wrong with that.
+Any other questions?
+
+ align:start position:0%
+Any other questions?
+ 
+
+ align:start position:0%
+Any other questions?
+Yeah, you can see why it was a messy
+
+ align:start position:0%
+Yeah, you can see why it was a messy
+ 
+
+ align:start position:0%
+Yeah, you can see why it was a messy
+homework problem.
+
+ align:start position:0%
+homework problem.
+ 
+
+ align:start position:0%
+homework problem.
+All right. Uh so far we've seen examples
+
+ align:start position:0%
+All right. Uh so far we've seen examples
+ 
+
+ align:start position:0%
+All right. Uh so far we've seen examples
+of how induction is useful in proving
+
+ align:start position:0%
+of how induction is useful in proving
+ 
+
+ align:start position:0%
+of how induction is useful in proving
+the hypothesis is true but not in
+
+ align:start position:0%
+the hypothesis is true but not in
+ 
+
+ align:start position:0%
+the hypothesis is true but not in
+solving the problem per se
+
+ align:start position:0%
+solving the problem per se
+ 
+
+ align:start position:0%
+solving the problem per se
+or even figuring out what the hypothesis
+
+ align:start position:0%
+or even figuring out what the hypothesis
+ 
+
+ align:start position:0%
+or even figuring out what the hypothesis
+should be. Now in the last example we're
+
+ align:start position:0%
+should be. Now in the last example we're
+ 
+
+ align:start position:0%
+should be. Now in the last example we're
+going to show you how induction can be
+
+ align:start position:0%
+going to show you how induction can be
+ 
+
+ align:start position:0%
+going to show you how induction can be
+used to prove there is a solution to a
+
+ align:start position:0%
+used to prove there is a solution to a
+ 
+
+ align:start position:0%
+used to prove there is a solution to a
+problem and also how to find the
+
+ align:start position:0%
+problem and also how to find the
+ 
+
+ align:start position:0%
+problem and also how to find the
+solution. So it's actually going to be a
+
+ align:start position:0%
+solution. So it's actually going to be a
+ 
+
+ align:start position:0%
+solution. So it's actually going to be a
+very useful constructive thing in this
+
+ align:start position:0%
+very useful constructive thing in this
+ 
+
+ align:start position:0%
+very useful constructive thing in this
+case. Now, this problem arose in the
+
+ align:start position:0%
+case. Now, this problem arose in the
+ 
+
+ align:start position:0%
+case. Now, this problem arose in the
+construction of the Stata Center, the
+
+ align:start position:0%
+construction of the Stata Center, the
+ 
+
+ align:start position:0%
+construction of the Stata Center, the
+building we're in now. Uh, this whole
+
+ align:start position:0%
+building we're in now. Uh, this whole
+ 
+
+ align:start position:0%
+building we're in now. Uh, this whole
+building was originally supposed to cost
+
+ align:start position:0%
+building was originally supposed to cost
+ 
+
+ align:start position:0%
+building was originally supposed to cost
+completely furnished under $und00
+
+ align:start position:0%
+completely furnished under $und00
+ 
+
+ align:start position:0%
+completely furnished under $und00
+million. That was the goal. But the
+
+ align:start position:0%
+million. That was the goal. But the
+ 
+
+ align:start position:0%
+million. That was the goal. But the
+first mistake they made was the first
+
+ align:start position:0%
+first mistake they made was the first
+ 
+
+ align:start position:0%
+first mistake they made was the first
+step was hiring the architect and they
+
+ align:start position:0%
+step was hiring the architect and they
+ 
+
+ align:start position:0%
+step was hiring the architect and they
+hired Frank Giri. I think MIT is now in
+
+ align:start position:0%
+hired Frank Giri. I think MIT is now in
+ 
+
+ align:start position:0%
+hired Frank Giri. I think MIT is now in
+a lawsuit with Frank Giri. Uh, so he was
+
+ align:start position:0%
+a lawsuit with Frank Giri. Uh, so he was
+ 
+
+ align:start position:0%
+a lawsuit with Frank Giri. Uh, so he was
+the architect and cost just went nuts.
+
+ align:start position:0%
+the architect and cost just went nuts.
+ 
+
+ align:start position:0%
+the architect and cost just went nuts.
+You know, as you can imagine, you know,
+
+ align:start position:0%
+You know, as you can imagine, you know,
+ 
+
+ align:start position:0%
+You know, as you can imagine, you know,
+all these slanted walls and crazy things
+
+ align:start position:0%
+all these slanted walls and crazy things
+ 
+
+ align:start position:0%
+all these slanted walls and crazy things
+happening actually are expensive. And uh
+
+ align:start position:0%
+happening actually are expensive. And uh
+ 
+
+ align:start position:0%
+happening actually are expensive. And uh
+the cost quickly got over $300 million.
+
+ align:start position:0%
+the cost quickly got over $300 million.
+ 
+
+ align:start position:0%
+the cost quickly got over $300 million.
+Literally, that that part's true. Now,
+
+ align:start position:0%
+Literally, that that part's true. Now,
+ 
+
+ align:start position:0%
+Literally, that that part's true. Now,
+I'm going to fabricate a little bit. Uh
+
+ align:start position:0%
+I'm going to fabricate a little bit. Uh
+ 
+
+ align:start position:0%
+I'm going to fabricate a little bit. Uh
+now, actually fundraising became a huge
+
+ align:start position:0%
+now, actually fundraising became a huge
+ 
+
+ align:start position:0%
+now, actually fundraising became a huge
+priority once they're more than 200
+
+ align:start position:0%
+priority once they're more than 200
+ 
+
+ align:start position:0%
+priority once they're more than 200
+million over budget and they haven't
+
+ align:start position:0%
+million over budget and they haven't
+ 
+
+ align:start position:0%
+million over budget and they haven't
+even bought the furniture yet. So, some
+
+ align:start position:0%
+even bought the furniture yet. So, some
+ 
+
+ align:start position:0%
+even bought the furniture yet. So, some
+pretty radical ideas were proposed and
+
+ align:start position:0%
+pretty radical ideas were proposed and
+ 
+
+ align:start position:0%
+pretty radical ideas were proposed and
+one of them was to build a large 2 to
+
+ align:start position:0%
+one of them was to build a large 2 to
+ 
+
+ align:start position:0%
+one of them was to build a large 2 to
+the n by 2 to the n courtyard and put a
+
+ align:start position:0%
+the n by 2 to the n courtyard and put a
+ 
+
+ align:start position:0%
+the n by 2 to the n courtyard and put a
+statue of a wealthy potential donor in
+
+ align:start position:0%
+statue of a wealthy potential donor in
+ 
+
+ align:start position:0%
+statue of a wealthy potential donor in
+the center of the courtyard. So let's
+
+ align:start position:0%
+the center of the courtyard. So let's
+ 
+
+ align:start position:0%
+the center of the courtyard. So let's
+draw this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the courtyard
+
+ align:start position:0%
+So the courtyard
+ 
+
+ align:start position:0%
+So the courtyard
+and of course you know it's computer
+
+ align:start position:0%
+and of course you know it's computer
+ 
+
+ align:start position:0%
+and of course you know it's computer
+science so it has to be a power of two.
+
+ align:start position:0%
+science so it has to be a power of two.
+ 
+
+ align:start position:0%
+science so it has to be a power of two.
+So, it's 2 the n by 2 to the n.
+
+ align:start position:0%
+So, it's 2 the n by 2 to the n.
+ 
+
+ align:start position:0%
+So, it's 2 the n by 2 to the n.
+And I've drawn here the case n= 2.
+
+ align:start position:0%
+And I've drawn here the case n= 2.
+ 
+
+ align:start position:0%
+And I've drawn here the case n= 2.
+And we've got to get uh the statue of
+
+ align:start position:0%
+And we've got to get uh the statue of
+ 
+
+ align:start position:0%
+And we've got to get uh the statue of
+the wealthy guy in the middle. And I'm
+
+ align:start position:0%
+the wealthy guy in the middle. And I'm
+ 
+
+ align:start position:0%
+the wealthy guy in the middle. And I'm
+not supposed to reveal his name. So,
+
+ align:start position:0%
+not supposed to reveal his name. So,
+ 
+
+ align:start position:0%
+not supposed to reveal his name. So,
+we're just going to call him Bill.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, Bill's got to go in the
+
+ align:start position:0%
+All right. So, Bill's got to go in the
+ 
+
+ align:start position:0%
+All right. So, Bill's got to go in the
+center. Now, this would be fine except
+
+ align:start position:0%
+center. Now, this would be fine except
+ 
+
+ align:start position:0%
+center. Now, this would be fine except
+that nothing was easy with Frank Gary.
+
+ align:start position:0%
+that nothing was easy with Frank Gary.
+ 
+
+ align:start position:0%
+that nothing was easy with Frank Gary.
+everything is some weird weird thing
+
+ align:start position:0%
+everything is some weird weird thing
+ 
+
+ align:start position:0%
+everything is some weird weird thing
+going on. And he insisted on using
+
+ align:start position:0%
+going on. And he insisted on using
+ 
+
+ align:start position:0%
+going on. And he insisted on using
+L-shaped tiles for the courtyard.
+
+ align:start position:0%
+L-shaped tiles for the courtyard.
+ 
+
+ align:start position:0%
+L-shaped tiles for the courtyard.
+So, the tiles that we're going to use
+
+ align:start position:0%
+So, the tiles that we're going to use
+ 
+
+ align:start position:0%
+So, the tiles that we're going to use
+look like this. So, it's, you know,
+
+ align:start position:0%
+look like this. So, it's, you know,
+ 
+
+ align:start position:0%
+look like this. So, it's, you know,
+almost a 2 by two except you're missing
+
+ align:start position:0%
+almost a 2 by two except you're missing
+ 
+
+ align:start position:0%
+almost a 2 by two except you're missing
+that piece.
+
+ align:start position:0%
+that piece.
+ 
+
+ align:start position:0%
+that piece.
+So, what you need to figure out how to
+
+ align:start position:0%
+So, what you need to figure out how to
+ 
+
+ align:start position:0%
+So, what you need to figure out how to
+do is tile this courtyard perfectly,
+
+ align:start position:0%
+do is tile this courtyard perfectly,
+ 
+
+ align:start position:0%
+do is tile this courtyard perfectly,
+leaving one spot for Bill using tiles
+
+ align:start position:0%
+leaving one spot for Bill using tiles
+ 
+
+ align:start position:0%
+leaving one spot for Bill using tiles
+like this. these L-shaped tiles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is 2 x two here.
+
+ align:start position:0%
+and this is 2 x two here.
+ 
+
+ align:start position:0%
+and this is 2 x two here.
+So that's the task. So let's see if we
+
+ align:start position:0%
+So that's the task. So let's see if we
+ 
+
+ align:start position:0%
+So that's the task. So let's see if we
+can do that for n equals 2 here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um let's see. We can do a tile here.
+
+ align:start position:0%
+Um let's see. We can do a tile here.
+ 
+
+ align:start position:0%
+Um let's see. We can do a tile here.
+We can do a tile here.
+
+ align:start position:0%
+We can do a tile here.
+ 
+
+ align:start position:0%
+We can do a tile here.
+a tile here, a tile here, and a tile
+
+ align:start position:0%
+a tile here, a tile here, and a tile
+ 
+
+ align:start position:0%
+a tile here, a tile here, and a tile
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+So, we can in this case, we can tile the
+
+ align:start position:0%
+So, we can in this case, we can tile the
+ 
+
+ align:start position:0%
+So, we can in this case, we can tile the
+courtyard perfectly using these L-shaped
+
+ align:start position:0%
+courtyard perfectly using these L-shaped
+ 
+
+ align:start position:0%
+courtyard perfectly using these L-shaped
+tiles, leaving one square in the center
+
+ align:start position:0%
+tiles, leaving one square in the center
+ 
+
+ align:start position:0%
+tiles, leaving one square in the center
+for the statue.
+
+ align:start position:0%
+for the statue.
+ 
+
+ align:start position:0%
+for the statue.
+All right, everybody understand what
+
+ align:start position:0%
+All right, everybody understand what
+ 
+
+ align:start position:0%
+All right, everybody understand what
+we're trying to do? The goal? Now, I
+
+ align:start position:0%
+we're trying to do? The goal? Now, I
+ 
+
+ align:start position:0%
+we're trying to do? The goal? Now, I
+want to do it for n.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh so let's start proving it by
+
+ align:start position:0%
+Uh so let's start proving it by
+ 
+
+ align:start position:0%
+Uh so let's start proving it by
+induction even though we don't know how
+
+ align:start position:0%
+induction even though we don't know how
+ 
+
+ align:start position:0%
+induction even though we don't know how
+to do it yet because we're going to see
+
+ align:start position:0%
+to do it yet because we're going to see
+ 
+
+ align:start position:0%
+to do it yet because we're going to see
+how induction is going to help us show
+
+ align:start position:0%
+how induction is going to help us show
+ 
+
+ align:start position:0%
+how induction is going to help us show
+it's possible and maybe even show us how
+
+ align:start position:0%
+it's possible and maybe even show us how
+ 
+
+ align:start position:0%
+it's possible and maybe even show us how
+to do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So let's state a theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n.
+
+ align:start position:0%
+for all n.
+ 
+
+ align:start position:0%
+for all n.
+There exists a way
+
+ align:start position:0%
+There exists a way
+ 
+
+ align:start position:0%
+There exists a way
+to tile
+
+ align:start position:0%
+to tile
+ 
+
+ align:start position:0%
+to tile
+a 2 to the n by 2 to the n
+
+ align:start position:0%
+a 2 to the n by 2 to the n
+ 
+
+ align:start position:0%
+a 2 to the n by 2 to the n
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+or courtyard
+
+ align:start position:0%
+or courtyard
+ 
+
+ align:start position:0%
+or courtyard
+with a center square missing for Bill.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the proof will be by induction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And our induction hypothesis, the
+
+ align:start position:0%
+And our induction hypothesis, the
+ 
+
+ align:start position:0%
+And our induction hypothesis, the
+predicate
+
+ align:start position:0%
+predicate
+ 
+
+ align:start position:0%
+predicate
+PN is going to be what we're trying to
+
+ align:start position:0%
+PN is going to be what we're trying to
+ 
+
+ align:start position:0%
+PN is going to be what we're trying to
+prove.
+
+ align:start position:0%
+prove.
+ 
+
+ align:start position:0%
+prove.
+All right? So this is the induction
+
+ align:start position:0%
+All right? So this is the induction
+ 
+
+ align:start position:0%
+All right? So this is the induction
+hypothesis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Almost always when you do the induction,
+
+ align:start position:0%
+Almost always when you do the induction,
+ 
+
+ align:start position:0%
+Almost always when you do the induction,
+you want to start out with that as your
+
+ align:start position:0%
+you want to start out with that as your
+ 
+
+ align:start position:0%
+you want to start out with that as your
+hypothesis.
+
+ align:start position:0%
+hypothesis.
+ 
+
+ align:start position:0%
+hypothesis.
+What's the next step?
+
+ align:start position:0%
+What's the next step?
+ 
+
+ align:start position:0%
+What's the next step?
+Base case. Never ever forget the base
+
+ align:start position:0%
+Base case. Never ever forget the base
+ 
+
+ align:start position:0%
+Base case. Never ever forget the base
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+or you'll be thinking all horses are the
+
+ align:start position:0%
+or you'll be thinking all horses are the
+ 
+
+ align:start position:0%
+or you'll be thinking all horses are the
+same color.
+
+ align:start position:0%
+same color.
+ 
+
+ align:start position:0%
+same color.
+P 0.
+
+ align:start position:0%
+P 0.
+ 
+
+ align:start position:0%
+P 0.
+Well, the courtyard for N equals 0 is
+
+ align:start position:0%
+Well, the courtyard for N equals 0 is
+ 
+
+ align:start position:0%
+Well, the courtyard for N equals 0 is
+just one square.
+
+ align:start position:0%
+just one square.
+ 
+
+ align:start position:0%
+just one square.
+And that's for Bill.
+
+ align:start position:0%
+And that's for Bill.
+ 
+
+ align:start position:0%
+And that's for Bill.
+So you're done. There's no tiles at all
+
+ align:start position:0%
+So you're done. There's no tiles at all
+ 
+
+ align:start position:0%
+So you're done. There's no tiles at all
+to worry about. That's easy. So that's
+
+ align:start position:0%
+to worry about. That's easy. So that's
+ 
+
+ align:start position:0%
+to worry about. That's easy. So that's
+true.
+
+ align:start position:0%
+true.
+ 
+
+ align:start position:0%
+true.
+And then we do the inductive step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+inductive step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for n bigger than equal to zero. Got to
+
+ align:start position:0%
+for n bigger than equal to zero. Got to
+ 
+
+ align:start position:0%
+for n bigger than equal to zero. Got to
+remember to keep track of that. Now we
+
+ align:start position:0%
+remember to keep track of that. Now we
+ 
+
+ align:start position:0%
+remember to keep track of that. Now we
+assume
+
+ align:start position:0%
+assume
+ 
+
+ align:start position:0%
+assume
+PN
+
+ align:start position:0%
+PN
+ 
+
+ align:start position:0%
+PN
+to verify the inductive hypothesis or to
+
+ align:start position:0%
+to verify the inductive hypothesis or to
+ 
+
+ align:start position:0%
+to verify the inductive hypothesis or to
+prove PN plus one.
+
+ align:start position:0%
+prove PN plus one.
+ 
+
+ align:start position:0%
+prove PN plus one.
+A lot of ways to write this down, but
+
+ align:start position:0%
+A lot of ways to write this down, but
+ 
+
+ align:start position:0%
+A lot of ways to write this down, but
+you always want to say what you're
+
+ align:start position:0%
+you always want to say what you're
+ 
+
+ align:start position:0%
+you always want to say what you're
+assuming and why.
+
+ align:start position:0%
+assuming and why.
+ 
+
+ align:start position:0%
+assuming and why.
+So we need to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PN plus one is true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, so let's look at a 2 to the n by 2
+
+ align:start position:0%
+Well, so let's look at a 2 to the n by 2
+ 
+
+ align:start position:0%
+Well, so let's look at a 2 to the n by 2
+the n +1 by 2 the n +1 courtyard.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So let's draw it out here.
+
+ align:start position:0%
+All right. So let's draw it out here.
+ 
+
+ align:start position:0%
+All right. So let's draw it out here.
+2 the n +1 by 2 the n +1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What are we going to do to use our
+
+ align:start position:0%
+What are we going to do to use our
+ 
+
+ align:start position:0%
+What are we going to do to use our
+inductive hypothesis? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for them. Yeah. So that you're on a good
+
+ align:start position:0%
+for them. Yeah. So that you're on a good
+ 
+
+ align:start position:0%
+for them. Yeah. So that you're on a good
+track there for sure, but I got to apply
+
+ align:start position:0%
+track there for sure, but I got to apply
+ 
+
+ align:start position:0%
+track there for sure, but I got to apply
+I'm not going from one to two. I want to
+
+ align:start position:0%
+I'm not going from one to two. I want to
+ 
+
+ align:start position:0%
+I'm not going from one to two. I want to
+get I want to use PN here. So I got a
+
+ align:start position:0%
+get I want to use PN here. So I got a
+ 
+
+ align:start position:0%
+get I want to use PN here. So I got a
+two to the n plus one by two to the n
+
+ align:start position:0%
+two to the n plus one by two to the n
+ 
+
+ align:start position:0%
+two to the n plus one by two to the n
+plus one courtyard. How do I use PN?
+
+ align:start position:0%
+plus one courtyard. How do I use PN?
+ 
+
+ align:start position:0%
+plus one courtyard. How do I use PN?
+Two to the n by two to the n courtyard.
+
+ align:start position:0%
+Two to the n by two to the n courtyard.
+ 
+
+ align:start position:0%
+Two to the n by two to the n courtyard.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Oh, never mind. I don't think it works.
+
+ align:start position:0%
+Oh, never mind. I don't think it works.
+ 
+
+ align:start position:0%
+Oh, never mind. I don't think it works.
+I was about to say that would be as if
+
+ align:start position:0%
+I was about to say that would be as if
+ 
+
+ align:start position:0%
+I was about to say that would be as if
+two to the n would divide that into four
+
+ align:start position:0%
+two to the n would divide that into four
+ 
+
+ align:start position:0%
+two to the n would divide that into four
+blocks. Good idea. Yeah, let's divide
+
+ align:start position:0%
+blocks. Good idea. Yeah, let's divide
+ 
+
+ align:start position:0%
+blocks. Good idea. Yeah, let's divide
+our courtyard into four blocks. That's a
+
+ align:start position:0%
+our courtyard into four blocks. That's a
+ 
+
+ align:start position:0%
+our courtyard into four blocks. That's a
+great idea. And now each of these is 2
+
+ align:start position:0%
+great idea. And now each of these is 2
+ 
+
+ align:start position:0%
+great idea. And now each of these is 2
+to the n by 2 to the n,
+
+ align:start position:0%
+to the n by 2 to the n,
+ 
+
+ align:start position:0%
+to the n by 2 to the n,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And I can apply the inductive hypothesis
+
+ align:start position:0%
+And I can apply the inductive hypothesis
+ 
+
+ align:start position:0%
+And I can apply the inductive hypothesis
+there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah. Something. Yeah. It doesn't quite
+
+ align:start position:0%
+Yeah. Something. Yeah. It doesn't quite
+ 
+
+ align:start position:0%
+Yeah. Something. Yeah. It doesn't quite
+work because Bill wants to be here.
+
+ align:start position:0%
+work because Bill wants to be here.
+ 
+
+ align:start position:0%
+work because Bill wants to be here.
+Got a little square for Bill there. But
+
+ align:start position:0%
+Got a little square for Bill there. But
+ 
+
+ align:start position:0%
+Got a little square for Bill there. But
+I can't I can't use my inductive
+
+ align:start position:0%
+I can't I can't use my inductive
+ 
+
+ align:start position:0%
+I can't I can't use my inductive
+hypothesis to tile this
+
+ align:start position:0%
+hypothesis to tile this
+ 
+
+ align:start position:0%
+hypothesis to tile this
+because there's no square missing. In
+
+ align:start position:0%
+because there's no square missing. In
+ 
+
+ align:start position:0%
+because there's no square missing. In
+fact, even if there wasn't a square
+
+ align:start position:0%
+fact, even if there wasn't a square
+ 
+
+ align:start position:0%
+fact, even if there wasn't a square
+missing, I'm in trouble. If I've got say
+
+ align:start position:0%
+missing, I'm in trouble. If I've got say
+ 
+
+ align:start position:0%
+missing, I'm in trouble. If I've got say
+this is size 16, 4x4 here, can I tile a
+
+ align:start position:0%
+this is size 16, 4x4 here, can I tile a
+ 
+
+ align:start position:0%
+this is size 16, 4x4 here, can I tile a
+4x4 region with L-shaped tiles?
+
+ align:start position:0%
+4x4 region with L-shaped tiles?
+ 
+
+ align:start position:0%
+4x4 region with L-shaped tiles?
+No, they're size three. Three doesn't
+
+ align:start position:0%
+No, they're size three. Three doesn't
+ 
+
+ align:start position:0%
+No, they're size three. Three doesn't
+divide 16. Yeah,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a great idea. All right, we're
+
+ align:start position:0%
+there's a great idea. All right, we're
+ 
+
+ align:start position:0%
+there's a great idea. All right, we're
+we're making progress now. Take a corner
+
+ align:start position:0%
+we're making progress now. Take a corner
+ 
+
+ align:start position:0%
+we're making progress now. Take a corner
+out of each of them. Put my L-shaped
+
+ align:start position:0%
+out of each of them. Put my L-shaped
+ 
+
+ align:start position:0%
+out of each of them. Put my L-shaped
+tile here.
+
+ align:start position:0%
+tile here.
+ 
+
+ align:start position:0%
+tile here.
+Now I can use the inductive hypothesis
+
+ align:start position:0%
+Now I can use the inductive hypothesis
+ 
+
+ align:start position:0%
+Now I can use the inductive hypothesis
+to tile each one of these.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Why can't you put like a a four in the
+
+ align:start position:0%
+Why can't you put like a a four in the
+ 
+
+ align:start position:0%
+Why can't you put like a a four in the
+center and then you have a bunch of twos
+
+ align:start position:0%
+center and then you have a bunch of twos
+ 
+
+ align:start position:0%
+center and then you have a bunch of twos
+on the side?
+
+ align:start position:0%
+on the side?
+ 
+
+ align:start position:0%
+on the side?
+Four in the center and a bunch.
+
+ align:start position:0%
+Four in the center and a bunch.
+ 
+
+ align:start position:0%
+Four in the center and a bunch.
+A two by two in the center.
+
+ align:start position:0%
+A two by two in the center.
+ 
+
+ align:start position:0%
+A two by two in the center.
+I got that. I got bill and a tile
+
+ align:start position:0%
+I got that. I got bill and a tile
+ 
+
+ align:start position:0%
+I got that. I got bill and a tile
+and then but like make it bigger. Not
+
+ align:start position:0%
+and then but like make it bigger. Not
+ 
+
+ align:start position:0%
+and then but like make it bigger. Not
+just like four single tiles, but like
+
+ align:start position:0%
+just like four single tiles, but like
+ 
+
+ align:start position:0%
+just like four single tiles, but like
+you have So you have something like that
+
+ align:start position:0%
+you have So you have something like that
+ 
+
+ align:start position:0%
+you have So you have something like that
+over there, right? Put that in the
+
+ align:start position:0%
+over there, right? Put that in the
+ 
+
+ align:start position:0%
+over there, right? Put that in the
+center.
+
+ align:start position:0%
+center.
+ 
+
+ align:start position:0%
+center.
+Put that in the center. Okay. The rest
+
+ align:start position:0%
+Put that in the center. Okay. The rest
+ 
+
+ align:start position:0%
+Put that in the center. Okay. The rest
+of them will have like 2 by two which
+
+ align:start position:0%
+of them will have like 2 by two which
+ 
+
+ align:start position:0%
+of them will have like 2 by two which
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+well the rest of them aren't 2 by two
+
+ align:start position:0%
+well the rest of them aren't 2 by two
+ 
+
+ align:start position:0%
+well the rest of them aren't 2 by two
+because this is n I got to use PN here
+
+ align:start position:0%
+because this is n I got to use PN here
+ 
+
+ align:start position:0%
+because this is n I got to use PN here
+and PN says that I can in a region 2 to
+
+ align:start position:0%
+and PN says that I can in a region 2 to
+ 
+
+ align:start position:0%
+and PN says that I can in a region 2 to
+the n by two to the n with a square out
+
+ align:start position:0%
+the n by two to the n with a square out
+ 
+
+ align:start position:0%
+the n by two to the n with a square out
+of the center I can tile it.
+
+ align:start position:0%
+of the center I can tile it.
+ 
+
+ align:start position:0%
+of the center I can tile it.
+Did I make am I good here so far? Did I
+
+ align:start position:0%
+Did I make am I good here so far? Did I
+ 
+
+ align:start position:0%
+Did I make am I good here so far? Did I
+claimed I was sort of done? Yeah. What?
+
+ align:start position:0%
+claimed I was sort of done? Yeah. What?
+ 
+
+ align:start position:0%
+claimed I was sort of done? Yeah. What?
+No, because P of N tells us well P of N
+
+ align:start position:0%
+No, because P of N tells us well P of N
+ 
+
+ align:start position:0%
+No, because P of N tells us well P of N
+tells us that we can set up a 2 by 2
+
+ align:start position:0%
+tells us that we can set up a 2 by 2
+ 
+
+ align:start position:0%
+tells us that we can set up a 2 by 2
+piece.
+
+ align:start position:0%
+piece.
+ 
+
+ align:start position:0%
+piece.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah. And what's the problem for this 2
+
+ align:start position:0%
+Yeah. And what's the problem for this 2
+ 
+
+ align:start position:0%
+Yeah. And what's the problem for this 2
+to the N by two to the N region?
+
+ align:start position:0%
+to the N by two to the N region?
+ 
+
+ align:start position:0%
+to the N by two to the N region?
+Bill's not in the center. He wants to be
+
+ align:start position:0%
+Bill's not in the center. He wants to be
+ 
+
+ align:start position:0%
+Bill's not in the center. He wants to be
+in the center. We put Bill in the
+
+ align:start position:0%
+in the center. We put Bill in the
+ 
+
+ align:start position:0%
+in the center. We put Bill in the
+corner. So, you can't use the inductive
+
+ align:start position:0%
+corner. So, you can't use the inductive
+ 
+
+ align:start position:0%
+corner. So, you can't use the inductive
+hypothesis here.
+
+ align:start position:0%
+hypothesis here.
+ 
+
+ align:start position:0%
+hypothesis here.
+Ah, so I I went a little too fast here.
+
+ align:start position:0%
+Ah, so I I went a little too fast here.
+ 
+
+ align:start position:0%
+Ah, so I I went a little too fast here.
+That's This is not a proof so far. I got
+
+ align:start position:0%
+That's This is not a proof so far. I got
+ 
+
+ align:start position:0%
+That's This is not a proof so far. I got
+a problem. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Great. Okay. Let's then change the
+
+ align:start position:0%
+Great. Okay. Let's then change the
+ 
+
+ align:start position:0%
+Great. Okay. Let's then change the
+inductive hypothesis.
+
+ align:start position:0%
+inductive hypothesis.
+ 
+
+ align:start position:0%
+inductive hypothesis.
+Good. Let's say there exists a way to
+
+ align:start position:0%
+Good. Let's say there exists a way to
+ 
+
+ align:start position:0%
+Good. Let's say there exists a way to
+tile a two to the n by two to the n
+
+ align:start position:0%
+tile a two to the n by two to the n
+ 
+
+ align:start position:0%
+tile a two to the n by two to the n
+region with a corner square missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for bill.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Oh, but I got to put Oh, but I can make
+
+ align:start position:0%
+Oh, but I got to put Oh, but I can make
+ 
+
+ align:start position:0%
+Oh, but I got to put Oh, but I can make
+this work. Yeah. Yeah, we can make some
+
+ align:start position:0%
+this work. Yeah. Yeah, we can make some
+ 
+
+ align:start position:0%
+this work. Yeah. Yeah, we can make some
+we can prove this. Now, the inductive
+
+ align:start position:0%
+we can prove this. Now, the inductive
+ 
+
+ align:start position:0%
+we can prove this. Now, the inductive
+step's going to work because I'll put
+
+ align:start position:0%
+step's going to work because I'll put
+ 
+
+ align:start position:0%
+step's going to work because I'll put
+Bill say he's in one of the four
+
+ align:start position:0%
+Bill say he's in one of the four
+ 
+
+ align:start position:0%
+Bill say he's in one of the four
+regions. Then use the L down here.
+
+ align:start position:0%
+regions. Then use the L down here.
+ 
+
+ align:start position:0%
+regions. Then use the L down here.
+Put the L here. And now I've got a
+
+ align:start position:0%
+Put the L here. And now I've got a
+ 
+
+ align:start position:0%
+Put the L here. And now I've got a
+corner out of each one. And now I'm done
+
+ align:start position:0%
+corner out of each one. And now I'm done
+ 
+
+ align:start position:0%
+corner out of each one. And now I'm done
+by induction.
+
+ align:start position:0%
+by induction.
+ 
+
+ align:start position:0%
+by induction.
+I have proved there's a way to tile any
+
+ align:start position:0%
+I have proved there's a way to tile any
+ 
+
+ align:start position:0%
+I have proved there's a way to tile any
+two to the n by two to the n region with
+
+ align:start position:0%
+two to the n by two to the n region with
+ 
+
+ align:start position:0%
+two to the n by two to the n region with
+a corner square missing.
+
+ align:start position:0%
+a corner square missing.
+ 
+
+ align:start position:0%
+a corner square missing.
+I think that proof works. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bill in the middle because you prove
+
+ align:start position:0%
+Bill in the middle because you prove
+ 
+
+ align:start position:0%
+Bill in the middle because you prove
+that you can put in the corner. 2x2 case
+
+ align:start position:0%
+that you can put in the corner. 2x2 case
+ 
+
+ align:start position:0%
+that you can put in the corner. 2x2 case
+you can just blow that square up and
+
+ align:start position:0%
+you can just blow that square up and
+ 
+
+ align:start position:0%
+you can just blow that square up and
+that square where Bill was becomes just
+
+ align:start position:0%
+that square where Bill was becomes just
+ 
+
+ align:start position:0%
+that square where Bill was becomes just
+another square which is 4x4 and then you
+
+ align:start position:0%
+another square which is 4x4 and then you
+ 
+
+ align:start position:0%
+another square which is 4x4 and then you
+can put them in the middle. That is
+
+ align:start position:0%
+can put them in the middle. That is
+ 
+
+ align:start position:0%
+can put them in the middle. That is
+true. So you jumped ahead. Uh we have
+
+ align:start position:0%
+true. So you jumped ahead. Uh we have
+ 
+
+ align:start position:0%
+true. So you jumped ahead. Uh we have
+successfully now proved this is true for
+
+ align:start position:0%
+successfully now proved this is true for
+ 
+
+ align:start position:0%
+successfully now proved this is true for
+P of N but Bill didn't want to be in the
+
+ align:start position:0%
+P of N but Bill didn't want to be in the
+ 
+
+ align:start position:0%
+P of N but Bill didn't want to be in the
+corner. We're trying to prove there's a
+
+ align:start position:0%
+corner. We're trying to prove there's a
+ 
+
+ align:start position:0%
+corner. We're trying to prove there's a
+way to do it with Bill in the center
+
+ align:start position:0%
+way to do it with Bill in the center
+ 
+
+ align:start position:0%
+way to do it with Bill in the center
+which is not what we proved. And you
+
+ align:start position:0%
+which is not what we proved. And you
+ 
+
+ align:start position:0%
+which is not what we proved. And you
+come up with a way yeah that might be
+
+ align:start position:0%
+come up with a way yeah that might be
+ 
+
+ align:start position:0%
+come up with a way yeah that might be
+doable. First prove you can put Bill in
+
+ align:start position:0%
+doable. First prove you can put Bill in
+ 
+
+ align:start position:0%
+doable. First prove you can put Bill in
+the corner and
+
+ align:start position:0%
+the corner and
+ 
+
+ align:start position:0%
+the corner and
+do it in two to the n by two to the n's.
+
+ align:start position:0%
+do it in two to the n by two to the n's.
+ 
+
+ align:start position:0%
+do it in two to the n by two to the n's.
+Oh, I don't know about this actually.
+
+ align:start position:0%
+Oh, I don't know about this actually.
+ 
+
+ align:start position:0%
+Oh, I don't know about this actually.
+I got bill in the corner. There's some
+
+ align:start position:0%
+I got bill in the corner. There's some
+ 
+
+ align:start position:0%
+I got bill in the corner. There's some
+way to do it, but it might have involved
+
+ align:start position:0%
+way to do it, but it might have involved
+ 
+
+ align:start position:0%
+way to do it, but it might have involved
+doing this. And now I can't rotate that.
+
+ align:start position:0%
+doing this. And now I can't rotate that.
+ 
+
+ align:start position:0%
+doing this. And now I can't rotate that.
+I don't think we have I don't think that
+
+ align:start position:0%
+I don't think we have I don't think that
+ 
+
+ align:start position:0%
+I don't think we have I don't think that
+proof necessarily works.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that he could be here. But likewise, we
+
+ align:start position:0%
+that he could be here. But likewise, we
+ 
+
+ align:start position:0%
+that he could be here. But likewise, we
+could prove that if the block just
+
+ align:start position:0%
+could prove that if the block just
+ 
+
+ align:start position:0%
+could prove that if the block just
+rotates, you can
+
+ align:start position:0%
+rotates, you can
+ 
+
+ align:start position:0%
+rotates, you can
+Yes, I agree with you. And I like it
+
+ align:start position:0%
+Yes, I agree with you. And I like it
+ 
+
+ align:start position:0%
+Yes, I agree with you. And I like it
+when I first heard it, and you might
+
+ align:start position:0%
+when I first heard it, and you might
+ 
+
+ align:start position:0%
+when I first heard it, and you might
+still convince me, but all we've proved
+
+ align:start position:0%
+still convince me, but all we've proved
+ 
+
+ align:start position:0%
+still convince me, but all we've proved
+is is this. There's a two to the n by
+
+ align:start position:0%
+is is this. There's a two to the n by
+ 
+
+ align:start position:0%
+is is this. There's a two to the n by
+two to the n any two to the n by two to
+
+ align:start position:0%
+two to the n any two to the n by two to
+ 
+
+ align:start position:0%
+two to the n any two to the n by two to
+the n region. We can tile it with a
+
+ align:start position:0%
+the n region. We can tile it with a
+ 
+
+ align:start position:0%
+the n region. We can tile it with a
+corner bill in a corner. Any corner
+
+ align:start position:0%
+corner bill in a corner. Any corner
+ 
+
+ align:start position:0%
+corner bill in a corner. Any corner
+square missing.
+
+ align:start position:0%
+square missing.
+ 
+
+ align:start position:0%
+square missing.
+Good. So now you want to say I can get
+
+ align:start position:0%
+Good. So now you want to say I can get
+ 
+
+ align:start position:0%
+Good. So now you want to say I can get
+Bill in the middle. And what you want to
+
+ align:start position:0%
+Bill in the middle. And what you want to
+ 
+
+ align:start position:0%
+Bill in the middle. And what you want to
+say is okay, I tile this region with
+
+ align:start position:0%
+say is okay, I tile this region with
+ 
+
+ align:start position:0%
+say is okay, I tile this region with
+Bill here, you know, two to the n by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe you're right. So then I would
+
+ align:start position:0%
+maybe you're right. So then I would
+ 
+
+ align:start position:0%
+maybe you're right. So then I would
+apply the I'd apply the theorem here
+
+ align:start position:0%
+apply the I'd apply the theorem here
+ 
+
+ align:start position:0%
+apply the I'd apply the theorem here
+with Bill here. Oh, Bill here. No, I
+
+ align:start position:0%
+with Bill here. Oh, Bill here. No, I
+ 
+
+ align:start position:0%
+with Bill here. Oh, Bill here. No, I
+think I like it now. There. And then I
+
+ align:start position:0%
+think I like it now. There. And then I
+ 
+
+ align:start position:0%
+think I like it now. There. And then I
+would take these out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three blocks
+
+ align:start position:0%
+three blocks
+ 
+
+ align:start position:0%
+three blocks
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that big square is just like a zoom a
+
+ align:start position:0%
+that big square is just like a zoom a
+ 
+
+ align:start position:0%
+that big square is just like a zoom a
+zoomed out version of like the little
+
+ align:start position:0%
+zoomed out version of like the little
+ 
+
+ align:start position:0%
+zoomed out version of like the little
+square.
+
+ align:start position:0%
+square.
+ 
+
+ align:start position:0%
+square.
+I like that.
+
+ align:start position:0%
+I like that.
+ 
+
+ align:start position:0%
+I like that.
+You know that little square fits in like
+
+ align:start position:0%
+You know that little square fits in like
+ 
+
+ align:start position:0%
+You know that little square fits in like
+a 2 by two like for example in the
+
+ align:start position:0%
+a 2 by two like for example in the
+ 
+
+ align:start position:0%
+a 2 by two like for example in the
+um in the four uh 4x4 case in the like
+
+ align:start position:0%
+um in the four uh 4x4 case in the like
+ 
+
+ align:start position:0%
+um in the four uh 4x4 case in the like
+we proved the 2 by two case in the 4x4
+
+ align:start position:0%
+we proved the 2 by two case in the 4x4
+ 
+
+ align:start position:0%
+we proved the 2 by two case in the 4x4
+case you have and you have like a big
+
+ align:start position:0%
+case you have and you have like a big
+ 
+
+ align:start position:0%
+case you have and you have like a big
+size. It's just like a you have four
+
+ align:start position:0%
+size. It's just like a you have four
+ 
+
+ align:start position:0%
+size. It's just like a you have four
+squares, right? And each of the each of
+
+ align:start position:0%
+squares, right? And each of the each of
+ 
+
+ align:start position:0%
+squares, right? And each of the each of
+those four squares has four squares.
+
+ align:start position:0%
+those four squares has four squares.
+ 
+
+ align:start position:0%
+those four squares has four squares.
+So you take that right top right square
+
+ align:start position:0%
+So you take that right top right square
+ 
+
+ align:start position:0%
+So you take that right top right square
+and you put fill within
+
+ align:start position:0%
+and you put fill within
+ 
+
+ align:start position:0%
+and you put fill within
+the smaller square
+
+ align:start position:0%
+the smaller square
+ 
+
+ align:start position:0%
+the smaller square
+where exactly where you want them to be
+
+ align:start position:0%
+where exactly where you want them to be
+ 
+
+ align:start position:0%
+where exactly where you want them to be
+and then you fill those other like all
+
+ align:start position:0%
+and then you fill those other like all
+ 
+
+ align:start position:0%
+and then you fill those other like all
+those empty spaces with
+
+ align:start position:0%
+those empty spaces with
+ 
+
+ align:start position:0%
+those empty spaces with
+I agree you can make a proof and so in
+
+ align:start position:0%
+I agree you can make a proof and so in
+ 
+
+ align:start position:0%
+I agree you can make a proof and so in
+this case you'd make a lema that uses
+
+ align:start position:0%
+this case you'd make a lema that uses
+ 
+
+ align:start position:0%
+this case you'd make a lema that uses
+induction that says you can do it with
+
+ align:start position:0%
+induction that says you can do it with
+ 
+
+ align:start position:0%
+induction that says you can do it with
+Bill in the corner and then as a
+
+ align:start position:0%
+Bill in the corner and then as a
+ 
+
+ align:start position:0%
+Bill in the corner and then as a
+correlary or a theorem you'd take that
+
+ align:start position:0%
+correlary or a theorem you'd take that
+ 
+
+ align:start position:0%
+correlary or a theorem you'd take that
+and apply it to four sub squares, put
+
+ align:start position:0%
+and apply it to four sub squares, put
+ 
+
+ align:start position:0%
+and apply it to four sub squares, put
+Bill in here, take these out, and then
+
+ align:start position:0%
+Bill in here, take these out, and then
+ 
+
+ align:start position:0%
+Bill in here, take these out, and then
+now you have your result with Bill in
+
+ align:start position:0%
+now you have your result with Bill in
+ 
+
+ align:start position:0%
+now you have your result with Bill in
+the center. So that is a way to do it.
+
+ align:start position:0%
+the center. So that is a way to do it.
+ 
+
+ align:start position:0%
+the center. So that is a way to do it.
+It ends up being more complicated. There
+
+ align:start position:0%
+It ends up being more complicated. There
+ 
+
+ align:start position:0%
+It ends up being more complicated. There
+is a simpler approach, but that is that
+
+ align:start position:0%
+is a simpler approach, but that is that
+ 
+
+ align:start position:0%
+is a simpler approach, but that is that
+is a way that works and is a natural
+
+ align:start position:0%
+is a way that works and is a natural
+ 
+
+ align:start position:0%
+is a way that works and is a natural
+thing you would do if you had this on
+
+ align:start position:0%
+thing you would do if you had this on
+ 
+
+ align:start position:0%
+thing you would do if you had this on
+homework is you'd think of a different
+
+ align:start position:0%
+homework is you'd think of a different
+ 
+
+ align:start position:0%
+homework is you'd think of a different
+thing to prove by induction, then use
+
+ align:start position:0%
+thing to prove by induction, then use
+ 
+
+ align:start position:0%
+thing to prove by induction, then use
+that as a lema to get you where you
+
+ align:start position:0%
+that as a lema to get you where you
+ 
+
+ align:start position:0%
+that as a lema to get you where you
+wanted to go. There's another way to do
+
+ align:start position:0%
+wanted to go. There's another way to do
+ 
+
+ align:start position:0%
+wanted to go. There's another way to do
+it without having that first step.
+
+ align:start position:0%
+it without having that first step.
+ 
+
+ align:start position:0%
+it without having that first step.
+All right? And that's Yeah.
+
+ align:start position:0%
+All right? And that's Yeah.
+ 
+
+ align:start position:0%
+All right? And that's Yeah.
+that courtyard.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Divide each cell into a 2 by two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Well, yeah. Yeah.
+
+ align:start position:0%
+Well, yeah. Yeah.
+ 
+
+ align:start position:0%
+Well, yeah. Yeah.
+Or you want to do it bottoms up. You
+
+ align:start position:0%
+Or you want to do it bottoms up. You
+ 
+
+ align:start position:0%
+Or you want to do it bottoms up. You
+want to take it and divide and that make
+
+ align:start position:0%
+want to take it and divide and that make
+ 
+
+ align:start position:0%
+want to take it and divide and that make
+that your your inductive step by two by
+
+ align:start position:0%
+that your your inductive step by two by
+ 
+
+ align:start position:0%
+that your your inductive step by two by
+twos inside. I haven't thought about
+
+ align:start position:0%
+twos inside. I haven't thought about
+ 
+
+ align:start position:0%
+twos inside. I haven't thought about
+that approach.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you do that,
+
+ align:start position:0%
+If you do that,
+ 
+
+ align:start position:0%
+If you do that,
+then you're all set except for the 2 by
+
+ align:start position:0%
+then you're all set except for the 2 by
+ 
+
+ align:start position:0%
+then you're all set except for the 2 by
+two where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm worried about a lot of 2 by twos
+
+ align:start position:0%
+I'm worried about a lot of 2 by twos
+ 
+
+ align:start position:0%
+I'm worried about a lot of 2 by twos
+with a corner missing if I do it that
+
+ align:start position:0%
+with a corner missing if I do it that
+ 
+
+ align:start position:0%
+with a corner missing if I do it that
+way. Think about that. Um there is let
+
+ align:start position:0%
+way. Think about that. Um there is let
+ 
+
+ align:start position:0%
+way. Think about that. Um there is let
+me get to a
+
+ align:start position:0%
+me get to a
+ 
+
+ align:start position:0%
+me get to a
+uh another approach here.
+
+ align:start position:0%
+uh another approach here.
+ 
+
+ align:start position:0%
+uh another approach here.
+We couldn't make it work with the
+
+ align:start position:0%
+We couldn't make it work with the
+ 
+
+ align:start position:0%
+We couldn't make it work with the
+center. We could make it work with a
+
+ align:start position:0%
+center. We could make it work with a
+ 
+
+ align:start position:0%
+center. We could make it work with a
+corner but then we had to do more work
+
+ align:start position:0%
+corner but then we had to do more work
+ 
+
+ align:start position:0%
+corner but then we had to do more work
+after.
+
+ align:start position:0%
+after.
+ 
+
+ align:start position:0%
+after.
+One general technique to use with
+
+ align:start position:0%
+One general technique to use with
+ 
+
+ align:start position:0%
+One general technique to use with
+induction when you're having struggling
+
+ align:start position:0%
+induction when you're having struggling
+ 
+
+ align:start position:0%
+induction when you're having struggling
+what's the induction hypothesis to use.
+
+ align:start position:0%
+what's the induction hypothesis to use.
+ 
+
+ align:start position:0%
+what's the induction hypothesis to use.
+If what you got doesn't work you could
+
+ align:start position:0%
+If what you got doesn't work you could
+ 
+
+ align:start position:0%
+If what you got doesn't work you could
+pick a different one but better to pick
+
+ align:start position:0%
+pick a different one but better to pick
+ 
+
+ align:start position:0%
+pick a different one but better to pick
+a stronger one. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes, you could, and that is a good thing
+
+ align:start position:0%
+Yes, you could, and that is a good thing
+ 
+
+ align:start position:0%
+Yes, you could, and that is a good thing
+to do. Make the induction hypothesis be
+
+ align:start position:0%
+to do. Make the induction hypothesis be
+ 
+
+ align:start position:0%
+to do. Make the induction hypothesis be
+much stronger.
+
+ align:start position:0%
+much stronger.
+ 
+
+ align:start position:0%
+much stronger.
+I had trouble proving there's a way to
+
+ align:start position:0%
+I had trouble proving there's a way to
+ 
+
+ align:start position:0%
+I had trouble proving there's a way to
+do it with a center square missing.
+
+ align:start position:0%
+do it with a center square missing.
+ 
+
+ align:start position:0%
+do it with a center square missing.
+Turns out to be easier to prove it where
+
+ align:start position:0%
+Turns out to be easier to prove it where
+ 
+
+ align:start position:0%
+Turns out to be easier to prove it where
+you assume any square could be missing.
+
+ align:start position:0%
+you assume any square could be missing.
+ 
+
+ align:start position:0%
+you assume any square could be missing.
+Seems like this should be harder, right?
+
+ align:start position:0%
+Seems like this should be harder, right?
+ 
+
+ align:start position:0%
+Seems like this should be harder, right?
+We had a hard enough time just showing
+
+ align:start position:0%
+We had a hard enough time just showing
+ 
+
+ align:start position:0%
+We had a hard enough time just showing
+this square missing was doable. But by
+
+ align:start position:0%
+this square missing was doable. But by
+ 
+
+ align:start position:0%
+this square missing was doable. But by
+assuming something by trying to prove a
+
+ align:start position:0%
+assuming something by trying to prove a
+ 
+
+ align:start position:0%
+assuming something by trying to prove a
+harder problem assuming something
+
+ align:start position:0%
+harder problem assuming something
+ 
+
+ align:start position:0%
+harder problem assuming something
+stronger in PN it gets easier to prove.
+
+ align:start position:0%
+stronger in PN it gets easier to prove.
+ 
+
+ align:start position:0%
+stronger in PN it gets easier to prove.
+All right. Now we better check the base
+
+ align:start position:0%
+All right. Now we better check the base
+ 
+
+ align:start position:0%
+All right. Now we better check the base
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+P 0. But that's easy. There's only one
+
+ align:start position:0%
+P 0. But that's easy. There's only one
+ 
+
+ align:start position:0%
+P 0. But that's easy. There's only one
+square bill can be.
+
+ align:start position:0%
+square bill can be.
+ 
+
+ align:start position:0%
+square bill can be.
+All right. But now let's look at PN
+
+ align:start position:0%
+All right. But now let's look at PN
+ 
+
+ align:start position:0%
+All right. But now let's look at PN
+implies PN plus one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So we go back to this. We've
+
+ align:start position:0%
+All right. So we go back to this. We've
+ 
+
+ align:start position:0%
+All right. So we go back to this. We've
+got a 2 to the n plus1 by 2 to the n
+
+ align:start position:0%
+got a 2 to the n plus1 by 2 to the n
+ 
+
+ align:start position:0%
+got a 2 to the n plus1 by 2 to the n
+plus1 courtyard.
+
+ align:start position:0%
+plus1 courtyard.
+ 
+
+ align:start position:0%
+plus1 courtyard.
+And now Bill can be anywhere.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Put him here. There's Bill.
+
+ align:start position:0%
+Put him here. There's Bill.
+ 
+
+ align:start position:0%
+Put him here. There's Bill.
+Now I'm going to place my first L-shaped
+
+ align:start position:0%
+Now I'm going to place my first L-shaped
+ 
+
+ align:start position:0%
+Now I'm going to place my first L-shaped
+tile here in the other three regions.
+
+ align:start position:0%
+tile here in the other three regions.
+ 
+
+ align:start position:0%
+tile here in the other three regions.
+And now I apply PN to each region.
+
+ align:start position:0%
+And now I apply PN to each region.
+ 
+
+ align:start position:0%
+And now I apply PN to each region.
+Well, PN says I can do it with any
+
+ align:start position:0%
+Well, PN says I can do it with any
+ 
+
+ align:start position:0%
+Well, PN says I can do it with any
+square missing. So I'll pick this one
+
+ align:start position:0%
+square missing. So I'll pick this one
+ 
+
+ align:start position:0%
+square missing. So I'll pick this one
+out here, this one out here, that one
+
+ align:start position:0%
+out here, this one out here, that one
+ 
+
+ align:start position:0%
+out here, this one out here, that one
+there, and that one there. And now I'm
+
+ align:start position:0%
+there, and that one there. And now I'm
+ 
+
+ align:start position:0%
+there, and that one there. And now I'm
+done. And that was easy.
+
+ align:start position:0%
+done. And that was easy.
+ 
+
+ align:start position:0%
+done. And that was easy.
+No extra steps.
+
+ align:start position:0%
+No extra steps.
+ 
+
+ align:start position:0%
+No extra steps.
+Now, how is it possible that it was
+
+ align:start position:0%
+Now, how is it possible that it was
+ 
+
+ align:start position:0%
+Now, how is it possible that it was
+easier to prove something that was
+
+ align:start position:0%
+easier to prove something that was
+ 
+
+ align:start position:0%
+easier to prove something that was
+harder?
+
+ align:start position:0%
+harder?
+ 
+
+ align:start position:0%
+harder?
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+By being in the center of the
+
+ align:start position:0%
+By being in the center of the
+ 
+
+ align:start position:0%
+By being in the center of the
+constraint.
+
+ align:start position:0%
+constraint.
+ 
+
+ align:start position:0%
+constraint.
+Yes, that is true. But but by allowing
+
+ align:start position:0%
+Yes, that is true. But but by allowing
+ 
+
+ align:start position:0%
+Yes, that is true. But but by allowing
+him to be anywhere, I could have
+
+ align:start position:0%
+him to be anywhere, I could have
+ 
+
+ align:start position:0%
+him to be anywhere, I could have
+started. I have to that's a possibility.
+
+ align:start position:0%
+started. I have to that's a possibility.
+ 
+
+ align:start position:0%
+started. I have to that's a possibility.
+See what I'm trying to do here. This
+
+ align:start position:0%
+See what I'm trying to do here. This
+ 
+
+ align:start position:0%
+See what I'm trying to do here. This
+inductive step is all about proving PN
+
+ align:start position:0%
+inductive step is all about proving PN
+ 
+
+ align:start position:0%
+inductive step is all about proving PN
+implies PN plus one is true.
+
+ align:start position:0%
+implies PN plus one is true.
+ 
+
+ align:start position:0%
+implies PN plus one is true.
+That's what I'm trying to show.
+
+ align:start position:0%
+That's what I'm trying to show.
+ 
+
+ align:start position:0%
+That's what I'm trying to show.
+Now, how is it useful for me if PN is
+
+ align:start position:0%
+Now, how is it useful for me if PN is
+ 
+
+ align:start position:0%
+Now, how is it useful for me if PN is
+stronger has more
+
+ align:start position:0%
+stronger has more
+ 
+
+ align:start position:0%
+stronger has more
+you grow it? You prove that it can be in
+
+ align:start position:0%
+you grow it? You prove that it can be in
+ 
+
+ align:start position:0%
+you grow it? You prove that it can be in
+say the corner. Well, but when you grow
+
+ align:start position:0%
+say the corner. Well, but when you grow
+ 
+
+ align:start position:0%
+say the corner. Well, but when you grow
+it, the corner moves. But since we
+
+ align:start position:0%
+it, the corner moves. But since we
+ 
+
+ align:start position:0%
+it, the corner moves. But since we
+proved that it can be in any, it's fine
+
+ align:start position:0%
+proved that it can be in any, it's fine
+ 
+
+ align:start position:0%
+proved that it can be in any, it's fine
+if it moves.
+
+ align:start position:0%
+if it moves.
+ 
+
+ align:start position:0%
+if it moves.
+Exactly. That's exactly right.
+
+ align:start position:0%
+Exactly. That's exactly right.
+ 
+
+ align:start position:0%
+Exactly. That's exactly right.
+PN got more powerful
+
+ align:start position:0%
+PN got more powerful
+ 
+
+ align:start position:0%
+PN got more powerful
+which means I get more to assume here in
+
+ align:start position:0%
+which means I get more to assume here in
+ 
+
+ align:start position:0%
+which means I get more to assume here in
+the recursive problem. Bill can be
+
+ align:start position:0%
+the recursive problem. Bill can be
+ 
+
+ align:start position:0%
+the recursive problem. Bill can be
+anywhere now. Gives me more power. I can
+
+ align:start position:0%
+anywhere now. Gives me more power. I can
+ 
+
+ align:start position:0%
+anywhere now. Gives me more power. I can
+tile any courtyard with a a courtyard
+
+ align:start position:0%
+tile any courtyard with a a courtyard
+ 
+
+ align:start position:0%
+tile any courtyard with a a courtyard
+with any square missing. This is more
+
+ align:start position:0%
+with any square missing. This is more
+ 
+
+ align:start position:0%
+with any square missing. This is more
+powerful. So this got more powerful. So
+
+ align:start position:0%
+powerful. So this got more powerful. So
+ 
+
+ align:start position:0%
+powerful. So this got more powerful. So
+did this. So what it means is my tool
+
+ align:start position:0%
+did this. So what it means is my tool
+ 
+
+ align:start position:0%
+did this. So what it means is my tool
+set is bigger with a stronger PN. And
+
+ align:start position:0%
+set is bigger with a stronger PN. And
+ 
+
+ align:start position:0%
+set is bigger with a stronger PN. And
+what I'm trying to construct or prove
+
+ align:start position:0%
+what I'm trying to construct or prove
+ 
+
+ align:start position:0%
+what I'm trying to construct or prove
+got harder. And sometimes
+
+ align:start position:0%
+got harder. And sometimes
+ 
+
+ align:start position:0%
+got harder. And sometimes
+if I've got more tools, it becomes
+
+ align:start position:0%
+if I've got more tools, it becomes
+ 
+
+ align:start position:0%
+if I've got more tools, it becomes
+easier to prove even a harder thing. And
+
+ align:start position:0%
+easier to prove even a harder thing. And
+ 
+
+ align:start position:0%
+easier to prove even a harder thing. And
+so a general rule with induction is if
+
+ align:start position:0%
+so a general rule with induction is if
+ 
+
+ align:start position:0%
+so a general rule with induction is if
+it you don't first succeed, try try
+
+ align:start position:0%
+it you don't first succeed, try try
+ 
+
+ align:start position:0%
+it you don't first succeed, try try
+again. Well, the rule with induction is
+
+ align:start position:0%
+again. Well, the rule with induction is
+ 
+
+ align:start position:0%
+again. Well, the rule with induction is
+if you don't succeed at first, try
+
+ align:start position:0%
+if you don't succeed at first, try
+ 
+
+ align:start position:0%
+if you don't succeed at first, try
+something harder.
+
+ align:start position:0%
+something harder.
+ 
+
+ align:start position:0%
+something harder.
+All right? And it's amazing, but it
+
+ align:start position:0%
+All right? And it's amazing, but it
+ 
+
+ align:start position:0%
+All right? And it's amazing, but it
+actually works a lot of the time, as it
+
+ align:start position:0%
+actually works a lot of the time, as it
+ 
+
+ align:start position:0%
+actually works a lot of the time, as it
+did here. If I don't assume something
+
+ align:start position:0%
+did here. If I don't assume something
+ 
+
+ align:start position:0%
+did here. If I don't assume something
+strong enough and pee in some little
+
+ align:start position:0%
+strong enough and pee in some little
+ 
+
+ align:start position:0%
+strong enough and pee in some little
+weak thing like Bill just in the in the
+
+ align:start position:0%
+weak thing like Bill just in the in the
+ 
+
+ align:start position:0%
+weak thing like Bill just in the in the
+center, it's not enough to go anywhere.
+
+ align:start position:0%
+center, it's not enough to go anywhere.
+ 
+
+ align:start position:0%
+center, it's not enough to go anywhere.
+But if I can assume a lot more like Bill
+
+ align:start position:0%
+But if I can assume a lot more like Bill
+ 
+
+ align:start position:0%
+But if I can assume a lot more like Bill
+can be anywhere he pleases,
+
+ align:start position:0%
+can be anywhere he pleases,
+ 
+
+ align:start position:0%
+can be anywhere he pleases,
+then I can prove lots of things here.
+
+ align:start position:0%
+then I can prove lots of things here.
+ 
+
+ align:start position:0%
+then I can prove lots of things here.
+All right? So you see, so it's all the
+
+ align:start position:0%
+All right? So you see, so it's all the
+ 
+
+ align:start position:0%
+All right? So you see, so it's all the
+art, and you're going to learn this over
+
+ align:start position:0%
+art, and you're going to learn this over
+ 
+
+ align:start position:0%
+art, and you're going to learn this over
+the next several weeks. It's all the art
+
+ align:start position:0%
+the next several weeks. It's all the art
+ 
+
+ align:start position:0%
+the next several weeks. It's all the art
+of what's your induction hypothesis.
+
+ align:start position:0%
+of what's your induction hypothesis.
+ 
+
+ align:start position:0%
+of what's your induction hypothesis.
+Picking a good one, life is easy.
+
+ align:start position:0%
+Picking a good one, life is easy.
+ 
+
+ align:start position:0%
+Picking a good one, life is easy.
+picking up the wrong one. Very painful
+
+ align:start position:0%
+picking up the wrong one. Very painful
+ 
+
+ align:start position:0%
+picking up the wrong one. Very painful
+as you'll see with beaver flu.
+
+ align:start position:0%
+as you'll see with beaver flu.
+ 
+
+ align:start position:0%
+as you'll see with beaver flu.
+Okay, that's it for today.
\ No newline at end of file
diff --git a/z9XQpjNgeBI.txt b/z9XQpjNgeBI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f2fa9970058ef22d143751845a2ae413e879fcf
--- /dev/null
+++ b/z9XQpjNgeBI.txt
@@ -0,0 +1,4325 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: What stresses you?
+
+You don't have to divulge
+something deeply personal, but
+
+in a general way stresses
+people?
+
+AUDIENCE: Lack of sleep
+
+PROFESSOR: Yeah,
+lack of sleep's
+
+a pretty good stressor.
+
+AUDIENCE: Exams.
+
+PROFESSOR: Exams and
+stuff like that,
+
+grades stuff like that.
+
+What else?
+
+So let's make up some things.
+
+Exams and grades if you're
+student, right?
+
+Deadlines of any kind throughout
+your life will
+
+stress you.
+
+Traffic when you're trying to
+get to the airport to make
+
+that flight, or trying to get
+to your job interview and
+
+traffic is twice as bad
+as you thought.
+
+Somebody in front of you
+seem to be driving
+
+exceptionally slowly.
+
+Sometimes family relationships,
+I think even in
+
+happy families, there's points
+of stress in terms of a how
+
+different views are
+dealt with.
+
+Maybe if you're a college
+student, what the rest of your
+
+life will be like, where it's
+not four years all set out in
+
+front of you approximately,
+right?
+
+But what the rest of your life
+will be about and mean that
+
+can be a stress if people talk
+too much it to you about that.
+
+What does not stress you
+compared to what we might
+
+imagine throughout evolution
+was stressful for
+
+mammals like us?
+
+You're mostly not worrying about
+being eaten or eating
+
+another person for
+dinner, right?
+
+OK that's not an everyday stress
+for you, but that's an
+
+everyday stress for mammals
+who're trying to survive
+
+because they're the food of
+another group, right?
+
+And trying to get their
+own food to live.
+
+So the kinds of stressors we now
+have in an industrialized
+
+economy or post-industrial
+economy is incredibly
+
+different than the stressors
+that occurred
+
+for most of our evolution.
+
+And I'm going to take a lot of
+these points from a wonderful
+
+book from a wonderful researcher
+and writer, Robert
+
+Sapolsky, Why Zebras
+Don't Get Ulcers.
+
+He asks in that sense what
+stresses a zebra?
+
+They're not worried about exams
+and deadlines and MCATS
+
+and things like this, right?
+
+OK what are the forms of
+stress that they face.
+
+And they're things like serious
+physical injury,
+
+predators and starvation, very
+fundamental things about
+
+living and surviving.
+
+Not careers, jobs, timetables,
+the kind of world we mostly
+
+live in, unless we have
+a health threat.
+
+And so what stress is, is
+the psychological and
+
+physiological response to a
+stimulus, a stressor, that
+
+alters the body's equilibrium.
+
+And when we talk about stress we
+can talk about two forms of
+
+it-- acute, what's
+instantaneous; and chronic
+
+what's consistent and goes on.
+
+So acute, physical stress would
+be an injury, chronic
+
+things are hunger or cancer,
+long term problems.
+
+An acute psychological stress
+would be a deadline, a chronic
+
+one would be chronic work
+pressure if you have it
+
+throughout the semester.
+
+An acute stressor socially is
+humiliation, a chronic one
+
+might be isolation.
+
+And we'll come back a little
+bit actually to social
+
+rejection as a stressor
+later on.
+
+So, Sapolsky's idea is this,
+that for animals in the
+
+wilderness, and for us maybe for
+a long time in evolution,
+
+stress is typically acute,
+physical, and responsive.
+
+Something happens, it's about
+your bodily survival,
+
+and then you act.
+
+For people in the world we live
+in, in this room, stress
+
+is often chronic,
+psychosocial--
+
+it's not a physical threat
+mostly that's happening to
+
+you, it's something about your
+sense of yourself in the
+
+world, how you relate
+to people, how you
+
+relate to your goals--
+
+and it's anticipatory--
+
+we talked about it for
+pleasure also, the
+
+anticipation of reward turns on
+your dopamine system once
+
+you know what the reward will
+be, not the reward itself.
+
+But when it comes to fearful
+things, we also know that we
+
+can have dread.
+
+We dread upcoming things for
+quite some time before they
+
+even get here if we think
+they're going to be pretty
+
+unpleasant.
+
+And there's a neat study from
+Greg Berns about the
+
+neurobiology of dread
+in people.
+
+So it's an fMRI study, and in
+a way that was approved by
+
+human subjects.
+
+They were waiting for a
+cutaneous electrical
+
+shock to the foot.
+
+So it's a shock that's enough
+to be unpleasant but not
+
+enough to be dangerous.
+
+And people signed up voluntarily
+to do it, and at
+
+each trial you sit
+in the scanner.
+
+You're told what's the voltage
+level is going to be, compared
+
+to the most unpleasant they use
+in that experiment, and
+
+how long until it comes.
+
+So the voltage is how painful
+it's going to be, the duration
+
+of time, and something about how
+long dread can develop in
+
+anticipation of a painful
+stimulus.
+
+And at first you just got the
+got the warning, and here
+
+comes the pain.
+
+After a while, you get a
+choice and this is the
+
+interesting thing.
+
+Would you rather get, for
+example you could think about
+
+this, 90% voltage, that is,
+9/10 as bad as the whole
+
+experiment ever has it,
+in three seconds--
+
+so something pretty painful,
+pretty fast--
+
+or would you rather have 60%
+voltage in 27 seconds.
+
+So you can decide for yourself,
+which would you
+
+rather have?
+
+And you can see the
+
+trading-off in people's choices--
+
+the actual physical pain, which
+is greater than 90%
+
+versus the period of dread, the
+anticipation of something
+
+miserable coming up in the case
+where it's less pain but
+
+a longer run up.
+
+And what they found is that
+people varied in interesting
+
+ways, and they find
+some [INAUDIBLE]
+
+of this, but they found that
+what they call the extreme
+
+dreaders, that they would prefer
+more voltage now than
+
+to wait for any shock
+later on.
+
+Like, get it over with now, it's
+more painful for me to
+
+sit there and wait for something
+even though there's
+
+no painful stimulus than to
+just get it over with now.
+
+And maybe we all know the relief
+that when we anticipate
+
+something bad, having it happen
+sometimes is almost a
+
+relief to be past all that
+miserable dread.
+
+So, where in the brain does
+some of this occur?
+
+So, one area that we'll come
+back to-- a couple different
+
+areas-- one area I want to focus
+on is this middle of the
+
+brain, this area called
+the cingulate.
+
+And here, regardless of time and
+in all subjects, the more
+
+voltage you got, the bigger
+the brain response.
+
+OK, that's not very surprising,
+it's in a part of
+
+the brain-- we'll come to this
+a little bit later-- that's
+
+involved in the interpretation
+of pain.
+
+More voltage you get, it's easy
+to interpret it as worse.
+
+And then you say, what's the
+difference in the people who
+
+are the extreme dreaders, the
+people who would say no matter
+
+how bad the pain, I would rather
+have it now than wait
+
+for a lesser pain for
+a few more seconds.
+
+Give me the worst now, I have
+to get it over with.
+
+And what they found in the
+brains of those individuals,
+
+shown in red in this figure, is
+that even before anything
+
+was coming on in the same brain
+areas that responded to
+
+the pain, there was a rise in
+activation as if the pain was
+
+already happening.
+
+The same areas that are involved
+in responding to the
+
+pain, especially in the people
+who dreaded it the most, who
+
+would take more pain now to
+avoid the wait, those parts of
+
+the brain are already showing
+a pain-like response before
+
+anything has arrived,
+a physical
+
+manifestation of dread.
+
+So let's go back to mortality
+for a moment.
+
+So, in 1900, think about this,
+what were the major causes of
+
+death in the United States?
+
+And they were mostly from
+infectious disease and
+
+childbirth.
+
+Childbirth was extremely
+dangerous in 1900.
+
+So the most common causes
+of death were pneumonia,
+
+tuberculosis,--
+
+if you know about this it won't
+surprise you, but if you
+
+haven't studied this in
+history recently--
+
+influenza, flu, in 1918 it
+killed more Americans than
+
+World War I, which was high at
+that year it was killing many,
+
+many people, and childbirth
+and especially of course,
+
+that's going to be
+in young women.
+
+How about a few years ago in
+2007, which is roughly now,
+
+how many people are dying
+of these things?
+
+Not so many in the United
+States, they're dying of
+
+diseases that are conceptualized
+as cumulative
+
+damage diseases, not an
+infection but things like
+
+heart disease, where over many
+years a combination of
+
+lifestyle and stress might
+harm your heart function,
+
+might promote the growth of
+cancer, might promote a stroke
+
+or cerebral-vascular disorders
+including stroke.
+
+And many of these diseases are
+viewed as a combination of
+
+long-term lifestyle things,
+maybe exposure to toxins in
+
+the environment, and some
+mixtures of those.
+
+Not a one-time, one-shot
+infection or child delivery,
+
+but long slow processes
+that finally
+
+culminate in mortality.
+
+So, many of our current ideas
+about stress come from a
+
+researcher named Hans Selye And
+in the 1930's, it turns
+
+out, he's one of the main people
+thinking about stress
+
+as an important thing in our
+life, but he was infamously
+
+not good for his handling of
+rats in the laboratory.
+
+Now have any of you
+handled rats in a
+
+laboratory by your hands?
+
+I see one hand going up
+there, any others?
+
+OK, how easy is it
+to handle them ?
+
+When you pick them up and do
+stuff, are they like thank you
+
+very much, I knew it was time
+for injection or time for
+
+feeding or whatever
+you do with them?
+
+No?
+
+Are they kind of squirreling
+around a lot and wiggling and
+
+not very happy when you pick
+them up, on the whole?
+
+About as happy as we would be
+if a giant picked us up and
+
+shook us, and injected us with
+the stuff for the day?
+
+I was only involved in one rat
+experiment ever and I can't
+
+claim to be a great success like
+Selye , but I can claim
+
+to be as bad as he was
+with handling rats.
+
+Because it was kind of scary,
+they were really mean and want
+
+to get out of your hand.
+
+Of course, from their
+perspective they're just
+
+trying to live the life they
+were meant to lead and you're
+
+fighting with them and you're
+forcing them into this thing
+
+that thing to get injected, and
+
+they're squirreling around.
+
+So, he was doing an experiment
+where they had extracted
+
+ovarian chemical, and they were
+trying to figure out what
+
+it does at the time.
+
+He injected the rats daily.
+
+And he was pretty bad, by his
+own admission, he would drop
+
+them on the floor and they would
+scurry behind tables.
+
+He would hunt them down
+and drag them out.
+
+And he would do this day in,
+day out for months because
+
+they were on a daily
+experimental schedule.
+
+And what he found, after
+months of this sort of
+
+inadvertent nonstop stressing of
+the rats, because of course
+
+the better thing to do if you're
+skilled is to just pick
+
+them up with authority,
+inject them, and
+
+put them back, right?
+
+All the fighting and stuff from
+the poor handling is not
+
+making them any happier.
+
+What he found in them is peptic
+ulcers, ulcers in their
+
+eating system, enlarged adrenal
+glands, shrunken
+
+immune tissue, but it wasn't
+about the ovarian chemical, it
+
+was also in his control rats.
+
+Basically he was giving all
+of them stress-induced
+
+physiological changes.
+
+And what he was impressed by,
+and many other people too, is
+
+that you can expose rats to a
+whole huge range of stressors,
+
+different things you do in their
+environment, and they
+
+all seem to converge on these
+ulcers, these enlarged adrenal
+
+glands, and shrunken
+immune tissue.
+
+A lot of different things that
+can stress you seem to
+
+converge upon a common
+biological pathway and
+
+consequences for the animal.
+
+So stress response is similar in
+a broad array of stressors,
+
+and if they go on for too long,
+people get sick, the
+
+chronic stress.
+
+So, you remember from your
+introductory biology courses
+
+and so on, that when we talk
+about the autonomic nervous
+
+system in people, there's
+a sympathetic and
+
+parasympathetic branch.
+
+The sympathetic goes from the
+brain to the spine to organs
+
+to blood vessels to sweat glands
+to muscles and hairs,
+
+that's why you get goosebumps
+when you're scared.
+
+That's the nerves innervating,
+that's when your
+
+hair stands on end.
+
+It turns on for emergency
+situations, arousal,
+
+activation--
+
+the famous joke that it's
+related to the four F's,
+
+flight fright, and sex.
+
+I was so afraid I'd mess
+it up, I couldn't
+
+read the four word--
+
+flight, fright fight, and sex.
+
+And it releases epinephrine
+and norepinephrine.
+
+Epinephrine and norepinephrine
+is the same thing as
+
+adrenaline and noradrenaline,
+one's English-American, and
+
+one's American-American,
+same thing.
+
+The parasympathetic is your
+zen, couch-potato system.
+
+It operates highly when you're
+asleep or you're eating or
+
+you're relaxing.
+
+And so you can talk about
+different organs and how
+
+they're responding to the two
+kinds of systems when one is
+
+up and one is down they're in
+mutual opposition or balance.
+
+So in the heart, when you're
+sympathetic, when you have to
+
+activate a run from being
+attacked and your heart rate
+
+speeds up, your parasympathetic
+system will
+
+turn it down.
+
+For the blood it's seceded to
+muscles, and when you're in
+
+sympathetic action and when
+you're in parasympathetic
+
+relaxation it's drawn from the
+muscles to other organs.
+
+Part of that response too is
+the hypothalamus, which
+
+releases corticotropin releasing
+hormone to the
+
+anterior pituitary.
+
+In about 15 seconds that
+releases ACTH into the blood,
+
+that reaches the kidney and
+a few minutes later that
+
+produces glucocorticoids, or
+steroids, or cortisol, that's
+
+often used as a marker for
+stress response, a brain to
+
+hypothalamus to pituitary
+to kidney circuit.
+
+And then we can talk about how
+what can be adaptive response
+
+in an acute emergency can become
+maladaptive if it's
+
+chronic and happens over
+and over again.
+
+So mobilization of energy good
+when you're escaping danger,
+
+but if you have it all the time
+maybe it leads to muscle
+
+weakness, myopathy, fatigue
+or diabetes.
+
+Increased cardiovascular tone
+good for escaping danger,
+
+stress-induced hypertension
+not good.
+
+Suppression of digestion, you
+don't want to start to spend
+
+energy on digestion when you're
+running for your life
+
+but if you suppress it too
+much it's associated with
+
+ulceration and colitis.
+
+Suppression of growth-- we'll
+come to that-- if you're in a
+
+growth period of your life,
+that's metabolically expensive
+
+to do, growth.
+
+You turn off growth mechanisms
+briefly when you're in
+
+sympathetic action.
+
+Reproduction is turned off or
+down, too much of that may
+
+lead to impotency
+loss of libido.
+
+Suppression of the immune
+system, again you're turning
+
+down energy spent on immune
+processes temporarily for
+
+emergency, too much of that
+you could have increased
+
+disease risk.
+
+Sharpening of cognition,
+you want to be as smart
+
+as you can be, right?
+
+Under danger circumstances,
+having your system in high
+
+gear all the time can lead to
+neuronal death, and I'll show
+
+you an example of hippocampal
+shrinkage that occurs with
+
+stress in that way.
+
+So everything that can be
+adaptive in one hand, can be
+
+related to stress-related
+disorders on the other hand in
+
+the heart or in the arteries.
+
+And here's a picture
+of a stomach ulcer.
+
+We'll come back to that because
+the ulcer is one of
+
+the great interesting stories of
+the second half of the last
+
+century, is the complete
+re-interpretation of why
+
+people get ulcers.
+
+So, let's talk about that now.
+
+So, the adaptive response when
+you're in an emergency is to
+
+suppress digestion,
+that's part of
+
+the sympathetic response.
+
+And stress has long been
+associated with getting ulcers
+
+which are holes in the
+walls of your organ.
+
+Now, for many, many, many
+years, physicians and
+
+scientists thought that getting
+ulcers in adults was
+
+associated with a combination
+of stress and diet.
+
+And people who had ulcers were
+told try to have less stress
+
+in your life and eat
+more bland food.
+
+And then Robert Warren and Barry
+Marshall won the Nobel
+
+Prize in 2005.
+
+But this is one of those stories
+in science where
+
+everybody literally ridiculed
+these people in conferences
+
+and papers they were literally
+ridiculed by the entire
+
+orthodox scientific field,
+because they put forth the
+
+idea, which had been around a
+little bit but they really
+
+pushed it, that this was due not
+to the combination of diet
+
+and stress but it was due to an
+actual specific bacterium.
+
+And people thought that's
+ridiculous because our
+
+stomachs are so acidic that no
+bacterium would survive in the
+
+acidic environment of our
+stomachs long enough to do any
+
+harm in this sort
+of chronic way.
+
+And part of the way, as they
+struggled to get data, they
+
+did these kind of funny
+experiments where Marshall
+
+went and took the bacterium they
+suspected and actually
+
+swallowed it to see what
+would happen, OK?
+
+This kind of weird, heroic
+self medical experiment.
+
+And he thought, like in 10 years
+I'll see if I have an
+
+ulcer, but what happened is
+within a couple of days he was
+
+having severe gastritis, severe
+disturbance of the
+
+stomach, and that was
+the first piece of
+
+evidence they could do.
+
+He couldn't find out if he would
+have an ulcer in the
+
+long run because his wife made
+him take medications right
+
+away after that.
+
+But still, that built up the
+case that it's a bacterium
+
+that's swallowed that
+causes the gastritis
+
+that leads to ulcers.
+
+And that if you get people
+antibiotic treatments that
+
+will treat the bacterium,
+they improve a lot.
+
+So, a complete re-understanding
+of what
+
+caused the disorder and
+how to treat it.
+
+So, some people say, well it was
+never about stress, it was
+
+always about the bacterium,
+that's it, it's a simple
+
+biological story.
+
+But there's two ways in which
+probably stress is relevant.
+
+One of them, the milder one,
+is that out 15% of cases of
+
+ulcer don't have any measurable
+bacterium, they
+
+don't seem to have that, OK?
+
+So who knows about that 15%.
+
+But here's the more
+amazing piece--
+
+many, many, many of us have
+this bacterium, it's
+
+incredibly common widespread
+bacterium.
+
+But only 10% of the people
+who have the
+
+bacterium have ulcers.
+
+OK, so it seems like it's not
+just about having the
+
+bacterium, but it's interaction
+perhaps, between
+
+the bacterium and the stressors
+of your environment.
+
+There's not many stories about
+suppression of growth, but
+
+there's one historically
+interesting one, so this is at
+
+the edge of science, this
+is an anecdote.
+
+I'll show a clinical case, you
+can't do many experiments
+
+about this, about what's called
+psychogenic dwarfism,
+
+an inability to get to standard
+height that's thought
+
+to be based on psychological
+principles.
+
+So this is a story of a British
+Victorian family,
+
+their favorite son was
+killed at age 13, a
+
+tragic loss of a son.
+
+The bereaved mother takes to her
+bed for years, she doesn't
+
+leave her room or bad, and
+she ignores her surviving
+
+six-year-old son, constantly
+idealizing the boy who passed
+
+away, having almost no interest
+in the surviving son.
+
+And when he would come into the
+room, bringing her food to
+
+her room as she lay in her bed
+in severe depression, she
+
+would say to him David--
+
+that's the boy who
+passed away--
+
+oh David is that you?
+
+Oh, it's only you, she would
+say to the surviving son.
+
+So, depressed and discounting
+her surviving son.
+
+David was always perfect,
+the surviving son was an
+
+irritating reminder.
+
+He grew to only 5 feet as an
+adult, and he's famous for
+
+writing the play Peter Pan.
+
+So the next time you see the
+play, or see the movie, think
+
+about what childhood means to a
+person who had this kind of
+
+childhood, and grew to
+a very short stature.
+
+It was interpreted as a
+psychological response to a
+
+long period of stress,
+the lack of
+
+attachment from his mother.
+
+And here's a clinical case of
+a child who went into a
+
+hospital, you can see this
+picture of this child growing,
+
+he was in obviously a
+non-supportive environment.
+
+He enters a hospital and his
+growth hormone level is 5.9,
+
+it's very low.
+
+He takes to a nurse, and 100
+days later it goes to 13, it
+
+more than doubles.
+
+He's gaining height
+considerably.
+
+The nurse goes on vacation, he
+goes back to his low levels of
+
+growth hormone and growth.
+
+She returns and he goes back to
+typical growth of height.
+
+So, very psychological
+relationship between his
+
+physical growth and his
+relationship to the nurse.
+
+And so we understand this to be
+extreme cases of emotional
+
+neglect or something like that
+in the homes, these are not
+
+small spats with your parents.
+
+But again, a relationship
+between a very chronic stress,
+
+an emotional one, and then
+physical growth.
+
+Now this is a famous chair, and
+the story goes like this.
+
+In the mid-1950's Meyer Friedman
+and Ray Rosenman were
+
+cardiologists on the West
+coast, and they had a
+
+cardiology practice.
+
+And they had a chair, and this
+is the chair, that sat in
+
+their waiting room.
+
+And they had a guy who came, in
+his name is lost to history
+
+although everybody agrees he
+gets credit for beginning this
+
+idea, and his job was to
+re-upholster the chairs.
+
+And he told these two
+physicians, I go to a lot of
+
+places and I work in a lot of
+offices, and nowhere do I go
+
+do I have to re upholster chairs
+as often as I do in
+
+your office.
+
+And this triggered a thought in
+these two people, because,
+
+don't forget that for many
+physicians, understandably,
+
+and maybe less so now,
+cardiology is like real
+
+biology and psychological stuff
+is kind of peripheral
+
+and edgy, may not
+really matter.
+
+OK so to Friedman and Rosenman's
+credit they say
+
+what is going on?
+
+Why does our chairs
+look like this?
+
+Now, sometimes you might have
+that experience yourself, have
+
+you ever stood in line in a
+way that's unbelievably
+
+irritating because you have
+somewhere to go, and there's
+
+somebody really slow in front of
+you or somebody working the
+
+line who's really slow?
+
+And you're going come on, I've
+got like minutes to go here,
+
+can't I get my coffee or
+my tea or whatever.
+
+Have you ever seen people jump
+from line to line in grocery
+
+stores because they cannot bear,
+they dread that moment
+
+when they get somebody who
+gets into the line where
+
+you're supposed to have
+10 and they have 12?
+
+Have you seen that?
+
+None of us think that's quite
+fair play, but some of us say
+
+OK, wish they had 10 items,
+and some people are really
+
+mad, right?
+
+OK, so that's type A personality
+and we'll talk
+
+about that in a moment.
+
+And what they began to say is
+the patients are sitting in
+
+the office, fidgeting,
+fidgeting, fidgeting, where's
+
+the doctor?
+
+Where's the doctor?
+
+I have important things to do.
+
+And they're wearing down the
+arms and the chair because
+
+they're so fidgety waiting for
+that appointment to happen.
+
+Not just for one moment but for
+a long time and they're
+
+literally wearing
+down the chair.
+
+And they're showing up at a
+high rate to a cardiology
+
+practice of people with
+heart problems.
+
+And that's developed this idea
+that a huge threat--
+
+and I'll qualify this
+in a moment
+
+with subsequent studies--
+
+but in the 1960's, that type A
+personality, you've heard that
+
+phrase perhaps, type A
+personalities, this is where
+
+that began.
+
+It's become a widespread term.
+
+These are people who are
+immensely competitive,
+
+over-achieving, time-pressured,
+impatient,
+
+hostile, and they have
+increased risk of
+
+cardiovascular disease.
+
+And in the first analyses, the
+risk if you had this kind of
+
+personality was equal to
+smoking or very high
+
+cholesterol.
+
+I mean, there's a very high
+risk and that's why these
+
+chairs were being worn down by
+the type A personalities
+
+showing up with cardiac problems
+because they were
+
+stressing themselves all the
+time by everyday life events.
+
+And this picture sort of--
+
+they had anecdotal things,
+they had a early morning
+
+group, a patient support group
+for type A individuals with
+
+cardiovascular disease to get
+together and say, OK when I'm
+
+really stressed out, I'm
+going to count to
+
+5 and relax, right?
+
+It was a support group.
+
+So, here is your car.
+
+So, now when you go park your
+car sometimes, there's some
+
+people depending on the
+situation who park forward
+
+into their spots.
+
+But if you know you have to get
+away super fast and you
+
+don't have a minute to waste,
+how do you park?
+
+You park backwards, right?
+
+So when you jump into your car
+you can hit that accelerator
+
+and you're out in two seconds.
+
+So all of the type A people are
+all lined up here, ready
+
+to race away out after
+the session.
+
+And here's the middle of the day
+mixed parking, some people
+
+front-end in, some people
+rear-end in.
+
+These are anecdotal, but this is
+the kind of thing they were
+
+noticing, that led
+to these ideas.
+
+So it turns out, in subsequent
+studies, that a lot of the
+
+effect wasn't as broad as they
+thought, but it does apply to
+
+people who are relatively young
+with cardiovascular
+
+problems, and the key
+psychological aspect is not
+
+the impatience and
+aggressiveness.
+
+Although if you work for
+somebody like that, you don't
+
+enjoy that, probably.
+
+But the key thing is whether the
+person feels in themselves
+
+hostility, not impatience but
+hostility, and especially when
+
+they suppress it.
+
+Like, they go, I'm so mad, I'm
+so mad, I'm so mad but I can't
+
+really hit the person in
+front of the line.
+
+And that person brewing with
+hostility and suppressing that
+
+rage is actually pushing
+up their risk of
+
+cardiovascular disorders.
+
+So again we talked about to
+adaptive stress-responses and
+
+for practically every one of
+them, what can be understood
+
+to be a stress-related disease
+when that form of stress
+
+continues chronically
+and unabated.
+
+And here's a picture of a neuron
+in a healthy animal
+
+with lots of dendrites and
+arborization, and the
+
+whithered neuron in a
+hippocampal animal given lots
+
+of stress in laboratory
+experiments.
+
+So you can see it at the
+neuronal level, you can see it
+
+at the behavioral level, you
+can see it at the disease
+
+level, chronic stress is
+toxic in many ways.
+
+So one form of stress that
+occurs after really terrible
+
+experiences is post-traumatic
+stress disorder.
+
+And you may have heard--
+
+where do you hear it these
+days most of all, about
+
+post-traumatic stress
+disorder?
+
+AUDIENCE: The wars.
+
+PROFESSOR: The wars, right.
+
+The unabated wars in the Middle
+East, for American
+
+soldiers going over there under
+many tours of duty,
+
+under constant fear
+of explosion.
+
+For the civilian populations
+in those parts of the world
+
+under nonstop war threat
+for many, many years.
+
+So, if you did a brutal, vicious
+experiment of people
+
+under constant threat for their
+life, unfortunately you
+
+couldn't create a more perfect
+one than the Middle East, for
+
+both soldiers and civilians for
+the last decade, right?
+
+Constant threat and
+danger for people,
+
+everywhere, all the time.
+
+I was reading a story about
+one soldier, for example,
+
+civilians as well, who was
+standing in line to get his
+
+toothpaste, IED blows up
+and he loses his leg.
+
+That's what the life is like
+for those soldiers.
+
+And as you know, because in
+the US we have a volunteer
+
+army, soldiers are sent again
+and again for years
+
+altogether.
+
+And the civilians living there
+all the time, that's the world
+
+they're in, brutal
+stress induction.
+
+Just a few months ago, the
+number of American soldiers
+
+who died from suicide is now, on
+a monthly basis, exceeding
+
+those who die from
+war injuries.
+
+Think about that.
+
+The number of active American
+soldier who die from suicide
+
+is equal to or higher in many
+months nowadays than the
+
+number who died from war
+consequences of bombs and
+
+things like that.
+
+So, there's a lot of interest
+in PTSD from the war, from
+
+civilians having been exposed
+to the war, and then from
+
+individuals who have brutal
+episodes in their lives,
+
+tragically, of assault
+or rape.
+
+It's a severe anxiety disorder
+that can develop after
+
+exposure to any event
+which results in
+
+psychological trauma.
+
+People re-experience the
+original trauma through
+
+flashbacks, dreams, increased
+arousal, hyper-vigilance.
+
+And it's very common for anybody
+who goes through an
+
+emotionally brutal experience
+and it persists strongly in
+
+what's estimated about 20%
+of people who go through
+
+something like that.
+
+So people have tried to
+understand, what is the brain
+
+basis of PTSD, who is at risk
+for it, and how does it happen
+
+in the brain in a way that
+treatment might become more
+
+effective to help people.
+
+So one thing that was observed,
+and not everybody
+
+guessed this finding, is that
+individuals with smaller
+
+volumes of the hippocampus--
+
+when they look at soldiers with
+PTSD they tend to smaller
+
+hippocampal volumes.
+
+So, let's ask the question, how
+could this be a cause or
+
+how could this be a consequence
+of a severely
+
+traumatic experience you have,
+like serving in a particularly
+
+brutal and nasty war--
+
+or being a civilian in one.
+
+But these are soldier studies,
+so we'll focus on that.
+
+How can you tell?
+
+They come back from the war,
+they have PTSD they have
+
+smaller hippocampi.
+
+Was that a risk factor for
+becoming somebody with PTSD
+
+into a high-stress situation, or
+was it the way that the war
+
+situation made you have PTSD?
+
+Is it the cause, or
+the consequence?
+
+Does that make sense?
+
+OK, so here's an approach
+that people have taken.
+
+They did a twin study--
+
+I'll show you the graph
+in a moment--
+
+where one twin, this was for
+Vietnam now, went to serve in
+
+Vietnam, and one twin did not
+serve in the military at all.
+
+And these are identical twins.
+
+And then they asked is the
+hippocampus smaller in the
+
+twin who never went?
+
+And the logic was--
+
+it's not a complete
+certainty--
+
+but the logic is, if the twin
+who stays home in the US also
+
+has a smaller hippocampus, that
+suggests that it's a risk
+
+factor for PTSD, rather
+than the way that PTSD
+
+develops in the brain.
+
+Does that make sense?
+
+It might also play a role in
+that, but it's present even
+
+before that.
+
+And that's exactly
+what they found--
+
+these graphs, I really have to
+get the projector fixed-- but
+
+there's two steep lines here
+on your notes you'll see.
+
+They're both pretty steep.
+
+The top one is the correlation
+between severity of PTSD in
+
+the soldiers who went and
+hippocampal volume.
+
+And the bottom is hippocampal
+volume in the twins who didn't
+
+go, and they look incredibly
+similar.
+
+That is, the larger hippocampus
+of either the twin
+
+who went to war or the twin who
+stayed home, the larger of
+
+either one correlated
+with the PTSD in the
+
+twin who went to war.
+
+Does that make sense?
+
+OK.
+
+So it's as if the genetic
+influence, or the early
+
+environmental influence
+at home, or both--
+
+if you have a smaller
+hippocampus, you're at high
+
+risk for PTSD.
+
+Now, if you're not sent
+into war, you won't
+
+necessarily get PTSD.
+
+But if you're sent into war,
+then you're at high risk for
+
+getting PTSD.
+
+Is that OK?
+
+So, more recently people have
+begun to do pre/post studies,
+
+and this is one done in the
+Israeli military, 50 recruits
+
+before and after they did
+military service as
+
+paramedics.
+
+And what they found was that
+there was increased stress
+
+associated with a greater
+amygdala and hippocampal
+
+response fMRI to stress-related
+content.
+
+But the amygdala reactivity
+before stress-related contact
+
+predicted how many stress
+symptoms you have, and the
+
+hippocampus change over time
+
+correlated with stress symptoms.
+
+So now this goes a little bit
+differently, it says the
+
+amygdala function predicts who's
+at risk for having PTSD,
+
+and the hippocampal changes
+over time before and after
+
+your initial service go with
+the degree to which you
+
+exhibit the PTSD.
+
+I'll just say that.
+
+So, there's been a lot of work
+on understanding what can
+
+positively modify stress.
+
+What can you do, given stress
+you can't avoid, to do better
+
+and cope better with that?
+
+What can be the sources
+of resilience?
+
+And I'm going to give you
+examples, but I'm going to
+
+tell you the following, these
+are the categories that have
+
+come up in pretty
+well-controlled studies.
+
+Outlets for frustration, if
+you have a good outlet for
+
+frustration, that diminishes the
+toxic effects of stress.
+
+If you can predict bad things
+and feel you have control,
+
+even if you have bad things
+happen, you can cope with the
+
+consequences better.
+
+We talked about that in learned
+helplessness before,
+
+this was our theme before.
+
+If things seem to be getting
+better, even if they're pretty
+
+bad, if they seem to be getting
+better, that's a huge
+
+source of resilience.
+
+And social support
+is very powerful.
+
+So let me show you
+the empirical
+
+evidence for these things.
+
+So, here's a study where
+rats received shocks.
+
+They had a prolonged stress
+response, because they were in
+
+a situation of getting shocks
+and shocks and shocks.
+
+Heart rate goes up,
+glucocorticoid cortical
+
+secretion goes up, high
+rate of ulcers.
+
+Now you have other rats getting
+a similar thing, but
+
+they can gnaw on a wooden
+bar, or eat or
+
+drink, or run on a wheel.
+
+So, they have outlets
+for frustration.
+
+It doesn't prevent the shocks,
+it's just after they get a
+
+shock they'll go for a quick
+angry run on the wheel, OK, or
+
+they'll bite on something, OK?
+
+And they have fewer ulcers.
+
+So, just having an outlet
+for frustration
+
+reduces the toxic effects.
+
+Even another rat in the
+cage that they can go
+
+and bite helps, OK?
+
+Now that's not a nice thing for
+the other rats, but it's
+
+just like this common thing
+that we have, it's not the
+
+best human trait, this is an
+example of a rat trait as an
+
+example, but if somebody is as
+miserable as you, you feel
+
+better about things, OK?
+
+And baboons will attack
+bystanders
+
+after losing a fight.
+
+So, baboons, depending on
+where they are in the
+
+hierarchy, alpha male and so
+on, they lose a fight, they
+
+get themselves healthier in
+terms of glucocorticoids if
+
+after they lose a fight
+they go beat up a
+
+lower-ranking baboon.
+
+we're not recommending that as
+a nice way to behave, we're
+
+just saying, weirdly enough,
+these kinds of actions some
+
+outlet for frustration--
+
+some are more constructive
+than others--
+
+result in resilience
+in these animals.
+
+Fewer ulcers, lowering
+of glucocorticoids.
+
+So, some kind of outlet
+for stress.
+
+How about predictability
+and control?
+
+So if rats hear a warning before
+a shock, even though
+
+they get an equal number
+of shocks,
+
+they have fewer ulcers.
+
+So, as long as they can know the
+shock is coming, they have
+
+all the dread of that too, but
+they feel like I know what's
+
+going on, and that literally
+results in fewer ulcers.
+
+If food is delivered to a rat at
+intermittent intervals they
+
+can predict versus random
+delivery, they're more
+
+stressed with the
+random delivery.
+
+Again, prediction--
+
+equal amount of food, but if
+they can predict it, they feel
+
+like they know what's
+going on.
+
+Rats are given a lever to avoid
+the shock, even if the
+
+lever is disconnected
+to the shocks, the
+
+stress response is reduced.
+
+So, it's kind of an outlet too,
+like here's a lever I'm
+
+pushing, it doesn't do
+anything, but they
+
+feel like, who knows?
+
+I feel like I have
+some control.
+
+Same thing with people, they
+did experiments where they
+
+give obnoxious noises,
+and one person has a
+
+button to stop the noise.
+
+They're less hypertensive
+whether the button
+
+is pressed or not.
+
+So they don't even have to
+press, but if they feel like,
+
+they feel like they might have
+control that's already a
+
+protective measure for stress.
+
+And there's famous studies
+looking at occupational
+
+stress, because some
+jobs have very high
+
+demand and low control.
+
+The most famous one that I
+know of is from pilots in
+
+World War II in the
+British Air Force.
+
+And they compared the pilot, who
+sat up front and rode the
+
+plane, versus the gunner--
+
+and if you think of those
+airplanes from books or movies
+
+there's a little turret down and
+there's a gunner shooting
+
+at the other planes and they're
+shooting back at him--
+
+does he feel like he
+has any control?
+
+No.
+
+Wherever the pilot's going he's
+like, no don't go there,
+
+don't go there they're all
+just shooting at him.
+
+So, and then they look at the
+life expectancy and health of
+
+the people and the pilots did a
+lot better than the gunners
+
+after the war.
+
+Because the gunners just went
+out day-in, day-out and they
+
+just went wherever the pilot
+took them and the shots were
+
+coming out.
+
+So everybody was at risk, but
+the pilots felt they had
+
+control and the gunners felt
+they had no control.
+
+So, many different examples.
+
+Here's a very famous one, and
+I read somewhere they're
+
+making a movie of this, I don't
+know exactly how they'll
+
+make compelling,
+but here we go.
+
+So this is a study from Judy
+Rodin and Ellen Langer where
+
+they looked at the sense
+of predictability
+
+in a nursing home.
+
+And they took people at randomly
+assigned, from
+
+randomly selected different
+floors.
+
+And group A, in the nursing
+home, got to make many
+
+decisions for themselves.
+
+They got to decide where to
+receive their visitors, when
+
+to watch a movie, what house
+plant to take care of-- they
+
+all took care of
+a house plant.
+
+These are sort of minor things
+but people in a nursing home
+
+don't have a huge
+range of things
+
+they can control anyway.
+
+But they took these things they
+could put under their
+
+control, and group B got no
+
+instructions to make decisions.
+
+They got a plant, but the staff
+took care of the plants.
+
+So everybody gets a plant, but
+one group, they're saying make
+
+the decisions you can
+for yourself.
+
+And the other group, the nurses
+and doctors made all
+
+the decisions they could
+for those individuals.
+
+They look at what happened
+one and a half
+
+years later after this.
+
+Not only the group A, the
+people who are making
+
+decisions for themselves in
+the nursing home, report
+
+themselves to be more cheerful,
+
+more active, and alert.
+
+They were also objectively
+healthier and, kind of
+
+amazingly, only half as many
+had died, literally died.
+
+So it's an extremely
+compelling--
+
+I've shown you so many sources
+of evidence, from controlled
+
+animal things to anecdotal
+things to kind of a controlled
+
+experiment with humans with
+random assignment here, where
+
+the sense that a person has
+control is incredibly powerful
+
+not only for their happiness,
+but it literally seems to
+
+fight off stress-related
+diseases in their body, in
+
+their hearts and their
+life expectancy.
+
+Now the psychological modifiers
+of the stress
+
+response are going to vary
+depending on who you are and
+
+the culture you're in.
+
+I'm going to show you one
+experiment about that, we'll
+
+talk a little bit later about
+different cultures.
+
+But here's one about what counts
+as predictably and
+
+control, it'll vary
+by culture.
+
+So, we'll talk more about this
+in social psychology, but
+
+social psychologists like
+to talk about one giant
+
+distinction around the world
+as a simplified way of
+
+organizing a huge complexity
+of cultures--
+
+individualist cultures and
+collectivist cultures.
+
+Individualist cultures tend to
+emphasize the individual--
+
+be yourself, be all that
+you can be, OK?
+
+You're the one, you're
+the special person.
+
+That's thought to be common
+as a cultural mode in
+
+the US and in Europe.
+
+Over time, just in the last
+decade, people decided the US
+
+is like way, way out of control,
+different than the
+
+rest of the world in this.
+
+The US would send this message
+to everybody, the way to be
+
+happy and successful is to
+be super individualistic.
+
+Europe, a little less so.
+
+And other cultures, Japan South
+Korea, China received a
+
+lot of attention--
+and East Asia--
+
+tend to be more like we're
+in this together.
+
+Now this is super simplifying
+over many people, many
+
+situations.
+
+But cultures do send messages.
+
+Where you grow up, everything
+from your household to your
+
+town you're in, the school
+you're in, the
+
+country you're in.
+
+They send you messages
+of ways to be.
+
+I mean, we live in them.
+
+And here's an example, an
+experiment that shows,
+
+depending on the cultural
+influences, roughly speaking,
+
+averaging out across people and
+families, you can view one
+
+thing or another as a better,
+healthier, happier control.
+
+So here's the experiment--
+
+and there's a bunch these,
+but this is one.
+
+In an elementary school, I think
+it was in San Francisco,
+
+7 to 9 year olds who are either
+from Asian-American
+
+families or Anglo-American
+families.
+
+So that's the cultural thing,
+trying to look at this
+
+cultural versus individualist.
+
+Parenthetically, Asian-American
+families in the
+
+US are probably somewhere
+in-between Asian families in
+
+Asia and Anglo-American families
+in the US, right?
+
+Probably somewhere in between.
+
+So they did an experiment with
+Ms. Smith, the teacher, and
+
+she has six markers and six
+piles of anagrams, and
+
+somebody got to pick which
+anagrams you would work on to
+
+do your best and solve, OK?
+
+So, typical school little
+exercise, you try to do well.
+
+And they divided all these
+children into three groups.
+
+In one group the children chose
+which anagrams they
+
+would you do.
+
+In one group, the teacher
+chose it.
+
+And one, they said we've
+communicated with your mother
+
+and she says this is the
+anagram set for you.
+
+OK, so you could think
+in your own life.
+
+If you arrive to class tomorrow
+at MIT and people
+
+told you, here's
+a problem set.
+
+You pick the problems, I pick
+the problems, or I emailed
+
+your mother and she said you
+should really try those
+
+problems, OK?
+
+Well you're older
+you wouldn't--
+
+you'd be weirded out, right?
+
+But 7 to 9 year olds.
+
+They sort of take that, right?
+
+Alright, here's the
+interesting thing.
+
+So we're going to talk about
+performance on the anagrams.
+
+So this is actual performance,
+what seems like a
+
+self-controlled thing.
+
+For the children who are from
+Anglo-American families, they
+
+performed best when they picked
+the anagrams set.
+
+The anagram sets were all
+equal difficulty.
+
+Just like, I picked it I know
+what I'm doing, OK?
+
+Four times better than the
+teacher and two and a half
+
+times better than when
+the mother picked.
+
+That is, there's something about
+picking that set that
+
+makes them feel like that's the
+right set for them, and
+
+they perform best.
+
+For the children from
+Asian-American families, on
+
+average they perform best when
+the mother had selected the
+
+anagram set.
+
+30% better than themselves,
+and twice
+
+as well as the teacher.
+
+So all this is saying is,
+culture influences all of us
+
+in various ways, in
+complicated ways.
+
+This is one of the easiest
+things to identify, is this
+
+kind of a cultural difference.
+
+But the important thing is, it's
+psychological what you
+
+perceive as a source
+of control, right?
+
+So the way we interpret this
+is, for children who are
+
+exposed heavily to an
+Anglo-American emphasis on
+
+independent selfness.
+
+You're the one, you believe you
+do best the most control
+
+is exerted, when you choose.
+
+And, apparently, for these
+Asian-American children, they
+
+feel the best control has been
+exerted when their mother had
+
+selected for them the
+anagram they're most
+
+likely to succeed on.
+
+And the performance goes
+with that belief for
+
+both groups of children.
+
+I always worry about these
+things, and we're going to
+
+talk a little more about
+stereotypes, because you
+
+sometimes feel like you're
+supporting stereotypes, but
+
+these are real studies and
+they didn't have to
+
+play out that way.
+
+And it's obviously this
+doesn't say every
+
+Anglo-American is this
+way, and every
+
+Asian-American is that way.
+
+But cultures do influence us,
+otherwise the other choice is
+
+cultures don't influence us.
+
+And all the data says that
+culture matters.
+
+The world we grow up in, the
+values we're exposed to.
+
+OK here's another kind of brutal
+experiment about sense
+
+of control from 1957.
+
+This is truly life and death.
+
+So, they were interested in
+understanding really about
+
+survival for animals for water
+temperature and endurance.
+
+And they put the rats in a jar,
+and they asked, brutally,
+
+how long does a rat swim
+before drowns?
+
+OK, this is a brutal experiment,
+as you can--
+
+And the goal there was more
+to understand things about
+
+temperature, and whether people
+could survive different
+
+temperatures.
+
+It wasn't just to be
+mean to rats, OK?
+
+The science goal was to
+understand thermal survival
+
+for people, in the long run.
+
+But one thing they noticed
+was this--
+
+some rats gave up in about 15
+minutes, others would struggle
+
+as long as possible, and
+would go for an hour
+
+before they gave up.
+
+Some would surrender quickly,
+and some would fight as long
+
+as a rat can possibly
+flight, OK?
+
+Now what's the difference
+between those
+
+rats who give up early--
+
+Yeah?
+
+AUDIENCE: Did they give up after
+60 minutes or 60 hours?
+
+PROFESSOR: 60 hours, I'm
+sorry, it is 60 hours.
+
+OK?
+
+Yeah it is fantastic,
+I'm sorry.
+
+Yes, you're right, I mis-said
+that because--
+
+yes that's correct.
+
+But it's huge, OK,
+and yes 60 hours.
+
+There we go, it is hours.
+
+OK, thank you.
+
+Is that unbelievable?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: But for life and
+death you might do that.
+
+For life and death?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: But you can't
+do anything else.
+
+I know, it's kind of amazing.
+
+What's amazing to them is not
+necessarily the 60 hours,
+
+which is pretty impressive
+itself, it's that some just
+
+gave up really fast and some
+just went as long as you could
+
+go before you would expire,
+no matter what.
+
+And I think what it is, they did
+an experiment-- this is a
+
+little bit like the Seyle
+experiment, but on purpose.
+
+But before they put the rats
+into here, they picked up the
+
+rats they let them wiggle
+around, and they would put
+
+them in and out of the water,
+and then they would put them
+
+in this fatal final
+experiment.
+
+And then practically all
+of the rest went for
+
+the 60 hours of effort.
+
+Why?
+
+You can't really know, you
+can't ask the rat, right?
+
+But the interpretation is they
+went in and out, they went in
+
+and out, they struggle--
+
+they had hope.
+
+Literally, as far as we can
+understand, they had hope.
+
+Because before they were
+taken out, OK?
+
+And if you have hope,
+you struggle for
+
+a long, long time.
+
+And if you're hopeless for some
+reason if you don't have
+
+hope, you give up fast.
+
+So it's very compelling that
+this sense of self control,
+
+including hope, makes a
+tremendous difference in
+
+performance.
+
+And it's very psychologically
+malleable in people, what
+
+counts, for them, as sources
+of hope and control.
+
+How about social support?
+
+So in primates, after a stress
+response, among strangers,
+
+they're worse.
+
+If they're among animals they
+know, they're better.
+
+And this is measured by
+glucocorticoids, an objective
+
+measure in monkeys.
+
+That they're better if they're
+among monkeys they know.
+
+So, you could think in your
+own life, family, friends.
+
+Intuitively are they
+sources of support?
+
+Yes.
+
+So, they do stressor experiments
+with people.
+
+A really good one is to tell
+somebody they're about to do
+
+public speaking task, that turns
+out to scare people, or
+
+a difficult math task, or
+they're about to argue with a
+
+stranger about a controversial
+topic.
+
+They have less cardiovascular
+response if they're with a
+
+supportive friend present when
+they get the instruction, OK?
+
+So if you're told you're going
+to do something, like have a
+
+really unpleasant argument with
+somebody, but there's
+
+somebody you know with you, who
+you know, you have less of
+
+a physiological response for the
+dread, if you want, or the
+
+stress of the upcoming event.
+
+And then, so those
+are controlled
+
+experiment with people.
+
+And there's epidemiological
+observation that people with
+
+spouses and close friends live
+longer, that when spouses die,
+
+the risk of dying increases for
+the surviving spouse, that
+
+parents of children killed in
+war have a higher risk of
+
+disease and mortality but only
+if they're divorced and
+
+widowed, that patients with
+severe coronary disease had
+
+three times the death rate over
+five years if they lack
+
+social support.
+
+So these are all correlation
+studies, all of them would
+
+have alternative
+interpretations, but they are
+
+all consistent with these
+experimental studies that
+
+social support is an incredibly
+powerful buffer for
+
+resilience for stress
+and threat.
+
+Here's another one, perception
+of life improving.
+
+So, rats getting shocks.
+
+Rat number one got 10 hours
+a day, rat number
+
+two got 50 per hour.
+
+And day two, all rats
+get 25 per hour.
+
+So rat number one, life
+is getting worse.
+
+Rat number two, life
+is getting better.
+
+And it's the group that goes
+from 10 to 25 that gets
+
+hypertensive, OK?
+
+So if you think things are
+getting better things can
+
+still be pretty bad.
+
+But if they feel like they're
+better, then you're going to
+
+be happier.
+
+As a side note--
+
+I should have put this in as a
+note but-- there's a work from
+
+Danny Kahneman on perception
+of pain.
+
+So he talked about people who
+went in to dentists, which can
+
+be sometimes unpleasant, and
+had them rate the pain
+
+periodically.
+
+And what he found is that, when
+you look back in your
+
+memory of how bad your
+experience was, he could
+
+predict it largely
+by two numbers--
+
+the peak pain response you
+report and the change near the
+
+end if it's getting better.
+
+So what he discovers, weirdly
+enough, is this--
+
+if you have peak pain responses
+that are similar
+
+with the dentist, if you add
+more pain but it's getting
+
+lower, people will feel like
+they had less pain overall,
+
+even though you added pain.
+
+Because if you just stop,
+it just stops.
+
+But now you've got a little bit
+of pain, and it's getting
+
+better and better and better.
+
+So you're adding pain, but the
+perception is, at the end it
+
+was getting better.
+
+Does that make sense?
+
+OK, you're adding pain,
+but it's getting less
+
+and less and less.
+
+But it's still an add, because
+you're adding it.
+
+People, in their mind,
+they'll say it was
+
+less painful overall.
+
+Because, what counts for
+them at the end is the
+
+getting-betterness.
+
+Getting better, even if it's
+bad, is a hugely powerful way
+
+the people view things
+in terms of how
+
+miserable life can be.
+
+So here's a graph that
+summarizes, here's risk of
+
+ulcer in rats.
+
+If there's another rat present,
+if they get a warning
+
+signal for control, a lever for
+responsive, if things seem
+
+to be getting better, if
+they have friends.
+
+All these things change the
+physiological consequence of
+
+very rough structures
+in the laboratory.
+
+And, as far as we could measure,
+it seems to happen in
+
+people as well.
+
+So it's kind of a dual
+story, right?
+
+There's fantastic stressors that
+we have in daily life in
+
+the world we live in that are
+chronic and unabating in many
+
+ways, but quite well-identified
+things they
+
+can help us manage those
+much, much better.
+
+Or become victims of them,
+much, much more likely.
+
+OK, I'm going to talk a bit
+about a couple studies about
+
+pain and romance.
+
+So, and this goes back to an
+idea we talked about before,
+
+but let me just remind you.
+
+This idea of embodied
+cognition.
+
+That the nature of the human
+mind largely determined by the
+
+form of the human body.
+
+That bottom-up physiology has
+a bigger role in our mental
+
+life than we might think.
+
+And I'm going to talk about
+emotional pain.
+
+And two things that are very
+painful emotionally--
+
+and if you've gone through
+, you know this-- they're
+
+shockingly painful sometimes.
+
+If you haven't had it recently,
+they're social
+
+rejection or romantic
+rejection, right?
+
+It's a sad thing, but it's true
+that I think those are
+
+shockingly painful for many
+people, even if you didn't
+
+think it was going
+to be that bad.
+
+The shock of being rejected
+socially or romantically is a
+
+pretty brutal experience
+emotionally.
+
+I'm going to show you guys from
+pretty strong evidence
+
+that it's because, when you
+have that kind of pain it
+
+literally turns on the same pain
+system as heat or shocks.
+
+OK?
+
+Literally the same one gets
+turned on as far as we can
+
+measure it.
+
+So, here's a thing just remind
+you that pain has is comprised
+
+of having two part.
+
+A sensory one that's the
+objective response to the
+
+pain, and what people call
+affective, that is, how much
+
+you suffer from that pain.
+
+So we could measure the
+objective one and the
+
+subjective one.
+
+And a bunch of studies have
+suggested that, for example
+
+somatosensory cortex, this the
+cortex that represents your
+
+body, if you get physical pain
+like a shock or heat gun,
+
+responds to the amount
+of that.
+
+Whereas something like the
+anterior sineal, this part of
+
+the brain viewed from the top,
+or this part viewed from the
+
+side, interprets that pain.
+
+So we know that people can
+withstand pain sometimes, we
+
+think this doesn't
+care about that.
+
+This is a part of your mind, or
+a component of your mind,
+
+supported by this part of the
+brain, that tells you how much
+
+you suffer subjectively from
+an objective thing.
+
+And part of reason they
+think that is the
+
+study, a hypnosis study.
+
+So we talked before, is
+hypnosis real or not?
+
+This is one of the things
+that should convince
+
+you a little bit.
+
+I was as skeptical as anybody
+but this is me apart
+
+So these are individuals who
+are highly hypnotic, only
+
+those are in this kind of
+a study, who get pain.
+
+And they're told to
+imagine that the
+
+pain is always identical.
+
+it's always identical, but
+they're hypnotically suggested
+
+that it's high or low.
+
+So in this primary response to
+pain in the somatosensory
+
+cortex, not much difference.
+
+But in the interior cingulate in
+the interpretation of pain,
+
+a big difference.
+
+Here's how much it is when they
+think it's a low pain by
+
+hypnotic suggestion, here's the
+response when they think
+
+it's high pain.
+
+So this change in brain
+response is
+
+purely hypnotic effect.
+
+The painful stimulus
+is always constant.
+
+Right?
+
+But that supports of you that
+this part is brain response is
+
+an interpretation rather than a
+simple objective response to
+
+the pain itself.
+
+There's many sources of
+evidence for that.
+
+So here's a study from Matt
+Lieberman at UCLA, where you
+
+come into a scanner and you're
+playing a game with somebody.
+
+Sometimes they tell you
+there's a person
+
+playing with you.
+
+It's very simple and it just
+shows you that even as adults
+
+we retain some of our childhood
+feelings, which is a
+
+game very simple computerized
+catch.
+
+And sometimes a person who's
+supposedly playing with you
+
+outside the room throws
+the ball back to you.
+
+And sometimes the person is
+really mean and they exclude
+
+you from playing catch
+on the computer.
+
+So, this is about as silly a
+version as you can get for
+
+young adults participants for
+pain, but hey we don't like
+
+being left out even when it's
+some weird experiment.
+
+And set up a little bit so you
+really believe the other
+
+people in the experiment have
+left you out of the ball
+
+tossing game.
+
+And here's what turns on, right
+in the middle of this
+
+pain region, the interior
+cingulate for this pain of
+
+social rejection under such
+a mild circumstance, OK?
+
+And, by the way, they do the
+same experiment and they tell
+
+you it's a computer who's
+deciding whether to toss you
+
+the ball, you don't
+have a problem.
+
+It's only when you believe it's
+a person who's choosing
+
+to exclude you.
+
+OK?
+
+So this was published in Science
+because they said,
+
+look being left out of a group
+is as painful as if we had
+
+given you a shock
+or thermal gun.
+
+And it could sound ridiculous,
+but look it's the same system
+
+that's responding.
+
+OK so just recently a paper was
+published where they said,
+
+let's go all the way, this is
+just a little laboratory
+
+experiment.
+
+Let's grab people who recently
+self report a very unhappy
+
+romantic breakup, OK, where
+somebody left them.
+
+So they gave them both physical
+pain and they looked
+
+at its relation to
+romantic pain.
+
+So participants felt intensely
+rejected as a result of
+
+recently experiencing
+an unwanted romantic
+
+relationship breakup.
+
+What's the word we use for
+that when somebody--
+
+isn't there a word?
+
+Help me out here.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Dumped.
+
+Yeah, this is when somebody
+dumps you.
+
+Oh my god, I'm really hurt.
+
+And what's wrong with me?
+
+It's easy to laugh about
+years later.
+
+I could tell, I have a story
+or two, but I won't
+
+drag you into my--
+
+but almost everybody lives
+through a version of this some
+
+time in their lives.
+
+So it's surprisingly intense.
+
+So what they did, this is
+a tough experiment.
+
+They had them view pictures
+of ex-partners, the
+
+person who left them.
+
+OK?
+
+I don't even know how they're
+going to-- please bring us all
+
+the pictures that are
+now covered with
+
+tears and stuff, right?
+
+And you view those pictures,
+they also had you bring in
+
+pictures of other friends,
+people you knew.
+
+And you and either thought about
+the ex-partners and how
+
+you were rejected, or you
+viewed pictures of your
+
+friends and you thought
+about good
+
+things about your friends.
+
+So they controlled for
+looking at a face.
+
+And here's where they find.
+
+Here's physical pain
+and social pain in
+
+the anterior cingulate.
+
+Pretty much turning on the
+same part of the brain.
+
+When you see the person who
+dumped you and when you get a
+
+heat gun applied to you that
+exerts physical pain.
+
+And in brain region after
+brain region that which
+
+responds to physical pain is
+also turned on with the pain
+
+of looking at somebody who
+dumped you recently and you
+
+still feel that feeling
+of rejection.
+
+So now all of this is social
+rejection is very painful.
+
+Romantic rejection is very
+painful, painful literally.
+
+OK?
+
+It's not a metaphor,
+it's not a story.
+
+It's literally the same system
+in your brain that feels
+
+physical pain, feels
+this emotion pain.
+
+Emotional pain is
+very powerful.
+
+And here's an amazing
+follow up with this.
+
+And this is the kind of study--
+it'd be interesting to
+
+see this replicated--
+
+but it kind of makes sense.
+
+So they randomly assign people
+to 2000 milligrams a pain
+
+medication like Tylenol,
+Excedrin for three weeks or
+
+they got placebos.
+
+So you don't know what you've
+got, a double blind study.
+
+They provide daily reports
+of how their day was.
+
+By day 15, they reported less
+painful responses to rejection
+
+in their daily lives.
+
+And they also had less brain
+response to social rejection,
+
+by taking drugs that
+work on pain.
+
+And they don't even know it's
+a double blind comparison.
+
+Now there's all kinds
+of issues--
+
+for those of you, I've just
+got to tell you this-- to
+
+chronically take these
+drugs, you get ulcers
+
+and things like this.
+
+so don't do that.
+
+But it just pushes the point
+that there's some incredibly
+
+interesting relationship between
+emotional pain and
+
+physical pain that's
+very striking.
+
+OK now I'm going to go on for
+the last few minutes to
+
+another topic.
+
+And again it's one of these
+topics about racial relations
+
+in the US that's always
+a very difficult
+
+topic in our culture.
+
+And I hope I communicate it
+correctly, and appropriately.
+
+So we talked before about
+stereotyped threat, and this
+
+is a threat that a
+person feels--
+
+this is another form
+of stress--
+
+that others' judgments or one's
+own actions will confirm
+
+a negative stereotype
+about one's group.
+
+And that, for example, in
+multiple studies that
+
+African-Americans when a test
+framed about a kind of a test
+
+of people might think
+African-Americans won't do
+
+well, do less well, when they
+just take the test they do
+
+perfectly well.
+
+And then we talked about that
+whatever stereotype might
+
+apply to you, when it's invoked
+people under-perform
+
+in that area.
+
+And we interpret that as a sort
+of a stress that's not
+
+letting people perform
+at their best.
+
+So I'm going to talk about that
+stress element, but we're
+
+going to do an exercise.
+
+And I need you to be sensitive
+on this, and
+
+hopefully I'll do it.
+
+This is the most common way
+that psychologists measure
+
+attitude something about the
+stereotypes that inhabit the
+
+minds of people who live
+in this country.
+
+So we're going to do it as an
+exercise if you're willing to
+
+do, you just tap with one
+hand or the other.
+
+And we'll just try it
+you don't have to do
+
+this at your desk.
+
+I read about this kind of
+research for a number of years
+
+before I ever did it as a
+demonstration when I was at a
+
+conference.
+
+And somebody works in this field
+did it and i it was kind
+
+of striking when it happened.
+
+So it's up to you anyway.
+
+So think about whether you want
+to do this, but here's
+
+what we're going to do.
+
+So the experiment has two kinds
+of stimuli, basically.
+
+One of them are adjectives
+that are pleasant or
+
+unpleasant.
+
+everybody agrees that murderer
+or sicknesses is unpleasant,
+
+everybody agrees cheer and
+peace are pleasant.
+
+The second category or stimuli
+that are relevant are names
+
+that are selected in these
+experiments to be usually
+
+thought of-- and of course
+it's a generalization--
+
+to be found for people who are
+European-Americans and more
+
+likely to be associated with
+African-Americans.
+
+OK?
+
+All right, I mean you'll see,
+the experiment has to work
+
+this way but I'll talk with you
+about other versions of it
+
+that don't depend
+on exactly this.
+
+OK?
+
+it doesn't really matter.
+
+you can think about things and
+ask questions in a minute.
+
+So what I'm going to ask you
+to do, This you're going to
+
+see a list like this
+of adjectives.
+
+Go from top to bottom if it's
+an unpleasant word you tap
+
+with your left on your desk, it
+it's a pleasant word with
+
+the right hand.
+
+From top to bottom.
+
+And I'll just read
+you the times
+
+as we go, on a stopwatch.
+
+Ready?
+
+So left hand if it's unpleasant,
+right hand if it's
+
+pleasant, OK?
+
+Here we go 9 seconds, 10
+seconds, or 11 seconds, 13
+
+seconds, 14.
+
+OK all right, there's
+some practice effect
+
+and all that stuff.
+
+OK now you're going
+to have the names.
+
+Tap with you left hand if it's
+a name that's more typical of
+
+an African-American, your
+right hand if it's more
+
+typical of a European-American.
+
+Ready?
+
+Go.
+
+5,6,7,9,10,11,12,13 OK.
+
+OK, tap with your left hand if
+the adjective is an unpleasant
+
+adjective or the name of an
+African-American, your right
+
+hand if it's pleasant
+or the name of a
+
+typical white American.
+
+OK so now it's a mixed list.
+
+Ready?
+
+Go 5 10 12,13,14,15.
+
+OK, so by about 15 we got
+pretty much everybody.
+
+OK, we'll do this now, left
+for a name typically
+
+associated in this kind of
+experiment for a white
+
+American, right for
+a black American.
+
+Ready?
+
+Go.
+
+8, 9, 10, 11, 12,13,14 OK.
+
+Now this is the last
+one coming up.
+
+So now it's going to be left
+hand if it's a unpleasant
+
+adjective or a white American
+name, on the right if it's a
+
+pleasant or a black
+American name.
+
+Ready?
+
+Go.
+
+8 9, 10, 11, 12,13, 14,15
+,16, 17,18,19, 20, 21,
+
+Still tapping, right?
+
+All right, so this is
+a shock, right?
+
+I mean if you don't know this
+lecture, it's a shock.
+
+And it's a shock because this
+effect, which you heard
+
+yourself, happens in
+
+undergraduates across this country.
+
+People who are very convinced
+that racism is wrong, they
+
+hold no stereotypes themselves
+and with racism is wrong,
+
+they're definitely
+right about that.
+
+Definitely don't foster
+a stereotype, I
+
+mean you don't either.
+
+But in experiment after
+experiment in a country, and
+
+there's literally hundreds of
+these published, people on
+
+average are faster when they
+have to do unpleasant and
+
+black or unpleasant white as if
+it were easier to associate
+
+these two concepts.
+
+And we just did now you are the
+easy condition you were
+
+all done in about 15 seconds.
+
+In the more difficult condition,
+the unpleasant or
+
+white condition, there was still
+tapping occurring at 20
+
+could have gone to 25 or 30.
+
+OK so you had that
+experience, too.
+
+I heard you going I think
+giggling, I think
+
+just because of shock.
+
+Because you say, if you're like
+me, you say I harbor no
+
+prejudices, how did
+this happen to me?
+
+So this experiment, and you
+could look up a lot of
+
+information about this from
+Mazarin Banaji at Harvard,
+
+who's sort of the leader of
+this, with Tony Greenwald.
+
+They have a huge amount of
+evidence about this.
+
+So one thing you kind of laughed
+at, because it was so
+
+silly almost, the way
+we set up here,
+
+were the names, right?
+
+Because it was kind of a
+funny list of names.
+
+I could tell you the experiment
+work identically,
+
+just about, if you
+show pictures of
+
+white or black people.
+
+So the names is not an issue
+in that case, OK?
+
+So it's a shocking thing.
+
+And where does it come from
+that people are faster for
+
+white and pleasant than
+black and pleasant?
+
+That occurs in 75% or people who
+are white and about 50% of
+
+people who are black.
+
+So it's not as if black people
+reverse that pattern, it's
+
+just they're even.
+
+And on average for white people
+they find just easier
+
+to associate white things with
+pleasant things than black
+
+names or faces with
+pleasant things.
+
+Yeah?
+
+AUDIENCE: Was the experiment
+ever done any other way, where
+
+you would tap first
+or [INAUDIBLE]?
+
+PROFESSOR: Yes, yes.
+
+So you are absolutely correct
+that in the demonstration now,
+
+I slightly loaded up
+the order of these
+
+things to make it work.
+
+But why I give you this website
+is to tell you that in
+
+hundreds of experiments where
+that's all controlled for by
+
+reversing the order, half
+the time and stuff,
+
+it all plays out.
+
+OK?
+
+It's a demonstration today,
+slightly loaded it that way
+
+but there's hundreds of
+experiments where
+
+it all plays out.
+
+In these numbers are first the
+actual experiments where it
+
+all plays out.
+
+People worry about whether the
+frequency of the names, that a
+
+name like Chip might be more
+frequent, common than a name
+
+that's an African American name,
+just by shear number.
+
+So therefore the pictures get
+it out of the equation.
+
+People have worried about lots
+of things about this.
+
+I think almost everybody agrees
+the basic phenomenon
+
+holds up under well-controlled
+experimental designs.
+
+That's an excellent question.
+
+Any other questions
+about this?
+
+It's a very disturbing thing,
+partly it shows you that
+
+stereotypes are out there,
+unfortunately, to this day.
+
+Even with an African American
+president, stereotypes are out
+
+there, in people's heads.
+
+They used to call it
+a test of implicit
+
+attitudes because it--
+
+but now is this really an
+attitude to the person has in
+
+their head?
+
+Or is it really they
+know about a
+
+stereotype that's out there?
+
+It's still problematic to have
+the stereotypes out there,
+
+even if it's not the
+one you believe in,
+
+subscribe to, or live by.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE] actually
+[INAUDIBLE] for the
+
+experiment.
+
+And whether they found that it
+was more associated with your
+
+own proof--
+
+PROFESSOR: So with African
+Americans it's about 50-50 on
+
+average, across them.
+
+It not reverse.
+
+It's not like, my group is
+awesome, all other groups are
+
+not so awesome as my group
+because I'm in my group.
+
+It could be that, and that also
+would be problematic as
+
+much as anything.
+
+But it doesn't seem to
+play out that way.
+
+It seems to play out a little
+bit to what you might call--
+
+and then this will change, my
+guess is-- to what is the
+
+dominant group in a society.
+
+And now the US is changing
+in this regard, OK?
+
+But it's not changed yet.
+
+And you get these kinds of
+things in lots of domains,
+
+we've talked about that
+before it's not just
+
+about black and white.
+
+But the last thing
+I'll show you--
+
+we'll be done in five minutes,
+it's just two slides.
+
+It's sort of a follow
+up on this.
+
+So here's an experiment that
+was done at Dartmouth.
+
+And they had white participants
+complete this
+
+task that you just did under
+better control circumstances.
+
+So for each person they could
+measure by how quickly they
+
+responded in the computer the
+difference between responding
+
+to black and white names in
+relation to pleasantness.
+
+So some person might be 10
+milliseconds, different
+
+somebody might be 200
+milliseconds different.
+
+People vary.
+
+But then they had them go
+to a different room--
+
+and this is the critical thing--
+to interact with
+
+either a black or white
+experimenter.
+
+All the participants in this
+experiment were white.
+
+Then they were told the reason
+we're doing this is, we want
+
+to videotape you making comments
+about the college
+
+fraternity system and racial
+profiling after 9/11.
+
+That's kind of a cover story,
+although the racial word was
+
+probably meant for them to think
+a little bit about the
+
+test they did.
+
+They go into a room they
+interact with a black or white
+
+experiment then they go back to
+the original room and they
+
+perform a cognitively demanding
+task, the Stroop
+
+task where you have to name
+colors that are in the wrong
+
+color, which you've
+seen many times in
+
+this course you already.
+
+And here's what they find.
+
+if you're a white person and you
+had a white experimenter,
+
+this is the performance
+on the Stroop task.
+
+It's unrelated to how you
+did on the IAT test.
+
+This is the IAT test, the people
+who are more along here
+
+had a bigger gap between
+black and white, OK?
+
+So they varied.
+
+But look at the people who went
+and took the IAT test
+
+like you just did, again under
+more controlled circumstances.
+
+Now they go and do the Stroop
+and look at the more their
+
+score reflected knowledge of the
+stereotype, the more the
+
+knowledge of that stereotype
+influenced in some way their
+
+performance--
+
+that's along this axis--
+
+the worse they did on the sort
+of cognitively demanding task.
+
+As if the stress that harms
+performance is occurring on
+
+both sides of racial
+groups, right?
+
+We already said that stereotype
+threat can diminish
+
+performance for people when
+they're working in the area
+
+where there's a stereotypes
+that they're not
+
+supposed to do well.
+
+Just thinking about that
+diminishes their performance.
+
+And now for the other group for
+the white participants,
+
+just thinking about
+the stereotyping--
+
+and you may have that too.
+
+Just thinking like, what I do?
+
+Why was I slower for that?
+
+I'm not a prejudiced person,
+how did I do that?
+
+The more their performance
+looked like that, the worse
+
+they did on this task.
+
+As if again, now they were
+having a part of their mind in
+
+the wrong place or
+over-aroused and
+
+under-performing.
+
+So everybody's falling victim,
+on both sides of this
+
+prospective, to these
+racial stereotypes.
+
+Whether you're black or white,
+it's disturbing to have that
+
+thought and it diminishes your
+ability think clearly.
+
+So in that sense stereotypes
+makes you stupider on
+
+performance in a cognitively
+demanding task.
+
+there's so many forms of stress
+and the one good thing
+
+is, psychologists are getting
+better and better at
+
+discovering sources
+of resilience.
+
+And we talked earlier in the
+course, it includes resilience
+
+from stereotyped threat.
+
+We'd like to just get rid of
+stereotypes today, but pending
+
+that we've talked about things
+like essays and so on that
+
+work surprisingly risk
+effectively sometimes.
+
+OK thanks very much.
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